Properties

Label 980.2.x.k.667.16
Level $980$
Weight $2$
Character 980.667
Analytic conductor $7.825$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(67,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.x (of order \(12\), degree \(4\), 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: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 667.16
Character \(\chi\) \(=\) 980.667
Dual form 980.2.x.k.263.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.19055 - 0.763272i) q^{2} +(0.835136 - 3.11677i) q^{3} +(0.834830 - 1.81743i) q^{4} +(1.91459 + 1.15514i) q^{5} +(-1.38467 - 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(-6.41872 - 3.70585i) q^{9} +O(q^{10})\) \(q+(1.19055 - 0.763272i) q^{2} +(0.835136 - 3.11677i) q^{3} +(0.834830 - 1.81743i) q^{4} +(1.91459 + 1.15514i) q^{5} +(-1.38467 - 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(-6.41872 - 3.70585i) q^{9} +(3.16111 - 0.0861032i) q^{10} +(1.21832 - 0.703395i) q^{11} +(-4.96732 - 4.11978i) q^{12} +(-0.699298 + 0.699298i) q^{13} +(5.19924 - 5.00264i) q^{15} +(-2.60612 - 3.03449i) q^{16} +(-1.19641 + 4.46506i) q^{17} +(-10.4704 + 0.487224i) q^{18} +(-1.40337 + 2.43071i) q^{19} +(3.69774 - 2.51529i) q^{20} +(0.913587 - 1.76734i) q^{22} +(2.03016 - 0.543980i) q^{23} +(-9.05837 - 1.11339i) q^{24} +(2.33132 + 4.42323i) q^{25} +(-0.298796 + 1.36631i) q^{26} +(-10.0659 + 10.0659i) q^{27} -4.85706i q^{29} +(2.37159 - 9.92434i) q^{30} +(3.18470 - 1.83869i) q^{31} +(-5.41886 - 1.62355i) q^{32} +(-1.17486 - 4.38464i) q^{33} +(1.98367 + 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(7.99714 - 2.14283i) q^{37} +(0.184507 + 3.96504i) q^{38} +(1.59554 + 2.76356i) q^{39} +(2.48250 - 5.81697i) q^{40} +3.53368 q^{41} +(-2.49869 - 2.49869i) q^{43} +(-0.261285 - 2.80142i) q^{44} +(-8.00846 - 14.5097i) q^{45} +(2.00181 - 2.19720i) q^{46} +(0.684106 + 2.55312i) q^{47} +(-11.6343 + 5.58845i) q^{48} +(6.15168 + 3.48666i) q^{50} +(12.9174 + 7.45786i) q^{51} +(0.687131 + 1.85472i) q^{52} +(0.951495 + 0.254952i) q^{53} +(-4.30095 + 19.6670i) q^{54} +(3.14510 + 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(-3.70726 - 5.78258i) q^{58} +(3.53286 + 6.11910i) q^{59} +(-4.75148 - 13.6256i) q^{60} +(-1.09916 + 1.90379i) q^{61} +(2.38814 - 4.61985i) q^{62} +(-7.69065 + 2.20315i) q^{64} +(-2.14665 + 0.531084i) q^{65} +(-4.74541 - 4.32341i) q^{66} +(-3.08671 - 0.827081i) q^{67} +(7.11614 + 5.90196i) q^{68} -6.78184i q^{69} +12.1891i q^{71} +(-7.85551 + 19.4360i) q^{72} +(-6.40469 - 1.71613i) q^{73} +(7.88545 - 8.65515i) q^{74} +(15.7332 - 3.57218i) q^{75} +(3.24607 + 4.57976i) q^{76} +(4.00892 + 2.07233i) q^{78} +(0.299644 - 0.518999i) q^{79} +(-1.48439 - 8.82024i) q^{80} +(11.8491 + 20.5233i) q^{81} +(4.20703 - 2.69716i) q^{82} +(4.53764 + 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(-4.88200 - 1.06764i) q^{86} +(-15.1383 - 4.05630i) q^{87} +(-2.44932 - 3.13581i) q^{88} +(0.401553 + 0.231837i) q^{89} +(-20.6093 - 11.1619i) q^{90} +(0.706194 - 4.14381i) q^{92} +(-3.07111 - 11.4615i) q^{93} +(2.76319 + 2.51746i) q^{94} +(-5.49468 + 3.03273i) q^{95} +(-9.58571 + 15.5335i) q^{96} +(8.00558 + 8.00558i) q^{97} -10.4267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48} + 80 q^{50} - 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} + 64 q^{61} + 80 q^{62} - 4 q^{65} - 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 16 q^{76} - 152 q^{78} + 20 q^{80} + 36 q^{81} - 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} - 32 q^{90} - 112 q^{92} - 32 q^{93} - 120 q^{96} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19055 0.763272i 0.841848 0.539715i
\(3\) 0.835136 3.11677i 0.482166 1.79947i −0.110331 0.993895i \(-0.535191\pi\)
0.592497 0.805573i \(-0.298142\pi\)
\(4\) 0.834830 1.81743i 0.417415 0.908716i
\(5\) 1.91459 + 1.15514i 0.856231 + 0.516593i
\(6\) −1.38467 4.34811i −0.565290 1.77511i
\(7\) 0 0
\(8\) −0.393286 2.80095i −0.139048 0.990286i
\(9\) −6.41872 3.70585i −2.13957 1.23528i
\(10\) 3.16111 0.0861032i 0.999629 0.0272282i
\(11\) 1.21832 0.703395i 0.367336 0.212082i −0.304958 0.952366i \(-0.598642\pi\)
0.672294 + 0.740284i \(0.265309\pi\)
\(12\) −4.96732 4.11978i −1.43394 1.18928i
\(13\) −0.699298 + 0.699298i −0.193950 + 0.193950i −0.797401 0.603450i \(-0.793792\pi\)
0.603450 + 0.797401i \(0.293792\pi\)
\(14\) 0 0
\(15\) 5.19924 5.00264i 1.34244 1.29168i
\(16\) −2.60612 3.03449i −0.651529 0.758624i
\(17\) −1.19641 + 4.46506i −0.290172 + 1.08294i 0.654805 + 0.755798i \(0.272751\pi\)
−0.944977 + 0.327138i \(0.893916\pi\)
\(18\) −10.4704 + 0.487224i −2.46790 + 0.114840i
\(19\) −1.40337 + 2.43071i −0.321955 + 0.557643i −0.980891 0.194556i \(-0.937673\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(20\) 3.69774 2.51529i 0.826840 0.562437i
\(21\) 0 0
\(22\) 0.913587 1.76734i 0.194777 0.376797i
\(23\) 2.03016 0.543980i 0.423318 0.113428i −0.0408699 0.999164i \(-0.513013\pi\)
0.464188 + 0.885737i \(0.346346\pi\)
\(24\) −9.05837 1.11339i −1.84903 0.227270i
\(25\) 2.33132 + 4.42323i 0.466263 + 0.884646i
\(26\) −0.298796 + 1.36631i −0.0585987 + 0.267954i
\(27\) −10.0659 + 10.0659i −1.93718 + 1.93718i
\(28\) 0 0
\(29\) 4.85706i 0.901933i −0.892541 0.450967i \(-0.851079\pi\)
0.892541 0.450967i \(-0.148921\pi\)
\(30\) 2.37159 9.92434i 0.432991 1.81193i
\(31\) 3.18470 1.83869i 0.571990 0.330238i −0.185954 0.982558i \(-0.559538\pi\)
0.757944 + 0.652320i \(0.226204\pi\)
\(32\) −5.41886 1.62355i −0.957929 0.287005i
\(33\) −1.17486 4.38464i −0.204517 0.763268i
\(34\) 1.98367 + 6.22907i 0.340196 + 1.06828i
\(35\) 0 0
\(36\) −12.0937 + 8.57184i −2.01561 + 1.42864i
\(37\) 7.99714 2.14283i 1.31472 0.352279i 0.467724 0.883875i \(-0.345074\pi\)
0.846998 + 0.531596i \(0.178408\pi\)
\(38\) 0.184507 + 3.96504i 0.0299310 + 0.643214i
\(39\) 1.59554 + 2.76356i 0.255491 + 0.442523i
\(40\) 2.48250 5.81697i 0.392518 0.919744i
\(41\) 3.53368 0.551868 0.275934 0.961177i \(-0.411013\pi\)
0.275934 + 0.961177i \(0.411013\pi\)
\(42\) 0 0
\(43\) −2.49869 2.49869i −0.381046 0.381046i 0.490433 0.871479i \(-0.336839\pi\)
−0.871479 + 0.490433i \(0.836839\pi\)
\(44\) −0.261285 2.80142i −0.0393903 0.422330i
\(45\) −8.00846 14.5097i −1.19383 2.16298i
\(46\) 2.00181 2.19720i 0.295151 0.323960i
\(47\) 0.684106 + 2.55312i 0.0997872 + 0.372411i 0.997702 0.0677590i \(-0.0215849\pi\)
−0.897915 + 0.440170i \(0.854918\pi\)
\(48\) −11.6343 + 5.58845i −1.67926 + 0.806623i
\(49\) 0 0
\(50\) 6.15168 + 3.48666i 0.869980 + 0.493088i
\(51\) 12.9174 + 7.45786i 1.80880 + 1.04431i
\(52\) 0.687131 + 1.85472i 0.0952879 + 0.257203i
\(53\) 0.951495 + 0.254952i 0.130698 + 0.0350204i 0.323575 0.946203i \(-0.395115\pi\)
−0.192877 + 0.981223i \(0.561782\pi\)
\(54\) −4.30095 + 19.6670i −0.585286 + 2.67634i
\(55\) 3.14510 + 0.0606082i 0.424085 + 0.00817240i
\(56\) 0 0
\(57\) 6.40395 + 6.40395i 0.848224 + 0.848224i
\(58\) −3.70726 5.78258i −0.486787 0.759291i
\(59\) 3.53286 + 6.11910i 0.459940 + 0.796639i 0.998957 0.0456557i \(-0.0145377\pi\)
−0.539018 + 0.842294i \(0.681204\pi\)
\(60\) −4.75148 13.6256i −0.613413 1.75906i
\(61\) −1.09916 + 1.90379i −0.140732 + 0.243756i −0.927773 0.373146i \(-0.878279\pi\)
0.787040 + 0.616902i \(0.211612\pi\)
\(62\) 2.38814 4.61985i 0.303294 0.586722i
\(63\) 0 0
\(64\) −7.69065 + 2.20315i −0.961331 + 0.275394i
\(65\) −2.14665 + 0.531084i −0.266260 + 0.0658729i
\(66\) −4.74541 4.32341i −0.584120 0.532175i
\(67\) −3.08671 0.827081i −0.377101 0.101044i 0.0652895 0.997866i \(-0.479203\pi\)
−0.442391 + 0.896822i \(0.645870\pi\)
\(68\) 7.11614 + 5.90196i 0.862959 + 0.715717i
\(69\) 6.78184i 0.816438i
\(70\) 0 0
\(71\) 12.1891i 1.44658i 0.690546 + 0.723289i \(0.257370\pi\)
−0.690546 + 0.723289i \(0.742630\pi\)
\(72\) −7.85551 + 19.4360i −0.925781 + 2.29055i
\(73\) −6.40469 1.71613i −0.749612 0.200858i −0.136266 0.990672i \(-0.543510\pi\)
−0.613346 + 0.789814i \(0.710177\pi\)
\(74\) 7.88545 8.65515i 0.916665 1.00614i
\(75\) 15.7332 3.57218i 1.81671 0.412480i
\(76\) 3.24607 + 4.57976i 0.372350 + 0.525334i
\(77\) 0 0
\(78\) 4.00892 + 2.07233i 0.453921 + 0.234645i
\(79\) 0.299644 0.518999i 0.0337126 0.0583919i −0.848677 0.528912i \(-0.822600\pi\)
0.882389 + 0.470520i \(0.155934\pi\)
\(80\) −1.48439 8.82024i −0.165960 0.986133i
\(81\) 11.8491 + 20.5233i 1.31657 + 2.28036i
\(82\) 4.20703 2.69716i 0.464589 0.297852i
\(83\) 4.53764 + 4.53764i 0.498071 + 0.498071i 0.910837 0.412766i \(-0.135437\pi\)
−0.412766 + 0.910837i \(0.635437\pi\)
\(84\) 0 0
\(85\) −7.44839 + 7.16674i −0.807891 + 0.777342i
\(86\) −4.88200 1.06764i −0.526440 0.115127i
\(87\) −15.1383 4.05630i −1.62300 0.434882i
\(88\) −2.44932 3.13581i −0.261099 0.334278i
\(89\) 0.401553 + 0.231837i 0.0425645 + 0.0245746i 0.521131 0.853477i \(-0.325510\pi\)
−0.478567 + 0.878051i \(0.658844\pi\)
\(90\) −20.6093 11.1619i −2.17242 1.17657i
\(91\) 0 0
\(92\) 0.706194 4.14381i 0.0736258 0.432022i
\(93\) −3.07111 11.4615i −0.318459 1.18851i
\(94\) 2.76319 + 2.51746i 0.285001 + 0.259657i
\(95\) −5.49468 + 3.03273i −0.563742 + 0.311151i
\(96\) −9.58571 + 15.5335i −0.978338 + 1.58538i
\(97\) 8.00558 + 8.00558i 0.812843 + 0.812843i 0.985059 0.172216i \(-0.0550927\pi\)
−0.172216 + 0.985059i \(0.555093\pi\)
\(98\) 0 0
\(99\) −10.4267 −1.04792
\(100\) 9.98517 0.544363i 0.998517 0.0544363i
\(101\) 3.01549 + 5.22299i 0.300053 + 0.519707i 0.976148 0.217108i \(-0.0696624\pi\)
−0.676095 + 0.736815i \(0.736329\pi\)
\(102\) 21.0712 0.980516i 2.08636 0.0970856i
\(103\) −13.5932 + 3.64227i −1.33937 + 0.358884i −0.856202 0.516642i \(-0.827182\pi\)
−0.483171 + 0.875526i \(0.660515\pi\)
\(104\) 2.23372 + 1.68367i 0.219035 + 0.165098i
\(105\) 0 0
\(106\) 1.32740 0.422716i 0.128929 0.0410578i
\(107\) −5.19174 19.3758i −0.501905 1.87313i −0.487290 0.873240i \(-0.662015\pi\)
−0.0146144 0.999893i \(-0.504652\pi\)
\(108\) 9.89076 + 26.6974i 0.951739 + 2.56896i
\(109\) −0.879139 + 0.507571i −0.0842062 + 0.0486165i −0.541512 0.840693i \(-0.682148\pi\)
0.457306 + 0.889310i \(0.348815\pi\)
\(110\) 3.79066 2.32841i 0.361425 0.222005i
\(111\) 26.7148i 2.53566i
\(112\) 0 0
\(113\) 7.39345 7.39345i 0.695518 0.695518i −0.267923 0.963440i \(-0.586337\pi\)
0.963440 + 0.267923i \(0.0863372\pi\)
\(114\) 12.5122 + 2.73628i 1.17188 + 0.256276i
\(115\) 4.51530 + 1.30362i 0.421054 + 0.121563i
\(116\) −8.82737 4.05482i −0.819601 0.376481i
\(117\) 7.08009 1.89711i 0.654555 0.175387i
\(118\) 8.87660 + 4.58857i 0.817157 + 0.422412i
\(119\) 0 0
\(120\) −16.0569 12.5953i −1.46579 1.14979i
\(121\) −4.51047 + 7.81236i −0.410043 + 0.710215i
\(122\) 0.144511 + 3.10552i 0.0130834 + 0.281161i
\(123\) 2.95110 11.0137i 0.266092 0.993069i
\(124\) −0.683006 7.32298i −0.0613357 0.657623i
\(125\) −0.645919 + 11.1617i −0.0577727 + 0.998330i
\(126\) 0 0
\(127\) −8.87092 + 8.87092i −0.787167 + 0.787167i −0.981029 0.193862i \(-0.937899\pi\)
0.193862 + 0.981029i \(0.437899\pi\)
\(128\) −7.47452 + 8.49303i −0.660661 + 0.750685i
\(129\) −9.87458 + 5.70109i −0.869408 + 0.501953i
\(130\) −2.15034 + 2.27077i −0.188597 + 0.199159i
\(131\) −11.3871 6.57436i −0.994898 0.574404i −0.0881630 0.996106i \(-0.528100\pi\)
−0.906735 + 0.421702i \(0.861433\pi\)
\(132\) −8.94960 1.52520i −0.778962 0.132752i
\(133\) 0 0
\(134\) −4.30618 + 1.37132i −0.371997 + 0.118464i
\(135\) −30.8996 + 7.64458i −2.65941 + 0.657941i
\(136\) 12.9769 + 1.59504i 1.11276 + 0.136773i
\(137\) 1.80890 6.75090i 0.154545 0.576769i −0.844599 0.535399i \(-0.820161\pi\)
0.999144 0.0413695i \(-0.0131721\pi\)
\(138\) −5.17640 8.07414i −0.440644 0.687317i
\(139\) 21.2377 1.80136 0.900679 0.434485i \(-0.143069\pi\)
0.900679 + 0.434485i \(0.143069\pi\)
\(140\) 0 0
\(141\) 8.52881 0.718255
\(142\) 9.30359 + 14.5117i 0.780740 + 1.21780i
\(143\) −0.360083 + 1.34385i −0.0301117 + 0.112378i
\(144\) 5.48256 + 29.1355i 0.456880 + 2.42796i
\(145\) 5.61057 9.29928i 0.465932 0.772263i
\(146\) −8.93499 + 2.84538i −0.739465 + 0.235485i
\(147\) 0 0
\(148\) 2.78181 16.3232i 0.228664 1.34176i
\(149\) 5.75434 + 3.32227i 0.471414 + 0.272171i 0.716831 0.697247i \(-0.245592\pi\)
−0.245418 + 0.969417i \(0.578925\pi\)
\(150\) 16.0046 16.2615i 1.30677 1.32775i
\(151\) −17.6555 + 10.1934i −1.43679 + 0.829529i −0.997625 0.0688796i \(-0.978058\pi\)
−0.439161 + 0.898408i \(0.644724\pi\)
\(152\) 7.36022 + 2.97481i 0.596993 + 0.241289i
\(153\) 24.2263 24.2263i 1.95858 1.95858i
\(154\) 0 0
\(155\) 8.22134 + 0.158431i 0.660354 + 0.0127255i
\(156\) 6.35458 0.592685i 0.508774 0.0474528i
\(157\) 4.59905 17.1639i 0.367044 1.36983i −0.497584 0.867416i \(-0.665779\pi\)
0.864628 0.502412i \(-0.167554\pi\)
\(158\) −0.0393955 0.846605i −0.00313413 0.0673523i
\(159\) 1.58925 2.75267i 0.126036 0.218301i
\(160\) −8.49949 9.36796i −0.671944 0.740602i
\(161\) 0 0
\(162\) 29.7719 + 15.3899i 2.33910 + 1.20915i
\(163\) 16.7957 4.50039i 1.31554 0.352498i 0.468235 0.883604i \(-0.344890\pi\)
0.847305 + 0.531106i \(0.178224\pi\)
\(164\) 2.95002 6.42222i 0.230358 0.501491i
\(165\) 2.81548 9.75192i 0.219185 0.759186i
\(166\) 8.86575 + 1.93884i 0.688116 + 0.150483i
\(167\) 6.88960 6.88960i 0.533133 0.533133i −0.388370 0.921503i \(-0.626962\pi\)
0.921503 + 0.388370i \(0.126962\pi\)
\(168\) 0 0
\(169\) 12.0220i 0.924767i
\(170\) −3.39752 + 14.2175i −0.260578 + 1.09044i
\(171\) 18.0157 10.4014i 1.37769 0.795412i
\(172\) −6.62718 + 2.45521i −0.505318 + 0.187208i
\(173\) −6.40337 23.8977i −0.486839 1.81691i −0.571632 0.820510i \(-0.693689\pi\)
0.0847922 0.996399i \(-0.472977\pi\)
\(174\) −21.1190 + 6.72543i −1.60103 + 0.509854i
\(175\) 0 0
\(176\) −5.30952 1.86384i −0.400220 0.140493i
\(177\) 22.0222 5.90084i 1.65529 0.443534i
\(178\) 0.655024 0.0304805i 0.0490961 0.00228461i
\(179\) 10.2777 + 17.8015i 0.768192 + 1.33055i 0.938542 + 0.345164i \(0.112177\pi\)
−0.170350 + 0.985384i \(0.554490\pi\)
\(180\) −33.0561 + 2.44170i −2.46386 + 0.181994i
\(181\) −7.85989 −0.584221 −0.292110 0.956385i \(-0.594357\pi\)
−0.292110 + 0.956385i \(0.594357\pi\)
\(182\) 0 0
\(183\) 5.01574 + 5.01574i 0.370774 + 0.370774i
\(184\) −2.32210 5.47244i −0.171187 0.403434i
\(185\) 17.7865 + 5.13516i 1.30769 + 0.377544i
\(186\) −12.4046 11.3015i −0.909549 0.828664i
\(187\) 1.68310 + 6.28140i 0.123080 + 0.459342i
\(188\) 5.21123 + 0.888105i 0.380068 + 0.0647717i
\(189\) 0 0
\(190\) −4.22691 + 7.80456i −0.306652 + 0.566202i
\(191\) −7.51061 4.33625i −0.543449 0.313760i 0.203027 0.979173i \(-0.434922\pi\)
−0.746475 + 0.665413i \(0.768255\pi\)
\(192\) 0.443974 + 25.8099i 0.0320411 + 1.86267i
\(193\) 5.12478 + 1.37318i 0.368890 + 0.0988437i 0.438502 0.898730i \(-0.355509\pi\)
−0.0696118 + 0.997574i \(0.522176\pi\)
\(194\) 15.6415 + 3.42062i 1.12299 + 0.245586i
\(195\) −0.137480 + 7.13415i −0.00984515 + 0.510887i
\(196\) 0 0
\(197\) −12.3437 12.3437i −0.879452 0.879452i 0.114026 0.993478i \(-0.463625\pi\)
−0.993478 + 0.114026i \(0.963625\pi\)
\(198\) −12.4136 + 7.95842i −0.882193 + 0.565581i
\(199\) −2.14941 3.72289i −0.152368 0.263909i 0.779730 0.626116i \(-0.215356\pi\)
−0.932097 + 0.362208i \(0.882023\pi\)
\(200\) 11.4724 8.26950i 0.811219 0.584742i
\(201\) −5.15564 + 8.92983i −0.363651 + 0.629862i
\(202\) 7.57667 + 3.91660i 0.533092 + 0.275571i
\(203\) 0 0
\(204\) 24.3380 17.2504i 1.70400 1.20777i
\(205\) 6.76555 + 4.08188i 0.472527 + 0.285091i
\(206\) −13.4033 + 14.7116i −0.933853 + 1.02501i
\(207\) −15.0470 4.03182i −1.04584 0.280231i
\(208\) 3.94447 + 0.299564i 0.273500 + 0.0207710i
\(209\) 3.94849i 0.273123i
\(210\) 0 0
\(211\) 19.5494i 1.34583i −0.739718 0.672917i \(-0.765041\pi\)
0.739718 0.672917i \(-0.234959\pi\)
\(212\) 1.25769 1.51643i 0.0863788 0.104149i
\(213\) 37.9906 + 10.1795i 2.60307 + 0.697490i
\(214\) −20.9701 19.1052i −1.43349 1.30601i
\(215\) −1.89764 7.67029i −0.129418 0.523110i
\(216\) 32.1528 + 24.2353i 2.18772 + 1.64900i
\(217\) 0 0
\(218\) −0.659246 + 1.27531i −0.0446498 + 0.0863751i
\(219\) −10.6976 + 18.5287i −0.722875 + 1.25206i
\(220\) 2.73577 5.66540i 0.184446 0.381961i
\(221\) −2.28576 3.95905i −0.153757 0.266315i
\(222\) −20.3907 31.8054i −1.36853 2.13464i
\(223\) −9.54503 9.54503i −0.639183 0.639183i 0.311171 0.950354i \(-0.399279\pi\)
−0.950354 + 0.311171i \(0.899279\pi\)
\(224\) 0 0
\(225\) 1.42776 37.0310i 0.0951838 2.46873i
\(226\) 3.15908 14.4455i 0.210139 0.960901i
\(227\) −17.8221 4.77541i −1.18289 0.316955i −0.386819 0.922155i \(-0.626426\pi\)
−0.796073 + 0.605200i \(0.793093\pi\)
\(228\) 16.9850 6.29253i 1.12486 0.416733i
\(229\) 13.5250 + 7.80865i 0.893755 + 0.516010i 0.875169 0.483817i \(-0.160750\pi\)
0.0185864 + 0.999827i \(0.494083\pi\)
\(230\) 6.37072 1.89438i 0.420073 0.124912i
\(231\) 0 0
\(232\) −13.6044 + 1.91021i −0.893172 + 0.125412i
\(233\) 0.989436 + 3.69263i 0.0648201 + 0.241912i 0.990733 0.135826i \(-0.0433688\pi\)
−0.925913 + 0.377738i \(0.876702\pi\)
\(234\) 6.98121 7.66264i 0.456376 0.500923i
\(235\) −1.63942 + 5.67842i −0.106944 + 0.370419i
\(236\) 14.0704 1.31233i 0.915904 0.0854253i
\(237\) −1.36736 1.36736i −0.0888193 0.0888193i
\(238\) 0 0
\(239\) 15.4752 1.00101 0.500505 0.865734i \(-0.333148\pi\)
0.500505 + 0.865734i \(0.333148\pi\)
\(240\) −28.7303 2.73960i −1.85453 0.176840i
\(241\) −14.3810 24.9086i −0.926361 1.60450i −0.789357 0.613934i \(-0.789586\pi\)
−0.137004 0.990570i \(-0.543747\pi\)
\(242\) 0.593010 + 12.7437i 0.0381202 + 0.819199i
\(243\) 32.6112 8.73814i 2.09201 0.560552i
\(244\) 2.54241 + 3.58699i 0.162761 + 0.229633i
\(245\) 0 0
\(246\) −4.89298 15.3648i −0.311965 0.979626i
\(247\) −0.718415 2.68116i −0.0457117 0.170598i
\(248\) −6.40258 8.19707i −0.406564 0.520514i
\(249\) 17.9323 10.3532i 1.13641 0.656109i
\(250\) 7.75039 + 13.7816i 0.490178 + 0.871622i
\(251\) 26.0285i 1.64291i 0.570277 + 0.821453i \(0.306836\pi\)
−0.570277 + 0.821453i \(0.693164\pi\)
\(252\) 0 0
\(253\) 2.09075 2.09075i 0.131444 0.131444i
\(254\) −3.79037 + 17.3322i −0.237829 + 1.08752i
\(255\) 16.1167 + 29.2001i 1.00927 + 1.82858i
\(256\) −2.41631 + 15.8165i −0.151020 + 0.988531i
\(257\) −22.2935 + 5.97352i −1.39063 + 0.372618i −0.874971 0.484176i \(-0.839119\pi\)
−0.515659 + 0.856794i \(0.672453\pi\)
\(258\) −7.40472 + 14.3244i −0.460998 + 0.891801i
\(259\) 0 0
\(260\) −0.826882 + 4.34476i −0.0512811 + 0.269451i
\(261\) −17.9995 + 31.1761i −1.11414 + 1.92975i
\(262\) −18.5750 + 0.864358i −1.14757 + 0.0534002i
\(263\) 2.93759 10.9633i 0.181140 0.676023i −0.814284 0.580466i \(-0.802870\pi\)
0.995424 0.0955566i \(-0.0304631\pi\)
\(264\) −11.8191 + 5.01515i −0.727416 + 0.308661i
\(265\) 1.52722 + 1.58724i 0.0938163 + 0.0975031i
\(266\) 0 0
\(267\) 1.05793 1.05793i 0.0647444 0.0647444i
\(268\) −4.08004 + 4.91941i −0.249228 + 0.300501i
\(269\) −23.5713 + 13.6089i −1.43717 + 0.829749i −0.997652 0.0684854i \(-0.978183\pi\)
−0.439516 + 0.898235i \(0.644850\pi\)
\(270\) −30.9526 + 32.6861i −1.88372 + 1.98921i
\(271\) 0.134959 + 0.0779185i 0.00819817 + 0.00473321i 0.504093 0.863649i \(-0.331827\pi\)
−0.495895 + 0.868382i \(0.665160\pi\)
\(272\) 16.6672 8.00597i 1.01060 0.485433i
\(273\) 0 0
\(274\) −2.99919 9.41799i −0.181188 0.568961i
\(275\) 5.95156 + 3.74906i 0.358893 + 0.226077i
\(276\) −12.3255 5.66169i −0.741910 0.340794i
\(277\) −5.41783 + 20.2196i −0.325526 + 1.21488i 0.588256 + 0.808674i \(0.299815\pi\)
−0.913782 + 0.406204i \(0.866852\pi\)
\(278\) 25.2846 16.2102i 1.51647 0.972220i
\(279\) −27.2556 −1.63175
\(280\) 0 0
\(281\) −2.56355 −0.152929 −0.0764644 0.997072i \(-0.524363\pi\)
−0.0764644 + 0.997072i \(0.524363\pi\)
\(282\) 10.1540 6.50980i 0.604661 0.387653i
\(283\) −5.32518 + 19.8738i −0.316549 + 1.18138i 0.605990 + 0.795472i \(0.292777\pi\)
−0.922539 + 0.385904i \(0.873889\pi\)
\(284\) 22.1528 + 10.1758i 1.31453 + 0.603824i
\(285\) 4.86351 + 19.6584i 0.288089 + 1.16446i
\(286\) 0.597025 + 1.87476i 0.0353028 + 0.110857i
\(287\) 0 0
\(288\) 28.7656 + 30.5026i 1.69503 + 1.79738i
\(289\) −3.78292 2.18407i −0.222525 0.128475i
\(290\) −0.418208 15.3537i −0.0245580 0.901599i
\(291\) 31.6373 18.2658i 1.85461 1.07076i
\(292\) −8.46578 + 10.2074i −0.495422 + 0.597343i
\(293\) 4.71102 4.71102i 0.275221 0.275221i −0.555977 0.831198i \(-0.687656\pi\)
0.831198 + 0.555977i \(0.187656\pi\)
\(294\) 0 0
\(295\) −0.304410 + 15.7965i −0.0177234 + 0.919708i
\(296\) −9.14712 21.5569i −0.531666 1.25297i
\(297\) −5.18314 + 19.3437i −0.300756 + 1.12244i
\(298\) 9.38664 0.436793i 0.543753 0.0253027i
\(299\) −1.03928 + 1.80009i −0.0601033 + 0.104102i
\(300\) 6.64232 31.5761i 0.383495 1.82305i
\(301\) 0 0
\(302\) −13.2395 + 25.6118i −0.761846 + 1.47379i
\(303\) 18.7972 5.03669i 1.07987 0.289350i
\(304\) 11.0333 2.07619i 0.632804 0.119078i
\(305\) −4.30358 + 2.37531i −0.246422 + 0.136010i
\(306\) 10.3514 47.3339i 0.591750 2.70590i
\(307\) −16.8508 + 16.8508i −0.961723 + 0.961723i −0.999294 0.0375706i \(-0.988038\pi\)
0.0375706 + 0.999294i \(0.488038\pi\)
\(308\) 0 0
\(309\) 45.4085i 2.58320i
\(310\) 9.90887 6.08651i 0.562786 0.345690i
\(311\) −15.7287 + 9.08099i −0.891895 + 0.514936i −0.874562 0.484914i \(-0.838851\pi\)
−0.0173329 + 0.999850i \(0.505518\pi\)
\(312\) 7.11309 5.55590i 0.402699 0.314541i
\(313\) −0.405938 1.51498i −0.0229450 0.0856319i 0.953504 0.301381i \(-0.0974475\pi\)
−0.976449 + 0.215749i \(0.930781\pi\)
\(314\) −7.62532 23.9449i −0.430322 1.35129i
\(315\) 0 0
\(316\) −0.693093 0.977859i −0.0389895 0.0550088i
\(317\) −28.5334 + 7.64549i −1.60259 + 0.429414i −0.945825 0.324678i \(-0.894744\pi\)
−0.656769 + 0.754092i \(0.728077\pi\)
\(318\) −0.208946 4.49023i −0.0117171 0.251800i
\(319\) −3.41643 5.91743i −0.191283 0.331313i
\(320\) −17.2694 4.66562i −0.965388 0.260816i
\(321\) −64.7258 −3.61264
\(322\) 0 0
\(323\) −9.17425 9.17425i −0.510469 0.510469i
\(324\) 47.1917 4.40151i 2.62176 0.244528i
\(325\) −4.72344 1.46287i −0.262009 0.0811454i
\(326\) 16.5611 18.1776i 0.917236 1.00677i
\(327\) 0.847782 + 3.16396i 0.0468824 + 0.174968i
\(328\) −1.38975 9.89766i −0.0767360 0.546507i
\(329\) 0 0
\(330\) −4.09139 13.7592i −0.225224 0.757416i
\(331\) 10.9400 + 6.31623i 0.601319 + 0.347172i 0.769560 0.638574i \(-0.220475\pi\)
−0.168241 + 0.985746i \(0.553809\pi\)
\(332\) 12.0350 4.45869i 0.660507 0.244703i
\(333\) −59.2724 15.8820i −3.24811 0.870328i
\(334\) 2.94379 13.4611i 0.161077 0.736557i
\(335\) −4.95439 5.14909i −0.270687 0.281325i
\(336\) 0 0
\(337\) 4.10542 + 4.10542i 0.223636 + 0.223636i 0.810028 0.586391i \(-0.199452\pi\)
−0.586391 + 0.810028i \(0.699452\pi\)
\(338\) 9.17603 + 14.3128i 0.499111 + 0.778513i
\(339\) −16.8692 29.2182i −0.916207 1.58692i
\(340\) 6.80693 + 19.5200i 0.369157 + 1.05862i
\(341\) 2.58665 4.48021i 0.140075 0.242617i
\(342\) 13.5095 26.1342i 0.730513 1.41318i
\(343\) 0 0
\(344\) −6.01600 + 7.98140i −0.324361 + 0.430328i
\(345\) 7.83396 12.9845i 0.421766 0.699060i
\(346\) −25.8640 23.5640i −1.39046 1.26681i
\(347\) 14.2660 + 3.82255i 0.765837 + 0.205205i 0.620531 0.784182i \(-0.286917\pi\)
0.145305 + 0.989387i \(0.453584\pi\)
\(348\) −20.0100 + 24.1266i −1.07265 + 1.29332i
\(349\) 5.05181i 0.270417i −0.990817 0.135209i \(-0.956830\pi\)
0.990817 0.135209i \(-0.0431705\pi\)
\(350\) 0 0
\(351\) 14.0781i 0.751434i
\(352\) −7.74389 + 1.83361i −0.412751 + 0.0977317i
\(353\) −10.5040 2.81454i −0.559072 0.149803i −0.0317919 0.999495i \(-0.510121\pi\)
−0.527280 + 0.849692i \(0.676788\pi\)
\(354\) 21.7147 23.8342i 1.15412 1.26677i
\(355\) −14.0801 + 23.3371i −0.747292 + 1.23860i
\(356\) 0.756576 0.536251i 0.0400984 0.0284212i
\(357\) 0 0
\(358\) 25.8236 + 13.3489i 1.36482 + 0.705514i
\(359\) 2.49329 4.31850i 0.131591 0.227922i −0.792699 0.609613i \(-0.791325\pi\)
0.924290 + 0.381691i \(0.124658\pi\)
\(360\) −37.4913 + 28.1378i −1.97597 + 1.48299i
\(361\) 5.56111 + 9.63212i 0.292690 + 0.506954i
\(362\) −9.35761 + 5.99923i −0.491825 + 0.315313i
\(363\) 20.5825 + 20.5825i 1.08030 + 1.08030i
\(364\) 0 0
\(365\) −10.2800 10.6840i −0.538079 0.559225i
\(366\) 9.79988 + 2.14313i 0.512248 + 0.112023i
\(367\) 15.3917 + 4.12420i 0.803442 + 0.215282i 0.637094 0.770786i \(-0.280136\pi\)
0.166347 + 0.986067i \(0.446803\pi\)
\(368\) −6.94154 4.74284i −0.361853 0.247238i
\(369\) −22.6817 13.0953i −1.18076 0.681714i
\(370\) 25.0953 7.46228i 1.30464 0.387946i
\(371\) 0 0
\(372\) −23.3944 3.98691i −1.21294 0.206712i
\(373\) −0.152497 0.569126i −0.00789599 0.0294682i 0.961865 0.273523i \(-0.0881890\pi\)
−0.969761 + 0.244055i \(0.921522\pi\)
\(374\) 6.79823 + 6.19368i 0.351528 + 0.320267i
\(375\) 34.2489 + 11.3347i 1.76861 + 0.585321i
\(376\) 6.88211 2.92025i 0.354918 0.150601i
\(377\) 3.39653 + 3.39653i 0.174930 + 0.174930i
\(378\) 0 0
\(379\) 23.7583 1.22038 0.610191 0.792254i \(-0.291093\pi\)
0.610191 + 0.792254i \(0.291093\pi\)
\(380\) 0.924648 + 12.5180i 0.0474335 + 0.642161i
\(381\) 20.2402 + 35.0570i 1.03694 + 1.79603i
\(382\) −12.2515 + 0.570105i −0.626842 + 0.0291691i
\(383\) −4.14964 + 1.11189i −0.212037 + 0.0568151i −0.363274 0.931682i \(-0.618341\pi\)
0.151237 + 0.988498i \(0.451674\pi\)
\(384\) 20.2286 + 30.3892i 1.03229 + 1.55079i
\(385\) 0 0
\(386\) 7.14943 2.27676i 0.363896 0.115884i
\(387\) 6.77862 + 25.2982i 0.344577 + 1.28598i
\(388\) 21.2329 7.86629i 1.07794 0.399350i
\(389\) −21.8152 + 12.5950i −1.10608 + 0.638593i −0.937810 0.347148i \(-0.887150\pi\)
−0.168266 + 0.985742i \(0.553817\pi\)
\(390\) 5.28162 + 8.59852i 0.267445 + 0.435403i
\(391\) 9.71561i 0.491340i
\(392\) 0 0
\(393\) −30.0006 + 30.0006i −1.51333 + 1.51333i
\(394\) −24.1174 5.27421i −1.21502 0.265711i
\(395\) 1.17321 0.647540i 0.0590306 0.0325813i
\(396\) −8.70454 + 18.9498i −0.437419 + 0.952265i
\(397\) 3.73802 1.00160i 0.187606 0.0502689i −0.163793 0.986495i \(-0.552373\pi\)
0.351399 + 0.936226i \(0.385706\pi\)
\(398\) −5.40057 2.79171i −0.270706 0.139936i
\(399\) 0 0
\(400\) 7.34658 18.6018i 0.367329 0.930091i
\(401\) 2.74364 4.75213i 0.137011 0.237310i −0.789353 0.613940i \(-0.789584\pi\)
0.926364 + 0.376630i \(0.122917\pi\)
\(402\) 0.677834 + 14.5666i 0.0338073 + 0.726516i
\(403\) −0.941265 + 3.51285i −0.0468877 + 0.174987i
\(404\) 12.0098 1.12014i 0.597512 0.0557293i
\(405\) −1.02098 + 52.9811i −0.0507330 + 2.63265i
\(406\) 0 0
\(407\) 8.23579 8.23579i 0.408233 0.408233i
\(408\) 15.8089 39.1141i 0.782656 1.93643i
\(409\) 14.7164 8.49650i 0.727678 0.420125i −0.0898942 0.995951i \(-0.528653\pi\)
0.817572 + 0.575826i \(0.195320\pi\)
\(410\) 11.1703 0.304261i 0.551663 0.0150264i
\(411\) −19.5303 11.2758i −0.963360 0.556196i
\(412\) −4.72839 + 27.7453i −0.232951 + 1.36691i
\(413\) 0 0
\(414\) −20.9916 + 6.68484i −1.03168 + 0.328542i
\(415\) 3.44613 + 13.9293i 0.169164 + 0.683764i
\(416\) 4.92474 2.65406i 0.241455 0.130126i
\(417\) 17.7364 66.1930i 0.868554 3.24149i
\(418\) 3.01378 + 4.70089i 0.147409 + 0.229928i
\(419\) 3.87556 0.189334 0.0946668 0.995509i \(-0.469821\pi\)
0.0946668 + 0.995509i \(0.469821\pi\)
\(420\) 0 0
\(421\) 20.7160 1.00964 0.504818 0.863226i \(-0.331560\pi\)
0.504818 + 0.863226i \(0.331560\pi\)
\(422\) −14.9215 23.2745i −0.726367 1.13299i
\(423\) 5.07039 18.9230i 0.246531 0.920066i
\(424\) 0.339899 2.76536i 0.0165069 0.134298i
\(425\) −22.5392 + 5.11747i −1.09331 + 0.248234i
\(426\) 52.9995 16.8779i 2.56783 0.817735i
\(427\) 0 0
\(428\) −39.5485 6.73991i −1.91165 0.325786i
\(429\) 3.88775 + 2.24459i 0.187702 + 0.108370i
\(430\) −8.11376 7.68347i −0.391280 0.370530i
\(431\) −8.46015 + 4.88447i −0.407511 + 0.235277i −0.689720 0.724076i \(-0.742266\pi\)
0.282209 + 0.959353i \(0.408933\pi\)
\(432\) 56.7778 + 4.31201i 2.73172 + 0.207462i
\(433\) 7.00877 7.00877i 0.336820 0.336820i −0.518349 0.855169i \(-0.673453\pi\)
0.855169 + 0.518349i \(0.173453\pi\)
\(434\) 0 0
\(435\) −24.2981 25.2530i −1.16501 1.21079i
\(436\) 0.188544 + 2.02151i 0.00902962 + 0.0968128i
\(437\) −1.52681 + 5.69814i −0.0730373 + 0.272579i
\(438\) 1.40645 + 30.2246i 0.0672030 + 1.44419i
\(439\) 2.21290 3.83285i 0.105616 0.182932i −0.808374 0.588670i \(-0.799652\pi\)
0.913990 + 0.405737i \(0.132985\pi\)
\(440\) −1.06716 8.83309i −0.0508750 0.421101i
\(441\) 0 0
\(442\) −5.74315 2.96880i −0.273174 0.141211i
\(443\) −4.25183 + 1.13928i −0.202011 + 0.0541286i −0.358405 0.933566i \(-0.616679\pi\)
0.156395 + 0.987695i \(0.450013\pi\)
\(444\) −48.5523 22.3023i −2.30419 1.05842i
\(445\) 0.501006 + 0.907721i 0.0237500 + 0.0430301i
\(446\) −18.6493 4.07840i −0.883071 0.193118i
\(447\) 15.1604 15.1604i 0.717062 0.717062i
\(448\) 0 0
\(449\) 21.8355i 1.03048i −0.857046 0.515240i \(-0.827703\pi\)
0.857046 0.515240i \(-0.172297\pi\)
\(450\) −26.5649 45.1771i −1.25228 2.12967i
\(451\) 4.30514 2.48557i 0.202721 0.117041i
\(452\) −7.26482 19.6094i −0.341708 0.922348i
\(453\) 17.0258 + 63.5411i 0.799941 + 2.98542i
\(454\) −24.8631 + 7.91772i −1.16688 + 0.371597i
\(455\) 0 0
\(456\) 15.4186 20.4557i 0.722041 0.957928i
\(457\) 21.2792 5.70175i 0.995400 0.266717i 0.275883 0.961191i \(-0.411030\pi\)
0.719517 + 0.694475i \(0.244363\pi\)
\(458\) 22.0623 1.02664i 1.03090 0.0479715i
\(459\) −32.9019 56.9877i −1.53573 2.65996i
\(460\) 6.13874 7.11795i 0.286220 0.331876i
\(461\) −19.7670 −0.920641 −0.460321 0.887753i \(-0.652266\pi\)
−0.460321 + 0.887753i \(0.652266\pi\)
\(462\) 0 0
\(463\) 14.5239 + 14.5239i 0.674983 + 0.674983i 0.958861 0.283877i \(-0.0916209\pi\)
−0.283877 + 0.958861i \(0.591621\pi\)
\(464\) −14.7387 + 12.6581i −0.684228 + 0.587636i
\(465\) 7.35973 25.4917i 0.341299 1.18215i
\(466\) 3.99645 + 3.64106i 0.185132 + 0.168669i
\(467\) 7.29665 + 27.2315i 0.337649 + 1.26012i 0.900969 + 0.433884i \(0.142857\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(468\) 2.46282 14.4513i 0.113844 0.668014i
\(469\) 0 0
\(470\) 2.38236 + 8.01178i 0.109890 + 0.369556i
\(471\) −49.6551 28.6684i −2.28799 1.32097i
\(472\) 15.7499 12.3019i 0.724946 0.566242i
\(473\) −4.80176 1.28663i −0.220785 0.0591592i
\(474\) −2.67157 0.584244i −0.122709 0.0268352i
\(475\) −14.0233 0.540678i −0.643432 0.0248080i
\(476\) 0 0
\(477\) −5.16257 5.16257i −0.236378 0.236378i
\(478\) 18.4241 11.8118i 0.842698 0.540260i
\(479\) 0.709375 + 1.22867i 0.0324122 + 0.0561395i 0.881776 0.471668i \(-0.156348\pi\)
−0.849364 + 0.527807i \(0.823014\pi\)
\(480\) −36.2960 + 18.6674i −1.65668 + 0.852047i
\(481\) −4.09391 + 7.09086i −0.186666 + 0.323315i
\(482\) −36.1334 18.6784i −1.64583 0.850777i
\(483\) 0 0
\(484\) 10.4330 + 14.7195i 0.474225 + 0.669067i
\(485\) 6.07987 + 24.5749i 0.276072 + 1.11589i
\(486\) 32.1557 35.2944i 1.45861 1.60099i
\(487\) 32.5132 + 8.71188i 1.47331 + 0.394773i 0.904066 0.427393i \(-0.140568\pi\)
0.569247 + 0.822166i \(0.307235\pi\)
\(488\) 5.76471 + 2.32995i 0.260956 + 0.105472i
\(489\) 56.1067i 2.53723i
\(490\) 0 0
\(491\) 3.16673i 0.142913i −0.997444 0.0714563i \(-0.977235\pi\)
0.997444 0.0714563i \(-0.0227647\pi\)
\(492\) −17.5529 14.5580i −0.791346 0.656324i
\(493\) 21.6871 + 5.81103i 0.976736 + 0.261716i
\(494\) −2.90177 2.64372i −0.130557 0.118946i
\(495\) −19.9629 12.0443i −0.897265 0.541350i
\(496\) −13.8792 4.87213i −0.623195 0.218765i
\(497\) 0 0
\(498\) 13.4470 26.0133i 0.602576 1.16568i
\(499\) −3.72451 + 6.45105i −0.166732 + 0.288789i −0.937269 0.348607i \(-0.886655\pi\)
0.770537 + 0.637395i \(0.219988\pi\)
\(500\) 19.7463 + 10.4920i 0.883083 + 0.469217i
\(501\) −15.7195 27.2270i −0.702297 1.21641i
\(502\) 19.8668 + 30.9883i 0.886701 + 1.38308i
\(503\) −19.3043 19.3043i −0.860736 0.860736i 0.130687 0.991424i \(-0.458282\pi\)
−0.991424 + 0.130687i \(0.958282\pi\)
\(504\) 0 0
\(505\) −0.259830 + 13.4832i −0.0115623 + 0.599994i
\(506\) 0.893334 4.08495i 0.0397135 0.181598i
\(507\) 37.4697 + 10.0400i 1.66409 + 0.445891i
\(508\) 8.71658 + 23.5280i 0.386736 + 1.04389i
\(509\) −9.85817 5.69161i −0.436956 0.252276i 0.265350 0.964152i \(-0.414513\pi\)
−0.702305 + 0.711876i \(0.747846\pi\)
\(510\) 41.4754 + 22.4629i 1.83656 + 0.994672i
\(511\) 0 0
\(512\) 9.19554 + 20.6747i 0.406390 + 0.913700i
\(513\) −10.3411 38.5934i −0.456570 1.70394i
\(514\) −21.9821 + 24.1278i −0.969590 + 1.06423i
\(515\) −30.2326 8.72849i −1.33221 0.384623i
\(516\) 2.11775 + 22.7058i 0.0932286 + 0.999568i
\(517\) 2.62931 + 2.62931i 0.115637 + 0.115637i
\(518\) 0 0
\(519\) −79.8313 −3.50421
\(520\) 2.33179 + 5.80380i 0.102256 + 0.254514i
\(521\) 0.617798 + 1.07006i 0.0270662 + 0.0468801i 0.879241 0.476377i \(-0.158050\pi\)
−0.852175 + 0.523257i \(0.824717\pi\)
\(522\) 2.36648 + 50.8554i 0.103578 + 2.22588i
\(523\) −6.09797 + 1.63395i −0.266646 + 0.0714474i −0.389665 0.920957i \(-0.627409\pi\)
0.123019 + 0.992404i \(0.460742\pi\)
\(524\) −21.4548 + 15.2068i −0.937256 + 0.664314i
\(525\) 0 0
\(526\) −4.87059 15.2945i −0.212368 0.666872i
\(527\) 4.39965 + 16.4197i 0.191652 + 0.715254i
\(528\) −10.2433 + 14.9920i −0.445784 + 0.652443i
\(529\) −16.0929 + 9.29126i −0.699693 + 0.403968i
\(530\) 3.02973 + 0.724004i 0.131603 + 0.0314487i
\(531\) 52.3691i 2.27262i
\(532\) 0 0
\(533\) −2.47109 + 2.47109i −0.107035 + 0.107035i
\(534\) 0.452033 2.06702i 0.0195614 0.0894485i
\(535\) 12.4417 43.0940i 0.537901 1.86312i
\(536\) −1.10265 + 8.97100i −0.0476274 + 0.387488i
\(537\) 64.0665 17.1666i 2.76467 0.740792i
\(538\) −17.6756 + 34.1934i −0.762048 + 1.47418i
\(539\) 0 0
\(540\) −11.9024 + 62.5398i −0.512197 + 2.69128i
\(541\) 16.1355 27.9475i 0.693719 1.20156i −0.276891 0.960901i \(-0.589304\pi\)
0.970611 0.240656i \(-0.0773624\pi\)
\(542\) 0.220149 0.0102443i 0.00945620 0.000440029i
\(543\) −6.56407 + 24.4975i −0.281691 + 1.05129i
\(544\) 13.7324 22.2531i 0.588772 0.954095i
\(545\) −2.26951 0.0437350i −0.0972150 0.00187340i
\(546\) 0 0
\(547\) −17.6256 + 17.6256i −0.753617 + 0.753617i −0.975152 0.221536i \(-0.928893\pi\)
0.221536 + 0.975152i \(0.428893\pi\)
\(548\) −10.7592 8.92341i −0.459609 0.381189i
\(549\) 14.1104 8.14662i 0.602215 0.347689i
\(550\) 9.94719 0.0792139i 0.424150 0.00337769i
\(551\) 11.8061 + 6.81625i 0.502957 + 0.290382i
\(552\) −18.9956 + 2.66721i −0.808507 + 0.113524i
\(553\) 0 0
\(554\) 8.98286 + 28.2078i 0.381645 + 1.19843i
\(555\) 30.8593 51.1479i 1.30990 2.17111i
\(556\) 17.7299 38.5981i 0.751914 1.63692i
\(557\) 1.60273 5.98149i 0.0679101 0.253444i −0.923622 0.383304i \(-0.874786\pi\)
0.991532 + 0.129860i \(0.0414528\pi\)
\(558\) −32.4493 + 20.8035i −1.37369 + 0.880682i
\(559\) 3.49465 0.147808
\(560\) 0 0
\(561\) 20.9833 0.885915
\(562\) −3.05205 + 1.95669i −0.128743 + 0.0825380i
\(563\) −1.32949 + 4.96172i −0.0560313 + 0.209112i −0.988266 0.152742i \(-0.951189\pi\)
0.932235 + 0.361854i \(0.117856\pi\)
\(564\) 7.12011 15.5005i 0.299811 0.652690i
\(565\) 22.6959 5.61499i 0.954823 0.236224i
\(566\) 8.82925 + 27.7254i 0.371121 + 1.16539i
\(567\) 0 0
\(568\) 34.1410 4.79380i 1.43253 0.201143i
\(569\) −30.0136 17.3284i −1.25824 0.726442i −0.285504 0.958378i \(-0.592161\pi\)
−0.972731 + 0.231935i \(0.925494\pi\)
\(570\) 20.7950 + 19.6922i 0.871005 + 0.824814i
\(571\) −28.9237 + 16.6991i −1.21042 + 0.698836i −0.962851 0.270034i \(-0.912965\pi\)
−0.247569 + 0.968870i \(0.579632\pi\)
\(572\) 2.14174 + 1.77631i 0.0895508 + 0.0742713i
\(573\) −19.7875 + 19.7875i −0.826634 + 0.826634i
\(574\) 0 0
\(575\) 7.13910 + 7.71168i 0.297721 + 0.321599i
\(576\) 57.5287 + 14.3590i 2.39703 + 0.598292i
\(577\) −8.91664 + 33.2773i −0.371204 + 1.38535i 0.487608 + 0.873063i \(0.337870\pi\)
−0.858812 + 0.512291i \(0.828797\pi\)
\(578\) −6.17080 + 0.287149i −0.256672 + 0.0119438i
\(579\) 8.55978 14.8260i 0.355732 0.616146i
\(580\) −12.2169 17.9602i −0.507281 0.745755i
\(581\) 0 0
\(582\) 23.7241 45.8942i 0.983394 1.90238i
\(583\) 1.33855 0.358664i 0.0554372 0.0148544i
\(584\) −2.28792 + 18.6141i −0.0946749 + 0.770259i
\(585\) 15.7469 + 4.54630i 0.651054 + 0.187966i
\(586\) 2.01292 9.20450i 0.0831531 0.380234i
\(587\) 23.3690 23.3690i 0.964544 0.964544i −0.0348489 0.999393i \(-0.511095\pi\)
0.999393 + 0.0348489i \(0.0110950\pi\)
\(588\) 0 0
\(589\) 10.3214i 0.425288i
\(590\) 11.6946 + 19.0389i 0.481460 + 0.783820i
\(591\) −48.7811 + 28.1638i −2.00659 + 1.15850i
\(592\) −27.3439 18.6828i −1.12383 0.767859i
\(593\) −1.67934 6.26739i −0.0689623 0.257371i 0.922834 0.385197i \(-0.125867\pi\)
−0.991797 + 0.127826i \(0.959200\pi\)
\(594\) 8.59374 + 26.9859i 0.352606 + 1.10724i
\(595\) 0 0
\(596\) 10.8419 7.68459i 0.444101 0.314773i
\(597\) −13.3984 + 3.59010i −0.548362 + 0.146933i
\(598\) 0.136639 + 2.93636i 0.00558758 + 0.120077i
\(599\) 8.75860 + 15.1703i 0.357867 + 0.619843i 0.987604 0.156965i \(-0.0501709\pi\)
−0.629737 + 0.776808i \(0.716838\pi\)
\(600\) −16.1931 42.6629i −0.661082 1.74171i
\(601\) 2.55297 0.104138 0.0520689 0.998643i \(-0.483418\pi\)
0.0520689 + 0.998643i \(0.483418\pi\)
\(602\) 0 0
\(603\) 16.7477 + 16.7477i 0.682018 + 0.682018i
\(604\) 3.78648 + 40.5975i 0.154070 + 1.65189i
\(605\) −17.6601 + 9.74727i −0.717983 + 0.396283i
\(606\) 18.5347 20.3438i 0.752920 0.826412i
\(607\) −5.72830 21.3783i −0.232504 0.867718i −0.979258 0.202617i \(-0.935055\pi\)
0.746754 0.665101i \(-0.231611\pi\)
\(608\) 11.5510 10.8932i 0.468457 0.441779i
\(609\) 0 0
\(610\) −3.31062 + 6.11273i −0.134043 + 0.247497i
\(611\) −2.26378 1.30700i −0.0915829 0.0528754i
\(612\) −23.8048 64.2544i −0.962250 2.59733i
\(613\) −7.79104 2.08760i −0.314677 0.0843175i 0.0980238 0.995184i \(-0.468748\pi\)
−0.412701 + 0.910867i \(0.635415\pi\)
\(614\) −7.19999 + 32.9234i −0.290568 + 1.32868i
\(615\) 18.3724 17.6777i 0.740849 0.712835i
\(616\) 0 0
\(617\) −20.7105 20.7105i −0.833772 0.833772i 0.154258 0.988031i \(-0.450701\pi\)
−0.988031 + 0.154258i \(0.950701\pi\)
\(618\) 34.6591 + 54.0612i 1.39419 + 2.17466i
\(619\) 15.2502 + 26.4141i 0.612956 + 1.06167i 0.990739 + 0.135777i \(0.0433530\pi\)
−0.377784 + 0.925894i \(0.623314\pi\)
\(620\) 7.15137 14.8095i 0.287206 0.594763i
\(621\) −14.9597 + 25.9110i −0.600314 + 1.03977i
\(622\) −11.7946 + 22.8167i −0.472921 + 0.914866i
\(623\) 0 0
\(624\) 4.22784 12.0438i 0.169249 0.482138i
\(625\) −14.1299 + 20.6239i −0.565197 + 0.824956i
\(626\) −1.63964 1.49382i −0.0655330 0.0597052i
\(627\) 12.3065 + 3.29753i 0.491476 + 0.131691i
\(628\) −27.3548 22.6874i −1.09157 0.905326i
\(629\) 38.2714i 1.52598i
\(630\) 0 0
\(631\) 24.2931i 0.967092i 0.875319 + 0.483546i \(0.160651\pi\)
−0.875319 + 0.483546i \(0.839349\pi\)
\(632\) −1.57154 0.635173i −0.0625123 0.0252658i
\(633\) −60.9309 16.3264i −2.42178 0.648915i
\(634\) −28.1349 + 30.8811i −1.11738 + 1.22644i
\(635\) −27.2313 + 6.73706i −1.08064 + 0.267352i
\(636\) −3.67603 5.18637i −0.145764 0.205653i
\(637\) 0 0
\(638\) −8.58406 4.43735i −0.339846 0.175676i
\(639\) 45.1709 78.2383i 1.78693 3.09506i
\(640\) −24.1213 + 7.62658i −0.953477 + 0.301467i
\(641\) −11.2086 19.4138i −0.442712 0.766800i 0.555178 0.831732i \(-0.312650\pi\)
−0.997890 + 0.0649320i \(0.979317\pi\)
\(642\) −77.0595 + 49.4035i −3.04130 + 1.94980i
\(643\) 3.56268 + 3.56268i 0.140498 + 0.140498i 0.773858 0.633359i \(-0.218325\pi\)
−0.633359 + 0.773858i \(0.718325\pi\)
\(644\) 0 0
\(645\) −25.4913 0.491236i −1.00372 0.0193424i
\(646\) −17.9249 3.91997i −0.705245 0.154229i
\(647\) −16.0227 4.29327i −0.629918 0.168786i −0.0702854 0.997527i \(-0.522391\pi\)
−0.559632 + 0.828741i \(0.689058\pi\)
\(648\) 52.8246 41.2603i 2.07515 1.62086i
\(649\) 8.60829 + 4.97000i 0.337905 + 0.195089i
\(650\) −6.74007 + 1.86365i −0.264367 + 0.0730983i
\(651\) 0 0
\(652\) 5.84240 34.2821i 0.228806 1.34259i
\(653\) −3.24782 12.1210i −0.127097 0.474332i 0.872809 0.488062i \(-0.162296\pi\)
−0.999906 + 0.0137300i \(0.995629\pi\)
\(654\) 3.42430 + 3.11978i 0.133901 + 0.121993i
\(655\) −14.2074 25.7409i −0.555129 1.00578i
\(656\) −9.20918 10.7229i −0.359558 0.418660i
\(657\) 34.7502 + 34.7502i 1.35573 + 1.35573i
\(658\) 0 0
\(659\) 33.3787 1.30025 0.650126 0.759827i \(-0.274716\pi\)
0.650126 + 0.759827i \(0.274716\pi\)
\(660\) −15.3730 13.2581i −0.598393 0.516073i
\(661\) 3.47890 + 6.02563i 0.135313 + 0.234370i 0.925717 0.378217i \(-0.123463\pi\)
−0.790404 + 0.612586i \(0.790129\pi\)
\(662\) 17.8457 0.830422i 0.693593 0.0322753i
\(663\) −14.2484 + 3.81784i −0.553361 + 0.148273i
\(664\) 10.9251 14.4943i 0.423977 0.562488i
\(665\) 0 0
\(666\) −82.6892 + 26.3327i −3.20414 + 1.02037i
\(667\) −2.64214 9.86062i −0.102304 0.381805i
\(668\) −6.76973 18.2730i −0.261929 0.707005i
\(669\) −37.7211 + 21.7783i −1.45838 + 0.841997i
\(670\) −9.82862 2.34871i −0.379713 0.0907387i
\(671\) 3.09256i 0.119387i
\(672\) 0 0
\(673\) −5.34897 + 5.34897i −0.206188 + 0.206188i −0.802645 0.596457i \(-0.796575\pi\)
0.596457 + 0.802645i \(0.296575\pi\)
\(674\) 8.02127 + 1.75416i 0.308968 + 0.0675679i
\(675\) −67.9905 21.0570i −2.61696 0.810483i
\(676\) 21.8491 + 10.0363i 0.840350 + 0.386012i
\(677\) −28.9931 + 7.76868i −1.11430 + 0.298575i −0.768573 0.639762i \(-0.779033\pi\)
−0.345723 + 0.938337i \(0.612366\pi\)
\(678\) −42.3851 21.9101i −1.62779 0.841451i
\(679\) 0 0
\(680\) 23.0030 + 18.0440i 0.882127 + 0.691955i
\(681\) −29.7677 + 51.5592i −1.14070 + 1.97575i
\(682\) −0.340078 7.30825i −0.0130223 0.279847i
\(683\) 4.92938 18.3967i 0.188618 0.703930i −0.805210 0.592990i \(-0.797947\pi\)
0.993827 0.110940i \(-0.0353861\pi\)
\(684\) −3.86372 41.4257i −0.147733 1.58395i
\(685\) 11.2615 10.8357i 0.430281 0.414010i
\(686\) 0 0
\(687\) 35.6329 35.6329i 1.35948 1.35948i
\(688\) −1.07038 + 14.0941i −0.0408080 + 0.537334i
\(689\) −0.843665 + 0.487090i −0.0321411 + 0.0185567i
\(690\) −0.583938 21.4381i −0.0222302 0.816135i
\(691\) 24.4705 + 14.1281i 0.930903 + 0.537457i 0.887097 0.461583i \(-0.152718\pi\)
0.0438058 + 0.999040i \(0.486052\pi\)
\(692\) −48.7782 8.31284i −1.85427 0.316007i
\(693\) 0 0
\(694\) 19.9020 6.33786i 0.755470 0.240582i
\(695\) 40.6615 + 24.5325i 1.54238 + 0.930569i
\(696\) −5.40781 + 43.9970i −0.204983 + 1.66770i
\(697\) −4.22772 + 15.7781i −0.160136 + 0.597638i
\(698\) −3.85591 6.01445i −0.145948 0.227650i
\(699\) 12.3354 0.466567
\(700\) 0 0
\(701\) −26.0149 −0.982568 −0.491284 0.871000i \(-0.663472\pi\)
−0.491284 + 0.871000i \(0.663472\pi\)
\(702\) −10.7454 16.7607i −0.405560 0.632593i
\(703\) −6.01436 + 22.4459i −0.226836 + 0.846563i
\(704\) −7.81996 + 8.09370i −0.294726 + 0.305043i
\(705\) 16.3292 + 9.85194i 0.614992 + 0.371046i
\(706\) −14.6538 + 4.66656i −0.551504 + 0.175628i
\(707\) 0 0
\(708\) 7.66046 44.9501i 0.287898 1.68933i
\(709\) −15.2471 8.80290i −0.572616 0.330600i 0.185578 0.982630i \(-0.440584\pi\)
−0.758193 + 0.652030i \(0.773918\pi\)
\(710\) 1.04952 + 38.5310i 0.0393877 + 1.44604i
\(711\) −3.84667 + 2.22087i −0.144261 + 0.0832893i
\(712\) 0.491438 1.21591i 0.0184174 0.0455681i
\(713\) 5.46525 5.46525i 0.204675 0.204675i
\(714\) 0 0
\(715\) −2.24174 + 2.15697i −0.0838363 + 0.0806663i
\(716\) 40.9332 3.81779i 1.52975 0.142678i
\(717\) 12.9239 48.2328i 0.482653 1.80129i
\(718\) −0.327803 7.04445i −0.0122335 0.262897i
\(719\) 11.5866 20.0685i 0.432106 0.748429i −0.564949 0.825126i \(-0.691104\pi\)
0.997054 + 0.0766969i \(0.0244374\pi\)
\(720\) −23.1586 + 62.1156i −0.863070 + 2.31491i
\(721\) 0 0
\(722\) 13.9727 + 7.22290i 0.520011 + 0.268809i
\(723\) −89.6445 + 24.0202i −3.33391 + 0.893320i
\(724\) −6.56167 + 14.2848i −0.243863 + 0.530891i
\(725\) 21.4839 11.3233i 0.797892 0.420538i
\(726\) 40.2146 + 8.79448i 1.49250 + 0.326394i
\(727\) −15.3777 + 15.3777i −0.570326 + 0.570326i −0.932220 0.361893i \(-0.882131\pi\)
0.361893 + 0.932220i \(0.382131\pi\)
\(728\) 0 0
\(729\) 37.8443i 1.40164i
\(730\) −20.3937 4.87341i −0.754803 0.180373i
\(731\) 14.1462 8.16734i 0.523218 0.302080i
\(732\) 13.3031 4.92847i 0.491695 0.182162i
\(733\) −10.8115 40.3490i −0.399331 1.49032i −0.814276 0.580478i \(-0.802866\pi\)
0.414944 0.909847i \(-0.363801\pi\)
\(734\) 21.4725 6.83800i 0.792566 0.252395i
\(735\) 0 0
\(736\) −11.8844 0.348310i −0.438063 0.0128389i
\(737\) −4.34235 + 1.16353i −0.159953 + 0.0428592i
\(738\) −36.9990 + 1.72169i −1.36195 + 0.0633764i
\(739\) 14.4738 + 25.0693i 0.532426 + 0.922189i 0.999283 + 0.0378565i \(0.0120530\pi\)
−0.466857 + 0.884333i \(0.654614\pi\)
\(740\) 24.1815 28.0388i 0.888930 1.03073i
\(741\) −8.95654 −0.329027
\(742\) 0 0
\(743\) −23.4115 23.4115i −0.858885 0.858885i 0.132322 0.991207i \(-0.457757\pi\)
−0.991207 + 0.132322i \(0.957757\pi\)
\(744\) −30.8954 + 13.1097i −1.13268 + 0.480625i
\(745\) 7.17953 + 13.0078i 0.263038 + 0.476570i
\(746\) −0.615954 0.561178i −0.0225517 0.0205462i
\(747\) −12.3100 45.9417i −0.450401 1.68092i
\(748\) 12.8211 + 2.18499i 0.468786 + 0.0798912i
\(749\) 0 0
\(750\) 49.4266 12.6467i 1.80480 0.461793i
\(751\) −38.1178 22.0073i −1.39094 0.803059i −0.397520 0.917593i \(-0.630129\pi\)
−0.993419 + 0.114534i \(0.963462\pi\)
\(752\) 5.96457 8.72964i 0.217505 0.318337i
\(753\) 81.1249 + 21.7373i 2.95636 + 0.792153i
\(754\) 6.63623 + 1.45127i 0.241677 + 0.0528521i
\(755\) −45.5779 0.878318i −1.65875 0.0319653i
\(756\) 0 0
\(757\) 24.7062 + 24.7062i 0.897961 + 0.897961i 0.995256 0.0972943i \(-0.0310188\pi\)
−0.0972943 + 0.995256i \(0.531019\pi\)
\(758\) 28.2855 18.1341i 1.02738 0.658659i
\(759\) −4.77032 8.26243i −0.173152 0.299907i
\(760\) 10.6555 + 14.1976i 0.386516 + 0.515001i
\(761\) 2.24848 3.89448i 0.0815073 0.141175i −0.822390 0.568924i \(-0.807360\pi\)
0.903898 + 0.427749i \(0.140693\pi\)
\(762\) 50.8551 + 26.2885i 1.84229 + 0.952331i
\(763\) 0 0
\(764\) −14.1509 + 10.0300i −0.511963 + 0.362872i
\(765\) 74.3680 18.3987i 2.68878 0.665207i
\(766\) −4.09169 + 4.49108i −0.147839 + 0.162269i
\(767\) −6.74959 1.80855i −0.243714 0.0653029i
\(768\) 47.2784 + 20.7400i 1.70601 + 0.748391i
\(769\) 14.9079i 0.537593i −0.963197 0.268797i \(-0.913374\pi\)
0.963197 0.268797i \(-0.0866259\pi\)
\(770\) 0 0
\(771\) 74.4723i 2.68206i
\(772\) 6.77398 8.16757i 0.243801 0.293957i
\(773\) −26.7544 7.16881i −0.962287 0.257844i −0.256719 0.966486i \(-0.582642\pi\)
−0.705568 + 0.708642i \(0.749308\pi\)
\(774\) 27.3797 + 24.9449i 0.984143 + 0.896624i
\(775\) 15.5575 + 9.80011i 0.558842 + 0.352030i
\(776\) 19.2747 25.5717i 0.691923 0.917971i
\(777\) 0 0
\(778\) −16.3587 + 31.6460i −0.586489 + 1.13456i
\(779\) −4.95906 + 8.58934i −0.177677 + 0.307745i
\(780\) 12.8511 + 6.20567i 0.460142 + 0.222199i
\(781\) 8.57374 + 14.8502i 0.306793 + 0.531380i
\(782\) 7.41566 + 11.5669i 0.265183 + 0.413633i
\(783\) 48.8906 + 48.8906i 1.74721 + 1.74721i
\(784\) 0 0
\(785\) 28.6320 27.5493i 1.02192 0.983277i
\(786\) −12.8186 + 58.6158i −0.457226 + 2.09076i
\(787\) −5.43008 1.45499i −0.193561 0.0518646i 0.160736 0.986997i \(-0.448613\pi\)
−0.354297 + 0.935133i \(0.615280\pi\)
\(788\) −32.7387 + 12.1289i −1.16627 + 0.432075i
\(789\) −31.7166 18.3116i −1.12914 0.651911i
\(790\) 0.902519 1.66641i 0.0321102 0.0592882i
\(791\) 0 0
\(792\) 4.10068 + 29.2047i 0.145711 + 1.03774i
\(793\) −0.562681 2.09996i −0.0199814 0.0745716i
\(794\) 3.68582 4.04559i 0.130805 0.143572i
\(795\) 6.22248 3.43443i 0.220689 0.121807i
\(796\) −8.56049 + 0.798427i −0.303419 + 0.0282995i
\(797\) −10.9874 10.9874i −0.389195 0.389195i 0.485205 0.874400i \(-0.338745\pi\)
−0.874400 + 0.485205i \(0.838745\pi\)
\(798\) 0 0
\(799\) −12.2183 −0.432252
\(800\) −5.45176 27.7539i −0.192749 0.981248i
\(801\) −1.71830 2.97619i −0.0607133 0.105159i
\(802\) −0.360718 7.75180i −0.0127374 0.273726i
\(803\) −9.01005 + 2.41424i −0.317958 + 0.0851965i
\(804\) 11.9253 + 16.8249i 0.420572 + 0.593369i
\(805\) 0 0
\(806\) 1.56063 + 4.90067i 0.0549710 + 0.172619i
\(807\) 22.7306 + 84.8316i 0.800154 + 2.98621i
\(808\) 13.4434 10.5004i 0.472936 0.369402i
\(809\) 14.4297 8.33096i 0.507320 0.292901i −0.224412 0.974494i \(-0.572046\pi\)
0.731731 + 0.681593i \(0.238713\pi\)
\(810\) 39.2234 + 63.8560i 1.37817 + 2.24367i
\(811\) 30.5372i 1.07231i −0.844120 0.536154i \(-0.819877\pi\)
0.844120 0.536154i \(-0.180123\pi\)
\(812\) 0 0
\(813\) 0.355563 0.355563i 0.0124701 0.0124701i
\(814\) 3.51899 16.0913i 0.123341 0.564000i
\(815\) 37.3554 + 10.7849i 1.30850 + 0.377779i
\(816\) −11.0334 58.6338i −0.386246 2.05259i
\(817\) 9.58017 2.56700i 0.335168 0.0898079i
\(818\) 11.0355 21.3481i 0.385846 0.746420i
\(819\) 0 0
\(820\) 13.0666 8.88825i 0.456307 0.310391i
\(821\) 9.24225 16.0080i 0.322557 0.558685i −0.658458 0.752617i \(-0.728791\pi\)
0.981015 + 0.193933i \(0.0621243\pi\)
\(822\) −31.8584 + 1.48248i −1.11119 + 0.0517075i
\(823\) 11.0750 41.3323i 0.386049 1.44075i −0.450457 0.892798i \(-0.648739\pi\)
0.836507 0.547957i \(-0.184594\pi\)
\(824\) 15.5478 + 36.6413i 0.541634 + 1.27646i
\(825\) 16.6553 15.4187i 0.579863 0.536809i
\(826\) 0 0
\(827\) 22.7990 22.7990i 0.792801 0.792801i −0.189148 0.981949i \(-0.560573\pi\)
0.981949 + 0.189148i \(0.0605726\pi\)
\(828\) −19.8892 + 23.9809i −0.691198 + 0.833395i
\(829\) 29.0025 16.7446i 1.00730 0.581563i 0.0968981 0.995294i \(-0.469108\pi\)
0.910399 + 0.413731i \(0.135775\pi\)
\(830\) 14.7347 + 13.9533i 0.511448 + 0.484324i
\(831\) 58.4953 + 33.7723i 2.02918 + 1.17155i
\(832\) 3.83740 6.91871i 0.133038 0.239863i
\(833\) 0 0
\(834\) −29.4072 92.3440i −1.01829 3.19761i
\(835\) 21.1492 5.23233i 0.731898 0.181072i
\(836\) 7.17612 + 3.29632i 0.248191 + 0.114006i
\(837\) −13.5488 + 50.5649i −0.468316 + 1.74778i
\(838\) 4.61406 2.95811i 0.159390 0.102186i
\(839\) −6.43773 −0.222255 −0.111127 0.993806i \(-0.535446\pi\)
−0.111127 + 0.993806i \(0.535446\pi\)
\(840\) 0 0
\(841\) 5.40897 0.186516
\(842\) 24.6635 15.8119i 0.849959 0.544916i
\(843\) −2.14092 + 7.99001i −0.0737371 + 0.275190i
\(844\) −35.5296 16.3204i −1.22298 0.561772i
\(845\) −13.8870 + 23.0171i −0.477728 + 0.791814i
\(846\) −8.40681 26.3989i −0.289032 0.907612i
\(847\) 0 0
\(848\) −1.70605 3.55174i −0.0585862 0.121967i
\(849\) 57.4949 + 33.1947i 1.97322 + 1.13924i
\(850\) −22.9281 + 23.2962i −0.786426 + 0.799052i
\(851\) 15.0698 8.70057i 0.516587 0.298252i
\(852\) 50.2163 60.5471i 1.72038 2.07431i
\(853\) 10.0581 10.0581i 0.344383 0.344383i −0.513629 0.858012i \(-0.671699\pi\)
0.858012 + 0.513629i \(0.171699\pi\)
\(854\) 0 0
\(855\) 46.5077 + 0.896235i 1.59053 + 0.0306506i
\(856\) −52.2289 + 22.1621i −1.78515 + 0.757484i
\(857\) −0.134823 + 0.503168i −0.00460548 + 0.0171879i −0.968190 0.250215i \(-0.919499\pi\)
0.963585 + 0.267403i \(0.0861654\pi\)
\(858\) 6.34180 0.295106i 0.216506 0.0100747i
\(859\) 2.00473 3.47230i 0.0684006 0.118473i −0.829797 0.558066i \(-0.811544\pi\)
0.898197 + 0.439592i \(0.144877\pi\)
\(860\) −15.5244 2.95457i −0.529379 0.100750i
\(861\) 0 0
\(862\) −6.34407 + 12.2726i −0.216080 + 0.418007i
\(863\) −14.3236 + 3.83800i −0.487581 + 0.130647i −0.494231 0.869331i \(-0.664550\pi\)
0.00664926 + 0.999978i \(0.497883\pi\)
\(864\) 70.8882 38.2032i 2.41166 1.29970i
\(865\) 15.3453 53.1511i 0.521756 1.80719i
\(866\) 2.99471 13.6939i 0.101764 0.465338i
\(867\) −9.96649 + 9.96649i −0.338480 + 0.338480i
\(868\) 0 0
\(869\) 0.843073i 0.0285993i
\(870\) −48.2031 11.5189i −1.63424 0.390529i
\(871\) 2.73690 1.58015i 0.0927364 0.0535414i
\(872\) 1.76744 + 2.26280i 0.0598529 + 0.0766282i
\(873\) −21.7181 81.0531i −0.735046 2.74323i
\(874\) 2.53148 + 7.94930i 0.0856287 + 0.268889i
\(875\) 0 0
\(876\) 24.7440 + 34.9104i 0.836024 + 1.17951i
\(877\) 29.9552 8.02646i 1.01151 0.271034i 0.285252 0.958453i \(-0.407923\pi\)
0.726262 + 0.687418i \(0.241256\pi\)
\(878\) −0.290939 6.25225i −0.00981871 0.211003i
\(879\) −10.7488 18.6175i −0.362548 0.627952i
\(880\) −8.01257 9.70173i −0.270104 0.327045i
\(881\) 26.6186 0.896802 0.448401 0.893833i \(-0.351994\pi\)
0.448401 + 0.893833i \(0.351994\pi\)
\(882\) 0 0
\(883\) −20.2772 20.2772i −0.682383 0.682383i 0.278154 0.960537i \(-0.410278\pi\)
−0.960537 + 0.278154i \(0.910278\pi\)
\(884\) −9.10352 + 0.849075i −0.306185 + 0.0285575i
\(885\) 48.9799 + 14.1410i 1.64644 + 0.475345i
\(886\) −4.19245 + 4.60167i −0.140848 + 0.154596i
\(887\) −11.0601 41.2767i −0.371361 1.38594i −0.858590 0.512663i \(-0.828659\pi\)
0.487229 0.873274i \(-0.338008\pi\)
\(888\) −74.8268 + 10.5066i −2.51102 + 0.352577i
\(889\) 0 0
\(890\) 1.28931 + 0.698285i 0.0432179 + 0.0234066i
\(891\) 28.8720 + 16.6692i 0.967247 + 0.558440i
\(892\) −25.3159 + 9.37896i −0.847640 + 0.314031i
\(893\) −7.16594 1.92011i −0.239799 0.0642540i
\(894\) 6.47774 29.6208i 0.216648 0.990667i
\(895\) −0.885581 + 45.9548i −0.0296017 + 1.53610i
\(896\) 0 0
\(897\) 4.74253 + 4.74253i 0.158348 + 0.158348i
\(898\) −16.6664 25.9963i −0.556166 0.867508i
\(899\) −8.93063 15.4683i −0.297853 0.515897i
\(900\) −66.1094 33.5095i −2.20365 1.11698i
\(901\) −2.27675 + 3.94345i −0.0758496 + 0.131375i
\(902\) 3.22832 6.24520i 0.107491 0.207942i
\(903\) 0 0
\(904\) −23.6164 17.8010i −0.785471 0.592051i
\(905\) −15.0485 9.07925i −0.500228 0.301804i
\(906\) 68.7692 + 62.6537i 2.28471 + 2.08153i
\(907\) 1.18466 + 0.317430i 0.0393361 + 0.0105401i 0.278433 0.960456i \(-0.410185\pi\)
−0.239097 + 0.970996i \(0.576852\pi\)
\(908\) −23.5574 + 28.4037i −0.781780 + 0.942611i
\(909\) 44.6999i 1.48260i
\(910\) 0 0
\(911\) 13.4236i 0.444743i −0.974962 0.222372i \(-0.928620\pi\)
0.974962 0.222372i \(-0.0713799\pi\)
\(912\) 2.74331 36.1222i 0.0908401 1.19613i
\(913\) 8.72004 + 2.33653i 0.288591 + 0.0773277i
\(914\) 20.9820 23.0301i 0.694024 0.761767i
\(915\) 3.80922 + 15.3970i 0.125929 + 0.509008i
\(916\) 25.4827 18.0618i 0.841974 0.596779i
\(917\) 0 0
\(918\) −82.6686 42.7338i −2.72847 1.41042i
\(919\) −13.1243 + 22.7320i −0.432931 + 0.749858i −0.997124 0.0757845i \(-0.975854\pi\)
0.564193 + 0.825643i \(0.309187\pi\)
\(920\) 1.87556 13.1598i 0.0618353 0.433867i
\(921\) 38.4473 + 66.5926i 1.26688 + 2.19430i
\(922\) −23.5337 + 15.0876i −0.775040 + 0.496884i
\(923\) −8.52380 8.52380i −0.280564 0.280564i
\(924\) 0 0
\(925\) 28.1221 + 30.3776i 0.924649 + 0.998809i
\(926\) 28.3772 + 6.20577i 0.932532 + 0.203934i
\(927\) 100.748 + 26.9955i 3.30901 + 0.886647i
\(928\) −7.88567 + 26.3197i −0.258860 + 0.863988i
\(929\) −17.2412 9.95422i −0.565666 0.326587i 0.189751 0.981832i \(-0.439232\pi\)
−0.755416 + 0.655245i \(0.772565\pi\)
\(930\) −10.6950 35.9667i −0.350702 1.17940i
\(931\) 0 0
\(932\) 7.53711 + 1.28448i 0.246886 + 0.0420747i
\(933\) 15.1677 + 56.6067i 0.496569 + 1.85322i
\(934\) 29.4721 + 26.8512i 0.964356 + 0.878597i
\(935\) −4.03344 + 13.9705i −0.131908 + 0.456885i
\(936\) −8.09820 19.0849i −0.264698 0.623809i
\(937\) −3.76752 3.76752i −0.123080 0.123080i 0.642884 0.765964i \(-0.277738\pi\)
−0.765964 + 0.642884i \(0.777738\pi\)
\(938\) 0 0
\(939\) −5.06087 −0.165155
\(940\) 8.95150 + 7.72005i 0.291966 + 0.251800i
\(941\) −2.41962 4.19090i −0.0788772 0.136619i 0.823889 0.566752i \(-0.191800\pi\)
−0.902766 + 0.430133i \(0.858467\pi\)
\(942\) −80.9988 + 3.76915i −2.63908 + 0.122806i
\(943\) 7.17394 1.92225i 0.233616 0.0625971i
\(944\) 9.36132 26.6675i 0.304685 0.867954i
\(945\) 0 0
\(946\) −6.69879 + 2.13325i −0.217797 + 0.0693580i
\(947\) −8.02761 29.9595i −0.260862 0.973551i −0.964735 0.263225i \(-0.915214\pi\)
0.703872 0.710327i \(-0.251453\pi\)
\(948\) −3.62659 + 1.34357i −0.117786 + 0.0436370i
\(949\) 5.67887 3.27870i 0.184344 0.106431i
\(950\) −17.1081 + 10.0599i −0.555061 + 0.326386i
\(951\) 95.3170i 3.09086i
\(952\) 0 0
\(953\) 22.3422 22.3422i 0.723734 0.723734i −0.245630 0.969364i \(-0.578995\pi\)
0.969364 + 0.245630i \(0.0789947\pi\)
\(954\) −10.0868 2.20586i −0.326571 0.0714174i
\(955\) −9.37078 16.9779i −0.303231 0.549393i
\(956\) 12.9192 28.1252i 0.417837 0.909634i
\(957\) −21.2965 + 5.70637i −0.688417 + 0.184461i
\(958\) 1.78236 + 0.921354i 0.0575855 + 0.0297676i
\(959\) 0 0
\(960\) −28.9640 + 49.9283i −0.934808 + 1.61143i
\(961\) −8.73844 + 15.1354i −0.281885 + 0.488239i
\(962\) 0.538243 + 11.5668i 0.0173537 + 0.372929i
\(963\) −38.4796 + 143.608i −1.23999 + 4.62770i
\(964\) −57.2754 + 5.34201i −1.84472 + 0.172055i
\(965\) 8.22565 + 8.54890i 0.264793 + 0.275199i
\(966\) 0 0
\(967\) 8.85634 8.85634i 0.284801 0.284801i −0.550219 0.835020i \(-0.685456\pi\)
0.835020 + 0.550219i \(0.185456\pi\)
\(968\) 23.6560 + 9.56111i 0.760331 + 0.307306i
\(969\) −36.2558 + 20.9323i −1.16470 + 0.672442i
\(970\) 25.9958 + 24.6172i 0.834674 + 0.790409i
\(971\) 8.19063 + 4.72886i 0.262850 + 0.151756i 0.625634 0.780117i \(-0.284840\pi\)
−0.362784 + 0.931873i \(0.618174\pi\)
\(972\) 11.3438 66.5634i 0.363854 2.13502i
\(973\) 0 0
\(974\) 45.3582 14.4445i 1.45337 0.462831i
\(975\) −8.50414 + 13.5002i −0.272350 + 0.432352i
\(976\) 8.64158 1.62613i 0.276610 0.0520510i
\(977\) −15.9873 + 59.6654i −0.511479 + 1.90886i −0.107173 + 0.994240i \(0.534180\pi\)
−0.404305 + 0.914624i \(0.632487\pi\)
\(978\) −42.8247 66.7980i −1.36938 2.13596i
\(979\) 0.652291 0.0208473
\(980\) 0 0
\(981\) 7.52393 0.240221
\(982\) −2.41708 3.77016i −0.0771321 0.120311i
\(983\) 15.3538 57.3012i 0.489710 1.82762i −0.0681315 0.997676i \(-0.521704\pi\)
0.557842 0.829947i \(-0.311630\pi\)
\(984\) −32.0094 3.93437i −1.02042 0.125423i
\(985\) −9.37447 37.8918i −0.298695 1.20733i
\(986\) 30.2550 9.63480i 0.963515 0.306834i
\(987\) 0 0
\(988\) −5.47258 0.932645i −0.174106 0.0296714i
\(989\) −6.43198 3.71351i −0.204525 0.118083i
\(990\) −32.9599 + 0.897773i −1.04754 + 0.0285331i
\(991\) −15.0202 + 8.67190i −0.477131 + 0.275472i −0.719220 0.694782i \(-0.755501\pi\)
0.242089 + 0.970254i \(0.422167\pi\)
\(992\) −20.2427 + 4.79309i −0.642706 + 0.152181i
\(993\) 28.8227 28.8227i 0.914660 0.914660i
\(994\) 0 0
\(995\) 0.185204 9.61068i 0.00587137 0.304679i
\(996\) −3.84584 41.2340i −0.121860 1.30655i
\(997\) 3.99308 14.9024i 0.126462 0.471964i −0.873425 0.486958i \(-0.838106\pi\)
0.999888 + 0.0149945i \(0.00477309\pi\)
\(998\) 0.489677 + 10.5231i 0.0155005 + 0.333104i
\(999\) −58.9289 + 102.068i −1.86443 + 3.22928i
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 980.2.x.k.667.16 72
4.3 odd 2 inner 980.2.x.k.667.18 72
5.3 odd 4 inner 980.2.x.k.863.7 72
7.2 even 3 140.2.k.a.127.3 yes 36
7.3 odd 6 980.2.x.l.67.10 72
7.4 even 3 inner 980.2.x.k.67.10 72
7.5 odd 6 980.2.k.l.687.3 36
7.6 odd 2 980.2.x.l.667.16 72
20.3 even 4 inner 980.2.x.k.863.10 72
28.3 even 6 980.2.x.l.67.7 72
28.11 odd 6 inner 980.2.x.k.67.7 72
28.19 even 6 980.2.k.l.687.6 36
28.23 odd 6 140.2.k.a.127.6 yes 36
28.27 even 2 980.2.x.l.667.18 72
35.2 odd 12 700.2.k.b.43.13 36
35.3 even 12 980.2.x.l.263.18 72
35.9 even 6 700.2.k.b.407.16 36
35.13 even 4 980.2.x.l.863.7 72
35.18 odd 12 inner 980.2.x.k.263.18 72
35.23 odd 12 140.2.k.a.43.6 yes 36
35.33 even 12 980.2.k.l.883.6 36
140.3 odd 12 980.2.x.l.263.16 72
140.23 even 12 140.2.k.a.43.3 36
140.79 odd 6 700.2.k.b.407.13 36
140.83 odd 4 980.2.x.l.863.10 72
140.103 odd 12 980.2.k.l.883.3 36
140.107 even 12 700.2.k.b.43.16 36
140.123 even 12 inner 980.2.x.k.263.16 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.k.a.43.3 36 140.23 even 12
140.2.k.a.43.6 yes 36 35.23 odd 12
140.2.k.a.127.3 yes 36 7.2 even 3
140.2.k.a.127.6 yes 36 28.23 odd 6
700.2.k.b.43.13 36 35.2 odd 12
700.2.k.b.43.16 36 140.107 even 12
700.2.k.b.407.13 36 140.79 odd 6
700.2.k.b.407.16 36 35.9 even 6
980.2.k.l.687.3 36 7.5 odd 6
980.2.k.l.687.6 36 28.19 even 6
980.2.k.l.883.3 36 140.103 odd 12
980.2.k.l.883.6 36 35.33 even 12
980.2.x.k.67.7 72 28.11 odd 6 inner
980.2.x.k.67.10 72 7.4 even 3 inner
980.2.x.k.263.16 72 140.123 even 12 inner
980.2.x.k.263.18 72 35.18 odd 12 inner
980.2.x.k.667.16 72 1.1 even 1 trivial
980.2.x.k.667.18 72 4.3 odd 2 inner
980.2.x.k.863.7 72 5.3 odd 4 inner
980.2.x.k.863.10 72 20.3 even 4 inner
980.2.x.l.67.7 72 28.3 even 6
980.2.x.l.67.10 72 7.3 odd 6
980.2.x.l.263.16 72 140.3 odd 12
980.2.x.l.263.18 72 35.3 even 12
980.2.x.l.667.16 72 7.6 odd 2
980.2.x.l.667.18 72 28.27 even 2
980.2.x.l.863.7 72 35.13 even 4
980.2.x.l.863.10 72 140.83 odd 4