Properties

Label 105.2.x.a.23.10
Level $105$
Weight $2$
Character 105.23
Analytic conductor $0.838$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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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 23.10
Character \(\chi\) \(=\) 105.23
Dual form 105.2.x.a.32.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.46015 - 0.391246i) q^{2} +(-0.852980 - 1.50746i) q^{3} +(0.246919 - 0.142558i) q^{4} +(0.207883 - 2.22638i) q^{5} +(-1.83527 - 1.86739i) q^{6} +(2.36949 + 1.17707i) q^{7} +(-1.83305 + 1.83305i) q^{8} +(-1.54485 + 2.57166i) q^{9} +O(q^{10})\) \(q+(1.46015 - 0.391246i) q^{2} +(-0.852980 - 1.50746i) q^{3} +(0.246919 - 0.142558i) q^{4} +(0.207883 - 2.22638i) q^{5} +(-1.83527 - 1.86739i) q^{6} +(2.36949 + 1.17707i) q^{7} +(-1.83305 + 1.83305i) q^{8} +(-1.54485 + 2.57166i) q^{9} +(-0.567525 - 3.33219i) q^{10} +(0.791646 - 0.457057i) q^{11} +(-0.425517 - 0.250619i) q^{12} +(3.07974 + 3.07974i) q^{13} +(3.92035 + 0.791646i) q^{14} +(-3.53350 + 1.58569i) q^{15} +(-2.24447 + 3.88754i) q^{16} +(-0.311437 + 1.16230i) q^{17} +(-1.24956 + 4.35943i) 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} +(0.505926 + 1.88814i) q^{23} +(4.32679 + 1.19969i) q^{24} +(-4.91357 - 0.925653i) q^{25} +(5.70182 + 3.29195i) q^{26} +(5.19439 + 0.135217i) q^{27} +(0.752874 - 0.0471508i) q^{28} +2.72261 q^{29} +(-4.53905 + 3.69781i) q^{30} +(-2.31688 - 4.01295i) q^{31} +(-0.414399 + 1.54656i) q^{32} +(-1.36425 - 0.803512i) q^{33} +1.81898i q^{34} +(3.11319 - 5.03071i) q^{35} +(-0.0148398 + 0.855222i) q^{36} +(0.207656 + 0.774982i) q^{37} +(-10.0376 - 2.68957i) q^{38} +(2.01562 - 7.26953i) q^{39} +(3.70001 + 4.46213i) q^{40} -0.922837i q^{41} +(-2.15061 - 6.58501i) q^{42} +(-4.80893 - 4.80893i) q^{43} +(0.130315 - 0.225712i) q^{44} +(5.40436 + 3.97403i) q^{45} +(1.47746 + 2.55903i) q^{46} +(-10.1240 + 2.71272i) q^{47} +(7.77478 + 0.0674490i) q^{48} +(4.22901 + 5.57813i) q^{49} +(-7.53672 + 0.570823i) q^{50} +(2.01776 - 0.521940i) q^{51} +(1.19949 + 0.321402i) q^{52} +(10.6535 + 2.85459i) q^{53} +(7.63750 - 1.83485i) q^{54} +(-0.853015 - 1.85752i) q^{55} +(-6.50102 + 2.18577i) q^{56} +(-0.103291 + 11.9063i) q^{57} +(3.97543 - 1.06521i) q^{58} +(-4.94023 - 8.55672i) q^{59} +(-0.646432 + 0.895265i) q^{60} +(0.533944 - 0.924818i) q^{61} +(-4.95304 - 4.95304i) q^{62} +(-6.68754 + 4.27514i) q^{63} -6.55754i q^{64} +(7.49690 - 6.21646i) q^{65} +(-2.30639 - 0.639490i) q^{66} +(6.83458 + 1.83132i) q^{67} +(0.0887959 + 0.331391i) q^{68} +(2.41475 - 2.37321i) q^{69} +(2.57748 - 8.56363i) q^{70} -0.557759i q^{71} +(-1.88219 - 7.54576i) q^{72} +(-0.564147 + 2.10543i) q^{73} +(0.606418 + 1.05035i) q^{74} +(2.79580 + 8.19656i) q^{75} -1.96000 q^{76} +(2.41379 - 0.151170i) q^{77} +(0.0989269 - 11.4032i) q^{78} +(-2.62503 - 1.51556i) q^{79} +(8.18857 + 5.80521i) q^{80} +(-4.22688 - 7.94566i) q^{81} +(-0.361057 - 1.34748i) 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} +(-2.32233 - 4.10422i) q^{87} +(-0.613318 + 2.28893i) q^{88} +(-5.64725 + 9.78132i) q^{89} +(9.44601 + 3.68825i) q^{90} +(3.67235 + 10.9225i) q^{91} +(0.394093 + 0.394093i) q^{92} +(-4.07310 + 6.91556i) q^{93} +(-13.7213 + 7.92197i) q^{94} +(-8.89008 + 12.5400i) q^{95} +(2.68484 - 0.694495i) q^{96} +(-1.58805 + 1.58805i) q^{97} +(8.35741 + 6.49033i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46015 0.391246i 1.03248 0.276653i 0.297488 0.954726i \(-0.403851\pi\)
0.734995 + 0.678072i \(0.237184\pi\)
\(3\) −0.852980 1.50746i −0.492468 0.870330i
\(4\) 0.246919 0.142558i 0.123459 0.0712792i
\(5\) 0.207883 2.22638i 0.0929679 0.995669i
\(6\) −1.83527 1.86739i −0.749245 0.762359i
\(7\) 2.36949 + 1.17707i 0.895585 + 0.444891i
\(8\) −1.83305 + 1.83305i −0.648080 + 0.648080i
\(9\) −1.54485 + 2.57166i −0.514950 + 0.857220i
\(10\) −0.567525 3.33219i −0.179467 1.05373i
\(11\) 0.791646 0.457057i 0.238690 0.137808i −0.375884 0.926667i \(-0.622661\pi\)
0.614575 + 0.788859i \(0.289328\pi\)
\(12\) −0.425517 0.250619i −0.122836 0.0723476i
\(13\) 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
\(15\) −3.53350 + 1.58569i −0.912345 + 0.409423i
\(16\) −2.24447 + 3.88754i −0.561118 + 0.971885i
\(17\) −0.311437 + 1.16230i −0.0755345 + 0.281899i −0.993354 0.115099i \(-0.963281\pi\)
0.917819 + 0.396998i \(0.129948\pi\)
\(18\) −1.24956 + 4.35943i −0.294524 + 1.02753i
\(19\) −5.95337 3.43718i −1.36580 0.788543i −0.375409 0.926859i \(-0.622498\pi\)
−0.990388 + 0.138316i \(0.955831\pi\)
\(20\) −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
\(23\) 0.505926 + 1.88814i 0.105493 + 0.393705i 0.998401 0.0565348i \(-0.0180052\pi\)
−0.892908 + 0.450240i \(0.851339\pi\)
\(24\) 4.32679 + 1.19969i 0.883203 + 0.244885i
\(25\) −4.91357 0.925653i −0.982714 0.185131i
\(26\) 5.70182 + 3.29195i 1.11822 + 0.645604i
\(27\) 5.19439 + 0.135217i 0.999661 + 0.0260225i
\(28\) 0.752874 0.0471508i 0.142280 0.00891066i
\(29\) 2.72261 0.505576 0.252788 0.967522i \(-0.418652\pi\)
0.252788 + 0.967522i \(0.418652\pi\)
\(30\) −4.53905 + 3.69781i −0.828713 + 0.675125i
\(31\) −2.31688 4.01295i −0.416123 0.720747i 0.579422 0.815028i \(-0.303278\pi\)
−0.995546 + 0.0942806i \(0.969945\pi\)
\(32\) −0.414399 + 1.54656i −0.0732561 + 0.273395i
\(33\) −1.36425 0.803512i −0.237486 0.139873i
\(34\) 1.81898i 0.311952i
\(35\) 3.11319 5.03071i 0.526225 0.850345i
\(36\) −0.0148398 + 0.855222i −0.00247330 + 0.142537i
\(37\) 0.207656 + 0.774982i 0.0341384 + 0.127406i 0.980892 0.194552i \(-0.0623255\pi\)
−0.946754 + 0.321959i \(0.895659\pi\)
\(38\) −10.0376 2.68957i −1.62832 0.436306i
\(39\) 2.01562 7.26953i 0.322757 1.16406i
\(40\) 3.70001 + 4.46213i 0.585023 + 0.705524i
\(41\) 0.922837i 0.144123i −0.997400 0.0720615i \(-0.977042\pi\)
0.997400 0.0720615i \(-0.0229578\pi\)
\(42\) −2.15061 6.58501i −0.331846 1.01609i
\(43\) −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
\(45\) 5.40436 + 3.97403i 0.805634 + 0.592414i
\(46\) 1.47746 + 2.55903i 0.217839 + 0.377309i
\(47\) −10.1240 + 2.71272i −1.47674 + 0.395691i −0.905236 0.424909i \(-0.860306\pi\)
−0.571503 + 0.820600i \(0.693640\pi\)
\(48\) 7.77478 + 0.0674490i 1.12219 + 0.00973542i
\(49\) 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
\(52\) 1.19949 + 0.321402i 0.166339 + 0.0445704i
\(53\) 10.6535 + 2.85459i 1.46336 + 0.392107i 0.900651 0.434544i \(-0.143090\pi\)
0.562714 + 0.826651i \(0.309757\pi\)
\(54\) 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
\(57\) −0.103291 + 11.9063i −0.0136813 + 1.57703i
\(58\) 3.97543 1.06521i 0.521999 0.139869i
\(59\) −4.94023 8.55672i −0.643163 1.11399i −0.984723 0.174130i \(-0.944289\pi\)
0.341560 0.939860i \(-0.389045\pi\)
\(60\) −0.646432 + 0.895265i −0.0834541 + 0.115578i
\(61\) 0.533944 0.924818i 0.0683645 0.118411i −0.829817 0.558036i \(-0.811555\pi\)
0.898182 + 0.439625i \(0.144889\pi\)
\(62\) −4.95304 4.95304i −0.629037 0.629037i
\(63\) −6.68754 + 4.27514i −0.842551 + 0.538617i
\(64\) 6.55754i 0.819693i
\(65\) 7.49690 6.21646i 0.929877 0.771057i
\(66\) −2.30639 0.639490i −0.283897 0.0787158i
\(67\) 6.83458 + 1.83132i 0.834977 + 0.223732i 0.650884 0.759177i \(-0.274398\pi\)
0.184093 + 0.982909i \(0.441065\pi\)
\(68\) 0.0887959 + 0.331391i 0.0107681 + 0.0401870i
\(69\) 2.41475 2.37321i 0.290701 0.285701i
\(70\) 2.57748 8.56363i 0.308068 1.02355i
\(71\) 0.557759i 0.0661938i −0.999452 0.0330969i \(-0.989463\pi\)
0.999452 0.0330969i \(-0.0105370\pi\)
\(72\) −1.88219 7.54576i −0.221819 0.889276i
\(73\) −0.564147 + 2.10543i −0.0660284 + 0.246421i −0.991050 0.133494i \(-0.957380\pi\)
0.925021 + 0.379915i \(0.124047\pi\)
\(74\) 0.606418 + 1.05035i 0.0704946 + 0.122100i
\(75\) 2.79580 + 8.19656i 0.322831 + 0.946457i
\(76\) −1.96000 −0.224827
\(77\) 2.41379 0.151170i 0.275077 0.0172275i
\(78\) 0.0989269 11.4032i 0.0112013 1.29116i
\(79\) −2.62503 1.51556i −0.295339 0.170514i 0.345008 0.938600i \(-0.387876\pi\)
−0.640347 + 0.768086i \(0.721210\pi\)
\(80\) 8.18857 + 5.80521i 0.915509 + 0.649042i
\(81\) −4.22688 7.94566i −0.469653 0.882851i
\(82\) −0.361057 1.34748i −0.0398720 0.148805i
\(83\) −2.38102 + 2.38102i −0.261351 + 0.261351i −0.825603 0.564252i \(-0.809165\pi\)
0.564252 + 0.825603i \(0.309165\pi\)
\(84\) −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
\(87\) −2.32233 4.10422i −0.248980 0.440018i
\(88\) −0.613318 + 2.28893i −0.0653799 + 0.244001i
\(89\) −5.64725 + 9.78132i −0.598607 + 1.03682i 0.394420 + 0.918930i \(0.370946\pi\)
−0.993027 + 0.117888i \(0.962388\pi\)
\(90\) 9.44601 + 3.68825i 0.995697 + 0.388776i
\(91\) 3.67235 + 10.9225i 0.384967 + 1.14499i
\(92\) 0.394093 + 0.394093i 0.0410871 + 0.0410871i
\(93\) −4.07310 + 6.91556i −0.422360 + 0.717110i
\(94\) −13.7213 + 7.92197i −1.41524 + 0.817089i
\(95\) −8.89008 + 12.5400i −0.912103 + 1.28657i
\(96\) 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 \(0.286371\pi\)
\(98\) 8.35741 + 6.49033i 0.844226 + 0.655622i
\(99\) −0.0475780 + 2.74193i −0.00478177 + 0.275574i
\(100\) −1.34521 + 0.471910i −0.134521 + 0.0471910i
\(101\) 4.02299 2.32267i 0.400302 0.231114i −0.286312 0.958136i \(-0.592429\pi\)
0.686614 + 0.727022i \(0.259096\pi\)
\(102\) 2.74203 1.55155i 0.271502 0.153627i
\(103\) 10.1719 2.72555i 1.00227 0.268556i 0.279871 0.960037i \(-0.409708\pi\)
0.722395 + 0.691481i \(0.243041\pi\)
\(104\) −11.2906 −1.10714
\(105\) −10.2391 0.401900i −0.999231 0.0392214i
\(106\) 16.6725 1.61938
\(107\) 6.11150 1.63757i 0.590821 0.158310i 0.0489927 0.998799i \(-0.484399\pi\)
0.541829 + 0.840489i \(0.317732\pi\)
\(108\) 1.30187 0.707117i 0.125272 0.0680424i
\(109\) −7.46435 + 4.30954i −0.714955 + 0.412779i −0.812893 0.582413i \(-0.802109\pi\)
0.0979381 + 0.995193i \(0.468775\pi\)
\(110\) −1.97228 2.37853i −0.188050 0.226784i
\(111\) 0.991125 0.974076i 0.0940734 0.0924552i
\(112\) −9.89417 + 6.56960i −0.934911 + 0.620769i
\(113\) 7.44178 7.44178i 0.700064 0.700064i −0.264360 0.964424i \(-0.585161\pi\)
0.964424 + 0.264360i \(0.0851608\pi\)
\(114\) 4.50747 + 17.4254i 0.422164 + 1.63204i
\(115\) 4.30890 0.733874i 0.401807 0.0684341i
\(116\) 0.672263 0.388131i 0.0624181 0.0360371i
\(117\) −12.6778 + 3.16231i −1.17206 + 0.292356i
\(118\) −10.5613 10.5613i −0.972243 0.972243i
\(119\) −2.10605 + 2.38747i −0.193062 + 0.218859i
\(120\) 3.57043 9.38371i 0.325934 0.856611i
\(121\) −5.08220 + 8.80262i −0.462018 + 0.800239i
\(122\) 0.417807 1.55928i 0.0378265 0.141170i
\(123\) −1.39114 + 0.787162i −0.125435 + 0.0709760i
\(124\) −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 \(0.339637\pi\)
\(128\) −3.39441 12.6681i −0.300027 1.11971i
\(129\) −3.14733 + 11.3512i −0.277107 + 0.999416i
\(130\) 8.51445 12.0101i 0.746767 1.05336i
\(131\) 7.37260 + 4.25658i 0.644147 + 0.371899i 0.786210 0.617959i \(-0.212040\pi\)
−0.142063 + 0.989858i \(0.545374\pi\)
\(132\) −0.451407 0.00391611i −0.0392899 0.000340854i
\(133\) −10.0607 15.1519i −0.872371 1.31384i
\(134\) 10.6960 0.923996
\(135\) 1.38087 11.5366i 0.118846 0.992913i
\(136\) −1.55967 2.70143i −0.133740 0.231645i
\(137\) 2.67426 9.98048i 0.228478 0.852690i −0.752504 0.658588i \(-0.771154\pi\)
0.980981 0.194102i \(-0.0621793\pi\)
\(138\) 2.59739 4.41001i 0.221104 0.375405i
\(139\) 3.03547i 0.257465i 0.991679 + 0.128733i \(0.0410909\pi\)
−0.991679 + 0.128733i \(0.958909\pi\)
\(140\) 0.0515336 1.68599i 0.00435539 0.142492i
\(141\) 12.7249 + 12.9476i 1.07163 + 1.09039i
\(142\) −0.218221 0.814412i −0.0183127 0.0683440i
\(143\) 3.84568 + 1.03045i 0.321592 + 0.0861703i
\(144\) −6.53006 11.7777i −0.544172 0.981473i
\(145\) 0.565984 6.06158i 0.0470024 0.503387i
\(146\) 3.29496i 0.272693i
\(147\) 4.80152 11.1331i 0.396023 0.918241i
\(148\) 0.161754 + 0.161754i 0.0132961 + 0.0132961i
\(149\) 6.44006 11.1545i 0.527590 0.913813i −0.471892 0.881656i \(-0.656429\pi\)
0.999483 0.0321573i \(-0.0102377\pi\)
\(150\) 7.28916 + 10.8744i 0.595157 + 0.887889i
\(151\) −5.94939 10.3046i −0.484154 0.838580i 0.515680 0.856781i \(-0.327539\pi\)
−0.999834 + 0.0182013i \(0.994206\pi\)
\(152\) 17.2133 4.61230i 1.39619 0.374107i
\(153\) −2.50791 2.59648i −0.202753 0.209913i
\(154\) 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
\(157\) 13.4384 + 3.60080i 1.07250 + 0.287375i 0.751520 0.659711i \(-0.229321\pi\)
0.320980 + 0.947086i \(0.395988\pi\)
\(158\) −4.42591 1.18592i −0.352106 0.0943466i
\(159\) −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
\(162\) −9.28060 9.94811i −0.729153 0.781598i
\(163\) 23.2728 6.23594i 1.82287 0.488436i 0.825733 0.564061i \(-0.190762\pi\)
0.997136 + 0.0756252i \(0.0240953\pi\)
\(164\) −0.131558 0.227866i −0.0102730 0.0177933i
\(165\) −2.07253 + 2.87031i −0.161346 + 0.223454i
\(166\) −2.54508 + 4.40821i −0.197537 + 0.342144i
\(167\) 4.98846 + 4.98846i 0.386018 + 0.386018i 0.873265 0.487246i \(-0.161999\pi\)
−0.487246 + 0.873265i \(0.661999\pi\)
\(168\) 8.84019 + 7.93559i 0.682036 + 0.612244i
\(169\) 5.96958i 0.459199i
\(170\) 4.04975 + 0.378134i 0.310601 + 0.0290016i
\(171\) 18.0363 10.0001i 1.37927 0.764729i
\(172\) −1.87297 0.501860i −0.142813 0.0382665i
\(173\) −6.22848 23.2450i −0.473543 1.76728i −0.626885 0.779112i \(-0.715670\pi\)
0.153342 0.988173i \(-0.450996\pi\)
\(174\) −4.99672 5.08418i −0.378800 0.385430i
\(175\) −10.5531 7.97695i −0.797741 0.603001i
\(176\) 4.10341i 0.309306i
\(177\) −8.68497 + 14.7459i −0.652802 + 1.10837i
\(178\) −4.41893 + 16.4917i −0.331213 + 1.23610i
\(179\) 2.55927 + 4.43279i 0.191289 + 0.331322i 0.945678 0.325106i \(-0.105400\pi\)
−0.754389 + 0.656428i \(0.772067\pi\)
\(180\) 1.90097 + 0.210825i 0.141690 + 0.0157140i
\(181\) −1.77024 −0.131581 −0.0657906 0.997833i \(-0.520957\pi\)
−0.0657906 + 0.997833i \(0.520957\pi\)
\(182\) 9.63558 + 14.5117i 0.714237 + 1.07568i
\(183\) −1.84957 0.0160456i −0.136724 0.00118613i
\(184\) −4.38844 2.53367i −0.323520 0.186784i
\(185\) 1.76857 0.301216i 0.130028 0.0221458i
\(186\) −3.24165 + 11.6913i −0.237689 + 0.857251i
\(187\) 0.284689 + 1.06247i 0.0208185 + 0.0776957i
\(188\) −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 0.184028 0.982921i \(-0.441086\pi\)
−0.759221 + 0.650833i \(0.774420\pi\)
\(192\) −9.88521 + 5.59345i −0.713404 + 0.403673i
\(193\) −1.83608 + 6.85235i −0.132164 + 0.493243i −0.999993 0.00361952i \(-0.998848\pi\)
0.867829 + 0.496862i \(0.165515\pi\)
\(194\) −1.69748 + 2.94012i −0.121872 + 0.211088i
\(195\) −15.7657 5.99874i −1.12901 0.429579i
\(196\) 1.83943 + 0.774462i 0.131388 + 0.0553187i
\(197\) −12.5538 12.5538i −0.894420 0.894420i 0.100516 0.994935i \(-0.467951\pi\)
−0.994935 + 0.100516i \(0.967951\pi\)
\(198\) 1.00330 + 4.02225i 0.0713014 + 0.285849i
\(199\) 14.9099 8.60825i 1.05694 0.610222i 0.132353 0.991203i \(-0.457747\pi\)
0.924583 + 0.380980i \(0.124413\pi\)
\(200\) 10.7036 7.31004i 0.756857 0.516898i
\(201\) −3.06913 11.8649i −0.216480 0.836887i
\(202\) 4.96543 4.96543i 0.349367 0.349367i
\(203\) 6.45121 + 3.20471i 0.452786 + 0.224926i
\(204\) 0.423816 0.416526i 0.0296731 0.0291626i
\(205\) −2.05459 0.191842i −0.143499 0.0133988i
\(206\) 13.7861 7.95943i 0.960526 0.554560i
\(207\) −5.63724 1.61582i −0.391815 0.112308i
\(208\) −18.8850 + 5.06022i −1.30944 + 0.350863i
\(209\) −6.28395 −0.434670
\(210\) −15.1078 + 3.41916i −1.04254 + 0.235945i
\(211\) −9.75343 −0.671454 −0.335727 0.941959i \(-0.608982\pi\)
−0.335727 + 0.941959i \(0.608982\pi\)
\(212\) 3.03748 0.813891i 0.208615 0.0558982i
\(213\) −0.840797 + 0.475757i −0.0576105 + 0.0325983i
\(214\) 8.28303 4.78221i 0.566216 0.326905i
\(215\) −11.7062 + 9.70683i −0.798358 + 0.662001i
\(216\) −9.76943 + 9.27371i −0.664725 + 0.630996i
\(217\) −0.766300 12.2358i −0.0520198 0.830620i
\(218\) −9.21299 + 9.21299i −0.623982 + 0.623982i
\(219\) 3.65504 0.945459i 0.246985 0.0638882i
\(220\) −0.475431 0.337052i −0.0320536 0.0227241i
\(221\) −4.53872 + 2.62043i −0.305307 + 0.176269i
\(222\) 1.06609 1.81007i 0.0715512 0.121484i
\(223\) 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
\(225\) 9.97119 11.2060i 0.664746 0.747069i
\(226\) 7.95456 13.7777i 0.529129 0.916479i
\(227\) −6.22238 + 23.2222i −0.412994 + 1.54131i 0.375826 + 0.926690i \(0.377359\pi\)
−0.788820 + 0.614624i \(0.789308\pi\)
\(228\) 1.67184 + 2.95461i 0.110720 + 0.195674i
\(229\) 2.82056 + 1.62845i 0.186388 + 0.107611i 0.590290 0.807191i \(-0.299013\pi\)
−0.403903 + 0.914802i \(0.632347\pi\)
\(230\) 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
\(233\) 4.31679 + 16.1105i 0.282802 + 1.05543i 0.950430 + 0.310938i \(0.100643\pi\)
−0.667628 + 0.744495i \(0.732690\pi\)
\(234\) −17.2742 + 9.57759i −1.12925 + 0.626107i
\(235\) 3.93495 + 23.1039i 0.256688 + 1.50713i
\(236\) −2.43967 1.40854i −0.158809 0.0916883i
\(237\) −0.0455445 + 5.24987i −0.00295843 + 0.341016i
\(238\) −2.14107 + 4.31006i −0.138785 + 0.279380i
\(239\) 15.1824 0.982070 0.491035 0.871140i \(-0.336619\pi\)
0.491035 + 0.871140i \(0.336619\pi\)
\(240\) 1.76641 17.2956i 0.114021 1.11643i
\(241\) −0.0593822 0.102853i −0.00382515 0.00662535i 0.864106 0.503309i \(-0.167884\pi\)
−0.867932 + 0.496684i \(0.834551\pi\)
\(242\) −3.97678 + 14.8416i −0.255637 + 0.954052i
\(243\) −8.37229 + 13.1493i −0.537082 + 0.843530i
\(244\) 0.304473i 0.0194919i
\(245\) 13.2982 8.25579i 0.849590 0.527443i
\(246\) −1.72330 + 1.69365i −0.109873 + 0.107983i
\(247\) −7.74921 28.9204i −0.493070 1.84016i
\(248\) 11.6029 + 3.10898i 0.736783 + 0.197420i
\(249\) 5.62024 + 1.55832i 0.356168 + 0.0987544i
\(250\) −0.295882 + 16.8983i −0.0187132 + 1.06874i
\(251\) 16.8255i 1.06202i −0.847367 0.531008i \(-0.821813\pi\)
0.847367 0.531008i \(-0.178187\pi\)
\(252\) −1.04182 + 2.00898i −0.0656285 + 0.126554i
\(253\) 1.26350 + 1.26350i 0.0794358 + 0.0794358i
\(254\) −4.73413 + 8.19975i −0.297046 + 0.514498i
\(255\) −0.742580 4.60082i −0.0465022 0.288114i
\(256\) −3.35517 5.81133i −0.209698 0.363208i
\(257\) 13.4428 3.60198i 0.838538 0.224686i 0.186103 0.982530i \(-0.440414\pi\)
0.652435 + 0.757845i \(0.273748\pi\)
\(258\) −0.154472 + 17.8058i −0.00961699 + 1.10854i
\(259\) −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
\(262\) 12.4305 + 3.33074i 0.767958 + 0.205774i
\(263\) −20.7766 5.56707i −1.28114 0.343280i −0.446851 0.894608i \(-0.647455\pi\)
−0.834288 + 0.551328i \(0.814121\pi\)
\(264\) 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
\(267\) 19.5619 + 0.169706i 1.19717 + 0.0103859i
\(268\) 1.94866 0.522141i 0.119033 0.0318948i
\(269\) −9.44119 16.3526i −0.575639 0.997036i −0.995972 0.0896663i \(-0.971420\pi\)
0.420333 0.907370i \(-0.361913\pi\)
\(270\) −2.49738 17.3855i −0.151986 1.05804i
\(271\) 1.85591 3.21453i 0.112739 0.195269i −0.804135 0.594447i \(-0.797371\pi\)
0.916874 + 0.399178i \(0.130704\pi\)
\(272\) −3.81947 3.81947i −0.231589 0.231589i
\(273\) 13.3327 14.8526i 0.806934 0.898919i
\(274\) 15.6193i 0.943597i
\(275\) −4.31289 + 1.51299i −0.260077 + 0.0912369i
\(276\) 0.257925 0.930232i 0.0155252 0.0559934i
\(277\) −7.30397 1.95709i −0.438853 0.117590i 0.0326260 0.999468i \(-0.489613\pi\)
−0.471479 + 0.881877i \(0.656280\pi\)
\(278\) 1.18762 + 4.43225i 0.0712286 + 0.265829i
\(279\) 13.8992 + 0.241178i 0.832122 + 0.0144390i
\(280\) 3.51491 + 14.9282i 0.210056 + 0.892128i
\(281\) 12.0546i 0.719117i 0.933122 + 0.359559i \(0.117073\pi\)
−0.933122 + 0.359559i \(0.882927\pi\)
\(282\) 23.6460 + 13.9269i 1.40810 + 0.829335i
\(283\) −6.21514 + 23.1952i −0.369452 + 1.37881i 0.491833 + 0.870690i \(0.336327\pi\)
−0.861285 + 0.508123i \(0.830340\pi\)
\(284\) −0.0795132 0.137721i −0.00471824 0.00817224i
\(285\) 26.4865 + 2.70508i 1.56893 + 0.160235i
\(286\) 6.01844 0.355878
\(287\) 1.08625 2.18666i 0.0641190 0.129074i
\(288\) −3.33704 3.45489i −0.196637 0.203581i
\(289\) 13.4685 + 7.77604i 0.792264 + 0.457414i
\(290\) −1.54515 9.07226i −0.0907343 0.532742i
\(291\) 3.74850 + 1.03934i 0.219741 + 0.0609273i
\(292\) 0.160848 + 0.600292i 0.00941291 + 0.0351295i
\(293\) −12.2498 + 12.2498i −0.715644 + 0.715644i −0.967710 0.252066i \(-0.918890\pi\)
0.252066 + 0.967710i \(0.418890\pi\)
\(294\) 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
\(297\) 4.17392 2.26709i 0.242196 0.131550i
\(298\) 5.03930 18.8069i 0.291919 1.08946i
\(299\) −4.25687 + 7.37311i −0.246181 + 0.426398i
\(300\) 1.85882 + 1.62532i 0.107319 + 0.0938377i
\(301\) −5.73428 17.0552i −0.330518 0.983045i
\(302\) −12.7187 12.7187i −0.731877 0.731877i
\(303\) −6.93285 4.08328i −0.398282 0.234578i
\(304\) 26.7243 15.4293i 1.53275 0.884931i
\(305\) −1.94800 1.38102i −0.111542 0.0790769i
\(306\) −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 \(0.418349\pi\)
\(308\) 0.574459 0.381433i 0.0327328 0.0217342i
\(309\) −12.7851 13.0088i −0.727317 0.740047i
\(310\) −12.0570 + 9.99773i −0.684793 + 0.567833i
\(311\) −20.2993 + 11.7198i −1.15107 + 0.664569i −0.949147 0.314833i \(-0.898051\pi\)
−0.201920 + 0.979402i \(0.564718\pi\)
\(312\) 9.63067 + 17.0201i 0.545229 + 0.963574i
\(313\) 10.2390 2.74353i 0.578742 0.155073i 0.0424390 0.999099i \(-0.486487\pi\)
0.536303 + 0.844026i \(0.319821\pi\)
\(314\) 21.0309 1.18684
\(315\) 8.12788 + 15.7778i 0.457954 + 0.888976i
\(316\) −0.864226 −0.0486165
\(317\) −19.8428 + 5.31686i −1.11448 + 0.298625i −0.768649 0.639671i \(-0.779071\pi\)
−0.345834 + 0.938296i \(0.612404\pi\)
\(318\) −14.2213 25.1331i −0.797492 1.40939i
\(319\) 2.15535 1.24439i 0.120676 0.0696724i
\(320\) −14.5996 1.36320i −0.816143 0.0762052i
\(321\) −7.68156 7.81601i −0.428743 0.436247i
\(322\) 0.488665 + 7.80269i 0.0272322 + 0.434827i
\(323\) 5.84912 5.84912i 0.325454 0.325454i
\(324\) −2.17642 1.35935i −0.120912 0.0755196i
\(325\) −12.2817 17.9833i −0.681268 0.997533i
\(326\) 31.5421 18.2108i 1.74695 1.00860i
\(327\) 12.8634 + 7.57622i 0.711347 + 0.418966i
\(328\) 1.69160 + 1.69160i 0.0934032 + 0.0934032i
\(329\) −27.1819 5.48891i −1.49858 0.302613i
\(330\) −1.90321 + 5.00196i −0.104768 + 0.275349i
\(331\) −15.9659 + 27.6537i −0.877564 + 1.51998i −0.0235570 + 0.999722i \(0.507499\pi\)
−0.854007 + 0.520262i \(0.825834\pi\)
\(332\) −0.248483 + 0.927351i −0.0136373 + 0.0508950i
\(333\) −2.31379 0.663210i −0.126795 0.0363437i
\(334\) 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 \(0.132047\pi\)
\(338\) 2.33558 + 8.71650i 0.127039 + 0.474115i
\(339\) −17.5659 4.87047i −0.954046 0.264527i
\(340\) 0.756262 0.128803i 0.0410141 0.00698534i
\(341\) −3.66830 2.11789i −0.198649 0.114690i
\(342\) 22.4233 21.6584i 1.21251 1.17115i
\(343\) 3.45475 + 18.1952i 0.186539 + 0.982448i
\(344\) 17.6300 0.950546
\(345\) −4.78169 5.86950i −0.257438 0.316003i
\(346\) −18.1891 31.5044i −0.977850 1.69369i
\(347\) 4.16271 15.5354i 0.223466 0.833986i −0.759547 0.650452i \(-0.774579\pi\)
0.983013 0.183534i \(-0.0587538\pi\)
\(348\) −1.15852 0.682339i −0.0621031 0.0365772i
\(349\) 9.21013i 0.493007i 0.969142 + 0.246503i \(0.0792817\pi\)
−0.969142 + 0.246503i \(0.920718\pi\)
\(350\) −18.5301 7.51869i −0.990476 0.401891i
\(351\) 15.5809 + 16.4138i 0.831649 + 0.876104i
\(352\) 0.378808 + 1.41373i 0.0201905 + 0.0753521i
\(353\) −10.0918 2.70409i −0.537133 0.143924i −0.0199530 0.999801i \(-0.506352\pi\)
−0.517180 + 0.855876i \(0.673018\pi\)
\(354\) −6.91210 + 24.9292i −0.367374 + 1.32497i
\(355\) −1.24179 0.115948i −0.0659071 0.00615390i
\(356\) 3.22025i 0.170673i
\(357\) 5.39544 + 1.13832i 0.285557 + 0.0602461i
\(358\) 5.47124 + 5.47124i 0.289164 + 0.289164i
\(359\) 0.770883 1.33521i 0.0406857 0.0704697i −0.844965 0.534821i \(-0.820379\pi\)
0.885651 + 0.464351i \(0.153712\pi\)
\(360\) −17.1910 + 2.62186i −0.906047 + 0.138184i
\(361\) 14.1284 + 24.4711i 0.743601 + 1.28795i
\(362\) −2.58482 + 0.692602i −0.135855 + 0.0364023i
\(363\) 17.6046 + 0.152726i 0.924001 + 0.00801603i
\(364\) 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
\(367\) −15.4881 4.15004i −0.808475 0.216630i −0.169173 0.985586i \(-0.554110\pi\)
−0.639301 + 0.768956i \(0.720776\pi\)
\(368\) −8.47576 2.27107i −0.441830 0.118388i
\(369\) 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
\(372\) −0.0198512 + 2.28823i −0.00102924 + 0.118639i
\(373\) −27.1057 + 7.26294i −1.40348 + 0.376061i −0.879592 0.475728i \(-0.842185\pi\)
−0.523885 + 0.851789i \(0.675518\pi\)
\(374\) 0.831378 + 1.43999i 0.0429895 + 0.0744600i
\(375\) 18.8299 4.52059i 0.972371 0.233442i
\(376\) 13.5853 23.5304i 0.700606 1.21349i
\(377\) 8.38493 + 8.38493i 0.431846 + 0.431846i
\(378\) 20.2568 + 4.64222i 1.04190 + 0.238770i
\(379\) 18.6208i 0.956485i −0.878228 0.478243i \(-0.841274\pi\)
0.878228 0.478243i \(-0.158726\pi\)
\(380\) −0.407449 + 4.36371i −0.0209017 + 0.223853i
\(381\) 10.4543 + 2.89864i 0.535588 + 0.148502i
\(382\) −13.4029 3.59129i −0.685750 0.183746i
\(383\) 4.19755 + 15.6655i 0.214485 + 0.800469i 0.986347 + 0.164679i \(0.0526588\pi\)
−0.771862 + 0.635790i \(0.780674\pi\)
\(384\) −16.2013 + 15.9226i −0.826768 + 0.812546i
\(385\) 0.165222 5.40545i 0.00842050 0.275487i
\(386\) 10.7238i 0.545828i
\(387\) 19.7960 4.93787i 1.00629 0.251006i
\(388\) −0.165729 + 0.618510i −0.00841362 + 0.0314001i
\(389\) 16.7445 + 29.0023i 0.848980 + 1.47048i 0.882120 + 0.471025i \(0.156116\pi\)
−0.0331402 + 0.999451i \(0.510551\pi\)
\(390\) −25.3674 2.59078i −1.28453 0.131189i
\(391\) −2.35215 −0.118953
\(392\) −17.9769 2.47300i −0.907973 0.124906i
\(393\) 0.127915 14.7447i 0.00645246 0.743769i
\(394\) −23.2420 13.4188i −1.17092 0.676029i
\(395\) −3.91993 + 5.52927i −0.197233 + 0.278208i
\(396\) 0.379138 + 0.683816i 0.0190524 + 0.0343631i
\(397\) 2.75129 + 10.2680i 0.138084 + 0.515335i 0.999966 + 0.00822688i \(0.00261873\pi\)
−0.861883 + 0.507108i \(0.830715\pi\)
\(398\) 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 0.970749 + 0.240096i \(0.0771788\pi\)
0.693304 + 0.720646i \(0.256155\pi\)
\(402\) −9.12350 16.1238i −0.455039 0.804182i
\(403\) 5.22346 19.4942i 0.260199 0.971076i
\(404\) 0.662233 1.14702i 0.0329473 0.0570664i
\(405\) −18.5688 + 7.75890i −0.922690 + 0.385543i
\(406\) 10.6736 + 2.15535i 0.529721 + 0.106968i
\(407\) 0.518601 + 0.518601i 0.0257061 + 0.0257061i
\(408\) −2.74191 + 4.65539i −0.135745 + 0.230476i
\(409\) −0.838832 + 0.484300i −0.0414776 + 0.0239471i −0.520595 0.853804i \(-0.674290\pi\)
0.479118 + 0.877751i \(0.340957\pi\)
\(410\) −3.07507 + 0.523733i −0.151867 + 0.0258653i
\(411\) −17.3262 + 4.48182i −0.854640 + 0.221072i
\(412\) 2.12308 2.12308i 0.104597 0.104597i
\(413\) −1.63396 26.0901i −0.0804021 1.28381i
\(414\) −8.86342 0.153798i −0.435613 0.00755876i
\(415\) 4.80609 + 5.79603i 0.235921 + 0.284516i
\(416\) −6.03923 + 3.48675i −0.296098 + 0.170952i
\(417\) 4.57584 2.58920i 0.224080 0.126794i
\(418\) −9.17553 + 2.45857i −0.448790 + 0.120253i
\(419\) 24.3482 1.18949 0.594743 0.803916i \(-0.297254\pi\)
0.594743 + 0.803916i \(0.297254\pi\)
\(420\) −2.58551 + 1.36043i −0.126160 + 0.0663821i
\(421\) 1.75923 0.0857395 0.0428698 0.999081i \(-0.486350\pi\)
0.0428698 + 0.999081i \(0.486350\pi\)
\(422\) −14.2415 + 3.81600i −0.693265 + 0.185760i
\(423\) 8.66388 30.2263i 0.421252 1.46965i
\(424\) −24.7609 + 14.2957i −1.20249 + 0.694261i
\(425\) 2.60615 5.42275i 0.126417 0.263042i
\(426\) −1.04155 + 1.02364i −0.0504634 + 0.0495954i
\(427\) 2.35375 1.56286i 0.113906 0.0756322i
\(428\) 1.27559 1.27559i 0.0616581 0.0616581i
\(429\) −1.72694 6.67615i −0.0833773 0.322327i
\(430\) −13.2951 + 18.7535i −0.641146 + 0.904373i
\(431\) −18.5687 + 10.7206i −0.894422 + 0.516395i −0.875386 0.483424i \(-0.839393\pi\)
−0.0190357 + 0.999819i \(0.506060\pi\)
\(432\) −12.1843 + 19.8899i −0.586219 + 0.956954i
\(433\) −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
\(435\) −9.62034 + 4.31721i −0.461260 + 0.206994i
\(436\) −1.22872 + 2.12821i −0.0588452 + 0.101923i
\(437\) 3.47792 12.9798i 0.166371 0.620907i
\(438\) 4.96701 2.81054i 0.237333 0.134293i
\(439\) −2.05458 1.18621i −0.0980598 0.0566149i 0.450168 0.892944i \(-0.351364\pi\)
−0.548228 + 0.836329i \(0.684697\pi\)
\(440\) 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
\(443\) 5.63107 + 21.0154i 0.267540 + 0.998473i 0.960677 + 0.277668i \(0.0895614\pi\)
−0.693137 + 0.720806i \(0.743772\pi\)
\(444\) 0.105864 0.381811i 0.00502410 0.0181199i
\(445\) 20.6030 + 14.6063i 0.976677 + 0.692406i
\(446\) 16.9826 + 9.80492i 0.804150 + 0.464276i
\(447\) −22.3082 0.193531i −1.05514 0.00915372i
\(448\) 7.71870 15.5381i 0.364674 0.734104i
\(449\) −28.8886 −1.36334 −0.681669 0.731661i \(-0.738746\pi\)
−0.681669 + 0.731661i \(0.738746\pi\)
\(450\) 10.1751 20.2637i 0.479660 0.955241i
\(451\) −0.421789 0.730561i −0.0198613 0.0344008i
\(452\) 0.776625 2.89840i 0.0365293 0.136329i
\(453\) −10.4591 + 17.7581i −0.491411 + 0.834348i
\(454\) 36.3425i 1.70564i
\(455\) 25.0811 5.90547i 1.17582 0.276853i
\(456\) −21.6355 22.0141i −1.01317 1.03091i
\(457\) −0.508794 1.89885i −0.0238004 0.0888242i 0.953004 0.302957i \(-0.0979740\pi\)
−0.976804 + 0.214133i \(0.931307\pi\)
\(458\) 4.75557 + 1.27425i 0.222213 + 0.0595419i
\(459\) −1.77489 + 5.99532i −0.0828446 + 0.279838i
\(460\) 0.959328 0.795478i 0.0447289 0.0370893i
\(461\) 17.4281i 0.811709i −0.913938 0.405854i \(-0.866974\pi\)
0.913938 0.405854i \(-0.133026\pi\)
\(462\) −4.71225 4.23005i −0.219234 0.196800i
\(463\) 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
\(465\) 14.5500 + 10.5059i 0.674738 + 0.487199i
\(466\) 12.6063 + 21.8348i 0.583977 + 1.01148i
\(467\) 12.1766 3.26272i 0.563468 0.150981i 0.0341687 0.999416i \(-0.489122\pi\)
0.529299 + 0.848435i \(0.322455\pi\)
\(468\) −2.67956 + 2.58816i −0.123863 + 0.119638i
\(469\) 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
\(472\) 24.7405 + 6.62921i 1.13878 + 0.305134i
\(473\) −6.00493 1.60902i −0.276107 0.0739827i
\(474\) 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
\(477\) −23.7990 + 22.9872i −1.08968 + 1.05251i
\(478\) 22.1687 5.94008i 1.01397 0.271693i
\(479\) 5.14393 + 8.90955i 0.235032 + 0.407088i 0.959282 0.282450i \(-0.0911471\pi\)
−0.724250 + 0.689538i \(0.757814\pi\)
\(480\) −0.988080 6.12186i −0.0450995 0.279424i
\(481\) −1.74722 + 3.02627i −0.0796662 + 0.137986i
\(482\) −0.126948 0.126948i −0.00578232 0.00578232i
\(483\) 8.51517 2.78098i 0.387454 0.126539i
\(484\) 2.89804i 0.131729i
\(485\) 3.20548 + 3.86574i 0.145554 + 0.175534i
\(486\) −7.08018 + 22.4756i −0.321163 + 1.01952i
\(487\) −18.0099 4.82573i −0.816105 0.218675i −0.173462 0.984841i \(-0.555495\pi\)
−0.642643 + 0.766166i \(0.722162\pi\)
\(488\) 0.716491 + 2.67398i 0.0324340 + 0.121045i
\(489\) −29.2517 29.7637i −1.32281 1.34596i
\(490\) 16.1873 17.2576i 0.731269 0.779618i
\(491\) 24.6940i 1.11442i −0.830370 0.557212i \(-0.811871\pi\)
0.830370 0.557212i \(-0.188129\pi\)
\(492\) −0.231281 + 0.392683i −0.0104269 + 0.0177035i
\(493\) −0.847921 + 3.16448i −0.0381884 + 0.142521i
\(494\) −22.6300 39.1964i −1.01817 1.76353i
\(495\) 6.09470 + 0.675927i 0.273936 + 0.0303806i
\(496\) 20.8007 0.933977
\(497\) 0.656522 1.32161i 0.0294490 0.0592821i
\(498\) 8.81609 + 0.0764827i 0.395058 + 0.00342727i
\(499\) 11.1524 + 6.43883i 0.499249 + 0.288242i 0.728403 0.685148i \(-0.240263\pi\)
−0.229154 + 0.973390i \(0.573596\pi\)
\(500\) 0.771007 + 3.09306i 0.0344805 + 0.138326i
\(501\) 3.26482 11.7749i 0.145862 0.526065i
\(502\) −6.58292 24.5678i −0.293810 1.09651i
\(503\) −2.81929 + 2.81929i −0.125706 + 0.125706i −0.767161 0.641455i \(-0.778331\pi\)
0.641455 + 0.767161i \(0.278331\pi\)
\(504\) 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
\(507\) 8.99888 5.09194i 0.399654 0.226141i
\(508\) −0.462205 + 1.72497i −0.0205070 + 0.0765333i
\(509\) 20.2795 35.1250i 0.898871 1.55689i 0.0699315 0.997552i \(-0.477722\pi\)
0.828939 0.559338i \(-0.188945\pi\)
\(510\) −2.88433 6.42736i −0.127720 0.284608i
\(511\) −3.81498 + 4.32475i −0.168765 + 0.191316i
\(512\) 11.3747 + 11.3747i 0.502695 + 0.502695i
\(513\) −30.4594 18.6591i −1.34481 0.823818i
\(514\) 18.2192 10.5189i 0.803616 0.463968i
\(515\) −3.95356 23.2131i −0.174215 1.02289i
\(516\) 0.841073 + 3.25150i 0.0370262 + 0.143139i
\(517\) −6.77477 + 6.77477i −0.297954 + 0.297954i
\(518\) 0.200571 + 3.20259i 0.00881258 + 0.140714i
\(519\) −29.7281 + 29.2167i −1.30492 + 1.28247i
\(520\) −2.34712 + 25.1372i −0.102928 + 1.10234i
\(521\) −13.7175 + 7.91980i −0.600974 + 0.346973i −0.769425 0.638738i \(-0.779457\pi\)
0.168451 + 0.985710i \(0.446124\pi\)
\(522\) −3.40207 + 11.8690i −0.148905 + 0.519494i
\(523\) −13.0100 + 3.48603i −0.568889 + 0.152433i −0.531787 0.846878i \(-0.678479\pi\)
−0.0371021 + 0.999311i \(0.511813\pi\)
\(524\) 2.42724 0.106035
\(525\) −3.02331 + 22.7125i −0.131948 + 0.991257i
\(526\) −32.5151 −1.41772
\(527\) 5.38580 1.44312i 0.234609 0.0628633i
\(528\) 6.18571 3.50013i 0.269198 0.152323i
\(529\) 16.6095 9.58948i 0.722151 0.416934i
\(530\) 3.46593 37.1194i 0.150550 1.61236i
\(531\) 29.6369 + 0.514259i 1.28613 + 0.0223170i
\(532\) −4.64420 2.30706i −0.201352 0.100024i
\(533\) 2.84210 2.84210i 0.123105 0.123105i
\(534\) 28.6298 7.40573i 1.23893 0.320477i
\(535\) −2.37539 13.9470i −0.102697 0.602980i
\(536\) −15.8850 + 9.17122i −0.686128 + 0.396136i
\(537\) 4.49923 7.63908i 0.194156 0.329650i
\(538\) −20.1835 20.1835i −0.870171 0.870171i
\(539\) 5.89740 + 2.48301i 0.254019 + 0.106951i
\(540\) −1.30368 3.04546i −0.0561014 0.131056i
\(541\) 15.9766 27.6722i 0.686887 1.18972i −0.285953 0.958244i \(-0.592310\pi\)
0.972840 0.231479i \(-0.0743565\pi\)
\(542\) 1.45224 5.41983i 0.0623790 0.232801i
\(543\) 1.50998 + 2.66856i 0.0647996 + 0.114519i
\(544\) −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 \(-0.0188420\pi\)
\(548\) −0.762477 2.84560i −0.0325714 0.121558i
\(549\) 1.55346 + 2.80183i 0.0662999 + 0.119579i
\(550\) −5.70552 + 3.89660i −0.243284 + 0.166152i
\(551\) −16.2087 9.35811i −0.690515 0.398669i
\(552\) −0.0761397 + 8.77655i −0.00324072 + 0.373555i
\(553\) −4.43608 6.68097i −0.188641 0.284104i
\(554\) −11.4306 −0.485640
\(555\) −1.96263 2.40912i −0.0833090 0.102261i
\(556\) 0.432732 + 0.749514i 0.0183519 + 0.0317865i
\(557\) 1.00229 3.74061i 0.0424686 0.158495i −0.941435 0.337194i \(-0.890522\pi\)
0.983904 + 0.178699i \(0.0571888\pi\)
\(558\) 20.3893 5.08584i 0.863146 0.215301i
\(559\) 29.6205i 1.25281i
\(560\) 12.5696 + 23.3939i 0.531163 + 0.988574i
\(561\) 1.35880 1.33542i 0.0573685 0.0563817i
\(562\) 4.71632 + 17.6016i 0.198946 + 0.742477i
\(563\) 35.3104 + 9.46140i 1.48816 + 0.398751i 0.909114 0.416547i \(-0.136760\pi\)
0.579043 + 0.815297i \(0.303426\pi\)
\(564\) 4.98780 + 1.38296i 0.210024 + 0.0582333i
\(565\) −15.0212 18.1153i −0.631948 0.762115i
\(566\) 36.3002i 1.52581i
\(567\) −0.662966 23.8025i −0.0278419 0.999612i
\(568\) 1.02240 + 1.02240i 0.0428989 + 0.0428989i
\(569\) −8.11965 + 14.0636i −0.340393 + 0.589579i −0.984506 0.175352i \(-0.943894\pi\)
0.644112 + 0.764931i \(0.277227\pi\)
\(570\) 39.7327 6.41293i 1.66422 0.268608i
\(571\) −20.1402 34.8839i −0.842843 1.45985i −0.887481 0.460844i \(-0.847547\pi\)
0.0446382 0.999003i \(-0.485786\pi\)
\(572\) 1.09647 0.293798i 0.0458457 0.0122843i
\(573\) −0.137921 + 15.8980i −0.00576174 + 0.664151i
\(574\) 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
\(577\) −16.6936 4.47305i −0.694965 0.186215i −0.105991 0.994367i \(-0.533801\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(578\) 22.7084 + 6.08469i 0.944544 + 0.253090i
\(579\) 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
\(582\) 5.88001 + 0.0510111i 0.243734 + 0.00211448i
\(583\) 9.73848 2.60942i 0.403327 0.108071i
\(584\) −2.82524 4.89345i −0.116909 0.202492i
\(585\) 4.40503 + 28.8830i 0.182126 + 1.19416i
\(586\) −13.0939 + 22.6793i −0.540905 + 0.936875i
\(587\) −0.596922 0.596922i −0.0246376 0.0246376i 0.694681 0.719318i \(-0.255546\pi\)
−0.719318 + 0.694681i \(0.755546\pi\)
\(588\) −0.401529 3.43346i −0.0165588 0.141594i
\(589\) 31.8541i 1.31253i
\(590\) −25.7089 + 21.3179i −1.05842 + 0.877645i
\(591\) −8.21615 + 29.6324i −0.337967 + 1.21891i
\(592\) −3.47885 0.932155i −0.142980 0.0383113i
\(593\) −2.42881 9.06443i −0.0997391 0.372232i 0.897956 0.440085i \(-0.145052\pi\)
−0.997695 + 0.0678534i \(0.978385\pi\)
\(594\) 5.20757 4.94333i 0.213669 0.202827i
\(595\) 4.87762 + 5.18520i 0.199963 + 0.212572i
\(596\) 3.67234i 0.150425i
\(597\) −25.6944 15.1334i −1.05160 0.619368i
\(598\) −3.33097 + 12.4313i −0.136213 + 0.508355i
\(599\) −3.14342 5.44456i −0.128437 0.222459i 0.794634 0.607088i \(-0.207663\pi\)
−0.923071 + 0.384629i \(0.874329\pi\)
\(600\) −20.1495 9.89985i −0.822600 0.404160i
\(601\) 9.39584 0.383264 0.191632 0.981467i \(-0.438622\pi\)
0.191632 + 0.981467i \(0.438622\pi\)
\(602\) −15.0457 22.6597i −0.613217 0.923539i
\(603\) −15.2679 + 14.7471i −0.621759 + 0.600549i
\(604\) −2.93803 1.69627i −0.119547 0.0690203i
\(605\) 18.5415 + 13.1448i 0.753820 + 0.534414i
\(606\) −11.7206 3.24976i −0.476116 0.132012i
\(607\) 3.66495 + 13.6778i 0.148756 + 0.555164i 0.999559 + 0.0296803i \(0.00944893\pi\)
−0.850804 + 0.525484i \(0.823884\pi\)
\(608\) 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
\(612\) −0.989401 0.283596i −0.0399942 0.0114637i
\(613\) −1.12348 + 4.19289i −0.0453770 + 0.169349i −0.984896 0.173148i \(-0.944606\pi\)
0.939519 + 0.342497i \(0.111273\pi\)
\(614\) −13.3643 + 23.1476i −0.539339 + 0.934162i
\(615\) 1.46333 + 3.26084i 0.0590072 + 0.131490i
\(616\) −4.14749 + 4.70170i −0.167107 + 0.189437i
\(617\) −3.80377 3.80377i −0.153134 0.153134i 0.626382 0.779516i \(-0.284535\pi\)
−0.779516 + 0.626382i \(0.784535\pi\)
\(618\) −23.7578 13.9928i −0.955679 0.562872i
\(619\) −18.8856 + 10.9036i −0.759075 + 0.438252i −0.828964 0.559303i \(-0.811069\pi\)
0.0698884 + 0.997555i \(0.477736\pi\)
\(620\) −1.70856 + 2.41002i −0.0686173 + 0.0967886i
\(621\) 2.37267 + 9.87616i 0.0952120 + 0.396317i
\(622\) −25.0547 + 25.0547i −1.00460 + 1.00460i
\(623\) −24.8944 + 16.5296i −0.997375 + 0.662243i
\(624\) 23.7366 + 24.1520i 0.950224 + 0.966855i
\(625\) 23.2863 + 9.09652i 0.931453 + 0.363861i
\(626\) 13.8771 8.01194i 0.554640 0.320221i
\(627\) 5.36009 + 9.47279i 0.214061 + 0.378307i
\(628\) 3.83151 1.02665i 0.152894 0.0409678i
\(629\) −0.965431 −0.0384943
\(630\) 18.0409 + 19.8579i 0.718768 + 0.791158i
\(631\) 8.91815 0.355026 0.177513 0.984118i \(-0.443195\pi\)
0.177513 + 0.984118i \(0.443195\pi\)
\(632\) 7.58991 2.03371i 0.301911 0.0808967i
\(633\) 8.31949 + 14.7029i 0.330670 + 0.584387i
\(634\) −26.8933 + 15.5268i −1.06807 + 0.616650i
\(635\) 8.93984 + 10.7812i 0.354767 + 0.427841i
\(636\) −3.81782 3.88464i −0.151386 0.154036i
\(637\) −4.15494 + 30.2034i −0.164625 + 1.19670i
\(638\) 2.66027 2.66027i 0.105321 0.105321i
\(639\) 1.43437 + 0.861653i 0.0567427 + 0.0340865i
\(640\) −28.9097 + 4.92378i −1.14276 + 0.194630i
\(641\) 33.8421 19.5388i 1.33668 0.771735i 0.350370 0.936611i \(-0.386056\pi\)
0.986314 + 0.164876i \(0.0527224\pi\)
\(642\) −14.2742 8.40717i −0.563359 0.331805i
\(643\) 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
\(645\) 24.6178 + 9.36688i 0.969325 + 0.368821i
\(646\) 6.25216 10.8291i 0.245988 0.426064i
\(647\) −3.73697 + 13.9465i −0.146915 + 0.548295i 0.852747 + 0.522324i \(0.174935\pi\)
−0.999663 + 0.0259718i \(0.991732\pi\)
\(648\) 22.3128 + 6.81669i 0.876531 + 0.267785i
\(649\) −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
\(653\) −4.53005 16.9064i −0.177274 0.661597i −0.996153 0.0876304i \(-0.972071\pi\)
0.818879 0.573967i \(-0.194596\pi\)
\(654\) 21.7467 + 6.02968i 0.850362 + 0.235779i
\(655\) 11.0094 15.5294i 0.430173 0.606783i
\(656\) 3.58756 + 2.07128i 0.140071 + 0.0808699i
\(657\) −4.54292 4.70336i −0.177236 0.183496i
\(658\) −41.8372 + 2.62017i −1.63098 + 0.102145i
\(659\) −7.49888 −0.292115 −0.146057 0.989276i \(-0.546658\pi\)
−0.146057 + 0.989276i \(0.546658\pi\)
\(660\) −0.102558 + 1.00419i −0.00399208 + 0.0390881i
\(661\) 12.8552 + 22.2658i 0.500008 + 0.866038i 1.00000 8.71032e-6i \(2.77258e-6\pi\)
−0.499992 + 0.866030i \(0.666664\pi\)
\(662\) −12.4932 + 46.6252i −0.485561 + 1.81214i
\(663\) 7.82162 + 4.60674i 0.303766 + 0.178911i
\(664\) 8.72904i 0.338752i
\(665\) −35.8254 + 19.2491i −1.38925 + 0.746448i
\(666\) −3.63796 0.0631259i −0.140968 0.00244608i
\(667\) 1.37744 + 5.14068i 0.0533347 + 0.199048i
\(668\) 1.94289 + 0.520595i 0.0751726 + 0.0201424i
\(669\) 6.00342 21.6519i 0.232105 0.837113i
\(670\) 2.22352 23.8135i 0.0859020 0.919994i
\(671\) 0.976172i 0.0376847i
\(672\) 7.17919 + 1.51465i 0.276943 + 0.0584289i
\(673\) 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
\(675\) −25.3978 5.47260i −0.977564 0.210641i
\(676\) 0.851014 + 1.47400i 0.0327313 + 0.0566923i
\(677\) −32.9885 + 8.83924i −1.26785 + 0.339719i −0.829207 0.558942i \(-0.811208\pi\)
−0.438643 + 0.898661i \(0.644541\pi\)
\(678\) −27.5544 0.239044i −1.05822 0.00918042i
\(679\) −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
\(682\) −6.18489 1.65724i −0.236832 0.0634588i
\(683\) −23.0820 6.18479i −0.883206 0.236654i −0.211416 0.977396i \(-0.567808\pi\)
−0.671790 + 0.740742i \(0.734474\pi\)
\(684\) 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
\(687\) 0.0489368 5.64091i 0.00186706 0.215214i
\(688\) 29.4884 7.90140i 1.12424 0.301238i
\(689\) 24.0185 + 41.6012i 0.915031 + 1.58488i
\(690\) −9.27842 6.69955i −0.353223 0.255047i
\(691\) −10.0976 + 17.4895i −0.384129 + 0.665332i −0.991648 0.128974i \(-0.958832\pi\)
0.607519 + 0.794305i \(0.292165\pi\)
\(692\) −4.85170 4.85170i −0.184434 0.184434i
\(693\) −3.34018 + 6.44099i −0.126883 + 0.244673i
\(694\) 24.3128i 0.922899i
\(695\) 6.75813 + 0.631022i 0.256350 + 0.0239360i
\(696\) 11.7802 + 3.26628i 0.446526 + 0.123808i
\(697\) 1.07261 + 0.287405i 0.0406281 + 0.0108863i
\(698\) 3.60343 + 13.4482i 0.136392 + 0.509021i
\(699\) 20.6037 20.2493i 0.779304 0.765899i
\(700\) −3.74294 0.465221i −0.141470 0.0175837i
\(701\) 49.4540i 1.86785i −0.357467 0.933926i \(-0.616360\pi\)
0.357467 0.933926i \(-0.383640\pi\)
\(702\) 29.1724 + 17.8707i 1.10104 + 0.674485i
\(703\) 1.42750 5.32750i 0.0538392 0.200931i
\(704\) −2.99717 5.19126i −0.112960 0.195653i
\(705\) 31.4716 25.6389i 1.18529 0.965617i
\(706\) −15.7936 −0.594398
\(707\) 12.2664 0.768217i 0.461325 0.0288918i
\(708\) −0.0423283 + 4.87915i −0.00159080 + 0.183370i
\(709\) −33.9663 19.6105i −1.27563 0.736486i −0.299589 0.954068i \(-0.596850\pi\)
−0.976042 + 0.217582i \(0.930183\pi\)
\(710\) −1.85856 + 0.316542i −0.0697505 + 0.0118796i
\(711\) 7.95280 4.40938i 0.298253 0.165365i
\(712\) −7.57795 28.2813i −0.283996 1.05989i
\(713\) 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
\(717\) −12.9503 22.8869i −0.483639 0.854726i
\(718\) 0.603211 2.25121i 0.0225116 0.0840145i
\(719\) 0.965960 1.67309i 0.0360242 0.0623958i −0.847451 0.530873i \(-0.821864\pi\)
0.883475 + 0.468478i \(0.155197\pi\)
\(720\) −27.5791 + 12.0900i −1.02781 + 0.450569i
\(721\) 27.3104 + 5.51486i 1.01709 + 0.205384i
\(722\) 30.2039 + 30.2039i 1.12407 + 1.12407i
\(723\) −0.104395 + 0.177248i −0.00388248 + 0.00659191i
\(724\) −0.437106 + 0.252363i −0.0162449 + 0.00937901i
\(725\) −13.3777 2.52019i −0.496837 0.0935977i
\(726\) 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 \(0.113340\pi\)
\(728\) −26.7530 13.2899i −0.991534 0.492555i
\(729\) 26.9634 + 1.40474i 0.998646 + 0.0520273i
\(730\) 7.33585 + 0.684965i 0.271512 + 0.0253517i
\(731\) 7.08709 4.09173i 0.262125 0.151338i
\(732\) −0.458980 + 0.259709i −0.0169644 + 0.00959914i
\(733\) 42.0106 11.2567i 1.55170 0.415776i 0.621673 0.783277i \(-0.286453\pi\)
0.930023 + 0.367502i \(0.119787\pi\)
\(734\) −24.2387 −0.894668
\(735\) −23.7883 13.0044i −0.877446 0.479675i
\(736\) −3.12978 −0.115365
\(737\) 6.24759 1.67404i 0.230133 0.0616640i
\(738\) 4.02305 + 1.15314i 0.148090 + 0.0424477i
\(739\) 23.4387 13.5324i 0.862208 0.497796i −0.00254291 0.999997i \(-0.500809\pi\)
0.864751 + 0.502201i \(0.167476\pi\)
\(740\) 0.393753 0.326501i 0.0144746 0.0120024i
\(741\) −36.9864 + 36.3502i −1.35873 + 1.33536i
\(742\) 39.5054 + 19.6247i 1.45029 + 0.720447i
\(743\) 2.20467 2.20467i 0.0808816 0.0808816i −0.665509 0.746390i \(-0.731785\pi\)
0.746390 + 0.665509i \(0.231785\pi\)
\(744\) −5.21037 20.1427i −0.191021 0.738468i
\(745\) −23.4955 16.6569i −0.860807 0.610261i
\(746\) −36.7368 + 21.2100i −1.34503 + 0.776553i
\(747\) −2.44486 9.80148i −0.0894526 0.358617i
\(748\) 0.221760 + 0.221760i 0.00810833 + 0.00810833i
\(749\) 16.4087 + 3.31346i 0.599561 + 0.121071i
\(750\) 25.7258 13.9679i 0.939374 0.510035i
\(751\) −11.9640 + 20.7223i −0.436574 + 0.756168i −0.997423 0.0717501i \(-0.977142\pi\)
0.560849 + 0.827918i \(0.310475\pi\)
\(752\) 12.1773 45.4461i 0.444059 1.65725i
\(753\) −25.3637 + 14.3518i −0.924305 + 0.523009i
\(754\) 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 \(-0.0890977\pi\)
\(758\) −7.28531 27.1892i −0.264615 0.987555i
\(759\) 0.826933 2.98242i 0.0300158 0.108255i
\(760\) −6.69039 39.2823i −0.242686 1.42492i
\(761\) 5.74841 + 3.31885i 0.208380 + 0.120308i 0.600558 0.799581i \(-0.294945\pi\)
−0.392178 + 0.919889i \(0.628278\pi\)
\(762\) 16.3989 + 0.142266i 0.594069 + 0.00515375i
\(763\) −22.7594 + 1.42537i −0.823944 + 0.0516018i
\(764\) −2.61711 −0.0946838
\(765\) −6.30212 + 5.04381i −0.227854 + 0.182359i
\(766\) 12.2581 + 21.2317i 0.442904 + 0.767133i
\(767\) 11.1379 41.5671i 0.402165 1.50090i
\(768\) −5.89843 + 10.0147i −0.212841 + 0.361376i
\(769\) 22.0730i 0.795972i 0.917391 + 0.397986i \(0.130291\pi\)
−0.917391 + 0.397986i \(0.869709\pi\)
\(770\) −1.87361 7.95742i −0.0675204 0.286766i
\(771\) −16.8963 17.1920i −0.608504 0.619155i
\(772\) 0.523498 + 1.95372i 0.0188411 + 0.0703159i
\(773\) −31.6080 8.46934i −1.13686 0.304621i −0.359173 0.933271i \(-0.616941\pi\)
−0.777688 + 0.628650i \(0.783608\pi\)
\(774\) 26.9733 14.9552i 0.969534 0.537552i
\(775\) 7.66954 + 21.8625i 0.275498 + 0.785325i
\(776\) 5.82195i 0.208996i
\(777\) 3.49502 1.14144i 0.125383 0.0409490i
\(778\) 35.7966 + 35.7966i 1.28337 + 1.28337i
\(779\) −3.17196 + 5.49399i −0.113647 + 0.196843i
\(780\) −4.74803 + 0.766341i −0.170007 + 0.0274394i
\(781\) −0.254928 0.441548i −0.00912203 0.0157998i
\(782\) −3.43449 + 0.920269i −0.122817 + 0.0329088i
\(783\) 14.1423 + 0.368142i 0.505405 + 0.0131563i
\(784\) −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
\(787\) 11.8480 + 3.17466i 0.422335 + 0.113164i 0.463726 0.885979i \(-0.346512\pi\)
−0.0413909 + 0.999143i \(0.513179\pi\)
\(788\) −4.88941 1.31011i −0.174178 0.0466708i
\(789\) 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
\(792\) −4.93888 5.11330i −0.175495 0.181693i
\(793\) 4.49261 1.20379i 0.159537 0.0427478i
\(794\) 8.03461 + 13.9164i 0.285138 + 0.493873i
\(795\) −42.1704 + 6.80639i −1.49563 + 0.241398i
\(796\) 2.45436 4.25107i 0.0869924 0.150675i
\(797\) 27.2098 + 27.2098i 0.963820 + 0.963820i 0.999368 0.0355479i \(-0.0113176\pi\)
−0.0355479 + 0.999368i \(0.511318\pi\)
\(798\) −9.83051 + 46.5950i −0.347996 + 1.64945i
\(799\) 12.6120i 0.446179i
\(800\) 3.46775 7.21553i 0.122604 0.255108i
\(801\) −16.4301 29.6335i −0.580529 1.04705i
\(802\) 56.1832 + 15.0542i 1.98390 + 0.531584i
\(803\) 0.515695 + 1.92460i 0.0181985 + 0.0679177i
\(804\) −2.44927 2.49214i −0.0863791 0.0878909i
\(805\) 11.0737 + 3.33298i 0.390298 + 0.117472i
\(806\) 30.5082i 1.07460i
\(807\) −16.5977 + 28.1806i −0.584267 + 0.992005i
\(808\) −3.11676 + 11.6319i −0.109647 + 0.409208i
\(809\) 19.1786 + 33.2184i 0.674285 + 1.16790i 0.976677 + 0.214712i \(0.0688813\pi\)
−0.302393 + 0.953183i \(0.597785\pi\)
\(810\) −24.0776 + 18.5941i −0.846000 + 0.653331i
\(811\) 3.87781 0.136168 0.0680841 0.997680i \(-0.478311\pi\)
0.0680841 + 0.997680i \(0.478311\pi\)
\(812\) 2.04978 0.128373i 0.0719333 0.00450502i
\(813\) −6.42883 0.0557723i −0.225469 0.00195602i
\(814\) 0.960137 + 0.554335i 0.0336528 + 0.0194294i
\(815\) −9.04557 53.1106i −0.316853 1.86038i
\(816\) −2.49975 + 9.01561i −0.0875087 + 0.315609i
\(817\) 12.1002 + 45.1585i 0.423332 + 1.57990i
\(818\) −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 0.616664 0.787226i \(-0.288484\pi\)
−0.373426 + 0.927660i \(0.621817\pi\)
\(822\) −23.5454 + 13.3230i −0.821241 + 0.464692i
\(823\) 0.468179 1.74727i 0.0163197 0.0609059i −0.957286 0.289143i \(-0.906630\pi\)
0.973606 + 0.228237i \(0.0732962\pi\)
\(824\) −13.6495 + 23.6416i −0.475503 + 0.823595i
\(825\) 5.95958 + 5.21094i 0.207486 + 0.181421i
\(826\) −12.5935 37.4562i −0.438184 1.30327i
\(827\) 27.7405 + 27.7405i 0.964633 + 0.964633i 0.999396 0.0347627i \(-0.0110676\pi\)
−0.0347627 + 0.999396i \(0.511068\pi\)
\(828\) −1.62229 + 0.404660i −0.0563784 + 0.0140629i
\(829\) −8.07960 + 4.66476i −0.280616 + 0.162014i −0.633702 0.773577i \(-0.718466\pi\)
0.353086 + 0.935591i \(0.385132\pi\)
\(830\) 9.28529 + 6.58272i 0.322297 + 0.228490i
\(831\) 3.27991 + 12.6798i 0.113779 + 0.439856i
\(832\) 20.1955 20.1955i 0.700154 0.700154i
\(833\) −7.80051 + 3.17813i −0.270272 + 0.110116i
\(834\) 5.66841 5.57090i 0.196281 0.192905i
\(835\) 12.1432 10.0692i 0.420234 0.348459i
\(836\) −1.55162 + 0.895831i −0.0536641 + 0.0309830i
\(837\) −11.4922 21.1581i −0.397227 0.731331i
\(838\) 35.5520 9.52614i 1.22812 0.329075i
\(839\) −3.18996 −0.110130 −0.0550649 0.998483i \(-0.517537\pi\)
−0.0550649 + 0.998483i \(0.517537\pi\)
\(840\) 19.5054 18.0320i 0.673000 0.622163i
\(841\) −21.5874 −0.744393
\(842\) 2.56874 0.688292i 0.0885246 0.0237201i
\(843\) 18.1718 10.2823i 0.625870 0.354143i
\(844\) −2.40830 + 1.39043i −0.0828972 + 0.0478607i
\(845\) 13.2906 + 1.24097i 0.457210 + 0.0426908i
\(846\) 0.824648 47.5247i 0.0283520 1.63393i
\(847\) −22.4036 + 14.8757i −0.769795 + 0.511134i
\(848\) −35.0087 + 35.0087i −1.20220 + 1.20220i
\(849\) 40.2672 10.4160i 1.38197 0.357477i
\(850\) 1.68374 8.93768i 0.0577519 0.306560i
\(851\) −1.35822 + 0.784167i −0.0465591 + 0.0268809i
\(852\) −0.139785 + 0.237336i −0.00478896 + 0.00813100i
\(853\) −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
\(855\) −18.5147 42.2346i −0.633189 1.44439i
\(856\) −8.20093 + 14.2044i −0.280302 + 0.485497i
\(857\) −2.99394 + 11.1736i −0.102271 + 0.381681i −0.998021 0.0628767i \(-0.979973\pi\)
0.895750 + 0.444558i \(0.146639\pi\)
\(858\) −5.13361 9.07253i −0.175258 0.309731i
\(859\) −24.0944 13.9109i −0.822092 0.474635i 0.0290454 0.999578i \(-0.490753\pi\)
−0.851137 + 0.524943i \(0.824087\pi\)
\(860\) −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
\(863\) −2.02145 7.54415i −0.0688109 0.256806i 0.922948 0.384925i \(-0.125773\pi\)
−0.991759 + 0.128119i \(0.959106\pi\)
\(864\) −2.36167 + 7.97740i −0.0803457 + 0.271397i
\(865\) −53.0471 + 9.03475i −1.80366 + 0.307191i
\(866\) −49.6242 28.6505i −1.68630 0.973585i
\(867\) 0.233679 26.9360i 0.00793615 0.914793i
\(868\) −1.93353 2.91200i −0.0656283 0.0988397i
\(869\) −2.77080 −0.0939929
\(870\) −12.3581 + 10.0677i −0.418977 + 0.341327i
\(871\) 15.4087 + 26.6887i 0.522105 + 0.904313i
\(872\) 5.78291 21.5821i 0.195834 0.730862i
\(873\) −1.63063 6.53723i −0.0551885 0.221252i
\(874\) 20.3132i 0.687103i
\(875\) −19.9536 + 21.8370i −0.674554 + 0.738226i
\(876\) 0.767715 0.754509i 0.0259387 0.0254925i
\(877\) −4.03404 15.0553i −0.136220 0.508380i −0.999990 0.00449350i \(-0.998570\pi\)
0.863770 0.503886i \(-0.168097\pi\)
\(878\) −3.46410 0.928204i −0.116908 0.0313254i
\(879\) 28.9150 + 8.01723i 0.975278 + 0.270414i
\(880\) 9.13576 + 0.853027i 0.307966 + 0.0287555i
\(881\) 8.59639i 0.289620i 0.989459 + 0.144810i \(0.0462571\pi\)
−0.989459 + 0.144810i \(0.953743\pi\)
\(882\) −29.6019 + 11.4659i −0.996747 + 0.386075i
\(883\) −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
\(885\) 31.0246 + 22.4015i 1.04288 + 0.753018i
\(886\) 16.4444 + 28.4826i 0.552461 + 0.956891i
\(887\) −1.93852 + 0.519425i −0.0650891 + 0.0174406i −0.291217 0.956657i \(-0.594060\pi\)
0.226128 + 0.974098i \(0.427393\pi\)
\(888\) −0.0312513 + 3.60231i −0.00104872 + 0.120885i
\(889\) −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
\(892\) 3.57262 + 0.957280i 0.119620 + 0.0320521i
\(893\) 69.5961 + 18.6482i 2.32895 + 0.624039i
\(894\) −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
\(897\) 14.7457 + 0.127924i 0.492343 + 0.00427125i
\(898\) −42.1818 + 11.3026i −1.40762 + 0.377172i
\(899\) −6.30796 10.9257i −0.210382 0.364393i
\(900\) 0.864555 4.18846i 0.0288185 0.139615i
\(901\) −6.63575 + 11.4935i −0.221069 + 0.382903i
\(902\) −0.901706 0.901706i −0.0300235 0.0300235i
\(903\) −20.8187 + 23.1919i −0.692804 + 0.771779i
\(904\) 27.2823i 0.907395i
\(905\) −0.368003 + 3.94124i −0.0122328 + 0.131011i
\(906\) −8.32406 + 30.0216i −0.276548 + 0.997401i
\(907\) −8.89437 2.38324i −0.295333 0.0791341i 0.108110 0.994139i \(-0.465520\pi\)
−0.403443 + 0.915005i \(0.632187\pi\)
\(908\) 1.77411 + 6.62106i 0.0588758 + 0.219727i
\(909\) −0.241782 + 13.9339i −0.00801939 + 0.462159i
\(910\) 34.3117 18.4358i 1.13742 0.611140i
\(911\) 32.1044i 1.06367i 0.846849 + 0.531834i \(0.178497\pi\)
−0.846849 + 0.531834i \(0.821503\pi\)
\(912\) −46.0543 27.1249i −1.52501 0.898195i
\(913\) −0.796663 + 2.97319i −0.0263657 + 0.0983981i
\(914\) −1.48583 2.57354i −0.0491470 0.0851251i
\(915\) −0.420217 + 4.11451i −0.0138919 + 0.136022i
\(916\) 0.928598 0.0306817
\(917\) 12.4591 + 18.7640i 0.411434 + 0.619642i
\(918\) −0.245956 + 9.44849i −0.00811777 + 0.311847i
\(919\) −30.6447 17.6927i −1.01088 0.583630i −0.0994284 0.995045i \(-0.531701\pi\)
−0.911448 + 0.411415i \(0.865035\pi\)
\(920\) −6.55320 + 9.24365i −0.216053 + 0.304754i
\(921\) 29.5120 + 8.18277i 0.972454 + 0.269631i
\(922\) −6.81869 25.4477i −0.224562 0.838076i
\(923\) 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
\(927\) −8.70485 + 30.3692i −0.285905 + 0.997456i
\(928\) −1.12825 + 4.21068i −0.0370365 + 0.138222i
\(929\) 22.6551 39.2398i 0.743290 1.28742i −0.207699 0.978193i \(-0.566597\pi\)
0.950989 0.309224i \(-0.100069\pi\)
\(930\) 25.3555 + 9.64758i 0.831441 + 0.316357i
\(931\) −6.00381 47.7445i −0.196767 1.56476i
\(932\) 3.36258 + 3.36258i 0.110145 + 0.110145i
\(933\) 34.9820 + 20.6035i 1.14526 + 0.674530i
\(934\) 16.5032 9.52814i 0.540002 0.311770i
\(935\) 2.42465 0.412957i 0.0792947 0.0135051i
\(936\) 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 \(0.269411\pi\)
\(938\) 25.3442 + 12.5900i 0.827517 + 0.411078i
\(939\) −12.8694 13.0947i −0.419977 0.427328i
\(940\) 4.26527 + 5.14381i 0.139118 + 0.167773i
\(941\) −23.3880 + 13.5031i −0.762428 + 0.440188i −0.830167 0.557515i \(-0.811755\pi\)
0.0677386 + 0.997703i \(0.478422\pi\)
\(942\) −17.9389 31.7031i −0.584482 1.03294i
\(943\) 1.74245 0.466888i 0.0567419 0.0152039i
\(944\) 44.3528 1.44356
\(945\) 16.8514 25.7105i 0.548175 0.836364i
\(946\) −9.39763 −0.305543
\(947\) 13.4359 3.60013i 0.436607 0.116988i −0.0338191 0.999428i \(-0.510767\pi\)
0.470426 + 0.882440i \(0.344100\pi\)
\(948\) 0.737168 + 1.30278i 0.0239421 + 0.0423124i
\(949\) −8.22158 + 4.74673i −0.266884 + 0.154086i
\(950\) 46.8309 + 22.5067i 1.51939 + 0.730215i
\(951\) 24.9405 + 25.3770i 0.808750 + 0.822905i
\(952\) −0.515856 8.23685i −0.0167190 0.266958i
\(953\) −20.8791 + 20.8791i −0.676342 + 0.676342i −0.959170 0.282829i \(-0.908727\pi\)
0.282829 + 0.959170i \(0.408727\pi\)
\(954\) −25.7565 + 42.8760i −0.833898 + 1.38816i
\(955\) −11.8706 + 16.7442i −0.384124 + 0.541828i
\(956\) 3.74883 2.16439i 0.121246 0.0700012i
\(957\) −3.71433 2.18765i −0.120067 0.0707167i
\(958\) 10.9968 + 10.9968i 0.355289 + 0.355289i
\(959\) 18.0844 20.5009i 0.583975 0.662008i
\(960\) 10.3982 + 23.1711i 0.335601 + 0.747843i
\(961\) 4.76416 8.25177i 0.153683 0.266186i
\(962\) −1.36718 + 5.10240i −0.0440798 + 0.164508i
\(963\) −5.23007 + 18.2465i −0.168537 + 0.587986i
\(964\) −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 \(0.909255\pi\)
\(968\) −6.81972 25.4515i −0.219194 0.818043i
\(969\) −13.8065 3.82811i −0.443528 0.122977i
\(970\) 6.19295 + 4.39043i 0.198844 + 0.140968i
\(971\) 18.6146 + 10.7472i 0.597372 + 0.344893i 0.768007 0.640441i \(-0.221248\pi\)
−0.170635 + 0.985334i \(0.554582\pi\)
\(972\) −0.192724 + 4.44035i −0.00618163 + 0.142424i
\(973\) −3.57297 + 7.19253i −0.114544 + 0.230582i
\(974\) −28.1852 −0.903112
\(975\) −16.6329 + 33.8536i −0.532680 + 1.08418i
\(976\) 2.39684 + 4.15146i 0.0767211 + 0.132885i
\(977\) −11.5650 + 43.1613i −0.369998 + 1.38085i 0.490520 + 0.871430i \(0.336807\pi\)
−0.860518 + 0.509421i \(0.829860\pi\)
\(978\) −54.3568 32.0148i −1.73814 1.02372i
\(979\) 10.3245i 0.329971i
\(980\) 2.10664 3.93428i 0.0672940 0.125676i
\(981\) 0.448608 25.8534i 0.0143229 0.825435i
\(982\) −9.66143 36.0570i −0.308309 1.15062i
\(983\) −12.5692 3.36791i −0.400896 0.107420i 0.0527371 0.998608i \(-0.483205\pi\)
−0.453633 + 0.891189i \(0.649872\pi\)
\(984\) 1.10711 3.99292i 0.0352935 0.127290i
\(985\) −30.5592 + 25.3398i −0.973698 + 0.807394i
\(986\) 4.95237i 0.157716i
\(987\) 14.9113 + 45.6574i 0.474632 + 1.45329i
\(988\) −6.03628 6.03628i −0.192040 0.192040i
\(989\) 6.64698 11.5129i 0.211362 0.366089i
\(990\) 9.16364 1.39757i 0.291240 0.0444178i
\(991\) −6.73127 11.6589i −0.213826 0.370357i 0.739083 0.673615i \(-0.235259\pi\)
−0.952909 + 0.303257i \(0.901926\pi\)
\(992\) 7.16637 1.92022i 0.227532 0.0609671i
\(993\) 55.3053 + 0.479793i 1.75506 + 0.0152258i
\(994\) 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
\(997\) 36.7071 + 9.83565i 1.16253 + 0.311498i 0.787975 0.615708i \(-0.211130\pi\)
0.374552 + 0.927206i \(0.377797\pi\)
\(998\) 18.8033 + 5.03834i 0.595209 + 0.159486i
\(999\) 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.23.10 yes 48
3.2 odd 2 inner 105.2.x.a.23.3 yes 48
5.2 odd 4 inner 105.2.x.a.2.10 yes 48
5.3 odd 4 525.2.bf.f.107.3 48
5.4 even 2 525.2.bf.f.443.3 48
7.2 even 3 735.2.j.g.638.3 24
7.3 odd 6 735.2.y.i.263.3 48
7.4 even 3 inner 105.2.x.a.53.3 yes 48
7.5 odd 6 735.2.j.e.638.3 24
7.6 odd 2 735.2.y.i.128.10 48
15.2 even 4 inner 105.2.x.a.2.3 48
15.8 even 4 525.2.bf.f.107.10 48
15.14 odd 2 525.2.bf.f.443.10 48
21.2 odd 6 735.2.j.g.638.10 24
21.5 even 6 735.2.j.e.638.10 24
21.11 odd 6 inner 105.2.x.a.53.10 yes 48
21.17 even 6 735.2.y.i.263.10 48
21.20 even 2 735.2.y.i.128.3 48
35.2 odd 12 735.2.j.g.197.10 24
35.4 even 6 525.2.bf.f.368.10 48
35.12 even 12 735.2.j.e.197.10 24
35.17 even 12 735.2.y.i.557.3 48
35.18 odd 12 525.2.bf.f.32.10 48
35.27 even 4 735.2.y.i.422.10 48
35.32 odd 12 inner 105.2.x.a.32.3 yes 48
105.2 even 12 735.2.j.g.197.3 24
105.17 odd 12 735.2.y.i.557.10 48
105.32 even 12 inner 105.2.x.a.32.10 yes 48
105.47 odd 12 735.2.j.e.197.3 24
105.53 even 12 525.2.bf.f.32.3 48
105.62 odd 4 735.2.y.i.422.3 48
105.74 odd 6 525.2.bf.f.368.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.3 48 15.2 even 4 inner
105.2.x.a.2.10 yes 48 5.2 odd 4 inner
105.2.x.a.23.3 yes 48 3.2 odd 2 inner
105.2.x.a.23.10 yes 48 1.1 even 1 trivial
105.2.x.a.32.3 yes 48 35.32 odd 12 inner
105.2.x.a.32.10 yes 48 105.32 even 12 inner
105.2.x.a.53.3 yes 48 7.4 even 3 inner
105.2.x.a.53.10 yes 48 21.11 odd 6 inner
525.2.bf.f.32.3 48 105.53 even 12
525.2.bf.f.32.10 48 35.18 odd 12
525.2.bf.f.107.3 48 5.3 odd 4
525.2.bf.f.107.10 48 15.8 even 4
525.2.bf.f.368.3 48 105.74 odd 6
525.2.bf.f.368.10 48 35.4 even 6
525.2.bf.f.443.3 48 5.4 even 2
525.2.bf.f.443.10 48 15.14 odd 2
735.2.j.e.197.3 24 105.47 odd 12
735.2.j.e.197.10 24 35.12 even 12
735.2.j.e.638.3 24 7.5 odd 6
735.2.j.e.638.10 24 21.5 even 6
735.2.j.g.197.3 24 105.2 even 12
735.2.j.g.197.10 24 35.2 odd 12
735.2.j.g.638.3 24 7.2 even 3
735.2.j.g.638.10 24 21.2 odd 6
735.2.y.i.128.3 48 21.20 even 2
735.2.y.i.128.10 48 7.6 odd 2
735.2.y.i.263.3 48 7.3 odd 6
735.2.y.i.263.10 48 21.17 even 6
735.2.y.i.422.3 48 105.62 odd 4
735.2.y.i.422.10 48 35.27 even 4
735.2.y.i.557.3 48 35.17 even 12
735.2.y.i.557.10 48 105.17 odd 12