Properties

Label 105.2.x.a.53.10
Level $105$
Weight $2$
Character 105.53
Analytic conductor $0.838$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(2,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 53.10
Character \(\chi\) \(=\) 105.53
Dual form 105.2.x.a.2.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.391246 - 1.46015i) q^{2} +(-1.50746 - 0.852980i) q^{3} +(-0.246919 - 0.142558i) q^{4} +(-1.82416 - 1.29322i) q^{5} +(-1.83527 + 1.86739i) q^{6} +(-1.17707 - 2.36949i) q^{7} +(1.83305 - 1.83305i) q^{8} +(1.54485 + 2.57166i) q^{9} +O(q^{10})\) \(q+(0.391246 - 1.46015i) q^{2} +(-1.50746 - 0.852980i) q^{3} +(-0.246919 - 0.142558i) q^{4} +(-1.82416 - 1.29322i) q^{5} +(-1.83527 + 1.86739i) q^{6} +(-1.17707 - 2.36949i) q^{7} +(1.83305 - 1.83305i) q^{8} +(1.54485 + 2.57166i) q^{9} +(-2.60200 + 2.15759i) q^{10} +(0.791646 + 0.457057i) q^{11} +(0.250619 + 0.425517i) q^{12} +(3.07974 + 3.07974i) q^{13} +(-3.92035 + 0.791646i) q^{14} +(1.64675 + 3.50545i) q^{15} +(-2.24447 - 3.88754i) q^{16} +(-1.16230 + 0.311437i) q^{17} +(4.35943 - 1.24956i) q^{18} +(5.95337 - 3.43718i) q^{19} +(0.266060 + 0.579371i) q^{20} +(-0.246748 + 4.57593i) q^{21} +(0.977102 - 0.977102i) q^{22} +(1.88814 + 0.505926i) q^{23} +(-4.32679 + 1.19969i) q^{24} +(1.65515 + 4.71810i) q^{25} +(5.70182 - 3.29195i) q^{26} +(-0.135217 - 5.19439i) q^{27} +(-0.0471508 + 0.752874i) q^{28} -2.72261 q^{29} +(5.76278 - 1.03301i) q^{30} +(-2.31688 + 4.01295i) q^{31} +(-1.54656 + 0.414399i) q^{32} +(-0.803512 - 1.36425i) q^{33} +1.81898i q^{34} +(-0.917115 + 5.84456i) q^{35} +(-0.0148398 - 0.855222i) q^{36} +(-0.774982 - 0.207656i) q^{37} +(-2.68957 - 10.0376i) q^{38} +(-2.01562 - 7.26953i) q^{39} +(-5.71432 + 0.973238i) q^{40} +0.922837i q^{41} +(6.58501 + 2.15061i) q^{42} +(-4.80893 - 4.80893i) q^{43} +(-0.130315 - 0.225712i) q^{44} +(0.507675 - 6.68897i) q^{45} +(1.47746 - 2.55903i) q^{46} +(-2.71272 + 10.1240i) q^{47} +(0.0674490 + 7.77478i) q^{48} +(-4.22901 + 5.57813i) q^{49} +(7.53672 - 0.570823i) q^{50} +(2.01776 + 0.521940i) q^{51} +(-0.321402 - 1.19949i) q^{52} +(2.85459 + 10.6535i) q^{53} +(-7.63750 - 1.83485i) q^{54} +(-0.853015 - 1.85752i) q^{55} +(-6.50102 - 2.18577i) q^{56} +(-11.9063 + 0.103291i) q^{57} +(-1.06521 + 3.97543i) q^{58} +(4.94023 - 8.55672i) q^{59} +(0.0931184 - 1.10032i) q^{60} +(0.533944 + 0.924818i) q^{61} +(4.95304 + 4.95304i) q^{62} +(4.27514 - 6.68754i) q^{63} -6.55754i q^{64} +(-1.63516 - 9.60074i) q^{65} +(-2.30639 + 0.639490i) q^{66} +(-1.83132 - 6.83458i) q^{67} +(0.331391 + 0.0887959i) q^{68} +(-2.41475 - 2.37321i) q^{69} +(8.17513 + 3.62579i) q^{70} +0.557759i q^{71} +(7.54576 + 1.88219i) q^{72} +(2.10543 - 0.564147i) q^{73} +(-0.606418 + 1.05035i) q^{74} +(1.52939 - 8.52414i) q^{75} -1.96000 q^{76} +(0.151170 - 2.41379i) q^{77} +(-11.4032 + 0.0989269i) q^{78} +(2.62503 - 1.51556i) q^{79} +(-0.933173 + 9.99411i) q^{80} +(-4.22688 + 7.94566i) q^{81} +(1.34748 + 0.361057i) q^{82} +(2.38102 - 2.38102i) q^{83} +(0.713264 - 1.09471i) q^{84} +(2.52298 + 0.934999i) q^{85} +(-8.90325 + 5.14029i) q^{86} +(4.10422 + 2.32233i) q^{87} +(2.28893 - 0.613318i) q^{88} +(5.64725 + 9.78132i) q^{89} +(-9.56828 - 3.35832i) q^{90} +(3.67235 - 10.9225i) q^{91} +(-0.394093 - 0.394093i) q^{92} +(6.91556 - 4.07310i) q^{93} +(13.7213 + 7.92197i) q^{94} +(-15.3050 - 1.42906i) q^{95} +(2.68484 + 0.694495i) q^{96} +(-1.58805 + 1.58805i) q^{97} +(6.49033 + 8.35741i) q^{98} +(0.0475780 + 2.74193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 2 q^{3} - 24 q^{6} - 12 q^{7} - 8 q^{10} - 10 q^{12} - 16 q^{13} + 4 q^{15} - 8 q^{16} + 14 q^{18} - 28 q^{21} - 8 q^{22} + 4 q^{25} + 40 q^{27} - 60 q^{28} + 40 q^{30} - 24 q^{31} - 4 q^{33} + 8 q^{36} + 4 q^{37} - 16 q^{40} + 14 q^{42} + 16 q^{43} + 40 q^{45} - 32 q^{46} + 44 q^{48} + 8 q^{51} + 36 q^{52} - 40 q^{55} - 88 q^{57} + 56 q^{58} - 50 q^{60} - 8 q^{61} + 44 q^{63} + 76 q^{66} + 12 q^{67} + 140 q^{70} - 34 q^{72} + 52 q^{73} + 6 q^{75} + 64 q^{76} - 120 q^{78} + 20 q^{81} + 104 q^{82} - 24 q^{85} - 46 q^{87} - 84 q^{90} + 72 q^{91} - 44 q^{93} + 12 q^{96} - 120 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.391246 1.46015i 0.276653 1.03248i −0.678072 0.734995i \(-0.737184\pi\)
0.954726 0.297488i \(-0.0961489\pi\)
\(3\) −1.50746 0.852980i −0.870330 0.492468i
\(4\) −0.246919 0.142558i −0.123459 0.0712792i
\(5\) −1.82416 1.29322i −0.815791 0.578347i
\(6\) −1.83527 + 1.86739i −0.749245 + 0.762359i
\(7\) −1.17707 2.36949i −0.444891 0.895585i
\(8\) 1.83305 1.83305i 0.648080 0.648080i
\(9\) 1.54485 + 2.57166i 0.514950 + 0.857220i
\(10\) −2.60200 + 2.15759i −0.822825 + 0.682289i
\(11\) 0.791646 + 0.457057i 0.238690 + 0.137808i 0.614575 0.788859i \(-0.289328\pi\)
−0.375884 + 0.926667i \(0.622661\pi\)
\(12\) 0.250619 + 0.425517i 0.0723476 + 0.122836i
\(13\) 3.07974 + 3.07974i 0.854166 + 0.854166i 0.990643 0.136477i \(-0.0435781\pi\)
−0.136477 + 0.990643i \(0.543578\pi\)
\(14\) −3.92035 + 0.791646i −1.04776 + 0.211576i
\(15\) 1.64675 + 3.50545i 0.425190 + 0.905104i
\(16\) −2.24447 3.88754i −0.561118 0.971885i
\(17\) −1.16230 + 0.311437i −0.281899 + 0.0755345i −0.396998 0.917819i \(-0.629948\pi\)
0.115099 + 0.993354i \(0.463281\pi\)
\(18\) 4.35943 1.24956i 1.02753 0.294524i
\(19\) 5.95337 3.43718i 1.36580 0.788543i 0.375409 0.926859i \(-0.377502\pi\)
0.990388 + 0.138316i \(0.0441690\pi\)
\(20\) 0.266060 + 0.579371i 0.0594928 + 0.129551i
\(21\) −0.246748 + 4.57593i −0.0538449 + 0.998549i
\(22\) 0.977102 0.977102i 0.208319 0.208319i
\(23\) 1.88814 + 0.505926i 0.393705 + 0.105493i 0.450240 0.892908i \(-0.351339\pi\)
−0.0565348 + 0.998401i \(0.518005\pi\)
\(24\) −4.32679 + 1.19969i −0.883203 + 0.244885i
\(25\) 1.65515 + 4.71810i 0.331029 + 0.943621i
\(26\) 5.70182 3.29195i 1.11822 0.645604i
\(27\) −0.135217 5.19439i −0.0260225 0.999661i
\(28\) −0.0471508 + 0.752874i −0.00891066 + 0.142280i
\(29\) −2.72261 −0.505576 −0.252788 0.967522i \(-0.581348\pi\)
−0.252788 + 0.967522i \(0.581348\pi\)
\(30\) 5.76278 1.03301i 1.05213 0.188601i
\(31\) −2.31688 + 4.01295i −0.416123 + 0.720747i −0.995546 0.0942806i \(-0.969945\pi\)
0.579422 + 0.815028i \(0.303278\pi\)
\(32\) −1.54656 + 0.414399i −0.273395 + 0.0732561i
\(33\) −0.803512 1.36425i −0.139873 0.237486i
\(34\) 1.81898i 0.311952i
\(35\) −0.917115 + 5.84456i −0.155021 + 0.987911i
\(36\) −0.0148398 0.855222i −0.00247330 0.142537i
\(37\) −0.774982 0.207656i −0.127406 0.0341384i 0.194552 0.980892i \(-0.437675\pi\)
−0.321959 + 0.946754i \(0.604341\pi\)
\(38\) −2.68957 10.0376i −0.436306 1.62832i
\(39\) −2.01562 7.26953i −0.322757 1.16406i
\(40\) −5.71432 + 0.973238i −0.903513 + 0.153882i
\(41\) 0.922837i 0.144123i 0.997400 + 0.0720615i \(0.0229578\pi\)
−0.997400 + 0.0720615i \(0.977042\pi\)
\(42\) 6.58501 + 2.15061i 1.01609 + 0.331846i
\(43\) −4.80893 4.80893i −0.733355 0.733355i 0.237928 0.971283i \(-0.423532\pi\)
−0.971283 + 0.237928i \(0.923532\pi\)
\(44\) −0.130315 0.225712i −0.0196457 0.0340273i
\(45\) 0.507675 6.68897i 0.0756797 0.997132i
\(46\) 1.47746 2.55903i 0.217839 0.377309i
\(47\) −2.71272 + 10.1240i −0.395691 + 1.47674i 0.424909 + 0.905236i \(0.360306\pi\)
−0.820600 + 0.571503i \(0.806360\pi\)
\(48\) 0.0674490 + 7.77478i 0.00973542 + 1.12219i
\(49\) −4.22901 + 5.57813i −0.604144 + 0.796875i
\(50\) 7.53672 0.570823i 1.06585 0.0807265i
\(51\) 2.01776 + 0.521940i 0.282543 + 0.0730862i
\(52\) −0.321402 1.19949i −0.0445704 0.166339i
\(53\) 2.85459 + 10.6535i 0.392107 + 1.46336i 0.826651 + 0.562714i \(0.190243\pi\)
−0.434544 + 0.900651i \(0.643090\pi\)
\(54\) −7.63750 1.83485i −1.03933 0.249692i
\(55\) −0.853015 1.85752i −0.115021 0.250468i
\(56\) −6.50102 2.18577i −0.868736 0.292086i
\(57\) −11.9063 + 0.103291i −1.57703 + 0.0136813i
\(58\) −1.06521 + 3.97543i −0.139869 + 0.521999i
\(59\) 4.94023 8.55672i 0.643163 1.11399i −0.341560 0.939860i \(-0.610955\pi\)
0.984723 0.174130i \(-0.0557114\pi\)
\(60\) 0.0931184 1.10032i 0.0120215 0.142051i
\(61\) 0.533944 + 0.924818i 0.0683645 + 0.118411i 0.898182 0.439625i \(-0.144889\pi\)
−0.829817 + 0.558036i \(0.811555\pi\)
\(62\) 4.95304 + 4.95304i 0.629037 + 0.629037i
\(63\) 4.27514 6.68754i 0.538617 0.842551i
\(64\) 6.55754i 0.819693i
\(65\) −1.63516 9.60074i −0.202816 1.19082i
\(66\) −2.30639 + 0.639490i −0.283897 + 0.0787158i
\(67\) −1.83132 6.83458i −0.223732 0.834977i −0.982909 0.184093i \(-0.941065\pi\)
0.759177 0.650884i \(-0.225602\pi\)
\(68\) 0.331391 + 0.0887959i 0.0401870 + 0.0107681i
\(69\) −2.41475 2.37321i −0.290701 0.285701i
\(70\) 8.17513 + 3.62579i 0.977115 + 0.433365i
\(71\) 0.557759i 0.0661938i 0.999452 + 0.0330969i \(0.0105370\pi\)
−0.999452 + 0.0330969i \(0.989463\pi\)
\(72\) 7.54576 + 1.88219i 0.889276 + 0.221819i
\(73\) 2.10543 0.564147i 0.246421 0.0660284i −0.133494 0.991050i \(-0.542620\pi\)
0.379915 + 0.925021i \(0.375953\pi\)
\(74\) −0.606418 + 1.05035i −0.0704946 + 0.122100i
\(75\) 1.52939 8.52414i 0.176599 0.984283i
\(76\) −1.96000 −0.224827
\(77\) 0.151170 2.41379i 0.0172275 0.275077i
\(78\) −11.4032 + 0.0989269i −1.29116 + 0.0112013i
\(79\) 2.62503 1.51556i 0.295339 0.170514i −0.345008 0.938600i \(-0.612124\pi\)
0.640347 + 0.768086i \(0.278790\pi\)
\(80\) −0.933173 + 9.99411i −0.104332 + 1.11738i
\(81\) −4.22688 + 7.94566i −0.469653 + 0.882851i
\(82\) 1.34748 + 0.361057i 0.148805 + 0.0398720i
\(83\) 2.38102 2.38102i 0.261351 0.261351i −0.564252 0.825603i \(-0.690835\pi\)
0.825603 + 0.564252i \(0.190835\pi\)
\(84\) 0.713264 1.09471i 0.0778235 0.119442i
\(85\) 2.52298 + 0.934999i 0.273655 + 0.101415i
\(86\) −8.90325 + 5.14029i −0.960062 + 0.554292i
\(87\) 4.10422 + 2.32233i 0.440018 + 0.248980i
\(88\) 2.28893 0.613318i 0.244001 0.0653799i
\(89\) 5.64725 + 9.78132i 0.598607 + 1.03682i 0.993027 + 0.117888i \(0.0376123\pi\)
−0.394420 + 0.918930i \(0.629054\pi\)
\(90\) −9.56828 3.35832i −1.00859 0.353998i
\(91\) 3.67235 10.9225i 0.384967 1.14499i
\(92\) −0.394093 0.394093i −0.0410871 0.0410871i
\(93\) 6.91556 4.07310i 0.717110 0.422360i
\(94\) 13.7213 + 7.92197i 1.41524 + 0.817089i
\(95\) −15.3050 1.42906i −1.57026 0.146618i
\(96\) 2.68484 + 0.694495i 0.274021 + 0.0708816i
\(97\) −1.58805 + 1.58805i −0.161242 + 0.161242i −0.783117 0.621875i \(-0.786371\pi\)
0.621875 + 0.783117i \(0.286371\pi\)
\(98\) 6.49033 + 8.35741i 0.655622 + 0.844226i
\(99\) 0.0475780 + 2.74193i 0.00478177 + 0.275574i
\(100\) 0.263919 1.40094i 0.0263919 0.140094i
\(101\) 4.02299 + 2.32267i 0.400302 + 0.231114i 0.686614 0.727022i \(-0.259096\pi\)
−0.286312 + 0.958136i \(0.592429\pi\)
\(102\) 1.55155 2.74203i 0.153627 0.271502i
\(103\) −2.72555 + 10.1719i −0.268556 + 1.00227i 0.691481 + 0.722395i \(0.256959\pi\)
−0.960037 + 0.279871i \(0.909708\pi\)
\(104\) 11.2906 1.10714
\(105\) 6.36781 8.02814i 0.621434 0.783466i
\(106\) 16.6725 1.61938
\(107\) 1.63757 6.11150i 0.158310 0.590821i −0.840489 0.541829i \(-0.817732\pi\)
0.998799 0.0489927i \(-0.0156011\pi\)
\(108\) −0.707117 + 1.30187i −0.0680424 + 0.125272i
\(109\) 7.46435 + 4.30954i 0.714955 + 0.412779i 0.812893 0.582413i \(-0.197891\pi\)
−0.0979381 + 0.995193i \(0.531225\pi\)
\(110\) −3.04600 + 0.518783i −0.290425 + 0.0494640i
\(111\) 0.991125 + 0.974076i 0.0940734 + 0.0924552i
\(112\) −6.56960 + 9.89417i −0.620769 + 0.934911i
\(113\) −7.44178 + 7.44178i −0.700064 + 0.700064i −0.964424 0.264360i \(-0.914839\pi\)
0.264360 + 0.964424i \(0.414839\pi\)
\(114\) −4.50747 + 17.4254i −0.422164 + 1.63204i
\(115\) −2.79001 3.36468i −0.260169 0.313758i
\(116\) 0.672263 + 0.388131i 0.0624181 + 0.0360371i
\(117\) −3.16231 + 12.6778i −0.292356 + 1.17206i
\(118\) −10.5613 10.5613i −0.972243 0.972243i
\(119\) 2.10605 + 2.38747i 0.193062 + 0.218859i
\(120\) 9.44424 + 3.40709i 0.862137 + 0.311023i
\(121\) −5.08220 8.80262i −0.462018 0.800239i
\(122\) 1.55928 0.417807i 0.141170 0.0378265i
\(123\) 0.787162 1.39114i 0.0709760 0.125435i
\(124\) 1.14416 0.660581i 0.102749 0.0593219i
\(125\) 3.08230 10.7471i 0.275690 0.961247i
\(126\) −8.09219 8.85883i −0.720910 0.789207i
\(127\) −4.42895 + 4.42895i −0.393006 + 0.393006i −0.875757 0.482752i \(-0.839637\pi\)
0.482752 + 0.875757i \(0.339637\pi\)
\(128\) −12.6681 3.39441i −1.11971 0.300027i
\(129\) 3.14733 + 11.3512i 0.277107 + 0.999416i
\(130\) −14.6583 1.36868i −1.28562 0.120041i
\(131\) 7.37260 4.25658i 0.644147 0.371899i −0.142063 0.989858i \(-0.545374\pi\)
0.786210 + 0.617959i \(0.212040\pi\)
\(132\) 0.00391611 + 0.451407i 0.000340854 + 0.0392899i
\(133\) −15.1519 10.0607i −1.31384 0.872371i
\(134\) −10.6960 −0.923996
\(135\) −6.47085 + 9.65029i −0.556922 + 0.830565i
\(136\) −1.55967 + 2.70143i −0.133740 + 0.231645i
\(137\) 9.98048 2.67426i 0.852690 0.228478i 0.194102 0.980981i \(-0.437821\pi\)
0.658588 + 0.752504i \(0.271154\pi\)
\(138\) −4.41001 + 2.59739i −0.375405 + 0.221104i
\(139\) 3.03547i 0.257465i 0.991679 + 0.128733i \(0.0410909\pi\)
−0.991679 + 0.128733i \(0.958909\pi\)
\(140\) 1.05964 1.31239i 0.0895563 0.110917i
\(141\) 12.7249 12.9476i 1.07163 1.09039i
\(142\) 0.814412 + 0.218221i 0.0683440 + 0.0183127i
\(143\) 1.03045 + 3.84568i 0.0861703 + 0.321592i
\(144\) 6.53006 11.7777i 0.544172 0.981473i
\(145\) 4.96649 + 3.52095i 0.412444 + 0.292399i
\(146\) 3.29496i 0.272693i
\(147\) 11.1331 4.80152i 0.918241 0.396023i
\(148\) 0.161754 + 0.161754i 0.0132961 + 0.0132961i
\(149\) −6.44006 11.1545i −0.527590 0.913813i −0.999483 0.0321573i \(-0.989762\pi\)
0.471892 0.881656i \(-0.343571\pi\)
\(150\) −11.8482 5.56818i −0.967399 0.454640i
\(151\) −5.94939 + 10.3046i −0.484154 + 0.838580i −0.999834 0.0182013i \(-0.994206\pi\)
0.515680 + 0.856781i \(0.327539\pi\)
\(152\) 4.61230 17.2133i 0.374107 1.39619i
\(153\) −2.59648 2.50791i −0.209913 0.202753i
\(154\) −3.46536 1.16512i −0.279246 0.0938879i
\(155\) 9.41600 4.32404i 0.756312 0.347315i
\(156\) −0.538640 + 2.08232i −0.0431257 + 0.166719i
\(157\) −3.60080 13.4384i −0.287375 1.07250i −0.947086 0.320980i \(-0.895988\pi\)
0.659711 0.751520i \(-0.270679\pi\)
\(158\) −1.18592 4.42591i −0.0943466 0.352106i
\(159\) 4.78403 18.4945i 0.379398 1.46671i
\(160\) 3.35709 + 1.24411i 0.265401 + 0.0983558i
\(161\) −1.02369 5.06945i −0.0806780 0.399529i
\(162\) 9.94811 + 9.28060i 0.781598 + 0.729153i
\(163\) −6.23594 + 23.2728i −0.488436 + 1.82287i 0.0756252 + 0.997136i \(0.475905\pi\)
−0.564061 + 0.825733i \(0.690762\pi\)
\(164\) 0.131558 0.227866i 0.0102730 0.0177933i
\(165\) −0.298547 + 3.52774i −0.0232419 + 0.274634i
\(166\) −2.54508 4.40821i −0.197537 0.342144i
\(167\) −4.98846 4.98846i −0.386018 0.386018i 0.487246 0.873265i \(-0.338001\pi\)
−0.873265 + 0.487246i \(0.838001\pi\)
\(168\) 7.93559 + 8.84019i 0.612244 + 0.682036i
\(169\) 5.96958i 0.459199i
\(170\) 2.35235 3.31812i 0.180417 0.254488i
\(171\) 18.0363 + 10.0001i 1.37927 + 0.764729i
\(172\) 0.501860 + 1.87297i 0.0382665 + 0.142813i
\(173\) −23.2450 6.22848i −1.76728 0.473543i −0.779112 0.626885i \(-0.784330\pi\)
−0.988173 + 0.153342i \(0.950996\pi\)
\(174\) 4.99672 5.08418i 0.378800 0.385430i
\(175\) 9.23129 9.47540i 0.697820 0.716273i
\(176\) 4.10341i 0.309306i
\(177\) −14.7459 + 8.68497i −1.10837 + 0.652802i
\(178\) 16.4917 4.41893i 1.23610 0.331213i
\(179\) −2.55927 + 4.43279i −0.191289 + 0.331322i −0.945678 0.325106i \(-0.894600\pi\)
0.754389 + 0.656428i \(0.227933\pi\)
\(180\) −1.07892 + 1.57926i −0.0804182 + 0.117711i
\(181\) −1.77024 −0.131581 −0.0657906 0.997833i \(-0.520957\pi\)
−0.0657906 + 0.997833i \(0.520957\pi\)
\(182\) −14.5117 9.63558i −1.07568 0.714237i
\(183\) −0.0160456 1.84957i −0.00118613 0.136724i
\(184\) 4.38844 2.53367i 0.323520 0.186784i
\(185\) 1.14515 + 1.38102i 0.0841930 + 0.101535i
\(186\) −3.24165 11.6913i −0.237689 0.857251i
\(187\) −1.06247 0.284689i −0.0776957 0.0208185i
\(188\) 2.11309 2.11309i 0.154113 0.154113i
\(189\) −12.1489 + 6.43457i −0.883704 + 0.468046i
\(190\) −8.07466 + 21.7885i −0.585797 + 1.58070i
\(191\) −7.94932 + 4.58954i −0.575193 + 0.332088i −0.759221 0.650833i \(-0.774420\pi\)
0.184028 + 0.982921i \(0.441086\pi\)
\(192\) −5.59345 + 9.88521i −0.403673 + 0.713404i
\(193\) 6.85235 1.83608i 0.493243 0.132164i −0.00361952 0.999993i \(-0.501152\pi\)
0.496862 + 0.867829i \(0.334485\pi\)
\(194\) 1.69748 + 2.94012i 0.121872 + 0.211088i
\(195\) −5.72431 + 15.8674i −0.409927 + 1.13629i
\(196\) 1.83943 0.774462i 0.131388 0.0553187i
\(197\) 12.5538 + 12.5538i 0.894420 + 0.894420i 0.994935 0.100516i \(-0.0320493\pi\)
−0.100516 + 0.994935i \(0.532049\pi\)
\(198\) 4.02225 + 1.00330i 0.285849 + 0.0713014i
\(199\) −14.9099 8.60825i −1.05694 0.610222i −0.132353 0.991203i \(-0.542253\pi\)
−0.924583 + 0.380980i \(0.875587\pi\)
\(200\) 11.6825 + 5.61455i 0.826075 + 0.397008i
\(201\) −3.06913 + 11.8649i −0.216480 + 0.836887i
\(202\) 4.96543 4.96543i 0.349367 0.349367i
\(203\) 3.20471 + 6.45121i 0.224926 + 0.452786i
\(204\) −0.423816 0.416526i −0.0296731 0.0291626i
\(205\) 1.19343 1.68341i 0.0833531 0.117574i
\(206\) 13.7861 + 7.95943i 0.960526 + 0.554560i
\(207\) 1.61582 + 5.63724i 0.112308 + 0.391815i
\(208\) 5.06022 18.8850i 0.350863 1.30944i
\(209\) 6.28395 0.434670
\(210\) −9.23092 12.4389i −0.636994 0.858369i
\(211\) −9.75343 −0.671454 −0.335727 0.941959i \(-0.608982\pi\)
−0.335727 + 0.941959i \(0.608982\pi\)
\(212\) 0.813891 3.03748i 0.0558982 0.208615i
\(213\) 0.475757 0.840797i 0.0325983 0.0576105i
\(214\) −8.28303 4.78221i −0.566216 0.326905i
\(215\) 2.55325 + 14.9913i 0.174131 + 1.02240i
\(216\) −9.76943 9.27371i −0.664725 0.630996i
\(217\) 12.2358 + 0.766300i 0.830620 + 0.0520198i
\(218\) 9.21299 9.21299i 0.623982 0.623982i
\(219\) −3.65504 0.945459i −0.246985 0.0638882i
\(220\) −0.0541804 + 0.580261i −0.00365284 + 0.0391212i
\(221\) −4.53872 2.62043i −0.305307 0.176269i
\(222\) 1.81007 1.06609i 0.121484 0.0715512i
\(223\) 9.17286 + 9.17286i 0.614260 + 0.614260i 0.944053 0.329793i \(-0.106979\pi\)
−0.329793 + 0.944053i \(0.606979\pi\)
\(224\) 2.80232 + 3.17678i 0.187238 + 0.212258i
\(225\) −9.57641 + 11.5452i −0.638427 + 0.769682i
\(226\) 7.95456 + 13.7777i 0.529129 + 0.916479i
\(227\) −23.2222 + 6.22238i −1.54131 + 0.412994i −0.926690 0.375826i \(-0.877359\pi\)
−0.614624 + 0.788820i \(0.710692\pi\)
\(228\) 2.95461 + 1.67184i 0.195674 + 0.110720i
\(229\) −2.82056 + 1.62845i −0.186388 + 0.107611i −0.590290 0.807191i \(-0.700987\pi\)
0.403903 + 0.914802i \(0.367653\pi\)
\(230\) −6.00453 + 2.75741i −0.395927 + 0.181818i
\(231\) −2.28680 + 3.50974i −0.150460 + 0.230924i
\(232\) −4.99068 + 4.99068i −0.327654 + 0.327654i
\(233\) 16.1105 + 4.31679i 1.05543 + 0.282802i 0.744495 0.667628i \(-0.232690\pi\)
0.310938 + 0.950430i \(0.399357\pi\)
\(234\) 17.2742 + 9.57759i 1.12925 + 0.626107i
\(235\) 18.0411 14.9597i 1.17687 0.975864i
\(236\) −2.43967 + 1.40854i −0.158809 + 0.0916883i
\(237\) −5.24987 + 0.0455445i −0.341016 + 0.00295843i
\(238\) 4.31006 2.14107i 0.279380 0.138785i
\(239\) −15.1824 −0.982070 −0.491035 0.871140i \(-0.663381\pi\)
−0.491035 + 0.871140i \(0.663381\pi\)
\(240\) 9.93150 14.2697i 0.641075 0.921105i
\(241\) −0.0593822 + 0.102853i −0.00382515 + 0.00662535i −0.867932 0.496684i \(-0.834551\pi\)
0.864106 + 0.503309i \(0.167884\pi\)
\(242\) −14.8416 + 3.97678i −0.954052 + 0.255637i
\(243\) 13.1493 8.37229i 0.843530 0.537082i
\(244\) 0.304473i 0.0194919i
\(245\) 14.9282 4.70637i 0.953725 0.300679i
\(246\) −1.72330 1.69365i −0.109873 0.107983i
\(247\) 28.9204 + 7.74921i 1.84016 + 0.493070i
\(248\) 3.10898 + 11.6029i 0.197420 + 0.736783i
\(249\) −5.62024 + 1.55832i −0.356168 + 0.0987544i
\(250\) −14.4864 8.70538i −0.916201 0.550577i
\(251\) 16.8255i 1.06202i 0.847367 + 0.531008i \(0.178187\pi\)
−0.847367 + 0.531008i \(0.821813\pi\)
\(252\) −2.00898 + 1.04182i −0.126554 + 0.0656285i
\(253\) 1.26350 + 1.26350i 0.0794358 + 0.0794358i
\(254\) 4.73413 + 8.19975i 0.297046 + 0.514498i
\(255\) −3.00574 3.56152i −0.188227 0.223031i
\(256\) −3.35517 + 5.81133i −0.209698 + 0.363208i
\(257\) 3.60198 13.4428i 0.224686 0.838538i −0.757845 0.652435i \(-0.773748\pi\)
0.982530 0.186103i \(-0.0595858\pi\)
\(258\) 17.8058 0.154472i 1.10854 0.00961699i
\(259\) 0.420170 + 2.08074i 0.0261081 + 0.129291i
\(260\) −0.964916 + 2.60371i −0.0598416 + 0.161475i
\(261\) −4.20602 7.00163i −0.260346 0.433390i
\(262\) −3.33074 12.4305i −0.205774 0.767958i
\(263\) −5.56707 20.7766i −0.343280 1.28114i −0.894608 0.446851i \(-0.852545\pi\)
0.551328 0.834288i \(-0.314121\pi\)
\(264\) −3.97362 1.02787i −0.244559 0.0632607i
\(265\) 8.57007 23.1253i 0.526455 1.42057i
\(266\) −20.6182 + 18.1879i −1.26419 + 1.11517i
\(267\) −0.169706 19.5619i −0.0103859 1.19717i
\(268\) −0.522141 + 1.94866i −0.0318948 + 0.119033i
\(269\) 9.44119 16.3526i 0.575639 0.997036i −0.420333 0.907370i \(-0.638087\pi\)
0.995972 0.0896663i \(-0.0285801\pi\)
\(270\) 11.5592 + 13.2241i 0.703470 + 0.804791i
\(271\) 1.85591 + 3.21453i 0.112739 + 0.195269i 0.916874 0.399178i \(-0.130704\pi\)
−0.804135 + 0.594447i \(0.797371\pi\)
\(272\) 3.81947 + 3.81947i 0.231589 + 0.231589i
\(273\) −14.8526 + 13.3327i −0.898919 + 0.806934i
\(274\) 15.6193i 0.943597i
\(275\) −0.846153 + 4.49157i −0.0510249 + 0.270852i
\(276\) 0.257925 + 0.930232i 0.0155252 + 0.0559934i
\(277\) 1.95709 + 7.30397i 0.117590 + 0.438853i 0.999468 0.0326260i \(-0.0103870\pi\)
−0.881877 + 0.471479i \(0.843720\pi\)
\(278\) 4.43225 + 1.18762i 0.265829 + 0.0712286i
\(279\) −13.8992 + 0.241178i −0.832122 + 0.0144390i
\(280\) 9.03224 + 12.3945i 0.539780 + 0.740712i
\(281\) 12.0546i 0.719117i −0.933122 0.359559i \(-0.882927\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(282\) −13.9269 23.6460i −0.829335 1.40810i
\(283\) 23.1952 6.21514i 1.37881 0.369452i 0.508123 0.861285i \(-0.330340\pi\)
0.870690 + 0.491833i \(0.163673\pi\)
\(284\) 0.0795132 0.137721i 0.00471824 0.00817224i
\(285\) 21.8526 + 15.2091i 1.29444 + 0.900908i
\(286\) 6.01844 0.355878
\(287\) 2.18666 1.08625i 0.129074 0.0641190i
\(288\) −3.45489 3.33704i −0.203581 0.196637i
\(289\) −13.4685 + 7.77604i −0.792264 + 0.457414i
\(290\) 7.08424 5.87427i 0.416001 0.344949i
\(291\) 3.74850 1.03934i 0.219741 0.0609273i
\(292\) −0.600292 0.160848i −0.0351295 0.00941291i
\(293\) 12.2498 12.2498i 0.715644 0.715644i −0.252066 0.967710i \(-0.581110\pi\)
0.967710 + 0.252066i \(0.0811101\pi\)
\(294\) −2.65518 18.1346i −0.154853 1.05763i
\(295\) −20.0775 + 9.22004i −1.16896 + 0.536812i
\(296\) −1.80122 + 1.03994i −0.104694 + 0.0604450i
\(297\) 2.26709 4.17392i 0.131550 0.242196i
\(298\) −18.8069 + 5.03930i −1.08946 + 0.291919i
\(299\) 4.25687 + 7.37311i 0.246181 + 0.426398i
\(300\) −1.59282 + 1.88674i −0.0919617 + 0.108931i
\(301\) −5.73428 + 17.0552i −0.330518 + 0.983045i
\(302\) 12.7187 + 12.7187i 0.731877 + 0.731877i
\(303\) −4.08328 6.93285i −0.234578 0.398282i
\(304\) −26.7243 15.4293i −1.53275 0.884931i
\(305\) 0.221995 2.37753i 0.0127114 0.136137i
\(306\) −4.67780 + 2.81005i −0.267412 + 0.160640i
\(307\) −12.5028 + 12.5028i −0.713571 + 0.713571i −0.967280 0.253709i \(-0.918349\pi\)
0.253709 + 0.967280i \(0.418349\pi\)
\(308\) −0.381433 + 0.574459i −0.0217342 + 0.0327328i
\(309\) 12.7851 13.0088i 0.727317 0.740047i
\(310\) −2.62977 15.4406i −0.149361 0.876965i
\(311\) −20.2993 11.7198i −1.15107 0.664569i −0.201920 0.979402i \(-0.564718\pi\)
−0.949147 + 0.314833i \(0.898051\pi\)
\(312\) −17.0201 9.63067i −0.963574 0.545229i
\(313\) −2.74353 + 10.2390i −0.155073 + 0.578742i 0.844026 + 0.536303i \(0.180179\pi\)
−0.999099 + 0.0424390i \(0.986487\pi\)
\(314\) −21.0309 −1.18684
\(315\) −16.4470 + 6.67046i −0.926686 + 0.375838i
\(316\) −0.864226 −0.0486165
\(317\) −5.31686 + 19.8428i −0.298625 + 1.11448i 0.639671 + 0.768649i \(0.279071\pi\)
−0.938296 + 0.345834i \(0.887596\pi\)
\(318\) −25.1331 14.2213i −1.40939 0.797492i
\(319\) −2.15535 1.24439i −0.120676 0.0696724i
\(320\) −8.48037 + 11.9620i −0.474067 + 0.668698i
\(321\) −7.68156 + 7.81601i −0.428743 + 0.436247i
\(322\) −7.80269 0.488665i −0.434827 0.0272322i
\(323\) −5.84912 + 5.84912i −0.325454 + 0.325454i
\(324\) 2.17642 1.35935i 0.120912 0.0755196i
\(325\) −9.43311 + 19.6279i −0.523255 + 1.08876i
\(326\) 31.5421 + 18.2108i 1.74695 + 1.00860i
\(327\) −7.57622 12.8634i −0.418966 0.711347i
\(328\) 1.69160 + 1.69160i 0.0934032 + 0.0934032i
\(329\) 27.1819 5.48891i 1.49858 0.302613i
\(330\) 5.03423 + 1.81614i 0.277125 + 0.0999752i
\(331\) −15.9659 27.6537i −0.877564 1.51998i −0.854007 0.520262i \(-0.825834\pi\)
−0.0235570 0.999722i \(-0.507499\pi\)
\(332\) −0.927351 + 0.248483i −0.0508950 + 0.0136373i
\(333\) −0.663210 2.31379i −0.0363437 0.126795i
\(334\) −9.23562 + 5.33219i −0.505351 + 0.291764i
\(335\) −5.49802 + 14.8357i −0.300389 + 0.810561i
\(336\) 18.3429 9.31129i 1.00069 0.507973i
\(337\) 9.40161 9.40161i 0.512139 0.512139i −0.403043 0.915181i \(-0.632047\pi\)
0.915181 + 0.403043i \(0.132047\pi\)
\(338\) 8.71650 + 2.33558i 0.474115 + 0.127039i
\(339\) 17.5659 4.87047i 0.954046 0.264527i
\(340\) −0.489678 0.590541i −0.0265565 0.0320266i
\(341\) −3.66830 + 2.11789i −0.198649 + 0.114690i
\(342\) 21.6584 22.4233i 1.17115 1.21251i
\(343\) 18.1952 + 3.45475i 0.982448 + 0.186539i
\(344\) −17.6300 −0.950546
\(345\) 1.33580 + 7.45193i 0.0719172 + 0.401199i
\(346\) −18.1891 + 31.5044i −0.977850 + 1.69369i
\(347\) 15.5354 4.16271i 0.833986 0.223466i 0.183534 0.983013i \(-0.441246\pi\)
0.650452 + 0.759547i \(0.274579\pi\)
\(348\) −0.682339 1.15852i −0.0365772 0.0621031i
\(349\) 9.21013i 0.493007i 0.969142 + 0.246503i \(0.0792817\pi\)
−0.969142 + 0.246503i \(0.920718\pi\)
\(350\) −10.2238 17.1863i −0.546486 0.918647i
\(351\) 15.5809 16.4138i 0.831649 0.876104i
\(352\) −1.41373 0.378808i −0.0753521 0.0201905i
\(353\) −2.70409 10.0918i −0.143924 0.537133i −0.999801 0.0199530i \(-0.993648\pi\)
0.855876 0.517180i \(-0.173018\pi\)
\(354\) 6.91210 + 24.9292i 0.367374 + 1.32497i
\(355\) 0.721307 1.01744i 0.0382830 0.0540003i
\(356\) 3.22025i 0.170673i
\(357\) −1.13832 5.39544i −0.0602461 0.285557i
\(358\) 5.47124 + 5.47124i 0.289164 + 0.289164i
\(359\) −0.770883 1.33521i −0.0406857 0.0704697i 0.844965 0.534821i \(-0.179621\pi\)
−0.885651 + 0.464351i \(0.846288\pi\)
\(360\) −11.3306 13.1918i −0.597175 0.695268i
\(361\) 14.1284 24.4711i 0.743601 1.28795i
\(362\) −0.692602 + 2.58482i −0.0364023 + 0.135855i
\(363\) 0.152726 + 17.6046i 0.00801603 + 0.924001i
\(364\) −2.46387 + 2.17344i −0.129142 + 0.113919i
\(365\) −4.57021 1.69369i −0.239216 0.0886517i
\(366\) −2.70693 0.700207i −0.141493 0.0366004i
\(367\) 4.15004 + 15.4881i 0.216630 + 0.808475i 0.985586 + 0.169173i \(0.0541097\pi\)
−0.768956 + 0.639301i \(0.779224\pi\)
\(368\) −2.27107 8.47576i −0.118388 0.441830i
\(369\) −2.37322 + 1.42564i −0.123545 + 0.0742161i
\(370\) 2.46454 1.13177i 0.128125 0.0588379i
\(371\) 21.8833 19.3038i 1.13612 1.00220i
\(372\) −2.28823 + 0.0198512i −0.118639 + 0.00102924i
\(373\) 7.26294 27.1057i 0.376061 1.40348i −0.475728 0.879592i \(-0.657815\pi\)
0.851789 0.523885i \(-0.175518\pi\)
\(374\) −0.831378 + 1.43999i −0.0429895 + 0.0744600i
\(375\) −13.8135 + 13.5716i −0.713325 + 0.700834i
\(376\) 13.5853 + 23.5304i 0.700606 + 1.21349i
\(377\) −8.38493 8.38493i −0.431846 0.431846i
\(378\) 4.64222 + 20.2568i 0.238770 + 1.04190i
\(379\) 18.6208i 0.956485i −0.878228 0.478243i \(-0.841274\pi\)
0.878228 0.478243i \(-0.158726\pi\)
\(380\) 3.57535 + 2.53471i 0.183412 + 0.130028i
\(381\) 10.4543 2.89864i 0.535588 0.148502i
\(382\) 3.59129 + 13.4029i 0.183746 + 0.685750i
\(383\) 15.6655 + 4.19755i 0.800469 + 0.214485i 0.635790 0.771862i \(-0.280674\pi\)
0.164679 + 0.986347i \(0.447341\pi\)
\(384\) 16.2013 + 15.9226i 0.826768 + 0.812546i
\(385\) −3.39733 + 4.20765i −0.173144 + 0.214442i
\(386\) 10.7238i 0.545828i
\(387\) 4.93787 19.7960i 0.251006 1.00629i
\(388\) 0.618510 0.165729i 0.0314001 0.00841362i
\(389\) −16.7445 + 29.0023i −0.848980 + 1.47048i 0.0331402 + 0.999451i \(0.489449\pi\)
−0.882120 + 0.471025i \(0.843884\pi\)
\(390\) 20.9293 + 14.5664i 1.05979 + 0.737601i
\(391\) −2.35215 −0.118953
\(392\) 2.47300 + 17.9769i 0.124906 + 0.907973i
\(393\) −14.7447 + 0.127915i −0.743769 + 0.00645246i
\(394\) 23.2420 13.4188i 1.17092 0.676029i
\(395\) −6.74845 0.630119i −0.339552 0.0317047i
\(396\) 0.379138 0.683816i 0.0190524 0.0343631i
\(397\) −10.2680 2.75129i −0.515335 0.138084i −0.00822688 0.999966i \(-0.502619\pi\)
−0.507108 + 0.861883i \(0.669285\pi\)
\(398\) −18.4028 + 18.4028i −0.922449 + 0.922449i
\(399\) 14.2593 + 28.0903i 0.713858 + 1.40627i
\(400\) 14.6269 17.0241i 0.731344 0.851204i
\(401\) 33.3226 19.2388i 1.66405 0.960741i 0.693304 0.720646i \(-0.256155\pi\)
0.970749 0.240096i \(-0.0771788\pi\)
\(402\) 16.1238 + 9.12350i 0.804182 + 0.455039i
\(403\) −19.4942 + 5.22346i −0.971076 + 0.260199i
\(404\) −0.662233 1.14702i −0.0329473 0.0570664i
\(405\) 17.9860 9.02788i 0.893733 0.448599i
\(406\) 10.6736 2.15535i 0.529721 0.106968i
\(407\) −0.518601 0.518601i −0.0257061 0.0257061i
\(408\) 4.65539 2.74191i 0.230476 0.135745i
\(409\) 0.838832 + 0.484300i 0.0414776 + 0.0239471i 0.520595 0.853804i \(-0.325710\pi\)
−0.479118 + 0.877751i \(0.659043\pi\)
\(410\) −1.99110 2.40122i −0.0983335 0.118588i
\(411\) −17.3262 4.48182i −0.854640 0.221072i
\(412\) 2.12308 2.12308i 0.104597 0.104597i
\(413\) −26.0901 1.63396i −1.28381 0.0804021i
\(414\) 8.86342 0.153798i 0.435613 0.00755876i
\(415\) −7.42255 + 1.26418i −0.364359 + 0.0620560i
\(416\) −6.03923 3.48675i −0.296098 0.170952i
\(417\) 2.58920 4.57584i 0.126794 0.224080i
\(418\) 2.45857 9.17553i 0.120253 0.448790i
\(419\) −24.3482 −1.18949 −0.594743 0.803916i \(-0.702746\pi\)
−0.594743 + 0.803916i \(0.702746\pi\)
\(420\) −2.71681 + 1.07451i −0.132567 + 0.0524308i
\(421\) 1.75923 0.0857395 0.0428698 0.999081i \(-0.486350\pi\)
0.0428698 + 0.999081i \(0.486350\pi\)
\(422\) −3.81600 + 14.2415i −0.185760 + 0.693265i
\(423\) −30.2263 + 8.66388i −1.46965 + 0.421252i
\(424\) 24.7609 + 14.2957i 1.20249 + 0.694261i
\(425\) −3.39316 4.96837i −0.164593 0.241001i
\(426\) −1.04155 1.02364i −0.0504634 0.0495954i
\(427\) 1.56286 2.35375i 0.0756322 0.113906i
\(428\) −1.27559 + 1.27559i −0.0616581 + 0.0616581i
\(429\) 1.72694 6.67615i 0.0833773 0.322327i
\(430\) 22.8885 + 2.13716i 1.10378 + 0.103063i
\(431\) −18.5687 10.7206i −0.894422 0.516395i −0.0190357 0.999819i \(-0.506060\pi\)
−0.875386 + 0.483424i \(0.839393\pi\)
\(432\) −19.8899 + 12.1843i −0.956954 + 0.586219i
\(433\) −26.8036 26.8036i −1.28810 1.28810i −0.935940 0.352161i \(-0.885447\pi\)
−0.352161 0.935940i \(-0.614553\pi\)
\(434\) 5.90612 17.5663i 0.283503 0.843209i
\(435\) −4.48347 9.54399i −0.214966 0.457599i
\(436\) −1.22872 2.12821i −0.0588452 0.101923i
\(437\) 12.9798 3.47792i 0.620907 0.166371i
\(438\) −2.81054 + 4.96701i −0.134293 + 0.237333i
\(439\) 2.05458 1.18621i 0.0980598 0.0566149i −0.450168 0.892944i \(-0.648636\pi\)
0.548228 + 0.836329i \(0.315303\pi\)
\(440\) −4.96855 1.84131i −0.236866 0.0877810i
\(441\) −20.8782 2.25820i −0.994201 0.107534i
\(442\) −5.60198 + 5.60198i −0.266459 + 0.266459i
\(443\) 21.0154 + 5.63107i 0.998473 + 0.267540i 0.720806 0.693137i \(-0.243772\pi\)
0.277668 + 0.960677i \(0.410439\pi\)
\(444\) −0.105864 0.381811i −0.00502410 0.0181199i
\(445\) 2.34793 25.1459i 0.111303 1.19203i
\(446\) 16.9826 9.80492i 0.804150 0.464276i
\(447\) 0.193531 + 22.3082i 0.00915372 + 1.05514i
\(448\) −15.5381 + 7.71870i −0.734104 + 0.364674i
\(449\) 28.8886 1.36334 0.681669 0.731661i \(-0.261254\pi\)
0.681669 + 0.731661i \(0.261254\pi\)
\(450\) 13.1111 + 18.5000i 0.618061 + 0.872100i
\(451\) −0.421789 + 0.730561i −0.0198613 + 0.0344008i
\(452\) 2.89840 0.776625i 0.136329 0.0365293i
\(453\) 17.7581 10.4591i 0.834348 0.491411i
\(454\) 36.3425i 1.70564i
\(455\) −20.8242 + 15.1752i −0.976253 + 0.711427i
\(456\) −21.6355 + 22.0141i −1.01317 + 1.03091i
\(457\) 1.89885 + 0.508794i 0.0888242 + 0.0238004i 0.302957 0.953004i \(-0.402026\pi\)
−0.214133 + 0.976804i \(0.568693\pi\)
\(458\) 1.27425 + 4.75557i 0.0595419 + 0.222213i
\(459\) 1.77489 + 5.99532i 0.0828446 + 0.279838i
\(460\) 0.209240 + 1.22854i 0.00975586 + 0.0572810i
\(461\) 17.4281i 0.811709i 0.913938 + 0.405854i \(0.133026\pi\)
−0.913938 + 0.405854i \(0.866974\pi\)
\(462\) 4.23005 + 4.71225i 0.196800 + 0.219234i
\(463\) 14.8405 + 14.8405i 0.689698 + 0.689698i 0.962165 0.272467i \(-0.0878395\pi\)
−0.272467 + 0.962165i \(0.587840\pi\)
\(464\) 6.11082 + 10.5843i 0.283688 + 0.491362i
\(465\) −17.8825 1.51337i −0.829283 0.0701809i
\(466\) 12.6063 21.8348i 0.583977 1.01148i
\(467\) 3.26272 12.1766i 0.150981 0.563468i −0.848435 0.529299i \(-0.822455\pi\)
0.999416 0.0341687i \(-0.0108784\pi\)
\(468\) 2.58816 2.67956i 0.119638 0.123863i
\(469\) −14.0389 + 12.3841i −0.648257 + 0.571845i
\(470\) −14.7849 32.1956i −0.681978 1.48507i
\(471\) −6.03462 + 23.3292i −0.278061 + 1.07495i
\(472\) −6.62921 24.7405i −0.305134 1.13878i
\(473\) −1.60902 6.00493i −0.0739827 0.276107i
\(474\) −1.98749 + 7.68343i −0.0912885 + 0.352911i
\(475\) 26.0707 + 22.3996i 1.19620 + 1.02776i
\(476\) −0.179669 0.889748i −0.00823512 0.0407815i
\(477\) −22.9872 + 23.7990i −1.05251 + 1.08968i
\(478\) −5.94008 + 22.1687i −0.271693 + 1.01397i
\(479\) −5.14393 + 8.90955i −0.235032 + 0.407088i −0.959282 0.282450i \(-0.908853\pi\)
0.724250 + 0.689538i \(0.242186\pi\)
\(480\) −3.99945 4.73897i −0.182549 0.216304i
\(481\) −1.74722 3.02627i −0.0796662 0.137986i
\(482\) 0.126948 + 0.126948i 0.00578232 + 0.00578232i
\(483\) −2.78098 + 8.51517i −0.126539 + 0.387454i
\(484\) 2.89804i 0.131729i
\(485\) 4.95057 0.843160i 0.224794 0.0382859i
\(486\) −7.08018 22.4756i −0.321163 1.01952i
\(487\) 4.82573 + 18.0099i 0.218675 + 0.816105i 0.984841 + 0.173462i \(0.0554954\pi\)
−0.766166 + 0.642643i \(0.777838\pi\)
\(488\) 2.67398 + 0.716491i 0.121045 + 0.0324340i
\(489\) 29.2517 29.7637i 1.32281 1.34596i
\(490\) −1.03142 23.6387i −0.0465947 1.06789i
\(491\) 24.6940i 1.11442i 0.830370 + 0.557212i \(0.188129\pi\)
−0.830370 + 0.557212i \(0.811871\pi\)
\(492\) −0.392683 + 0.231281i −0.0177035 + 0.0104269i
\(493\) 3.16448 0.847921i 0.142521 0.0381884i
\(494\) 22.6300 39.1964i 1.01817 1.76353i
\(495\) 3.45914 5.06326i 0.155477 0.227577i
\(496\) 20.8007 0.933977
\(497\) 1.32161 0.656522i 0.0592821 0.0294490i
\(498\) 0.0764827 + 8.81609i 0.00342727 + 0.395058i
\(499\) −11.1524 + 6.43883i −0.499249 + 0.288242i −0.728403 0.685148i \(-0.759737\pi\)
0.229154 + 0.973390i \(0.426404\pi\)
\(500\) −2.29316 + 2.21424i −0.102553 + 0.0990239i
\(501\) 3.26482 + 11.7749i 0.145862 + 0.526065i
\(502\) 24.5678 + 6.58292i 1.09651 + 0.293810i
\(503\) 2.81929 2.81929i 0.125706 0.125706i −0.641455 0.767161i \(-0.721669\pi\)
0.767161 + 0.641455i \(0.221669\pi\)
\(504\) −4.42205 20.0951i −0.196974 0.895107i
\(505\) −4.33485 9.43955i −0.192898 0.420055i
\(506\) 2.33925 1.35057i 0.103992 0.0600400i
\(507\) 5.09194 8.99888i 0.226141 0.399654i
\(508\) 1.72497 0.462205i 0.0765333 0.0205070i
\(509\) −20.2795 35.1250i −0.898871 1.55689i −0.828939 0.559338i \(-0.811055\pi\)
−0.0699315 0.997552i \(-0.522278\pi\)
\(510\) −6.37635 + 2.99541i −0.282349 + 0.132639i
\(511\) −3.81498 4.32475i −0.168765 0.191316i
\(512\) −11.3747 11.3747i −0.502695 0.502695i
\(513\) −18.6591 30.4594i −0.823818 1.34481i
\(514\) −18.2192 10.5189i −0.803616 0.463968i
\(515\) 18.1264 15.0304i 0.798743 0.662321i
\(516\) 0.841073 3.25150i 0.0370262 0.143139i
\(517\) −6.77477 + 6.77477i −0.297954 + 0.297954i
\(518\) 3.20259 + 0.200571i 0.140714 + 0.00881258i
\(519\) 29.7281 + 29.2167i 1.30492 + 1.28247i
\(520\) −20.5959 14.6013i −0.903191 0.640309i
\(521\) −13.7175 7.91980i −0.600974 0.346973i 0.168451 0.985710i \(-0.446124\pi\)
−0.769425 + 0.638738i \(0.779457\pi\)
\(522\) −11.8690 + 3.40207i −0.519494 + 0.148905i
\(523\) 3.48603 13.0100i 0.152433 0.568889i −0.846878 0.531787i \(-0.821521\pi\)
0.999311 0.0371021i \(-0.0118127\pi\)
\(524\) −2.42724 −0.106035
\(525\) −21.9981 + 6.40964i −0.960076 + 0.279740i
\(526\) −32.5151 −1.41772
\(527\) 1.44312 5.38580i 0.0628633 0.234609i
\(528\) −3.50013 + 6.18571i −0.152323 + 0.269198i
\(529\) −16.6095 9.58948i −0.722151 0.416934i
\(530\) −30.4134 21.5613i −1.32107 0.936562i
\(531\) 29.6369 0.514259i 1.28613 0.0223170i
\(532\) 2.30706 + 4.64420i 0.100024 + 0.201352i
\(533\) −2.84210 + 2.84210i −0.123105 + 0.123105i
\(534\) −28.6298 7.40573i −1.23893 0.320477i
\(535\) −10.8907 + 9.03063i −0.470848 + 0.390428i
\(536\) −15.8850 9.17122i −0.686128 0.396136i
\(537\) 7.63908 4.49923i 0.329650 0.194156i
\(538\) −20.1835 20.1835i −0.870171 0.870171i
\(539\) −5.89740 + 2.48301i −0.254019 + 0.106951i
\(540\) 2.97350 1.46036i 0.127959 0.0628439i
\(541\) 15.9766 + 27.6722i 0.686887 + 1.18972i 0.972840 + 0.231479i \(0.0743565\pi\)
−0.285953 + 0.958244i \(0.592310\pi\)
\(542\) 5.41983 1.45224i 0.232801 0.0623790i
\(543\) 2.66856 + 1.50998i 0.114519 + 0.0647996i
\(544\) 1.66850 0.963310i 0.0715364 0.0413016i
\(545\) −8.04299 17.5144i −0.344524 0.750234i
\(546\) 13.6568 + 26.9034i 0.584457 + 1.15136i
\(547\) 24.7307 24.7307i 1.05741 1.05741i 0.0591593 0.998249i \(-0.481158\pi\)
0.998249 0.0591593i \(-0.0188420\pi\)
\(548\) −2.84560 0.762477i −0.121558 0.0325714i
\(549\) −1.55346 + 2.80183i −0.0662999 + 0.119579i
\(550\) 6.22731 + 2.99282i 0.265534 + 0.127614i
\(551\) −16.2087 + 9.35811i −0.690515 + 0.398669i
\(552\) −8.77655 + 0.0761397i −0.373555 + 0.00324072i
\(553\) −6.68097 4.43608i −0.284104 0.188641i
\(554\) 11.4306 0.485640
\(555\) −0.548276 3.05862i −0.0232730 0.129831i
\(556\) 0.432732 0.749514i 0.0183519 0.0317865i
\(557\) 3.74061 1.00229i 0.158495 0.0424686i −0.178699 0.983904i \(-0.557189\pi\)
0.337194 + 0.941435i \(0.390522\pi\)
\(558\) −5.08584 + 20.3893i −0.215301 + 0.863146i
\(559\) 29.6205i 1.25281i
\(560\) 24.7794 9.55263i 1.04712 0.403672i
\(561\) 1.35880 + 1.33542i 0.0573685 + 0.0563817i
\(562\) −17.6016 4.71632i −0.742477 0.198946i
\(563\) 9.46140 + 35.3104i 0.398751 + 1.48816i 0.815297 + 0.579043i \(0.196574\pi\)
−0.416547 + 0.909114i \(0.636760\pi\)
\(564\) −4.98780 + 1.38296i −0.210024 + 0.0582333i
\(565\) 23.1989 3.95114i 0.975986 0.166226i
\(566\) 36.3002i 1.52581i
\(567\) 23.8025 + 0.662966i 0.999612 + 0.0278419i
\(568\) 1.02240 + 1.02240i 0.0428989 + 0.0428989i
\(569\) 8.11965 + 14.0636i 0.340393 + 0.589579i 0.984506 0.175352i \(-0.0561064\pi\)
−0.644112 + 0.764931i \(0.722773\pi\)
\(570\) 30.7573 25.9576i 1.28828 1.08725i
\(571\) −20.1402 + 34.8839i −0.842843 + 1.45985i 0.0446382 + 0.999003i \(0.485786\pi\)
−0.887481 + 0.460844i \(0.847547\pi\)
\(572\) 0.293798 1.09647i 0.0122843 0.0458457i
\(573\) 15.8980 0.137921i 0.664151 0.00576174i
\(574\) −0.730561 3.61784i −0.0304930 0.151006i
\(575\) 0.738139 + 9.74583i 0.0307825 + 0.406429i
\(576\) 16.8638 10.1304i 0.702657 0.422101i
\(577\) 4.47305 + 16.6936i 0.186215 + 0.694965i 0.994367 + 0.105991i \(0.0338014\pi\)
−0.808152 + 0.588974i \(0.799532\pi\)
\(578\) 6.08469 + 22.7084i 0.253090 + 0.944544i
\(579\) −11.8958 3.07710i −0.494371 0.127880i
\(580\) −0.724378 1.57740i −0.0300781 0.0654980i
\(581\) −8.44443 2.83918i −0.350334 0.117789i
\(582\) −0.0510111 5.88001i −0.00211448 0.243734i
\(583\) −2.60942 + 9.73848i −0.108071 + 0.403327i
\(584\) 2.82524 4.89345i 0.116909 0.202492i
\(585\) 22.1638 19.0368i 0.916359 0.787073i
\(586\) −13.0939 22.6793i −0.540905 0.936875i
\(587\) 0.596922 + 0.596922i 0.0246376 + 0.0246376i 0.719318 0.694681i \(-0.244454\pi\)
−0.694681 + 0.719318i \(0.744454\pi\)
\(588\) −3.43346 0.401529i −0.141594 0.0165588i
\(589\) 31.8541i 1.31253i
\(590\) 5.60740 + 32.9236i 0.230853 + 1.35544i
\(591\) −8.21615 29.6324i −0.337967 1.21891i
\(592\) 0.932155 + 3.47885i 0.0383113 + 0.142980i
\(593\) −9.06443 2.42881i −0.372232 0.0997391i 0.0678534 0.997695i \(-0.478385\pi\)
−0.440085 + 0.897956i \(0.645052\pi\)
\(594\) −5.20757 4.94333i −0.213669 0.202827i
\(595\) −0.754250 7.07874i −0.0309212 0.290200i
\(596\) 3.67234i 0.150425i
\(597\) 15.1334 + 25.6944i 0.619368 + 1.05160i
\(598\) 12.4313 3.33097i 0.508355 0.136213i
\(599\) 3.14342 5.44456i 0.128437 0.222459i −0.794634 0.607088i \(-0.792337\pi\)
0.923071 + 0.384629i \(0.125671\pi\)
\(600\) −12.8217 18.4286i −0.523444 0.752344i
\(601\) 9.39584 0.383264 0.191632 0.981467i \(-0.438622\pi\)
0.191632 + 0.981467i \(0.438622\pi\)
\(602\) 22.6597 + 15.0457i 0.923539 + 0.613217i
\(603\) 14.7471 15.2679i 0.600549 0.621759i
\(604\) 2.93803 1.69627i 0.119547 0.0690203i
\(605\) −2.11300 + 22.6298i −0.0859057 + 0.920034i
\(606\) −11.7206 + 3.24976i −0.476116 + 0.132012i
\(607\) −13.6778 3.66495i −0.555164 0.148756i −0.0296803 0.999559i \(-0.509449\pi\)
−0.525484 + 0.850804i \(0.676116\pi\)
\(608\) −7.78287 + 7.78287i −0.315637 + 0.315637i
\(609\) 0.671800 12.4585i 0.0272227 0.504843i
\(610\) −3.38470 1.25435i −0.137042 0.0507870i
\(611\) −39.5338 + 22.8248i −1.59937 + 0.923395i
\(612\) 0.283596 + 0.989401i 0.0114637 + 0.0399942i
\(613\) 4.19289 1.12348i 0.169349 0.0453770i −0.173148 0.984896i \(-0.555394\pi\)
0.342497 + 0.939519i \(0.388727\pi\)
\(614\) 13.3643 + 23.1476i 0.539339 + 0.934162i
\(615\) −3.23496 + 1.51968i −0.130446 + 0.0612796i
\(616\) −4.14749 4.70170i −0.167107 0.189437i
\(617\) 3.80377 + 3.80377i 0.153134 + 0.153134i 0.779516 0.626382i \(-0.215465\pi\)
−0.626382 + 0.779516i \(0.715465\pi\)
\(618\) −13.9928 23.7578i −0.562872 0.955679i
\(619\) 18.8856 + 10.9036i 0.759075 + 0.438252i 0.828964 0.559303i \(-0.188931\pi\)
−0.0698884 + 0.997555i \(0.522264\pi\)
\(620\) −2.94141 0.274647i −0.118130 0.0110301i
\(621\) 2.37267 9.87616i 0.0952120 0.396317i
\(622\) −25.0547 + 25.0547i −1.00460 + 1.00460i
\(623\) 16.5296 24.8944i 0.662243 0.997375i
\(624\) −23.7366 + 24.1520i −0.950224 + 0.966855i
\(625\) −19.5210 + 15.6183i −0.780839 + 0.624732i
\(626\) 13.8771 + 8.01194i 0.554640 + 0.320221i
\(627\) −9.47279 5.36009i −0.378307 0.214061i
\(628\) −1.02665 + 3.83151i −0.0409678 + 0.152894i
\(629\) 0.965431 0.0384943
\(630\) 3.30504 + 26.6250i 0.131676 + 1.06076i
\(631\) 8.91815 0.355026 0.177513 0.984118i \(-0.443195\pi\)
0.177513 + 0.984118i \(0.443195\pi\)
\(632\) 2.03371 7.58991i 0.0808967 0.301911i
\(633\) 14.7029 + 8.31949i 0.584387 + 0.330670i
\(634\) 26.8933 + 15.5268i 1.06807 + 0.616650i
\(635\) 13.8067 2.35151i 0.547904 0.0933167i
\(636\) −3.81782 + 3.88464i −0.151386 + 0.154036i
\(637\) −30.2034 + 4.15494i −1.19670 + 0.164625i
\(638\) −2.66027 + 2.66027i −0.105321 + 0.105321i
\(639\) −1.43437 + 0.861653i −0.0567427 + 0.0340865i
\(640\) 18.7190 + 22.5747i 0.739933 + 0.892343i
\(641\) 33.8421 + 19.5388i 1.33668 + 0.771735i 0.986314 0.164876i \(-0.0527224\pi\)
0.350370 + 0.936611i \(0.386056\pi\)
\(642\) 8.40717 + 14.2742i 0.331805 + 0.563359i
\(643\) 10.9666 + 10.9666i 0.432481 + 0.432481i 0.889471 0.456991i \(-0.151073\pi\)
−0.456991 + 0.889471i \(0.651073\pi\)
\(644\) −0.469926 + 1.39768i −0.0185177 + 0.0550762i
\(645\) 8.93837 24.7766i 0.351948 0.975578i
\(646\) 6.25216 + 10.8291i 0.245988 + 0.426064i
\(647\) −13.9465 + 3.73697i −0.548295 + 0.146915i −0.522324 0.852747i \(-0.674935\pi\)
−0.0259718 + 0.999663i \(0.508268\pi\)
\(648\) 6.81669 + 22.3128i 0.267785 + 0.876531i
\(649\) 7.82182 4.51593i 0.307033 0.177266i
\(650\) 24.9691 + 21.4531i 0.979369 + 0.841461i
\(651\) −17.7913 11.5921i −0.697295 0.454328i
\(652\) 4.85751 4.85751i 0.190235 0.190235i
\(653\) −16.9064 4.53005i −0.661597 0.177274i −0.0876304 0.996153i \(-0.527929\pi\)
−0.573967 + 0.818879i \(0.694596\pi\)
\(654\) −21.7467 + 6.02968i −0.850362 + 0.235779i
\(655\) −18.9535 1.76974i −0.740576 0.0691493i
\(656\) 3.58756 2.07128i 0.140071 0.0808699i
\(657\) 4.70336 + 4.54292i 0.183496 + 0.177236i
\(658\) 2.62017 41.8372i 0.102145 1.63098i
\(659\) 7.49888 0.292115 0.146057 0.989276i \(-0.453342\pi\)
0.146057 + 0.989276i \(0.453342\pi\)
\(660\) 0.576626 0.828504i 0.0224451 0.0322495i
\(661\) 12.8552 22.2658i 0.500008 0.866038i −0.499992 0.866030i \(-0.666664\pi\)
1.00000 8.71032e-6i \(-2.77258e-6\pi\)
\(662\) −46.6252 + 12.4932i −1.81214 + 0.485561i
\(663\) 4.60674 + 7.82162i 0.178911 + 0.303766i
\(664\) 8.72904i 0.338752i
\(665\) 14.6289 + 37.9471i 0.567284 + 1.47153i
\(666\) −3.63796 + 0.0631259i −0.140968 + 0.00244608i
\(667\) −5.14068 1.37744i −0.199048 0.0533347i
\(668\) 0.520595 + 1.94289i 0.0201424 + 0.0751726i
\(669\) −6.00342 21.6519i −0.232105 0.837113i
\(670\) 19.5113 + 13.8324i 0.753787 + 0.534391i
\(671\) 0.976172i 0.0376847i
\(672\) −1.51465 7.17919i −0.0584289 0.276943i
\(673\) 9.04384 + 9.04384i 0.348614 + 0.348614i 0.859593 0.510979i \(-0.170717\pi\)
−0.510979 + 0.859593i \(0.670717\pi\)
\(674\) −10.0494 17.4061i −0.387090 0.670459i
\(675\) 24.2839 9.23544i 0.934687 0.355472i
\(676\) 0.851014 1.47400i 0.0327313 0.0566923i
\(677\) −8.83924 + 32.9885i −0.339719 + 1.26785i 0.558942 + 0.829207i \(0.311208\pi\)
−0.898661 + 0.438643i \(0.855459\pi\)
\(678\) −0.239044 27.5544i −0.00918042 1.05822i
\(679\) 5.63213 + 1.89363i 0.216141 + 0.0726708i
\(680\) 6.33864 2.91084i 0.243076 0.111626i
\(681\) 40.3141 + 10.4281i 1.54484 + 0.399608i
\(682\) 1.65724 + 6.18489i 0.0634588 + 0.236832i
\(683\) −6.18479 23.0820i −0.236654 0.883206i −0.977396 0.211416i \(-0.932192\pi\)
0.740742 0.671790i \(-0.234474\pi\)
\(684\) −3.02790 5.04045i −0.115775 0.192726i
\(685\) −21.6644 8.02870i −0.827756 0.306761i
\(686\) 12.1633 25.2161i 0.464396 0.962754i
\(687\) 5.64091 0.0489368i 0.215214 0.00186706i
\(688\) −7.90140 + 29.4884i −0.301238 + 1.12424i
\(689\) −24.0185 + 41.6012i −0.915031 + 1.58488i
\(690\) 11.4036 + 0.965067i 0.434127 + 0.0367395i
\(691\) −10.0976 17.4895i −0.384129 0.665332i 0.607519 0.794305i \(-0.292165\pi\)
−0.991648 + 0.128974i \(0.958832\pi\)
\(692\) 4.85170 + 4.85170i 0.184434 + 0.184434i
\(693\) 6.44099 3.34018i 0.244673 0.126883i
\(694\) 24.3128i 0.922899i
\(695\) 3.92554 5.53720i 0.148904 0.210038i
\(696\) 11.7802 3.26628i 0.446526 0.123808i
\(697\) −0.287405 1.07261i −0.0108863 0.0406281i
\(698\) 13.4482 + 3.60343i 0.509021 + 0.136392i
\(699\) −20.6037 20.2493i −0.779304 0.765899i
\(700\) −3.63018 + 1.02365i −0.137208 + 0.0386905i
\(701\) 49.4540i 1.86785i 0.357467 + 0.933926i \(0.383640\pi\)
−0.357467 + 0.933926i \(0.616360\pi\)
\(702\) −17.8707 29.1724i −0.674485 1.10104i
\(703\) −5.32750 + 1.42750i −0.200931 + 0.0538392i
\(704\) 2.99717 5.19126i 0.112960 0.195653i
\(705\) −39.9565 + 7.16243i −1.50485 + 0.269753i
\(706\) −15.7936 −0.594398
\(707\) 0.768217 12.2664i 0.0288918 0.461325i
\(708\) 4.87915 0.0423283i 0.183370 0.00159080i
\(709\) 33.9663 19.6105i 1.27563 0.736486i 0.299589 0.954068i \(-0.403150\pi\)
0.976042 + 0.217582i \(0.0698170\pi\)
\(710\) −1.20341 1.45129i −0.0451633 0.0544659i
\(711\) 7.95280 + 4.40938i 0.298253 + 0.165365i
\(712\) 28.2813 + 7.57795i 1.05989 + 0.283996i
\(713\) −6.40485 + 6.40485i −0.239864 + 0.239864i
\(714\) −8.32352 0.448830i −0.311500 0.0167970i
\(715\) 3.09362 8.34775i 0.115695 0.312188i
\(716\) 1.26386 0.729692i 0.0472328 0.0272699i
\(717\) 22.8869 + 12.9503i 0.854726 + 0.483639i
\(718\) −2.25121 + 0.603211i −0.0840145 + 0.0225116i
\(719\) −0.965960 1.67309i −0.0360242 0.0623958i 0.847451 0.530873i \(-0.178136\pi\)
−0.883475 + 0.468478i \(0.844803\pi\)
\(720\) −27.1431 + 13.0396i −1.01156 + 0.485957i
\(721\) 27.3104 5.51486i 1.01709 0.205384i
\(722\) −30.2039 30.2039i −1.12407 1.12407i
\(723\) 0.177248 0.104395i 0.00659191 0.00388248i
\(724\) 0.437106 + 0.252363i 0.0162449 + 0.00937901i
\(725\) −4.50632 12.8456i −0.167360 0.477072i
\(726\) 25.7651 + 6.66473i 0.956233 + 0.247351i
\(727\) 15.8726 15.8726i 0.588684 0.588684i −0.348591 0.937275i \(-0.613340\pi\)
0.937275 + 0.348591i \(0.113340\pi\)
\(728\) −13.2899 26.7530i −0.492555 0.991534i
\(729\) −26.9634 + 1.40474i −0.998646 + 0.0520273i
\(730\) −4.26112 + 6.01055i −0.157711 + 0.222460i
\(731\) 7.08709 + 4.09173i 0.262125 + 0.151338i
\(732\) −0.259709 + 0.458980i −0.00959914 + 0.0169644i
\(733\) −11.2567 + 42.0106i −0.415776 + 1.55170i 0.367502 + 0.930023i \(0.380213\pi\)
−0.783277 + 0.621673i \(0.786453\pi\)
\(734\) 24.2387 0.894668
\(735\) −26.5180 5.63879i −0.978131 0.207990i
\(736\) −3.12978 −0.115365
\(737\) 1.67404 6.24759i 0.0616640 0.230133i
\(738\) 1.15314 + 4.02305i 0.0424477 + 0.148090i
\(739\) −23.4387 13.5324i −0.862208 0.497796i 0.00254291 0.999997i \(-0.499191\pi\)
−0.864751 + 0.502201i \(0.832524\pi\)
\(740\) −0.0858818 0.504251i −0.00315708 0.0185366i
\(741\) −36.9864 36.3502i −1.35873 1.33536i
\(742\) −19.6247 39.5054i −0.720447 1.45029i
\(743\) −2.20467 + 2.20467i −0.0808816 + 0.0808816i −0.746390 0.665509i \(-0.768215\pi\)
0.665509 + 0.746390i \(0.268215\pi\)
\(744\) 5.21037 20.1427i 0.191021 0.738468i
\(745\) −2.67755 + 28.6761i −0.0980980 + 1.05061i
\(746\) −36.7368 21.2100i −1.34503 0.776553i
\(747\) 9.80148 + 2.44486i 0.358617 + 0.0894526i
\(748\) 0.221760 + 0.221760i 0.00810833 + 0.00810833i
\(749\) −16.4087 + 3.31346i −0.599561 + 0.121071i
\(750\) 14.4121 + 25.4796i 0.526256 + 0.930384i
\(751\) −11.9640 20.7223i −0.436574 0.756168i 0.560849 0.827918i \(-0.310475\pi\)
−0.997423 + 0.0717501i \(0.977142\pi\)
\(752\) 45.4461 12.1773i 1.65725 0.444059i
\(753\) 14.3518 25.3637i 0.523009 0.924305i
\(754\) −15.5238 + 8.96270i −0.565345 + 0.326402i
\(755\) 24.1789 11.1035i 0.879959 0.404096i
\(756\) 3.91710 + 0.143119i 0.142463 + 0.00520517i
\(757\) 34.0440 34.0440i 1.23735 1.23735i 0.276268 0.961081i \(-0.410902\pi\)
0.961081 0.276268i \(-0.0890977\pi\)
\(758\) −27.1892 7.28531i −0.987555 0.264615i
\(759\) −0.826933 2.98242i −0.0300158 0.108255i
\(760\) −30.6743 + 25.4352i −1.11267 + 0.922631i
\(761\) 5.74841 3.31885i 0.208380 0.120308i −0.392178 0.919889i \(-0.628278\pi\)
0.600558 + 0.799581i \(0.294945\pi\)
\(762\) −0.142266 16.3989i −0.00515375 0.594069i
\(763\) 1.42537 22.7594i 0.0516018 0.823944i
\(764\) 2.61711 0.0946838
\(765\) 1.49312 + 7.93268i 0.0539839 + 0.286807i
\(766\) 12.2581 21.2317i 0.442904 0.767133i
\(767\) 41.5671 11.1379i 1.50090 0.402165i
\(768\) 10.0147 5.89843i 0.361376 0.212841i
\(769\) 22.0730i 0.795972i 0.917391 + 0.397986i \(0.130291\pi\)
−0.917391 + 0.397986i \(0.869709\pi\)
\(770\) 4.81462 + 6.60685i 0.173507 + 0.238094i
\(771\) −16.8963 + 17.1920i −0.608504 + 0.619155i
\(772\) −1.95372 0.523498i −0.0703159 0.0188411i
\(773\) −8.46934 31.6080i −0.304621 1.13686i −0.933271 0.359173i \(-0.883059\pi\)
0.628650 0.777688i \(-0.283608\pi\)
\(774\) −26.9733 14.9552i −0.969534 0.537552i
\(775\) −22.7683 4.28925i −0.817861 0.154074i
\(776\) 5.82195i 0.208996i
\(777\) 1.14144 3.49502i 0.0409490 0.125383i
\(778\) 35.7966 + 35.7966i 1.28337 + 1.28337i
\(779\) 3.17196 + 5.49399i 0.113647 + 0.196843i
\(780\) 3.67548 3.10192i 0.131603 0.111066i
\(781\) −0.254928 + 0.441548i −0.00912203 + 0.0157998i
\(782\) −0.920269 + 3.43449i −0.0329088 + 0.122817i
\(783\) 0.368142 + 14.1423i 0.0131563 + 0.505405i
\(784\) 31.1771 + 3.92048i 1.11347 + 0.140017i
\(785\) −10.8104 + 29.1705i −0.385839 + 1.04114i
\(786\) −5.58202 + 21.5795i −0.199104 + 0.769715i
\(787\) −3.17466 11.8480i −0.113164 0.422335i 0.885979 0.463726i \(-0.153488\pi\)
−0.999143 + 0.0413909i \(0.986821\pi\)
\(788\) −1.31011 4.88941i −0.0466708 0.174178i
\(789\) −9.32990 + 36.0684i −0.332153 + 1.28407i
\(790\) −3.56038 + 9.60724i −0.126673 + 0.341810i
\(791\) 26.3928 + 8.87375i 0.938419 + 0.315514i
\(792\) 5.11330 + 4.93888i 0.181693 + 0.175495i
\(793\) −1.20379 + 4.49261i −0.0427478 + 0.159537i
\(794\) −8.03461 + 13.9164i −0.285138 + 0.493873i
\(795\) −32.6444 + 27.5502i −1.15778 + 0.977106i
\(796\) 2.45436 + 4.25107i 0.0869924 + 0.150675i
\(797\) −27.2098 27.2098i −0.963820 0.963820i 0.0355479 0.999368i \(-0.488682\pi\)
−0.999368 + 0.0355479i \(0.988682\pi\)
\(798\) 46.5950 9.83051i 1.64945 0.347996i
\(799\) 12.6120i 0.446179i
\(800\) −4.51496 6.61093i −0.159628 0.233732i
\(801\) −16.4301 + 29.6335i −0.580529 + 1.04705i
\(802\) −15.0542 56.1832i −0.531584 1.98390i
\(803\) 1.92460 + 0.515695i 0.0679177 + 0.0181985i
\(804\) 2.44927 2.49214i 0.0863791 0.0878909i
\(805\) −4.68856 + 10.5714i −0.165250 + 0.372592i
\(806\) 30.5082i 1.07460i
\(807\) −28.1806 + 16.5977i −0.992005 + 0.584267i
\(808\) 11.6319 3.11676i 0.409208 0.109647i
\(809\) −19.1786 + 33.2184i −0.674285 + 1.16790i 0.302393 + 0.953183i \(0.402215\pi\)
−0.976677 + 0.214712i \(0.931119\pi\)
\(810\) −6.14510 29.7945i −0.215917 1.04687i
\(811\) 3.87781 0.136168 0.0680841 0.997680i \(-0.478311\pi\)
0.0680841 + 0.997680i \(0.478311\pi\)
\(812\) 0.128373 2.04978i 0.00450502 0.0719333i
\(813\) −0.0557723 6.42883i −0.00195602 0.225469i
\(814\) −0.960137 + 0.554335i −0.0336528 + 0.0194294i
\(815\) 41.4723 34.3890i 1.45271 1.20459i
\(816\) −2.49975 9.01561i −0.0875087 0.315609i
\(817\) −45.1585 12.1002i −1.57990 0.423332i
\(818\) 1.03534 1.03534i 0.0361999 0.0361999i
\(819\) 33.7622 7.42957i 1.17975 0.259610i
\(820\) −0.534665 + 0.245530i −0.0186713 + 0.00857427i
\(821\) 6.96953 4.02386i 0.243238 0.140434i −0.373426 0.927660i \(-0.621817\pi\)
0.616664 + 0.787226i \(0.288484\pi\)
\(822\) −13.3230 + 23.5454i −0.464692 + 0.821241i
\(823\) −1.74727 + 0.468179i −0.0609059 + 0.0163197i −0.289143 0.957286i \(-0.593370\pi\)
0.228237 + 0.973606i \(0.426704\pi\)
\(824\) 13.6495 + 23.6416i 0.475503 + 0.823595i
\(825\) 5.10676 6.04909i 0.177794 0.210602i
\(826\) −12.5935 + 37.4562i −0.438184 + 1.30327i
\(827\) −27.7405 27.7405i −0.964633 0.964633i 0.0347627 0.999396i \(-0.488932\pi\)
−0.999396 + 0.0347627i \(0.988932\pi\)
\(828\) 0.404660 1.62229i 0.0140629 0.0563784i
\(829\) 8.07960 + 4.66476i 0.280616 + 0.162014i 0.633702 0.773577i \(-0.281534\pi\)
−0.353086 + 0.935591i \(0.614868\pi\)
\(830\) −1.05816 + 11.3327i −0.0367292 + 0.393362i
\(831\) 3.27991 12.6798i 0.113779 0.439856i
\(832\) 20.1955 20.1955i 0.700154 0.700154i
\(833\) 3.17813 7.80051i 0.110116 0.270272i
\(834\) −5.66841 5.57090i −0.196281 0.192905i
\(835\) 2.64857 + 15.5509i 0.0916576 + 0.538163i
\(836\) −1.55162 0.895831i −0.0536641 0.0309830i
\(837\) 21.1581 + 11.4922i 0.731331 + 0.397227i
\(838\) −9.52614 + 35.5520i −0.329075 + 1.22812i
\(839\) 3.18996 0.110130 0.0550649 0.998483i \(-0.482463\pi\)
0.0550649 + 0.998483i \(0.482463\pi\)
\(840\) −3.04347 26.3885i −0.105010 0.910488i
\(841\) −21.5874 −0.744393
\(842\) 0.688292 2.56874i 0.0237201 0.0885246i
\(843\) −10.2823 + 18.1718i −0.354143 + 0.625870i
\(844\) 2.40830 + 1.39043i 0.0828972 + 0.0478607i
\(845\) 7.72000 10.8895i 0.265576 0.374610i
\(846\) 0.824648 + 47.5247i 0.0283520 + 1.63393i
\(847\) −14.8757 + 22.4036i −0.511134 + 0.769795i
\(848\) 35.0087 35.0087i 1.20220 1.20220i
\(849\) −40.2672 10.4160i −1.38197 0.357477i
\(850\) −8.58213 + 3.01068i −0.294365 + 0.103265i
\(851\) −1.35822 0.784167i −0.0465591 0.0268809i
\(852\) −0.237336 + 0.139785i −0.00813100 + 0.00478896i
\(853\) −5.14974 5.14974i −0.176324 0.176324i 0.613427 0.789751i \(-0.289790\pi\)
−0.789751 + 0.613427i \(0.789790\pi\)
\(854\) −2.82537 3.20291i −0.0966823 0.109601i
\(855\) −19.9688 41.5669i −0.682919 1.42156i
\(856\) −8.20093 14.2044i −0.280302 0.485497i
\(857\) −11.1736 + 2.99394i −0.381681 + 0.102271i −0.444558 0.895750i \(-0.646639\pi\)
0.0628767 + 0.998021i \(0.479973\pi\)
\(858\) −9.07253 5.13361i −0.309731 0.175258i
\(859\) 24.0944 13.9109i 0.822092 0.474635i −0.0290454 0.999578i \(-0.509247\pi\)
0.851137 + 0.524943i \(0.175913\pi\)
\(860\) 1.50669 4.06562i 0.0513778 0.138636i
\(861\) −4.22284 0.227708i −0.143914 0.00776028i
\(862\) −22.9187 + 22.9187i −0.780613 + 0.780613i
\(863\) −7.54415 2.02145i −0.256806 0.0688109i 0.128119 0.991759i \(-0.459106\pi\)
−0.384925 + 0.922948i \(0.625773\pi\)
\(864\) 2.36167 + 7.97740i 0.0803457 + 0.271397i
\(865\) 34.3479 + 41.4228i 1.16786 + 1.40842i
\(866\) −49.6242 + 28.6505i −1.68630 + 0.973585i
\(867\) 26.9360 0.233679i 0.914793 0.00793615i
\(868\) −2.91200 1.93353i −0.0988397 0.0656283i
\(869\) 2.77080 0.0939929
\(870\) −15.6898 + 2.81249i −0.531934 + 0.0953524i
\(871\) 15.4087 26.6887i 0.522105 0.904313i
\(872\) 21.5821 5.78291i 0.730862 0.195834i
\(873\) −6.53723 1.63063i −0.221252 0.0551885i
\(874\) 20.3132i 0.687103i
\(875\) −29.0932 + 5.34656i −0.983530 + 0.180747i
\(876\) 0.767715 + 0.754509i 0.0259387 + 0.0254925i
\(877\) 15.0553 + 4.03404i 0.508380 + 0.136220i 0.503886 0.863770i \(-0.331903\pi\)
0.00449350 + 0.999990i \(0.498570\pi\)
\(878\) −0.928204 3.46410i −0.0313254 0.116908i
\(879\) −28.9150 + 8.01723i −0.975278 + 0.270414i
\(880\) −5.30662 + 7.48529i −0.178886 + 0.252329i
\(881\) 8.59639i 0.289620i −0.989459 0.144810i \(-0.953743\pi\)
0.989459 0.144810i \(-0.0462571\pi\)
\(882\) −11.4659 + 29.6019i −0.386075 + 0.996747i
\(883\) −31.4000 31.4000i −1.05670 1.05670i −0.998293 0.0584026i \(-0.981399\pi\)
−0.0584026 0.998293i \(-0.518601\pi\)
\(884\) 0.747129 + 1.29407i 0.0251287 + 0.0435241i
\(885\) 38.1305 + 3.22693i 1.28174 + 0.108472i
\(886\) 16.4444 28.4826i 0.552461 0.956891i
\(887\) −0.519425 + 1.93852i −0.0174406 + 0.0650891i −0.974098 0.226128i \(-0.927393\pi\)
0.956657 + 0.291217i \(0.0940600\pi\)
\(888\) 3.60231 0.0312513i 0.120885 0.00104872i
\(889\) 15.7076 + 5.28118i 0.526815 + 0.177125i
\(890\) −35.7982 13.2666i −1.19996 0.444697i
\(891\) −6.97782 + 4.35822i −0.233766 + 0.146006i
\(892\) −0.957280 3.57262i −0.0320521 0.119620i
\(893\) 18.6482 + 69.5961i 0.624039 + 2.32895i
\(894\) 32.6491 + 8.44542i 1.09195 + 0.282457i
\(895\) 10.4011 4.77642i 0.347671 0.159658i
\(896\) 6.86824 + 34.0125i 0.229452 + 1.13628i
\(897\) −0.127924 14.7457i −0.00427125 0.492343i
\(898\) 11.3026 42.1818i 0.377172 1.40762i
\(899\) 6.30796 10.9257i 0.210382 0.364393i
\(900\) 4.01046 1.48553i 0.133682 0.0495178i
\(901\) −6.63575 11.4935i −0.221069 0.382903i
\(902\) 0.901706 + 0.901706i 0.0300235 + 0.0300235i
\(903\) 23.1919 20.8187i 0.771779 0.692804i
\(904\) 27.2823i 0.907395i
\(905\) 3.22921 + 2.28932i 0.107343 + 0.0760996i
\(906\) −8.32406 30.0216i −0.276548 0.997401i
\(907\) 2.38324 + 8.89437i 0.0791341 + 0.295333i 0.994139 0.108110i \(-0.0344800\pi\)
−0.915005 + 0.403443i \(0.867813\pi\)
\(908\) 6.62106 + 1.77411i 0.219727 + 0.0588758i
\(909\) 0.241782 + 13.9339i 0.00801939 + 0.462159i
\(910\) 14.0108 + 36.3438i 0.464453 + 1.20478i
\(911\) 32.1044i 1.06367i −0.846849 0.531834i \(-0.821503\pi\)
0.846849 0.531834i \(-0.178497\pi\)
\(912\) 27.1249 + 46.0543i 0.898195 + 1.52501i
\(913\) 2.97319 0.796663i 0.0983981 0.0263657i
\(914\) 1.48583 2.57354i 0.0491470 0.0851251i
\(915\) −2.36263 + 3.39466i −0.0781063 + 0.112224i
\(916\) 0.928598 0.0306817
\(917\) −18.7640 12.4591i −0.619642 0.411434i
\(918\) 9.44849 0.245956i 0.311847 0.00811777i
\(919\) 30.6447 17.6927i 1.01088 0.583630i 0.0994284 0.995045i \(-0.468299\pi\)
0.911448 + 0.411415i \(0.134965\pi\)
\(920\) −11.2818 1.05341i −0.371951 0.0347299i
\(921\) 29.5120 8.18277i 0.972454 0.269631i
\(922\) 25.4477 + 6.81869i 0.838076 + 0.224562i
\(923\) −1.71775 + 1.71775i −0.0565405 + 0.0565405i
\(924\) 1.06500 0.540617i 0.0350358 0.0177850i
\(925\) −0.302967 4.00014i −0.00996148 0.131524i
\(926\) 27.4757 15.8631i 0.902909 0.521295i
\(927\) −30.3692 + 8.70485i −0.997456 + 0.285905i
\(928\) 4.21068 1.12825i 0.138222 0.0370365i
\(929\) −22.6551 39.2398i −0.743290 1.28742i −0.950989 0.309224i \(-0.899931\pi\)
0.207699 0.978193i \(-0.433403\pi\)
\(930\) −9.20623 + 25.5191i −0.301884 + 0.836805i
\(931\) −6.00381 + 47.7445i −0.196767 + 1.56476i
\(932\) −3.36258 3.36258i −0.110145 0.110145i
\(933\) 20.6035 + 34.9820i 0.674530 + 1.14526i
\(934\) −16.5032 9.52814i −0.540002 0.311770i
\(935\) 1.56996 + 1.89333i 0.0513431 + 0.0619187i
\(936\) 17.4423 + 29.0356i 0.570119 + 0.949059i
\(937\) −2.63830 + 2.63830i −0.0861894 + 0.0861894i −0.748887 0.662698i \(-0.769411\pi\)
0.662698 + 0.748887i \(0.269411\pi\)
\(938\) 12.5900 + 25.3442i 0.411078 + 0.827517i
\(939\) 12.8694 13.0947i 0.419977 0.427328i
\(940\) −6.58731 + 1.12192i −0.214854 + 0.0365931i
\(941\) −23.3880 13.5031i −0.762428 0.440188i 0.0677386 0.997703i \(-0.478422\pi\)
−0.830167 + 0.557515i \(0.811755\pi\)
\(942\) 31.7031 + 17.9389i 1.03294 + 0.584482i
\(943\) −0.466888 + 1.74245i −0.0152039 + 0.0567419i
\(944\) −44.3528 −1.44356
\(945\) 30.4830 + 3.97357i 0.991611 + 0.129260i
\(946\) −9.39763 −0.305543
\(947\) 3.60013 13.4359i 0.116988 0.436607i −0.882440 0.470426i \(-0.844100\pi\)
0.999428 + 0.0338191i \(0.0107670\pi\)
\(948\) 1.30278 + 0.737168i 0.0423124 + 0.0239421i
\(949\) 8.22158 + 4.74673i 0.266884 + 0.154086i
\(950\) 42.9068 29.3034i 1.39208 0.950727i
\(951\) 24.9405 25.3770i 0.808750 0.822905i
\(952\) 8.23685 + 0.515856i 0.266958 + 0.0167190i
\(953\) 20.8791 20.8791i 0.676342 0.676342i −0.282829 0.959170i \(-0.591273\pi\)
0.959170 + 0.282829i \(0.0912728\pi\)
\(954\) 25.7565 + 42.8760i 0.833898 + 1.38816i
\(955\) 20.4362 + 1.90817i 0.661299 + 0.0617470i
\(956\) 3.74883 + 2.16439i 0.121246 + 0.0700012i
\(957\) 2.18765 + 3.71433i 0.0707167 + 0.120067i
\(958\) 10.9968 + 10.9968i 0.355289 + 0.355289i
\(959\) −18.0844 20.5009i −0.583975 0.662008i
\(960\) 22.9872 10.7987i 0.741908 0.348525i
\(961\) 4.76416 + 8.25177i 0.153683 + 0.266186i
\(962\) −5.10240 + 1.36718i −0.164508 + 0.0440798i
\(963\) 18.2465 5.23007i 0.587986 0.168537i
\(964\) 0.0293251 0.0169309i 0.000944499 0.000545307i
\(965\) −14.8743 5.51230i −0.478819 0.177447i
\(966\) 11.3454 + 7.39218i 0.365032 + 0.237839i
\(967\) −38.5871 + 38.5871i −1.24088 + 1.24088i −0.281238 + 0.959638i \(0.590745\pi\)
−0.959638 + 0.281238i \(0.909255\pi\)
\(968\) −25.4515 6.81972i −0.818043 0.219194i
\(969\) 13.8065 3.82811i 0.443528 0.122977i
\(970\) 0.705752 7.55847i 0.0226603 0.242688i
\(971\) 18.6146 10.7472i 0.597372 0.344893i −0.170635 0.985334i \(-0.554582\pi\)
0.768007 + 0.640441i \(0.221248\pi\)
\(972\) −4.44035 + 0.192724i −0.142424 + 0.00618163i
\(973\) 7.19253 3.57297i 0.230582 0.114544i
\(974\) 28.1852 0.903112
\(975\) 30.9622 21.5420i 0.991585 0.689896i
\(976\) 2.39684 4.15146i 0.0767211 0.132885i
\(977\) −43.1613 + 11.5650i −1.38085 + 0.369998i −0.871430 0.490520i \(-0.836807\pi\)
−0.509421 + 0.860518i \(0.670140\pi\)
\(978\) −32.0148 54.3568i −1.02372 1.73814i
\(979\) 10.3245i 0.329971i
\(980\) −4.35697 0.966047i −0.139178 0.0308593i
\(981\) 0.448608 + 25.8534i 0.0143229 + 0.825435i
\(982\) 36.0570 + 9.66143i 1.15062 + 0.308309i
\(983\) −3.36791 12.5692i −0.107420 0.400896i 0.891189 0.453633i \(-0.149872\pi\)
−0.998608 + 0.0527371i \(0.983205\pi\)
\(984\) −1.10711 3.99292i −0.0352935 0.127290i
\(985\) −6.66530 39.1350i −0.212374 1.24694i
\(986\) 4.95237i 0.157716i
\(987\) −45.6574 14.9113i −1.45329 0.474632i
\(988\) −6.03628 6.03628i −0.192040 0.192040i
\(989\) −6.64698 11.5129i −0.211362 0.366089i
\(990\) −6.03975 7.03185i −0.191956 0.223487i
\(991\) −6.73127 + 11.6589i −0.213826 + 0.370357i −0.952909 0.303257i \(-0.901926\pi\)
0.739083 + 0.673615i \(0.235259\pi\)
\(992\) 1.92022 7.16637i 0.0609671 0.227532i
\(993\) 0.479793 + 55.3053i 0.0152258 + 1.75506i
\(994\) −0.441548 2.18661i −0.0140050 0.0693550i
\(995\) 16.0657 + 34.9847i 0.509318 + 1.10909i
\(996\) 1.60989 + 0.416435i 0.0510114 + 0.0131953i
\(997\) −9.83565 36.7071i −0.311498 1.16253i −0.927206 0.374552i \(-0.877797\pi\)
0.615708 0.787975i \(-0.288870\pi\)
\(998\) 5.03834 + 18.8033i 0.159486 + 0.595209i
\(999\) −0.973855 + 4.05364i −0.0308114 + 0.128251i
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 105.2.x.a.53.10 yes 48
3.2 odd 2 inner 105.2.x.a.53.3 yes 48
5.2 odd 4 inner 105.2.x.a.32.10 yes 48
5.3 odd 4 525.2.bf.f.32.3 48
5.4 even 2 525.2.bf.f.368.3 48
7.2 even 3 inner 105.2.x.a.23.3 yes 48
7.3 odd 6 735.2.j.e.638.10 24
7.4 even 3 735.2.j.g.638.10 24
7.5 odd 6 735.2.y.i.128.3 48
7.6 odd 2 735.2.y.i.263.10 48
15.2 even 4 inner 105.2.x.a.32.3 yes 48
15.8 even 4 525.2.bf.f.32.10 48
15.14 odd 2 525.2.bf.f.368.10 48
21.2 odd 6 inner 105.2.x.a.23.10 yes 48
21.5 even 6 735.2.y.i.128.10 48
21.11 odd 6 735.2.j.g.638.3 24
21.17 even 6 735.2.j.e.638.3 24
21.20 even 2 735.2.y.i.263.3 48
35.2 odd 12 inner 105.2.x.a.2.3 48
35.9 even 6 525.2.bf.f.443.10 48
35.12 even 12 735.2.y.i.422.3 48
35.17 even 12 735.2.j.e.197.3 24
35.23 odd 12 525.2.bf.f.107.10 48
35.27 even 4 735.2.y.i.557.10 48
35.32 odd 12 735.2.j.g.197.3 24
105.2 even 12 inner 105.2.x.a.2.10 yes 48
105.17 odd 12 735.2.j.e.197.10 24
105.23 even 12 525.2.bf.f.107.3 48
105.32 even 12 735.2.j.g.197.10 24
105.44 odd 6 525.2.bf.f.443.3 48
105.47 odd 12 735.2.y.i.422.10 48
105.62 odd 4 735.2.y.i.557.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.3 48 35.2 odd 12 inner
105.2.x.a.2.10 yes 48 105.2 even 12 inner
105.2.x.a.23.3 yes 48 7.2 even 3 inner
105.2.x.a.23.10 yes 48 21.2 odd 6 inner
105.2.x.a.32.3 yes 48 15.2 even 4 inner
105.2.x.a.32.10 yes 48 5.2 odd 4 inner
105.2.x.a.53.3 yes 48 3.2 odd 2 inner
105.2.x.a.53.10 yes 48 1.1 even 1 trivial
525.2.bf.f.32.3 48 5.3 odd 4
525.2.bf.f.32.10 48 15.8 even 4
525.2.bf.f.107.3 48 105.23 even 12
525.2.bf.f.107.10 48 35.23 odd 12
525.2.bf.f.368.3 48 5.4 even 2
525.2.bf.f.368.10 48 15.14 odd 2
525.2.bf.f.443.3 48 105.44 odd 6
525.2.bf.f.443.10 48 35.9 even 6
735.2.j.e.197.3 24 35.17 even 12
735.2.j.e.197.10 24 105.17 odd 12
735.2.j.e.638.3 24 21.17 even 6
735.2.j.e.638.10 24 7.3 odd 6
735.2.j.g.197.3 24 35.32 odd 12
735.2.j.g.197.10 24 105.32 even 12
735.2.j.g.638.3 24 21.11 odd 6
735.2.j.g.638.10 24 7.4 even 3
735.2.y.i.128.3 48 7.5 odd 6
735.2.y.i.128.10 48 21.5 even 6
735.2.y.i.263.3 48 21.20 even 2
735.2.y.i.263.10 48 7.6 odd 2
735.2.y.i.422.3 48 35.12 even 12
735.2.y.i.422.10 48 105.47 odd 12
735.2.y.i.557.3 48 105.62 odd 4
735.2.y.i.557.10 48 35.27 even 4