Properties

Label 315.2.bh.c.169.14
Level $315$
Weight $2$
Character 315.169
Analytic conductor $2.515$
Analytic rank $0$
Dimension $64$
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] = [315,2,Mod(169,315)]
 
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([4, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bh (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: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 169.14
Character \(\chi\) \(=\) 315.169
Dual form 315.2.bh.c.274.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.293339 - 0.169359i) q^{2} +(0.530399 + 1.64884i) q^{3} +(-0.942635 - 1.63269i) q^{4} +(-2.22372 - 0.234648i) q^{5} +(0.123660 - 0.573497i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.31601i q^{8} +(-2.43735 + 1.74909i) q^{9} +O(q^{10})\) \(q+(-0.293339 - 0.169359i) q^{2} +(0.530399 + 1.64884i) q^{3} +(-0.942635 - 1.63269i) q^{4} +(-2.22372 - 0.234648i) q^{5} +(0.123660 - 0.573497i) q^{6} +(0.866025 + 0.500000i) q^{7} +1.31601i q^{8} +(-2.43735 + 1.74909i) q^{9} +(0.612564 + 0.445440i) q^{10} +(-2.50084 + 4.33159i) q^{11} +(2.19208 - 2.42023i) q^{12} +(-1.80151 + 1.04011i) q^{13} +(-0.169359 - 0.293339i) q^{14} +(-0.792563 - 3.79102i) q^{15} +(-1.66239 + 2.87934i) q^{16} +1.41082i q^{17} +(1.01120 - 0.100287i) q^{18} -0.0403908 q^{19} +(1.71305 + 3.85184i) q^{20} +(-0.365081 + 1.69314i) q^{21} +(1.46719 - 0.847082i) q^{22} +(-6.00558 + 3.46732i) q^{23} +(-2.16990 + 0.698012i) q^{24} +(4.88988 + 1.04358i) q^{25} +0.704606 q^{26} +(-4.17674 - 3.09109i) q^{27} -1.88527i q^{28} +(3.39829 - 5.88601i) q^{29} +(-0.409555 + 1.24628i) q^{30} +(-5.17476 - 8.96294i) q^{31} +(3.25469 - 1.87910i) q^{32} +(-8.46855 - 1.82602i) q^{33} +(0.238936 - 0.413849i) q^{34} +(-1.80848 - 1.31507i) q^{35} +(5.15326 + 2.33069i) q^{36} +2.86105i q^{37} +(0.0118482 + 0.00684056i) q^{38} +(-2.67049 - 2.41874i) q^{39} +(0.308800 - 2.92645i) q^{40} +(4.37745 + 7.58197i) q^{41} +(0.393841 - 0.434833i) q^{42} +(7.27932 + 4.20272i) q^{43} +9.42953 q^{44} +(5.83042 - 3.31757i) q^{45} +2.34889 q^{46} +(-6.55370 - 3.78378i) q^{47} +(-5.62931 - 1.21382i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.25765 - 1.13427i) q^{50} +(-2.32622 + 0.748298i) q^{51} +(3.39634 + 1.96088i) q^{52} +9.89525i q^{53} +(0.701695 + 1.61411i) q^{54} +(6.57758 - 9.04543i) q^{55} +(-0.658007 + 1.13970i) q^{56} +(-0.0214233 - 0.0665980i) q^{57} +(-1.99370 + 1.15106i) q^{58} +(2.86271 + 4.95837i) q^{59} +(-5.44247 + 4.86756i) q^{60} +(3.19419 - 5.53251i) q^{61} +3.50557i q^{62} +(-2.98535 + 0.296078i) q^{63} +5.37659 q^{64} +(4.25013 - 1.89018i) q^{65} +(2.17490 + 1.96987i) q^{66} +(6.22427 - 3.59358i) q^{67} +(2.30343 - 1.32989i) q^{68} +(-8.90242 - 8.06318i) q^{69} +(0.307777 + 0.692044i) q^{70} +0.459791 q^{71} +(-2.30182 - 3.20759i) q^{72} -1.72878i q^{73} +(0.484545 - 0.839256i) q^{74} +(0.872884 + 8.61615i) q^{75} +(0.0380738 + 0.0659457i) q^{76} +(-4.33159 + 2.50084i) q^{77} +(0.373722 + 1.16178i) q^{78} +(-6.43143 + 11.1396i) q^{79} +(4.37233 - 6.01279i) q^{80} +(2.88138 - 8.52629i) q^{81} -2.96545i q^{82} +(-6.02917 - 3.48094i) q^{83} +(3.10851 - 0.999946i) q^{84} +(0.331046 - 3.13727i) q^{85} +(-1.42354 - 2.46564i) q^{86} +(11.5075 + 2.48130i) q^{87} +(-5.70043 - 3.29114i) q^{88} +1.10154 q^{89} +(-2.27215 - 0.0142643i) q^{90} -2.08021 q^{91} +(11.3221 + 6.53684i) q^{92} +(12.0338 - 13.2863i) q^{93} +(1.28164 + 2.21986i) q^{94} +(0.0898179 + 0.00947763i) q^{95} +(4.82462 + 4.36979i) q^{96} +(-1.56345 - 0.902656i) q^{97} -0.338719i q^{98} +(-1.48089 - 14.9318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.293339 0.169359i −0.207422 0.119755i 0.392691 0.919671i \(-0.371544\pi\)
−0.600113 + 0.799915i \(0.704878\pi\)
\(3\) 0.530399 + 1.64884i 0.306226 + 0.951959i
\(4\) −0.942635 1.63269i −0.471317 0.816346i
\(5\) −2.22372 0.234648i −0.994479 0.104938i
\(6\) 0.123660 0.573497i 0.0504839 0.234129i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.31601i 0.465281i
\(9\) −2.43735 + 1.74909i −0.812451 + 0.583029i
\(10\) 0.612564 + 0.445440i 0.193710 + 0.140860i
\(11\) −2.50084 + 4.33159i −0.754033 + 1.30602i 0.191821 + 0.981430i \(0.438561\pi\)
−0.945854 + 0.324593i \(0.894773\pi\)
\(12\) 2.19208 2.42023i 0.632798 0.698661i
\(13\) −1.80151 + 1.04011i −0.499650 + 0.288473i −0.728569 0.684972i \(-0.759814\pi\)
0.228919 + 0.973446i \(0.426481\pi\)
\(14\) −0.169359 0.293339i −0.0452632 0.0783981i
\(15\) −0.792563 3.79102i −0.204639 0.978838i
\(16\) −1.66239 + 2.87934i −0.415598 + 0.719836i
\(17\) 1.41082i 0.342174i 0.985256 + 0.171087i \(0.0547280\pi\)
−0.985256 + 0.171087i \(0.945272\pi\)
\(18\) 1.01120 0.100287i 0.238341 0.0236379i
\(19\) −0.0403908 −0.00926628 −0.00463314 0.999989i \(-0.501475\pi\)
−0.00463314 + 0.999989i \(0.501475\pi\)
\(20\) 1.71305 + 3.85184i 0.383050 + 0.861298i
\(21\) −0.365081 + 1.69314i −0.0796673 + 0.369473i
\(22\) 1.46719 0.847082i 0.312806 0.180599i
\(23\) −6.00558 + 3.46732i −1.25225 + 0.722987i −0.971556 0.236811i \(-0.923898\pi\)
−0.280694 + 0.959797i \(0.590565\pi\)
\(24\) −2.16990 + 0.698012i −0.442928 + 0.142481i
\(25\) 4.88988 + 1.04358i 0.977976 + 0.208717i
\(26\) 0.704606 0.138185
\(27\) −4.17674 3.09109i −0.803814 0.594881i
\(28\) 1.88527i 0.356282i
\(29\) 3.39829 5.88601i 0.631046 1.09300i −0.356292 0.934375i \(-0.615959\pi\)
0.987338 0.158630i \(-0.0507076\pi\)
\(30\) −0.409555 + 1.24628i −0.0747742 + 0.227539i
\(31\) −5.17476 8.96294i −0.929413 1.60979i −0.784305 0.620376i \(-0.786980\pi\)
−0.145109 0.989416i \(-0.546353\pi\)
\(32\) 3.25469 1.87910i 0.575353 0.332180i
\(33\) −8.46855 1.82602i −1.47418 0.317870i
\(34\) 0.238936 0.413849i 0.0409771 0.0709744i
\(35\) −1.80848 1.31507i −0.305688 0.222288i
\(36\) 5.15326 + 2.33069i 0.858876 + 0.388449i
\(37\) 2.86105i 0.470353i 0.971953 + 0.235177i \(0.0755668\pi\)
−0.971953 + 0.235177i \(0.924433\pi\)
\(38\) 0.0118482 + 0.00684056i 0.00192203 + 0.00110969i
\(39\) −2.67049 2.41874i −0.427621 0.387308i
\(40\) 0.308800 2.92645i 0.0488256 0.462712i
\(41\) 4.37745 + 7.58197i 0.683644 + 1.18411i 0.973861 + 0.227145i \(0.0729390\pi\)
−0.290217 + 0.956961i \(0.593728\pi\)
\(42\) 0.393841 0.434833i 0.0607710 0.0670962i
\(43\) 7.27932 + 4.20272i 1.11009 + 0.640908i 0.938852 0.344322i \(-0.111891\pi\)
0.171234 + 0.985230i \(0.445225\pi\)
\(44\) 9.42953 1.42155
\(45\) 5.83042 3.31757i 0.869147 0.494553i
\(46\) 2.34889 0.346325
\(47\) −6.55370 3.78378i −0.955956 0.551921i −0.0610297 0.998136i \(-0.519438\pi\)
−0.894926 + 0.446215i \(0.852772\pi\)
\(48\) −5.62931 1.21382i −0.812521 0.175199i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −1.25765 1.13427i −0.177859 0.160410i
\(51\) −2.32622 + 0.748298i −0.325736 + 0.104783i
\(52\) 3.39634 + 1.96088i 0.470988 + 0.271925i
\(53\) 9.89525i 1.35922i 0.733575 + 0.679608i \(0.237850\pi\)
−0.733575 + 0.679608i \(0.762150\pi\)
\(54\) 0.701695 + 1.61411i 0.0954886 + 0.219652i
\(55\) 6.57758 9.04543i 0.886921 1.21969i
\(56\) −0.658007 + 1.13970i −0.0879298 + 0.152299i
\(57\) −0.0214233 0.0665980i −0.00283758 0.00882112i
\(58\) −1.99370 + 1.15106i −0.261786 + 0.151142i
\(59\) 2.86271 + 4.95837i 0.372694 + 0.645524i 0.989979 0.141215i \(-0.0451009\pi\)
−0.617285 + 0.786739i \(0.711768\pi\)
\(60\) −5.44247 + 4.86756i −0.702620 + 0.628399i
\(61\) 3.19419 5.53251i 0.408975 0.708365i −0.585800 0.810455i \(-0.699220\pi\)
0.994775 + 0.102090i \(0.0325531\pi\)
\(62\) 3.50557i 0.445208i
\(63\) −2.98535 + 0.296078i −0.376119 + 0.0373023i
\(64\) 5.37659 0.672074
\(65\) 4.25013 1.89018i 0.527163 0.234448i
\(66\) 2.17490 + 1.96987i 0.267712 + 0.242474i
\(67\) 6.22427 3.59358i 0.760415 0.439026i −0.0690296 0.997615i \(-0.521990\pi\)
0.829445 + 0.558589i \(0.188657\pi\)
\(68\) 2.30343 1.32989i 0.279332 0.161273i
\(69\) −8.90242 8.06318i −1.07173 0.970693i
\(70\) 0.307777 + 0.692044i 0.0367863 + 0.0827151i
\(71\) 0.459791 0.0545672 0.0272836 0.999628i \(-0.491314\pi\)
0.0272836 + 0.999628i \(0.491314\pi\)
\(72\) −2.30182 3.20759i −0.271272 0.378018i
\(73\) 1.72878i 0.202338i −0.994869 0.101169i \(-0.967742\pi\)
0.994869 0.101169i \(-0.0322583\pi\)
\(74\) 0.484545 0.839256i 0.0563272 0.0975616i
\(75\) 0.872884 + 8.61615i 0.100792 + 0.994908i
\(76\) 0.0380738 + 0.0659457i 0.00436736 + 0.00756449i
\(77\) −4.33159 + 2.50084i −0.493630 + 0.284998i
\(78\) 0.373722 + 1.16178i 0.0423157 + 0.131546i
\(79\) −6.43143 + 11.1396i −0.723592 + 1.25330i 0.235959 + 0.971763i \(0.424177\pi\)
−0.959551 + 0.281535i \(0.909156\pi\)
\(80\) 4.37233 6.01279i 0.488841 0.672250i
\(81\) 2.88138 8.52629i 0.320154 0.947366i
\(82\) 2.96545i 0.327479i
\(83\) −6.02917 3.48094i −0.661787 0.382083i 0.131170 0.991360i \(-0.458126\pi\)
−0.792958 + 0.609277i \(0.791460\pi\)
\(84\) 3.10851 0.999946i 0.339166 0.109103i
\(85\) 0.331046 3.13727i 0.0359070 0.340285i
\(86\) −1.42354 2.46564i −0.153504 0.265877i
\(87\) 11.5075 + 2.48130i 1.23374 + 0.266024i
\(88\) −5.70043 3.29114i −0.607668 0.350837i
\(89\) 1.10154 0.116763 0.0583816 0.998294i \(-0.481406\pi\)
0.0583816 + 0.998294i \(0.481406\pi\)
\(90\) −2.27215 0.0142643i −0.239506 0.00150359i
\(91\) −2.08021 −0.218065
\(92\) 11.3221 + 6.53684i 1.18041 + 0.681512i
\(93\) 12.0338 13.2863i 1.24784 1.37772i
\(94\) 1.28164 + 2.21986i 0.132191 + 0.228961i
\(95\) 0.0898179 + 0.00947763i 0.00921512 + 0.000972384i
\(96\) 4.82462 + 4.36979i 0.492410 + 0.445990i
\(97\) −1.56345 0.902656i −0.158744 0.0916509i 0.418524 0.908206i \(-0.362548\pi\)
−0.577268 + 0.816555i \(0.695881\pi\)
\(98\) 0.338719i 0.0342157i
\(99\) −1.48089 14.9318i −0.148835 1.50070i
\(100\) −2.90552 8.96739i −0.290552 0.896739i
\(101\) 3.44435 5.96579i 0.342725 0.593618i −0.642212 0.766527i \(-0.721983\pi\)
0.984938 + 0.172909i \(0.0553166\pi\)
\(102\) 0.809102 + 0.174462i 0.0801130 + 0.0172743i
\(103\) −12.2796 + 7.08965i −1.20995 + 0.698564i −0.962748 0.270401i \(-0.912844\pi\)
−0.247200 + 0.968965i \(0.579510\pi\)
\(104\) −1.36879 2.37082i −0.134221 0.232478i
\(105\) 1.20913 3.67940i 0.117999 0.359073i
\(106\) 1.67585 2.90266i 0.162773 0.281931i
\(107\) 10.6090i 1.02561i −0.858504 0.512807i \(-0.828606\pi\)
0.858504 0.512807i \(-0.171394\pi\)
\(108\) −1.10966 + 9.73310i −0.106777 + 0.936568i
\(109\) 12.3046 1.17857 0.589283 0.807927i \(-0.299410\pi\)
0.589283 + 0.807927i \(0.299410\pi\)
\(110\) −3.46139 + 1.53940i −0.330030 + 0.146776i
\(111\) −4.71741 + 1.51750i −0.447757 + 0.144034i
\(112\) −2.87934 + 1.66239i −0.272073 + 0.157081i
\(113\) −3.70732 + 2.14042i −0.348755 + 0.201354i −0.664137 0.747611i \(-0.731201\pi\)
0.315382 + 0.948965i \(0.397867\pi\)
\(114\) −0.00499472 + 0.0231640i −0.000467798 + 0.00216951i
\(115\) 14.1683 6.30116i 1.32120 0.587586i
\(116\) −12.8134 −1.18969
\(117\) 2.57169 5.68611i 0.237753 0.525681i
\(118\) 1.93931i 0.178528i
\(119\) −0.705410 + 1.22181i −0.0646648 + 0.112003i
\(120\) 4.98903 1.04302i 0.455434 0.0952146i
\(121\) −7.00844 12.1390i −0.637130 1.10354i
\(122\) −1.87396 + 1.08193i −0.169661 + 0.0979536i
\(123\) −10.1797 + 11.2392i −0.917870 + 1.01340i
\(124\) −9.75581 + 16.8976i −0.876098 + 1.51745i
\(125\) −10.6289 3.46804i −0.950674 0.310191i
\(126\) 0.925864 + 0.418746i 0.0824825 + 0.0373049i
\(127\) 7.37319i 0.654264i 0.944979 + 0.327132i \(0.106082\pi\)
−0.944979 + 0.327132i \(0.893918\pi\)
\(128\) −8.08654 4.66877i −0.714756 0.412665i
\(129\) −3.06867 + 14.2316i −0.270181 + 1.25302i
\(130\) −1.56685 0.165335i −0.137422 0.0145008i
\(131\) 1.87182 + 3.24209i 0.163542 + 0.283262i 0.936136 0.351637i \(-0.114375\pi\)
−0.772595 + 0.634899i \(0.781042\pi\)
\(132\) 5.00141 + 15.5478i 0.435317 + 1.35326i
\(133\) −0.0349795 0.0201954i −0.00303310 0.00175116i
\(134\) −2.43443 −0.210302
\(135\) 8.56259 + 7.85380i 0.736950 + 0.675947i
\(136\) −1.85666 −0.159207
\(137\) −5.67442 3.27613i −0.484798 0.279898i 0.237616 0.971359i \(-0.423634\pi\)
−0.722414 + 0.691461i \(0.756967\pi\)
\(138\) 1.24585 + 3.87295i 0.106054 + 0.329688i
\(139\) 8.46026 + 14.6536i 0.717590 + 1.24290i 0.961952 + 0.273218i \(0.0880880\pi\)
−0.244362 + 0.969684i \(0.578579\pi\)
\(140\) −0.442375 + 4.19232i −0.0373875 + 0.354315i
\(141\) 2.76278 12.8129i 0.232668 1.07904i
\(142\) −0.134875 0.0778699i −0.0113184 0.00653470i
\(143\) 10.4046i 0.870073i
\(144\) −0.984395 9.92565i −0.0820329 0.827137i
\(145\) −8.93799 + 12.2914i −0.742260 + 1.02075i
\(146\) −0.292785 + 0.507118i −0.0242310 + 0.0419694i
\(147\) −1.16274 + 1.28376i −0.0959011 + 0.105883i
\(148\) 4.67121 2.69692i 0.383971 0.221686i
\(149\) −0.759296 1.31514i −0.0622040 0.107740i 0.833246 0.552902i \(-0.186480\pi\)
−0.895450 + 0.445162i \(0.853146\pi\)
\(150\) 1.20317 2.67528i 0.0982388 0.218436i
\(151\) −4.82908 + 8.36421i −0.392985 + 0.680670i −0.992842 0.119437i \(-0.961891\pi\)
0.599857 + 0.800107i \(0.295224\pi\)
\(152\) 0.0531548i 0.00431143i
\(153\) −2.46765 3.43867i −0.199498 0.278000i
\(154\) 1.69416 0.136520
\(155\) 9.40408 + 21.1453i 0.755354 + 1.69843i
\(156\) −1.43176 + 6.64008i −0.114633 + 0.531632i
\(157\) −17.5682 + 10.1430i −1.40210 + 0.809500i −0.994608 0.103710i \(-0.966929\pi\)
−0.407488 + 0.913211i \(0.633595\pi\)
\(158\) 3.77318 2.17844i 0.300178 0.173308i
\(159\) −16.3157 + 5.24843i −1.29392 + 0.416228i
\(160\) −7.67845 + 3.41488i −0.607035 + 0.269970i
\(161\) −6.93464 −0.546527
\(162\) −2.28923 + 2.01310i −0.179859 + 0.158164i
\(163\) 21.1677i 1.65798i 0.559260 + 0.828992i \(0.311085\pi\)
−0.559260 + 0.828992i \(0.688915\pi\)
\(164\) 8.25268 14.2941i 0.644426 1.11618i
\(165\) 18.4032 + 6.04769i 1.43269 + 0.470812i
\(166\) 1.17906 + 2.04219i 0.0915128 + 0.158505i
\(167\) 8.53873 4.92984i 0.660747 0.381482i −0.131815 0.991274i \(-0.542080\pi\)
0.792562 + 0.609792i \(0.208747\pi\)
\(168\) −2.22819 0.480452i −0.171909 0.0370677i
\(169\) −4.33636 + 7.51080i −0.333566 + 0.577754i
\(170\) −0.628435 + 0.864218i −0.0481988 + 0.0662825i
\(171\) 0.0984466 0.0706471i 0.00752840 0.00540252i
\(172\) 15.8465i 1.20828i
\(173\) 11.3362 + 6.54495i 0.861875 + 0.497604i 0.864640 0.502393i \(-0.167547\pi\)
−0.00276491 + 0.999996i \(0.500880\pi\)
\(174\) −2.95538 2.67677i −0.224047 0.202926i
\(175\) 3.71297 + 3.34871i 0.280674 + 0.253139i
\(176\) −8.31476 14.4016i −0.626748 1.08556i
\(177\) −6.65718 + 7.35008i −0.500384 + 0.552466i
\(178\) −0.323125 0.186556i −0.0242192 0.0139830i
\(179\) 9.85401 0.736523 0.368262 0.929722i \(-0.379953\pi\)
0.368262 + 0.929722i \(0.379953\pi\)
\(180\) −10.9125 6.39202i −0.813371 0.476433i
\(181\) 8.41154 0.625225 0.312612 0.949881i \(-0.398796\pi\)
0.312612 + 0.949881i \(0.398796\pi\)
\(182\) 0.610207 + 0.352303i 0.0452315 + 0.0261144i
\(183\) 10.8164 + 2.33228i 0.799573 + 0.172407i
\(184\) −4.56304 7.90342i −0.336392 0.582648i
\(185\) 0.671339 6.36217i 0.0493578 0.467756i
\(186\) −5.78013 + 1.85935i −0.423820 + 0.136334i
\(187\) −6.11109 3.52824i −0.446887 0.258011i
\(188\) 14.2669i 1.04052i
\(189\) −2.07162 4.76533i −0.150688 0.346627i
\(190\) −0.0247420 0.0179917i −0.00179497 0.00130525i
\(191\) −2.23497 + 3.87109i −0.161717 + 0.280102i −0.935485 0.353368i \(-0.885036\pi\)
0.773768 + 0.633470i \(0.218370\pi\)
\(192\) 2.85174 + 8.86515i 0.205807 + 0.639787i
\(193\) 6.66949 3.85063i 0.480081 0.277175i −0.240370 0.970681i \(-0.577269\pi\)
0.720450 + 0.693507i \(0.243935\pi\)
\(194\) 0.305747 + 0.529569i 0.0219513 + 0.0380208i
\(195\) 5.37087 + 6.00523i 0.384616 + 0.430044i
\(196\) 0.942635 1.63269i 0.0673311 0.116621i
\(197\) 3.01080i 0.214511i 0.994231 + 0.107255i \(0.0342063\pi\)
−0.994231 + 0.107255i \(0.965794\pi\)
\(198\) −2.09444 + 4.63088i −0.148845 + 0.329102i
\(199\) −25.8065 −1.82938 −0.914688 0.404160i \(-0.867564\pi\)
−0.914688 + 0.404160i \(0.867564\pi\)
\(200\) −1.37337 + 6.43515i −0.0971120 + 0.455034i
\(201\) 9.22659 + 8.35679i 0.650794 + 0.589443i
\(202\) −2.02072 + 1.16666i −0.142178 + 0.0820862i
\(203\) 5.88601 3.39829i 0.413117 0.238513i
\(204\) 3.41451 + 3.09263i 0.239064 + 0.216527i
\(205\) −7.95515 17.8874i −0.555612 1.24931i
\(206\) 4.80279 0.334626
\(207\) 8.57306 18.9554i 0.595869 1.31749i
\(208\) 6.91624i 0.479555i
\(209\) 0.101011 0.174956i 0.00698708 0.0121020i
\(210\) −0.977826 + 0.874534i −0.0674764 + 0.0603486i
\(211\) 9.45426 + 16.3753i 0.650858 + 1.12732i 0.982915 + 0.184060i \(0.0589241\pi\)
−0.332057 + 0.943259i \(0.607743\pi\)
\(212\) 16.1559 9.32760i 1.10959 0.640623i
\(213\) 0.243873 + 0.758122i 0.0167099 + 0.0519457i
\(214\) −1.79674 + 3.11204i −0.122822 + 0.212735i
\(215\) −15.2010 11.0538i −1.03670 0.753860i
\(216\) 4.06792 5.49664i 0.276787 0.373999i
\(217\) 10.3495i 0.702571i
\(218\) −3.60941 2.08390i −0.244460 0.141139i
\(219\) 2.85048 0.916943i 0.192618 0.0619613i
\(220\) −20.9687 2.21262i −1.41371 0.149175i
\(221\) −1.46740 2.54161i −0.0987081 0.170967i
\(222\) 1.64080 + 0.353796i 0.110123 + 0.0237453i
\(223\) 3.60716 + 2.08260i 0.241553 + 0.139461i 0.615891 0.787832i \(-0.288796\pi\)
−0.374337 + 0.927293i \(0.622130\pi\)
\(224\) 3.75819 0.251105
\(225\) −13.7437 + 6.00925i −0.916246 + 0.400616i
\(226\) 1.45000 0.0964526
\(227\) −14.5855 8.42095i −0.968075 0.558918i −0.0694261 0.997587i \(-0.522117\pi\)
−0.898649 + 0.438669i \(0.855450\pi\)
\(228\) −0.0885397 + 0.0977552i −0.00586368 + 0.00647399i
\(229\) −1.96739 3.40761i −0.130009 0.225181i 0.793671 0.608347i \(-0.208167\pi\)
−0.923680 + 0.383166i \(0.874834\pi\)
\(230\) −5.22329 0.551164i −0.344413 0.0363427i
\(231\) −6.42096 5.81565i −0.422468 0.382642i
\(232\) 7.74607 + 4.47219i 0.508554 + 0.293614i
\(233\) 9.05613i 0.593287i −0.954988 0.296643i \(-0.904133\pi\)
0.954988 0.296643i \(-0.0958672\pi\)
\(234\) −1.71737 + 1.23242i −0.112268 + 0.0805657i
\(235\) 13.6858 + 9.95189i 0.892760 + 0.649190i
\(236\) 5.39699 9.34786i 0.351314 0.608494i
\(237\) −21.7786 4.69599i −1.41467 0.305037i
\(238\) 0.413849 0.238936i 0.0268258 0.0154879i
\(239\) 0.266785 + 0.462085i 0.0172569 + 0.0298898i 0.874525 0.484981i \(-0.161173\pi\)
−0.857268 + 0.514870i \(0.827840\pi\)
\(240\) 12.2332 + 4.02010i 0.789650 + 0.259496i
\(241\) −3.73632 + 6.47149i −0.240677 + 0.416866i −0.960907 0.276870i \(-0.910703\pi\)
0.720230 + 0.693735i \(0.244036\pi\)
\(242\) 4.74778i 0.305199i
\(243\) 15.5868 + 0.228602i 0.999892 + 0.0146648i
\(244\) −12.0438 −0.771027
\(245\) −0.908650 2.04312i −0.0580515 0.130530i
\(246\) 4.88956 1.57287i 0.311747 0.100283i
\(247\) 0.0727646 0.0420107i 0.00462990 0.00267308i
\(248\) 11.7953 6.81005i 0.749005 0.432438i
\(249\) 2.54165 11.7874i 0.161071 0.746998i
\(250\) 2.53051 + 2.81741i 0.160044 + 0.178189i
\(251\) −17.3364 −1.09427 −0.547133 0.837045i \(-0.684281\pi\)
−0.547133 + 0.837045i \(0.684281\pi\)
\(252\) 3.29750 + 4.59507i 0.207723 + 0.289462i
\(253\) 34.6849i 2.18062i
\(254\) 1.24872 2.16284i 0.0783515 0.135709i
\(255\) 5.34845 1.11816i 0.334933 0.0700222i
\(256\) −3.79519 6.57347i −0.237200 0.410842i
\(257\) 0.864116 0.498898i 0.0539021 0.0311204i −0.472807 0.881166i \(-0.656759\pi\)
0.526709 + 0.850046i \(0.323426\pi\)
\(258\) 3.31041 3.65496i 0.206097 0.227548i
\(259\) −1.43052 + 2.47774i −0.0888884 + 0.153959i
\(260\) −7.09240 5.15739i −0.439852 0.319848i
\(261\) 2.01232 + 20.2902i 0.124559 + 1.25593i
\(262\) 1.26804i 0.0783398i
\(263\) 7.41405 + 4.28050i 0.457170 + 0.263947i 0.710854 0.703340i \(-0.248309\pi\)
−0.253684 + 0.967287i \(0.581642\pi\)
\(264\) 2.40307 11.1447i 0.147899 0.685910i
\(265\) 2.32190 22.0043i 0.142633 1.35171i
\(266\) 0.00684056 + 0.0118482i 0.000419422 + 0.000726459i
\(267\) 0.584257 + 1.81627i 0.0357559 + 0.111154i
\(268\) −11.7344 6.77487i −0.716794 0.413841i
\(269\) 27.2006 1.65845 0.829224 0.558917i \(-0.188783\pi\)
0.829224 + 0.558917i \(0.188783\pi\)
\(270\) −1.18163 3.75398i −0.0719115 0.228460i
\(271\) 23.1357 1.40540 0.702698 0.711488i \(-0.251978\pi\)
0.702698 + 0.711488i \(0.251978\pi\)
\(272\) −4.06224 2.34533i −0.246309 0.142207i
\(273\) −1.10334 3.42994i −0.0667773 0.207589i
\(274\) 1.10968 + 1.92203i 0.0670385 + 0.116114i
\(275\) −16.7492 + 18.5711i −1.01002 + 1.11988i
\(276\) −4.77295 + 22.1355i −0.287298 + 1.33240i
\(277\) −5.45413 3.14895i −0.327707 0.189202i 0.327116 0.944984i \(-0.393923\pi\)
−0.654823 + 0.755783i \(0.727257\pi\)
\(278\) 5.73130i 0.343740i
\(279\) 28.2897 + 12.7947i 1.69366 + 0.766001i
\(280\) 1.73065 2.37998i 0.103426 0.142231i
\(281\) −9.94700 + 17.2287i −0.593388 + 1.02778i 0.400384 + 0.916347i \(0.368877\pi\)
−0.993772 + 0.111431i \(0.964457\pi\)
\(282\) −2.98042 + 3.29063i −0.177481 + 0.195954i
\(283\) −5.22468 + 3.01647i −0.310575 + 0.179310i −0.647184 0.762334i \(-0.724053\pi\)
0.336609 + 0.941645i \(0.390720\pi\)
\(284\) −0.433415 0.750697i −0.0257185 0.0445457i
\(285\) 0.0320123 + 0.153122i 0.00189624 + 0.00907019i
\(286\) −1.76211 + 3.05206i −0.104196 + 0.180472i
\(287\) 8.75491i 0.516786i
\(288\) −4.64612 + 10.2728i −0.273775 + 0.605328i
\(289\) 15.0096 0.882917
\(290\) 4.70353 2.09183i 0.276201 0.122836i
\(291\) 0.659086 3.05664i 0.0386363 0.179184i
\(292\) −2.82256 + 1.62961i −0.165178 + 0.0953655i
\(293\) 10.8660 6.27351i 0.634801 0.366502i −0.147808 0.989016i \(-0.547222\pi\)
0.782609 + 0.622514i \(0.213888\pi\)
\(294\) 0.558493 0.179656i 0.0325720 0.0104778i
\(295\) −5.20241 11.6978i −0.302896 0.681070i
\(296\) −3.76517 −0.218846
\(297\) 23.8347 10.3616i 1.38303 0.601239i
\(298\) 0.514375i 0.0297970i
\(299\) 7.21276 12.4929i 0.417125 0.722481i
\(300\) 13.2447 9.54703i 0.764684 0.551198i
\(301\) 4.20272 + 7.27932i 0.242241 + 0.419573i
\(302\) 2.83312 1.63570i 0.163027 0.0941239i
\(303\) 11.6635 + 2.51493i 0.670051 + 0.144479i
\(304\) 0.0671453 0.116299i 0.00385105 0.00667021i
\(305\) −8.40119 + 11.5532i −0.481051 + 0.661537i
\(306\) 0.141487 + 1.42661i 0.00808828 + 0.0815541i
\(307\) 10.0210i 0.571929i 0.958240 + 0.285964i \(0.0923139\pi\)
−0.958240 + 0.285964i \(0.907686\pi\)
\(308\) 8.16621 + 4.71476i 0.465313 + 0.268649i
\(309\) −18.2028 16.4868i −1.03552 0.937902i
\(310\) 0.822576 7.79542i 0.0467192 0.442750i
\(311\) −2.40863 4.17186i −0.136581 0.236565i 0.789619 0.613597i \(-0.210278\pi\)
−0.926200 + 0.377032i \(0.876945\pi\)
\(312\) 3.18309 3.51440i 0.180207 0.198964i
\(313\) 4.62029 + 2.66753i 0.261155 + 0.150778i 0.624861 0.780736i \(-0.285156\pi\)
−0.363707 + 0.931514i \(0.618489\pi\)
\(314\) 6.87125 0.387767
\(315\) 6.70807 + 0.0421125i 0.377957 + 0.00237277i
\(316\) 24.2500 1.36417
\(317\) −7.91489 4.56966i −0.444544 0.256658i 0.260979 0.965345i \(-0.415955\pi\)
−0.705523 + 0.708687i \(0.749288\pi\)
\(318\) 5.67490 + 1.22364i 0.318232 + 0.0686186i
\(319\) 16.9972 + 29.4400i 0.951659 + 1.64832i
\(320\) −11.9560 1.26161i −0.668363 0.0705260i
\(321\) 17.4926 5.62702i 0.976341 0.314070i
\(322\) 2.03420 + 1.17445i 0.113362 + 0.0654494i
\(323\) 0.0569842i 0.00317068i
\(324\) −16.6369 + 3.33277i −0.924272 + 0.185154i
\(325\) −9.89463 + 3.20596i −0.548855 + 0.177834i
\(326\) 3.58495 6.20932i 0.198552 0.343902i
\(327\) 6.52634 + 20.2883i 0.360908 + 1.12195i
\(328\) −9.97798 + 5.76079i −0.550942 + 0.318086i
\(329\) −3.78378 6.55370i −0.208607 0.361317i
\(330\) −4.37415 4.89078i −0.240789 0.269229i
\(331\) −2.08484 + 3.61105i −0.114593 + 0.198481i −0.917617 0.397466i \(-0.869890\pi\)
0.803024 + 0.595947i \(0.203223\pi\)
\(332\) 13.1250i 0.720329i
\(333\) −5.00422 6.97338i −0.274230 0.382139i
\(334\) −3.33966 −0.182738
\(335\) −14.6843 + 6.53061i −0.802287 + 0.356806i
\(336\) −4.26822 3.86585i −0.232850 0.210899i
\(337\) −9.40591 + 5.43050i −0.512372 + 0.295818i −0.733808 0.679357i \(-0.762259\pi\)
0.221436 + 0.975175i \(0.428926\pi\)
\(338\) 2.54405 1.46881i 0.138378 0.0798926i
\(339\) −5.49557 4.97750i −0.298478 0.270341i
\(340\) −5.43425 + 2.41681i −0.294714 + 0.131070i
\(341\) 51.7650 2.80323
\(342\) −0.0408430 + 0.00405068i −0.00220854 + 0.000219036i
\(343\) 1.00000i 0.0539949i
\(344\) −5.53083 + 9.57968i −0.298202 + 0.516502i
\(345\) 17.9045 + 20.0192i 0.963945 + 1.07780i
\(346\) −2.21690 3.83978i −0.119181 0.206428i
\(347\) 0.00153397 0.000885640i 8.23480e−5 4.75437e-5i −0.499959 0.866049i \(-0.666652\pi\)
0.500041 + 0.866002i \(0.333318\pi\)
\(348\) −6.79621 21.1272i −0.364315 1.13254i
\(349\) 0.301876 0.522865i 0.0161591 0.0279883i −0.857833 0.513929i \(-0.828190\pi\)
0.873992 + 0.485941i \(0.161523\pi\)
\(350\) −0.522023 1.61113i −0.0279033 0.0861187i
\(351\) 10.7395 + 1.22440i 0.573233 + 0.0653538i
\(352\) 18.7973i 1.00190i
\(353\) −22.0607 12.7367i −1.17417 0.677908i −0.219512 0.975610i \(-0.570447\pi\)
−0.954659 + 0.297702i \(0.903780\pi\)
\(354\) 3.19761 1.02861i 0.169951 0.0546699i
\(355\) −1.02245 0.107889i −0.0542659 0.00572616i
\(356\) −1.03835 1.79848i −0.0550325 0.0953191i
\(357\) −2.38871 0.515064i −0.126424 0.0272601i
\(358\) −2.89056 1.66887i −0.152771 0.0882024i
\(359\) −0.544571 −0.0287414 −0.0143707 0.999897i \(-0.504574\pi\)
−0.0143707 + 0.999897i \(0.504574\pi\)
\(360\) 4.36596 + 7.67291i 0.230106 + 0.404398i
\(361\) −18.9984 −0.999914
\(362\) −2.46743 1.42457i −0.129685 0.0748739i
\(363\) 16.2980 17.9943i 0.855421 0.944456i
\(364\) 1.96088 + 3.39634i 0.102778 + 0.178017i
\(365\) −0.405655 + 3.84432i −0.0212329 + 0.201221i
\(366\) −2.77788 2.51601i −0.145202 0.131514i
\(367\) −1.58410 0.914582i −0.0826895 0.0477408i 0.458085 0.888908i \(-0.348535\pi\)
−0.540775 + 0.841168i \(0.681869\pi\)
\(368\) 23.0562i 1.20189i
\(369\) −23.9309 10.8234i −1.24580 0.563443i
\(370\) −1.27442 + 1.75258i −0.0662541 + 0.0911120i
\(371\) −4.94762 + 8.56954i −0.256868 + 0.444908i
\(372\) −33.0359 7.12333i −1.71283 0.369327i
\(373\) 27.6925 15.9883i 1.43387 0.827843i 0.436453 0.899727i \(-0.356235\pi\)
0.997413 + 0.0718846i \(0.0229013\pi\)
\(374\) 1.19508 + 2.06994i 0.0617962 + 0.107034i
\(375\) 0.0807141 19.3647i 0.00416806 0.999991i
\(376\) 4.97951 8.62476i 0.256798 0.444788i
\(377\) 14.1383i 0.728160i
\(378\) −0.199368 + 1.74871i −0.0102544 + 0.0899437i
\(379\) 5.62286 0.288827 0.144413 0.989517i \(-0.453871\pi\)
0.144413 + 0.989517i \(0.453871\pi\)
\(380\) −0.0691915 0.155579i −0.00354945 0.00798103i
\(381\) −12.1572 + 3.91073i −0.622833 + 0.200353i
\(382\) 1.31121 0.757027i 0.0670873 0.0387329i
\(383\) 14.3399 8.27915i 0.732735 0.423045i −0.0866870 0.996236i \(-0.527628\pi\)
0.819422 + 0.573191i \(0.194295\pi\)
\(384\) 3.40896 15.8097i 0.173963 0.806787i
\(385\) 10.2191 4.54478i 0.520812 0.231624i
\(386\) −2.60856 −0.132772
\(387\) −25.0932 + 2.48866i −1.27556 + 0.126506i
\(388\) 3.40350i 0.172787i
\(389\) −8.97007 + 15.5366i −0.454801 + 0.787738i −0.998677 0.0514278i \(-0.983623\pi\)
0.543876 + 0.839165i \(0.316956\pi\)
\(390\) −0.558445 2.67118i −0.0282779 0.135260i
\(391\) −4.89177 8.47279i −0.247387 0.428488i
\(392\) −1.13970 + 0.658007i −0.0575636 + 0.0332344i
\(393\) −4.35287 + 4.80593i −0.219573 + 0.242427i
\(394\) 0.509908 0.883186i 0.0256888 0.0444943i
\(395\) 16.9156 23.2622i 0.851116 1.17045i
\(396\) −22.9831 + 16.4931i −1.15494 + 0.828808i
\(397\) 16.6585i 0.836067i −0.908432 0.418033i \(-0.862720\pi\)
0.908432 0.418033i \(-0.137280\pi\)
\(398\) 7.57006 + 4.37058i 0.379453 + 0.219077i
\(399\) 0.0147459 0.0683872i 0.000738220 0.00342364i
\(400\) −11.1337 + 12.3448i −0.556687 + 0.617240i
\(401\) −3.21695 5.57192i −0.160647 0.278249i 0.774454 0.632630i \(-0.218025\pi\)
−0.935101 + 0.354382i \(0.884691\pi\)
\(402\) −1.29122 4.01398i −0.0644001 0.200199i
\(403\) 18.6448 + 10.7646i 0.928764 + 0.536222i
\(404\) −12.9870 −0.646130
\(405\) −8.40807 + 18.2840i −0.417800 + 0.908539i
\(406\) −2.30213 −0.114253
\(407\) −12.3929 7.15503i −0.614292 0.354662i
\(408\) −0.984770 3.06133i −0.0487534 0.151559i
\(409\) 1.27356 + 2.20587i 0.0629735 + 0.109073i 0.895793 0.444471i \(-0.146608\pi\)
−0.832820 + 0.553544i \(0.813275\pi\)
\(410\) −0.695838 + 6.59434i −0.0343650 + 0.325671i
\(411\) 2.39210 11.0939i 0.117994 0.547220i
\(412\) 23.1504 + 13.3659i 1.14054 + 0.658490i
\(413\) 5.72543i 0.281730i
\(414\) −5.72508 + 4.10842i −0.281372 + 0.201918i
\(415\) 12.5904 + 9.15538i 0.618038 + 0.449420i
\(416\) −3.90891 + 6.77044i −0.191650 + 0.331948i
\(417\) −19.6741 + 21.7219i −0.963447 + 1.06373i
\(418\) −0.0592610 + 0.0342143i −0.00289855 + 0.00167348i
\(419\) −6.36378 11.0224i −0.310891 0.538479i 0.667664 0.744462i \(-0.267294\pi\)
−0.978556 + 0.205983i \(0.933961\pi\)
\(420\) −7.14710 + 1.49420i −0.348743 + 0.0729093i
\(421\) 3.88511 6.72920i 0.189348 0.327961i −0.755685 0.654936i \(-0.772696\pi\)
0.945033 + 0.326974i \(0.106029\pi\)
\(422\) 6.40467i 0.311774i
\(423\) 22.5919 2.24059i 1.09845 0.108941i
\(424\) −13.0223 −0.632418
\(425\) −1.47231 + 6.89874i −0.0714176 + 0.334638i
\(426\) 0.0568577 0.263689i 0.00275476 0.0127758i
\(427\) 5.53251 3.19419i 0.267737 0.154578i
\(428\) −17.3213 + 10.0004i −0.837255 + 0.483389i
\(429\) 17.1555 5.51857i 0.828274 0.266439i
\(430\) 2.58700 + 5.81693i 0.124756 + 0.280517i
\(431\) −28.9341 −1.39371 −0.696853 0.717214i \(-0.745417\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(432\) 15.8437 6.88767i 0.762280 0.331383i
\(433\) 8.32708i 0.400174i 0.979778 + 0.200087i \(0.0641224\pi\)
−0.979778 + 0.200087i \(0.935878\pi\)
\(434\) −1.75279 + 3.03591i −0.0841364 + 0.145729i
\(435\) −25.0073 8.21795i −1.19901 0.394021i
\(436\) −11.5987 20.0896i −0.555478 0.962117i
\(437\) 0.242570 0.140048i 0.0116037 0.00669940i
\(438\) −0.991450 0.213780i −0.0473733 0.0102148i
\(439\) 14.8208 25.6704i 0.707359 1.22518i −0.258474 0.966018i \(-0.583220\pi\)
0.965833 0.259164i \(-0.0834471\pi\)
\(440\) 11.9039 + 8.65618i 0.567496 + 0.412667i
\(441\) −2.73343 1.23627i −0.130163 0.0588698i
\(442\) 0.994072i 0.0472832i
\(443\) 33.0635 + 19.0892i 1.57089 + 0.906956i 0.996060 + 0.0886873i \(0.0282672\pi\)
0.574835 + 0.818269i \(0.305066\pi\)
\(444\) 6.92440 + 6.27163i 0.328617 + 0.297638i
\(445\) −2.44952 0.258475i −0.116118 0.0122529i
\(446\) −0.705414 1.22181i −0.0334023 0.0578545i
\(447\) 1.76573 1.94951i 0.0835160 0.0922085i
\(448\) 4.65627 + 2.68830i 0.219988 + 0.127010i
\(449\) −6.74489 −0.318311 −0.159155 0.987254i \(-0.550877\pi\)
−0.159155 + 0.987254i \(0.550877\pi\)
\(450\) 5.04928 + 0.564875i 0.238025 + 0.0266285i
\(451\) −43.7893 −2.06196
\(452\) 6.98929 + 4.03527i 0.328749 + 0.189803i
\(453\) −16.3526 3.52601i −0.768312 0.165667i
\(454\) 2.85233 + 4.94039i 0.133867 + 0.231864i
\(455\) 4.62581 + 0.488118i 0.216861 + 0.0228833i
\(456\) 0.0876439 0.0281933i 0.00410430 0.00132027i
\(457\) 13.8348 + 7.98752i 0.647164 + 0.373640i 0.787369 0.616482i \(-0.211443\pi\)
−0.140205 + 0.990123i \(0.544776\pi\)
\(458\) 1.33278i 0.0622768i
\(459\) 4.36098 5.89263i 0.203553 0.275044i
\(460\) −23.6434 17.1928i −1.10238 0.801620i
\(461\) 12.1202 20.9928i 0.564493 0.977730i −0.432604 0.901584i \(-0.642405\pi\)
0.997097 0.0761461i \(-0.0242615\pi\)
\(462\) 0.898584 + 2.79341i 0.0418059 + 0.129961i
\(463\) 32.3985 18.7053i 1.50568 0.869307i 0.505706 0.862706i \(-0.331232\pi\)
0.999978 0.00660146i \(-0.00210133\pi\)
\(464\) 11.2986 + 19.5697i 0.524523 + 0.908500i
\(465\) −29.8774 + 26.7213i −1.38553 + 1.23917i
\(466\) −1.53374 + 2.65651i −0.0710491 + 0.123061i
\(467\) 27.2968i 1.26315i 0.775316 + 0.631574i \(0.217591\pi\)
−0.775316 + 0.631574i \(0.782409\pi\)
\(468\) −11.7078 + 1.16115i −0.541195 + 0.0536740i
\(469\) 7.18716 0.331872
\(470\) −2.32912 5.23709i −0.107434 0.241569i
\(471\) −26.0424 23.5873i −1.19997 1.08685i
\(472\) −6.52528 + 3.76737i −0.300350 + 0.173407i
\(473\) −36.4089 + 21.0207i −1.67408 + 0.966531i
\(474\) 5.59320 + 5.06592i 0.256904 + 0.232686i
\(475\) −0.197506 0.0421512i −0.00906221 0.00193403i
\(476\) 2.65978 0.121911
\(477\) −17.3077 24.1182i −0.792463 1.10430i
\(478\) 0.180730i 0.00826639i
\(479\) 9.26801 16.0527i 0.423466 0.733465i −0.572810 0.819689i \(-0.694147\pi\)
0.996276 + 0.0862233i \(0.0274799\pi\)
\(480\) −9.70324 10.8493i −0.442890 0.495200i
\(481\) −2.97579 5.15422i −0.135684 0.235012i
\(482\) 2.19202 1.26556i 0.0998436 0.0576447i
\(483\) −3.67813 11.4341i −0.167361 0.520271i
\(484\) −13.2128 + 22.8852i −0.600581 + 1.04024i
\(485\) 3.26486 + 2.37412i 0.148250 + 0.107803i
\(486\) −4.53349 2.70682i −0.205643 0.122784i
\(487\) 8.46107i 0.383408i 0.981453 + 0.191704i \(0.0614013\pi\)
−0.981453 + 0.191704i \(0.938599\pi\)
\(488\) 7.28085 + 4.20360i 0.329589 + 0.190288i
\(489\) −34.9022 + 11.2273i −1.57833 + 0.507718i
\(490\) −0.0794797 + 0.753216i −0.00359053 + 0.0340268i
\(491\) 13.3499 + 23.1227i 0.602471 + 1.04351i 0.992446 + 0.122685i \(0.0391505\pi\)
−0.389974 + 0.920826i \(0.627516\pi\)
\(492\) 27.9459 + 6.02580i 1.25990 + 0.271664i
\(493\) 8.30410 + 4.79438i 0.373998 + 0.215928i
\(494\) −0.0284596 −0.00128046
\(495\) −0.210633 + 33.5517i −0.00946727 + 1.50804i
\(496\) 34.4099 1.54505
\(497\) 0.398191 + 0.229896i 0.0178613 + 0.0103122i
\(498\) −2.74188 + 3.02726i −0.122866 + 0.135655i
\(499\) −9.85973 17.0776i −0.441382 0.764496i 0.556410 0.830908i \(-0.312178\pi\)
−0.997792 + 0.0664114i \(0.978845\pi\)
\(500\) 4.35689 + 20.6227i 0.194846 + 0.922277i
\(501\) 12.6575 + 11.4642i 0.565494 + 0.512184i
\(502\) 5.08546 + 2.93609i 0.226975 + 0.131044i
\(503\) 1.69130i 0.0754113i 0.999289 + 0.0377056i \(0.0120049\pi\)
−0.999289 + 0.0377056i \(0.987995\pi\)
\(504\) −0.389643 3.92877i −0.0173561 0.175001i
\(505\) −9.05913 + 12.4580i −0.403126 + 0.554375i
\(506\) −5.87421 + 10.1744i −0.261141 + 0.452309i
\(507\) −14.6841 3.16625i −0.652145 0.140618i
\(508\) 12.0381 6.95022i 0.534106 0.308366i
\(509\) 12.9575 + 22.4431i 0.574333 + 0.994773i 0.996114 + 0.0880756i \(0.0280717\pi\)
−0.421781 + 0.906698i \(0.638595\pi\)
\(510\) −1.75828 0.577809i −0.0778580 0.0255858i
\(511\) 0.864389 1.49717i 0.0382383 0.0662307i
\(512\) 21.2461i 0.938953i
\(513\) 0.168702 + 0.124852i 0.00744837 + 0.00551234i
\(514\) −0.337972 −0.0149073
\(515\) 28.9701 12.8840i 1.27657 0.567737i
\(516\) 26.1284 8.40498i 1.15024 0.370008i
\(517\) 32.7796 18.9253i 1.44164 0.832333i
\(518\) 0.839256 0.484545i 0.0368748 0.0212897i
\(519\) −4.77888 + 22.1630i −0.209770 + 0.972848i
\(520\) 2.48751 + 5.59322i 0.109084 + 0.245279i
\(521\) −1.68614 −0.0738711 −0.0369355 0.999318i \(-0.511760\pi\)
−0.0369355 + 0.999318i \(0.511760\pi\)
\(522\) 2.84604 6.29271i 0.124568 0.275424i
\(523\) 41.0414i 1.79461i 0.441408 + 0.897307i \(0.354479\pi\)
−0.441408 + 0.897307i \(0.645521\pi\)
\(524\) 3.52888 6.11221i 0.154160 0.267013i
\(525\) −3.55214 + 7.89825i −0.155028 + 0.344708i
\(526\) −1.44989 2.51128i −0.0632181 0.109497i
\(527\) 12.6451 7.30065i 0.550829 0.318021i
\(528\) 19.3358 21.3483i 0.841482 0.929066i
\(529\) 12.5446 21.7280i 0.545419 0.944694i
\(530\) −4.40773 + 6.06148i −0.191460 + 0.263294i
\(531\) −15.6501 7.07815i −0.679155 0.307166i
\(532\) 0.0761475i 0.00330141i
\(533\) −15.7721 9.10603i −0.683165 0.394426i
\(534\) 0.136216 0.631731i 0.00589466 0.0273377i
\(535\) −2.48939 + 23.5915i −0.107626 + 1.01995i
\(536\) 4.72920 + 8.19122i 0.204270 + 0.353807i
\(537\) 5.22656 + 16.2477i 0.225543 + 0.701140i
\(538\) −7.97898 4.60667i −0.343998 0.198608i
\(539\) −5.00169 −0.215438
\(540\) 4.75143 21.3833i 0.204469 0.920192i
\(541\) −35.0774 −1.50809 −0.754047 0.656821i \(-0.771901\pi\)
−0.754047 + 0.656821i \(0.771901\pi\)
\(542\) −6.78662 3.91825i −0.291510 0.168303i
\(543\) 4.46147 + 13.8693i 0.191460 + 0.595188i
\(544\) 2.65107 + 4.59178i 0.113664 + 0.196871i
\(545\) −27.3620 2.88725i −1.17206 0.123676i
\(546\) −0.257238 + 1.19300i −0.0110088 + 0.0510555i
\(547\) −36.5290 21.0900i −1.56187 0.901744i −0.997068 0.0765154i \(-0.975621\pi\)
−0.564798 0.825229i \(-0.691046\pi\)
\(548\) 12.3528i 0.527684i
\(549\) 1.89146 + 19.0716i 0.0807256 + 0.813956i
\(550\) 8.05838 2.61099i 0.343611 0.111333i
\(551\) −0.137260 + 0.237741i −0.00584746 + 0.0101281i
\(552\) 10.6112 11.7157i 0.451645 0.498653i
\(553\) −11.1396 + 6.43143i −0.473702 + 0.273492i
\(554\) 1.06661 + 1.84742i 0.0453158 + 0.0784892i
\(555\) 10.8463 2.26756i 0.460399 0.0962525i
\(556\) 15.9499 27.6260i 0.676425 1.17160i
\(557\) 36.2511i 1.53601i 0.640444 + 0.768005i \(0.278750\pi\)
−0.640444 + 0.768005i \(0.721250\pi\)
\(558\) −6.13155 8.54432i −0.259569 0.361710i
\(559\) −17.4851 −0.739539
\(560\) 6.79294 3.02106i 0.287054 0.127663i
\(561\) 2.57619 11.9476i 0.108767 0.504428i
\(562\) 5.83568 3.36923i 0.246163 0.142123i
\(563\) −37.3071 + 21.5393i −1.57231 + 0.907772i −0.576422 + 0.817152i \(0.695552\pi\)
−0.995886 + 0.0906202i \(0.971115\pi\)
\(564\) −23.5238 + 7.56715i −0.990533 + 0.318635i
\(565\) 8.74628 3.88978i 0.367959 0.163644i
\(566\) 2.04347 0.0858934
\(567\) 6.75850 5.94329i 0.283830 0.249595i
\(568\) 0.605091i 0.0253891i
\(569\) 22.1047 38.2865i 0.926679 1.60505i 0.137840 0.990455i \(-0.455984\pi\)
0.788839 0.614600i \(-0.210683\pi\)
\(570\) 0.0165423 0.0503383i 0.000692879 0.00210844i
\(571\) 6.56750 + 11.3752i 0.274841 + 0.476039i 0.970095 0.242725i \(-0.0780413\pi\)
−0.695254 + 0.718764i \(0.744708\pi\)
\(572\) −16.9874 + 9.80770i −0.710280 + 0.410081i
\(573\) −7.56823 1.63189i −0.316167 0.0681733i
\(574\) 1.48273 2.56816i 0.0618878 0.107193i
\(575\) −32.9850 + 10.6875i −1.37557 + 0.445698i
\(576\) −13.1047 + 9.40413i −0.546027 + 0.391839i
\(577\) 23.4282i 0.975327i −0.873032 0.487664i \(-0.837849\pi\)
0.873032 0.487664i \(-0.162151\pi\)
\(578\) −4.40290 2.54201i −0.183136 0.105734i
\(579\) 9.88657 + 8.95456i 0.410872 + 0.372139i
\(580\) 28.4934 + 3.00664i 1.18312 + 0.124844i
\(581\) −3.48094 6.02917i −0.144414 0.250132i
\(582\) −0.711007 + 0.785010i −0.0294722 + 0.0325397i
\(583\) −42.8621 24.7465i −1.77517 1.02489i
\(584\) 2.27510 0.0941441
\(585\) −7.05297 + 12.0409i −0.291604 + 0.497830i
\(586\) −4.24991 −0.175562
\(587\) −18.8578 10.8875i −0.778343 0.449376i 0.0574999 0.998346i \(-0.481687\pi\)
−0.835843 + 0.548969i \(0.815020\pi\)
\(588\) 3.19202 + 0.688277i 0.131637 + 0.0283840i
\(589\) 0.209013 + 0.362020i 0.00861221 + 0.0149168i
\(590\) −0.455056 + 4.31249i −0.0187343 + 0.177542i
\(591\) −4.96434 + 1.59693i −0.204206 + 0.0656888i
\(592\) −8.23794 4.75618i −0.338577 0.195478i
\(593\) 20.0469i 0.823226i −0.911359 0.411613i \(-0.864966\pi\)
0.911359 0.411613i \(-0.135034\pi\)
\(594\) −8.74648 0.997178i −0.358872 0.0409147i
\(595\) 1.85533 2.55143i 0.0760612 0.104599i
\(596\) −1.43148 + 2.47939i −0.0586356 + 0.101560i
\(597\) −13.6878 42.5509i −0.560203 1.74149i
\(598\) −4.23157 + 2.44310i −0.173042 + 0.0999056i
\(599\) −2.88211 4.99197i −0.117760 0.203966i 0.801120 0.598504i \(-0.204238\pi\)
−0.918880 + 0.394538i \(0.870905\pi\)
\(600\) −11.3390 + 1.14873i −0.462912 + 0.0468966i
\(601\) 1.91782 3.32177i 0.0782296 0.135498i −0.824257 0.566217i \(-0.808407\pi\)
0.902486 + 0.430719i \(0.141740\pi\)
\(602\) 2.84708i 0.116038i
\(603\) −8.88524 + 19.6456i −0.361835 + 0.800031i
\(604\) 18.2082 0.740883
\(605\) 12.7364 + 28.6382i 0.517809 + 1.16431i
\(606\) −2.99543 2.71305i −0.121681 0.110210i
\(607\) 17.0492 9.84338i 0.692007 0.399531i −0.112356 0.993668i \(-0.535840\pi\)
0.804364 + 0.594137i \(0.202506\pi\)
\(608\) −0.131460 + 0.0758982i −0.00533139 + 0.00307808i
\(609\) 8.72517 + 7.90264i 0.353562 + 0.320231i
\(610\) 4.42105 1.96620i 0.179003 0.0796090i
\(611\) 15.7421 0.636858
\(612\) −3.28819 + 7.27032i −0.132917 + 0.293885i
\(613\) 18.0267i 0.728090i −0.931381 0.364045i \(-0.881395\pi\)
0.931381 0.364045i \(-0.118605\pi\)
\(614\) 1.69715 2.93955i 0.0684914 0.118631i
\(615\) 25.2740 22.6042i 1.01915 0.911490i
\(616\) −3.29114 5.70043i −0.132604 0.229677i
\(617\) 36.7976 21.2451i 1.48142 0.855296i 0.481637 0.876371i \(-0.340042\pi\)
0.999778 + 0.0210751i \(0.00670891\pi\)
\(618\) 2.54740 + 7.91904i 0.102471 + 0.318550i
\(619\) 14.3022 24.7722i 0.574855 0.995677i −0.421203 0.906967i \(-0.638392\pi\)
0.996057 0.0887110i \(-0.0282748\pi\)
\(620\) 25.6592 35.2863i 1.03050 1.41713i
\(621\) 35.8015 + 4.08170i 1.43667 + 0.163793i
\(622\) 1.63169i 0.0654250i
\(623\) 0.953963 + 0.550771i 0.0382197 + 0.0220662i
\(624\) 11.4038 3.66837i 0.456517 0.146852i
\(625\) 22.8219 + 10.2060i 0.912874 + 0.408240i
\(626\) −0.903542 1.56498i −0.0361128 0.0625492i
\(627\) 0.342051 + 0.0737545i 0.0136602 + 0.00294547i
\(628\) 33.1208 + 19.1223i 1.32166 + 0.763063i
\(629\) −4.03642 −0.160943
\(630\) −1.96061 1.14843i −0.0781124 0.0457545i
\(631\) −11.6101 −0.462192 −0.231096 0.972931i \(-0.574231\pi\)
−0.231096 + 0.972931i \(0.574231\pi\)
\(632\) −14.6598 8.46385i −0.583136 0.336674i
\(633\) −21.9857 + 24.2740i −0.873852 + 0.964805i
\(634\) 1.54783 + 2.68092i 0.0614722 + 0.106473i
\(635\) 1.73010 16.3959i 0.0686571 0.650652i
\(636\) 23.9488 + 21.6911i 0.949632 + 0.860109i
\(637\) −1.80151 1.04011i −0.0713786 0.0412105i
\(638\) 11.5145i 0.455864i
\(639\) −1.12067 + 0.804215i −0.0443331 + 0.0318143i
\(640\) 16.8867 + 12.2795i 0.667506 + 0.485391i
\(641\) −6.01131 + 10.4119i −0.237433 + 0.411245i −0.959977 0.280079i \(-0.909639\pi\)
0.722544 + 0.691325i \(0.242973\pi\)
\(642\) −6.08425 1.31191i −0.240126 0.0517770i
\(643\) 4.12908 2.38393i 0.162835 0.0940129i −0.416368 0.909196i \(-0.636697\pi\)
0.579203 + 0.815183i \(0.303364\pi\)
\(644\) 6.53684 + 11.3221i 0.257587 + 0.446155i
\(645\) 10.1633 30.9270i 0.400178 1.21775i
\(646\) −0.00965080 + 0.0167157i −0.000379706 + 0.000657669i
\(647\) 12.8704i 0.505989i −0.967468 0.252995i \(-0.918585\pi\)
0.967468 0.252995i \(-0.0814155\pi\)
\(648\) 11.2207 + 3.79194i 0.440791 + 0.148961i
\(649\) −28.6368 −1.12409
\(650\) 3.44544 + 0.735316i 0.135141 + 0.0288415i
\(651\) 17.0647 5.48937i 0.668818 0.215145i
\(652\) 34.5604 19.9534i 1.35349 0.781437i
\(653\) 18.9241 10.9258i 0.740557 0.427561i −0.0817150 0.996656i \(-0.526040\pi\)
0.822272 + 0.569095i \(0.192706\pi\)
\(654\) 1.52158 7.05665i 0.0594986 0.275937i
\(655\) −3.40166 7.64872i −0.132914 0.298860i
\(656\) −29.1082 −1.13648
\(657\) 3.02379 + 4.21364i 0.117969 + 0.164390i
\(658\) 2.56327i 0.0999269i
\(659\) −19.5372 + 33.8395i −0.761062 + 1.31820i 0.181242 + 0.983439i \(0.441988\pi\)
−0.942304 + 0.334759i \(0.891345\pi\)
\(660\) −7.47350 35.7475i −0.290905 1.39147i
\(661\) 6.07402 + 10.5205i 0.236252 + 0.409201i 0.959636 0.281246i \(-0.0907476\pi\)
−0.723384 + 0.690446i \(0.757414\pi\)
\(662\) 1.22313 0.706175i 0.0475383 0.0274463i
\(663\) 3.41241 3.76758i 0.132527 0.146321i
\(664\) 4.58096 7.93446i 0.177776 0.307917i
\(665\) 0.0730458 + 0.0531168i 0.00283259 + 0.00205978i
\(666\) 0.286926 + 2.89308i 0.0111182 + 0.112104i
\(667\) 47.1318i 1.82495i
\(668\) −16.0978 9.29408i −0.622843 0.359599i
\(669\) −1.52063 + 7.05225i −0.0587911 + 0.272656i
\(670\) 5.41349 + 0.571234i 0.209141 + 0.0220687i
\(671\) 15.9764 + 27.6719i 0.616760 + 1.06826i
\(672\) 1.99334 + 6.19666i 0.0768948 + 0.239041i
\(673\) −11.7942 6.80937i −0.454632 0.262482i 0.255152 0.966901i \(-0.417874\pi\)
−0.709785 + 0.704419i \(0.751208\pi\)
\(674\) 3.67883 0.141703
\(675\) −17.1979 19.4739i −0.661949 0.749549i
\(676\) 16.3504 0.628863
\(677\) −12.5600 7.25152i −0.482720 0.278699i 0.238829 0.971062i \(-0.423236\pi\)
−0.721549 + 0.692363i \(0.756570\pi\)
\(678\) 0.769079 + 2.39082i 0.0295363 + 0.0918189i
\(679\) −0.902656 1.56345i −0.0346408 0.0599996i
\(680\) 4.12869 + 0.435662i 0.158328 + 0.0167069i
\(681\) 6.14866 28.5157i 0.235617 1.09272i
\(682\) −15.1847 8.76689i −0.581452 0.335701i
\(683\) 17.4035i 0.665925i −0.942940 0.332963i \(-0.891952\pi\)
0.942940 0.332963i \(-0.108048\pi\)
\(684\) −0.208144 0.0941386i −0.00795859 0.00359948i
\(685\) 11.8496 + 8.61669i 0.452750 + 0.329227i
\(686\) 0.169359 0.293339i 0.00646617 0.0111997i
\(687\) 4.57511 5.05130i 0.174551 0.192719i
\(688\) −24.2021 + 13.9731i −0.922698 + 0.532720i
\(689\) −10.2921 17.8264i −0.392098 0.679133i
\(690\) −1.86165 8.90470i −0.0708716 0.338996i
\(691\) 11.4467 19.8263i 0.435453 0.754228i −0.561879 0.827219i \(-0.689921\pi\)
0.997333 + 0.0729918i \(0.0232547\pi\)
\(692\) 24.6780i 0.938117i
\(693\) 6.18341 13.6718i 0.234888 0.519348i
\(694\) −0.000599966 0 −2.27744e−5 0
\(695\) −15.3748 34.5707i −0.583200 1.31134i
\(696\) −3.26543 + 15.1441i −0.123776 + 0.574035i
\(697\) −10.6968 + 6.17580i −0.405170 + 0.233925i
\(698\) −0.177104 + 0.102251i −0.00670349 + 0.00387026i
\(699\) 14.9321 4.80336i 0.564784 0.181680i
\(700\) 1.96744 9.21874i 0.0743622 0.348436i
\(701\) 44.2233 1.67029 0.835146 0.550028i \(-0.185383\pi\)
0.835146 + 0.550028i \(0.185383\pi\)
\(702\) −2.94295 2.17800i −0.111075 0.0822034i
\(703\) 0.115560i 0.00435843i
\(704\) −13.4460 + 23.2892i −0.506766 + 0.877744i
\(705\) −9.15018 + 27.8441i −0.344616 + 1.04867i
\(706\) 4.31417 + 7.47236i 0.162366 + 0.281226i
\(707\) 5.96579 3.44435i 0.224366 0.129538i
\(708\) 18.2757 + 3.94068i 0.686843 + 0.148100i
\(709\) −5.01095 + 8.67921i −0.188190 + 0.325955i −0.944647 0.328089i \(-0.893595\pi\)
0.756457 + 0.654044i \(0.226929\pi\)
\(710\) 0.281652 + 0.204809i 0.0105702 + 0.00768635i
\(711\) −3.80841 38.4002i −0.142827 1.44012i
\(712\) 1.44964i 0.0543277i
\(713\) 62.1548 + 35.8851i 2.32772 + 1.34391i
\(714\) 0.613472 + 0.555639i 0.0229586 + 0.0207943i
\(715\) −2.44141 + 23.1369i −0.0913036 + 0.865269i
\(716\) −9.28873 16.0886i −0.347136 0.601258i
\(717\) −0.620402 + 0.684975i −0.0231693 + 0.0255809i
\(718\) 0.159744 + 0.0922282i 0.00596159 + 0.00344192i
\(719\) −26.6950 −0.995556 −0.497778 0.867304i \(-0.665851\pi\)
−0.497778 + 0.867304i \(0.665851\pi\)
\(720\) −0.140015 + 22.3029i −0.00521804 + 0.831179i
\(721\) −14.1793 −0.528064
\(722\) 5.57296 + 3.21755i 0.207404 + 0.119745i
\(723\) −12.6522 2.72812i −0.470541 0.101460i
\(724\) −7.92901 13.7335i −0.294679 0.510400i
\(725\) 22.7598 25.2355i 0.845277 0.937222i
\(726\) −7.82833 + 2.51822i −0.290536 + 0.0934598i
\(727\) −36.9504 21.3333i −1.37041 0.791209i −0.379434 0.925219i \(-0.623881\pi\)
−0.990980 + 0.134010i \(0.957215\pi\)
\(728\) 2.73758i 0.101462i
\(729\) 7.89029 + 25.8214i 0.292233 + 0.956347i
\(730\) 0.770066 1.05899i 0.0285014 0.0391949i
\(731\) −5.92928 + 10.2698i −0.219302 + 0.379843i
\(732\) −6.38804 19.8584i −0.236109 0.733986i
\(733\) −31.9343 + 18.4373i −1.17952 + 0.680997i −0.955904 0.293680i \(-0.905120\pi\)
−0.223618 + 0.974677i \(0.571787\pi\)
\(734\) 0.309786 + 0.536565i 0.0114344 + 0.0198050i
\(735\) 2.88684 2.58189i 0.106483 0.0952345i
\(736\) −13.0309 + 22.5701i −0.480324 + 0.831945i
\(737\) 35.9479i 1.32416i
\(738\) 5.18683 + 7.22785i 0.190930 + 0.266061i
\(739\) −0.581344 −0.0213851 −0.0106925 0.999943i \(-0.503404\pi\)
−0.0106925 + 0.999943i \(0.503404\pi\)
\(740\) −11.0203 + 4.90111i −0.405114 + 0.180169i
\(741\) 0.107863 + 0.0976949i 0.00396245 + 0.00358891i
\(742\) 2.90266 1.67585i 0.106560 0.0615225i
\(743\) −45.9775 + 26.5451i −1.68675 + 0.973847i −0.729773 + 0.683690i \(0.760374\pi\)
−0.956979 + 0.290157i \(0.906293\pi\)
\(744\) 17.4849 + 15.8366i 0.641029 + 0.580598i
\(745\) 1.37987 + 3.10267i 0.0505545 + 0.113673i
\(746\) −10.8311 −0.396554
\(747\) 20.7837 2.06126i 0.760435 0.0754176i
\(748\) 13.3034i 0.486419i
\(749\) 5.30451 9.18768i 0.193823 0.335711i
\(750\) −3.30328 + 5.66677i −0.120619 + 0.206921i
\(751\) 17.3812 + 30.1051i 0.634248 + 1.09855i 0.986674 + 0.162710i \(0.0520235\pi\)
−0.352426 + 0.935840i \(0.614643\pi\)
\(752\) 21.7896 12.5802i 0.794586 0.458754i
\(753\) −9.19524 28.5850i −0.335093 1.04170i
\(754\) 2.39445 4.14732i 0.0872009 0.151036i
\(755\) 12.7012 17.4666i 0.462243 0.635673i
\(756\) −5.82754 + 7.87428i −0.211946 + 0.286385i
\(757\) 27.7090i 1.00710i 0.863966 + 0.503551i \(0.167973\pi\)
−0.863966 + 0.503551i \(0.832027\pi\)
\(758\) −1.64940 0.952283i −0.0599090 0.0345885i
\(759\) 57.1899 18.3969i 2.07586 0.667764i
\(760\) −0.0124727 + 0.118202i −0.000452432 + 0.00428762i
\(761\) 8.38181 + 14.5177i 0.303841 + 0.526267i 0.977003 0.213228i \(-0.0683977\pi\)
−0.673162 + 0.739495i \(0.735064\pi\)
\(762\) 4.22850 + 0.911767i 0.153182 + 0.0330298i
\(763\) 10.6561 + 6.15229i 0.385776 + 0.222728i
\(764\) 8.42705 0.304880
\(765\) 4.68049 + 8.22567i 0.169223 + 0.297400i
\(766\) −5.60860 −0.202647
\(767\) −10.3144 5.95505i −0.372433 0.215024i
\(768\) 8.82564 9.74423i 0.318468 0.351615i
\(769\) −0.244121 0.422830i −0.00880323 0.0152476i 0.861590 0.507604i \(-0.169469\pi\)
−0.870393 + 0.492357i \(0.836136\pi\)
\(770\) −3.76735 0.397533i −0.135766 0.0143261i
\(771\) 1.28093 + 1.16018i 0.0461316 + 0.0417827i
\(772\) −12.5738 7.25948i −0.452541 0.261274i
\(773\) 26.3957i 0.949388i −0.880151 0.474694i \(-0.842559\pi\)
0.880151 0.474694i \(-0.157441\pi\)
\(774\) 7.78229 + 3.51974i 0.279729 + 0.126515i
\(775\) −15.9503 49.2280i −0.572953 1.76832i
\(776\) 1.18791 2.05752i 0.0426434 0.0738605i
\(777\) −4.84415 1.04451i −0.173783 0.0374717i
\(778\) 5.26254 3.03833i 0.188671 0.108929i
\(779\) −0.176809 0.306242i −0.00633484 0.0109723i
\(780\) 4.74192 14.4297i 0.169788 0.516667i
\(781\) −1.14987 + 1.99163i −0.0411454 + 0.0712660i
\(782\) 3.31387i 0.118504i
\(783\) −32.3880 + 14.0799i −1.15745 + 0.503174i
\(784\) −3.32478 −0.118742
\(785\) 41.4468 18.4329i 1.47930 0.657898i
\(786\) 2.09080 0.672567i 0.0745762 0.0239897i
\(787\) −0.661933 + 0.382167i −0.0235954 + 0.0136228i −0.511751 0.859134i \(-0.671003\pi\)
0.488156 + 0.872756i \(0.337670\pi\)
\(788\) 4.91571 2.83809i 0.175115 0.101103i
\(789\) −3.12546 + 14.4950i −0.111269 + 0.516035i
\(790\) −8.90167 + 3.95889i −0.316707 + 0.140851i
\(791\) −4.28084 −0.152209
\(792\) 19.6505 1.94887i 0.698248 0.0692501i
\(793\) 13.2892i 0.471913i
\(794\) −2.82127 + 4.88659i −0.100123 + 0.173419i
\(795\) 37.5131 7.84261i 1.33045 0.278149i
\(796\) 24.3261 + 42.1341i 0.862217 + 1.49340i
\(797\) 14.7430 8.51189i 0.522225 0.301507i −0.215619 0.976477i \(-0.569177\pi\)
0.737845 + 0.674971i \(0.235844\pi\)
\(798\) −0.0159076 + 0.0175633i −0.000563122 + 0.000621733i
\(799\) 5.33824 9.24610i 0.188853 0.327103i
\(800\) 17.8760 5.79201i 0.632013 0.204778i
\(801\) −2.68484 + 1.92669i −0.0948643 + 0.0680763i
\(802\) 2.17928i 0.0769532i
\(803\) 7.48836 + 4.32341i 0.264258 + 0.152570i
\(804\) 4.94676 22.9416i 0.174459 0.809087i
\(805\) 15.4207 + 1.62720i 0.543509 + 0.0573513i
\(806\) −3.64616 6.31534i −0.128431 0.222448i
\(807\) 14.4272 + 44.8494i 0.507860 + 1.57877i
\(808\) 7.85105 + 4.53281i 0.276199 + 0.159464i
\(809\) 6.38947 0.224642 0.112321 0.993672i \(-0.464172\pi\)
0.112321 + 0.993672i \(0.464172\pi\)
\(810\) 5.56298 3.93942i 0.195463 0.138417i
\(811\) −16.3920 −0.575601 −0.287800 0.957690i \(-0.592924\pi\)
−0.287800 + 0.957690i \(0.592924\pi\)
\(812\) −11.0967 6.40669i −0.389418 0.224831i
\(813\) 12.2712 + 38.1472i 0.430369 + 1.33788i
\(814\) 2.42354 + 4.19770i 0.0849451 + 0.147129i
\(815\) 4.96697 47.0712i 0.173985 1.64883i
\(816\) 1.71248 7.94195i 0.0599486 0.278024i
\(817\) −0.294017 0.169751i −0.0102864 0.00593884i
\(818\) 0.862757i 0.0301656i
\(819\) 5.07021 3.63847i 0.177167 0.127138i
\(820\) −21.7057 + 29.8496i −0.757998 + 1.04239i
\(821\) −3.24566 + 5.62165i −0.113274 + 0.196197i −0.917089 0.398683i \(-0.869467\pi\)
0.803814 + 0.594880i \(0.202801\pi\)
\(822\) −2.58055 + 2.84914i −0.0900069 + 0.0993751i
\(823\) −32.6474 + 18.8490i −1.13802 + 0.657033i −0.945938 0.324346i \(-0.894856\pi\)
−0.192077 + 0.981380i \(0.561522\pi\)
\(824\) −9.33007 16.1602i −0.325028 0.562966i
\(825\) −39.5046 17.7667i −1.37537 0.618556i
\(826\) 0.969655 1.67949i 0.0337386 0.0584370i
\(827\) 20.6768i 0.719002i −0.933145 0.359501i \(-0.882947\pi\)
0.933145 0.359501i \(-0.117053\pi\)
\(828\) −39.0295 + 3.87083i −1.35637 + 0.134521i
\(829\) 9.94279 0.345327 0.172664 0.984981i \(-0.444763\pi\)
0.172664 + 0.984981i \(0.444763\pi\)
\(830\) −2.14270 4.81793i −0.0743744 0.167233i
\(831\) 2.29924 10.6632i 0.0797598 0.369902i
\(832\) −9.68601 + 5.59222i −0.335802 + 0.193875i
\(833\) −1.22181 + 0.705410i −0.0423331 + 0.0244410i
\(834\) 9.44999 3.03987i 0.327227 0.105262i
\(835\) −20.1445 + 8.95900i −0.697131 + 0.310039i
\(836\) −0.380866 −0.0131725
\(837\) −6.09168 + 53.4315i −0.210559 + 1.84686i
\(838\) 4.31106i 0.148923i
\(839\) −22.2977 + 38.6208i −0.769804 + 1.33334i 0.167866 + 0.985810i \(0.446313\pi\)
−0.937669 + 0.347529i \(0.887021\pi\)
\(840\) 4.84214 + 1.59123i 0.167070 + 0.0549027i
\(841\) −8.59674 14.8900i −0.296439 0.513448i
\(842\) −2.27931 + 1.31596i −0.0785501 + 0.0453509i
\(843\) −33.6833 7.26292i −1.16011 0.250148i
\(844\) 17.8238 30.8718i 0.613522 1.06265i
\(845\) 11.4053 15.6844i 0.392353 0.539560i
\(846\) −7.00654 3.16889i −0.240890 0.108949i
\(847\) 14.0169i 0.481625i
\(848\) −28.4918 16.4498i −0.978413 0.564887i
\(849\) −7.74484 7.01473i −0.265802 0.240745i
\(850\) 1.60025 1.77432i 0.0548882 0.0608587i
\(851\) −9.92017 17.1822i −0.340059 0.588999i
\(852\) 1.00790 1.11280i 0.0345300 0.0381240i
\(853\) −43.6846 25.2213i −1.49573 0.863562i −0.495746 0.868468i \(-0.665105\pi\)
−0.999988 + 0.00490532i \(0.998439\pi\)
\(854\) −2.16387 −0.0740460
\(855\) −0.235495 + 0.133999i −0.00805377 + 0.00458267i
\(856\) 13.9616 0.477198
\(857\) 37.8817 + 21.8710i 1.29401 + 0.747099i 0.979363 0.202108i \(-0.0647792\pi\)
0.314651 + 0.949207i \(0.398113\pi\)
\(858\) −5.96699 1.28663i −0.203710 0.0439247i
\(859\) −7.60690 13.1755i −0.259544 0.449544i 0.706576 0.707637i \(-0.250239\pi\)
−0.966120 + 0.258094i \(0.916906\pi\)
\(860\) −3.71835 + 35.2382i −0.126795 + 1.20161i
\(861\) −14.4355 + 4.64360i −0.491959 + 0.158253i
\(862\) 8.48750 + 4.90026i 0.289085 + 0.166903i
\(863\) 5.44163i 0.185235i 0.995702 + 0.0926177i \(0.0295234\pi\)
−0.995702 + 0.0926177i \(0.970477\pi\)
\(864\) −19.4024 2.21206i −0.660085 0.0752557i
\(865\) −23.6728 17.2142i −0.804899 0.585300i
\(866\) 1.41027 2.44266i 0.0479229 0.0830048i
\(867\) 7.96107 + 24.7484i 0.270372 + 0.840500i
\(868\) −16.8976 + 9.75581i −0.573540 + 0.331134i
\(869\) −32.1680 55.7166i −1.09122 1.89006i
\(870\) 5.94384 + 6.64587i 0.201515 + 0.225316i
\(871\) −7.47541 + 12.9478i −0.253294 + 0.438719i
\(872\) 16.1930i 0.548364i
\(873\) 5.38950 0.534514i 0.182407 0.0180905i
\(874\) −0.0948737 −0.00320915
\(875\) −7.47084 8.31784i −0.252561 0.281194i
\(876\) −4.18405 3.78961i −0.141366 0.128039i
\(877\) 35.0971 20.2633i 1.18514 0.684243i 0.227945 0.973674i \(-0.426799\pi\)
0.957199 + 0.289430i \(0.0934659\pi\)
\(878\) −8.69505 + 5.02009i −0.293444 + 0.169420i
\(879\) 16.1074 + 14.5889i 0.543288 + 0.492072i
\(880\) 15.1104 + 33.9762i 0.509372 + 1.14534i
\(881\) −10.2204 −0.344333 −0.172167 0.985068i \(-0.555077\pi\)
−0.172167 + 0.985068i \(0.555077\pi\)
\(882\) 0.592449 + 0.825577i 0.0199488 + 0.0277986i
\(883\) 30.6526i 1.03154i −0.856727 0.515770i \(-0.827506\pi\)
0.856727 0.515770i \(-0.172494\pi\)
\(884\) −2.76645 + 4.79163i −0.0930457 + 0.161160i
\(885\) 16.5284 14.7824i 0.555596 0.496906i
\(886\) −6.46588 11.1992i −0.217225 0.376245i
\(887\) 26.6715 15.3988i 0.895542 0.517042i 0.0197910 0.999804i \(-0.493700\pi\)
0.875751 + 0.482763i \(0.160367\pi\)
\(888\) −1.99705 6.20817i −0.0670165 0.208333i
\(889\) −3.68659 + 6.38537i −0.123644 + 0.214158i
\(890\) 0.674765 + 0.490670i 0.0226182 + 0.0164473i
\(891\) 29.7265 + 33.8039i 0.995875 + 1.13247i
\(892\) 7.85251i 0.262922i
\(893\) 0.264709 + 0.152830i 0.00885816 + 0.00511426i
\(894\) −0.848123 + 0.272824i −0.0283655 + 0.00912461i
\(895\) −21.9126 2.31223i −0.732457 0.0772892i
\(896\) −4.66877 8.08654i −0.155973 0.270152i
\(897\) 24.4244 + 5.26649i 0.815507 + 0.175843i
\(898\) 1.97854 + 1.14231i 0.0660247 + 0.0381194i
\(899\) −70.3413 −2.34601
\(900\) 22.7665 + 16.7747i 0.758884 + 0.559156i
\(901\) −13.9604 −0.465089
\(902\) 12.8451 + 7.41613i 0.427695 + 0.246930i
\(903\) −9.77332 + 10.7906i −0.325236 + 0.359087i
\(904\) −2.81682 4.87888i −0.0936861 0.162269i
\(905\) −18.7049 1.97375i −0.621773 0.0656098i
\(906\) 4.19969 + 3.80378i 0.139525 + 0.126372i
\(907\) 40.5636 + 23.4194i 1.34689 + 0.777629i 0.987808 0.155675i \(-0.0497554\pi\)
0.359085 + 0.933305i \(0.383089\pi\)
\(908\) 31.7515i 1.05371i
\(909\) 2.03959 + 20.5652i 0.0676490 + 0.682104i
\(910\) −1.27426 0.926608i −0.0422414 0.0307168i
\(911\) 25.4261 44.0393i 0.842405 1.45909i −0.0454504 0.998967i \(-0.514472\pi\)
0.887856 0.460122i \(-0.152194\pi\)
\(912\) 0.227372 + 0.0490270i 0.00752905 + 0.00162345i
\(913\) 30.1560 17.4106i 0.998018 0.576206i
\(914\) −2.70552 4.68610i −0.0894907 0.155002i
\(915\) −23.5055 7.72440i −0.777066 0.255361i
\(916\) −3.70905 + 6.42427i −0.122551 + 0.212264i
\(917\) 3.74364i 0.123626i
\(918\) −2.27722 + 0.989965i −0.0751593 + 0.0326737i
\(919\) 26.6976 0.880671 0.440336 0.897833i \(-0.354860\pi\)
0.440336 + 0.897833i \(0.354860\pi\)
\(920\) 8.29241 + 18.6457i 0.273393 + 0.614731i
\(921\) −16.5230 + 5.31513i −0.544453 + 0.175140i
\(922\) −7.11064 + 4.10533i −0.234176 + 0.135202i
\(923\) −0.828320 + 0.478231i −0.0272645 + 0.0157412i
\(924\) −3.44254 + 15.9655i −0.113251 + 0.525226i
\(925\) −2.98574 + 13.9902i −0.0981707 + 0.459994i
\(926\) −12.6716 −0.416416
\(927\) 17.5294 38.7581i 0.575740 1.27298i
\(928\) 25.5428i 0.838485i
\(929\) −12.8946 + 22.3341i −0.423058 + 0.732758i −0.996237 0.0866721i \(-0.972377\pi\)
0.573179 + 0.819430i \(0.305710\pi\)
\(930\) 13.2897 2.77839i 0.435786 0.0911069i
\(931\) −0.0201954 0.0349795i −0.000661877 0.00114641i
\(932\) −14.7859 + 8.53662i −0.484327 + 0.279626i
\(933\) 5.60121 6.18420i 0.183375 0.202462i
\(934\) 4.62297 8.00723i 0.151268 0.262004i
\(935\) 12.7615 + 9.27978i 0.417345 + 0.303481i
\(936\) 7.48300 + 3.38438i 0.244589 + 0.110622i
\(937\) 13.8416i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(938\) −2.10827 1.21721i −0.0688376 0.0397434i
\(939\) −1.94773 + 9.03299i −0.0635617 + 0.294780i
\(940\) 3.34770 31.7256i 0.109190 1.03478i
\(941\) 10.9224 + 18.9181i 0.356059 + 0.616712i 0.987299 0.158876i \(-0.0507870\pi\)
−0.631240 + 0.775588i \(0.717454\pi\)
\(942\) 3.64451 + 11.3296i 0.118744 + 0.369138i
\(943\) −52.5783 30.3561i −1.71218 0.988530i
\(944\) −19.0358 −0.619563
\(945\) 3.48852 + 11.0829i 0.113482 + 0.360526i
\(946\) 14.2402 0.462988
\(947\) −16.9340 9.77685i −0.550281 0.317705i 0.198954 0.980009i \(-0.436245\pi\)
−0.749235 + 0.662304i \(0.769579\pi\)
\(948\) 12.8622 + 39.9843i 0.417743 + 1.29863i
\(949\) 1.79811 + 3.11442i 0.0583692 + 0.101098i
\(950\) 0.0507976 + 0.0458141i 0.00164809 + 0.00148641i
\(951\) 3.33660 15.4741i 0.108197 0.501783i
\(952\) −1.60791 0.928329i −0.0521128 0.0300873i
\(953\) 10.4366i 0.338076i −0.985610 0.169038i \(-0.945934\pi\)
0.985610 0.169038i \(-0.0540661\pi\)
\(954\) 0.992366 + 10.0060i 0.0321290 + 0.323957i
\(955\) 5.87830 8.08379i 0.190217 0.261585i
\(956\) 0.502961 0.871154i 0.0162669 0.0281751i
\(957\) −39.5265 + 43.6406i −1.27771 + 1.41070i
\(958\) −5.43734 + 3.13925i −0.175672 + 0.101425i
\(959\) −3.27613 5.67442i −0.105792 0.183236i
\(960\) −4.26129 20.3828i −0.137532 0.657851i
\(961\) −38.0562 + 65.9152i −1.22762 + 2.12630i
\(962\) 2.01591i 0.0649956i
\(963\) 18.5561 + 25.8579i 0.597963 + 0.833260i
\(964\) 14.0879 0.453742
\(965\) −15.7346 + 6.99775i −0.506516 + 0.225266i
\(966\) −0.857537 + 3.97700i −0.0275908 + 0.127958i
\(967\) −46.4167 + 26.7987i −1.49266 + 0.861788i −0.999965 0.00841431i \(-0.997322\pi\)
−0.492695 + 0.870202i \(0.663988\pi\)
\(968\) 15.9750 9.22319i 0.513457 0.296445i
\(969\) 0.0939578 0.0302244i 0.00301836 0.000970946i
\(970\) −0.555633 1.24936i −0.0178403 0.0401144i
\(971\) 48.6157 1.56015 0.780077 0.625684i \(-0.215180\pi\)
0.780077 + 0.625684i \(0.215180\pi\)
\(972\) −14.3194 25.6639i −0.459295 0.823170i
\(973\) 16.9205i 0.542447i
\(974\) 1.43296 2.48196i 0.0459150 0.0795272i
\(975\) −10.5342 14.6142i −0.337365 0.468030i
\(976\) 10.6200 + 18.3944i 0.339938 + 0.588790i
\(977\) 20.3875 11.7707i 0.652255 0.376579i −0.137065 0.990562i \(-0.543767\pi\)
0.789319 + 0.613983i \(0.210434\pi\)
\(978\) 12.1396 + 2.61760i 0.388183 + 0.0837016i
\(979\) −2.75478 + 4.77142i −0.0880432 + 0.152495i
\(980\) −2.47927 + 3.40946i −0.0791973 + 0.108911i
\(981\) −29.9906 + 21.5218i −0.957527 + 0.687138i
\(982\) 9.04370i 0.288596i
\(983\) 28.8136 + 16.6355i 0.919010 + 0.530591i 0.883319 0.468772i \(-0.155303\pi\)
0.0356911 + 0.999363i \(0.488637\pi\)
\(984\) −14.7909 13.3966i −0.471518 0.427067i
\(985\) 0.706480 6.69519i 0.0225103 0.213326i
\(986\) −1.62394 2.81275i −0.0517169 0.0895763i
\(987\) 8.79910 9.71493i 0.280078 0.309230i
\(988\) −0.137181 0.0792015i −0.00436431 0.00251973i
\(989\) −58.2887 −1.85347
\(990\) 5.74408 9.80634i 0.182559 0.311666i
\(991\) −41.7491 −1.32620 −0.663102 0.748529i \(-0.730761\pi\)
−0.663102 + 0.748529i \(0.730761\pi\)
\(992\) −33.6844 19.4477i −1.06948 0.617466i
\(993\) −7.05985 1.52227i −0.224038 0.0483079i
\(994\) −0.0778699 0.134875i −0.00246988 0.00427796i
\(995\) 57.3866 + 6.05546i 1.81928 + 0.191971i
\(996\) −21.6411 + 6.96150i −0.685724 + 0.220584i
\(997\) 29.6361 + 17.1104i 0.938586 + 0.541893i 0.889517 0.456903i \(-0.151041\pi\)
0.0490691 + 0.998795i \(0.484375\pi\)
\(998\) 6.67935i 0.211431i
\(999\) 8.84376 11.9498i 0.279804 0.378076i
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.bh.c.169.14 64
3.2 odd 2 945.2.bh.c.694.19 64
5.4 even 2 inner 315.2.bh.c.169.19 yes 64
9.4 even 3 inner 315.2.bh.c.274.19 yes 64
9.5 odd 6 945.2.bh.c.64.14 64
15.14 odd 2 945.2.bh.c.694.14 64
45.4 even 6 inner 315.2.bh.c.274.14 yes 64
45.14 odd 6 945.2.bh.c.64.19 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bh.c.169.14 64 1.1 even 1 trivial
315.2.bh.c.169.19 yes 64 5.4 even 2 inner
315.2.bh.c.274.14 yes 64 45.4 even 6 inner
315.2.bh.c.274.19 yes 64 9.4 even 3 inner
945.2.bh.c.64.14 64 9.5 odd 6
945.2.bh.c.64.19 64 45.14 odd 6
945.2.bh.c.694.14 64 15.14 odd 2
945.2.bh.c.694.19 64 3.2 odd 2