Properties

Label 287.2.j.a.81.17
Level $287$
Weight $2$
Character 287.81
Analytic conductor $2.292$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(81,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.j (of order \(6\), 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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 81.17
Character \(\chi\) \(=\) 287.81
Dual form 287.2.j.a.163.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.467463 + 0.809670i) q^{2} +(-0.691950 - 0.399498i) q^{3} +(0.562956 - 0.975068i) q^{4} +(1.41567 + 2.45201i) q^{5} -0.747002i q^{6} +(-0.561364 - 2.58551i) q^{7} +2.92250 q^{8} +(-1.18080 - 2.04521i) q^{9} +O(q^{10})\) \(q+(0.467463 + 0.809670i) q^{2} +(-0.691950 - 0.399498i) q^{3} +(0.562956 - 0.975068i) q^{4} +(1.41567 + 2.45201i) q^{5} -0.747002i q^{6} +(-0.561364 - 2.58551i) q^{7} +2.92250 q^{8} +(-1.18080 - 2.04521i) q^{9} +(-1.32355 + 2.29245i) q^{10} +(4.46876 + 2.58004i) q^{11} +(-0.779075 + 0.449799i) q^{12} +1.56869i q^{13} +(1.83099 - 1.66315i) q^{14} -2.26223i q^{15} +(0.240249 + 0.416123i) q^{16} +(-2.26946 - 1.31027i) q^{17} +(1.10396 - 1.91212i) q^{18} +(1.80953 - 1.04473i) q^{19} +3.18784 q^{20} +(-0.644470 + 2.01331i) q^{21} +4.82430i q^{22} +(2.54876 + 4.41457i) q^{23} +(-2.02222 - 1.16753i) q^{24} +(-1.50824 + 2.61235i) q^{25} +(-1.27012 + 0.733306i) q^{26} +4.28390i q^{27} +(-2.83707 - 0.908161i) q^{28} -0.269442i q^{29} +(1.83166 - 1.05751i) q^{30} +(-1.20558 + 2.08812i) q^{31} +(2.69788 - 4.67287i) q^{32} +(-2.06144 - 3.57052i) q^{33} -2.45002i q^{34} +(5.54500 - 5.03670i) q^{35} -2.65896 q^{36} +(-4.60356 - 7.97361i) q^{37} +(1.69178 + 0.976749i) q^{38} +(0.626689 - 1.08546i) q^{39} +(4.13729 + 7.16600i) q^{40} +(-2.37929 + 5.94466i) q^{41} +(-1.93138 + 0.419340i) q^{42} -7.57662 q^{43} +(5.03143 - 2.90490i) q^{44} +(3.34325 - 5.79069i) q^{45} +(-2.38290 + 4.12730i) q^{46} +(-6.88968 + 3.97776i) q^{47} -0.383915i q^{48} +(-6.36974 + 2.90283i) q^{49} -2.82018 q^{50} +(1.04690 + 1.81329i) q^{51} +(1.52958 + 0.883105i) q^{52} +(-9.66900 - 5.58240i) q^{53} +(-3.46855 + 2.00257i) q^{54} +14.6099i q^{55} +(-1.64059 - 7.55615i) q^{56} -1.66947 q^{57} +(0.218159 - 0.125954i) q^{58} +(1.00611 - 1.74263i) q^{59} +(-2.20583 - 1.27353i) q^{60} +(-2.52766 - 4.37803i) q^{61} -2.25426 q^{62} +(-4.62506 + 4.20109i) q^{63} +6.00564 q^{64} +(-3.84645 + 2.22075i) q^{65} +(1.92729 - 3.33817i) q^{66} +(7.26159 + 4.19248i) q^{67} +(-2.55521 + 1.47525i) q^{68} -4.07289i q^{69} +(6.67015 + 2.13515i) q^{70} -8.62936i q^{71} +(-3.45090 - 5.97713i) q^{72} +(-0.469846 + 0.813797i) q^{73} +(4.30400 - 7.45474i) q^{74} +(2.08725 - 1.20508i) q^{75} -2.35255i q^{76} +(4.16212 - 13.0024i) q^{77} +1.17182 q^{78} +(-0.429949 + 0.248231i) q^{79} +(-0.680226 + 1.17819i) q^{80} +(-1.83100 + 3.17139i) q^{81} +(-5.92545 + 0.852470i) q^{82} -5.21421 q^{83} +(1.60031 + 1.76181i) q^{84} -7.41965i q^{85} +(-3.54179 - 6.13456i) q^{86} +(-0.107641 + 0.186440i) q^{87} +(13.0599 + 7.54016i) q^{88} +(-7.13866 + 4.12151i) q^{89} +6.25139 q^{90} +(4.05587 - 0.880608i) q^{91} +5.73935 q^{92} +(1.66840 - 0.963252i) q^{93} +(-6.44135 - 3.71891i) q^{94} +(5.12339 + 2.95799i) q^{95} +(-3.73360 + 2.15560i) q^{96} -10.0991i q^{97} +(-5.32795 - 3.80042i) q^{98} -12.1861i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 2 q^{2} - 26 q^{4} - 6 q^{5} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 2 q^{2} - 26 q^{4} - 6 q^{5} - 12 q^{8} + 16 q^{9} + 16 q^{10} - 26 q^{16} + 12 q^{18} + 16 q^{20} - 48 q^{21} - 32 q^{25} + 6 q^{31} + 20 q^{32} - 20 q^{33} - 4 q^{36} - 24 q^{37} + 14 q^{39} + 44 q^{40} + 24 q^{41} - 2 q^{42} - 32 q^{43} + 26 q^{45} + 12 q^{46} + 16 q^{49} - 12 q^{51} + 8 q^{57} + 2 q^{59} + 14 q^{61} - 20 q^{62} - 20 q^{64} - 4 q^{66} - 42 q^{72} - 16 q^{73} - 22 q^{74} - 32 q^{77} + 88 q^{78} - 52 q^{80} - 46 q^{81} - 42 q^{82} - 112 q^{83} + 72 q^{84} + 16 q^{86} - 18 q^{87} + 224 q^{90} + 86 q^{91} - 32 q^{92} - 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.467463 + 0.809670i 0.330546 + 0.572523i 0.982619 0.185633i \(-0.0594336\pi\)
−0.652073 + 0.758157i \(0.726100\pi\)
\(3\) −0.691950 0.399498i −0.399498 0.230650i 0.286770 0.958000i \(-0.407419\pi\)
−0.686267 + 0.727350i \(0.740752\pi\)
\(4\) 0.562956 0.975068i 0.281478 0.487534i
\(5\) 1.41567 + 2.45201i 0.633107 + 1.09657i 0.986913 + 0.161254i \(0.0515538\pi\)
−0.353806 + 0.935319i \(0.615113\pi\)
\(6\) 0.747002i 0.304962i
\(7\) −0.561364 2.58551i −0.212176 0.977232i
\(8\) 2.92250 1.03326
\(9\) −1.18080 2.04521i −0.393601 0.681737i
\(10\) −1.32355 + 2.29245i −0.418542 + 0.724936i
\(11\) 4.46876 + 2.58004i 1.34738 + 0.777911i 0.987878 0.155233i \(-0.0496127\pi\)
0.359504 + 0.933144i \(0.382946\pi\)
\(12\) −0.779075 + 0.449799i −0.224900 + 0.129846i
\(13\) 1.56869i 0.435077i 0.976052 + 0.217539i \(0.0698028\pi\)
−0.976052 + 0.217539i \(0.930197\pi\)
\(14\) 1.83099 1.66315i 0.489354 0.444496i
\(15\) 2.26223i 0.584104i
\(16\) 0.240249 + 0.416123i 0.0600622 + 0.104031i
\(17\) −2.26946 1.31027i −0.550425 0.317788i 0.198869 0.980026i \(-0.436273\pi\)
−0.749293 + 0.662238i \(0.769607\pi\)
\(18\) 1.10396 1.91212i 0.260207 0.450692i
\(19\) 1.80953 1.04473i 0.415135 0.239678i −0.277859 0.960622i \(-0.589625\pi\)
0.692994 + 0.720944i \(0.256291\pi\)
\(20\) 3.18784 0.712822
\(21\) −0.644470 + 2.01331i −0.140635 + 0.439340i
\(22\) 4.82430i 1.02854i
\(23\) 2.54876 + 4.41457i 0.531452 + 0.920502i 0.999326 + 0.0367069i \(0.0116868\pi\)
−0.467874 + 0.883795i \(0.654980\pi\)
\(24\) −2.02222 1.16753i −0.412785 0.238321i
\(25\) −1.50824 + 2.61235i −0.301648 + 0.522469i
\(26\) −1.27012 + 0.733306i −0.249092 + 0.143813i
\(27\) 4.28390i 0.824437i
\(28\) −2.83707 0.908161i −0.536157 0.171626i
\(29\) 0.269442i 0.0500340i −0.999687 0.0250170i \(-0.992036\pi\)
0.999687 0.0250170i \(-0.00796400\pi\)
\(30\) 1.83166 1.05751i 0.334413 0.193074i
\(31\) −1.20558 + 2.08812i −0.216528 + 0.375038i −0.953744 0.300619i \(-0.902807\pi\)
0.737216 + 0.675657i \(0.236140\pi\)
\(32\) 2.69788 4.67287i 0.476923 0.826055i
\(33\) −2.06144 3.57052i −0.358851 0.621547i
\(34\) 2.45002i 0.420174i
\(35\) 5.54500 5.03670i 0.937275 0.851358i
\(36\) −2.65896 −0.443160
\(37\) −4.60356 7.97361i −0.756821 1.31085i −0.944464 0.328616i \(-0.893418\pi\)
0.187642 0.982237i \(-0.439915\pi\)
\(38\) 1.69178 + 0.976749i 0.274443 + 0.158450i
\(39\) 0.626689 1.08546i 0.100351 0.173812i
\(40\) 4.13729 + 7.16600i 0.654163 + 1.13304i
\(41\) −2.37929 + 5.94466i −0.371583 + 0.928400i
\(42\) −1.93138 + 0.419340i −0.298019 + 0.0647056i
\(43\) −7.57662 −1.15542 −0.577712 0.816241i \(-0.696054\pi\)
−0.577712 + 0.816241i \(0.696054\pi\)
\(44\) 5.03143 2.90490i 0.758517 0.437930i
\(45\) 3.34325 5.79069i 0.498383 0.863224i
\(46\) −2.38290 + 4.12730i −0.351339 + 0.608538i
\(47\) −6.88968 + 3.97776i −1.00496 + 0.580216i −0.909713 0.415237i \(-0.863698\pi\)
−0.0952503 + 0.995453i \(0.530365\pi\)
\(48\) 0.383915i 0.0554134i
\(49\) −6.36974 + 2.90283i −0.909963 + 0.414690i
\(50\) −2.82018 −0.398834
\(51\) 1.04690 + 1.81329i 0.146596 + 0.253911i
\(52\) 1.52958 + 0.883105i 0.212115 + 0.122465i
\(53\) −9.66900 5.58240i −1.32814 0.766801i −0.343127 0.939289i \(-0.611486\pi\)
−0.985012 + 0.172487i \(0.944820\pi\)
\(54\) −3.46855 + 2.00257i −0.472009 + 0.272515i
\(55\) 14.6099i 1.97000i
\(56\) −1.64059 7.55615i −0.219233 1.00973i
\(57\) −1.66947 −0.221127
\(58\) 0.218159 0.125954i 0.0286457 0.0165386i
\(59\) 1.00611 1.74263i 0.130984 0.226871i −0.793072 0.609128i \(-0.791520\pi\)
0.924056 + 0.382257i \(0.124853\pi\)
\(60\) −2.20583 1.27353i −0.284771 0.164413i
\(61\) −2.52766 4.37803i −0.323633 0.560549i 0.657602 0.753366i \(-0.271571\pi\)
−0.981235 + 0.192817i \(0.938238\pi\)
\(62\) −2.25426 −0.286291
\(63\) −4.62506 + 4.20109i −0.582702 + 0.529287i
\(64\) 6.00564 0.750705
\(65\) −3.84645 + 2.22075i −0.477094 + 0.275450i
\(66\) 1.92729 3.33817i 0.237234 0.410901i
\(67\) 7.26159 + 4.19248i 0.887144 + 0.512193i 0.873007 0.487707i \(-0.162167\pi\)
0.0141368 + 0.999900i \(0.495500\pi\)
\(68\) −2.55521 + 1.47525i −0.309865 + 0.178901i
\(69\) 4.07289i 0.490318i
\(70\) 6.67015 + 2.13515i 0.797235 + 0.255199i
\(71\) 8.62936i 1.02412i −0.858951 0.512058i \(-0.828883\pi\)
0.858951 0.512058i \(-0.171117\pi\)
\(72\) −3.45090 5.97713i −0.406692 0.704411i
\(73\) −0.469846 + 0.813797i −0.0549913 + 0.0952477i −0.892211 0.451620i \(-0.850846\pi\)
0.837219 + 0.546867i \(0.184180\pi\)
\(74\) 4.30400 7.45474i 0.500329 0.866596i
\(75\) 2.08725 1.20508i 0.241015 0.139150i
\(76\) 2.35255i 0.269857i
\(77\) 4.16212 13.0024i 0.474318 1.48176i
\(78\) 1.17182 0.132682
\(79\) −0.429949 + 0.248231i −0.0483730 + 0.0279282i −0.523991 0.851724i \(-0.675558\pi\)
0.475618 + 0.879652i \(0.342224\pi\)
\(80\) −0.680226 + 1.17819i −0.0760516 + 0.131725i
\(81\) −1.83100 + 3.17139i −0.203445 + 0.352377i
\(82\) −5.92545 + 0.852470i −0.654356 + 0.0941396i
\(83\) −5.21421 −0.572334 −0.286167 0.958180i \(-0.592381\pi\)
−0.286167 + 0.958180i \(0.592381\pi\)
\(84\) 1.60031 + 1.76181i 0.174608 + 0.192229i
\(85\) 7.41965i 0.804774i
\(86\) −3.54179 6.13456i −0.381921 0.661507i
\(87\) −0.107641 + 0.186440i −0.0115404 + 0.0199885i
\(88\) 13.0599 + 7.54016i 1.39219 + 0.803784i
\(89\) −7.13866 + 4.12151i −0.756696 + 0.436879i −0.828108 0.560568i \(-0.810583\pi\)
0.0714120 + 0.997447i \(0.477249\pi\)
\(90\) 6.25139 0.658955
\(91\) 4.05587 0.880608i 0.425171 0.0923128i
\(92\) 5.73935 0.598368
\(93\) 1.66840 0.963252i 0.173005 0.0998846i
\(94\) −6.44135 3.71891i −0.664374 0.383577i
\(95\) 5.12339 + 2.95799i 0.525649 + 0.303484i
\(96\) −3.73360 + 2.15560i −0.381059 + 0.220005i
\(97\) 10.0991i 1.02541i −0.858564 0.512706i \(-0.828643\pi\)
0.858564 0.512706i \(-0.171357\pi\)
\(98\) −5.32795 3.80042i −0.538205 0.383901i
\(99\) 12.1861i 1.22475i
\(100\) 1.69814 + 2.94127i 0.169814 + 0.294127i
\(101\) 9.64523 + 5.56868i 0.959736 + 0.554104i 0.896092 0.443869i \(-0.146394\pi\)
0.0636443 + 0.997973i \(0.479728\pi\)
\(102\) −0.978776 + 1.69529i −0.0969133 + 0.167859i
\(103\) 7.94399 + 13.7594i 0.782744 + 1.35575i 0.930337 + 0.366705i \(0.119514\pi\)
−0.147593 + 0.989048i \(0.547153\pi\)
\(104\) 4.58450i 0.449547i
\(105\) −5.84901 + 1.26993i −0.570805 + 0.123933i
\(106\) 10.4383i 1.01385i
\(107\) 5.96425 + 10.3304i 0.576586 + 0.998676i 0.995867 + 0.0908200i \(0.0289488\pi\)
−0.419281 + 0.907856i \(0.637718\pi\)
\(108\) 4.17709 + 2.41165i 0.401941 + 0.232061i
\(109\) 9.02809 + 5.21237i 0.864734 + 0.499254i 0.865595 0.500745i \(-0.166941\pi\)
−0.000860769 1.00000i \(0.500274\pi\)
\(110\) −11.8292 + 6.82961i −1.12787 + 0.651177i
\(111\) 7.35645i 0.698244i
\(112\) 0.941024 0.854763i 0.0889184 0.0807675i
\(113\) −10.5872 −0.995960 −0.497980 0.867189i \(-0.665925\pi\)
−0.497980 + 0.867189i \(0.665925\pi\)
\(114\) −0.780418 1.35172i −0.0730928 0.126600i
\(115\) −7.21639 + 12.4992i −0.672932 + 1.16555i
\(116\) −0.262724 0.151684i −0.0243933 0.0140835i
\(117\) 3.20831 1.85232i 0.296608 0.171247i
\(118\) 1.88127 0.173185
\(119\) −2.11373 + 6.60325i −0.193765 + 0.605319i
\(120\) 6.61135i 0.603531i
\(121\) 7.81321 + 13.5329i 0.710292 + 1.23026i
\(122\) 2.36317 4.09313i 0.213952 0.370575i
\(123\) 4.02123 3.16289i 0.362582 0.285188i
\(124\) 1.35738 + 2.35104i 0.121896 + 0.211130i
\(125\) 5.61602 0.502313
\(126\) −5.56354 1.78092i −0.495640 0.158657i
\(127\) −6.60247 −0.585875 −0.292937 0.956132i \(-0.594633\pi\)
−0.292937 + 0.956132i \(0.594633\pi\)
\(128\) −2.58835 4.48315i −0.228780 0.396258i
\(129\) 5.24264 + 3.02684i 0.461589 + 0.266498i
\(130\) −3.59615 2.07624i −0.315403 0.182098i
\(131\) −1.07657 1.86467i −0.0940603 0.162917i 0.815156 0.579242i \(-0.196651\pi\)
−0.909216 + 0.416325i \(0.863318\pi\)
\(132\) −4.64200 −0.404034
\(133\) −3.71697 4.09209i −0.322303 0.354829i
\(134\) 7.83932i 0.677214i
\(135\) −10.5042 + 6.06458i −0.904055 + 0.521956i
\(136\) −6.63249 3.82927i −0.568731 0.328357i
\(137\) 8.65484 + 4.99687i 0.739433 + 0.426912i 0.821863 0.569685i \(-0.192935\pi\)
−0.0824303 + 0.996597i \(0.526268\pi\)
\(138\) 3.29770 1.90393i 0.280718 0.162073i
\(139\) 10.4555 0.886826 0.443413 0.896317i \(-0.353768\pi\)
0.443413 + 0.896317i \(0.353768\pi\)
\(140\) −1.78954 8.24219i −0.151244 0.696592i
\(141\) 6.35642 0.535307
\(142\) 6.98694 4.03391i 0.586331 0.338518i
\(143\) −4.04729 + 7.01011i −0.338451 + 0.586215i
\(144\) 0.567373 0.982719i 0.0472811 0.0818933i
\(145\) 0.660674 0.381440i 0.0548660 0.0316769i
\(146\) −0.878543 −0.0727087
\(147\) 5.56722 + 0.536084i 0.459176 + 0.0442154i
\(148\) −10.3664 −0.852114
\(149\) −19.8885 + 11.4827i −1.62933 + 0.940696i −0.645041 + 0.764148i \(0.723160\pi\)
−0.984292 + 0.176547i \(0.943507\pi\)
\(150\) 1.95143 + 1.12666i 0.159333 + 0.0919912i
\(151\) 6.18581 + 3.57138i 0.503394 + 0.290635i 0.730114 0.683325i \(-0.239467\pi\)
−0.226720 + 0.973960i \(0.572800\pi\)
\(152\) 5.28835 3.05323i 0.428942 0.247650i
\(153\) 6.18870i 0.500326i
\(154\) 12.4733 2.70819i 1.00512 0.218232i
\(155\) −6.82680 −0.548342
\(156\) −0.705597 1.22213i −0.0564930 0.0978487i
\(157\) −19.1087 11.0324i −1.52504 0.880484i −0.999559 0.0296795i \(-0.990551\pi\)
−0.525483 0.850804i \(-0.676115\pi\)
\(158\) −0.401970 0.232078i −0.0319790 0.0184631i
\(159\) 4.46031 + 7.72548i 0.353726 + 0.612671i
\(160\) 15.2772 1.20777
\(161\) 9.98315 9.06802i 0.786782 0.714660i
\(162\) −3.42371 −0.268992
\(163\) 4.02438 + 6.97042i 0.315213 + 0.545966i 0.979483 0.201528i \(-0.0645906\pi\)
−0.664269 + 0.747493i \(0.731257\pi\)
\(164\) 4.45701 + 5.66655i 0.348034 + 0.442483i
\(165\) 5.83663 10.1093i 0.454381 0.787011i
\(166\) −2.43745 4.22179i −0.189183 0.327675i
\(167\) 23.2127i 1.79625i −0.439741 0.898124i \(-0.644930\pi\)
0.439741 0.898124i \(-0.355070\pi\)
\(168\) −1.88346 + 5.88389i −0.145312 + 0.453952i
\(169\) 10.5392 0.810708
\(170\) 6.00747 3.46841i 0.460752 0.266015i
\(171\) −4.27340 2.46725i −0.326795 0.188675i
\(172\) −4.26530 + 7.38772i −0.325226 + 0.563308i
\(173\) 7.73197 + 13.3922i 0.587850 + 1.01819i 0.994513 + 0.104609i \(0.0333590\pi\)
−0.406663 + 0.913578i \(0.633308\pi\)
\(174\) −0.201273 −0.0152585
\(175\) 7.60092 + 2.43309i 0.574576 + 0.183924i
\(176\) 2.47941i 0.186892i
\(177\) −1.39235 + 0.803873i −0.104655 + 0.0604228i
\(178\) −6.67412 3.85331i −0.500247 0.288818i
\(179\) 2.02925 + 1.17159i 0.151673 + 0.0875685i 0.573916 0.818914i \(-0.305424\pi\)
−0.422243 + 0.906483i \(0.638757\pi\)
\(180\) −3.76421 6.51980i −0.280568 0.485957i
\(181\) 12.8743i 0.956938i −0.878104 0.478469i \(-0.841192\pi\)
0.878104 0.478469i \(-0.158808\pi\)
\(182\) 2.60897 + 2.87227i 0.193390 + 0.212907i
\(183\) 4.03917i 0.298584i
\(184\) 7.44873 + 12.9016i 0.549128 + 0.951117i
\(185\) 13.0342 22.5760i 0.958297 1.65982i
\(186\) 1.55983 + 0.900570i 0.114372 + 0.0660330i
\(187\) −6.76111 11.7106i −0.494421 0.856363i
\(188\) 8.95722i 0.653272i
\(189\) 11.0761 2.40483i 0.805665 0.174925i
\(190\) 5.53101i 0.401262i
\(191\) 12.8592 7.42426i 0.930459 0.537201i 0.0435025 0.999053i \(-0.486148\pi\)
0.886957 + 0.461852i \(0.152815\pi\)
\(192\) −4.15561 2.39924i −0.299905 0.173150i
\(193\) −0.996679 0.575433i −0.0717425 0.0414206i 0.463700 0.885992i \(-0.346522\pi\)
−0.535442 + 0.844572i \(0.679855\pi\)
\(194\) 8.17697 4.72097i 0.587072 0.338946i
\(195\) 3.54874 0.254130
\(196\) −0.755428 + 7.84510i −0.0539591 + 0.560364i
\(197\) 8.28961 0.590610 0.295305 0.955403i \(-0.404579\pi\)
0.295305 + 0.955403i \(0.404579\pi\)
\(198\) 9.86670 5.69654i 0.701196 0.404836i
\(199\) −1.03360 0.596751i −0.0732702 0.0423026i 0.462917 0.886401i \(-0.346803\pi\)
−0.536188 + 0.844099i \(0.680136\pi\)
\(200\) −4.40782 + 7.63458i −0.311680 + 0.539846i
\(201\) −3.34977 5.80197i −0.236275 0.409240i
\(202\) 10.4126i 0.732628i
\(203\) −0.696644 + 0.151255i −0.0488948 + 0.0106160i
\(204\) 2.35744 0.165054
\(205\) −17.9447 + 2.58163i −1.25331 + 0.180309i
\(206\) −7.42705 + 12.8640i −0.517467 + 0.896279i
\(207\) 6.01916 10.4255i 0.418360 0.724621i
\(208\) −0.652770 + 0.376877i −0.0452614 + 0.0261317i
\(209\) 10.7818 0.745793
\(210\) −3.76243 4.14212i −0.259632 0.285834i
\(211\) 11.5389i 0.794369i 0.917739 + 0.397184i \(0.130013\pi\)
−0.917739 + 0.397184i \(0.869987\pi\)
\(212\) −10.8864 + 6.28529i −0.747684 + 0.431676i
\(213\) −3.44741 + 5.97109i −0.236213 + 0.409132i
\(214\) −5.57614 + 9.65816i −0.381177 + 0.660218i
\(215\) −10.7260 18.5779i −0.731506 1.26701i
\(216\) 12.5197i 0.851857i
\(217\) 6.07564 + 1.94484i 0.412441 + 0.132024i
\(218\) 9.74637i 0.660107i
\(219\) 0.650220 0.375405i 0.0439378 0.0253675i
\(220\) 14.2457 + 8.22475i 0.960444 + 0.554512i
\(221\) 2.05541 3.56008i 0.138262 0.239477i
\(222\) −5.95630 + 3.43887i −0.399761 + 0.230802i
\(223\) −23.7312 −1.58916 −0.794579 0.607161i \(-0.792308\pi\)
−0.794579 + 0.607161i \(0.792308\pi\)
\(224\) −13.5963 4.35223i −0.908438 0.290795i
\(225\) 7.12373 0.474915
\(226\) −4.94913 8.57214i −0.329211 0.570210i
\(227\) −16.3187 9.42159i −1.08311 0.625333i −0.151375 0.988476i \(-0.548370\pi\)
−0.931733 + 0.363144i \(0.881703\pi\)
\(228\) −0.939840 + 1.62785i −0.0622424 + 0.107807i
\(229\) 24.8440 14.3437i 1.64174 0.947857i 0.661519 0.749928i \(-0.269912\pi\)
0.980216 0.197928i \(-0.0634213\pi\)
\(230\) −13.4936 −0.889741
\(231\) −8.07440 + 7.33424i −0.531256 + 0.482557i
\(232\) 0.787443i 0.0516981i
\(233\) 0.174969 0.101019i 0.0114626 0.00661795i −0.494258 0.869315i \(-0.664560\pi\)
0.505720 + 0.862697i \(0.331227\pi\)
\(234\) 2.99953 + 1.73178i 0.196086 + 0.113210i
\(235\) −19.5070 11.2624i −1.27250 0.734677i
\(236\) −1.13279 1.96204i −0.0737381 0.127718i
\(237\) 0.396671 0.0257665
\(238\) −6.33455 + 1.37535i −0.410608 + 0.0891509i
\(239\) 29.9628i 1.93813i −0.246796 0.969067i \(-0.579378\pi\)
0.246796 0.969067i \(-0.420622\pi\)
\(240\) 0.941365 0.543497i 0.0607648 0.0350826i
\(241\) −0.176305 + 0.305370i −0.0113568 + 0.0196706i −0.871648 0.490132i \(-0.836948\pi\)
0.860291 + 0.509803i \(0.170282\pi\)
\(242\) −7.30478 + 12.6522i −0.469569 + 0.813317i
\(243\) 13.6638 7.88881i 0.876534 0.506067i
\(244\) −5.69184 −0.364382
\(245\) −16.1352 11.5092i −1.03084 0.735298i
\(246\) 4.44067 + 1.77733i 0.283127 + 0.113319i
\(247\) 1.63886 + 2.83860i 0.104278 + 0.180616i
\(248\) −3.52330 + 6.10254i −0.223730 + 0.387512i
\(249\) 3.60798 + 2.08307i 0.228646 + 0.132009i
\(250\) 2.62529 + 4.54713i 0.166038 + 0.287586i
\(251\) 2.20729 0.139323 0.0696615 0.997571i \(-0.477808\pi\)
0.0696615 + 0.997571i \(0.477808\pi\)
\(252\) 1.49265 + 6.87478i 0.0940279 + 0.433070i
\(253\) 26.3036i 1.65369i
\(254\) −3.08641 5.34583i −0.193659 0.335427i
\(255\) −2.96413 + 5.13403i −0.185621 + 0.321505i
\(256\) 8.42556 14.5935i 0.526597 0.912094i
\(257\) 0.628436 0.362828i 0.0392007 0.0226326i −0.480272 0.877120i \(-0.659462\pi\)
0.519472 + 0.854487i \(0.326129\pi\)
\(258\) 5.65975i 0.352361i
\(259\) −18.0316 + 16.3787i −1.12043 + 1.01772i
\(260\) 5.00074i 0.310133i
\(261\) −0.551065 + 0.318157i −0.0341101 + 0.0196935i
\(262\) 1.00651 1.74333i 0.0621826 0.107703i
\(263\) 16.4540 + 9.49973i 1.01460 + 0.585778i 0.912535 0.409000i \(-0.134122\pi\)
0.102063 + 0.994778i \(0.467456\pi\)
\(264\) −6.02455 10.4348i −0.370786 0.642220i
\(265\) 31.6113i 1.94187i
\(266\) 1.57569 4.92242i 0.0966118 0.301813i
\(267\) 6.58613 0.403065
\(268\) 8.17591 4.72036i 0.499423 0.288342i
\(269\) 14.2111 24.6143i 0.866464 1.50076i 0.000877771 1.00000i \(-0.499721\pi\)
0.865586 0.500760i \(-0.166946\pi\)
\(270\) −9.82062 5.66994i −0.597664 0.345062i
\(271\) 2.66994 + 4.62448i 0.162187 + 0.280917i 0.935653 0.352922i \(-0.114812\pi\)
−0.773465 + 0.633838i \(0.781478\pi\)
\(272\) 1.25917i 0.0763481i
\(273\) −3.15826 1.01097i −0.191147 0.0611870i
\(274\) 9.34342i 0.564457i
\(275\) −13.4799 + 7.78263i −0.812869 + 0.469310i
\(276\) −3.97134 2.29286i −0.239047 0.138014i
\(277\) 4.55841 7.89540i 0.273888 0.474388i −0.695966 0.718075i \(-0.745023\pi\)
0.969854 + 0.243687i \(0.0783568\pi\)
\(278\) 4.88757 + 8.46553i 0.293137 + 0.507729i
\(279\) 5.69421 0.340903
\(280\) 16.2052 14.7198i 0.968449 0.879673i
\(281\) 12.6932i 0.757213i 0.925558 + 0.378607i \(0.123597\pi\)
−0.925558 + 0.378607i \(0.876403\pi\)
\(282\) 2.97139 + 5.14661i 0.176944 + 0.306476i
\(283\) −1.41791 + 2.45589i −0.0842861 + 0.145988i −0.905087 0.425227i \(-0.860194\pi\)
0.820801 + 0.571215i \(0.193528\pi\)
\(284\) −8.41422 4.85795i −0.499292 0.288266i
\(285\) −2.36342 4.09357i −0.139997 0.242482i
\(286\) −7.56784 −0.447496
\(287\) 16.7056 + 2.81456i 0.986102 + 0.166138i
\(288\) −12.7427 −0.750870
\(289\) −5.06637 8.77521i −0.298022 0.516189i
\(290\) 0.617681 + 0.356619i 0.0362715 + 0.0209414i
\(291\) −4.03458 + 6.98810i −0.236511 + 0.409649i
\(292\) 0.529005 + 0.916264i 0.0309577 + 0.0536203i
\(293\) 15.0226i 0.877632i −0.898577 0.438816i \(-0.855398\pi\)
0.898577 0.438816i \(-0.144602\pi\)
\(294\) 2.16842 + 4.75821i 0.126465 + 0.277504i
\(295\) 5.69725 0.331707
\(296\) −13.4539 23.3029i −0.781993 1.35445i
\(297\) −11.0526 + 19.1437i −0.641338 + 1.11083i
\(298\) −18.5943 10.7354i −1.07714 0.621887i
\(299\) −6.92511 + 3.99821i −0.400489 + 0.231223i
\(300\) 2.71362i 0.156671i
\(301\) 4.25324 + 19.5894i 0.245153 + 1.12912i
\(302\) 6.67795i 0.384273i
\(303\) −4.44935 7.70649i −0.255608 0.442726i
\(304\) 0.869475 + 0.501992i 0.0498678 + 0.0287912i
\(305\) 7.15665 12.3957i 0.409788 0.709774i
\(306\) −5.01080 + 2.89299i −0.286449 + 0.165381i
\(307\) −31.7863 −1.81414 −0.907069 0.420981i \(-0.861686\pi\)
−0.907069 + 0.420981i \(0.861686\pi\)
\(308\) −10.3351 11.3781i −0.588898 0.648328i
\(309\) 12.6944i 0.722160i
\(310\) −3.19128 5.52746i −0.181253 0.313939i
\(311\) 14.6550 + 8.46104i 0.831006 + 0.479782i 0.854197 0.519949i \(-0.174049\pi\)
−0.0231909 + 0.999731i \(0.507383\pi\)
\(312\) 1.83150 3.17225i 0.103688 0.179593i
\(313\) −27.6354 + 15.9553i −1.56204 + 0.901846i −0.564994 + 0.825095i \(0.691121\pi\)
−0.997050 + 0.0767511i \(0.975545\pi\)
\(314\) 20.6290i 1.16416i
\(315\) −16.8487 5.39334i −0.949315 0.303880i
\(316\) 0.558972i 0.0314446i
\(317\) −24.1827 + 13.9619i −1.35824 + 0.784179i −0.989386 0.145309i \(-0.953582\pi\)
−0.368852 + 0.929488i \(0.620249\pi\)
\(318\) −4.17006 + 7.22276i −0.233846 + 0.405032i
\(319\) 0.695170 1.20407i 0.0389220 0.0674149i
\(320\) 8.50200 + 14.7259i 0.475276 + 0.823203i
\(321\) 9.53082i 0.531959i
\(322\) 12.0089 + 3.84409i 0.669228 + 0.214223i
\(323\) −5.47554 −0.304667
\(324\) 2.06155 + 3.57071i 0.114530 + 0.198373i
\(325\) −4.09797 2.36596i −0.227314 0.131240i
\(326\) −3.76250 + 6.51684i −0.208385 + 0.360934i
\(327\) −4.16466 7.21340i −0.230306 0.398902i
\(328\) −6.95347 + 17.3733i −0.383941 + 0.959278i
\(329\) 14.1522 + 15.5804i 0.780234 + 0.858974i
\(330\) 10.9136 0.600776
\(331\) 9.49493 5.48190i 0.521889 0.301313i −0.215818 0.976434i \(-0.569242\pi\)
0.737707 + 0.675121i \(0.235909\pi\)
\(332\) −2.93537 + 5.08421i −0.161100 + 0.279033i
\(333\) −10.8718 + 18.8305i −0.595771 + 1.03191i
\(334\) 18.7946 10.8511i 1.02839 0.593744i
\(335\) 23.7407i 1.29709i
\(336\) −0.992618 + 0.215516i −0.0541517 + 0.0117574i
\(337\) −0.458974 −0.0250019 −0.0125009 0.999922i \(-0.503979\pi\)
−0.0125009 + 0.999922i \(0.503979\pi\)
\(338\) 4.92669 + 8.53328i 0.267977 + 0.464149i
\(339\) 7.32581 + 4.22956i 0.397884 + 0.229718i
\(340\) −7.23467 4.17694i −0.392355 0.226526i
\(341\) −10.7749 + 6.22088i −0.583493 + 0.336880i
\(342\) 4.61339i 0.249464i
\(343\) 11.0810 + 14.8395i 0.598320 + 0.801257i
\(344\) −22.1427 −1.19385
\(345\) 9.98676 5.76586i 0.537669 0.310423i
\(346\) −7.22882 + 12.5207i −0.388624 + 0.673116i
\(347\) 14.1979 + 8.19716i 0.762183 + 0.440047i 0.830079 0.557646i \(-0.188295\pi\)
−0.0678959 + 0.997692i \(0.521629\pi\)
\(348\) 0.121195 + 0.209915i 0.00649671 + 0.0112526i
\(349\) −31.0306 −1.66103 −0.830514 0.556997i \(-0.811953\pi\)
−0.830514 + 0.556997i \(0.811953\pi\)
\(350\) 1.58315 + 7.29162i 0.0846230 + 0.389754i
\(351\) −6.72012 −0.358693
\(352\) 24.1124 13.9213i 1.28519 0.742007i
\(353\) 4.70228 8.14459i 0.250277 0.433493i −0.713325 0.700833i \(-0.752812\pi\)
0.963602 + 0.267341i \(0.0861449\pi\)
\(354\) −1.30174 0.751563i −0.0691870 0.0399451i
\(355\) 21.1593 12.2163i 1.12302 0.648375i
\(356\) 9.28091i 0.491887i
\(357\) 4.10058 3.72469i 0.217026 0.197132i
\(358\) 2.19070i 0.115782i
\(359\) 13.9731 + 24.2020i 0.737470 + 1.27733i 0.953631 + 0.300977i \(0.0973129\pi\)
−0.216162 + 0.976358i \(0.569354\pi\)
\(360\) 9.77065 16.9233i 0.514959 0.891935i
\(361\) −7.31707 + 12.6735i −0.385109 + 0.667028i
\(362\) 10.4239 6.01826i 0.547869 0.316312i
\(363\) 12.4854i 0.655315i
\(364\) 1.42463 4.45050i 0.0746706 0.233269i
\(365\) −2.66059 −0.139261
\(366\) −3.27040 + 1.88816i −0.170946 + 0.0986959i
\(367\) 15.1592 26.2565i 0.791304 1.37058i −0.133855 0.991001i \(-0.542736\pi\)
0.925160 0.379578i \(-0.123931\pi\)
\(368\) −1.22467 + 2.12119i −0.0638404 + 0.110575i
\(369\) 14.9676 2.15332i 0.779180 0.112097i
\(370\) 24.3721 1.26705
\(371\) −9.00553 + 28.1331i −0.467544 + 1.46060i
\(372\) 2.16907i 0.112461i
\(373\) −4.92455 8.52957i −0.254983 0.441644i 0.709908 0.704295i \(-0.248737\pi\)
−0.964891 + 0.262651i \(0.915403\pi\)
\(374\) 6.32114 10.9485i 0.326858 0.566135i
\(375\) −3.88601 2.24359i −0.200673 0.115858i
\(376\) −20.1351 + 11.6250i −1.03839 + 0.599513i
\(377\) 0.422671 0.0217687
\(378\) 7.12477 + 7.84379i 0.366459 + 0.403441i
\(379\) 27.7924 1.42760 0.713800 0.700350i \(-0.246973\pi\)
0.713800 + 0.700350i \(0.246973\pi\)
\(380\) 5.76849 3.33044i 0.295917 0.170848i
\(381\) 4.56858 + 2.63767i 0.234056 + 0.135132i
\(382\) 12.0224 + 6.94114i 0.615120 + 0.355140i
\(383\) 10.6665 6.15833i 0.545035 0.314676i −0.202082 0.979369i \(-0.564771\pi\)
0.747117 + 0.664692i \(0.231437\pi\)
\(384\) 4.13616i 0.211072i
\(385\) 37.7741 8.20149i 1.92515 0.417987i
\(386\) 1.07598i 0.0547657i
\(387\) 8.94649 + 15.4958i 0.454776 + 0.787695i
\(388\) −9.84734 5.68537i −0.499923 0.288631i
\(389\) 9.62350 16.6684i 0.487931 0.845121i −0.511973 0.859002i \(-0.671085\pi\)
0.999904 + 0.0138808i \(0.00441852\pi\)
\(390\) 1.65890 + 2.87331i 0.0840019 + 0.145496i
\(391\) 13.3583i 0.675556i
\(392\) −18.6156 + 8.48351i −0.940228 + 0.428482i
\(393\) 1.72035i 0.0867800i
\(394\) 3.87509 + 6.71185i 0.195224 + 0.338138i
\(395\) −1.21733 0.702826i −0.0612505 0.0353630i
\(396\) −11.8823 6.86023i −0.597106 0.344739i
\(397\) −16.7407 + 9.66523i −0.840190 + 0.485084i −0.857329 0.514769i \(-0.827878\pi\)
0.0171389 + 0.999853i \(0.494544\pi\)
\(398\) 1.11584i 0.0559319i
\(399\) 0.937183 + 4.31644i 0.0469178 + 0.216092i
\(400\) −1.44941 −0.0724705
\(401\) 1.01532 + 1.75858i 0.0507024 + 0.0878192i 0.890263 0.455447i \(-0.150521\pi\)
−0.839560 + 0.543267i \(0.817187\pi\)
\(402\) 3.13179 5.42442i 0.156200 0.270545i
\(403\) −3.27563 1.89118i −0.163171 0.0942065i
\(404\) 10.8597 6.26984i 0.540289 0.311936i
\(405\) −10.3684 −0.515209
\(406\) −0.448122 0.493346i −0.0222399 0.0244844i
\(407\) 47.5095i 2.35496i
\(408\) 3.05957 + 5.29933i 0.151471 + 0.262356i
\(409\) 0.428284 0.741810i 0.0211773 0.0366802i −0.855243 0.518228i \(-0.826592\pi\)
0.876420 + 0.481548i \(0.159925\pi\)
\(410\) −10.4787 13.3224i −0.517508 0.657948i
\(411\) −3.99248 6.91518i −0.196934 0.341100i
\(412\) 17.8885 0.881301
\(413\) −5.07037 1.62305i −0.249497 0.0798650i
\(414\) 11.2549 0.553150
\(415\) −7.38160 12.7853i −0.362349 0.627606i
\(416\) 7.33030 + 4.23215i 0.359397 + 0.207498i
\(417\) −7.23470 4.17696i −0.354285 0.204546i
\(418\) 5.04010 + 8.72971i 0.246519 + 0.426984i
\(419\) 39.0433 1.90739 0.953694 0.300777i \(-0.0972461\pi\)
0.953694 + 0.300777i \(0.0972461\pi\)
\(420\) −2.05446 + 6.41810i −0.100248 + 0.313171i
\(421\) 3.00608i 0.146508i 0.997313 + 0.0732538i \(0.0233383\pi\)
−0.997313 + 0.0732538i \(0.976662\pi\)
\(422\) −9.34268 + 5.39400i −0.454795 + 0.262576i
\(423\) 16.2707 + 9.39390i 0.791109 + 0.456747i
\(424\) −28.2576 16.3146i −1.37231 0.792305i
\(425\) 6.84577 3.95241i 0.332069 0.191720i
\(426\) −6.44615 −0.312317
\(427\) −9.90051 + 8.99295i −0.479119 + 0.435199i
\(428\) 13.4304 0.649185
\(429\) 5.60104 3.23376i 0.270421 0.156128i
\(430\) 10.0280 17.3690i 0.483593 0.837608i
\(431\) −6.60964 + 11.4482i −0.318375 + 0.551442i −0.980149 0.198262i \(-0.936470\pi\)
0.661774 + 0.749703i \(0.269804\pi\)
\(432\) −1.78263 + 1.02920i −0.0857668 + 0.0495175i
\(433\) 31.4496 1.51137 0.755687 0.654933i \(-0.227303\pi\)
0.755687 + 0.654933i \(0.227303\pi\)
\(434\) 1.26546 + 5.82841i 0.0607440 + 0.279772i
\(435\) −0.609538 −0.0292251
\(436\) 10.1648 5.86867i 0.486807 0.281058i
\(437\) 9.22410 + 5.32554i 0.441249 + 0.254755i
\(438\) 0.607908 + 0.350976i 0.0290470 + 0.0167703i
\(439\) −9.79931 + 5.65763i −0.467695 + 0.270024i −0.715275 0.698844i \(-0.753698\pi\)
0.247579 + 0.968868i \(0.420365\pi\)
\(440\) 42.6975i 2.03552i
\(441\) 13.4583 + 9.59980i 0.640872 + 0.457133i
\(442\) 3.84332 0.182808
\(443\) −11.4562 19.8427i −0.544299 0.942754i −0.998651 0.0519315i \(-0.983462\pi\)
0.454351 0.890823i \(-0.349871\pi\)
\(444\) 7.17304 + 4.14136i 0.340418 + 0.196540i
\(445\) −20.2120 11.6694i −0.958139 0.553182i
\(446\) −11.0935 19.2144i −0.525290 0.909830i
\(447\) 18.3492 0.867886
\(448\) −3.37135 15.5277i −0.159281 0.733613i
\(449\) −33.6809 −1.58950 −0.794750 0.606938i \(-0.792398\pi\)
−0.794750 + 0.606938i \(0.792398\pi\)
\(450\) 3.33008 + 5.76787i 0.156982 + 0.271900i
\(451\) −25.9699 + 20.4266i −1.22288 + 0.961851i
\(452\) −5.96013 + 10.3232i −0.280341 + 0.485565i
\(453\) −2.85351 4.94243i −0.134070 0.232216i
\(454\) 17.6170i 0.826806i
\(455\) 7.90104 + 8.69840i 0.370406 + 0.407787i
\(456\) −4.87903 −0.228482
\(457\) 7.87162 4.54468i 0.368219 0.212591i −0.304461 0.952525i \(-0.598476\pi\)
0.672680 + 0.739933i \(0.265143\pi\)
\(458\) 23.2273 + 13.4103i 1.08534 + 0.626621i
\(459\) 5.61307 9.72213i 0.261996 0.453790i
\(460\) 8.12502 + 14.0729i 0.378831 + 0.656154i
\(461\) −15.0466 −0.700789 −0.350394 0.936602i \(-0.613952\pi\)
−0.350394 + 0.936602i \(0.613952\pi\)
\(462\) −9.71280 3.10911i −0.451880 0.144649i
\(463\) 20.3416i 0.945356i 0.881235 + 0.472678i \(0.156713\pi\)
−0.881235 + 0.472678i \(0.843287\pi\)
\(464\) 0.112121 0.0647330i 0.00520508 0.00300516i
\(465\) 4.72381 + 2.72729i 0.219061 + 0.126475i
\(466\) 0.163584 + 0.0944450i 0.00757786 + 0.00437508i
\(467\) 19.3713 + 33.5520i 0.896395 + 1.55260i 0.832069 + 0.554673i \(0.187156\pi\)
0.0643262 + 0.997929i \(0.479510\pi\)
\(468\) 4.17109i 0.192809i
\(469\) 6.76331 21.1284i 0.312301 0.975620i
\(470\) 21.0590i 0.971380i
\(471\) 8.81486 + 15.2678i 0.406167 + 0.703502i
\(472\) 2.94034 5.09282i 0.135340 0.234416i
\(473\) −33.8581 19.5480i −1.55680 0.898817i
\(474\) 0.185429 + 0.321172i 0.00851703 + 0.0147519i
\(475\) 6.30283i 0.289193i
\(476\) 5.24868 + 5.77837i 0.240573 + 0.264851i
\(477\) 26.3669i 1.20726i
\(478\) 24.2600 14.0065i 1.10963 0.640644i
\(479\) 10.7050 + 6.18054i 0.489125 + 0.282396i 0.724211 0.689578i \(-0.242204\pi\)
−0.235087 + 0.971974i \(0.575537\pi\)
\(480\) −10.5711 6.10322i −0.482502 0.278573i
\(481\) 12.5081 7.22158i 0.570322 0.329276i
\(482\) −0.329665 −0.0150158
\(483\) −10.5305 + 2.28637i −0.479154 + 0.104034i
\(484\) 17.5940 0.799726
\(485\) 24.7632 14.2970i 1.12444 0.649195i
\(486\) 12.7747 + 7.37546i 0.579471 + 0.334558i
\(487\) 5.91089 10.2380i 0.267848 0.463926i −0.700458 0.713694i \(-0.747021\pi\)
0.968306 + 0.249768i \(0.0803542\pi\)
\(488\) −7.38707 12.7948i −0.334397 0.579192i
\(489\) 6.43092i 0.290816i
\(490\) 1.77606 18.4443i 0.0802342 0.833230i
\(491\) 28.6656 1.29366 0.646830 0.762634i \(-0.276094\pi\)
0.646830 + 0.762634i \(0.276094\pi\)
\(492\) −0.820258 5.70154i −0.0369801 0.257045i
\(493\) −0.353042 + 0.611486i −0.0159002 + 0.0275400i
\(494\) −1.53222 + 2.65388i −0.0689378 + 0.119404i
\(495\) 29.8804 17.2515i 1.34302 0.775395i
\(496\) −1.15856 −0.0520207
\(497\) −22.3113 + 4.84421i −1.00080 + 0.217293i
\(498\) 3.89503i 0.174540i
\(499\) −2.05611 + 1.18710i −0.0920442 + 0.0531417i −0.545316 0.838231i \(-0.683590\pi\)
0.453271 + 0.891373i \(0.350257\pi\)
\(500\) 3.16158 5.47601i 0.141390 0.244895i
\(501\) −9.27340 + 16.0620i −0.414305 + 0.717597i
\(502\) 1.03183 + 1.78718i 0.0460528 + 0.0797657i
\(503\) 9.11407i 0.406376i −0.979140 0.203188i \(-0.934870\pi\)
0.979140 0.203188i \(-0.0651303\pi\)
\(504\) −13.5167 + 12.2777i −0.602083 + 0.546891i
\(505\) 31.5336i 1.40323i
\(506\) −21.2972 + 12.2959i −0.946776 + 0.546622i
\(507\) −7.29260 4.21039i −0.323876 0.186990i
\(508\) −3.71690 + 6.43786i −0.164911 + 0.285634i
\(509\) 0.949168 0.548002i 0.0420711 0.0242898i −0.478817 0.877915i \(-0.658934\pi\)
0.520888 + 0.853625i \(0.325601\pi\)
\(510\) −5.54249 −0.245426
\(511\) 2.36784 + 0.757955i 0.104747 + 0.0335300i
\(512\) 5.40116 0.238700
\(513\) 4.47553 + 7.75184i 0.197599 + 0.342252i
\(514\) 0.587541 + 0.339217i 0.0259153 + 0.0149622i
\(515\) −22.4921 + 38.9575i −0.991121 + 1.71667i
\(516\) 5.90275 3.40796i 0.259854 0.150027i
\(517\) −41.0511 −1.80543
\(518\) −21.6904 6.94320i −0.953022 0.305067i
\(519\) 12.3556i 0.542351i
\(520\) −11.2412 + 6.49014i −0.492961 + 0.284611i
\(521\) −25.0920 14.4869i −1.09930 0.634682i −0.163264 0.986582i \(-0.552202\pi\)
−0.936038 + 0.351900i \(0.885536\pi\)
\(522\) −0.515205 0.297454i −0.0225499 0.0130192i
\(523\) −15.5893 27.0014i −0.681672 1.18069i −0.974470 0.224516i \(-0.927920\pi\)
0.292798 0.956174i \(-0.405414\pi\)
\(524\) −2.42424 −0.105904
\(525\) −4.28745 4.72013i −0.187119 0.206003i
\(526\) 17.7631i 0.774508i
\(527\) 5.47202 3.15927i 0.238365 0.137620i
\(528\) 0.990517 1.71563i 0.0431067 0.0746630i
\(529\) −1.49231 + 2.58475i −0.0648829 + 0.112380i
\(530\) 25.5947 14.7771i 1.11176 0.641878i
\(531\) −4.75205 −0.206221
\(532\) −6.08256 + 1.32064i −0.263712 + 0.0572570i
\(533\) −9.32534 3.73238i −0.403925 0.161667i
\(534\) 3.07877 + 5.33259i 0.133232 + 0.230764i
\(535\) −16.8868 + 29.2488i −0.730081 + 1.26454i
\(536\) 21.2220 + 12.2525i 0.916650 + 0.529228i
\(537\) −0.936092 1.62136i −0.0403954 0.0699668i
\(538\) 26.5726 1.14563
\(539\) −35.9542 3.46214i −1.54866 0.149125i
\(540\) 13.6564i 0.587677i
\(541\) −12.0284 20.8338i −0.517142 0.895716i −0.999802 0.0199082i \(-0.993663\pi\)
0.482660 0.875808i \(-0.339671\pi\)
\(542\) −2.49620 + 4.32355i −0.107221 + 0.185712i
\(543\) −5.14325 + 8.90836i −0.220718 + 0.382294i
\(544\) −12.2455 + 7.06992i −0.525020 + 0.303121i
\(545\) 29.5160i 1.26432i
\(546\) −0.657816 3.02975i −0.0281519 0.129661i
\(547\) 27.3582i 1.16975i 0.811123 + 0.584876i \(0.198857\pi\)
−0.811123 + 0.584876i \(0.801143\pi\)
\(548\) 9.74459 5.62604i 0.416268 0.240333i
\(549\) −5.96933 + 10.3392i −0.254765 + 0.441265i
\(550\) −12.6027 7.27619i −0.537382 0.310258i
\(551\) −0.281494 0.487563i −0.0119921 0.0207709i
\(552\) 11.9030i 0.506626i
\(553\) 0.883162 + 0.972289i 0.0375559 + 0.0413459i
\(554\) 8.52356 0.362131
\(555\) −18.0381 + 10.4143i −0.765675 + 0.442063i
\(556\) 5.88600 10.1949i 0.249622 0.432358i
\(557\) 18.4992 + 10.6805i 0.783836 + 0.452548i 0.837788 0.545996i \(-0.183849\pi\)
−0.0539522 + 0.998544i \(0.517182\pi\)
\(558\) 2.66183 + 4.61043i 0.112684 + 0.195175i
\(559\) 11.8854i 0.502698i
\(560\) 3.42807 + 1.09734i 0.144862 + 0.0463711i
\(561\) 10.8042i 0.456153i
\(562\) −10.2773 + 5.93361i −0.433522 + 0.250294i
\(563\) 22.9403 + 13.2446i 0.966820 + 0.558194i 0.898265 0.439454i \(-0.144828\pi\)
0.0685545 + 0.997647i \(0.478161\pi\)
\(564\) 3.57839 6.19795i 0.150677 0.260981i
\(565\) −14.9880 25.9599i −0.630549 1.09214i
\(566\) −2.65129 −0.111442
\(567\) 9.22752 + 2.95377i 0.387520 + 0.124047i
\(568\) 25.2193i 1.05818i
\(569\) −1.60599 2.78165i −0.0673265 0.116613i 0.830397 0.557172i \(-0.188114\pi\)
−0.897724 + 0.440559i \(0.854780\pi\)
\(570\) 2.20963 3.82718i 0.0925511 0.160303i
\(571\) −10.0684 5.81301i −0.421350 0.243267i 0.274305 0.961643i \(-0.411552\pi\)
−0.695655 + 0.718376i \(0.744886\pi\)
\(572\) 4.55689 + 7.89277i 0.190533 + 0.330013i
\(573\) −11.8639 −0.495622
\(574\) 5.53040 + 14.8418i 0.230835 + 0.619483i
\(575\) −15.3765 −0.641245
\(576\) −7.09148 12.2828i −0.295478 0.511784i
\(577\) 25.0722 + 14.4755i 1.04377 + 0.602621i 0.920899 0.389802i \(-0.127456\pi\)
0.122871 + 0.992423i \(0.460790\pi\)
\(578\) 4.73669 8.20418i 0.197020 0.341249i
\(579\) 0.459768 + 0.796342i 0.0191073 + 0.0330948i
\(580\) 0.858936i 0.0356654i
\(581\) 2.92707 + 13.4814i 0.121435 + 0.559303i
\(582\) −7.54407 −0.312712
\(583\) −28.8056 49.8928i −1.19301 2.06635i
\(584\) −1.37312 + 2.37832i −0.0568203 + 0.0984156i
\(585\) 9.08381 + 5.24454i 0.375569 + 0.216835i
\(586\) 12.1634 7.02253i 0.502465 0.290098i
\(587\) 21.5525i 0.889568i 0.895638 + 0.444784i \(0.146719\pi\)
−0.895638 + 0.444784i \(0.853281\pi\)
\(588\) 3.65682 5.12663i 0.150805 0.211418i
\(589\) 5.03803i 0.207589i
\(590\) 2.66326 + 4.61289i 0.109644 + 0.189910i
\(591\) −5.73600 3.31168i −0.235947 0.136224i
\(592\) 2.21200 3.83130i 0.0909127 0.157465i
\(593\) 21.7609 12.5637i 0.893614 0.515928i 0.0184911 0.999829i \(-0.494114\pi\)
0.875123 + 0.483901i \(0.160780\pi\)
\(594\) −20.6668 −0.847969
\(595\) −19.1836 + 4.16513i −0.786450 + 0.170754i
\(596\) 25.8569i 1.05914i
\(597\) 0.476801 + 0.825844i 0.0195142 + 0.0337996i
\(598\) −6.47447 3.73804i −0.264761 0.152860i
\(599\) 10.9830 19.0231i 0.448752 0.777261i −0.549553 0.835459i \(-0.685202\pi\)
0.998305 + 0.0581978i \(0.0185354\pi\)
\(600\) 6.09999 3.52183i 0.249031 0.143778i
\(601\) 36.7762i 1.50013i −0.661362 0.750067i \(-0.730021\pi\)
0.661362 0.750067i \(-0.269979\pi\)
\(602\) −13.8727 + 12.6011i −0.565411 + 0.513581i
\(603\) 19.8020i 0.806399i
\(604\) 6.96468 4.02106i 0.283389 0.163614i
\(605\) −22.1218 + 38.3161i −0.899380 + 1.55777i
\(606\) 4.15981 7.20501i 0.168981 0.292683i
\(607\) −5.38324 9.32404i −0.218499 0.378451i 0.735850 0.677144i \(-0.236783\pi\)
−0.954349 + 0.298693i \(0.903449\pi\)
\(608\) 11.2743i 0.457232i
\(609\) 0.542469 + 0.173647i 0.0219820 + 0.00703653i
\(610\) 13.3819 0.541817
\(611\) −6.23988 10.8078i −0.252439 0.437237i
\(612\) 6.03440 + 3.48396i 0.243926 + 0.140831i
\(613\) −3.27709 + 5.67609i −0.132360 + 0.229255i −0.924586 0.380973i \(-0.875589\pi\)
0.792226 + 0.610228i \(0.208922\pi\)
\(614\) −14.8589 25.7364i −0.599657 1.03864i
\(615\) 13.4482 + 5.38249i 0.542282 + 0.217043i
\(616\) 12.1638 37.9994i 0.490093 1.53104i
\(617\) 28.6247 1.15239 0.576193 0.817313i \(-0.304538\pi\)
0.576193 + 0.817313i \(0.304538\pi\)
\(618\) 10.2783 5.93417i 0.413454 0.238707i
\(619\) 19.9590 34.5700i 0.802220 1.38949i −0.115932 0.993257i \(-0.536985\pi\)
0.918152 0.396229i \(-0.129681\pi\)
\(620\) −3.84319 + 6.65660i −0.154346 + 0.267336i
\(621\) −18.9116 + 10.9186i −0.758896 + 0.438149i
\(622\) 15.8209i 0.634361i
\(623\) 14.6636 + 16.1434i 0.587484 + 0.646772i
\(624\) 0.602245 0.0241091
\(625\) 15.4916 + 26.8323i 0.619665 + 1.07329i
\(626\) −25.8371 14.9170i −1.03266 0.596204i
\(627\) −7.46047 4.30731i −0.297943 0.172017i
\(628\) −21.5147 + 12.4215i −0.858532 + 0.495674i
\(629\) 24.1277i 0.962034i
\(630\) −3.50931 16.1631i −0.139814 0.643951i
\(631\) −26.3805 −1.05019 −0.525096 0.851043i \(-0.675971\pi\)
−0.525096 + 0.851043i \(0.675971\pi\)
\(632\) −1.25652 + 0.725454i −0.0499818 + 0.0288570i
\(633\) 4.60975 7.98433i 0.183221 0.317348i
\(634\) −22.6091 13.0534i −0.897922 0.518415i
\(635\) −9.34692 16.1893i −0.370921 0.642454i
\(636\) 10.0438 0.398264
\(637\) −4.55365 9.99216i −0.180422 0.395904i
\(638\) 1.29987 0.0514622
\(639\) −17.6489 + 10.1896i −0.698178 + 0.403093i
\(640\) 7.32849 12.6933i 0.289684 0.501748i
\(641\) −5.25016 3.03118i −0.207369 0.119724i 0.392719 0.919658i \(-0.371534\pi\)
−0.600088 + 0.799934i \(0.704868\pi\)
\(642\) 7.71682 4.45531i 0.304559 0.175837i
\(643\) 7.51885i 0.296514i −0.988949 0.148257i \(-0.952634\pi\)
0.988949 0.148257i \(-0.0473663\pi\)
\(644\) −3.22187 14.8392i −0.126959 0.584745i
\(645\) 17.1400i 0.674888i
\(646\) −2.55961 4.43338i −0.100707 0.174429i
\(647\) −7.93053 + 13.7361i −0.311781 + 0.540021i −0.978748 0.205067i \(-0.934259\pi\)
0.666967 + 0.745087i \(0.267592\pi\)
\(648\) −5.35110 + 9.26838i −0.210211 + 0.364096i
\(649\) 8.99208 5.19158i 0.352970 0.203787i
\(650\) 4.42400i 0.173524i
\(651\) −3.42708 3.77294i −0.134318 0.147873i
\(652\) 9.06219 0.354903
\(653\) 29.6483 17.1175i 1.16023 0.669858i 0.208870 0.977943i \(-0.433021\pi\)
0.951359 + 0.308085i \(0.0996881\pi\)
\(654\) 3.89365 6.74400i 0.152254 0.263711i
\(655\) 3.04813 5.27952i 0.119100 0.206288i
\(656\) −3.04533 + 0.438120i −0.118900 + 0.0171057i
\(657\) 2.21918 0.0865786
\(658\) −5.99935 + 18.7418i −0.233879 + 0.730633i
\(659\) 4.57842i 0.178350i 0.996016 + 0.0891750i \(0.0284230\pi\)
−0.996016 + 0.0891750i \(0.971577\pi\)
\(660\) −6.57153 11.3822i −0.255797 0.443053i
\(661\) 3.94695 6.83631i 0.153518 0.265902i −0.779000 0.627024i \(-0.784273\pi\)
0.932519 + 0.361122i \(0.117606\pi\)
\(662\) 8.87706 + 5.12518i 0.345017 + 0.199196i
\(663\) −2.84449 + 1.64227i −0.110471 + 0.0637804i
\(664\) −15.2385 −0.591370
\(665\) 4.77183 14.9071i 0.185044 0.578073i
\(666\) −20.3287 −0.787721
\(667\) 1.18947 0.686741i 0.0460564 0.0265907i
\(668\) −22.6339 13.0677i −0.875733 0.505605i
\(669\) 16.4208 + 9.48055i 0.634865 + 0.366539i
\(670\) −19.2221 + 11.0979i −0.742615 + 0.428749i
\(671\) 26.0858i 1.00703i
\(672\) 7.66923 + 8.44320i 0.295847 + 0.325703i
\(673\) 36.3385i 1.40075i 0.713776 + 0.700374i \(0.246983\pi\)
−0.713776 + 0.700374i \(0.753017\pi\)
\(674\) −0.214553 0.371617i −0.00826428 0.0143142i
\(675\) −11.1910 6.46114i −0.430743 0.248689i
\(676\) 5.93311 10.2764i 0.228196 0.395248i
\(677\) 8.99933 + 15.5873i 0.345872 + 0.599069i 0.985512 0.169606i \(-0.0542497\pi\)
−0.639639 + 0.768675i \(0.720916\pi\)
\(678\) 7.90866i 0.303730i
\(679\) −26.1114 + 5.66929i −1.00206 + 0.217567i
\(680\) 21.6839i 0.831540i
\(681\) 7.52780 + 13.0385i 0.288466 + 0.499638i
\(682\) −10.0737 5.81607i −0.385743 0.222709i
\(683\) 4.07132 + 2.35058i 0.155785 + 0.0899423i 0.575866 0.817544i \(-0.304665\pi\)
−0.420081 + 0.907487i \(0.637998\pi\)
\(684\) −4.81147 + 2.77790i −0.183971 + 0.106216i
\(685\) 28.2957i 1.08112i
\(686\) −6.83512 + 15.9089i −0.260966 + 0.607405i
\(687\) −22.9211 −0.874493
\(688\) −1.82027 3.15281i −0.0693973 0.120200i
\(689\) 8.75707 15.1677i 0.333618 0.577843i
\(690\) 9.33689 + 5.39066i 0.355449 + 0.205219i
\(691\) 25.0435 14.4589i 0.952699 0.550041i 0.0587808 0.998271i \(-0.481279\pi\)
0.893918 + 0.448230i \(0.147945\pi\)
\(692\) 17.4110 0.661868
\(693\) −31.5072 + 6.84083i −1.19686 + 0.259862i
\(694\) 15.3275i 0.581823i
\(695\) 14.8016 + 25.6371i 0.561455 + 0.972469i
\(696\) −0.314581 + 0.544871i −0.0119242 + 0.0206533i
\(697\) 13.1888 10.3736i 0.499562 0.392930i
\(698\) −14.5057 25.1245i −0.549047 0.950978i
\(699\) −0.161427 −0.00610572
\(700\) 6.65141 6.04170i 0.251400 0.228355i
\(701\) −27.6401 −1.04395 −0.521977 0.852960i \(-0.674805\pi\)
−0.521977 + 0.852960i \(0.674805\pi\)
\(702\) −3.14141 5.44108i −0.118565 0.205360i
\(703\) −16.6606 9.61899i −0.628366 0.362787i
\(704\) 26.8378 + 15.4948i 1.01149 + 0.583982i
\(705\) 8.99859 + 15.5860i 0.338907 + 0.587003i
\(706\) 8.79257 0.330913
\(707\) 8.98339 28.0639i 0.337855 1.05545i
\(708\) 1.81018i 0.0680308i
\(709\) −10.8151 + 6.24413i −0.406171 + 0.234503i −0.689143 0.724625i \(-0.742013\pi\)
0.282972 + 0.959128i \(0.408680\pi\)
\(710\) 19.7824 + 11.4214i 0.742419 + 0.428636i
\(711\) 1.01537 + 0.586224i 0.0380793 + 0.0219851i
\(712\) −20.8627 + 12.0451i −0.781864 + 0.451409i
\(713\) −12.2909 −0.460298
\(714\) 4.93264 + 1.57896i 0.184599 + 0.0590912i
\(715\) −22.9185 −0.857103
\(716\) 2.28475 1.31910i 0.0853853 0.0492972i
\(717\) −11.9701 + 20.7328i −0.447031 + 0.774280i
\(718\) −13.0638 + 22.6271i −0.487536 + 0.844437i
\(719\) −39.0459 + 22.5431i −1.45617 + 0.840717i −0.998820 0.0485717i \(-0.984533\pi\)
−0.457346 + 0.889289i \(0.651200\pi\)
\(720\) 3.21285 0.119736
\(721\) 31.1156 28.2633i 1.15881 1.05258i
\(722\) −13.6818 −0.509185
\(723\) 0.243989 0.140867i 0.00907406 0.00523891i
\(724\) −12.5533 7.24766i −0.466540 0.269357i
\(725\) 0.703874 + 0.406382i 0.0261412 + 0.0150927i
\(726\) 10.1091 5.83648i 0.375183 0.216612i
\(727\) 35.6238i 1.32121i −0.750732 0.660607i \(-0.770299\pi\)
0.750732 0.660607i \(-0.229701\pi\)
\(728\) 11.8533 2.57358i 0.439312 0.0953831i
\(729\) −1.62023 −0.0600085
\(730\) −1.24373 2.15420i −0.0460324 0.0797304i
\(731\) 17.1948 + 9.92743i 0.635973 + 0.367179i
\(732\) 3.93847 + 2.27387i 0.145570 + 0.0840448i
\(733\) 7.78442 + 13.4830i 0.287524 + 0.498006i 0.973218 0.229883i \(-0.0738345\pi\)
−0.685694 + 0.727890i \(0.740501\pi\)
\(734\) 28.3455 1.04625
\(735\) 6.56685 + 14.4098i 0.242222 + 0.531513i
\(736\) 27.5050 1.01385
\(737\) 21.6335 + 37.4704i 0.796881 + 1.38024i
\(738\) 8.74027 + 11.1122i 0.321734 + 0.409045i
\(739\) −7.31123 + 12.6634i −0.268948 + 0.465832i −0.968590 0.248661i \(-0.920009\pi\)
0.699642 + 0.714493i \(0.253343\pi\)
\(740\) −14.6754 25.4186i −0.539479 0.934405i
\(741\) 2.61889i 0.0962074i
\(742\) −26.9883 + 5.85967i −0.990770 + 0.215115i
\(743\) 17.5545 0.644011 0.322005 0.946738i \(-0.395643\pi\)
0.322005 + 0.946738i \(0.395643\pi\)
\(744\) 4.87590 2.81510i 0.178759 0.103207i
\(745\) −56.3112 32.5113i −2.06308 1.19112i
\(746\) 4.60409 7.97452i 0.168568 0.291968i
\(747\) 6.15696 + 10.6642i 0.225271 + 0.390181i
\(748\) −15.2248 −0.556675
\(749\) 23.3612 21.2198i 0.853601 0.775353i
\(750\) 4.19518i 0.153186i
\(751\) −45.1366 + 26.0596i −1.64706 + 0.950929i −0.668824 + 0.743421i \(0.733202\pi\)
−0.978233 + 0.207508i \(0.933465\pi\)
\(752\) −3.31048 1.91130i −0.120721 0.0696981i
\(753\) −1.52734 0.881808i −0.0556592 0.0321349i
\(754\) 0.197583 + 0.342224i 0.00719556 + 0.0124631i
\(755\) 20.2236i 0.736011i
\(756\) 3.89047 12.1537i 0.141495 0.442027i
\(757\) 6.56451i 0.238591i −0.992859 0.119296i \(-0.961936\pi\)
0.992859 0.119296i \(-0.0380636\pi\)
\(758\) 12.9919 + 22.5027i 0.471888 + 0.817334i
\(759\) 10.5082 18.2008i 0.381424 0.660645i
\(760\) 14.9731 + 8.64473i 0.543132 + 0.313577i
\(761\) 21.9319 + 37.9872i 0.795032 + 1.37704i 0.922819 + 0.385235i \(0.125880\pi\)
−0.127786 + 0.991802i \(0.540787\pi\)
\(762\) 4.93206i 0.178670i
\(763\) 8.40859 26.2683i 0.304412 0.950975i
\(764\) 16.7181i 0.604841i
\(765\) −15.1747 + 8.76115i −0.548644 + 0.316760i
\(766\) 9.97244 + 5.75759i 0.360319 + 0.208030i
\(767\) 2.73364 + 1.57827i 0.0987062 + 0.0569880i
\(768\) −11.6601 + 6.73198i −0.420749 + 0.242919i
\(769\) 23.3701 0.842747 0.421373 0.906887i \(-0.361548\pi\)
0.421373 + 0.906887i \(0.361548\pi\)
\(770\) 24.2985 + 26.7507i 0.875658 + 0.964028i
\(771\) −0.579795 −0.0208808
\(772\) −1.12217 + 0.647887i −0.0403879 + 0.0233180i
\(773\) −12.9930 7.50149i −0.467324 0.269810i 0.247795 0.968813i \(-0.420294\pi\)
−0.715119 + 0.699003i \(0.753627\pi\)
\(774\) −8.36432 + 14.4874i −0.300649 + 0.520740i
\(775\) −3.63660 6.29878i −0.130631 0.226259i
\(776\) 29.5147i 1.05952i
\(777\) 19.0202 4.12965i 0.682346 0.148150i
\(778\) 17.9945 0.645135
\(779\) 1.90518 + 13.2428i 0.0682603 + 0.474471i
\(780\) 1.99778 3.46026i 0.0715321 0.123897i
\(781\) 22.2641 38.5625i 0.796672 1.37988i
\(782\) 10.8158 6.24449i 0.386772 0.223303i
\(783\) 1.15426 0.0412499
\(784\) −2.73826 1.95320i −0.0977949 0.0697570i
\(785\) 62.4731i 2.22976i
\(786\) −1.39291 + 0.804199i −0.0496836 + 0.0286848i
\(787\) 10.4644 18.1248i 0.373015 0.646080i −0.617013 0.786953i \(-0.711657\pi\)
0.990028 + 0.140873i \(0.0449908\pi\)
\(788\) 4.66669 8.08294i 0.166244 0.287943i
\(789\) −7.59024 13.1467i −0.270220 0.468034i
\(790\) 1.31418i 0.0467565i
\(791\) 5.94328 + 27.3733i 0.211319 + 0.973283i
\(792\) 35.6138i 1.26548i
\(793\) 6.86778 3.96511i 0.243882 0.140805i
\(794\) −15.6513 9.03628i −0.555444 0.320686i
\(795\) −12.6286 + 21.8735i −0.447892 + 0.775772i
\(796\) −1.16375 + 0.671889i −0.0412479 + 0.0238145i
\(797\) −6.22453 −0.220484 −0.110242 0.993905i \(-0.535163\pi\)
−0.110242 + 0.993905i \(0.535163\pi\)
\(798\) −3.05680 + 2.77659i −0.108209 + 0.0982901i
\(799\) 20.8478 0.737542
\(800\) 8.13810 + 14.0956i 0.287725 + 0.498355i
\(801\) 16.8587 + 9.73338i 0.595673 + 0.343912i
\(802\) −0.949246 + 1.64414i −0.0335190 + 0.0580567i
\(803\) −4.19926 + 2.42444i −0.148189 + 0.0855567i
\(804\) −7.54310 −0.266024
\(805\) 36.3677 + 11.6415i 1.28179 + 0.410308i
\(806\) 3.53623i 0.124559i
\(807\) −19.6667 + 11.3546i −0.692301 + 0.399700i
\(808\) 28.1882 + 16.2744i 0.991656 + 0.572533i
\(809\) −7.05198 4.07146i −0.247934 0.143145i 0.370884 0.928679i \(-0.379055\pi\)
−0.618818 + 0.785534i \(0.712388\pi\)
\(810\) −4.84684 8.39497i −0.170300 0.294969i
\(811\) 30.7997 1.08152 0.540762 0.841176i \(-0.318136\pi\)
0.540762 + 0.841176i \(0.318136\pi\)
\(812\) −0.244696 + 0.764426i −0.00858715 + 0.0268261i
\(813\) 4.26654i 0.149634i
\(814\) 38.4670 22.2090i 1.34827 0.778423i
\(815\) −11.3944 + 19.7356i −0.399127 + 0.691309i
\(816\) −0.503034 + 0.871280i −0.0176097 + 0.0305009i
\(817\) −13.7101 + 7.91554i −0.479656 + 0.276930i
\(818\) 0.800829 0.0280003
\(819\) −6.59022 7.25529i −0.230281 0.253520i
\(820\) −7.58479 + 18.9506i −0.264872 + 0.661784i
\(821\) −0.921569 1.59620i −0.0321630 0.0557079i 0.849496 0.527595i \(-0.176906\pi\)
−0.881659 + 0.471887i \(0.843573\pi\)
\(822\) 3.73267 6.46518i 0.130192 0.225499i
\(823\) −9.15804 5.28740i −0.319229 0.184307i 0.331820 0.943343i \(-0.392337\pi\)
−0.651049 + 0.759036i \(0.725671\pi\)
\(824\) 23.2163 + 40.2118i 0.808778 + 1.40084i
\(825\) 12.4366 0.432986
\(826\) −1.05608 4.86404i −0.0367456 0.169242i
\(827\) 14.1020i 0.490374i −0.969476 0.245187i \(-0.921151\pi\)
0.969476 0.245187i \(-0.0788493\pi\)
\(828\) −6.77704 11.7382i −0.235518 0.407930i
\(829\) −1.27104 + 2.20150i −0.0441449 + 0.0764612i −0.887254 0.461282i \(-0.847390\pi\)
0.843109 + 0.537743i \(0.180723\pi\)
\(830\) 6.90126 11.9533i 0.239546 0.414906i
\(831\) −6.30839 + 3.64215i −0.218835 + 0.126345i
\(832\) 9.42101i 0.326615i
\(833\) 18.2594 + 1.75825i 0.632649 + 0.0609197i
\(834\) 7.81030i 0.270448i
\(835\) 56.9177 32.8614i 1.96972 1.13722i
\(836\) 6.06968 10.5130i 0.209924 0.363600i
\(837\) −8.94531 5.16458i −0.309195 0.178514i
\(838\) 18.2513 + 31.6122i 0.630481 + 1.09202i
\(839\) 22.0506i 0.761272i 0.924725 + 0.380636i \(0.124295\pi\)
−0.924725 + 0.380636i \(0.875705\pi\)
\(840\) −17.0937 + 3.71138i −0.589790 + 0.128055i
\(841\) 28.9274 0.997497
\(842\) −2.43394 + 1.40523i −0.0838790 + 0.0484276i
\(843\) 5.07091 8.78307i 0.174651 0.302505i
\(844\) 11.2512 + 6.49588i 0.387282 + 0.223597i
\(845\) 14.9200 + 25.8422i 0.513264 + 0.889000i
\(846\) 17.5652i 0.603905i
\(847\) 30.6033 27.7980i 1.05154 0.955151i
\(848\) 5.36466i 0.184223i
\(849\) 1.96225 1.13290i 0.0673442 0.0388812i
\(850\) 6.40029 + 3.69521i 0.219528 + 0.126745i
\(851\) 23.4667 40.6455i 0.804429 1.39331i
\(852\) 3.88148 + 6.72292i 0.132977 + 0.230323i
\(853\) −36.4227 −1.24709 −0.623546 0.781787i \(-0.714308\pi\)
−0.623546 + 0.781787i \(0.714308\pi\)
\(854\) −11.9094 3.81227i −0.407533 0.130453i
\(855\) 13.9712i 0.477806i
\(856\) 17.4305 + 30.1905i 0.595763 + 1.03189i
\(857\) −16.7007 + 28.9265i −0.570486 + 0.988110i 0.426030 + 0.904709i \(0.359912\pi\)
−0.996516 + 0.0834013i \(0.973422\pi\)
\(858\) 5.23657 + 3.02333i 0.178773 + 0.103215i
\(859\) −20.0370 34.7051i −0.683653 1.18412i −0.973858 0.227157i \(-0.927057\pi\)
0.290205 0.956964i \(-0.406276\pi\)
\(860\) −24.1530 −0.823611
\(861\) −10.4351 8.62140i −0.355626 0.293816i
\(862\) −12.3591 −0.420951
\(863\) −19.8954 34.4598i −0.677247 1.17303i −0.975807 0.218636i \(-0.929839\pi\)
0.298559 0.954391i \(-0.403494\pi\)
\(864\) 20.0181 + 11.5575i 0.681030 + 0.393193i
\(865\) −21.8918 + 37.9177i −0.744344 + 1.28924i
\(866\) 14.7016 + 25.4638i 0.499579 + 0.865297i
\(867\) 8.09602i 0.274955i
\(868\) 5.31667 4.82930i 0.180460 0.163917i
\(869\) −2.56178 −0.0869025
\(870\) −0.284937 0.493525i −0.00966025 0.0167320i
\(871\) −6.57671 + 11.3912i −0.222843 + 0.385976i
\(872\) 26.3846 + 15.2331i 0.893494 + 0.515859i
\(873\) −20.6549 + 11.9251i −0.699061 + 0.403603i
\(874\) 9.95797i 0.336833i
\(875\) −3.15264 14.5203i −0.106579 0.490876i
\(876\) 0.845345i 0.0285616i
\(877\) −17.7997 30.8300i −0.601054 1.04106i −0.992662 0.120924i \(-0.961414\pi\)
0.391608 0.920132i \(-0.371919\pi\)
\(878\) −9.16163 5.28947i −0.309190 0.178511i
\(879\) −6.00151 + 10.3949i −0.202426 + 0.350612i
\(880\) −6.07953 + 3.51002i −0.204941 + 0.118323i
\(881\) 9.30281 0.313420 0.156710 0.987645i \(-0.449911\pi\)
0.156710 + 0.987645i \(0.449911\pi\)
\(882\) −1.48140 + 15.3843i −0.0498815 + 0.518018i
\(883\) 52.4893i 1.76641i 0.468990 + 0.883203i \(0.344618\pi\)
−0.468990 + 0.883203i \(0.655382\pi\)
\(884\) −2.31422 4.00834i −0.0778355 0.134815i
\(885\) −3.94221 2.27604i −0.132516 0.0765082i
\(886\) 10.7107 18.5514i 0.359832 0.623248i
\(887\) −4.93760 + 2.85072i −0.165788 + 0.0957179i −0.580598 0.814190i \(-0.697181\pi\)
0.414810 + 0.909908i \(0.363848\pi\)
\(888\) 21.4992i 0.721467i
\(889\) 3.70639 + 17.0708i 0.124308 + 0.572535i
\(890\) 21.8200i 0.731409i
\(891\) −16.3646 + 9.44812i −0.548235 + 0.316524i
\(892\) −13.3596 + 23.1395i −0.447313 + 0.774769i
\(893\) −8.31139 + 14.3958i −0.278130 + 0.481736i
\(894\) 8.57757 + 14.8568i 0.286877 + 0.496885i
\(895\) 6.63432i 0.221761i
\(896\) −10.1382 + 9.20889i −0.338695 + 0.307647i
\(897\) 6.38911 0.213326
\(898\) −15.7446 27.2704i −0.525403 0.910025i
\(899\) 0.562627 + 0.324833i 0.0187647 + 0.0108338i
\(900\) 4.01035 6.94613i 0.133678 0.231538i
\(901\) 14.6289 + 25.3380i 0.487360 + 0.844133i
\(902\) −28.6788 11.4784i −0.954899 0.382189i
\(903\) 4.88290 15.2541i 0.162493 0.507624i
\(904\) −30.9411 −1.02908
\(905\) 31.5679 18.2257i 1.04935 0.605844i
\(906\) 2.66783 4.62081i 0.0886326 0.153516i
\(907\) −2.06751 + 3.58103i −0.0686504 + 0.118906i −0.898307 0.439367i \(-0.855203\pi\)
0.829657 + 0.558273i \(0.188536\pi\)
\(908\) −18.3734 + 10.6079i −0.609742 + 0.352035i
\(909\) 26.3020i 0.872384i
\(910\) −3.34939 + 10.4634i −0.111031 + 0.346859i
\(911\) −38.4184 −1.27286 −0.636430 0.771335i \(-0.719590\pi\)
−0.636430 + 0.771335i \(0.719590\pi\)
\(912\) −0.401089 0.694707i −0.0132814 0.0230040i
\(913\) −23.3011 13.4529i −0.771153 0.445225i
\(914\) 7.35939 + 4.24894i 0.243427 + 0.140543i
\(915\) −9.90409 + 5.71813i −0.327419 + 0.189035i
\(916\) 32.2994i 1.06720i
\(917\) −4.21678 + 3.83024i −0.139250 + 0.126486i
\(918\) 10.4956 0.346407
\(919\) −18.7736 + 10.8389i −0.619283 + 0.357543i −0.776590 0.630006i \(-0.783052\pi\)
0.157307 + 0.987550i \(0.449719\pi\)
\(920\) −21.0899 + 36.5288i −0.695313 + 1.20432i
\(921\) 21.9945 + 12.6985i 0.724744 + 0.418431i
\(922\) −7.03372 12.1828i −0.231643 0.401218i
\(923\) 13.5368 0.445570
\(924\) 2.60585 + 12.0019i 0.0857263 + 0.394835i
\(925\) 27.7731 0.913174
\(926\) −16.4700 + 9.50897i −0.541238 + 0.312484i
\(927\) 18.7606 32.4943i 0.616178 1.06725i
\(928\) −1.25907 0.726922i −0.0413309 0.0238624i
\(929\) −1.92665 + 1.11235i −0.0632113 + 0.0364951i −0.531273 0.847201i \(-0.678286\pi\)
0.468061 + 0.883696i \(0.344953\pi\)
\(930\) 5.09964i 0.167224i
\(931\) −8.49356 + 11.9074i −0.278365 + 0.390250i
\(932\) 0.227476i 0.00745123i
\(933\) −6.76033 11.7092i −0.221323 0.383343i
\(934\) −18.1107 + 31.3687i −0.592600 + 1.02641i
\(935\) 19.1430 33.1566i 0.626043 1.08434i
\(936\) 9.37628 5.41340i 0.306473 0.176942i
\(937\) 6.96322i 0.227479i 0.993511 + 0.113739i \(0.0362829\pi\)
−0.993511 + 0.113739i \(0.963717\pi\)
\(938\) 20.2687 4.40072i 0.661795 0.143688i
\(939\) 25.4964 0.832044
\(940\) −21.9632 + 12.6805i −0.716360 + 0.413591i
\(941\) −25.7052 + 44.5227i −0.837965 + 1.45140i 0.0536282 + 0.998561i \(0.482921\pi\)
−0.891593 + 0.452837i \(0.850412\pi\)
\(942\) −8.24125 + 14.2743i −0.268514 + 0.465080i
\(943\) −32.3074 + 4.64793i −1.05207 + 0.151357i
\(944\) 0.966863 0.0314687
\(945\) 21.5767 + 23.7542i 0.701891 + 0.772724i
\(946\) 36.5518i 1.18840i
\(947\) −3.99412 6.91801i −0.129791 0.224805i 0.793804 0.608173i \(-0.208097\pi\)
−0.923596 + 0.383368i \(0.874764\pi\)
\(948\) 0.223308 0.386781i 0.00725271 0.0125621i
\(949\) −1.27660 0.737044i −0.0414401 0.0239255i
\(950\) −5.10321 + 2.94634i −0.165570 + 0.0955919i
\(951\) 22.3110 0.723484
\(952\) −6.17738 + 19.2980i −0.200210 + 0.625452i
\(953\) 15.6112 0.505695 0.252847 0.967506i \(-0.418633\pi\)
0.252847 + 0.967506i \(0.418633\pi\)
\(954\) −21.3485 + 12.3255i −0.691182 + 0.399054i
\(955\) 36.4088 + 21.0206i 1.17816 + 0.680211i
\(956\) −29.2158 16.8678i −0.944907 0.545542i
\(957\) −0.962046 + 0.555437i −0.0310985 + 0.0179547i
\(958\) 11.5567i 0.373380i
\(959\) 8.06096 25.1823i 0.260302 0.813177i
\(960\) 13.5861i 0.438490i
\(961\) 12.5932 + 21.8120i 0.406231 + 0.703613i
\(962\) 11.6942 + 6.75165i 0.377036 + 0.217682i
\(963\) 14.0852 24.3963i 0.453890 0.786160i
\(964\) 0.198504 + 0.343820i 0.00639340 + 0.0110737i
\(965\) 3.25849i 0.104895i
\(966\) −6.77383 7.45743i −0.217944 0.239939i
\(967\) 38.4050i 1.23502i −0.786562 0.617511i \(-0.788141\pi\)
0.786562 0.617511i \(-0.211859\pi\)
\(968\) 22.8341 + 39.5498i 0.733915 + 1.27118i
\(969\) 3.78880 + 2.18746i 0.121714 + 0.0702715i
\(970\) 23.1518 + 13.3667i 0.743358 + 0.429178i
\(971\) 23.4682 13.5493i 0.753129 0.434819i −0.0736944 0.997281i \(-0.523479\pi\)
0.826823 + 0.562462i \(0.190146\pi\)
\(972\) 17.7642i 0.569787i
\(973\) −5.86936 27.0329i −0.188163 0.866634i
\(974\) 11.0525 0.354145
\(975\) 1.89039 + 3.27426i 0.0605410 + 0.104860i
\(976\) 1.21453 2.10363i 0.0388762 0.0673356i
\(977\) −3.52910 2.03753i −0.112906 0.0651863i 0.442484 0.896777i \(-0.354097\pi\)
−0.555390 + 0.831590i \(0.687431\pi\)
\(978\) 5.20692 3.00622i 0.166499 0.0961282i
\(979\) −42.5346 −1.35941
\(980\) −20.3057 + 9.25375i −0.648642 + 0.295600i
\(981\) 24.6191i 0.786028i
\(982\) 13.4001 + 23.2097i 0.427615 + 0.740651i
\(983\) 26.8277 46.4669i 0.855671 1.48207i −0.0203505 0.999793i \(-0.506478\pi\)
0.876021 0.482272i \(-0.160188\pi\)
\(984\) 11.7520 9.24353i 0.374641 0.294673i
\(985\) 11.7353 + 20.3262i 0.373919 + 0.647647i
\(986\) −0.660136 −0.0210230
\(987\) −3.56827 16.4346i −0.113579 0.523119i
\(988\) 3.69044 0.117408
\(989\) −19.3109 33.4475i −0.614052 1.06357i
\(990\) 27.9360 + 16.1288i 0.887864 + 0.512608i
\(991\) 6.14503 + 3.54783i 0.195203 + 0.112701i 0.594416 0.804158i \(-0.297383\pi\)
−0.399213 + 0.916858i \(0.630717\pi\)
\(992\) 6.50502 + 11.2670i 0.206535 + 0.357729i
\(993\) −8.76003 −0.277991
\(994\) −14.3519 15.8003i −0.455216 0.501155i
\(995\) 3.37921i 0.107128i
\(996\) 4.06226 2.34535i 0.128718 0.0743152i
\(997\) −44.9623 25.9590i −1.42397 0.822130i −0.427336 0.904093i \(-0.640548\pi\)
−0.996635 + 0.0819630i \(0.973881\pi\)
\(998\) −1.92231 1.10985i −0.0608498 0.0351316i
\(999\) 34.1581 19.7212i 1.08072 0.623951i
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 287.2.j.a.81.17 52
7.2 even 3 inner 287.2.j.a.163.18 yes 52
41.40 even 2 inner 287.2.j.a.81.18 yes 52
287.163 even 6 inner 287.2.j.a.163.17 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.j.a.81.17 52 1.1 even 1 trivial
287.2.j.a.81.18 yes 52 41.40 even 2 inner
287.2.j.a.163.17 yes 52 287.163 even 6 inner
287.2.j.a.163.18 yes 52 7.2 even 3 inner