Properties

Label 475.2.e.d.201.3
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.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: \(3.79289409601\)
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: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.3
Root \(1.14257 - 1.97899i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.d.26.3

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14257 1.97899i 0.807920 1.39936i −0.106382 0.994325i \(-0.533927\pi\)
0.914302 0.405033i \(-0.132740\pi\)
\(3\) −1.25351 + 2.17114i −0.723714 + 1.25351i 0.235787 + 0.971805i \(0.424233\pi\)
−0.959501 + 0.281705i \(0.909100\pi\)
\(4\) −1.61094 2.79023i −0.805469 1.39511i
\(5\) 0 0
\(6\) 2.86445 + 4.96137i 1.16941 + 2.02547i
\(7\) −3.50702 −1.32553 −0.662764 0.748828i \(-0.730617\pi\)
−0.662764 + 0.748828i \(0.730617\pi\)
\(8\) −2.79216 −0.987178
\(9\) −1.64257 2.84502i −0.547524 0.948339i
\(10\) 0 0
\(11\) −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 \(-0.922790\pi\)
0.277350 0.960769i \(-0.410544\pi\)
\(14\) −4.00702 + 6.94036i −1.07092 + 1.85489i
\(15\) 0 0
\(16\) 0.0316332 0.0547902i 0.00790829 0.0136976i
\(17\) 0.0793049 0.137360i 0.0192343 0.0333147i −0.856248 0.516565i \(-0.827210\pi\)
0.875482 + 0.483250i \(0.160544\pi\)
\(18\) −7.50702 −1.76942
\(19\) −4.26053 + 0.920816i −0.977432 + 0.211250i
\(20\) 0 0
\(21\) 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 0.920081 0.391729i \(-0.128123\pi\)
−0.799287 + 0.600949i \(0.794789\pi\)
\(24\) 3.50000 6.06218i 0.714435 1.23744i
\(25\) 0 0
\(26\) −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 \(0.727761\pi\)
\(30\) 0 0
\(31\) −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
\(35\) 0 0
\(36\) −5.29216 + 9.16629i −0.882027 + 1.52772i
\(37\) 10.9648 1.80260 0.901302 0.433192i \(-0.142613\pi\)
0.901302 + 0.433192i \(0.142613\pi\)
\(38\) −3.04567 + 9.48365i −0.494073 + 1.53845i
\(39\) 12.5351 2.00722
\(40\) 0 0
\(41\) −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 −0.964981 0.262321i \(-0.915512\pi\)
0.709667 + 0.704537i \(0.248845\pi\)
\(44\) 7.26053 + 12.5756i 1.09457 + 1.89584i
\(45\) 0 0
\(46\) 2.64759 0.390366
\(47\) 1.53163 + 2.65287i 0.223412 + 0.386960i 0.955842 0.293882i \(-0.0949472\pi\)
−0.732430 + 0.680842i \(0.761614\pi\)
\(48\) 0.0793049 + 0.137360i 0.0114467 + 0.0198262i
\(49\) 5.29918 0.757026
\(50\) 0 0
\(51\) 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 0.598602 0.801047i \(-0.295723\pi\)
−0.993028 + 0.117881i \(0.962390\pi\)
\(54\) 0.816776 1.41470i 0.111149 0.192516i
\(55\) 0 0
\(56\) 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 \(0.230567\pi\)
\(60\) 0 0
\(61\) 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
\(65\) 0 0
\(66\) −12.9101 22.3610i −1.58913 2.75245i
\(67\) −4.22188 7.31250i −0.515784 0.893365i −0.999832 0.0183230i \(-0.994167\pi\)
0.484048 0.875042i \(-0.339166\pi\)
\(68\) −0.511021 −0.0619704
\(69\) −2.90466 −0.349680
\(70\) 0 0
\(71\) 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 −0.995832 0.0912097i \(-0.970927\pi\)
0.576906 + 0.816811i \(0.304260\pi\)
\(74\) 12.5281 21.6993i 1.45636 2.52249i
\(75\) 0 0
\(76\) 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 0
\(81\) 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 \(-0.585859\pi\)
−0.266476 + 0.963841i \(0.585859\pi\)
\(84\) −28.3273 −3.09076
\(85\) 0 0
\(86\) 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 \(0.814554\pi\)
\(90\) 0 0
\(91\) 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
\(95\) 0 0
\(96\) 14.3624 1.46586
\(97\) 0.809757 1.40254i 0.0822184 0.142406i −0.821984 0.569510i \(-0.807133\pi\)
0.904203 + 0.427104i \(0.140466\pi\)
\(98\) 6.05469 10.4870i 0.611616 1.05935i
\(99\) 7.40310 + 12.8225i 0.744039 + 1.28871i
\(100\) 0 0
\(101\) −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 \(-0.675199\pi\)
−0.523032 + 0.852313i \(0.675199\pi\)
\(104\) 6.98040 + 12.0904i 0.684485 + 1.18556i
\(105\) 0 0
\(106\) −13.1234 −1.27466
\(107\) 2.17265 0.210038 0.105019 0.994470i \(-0.466510\pi\)
0.105019 + 0.994470i \(0.466510\pi\)
\(108\) −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 \(0.893013\pi\)
\(110\) 0 0
\(111\) −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 \(-0.653139\pi\)
−0.462754 + 0.886487i \(0.653139\pi\)
\(114\) −16.7726 18.5004i −1.57089 1.73272i
\(115\) 0 0
\(116\) 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
\(120\) 0 0
\(121\) 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
\(125\) 0 0
\(126\) 26.3273 2.34542
\(127\) 7.85543 + 13.6060i 0.697056 + 1.20734i 0.969483 + 0.245160i \(0.0788407\pi\)
−0.272426 + 0.962177i \(0.587826\pi\)
\(128\) −9.08432 + 15.7345i −0.802948 + 1.39075i
\(129\) −4.19726 7.26987i −0.369548 0.640076i
\(130\) 0 0
\(131\) 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 0
\(136\) −0.221432 + 0.383532i −0.0189876 + 0.0328876i
\(137\) 0.0546904 + 0.0947266i 0.00467252 + 0.00809304i 0.868352 0.495948i \(-0.165179\pi\)
−0.863680 + 0.504041i \(0.831846\pi\)
\(138\) −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 \(0.852835\pi\)
\(140\) 0 0
\(141\) −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
\(145\) 0 0
\(146\) 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 \(0.189228\pi\)
\(150\) 0 0
\(151\) −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
\(155\) 0 0
\(156\) −20.1933 34.9758i −1.61675 2.80030i
\(157\) 1.88906 3.27195i 0.150764 0.261130i −0.780745 0.624850i \(-0.785160\pi\)
0.931508 + 0.363720i \(0.118493\pi\)
\(158\) −11.5703 20.0403i −0.920482 1.59432i
\(159\) 14.3976 1.14181
\(160\) 0 0
\(161\) −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 \(-0.479837\pi\)
0.0633031 + 0.997994i \(0.479837\pi\)
\(164\) 19.5803 1.52897
\(165\) 0 0
\(166\) −5.54767 + 9.60885i −0.430583 + 0.745791i
\(167\) 3.24649 + 5.62309i 0.251221 + 0.435128i 0.963862 0.266401i \(-0.0858346\pi\)
−0.712641 + 0.701529i \(0.752501\pi\)
\(168\) −12.2746 + 21.2602i −0.947003 + 1.64026i
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 9.61796 + 10.6088i 0.735504 + 0.811273i
\(172\) 10.7882 0.822589
\(173\) 4.26053 7.37945i 0.323922 0.561049i −0.657372 0.753567i \(-0.728332\pi\)
0.981294 + 0.192517i \(0.0616651\pi\)
\(174\) −10.0457 + 17.3996i −0.761560 + 1.31906i
\(175\) 0 0
\(176\) −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 \(0.625402\pi\)
\(180\) 0 0
\(181\) −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
\(185\) 0 0
\(186\) −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
\(190\) 0 0
\(191\) 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 −0.988875 0.148750i \(-0.952475\pi\)
0.623259 + 0.782016i \(0.285808\pi\)
\(194\) −1.85041 3.20500i −0.132852 0.230106i
\(195\) 0 0
\(196\) −8.53665 14.7859i −0.609761 1.05614i
\(197\) −16.2038 −1.15448 −0.577238 0.816576i \(-0.695869\pi\)
−0.577238 + 0.816576i \(0.695869\pi\)
\(198\) 33.8343 2.40450
\(199\) −0.167186 0.289574i −0.0118515 0.0205274i 0.860039 0.510229i \(-0.170439\pi\)
−0.871890 + 0.489701i \(0.837106\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) −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
\(210\) 0 0
\(211\) −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
\(215\) 0 0
\(216\) −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
\(220\) 0 0
\(221\) −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 \(0.389365\pi\)
−0.984547 + 0.175120i \(0.943969\pi\)
\(224\) 10.0457 + 17.3996i 0.671205 + 1.16256i
\(225\) 0 0
\(226\) −11.2409 + 19.4699i −0.747736 + 1.29512i
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) −34.4136 + 7.43771i −2.27909 + 0.492574i
\(229\) −12.9788 −0.857666 −0.428833 0.903384i \(-0.641075\pi\)
−0.428833 + 0.903384i \(0.641075\pi\)
\(230\) 0 0
\(231\) −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 \(-0.486246\pi\)
0.843619 0.536943i \(-0.180421\pi\)
\(234\) 18.7675 + 32.5063i 1.22687 + 2.12501i
\(235\) 0 0
\(236\) 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 0
\(241\) 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
\(245\) 0 0
\(246\) −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
\(250\) 0 0
\(251\) 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 0
\(256\) 7.79416 + 13.4999i 0.487135 + 0.843743i
\(257\) 7.53865 + 13.0573i 0.470248 + 0.814494i 0.999421 0.0340202i \(-0.0108311\pi\)
−0.529173 + 0.848514i \(0.677498\pi\)
\(258\) −19.1827 −1.19426
\(259\) −38.4538 −2.38940
\(260\) 0 0
\(261\) 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 \(-0.619900\pi\)
0.989227 0.146393i \(-0.0467663\pi\)
\(264\) −15.7746 + 27.3223i −0.970857 + 1.68157i
\(265\) 0 0
\(266\) 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 0
\(271\) 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
\(275\) 0 0
\(276\) 4.67922 + 8.10465i 0.281656 + 0.487843i
\(277\) −30.6264 −1.84016 −0.920082 0.391726i \(-0.871878\pi\)
−0.920082 + 0.391726i \(0.871878\pi\)
\(278\) −3.29918 −0.197872
\(279\) 3.75351 + 6.50127i 0.224717 + 0.389221i
\(280\) 0 0
\(281\) −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 −0.798725 0.601696i \(-0.794492\pi\)
0.920447 + 0.390868i \(0.127825\pi\)
\(284\) −52.3101 −3.10403
\(285\) 0 0
\(286\) 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
\(290\) 0 0
\(291\) 2.03008 + 3.51619i 0.119005 + 0.206123i
\(292\) 23.0642 1.34973
\(293\) −12.1726 −0.711134 −0.355567 0.934651i \(-0.615712\pi\)
−0.355567 + 0.934651i \(0.615712\pi\)
\(294\) 15.1792 + 26.2912i 0.885270 + 1.53333i
\(295\) 0 0
\(296\) −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
\(300\) 0 0
\(301\) 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 0
\(306\) −0.595344 + 1.03117i −0.0340335 + 0.0589478i
\(307\) 12.2675 21.2480i 0.700146 1.21269i −0.268269 0.963344i \(-0.586452\pi\)
0.968415 0.249344i \(-0.0802150\pi\)
\(308\) −25.4628 44.1029i −1.45088 2.51299i
\(309\) 13.3078 23.0497i 0.757052 1.31125i
\(310\) 0 0
\(311\) −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 \(-0.807385\pi\)
−0.0814282 0.996679i \(-0.525948\pi\)
\(314\) −4.31678 7.47687i −0.243610 0.421944i
\(315\) 0 0
\(316\) −32.6264 −1.83538
\(317\) 1.11796 + 1.93636i 0.0627907 + 0.108757i 0.895712 0.444635i \(-0.146667\pi\)
−0.832921 + 0.553392i \(0.813333\pi\)
\(318\) 16.4503 28.4928i 0.922489 1.59780i
\(319\) −7.90310 13.6886i −0.442489 0.766413i
\(320\) 0 0
\(321\) −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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) −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
\(335\) 0 0
\(336\) −0.278124 0.481725i −0.0151729 0.0262802i
\(337\) 2.80620 4.86048i 0.152863 0.264767i −0.779416 0.626507i \(-0.784484\pi\)
0.932279 + 0.361740i \(0.117817\pi\)
\(338\) 13.7109 + 23.7479i 0.745772 + 1.29172i
\(339\) 12.3324 21.3603i 0.669802 1.16013i
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) −9.73591 16.8631i −0.523406 0.906566i
\(347\) 2.73747 4.74144i 0.146955 0.254534i −0.783146 0.621838i \(-0.786386\pi\)
0.930101 + 0.367305i \(0.119719\pi\)
\(348\) 14.1636 + 24.5321i 0.759250 + 1.31506i
\(349\) −18.8202 −1.00742 −0.503712 0.863872i \(-0.668033\pi\)
−0.503712 + 0.863872i \(0.668033\pi\)
\(350\) 0 0
\(351\) −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 \(-0.390250\pi\)
0.337998 + 0.941147i \(0.390250\pi\)
\(354\) −17.5491 −0.932726
\(355\) 0 0
\(356\) 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 \(0.0722125\pi\)
\(360\) 0 0
\(361\) 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
\(365\) 0 0
\(366\) −2.50200 + 4.33359i −0.130782 + 0.226521i
\(367\) −10.3202 17.8752i −0.538712 0.933076i −0.998974 0.0452932i \(-0.985578\pi\)
0.460262 0.887783i \(-0.347756\pi\)
\(368\) 0.0733010 0.00382108
\(369\) 19.9648 1.03933
\(370\) 0 0
\(371\) 10.0703 + 17.4422i 0.522823 + 0.905556i
\(372\) −18.4578 −0.956992
\(373\) −4.55313 −0.235752 −0.117876 0.993028i \(-0.537609\pi\)
−0.117876 + 0.993028i \(0.537609\pi\)
\(374\) 0.816776 + 1.41470i 0.0422345 + 0.0731522i
\(375\) 0 0
\(376\) −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 \(0.670939\pi\)
\(380\) 0 0
\(381\) −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 \(0.337145\pi\)
−0.999928 + 0.0119734i \(0.996189\pi\)
\(384\) −22.7746 39.4467i −1.16221 2.01301i
\(385\) 0 0
\(386\) 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 \(0.947118\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) 23.8519 41.3126i 1.19860 2.07604i
\(397\) −8.27457 + 14.3320i −0.415289 + 0.719301i −0.995459 0.0951945i \(-0.969653\pi\)
0.580170 + 0.814495i \(0.302986\pi\)
\(398\) −0.764087 −0.0383002
\(399\) −11.7183 + 36.4886i −0.586650 + 1.82672i
\(400\) 0 0
\(401\) −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
\(405\) 0 0
\(406\) −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 \(0.741022\pi\)
\(410\) 0 0
\(411\) −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
\(415\) 0 0
\(416\) −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 \(0.677966\pi\)
\(420\) 0 0
\(421\) 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 0
\(426\) 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
\(430\) 0 0
\(431\) 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 0.931328 0.364182i \(-0.118651\pi\)
−0.781055 + 0.624462i \(0.785318\pi\)
\(434\) 9.15661 15.8597i 0.439531 0.761290i
\(435\) 0 0
\(436\) 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 \(0.899359\pi\)
\(440\) 0 0
\(441\) −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 \(-0.883457\pi\)
0.156819 0.987627i \(-0.449876\pi\)
\(444\) 88.5661 4.20316
\(445\) 0 0
\(446\) 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 \(0.293258\pi\)
\(450\) 0 0
\(451\) 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
\(455\) 0 0
\(456\) −9.32970 + 29.0509i −0.436903 + 1.36043i
\(457\) −33.1646 −1.55138 −0.775688 0.631116i \(-0.782597\pi\)
−0.775688 + 0.631116i \(0.782597\pi\)
\(458\) −14.8293 + 25.6850i −0.692926 + 1.20018i
\(459\) 0.0566917 0.0981929i 0.00264614 0.00458325i
\(460\) 0 0
\(461\) −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 \(-0.453976\pi\)
0.144086 + 0.989565i \(0.453976\pi\)
\(464\) 0.221876 0.0103003
\(465\) 0 0
\(466\) −30.9332 53.5778i −1.43295 2.48195i
\(467\) 17.1546 0.793821 0.396910 0.917857i \(-0.370082\pi\)
0.396910 + 0.917857i \(0.370082\pi\)
\(468\) 52.9216 2.44630
\(469\) 14.8062 + 25.6451i 0.683687 + 1.18418i
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 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 \(0.528763\pi\)
\(480\) 0 0
\(481\) −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 0
\(486\) 51.0943 2.31768
\(487\) 23.7149 1.07462 0.537311 0.843384i \(-0.319440\pi\)
0.537311 + 0.843384i \(0.319440\pi\)
\(488\) −1.21943 2.11212i −0.0552010 0.0956110i
\(489\) −2.02617 + 3.50943i −0.0916267 + 0.158702i
\(490\) 0 0
\(491\) 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
\(495\) 0 0
\(496\) −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 \(0.0993611\pi\)
\(500\) 0 0
\(501\) −16.2780 −0.727249
\(502\) 16.6084 0.741269
\(503\) 6.74649 + 11.6853i 0.300811 + 0.521020i 0.976320 0.216332i \(-0.0694093\pi\)
−0.675509 + 0.737352i \(0.736076\pi\)
\(504\) −16.0843 27.8589i −0.716453 1.24093i
\(505\) 0 0
\(506\) −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 0
\(511\) 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
\(515\) 0 0
\(516\) −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
\(520\) 0 0
\(521\) −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 \(0.150526\pi\)
−0.0506855 + 0.998715i \(0.516141\pi\)
\(524\) −37.1646 −1.62354
\(525\) 0 0
\(526\) −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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 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
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) −50.2284 + 86.9981i −2.14958 + 3.72317i
\(547\) −9.12853 15.8111i −0.390308 0.676033i 0.602182 0.798359i \(-0.294298\pi\)
−0.992490 + 0.122326i \(0.960965\pi\)
\(548\) 0.176206 0.305197i 0.00752714 0.0130374i
\(549\) 1.43473 2.48503i 0.0612329 0.106058i
\(550\) 0 0
\(551\) −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
\(555\) 0 0
\(556\) −2.32580 + 4.02840i −0.0986357 + 0.170842i
\(557\) 7.45233 + 12.9078i 0.315765 + 0.546922i 0.979600 0.200958i \(-0.0644054\pi\)
−0.663835 + 0.747879i \(0.731072\pi\)
\(558\) 17.1546 0.726212
\(559\) 16.7420 0.708113
\(560\) 0 0
\(561\) −0.896081 1.55206i −0.0378326 0.0655279i
\(562\) −30.5351 −1.28805
\(563\) −45.7810 −1.92944 −0.964720 0.263276i \(-0.915197\pi\)
−0.964720 + 0.263276i \(0.915197\pi\)
\(564\) 12.3715 + 21.4280i 0.520933 + 0.902282i
\(565\) 0 0
\(566\) −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 \(0.497467\pi\)
\(570\) 0 0
\(571\) −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 0
\(576\) 21.2956 + 36.8851i 0.887318 + 1.53688i
\(577\) 19.2350 0.800765 0.400382 0.916348i \(-0.368877\pi\)
0.400382 + 0.916348i \(0.368877\pi\)
\(578\) 38.7899 1.61345
\(579\) −12.7339 22.0558i −0.529203 0.916607i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) −13.9081 + 24.0896i −0.574539 + 0.995131i
\(587\) 20.4242 35.3757i 0.842995 1.46011i −0.0443559 0.999016i \(-0.514124\pi\)
0.887351 0.461095i \(-0.152543\pi\)
\(588\) 42.8031 1.76517
\(589\) 9.73591 2.10419i 0.401161 0.0867018i
\(590\) 0 0
\(591\) 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 0.681882 0.731462i \(-0.261162\pi\)
−0.974406 + 0.224796i \(0.927828\pi\)
\(594\) −3.68122 + 6.37607i −0.151042 + 0.261613i
\(595\) 0 0
\(596\) 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 \(0.728361\pi\)
\(600\) 0 0
\(601\) 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
\(605\) 0 0
\(606\) 35.2706 61.0904i 1.43277 2.48163i
\(607\) 10.3914 0.421774 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(608\) 16.7726 + 18.5004i 0.680217 + 0.750291i
\(609\) 30.8343 1.24947
\(610\) 0 0
\(611\) 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 −0.997685 0.0680090i \(-0.978335\pi\)
0.557740 + 0.830016i \(0.311669\pi\)
\(614\) −28.0331 48.5547i −1.13132 1.95951i
\(615\) 0 0
\(616\) −44.1335 −1.77819
\(617\) −21.3855 37.0408i −0.860948 1.49121i −0.871015 0.491256i \(-0.836538\pi\)
0.0100671 0.999949i \(-0.496795\pi\)
\(618\) −30.4101 52.6719i −1.22327 2.11877i
\(619\) 28.7882 1.15709 0.578547 0.815649i \(-0.303620\pi\)
0.578547 + 0.815649i \(0.303620\pi\)
\(620\) 0 0
\(621\) 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 0
\(626\) −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
\(630\) 0 0
\(631\) 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
\(635\) 0 0
\(636\) −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
\(640\) 0 0
\(641\) −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 \(0.401443\pi\)
−0.977195 + 0.212344i \(0.931890\pi\)
\(644\) −6.54567 + 11.3374i −0.257936 + 0.446757i
\(645\) 0 0
\(646\) 1.06114 + 1.17045i 0.0417499 + 0.0460509i
\(647\) 48.0029 1.88719 0.943595 0.331103i \(-0.107421\pi\)
0.943595 + 0.331103i \(0.107421\pi\)
\(648\) −11.2570 + 19.4976i −0.442216 + 0.765940i
\(649\) 6.90310 11.9565i 0.270970 0.469334i
\(650\) 0 0
\(651\) −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 \(-0.524368\pi\)
−0.0764788 + 0.997071i \(0.524368\pi\)
\(654\) −90.6325 −3.54401
\(655\) 0 0
\(656\) 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 \(0.915383\pi\)
\(660\) 0 0
\(661\) 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
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) −1.96837 3.40931i −0.0759880 0.131615i
\(672\) −50.3694 −1.94304
\(673\) 11.3304 0.436754 0.218377 0.975865i \(-0.429924\pi\)
0.218377 + 0.975865i \(0.429924\pi\)
\(674\) −6.41256 11.1069i −0.247003 0.427821i
\(675\) 0 0
\(676\) 38.6625 1.48702
\(677\) −8.90466 −0.342234 −0.171117 0.985251i \(-0.554738\pi\)
−0.171117 + 0.985251i \(0.554738\pi\)
\(678\) −28.1812 48.8113i −1.08229 1.87459i
\(679\) −2.83983 + 4.91873i −0.108983 + 0.188764i
\(680\) 0 0
\(681\) 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 \(-0.329357\pi\)
0.510780 + 0.859712i \(0.329357\pi\)
\(684\) 14.1069 43.9263i 0.539392 1.67957i
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) 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
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) −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
\(705\) 0 0
\(706\) 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 \(0.440070\pi\)
\(710\) 0 0
\(711\) −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
\(715\) 0 0
\(716\) 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 0
\(721\) 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
\(725\) 0 0
\(726\) 26.6772 + 46.2063i 0.990085 + 1.71488i
\(727\) −8.33983 + 14.4450i −0.309307 + 0.535736i −0.978211 0.207613i \(-0.933430\pi\)
0.668904 + 0.743349i \(0.266764\pi\)
\(728\) −24.4804 42.4013i −0.907304 1.57150i
\(729\) −31.8655 −1.18020
\(730\) 0 0
\(731\) 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 \(-0.475677\pi\)
0.0763399 + 0.997082i \(0.475677\pi\)
\(734\) −47.1664 −1.74094
\(735\) 0 0
\(736\) 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 \(0.834629\pi\)
\(740\) 0 0
\(741\) −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 \(-0.560487\pi\)
0.944878 0.327422i \(-0.106180\pi\)
\(744\) −7.99800 + 13.8529i −0.293221 + 0.507873i
\(745\) 0 0
\(746\) −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
\(750\) 0 0
\(751\) −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
\(755\) 0 0
\(756\) 4.03865 + 6.99515i 0.146884 + 0.254411i
\(757\) 18.1968 31.5178i 0.661375 1.14553i −0.318880 0.947795i \(-0.603307\pi\)
0.980255 0.197739i \(-0.0633599\pi\)
\(758\) −22.7585 + 39.4189i −0.826627 + 1.43176i
\(759\) 13.0913 0.475186
\(760\) 0 0
\(761\) −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 0
\(766\) 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 \(-0.421424\pi\)
\(770\) 0 0
\(771\) −37.7991 −1.36130
\(772\) 32.7298 1.17797
\(773\) 22.4874 + 38.9494i 0.808816 + 1.40091i 0.913684 + 0.406425i \(0.133225\pi\)
−0.104868 + 0.994486i \(0.533442\pi\)
\(774\) 12.5683 21.7689i 0.451758 0.782467i
\(775\) 0 0
\(776\) −2.26097 + 3.91612i −0.0811642 + 0.140580i
\(777\) 48.2022 83.4886i 1.72924 2.99514i