Properties

Label 171.2.h.c.7.9
Level $171$
Weight $2$
Character 171.7
Analytic conductor $1.365$
Analytic rank $0$
Dimension $32$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [171,2,Mod(7,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.h (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.36544187456\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.9
Character \(\chi\) \(=\) 171.7
Dual form 171.2.h.c.49.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.370889 q^{2} +(1.73173 - 0.0335006i) q^{3} -1.86244 q^{4} +(1.77761 - 3.07890i) q^{5} +(0.642278 - 0.0124250i) q^{6} +(-0.124876 + 0.216291i) q^{7} -1.43254 q^{8} +(2.99776 - 0.116028i) q^{9} +(0.659294 - 1.14193i) q^{10} +(-0.815815 + 1.41303i) q^{11} +(-3.22524 + 0.0623929i) q^{12} -1.32541 q^{13} +(-0.0463150 + 0.0802199i) q^{14} +(2.97518 - 5.39137i) q^{15} +3.19357 q^{16} +(3.73000 + 6.46055i) q^{17} +(1.11183 - 0.0430334i) q^{18} +(-4.07660 + 1.54315i) q^{19} +(-3.31069 + 5.73428i) q^{20} +(-0.209005 + 0.378740i) q^{21} +(-0.302577 + 0.524078i) q^{22} -4.49143 q^{23} +(-2.48076 + 0.0479909i) q^{24} +(-3.81976 - 6.61602i) q^{25} -0.491582 q^{26} +(5.18741 - 0.301355i) q^{27} +(0.232573 - 0.402829i) q^{28} +(2.06363 + 3.57430i) q^{29} +(1.10346 - 1.99960i) q^{30} +(-4.32871 - 7.49755i) q^{31} +4.04953 q^{32} +(-1.36543 + 2.47432i) q^{33} +(1.38342 + 2.39615i) q^{34} +(0.443959 + 0.768960i) q^{35} +(-5.58314 + 0.216095i) q^{36} +3.10599 q^{37} +(-1.51197 + 0.572336i) q^{38} +(-2.29526 + 0.0444022i) q^{39} +(-2.54649 + 4.41064i) q^{40} +(-2.77461 + 4.80577i) q^{41} +(-0.0775175 + 0.140471i) q^{42} -10.0406 q^{43} +(1.51941 - 2.63169i) q^{44} +(4.97159 - 9.43605i) q^{45} -1.66582 q^{46} +(-1.68288 - 2.91483i) q^{47} +(5.53039 - 0.106987i) q^{48} +(3.46881 + 6.00816i) q^{49} +(-1.41671 - 2.45381i) q^{50} +(6.67577 + 11.0629i) q^{51} +2.46851 q^{52} +(0.254182 - 0.440256i) q^{53} +(1.92395 - 0.111769i) q^{54} +(2.90039 + 5.02363i) q^{55} +(0.178889 - 0.309845i) q^{56} +(-7.00787 + 2.80888i) q^{57} +(0.765376 + 1.32567i) q^{58} +(5.23121 - 9.06071i) q^{59} +(-5.54110 + 10.0411i) q^{60} +(-2.07050 - 3.58621i) q^{61} +(-1.60547 - 2.78076i) q^{62} +(-0.349251 + 0.662876i) q^{63} -4.88521 q^{64} +(-2.35606 + 4.08082i) q^{65} +(-0.506423 + 0.917697i) q^{66} -0.799350 q^{67} +(-6.94690 - 12.0324i) q^{68} +(-7.77793 + 0.150466i) q^{69} +(0.164660 + 0.285199i) q^{70} +(5.60051 + 9.70037i) q^{71} +(-4.29440 + 0.166214i) q^{72} +(-1.84754 - 3.20004i) q^{73} +1.15198 q^{74} +(-6.83642 - 11.3292i) q^{75} +(7.59244 - 2.87402i) q^{76} +(-0.203751 - 0.352907i) q^{77} +(-0.851285 + 0.0164683i) q^{78} +9.85529 q^{79} +(5.67691 - 9.83269i) q^{80} +(8.97308 - 0.695646i) q^{81} +(-1.02907 + 1.78241i) q^{82} +(0.185251 - 0.320865i) q^{83} +(0.389259 - 0.705381i) q^{84} +26.5219 q^{85} -3.72396 q^{86} +(3.69338 + 6.12059i) q^{87} +(1.16868 - 2.02422i) q^{88} +(4.01034 - 6.94611i) q^{89} +(1.84391 - 3.49973i) q^{90} +(0.165512 - 0.286675i) q^{91} +8.36503 q^{92} +(-7.74732 - 12.8387i) q^{93} +(-0.624161 - 1.08108i) q^{94} +(-2.49539 + 15.2946i) q^{95} +(7.01269 - 0.135662i) q^{96} +6.43155 q^{97} +(1.28654 + 2.22836i) q^{98} +(-2.28166 + 4.33058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.370889 0.262258 0.131129 0.991365i \(-0.458140\pi\)
0.131129 + 0.991365i \(0.458140\pi\)
\(3\) 1.73173 0.0335006i 0.999813 0.0193416i
\(4\) −1.86244 −0.931221
\(5\) 1.77761 3.07890i 0.794969 1.37693i −0.127889 0.991788i \(-0.540820\pi\)
0.922859 0.385139i \(-0.125846\pi\)
\(6\) 0.642278 0.0124250i 0.262209 0.00507249i
\(7\) −0.124876 + 0.216291i −0.0471985 + 0.0817503i −0.888660 0.458568i \(-0.848363\pi\)
0.841461 + 0.540318i \(0.181696\pi\)
\(8\) −1.43254 −0.506478
\(9\) 2.99776 0.116028i 0.999252 0.0386759i
\(10\) 0.659294 1.14193i 0.208487 0.361110i
\(11\) −0.815815 + 1.41303i −0.245977 + 0.426045i −0.962406 0.271615i \(-0.912442\pi\)
0.716429 + 0.697660i \(0.245776\pi\)
\(12\) −3.22524 + 0.0623929i −0.931046 + 0.0180113i
\(13\) −1.32541 −0.367604 −0.183802 0.982963i \(-0.558841\pi\)
−0.183802 + 0.982963i \(0.558841\pi\)
\(14\) −0.0463150 + 0.0802199i −0.0123782 + 0.0214397i
\(15\) 2.97518 5.39137i 0.768189 1.39205i
\(16\) 3.19357 0.798393
\(17\) 3.73000 + 6.46055i 0.904658 + 1.56691i 0.821376 + 0.570387i \(0.193207\pi\)
0.0832816 + 0.996526i \(0.473460\pi\)
\(18\) 1.11183 0.0430334i 0.262062 0.0101431i
\(19\) −4.07660 + 1.54315i −0.935237 + 0.354022i
\(20\) −3.31069 + 5.73428i −0.740292 + 1.28222i
\(21\) −0.209005 + 0.378740i −0.0456085 + 0.0826479i
\(22\) −0.302577 + 0.524078i −0.0645096 + 0.111734i
\(23\) −4.49143 −0.936528 −0.468264 0.883589i \(-0.655120\pi\)
−0.468264 + 0.883589i \(0.655120\pi\)
\(24\) −2.48076 + 0.0479909i −0.506384 + 0.00979609i
\(25\) −3.81976 6.61602i −0.763952 1.32320i
\(26\) −0.491582 −0.0964071
\(27\) 5.18741 0.301355i 0.998317 0.0579958i
\(28\) 0.232573 0.402829i 0.0439522 0.0761275i
\(29\) 2.06363 + 3.57430i 0.383206 + 0.663732i 0.991518 0.129966i \(-0.0414867\pi\)
−0.608313 + 0.793697i \(0.708153\pi\)
\(30\) 1.10346 1.99960i 0.201464 0.365075i
\(31\) −4.32871 7.49755i −0.777460 1.34660i −0.933401 0.358834i \(-0.883174\pi\)
0.155941 0.987766i \(-0.450159\pi\)
\(32\) 4.04953 0.715863
\(33\) −1.36543 + 2.47432i −0.237691 + 0.430723i
\(34\) 1.38342 + 2.39615i 0.237254 + 0.410936i
\(35\) 0.443959 + 0.768960i 0.0750428 + 0.129978i
\(36\) −5.58314 + 0.216095i −0.930524 + 0.0360158i
\(37\) 3.10599 0.510622 0.255311 0.966859i \(-0.417822\pi\)
0.255311 + 0.966859i \(0.417822\pi\)
\(38\) −1.51197 + 0.572336i −0.245274 + 0.0928452i
\(39\) −2.29526 + 0.0444022i −0.367535 + 0.00711004i
\(40\) −2.54649 + 4.41064i −0.402635 + 0.697384i
\(41\) −2.77461 + 4.80577i −0.433322 + 0.750535i −0.997157 0.0753521i \(-0.975992\pi\)
0.563835 + 0.825887i \(0.309325\pi\)
\(42\) −0.0775175 + 0.140471i −0.0119612 + 0.0216751i
\(43\) −10.0406 −1.53118 −0.765591 0.643328i \(-0.777553\pi\)
−0.765591 + 0.643328i \(0.777553\pi\)
\(44\) 1.51941 2.63169i 0.229059 0.396742i
\(45\) 4.97159 9.43605i 0.741121 1.40664i
\(46\) −1.66582 −0.245612
\(47\) −1.68288 2.91483i −0.245473 0.425171i 0.716792 0.697287i \(-0.245610\pi\)
−0.962264 + 0.272116i \(0.912277\pi\)
\(48\) 5.53039 0.106987i 0.798243 0.0154422i
\(49\) 3.46881 + 6.00816i 0.495545 + 0.858308i
\(50\) −1.41671 2.45381i −0.200353 0.347021i
\(51\) 6.67577 + 11.0629i 0.934795 + 1.54912i
\(52\) 2.46851 0.342320
\(53\) 0.254182 0.440256i 0.0349146 0.0604739i −0.848040 0.529932i \(-0.822217\pi\)
0.882955 + 0.469458i \(0.155551\pi\)
\(54\) 1.92395 0.111769i 0.261817 0.0152099i
\(55\) 2.90039 + 5.02363i 0.391089 + 0.677386i
\(56\) 0.178889 0.309845i 0.0239050 0.0414047i
\(57\) −7.00787 + 2.80888i −0.928215 + 0.372045i
\(58\) 0.765376 + 1.32567i 0.100499 + 0.174069i
\(59\) 5.23121 9.06071i 0.681045 1.17960i −0.293617 0.955923i \(-0.594859\pi\)
0.974662 0.223681i \(-0.0718075\pi\)
\(60\) −5.54110 + 10.0411i −0.715353 + 1.29630i
\(61\) −2.07050 3.58621i −0.265100 0.459168i 0.702489 0.711694i \(-0.252072\pi\)
−0.967590 + 0.252527i \(0.918738\pi\)
\(62\) −1.60547 2.78076i −0.203895 0.353157i
\(63\) −0.349251 + 0.662876i −0.0440015 + 0.0835145i
\(64\) −4.88521 −0.610652
\(65\) −2.35606 + 4.08082i −0.292234 + 0.506164i
\(66\) −0.506423 + 0.917697i −0.0623364 + 0.112961i
\(67\) −0.799350 −0.0976561 −0.0488281 0.998807i \(-0.515549\pi\)
−0.0488281 + 0.998807i \(0.515549\pi\)
\(68\) −6.94690 12.0324i −0.842436 1.45914i
\(69\) −7.77793 + 0.150466i −0.936353 + 0.0181139i
\(70\) 0.164660 + 0.285199i 0.0196806 + 0.0340878i
\(71\) 5.60051 + 9.70037i 0.664658 + 1.15122i 0.979378 + 0.202037i \(0.0647563\pi\)
−0.314719 + 0.949185i \(0.601910\pi\)
\(72\) −4.29440 + 0.166214i −0.506099 + 0.0195885i
\(73\) −1.84754 3.20004i −0.216239 0.374537i 0.737416 0.675439i \(-0.236046\pi\)
−0.953655 + 0.300902i \(0.902712\pi\)
\(74\) 1.15198 0.133915
\(75\) −6.83642 11.3292i −0.789402 1.30818i
\(76\) 7.59244 2.87402i 0.870912 0.329673i
\(77\) −0.203751 0.352907i −0.0232195 0.0402174i
\(78\) −0.851285 + 0.0164683i −0.0963891 + 0.00186467i
\(79\) 9.85529 1.10881 0.554403 0.832248i \(-0.312947\pi\)
0.554403 + 0.832248i \(0.312947\pi\)
\(80\) 5.67691 9.83269i 0.634698 1.09933i
\(81\) 8.97308 0.695646i 0.997008 0.0772940i
\(82\) −1.02907 + 1.78241i −0.113642 + 0.196834i
\(83\) 0.185251 0.320865i 0.0203340 0.0352195i −0.855679 0.517506i \(-0.826860\pi\)
0.876013 + 0.482287i \(0.160194\pi\)
\(84\) 0.389259 0.705381i 0.0424716 0.0769634i
\(85\) 26.5219 2.87670
\(86\) −3.72396 −0.401565
\(87\) 3.69338 + 6.12059i 0.395972 + 0.656196i
\(88\) 1.16868 2.02422i 0.124582 0.215783i
\(89\) 4.01034 6.94611i 0.425095 0.736286i −0.571334 0.820717i \(-0.693574\pi\)
0.996429 + 0.0844315i \(0.0269074\pi\)
\(90\) 1.84391 3.49973i 0.194365 0.368904i
\(91\) 0.165512 0.286675i 0.0173504 0.0300517i
\(92\) 8.36503 0.872115
\(93\) −7.74732 12.8387i −0.803360 1.33131i
\(94\) −0.624161 1.08108i −0.0643772 0.111505i
\(95\) −2.49539 + 15.2946i −0.256022 + 1.56919i
\(96\) 7.01269 0.135662i 0.715729 0.0138459i
\(97\) 6.43155 0.653024 0.326512 0.945193i \(-0.394127\pi\)
0.326512 + 0.945193i \(0.394127\pi\)
\(98\) 1.28654 + 2.22836i 0.129961 + 0.225098i
\(99\) −2.28166 + 4.33058i −0.229316 + 0.435240i
\(100\) 7.11408 + 12.3220i 0.711408 + 1.23220i
\(101\) −3.78177 6.55021i −0.376300 0.651771i 0.614221 0.789134i \(-0.289470\pi\)
−0.990521 + 0.137364i \(0.956137\pi\)
\(102\) 2.47597 + 4.10313i 0.245158 + 0.406270i
\(103\) −6.90927 11.9672i −0.680791 1.17916i −0.974740 0.223343i \(-0.928303\pi\)
0.293949 0.955821i \(-0.405030\pi\)
\(104\) 1.89871 0.186183
\(105\) 0.794576 + 1.31675i 0.0775427 + 0.128502i
\(106\) 0.0942734 0.163286i 0.00915664 0.0158598i
\(107\) 12.0119 1.16123 0.580616 0.814177i \(-0.302812\pi\)
0.580616 + 0.814177i \(0.302812\pi\)
\(108\) −9.66124 + 0.561256i −0.929653 + 0.0540069i
\(109\) −7.62598 13.2086i −0.730436 1.26515i −0.956697 0.291086i \(-0.905984\pi\)
0.226261 0.974067i \(-0.427350\pi\)
\(110\) 1.07572 + 1.86321i 0.102566 + 0.177650i
\(111\) 5.37873 0.104053i 0.510526 0.00987623i
\(112\) −0.398799 + 0.690740i −0.0376830 + 0.0652688i
\(113\) −1.46481 2.53713i −0.137798 0.238673i 0.788865 0.614567i \(-0.210669\pi\)
−0.926663 + 0.375894i \(0.877336\pi\)
\(114\) −2.59914 + 1.04178i −0.243432 + 0.0975718i
\(115\) −7.98399 + 13.8287i −0.744511 + 1.28953i
\(116\) −3.84338 6.65693i −0.356849 0.618081i
\(117\) −3.97327 + 0.153785i −0.367329 + 0.0142174i
\(118\) 1.94020 3.36052i 0.178610 0.309361i
\(119\) −1.86314 −0.170794
\(120\) −4.26206 + 7.72334i −0.389071 + 0.705041i
\(121\) 4.16889 + 7.22073i 0.378990 + 0.656430i
\(122\) −0.767926 1.33009i −0.0695248 0.120420i
\(123\) −4.64387 + 8.41523i −0.418724 + 0.758776i
\(124\) 8.06198 + 13.9638i 0.723987 + 1.25398i
\(125\) −9.38406 −0.839336
\(126\) −0.129533 + 0.245853i −0.0115397 + 0.0219024i
\(127\) −0.949181 + 1.64403i −0.0842262 + 0.145884i −0.905061 0.425281i \(-0.860175\pi\)
0.820835 + 0.571165i \(0.193509\pi\)
\(128\) −9.91094 −0.876012
\(129\) −17.3876 + 0.336367i −1.53090 + 0.0296155i
\(130\) −0.873838 + 1.51353i −0.0766407 + 0.132746i
\(131\) 1.51445 2.62310i 0.132318 0.229181i −0.792252 0.610194i \(-0.791091\pi\)
0.924570 + 0.381013i \(0.124425\pi\)
\(132\) 2.54304 4.60827i 0.221343 0.401098i
\(133\) 0.175300 1.07443i 0.0152004 0.0931652i
\(134\) −0.296470 −0.0256111
\(135\) 8.29332 16.5072i 0.713775 1.42071i
\(136\) −5.34336 9.25497i −0.458190 0.793608i
\(137\) −2.12874 3.68708i −0.181870 0.315009i 0.760647 0.649166i \(-0.224882\pi\)
−0.942517 + 0.334157i \(0.891548\pi\)
\(138\) −2.88475 + 0.0558061i −0.245566 + 0.00475053i
\(139\) −17.2721 −1.46500 −0.732502 0.680765i \(-0.761648\pi\)
−0.732502 + 0.680765i \(0.761648\pi\)
\(140\) −0.826848 1.43214i −0.0698814 0.121038i
\(141\) −3.01193 4.99131i −0.253650 0.420344i
\(142\) 2.07717 + 3.59776i 0.174312 + 0.301917i
\(143\) 1.08129 1.87285i 0.0904222 0.156616i
\(144\) 9.57354 0.370543i 0.797795 0.0308786i
\(145\) 14.6732 1.21855
\(146\) −0.685234 1.18686i −0.0567104 0.0982253i
\(147\) 6.20831 + 10.2883i 0.512053 + 0.848563i
\(148\) −5.78473 −0.475501
\(149\) −0.923073 + 1.59881i −0.0756211 + 0.130980i −0.901356 0.433079i \(-0.857427\pi\)
0.825735 + 0.564058i \(0.190761\pi\)
\(150\) −2.53555 4.20187i −0.207027 0.343081i
\(151\) −5.59926 + 9.69820i −0.455661 + 0.789228i −0.998726 0.0504626i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(152\) 5.83989 2.21061i 0.473677 0.179305i
\(153\) 11.9312 + 18.9344i 0.964583 + 1.53075i
\(154\) −0.0755689 0.130889i −0.00608952 0.0105473i
\(155\) −30.7790 −2.47223
\(156\) 4.27478 0.0826965i 0.342256 0.00662102i
\(157\) −10.3856 + 17.9883i −0.828858 + 1.43562i 0.0700766 + 0.997542i \(0.477676\pi\)
−0.898935 + 0.438083i \(0.855658\pi\)
\(158\) 3.65522 0.290794
\(159\) 0.425425 0.770919i 0.0337384 0.0611379i
\(160\) 7.19847 12.4681i 0.569089 0.985692i
\(161\) 0.560870 0.971456i 0.0442028 0.0765614i
\(162\) 3.32801 0.258007i 0.261474 0.0202710i
\(163\) −5.41671 −0.424269 −0.212135 0.977240i \(-0.568042\pi\)
−0.212135 + 0.977240i \(0.568042\pi\)
\(164\) 5.16755 8.95046i 0.403518 0.698914i
\(165\) 5.19098 + 8.60239i 0.404118 + 0.669695i
\(166\) 0.0687077 0.119005i 0.00533275 0.00923660i
\(167\) −1.50006 −0.116078 −0.0580392 0.998314i \(-0.518485\pi\)
−0.0580392 + 0.998314i \(0.518485\pi\)
\(168\) 0.299407 0.542559i 0.0230997 0.0418594i
\(169\) −11.2433 −0.864867
\(170\) 9.83667 0.754438
\(171\) −12.0416 + 5.09898i −0.920845 + 0.389928i
\(172\) 18.7001 1.42587
\(173\) 22.4134 1.70406 0.852031 0.523491i \(-0.175371\pi\)
0.852031 + 0.523491i \(0.175371\pi\)
\(174\) 1.36983 + 2.27006i 0.103847 + 0.172093i
\(175\) 1.90798 0.144230
\(176\) −2.60536 + 4.51262i −0.196387 + 0.340151i
\(177\) 8.75548 15.8659i 0.658102 1.19256i
\(178\) 1.48739 2.57623i 0.111485 0.193097i
\(179\) −12.7134 −0.950242 −0.475121 0.879920i \(-0.657596\pi\)
−0.475121 + 0.879920i \(0.657596\pi\)
\(180\) −9.25929 + 17.5741i −0.690147 + 1.30990i
\(181\) 1.31157 2.27170i 0.0974880 0.168854i −0.813156 0.582045i \(-0.802253\pi\)
0.910644 + 0.413191i \(0.135586\pi\)
\(182\) 0.0613866 0.106325i 0.00455027 0.00788131i
\(183\) −3.70568 6.14098i −0.273932 0.453954i
\(184\) 6.43414 0.474331
\(185\) 5.52123 9.56304i 0.405929 0.703089i
\(186\) −2.87340 4.76173i −0.210688 0.349147i
\(187\) −12.1720 −0.890101
\(188\) 3.13426 + 5.42870i 0.228589 + 0.395928i
\(189\) −0.582600 + 1.15962i −0.0423779 + 0.0843500i
\(190\) −0.925514 + 5.67259i −0.0671439 + 0.411533i
\(191\) −1.70417 + 2.95170i −0.123309 + 0.213578i −0.921071 0.389395i \(-0.872684\pi\)
0.797762 + 0.602973i \(0.206017\pi\)
\(192\) −8.45985 + 0.163658i −0.610537 + 0.0118110i
\(193\) −0.248883 + 0.431077i −0.0179150 + 0.0310296i −0.874844 0.484405i \(-0.839036\pi\)
0.856929 + 0.515435i \(0.172369\pi\)
\(194\) 2.38539 0.171261
\(195\) −3.94335 + 7.14580i −0.282389 + 0.511721i
\(196\) −6.46046 11.1898i −0.461461 0.799275i
\(197\) −2.64398 −0.188376 −0.0941880 0.995554i \(-0.530025\pi\)
−0.0941880 + 0.995554i \(0.530025\pi\)
\(198\) −0.846243 + 1.60617i −0.0601399 + 0.114145i
\(199\) 0.106311 0.184136i 0.00753617 0.0130530i −0.862233 0.506512i \(-0.830934\pi\)
0.869769 + 0.493459i \(0.164268\pi\)
\(200\) 5.47195 + 9.47770i 0.386925 + 0.670174i
\(201\) −1.38426 + 0.0267787i −0.0976379 + 0.00188882i
\(202\) −1.40262 2.42940i −0.0986877 0.170932i
\(203\) −1.03079 −0.0723470
\(204\) −12.4332 20.6041i −0.870500 1.44257i
\(205\) 9.86433 + 17.0855i 0.688955 + 1.19330i
\(206\) −2.56257 4.43851i −0.178543 0.309245i
\(207\) −13.4642 + 0.521131i −0.935828 + 0.0362211i
\(208\) −4.23280 −0.293492
\(209\) 1.14524 7.01930i 0.0792177 0.485535i
\(210\) 0.294700 + 0.488370i 0.0203362 + 0.0337007i
\(211\) 4.26187 7.38178i 0.293400 0.508183i −0.681212 0.732086i \(-0.738547\pi\)
0.974611 + 0.223903i \(0.0718800\pi\)
\(212\) −0.473399 + 0.819952i −0.0325132 + 0.0563145i
\(213\) 10.0235 + 16.6108i 0.686801 + 1.13815i
\(214\) 4.45508 0.304543
\(215\) −17.8483 + 30.9141i −1.21724 + 2.10833i
\(216\) −7.43115 + 0.431702i −0.505626 + 0.0293736i
\(217\) 2.16220 0.146780
\(218\) −2.82839 4.89892i −0.191563 0.331797i
\(219\) −3.30665 5.47970i −0.223442 0.370284i
\(220\) −5.40181 9.35621i −0.364190 0.630796i
\(221\) −4.94380 8.56290i −0.332556 0.576003i
\(222\) 1.99491 0.0385920i 0.133890 0.00259012i
\(223\) 15.6032 1.04487 0.522433 0.852680i \(-0.325025\pi\)
0.522433 + 0.852680i \(0.325025\pi\)
\(224\) −0.505688 + 0.875877i −0.0337877 + 0.0585220i
\(225\) −12.2184 19.3900i −0.814557 1.29267i
\(226\) −0.543283 0.940994i −0.0361386 0.0625940i
\(227\) −0.595426 + 1.03131i −0.0395198 + 0.0684503i −0.885109 0.465384i \(-0.845916\pi\)
0.845589 + 0.533835i \(0.179249\pi\)
\(228\) 13.0517 5.23137i 0.864373 0.346456i
\(229\) −9.98443 17.2935i −0.659790 1.14279i −0.980670 0.195669i \(-0.937312\pi\)
0.320880 0.947120i \(-0.396021\pi\)
\(230\) −2.96118 + 5.12891i −0.195254 + 0.338190i
\(231\) −0.364663 0.604312i −0.0239931 0.0397608i
\(232\) −2.95622 5.12032i −0.194085 0.336166i
\(233\) 6.18432 + 10.7115i 0.405148 + 0.701737i 0.994339 0.106257i \(-0.0338867\pi\)
−0.589191 + 0.807994i \(0.700553\pi\)
\(234\) −1.47364 + 0.0570371i −0.0963350 + 0.00372863i
\(235\) −11.9660 −0.780573
\(236\) −9.74281 + 16.8750i −0.634203 + 1.09847i
\(237\) 17.0667 0.330158i 1.10860 0.0214461i
\(238\) −0.691019 −0.0447921
\(239\) 8.11631 + 14.0579i 0.525000 + 0.909327i 0.999576 + 0.0291128i \(0.00926819\pi\)
−0.474576 + 0.880215i \(0.657398\pi\)
\(240\) 9.50145 17.2177i 0.613316 1.11140i
\(241\) −5.24347 9.08196i −0.337762 0.585020i 0.646250 0.763126i \(-0.276336\pi\)
−0.984011 + 0.178106i \(0.943003\pi\)
\(242\) 1.54620 + 2.67809i 0.0993933 + 0.172154i
\(243\) 15.5156 1.50527i 0.995327 0.0965633i
\(244\) 3.85619 + 6.67911i 0.246867 + 0.427586i
\(245\) 24.6647 1.57577
\(246\) −1.72236 + 3.12112i −0.109814 + 0.198995i
\(247\) 5.40319 2.04531i 0.343797 0.130140i
\(248\) 6.20104 + 10.7405i 0.393767 + 0.682024i
\(249\) 0.310056 0.561856i 0.0196490 0.0356062i
\(250\) −3.48044 −0.220123
\(251\) −7.02198 + 12.1624i −0.443223 + 0.767685i −0.997927 0.0643630i \(-0.979498\pi\)
0.554703 + 0.832048i \(0.312832\pi\)
\(252\) 0.650459 1.23457i 0.0409751 0.0777705i
\(253\) 3.66418 6.34654i 0.230365 0.399004i
\(254\) −0.352041 + 0.609753i −0.0220890 + 0.0382593i
\(255\) 45.9286 0.888499i 2.87616 0.0556399i
\(256\) 6.09457 0.380910
\(257\) 17.1607 1.07045 0.535227 0.844709i \(-0.320226\pi\)
0.535227 + 0.844709i \(0.320226\pi\)
\(258\) −6.44888 + 0.124755i −0.401490 + 0.00776690i
\(259\) −0.387862 + 0.671797i −0.0241006 + 0.0417435i
\(260\) 4.38803 7.60029i 0.272134 0.471350i
\(261\) 6.60096 + 10.4755i 0.408589 + 0.648414i
\(262\) 0.561691 0.972878i 0.0347014 0.0601046i
\(263\) 19.4995 1.20239 0.601194 0.799103i \(-0.294692\pi\)
0.601194 + 0.799103i \(0.294692\pi\)
\(264\) 1.95603 3.54455i 0.120385 0.218152i
\(265\) −0.903671 1.56520i −0.0555121 0.0961498i
\(266\) 0.0650167 0.398496i 0.00398643 0.0244333i
\(267\) 6.71211 12.1631i 0.410774 0.744370i
\(268\) 1.48874 0.0909394
\(269\) −11.5796 20.0564i −0.706020 1.22286i −0.966322 0.257335i \(-0.917156\pi\)
0.260303 0.965527i \(-0.416178\pi\)
\(270\) 3.07590 6.12234i 0.187193 0.372594i
\(271\) −11.0388 19.1197i −0.670557 1.16144i −0.977746 0.209790i \(-0.932722\pi\)
0.307190 0.951648i \(-0.400611\pi\)
\(272\) 11.9120 + 20.6322i 0.722272 + 1.25101i
\(273\) 0.277018 0.501988i 0.0167659 0.0303817i
\(274\) −0.789525 1.36750i −0.0476970 0.0826136i
\(275\) 12.4649 0.751660
\(276\) 14.4859 0.280234i 0.871951 0.0168681i
\(277\) 14.7992 25.6330i 0.889199 1.54014i 0.0483752 0.998829i \(-0.484596\pi\)
0.840824 0.541309i \(-0.182071\pi\)
\(278\) −6.40605 −0.384209
\(279\) −13.8464 21.9736i −0.828959 1.31552i
\(280\) −0.635988 1.10156i −0.0380075 0.0658310i
\(281\) −14.4042 24.9487i −0.859280 1.48832i −0.872617 0.488406i \(-0.837579\pi\)
0.0133368 0.999911i \(-0.495755\pi\)
\(282\) −1.11709 1.85122i −0.0665219 0.110239i
\(283\) −8.01020 + 13.8741i −0.476157 + 0.824728i −0.999627 0.0273162i \(-0.991304\pi\)
0.523470 + 0.852044i \(0.324637\pi\)
\(284\) −10.4306 18.0664i −0.618944 1.07204i
\(285\) −3.80896 + 26.5696i −0.225623 + 1.57385i
\(286\) 0.401040 0.694621i 0.0237140 0.0410738i
\(287\) −0.692963 1.20025i −0.0409043 0.0708483i
\(288\) 12.1395 0.469859i 0.715328 0.0276867i
\(289\) −19.3258 + 33.4732i −1.13681 + 1.96901i
\(290\) 5.44215 0.319574
\(291\) 11.1377 0.215461i 0.652902 0.0126305i
\(292\) 3.44094 + 5.95989i 0.201366 + 0.348776i
\(293\) −0.400378 0.693475i −0.0233903 0.0405132i 0.854093 0.520120i \(-0.174113\pi\)
−0.877484 + 0.479607i \(0.840779\pi\)
\(294\) 2.30259 + 3.81581i 0.134290 + 0.222543i
\(295\) −18.5980 32.2127i −1.08282 1.87550i
\(296\) −4.44945 −0.258619
\(297\) −3.80614 + 7.57582i −0.220855 + 0.439594i
\(298\) −0.342358 + 0.592981i −0.0198322 + 0.0343504i
\(299\) 5.95301 0.344271
\(300\) 12.7324 + 21.0999i 0.735108 + 1.21820i
\(301\) 1.25383 2.17170i 0.0722696 0.125175i
\(302\) −2.07670 + 3.59696i −0.119501 + 0.206982i
\(303\) −6.76842 11.2165i −0.388836 0.644370i
\(304\) −13.0189 + 4.92815i −0.746686 + 0.282649i
\(305\) −14.7221 −0.842987
\(306\) 4.42516 + 7.02255i 0.252970 + 0.401452i
\(307\) 2.29987 + 3.98349i 0.131260 + 0.227350i 0.924163 0.381999i \(-0.124764\pi\)
−0.792902 + 0.609349i \(0.791431\pi\)
\(308\) 0.379474 + 0.657268i 0.0216225 + 0.0374513i
\(309\) −12.3659 20.4925i −0.703470 1.16578i
\(310\) −11.4156 −0.648362
\(311\) 16.4116 + 28.4257i 0.930615 + 1.61187i 0.782273 + 0.622936i \(0.214060\pi\)
0.148342 + 0.988936i \(0.452606\pi\)
\(312\) 3.28804 0.0636078i 0.186149 0.00360108i
\(313\) 9.19380 + 15.9241i 0.519664 + 0.900085i 0.999739 + 0.0228573i \(0.00727633\pi\)
−0.480074 + 0.877228i \(0.659390\pi\)
\(314\) −3.85189 + 6.67167i −0.217375 + 0.376504i
\(315\) 1.42010 + 2.25364i 0.0800136 + 0.126978i
\(316\) −18.3549 −1.03254
\(317\) −0.679102 1.17624i −0.0381422 0.0660642i 0.846324 0.532668i \(-0.178811\pi\)
−0.884466 + 0.466604i \(0.845477\pi\)
\(318\) 0.157786 0.285925i 0.00884817 0.0160339i
\(319\) −6.73415 −0.377040
\(320\) −8.68398 + 15.0411i −0.485449 + 0.840823i
\(321\) 20.8013 0.402405i 1.16102 0.0224601i
\(322\) 0.208021 0.360302i 0.0115925 0.0200789i
\(323\) −25.1753 20.5812i −1.40079 1.14517i
\(324\) −16.7118 + 1.29560i −0.928435 + 0.0719778i
\(325\) 5.06277 + 8.76897i 0.280832 + 0.486415i
\(326\) −2.00900 −0.111268
\(327\) −13.6486 22.6182i −0.754770 1.25079i
\(328\) 3.97473 6.88444i 0.219468 0.380130i
\(329\) 0.840601 0.0463438
\(330\) 1.92528 + 3.19053i 0.105983 + 0.175633i
\(331\) 8.39869 14.5470i 0.461634 0.799573i −0.537409 0.843322i \(-0.680597\pi\)
0.999043 + 0.0437490i \(0.0139302\pi\)
\(332\) −0.345020 + 0.597592i −0.0189354 + 0.0327971i
\(333\) 9.31100 0.360381i 0.510240 0.0197488i
\(334\) −0.556357 −0.0304425
\(335\) −1.42093 + 2.46112i −0.0776336 + 0.134465i
\(336\) −0.667471 + 1.20953i −0.0364135 + 0.0659854i
\(337\) −18.2612 + 31.6293i −0.994750 + 1.72296i −0.408751 + 0.912646i \(0.634035\pi\)
−0.585999 + 0.810312i \(0.699298\pi\)
\(338\) −4.17001 −0.226819
\(339\) −2.62165 4.34454i −0.142389 0.235963i
\(340\) −49.3954 −2.67884
\(341\) 14.1257 0.764951
\(342\) −4.46610 + 1.89115i −0.241499 + 0.102262i
\(343\) −3.48094 −0.187953
\(344\) 14.3836 0.775511
\(345\) −13.3628 + 24.2150i −0.719430 + 1.30369i
\(346\) 8.31290 0.446904
\(347\) 5.07542 8.79089i 0.272463 0.471920i −0.697029 0.717043i \(-0.745495\pi\)
0.969492 + 0.245123i \(0.0788284\pi\)
\(348\) −6.87870 11.3992i −0.368737 0.611063i
\(349\) 8.63614 14.9582i 0.462282 0.800696i −0.536792 0.843715i \(-0.680364\pi\)
0.999074 + 0.0430183i \(0.0136974\pi\)
\(350\) 0.707649 0.0378254
\(351\) −6.87546 + 0.399420i −0.366985 + 0.0213195i
\(352\) −3.30367 + 5.72212i −0.176086 + 0.304990i
\(353\) −8.45158 + 14.6386i −0.449832 + 0.779132i −0.998375 0.0569905i \(-0.981850\pi\)
0.548543 + 0.836123i \(0.315183\pi\)
\(354\) 3.24731 5.88450i 0.172593 0.312758i
\(355\) 39.8220 2.11353
\(356\) −7.46902 + 12.9367i −0.395857 + 0.685645i
\(357\) −3.22646 + 0.0624164i −0.170762 + 0.00330343i
\(358\) −4.71525 −0.249209
\(359\) 3.82747 + 6.62938i 0.202006 + 0.349885i 0.949175 0.314750i \(-0.101921\pi\)
−0.747168 + 0.664635i \(0.768587\pi\)
\(360\) −7.12198 + 13.5175i −0.375361 + 0.712434i
\(361\) 14.2374 12.5816i 0.749337 0.662189i
\(362\) 0.486446 0.842549i 0.0255670 0.0442834i
\(363\) 7.46128 + 12.3647i 0.391616 + 0.648977i
\(364\) −0.308256 + 0.533915i −0.0161570 + 0.0279848i
\(365\) −13.1368 −0.687613
\(366\) −1.37440 2.27762i −0.0718409 0.119053i
\(367\) 12.3888 + 21.4579i 0.646688 + 1.12010i 0.983909 + 0.178670i \(0.0571796\pi\)
−0.337221 + 0.941425i \(0.609487\pi\)
\(368\) −14.3437 −0.747717
\(369\) −7.76001 + 14.7285i −0.403970 + 0.766733i
\(370\) 2.04776 3.54683i 0.106458 0.184391i
\(371\) 0.0634823 + 0.109955i 0.00329584 + 0.00570856i
\(372\) 14.4289 + 23.9113i 0.748105 + 1.23974i
\(373\) 11.5863 + 20.0681i 0.599917 + 1.03909i 0.992833 + 0.119512i \(0.0381330\pi\)
−0.392916 + 0.919574i \(0.628534\pi\)
\(374\) −4.51444 −0.233436
\(375\) −16.2506 + 0.314372i −0.839179 + 0.0162341i
\(376\) 2.41078 + 4.17560i 0.124327 + 0.215340i
\(377\) −2.73516 4.73744i −0.140868 0.243990i
\(378\) −0.216080 + 0.430090i −0.0111140 + 0.0221215i
\(379\) 29.0801 1.49374 0.746871 0.664969i \(-0.231555\pi\)
0.746871 + 0.664969i \(0.231555\pi\)
\(380\) 4.64752 28.4852i 0.238413 1.46126i
\(381\) −1.58865 + 2.87881i −0.0813888 + 0.147486i
\(382\) −0.632057 + 1.09475i −0.0323388 + 0.0560125i
\(383\) 1.41428 2.44960i 0.0722662 0.125169i −0.827628 0.561277i \(-0.810310\pi\)
0.899894 + 0.436108i \(0.143644\pi\)
\(384\) −17.1630 + 0.332023i −0.875848 + 0.0169435i
\(385\) −1.44875 −0.0738353
\(386\) −0.0923078 + 0.159882i −0.00469834 + 0.00813777i
\(387\) −30.0994 + 1.16499i −1.53004 + 0.0592199i
\(388\) −11.9784 −0.608110
\(389\) −9.58295 16.5982i −0.485875 0.841560i 0.513993 0.857794i \(-0.328166\pi\)
−0.999868 + 0.0162341i \(0.994832\pi\)
\(390\) −1.46254 + 2.65030i −0.0740588 + 0.134203i
\(391\) −16.7530 29.0171i −0.847238 1.46746i
\(392\) −4.96920 8.60691i −0.250983 0.434715i
\(393\) 2.53473 4.59322i 0.127860 0.231697i
\(394\) −0.980624 −0.0494031
\(395\) 17.5188 30.3435i 0.881467 1.52675i
\(396\) 4.24946 8.06546i 0.213544 0.405305i
\(397\) 15.9590 + 27.6417i 0.800958 + 1.38730i 0.918986 + 0.394289i \(0.129009\pi\)
−0.118029 + 0.993010i \(0.537658\pi\)
\(398\) 0.0394295 0.0682939i 0.00197642 0.00342326i
\(399\) 0.267577 1.86650i 0.0133956 0.0934418i
\(400\) −12.1987 21.1287i −0.609934 1.05644i
\(401\) −19.1703 + 33.2040i −0.957320 + 1.65813i −0.228353 + 0.973578i \(0.573334\pi\)
−0.728967 + 0.684548i \(0.759999\pi\)
\(402\) −0.513405 + 0.00993193i −0.0256063 + 0.000495360i
\(403\) 5.73734 + 9.93737i 0.285797 + 0.495015i
\(404\) 7.04332 + 12.1994i 0.350418 + 0.606942i
\(405\) 13.8088 28.8638i 0.686163 1.43425i
\(406\) −0.382307 −0.0189736
\(407\) −2.53391 + 4.38887i −0.125601 + 0.217548i
\(408\) −9.56329 15.8481i −0.473453 0.784597i
\(409\) 2.29288 0.113375 0.0566877 0.998392i \(-0.481946\pi\)
0.0566877 + 0.998392i \(0.481946\pi\)
\(410\) 3.65857 + 6.33683i 0.180684 + 0.312954i
\(411\) −3.80991 6.31370i −0.187929 0.311432i
\(412\) 12.8681 + 22.2882i 0.633966 + 1.09806i
\(413\) 1.30650 + 2.26292i 0.0642886 + 0.111351i
\(414\) −4.99373 + 0.193282i −0.245428 + 0.00949928i
\(415\) −0.658608 1.14074i −0.0323298 0.0559968i
\(416\) −5.36731 −0.263154
\(417\) −29.9106 + 0.578627i −1.46473 + 0.0283355i
\(418\) 0.424756 2.60338i 0.0207755 0.127335i
\(419\) 5.32211 + 9.21817i 0.260002 + 0.450337i 0.966242 0.257636i \(-0.0829434\pi\)
−0.706240 + 0.707972i \(0.749610\pi\)
\(420\) −1.47985 2.45238i −0.0722094 0.119664i
\(421\) 25.8645 1.26056 0.630280 0.776367i \(-0.282940\pi\)
0.630280 + 0.776367i \(0.282940\pi\)
\(422\) 1.58068 2.73782i 0.0769464 0.133275i
\(423\) −5.38305 8.54268i −0.261733 0.415359i
\(424\) −0.364125 + 0.630684i −0.0176835 + 0.0306287i
\(425\) 28.4954 49.3555i 1.38223 2.39409i
\(426\) 3.71762 + 6.16075i 0.180119 + 0.298489i
\(427\) 1.03422 0.0500494
\(428\) −22.3714 −1.08136
\(429\) 1.80976 3.27950i 0.0873761 0.158336i
\(430\) −6.61973 + 11.4657i −0.319232 + 0.552926i
\(431\) −9.52984 + 16.5062i −0.459036 + 0.795074i −0.998910 0.0466716i \(-0.985139\pi\)
0.539874 + 0.841746i \(0.318472\pi\)
\(432\) 16.5663 0.962399i 0.797049 0.0463034i
\(433\) 13.3288 23.0861i 0.640540 1.10945i −0.344773 0.938686i \(-0.612044\pi\)
0.985312 0.170761i \(-0.0546226\pi\)
\(434\) 0.801937 0.0384942
\(435\) 25.4101 0.491563i 1.21832 0.0235686i
\(436\) 14.2029 + 24.6002i 0.680197 + 1.17814i
\(437\) 18.3098 6.93094i 0.875876 0.331552i
\(438\) −1.22640 2.03236i −0.0585996 0.0971100i
\(439\) −1.94705 −0.0929274 −0.0464637 0.998920i \(-0.514795\pi\)
−0.0464637 + 0.998920i \(0.514795\pi\)
\(440\) −4.15492 7.19653i −0.198078 0.343081i
\(441\) 11.0958 + 17.6085i 0.528370 + 0.838501i
\(442\) −1.83360 3.17589i −0.0872154 0.151062i
\(443\) −3.28115 5.68312i −0.155892 0.270013i 0.777491 0.628894i \(-0.216492\pi\)
−0.933384 + 0.358880i \(0.883159\pi\)
\(444\) −10.0176 + 0.193792i −0.475413 + 0.00919695i
\(445\) −14.2576 24.6949i −0.675875 1.17065i
\(446\) 5.78704 0.274024
\(447\) −1.54495 + 2.79962i −0.0730736 + 0.132418i
\(448\) 0.610044 1.05663i 0.0288219 0.0499209i
\(449\) −35.5348 −1.67699 −0.838495 0.544910i \(-0.816564\pi\)
−0.838495 + 0.544910i \(0.816564\pi\)
\(450\) −4.53165 7.19154i −0.213624 0.339013i
\(451\) −4.52714 7.84124i −0.213175 0.369229i
\(452\) 2.72813 + 4.72526i 0.128320 + 0.222257i
\(453\) −9.37149 + 16.9822i −0.440311 + 0.797894i
\(454\) −0.220837 + 0.382501i −0.0103644 + 0.0179516i
\(455\) −0.588430 1.01919i −0.0275860 0.0477804i
\(456\) 10.0390 4.02382i 0.470121 0.188433i
\(457\) −3.32444 + 5.75809i −0.155511 + 0.269352i −0.933245 0.359241i \(-0.883036\pi\)
0.777734 + 0.628593i \(0.216369\pi\)
\(458\) −3.70311 6.41398i −0.173035 0.299706i
\(459\) 21.2959 + 32.3894i 0.994009 + 1.51181i
\(460\) 14.8697 25.7551i 0.693304 1.20084i
\(461\) −6.97181 −0.324709 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(462\) −0.135250 0.224133i −0.00629238 0.0104276i
\(463\) 8.59691 + 14.8903i 0.399532 + 0.692010i 0.993668 0.112354i \(-0.0358392\pi\)
−0.594136 + 0.804365i \(0.702506\pi\)
\(464\) 6.59033 + 11.4148i 0.305949 + 0.529919i
\(465\) −53.3008 + 1.03111i −2.47177 + 0.0478168i
\(466\) 2.29369 + 3.97280i 0.106253 + 0.184036i
\(467\) 36.5485 1.69126 0.845632 0.533766i \(-0.179224\pi\)
0.845632 + 0.533766i \(0.179224\pi\)
\(468\) 7.39998 0.286415i 0.342064 0.0132396i
\(469\) 0.0998193 0.172892i 0.00460923 0.00798341i
\(470\) −4.43804 −0.204712
\(471\) −17.3823 + 31.4988i −0.800936 + 1.45139i
\(472\) −7.49390 + 12.9798i −0.344935 + 0.597444i
\(473\) 8.19130 14.1877i 0.376636 0.652353i
\(474\) 6.32984 0.122452i 0.290739 0.00562441i
\(475\) 25.7811 + 21.0764i 1.18292 + 0.967054i
\(476\) 3.47000 0.159047
\(477\) 0.710894 1.34927i 0.0325496 0.0617790i
\(478\) 3.01025 + 5.21391i 0.137686 + 0.238479i
\(479\) 9.98270 + 17.2905i 0.456121 + 0.790025i 0.998752 0.0499464i \(-0.0159050\pi\)
−0.542631 + 0.839971i \(0.682572\pi\)
\(480\) 12.0481 21.8325i 0.549918 0.996514i
\(481\) −4.11673 −0.187707
\(482\) −1.94475 3.36840i −0.0885807 0.153426i
\(483\) 0.938730 1.70109i 0.0427137 0.0774021i
\(484\) −7.76432 13.4482i −0.352924 0.611281i
\(485\) 11.4327 19.8021i 0.519134 0.899167i
\(486\) 5.75457 0.558289i 0.261033 0.0253245i
\(487\) 0.541412 0.0245337 0.0122669 0.999925i \(-0.496095\pi\)
0.0122669 + 0.999925i \(0.496095\pi\)
\(488\) 2.96607 + 5.13738i 0.134268 + 0.232558i
\(489\) −9.38026 + 0.181463i −0.424190 + 0.00820604i
\(490\) 9.14787 0.413259
\(491\) 3.67184 6.35982i 0.165708 0.287015i −0.771199 0.636595i \(-0.780342\pi\)
0.936906 + 0.349580i \(0.113676\pi\)
\(492\) 8.64894 15.6729i 0.389924 0.706588i
\(493\) −15.3946 + 26.6643i −0.693340 + 1.20090i
\(494\) 2.00398 0.758583i 0.0901635 0.0341302i
\(495\) 9.27755 + 14.7231i 0.416995 + 0.661753i
\(496\) −13.8241 23.9440i −0.620718 1.07512i
\(497\) −2.79747 −0.125484
\(498\) 0.114996 0.208386i 0.00515310 0.00933801i
\(499\) 5.97373 10.3468i 0.267421 0.463187i −0.700774 0.713383i \(-0.747162\pi\)
0.968195 + 0.250197i \(0.0804952\pi\)
\(500\) 17.4773 0.781607
\(501\) −2.59770 + 0.0502530i −0.116057 + 0.00224514i
\(502\) −2.60437 + 4.51091i −0.116239 + 0.201332i
\(503\) 14.7358 25.5232i 0.657038 1.13802i −0.324341 0.945940i \(-0.605142\pi\)
0.981379 0.192083i \(-0.0615242\pi\)
\(504\) 0.500315 0.949595i 0.0222858 0.0422983i
\(505\) −26.8900 −1.19659
\(506\) 1.35900 2.35386i 0.0604151 0.104642i
\(507\) −19.4703 + 0.376657i −0.864706 + 0.0167279i
\(508\) 1.76779 3.06191i 0.0784332 0.135850i
\(509\) 17.9044 0.793600 0.396800 0.917905i \(-0.370121\pi\)
0.396800 + 0.917905i \(0.370121\pi\)
\(510\) 17.0344 0.329534i 0.754297 0.0145920i
\(511\) 0.922853 0.0408246
\(512\) 22.0823 0.975909
\(513\) −20.6820 + 9.23343i −0.913131 + 0.407666i
\(514\) 6.36470 0.280735
\(515\) −49.1278 −2.16483
\(516\) 32.3834 0.626464i 1.42560 0.0275786i
\(517\) 5.49166 0.241523
\(518\) −0.143854 + 0.249162i −0.00632058 + 0.0109476i
\(519\) 38.8139 0.750864i 1.70374 0.0329593i
\(520\) 3.37515 5.84593i 0.148010 0.256361i
\(521\) −27.8411 −1.21974 −0.609871 0.792501i \(-0.708779\pi\)
−0.609871 + 0.792501i \(0.708779\pi\)
\(522\) 2.44823 + 3.88523i 0.107156 + 0.170052i
\(523\) −12.9624 + 22.4515i −0.566805 + 0.981735i 0.430074 + 0.902794i \(0.358487\pi\)
−0.996879 + 0.0789417i \(0.974846\pi\)
\(524\) −2.82057 + 4.88537i −0.123217 + 0.213418i
\(525\) 3.30410 0.0639185i 0.144203 0.00278963i
\(526\) 7.23214 0.315336
\(527\) 32.2922 55.9317i 1.40667 2.43642i
\(528\) −4.36060 + 7.90191i −0.189771 + 0.343886i
\(529\) −2.82704 −0.122915
\(530\) −0.335162 0.580517i −0.0145585 0.0252161i
\(531\) 14.6306 27.7688i 0.634913 1.20506i
\(532\) −0.326485 + 2.00107i −0.0141549 + 0.0867574i
\(533\) 3.67751 6.36964i 0.159291 0.275900i
\(534\) 2.48945 4.51116i 0.107729 0.195217i
\(535\) 21.3524 36.9834i 0.923144 1.59893i
\(536\) 1.14510 0.0494607
\(537\) −22.0161 + 0.425906i −0.950064 + 0.0183792i
\(538\) −4.29474 7.43871i −0.185159 0.320705i
\(539\) −11.3196 −0.487571
\(540\) −15.4458 + 30.7437i −0.664682 + 1.32300i
\(541\) −12.3043 + 21.3116i −0.529001 + 0.916257i 0.470427 + 0.882439i \(0.344100\pi\)
−0.999428 + 0.0338181i \(0.989233\pi\)
\(542\) −4.09415 7.09128i −0.175859 0.304597i
\(543\) 2.19517 3.97790i 0.0942038 0.170708i
\(544\) 15.1048 + 26.1622i 0.647611 + 1.12170i
\(545\) −54.2239 −2.32270
\(546\) 0.102743 0.186182i 0.00439699 0.00796784i
\(547\) −6.44357 11.1606i −0.275507 0.477192i 0.694756 0.719246i \(-0.255512\pi\)
−0.970263 + 0.242054i \(0.922179\pi\)
\(548\) 3.96465 + 6.86697i 0.169361 + 0.293343i
\(549\) −6.62296 10.5104i −0.282661 0.448571i
\(550\) 4.62308 0.197129
\(551\) −13.9283 11.3865i −0.593364 0.485083i
\(552\) 11.1422 0.215548i 0.474243 0.00917432i
\(553\) −1.23068 + 2.13161i −0.0523340 + 0.0906452i
\(554\) 5.48887 9.50700i 0.233200 0.403914i
\(555\) 9.24089 16.7455i 0.392254 0.710809i
\(556\) 32.1684 1.36424
\(557\) −11.8767 + 20.5710i −0.503231 + 0.871622i 0.496762 + 0.867887i \(0.334522\pi\)
−0.999993 + 0.00373498i \(0.998811\pi\)
\(558\) −5.13546 8.14976i −0.217401 0.345007i
\(559\) 13.3080 0.562868
\(560\) 1.41781 + 2.45573i 0.0599136 + 0.103773i
\(561\) −21.0785 + 0.407768i −0.889935 + 0.0172160i
\(562\) −5.34234 9.25321i −0.225353 0.390323i
\(563\) 13.3440 + 23.1125i 0.562383 + 0.974077i 0.997288 + 0.0735999i \(0.0234488\pi\)
−0.434904 + 0.900477i \(0.643218\pi\)
\(564\) 5.60955 + 9.29602i 0.236204 + 0.391433i
\(565\) −10.4154 −0.438181
\(566\) −2.97090 + 5.14574i −0.124876 + 0.216292i
\(567\) −0.970056 + 2.02766i −0.0407385 + 0.0851539i
\(568\) −8.02294 13.8961i −0.336635 0.583069i
\(569\) 6.57047 11.3804i 0.275448 0.477090i −0.694800 0.719203i \(-0.744507\pi\)
0.970248 + 0.242113i \(0.0778404\pi\)
\(570\) −1.41270 + 9.85438i −0.0591716 + 0.412755i
\(571\) −1.08070 1.87182i −0.0452258 0.0783333i 0.842526 0.538655i \(-0.181067\pi\)
−0.887752 + 0.460322i \(0.847734\pi\)
\(572\) −2.01384 + 3.48808i −0.0842031 + 0.145844i
\(573\) −2.85227 + 5.16863i −0.119155 + 0.215923i
\(574\) −0.257012 0.445158i −0.0107275 0.0185805i
\(575\) 17.1562 + 29.7154i 0.715463 + 1.23922i
\(576\) −14.6447 + 0.566821i −0.610195 + 0.0236175i
\(577\) 4.53956 0.188985 0.0944923 0.995526i \(-0.469877\pi\)
0.0944923 + 0.995526i \(0.469877\pi\)
\(578\) −7.16772 + 12.4149i −0.298138 + 0.516390i
\(579\) −0.416555 + 0.754846i −0.0173114 + 0.0313703i
\(580\) −27.3281 −1.13474
\(581\) 0.0462667 + 0.0801364i 0.00191947 + 0.00332462i
\(582\) 4.13084 0.0799120i 0.171229 0.00331246i
\(583\) 0.414731 + 0.718336i 0.0171764 + 0.0297504i
\(584\) 2.64668 + 4.58418i 0.109520 + 0.189695i
\(585\) −6.58941 + 12.5067i −0.272439 + 0.517087i
\(586\) −0.148496 0.257202i −0.00613430 0.0106249i
\(587\) 24.2678 1.00164 0.500819 0.865552i \(-0.333032\pi\)
0.500819 + 0.865552i \(0.333032\pi\)
\(588\) −11.5626 19.1613i −0.476834 0.790200i
\(589\) 29.2163 + 23.8847i 1.20384 + 0.984152i
\(590\) −6.89781 11.9474i −0.283978 0.491865i
\(591\) −4.57866 + 0.0885750i −0.188341 + 0.00364349i
\(592\) 9.91920 0.407677
\(593\) 16.5350 28.6395i 0.679013 1.17608i −0.296266 0.955106i \(-0.595741\pi\)
0.975279 0.220979i \(-0.0709252\pi\)
\(594\) −1.41165 + 2.80979i −0.0579209 + 0.115287i
\(595\) −3.31193 + 5.73644i −0.135776 + 0.235171i
\(596\) 1.71917 2.97769i 0.0704199 0.121971i
\(597\) 0.177932 0.322434i 0.00728229 0.0131963i
\(598\) 2.20791 0.0902880
\(599\) −13.2848 −0.542803 −0.271401 0.962466i \(-0.587487\pi\)
−0.271401 + 0.962466i \(0.587487\pi\)
\(600\) 9.79343 + 16.2295i 0.399815 + 0.662565i
\(601\) −7.35146 + 12.7331i −0.299872 + 0.519394i −0.976106 0.217293i \(-0.930277\pi\)
0.676234 + 0.736687i \(0.263611\pi\)
\(602\) 0.465032 0.805459i 0.0189533 0.0328280i
\(603\) −2.39626 + 0.0927468i −0.0975831 + 0.00377694i
\(604\) 10.4283 18.0623i 0.424321 0.734946i
\(605\) 29.6426 1.20514
\(606\) −2.51033 4.16007i −0.101975 0.168991i
\(607\) −1.19304 2.06641i −0.0484241 0.0838729i 0.840797 0.541350i \(-0.182087\pi\)
−0.889221 + 0.457477i \(0.848753\pi\)
\(608\) −16.5083 + 6.24903i −0.669502 + 0.253431i
\(609\) −1.78504 + 0.0345320i −0.0723335 + 0.00139931i
\(610\) −5.46028 −0.221080
\(611\) 2.23051 + 3.86336i 0.0902368 + 0.156295i
\(612\) −22.2212 35.2641i −0.898239 1.42547i
\(613\) 2.16079 + 3.74260i 0.0872736 + 0.151162i 0.906358 0.422511i \(-0.138851\pi\)
−0.819084 + 0.573673i \(0.805518\pi\)
\(614\) 0.852996 + 1.47743i 0.0344241 + 0.0596243i
\(615\) 17.6547 + 29.2570i 0.711906 + 1.17976i
\(616\) 0.291880 + 0.505552i 0.0117602 + 0.0203693i
\(617\) −9.61045 −0.386902 −0.193451 0.981110i \(-0.561968\pi\)
−0.193451 + 0.981110i \(0.561968\pi\)
\(618\) −4.58637 7.60043i −0.184491 0.305734i
\(619\) −1.79677 + 3.11209i −0.0722182 + 0.125086i −0.899873 0.436152i \(-0.856341\pi\)
0.827655 + 0.561237i \(0.189674\pi\)
\(620\) 57.3241 2.30219
\(621\) −23.2989 + 1.35352i −0.934952 + 0.0543147i
\(622\) 6.08687 + 10.5428i 0.244061 + 0.422727i
\(623\) 1.00159 + 1.73480i 0.0401277 + 0.0695032i
\(624\) −7.33006 + 0.141802i −0.293437 + 0.00567660i
\(625\) 2.41765 4.18750i 0.0967061 0.167500i
\(626\) 3.40988 + 5.90608i 0.136286 + 0.236055i
\(627\) 1.74809 12.1939i 0.0698119 0.486976i
\(628\) 19.3425 33.5022i 0.771850 1.33688i
\(629\) 11.5853 + 20.0664i 0.461938 + 0.800100i
\(630\) 0.526700 + 0.835851i 0.0209842 + 0.0333011i
\(631\) 12.6319 21.8792i 0.502870 0.870996i −0.497125 0.867679i \(-0.665611\pi\)
0.999994 0.00331669i \(-0.00105574\pi\)
\(632\) −14.1181 −0.561586
\(633\) 7.13311 12.9260i 0.283516 0.513763i
\(634\) −0.251872 0.436254i −0.0100031 0.0173259i
\(635\) 3.37454 + 5.84487i 0.133915 + 0.231947i
\(636\) −0.792330 + 1.43579i −0.0314179 + 0.0569328i
\(637\) −4.59761 7.96330i −0.182164 0.315517i
\(638\) −2.49762 −0.0988818
\(639\) 17.9145 + 28.4295i 0.708686 + 1.12465i
\(640\) −17.6177 + 30.5148i −0.696402 + 1.20620i
\(641\) −23.3043 −0.920463 −0.460231 0.887799i \(-0.652234\pi\)
−0.460231 + 0.887799i \(0.652234\pi\)
\(642\) 7.71498 0.149248i 0.304486 0.00589034i
\(643\) −8.62978 + 14.9472i −0.340325 + 0.589461i −0.984493 0.175423i \(-0.943871\pi\)
0.644168 + 0.764884i \(0.277204\pi\)
\(644\) −1.04459 + 1.80928i −0.0411625 + 0.0712956i
\(645\) −29.8727 + 54.1328i −1.17624 + 2.13148i
\(646\) −9.33724 7.63333i −0.367369 0.300329i
\(647\) −35.6673 −1.40223 −0.701114 0.713049i \(-0.747314\pi\)
−0.701114 + 0.713049i \(0.747314\pi\)
\(648\) −12.8543 + 0.996539i −0.504963 + 0.0391477i
\(649\) 8.53539 + 14.7837i 0.335043 + 0.580312i
\(650\) 1.87772 + 3.25231i 0.0736504 + 0.127566i
\(651\) 3.74434 0.0724351i 0.146752 0.00283896i
\(652\) 10.0883 0.395088
\(653\) −8.46548 14.6626i −0.331280 0.573794i 0.651483 0.758663i \(-0.274147\pi\)
−0.982763 + 0.184869i \(0.940814\pi\)
\(654\) −5.06212 8.38883i −0.197944 0.328029i
\(655\) −5.38418 9.32566i −0.210377 0.364384i
\(656\) −8.86092 + 15.3476i −0.345961 + 0.599222i
\(657\) −5.90978 9.37858i −0.230563 0.365893i
\(658\) 0.311770 0.0121540
\(659\) 2.26182 + 3.91760i 0.0881082 + 0.152608i 0.906711 0.421752i \(-0.138585\pi\)
−0.818603 + 0.574359i \(0.805251\pi\)
\(660\) −9.66790 16.0214i −0.376323 0.623634i
\(661\) 20.0800 0.781021 0.390510 0.920599i \(-0.372299\pi\)
0.390510 + 0.920599i \(0.372299\pi\)
\(662\) 3.11498 5.39530i 0.121067 0.209694i
\(663\) −8.84817 14.6630i −0.343634 0.569463i
\(664\) −0.265379 + 0.459651i −0.0102987 + 0.0178379i
\(665\) −2.99646 2.44965i −0.116198 0.0949933i
\(666\) 3.45335 0.133661i 0.133815 0.00517928i
\(667\) −9.26864 16.0537i −0.358883 0.621604i
\(668\) 2.79378 0.108095
\(669\) 27.0204 0.522716i 1.04467 0.0202094i
\(670\) −0.527007 + 0.912803i −0.0203600 + 0.0352646i
\(671\) 6.75658 0.260835
\(672\) −0.846371 + 1.53372i −0.0326495 + 0.0591646i
\(673\) 8.72911 15.1193i 0.336482 0.582805i −0.647286 0.762247i \(-0.724096\pi\)
0.983768 + 0.179443i \(0.0574294\pi\)
\(674\) −6.77287 + 11.7310i −0.260881 + 0.451860i
\(675\) −21.8084 33.1689i −0.839407 1.27667i
\(676\) 20.9399 0.805382
\(677\) −20.4904 + 35.4905i −0.787511 + 1.36401i 0.139976 + 0.990155i \(0.455297\pi\)
−0.927487 + 0.373854i \(0.878036\pi\)
\(678\) −0.972341 1.61134i −0.0373425 0.0618833i
\(679\) −0.803143 + 1.39108i −0.0308218 + 0.0533849i
\(680\) −37.9936 −1.45699
\(681\) −0.996565 + 1.80589i −0.0381885 + 0.0692018i
\(682\) 5.23907 0.200614
\(683\) 20.9461 0.801480 0.400740 0.916192i \(-0.368753\pi\)
0.400740 + 0.916192i \(0.368753\pi\)
\(684\) 22.4268 9.49654i 0.857510 0.363109i
\(685\) −15.1362 −0.578325
\(686\) −1.29104 −0.0492922
\(687\) −17.8696 29.6132i −0.681769 1.12981i
\(688\) −32.0655 −1.22248
\(689\) −0.336897 + 0.583522i −0.0128347 + 0.0222304i
\(690\) −4.95613 + 8.98107i −0.188676 + 0.341903i
\(691\) −10.5768 + 18.3195i −0.402359 + 0.696907i −0.994010 0.109288i \(-0.965143\pi\)
0.591651 + 0.806194i \(0.298476\pi\)
\(692\) −41.7437 −1.58686
\(693\) −0.651742 1.03429i −0.0247576 0.0392893i
\(694\) 1.88242 3.26044i 0.0714556 0.123765i
\(695\) −30.7031 + 53.1793i −1.16463 + 2.01720i
\(696\) −5.29090 8.76797i −0.200551 0.332349i
\(697\) −41.3972 −1.56803
\(698\) 3.20305 5.54785i 0.121237 0.209989i
\(699\) 11.0684 + 18.3423i 0.418645 + 0.693769i
\(700\) −3.55350 −0.134310
\(701\) −1.32346 2.29231i −0.0499865 0.0865792i 0.839950 0.542665i \(-0.182585\pi\)
−0.889936 + 0.456085i \(0.849251\pi\)
\(702\) −2.55003 + 0.148141i −0.0962448 + 0.00559121i
\(703\) −12.6619 + 4.79300i −0.477552 + 0.180771i
\(704\) 3.98543 6.90297i 0.150207 0.260165i
\(705\) −20.7218 + 0.400867i −0.780427 + 0.0150975i
\(706\) −3.13460 + 5.42928i −0.117972 + 0.204334i
\(707\) 1.88900 0.0710432
\(708\) −16.3066 + 29.5494i −0.612838 + 1.11053i
\(709\) −13.4226 23.2486i −0.504097 0.873121i −0.999989 0.00473700i \(-0.998492\pi\)
0.495892 0.868384i \(-0.334841\pi\)
\(710\) 14.7695 0.554291
\(711\) 29.5437 1.14349i 1.10798 0.0428841i
\(712\) −5.74496 + 9.95056i −0.215301 + 0.372913i
\(713\) 19.4421 + 33.6748i 0.728113 + 1.26113i
\(714\) −1.19666 + 0.0231496i −0.0447838 + 0.000866351i
\(715\) −3.84422 6.65839i −0.143766 0.249010i
\(716\) 23.6779 0.884885
\(717\) 14.5262 + 24.0725i 0.542490 + 0.899003i
\(718\) 1.41957 + 2.45876i 0.0529778 + 0.0917602i
\(719\) 1.94193 + 3.36352i 0.0724217 + 0.125438i 0.899962 0.435968i \(-0.143594\pi\)
−0.827540 + 0.561406i \(0.810261\pi\)
\(720\) 15.8771 30.1347i 0.591705 1.12305i
\(721\) 3.45120 0.128529
\(722\) 5.28049 4.66638i 0.196520 0.173665i
\(723\) −9.38451 15.5518i −0.349014 0.578378i
\(724\) −2.44272 + 4.23091i −0.0907828 + 0.157240i
\(725\) 15.7651 27.3060i 0.585502 1.01412i
\(726\) 2.76731 + 4.58592i 0.102704 + 0.170200i
\(727\) −52.3039 −1.93984 −0.969922 0.243417i \(-0.921732\pi\)
−0.969922 + 0.243417i \(0.921732\pi\)
\(728\) −0.237102 + 0.410673i −0.00878758 + 0.0152205i
\(729\) 26.8184 3.12650i 0.993273 0.115796i
\(730\) −4.87230 −0.180332
\(731\) −37.4516 64.8680i −1.38520 2.39923i
\(732\) 6.90162 + 11.4372i 0.255091 + 0.422731i
\(733\) 3.06517 + 5.30902i 0.113215 + 0.196093i 0.917065 0.398739i \(-0.130552\pi\)
−0.803850 + 0.594832i \(0.797219\pi\)
\(734\) 4.59485 + 7.95852i 0.169599 + 0.293754i
\(735\) 42.7125 0.826283i 1.57548 0.0304779i
\(736\) −18.1882 −0.670426
\(737\) 0.652121 1.12951i 0.0240212 0.0416059i
\(738\) −2.87810 + 5.46262i −0.105944 + 0.201082i
\(739\) −6.68714 11.5825i −0.245990 0.426068i 0.716419 0.697670i \(-0.245780\pi\)
−0.962410 + 0.271602i \(0.912447\pi\)
\(740\) −10.2830 + 17.8106i −0.378009 + 0.654731i
\(741\) 9.28833 3.72293i 0.341215 0.136765i
\(742\) 0.0235449 + 0.0407809i 0.000864360 + 0.00149712i
\(743\) 1.37195 2.37629i 0.0503321 0.0871778i −0.839762 0.542955i \(-0.817305\pi\)
0.890094 + 0.455777i \(0.150639\pi\)
\(744\) 11.0983 + 18.3919i 0.406884 + 0.674280i
\(745\) 3.28172 + 5.68410i 0.120233 + 0.208249i
\(746\) 4.29724 + 7.44304i 0.157333 + 0.272509i
\(747\) 0.518109 0.983368i 0.0189566 0.0359796i
\(748\) 22.6696 0.828881
\(749\) −1.49999 + 2.59806i −0.0548085 + 0.0949311i
\(750\) −6.02718 + 0.116597i −0.220081 + 0.00425752i
\(751\) −20.9472 −0.764374 −0.382187 0.924085i \(-0.624829\pi\)
−0.382187 + 0.924085i \(0.624829\pi\)
\(752\) −5.37439 9.30871i −0.195984 0.339454i
\(753\) −11.7527 + 21.2972i −0.428292 + 0.776114i
\(754\) −1.01444 1.75706i −0.0369438 0.0639885i
\(755\) 19.9065 + 34.4791i 0.724473 + 1.25482i
\(756\) 1.08506 2.15973i 0.0394632 0.0785484i
\(757\) 3.65990 + 6.33913i 0.133021 + 0.230400i 0.924840 0.380357i \(-0.124199\pi\)
−0.791819 + 0.610756i \(0.790865\pi\)
\(758\) 10.7855 0.391746
\(759\) 6.13274 11.1132i 0.222604 0.403385i
\(760\) 3.57474 21.9100i 0.129670 0.794761i
\(761\) 6.05266 + 10.4835i 0.219409 + 0.380027i 0.954627 0.297803i \(-0.0962539\pi\)
−0.735219 + 0.677830i \(0.762921\pi\)
\(762\) −0.589212 + 1.06772i −0.0213449 + 0.0386794i
\(763\) 3.80919 0.137902
\(764\) 3.17391 5.49737i 0.114828 0.198888i
\(765\) 79.5061 3.07727i 2.87455 0.111259i
\(766\) 0.524540 0.908530i 0.0189524 0.0328265i
\(767\) −6.93352 + 12.0092i −0.250355 + 0.433627i
\(768\) 10.5541 0.204172i 0.380839 0.00736741i
\(769\) −28.9659 −1.04454 −0.522269 0.852781i \(-0.674914\pi\)
−0.522269 + 0.852781i \(0.674914\pi\)
\(770\) −0.537327 −0.0193639
\(771\) 29.7176 0.574893i 1.07025 0.0207043i
\(772\) 0.463529 0.802856i 0.0166828 0.0288954i
\(773\) 21.7876 37.7372i 0.783645 1.35731i −0.146160 0.989261i \(-0.546691\pi\)
0.929805 0.368052i \(-0.119975\pi\)
\(774\) −11.1635 + 0.432083i −0.401265 + 0.0155309i
\(775\) −33.0693 + 57.2777i −1.18788 + 2.05748i
\(776\) −9.21343 −0.330743
\(777\) −0.649166 + 1.17636i −0.0232887 + 0.0422018i
\(778\) −3.55421 6.15608i −0.127425 0.220706i
\(779\) 3.89499 23.8729i 0.139552 0.855334i
\(780\) 7.34426 13.3086i 0.262967 0.476525i
\(781\) −18.2759 −0.653964
\(782\) −6.21352 10.7621i −0.222195 0.384853i
\(783\) 11.7820 + 17.9195i 0.421054 + 0.640390i
\(784\) 11.0779 + 19.1875i 0.395639 + 0.685267i
\(785\) 36.9229 + 63.9523i 1.31783 + 2.28255i
\(786\) 0.940104 1.70358i 0.0335324 0.0607645i
\(787\) 3.10060 + 5.37040i 0.110525 + 0.191434i 0.915982 0.401220i \(-0.131414\pi\)
−0.805457 + 0.592654i \(0.798080\pi\)
\(788\) 4.92426 0.175420
\(789\) 33.7677 0.653244i 1.20216 0.0232561i
\(790\) 6.49754 11.2541i 0.231172 0.400402i
\(791\) 0.731677 0.0260155
\(792\) 3.26857 6.20372i 0.116143 0.220440i
\(793\) 2.74427 + 4.75322i 0.0974520 + 0.168792i
\(794\) 5.91901 + 10.2520i 0.210058 + 0.363831i
\(795\) −1.61735 2.68023i −0.0573614 0.0950581i
\(796\) −0.197997 + 0.342942i −0.00701784 + 0.0121552i
\(797\) −19.1606 33.1871i −0.678702 1.17555i −0.975372 0.220566i \(-0.929210\pi\)
0.296671 0.954980i \(-0.404124\pi\)
\(798\) 0.0992414 0.692264i 0.00351311 0.0245059i
\(799\) 12.5543 21.7446i 0.444138 0.769269i
\(800\) −15.4683 26.7918i −0.546885 0.947233i
\(801\) 11.2161 21.2880i 0.396300 0.752176i
\(802\) −7.11006 + 12.3150i −0.251065 + 0.434857i
\(803\) 6.02902 0.212759
\(804\) 2.57809 0.0498738i 0.0909224 0.00175891i
\(805\) −1.99401 3.45373i −0.0702797 0.121728i
\(806\) 2.12792 + 3.68566i 0.0749527 + 0.129822i
\(807\) −20.7246 34.3443i −0.729540 1.20898i
\(808\) 5.41752 + 9.38342i 0.190588 + 0.330108i
\(809\) −36.9557 −1.29929 −0.649647 0.760236i \(-0.725083\pi\)
−0.649647 + 0.760236i \(0.725083\pi\)
\(810\) 5.12152 10.7053i 0.179952 0.376145i
\(811\) 21.0016 36.3759i 0.737467 1.27733i −0.216165 0.976357i \(-0.569355\pi\)
0.953632 0.300974i \(-0.0973118\pi\)
\(812\) 1.91978 0.0673710
\(813\) −19.7566 32.7403i −0.692895 1.14825i
\(814\) −0.939801 + 1.62778i −0.0329400 + 0.0570537i
\(815\) −9.62877 + 16.6775i −0.337281 + 0.584188i
\(816\) 21.3195 + 35.3303i 0.746333 + 1.23681i
\(817\) 40.9317 15.4942i 1.43202 0.542072i
\(818\) 0.850402 0.0297336
\(819\) 0.462902 0.878586i 0.0161751 0.0307003i
\(820\) −18.3717 31.8208i −0.641569 1.11123i
\(821\) 8.86017 + 15.3463i 0.309222 + 0.535588i 0.978192 0.207701i \(-0.0665981\pi\)
−0.668970 + 0.743289i \(0.733265\pi\)
\(822\) −1.41305 2.34168i −0.0492859 0.0816756i
\(823\) −29.2027 −1.01794 −0.508971 0.860784i \(-0.669974\pi\)
−0.508971 + 0.860784i \(0.669974\pi\)
\(824\) 9.89779 + 17.1435i 0.344806 + 0.597221i
\(825\) 21.5858 0.417581i 0.751519 0.0145383i
\(826\) 0.484566 + 0.839294i 0.0168602 + 0.0292028i
\(827\) 7.34515 12.7222i 0.255416 0.442393i −0.709593 0.704612i \(-0.751121\pi\)
0.965008 + 0.262219i \(0.0844543\pi\)
\(828\) 25.0763 0.970576i 0.871462 0.0337298i
\(829\) −2.88680 −0.100263 −0.0501314 0.998743i \(-0.515964\pi\)
−0.0501314 + 0.998743i \(0.515964\pi\)
\(830\) −0.244270 0.423089i −0.00847875 0.0146856i
\(831\) 24.7695 44.8851i 0.859244 1.55705i
\(832\) 6.47493 0.224478
\(833\) −25.8773 + 44.8209i −0.896596 + 1.55295i
\(834\) −11.0935 + 0.214607i −0.384137 + 0.00743122i
\(835\) −2.66652 + 4.61855i −0.0922788 + 0.159831i
\(836\) −2.13294 + 13.0730i −0.0737692 + 0.452140i
\(837\) −24.7142 37.5884i −0.854249 1.29924i
\(838\) 1.97391 + 3.41892i 0.0681877 + 0.118105i
\(839\) −15.1184 −0.521946 −0.260973 0.965346i \(-0.584043\pi\)
−0.260973 + 0.965346i \(0.584043\pi\)
\(840\) −1.13826 1.88630i −0.0392737 0.0650835i
\(841\) 5.98290 10.3627i 0.206307 0.357334i
\(842\) 9.59288 0.330592
\(843\) −25.7799 42.7218i −0.887906 1.47142i
\(844\) −7.93749 + 13.7481i −0.273220 + 0.473230i
\(845\) −19.9861 + 34.6170i −0.687543 + 1.19086i
\(846\) −1.99652 3.16839i −0.0686416 0.108931i
\(847\) −2.08237 −0.0715511
\(848\) 0.811749 1.40599i 0.0278756 0.0482819i
\(849\) −13.4067 + 24.2945i −0.460116 + 0.833783i
\(850\) 10.5686 18.3054i 0.362501 0.627871i
\(851\) −13.9503 −0.478212
\(852\) −18.6682 30.9366i −0.639563 1.05987i
\(853\) 26.1014 0.893696 0.446848 0.894610i \(-0.352546\pi\)
0.446848 + 0.894610i \(0.352546\pi\)
\(854\) 0.383581 0.0131259
\(855\) −5.70598 + 46.1389i −0.195141 + 1.57792i
\(856\) −17.2075 −0.588139
\(857\) 41.6454 1.42258 0.711291 0.702898i \(-0.248111\pi\)
0.711291 + 0.702898i \(0.248111\pi\)
\(858\) 0.671221 1.21633i 0.0229151 0.0415248i
\(859\) 9.44030 0.322099 0.161049 0.986946i \(-0.448512\pi\)
0.161049 + 0.986946i \(0.448512\pi\)
\(860\) 33.2414 57.5758i 1.13352 1.96332i
\(861\) −1.24023 2.05528i −0.0422670 0.0700439i
\(862\) −3.53451 + 6.12196i −0.120386 + 0.208515i
\(863\) 31.0403 1.05662 0.528311 0.849051i \(-0.322825\pi\)
0.528311 + 0.849051i \(0.322825\pi\)
\(864\) 21.0066 1.22035i 0.714658 0.0415171i
\(865\) 39.8422 69.0088i 1.35468 2.34637i
\(866\) 4.94349 8.56238i 0.167987 0.290962i
\(867\) −32.3456 + 58.6139i −1.09851 + 1.99063i
\(868\) −4.02698 −0.136684
\(869\) −8.04009 + 13.9258i −0.272741 + 0.472402i
\(870\) 9.42431 0.182315i 0.319514 0.00618107i
\(871\) 1.05947 0.0358988
\(872\) 10.9245 + 18.9218i 0.369950 + 0.640772i
\(873\) 19.2802 0.746238i 0.652536 0.0252563i
\(874\) 6.79090 2.57061i 0.229706 0.0869522i
\(875\) 1.17184 2.02969i 0.0396154 0.0686159i
\(876\) 6.15843 + 10.2056i 0.208074 + 0.344816i
\(877\) 20.7277 35.9014i 0.699924 1.21230i −0.268568 0.963261i \(-0.586550\pi\)
0.968492 0.249044i \(-0.0801163\pi\)
\(878\) −0.722138 −0.0243710
\(879\) −0.716577 1.18750i −0.0241695 0.0400532i
\(880\) 9.26261 + 16.0433i 0.312243 + 0.540820i
\(881\) 15.2233 0.512886 0.256443 0.966559i \(-0.417449\pi\)
0.256443 + 0.966559i \(0.417449\pi\)
\(882\) 4.11530 + 6.53080i 0.138569 + 0.219904i
\(883\) −0.314882 + 0.545392i −0.0105966 + 0.0183539i −0.871275 0.490795i \(-0.836706\pi\)
0.860678 + 0.509149i \(0.170040\pi\)
\(884\) 9.20753 + 15.9479i 0.309683 + 0.536386i
\(885\) −33.2859 55.1606i −1.11889 1.85420i
\(886\) −1.21694 2.10781i −0.0408840 0.0708132i
\(887\) −1.12719 −0.0378474 −0.0189237 0.999821i \(-0.506024\pi\)
−0.0189237 + 0.999821i \(0.506024\pi\)
\(888\) −7.70523 + 0.149059i −0.258570 + 0.00500210i
\(889\) −0.237059 0.410599i −0.00795071 0.0137710i
\(890\) −5.28798 9.15906i −0.177254 0.307012i
\(891\) −6.33740 + 13.2468i −0.212311 + 0.443783i
\(892\) −29.0600 −0.973000
\(893\) 11.3584 + 9.28567i 0.380095 + 0.310733i
\(894\) −0.573004 + 1.03835i −0.0191641 + 0.0347276i
\(895\) −22.5994 + 39.1432i −0.755413 + 1.30841i
\(896\) 1.23763 2.14365i 0.0413465 0.0716142i
\(897\) 10.3090 0.199429i 0.344207 0.00665876i
\(898\) −13.1795 −0.439804
\(899\) 17.8657 30.9443i 0.595854 1.03205i
\(900\) 22.7560 + 36.1128i 0.758532 + 1.20376i
\(901\) 3.79240 0.126343
\(902\) −1.67907 2.90823i −0.0559068 0.0968334i
\(903\) 2.09854 3.80279i 0.0698350 0.126549i
\(904\) 2.09840 + 3.63453i 0.0697917 + 0.120883i
\(905\) −4.66290 8.07637i −0.155000 0.268468i
\(906\) −3.47578 + 6.29851i −0.115475 + 0.209254i
\(907\) 28.7319 0.954028 0.477014 0.878896i \(-0.341719\pi\)
0.477014 + 0.878896i \(0.341719\pi\)
\(908\) 1.10895 1.92075i 0.0368016 0.0637423i
\(909\) −12.0968 19.1971i −0.401226 0.636729i
\(910\) −0.218242 0.378006i −0.00723466 0.0125308i
\(911\) −19.6724 + 34.0735i −0.651774 + 1.12891i 0.330918 + 0.943660i \(0.392642\pi\)
−0.982692 + 0.185246i \(0.940692\pi\)
\(912\) −22.3801 + 8.97035i −0.741080 + 0.297038i
\(913\) 0.302262 + 0.523532i 0.0100034 + 0.0173264i
\(914\) −1.23300 + 2.13561i −0.0407839 + 0.0706398i
\(915\) −25.4947 + 0.493200i −0.842829 + 0.0163047i
\(916\) 18.5954 + 32.2082i 0.614410 + 1.06419i
\(917\) 0.378235 + 0.655122i 0.0124904 + 0.0216340i
\(918\) 7.89843 + 12.0129i 0.260687 + 0.396484i
\(919\) 14.3218 0.472433 0.236217 0.971700i \(-0.424093\pi\)
0.236217 + 0.971700i \(0.424093\pi\)
\(920\) 11.4374 19.8101i 0.377079 0.653120i
\(921\) 4.11619 + 6.82127i 0.135633 + 0.224768i
\(922\) −2.58577 −0.0851577
\(923\) −7.42300 12.8570i −0.244331 0.423194i
\(924\) 0.679164 + 1.12550i 0.0223428 + 0.0370261i
\(925\) −11.8641 20.5493i −0.390091 0.675657i
\(926\) 3.18850 + 5.52264i 0.104781 + 0.181485i
\(927\) −22.1008 35.0731i −0.725887 1.15195i
\(928\) 8.35672 + 14.4743i 0.274323 + 0.475141i
\(929\) 1.78788 0.0586586 0.0293293 0.999570i \(-0.490663\pi\)
0.0293293 + 0.999570i \(0.490663\pi\)
\(930\) −19.7687 + 0.382429i −0.648240 + 0.0125403i
\(931\) −23.4124 19.1400i −0.767312 0.627288i
\(932\) −11.5179 19.9496i −0.377282 0.653472i
\(933\) 29.3726 + 48.6757i 0.961617 + 1.59357i
\(934\) 13.5555 0.443548
\(935\) −21.6369 + 37.4763i −0.707603 + 1.22560i
\(936\) 5.69185 0.220303i 0.186044 0.00720082i
\(937\) 6.96721 12.0676i 0.227609 0.394230i −0.729490 0.683991i \(-0.760243\pi\)
0.957099 + 0.289761i \(0.0935759\pi\)
\(938\) 0.0370219 0.0641238i 0.00120881 0.00209372i
\(939\) 16.4546 + 27.2682i 0.536976 + 0.889866i
\(940\) 22.2859 0.726886
\(941\) −45.4329 −1.48107 −0.740535 0.672017i \(-0.765428\pi\)
−0.740535 + 0.672017i \(0.765428\pi\)
\(942\) −6.44692 + 11.6826i −0.210052 + 0.380638i
\(943\) 12.4620 21.5848i 0.405818 0.702897i
\(944\) 16.7062 28.9360i 0.543741 0.941787i
\(945\) 2.53473 + 3.85512i 0.0824546 + 0.125407i
\(946\) 3.03806 5.26208i 0.0987759 0.171085i
\(947\) −5.17499 −0.168165 −0.0840823 0.996459i \(-0.526796\pi\)
−0.0840823 + 0.996459i \(0.526796\pi\)
\(948\) −31.7857 + 0.614900i −1.03235 + 0.0199710i
\(949\) 2.44876 + 4.24138i 0.0794902 + 0.137681i
\(950\) 9.56194 + 7.81702i 0.310230 + 0.253618i
\(951\) −1.21542 2.01418i −0.0394128 0.0653141i
\(952\) 2.66902 0.0865035
\(953\) 12.9234 + 22.3840i 0.418630 + 0.725088i 0.995802 0.0915347i \(-0.0291772\pi\)
−0.577172 + 0.816622i \(0.695844\pi\)
\(954\) 0.263663 0.500431i 0.00853640 0.0162020i
\(955\) 6.05867 + 10.4939i 0.196054 + 0.339575i
\(956\) −15.1162 26.1819i −0.488891 0.846785i
\(957\) −11.6617 + 0.225598i −0.376969 + 0.00729255i
\(958\) 3.70247 + 6.41287i 0.119621 + 0.207190i
\(959\) 1.06331 0.0343360
\(960\) −14.5344 + 26.3380i −0.469096 + 0.850055i
\(961\) −21.9755 + 38.0628i −0.708888 + 1.22783i
\(962\) −1.52685 −0.0492276
\(963\) 36.0087 1.39371i 1.16036 0.0449118i
\(964\) 9.76565 + 16.9146i 0.314531 + 0.544783i
\(965\) 0.884830 + 1.53257i 0.0284837 + 0.0493352i
\(966\) 0.348165 0.630914i 0.0112020 0.0202993i
\(967\) −13.0699 + 22.6377i −0.420299 + 0.727979i −0.995969 0.0897035i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(968\) −5.97209 10.3440i −0.191950 0.332468i
\(969\) −44.2862 34.7976i −1.42268 1.11786i
\(970\) 4.24028 7.34438i 0.136147 0.235814i
\(971\) 6.28902 + 10.8929i 0.201824 + 0.349570i 0.949116 0.314926i \(-0.101980\pi\)
−0.747292 + 0.664496i \(0.768646\pi\)
\(972\) −28.8969 + 2.80348i −0.926869 + 0.0899217i
\(973\) 2.15687 3.73581i 0.0691461 0.119764i
\(974\) 0.200804 0.00643417
\(975\) 9.06110 + 15.0159i 0.290187 + 0.480892i
\(976\) −6.61229 11.4528i −0.211654 0.366596i
\(977\) 18.8495 + 32.6483i 0.603050 + 1.04451i 0.992356 + 0.123405i \(0.0393813\pi\)
−0.389307 + 0.921108i \(0.627285\pi\)
\(978\) −3.47904 + 0.0673027i −0.111247 + 0.00215210i
\(979\) 6.54338 + 11.3335i 0.209127 + 0.362219i
\(980\) −45.9366 −1.46739
\(981\) −24.3934 38.7113i −0.778821 1.23596i
\(982\) 1.36185 2.35879i 0.0434583 0.0752719i
\(983\) −23.2447 −0.741390 −0.370695 0.928755i \(-0.620881\pi\)
−0.370695 + 0.928755i \(0.620881\pi\)
\(984\) 6.65252 12.0551i 0.212075 0.384304i
\(985\) −4.69996 + 8.14056i −0.149753 + 0.259380i
\(986\) −5.70970 + 9.88950i −0.181834 + 0.314946i
\(987\) 1.45569 0.0281606i 0.0463352 0.000896363i
\(988\) −10.0631 + 3.80927i −0.320151 + 0.121189i
\(989\) 45.0968 1.43400
\(990\) 3.44094 + 5.46063i 0.109360 + 0.173550i
\(991\) −11.8484 20.5220i −0.376376 0.651903i 0.614156 0.789185i \(-0.289497\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(992\) −17.5293 30.3616i −0.556555 0.963982i
\(993\) 14.0569 25.4727i 0.446082 0.808352i
\(994\) −1.03755 −0.0329091
\(995\) −0.377957 0.654641i −0.0119820 0.0207535i
\(996\) −0.577460 + 1.04642i −0.0182975 + 0.0331572i
\(997\) 9.46564 + 16.3950i 0.299780 + 0.519234i 0.976085 0.217387i \(-0.0697535\pi\)
−0.676306 + 0.736621i \(0.736420\pi\)
\(998\) 2.21559 3.83752i 0.0701333 0.121475i
\(999\) 16.1120 0.936006i 0.509762 0.0296139i
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 171.2.h.c.7.9 yes 32
3.2 odd 2 513.2.h.c.235.8 32
9.4 even 3 171.2.g.c.121.8 yes 32
9.5 odd 6 513.2.g.c.64.9 32
19.11 even 3 171.2.g.c.106.8 32
57.11 odd 6 513.2.g.c.505.9 32
171.49 even 3 inner 171.2.h.c.49.9 yes 32
171.68 odd 6 513.2.h.c.334.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.g.c.106.8 32 19.11 even 3
171.2.g.c.121.8 yes 32 9.4 even 3
171.2.h.c.7.9 yes 32 1.1 even 1 trivial
171.2.h.c.49.9 yes 32 171.49 even 3 inner
513.2.g.c.64.9 32 9.5 odd 6
513.2.g.c.505.9 32 57.11 odd 6
513.2.h.c.235.8 32 3.2 odd 2
513.2.h.c.334.8 32 171.68 odd 6