Properties

Label 315.2.z.b.104.10
Level $315$
Weight $2$
Character 315.104
Analytic conductor $2.515$
Analytic rank $0$
Dimension $80$
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] = [315,2,Mod(104,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.104");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.z (of order \(6\), degree \(2\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 104.10
Character \(\chi\) \(=\) 315.104
Dual form 315.2.z.b.209.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.938003 - 1.62467i) q^{2} +(1.62365 + 0.603134i) q^{3} +(-0.759700 + 1.31584i) q^{4} +(1.09295 - 1.95076i) q^{5} +(-0.543094 - 3.20363i) q^{6} +(-0.0240802 - 2.64564i) q^{7} -0.901609 q^{8} +(2.27246 + 1.95855i) q^{9} +O(q^{10})\) \(q+(-0.938003 - 1.62467i) q^{2} +(1.62365 + 0.603134i) q^{3} +(-0.759700 + 1.31584i) q^{4} +(1.09295 - 1.95076i) q^{5} +(-0.543094 - 3.20363i) q^{6} +(-0.0240802 - 2.64564i) q^{7} -0.901609 q^{8} +(2.27246 + 1.95855i) q^{9} +(-4.19453 + 0.0541402i) q^{10} +(1.72215 - 0.994281i) q^{11} +(-2.02711 + 1.67826i) q^{12} +(-2.28487 + 3.95751i) q^{13} +(-4.27571 + 2.52074i) q^{14} +(2.95113 - 2.50815i) q^{15} +(2.36511 + 4.09649i) q^{16} -6.36210i q^{17} +(1.05043 - 5.52912i) q^{18} +2.43428i q^{19} +(1.73657 + 2.92014i) q^{20} +(1.55658 - 4.31011i) q^{21} +(-3.23076 - 1.86528i) q^{22} +(0.00774549 - 0.0134156i) q^{23} +(-1.46389 - 0.543790i) q^{24} +(-2.61093 - 4.26416i) q^{25} +8.57286 q^{26} +(2.50840 + 4.55059i) q^{27} +(3.49953 + 1.97821i) q^{28} +(4.97858 - 2.87439i) q^{29} +(-6.84309 - 2.44196i) q^{30} +(-4.68768 - 2.70644i) q^{31} +(3.53536 - 6.12342i) q^{32} +(3.39584 - 0.575678i) q^{33} +(-10.3363 + 5.96767i) q^{34} +(-5.18733 - 2.84457i) q^{35} +(-4.30353 + 1.50228i) q^{36} +11.1208i q^{37} +(3.95490 - 2.28336i) q^{38} +(-6.09673 + 5.04752i) q^{39} +(-0.985411 + 1.75882i) q^{40} +(-3.35005 + 5.80246i) q^{41} +(-8.46258 + 1.51397i) q^{42} +(7.95328 - 4.59183i) q^{43} +3.02142i q^{44} +(6.30435 - 2.29243i) q^{45} -0.0290612 q^{46} +(-4.89285 + 2.82489i) q^{47} +(1.36937 + 8.07774i) q^{48} +(-6.99884 + 0.127415i) q^{49} +(-4.47879 + 8.24169i) q^{50} +(3.83720 - 10.3298i) q^{51} +(-3.47163 - 6.01304i) q^{52} +1.35986 q^{53} +(5.04032 - 8.34380i) q^{54} +(-0.0573885 - 4.44619i) q^{55} +(0.0217109 + 2.38533i) q^{56} +(-1.46820 + 3.95241i) q^{57} +(-9.33985 - 5.39237i) q^{58} +(-1.12770 + 1.95323i) q^{59} +(1.05835 + 5.78866i) q^{60} +(7.04872 - 4.06958i) q^{61} +10.1546i q^{62} +(5.12691 - 6.05928i) q^{63} -3.80426 q^{64} +(5.22291 + 8.78258i) q^{65} +(-4.12059 - 4.97713i) q^{66} +(9.56621 + 5.52305i) q^{67} +(8.37151 + 4.83329i) q^{68} +(0.0206673 - 0.0171106i) q^{69} +(0.244241 + 11.0959i) q^{70} +7.78322i q^{71} +(-2.04887 - 1.76585i) q^{72} +5.71111 q^{73} +(18.0676 - 10.4313i) q^{74} +(-1.66737 - 8.49823i) q^{75} +(-3.20312 - 1.84932i) q^{76} +(-2.67198 - 4.53224i) q^{77} +(13.9193 + 5.17058i) q^{78} +(1.56365 + 2.70833i) q^{79} +(10.5762 - 0.136511i) q^{80} +(1.32815 + 8.90146i) q^{81} +12.5694 q^{82} +(3.26803 - 1.88680i) q^{83} +(4.48888 + 5.32260i) q^{84} +(-12.4109 - 6.95345i) q^{85} +(-14.9204 - 8.61430i) q^{86} +(9.81710 - 1.66424i) q^{87} +(-1.55270 + 0.896452i) q^{88} -2.80146 q^{89} +(-9.63793 - 8.09217i) q^{90} +(10.5252 + 5.94965i) q^{91} +(0.0117685 + 0.0203836i) q^{92} +(-5.97880 - 7.22160i) q^{93} +(9.17902 + 5.29951i) q^{94} +(4.74870 + 2.66054i) q^{95} +(9.43341 - 7.80998i) q^{96} +(4.13759 + 7.16652i) q^{97} +(6.77194 + 11.2513i) q^{98} +(5.86086 + 1.11345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 52 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 52 q^{4} - 4 q^{9} - 24 q^{11} - 12 q^{14} - 34 q^{15} - 28 q^{16} + 20 q^{21} - 22 q^{25} - 48 q^{29} + 36 q^{30} - 40 q^{36} + 16 q^{39} - 24 q^{46} + 20 q^{49} - 42 q^{50} - 8 q^{51} + 24 q^{56} + 116 q^{60} + 128 q^{64} + 90 q^{65} - 6 q^{70} + 12 q^{74} - 32 q^{79} + 68 q^{81} - 4 q^{84} - 2 q^{85} + 156 q^{86} - 8 q^{91} - 24 q^{95} - 116 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.938003 1.62467i −0.663268 1.14881i −0.979752 0.200217i \(-0.935835\pi\)
0.316483 0.948598i \(-0.397498\pi\)
\(3\) 1.62365 + 0.603134i 0.937413 + 0.348219i
\(4\) −0.759700 + 1.31584i −0.379850 + 0.657920i
\(5\) 1.09295 1.95076i 0.488781 0.872406i
\(6\) −0.543094 3.20363i −0.221717 1.30788i
\(7\) −0.0240802 2.64564i −0.00910147 0.999959i
\(8\) −0.901609 −0.318767
\(9\) 2.27246 + 1.95855i 0.757487 + 0.652851i
\(10\) −4.19453 + 0.0541402i −1.32643 + 0.0171206i
\(11\) 1.72215 0.994281i 0.519246 0.299787i −0.217380 0.976087i \(-0.569751\pi\)
0.736626 + 0.676300i \(0.236418\pi\)
\(12\) −2.02711 + 1.67826i −0.585177 + 0.484471i
\(13\) −2.28487 + 3.95751i −0.633709 + 1.09762i 0.353078 + 0.935594i \(0.385135\pi\)
−0.986787 + 0.162022i \(0.948198\pi\)
\(14\) −4.27571 + 2.52074i −1.14273 + 0.673697i
\(15\) 2.95113 2.50815i 0.761979 0.647602i
\(16\) 2.36511 + 4.09649i 0.591278 + 1.02412i
\(17\) 6.36210i 1.54304i −0.636207 0.771519i \(-0.719498\pi\)
0.636207 0.771519i \(-0.280502\pi\)
\(18\) 1.05043 5.52912i 0.247588 1.30323i
\(19\) 2.43428i 0.558463i 0.960224 + 0.279231i \(0.0900796\pi\)
−0.960224 + 0.279231i \(0.909920\pi\)
\(20\) 1.73657 + 2.92014i 0.388310 + 0.652962i
\(21\) 1.55658 4.31011i 0.339673 0.940544i
\(22\) −3.23076 1.86528i −0.688799 0.397678i
\(23\) 0.00774549 0.0134156i 0.00161505 0.00279734i −0.865217 0.501398i \(-0.832819\pi\)
0.866832 + 0.498601i \(0.166153\pi\)
\(24\) −1.46389 0.543790i −0.298816 0.111001i
\(25\) −2.61093 4.26416i −0.522186 0.852832i
\(26\) 8.57286 1.68128
\(27\) 2.50840 + 4.55059i 0.482742 + 0.875762i
\(28\) 3.49953 + 1.97821i 0.661349 + 0.373846i
\(29\) 4.97858 2.87439i 0.924500 0.533760i 0.0394318 0.999222i \(-0.487445\pi\)
0.885068 + 0.465462i \(0.154112\pi\)
\(30\) −6.84309 2.44196i −1.24937 0.445838i
\(31\) −4.68768 2.70644i −0.841933 0.486090i 0.0159878 0.999872i \(-0.494911\pi\)
−0.857921 + 0.513782i \(0.828244\pi\)
\(32\) 3.53536 6.12342i 0.624969 1.08248i
\(33\) 3.39584 0.575678i 0.591140 0.100213i
\(34\) −10.3363 + 5.96767i −1.77266 + 1.02345i
\(35\) −5.18733 2.84457i −0.876819 0.480821i
\(36\) −4.30353 + 1.50228i −0.717255 + 0.250380i
\(37\) 11.1208i 1.82824i 0.405442 + 0.914121i \(0.367118\pi\)
−0.405442 + 0.914121i \(0.632882\pi\)
\(38\) 3.95490 2.28336i 0.641570 0.370411i
\(39\) −6.09673 + 5.04752i −0.976258 + 0.808250i
\(40\) −0.985411 + 1.75882i −0.155807 + 0.278094i
\(41\) −3.35005 + 5.80246i −0.523190 + 0.906192i 0.476446 + 0.879204i \(0.341925\pi\)
−0.999636 + 0.0269879i \(0.991408\pi\)
\(42\) −8.46258 + 1.51397i −1.30580 + 0.233611i
\(43\) 7.95328 4.59183i 1.21286 0.700247i 0.249482 0.968379i \(-0.419740\pi\)
0.963382 + 0.268132i \(0.0864063\pi\)
\(44\) 3.02142i 0.455496i
\(45\) 6.30435 2.29243i 0.939796 0.341735i
\(46\) −0.0290612 −0.00428483
\(47\) −4.89285 + 2.82489i −0.713696 + 0.412052i −0.812428 0.583062i \(-0.801855\pi\)
0.0987323 + 0.995114i \(0.468521\pi\)
\(48\) 1.36937 + 8.07774i 0.197652 + 1.16592i
\(49\) −6.99884 + 0.127415i −0.999834 + 0.0182022i
\(50\) −4.47879 + 8.24169i −0.633396 + 1.16555i
\(51\) 3.83720 10.3298i 0.537315 1.44646i
\(52\) −3.47163 6.01304i −0.481429 0.833859i
\(53\) 1.35986 0.186791 0.0933955 0.995629i \(-0.470228\pi\)
0.0933955 + 0.995629i \(0.470228\pi\)
\(54\) 5.04032 8.34380i 0.685901 1.13545i
\(55\) −0.0573885 4.44619i −0.00773826 0.599524i
\(56\) 0.0217109 + 2.38533i 0.00290125 + 0.318754i
\(57\) −1.46820 + 3.95241i −0.194467 + 0.523510i
\(58\) −9.33985 5.39237i −1.22638 0.708052i
\(59\) −1.12770 + 1.95323i −0.146814 + 0.254289i −0.930048 0.367438i \(-0.880235\pi\)
0.783234 + 0.621727i \(0.213569\pi\)
\(60\) 1.05835 + 5.78866i 0.136632 + 0.747312i
\(61\) 7.04872 4.06958i 0.902495 0.521056i 0.0244865 0.999700i \(-0.492205\pi\)
0.878009 + 0.478644i \(0.158872\pi\)
\(62\) 10.1546i 1.28963i
\(63\) 5.12691 6.05928i 0.645929 0.763397i
\(64\) −3.80426 −0.475532
\(65\) 5.22291 + 8.78258i 0.647822 + 1.08935i
\(66\) −4.12059 4.97713i −0.507210 0.612642i
\(67\) 9.56621 + 5.52305i 1.16870 + 0.674748i 0.953373 0.301794i \(-0.0975855\pi\)
0.215325 + 0.976542i \(0.430919\pi\)
\(68\) 8.37151 + 4.83329i 1.01519 + 0.586123i
\(69\) 0.0206673 0.0171106i 0.00248805 0.00205987i
\(70\) 0.244241 + 11.0959i 0.0291923 + 1.32622i
\(71\) 7.78322i 0.923698i 0.886958 + 0.461849i \(0.152814\pi\)
−0.886958 + 0.461849i \(0.847186\pi\)
\(72\) −2.04887 1.76585i −0.241462 0.208107i
\(73\) 5.71111 0.668435 0.334217 0.942496i \(-0.391528\pi\)
0.334217 + 0.942496i \(0.391528\pi\)
\(74\) 18.0676 10.4313i 2.10031 1.21262i
\(75\) −1.66737 8.49823i −0.192531 0.981291i
\(76\) −3.20312 1.84932i −0.367423 0.212132i
\(77\) −2.67198 4.53224i −0.304500 0.516496i
\(78\) 13.9193 + 5.17058i 1.57605 + 0.585453i
\(79\) 1.56365 + 2.70833i 0.175925 + 0.304711i 0.940481 0.339846i \(-0.110375\pi\)
−0.764556 + 0.644557i \(0.777042\pi\)
\(80\) 10.5762 0.136511i 1.18246 0.0152624i
\(81\) 1.32815 + 8.90146i 0.147572 + 0.989051i
\(82\) 12.5694 1.38806
\(83\) 3.26803 1.88680i 0.358713 0.207103i −0.309803 0.950801i \(-0.600263\pi\)
0.668516 + 0.743698i \(0.266930\pi\)
\(84\) 4.48888 + 5.32260i 0.489777 + 0.580743i
\(85\) −12.4109 6.95345i −1.34616 0.754208i
\(86\) −14.9204 8.61430i −1.60891 0.928904i
\(87\) 9.81710 1.66424i 1.05250 0.178425i
\(88\) −1.55270 + 0.896452i −0.165518 + 0.0955621i
\(89\) −2.80146 −0.296954 −0.148477 0.988916i \(-0.547437\pi\)
−0.148477 + 0.988916i \(0.547437\pi\)
\(90\) −9.63793 8.09217i −1.01593 0.852990i
\(91\) 10.5252 + 5.94965i 1.10334 + 0.623693i
\(92\) 0.0117685 + 0.0203836i 0.00122695 + 0.00212514i
\(93\) −5.97880 7.22160i −0.619973 0.748845i
\(94\) 9.17902 + 5.29951i 0.946743 + 0.546603i
\(95\) 4.74870 + 2.66054i 0.487206 + 0.272966i
\(96\) 9.43341 7.80998i 0.962793 0.797102i
\(97\) 4.13759 + 7.16652i 0.420109 + 0.727650i 0.995950 0.0899118i \(-0.0286585\pi\)
−0.575841 + 0.817562i \(0.695325\pi\)
\(98\) 6.77194 + 11.2513i 0.684069 + 1.13655i
\(99\) 5.86086 + 1.11345i 0.589038 + 0.111906i
\(100\) 7.59447 0.196081i 0.759447 0.0196081i
\(101\) 0.942877 + 1.63311i 0.0938198 + 0.162501i 0.909115 0.416544i \(-0.136759\pi\)
−0.815296 + 0.579045i \(0.803426\pi\)
\(102\) −20.3818 + 3.45522i −2.01810 + 0.342118i
\(103\) 0.522627 0.905216i 0.0514959 0.0891936i −0.839128 0.543933i \(-0.816934\pi\)
0.890624 + 0.454740i \(0.150268\pi\)
\(104\) 2.06006 3.56812i 0.202005 0.349883i
\(105\) −6.70674 7.74724i −0.654510 0.756053i
\(106\) −1.27555 2.20932i −0.123893 0.214588i
\(107\) 11.7173 1.13275 0.566376 0.824147i \(-0.308345\pi\)
0.566376 + 0.824147i \(0.308345\pi\)
\(108\) −7.89348 0.156431i −0.759551 0.0150526i
\(109\) −18.1511 −1.73856 −0.869281 0.494319i \(-0.835418\pi\)
−0.869281 + 0.494319i \(0.835418\pi\)
\(110\) −7.16976 + 4.26378i −0.683609 + 0.406535i
\(111\) −6.70731 + 18.0562i −0.636629 + 1.71382i
\(112\) 10.7809 6.35588i 1.01870 0.600574i
\(113\) −5.75934 + 9.97546i −0.541793 + 0.938413i 0.457008 + 0.889462i \(0.348921\pi\)
−0.998801 + 0.0489502i \(0.984412\pi\)
\(114\) 7.79854 1.32204i 0.730400 0.123821i
\(115\) −0.0177052 0.0297721i −0.00165101 0.00277626i
\(116\) 8.73468i 0.810995i
\(117\) −12.9433 + 4.51824i −1.19661 + 0.417712i
\(118\) 4.23114 0.389508
\(119\) −16.8318 + 0.153201i −1.54297 + 0.0140439i
\(120\) −2.66076 + 2.26137i −0.242893 + 0.206434i
\(121\) −3.52281 + 6.10169i −0.320256 + 0.554699i
\(122\) −13.2234 7.63455i −1.19719 0.691200i
\(123\) −8.93896 + 7.40062i −0.805999 + 0.667291i
\(124\) 7.12247 4.11216i 0.639617 0.369283i
\(125\) −11.1720 + 0.432793i −0.999250 + 0.0387102i
\(126\) −14.6534 2.64591i −1.30543 0.235716i
\(127\) 2.53008i 0.224509i −0.993680 0.112254i \(-0.964193\pi\)
0.993680 0.112254i \(-0.0358071\pi\)
\(128\) −3.50231 6.06618i −0.309563 0.536179i
\(129\) 15.6828 2.65862i 1.38079 0.234078i
\(130\) 9.36969 16.7236i 0.821776 1.46676i
\(131\) −0.754568 + 1.30695i −0.0659269 + 0.114189i −0.897105 0.441818i \(-0.854334\pi\)
0.831178 + 0.556007i \(0.187667\pi\)
\(132\) −1.82232 + 4.90572i −0.158613 + 0.426988i
\(133\) 6.44024 0.0586180i 0.558439 0.00508283i
\(134\) 20.7226i 1.79016i
\(135\) 11.6187 + 0.0802698i 0.999976 + 0.00690853i
\(136\) 5.73613i 0.491869i
\(137\) −3.18375 5.51442i −0.272006 0.471129i 0.697369 0.716712i \(-0.254354\pi\)
−0.969375 + 0.245583i \(0.921021\pi\)
\(138\) −0.0471851 0.0175278i −0.00401666 0.00149206i
\(139\) 14.5759 + 8.41540i 1.23631 + 0.713785i 0.968338 0.249642i \(-0.0803129\pi\)
0.267973 + 0.963426i \(0.413646\pi\)
\(140\) 7.68382 4.66467i 0.649401 0.394236i
\(141\) −9.64805 + 1.63558i −0.812512 + 0.137741i
\(142\) 12.6452 7.30069i 1.06116 0.612660i
\(143\) 9.08721i 0.759911i
\(144\) −2.64858 + 13.9413i −0.220715 + 1.16178i
\(145\) −0.165905 12.8536i −0.0137777 1.06743i
\(146\) −5.35704 9.27866i −0.443352 0.767908i
\(147\) −11.4405 4.01436i −0.943596 0.331099i
\(148\) −14.6331 8.44844i −1.20284 0.694458i
\(149\) −7.71964 4.45693i −0.632417 0.365126i 0.149270 0.988796i \(-0.452308\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(150\) −12.2428 + 10.6803i −0.999621 + 0.872042i
\(151\) −5.74142 9.94442i −0.467230 0.809266i 0.532069 0.846701i \(-0.321415\pi\)
−0.999299 + 0.0374351i \(0.988081\pi\)
\(152\) 2.19477i 0.178019i
\(153\) 12.4605 14.4576i 1.00737 1.16883i
\(154\) −4.85706 + 8.59234i −0.391393 + 0.692390i
\(155\) −10.4030 + 6.18655i −0.835589 + 0.496916i
\(156\) −2.01004 11.8569i −0.160932 0.949313i
\(157\) −5.84027 + 10.1156i −0.466104 + 0.807316i −0.999251 0.0387068i \(-0.987676\pi\)
0.533146 + 0.846023i \(0.321010\pi\)
\(158\) 2.93342 5.08084i 0.233371 0.404210i
\(159\) 2.20793 + 0.820176i 0.175100 + 0.0650442i
\(160\) −8.08136 13.5892i −0.638887 1.07432i
\(161\) −0.0356793 0.0201687i −0.00281192 0.00158952i
\(162\) 13.2161 10.5074i 1.03836 0.825539i
\(163\) 8.04946i 0.630482i −0.949012 0.315241i \(-0.897915\pi\)
0.949012 0.315241i \(-0.102085\pi\)
\(164\) −5.09007 8.81626i −0.397468 0.688434i
\(165\) 2.58847 7.25365i 0.201512 0.564696i
\(166\) −6.13085 3.53965i −0.475846 0.274730i
\(167\) −11.8147 6.82123i −0.914251 0.527843i −0.0324544 0.999473i \(-0.510332\pi\)
−0.881796 + 0.471630i \(0.843666\pi\)
\(168\) −1.40342 + 3.88603i −0.108276 + 0.299814i
\(169\) −3.94126 6.82645i −0.303174 0.525112i
\(170\) 0.344446 + 26.6860i 0.0264178 + 2.04673i
\(171\) −4.76767 + 5.53181i −0.364593 + 0.423028i
\(172\) 13.9537i 1.06396i
\(173\) −1.90414 + 1.09935i −0.144769 + 0.0835824i −0.570635 0.821204i \(-0.693303\pi\)
0.425866 + 0.904786i \(0.359970\pi\)
\(174\) −11.9123 14.3885i −0.903070 1.09079i
\(175\) −11.2186 + 7.01027i −0.848044 + 0.529926i
\(176\) 8.14613 + 4.70317i 0.614038 + 0.354515i
\(177\) −3.00904 + 2.49121i −0.226174 + 0.187250i
\(178\) 2.62778 + 4.55144i 0.196960 + 0.341145i
\(179\) 8.92870i 0.667363i −0.942686 0.333681i \(-0.891709\pi\)
0.942686 0.333681i \(-0.108291\pi\)
\(180\) −1.77295 + 10.0371i −0.132148 + 0.748118i
\(181\) 2.80304i 0.208349i −0.994559 0.104174i \(-0.966780\pi\)
0.994559 0.104174i \(-0.0332200\pi\)
\(182\) −0.206436 22.6807i −0.0153021 1.68121i
\(183\) 13.8991 2.35624i 1.02745 0.174178i
\(184\) −0.00698340 + 0.0120956i −0.000514823 + 0.000891699i
\(185\) 21.6939 + 12.1544i 1.59497 + 0.893610i
\(186\) −6.12457 + 16.4875i −0.449075 + 1.20892i
\(187\) −6.32572 10.9565i −0.462582 0.801216i
\(188\) 8.58427i 0.626072i
\(189\) 11.9788 6.74592i 0.871332 0.490693i
\(190\) −0.131792 10.2107i −0.00956123 0.740759i
\(191\) −2.67708 + 1.54562i −0.193707 + 0.111837i −0.593717 0.804674i \(-0.702340\pi\)
0.400010 + 0.916511i \(0.369007\pi\)
\(192\) −6.17677 2.29447i −0.445770 0.165589i
\(193\) 2.45619 + 1.41808i 0.176800 + 0.102076i 0.585788 0.810464i \(-0.300785\pi\)
−0.408988 + 0.912540i \(0.634118\pi\)
\(194\) 7.76215 13.4444i 0.557290 0.965255i
\(195\) 3.18309 + 17.4099i 0.227946 + 1.24675i
\(196\) 5.14936 9.30614i 0.367812 0.664725i
\(197\) −14.9273 −1.06352 −0.531762 0.846894i \(-0.678470\pi\)
−0.531762 + 0.846894i \(0.678470\pi\)
\(198\) −3.68852 10.5664i −0.262132 0.750919i
\(199\) 23.0264i 1.63230i −0.577842 0.816148i \(-0.696105\pi\)
0.577842 0.816148i \(-0.303895\pi\)
\(200\) 2.35404 + 3.84460i 0.166455 + 0.271854i
\(201\) 12.2010 + 14.7372i 0.860593 + 1.03948i
\(202\) 1.76884 3.06373i 0.124455 0.215563i
\(203\) −7.72448 13.1023i −0.542152 0.919603i
\(204\) 10.6773 + 12.8967i 0.747557 + 0.902949i
\(205\) 7.65777 + 12.8769i 0.534842 + 0.899364i
\(206\) −1.96090 −0.136623
\(207\) 0.0438764 0.0153164i 0.00304962 0.00106456i
\(208\) −21.6159 −1.49879
\(209\) 2.42036 + 4.19219i 0.167420 + 0.289980i
\(210\) −6.29576 + 18.1632i −0.434449 + 1.25338i
\(211\) 5.31019 9.19753i 0.365569 0.633184i −0.623298 0.781984i \(-0.714208\pi\)
0.988867 + 0.148800i \(0.0475411\pi\)
\(212\) −1.03308 + 1.78935i −0.0709525 + 0.122893i
\(213\) −4.69432 + 12.6372i −0.321650 + 0.865887i
\(214\) −10.9908 19.0367i −0.751318 1.30132i
\(215\) −0.265034 20.5336i −0.0180752 1.40038i
\(216\) −2.26160 4.10285i −0.153882 0.279164i
\(217\) −7.04738 + 12.4671i −0.478407 + 0.846322i
\(218\) 17.0258 + 29.4896i 1.15313 + 1.99728i
\(219\) 9.27283 + 3.44456i 0.626599 + 0.232762i
\(220\) 5.89407 + 3.30226i 0.397378 + 0.222638i
\(221\) 25.1781 + 14.5366i 1.69366 + 0.977836i
\(222\) 35.6268 6.03961i 2.39112 0.405352i
\(223\) −4.01295 6.95063i −0.268727 0.465449i 0.699806 0.714333i \(-0.253270\pi\)
−0.968533 + 0.248884i \(0.919936\pi\)
\(224\) −16.2855 9.20583i −1.08812 0.615091i
\(225\) 2.41835 14.8038i 0.161223 0.986918i
\(226\) 21.6091 1.43742
\(227\) −4.95788 + 2.86243i −0.329066 + 0.189986i −0.655426 0.755259i \(-0.727511\pi\)
0.326360 + 0.945245i \(0.394178\pi\)
\(228\) −4.08535 4.93456i −0.270559 0.326799i
\(229\) 6.34119 + 3.66109i 0.419038 + 0.241932i 0.694666 0.719333i \(-0.255552\pi\)
−0.275628 + 0.961264i \(0.588886\pi\)
\(230\) −0.0317623 + 0.0566913i −0.00209435 + 0.00373812i
\(231\) −1.60481 8.97031i −0.105589 0.590203i
\(232\) −4.48873 + 2.59157i −0.294700 + 0.170145i
\(233\) −26.2522 −1.71984 −0.859919 0.510431i \(-0.829486\pi\)
−0.859919 + 0.510431i \(0.829486\pi\)
\(234\) 19.4815 + 16.7904i 1.27354 + 1.09762i
\(235\) 0.163048 + 12.6322i 0.0106361 + 0.824036i
\(236\) −1.71343 2.96774i −0.111535 0.193183i
\(237\) 0.905338 + 5.34046i 0.0588080 + 0.346900i
\(238\) 16.0372 + 27.2025i 1.03954 + 1.76328i
\(239\) 11.6421 + 6.72155i 0.753063 + 0.434781i 0.826799 0.562497i \(-0.190159\pi\)
−0.0737368 + 0.997278i \(0.523492\pi\)
\(240\) 17.2544 + 6.15723i 1.11377 + 0.397447i
\(241\) 5.16398 2.98143i 0.332641 0.192051i −0.324372 0.945930i \(-0.605153\pi\)
0.657013 + 0.753879i \(0.271820\pi\)
\(242\) 13.2176 0.849662
\(243\) −3.21233 + 15.2539i −0.206071 + 0.978537i
\(244\) 12.3666i 0.791693i
\(245\) −7.40081 + 13.7923i −0.472821 + 0.881159i
\(246\) 20.4083 + 7.58105i 1.30119 + 0.483350i
\(247\) −9.63369 5.56202i −0.612977 0.353903i
\(248\) 4.22646 + 2.44015i 0.268380 + 0.154949i
\(249\) 6.44412 1.09244i 0.408380 0.0692303i
\(250\) 11.1825 + 17.7448i 0.707242 + 1.12228i
\(251\) −5.42779 −0.342599 −0.171300 0.985219i \(-0.554797\pi\)
−0.171300 + 0.985219i \(0.554797\pi\)
\(252\) 4.07812 + 11.3494i 0.256898 + 0.714946i
\(253\) 0.0308048i 0.00193668i
\(254\) −4.11055 + 2.37323i −0.257919 + 0.148910i
\(255\) −15.9571 18.7754i −0.999274 1.17576i
\(256\) −10.3746 + 17.9694i −0.648413 + 1.12308i
\(257\) 14.5364 + 8.39259i 0.906755 + 0.523515i 0.879386 0.476110i \(-0.157954\pi\)
0.0273696 + 0.999625i \(0.491287\pi\)
\(258\) −19.0299 22.9856i −1.18475 1.43102i
\(259\) 29.4216 0.267790i 1.82817 0.0166397i
\(260\) −15.5243 + 0.200377i −0.962777 + 0.0124269i
\(261\) 16.9433 + 3.21889i 1.04876 + 0.199244i
\(262\) 2.83115 0.174909
\(263\) −12.8188 22.2028i −0.790439 1.36908i −0.925695 0.378270i \(-0.876519\pi\)
0.135256 0.990811i \(-0.456814\pi\)
\(264\) −3.06172 + 0.519036i −0.188436 + 0.0319445i
\(265\) 1.48625 2.65276i 0.0912999 0.162958i
\(266\) −6.13620 10.4083i −0.376234 0.638172i
\(267\) −4.54858 1.68965i −0.278369 0.103405i
\(268\) −14.5349 + 8.39173i −0.887860 + 0.512606i
\(269\) −29.6439 −1.80742 −0.903710 0.428144i \(-0.859168\pi\)
−0.903710 + 0.428144i \(0.859168\pi\)
\(270\) −10.7679 18.9518i −0.655316 1.15337i
\(271\) 9.38040i 0.569819i 0.958554 + 0.284909i \(0.0919635\pi\)
−0.958554 + 0.284909i \(0.908036\pi\)
\(272\) 26.0623 15.0471i 1.58026 0.912364i
\(273\) 13.5007 + 16.0082i 0.817102 + 0.968861i
\(274\) −5.97274 + 10.3451i −0.360826 + 0.624970i
\(275\) −8.73617 4.74750i −0.526811 0.286285i
\(276\) 0.00681383 + 0.0401938i 0.000410144 + 0.00241938i
\(277\) 5.58263 3.22314i 0.335428 0.193659i −0.322820 0.946460i \(-0.604631\pi\)
0.658248 + 0.752801i \(0.271298\pi\)
\(278\) 31.5747i 1.89372i
\(279\) −5.35188 15.3313i −0.320409 0.917863i
\(280\) 4.67694 + 2.56469i 0.279501 + 0.153270i
\(281\) −4.83381 + 2.79080i −0.288361 + 0.166485i −0.637202 0.770696i \(-0.719908\pi\)
0.348841 + 0.937182i \(0.386575\pi\)
\(282\) 11.7072 + 14.1407i 0.697152 + 0.842067i
\(283\) 4.49792 7.79062i 0.267373 0.463104i −0.700809 0.713349i \(-0.747178\pi\)
0.968183 + 0.250244i \(0.0805109\pi\)
\(284\) −10.2415 5.91291i −0.607719 0.350867i
\(285\) 6.10555 + 7.18388i 0.361662 + 0.425537i
\(286\) 14.7637 8.52383i 0.872996 0.504025i
\(287\) 15.4319 + 8.72331i 0.910916 + 0.514921i
\(288\) 20.0270 6.99104i 1.18010 0.411951i
\(289\) −23.4764 −1.38096
\(290\) −20.7272 + 12.3262i −1.21714 + 0.723821i
\(291\) 2.39562 + 14.1314i 0.140434 + 0.828399i
\(292\) −4.33873 + 7.51490i −0.253905 + 0.439776i
\(293\) −15.2457 8.80210i −0.890662 0.514224i −0.0165034 0.999864i \(-0.505253\pi\)
−0.874159 + 0.485640i \(0.838587\pi\)
\(294\) 4.20922 + 22.3525i 0.245486 + 1.30362i
\(295\) 2.57777 + 4.33465i 0.150084 + 0.252373i
\(296\) 10.0266i 0.582783i
\(297\) 8.84440 + 5.34273i 0.513204 + 0.310016i
\(298\) 16.7225i 0.968707i
\(299\) 0.0353948 + 0.0613057i 0.00204694 + 0.00354540i
\(300\) 12.4490 + 4.26211i 0.718743 + 0.246073i
\(301\) −12.3399 20.9310i −0.711257 1.20644i
\(302\) −10.7709 + 18.6558i −0.619797 + 1.07352i
\(303\) 0.545916 + 3.22028i 0.0313620 + 0.185000i
\(304\) −9.97202 + 5.75735i −0.571935 + 0.330207i
\(305\) −0.234890 18.1982i −0.0134498 1.04203i
\(306\) −35.1769 6.68292i −2.01093 0.382037i
\(307\) −2.48249 −0.141683 −0.0708416 0.997488i \(-0.522568\pi\)
−0.0708416 + 0.997488i \(0.522568\pi\)
\(308\) 7.99360 0.0727565i 0.455477 0.00414569i
\(309\) 1.39453 1.15454i 0.0793319 0.0656793i
\(310\) 19.8092 + 11.0984i 1.12508 + 0.630348i
\(311\) 12.9774 22.4774i 0.735878 1.27458i −0.218459 0.975846i \(-0.570103\pi\)
0.954337 0.298732i \(-0.0965638\pi\)
\(312\) 5.49686 4.55088i 0.311199 0.257643i
\(313\) −10.1190 17.5265i −0.571957 0.990659i −0.996365 0.0851877i \(-0.972851\pi\)
0.424408 0.905471i \(-0.360482\pi\)
\(314\) 21.9128 1.23661
\(315\) −6.21675 16.6238i −0.350274 0.936647i
\(316\) −4.75163 −0.267300
\(317\) 5.21345 + 9.02996i 0.292817 + 0.507173i 0.974475 0.224498i \(-0.0720741\pi\)
−0.681658 + 0.731671i \(0.738741\pi\)
\(318\) −0.738530 4.35648i −0.0414147 0.244299i
\(319\) 5.71589 9.90022i 0.320029 0.554306i
\(320\) −4.15785 + 7.42119i −0.232431 + 0.414857i
\(321\) 19.0247 + 7.06708i 1.06186 + 0.394446i
\(322\) 0.000699799 0.0768854i 3.89983e−5 0.00428466i
\(323\) 15.4872 0.861728
\(324\) −12.7219 5.01482i −0.706771 0.278601i
\(325\) 22.8411 0.589733i 1.26700 0.0327125i
\(326\) −13.0777 + 7.55042i −0.724307 + 0.418179i
\(327\) −29.4710 10.9475i −1.62975 0.605401i
\(328\) 3.02043 5.23155i 0.166776 0.288864i
\(329\) 7.59146 + 12.8767i 0.418531 + 0.709916i
\(330\) −14.2128 + 2.59855i −0.782388 + 0.143045i
\(331\) −14.9466 25.8883i −0.821542 1.42295i −0.904534 0.426402i \(-0.859781\pi\)
0.0829919 0.996550i \(-0.473552\pi\)
\(332\) 5.73360i 0.314672i
\(333\) −21.7806 + 25.2715i −1.19357 + 1.38487i
\(334\) 25.5934i 1.40041i
\(335\) 21.2295 12.6250i 1.15989 0.689776i
\(336\) 21.3378 3.81739i 1.16407 0.208255i
\(337\) −20.0363 11.5680i −1.09145 0.630148i −0.157486 0.987521i \(-0.550339\pi\)
−0.933962 + 0.357373i \(0.883672\pi\)
\(338\) −7.39382 + 12.8065i −0.402171 + 0.696580i
\(339\) −15.3677 + 12.7230i −0.834657 + 0.691018i
\(340\) 18.5782 11.0483i 1.00755 0.599176i
\(341\) −10.7638 −0.582894
\(342\) 13.4594 + 2.55703i 0.727803 + 0.138268i
\(343\) 0.505629 + 18.5134i 0.0273014 + 0.999627i
\(344\) −7.17075 + 4.14003i −0.386621 + 0.223216i
\(345\) −0.0107904 0.0590180i −0.000580933 0.00317742i
\(346\) 3.57218 + 2.06240i 0.192041 + 0.110875i
\(347\) 2.30614 3.99435i 0.123800 0.214428i −0.797463 0.603368i \(-0.793825\pi\)
0.921263 + 0.388940i \(0.127159\pi\)
\(348\) −5.26818 + 14.1820i −0.282404 + 0.760237i
\(349\) −30.9578 + 17.8735i −1.65713 + 0.956745i −0.683101 + 0.730324i \(0.739369\pi\)
−0.974030 + 0.226421i \(0.927297\pi\)
\(350\) 21.9124 + 11.6508i 1.17127 + 0.622762i
\(351\) −23.7404 0.470482i −1.26717 0.0251125i
\(352\) 14.0605i 0.749430i
\(353\) −2.77278 + 1.60086i −0.147580 + 0.0852054i −0.571972 0.820273i \(-0.693821\pi\)
0.424392 + 0.905479i \(0.360488\pi\)
\(354\) 6.86988 + 2.55194i 0.365130 + 0.135634i
\(355\) 15.1832 + 8.50666i 0.805840 + 0.451486i
\(356\) 2.12827 3.68627i 0.112798 0.195372i
\(357\) −27.4214 9.90311i −1.45129 0.524128i
\(358\) −14.5062 + 8.37515i −0.766676 + 0.442641i
\(359\) 25.4583i 1.34364i −0.740716 0.671818i \(-0.765513\pi\)
0.740716 0.671818i \(-0.234487\pi\)
\(360\) −5.68405 + 2.06687i −0.299576 + 0.108934i
\(361\) 13.0743 0.688120
\(362\) −4.55402 + 2.62927i −0.239354 + 0.138191i
\(363\) −9.39993 + 7.78226i −0.493369 + 0.408463i
\(364\) −15.8248 + 9.32949i −0.829442 + 0.488998i
\(365\) 6.24195 11.1410i 0.326718 0.583147i
\(366\) −16.8655 20.3713i −0.881576 1.06483i
\(367\) 11.7133 + 20.2880i 0.611427 + 1.05902i 0.991000 + 0.133861i \(0.0427376\pi\)
−0.379573 + 0.925162i \(0.623929\pi\)
\(368\) 0.0732758 0.00381976
\(369\) −18.9773 + 6.62460i −0.987917 + 0.344863i
\(370\) −0.602080 46.6463i −0.0313007 2.42503i
\(371\) −0.0327457 3.59770i −0.00170007 0.186783i
\(372\) 14.0446 2.38089i 0.728176 0.123444i
\(373\) −15.5861 8.99863i −0.807017 0.465931i 0.0389022 0.999243i \(-0.487614\pi\)
−0.845919 + 0.533312i \(0.820947\pi\)
\(374\) −11.8671 + 20.5544i −0.613633 + 1.06284i
\(375\) −18.4004 6.03548i −0.950190 0.311671i
\(376\) 4.41144 2.54694i 0.227502 0.131349i
\(377\) 26.2704i 1.35299i
\(378\) −22.1961 13.1340i −1.14164 0.675538i
\(379\) −0.827213 −0.0424911 −0.0212455 0.999774i \(-0.506763\pi\)
−0.0212455 + 0.999774i \(0.506763\pi\)
\(380\) −7.10843 + 4.22731i −0.364655 + 0.216856i
\(381\) 1.52598 4.10796i 0.0781783 0.210457i
\(382\) 5.02223 + 2.89958i 0.256959 + 0.148356i
\(383\) 22.0310 + 12.7196i 1.12573 + 0.649942i 0.942858 0.333194i \(-0.108126\pi\)
0.182875 + 0.983136i \(0.441460\pi\)
\(384\) −2.02780 11.9617i −0.103481 0.610418i
\(385\) −11.7616 + 0.258895i −0.599429 + 0.0131945i
\(386\) 5.32066i 0.270814i
\(387\) 27.0669 + 5.14217i 1.37589 + 0.261391i
\(388\) −12.5733 −0.638314
\(389\) 5.70871 3.29592i 0.289443 0.167110i −0.348248 0.937403i \(-0.613223\pi\)
0.637691 + 0.770293i \(0.279890\pi\)
\(390\) 25.2996 21.5020i 1.28110 1.08880i
\(391\) −0.0853513 0.0492776i −0.00431640 0.00249207i
\(392\) 6.31021 0.114879i 0.318714 0.00580225i
\(393\) −2.01342 + 1.66692i −0.101563 + 0.0840850i
\(394\) 14.0018 + 24.2519i 0.705402 + 1.22179i
\(395\) 6.99229 0.0902518i 0.351820 0.00454106i
\(396\) −5.91761 + 6.86606i −0.297371 + 0.345032i
\(397\) 7.24750 0.363742 0.181871 0.983322i \(-0.441785\pi\)
0.181871 + 0.983322i \(0.441785\pi\)
\(398\) −37.4103 + 21.5988i −1.87521 + 1.08265i
\(399\) 10.4920 + 3.78915i 0.525258 + 0.189695i
\(400\) 11.2930 20.7809i 0.564648 1.03904i
\(401\) 21.6860 + 12.5204i 1.08295 + 0.625239i 0.931689 0.363256i \(-0.118335\pi\)
0.151256 + 0.988495i \(0.451668\pi\)
\(402\) 12.4985 33.6461i 0.623367 1.67812i
\(403\) 21.4215 12.3677i 1.06708 0.616079i
\(404\) −2.86522 −0.142550
\(405\) 18.8162 + 7.13794i 0.934985 + 0.354687i
\(406\) −14.0414 + 24.8398i −0.696861 + 1.23278i
\(407\) 11.0572 + 19.1516i 0.548083 + 0.949308i
\(408\) −3.45965 + 9.31345i −0.171278 + 0.461084i
\(409\) 9.11823 + 5.26441i 0.450868 + 0.260308i 0.708197 0.706015i \(-0.249509\pi\)
−0.257329 + 0.966324i \(0.582842\pi\)
\(410\) 13.7377 24.5200i 0.678459 1.21095i
\(411\) −1.84336 10.8737i −0.0909261 0.536360i
\(412\) 0.794079 + 1.37539i 0.0391215 + 0.0677604i
\(413\) 5.19471 + 2.93645i 0.255615 + 0.144493i
\(414\) −0.0660403 0.0569178i −0.00324570 0.00279736i
\(415\) −0.108903 8.43732i −0.00534585 0.414172i
\(416\) 16.1557 + 27.9824i 0.792096 + 1.37195i
\(417\) 18.5905 + 22.4548i 0.910381 + 1.09962i
\(418\) 4.54061 7.86457i 0.222089 0.384669i
\(419\) 9.50459 16.4624i 0.464330 0.804243i −0.534841 0.844953i \(-0.679629\pi\)
0.999171 + 0.0407098i \(0.0129619\pi\)
\(420\) 15.2892 2.93941i 0.746038 0.143428i
\(421\) 6.62782 + 11.4797i 0.323020 + 0.559487i 0.981110 0.193453i \(-0.0619685\pi\)
−0.658090 + 0.752940i \(0.728635\pi\)
\(422\) −19.9239 −0.969881
\(423\) −16.6515 3.16346i −0.809623 0.153813i
\(424\) −1.22606 −0.0595427
\(425\) −27.1290 + 16.6110i −1.31595 + 0.805752i
\(426\) 24.9346 4.22702i 1.20808 0.204800i
\(427\) −10.9364 18.5504i −0.529248 0.897716i
\(428\) −8.90161 + 15.4180i −0.430276 + 0.745259i
\(429\) −5.48080 + 14.7544i −0.264616 + 0.712350i
\(430\) −33.1117 + 19.6912i −1.59679 + 0.949592i
\(431\) 7.25892i 0.349650i 0.984600 + 0.174825i \(0.0559360\pi\)
−0.984600 + 0.174825i \(0.944064\pi\)
\(432\) −12.7088 + 21.0383i −0.611454 + 1.01221i
\(433\) 15.5951 0.749453 0.374726 0.927135i \(-0.377737\pi\)
0.374726 + 0.927135i \(0.377737\pi\)
\(434\) 26.8654 0.244525i 1.28958 0.0117376i
\(435\) 7.48305 20.9697i 0.358785 1.00542i
\(436\) 13.7894 23.8839i 0.660393 1.14383i
\(437\) 0.0326573 + 0.0188547i 0.00156221 + 0.000901942i
\(438\) −3.10167 18.2963i −0.148203 0.874230i
\(439\) −28.7023 + 16.5713i −1.36989 + 0.790904i −0.990913 0.134505i \(-0.957056\pi\)
−0.378972 + 0.925408i \(0.623722\pi\)
\(440\) 0.0517419 + 4.00872i 0.00246670 + 0.191108i
\(441\) −16.1541 13.4180i −0.769244 0.638955i
\(442\) 54.5414i 2.59427i
\(443\) −2.58558 4.47836i −0.122845 0.212773i 0.798044 0.602600i \(-0.205868\pi\)
−0.920888 + 0.389826i \(0.872535\pi\)
\(444\) −18.6635 22.5430i −0.885731 1.06984i
\(445\) −3.06185 + 5.46497i −0.145146 + 0.259065i
\(446\) −7.52832 + 13.0394i −0.356476 + 0.617435i
\(447\) −9.84584 11.8925i −0.465692 0.562494i
\(448\) 0.0916073 + 10.0647i 0.00432804 + 0.475512i
\(449\) 5.53014i 0.260984i 0.991449 + 0.130492i \(0.0416556\pi\)
−0.991449 + 0.130492i \(0.958344\pi\)
\(450\) −26.3196 + 9.95697i −1.24072 + 0.469376i
\(451\) 13.3236i 0.627382i
\(452\) −8.75074 15.1567i −0.411600 0.712912i
\(453\) −3.32422 19.6091i −0.156185 0.921315i
\(454\) 9.30101 + 5.36994i 0.436518 + 0.252024i
\(455\) 23.1098 14.0294i 1.08340 0.657710i
\(456\) 1.32374 3.56353i 0.0619898 0.166878i
\(457\) −6.13724 + 3.54334i −0.287088 + 0.165750i −0.636628 0.771171i \(-0.719671\pi\)
0.349540 + 0.936921i \(0.386338\pi\)
\(458\) 13.7365i 0.641863i
\(459\) 28.9514 15.9587i 1.35133 0.744890i
\(460\) 0.0526259 0.000679260i 0.00245370 3.16707e-5i
\(461\) 11.9627 + 20.7199i 0.557157 + 0.965024i 0.997732 + 0.0673082i \(0.0214411\pi\)
−0.440575 + 0.897716i \(0.645226\pi\)
\(462\) −13.0685 + 11.0215i −0.608001 + 0.512765i
\(463\) 17.6719 + 10.2029i 0.821285 + 0.474169i 0.850859 0.525394i \(-0.176082\pi\)
−0.0295746 + 0.999563i \(0.509415\pi\)
\(464\) 23.5498 + 13.5965i 1.09327 + 0.631201i
\(465\) −20.6221 + 3.77038i −0.956328 + 0.174847i
\(466\) 24.6246 + 42.6511i 1.14071 + 1.97577i
\(467\) 18.8109i 0.870464i 0.900318 + 0.435232i \(0.143334\pi\)
−0.900318 + 0.435232i \(0.856666\pi\)
\(468\) 3.88771 20.4638i 0.179710 0.945938i
\(469\) 14.3817 25.4418i 0.664084 1.17479i
\(470\) 20.3703 12.1140i 0.939610 0.558776i
\(471\) −15.5836 + 12.9018i −0.718055 + 0.594482i
\(472\) 1.01674 1.76105i 0.0467994 0.0810589i
\(473\) 9.13114 15.8156i 0.419850 0.727202i
\(474\) 7.82727 6.48024i 0.359518 0.297647i
\(475\) 10.3802 6.35574i 0.476275 0.291621i
\(476\) 12.5856 22.2644i 0.576859 1.02049i
\(477\) 3.09022 + 2.66335i 0.141492 + 0.121947i
\(478\) 25.2193i 1.15351i
\(479\) −2.31069 4.00223i −0.105578 0.182866i 0.808396 0.588639i \(-0.200336\pi\)
−0.913974 + 0.405772i \(0.867003\pi\)
\(480\) −4.92516 26.9382i −0.224802 1.22956i
\(481\) −44.0105 25.4095i −2.00671 1.15857i
\(482\) −9.68767 5.59318i −0.441261 0.254762i
\(483\) −0.0457662 0.0542663i −0.00208243 0.00246920i
\(484\) −5.35256 9.27090i −0.243298 0.421405i
\(485\) 18.5023 0.238816i 0.840148 0.0108441i
\(486\) 27.7957 9.08921i 1.26084 0.412295i
\(487\) 28.6422i 1.29790i −0.760831 0.648951i \(-0.775208\pi\)
0.760831 0.648951i \(-0.224792\pi\)
\(488\) −6.35518 + 3.66917i −0.287686 + 0.166095i
\(489\) 4.85490 13.0695i 0.219546 0.591023i
\(490\) 29.3499 0.913366i 1.32589 0.0412616i
\(491\) −16.6816 9.63112i −0.752830 0.434646i 0.0738857 0.997267i \(-0.476460\pi\)
−0.826715 + 0.562620i \(0.809793\pi\)
\(492\) −2.94709 17.3845i −0.132865 0.783753i
\(493\) −18.2871 31.6743i −0.823612 1.42654i
\(494\) 20.8688i 0.938930i
\(495\) 8.57768 10.2162i 0.385538 0.459183i
\(496\) 25.6041i 1.14966i
\(497\) 20.5916 0.187422i 0.923660 0.00840701i
\(498\) −7.81945 9.44486i −0.350398 0.423234i
\(499\) −11.1319 + 19.2810i −0.498331 + 0.863134i −0.999998 0.00192627i \(-0.999387\pi\)
0.501667 + 0.865061i \(0.332720\pi\)
\(500\) 7.91785 15.0293i 0.354097 0.672130i
\(501\) −15.0688 18.2011i −0.673226 0.813167i
\(502\) 5.09129 + 8.81836i 0.227235 + 0.393583i
\(503\) 31.0638i 1.38507i 0.721387 + 0.692533i \(0.243505\pi\)
−0.721387 + 0.692533i \(0.756495\pi\)
\(504\) −4.62246 + 5.46310i −0.205901 + 0.243346i
\(505\) 4.21632 0.0544215i 0.187624 0.00242173i
\(506\) −0.0500475 + 0.0288950i −0.00222488 + 0.00128454i
\(507\) −2.28194 13.4609i −0.101345 0.597818i
\(508\) 3.32918 + 1.92211i 0.147709 + 0.0852796i
\(509\) −14.0551 + 24.3442i −0.622982 + 1.07904i 0.365946 + 0.930636i \(0.380746\pi\)
−0.988927 + 0.148400i \(0.952588\pi\)
\(510\) −15.5360 + 43.5364i −0.687945 + 1.92783i
\(511\) −0.137525 15.1095i −0.00608374 0.668407i
\(512\) 24.9164 1.10116
\(513\) −11.0774 + 6.10616i −0.489080 + 0.269594i
\(514\) 31.4891i 1.38893i
\(515\) −1.19466 2.00887i −0.0526428 0.0885215i
\(516\) −8.41592 + 22.6558i −0.370490 + 0.997366i
\(517\) −5.61747 + 9.72974i −0.247056 + 0.427913i
\(518\) −28.0326 47.5491i −1.23168 2.08919i
\(519\) −3.75471 + 0.636514i −0.164813 + 0.0279399i
\(520\) −4.70902 7.91845i −0.206504 0.347247i
\(521\) 28.0333 1.22816 0.614080 0.789244i \(-0.289527\pi\)
0.614080 + 0.789244i \(0.289527\pi\)
\(522\) −10.6632 30.5465i −0.466716 1.33699i
\(523\) 6.23624 0.272692 0.136346 0.990661i \(-0.456464\pi\)
0.136346 + 0.990661i \(0.456464\pi\)
\(524\) −1.14649 1.98578i −0.0500847 0.0867492i
\(525\) −22.4431 + 4.61590i −0.979498 + 0.201455i
\(526\) −24.0481 + 41.6525i −1.04855 + 1.81614i
\(527\) −17.2186 + 29.8235i −0.750055 + 1.29913i
\(528\) 10.3898 + 12.5495i 0.452158 + 0.546147i
\(529\) 11.4999 + 19.9184i 0.499995 + 0.866016i
\(530\) −5.70396 + 0.0736230i −0.247764 + 0.00319798i
\(531\) −6.38816 + 2.22998i −0.277222 + 0.0967730i
\(532\) −4.81552 + 8.51885i −0.208779 + 0.369339i
\(533\) −15.3089 26.5157i −0.663100 1.14852i
\(534\) 1.52145 + 8.97484i 0.0658398 + 0.388379i
\(535\) 12.8064 22.8576i 0.553668 0.988219i
\(536\) −8.62498 4.97963i −0.372542 0.215087i
\(537\) 5.38520 14.4971i 0.232389 0.625594i
\(538\) 27.8061 + 48.1615i 1.19881 + 2.07639i
\(539\) −11.9263 + 7.17824i −0.513703 + 0.309189i
\(540\) −8.93233 + 15.2273i −0.384386 + 0.655280i
\(541\) −18.2151 −0.783127 −0.391564 0.920151i \(-0.628066\pi\)
−0.391564 + 0.920151i \(0.628066\pi\)
\(542\) 15.2401 8.79885i 0.654616 0.377943i
\(543\) 1.69061 4.55116i 0.0725510 0.195309i
\(544\) −38.9578 22.4923i −1.67030 0.964350i
\(545\) −19.8382 + 35.4085i −0.849776 + 1.51673i
\(546\) 13.3443 36.9500i 0.571084 1.58131i
\(547\) −22.6534 + 13.0789i −0.968589 + 0.559215i −0.898806 0.438347i \(-0.855564\pi\)
−0.0697830 + 0.997562i \(0.522231\pi\)
\(548\) 9.67479 0.413286
\(549\) 23.9884 + 4.55733i 1.02380 + 0.194502i
\(550\) 0.481435 + 18.6466i 0.0205285 + 0.795092i
\(551\) 6.99707 + 12.1193i 0.298085 + 0.516298i
\(552\) −0.0186338 + 0.0154271i −0.000793109 + 0.000656619i
\(553\) 7.12761 4.20208i 0.303097 0.178691i
\(554\) −10.4731 6.04662i −0.444958 0.256896i
\(555\) 27.8926 + 32.8188i 1.18397 + 1.39308i
\(556\) −22.1466 + 12.7864i −0.939226 + 0.542262i
\(557\) 4.94802 0.209654 0.104827 0.994490i \(-0.466571\pi\)
0.104827 + 0.994490i \(0.466571\pi\)
\(558\) −19.8883 + 23.0759i −0.841938 + 0.976880i
\(559\) 41.9669i 1.77501i
\(560\) −0.615836 27.9776i −0.0260238 1.18227i
\(561\) −3.66252 21.6047i −0.154632 0.912151i
\(562\) 9.06826 + 5.23556i 0.382522 + 0.220849i
\(563\) 3.54967 + 2.04940i 0.149601 + 0.0863720i 0.572932 0.819603i \(-0.305806\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(564\) 5.17746 13.9378i 0.218011 0.586888i
\(565\) 13.1651 + 22.1377i 0.553859 + 0.931342i
\(566\) −16.8762 −0.709361
\(567\) 23.5181 3.72815i 0.987667 0.156567i
\(568\) 7.01742i 0.294444i
\(569\) 24.3155 14.0386i 1.01936 0.588527i 0.105440 0.994426i \(-0.466375\pi\)
0.913918 + 0.405899i \(0.133041\pi\)
\(570\) 5.94441 16.6580i 0.248984 0.697727i
\(571\) −13.2089 + 22.8785i −0.552776 + 0.957436i 0.445297 + 0.895383i \(0.353098\pi\)
−0.998073 + 0.0620529i \(0.980235\pi\)
\(572\) −11.9573 6.90355i −0.499960 0.288652i
\(573\) −5.27885 + 0.894894i −0.220527 + 0.0373847i
\(574\) −0.302675 33.2542i −0.0126334 1.38800i
\(575\) −0.0774290 + 0.00199914i −0.00322901 + 8.33698e-5i
\(576\) −8.64502 7.45083i −0.360209 0.310451i
\(577\) −20.5348 −0.854875 −0.427437 0.904045i \(-0.640584\pi\)
−0.427437 + 0.904045i \(0.640584\pi\)
\(578\) 22.0209 + 38.1413i 0.915949 + 1.58647i
\(579\) 3.13269 + 3.78387i 0.130190 + 0.157252i
\(580\) 17.0393 + 9.54656i 0.707517 + 0.396399i
\(581\) −5.07049 8.60060i −0.210359 0.356813i
\(582\) 20.7118 17.1474i 0.858531 0.710783i
\(583\) 2.34187 1.35208i 0.0969905 0.0559975i
\(584\) −5.14918 −0.213075
\(585\) −5.33230 + 30.1874i −0.220464 + 1.24810i
\(586\) 33.0256i 1.36427i
\(587\) 27.2457 15.7303i 1.12455 0.649259i 0.181991 0.983300i \(-0.441746\pi\)
0.942558 + 0.334041i \(0.108412\pi\)
\(588\) 13.9736 12.0041i 0.576261 0.495042i
\(589\) 6.58823 11.4111i 0.271463 0.470188i
\(590\) 4.62442 8.25394i 0.190384 0.339809i
\(591\) −24.2366 9.00314i −0.996962 0.370340i
\(592\) −45.5561 + 26.3018i −1.87235 + 1.08100i
\(593\) 25.5323i 1.04848i −0.851569 0.524242i \(-0.824349\pi\)
0.851569 0.524242i \(-0.175651\pi\)
\(594\) 0.384083 19.3807i 0.0157591 0.795201i
\(595\) −18.0975 + 33.0023i −0.741924 + 1.35296i
\(596\) 11.7292 6.77187i 0.480447 0.277386i
\(597\) 13.8880 37.3867i 0.568397 1.53014i
\(598\) 0.0664010 0.115010i 0.00271534 0.00470310i
\(599\) −38.7855 22.3928i −1.58473 0.914945i −0.994155 0.107964i \(-0.965567\pi\)
−0.590577 0.806982i \(-0.701100\pi\)
\(600\) 1.50332 + 7.66207i 0.0613726 + 0.312803i
\(601\) 9.78512 5.64944i 0.399143 0.230446i −0.286971 0.957939i \(-0.592648\pi\)
0.686114 + 0.727494i \(0.259315\pi\)
\(602\) −22.4311 + 39.6815i −0.914222 + 1.61730i
\(603\) 10.9216 + 31.2868i 0.444763 + 1.27410i
\(604\) 17.4470 0.709909
\(605\) 8.05268 + 13.5410i 0.327388 + 0.550519i
\(606\) 4.71981 3.90756i 0.191729 0.158734i
\(607\) −0.921022 + 1.59526i −0.0373831 + 0.0647495i −0.884112 0.467276i \(-0.845236\pi\)
0.846728 + 0.532025i \(0.178569\pi\)
\(608\) 14.9061 + 8.60605i 0.604523 + 0.349022i
\(609\) −4.63937 25.9325i −0.187997 1.05084i
\(610\) −29.3457 + 17.4516i −1.18817 + 0.706594i
\(611\) 25.8180i 1.04448i
\(612\) 9.55766 + 27.3795i 0.386345 + 1.10675i
\(613\) 9.18979i 0.371172i 0.982628 + 0.185586i \(0.0594184\pi\)
−0.982628 + 0.185586i \(0.940582\pi\)
\(614\) 2.32858 + 4.03322i 0.0939740 + 0.162768i
\(615\) 4.66701 + 25.5263i 0.188192 + 1.02932i
\(616\) 2.40908 + 4.08630i 0.0970646 + 0.164642i
\(617\) −20.9885 + 36.3531i −0.844965 + 1.46352i 0.0406875 + 0.999172i \(0.487045\pi\)
−0.885652 + 0.464350i \(0.846288\pi\)
\(618\) −3.18381 1.18269i −0.128072 0.0475746i
\(619\) 5.76384 3.32775i 0.231668 0.133754i −0.379673 0.925121i \(-0.623964\pi\)
0.611341 + 0.791367i \(0.290630\pi\)
\(620\) −0.237348 18.3886i −0.00953212 0.738504i
\(621\) 0.0804776 + 0.00159489i 0.00322946 + 6.40007e-5i
\(622\) −48.6912 −1.95234
\(623\) 0.0674598 + 7.41166i 0.00270272 + 0.296942i
\(624\) −35.0966 13.0373i −1.40499 0.521908i
\(625\) −11.3661 + 22.2668i −0.454644 + 0.890673i
\(626\) −18.9832 + 32.8799i −0.758722 + 1.31415i
\(627\) 1.40136 + 8.26643i 0.0559650 + 0.330129i
\(628\) −8.87371 15.3697i −0.354099 0.613318i
\(629\) 70.7514 2.82104
\(630\) −21.1769 + 25.6934i −0.843708 + 1.02365i
\(631\) 40.6463 1.61810 0.809051 0.587738i \(-0.199982\pi\)
0.809051 + 0.587738i \(0.199982\pi\)
\(632\) −1.40980 2.44185i −0.0560790 0.0971316i
\(633\) 14.1692 11.7308i 0.563176 0.466257i
\(634\) 9.78047 16.9403i 0.388432 0.672784i
\(635\) −4.93559 2.76525i −0.195863 0.109736i
\(636\) −2.75658 + 2.28219i −0.109306 + 0.0904948i
\(637\) 15.4872 27.9891i 0.613625 1.10897i
\(638\) −21.4461 −0.849060
\(639\) −15.2438 + 17.6871i −0.603037 + 0.699689i
\(640\) −15.6615 + 0.202148i −0.619075 + 0.00799061i
\(641\) −35.8005 + 20.6694i −1.41403 + 0.816393i −0.995765 0.0919301i \(-0.970696\pi\)
−0.418269 + 0.908323i \(0.637363\pi\)
\(642\) −6.36357 37.5378i −0.251150 1.48150i
\(643\) −4.89772 + 8.48311i −0.193147 + 0.334541i −0.946292 0.323314i \(-0.895203\pi\)
0.753144 + 0.657855i \(0.228536\pi\)
\(644\) 0.0536444 0.0316261i 0.00211388 0.00124624i
\(645\) 11.9542 33.4991i 0.470695 1.31903i
\(646\) −14.5270 25.1615i −0.571557 0.989966i
\(647\) 32.9147i 1.29401i −0.762486 0.647005i \(-0.776021\pi\)
0.762486 0.647005i \(-0.223979\pi\)
\(648\) −1.19747 8.02563i −0.0470410 0.315277i
\(649\) 4.48500i 0.176052i
\(650\) −22.3831 36.5560i −0.877939 1.43385i
\(651\) −18.9618 + 15.9917i −0.743171 + 0.626763i
\(652\) 10.5918 + 6.11518i 0.414807 + 0.239489i
\(653\) 15.2724 26.4526i 0.597655 1.03517i −0.395511 0.918461i \(-0.629432\pi\)
0.993166 0.116708i \(-0.0372343\pi\)
\(654\) 9.85775 + 58.1495i 0.385469 + 2.27382i
\(655\) 1.72484 + 2.90041i 0.0673952 + 0.113328i
\(656\) −31.6930 −1.23740
\(657\) 12.9783 + 11.1855i 0.506330 + 0.436388i
\(658\) 13.7996 24.4120i 0.537963 0.951679i
\(659\) −17.3536 + 10.0191i −0.676001 + 0.390289i −0.798347 0.602198i \(-0.794292\pi\)
0.122346 + 0.992488i \(0.460958\pi\)
\(660\) 7.57818 + 8.91661i 0.294980 + 0.347079i
\(661\) 21.5858 + 12.4625i 0.839588 + 0.484737i 0.857124 0.515110i \(-0.172249\pi\)
−0.0175359 + 0.999846i \(0.505582\pi\)
\(662\) −28.0400 + 48.5667i −1.08981 + 1.88760i
\(663\) 32.1128 + 38.7880i 1.24716 + 1.50640i
\(664\) −2.94648 + 1.70115i −0.114346 + 0.0660176i
\(665\) 6.92449 12.6274i 0.268520 0.489671i
\(666\) 61.4881 + 11.6815i 2.38261 + 0.452650i
\(667\) 0.0890541i 0.00344819i
\(668\) 17.9513 10.3642i 0.694556 0.401002i
\(669\) −2.32345 13.7057i −0.0898299 0.529894i
\(670\) −40.4248 22.6487i −1.56174 0.874995i
\(671\) 8.09261 14.0168i 0.312412 0.541113i
\(672\) −20.8896 24.7694i −0.805832 0.955499i
\(673\) 15.4480 8.91892i 0.595477 0.343799i −0.171783 0.985135i \(-0.554953\pi\)
0.767260 + 0.641336i \(0.221619\pi\)
\(674\) 43.4032i 1.67183i
\(675\) 12.8552 22.5775i 0.494797 0.869009i
\(676\) 11.9767 0.460642
\(677\) 5.06781 2.92590i 0.194772 0.112452i −0.399443 0.916758i \(-0.630796\pi\)
0.594214 + 0.804307i \(0.297463\pi\)
\(678\) 35.0856 + 13.0332i 1.34745 + 0.500536i
\(679\) 18.8604 11.1192i 0.723796 0.426714i
\(680\) 11.1898 + 6.26929i 0.429110 + 0.240416i
\(681\) −9.77627 + 1.65732i −0.374627 + 0.0635085i
\(682\) 10.0965 + 17.4877i 0.386615 + 0.669637i
\(683\) −28.5292 −1.09164 −0.545819 0.837903i \(-0.683782\pi\)
−0.545819 + 0.837903i \(0.683782\pi\)
\(684\) −3.65697 10.4760i −0.139828 0.400560i
\(685\) −14.2370 + 0.183762i −0.543967 + 0.00702117i
\(686\) 29.6038 18.1871i 1.13028 0.694385i
\(687\) 8.08774 + 9.76891i 0.308566 + 0.372707i
\(688\) 37.6208 + 21.7204i 1.43428 + 0.828082i
\(689\) −3.10710 + 5.38165i −0.118371 + 0.205025i
\(690\) −0.0857633 + 0.0728898i −0.00326495 + 0.00277487i
\(691\) 18.2090 10.5130i 0.692703 0.399932i −0.111921 0.993717i \(-0.535700\pi\)
0.804624 + 0.593785i \(0.202367\pi\)
\(692\) 3.34072i 0.126995i
\(693\) 2.80465 15.5325i 0.106540 0.590032i
\(694\) −8.65266 −0.328450
\(695\) 32.3471 19.2365i 1.22700 0.729681i
\(696\) −8.85118 + 1.50049i −0.335503 + 0.0568760i
\(697\) 36.9159 + 21.3134i 1.39829 + 0.807302i
\(698\) 58.0769 + 33.5307i 2.19824 + 1.26916i
\(699\) −42.6243 15.8336i −1.61220 0.598881i
\(700\) −0.701638 20.0875i −0.0265194 0.759237i
\(701\) 43.0100i 1.62446i 0.583335 + 0.812232i \(0.301748\pi\)
−0.583335 + 0.812232i \(0.698252\pi\)
\(702\) 21.5042 + 39.0116i 0.811623 + 1.47240i
\(703\) −27.0711 −1.02100
\(704\) −6.55148 + 3.78250i −0.246918 + 0.142558i
\(705\) −7.35419 + 20.6086i −0.276975 + 0.776166i
\(706\) 5.20175 + 3.00323i 0.195770 + 0.113028i
\(707\) 4.29792 2.53384i 0.161640 0.0952949i
\(708\) −0.992055 5.85199i −0.0372837 0.219931i
\(709\) −14.3836 24.9131i −0.540187 0.935632i −0.998893 0.0470434i \(-0.985020\pi\)
0.458706 0.888588i \(-0.348313\pi\)
\(710\) −0.421385 32.6469i −0.0158143 1.22522i
\(711\) −1.75106 + 9.21706i −0.0656699 + 0.345667i
\(712\) 2.52582 0.0946591
\(713\) −0.0726168 + 0.0419253i −0.00271952 + 0.00157012i
\(714\) 9.63207 + 53.8398i 0.360471 + 2.01490i
\(715\) 17.7270 + 9.93185i 0.662951 + 0.371430i
\(716\) 11.7487 + 6.78314i 0.439071 + 0.253498i
\(717\) 14.8486 + 17.9351i 0.554532 + 0.669800i
\(718\) −41.3613 + 23.8800i −1.54359 + 0.891192i
\(719\) 38.4513 1.43399 0.716996 0.697077i \(-0.245517\pi\)
0.716996 + 0.697077i \(0.245517\pi\)
\(720\) 24.3014 + 20.4039i 0.905660 + 0.760407i
\(721\) −2.40746 1.36089i −0.0896586 0.0506820i
\(722\) −12.2637 21.2414i −0.456408 0.790522i
\(723\) 10.1827 1.72621i 0.378698 0.0641986i
\(724\) 3.68836 + 2.12947i 0.137077 + 0.0791413i
\(725\) −25.2556 13.7246i −0.937968 0.509721i
\(726\) 21.4608 + 7.97200i 0.796484 + 0.295869i
\(727\) −10.8862 18.8555i −0.403747 0.699310i 0.590428 0.807091i \(-0.298959\pi\)
−0.994175 + 0.107780i \(0.965626\pi\)
\(728\) −9.48959 5.36425i −0.351707 0.198812i
\(729\) −14.4158 + 22.8295i −0.533919 + 0.845535i
\(730\) −23.9554 + 0.309200i −0.886629 + 0.0114440i
\(731\) −29.2137 50.5996i −1.08051 1.87149i
\(732\) −7.45873 + 20.0790i −0.275683 + 0.742143i
\(733\) 9.32775 16.1561i 0.344528 0.596741i −0.640740 0.767758i \(-0.721372\pi\)
0.985268 + 0.171018i \(0.0547055\pi\)
\(734\) 21.9741 38.0603i 0.811081 1.40483i
\(735\) −20.3349 + 17.9302i −0.750065 + 0.661364i
\(736\) −0.0547661 0.0948577i −0.00201871 0.00349650i
\(737\) 21.9659 0.809123
\(738\) 28.5635 + 24.6179i 1.05144 + 0.906197i
\(739\) 37.9840 1.39727 0.698633 0.715480i \(-0.253792\pi\)
0.698633 + 0.715480i \(0.253792\pi\)
\(740\) −32.4741 + 19.3120i −1.19377 + 0.709924i
\(741\) −12.2871 14.8412i −0.451377 0.545203i
\(742\) −5.81435 + 3.42785i −0.213452 + 0.125840i
\(743\) 11.1994 19.3979i 0.410865 0.711640i −0.584119 0.811668i \(-0.698560\pi\)
0.994985 + 0.100028i \(0.0318933\pi\)
\(744\) 5.39054 + 6.51105i 0.197627 + 0.238707i
\(745\) −17.1316 + 10.1880i −0.627652 + 0.373258i
\(746\) 33.7630i 1.23615i
\(747\) 11.1219 + 2.11294i 0.406928 + 0.0773083i
\(748\) 19.2226 0.702848
\(749\) −0.282154 30.9997i −0.0103097 1.13270i
\(750\) 7.45393 + 35.5558i 0.272179 + 1.29831i
\(751\) 15.9993 27.7115i 0.583821 1.01121i −0.411200 0.911545i \(-0.634890\pi\)
0.995021 0.0996631i \(-0.0317765\pi\)
\(752\) −23.1443 13.3624i −0.843985 0.487275i
\(753\) −8.81282 3.27368i −0.321157 0.119300i
\(754\) 42.6807 24.6417i 1.55434 0.897398i
\(755\) −25.6743 + 0.331386i −0.934382 + 0.0120604i
\(756\) −0.223785 + 20.8871i −0.00813897 + 0.759656i
\(757\) 27.6125i 1.00359i 0.864985 + 0.501797i \(0.167328\pi\)
−0.864985 + 0.501797i \(0.832672\pi\)
\(758\) 0.775928 + 1.34395i 0.0281830 + 0.0488143i
\(759\) 0.0185794 0.0500160i 0.000674389 0.00181547i
\(760\) −4.28147 2.39877i −0.155305 0.0870125i
\(761\) 5.85711 10.1448i 0.212320 0.367749i −0.740120 0.672475i \(-0.765231\pi\)
0.952440 + 0.304725i \(0.0985647\pi\)
\(762\) −8.10546 + 1.37407i −0.293630 + 0.0497774i
\(763\) 0.437083 + 48.0213i 0.0158235 + 1.73849i
\(764\) 4.69682i 0.169925i
\(765\) −14.5847 40.1089i −0.527310 1.45014i
\(766\) 47.7242i 1.72435i
\(767\) −5.15329 8.92576i −0.186074 0.322290i
\(768\) −27.6826 + 22.9186i −0.998911 + 0.827004i
\(769\) −7.29834 4.21370i −0.263185 0.151950i 0.362602 0.931944i \(-0.381889\pi\)
−0.625787 + 0.779994i \(0.715222\pi\)
\(770\) 11.4531 + 18.8659i 0.412740 + 0.679881i
\(771\) 18.5401 + 22.3940i 0.667706 + 0.806500i
\(772\) −3.73193 + 2.15463i −0.134315 + 0.0775469i
\(773\) 17.3296i 0.623303i −0.950197 0.311651i \(-0.899118\pi\)
0.950197 0.311651i \(-0.100882\pi\)
\(774\) −17.0345 48.7981i −0.612291 1.75401i
\(775\) 0.698541 + 27.0553i 0.0250923 + 0.971857i
\(776\) −3.73049 6.46140i −0.133917 0.231951i
\(777\) 47.9317 + 17.3103i 1.71954 + 0.621005i
\(778\) −10.7096 6.18317i −0.383957 0.221678i
\(779\) −14.1248 8.15497i −0.506074 0.292182i
\(780\) −25.3269 9.03789i −0.906847 0.323608i
\(781\) 7.73871 + 13.4038i 0.276913 + 0.479627i
\(782\) 0.184890i 0.00661166i
\(783\) 25.5685 + 15.4454i 0.913742 + 0.551973i
\(784\) −17.0750 28.3694i −0.609821 1.01319i
\(785\) 13.3501 + 22.4488i 0.476485 + 0.801233i
\(786\) 4.59679 + 1.70756i 0.163962 + 0.0609067i
\(787\) −21.4506 + 37.1536i −0.764633 + 1.32438i 0.175808 + 0.984425i \(0.443746\pi\)
−0.940440 + 0.339959i \(0.889587\pi\)
\(788\) 11.3403 19.6419i 0.403980 0.699714i
\(789\) −7.42193 43.7809i −0.264228 1.55864i
\(790\) −6.70542 11.2755i −0.238568 0.401164i
\(791\) 26.5302 + 14.9969i 0.943305 + 0.533229i
\(792\) −5.28420 1.00389i −0.187766 0.0356718i
\(793\) 37.1938i 1.32079i
\(794\) −6.79818 11.7748i −0.241258 0.417872i
\(795\) 4.01312 3.41073i 0.142331 0.120966i
\(796\) 30.2990 + 17.4931i 1.07392 + 0.620028i
\(797\) −32.8167 18.9467i −1.16243 0.671127i −0.210542 0.977585i \(-0.567523\pi\)
−0.951884 + 0.306458i \(0.900856\pi\)
\(798\) −3.68544 20.6003i −0.130463 0.729243i
\(799\) 17.9722 + 31.1288i 0.635812 + 1.10126i
\(800\) −35.3418 + 0.912489i −1.24952 + 0.0322613i
\(801\) −6.36620 5.48680i −0.224939 0.193867i
\(802\) 46.9767i 1.65880i
\(803\) 9.83536 5.67845i 0.347082 0.200388i
\(804\) −28.6609 + 4.85872i −1.01079 + 0.171354i
\(805\) −0.0783400 + 0.0475584i −0.00276112 + 0.00167621i
\(806\) −40.1869 23.2019i −1.41552 0.817252i
\(807\) −48.1312 17.8792i −1.69430 0.629379i
\(808\) −0.850106 1.47243i −0.0299066 0.0517998i
\(809\) 7.63719i 0.268509i 0.990947 + 0.134255i \(0.0428640\pi\)
−0.990947 + 0.134255i \(0.957136\pi\)
\(810\) −6.05287 37.2655i −0.212676 1.30938i
\(811\) 4.82929i 0.169579i 0.996399 + 0.0847897i \(0.0270218\pi\)
−0.996399 + 0.0847897i \(0.972978\pi\)
\(812\) 23.1088 0.210333i 0.810961 0.00738125i
\(813\) −5.65764 + 15.2305i −0.198422 + 0.534156i
\(814\) 20.7433 35.9285i 0.727052 1.25929i
\(815\) −15.7026 8.79764i −0.550037 0.308168i
\(816\) 51.3914 8.71210i 1.79906 0.304984i
\(817\) 11.1778 + 19.3605i 0.391062 + 0.677339i
\(818\) 19.7521i 0.690618i
\(819\) 12.2653 + 34.1344i 0.428585 + 1.19275i
\(820\) −22.7616 + 0.293791i −0.794869 + 0.0102596i
\(821\) 21.0849 12.1734i 0.735869 0.424854i −0.0846966 0.996407i \(-0.526992\pi\)
0.820565 + 0.571553i \(0.193659\pi\)
\(822\) −15.9371 + 13.1944i −0.555870 + 0.460208i
\(823\) 14.8597 + 8.57926i 0.517977 + 0.299054i 0.736106 0.676866i \(-0.236662\pi\)
−0.218130 + 0.975920i \(0.569996\pi\)
\(824\) −0.471205 + 0.816150i −0.0164152 + 0.0284319i
\(825\) −11.3211 12.9773i −0.394149 0.451813i
\(826\) −0.101887 11.1941i −0.00354510 0.389492i
\(827\) −14.8501 −0.516388 −0.258194 0.966093i \(-0.583127\pi\)
−0.258194 + 0.966093i \(0.583127\pi\)
\(828\) −0.0131790 + 0.0693702i −0.000458001 + 0.00241078i
\(829\) 53.9443i 1.87356i −0.349915 0.936781i \(-0.613790\pi\)
0.349915 0.936781i \(-0.386210\pi\)
\(830\) −13.6057 + 8.09116i −0.472261 + 0.280848i
\(831\) 11.0082 1.86616i 0.381871 0.0647364i
\(832\) 8.69223 15.0554i 0.301349 0.521951i
\(833\) 0.810629 + 44.5274i 0.0280866 + 1.54278i
\(834\) 19.0437 51.2661i 0.659431 1.77520i
\(835\) −26.2195 + 15.5924i −0.907362 + 0.539599i
\(836\) −7.35499 −0.254378
\(837\) 0.557288 28.1206i 0.0192627 0.971990i
\(838\) −35.6614 −1.23190
\(839\) 18.3115 + 31.7164i 0.632182 + 1.09497i 0.987105 + 0.160076i \(0.0511738\pi\)
−0.354923 + 0.934896i \(0.615493\pi\)
\(840\) 6.04685 + 6.98498i 0.208636 + 0.241005i
\(841\) 2.02419 3.50600i 0.0697996 0.120896i
\(842\) 12.4338 21.5360i 0.428498 0.742180i
\(843\) −9.53163 + 1.61584i −0.328287 + 0.0556526i
\(844\) 8.06831 + 13.9747i 0.277723 + 0.481030i
\(845\) −17.6244 + 0.227484i −0.606297 + 0.00782567i
\(846\) 10.4796 + 30.0205i 0.360295 + 1.03213i
\(847\) 16.2277 + 9.17317i 0.557591 + 0.315194i
\(848\) 3.21622 + 5.57065i 0.110445 + 0.191297i
\(849\) 12.0018 9.93637i 0.411901 0.341015i
\(850\) 52.4345 + 28.4945i 1.79849 + 0.977354i
\(851\) 0.149191 + 0.0861357i 0.00511422 + 0.00295269i
\(852\) −13.0622 15.7775i −0.447505 0.540527i
\(853\) 2.99570 + 5.18871i 0.102571 + 0.177658i 0.912743 0.408534i \(-0.133960\pi\)
−0.810172 + 0.586192i \(0.800626\pi\)
\(854\) −19.8799 + 35.1683i −0.680275 + 1.20343i
\(855\) 5.58041 + 15.3466i 0.190846 + 0.524841i
\(856\) −10.5644 −0.361083
\(857\) −11.2002 + 6.46642i −0.382590 + 0.220889i −0.678945 0.734189i \(-0.737562\pi\)
0.296354 + 0.955078i \(0.404229\pi\)
\(858\) 29.1121 4.93520i 0.993869 0.168485i
\(859\) 47.2402 + 27.2741i 1.61181 + 0.930582i 0.988950 + 0.148252i \(0.0473647\pi\)
0.622865 + 0.782329i \(0.285969\pi\)
\(860\) 27.2202 + 15.2506i 0.928202 + 0.520042i
\(861\) 19.7946 + 23.4711i 0.674599 + 0.799892i
\(862\) 11.7934 6.80889i 0.401683 0.231912i
\(863\) 36.1168 1.22943 0.614714 0.788750i \(-0.289271\pi\)
0.614714 + 0.788750i \(0.289271\pi\)
\(864\) 36.7333 + 0.727973i 1.24969 + 0.0247661i
\(865\) 0.0634532 + 4.91605i 0.00215747 + 0.167151i
\(866\) −14.6283 25.3369i −0.497088 0.860982i
\(867\) −38.1174 14.1594i −1.29453 0.480878i
\(868\) −11.0508 18.7445i −0.375089 0.636229i
\(869\) 5.38568 + 3.10942i 0.182697 + 0.105480i
\(870\) −41.0880 + 7.51219i −1.39301 + 0.254687i
\(871\) −43.7151 + 25.2389i −1.48123 + 0.855188i
\(872\) 16.3652 0.554196
\(873\) −4.63349 + 24.3893i −0.156820 + 0.825454i
\(874\) 0.0707431i 0.00239292i
\(875\) 1.41404 + 29.5466i 0.0478032 + 0.998857i
\(876\) −11.5771 + 9.58471i −0.391152 + 0.323837i
\(877\) −42.8491 24.7389i −1.44691 0.835375i −0.448615 0.893725i \(-0.648083\pi\)
−0.998296 + 0.0583505i \(0.981416\pi\)
\(878\) 53.8457 + 31.0878i 1.81720 + 1.04916i
\(879\) −19.4448 23.4867i −0.655856 0.792186i
\(880\) 18.0781 10.7508i 0.609411 0.362410i
\(881\) −31.2573 −1.05309 −0.526543 0.850148i \(-0.676512\pi\)
−0.526543 + 0.850148i \(0.676512\pi\)
\(882\) −6.64726 + 38.8313i −0.223825 + 1.30752i
\(883\) 27.7767i 0.934761i −0.884056 0.467380i \(-0.845198\pi\)
0.884056 0.467380i \(-0.154802\pi\)
\(884\) −38.2556 + 22.0869i −1.28667 + 0.742862i
\(885\) 1.57102 + 8.59268i 0.0528091 + 0.288840i
\(886\) −4.85057 + 8.40144i −0.162958 + 0.282252i
\(887\) −14.8268 8.56024i −0.497834 0.287425i 0.229984 0.973194i \(-0.426132\pi\)
−0.727819 + 0.685769i \(0.759466\pi\)
\(888\) 6.04736 16.2796i 0.202936 0.546308i
\(889\) −6.69370 + 0.0609250i −0.224499 + 0.00204336i
\(890\) 11.7508 0.151672i 0.393888 0.00508404i
\(891\) 11.1378 + 14.0091i 0.373131 + 0.469321i
\(892\) 12.1945 0.408304
\(893\) −6.87657 11.9106i −0.230116 0.398572i
\(894\) −10.0859 + 27.1514i −0.337322 + 0.908078i
\(895\) −17.4178 9.75861i −0.582211 0.326194i
\(896\) −15.9646 + 9.41193i −0.533340 + 0.314431i
\(897\) 0.0204932 + 0.120887i 0.000684249 + 0.00403629i
\(898\) 8.98465 5.18729i 0.299822 0.173102i
\(899\) −31.1174 −1.03782
\(900\) 17.6422 + 14.4286i 0.588072 + 0.480953i
\(901\) 8.65156i 0.288225i
\(902\) 21.6464 12.4975i 0.720746 0.416123i
\(903\) −7.41140 41.4271i −0.246636 1.37861i
\(904\) 5.19267 8.99396i 0.172706 0.299135i
\(905\) −5.46807 3.06358i −0.181765 0.101837i
\(906\) −28.7401 + 23.7941i −0.954827 + 0.790507i
\(907\) −1.51269 + 0.873352i −0.0502280 + 0.0289992i −0.524904 0.851162i \(-0.675899\pi\)
0.474676 + 0.880161i \(0.342565\pi\)
\(908\) 8.69836i 0.288665i
\(909\) −1.05588 + 5.55785i −0.0350214 + 0.184342i
\(910\) −44.4703 24.3861i −1.47417 0.808392i
\(911\) 36.4462 21.0422i 1.20752 0.697161i 0.245301 0.969447i \(-0.421113\pi\)
0.962216 + 0.272286i \(0.0877798\pi\)
\(912\) −19.6635 + 3.33344i −0.651123 + 0.110381i
\(913\) 3.75202 6.49868i 0.124174 0.215075i
\(914\) 11.5135 + 6.64732i 0.380833 + 0.219874i
\(915\) 10.5946 29.6891i 0.350245 0.981492i
\(916\) −9.63481 + 5.56266i −0.318343 + 0.183795i
\(917\) 3.47589 + 1.96484i 0.114784 + 0.0648849i
\(918\) −53.0841 32.0670i −1.75204 1.05837i
\(919\) −31.6249 −1.04321 −0.521604 0.853187i \(-0.674666\pi\)
−0.521604 + 0.853187i \(0.674666\pi\)
\(920\) 0.0159631 + 0.0268428i 0.000526288 + 0.000884980i
\(921\) −4.03069 1.49727i −0.132816 0.0493368i
\(922\) 22.4420 38.8707i 0.739089 1.28014i
\(923\) −30.8022 17.7836i −1.01387 0.585356i
\(924\) 13.0227 + 4.70308i 0.428414 + 0.154720i
\(925\) 47.4207 29.0355i 1.55918 0.954682i
\(926\) 38.2814i 1.25801i
\(927\) 2.96056 1.03348i 0.0972376 0.0339438i
\(928\) 40.6479i 1.33433i
\(929\) −9.90204 17.1508i −0.324875 0.562701i 0.656612 0.754229i \(-0.271989\pi\)
−0.981487 + 0.191528i \(0.938656\pi\)
\(930\) 25.4692 + 29.9675i 0.835169 + 0.982673i
\(931\) −0.310165 17.0371i −0.0101652 0.558370i
\(932\) 19.9438 34.5436i 0.653280 1.13151i
\(933\) 34.6275 28.6683i 1.13365 0.938560i
\(934\) 30.5615 17.6447i 1.00000 0.577351i
\(935\) −28.2871 + 0.365111i −0.925088 + 0.0119404i
\(936\) 11.6698 4.07369i 0.381438 0.133153i
\(937\) 37.2793 1.21786 0.608932 0.793223i \(-0.291598\pi\)
0.608932 + 0.793223i \(0.291598\pi\)
\(938\) −54.8245 + 0.499004i −1.79008 + 0.0162931i
\(939\) −5.85876 34.5600i −0.191194 1.12782i
\(940\) −16.7459 9.38216i −0.546189 0.306012i
\(941\) 7.34570 12.7231i 0.239463 0.414762i −0.721097 0.692834i \(-0.756362\pi\)
0.960560 + 0.278072i \(0.0896953\pi\)
\(942\) 35.5786 + 13.2163i 1.15921 + 0.430611i
\(943\) 0.0518955 + 0.0898857i 0.00168995 + 0.00292708i
\(944\) −10.6685 −0.347231
\(945\) −0.0674150 30.7408i −0.00219301 0.999998i
\(946\) −34.2601 −1.11389
\(947\) −5.59021 9.68252i −0.181657 0.314640i 0.760788 0.649001i \(-0.224813\pi\)
−0.942445 + 0.334361i \(0.891479\pi\)
\(948\) −7.71497 2.86587i −0.250571 0.0930791i
\(949\) −13.0491 + 22.6018i −0.423593 + 0.733684i
\(950\) −20.0626 10.9026i −0.650917 0.353728i
\(951\) 3.01853 + 17.8059i 0.0978826 + 0.577395i
\(952\) 15.1757 0.138127i 0.491849 0.00447673i
\(953\) −23.5964 −0.764363 −0.382182 0.924087i \(-0.624827\pi\)
−0.382182 + 0.924087i \(0.624827\pi\)
\(954\) 1.42843 7.51882i 0.0462471 0.243431i
\(955\) 0.0892107 + 6.91163i 0.00288679 + 0.223655i
\(956\) −17.6890 + 10.2127i −0.572102 + 0.330303i
\(957\) 15.2517 12.6270i 0.493019 0.408173i
\(958\) −4.33486 + 7.50820i −0.140053 + 0.242579i
\(959\) −14.5125 + 8.55586i −0.468634 + 0.276283i
\(960\) −11.2269 + 9.54165i −0.362345 + 0.307955i
\(961\) −0.850410 1.47295i −0.0274326 0.0475146i
\(962\) 95.3367i 3.07378i
\(963\) 26.6270 + 22.9489i 0.858044 + 0.739518i
\(964\) 9.05996i 0.291802i
\(965\) 5.45082 3.24155i 0.175468 0.104349i
\(966\) −0.0452360 + 0.125257i −0.00145544 + 0.00403007i
\(967\) 18.4286 + 10.6397i 0.592623 + 0.342151i 0.766134 0.642681i \(-0.222178\pi\)
−0.173511 + 0.984832i \(0.555511\pi\)
\(968\) 3.17620 5.50133i 0.102087 0.176820i
\(969\) 25.1457 + 9.34082i 0.807795 + 0.300071i
\(970\) −17.7432 29.8362i −0.569701 0.957982i
\(971\) 33.6174 1.07884 0.539418 0.842038i \(-0.318644\pi\)
0.539418 + 0.842038i \(0.318644\pi\)
\(972\) −17.6312 15.8153i −0.565522 0.507276i
\(973\) 21.9131 38.7652i 0.702503 1.24276i
\(974\) −46.5341 + 26.8665i −1.49105 + 0.860857i
\(975\) 37.4415 + 12.8187i 1.19909 + 0.410527i
\(976\) 33.3420 + 19.2500i 1.06725 + 0.616178i
\(977\) 24.4165 42.2905i 0.781151 1.35299i −0.150120 0.988668i \(-0.547966\pi\)
0.931271 0.364326i \(-0.118701\pi\)
\(978\) −25.7875 + 4.37161i −0.824593 + 0.139789i
\(979\) −4.82452 + 2.78544i −0.154192 + 0.0890230i
\(980\) −12.5261 20.2163i −0.400131 0.645786i
\(981\) −41.2477 35.5499i −1.31694 1.13502i
\(982\) 36.1361i 1.15315i
\(983\) −35.7407 + 20.6349i −1.13995 + 0.658152i −0.946419 0.322942i \(-0.895328\pi\)
−0.193533 + 0.981094i \(0.561995\pi\)
\(984\) 8.05944 6.67246i 0.256926 0.212710i
\(985\) −16.3147 + 29.1195i −0.519831 + 0.927826i
\(986\) −34.3068 + 59.4211i −1.09255 + 1.89235i
\(987\) 4.55948 + 25.4859i 0.145130 + 0.811225i
\(988\) 14.6374 8.45093i 0.465679 0.268860i
\(989\) 0.142264i 0.00452373i
\(990\) −24.6438 4.35308i −0.783232 0.138350i
\(991\) −23.2358 −0.738109 −0.369054 0.929408i \(-0.620318\pi\)
−0.369054 + 0.929408i \(0.620318\pi\)
\(992\) −33.1453 + 19.1364i −1.05236 + 0.607582i
\(993\) −8.65394 51.0484i −0.274625 1.61997i
\(994\) −19.6195 33.2788i −0.622293 1.05554i
\(995\) −44.9189 25.1666i −1.42403 0.797836i
\(996\) −3.45813 + 9.30935i −0.109575 + 0.294978i
\(997\) −15.2901 26.4833i −0.484243 0.838733i 0.515593 0.856834i \(-0.327572\pi\)
−0.999836 + 0.0181001i \(0.994238\pi\)
\(998\) 41.7669 1.32211
\(999\) −50.6061 + 27.8954i −1.60111 + 0.882570i
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 315.2.z.b.104.10 yes 80
3.2 odd 2 945.2.z.b.314.31 80
5.4 even 2 inner 315.2.z.b.104.31 yes 80
7.6 odd 2 inner 315.2.z.b.104.9 80
9.2 odd 6 inner 315.2.z.b.209.32 yes 80
9.7 even 3 945.2.z.b.629.10 80
15.14 odd 2 945.2.z.b.314.9 80
21.20 even 2 945.2.z.b.314.32 80
35.34 odd 2 inner 315.2.z.b.104.32 yes 80
45.29 odd 6 inner 315.2.z.b.209.9 yes 80
45.34 even 6 945.2.z.b.629.32 80
63.20 even 6 inner 315.2.z.b.209.31 yes 80
63.34 odd 6 945.2.z.b.629.9 80
105.104 even 2 945.2.z.b.314.10 80
315.34 odd 6 945.2.z.b.629.31 80
315.209 even 6 inner 315.2.z.b.209.10 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.z.b.104.9 80 7.6 odd 2 inner
315.2.z.b.104.10 yes 80 1.1 even 1 trivial
315.2.z.b.104.31 yes 80 5.4 even 2 inner
315.2.z.b.104.32 yes 80 35.34 odd 2 inner
315.2.z.b.209.9 yes 80 45.29 odd 6 inner
315.2.z.b.209.10 yes 80 315.209 even 6 inner
315.2.z.b.209.31 yes 80 63.20 even 6 inner
315.2.z.b.209.32 yes 80 9.2 odd 6 inner
945.2.z.b.314.9 80 15.14 odd 2
945.2.z.b.314.10 80 105.104 even 2
945.2.z.b.314.31 80 3.2 odd 2
945.2.z.b.314.32 80 21.20 even 2
945.2.z.b.629.9 80 63.34 odd 6
945.2.z.b.629.10 80 9.7 even 3
945.2.z.b.629.31 80 315.34 odd 6
945.2.z.b.629.32 80 45.34 even 6