Properties

Label 429.2.p.b.230.3
Level $429$
Weight $2$
Character 429.230
Analytic conductor $3.426$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(230,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.230");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.p (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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 230.3
Character \(\chi\) \(=\) 429.230
Dual form 429.2.p.b.263.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23621 + 2.14118i) q^{2} +(-1.16044 + 1.28584i) q^{3} +(-2.05645 - 3.56187i) q^{4} +2.31580i q^{5} +(-1.31867 - 4.07429i) q^{6} +(-3.20654 + 1.85129i) q^{7} +5.22398 q^{8} +(-0.306758 - 2.98428i) q^{9} +O(q^{10})\) \(q+(-1.23621 + 2.14118i) q^{2} +(-1.16044 + 1.28584i) q^{3} +(-2.05645 - 3.56187i) q^{4} +2.31580i q^{5} +(-1.31867 - 4.07429i) q^{6} +(-3.20654 + 1.85129i) q^{7} +5.22398 q^{8} +(-0.306758 - 2.98428i) q^{9} +(-4.95856 - 2.86283i) q^{10} +(-0.00334847 + 3.31662i) q^{11} +(6.96638 + 1.48908i) q^{12} +(-2.99673 - 2.00489i) q^{13} -9.15438i q^{14} +(-2.97775 - 2.68735i) q^{15} +(-2.34506 + 4.06177i) q^{16} +(1.81821 + 3.14922i) q^{17} +(6.76910 + 3.03238i) q^{18} +(1.23762 - 0.714538i) q^{19} +(8.24860 - 4.76233i) q^{20} +(1.34053 - 6.27140i) q^{21} +(-7.09736 - 4.10722i) q^{22} +(-4.95627 - 2.86150i) q^{23} +(-6.06212 + 6.71720i) q^{24} -0.362948 q^{25} +(7.99745 - 3.93808i) q^{26} +(4.19327 + 3.06863i) q^{27} +(13.1881 + 7.61418i) q^{28} +(0.195179 - 0.338060i) q^{29} +(9.43525 - 3.05377i) q^{30} +7.44153 q^{31} +(-0.574015 - 0.994224i) q^{32} +(-4.26075 - 3.85305i) q^{33} -8.99076 q^{34} +(-4.28723 - 7.42571i) q^{35} +(-9.99878 + 7.22964i) q^{36} +(-2.18584 + 3.78599i) q^{37} +3.53329i q^{38} +(6.05550 - 1.52675i) q^{39} +12.0977i q^{40} +(2.49288 - 4.31779i) q^{41} +(11.7710 + 10.6231i) q^{42} +(-6.34232 + 3.66174i) q^{43} +(11.8203 - 6.80854i) q^{44} +(6.91100 - 0.710392i) q^{45} +(12.2540 - 7.07485i) q^{46} +9.51675i q^{47} +(-2.50147 - 7.72881i) q^{48} +(3.35458 - 5.81030i) q^{49} +(0.448682 - 0.777140i) q^{50} +(-6.15931 - 1.31657i) q^{51} +(-0.978559 + 14.7969i) q^{52} -4.53927i q^{53} +(-11.7543 + 5.18508i) q^{54} +(-7.68065 - 0.00775439i) q^{55} +(-16.7509 + 9.67113i) q^{56} +(-0.517399 + 2.42055i) q^{57} +(0.482567 + 0.835830i) q^{58} +(-1.96442 + 1.13416i) q^{59} +(-3.44842 + 16.1328i) q^{60} +(7.11598 - 4.10841i) q^{61} +(-9.19932 + 15.9337i) q^{62} +(6.50840 + 9.00128i) q^{63} -6.54183 q^{64} +(4.64294 - 6.93984i) q^{65} +(13.5173 - 4.35987i) q^{66} +(1.25601 - 2.17547i) q^{67} +(7.47809 - 12.9524i) q^{68} +(9.43088 - 3.05235i) q^{69} +21.1998 q^{70} +(-12.1268 + 7.00140i) q^{71} +(-1.60250 - 15.5898i) q^{72} -13.6341i q^{73} +(-5.40433 - 9.36058i) q^{74} +(0.421180 - 0.466693i) q^{75} +(-5.09019 - 2.93882i) q^{76} +(-6.12931 - 10.6411i) q^{77} +(-4.21683 + 14.8533i) q^{78} -9.28575i q^{79} +(-9.40626 - 5.43071i) q^{80} +(-8.81180 + 1.83090i) q^{81} +(6.16346 + 10.6754i) q^{82} -1.73616 q^{83} +(-25.0947 + 8.12202i) q^{84} +(-7.29298 + 4.21061i) q^{85} -18.1068i q^{86} +(0.208197 + 0.643268i) q^{87} +(-0.0174923 + 17.3260i) q^{88} +(-9.51379 - 5.49279i) q^{89} +(-7.02239 + 15.6759i) q^{90} +(13.3208 + 0.880936i) q^{91} +23.5381i q^{92} +(-8.63545 + 9.56860i) q^{93} +(-20.3771 - 11.7647i) q^{94} +(1.65473 + 2.86608i) q^{95} +(1.94452 + 0.415646i) q^{96} +(-8.03552 - 13.9179i) q^{97} +(8.29395 + 14.3656i) q^{98} +(9.89874 - 1.00741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9} + 28 q^{12} - 8 q^{15} - 44 q^{16} + 16 q^{22} - 56 q^{25} + 44 q^{27} - 40 q^{31} - 16 q^{33} - 56 q^{34} + 40 q^{36} + 28 q^{37} - 22 q^{42} - 10 q^{45} + 24 q^{48} - 8 q^{49} - 12 q^{55} - 16 q^{58} - 76 q^{60} + 104 q^{64} + 68 q^{66} - 24 q^{67} + 30 q^{69} + 88 q^{70} - 66 q^{75} - 28 q^{78} - 66 q^{81} + 32 q^{82} - 8 q^{88} - 80 q^{91} + 30 q^{93} - 80 q^{97} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23621 + 2.14118i −0.874135 + 1.51405i −0.0164538 + 0.999865i \(0.505238\pi\)
−0.857681 + 0.514182i \(0.828096\pi\)
\(3\) −1.16044 + 1.28584i −0.669980 + 0.742379i
\(4\) −2.05645 3.56187i −1.02822 1.78094i
\(5\) 2.31580i 1.03566i 0.855484 + 0.517830i \(0.173260\pi\)
−0.855484 + 0.517830i \(0.826740\pi\)
\(6\) −1.31867 4.07429i −0.538343 1.66332i
\(7\) −3.20654 + 1.85129i −1.21196 + 0.699723i −0.963185 0.268839i \(-0.913360\pi\)
−0.248771 + 0.968562i \(0.580027\pi\)
\(8\) 5.22398 1.84696
\(9\) −0.306758 2.98428i −0.102253 0.994758i
\(10\) −4.95856 2.86283i −1.56804 0.905306i
\(11\) −0.00334847 + 3.31662i −0.00100960 + 0.999999i
\(12\) 6.96638 + 1.48908i 2.01102 + 0.429860i
\(13\) −2.99673 2.00489i −0.831144 0.556058i
\(14\) 9.15438i 2.44661i
\(15\) −2.97775 2.68735i −0.768851 0.693871i
\(16\) −2.34506 + 4.06177i −0.586266 + 1.01544i
\(17\) 1.81821 + 3.14922i 0.440979 + 0.763799i 0.997762 0.0668592i \(-0.0212978\pi\)
−0.556783 + 0.830658i \(0.687964\pi\)
\(18\) 6.76910 + 3.03238i 1.59549 + 0.714738i
\(19\) 1.23762 0.714538i 0.283929 0.163926i −0.351272 0.936273i \(-0.614251\pi\)
0.635201 + 0.772347i \(0.280917\pi\)
\(20\) 8.24860 4.76233i 1.84444 1.06489i
\(21\) 1.34053 6.27140i 0.292527 1.36853i
\(22\) −7.09736 4.10722i −1.51316 0.875663i
\(23\) −4.95627 2.86150i −1.03345 0.596664i −0.115481 0.993310i \(-0.536841\pi\)
−0.917972 + 0.396645i \(0.870174\pi\)
\(24\) −6.06212 + 6.71720i −1.23743 + 1.37114i
\(25\) −0.362948 −0.0725897
\(26\) 7.99745 3.93808i 1.56843 0.772320i
\(27\) 4.19327 + 3.06863i 0.806995 + 0.590558i
\(28\) 13.1881 + 7.61418i 2.49233 + 1.43895i
\(29\) 0.195179 0.338060i 0.0362439 0.0627762i −0.847334 0.531060i \(-0.821794\pi\)
0.883578 + 0.468283i \(0.155127\pi\)
\(30\) 9.43525 3.05377i 1.72263 0.557540i
\(31\) 7.44153 1.33654 0.668269 0.743920i \(-0.267035\pi\)
0.668269 + 0.743920i \(0.267035\pi\)
\(32\) −0.574015 0.994224i −0.101473 0.175756i
\(33\) −4.26075 3.85305i −0.741702 0.670729i
\(34\) −8.99076 −1.54190
\(35\) −4.28723 7.42571i −0.724675 1.25517i
\(36\) −9.99878 + 7.22964i −1.66646 + 1.20494i
\(37\) −2.18584 + 3.78599i −0.359350 + 0.622413i −0.987852 0.155395i \(-0.950335\pi\)
0.628502 + 0.777808i \(0.283668\pi\)
\(38\) 3.53329i 0.573175i
\(39\) 6.05550 1.52675i 0.969655 0.244476i
\(40\) 12.0977i 1.91282i
\(41\) 2.49288 4.31779i 0.389322 0.674326i −0.603036 0.797714i \(-0.706043\pi\)
0.992359 + 0.123388i \(0.0393759\pi\)
\(42\) 11.7710 + 10.6231i 1.81631 + 1.63918i
\(43\) −6.34232 + 3.66174i −0.967194 + 0.558410i −0.898380 0.439220i \(-0.855255\pi\)
−0.0688144 + 0.997629i \(0.521922\pi\)
\(44\) 11.8203 6.80854i 1.78197 1.02643i
\(45\) 6.91100 0.710392i 1.03023 0.105899i
\(46\) 12.2540 7.07485i 1.80675 1.04313i
\(47\) 9.51675i 1.38816i 0.719897 + 0.694081i \(0.244189\pi\)
−0.719897 + 0.694081i \(0.755811\pi\)
\(48\) −2.50147 7.72881i −0.361056 1.11556i
\(49\) 3.35458 5.81030i 0.479226 0.830043i
\(50\) 0.448682 0.777140i 0.0634532 0.109904i
\(51\) −6.15931 1.31657i −0.862476 0.184356i
\(52\) −0.978559 + 14.7969i −0.135702 + 2.05197i
\(53\) 4.53927i 0.623517i −0.950161 0.311759i \(-0.899082\pi\)
0.950161 0.311759i \(-0.100918\pi\)
\(54\) −11.7543 + 5.18508i −1.59956 + 0.705600i
\(55\) −7.68065 0.00775439i −1.03566 0.00104560i
\(56\) −16.7509 + 9.67113i −2.23843 + 1.29236i
\(57\) −0.517399 + 2.42055i −0.0685312 + 0.320610i
\(58\) 0.482567 + 0.835830i 0.0633641 + 0.109750i
\(59\) −1.96442 + 1.13416i −0.255746 + 0.147655i −0.622392 0.782705i \(-0.713839\pi\)
0.366646 + 0.930360i \(0.380506\pi\)
\(60\) −3.44842 + 16.1328i −0.445189 + 2.08273i
\(61\) 7.11598 4.10841i 0.911108 0.526029i 0.0303207 0.999540i \(-0.490347\pi\)
0.880788 + 0.473512i \(0.157014\pi\)
\(62\) −9.19932 + 15.9337i −1.16831 + 2.02358i
\(63\) 6.50840 + 9.00128i 0.819982 + 1.13406i
\(64\) −6.54183 −0.817729
\(65\) 4.64294 6.93984i 0.575886 0.860781i
\(66\) 13.5173 4.35987i 1.66386 0.536663i
\(67\) 1.25601 2.17547i 0.153446 0.265776i −0.779046 0.626967i \(-0.784296\pi\)
0.932492 + 0.361191i \(0.117630\pi\)
\(68\) 7.47809 12.9524i 0.906852 1.57071i
\(69\) 9.43088 3.05235i 1.13534 0.367460i
\(70\) 21.1998 2.53385
\(71\) −12.1268 + 7.00140i −1.43918 + 0.830913i −0.997793 0.0664013i \(-0.978848\pi\)
−0.441391 + 0.897315i \(0.645515\pi\)
\(72\) −1.60250 15.5898i −0.188857 1.83728i
\(73\) 13.6341i 1.59575i −0.602822 0.797875i \(-0.705957\pi\)
0.602822 0.797875i \(-0.294043\pi\)
\(74\) −5.40433 9.36058i −0.628241 1.08815i
\(75\) 0.421180 0.466693i 0.0486337 0.0538891i
\(76\) −5.09019 2.93882i −0.583885 0.337106i
\(77\) −6.12931 10.6411i −0.698499 1.21266i
\(78\) −4.21683 + 14.8533i −0.477462 + 1.68181i
\(79\) 9.28575i 1.04473i −0.852723 0.522364i \(-0.825050\pi\)
0.852723 0.522364i \(-0.174950\pi\)
\(80\) −9.40626 5.43071i −1.05165 0.607172i
\(81\) −8.81180 + 1.83090i −0.979089 + 0.203434i
\(82\) 6.16346 + 10.6754i 0.680641 + 1.17890i
\(83\) −1.73616 −0.190569 −0.0952843 0.995450i \(-0.530376\pi\)
−0.0952843 + 0.995450i \(0.530376\pi\)
\(84\) −25.0947 + 8.12202i −2.73805 + 0.886185i
\(85\) −7.29298 + 4.21061i −0.791035 + 0.456704i
\(86\) 18.1068i 1.95250i
\(87\) 0.208197 + 0.643268i 0.0223211 + 0.0689655i
\(88\) −0.0174923 + 17.3260i −0.00186469 + 1.84696i
\(89\) −9.51379 5.49279i −1.00846 0.582234i −0.0977191 0.995214i \(-0.531155\pi\)
−0.910740 + 0.412980i \(0.864488\pi\)
\(90\) −7.02239 + 15.6759i −0.740225 + 1.65239i
\(91\) 13.3208 + 0.880936i 1.39640 + 0.0923472i
\(92\) 23.5381i 2.45402i
\(93\) −8.63545 + 9.56860i −0.895454 + 0.992218i
\(94\) −20.3771 11.7647i −2.10174 1.21344i
\(95\) 1.65473 + 2.86608i 0.169772 + 0.294053i
\(96\) 1.94452 + 0.415646i 0.198462 + 0.0424217i
\(97\) −8.03552 13.9179i −0.815884 1.41315i −0.908692 0.417468i \(-0.862918\pi\)
0.0928080 0.995684i \(-0.470416\pi\)
\(98\) 8.29395 + 14.3656i 0.837816 + 1.45114i
\(99\) 9.89874 1.00741i 0.994861 0.101248i
\(100\) 0.746385 + 1.29278i 0.0746385 + 0.129278i
\(101\) −3.58744 + 6.21363i −0.356964 + 0.618279i −0.987452 0.157920i \(-0.949521\pi\)
0.630488 + 0.776199i \(0.282855\pi\)
\(102\) 10.4332 11.5607i 1.03304 1.14468i
\(103\) −14.0291 −1.38233 −0.691164 0.722698i \(-0.742902\pi\)
−0.691164 + 0.722698i \(0.742902\pi\)
\(104\) −15.6549 10.4735i −1.53509 1.02702i
\(105\) 14.5233 + 3.10440i 1.41733 + 0.302958i
\(106\) 9.71942 + 5.61151i 0.944034 + 0.545038i
\(107\) 6.17838 10.7013i 0.597286 1.03453i −0.395934 0.918279i \(-0.629579\pi\)
0.993220 0.116251i \(-0.0370877\pi\)
\(108\) 2.30683 21.2464i 0.221975 2.04443i
\(109\) 9.25995i 0.886942i 0.896289 + 0.443471i \(0.146253\pi\)
−0.896289 + 0.443471i \(0.853747\pi\)
\(110\) 9.51153 16.4361i 0.906889 1.56712i
\(111\) −2.33163 7.20405i −0.221309 0.683778i
\(112\) 17.3656i 1.64090i
\(113\) 6.38795 3.68809i 0.600928 0.346946i −0.168479 0.985705i \(-0.553885\pi\)
0.769407 + 0.638759i \(0.220552\pi\)
\(114\) −4.54323 4.10017i −0.425513 0.384016i
\(115\) 6.62668 11.4777i 0.617941 1.07030i
\(116\) −1.60550 −0.149067
\(117\) −5.06389 + 9.55809i −0.468156 + 0.883646i
\(118\) 5.60825i 0.516282i
\(119\) −11.6603 6.73206i −1.06890 0.617127i
\(120\) −15.5557 14.0387i −1.42004 1.28155i
\(121\) −11.0000 0.0222112i −0.999998 0.00201920i
\(122\) 20.3155i 1.83928i
\(123\) 2.65915 + 8.21598i 0.239767 + 0.740810i
\(124\) −15.3031 26.5058i −1.37426 2.38029i
\(125\) 10.7385i 0.960481i
\(126\) −27.3192 + 2.80818i −2.43379 + 0.250173i
\(127\) 4.58910 + 2.64952i 0.407216 + 0.235107i 0.689593 0.724197i \(-0.257789\pi\)
−0.282377 + 0.959304i \(0.591123\pi\)
\(128\) 9.23513 15.9957i 0.816278 1.41384i
\(129\) 2.65148 12.4044i 0.233449 1.09215i
\(130\) 9.11981 + 18.5205i 0.799861 + 1.62436i
\(131\) −13.4978 −1.17931 −0.589653 0.807657i \(-0.700735\pi\)
−0.589653 + 0.807657i \(0.700735\pi\)
\(132\) −4.96205 + 23.0999i −0.431891 + 2.01058i
\(133\) −2.64564 + 4.58238i −0.229406 + 0.397343i
\(134\) 3.10539 + 5.37869i 0.268265 + 0.464648i
\(135\) −7.10635 + 9.71079i −0.611617 + 0.835772i
\(136\) 9.49827 + 16.4515i 0.814470 + 1.41070i
\(137\) −1.54454 + 0.891738i −0.131959 + 0.0761863i −0.564526 0.825415i \(-0.690941\pi\)
0.432567 + 0.901602i \(0.357608\pi\)
\(138\) −5.12292 + 23.9666i −0.436092 + 2.04017i
\(139\) −5.31782 + 3.07024i −0.451052 + 0.260415i −0.708274 0.705937i \(-0.750526\pi\)
0.257223 + 0.966352i \(0.417193\pi\)
\(140\) −17.6330 + 30.5412i −1.49026 + 2.58120i
\(141\) −12.2370 11.0436i −1.03054 0.930041i
\(142\) 34.6209i 2.90532i
\(143\) 6.65952 9.93231i 0.556897 0.830582i
\(144\) 12.8408 + 5.75233i 1.07007 + 0.479361i
\(145\) 0.782882 + 0.451997i 0.0650148 + 0.0375363i
\(146\) 29.1931 + 16.8547i 2.41604 + 1.39490i
\(147\) 3.57832 + 11.0560i 0.295135 + 0.911880i
\(148\) 17.9803 1.47797
\(149\) −1.90432 3.29837i −0.156008 0.270213i 0.777418 0.628985i \(-0.216529\pi\)
−0.933425 + 0.358771i \(0.883196\pi\)
\(150\) 0.478607 + 1.47876i 0.0390781 + 0.120740i
\(151\) 6.89118i 0.560797i 0.959884 + 0.280398i \(0.0904665\pi\)
−0.959884 + 0.280398i \(0.909533\pi\)
\(152\) 6.46529 3.73274i 0.524404 0.302765i
\(153\) 8.84040 6.39208i 0.714704 0.516769i
\(154\) 30.3616 + 0.0306531i 2.44661 + 0.00247010i
\(155\) 17.2331i 1.38420i
\(156\) −17.8909 18.4292i −1.43242 1.47552i
\(157\) −6.66314 −0.531776 −0.265888 0.964004i \(-0.585665\pi\)
−0.265888 + 0.964004i \(0.585665\pi\)
\(158\) 19.8825 + 11.4792i 1.58177 + 0.913234i
\(159\) 5.83677 + 5.26755i 0.462886 + 0.417744i
\(160\) 2.30243 1.32931i 0.182023 0.105091i
\(161\) 21.1899 1.67000
\(162\) 6.97296 21.1311i 0.547848 1.66021i
\(163\) 11.5455 + 19.9975i 0.904316 + 1.56632i 0.821833 + 0.569729i \(0.192952\pi\)
0.0824833 + 0.996592i \(0.473715\pi\)
\(164\) −20.5059 −1.60124
\(165\) 8.92290 9.86707i 0.694647 0.768150i
\(166\) 2.14627 3.71744i 0.166583 0.288530i
\(167\) 0.132034 0.228690i 0.0102171 0.0176966i −0.860872 0.508822i \(-0.830081\pi\)
0.871089 + 0.491126i \(0.163414\pi\)
\(168\) 7.00289 32.7617i 0.540285 2.52762i
\(169\) 4.96079 + 12.0163i 0.381599 + 0.924328i
\(170\) 20.8208i 1.59689i
\(171\) −2.51203 3.47420i −0.192100 0.265678i
\(172\) 26.0853 + 15.0604i 1.98898 + 1.14834i
\(173\) 11.7184 + 20.2968i 0.890932 + 1.54314i 0.838760 + 0.544501i \(0.183281\pi\)
0.0521714 + 0.998638i \(0.483386\pi\)
\(174\) −1.63473 0.349428i −0.123929 0.0264901i
\(175\) 1.16381 0.671924i 0.0879755 0.0507927i
\(176\) −13.4635 7.79129i −1.01485 0.587291i
\(177\) 0.821248 3.84205i 0.0617288 0.288786i
\(178\) 23.5221 13.5805i 1.76306 1.01790i
\(179\) 16.7444 + 9.66739i 1.25154 + 0.722575i 0.971414 0.237390i \(-0.0762919\pi\)
0.280122 + 0.959965i \(0.409625\pi\)
\(180\) −16.7424 23.1552i −1.24791 1.72589i
\(181\) −23.8199 −1.77052 −0.885258 0.465100i \(-0.846018\pi\)
−0.885258 + 0.465100i \(0.846018\pi\)
\(182\) −18.3536 + 27.4332i −1.36046 + 2.03349i
\(183\) −2.97492 + 13.9176i −0.219912 + 1.02882i
\(184\) −25.8915 14.9484i −1.90874 1.10201i
\(185\) −8.76761 5.06198i −0.644607 0.372164i
\(186\) −9.81288 30.3189i −0.719516 2.22309i
\(187\) −10.4509 + 6.01976i −0.764244 + 0.440208i
\(188\) 33.8975 19.5707i 2.47223 1.42734i
\(189\) −19.1268 2.07670i −1.39127 0.151058i
\(190\) −8.18240 −0.593614
\(191\) −5.49010 + 3.16971i −0.397250 + 0.229352i −0.685297 0.728264i \(-0.740327\pi\)
0.288047 + 0.957616i \(0.406994\pi\)
\(192\) 7.59140 8.41174i 0.547862 0.607065i
\(193\) −1.12988 0.652334i −0.0813302 0.0469560i 0.458783 0.888548i \(-0.348285\pi\)
−0.540114 + 0.841592i \(0.681619\pi\)
\(194\) 39.7345 2.85277
\(195\) 3.53565 + 14.0233i 0.253193 + 1.00423i
\(196\) −27.5941 −1.97101
\(197\) −2.11756 + 3.66773i −0.150870 + 0.261315i −0.931548 0.363619i \(-0.881541\pi\)
0.780677 + 0.624934i \(0.214874\pi\)
\(198\) −10.0799 + 22.4404i −0.716348 + 1.59477i
\(199\) 8.81144 + 15.2619i 0.624626 + 1.08188i 0.988613 + 0.150481i \(0.0480821\pi\)
−0.363987 + 0.931404i \(0.618585\pi\)
\(200\) −1.89604 −0.134070
\(201\) 1.33978 + 4.13953i 0.0945008 + 0.291980i
\(202\) −8.86968 15.3627i −0.624069 1.08092i
\(203\) 1.44534i 0.101443i
\(204\) 7.97685 + 24.6461i 0.558491 + 1.72557i
\(205\) 9.99916 + 5.77302i 0.698372 + 0.403205i
\(206\) 17.3430 30.0389i 1.20834 2.09291i
\(207\) −7.01913 + 15.6687i −0.487863 + 1.08905i
\(208\) 15.1709 7.47042i 1.05192 0.517981i
\(209\) 2.36571 + 4.10710i 0.163640 + 0.284094i
\(210\) −24.6010 + 27.2594i −1.69763 + 1.88108i
\(211\) −0.446183 0.257604i −0.0307165 0.0177342i 0.484563 0.874756i \(-0.338979\pi\)
−0.515280 + 0.857022i \(0.672312\pi\)
\(212\) −16.1683 + 9.33478i −1.11044 + 0.641116i
\(213\) 5.06973 23.7178i 0.347373 1.62512i
\(214\) 15.2756 + 26.4581i 1.04422 + 1.80864i
\(215\) −8.47987 14.6876i −0.578322 1.00168i
\(216\) 21.9056 + 16.0305i 1.49049 + 1.09074i
\(217\) −23.8615 + 13.7765i −1.61983 + 0.935207i
\(218\) −19.8273 11.4473i −1.34287 0.775307i
\(219\) 17.5312 + 15.8216i 1.18465 + 1.06912i
\(220\) 15.7672 + 27.3734i 1.06303 + 1.84552i
\(221\) 0.865191 13.0827i 0.0581990 0.880037i
\(222\) 18.3076 + 3.91329i 1.22873 + 0.262643i
\(223\) 7.83072 13.5632i 0.524384 0.908260i −0.475213 0.879871i \(-0.657629\pi\)
0.999597 0.0283889i \(-0.00903769\pi\)
\(224\) 3.68120 + 2.12534i 0.245961 + 0.142005i
\(225\) 0.111338 + 1.08314i 0.00742250 + 0.0722092i
\(226\) 18.2370i 1.21311i
\(227\) −10.9081 18.8934i −0.723995 1.25400i −0.959386 0.282096i \(-0.908970\pi\)
0.235391 0.971901i \(-0.424363\pi\)
\(228\) 9.68571 3.13483i 0.641452 0.207609i
\(229\) 13.4538 0.889054 0.444527 0.895765i \(-0.353372\pi\)
0.444527 + 0.895765i \(0.353372\pi\)
\(230\) 16.3840 + 28.3779i 1.08033 + 1.87118i
\(231\) 20.7954 + 4.46702i 1.36824 + 0.293909i
\(232\) 1.01961 1.76602i 0.0669409 0.115945i
\(233\) −5.12618 −0.335827 −0.167913 0.985802i \(-0.553703\pi\)
−0.167913 + 0.985802i \(0.553703\pi\)
\(234\) −14.2056 22.6586i −0.928648 1.48124i
\(235\) −22.0389 −1.43766
\(236\) 8.07947 + 4.66468i 0.525928 + 0.303645i
\(237\) 11.9400 + 10.7756i 0.775584 + 0.699947i
\(238\) 28.8292 16.6445i 1.86872 1.07891i
\(239\) −24.2427 −1.56813 −0.784066 0.620677i \(-0.786858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(240\) 17.8984 5.79292i 1.15534 0.373931i
\(241\) 15.6267 9.02205i 1.00660 0.581161i 0.0964064 0.995342i \(-0.469265\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(242\) 13.6459 23.5255i 0.877190 1.51228i
\(243\) 7.87132 13.4552i 0.504945 0.863151i
\(244\) −29.2673 16.8975i −1.87365 1.08175i
\(245\) 13.4555 + 7.76855i 0.859642 + 0.496314i
\(246\) −20.8792 4.46298i −1.33121 0.284549i
\(247\) −5.14138 0.340012i −0.327138 0.0216345i
\(248\) 38.8744 2.46853
\(249\) 2.01471 2.23242i 0.127677 0.141474i
\(250\) −22.9931 13.2751i −1.45421 0.839590i
\(251\) 5.01922 2.89785i 0.316810 0.182911i −0.333160 0.942870i \(-0.608115\pi\)
0.649970 + 0.759960i \(0.274781\pi\)
\(252\) 18.6772 41.6928i 1.17656 2.62640i
\(253\) 9.50712 16.4285i 0.597707 1.03285i
\(254\) −11.3462 + 6.55074i −0.711924 + 0.411030i
\(255\) 3.04891 14.2638i 0.190930 0.893231i
\(256\) 16.2914 + 28.2175i 1.01821 + 1.76359i
\(257\) −21.7456 12.5548i −1.35645 0.783150i −0.367311 0.930098i \(-0.619721\pi\)
−0.989144 + 0.146949i \(0.953055\pi\)
\(258\) 23.2824 + 21.0118i 1.44950 + 1.30814i
\(259\) 16.1865i 1.00578i
\(260\) −34.2668 2.26615i −2.12514 0.140541i
\(261\) −1.06874 0.478766i −0.0661532 0.0296349i
\(262\) 16.6861 28.9012i 1.03087 1.78552i
\(263\) −4.85093 + 8.40205i −0.299121 + 0.518093i −0.975935 0.218061i \(-0.930027\pi\)
0.676814 + 0.736154i \(0.263360\pi\)
\(264\) −22.2581 20.1283i −1.36989 1.23881i
\(265\) 10.5121 0.645751
\(266\) −6.54115 11.3296i −0.401064 0.694663i
\(267\) 18.1030 5.85914i 1.10789 0.358573i
\(268\) −10.3317 −0.631107
\(269\) −9.27986 + 5.35773i −0.565803 + 0.326666i −0.755471 0.655182i \(-0.772592\pi\)
0.189668 + 0.981848i \(0.439259\pi\)
\(270\) −12.0076 27.2206i −0.730761 1.65659i
\(271\) −2.68341 1.54927i −0.163005 0.0941113i 0.416278 0.909237i \(-0.363334\pi\)
−0.579284 + 0.815126i \(0.696668\pi\)
\(272\) −17.0552 −1.03413
\(273\) −16.5907 + 16.1061i −1.00411 + 0.974785i
\(274\) 4.40952i 0.266389i
\(275\) 0.00121532 1.20376i 7.32866e−5 0.0725897i
\(276\) −30.2662 27.3146i −1.82181 1.64414i
\(277\) 12.4789 7.20471i 0.749786 0.432889i −0.0758306 0.997121i \(-0.524161\pi\)
0.825617 + 0.564232i \(0.190827\pi\)
\(278\) 15.1819i 0.910551i
\(279\) −2.28275 22.2076i −0.136665 1.32953i
\(280\) −22.3964 38.7918i −1.33844 2.31825i
\(281\) −1.82943 −0.109135 −0.0545675 0.998510i \(-0.517378\pi\)
−0.0545675 + 0.998510i \(0.517378\pi\)
\(282\) 38.7740 12.5494i 2.30896 0.747307i
\(283\) 4.76401 + 2.75050i 0.283191 + 0.163500i 0.634867 0.772621i \(-0.281055\pi\)
−0.351676 + 0.936122i \(0.614388\pi\)
\(284\) 49.8762 + 28.7960i 2.95961 + 1.70873i
\(285\) −5.60553 1.19820i −0.332043 0.0709749i
\(286\) 13.0343 + 26.5377i 0.770736 + 1.56921i
\(287\) 18.4602i 1.08967i
\(288\) −2.79095 + 2.01801i −0.164459 + 0.118912i
\(289\) 1.88826 3.27056i 0.111074 0.192386i
\(290\) −1.93562 + 1.11753i −0.113663 + 0.0656236i
\(291\) 27.2209 + 5.81855i 1.59572 + 0.341089i
\(292\) −48.5629 + 28.0378i −2.84193 + 1.64079i
\(293\) 0.387256 + 0.670747i 0.0226237 + 0.0391855i 0.877116 0.480279i \(-0.159465\pi\)
−0.854492 + 0.519465i \(0.826131\pi\)
\(294\) −28.0964 6.00568i −1.63862 0.350258i
\(295\) −2.62649 4.54922i −0.152920 0.264866i
\(296\) −11.4188 + 19.7779i −0.663704 + 1.14957i
\(297\) −10.1915 + 13.8972i −0.591373 + 0.806398i
\(298\) 9.41657 0.545487
\(299\) 9.11559 + 18.5119i 0.527168 + 1.07057i
\(300\) −2.52844 0.540459i −0.145979 0.0312034i
\(301\) 13.5579 23.4830i 0.781465 1.35354i
\(302\) −14.7553 8.51898i −0.849072 0.490212i
\(303\) −3.82671 11.8234i −0.219839 0.679237i
\(304\) 6.70255i 0.384418i
\(305\) 9.51428 + 16.4792i 0.544786 + 0.943598i
\(306\) 2.75799 + 26.8309i 0.157664 + 1.53382i
\(307\) 25.7122i 1.46747i 0.679434 + 0.733737i \(0.262225\pi\)
−0.679434 + 0.733737i \(0.737775\pi\)
\(308\) −25.2975 + 43.7146i −1.44146 + 2.49087i
\(309\) 16.2799 18.0392i 0.926133 1.02621i
\(310\) −36.8993 21.3038i −2.09574 1.20998i
\(311\) 2.62026i 0.148581i −0.997237 0.0742905i \(-0.976331\pi\)
0.997237 0.0742905i \(-0.0236692\pi\)
\(312\) 31.6338 7.97572i 1.79091 0.451536i
\(313\) 4.89272 0.276553 0.138276 0.990394i \(-0.455844\pi\)
0.138276 + 0.990394i \(0.455844\pi\)
\(314\) 8.23706 14.2670i 0.464844 0.805134i
\(315\) −20.8452 + 15.0722i −1.17449 + 0.849222i
\(316\) −33.0747 + 19.0957i −1.86059 + 1.07421i
\(317\) 4.04149i 0.226993i 0.993538 + 0.113496i \(0.0362050\pi\)
−0.993538 + 0.113496i \(0.963795\pi\)
\(318\) −18.4943 + 5.98578i −1.03711 + 0.335666i
\(319\) 1.12057 + 0.648468i 0.0627396 + 0.0363072i
\(320\) 15.1496i 0.846888i
\(321\) 6.59046 + 20.3626i 0.367843 + 1.13653i
\(322\) −26.1953 + 45.3715i −1.45981 + 2.52846i
\(323\) 4.50048 + 2.59835i 0.250413 + 0.144576i
\(324\) 24.6425 + 27.6214i 1.36903 + 1.53452i
\(325\) 1.08766 + 0.727673i 0.0603325 + 0.0403641i
\(326\) −57.0910 −3.16198
\(327\) −11.9068 10.7456i −0.658447 0.594234i
\(328\) 13.0228 22.5561i 0.719062 1.24545i
\(329\) −17.6183 30.5158i −0.971329 1.68239i
\(330\) 10.0966 + 31.3034i 0.555800 + 1.72320i
\(331\) −0.779830 1.35071i −0.0428633 0.0742415i 0.843798 0.536661i \(-0.180315\pi\)
−0.886661 + 0.462420i \(0.846981\pi\)
\(332\) 3.57033 + 6.18399i 0.195947 + 0.339391i
\(333\) 11.9690 + 5.36177i 0.655895 + 0.293823i
\(334\) 0.326446 + 0.565420i 0.0178623 + 0.0309384i
\(335\) 5.03796 + 2.90867i 0.275253 + 0.158918i
\(336\) 22.3294 + 20.1517i 1.21817 + 1.09937i
\(337\) 27.2822i 1.48616i 0.669204 + 0.743079i \(0.266635\pi\)
−0.669204 + 0.743079i \(0.733365\pi\)
\(338\) −31.8616 4.23269i −1.73304 0.230228i
\(339\) −2.67055 + 12.4937i −0.145045 + 0.678563i
\(340\) 29.9953 + 17.3178i 1.62672 + 0.939189i
\(341\) −0.0249177 + 24.6807i −0.00134937 + 1.33654i
\(342\) 10.5443 1.08387i 0.570171 0.0586087i
\(343\) 1.07686i 0.0581451i
\(344\) −33.1322 + 19.1289i −1.78637 + 1.03136i
\(345\) 7.06865 + 21.8401i 0.380564 + 1.17583i
\(346\) −57.9457 −3.11518
\(347\) 3.08735 + 5.34746i 0.165738 + 0.287066i 0.936917 0.349552i \(-0.113666\pi\)
−0.771179 + 0.636618i \(0.780333\pi\)
\(348\) 1.86309 2.06442i 0.0998722 0.110664i
\(349\) −18.1454 10.4763i −0.971301 0.560781i −0.0716686 0.997428i \(-0.522832\pi\)
−0.899633 + 0.436647i \(0.856166\pi\)
\(350\) 3.32257i 0.177599i
\(351\) −6.41382 17.6029i −0.342344 0.939575i
\(352\) 3.29939 1.90046i 0.175858 0.101295i
\(353\) 19.3547 + 11.1744i 1.03015 + 0.594755i 0.917027 0.398826i \(-0.130582\pi\)
0.113120 + 0.993581i \(0.463916\pi\)
\(354\) 7.21131 + 6.50804i 0.383277 + 0.345899i
\(355\) −16.2139 28.0833i −0.860543 1.49050i
\(356\) 45.1825i 2.39467i
\(357\) 22.1874 7.18107i 1.17428 0.380063i
\(358\) −41.3993 + 23.9019i −2.18802 + 1.26326i
\(359\) 2.14210 0.113056 0.0565279 0.998401i \(-0.481997\pi\)
0.0565279 + 0.998401i \(0.481997\pi\)
\(360\) 36.1029 3.71108i 1.90279 0.195591i
\(361\) −8.47887 + 14.6858i −0.446256 + 0.772939i
\(362\) 29.4464 51.0027i 1.54767 2.68064i
\(363\) 12.7934 14.1184i 0.671478 0.741025i
\(364\) −24.2557 49.2585i −1.27134 2.58185i
\(365\) 31.5739 1.65265
\(366\) −26.1225 23.5749i −1.36544 1.23228i
\(367\) 4.96066 8.59211i 0.258944 0.448505i −0.707015 0.707198i \(-0.749959\pi\)
0.965959 + 0.258694i \(0.0832921\pi\)
\(368\) 23.2455 13.4208i 1.21176 0.699608i
\(369\) −13.6502 6.11492i −0.710601 0.318330i
\(370\) 21.6773 12.5154i 1.12695 0.650644i
\(371\) 8.40353 + 14.5553i 0.436290 + 0.755676i
\(372\) 51.8405 + 11.0810i 2.68780 + 0.574525i
\(373\) 15.3434 8.85854i 0.794453 0.458678i −0.0470748 0.998891i \(-0.514990\pi\)
0.841528 + 0.540214i \(0.181657\pi\)
\(374\) 0.0301053 29.8190i 0.00155671 1.54190i
\(375\) −13.8080 12.4614i −0.713041 0.643503i
\(376\) 49.7154i 2.56387i
\(377\) −1.26268 + 0.621762i −0.0650311 + 0.0320224i
\(378\) 28.0914 38.3868i 1.44487 1.97440i
\(379\) −5.96882 + 10.3383i −0.306598 + 0.531043i −0.977616 0.210398i \(-0.932524\pi\)
0.671018 + 0.741441i \(0.265857\pi\)
\(380\) 6.80573 11.7879i 0.349127 0.604705i
\(381\) −8.73222 + 2.82623i −0.447365 + 0.144792i
\(382\) 15.6738i 0.801940i
\(383\) −29.8752 + 17.2485i −1.52655 + 0.881356i −0.527050 + 0.849834i \(0.676702\pi\)
−0.999503 + 0.0315212i \(0.989965\pi\)
\(384\) 9.85109 + 30.4370i 0.502711 + 1.55323i
\(385\) 24.6426 14.1943i 1.25590 0.723407i
\(386\) 2.79353 1.61285i 0.142187 0.0820918i
\(387\) 12.8732 + 17.8039i 0.654381 + 0.905026i
\(388\) −33.0493 + 57.2430i −1.67782 + 2.90607i
\(389\) 8.07746i 0.409543i −0.978810 0.204772i \(-0.934355\pi\)
0.978810 0.204772i \(-0.0656452\pi\)
\(390\) −34.3974 9.76536i −1.74178 0.494488i
\(391\) 20.8112i 1.05247i
\(392\) 17.5243 30.3529i 0.885109 1.53305i
\(393\) 15.6633 17.3559i 0.790111 0.875491i
\(394\) −5.23552 9.06819i −0.263762 0.456849i
\(395\) 21.5040 1.08198
\(396\) −23.9445 33.1864i −1.20326 1.66768i
\(397\) 0.187144 + 0.324144i 0.00939251 + 0.0162683i 0.870683 0.491844i \(-0.163677\pi\)
−0.861291 + 0.508112i \(0.830344\pi\)
\(398\) −43.5713 −2.18403
\(399\) −2.82210 8.71945i −0.141282 0.436518i
\(400\) 0.851137 1.47421i 0.0425569 0.0737106i
\(401\) 0.872340 + 0.503646i 0.0435626 + 0.0251509i 0.521623 0.853176i \(-0.325327\pi\)
−0.478061 + 0.878327i \(0.658660\pi\)
\(402\) −10.5197 2.24862i −0.524677 0.112151i
\(403\) −22.3003 14.9195i −1.11086 0.743192i
\(404\) 29.5095 1.46815
\(405\) −4.24001 20.4064i −0.210688 1.01400i
\(406\) −3.09473 1.78675i −0.153589 0.0886747i
\(407\) −12.5494 7.26229i −0.622050 0.359978i
\(408\) −32.1761 6.87773i −1.59296 0.340498i
\(409\) −13.6305 + 7.86959i −0.673987 + 0.389126i −0.797585 0.603206i \(-0.793890\pi\)
0.123599 + 0.992332i \(0.460556\pi\)
\(410\) −24.7222 + 14.2734i −1.22094 + 0.704912i
\(411\) 0.645710 3.02083i 0.0318505 0.149007i
\(412\) 28.8501 + 49.9699i 1.42134 + 2.46184i
\(413\) 4.19933 7.27345i 0.206635 0.357903i
\(414\) −24.8723 34.3991i −1.22241 1.69062i
\(415\) 4.02061i 0.197364i
\(416\) −0.273145 + 4.13026i −0.0133920 + 0.202503i
\(417\) 2.22317 10.4007i 0.108869 0.509324i
\(418\) −11.7186 0.0118311i −0.573175 0.000578678i
\(419\) 19.0181 + 10.9801i 0.929093 + 0.536412i 0.886525 0.462681i \(-0.153113\pi\)
0.0425684 + 0.999094i \(0.486446\pi\)
\(420\) −18.8090 58.1143i −0.917786 2.83569i
\(421\) 5.93199 0.289108 0.144554 0.989497i \(-0.453825\pi\)
0.144554 + 0.989497i \(0.453825\pi\)
\(422\) 1.10316 0.636907i 0.0537008 0.0310042i
\(423\) 28.4006 2.91934i 1.38089 0.141943i
\(424\) 23.7131i 1.15161i
\(425\) −0.659915 1.14301i −0.0320106 0.0554439i
\(426\) 44.5169 + 40.1755i 2.15685 + 1.94651i
\(427\) −15.2118 + 26.3476i −0.736149 + 1.27505i
\(428\) −50.8221 −2.45658
\(429\) 5.04338 + 20.0889i 0.243497 + 0.969902i
\(430\) 41.9317 2.02213
\(431\) −14.5033 + 25.1205i −0.698601 + 1.21001i 0.270350 + 0.962762i \(0.412860\pi\)
−0.968952 + 0.247251i \(0.920473\pi\)
\(432\) −22.2976 + 9.83596i −1.07279 + 0.473233i
\(433\) −0.286323 0.495926i −0.0137598 0.0238327i 0.859064 0.511869i \(-0.171047\pi\)
−0.872823 + 0.488036i \(0.837713\pi\)
\(434\) 68.1226i 3.26999i
\(435\) −1.48968 + 0.482144i −0.0714248 + 0.0231170i
\(436\) 32.9828 19.0426i 1.57959 0.911975i
\(437\) −8.17861 −0.391236
\(438\) −55.5492 + 17.9788i −2.65425 + 0.859061i
\(439\) 0.649189 + 0.374810i 0.0309841 + 0.0178887i 0.515412 0.856942i \(-0.327639\pi\)
−0.484428 + 0.874831i \(0.660972\pi\)
\(440\) −40.1236 0.0405088i −1.91282 0.00193118i
\(441\) −18.3686 8.22863i −0.874695 0.391840i
\(442\) 26.9429 + 18.0255i 1.28154 + 0.857387i
\(443\) 0.139797i 0.00664197i 0.999994 + 0.00332099i \(0.00105710\pi\)
−0.999994 + 0.00332099i \(0.998943\pi\)
\(444\) −20.8650 + 23.1197i −0.990211 + 1.09721i
\(445\) 12.7202 22.0321i 0.602996 1.04442i
\(446\) 19.3609 + 33.5341i 0.916765 + 1.58788i
\(447\) 6.45102 + 1.37892i 0.305123 + 0.0652207i
\(448\) 20.9766 12.1109i 0.991052 0.572184i
\(449\) 10.2530 5.91959i 0.483870 0.279363i −0.238158 0.971227i \(-0.576543\pi\)
0.722028 + 0.691864i \(0.243210\pi\)
\(450\) −2.45684 1.10060i −0.115816 0.0518826i
\(451\) 14.3121 + 8.28240i 0.673933 + 0.390003i
\(452\) −26.2730 15.1687i −1.23578 0.713476i
\(453\) −8.86095 7.99680i −0.416324 0.375723i
\(454\) 53.9389 2.53148
\(455\) −2.04008 + 30.8483i −0.0956402 + 1.44619i
\(456\) −2.70288 + 12.6449i −0.126574 + 0.592153i
\(457\) 25.2592 + 14.5834i 1.18158 + 0.682184i 0.956379 0.292129i \(-0.0943638\pi\)
0.225198 + 0.974313i \(0.427697\pi\)
\(458\) −16.6318 + 28.8071i −0.777154 + 1.34607i
\(459\) −2.03958 + 18.7849i −0.0951995 + 0.876806i
\(460\) −54.5097 −2.54153
\(461\) −4.42794 7.66941i −0.206230 0.357200i 0.744294 0.667852i \(-0.232786\pi\)
−0.950524 + 0.310652i \(0.899453\pi\)
\(462\) −35.2723 + 39.0046i −1.64101 + 1.81466i
\(463\) −26.3101 −1.22273 −0.611367 0.791347i \(-0.709380\pi\)
−0.611367 + 0.791347i \(0.709380\pi\)
\(464\) 0.915416 + 1.58555i 0.0424971 + 0.0736071i
\(465\) −22.1590 19.9980i −1.02760 0.927385i
\(466\) 6.33705 10.9761i 0.293558 0.508458i
\(467\) 29.3379i 1.35760i −0.734324 0.678799i \(-0.762501\pi\)
0.734324 0.678799i \(-0.237499\pi\)
\(468\) 44.4583 1.61880i 2.05509 0.0748290i
\(469\) 9.30096i 0.429479i
\(470\) 27.2448 47.1894i 1.25671 2.17669i
\(471\) 7.73217 8.56771i 0.356280 0.394779i
\(472\) −10.2621 + 5.92483i −0.472352 + 0.272713i
\(473\) −12.1234 21.0473i −0.557433 0.967757i
\(474\) −37.8328 + 12.2448i −1.73772 + 0.562422i
\(475\) −0.449191 + 0.259340i −0.0206103 + 0.0118994i
\(476\) 55.3766i 2.53818i
\(477\) −13.5464 + 1.39246i −0.620249 + 0.0637564i
\(478\) 29.9692 51.9082i 1.37076 2.37423i
\(479\) −17.3828 + 30.1080i −0.794242 + 1.37567i 0.129077 + 0.991635i \(0.458799\pi\)
−0.923319 + 0.384033i \(0.874535\pi\)
\(480\) −0.962555 + 4.50313i −0.0439344 + 0.205539i
\(481\) 14.1409 6.96321i 0.644769 0.317495i
\(482\) 44.6127i 2.03205i
\(483\) −24.5896 + 27.2468i −1.11887 + 1.23977i
\(484\) 22.5418 + 39.2262i 1.02463 + 1.78301i
\(485\) 32.2312 18.6087i 1.46354 0.844977i
\(486\) 19.0794 + 33.4874i 0.865461 + 1.51902i
\(487\) −8.12787 14.0779i −0.368309 0.637929i 0.620993 0.783816i \(-0.286730\pi\)
−0.989301 + 0.145887i \(0.953396\pi\)
\(488\) 37.1738 21.4623i 1.68278 0.971552i
\(489\) −39.1114 8.36016i −1.76868 0.378059i
\(490\) −33.2678 + 19.2072i −1.50289 + 0.867692i
\(491\) 6.73824 11.6710i 0.304093 0.526704i −0.672966 0.739673i \(-0.734980\pi\)
0.977059 + 0.212969i \(0.0683135\pi\)
\(492\) 23.7959 26.3673i 1.07280 1.18873i
\(493\) 1.41950 0.0639312
\(494\) 7.08387 10.5883i 0.318718 0.476391i
\(495\) 2.33296 + 22.9236i 0.104859 + 1.03034i
\(496\) −17.4509 + 30.2258i −0.783567 + 1.35718i
\(497\) 25.9233 44.9005i 1.16282 2.01406i
\(498\) 2.28942 + 7.07362i 0.102591 + 0.316977i
\(499\) 8.03905 0.359877 0.179939 0.983678i \(-0.442410\pi\)
0.179939 + 0.983678i \(0.442410\pi\)
\(500\) 38.2492 22.0832i 1.71056 0.987590i
\(501\) 0.140841 + 0.435156i 0.00629230 + 0.0194414i
\(502\) 14.3294i 0.639554i
\(503\) −18.1322 31.4060i −0.808477 1.40032i −0.913919 0.405898i \(-0.866959\pi\)
0.105442 0.994425i \(-0.466374\pi\)
\(504\) 33.9998 + 47.0226i 1.51447 + 2.09455i
\(505\) −14.3895 8.30781i −0.640326 0.369693i
\(506\) 23.4236 + 40.6656i 1.04131 + 1.80781i
\(507\) −21.2077 7.56537i −0.941866 0.335990i
\(508\) 21.7944i 0.966969i
\(509\) 26.8544 + 15.5044i 1.19030 + 0.687221i 0.958375 0.285512i \(-0.0921636\pi\)
0.231927 + 0.972733i \(0.425497\pi\)
\(510\) 26.7722 + 24.1613i 1.18549 + 1.06988i
\(511\) 25.2407 + 43.7182i 1.11658 + 1.93398i
\(512\) −43.6179 −1.92766
\(513\) 7.38231 + 0.801537i 0.325937 + 0.0353887i
\(514\) 53.7645 31.0409i 2.37145 1.36916i
\(515\) 32.4887i 1.43162i
\(516\) −49.6356 + 16.0648i −2.18508 + 0.707215i
\(517\) −31.5635 0.0318665i −1.38816 0.00140149i
\(518\) 34.6584 + 20.0100i 1.52280 + 0.879190i
\(519\) −39.6969 8.48531i −1.74250 0.372464i
\(520\) 24.2547 36.2536i 1.06364 1.58983i
\(521\) 15.3032i 0.670444i 0.942139 + 0.335222i \(0.108811\pi\)
−0.942139 + 0.335222i \(0.891189\pi\)
\(522\) 2.34631 1.69651i 0.102695 0.0742542i
\(523\) 25.8794 + 14.9415i 1.13163 + 0.653345i 0.944344 0.328961i \(-0.106698\pi\)
0.187283 + 0.982306i \(0.440032\pi\)
\(524\) 27.7575 + 48.0773i 1.21259 + 2.10027i
\(525\) −0.486542 + 2.27620i −0.0212344 + 0.0993413i
\(526\) −11.9936 20.7735i −0.522944 0.905766i
\(527\) 13.5302 + 23.4350i 0.589386 + 1.02085i
\(528\) 25.6419 8.27056i 1.11592 0.359930i
\(529\) 4.87638 + 8.44614i 0.212017 + 0.367224i
\(530\) −12.9952 + 22.5083i −0.564474 + 0.977697i
\(531\) 3.98725 + 5.51446i 0.173032 + 0.239307i
\(532\) 21.7625 0.943524
\(533\) −16.1272 + 7.94130i −0.698547 + 0.343976i
\(534\) −9.83369 + 46.0050i −0.425545 + 1.99083i
\(535\) 24.7820 + 14.3079i 1.07142 + 0.618585i
\(536\) 6.56137 11.3646i 0.283408 0.490877i
\(537\) −31.8616 + 10.3122i −1.37493 + 0.445003i
\(538\) 26.4932i 1.14220i
\(539\) 19.2594 + 11.1453i 0.829559 + 0.480063i
\(540\) 49.2024 + 5.34217i 2.11734 + 0.229890i
\(541\) 0.0554765i 0.00238512i −0.999999 0.00119256i \(-0.999620\pi\)
0.999999 0.00119256i \(-0.000379604\pi\)
\(542\) 6.63453 3.83045i 0.284978 0.164532i
\(543\) 27.6415 30.6285i 1.18621 1.31439i
\(544\) 2.08736 3.61541i 0.0894946 0.155009i
\(545\) −21.4442 −0.918569
\(546\) −13.9765 55.4343i −0.598137 2.37237i
\(547\) 1.16971i 0.0500131i −0.999687 0.0250066i \(-0.992039\pi\)
0.999687 0.0250066i \(-0.00796067\pi\)
\(548\) 6.35252 + 3.66763i 0.271366 + 0.156673i
\(549\) −14.4435 19.9758i −0.616435 0.852545i
\(550\) 2.57598 + 1.49071i 0.109840 + 0.0635641i
\(551\) 0.557852i 0.0237653i
\(552\) 49.2668 15.9455i 2.09693 0.678683i
\(553\) 17.1907 + 29.7751i 0.731021 + 1.26617i
\(554\) 35.6262i 1.51361i
\(555\) 16.6832 5.39960i 0.708161 0.229200i
\(556\) 21.8716 + 12.6276i 0.927564 + 0.535530i
\(557\) −10.7382 + 18.5991i −0.454993 + 0.788071i −0.998688 0.0512122i \(-0.983692\pi\)
0.543695 + 0.839283i \(0.317025\pi\)
\(558\) 50.3725 + 22.5655i 2.13244 + 0.955274i
\(559\) 26.3476 + 1.74243i 1.11439 + 0.0736971i
\(560\) 40.2154 1.69941
\(561\) 4.38718 20.4237i 0.185227 0.862289i
\(562\) 2.26157 3.91716i 0.0953987 0.165235i
\(563\) −7.34568 12.7231i −0.309583 0.536214i 0.668688 0.743543i \(-0.266856\pi\)
−0.978271 + 0.207329i \(0.933523\pi\)
\(564\) −14.1712 + 66.2973i −0.596716 + 2.79162i
\(565\) 8.54088 + 14.7932i 0.359318 + 0.622356i
\(566\) −11.7787 + 6.80042i −0.495095 + 0.285843i
\(567\) 24.8658 22.1841i 1.04427 0.931644i
\(568\) −63.3501 + 36.5752i −2.65811 + 1.53466i
\(569\) −2.01217 + 3.48518i −0.0843546 + 0.146107i −0.905116 0.425165i \(-0.860216\pi\)
0.820761 + 0.571271i \(0.193550\pi\)
\(570\) 9.49518 10.5212i 0.397709 0.440686i
\(571\) 14.5414i 0.608539i −0.952586 0.304269i \(-0.901588\pi\)
0.952586 0.304269i \(-0.0984123\pi\)
\(572\) −49.0726 3.29506i −2.05183 0.137773i
\(573\) 2.29520 10.7376i 0.0958833 0.448572i
\(574\) −39.5267 22.8208i −1.64981 0.952520i
\(575\) 1.79887 + 1.03858i 0.0750180 + 0.0433117i
\(576\) 2.00676 + 19.5226i 0.0836151 + 0.813443i
\(577\) −13.1988 −0.549472 −0.274736 0.961520i \(-0.588591\pi\)
−0.274736 + 0.961520i \(0.588591\pi\)
\(578\) 4.66859 + 8.08623i 0.194188 + 0.336343i
\(579\) 2.14995 0.695842i 0.0893488 0.0289182i
\(580\) 3.71803i 0.154383i
\(581\) 5.56707 3.21415i 0.230961 0.133345i
\(582\) −46.1095 + 51.0921i −1.91130 + 2.11784i
\(583\) 15.0551 + 0.0151996i 0.623517 + 0.000629504i
\(584\) 71.2243i 2.94728i
\(585\) −22.1347 11.7270i −0.915156 0.484850i
\(586\) −1.91492 −0.0791048
\(587\) −39.5978 22.8618i −1.63438 0.943608i −0.982721 0.185092i \(-0.940742\pi\)
−0.651655 0.758515i \(-0.725925\pi\)
\(588\) 32.0213 35.4815i 1.32054 1.46323i
\(589\) 9.20976 5.31726i 0.379481 0.219094i
\(590\) 12.9876 0.534692
\(591\) −2.25880 6.97902i −0.0929145 0.287078i
\(592\) −10.2519 17.7568i −0.421350 0.729799i
\(593\) 1.84220 0.0756500 0.0378250 0.999284i \(-0.487957\pi\)
0.0378250 + 0.999284i \(0.487957\pi\)
\(594\) −17.1576 39.0019i −0.703985 1.60027i
\(595\) 15.5901 27.0029i 0.639134 1.10701i
\(596\) −7.83226 + 13.5659i −0.320822 + 0.555680i
\(597\) −29.8494 6.38039i −1.22166 0.261132i
\(598\) −50.9063 3.36656i −2.08171 0.137669i
\(599\) 4.33911i 0.177291i −0.996063 0.0886457i \(-0.971746\pi\)
0.996063 0.0886457i \(-0.0282539\pi\)
\(600\) 2.20024 2.43800i 0.0898243 0.0995308i
\(601\) −30.7221 17.7374i −1.25318 0.723524i −0.281441 0.959579i \(-0.590812\pi\)
−0.971740 + 0.236054i \(0.924146\pi\)
\(602\) 33.5209 + 58.0600i 1.36621 + 2.36635i
\(603\) −6.87749 3.08093i −0.280073 0.125465i
\(604\) 24.5455 14.1714i 0.998743 0.576625i
\(605\) 0.0514368 25.4738i 0.00209120 1.03566i
\(606\) 30.0467 + 6.42256i 1.22057 + 0.260899i
\(607\) −2.88163 + 1.66371i −0.116962 + 0.0675279i −0.557340 0.830285i \(-0.688178\pi\)
0.440378 + 0.897813i \(0.354845\pi\)
\(608\) −1.42082 0.820312i −0.0576219 0.0332680i
\(609\) −1.85847 1.67723i −0.0753090 0.0679647i
\(610\) −47.0467 −1.90487
\(611\) 19.0801 28.5192i 0.771898 1.15376i
\(612\) −40.9476 18.3434i −1.65521 0.741488i
\(613\) −0.938235 0.541690i −0.0378949 0.0218787i 0.480933 0.876757i \(-0.340298\pi\)
−0.518828 + 0.854879i \(0.673631\pi\)
\(614\) −55.0546 31.7858i −2.22182 1.28277i
\(615\) −19.0266 + 6.15806i −0.767226 + 0.248317i
\(616\) −32.0194 55.5888i −1.29010 2.23974i
\(617\) −21.0322 + 12.1430i −0.846726 + 0.488857i −0.859545 0.511061i \(-0.829253\pi\)
0.0128191 + 0.999918i \(0.495919\pi\)
\(618\) 18.4997 + 57.1586i 0.744167 + 2.29926i
\(619\) 3.72197 0.149599 0.0747993 0.997199i \(-0.476168\pi\)
0.0747993 + 0.997199i \(0.476168\pi\)
\(620\) 61.3822 35.4390i 2.46517 1.42327i
\(621\) −12.0021 27.2080i −0.481626 1.09182i
\(622\) 5.61045 + 3.23920i 0.224959 + 0.129880i
\(623\) 40.6751 1.62961
\(624\) −7.99922 + 28.1764i −0.320225 + 1.12796i
\(625\) −26.6830 −1.06732
\(626\) −6.04844 + 10.4762i −0.241744 + 0.418714i
\(627\) −8.02633 1.72412i −0.320541 0.0688548i
\(628\) 13.7024 + 23.7332i 0.546785 + 0.947060i
\(629\) −15.8972 −0.633864
\(630\) −6.50320 63.2659i −0.259094 2.52057i
\(631\) 10.8592 + 18.8086i 0.432297 + 0.748760i 0.997071 0.0764859i \(-0.0243700\pi\)
−0.564774 + 0.825246i \(0.691037\pi\)
\(632\) 48.5086i 1.92957i
\(633\) 0.849006 0.274785i 0.0337450 0.0109217i
\(634\) −8.65358 4.99615i −0.343678 0.198422i
\(635\) −6.13576 + 10.6274i −0.243490 + 0.421737i
\(636\) 6.75934 31.6223i 0.268025 1.25391i
\(637\) −21.7018 + 10.6863i −0.859857 + 0.423408i
\(638\) −2.77375 + 1.59769i −0.109814 + 0.0632533i
\(639\) 24.6141 + 34.0419i 0.973719 + 1.34668i
\(640\) 37.0430 + 21.3868i 1.46425 + 0.845386i
\(641\) 23.1524 13.3670i 0.914463 0.527966i 0.0325988 0.999469i \(-0.489622\pi\)
0.881865 + 0.471503i \(0.156288\pi\)
\(642\) −51.7472 11.0611i −2.04230 0.436547i
\(643\) −7.20749 12.4837i −0.284236 0.492311i 0.688188 0.725533i \(-0.258407\pi\)
−0.972424 + 0.233222i \(0.925073\pi\)
\(644\) −43.5760 75.4758i −1.71713 2.97416i
\(645\) 28.7262 + 6.14030i 1.13109 + 0.241774i
\(646\) −11.1271 + 6.42424i −0.437790 + 0.252758i
\(647\) −5.74259 3.31548i −0.225764 0.130345i 0.382852 0.923810i \(-0.374942\pi\)
−0.608617 + 0.793464i \(0.708275\pi\)
\(648\) −46.0327 + 9.56461i −1.80834 + 0.375733i
\(649\) −3.75500 6.51905i −0.147397 0.255895i
\(650\) −2.90266 + 1.42932i −0.113852 + 0.0560625i
\(651\) 9.97557 46.6688i 0.390974 1.82909i
\(652\) 47.4856 82.2475i 1.85968 3.22106i
\(653\) 11.4843 + 6.63046i 0.449415 + 0.259470i 0.707583 0.706630i \(-0.249785\pi\)
−0.258168 + 0.966100i \(0.583119\pi\)
\(654\) 37.7277 12.2108i 1.47527 0.477479i
\(655\) 31.2582i 1.22136i
\(656\) 11.6919 + 20.2510i 0.456493 + 0.790669i
\(657\) −40.6879 + 4.18238i −1.58739 + 0.163170i
\(658\) 87.1200 3.39629
\(659\) 9.07488 + 15.7182i 0.353507 + 0.612293i 0.986861 0.161570i \(-0.0516556\pi\)
−0.633354 + 0.773862i \(0.718322\pi\)
\(660\) −53.4947 11.4911i −2.08228 0.447291i
\(661\) −22.5077 + 38.9844i −0.875447 + 1.51632i −0.0191618 + 0.999816i \(0.506100\pi\)
−0.856286 + 0.516503i \(0.827234\pi\)
\(662\) 3.85615 0.149873
\(663\) 15.8182 + 16.2942i 0.614328 + 0.632813i
\(664\) −9.06969 −0.351972
\(665\) −10.6119 6.12678i −0.411512 0.237587i
\(666\) −26.2767 + 18.9995i −1.01820 + 0.736214i
\(667\) −1.93472 + 1.11701i −0.0749127 + 0.0432509i
\(668\) −1.08609 −0.0420220
\(669\) 8.35301 + 25.8083i 0.322946 + 0.997808i
\(670\) −12.4560 + 7.19147i −0.481217 + 0.277831i
\(671\) 13.6022 + 23.6148i 0.525108 + 0.911639i
\(672\) −7.00466 + 2.26710i −0.270211 + 0.0874551i
\(673\) 19.2627 + 11.1213i 0.742523 + 0.428696i 0.822986 0.568062i \(-0.192307\pi\)
−0.0804630 + 0.996758i \(0.525640\pi\)
\(674\) −58.4163 33.7267i −2.25011 1.29910i
\(675\) −1.52194 1.11375i −0.0585795 0.0428684i
\(676\) 32.5988 42.3805i 1.25380 1.63002i
\(677\) 39.8731 1.53245 0.766224 0.642574i \(-0.222133\pi\)
0.766224 + 0.642574i \(0.222133\pi\)
\(678\) −23.4499 21.1630i −0.900587 0.812760i
\(679\) 51.5324 + 29.7522i 1.97763 + 1.14179i
\(680\) −38.0984 + 21.9961i −1.46101 + 0.843514i
\(681\) 36.9520 + 7.89858i 1.41600 + 0.302674i
\(682\) −52.8152 30.5640i −2.02240 1.17036i
\(683\) 18.6392 10.7613i 0.713208 0.411771i −0.0990400 0.995083i \(-0.531577\pi\)
0.812248 + 0.583313i \(0.198244\pi\)
\(684\) −7.20879 + 16.0920i −0.275635 + 0.615294i
\(685\) −2.06509 3.57684i −0.0789031 0.136664i
\(686\) 2.30576 + 1.33123i 0.0880344 + 0.0508267i
\(687\) −15.6124 + 17.2995i −0.595649 + 0.660015i
\(688\) 34.3480i 1.30951i
\(689\) −9.10077 + 13.6030i −0.346712 + 0.518232i
\(690\) −55.5020 11.8637i −2.11292 0.451643i
\(691\) 9.36312 16.2174i 0.356190 0.616939i −0.631131 0.775676i \(-0.717409\pi\)
0.987321 + 0.158737i \(0.0507423\pi\)
\(692\) 48.1965 83.4787i 1.83216 3.17339i
\(693\) −29.8757 + 21.5558i −1.13488 + 0.818836i
\(694\) −15.2665 −0.579509
\(695\) −7.11009 12.3150i −0.269701 0.467136i
\(696\) 1.08762 + 3.36042i 0.0412261 + 0.127376i
\(697\) 18.1303 0.686733
\(698\) 44.8632 25.9018i 1.69810 0.980397i
\(699\) 5.94862 6.59143i 0.224997 0.249311i
\(700\) −4.78662 2.76356i −0.180917 0.104453i
\(701\) −42.5649 −1.60766 −0.803828 0.594862i \(-0.797207\pi\)
−0.803828 + 0.594862i \(0.797207\pi\)
\(702\) 45.6200 + 8.02781i 1.72181 + 0.302990i
\(703\) 6.24747i 0.235628i
\(704\) 0.0219051 21.6968i 0.000825580 0.817729i
\(705\) 25.5749 28.3385i 0.963205 1.06729i
\(706\) −47.8531 + 27.6280i −1.80097 + 1.03979i
\(707\) 26.5656i 0.999103i
\(708\) −15.3738 + 4.97580i −0.577781 + 0.187002i
\(709\) −15.0049 25.9892i −0.563519 0.976044i −0.997186 0.0749705i \(-0.976114\pi\)
0.433667 0.901073i \(-0.357220\pi\)
\(710\) 80.1752 3.00892
\(711\) −27.7112 + 2.84848i −1.03925 + 0.106826i
\(712\) −49.6999 28.6942i −1.86258 1.07536i
\(713\) −36.8822 21.2939i −1.38125 0.797465i
\(714\) −12.0524 + 56.3847i −0.451048 + 2.11014i
\(715\) 23.0013 + 15.4221i 0.860200 + 0.576755i
\(716\) 79.5220i 2.97188i
\(717\) 28.1323 31.1722i 1.05062 1.16415i
\(718\) −2.64810 + 4.58664i −0.0988261 + 0.171172i
\(719\) −42.9331 + 24.7874i −1.60113 + 0.924415i −0.609873 + 0.792499i \(0.708779\pi\)
−0.991261 + 0.131916i \(0.957887\pi\)
\(720\) −13.3213 + 29.7368i −0.496455 + 1.10822i
\(721\) 44.9848 25.9720i 1.67532 0.967248i
\(722\) −20.9634 36.3097i −0.780177 1.35131i
\(723\) −6.53289 + 30.5629i −0.242961 + 1.13665i
\(724\) 48.9843 + 84.8433i 1.82049 + 3.15318i
\(725\) −0.0708400 + 0.122699i −0.00263093 + 0.00455691i
\(726\) 14.4148 + 44.8464i 0.534983 + 1.66440i
\(727\) −0.679238 −0.0251915 −0.0125958 0.999921i \(-0.504009\pi\)
−0.0125958 + 0.999921i \(0.504009\pi\)
\(728\) 69.5875 + 4.60200i 2.57908 + 0.170561i
\(729\) 8.16701 + 25.7352i 0.302482 + 0.953155i
\(730\) −39.0321 + 67.6056i −1.44464 + 2.50219i
\(731\) −23.0633 13.3156i −0.853026 0.492495i
\(732\) 55.6904 18.0245i 2.05838 0.666204i
\(733\) 23.3555i 0.862654i 0.902196 + 0.431327i \(0.141954\pi\)
−0.902196 + 0.431327i \(0.858046\pi\)
\(734\) 12.2649 + 21.2434i 0.452705 + 0.784107i
\(735\) −25.6034 + 8.28669i −0.944396 + 0.305659i
\(736\) 6.57019i 0.242180i
\(737\) 7.21101 + 4.17299i 0.265621 + 0.153714i
\(738\) 29.9677 21.6682i 1.10313 0.797619i
\(739\) 19.2960 + 11.1405i 0.709814 + 0.409811i 0.810992 0.585057i \(-0.198928\pi\)
−0.101178 + 0.994868i \(0.532261\pi\)
\(740\) 41.6388i 1.53067i
\(741\) 6.40346 6.21641i 0.235237 0.228366i
\(742\) −41.5542 −1.52550
\(743\) 4.30681 7.45961i 0.158002 0.273667i −0.776146 0.630553i \(-0.782828\pi\)
0.934148 + 0.356886i \(0.116162\pi\)
\(744\) −45.1114 + 49.9862i −1.65387 + 1.83258i
\(745\) 7.63839 4.41002i 0.279849 0.161571i
\(746\) 43.8042i 1.60379i
\(747\) 0.532583 + 5.18119i 0.0194862 + 0.189570i
\(748\) 42.9333 + 24.8454i 1.56980 + 0.908437i
\(749\) 45.7520i 1.67174i
\(750\) 43.7517 14.1605i 1.59759 0.517068i
\(751\) 1.46013 2.52902i 0.0532809 0.0922853i −0.838155 0.545432i \(-0.816365\pi\)
0.891436 + 0.453147i \(0.149699\pi\)
\(752\) −38.6549 22.3174i −1.40960 0.813832i
\(753\) −2.09834 + 9.81668i −0.0764678 + 0.357740i
\(754\) 0.229629 3.47225i 0.00836258 0.126452i
\(755\) −15.9586 −0.580794
\(756\) 31.9364 + 72.3979i 1.16151 + 2.63309i
\(757\) −11.2830 + 19.5427i −0.410088 + 0.710293i −0.994899 0.100877i \(-0.967835\pi\)
0.584811 + 0.811170i \(0.301169\pi\)
\(758\) −14.7575 25.5607i −0.536016 0.928407i
\(759\) 10.0919 + 31.2889i 0.366314 + 1.13571i
\(760\) 8.64428 + 14.9723i 0.313561 + 0.543104i
\(761\) −2.92561 5.06731i −0.106053 0.183690i 0.808115 0.589025i \(-0.200488\pi\)
−0.914168 + 0.405335i \(0.867155\pi\)
\(762\) 4.74341 22.1911i 0.171836 0.803899i
\(763\) −17.1429 29.6923i −0.620614 1.07494i
\(764\) 22.5802 + 13.0367i 0.816924 + 0.471651i
\(765\) 14.8028 + 20.4726i 0.535196 + 0.740190i
\(766\) 85.2912i 3.08170i
\(767\) 8.16072 + 0.539689i 0.294666 + 0.0194870i
\(768\) −55.1882 11.7966i −1.99143 0.425674i
\(769\) 35.9163 + 20.7363i 1.29517 + 0.747769i 0.979566 0.201121i \(-0.0644583\pi\)
0.315608 + 0.948890i \(0.397792\pi\)
\(770\) −0.0709867 + 70.3116i −0.00255818 + 2.53385i
\(771\) 41.3780 13.3922i 1.49019 0.482309i
\(772\) 5.36596i 0.193125i
\(773\) −5.92843 + 3.42278i −0.213231 + 0.123109i −0.602812 0.797883i \(-0.705953\pi\)
0.389581 + 0.920992i \(0.372620\pi\)
\(774\) −54.0356 + 5.55440i −1.94227 + 0.199649i
\(775\) −2.70089 −0.0970189
\(776\) −41.9774 72.7071i −1.50690 2.61003i
\(777\) 20.8133 + 18.7835i 0.746672 + 0.673855i
\(778\) 17.2953 + 9.98546i 0.620068 + 0.357996i
\(779\) 7.12503i 0.255281i
\(780\) 42.6785 41.4318i 1.52813 1.48350i
\(781\) −23.1804 40.2434i −0.829460 1.44002i
\(782\) 44.5606 + 25.7271i 1.59348 + 0.919998i
\(783\) 1.85582 0.818645i 0.0663217 0.0292560i
\(784\) 15.7334 + 27.2511i 0.561907 + 0.973252i
\(785\) 15.4305i 0.550739i
\(786\) 17.7990 + 54.9938i 0.634870 + 1.96156i
\(787\) −46.6245 + 26.9186i −1.66198 + 0.959546i −0.690215 + 0.723604i \(0.742484\pi\)
−0.971767 + 0.235942i \(0.924183\pi\)
\(788\) 17.4186 0.620513
\(789\) −5.17447 15.9876i −0.184216 0.569173i
\(790\) −26.5835 + 46.0440i −0.945799 + 1.63817i
\(791\) −13.6555 + 23.6520i −0.485532 + 0.840967i
\(792\) 51.7109 5.26269i 1.83747 0.187002i
\(793\) −29.5616 1.95498i −1.04976 0.0694235i
\(794\) −0.925402 −0.0328413
\(795\) −12.1986 + 13.5168i −0.432641 + 0.479392i
\(796\) 36.2405 62.7705i 1.28451 2.22484i
\(797\) −11.9010 + 6.87106i −0.421556 + 0.243386i −0.695743 0.718291i \(-0.744925\pi\)
0.274187 + 0.961676i \(0.411591\pi\)
\(798\) 22.1587 + 4.73647i 0.784408 + 0.167669i
\(799\) −29.9704 + 17.3034i −1.06028 + 0.612151i
\(800\) 0.208338 + 0.360852i 0.00736586 + 0.0127580i
\(801\) −13.4736 + 30.0767i −0.476065 + 1.06271i
\(802\) −2.15680 + 1.24523i −0.0761591 + 0.0439705i
\(803\) 45.2192 + 0.0456533i 1.59575 + 0.00161107i
\(804\) 11.9893 13.2848i 0.422829 0.468520i
\(805\) 49.0717i 1.72955i
\(806\) 59.5133 29.3053i 2.09627 1.03224i
\(807\) 3.87955 18.1497i 0.136567 0.638900i
\(808\) −18.7407 + 32.4599i −0.659297 + 1.14194i
\(809\) −11.8217 + 20.4757i −0.415627 + 0.719888i −0.995494 0.0948235i \(-0.969771\pi\)
0.579867 + 0.814711i \(0.303105\pi\)
\(810\) 48.9354 + 16.1480i 1.71942 + 0.567383i
\(811\) 4.85443i 0.170462i 0.996361 + 0.0852311i \(0.0271629\pi\)
−0.996361 + 0.0852311i \(0.972837\pi\)
\(812\) 5.14811 2.97226i 0.180663 0.104306i
\(813\) 5.10604 1.65260i 0.179077 0.0579591i
\(814\) 31.0636 17.8928i 1.08878 0.627142i
\(815\) −46.3102 + 26.7372i −1.62217 + 0.936563i
\(816\) 19.7916 21.9303i 0.692843 0.767713i
\(817\) −5.23290 + 9.06365i −0.183076 + 0.317097i
\(818\) 38.9140i 1.36060i
\(819\) −1.45730 40.0231i −0.0509223 1.39852i
\(820\) 47.4877i 1.65834i
\(821\) −23.5087 + 40.7182i −0.820458 + 1.42107i 0.0848840 + 0.996391i \(0.472948\pi\)
−0.905342 + 0.424684i \(0.860385\pi\)
\(822\) 5.66992 + 5.11698i 0.197761 + 0.178475i
\(823\) −17.7481 30.7406i −0.618659 1.07155i −0.989731 0.142945i \(-0.954343\pi\)
0.371072 0.928604i \(-0.378990\pi\)
\(824\) −73.2878 −2.55310
\(825\) 1.54643 + 1.39846i 0.0538399 + 0.0486880i
\(826\) 10.3825 + 17.9831i 0.361254 + 0.625711i
\(827\) −0.0190957 −0.000664022 −0.000332011 1.00000i \(-0.500106\pi\)
−0.000332011 1.00000i \(0.500106\pi\)
\(828\) 70.2442 7.22052i 2.44116 0.250930i
\(829\) −5.22732 + 9.05399i −0.181552 + 0.314458i −0.942409 0.334462i \(-0.891446\pi\)
0.760857 + 0.648920i \(0.224779\pi\)
\(830\) 8.60887 + 4.97034i 0.298818 + 0.172523i
\(831\) −5.21695 + 24.4065i −0.180974 + 0.846652i
\(832\) 19.6041 + 13.1157i 0.679650 + 0.454705i
\(833\) 24.3973 0.845315
\(834\) 19.5215 + 17.6177i 0.675974 + 0.610051i
\(835\) 0.529602 + 0.305766i 0.0183276 + 0.0105815i
\(836\) 9.76401 16.8724i 0.337695 0.583544i
\(837\) 31.2043 + 22.8353i 1.07858 + 0.789304i
\(838\) −47.0208 + 27.1475i −1.62431 + 0.937793i
\(839\) 2.54653 1.47024i 0.0879159 0.0507583i −0.455398 0.890288i \(-0.650503\pi\)
0.543313 + 0.839530i \(0.317170\pi\)
\(840\) 75.8697 + 16.2173i 2.61775 + 0.559551i
\(841\) 14.4238 + 24.9828i 0.497373 + 0.861475i
\(842\) −7.33321 + 12.7015i −0.252719 + 0.437722i
\(843\) 2.12295 2.35236i 0.0731182 0.0810195i
\(844\) 2.11900i 0.0729389i
\(845\) −27.8273 + 11.4882i −0.957288 + 0.395207i
\(846\) −28.8584 + 64.4199i −0.992171 + 2.21480i
\(847\) 35.3129 20.2930i 1.21337 0.697275i
\(848\) 18.4375 + 10.6449i 0.633146 + 0.365547i
\(849\) −9.06505 + 2.93395i −0.311112 + 0.100693i
\(850\) 3.26318 0.111926
\(851\) 21.6672 12.5096i 0.742743 0.428823i
\(852\) −94.9054 + 30.7166i −3.25140 + 1.05233i
\(853\) 15.6357i 0.535356i −0.963508 0.267678i \(-0.913744\pi\)
0.963508 0.267678i \(-0.0862563\pi\)
\(854\) −37.6100 65.1424i −1.28699 2.22913i
\(855\) 8.04556 5.81736i 0.275152 0.198950i
\(856\) 32.2757 55.9032i 1.10316 1.91073i
\(857\) −29.0261 −0.991514 −0.495757 0.868461i \(-0.665109\pi\)
−0.495757 + 0.868461i \(0.665109\pi\)
\(858\) −49.2488 14.0354i −1.68133 0.479160i
\(859\) 18.6927 0.637785 0.318893 0.947791i \(-0.396689\pi\)
0.318893 + 0.947791i \(0.396689\pi\)
\(860\) −34.8768 + 60.4084i −1.18929 + 2.05991i
\(861\) −23.7368 21.4220i −0.808949 0.730059i
\(862\) −35.8584 62.1086i −1.22134 2.11543i
\(863\) 39.6741i 1.35052i 0.737579 + 0.675260i \(0.235969\pi\)
−0.737579 + 0.675260i \(0.764031\pi\)
\(864\) 0.643905 5.93049i 0.0219061 0.201759i
\(865\) −47.0035 + 27.1375i −1.59817 + 0.922701i
\(866\) 1.41583 0.0481117
\(867\) 2.01420 + 6.22329i 0.0684059 + 0.211354i
\(868\) 98.1400 + 56.6612i 3.33109 + 1.92321i
\(869\) 30.7973 + 0.0310930i 1.04473 + 0.00105476i
\(870\) 0.809206 3.78572i 0.0274347 0.128348i
\(871\) −8.12551 + 4.00113i −0.275322 + 0.135573i
\(872\) 48.3738i 1.63814i
\(873\) −39.0700 + 28.2497i −1.32232 + 0.956106i
\(874\) 10.1105 17.5119i 0.341993 0.592349i
\(875\) −19.8801 34.4334i −0.672071 1.16406i
\(876\) 20.3023 94.9803i 0.685950 3.20909i
\(877\) −4.33737 + 2.50418i −0.146462 + 0.0845601i −0.571440 0.820644i \(-0.693615\pi\)
0.424978 + 0.905204i \(0.360282\pi\)
\(878\) −1.60507 + 0.926690i −0.0541686 + 0.0312743i
\(879\) −1.31186 0.280413i −0.0442479 0.00945810i
\(880\) 18.0431 31.1788i 0.608233 1.05104i
\(881\) −40.3122 23.2742i −1.35815 0.784129i −0.368776 0.929518i \(-0.620223\pi\)
−0.989375 + 0.145389i \(0.953557\pi\)
\(882\) 40.3265 29.1582i 1.35786 0.981808i
\(883\) −26.4621 −0.890522 −0.445261 0.895401i \(-0.646889\pi\)
−0.445261 + 0.895401i \(0.646889\pi\)
\(884\) −48.3781 + 23.8222i −1.62713 + 0.801226i
\(885\) 8.89744 + 1.90185i 0.299084 + 0.0639300i
\(886\) −0.299332 0.172819i −0.0100563 0.00580598i
\(887\) 11.1436 19.3013i 0.374166 0.648075i −0.616036 0.787718i \(-0.711262\pi\)
0.990202 + 0.139643i \(0.0445956\pi\)
\(888\) −12.1804 37.6338i −0.408747 1.26291i
\(889\) −19.6201 −0.658038
\(890\) 31.4498 + 54.4727i 1.05420 + 1.82593i
\(891\) −6.04291 29.2315i −0.202445 0.979294i
\(892\) −64.4139 −2.15674
\(893\) 6.80008 + 11.7781i 0.227556 + 0.394139i
\(894\) −10.9274 + 12.1082i −0.365466 + 0.404958i
\(895\) −22.3878 + 38.7768i −0.748341 + 1.29616i
\(896\) 68.3878i 2.28468i
\(897\) −34.3814 9.76083i −1.14796 0.325905i
\(898\) 29.2715i 0.976803i
\(899\) 1.45243 2.51569i 0.0484413 0.0839028i
\(900\) 3.62904 2.62399i 0.120968 0.0874663i
\(901\) 14.2952 8.25333i 0.476242 0.274958i
\(902\) −35.4270 + 20.4061i −1.17959 + 0.679450i
\(903\) 14.4622 + 44.6839i 0.481271 + 1.48699i
\(904\) 33.3706 19.2665i 1.10989 0.640794i
\(905\) 55.1621i 1.83365i
\(906\) 28.0767 9.08716i 0.932784 0.301901i
\(907\) 8.12560 14.0740i 0.269806 0.467318i −0.699006 0.715116i \(-0.746374\pi\)
0.968812 + 0.247798i \(0.0797071\pi\)
\(908\) −44.8638 + 77.7065i −1.48886 + 2.57878i
\(909\) 19.6437 + 8.79983i 0.651539 + 0.291872i
\(910\) −63.5300 42.5033i −2.10600 1.40897i
\(911\) 30.1340i 0.998383i −0.866492 0.499191i \(-0.833630\pi\)
0.866492 0.499191i \(-0.166370\pi\)
\(912\) −8.61839 7.77791i −0.285383 0.257552i
\(913\) 0.00581348 5.75820i 0.000192398 0.190568i
\(914\) −62.4516 + 36.0565i −2.06572 + 1.19264i
\(915\) −32.2304 6.88932i −1.06550 0.227754i
\(916\) −27.6671 47.9209i −0.914147 1.58335i
\(917\) 43.2811 24.9883i 1.42927 0.825187i
\(918\) −37.7007 27.5893i −1.24431 0.910583i
\(919\) 0.220789 0.127473i 0.00728315 0.00420493i −0.496354 0.868120i \(-0.665328\pi\)
0.503637 + 0.863915i \(0.331995\pi\)
\(920\) 34.6177 59.9595i 1.14131 1.97681i
\(921\) −33.0617 29.8375i −1.08942 0.983178i
\(922\) 21.8955 0.721090
\(923\) 50.3778 + 3.33161i 1.65820 + 0.109661i
\(924\) −26.8537 83.2567i −0.883421 2.73895i
\(925\) 0.793348 1.37412i 0.0260851 0.0451807i
\(926\) 32.5249 56.3348i 1.06883 1.85128i
\(927\) 4.30355 + 41.8667i 0.141347 + 1.37508i
\(928\) −0.448144 −0.0147110
\(929\) 40.3841 23.3158i 1.32496 0.764966i 0.340445 0.940264i \(-0.389422\pi\)
0.984515 + 0.175298i \(0.0560889\pi\)
\(930\) 70.2127 22.7247i 2.30236 0.745173i
\(931\) 9.58790i 0.314231i
\(932\) 10.5417 + 18.2588i 0.345305 + 0.598086i
\(933\) 3.36922 + 3.04065i 0.110303 + 0.0995464i
\(934\) 62.8180 + 36.2680i 2.05547 + 1.18672i
\(935\) −13.9406 24.2022i −0.455906 0.791496i
\(936\) −26.4537 + 49.9313i −0.864665 + 1.63206i
\(937\) 9.76109i 0.318881i 0.987208 + 0.159441i \(0.0509690\pi\)
−0.987208 + 0.159441i \(0.949031\pi\)
\(938\) −19.9151 11.4980i −0.650251 0.375422i
\(939\) −5.67770 + 6.29124i −0.185285 + 0.205307i
\(940\) 45.3219 + 78.4999i 1.47824 + 2.56038i
\(941\) 26.4931 0.863650 0.431825 0.901957i \(-0.357870\pi\)
0.431825 + 0.901957i \(0.357870\pi\)
\(942\) 8.78645 + 27.1475i 0.286278 + 0.884514i
\(943\) −24.7107 + 14.2668i −0.804693 + 0.464589i
\(944\) 10.6387i 0.346260i
\(945\) 4.80923 44.2939i 0.156444 1.44088i
\(946\) 60.0533 + 0.0606299i 1.95250 + 0.00197125i
\(947\) −1.22181 0.705411i −0.0397034 0.0229228i 0.480017 0.877259i \(-0.340631\pi\)
−0.519720 + 0.854336i \(0.673964\pi\)
\(948\) 13.8272 64.6880i 0.449087 2.10097i
\(949\) −27.3349 + 40.8577i −0.887330 + 1.32630i
\(950\) 1.28240i 0.0416066i
\(951\) −5.19670 4.68991i −0.168515 0.152081i
\(952\) −60.9131 35.1682i −1.97421 1.13981i
\(953\) 24.2967 + 42.0831i 0.787048 + 1.36321i 0.927768 + 0.373157i \(0.121725\pi\)
−0.140721 + 0.990049i \(0.544942\pi\)
\(954\) 13.7648 30.7268i 0.445651 0.994818i
\(955\) −7.34043 12.7140i −0.237531 0.411416i
\(956\) 49.8540 + 86.3496i 1.61239 + 2.79275i
\(957\) −2.13417 + 0.688357i −0.0689880 + 0.0222514i
\(958\) −42.9778 74.4397i −1.38855 2.40504i
\(959\) 3.30174 5.71878i 0.106619 0.184669i
\(960\) 19.4799 + 17.5802i 0.628712 + 0.567399i
\(961\) 24.3764 0.786334
\(962\) −2.57165 + 38.8863i −0.0829132 + 1.25374i
\(963\) −33.8308 15.1553i −1.09018 0.488372i
\(964\) −64.2708 37.1068i −2.07002 1.19513i
\(965\) 1.51068 2.61657i 0.0486304 0.0842304i
\(966\) −27.9424 86.3338i −0.899032 2.77775i
\(967\) 44.3067i 1.42481i 0.701770 + 0.712404i \(0.252393\pi\)
−0.701770 + 0.712404i \(0.747607\pi\)
\(968\) −57.4637 0.116031i −1.84695 0.00372938i
\(969\) −8.56360 + 2.77166i −0.275102 + 0.0890384i
\(970\) 92.0173i 2.95450i
\(971\) 18.5387 10.7033i 0.594935 0.343486i −0.172111 0.985077i \(-0.555059\pi\)
0.767046 + 0.641592i \(0.221726\pi\)
\(972\) −64.1127 0.366714i −2.05641 0.0117624i
\(973\) 11.3679 19.6897i 0.364437 0.631223i
\(974\) 40.1911 1.28781
\(975\) −2.19783 + 0.554132i −0.0703870 + 0.0177464i
\(976\) 38.5380i 1.23357i
\(977\) 33.0568 + 19.0853i 1.05758 + 0.610594i 0.924762 0.380546i \(-0.124264\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(978\) 66.2507 73.4098i 2.11846 2.34739i
\(979\) 18.2494 31.5352i 0.583252 1.00787i
\(980\) 63.9025i 2.04129i
\(981\) 27.6342 2.84057i 0.882293 0.0906923i
\(982\) 16.6598 + 28.8556i 0.531636 + 0.920820i
\(983\) 20.6274i 0.657911i −0.944346 0.328955i \(-0.893303\pi\)
0.944346 0.328955i \(-0.106697\pi\)
\(984\) 13.8913 + 42.9201i 0.442840 + 1.36824i
\(985\) −8.49374 4.90386i −0.270633 0.156250i
\(986\) −1.75481 + 3.03942i −0.0558845 + 0.0967948i
\(987\) 59.6834 + 12.7575i 1.89974 + 0.406075i
\(988\) 9.36190 + 19.0122i 0.297842 + 0.604857i
\(989\) 41.9123 1.33273
\(990\) −51.9676 23.3431i −1.65164 0.741892i
\(991\) 6.40435 11.0927i 0.203441 0.352370i −0.746194 0.665729i \(-0.768121\pi\)
0.949635 + 0.313359i \(0.101454\pi\)
\(992\) −4.27155 7.39855i −0.135622 0.234904i
\(993\) 2.64173 + 0.564677i 0.0838329 + 0.0179195i
\(994\) 64.0935 + 111.013i 2.03292 + 3.52112i
\(995\) −35.3435 + 20.4056i −1.12046 + 0.646900i
\(996\) −12.0948 2.58529i −0.383237 0.0819179i
\(997\) 38.7630 22.3798i 1.22764 0.708776i 0.261101 0.965311i \(-0.415914\pi\)
0.966535 + 0.256536i \(0.0825811\pi\)
\(998\) −9.93798 + 17.2131i −0.314581 + 0.544871i
\(999\) −20.7836 + 9.16813i −0.657565 + 0.290067i
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 429.2.p.b.230.3 96
3.2 odd 2 inner 429.2.p.b.230.46 yes 96
11.10 odd 2 inner 429.2.p.b.230.45 yes 96
13.3 even 3 inner 429.2.p.b.263.4 yes 96
33.32 even 2 inner 429.2.p.b.230.4 yes 96
39.29 odd 6 inner 429.2.p.b.263.45 yes 96
143.120 odd 6 inner 429.2.p.b.263.46 yes 96
429.263 even 6 inner 429.2.p.b.263.3 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.p.b.230.3 96 1.1 even 1 trivial
429.2.p.b.230.4 yes 96 33.32 even 2 inner
429.2.p.b.230.45 yes 96 11.10 odd 2 inner
429.2.p.b.230.46 yes 96 3.2 odd 2 inner
429.2.p.b.263.3 yes 96 429.263 even 6 inner
429.2.p.b.263.4 yes 96 13.3 even 3 inner
429.2.p.b.263.45 yes 96 39.29 odd 6 inner
429.2.p.b.263.46 yes 96 143.120 odd 6 inner