Properties

Label 95.2.e.b.11.1
Level $95$
Weight $2$
Character 95.11
Analytic conductor $0.759$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(11,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\), 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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3518667.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(1.14257 - 1.97899i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.2.e.b.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.14257 + 1.97899i) q^{2} +(1.25351 - 2.17114i) q^{3} +(-1.61094 - 2.79023i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.86445 + 4.96137i) q^{6} +3.50702 q^{7} +2.79216 q^{8} +(-1.64257 - 2.84502i) q^{9} +O(q^{10})\) \(q+(-1.14257 + 1.97899i) q^{2} +(1.25351 - 2.17114i) q^{3} +(-1.61094 - 2.79023i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.86445 + 4.96137i) q^{6} +3.50702 q^{7} +2.79216 q^{8} +(-1.64257 - 2.84502i) q^{9} +(1.14257 + 1.97899i) q^{10} -4.50702 q^{11} -8.07730 q^{12} +(2.50000 + 4.33013i) q^{13} +(-4.00702 + 6.94036i) q^{14} +(-1.25351 - 2.17114i) q^{15} +(0.0316332 - 0.0547902i) q^{16} +(-0.0793049 + 0.137360i) q^{17} +7.50702 q^{18} +(-4.26053 + 0.920816i) q^{19} -3.22188 q^{20} +(4.39608 - 7.61423i) q^{21} +(5.14959 - 8.91935i) q^{22} +(-0.579305 - 1.00339i) q^{23} +(3.50000 - 6.06218i) q^{24} +(-0.500000 - 0.866025i) q^{25} -11.4257 q^{26} -0.714858 q^{27} +(-5.64959 - 9.78538i) q^{28} +(1.75351 + 3.03717i) q^{29} +5.72889 q^{30} -2.28514 q^{31} +(2.86445 + 4.96137i) q^{32} +(-5.64959 + 9.78538i) q^{33} +(-0.181223 - 0.313888i) q^{34} +(1.75351 - 3.03717i) q^{35} +(-5.29216 + 9.16629i) q^{36} -10.9648 q^{37} +(3.04567 - 9.48365i) q^{38} +12.5351 q^{39} +(1.39608 - 2.41808i) q^{40} +(-3.03865 + 5.26310i) q^{41} +(10.0457 + 17.3996i) q^{42} +(1.67420 - 2.89981i) q^{43} +(7.26053 + 12.5756i) q^{44} -3.28514 q^{45} +2.64759 q^{46} +(-1.53163 - 2.65287i) q^{47} +(-0.0793049 - 0.137360i) q^{48} +5.29918 q^{49} +2.28514 q^{50} +(0.198819 + 0.344364i) q^{51} +(8.05469 - 13.9511i) q^{52} +(2.87147 + 4.97353i) q^{53} +(0.816776 - 1.41470i) q^{54} +(-2.25351 + 3.90319i) q^{55} +9.79216 q^{56} +(-3.34139 + 10.4045i) q^{57} -8.01404 q^{58} +(-1.53163 + 2.65287i) q^{59} +(-4.03865 + 6.99515i) q^{60} +(0.436734 + 0.756445i) q^{61} +(2.61094 - 4.52228i) q^{62} +(-5.76053 - 9.97753i) q^{63} -12.9648 q^{64} +5.00000 q^{65} +(-12.9101 - 22.3610i) q^{66} +(4.22188 + 7.31250i) q^{67} +0.511021 q^{68} -2.90466 q^{69} +(4.00702 + 6.94036i) q^{70} +(8.11796 - 14.0607i) q^{71} +(-4.58632 - 7.94375i) q^{72} +(3.57930 - 6.19954i) q^{73} +(12.5281 - 21.6993i) q^{74} -2.50702 q^{75} +(9.43273 + 10.4045i) q^{76} -15.8062 q^{77} +(-14.3222 + 24.8068i) q^{78} +(5.06327 - 8.76983i) q^{79} +(-0.0316332 - 0.0547902i) q^{80} +(4.03163 - 6.98299i) q^{81} +(-6.94375 - 12.0269i) q^{82} +4.85543 q^{83} -28.3273 q^{84} +(0.0793049 + 0.137360i) q^{85} +(3.82580 + 6.62647i) q^{86} +8.79216 q^{87} -12.5843 q^{88} +(0.556248 + 0.963449i) q^{89} +(3.75351 - 6.50127i) q^{90} +(8.76755 + 15.1858i) q^{91} +(-1.86645 + 3.23278i) q^{92} +(-2.86445 + 4.96137i) q^{93} +7.00000 q^{94} +(-1.33281 + 4.15013i) q^{95} +14.3624 q^{96} +(-0.809757 + 1.40254i) q^{97} +(-6.05469 + 10.4870i) q^{98} +(7.40310 + 12.8225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - q^{3} - 7 q^{4} + 3 q^{5} + 6 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - q^{3} - 7 q^{4} + 3 q^{5} + 6 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + q^{10} - 10 q^{11} - 8 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 3 q^{16} - q^{17} + 28 q^{18} - 14 q^{20} + 12 q^{21} + 8 q^{22} - 4 q^{23} + 21 q^{24} - 3 q^{25} - 10 q^{26} - 16 q^{27} - 11 q^{28} + 2 q^{29} + 12 q^{30} - 2 q^{31} + 6 q^{32} - 11 q^{33} + 25 q^{34} + 2 q^{35} - 3 q^{36} - 4 q^{37} - 19 q^{38} - 10 q^{39} - 6 q^{40} + 2 q^{41} + 23 q^{42} + q^{43} + 18 q^{44} - 8 q^{45} - 48 q^{46} - 6 q^{47} - q^{48} - 14 q^{49} + 2 q^{50} + 6 q^{51} + 35 q^{52} - 11 q^{53} - 10 q^{54} - 5 q^{55} + 30 q^{56} - 19 q^{57} - 14 q^{58} - 6 q^{59} - 4 q^{60} + 9 q^{61} + 13 q^{62} - 9 q^{63} - 16 q^{64} + 30 q^{65} - 29 q^{66} + 20 q^{67} + 68 q^{68} - 10 q^{69} + 7 q^{70} + 29 q^{71} - 11 q^{72} + 22 q^{73} + 7 q^{74} + 2 q^{75} - 19 q^{76} - 32 q^{77} - 30 q^{78} + 24 q^{79} + 3 q^{80} + 21 q^{81} - 31 q^{82} - 6 q^{83} - 56 q^{84} + q^{85} + 32 q^{86} + 24 q^{87} - 18 q^{88} + 14 q^{89} + 14 q^{90} + 10 q^{91} - 41 q^{92} - 6 q^{93} + 42 q^{94} + 34 q^{96} - 7 q^{97} - 23 q^{98} + 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14257 + 1.97899i −0.807920 + 1.39936i 0.106382 + 0.994325i \(0.466073\pi\)
−0.914302 + 0.405033i \(0.867260\pi\)
\(3\) 1.25351 2.17114i 0.723714 1.25351i −0.235787 0.971805i \(-0.575767\pi\)
0.959501 0.281705i \(-0.0908998\pi\)
\(4\) −1.61094 2.79023i −0.805469 1.39511i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 2.86445 + 4.96137i 1.16941 + 2.02547i
\(7\) 3.50702 1.32553 0.662764 0.748828i \(-0.269383\pi\)
0.662764 + 0.748828i \(0.269383\pi\)
\(8\) 2.79216 0.987178
\(9\) −1.64257 2.84502i −0.547524 0.948339i
\(10\) 1.14257 + 1.97899i 0.361313 + 0.625812i
\(11\) −4.50702 −1.35892 −0.679459 0.733714i \(-0.737785\pi\)
−0.679459 + 0.733714i \(0.737785\pi\)
\(12\) −8.07730 −2.33172
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −4.00702 + 6.94036i −1.07092 + 1.85489i
\(15\) −1.25351 2.17114i −0.323655 0.560586i
\(16\) 0.0316332 0.0547902i 0.00790829 0.0136976i
\(17\) −0.0793049 + 0.137360i −0.0192343 + 0.0333147i −0.875482 0.483250i \(-0.839456\pi\)
0.856248 + 0.516565i \(0.172790\pi\)
\(18\) 7.50702 1.76942
\(19\) −4.26053 + 0.920816i −0.977432 + 0.211250i
\(20\) −3.22188 −0.720433
\(21\) 4.39608 7.61423i 0.959303 1.66156i
\(22\) 5.14959 8.91935i 1.09790 1.90161i
\(23\) −0.579305 1.00339i −0.120793 0.209220i 0.799287 0.600949i \(-0.205211\pi\)
−0.920081 + 0.391729i \(0.871877\pi\)
\(24\) 3.50000 6.06218i 0.714435 1.23744i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −11.4257 −2.24077
\(27\) −0.714858 −0.137574
\(28\) −5.64959 9.78538i −1.06767 1.84926i
\(29\) 1.75351 + 3.03717i 0.325619 + 0.563988i 0.981637 0.190757i \(-0.0610942\pi\)
−0.656019 + 0.754745i \(0.727761\pi\)
\(30\) 5.72889 1.04595
\(31\) −2.28514 −0.410424 −0.205212 0.978718i \(-0.565788\pi\)
−0.205212 + 0.978718i \(0.565788\pi\)
\(32\) 2.86445 + 4.96137i 0.506368 + 0.877054i
\(33\) −5.64959 + 9.78538i −0.983467 + 1.70342i
\(34\) −0.181223 0.313888i −0.0310795 0.0538313i
\(35\) 1.75351 3.03717i 0.296397 0.513375i
\(36\) −5.29216 + 9.16629i −0.882027 + 1.52772i
\(37\) −10.9648 −1.80260 −0.901302 0.433192i \(-0.857387\pi\)
−0.901302 + 0.433192i \(0.857387\pi\)
\(38\) 3.04567 9.48365i 0.494073 1.53845i
\(39\) 12.5351 2.00722
\(40\) 1.39608 2.41808i 0.220740 0.382332i
\(41\) −3.03865 + 5.26310i −0.474558 + 0.821958i −0.999576 0.0291332i \(-0.990725\pi\)
0.525018 + 0.851091i \(0.324059\pi\)
\(42\) 10.0457 + 17.3996i 1.55008 + 2.68482i
\(43\) 1.67420 2.89981i 0.255314 0.442216i −0.709667 0.704537i \(-0.751155\pi\)
0.964981 + 0.262321i \(0.0844879\pi\)
\(44\) 7.26053 + 12.5756i 1.09457 + 1.89584i
\(45\) −3.28514 −0.489720
\(46\) 2.64759 0.390366
\(47\) −1.53163 2.65287i −0.223412 0.386960i 0.732430 0.680842i \(-0.238386\pi\)
−0.955842 + 0.293882i \(0.905053\pi\)
\(48\) −0.0793049 0.137360i −0.0114467 0.0198262i
\(49\) 5.29918 0.757026
\(50\) 2.28514 0.323168
\(51\) 0.198819 + 0.344364i 0.0278402 + 0.0482207i
\(52\) 8.05469 13.9511i 1.11698 1.93467i
\(53\) 2.87147 + 4.97353i 0.394426 + 0.683166i 0.993028 0.117881i \(-0.0376100\pi\)
−0.598602 + 0.801047i \(0.704277\pi\)
\(54\) 0.816776 1.41470i 0.111149 0.192516i
\(55\) −2.25351 + 3.90319i −0.303863 + 0.526306i
\(56\) 9.79216 1.30853
\(57\) −3.34139 + 10.4045i −0.442578 + 1.37810i
\(58\) −8.01404 −1.05229
\(59\) −1.53163 + 2.65287i −0.199402 + 0.345374i −0.948335 0.317272i \(-0.897233\pi\)
0.748933 + 0.662646i \(0.230567\pi\)
\(60\) −4.03865 + 6.99515i −0.521388 + 0.903070i
\(61\) 0.436734 + 0.756445i 0.0559180 + 0.0968528i 0.892629 0.450791i \(-0.148858\pi\)
−0.836711 + 0.547644i \(0.815525\pi\)
\(62\) 2.61094 4.52228i 0.331589 0.574330i
\(63\) −5.76053 9.97753i −0.725758 1.25705i
\(64\) −12.9648 −1.62060
\(65\) 5.00000 0.620174
\(66\) −12.9101 22.3610i −1.58913 2.75245i
\(67\) 4.22188 + 7.31250i 0.515784 + 0.893365i 0.999832 + 0.0183230i \(0.00583273\pi\)
−0.484048 + 0.875042i \(0.660834\pi\)
\(68\) 0.511021 0.0619704
\(69\) −2.90466 −0.349680
\(70\) 4.00702 + 6.94036i 0.478930 + 0.829532i
\(71\) 8.11796 14.0607i 0.963424 1.66870i 0.249634 0.968340i \(-0.419690\pi\)
0.713790 0.700359i \(-0.246977\pi\)
\(72\) −4.58632 7.94375i −0.540503 0.936179i
\(73\) 3.57930 6.19954i 0.418926 0.725601i −0.576906 0.816811i \(-0.695740\pi\)
0.995832 + 0.0912097i \(0.0290733\pi\)
\(74\) 12.5281 21.6993i 1.45636 2.52249i
\(75\) −2.50702 −0.289486
\(76\) 9.43273 + 10.4045i 1.08201 + 1.19347i
\(77\) −15.8062 −1.80128
\(78\) −14.3222 + 24.8068i −1.62167 + 2.80882i
\(79\) 5.06327 8.76983i 0.569662 0.986683i −0.426937 0.904281i \(-0.640407\pi\)
0.996599 0.0824022i \(-0.0262592\pi\)
\(80\) −0.0316332 0.0547902i −0.00353669 0.00612574i
\(81\) 4.03163 6.98299i 0.447959 0.775888i
\(82\) −6.94375 12.0269i −0.766809 1.32815i
\(83\) 4.85543 0.532952 0.266476 0.963841i \(-0.414141\pi\)
0.266476 + 0.963841i \(0.414141\pi\)
\(84\) −28.3273 −3.09076
\(85\) 0.0793049 + 0.137360i 0.00860183 + 0.0148988i
\(86\) 3.82580 + 6.62647i 0.412546 + 0.714551i
\(87\) 8.79216 0.942619
\(88\) −12.5843 −1.34149
\(89\) 0.556248 + 0.963449i 0.0589621 + 0.102125i 0.894000 0.448067i \(-0.147888\pi\)
−0.835038 + 0.550193i \(0.814554\pi\)
\(90\) 3.75351 6.50127i 0.395655 0.685294i
\(91\) 8.76755 + 15.1858i 0.919089 + 1.59191i
\(92\) −1.86645 + 3.23278i −0.194591 + 0.337041i
\(93\) −2.86445 + 4.96137i −0.297029 + 0.514470i
\(94\) 7.00000 0.721995
\(95\) −1.33281 + 4.15013i −0.136744 + 0.425795i
\(96\) 14.3624 1.46586
\(97\) −0.809757 + 1.40254i −0.0822184 + 0.142406i −0.904203 0.427104i \(-0.859534\pi\)
0.821984 + 0.569510i \(0.192867\pi\)
\(98\) −6.05469 + 10.4870i −0.611616 + 1.05935i
\(99\) 7.40310 + 12.8225i 0.744039 + 1.28871i
\(100\) −1.61094 + 2.79023i −0.161094 + 0.279023i
\(101\) −6.15661 10.6636i −0.612605 1.06106i −0.990800 0.135337i \(-0.956788\pi\)
0.378194 0.925726i \(-0.376545\pi\)
\(102\) −0.908659 −0.0899707
\(103\) 10.6164 1.04606 0.523032 0.852313i \(-0.324801\pi\)
0.523032 + 0.852313i \(0.324801\pi\)
\(104\) 6.98040 + 12.0904i 0.684485 + 1.18556i
\(105\) −4.39608 7.61423i −0.429014 0.743073i
\(106\) −13.1234 −1.27466
\(107\) −2.17265 −0.210038 −0.105019 0.994470i \(-0.533490\pi\)
−0.105019 + 0.994470i \(0.533490\pi\)
\(108\) 1.15159 + 1.99461i 0.110812 + 0.191932i
\(109\) −7.91012 + 13.7007i −0.757652 + 1.31229i 0.186393 + 0.982475i \(0.440320\pi\)
−0.944045 + 0.329816i \(0.893013\pi\)
\(110\) −5.14959 8.91935i −0.490994 0.850427i
\(111\) −13.7445 + 23.8062i −1.30457 + 2.25958i
\(112\) 0.110938 0.192150i 0.0104827 0.0181565i
\(113\) 9.83828 0.925507 0.462754 0.886487i \(-0.346861\pi\)
0.462754 + 0.886487i \(0.346861\pi\)
\(114\) −16.7726 18.5004i −1.57089 1.73272i
\(115\) −1.15861 −0.108041
\(116\) 5.64959 9.78538i 0.524551 0.908549i
\(117\) 8.21286 14.2251i 0.759279 1.31511i
\(118\) −3.50000 6.06218i −0.322201 0.558069i
\(119\) −0.278124 + 0.481725i −0.0254956 + 0.0441596i
\(120\) −3.50000 6.06218i −0.319505 0.553399i
\(121\) 9.31322 0.846656
\(122\) −1.99600 −0.180709
\(123\) 7.61796 + 13.1947i 0.686888 + 1.18972i
\(124\) 3.68122 + 6.37607i 0.330584 + 0.572588i
\(125\) −1.00000 −0.0894427
\(126\) 26.3273 2.34542
\(127\) −7.85543 13.6060i −0.697056 1.20734i −0.969483 0.245160i \(-0.921159\pi\)
0.272426 0.962177i \(-0.412174\pi\)
\(128\) 9.08432 15.7345i 0.802948 1.39075i
\(129\) −4.19726 7.26987i −0.369548 0.640076i
\(130\) −5.71286 + 9.89496i −0.501051 + 0.867845i
\(131\) 5.76755 9.98968i 0.503913 0.872803i −0.496077 0.868279i \(-0.665227\pi\)
0.999990 0.00452412i \(-0.00144008\pi\)
\(132\) 36.4046 3.16861
\(133\) −14.9418 + 3.22932i −1.29561 + 0.280017i
\(134\) −19.2952 −1.66685
\(135\) −0.357429 + 0.619085i −0.0307626 + 0.0532823i
\(136\) −0.221432 + 0.383532i −0.0189876 + 0.0328876i
\(137\) −0.0546904 0.0947266i −0.00467252 0.00809304i 0.863680 0.504041i \(-0.168154\pi\)
−0.868352 + 0.495948i \(0.834821\pi\)
\(138\) 3.31878 5.74829i 0.282513 0.489327i
\(139\) −0.721876 1.25033i −0.0612287 0.106051i 0.833786 0.552088i \(-0.186169\pi\)
−0.895015 + 0.446036i \(0.852835\pi\)
\(140\) −11.2992 −0.954955
\(141\) −7.67967 −0.646745
\(142\) 18.5507 + 32.1307i 1.55674 + 2.69635i
\(143\) −11.2675 19.5160i −0.942240 1.63201i
\(144\) −0.207839 −0.0173199
\(145\) 3.50702 0.291242
\(146\) 8.17922 + 14.1668i 0.676917 + 1.17245i
\(147\) 6.64257 11.5053i 0.547870 0.948939i
\(148\) 17.6636 + 30.5943i 1.45194 + 2.51484i
\(149\) −0.864447 + 1.49727i −0.0708183 + 0.122661i −0.899260 0.437414i \(-0.855894\pi\)
0.828442 + 0.560075i \(0.189228\pi\)
\(150\) 2.86445 4.96137i 0.233881 0.405094i
\(151\) −20.1406 −1.63902 −0.819508 0.573068i \(-0.805753\pi\)
−0.819508 + 0.573068i \(0.805753\pi\)
\(152\) −11.8961 + 2.57107i −0.964900 + 0.208541i
\(153\) 0.521056 0.0421249
\(154\) 18.0597 31.2803i 1.45529 2.52064i
\(155\) −1.14257 + 1.97899i −0.0917735 + 0.158956i
\(156\) −20.1933 34.9758i −1.61675 2.80030i
\(157\) −1.88906 + 3.27195i −0.150764 + 0.261130i −0.931508 0.363720i \(-0.881507\pi\)
0.780745 + 0.624850i \(0.214840\pi\)
\(158\) 11.5703 + 20.0403i 0.920482 + 1.59432i
\(159\) 14.3976 1.14181
\(160\) 5.72889 0.452909
\(161\) −2.03163 3.51889i −0.160115 0.277328i
\(162\) 9.21286 + 15.9571i 0.723830 + 1.25371i
\(163\) −1.61640 −0.126606 −0.0633031 0.997994i \(-0.520163\pi\)
−0.0633031 + 0.997994i \(0.520163\pi\)
\(164\) 19.5803 1.52897
\(165\) 5.64959 + 9.78538i 0.439820 + 0.761791i
\(166\) −5.54767 + 9.60885i −0.430583 + 0.745791i
\(167\) −3.24649 5.62309i −0.251221 0.435128i 0.712641 0.701529i \(-0.247499\pi\)
−0.963862 + 0.266401i \(0.914165\pi\)
\(168\) 12.2746 21.2602i 0.947003 1.64026i
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) −0.362446 −0.0277983
\(171\) 9.61796 + 10.6088i 0.735504 + 0.811273i
\(172\) −10.7882 −0.822589
\(173\) −4.26053 + 7.37945i −0.323922 + 0.561049i −0.981294 0.192517i \(-0.938335\pi\)
0.657372 + 0.753567i \(0.271668\pi\)
\(174\) −10.0457 + 17.3996i −0.761560 + 1.31906i
\(175\) −1.75351 3.03717i −0.132553 0.229588i
\(176\) −0.142571 + 0.246941i −0.0107467 + 0.0186139i
\(177\) 3.83983 + 6.65079i 0.288620 + 0.499904i
\(178\) −2.54221 −0.190547
\(179\) −10.2711 −0.767698 −0.383849 0.923396i \(-0.625402\pi\)
−0.383849 + 0.923396i \(0.625402\pi\)
\(180\) 5.29216 + 9.16629i 0.394454 + 0.683215i
\(181\) −6.13355 10.6236i −0.455903 0.789648i 0.542836 0.839838i \(-0.317350\pi\)
−0.998740 + 0.0501908i \(0.984017\pi\)
\(182\) −40.0702 −2.97020
\(183\) 2.18980 0.161875
\(184\) −1.61751 2.80161i −0.119245 0.206538i
\(185\) −5.48240 + 9.49580i −0.403074 + 0.698145i
\(186\) −6.54567 11.3374i −0.479952 0.831301i
\(187\) 0.357429 0.619085i 0.0261378 0.0452720i
\(188\) −4.93473 + 8.54721i −0.359902 + 0.623369i
\(189\) −2.50702 −0.182359
\(190\) −6.69024 7.37945i −0.485361 0.535362i
\(191\) 5.71085 0.413223 0.206611 0.978423i \(-0.433756\pi\)
0.206611 + 0.978423i \(0.433756\pi\)
\(192\) −16.2515 + 28.1484i −1.17285 + 2.03144i
\(193\) 5.07930 8.79761i 0.365616 0.633266i −0.623259 0.782016i \(-0.714192\pi\)
0.988875 + 0.148750i \(0.0475249\pi\)
\(194\) −1.85041 3.20500i −0.132852 0.230106i
\(195\) 6.26755 10.8557i 0.448828 0.777393i
\(196\) −8.53665 14.7859i −0.609761 1.05614i
\(197\) 16.2038 1.15448 0.577238 0.816576i \(-0.304131\pi\)
0.577238 + 0.816576i \(0.304131\pi\)
\(198\) −33.8343 −2.40450
\(199\) −0.167186 0.289574i −0.0118515 0.0205274i 0.860039 0.510229i \(-0.170439\pi\)
−0.871890 + 0.489701i \(0.837106\pi\)
\(200\) −1.39608 2.41808i −0.0987178 0.170984i
\(201\) 21.1686 1.49312
\(202\) 28.1375 1.97974
\(203\) 6.14959 + 10.6514i 0.431617 + 0.747582i
\(204\) 0.640570 1.10950i 0.0448489 0.0776805i
\(205\) 3.03865 + 5.26310i 0.212229 + 0.367591i
\(206\) −12.1300 + 21.0098i −0.845137 + 1.46382i
\(207\) −1.90310 + 3.29626i −0.132275 + 0.229106i
\(208\) 0.316332 0.0219336
\(209\) 19.2023 4.15013i 1.32825 0.287071i
\(210\) 20.0913 1.38643
\(211\) −1.01404 + 1.75636i −0.0698092 + 0.120913i −0.898817 0.438324i \(-0.855572\pi\)
0.829008 + 0.559237i \(0.188906\pi\)
\(212\) 9.25151 16.0241i 0.635396 1.10054i
\(213\) −20.3519 35.2505i −1.39449 2.41532i
\(214\) 2.48240 4.29965i 0.169694 0.293918i
\(215\) −1.67420 2.89981i −0.114180 0.197765i
\(216\) −1.99600 −0.135810
\(217\) −8.01404 −0.544028
\(218\) −18.0757 31.3081i −1.22424 2.12045i
\(219\) −8.97338 15.5424i −0.606365 1.05026i
\(220\) 14.5211 0.979009
\(221\) −0.793049 −0.0533463
\(222\) −31.4081 54.4005i −2.10797 3.65112i
\(223\) 9.61596 16.6553i 0.643932 1.11532i −0.340615 0.940203i \(-0.610635\pi\)
0.984547 0.175120i \(-0.0560314\pi\)
\(224\) 10.0457 + 17.3996i 0.671205 + 1.16256i
\(225\) −1.64257 + 2.84502i −0.109505 + 0.189668i
\(226\) −11.2409 + 19.4699i −0.747736 + 1.29512i
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 34.4136 7.43771i 2.27909 0.492574i
\(229\) −12.9788 −0.857666 −0.428833 0.903384i \(-0.641075\pi\)
−0.428833 + 0.903384i \(0.641075\pi\)
\(230\) 1.32379 2.29288i 0.0872884 0.151188i
\(231\) −19.8132 + 34.3175i −1.30361 + 2.25793i
\(232\) 4.89608 + 8.48026i 0.321443 + 0.556756i
\(233\) −13.5367 + 23.4462i −0.886815 + 1.53601i −0.0431968 + 0.999067i \(0.513754\pi\)
−0.843619 + 0.536943i \(0.819579\pi\)
\(234\) 18.7675 + 32.5063i 1.22687 + 2.12501i
\(235\) −3.06327 −0.199825
\(236\) 9.86946 0.642447
\(237\) −12.6937 21.9861i −0.824545 1.42815i
\(238\) −0.635553 1.10081i −0.0411968 0.0713549i
\(239\) 20.0602 1.29758 0.648792 0.760966i \(-0.275275\pi\)
0.648792 + 0.760966i \(0.275275\pi\)
\(240\) −0.158610 −0.0102382
\(241\) 10.7922 + 18.6926i 0.695184 + 1.20409i 0.970119 + 0.242631i \(0.0780105\pi\)
−0.274934 + 0.961463i \(0.588656\pi\)
\(242\) −10.6410 + 18.4308i −0.684030 + 1.18478i
\(243\) −11.1797 19.3637i −0.717176 1.24219i
\(244\) 1.40710 2.43717i 0.0900805 0.156024i
\(245\) 2.64959 4.58922i 0.169276 0.293195i
\(246\) −34.8162 −2.21980
\(247\) −14.6386 16.1466i −0.931430 1.02738i
\(248\) −6.38049 −0.405161
\(249\) 6.08632 10.5418i 0.385705 0.668061i
\(250\) 1.14257 1.97899i 0.0722626 0.125162i
\(251\) 3.63400 + 6.29426i 0.229376 + 0.397290i 0.957623 0.288024i \(-0.0929982\pi\)
−0.728248 + 0.685314i \(0.759665\pi\)
\(252\) −18.5597 + 32.1464i −1.16915 + 2.02503i
\(253\) 2.61094 + 4.52228i 0.164148 + 0.284313i
\(254\) 35.9015 2.25266
\(255\) 0.397638 0.0249010
\(256\) 7.79416 + 13.4999i 0.487135 + 0.843743i
\(257\) −7.53865 13.0573i −0.470248 0.814494i 0.529173 0.848514i \(-0.322502\pi\)
−0.999421 + 0.0340202i \(0.989169\pi\)
\(258\) 19.1827 1.19426
\(259\) −38.4538 −2.38940
\(260\) −8.05469 13.9511i −0.499531 0.865213i
\(261\) 5.76053 9.97753i 0.356568 0.617593i
\(262\) 13.1797 + 22.8279i 0.814242 + 1.41031i
\(263\) −10.0773 + 17.4544i −0.621393 + 1.07628i 0.367833 + 0.929892i \(0.380100\pi\)
−0.989227 + 0.146393i \(0.953234\pi\)
\(264\) −15.7746 + 27.3223i −0.970857 + 1.68157i
\(265\) 5.74293 0.352786
\(266\) 10.6812 33.2593i 0.654908 2.03926i
\(267\) 2.78905 0.170687
\(268\) 13.6024 23.5600i 0.830897 1.43915i
\(269\) 3.86245 6.68995i 0.235497 0.407894i −0.723920 0.689884i \(-0.757661\pi\)
0.959417 + 0.281991i \(0.0909947\pi\)
\(270\) −0.816776 1.41470i −0.0497074 0.0860957i
\(271\) 2.64257 4.57707i 0.160525 0.278037i −0.774532 0.632534i \(-0.782015\pi\)
0.935057 + 0.354497i \(0.115348\pi\)
\(272\) 0.00501733 + 0.00869027i 0.000304220 + 0.000526925i
\(273\) 43.9608 2.66063
\(274\) 0.249951 0.0151001
\(275\) 2.25351 + 3.90319i 0.135892 + 0.235371i
\(276\) 4.67922 + 8.10465i 0.281656 + 0.487843i
\(277\) 30.6264 1.84016 0.920082 0.391726i \(-0.128122\pi\)
0.920082 + 0.391726i \(0.128122\pi\)
\(278\) 3.29918 0.197872
\(279\) 3.75351 + 6.50127i 0.224717 + 0.389221i
\(280\) 4.89608 8.48026i 0.292597 0.506792i
\(281\) −6.68122 11.5722i −0.398568 0.690341i 0.594981 0.803740i \(-0.297159\pi\)
−0.993550 + 0.113399i \(0.963826\pi\)
\(282\) 8.77457 15.1980i 0.522518 0.905027i
\(283\) −2.04767 + 3.54667i −0.121721 + 0.210828i −0.920447 0.390868i \(-0.872175\pi\)
0.798725 + 0.601696i \(0.205508\pi\)
\(284\) −52.3101 −3.10403
\(285\) 7.33983 + 8.09596i 0.434774 + 0.479563i
\(286\) 51.4959 3.04502
\(287\) −10.6566 + 18.4578i −0.629040 + 1.08953i
\(288\) 9.41012 16.2988i 0.554497 0.960416i
\(289\) 8.48742 + 14.7006i 0.499260 + 0.864744i
\(290\) −4.00702 + 6.94036i −0.235300 + 0.407552i
\(291\) 2.03008 + 3.51619i 0.119005 + 0.206123i
\(292\) −23.0642 −1.34973
\(293\) 12.1726 0.711134 0.355567 0.934651i \(-0.384288\pi\)
0.355567 + 0.934651i \(0.384288\pi\)
\(294\) 15.1792 + 26.2912i 0.885270 + 1.53333i
\(295\) 1.53163 + 2.65287i 0.0891751 + 0.154456i
\(296\) −30.6155 −1.77949
\(297\) 3.22188 0.186952
\(298\) −1.97539 3.42147i −0.114431 0.198200i
\(299\) 2.89652 5.01693i 0.167510 0.290136i
\(300\) 4.03865 + 6.99515i 0.233172 + 0.403865i
\(301\) 5.87147 10.1697i 0.338426 0.586170i
\(302\) 23.0120 39.8580i 1.32419 2.29357i
\(303\) −30.8695 −1.77340
\(304\) −0.0843223 + 0.262564i −0.00483621 + 0.0150591i
\(305\) 0.873467 0.0500146
\(306\) −0.595344 + 1.03117i −0.0340335 + 0.0589478i
\(307\) −12.2675 + 21.2480i −0.700146 + 1.21269i 0.268269 + 0.963344i \(0.413548\pi\)
−0.968415 + 0.249344i \(0.919785\pi\)
\(308\) 25.4628 + 44.1029i 1.45088 + 2.51299i
\(309\) 13.3078 23.0497i 0.757052 1.31125i
\(310\) −2.61094 4.52228i −0.148291 0.256848i
\(311\) −10.2038 −0.578606 −0.289303 0.957238i \(-0.593424\pi\)
−0.289303 + 0.957238i \(0.593424\pi\)
\(312\) 35.0000 1.98148
\(313\) 15.9910 + 27.6972i 0.903864 + 1.56554i 0.822435 + 0.568859i \(0.192615\pi\)
0.0814282 + 0.996679i \(0.474052\pi\)
\(314\) −4.31678 7.47687i −0.243610 0.421944i
\(315\) −11.5211 −0.649138
\(316\) −32.6264 −1.83538
\(317\) −1.11796 1.93636i −0.0627907 0.108757i 0.832921 0.553392i \(-0.186667\pi\)
−0.895712 + 0.444635i \(0.853333\pi\)
\(318\) −16.4503 + 28.4928i −0.922489 + 1.59780i
\(319\) −7.90310 13.6886i −0.442489 0.766413i
\(320\) −6.48240 + 11.2279i −0.362377 + 0.627656i
\(321\) −2.72343 + 4.71713i −0.152007 + 0.263284i
\(322\) 9.28514 0.517441
\(323\) 0.211397 0.658252i 0.0117625 0.0366261i
\(324\) −25.9788 −1.44327
\(325\) 2.50000 4.33013i 0.138675 0.240192i
\(326\) 1.84685 3.19884i 0.102288 0.177167i
\(327\) 19.8308 + 34.3480i 1.09665 + 1.89945i
\(328\) −8.48441 + 14.6954i −0.468473 + 0.811419i
\(329\) −5.37147 9.30365i −0.296139 0.512927i
\(330\) −25.8202 −1.42136
\(331\) −10.0913 −0.554670 −0.277335 0.960773i \(-0.589451\pi\)
−0.277335 + 0.960773i \(0.589451\pi\)
\(332\) −7.82179 13.5477i −0.429277 0.743529i
\(333\) 18.0105 + 31.1951i 0.986968 + 1.70948i
\(334\) 14.8374 0.811866
\(335\) 8.44375 0.461331
\(336\) −0.278124 0.481725i −0.0151729 0.0262802i
\(337\) −2.80620 + 4.86048i −0.152863 + 0.264767i −0.932279 0.361740i \(-0.882183\pi\)
0.779416 + 0.626507i \(0.215516\pi\)
\(338\) −13.7109 23.7479i −0.745772 1.29172i
\(339\) 12.3324 21.3603i 0.669802 1.16013i
\(340\) 0.255511 0.442557i 0.0138570 0.0240010i
\(341\) 10.2992 0.557732
\(342\) −31.9839 + 6.91258i −1.72949 + 0.373790i
\(343\) −5.96481 −0.322069
\(344\) 4.67465 8.09673i 0.252040 0.436546i
\(345\) −1.45233 + 2.51551i −0.0781907 + 0.135430i
\(346\) −9.73591 16.8631i −0.523406 0.906566i
\(347\) −2.73747 + 4.74144i −0.146955 + 0.254534i −0.930101 0.367305i \(-0.880281\pi\)
0.783146 + 0.621838i \(0.213614\pi\)
\(348\) −14.1636 24.5321i −0.759250 1.31506i
\(349\) −18.8202 −1.00742 −0.503712 0.863872i \(-0.668033\pi\)
−0.503712 + 0.863872i \(0.668033\pi\)
\(350\) 8.01404 0.428368
\(351\) −1.78714 3.09542i −0.0953907 0.165222i
\(352\) −12.9101 22.3610i −0.688112 1.19184i
\(353\) −12.7008 −0.675996 −0.337998 0.941147i \(-0.609750\pi\)
−0.337998 + 0.941147i \(0.609750\pi\)
\(354\) −17.5491 −0.932726
\(355\) −8.11796 14.0607i −0.430856 0.746265i
\(356\) 1.79216 3.10411i 0.0949843 0.164518i
\(357\) 0.697262 + 1.20769i 0.0369030 + 0.0639179i
\(358\) 11.7355 20.3264i 0.620239 1.07429i
\(359\) 5.54021 9.59592i 0.292401 0.506453i −0.681976 0.731375i \(-0.738879\pi\)
0.974377 + 0.224921i \(0.0722125\pi\)
\(360\) −9.17265 −0.483441
\(361\) 17.3042 7.84632i 0.910747 0.412964i
\(362\) 28.0321 1.47333
\(363\) 11.6742 20.2203i 0.612737 1.06129i
\(364\) 28.2479 48.9269i 1.48059 2.56447i
\(365\) −3.57930 6.19954i −0.187349 0.324499i
\(366\) −2.50200 + 4.33359i −0.130782 + 0.226521i
\(367\) 10.3202 + 17.8752i 0.538712 + 0.933076i 0.998974 + 0.0452932i \(0.0144222\pi\)
−0.460262 + 0.887783i \(0.652244\pi\)
\(368\) −0.0733010 −0.00382108
\(369\) 19.9648 1.03933
\(370\) −12.5281 21.6993i −0.651304 1.12809i
\(371\) 10.0703 + 17.4422i 0.522823 + 0.905556i
\(372\) 18.4578 0.956992
\(373\) 4.55313 0.235752 0.117876 0.993028i \(-0.462391\pi\)
0.117876 + 0.993028i \(0.462391\pi\)
\(374\) 0.816776 + 1.41470i 0.0422345 + 0.0731522i
\(375\) −1.25351 + 2.17114i −0.0647309 + 0.112117i
\(376\) −4.27657 7.40723i −0.220547 0.381999i
\(377\) −8.76755 + 15.1858i −0.451552 + 0.782110i
\(378\) 2.86445 4.96137i 0.147331 0.255185i
\(379\) −19.9187 −1.02315 −0.511577 0.859237i \(-0.670939\pi\)
−0.511577 + 0.859237i \(0.670939\pi\)
\(380\) 13.7269 2.96675i 0.704175 0.152191i
\(381\) −39.3874 −2.01788
\(382\) −6.52506 + 11.3017i −0.333851 + 0.578247i
\(383\) 9.98742 17.2987i 0.510333 0.883923i −0.489595 0.871950i \(-0.662855\pi\)
0.999928 0.0119734i \(-0.00381133\pi\)
\(384\) −22.7746 39.4467i −1.16221 2.01301i
\(385\) −7.90310 + 13.6886i −0.402779 + 0.697634i
\(386\) 11.6069 + 20.1038i 0.590777 + 1.02326i
\(387\) −11.0000 −0.559161
\(388\) 5.21787 0.264897
\(389\) −6.90110 11.9531i −0.349900 0.606044i 0.636332 0.771416i \(-0.280451\pi\)
−0.986231 + 0.165372i \(0.947118\pi\)
\(390\) 14.3222 + 24.8068i 0.725235 + 1.25614i
\(391\) 0.183767 0.00929349
\(392\) 14.7962 0.747319
\(393\) −14.4593 25.0443i −0.729378 1.26332i
\(394\) −18.5140 + 32.0673i −0.932724 + 1.61552i
\(395\) −5.06327 8.76983i −0.254761 0.441258i
\(396\) 23.8519 41.3126i 1.19860 2.07604i
\(397\) 8.27457 14.3320i 0.415289 0.719301i −0.580170 0.814495i \(-0.697014\pi\)
0.995459 + 0.0951945i \(0.0303473\pi\)
\(398\) 0.764087 0.0383002
\(399\) −11.7183 + 36.4886i −0.586650 + 1.82672i
\(400\) −0.0632663 −0.00316332
\(401\) −4.26253 + 7.38292i −0.212861 + 0.368685i −0.952609 0.304199i \(-0.901611\pi\)
0.739748 + 0.672884i \(0.234945\pi\)
\(402\) −24.1867 + 41.8926i −1.20632 + 2.08941i
\(403\) −5.71286 9.89496i −0.284578 0.492903i
\(404\) −19.8358 + 34.3567i −0.986869 + 1.70931i
\(405\) −4.03163 6.98299i −0.200333 0.346988i
\(406\) −28.1054 −1.39485
\(407\) 49.4186 2.44959
\(408\) 0.555134 + 0.961521i 0.0274833 + 0.0476024i
\(409\) 5.78314 + 10.0167i 0.285958 + 0.495294i 0.972841 0.231474i \(-0.0743549\pi\)
−0.686883 + 0.726768i \(0.741022\pi\)
\(410\) −13.8875 −0.685855
\(411\) −0.274220 −0.0135263
\(412\) −17.1024 29.6222i −0.842573 1.45938i
\(413\) −5.37147 + 9.30365i −0.264313 + 0.457803i
\(414\) −4.34885 7.53243i −0.213734 0.370199i
\(415\) 2.42771 4.20492i 0.119172 0.206412i
\(416\) −14.3222 + 24.8068i −0.702205 + 1.21626i
\(417\) −3.61951 −0.177248
\(418\) −13.7269 + 42.7430i −0.671404 + 2.09063i
\(419\) −21.7149 −1.06084 −0.530420 0.847735i \(-0.677966\pi\)
−0.530420 + 0.847735i \(0.677966\pi\)
\(420\) −14.1636 + 24.5321i −0.691114 + 1.19704i
\(421\) 3.46135 5.99523i 0.168696 0.292190i −0.769266 0.638929i \(-0.779378\pi\)
0.937962 + 0.346739i \(0.112711\pi\)
\(422\) −2.31722 4.01354i −0.112800 0.195376i
\(423\) −5.03163 + 8.71504i −0.244646 + 0.423740i
\(424\) 8.01760 + 13.8869i 0.389369 + 0.674407i
\(425\) 0.158610 0.00769371
\(426\) 93.0138 4.50654
\(427\) 1.53163 + 2.65287i 0.0741209 + 0.128381i
\(428\) 3.50000 + 6.06218i 0.169179 + 0.293026i
\(429\) −56.4959 −2.72765
\(430\) 7.65159 0.368992
\(431\) 13.9894 + 24.2304i 0.673847 + 1.16714i 0.976805 + 0.214133i \(0.0686926\pi\)
−0.302958 + 0.953004i \(0.597974\pi\)
\(432\) −0.0226132 + 0.0391672i −0.00108798 + 0.00188443i
\(433\) −3.12698 5.41608i −0.150273 0.260280i 0.781055 0.624462i \(-0.214682\pi\)
−0.931328 + 0.364182i \(0.881349\pi\)
\(434\) 9.15661 15.8597i 0.439531 0.761290i
\(435\) 4.39608 7.61423i 0.210776 0.365075i
\(436\) 50.9708 2.44106
\(437\) 3.39208 + 3.74152i 0.162265 + 0.178981i
\(438\) 41.0109 1.95958
\(439\) −15.5988 + 27.0179i −0.744490 + 1.28949i 0.205942 + 0.978564i \(0.433974\pi\)
−0.950433 + 0.310931i \(0.899359\pi\)
\(440\) −6.29216 + 10.8983i −0.299967 + 0.519558i
\(441\) −8.70428 15.0763i −0.414490 0.717917i
\(442\) 0.906115 1.56944i 0.0430995 0.0746505i
\(443\) 16.3519 + 28.3223i 0.776901 + 1.34563i 0.933720 + 0.358004i \(0.116543\pi\)
−0.156819 + 0.987627i \(0.550124\pi\)
\(444\) 88.5661 4.20316
\(445\) 1.11250 0.0527373
\(446\) 21.9738 + 38.0598i 1.04049 + 1.80218i
\(447\) 2.16719 + 3.75368i 0.102504 + 0.177543i
\(448\) −45.4678 −2.14815
\(449\) 25.6304 1.20958 0.604788 0.796387i \(-0.293258\pi\)
0.604788 + 0.796387i \(0.293258\pi\)
\(450\) −3.75351 6.50127i −0.176942 0.306473i
\(451\) 13.6953 23.7209i 0.644885 1.11697i
\(452\) −15.8489 27.4510i −0.745467 1.29119i
\(453\) −25.2464 + 43.7280i −1.18618 + 2.05452i
\(454\) −4.57028 + 7.91597i −0.214494 + 0.371515i
\(455\) 17.5351 0.822058
\(456\) −9.32970 + 29.0509i −0.436903 + 1.36043i
\(457\) 33.1646 1.55138 0.775688 0.631116i \(-0.217403\pi\)
0.775688 + 0.631116i \(0.217403\pi\)
\(458\) 14.8293 25.6850i 0.692926 1.20018i
\(459\) 0.0566917 0.0981929i 0.00264614 0.00458325i
\(460\) 1.86645 + 3.23278i 0.0870236 + 0.150729i
\(461\) −1.08788 + 1.88426i −0.0506677 + 0.0877590i −0.890247 0.455478i \(-0.849468\pi\)
0.839579 + 0.543237i \(0.182802\pi\)
\(462\) −45.2760 78.4204i −2.10643 3.64845i
\(463\) −6.20072 −0.288172 −0.144086 0.989565i \(-0.546024\pi\)
−0.144086 + 0.989565i \(0.546024\pi\)
\(464\) 0.221876 0.0103003
\(465\) 2.86445 + 4.96137i 0.132836 + 0.230078i
\(466\) −30.9332 53.5778i −1.43295 2.48195i
\(467\) −17.1546 −0.793821 −0.396910 0.917857i \(-0.629918\pi\)
−0.396910 + 0.917857i \(0.629918\pi\)
\(468\) −52.9216 −2.44630
\(469\) 14.8062 + 25.6451i 0.683687 + 1.18418i
\(470\) 3.50000 6.06218i 0.161443 0.279627i
\(471\) 4.73591 + 8.20284i 0.218219 + 0.377967i
\(472\) −4.27657 + 7.40723i −0.196845 + 0.340945i
\(473\) −7.54567 + 13.0695i −0.346950 + 0.600936i
\(474\) 58.0138 2.66466
\(475\) 2.92771 + 3.22932i 0.134333 + 0.148171i
\(476\) 1.79216 0.0821436
\(477\) 9.43318 16.3387i 0.431915 0.748099i
\(478\) −22.9202 + 39.6989i −1.04834 + 1.81578i
\(479\) 17.8891 + 30.9848i 0.817372 + 1.41573i 0.907612 + 0.419810i \(0.137903\pi\)
−0.0902399 + 0.995920i \(0.528763\pi\)
\(480\) 7.18122 12.4382i 0.327776 0.567726i
\(481\) −27.4120 47.4790i −1.24988 2.16486i
\(482\) −49.3233 −2.24661
\(483\) −10.1867 −0.463510
\(484\) −15.0030 25.9860i −0.681955 1.18118i
\(485\) 0.809757 + 1.40254i 0.0367692 + 0.0636861i
\(486\) 51.0943 2.31768
\(487\) −23.7149 −1.07462 −0.537311 0.843384i \(-0.680560\pi\)
−0.537311 + 0.843384i \(0.680560\pi\)
\(488\) 1.21943 + 2.11212i 0.0552010 + 0.0956110i
\(489\) −2.02617 + 3.50943i −0.0916267 + 0.158702i
\(490\) 6.05469 + 10.4870i 0.273523 + 0.473756i
\(491\) 19.5933 33.9367i 0.884235 1.53154i 0.0376474 0.999291i \(-0.488014\pi\)
0.846588 0.532249i \(-0.178653\pi\)
\(492\) 24.5441 42.5117i 1.10653 1.91657i
\(493\) −0.556248 −0.0250521
\(494\) 48.6796 10.5210i 2.19020 0.473361i
\(495\) 14.8062 0.665489
\(496\) −0.0722863 + 0.125204i −0.00324575 + 0.00562180i
\(497\) 28.4698 49.3112i 1.27705 2.21191i
\(498\) 13.9081 + 24.0896i 0.623238 + 1.07948i
\(499\) 4.68824 8.12027i 0.209875 0.363513i −0.741800 0.670621i \(-0.766028\pi\)
0.951675 + 0.307107i \(0.0993611\pi\)
\(500\) 1.61094 + 2.79023i 0.0720433 + 0.124783i
\(501\) −16.2780 −0.727249
\(502\) −16.6084 −0.741269
\(503\) −6.74649 11.6853i −0.300811 0.521020i 0.675509 0.737352i \(-0.263924\pi\)
−0.976320 + 0.216332i \(0.930591\pi\)
\(504\) −16.0843 27.8589i −0.716453 1.24093i
\(505\) −12.3132 −0.547931
\(506\) −11.9327 −0.530475
\(507\) 15.0421 + 26.0537i 0.668044 + 1.15709i
\(508\) −25.3092 + 43.8368i −1.12291 + 1.94495i
\(509\) −12.8534 22.2628i −0.569718 0.986781i −0.996594 0.0824703i \(-0.973719\pi\)
0.426875 0.904310i \(-0.359614\pi\)
\(510\) −0.454330 + 0.786922i −0.0201181 + 0.0348455i
\(511\) 12.5527 21.7419i 0.555298 0.961805i
\(512\) 0.715746 0.0316318
\(513\) 3.04567 0.658252i 0.134470 0.0290625i
\(514\) 34.4538 1.51969
\(515\) 5.30820 9.19407i 0.233907 0.405139i
\(516\) −13.5231 + 23.4226i −0.595319 + 1.03112i
\(517\) 6.90310 + 11.9565i 0.303598 + 0.525847i
\(518\) 43.9362 76.0997i 1.93045 3.34363i
\(519\) 10.6812 + 18.5004i 0.468854 + 0.812078i
\(520\) 13.9608 0.612222
\(521\) −37.7358 −1.65324 −0.826618 0.562763i \(-0.809738\pi\)
−0.826618 + 0.562763i \(0.809738\pi\)
\(522\) 13.1636 + 22.8001i 0.576156 + 0.997932i
\(523\) −19.2003 33.2559i −0.839570 1.45418i −0.890255 0.455462i \(-0.849474\pi\)
0.0506855 0.998715i \(-0.483859\pi\)
\(524\) −37.1646 −1.62354
\(525\) −8.79216 −0.383721
\(526\) −23.0281 39.8858i −1.00407 1.73910i
\(527\) 0.181223 0.313888i 0.00789420 0.0136732i
\(528\) 0.357429 + 0.619085i 0.0155551 + 0.0269422i
\(529\) 10.8288 18.7561i 0.470818 0.815481i
\(530\) −6.56171 + 11.3652i −0.285022 + 0.493673i
\(531\) 10.0633 0.436709
\(532\) 33.0808 + 36.4886i 1.43423 + 1.58198i
\(533\) −30.3865 −1.31619
\(534\) −3.18668 + 5.51950i −0.137901 + 0.238852i
\(535\) −1.08632 + 1.88157i −0.0469659 + 0.0813473i
\(536\) 11.7882 + 20.4177i 0.509171 + 0.881910i
\(537\) −12.8749 + 22.3000i −0.555594 + 0.962317i
\(538\) 8.82624 + 15.2875i 0.380526 + 0.659091i
\(539\) −23.8835 −1.02874
\(540\) 2.30318 0.0991132
\(541\) 6.40310 + 11.0905i 0.275291 + 0.476818i 0.970208 0.242272i \(-0.0778926\pi\)
−0.694918 + 0.719089i \(0.744559\pi\)
\(542\) 6.03865 + 10.4593i 0.259382 + 0.449263i
\(543\) −30.7539 −1.31977
\(544\) −0.908659 −0.0389584
\(545\) 7.91012 + 13.7007i 0.338832 + 0.586875i
\(546\) −50.2284 + 86.9981i −2.14958 + 3.72317i
\(547\) 9.12853 + 15.8111i 0.390308 + 0.676033i 0.992490 0.122326i \(-0.0390352\pi\)
−0.602182 + 0.798359i \(0.705702\pi\)
\(548\) −0.176206 + 0.305197i −0.00752714 + 0.0130374i
\(549\) 1.43473 2.48503i 0.0612329 0.106058i
\(550\) −10.2992 −0.439159
\(551\) −10.2675 11.3253i −0.437412 0.482473i
\(552\) −8.11027 −0.345196
\(553\) 17.7570 30.7560i 0.755103 1.30788i
\(554\) −34.9929 + 60.6095i −1.48671 + 2.57505i
\(555\) 13.7445 + 23.8062i 0.583421 + 1.01051i
\(556\) −2.32580 + 4.02840i −0.0986357 + 0.170842i
\(557\) −7.45233 12.9078i −0.315765 0.546922i 0.663835 0.747879i \(-0.268928\pi\)
−0.979600 + 0.200958i \(0.935595\pi\)
\(558\) −17.1546 −0.726212
\(559\) 16.7420 0.708113
\(560\) −0.110938 0.192150i −0.00468799 0.00811984i
\(561\) −0.896081 1.55206i −0.0378326 0.0655279i
\(562\) 30.5351 1.28805
\(563\) 45.7810 1.92944 0.964720 0.263276i \(-0.0848031\pi\)
0.964720 + 0.263276i \(0.0848031\pi\)
\(564\) 12.3715 + 21.4280i 0.520933 + 0.902282i
\(565\) 4.91914 8.52020i 0.206950 0.358447i
\(566\) −4.67922 8.10465i −0.196682 0.340664i
\(567\) 14.1390 24.4895i 0.593783 1.02846i
\(568\) 22.6666 39.2598i 0.951071 1.64730i
\(569\) 0.379598 0.0159136 0.00795679 0.999968i \(-0.497467\pi\)
0.00795679 + 0.999968i \(0.497467\pi\)
\(570\) −24.4081 + 5.27526i −1.02234 + 0.220956i
\(571\) −15.8514 −0.663361 −0.331681 0.943392i \(-0.607616\pi\)
−0.331681 + 0.943392i \(0.607616\pi\)
\(572\) −36.3026 + 62.8780i −1.51789 + 2.62906i
\(573\) 7.15861 12.3991i 0.299055 0.517979i
\(574\) −24.3519 42.1787i −1.01643 1.76050i
\(575\) −0.579305 + 1.00339i −0.0241587 + 0.0418441i
\(576\) 21.2956 + 36.8851i 0.887318 + 1.53688i
\(577\) −19.2350 −0.800765 −0.400382 0.916348i \(-0.631123\pi\)
−0.400382 + 0.916348i \(0.631123\pi\)
\(578\) −38.7899 −1.61345
\(579\) −12.7339 22.0558i −0.529203 0.916607i
\(580\) −5.64959 9.78538i −0.234586 0.406316i
\(581\) 17.0281 0.706444
\(582\) −9.27803 −0.384587
\(583\) −12.9418 22.4158i −0.535993 0.928366i
\(584\) 9.99400 17.3101i 0.413554 0.716297i
\(585\) −8.21286 14.2251i −0.339560 0.588135i
\(586\) −13.9081 + 24.0896i −0.574539 + 0.995131i
\(587\) −20.4242 + 35.3757i −0.842995 + 1.46011i 0.0443559 + 0.999016i \(0.485876\pi\)
−0.887351 + 0.461095i \(0.847457\pi\)
\(588\) −42.8031 −1.76517
\(589\) 9.73591 2.10419i 0.401161 0.0867018i
\(590\) −7.00000 −0.288185
\(591\) 20.3117 35.1808i 0.835510 1.44715i
\(592\) −0.346852 + 0.600764i −0.0142555 + 0.0246913i
\(593\) 7.12342 + 12.3381i 0.292524 + 0.506666i 0.974406 0.224796i \(-0.0721716\pi\)
−0.681882 + 0.731462i \(0.738838\pi\)
\(594\) −3.68122 + 6.37607i −0.151042 + 0.261613i
\(595\) 0.278124 + 0.481725i 0.0114020 + 0.0197488i
\(596\) 5.57028 0.228168
\(597\) −0.838276 −0.0343083
\(598\) 6.61897 + 11.4644i 0.270670 + 0.468814i
\(599\) 7.92571 + 13.7277i 0.323836 + 0.560900i 0.981276 0.192607i \(-0.0616941\pi\)
−0.657440 + 0.753507i \(0.728361\pi\)
\(600\) −7.00000 −0.285774
\(601\) 16.4718 0.671900 0.335950 0.941880i \(-0.390943\pi\)
0.335950 + 0.941880i \(0.390943\pi\)
\(602\) 13.4171 + 23.2392i 0.546842 + 0.947158i
\(603\) 13.8695 24.0226i 0.564808 0.978277i
\(604\) 32.4452 + 56.1968i 1.32018 + 2.28661i
\(605\) 4.65661 8.06548i 0.189318 0.327908i
\(606\) 35.2706 61.0904i 1.43277 2.48163i
\(607\) −10.3914 −0.421774 −0.210887 0.977510i \(-0.567635\pi\)
−0.210887 + 0.977510i \(0.567635\pi\)
\(608\) −16.7726 18.5004i −0.680217 0.750291i
\(609\) 30.8343 1.24947
\(610\) −0.997999 + 1.72858i −0.0404078 + 0.0699883i
\(611\) 7.65817 13.2643i 0.309816 0.536617i
\(612\) −0.839389 1.45386i −0.0339303 0.0587690i
\(613\) 10.8925 18.8664i 0.439945 0.762007i −0.557740 0.830016i \(-0.688331\pi\)
0.997685 + 0.0680090i \(0.0216647\pi\)
\(614\) −28.0331 48.5547i −1.13132 1.95951i
\(615\) 15.2359 0.614371
\(616\) −44.1335 −1.77819
\(617\) 21.3855 + 37.0408i 0.860948 + 1.49121i 0.871015 + 0.491256i \(0.163462\pi\)
−0.0100671 + 0.999949i \(0.503205\pi\)
\(618\) 30.4101 + 52.6719i 1.22327 + 2.11877i
\(619\) 28.7882 1.15709 0.578547 0.815649i \(-0.303620\pi\)
0.578547 + 0.815649i \(0.303620\pi\)
\(620\) 7.36245 0.295683
\(621\) 0.414120 + 0.717278i 0.0166181 + 0.0287834i
\(622\) 11.6586 20.1933i 0.467468 0.809678i
\(623\) 1.95077 + 3.37883i 0.0781560 + 0.135370i
\(624\) 0.396525 0.686801i 0.0158737 0.0274940i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −73.0833 −2.92100
\(627\) 15.0597 46.8931i 0.601427 1.87273i
\(628\) 12.1726 0.485742
\(629\) 0.869563 1.50613i 0.0346718 0.0600532i
\(630\) 13.1636 22.8001i 0.524451 0.908377i
\(631\) 9.69370 + 16.7900i 0.385900 + 0.668399i 0.991894 0.127071i \(-0.0405576\pi\)
−0.605993 + 0.795470i \(0.707224\pi\)
\(632\) 14.1375 24.4868i 0.562358 0.974032i
\(633\) 2.54221 + 4.40324i 0.101044 + 0.175013i
\(634\) 5.10938 0.202919
\(635\) −15.7109 −0.623466
\(636\) −23.1937 40.1727i −0.919690 1.59295i
\(637\) 13.2479 + 22.9461i 0.524903 + 0.909158i
\(638\) 36.1194 1.42998
\(639\) −53.3373 −2.10999
\(640\) −9.08432 15.7345i −0.359089 0.621961i
\(641\) −20.3433 + 35.2356i −0.803512 + 1.39172i 0.113779 + 0.993506i \(0.463704\pi\)
−0.917291 + 0.398217i \(0.869629\pi\)
\(642\) −6.22343 10.7793i −0.245619 0.425425i
\(643\) 17.0527 29.5361i 0.672492 1.16479i −0.304703 0.952448i \(-0.598557\pi\)
0.977195 0.212344i \(-0.0681096\pi\)
\(644\) −6.54567 + 11.3374i −0.257936 + 0.446757i
\(645\) −8.39452 −0.330534
\(646\) 1.06114 + 1.17045i 0.0417499 + 0.0460509i
\(647\) −48.0029 −1.88719 −0.943595 0.331103i \(-0.892579\pi\)
−0.943595 + 0.331103i \(0.892579\pi\)
\(648\) 11.2570 19.4976i 0.442216 0.765940i
\(649\) 6.90310 11.9565i 0.270970 0.469334i
\(650\) 5.71286 + 9.89496i 0.224077 + 0.388112i
\(651\) −10.0457 + 17.3996i −0.393721 + 0.681945i
\(652\) 2.60392 + 4.51012i 0.101977 + 0.176630i
\(653\) 3.90866 0.152958 0.0764788 0.997071i \(-0.475632\pi\)
0.0764788 + 0.997071i \(0.475632\pi\)
\(654\) −90.6325 −3.54401
\(655\) −5.76755 9.98968i −0.225357 0.390329i
\(656\) 0.192244 + 0.332977i 0.00750588 + 0.0130006i
\(657\) −23.5171 −0.917488
\(658\) 24.5491 0.957025
\(659\) −6.54411 11.3347i −0.254922 0.441539i 0.709952 0.704250i \(-0.248717\pi\)
−0.964874 + 0.262711i \(0.915383\pi\)
\(660\) 18.2023 31.5273i 0.708523 1.22720i
\(661\) 11.9714 + 20.7350i 0.465633 + 0.806500i 0.999230 0.0392391i \(-0.0124934\pi\)
−0.533597 + 0.845739i \(0.679160\pi\)
\(662\) 11.5301 19.9707i 0.448129 0.776182i
\(663\) −0.994095 + 1.72182i −0.0386074 + 0.0668700i
\(664\) 13.5571 0.526119
\(665\) −4.67420 + 14.5546i −0.181258 + 0.564403i
\(666\) −82.3130 −3.18956
\(667\) 2.03163 3.51889i 0.0786652 0.136252i
\(668\) −10.4598 + 18.1169i −0.404701 + 0.700963i
\(669\) −24.1074 41.7552i −0.932045 1.61435i
\(670\) −9.64759 + 16.7101i −0.372719 + 0.645568i
\(671\) −1.96837 3.40931i −0.0759880 0.131615i
\(672\) 50.3694 1.94304
\(673\) −11.3304 −0.436754 −0.218377 0.975865i \(-0.570076\pi\)
−0.218377 + 0.975865i \(0.570076\pi\)
\(674\) −6.41256 11.1069i −0.247003 0.427821i
\(675\) 0.357429 + 0.619085i 0.0137574 + 0.0238286i
\(676\) 38.6625 1.48702
\(677\) 8.90466 0.342234 0.171117 0.985251i \(-0.445262\pi\)
0.171117 + 0.985251i \(0.445262\pi\)
\(678\) 28.1812 + 48.8113i 1.08229 + 1.87459i
\(679\) −2.83983 + 4.91873i −0.108983 + 0.188764i
\(680\) 0.221432 + 0.383532i 0.00849153 + 0.0147078i
\(681\) 5.01404 8.68457i 0.192138 0.332793i
\(682\) −11.7675 + 20.3820i −0.450603 + 0.780467i
\(683\) −26.6977 −1.02156 −0.510780 0.859712i \(-0.670643\pi\)
−0.510780 + 0.859712i \(0.670643\pi\)
\(684\) 14.1069 43.9263i 0.539392 1.67957i
\(685\) −0.109381 −0.00417923
\(686\) 6.81522 11.8043i 0.260206 0.450690i
\(687\) −16.2691 + 28.1789i −0.620705 + 1.07509i
\(688\) −0.105921 0.183460i −0.00403819 0.00699435i
\(689\) −14.3573 + 24.8676i −0.546971 + 0.947381i
\(690\) −3.31878 5.74829i −0.126344 0.218834i
\(691\) 35.9708 1.36840 0.684198 0.729297i \(-0.260153\pi\)
0.684198 + 0.729297i \(0.260153\pi\)
\(692\) 27.4538 1.04364
\(693\) 25.9628 + 44.9689i 0.986245 + 1.70823i
\(694\) −6.25551 10.8349i −0.237456 0.411286i
\(695\) −1.44375 −0.0547646
\(696\) 24.5491 0.930532
\(697\) −0.481960 0.834779i −0.0182555 0.0316195i
\(698\) 21.5035 37.2451i 0.813918 1.40975i
\(699\) 33.9366 + 58.7800i 1.28360 + 2.22326i
\(700\) −5.64959 + 9.78538i −0.213534 + 0.369852i
\(701\) −1.22543 + 2.12252i −0.0462840 + 0.0801663i −0.888239 0.459381i \(-0.848071\pi\)
0.841955 + 0.539547i \(0.181405\pi\)
\(702\) 8.16776 0.308272
\(703\) 46.7159 10.0966i 1.76192 0.380799i
\(704\) 58.4326 2.20226
\(705\) −3.83983 + 6.65079i −0.144616 + 0.250483i
\(706\) 14.5116 25.1348i 0.546151 0.945961i
\(707\) −21.5913 37.3973i −0.812026 1.40647i
\(708\) 12.3715 21.4280i 0.464948 0.805314i
\(709\) 25.1440 + 43.5507i 0.944304 + 1.63558i 0.757139 + 0.653254i \(0.226597\pi\)
0.187165 + 0.982329i \(0.440070\pi\)
\(710\) 37.1014 1.39239
\(711\) −33.2671 −1.24761
\(712\) 1.55313 + 2.69011i 0.0582061 + 0.100816i
\(713\) 1.32379 + 2.29288i 0.0495765 + 0.0858690i
\(714\) −3.18668 −0.119259
\(715\) −22.5351 −0.842765
\(716\) 16.5461 + 28.6587i 0.618357 + 1.07103i
\(717\) 25.1456 43.5534i 0.939079 1.62653i
\(718\) 12.6602 + 21.9281i 0.472473 + 0.818348i
\(719\) 24.0491 41.6543i 0.896881 1.55344i 0.0654223 0.997858i \(-0.479161\pi\)
0.831459 0.555586i \(-0.187506\pi\)
\(720\) −0.103919 + 0.179994i −0.00387285 + 0.00670797i
\(721\) 37.2319 1.38659
\(722\) −4.24347 + 43.2098i −0.157926 + 1.60810i
\(723\) 54.1123 2.01246
\(724\) −19.7615 + 34.2280i −0.734432 + 1.27207i
\(725\) 1.75351 3.03717i 0.0651237 0.112798i
\(726\) 26.6772 + 46.2063i 0.990085 + 1.71488i
\(727\) 8.33983 14.4450i 0.309307 0.535736i −0.668904 0.743349i \(-0.733236\pi\)
0.978211 + 0.207613i \(0.0665695\pi\)
\(728\) 24.4804 + 42.4013i 0.907304 + 1.57150i
\(729\) −31.8655 −1.18020
\(730\) 16.3584 0.605453
\(731\) 0.265545 + 0.459938i 0.00982155 + 0.0170114i
\(732\) −3.52763 6.11004i −0.130385 0.225833i
\(733\) −4.13365 −0.152680 −0.0763399 0.997082i \(-0.524323\pi\)
−0.0763399 + 0.997082i \(0.524323\pi\)
\(734\) −47.1664 −1.74094
\(735\) −6.64257 11.5053i −0.245015 0.424378i
\(736\) 3.31878 5.74829i 0.122332 0.211885i
\(737\) −19.0281 32.9576i −0.700908 1.21401i
\(738\) −22.8112 + 39.5102i −0.839692 + 1.45439i
\(739\) −23.4870 + 40.6806i −0.863982 + 1.49646i 0.00407159 + 0.999992i \(0.498704\pi\)
−0.868054 + 0.496470i \(0.834629\pi\)
\(740\) 35.3273 1.29866
\(741\) −53.4061 + 11.5425i −1.96192 + 0.424025i
\(742\) −46.0241 −1.68960
\(743\) −20.6069 + 35.6923i −0.755995 + 1.30942i 0.188883 + 0.982000i \(0.439513\pi\)
−0.944878 + 0.327422i \(0.893820\pi\)
\(744\) −7.99800 + 13.8529i −0.293221 + 0.507873i
\(745\) 0.864447 + 1.49727i 0.0316709 + 0.0548556i
\(746\) −5.20228 + 9.01061i −0.190469 + 0.329902i
\(747\) −7.97539 13.8138i −0.291804 0.505420i
\(748\) −2.30318 −0.0842127
\(749\) −7.61951 −0.278411
\(750\) −2.86445 4.96137i −0.104595 0.181164i
\(751\) −2.98942 5.17783i −0.109086 0.188942i 0.806314 0.591487i \(-0.201459\pi\)
−0.915400 + 0.402545i \(0.868126\pi\)
\(752\) −0.193802 −0.00706722
\(753\) 18.2210 0.664010
\(754\) −20.0351 34.7018i −0.729635 1.26376i
\(755\) −10.0703 + 17.4422i −0.366495 + 0.634788i
\(756\) 4.03865 + 6.99515i 0.146884 + 0.254411i
\(757\) −18.1968 + 31.5178i −0.661375 + 1.14553i 0.318880 + 0.947795i \(0.396693\pi\)
−0.980255 + 0.197739i \(0.936640\pi\)
\(758\) 22.7585 39.4189i 0.826627 1.43176i
\(759\) 13.0913 0.475186
\(760\) −3.72143 + 11.5878i −0.134991 + 0.420335i
\(761\) −2.71397 −0.0983813 −0.0491907 0.998789i \(-0.515664\pi\)
−0.0491907 + 0.998789i \(0.515664\pi\)
\(762\) 45.0029 77.9473i 1.63028 2.82373i
\(763\) −27.7409 + 48.0487i −1.00429 + 1.73948i
\(764\) −9.19983 15.9346i −0.332838 0.576493i
\(765\) 0.260528 0.451248i 0.00941941 0.0163149i
\(766\) 22.8227 + 39.5300i 0.824617 + 1.42828i
\(767\) −15.3163 −0.553041
\(768\) 39.0802 1.41019
\(769\) −19.8995 34.4670i −0.717596 1.24291i −0.961950 0.273226i \(-0.911909\pi\)
0.244354 0.969686i \(-0.421424\pi\)
\(770\) −18.0597 31.2803i −0.650827 1.12726i
\(771\) −37.7991 −1.36130
\(772\) −32.7298 −1.17797
\(773\) −22.4874 38.9494i −0.808816 1.40091i −0.913684 0.406425i \(-0.866775\pi\)
0.104868 0.994486i \(-0.466558\pi\)
\(774\) 12.5683 21.7689i 0.451758 0.782467i
\(775\) 1.14257 + 1.97899i 0.0410424 + 0.0710875i
\(776\) −2.26097 + 3.91612i −0.0811642 + 0.140580i
\(777\) −48.2022 + 83.4886i −1.72924 + 2.99514i
\(778\) 31.5400 1.13076
\(779\) 8.09992 25.2216i 0.290210 0.903658i
\(780\) −40.3865 −1.44607
\(781\) −36.5878 + 63.3719i −1.30921 + 2.26762i
\(782\) −0.209967 + 0.363673i −0.00750840 + 0.0130049i
\(783\) −1.25351 2.17114i −0.0447968 0.0775903i
\(784\) 0.167630 0.290343i 0.00598678 0.0103694i
\(785\) 1.88906 + 3.27195i 0.0674235 + 0.116781i
\(786\) 66.0833 2.35711
\(787\) −17.7149 −0.631466 −0.315733 0.948848i \(-0.602250\pi\)
−0.315733 + 0.948848i \(0.602250\pi\)
\(788\) −26.1034 45.2124i −0.929894 1.61062i
\(789\) 25.2640 + 43.7585i 0.899422 + 1.55784i
\(790\) 23.1406 0.823305
\(791\) 34.5030 1.22679
\(792\) 20.6706 + 35.8026i 0.734499 + 1.27219i
\(793\) −2.18367 + 3.78222i −0.0775443 + 0.134311i
\(794\) 18.9086 + 32.7506i 0.671040 + 1.16227i
\(795\) 7.19882 12.4687i 0.255316 0.442220i
\(796\) −0.538652 + 0.932972i −0.0190920 + 0.0330683i
\(797\) 25.4930 0.903008 0.451504 0.892269i \(-0.350888\pi\)
0.451504 + 0.892269i \(0.350888\pi\)
\(798\) −58.8217 64.8813i −2.08227 2.29677i
\(799\) 0.485864 0.0171886
\(800\) 2.86445 4.96137i 0.101274 0.175411i
\(801\) 1.82735 3.16507i 0.0645663 0.111832i
\(802\) −9.74049 16.8710i −0.343949 0.595736i
\(803\) −16.1320 + 27.9414i −0.569286 + 0.986032i
\(804\) −34.1014 59.0653i −1.20266 2.08307i
\(805\) −4.06327 −0.143211
\(806\) 26.1094 0.919664
\(807\) −9.68322 16.7718i −0.340866 0.590397i
\(808\) −17.1902 29.7744i −0.604751 1.04746i
\(809\) −20.4678 −0.719610 −0.359805 0.933027i \(-0.617157\pi\)
−0.359805 + 0.933027i \(0.617157\pi\)
\(810\) 18.4257 0.647414
\(811\) 11.4508 + 19.8333i 0.402091 + 0.696442i 0.993978 0.109579i \(-0.0349502\pi\)
−0.591887 + 0.806021i \(0.701617\pi\)
\(812\) 19.8132 34.3175i 0.695308 1.20431i
\(813\) −6.62498 11.4748i −0.232348 0.402439i
\(814\) −56.4643 + 97.7990i −1.97907 + 3.42785i
\(815\) −0.808200 + 1.39984i −0.0283100 + 0.0490344i
\(816\) 0.0251571 0.000880674
\(817\) −4.46281 + 13.8963i −0.156134 + 0.486171i
\(818\) −26.4306 −0.924124
\(819\) 28.8026 49.8876i 1.00645 1.74322i
\(820\) 9.79016 16.9571i 0.341887 0.592166i
\(821\) −15.3609 26.6058i −0.536099 0.928550i −0.999109 0.0421975i \(-0.986564\pi\)
0.463011 0.886353i \(-0.346769\pi\)
\(822\) 0.313316 0.542679i 0.0109281 0.0189281i
\(823\) −2.09846 3.63464i −0.0731476 0.126695i 0.827132 0.562008i \(-0.189971\pi\)
−0.900279 + 0.435313i \(0.856638\pi\)
\(824\) 29.6427 1.03265
\(825\) 11.2992 0.393387
\(826\) −12.2746 21.2602i −0.427087 0.739736i
\(827\) 10.6652 + 18.4726i 0.370865 + 0.642357i 0.989699 0.143165i \(-0.0457280\pi\)
−0.618834 + 0.785522i \(0.712395\pi\)
\(828\) 12.2631 0.426172
\(829\) 34.0390 1.18222 0.591112 0.806590i \(-0.298689\pi\)
0.591112 + 0.806590i \(0.298689\pi\)
\(830\) 5.54767 + 9.60885i 0.192562 + 0.333528i
\(831\) 38.3905 66.4943i 1.33175 2.30666i
\(832\) −32.4120 56.1393i −1.12368 1.94628i
\(833\) −0.420251 + 0.727896i −0.0145608 + 0.0252201i
\(834\) 4.13555 7.16299i 0.143202 0.248034i
\(835\) −6.49298 −0.224699
\(836\) −42.5135 46.8931i −1.47036 1.62183i
\(837\) 1.63355 0.0564638
\(838\) 24.8108 42.9735i 0.857074 1.48450i
\(839\) −5.20584 + 9.01678i −0.179725 + 0.311294i −0.941786 0.336212i \(-0.890854\pi\)
0.762061 + 0.647505i \(0.224188\pi\)
\(840\) −12.2746 21.2602i −0.423513 0.733546i
\(841\) 8.35041 14.4633i 0.287945 0.498736i
\(842\) 7.90967 + 13.7000i 0.272585 + 0.472132i
\(843\) −33.4999 −1.15380
\(844\) 6.53421 0.224917
\(845\) 6.00000 + 10.3923i 0.206406 + 0.357506i
\(846\) −11.4980 19.9151i −0.395309 0.684696i
\(847\) 32.6616 1.12227
\(848\) 0.363334 0.0124769
\(849\) 5.13355 + 8.89157i 0.176183 + 0.305158i
\(850\) −0.181223 + 0.313888i −0.00621590 + 0.0107663i
\(851\) 6.35197 + 11.0019i 0.217743 + 0.377141i
\(852\) −65.5712 + 113.573i −2.24643 + 3.89093i
\(853\) 6.56527 11.3714i 0.224790 0.389349i −0.731466 0.681878i \(-0.761164\pi\)
0.956257 + 0.292529i \(0.0944969\pi\)
\(854\) −7.00000 −0.239535
\(855\) 13.9964 3.02501i 0.478668 0.103453i
\(856\) −6.06638 −0.207345
\(857\) 21.6230 37.4521i 0.738627 1.27934i −0.214487 0.976727i \(-0.568808\pi\)
0.953114 0.302612i \(-0.0978587\pi\)
\(858\) 64.5506 111.805i 2.20372 3.81696i
\(859\) −15.7344 27.2527i −0.536849 0.929850i −0.999071 0.0430861i \(-0.986281\pi\)
0.462222 0.886764i \(-0.347052\pi\)
\(860\) −5.39408 + 9.34282i −0.183937 + 0.318587i
\(861\) 26.7163 + 46.2740i 0.910490 + 1.57701i
\(862\) −63.9356 −2.17766
\(863\) −23.7842 −0.809622 −0.404811 0.914400i \(-0.632663\pi\)
−0.404811 + 0.914400i \(0.632663\pi\)
\(864\) −2.04767 3.54667i −0.0696632 0.120660i
\(865\) 4.26053 + 7.37945i 0.144862 + 0.250909i
\(866\) 14.2912 0.485634
\(867\) 42.5562 1.44529
\(868\) 12.9101 + 22.3610i 0.438198 + 0.758981i
\(869\) −22.8202 + 39.5258i −0.774123 + 1.34082i
\(870\) 10.0457 + 17.3996i 0.340580 + 0.589902i
\(871\) −21.1094 + 36.5625i −0.715264 + 1.23887i
\(872\) −22.0863 + 38.2546i −0.747937 + 1.29547i
\(873\) 5.32033 0.180066
\(874\) −11.2801 + 2.43794i −0.381556 + 0.0824646i
\(875\) −3.50702 −0.118559
\(876\) −28.9111 + 50.0756i −0.976817 + 1.69190i
\(877\) 19.0848 33.0558i 0.644447 1.11621i −0.339982 0.940432i \(-0.610421\pi\)
0.984429 0.175783i \(-0.0562456\pi\)
\(878\) −35.6455 61.7398i −1.20298 2.08362i
\(879\) 15.2585 26.4285i 0.514657 0.891413i
\(880\) 0.142571 + 0.246941i 0.00480608 + 0.00832437i
\(881\) 5.49209 0.185033 0.0925167 0.995711i \(-0.470509\pi\)
0.0925167 + 0.995711i \(0.470509\pi\)
\(882\) 39.7810 1.33950
\(883\) 17.1491 + 29.7032i 0.577115 + 0.999592i 0.995808 + 0.0914644i \(0.0291548\pi\)
−0.418694 + 0.908128i \(0.637512\pi\)
\(884\) 1.27755 + 2.21279i 0.0429688 + 0.0744241i
\(885\) 7.67967 0.258149
\(886\) −74.7327 −2.51069
\(887\) 18.7585 + 32.4907i 0.629850 + 1.09093i 0.987582 + 0.157107i \(0.0502169\pi\)
−0.357732 + 0.933824i \(0.616450\pi\)
\(888\) −38.3768 + 66.4706i −1.28784 + 2.23061i
\(889\) −27.5491 47.7165i −0.923968 1.60036i
\(890\) −1.27111 + 2.20162i −0.0426075 + 0.0737984i
\(891\) −18.1706 + 31.4725i −0.608740 + 1.05437i
\(892\) −61.9628 −2.07467
\(893\) 8.96837 + 9.89226i 0.300115 + 0.331032i
\(894\) −9.90466 −0.331261
\(895\) −5.13555 + 8.89504i −0.171663 + 0.297328i
\(896\) 31.8589 55.1812i 1.06433 1.84347i
\(897\) −7.26164 12.5775i −0.242459 0.419952i
\(898\) −29.2846 + 50.7224i −0.977240 + 1.69263i
\(899\) −4.00702 6.94036i −0.133642 0.231474i
\(900\) 10.5843 0.352811
\(901\) −0.910886 −0.0303460
\(902\) 31.2956 + 54.2056i 1.04203 + 1.80485i
\(903\) −14.7199 25.4956i −0.489847 0.848439i
\(904\) 27.4701 0.913640
\(905\) −12.2671 −0.407772
\(906\) −57.6916 99.9248i −1.91668 3.31978i
\(907\) 11.1265 19.2717i 0.369450 0.639907i −0.620029 0.784579i \(-0.712879\pi\)
0.989480 + 0.144672i \(0.0462126\pi\)
\(908\) −6.44375 11.1609i −0.213843 0.370388i
\(909\) −20.2253 + 35.0313i −0.670832 + 1.16192i
\(910\) −20.0351 + 34.7018i −0.664157 + 1.15035i
\(911\) 10.0421 0.332710 0.166355 0.986066i \(-0.446800\pi\)
0.166355 + 0.986066i \(0.446800\pi\)
\(912\) 0.464364 + 0.512202i 0.0153766 + 0.0169607i
\(913\) −21.8835 −0.724238
\(914\) −37.8930 + 65.6325i −1.25339 + 2.17093i
\(915\) 1.09490 1.89642i 0.0361963 0.0626938i
\(916\) 20.9081 + 36.2139i 0.690824 + 1.19654i
\(917\) 20.2269 35.0340i 0.667951 1.15692i
\(918\) 0.129549 + 0.224385i 0.00427574 + 0.00740580i
\(919\) 6.06104 0.199935 0.0999676 0.994991i \(-0.468126\pi\)
0.0999676 + 0.994991i \(0.468126\pi\)
\(920\) −3.23503 −0.106656
\(921\) 30.7550 + 53.2692i 1.01341 + 1.75528i
\(922\) −2.48596 4.30581i −0.0818708 0.141804i
\(923\) 81.1796 2.67206
\(924\) 127.671 4.20008
\(925\) 5.48240 + 9.49580i 0.180260 + 0.312220i
\(926\) 7.08477 12.2712i 0.232820 0.403256i
\(927\) −17.4382 30.2038i −0.572745 0.992024i
\(928\) −10.0457 + 17.3996i −0.329765 + 0.571170i
\(929\) 25.9382 44.9263i 0.851004 1.47398i −0.0292983 0.999571i \(-0.509327\pi\)
0.880303 0.474412i \(-0.157339\pi\)
\(930\) −13.0913 −0.429282
\(931\) −22.5773 + 4.87957i −0.739941 + 0.159921i
\(932\) 87.2268 2.85721
\(933\) −12.7906 + 22.1540i −0.418746 + 0.725289i
\(934\) 19.6004 33.9488i 0.641343 1.11084i
\(935\) −0.357429 0.619085i −0.0116892 0.0202462i
\(936\) 22.9316 39.7187i 0.749543 1.29825i
\(937\) −12.5999 21.8237i −0.411621 0.712949i 0.583446 0.812152i \(-0.301704\pi\)
−0.995067 + 0.0992029i \(0.968371\pi\)
\(938\) −67.6685 −2.20946
\(939\) 80.1794 2.61655
\(940\) 4.93473 + 8.54721i 0.160953 + 0.278779i
\(941\) 0.967923 + 1.67649i 0.0315534 + 0.0546521i 0.881371 0.472425i \(-0.156621\pi\)
−0.849817 + 0.527077i \(0.823288\pi\)
\(942\) −21.6445 −0.705215
\(943\) 7.04122 0.229294
\(944\) 0.0969008 + 0.167837i 0.00315385 + 0.00546263i
\(945\) −1.25351 + 2.17114i −0.0407767 + 0.0706272i
\(946\) −17.2429 29.8656i −0.560616 0.971016i
\(947\) −15.6812 + 27.1607i −0.509571 + 0.882603i 0.490367 + 0.871516i \(0.336863\pi\)
−0.999939 + 0.0110875i \(0.996471\pi\)
\(948\) −40.8975 + 70.8366i −1.32829 + 2.30067i
\(949\) 35.7930 1.16189
\(950\) −9.73591 + 2.10419i −0.315875 + 0.0682691i
\(951\) −5.60548 −0.181770
\(952\) −0.776567 + 1.34505i −0.0251687 + 0.0435934i
\(953\) −26.4542 + 45.8201i −0.856937 + 1.48426i 0.0179001 + 0.999840i \(0.494302\pi\)
−0.874837 + 0.484418i \(0.839031\pi\)
\(954\) 21.5561 + 37.3363i 0.697906 + 1.20881i
\(955\) 2.85543 4.94575i 0.0923995 0.160041i
\(956\) −32.3157 55.9724i −1.04516 1.81028i
\(957\) −39.6264 −1.28094
\(958\) −81.7581 −2.64148
\(959\) −0.191800 0.332208i −0.00619355 0.0107275i
\(960\) 16.2515 + 28.1484i 0.524515 + 0.908487i
\(961\) −25.7781 −0.831552
\(962\) 125.281 4.03921
\(963\) 3.56873 + 6.18122i 0.115001 + 0.199187i
\(964\) 34.7710 60.2252i 1.11990 1.93972i
\(965\) −5.07930 8.79761i −0.163509 0.283205i
\(966\) 11.6390 20.1594i 0.374479 0.648617i
\(967\) 30.0140 51.9858i 0.965186 1.67175i 0.256073 0.966657i \(-0.417571\pi\)
0.709113 0.705094i \(-0.249095\pi\)
\(968\) 26.0040 0.835800
\(969\) −1.16417 1.28410i −0.0373985 0.0412512i
\(970\) −3.70082 −0.118826
\(971\) −0.875025 + 1.51559i −0.0280809 + 0.0486375i −0.879724 0.475484i \(-0.842273\pi\)
0.851643 + 0.524122i \(0.175606\pi\)
\(972\) −36.0195 + 62.3876i −1.15533 + 2.00108i
\(973\) −2.53163 4.38492i −0.0811604 0.140574i
\(974\) 27.0959 46.9315i 0.868209 1.50378i
\(975\) −6.26755 10.8557i −0.200722 0.347661i
\(976\) 0.0552611 0.00176886
\(977\) 5.47583 0.175187 0.0875937 0.996156i \(-0.472082\pi\)
0.0875937 + 0.996156i \(0.472082\pi\)
\(978\) −4.63009 8.01955i −0.148054 0.256437i
\(979\) −2.50702 4.34228i −0.0801247 0.138780i
\(980\) −17.0733 −0.545387
\(981\) 51.9717 1.65933
\(982\) 44.7736 + 77.5501i 1.42878 + 2.47472i
\(983\) −2.52963 + 4.38145i −0.0806827 + 0.139747i −0.903543 0.428497i \(-0.859043\pi\)
0.822861 + 0.568243i \(0.192377\pi\)
\(984\) 21.2706 + 36.8417i 0.678081 + 1.17447i
\(985\) 8.10192 14.0329i 0.258149 0.447126i
\(986\) 0.635553 1.10081i 0.0202401 0.0350569i
\(987\) −26.9327 −0.857278
\(988\) −21.4708 + 66.8561i −0.683078 + 2.12698i
\(989\) −3.87950 −0.123361
\(990\) −16.9171 + 29.3013i −0.537662 + 0.931258i
\(991\) −0.0492290 + 0.0852672i −0.00156381 + 0.00270860i −0.866806 0.498645i \(-0.833831\pi\)
0.865242 + 0.501354i \(0.167164\pi\)
\(992\) −6.54567 11.3374i −0.207825 0.359964i
\(993\) −12.6496 + 21.9097i −0.401423 + 0.695284i
\(994\) 65.0576 + 112.683i 2.06350 + 3.57409i
\(995\) −0.334372 −0.0106003
\(996\) −39.2188 −1.24269
\(997\) −9.17967 15.8996i −0.290723 0.503547i 0.683258 0.730177i \(-0.260562\pi\)
−0.973981 + 0.226630i \(0.927229\pi\)
\(998\) 10.7133 + 18.5560i 0.339124 + 0.587379i
\(999\) 7.83828 0.247992
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 95.2.e.b.11.1 6
3.2 odd 2 855.2.k.g.676.3 6
4.3 odd 2 1520.2.q.j.961.1 6
5.2 odd 4 475.2.j.b.49.2 12
5.3 odd 4 475.2.j.b.49.5 12
5.4 even 2 475.2.e.d.201.3 6
19.7 even 3 inner 95.2.e.b.26.1 yes 6
19.8 odd 6 1805.2.a.g.1.1 3
19.11 even 3 1805.2.a.h.1.3 3
57.26 odd 6 855.2.k.g.406.3 6
76.7 odd 6 1520.2.q.j.881.1 6
95.7 odd 12 475.2.j.b.349.5 12
95.49 even 6 9025.2.a.z.1.1 3
95.64 even 6 475.2.e.d.26.3 6
95.83 odd 12 475.2.j.b.349.2 12
95.84 odd 6 9025.2.a.ba.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.b.11.1 6 1.1 even 1 trivial
95.2.e.b.26.1 yes 6 19.7 even 3 inner
475.2.e.d.26.3 6 95.64 even 6
475.2.e.d.201.3 6 5.4 even 2
475.2.j.b.49.2 12 5.2 odd 4
475.2.j.b.49.5 12 5.3 odd 4
475.2.j.b.349.2 12 95.83 odd 12
475.2.j.b.349.5 12 95.7 odd 12
855.2.k.g.406.3 6 57.26 odd 6
855.2.k.g.676.3 6 3.2 odd 2
1520.2.q.j.881.1 6 76.7 odd 6
1520.2.q.j.961.1 6 4.3 odd 2
1805.2.a.g.1.1 3 19.8 odd 6
1805.2.a.h.1.3 3 19.11 even 3
9025.2.a.z.1.1 3 95.49 even 6
9025.2.a.ba.1.3 3 95.84 odd 6