Properties

Label 171.2.g.c.121.8
Level $171$
Weight $2$
Character 171.121
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(106,171)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.g (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 121.8
Character \(\chi\) \(=\) 171.121
Dual form 171.2.g.c.106.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.185445 + 0.321199i) q^{2} +(-0.894876 + 1.48297i) q^{3} +(0.931221 + 1.61292i) q^{4} -3.55521 q^{5} +(-0.310379 - 0.562442i) q^{6} +(-0.124876 - 0.216291i) q^{7} -1.43254 q^{8} +(-1.39839 - 2.65415i) q^{9} +(0.659294 - 1.14193i) q^{10} +(-0.815815 - 1.41303i) q^{11} +(-3.22524 - 0.0623929i) q^{12} +(0.662707 + 1.14784i) q^{13} +0.0926300 q^{14} +(3.18147 - 5.27227i) q^{15} +(-1.59679 + 2.76571i) 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} +(0.432501 + 0.00836682i) q^{21} +0.605154 q^{22} +(2.24572 + 3.88969i) q^{23} +(1.28194 - 2.12441i) q^{24} +7.63952 q^{25} -0.491582 q^{26} +(5.18741 + 0.301355i) q^{27} +(0.232573 - 0.402829i) q^{28} -4.12725 q^{29} +(1.10346 + 1.99960i) q^{30} +(-4.32871 + 7.49755i) q^{31} +(-2.02477 - 3.50700i) q^{32} +(2.82554 + 0.0546606i) q^{33} -2.76683 q^{34} +(0.443959 + 0.768960i) q^{35} +(2.97872 - 4.72710i) q^{36} +3.10599 q^{37} +(0.260326 - 1.59557i) q^{38} +(-2.29526 - 0.0444022i) q^{39} +5.09297 q^{40} +5.54922 q^{41} +(-0.0828923 + 0.137367i) q^{42} +(5.02032 - 8.69544i) q^{43} +(1.51941 - 2.63169i) q^{44} +(4.97159 + 9.43605i) q^{45} -1.66582 q^{46} +3.36575 q^{47} +(-2.67254 - 4.84295i) q^{48} +(3.46881 - 6.00816i) q^{49} +(-1.41671 + 2.45381i) q^{50} +(-12.9187 - 0.249914i) q^{51} +(-1.23425 + 2.13779i) q^{52} +(0.254182 - 0.440256i) q^{53} +(-1.05877 + 1.61031i) q^{54} +(2.90039 + 5.02363i) q^{55} +(0.178889 + 0.309845i) q^{56} +(1.35962 - 7.42640i) q^{57} +(0.765376 - 1.32567i) q^{58} -10.4624 q^{59} +(11.4664 + 0.221820i) q^{60} +4.14100 q^{61} +(-1.60547 - 2.78076i) q^{62} +(-0.399442 + 0.633898i) q^{63} -4.88521 q^{64} +(-2.35606 - 4.08082i) q^{65} +(-0.541537 + 0.897424i) q^{66} +(0.399675 + 0.692257i) q^{67} +(-6.94690 + 12.0324i) q^{68} +(-7.77793 - 0.150466i) q^{69} -0.329319 q^{70} +(5.60051 + 9.70037i) q^{71} +(2.00325 + 3.80216i) q^{72} +(-1.84754 - 3.20004i) q^{73} +(-0.575989 + 0.997642i) q^{74} +(-6.83642 + 11.3292i) q^{75} +(-6.28519 - 5.13823i) q^{76} +(-0.203751 + 0.352907i) q^{77} +(0.439905 - 0.729000i) q^{78} +(-4.92764 + 8.53493i) q^{79} +(5.67691 - 9.83269i) q^{80} +(-5.08898 + 7.42309i) q^{81} +(-1.02907 + 1.78241i) q^{82} +(0.185251 + 0.320865i) q^{83} +(0.389259 + 0.705381i) q^{84} +(-13.2609 - 22.9686i) q^{85} +(1.86198 + 3.22504i) q^{86} +(3.69338 - 6.12059i) q^{87} +(1.16868 + 2.02422i) q^{88} +(4.01034 - 6.94611i) q^{89} +(-3.95281 - 0.152993i) q^{90} +(0.165512 - 0.286675i) q^{91} +(-4.18251 + 7.24433i) q^{92} +(-7.24498 - 13.1287i) q^{93} +(-0.624161 + 1.08108i) q^{94} +(14.4932 - 5.48621i) q^{95} +(7.01269 + 0.135662i) q^{96} +(-3.21577 + 5.56988i) q^{97} +(1.28654 + 2.22836i) q^{98} +(-2.60956 + 4.14127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} + q^{15} - 11 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.185445 + 0.321199i −0.131129 + 0.227122i −0.924112 0.382122i \(-0.875194\pi\)
0.792983 + 0.609244i \(0.208527\pi\)
\(3\) −0.894876 + 1.48297i −0.516657 + 0.856193i
\(4\) 0.931221 + 1.61292i 0.465610 + 0.806461i
\(5\) −3.55521 −1.58994 −0.794969 0.606650i \(-0.792513\pi\)
−0.794969 + 0.606650i \(0.792513\pi\)
\(6\) −0.310379 0.562442i −0.126712 0.229616i
\(7\) −0.124876 0.216291i −0.0471985 0.0817503i 0.841461 0.540318i \(-0.181696\pi\)
−0.888660 + 0.458568i \(0.848363\pi\)
\(8\) −1.43254 −0.506478
\(9\) −1.39839 2.65415i −0.466132 0.884715i
\(10\) 0.659294 1.14193i 0.208487 0.361110i
\(11\) −0.815815 1.41303i −0.245977 0.426045i 0.716429 0.697660i \(-0.245776\pi\)
−0.962406 + 0.271615i \(0.912442\pi\)
\(12\) −3.22524 0.0623929i −0.931046 0.0180113i
\(13\) 0.662707 + 1.14784i 0.183802 + 0.318354i 0.943172 0.332305i \(-0.107826\pi\)
−0.759370 + 0.650659i \(0.774493\pi\)
\(14\) 0.0926300 0.0247564
\(15\) 3.18147 5.27227i 0.821453 1.36129i
\(16\) −1.59679 + 2.76571i −0.399196 + 0.691428i
\(17\) 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
\(21\) 0.432501 + 0.00836682i 0.0943794 + 0.00182579i
\(22\) 0.605154 0.129019
\(23\) 2.24572 + 3.88969i 0.468264 + 0.811057i 0.999342 0.0362656i \(-0.0115462\pi\)
−0.531078 + 0.847323i \(0.678213\pi\)
\(24\) 1.28194 2.12441i 0.261675 0.433643i
\(25\) 7.63952 1.52790
\(26\) −0.491582 −0.0964071
\(27\) 5.18741 + 0.301355i 0.998317 + 0.0579958i
\(28\) 0.232573 0.402829i 0.0439522 0.0761275i
\(29\) −4.12725 −0.766411 −0.383206 0.923663i \(-0.625180\pi\)
−0.383206 + 0.923663i \(0.625180\pi\)
\(30\) 1.10346 + 1.99960i 0.201464 + 0.365075i
\(31\) −4.32871 + 7.49755i −0.777460 + 1.34660i 0.155941 + 0.987766i \(0.450159\pi\)
−0.933401 + 0.358834i \(0.883174\pi\)
\(32\) −2.02477 3.50700i −0.357932 0.619956i
\(33\) 2.82554 + 0.0546606i 0.491863 + 0.00951519i
\(34\) −2.76683 −0.474508
\(35\) 0.443959 + 0.768960i 0.0750428 + 0.129978i
\(36\) 2.97872 4.72710i 0.496453 0.787849i
\(37\) 3.10599 0.510622 0.255311 0.966859i \(-0.417822\pi\)
0.255311 + 0.966859i \(0.417822\pi\)
\(38\) 0.260326 1.59557i 0.0422305 0.258836i
\(39\) −2.29526 0.0444022i −0.367535 0.00711004i
\(40\) 5.09297 0.805269
\(41\) 5.54922 0.866643 0.433322 0.901239i \(-0.357341\pi\)
0.433322 + 0.901239i \(0.357341\pi\)
\(42\) −0.0828923 + 0.137367i −0.0127906 + 0.0211962i
\(43\) 5.02032 8.69544i 0.765591 1.32604i −0.174342 0.984685i \(-0.555780\pi\)
0.939934 0.341358i \(-0.110887\pi\)
\(44\) 1.51941 2.63169i 0.229059 0.396742i
\(45\) 4.97159 + 9.43605i 0.741121 + 1.40664i
\(46\) −1.66582 −0.245612
\(47\) 3.36575 0.490946 0.245473 0.969403i \(-0.421057\pi\)
0.245473 + 0.969403i \(0.421057\pi\)
\(48\) −2.67254 4.84295i −0.385748 0.699020i
\(49\) 3.46881 6.00816i 0.495545 0.858308i
\(50\) −1.41671 + 2.45381i −0.200353 + 0.347021i
\(51\) −12.9187 0.249914i −1.80898 0.0349950i
\(52\) −1.23425 + 2.13779i −0.171160 + 0.296458i
\(53\) 0.254182 0.440256i 0.0349146 0.0604739i −0.848040 0.529932i \(-0.822217\pi\)
0.882955 + 0.469458i \(0.155551\pi\)
\(54\) −1.05877 + 1.61031i −0.144080 + 0.219135i
\(55\) 2.90039 + 5.02363i 0.391089 + 0.677386i
\(56\) 0.178889 + 0.309845i 0.0239050 + 0.0414047i
\(57\) 1.35962 7.42640i 0.180085 0.983651i
\(58\) 0.765376 1.32567i 0.100499 0.174069i
\(59\) −10.4624 −1.36209 −0.681045 0.732242i \(-0.738474\pi\)
−0.681045 + 0.732242i \(0.738474\pi\)
\(60\) 11.4664 + 0.221820i 1.48031 + 0.0286368i
\(61\) 4.14100 0.530201 0.265100 0.964221i \(-0.414595\pi\)
0.265100 + 0.964221i \(0.414595\pi\)
\(62\) −1.60547 2.78076i −0.203895 0.353157i
\(63\) −0.399442 + 0.633898i −0.0503250 + 0.0798636i
\(64\) −4.88521 −0.610652
\(65\) −2.35606 4.08082i −0.292234 0.506164i
\(66\) −0.541537 + 0.897424i −0.0666586 + 0.110465i
\(67\) 0.399675 + 0.692257i 0.0488281 + 0.0845727i 0.889406 0.457117i \(-0.151118\pi\)
−0.840578 + 0.541690i \(0.817785\pi\)
\(68\) −6.94690 + 12.0324i −0.842436 + 1.45914i
\(69\) −7.77793 0.150466i −0.936353 0.0181139i
\(70\) −0.329319 −0.0393612
\(71\) 5.60051 + 9.70037i 0.664658 + 1.15122i 0.979378 + 0.202037i \(0.0647563\pi\)
−0.314719 + 0.949185i \(0.601910\pi\)
\(72\) 2.00325 + 3.80216i 0.236086 + 0.448089i
\(73\) −1.84754 3.20004i −0.216239 0.374537i 0.737416 0.675439i \(-0.236046\pi\)
−0.953655 + 0.300902i \(0.902712\pi\)
\(74\) −0.575989 + 0.997642i −0.0669573 + 0.115974i
\(75\) −6.83642 + 11.3292i −0.789402 + 1.30818i
\(76\) −6.28519 5.13823i −0.720961 0.589396i
\(77\) −0.203751 + 0.352907i −0.0232195 + 0.0402174i
\(78\) 0.439905 0.729000i 0.0498094 0.0825430i
\(79\) −4.92764 + 8.53493i −0.554403 + 0.960255i 0.443546 + 0.896251i \(0.353720\pi\)
−0.997950 + 0.0640032i \(0.979613\pi\)
\(80\) 5.67691 9.83269i 0.634698 1.09933i
\(81\) −5.08898 + 7.42309i −0.565443 + 0.824788i
\(82\) −1.02907 + 1.78241i −0.113642 + 0.196834i
\(83\) 0.185251 + 0.320865i 0.0203340 + 0.0352195i 0.876013 0.482287i \(-0.160194\pi\)
−0.855679 + 0.517506i \(0.826860\pi\)
\(84\) 0.389259 + 0.705381i 0.0424716 + 0.0769634i
\(85\) −13.2609 22.9686i −1.43835 2.49130i
\(86\) 1.86198 + 3.22504i 0.200782 + 0.347765i
\(87\) 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 \(0.0269074\pi\)
\(90\) −3.95281 0.152993i −0.416662 0.0161269i
\(91\) 0.165512 0.286675i 0.0173504 0.0300517i
\(92\) −4.18251 + 7.24433i −0.436057 + 0.755273i
\(93\) −7.24498 13.1287i −0.751269 1.36139i
\(94\) −0.624161 + 1.08108i −0.0643772 + 0.111505i
\(95\) 14.4932 5.48621i 1.48697 0.562873i
\(96\) 7.01269 + 0.135662i 0.715729 + 0.0138459i
\(97\) −3.21577 + 5.56988i −0.326512 + 0.565536i −0.981817 0.189829i \(-0.939207\pi\)
0.655305 + 0.755364i \(0.272540\pi\)
\(98\) 1.28654 + 2.22836i 0.129961 + 0.225098i
\(99\) −2.60956 + 4.14127i −0.262271 + 0.416213i
\(100\) 7.11408 + 12.3220i 0.711408 + 1.23220i
\(101\) 7.56353 0.752600 0.376300 0.926498i \(-0.377196\pi\)
0.376300 + 0.926498i \(0.377196\pi\)
\(102\) 2.47597 4.10313i 0.245158 0.406270i
\(103\) −6.90927 + 11.9672i −0.680791 + 1.17916i 0.293949 + 0.955821i \(0.405030\pi\)
−0.974740 + 0.223343i \(0.928303\pi\)
\(104\) −0.949353 1.64433i −0.0930917 0.161240i
\(105\) −1.53763 0.0297458i −0.150057 0.00290289i
\(106\) 0.0942734 + 0.163286i 0.00915664 + 0.0158598i
\(107\) 12.0119 1.16123 0.580616 0.814177i \(-0.302812\pi\)
0.580616 + 0.814177i \(0.302812\pi\)
\(108\) 4.34456 + 8.64751i 0.418055 + 0.832107i
\(109\) −7.62598 13.2086i −0.730436 1.26515i −0.956697 0.291086i \(-0.905984\pi\)
0.226261 0.974067i \(-0.427350\pi\)
\(110\) −2.15145 −0.205133
\(111\) −2.77948 + 4.60609i −0.263816 + 0.437191i
\(112\) 0.797598 0.0753659
\(113\) −1.46481 + 2.53713i −0.137798 + 0.238673i −0.926663 0.375894i \(-0.877336\pi\)
0.788865 + 0.614567i \(0.210669\pi\)
\(114\) 2.13322 + 1.81389i 0.199795 + 0.169887i
\(115\) −7.98399 13.8287i −0.744511 1.28953i
\(116\) −3.84338 6.65693i −0.356849 0.618081i
\(117\) 2.11982 3.36406i 0.195977 0.311007i
\(118\) 1.94020 3.36052i 0.178610 0.309361i
\(119\) 0.931572 1.61353i 0.0853970 0.147912i
\(120\) −4.55758 + 7.55272i −0.416048 + 0.689466i
\(121\) 4.16889 7.22073i 0.378990 0.656430i
\(122\) −0.767926 + 1.33009i −0.0695248 + 0.120420i
\(123\) −4.96587 + 8.22933i −0.447757 + 0.742014i
\(124\) −16.1240 −1.44797
\(125\) −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 \(0.193509\pi\)
\(128\) 4.95547 8.58313i 0.438006 0.758648i
\(129\) 8.40251 + 15.2263i 0.739800 + 1.34060i
\(130\) 1.74768 0.153281
\(131\) −3.02889 −0.264636 −0.132318 0.991207i \(-0.542242\pi\)
−0.132318 + 0.991207i \(0.542242\pi\)
\(132\) 2.54304 + 4.60827i 0.221343 + 0.401098i
\(133\) 0.842837 + 0.689031i 0.0730832 + 0.0597465i
\(134\) −0.296470 −0.0256111
\(135\) −18.4423 1.07138i −1.58726 0.0922098i
\(136\) −5.34336 9.25497i −0.458190 0.793608i
\(137\) 4.25747 0.363741 0.181870 0.983323i \(-0.441785\pi\)
0.181870 + 0.983323i \(0.441785\pi\)
\(138\) 1.49070 2.47036i 0.126897 0.210291i
\(139\) 8.63607 + 14.9581i 0.732502 + 1.26873i 0.955811 + 0.293983i \(0.0949809\pi\)
−0.223308 + 0.974748i \(0.571686\pi\)
\(140\) −0.826848 + 1.43214i −0.0698814 + 0.121038i
\(141\) −3.01193 + 4.99131i −0.253650 + 0.420344i
\(142\) −4.15434 −0.348624
\(143\) 1.08129 1.87285i 0.0904222 0.156616i
\(144\) 9.57354 + 0.370543i 0.797795 + 0.0308786i
\(145\) 14.6732 1.21855
\(146\) 1.37047 0.113421
\(147\) 5.80576 + 10.5207i 0.478851 + 0.867732i
\(148\) 2.89236 + 5.00972i 0.237751 + 0.411796i
\(149\) 1.84615 0.151242 0.0756211 0.997137i \(-0.475906\pi\)
0.0756211 + 0.997137i \(0.475906\pi\)
\(150\) −2.37115 4.29679i −0.193603 0.350831i
\(151\) −5.59926 9.69820i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504626i \(0.983930\pi\)
\(152\) 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
\(155\) 15.3895 26.6554i 1.23611 2.14101i
\(156\) −2.06577 3.74342i −0.165394 0.299713i
\(157\) 20.7711 1.65772 0.828858 0.559459i \(-0.188991\pi\)
0.828858 + 0.559459i \(0.188991\pi\)
\(158\) −1.82761 3.16551i −0.145397 0.251835i
\(159\) 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
\(162\) −1.44057 3.01115i −0.113182 0.236578i
\(163\) −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
\(165\) −10.0454 0.194330i −0.782032 0.0151286i
\(166\) −0.137415 −0.0106655
\(167\) 0.750032 + 1.29909i 0.0580392 + 0.100527i 0.893585 0.448894i \(-0.148182\pi\)
−0.835546 + 0.549421i \(0.814848\pi\)
\(168\) −0.619573 0.0119858i −0.0478011 0.000924723i
\(169\) 5.62164 9.73696i 0.432434 0.748997i
\(170\) 9.83667 0.754438
\(171\) 9.79644 + 8.66197i 0.749152 + 0.662398i
\(172\) 18.7001 1.42587
\(173\) −11.2067 + 19.4106i −0.852031 + 1.47576i 0.0273414 + 0.999626i \(0.491296\pi\)
−0.879372 + 0.476135i \(0.842037\pi\)
\(174\) 1.28101 + 2.32134i 0.0971132 + 0.175980i
\(175\) −0.953990 1.65236i −0.0721149 0.124907i
\(176\) 5.21072 0.392773
\(177\) 9.36256 15.5154i 0.703733 1.16621i
\(178\) 1.48739 + 2.57623i 0.111485 + 0.193097i
\(179\) −12.7134 −0.950242 −0.475121 0.879920i \(-0.657596\pi\)
−0.475121 + 0.879920i \(0.657596\pi\)
\(180\) −10.5900 + 16.8058i −0.789329 + 1.25263i
\(181\) 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
\(184\) −3.21707 5.57213i −0.237166 0.410783i
\(185\) −11.0425 −0.811857
\(186\) 5.56048 + 0.107569i 0.407714 + 0.00788731i
\(187\) 6.08598 10.5412i 0.445051 0.770850i
\(188\) 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 0.797762 0.602973i \(-0.206017\pi\)
−0.921071 + 0.389395i \(0.872684\pi\)
\(192\) 4.37166 7.24462i 0.315497 0.522835i
\(193\) 0.497765 0.0358299 0.0179150 0.999840i \(-0.494297\pi\)
0.0179150 + 0.999840i \(0.494297\pi\)
\(194\) −1.19269 2.06581i −0.0856305 0.148316i
\(195\) 8.16012 + 0.157859i 0.584358 + 0.0113045i
\(196\) 12.9209 0.922923
\(197\) −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 \(0.164268\pi\)
\(200\) −10.9439 −0.773851
\(201\) −1.38426 0.0267787i −0.0976379 0.00188882i
\(202\) −1.40262 + 2.42940i −0.0986877 + 0.170932i
\(203\) 0.515393 + 0.892687i 0.0361735 + 0.0626543i
\(204\) −11.6270 21.0695i −0.814056 1.47516i
\(205\) −19.7287 −1.37791
\(206\) −2.56257 4.43851i −0.178543 0.309245i
\(207\) 7.18342 11.3998i 0.499282 0.792340i
\(208\) −4.23280 −0.293492
\(209\) 5.50627 + 4.50145i 0.380877 + 0.311372i
\(210\) 0.294700 0.488370i 0.0203362 0.0337007i
\(211\) −8.52375 −0.586799 −0.293400 0.955990i \(-0.594787\pi\)
−0.293400 + 0.955990i \(0.594787\pi\)
\(212\) 0.946799 0.0650264
\(213\) −19.3971 0.375241i −1.32907 0.0257111i
\(214\) −2.22754 + 3.85821i −0.152271 + 0.263742i
\(215\) −17.8483 + 30.9141i −1.21724 + 2.10833i
\(216\) −7.43115 0.431702i −0.505626 0.0293736i
\(217\) 2.16220 0.146780
\(218\) 5.65678 0.383126
\(219\) 6.39889 + 0.123788i 0.432397 + 0.00836480i
\(220\) −5.40181 + 9.35621i −0.364190 + 0.630796i
\(221\) −4.94380 + 8.56290i −0.332556 + 0.576003i
\(222\) −0.964034 1.74694i −0.0647017 0.117247i
\(223\) −7.80159 + 13.5127i −0.522433 + 0.904880i 0.477227 + 0.878780i \(0.341642\pi\)
−0.999659 + 0.0260998i \(0.991691\pi\)
\(224\) −0.505688 + 0.875877i −0.0337877 + 0.0585220i
\(225\) −10.6831 20.2764i −0.712205 1.35176i
\(226\) −0.543283 0.940994i −0.0361386 0.0625940i
\(227\) −0.595426 1.03131i −0.0395198 0.0684503i 0.845589 0.533835i \(-0.179249\pi\)
−0.885109 + 0.465384i \(0.845916\pi\)
\(228\) 13.2443 4.72267i 0.877126 0.312766i
\(229\) −9.98443 + 17.2935i −0.659790 + 1.14279i 0.320880 + 0.947120i \(0.396021\pi\)
−0.980670 + 0.195669i \(0.937312\pi\)
\(230\) 5.92235 0.390508
\(231\) −0.341018 0.617964i −0.0224373 0.0406590i
\(232\) 5.91244 0.388171
\(233\) 6.18432 + 10.7115i 0.405148 + 0.701737i 0.994339 0.106257i \(-0.0338867\pi\)
−0.589191 + 0.807994i \(0.700553\pi\)
\(234\) 0.687425 + 1.30473i 0.0449384 + 0.0852928i
\(235\) −11.9660 −0.780573
\(236\) −9.74281 16.8750i −0.634203 1.09847i
\(237\) −8.24741 14.9452i −0.535727 0.970798i
\(238\) 0.345510 + 0.598440i 0.0223961 + 0.0387911i
\(239\) 8.11631 14.0579i 0.525000 0.909327i −0.474576 0.880215i \(-0.657398\pi\)
0.999576 0.0291128i \(-0.00926819\pi\)
\(240\) 9.50145 + 17.2177i 0.613316 + 1.11140i
\(241\) 10.4869 0.675523 0.337762 0.941232i \(-0.390330\pi\)
0.337762 + 0.941232i \(0.390330\pi\)
\(242\) 1.54620 + 2.67809i 0.0993933 + 0.172154i
\(243\) −6.45420 14.1895i −0.414037 0.910260i
\(244\) 3.85619 + 6.67911i 0.246867 + 0.427586i
\(245\) −12.3324 + 21.3603i −0.787885 + 1.36466i
\(246\) −1.72236 3.12112i −0.109814 0.198995i
\(247\) −4.47288 3.65665i −0.284603 0.232667i
\(248\) 6.20104 10.7405i 0.393767 0.682024i
\(249\) −0.641609 0.0124121i −0.0406603 0.000786583i
\(250\) 1.74022 3.01415i 0.110061 0.190632i
\(251\) −7.02198 + 12.1624i −0.443223 + 0.767685i −0.997927 0.0643630i \(-0.979498\pi\)
0.554703 + 0.832048i \(0.312832\pi\)
\(252\) −1.39440 0.0539700i −0.0878387 0.00339979i
\(253\) 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
\(256\) −3.04728 5.27805i −0.190455 0.329878i
\(257\) −8.58033 14.8616i −0.535227 0.927040i −0.999152 0.0411655i \(-0.986893\pi\)
0.463926 0.885874i \(-0.346440\pi\)
\(258\) −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
\(261\) 5.77153 + 10.9543i 0.357249 + 0.678056i
\(262\) 0.561691 0.972878i 0.0347014 0.0601046i
\(263\) −9.74973 + 16.8870i −0.601194 + 1.04130i 0.391446 + 0.920201i \(0.371975\pi\)
−0.992641 + 0.121098i \(0.961358\pi\)
\(264\) −4.04769 0.0783033i −0.249118 0.00481924i
\(265\) −0.903671 + 1.56520i −0.0555121 + 0.0961498i
\(266\) −0.377616 + 0.142942i −0.0231531 + 0.00876431i
\(267\) 6.71211 + 12.1631i 0.410774 + 0.744370i
\(268\) −0.744371 + 1.28929i −0.0454697 + 0.0787558i
\(269\) −11.5796 20.0564i −0.706020 1.22286i −0.966322 0.257335i \(-0.917156\pi\)
0.260303 0.965527i \(-0.416178\pi\)
\(270\) 3.76415 5.72498i 0.229079 0.348411i
\(271\) −11.0388 19.1197i −0.670557 1.16144i −0.977746 0.209790i \(-0.932722\pi\)
0.307190 0.951648i \(-0.400611\pi\)
\(272\) −23.8240 −1.44454
\(273\) 0.277018 + 0.501988i 0.0167659 + 0.0303817i
\(274\) −0.789525 + 1.36750i −0.0476970 + 0.0826136i
\(275\) −6.23244 10.7949i −0.375830 0.650957i
\(276\) −7.00028 12.6853i −0.421368 0.763566i
\(277\) 14.7992 + 25.6330i 0.889199 + 1.54014i 0.840824 + 0.541309i \(0.182071\pi\)
0.0483752 + 0.998829i \(0.484596\pi\)
\(278\) −6.40605 −0.384209
\(279\) 25.9529 + 1.00450i 1.55376 + 0.0601380i
\(280\) −0.635988 1.10156i −0.0380075 0.0658310i
\(281\) 28.8083 1.71856 0.859280 0.511506i \(-0.170912\pi\)
0.859280 + 0.511506i \(0.170912\pi\)
\(282\) −1.04466 1.89304i −0.0622085 0.112729i
\(283\) 16.0204 0.952314 0.476157 0.879360i \(-0.342029\pi\)
0.476157 + 0.879360i \(0.342029\pi\)
\(284\) −10.4306 + 18.0664i −0.618944 + 1.07204i
\(285\) −4.83372 + 26.4024i −0.286325 + 1.56394i
\(286\) 0.401040 + 0.694621i 0.0237140 + 0.0410738i
\(287\) −0.692963 1.20025i −0.0409043 0.0708483i
\(288\) −6.47667 + 10.2782i −0.381641 + 0.605649i
\(289\) −19.3258 + 33.4732i −1.13681 + 1.96901i
\(290\) −2.72107 + 4.71304i −0.159787 + 0.276759i
\(291\) −5.38225 9.75324i −0.315513 0.571745i
\(292\) 3.44094 5.95989i 0.201366 0.348776i
\(293\) −0.400378 + 0.693475i −0.0233903 + 0.0405132i −0.877484 0.479607i \(-0.840779\pi\)
0.854093 + 0.520120i \(0.174113\pi\)
\(294\) −4.45589 0.0862000i −0.259873 0.00502729i
\(295\) 37.1961 2.16564
\(296\) −4.44945 −0.258619
\(297\) −3.80614 7.57582i −0.220855 0.439594i
\(298\) −0.342358 + 0.592981i −0.0198322 + 0.0343504i
\(299\) −2.97650 + 5.15546i −0.172136 + 0.298148i
\(300\) −24.6393 0.476652i −1.42255 0.0275195i
\(301\) −2.50766 −0.144539
\(302\) 4.15341 0.239002
\(303\) −6.76842 + 11.2165i −0.388836 + 0.644370i
\(304\) 2.24156 13.7388i 0.128562 0.787974i
\(305\) −14.7221 −0.842987
\(306\) 3.86912 + 7.34358i 0.221183 + 0.419804i
\(307\) 2.29987 + 3.98349i 0.131260 + 0.227350i 0.924163 0.381999i \(-0.124764\pi\)
−0.792902 + 0.609349i \(0.791431\pi\)
\(308\) −0.758947 −0.0432450
\(309\) −11.5641 20.9554i −0.657856 1.19211i
\(310\) 5.70779 + 9.88619i 0.324181 + 0.561498i
\(311\) 16.4116 28.4257i 0.930615 1.61187i 0.148342 0.988936i \(-0.452606\pi\)
0.782273 0.622936i \(-0.214060\pi\)
\(312\) 3.28804 + 0.0636078i 0.186149 + 0.00360108i
\(313\) −18.3876 −1.03933 −0.519664 0.854371i \(-0.673943\pi\)
−0.519664 + 0.854371i \(0.673943\pi\)
\(314\) −3.85189 + 6.67167i −0.217375 + 0.376504i
\(315\) 1.42010 2.25364i 0.0800136 0.126978i
\(316\) −18.3549 −1.03254
\(317\) 1.35820 0.0762844 0.0381422 0.999272i \(-0.487856\pi\)
0.0381422 + 0.999272i \(0.487856\pi\)
\(318\) −0.326511 0.00631643i −0.0183099 0.000354208i
\(319\) 3.36707 + 5.83194i 0.188520 + 0.326526i
\(320\) 17.3680 0.970899
\(321\) −10.7491 + 17.8133i −0.599959 + 0.994239i
\(322\) 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
\(326\) 1.00450 1.73984i 0.0556341 0.0963610i
\(327\) 26.4122 + 0.510950i 1.46060 + 0.0282556i
\(328\) −7.94947 −0.438936
\(329\) −0.420300 0.727982i −0.0231719 0.0401349i
\(330\) 1.92528 3.19053i 0.105983 0.175633i
\(331\) 8.39869 + 14.5470i 0.461634 + 0.799573i 0.999043 0.0437490i \(-0.0139302\pi\)
−0.537409 + 0.843322i \(0.680597\pi\)
\(332\) −0.345020 + 0.597592i −0.0189354 + 0.0327971i
\(333\) −4.34340 8.24375i −0.238017 0.451755i
\(334\) −0.556357 −0.0304425
\(335\) −1.42093 2.46112i −0.0776336 0.134465i
\(336\) −0.713751 + 1.18281i −0.0389383 + 0.0645277i
\(337\) 36.5224 1.98950 0.994750 0.102335i \(-0.0326312\pi\)
0.994750 + 0.102335i \(0.0326312\pi\)
\(338\) 2.08500 + 3.61133i 0.113409 + 0.196431i
\(339\) −2.45166 4.44269i −0.133156 0.241294i
\(340\) 24.6977 42.7777i 1.33942 2.31995i
\(341\) 14.1257 0.764951
\(342\) −4.59892 + 1.54029i −0.248681 + 0.0832895i
\(343\) −3.48094 −0.187953
\(344\) −7.19179 + 12.4565i −0.387755 + 0.671612i
\(345\) 27.6522 + 0.534937i 1.48874 + 0.0288001i
\(346\) −4.15645 7.19918i −0.223452 0.387030i
\(347\) −10.1508 −0.544926 −0.272463 0.962166i \(-0.587838\pi\)
−0.272463 + 0.962166i \(0.587838\pi\)
\(348\) 13.3114 + 0.257511i 0.713565 + 0.0138041i
\(349\) 8.63614 + 14.9582i 0.462282 + 0.800696i 0.999074 0.0430183i \(-0.0136974\pi\)
−0.536792 + 0.843715i \(0.680364\pi\)
\(350\) 0.707649 0.0378254
\(351\) 3.09182 + 6.15404i 0.165029 + 0.328478i
\(352\) −3.30367 + 5.72212i −0.176086 + 0.304990i
\(353\) −8.45158 14.6386i −0.449832 0.779132i 0.548543 0.836123i \(-0.315183\pi\)
−0.998375 + 0.0569905i \(0.981850\pi\)
\(354\) 3.24731 + 5.88450i 0.172593 + 0.312758i
\(355\) −19.9110 34.4869i −1.05677 1.83037i
\(356\) 14.9380 0.791714
\(357\) 1.55917 + 2.82540i 0.0825202 + 0.149536i
\(358\) 2.35762 4.08353i 0.124604 0.215821i
\(359\) 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
\(363\) 6.97748 + 12.6440i 0.366223 + 0.663638i
\(364\) 0.616512 0.0323140
\(365\) 6.56841 + 11.3768i 0.343806 + 0.595490i
\(366\) −1.28528 2.32907i −0.0671826 0.121743i
\(367\) −24.7775 −1.29338 −0.646688 0.762755i \(-0.723846\pi\)
−0.646688 + 0.762755i \(0.723846\pi\)
\(368\) −14.3437 −0.747717
\(369\) −7.76001 14.7285i −0.403970 0.766733i
\(370\) 2.04776 3.54683i 0.106458 0.184391i
\(371\) −0.126965 −0.00659167
\(372\) 14.4289 23.9113i 0.748105 1.23974i
\(373\) 11.5863 20.0681i 0.599917 1.03909i −0.392916 0.919574i \(-0.628534\pi\)
0.992833 0.119512i \(-0.0381330\pi\)
\(374\) 2.25722 + 3.90962i 0.116718 + 0.202162i
\(375\) 8.39757 13.9163i 0.433649 0.718633i
\(376\) −4.82157 −0.248653
\(377\) −2.73516 4.73744i −0.140868 0.243990i
\(378\) 0.480509 + 0.0279145i 0.0247147 + 0.00143577i
\(379\) 29.0801 1.49374 0.746871 0.664969i \(-0.231555\pi\)
0.746871 + 0.664969i \(0.231555\pi\)
\(380\) 22.3452 + 18.2675i 1.14628 + 0.937103i
\(381\) −1.58865 2.87881i −0.0813888 0.147486i
\(382\) 1.26411 0.0646777
\(383\) −2.82855 −0.144532 −0.0722662 0.997385i \(-0.523023\pi\)
−0.0722662 + 0.997385i \(0.523023\pi\)
\(384\) 8.29398 + 15.0296i 0.423250 + 0.766978i
\(385\) 0.724377 1.25466i 0.0369177 0.0639433i
\(386\) −0.0923078 + 0.159882i −0.00469834 + 0.00813777i
\(387\) −30.0994 1.16499i −1.53004 0.0592199i
\(388\) −11.9784 −0.608110
\(389\) 19.1659 0.971750 0.485875 0.874028i \(-0.338501\pi\)
0.485875 + 0.874028i \(0.338501\pi\)
\(390\) −1.56395 + 2.59175i −0.0791939 + 0.131238i
\(391\) −16.7530 + 29.0171i −0.847238 + 1.46746i
\(392\) −4.96920 + 8.60691i −0.250983 + 0.434715i
\(393\) 2.71048 4.49175i 0.136726 0.226579i
\(394\) 0.490312 0.849245i 0.0247016 0.0427844i
\(395\) 17.5188 30.3435i 0.881467 1.52675i
\(396\) −9.10962 0.352587i −0.457776 0.0177182i
\(397\) 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
\(399\) −1.77605 + 0.633304i −0.0889135 + 0.0317049i
\(400\) −12.1987 + 21.1287i −0.609934 + 1.05644i
\(401\) 38.3406 1.91464 0.957320 0.289030i \(-0.0933328\pi\)
0.957320 + 0.289030i \(0.0933328\pi\)
\(402\) 0.265304 0.439656i 0.0132322 0.0219280i
\(403\) −11.4747 −0.571595
\(404\) 7.04332 + 12.1994i 0.350418 + 0.606942i
\(405\) 18.0924 26.3906i 0.899019 1.31136i
\(406\) −0.382307 −0.0189736
\(407\) −2.53391 4.38887i −0.125601 0.217548i
\(408\) 18.5065 + 0.358012i 0.916208 + 0.0177242i
\(409\) −1.14644 1.98569i −0.0566877 0.0981860i 0.836289 0.548289i \(-0.184721\pi\)
−0.892977 + 0.450103i \(0.851387\pi\)
\(410\) 3.65857 6.33683i 0.180684 0.312954i
\(411\) −3.80991 + 6.31370i −0.187929 + 0.311432i
\(412\) −25.7362 −1.26793
\(413\) 1.30650 + 2.26292i 0.0642886 + 0.111351i
\(414\) 2.32948 + 4.42134i 0.114488 + 0.217297i
\(415\) −0.658608 1.14074i −0.0323298 0.0559968i
\(416\) 2.68366 4.64823i 0.131577 0.227898i
\(417\) −29.9106 0.578627i −1.46473 0.0283355i
\(418\) −2.46697 + 0.933841i −0.120663 + 0.0456756i
\(419\) 5.32211 9.21817i 0.260002 0.450337i −0.706240 0.707972i \(-0.749610\pi\)
0.966242 + 0.257636i \(0.0829434\pi\)
\(420\) −1.38390 2.50778i −0.0675272 0.122367i
\(421\) −12.9323 + 22.3994i −0.630280 + 1.09168i 0.357214 + 0.934023i \(0.383727\pi\)
−0.987494 + 0.157655i \(0.949607\pi\)
\(422\) 1.58068 2.73782i 0.0769464 0.133275i
\(423\) −4.70665 8.93320i −0.228845 0.434347i
\(424\) −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
\(427\) −0.517110 0.895661i −0.0250247 0.0433441i
\(428\) 11.1857 + 19.3742i 0.540682 + 0.936489i
\(429\) 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 \(0.318472\pi\)
\(432\) −9.11664 + 13.8657i −0.438624 + 0.667113i
\(433\) 13.3288 23.0861i 0.640540 1.10945i −0.344773 0.938686i \(-0.612044\pi\)
0.985312 0.170761i \(-0.0546226\pi\)
\(434\) −0.400969 + 0.694498i −0.0192471 + 0.0333370i
\(435\) −13.1307 + 21.7600i −0.629571 + 1.04331i
\(436\) 14.2029 24.6002i 0.680197 1.17814i
\(437\) −15.1573 12.3913i −0.725070 0.592755i
\(438\) −1.22640 + 2.03236i −0.0585996 + 0.0971100i
\(439\) 0.973523 1.68619i 0.0464637 0.0804775i −0.841858 0.539699i \(-0.818538\pi\)
0.888322 + 0.459221i \(0.151871\pi\)
\(440\) −4.15492 7.19653i −0.198078 0.343081i
\(441\) −20.7973 0.804957i −0.990348 0.0383313i
\(442\) −1.83360 3.17589i −0.0872154 0.151062i
\(443\) 6.56230 0.311784 0.155892 0.987774i \(-0.450175\pi\)
0.155892 + 0.987774i \(0.450175\pi\)
\(444\) −10.0176 0.193792i −0.475413 0.00919695i
\(445\) −14.2576 + 24.6949i −0.675875 + 1.17065i
\(446\) −2.89352 5.01173i −0.137012 0.237312i
\(447\) −1.65207 + 2.73778i −0.0781403 + 0.129492i
\(448\) 0.610044 + 1.05663i 0.0288219 + 0.0499209i
\(449\) −35.5348 −1.67699 −0.838495 0.544910i \(-0.816564\pi\)
−0.838495 + 0.544910i \(0.816564\pi\)
\(450\) 8.49389 + 0.328755i 0.400406 + 0.0154977i
\(451\) −4.52714 7.84124i −0.213175 0.369229i
\(452\) −5.45626 −0.256641
\(453\) 19.3928 + 0.375157i 0.911152 + 0.0176264i
\(454\) 0.441674 0.0207288
\(455\) −0.588430 + 1.01919i −0.0275860 + 0.0477804i
\(456\) −1.94770 + 10.6386i −0.0912094 + 0.498198i
\(457\) −3.32444 5.75809i −0.155511 0.269352i 0.777734 0.628593i \(-0.216369\pi\)
−0.933245 + 0.359241i \(0.883036\pi\)
\(458\) −3.70311 6.41398i −0.173035 0.299706i
\(459\) 17.4021 + 34.6375i 0.812261 + 1.61674i
\(460\) 14.8697 25.7551i 0.693304 1.20084i
\(461\) 3.48590 6.03776i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(462\) 0.261729 + 0.00506321i 0.0121768 + 0.000235562i
\(463\) 8.59691 14.8903i 0.399532 0.692010i −0.594136 0.804365i \(-0.702506\pi\)
0.993668 + 0.112354i \(0.0358392\pi\)
\(464\) 6.59033 11.4148i 0.305949 0.529919i
\(465\) 25.7574 + 46.6754i 1.19447 + 2.16452i
\(466\) −4.58739 −0.212507
\(467\) 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
\(470\) 2.21902 3.84346i 0.102356 0.177286i
\(471\) −18.5876 + 30.8029i −0.856470 + 1.41932i
\(472\) 14.9878 0.689869
\(473\) −16.3826 −0.753272
\(474\) 6.32984 + 0.122452i 0.290739 + 0.00562441i
\(475\) −31.1433 + 11.7889i −1.42895 + 0.540912i
\(476\) 3.47000 0.159047
\(477\) −1.52395 0.0589844i −0.0697770 0.00270071i
\(478\) 3.01025 + 5.21391i 0.137686 + 0.238479i
\(479\) −19.9654 −0.912242 −0.456121 0.889918i \(-0.650762\pi\)
−0.456121 + 0.889918i \(0.650762\pi\)
\(480\) −24.9316 0.482306i −1.13797 0.0220142i
\(481\) 2.05836 + 3.56519i 0.0938533 + 0.162559i
\(482\) −1.94475 + 3.36840i −0.0885807 + 0.153426i
\(483\) 0.938730 + 1.70109i 0.0427137 + 0.0774021i
\(484\) 15.5286 0.705847
\(485\) 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 \(0.496095\pi\)
\(488\) −5.93214 −0.268535
\(489\) 4.84728 8.03281i 0.219202 0.363256i
\(490\) −4.57394 7.92229i −0.206629 0.357893i
\(491\) −7.34369 −0.331416 −0.165708 0.986175i \(-0.552991\pi\)
−0.165708 + 0.986175i \(0.552991\pi\)
\(492\) −17.8976 0.346232i −0.806885 0.0156094i
\(493\) −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
\(497\) 1.39873 2.42268i 0.0627418 0.108672i
\(498\) 0.122970 0.203783i 0.00551040 0.00913172i
\(499\) −11.9475 −0.534842 −0.267421 0.963580i \(-0.586171\pi\)
−0.267421 + 0.963580i \(0.586171\pi\)
\(500\) −8.73863 15.1358i −0.390803 0.676891i
\(501\) −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 \(-0.0615242\pi\)
\(504\) 0.572216 0.908082i 0.0254885 0.0404492i
\(505\) −26.8900 −1.19659
\(506\) 1.35900 + 2.35386i 0.0604151 + 0.104642i
\(507\) 9.40895 + 17.0501i 0.417866 + 0.757221i
\(508\) −3.53559 −0.156866
\(509\) −8.95222 15.5057i −0.396800 0.687278i 0.596529 0.802592i \(-0.296546\pi\)
−0.993329 + 0.115314i \(0.963213\pi\)
\(510\) −8.80260 + 14.5875i −0.389786 + 0.645944i
\(511\) −0.461426 + 0.799214i −0.0204123 + 0.0353552i
\(512\) 22.0823 0.975909
\(513\) −21.6120 + 6.77642i −0.954195 + 0.299186i
\(514\) 6.36470 0.280735
\(515\) 24.5639 42.5459i 1.08242 1.87480i
\(516\) −16.7343 + 27.7317i −0.736685 + 1.22082i
\(517\) −2.74583 4.75592i −0.120762 0.209165i
\(518\) 0.287708 0.0126412
\(519\) −18.7567 33.9893i −0.823328 1.49196i
\(520\) 3.37515 + 5.84593i 0.148010 + 0.256361i
\(521\) −27.8411 −1.21974 −0.609871 0.792501i \(-0.708779\pi\)
−0.609871 + 0.792501i \(0.708779\pi\)
\(522\) −4.58882 0.177610i −0.200847 0.00777377i
\(523\) −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
\(526\) −3.61607 6.26321i −0.157668 0.273089i
\(527\) −64.5844 −2.81334
\(528\) −4.66295 + 7.72734i −0.202929 + 0.336289i
\(529\) 1.41352 2.44829i 0.0614573 0.106447i
\(530\) −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
\(534\) −5.15151 0.0996569i −0.222927 0.00431258i
\(535\) −42.7048 −1.84629
\(536\) −0.572549 0.991684i −0.0247304 0.0428342i
\(537\) 11.3769 18.8535i 0.490949 0.813590i
\(538\) 8.58948 0.370319
\(539\) −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 \(0.989233\pi\)
\(542\) 8.18831 0.351718
\(543\) 2.19517 + 3.97790i 0.0942038 + 0.170708i
\(544\) 15.1048 26.1622i 0.647611 1.12170i
\(545\) 27.1120 + 46.9593i 1.16135 + 2.01151i
\(546\) −0.212609 0.00411297i −0.00909885 0.000176019i
\(547\) 12.8871 0.551014 0.275507 0.961299i \(-0.411154\pi\)
0.275507 + 0.961299i \(0.411154\pi\)
\(548\) 3.96465 + 6.86697i 0.169361 + 0.293343i
\(549\) −5.79076 10.9908i −0.247143 0.469077i
\(550\) 4.62308 0.197129
\(551\) 16.8252 6.36895i 0.716776 0.271327i
\(552\) 11.1422 + 0.215548i 0.474243 + 0.00917432i
\(553\) 2.46137 0.104668
\(554\) −10.9777 −0.466399
\(555\) 9.88162 16.3756i 0.419451 0.695106i
\(556\) −16.0842 + 27.8586i −0.682121 + 1.18147i
\(557\) −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
\(560\) −2.83563 −0.119827
\(561\) 10.1861 + 18.4584i 0.430058 + 0.779314i
\(562\) −5.34234 + 9.25321i −0.225353 + 0.390323i
\(563\) 13.3440 23.1125i 0.562383 0.974077i −0.434904 0.900477i \(-0.643218\pi\)
0.997288 0.0735999i \(-0.0234488\pi\)
\(564\) −10.8554 0.209999i −0.457093 0.00884256i
\(565\) 5.20772 9.02003i 0.219090 0.379476i
\(566\) −2.97090 + 5.14574i −0.124876 + 0.216292i
\(567\) 2.24104 + 0.173738i 0.0941147 + 0.00729633i
\(568\) −8.02294 13.8961i −0.336635 0.583069i
\(569\) 6.57047 + 11.3804i 0.275448 + 0.477090i 0.970248 0.242113i \(-0.0778404\pi\)
−0.694800 + 0.719203i \(0.744507\pi\)
\(570\) −7.58405 6.44877i −0.317661 0.270109i
\(571\) −1.08070 + 1.87182i −0.0452258 + 0.0783333i −0.887752 0.460322i \(-0.847734\pi\)
0.842526 + 0.538655i \(0.181067\pi\)
\(572\) 4.02769 0.168406
\(573\) 5.90230 + 0.114181i 0.246572 + 0.00476999i
\(574\) 0.514024 0.0214550
\(575\) 17.1562 + 29.7154i 0.715463 + 1.23922i
\(576\) 6.83146 + 12.9661i 0.284644 + 0.540253i
\(577\) 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
\(579\) −0.445438 + 0.738170i −0.0185118 + 0.0306773i
\(580\) 13.6640 + 23.6668i 0.567368 + 0.982710i
\(581\) 0.0462667 0.0801364i 0.00191947 0.00332462i
\(582\) 4.13084 + 0.0799120i 0.171229 + 0.00331246i
\(583\) −0.829462 −0.0343528
\(584\) 2.64668 + 4.58418i 0.109520 + 0.189695i
\(585\) −7.53639 + 11.9599i −0.311591 + 0.494483i
\(586\) −0.148496 0.257202i −0.00613430 0.0106249i
\(587\) −12.1339 + 21.0165i −0.500819 + 0.867444i 0.499180 + 0.866498i \(0.333635\pi\)
−1.00000 0.000946197i \(0.999699\pi\)
\(588\) −11.5626 + 19.1613i −0.476834 + 0.790200i
\(589\) 6.07663 37.2444i 0.250383 1.53463i
\(590\) −6.89781 + 11.9474i −0.283978 + 0.491865i
\(591\) 2.36604 3.92094i 0.0973257 0.161286i
\(592\) −4.95960 + 8.59028i −0.203838 + 0.353058i
\(593\) 16.5350 28.6395i 0.679013 1.17608i −0.296266 0.955106i \(-0.595741\pi\)
0.975279 0.220979i \(-0.0709252\pi\)
\(594\) 3.13918 + 0.182366i 0.128802 + 0.00748257i
\(595\) −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
\(598\) −1.10395 1.91210i −0.0451440 0.0781917i
\(599\) 6.64241 + 11.5050i 0.271401 + 0.470081i 0.969221 0.246193i \(-0.0791796\pi\)
−0.697820 + 0.716274i \(0.745846\pi\)
\(600\) 9.79343 16.2295i 0.399815 0.662565i
\(601\) −7.35146 12.7331i −0.299872 0.519394i 0.676234 0.736687i \(-0.263611\pi\)
−0.976106 + 0.217293i \(0.930277\pi\)
\(602\) 0.465032 0.805459i 0.0189533 0.0328280i
\(603\) 1.27845 2.02884i 0.0520625 0.0826209i
\(604\) 10.4283 18.0623i 0.424321 0.734946i
\(605\) −14.8213 + 25.6712i −0.602571 + 1.04368i
\(606\) −2.34756 4.25405i −0.0953632 0.172809i
\(607\) −1.19304 + 2.06641i −0.0484241 + 0.0838729i −0.889221 0.457477i \(-0.848753\pi\)
0.840797 + 0.541350i \(0.182087\pi\)
\(608\) 13.6660 + 11.1721i 0.554229 + 0.453090i
\(609\) −1.78504 0.0345320i −0.0723335 0.00139931i
\(610\) 2.73014 4.72874i 0.110540 0.191461i
\(611\) 2.23051 + 3.86336i 0.0902368 + 0.156295i
\(612\) 41.6502 + 1.61207i 1.68361 + 0.0651640i
\(613\) 2.16079 + 3.74260i 0.0872736 + 0.151162i 0.906358 0.422511i \(-0.138851\pi\)
−0.819084 + 0.573673i \(0.805518\pi\)
\(614\) −1.70599 −0.0688482
\(615\) 17.6547 29.2570i 0.711906 1.17976i
\(616\) 0.291880 0.505552i 0.0117602 0.0203693i
\(617\) 4.80522 + 8.32289i 0.193451 + 0.335067i 0.946392 0.323021i \(-0.104699\pi\)
−0.752941 + 0.658088i \(0.771365\pi\)
\(618\) 8.87535 + 0.171695i 0.357019 + 0.00690661i
\(619\) −1.79677 3.11209i −0.0722182 0.125086i 0.827655 0.561237i \(-0.189674\pi\)
−0.899873 + 0.436152i \(0.856341\pi\)
\(620\) 57.3241 2.30219
\(621\) 10.4773 + 20.8542i 0.420438 + 0.836850i
\(622\) 6.08687 + 10.5428i 0.244061 + 0.422727i
\(623\) −2.00317 −0.0802554
\(624\) 3.78783 6.27712i 0.151635 0.251286i
\(625\) −4.83530 −0.193412
\(626\) 3.40988 5.90608i 0.136286 0.236055i
\(627\) −11.6029 + 4.13739i −0.463377 + 0.165231i
\(628\) 19.3425 + 33.5022i 0.771850 + 1.33688i
\(629\) 11.5853 + 20.0664i 0.461938 + 0.800100i
\(630\) 0.460518 + 0.874061i 0.0183475 + 0.0348234i
\(631\) 12.6319 21.8792i 0.502870 0.870996i −0.497125 0.867679i \(-0.665611\pi\)
0.999994 0.00331669i \(-0.00105574\pi\)
\(632\) 7.05903 12.2266i 0.280793 0.486348i
\(633\) 7.62770 12.6405i 0.303174 0.502413i
\(634\) −0.251872 + 0.436254i −0.0100031 + 0.0173259i
\(635\) 3.37454 5.84487i 0.133915 0.231947i
\(636\) −0.847267 + 1.40407i −0.0335963 + 0.0556751i
\(637\) 9.19523 0.364328
\(638\) −2.49762 −0.0988818
\(639\) 17.9145 28.4295i 0.708686 1.12465i
\(640\) −17.6177 + 30.5148i −0.696402 + 1.20620i
\(641\) 11.6521 20.1821i 0.460231 0.797144i −0.538741 0.842472i \(-0.681100\pi\)
0.998972 + 0.0453273i \(0.0144331\pi\)
\(642\) −3.72824 6.75599i −0.147142 0.266638i
\(643\) 17.2596 0.680651 0.340325 0.940308i \(-0.389463\pi\)
0.340325 + 0.940308i \(0.389463\pi\)
\(644\) 2.08918 0.0823251
\(645\) −29.8727 54.1328i −1.17624 2.13148i
\(646\) 11.2793 4.26963i 0.443777 0.167986i
\(647\) −35.6673 −1.40223 −0.701114 0.713049i \(-0.747314\pi\)
−0.701114 + 0.713049i \(0.747314\pi\)
\(648\) 7.29016 10.6338i 0.286384 0.417737i
\(649\) 8.53539 + 14.7837i 0.335043 + 0.580312i
\(650\) −3.75545 −0.147301
\(651\) −1.93490 + 3.20648i −0.0758348 + 0.125672i
\(652\) −5.04415 8.73673i −0.197544 0.342157i
\(653\) −8.46548 + 14.6626i −0.331280 + 0.573794i −0.982763 0.184869i \(-0.940814\pi\)
0.651483 + 0.758663i \(0.274147\pi\)
\(654\) −5.06212 + 8.38883i −0.197944 + 0.328029i
\(655\) 10.7684 0.420754
\(656\) −8.86092 + 15.3476i −0.345961 + 0.599222i
\(657\) −5.90978 + 9.37858i −0.230563 + 0.365893i
\(658\) 0.311770 0.0121540
\(659\) −4.52365 −0.176216 −0.0881082 0.996111i \(-0.528082\pi\)
−0.0881082 + 0.996111i \(0.528082\pi\)
\(660\) −9.04103 16.3834i −0.351921 0.637722i
\(661\) −10.0400 17.3898i −0.390510 0.676384i 0.602007 0.798491i \(-0.294368\pi\)
−0.992517 + 0.122107i \(0.961035\pi\)
\(662\) −6.22996 −0.242134
\(663\) −8.27444 14.9942i −0.321353 0.582328i
\(664\) −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
\(668\) −1.39689 + 2.41948i −0.0540473 + 0.0936127i
\(669\) −13.0575 23.6617i −0.504833 0.914816i
\(670\) 1.05401 0.0407201
\(671\) −3.37829 5.85137i −0.130417 0.225890i
\(672\) −0.846371 1.53372i −0.0326495 0.0591646i
\(673\) 8.72911 + 15.1193i 0.336482 + 0.582805i 0.983768 0.179443i \(-0.0574294\pi\)
−0.647286 + 0.762247i \(0.724096\pi\)
\(674\) −6.77287 + 11.7310i −0.260881 + 0.451860i
\(675\) 39.6293 + 2.30221i 1.52533 + 0.0886121i
\(676\) 20.9399 0.805382
\(677\) −20.4904 35.4905i −0.787511 1.36401i −0.927487 0.373854i \(-0.878036\pi\)
0.139976 0.990155i \(-0.455297\pi\)
\(678\) 1.88164 + 0.0364006i 0.0722638 + 0.00139796i
\(679\) 1.60629 0.0616436
\(680\) 18.9968 + 32.9034i 0.728493 + 1.26179i
\(681\) 2.06223 + 0.0398942i 0.0790248 + 0.00152875i
\(682\) −2.61954 + 4.53717i −0.100307 + 0.173737i
\(683\) 20.9461 0.801480 0.400740 0.916192i \(-0.368753\pi\)
0.400740 + 0.916192i \(0.368753\pi\)
\(684\) −4.84844 + 23.8671i −0.185385 + 0.912581i
\(685\) −15.1362 −0.578325
\(686\) 0.645521 1.11807i 0.0246461 0.0426883i
\(687\) −16.7110 30.2822i −0.637563 1.15534i
\(688\) 16.0327 + 27.7695i 0.611242 + 1.05870i
\(689\) 0.673794 0.0256695
\(690\) −5.29977 + 8.78266i −0.201759 + 0.334350i
\(691\) −10.5768 18.3195i −0.402359 0.696907i 0.591651 0.806194i \(-0.298476\pi\)
−0.994010 + 0.109288i \(0.965143\pi\)
\(692\) −41.7437 −1.58686
\(693\) 1.22159 + 0.0472815i 0.0464043 + 0.00179608i
\(694\) 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
\(697\) 20.6986 + 35.8510i 0.784015 + 1.35795i
\(698\) −6.40610 −0.242475
\(699\) −21.4191 0.414357i −0.810144 0.0156724i
\(700\) 1.77675 3.07742i 0.0671548 0.116316i
\(701\) −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
\(705\) 10.7081 17.7452i 0.403289 0.668321i
\(706\) 6.26920 0.235944
\(707\) −0.944501 1.63592i −0.0355216 0.0615252i
\(708\) 33.7438 + 0.652780i 1.26817 + 0.0245330i
\(709\) 26.8452 1.00819 0.504097 0.863647i \(-0.331825\pi\)
0.504097 + 0.863647i \(0.331825\pi\)
\(710\) 14.7695 0.554291
\(711\) 29.5437 + 1.14349i 1.10798 + 0.0428841i
\(712\) −5.74496 + 9.95056i −0.215301 + 0.372913i
\(713\) −38.8843 −1.45623
\(714\) −1.19666 0.0231496i −0.0447838 0.000866351i
\(715\) −3.84422 + 6.65839i −0.143766 + 0.249010i
\(716\) −11.8390 20.5057i −0.442442 0.766333i
\(717\) 13.5843 + 24.6163i 0.507314 + 0.919312i
\(718\) −2.83914 −0.105956
\(719\) 1.94193 + 3.36352i 0.0724217 + 0.125438i 0.899962 0.435968i \(-0.143594\pi\)
−0.827540 + 0.561406i \(0.810261\pi\)
\(720\) −34.0360 1.31736i −1.26845 0.0490950i
\(721\) 3.45120 0.128529
\(722\) 1.40095 + 6.90623i 0.0521381 + 0.257023i
\(723\) −9.38451 + 15.5518i −0.349014 + 0.578378i
\(724\) 4.88543 0.181566
\(725\) −31.5302 −1.17100
\(726\) −5.35518 0.103597i −0.198749 0.00384485i
\(727\) 26.1519 45.2965i 0.969922 1.67995i 0.274156 0.961685i \(-0.411602\pi\)
0.695766 0.718269i \(-0.255065\pi\)
\(728\) −0.237102 + 0.410673i −0.00878758 + 0.0152205i
\(729\) 26.8184 + 3.12650i 0.993273 + 0.115796i
\(730\) −4.87230 −0.180332
\(731\) 74.9031 2.77039
\(732\) −13.3557 0.258369i −0.493642 0.00954960i
\(733\) 3.06517 5.30902i 0.113215 0.196093i −0.803850 0.594832i \(-0.797219\pi\)
0.917065 + 0.398739i \(0.130552\pi\)
\(734\) 4.59485 7.95852i 0.169599 0.293754i
\(735\) −20.6407 37.4033i −0.761343 1.37964i
\(736\) 9.09410 15.7515i 0.335213 0.580606i
\(737\) 0.652121 1.12951i 0.0240212 0.0416059i
\(738\) 6.16982 + 0.238802i 0.227114 + 0.00879043i
\(739\) −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
\(741\) 9.42537 3.36091i 0.346250 0.123466i
\(742\) 0.0235449 0.0407809i 0.000864360 0.00149712i
\(743\) −2.74391 −0.100664 −0.0503321 0.998733i \(-0.516028\pi\)
−0.0503321 + 0.998733i \(0.516028\pi\)
\(744\) 10.3787 + 18.8074i 0.380502 + 0.689512i
\(745\) −6.56344 −0.240466
\(746\) 4.29724 + 7.44304i 0.157333 + 0.272509i
\(747\) 0.592568 0.940380i 0.0216809 0.0344067i
\(748\) 22.6696 0.828881
\(749\) −1.49999 2.59806i −0.0548085 0.0949311i
\(750\) 2.91261 + 5.27799i 0.106354 + 0.192725i
\(751\) 10.4736 + 18.1408i 0.382187 + 0.661967i 0.991375 0.131059i \(-0.0418377\pi\)
−0.609188 + 0.793026i \(0.708504\pi\)
\(752\) −5.37439 + 9.30871i −0.195984 + 0.339454i
\(753\) −11.7527 21.2972i −0.428292 0.776114i
\(754\) 2.02888 0.0738875
\(755\) 19.9065 + 34.4791i 0.724473 + 1.25482i
\(756\) 1.32785 2.01955i 0.0482933 0.0734503i
\(757\) 3.65990 + 6.33913i 0.133021 + 0.230400i 0.924840 0.380357i \(-0.124199\pi\)
−0.791819 + 0.610756i \(0.790865\pi\)
\(758\) −5.39274 + 9.34049i −0.195873 + 0.339262i
\(759\) 6.13274 + 11.1132i 0.222604 + 0.403385i
\(760\) −20.7620 + 7.85920i −0.753118 + 0.285083i
\(761\) 6.05266 10.4835i 0.219409 0.380027i −0.735219 0.677830i \(-0.762921\pi\)
0.954627 + 0.297803i \(0.0962539\pi\)
\(762\) 1.21928 + 0.0235872i 0.0441698 + 0.000854473i
\(763\) −1.90460 + 3.29886i −0.0689510 + 0.119427i
\(764\) 3.17391 5.49737i 0.114828 0.198888i
\(765\) −42.4180 + 67.3156i −1.53363 + 2.43380i
\(766\) 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
\(769\) 14.4830 + 25.0852i 0.522269 + 0.904597i 0.999664 + 0.0259081i \(0.00824772\pi\)
−0.477395 + 0.878689i \(0.658419\pi\)
\(770\) 0.268663 + 0.465339i 0.00968195 + 0.0167696i
\(771\) 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 \(-0.119975\pi\)
\(774\) 5.95596 9.45185i 0.214082 0.339740i
\(775\) −33.0693 + 57.2777i −1.18788 + 2.05748i
\(776\) 4.60671 7.97906i 0.165371 0.286432i
\(777\) 1.34334 + 0.0259873i 0.0481922 + 0.000932287i
\(778\) −3.55421 + 6.15608i −0.127425 + 0.220706i
\(779\) −22.6220 + 8.56327i −0.810517 + 0.306811i
\(780\) 7.34426 + 13.3086i 0.262967 + 0.476525i
\(781\) 9.13796 15.8274i 0.326982 0.566349i
\(782\) −6.21352 10.7621i −0.222195 0.384853i
\(783\) −21.4097 1.24377i −0.765121 0.0444487i
\(784\) 11.0779 + 19.1875i 0.395639 + 0.685267i
\(785\) −73.8457 −2.63567
\(786\) 0.940104 + 1.70358i 0.0335324 + 0.0607645i
\(787\) 3.10060 5.37040i 0.110525 0.191434i −0.805457 0.592654i \(-0.798080\pi\)
0.915982 + 0.401220i \(0.131414\pi\)
\(788\) −2.46213 4.26454i −0.0877098 0.151918i
\(789\) −16.3181 29.5703i −0.580941 1.05273i
\(790\) 6.49754 + 11.2541i 0.231172 + 0.400402i
\(791\) 0.731677 0.0260155
\(792\) 3.73830 5.93252i 0.132835 0.210803i
\(793\) 2.74427 + 4.75322i 0.0974520 + 0.168792i
\(794\) −11.8380 −0.420115
\(795\) −1.51248 2.74078i −0.0536420 0.0972055i
\(796\) 0.395995 0.0140357
\(797\) −19.1606 + 33.1871i −0.678702 + 1.17555i 0.296671 + 0.954980i \(0.404124\pi\)
−0.975372 + 0.220566i \(0.929210\pi\)
\(798\) 0.125941 0.687907i 0.00445827 0.0243517i
\(799\) 12.5543 + 21.7446i 0.444138 + 0.769269i
\(800\) −15.4683 26.7918i −0.546885 0.947233i
\(801\) −24.0440 0.930621i −0.849554 0.0328819i
\(802\) −7.11006 + 12.3150i −0.251065 + 0.434857i
\(803\) −3.01451 + 5.22128i −0.106380 + 0.184255i
\(804\) −1.24586 2.25763i −0.0439379 0.0796206i
\(805\) −1.99401 + 3.45373i −0.0702797 + 0.121728i
\(806\) 2.12792 3.68566i 0.0749527 0.129822i
\(807\) 40.1053 + 0.775846i 1.41177 + 0.0273111i
\(808\) −10.8350 −0.381175
\(809\) −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 \(-0.0973118\pi\)
\(812\) −0.959889 + 1.66258i −0.0336855 + 0.0583450i
\(813\) 38.2322 + 0.739610i 1.34086 + 0.0259393i
\(814\) 1.87960 0.0658800
\(815\) 19.2575 0.674562
\(816\) 21.3195 35.3303i 0.746333 1.23681i
\(817\) −7.04750 + 43.1950i −0.246561 + 1.51120i
\(818\) 0.850402 0.0297336
\(819\) −0.992328 0.0384080i −0.0346748 0.00134208i
\(820\) −18.3717 31.8208i −0.641569 1.11123i
\(821\) −17.7203 −0.618444 −0.309222 0.950990i \(-0.600069\pi\)
−0.309222 + 0.950990i \(0.600069\pi\)
\(822\) −1.32143 2.39458i −0.0460902 0.0835207i
\(823\) 14.6013 + 25.2903i 0.508971 + 0.881563i 0.999946 + 0.0103898i \(0.00330724\pi\)
−0.490975 + 0.871174i \(0.663359\pi\)
\(824\) 9.89779 17.1435i 0.344806 0.597221i
\(825\) 21.5858 + 0.417581i 0.751519 + 0.0145383i
\(826\) −0.969133 −0.0337204
\(827\) 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 \(0.515964\pi\)
\(830\) 0.488541 0.0169575
\(831\) −51.2564 0.991566i −1.77807 0.0343970i
\(832\) −3.23747 5.60746i −0.112239 0.194404i
\(833\) 51.7547 1.79319
\(834\) 5.73262 9.49997i 0.198504 0.328957i
\(835\) −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
\(839\) 7.55921 13.0929i 0.260973 0.452019i −0.705528 0.708682i \(-0.749290\pi\)
0.966501 + 0.256664i \(0.0826233\pi\)
\(840\) 2.20271 + 0.0426119i 0.0760009 + 0.00147025i
\(841\) −11.9658 −0.412614
\(842\) −4.79644 8.30768i −0.165296 0.286301i
\(843\) −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
\(846\) 3.74216 + 0.144840i 0.128658 + 0.00497970i
\(847\) −2.08237 −0.0715511
\(848\) 0.811749 + 1.40599i 0.0278756 + 0.0482819i
\(849\) −14.3363 + 23.7578i −0.492019 + 0.815364i
\(850\) −21.1373 −0.725002
\(851\) 6.97517 + 12.0814i 0.239106 + 0.414143i
\(852\) −17.4578 31.6355i −0.598093 1.08381i
\(853\) −13.0507 + 22.6045i −0.446848 + 0.773964i −0.998179 0.0603231i \(-0.980787\pi\)
0.551331 + 0.834287i \(0.314120\pi\)
\(854\) 0.383581 0.0131259
\(855\) −34.8284 30.7951i −1.19111 1.05317i
\(856\) −17.2075 −0.588139
\(857\) −20.8227 + 36.0660i −0.711291 + 1.23199i 0.253082 + 0.967445i \(0.418556\pi\)
−0.964373 + 0.264547i \(0.914778\pi\)
\(858\) −1.38898 0.0268701i −0.0474191 0.000917332i
\(859\) −4.72015 8.17554i −0.161049 0.278946i 0.774196 0.632946i \(-0.218155\pi\)
−0.935245 + 0.354000i \(0.884821\pi\)
\(860\) −66.4828 −2.26704
\(861\) 2.40004 + 0.0464293i 0.0817933 + 0.00158231i
\(862\) −3.53451 6.12196i −0.120386 0.208515i
\(863\) 31.0403 1.05662 0.528311 0.849051i \(-0.322825\pi\)
0.528311 + 0.849051i \(0.322825\pi\)
\(864\) −9.44644 18.8024i −0.321374 0.639671i
\(865\) 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
\(868\) 2.01349 + 3.48746i 0.0683422 + 0.118372i
\(869\) 16.0802 0.545483
\(870\) −4.55427 8.25285i −0.154404 0.279798i
\(871\) −0.529735 + 0.917528i −0.0179494 + 0.0310892i
\(872\) 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
\(876\) 5.75912 + 10.4362i 0.194582 + 0.352606i
\(877\) −41.4554 −1.39985 −0.699924 0.714217i \(-0.746783\pi\)
−0.699924 + 0.714217i \(0.746783\pi\)
\(878\) 0.361069 + 0.625390i 0.0121855 + 0.0211059i
\(879\) −0.670113 1.21432i −0.0226024 0.0409580i
\(880\) −18.5252 −0.624485
\(881\) 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 \(0.170040\pi\)
\(884\) −18.4151 −0.619365
\(885\) −33.2859 + 55.1606i −1.11889 + 1.85420i
\(886\) −1.21694 + 2.10781i −0.0408840 + 0.0708132i
\(887\) 0.563597 + 0.976178i 0.0189237 + 0.0327769i 0.875332 0.483522i \(-0.160643\pi\)
−0.856408 + 0.516299i \(0.827309\pi\)
\(888\) 3.98170 6.59839i 0.133617 0.221428i
\(889\) 0.474118 0.0159014
\(890\) −5.28798 9.15906i −0.177254 0.307012i
\(891\) 14.6407 + 1.13504i 0.490483 + 0.0380252i
\(892\) −29.0600 −0.973000
\(893\) −13.7208 + 5.19385i −0.459151 + 0.173806i
\(894\) −0.573004 1.03835i −0.0191641 0.0347276i
\(895\) 45.1987 1.51083
\(896\) −2.47527 −0.0826929
\(897\) −4.98178 9.02756i −0.166337 0.301421i
\(898\) 6.58973 11.4137i 0.219902 0.380881i
\(899\) 17.8657 30.9443i 0.595854 1.03205i
\(900\) 22.7560 36.1128i 0.758532 1.20376i
\(901\) 3.79240 0.126343
\(902\) 3.35813 0.111814
\(903\) 2.24404 3.71878i 0.0746771 0.123753i
\(904\) 2.09840 3.63453i 0.0697917 0.120883i
\(905\) −4.66290 + 8.07637i −0.155000 + 0.268468i
\(906\) −3.71678 + 6.15937i −0.123482 + 0.204631i
\(907\) −14.3660 + 24.8826i −0.477014 + 0.826213i −0.999653 0.0263414i \(-0.991614\pi\)
0.522639 + 0.852554i \(0.324948\pi\)
\(908\) 1.10895 1.92075i 0.0368016 0.0637423i
\(909\) −10.5768 20.0747i −0.350811 0.665837i
\(910\) −0.218242 0.378006i −0.00723466 0.0125308i
\(911\) −19.6724 34.0735i −0.651774 1.12891i −0.982692 0.185246i \(-0.940692\pi\)
0.330918 0.943660i \(-0.392642\pi\)
\(912\) 18.3683 + 15.6187i 0.608235 + 0.517186i
\(913\) 0.302262 0.523532i 0.0100034 0.0173264i
\(914\) 2.46599 0.0815678
\(915\) 13.1745 21.8325i 0.435535 0.721759i
\(916\) −37.1908 −1.22882
\(917\) 0.378235 + 0.655122i 0.0124904 + 0.0216340i
\(918\) −14.3527 0.833799i −0.473709 0.0275195i
\(919\) 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
\(921\) −7.96549 0.154094i −0.262472 0.00507757i
\(922\) 1.29288 + 2.23934i 0.0425788 + 0.0737487i
\(923\) −7.42300 + 12.8570i −0.244331 + 0.423194i
\(924\) 0.679164 1.12550i 0.0223428 0.0370261i
\(925\) 23.7283 0.780181
\(926\) 3.18850 + 5.52264i 0.104781 + 0.181485i
\(927\) 41.4246 + 1.60334i 1.36056 + 0.0526604i
\(928\) 8.35672 + 14.4743i 0.274323 + 0.475141i
\(929\) −0.893942 + 1.54835i −0.0293293 + 0.0507998i −0.880317 0.474385i \(-0.842670\pi\)
0.850988 + 0.525185i \(0.176004\pi\)
\(930\) −19.7687 0.382429i −0.648240 0.0125403i
\(931\) −4.86950 + 29.8458i −0.159591 + 0.978156i
\(932\) −11.5179 + 19.9496i −0.377282 + 0.653472i
\(933\) 27.4681 + 49.7753i 0.899265 + 1.62957i
\(934\) −6.77773 + 11.7394i −0.221774 + 0.384124i
\(935\) −21.6369 + 37.4763i −0.707603 + 1.22560i
\(936\) −3.03671 + 4.81914i −0.0992581 + 0.157518i
\(937\) 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
\(940\) −11.1430 19.3002i −0.363443 0.629502i
\(941\) 22.7165 + 39.3461i 0.740535 + 1.28264i 0.952252 + 0.305314i \(0.0987613\pi\)
−0.211717 + 0.977331i \(0.567905\pi\)
\(942\) −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
\(945\) 2.07127 + 4.12269i 0.0673783 + 0.134111i
\(946\) 3.03806 5.26208i 0.0987759 0.171085i
\(947\) 2.58749 4.48167i 0.0840823 0.145635i −0.820918 0.571047i \(-0.806537\pi\)
0.905000 + 0.425412i \(0.139871\pi\)
\(948\) 16.4254 27.2197i 0.533471 0.884056i
\(949\) 2.44876 4.24138i 0.0794902 0.137681i
\(950\) 1.98877 12.1894i 0.0645241 0.395476i
\(951\) −1.21542 + 2.01418i −0.0394128 + 0.0653141i
\(952\) −1.33451 + 2.31144i −0.0432517 + 0.0749142i
\(953\) 12.9234 + 22.3840i 0.418630 + 0.725088i 0.995802 0.0915347i \(-0.0291772\pi\)
−0.577172 + 0.816622i \(0.695844\pi\)
\(954\) 0.301554 0.478554i 0.00976318 0.0154938i
\(955\) 6.05867 + 10.4939i 0.196054 + 0.339575i
\(956\) 30.2323 0.977783
\(957\) −11.6617 0.225598i −0.376969 0.00729255i
\(958\) 3.70247 6.41287i 0.119621 0.207190i
\(959\) −0.531655 0.920853i −0.0171680 0.0297359i
\(960\) −15.5422 + 25.7562i −0.501621 + 0.831276i
\(961\) −21.9755 38.0628i −0.708888 1.22783i
\(962\) −1.52685 −0.0492276
\(963\) −16.7974 31.8813i −0.541287 1.02736i
\(964\) 9.76565 + 16.9146i 0.314531 + 0.544783i
\(965\) −1.76966 −0.0569674
\(966\) −0.720470 0.0139376i −0.0231807 0.000448436i
\(967\) 26.1397 0.840597 0.420299 0.907386i \(-0.361925\pi\)
0.420299 + 0.907386i \(0.361925\pi\)
\(968\) −5.97209 + 10.3440i −0.191950 + 0.332468i
\(969\) 53.0500 18.9166i 1.70421 0.607689i
\(970\) 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 \(0.768646\pi\)
\(972\) 16.8763 23.6237i 0.541309 0.757731i
\(973\) 2.15687 3.73581i 0.0691461 0.119764i
\(974\) −0.100402 + 0.173901i −0.00321708 + 0.00557215i
\(975\) −17.5347 0.339212i −0.561559 0.0108635i
\(976\) −6.61229 + 11.4528i −0.211654 + 0.366596i
\(977\) 18.8495 32.6483i 0.603050 1.04451i −0.389307 0.921108i \(-0.627285\pi\)
0.992356 0.123405i \(-0.0393813\pi\)
\(978\) 1.68123 + 3.04658i 0.0537599 + 0.0974190i
\(979\) −13.0868 −0.418255
\(980\) −45.9366 −1.46739
\(981\) −24.3934 + 38.7113i −0.778821 + 1.23596i
\(982\) 1.36185 2.35879i 0.0434583 0.0752719i
\(983\) 11.6223 20.1305i 0.370695 0.642063i −0.618977 0.785409i \(-0.712453\pi\)
0.989673 + 0.143346i \(0.0457861\pi\)
\(984\) 7.11379 11.7888i 0.226779 0.375814i
\(985\) 9.39991 0.299506
\(986\) 11.4194 0.363668
\(987\) 1.45569 + 0.0281606i 0.0463352 + 0.000896363i
\(988\) 1.73264 10.6196i 0.0551226 0.337853i
\(989\) 45.0968 1.43400
\(990\) 3.00857 + 5.71026i 0.0956188 + 0.181484i
\(991\) −11.8484 20.5220i −0.376376 0.651903i 0.614156 0.789185i \(-0.289497\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(992\) 35.0586 1.11311
\(993\) −29.0885 0.562722i −0.923094 0.0178574i
\(994\) 0.518775 + 0.898545i 0.0164545 + 0.0285001i
\(995\) −0.377957 + 0.654641i −0.0119820 + 0.0207535i
\(996\) −0.577460 1.04642i −0.0182975 0.0331572i
\(997\) −18.9313 −0.599559 −0.299780 0.954008i \(-0.596913\pi\)
−0.299780 + 0.954008i \(0.596913\pi\)
\(998\) 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.g.c.121.8 yes 32
3.2 odd 2 513.2.g.c.64.9 32
9.2 odd 6 513.2.h.c.235.8 32
9.7 even 3 171.2.h.c.7.9 yes 32
19.11 even 3 171.2.h.c.49.9 yes 32
57.11 odd 6 513.2.h.c.334.8 32
171.11 odd 6 513.2.g.c.505.9 32
171.106 even 3 inner 171.2.g.c.106.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.g.c.106.8 32 171.106 even 3 inner
171.2.g.c.121.8 yes 32 1.1 even 1 trivial
171.2.h.c.7.9 yes 32 9.7 even 3
171.2.h.c.49.9 yes 32 19.11 even 3
513.2.g.c.64.9 32 3.2 odd 2
513.2.g.c.505.9 32 171.11 odd 6
513.2.h.c.235.8 32 9.2 odd 6
513.2.h.c.334.8 32 57.11 odd 6