Properties

Label 429.2.t.a.296.2
Level $429$
Weight $2$
Character 429.296
Analytic conductor $3.426$
Analytic rank $0$
Dimension $104$
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(296,429)]
 
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, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.296");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.t (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: \(104\)
Relative dimension: \(52\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 296.2
Character \(\chi\) \(=\) 429.296
Dual form 429.2.t.a.329.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.31547 + 1.33684i) q^{2} +(1.48761 + 0.887132i) q^{3} +(2.57426 - 4.45876i) q^{4} -2.76446 q^{5} +(-4.63048 - 0.0654292i) q^{6} +(-0.565134 + 0.978841i) q^{7} +8.41814i q^{8} +(1.42599 + 2.63942i) q^{9} +O(q^{10})\) \(q+(-2.31547 + 1.33684i) q^{2} +(1.48761 + 0.887132i) q^{3} +(2.57426 - 4.45876i) q^{4} -2.76446 q^{5} +(-4.63048 - 0.0654292i) q^{6} +(-0.565134 + 0.978841i) q^{7} +8.41814i q^{8} +(1.42599 + 2.63942i) q^{9} +(6.40102 - 3.69563i) q^{10} +(3.16940 + 0.977207i) q^{11} +(7.78502 - 4.34920i) q^{12} +(-2.86710 + 2.18626i) q^{13} -3.02197i q^{14} +(-4.11245 - 2.45244i) q^{15} +(-6.10514 - 10.5744i) q^{16} +(1.85321 - 3.20985i) q^{17} +(-6.83032 - 4.20518i) q^{18} +(-0.848514 + 1.46967i) q^{19} +(-7.11645 + 12.3260i) q^{20} +(-1.70906 + 0.954790i) q^{21} +(-8.64500 + 1.97427i) q^{22} +(-7.29596 + 4.21232i) q^{23} +(-7.46800 + 12.5229i) q^{24} +2.64223 q^{25} +(3.71600 - 8.89507i) q^{26} +(-0.220186 + 5.19149i) q^{27} +(2.90961 + 5.03959i) q^{28} +(-0.295904 - 0.512520i) q^{29} +(12.8008 + 0.180876i) q^{30} -4.08080i q^{31} +(13.6919 + 7.90502i) q^{32} +(3.84793 + 4.26538i) q^{33} +9.90976i q^{34} +(1.56229 - 2.70597i) q^{35} +(15.4394 + 0.436409i) q^{36} +(-8.55581 + 4.93970i) q^{37} -4.53730i q^{38} +(-6.20464 + 0.708824i) q^{39} -23.2716i q^{40} +(-8.76317 + 5.05942i) q^{41} +(2.68089 - 4.49552i) q^{42} +(-7.31991 - 4.22615i) q^{43} +(12.5160 - 11.6160i) q^{44} +(-3.94210 - 7.29657i) q^{45} +(11.2624 - 19.5070i) q^{46} -1.04557 q^{47} +(0.298806 - 21.1467i) q^{48} +(2.86125 + 4.95582i) q^{49} +(-6.11801 + 3.53224i) q^{50} +(5.60443 - 3.13098i) q^{51} +(2.36735 + 18.4117i) q^{52} -1.18874i q^{53} +(-6.43033 - 12.3151i) q^{54} +(-8.76166 - 2.70145i) q^{55} +(-8.24002 - 4.75738i) q^{56} +(-2.56605 + 1.43356i) q^{57} +(1.37031 + 0.791149i) q^{58} +(1.43147 - 2.47938i) q^{59} +(-21.5214 + 12.0232i) q^{60} +(8.12322 + 4.68995i) q^{61} +(5.45536 + 9.44896i) q^{62} +(-3.38945 - 0.0958059i) q^{63} -17.8503 q^{64} +(7.92597 - 6.04384i) q^{65} +(-14.6119 - 4.73231i) q^{66} +(1.49115 - 0.860914i) q^{67} +(-9.54130 - 16.5260i) q^{68} +(-14.5905 - 0.206165i) q^{69} +8.35411i q^{70} +(4.35002 - 7.53446i) q^{71} +(-22.2190 + 12.0042i) q^{72} +7.15945 q^{73} +(13.2071 - 22.8754i) q^{74} +(3.93063 + 2.34401i) q^{75} +(4.36860 + 7.56663i) q^{76} +(-2.74766 + 2.55008i) q^{77} +(13.4191 - 9.93585i) q^{78} +1.41460i q^{79} +(16.8774 + 29.2325i) q^{80} +(-4.93309 + 7.52759i) q^{81} +(13.5272 - 23.4299i) q^{82} +6.53336i q^{83} +(-0.142406 + 10.0782i) q^{84} +(-5.12312 + 8.87351i) q^{85} +22.5987 q^{86} +(0.0144825 - 1.02494i) q^{87} +(-8.22626 + 26.6804i) q^{88} +(-3.41519 - 5.91528i) q^{89} +(18.8821 + 11.6250i) q^{90} +(-0.519711 - 4.04197i) q^{91} +43.3745i q^{92} +(3.62021 - 6.07066i) q^{93} +(2.42098 - 1.39775i) q^{94} +(2.34568 - 4.06284i) q^{95} +(13.3555 + 23.9061i) q^{96} +(4.33663 + 2.50376i) q^{97} +(-13.2503 - 7.65004i) q^{98} +(1.94027 + 9.75886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31547 + 1.33684i −1.63728 + 0.945286i −0.655521 + 0.755177i \(0.727551\pi\)
−0.981763 + 0.190109i \(0.939116\pi\)
\(3\) 1.48761 + 0.887132i 0.858875 + 0.512186i
\(4\) 2.57426 4.45876i 1.28713 2.22938i
\(5\) −2.76446 −1.23630 −0.618152 0.786059i \(-0.712118\pi\)
−0.618152 + 0.786059i \(0.712118\pi\)
\(6\) −4.63048 0.0654292i −1.89038 0.0267114i
\(7\) −0.565134 + 0.978841i −0.213601 + 0.369967i −0.952839 0.303477i \(-0.901852\pi\)
0.739238 + 0.673444i \(0.235186\pi\)
\(8\) 8.41814i 2.97626i
\(9\) 1.42599 + 2.63942i 0.475331 + 0.879807i
\(10\) 6.40102 3.69563i 2.02418 1.16866i
\(11\) 3.16940 + 0.977207i 0.955609 + 0.294639i
\(12\) 7.78502 4.34920i 2.24734 1.25551i
\(13\) −2.86710 + 2.18626i −0.795190 + 0.606361i
\(14\) 3.02197i 0.807655i
\(15\) −4.11245 2.45244i −1.06183 0.633217i
\(16\) −6.10514 10.5744i −1.52629 2.64360i
\(17\) 1.85321 3.20985i 0.449469 0.778504i −0.548882 0.835900i \(-0.684946\pi\)
0.998351 + 0.0573959i \(0.0182797\pi\)
\(18\) −6.83032 4.20518i −1.60992 0.991170i
\(19\) −0.848514 + 1.46967i −0.194662 + 0.337165i −0.946790 0.321853i \(-0.895694\pi\)
0.752127 + 0.659018i \(0.229028\pi\)
\(20\) −7.11645 + 12.3260i −1.59129 + 2.75619i
\(21\) −1.70906 + 0.954790i −0.372948 + 0.208352i
\(22\) −8.64500 + 1.97427i −1.84312 + 0.420916i
\(23\) −7.29596 + 4.21232i −1.52131 + 0.878330i −0.521628 + 0.853173i \(0.674675\pi\)
−0.999684 + 0.0251570i \(0.991991\pi\)
\(24\) −7.46800 + 12.5229i −1.52440 + 2.55623i
\(25\) 2.64223 0.528447
\(26\) 3.71600 8.89507i 0.728767 1.74447i
\(27\) −0.220186 + 5.19149i −0.0423749 + 0.999102i
\(28\) 2.90961 + 5.03959i 0.549865 + 0.952393i
\(29\) −0.295904 0.512520i −0.0549479 0.0951726i 0.837243 0.546831i \(-0.184166\pi\)
−0.892191 + 0.451658i \(0.850833\pi\)
\(30\) 12.8008 + 0.180876i 2.33709 + 0.0330234i
\(31\) 4.08080i 0.732933i −0.930431 0.366467i \(-0.880567\pi\)
0.930431 0.366467i \(-0.119433\pi\)
\(32\) 13.6919 + 7.90502i 2.42041 + 1.39742i
\(33\) 3.84793 + 4.26538i 0.669838 + 0.742507i
\(34\) 9.90976i 1.69951i
\(35\) 1.56229 2.70597i 0.264075 0.457392i
\(36\) 15.4394 + 0.436409i 2.57324 + 0.0727349i
\(37\) −8.55581 + 4.93970i −1.40657 + 0.812082i −0.995055 0.0993227i \(-0.968332\pi\)
−0.411512 + 0.911404i \(0.634999\pi\)
\(38\) 4.53730i 0.736047i
\(39\) −6.20464 + 0.708824i −0.993538 + 0.113503i
\(40\) 23.2716i 3.67956i
\(41\) −8.76317 + 5.05942i −1.36858 + 0.790148i −0.990746 0.135726i \(-0.956663\pi\)
−0.377831 + 0.925875i \(0.623330\pi\)
\(42\) 2.68089 4.49552i 0.413670 0.693674i
\(43\) −7.31991 4.22615i −1.11628 0.644482i −0.175828 0.984421i \(-0.556260\pi\)
−0.940448 + 0.339939i \(0.889594\pi\)
\(44\) 12.5160 11.6160i 1.88686 1.75117i
\(45\) −3.94210 7.29657i −0.587654 1.08771i
\(46\) 11.2624 19.5070i 1.66055 2.87615i
\(47\) −1.04557 −0.152512 −0.0762559 0.997088i \(-0.524297\pi\)
−0.0762559 + 0.997088i \(0.524297\pi\)
\(48\) 0.298806 21.1467i 0.0431289 3.05227i
\(49\) 2.86125 + 4.95582i 0.408749 + 0.707975i
\(50\) −6.11801 + 3.53224i −0.865217 + 0.499534i
\(51\) 5.60443 3.13098i 0.784777 0.438425i
\(52\) 2.36735 + 18.4117i 0.328293 + 2.55324i
\(53\) 1.18874i 0.163286i −0.996662 0.0816428i \(-0.973983\pi\)
0.996662 0.0816428i \(-0.0260167\pi\)
\(54\) −6.43033 12.3151i −0.875057 1.67587i
\(55\) −8.76166 2.70145i −1.18142 0.364263i
\(56\) −8.24002 4.75738i −1.10112 0.635731i
\(57\) −2.56605 + 1.43356i −0.339882 + 0.189879i
\(58\) 1.37031 + 0.791149i 0.179931 + 0.103883i
\(59\) 1.43147 2.47938i 0.186362 0.322788i −0.757673 0.652634i \(-0.773664\pi\)
0.944034 + 0.329847i \(0.106997\pi\)
\(60\) −21.5214 + 12.0232i −2.77840 + 1.55219i
\(61\) 8.12322 + 4.68995i 1.04007 + 0.600486i 0.919854 0.392261i \(-0.128307\pi\)
0.120219 + 0.992747i \(0.461640\pi\)
\(62\) 5.45536 + 9.44896i 0.692832 + 1.20002i
\(63\) −3.38945 0.0958059i −0.427031 0.0120704i
\(64\) −17.8503 −2.23129
\(65\) 7.92597 6.04384i 0.983096 0.749646i
\(66\) −14.6119 4.73231i −1.79860 0.582507i
\(67\) 1.49115 0.860914i 0.182173 0.105177i −0.406140 0.913811i \(-0.633126\pi\)
0.588313 + 0.808633i \(0.299792\pi\)
\(68\) −9.54130 16.5260i −1.15705 2.00407i
\(69\) −14.5905 0.206165i −1.75648 0.0248194i
\(70\) 8.35411i 0.998507i
\(71\) 4.35002 7.53446i 0.516253 0.894176i −0.483569 0.875306i \(-0.660660\pi\)
0.999822 0.0188697i \(-0.00600676\pi\)
\(72\) −22.2190 + 12.0042i −2.61853 + 1.41471i
\(73\) 7.15945 0.837950 0.418975 0.907998i \(-0.362389\pi\)
0.418975 + 0.907998i \(0.362389\pi\)
\(74\) 13.2071 22.8754i 1.53530 2.65922i
\(75\) 3.93063 + 2.34401i 0.453870 + 0.270663i
\(76\) 4.36860 + 7.56663i 0.501112 + 0.867952i
\(77\) −2.74766 + 2.55008i −0.313125 + 0.290609i
\(78\) 13.4191 9.93585i 1.51941 1.12501i
\(79\) 1.41460i 0.159155i 0.996829 + 0.0795776i \(0.0253571\pi\)
−0.996829 + 0.0795776i \(0.974643\pi\)
\(80\) 16.8774 + 29.2325i 1.88695 + 3.26830i
\(81\) −4.93309 + 7.52759i −0.548121 + 0.836399i
\(82\) 13.5272 23.4299i 1.49383 2.58739i
\(83\) 6.53336i 0.717129i 0.933505 + 0.358565i \(0.116734\pi\)
−0.933505 + 0.358565i \(0.883266\pi\)
\(84\) −0.142406 + 10.0782i −0.0155378 + 1.09962i
\(85\) −5.12312 + 8.87351i −0.555681 + 0.962467i
\(86\) 22.5987 2.43688
\(87\) 0.0144825 1.02494i 0.00155269 0.109885i
\(88\) −8.22626 + 26.6804i −0.876923 + 2.84414i
\(89\) −3.41519 5.91528i −0.362009 0.627019i 0.626282 0.779597i \(-0.284576\pi\)
−0.988291 + 0.152578i \(0.951242\pi\)
\(90\) 18.8821 + 11.6250i 1.99035 + 1.22539i
\(91\) −0.519711 4.04197i −0.0544805 0.423713i
\(92\) 43.3745i 4.52211i
\(93\) 3.62021 6.07066i 0.375398 0.629498i
\(94\) 2.42098 1.39775i 0.249705 0.144167i
\(95\) 2.34568 4.06284i 0.240662 0.416839i
\(96\) 13.3555 + 23.9061i 1.36309 + 2.43991i
\(97\) 4.33663 + 2.50376i 0.440318 + 0.254218i 0.703733 0.710465i \(-0.251515\pi\)
−0.263414 + 0.964683i \(0.584849\pi\)
\(98\) −13.2503 7.65004i −1.33848 0.772771i
\(99\) 1.94027 + 9.75886i 0.195005 + 0.980802i
\(100\) 6.80181 11.7811i 0.680181 1.17811i
\(101\) 6.27893 + 10.8754i 0.624777 + 1.08215i 0.988584 + 0.150671i \(0.0481436\pi\)
−0.363807 + 0.931474i \(0.618523\pi\)
\(102\) −8.79126 + 14.7419i −0.870465 + 1.45967i
\(103\) −4.21360 −0.415179 −0.207589 0.978216i \(-0.566562\pi\)
−0.207589 + 0.978216i \(0.566562\pi\)
\(104\) −18.4043 24.1356i −1.80469 2.36669i
\(105\) 4.72464 2.63948i 0.461077 0.257587i
\(106\) 1.58915 + 2.75248i 0.154352 + 0.267345i
\(107\) 9.09797 + 15.7581i 0.879534 + 1.52340i 0.851853 + 0.523780i \(0.175479\pi\)
0.0276802 + 0.999617i \(0.491188\pi\)
\(108\) 22.5807 + 14.3460i 2.17283 + 1.38045i
\(109\) 3.66800 0.351331 0.175666 0.984450i \(-0.443792\pi\)
0.175666 + 0.984450i \(0.443792\pi\)
\(110\) 23.8988 5.45779i 2.27866 0.520380i
\(111\) −17.1099 0.241765i −1.62400 0.0229474i
\(112\) 13.8009 1.30406
\(113\) 7.69319 + 4.44167i 0.723714 + 0.417837i 0.816118 0.577885i \(-0.196122\pi\)
−0.0924038 + 0.995722i \(0.529455\pi\)
\(114\) 4.02518 6.74975i 0.376993 0.632172i
\(115\) 20.1694 11.6448i 1.88080 1.08588i
\(116\) −3.04694 −0.282901
\(117\) −9.85893 4.44988i −0.911459 0.411391i
\(118\) 7.65457i 0.704660i
\(119\) 2.09462 + 3.62800i 0.192014 + 0.332578i
\(120\) 20.6450 34.6192i 1.88462 3.16028i
\(121\) 9.09013 + 6.19431i 0.826376 + 0.563119i
\(122\) −25.0788 −2.27052
\(123\) −17.5246 0.247625i −1.58014 0.0223276i
\(124\) −18.1953 10.5051i −1.63399 0.943382i
\(125\) 6.51795 0.582983
\(126\) 7.97625 4.30931i 0.710581 0.383904i
\(127\) −8.61325 + 4.97286i −0.764302 + 0.441270i −0.830838 0.556514i \(-0.812139\pi\)
0.0665360 + 0.997784i \(0.478805\pi\)
\(128\) 13.9481 8.05291i 1.23285 0.711784i
\(129\) −7.14005 12.7806i −0.628646 1.12527i
\(130\) −10.2727 + 24.5901i −0.900977 + 2.15669i
\(131\) −0.480341 −0.0419676 −0.0209838 0.999780i \(-0.506680\pi\)
−0.0209838 + 0.999780i \(0.506680\pi\)
\(132\) 28.9239 6.17675i 2.51750 0.537617i
\(133\) −0.959049 1.66112i −0.0831601 0.144037i
\(134\) −2.30180 + 3.98684i −0.198846 + 0.344411i
\(135\) 0.608696 14.3516i 0.0523882 1.23519i
\(136\) 27.0210 + 15.6006i 2.31703 + 1.33774i
\(137\) 1.34325 2.32658i 0.114761 0.198773i −0.802923 0.596083i \(-0.796723\pi\)
0.917684 + 0.397310i \(0.130056\pi\)
\(138\) 34.0594 19.0277i 2.89932 1.61974i
\(139\) −8.48434 4.89844i −0.719633 0.415480i 0.0949848 0.995479i \(-0.469720\pi\)
−0.814617 + 0.579999i \(0.803053\pi\)
\(140\) −8.04350 13.9317i −0.679800 1.17745i
\(141\) −1.55540 0.927557i −0.130988 0.0781144i
\(142\) 23.2611i 1.95203i
\(143\) −11.2234 + 4.12739i −0.938548 + 0.345149i
\(144\) 19.2044 31.1931i 1.60037 2.59942i
\(145\) 0.818013 + 1.41684i 0.0679323 + 0.117662i
\(146\) −16.5775 + 9.57101i −1.37196 + 0.792103i
\(147\) −0.140039 + 9.91066i −0.0115502 + 0.817417i
\(148\) 50.8644i 4.18103i
\(149\) −14.9158 8.61166i −1.22195 0.705494i −0.256618 0.966513i \(-0.582608\pi\)
−0.965334 + 0.261018i \(0.915942\pi\)
\(150\) −12.2348 0.172879i −0.998967 0.0141155i
\(151\) 5.40037 0.439476 0.219738 0.975559i \(-0.429480\pi\)
0.219738 + 0.975559i \(0.429480\pi\)
\(152\) −12.3719 7.14290i −1.00349 0.579366i
\(153\) 11.1148 + 0.314171i 0.898580 + 0.0253992i
\(154\) 2.95309 9.57781i 0.237967 0.771802i
\(155\) 11.2812i 0.906128i
\(156\) −12.8119 + 29.4897i −1.02577 + 2.36106i
\(157\) 3.51966 0.280900 0.140450 0.990088i \(-0.455145\pi\)
0.140450 + 0.990088i \(0.455145\pi\)
\(158\) −1.89109 3.27547i −0.150447 0.260582i
\(159\) 1.05457 1.76838i 0.0836325 0.140242i
\(160\) −37.8507 21.8531i −2.99236 1.72764i
\(161\) 9.52211i 0.750447i
\(162\) 1.35924 24.0246i 0.106792 1.88755i
\(163\) 13.2575 + 7.65423i 1.03841 + 0.599525i 0.919382 0.393366i \(-0.128689\pi\)
0.119026 + 0.992891i \(0.462023\pi\)
\(164\) 52.0971i 4.06810i
\(165\) −10.6374 11.7915i −0.828123 0.917965i
\(166\) −8.73403 15.1278i −0.677893 1.17414i
\(167\) 1.33893 0.773032i 0.103610 0.0598190i −0.447300 0.894384i \(-0.647614\pi\)
0.550909 + 0.834565i \(0.314281\pi\)
\(168\) −8.03755 14.3871i −0.620110 1.10999i
\(169\) 3.44050 12.5365i 0.264654 0.964344i
\(170\) 27.3951i 2.10111i
\(171\) −5.08905 0.143847i −0.389169 0.0110002i
\(172\) −37.6868 + 21.7585i −2.87359 + 1.65907i
\(173\) 0.247842 0.429275i 0.0188431 0.0326372i −0.856450 0.516230i \(-0.827335\pi\)
0.875293 + 0.483593i \(0.160668\pi\)
\(174\) 1.33664 + 2.39257i 0.101330 + 0.181380i
\(175\) −1.49322 + 2.58633i −0.112877 + 0.195508i
\(176\) −9.01621 39.4805i −0.679622 2.97595i
\(177\) 4.32901 2.41846i 0.325388 0.181782i
\(178\) 15.8155 + 9.13110i 1.18542 + 0.684405i
\(179\) −20.6337 + 11.9129i −1.54224 + 0.890410i −0.543538 + 0.839385i \(0.682916\pi\)
−0.998697 + 0.0510255i \(0.983751\pi\)
\(180\) −42.6816 1.20644i −3.18130 0.0899224i
\(181\) 5.91482 0.439645 0.219823 0.975540i \(-0.429452\pi\)
0.219823 + 0.975540i \(0.429452\pi\)
\(182\) 6.60682 + 8.66428i 0.489730 + 0.642239i
\(183\) 7.92362 + 14.1832i 0.585731 + 1.04845i
\(184\) −35.4599 61.4183i −2.61414 4.52782i
\(185\) 23.6522 13.6556i 1.73894 1.00398i
\(186\) −0.267004 + 18.8960i −0.0195777 + 1.38552i
\(187\) 9.01025 8.36232i 0.658895 0.611514i
\(188\) −2.69157 + 4.66193i −0.196303 + 0.340006i
\(189\) −4.95721 3.14941i −0.360584 0.229086i
\(190\) 12.5432i 0.909977i
\(191\) 2.58659 + 1.49337i 0.187159 + 0.108056i 0.590652 0.806926i \(-0.298871\pi\)
−0.403493 + 0.914983i \(0.632204\pi\)
\(192\) −26.5544 15.8356i −1.91640 1.14284i
\(193\) −7.45257 12.9082i −0.536448 0.929155i −0.999092 0.0426108i \(-0.986432\pi\)
0.462644 0.886544i \(-0.346901\pi\)
\(194\) −13.3885 −0.961235
\(195\) 17.1525 1.95952i 1.22831 0.140324i
\(196\) 29.4624 2.10446
\(197\) 11.0611 6.38612i 0.788069 0.454992i −0.0512130 0.998688i \(-0.516309\pi\)
0.839282 + 0.543696i \(0.182975\pi\)
\(198\) −17.5386 20.0025i −1.24642 1.42152i
\(199\) −1.65383 + 2.86452i −0.117237 + 0.203060i −0.918672 0.395022i \(-0.870737\pi\)
0.801435 + 0.598082i \(0.204070\pi\)
\(200\) 22.2427i 1.57280i
\(201\) 2.98200 + 0.0421360i 0.210334 + 0.00297205i
\(202\) −29.0774 16.7878i −2.04588 1.18119i
\(203\) 0.668901 0.0469476
\(204\) 0.466983 33.0487i 0.0326954 2.31388i
\(205\) 24.2254 13.9866i 1.69198 0.976863i
\(206\) 9.75646 5.63290i 0.679765 0.392463i
\(207\) −21.5221 13.2504i −1.49589 0.920963i
\(208\) 40.6225 + 16.9704i 2.81666 + 1.17669i
\(209\) −4.12545 + 3.82879i −0.285363 + 0.264843i
\(210\) −7.41120 + 12.4277i −0.511421 + 0.857592i
\(211\) 17.9917 10.3875i 1.23860 0.715105i 0.269790 0.962919i \(-0.413046\pi\)
0.968808 + 0.247814i \(0.0797123\pi\)
\(212\) −5.30029 3.06012i −0.364025 0.210170i
\(213\) 13.1552 7.34933i 0.901380 0.503568i
\(214\) −42.1321 24.3250i −2.88009 1.66282i
\(215\) 20.2356 + 11.6830i 1.38006 + 0.796776i
\(216\) −43.7026 1.85356i −2.97359 0.126119i
\(217\) 3.99445 + 2.30620i 0.271161 + 0.156555i
\(218\) −8.49315 + 4.90352i −0.575229 + 0.332108i
\(219\) 10.6505 + 6.35138i 0.719694 + 0.429186i
\(220\) −34.5999 + 32.1119i −2.33273 + 2.16498i
\(221\) 1.70426 + 13.2546i 0.114641 + 0.891599i
\(222\) 39.9407 22.3134i 2.68064 1.49757i
\(223\) 10.9221 6.30590i 0.731401 0.422274i −0.0875337 0.996162i \(-0.527899\pi\)
0.818934 + 0.573887i \(0.194565\pi\)
\(224\) −15.4755 + 8.93480i −1.03400 + 0.596981i
\(225\) 3.76781 + 6.97397i 0.251187 + 0.464931i
\(226\) −23.7511 −1.57990
\(227\) 13.7653 + 7.94738i 0.913633 + 0.527486i 0.881598 0.472001i \(-0.156468\pi\)
0.0320344 + 0.999487i \(0.489801\pi\)
\(228\) −0.213814 + 15.1318i −0.0141602 + 1.00212i
\(229\) 11.8755i 0.784754i 0.919804 + 0.392377i \(0.128347\pi\)
−0.919804 + 0.392377i \(0.871653\pi\)
\(230\) −31.1344 + 53.9263i −2.05294 + 3.55580i
\(231\) −6.34972 + 1.35600i −0.417781 + 0.0892180i
\(232\) 4.31446 2.49096i 0.283258 0.163539i
\(233\) −14.4815 −0.948718 −0.474359 0.880332i \(-0.657320\pi\)
−0.474359 + 0.880332i \(0.657320\pi\)
\(234\) 28.7768 2.87623i 1.88120 0.188025i
\(235\) 2.89043 0.188551
\(236\) −7.36996 12.7652i −0.479744 0.830941i
\(237\) −1.25494 + 2.10438i −0.0815171 + 0.136694i
\(238\) −9.70008 5.60034i −0.628763 0.363016i
\(239\) 0.372520i 0.0240963i −0.999927 0.0120482i \(-0.996165\pi\)
0.999927 0.0120482i \(-0.00383515\pi\)
\(240\) −0.826037 + 58.4593i −0.0533205 + 3.77353i
\(241\) −8.44225 + 14.6224i −0.543813 + 0.941912i 0.454868 + 0.890559i \(0.349687\pi\)
−0.998681 + 0.0513526i \(0.983647\pi\)
\(242\) −29.3287 2.19072i −1.88532 0.140825i
\(243\) −14.0165 + 6.82186i −0.899159 + 0.437622i
\(244\) 41.8227 24.1463i 2.67742 1.54581i
\(245\) −7.90980 13.7002i −0.505339 0.875272i
\(246\) 40.9087 22.8541i 2.60824 1.45713i
\(247\) −0.780313 6.06876i −0.0496501 0.386146i
\(248\) 34.3527 2.18140
\(249\) −5.79595 + 9.71912i −0.367304 + 0.615924i
\(250\) −15.0921 + 8.71343i −0.954508 + 0.551086i
\(251\) 16.0934 + 9.29153i 1.01581 + 0.586476i 0.912886 0.408214i \(-0.133848\pi\)
0.102920 + 0.994690i \(0.467181\pi\)
\(252\) −9.15252 + 14.8661i −0.576555 + 0.936477i
\(253\) −27.2401 + 6.22085i −1.71257 + 0.391101i
\(254\) 13.2958 23.0290i 0.834253 1.44497i
\(255\) −15.4932 + 8.65547i −0.970222 + 0.542027i
\(256\) −3.68054 + 6.37489i −0.230034 + 0.398430i
\(257\) 10.2321 5.90750i 0.638260 0.368500i −0.145684 0.989331i \(-0.546538\pi\)
0.783944 + 0.620831i \(0.213205\pi\)
\(258\) 33.6182 + 20.0480i 2.09298 + 1.24814i
\(259\) 11.1664i 0.693845i
\(260\) −6.54445 50.8984i −0.405870 3.15659i
\(261\) 0.930799 1.51186i 0.0576150 0.0935820i
\(262\) 1.11222 0.642138i 0.0687129 0.0396714i
\(263\) −5.58258 9.66932i −0.344237 0.596236i 0.640978 0.767559i \(-0.278529\pi\)
−0.985215 + 0.171324i \(0.945196\pi\)
\(264\) −35.9065 + 32.3924i −2.20990 + 1.99361i
\(265\) 3.28621i 0.201870i
\(266\) 4.44129 + 2.56418i 0.272313 + 0.157220i
\(267\) 0.167151 11.8294i 0.0102295 0.723946i
\(268\) 8.86489i 0.541509i
\(269\) −11.1760 6.45248i −0.681414 0.393414i 0.118974 0.992897i \(-0.462040\pi\)
−0.800388 + 0.599483i \(0.795373\pi\)
\(270\) 17.7764 + 34.0445i 1.08184 + 2.07188i
\(271\) 13.5276 + 23.4306i 0.821746 + 1.42331i 0.904381 + 0.426725i \(0.140333\pi\)
−0.0826357 + 0.996580i \(0.526334\pi\)
\(272\) −45.2564 −2.74408
\(273\) 2.81263 6.47394i 0.170228 0.391821i
\(274\) 7.18282i 0.433930i
\(275\) 8.37428 + 2.58201i 0.504988 + 0.155701i
\(276\) −38.4789 + 64.5246i −2.31616 + 3.88392i
\(277\) −0.416135 0.240255i −0.0250031 0.0144356i 0.487446 0.873153i \(-0.337928\pi\)
−0.512449 + 0.858717i \(0.671262\pi\)
\(278\) 26.1936 1.57099
\(279\) 10.7709 5.81919i 0.644840 0.348386i
\(280\) 22.7792 + 13.1516i 1.36132 + 0.785957i
\(281\) 13.2614i 0.791111i −0.918442 0.395555i \(-0.870552\pi\)
0.918442 0.395555i \(-0.129448\pi\)
\(282\) 4.84148 + 0.0684107i 0.288306 + 0.00407380i
\(283\) −0.259912 + 0.150060i −0.0154502 + 0.00892017i −0.507705 0.861531i \(-0.669506\pi\)
0.492255 + 0.870451i \(0.336173\pi\)
\(284\) −22.3962 38.7914i −1.32897 2.30184i
\(285\) 7.09375 3.96301i 0.420197 0.234748i
\(286\) 20.4698 24.5607i 1.21040 1.45230i
\(287\) 11.4370i 0.675105i
\(288\) −1.34012 + 47.4112i −0.0789674 + 2.79373i
\(289\) 1.63123 + 2.82537i 0.0959545 + 0.166198i
\(290\) −3.78817 2.18710i −0.222449 0.128431i
\(291\) 4.23008 + 7.57179i 0.247971 + 0.443866i
\(292\) 18.4303 31.9222i 1.07855 1.86811i
\(293\) 11.6147 + 6.70573i 0.678536 + 0.391753i 0.799303 0.600928i \(-0.205202\pi\)
−0.120767 + 0.992681i \(0.538535\pi\)
\(294\) −12.9247 23.1350i −0.753782 1.34926i
\(295\) −3.95724 + 6.85414i −0.230399 + 0.399064i
\(296\) −41.5831 72.0240i −2.41697 4.18631i
\(297\) −5.77102 + 16.2387i −0.334868 + 0.942265i
\(298\) 46.0495 2.66758
\(299\) 11.7090 28.0280i 0.677147 1.62090i
\(300\) 20.5698 11.4916i 1.18760 0.663468i
\(301\) 8.27347 4.77669i 0.476875 0.275324i
\(302\) −12.5044 + 7.21941i −0.719546 + 0.415430i
\(303\) −0.307312 + 21.7487i −0.0176546 + 1.24943i
\(304\) 20.7212 1.18844
\(305\) −22.4563 12.9652i −1.28585 0.742383i
\(306\) −26.1560 + 14.1312i −1.49524 + 0.807830i
\(307\) 20.5352 1.17201 0.586003 0.810309i \(-0.300701\pi\)
0.586003 + 0.810309i \(0.300701\pi\)
\(308\) 4.29698 + 18.8158i 0.244843 + 1.07213i
\(309\) −6.26822 3.73802i −0.356586 0.212649i
\(310\) −15.0811 26.1213i −0.856550 1.48359i
\(311\) 14.0325i 0.795710i 0.917448 + 0.397855i \(0.130245\pi\)
−0.917448 + 0.397855i \(0.869755\pi\)
\(312\) −5.96698 52.2315i −0.337814 2.95703i
\(313\) −21.6594 −1.22426 −0.612130 0.790757i \(-0.709687\pi\)
−0.612130 + 0.790757i \(0.709687\pi\)
\(314\) −8.14967 + 4.70522i −0.459913 + 0.265531i
\(315\) 9.37000 + 0.264852i 0.527940 + 0.0149227i
\(316\) 6.30737 + 3.64156i 0.354817 + 0.204854i
\(317\) 24.4539 1.37347 0.686735 0.726908i \(-0.259043\pi\)
0.686735 + 0.726908i \(0.259043\pi\)
\(318\) −0.0777781 + 5.50441i −0.00436158 + 0.308672i
\(319\) −0.436997 1.91354i −0.0244671 0.107138i
\(320\) 49.3465 2.75855
\(321\) −0.445285 + 31.5131i −0.0248534 + 1.75889i
\(322\) 12.7295 + 22.0481i 0.709388 + 1.22870i
\(323\) 3.14495 + 5.44721i 0.174990 + 0.303091i
\(324\) 20.8646 + 41.3734i 1.15915 + 2.29852i
\(325\) −7.57554 + 5.77662i −0.420216 + 0.320429i
\(326\) −40.9298 −2.26689
\(327\) 5.45658 + 3.25400i 0.301749 + 0.179947i
\(328\) −42.5909 73.7695i −2.35169 4.07324i
\(329\) 0.590886 1.02344i 0.0325766 0.0564243i
\(330\) 40.3939 + 13.0823i 2.22361 + 0.720155i
\(331\) −20.2155 11.6714i −1.11114 0.641519i −0.172018 0.985094i \(-0.555029\pi\)
−0.939125 + 0.343575i \(0.888362\pi\)
\(332\) 29.1307 + 16.8186i 1.59875 + 0.923040i
\(333\) −25.2385 15.5384i −1.38306 0.851500i
\(334\) −2.06683 + 3.57986i −0.113092 + 0.195881i
\(335\) −4.12222 + 2.37996i −0.225221 + 0.130031i
\(336\) 20.5304 + 12.2432i 1.12003 + 0.667923i
\(337\) 35.9796i 1.95993i −0.199165 0.979966i \(-0.563823\pi\)
0.199165 0.979966i \(-0.436177\pi\)
\(338\) 8.79285 + 33.6272i 0.478268 + 1.82908i
\(339\) 7.50416 + 13.4324i 0.407570 + 0.729546i
\(340\) 26.3765 + 45.6855i 1.43047 + 2.47764i
\(341\) 3.98779 12.9337i 0.215951 0.700397i
\(342\) 11.9758 6.47016i 0.647579 0.349866i
\(343\) −14.3798 −0.776438
\(344\) 35.5763 61.6200i 1.91815 3.32233i
\(345\) 40.3347 + 0.569935i 2.17155 + 0.0306843i
\(346\) 1.32530i 0.0712484i
\(347\) 15.4394 26.7417i 0.828828 1.43557i −0.0701302 0.997538i \(-0.522341\pi\)
0.898958 0.438034i \(-0.144325\pi\)
\(348\) −4.53267 2.70303i −0.242976 0.144898i
\(349\) −12.1184 20.9898i −0.648685 1.12356i −0.983437 0.181250i \(-0.941986\pi\)
0.334752 0.942306i \(-0.391347\pi\)
\(350\) 7.98475i 0.426803i
\(351\) −10.7187 15.3659i −0.572120 0.820170i
\(352\) 35.6702 + 38.4340i 1.90123 + 2.04854i
\(353\) −5.88781 10.1980i −0.313376 0.542784i 0.665715 0.746206i \(-0.268127\pi\)
−0.979091 + 0.203423i \(0.934793\pi\)
\(354\) −6.79061 + 11.3870i −0.360917 + 0.605214i
\(355\) −12.0255 + 20.8287i −0.638245 + 1.10547i
\(356\) −35.1664 −1.86382
\(357\) −0.102518 + 7.25527i −0.00542582 + 0.383990i
\(358\) 31.8511 55.1678i 1.68338 2.91571i
\(359\) 29.2458i 1.54354i 0.635904 + 0.771768i \(0.280628\pi\)
−0.635904 + 0.771768i \(0.719372\pi\)
\(360\) 61.4235 33.1851i 3.23730 1.74901i
\(361\) 8.06005 + 13.9604i 0.424213 + 0.734759i
\(362\) −13.6956 + 7.90715i −0.719824 + 0.415591i
\(363\) 8.02744 + 17.2789i 0.421331 + 0.906907i
\(364\) −19.3600 8.08783i −1.01474 0.423917i
\(365\) −19.7920 −1.03596
\(366\) −37.3075 22.2482i −1.95010 1.16293i
\(367\) 8.59155 + 14.8810i 0.448475 + 0.776782i 0.998287 0.0585069i \(-0.0186340\pi\)
−0.549812 + 0.835288i \(0.685301\pi\)
\(368\) 89.0857 + 51.4337i 4.64391 + 2.68116i
\(369\) −25.8502 15.9150i −1.34571 0.828502i
\(370\) −36.5106 + 63.2382i −1.89810 + 3.28760i
\(371\) 1.16358 + 0.671796i 0.0604103 + 0.0348779i
\(372\) −17.7482 31.7691i −0.920201 1.64715i
\(373\) −24.0932 13.9102i −1.24750 0.720243i −0.276888 0.960902i \(-0.589303\pi\)
−0.970610 + 0.240659i \(0.922637\pi\)
\(374\) −9.68389 + 31.4079i −0.500742 + 1.62407i
\(375\) 9.69619 + 5.78228i 0.500709 + 0.298596i
\(376\) 8.80173i 0.453915i
\(377\) 1.96889 + 0.822521i 0.101403 + 0.0423620i
\(378\) 15.6885 + 0.665396i 0.806930 + 0.0342243i
\(379\) −30.7429 + 17.7494i −1.57916 + 0.911726i −0.584178 + 0.811625i \(0.698583\pi\)
−0.994977 + 0.100101i \(0.968083\pi\)
\(380\) −12.0768 20.9176i −0.619527 1.07305i
\(381\) −17.2248 0.243388i −0.882452 0.0124692i
\(382\) −7.98556 −0.408577
\(383\) −0.861035 + 1.49136i −0.0439968 + 0.0762047i −0.887185 0.461413i \(-0.847342\pi\)
0.843188 + 0.537618i \(0.180676\pi\)
\(384\) 27.8933 + 0.394136i 1.42343 + 0.0201132i
\(385\) 7.59581 7.04960i 0.387118 0.359281i
\(386\) 34.5124 + 19.9257i 1.75663 + 1.01419i
\(387\) 0.716450 25.3468i 0.0364192 1.28845i
\(388\) 22.3273 12.8907i 1.13350 0.654424i
\(389\) 19.5377i 0.990600i 0.868722 + 0.495300i \(0.164942\pi\)
−0.868722 + 0.495300i \(0.835058\pi\)
\(390\) −37.0965 + 27.4673i −1.87845 + 1.39086i
\(391\) 31.2253i 1.57913i
\(392\) −41.7188 + 24.0864i −2.10712 + 1.21654i
\(393\) −0.714563 0.426126i −0.0360449 0.0214952i
\(394\) −17.0744 + 29.5737i −0.860196 + 1.48990i
\(395\) 3.91061i 0.196764i
\(396\) 48.5072 + 16.4707i 2.43758 + 0.827682i
\(397\) 26.8655 + 15.5108i 1.34834 + 0.778464i 0.988014 0.154364i \(-0.0493327\pi\)
0.360324 + 0.932827i \(0.382666\pi\)
\(398\) 8.84360i 0.443290i
\(399\) 0.0469390 3.32191i 0.00234989 0.166304i
\(400\) −16.1312 27.9401i −0.806561 1.39700i
\(401\) −5.00517 8.66921i −0.249946 0.432920i 0.713564 0.700590i \(-0.247080\pi\)
−0.963511 + 0.267670i \(0.913746\pi\)
\(402\) −6.96105 + 3.88888i −0.347186 + 0.193960i
\(403\) 8.92171 + 11.7000i 0.444422 + 0.582821i
\(404\) 64.6545 3.21668
\(405\) 13.6373 20.8097i 0.677644 1.03404i
\(406\) −1.54882 + 0.894211i −0.0768666 + 0.0443790i
\(407\) −31.9439 + 7.29506i −1.58340 + 0.361603i
\(408\) 26.3570 + 47.1788i 1.30487 + 2.33570i
\(409\) −17.7089 + 30.6727i −0.875648 + 1.51667i −0.0195767 + 0.999808i \(0.506232\pi\)
−0.856071 + 0.516858i \(0.827101\pi\)
\(410\) −37.3955 + 64.7709i −1.84683 + 3.19881i
\(411\) 4.06222 2.26941i 0.200374 0.111942i
\(412\) −10.8469 + 18.7874i −0.534390 + 0.925590i
\(413\) 1.61795 + 2.80236i 0.0796139 + 0.137895i
\(414\) 67.5473 + 1.90928i 3.31977 + 0.0938362i
\(415\) 18.0612i 0.886590i
\(416\) −56.5385 + 7.26964i −2.77203 + 0.356424i
\(417\) −8.27587 14.8137i −0.405271 0.725431i
\(418\) 4.43388 14.3805i 0.216868 0.703373i
\(419\) −2.45192 + 1.41562i −0.119784 + 0.0691573i −0.558695 0.829373i \(-0.688698\pi\)
0.438911 + 0.898531i \(0.355364\pi\)
\(420\) 0.393676 27.8607i 0.0192094 1.35946i
\(421\) 24.8977i 1.21344i −0.794915 0.606721i \(-0.792485\pi\)
0.794915 0.606721i \(-0.207515\pi\)
\(422\) −27.7728 + 48.1038i −1.35196 + 2.34166i
\(423\) −1.49097 2.75969i −0.0724936 0.134181i
\(424\) 10.0069 0.485980
\(425\) 4.89662 8.48119i 0.237521 0.411398i
\(426\) −20.6356 + 34.6035i −0.999800 + 1.67655i
\(427\) −9.18143 + 5.30090i −0.444320 + 0.256528i
\(428\) 93.6823 4.52830
\(429\) −20.3576 3.81668i −0.982875 0.184271i
\(430\) −62.4732 −3.01272
\(431\) 2.36616 1.36610i 0.113974 0.0658027i −0.441929 0.897050i \(-0.645706\pi\)
0.555903 + 0.831247i \(0.312373\pi\)
\(432\) 56.2412 29.3664i 2.70591 1.41289i
\(433\) 5.34129 9.25139i 0.256686 0.444594i −0.708666 0.705544i \(-0.750703\pi\)
0.965352 + 0.260951i \(0.0840360\pi\)
\(434\) −12.3320 −0.591957
\(435\) −0.0400363 + 2.83340i −0.00191959 + 0.135851i
\(436\) 9.44241 16.3547i 0.452210 0.783250i
\(437\) 14.2969i 0.683911i
\(438\) −33.1517 0.468437i −1.58405 0.0223828i
\(439\) 10.6889 6.17124i 0.510154 0.294537i −0.222743 0.974877i \(-0.571501\pi\)
0.732897 + 0.680340i \(0.238168\pi\)
\(440\) 22.7412 73.7569i 1.08414 3.51622i
\(441\) −9.00039 + 14.6190i −0.428590 + 0.696143i
\(442\) −21.6653 28.4122i −1.03052 1.35143i
\(443\) 5.22827i 0.248403i 0.992257 + 0.124201i \(0.0396369\pi\)
−0.992257 + 0.124201i \(0.960363\pi\)
\(444\) −45.1234 + 75.6666i −2.14146 + 3.59098i
\(445\) 9.44115 + 16.3526i 0.447553 + 0.775185i
\(446\) −16.8599 + 29.2022i −0.798340 + 1.38277i
\(447\) −14.5493 26.0431i −0.688159 1.23180i
\(448\) 10.0878 17.4726i 0.476605 0.825504i
\(449\) 12.0394 20.8529i 0.568175 0.984108i −0.428571 0.903508i \(-0.640983\pi\)
0.996747 0.0806003i \(-0.0256837\pi\)
\(450\) −18.0473 11.1111i −0.850758 0.523781i
\(451\) −32.7180 + 7.47186i −1.54063 + 0.351836i
\(452\) 39.6086 22.8680i 1.86303 1.07562i
\(453\) 8.03366 + 4.79084i 0.377454 + 0.225093i
\(454\) −42.4974 −1.99450
\(455\) 1.43672 + 11.1739i 0.0673544 + 0.523838i
\(456\) −12.0679 21.6014i −0.565130 1.01158i
\(457\) −0.324040 0.561253i −0.0151579 0.0262543i 0.858347 0.513070i \(-0.171492\pi\)
−0.873505 + 0.486815i \(0.838158\pi\)
\(458\) −15.8756 27.4973i −0.741817 1.28487i
\(459\) 16.2559 + 10.3277i 0.758758 + 0.482055i
\(460\) 119.907i 5.59070i
\(461\) 5.33706 + 3.08135i 0.248572 + 0.143513i 0.619110 0.785304i \(-0.287493\pi\)
−0.370538 + 0.928817i \(0.620827\pi\)
\(462\) 12.8898 11.6283i 0.599690 0.540998i
\(463\) 30.4408i 1.41471i 0.706861 + 0.707353i \(0.250111\pi\)
−0.706861 + 0.707353i \(0.749889\pi\)
\(464\) −3.61307 + 6.25802i −0.167732 + 0.290521i
\(465\) −10.0079 + 16.7821i −0.464106 + 0.778250i
\(466\) 33.5316 19.3595i 1.55332 0.896810i
\(467\) 5.89082i 0.272595i 0.990668 + 0.136297i \(0.0435202\pi\)
−0.990668 + 0.136297i \(0.956480\pi\)
\(468\) −45.2204 + 32.5034i −2.09031 + 1.50247i
\(469\) 1.94613i 0.0898639i
\(470\) −6.69270 + 3.86403i −0.308711 + 0.178235i
\(471\) 5.23590 + 3.12241i 0.241258 + 0.143873i
\(472\) 20.8717 + 12.0503i 0.960700 + 0.554660i
\(473\) −19.0699 20.5474i −0.876833 0.944771i
\(474\) 0.0925564 6.55028i 0.00425125 0.300864i
\(475\) −2.24197 + 3.88321i −0.102869 + 0.178174i
\(476\) 21.5685 0.988589
\(477\) 3.13758 1.69513i 0.143660 0.0776147i
\(478\) 0.497999 + 0.862560i 0.0227779 + 0.0394526i
\(479\) −0.349105 + 0.201556i −0.0159510 + 0.00920932i −0.507954 0.861384i \(-0.669598\pi\)
0.492003 + 0.870593i \(0.336265\pi\)
\(480\) −36.9207 66.0876i −1.68519 3.01647i
\(481\) 13.7309 32.8679i 0.626073 1.49865i
\(482\) 45.1436i 2.05624i
\(483\) 8.44737 14.1652i 0.384369 0.644540i
\(484\) 51.0193 24.5849i 2.31906 1.11749i
\(485\) −11.9884 6.92153i −0.544367 0.314291i
\(486\) 23.3351 34.5336i 1.05850 1.56647i
\(487\) −16.6034 9.58597i −0.752371 0.434382i 0.0741789 0.997245i \(-0.476366\pi\)
−0.826550 + 0.562863i \(0.809700\pi\)
\(488\) −39.4806 + 68.3824i −1.78720 + 3.09553i
\(489\) 12.9318 + 23.1477i 0.584794 + 1.04678i
\(490\) 36.6298 + 21.1482i 1.65477 + 0.955379i
\(491\) 3.27077 + 5.66514i 0.147608 + 0.255664i 0.930343 0.366691i \(-0.119509\pi\)
−0.782735 + 0.622355i \(0.786176\pi\)
\(492\) −46.2170 + 77.5004i −2.08362 + 3.49399i
\(493\) −2.19349 −0.0987896
\(494\) 9.91973 + 13.0089i 0.446310 + 0.585297i
\(495\) −5.36381 26.9780i −0.241085 1.21257i
\(496\) −43.1521 + 24.9139i −1.93759 + 1.11867i
\(497\) 4.91669 + 8.51596i 0.220544 + 0.381993i
\(498\) 0.427473 30.2526i 0.0191555 1.35565i
\(499\) 27.9317i 1.25039i 0.780467 + 0.625196i \(0.214981\pi\)
−0.780467 + 0.625196i \(0.785019\pi\)
\(500\) 16.7789 29.0619i 0.750376 1.29969i
\(501\) 2.67759 + 0.0378348i 0.119626 + 0.00169033i
\(502\) −49.6850 −2.21755
\(503\) −7.46410 + 12.9282i −0.332808 + 0.576440i −0.983061 0.183277i \(-0.941329\pi\)
0.650254 + 0.759717i \(0.274663\pi\)
\(504\) 0.806507 28.5329i 0.0359247 1.27095i
\(505\) −17.3579 30.0647i −0.772414 1.33786i
\(506\) 54.7573 50.8197i 2.43426 2.25921i
\(507\) 16.2396 15.5973i 0.721227 0.692698i
\(508\) 51.2058i 2.27189i
\(509\) 17.9447 + 31.0812i 0.795387 + 1.37765i 0.922593 + 0.385774i \(0.126065\pi\)
−0.127207 + 0.991876i \(0.540601\pi\)
\(510\) 24.3031 40.7534i 1.07616 1.80459i
\(511\) −4.04605 + 7.00796i −0.178987 + 0.310014i
\(512\) 12.5305i 0.553776i
\(513\) −7.44293 4.72865i −0.328614 0.208775i
\(514\) −15.7947 + 27.3573i −0.696675 + 1.20668i
\(515\) 11.6483 0.513287
\(516\) −75.3660 1.06493i −3.31780 0.0468810i
\(517\) −3.31382 1.02174i −0.145742 0.0449359i
\(518\) 14.9276 + 25.8554i 0.655882 + 1.13602i
\(519\) 0.749517 0.418727i 0.0329001 0.0183801i
\(520\) 50.8779 + 66.7219i 2.23114 + 2.92595i
\(521\) 32.3244i 1.41616i −0.706133 0.708079i \(-0.749562\pi\)
0.706133 0.708079i \(-0.250438\pi\)
\(522\) −0.134122 + 4.74500i −0.00587035 + 0.207683i
\(523\) 1.46718 0.847075i 0.0641551 0.0370400i −0.467579 0.883951i \(-0.654874\pi\)
0.531734 + 0.846911i \(0.321540\pi\)
\(524\) −1.23653 + 2.14172i −0.0540179 + 0.0935617i
\(525\) −4.51575 + 2.52278i −0.197083 + 0.110103i
\(526\) 25.8526 + 14.9260i 1.12723 + 0.650805i
\(527\) −13.0988 7.56258i −0.570591 0.329431i
\(528\) 21.6118 66.7303i 0.940532 2.90407i
\(529\) 23.9873 41.5472i 1.04293 1.80640i
\(530\) −4.39313 7.60912i −0.190825 0.330519i
\(531\) 8.58539 + 0.242674i 0.372574 + 0.0105311i
\(532\) −9.87538 −0.428152
\(533\) 14.0636 33.6645i 0.609164 1.45817i
\(534\) 15.4269 + 27.6140i 0.667588 + 1.19498i
\(535\) −25.1510 43.5627i −1.08737 1.88338i
\(536\) 7.24729 + 12.5527i 0.313035 + 0.542193i
\(537\) −41.2633 0.583056i −1.78064 0.0251607i
\(538\) 34.5036 1.48756
\(539\) 4.22555 + 18.5030i 0.182007 + 0.796980i
\(540\) −62.4236 39.6590i −2.68628 1.70665i
\(541\) −0.557105 −0.0239518 −0.0119759 0.999928i \(-0.503812\pi\)
−0.0119759 + 0.999928i \(0.503812\pi\)
\(542\) −62.6457 36.1685i −2.69086 1.55357i
\(543\) 8.79898 + 5.24723i 0.377600 + 0.225180i
\(544\) 50.7479 29.2993i 2.17580 1.25620i
\(545\) −10.1400 −0.434352
\(546\) 2.14205 + 18.7502i 0.0916711 + 0.802436i
\(547\) 39.2321i 1.67744i 0.544562 + 0.838721i \(0.316696\pi\)
−0.544562 + 0.838721i \(0.683304\pi\)
\(548\) −6.91575 11.9784i −0.295426 0.511693i
\(549\) −0.795076 + 28.1284i −0.0339330 + 1.20049i
\(550\) −22.8421 + 5.21648i −0.973991 + 0.222432i
\(551\) 1.00431 0.0427852
\(552\) 1.73553 122.824i 0.0738689 5.22775i
\(553\) −1.38467 0.799440i −0.0588822 0.0339957i
\(554\) 1.28473 0.0545829
\(555\) 47.2997 + 0.668351i 2.00776 + 0.0283699i
\(556\) −43.6819 + 25.2197i −1.85252 + 1.06956i
\(557\) 18.4169 10.6330i 0.780350 0.450535i −0.0562042 0.998419i \(-0.517900\pi\)
0.836554 + 0.547884i \(0.184566\pi\)
\(558\) −17.1605 + 27.8732i −0.726461 + 1.17996i
\(559\) 30.2264 3.88647i 1.27844 0.164380i
\(560\) −38.1520 −1.61222
\(561\) 20.8223 4.44663i 0.879117 0.187737i
\(562\) 17.7284 + 30.7064i 0.747826 + 1.29527i
\(563\) 3.66666 6.35084i 0.154531 0.267656i −0.778357 0.627822i \(-0.783947\pi\)
0.932888 + 0.360166i \(0.117280\pi\)
\(564\) −8.13976 + 4.54738i −0.342746 + 0.191479i
\(565\) −21.2675 12.2788i −0.894731 0.516573i
\(566\) 0.401213 0.694921i 0.0168642 0.0292097i
\(567\) −4.58046 9.08281i −0.192361 0.381442i
\(568\) 63.4261 + 36.6191i 2.66130 + 1.53650i
\(569\) −13.5513 23.4716i −0.568102 0.983982i −0.996754 0.0805117i \(-0.974345\pi\)
0.428652 0.903470i \(-0.358989\pi\)
\(570\) −11.1275 + 18.6594i −0.466078 + 0.781556i
\(571\) 13.8007i 0.577543i 0.957398 + 0.288771i \(0.0932467\pi\)
−0.957398 + 0.288771i \(0.906753\pi\)
\(572\) −10.4890 + 60.6674i −0.438566 + 2.53663i
\(573\) 2.52303 + 4.51620i 0.105401 + 0.188667i
\(574\) 15.2894 + 26.4820i 0.638167 + 1.10534i
\(575\) −19.2776 + 11.1299i −0.803932 + 0.464151i
\(576\) −25.4544 47.1145i −1.06060 1.96310i
\(577\) 25.4836i 1.06090i 0.847717 + 0.530449i \(0.177977\pi\)
−0.847717 + 0.530449i \(0.822023\pi\)
\(578\) −7.55411 4.36136i −0.314209 0.181409i
\(579\) 0.364754 25.8139i 0.0151586 1.07279i
\(580\) 8.42313 0.349751
\(581\) −6.39512 3.69223i −0.265314 0.153179i
\(582\) −19.9169 11.8773i −0.825580 0.492331i
\(583\) 1.16164 3.76758i 0.0481103 0.156037i
\(584\) 60.2692i 2.49396i
\(585\) 27.2546 + 12.3015i 1.12684 + 0.508605i
\(586\) −35.8579 −1.48128
\(587\) 9.66167 + 16.7345i 0.398780 + 0.690707i 0.993576 0.113170i \(-0.0361004\pi\)
−0.594796 + 0.803877i \(0.702767\pi\)
\(588\) 43.8287 + 26.1371i 1.80747 + 1.07787i
\(589\) 5.99742 + 3.46261i 0.247120 + 0.142675i
\(590\) 21.1607i 0.871174i
\(591\) 22.1200 + 0.312558i 0.909893 + 0.0128569i
\(592\) 104.469 + 60.3152i 4.29365 + 2.47894i
\(593\) 22.6629i 0.930652i 0.885139 + 0.465326i \(0.154063\pi\)
−0.885139 + 0.465326i \(0.845937\pi\)
\(594\) −8.34588 45.3151i −0.342436 1.85930i
\(595\) −5.79051 10.0294i −0.237388 0.411167i
\(596\) −76.7946 + 44.3374i −3.14563 + 1.81613i
\(597\) −5.00147 + 2.79413i −0.204696 + 0.114356i
\(598\) 10.3571 + 80.5510i 0.423535 + 3.29398i
\(599\) 9.06218i 0.370271i −0.982713 0.185135i \(-0.940728\pi\)
0.982713 0.185135i \(-0.0592724\pi\)
\(600\) −19.7322 + 33.0885i −0.805564 + 1.35083i
\(601\) 14.5938 8.42572i 0.595292 0.343692i −0.171895 0.985115i \(-0.554989\pi\)
0.767187 + 0.641423i \(0.221656\pi\)
\(602\) −12.7713 + 22.1205i −0.520519 + 0.901566i
\(603\) 4.39868 + 2.70811i 0.179128 + 0.110283i
\(604\) 13.9020 24.0789i 0.565663 0.979757i
\(605\) −25.1293 17.1239i −1.02165 0.696187i
\(606\) −28.3629 50.7692i −1.15216 2.06236i
\(607\) −37.1851 21.4689i −1.50930 0.871394i −0.999941 0.0108386i \(-0.996550\pi\)
−0.509357 0.860555i \(-0.670117\pi\)
\(608\) −23.2355 + 13.4150i −0.942325 + 0.544052i
\(609\) 0.995067 + 0.593403i 0.0403221 + 0.0240459i
\(610\) 69.3292 2.80706
\(611\) 2.99774 2.28589i 0.121276 0.0924771i
\(612\) 30.0133 48.7495i 1.21322 1.97058i
\(613\) 10.0723 + 17.4458i 0.406817 + 0.704628i 0.994531 0.104441i \(-0.0333053\pi\)
−0.587714 + 0.809069i \(0.699972\pi\)
\(614\) −47.5486 + 27.4522i −1.91891 + 1.10788i
\(615\) 48.4460 + 0.684549i 1.95353 + 0.0276037i
\(616\) −21.4669 23.1302i −0.864927 0.931943i
\(617\) 10.3940 18.0030i 0.418448 0.724773i −0.577336 0.816507i \(-0.695908\pi\)
0.995784 + 0.0917338i \(0.0292409\pi\)
\(618\) 19.5110 + 0.275693i 0.784847 + 0.0110900i
\(619\) 2.37921i 0.0956287i −0.998856 0.0478143i \(-0.984774\pi\)
0.998856 0.0478143i \(-0.0152256\pi\)
\(620\) 50.3001 + 29.0408i 2.02010 + 1.16631i
\(621\) −20.2617 38.8043i −0.813075 1.55716i
\(622\) −18.7592 32.4918i −0.752174 1.30280i
\(623\) 7.72016 0.309302
\(624\) 45.3756 + 61.2830i 1.81648 + 2.45328i
\(625\) −31.2298 −1.24919
\(626\) 50.1516 28.9550i 2.00446 1.15728i
\(627\) −9.53372 + 2.03594i −0.380740 + 0.0813078i
\(628\) 9.06054 15.6933i 0.361555 0.626232i
\(629\) 36.6172i 1.46002i
\(630\) −22.0500 + 11.9129i −0.878493 + 0.474621i
\(631\) −29.0167 16.7528i −1.15514 0.666919i −0.205004 0.978761i \(-0.565721\pi\)
−0.950134 + 0.311842i \(0.899054\pi\)
\(632\) −11.9083 −0.473687
\(633\) 35.9797 + 0.508399i 1.43007 + 0.0202070i
\(634\) −56.6224 + 32.6909i −2.24876 + 1.29832i
\(635\) 23.8110 13.7473i 0.944910 0.545544i
\(636\) −5.17005 9.25433i −0.205006 0.366958i
\(637\) −19.0382 7.95339i −0.754322 0.315125i
\(638\) 3.56994 + 3.84654i 0.141335 + 0.152286i
\(639\) 26.0897 + 0.737449i 1.03209 + 0.0291730i
\(640\) −38.5588 + 22.2620i −1.52417 + 0.879981i
\(641\) −9.30156 5.37026i −0.367390 0.212112i 0.304928 0.952375i \(-0.401368\pi\)
−0.672317 + 0.740263i \(0.734701\pi\)
\(642\) −41.0969 73.5630i −1.62196 2.90330i
\(643\) −19.7709 11.4147i −0.779688 0.450153i 0.0566314 0.998395i \(-0.481964\pi\)
−0.836320 + 0.548242i \(0.815297\pi\)
\(644\) −42.4568 24.5124i −1.67303 0.965925i
\(645\) 19.7384 + 35.3315i 0.777198 + 1.39118i
\(646\) −14.5641 8.40856i −0.573015 0.330831i
\(647\) 20.5076 11.8400i 0.806235 0.465480i −0.0394116 0.999223i \(-0.512548\pi\)
0.845647 + 0.533743i \(0.179215\pi\)
\(648\) −63.3683 41.5274i −2.48934 1.63135i
\(649\) 6.95976 6.45929i 0.273195 0.253549i
\(650\) 9.81853 23.5029i 0.385115 0.921858i
\(651\) 3.89630 + 6.97434i 0.152708 + 0.273346i
\(652\) 68.2567 39.4080i 2.67314 1.54334i
\(653\) 14.9752 8.64595i 0.586026 0.338342i −0.177499 0.984121i \(-0.556801\pi\)
0.763524 + 0.645779i \(0.223467\pi\)
\(654\) −16.9846 0.239995i −0.664151 0.00938454i
\(655\) 1.32788 0.0518847
\(656\) 107.001 + 61.7769i 4.17768 + 2.41198i
\(657\) 10.2093 + 18.8968i 0.398304 + 0.737234i
\(658\) 3.15967i 0.123177i
\(659\) −3.48802 + 6.04142i −0.135874 + 0.235340i −0.925931 0.377693i \(-0.876718\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(660\) −79.9588 + 17.0754i −3.11239 + 0.664658i
\(661\) 10.6436 6.14511i 0.413990 0.239017i −0.278513 0.960432i \(-0.589842\pi\)
0.692502 + 0.721416i \(0.256508\pi\)
\(662\) 62.4111 2.42568
\(663\) −9.22328 + 21.2296i −0.358202 + 0.824489i
\(664\) −54.9987 −2.13436
\(665\) 2.65125 + 4.59210i 0.102811 + 0.178074i
\(666\) 79.2112 + 2.23898i 3.06937 + 0.0867586i
\(667\) 4.31780 + 2.49288i 0.167186 + 0.0965248i
\(668\) 7.95995i 0.307980i
\(669\) 21.8421 + 0.308632i 0.844464 + 0.0119324i
\(670\) 6.36324 11.0215i 0.245834 0.425796i
\(671\) 21.1627 + 22.8024i 0.816975 + 0.880276i
\(672\) −30.9480 0.437299i −1.19384 0.0168692i
\(673\) −4.49827 + 2.59708i −0.173396 + 0.100110i −0.584186 0.811620i \(-0.698586\pi\)
0.410790 + 0.911730i \(0.365253\pi\)
\(674\) 48.0988 + 83.3096i 1.85270 + 3.20896i
\(675\) −0.581784 + 13.7171i −0.0223929 + 0.527972i
\(676\) −47.0403 47.6125i −1.80924 1.83125i
\(677\) −40.2631 −1.54744 −0.773718 0.633530i \(-0.781605\pi\)
−0.773718 + 0.633530i \(0.781605\pi\)
\(678\) −35.3325 21.0704i −1.35694 0.809203i
\(679\) −4.90156 + 2.82992i −0.188105 + 0.108602i
\(680\) −74.6984 43.1271i −2.86455 1.65385i
\(681\) 13.4270 + 24.0342i 0.514525 + 0.920994i
\(682\) 8.05660 + 35.2785i 0.308503 + 1.35088i
\(683\) −8.28121 + 14.3435i −0.316872 + 0.548838i −0.979834 0.199815i \(-0.935966\pi\)
0.662962 + 0.748653i \(0.269299\pi\)
\(684\) −13.7419 + 22.3205i −0.525436 + 0.853447i
\(685\) −3.71336 + 6.43172i −0.141880 + 0.245743i
\(686\) 33.2961 19.2235i 1.27125 0.733956i
\(687\) −10.5351 + 17.6661i −0.401940 + 0.674006i
\(688\) 103.205i 3.93466i
\(689\) 2.59889 + 3.40822i 0.0990099 + 0.129843i
\(690\) −94.1557 + 52.6013i −3.58445 + 2.00250i
\(691\) −1.43677 + 0.829518i −0.0546572 + 0.0315563i −0.527080 0.849816i \(-0.676713\pi\)
0.472422 + 0.881372i \(0.343380\pi\)
\(692\) −1.27602 2.21013i −0.0485071 0.0840167i
\(693\) −10.6489 3.61584i −0.404518 0.137355i
\(694\) 82.5596i 3.13392i
\(695\) 23.4546 + 13.5415i 0.889685 + 0.513660i
\(696\) 8.62806 + 0.121916i 0.327046 + 0.00462120i
\(697\) 37.5047i 1.42059i
\(698\) 56.1197 + 32.4007i 2.12416 + 1.22639i
\(699\) −21.5430 12.8470i −0.814829 0.485920i
\(700\) 7.68787 + 13.3158i 0.290574 + 0.503289i
\(701\) −1.95017 −0.0736571 −0.0368285 0.999322i \(-0.511726\pi\)
−0.0368285 + 0.999322i \(0.511726\pi\)
\(702\) 45.3604 + 21.2501i 1.71202 + 0.802034i
\(703\) 16.7656i 0.632327i
\(704\) −56.5747 17.4435i −2.13224 0.657425i
\(705\) 4.29984 + 2.56419i 0.161942 + 0.0965731i
\(706\) 27.2661 + 15.7421i 1.02617 + 0.592461i
\(707\) −14.1938 −0.533811
\(708\) 0.360711 25.5278i 0.0135563 0.959392i
\(709\) −16.9022 9.75846i −0.634774 0.366487i 0.147825 0.989014i \(-0.452773\pi\)
−0.782598 + 0.622527i \(0.786106\pi\)
\(710\) 64.3043i 2.41330i
\(711\) −3.73373 + 2.01721i −0.140026 + 0.0756514i
\(712\) 49.7956 28.7495i 1.86617 1.07743i
\(713\) 17.1896 + 29.7733i 0.643757 + 1.11502i
\(714\) −9.46173 16.9364i −0.354096 0.633829i
\(715\) 31.0266 11.4100i 1.16033 0.426709i
\(716\) 122.668i 4.58430i
\(717\) 0.330475 0.554167i 0.0123418 0.0206957i
\(718\) −39.0969 67.7179i −1.45908 2.52721i
\(719\) −11.1197 6.41995i −0.414694 0.239424i 0.278110 0.960549i \(-0.410292\pi\)
−0.692805 + 0.721125i \(0.743625\pi\)
\(720\) −53.0899 + 86.2320i −1.97854 + 3.21368i
\(721\) 2.38125 4.12445i 0.0886824 0.153602i
\(722\) −37.3256 21.5499i −1.38911 0.802006i
\(723\) −25.5308 + 14.2631i −0.949501 + 0.530451i
\(724\) 15.2263 26.3728i 0.565882 0.980136i
\(725\) −0.781847 1.35420i −0.0290371 0.0502936i
\(726\) −41.6863 29.2774i −1.54713 1.08659i
\(727\) 28.6628 1.06304 0.531522 0.847045i \(-0.321620\pi\)
0.531522 + 0.847045i \(0.321620\pi\)
\(728\) 34.0258 4.37500i 1.26108 0.162148i
\(729\) −26.9030 2.28619i −0.996409 0.0846737i
\(730\) 45.8278 26.4587i 1.69616 0.979280i
\(731\) −27.1307 + 15.6639i −1.00346 + 0.579350i
\(732\) 83.6370 + 1.18180i 3.09131 + 0.0436806i
\(733\) 24.3781 0.900424 0.450212 0.892922i \(-0.351348\pi\)
0.450212 + 0.892922i \(0.351348\pi\)
\(734\) −39.7869 22.9710i −1.46856 0.847875i
\(735\) 0.387132 27.3976i 0.0142796 1.01058i
\(736\) −133.194 −4.90960
\(737\) 5.56733 1.27142i 0.205075 0.0468333i
\(738\) 81.1310 + 2.29324i 2.98647 + 0.0844154i
\(739\) 8.78677 + 15.2191i 0.323226 + 0.559845i 0.981152 0.193239i \(-0.0618991\pi\)
−0.657925 + 0.753083i \(0.728566\pi\)
\(740\) 140.612i 5.16902i
\(741\) 4.22299 9.72022i 0.155135 0.357081i
\(742\) −3.59232 −0.131878
\(743\) −3.28116 + 1.89438i −0.120374 + 0.0694981i −0.558978 0.829182i \(-0.688806\pi\)
0.438604 + 0.898680i \(0.355473\pi\)
\(744\) 51.1036 + 30.4754i 1.87355 + 1.11728i
\(745\) 41.2342 + 23.8066i 1.51070 + 0.872205i
\(746\) 74.3827 2.72334
\(747\) −17.2443 + 9.31653i −0.630935 + 0.340874i
\(748\) −14.0908 61.7013i −0.515211 2.25602i
\(749\) −20.5663 −0.751476
\(750\) −30.1812 0.426464i −1.10206 0.0155723i
\(751\) −20.4312 35.3878i −0.745544 1.29132i −0.949940 0.312431i \(-0.898857\pi\)
0.204397 0.978888i \(-0.434477\pi\)
\(752\) 6.38334 + 11.0563i 0.232777 + 0.403181i
\(753\) 15.6980 + 28.0992i 0.572066 + 1.02399i
\(754\) −5.65848 + 0.727560i −0.206070 + 0.0264962i
\(755\) −14.9291 −0.543325
\(756\) −26.8036 + 13.9955i −0.974838 + 0.509013i
\(757\) 5.13256 + 8.88986i 0.186546 + 0.323108i 0.944096 0.329669i \(-0.106937\pi\)
−0.757550 + 0.652777i \(0.773604\pi\)
\(758\) 47.4561 82.1964i 1.72368 2.98551i
\(759\) −46.0414 14.9113i −1.67120 0.541247i
\(760\) 34.2015 + 19.7463i 1.24062 + 0.716272i
\(761\) −9.79680 5.65618i −0.355134 0.205037i 0.311810 0.950144i \(-0.399065\pi\)
−0.666944 + 0.745108i \(0.732398\pi\)
\(762\) 40.2088 22.4632i 1.45661 0.813754i
\(763\) −2.07292 + 3.59039i −0.0750446 + 0.129981i
\(764\) 13.3171 7.68865i 0.481797 0.278165i
\(765\) −30.7265 0.868512i −1.11092 0.0314011i
\(766\) 4.60425i 0.166358i
\(767\) 1.31641 + 10.2382i 0.0475329 + 0.369680i
\(768\) −11.1306 + 6.21825i −0.401641 + 0.224382i
\(769\) −12.6744 21.9527i −0.457050 0.791634i 0.541753 0.840537i \(-0.317761\pi\)
−0.998804 + 0.0489035i \(0.984427\pi\)
\(770\) −8.16370 + 26.4775i −0.294199 + 0.954182i
\(771\) 20.4621 + 0.289133i 0.736926 + 0.0104129i
\(772\) −76.7396 −2.76192
\(773\) −12.4782 + 21.6129i −0.448809 + 0.777361i −0.998309 0.0581334i \(-0.981485\pi\)
0.549499 + 0.835494i \(0.314818\pi\)
\(774\) 32.2256 + 59.6475i 1.15833 + 2.14398i
\(775\) 10.7824i 0.387316i
\(776\) −21.0770 + 36.5064i −0.756619 + 1.31050i
\(777\) 9.90605 16.6113i 0.355378 0.595926i
\(778\) −26.1187 45.2389i −0.936401 1.62189i
\(779\) 17.1719i 0.615249i
\(780\) 35.4180 81.5230i 1.26817 2.91899i
\(781\) 21.1497 19.6288i 0.756795 0.702374i
\(782\) −41.7431 72.3011i −1.49273 2.58548i
\(783\) 2.72589 1.42333i 0.0974155 0.0508656i
\(784\) 34.9366 60.5120i 1.24774 2.16114i
\(785\) −9.72997 −0.347277
\(786\) 2.22421 + 0.0314284i 0.0793349 + 0.00112101i
\(787\) −23.1672 + 40.1267i −0.825820 + 1.43036i 0.0754708 + 0.997148i \(0.475954\pi\)
−0.901291 + 0.433214i \(0.857379\pi\)
\(788\) 65.7582i 2.34254i
\(789\) 0.273230 19.3367i 0.00972725 0.688405i
\(790\) 5.22785 + 9.05490i 0.185998 + 0.322159i
\(791\) −8.69537 + 5.02027i −0.309172 + 0.178500i
\(792\) −82.1514 + 16.3335i −2.91912 + 0.580386i
\(793\) −33.5435 + 4.31298i −1.19117 + 0.153159i
\(794\) −82.9415 −2.94348
\(795\) −2.91531 + 4.88862i −0.103395 + 0.173381i
\(796\) 8.51479 + 14.7480i 0.301799 + 0.522731i
\(797\) −3.95180 2.28157i −0.139980 0.0808175i 0.428374 0.903601i \(-0.359086\pi\)
−0.568354 + 0.822784i \(0.692420\pi\)
\(798\) 4.33216 + 7.75453i 0.153357 + 0.274507i
\(799\) −1.93766 + 3.35612i −0.0685494 + 0.118731i
\(800\) 36.1772 + 20.8869i 1.27906 + 0.738464i
\(801\) 10.7429 17.4493i 0.379581 0.616540i
\(802\) 23.1786 + 13.3822i 0.818466 + 0.472541i
\(803\) 22.6911 + 6.99627i 0.800752 + 0.246893i
\(804\) 7.86432 13.1875i 0.277353 0.465088i
\(805\) 26.3235i 0.927781i
\(806\) −36.2990 15.1642i −1.27858 0.534137i
\(807\) −10.9014 19.5134i −0.383748 0.686904i
\(808\) −91.5509 + 52.8569i −3.22075 + 1.85950i
\(809\) 11.5826 + 20.0617i 0.407223 + 0.705331i 0.994577 0.103999i \(-0.0331638\pi\)
−0.587354 + 0.809330i \(0.699830\pi\)
\(810\) −3.75757 + 66.4151i −0.132028 + 2.33359i
\(811\) 37.6598 1.32242 0.661208 0.750203i \(-0.270044\pi\)
0.661208 + 0.750203i \(0.270044\pi\)
\(812\) 1.72193 2.98247i 0.0604278 0.104664i
\(813\) −0.662088 + 46.8564i −0.0232204 + 1.64333i
\(814\) 64.2127 59.5952i 2.25065 2.08881i
\(815\) −36.6498 21.1598i −1.28379 0.741195i
\(816\) −67.3241 40.1484i −2.35682 1.40548i
\(817\) 12.4221 7.17190i 0.434594 0.250913i
\(818\) 94.6955i 3.31095i
\(819\) 9.92735 7.13555i 0.346890 0.249336i
\(820\) 144.020i 5.02941i
\(821\) 7.75918 4.47977i 0.270797 0.156345i −0.358453 0.933548i \(-0.616696\pi\)
0.629250 + 0.777203i \(0.283362\pi\)
\(822\) −6.37211 + 10.6853i −0.222253 + 0.372691i
\(823\) 2.34668 4.06456i 0.0818000 0.141682i −0.822223 0.569165i \(-0.807266\pi\)
0.904023 + 0.427484i \(0.140600\pi\)
\(824\) 35.4707i 1.23568i
\(825\) 10.1671 + 11.2701i 0.353974 + 0.392376i
\(826\) −7.49260 4.32586i −0.260701 0.150516i
\(827\) 27.2442i 0.947375i −0.880693 0.473688i \(-0.842923\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(828\) −114.484 + 61.8518i −3.97858 + 2.14950i
\(829\) 9.71045 + 16.8190i 0.337258 + 0.584148i 0.983916 0.178632i \(-0.0571673\pi\)
−0.646658 + 0.762780i \(0.723834\pi\)
\(830\) 24.1449 + 41.8202i 0.838081 + 1.45160i
\(831\) −0.405910 0.726574i −0.0140808 0.0252046i
\(832\) 51.1786 39.0255i 1.77430 1.35297i
\(833\) 21.2100 0.734882
\(834\) 38.9660 + 23.2372i 1.34928 + 0.804639i
\(835\) −3.70142 + 2.13702i −0.128093 + 0.0739545i
\(836\) 6.45164 + 28.2507i 0.223135 + 0.977070i
\(837\) 21.1854 + 0.898536i 0.732275 + 0.0310580i
\(838\) 3.78489 6.55563i 0.130747 0.226460i
\(839\) 6.82812 11.8267i 0.235733 0.408301i −0.723752 0.690060i \(-0.757584\pi\)
0.959485 + 0.281758i \(0.0909176\pi\)
\(840\) 22.2195 + 39.7726i 0.766645 + 1.37229i
\(841\) 14.3249 24.8114i 0.493961 0.855566i
\(842\) 33.2842 + 57.6499i 1.14705 + 1.98675i
\(843\) 11.7646 19.7279i 0.405196 0.679465i
\(844\) 106.961i 3.68174i
\(845\) −9.51111 + 34.6565i −0.327192 + 1.19222i
\(846\) 7.14156 + 4.39680i 0.245532 + 0.151165i
\(847\) −11.2004 + 5.39718i −0.384850 + 0.185449i
\(848\) −12.5702 + 7.25741i −0.431662 + 0.249220i
\(849\) −0.519773 0.00734446i −0.0178386 0.000252061i
\(850\) 26.1839i 0.898100i
\(851\) 41.6152 72.0797i 1.42655 2.47086i
\(852\) 1.09615 77.5750i 0.0375533 2.65768i
\(853\) −1.58442 −0.0542496 −0.0271248 0.999632i \(-0.508635\pi\)
−0.0271248 + 0.999632i \(0.508635\pi\)
\(854\) 14.1729 24.5481i 0.484986 0.840020i
\(855\) 14.0685 + 0.397658i 0.481132 + 0.0135996i
\(856\) −132.654 + 76.5879i −4.53403 + 2.61772i
\(857\) −45.1473 −1.54220 −0.771101 0.636713i \(-0.780293\pi\)
−0.771101 + 0.636713i \(0.780293\pi\)
\(858\) 52.2397 18.3774i 1.78343 0.627395i
\(859\) −12.4759 −0.425673 −0.212836 0.977088i \(-0.568270\pi\)
−0.212836 + 0.977088i \(0.568270\pi\)
\(860\) 104.184 60.1504i 3.55263 2.05111i
\(861\) 10.1461 17.0139i 0.345779 0.579830i
\(862\) −3.65251 + 6.32633i −0.124405 + 0.215476i
\(863\) −44.5425 −1.51624 −0.758121 0.652113i \(-0.773883\pi\)
−0.758121 + 0.652113i \(0.773883\pi\)
\(864\) −44.0536 + 69.3407i −1.49873 + 2.35902i
\(865\) −0.685149 + 1.18671i −0.0232958 + 0.0403495i
\(866\) 28.5618i 0.970568i
\(867\) −0.0798376 + 5.65017i −0.00271143 + 0.191890i
\(868\) 20.5656 11.8735i 0.698041 0.403014i
\(869\) −1.38236 + 4.48343i −0.0468934 + 0.152090i
\(870\) −3.69509 6.61417i −0.125275 0.224241i
\(871\) −2.39308 + 5.72837i −0.0810864 + 0.194098i
\(872\) 30.8778i 1.04565i
\(873\) −0.424456 + 15.0165i −0.0143657 + 0.508233i
\(874\) 19.1126 + 33.1039i 0.646492 + 1.11976i
\(875\) −3.68352 + 6.38004i −0.124526 + 0.215685i
\(876\) 55.7364 31.1379i 1.88316 1.05205i
\(877\) 1.51193 2.61874i 0.0510542 0.0884285i −0.839369 0.543562i \(-0.817075\pi\)
0.890423 + 0.455134i \(0.150409\pi\)
\(878\) −16.4999 + 28.5786i −0.556844 + 0.964482i
\(879\) 11.3293 + 20.2793i 0.382127 + 0.684004i
\(880\) 24.9249 + 109.142i 0.840220 + 3.67918i
\(881\) −19.6662 + 11.3543i −0.662572 + 0.382536i −0.793256 0.608888i \(-0.791616\pi\)
0.130684 + 0.991424i \(0.458283\pi\)
\(882\) 1.29689 45.8819i 0.0436687 1.54492i
\(883\) −35.6943 −1.20121 −0.600605 0.799546i \(-0.705073\pi\)
−0.600605 + 0.799546i \(0.705073\pi\)
\(884\) 63.4861 + 26.5219i 2.13527 + 0.892028i
\(885\) −11.9674 + 6.68572i −0.402279 + 0.224738i
\(886\) −6.98934 12.1059i −0.234812 0.406706i
\(887\) 14.7296 + 25.5125i 0.494573 + 0.856626i 0.999980 0.00625508i \(-0.00199107\pi\)
−0.505407 + 0.862881i \(0.668658\pi\)
\(888\) 2.03521 144.034i 0.0682973 4.83345i
\(889\) 11.2413i 0.377022i
\(890\) −43.7214 25.2426i −1.46554 0.846132i
\(891\) −22.9909 + 19.0373i −0.770225 + 0.637773i
\(892\) 64.9322i 2.17409i
\(893\) 0.887179 1.53664i 0.0296883 0.0514217i
\(894\) 68.5039 + 40.8520i 2.29111 + 1.36630i
\(895\) 57.0410 32.9327i 1.90667 1.10082i
\(896\) 18.2039i 0.608150i
\(897\) 42.2830 31.3075i 1.41179 1.04533i
\(898\) 64.3789i 2.14835i
\(899\) −2.09149 + 1.20752i −0.0697551 + 0.0402731i
\(900\) 40.7946 + 1.15310i 1.35982 + 0.0384365i
\(901\) −3.81567 2.20298i −0.127118 0.0733918i
\(902\) 65.7690 61.0395i 2.18987 2.03239i
\(903\) 16.5453 + 0.233787i 0.550592 + 0.00777995i
\(904\) −37.3905 + 64.7623i −1.24359 + 2.15396i
\(905\) −16.3513 −0.543535
\(906\) −25.0063 0.353342i −0.830777 0.0117390i
\(907\) 2.60584 + 4.51345i 0.0865256 + 0.149867i 0.906040 0.423191i \(-0.139090\pi\)
−0.819515 + 0.573058i \(0.805757\pi\)
\(908\) 70.8708 40.9173i 2.35193 1.35789i
\(909\) −19.7511 + 32.0810i −0.655103 + 1.06406i
\(910\) −18.2643 23.9520i −0.605455 0.794003i
\(911\) 49.4367i 1.63791i 0.573858 + 0.818955i \(0.305446\pi\)
−0.573858 + 0.818955i \(0.694554\pi\)
\(912\) 30.8251 + 18.3824i 1.02072 + 0.608703i
\(913\) −6.38445 + 20.7068i −0.211294 + 0.685295i
\(914\) 1.50061 + 0.866376i 0.0496357 + 0.0286572i
\(915\) −21.9045 39.2089i −0.724142 1.29621i
\(916\) 52.9499 + 30.5706i 1.74951 + 1.01008i
\(917\) 0.271457 0.470178i 0.00896431 0.0155266i
\(918\) −51.4463 2.18199i −1.69798 0.0720165i
\(919\) 30.6269 + 17.6824i 1.01029 + 0.583289i 0.911276 0.411797i \(-0.135099\pi\)
0.0990113 + 0.995086i \(0.468432\pi\)
\(920\) 98.0274 + 169.788i 3.23187 + 5.59776i
\(921\) 30.5485 + 18.2174i 1.00661 + 0.600285i
\(922\) −16.4771 −0.542643
\(923\) 4.00038 + 31.1123i 0.131674 + 1.02407i
\(924\) −10.2998 + 31.8026i −0.338839 + 1.04623i
\(925\) −22.6065 + 13.0518i −0.743296 + 0.429142i
\(926\) −40.6944 70.4848i −1.33730 2.31627i
\(927\) −6.00857 11.1215i −0.197347 0.365277i
\(928\) 9.35650i 0.307142i
\(929\) −11.4659 + 19.8596i −0.376185 + 0.651572i −0.990504 0.137486i \(-0.956098\pi\)
0.614318 + 0.789058i \(0.289431\pi\)
\(930\) 0.738120 52.2373i 0.0242039 1.71293i
\(931\) −9.71123 −0.318273
\(932\) −37.2793 + 64.5697i −1.22112 + 2.11505i
\(933\) −12.4487 + 20.8749i −0.407551 + 0.683415i
\(934\) −7.87506 13.6400i −0.257680 0.446315i
\(935\) −24.9085 + 23.1173i −0.814594 + 0.756017i
\(936\) 37.4597 82.9938i 1.22441 2.71274i
\(937\) 19.1102i 0.624302i 0.950033 + 0.312151i \(0.101049\pi\)
−0.950033 + 0.312151i \(0.898951\pi\)
\(938\) −2.60166 4.50620i −0.0849471 0.147133i
\(939\) −32.2208 19.2147i −1.05149 0.627049i
\(940\) 7.44073 12.8877i 0.242690 0.420351i
\(941\) 0.00874113i 0.000284953i 1.00000 0.000142476i \(4.53516e-5\pi\)
−1.00000 0.000142476i \(0.999955\pi\)
\(942\) −16.2977 0.230289i −0.531008 0.00750322i
\(943\) 42.6238 73.8266i 1.38802 2.40412i
\(944\) −34.9573 −1.13776
\(945\) 13.7040 + 8.70643i 0.445791 + 0.283220i
\(946\) 71.6242 + 22.0836i 2.32870 + 0.718000i
\(947\) −8.81811 15.2734i −0.286550 0.496319i 0.686434 0.727192i \(-0.259175\pi\)
−0.972984 + 0.230873i \(0.925842\pi\)
\(948\) 6.15239 + 11.0127i 0.199820 + 0.357676i
\(949\) −20.5268 + 15.6524i −0.666329 + 0.508100i
\(950\) 11.9886i 0.388962i
\(951\) 36.3780 + 21.6939i 1.17964 + 0.703472i
\(952\) −30.5410 + 17.6328i −0.989838 + 0.571484i
\(953\) −13.8708 + 24.0249i −0.449319 + 0.778243i −0.998342 0.0575643i \(-0.981667\pi\)
0.549023 + 0.835807i \(0.315000\pi\)
\(954\) −4.99885 + 8.11945i −0.161844 + 0.262877i
\(955\) −7.15052 4.12835i −0.231385 0.133590i
\(956\) −1.66098 0.958966i −0.0537199 0.0310152i
\(957\) 1.04748 3.23428i 0.0338601 0.104549i
\(958\) 0.538894 0.933392i 0.0174109 0.0301565i
\(959\) 1.51823 + 2.62965i 0.0490263 + 0.0849160i
\(960\) 73.4085 + 43.7768i 2.36925 + 1.41289i
\(961\) 14.3471 0.462809
\(962\) 12.1456 + 94.4604i 0.391590 + 3.04553i
\(963\) −28.6187 + 46.4844i −0.922226 + 1.49794i
\(964\) 43.4651 + 75.2838i 1.39992 + 2.42473i
\(965\) 20.6023 + 35.6843i 0.663213 + 1.14872i
\(966\) −0.623024 + 44.0919i −0.0200455 + 1.41863i
\(967\) −14.4503 −0.464689 −0.232344 0.972634i \(-0.574640\pi\)
−0.232344 + 0.972634i \(0.574640\pi\)
\(968\) −52.1446 + 76.5220i −1.67599 + 2.45951i
\(969\) −0.153924 + 10.8933i −0.00494476 + 0.349944i
\(970\) 37.0118 1.18838
\(971\) 28.4712 + 16.4379i 0.913686 + 0.527517i 0.881615 0.471969i \(-0.156457\pi\)
0.0320706 + 0.999486i \(0.489790\pi\)
\(972\) −5.66516 + 80.0574i −0.181710 + 2.56784i
\(973\) 9.58959 5.53655i 0.307428 0.177494i
\(974\) 51.2595 1.64246
\(975\) −16.3941 + 1.87288i −0.525032 + 0.0599802i
\(976\) 114.531i 3.66605i
\(977\) 15.8490 + 27.4512i 0.507054 + 0.878243i 0.999967 + 0.00816400i \(0.00259871\pi\)
−0.492913 + 0.870079i \(0.664068\pi\)
\(978\) −60.8878 36.3101i −1.94698 1.16107i
\(979\) −5.04363 22.0852i −0.161195 0.705846i
\(980\) −81.4476 −2.60175
\(981\) 5.23055 + 9.68141i 0.166999 + 0.309104i
\(982\) −15.1467 8.74497i −0.483352 0.279063i
\(983\) −33.1591 −1.05761 −0.528806 0.848743i \(-0.677360\pi\)
−0.528806 + 0.848743i \(0.677360\pi\)
\(984\) 2.08454 147.524i 0.0664527 4.70291i
\(985\) −30.5779 + 17.6542i −0.974293 + 0.562508i
\(986\) 5.07895 2.93233i 0.161747 0.0933845i
\(987\) 1.78694 0.998297i 0.0568790 0.0317762i
\(988\) −29.0679 12.1434i −0.924772 0.386332i
\(989\) 71.2077 2.26427
\(990\) 48.4849 + 55.2961i 1.54095 + 1.75743i
\(991\) −8.51250 14.7441i −0.270408 0.468361i 0.698558 0.715553i \(-0.253825\pi\)
−0.968966 + 0.247192i \(0.920492\pi\)
\(992\) 32.2588 55.8739i 1.02422 1.77400i
\(993\) −19.7188 35.2964i −0.625756 1.12010i
\(994\) −22.7689 13.1456i −0.722186 0.416954i
\(995\) 4.57195 7.91884i 0.144940 0.251044i
\(996\) 28.4149 + 50.8623i 0.900360 + 1.61163i
\(997\) 26.5317 + 15.3181i 0.840269 + 0.485129i 0.857356 0.514725i \(-0.172106\pi\)
−0.0170869 + 0.999854i \(0.505439\pi\)
\(998\) −37.3401 64.6749i −1.18198 2.04725i
\(999\) −23.7605 45.5050i −0.751749 1.43972i
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.t.a.296.2 yes 104
3.2 odd 2 inner 429.2.t.a.296.51 yes 104
11.10 odd 2 inner 429.2.t.a.296.52 yes 104
13.4 even 6 inner 429.2.t.a.329.1 yes 104
33.32 even 2 inner 429.2.t.a.296.1 104
39.17 odd 6 inner 429.2.t.a.329.52 yes 104
143.43 odd 6 inner 429.2.t.a.329.51 yes 104
429.329 even 6 inner 429.2.t.a.329.2 yes 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.t.a.296.1 104 33.32 even 2 inner
429.2.t.a.296.2 yes 104 1.1 even 1 trivial
429.2.t.a.296.51 yes 104 3.2 odd 2 inner
429.2.t.a.296.52 yes 104 11.10 odd 2 inner
429.2.t.a.329.1 yes 104 13.4 even 6 inner
429.2.t.a.329.2 yes 104 429.329 even 6 inner
429.2.t.a.329.51 yes 104 143.43 odd 6 inner
429.2.t.a.329.52 yes 104 39.17 odd 6 inner