Properties

Label 847.2.f.p.148.2
Level $847$
Weight $2$
Character 847.148
Analytic conductor $6.763$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 148.2
Root \(-0.762262 - 2.34600i\) of defining polynomial
Character \(\chi\) \(=\) 847.148
Dual form 847.2.f.p.372.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.762262 + 2.34600i) q^{2} +(1.30902 + 0.951057i) q^{3} +(-3.30464 + 2.40097i) q^{4} +(-1.07128 + 3.29706i) q^{5} +(-1.23337 + 3.79591i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-4.16042 - 3.02272i) q^{8} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})\) \(q+(0.762262 + 2.34600i) q^{2} +(1.30902 + 0.951057i) q^{3} +(-3.30464 + 2.40097i) q^{4} +(-1.07128 + 3.29706i) q^{5} +(-1.23337 + 3.79591i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-4.16042 - 3.02272i) q^{8} +(-0.118034 - 0.363271i) q^{9} -8.55150 q^{10} -6.60929 q^{12} +(-0.202020 - 0.621755i) q^{13} +(1.99563 + 1.44991i) q^{14} +(-4.53801 + 3.29706i) q^{15} +(1.39545 - 4.29476i) q^{16} +(-0.351400 + 1.08150i) q^{17} +(0.762262 - 0.553816i) q^{18} +(4.91560 + 3.57140i) q^{19} +(-4.37592 - 13.4677i) q^{20} +1.61803 q^{21} -6.66708 q^{23} +(-2.57128 - 7.91358i) q^{24} +(-5.67787 - 4.12521i) q^{25} +(1.30464 - 0.947880i) q^{26} +(1.69098 - 5.20431i) q^{27} +(-1.26226 + 3.88484i) q^{28} +(3.70010 - 2.68828i) q^{29} +(-11.1941 - 8.13296i) q^{30} +(0.864107 + 2.65945i) q^{31} +0.854102 q^{32} -2.80505 q^{34} +(1.07128 + 3.29706i) q^{35} +(1.26226 + 0.917087i) q^{36} +(0.355772 - 0.258483i) q^{37} +(-4.63152 + 14.2544i) q^{38} +(0.326876 - 1.00602i) q^{39} +(14.4230 - 10.4790i) q^{40} +(4.77575 + 3.46978i) q^{41} +(1.23337 + 3.79591i) q^{42} +8.70820 q^{43} +1.32417 q^{45} +(-5.08206 - 15.6410i) q^{46} +(0.489215 + 0.355436i) q^{47} +(5.91123 - 4.29476i) q^{48} +(0.309017 - 0.951057i) q^{49} +(5.34973 - 16.4648i) q^{50} +(-1.48855 + 1.08150i) q^{51} +(2.16042 + 1.56963i) q^{52} +(3.03531 + 9.34172i) q^{53} +13.4983 q^{54} -5.14256 q^{56} +(3.03801 + 9.35004i) q^{57} +(9.12715 + 6.63126i) q^{58} +(-1.37052 + 0.995741i) q^{59} +(7.08039 - 21.7912i) q^{60} +(2.11930 - 6.52252i) q^{61} +(-5.58039 + 4.05439i) q^{62} +(-0.309017 - 0.224514i) q^{63} +(-2.13986 - 6.58580i) q^{64} +2.26638 q^{65} -6.17828 q^{67} +(-1.43539 - 4.41766i) q^{68} +(-8.72732 - 6.34077i) q^{69} +(-6.91831 + 5.02644i) q^{70} +(-1.67390 + 5.15175i) q^{71} +(-0.606997 + 1.86814i) q^{72} +(-5.42202 + 3.93933i) q^{73} +(0.877594 + 0.637609i) q^{74} +(-3.50911 - 10.7999i) q^{75} -24.8191 q^{76} +2.60929 q^{78} +(0.820054 + 2.52387i) q^{79} +(12.6652 + 9.20178i) q^{80} +(6.23607 - 4.53077i) q^{81} +(-4.49975 + 13.8488i) q^{82} +(2.06936 - 6.36882i) q^{83} +(-5.34703 + 3.88484i) q^{84} +(-3.18931 - 2.31717i) q^{85} +(6.63793 + 20.4295i) q^{86} +7.40020 q^{87} -0.698213 q^{89} +(1.00937 + 3.10651i) q^{90} +(-0.528896 - 0.384266i) q^{91} +(22.0323 - 16.0074i) q^{92} +(-1.39815 + 4.30308i) q^{93} +(-0.460942 + 1.41863i) q^{94} +(-17.0411 + 12.3811i) q^{95} +(1.11803 + 0.812299i) q^{96} +(-4.59159 - 14.1315i) q^{97} +2.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} - 12 q^{8} + 8 q^{9} - 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 16 q^{23} - 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} - 3 q^{28} + 6 q^{29} - 26 q^{30} + 14 q^{31} - 20 q^{32} - 24 q^{34} - 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} + 29 q^{40} + 18 q^{41} + 2 q^{42} + 16 q^{43} + 18 q^{45} - 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} + q^{50} + 8 q^{51} - 4 q^{52} + 7 q^{53} + 4 q^{54} - 18 q^{56} - 3 q^{57} + 36 q^{58} + 17 q^{60} + 12 q^{61} - 5 q^{62} + 2 q^{63} - 4 q^{64} + 24 q^{65} - 30 q^{67} - 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} + 3 q^{72} + 8 q^{73} + q^{74} - 52 q^{76} - 18 q^{78} + q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} - 22 q^{83} - 11 q^{84} - 5 q^{85} + 13 q^{86} + 12 q^{87} - 34 q^{89} - 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} + 50 q^{94} - 41 q^{95} - 15 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.762262 + 2.34600i 0.539001 + 1.65887i 0.734842 + 0.678238i \(0.237256\pi\)
−0.195842 + 0.980636i \(0.562744\pi\)
\(3\) 1.30902 + 0.951057i 0.755761 + 0.549093i 0.897607 0.440796i \(-0.145304\pi\)
−0.141846 + 0.989889i \(0.545304\pi\)
\(4\) −3.30464 + 2.40097i −1.65232 + 1.20048i
\(5\) −1.07128 + 3.29706i −0.479091 + 1.47449i 0.361270 + 0.932461i \(0.382343\pi\)
−0.840361 + 0.542028i \(0.817657\pi\)
\(6\) −1.23337 + 3.79591i −0.503520 + 1.54967i
\(7\) 0.809017 0.587785i 0.305780 0.222162i
\(8\) −4.16042 3.02272i −1.47093 1.06869i
\(9\) −0.118034 0.363271i −0.0393447 0.121090i
\(10\) −8.55150 −2.70422
\(11\) 0 0
\(12\) −6.60929 −1.90794
\(13\) −0.202020 0.621755i −0.0560304 0.172444i 0.919125 0.393966i \(-0.128897\pi\)
−0.975155 + 0.221523i \(0.928897\pi\)
\(14\) 1.99563 + 1.44991i 0.533354 + 0.387504i
\(15\) −4.53801 + 3.29706i −1.17171 + 0.851297i
\(16\) 1.39545 4.29476i 0.348863 1.07369i
\(17\) −0.351400 + 1.08150i −0.0852270 + 0.262302i −0.984584 0.174914i \(-0.944035\pi\)
0.899357 + 0.437216i \(0.144035\pi\)
\(18\) 0.762262 0.553816i 0.179667 0.130536i
\(19\) 4.91560 + 3.57140i 1.12772 + 0.819334i 0.985361 0.170481i \(-0.0545322\pi\)
0.142356 + 0.989816i \(0.454532\pi\)
\(20\) −4.37592 13.4677i −0.978486 3.01147i
\(21\) 1.61803 0.353084
\(22\) 0 0
\(23\) −6.66708 −1.39018 −0.695091 0.718921i \(-0.744636\pi\)
−0.695091 + 0.718921i \(0.744636\pi\)
\(24\) −2.57128 7.91358i −0.524860 1.61535i
\(25\) −5.67787 4.12521i −1.13557 0.825042i
\(26\) 1.30464 0.947880i 0.255862 0.185895i
\(27\) 1.69098 5.20431i 0.325430 1.00157i
\(28\) −1.26226 + 3.88484i −0.238545 + 0.734166i
\(29\) 3.70010 2.68828i 0.687091 0.499201i −0.188612 0.982052i \(-0.560399\pi\)
0.875703 + 0.482851i \(0.160399\pi\)
\(30\) −11.1941 8.13296i −2.04375 1.48487i
\(31\) 0.864107 + 2.65945i 0.155198 + 0.477651i 0.998181 0.0602896i \(-0.0192024\pi\)
−0.842983 + 0.537941i \(0.819202\pi\)
\(32\) 0.854102 0.150985
\(33\) 0 0
\(34\) −2.80505 −0.481063
\(35\) 1.07128 + 3.29706i 0.181079 + 0.557304i
\(36\) 1.26226 + 0.917087i 0.210377 + 0.152848i
\(37\) 0.355772 0.258483i 0.0584885 0.0424944i −0.558157 0.829735i \(-0.688491\pi\)
0.616645 + 0.787241i \(0.288491\pi\)
\(38\) −4.63152 + 14.2544i −0.751332 + 2.31236i
\(39\) 0.326876 1.00602i 0.0523420 0.161092i
\(40\) 14.4230 10.4790i 2.28048 1.65687i
\(41\) 4.77575 + 3.46978i 0.745847 + 0.541889i 0.894537 0.446995i \(-0.147506\pi\)
−0.148690 + 0.988884i \(0.547506\pi\)
\(42\) 1.23337 + 3.79591i 0.190312 + 0.585722i
\(43\) 8.70820 1.32799 0.663994 0.747738i \(-0.268860\pi\)
0.663994 + 0.747738i \(0.268860\pi\)
\(44\) 0 0
\(45\) 1.32417 0.197396
\(46\) −5.08206 15.6410i −0.749309 2.30614i
\(47\) 0.489215 + 0.355436i 0.0713594 + 0.0518456i 0.622893 0.782307i \(-0.285957\pi\)
−0.551534 + 0.834153i \(0.685957\pi\)
\(48\) 5.91123 4.29476i 0.853213 0.619895i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) 5.34973 16.4648i 0.756566 2.32847i
\(51\) −1.48855 + 1.08150i −0.208439 + 0.151440i
\(52\) 2.16042 + 1.56963i 0.299596 + 0.217669i
\(53\) 3.03531 + 9.34172i 0.416932 + 1.28318i 0.910512 + 0.413483i \(0.135688\pi\)
−0.493580 + 0.869700i \(0.664312\pi\)
\(54\) 13.4983 1.83688
\(55\) 0 0
\(56\) −5.14256 −0.687203
\(57\) 3.03801 + 9.35004i 0.402394 + 1.23844i
\(58\) 9.12715 + 6.63126i 1.19845 + 0.870727i
\(59\) −1.37052 + 0.995741i −0.178426 + 0.129634i −0.673414 0.739266i \(-0.735173\pi\)
0.494987 + 0.868900i \(0.335173\pi\)
\(60\) 7.08039 21.7912i 0.914075 2.81323i
\(61\) 2.11930 6.52252i 0.271348 0.835123i −0.718815 0.695202i \(-0.755315\pi\)
0.990163 0.139921i \(-0.0446850\pi\)
\(62\) −5.58039 + 4.05439i −0.708711 + 0.514908i
\(63\) −0.309017 0.224514i −0.0389325 0.0282861i
\(64\) −2.13986 6.58580i −0.267482 0.823225i
\(65\) 2.26638 0.281110
\(66\) 0 0
\(67\) −6.17828 −0.754797 −0.377398 0.926051i \(-0.623181\pi\)
−0.377398 + 0.926051i \(0.623181\pi\)
\(68\) −1.43539 4.41766i −0.174066 0.535721i
\(69\) −8.72732 6.34077i −1.05065 0.763339i
\(70\) −6.91831 + 5.02644i −0.826896 + 0.600775i
\(71\) −1.67390 + 5.15175i −0.198656 + 0.611400i 0.801259 + 0.598318i \(0.204164\pi\)
−0.999914 + 0.0130816i \(0.995836\pi\)
\(72\) −0.606997 + 1.86814i −0.0715352 + 0.220163i
\(73\) −5.42202 + 3.93933i −0.634599 + 0.461063i −0.857990 0.513666i \(-0.828287\pi\)
0.223391 + 0.974729i \(0.428287\pi\)
\(74\) 0.877594 + 0.637609i 0.102018 + 0.0741206i
\(75\) −3.50911 10.7999i −0.405198 1.24707i
\(76\) −24.8191 −2.84695
\(77\) 0 0
\(78\) 2.60929 0.295444
\(79\) 0.820054 + 2.52387i 0.0922633 + 0.283957i 0.986531 0.163576i \(-0.0523028\pi\)
−0.894267 + 0.447533i \(0.852303\pi\)
\(80\) 12.6652 + 9.20178i 1.41601 + 1.02879i
\(81\) 6.23607 4.53077i 0.692896 0.503419i
\(82\) −4.49975 + 13.8488i −0.496914 + 1.52934i
\(83\) 2.06936 6.36882i 0.227141 0.699069i −0.770926 0.636925i \(-0.780206\pi\)
0.998067 0.0621443i \(-0.0197939\pi\)
\(84\) −5.34703 + 3.88484i −0.583409 + 0.423871i
\(85\) −3.18931 2.31717i −0.345930 0.251333i
\(86\) 6.63793 + 20.4295i 0.715787 + 2.20297i
\(87\) 7.40020 0.793384
\(88\) 0 0
\(89\) −0.698213 −0.0740105 −0.0370052 0.999315i \(-0.511782\pi\)
−0.0370052 + 0.999315i \(0.511782\pi\)
\(90\) 1.00937 + 3.10651i 0.106397 + 0.327455i
\(91\) −0.528896 0.384266i −0.0554434 0.0402820i
\(92\) 22.0323 16.0074i 2.29703 1.66889i
\(93\) −1.39815 + 4.30308i −0.144982 + 0.446208i
\(94\) −0.460942 + 1.41863i −0.0475426 + 0.146321i
\(95\) −17.0411 + 12.3811i −1.74838 + 1.27027i
\(96\) 1.11803 + 0.812299i 0.114109 + 0.0829049i
\(97\) −4.59159 14.1315i −0.466205 1.43483i −0.857461 0.514550i \(-0.827959\pi\)
0.391256 0.920282i \(-0.372041\pi\)
\(98\) 2.46673 0.249178
\(99\) 0 0
\(100\) 28.6678 2.86678
\(101\) 2.66360 + 8.19772i 0.265038 + 0.815704i 0.991685 + 0.128692i \(0.0410779\pi\)
−0.726646 + 0.687012i \(0.758922\pi\)
\(102\) −3.67186 2.66776i −0.363569 0.264148i
\(103\) 0.754779 0.548379i 0.0743706 0.0540334i −0.549979 0.835179i \(-0.685364\pi\)
0.624349 + 0.781145i \(0.285364\pi\)
\(104\) −1.03890 + 3.19741i −0.101873 + 0.313532i
\(105\) −1.73337 + 5.33475i −0.169159 + 0.520618i
\(106\) −19.6020 + 14.2417i −1.90391 + 1.38327i
\(107\) −5.35740 3.89238i −0.517920 0.376291i 0.297900 0.954597i \(-0.403714\pi\)
−0.815820 + 0.578306i \(0.803714\pi\)
\(108\) 6.90727 + 21.2584i 0.664652 + 2.04559i
\(109\) −4.12507 −0.395110 −0.197555 0.980292i \(-0.563300\pi\)
−0.197555 + 0.980292i \(0.563300\pi\)
\(110\) 0 0
\(111\) 0.711544 0.0675368
\(112\) −1.39545 4.29476i −0.131858 0.405817i
\(113\) 15.2304 + 11.0655i 1.43276 + 1.04096i 0.989495 + 0.144564i \(0.0461781\pi\)
0.443260 + 0.896393i \(0.353822\pi\)
\(114\) −19.6194 + 14.2544i −1.83753 + 1.33504i
\(115\) 7.14231 21.9818i 0.666023 2.04981i
\(116\) −5.77305 + 17.7676i −0.536014 + 1.64968i
\(117\) −0.202020 + 0.146776i −0.0186768 + 0.0135695i
\(118\) −3.38070 2.45623i −0.311219 0.226114i
\(119\) 0.351400 + 1.08150i 0.0322128 + 0.0991407i
\(120\) 28.8461 2.63328
\(121\) 0 0
\(122\) 16.9173 1.53162
\(123\) 2.95158 + 9.08401i 0.266135 + 0.819078i
\(124\) −9.24081 6.71384i −0.829849 0.602921i
\(125\) 5.66042 4.11253i 0.506283 0.367836i
\(126\) 0.291158 0.896093i 0.0259384 0.0798303i
\(127\) −2.46174 + 7.57645i −0.218444 + 0.672301i 0.780447 + 0.625221i \(0.214991\pi\)
−0.998891 + 0.0470794i \(0.985009\pi\)
\(128\) 15.2011 11.0443i 1.34360 0.976185i
\(129\) 11.3992 + 8.28199i 1.00364 + 0.729189i
\(130\) 1.72758 + 5.31693i 0.151518 + 0.466326i
\(131\) −4.80505 −0.419819 −0.209910 0.977721i \(-0.567317\pi\)
−0.209910 + 0.977721i \(0.567317\pi\)
\(132\) 0 0
\(133\) 6.07602 0.526858
\(134\) −4.70947 14.4942i −0.406836 1.25211i
\(135\) 15.3474 + 11.1505i 1.32089 + 0.959685i
\(136\) 4.73103 3.43730i 0.405683 0.294746i
\(137\) −6.76059 + 20.8070i −0.577596 + 1.77766i 0.0495667 + 0.998771i \(0.484216\pi\)
−0.627163 + 0.778888i \(0.715784\pi\)
\(138\) 8.22295 25.3076i 0.699984 2.15433i
\(139\) 16.0296 11.6462i 1.35962 0.987819i 0.361147 0.932509i \(-0.382385\pi\)
0.998469 0.0553100i \(-0.0176147\pi\)
\(140\) −11.4563 8.32350i −0.968236 0.703464i
\(141\) 0.302352 + 0.930543i 0.0254626 + 0.0783658i
\(142\) −13.3620 −1.12131
\(143\) 0 0
\(144\) −1.72487 −0.143740
\(145\) 4.89957 + 15.0793i 0.406887 + 1.25227i
\(146\) −13.3747 9.71726i −1.10689 0.804206i
\(147\) 1.30902 0.951057i 0.107966 0.0784418i
\(148\) −0.555090 + 1.70839i −0.0456281 + 0.140429i
\(149\) 0.977146 3.00735i 0.0800509 0.246371i −0.903019 0.429600i \(-0.858655\pi\)
0.983070 + 0.183228i \(0.0586547\pi\)
\(150\) 22.6618 16.4648i 1.85033 1.34434i
\(151\) −7.22295 5.24778i −0.587795 0.427058i 0.253731 0.967275i \(-0.418342\pi\)
−0.841526 + 0.540217i \(0.818342\pi\)
\(152\) −9.65564 29.7170i −0.783175 2.41037i
\(153\) 0.434354 0.0351155
\(154\) 0 0
\(155\) −9.69406 −0.778645
\(156\) 1.33521 + 4.10936i 0.106902 + 0.329012i
\(157\) −0.922017 0.669885i −0.0735850 0.0534626i 0.550385 0.834911i \(-0.314481\pi\)
−0.623970 + 0.781449i \(0.714481\pi\)
\(158\) −5.29590 + 3.84770i −0.421319 + 0.306106i
\(159\) −4.91123 + 15.1152i −0.389486 + 1.19871i
\(160\) −0.914982 + 2.81602i −0.0723356 + 0.222626i
\(161\) −5.39378 + 3.91881i −0.425090 + 0.308846i
\(162\) 15.3827 + 11.1762i 1.20858 + 0.878084i
\(163\) −1.56587 4.81927i −0.122649 0.377474i 0.870817 0.491608i \(-0.163591\pi\)
−0.993465 + 0.114134i \(0.963591\pi\)
\(164\) −24.1130 −1.88291
\(165\) 0 0
\(166\) 16.5187 1.28210
\(167\) −6.08976 18.7424i −0.471240 1.45033i −0.850962 0.525227i \(-0.823981\pi\)
0.379722 0.925100i \(-0.376019\pi\)
\(168\) −6.73170 4.89086i −0.519362 0.377338i
\(169\) 10.1715 7.38999i 0.782420 0.568461i
\(170\) 3.00500 9.24842i 0.230473 0.709322i
\(171\) 0.717177 2.20724i 0.0548439 0.168792i
\(172\) −28.7775 + 20.9081i −2.19427 + 1.59423i
\(173\) 11.6456 + 8.46105i 0.885401 + 0.643281i 0.934675 0.355504i \(-0.115691\pi\)
−0.0492739 + 0.998785i \(0.515691\pi\)
\(174\) 5.64089 + 17.3609i 0.427635 + 1.31612i
\(175\) −7.01823 −0.530528
\(176\) 0 0
\(177\) −2.74104 −0.206029
\(178\) −0.532221 1.63801i −0.0398917 0.122774i
\(179\) 3.77342 + 2.74155i 0.282038 + 0.204913i 0.719806 0.694175i \(-0.244231\pi\)
−0.437768 + 0.899088i \(0.644231\pi\)
\(180\) −4.37592 + 3.17929i −0.326162 + 0.236971i
\(181\) 3.06176 9.42311i 0.227578 0.700415i −0.770441 0.637511i \(-0.779964\pi\)
0.998020 0.0629034i \(-0.0200360\pi\)
\(182\) 0.498330 1.53370i 0.0369387 0.113686i
\(183\) 8.97748 6.52252i 0.663634 0.482159i
\(184\) 27.7378 + 20.1527i 2.04486 + 1.48568i
\(185\) 0.471104 + 1.44991i 0.0346362 + 0.106599i
\(186\) −11.1608 −0.818349
\(187\) 0 0
\(188\) −2.47007 −0.180148
\(189\) −1.69098 5.20431i −0.123001 0.378558i
\(190\) −42.0358 30.5408i −3.04960 2.21566i
\(191\) −8.04401 + 5.84432i −0.582044 + 0.422880i −0.839461 0.543421i \(-0.817129\pi\)
0.257416 + 0.966301i \(0.417129\pi\)
\(192\) 3.46236 10.6560i 0.249874 0.769034i
\(193\) 1.14542 3.52523i 0.0824489 0.253752i −0.901331 0.433131i \(-0.857409\pi\)
0.983780 + 0.179379i \(0.0574089\pi\)
\(194\) 29.6524 21.5437i 2.12892 1.54675i
\(195\) 2.96673 + 2.15546i 0.212452 + 0.154355i
\(196\) 1.26226 + 3.88484i 0.0901616 + 0.277489i
\(197\) 5.91982 0.421770 0.210885 0.977511i \(-0.432365\pi\)
0.210885 + 0.977511i \(0.432365\pi\)
\(198\) 0 0
\(199\) 11.4842 0.814095 0.407047 0.913407i \(-0.366558\pi\)
0.407047 + 0.913407i \(0.366558\pi\)
\(200\) 11.1529 + 34.3252i 0.788632 + 2.42716i
\(201\) −8.08747 5.87589i −0.570446 0.414453i
\(202\) −17.2015 + 12.4976i −1.21029 + 0.879330i
\(203\) 1.41331 4.34973i 0.0991950 0.305291i
\(204\) 2.32250 7.14793i 0.162608 0.500455i
\(205\) −16.5562 + 12.0288i −1.15634 + 0.840129i
\(206\) 1.86184 + 1.35270i 0.129720 + 0.0942474i
\(207\) 0.786942 + 2.42196i 0.0546963 + 0.168338i
\(208\) −2.95220 −0.204698
\(209\) 0 0
\(210\) −13.8366 −0.954817
\(211\) 2.69613 + 8.29785i 0.185610 + 0.571247i 0.999958 0.00912833i \(-0.00290568\pi\)
−0.814349 + 0.580376i \(0.802906\pi\)
\(212\) −32.4598 23.5834i −2.22935 1.61971i
\(213\) −7.09077 + 5.15175i −0.485852 + 0.352992i
\(214\) 5.04779 15.5355i 0.345060 1.06198i
\(215\) −9.32892 + 28.7115i −0.636227 + 1.95810i
\(216\) −22.7664 + 16.5407i −1.54906 + 1.12545i
\(217\) 2.26226 + 1.64363i 0.153572 + 0.111577i
\(218\) −3.14438 9.67742i −0.212965 0.655438i
\(219\) −10.8440 −0.732772
\(220\) 0 0
\(221\) 0.743416 0.0500076
\(222\) 0.542383 + 1.66928i 0.0364024 + 0.112035i
\(223\) −8.35944 6.07349i −0.559790 0.406711i 0.271592 0.962412i \(-0.412450\pi\)
−0.831382 + 0.555701i \(0.812450\pi\)
\(224\) 0.690983 0.502029i 0.0461682 0.0335432i
\(225\) −0.828390 + 2.54952i −0.0552260 + 0.169968i
\(226\) −14.3502 + 44.1654i −0.954561 + 2.93784i
\(227\) 10.7348 7.79929i 0.712494 0.517657i −0.171483 0.985187i \(-0.554856\pi\)
0.883977 + 0.467530i \(0.154856\pi\)
\(228\) −32.4887 23.6044i −2.15161 1.56324i
\(229\) −0.771377 2.37405i −0.0509740 0.156882i 0.922329 0.386405i \(-0.126283\pi\)
−0.973303 + 0.229523i \(0.926283\pi\)
\(230\) 57.0135 3.75936
\(231\) 0 0
\(232\) −23.5199 −1.54415
\(233\) −2.96776 9.13384i −0.194425 0.598378i −0.999983 0.00586090i \(-0.998134\pi\)
0.805558 0.592517i \(-0.201866\pi\)
\(234\) −0.498330 0.362058i −0.0325769 0.0236685i
\(235\) −1.69598 + 1.23220i −0.110633 + 0.0803799i
\(236\) 2.13834 6.58114i 0.139194 0.428396i
\(237\) −1.32688 + 4.08370i −0.0861898 + 0.265265i
\(238\) −2.26934 + 1.64877i −0.147099 + 0.106874i
\(239\) −4.50078 3.27001i −0.291131 0.211519i 0.432627 0.901573i \(-0.357587\pi\)
−0.723758 + 0.690054i \(0.757587\pi\)
\(240\) 7.82750 + 24.0906i 0.505263 + 1.55504i
\(241\) 15.0208 0.967572 0.483786 0.875186i \(-0.339261\pi\)
0.483786 + 0.875186i \(0.339261\pi\)
\(242\) 0 0
\(243\) −3.94427 −0.253025
\(244\) 8.65682 + 26.6430i 0.554196 + 1.70564i
\(245\) 2.80464 + 2.03769i 0.179182 + 0.130183i
\(246\) −19.0612 + 13.8488i −1.21530 + 0.882967i
\(247\) 1.22748 3.77780i 0.0781027 0.240375i
\(248\) 4.44372 13.6764i 0.282177 0.868450i
\(249\) 8.76593 6.36882i 0.555519 0.403608i
\(250\) 13.9627 + 10.1445i 0.883081 + 0.641596i
\(251\) 8.53290 + 26.2616i 0.538592 + 1.65762i 0.735757 + 0.677246i \(0.236827\pi\)
−0.197165 + 0.980370i \(0.563173\pi\)
\(252\) 1.56024 0.0982860
\(253\) 0 0
\(254\) −19.6508 −1.23300
\(255\) −1.97110 6.06643i −0.123435 0.379895i
\(256\) 26.2927 + 19.1027i 1.64329 + 1.19392i
\(257\) 23.0311 16.7331i 1.43664 1.04378i 0.447908 0.894080i \(-0.352169\pi\)
0.988732 0.149700i \(-0.0478307\pi\)
\(258\) −10.7404 + 33.0556i −0.668668 + 2.05795i
\(259\) 0.135893 0.418235i 0.00844397 0.0259879i
\(260\) −7.48959 + 5.44150i −0.464484 + 0.337468i
\(261\) −1.41331 1.02683i −0.0874818 0.0635592i
\(262\) −3.66271 11.2727i −0.226283 0.696427i
\(263\) 14.1803 0.874397 0.437199 0.899365i \(-0.355971\pi\)
0.437199 + 0.899365i \(0.355971\pi\)
\(264\) 0 0
\(265\) −34.0519 −2.09179
\(266\) 4.63152 + 14.2544i 0.283977 + 0.873991i
\(267\) −0.913973 0.664040i −0.0559342 0.0406386i
\(268\) 20.4170 14.8338i 1.24717 0.906120i
\(269\) −7.47626 + 23.0095i −0.455835 + 1.40292i 0.414316 + 0.910133i \(0.364021\pi\)
−0.870152 + 0.492784i \(0.835979\pi\)
\(270\) −14.4604 + 44.5046i −0.880034 + 2.70847i
\(271\) −6.02697 + 4.37885i −0.366113 + 0.265996i −0.755597 0.655037i \(-0.772653\pi\)
0.389485 + 0.921033i \(0.372653\pi\)
\(272\) 4.15441 + 3.01836i 0.251898 + 0.183015i
\(273\) −0.326876 1.00602i −0.0197834 0.0608871i
\(274\) −53.9665 −3.26024
\(275\) 0 0
\(276\) 44.0647 2.65238
\(277\) −5.92973 18.2498i −0.356283 1.09653i −0.955262 0.295761i \(-0.904427\pi\)
0.598979 0.800765i \(-0.295573\pi\)
\(278\) 39.5408 + 28.7281i 2.37150 + 1.72300i
\(279\) 0.864107 0.627811i 0.0517327 0.0375860i
\(280\) 5.50911 16.9553i 0.329233 1.01327i
\(281\) −0.587326 + 1.80760i −0.0350370 + 0.107833i −0.967045 0.254604i \(-0.918055\pi\)
0.932009 + 0.362436i \(0.118055\pi\)
\(282\) −1.95258 + 1.41863i −0.116275 + 0.0844785i
\(283\) −5.86681 4.26249i −0.348746 0.253379i 0.399597 0.916691i \(-0.369150\pi\)
−0.748343 + 0.663312i \(0.769150\pi\)
\(284\) −6.83750 21.0437i −0.405731 1.24871i
\(285\) −34.0822 −2.01885
\(286\) 0 0
\(287\) 5.90315 0.348452
\(288\) −0.100813 0.310271i −0.00594047 0.0182829i
\(289\) 12.7071 + 9.23227i 0.747478 + 0.543075i
\(290\) −31.6414 + 22.9888i −1.85805 + 1.34995i
\(291\) 7.42934 22.8652i 0.435516 1.34038i
\(292\) 8.45966 26.0361i 0.495064 1.52365i
\(293\) 2.64627 1.92263i 0.154597 0.112321i −0.507798 0.861476i \(-0.669540\pi\)
0.662394 + 0.749155i \(0.269540\pi\)
\(294\) 3.22899 + 2.34600i 0.188319 + 0.136822i
\(295\) −1.81481 5.58540i −0.105662 0.325195i
\(296\) −2.26148 −0.131446
\(297\) 0 0
\(298\) 7.80008 0.451846
\(299\) 1.34689 + 4.14529i 0.0778924 + 0.239728i
\(300\) 37.5267 + 27.2647i 2.16660 + 1.57413i
\(301\) 7.04508 5.11855i 0.406072 0.295029i
\(302\) 6.80552 20.9452i 0.391614 1.20526i
\(303\) −4.30980 + 13.2642i −0.247591 + 0.762008i
\(304\) 22.1978 16.1276i 1.27313 0.924983i
\(305\) 19.2348 + 13.9749i 1.10138 + 0.800199i
\(306\) 0.331092 + 1.01900i 0.0189273 + 0.0582521i
\(307\) 31.6121 1.80420 0.902099 0.431530i \(-0.142026\pi\)
0.902099 + 0.431530i \(0.142026\pi\)
\(308\) 0 0
\(309\) 1.50956 0.0858758
\(310\) −7.38941 22.7423i −0.419690 1.29167i
\(311\) 7.31213 + 5.31257i 0.414633 + 0.301248i 0.775475 0.631379i \(-0.217511\pi\)
−0.360842 + 0.932627i \(0.617511\pi\)
\(312\) −4.40086 + 3.19741i −0.249149 + 0.181018i
\(313\) 4.48045 13.7894i 0.253250 0.779423i −0.740920 0.671594i \(-0.765610\pi\)
0.994169 0.107829i \(-0.0343900\pi\)
\(314\) 0.868732 2.67368i 0.0490254 0.150885i
\(315\) 1.07128 0.778330i 0.0603597 0.0438539i
\(316\) −8.76971 6.37156i −0.493335 0.358429i
\(317\) −5.69128 17.5160i −0.319654 0.983794i −0.973796 0.227423i \(-0.926970\pi\)
0.654142 0.756372i \(-0.273030\pi\)
\(318\) −39.2040 −2.19845
\(319\) 0 0
\(320\) 24.0061 1.34198
\(321\) −3.31106 10.1904i −0.184805 0.568772i
\(322\) −13.3050 9.66666i −0.741460 0.538702i
\(323\) −5.58980 + 4.06123i −0.311025 + 0.225973i
\(324\) −9.72977 + 29.9452i −0.540543 + 1.66362i
\(325\) −1.41783 + 4.36362i −0.0786468 + 0.242050i
\(326\) 10.1124 7.34709i 0.560074 0.406918i
\(327\) −5.39979 3.92317i −0.298609 0.216952i
\(328\) −9.38092 28.8715i −0.517975 1.59416i
\(329\) 0.604703 0.0333384
\(330\) 0 0
\(331\) −6.47653 −0.355982 −0.177991 0.984032i \(-0.556960\pi\)
−0.177991 + 0.984032i \(0.556960\pi\)
\(332\) 8.45284 + 26.0152i 0.463910 + 1.42777i
\(333\) −0.135893 0.0987319i −0.00744688 0.00541047i
\(334\) 39.3276 28.5732i 2.15191 1.56345i
\(335\) 6.61866 20.3701i 0.361616 1.11294i
\(336\) 2.25789 6.94907i 0.123178 0.379103i
\(337\) −5.06187 + 3.67767i −0.275738 + 0.200335i −0.717056 0.697015i \(-0.754511\pi\)
0.441318 + 0.897351i \(0.354511\pi\)
\(338\) 25.0902 + 18.2291i 1.36473 + 0.991534i
\(339\) 9.41290 + 28.9699i 0.511239 + 1.57343i
\(340\) 16.1030 0.873308
\(341\) 0 0
\(342\) 5.72487 0.309566
\(343\) −0.309017 0.951057i −0.0166853 0.0513522i
\(344\) −36.2298 26.3225i −1.95338 1.41921i
\(345\) 30.2553 21.9818i 1.62889 1.18346i
\(346\) −10.9726 + 33.7702i −0.589891 + 1.81550i
\(347\) 7.01951 21.6038i 0.376827 1.15976i −0.565410 0.824810i \(-0.691282\pi\)
0.942238 0.334945i \(-0.108718\pi\)
\(348\) −24.4550 + 17.7676i −1.31093 + 0.952444i
\(349\) −24.0230 17.4537i −1.28592 0.934277i −0.286207 0.958168i \(-0.592394\pi\)
−0.999715 + 0.0238912i \(0.992394\pi\)
\(350\) −5.34973 16.4648i −0.285955 0.880079i
\(351\) −3.57742 −0.190948
\(352\) 0 0
\(353\) −6.82506 −0.363262 −0.181631 0.983367i \(-0.558138\pi\)
−0.181631 + 0.983367i \(0.558138\pi\)
\(354\) −2.08939 6.43048i −0.111050 0.341776i
\(355\) −15.1924 11.0379i −0.806328 0.585832i
\(356\) 2.30735 1.67639i 0.122289 0.0888483i
\(357\) −0.568577 + 1.74990i −0.0300923 + 0.0926145i
\(358\) −3.55534 + 10.9422i −0.187906 + 0.578314i
\(359\) 5.87322 4.26715i 0.309977 0.225211i −0.421910 0.906638i \(-0.638640\pi\)
0.731887 + 0.681427i \(0.238640\pi\)
\(360\) −5.50911 4.00261i −0.290356 0.210956i
\(361\) 5.53698 + 17.0411i 0.291420 + 0.896898i
\(362\) 24.4405 1.28456
\(363\) 0 0
\(364\) 2.67042 0.139968
\(365\) −7.17969 22.0968i −0.375802 1.15660i
\(366\) 22.1450 + 16.0893i 1.15754 + 0.841002i
\(367\) 29.3969 21.3581i 1.53451 1.11488i 0.580842 0.814016i \(-0.302723\pi\)
0.953666 0.300869i \(-0.0972766\pi\)
\(368\) −9.30360 + 28.6335i −0.484984 + 1.49263i
\(369\) 0.696772 2.14444i 0.0362725 0.111635i
\(370\) −3.04238 + 2.21042i −0.158166 + 0.114914i
\(371\) 7.94654 + 5.77350i 0.412564 + 0.299745i
\(372\) −5.71114 17.5771i −0.296109 0.911328i
\(373\) −14.2913 −0.739977 −0.369989 0.929036i \(-0.620638\pi\)
−0.369989 + 0.929036i \(0.620638\pi\)
\(374\) 0 0
\(375\) 11.3208 0.584605
\(376\) −0.960957 2.95752i −0.0495576 0.152523i
\(377\) −2.41894 1.75747i −0.124582 0.0905141i
\(378\) 10.9203 7.93410i 0.561682 0.408086i
\(379\) −0.786533 + 2.42070i −0.0404015 + 0.124343i −0.969223 0.246184i \(-0.920823\pi\)
0.928821 + 0.370528i \(0.120823\pi\)
\(380\) 26.5882 81.8301i 1.36395 4.19780i
\(381\) −10.4281 + 7.57645i −0.534247 + 0.388153i
\(382\) −19.8424 14.4164i −1.01523 0.737605i
\(383\) −7.14963 22.0043i −0.365329 1.12437i −0.949775 0.312935i \(-0.898688\pi\)
0.584446 0.811433i \(-0.301312\pi\)
\(384\) 30.4023 1.55146
\(385\) 0 0
\(386\) 9.14330 0.465382
\(387\) −1.02786 3.16344i −0.0522493 0.160807i
\(388\) 49.1027 + 35.6752i 2.49281 + 1.81113i
\(389\) −24.4820 + 17.7872i −1.24129 + 0.901849i −0.997684 0.0680260i \(-0.978330\pi\)
−0.243605 + 0.969875i \(0.578330\pi\)
\(390\) −2.79528 + 8.60298i −0.141544 + 0.435629i
\(391\) 2.34281 7.21043i 0.118481 0.364647i
\(392\) −4.16042 + 3.02272i −0.210133 + 0.152670i
\(393\) −6.28990 4.56988i −0.317283 0.230520i
\(394\) 4.51245 + 13.8879i 0.227334 + 0.699663i
\(395\) −9.19985 −0.462894
\(396\) 0 0
\(397\) −22.6740 −1.13798 −0.568989 0.822345i \(-0.692665\pi\)
−0.568989 + 0.822345i \(0.692665\pi\)
\(398\) 8.75399 + 26.9420i 0.438798 + 1.35048i
\(399\) 7.95362 + 5.77864i 0.398179 + 0.289294i
\(400\) −25.6400 + 18.6285i −1.28200 + 0.931427i
\(401\) −5.01182 + 15.4248i −0.250278 + 0.770277i 0.744445 + 0.667684i \(0.232714\pi\)
−0.994723 + 0.102593i \(0.967286\pi\)
\(402\) 7.62007 23.4522i 0.380055 1.16969i
\(403\) 1.47896 1.07453i 0.0736721 0.0535259i
\(404\) −28.4847 20.6953i −1.41717 1.02963i
\(405\) 8.25764 + 25.4144i 0.410325 + 1.26285i
\(406\) 11.2818 0.559905
\(407\) 0 0
\(408\) 9.46207 0.468442
\(409\) −10.8346 33.3454i −0.535735 1.64882i −0.742055 0.670339i \(-0.766149\pi\)
0.206320 0.978485i \(-0.433851\pi\)
\(410\) −40.8398 29.6719i −2.01693 1.46539i
\(411\) −28.6383 + 20.8070i −1.41262 + 1.02633i
\(412\) −1.17764 + 3.62440i −0.0580181 + 0.178561i
\(413\) −0.523492 + 1.61114i −0.0257594 + 0.0792791i
\(414\) −5.08206 + 3.69234i −0.249770 + 0.181468i
\(415\) 18.7815 + 13.6456i 0.921949 + 0.669835i
\(416\) −0.172546 0.531042i −0.00845976 0.0260365i
\(417\) 32.0593 1.56995
\(418\) 0 0
\(419\) 28.2633 1.38075 0.690376 0.723451i \(-0.257445\pi\)
0.690376 + 0.723451i \(0.257445\pi\)
\(420\) −7.08039 21.7912i −0.345488 1.06330i
\(421\) 11.1601 + 8.10831i 0.543911 + 0.395175i 0.825536 0.564350i \(-0.190873\pi\)
−0.281624 + 0.959525i \(0.590873\pi\)
\(422\) −17.4116 + 12.6503i −0.847584 + 0.615806i
\(423\) 0.0713756 0.219671i 0.00347040 0.0106808i
\(424\) 15.6093 48.0403i 0.758052 2.33305i
\(425\) 6.45661 4.69100i 0.313192 0.227547i
\(426\) −17.4910 12.7080i −0.847443 0.615703i
\(427\) −2.11930 6.52252i −0.102560 0.315647i
\(428\) 27.0498 1.30750
\(429\) 0 0
\(430\) −74.4682 −3.59117
\(431\) 8.70502 + 26.7913i 0.419306 + 1.29049i 0.908342 + 0.418228i \(0.137349\pi\)
−0.489036 + 0.872264i \(0.662651\pi\)
\(432\) −19.9916 14.5247i −0.961846 0.698822i
\(433\) −11.4713 + 8.33440i −0.551276 + 0.400526i −0.828256 0.560350i \(-0.810667\pi\)
0.276979 + 0.960876i \(0.410667\pi\)
\(434\) −2.13152 + 6.56015i −0.102316 + 0.314897i
\(435\) −7.92767 + 24.3989i −0.380103 + 1.16984i
\(436\) 13.6319 9.90415i 0.652849 0.474323i
\(437\) −32.7727 23.8108i −1.56773 1.13902i
\(438\) −8.26600 25.4401i −0.394965 1.21558i
\(439\) 28.0185 1.33725 0.668625 0.743599i \(-0.266883\pi\)
0.668625 + 0.743599i \(0.266883\pi\)
\(440\) 0 0
\(441\) −0.381966 −0.0181889
\(442\) 0.566678 + 1.74406i 0.0269541 + 0.0829563i
\(443\) −14.0259 10.1904i −0.666392 0.484162i 0.202424 0.979298i \(-0.435118\pi\)
−0.868815 + 0.495136i \(0.835118\pi\)
\(444\) −2.35140 + 1.70839i −0.111593 + 0.0810767i
\(445\) 0.747981 2.30205i 0.0354577 0.109128i
\(446\) 7.87633 24.2409i 0.372955 1.14784i
\(447\) 4.13926 3.00735i 0.195780 0.142243i
\(448\) −5.60222 4.07025i −0.264680 0.192301i
\(449\) −9.12264 28.0766i −0.430524 1.32502i −0.897604 0.440802i \(-0.854694\pi\)
0.467080 0.884215i \(-0.345306\pi\)
\(450\) −6.61263 −0.311722
\(451\) 0 0
\(452\) −76.8990 −3.61702
\(453\) −4.46403 13.7389i −0.209738 0.645508i
\(454\) 26.4799 + 19.2388i 1.24276 + 0.902920i
\(455\) 1.83354 1.33215i 0.0859577 0.0624519i
\(456\) 15.6231 48.0831i 0.731621 2.25170i
\(457\) 2.99662 9.22263i 0.140176 0.431417i −0.856183 0.516672i \(-0.827171\pi\)
0.996359 + 0.0852555i \(0.0271706\pi\)
\(458\) 4.98154 3.61930i 0.232772 0.169119i
\(459\) 5.03424 + 3.65759i 0.234978 + 0.170722i
\(460\) 29.1746 + 89.7903i 1.36027 + 4.18650i
\(461\) −19.2216 −0.895240 −0.447620 0.894224i \(-0.647728\pi\)
−0.447620 + 0.894224i \(0.647728\pi\)
\(462\) 0 0
\(463\) 20.5327 0.954235 0.477117 0.878840i \(-0.341682\pi\)
0.477117 + 0.878840i \(0.341682\pi\)
\(464\) −6.38220 19.6424i −0.296286 0.911876i
\(465\) −12.6897 9.21959i −0.588470 0.427548i
\(466\) 19.1658 13.9248i 0.887838 0.645052i
\(467\) 10.4050 32.0234i 0.481488 1.48187i −0.355515 0.934671i \(-0.615695\pi\)
0.837003 0.547198i \(-0.184305\pi\)
\(468\) 0.315201 0.970088i 0.0145702 0.0448423i
\(469\) −4.99833 + 3.63150i −0.230801 + 0.167687i
\(470\) −4.18352 3.03951i −0.192972 0.140202i
\(471\) −0.569838 1.75378i −0.0262568 0.0808100i
\(472\) 8.71178 0.400992
\(473\) 0 0
\(474\) −10.5918 −0.486498
\(475\) −13.1774 40.5558i −0.604620 1.86083i
\(476\) −3.75789 2.73027i −0.172243 0.125142i
\(477\) 3.03531 2.20528i 0.138977 0.100973i
\(478\) 4.24067 13.0514i 0.193964 0.596959i
\(479\) 4.37901 13.4772i 0.200082 0.615789i −0.799797 0.600270i \(-0.795060\pi\)
0.999880 0.0155195i \(-0.00494021\pi\)
\(480\) −3.87592 + 2.81602i −0.176911 + 0.128533i
\(481\) −0.232586 0.168984i −0.0106050 0.00770501i
\(482\) 11.4497 + 35.2387i 0.521522 + 1.60508i
\(483\) −10.7876 −0.490851
\(484\) 0 0
\(485\) 51.5111 2.33900
\(486\) −3.00657 9.25327i −0.136381 0.419737i
\(487\) −22.4433 16.3060i −1.01700 0.738897i −0.0513373 0.998681i \(-0.516348\pi\)
−0.965667 + 0.259785i \(0.916348\pi\)
\(488\) −28.5329 + 20.7304i −1.29162 + 0.938420i
\(489\) 2.53364 7.79774i 0.114575 0.352626i
\(490\) −2.64256 + 8.13296i −0.119379 + 0.367410i
\(491\) 2.78541 2.02372i 0.125704 0.0913291i −0.523157 0.852236i \(-0.675246\pi\)
0.648861 + 0.760907i \(0.275246\pi\)
\(492\) −31.5643 22.9328i −1.42303 1.03389i
\(493\) 1.60715 + 4.94631i 0.0723825 + 0.222770i
\(494\) 9.79837 0.440850
\(495\) 0 0
\(496\) 12.6275 0.566992
\(497\) 1.67390 + 5.15175i 0.0750848 + 0.231087i
\(498\) 21.6232 + 15.7102i 0.968959 + 0.703990i
\(499\) 2.09473 1.52191i 0.0937731 0.0681302i −0.539911 0.841722i \(-0.681542\pi\)
0.633684 + 0.773592i \(0.281542\pi\)
\(500\) −8.83162 + 27.1809i −0.394962 + 1.21557i
\(501\) 9.85344 30.3258i 0.440219 1.35486i
\(502\) −55.1054 + 40.0364i −2.45947 + 1.78691i
\(503\) 18.5286 + 13.4618i 0.826151 + 0.600234i 0.918468 0.395496i \(-0.129427\pi\)
−0.0923170 + 0.995730i \(0.529427\pi\)
\(504\) 0.606997 + 1.86814i 0.0270378 + 0.0832137i
\(505\) −29.8818 −1.32972
\(506\) 0 0
\(507\) 20.3429 0.903460
\(508\) −10.0556 30.9480i −0.446146 1.37310i
\(509\) 19.4961 + 14.1648i 0.864150 + 0.627842i 0.929011 0.370052i \(-0.120660\pi\)
−0.0648607 + 0.997894i \(0.520660\pi\)
\(510\) 12.7294 9.24842i 0.563666 0.409527i
\(511\) −2.07103 + 6.37396i −0.0916168 + 0.281968i
\(512\) −13.1605 + 40.5040i −0.581619 + 1.79004i
\(513\) 26.8989 19.5432i 1.18761 0.862852i
\(514\) 56.8115 + 41.2760i 2.50585 + 1.82060i
\(515\) 0.999459 + 3.07602i 0.0440414 + 0.135546i
\(516\) −57.5550 −2.53372
\(517\) 0 0
\(518\) 1.08477 0.0476619
\(519\) 7.19740 + 22.1513i 0.315931 + 0.972334i
\(520\) −9.42909 6.85064i −0.413493 0.300420i
\(521\) 27.1067 19.6942i 1.18757 0.862817i 0.194561 0.980890i \(-0.437672\pi\)
0.993005 + 0.118073i \(0.0376718\pi\)
\(522\) 1.33163 4.09835i 0.0582840 0.179380i
\(523\) −9.62816 + 29.6324i −0.421010 + 1.29574i 0.485754 + 0.874096i \(0.338545\pi\)
−0.906764 + 0.421640i \(0.861455\pi\)
\(524\) 15.8790 11.5368i 0.693677 0.503986i
\(525\) −9.18698 6.67473i −0.400953 0.291309i
\(526\) 10.8091 + 33.2671i 0.471301 + 1.45051i
\(527\) −3.17983 −0.138516
\(528\) 0 0
\(529\) 21.4500 0.932608
\(530\) −25.9564 79.8857i −1.12748 3.47001i
\(531\) 0.523492 + 0.380339i 0.0227176 + 0.0165053i
\(532\) −20.0791 + 14.5883i −0.870539 + 0.632484i
\(533\) 1.19256 3.67031i 0.0516554 0.158979i
\(534\) 0.861152 2.65035i 0.0372657 0.114692i
\(535\) 18.5727 13.4938i 0.802967 0.583390i
\(536\) 25.7042 + 18.6752i 1.11025 + 0.806646i
\(537\) 2.33210 + 7.17747i 0.100638 + 0.309731i
\(538\) −59.6793 −2.57296
\(539\) 0 0
\(540\) −77.4898 −3.33463
\(541\) 6.98599 + 21.5007i 0.300351 + 0.924386i 0.981371 + 0.192121i \(0.0615367\pi\)
−0.681020 + 0.732265i \(0.738463\pi\)
\(542\) −14.8669 10.8015i −0.638589 0.463962i
\(543\) 12.9698 9.42311i 0.556588 0.404385i
\(544\) −0.300131 + 0.923709i −0.0128680 + 0.0396037i
\(545\) 4.41910 13.6006i 0.189293 0.582585i
\(546\) 2.11096 1.53370i 0.0903407 0.0656364i
\(547\) 22.2028 + 16.1313i 0.949324 + 0.689724i 0.950647 0.310275i \(-0.100421\pi\)
−0.00132275 + 0.999999i \(0.500421\pi\)
\(548\) −27.6154 84.9916i −1.17967 3.63066i
\(549\) −2.61959 −0.111801
\(550\) 0 0
\(551\) 27.7891 1.18386
\(552\) 17.1429 + 52.7605i 0.729651 + 2.24564i
\(553\) 2.14693 + 1.55984i 0.0912968 + 0.0663310i
\(554\) 38.2941 27.8223i 1.62696 1.18206i
\(555\) −0.762262 + 2.34600i −0.0323562 + 0.0995822i
\(556\) −25.0101 + 76.9732i −1.06066 + 3.26439i
\(557\) 24.4731 17.7807i 1.03696 0.753393i 0.0672679 0.997735i \(-0.478572\pi\)
0.969689 + 0.244341i \(0.0785718\pi\)
\(558\) 2.13152 + 1.54864i 0.0902345 + 0.0655592i
\(559\) −1.75923 5.41437i −0.0744077 0.229003i
\(560\) 15.6550 0.661544
\(561\) 0 0
\(562\) −4.68834 −0.197766
\(563\) 2.30599 + 7.09711i 0.0971859 + 0.299107i 0.987817 0.155619i \(-0.0497371\pi\)
−0.890631 + 0.454726i \(0.849737\pi\)
\(564\) −3.23337 2.34918i −0.136149 0.0989182i
\(565\) −52.7997 + 38.3612i −2.22130 + 1.61387i
\(566\) 5.52775 17.0127i 0.232349 0.715096i
\(567\) 2.38197 7.33094i 0.100033 0.307870i
\(568\) 22.5364 16.3737i 0.945607 0.687024i
\(569\) −28.8401 20.9536i −1.20904 0.878419i −0.213896 0.976856i \(-0.568616\pi\)
−0.995143 + 0.0984376i \(0.968616\pi\)
\(570\) −25.9795 79.9568i −1.08816 3.34902i
\(571\) 25.8902 1.08347 0.541737 0.840548i \(-0.317767\pi\)
0.541737 + 0.840548i \(0.317767\pi\)
\(572\) 0 0
\(573\) −16.0880 −0.672087
\(574\) 4.49975 + 13.8488i 0.187816 + 0.578038i
\(575\) 37.8548 + 27.5031i 1.57865 + 1.14696i
\(576\) −2.13986 + 1.55470i −0.0891607 + 0.0647790i
\(577\) 2.52276 7.76425i 0.105024 0.323230i −0.884712 0.466138i \(-0.845645\pi\)
0.989736 + 0.142908i \(0.0456452\pi\)
\(578\) −11.9728 + 36.8484i −0.498001 + 1.53269i
\(579\) 4.85206 3.52523i 0.201645 0.146504i
\(580\) −52.3963 38.0681i −2.17564 1.58069i
\(581\) −2.06936 6.36882i −0.0858514 0.264223i
\(582\) 59.3048 2.45826
\(583\) 0 0
\(584\) 34.4653 1.42619
\(585\) −0.267510 0.823311i −0.0110602 0.0340397i
\(586\) 6.52764 + 4.74260i 0.269654 + 0.195915i
\(587\) 10.0831 7.32580i 0.416174 0.302368i −0.359923 0.932982i \(-0.617197\pi\)
0.776097 + 0.630614i \(0.217197\pi\)
\(588\) −2.04238 + 6.28581i −0.0842265 + 0.259222i
\(589\) −5.25033 + 16.1589i −0.216336 + 0.665815i
\(590\) 11.7200 8.51508i 0.482505 0.350560i
\(591\) 7.74915 + 5.63008i 0.318757 + 0.231591i
\(592\) −0.613662 1.88866i −0.0252214 0.0776233i
\(593\) −23.6707 −0.972037 −0.486019 0.873948i \(-0.661551\pi\)
−0.486019 + 0.873948i \(0.661551\pi\)
\(594\) 0 0
\(595\) −3.94221 −0.161615
\(596\) 3.99141 + 12.2843i 0.163495 + 0.503185i
\(597\) 15.0330 + 10.9221i 0.615261 + 0.447014i
\(598\) −8.69818 + 6.31959i −0.355695 + 0.258427i
\(599\) 12.0458 37.0730i 0.492176 1.51476i −0.329136 0.944283i \(-0.606757\pi\)
0.821312 0.570480i \(-0.193243\pi\)
\(600\) −18.0458 + 55.5393i −0.736718 + 2.26738i
\(601\) −24.7163 + 17.9574i −1.00820 + 0.732499i −0.963830 0.266517i \(-0.914127\pi\)
−0.0443675 + 0.999015i \(0.514127\pi\)
\(602\) 17.3783 + 12.6261i 0.708288 + 0.514601i
\(603\) 0.729247 + 2.24439i 0.0296972 + 0.0913986i
\(604\) 36.4690 1.48390
\(605\) 0 0
\(606\) −34.4030 −1.39753
\(607\) 11.6244 + 35.7762i 0.471819 + 1.45211i 0.850200 + 0.526460i \(0.176481\pi\)
−0.378380 + 0.925650i \(0.623519\pi\)
\(608\) 4.19843 + 3.05034i 0.170269 + 0.123707i
\(609\) 5.98688 4.34973i 0.242601 0.176260i
\(610\) −18.1231 + 55.7773i −0.733785 + 2.25836i
\(611\) 0.122162 0.375977i 0.00494216 0.0152104i
\(612\) −1.43539 + 1.04287i −0.0580221 + 0.0421555i
\(613\) −14.2607 10.3610i −0.575985 0.418477i 0.261290 0.965260i \(-0.415852\pi\)
−0.837274 + 0.546783i \(0.815852\pi\)
\(614\) 24.0967 + 74.1620i 0.972464 + 2.99294i
\(615\) −33.1125 −1.33522
\(616\) 0 0
\(617\) −44.4849 −1.79089 −0.895447 0.445168i \(-0.853144\pi\)
−0.895447 + 0.445168i \(0.853144\pi\)
\(618\) 1.15068 + 3.54143i 0.0462871 + 0.142457i
\(619\) 5.01933 + 3.64676i 0.201744 + 0.146576i 0.684070 0.729416i \(-0.260208\pi\)
−0.482326 + 0.875992i \(0.660208\pi\)
\(620\) 32.0354 23.2751i 1.28657 0.934750i
\(621\) −11.2739 + 34.6976i −0.452407 + 1.39237i
\(622\) −6.88954 + 21.2038i −0.276246 + 0.850196i
\(623\) −0.564866 + 0.410399i −0.0226309 + 0.0164423i
\(624\) −3.86448 2.80771i −0.154703 0.112398i
\(625\) −3.34839 10.3053i −0.133935 0.412211i
\(626\) 35.7652 1.42947
\(627\) 0 0
\(628\) 4.65531 0.185767
\(629\) 0.154531 + 0.475598i 0.00616156 + 0.0189633i
\(630\) 2.64256 + 1.91993i 0.105282 + 0.0764919i
\(631\) −36.2486 + 26.3361i −1.44303 + 1.04843i −0.455636 + 0.890166i \(0.650588\pi\)
−0.987398 + 0.158259i \(0.949412\pi\)
\(632\) 4.21718 12.9791i 0.167750 0.516282i
\(633\) −4.36244 + 13.4262i −0.173391 + 0.533644i
\(634\) 36.7542 26.7035i 1.45970 1.06053i
\(635\) −22.3428 16.2330i −0.886646 0.644186i
\(636\) −20.0612 61.7421i −0.795480 2.44823i
\(637\) −0.653752 −0.0259026
\(638\) 0 0
\(639\) 2.06906 0.0818507
\(640\) 20.1289 + 61.9505i 0.795666 + 2.44881i
\(641\) 8.31316 + 6.03986i 0.328350 + 0.238560i 0.739730 0.672904i \(-0.234953\pi\)
−0.411380 + 0.911464i \(0.634953\pi\)
\(642\) 21.3828 15.5355i 0.843911 0.613137i
\(643\) −5.08165 + 15.6397i −0.200401 + 0.616771i 0.799470 + 0.600706i \(0.205114\pi\)
−0.999871 + 0.0160646i \(0.994886\pi\)
\(644\) 8.41560 25.9006i 0.331621 1.02063i
\(645\) −39.5179 + 28.7115i −1.55602 + 1.13051i
\(646\) −13.7885 10.0180i −0.542503 0.394151i
\(647\) −8.33377 25.6487i −0.327634 1.00835i −0.970237 0.242156i \(-0.922146\pi\)
0.642603 0.766199i \(-0.277854\pi\)
\(648\) −39.6399 −1.55720
\(649\) 0 0
\(650\) −11.3178 −0.443921
\(651\) 1.39815 + 4.30308i 0.0547980 + 0.168651i
\(652\) 16.7456 + 12.1664i 0.655806 + 0.476471i
\(653\) −5.74889 + 4.17682i −0.224972 + 0.163451i −0.694562 0.719433i \(-0.744402\pi\)
0.469590 + 0.882885i \(0.344402\pi\)
\(654\) 5.08772 15.6584i 0.198946 0.612292i
\(655\) 5.14755 15.8425i 0.201132 0.619019i
\(656\) 21.5662 15.6688i 0.842020 0.611763i
\(657\) 2.07103 + 1.50469i 0.0807984 + 0.0587035i
\(658\) 0.460942 + 1.41863i 0.0179694 + 0.0553041i
\(659\) −32.6279 −1.27100 −0.635502 0.772099i \(-0.719207\pi\)
−0.635502 + 0.772099i \(0.719207\pi\)
\(660\) 0 0
\(661\) −33.8165 −1.31531 −0.657654 0.753320i \(-0.728451\pi\)
−0.657654 + 0.753320i \(0.728451\pi\)
\(662\) −4.93681 15.1939i −0.191875 0.590530i
\(663\) 0.973144 + 0.707031i 0.0377938 + 0.0274588i
\(664\) −27.8606 + 20.2419i −1.08120 + 0.785537i
\(665\) −6.50911 + 20.0330i −0.252413 + 0.776846i
\(666\) 0.128039 0.394064i 0.00496142 0.0152697i
\(667\) −24.6689 + 17.9230i −0.955182 + 0.693980i
\(668\) 65.1242 + 47.3155i 2.51973 + 1.83069i
\(669\) −5.16642 15.9006i −0.199745 0.614753i
\(670\) 52.8335 2.04114
\(671\) 0 0
\(672\) 1.38197 0.0533105
\(673\) 7.33902 + 22.5872i 0.282898 + 0.870672i 0.987021 + 0.160593i \(0.0513406\pi\)
−0.704122 + 0.710079i \(0.748659\pi\)
\(674\) −12.4863 9.07182i −0.480954 0.349433i
\(675\) −31.0701 + 22.5737i −1.19589 + 0.868863i
\(676\) −15.8699 + 48.8426i −0.610382 + 1.87856i
\(677\) −14.1008 + 43.3978i −0.541938 + 1.66791i 0.186224 + 0.982507i \(0.440375\pi\)
−0.728162 + 0.685405i \(0.759625\pi\)
\(678\) −60.7884 + 44.1654i −2.33456 + 1.69616i
\(679\) −12.0209 8.73372i −0.461321 0.335169i
\(680\) 6.26471 + 19.2808i 0.240241 + 0.739385i
\(681\) 21.4696 0.822717
\(682\) 0 0
\(683\) −28.8727 −1.10478 −0.552392 0.833585i \(-0.686285\pi\)
−0.552392 + 0.833585i \(0.686285\pi\)
\(684\) 2.92950 + 9.01608i 0.112012 + 0.344738i
\(685\) −61.3593 44.5801i −2.34442 1.70332i
\(686\) 1.99563 1.44991i 0.0761934 0.0553578i
\(687\) 1.24811 3.84130i 0.0476185 0.146555i
\(688\) 12.1519 37.3997i 0.463286 1.42585i
\(689\) 5.19506 3.77444i 0.197916 0.143795i
\(690\) 74.6317 + 54.2231i 2.84118 + 2.06424i
\(691\) −8.36308 25.7389i −0.318146 0.979154i −0.974440 0.224648i \(-0.927877\pi\)
0.656294 0.754506i \(-0.272123\pi\)
\(692\) −58.7994 −2.23522
\(693\) 0 0
\(694\) 56.0334 2.12700
\(695\) 21.2260 + 65.3270i 0.805149 + 2.47799i
\(696\) −30.7879 22.3687i −1.16701 0.847884i
\(697\) −5.43076 + 3.94568i −0.205705 + 0.149453i
\(698\) 22.6347 69.6623i 0.856734 2.63676i
\(699\) 4.80194 14.7789i 0.181626 0.558988i
\(700\) 23.1928 16.8505i 0.876604 0.636890i
\(701\) −31.1598 22.6389i −1.17689 0.855060i −0.185071 0.982725i \(-0.559252\pi\)
−0.991817 + 0.127665i \(0.959252\pi\)
\(702\) −2.72693 8.39263i −0.102921 0.316759i
\(703\) 2.67198 0.100776
\(704\) 0 0
\(705\) −3.39196 −0.127748
\(706\) −5.20249 16.0116i −0.195798 0.602605i
\(707\) 6.97340 + 5.06647i 0.262262 + 0.190544i
\(708\) 9.05816 6.58114i 0.340427 0.247334i
\(709\) −0.585477 + 1.80191i −0.0219880 + 0.0676722i −0.961448 0.274985i \(-0.911327\pi\)
0.939460 + 0.342657i \(0.111327\pi\)
\(710\) 14.3144 44.0551i 0.537209 1.65336i
\(711\) 0.820054 0.595804i 0.0307544 0.0223444i
\(712\) 2.90486 + 2.11050i 0.108864 + 0.0790944i
\(713\) −5.76107 17.7308i −0.215754 0.664022i
\(714\) −4.53867 −0.169856
\(715\) 0 0
\(716\) −19.0522 −0.712013
\(717\) −2.78163 8.56099i −0.103882 0.319716i
\(718\) 14.4877 + 10.5259i 0.540675 + 0.392823i
\(719\) −11.7932 + 8.56828i −0.439813 + 0.319543i −0.785561 0.618785i \(-0.787625\pi\)
0.345748 + 0.938328i \(0.387625\pi\)
\(720\) 1.84782 5.68701i 0.0688643 0.211942i
\(721\) 0.288300 0.887296i 0.0107369 0.0330446i
\(722\) −35.7577 + 25.9795i −1.33077 + 0.966858i
\(723\) 19.6624 + 14.2856i 0.731253 + 0.531287i
\(724\) 12.5066 + 38.4912i 0.464802 + 1.43051i
\(725\) −32.0984 −1.19210
\(726\) 0 0
\(727\) 4.04780 0.150125 0.0750623 0.997179i \(-0.476084\pi\)
0.0750623 + 0.997179i \(0.476084\pi\)
\(728\) 1.03890 + 3.19741i 0.0385042 + 0.118504i
\(729\) −23.8713 17.3435i −0.884123 0.642353i
\(730\) 46.3664 33.6871i 1.71610 1.24682i
\(731\) −3.06006 + 9.41790i −0.113180 + 0.348334i
\(732\) −14.0070 + 43.1092i −0.517715 + 1.59336i
\(733\) 19.0128 13.8136i 0.702256 0.510219i −0.178410 0.983956i \(-0.557095\pi\)
0.880666 + 0.473738i \(0.157095\pi\)
\(734\) 72.5144 + 52.6848i 2.67655 + 1.94463i
\(735\) 1.73337 + 5.33475i 0.0639362 + 0.196775i
\(736\) −5.69437 −0.209897
\(737\) 0 0
\(738\) 5.56199 0.204740
\(739\) −10.0983 31.0792i −0.371470 1.14327i −0.945829 0.324664i \(-0.894749\pi\)
0.574359 0.818603i \(-0.305251\pi\)
\(740\) −5.03801 3.66033i −0.185201 0.134556i
\(741\) 5.19969 3.77780i 0.191015 0.138781i
\(742\) −7.48729 + 23.0435i −0.274867 + 0.845954i
\(743\) −5.59500 + 17.2196i −0.205261 + 0.631727i 0.794442 + 0.607340i \(0.207763\pi\)
−0.999703 + 0.0243872i \(0.992237\pi\)
\(744\) 18.8239 13.6764i 0.690118 0.501400i
\(745\) 8.86860 + 6.44341i 0.324920 + 0.236068i
\(746\) −10.8937 33.5275i −0.398848 1.22753i
\(747\) −2.55787 −0.0935874
\(748\) 0 0
\(749\) −6.62212 −0.241967
\(750\) 8.62944 + 26.5587i 0.315103 + 0.969786i
\(751\) −7.39730 5.37445i −0.269931 0.196117i 0.444582 0.895738i \(-0.353352\pi\)
−0.714514 + 0.699621i \(0.753352\pi\)
\(752\) 2.20919 1.60507i 0.0805608 0.0585309i
\(753\) −13.8065 + 42.4921i −0.503138 + 1.54850i
\(754\) 2.27915 7.01450i 0.0830017 0.255453i
\(755\) 25.0400 18.1927i 0.911300 0.662098i
\(756\) 18.0835 + 13.1384i 0.657689 + 0.477839i
\(757\) 14.6322 + 45.0334i 0.531818 + 1.63677i 0.750426 + 0.660954i \(0.229848\pi\)
−0.218608 + 0.975813i \(0.570152\pi\)
\(758\) −6.27851 −0.228046
\(759\) 0 0
\(760\) 108.323 3.92927
\(761\) 1.06558 + 3.27951i 0.0386271 + 0.118882i 0.968511 0.248972i \(-0.0800926\pi\)
−0.929884 + 0.367854i \(0.880093\pi\)
\(762\) −25.7233 18.6891i −0.931856 0.677033i
\(763\) −3.33725 + 2.42466i −0.120817 + 0.0877784i
\(764\) 12.5506 38.6268i 0.454065 1.39747i
\(765\) −0.465315 + 1.43209i −0.0168235 + 0.0517774i
\(766\) 46.1722 33.5461i 1.66827 1.21207i
\(767\) 0.895980 + 0.650967i 0.0323519 + 0.0235051i
\(768\) 16.2498 + 50.0116i 0.586363 + 1.80464i
\(769\) 34.9787 1.26137 0.630683 0.776041i \(-0.282775\pi\)
0.630683 + 0.776041i \(0.282775\pi\)
\(770\) 0 0
\(771\) 46.0622 1.65889
\(772\) 4.67876 + 14.3997i 0.168392 + 0.518258i
\(773\) −20.5323 14.9176i −0.738497 0.536549i 0.153743 0.988111i \(-0.450867\pi\)
−0.892240 + 0.451561i \(0.850867\pi\)
\(774\) 6.63793 4.82274i 0.238596 0.173350i
\(775\) 6.06450 18.6646i 0.217843 0.670453i
\(776\) −23.6125 + 72.6718i −0.847639 + 2.60877i
\(777\) 0.575651 0.418235i 0.0206514 0.0150041i
\(778\) −60.3906 43.8763i −2.16511 1.57304i
\(779\) 11.0837 + 34.1122i 0.397115 + 1.22220i
\(780\) −14.9792 −0.536340
\(781\) 0 0
\(782\) 18.7015 0.668765
\(783\) −7.73383 23.8023i −0.276385 0.850624i
\(784\) −3.65334 2.65431i −0.130477 0.0947967i
\(785\) 3.19639 2.32231i 0.114084 0.0828868i
\(786\) 5.92639 18.2396i 0.211387 0.650583i
\(787\) 9.19486 28.2989i 0.327761 1.00875i −0.642417 0.766355i \(-0.722068\pi\)
0.970179 0.242391i \(-0.0779316\pi\)
\(788\) −19.5629 + 14.2133i −0.696900 + 0.506327i
\(789\) 18.5623 + 13.4863i 0.660836 + 0.480125i
\(790\) −7.01269 21.5828i −0.249500 0.767883i
\(791\) 18.8258 0.669369
\(792\) 0 0
\(793\) −4.48355 −0.159215
\(794\) −17.2836 53.1933i −0.613371 1.88776i
\(795\) −44.5745 32.3852i −1.58089 1.14859i
\(796\) −37.9513 + 27.5732i −1.34515 + 0.977307i
\(797\) −1.92929 + 5.93773i −0.0683388 + 0.210325i −0.979394 0.201959i \(-0.935269\pi\)
0.911055 + 0.412285i \(0.135269\pi\)
\(798\) −7.49396 + 23.0640i −0.265283 + 0.816458i
\(799\) −0.556313 + 0.404185i −0.0196809 + 0.0142990i
\(800\) −4.84948 3.52335i −0.171455 0.124569i
\(801\) 0.0824129 + 0.253641i 0.00291192 + 0.00896196i
\(802\) −40.0069 −1.41269
\(803\) 0 0
\(804\) 40.8340 1.44010
\(805\) −7.14231 21.9818i −0.251733 0.774755i
\(806\) 3.64819 + 2.65057i 0.128502 + 0.0933622i
\(807\) −31.6699 + 23.0095i −1.11483 + 0.809974i
\(808\) 13.6977 42.1573i 0.481884 1.48309i
\(809\) 12.1091 37.2681i 0.425735 1.31028i −0.476554 0.879145i \(-0.658114\pi\)
0.902289 0.431132i \(-0.141886\pi\)
\(810\) −53.3277 + 38.7449i −1.87375 + 1.36136i
\(811\) 10.0164 + 7.27732i 0.351722 + 0.255541i 0.749591 0.661901i \(-0.230250\pi\)
−0.397869 + 0.917442i \(0.630250\pi\)
\(812\) 5.77305 + 17.7676i 0.202594 + 0.623521i
\(813\) −12.0539 −0.422750
\(814\) 0 0
\(815\) 17.5669 0.615341
\(816\) 2.56757 + 7.90216i 0.0898829 + 0.276631i
\(817\) 42.8061 + 31.1004i 1.49760 + 1.08807i
\(818\) 69.9695 50.8358i 2.44643 1.77743i
\(819\) −0.0771649 + 0.237489i −0.00269636 + 0.00829854i
\(820\) 25.8317 79.5019i 0.902083 2.77633i
\(821\) −38.5891 + 28.0366i −1.34677 + 0.978484i −0.347603 + 0.937642i \(0.613004\pi\)
−0.999166 + 0.0408426i \(0.986996\pi\)
\(822\) −70.6431 51.3252i −2.46396 1.79017i
\(823\) −4.48715 13.8100i −0.156412 0.481387i 0.841889 0.539651i \(-0.181444\pi\)
−0.998301 + 0.0582633i \(0.981444\pi\)
\(824\) −4.79779 −0.167139
\(825\) 0 0
\(826\) −4.17878 −0.145398
\(827\) −9.56013 29.4231i −0.332438 1.02314i −0.967970 0.251065i \(-0.919219\pi\)
0.635532 0.772075i \(-0.280781\pi\)
\(828\) −8.41560 6.11429i −0.292462 0.212486i
\(829\) −0.0694183 + 0.0504353i −0.00241100 + 0.00175169i −0.588990 0.808140i \(-0.700474\pi\)
0.586579 + 0.809892i \(0.300474\pi\)
\(830\) −17.6961 + 54.4630i −0.614240 + 1.89044i
\(831\) 9.59450 29.5288i 0.332830 1.02434i
\(832\) −3.66246 + 2.66093i −0.126973 + 0.0922512i
\(833\) 0.919977 + 0.668402i 0.0318753 + 0.0231588i
\(834\) 24.4376 + 75.2111i 0.846204 + 2.60435i
\(835\) 68.3185 2.36426
\(836\) 0 0
\(837\) 15.3018 0.528907
\(838\) 21.5440 + 66.3057i 0.744226 + 2.29049i
\(839\) −8.64881 6.28373i −0.298590 0.216939i 0.428395 0.903592i \(-0.359079\pi\)
−0.726985 + 0.686653i \(0.759079\pi\)
\(840\) 23.3370 16.9553i 0.805202 0.585014i
\(841\) −2.49761 + 7.68685i −0.0861245 + 0.265064i
\(842\) −10.5152 + 32.3623i −0.362376 + 1.11528i
\(843\) −2.48795 + 1.80760i −0.0856897 + 0.0622572i
\(844\) −28.8326 20.9481i −0.992459 0.721064i
\(845\) 13.4688 + 41.4526i 0.463340 + 1.42601i
\(846\) 0.569756 0.0195886
\(847\) 0 0
\(848\) 44.3561 1.52319
\(849\) −3.62589 11.1593i −0.124440 0.382987i
\(850\) 15.9267 + 11.5714i 0.546282 + 0.396897i
\(851\) −2.37196 + 1.72333i −0.0813098 + 0.0590750i
\(852\) 11.0633 34.0494i 0.379023 1.16651i
\(853\) 6.55124 20.1627i 0.224310 0.690356i −0.774051 0.633124i \(-0.781772\pi\)
0.998361 0.0572325i \(-0.0182276\pi\)
\(854\) 13.6864 9.94374i 0.468338 0.340268i
\(855\) 6.50911 + 4.72915i 0.222607 + 0.161733i
\(856\) 10.5235 + 32.3879i 0.359684 + 1.10699i
\(857\) −9.45359 −0.322929 −0.161464 0.986879i \(-0.551622\pi\)
−0.161464 + 0.986879i \(0.551622\pi\)
\(858\) 0 0
\(859\) −38.8261 −1.32473 −0.662365 0.749181i \(-0.730447\pi\)
−0.662365 + 0.749181i \(0.730447\pi\)
\(860\) −38.1064 117.280i −1.29942 3.99920i
\(861\) 7.72732 + 5.61423i 0.263346 + 0.191332i
\(862\) −56.2169 + 40.8440i −1.91476 + 1.39115i
\(863\) −11.6205 + 35.7641i −0.395565 + 1.21742i 0.532955 + 0.846144i \(0.321081\pi\)
−0.928520 + 0.371281i \(0.878919\pi\)
\(864\) 1.44427 4.44501i 0.0491351 0.151222i
\(865\) −40.3723 + 29.3322i −1.37270 + 0.997324i
\(866\) −28.2967 20.5587i −0.961560 0.698614i
\(867\) 7.85344 + 24.1704i 0.266717 + 0.820870i
\(868\) −11.4223 −0.387697
\(869\) 0 0
\(870\) −63.2828 −2.14549
\(871\) 1.24814 + 3.84137i 0.0422915 + 0.130160i
\(872\) 17.1620 + 12.4689i 0.581179 + 0.422251i
\(873\) −4.59159 + 3.33598i −0.155402 + 0.112906i
\(874\) 30.8787 95.0350i 1.04449 3.21461i
\(875\) 2.16209 6.65422i 0.0730919 0.224954i
\(876\) 35.8357 26.0361i 1.21078 0.879680i
\(877\) −17.8053 12.9363i −0.601243 0.436829i 0.245077 0.969504i \(-0.421187\pi\)
−0.846320 + 0.532675i \(0.821187\pi\)
\(878\) 21.3574 + 65.7315i 0.720779 + 2.21833i
\(879\) 5.29254 0.178513
\(880\) 0 0
\(881\) −6.92969 −0.233467 −0.116734 0.993163i \(-0.537242\pi\)
−0.116734 + 0.993163i \(0.537242\pi\)
\(882\) −0.291158 0.896093i −0.00980381 0.0301730i
\(883\) −34.2528 24.8861i −1.15270 0.837485i −0.163861 0.986483i \(-0.552395\pi\)
−0.988837 + 0.148999i \(0.952395\pi\)
\(884\) −2.45673 + 1.78492i −0.0826287 + 0.0600332i
\(885\) 2.93642 9.03737i 0.0987066 0.303788i
\(886\) 13.2153 40.6726i 0.443978 1.36642i
\(887\) −6.51782 + 4.73547i −0.218847 + 0.159002i −0.691807 0.722082i \(-0.743185\pi\)
0.472961 + 0.881084i \(0.343185\pi\)
\(888\) −2.96032 2.15080i −0.0993418 0.0721760i
\(889\) 2.46174 + 7.57645i 0.0825640 + 0.254106i
\(890\) 5.97077 0.200141
\(891\) 0 0
\(892\) 42.2072 1.41320
\(893\) 1.13539 + 3.49436i 0.0379943 + 0.116934i
\(894\) 10.2104 + 7.41832i 0.341488 + 0.248106i
\(895\) −13.0814 + 9.50421i −0.437264 + 0.317691i
\(896\) 5.80631 17.8700i 0.193975 0.596995i
\(897\) −2.17931 + 6.70722i −0.0727650 + 0.223948i
\(898\) 58.9139 42.8035i 1.96598 1.42837i
\(899\) 10.3466 + 7.51726i 0.345079 + 0.250715i
\(900\) −3.38378 10.4142i −0.112793 0.347140i
\(901\) −11.1697 −0.372115
\(902\) 0 0
\(903\) 14.0902 0.468891
\(904\) −29.9168 92.0744i −0.995018 3.06235i
\(905\) 27.7886 + 20.1896i 0.923723 + 0.671124i
\(906\) 28.8286 20.9452i 0.957768 0.695859i
\(907\) 0.894385 2.75263i 0.0296976 0.0913997i −0.935109 0.354360i \(-0.884699\pi\)
0.964807 + 0.262960i \(0.0846988\pi\)
\(908\) −16.7489 + 51.5478i −0.555832 + 1.71067i
\(909\) 2.66360 1.93522i 0.0883461 0.0641872i
\(910\) 4.52285 + 3.28605i 0.149931 + 0.108931i
\(911\) −6.25759 19.2589i −0.207323 0.638075i −0.999610 0.0279265i \(-0.991110\pi\)
0.792287 0.610149i \(-0.208890\pi\)
\(912\) 44.3956 1.47008
\(913\) 0 0
\(914\) 23.9205 0.791220
\(915\) 11.8877 + 36.5867i 0.392997 + 1.20952i
\(916\) 8.24915 + 5.99336i 0.272559 + 0.198026i
\(917\) −3.88737 + 2.82434i −0.128372 + 0.0932679i
\(918\) −4.74330 + 14.5984i −0.156552 + 0.481818i
\(919\) 5.78669 17.8096i 0.190885 0.587484i −0.809115 0.587651i \(-0.800053\pi\)
1.00000 0.000166260i \(5.29223e-5\pi\)
\(920\) −96.1597 + 69.8641i −3.17029 + 2.30335i
\(921\) 41.3808 + 30.0649i 1.36354 + 0.990672i
\(922\) −14.6519 45.0939i −0.482535 1.48509i
\(923\) 3.54128 0.116563
\(924\) 0 0
\(925\) −3.08632 −0.101478
\(926\) 15.6513 + 48.1697i 0.514333 + 1.58295i
\(927\) −0.288300 0.209462i −0.00946901 0.00687964i
\(928\) 3.16026 2.29606i 0.103741 0.0753720i
\(929\) −13.9892 + 43.0544i −0.458971 + 1.41257i 0.407437 + 0.913233i \(0.366423\pi\)
−0.866409 + 0.499336i \(0.833577\pi\)
\(930\) 11.9563 36.7978i 0.392063 1.20665i
\(931\) 4.91560 3.57140i 0.161102 0.117048i
\(932\) 31.7374 + 23.0586i 1.03959 + 0.755309i
\(933\) 4.51914 + 13.9085i 0.147950 + 0.455344i
\(934\) 83.0584 2.71775
\(935\) 0 0
\(936\) 1.28415 0.0419738
\(937\) 9.10361 + 28.0180i 0.297402 + 0.915309i 0.982404 + 0.186768i \(0.0598013\pi\)
−0.685002 + 0.728541i \(0.740199\pi\)
\(938\) −12.3295 8.95793i −0.402574 0.292487i
\(939\) 18.9795 13.7894i 0.619372 0.450000i
\(940\) 2.64614 8.14397i 0.0863074 0.265627i
\(941\) 17.9955 55.3844i 0.586636 1.80548i −0.00596369 0.999982i \(-0.501898\pi\)
0.592600 0.805497i \(-0.298102\pi\)
\(942\) 3.68001 2.67368i 0.119901 0.0871133i
\(943\) −31.8403 23.1333i −1.03686 0.753325i
\(944\) 2.36397 + 7.27557i 0.0769408 + 0.236800i
\(945\) 18.9704 0.617108
\(946\) 0 0
\(947\) 45.3642 1.47414 0.737069 0.675818i \(-0.236209\pi\)
0.737069 + 0.675818i \(0.236209\pi\)
\(948\) −5.41998 16.6810i −0.176033 0.541773i
\(949\) 3.54465 + 2.57534i 0.115064 + 0.0835991i
\(950\) 85.0994 61.8283i 2.76099 2.00598i
\(951\) 9.20869 28.3414i 0.298612 0.919034i
\(952\) 1.80709 5.56166i 0.0585683 0.180255i
\(953\) 33.4428 24.2976i 1.08332 0.787076i 0.105059 0.994466i \(-0.466497\pi\)
0.978258 + 0.207390i \(0.0664969\pi\)
\(954\) 7.48729 + 5.43984i 0.242410 + 0.176121i
\(955\) −10.6517 32.7825i −0.344680 1.06082i
\(956\) 22.7247 0.734968
\(957\) 0 0
\(958\) 34.9555 1.12936
\(959\) 6.76059 + 20.8070i 0.218311 + 0.671892i
\(960\) 31.4245 + 22.8312i 1.01422 + 0.736874i
\(961\) 18.7535 13.6252i 0.604953 0.439524i
\(962\) 0.219145 0.674458i 0.00706551 0.0217454i
\(963\) −0.781635 + 2.40562i −0.0251878 + 0.0775202i
\(964\) −49.6383 + 36.0643i −1.59874 + 1.16155i
\(965\) 10.3958 + 7.55301i 0.334653 + 0.243140i
\(966\) −8.22295 25.3076i −0.264569 0.814260i
\(967\) −6.52818 −0.209932 −0.104966 0.994476i \(-0.533473\pi\)
−0.104966 + 0.994476i \(0.533473\pi\)
\(968\) 0 0
\(969\) −11.1796 −0.359140
\(970\) 39.2649 + 120.845i 1.26072 + 3.88010i
\(971\) −23.3472 16.9627i −0.749246 0.544359i 0.146347 0.989233i \(-0.453248\pi\)
−0.895593 + 0.444874i \(0.853248\pi\)
\(972\) 13.0344 9.47006i 0.418079 0.303752i
\(973\) 6.12278 18.8440i 0.196287 0.604110i
\(974\) 21.1463 65.0815i 0.677570 2.08535i
\(975\) −6.00600 + 4.36362i −0.192346 + 0.139748i
\(976\) −25.0553 18.2037i −0.802000 0.582687i
\(977\) −2.77637 8.54479i −0.0888240 0.273372i 0.896771 0.442495i \(-0.145907\pi\)
−0.985595 + 0.169123i \(0.945907\pi\)
\(978\) 20.2248 0.646718
\(979\) 0 0
\(980\) −14.1608 −0.452350
\(981\) 0.486898 + 1.49852i 0.0155455 + 0.0478440i
\(982\) 6.87085 + 4.99197i 0.219258 + 0.159300i
\(983\) −29.8381 + 21.6786i −0.951687 + 0.691441i −0.951205 0.308559i \(-0.900153\pi\)
−0.000481513 1.00000i \(0.500153\pi\)
\(984\) 15.1786 46.7151i 0.483878 1.48922i
\(985\) −6.34178 + 19.5180i −0.202066 + 0.621895i
\(986\) −10.3790 + 7.54077i −0.330534 + 0.240147i
\(987\) 0.791567 + 0.575107i 0.0251959 + 0.0183059i
\(988\) 5.01397 + 15.4314i 0.159516 + 0.490938i
\(989\) −58.0583 −1.84615
\(990\) 0 0
\(991\) −2.98352 −0.0947746 −0.0473873 0.998877i \(-0.515089\pi\)
−0.0473873 + 0.998877i \(0.515089\pi\)
\(992\) 0.738036 + 2.27144i 0.0234327 + 0.0721183i
\(993\) −8.47789 6.15955i −0.269038 0.195467i
\(994\) −10.8100 + 7.85396i −0.342874 + 0.249112i
\(995\) −12.3028 + 37.8641i −0.390025 + 1.20037i
\(996\) −13.6770 + 42.0934i −0.433372 + 1.33378i
\(997\) −50.8510 + 36.9454i −1.61047 + 1.17007i −0.748458 + 0.663182i \(0.769205\pi\)
−0.862010 + 0.506891i \(0.830795\pi\)
\(998\) 5.16714 + 3.75415i 0.163563 + 0.118836i
\(999\) −0.743624 2.28864i −0.0235272 0.0724093i
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 847.2.f.p.148.2 8
11.2 odd 10 847.2.f.s.372.1 8
11.3 even 5 847.2.a.l.1.4 4
11.4 even 5 77.2.f.a.36.1 yes 8
11.5 even 5 77.2.f.a.15.1 8
11.6 odd 10 847.2.f.q.323.2 8
11.7 odd 10 847.2.f.q.729.2 8
11.8 odd 10 847.2.a.k.1.1 4
11.9 even 5 inner 847.2.f.p.372.2 8
11.10 odd 2 847.2.f.s.148.1 8
33.5 odd 10 693.2.m.g.631.2 8
33.8 even 10 7623.2.a.co.1.4 4
33.14 odd 10 7623.2.a.ch.1.1 4
33.26 odd 10 693.2.m.g.190.2 8
77.4 even 15 539.2.q.c.520.1 16
77.5 odd 30 539.2.q.b.312.1 16
77.16 even 15 539.2.q.c.312.1 16
77.26 odd 30 539.2.q.b.410.2 16
77.27 odd 10 539.2.f.d.246.1 8
77.37 even 15 539.2.q.c.410.2 16
77.38 odd 30 539.2.q.b.422.2 16
77.41 even 10 5929.2.a.bb.1.1 4
77.48 odd 10 539.2.f.d.344.1 8
77.59 odd 30 539.2.q.b.520.1 16
77.60 even 15 539.2.q.c.422.2 16
77.69 odd 10 5929.2.a.bi.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.15.1 8 11.5 even 5
77.2.f.a.36.1 yes 8 11.4 even 5
539.2.f.d.246.1 8 77.27 odd 10
539.2.f.d.344.1 8 77.48 odd 10
539.2.q.b.312.1 16 77.5 odd 30
539.2.q.b.410.2 16 77.26 odd 30
539.2.q.b.422.2 16 77.38 odd 30
539.2.q.b.520.1 16 77.59 odd 30
539.2.q.c.312.1 16 77.16 even 15
539.2.q.c.410.2 16 77.37 even 15
539.2.q.c.422.2 16 77.60 even 15
539.2.q.c.520.1 16 77.4 even 15
693.2.m.g.190.2 8 33.26 odd 10
693.2.m.g.631.2 8 33.5 odd 10
847.2.a.k.1.1 4 11.8 odd 10
847.2.a.l.1.4 4 11.3 even 5
847.2.f.p.148.2 8 1.1 even 1 trivial
847.2.f.p.372.2 8 11.9 even 5 inner
847.2.f.q.323.2 8 11.6 odd 10
847.2.f.q.729.2 8 11.7 odd 10
847.2.f.s.148.1 8 11.10 odd 2
847.2.f.s.372.1 8 11.2 odd 10
5929.2.a.bb.1.1 4 77.41 even 10
5929.2.a.bi.1.4 4 77.69 odd 10
7623.2.a.ch.1.1 4 33.14 odd 10
7623.2.a.co.1.4 4 33.8 even 10