Properties

Label 750.2.l.a.143.6
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [750,2,Mod(107,750)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(750, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("750.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 143.6
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.a.257.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(-1.70181 + 0.322239i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 + 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.79232 - 1.09678i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(-1.70181 + 0.322239i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.485490 + 1.66262i) q^{6} +(-0.0556476 + 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(2.79232 - 1.09678i) q^{9} +(-1.04749 + 0.340351i) q^{11} +(1.26100 + 1.18739i) q^{12} +(-4.54086 + 2.31368i) q^{13} +(0.0243189 + 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.491350 + 3.10226i) q^{17} +(0.290452 - 2.98591i) q^{18} +(0.824223 - 1.13445i) q^{19} +(0.0767699 - 0.112634i) q^{21} +(-0.172297 + 1.08784i) q^{22} +(-2.22575 - 1.13408i) q^{23} +(1.63045 - 0.584493i) q^{24} +5.09632i q^{26} +(-4.39859 + 2.76630i) q^{27} +(0.0777287 + 0.0123110i) q^{28} +(-5.66803 + 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.67296 - 0.916756i) q^{33} +(2.98720 + 0.970601i) q^{34} +(-2.52860 - 1.61437i) q^{36} +(4.70325 + 9.23065i) q^{37} +(-0.636609 - 1.24942i) q^{38} +(6.98213 - 5.40069i) q^{39} +(3.55210 + 1.15415i) q^{41} +(-0.0655044 - 0.119537i) q^{42} +(1.00563 + 1.00563i) q^{43} +(0.891050 + 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(-12.5515 - 1.98797i) q^{47} +(0.219422 - 1.71810i) q^{48} +6.99381i q^{49} +(-1.83585 - 5.12113i) q^{51} +(4.54086 + 2.31368i) q^{52} +(-1.06206 + 6.70559i) q^{53} +(0.467880 + 5.17504i) q^{54} +(0.0462573 - 0.0636677i) q^{56} +(-1.03711 + 2.19621i) q^{57} +(1.09599 + 6.91981i) q^{58} +(-2.03647 + 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(8.51329 - 4.33774i) q^{62} +(-0.0943531 + 0.216419i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.0573270 - 1.90682i) q^{66} +(6.57696 - 1.04169i) q^{67} +(2.22097 - 2.22097i) q^{68} +(4.15326 + 1.21276i) q^{69} +(-7.51096 - 10.3379i) q^{71} +(-2.58637 + 1.52009i) q^{72} +(0.602914 - 1.18329i) q^{73} +10.3598 q^{74} -1.40225 q^{76} +(0.0393507 - 0.0772302i) q^{77} +(-1.64223 - 8.67298i) q^{78} +(-5.85354 - 8.05671i) q^{79} +(6.59415 - 6.12512i) q^{81} +(2.64098 - 2.64098i) q^{82} +(-0.871279 + 0.137997i) q^{83} +(-0.136247 + 0.00409615i) q^{84} +(1.35257 - 0.439477i) q^{86} +(8.31892 - 8.83463i) q^{87} +(0.981353 - 0.500025i) q^{88} +(-1.01326 - 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(0.390777 + 2.46727i) q^{92} +(-14.9646 - 7.06668i) q^{93} +(-7.46957 + 10.2810i) q^{94} +(-1.43122 - 0.975505i) q^{96} +(1.62393 - 10.2531i) q^{97} +(6.23153 + 3.17512i) q^{98} +(-2.55165 + 2.09924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) −1.70181 + 0.322239i −0.982541 + 0.186045i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) −0.485490 + 1.66262i −0.198200 + 0.678761i
\(7\) −0.0556476 + 0.0556476i −0.0210328 + 0.0210328i −0.717545 0.696512i \(-0.754734\pi\)
0.696512 + 0.717545i \(0.254734\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) 2.79232 1.09678i 0.930775 0.365593i
\(10\) 0 0
\(11\) −1.04749 + 0.340351i −0.315831 + 0.102620i −0.462643 0.886545i \(-0.653099\pi\)
0.146812 + 0.989164i \(0.453099\pi\)
\(12\) 1.26100 + 1.18739i 0.364018 + 0.342769i
\(13\) −4.54086 + 2.31368i −1.25941 + 0.641700i −0.950893 0.309520i \(-0.899832\pi\)
−0.308514 + 0.951220i \(0.599832\pi\)
\(14\) 0.0243189 + 0.0748459i 0.00649950 + 0.0200034i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.491350 + 3.10226i 0.119170 + 0.752408i 0.972820 + 0.231562i \(0.0743836\pi\)
−0.853650 + 0.520846i \(0.825616\pi\)
\(18\) 0.290452 2.98591i 0.0684602 0.703785i
\(19\) 0.824223 1.13445i 0.189090 0.260260i −0.703938 0.710262i \(-0.748577\pi\)
0.893028 + 0.450002i \(0.148577\pi\)
\(20\) 0 0
\(21\) 0.0767699 0.112634i 0.0167526 0.0245787i
\(22\) −0.172297 + 1.08784i −0.0367338 + 0.231928i
\(23\) −2.22575 1.13408i −0.464102 0.236472i 0.206273 0.978495i \(-0.433867\pi\)
−0.670375 + 0.742023i \(0.733867\pi\)
\(24\) 1.63045 0.584493i 0.332814 0.119309i
\(25\) 0 0
\(26\) 5.09632i 0.999471i
\(27\) −4.39859 + 2.76630i −0.846508 + 0.532376i
\(28\) 0.0777287 + 0.0123110i 0.0146893 + 0.00232656i
\(29\) −5.66803 + 4.11807i −1.05253 + 0.764705i −0.972691 0.232103i \(-0.925440\pi\)
−0.0798355 + 0.996808i \(0.525440\pi\)
\(30\) 0 0
\(31\) 7.72991 + 5.61611i 1.38833 + 1.00868i 0.996046 + 0.0888399i \(0.0283160\pi\)
0.392287 + 0.919843i \(0.371684\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 1.67296 0.916756i 0.291225 0.159587i
\(34\) 2.98720 + 0.970601i 0.512301 + 0.166457i
\(35\) 0 0
\(36\) −2.52860 1.61437i −0.421433 0.269061i
\(37\) 4.70325 + 9.23065i 0.773210 + 1.51751i 0.853706 + 0.520755i \(0.174350\pi\)
−0.0804961 + 0.996755i \(0.525650\pi\)
\(38\) −0.636609 1.24942i −0.103272 0.202682i
\(39\) 6.98213 5.40069i 1.11803 0.864803i
\(40\) 0 0
\(41\) 3.55210 + 1.15415i 0.554745 + 0.180248i 0.572956 0.819586i \(-0.305797\pi\)
−0.0182101 + 0.999834i \(0.505797\pi\)
\(42\) −0.0655044 0.119537i −0.0101075 0.0184450i
\(43\) 1.00563 + 1.00563i 0.153357 + 0.153357i 0.779616 0.626258i \(-0.215414\pi\)
−0.626258 + 0.779616i \(0.715414\pi\)
\(44\) 0.891050 + 0.647386i 0.134331 + 0.0975971i
\(45\) 0 0
\(46\) −2.02094 + 1.46830i −0.297972 + 0.216489i
\(47\) −12.5515 1.98797i −1.83083 0.289975i −0.856674 0.515858i \(-0.827473\pi\)
−0.974154 + 0.225883i \(0.927473\pi\)
\(48\) 0.219422 1.71810i 0.0316708 0.247986i
\(49\) 6.99381i 0.999115i
\(50\) 0 0
\(51\) −1.83585 5.12113i −0.257071 0.717101i
\(52\) 4.54086 + 2.31368i 0.629704 + 0.320850i
\(53\) −1.06206 + 6.70559i −0.145885 + 0.921083i 0.800802 + 0.598929i \(0.204407\pi\)
−0.946687 + 0.322154i \(0.895593\pi\)
\(54\) 0.467880 + 5.17504i 0.0636704 + 0.704234i
\(55\) 0 0
\(56\) 0.0462573 0.0636677i 0.00618139 0.00850795i
\(57\) −1.03711 + 2.19621i −0.137369 + 0.290895i
\(58\) 1.09599 + 6.91981i 0.143911 + 0.908616i
\(59\) −2.03647 + 6.26761i −0.265126 + 0.815974i 0.726538 + 0.687126i \(0.241128\pi\)
−0.991664 + 0.128848i \(0.958872\pi\)
\(60\) 0 0
\(61\) 1.23324 + 3.79553i 0.157901 + 0.485968i 0.998443 0.0557774i \(-0.0177637\pi\)
−0.840543 + 0.541745i \(0.817764\pi\)
\(62\) 8.51329 4.33774i 1.08119 0.550894i
\(63\) −0.0943531 + 0.216419i −0.0118874 + 0.0272663i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) −0.0573270 1.90682i −0.00705647 0.234713i
\(67\) 6.57696 1.04169i 0.803504 0.127263i 0.258844 0.965919i \(-0.416659\pi\)
0.544660 + 0.838657i \(0.316659\pi\)
\(68\) 2.22097 2.22097i 0.269332 0.269332i
\(69\) 4.15326 + 1.21276i 0.499993 + 0.146000i
\(70\) 0 0
\(71\) −7.51096 10.3379i −0.891387 1.22689i −0.973135 0.230236i \(-0.926050\pi\)
0.0817481 0.996653i \(-0.473950\pi\)
\(72\) −2.58637 + 1.52009i −0.304807 + 0.179144i
\(73\) 0.602914 1.18329i 0.0705658 0.138493i −0.853029 0.521864i \(-0.825237\pi\)
0.923595 + 0.383371i \(0.125237\pi\)
\(74\) 10.3598 1.20430
\(75\) 0 0
\(76\) −1.40225 −0.160849
\(77\) 0.0393507 0.0772302i 0.00448443 0.00880119i
\(78\) −1.64223 8.67298i −0.185946 0.982022i
\(79\) −5.85354 8.05671i −0.658575 0.906451i 0.340858 0.940115i \(-0.389282\pi\)
−0.999433 + 0.0336639i \(0.989282\pi\)
\(80\) 0 0
\(81\) 6.59415 6.12512i 0.732684 0.680569i
\(82\) 2.64098 2.64098i 0.291647 0.291647i
\(83\) −0.871279 + 0.137997i −0.0956353 + 0.0151471i −0.204069 0.978957i \(-0.565417\pi\)
0.108433 + 0.994104i \(0.465417\pi\)
\(84\) −0.136247 + 0.00409615i −0.0148657 + 0.000446927i
\(85\) 0 0
\(86\) 1.35257 0.439477i 0.145851 0.0473900i
\(87\) 8.31892 8.83463i 0.891882 0.947172i
\(88\) 0.981353 0.500025i 0.104613 0.0533028i
\(89\) −1.01326 3.11850i −0.107406 0.330560i 0.882882 0.469595i \(-0.155600\pi\)
−0.990288 + 0.139035i \(0.955600\pi\)
\(90\) 0 0
\(91\) 0.123937 0.381439i 0.0129921 0.0399856i
\(92\) 0.390777 + 2.46727i 0.0407413 + 0.257230i
\(93\) −14.9646 7.06668i −1.55175 0.732781i
\(94\) −7.46957 + 10.2810i −0.770427 + 1.06040i
\(95\) 0 0
\(96\) −1.43122 0.975505i −0.146073 0.0995621i
\(97\) 1.62393 10.2531i 0.164885 1.04104i −0.756953 0.653469i \(-0.773313\pi\)
0.921838 0.387575i \(-0.126687\pi\)
\(98\) 6.23153 + 3.17512i 0.629479 + 0.320736i
\(99\) −2.55165 + 2.09924i −0.256450 + 0.210981i
\(100\) 0 0
\(101\) 14.0377i 1.39680i 0.715708 + 0.698399i \(0.246104\pi\)
−0.715708 + 0.698399i \(0.753896\pi\)
\(102\) −5.39642 0.689188i −0.534325 0.0682398i
\(103\) 13.0416 + 2.06559i 1.28503 + 0.203529i 0.761324 0.648371i \(-0.224549\pi\)
0.523705 + 0.851900i \(0.324549\pi\)
\(104\) 4.12301 2.99554i 0.404295 0.293737i
\(105\) 0 0
\(106\) 5.49256 + 3.99058i 0.533484 + 0.387599i
\(107\) −13.7619 13.7619i −1.33041 1.33041i −0.904999 0.425413i \(-0.860129\pi\)
−0.425413 0.904999i \(-0.639871\pi\)
\(108\) 4.82341 + 1.93254i 0.464133 + 0.185958i
\(109\) −11.7044 3.80299i −1.12108 0.364260i −0.310898 0.950443i \(-0.600630\pi\)
−0.810178 + 0.586183i \(0.800630\pi\)
\(110\) 0 0
\(111\) −10.9785 14.1933i −1.04204 1.34716i
\(112\) −0.0357280 0.0701201i −0.00337598 0.00662572i
\(113\) −3.46581 6.80204i −0.326036 0.639882i 0.668565 0.743654i \(-0.266909\pi\)
−0.994601 + 0.103771i \(0.966909\pi\)
\(114\) 1.48600 + 1.92113i 0.139177 + 0.179930i
\(115\) 0 0
\(116\) 6.66317 + 2.16499i 0.618660 + 0.201015i
\(117\) −10.1420 + 11.4409i −0.937624 + 1.05771i
\(118\) 4.65995 + 4.65995i 0.428983 + 0.428983i
\(119\) −0.199976 0.145291i −0.0183317 0.0133188i
\(120\) 0 0
\(121\) −7.91779 + 5.75261i −0.719799 + 0.522964i
\(122\) 3.94172 + 0.624308i 0.356867 + 0.0565222i
\(123\) −6.41692 0.819518i −0.578594 0.0738935i
\(124\) 9.55469i 0.858037i
\(125\) 0 0
\(126\) 0.149996 + 0.182322i 0.0133627 + 0.0162425i
\(127\) −2.87091 1.46280i −0.254752 0.129803i 0.321952 0.946756i \(-0.395661\pi\)
−0.576703 + 0.816954i \(0.695661\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) −2.03545 1.38734i −0.179211 0.122149i
\(130\) 0 0
\(131\) 3.12598 4.30255i 0.273118 0.375915i −0.650321 0.759660i \(-0.725366\pi\)
0.923439 + 0.383744i \(0.125366\pi\)
\(132\) −1.72501 0.814598i −0.150143 0.0709017i
\(133\) 0.0172632 + 0.108995i 0.00149690 + 0.00945109i
\(134\) 2.05773 6.33303i 0.177761 0.547091i
\(135\) 0 0
\(136\) −0.970601 2.98720i −0.0832283 0.256150i
\(137\) 10.2341 5.21451i 0.874354 0.445506i 0.0415907 0.999135i \(-0.486757\pi\)
0.832763 + 0.553629i \(0.186757\pi\)
\(138\) 2.96612 3.15000i 0.252493 0.268146i
\(139\) −10.3684 + 3.36891i −0.879440 + 0.285747i −0.713725 0.700426i \(-0.752993\pi\)
−0.165715 + 0.986174i \(0.552993\pi\)
\(140\) 0 0
\(141\) 22.0009 0.661442i 1.85281 0.0557034i
\(142\) −12.6211 + 1.99898i −1.05914 + 0.167751i
\(143\) 3.96905 3.96905i 0.331909 0.331909i
\(144\) 0.180223 + 2.99458i 0.0150186 + 0.249548i
\(145\) 0 0
\(146\) −0.780598 1.07440i −0.0646028 0.0889181i
\(147\) −2.25367 11.9021i −0.185880 0.981672i
\(148\) 4.70325 9.23065i 0.386605 0.758755i
\(149\) −14.3679 −1.17707 −0.588534 0.808472i \(-0.700295\pi\)
−0.588534 + 0.808472i \(0.700295\pi\)
\(150\) 0 0
\(151\) −0.326435 −0.0265649 −0.0132824 0.999912i \(-0.504228\pi\)
−0.0132824 + 0.999912i \(0.504228\pi\)
\(152\) −0.636609 + 1.24942i −0.0516358 + 0.101341i
\(153\) 4.77450 + 8.12361i 0.385995 + 0.656755i
\(154\) −0.0509477 0.0701235i −0.00410548 0.00565071i
\(155\) 0 0
\(156\) −8.47324 2.47421i −0.678402 0.198096i
\(157\) 3.47556 3.47556i 0.277380 0.277380i −0.554682 0.832062i \(-0.687160\pi\)
0.832062 + 0.554682i \(0.187160\pi\)
\(158\) −9.83604 + 1.55788i −0.782513 + 0.123938i
\(159\) −0.353372 11.7539i −0.0280242 0.932144i
\(160\) 0 0
\(161\) 0.186967 0.0607491i 0.0147350 0.00478770i
\(162\) −2.46384 8.65618i −0.193578 0.680094i
\(163\) −1.36590 + 0.695961i −0.106986 + 0.0545119i −0.506664 0.862143i \(-0.669122\pi\)
0.399679 + 0.916655i \(0.369122\pi\)
\(164\) −1.15415 3.55210i −0.0901239 0.277373i
\(165\) 0 0
\(166\) −0.272596 + 0.838964i −0.0211576 + 0.0651163i
\(167\) 3.50144 + 22.1072i 0.270949 + 1.71071i 0.629336 + 0.777133i \(0.283327\pi\)
−0.358387 + 0.933573i \(0.616673\pi\)
\(168\) −0.0582050 + 0.123256i −0.00449061 + 0.00950943i
\(169\) 7.62505 10.4950i 0.586542 0.807306i
\(170\) 0 0
\(171\) 1.05726 4.07173i 0.0808509 0.311373i
\(172\) 0.222477 1.40467i 0.0169637 0.107105i
\(173\) 12.6292 + 6.43491i 0.960182 + 0.489237i 0.862542 0.505985i \(-0.168871\pi\)
0.0976395 + 0.995222i \(0.468871\pi\)
\(174\) −4.09500 11.4230i −0.310441 0.865979i
\(175\) 0 0
\(176\) 1.10140i 0.0830211i
\(177\) 1.44602 11.3225i 0.108690 0.851053i
\(178\) −3.23861 0.512946i −0.242744 0.0384469i
\(179\) 12.2896 8.92889i 0.918565 0.667377i −0.0246011 0.999697i \(-0.507832\pi\)
0.943167 + 0.332320i \(0.107832\pi\)
\(180\) 0 0
\(181\) −8.30933 6.03708i −0.617627 0.448733i 0.234465 0.972125i \(-0.424666\pi\)
−0.852092 + 0.523392i \(0.824666\pi\)
\(182\) −0.283598 0.283598i −0.0210217 0.0210217i
\(183\) −3.32181 6.06188i −0.245556 0.448107i
\(184\) 2.37576 + 0.771931i 0.175143 + 0.0569075i
\(185\) 0 0
\(186\) −13.0902 + 10.1253i −0.959823 + 0.742425i
\(187\) −1.57054 3.08236i −0.114849 0.225405i
\(188\) 5.76930 + 11.3229i 0.420770 + 0.825807i
\(189\) 0.0908325 0.398709i 0.00660709 0.0290018i
\(190\) 0 0
\(191\) −10.3303 3.35652i −0.747475 0.242869i −0.0895805 0.995980i \(-0.528553\pi\)
−0.657894 + 0.753110i \(0.728553\pi\)
\(192\) −1.51894 + 0.832356i −0.109620 + 0.0600701i
\(193\) 13.7241 + 13.7241i 0.987880 + 0.987880i 0.999927 0.0120476i \(-0.00383498\pi\)
−0.0120476 + 0.999927i \(0.503835\pi\)
\(194\) −8.39833 6.10174i −0.602965 0.438080i
\(195\) 0 0
\(196\) 5.65811 4.11086i 0.404151 0.293633i
\(197\) 12.0795 + 1.91320i 0.860625 + 0.136310i 0.571120 0.820867i \(-0.306509\pi\)
0.289506 + 0.957176i \(0.406509\pi\)
\(198\) 0.712010 + 3.22657i 0.0506003 + 0.229302i
\(199\) 15.9356i 1.12965i 0.825212 + 0.564823i \(0.191056\pi\)
−0.825212 + 0.564823i \(0.808944\pi\)
\(200\) 0 0
\(201\) −10.8571 + 3.89211i −0.765799 + 0.274528i
\(202\) 12.5076 + 6.37296i 0.880034 + 0.448400i
\(203\) 0.0862519 0.544573i 0.00605369 0.0382215i
\(204\) −3.06399 + 4.49536i −0.214522 + 0.314738i
\(205\) 0 0
\(206\) 7.76123 10.6824i 0.540750 0.744279i
\(207\) −7.45886 0.725556i −0.518427 0.0504296i
\(208\) −0.797241 5.03358i −0.0552787 0.349016i
\(209\) −0.477258 + 1.46885i −0.0330126 + 0.101602i
\(210\) 0 0
\(211\) −3.41758 10.5182i −0.235276 0.724104i −0.997085 0.0763026i \(-0.975689\pi\)
0.761809 0.647802i \(-0.224311\pi\)
\(212\) 6.04920 3.08222i 0.415461 0.211688i
\(213\) 16.1135 + 15.1729i 1.10408 + 1.03963i
\(214\) −18.5097 + 6.01417i −1.26530 + 0.411120i
\(215\) 0 0
\(216\) 3.91169 3.42034i 0.266157 0.232724i
\(217\) −0.742674 + 0.117628i −0.0504160 + 0.00798511i
\(218\) −8.70216 + 8.70216i −0.589385 + 0.589385i
\(219\) −0.644746 + 2.20801i −0.0435679 + 0.149204i
\(220\) 0 0
\(221\) −9.40879 12.9501i −0.632904 0.871117i
\(222\) −17.6304 + 3.33833i −1.18328 + 0.224054i
\(223\) 2.49393 4.89460i 0.167006 0.327767i −0.792302 0.610129i \(-0.791118\pi\)
0.959308 + 0.282362i \(0.0911178\pi\)
\(224\) −0.0786976 −0.00525820
\(225\) 0 0
\(226\) −7.63411 −0.507814
\(227\) −3.07043 + 6.02606i −0.203792 + 0.399964i −0.970170 0.242426i \(-0.922057\pi\)
0.766378 + 0.642390i \(0.222057\pi\)
\(228\) 2.38637 0.451860i 0.158041 0.0299251i
\(229\) 1.78525 + 2.45719i 0.117973 + 0.162376i 0.863919 0.503630i \(-0.168003\pi\)
−0.745947 + 0.666006i \(0.768003\pi\)
\(230\) 0 0
\(231\) −0.0420810 + 0.144111i −0.00276873 + 0.00948184i
\(232\) 4.95404 4.95404i 0.325249 0.325249i
\(233\) −1.36565 + 0.216297i −0.0894666 + 0.0141701i −0.201007 0.979590i \(-0.564421\pi\)
0.111541 + 0.993760i \(0.464421\pi\)
\(234\) 5.58954 + 14.2306i 0.365400 + 0.930283i
\(235\) 0 0
\(236\) 6.26761 2.03647i 0.407987 0.132563i
\(237\) 12.5578 + 11.8248i 0.815717 + 0.768101i
\(238\) −0.220242 + 0.112219i −0.0142762 + 0.00727408i
\(239\) 3.51376 + 10.8143i 0.227287 + 0.699516i 0.998051 + 0.0623963i \(0.0198743\pi\)
−0.770765 + 0.637120i \(0.780126\pi\)
\(240\) 0 0
\(241\) −2.72661 + 8.39163i −0.175636 + 0.540552i −0.999662 0.0259998i \(-0.991723\pi\)
0.824026 + 0.566552i \(0.191723\pi\)
\(242\) 1.53101 + 9.66643i 0.0984172 + 0.621382i
\(243\) −9.24826 + 12.5487i −0.593276 + 0.804999i
\(244\) 2.34577 3.22867i 0.150172 0.206695i
\(245\) 0 0
\(246\) −3.64342 + 5.34547i −0.232296 + 0.340814i
\(247\) −1.11793 + 7.05835i −0.0711323 + 0.449112i
\(248\) −8.51329 4.33774i −0.540595 0.275447i
\(249\) 1.43828 0.515604i 0.0911475 0.0326751i
\(250\) 0 0
\(251\) 14.6104i 0.922197i 0.887349 + 0.461099i \(0.152545\pi\)
−0.887349 + 0.461099i \(0.847455\pi\)
\(252\) 0.230546 0.0508748i 0.0145230 0.00320481i
\(253\) 2.71745 + 0.430401i 0.170844 + 0.0270591i
\(254\) −2.60673 + 1.89390i −0.163561 + 0.118834i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −1.57229 1.57229i −0.0980767 0.0980767i 0.656366 0.754443i \(-0.272093\pi\)
−0.754443 + 0.656366i \(0.772093\pi\)
\(258\) −2.16020 + 1.18376i −0.134488 + 0.0736975i
\(259\) −0.775389 0.251939i −0.0481803 0.0156547i
\(260\) 0 0
\(261\) −11.3104 + 17.7155i −0.700095 + 1.09656i
\(262\) −2.41443 4.73859i −0.149164 0.292751i
\(263\) −8.79695 17.2650i −0.542443 1.06460i −0.985747 0.168233i \(-0.946194\pi\)
0.443304 0.896371i \(-0.353806\pi\)
\(264\) −1.50895 + 1.16718i −0.0928695 + 0.0718348i
\(265\) 0 0
\(266\) 0.104953 + 0.0341012i 0.00643507 + 0.00209088i
\(267\) 2.72928 + 4.98058i 0.167029 + 0.304807i
\(268\) −4.70859 4.70859i −0.287623 0.287623i
\(269\) −4.44596 3.23018i −0.271075 0.196948i 0.443940 0.896056i \(-0.353580\pi\)
−0.715015 + 0.699109i \(0.753580\pi\)
\(270\) 0 0
\(271\) 6.02194 4.37520i 0.365807 0.265774i −0.389663 0.920957i \(-0.627409\pi\)
0.755470 + 0.655183i \(0.227409\pi\)
\(272\) −3.10226 0.491350i −0.188102 0.0297924i
\(273\) −0.0880031 + 0.689074i −0.00532619 + 0.0417047i
\(274\) 11.4859i 0.693891i
\(275\) 0 0
\(276\) −1.46008 4.07290i −0.0878863 0.245160i
\(277\) −17.0144 8.66928i −1.02230 0.520886i −0.139293 0.990251i \(-0.544483\pi\)
−0.883004 + 0.469365i \(0.844483\pi\)
\(278\) −1.70545 + 10.7678i −0.102286 + 0.645810i
\(279\) 27.7440 + 7.20400i 1.66099 + 0.431292i
\(280\) 0 0
\(281\) 0.827936 1.13956i 0.0493905 0.0679802i −0.783607 0.621256i \(-0.786623\pi\)
0.832998 + 0.553276i \(0.186623\pi\)
\(282\) 9.39887 19.9033i 0.559694 1.18522i
\(283\) −1.49164 9.41786i −0.0886689 0.559834i −0.991528 0.129896i \(-0.958536\pi\)
0.902859 0.429937i \(-0.141464\pi\)
\(284\) −3.94874 + 12.1530i −0.234315 + 0.721147i
\(285\) 0 0
\(286\) −1.73454 5.33836i −0.102565 0.315664i
\(287\) −0.261892 + 0.133440i −0.0154590 + 0.00787674i
\(288\) 2.75001 + 1.19893i 0.162046 + 0.0706478i
\(289\) 6.78537 2.20470i 0.399139 0.129688i
\(290\) 0 0
\(291\) 0.540319 + 17.9721i 0.0316740 + 1.05355i
\(292\) −1.31168 + 0.207750i −0.0767604 + 0.0121577i
\(293\) 22.0266 22.0266i 1.28681 1.28681i 0.350091 0.936716i \(-0.386151\pi\)
0.936716 0.350091i \(-0.113849\pi\)
\(294\) −11.6280 3.39542i −0.678161 0.198025i
\(295\) 0 0
\(296\) −6.08934 8.38126i −0.353936 0.487151i
\(297\) 3.66597 4.39475i 0.212721 0.255009i
\(298\) −6.52291 + 12.8019i −0.377862 + 0.741596i
\(299\) 12.7307 0.736237
\(300\) 0 0
\(301\) −0.111922 −0.00645107
\(302\) −0.148198 + 0.290856i −0.00852785 + 0.0167369i
\(303\) −4.52347 23.8894i −0.259867 1.37241i
\(304\) 0.824223 + 1.13445i 0.0472724 + 0.0650649i
\(305\) 0 0
\(306\) 9.40577 0.566067i 0.537692 0.0323599i
\(307\) −1.56450 + 1.56450i −0.0892910 + 0.0892910i −0.750341 0.661050i \(-0.770111\pi\)
0.661050 + 0.750341i \(0.270111\pi\)
\(308\) −0.0856103 + 0.0135593i −0.00487810 + 0.000772615i
\(309\) −22.8600 + 0.687269i −1.30046 + 0.0390974i
\(310\) 0 0
\(311\) 12.9644 4.21240i 0.735145 0.238863i 0.0825681 0.996585i \(-0.473688\pi\)
0.652577 + 0.757722i \(0.273688\pi\)
\(312\) −6.05131 + 6.42644i −0.342588 + 0.363826i
\(313\) −17.0167 + 8.67043i −0.961839 + 0.490082i −0.863101 0.505032i \(-0.831481\pi\)
−0.0987386 + 0.995113i \(0.531481\pi\)
\(314\) −1.51888 4.67462i −0.0857152 0.263804i
\(315\) 0 0
\(316\) −3.07739 + 9.47123i −0.173117 + 0.532798i
\(317\) 1.42135 + 8.97408i 0.0798312 + 0.504034i 0.994911 + 0.100761i \(0.0321277\pi\)
−0.915079 + 0.403274i \(0.867872\pi\)
\(318\) −10.6332 5.02130i −0.596281 0.281580i
\(319\) 4.53563 6.24276i 0.253947 0.349528i
\(320\) 0 0
\(321\) 27.8548 + 18.9855i 1.55470 + 1.05967i
\(322\) 0.0307532 0.194168i 0.00171381 0.0108206i
\(323\) 3.92433 + 1.99954i 0.218355 + 0.111258i
\(324\) −8.83128 1.73453i −0.490626 0.0963625i
\(325\) 0 0
\(326\) 1.53299i 0.0849043i
\(327\) 21.1441 + 2.70036i 1.16927 + 0.149330i
\(328\) −3.68892 0.584268i −0.203687 0.0322608i
\(329\) 0.809088 0.587837i 0.0446065 0.0324085i
\(330\) 0 0
\(331\) 8.94485 + 6.49882i 0.491654 + 0.357207i 0.805820 0.592161i \(-0.201725\pi\)
−0.314166 + 0.949368i \(0.601725\pi\)
\(332\) 0.623767 + 0.623767i 0.0342336 + 0.0342336i
\(333\) 23.2570 + 20.6166i 1.27448 + 1.12978i
\(334\) 21.2873 + 6.91666i 1.16479 + 0.378463i
\(335\) 0 0
\(336\) 0.0833977 + 0.107818i 0.00454971 + 0.00588197i
\(337\) 7.85531 + 15.4169i 0.427906 + 0.839813i 0.999810 + 0.0194923i \(0.00620499\pi\)
−0.571904 + 0.820321i \(0.693795\pi\)
\(338\) −5.88940 11.5586i −0.320341 0.628705i
\(339\) 8.09004 + 10.4590i 0.439391 + 0.568054i
\(340\) 0 0
\(341\) −10.0085 3.25195i −0.541989 0.176103i
\(342\) −3.14795 2.79056i −0.170222 0.150896i
\(343\) −0.778722 0.778722i −0.0420470 0.0420470i
\(344\) −1.15057 0.835934i −0.0620343 0.0450706i
\(345\) 0 0
\(346\) 11.4671 8.33133i 0.616475 0.447895i
\(347\) −14.7693 2.33923i −0.792857 0.125576i −0.253148 0.967428i \(-0.581466\pi\)
−0.539709 + 0.841851i \(0.681466\pi\)
\(348\) −12.0371 1.53728i −0.645256 0.0824070i
\(349\) 0.345103i 0.0184729i 0.999957 + 0.00923647i \(0.00294010\pi\)
−0.999957 + 0.00923647i \(0.997060\pi\)
\(350\) 0 0
\(351\) 13.5730 22.7383i 0.724473 1.21368i
\(352\) −0.981353 0.500025i −0.0523063 0.0266514i
\(353\) 3.13409 19.7879i 0.166811 1.05320i −0.752190 0.658947i \(-0.771002\pi\)
0.919001 0.394256i \(-0.128998\pi\)
\(354\) −9.43196 6.42874i −0.501303 0.341683i
\(355\) 0 0
\(356\) −1.92734 + 2.65275i −0.102149 + 0.140596i
\(357\) 0.387139 + 0.182818i 0.0204896 + 0.00967574i
\(358\) −2.37636 15.0037i −0.125594 0.792971i
\(359\) 5.66877 17.4467i 0.299186 0.920800i −0.682597 0.730795i \(-0.739150\pi\)
0.981783 0.190005i \(-0.0608505\pi\)
\(360\) 0 0
\(361\) 5.26370 + 16.2000i 0.277037 + 0.852632i
\(362\) −9.15143 + 4.66289i −0.480989 + 0.245076i
\(363\) 11.6209 12.3413i 0.609937 0.647749i
\(364\) −0.381439 + 0.123937i −0.0199928 + 0.00649606i
\(365\) 0 0
\(366\) −6.90925 + 0.207721i −0.361152 + 0.0108578i
\(367\) −0.0192492 + 0.00304877i −0.00100480 + 0.000159144i −0.156937 0.987609i \(-0.550162\pi\)
0.155932 + 0.987768i \(0.450162\pi\)
\(368\) 1.76637 1.76637i 0.0920783 0.0920783i
\(369\) 11.1845 0.673114i 0.582240 0.0350409i
\(370\) 0 0
\(371\) −0.314049 0.432251i −0.0163046 0.0224414i
\(372\) 3.07889 + 16.2603i 0.159633 + 0.843057i
\(373\) −3.17602 + 6.23329i −0.164448 + 0.322748i −0.958495 0.285109i \(-0.907970\pi\)
0.794047 + 0.607856i \(0.207970\pi\)
\(374\) −3.45942 −0.178882
\(375\) 0 0
\(376\) 12.7080 0.655364
\(377\) 16.2098 31.8136i 0.834848 1.63848i
\(378\) −0.314015 0.261942i −0.0161512 0.0134729i
\(379\) 7.15293 + 9.84516i 0.367421 + 0.505712i 0.952198 0.305483i \(-0.0988178\pi\)
−0.584776 + 0.811194i \(0.698818\pi\)
\(380\) 0 0
\(381\) 5.35711 + 1.56429i 0.274453 + 0.0801412i
\(382\) −7.68054 + 7.68054i −0.392971 + 0.392971i
\(383\) −0.936062 + 0.148258i −0.0478305 + 0.00757561i −0.180304 0.983611i \(-0.557708\pi\)
0.132473 + 0.991187i \(0.457708\pi\)
\(384\) 0.0520493 + 1.73127i 0.00265613 + 0.0883484i
\(385\) 0 0
\(386\) 18.4588 5.99764i 0.939530 0.305272i
\(387\) 3.91100 + 1.70509i 0.198807 + 0.0866748i
\(388\) −9.24945 + 4.71283i −0.469570 + 0.239258i
\(389\) 6.14102 + 18.9001i 0.311362 + 0.958273i 0.977226 + 0.212200i \(0.0680630\pi\)
−0.665864 + 0.746073i \(0.731937\pi\)
\(390\) 0 0
\(391\) 2.42458 7.46210i 0.122616 0.377374i
\(392\) −1.09407 6.90770i −0.0552590 0.348892i
\(393\) −3.93339 + 8.32944i −0.198413 + 0.420164i
\(394\) 7.18863 9.89430i 0.362158 0.498468i
\(395\) 0 0
\(396\) 3.19814 + 0.830427i 0.160713 + 0.0417305i
\(397\) −4.21926 + 26.6394i −0.211759 + 1.33699i 0.621198 + 0.783654i \(0.286646\pi\)
−0.832957 + 0.553338i \(0.813354\pi\)
\(398\) 14.1987 + 7.23462i 0.711719 + 0.362639i
\(399\) −0.0645011 0.179927i −0.00322909 0.00900759i
\(400\) 0 0
\(401\) 33.9394i 1.69485i 0.530912 + 0.847427i \(0.321849\pi\)
−0.530912 + 0.847427i \(0.678151\pi\)
\(402\) −1.46112 + 11.4407i −0.0728739 + 0.570611i
\(403\) −48.0943 7.61739i −2.39575 0.379449i
\(404\) 11.3567 8.25112i 0.565017 0.410509i
\(405\) 0 0
\(406\) −0.446060 0.324082i −0.0221376 0.0160839i
\(407\) −8.06828 8.06828i −0.399930 0.399930i
\(408\) 2.61437 + 4.77089i 0.129431 + 0.236194i
\(409\) 15.1218 + 4.91338i 0.747726 + 0.242951i 0.658002 0.753016i \(-0.271402\pi\)
0.0897236 + 0.995967i \(0.471402\pi\)
\(410\) 0 0
\(411\) −15.7361 + 12.1719i −0.776205 + 0.600396i
\(412\) −5.99458 11.7650i −0.295332 0.579621i
\(413\) −0.235453 0.462102i −0.0115859 0.0227386i
\(414\) −4.03273 + 6.31650i −0.198198 + 0.310439i
\(415\) 0 0
\(416\) −4.84689 1.57485i −0.237638 0.0772134i
\(417\) 16.5595 9.07436i 0.810924 0.444373i
\(418\) 1.09208 + 1.09208i 0.0534155 + 0.0534155i
\(419\) 22.2455 + 16.1623i 1.08677 + 0.789582i 0.978850 0.204578i \(-0.0655823\pi\)
0.107916 + 0.994160i \(0.465582\pi\)
\(420\) 0 0
\(421\) 25.8507 18.7816i 1.25988 0.915359i 0.261132 0.965303i \(-0.415904\pi\)
0.998752 + 0.0499438i \(0.0159042\pi\)
\(422\) −10.9234 1.73009i −0.531741 0.0842194i
\(423\) −37.2283 + 8.21520i −1.81010 + 0.399437i
\(424\) 6.78917i 0.329711i
\(425\) 0 0
\(426\) 20.8346 7.46889i 1.00944 0.361869i
\(427\) −0.279839 0.142585i −0.0135424 0.00690018i
\(428\) −3.04457 + 19.2226i −0.147165 + 0.929162i
\(429\) −5.47559 + 8.03356i −0.264364 + 0.387864i
\(430\) 0 0
\(431\) −5.09101 + 7.00718i −0.245225 + 0.337524i −0.913832 0.406093i \(-0.866891\pi\)
0.668607 + 0.743616i \(0.266891\pi\)
\(432\) −1.27167 5.03814i −0.0611835 0.242398i
\(433\) −1.68664 10.6490i −0.0810548 0.511760i −0.994495 0.104786i \(-0.966584\pi\)
0.913440 0.406974i \(-0.133416\pi\)
\(434\) −0.232360 + 0.715129i −0.0111536 + 0.0343273i
\(435\) 0 0
\(436\) 3.80299 + 11.7044i 0.182130 + 0.560538i
\(437\) −3.12107 + 1.59026i −0.149301 + 0.0760726i
\(438\) 1.67464 + 1.57689i 0.0800176 + 0.0753467i
\(439\) 32.6251 10.6006i 1.55711 0.505937i 0.601078 0.799190i \(-0.294738\pi\)
0.956035 + 0.293253i \(0.0947379\pi\)
\(440\) 0 0
\(441\) 7.67066 + 19.5290i 0.365269 + 0.929951i
\(442\) −15.8101 + 2.50408i −0.752011 + 0.119107i
\(443\) −4.58214 + 4.58214i −0.217704 + 0.217704i −0.807530 0.589826i \(-0.799196\pi\)
0.589826 + 0.807530i \(0.299196\pi\)
\(444\) −5.02958 + 17.2244i −0.238693 + 0.817434i
\(445\) 0 0
\(446\) −3.22891 4.44421i −0.152893 0.210439i
\(447\) 24.4515 4.62991i 1.15652 0.218987i
\(448\) −0.0357280 + 0.0701201i −0.00168799 + 0.00331286i
\(449\) −22.7460 −1.07345 −0.536726 0.843756i \(-0.680339\pi\)
−0.536726 + 0.843756i \(0.680339\pi\)
\(450\) 0 0
\(451\) −4.11362 −0.193703
\(452\) −3.46581 + 6.80204i −0.163018 + 0.319941i
\(453\) 0.555530 0.105190i 0.0261011 0.00494225i
\(454\) 3.97531 + 5.47155i 0.186571 + 0.256792i
\(455\) 0 0
\(456\) 0.680779 2.33141i 0.0318804 0.109178i
\(457\) 6.28077 6.28077i 0.293802 0.293802i −0.544778 0.838580i \(-0.683386\pi\)
0.838580 + 0.544778i \(0.183386\pi\)
\(458\) 2.99986 0.475131i 0.140174 0.0222014i
\(459\) −10.7430 12.2863i −0.501442 0.573477i
\(460\) 0 0
\(461\) −21.3397 + 6.93369i −0.993889 + 0.322934i −0.760421 0.649430i \(-0.775007\pi\)
−0.233468 + 0.972364i \(0.575007\pi\)
\(462\) 0.109300 + 0.102920i 0.00508509 + 0.00478826i
\(463\) 21.5722 10.9916i 1.00255 0.510823i 0.125944 0.992037i \(-0.459804\pi\)
0.876603 + 0.481214i \(0.159804\pi\)
\(464\) −2.16499 6.66317i −0.100507 0.309330i
\(465\) 0 0
\(466\) −0.427269 + 1.31500i −0.0197929 + 0.0609161i
\(467\) −2.10730 13.3049i −0.0975140 0.615679i −0.987247 0.159197i \(-0.949109\pi\)
0.889733 0.456482i \(-0.150891\pi\)
\(468\) 15.2171 + 1.48024i 0.703413 + 0.0684240i
\(469\) −0.308025 + 0.423960i −0.0142233 + 0.0195766i
\(470\) 0 0
\(471\) −4.79479 + 7.03472i −0.220932 + 0.324143i
\(472\) 1.03093 6.50902i 0.0474523 0.299602i
\(473\) −1.39566 0.711123i −0.0641724 0.0326975i
\(474\) 16.2371 5.82076i 0.745793 0.267356i
\(475\) 0 0
\(476\) 0.247184i 0.0113296i
\(477\) 4.38893 + 19.8890i 0.200955 + 0.910656i
\(478\) 11.2308 + 1.77878i 0.513684 + 0.0813596i
\(479\) −13.9808 + 10.1576i −0.638797 + 0.464113i −0.859437 0.511242i \(-0.829186\pi\)
0.220639 + 0.975355i \(0.429186\pi\)
\(480\) 0 0
\(481\) −42.7136 31.0332i −1.94757 1.41499i
\(482\) 6.23914 + 6.23914i 0.284185 + 0.284185i
\(483\) −0.298606 + 0.163631i −0.0135871 + 0.00744549i
\(484\) 9.30791 + 3.02432i 0.423087 + 0.137469i
\(485\) 0 0
\(486\) 6.98235 + 13.9372i 0.316726 + 0.632206i
\(487\) 1.64469 + 3.22789i 0.0745281 + 0.146270i 0.925264 0.379324i \(-0.123843\pi\)
−0.850736 + 0.525593i \(0.823843\pi\)
\(488\) −1.81181 3.55588i −0.0820169 0.160967i
\(489\) 2.10024 1.62454i 0.0949761 0.0734643i
\(490\) 0 0
\(491\) −5.48953 1.78366i −0.247739 0.0804953i 0.182515 0.983203i \(-0.441576\pi\)
−0.430254 + 0.902708i \(0.641576\pi\)
\(492\) 3.10877 + 5.67310i 0.140154 + 0.255763i
\(493\) −15.5603 15.5603i −0.700800 0.700800i
\(494\) 5.78150 + 4.20051i 0.260122 + 0.188990i
\(495\) 0 0
\(496\) −7.72991 + 5.61611i −0.347083 + 0.252171i
\(497\) 0.993249 + 0.157315i 0.0445533 + 0.00705655i
\(498\) 0.193560 1.51560i 0.00867365 0.0679157i
\(499\) 28.5582i 1.27844i 0.769024 + 0.639220i \(0.220743\pi\)
−0.769024 + 0.639220i \(0.779257\pi\)
\(500\) 0 0
\(501\) −13.0826 36.4940i −0.584486 1.63043i
\(502\) 13.0179 + 6.63296i 0.581018 + 0.296044i
\(503\) −3.76856 + 23.7938i −0.168032 + 1.06091i 0.749138 + 0.662414i \(0.230468\pi\)
−0.917170 + 0.398497i \(0.869532\pi\)
\(504\) 0.0593360 0.228515i 0.00264304 0.0101789i
\(505\) 0 0
\(506\) 1.61718 2.22586i 0.0718926 0.0989517i
\(507\) −9.59451 + 20.3176i −0.426107 + 0.902335i
\(508\) 0.504047 + 3.18243i 0.0223635 + 0.141197i
\(509\) 1.35722 4.17708i 0.0601576 0.185146i −0.916462 0.400123i \(-0.868968\pi\)
0.976619 + 0.214977i \(0.0689675\pi\)
\(510\) 0 0
\(511\) 0.0322963 + 0.0993978i 0.00142870 + 0.00439710i
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) −0.487193 + 7.27001i −0.0215101 + 0.320979i
\(514\) −2.11472 + 0.687116i −0.0932765 + 0.0303074i
\(515\) 0 0
\(516\) 0.0740233 + 2.46217i 0.00325869 + 0.108391i
\(517\) 13.8242 2.18954i 0.607989 0.0962960i
\(518\) −0.576498 + 0.576498i −0.0253299 + 0.0253299i
\(519\) −23.5661 6.88138i −1.03444 0.302059i
\(520\) 0 0
\(521\) 3.85216 + 5.30205i 0.168766 + 0.232287i 0.885020 0.465553i \(-0.154145\pi\)
−0.716254 + 0.697840i \(0.754145\pi\)
\(522\) 10.6499 + 18.1203i 0.466132 + 0.793104i
\(523\) 4.06078 7.96973i 0.177566 0.348492i −0.785020 0.619471i \(-0.787347\pi\)
0.962585 + 0.270979i \(0.0873473\pi\)
\(524\) −5.31824 −0.232328
\(525\) 0 0
\(526\) −19.3769 −0.844875
\(527\) −13.6245 + 26.7397i −0.593494 + 1.16480i
\(528\) 0.354913 + 1.87437i 0.0154456 + 0.0815716i
\(529\) −9.85121 13.5590i −0.428314 0.589523i
\(530\) 0 0
\(531\) 1.18770 + 19.7348i 0.0515416 + 0.856416i
\(532\) 0.0780320 0.0780320i 0.00338312 0.00338312i
\(533\) −18.7999 + 2.97762i −0.814315 + 0.128975i
\(534\) 5.67680 0.170669i 0.245659 0.00738556i
\(535\) 0 0
\(536\) −6.33303 + 2.05773i −0.273545 + 0.0888803i
\(537\) −18.0373 + 19.1555i −0.778367 + 0.826619i
\(538\) −4.89653 + 2.49491i −0.211105 + 0.107563i
\(539\) −2.38035 7.32596i −0.102529 0.315551i
\(540\) 0 0
\(541\) 4.98127 15.3308i 0.214161 0.659121i −0.785051 0.619432i \(-0.787363\pi\)
0.999212 0.0396896i \(-0.0126369\pi\)
\(542\) −1.16442 7.35189i −0.0500163 0.315791i
\(543\) 16.0863 + 7.59639i 0.690329 + 0.325992i
\(544\) −1.84619 + 2.54107i −0.0791548 + 0.108947i
\(545\) 0 0
\(546\) 0.574017 + 0.391244i 0.0245657 + 0.0167437i
\(547\) 3.70025 23.3625i 0.158211 0.998907i −0.772994 0.634413i \(-0.781242\pi\)
0.931206 0.364494i \(-0.118758\pi\)
\(548\) −10.2341 5.21451i −0.437177 0.222753i
\(549\) 7.60647 + 9.24576i 0.324636 + 0.394599i
\(550\) 0 0
\(551\) 9.82428i 0.418528i
\(552\) −4.29184 0.548120i −0.182673 0.0233295i
\(553\) 0.774072 + 0.122601i 0.0329169 + 0.00521353i
\(554\) −15.4488 + 11.2242i −0.656355 + 0.476870i
\(555\) 0 0
\(556\) 8.81992 + 6.40805i 0.374048 + 0.271762i
\(557\) 27.5142 + 27.5142i 1.16581 + 1.16581i 0.983181 + 0.182634i \(0.0584623\pi\)
0.182634 + 0.983181i \(0.441538\pi\)
\(558\) 19.0143 21.4496i 0.804941 0.908033i
\(559\) −6.89314 2.23972i −0.291549 0.0947299i
\(560\) 0 0
\(561\) 3.66602 + 4.73951i 0.154780 + 0.200102i
\(562\) −0.639477 1.25504i −0.0269747 0.0529408i
\(563\) 11.3007 + 22.1789i 0.476267 + 0.934728i 0.996727 + 0.0808412i \(0.0257607\pi\)
−0.520460 + 0.853886i \(0.674239\pi\)
\(564\) −13.4669 17.4103i −0.567061 0.733108i
\(565\) 0 0
\(566\) −9.06857 2.94656i −0.381180 0.123853i
\(567\) −0.0261004 + 0.707797i −0.00109611 + 0.0297247i
\(568\) 9.03570 + 9.03570i 0.379129 + 0.379129i
\(569\) −25.9540 18.8567i −1.08805 0.790515i −0.108981 0.994044i \(-0.534759\pi\)
−0.979069 + 0.203529i \(0.934759\pi\)
\(570\) 0 0
\(571\) −34.1170 + 24.7874i −1.42775 + 1.03732i −0.437322 + 0.899305i \(0.644073\pi\)
−0.990430 + 0.138017i \(0.955927\pi\)
\(572\) −5.54398 0.878080i −0.231805 0.0367144i
\(573\) 18.6618 + 2.38334i 0.779609 + 0.0995655i
\(574\) 0.293928i 0.0122683i
\(575\) 0 0
\(576\) 2.31674 1.90597i 0.0965306 0.0794156i
\(577\) −19.6556 10.0150i −0.818274 0.416931i −0.00583873 0.999983i \(-0.501859\pi\)
−0.812435 + 0.583052i \(0.801859\pi\)
\(578\) 1.11609 7.04672i 0.0464233 0.293105i
\(579\) −27.7782 18.9333i −1.15442 0.786843i
\(580\) 0 0
\(581\) 0.0408054 0.0561638i 0.00169289 0.00233007i
\(582\) 16.2586 + 7.67775i 0.673940 + 0.318253i
\(583\) −1.16975 7.38553i −0.0484462 0.305877i
\(584\) −0.410385 + 1.26303i −0.0169818 + 0.0522647i
\(585\) 0 0
\(586\) −9.62597 29.6257i −0.397645 1.22383i
\(587\) −11.4960 + 5.85750i −0.474490 + 0.241765i −0.674846 0.737958i \(-0.735790\pi\)
0.200356 + 0.979723i \(0.435790\pi\)
\(588\) −8.30436 + 8.81916i −0.342466 + 0.363696i
\(589\) 12.7423 4.14024i 0.525039 0.170596i
\(590\) 0 0
\(591\) −21.1735 + 0.636564i −0.870960 + 0.0261848i
\(592\) −10.2323 + 1.62063i −0.420543 + 0.0666075i
\(593\) −3.75033 + 3.75033i −0.154007 + 0.154007i −0.779905 0.625898i \(-0.784733\pi\)
0.625898 + 0.779905i \(0.284733\pi\)
\(594\) −2.25143 5.26158i −0.0923774 0.215885i
\(595\) 0 0
\(596\) 8.44527 + 11.6239i 0.345932 + 0.476134i
\(597\) −5.13507 27.1194i −0.210165 1.10992i
\(598\) 5.77963 11.3432i 0.236347 0.463856i
\(599\) 29.8620 1.22013 0.610065 0.792352i \(-0.291143\pi\)
0.610065 + 0.792352i \(0.291143\pi\)
\(600\) 0 0
\(601\) 19.0008 0.775058 0.387529 0.921858i \(-0.373329\pi\)
0.387529 + 0.921858i \(0.373329\pi\)
\(602\) −0.0508115 + 0.0997231i −0.00207092 + 0.00406441i
\(603\) 17.2225 10.1222i 0.701355 0.412208i
\(604\) 0.191874 + 0.264091i 0.00780722 + 0.0107457i
\(605\) 0 0
\(606\) −23.3393 6.81513i −0.948092 0.276846i
\(607\) −29.8007 + 29.8007i −1.20957 + 1.20957i −0.238406 + 0.971165i \(0.576625\pi\)
−0.971165 + 0.238406i \(0.923375\pi\)
\(608\) 1.38499 0.219361i 0.0561687 0.00889625i
\(609\) 0.0286980 + 0.954554i 0.00116290 + 0.0386805i
\(610\) 0 0
\(611\) 61.5942 20.0132i 2.49184 0.809646i
\(612\) 3.76576 8.63759i 0.152222 0.349154i
\(613\) 1.17929 0.600877i 0.0476310 0.0242692i −0.430013 0.902823i \(-0.641491\pi\)
0.477644 + 0.878554i \(0.341491\pi\)
\(614\) 0.683714 + 2.10425i 0.0275924 + 0.0849208i
\(615\) 0 0
\(616\) −0.0267848 + 0.0824351i −0.00107919 + 0.00332141i
\(617\) −6.57400 41.5066i −0.264659 1.67099i −0.659087 0.752067i \(-0.729057\pi\)
0.394428 0.918927i \(-0.370943\pi\)
\(618\) −9.76586 + 20.6804i −0.392841 + 0.831889i
\(619\) 9.51877 13.1015i 0.382592 0.526592i −0.573677 0.819082i \(-0.694484\pi\)
0.956269 + 0.292489i \(0.0944836\pi\)
\(620\) 0 0
\(621\) 12.9274 1.16877i 0.518758 0.0469013i
\(622\) 2.13245 13.4638i 0.0855036 0.539848i
\(623\) 0.229923 + 0.117151i 0.00921165 + 0.00469357i
\(624\) 2.97877 + 8.30930i 0.119246 + 0.332638i
\(625\) 0 0
\(626\) 19.0983i 0.763320i
\(627\) 0.338883 2.65349i 0.0135337 0.105970i
\(628\) −4.85468 0.768905i −0.193723 0.0306827i
\(629\) −26.3249 + 19.1262i −1.04964 + 0.762611i
\(630\) 0 0
\(631\) −9.33690 6.78365i −0.371696 0.270053i 0.386218 0.922408i \(-0.373781\pi\)
−0.757914 + 0.652355i \(0.773781\pi\)
\(632\) 7.04182 + 7.04182i 0.280109 + 0.280109i
\(633\) 9.20545 + 16.7988i 0.365884 + 0.667691i
\(634\) 8.64124 + 2.80771i 0.343188 + 0.111508i
\(635\) 0 0
\(636\) −9.30139 + 7.19464i −0.368824 + 0.285286i
\(637\) −16.1814 31.7579i −0.641132 1.25829i
\(638\) −3.50321 6.87543i −0.138693 0.272201i
\(639\) −32.3115 20.6290i −1.27822 0.816073i
\(640\) 0 0
\(641\) −15.5088 5.03912i −0.612561 0.199033i −0.0137264 0.999906i \(-0.504369\pi\)
−0.598835 + 0.800873i \(0.704369\pi\)
\(642\) 29.5620 16.1995i 1.16672 0.639344i
\(643\) 12.8296 + 12.8296i 0.505952 + 0.505952i 0.913281 0.407330i \(-0.133540\pi\)
−0.407330 + 0.913281i \(0.633540\pi\)
\(644\) −0.159043 0.115552i −0.00626719 0.00455338i
\(645\) 0 0
\(646\) 3.56321 2.58883i 0.140193 0.101856i
\(647\) 25.1179 + 3.97829i 0.987488 + 0.156403i 0.629229 0.777220i \(-0.283371\pi\)
0.358259 + 0.933622i \(0.383371\pi\)
\(648\) −5.55479 + 7.08127i −0.218213 + 0.278178i
\(649\) 7.25839i 0.284917i
\(650\) 0 0
\(651\) 1.22599 0.439499i 0.0480502 0.0172253i
\(652\) 1.36590 + 0.695961i 0.0534928 + 0.0272559i
\(653\) −4.76127 + 30.0615i −0.186323 + 1.17640i 0.700281 + 0.713867i \(0.253058\pi\)
−0.886604 + 0.462529i \(0.846942\pi\)
\(654\) 12.0053 17.6136i 0.469443 0.688747i
\(655\) 0 0
\(656\) −2.19532 + 3.02160i −0.0857129 + 0.117974i
\(657\) 0.385730 3.96538i 0.0150488 0.154704i
\(658\) −0.156448 0.987775i −0.00609899 0.0385075i
\(659\) −3.19473 + 9.83236i −0.124449 + 0.383014i −0.993800 0.111180i \(-0.964537\pi\)
0.869351 + 0.494195i \(0.164537\pi\)
\(660\) 0 0
\(661\) 3.97825 + 12.2438i 0.154736 + 0.476229i 0.998134 0.0610606i \(-0.0194483\pi\)
−0.843398 + 0.537289i \(0.819448\pi\)
\(662\) 9.85137 5.01952i 0.382884 0.195089i
\(663\) 20.1850 + 19.0067i 0.783921 + 0.738161i
\(664\) 0.838964 0.272596i 0.0325581 0.0105788i
\(665\) 0 0
\(666\) 28.9279 11.3624i 1.12093 0.440284i
\(667\) 17.2859 2.73781i 0.669311 0.106008i
\(668\) 15.8270 15.8270i 0.612365 0.612365i
\(669\) −2.66696 + 9.13333i −0.103111 + 0.353115i
\(670\) 0 0
\(671\) −2.58363 3.55605i −0.0997397 0.137280i
\(672\) 0.133928 0.0253594i 0.00516640 0.000978260i
\(673\) 15.3006 30.0291i 0.589794 1.15754i −0.382540 0.923939i \(-0.624951\pi\)
0.972334 0.233596i \(-0.0750494\pi\)
\(674\) 17.3028 0.666479
\(675\) 0 0
\(676\) −12.9725 −0.498943
\(677\) −7.07682 + 13.8891i −0.271984 + 0.533800i −0.986085 0.166244i \(-0.946836\pi\)
0.714100 + 0.700044i \(0.246836\pi\)
\(678\) 12.9918 2.46001i 0.498948 0.0944759i
\(679\) 0.480192 + 0.660928i 0.0184281 + 0.0253641i
\(680\) 0 0
\(681\) 3.28346 11.2446i 0.125823 0.430895i
\(682\) −7.44126 + 7.44126i −0.284940 + 0.284940i
\(683\) −26.5524 + 4.20549i −1.01600 + 0.160919i −0.642157 0.766573i \(-0.721960\pi\)
−0.373844 + 0.927492i \(0.621960\pi\)
\(684\) −3.91554 + 1.53796i −0.149715 + 0.0588054i
\(685\) 0 0
\(686\) −1.04738 + 0.340314i −0.0399891 + 0.0129932i
\(687\) −3.82996 3.60640i −0.146122 0.137593i
\(688\) −1.26717 + 0.645655i −0.0483104 + 0.0246154i
\(689\) −10.6919 32.9064i −0.407330 1.25363i
\(690\) 0 0
\(691\) 7.00128 21.5477i 0.266341 0.819714i −0.725040 0.688707i \(-0.758179\pi\)
0.991381 0.131007i \(-0.0418212\pi\)
\(692\) −2.21732 13.9996i −0.0842898 0.532185i
\(693\) 0.0251756 0.258811i 0.000956343 0.00983141i
\(694\) −8.78938 + 12.0975i −0.333640 + 0.459217i
\(695\) 0 0
\(696\) −6.83446 + 10.0272i −0.259060 + 0.380081i
\(697\) −1.83514 + 11.5866i −0.0695110 + 0.438875i
\(698\) 0.307489 + 0.156673i 0.0116386 + 0.00593018i
\(699\) 2.25438 0.808162i 0.0852684 0.0305675i
\(700\) 0 0
\(701\) 37.8133i 1.42819i −0.700049 0.714095i \(-0.746839\pi\)
0.700049 0.714095i \(-0.253161\pi\)
\(702\) −14.0980 22.4166i −0.532094 0.846061i
\(703\) 14.3482 + 2.27253i 0.541153 + 0.0857102i
\(704\) −0.891050 + 0.647386i −0.0335827 + 0.0243993i
\(705\) 0 0
\(706\) −16.2083 11.7760i −0.610007 0.443196i
\(707\) −0.781162 0.781162i −0.0293786 0.0293786i
\(708\) −10.0101 + 5.48536i −0.376201 + 0.206152i
\(709\) −37.7779 12.2748i −1.41878 0.460989i −0.503565 0.863958i \(-0.667978\pi\)
−0.915214 + 0.402968i \(0.867978\pi\)
\(710\) 0 0
\(711\) −25.1814 16.0769i −0.944377 0.602931i
\(712\) 1.48863 + 2.92160i 0.0557887 + 0.109491i
\(713\) −10.8358 21.2664i −0.405803 0.796433i
\(714\) 0.338649 0.261946i 0.0126736 0.00980309i
\(715\) 0 0
\(716\) −14.4473 4.69420i −0.539919 0.175430i
\(717\) −9.46453 17.2716i −0.353459 0.645018i
\(718\) −12.9715 12.9715i −0.484093 0.484093i
\(719\) 25.6075 + 18.6049i 0.954998 + 0.693847i 0.951984 0.306149i \(-0.0990405\pi\)
0.00301445 + 0.999995i \(0.499040\pi\)
\(720\) 0 0
\(721\) −0.840680 + 0.610790i −0.0313086 + 0.0227470i
\(722\) 16.8240 + 2.66466i 0.626124 + 0.0991682i
\(723\) 1.93606 15.1596i 0.0720029 0.563791i
\(724\) 10.2709i 0.381715i
\(725\) 0 0
\(726\) −5.72039 15.9571i −0.212304 0.592223i
\(727\) −45.9671 23.4214i −1.70483 0.868652i −0.984580 0.174934i \(-0.944029\pi\)
−0.720246 0.693719i \(-0.755971\pi\)
\(728\) −0.0627409 + 0.396131i −0.00232533 + 0.0146816i
\(729\) 11.6951 24.3357i 0.433152 0.901321i
\(730\) 0 0
\(731\) −2.62561 + 3.61384i −0.0971117 + 0.133663i
\(732\) −2.95165 + 6.25049i −0.109096 + 0.231025i
\(733\) 3.31036 + 20.9008i 0.122271 + 0.771988i 0.970276 + 0.242000i \(0.0778035\pi\)
−0.848005 + 0.529988i \(0.822197\pi\)
\(734\) −0.00602247 + 0.0185352i −0.000222293 + 0.000684148i
\(735\) 0 0
\(736\) −0.771931 2.37576i −0.0284538 0.0875717i
\(737\) −6.53478 + 3.32964i −0.240712 + 0.122649i
\(738\) 4.47789 10.2710i 0.164834 0.378082i
\(739\) −11.8537 + 3.85150i −0.436046 + 0.141680i −0.518811 0.854889i \(-0.673625\pi\)
0.0827648 + 0.996569i \(0.473625\pi\)
\(740\) 0 0
\(741\) −0.371961 12.3722i −0.0136643 0.454505i
\(742\) −0.527714 + 0.0835816i −0.0193730 + 0.00306838i
\(743\) −2.30237 + 2.30237i −0.0844658 + 0.0844658i −0.748077 0.663612i \(-0.769023\pi\)
0.663612 + 0.748077i \(0.269023\pi\)
\(744\) 15.8858 + 4.63870i 0.582402 + 0.170063i
\(745\) 0 0
\(746\) 4.11202 + 5.65971i 0.150552 + 0.207217i
\(747\) −2.28154 + 1.34093i −0.0834772 + 0.0490621i
\(748\) −1.57054 + 3.08236i −0.0574247 + 0.112702i
\(749\) 1.53163 0.0559646
\(750\) 0 0
\(751\) 18.7652 0.684751 0.342375 0.939563i \(-0.388769\pi\)
0.342375 + 0.939563i \(0.388769\pi\)
\(752\) 5.76930 11.3229i 0.210385 0.412904i
\(753\) −4.70802 24.8641i −0.171570 0.906097i
\(754\) −20.9870 28.8861i −0.764301 1.05197i
\(755\) 0 0
\(756\) −0.375952 + 0.160870i −0.0136733 + 0.00585079i
\(757\) 7.02667 7.02667i 0.255389 0.255389i −0.567787 0.823176i \(-0.692200\pi\)
0.823176 + 0.567787i \(0.192200\pi\)
\(758\) 12.0195 1.90370i 0.436567 0.0691453i
\(759\) −4.76327 + 0.143204i −0.172896 + 0.00519798i
\(760\) 0 0
\(761\) 48.1462 15.6436i 1.74530 0.567081i 0.749782 0.661685i \(-0.230158\pi\)
0.995515 + 0.0946038i \(0.0301584\pi\)
\(762\) 3.82587 4.06305i 0.138597 0.147189i
\(763\) 0.862948 0.439694i 0.0312408 0.0159180i
\(764\) 3.35652 + 10.3303i 0.121435 + 0.373737i
\(765\) 0 0
\(766\) −0.292865 + 0.901344i −0.0105816 + 0.0325669i
\(767\) −5.25394 33.1721i −0.189709 1.19777i
\(768\) 1.56620 + 0.739603i 0.0565154 + 0.0266881i
\(769\) −21.2813 + 29.2912i −0.767422 + 1.05627i 0.229138 + 0.973394i \(0.426409\pi\)
−0.996560 + 0.0828721i \(0.973591\pi\)
\(770\) 0 0
\(771\) 3.18239 + 2.16909i 0.114611 + 0.0781178i
\(772\) 3.03620 19.1698i 0.109275 0.689936i
\(773\) 20.9544 + 10.6768i 0.753679 + 0.384019i 0.788227 0.615384i \(-0.210999\pi\)
−0.0345481 + 0.999403i \(0.510999\pi\)
\(774\) 3.29481 2.71063i 0.118429 0.0974317i
\(775\) 0 0
\(776\) 10.3809i 0.372653i
\(777\) 1.40075 + 0.178893i 0.0502516 + 0.00641774i
\(778\) 19.6281 + 3.10878i 0.703701 + 0.111455i
\(779\) 4.23704 3.07839i 0.151808 0.110295i
\(780\) 0 0
\(781\) 11.3862 + 8.27256i 0.407430 + 0.296015i
\(782\) −5.54804 5.54804i −0.198397 0.198397i
\(783\) 13.5395 33.7932i 0.483862 1.20767i
\(784\) −6.65151 2.16121i −0.237554 0.0771859i
\(785\) 0 0
\(786\) 5.63586 + 7.28616i 0.201025 + 0.259889i
\(787\) −14.2872 28.0403i −0.509285 0.999529i −0.992293 0.123913i \(-0.960456\pi\)
0.483008 0.875616i \(-0.339544\pi\)
\(788\) −5.55232 10.8970i −0.197793 0.388191i
\(789\) 20.5342 + 26.5470i 0.731036 + 0.945099i
\(790\) 0 0
\(791\) 0.571382 + 0.185653i 0.0203160 + 0.00660107i
\(792\) 2.19184 2.47256i 0.0778837 0.0878585i
\(793\) −14.3816 14.3816i −0.510707 0.510707i
\(794\) 21.8203 + 15.8534i 0.774375 + 0.562616i
\(795\) 0 0
\(796\) 12.8922 9.36672i 0.456952 0.331995i
\(797\) 6.24831 + 0.989635i 0.221326 + 0.0350547i 0.266113 0.963942i \(-0.414261\pi\)
−0.0447862 + 0.998997i \(0.514261\pi\)
\(798\) −0.189599 0.0242140i −0.00671172 0.000857167i
\(799\) 39.9149i 1.41209i
\(800\) 0 0
\(801\) −6.24966 7.59654i −0.220821 0.268410i
\(802\) 30.2402 + 15.4082i 1.06782 + 0.544081i
\(803\) −0.228816 + 1.44469i −0.00807473 + 0.0509818i
\(804\) 9.53041 + 6.49584i 0.336112 + 0.229091i
\(805\) 0 0
\(806\) −28.6215 + 39.3941i −1.00815 + 1.38760i
\(807\) 8.60707 + 4.06450i 0.302983 + 0.143077i
\(808\) −2.19597 13.8648i −0.0772540 0.487763i
\(809\) 10.4456 32.1483i 0.367249 1.13028i −0.581312 0.813681i \(-0.697461\pi\)
0.948561 0.316595i \(-0.102539\pi\)
\(810\) 0 0
\(811\) −11.3720 34.9993i −0.399324 1.22899i −0.925543 0.378643i \(-0.876391\pi\)
0.526219 0.850349i \(-0.323609\pi\)
\(812\) −0.491266 + 0.250313i −0.0172401 + 0.00878425i
\(813\) −8.83835 + 9.38626i −0.309975 + 0.329191i
\(814\) −10.8518 + 3.52597i −0.380356 + 0.123585i
\(815\) 0 0
\(816\) 5.43779 0.163483i 0.190361 0.00572306i
\(817\) 1.96970 0.311969i 0.0689110 0.0109144i
\(818\) 11.2430 11.2430i 0.393103 0.393103i
\(819\) −0.0722816 1.20103i −0.00252572 0.0419675i
\(820\) 0 0
\(821\) −1.94467 2.67661i −0.0678695 0.0934144i 0.773733 0.633512i \(-0.218387\pi\)
−0.841602 + 0.540098i \(0.818387\pi\)
\(822\) 3.70121 + 19.5469i 0.129095 + 0.681777i
\(823\) −16.1380 + 31.6727i −0.562537 + 1.10404i 0.418136 + 0.908385i \(0.362684\pi\)
−0.980673 + 0.195656i \(0.937316\pi\)
\(824\) −13.2042 −0.459990
\(825\) 0 0
\(826\) −0.518630 −0.0180454
\(827\) 4.05871 7.96567i 0.141135 0.276993i −0.809609 0.586969i \(-0.800321\pi\)
0.950744 + 0.309976i \(0.100321\pi\)
\(828\) 3.79722 + 6.46082i 0.131963 + 0.224529i
\(829\) 6.82593 + 9.39508i 0.237074 + 0.326305i 0.910932 0.412556i \(-0.135364\pi\)
−0.673858 + 0.738861i \(0.735364\pi\)
\(830\) 0 0
\(831\) 31.7489 + 9.27078i 1.10136 + 0.321600i
\(832\) −3.60364 + 3.60364i −0.124934 + 0.124934i
\(833\) −21.6966 + 3.43640i −0.751743 + 0.119064i
\(834\) −0.567443 18.8743i −0.0196489 0.653565i
\(835\) 0 0
\(836\) 1.46885 0.477258i 0.0508012 0.0165063i
\(837\) −49.5365 3.31965i −1.71223 0.114744i
\(838\) 24.5000 12.4834i 0.846339 0.431231i
\(839\) 1.99464 + 6.13888i 0.0688628 + 0.211938i 0.979566 0.201124i \(-0.0644594\pi\)
−0.910703 + 0.413062i \(0.864459\pi\)
\(840\) 0 0
\(841\) 6.20662 19.1020i 0.214021 0.658690i
\(842\) −4.99858 31.5598i −0.172262 1.08762i
\(843\) −1.04178 + 2.20610i −0.0358809 + 0.0759822i
\(844\) −6.50062 + 8.94734i −0.223761 + 0.307980i
\(845\) 0 0
\(846\) −9.58150 + 36.9003i −0.329419 + 1.26866i
\(847\) 0.120487 0.760725i 0.00413998 0.0261388i
\(848\) −6.04920 3.08222i −0.207730 0.105844i
\(849\) 5.57329 + 15.5468i 0.191275 + 0.533563i
\(850\) 0 0
\(851\) 25.8790i 0.887121i
\(852\) 2.80386 21.9545i 0.0960586 0.752150i
\(853\) 26.0890 + 4.13209i 0.893271 + 0.141480i 0.586162 0.810194i \(-0.300638\pi\)
0.307109 + 0.951674i \(0.400638\pi\)
\(854\) −0.254089 + 0.184606i −0.00869474 + 0.00631710i
\(855\) 0 0
\(856\) 15.7453 + 11.4396i 0.538163 + 0.390998i
\(857\) 21.7170 + 21.7170i 0.741840 + 0.741840i 0.972932 0.231092i \(-0.0742298\pi\)
−0.231092 + 0.972932i \(0.574230\pi\)
\(858\) 4.67208 + 8.52595i 0.159502 + 0.291071i
\(859\) 2.16755 + 0.704281i 0.0739560 + 0.0240298i 0.345761 0.938322i \(-0.387621\pi\)
−0.271805 + 0.962352i \(0.587621\pi\)
\(860\) 0 0
\(861\) 0.402691 0.311482i 0.0137237 0.0106153i
\(862\) 3.93217 + 7.71732i 0.133930 + 0.262853i
\(863\) −0.924026 1.81350i −0.0314542 0.0617324i 0.874745 0.484584i \(-0.161029\pi\)
−0.906199 + 0.422852i \(0.861029\pi\)
\(864\) −5.06634 1.15420i −0.172360 0.0392666i
\(865\) 0 0
\(866\) −10.2541 3.33175i −0.348448 0.113218i
\(867\) −10.8370 + 5.93849i −0.368043 + 0.201682i
\(868\) 0.531696 + 0.531696i 0.0180469 + 0.0180469i
\(869\) 8.87365 + 6.44709i 0.301018 + 0.218702i
\(870\) 0 0
\(871\) −27.4549 + 19.9472i −0.930274 + 0.675884i
\(872\) 12.1552 + 1.92520i 0.411627 + 0.0651953i
\(873\) −6.71083 30.4111i −0.227127 1.02926i
\(874\) 3.50286i 0.118486i
\(875\) 0 0
\(876\) 2.16529 0.776226i 0.0731584 0.0262263i
\(877\) −5.66858 2.88829i −0.191414 0.0975305i 0.355657 0.934617i \(-0.384257\pi\)
−0.547071 + 0.837086i \(0.684257\pi\)
\(878\) 5.36634 33.8818i 0.181105 1.14345i
\(879\) −30.3873 + 44.5829i −1.02494 + 1.50374i
\(880\) 0 0
\(881\) −3.61099 + 4.97010i −0.121657 + 0.167447i −0.865502 0.500906i \(-0.833000\pi\)
0.743844 + 0.668353i \(0.233000\pi\)
\(882\) 20.8829 + 2.03137i 0.703162 + 0.0683996i
\(883\) 6.19390 + 39.1067i 0.208441 + 1.31605i 0.840789 + 0.541362i \(0.182091\pi\)
−0.632348 + 0.774684i \(0.717909\pi\)
\(884\) −4.94649 + 15.2237i −0.166369 + 0.512030i
\(885\) 0 0
\(886\) 2.00247 + 6.16296i 0.0672742 + 0.207049i
\(887\) −43.0525 + 21.9363i −1.44556 + 0.736550i −0.988263 0.152763i \(-0.951183\pi\)
−0.457299 + 0.889313i \(0.651183\pi\)
\(888\) 13.0637 + 12.3011i 0.438388 + 0.412798i
\(889\) 0.241160 0.0783578i 0.00808826 0.00262804i
\(890\) 0 0
\(891\) −4.82263 + 8.66035i −0.161564 + 0.290133i
\(892\) −5.42571 + 0.859348i −0.181666 + 0.0287731i
\(893\) −12.6005 + 12.6005i −0.421660 + 0.421660i
\(894\) 6.97549 23.8884i 0.233295 0.798948i
\(895\) 0 0
\(896\) 0.0462573 + 0.0636677i 0.00154535 + 0.00212699i
\(897\) −21.6653 + 4.10233i −0.723383 + 0.136973i
\(898\) −10.3265 + 20.2669i −0.344599 + 0.676314i
\(899\) −66.9409 −2.23260
\(900\) 0 0
\(901\) −21.3243 −0.710416
\(902\) −1.86754 + 3.66526i −0.0621824 + 0.122040i
\(903\) 0.190470 0.0360655i 0.00633844 0.00120019i
\(904\) 4.48722 + 6.17613i 0.149243 + 0.205415i
\(905\) 0 0
\(906\) 0.158481 0.542736i 0.00526517 0.0180312i
\(907\) 24.7561 24.7561i 0.822014 0.822014i −0.164383 0.986397i \(-0.552563\pi\)
0.986397 + 0.164383i \(0.0525632\pi\)
\(908\) 6.67994 1.05800i 0.221682 0.0351109i
\(909\) 15.3962 + 39.1977i 0.510660 + 1.30010i
\(910\) 0 0
\(911\) 48.5335 15.7695i 1.60799 0.522466i 0.638921 0.769272i \(-0.279381\pi\)
0.969065 + 0.246806i \(0.0793810\pi\)
\(912\) −1.76823 1.66502i −0.0585521 0.0551342i
\(913\) 0.865690 0.441091i 0.0286502 0.0145980i
\(914\) −2.74480 8.44762i −0.0907898 0.279422i
\(915\) 0 0
\(916\) 0.938563 2.88860i 0.0310110 0.0954420i
\(917\) 0.0654729 + 0.413380i 0.00216211 + 0.0136510i
\(918\) −15.8244 + 3.99424i −0.522284 + 0.131830i
\(919\) −6.34757 + 8.73668i −0.209387 + 0.288196i −0.900774 0.434288i \(-0.857000\pi\)
0.691387 + 0.722485i \(0.257000\pi\)
\(920\) 0 0
\(921\) 2.15835 3.16664i 0.0711200 0.104344i
\(922\) −3.51006 + 22.1617i −0.115598 + 0.729855i
\(923\) 58.0249 + 29.5652i 1.90991 + 0.973150i
\(924\) 0.141323 0.0506624i 0.00464919 0.00166667i
\(925\) 0 0
\(926\) 24.2111i 0.795626i
\(927\) 38.6819 8.53597i 1.27048 0.280358i
\(928\) −6.91981 1.09599i −0.227154 0.0359777i
\(929\) 38.0194 27.6227i 1.24738 0.906272i 0.249310 0.968424i \(-0.419796\pi\)
0.998067 + 0.0621513i \(0.0197961\pi\)
\(930\) 0 0
\(931\) 7.93409 + 5.76446i 0.260029 + 0.188922i
\(932\) 0.977696 + 0.977696i 0.0320255 + 0.0320255i
\(933\) −20.7056 + 11.3463i −0.677871 + 0.371463i
\(934\) −12.8115 4.16270i −0.419204 0.136208i
\(935\) 0 0
\(936\) 8.22734 12.8866i 0.268919 0.421210i
\(937\) 20.7717 + 40.7667i 0.678581 + 1.33179i 0.931301 + 0.364250i \(0.118675\pi\)
−0.252721 + 0.967539i \(0.581325\pi\)
\(938\) 0.237911 + 0.466926i 0.00776806 + 0.0152457i
\(939\) 26.1652 20.2389i 0.853870 0.660470i
\(940\) 0 0
\(941\) −29.1364 9.46699i −0.949820 0.308615i −0.207177 0.978303i \(-0.566428\pi\)
−0.742642 + 0.669688i \(0.766428\pi\)
\(942\) 4.09119 + 7.46589i 0.133298 + 0.243252i
\(943\) −6.59721 6.59721i −0.214835 0.214835i
\(944\) −5.33155 3.87360i −0.173527 0.126075i
\(945\) 0 0
\(946\) −1.26723 + 0.920697i −0.0412012 + 0.0299344i
\(947\) 14.2493 + 2.25687i 0.463040 + 0.0733384i 0.383596 0.923501i \(-0.374685\pi\)
0.0794442 + 0.996839i \(0.474685\pi\)
\(948\) 2.18514 17.1099i 0.0709701 0.555704i
\(949\) 6.76809i 0.219701i
\(950\) 0 0
\(951\) −5.31067 14.8142i −0.172210 0.480382i
\(952\) 0.220242 + 0.112219i 0.00713809 + 0.00363704i
\(953\) 0.616563 3.89283i 0.0199724 0.126101i −0.975688 0.219166i \(-0.929666\pi\)
0.995660 + 0.0930649i \(0.0296664\pi\)
\(954\) 19.7138 + 5.11887i 0.638257 + 0.165729i
\(955\) 0 0
\(956\) 6.68358 9.19915i 0.216162 0.297522i
\(957\) −5.70713 + 12.0856i −0.184485 + 0.390671i
\(958\) 2.70337 + 17.0684i 0.0873420 + 0.551455i
\(959\) −0.279326 + 0.859676i −0.00901989 + 0.0277604i
\(960\) 0 0
\(961\) 18.6313 + 57.3413i 0.601010 + 1.84972i
\(962\) −47.0424 + 23.9693i −1.51671 + 0.772801i
\(963\) −53.5214 23.3339i −1.72470 0.751925i
\(964\) 8.39163 2.72661i 0.270276 0.0878181i
\(965\) 0 0
\(966\) 0.0102323 + 0.340347i 0.000329218 + 0.0109505i
\(967\) 51.5598 8.16627i 1.65805 0.262610i 0.743992 0.668189i \(-0.232930\pi\)
0.914060 + 0.405579i \(0.132930\pi\)
\(968\) 6.92040 6.92040i 0.222430 0.222430i
\(969\) −7.32280 2.13828i −0.235242 0.0686914i
\(970\) 0 0
\(971\) 2.69176 + 3.70489i 0.0863828 + 0.118896i 0.850021 0.526748i \(-0.176589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(972\) 15.5881 + 0.106057i 0.499988 + 0.00340179i
\(973\) 0.389507 0.764451i 0.0124870 0.0245072i
\(974\) 3.62274 0.116080
\(975\) 0 0
\(976\) −3.99086 −0.127744
\(977\) −1.87651 + 3.68285i −0.0600348 + 0.117825i −0.919074 0.394085i \(-0.871062\pi\)
0.859039 + 0.511910i \(0.171062\pi\)
\(978\) −0.493987 2.60885i −0.0157960 0.0834219i
\(979\) 2.12277 + 2.92174i 0.0678439 + 0.0933792i
\(980\) 0 0
\(981\) −36.8535 + 2.21795i −1.17664 + 0.0708137i
\(982\) −4.08144 + 4.08144i −0.130244 + 0.130244i
\(983\) 25.6200 4.05781i 0.817151 0.129424i 0.266153 0.963931i \(-0.414247\pi\)
0.550998 + 0.834507i \(0.314247\pi\)
\(984\) 6.46612 0.194399i 0.206132 0.00619722i
\(985\) 0 0
\(986\) −20.9285 + 6.80010i −0.666501 + 0.216559i
\(987\) −1.18749 + 1.26111i −0.0377983 + 0.0401415i
\(988\) 6.36743 3.24437i 0.202575 0.103217i
\(989\) −1.09782 3.37875i −0.0349087 0.107438i
\(990\) 0 0
\(991\) −7.36863 + 22.6783i −0.234072 + 0.720400i 0.763171 + 0.646197i \(0.223641\pi\)
−0.997243 + 0.0742035i \(0.976359\pi\)
\(992\) 1.49468 + 9.43706i 0.0474562 + 0.299627i
\(993\) −17.3166 8.17738i −0.549526 0.259501i
\(994\) 0.591094 0.813572i 0.0187484 0.0258049i
\(995\) 0 0
\(996\) −1.26253 0.860532i −0.0400049 0.0272670i
\(997\) −2.45546 + 15.5032i −0.0777652 + 0.490990i 0.917810 + 0.397020i \(0.129956\pi\)
−0.995575 + 0.0939699i \(0.970044\pi\)
\(998\) 25.4455 + 12.9651i 0.805464 + 0.410404i
\(999\) −46.2225 27.5912i −1.46241 0.872947i
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 750.2.l.a.143.6 80
3.2 odd 2 inner 750.2.l.a.143.1 80
5.2 odd 4 750.2.l.b.107.8 80
5.3 odd 4 150.2.l.a.17.3 80
5.4 even 2 750.2.l.c.143.5 80
15.2 even 4 750.2.l.b.107.2 80
15.8 even 4 150.2.l.a.17.9 yes 80
15.14 odd 2 750.2.l.c.143.10 80
25.3 odd 20 750.2.l.c.257.10 80
25.4 even 10 150.2.l.a.53.9 yes 80
25.21 even 5 750.2.l.b.743.2 80
25.22 odd 20 inner 750.2.l.a.257.1 80
75.29 odd 10 150.2.l.a.53.3 yes 80
75.47 even 20 inner 750.2.l.a.257.6 80
75.53 even 20 750.2.l.c.257.5 80
75.71 odd 10 750.2.l.b.743.8 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.17.3 80 5.3 odd 4
150.2.l.a.17.9 yes 80 15.8 even 4
150.2.l.a.53.3 yes 80 75.29 odd 10
150.2.l.a.53.9 yes 80 25.4 even 10
750.2.l.a.143.1 80 3.2 odd 2 inner
750.2.l.a.143.6 80 1.1 even 1 trivial
750.2.l.a.257.1 80 25.22 odd 20 inner
750.2.l.a.257.6 80 75.47 even 20 inner
750.2.l.b.107.2 80 15.2 even 4
750.2.l.b.107.8 80 5.2 odd 4
750.2.l.b.743.2 80 25.21 even 5
750.2.l.b.743.8 80 75.71 odd 10
750.2.l.c.143.5 80 5.4 even 2
750.2.l.c.143.10 80 15.14 odd 2
750.2.l.c.257.5 80 75.53 even 20
750.2.l.c.257.10 80 25.3 odd 20