Properties

Label 252.2.bj.b.103.1
Level $252$
Weight $2$
Character 252.103
Analytic conductor $2.012$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(103,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 103.1
Character \(\chi\) \(=\) 252.103
Dual form 252.2.bj.b.115.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41404 - 0.0221477i) q^{2} +(0.799650 + 1.53641i) q^{3} +(1.99902 + 0.0626353i) q^{4} +(-2.43207 + 1.40416i) q^{5} +(-1.09671 - 2.19026i) q^{6} +(-2.50476 - 0.852161i) q^{7} +(-2.82531 - 0.132842i) q^{8} +(-1.72112 + 2.45718i) q^{9} +O(q^{10})\) \(q+(-1.41404 - 0.0221477i) q^{2} +(0.799650 + 1.53641i) q^{3} +(1.99902 + 0.0626353i) q^{4} +(-2.43207 + 1.40416i) q^{5} +(-1.09671 - 2.19026i) q^{6} +(-2.50476 - 0.852161i) q^{7} +(-2.82531 - 0.132842i) q^{8} +(-1.72112 + 2.45718i) q^{9} +(3.47014 - 1.93167i) q^{10} +(-3.24154 - 1.87151i) q^{11} +(1.50228 + 3.12140i) q^{12} +(-0.529793 - 0.305876i) q^{13} +(3.52296 + 1.26046i) q^{14} +(-4.10216 - 2.61383i) q^{15} +(3.99215 + 0.250418i) q^{16} +(3.82616 - 2.20903i) q^{17} +(2.48815 - 3.43644i) q^{18} +(0.594752 - 1.03014i) q^{19} +(-4.94970 + 2.65460i) q^{20} +(-0.693661 - 4.52977i) q^{21} +(4.54222 + 2.71818i) q^{22} +(-6.22464 + 3.59380i) q^{23} +(-2.05515 - 4.44706i) q^{24} +(1.44331 - 2.49988i) q^{25} +(0.742374 + 0.444255i) q^{26} +(-5.15154 - 0.679462i) q^{27} +(-4.95369 - 1.86037i) q^{28} +(4.31175 + 7.46818i) q^{29} +(5.74274 + 3.78691i) q^{30} -4.01196 q^{31} +(-5.63952 - 0.442519i) q^{32} +(0.283303 - 6.47689i) q^{33} +(-5.45927 + 3.03892i) q^{34} +(7.28832 - 1.44456i) q^{35} +(-3.59446 + 4.80415i) q^{36} +(-4.72127 + 8.17748i) q^{37} +(-0.863818 + 1.44349i) q^{38} +(0.0463026 - 1.05857i) q^{39} +(7.05787 - 3.64409i) q^{40} +(-3.44593 - 1.98951i) q^{41} +(0.880541 + 6.42064i) q^{42} +(-1.57801 + 0.911063i) q^{43} +(-6.36269 - 3.94421i) q^{44} +(0.735615 - 8.39276i) q^{45} +(8.88149 - 4.94392i) q^{46} -2.42258 q^{47} +(2.80758 + 6.33384i) q^{48} +(5.54764 + 4.26892i) q^{49} +(-2.09626 + 3.50297i) q^{50} +(6.45358 + 4.11210i) q^{51} +(-1.03991 - 0.644636i) q^{52} +(0.171887 + 0.297717i) q^{53} +(7.26943 + 1.07488i) q^{54} +10.5115 q^{55} +(6.96351 + 2.74035i) q^{56} +(2.05831 + 0.0900318i) q^{57} +(-5.93159 - 10.6558i) q^{58} +13.0246 q^{59} +(-8.03659 - 5.48203i) q^{60} +2.17427i q^{61} +(5.67307 + 0.0888554i) q^{62} +(6.40491 - 4.68798i) q^{63} +(7.96471 + 0.750641i) q^{64} +1.71799 q^{65} +(-0.544050 + 9.15231i) q^{66} +14.7149i q^{67} +(7.78693 - 4.17625i) q^{68} +(-10.4991 - 6.68983i) q^{69} +(-10.3380 + 1.88124i) q^{70} -5.36830i q^{71} +(5.18911 - 6.71365i) q^{72} +(-1.51244 + 0.873205i) q^{73} +(6.85717 - 11.4587i) q^{74} +(4.99499 + 0.218484i) q^{75} +(1.25344 - 2.02202i) q^{76} +(6.52446 + 7.44999i) q^{77} +(-0.0889187 + 1.49584i) q^{78} -9.86194i q^{79} +(-10.0608 + 4.99657i) q^{80} +(-3.07549 - 8.45821i) q^{81} +(4.82861 + 2.88956i) q^{82} +(2.17733 + 3.77124i) q^{83} +(-1.10292 - 9.09855i) q^{84} +(-6.20366 + 10.7451i) q^{85} +(2.25154 - 1.25333i) q^{86} +(-8.02630 + 12.5966i) q^{87} +(8.90974 + 5.71819i) q^{88} +(0.865286 + 0.499573i) q^{89} +(-1.22607 + 11.8514i) q^{90} +(1.06635 + 1.21762i) q^{91} +(-12.6683 + 6.79419i) q^{92} +(-3.20816 - 6.16402i) q^{93} +(3.42563 + 0.0536546i) q^{94} +3.34050i q^{95} +(-3.82975 - 9.01848i) q^{96} +(-5.76933 + 3.33092i) q^{97} +(-7.75004 - 6.15929i) q^{98} +(10.1777 - 4.74398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41404 0.0221477i −0.999877 0.0156608i
\(3\) 0.799650 + 1.53641i 0.461678 + 0.887048i
\(4\) 1.99902 + 0.0626353i 0.999509 + 0.0313177i
\(5\) −2.43207 + 1.40416i −1.08765 + 0.627958i −0.932951 0.360003i \(-0.882776\pi\)
−0.154703 + 0.987961i \(0.549442\pi\)
\(6\) −1.09671 2.19026i −0.447730 0.894169i
\(7\) −2.50476 0.852161i −0.946710 0.322087i
\(8\) −2.82531 0.132842i −0.998896 0.0469669i
\(9\) −1.72112 + 2.45718i −0.573707 + 0.819061i
\(10\) 3.47014 1.93167i 1.09736 0.610847i
\(11\) −3.24154 1.87151i −0.977362 0.564280i −0.0758895 0.997116i \(-0.524180\pi\)
−0.901473 + 0.432836i \(0.857513\pi\)
\(12\) 1.50228 + 3.12140i 0.433671 + 0.901071i
\(13\) −0.529793 0.305876i −0.146938 0.0848348i 0.424728 0.905321i \(-0.360370\pi\)
−0.571667 + 0.820486i \(0.693703\pi\)
\(14\) 3.52296 + 1.26046i 0.941550 + 0.336873i
\(15\) −4.10216 2.61383i −1.05917 0.674887i
\(16\) 3.99215 + 0.250418i 0.998038 + 0.0626046i
\(17\) 3.82616 2.20903i 0.927980 0.535770i 0.0418081 0.999126i \(-0.486688\pi\)
0.886172 + 0.463356i \(0.153355\pi\)
\(18\) 2.48815 3.43644i 0.586463 0.809976i
\(19\) 0.594752 1.03014i 0.136445 0.236330i −0.789703 0.613489i \(-0.789765\pi\)
0.926149 + 0.377159i \(0.123099\pi\)
\(20\) −4.94970 + 2.65460i −1.10679 + 0.593587i
\(21\) −0.693661 4.52977i −0.151369 0.988477i
\(22\) 4.54222 + 2.71818i 0.968405 + 0.579517i
\(23\) −6.22464 + 3.59380i −1.29793 + 0.749359i −0.980046 0.198771i \(-0.936305\pi\)
−0.317882 + 0.948130i \(0.602972\pi\)
\(24\) −2.05515 4.44706i −0.419507 0.907752i
\(25\) 1.44331 2.49988i 0.288661 0.499976i
\(26\) 0.742374 + 0.444255i 0.145592 + 0.0871256i
\(27\) −5.15154 0.679462i −0.991414 0.130763i
\(28\) −4.95369 1.86037i −0.936159 0.351577i
\(29\) 4.31175 + 7.46818i 0.800673 + 1.38681i 0.919174 + 0.393852i \(0.128858\pi\)
−0.118501 + 0.992954i \(0.537809\pi\)
\(30\) 5.74274 + 3.78691i 1.04848 + 0.691392i
\(31\) −4.01196 −0.720569 −0.360284 0.932843i \(-0.617320\pi\)
−0.360284 + 0.932843i \(0.617320\pi\)
\(32\) −5.63952 0.442519i −0.996936 0.0782270i
\(33\) 0.283303 6.47689i 0.0493167 1.12748i
\(34\) −5.45927 + 3.03892i −0.936257 + 0.521171i
\(35\) 7.28832 1.44456i 1.23195 0.244175i
\(36\) −3.59446 + 4.80415i −0.599076 + 0.800692i
\(37\) −4.72127 + 8.17748i −0.776172 + 1.34437i 0.157962 + 0.987445i \(0.449508\pi\)
−0.934134 + 0.356923i \(0.883826\pi\)
\(38\) −0.863818 + 1.44349i −0.140130 + 0.234165i
\(39\) 0.0463026 1.05857i 0.00741436 0.169508i
\(40\) 7.05787 3.64409i 1.11595 0.576181i
\(41\) −3.44593 1.98951i −0.538163 0.310709i 0.206171 0.978516i \(-0.433900\pi\)
−0.744334 + 0.667807i \(0.767233\pi\)
\(42\) 0.880541 + 6.42064i 0.135870 + 0.990727i
\(43\) −1.57801 + 0.911063i −0.240644 + 0.138936i −0.615473 0.788158i \(-0.711035\pi\)
0.374829 + 0.927094i \(0.377701\pi\)
\(44\) −6.36269 3.94421i −0.959211 0.594612i
\(45\) 0.735615 8.39276i 0.109659 1.25112i
\(46\) 8.88149 4.94392i 1.30950 0.728941i
\(47\) −2.42258 −0.353370 −0.176685 0.984267i \(-0.556537\pi\)
−0.176685 + 0.984267i \(0.556537\pi\)
\(48\) 2.80758 + 6.33384i 0.405239 + 0.914211i
\(49\) 5.54764 + 4.26892i 0.792520 + 0.609845i
\(50\) −2.09626 + 3.50297i −0.296456 + 0.495394i
\(51\) 6.45358 + 4.11210i 0.903681 + 0.575809i
\(52\) −1.03991 0.644636i −0.144209 0.0893949i
\(53\) 0.171887 + 0.297717i 0.0236105 + 0.0408946i 0.877589 0.479413i \(-0.159151\pi\)
−0.853979 + 0.520308i \(0.825817\pi\)
\(54\) 7.26943 + 1.07488i 0.989244 + 0.146273i
\(55\) 10.5115 1.41738
\(56\) 6.96351 + 2.74035i 0.930538 + 0.366195i
\(57\) 2.05831 + 0.0900318i 0.272630 + 0.0119250i
\(58\) −5.93159 10.6558i −0.778856 1.39917i
\(59\) 13.0246 1.69566 0.847830 0.530268i \(-0.177909\pi\)
0.847830 + 0.530268i \(0.177909\pi\)
\(60\) −8.03659 5.48203i −1.03752 0.707727i
\(61\) 2.17427i 0.278387i 0.990265 + 0.139193i \(0.0444510\pi\)
−0.990265 + 0.139193i \(0.955549\pi\)
\(62\) 5.67307 + 0.0888554i 0.720480 + 0.0112847i
\(63\) 6.40491 4.68798i 0.806942 0.590630i
\(64\) 7.96471 + 0.750641i 0.995588 + 0.0938301i
\(65\) 1.71799 0.213091
\(66\) −0.544050 + 9.15231i −0.0669679 + 1.12657i
\(67\) 14.7149i 1.79771i 0.438243 + 0.898856i \(0.355601\pi\)
−0.438243 + 0.898856i \(0.644399\pi\)
\(68\) 7.78693 4.17625i 0.944304 0.506445i
\(69\) −10.4991 6.68983i −1.26394 0.805361i
\(70\) −10.3380 + 1.88124i −1.23562 + 0.224852i
\(71\) 5.36830i 0.637100i −0.947906 0.318550i \(-0.896804\pi\)
0.947906 0.318550i \(-0.103196\pi\)
\(72\) 5.18911 6.71365i 0.611542 0.791212i
\(73\) −1.51244 + 0.873205i −0.177017 + 0.102201i −0.585890 0.810390i \(-0.699255\pi\)
0.408873 + 0.912591i \(0.365922\pi\)
\(74\) 6.85717 11.4587i 0.797130 1.33205i
\(75\) 4.99499 + 0.218484i 0.576771 + 0.0252283i
\(76\) 1.25344 2.02202i 0.143780 0.231941i
\(77\) 6.52446 + 7.44999i 0.743532 + 0.849005i
\(78\) −0.0889187 + 1.49584i −0.0100681 + 0.169371i
\(79\) 9.86194i 1.10955i −0.831999 0.554777i \(-0.812803\pi\)
0.831999 0.554777i \(-0.187197\pi\)
\(80\) −10.0608 + 4.99657i −1.12483 + 0.558634i
\(81\) −3.07549 8.45821i −0.341721 0.939801i
\(82\) 4.82861 + 2.88956i 0.533231 + 0.319099i
\(83\) 2.17733 + 3.77124i 0.238993 + 0.413947i 0.960425 0.278537i \(-0.0898495\pi\)
−0.721433 + 0.692484i \(0.756516\pi\)
\(84\) −1.10292 9.09855i −0.120338 0.992733i
\(85\) −6.20366 + 10.7451i −0.672881 + 1.16546i
\(86\) 2.25154 1.25333i 0.242790 0.135150i
\(87\) −8.02630 + 12.5966i −0.860510 + 1.35049i
\(88\) 8.90974 + 5.71819i 0.949781 + 0.609561i
\(89\) 0.865286 + 0.499573i 0.0917201 + 0.0529546i 0.545159 0.838333i \(-0.316469\pi\)
−0.453438 + 0.891288i \(0.649803\pi\)
\(90\) −1.22607 + 11.8514i −0.129239 + 1.24925i
\(91\) 1.06635 + 1.21762i 0.111784 + 0.127641i
\(92\) −12.6683 + 6.79419i −1.32076 + 0.708343i
\(93\) −3.20816 6.16402i −0.332671 0.639179i
\(94\) 3.42563 + 0.0536546i 0.353327 + 0.00553405i
\(95\) 3.34050i 0.342728i
\(96\) −3.82975 9.01848i −0.390872 0.920445i
\(97\) −5.76933 + 3.33092i −0.585787 + 0.338204i −0.763430 0.645891i \(-0.776486\pi\)
0.177643 + 0.984095i \(0.443153\pi\)
\(98\) −7.75004 6.15929i −0.782873 0.622182i
\(99\) 10.1777 4.74398i 1.02290 0.476788i
\(100\) 3.04178 4.90691i 0.304178 0.490691i
\(101\) 6.16610 + 3.56000i 0.613550 + 0.354233i 0.774354 0.632753i \(-0.218075\pi\)
−0.160803 + 0.986986i \(0.551408\pi\)
\(102\) −9.03454 5.95761i −0.894553 0.589891i
\(103\) −5.36564 9.29356i −0.528692 0.915721i −0.999440 0.0334538i \(-0.989349\pi\)
0.470748 0.882268i \(-0.343984\pi\)
\(104\) 1.45619 + 0.934573i 0.142792 + 0.0916424i
\(105\) 8.04754 + 10.0427i 0.785359 + 0.980068i
\(106\) −0.236461 0.424790i −0.0229671 0.0412593i
\(107\) −12.5172 7.22680i −1.21008 0.698641i −0.247305 0.968938i \(-0.579545\pi\)
−0.962777 + 0.270296i \(0.912878\pi\)
\(108\) −10.2555 1.68093i −0.986832 0.161747i
\(109\) 0.384805 + 0.666502i 0.0368577 + 0.0638394i 0.883866 0.467741i \(-0.154932\pi\)
−0.847008 + 0.531580i \(0.821599\pi\)
\(110\) −14.8637 0.232806i −1.41720 0.0221972i
\(111\) −16.3393 0.714692i −1.55086 0.0678355i
\(112\) −9.78599 4.02920i −0.924689 0.380723i
\(113\) 3.50852 6.07693i 0.330054 0.571670i −0.652468 0.757816i \(-0.726266\pi\)
0.982522 + 0.186146i \(0.0595998\pi\)
\(114\) −2.90854 0.172895i −0.272410 0.0161931i
\(115\) 10.0925 17.4807i 0.941131 1.63009i
\(116\) 8.15151 + 15.1991i 0.756848 + 1.41120i
\(117\) 1.66343 0.775349i 0.153784 0.0716810i
\(118\) −18.4173 0.288464i −1.69545 0.0265553i
\(119\) −11.4661 + 2.27260i −1.05109 + 0.208329i
\(120\) 11.2426 + 7.92980i 1.02631 + 0.723888i
\(121\) 1.50507 + 2.60686i 0.136825 + 0.236987i
\(122\) 0.0481550 3.07450i 0.00435975 0.278353i
\(123\) 0.301166 6.88527i 0.0271552 0.620824i
\(124\) −8.01998 0.251290i −0.720215 0.0225665i
\(125\) 5.93505i 0.530847i
\(126\) −9.16062 + 6.48714i −0.816093 + 0.577920i
\(127\) 17.0935i 1.51680i 0.651789 + 0.758401i \(0.274019\pi\)
−0.651789 + 0.758401i \(0.725981\pi\)
\(128\) −11.2458 1.23784i −0.993997 0.109410i
\(129\) −2.66162 1.69594i −0.234343 0.149319i
\(130\) −2.42931 0.0380495i −0.213064 0.00333716i
\(131\) 7.88249 + 13.6529i 0.688696 + 1.19286i 0.972260 + 0.233904i \(0.0751500\pi\)
−0.283563 + 0.958954i \(0.591517\pi\)
\(132\) 0.972011 12.9297i 0.0846027 1.12539i
\(133\) −2.36756 + 2.07343i −0.205293 + 0.179789i
\(134\) 0.325901 20.8075i 0.0281535 1.79749i
\(135\) 13.4830 5.58106i 1.16043 0.480341i
\(136\) −11.1035 + 5.73292i −0.952120 + 0.491594i
\(137\) 1.50631 2.60900i 0.128693 0.222902i −0.794478 0.607293i \(-0.792255\pi\)
0.923170 + 0.384391i \(0.125589\pi\)
\(138\) 14.6980 + 9.69222i 1.25117 + 0.825057i
\(139\) −1.85082 + 3.20571i −0.156984 + 0.271905i −0.933780 0.357848i \(-0.883510\pi\)
0.776796 + 0.629753i \(0.216844\pi\)
\(140\) 14.6600 2.43119i 1.23899 0.205473i
\(141\) −1.93722 3.72209i −0.163143 0.313456i
\(142\) −0.118895 + 7.59099i −0.00997746 + 0.637022i
\(143\) 1.14490 + 1.98302i 0.0957412 + 0.165829i
\(144\) −7.48630 + 9.37845i −0.623858 + 0.781538i
\(145\) −20.9730 12.1088i −1.74171 1.00558i
\(146\) 2.15798 1.20125i 0.178596 0.0994162i
\(147\) −2.12264 + 11.9371i −0.175073 + 0.984556i
\(148\) −9.95010 + 16.0512i −0.817893 + 1.31940i
\(149\) 5.65016 + 9.78637i 0.462880 + 0.801731i 0.999103 0.0423452i \(-0.0134829\pi\)
−0.536224 + 0.844076i \(0.680150\pi\)
\(150\) −7.05827 0.419572i −0.576305 0.0342579i
\(151\) 4.22994 + 2.44216i 0.344228 + 0.198740i 0.662140 0.749380i \(-0.269648\pi\)
−0.317912 + 0.948120i \(0.602982\pi\)
\(152\) −1.81720 + 2.83145i −0.147395 + 0.229661i
\(153\) −1.15728 + 13.2036i −0.0935605 + 1.06745i
\(154\) −9.06085 10.6791i −0.730144 0.860545i
\(155\) 9.75736 5.63341i 0.783730 0.452487i
\(156\) 0.158864 2.11321i 0.0127193 0.169192i
\(157\) 11.6574i 0.930366i −0.885215 0.465183i \(-0.845989\pi\)
0.885215 0.465183i \(-0.154011\pi\)
\(158\) −0.218419 + 13.9452i −0.0173765 + 1.10942i
\(159\) −0.319966 + 0.502158i −0.0253750 + 0.0398237i
\(160\) 14.3371 6.84253i 1.13344 0.540949i
\(161\) 18.6537 3.69721i 1.47012 0.291381i
\(162\) 4.16154 + 12.0284i 0.326961 + 0.945038i
\(163\) 8.82016 + 5.09232i 0.690848 + 0.398861i 0.803930 0.594724i \(-0.202739\pi\)
−0.113081 + 0.993586i \(0.536072\pi\)
\(164\) −6.76386 4.19290i −0.528168 0.327410i
\(165\) 8.40556 + 16.1501i 0.654372 + 1.25728i
\(166\) −2.99530 5.38090i −0.232480 0.417639i
\(167\) 7.03763 12.1895i 0.544588 0.943254i −0.454045 0.890979i \(-0.650019\pi\)
0.998633 0.0522750i \(-0.0166472\pi\)
\(168\) 1.35806 + 12.8901i 0.104776 + 0.994496i
\(169\) −6.31288 10.9342i −0.485606 0.841094i
\(170\) 9.01020 15.0565i 0.691051 1.15478i
\(171\) 1.50760 + 3.23441i 0.115289 + 0.247342i
\(172\) −3.21153 + 1.72239i −0.244877 + 0.131331i
\(173\) 15.9908i 1.21576i −0.794030 0.607878i \(-0.792021\pi\)
0.794030 0.607878i \(-0.207979\pi\)
\(174\) 11.6285 17.6343i 0.881554 1.33685i
\(175\) −5.74544 + 5.03167i −0.434314 + 0.380359i
\(176\) −12.4721 8.28308i −0.940119 0.624361i
\(177\) 10.4151 + 20.0112i 0.782849 + 1.50413i
\(178\) −1.21248 0.725580i −0.0908795 0.0543845i
\(179\) −1.34673 + 0.777533i −0.100659 + 0.0581156i −0.549484 0.835504i \(-0.685176\pi\)
0.448825 + 0.893619i \(0.351843\pi\)
\(180\) 1.99619 16.7312i 0.148787 1.24707i
\(181\) 11.7809i 0.875665i −0.899056 0.437833i \(-0.855746\pi\)
0.899056 0.437833i \(-0.144254\pi\)
\(182\) −1.48089 1.74537i −0.109771 0.129376i
\(183\) −3.34057 + 1.73865i −0.246942 + 0.128525i
\(184\) 18.0639 9.32669i 1.33169 0.687572i
\(185\) 26.5176i 1.94961i
\(186\) 4.39995 + 8.78722i 0.322620 + 0.644310i
\(187\) −16.5369 −1.20930
\(188\) −4.84279 0.151739i −0.353197 0.0110667i
\(189\) 12.3244 + 6.09183i 0.896465 + 0.443115i
\(190\) 0.0739842 4.72360i 0.00536738 0.342686i
\(191\) 14.4891i 1.04840i 0.851596 + 0.524199i \(0.175635\pi\)
−0.851596 + 0.524199i \(0.824365\pi\)
\(192\) 5.21568 + 12.8373i 0.376410 + 0.926453i
\(193\) −9.21423 −0.663254 −0.331627 0.943410i \(-0.607598\pi\)
−0.331627 + 0.943410i \(0.607598\pi\)
\(194\) 8.23184 4.58228i 0.591011 0.328989i
\(195\) 1.37379 + 2.63954i 0.0983793 + 0.189021i
\(196\) 10.8225 + 8.88113i 0.773033 + 0.634366i
\(197\) −9.54933 −0.680361 −0.340181 0.940360i \(-0.610488\pi\)
−0.340181 + 0.940360i \(0.610488\pi\)
\(198\) −14.4968 + 6.48276i −1.03024 + 0.460710i
\(199\) −8.38058 14.5156i −0.594084 1.02898i −0.993675 0.112290i \(-0.964181\pi\)
0.399592 0.916693i \(-0.369152\pi\)
\(200\) −4.40987 + 6.87120i −0.311825 + 0.485867i
\(201\) −22.6082 + 11.7668i −1.59466 + 0.829965i
\(202\) −8.64027 5.17055i −0.607928 0.363799i
\(203\) −4.43582 22.3803i −0.311333 1.57079i
\(204\) 12.6433 + 8.62439i 0.885205 + 0.603828i
\(205\) 11.1743 0.780447
\(206\) 7.38140 + 13.2603i 0.514286 + 0.923889i
\(207\) 1.88274 21.4804i 0.130859 1.49299i
\(208\) −2.03842 1.35377i −0.141339 0.0938674i
\(209\) −3.85583 + 2.22616i −0.266713 + 0.153987i
\(210\) −11.1571 14.3790i −0.769914 0.992247i
\(211\) −7.48353 4.32062i −0.515187 0.297443i 0.219776 0.975550i \(-0.429467\pi\)
−0.734963 + 0.678107i \(0.762801\pi\)
\(212\) 0.324958 + 0.605908i 0.0223182 + 0.0416139i
\(213\) 8.24791 4.29276i 0.565138 0.294135i
\(214\) 17.5397 + 10.4962i 1.19899 + 0.717506i
\(215\) 2.55855 4.43153i 0.174491 0.302228i
\(216\) 14.4644 + 2.60403i 0.984178 + 0.177182i
\(217\) 10.0490 + 3.41883i 0.682170 + 0.232086i
\(218\) −0.529369 0.950984i −0.0358534 0.0644087i
\(219\) −2.55102 1.62546i −0.172382 0.109839i
\(220\) 21.0128 + 0.658394i 1.41668 + 0.0443889i
\(221\) −2.70276 −0.181808
\(222\) 23.0886 + 1.37248i 1.54961 + 0.0921148i
\(223\) 9.83962 + 17.0427i 0.658909 + 1.14126i 0.980898 + 0.194521i \(0.0623153\pi\)
−0.321989 + 0.946743i \(0.604351\pi\)
\(224\) 13.7485 + 5.91418i 0.918613 + 0.395158i
\(225\) 3.65856 + 7.84906i 0.243904 + 0.523271i
\(226\) −5.09578 + 8.51532i −0.338966 + 0.566431i
\(227\) −5.98741 + 10.3705i −0.397398 + 0.688314i −0.993404 0.114666i \(-0.963420\pi\)
0.596006 + 0.802980i \(0.296754\pi\)
\(228\) 4.10897 + 0.308898i 0.272123 + 0.0204573i
\(229\) 2.37393 1.37059i 0.156874 0.0905710i −0.419508 0.907752i \(-0.637797\pi\)
0.576382 + 0.817181i \(0.304464\pi\)
\(230\) −14.6584 + 24.4949i −0.966544 + 1.61515i
\(231\) −6.22896 + 15.9816i −0.409836 + 1.05152i
\(232\) −11.1899 21.6727i −0.734655 1.42288i
\(233\) −8.10740 + 14.0424i −0.531133 + 0.919950i 0.468206 + 0.883619i \(0.344900\pi\)
−0.999340 + 0.0363310i \(0.988433\pi\)
\(234\) −2.36933 + 1.05953i −0.154888 + 0.0692639i
\(235\) 5.89189 3.40169i 0.384345 0.221902i
\(236\) 26.0364 + 0.815801i 1.69483 + 0.0531041i
\(237\) 15.1520 7.88610i 0.984228 0.512257i
\(238\) 16.2638 2.95960i 1.05423 0.191842i
\(239\) 3.45217 + 1.99311i 0.223302 + 0.128924i 0.607478 0.794336i \(-0.292181\pi\)
−0.384176 + 0.923260i \(0.625514\pi\)
\(240\) −15.7219 11.4621i −1.01485 0.739872i
\(241\) 9.73779 + 5.62211i 0.627266 + 0.362152i 0.779692 0.626163i \(-0.215375\pi\)
−0.152426 + 0.988315i \(0.548709\pi\)
\(242\) −2.07050 3.71954i −0.133096 0.239101i
\(243\) 10.5360 11.4888i 0.675883 0.737009i
\(244\) −0.136186 + 4.34641i −0.00871842 + 0.278250i
\(245\) −19.4865 2.59255i −1.24495 0.165632i
\(246\) −0.578353 + 9.72937i −0.0368744 + 0.620322i
\(247\) −0.630191 + 0.363841i −0.0400981 + 0.0231506i
\(248\) 11.3350 + 0.532958i 0.719774 + 0.0338429i
\(249\) −4.05308 + 6.36094i −0.256853 + 0.403108i
\(250\) −0.131447 + 8.39240i −0.00831346 + 0.530782i
\(251\) −10.3057 −0.650492 −0.325246 0.945629i \(-0.605447\pi\)
−0.325246 + 0.945629i \(0.605447\pi\)
\(252\) 13.0972 8.97019i 0.825044 0.565069i
\(253\) 26.9033 1.69139
\(254\) 0.378580 24.1709i 0.0237543 1.51662i
\(255\) −21.4696 0.939091i −1.34448 0.0588082i
\(256\) 15.8746 + 1.99942i 0.992161 + 0.124964i
\(257\) −20.9853 + 12.1158i −1.30902 + 0.755766i −0.981933 0.189227i \(-0.939402\pi\)
−0.327091 + 0.944993i \(0.606068\pi\)
\(258\) 3.72608 + 2.45707i 0.231975 + 0.152971i
\(259\) 18.7942 16.4593i 1.16781 1.02273i
\(260\) 3.43430 + 0.107607i 0.212986 + 0.00667350i
\(261\) −25.7717 2.25886i −1.59523 0.139820i
\(262\) −10.8438 19.4803i −0.669931 1.20350i
\(263\) 6.38149 + 3.68435i 0.393499 + 0.227187i 0.683675 0.729786i \(-0.260380\pi\)
−0.290176 + 0.956973i \(0.593714\pi\)
\(264\) −1.66082 + 18.2616i −0.102217 + 1.12392i
\(265\) −0.836082 0.482712i −0.0513601 0.0296528i
\(266\) 3.39374 2.87948i 0.208084 0.176552i
\(267\) −0.0756239 + 1.72892i −0.00462811 + 0.105808i
\(268\) −0.921673 + 29.4154i −0.0563002 + 1.79683i
\(269\) −26.6977 + 15.4139i −1.62778 + 0.939802i −0.643032 + 0.765839i \(0.722324\pi\)
−0.984752 + 0.173963i \(0.944343\pi\)
\(270\) −19.1891 + 7.59323i −1.16781 + 0.462109i
\(271\) −9.52600 + 16.4995i −0.578664 + 1.00227i 0.416969 + 0.908920i \(0.363092\pi\)
−0.995633 + 0.0933541i \(0.970241\pi\)
\(272\) 15.8278 7.86067i 0.959702 0.476623i
\(273\) −1.01805 + 2.61202i −0.0616154 + 0.158086i
\(274\) −2.18776 + 3.65587i −0.132168 + 0.220859i
\(275\) −9.35708 + 5.40232i −0.564253 + 0.325772i
\(276\) −20.5689 14.0307i −1.23810 0.844550i
\(277\) 0.125651 0.217634i 0.00754964 0.0130764i −0.862226 0.506524i \(-0.830930\pi\)
0.869776 + 0.493448i \(0.164264\pi\)
\(278\) 2.68813 4.49201i 0.161223 0.269413i
\(279\) 6.90506 9.85811i 0.413395 0.590190i
\(280\) −20.7836 + 3.11312i −1.24206 + 0.186045i
\(281\) −5.87455 10.1750i −0.350447 0.606991i 0.635881 0.771787i \(-0.280637\pi\)
−0.986328 + 0.164796i \(0.947304\pi\)
\(282\) 2.65687 + 5.30608i 0.158214 + 0.315973i
\(283\) −8.70892 −0.517692 −0.258846 0.965919i \(-0.583342\pi\)
−0.258846 + 0.965919i \(0.583342\pi\)
\(284\) 0.336245 10.7313i 0.0199525 0.636787i
\(285\) −5.13238 + 2.67123i −0.304016 + 0.158230i
\(286\) −1.57501 2.82943i −0.0931325 0.167308i
\(287\) 6.93584 + 7.91972i 0.409409 + 0.467486i
\(288\) 10.7936 13.0957i 0.636021 0.771672i
\(289\) 1.25967 2.18181i 0.0740983 0.128342i
\(290\) 29.3884 + 17.5868i 1.72575 + 1.03273i
\(291\) −9.73111 6.20049i −0.570448 0.363479i
\(292\) −3.07808 + 1.65082i −0.180131 + 0.0966070i
\(293\) 10.0622 + 5.80944i 0.587842 + 0.339391i 0.764244 0.644927i \(-0.223112\pi\)
−0.176402 + 0.984318i \(0.556446\pi\)
\(294\) 3.26588 16.8325i 0.190470 0.981693i
\(295\) −31.6767 + 18.2886i −1.84429 + 1.06480i
\(296\) 14.4253 22.4767i 0.838456 1.30643i
\(297\) 15.4273 + 11.8436i 0.895184 + 0.687238i
\(298\) −7.77281 13.9635i −0.450267 0.808882i
\(299\) 4.39703 0.254287
\(300\) 9.97139 + 0.749615i 0.575698 + 0.0432791i
\(301\) 4.72890 0.937277i 0.272569 0.0540237i
\(302\) −5.92722 3.54699i −0.341073 0.204106i
\(303\) −0.538903 + 12.3204i −0.0309591 + 0.707790i
\(304\) 2.63231 3.96354i 0.150973 0.227325i
\(305\) −3.05301 5.28797i −0.174815 0.302789i
\(306\) 1.92887 18.6448i 0.110266 1.06585i
\(307\) 23.8074 1.35876 0.679380 0.733787i \(-0.262249\pi\)
0.679380 + 0.733787i \(0.262249\pi\)
\(308\) 12.5759 + 15.3013i 0.716578 + 0.871875i
\(309\) 9.98809 15.6754i 0.568203 0.891743i
\(310\) −13.9221 + 7.74977i −0.790720 + 0.440157i
\(311\) −23.9640 −1.35887 −0.679436 0.733734i \(-0.737776\pi\)
−0.679436 + 0.733734i \(0.737776\pi\)
\(312\) −0.271443 + 2.98464i −0.0153674 + 0.168972i
\(313\) 10.3095i 0.582728i 0.956612 + 0.291364i \(0.0941090\pi\)
−0.956612 + 0.291364i \(0.905891\pi\)
\(314\) −0.258185 + 16.4841i −0.0145702 + 0.930252i
\(315\) −8.99452 + 20.3950i −0.506784 + 1.14913i
\(316\) 0.617706 19.7142i 0.0347487 1.10901i
\(317\) −12.7739 −0.717451 −0.358726 0.933443i \(-0.616789\pi\)
−0.358726 + 0.933443i \(0.616789\pi\)
\(318\) 0.463567 0.702985i 0.0259955 0.0394215i
\(319\) 32.2779i 1.80722i
\(320\) −20.4247 + 9.35808i −1.14178 + 0.523132i
\(321\) 1.09397 25.0105i 0.0610596 1.39595i
\(322\) −26.4590 + 4.81486i −1.47450 + 0.268322i
\(323\) 5.25531i 0.292413i
\(324\) −5.61818 17.1008i −0.312121 0.950042i
\(325\) −1.52931 + 0.882946i −0.0848307 + 0.0489771i
\(326\) −12.3593 7.39609i −0.684517 0.409632i
\(327\) −0.716312 + 1.12419i −0.0396122 + 0.0621677i
\(328\) 9.47150 + 6.07873i 0.522976 + 0.335642i
\(329\) 6.06799 + 2.06443i 0.334539 + 0.113816i
\(330\) −11.5281 23.0230i −0.634601 1.26737i
\(331\) 18.9845i 1.04348i −0.853104 0.521741i \(-0.825283\pi\)
0.853104 0.521741i \(-0.174717\pi\)
\(332\) 4.11630 + 7.67515i 0.225911 + 0.421229i
\(333\) −11.9677 25.6754i −0.655825 1.40700i
\(334\) −10.2215 + 17.0806i −0.559293 + 0.934610i
\(335\) −20.6620 35.7877i −1.12889 1.95529i
\(336\) −1.63486 18.2573i −0.0891891 0.996015i
\(337\) 9.58901 16.6086i 0.522347 0.904731i −0.477315 0.878732i \(-0.658390\pi\)
0.999662 0.0259987i \(-0.00827657\pi\)
\(338\) 8.68450 + 15.6013i 0.472374 + 0.848596i
\(339\) 12.1423 + 0.531109i 0.659477 + 0.0288459i
\(340\) −13.0743 + 21.0910i −0.709051 + 1.14382i
\(341\) 13.0049 + 7.50840i 0.704257 + 0.406603i
\(342\) −2.06018 4.60698i −0.111402 0.249117i
\(343\) −10.2577 15.4201i −0.553864 0.832607i
\(344\) 4.57938 2.36440i 0.246904 0.127480i
\(345\) 34.9281 + 1.52777i 1.88046 + 0.0822526i
\(346\) −0.354158 + 22.6116i −0.0190397 + 1.21561i
\(347\) 27.5615i 1.47958i 0.672839 + 0.739789i \(0.265074\pi\)
−0.672839 + 0.739789i \(0.734926\pi\)
\(348\) −16.8337 + 24.6780i −0.902382 + 1.32288i
\(349\) 15.9615 9.21538i 0.854400 0.493288i −0.00773296 0.999970i \(-0.502462\pi\)
0.862133 + 0.506682i \(0.169128\pi\)
\(350\) 8.23572 6.98774i 0.440218 0.373510i
\(351\) 2.52142 + 1.93571i 0.134583 + 0.103320i
\(352\) 17.4526 + 11.9888i 0.930225 + 0.639007i
\(353\) 16.3377 + 9.43255i 0.869566 + 0.502044i 0.867204 0.497953i \(-0.165915\pi\)
0.00236195 + 0.999997i \(0.499248\pi\)
\(354\) −14.2842 28.5272i −0.759197 1.51621i
\(355\) 7.53793 + 13.0561i 0.400072 + 0.692944i
\(356\) 1.69843 + 1.05285i 0.0900167 + 0.0558011i
\(357\) −12.6605 15.7993i −0.670064 0.836188i
\(358\) 1.92155 1.06964i 0.101557 0.0565320i
\(359\) 10.1985 + 5.88809i 0.538254 + 0.310761i 0.744371 0.667766i \(-0.232749\pi\)
−0.206117 + 0.978527i \(0.566083\pi\)
\(360\) −3.19325 + 23.6144i −0.168299 + 1.24459i
\(361\) 8.79254 + 15.2291i 0.462765 + 0.801533i
\(362\) −0.260919 + 16.6586i −0.0137136 + 0.875558i
\(363\) −2.80168 + 4.39698i −0.147050 + 0.230782i
\(364\) 2.05539 + 2.50083i 0.107731 + 0.131079i
\(365\) 2.45223 4.24739i 0.128356 0.222319i
\(366\) 4.76221 2.38454i 0.248925 0.124642i
\(367\) 11.3992 19.7440i 0.595034 1.03063i −0.398509 0.917165i \(-0.630472\pi\)
0.993542 0.113464i \(-0.0361946\pi\)
\(368\) −25.7497 + 12.7882i −1.34230 + 0.666633i
\(369\) 10.8194 5.04309i 0.563237 0.262533i
\(370\) −0.587302 + 37.4969i −0.0305324 + 1.94937i
\(371\) −0.176833 0.892185i −0.00918069 0.0463199i
\(372\) −6.02709 12.5229i −0.312490 0.649284i
\(373\) −2.49678 4.32454i −0.129278 0.223916i 0.794119 0.607762i \(-0.207933\pi\)
−0.923397 + 0.383846i \(0.874599\pi\)
\(374\) 23.3838 + 0.366253i 1.20915 + 0.0189385i
\(375\) 9.11867 4.74596i 0.470886 0.245080i
\(376\) 6.84454 + 0.321822i 0.352980 + 0.0165967i
\(377\) 5.27545i 0.271700i
\(378\) −17.2922 8.88705i −0.889415 0.457100i
\(379\) 32.2808i 1.65815i 0.559135 + 0.829077i \(0.311133\pi\)
−0.559135 + 0.829077i \(0.688867\pi\)
\(380\) −0.209233 + 6.67772i −0.0107334 + 0.342560i
\(381\) −26.2626 + 13.6688i −1.34547 + 0.700274i
\(382\) 0.320900 20.4882i 0.0164187 1.04827i
\(383\) −8.82152 15.2793i −0.450759 0.780737i 0.547675 0.836691i \(-0.315513\pi\)
−0.998433 + 0.0559544i \(0.982180\pi\)
\(384\) −7.09087 18.2680i −0.361854 0.932235i
\(385\) −26.3289 8.95753i −1.34184 0.456518i
\(386\) 13.0293 + 0.204073i 0.663173 + 0.0103871i
\(387\) 0.477292 5.44550i 0.0242621 0.276810i
\(388\) −11.7416 + 6.29722i −0.596091 + 0.319693i
\(389\) −7.75525 + 13.4325i −0.393207 + 0.681054i −0.992871 0.119198i \(-0.961968\pi\)
0.599664 + 0.800252i \(0.295301\pi\)
\(390\) −1.88414 3.76284i −0.0954070 0.190539i
\(391\) −15.8777 + 27.5009i −0.802968 + 1.39078i
\(392\) −15.1067 12.7980i −0.763003 0.646395i
\(393\) −14.6732 + 23.0283i −0.740165 + 1.16162i
\(394\) 13.5031 + 0.211495i 0.680278 + 0.0106550i
\(395\) 13.8477 + 23.9849i 0.696753 + 1.20681i
\(396\) 20.6426 8.84582i 1.03733 0.444519i
\(397\) 29.6794 + 17.1354i 1.48957 + 0.860002i 0.999929 0.0119229i \(-0.00379527\pi\)
0.489639 + 0.871925i \(0.337129\pi\)
\(398\) 11.5290 + 20.7112i 0.577896 + 1.03816i
\(399\) −5.07886 1.97952i −0.254261 0.0991001i
\(400\) 6.38792 9.61848i 0.319396 0.480924i
\(401\) −3.42451 5.93142i −0.171012 0.296201i 0.767762 0.640735i \(-0.221370\pi\)
−0.938774 + 0.344534i \(0.888037\pi\)
\(402\) 32.2294 16.1380i 1.60746 0.804889i
\(403\) 2.12551 + 1.22716i 0.105879 + 0.0611293i
\(404\) 12.1032 + 7.50273i 0.602156 + 0.373275i
\(405\) 19.3565 + 16.2525i 0.961830 + 0.807592i
\(406\) 5.77675 + 31.7449i 0.286695 + 1.57547i
\(407\) 30.6084 17.6718i 1.51720 0.875957i
\(408\) −17.6871 12.4753i −0.875640 0.617617i
\(409\) 34.2017i 1.69116i −0.533846 0.845582i \(-0.679254\pi\)
0.533846 0.845582i \(-0.320746\pi\)
\(410\) −15.8009 0.247485i −0.780352 0.0122224i
\(411\) 5.21302 + 0.228020i 0.257139 + 0.0112474i
\(412\) −10.1439 18.9141i −0.499754 0.931830i
\(413\) −32.6235 11.0991i −1.60530 0.546149i
\(414\) −3.13801 + 30.3325i −0.154225 + 1.49076i
\(415\) −10.5908 6.11461i −0.519883 0.300154i
\(416\) 2.85242 + 1.95944i 0.139852 + 0.0960694i
\(417\) −6.40529 0.280171i −0.313668 0.0137200i
\(418\) 5.50160 3.06249i 0.269092 0.149791i
\(419\) 10.0572 17.4195i 0.491325 0.851000i −0.508625 0.860988i \(-0.669846\pi\)
0.999950 + 0.00998821i \(0.00317940\pi\)
\(420\) 15.4581 + 20.5796i 0.754280 + 1.00418i
\(421\) 3.04994 + 5.28265i 0.148645 + 0.257461i 0.930727 0.365715i \(-0.119175\pi\)
−0.782082 + 0.623176i \(0.785842\pi\)
\(422\) 10.4863 + 6.27527i 0.510466 + 0.305475i
\(423\) 4.16956 5.95273i 0.202731 0.289432i
\(424\) −0.446084 0.863975i −0.0216637 0.0419583i
\(425\) 12.7533i 0.618624i
\(426\) −11.7580 + 5.88746i −0.569675 + 0.285248i
\(427\) 1.85283 5.44602i 0.0896646 0.263552i
\(428\) −24.5694 15.2305i −1.18761 0.736195i
\(429\) −2.13122 + 3.34476i −0.102896 + 0.161486i
\(430\) −3.71604 + 6.20970i −0.179203 + 0.299458i
\(431\) −23.2792 + 13.4402i −1.12132 + 0.647393i −0.941737 0.336350i \(-0.890807\pi\)
−0.179581 + 0.983743i \(0.557474\pi\)
\(432\) −20.3956 4.00256i −0.981283 0.192573i
\(433\) 16.0304i 0.770372i 0.922839 + 0.385186i \(0.125863\pi\)
−0.922839 + 0.385186i \(0.874137\pi\)
\(434\) −14.1340 5.05693i −0.678452 0.242740i
\(435\) 1.83299 41.9059i 0.0878850 2.00923i
\(436\) 0.727487 + 1.35645i 0.0348403 + 0.0649623i
\(437\) 8.54968i 0.408987i
\(438\) 3.57125 + 2.35497i 0.170641 + 0.112525i
\(439\) 19.6894 0.939723 0.469861 0.882740i \(-0.344304\pi\)
0.469861 + 0.882740i \(0.344304\pi\)
\(440\) −29.6983 1.39638i −1.41581 0.0665698i
\(441\) −20.0377 + 6.28425i −0.954175 + 0.299250i
\(442\) 3.82182 + 0.0598599i 0.181785 + 0.00284724i
\(443\) 7.20419i 0.342281i 0.985247 + 0.171141i \(0.0547453\pi\)
−0.985247 + 0.171141i \(0.945255\pi\)
\(444\) −32.6179 2.45210i −1.54798 0.116372i
\(445\) −2.80591 −0.133013
\(446\) −13.5362 24.3170i −0.640955 1.15144i
\(447\) −10.5177 + 16.5066i −0.497472 + 0.780738i
\(448\) −19.3100 8.66739i −0.912312 0.409496i
\(449\) 6.42464 0.303198 0.151599 0.988442i \(-0.451558\pi\)
0.151599 + 0.988442i \(0.451558\pi\)
\(450\) −4.99951 11.1799i −0.235679 0.527026i
\(451\) 7.44675 + 12.8981i 0.350654 + 0.607350i
\(452\) 7.39423 11.9281i 0.347795 0.561053i
\(453\) −0.369687 + 8.45180i −0.0173694 + 0.397100i
\(454\) 8.69612 14.5317i 0.408129 0.682006i
\(455\) −4.30316 1.46401i −0.201735 0.0686336i
\(456\) −5.80340 0.527799i −0.271769 0.0247164i
\(457\) −36.4381 −1.70450 −0.852250 0.523134i \(-0.824763\pi\)
−0.852250 + 0.523134i \(0.824763\pi\)
\(458\) −3.38718 + 1.88549i −0.158273 + 0.0881031i
\(459\) −21.2116 + 8.78019i −0.990071 + 0.409824i
\(460\) 21.2700 34.3122i 0.991720 1.59981i
\(461\) −1.90388 + 1.09920i −0.0886725 + 0.0511951i −0.543681 0.839292i \(-0.682970\pi\)
0.455008 + 0.890487i \(0.349636\pi\)
\(462\) 9.16196 22.4607i 0.426253 1.04497i
\(463\) −2.98183 1.72156i −0.138577 0.0800077i 0.429108 0.903253i \(-0.358828\pi\)
−0.567686 + 0.823245i \(0.692161\pi\)
\(464\) 15.3430 + 30.8939i 0.712282 + 1.43421i
\(465\) 16.4577 + 10.4866i 0.763208 + 0.486302i
\(466\) 11.7752 19.6770i 0.545475 0.911519i
\(467\) 0.234638 0.406404i 0.0108577 0.0188061i −0.860545 0.509374i \(-0.829877\pi\)
0.871403 + 0.490567i \(0.163210\pi\)
\(468\) 3.37379 1.44575i 0.155954 0.0668297i
\(469\) 12.5395 36.8573i 0.579019 1.70191i
\(470\) −8.40671 + 4.67963i −0.387773 + 0.215855i
\(471\) 17.9106 9.32188i 0.825279 0.429529i
\(472\) −36.7985 1.73022i −1.69379 0.0796399i
\(473\) 6.82024 0.313595
\(474\) −21.6002 + 10.8157i −0.992129 + 0.496781i
\(475\) −1.71682 2.97362i −0.0787731 0.136439i
\(476\) −23.0632 + 3.82478i −1.05710 + 0.175309i
\(477\) −1.02738 0.0900489i −0.0470406 0.00412306i
\(478\) −4.83736 2.89480i −0.221256 0.132405i
\(479\) 3.75827 6.50952i 0.171720 0.297427i −0.767301 0.641287i \(-0.778401\pi\)
0.939021 + 0.343859i \(0.111734\pi\)
\(480\) 21.9776 + 16.5560i 1.00313 + 0.755675i
\(481\) 5.00259 2.88825i 0.228098 0.131693i
\(482\) −13.6451 8.16556i −0.621518 0.371931i
\(483\) 20.5969 + 25.7033i 0.937191 + 1.16954i
\(484\) 2.84538 + 5.30543i 0.129336 + 0.241156i
\(485\) 9.35427 16.2021i 0.424756 0.735698i
\(486\) −15.1527 + 16.0123i −0.687342 + 0.726334i
\(487\) 11.0384 6.37304i 0.500199 0.288790i −0.228597 0.973521i \(-0.573414\pi\)
0.728796 + 0.684731i \(0.240080\pi\)
\(488\) 0.288835 6.14298i 0.0130750 0.278079i
\(489\) −0.770861 + 17.6235i −0.0348595 + 0.796961i
\(490\) 27.4972 + 4.09755i 1.24220 + 0.185108i
\(491\) 16.7854 + 9.69106i 0.757515 + 0.437351i 0.828403 0.560133i \(-0.189250\pi\)
−0.0708879 + 0.997484i \(0.522583\pi\)
\(492\) 1.03330 13.7449i 0.0465846 0.619669i
\(493\) 32.9949 + 19.0496i 1.48602 + 0.857952i
\(494\) 0.899174 0.500528i 0.0404557 0.0225198i
\(495\) −18.0916 + 25.8288i −0.813158 + 1.16092i
\(496\) −16.0164 1.00467i −0.719155 0.0451109i
\(497\) −4.57465 + 13.4463i −0.205201 + 0.603149i
\(498\) 5.87209 8.90486i 0.263135 0.399036i
\(499\) −18.2465 + 10.5346i −0.816826 + 0.471594i −0.849321 0.527877i \(-0.822988\pi\)
0.0324950 + 0.999472i \(0.489655\pi\)
\(500\) 0.371744 11.8643i 0.0166249 0.530586i
\(501\) 24.3558 + 1.06534i 1.08814 + 0.0475957i
\(502\) 14.5727 + 0.228248i 0.650412 + 0.0101872i
\(503\) 29.8779 1.33219 0.666095 0.745867i \(-0.267965\pi\)
0.666095 + 0.745867i \(0.267965\pi\)
\(504\) −18.7186 + 12.3941i −0.833792 + 0.552079i
\(505\) −19.9952 −0.889774
\(506\) −38.0423 0.595844i −1.69119 0.0264885i
\(507\) 11.7514 18.4427i 0.521897 0.819071i
\(508\) −1.07066 + 34.1702i −0.0475027 + 1.51606i
\(509\) −29.9207 + 17.2747i −1.32621 + 0.765688i −0.984711 0.174195i \(-0.944268\pi\)
−0.341498 + 0.939882i \(0.610934\pi\)
\(510\) 30.3380 + 1.80341i 1.34339 + 0.0798565i
\(511\) 4.53240 0.898330i 0.200502 0.0397398i
\(512\) −22.4030 3.17884i −0.990083 0.140486i
\(513\) −3.76383 + 4.90270i −0.166177 + 0.216459i
\(514\) 29.9423 16.6675i 1.32070 0.735173i
\(515\) 26.0992 + 15.0684i 1.15007 + 0.663992i
\(516\) −5.21440 3.55692i −0.229551 0.156585i
\(517\) 7.85291 + 4.53388i 0.345371 + 0.199400i
\(518\) −26.9402 + 22.8579i −1.18369 + 1.00432i
\(519\) 24.5684 12.7870i 1.07843 0.561288i
\(520\) −4.85385 0.228222i −0.212855 0.0100082i
\(521\) 6.83068 3.94369i 0.299257 0.172776i −0.342852 0.939389i \(-0.611393\pi\)
0.642109 + 0.766613i \(0.278060\pi\)
\(522\) 36.3922 + 3.76490i 1.59284 + 0.164785i
\(523\) 8.08449 14.0027i 0.353510 0.612297i −0.633352 0.773864i \(-0.718321\pi\)
0.986862 + 0.161567i \(0.0516547\pi\)
\(524\) 14.9021 + 27.7861i 0.651001 + 1.21384i
\(525\) −12.3251 4.80378i −0.537910 0.209654i
\(526\) −8.94208 5.35116i −0.389893 0.233322i
\(527\) −15.3504 + 8.86255i −0.668674 + 0.386059i
\(528\) 2.75292 25.7858i 0.119806 1.12218i
\(529\) 14.3308 24.8217i 0.623078 1.07920i
\(530\) 1.17156 + 0.701091i 0.0508894 + 0.0304535i
\(531\) −22.4169 + 32.0038i −0.972811 + 1.38885i
\(532\) −4.86266 + 3.99653i −0.210823 + 0.173272i
\(533\) 1.21709 + 2.10805i 0.0527178 + 0.0913099i
\(534\) 0.145227 2.44308i 0.00628457 0.105723i
\(535\) 40.5902 1.75487
\(536\) 1.95476 41.5741i 0.0844330 1.79573i
\(537\) −2.27152 1.44737i −0.0980234 0.0624587i
\(538\) 38.0929 21.2046i 1.64230 0.914194i
\(539\) −9.99362 24.2203i −0.430456 1.04324i
\(540\) 27.3023 10.3121i 1.17490 0.443764i
\(541\) 15.1006 26.1550i 0.649224 1.12449i −0.334084 0.942543i \(-0.608427\pi\)
0.983308 0.181946i \(-0.0582397\pi\)
\(542\) 13.8356 23.1200i 0.594289 0.993089i
\(543\) 18.1003 9.42057i 0.776757 0.404275i
\(544\) −22.5552 + 10.7647i −0.967048 + 0.461535i
\(545\) −1.87175 1.08065i −0.0801768 0.0462901i
\(546\) 1.49742 3.67095i 0.0640835 0.157102i
\(547\) −5.67357 + 3.27564i −0.242584 + 0.140056i −0.616364 0.787461i \(-0.711395\pi\)
0.373780 + 0.927518i \(0.378062\pi\)
\(548\) 3.17455 5.12110i 0.135610 0.218762i
\(549\) −5.34258 3.74218i −0.228016 0.159712i
\(550\) 13.3509 7.43185i 0.569286 0.316895i
\(551\) 10.2577 0.436993
\(552\) 28.7744 + 20.2955i 1.22472 + 0.863836i
\(553\) −8.40396 + 24.7018i −0.357373 + 1.05043i
\(554\) −0.182496 + 0.304960i −0.00775350 + 0.0129565i
\(555\) 40.7419 21.2048i 1.72940 0.900093i
\(556\) −3.90061 + 6.29234i −0.165423 + 0.266855i
\(557\) 0.158409 + 0.274372i 0.00671199 + 0.0116255i 0.869362 0.494176i \(-0.164530\pi\)
−0.862650 + 0.505801i \(0.831197\pi\)
\(558\) −9.98237 + 13.7868i −0.422587 + 0.583643i
\(559\) 1.11469 0.0471463
\(560\) 29.4578 3.94177i 1.24482 0.166570i
\(561\) −13.2237 25.4075i −0.558306 1.07270i
\(562\) 8.08150 + 14.5180i 0.340898 + 0.612405i
\(563\) 6.73380 0.283796 0.141898 0.989881i \(-0.454680\pi\)
0.141898 + 0.989881i \(0.454680\pi\)
\(564\) −3.63940 7.56186i −0.153247 0.318412i
\(565\) 19.7060i 0.829039i
\(566\) 12.3148 + 0.192882i 0.517628 + 0.00810744i
\(567\) 0.495610 + 23.8066i 0.0208137 + 0.999783i
\(568\) −0.713138 + 15.1671i −0.0299226 + 0.636397i
\(569\) 3.35568 0.140677 0.0703387 0.997523i \(-0.477592\pi\)
0.0703387 + 0.997523i \(0.477592\pi\)
\(570\) 7.31655 3.66355i 0.306457 0.153449i
\(571\) 24.1300i 1.00981i 0.863175 + 0.504904i \(0.168472\pi\)
−0.863175 + 0.504904i \(0.831528\pi\)
\(572\) 2.16447 + 4.03581i 0.0905009 + 0.168746i
\(573\) −22.2613 + 11.5862i −0.929979 + 0.484022i
\(574\) −9.63215 11.3524i −0.402038 0.473841i
\(575\) 20.7478i 0.865244i
\(576\) −15.5527 + 18.2788i −0.648028 + 0.761616i
\(577\) −32.0115 + 18.4819i −1.33266 + 0.769410i −0.985706 0.168473i \(-0.946116\pi\)
−0.346951 + 0.937883i \(0.612783\pi\)
\(578\) −1.82955 + 3.05727i −0.0760991 + 0.127166i
\(579\) −7.36816 14.1568i −0.306210 0.588338i
\(580\) −41.1669 25.5193i −1.70936 1.05963i
\(581\) −2.23997 11.3015i −0.0929298 0.468864i
\(582\) 13.6229 + 8.98326i 0.564686 + 0.372368i
\(583\) 1.28675i 0.0532917i
\(584\) 4.38909 2.26616i 0.181622 0.0937742i
\(585\) −2.95687 + 4.22142i −0.122251 + 0.174534i
\(586\) −14.0997 8.43763i −0.582455 0.348555i
\(587\) −7.18018 12.4364i −0.296358 0.513307i 0.678942 0.734192i \(-0.262439\pi\)
−0.975300 + 0.220885i \(0.929105\pi\)
\(588\) −4.99089 + 23.7295i −0.205821 + 0.978590i
\(589\) −2.38612 + 4.13288i −0.0983184 + 0.170292i
\(590\) 45.1972 25.1592i 1.86074 1.03579i
\(591\) −7.63612 14.6717i −0.314108 0.603513i
\(592\) −20.8958 + 31.4634i −0.858813 + 1.29314i
\(593\) 29.2573 + 16.8917i 1.20146 + 0.693660i 0.960879 0.276970i \(-0.0893302\pi\)
0.240577 + 0.970630i \(0.422664\pi\)
\(594\) −21.5525 17.0891i −0.884311 0.701173i
\(595\) 24.6952 21.6273i 1.01240 0.886631i
\(596\) 10.6818 + 19.9170i 0.437544 + 0.815834i
\(597\) 15.6004 24.4834i 0.638481 1.00204i
\(598\) −6.21758 0.0973839i −0.254256 0.00398232i
\(599\) 29.3444i 1.19898i 0.800382 + 0.599490i \(0.204630\pi\)
−0.800382 + 0.599490i \(0.795370\pi\)
\(600\) −14.0833 1.28083i −0.574950 0.0522896i
\(601\) −2.28904 + 1.32158i −0.0933717 + 0.0539082i −0.545959 0.837812i \(-0.683834\pi\)
0.452587 + 0.891720i \(0.350501\pi\)
\(602\) −6.70761 + 1.22061i −0.273382 + 0.0497485i
\(603\) −36.1572 25.3261i −1.47244 1.03136i
\(604\) 8.30277 + 5.14686i 0.337835 + 0.209423i
\(605\) −7.32088 4.22671i −0.297636 0.171840i
\(606\) 1.03490 17.4096i 0.0420399 0.707218i
\(607\) 7.14641 + 12.3779i 0.290064 + 0.502405i 0.973825 0.227301i \(-0.0729901\pi\)
−0.683761 + 0.729706i \(0.739657\pi\)
\(608\) −3.80997 + 5.54631i −0.154515 + 0.224933i
\(609\) 30.8382 24.7116i 1.24963 1.00137i
\(610\) 4.19997 + 7.54502i 0.170052 + 0.305489i
\(611\) 1.28347 + 0.741011i 0.0519236 + 0.0299781i
\(612\) −3.14043 + 26.3217i −0.126945 + 1.06399i
\(613\) −8.49136 14.7075i −0.342963 0.594029i 0.642019 0.766689i \(-0.278097\pi\)
−0.984981 + 0.172660i \(0.944764\pi\)
\(614\) −33.6646 0.527278i −1.35859 0.0212792i
\(615\) 8.93553 + 17.1683i 0.360315 + 0.692294i
\(616\) −17.4439 21.9152i −0.702836 0.882990i
\(617\) 6.62896 11.4817i 0.266872 0.462235i −0.701181 0.712984i \(-0.747343\pi\)
0.968052 + 0.250748i \(0.0806767\pi\)
\(618\) −14.4707 + 21.9445i −0.582099 + 0.882736i
\(619\) −20.1710 + 34.9372i −0.810741 + 1.40425i 0.101605 + 0.994825i \(0.467602\pi\)
−0.912346 + 0.409420i \(0.865731\pi\)
\(620\) 19.8580 10.6501i 0.797516 0.427720i
\(621\) 34.5083 14.2842i 1.38477 0.573204i
\(622\) 33.8860 + 0.530746i 1.35871 + 0.0212810i
\(623\) −1.74162 1.98867i −0.0697764 0.0796745i
\(624\) 0.449934 4.21440i 0.0180118 0.168711i
\(625\) 15.5503 + 26.9338i 0.622011 + 1.07735i
\(626\) 0.228331 14.5781i 0.00912595 0.582656i
\(627\) −6.50362 4.14399i −0.259729 0.165495i
\(628\) 0.730168 23.3035i 0.0291369 0.929909i
\(629\) 41.7178i 1.66340i
\(630\) 13.1703 28.6401i 0.524718 1.14105i
\(631\) 10.1900i 0.405658i −0.979214 0.202829i \(-0.934986\pi\)
0.979214 0.202829i \(-0.0650136\pi\)
\(632\) −1.31008 + 27.8630i −0.0521123 + 1.10833i
\(633\) 0.654042 14.9528i 0.0259958 0.594319i
\(634\) 18.0627 + 0.282911i 0.717363 + 0.0112358i
\(635\) −24.0019 41.5725i −0.952487 1.64976i
\(636\) −0.671071 + 0.983783i −0.0266097 + 0.0390095i
\(637\) −1.63334 3.95854i −0.0647154 0.156843i
\(638\) −0.714880 + 45.6423i −0.0283024 + 1.80699i
\(639\) 13.1909 + 9.23948i 0.521823 + 0.365508i
\(640\) 29.0887 12.7803i 1.14983 0.505187i
\(641\) 6.30398 10.9188i 0.248992 0.431267i −0.714254 0.699886i \(-0.753234\pi\)
0.963246 + 0.268619i \(0.0865673\pi\)
\(642\) −2.10084 + 35.3416i −0.0829137 + 1.39482i
\(643\) 20.9389 36.2672i 0.825749 1.43024i −0.0755963 0.997139i \(-0.524086\pi\)
0.901345 0.433101i \(-0.142581\pi\)
\(644\) 37.5207 6.22240i 1.47852 0.245197i
\(645\) 8.85460 + 0.387305i 0.348650 + 0.0152501i
\(646\) −0.116393 + 7.43122i −0.00457941 + 0.292378i
\(647\) −4.79985 8.31358i −0.188702 0.326841i 0.756116 0.654438i \(-0.227095\pi\)
−0.944818 + 0.327597i \(0.893761\pi\)
\(648\) 7.56560 + 24.3056i 0.297205 + 0.954814i
\(649\) −42.2198 24.3756i −1.65727 0.956827i
\(650\) 2.18206 1.21465i 0.0855874 0.0476425i
\(651\) 2.78294 + 18.1733i 0.109072 + 0.712266i
\(652\) 17.3127 + 10.7321i 0.678018 + 0.420302i
\(653\) −2.86038 4.95432i −0.111935 0.193878i 0.804615 0.593797i \(-0.202372\pi\)
−0.916551 + 0.399919i \(0.869038\pi\)
\(654\) 1.03779 1.57378i 0.0405809 0.0615398i
\(655\) −38.3415 22.1365i −1.49813 0.864944i
\(656\) −13.2585 8.80534i −0.517656 0.343791i
\(657\) 0.457459 5.21922i 0.0178472 0.203621i
\(658\) −8.53466 3.05358i −0.332716 0.119041i
\(659\) −29.4052 + 16.9771i −1.14546 + 0.661334i −0.947778 0.318932i \(-0.896676\pi\)
−0.197686 + 0.980265i \(0.563343\pi\)
\(660\) 15.7913 + 32.8108i 0.614676 + 1.27716i
\(661\) 39.1649i 1.52334i 0.647966 + 0.761669i \(0.275620\pi\)
−0.647966 + 0.761669i \(0.724380\pi\)
\(662\) −0.420462 + 26.8448i −0.0163417 + 1.04335i
\(663\) −2.16127 4.15256i −0.0839366 0.161272i
\(664\) −5.65063 10.9441i −0.219287 0.424715i
\(665\) 2.84664 8.36714i 0.110388 0.324464i
\(666\) 16.3541 + 36.5711i 0.633710 + 1.41710i
\(667\) −53.6783 30.9912i −2.07843 1.19998i
\(668\) 14.8318 23.9263i 0.573861 0.925736i
\(669\) −18.3164 + 28.7459i −0.708152 + 1.11138i
\(670\) 28.4243 + 51.0628i 1.09813 + 1.97273i
\(671\) 4.06916 7.04799i 0.157088 0.272085i
\(672\) 1.90741 + 25.8527i 0.0735798 + 0.997289i
\(673\) −4.87986 8.45217i −0.188105 0.325807i 0.756513 0.653978i \(-0.226901\pi\)
−0.944618 + 0.328171i \(0.893568\pi\)
\(674\) −13.9271 + 23.2729i −0.536451 + 0.896439i
\(675\) −9.13382 + 11.8976i −0.351561 + 0.457937i
\(676\) −11.9347 22.2531i −0.459027 0.855890i
\(677\) 28.1225i 1.08084i −0.841397 0.540418i \(-0.818266\pi\)
0.841397 0.540418i \(-0.181734\pi\)
\(678\) −17.1579 1.01993i −0.658944 0.0391703i
\(679\) 17.2893 3.42677i 0.663501 0.131507i
\(680\) 18.9546 29.5339i 0.726877 1.13258i
\(681\) −20.7212 0.906357i −0.794038 0.0347317i
\(682\) −18.2232 10.9052i −0.697803 0.417582i
\(683\) −12.9477 + 7.47537i −0.495431 + 0.286037i −0.726825 0.686823i \(-0.759005\pi\)
0.231394 + 0.972860i \(0.425671\pi\)
\(684\) 2.81114 + 6.56008i 0.107487 + 0.250831i
\(685\) 8.46037i 0.323254i
\(686\) 14.1633 + 22.0318i 0.540757 + 0.841179i
\(687\) 4.00410 + 2.55134i 0.152766 + 0.0973397i
\(688\) −6.52779 + 3.24194i −0.248870 + 0.123598i
\(689\) 0.210304i 0.00801196i
\(690\) −49.3559 2.93391i −1.87895 0.111692i
\(691\) −13.8627 −0.527361 −0.263680 0.964610i \(-0.584936\pi\)
−0.263680 + 0.964610i \(0.584936\pi\)
\(692\) 1.00159 31.9659i 0.0380747 1.21516i
\(693\) −29.5354 + 3.20947i −1.12196 + 0.121918i
\(694\) 0.610422 38.9730i 0.0231713 1.47940i
\(695\) 10.3953i 0.394318i
\(696\) 24.3501 34.5229i 0.922988 1.30859i
\(697\) −17.5796 −0.665873
\(698\) −22.7743 + 12.6774i −0.862021 + 0.479847i
\(699\) −28.0580 1.22727i −1.06125 0.0464198i
\(700\) −11.8004 + 9.69854i −0.446013 + 0.366570i
\(701\) −23.4800 −0.886829 −0.443414 0.896317i \(-0.646233\pi\)
−0.443414 + 0.896317i \(0.646233\pi\)
\(702\) −3.52251 2.79301i −0.132949 0.105415i
\(703\) 5.61597 + 9.72714i 0.211810 + 0.366866i
\(704\) −24.4131 17.3392i −0.920104 0.653497i
\(705\) 9.93784 + 6.33221i 0.374281 + 0.238485i
\(706\) −22.8932 13.6998i −0.861597 0.515601i
\(707\) −12.4109 14.1715i −0.466760 0.532973i
\(708\) 19.5666 + 40.6550i 0.735359 + 1.52791i
\(709\) 21.8896 0.822083 0.411042 0.911617i \(-0.365165\pi\)
0.411042 + 0.911617i \(0.365165\pi\)
\(710\) −10.3698 18.6288i −0.389170 0.699125i
\(711\) 24.2326 + 16.9736i 0.908793 + 0.636559i
\(712\) −2.37833 1.52639i −0.0891318 0.0572040i
\(713\) 24.9730 14.4182i 0.935246 0.539965i
\(714\) 17.5525 + 22.6213i 0.656886 + 0.846580i
\(715\) −5.56894 3.21523i −0.208267 0.120243i
\(716\) −2.74083 + 1.46995i −0.102430 + 0.0549347i
\(717\) −0.301711 + 6.89774i −0.0112676 + 0.257601i
\(718\) −14.2906 8.55186i −0.533322 0.319153i
\(719\) 0.739214 1.28036i 0.0275680 0.0477492i −0.851912 0.523685i \(-0.824557\pi\)
0.879480 + 0.475935i \(0.157890\pi\)
\(720\) 5.03839 33.3210i 0.187770 1.24180i
\(721\) 5.52002 + 27.8505i 0.205576 + 1.03721i
\(722\) −12.0957 21.7293i −0.450156 0.808682i
\(723\) −0.851059 + 19.4570i −0.0316512 + 0.723613i
\(724\) 0.737899 23.5502i 0.0274238 0.875236i
\(725\) 24.8927 0.924493
\(726\) 4.05907 6.15546i 0.150646 0.228451i
\(727\) 21.0883 + 36.5260i 0.782121 + 1.35467i 0.930704 + 0.365773i \(0.119195\pi\)
−0.148583 + 0.988900i \(0.547471\pi\)
\(728\) −2.85101 3.58179i −0.105665 0.132750i
\(729\) 26.0767 + 7.00055i 0.965802 + 0.259280i
\(730\) −3.56162 + 5.95167i −0.131822 + 0.220281i
\(731\) −4.02514 + 6.97174i −0.148875 + 0.257859i
\(732\) −6.78677 + 3.26637i −0.250846 + 0.120728i
\(733\) 34.8533 20.1226i 1.28734 0.743244i 0.309159 0.951011i \(-0.399953\pi\)
0.978179 + 0.207766i \(0.0666193\pi\)
\(734\) −16.5562 + 27.6663i −0.611101 + 1.02118i
\(735\) −11.5991 32.0124i −0.427841 1.18079i
\(736\) 36.6943 17.5128i 1.35257 0.645530i
\(737\) 27.5390 47.6990i 1.01441 1.75702i
\(738\) −15.4108 + 6.89151i −0.567279 + 0.253680i
\(739\) −24.9157 + 14.3851i −0.916540 + 0.529165i −0.882530 0.470257i \(-0.844161\pi\)
−0.0340104 + 0.999421i \(0.510828\pi\)
\(740\) 1.66094 53.0091i 0.0610573 1.94865i
\(741\) −1.06294 0.677287i −0.0390481 0.0248808i
\(742\) 0.230289 + 1.26550i 0.00845416 + 0.0464580i
\(743\) 17.6335 + 10.1807i 0.646910 + 0.373494i 0.787272 0.616606i \(-0.211493\pi\)
−0.140361 + 0.990100i \(0.544826\pi\)
\(744\) 8.24519 + 17.8414i 0.302283 + 0.654098i
\(745\) −27.4832 15.8674i −1.00691 0.581337i
\(746\) 3.43476 + 6.17037i 0.125756 + 0.225913i
\(747\) −13.0141 1.14067i −0.476160 0.0417348i
\(748\) −33.0576 1.03579i −1.20870 0.0378724i
\(749\) 25.1941 + 28.7681i 0.920574 + 1.05116i
\(750\) −12.9993 + 6.50902i −0.474667 + 0.237676i
\(751\) 3.94952 2.28026i 0.144120 0.0832077i −0.426206 0.904626i \(-0.640150\pi\)
0.570326 + 0.821418i \(0.306817\pi\)
\(752\) −9.67133 0.606660i −0.352677 0.0221226i
\(753\) −8.24098 15.8338i −0.300318 0.577017i
\(754\) −0.116839 + 7.45970i −0.00425502 + 0.271666i
\(755\) −13.7167 −0.499201
\(756\) 24.2550 + 12.9496i 0.882148 + 0.470973i
\(757\) −33.7462 −1.22653 −0.613264 0.789878i \(-0.710144\pi\)
−0.613264 + 0.789878i \(0.710144\pi\)
\(758\) 0.714944 45.6463i 0.0259679 1.65795i
\(759\) 21.5132 + 41.3345i 0.780880 + 1.50035i
\(760\) 0.443760 9.43793i 0.0160969 0.342350i
\(761\) 38.9857 22.5084i 1.41323 0.815929i 0.417539 0.908659i \(-0.362893\pi\)
0.995691 + 0.0927296i \(0.0295592\pi\)
\(762\) 37.4391 18.7466i 1.35628 0.679117i
\(763\) −0.395877 1.99734i −0.0143317 0.0723087i
\(764\) −0.907532 + 28.9641i −0.0328334 + 1.04788i
\(765\) −15.7253 33.7370i −0.568550 1.21977i
\(766\) 12.1356 + 21.8010i 0.438477 + 0.787701i
\(767\) −6.90035 3.98392i −0.249157 0.143851i
\(768\) 9.62218 + 25.9887i 0.347211 + 0.937787i
\(769\) −16.8566 9.73214i −0.607863 0.350950i 0.164265 0.986416i \(-0.447475\pi\)
−0.772129 + 0.635466i \(0.780808\pi\)
\(770\) 37.0317 + 13.2494i 1.33453 + 0.477476i
\(771\) −35.3958 22.5536i −1.27475 0.812247i
\(772\) −18.4194 0.577136i −0.662929 0.0207716i
\(773\) −1.15063 + 0.664319i −0.0413855 + 0.0238939i −0.520550 0.853831i \(-0.674273\pi\)
0.479165 + 0.877725i \(0.340940\pi\)
\(774\) −0.795514 + 7.68958i −0.0285942 + 0.276396i
\(775\) −5.79049 + 10.0294i −0.208000 + 0.360267i
\(776\) 16.7426 8.64447i 0.601025 0.310318i
\(777\) 40.3171 + 15.7139i 1.44637 + 0.563732i
\(778\) 11.2637 18.8223i 0.403824 0.674813i
\(779\) −4.09894 + 2.36653i −0.146860 + 0.0847896i
\(780\) 2.58091 + 5.36254i 0.0924113 + 0.192010i
\(781\) −10.0468 + 17.4016i −0.359503 + 0.622677i
\(782\) 23.0607 38.5357i 0.824650 1.37804i
\(783\) −17.1378 41.4023i −0.612456 1.47960i
\(784\) 21.0780 + 18.4314i 0.752787 + 0.658265i
\(785\) 16.3689 + 28.3517i 0.584230 + 1.01192i
\(786\) 21.2585 32.2379i 0.758266 1.14989i
\(787\) −34.4903 −1.22945 −0.614724 0.788743i \(-0.710732\pi\)
−0.614724 + 0.788743i \(0.710732\pi\)
\(788\) −19.0893 0.598125i −0.680028 0.0213073i
\(789\) −0.557726 + 12.7508i −0.0198556 + 0.453940i
\(790\) −19.0500 34.2223i −0.677768 1.21758i
\(791\) −13.9665 + 12.2314i −0.496592 + 0.434900i
\(792\) −29.3854 + 12.0512i −1.04416 + 0.428219i
\(793\) 0.665057 1.15191i 0.0236169 0.0409056i
\(794\) −41.5884 24.8875i −1.47592 0.883225i
\(795\) 0.0730715 1.67057i 0.00259158 0.0592489i
\(796\) −15.8438 29.5419i −0.561567 1.04708i
\(797\) −18.1134 10.4578i −0.641608 0.370433i 0.143625 0.989632i \(-0.454124\pi\)
−0.785234 + 0.619199i \(0.787457\pi\)
\(798\) 7.13787 + 2.91161i 0.252678 + 0.103070i
\(799\) −9.26920 + 5.35157i −0.327921 + 0.189325i
\(800\) −9.24580 + 13.4594i −0.326888 + 0.475863i
\(801\) −2.71680 + 1.26634i −0.0959935 + 0.0447439i
\(802\) 4.71102 + 8.46311i 0.166352 + 0.298843i
\(803\) 6.53683 0.230680
\(804\) −45.9312 + 22.1059i −1.61987 + 0.779617i
\(805\) −40.1757 + 35.1846i −1.41601 + 1.24009i
\(806\) −2.97837 1.78233i −0.104909 0.0627800i
\(807\) −45.0309 28.6929i −1.58516 1.01004i
\(808\) −16.9482 10.8772i −0.596236 0.382659i
\(809\) 1.33919 + 2.31955i 0.0470835 + 0.0815510i 0.888607 0.458670i \(-0.151674\pi\)
−0.841523 + 0.540221i \(0.818341\pi\)
\(810\) −27.0109 23.4104i −0.949065 0.822556i
\(811\) −4.16084 −0.146107 −0.0730534 0.997328i \(-0.523274\pi\)
−0.0730534 + 0.997328i \(0.523274\pi\)
\(812\) −7.46549 45.0165i −0.261987 1.57977i
\(813\) −32.9675 1.44202i −1.15622 0.0505738i
\(814\) −43.6729 + 24.3107i −1.53073 + 0.852089i
\(815\) −28.6017 −1.00187
\(816\) 24.7339 + 18.0322i 0.865860 + 0.631255i
\(817\) 2.16743i 0.0758286i
\(818\) −0.757487 + 48.3625i −0.0264849 + 1.69096i
\(819\) −4.82722 + 0.524551i −0.168677 + 0.0183293i
\(820\) 22.3376 + 0.699906i 0.780064 + 0.0244418i
\(821\) 11.6582 0.406875 0.203437 0.979088i \(-0.434789\pi\)
0.203437 + 0.979088i \(0.434789\pi\)
\(822\) −7.36637 0.437886i −0.256932 0.0152730i
\(823\) 24.4516i 0.852329i −0.904646 0.426164i \(-0.859864\pi\)
0.904646 0.426164i \(-0.140136\pi\)
\(824\) 13.9250 + 26.9699i 0.485100 + 0.939542i
\(825\) −15.7826 10.0564i −0.549479 0.350118i
\(826\) 45.8851 + 16.4171i 1.59655 + 0.571223i
\(827\) 1.50378i 0.0522917i −0.999658 0.0261458i \(-0.991677\pi\)
0.999658 0.0261458i \(-0.00832343\pi\)
\(828\) 5.10906 42.8219i 0.177552 1.48816i
\(829\) −41.9427 + 24.2157i −1.45673 + 0.841044i −0.998849 0.0479683i \(-0.984725\pi\)
−0.457883 + 0.889013i \(0.651392\pi\)
\(830\) 14.8404 + 8.88086i 0.515118 + 0.308259i
\(831\) 0.434852 + 0.0190207i 0.0150848 + 0.000659820i
\(832\) −3.99004 2.83390i −0.138330 0.0982478i
\(833\) 30.6564 + 4.07863i 1.06218 + 0.141316i
\(834\) 9.05113 + 0.538035i 0.313415 + 0.0186306i
\(835\) 39.5277i 1.36791i
\(836\) −7.84731 + 4.20863i −0.271405 + 0.145559i
\(837\) 20.6677 + 2.72597i 0.714382 + 0.0942234i
\(838\) −14.6070 + 24.4092i −0.504592 + 0.843201i
\(839\) 5.29494 + 9.17110i 0.182801 + 0.316621i 0.942833 0.333264i \(-0.108150\pi\)
−0.760032 + 0.649886i \(0.774817\pi\)
\(840\) −21.4027 29.4428i −0.738462 1.01587i
\(841\) −22.6825 + 39.2872i −0.782154 + 1.35473i
\(842\) −4.19574 7.53743i −0.144595 0.259757i
\(843\) 10.9354 17.1622i 0.376637 0.591097i
\(844\) −14.6891 9.10573i −0.505619 0.313432i
\(845\) 30.7067 + 17.7285i 1.05634 + 0.609880i
\(846\) −6.02776 + 8.32506i −0.207239 + 0.286221i
\(847\) −1.54838 7.81212i −0.0532029 0.268428i
\(848\) 0.611645 + 1.23158i 0.0210040 + 0.0422925i
\(849\) −6.96409 13.3805i −0.239007 0.459217i
\(850\) −0.282455 + 18.0336i −0.00968812 + 0.618548i
\(851\) 67.8692i 2.32652i
\(852\) 16.7566 8.06470i 0.574072 0.276292i
\(853\) −32.3692 + 18.6884i −1.10830 + 0.639877i −0.938389 0.345582i \(-0.887682\pi\)
−0.169912 + 0.985459i \(0.554348\pi\)
\(854\) −2.74059 + 7.65986i −0.0937811 + 0.262115i
\(855\) −8.20821 5.74940i −0.280715 0.196625i
\(856\) 34.4049 + 22.0807i 1.17593 + 0.754704i
\(857\) 5.95532 + 3.43830i 0.203430 + 0.117450i 0.598254 0.801306i \(-0.295861\pi\)
−0.394825 + 0.918757i \(0.629195\pi\)
\(858\) 3.08771 4.68242i 0.105413 0.159855i
\(859\) −4.32467 7.49055i −0.147556 0.255574i 0.782768 0.622314i \(-0.213807\pi\)
−0.930324 + 0.366740i \(0.880474\pi\)
\(860\) 5.39216 8.69847i 0.183871 0.296615i
\(861\) −6.62170 + 16.9893i −0.225667 + 0.578994i
\(862\) 33.2153 18.4894i 1.13132 0.629753i
\(863\) 26.5454 + 15.3260i 0.903617 + 0.521703i 0.878372 0.477978i \(-0.158630\pi\)
0.0252448 + 0.999681i \(0.491963\pi\)
\(864\) 28.7515 + 6.11149i 0.978146 + 0.207917i
\(865\) 22.4535 + 38.8907i 0.763443 + 1.32232i
\(866\) 0.355036 22.6676i 0.0120646 0.770277i
\(867\) 4.35946 + 0.190685i 0.148055 + 0.00647601i
\(868\) 19.8740 + 7.46374i 0.674567 + 0.253336i
\(869\) −18.4567 + 31.9679i −0.626100 + 1.08444i
\(870\) −3.52003 + 59.2160i −0.119340 + 2.00761i
\(871\) 4.50094 7.79586i 0.152509 0.264153i
\(872\) −0.998653 1.93419i −0.0338187 0.0655000i
\(873\) 1.74502 19.9092i 0.0590600 0.673825i
\(874\) 0.189355 12.0896i 0.00640504 0.408936i
\(875\) −5.05762 + 14.8659i −0.170979 + 0.502558i
\(876\) −4.99773 3.40912i −0.168858 0.115183i
\(877\) −21.6550 37.5076i −0.731239 1.26654i −0.956354 0.292211i \(-0.905609\pi\)
0.225115 0.974332i \(-0.427724\pi\)
\(878\) −27.8416 0.436074i −0.939608 0.0147168i
\(879\) −0.879415 + 20.1053i −0.0296619 + 0.678133i
\(880\) 41.9637 + 2.63228i 1.41460 + 0.0887343i
\(881\) 16.8008i 0.566034i −0.959115 0.283017i \(-0.908665\pi\)
0.959115 0.283017i \(-0.0913353\pi\)
\(882\) 28.4732 8.44240i 0.958744 0.284270i
\(883\) 12.8684i 0.433055i −0.976277 0.216527i \(-0.930527\pi\)
0.976277 0.216527i \(-0.0694731\pi\)
\(884\) −5.40288 0.169289i −0.181718 0.00569379i
\(885\) −53.4291 34.0441i −1.79600 1.14438i
\(886\) 0.159556 10.1870i 0.00536038 0.342239i
\(887\) 24.4526 + 42.3532i 0.821039 + 1.42208i 0.904910 + 0.425604i \(0.139938\pi\)
−0.0838710 + 0.996477i \(0.526728\pi\)
\(888\) 46.0687 + 4.18978i 1.54596 + 0.140600i
\(889\) 14.5664 42.8151i 0.488541 1.43597i
\(890\) 3.96767 + 0.0621444i 0.132997 + 0.00208308i
\(891\) −5.86025 + 33.1735i −0.196326 + 1.11135i
\(892\) 18.6021 + 34.6850i 0.622844 + 1.16134i
\(893\) −1.44084 + 2.49560i −0.0482158 + 0.0835122i
\(894\) 15.2381 23.1081i 0.509638 0.772851i
\(895\) 2.18356 3.78203i 0.0729882 0.126419i
\(896\) 27.1132 + 12.6837i 0.905787 + 0.423733i
\(897\) 3.51609 + 6.75565i 0.117399 + 0.225565i
\(898\) −9.08470 0.142291i −0.303160 0.00474830i
\(899\) −17.2986 29.9620i −0.576940 0.999289i
\(900\) 6.82190 + 15.9196i 0.227397 + 0.530653i
\(901\) 1.31533 + 0.759408i 0.0438201 + 0.0252996i
\(902\) −10.2443 18.4034i −0.341099 0.612767i
\(903\) 5.22151 + 6.51604i 0.173761 + 0.216840i
\(904\) −10.7199 + 16.7031i −0.356539 + 0.555537i
\(905\) 16.5422 + 28.6519i 0.549881 + 0.952421i
\(906\) 0.709939 11.9430i 0.0235861 0.396779i
\(907\) 3.37721 + 1.94983i 0.112138 + 0.0647431i 0.555020 0.831837i \(-0.312711\pi\)
−0.442882 + 0.896580i \(0.646044\pi\)
\(908\) −12.6185 + 20.3558i −0.418760 + 0.675531i
\(909\) −19.3602 + 9.02405i −0.642137 + 0.299309i
\(910\) 6.05241 + 2.16547i 0.200635 + 0.0717845i
\(911\) 19.4469 11.2277i 0.644305 0.371990i −0.141966 0.989872i \(-0.545342\pi\)
0.786271 + 0.617882i \(0.212009\pi\)
\(912\) 8.19456 + 0.874860i 0.271349 + 0.0289695i
\(913\) 16.2995i 0.539435i
\(914\) 51.5249 + 0.807018i 1.70429 + 0.0266938i
\(915\) 5.68316 8.91921i 0.187880 0.294860i
\(916\) 4.83137 2.59114i 0.159633 0.0856136i
\(917\) −8.10930 40.9143i −0.267793 1.35111i
\(918\) 30.1885 11.9458i 0.996368 0.394269i
\(919\) 27.1929 + 15.6998i 0.897012 + 0.517890i 0.876229 0.481894i \(-0.160051\pi\)
0.0207822 + 0.999784i \(0.493384\pi\)
\(920\) −30.8366 + 48.0477i −1.01665 + 1.58409i
\(921\) 19.0376 + 36.5780i 0.627310 + 1.20528i
\(922\) 2.71651 1.51215i 0.0894633 0.0498001i
\(923\) −1.64203 + 2.84409i −0.0540482 + 0.0936143i
\(924\) −13.4528 + 31.5575i −0.442566 + 1.03816i
\(925\) 13.6285 + 23.6052i 0.448101 + 0.776135i
\(926\) 4.17830 + 2.50039i 0.137307 + 0.0821681i
\(927\) 32.0709 + 2.81097i 1.05335 + 0.0923245i
\(928\) −21.0114 44.0250i −0.689734 1.44519i
\(929\) 25.1004i 0.823516i 0.911293 + 0.411758i \(0.135085\pi\)
−0.911293 + 0.411758i \(0.864915\pi\)
\(930\) −23.0396 15.1929i −0.755499 0.498195i
\(931\) 7.69706 3.17591i 0.252261 0.104086i
\(932\) −17.0864 + 27.5633i −0.559684 + 0.902865i
\(933\) −19.1628 36.8185i −0.627362 1.20538i
\(934\) −0.340788 + 0.569475i −0.0111509 + 0.0186338i
\(935\) 40.2189 23.2204i 1.31530 0.759387i
\(936\) −4.80270 + 1.96962i −0.156981 + 0.0643791i
\(937\) 19.0090i 0.620996i −0.950574 0.310498i \(-0.899504\pi\)
0.950574 0.310498i \(-0.100496\pi\)
\(938\) −18.5476 + 51.8400i −0.605601 + 1.69264i
\(939\) −15.8396 + 8.24400i −0.516907 + 0.269033i
\(940\) 11.9911 6.43099i 0.391106 0.209756i
\(941\) 37.4081i 1.21947i 0.792606 + 0.609734i \(0.208724\pi\)
−0.792606 + 0.609734i \(0.791276\pi\)
\(942\) −25.5328 + 12.7848i −0.831904 + 0.416552i
\(943\) 28.5995 0.931329
\(944\) 51.9962 + 3.26160i 1.69233 + 0.106156i
\(945\) −38.5275 + 2.48956i −1.25330 + 0.0809853i
\(946\) −9.64409 0.151052i −0.313556 0.00491113i
\(947\) 27.1934i 0.883668i 0.897097 + 0.441834i \(0.145672\pi\)
−0.897097 + 0.441834i \(0.854328\pi\)
\(948\) 30.7831 14.8154i 0.999788 0.481182i
\(949\) 1.06837 0.0346808
\(950\) 2.36179 + 4.24284i 0.0766267 + 0.137656i
\(951\) −10.2146 19.6259i −0.331232 0.636413i
\(952\) 32.6970 4.89760i 1.05972 0.158732i
\(953\) 25.8339 0.836841 0.418420 0.908253i \(-0.362584\pi\)
0.418420 + 0.908253i \(0.362584\pi\)
\(954\) 1.45077 + 0.150087i 0.0469703 + 0.00485924i
\(955\) −20.3450 35.2386i −0.658349 1.14029i
\(956\) 6.77611 + 4.20049i 0.219155 + 0.135854i
\(957\) 49.5921 25.8110i 1.60309 0.834352i
\(958\) −5.45852 + 9.12148i −0.176357 + 0.294702i
\(959\) −5.99623 + 5.25131i −0.193628 + 0.169574i
\(960\) −30.7105 23.8976i −0.991177 0.771292i
\(961\) −14.9042 −0.480781
\(962\) −7.13783 + 3.97330i −0.230133 + 0.128104i
\(963\) 39.3011 18.3188i 1.26646 0.590316i
\(964\) 19.1139 + 11.8486i 0.615617 + 0.381619i
\(965\) 22.4096 12.9382i 0.721392 0.416496i
\(966\) −28.5556 36.8017i −0.918760 1.18408i
\(967\) 38.1504 + 22.0262i 1.22683 + 0.708313i 0.966366 0.257169i \(-0.0827897\pi\)
0.260468 + 0.965482i \(0.416123\pi\)
\(968\) −3.90599 7.56511i −0.125543 0.243152i
\(969\) 8.07432 4.20241i 0.259385 0.135001i
\(970\) −13.5862 + 22.7032i −0.436225 + 0.728956i
\(971\) −17.9137 + 31.0274i −0.574877 + 0.995716i 0.421178 + 0.906978i \(0.361617\pi\)
−0.996055 + 0.0887384i \(0.971716\pi\)
\(972\) 21.7812 22.3065i 0.698633 0.715480i
\(973\) 7.36763 6.45233i 0.236195 0.206852i
\(974\) −15.7499 + 8.76726i −0.504660 + 0.280921i
\(975\) −2.57948 1.64360i −0.0826095 0.0526373i
\(976\) −0.544477 + 8.68002i −0.0174283 + 0.277841i
\(977\) −39.7811 −1.27271 −0.636355 0.771396i \(-0.719559\pi\)
−0.636355 + 0.771396i \(0.719559\pi\)
\(978\) 1.48035 24.9032i 0.0473363 0.796317i
\(979\) −1.86991 3.23877i −0.0597625 0.103512i
\(980\) −38.7915 6.40310i −1.23915 0.204539i
\(981\) −2.30001 0.201594i −0.0734338 0.00643639i
\(982\) −23.5206 14.0753i −0.750573 0.449161i
\(983\) 1.44927 2.51020i 0.0462244 0.0800630i −0.841988 0.539497i \(-0.818614\pi\)
0.888212 + 0.459434i \(0.151948\pi\)
\(984\) −1.76554 + 19.4130i −0.0562834 + 0.618863i
\(985\) 23.2246 13.4087i 0.739998 0.427238i
\(986\) −46.2343 27.6677i −1.47240 0.881119i
\(987\) 1.68045 + 10.9738i 0.0534894 + 0.349298i
\(988\) −1.28255 + 0.687853i −0.0408035 + 0.0218835i
\(989\) 6.54835 11.3421i 0.208226 0.360657i
\(990\) 26.1543 36.1223i 0.831239 1.14804i
\(991\) −35.6534 + 20.5845i −1.13257 + 0.653888i −0.944579 0.328283i \(-0.893530\pi\)
−0.187988 + 0.982171i \(0.560197\pi\)
\(992\) 22.6255 + 1.77537i 0.718361 + 0.0563679i
\(993\) 29.1680 15.1809i 0.925618 0.481753i
\(994\) 6.76655 18.9123i 0.214622 0.599861i
\(995\) 40.7643 + 23.5353i 1.29232 + 0.746119i
\(996\) −8.50059 + 12.4618i −0.269352 + 0.394866i
\(997\) 22.2201 + 12.8288i 0.703719 + 0.406292i 0.808731 0.588179i \(-0.200155\pi\)
−0.105012 + 0.994471i \(0.533488\pi\)
\(998\) 26.0346 14.4923i 0.824111 0.458745i
\(999\) 29.8781 38.9186i 0.945300 1.23133i
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 252.2.bj.b.103.1 yes 84
3.2 odd 2 756.2.bj.b.523.42 84
4.3 odd 2 inner 252.2.bj.b.103.2 yes 84
7.3 odd 6 252.2.n.b.31.29 yes 84
9.2 odd 6 756.2.n.b.19.15 84
9.7 even 3 252.2.n.b.187.28 yes 84
12.11 even 2 756.2.bj.b.523.41 84
21.17 even 6 756.2.n.b.199.14 84
28.3 even 6 252.2.n.b.31.28 84
36.7 odd 6 252.2.n.b.187.29 yes 84
36.11 even 6 756.2.n.b.19.14 84
63.38 even 6 756.2.bj.b.451.42 84
63.52 odd 6 inner 252.2.bj.b.115.1 yes 84
84.59 odd 6 756.2.n.b.199.15 84
252.115 even 6 inner 252.2.bj.b.115.2 yes 84
252.227 odd 6 756.2.bj.b.451.41 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.28 84 28.3 even 6
252.2.n.b.31.29 yes 84 7.3 odd 6
252.2.n.b.187.28 yes 84 9.7 even 3
252.2.n.b.187.29 yes 84 36.7 odd 6
252.2.bj.b.103.1 yes 84 1.1 even 1 trivial
252.2.bj.b.103.2 yes 84 4.3 odd 2 inner
252.2.bj.b.115.1 yes 84 63.52 odd 6 inner
252.2.bj.b.115.2 yes 84 252.115 even 6 inner
756.2.n.b.19.14 84 36.11 even 6
756.2.n.b.19.15 84 9.2 odd 6
756.2.n.b.199.14 84 21.17 even 6
756.2.n.b.199.15 84 84.59 odd 6
756.2.bj.b.451.41 84 252.227 odd 6
756.2.bj.b.451.42 84 63.38 even 6
756.2.bj.b.523.41 84 12.11 even 2
756.2.bj.b.523.42 84 3.2 odd 2