Properties

Label 980.2.x.l.263.18
Level $980$
Weight $2$
Character 980.263
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 263.18
Character \(\chi\) \(=\) 980.263
Dual form 980.2.x.l.667.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41268 - 0.0657371i) q^{2} +(0.835136 + 3.11677i) q^{3} +(1.99136 - 0.185732i) q^{4} +(-1.91459 + 1.15514i) q^{5} +(1.38467 + 4.34811i) q^{6} +(2.80095 - 0.393286i) q^{8} +(-6.41872 + 3.70585i) q^{9} +O(q^{10})\) \(q+(1.41268 - 0.0657371i) q^{2} +(0.835136 + 3.11677i) q^{3} +(1.99136 - 0.185732i) q^{4} +(-1.91459 + 1.15514i) q^{5} +(1.38467 + 4.34811i) q^{6} +(2.80095 - 0.393286i) q^{8} +(-6.41872 + 3.70585i) q^{9} +(-2.62878 + 1.75770i) q^{10} +(-1.21832 - 0.703395i) q^{11} +(2.24194 + 6.05149i) q^{12} +(0.699298 + 0.699298i) q^{13} +(-5.19924 - 5.00264i) q^{15} +(3.93101 - 0.739716i) q^{16} +(1.19641 + 4.46506i) q^{17} +(-8.82402 + 5.65715i) q^{18} +(-1.40337 - 2.43071i) q^{19} +(-3.59809 + 2.65589i) q^{20} +(-1.76734 - 0.913587i) q^{22} +(-2.03016 - 0.543980i) q^{23} +(3.56496 + 8.40147i) q^{24} +(2.33132 - 4.42323i) q^{25} +(1.03386 + 0.941917i) q^{26} +(-10.0659 - 10.0659i) q^{27} +4.85706i q^{29} +(-7.67375 - 6.72537i) q^{30} +(3.18470 + 1.83869i) q^{31} +(5.50465 - 1.30340i) 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} +(-2.14231 - 3.34157i) q^{38} +(-1.59554 + 2.76356i) q^{39} +(-4.90838 + 3.98846i) q^{40} -3.53368 q^{41} +(2.49869 - 2.49869i) q^{43} +(-2.55675 - 1.17443i) q^{44} +(8.00846 - 14.5097i) q^{45} +(-2.90374 - 0.635016i) q^{46} +(0.684106 - 2.55312i) q^{47} +(5.58845 + 11.6343i) q^{48} +(3.00265 - 6.40188i) q^{50} +(-12.9174 + 7.45786i) q^{51} +(1.52243 + 1.26267i) q^{52} +(0.951495 - 0.254952i) q^{53} +(-14.8816 - 13.5582i) q^{54} +(3.14510 - 0.0606082i) q^{55} +(6.40395 - 6.40395i) q^{57} +(0.319289 + 6.86149i) q^{58} +(3.53286 - 6.11910i) q^{59} +(-11.2827 - 8.99638i) q^{60} +(1.09916 + 1.90379i) q^{61} +(4.61985 + 2.38814i) q^{62} +(7.69065 - 2.20315i) q^{64} +(-2.14665 - 0.531084i) q^{65} +(1.37148 - 6.27135i) q^{66} +(3.08671 - 0.827081i) q^{67} +(3.21178 + 8.66931i) q^{68} -6.78184i q^{69} +12.1891i q^{71} +(-16.5211 + 12.9043i) q^{72} +(6.40469 - 1.71613i) q^{73} +(11.4383 + 2.50143i) q^{74} +(15.7332 + 3.57218i) q^{75} +(-3.24607 - 4.57976i) q^{76} +(-2.07233 + 4.00892i) q^{78} +(-0.299644 - 0.518999i) q^{79} +(-6.67180 + 5.95711i) q^{80} +(11.8491 - 20.5233i) q^{81} +(-4.99198 + 0.232294i) q^{82} +(4.53764 - 4.53764i) q^{83} +(-7.44839 - 7.16674i) q^{85} +(3.36560 - 3.69412i) q^{86} +(-15.1383 + 4.05630i) q^{87} +(-3.68908 - 1.49103i) q^{88} +(-0.401553 + 0.231837i) q^{89} +(10.3596 - 21.0241i) q^{90} +(-4.14381 - 0.706194i) q^{92} +(-3.07111 + 11.4615i) q^{93} +(0.798592 - 3.65172i) q^{94} +(5.49468 + 3.03273i) q^{95} +(8.65952 + 16.0682i) 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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41268 0.0657371i 0.998919 0.0464831i
\(3\) 0.835136 + 3.11677i 0.482166 + 1.79947i 0.592497 + 0.805573i \(0.298142\pi\)
−0.110331 + 0.993895i \(0.535191\pi\)
\(4\) 1.99136 0.185732i 0.995679 0.0928658i
\(5\) −1.91459 + 1.15514i −0.856231 + 0.516593i
\(6\) 1.38467 + 4.34811i 0.565290 + 1.77511i
\(7\) 0 0
\(8\) 2.80095 0.393286i 0.990286 0.139048i
\(9\) −6.41872 + 3.70585i −2.13957 + 1.23528i
\(10\) −2.62878 + 1.75770i −0.831293 + 0.555835i
\(11\) −1.21832 0.703395i −0.367336 0.212082i 0.304958 0.952366i \(-0.401358\pi\)
−0.672294 + 0.740284i \(0.734691\pi\)
\(12\) 2.24194 + 6.05149i 0.647191 + 1.74691i
\(13\) 0.699298 + 0.699298i 0.193950 + 0.193950i 0.797401 0.603450i \(-0.206208\pi\)
−0.603450 + 0.797401i \(0.706208\pi\)
\(14\) 0 0
\(15\) −5.19924 5.00264i −1.34244 1.29168i
\(16\) 3.93101 0.739716i 0.982752 0.184929i
\(17\) 1.19641 + 4.46506i 0.290172 + 1.08294i 0.944977 + 0.327138i \(0.106084\pi\)
−0.654805 + 0.755798i \(0.727249\pi\)
\(18\) −8.82402 + 5.65715i −2.07984 + 1.33340i
\(19\) −1.40337 2.43071i −0.321955 0.557643i 0.658936 0.752199i \(-0.271007\pi\)
−0.980891 + 0.194556i \(0.937673\pi\)
\(20\) −3.59809 + 2.65589i −0.804557 + 0.593875i
\(21\) 0 0
\(22\) −1.76734 0.913587i −0.376797 0.194777i
\(23\) −2.03016 0.543980i −0.423318 0.113428i 0.0408699 0.999164i \(-0.486987\pi\)
−0.464188 + 0.885737i \(0.653654\pi\)
\(24\) 3.56496 + 8.40147i 0.727694 + 1.71494i
\(25\) 2.33132 4.42323i 0.466263 0.884646i
\(26\) 1.03386 + 0.941917i 0.202756 + 0.184725i
\(27\) −10.0659 10.0659i −1.93718 1.93718i
\(28\) 0 0
\(29\) 4.85706i 0.901933i 0.892541 + 0.450967i \(0.148921\pi\)
−0.892541 + 0.450967i \(0.851079\pi\)
\(30\) −7.67375 6.72537i −1.40103 1.22788i
\(31\) 3.18470 + 1.83869i 0.571990 + 0.330238i 0.757944 0.652320i \(-0.226204\pi\)
−0.185954 + 0.982558i \(0.559538\pi\)
\(32\) 5.50465 1.30340i 0.973094 0.230410i
\(33\) 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 0.846998 0.531596i \(-0.178408\pi\)
0.467724 + 0.883875i \(0.345074\pi\)
\(38\) −2.14231 3.34157i −0.347528 0.542074i
\(39\) −1.59554 + 2.76356i −0.255491 + 0.442523i
\(40\) −4.90838 + 3.98846i −0.776082 + 0.630632i
\(41\) −3.53368 −0.551868 −0.275934 0.961177i \(-0.588987\pi\)
−0.275934 + 0.961177i \(0.588987\pi\)
\(42\) 0 0
\(43\) 2.49869 2.49869i 0.381046 0.381046i −0.490433 0.871479i \(-0.663161\pi\)
0.871479 + 0.490433i \(0.163161\pi\)
\(44\) −2.55675 1.17443i −0.385444 0.177052i
\(45\) 8.00846 14.5097i 1.19383 2.16298i
\(46\) −2.90374 0.635016i −0.428133 0.0936280i
\(47\) 0.684106 2.55312i 0.0997872 0.372411i −0.897915 0.440170i \(-0.854918\pi\)
0.997702 + 0.0677590i \(0.0215849\pi\)
\(48\) 5.58845 + 11.6343i 0.806623 + 1.67926i
\(49\) 0 0
\(50\) 3.00265 6.40188i 0.424638 0.905363i
\(51\) −12.9174 + 7.45786i −1.80880 + 1.04431i
\(52\) 1.52243 + 1.26267i 0.211123 + 0.175101i
\(53\) 0.951495 0.254952i 0.130698 0.0350204i −0.192877 0.981223i \(-0.561782\pi\)
0.323575 + 0.946203i \(0.395115\pi\)
\(54\) −14.8816 13.5582i −2.02513 1.84504i
\(55\) 3.14510 0.0606082i 0.424085 0.00817240i
\(56\) 0 0
\(57\) 6.40395 6.40395i 0.848224 0.848224i
\(58\) 0.319289 + 6.86149i 0.0419247 + 0.900958i
\(59\) 3.53286 6.11910i 0.459940 0.796639i −0.539018 0.842294i \(-0.681204\pi\)
0.998957 + 0.0456557i \(0.0145377\pi\)
\(60\) −11.2827 8.99638i −1.45659 1.16143i
\(61\) 1.09916 + 1.90379i 0.140732 + 0.243756i 0.927773 0.373146i \(-0.121721\pi\)
−0.787040 + 0.616902i \(0.788388\pi\)
\(62\) 4.61985 + 2.38814i 0.586722 + 0.303294i
\(63\) 0 0
\(64\) 7.69065 2.20315i 0.961331 0.275394i
\(65\) −2.14665 0.531084i −0.266260 0.0658729i
\(66\) 1.37148 6.27135i 0.168817 0.771950i
\(67\) 3.08671 0.827081i 0.377101 0.101044i −0.0652895 0.997866i \(-0.520797\pi\)
0.442391 + 0.896822i \(0.354130\pi\)
\(68\) 3.21178 + 8.66931i 0.389485 + 1.05131i
\(69\) 6.78184i 0.816438i
\(70\) 0 0
\(71\) 12.1891i 1.44658i 0.690546 + 0.723289i \(0.257370\pi\)
−0.690546 + 0.723289i \(0.742630\pi\)
\(72\) −16.5211 + 12.9043i −1.94703 + 1.52079i
\(73\) 6.40469 1.71613i 0.749612 0.200858i 0.136266 0.990672i \(-0.456490\pi\)
0.613346 + 0.789814i \(0.289823\pi\)
\(74\) 11.4383 + 2.50143i 1.32968 + 0.290785i
\(75\) 15.7332 + 3.57218i 1.81671 + 0.412480i
\(76\) −3.24607 4.57976i −0.372350 0.525334i
\(77\) 0 0
\(78\) −2.07233 + 4.00892i −0.234645 + 0.453921i
\(79\) −0.299644 0.518999i −0.0337126 0.0583919i 0.848677 0.528912i \(-0.177400\pi\)
−0.882389 + 0.470520i \(0.844066\pi\)
\(80\) −6.67180 + 5.95711i −0.745930 + 0.666025i
\(81\) 11.8491 20.5233i 1.31657 2.28036i
\(82\) −4.99198 + 0.232294i −0.551271 + 0.0256526i
\(83\) 4.53764 4.53764i 0.498071 0.498071i −0.412766 0.910837i \(-0.635437\pi\)
0.910837 + 0.412766i \(0.135437\pi\)
\(84\) 0 0
\(85\) −7.44839 7.16674i −0.807891 0.777342i
\(86\) 3.36560 3.69412i 0.362922 0.398347i
\(87\) −15.1383 + 4.05630i −1.62300 + 0.434882i
\(88\) −3.68908 1.49103i −0.393257 0.158944i
\(89\) −0.401553 + 0.231837i −0.0425645 + 0.0245746i −0.521131 0.853477i \(-0.674490\pi\)
0.478567 + 0.878051i \(0.341156\pi\)
\(90\) 10.3596 21.0241i 1.09200 2.21613i
\(91\) 0 0
\(92\) −4.14381 0.706194i −0.432022 0.0736258i
\(93\) −3.07111 + 11.4615i −0.318459 + 1.18851i
\(94\) 0.798592 3.65172i 0.0823685 0.376647i
\(95\) 5.49468 + 3.03273i 0.563742 + 0.311151i
\(96\) 8.65952 + 16.0682i 0.883809 + 1.63995i
\(97\) −8.00558 + 8.00558i −0.812843 + 0.812843i −0.985059 0.172216i \(-0.944907\pi\)
0.172216 + 0.985059i \(0.444907\pi\)
\(98\) 0 0
\(99\) 10.4267 1.04792
\(100\) 3.82095 9.24123i 0.382095 0.924123i
\(101\) −3.01549 + 5.22299i −0.300053 + 0.519707i −0.976148 0.217108i \(-0.930338\pi\)
0.676095 + 0.736815i \(0.263671\pi\)
\(102\) −17.7579 + 11.3848i −1.75830 + 1.12726i
\(103\) −13.5932 3.64227i −1.33937 0.358884i −0.483171 0.875526i \(-0.660515\pi\)
−0.856202 + 0.516642i \(0.827182\pi\)
\(104\) 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 0.0146144 0.999893i \(-0.495348\pi\)
0.487290 0.873240i \(-0.337985\pi\)
\(108\) −21.9143 18.1752i −2.10871 1.74891i
\(109\) −0.879139 0.507571i −0.0842062 0.0486165i 0.457306 0.889310i \(-0.348815\pi\)
−0.541512 + 0.840693i \(0.682148\pi\)
\(110\) 4.43904 0.292370i 0.423246 0.0278764i
\(111\) 26.7148i 2.53566i
\(112\) 0 0
\(113\) 7.39345 + 7.39345i 0.695518 + 0.695518i 0.963440 0.267923i \(-0.0863372\pi\)
−0.267923 + 0.963440i \(0.586337\pi\)
\(114\) 8.62579 9.46774i 0.807879 0.886735i
\(115\) 4.51530 1.30362i 0.421054 0.121563i
\(116\) 0.902109 + 9.67214i 0.0837588 + 0.898036i
\(117\) −7.08009 1.89711i −0.654555 0.175387i
\(118\) 4.58857 8.87660i 0.422412 0.817157i
\(119\) 0 0
\(120\) −16.5303 11.9674i −1.50900 1.09247i
\(121\) −4.51047 7.81236i −0.410043 0.710215i
\(122\) 1.67791 + 2.61721i 0.151911 + 0.236951i
\(123\) −2.95110 11.0137i −0.266092 0.993069i
\(124\) 6.68339 + 3.06999i 0.600186 + 0.275693i
\(125\) 0.645919 + 11.1617i 0.0577727 + 0.998330i
\(126\) 0 0
\(127\) 8.87092 + 8.87092i 0.787167 + 0.787167i 0.981029 0.193862i \(-0.0621014\pi\)
−0.193862 + 0.981029i \(0.562101\pi\)
\(128\) 10.7196 3.61792i 0.947491 0.319782i
\(129\) 9.87458 + 5.70109i 0.869408 + 0.501953i
\(130\) −3.06746 0.609140i −0.269034 0.0534251i
\(131\) −11.3871 + 6.57436i −0.994898 + 0.574404i −0.906735 0.421702i \(-0.861433\pi\)
−0.0881630 + 0.996106i \(0.528100\pi\)
\(132\) 1.52520 8.94960i 0.132752 0.778962i
\(133\) 0 0
\(134\) 4.30618 1.37132i 0.371997 0.118464i
\(135\) 30.8996 + 7.64458i 2.65941 + 0.657941i
\(136\) 5.10713 + 12.0359i 0.437933 + 1.03207i
\(137\) 1.80890 + 6.75090i 0.154545 + 0.576769i 0.999144 + 0.0413695i \(0.0131721\pi\)
−0.844599 + 0.535399i \(0.820161\pi\)
\(138\) −0.445819 9.58061i −0.0379506 0.815556i
\(139\) 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
\(142\) 0.801275 + 17.2193i 0.0672415 + 1.44501i
\(143\) −0.360083 1.34385i −0.0301117 0.112378i
\(144\) −22.4908 + 19.3158i −1.87423 + 1.60965i
\(145\) −5.61057 9.29928i −0.465932 0.772263i
\(146\) 8.93499 2.84538i 0.739465 0.235485i
\(147\) 0 0
\(148\) 16.3232 + 2.78181i 1.34176 + 0.228664i
\(149\) 5.75434 3.32227i 0.471414 0.272171i −0.245418 0.969417i \(-0.578925\pi\)
0.716831 + 0.697247i \(0.245592\pi\)
\(150\) 22.4608 + 4.01211i 1.83392 + 0.327588i
\(151\) 17.6555 + 10.1934i 1.43679 + 0.829529i 0.997625 0.0688796i \(-0.0219424\pi\)
0.439161 + 0.898408i \(0.355276\pi\)
\(152\) −4.88673 6.25637i −0.396367 0.507458i
\(153\) −24.2263 24.2263i −1.95858 1.95858i
\(154\) 0 0
\(155\) −8.22134 + 0.158431i −0.660354 + 0.0127255i
\(156\) −2.66401 + 5.79957i −0.213292 + 0.464338i
\(157\) −4.59905 17.1639i −0.367044 1.36983i −0.864628 0.502412i \(-0.832446\pi\)
0.497584 0.867416i \(-0.334221\pi\)
\(158\) −0.457420 0.713484i −0.0363904 0.0567617i
\(159\) 1.58925 + 2.75267i 0.126036 + 0.218301i
\(160\) −9.03355 + 8.85410i −0.714164 + 0.699978i
\(161\) 0 0
\(162\) 15.3899 29.7719i 1.20915 2.33910i
\(163\) −16.7957 4.50039i −1.31554 0.352498i −0.468235 0.883604i \(-0.655110\pi\)
−0.847305 + 0.531106i \(0.821776\pi\)
\(164\) −7.03682 + 0.656316i −0.549483 + 0.0512497i
\(165\) 2.81548 + 9.75192i 0.219185 + 0.759186i
\(166\) 6.11196 6.70855i 0.474380 0.520684i
\(167\) 6.88960 + 6.88960i 0.533133 + 0.533133i 0.921503 0.388370i \(-0.126962\pi\)
−0.388370 + 0.921503i \(0.626962\pi\)
\(168\) 0 0
\(169\) 12.0220i 0.924767i
\(170\) −10.9933 9.63472i −0.843151 0.738949i
\(171\) 18.0157 + 10.4014i 1.37769 + 0.795412i
\(172\) 4.51170 5.43987i 0.344014 0.414786i
\(173\) 6.40337 23.8977i 0.486839 1.81691i −0.0847922 0.996399i \(-0.527023\pi\)
0.571632 0.820510i \(-0.306311\pi\)
\(174\) −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
\(178\) −0.552027 + 0.353909i −0.0413762 + 0.0265266i
\(179\) −10.2777 + 17.8015i −0.768192 + 1.33055i 0.170350 + 0.985384i \(0.445510\pi\)
−0.938542 + 0.345164i \(0.887823\pi\)
\(180\) 13.2528 30.3814i 0.987806 2.26450i
\(181\) 7.85989 0.584221 0.292110 0.956385i \(-0.405643\pi\)
0.292110 + 0.956385i \(0.405643\pi\)
\(182\) 0 0
\(183\) −5.01574 + 5.01574i −0.370774 + 0.370774i
\(184\) −5.90032 0.725227i −0.434978 0.0534645i
\(185\) −17.7865 + 5.13516i −1.30769 + 0.377544i
\(186\) −3.58506 + 16.3934i −0.262870 + 1.20203i
\(187\) 1.68310 6.28140i 0.123080 0.459342i
\(188\) 0.888105 5.21123i 0.0647717 0.380068i
\(189\) 0 0
\(190\) 7.96161 + 3.92308i 0.577596 + 0.284610i
\(191\) 7.51061 4.33625i 0.543449 0.313760i −0.203027 0.979173i \(-0.565078\pi\)
0.746475 + 0.665413i \(0.231745\pi\)
\(192\) 13.2895 + 22.1301i 0.959084 + 1.59710i
\(193\) 5.12478 1.37318i 0.368890 0.0988437i −0.0696118 0.997574i \(-0.522176\pi\)
0.438502 + 0.898730i \(0.355509\pi\)
\(194\) −10.7831 + 11.8356i −0.774181 + 0.849748i
\(195\) −0.137480 7.13415i −0.00984515 0.510887i
\(196\) 0 0
\(197\) −12.3437 + 12.3437i −0.879452 + 0.879452i −0.993478 0.114026i \(-0.963625\pi\)
0.114026 + 0.993478i \(0.463625\pi\)
\(198\) 14.7297 0.685422i 1.04679 0.0487108i
\(199\) −2.14941 + 3.72289i −0.152368 + 0.263909i −0.932097 0.362208i \(-0.882023\pi\)
0.779730 + 0.626116i \(0.215356\pi\)
\(200\) 4.79031 13.3061i 0.338726 0.940885i
\(201\) 5.15564 + 8.92983i 0.363651 + 0.629862i
\(202\) −3.91660 + 7.57667i −0.275571 + 0.533092i
\(203\) 0 0
\(204\) −24.3380 + 17.2504i −1.70400 + 1.20777i
\(205\) 6.76555 4.08188i 0.472527 0.285091i
\(206\) −19.4423 4.25181i −1.35461 0.296238i
\(207\) 15.0470 4.03182i 1.04584 0.280231i
\(208\) 3.26623 + 2.23166i 0.226472 + 0.154738i
\(209\) 3.94849i 0.273123i
\(210\) 0 0
\(211\) 19.5494i 1.34583i −0.739718 0.672917i \(-0.765041\pi\)
0.739718 0.672917i \(-0.234959\pi\)
\(212\) 1.84741 0.684424i 0.126881 0.0470064i
\(213\) −37.9906 + 10.1795i −2.60307 + 0.697490i
\(214\) 6.06058 27.7132i 0.414293 1.89444i
\(215\) −1.89764 + 7.67029i −0.129418 + 0.523110i
\(216\) −32.1528 24.2353i −2.18772 1.64900i
\(217\) 0 0
\(218\) −1.27531 0.659246i −0.0863751 0.0446498i
\(219\) 10.6976 + 18.5287i 0.722875 + 1.25206i
\(220\) 6.25175 0.704836i 0.421493 0.0475200i
\(221\) −2.28576 + 3.95905i −0.153757 + 0.266315i
\(222\) 1.75615 + 37.7396i 0.117865 + 2.53292i
\(223\) −9.54503 + 9.54503i −0.639183 + 0.639183i −0.950354 0.311171i \(-0.899279\pi\)
0.311171 + 0.950354i \(0.399279\pi\)
\(224\) 0 0
\(225\) 1.42776 + 37.0310i 0.0951838 + 2.46873i
\(226\) 10.9306 + 9.95860i 0.727096 + 0.662436i
\(227\) −17.8221 + 4.77541i −1.18289 + 0.316955i −0.796073 0.605200i \(-0.793093\pi\)
−0.386819 + 0.922155i \(0.626426\pi\)
\(228\) 11.5631 13.9420i 0.765788 0.923330i
\(229\) −13.5250 + 7.80865i −0.893755 + 0.516010i −0.875169 0.483817i \(-0.839250\pi\)
−0.0185864 + 0.999827i \(0.505917\pi\)
\(230\) 6.29300 2.13842i 0.414948 0.141003i
\(231\) 0 0
\(232\) 1.91021 + 13.6044i 0.125412 + 0.893172i
\(233\) 0.989436 3.69263i 0.0648201 0.241912i −0.925913 0.377738i \(-0.876702\pi\)
0.990733 + 0.135826i \(0.0433688\pi\)
\(234\) −10.1266 2.21459i −0.662000 0.144772i
\(235\) 1.63942 + 5.67842i 0.106944 + 0.370419i
\(236\) 5.89868 12.8415i 0.383972 0.835909i
\(237\) 1.36736 1.36736i 0.0888193 0.0888193i
\(238\) 0 0
\(239\) −15.4752 −1.00101 −0.500505 0.865734i \(-0.666852\pi\)
−0.500505 + 0.865734i \(0.666852\pi\)
\(240\) −24.1388 15.8195i −1.55815 1.02114i
\(241\) 14.3810 24.9086i 0.926361 1.60450i 0.137004 0.990570i \(-0.456253\pi\)
0.789357 0.613934i \(-0.210414\pi\)
\(242\) −6.88544 10.7399i −0.442613 0.690387i
\(243\) 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
\(248\) 9.64333 + 3.89758i 0.612352 + 0.247497i
\(249\) 17.9323 + 10.3532i 1.13641 + 0.656109i
\(250\) 1.64622 + 15.7255i 0.104116 + 0.994565i
\(251\) 26.0285i 1.64291i −0.570277 0.821453i \(-0.693164\pi\)
0.570277 0.821453i \(-0.306836\pi\)
\(252\) 0 0
\(253\) 2.09075 + 2.09075i 0.131444 + 0.131444i
\(254\) 13.1150 + 11.9487i 0.822906 + 0.749726i
\(255\) 16.1167 29.2001i 1.00927 1.82858i
\(256\) 14.9056 5.81566i 0.931603 0.363479i
\(257\) 22.2935 + 5.97352i 1.39063 + 0.372618i 0.874971 0.484176i \(-0.160881\pi\)
0.515659 + 0.856794i \(0.327547\pi\)
\(258\) 14.3244 + 7.40472i 0.891801 + 0.460998i
\(259\) 0 0
\(260\) −4.37339 0.658877i −0.271226 0.0408618i
\(261\) −17.9995 31.1761i −1.11414 1.92975i
\(262\) −15.6542 + 10.0361i −0.967122 + 0.620029i
\(263\) −2.93759 10.9633i −0.181140 0.676023i −0.995424 0.0955566i \(-0.969537\pi\)
0.814284 0.580466i \(-0.197130\pi\)
\(264\) 1.56631 12.7432i 0.0963997 0.784291i
\(265\) −1.52722 + 1.58724i −0.0938163 + 0.0975031i
\(266\) 0 0
\(267\) −1.05793 1.05793i −0.0647444 0.0647444i
\(268\) 5.99312 2.22031i 0.366088 0.135627i
\(269\) 23.5713 + 13.6089i 1.43717 + 0.829749i 0.997652 0.0684854i \(-0.0218167\pi\)
0.439516 + 0.898235i \(0.355150\pi\)
\(270\) 44.1539 + 8.76814i 2.68712 + 0.533612i
\(271\) 0.134959 0.0779185i 0.00819817 0.00473321i −0.495895 0.868382i \(-0.665160\pi\)
0.504093 + 0.863649i \(0.331827\pi\)
\(272\) 8.00597 + 16.6672i 0.485433 + 1.01060i
\(273\) 0 0
\(274\) 2.99919 + 9.41799i 0.181188 + 0.568961i
\(275\) −5.95156 + 3.74906i −0.358893 + 0.226077i
\(276\) −1.25960 13.5051i −0.0758192 0.812910i
\(277\) −5.41783 20.2196i −0.325526 1.21488i −0.913782 0.406204i \(-0.866852\pi\)
0.588256 0.808674i \(-0.299815\pi\)
\(278\) 30.0022 1.39610i 1.79941 0.0837328i
\(279\) −27.2556 −1.63175
\(280\) 0 0
\(281\) −2.56355 −0.152929 −0.0764644 0.997072i \(-0.524363\pi\)
−0.0764644 + 0.997072i \(0.524363\pi\)
\(282\) 12.0485 0.560659i 0.717479 0.0333868i
\(283\) −5.32518 19.8738i −0.316549 1.18138i −0.922539 0.385904i \(-0.873889\pi\)
0.605990 0.795472i \(-0.292777\pi\)
\(284\) 2.26390 + 24.2728i 0.134338 + 1.44033i
\(285\) −4.86351 + 19.6584i −0.288089 + 1.16446i
\(286\) −0.597025 1.87476i −0.0353028 0.110857i
\(287\) 0 0
\(288\) −30.5026 + 28.7656i −1.79738 + 1.69503i
\(289\) −3.78292 + 2.18407i −0.222525 + 0.128475i
\(290\) −8.53727 12.7681i −0.501326 0.749771i
\(291\) −31.6373 18.2658i −1.85461 1.07076i
\(292\) 12.4353 4.60698i 0.727720 0.269603i
\(293\) −4.71102 4.71102i −0.275221 0.275221i 0.555977 0.831198i \(-0.312344\pi\)
−0.831198 + 0.555977i \(0.812344\pi\)
\(294\) 0 0
\(295\) 0.304410 + 15.7965i 0.0177234 + 0.919708i
\(296\) 23.2423 + 2.85679i 1.35093 + 0.166047i
\(297\) 5.18314 + 19.3437i 0.300756 + 1.12244i
\(298\) 7.91067 5.07159i 0.458253 0.293790i
\(299\) −1.03928 1.80009i −0.0601033 0.104102i
\(300\) 31.9938 + 4.19134i 1.84716 + 0.241987i
\(301\) 0 0
\(302\) 25.6118 + 13.2395i 1.47379 + 0.761846i
\(303\) −18.7972 5.03669i −1.07987 0.289350i
\(304\) −7.31469 8.51704i −0.419526 0.488486i
\(305\) −4.30358 2.37531i −0.246422 0.136010i
\(306\) −35.8166 32.6315i −2.04750 1.86542i
\(307\) −16.8508 16.8508i −0.961723 0.961723i 0.0375706 0.999294i \(-0.488038\pi\)
−0.999294 + 0.0375706i \(0.988038\pi\)
\(308\) 0 0
\(309\) 45.4085i 2.58320i
\(310\) −11.6038 + 0.764260i −0.659049 + 0.0434071i
\(311\) −15.7287 9.08099i −0.891895 0.514936i −0.0173329 0.999850i \(-0.505518\pi\)
−0.874562 + 0.484914i \(0.838851\pi\)
\(312\) −3.38216 + 8.36809i −0.191477 + 0.473750i
\(313\) 0.405938 1.51498i 0.0229450 0.0856319i −0.953504 0.301381i \(-0.902553\pi\)
0.976449 + 0.215749i \(0.0692192\pi\)
\(314\) −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 −0.656769 0.754092i \(-0.728077\pi\)
−0.945825 + 0.324678i \(0.894744\pi\)
\(318\) 2.42607 + 3.78418i 0.136047 + 0.212206i
\(319\) 3.41643 5.91743i 0.191283 0.331313i
\(320\) −12.1795 + 13.1019i −0.680855 + 0.732418i
\(321\) 64.7258 3.61264
\(322\) 0 0
\(323\) 9.17425 9.17425i 0.510469 0.510469i
\(324\) 19.7840 43.0699i 1.09911 2.39277i
\(325\) 4.72344 1.46287i 0.262009 0.0811454i
\(326\) −24.0229 5.25353i −1.33050 0.290966i
\(327\) 0.847782 3.16396i 0.0468824 0.174968i
\(328\) −9.89766 + 1.38975i −0.546507 + 0.0767360i
\(329\) 0 0
\(330\) 4.61845 + 13.5913i 0.254238 + 0.748177i
\(331\) −10.9400 + 6.31623i −0.601319 + 0.347172i −0.769560 0.638574i \(-0.779525\pi\)
0.168241 + 0.985746i \(0.446191\pi\)
\(332\) 8.19328 9.87885i 0.449665 0.542172i
\(333\) −59.2724 + 15.8820i −3.24811 + 0.870328i
\(334\) 10.1857 + 9.27993i 0.557339 + 0.507775i
\(335\) −4.95439 + 5.14909i −0.270687 + 0.281325i
\(336\) 0 0
\(337\) 4.10542 4.10542i 0.223636 0.223636i −0.586391 0.810028i \(-0.699452\pi\)
0.810028 + 0.586391i \(0.199452\pi\)
\(338\) −0.790289 16.9832i −0.0429861 0.923767i
\(339\) −16.8692 + 29.2182i −0.916207 + 1.58692i
\(340\) −16.1635 12.8881i −0.876588 0.698958i
\(341\) −2.58665 4.48021i −0.140075 0.242617i
\(342\) 26.1342 + 13.5095i 1.41318 + 0.730513i
\(343\) 0 0
\(344\) 6.01600 7.98140i 0.324361 0.430328i
\(345\) 7.83396 + 12.9845i 0.421766 + 0.699060i
\(346\) 7.47498 34.1809i 0.401857 1.83757i
\(347\) −14.2660 + 3.82255i −0.765837 + 0.205205i −0.620531 0.784182i \(-0.713083\pi\)
−0.145305 + 0.989387i \(0.546416\pi\)
\(348\) −29.3925 + 10.8892i −1.57560 + 0.583723i
\(349\) 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
\(352\) −7.62321 2.28399i −0.406318 0.121737i
\(353\) 10.5040 2.81454i 0.559072 0.149803i 0.0317919 0.999495i \(-0.489879\pi\)
0.527280 + 0.849692i \(0.323212\pi\)
\(354\) 31.4984 + 6.88835i 1.67412 + 0.366112i
\(355\) −14.0801 23.3371i −0.747292 1.23860i
\(356\) −0.756576 + 0.536251i −0.0400984 + 0.0284212i
\(357\) 0 0
\(358\) −13.3489 + 25.8236i −0.705514 + 1.36482i
\(359\) −2.49329 4.31850i −0.131591 0.227922i 0.792699 0.609613i \(-0.208675\pi\)
−0.924290 + 0.381691i \(0.875342\pi\)
\(360\) 16.7248 43.7906i 0.881477 2.30797i
\(361\) 5.56111 9.63212i 0.292690 0.506954i
\(362\) 11.1035 0.516686i 0.583589 0.0271564i
\(363\) 20.5825 20.5825i 1.08030 1.08030i
\(364\) 0 0
\(365\) −10.2800 + 10.6840i −0.538079 + 0.559225i
\(366\) −6.75594 + 7.41538i −0.353139 + 0.387608i
\(367\) 15.3917 4.12420i 0.803442 0.215282i 0.166347 0.986067i \(-0.446803\pi\)
0.637094 + 0.770786i \(0.280136\pi\)
\(368\) −8.38297 0.636648i −0.436993 0.0331875i
\(369\) 22.6817 13.0953i 1.18076 0.681714i
\(370\) −24.7892 + 8.42359i −1.28873 + 0.437922i
\(371\) 0 0
\(372\) −3.98691 + 23.3944i −0.206712 + 1.21294i
\(373\) −0.152497 + 0.569126i −0.00789599 + 0.0294682i −0.969761 0.244055i \(-0.921522\pi\)
0.961865 + 0.273523i \(0.0881890\pi\)
\(374\) 1.96476 8.98428i 0.101596 0.464566i
\(375\) −34.2489 + 11.3347i −1.76861 + 0.585321i
\(376\) 0.912041 7.42021i 0.0470349 0.382668i
\(377\) −3.39653 + 3.39653i −0.174930 + 0.174930i
\(378\) 0 0
\(379\) −23.7583 −1.22038 −0.610191 0.792254i \(-0.708907\pi\)
−0.610191 + 0.792254i \(0.708907\pi\)
\(380\) 11.5051 + 5.01871i 0.590201 + 0.257454i
\(381\) −20.2402 + 35.0570i −1.03694 + 1.79603i
\(382\) 10.3251 6.61948i 0.528277 0.338682i
\(383\) −4.14964 1.11189i −0.212037 0.0568151i 0.151237 0.988498i \(-0.451674\pi\)
−0.363274 + 0.931682i \(0.618341\pi\)
\(384\) 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
\(388\) −14.4551 + 17.4289i −0.733845 + 0.884816i
\(389\) −21.8152 12.5950i −1.10608 0.638593i −0.168266 0.985742i \(-0.553817\pi\)
−0.937810 + 0.347148i \(0.887150\pi\)
\(390\) −0.663194 10.0693i −0.0335822 0.509877i
\(391\) 9.71561i 0.491340i
\(392\) 0 0
\(393\) −30.0006 30.0006i −1.51333 1.51333i
\(394\) −16.6263 + 18.2492i −0.837622 + 0.919381i
\(395\) 1.17321 + 0.647540i 0.0590306 + 0.0325813i
\(396\) 20.7633 1.93657i 1.04340 0.0973163i
\(397\) −3.73802 1.00160i −0.187606 0.0502689i 0.163793 0.986495i \(-0.447627\pi\)
−0.351399 + 0.936226i \(0.614294\pi\)
\(398\) −2.79171 + 5.40057i −0.139936 + 0.270706i
\(399\) 0 0
\(400\) 5.89249 19.1123i 0.294625 0.955613i
\(401\) 2.74364 + 4.75213i 0.137011 + 0.237310i 0.926364 0.376630i \(-0.122917\pi\)
−0.789353 + 0.613940i \(0.789584\pi\)
\(402\) 7.87032 + 12.2761i 0.392536 + 0.612277i
\(403\) 0.941265 + 3.51285i 0.0468877 + 0.174987i
\(404\) −5.03485 + 10.9609i −0.250493 + 0.545325i
\(405\) 1.02098 + 52.9811i 0.0507330 + 2.63265i
\(406\) 0 0
\(407\) −8.23579 8.23579i −0.408233 0.408233i
\(408\) −33.2479 + 25.9693i −1.64602 + 1.28567i
\(409\) −14.7164 8.49650i −0.727678 0.420125i 0.0898942 0.995951i \(-0.471347\pi\)
−0.817572 + 0.575826i \(0.804680\pi\)
\(410\) 9.28926 6.21116i 0.458764 0.306747i
\(411\) −19.5303 + 11.2758i −0.963360 + 0.556196i
\(412\) −27.7453 4.72839i −1.36691 0.232951i
\(413\) 0 0
\(414\) 20.9916 6.68484i 1.03168 0.328542i
\(415\) −3.44613 + 13.9293i −0.169164 + 0.683764i
\(416\) 4.76085 + 2.93792i 0.233420 + 0.144044i
\(417\) 17.7364 + 66.1930i 0.868554 + 3.24149i
\(418\) 0.259563 + 5.57798i 0.0126956 + 0.272828i
\(419\) 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 \(0.331560\pi\)
\(422\) −1.28512 27.6171i −0.0625586 1.34438i
\(423\) 5.07039 + 18.9230i 0.246531 + 0.920066i
\(424\) 2.56482 1.08832i 0.124559 0.0528534i
\(425\) 22.5392 + 5.11747i 1.09331 + 0.248234i
\(426\) −52.9995 + 16.8779i −2.56783 + 0.817735i
\(427\) 0 0
\(428\) 6.73991 39.5485i 0.325786 1.91165i
\(429\) 3.88775 2.24459i 0.187702 0.108370i
\(430\) −2.17654 + 10.9605i −0.104962 + 0.528560i
\(431\) 8.46015 + 4.88447i 0.407511 + 0.235277i 0.689720 0.724076i \(-0.257734\pi\)
−0.282209 + 0.959353i \(0.591067\pi\)
\(432\) −47.0150 32.1232i −2.26201 1.54553i
\(433\) −7.00877 7.00877i −0.336820 0.336820i 0.518349 0.855169i \(-0.326547\pi\)
−0.855169 + 0.518349i \(0.826547\pi\)
\(434\) 0 0
\(435\) 24.2981 25.2530i 1.16501 1.21079i
\(436\) −1.84495 0.847472i −0.0883572 0.0405865i
\(437\) 1.52681 + 5.69814i 0.0730373 + 0.272579i
\(438\) 16.3303 + 25.4720i 0.780293 + 1.21710i
\(439\) 2.21290 + 3.83285i 0.105616 + 0.182932i 0.913990 0.405737i \(-0.132985\pi\)
−0.808374 + 0.588670i \(0.799652\pi\)
\(440\) 8.78542 1.40668i 0.418828 0.0670610i
\(441\) 0 0
\(442\) −2.96880 + 5.74315i −0.141211 + 0.273174i
\(443\) 4.25183 + 1.13928i 0.202011 + 0.0541286i 0.358405 0.933566i \(-0.383321\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(444\) 4.96178 + 53.1987i 0.235476 + 2.52470i
\(445\) 0.501006 0.907721i 0.0237500 0.0430301i
\(446\) −12.8567 + 14.1116i −0.608781 + 0.668203i
\(447\) 15.1604 + 15.1604i 0.717062 + 0.717062i
\(448\) 0 0
\(449\) 21.8355i 1.03048i 0.857046 + 0.515240i \(0.172297\pi\)
−0.857046 + 0.515240i \(0.827703\pi\)
\(450\) 4.45128 + 52.2193i 0.209835 + 2.46164i
\(451\) 4.30514 + 2.48557i 0.202721 + 0.117041i
\(452\) 16.0962 + 13.3498i 0.757102 + 0.627922i
\(453\) −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 0.719517 0.694475i \(-0.244363\pi\)
0.275883 + 0.961191i \(0.411030\pi\)
\(458\) −18.5932 + 11.9203i −0.868804 + 0.556997i
\(459\) 32.9019 56.9877i 1.53573 2.65996i
\(460\) 8.74946 3.43460i 0.407945 0.160139i
\(461\) 19.7670 0.920641 0.460321 0.887753i \(-0.347734\pi\)
0.460321 + 0.887753i \(0.347734\pi\)
\(462\) 0 0
\(463\) −14.5239 + 14.5239i −0.674983 + 0.674983i −0.958861 0.283877i \(-0.908379\pi\)
0.283877 + 0.958861i \(0.408379\pi\)
\(464\) 3.59284 + 19.0931i 0.166794 + 0.886377i
\(465\) −7.35973 25.4917i −0.341299 1.18215i
\(466\) 1.15502 5.28156i 0.0535052 0.244663i
\(467\) 7.29665 27.2315i 0.337649 1.26012i −0.563320 0.826239i \(-0.690476\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(468\) −14.4513 2.46282i −0.668014 0.113844i
\(469\) 0 0
\(470\) 2.68927 + 7.91404i 0.124047 + 0.365048i
\(471\) 49.6551 28.6684i 2.28799 1.32097i
\(472\) 7.48882 18.5287i 0.344701 0.852853i
\(473\) −4.80176 + 1.28663i −0.220785 + 0.0591592i
\(474\) 1.84176 2.02153i 0.0845947 0.0928519i
\(475\) −14.0233 + 0.540678i −0.643432 + 0.0248080i
\(476\) 0 0
\(477\) −5.16257 + 5.16257i −0.236378 + 0.236378i
\(478\) −21.8616 + 1.01730i −0.999928 + 0.0465301i
\(479\) 0.709375 1.22867i 0.0324122 0.0561395i −0.849364 0.527807i \(-0.823014\pi\)
0.881776 + 0.471668i \(0.156348\pi\)
\(480\) −35.1404 20.7611i −1.60393 0.947610i
\(481\) 4.09391 + 7.09086i 0.186666 + 0.323315i
\(482\) 18.6784 36.1334i 0.850777 1.64583i
\(483\) 0 0
\(484\) −10.4330 14.7195i −0.474225 0.669067i
\(485\) 6.07987 24.5749i 0.276072 1.11589i
\(486\) 46.6437 + 10.2005i 2.11580 + 0.462703i
\(487\) −32.5132 + 8.71188i −1.47331 + 0.394773i −0.904066 0.427393i \(-0.859432\pi\)
−0.569247 + 0.822166i \(0.692765\pi\)
\(488\) 3.82742 + 4.90015i 0.173259 + 0.221819i
\(489\) 56.1067i 2.53723i
\(490\) 0 0
\(491\) 3.16673i 0.142913i −0.997444 0.0714563i \(-0.977235\pi\)
0.997444 0.0714563i \(-0.0227647\pi\)
\(492\) −7.92228 21.3840i −0.357164 0.964066i
\(493\) −21.6871 + 5.81103i −0.976736 + 0.261716i
\(494\) 0.838642 3.83486i 0.0377323 0.172539i
\(495\) −19.9629 + 12.0443i −0.897265 + 0.541350i
\(496\) 13.8792 + 4.87213i 0.623195 + 0.218765i
\(497\) 0 0
\(498\) 26.0133 + 13.4470i 1.16568 + 0.602576i
\(499\) 3.72451 + 6.45105i 0.166732 + 0.288789i 0.937269 0.348607i \(-0.113345\pi\)
−0.770537 + 0.637395i \(0.780012\pi\)
\(500\) 3.35933 + 22.1069i 0.150234 + 0.988651i
\(501\) −15.7195 + 27.2270i −0.702297 + 1.21641i
\(502\) −1.71104 36.7701i −0.0763674 1.64113i
\(503\) −19.3043 + 19.3043i −0.860736 + 0.860736i −0.991424 0.130687i \(-0.958282\pi\)
0.130687 + 0.991424i \(0.458282\pi\)
\(504\) 0 0
\(505\) −0.259830 13.4832i −0.0115623 0.599994i
\(506\) 3.09101 + 2.81613i 0.137412 + 0.125192i
\(507\) 37.4697 10.0400i 1.66409 0.445891i
\(508\) 19.3128 + 16.0176i 0.856866 + 0.710664i
\(509\) 9.85817 5.69161i 0.436956 0.252276i −0.265350 0.964152i \(-0.585487\pi\)
0.702305 + 0.711876i \(0.252154\pi\)
\(510\) 20.8482 42.3100i 0.923176 1.87352i
\(511\) 0 0
\(512\) 20.6747 9.19554i 0.913700 0.406390i
\(513\) −10.3411 + 38.5934i −0.456570 + 1.70394i
\(514\) 31.8863 + 6.97319i 1.40645 + 0.307574i
\(515\) 30.2326 8.72849i 1.33221 0.384623i
\(516\) 20.7227 + 9.51889i 0.912266 + 0.419046i
\(517\) −2.62931 + 2.62931i −0.115637 + 0.115637i
\(518\) 0 0
\(519\) 79.8313 3.50421
\(520\) −6.22154 0.643292i −0.272833 0.0282102i
\(521\) −0.617798 + 1.07006i −0.0270662 + 0.0468801i −0.879241 0.476377i \(-0.841950\pi\)
0.852175 + 0.523257i \(0.175283\pi\)
\(522\) −27.4771 42.8588i −1.20264 1.87588i
\(523\) −6.09797 1.63395i −0.266646 0.0714474i 0.123019 0.992404i \(-0.460742\pi\)
−0.389665 + 0.920957i \(0.627409\pi\)
\(524\) −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
\(528\) 1.37500 18.1051i 0.0598392 0.787924i
\(529\) −16.0929 9.29126i −0.699693 0.403968i
\(530\) −2.05314 + 2.34266i −0.0891826 + 0.101759i
\(531\) 52.3691i 2.27262i
\(532\) 0 0
\(533\) −2.47109 2.47109i −0.107035 0.107035i
\(534\) −1.56407 1.42498i −0.0676840 0.0616649i
\(535\) 12.4417 + 43.0940i 0.537901 + 1.86312i
\(536\) 8.32044 3.53057i 0.359388 0.152497i
\(537\) −64.0665 17.1666i −2.76467 0.740792i
\(538\) 34.1934 + 17.6756i 1.47418 + 0.762048i
\(539\) 0 0
\(540\) 62.9519 + 9.48407i 2.70902 + 0.408129i
\(541\) 16.1355 + 27.9475i 0.693719 + 1.20156i 0.970611 + 0.240656i \(0.0773624\pi\)
−0.276891 + 0.960901i \(0.589304\pi\)
\(542\) 0.185532 0.118946i 0.00796929 0.00510917i
\(543\) 6.56407 + 24.4975i 0.281691 + 1.05129i
\(544\) 12.4056 + 23.0192i 0.531884 + 0.986939i
\(545\) 2.26951 0.0437350i 0.0972150 0.00187340i
\(546\) 0 0
\(547\) 17.6256 + 17.6256i 0.753617 + 0.753617i 0.975152 0.221536i \(-0.0711069\pi\)
−0.221536 + 0.975152i \(0.571107\pi\)
\(548\) 4.85602 + 13.1075i 0.207439 + 0.559924i
\(549\) −14.1104 8.14662i −0.602215 0.347689i
\(550\) −8.16123 + 5.68747i −0.347996 + 0.242515i
\(551\) 11.8061 6.81625i 0.502957 0.290382i
\(552\) −2.66721 18.9956i −0.113524 0.808507i
\(553\) 0 0
\(554\) −8.98286 28.2078i −0.381645 1.19843i
\(555\) −30.8593 51.1479i −1.30990 2.17111i
\(556\) 42.2919 3.94451i 1.79357 0.167285i
\(557\) 1.60273 + 5.98149i 0.0679101 + 0.253444i 0.991532 0.129860i \(-0.0414528\pi\)
−0.923622 + 0.383304i \(0.874786\pi\)
\(558\) −38.5036 + 1.79171i −1.62999 + 0.0758490i
\(559\) 3.49465 0.147808
\(560\) 0 0
\(561\) 20.9833 0.885915
\(562\) −3.62149 + 0.168521i −0.152764 + 0.00710861i
\(563\) −1.32949 4.96172i −0.0560313 0.209112i 0.932235 0.361854i \(-0.117856\pi\)
−0.988266 + 0.152742i \(0.951189\pi\)
\(564\) 16.9839 1.58407i 0.715151 0.0667013i
\(565\) −22.6959 5.61499i −0.954823 0.236224i
\(566\) −8.82925 27.7254i −0.371121 1.16539i
\(567\) 0 0
\(568\) 4.79380 + 34.1410i 0.201143 + 1.43253i
\(569\) −30.0136 + 17.3284i −1.25824 + 0.726442i −0.972731 0.231935i \(-0.925494\pi\)
−0.285504 + 0.958378i \(0.592161\pi\)
\(570\) −5.57832 + 28.0908i −0.233650 + 1.17660i
\(571\) 28.9237 + 16.6991i 1.21042 + 0.698836i 0.962851 0.270034i \(-0.0870350\pi\)
0.247569 + 0.968870i \(0.420368\pi\)
\(572\) −0.966649 2.60920i −0.0404176 0.109096i
\(573\) 19.7875 + 19.7875i 0.826634 + 0.826634i
\(574\) 0 0
\(575\) −7.13910 + 7.71168i −0.297721 + 0.321599i
\(576\) −41.1996 + 42.6418i −1.71665 + 1.77674i
\(577\) 8.91664 + 33.2773i 0.371204 + 1.38535i 0.858812 + 0.512291i \(0.171203\pi\)
−0.487608 + 0.873063i \(0.662130\pi\)
\(578\) −5.20050 + 3.33408i −0.216312 + 0.138679i
\(579\) 8.55978 + 14.8260i 0.355732 + 0.616146i
\(580\) −12.8998 17.4761i −0.535636 0.725657i
\(581\) 0 0
\(582\) −45.8942 23.7241i −1.90238 0.983394i
\(583\) −1.33855 0.358664i −0.0554372 0.0148544i
\(584\) 17.2643 7.32567i 0.714401 0.303138i
\(585\) 15.7469 4.54630i 0.651054 0.187966i
\(586\) −6.96487 6.34549i −0.287716 0.262130i
\(587\) 23.3690 + 23.3690i 0.964544 + 0.964544i 0.999393 0.0348489i \(-0.0110950\pi\)
−0.0348489 + 0.999393i \(0.511095\pi\)
\(588\) 0 0
\(589\) 10.3214i 0.425288i
\(590\) 1.46845 + 22.2955i 0.0604552 + 0.917890i
\(591\) −48.7811 28.1638i −2.00659 1.15850i
\(592\) 33.0219 + 2.50786i 1.35719 + 0.103072i
\(593\) 1.67934 6.26739i 0.0689623 0.257371i −0.922834 0.385197i \(-0.874133\pi\)
0.991797 + 0.127826i \(0.0408000\pi\)
\(594\) 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
\(598\) −1.58651 2.47464i −0.0648773 0.101196i
\(599\) −8.75860 + 15.1703i −0.357867 + 0.619843i −0.987604 0.156965i \(-0.949829\pi\)
0.629737 + 0.776808i \(0.283162\pi\)
\(600\) 45.4727 + 3.81787i 1.85641 + 0.155864i
\(601\) −2.55297 −0.104138 −0.0520689 0.998643i \(-0.516582\pi\)
−0.0520689 + 0.998643i \(0.516582\pi\)
\(602\) 0 0
\(603\) −16.7477 + 16.7477i −0.682018 + 0.682018i
\(604\) 37.0517 + 17.0196i 1.50761 + 0.692516i
\(605\) 17.6601 + 9.74727i 0.717983 + 0.396283i
\(606\) −26.8856 5.87959i −1.09215 0.238842i
\(607\) −5.72830 + 21.3783i −0.232504 + 0.867718i 0.746754 + 0.665101i \(0.231611\pi\)
−0.979258 + 0.202617i \(0.935055\pi\)
\(608\) −10.8932 11.5510i −0.441779 0.468457i
\(609\) 0 0
\(610\) −6.23574 3.07266i −0.252478 0.124408i
\(611\) 2.26378 1.30700i 0.0915829 0.0528754i
\(612\) −52.7427 43.7436i −2.13200 1.76823i
\(613\) −7.79104 + 2.08760i −0.314677 + 0.0843175i −0.412701 0.910867i \(-0.635415\pi\)
0.0980238 + 0.995184i \(0.468748\pi\)
\(614\) −24.9125 22.6971i −1.00539 0.915980i
\(615\) 18.3724 + 17.6777i 0.740849 + 0.712835i
\(616\) 0 0
\(617\) −20.7105 + 20.7105i −0.833772 + 0.833772i −0.988031 0.154258i \(-0.950701\pi\)
0.154258 + 0.988031i \(0.450701\pi\)
\(618\) −2.98502 64.1479i −0.120075 2.58041i
\(619\) 15.2502 26.4141i 0.612956 1.06167i −0.377784 0.925894i \(-0.623314\pi\)
0.990739 0.135777i \(-0.0433530\pi\)
\(620\) −16.3422 + 1.84246i −0.656319 + 0.0739948i
\(621\) 14.9597 + 25.9110i 0.600314 + 1.03977i
\(622\) −22.8167 11.7946i −0.914866 0.472921i
\(623\) 0 0
\(624\) −4.22784 + 12.0438i −0.169249 + 0.482138i
\(625\) −14.1299 20.6239i −0.565197 0.824956i
\(626\) 0.473872 2.16688i 0.0189398 0.0866059i
\(627\) −12.3065 + 3.29753i −0.491476 + 0.131691i
\(628\) −12.3462 33.3253i −0.492668 1.32982i
\(629\) 38.2714i 1.52598i
\(630\) 0 0
\(631\) 24.2931i 0.967092i 0.875319 + 0.483546i \(0.160651\pi\)
−0.875319 + 0.483546i \(0.839349\pi\)
\(632\) −1.04340 1.33584i −0.0415044 0.0531370i
\(633\) 60.9309 16.3264i 2.42178 0.648915i
\(634\) −40.8113 8.92497i −1.62082 0.354456i
\(635\) −27.2313 6.73706i −1.08064 0.267352i
\(636\) 3.67603 + 5.18637i 0.145764 + 0.205653i
\(637\) 0 0
\(638\) 4.43735 8.58406i 0.175676 0.339846i
\(639\) −45.1709 78.2383i −1.78693 3.09506i
\(640\) −16.3445 + 19.3095i −0.646074 + 0.763274i
\(641\) −11.2086 + 19.4138i −0.442712 + 0.766800i −0.997890 0.0649320i \(-0.979317\pi\)
0.555178 + 0.831732i \(0.312650\pi\)
\(642\) 91.4372 4.25489i 3.60874 0.167927i
\(643\) 3.56268 3.56268i 0.140498 0.140498i −0.633359 0.773858i \(-0.718325\pi\)
0.773858 + 0.633359i \(0.218325\pi\)
\(644\) 0 0
\(645\) −25.4913 + 0.491236i −1.00372 + 0.0193424i
\(646\) 12.3572 13.5634i 0.486189 0.533645i
\(647\) −16.0227 + 4.29327i −0.629918 + 0.168786i −0.559632 0.828741i \(-0.689058\pi\)
−0.0702854 + 0.997527i \(0.522391\pi\)
\(648\) 25.1173 62.1448i 0.986700 2.44128i
\(649\) −8.60829 + 4.97000i −0.337905 + 0.195089i
\(650\) 6.57657 2.37708i 0.257954 0.0932367i
\(651\) 0 0
\(652\) −34.2821 5.84240i −1.34259 0.228806i
\(653\) −3.24782 + 12.1210i −0.127097 + 0.474332i −0.999906 0.0137300i \(-0.995629\pi\)
0.872809 + 0.488062i \(0.162296\pi\)
\(654\) 0.989659 4.52542i 0.0386987 0.176958i
\(655\) 14.2074 25.7409i 0.555129 1.00578i
\(656\) −13.8909 + 2.61392i −0.542349 + 0.102056i
\(657\) −34.7502 + 34.7502i −1.35573 + 1.35573i
\(658\) 0 0
\(659\) −33.3787 −1.30025 −0.650126 0.759827i \(-0.725284\pi\)
−0.650126 + 0.759827i \(0.725284\pi\)
\(660\) 7.41787 + 18.8966i 0.288740 + 0.735550i
\(661\) −3.47890 + 6.02563i −0.135313 + 0.234370i −0.925717 0.378217i \(-0.876537\pi\)
0.790404 + 0.612586i \(0.209871\pi\)
\(662\) −15.0396 + 9.64201i −0.584531 + 0.374748i
\(663\) −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
\(668\) 14.9993 + 12.4400i 0.580339 + 0.481320i
\(669\) −37.7211 21.7783i −1.45838 0.841997i
\(670\) −6.66051 + 7.59973i −0.257318 + 0.293603i
\(671\) 3.09256i 0.119387i
\(672\) 0 0
\(673\) −5.34897 5.34897i −0.206188 0.206188i 0.596457 0.802645i \(-0.296575\pi\)
−0.802645 + 0.596457i \(0.796575\pi\)
\(674\) 5.52979 6.06954i 0.212999 0.233790i
\(675\) −67.9905 + 21.0570i −2.61696 + 0.810483i
\(676\) −2.23286 23.9400i −0.0858792 0.920770i
\(677\) 28.9931 + 7.76868i 1.11430 + 0.298575i 0.768573 0.639762i \(-0.220967\pi\)
0.345723 + 0.938337i \(0.387634\pi\)
\(678\) −21.9101 + 42.3851i −0.841451 + 1.62779i
\(679\) 0 0
\(680\) −23.6811 17.1443i −0.908131 0.657456i
\(681\) −29.7677 51.5592i −1.14070 1.97575i
\(682\) −3.94864 6.15909i −0.151201 0.235844i
\(683\) −4.92938 18.3967i −0.188618 0.703930i −0.993827 0.110940i \(-0.964614\pi\)
0.805210 0.592990i \(-0.202053\pi\)
\(684\) 37.8075 + 17.3667i 1.44561 + 0.664034i
\(685\) −11.2615 10.8357i −0.430281 0.414010i
\(686\) 0 0
\(687\) −35.6329 35.6329i −1.35948 1.35948i
\(688\) 7.97404 11.6707i 0.304008 0.444941i
\(689\) 0.843665 + 0.487090i 0.0321411 + 0.0185567i
\(690\) 11.9205 + 17.8280i 0.453805 + 0.678699i
\(691\) 24.4705 14.1281i 0.930903 0.537457i 0.0438058 0.999040i \(-0.486052\pi\)
0.887097 + 0.461583i \(0.152718\pi\)
\(692\) 8.31284 48.7782i 0.316007 1.85427i
\(693\) 0 0
\(694\) −19.9020 + 6.33786i −0.755470 + 0.240582i
\(695\) −40.6615 + 24.5325i −1.54238 + 0.930569i
\(696\) −40.8064 + 17.3152i −1.54676 + 0.656331i
\(697\) −4.22772 15.7781i −0.160136 0.597638i
\(698\) −0.332091 7.13662i −0.0125698 0.270125i
\(699\) 12.3354 0.466567
\(700\) 0 0
\(701\) −26.0149 −0.982568 −0.491284 0.871000i \(-0.663472\pi\)
−0.491284 + 0.871000i \(0.663472\pi\)
\(702\) −0.925454 19.8879i −0.0349290 0.750622i
\(703\) −6.01436 22.4459i −0.226836 0.846563i
\(704\) −10.9193 2.72543i −0.411538 0.102719i
\(705\) −16.3292 + 9.85194i −0.614992 + 0.371046i
\(706\) 14.6538 4.66656i 0.551504 0.175628i
\(707\) 0 0
\(708\) 44.9501 + 7.66046i 1.68933 + 0.287898i
\(709\) −15.2471 + 8.80290i −0.572616 + 0.330600i −0.758193 0.652030i \(-0.773918\pi\)
0.185578 + 0.982630i \(0.440584\pi\)
\(710\) −21.4248 32.0424i −0.804058 1.20253i
\(711\) 3.84667 + 2.22087i 0.144261 + 0.0832893i
\(712\) −1.03355 + 0.807288i −0.0387340 + 0.0302544i
\(713\) −5.46525 5.46525i −0.204675 0.204675i
\(714\) 0 0
\(715\) 2.24174 + 2.15697i 0.0838363 + 0.0806663i
\(716\) −17.1603 + 37.3581i −0.641310 + 1.39614i
\(717\) −12.9239 48.2328i −0.482653 1.80129i
\(718\) −3.80611 5.93678i −0.142043 0.221558i
\(719\) 11.5866 + 20.0685i 0.432106 + 0.748429i 0.997054 0.0766969i \(-0.0244374\pi\)
−0.564949 + 0.825126i \(0.691104\pi\)
\(720\) 20.7483 62.9617i 0.773243 2.34644i
\(721\) 0 0
\(722\) 7.22290 13.9727i 0.268809 0.520011i
\(723\) 89.6445 + 24.0202i 3.33391 + 0.893320i
\(724\) 15.6518 1.45983i 0.581696 0.0542541i
\(725\) 21.4839 + 11.3233i 0.797892 + 0.420538i
\(726\) 27.7235 30.4296i 1.02892 1.12935i
\(727\) −15.3777 15.3777i −0.570326 0.570326i 0.361893 0.932220i \(-0.382131\pi\)
−0.932220 + 0.361893i \(0.882131\pi\)
\(728\) 0 0
\(729\) 37.8443i 1.40164i
\(730\) −13.8201 + 15.7689i −0.511503 + 0.583632i
\(731\) 14.1462 + 8.16734i 0.523218 + 0.302080i
\(732\) −9.05655 + 10.9197i −0.334740 + 0.403604i
\(733\) 10.8115 40.3490i 0.399331 1.49032i −0.414944 0.909847i \(-0.636199\pi\)
0.814276 0.580478i \(-0.197134\pi\)
\(734\) 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
\(738\) 31.1813 19.9906i 1.14780 0.735862i
\(739\) −14.4738 + 25.0693i −0.532426 + 0.922189i 0.466857 + 0.884333i \(0.345386\pi\)
−0.999283 + 0.0378565i \(0.987947\pi\)
\(740\) −34.4655 + 13.5294i −1.26698 + 0.497352i
\(741\) 8.95654 0.329027
\(742\) 0 0
\(743\) 23.4115 23.4115i 0.858885 0.858885i −0.132322 0.991207i \(-0.542243\pi\)
0.991207 + 0.132322i \(0.0422432\pi\)
\(744\) −4.09437 + 33.3111i −0.150107 + 1.22124i
\(745\) −7.17953 + 13.0078i −0.263038 + 0.476570i
\(746\) −0.178017 + 0.814021i −0.00651768 + 0.0298034i
\(747\) −12.3100 + 45.9417i −0.450401 + 1.68092i
\(748\) 2.18499 12.8211i 0.0798912 0.468786i
\(749\) 0 0
\(750\) −47.6378 + 18.2638i −1.73949 + 0.666898i
\(751\) 38.1178 22.0073i 1.39094 0.803059i 0.397520 0.917593i \(-0.369871\pi\)
0.993419 + 0.114534i \(0.0365376\pi\)
\(752\) 0.800644 10.5424i 0.0291965 0.384441i
\(753\) 81.1249 21.7373i 2.95636 0.792153i
\(754\) −4.57495 + 5.02151i −0.166610 + 0.182872i
\(755\) −45.5779 + 0.878318i −1.65875 + 0.0319653i
\(756\) 0 0
\(757\) 24.7062 24.7062i 0.897961 0.897961i −0.0972943 0.995256i \(-0.531019\pi\)
0.995256 + 0.0972943i \(0.0310188\pi\)
\(758\) −33.5630 + 1.56180i −1.21906 + 0.0567272i
\(759\) −4.77032 + 8.26243i −0.173152 + 0.299907i
\(760\) 16.5831 + 6.33354i 0.601531 + 0.229742i
\(761\) −2.24848 3.89448i −0.0815073 0.141175i 0.822390 0.568924i \(-0.192640\pi\)
−0.903898 + 0.427749i \(0.859307\pi\)
\(762\) −26.2885 + 50.8551i −0.952331 + 1.84229i
\(763\) 0 0
\(764\) 14.1509 10.0300i 0.511963 0.362872i
\(765\) 74.3680 + 18.3987i 2.68878 + 0.665207i
\(766\) −5.93523 1.29797i −0.214449 0.0468975i
\(767\) 6.74959 1.80855i 0.243714 0.0653029i
\(768\) 30.5743 + 41.6006i 1.10325 + 1.50113i
\(769\) 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
\(772\) 9.95023 3.68633i 0.358116 0.132674i
\(773\) 26.7544 7.16881i 0.962287 0.257844i 0.256719 0.966486i \(-0.417358\pi\)
0.705568 + 0.708642i \(0.250692\pi\)
\(774\) −7.91303 + 36.1839i −0.284428 + 1.30060i
\(775\) 15.5575 9.80011i 0.558842 0.352030i
\(776\) −19.2747 + 25.5717i −0.691923 + 0.917971i
\(777\) 0 0
\(778\) −31.6460 16.3587i −1.13456 0.586489i
\(779\) 4.95906 + 8.58934i 0.177677 + 0.307745i
\(780\) −1.59881 14.1811i −0.0572466 0.507765i
\(781\) 8.57374 14.8502i 0.306793 0.531380i
\(782\) −0.638676 13.7251i −0.0228390 0.490809i
\(783\) 48.8906 48.8906i 1.74721 1.74721i
\(784\) 0 0
\(785\) 28.6320 + 27.5493i 1.02192 + 0.983277i
\(786\) −44.3535 40.4092i −1.58204 1.44135i
\(787\) −5.43008 + 1.45499i −0.193561 + 0.0518646i −0.354297 0.935133i \(-0.615280\pi\)
0.160736 + 0.986997i \(0.448613\pi\)
\(788\) −22.2881 + 26.8733i −0.793980 + 0.957322i
\(789\) 31.7166 18.3116i 1.12914 0.651911i
\(790\) 1.69994 + 0.837647i 0.0604813 + 0.0298021i
\(791\) 0 0
\(792\) 29.2047 4.10068i 1.03774 0.145711i
\(793\) −0.562681 + 2.09996i −0.0199814 + 0.0745716i
\(794\) −5.34649 1.16922i −0.189740 0.0414940i
\(795\) −6.22248 3.43443i −0.220689 0.121807i
\(796\) −3.58879 + 7.81282i −0.127201 + 0.276918i
\(797\) 10.9874 10.9874i 0.389195 0.389195i −0.485205 0.874400i \(-0.661255\pi\)
0.874400 + 0.485205i \(0.161255\pi\)
\(798\) 0 0
\(799\) 12.2183 0.432252
\(800\) 7.06785 27.3870i 0.249886 0.968275i
\(801\) 1.71830 2.97619i 0.0607133 0.105159i
\(802\) 4.18829 + 6.53290i 0.147894 + 0.230685i
\(803\) −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
\(808\) −6.39212 + 15.8153i −0.224874 + 0.556380i
\(809\) 14.4297 + 8.33096i 0.507320 + 0.292901i 0.731731 0.681593i \(-0.238713\pi\)
−0.224412 + 0.974494i \(0.572046\pi\)
\(810\) 4.92515 + 74.7784i 0.173052 + 2.62745i
\(811\) 30.5372i 1.07231i 0.844120 + 0.536154i \(0.180123\pi\)
−0.844120 + 0.536154i \(0.819877\pi\)
\(812\) 0 0
\(813\) 0.355563 + 0.355563i 0.0124701 + 0.0124701i
\(814\) −12.1760 11.0932i −0.426768 0.388816i
\(815\) 37.3554 10.7849i 1.30850 0.377779i
\(816\) −45.2617 + 38.8721i −1.58448 + 1.36080i
\(817\) −9.58017 2.56700i −0.335168 0.0898079i
\(818\) −21.3481 11.0355i −0.746420 0.385846i
\(819\) 0 0
\(820\) 12.7145 9.38507i 0.444009 0.327741i
\(821\) 9.24225 + 16.0080i 0.322557 + 0.558685i 0.981015 0.193933i \(-0.0621243\pi\)
−0.658458 + 0.752617i \(0.728791\pi\)
\(822\) −26.8490 + 17.2131i −0.936465 + 0.600375i
\(823\) −11.0750 41.3323i −0.386049 1.44075i −0.836507 0.547957i \(-0.815406\pi\)
0.450457 0.892798i \(-0.351261\pi\)
\(824\) −39.5062 4.85583i −1.37626 0.169161i
\(825\) −16.6553 15.4187i −0.579863 0.536809i
\(826\) 0 0
\(827\) −22.7990 22.7990i −0.792801 0.792801i 0.189148 0.981949i \(-0.439427\pi\)
−0.981949 + 0.189148i \(0.939427\pi\)
\(828\) 29.2150 10.8235i 1.01529 0.376142i
\(829\) −29.0025 16.7446i −1.00730 0.581563i −0.0968981 0.995294i \(-0.530892\pi\)
−0.910399 + 0.413731i \(0.864225\pi\)
\(830\) −3.95262 + 19.9043i −0.137197 + 0.690888i
\(831\) 58.4953 33.7723i 2.02918 1.17155i
\(832\) 6.91871 + 3.83740i 0.239863 + 0.133038i
\(833\) 0 0
\(834\) 29.4072 + 92.3440i 1.01829 + 3.19761i
\(835\) −21.1492 5.23233i −0.731898 0.181072i
\(836\) 0.733360 + 7.86286i 0.0253638 + 0.271943i
\(837\) −13.5488 50.5649i −0.468316 1.74778i
\(838\) 5.47495 0.254768i 0.189129 0.00880082i
\(839\) −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
\(842\) 29.2652 1.36181i 1.00854 0.0469310i
\(843\) −2.14092 7.99001i −0.0737371 0.275190i
\(844\) −3.63094 38.9298i −0.124982 1.34002i
\(845\) 13.8870 + 23.0171i 0.477728 + 0.791814i
\(846\) 8.40681 + 26.3989i 0.289032 + 0.907612i
\(847\) 0 0
\(848\) 3.55174 1.70605i 0.121967 0.0585862i
\(849\) 57.4949 33.1947i 1.97322 1.13924i
\(850\) 32.1772 + 5.74772i 1.10367 + 0.197145i
\(851\) −15.0698 8.70057i −0.516587 0.298252i
\(852\) −73.7621 + 27.3271i −2.52705 + 0.936213i
\(853\) −10.0581 10.0581i −0.344383 0.344383i 0.513629 0.858012i \(-0.328301\pi\)
−0.858012 + 0.513629i \(0.828301\pi\)
\(854\) 0 0
\(855\) −46.5077 + 0.896235i −1.59053 + 0.0306506i
\(856\) 6.92156 56.3126i 0.236574 1.92473i
\(857\) 0.134823 + 0.503168i 0.00460548 + 0.0171879i 0.968190 0.250215i \(-0.0805013\pi\)
−0.963585 + 0.267403i \(0.913835\pi\)
\(858\) 5.34461 3.42647i 0.182462 0.116978i
\(859\) 2.00473 + 3.47230i 0.0684006 + 0.118473i 0.898197 0.439592i \(-0.144877\pi\)
−0.829797 + 0.558066i \(0.811544\pi\)
\(860\) −2.35426 + 15.6267i −0.0802796 + 0.532868i
\(861\) 0 0
\(862\) 12.2726 + 6.34407i 0.418007 + 0.216080i
\(863\) 14.3236 + 3.83800i 0.487581 + 0.130647i 0.494231 0.869331i \(-0.335450\pi\)
−0.00664926 + 0.999978i \(0.502117\pi\)
\(864\) −68.5291 42.2893i −2.33141 1.43871i
\(865\) 15.3453 + 53.1511i 0.521756 + 1.80719i
\(866\) −10.3619 9.44045i −0.352113 0.320800i
\(867\) −9.96649 9.96649i −0.338480 0.338480i
\(868\) 0 0
\(869\) 0.843073i 0.0285993i
\(870\) 32.6655 37.2718i 1.10747 1.26363i
\(871\) 2.73690 + 1.58015i 0.0927364 + 0.0535414i
\(872\) −2.66205 1.07593i −0.0901483 0.0364355i
\(873\) 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 0.726262 0.687418i \(-0.241256\pi\)
0.285252 + 0.958453i \(0.407923\pi\)
\(878\) 3.37809 + 5.26914i 0.114005 + 0.177825i
\(879\) 10.7488 18.6175i 0.362548 0.627952i
\(880\) 12.3186 2.56473i 0.415259 0.0864570i
\(881\) −26.6186 −0.896802 −0.448401 0.893833i \(-0.648006\pi\)
−0.448401 + 0.893833i \(0.648006\pi\)
\(882\) 0 0
\(883\) 20.2772 20.2772i 0.682383 0.682383i −0.278154 0.960537i \(-0.589722\pi\)
0.960537 + 0.278154i \(0.0897224\pi\)
\(884\) −3.81644 + 8.30842i −0.128361 + 0.279442i
\(885\) −48.9799 + 14.1410i −1.64644 + 0.475345i
\(886\) 6.08139 + 1.32993i 0.204308 + 0.0446800i
\(887\) −11.0601 + 41.2767i −0.371361 + 1.38594i 0.487229 + 0.873274i \(0.338008\pi\)
−0.858590 + 0.512663i \(0.828659\pi\)
\(888\) 10.5066 + 74.8268i 0.352577 + 2.51102i
\(889\) 0 0
\(890\) 0.648093 1.31526i 0.0217241 0.0440876i
\(891\) −28.8720 + 16.6692i −0.967247 + 0.558440i
\(892\) −17.2348 + 20.7804i −0.577062 + 0.695779i
\(893\) −7.16594 + 1.92011i −0.239799 + 0.0642540i
\(894\) 22.4135 + 20.4203i 0.749619 + 0.682956i
\(895\) −0.885581 45.9548i −0.0296017 1.53610i
\(896\) 0 0
\(897\) 4.74253 4.74253i 0.158348 0.158348i
\(898\) 1.43540 + 30.8467i 0.0479000 + 1.02937i
\(899\) −8.93063 + 15.4683i −0.297853 + 0.515897i
\(900\) 9.72100 + 73.4768i 0.324033 + 2.44923i
\(901\) 2.27675 + 3.94345i 0.0758496 + 0.131375i
\(902\) 6.24520 + 3.22832i 0.207942 + 0.107491i
\(903\) 0 0
\(904\) 23.6164 + 17.8010i 0.785471 + 0.592051i
\(905\) −15.0485 + 9.07925i −0.500228 + 0.301804i
\(906\) −19.8751 + 90.8828i −0.660305 + 3.01938i
\(907\) −1.18466 + 0.317430i −0.0393361 + 0.0105401i −0.278433 0.960456i \(-0.589815\pi\)
0.239097 + 0.970996i \(0.423148\pi\)
\(908\) −34.6032 + 12.8197i −1.14835 + 0.425436i
\(909\) 44.6999i 1.48260i
\(910\) 0 0
\(911\) 13.4236i 0.444743i −0.974962 0.222372i \(-0.928620\pi\)
0.974962 0.222372i \(-0.0713799\pi\)
\(912\) 20.4369 29.9111i 0.676733 0.990455i
\(913\) −8.72004 + 2.33653i −0.288591 + 0.0773277i
\(914\) 30.4357 + 6.65594i 1.00672 + 0.220159i
\(915\) 3.80922 15.3970i 0.125929 0.509008i
\(916\) −25.4827 + 18.0618i −0.841974 + 0.596779i
\(917\) 0 0
\(918\) 42.7338 82.6686i 1.41042 2.72847i
\(919\) 13.1243 + 22.7320i 0.432931 + 0.749858i 0.997124 0.0757845i \(-0.0241461\pi\)
−0.564193 + 0.825643i \(0.690813\pi\)
\(920\) 12.1344 5.42717i 0.400061 0.178928i
\(921\) 38.4473 66.5926i 1.26688 2.19430i
\(922\) 27.9246 1.29943i 0.919646 0.0427943i
\(923\) −8.52380 + 8.52380i −0.280564 + 0.280564i
\(924\) 0 0
\(925\) 28.1221 30.3776i 0.924649 0.998809i
\(926\) −19.5629 + 21.4725i −0.642878 + 0.705629i
\(927\) 100.748 26.9955i 3.30901 0.886647i
\(928\) 6.33068 + 26.7364i 0.207815 + 0.877666i
\(929\) 17.2412 9.95422i 0.565666 0.326587i −0.189751 0.981832i \(-0.560768\pi\)
0.755416 + 0.655245i \(0.227435\pi\)
\(930\) −12.0727 35.5280i −0.395881 1.16501i
\(931\) 0 0
\(932\) 1.28448 7.53711i 0.0420747 0.246886i
\(933\) 15.1677 56.6067i 0.496569 1.85322i
\(934\) 8.51775 38.9491i 0.278709 1.27446i
\(935\) 4.03344 + 13.9705i 0.131908 + 0.456885i
\(936\) −20.5771 2.52920i −0.672583 0.0826693i
\(937\) 3.76752 3.76752i 0.123080 0.123080i −0.642884 0.765964i \(-0.722262\pi\)
0.765964 + 0.642884i \(0.222262\pi\)
\(938\) 0 0
\(939\) 5.06087 0.165155
\(940\) 4.31933 + 11.0033i 0.140881 + 0.358887i
\(941\) 2.41962 4.19090i 0.0788772 0.136619i −0.823889 0.566752i \(-0.808200\pi\)
0.902766 + 0.430133i \(0.141533\pi\)
\(942\) 68.2624 43.7636i 2.22411 1.42589i
\(943\) 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 −0.703872 0.710327i \(-0.748547\pi\)
0.964735 0.263225i \(-0.0847861\pi\)
\(948\) 2.46893 2.97686i 0.0801872 0.0966838i
\(949\) 5.67887 + 3.27870i 0.184344 + 0.106431i
\(950\) −19.7749 + 1.68566i −0.641584 + 0.0546899i
\(951\) 95.3170i 3.09086i
\(952\) 0 0
\(953\) 22.3422 + 22.3422i 0.723734 + 0.723734i 0.969364 0.245630i \(-0.0789947\pi\)
−0.245630 + 0.969364i \(0.578995\pi\)
\(954\) −6.95371 + 7.63245i −0.225135 + 0.247110i
\(955\) −9.37078 + 16.9779i −0.303231 + 0.549393i
\(956\) −30.8167 + 2.87424i −0.996684 + 0.0929596i
\(957\) 21.2965 + 5.70637i 0.688417 + 0.184461i
\(958\) 0.921354 1.78236i 0.0297676 0.0575855i
\(959\) 0 0
\(960\) −51.0071 27.0189i −1.64625 0.872030i
\(961\) −8.73844 15.1354i −0.281885 0.488239i
\(962\) 6.24953 + 9.74802i 0.201493 + 0.314289i
\(963\) 38.4796 + 143.608i 1.23999 + 4.62770i
\(964\) 24.0114 52.2729i 0.773354 1.68360i
\(965\) −8.22565 + 8.54890i −0.264793 + 0.275199i
\(966\) 0 0
\(967\) −8.85634 8.85634i −0.284801 0.284801i 0.550219 0.835020i \(-0.314544\pi\)
−0.835020 + 0.550219i \(0.814544\pi\)
\(968\) −15.7061 20.1081i −0.504813 0.646300i
\(969\) 36.2558 + 20.9323i 1.16470 + 0.672442i
\(970\) 6.97345 35.1163i 0.223904 1.12752i
\(971\) 8.19063 4.72886i 0.262850 0.151756i −0.362784 0.931873i \(-0.618174\pi\)
0.625634 + 0.780117i \(0.284840\pi\)
\(972\) 66.5634 + 11.3438i 2.13502 + 0.363854i
\(973\) 0 0
\(974\) −45.3582 + 14.4445i −1.45337 + 0.462831i
\(975\) 8.50414 + 13.5002i 0.272350 + 0.432352i
\(976\) 5.72906 + 6.67076i 0.183383 + 0.213526i
\(977\) −15.9873 59.6654i −0.511479 1.90886i −0.404305 0.914624i \(-0.632487\pi\)
−0.107173 0.994240i \(-0.534180\pi\)
\(978\) −3.68829 79.2611i −0.117939 2.53449i
\(979\) 0.652291 0.0208473
\(980\) 0 0
\(981\) 7.52393 0.240221
\(982\) −0.208172 4.47359i −0.00664303 0.142758i
\(983\) 15.3538 + 57.3012i 0.489710 + 1.82762i 0.557842 + 0.829947i \(0.311630\pi\)
−0.0681315 + 0.997676i \(0.521704\pi\)
\(984\) −12.5974 29.6881i −0.401591 0.946422i
\(985\) 9.37447 37.8918i 0.298695 1.20733i
\(986\) −30.2550 + 9.63480i −0.963515 + 0.306834i
\(987\) 0 0
\(988\) 0.932645 5.47258i 0.0296714 0.174106i
\(989\) −6.43198 + 3.71351i −0.204525 + 0.118083i
\(990\) −27.4095 + 18.3271i −0.871132 + 0.582473i
\(991\) 15.0202 + 8.67190i 0.477131 + 0.275472i 0.719220 0.694782i \(-0.244499\pi\)
−0.242089 + 0.970254i \(0.577833\pi\)
\(992\) 19.9272 + 5.97040i 0.632690 + 0.189560i
\(993\) −28.8227 28.8227i −0.914660 0.914660i
\(994\) 0 0
\(995\) −0.185204 9.61068i −0.00587137 0.304679i
\(996\) 37.6326 + 17.2864i 1.19243 + 0.547740i
\(997\) −3.99308 14.9024i −0.126462 0.471964i 0.873425 0.486958i \(-0.161894\pi\)
−0.999888 + 0.0149945i \(0.995227\pi\)
\(998\) 5.68564 + 8.86846i 0.179976 + 0.280726i
\(999\) −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.l.263.18 72
4.3 odd 2 inner 980.2.x.l.263.16 72
5.2 odd 4 inner 980.2.x.l.67.10 72
7.2 even 3 inner 980.2.x.l.863.7 72
7.3 odd 6 140.2.k.a.43.6 yes 36
7.4 even 3 980.2.k.l.883.6 36
7.5 odd 6 980.2.x.k.863.7 72
7.6 odd 2 980.2.x.k.263.18 72
20.7 even 4 inner 980.2.x.l.67.7 72
28.3 even 6 140.2.k.a.43.3 36
28.11 odd 6 980.2.k.l.883.3 36
28.19 even 6 980.2.x.k.863.10 72
28.23 odd 6 inner 980.2.x.l.863.10 72
28.27 even 2 980.2.x.k.263.16 72
35.2 odd 12 inner 980.2.x.l.667.16 72
35.3 even 12 700.2.k.b.407.16 36
35.12 even 12 980.2.x.k.667.16 72
35.17 even 12 140.2.k.a.127.3 yes 36
35.24 odd 6 700.2.k.b.43.13 36
35.27 even 4 980.2.x.k.67.10 72
35.32 odd 12 980.2.k.l.687.3 36
140.3 odd 12 700.2.k.b.407.13 36
140.27 odd 4 980.2.x.k.67.7 72
140.47 odd 12 980.2.x.k.667.18 72
140.59 even 6 700.2.k.b.43.16 36
140.67 even 12 980.2.k.l.687.6 36
140.87 odd 12 140.2.k.a.127.6 yes 36
140.107 even 12 inner 980.2.x.l.667.18 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.k.a.43.3 36 28.3 even 6
140.2.k.a.43.6 yes 36 7.3 odd 6
140.2.k.a.127.3 yes 36 35.17 even 12
140.2.k.a.127.6 yes 36 140.87 odd 12
700.2.k.b.43.13 36 35.24 odd 6
700.2.k.b.43.16 36 140.59 even 6
700.2.k.b.407.13 36 140.3 odd 12
700.2.k.b.407.16 36 35.3 even 12
980.2.k.l.687.3 36 35.32 odd 12
980.2.k.l.687.6 36 140.67 even 12
980.2.k.l.883.3 36 28.11 odd 6
980.2.k.l.883.6 36 7.4 even 3
980.2.x.k.67.7 72 140.27 odd 4
980.2.x.k.67.10 72 35.27 even 4
980.2.x.k.263.16 72 28.27 even 2
980.2.x.k.263.18 72 7.6 odd 2
980.2.x.k.667.16 72 35.12 even 12
980.2.x.k.667.18 72 140.47 odd 12
980.2.x.k.863.7 72 7.5 odd 6
980.2.x.k.863.10 72 28.19 even 6
980.2.x.l.67.7 72 20.7 even 4 inner
980.2.x.l.67.10 72 5.2 odd 4 inner
980.2.x.l.263.16 72 4.3 odd 2 inner
980.2.x.l.263.18 72 1.1 even 1 trivial
980.2.x.l.667.16 72 35.2 odd 12 inner
980.2.x.l.667.18 72 140.107 even 12 inner
980.2.x.l.863.7 72 7.2 even 3 inner
980.2.x.l.863.10 72 28.23 odd 6 inner