Properties

Label 315.2.bl.i.41.9
Level $315$
Weight $2$
Character 315.41
Analytic conductor $2.515$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(41,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bl (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.9
Character \(\chi\) \(=\) 315.41
Dual form 315.2.bl.i.146.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58089 - 0.912729i) q^{2} +(0.791176 - 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.155560 - 3.15796i) q^{6} +(2.11583 + 1.58847i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} +O(q^{10})\) \(q+(1.58089 - 0.912729i) q^{2} +(0.791176 - 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.155560 - 3.15796i) q^{6} +(2.11583 + 1.58847i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} -1.82546i q^{10} +(-0.549675 + 0.317355i) q^{11} +(-1.25073 - 1.93925i) q^{12} +(-2.73324 - 1.57804i) q^{13} +(4.79475 + 0.580024i) q^{14} +(-0.938777 - 1.45557i) q^{15} +(2.44479 + 4.23450i) q^{16} -2.83015 q^{17} +(-4.98883 - 2.25881i) q^{18} +4.89715i q^{19} +(-0.666147 - 1.15380i) q^{20} +(4.12150 - 2.00330i) q^{21} +(-0.579318 + 1.00341i) q^{22} +(-3.83011 - 2.21132i) q^{23} +(1.87802 + 0.964339i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.76127 q^{26} +(-5.13961 + 0.764479i) q^{27} +(3.24224 - 1.38309i) q^{28} +(0.0996181 - 0.0575146i) q^{29} +(-2.81265 - 1.44426i) q^{30} +(0.272686 + 0.157435i) q^{31} +(5.61876 + 3.24399i) q^{32} +(0.0540882 + 1.09802i) q^{33} +(-4.47417 + 2.58316i) q^{34} +(2.43358 - 1.03813i) q^{35} +(-3.97753 + 0.392818i) q^{36} +10.7800 q^{37} +(4.46977 + 7.74186i) q^{38} +(-4.59390 + 2.96285i) q^{39} +(1.05557 + 0.609434i) q^{40} +(-1.11318 + 1.92808i) q^{41} +(4.68719 - 6.92881i) q^{42} +(-0.870817 - 1.50830i) q^{43} +0.845620i q^{44} +(-2.98548 + 0.294843i) q^{45} -8.07333 q^{46} +(3.95084 + 6.84306i) q^{47} +(8.45874 - 0.416676i) q^{48} +(1.95350 + 6.72189i) q^{49} +(-1.58089 - 0.912729i) q^{50} +(-2.23915 + 4.36068i) q^{51} +(-3.64148 + 2.10241i) q^{52} -8.63571i q^{53} +(-7.42741 + 5.89963i) q^{54} +0.634710i q^{55} +(-1.93614 + 2.57892i) q^{56} +(7.54548 + 3.87451i) q^{57} +(0.104990 - 0.181849i) q^{58} +(7.65048 - 13.2510i) q^{59} +(-2.30481 + 0.113534i) q^{60} +(-8.94576 + 5.16484i) q^{61} +0.574783 q^{62} +(0.174174 - 7.93534i) q^{63} +2.06438 q^{64} +(-2.73324 + 1.57804i) q^{65} +(1.08770 + 1.68648i) q^{66} +(-2.40584 + 4.16704i) q^{67} +(-1.88530 + 3.26543i) q^{68} +(-6.43747 + 4.15186i) q^{69} +(2.89969 - 3.86236i) q^{70} -12.9744i q^{71} +(2.97169 - 2.13068i) q^{72} -6.45973i q^{73} +(17.0421 - 9.83926i) q^{74} +(-1.72995 + 0.0852172i) q^{75} +(5.65033 + 3.26222i) q^{76} +(-1.66713 - 0.201674i) q^{77} +(-4.55818 + 8.87692i) q^{78} +(6.51973 + 11.2925i) q^{79} +4.88958 q^{80} +(-2.88843 + 8.52391i) q^{81} +4.06412i q^{82} +(2.25090 + 3.89867i) q^{83} +(0.434124 - 6.08989i) q^{84} +(-1.41508 + 2.45099i) q^{85} +(-2.75334 - 1.58964i) q^{86} +(-0.00980246 - 0.198995i) q^{87} +(-0.386814 - 0.669981i) q^{88} -11.1029 q^{89} +(-4.45060 + 3.19105i) q^{90} +(-3.27641 - 7.68054i) q^{91} +(-5.10284 + 2.94612i) q^{92} +(0.458318 - 0.295593i) q^{93} +(12.4917 + 7.21210i) q^{94} +(4.24105 + 2.44857i) q^{95} +(9.44375 - 6.09077i) q^{96} +(0.266943 - 0.154120i) q^{97} +(9.22354 + 8.84357i) q^{98} +(1.73461 + 0.785387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.58089 0.912729i 1.11786 0.645397i 0.177006 0.984210i \(-0.443359\pi\)
0.940854 + 0.338813i \(0.110025\pi\)
\(3\) 0.791176 1.54079i 0.456786 0.889577i
\(4\) 0.666147 1.15380i 0.333074 0.576901i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −0.155560 3.15796i −0.0635072 1.28923i
\(7\) 2.11583 + 1.58847i 0.799710 + 0.600387i
\(8\) 1.21887i 0.430935i
\(9\) −1.74808 2.43808i −0.582693 0.812692i
\(10\) 1.82546i 0.577260i
\(11\) −0.549675 + 0.317355i −0.165733 + 0.0956861i −0.580572 0.814209i \(-0.697171\pi\)
0.414839 + 0.909895i \(0.363838\pi\)
\(12\) −1.25073 1.93925i −0.361054 0.559815i
\(13\) −2.73324 1.57804i −0.758064 0.437668i 0.0705364 0.997509i \(-0.477529\pi\)
−0.828600 + 0.559841i \(0.810862\pi\)
\(14\) 4.79475 + 0.580024i 1.28145 + 0.155018i
\(15\) −0.938777 1.45557i −0.242391 0.375828i
\(16\) 2.44479 + 4.23450i 0.611198 + 1.05863i
\(17\) −2.83015 −0.686413 −0.343207 0.939260i \(-0.611513\pi\)
−0.343207 + 0.939260i \(0.611513\pi\)
\(18\) −4.98883 2.25881i −1.17588 0.532408i
\(19\) 4.89715i 1.12348i 0.827313 + 0.561741i \(0.189868\pi\)
−0.827313 + 0.561741i \(0.810132\pi\)
\(20\) −0.666147 1.15380i −0.148955 0.257998i
\(21\) 4.12150 2.00330i 0.899386 0.437155i
\(22\) −0.579318 + 1.00341i −0.123511 + 0.213927i
\(23\) −3.83011 2.21132i −0.798633 0.461091i 0.0443596 0.999016i \(-0.485875\pi\)
−0.842993 + 0.537924i \(0.819209\pi\)
\(24\) 1.87802 + 0.964339i 0.383350 + 0.196845i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −5.76127 −1.12988
\(27\) −5.13961 + 0.764479i −0.989118 + 0.147124i
\(28\) 3.24224 1.38309i 0.612726 0.261380i
\(29\) 0.0996181 0.0575146i 0.0184986 0.0106802i −0.490722 0.871316i \(-0.663267\pi\)
0.509221 + 0.860636i \(0.329934\pi\)
\(30\) −2.81265 1.44426i −0.513517 0.263684i
\(31\) 0.272686 + 0.157435i 0.0489759 + 0.0282762i 0.524288 0.851541i \(-0.324332\pi\)
−0.475312 + 0.879817i \(0.657665\pi\)
\(32\) 5.61876 + 3.24399i 0.993266 + 0.573462i
\(33\) 0.0540882 + 1.09802i 0.00941554 + 0.191140i
\(34\) −4.47417 + 2.58316i −0.767314 + 0.443009i
\(35\) 2.43358 1.03813i 0.411349 0.175476i
\(36\) −3.97753 + 0.392818i −0.662922 + 0.0654697i
\(37\) 10.7800 1.77223 0.886115 0.463466i \(-0.153395\pi\)
0.886115 + 0.463466i \(0.153395\pi\)
\(38\) 4.46977 + 7.74186i 0.725092 + 1.25590i
\(39\) −4.59390 + 2.96285i −0.735612 + 0.474435i
\(40\) 1.05557 + 0.609434i 0.166900 + 0.0963599i
\(41\) −1.11318 + 1.92808i −0.173849 + 0.301115i −0.939762 0.341828i \(-0.888954\pi\)
0.765913 + 0.642944i \(0.222287\pi\)
\(42\) 4.68719 6.92881i 0.723249 1.06914i
\(43\) −0.870817 1.50830i −0.132798 0.230013i 0.791956 0.610578i \(-0.209063\pi\)
−0.924754 + 0.380565i \(0.875730\pi\)
\(44\) 0.845620i 0.127482i
\(45\) −2.98548 + 0.294843i −0.445048 + 0.0439527i
\(46\) −8.07333 −1.19035
\(47\) 3.95084 + 6.84306i 0.576290 + 0.998163i 0.995900 + 0.0904591i \(0.0288334\pi\)
−0.419610 + 0.907704i \(0.637833\pi\)
\(48\) 8.45874 0.416676i 1.22091 0.0601420i
\(49\) 1.95350 + 6.72189i 0.279072 + 0.960270i
\(50\) −1.58089 0.912729i −0.223572 0.129079i
\(51\) −2.23915 + 4.36068i −0.313544 + 0.610617i
\(52\) −3.64148 + 2.10241i −0.504982 + 0.291552i
\(53\) 8.63571i 1.18621i −0.805127 0.593103i \(-0.797903\pi\)
0.805127 0.593103i \(-0.202097\pi\)
\(54\) −7.42741 + 5.89963i −1.01074 + 0.802838i
\(55\) 0.634710i 0.0855842i
\(56\) −1.93614 + 2.57892i −0.258727 + 0.344623i
\(57\) 7.54548 + 3.87451i 0.999424 + 0.513191i
\(58\) 0.104990 0.181849i 0.0137859 0.0238779i
\(59\) 7.65048 13.2510i 0.996008 1.72514i 0.420699 0.907200i \(-0.361785\pi\)
0.575309 0.817936i \(-0.304882\pi\)
\(60\) −2.30481 + 0.113534i −0.297549 + 0.0146572i
\(61\) −8.94576 + 5.16484i −1.14539 + 0.661290i −0.947759 0.318987i \(-0.896657\pi\)
−0.197628 + 0.980277i \(0.563324\pi\)
\(62\) 0.574783 0.0729975
\(63\) 0.174174 7.93534i 0.0219438 0.999759i
\(64\) 2.06438 0.258048
\(65\) −2.73324 + 1.57804i −0.339016 + 0.195731i
\(66\) 1.08770 + 1.68648i 0.133887 + 0.207591i
\(67\) −2.40584 + 4.16704i −0.293920 + 0.509084i −0.974733 0.223373i \(-0.928293\pi\)
0.680813 + 0.732457i \(0.261627\pi\)
\(68\) −1.88530 + 3.26543i −0.228626 + 0.395992i
\(69\) −6.43747 + 4.15186i −0.774981 + 0.499826i
\(70\) 2.89969 3.86236i 0.346579 0.461641i
\(71\) 12.9744i 1.53978i −0.638175 0.769892i \(-0.720310\pi\)
0.638175 0.769892i \(-0.279690\pi\)
\(72\) 2.97169 2.13068i 0.350217 0.251103i
\(73\) 6.45973i 0.756054i −0.925794 0.378027i \(-0.876603\pi\)
0.925794 0.378027i \(-0.123397\pi\)
\(74\) 17.0421 9.83926i 1.98110 1.14379i
\(75\) −1.72995 + 0.0852172i −0.199758 + 0.00984003i
\(76\) 5.65033 + 3.26222i 0.648138 + 0.374202i
\(77\) −1.66713 0.201674i −0.189987 0.0229829i
\(78\) −4.55818 + 8.87692i −0.516113 + 1.00511i
\(79\) 6.51973 + 11.2925i 0.733527 + 1.27051i 0.955366 + 0.295423i \(0.0954606\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(80\) 4.88958 0.546672
\(81\) −2.88843 + 8.52391i −0.320937 + 0.947101i
\(82\) 4.06412i 0.448807i
\(83\) 2.25090 + 3.89867i 0.247068 + 0.427935i 0.962711 0.270532i \(-0.0871995\pi\)
−0.715643 + 0.698466i \(0.753866\pi\)
\(84\) 0.434124 6.08989i 0.0473668 0.664461i
\(85\) −1.41508 + 2.45099i −0.153487 + 0.265847i
\(86\) −2.75334 1.58964i −0.296900 0.171415i
\(87\) −0.00980246 0.198995i −0.00105093 0.0213345i
\(88\) −0.386814 0.669981i −0.0412345 0.0714202i
\(89\) −11.1029 −1.17691 −0.588454 0.808531i \(-0.700263\pi\)
−0.588454 + 0.808531i \(0.700263\pi\)
\(90\) −4.45060 + 3.19105i −0.469135 + 0.336366i
\(91\) −3.27641 7.68054i −0.343461 0.805139i
\(92\) −5.10284 + 2.94612i −0.532008 + 0.307155i
\(93\) 0.458318 0.295593i 0.0475254 0.0306516i
\(94\) 12.4917 + 7.21210i 1.28842 + 0.743871i
\(95\) 4.24105 + 2.44857i 0.435123 + 0.251218i
\(96\) 9.44375 6.09077i 0.963848 0.621637i
\(97\) 0.266943 0.154120i 0.0271040 0.0156485i −0.486387 0.873744i \(-0.661685\pi\)
0.513491 + 0.858095i \(0.328352\pi\)
\(98\) 9.22354 + 8.84357i 0.931718 + 0.893335i
\(99\) 1.73461 + 0.785387i 0.174335 + 0.0789344i
\(100\) −1.33229 −0.133229
\(101\) 0.986427 + 1.70854i 0.0981531 + 0.170006i 0.910920 0.412583i \(-0.135373\pi\)
−0.812767 + 0.582589i \(0.802040\pi\)
\(102\) 0.440260 + 8.93750i 0.0435922 + 0.884945i
\(103\) −13.9294 8.04212i −1.37250 0.792413i −0.381258 0.924469i \(-0.624509\pi\)
−0.991242 + 0.132056i \(0.957842\pi\)
\(104\) 1.92342 3.33145i 0.188606 0.326676i
\(105\) 0.325847 4.57098i 0.0317994 0.446082i
\(106\) −7.88206 13.6521i −0.765573 1.32601i
\(107\) 10.0764i 0.974121i −0.873368 0.487061i \(-0.838069\pi\)
0.873368 0.487061i \(-0.161931\pi\)
\(108\) −2.54168 + 6.43934i −0.244573 + 0.619626i
\(109\) −14.2509 −1.36499 −0.682496 0.730889i \(-0.739106\pi\)
−0.682496 + 0.730889i \(0.739106\pi\)
\(110\) 0.579318 + 1.00341i 0.0552358 + 0.0956712i
\(111\) 8.52892 16.6098i 0.809529 1.57653i
\(112\) −1.55362 + 12.8430i −0.146804 + 1.21355i
\(113\) 0.175863 + 0.101534i 0.0165438 + 0.00955155i 0.508249 0.861210i \(-0.330293\pi\)
−0.491705 + 0.870762i \(0.663626\pi\)
\(114\) 15.4650 0.761802i 1.44843 0.0713493i
\(115\) −3.83011 + 2.21132i −0.357160 + 0.206206i
\(116\) 0.153253i 0.0142292i
\(117\) 0.930547 + 9.42237i 0.0860291 + 0.871099i
\(118\) 27.9313i 2.57128i
\(119\) −5.98814 4.49562i −0.548931 0.412113i
\(120\) 1.77415 1.14424i 0.161957 0.104455i
\(121\) −5.29857 + 9.17740i −0.481688 + 0.834309i
\(122\) −9.42819 + 16.3301i −0.853588 + 1.47846i
\(123\) 2.09005 + 3.24063i 0.188453 + 0.292197i
\(124\) 0.363298 0.209750i 0.0326251 0.0188361i
\(125\) −1.00000 −0.0894427
\(126\) −6.96747 12.7039i −0.620711 1.13175i
\(127\) 4.60267 0.408421 0.204211 0.978927i \(-0.434537\pi\)
0.204211 + 0.978927i \(0.434537\pi\)
\(128\) −7.97396 + 4.60377i −0.704805 + 0.406919i
\(129\) −3.01295 + 0.148417i −0.265275 + 0.0130674i
\(130\) −2.88064 + 4.98941i −0.252649 + 0.437600i
\(131\) 0.755338 1.30828i 0.0659942 0.114305i −0.831140 0.556063i \(-0.812311\pi\)
0.897135 + 0.441757i \(0.145645\pi\)
\(132\) 1.30293 + 0.669035i 0.113405 + 0.0582320i
\(133\) −7.77899 + 10.3615i −0.674524 + 0.898460i
\(134\) 8.78351i 0.758780i
\(135\) −1.90775 + 4.83327i −0.164193 + 0.415982i
\(136\) 3.44958i 0.295799i
\(137\) 10.9225 6.30611i 0.933172 0.538767i 0.0453589 0.998971i \(-0.485557\pi\)
0.887814 + 0.460203i \(0.152224\pi\)
\(138\) −6.38742 + 12.4393i −0.543734 + 1.05890i
\(139\) 4.86731 + 2.81014i 0.412840 + 0.238353i 0.692009 0.721889i \(-0.256726\pi\)
−0.279169 + 0.960242i \(0.590059\pi\)
\(140\) 0.423326 3.49941i 0.0357775 0.295754i
\(141\) 13.6696 0.673360i 1.15118 0.0567071i
\(142\) −11.8421 20.5112i −0.993771 1.72126i
\(143\) 2.00319 0.167515
\(144\) 6.05035 13.3628i 0.504196 1.11357i
\(145\) 0.115029i 0.00955265i
\(146\) −5.89598 10.2121i −0.487955 0.845163i
\(147\) 11.9026 + 2.30826i 0.981710 + 0.190382i
\(148\) 7.18110 12.4380i 0.590283 1.02240i
\(149\) −10.8483 6.26327i −0.888727 0.513107i −0.0152013 0.999884i \(-0.504839\pi\)
−0.873526 + 0.486778i \(0.838172\pi\)
\(150\) −2.65709 + 1.71370i −0.216950 + 0.139923i
\(151\) −4.44709 7.70259i −0.361899 0.626828i 0.626374 0.779523i \(-0.284538\pi\)
−0.988273 + 0.152695i \(0.951205\pi\)
\(152\) −5.96897 −0.484148
\(153\) 4.94734 + 6.90013i 0.399968 + 0.557843i
\(154\) −2.81963 + 1.20281i −0.227212 + 0.0969254i
\(155\) 0.272686 0.157435i 0.0219027 0.0126455i
\(156\) 0.358323 + 7.27414i 0.0286888 + 0.582397i
\(157\) 1.47404 + 0.851038i 0.117641 + 0.0679202i 0.557666 0.830065i \(-0.311697\pi\)
−0.440025 + 0.897986i \(0.645030\pi\)
\(158\) 20.6140 + 11.9015i 1.63996 + 0.946832i
\(159\) −13.3058 6.83237i −1.05522 0.541842i
\(160\) 5.61876 3.24399i 0.444202 0.256460i
\(161\) −4.59126 10.7628i −0.361842 0.848228i
\(162\) 3.21371 + 16.1117i 0.252493 + 1.26586i
\(163\) 18.8951 1.47998 0.739988 0.672620i \(-0.234831\pi\)
0.739988 + 0.672620i \(0.234831\pi\)
\(164\) 1.48308 + 2.56877i 0.115809 + 0.200587i
\(165\) 0.977956 + 0.502167i 0.0761337 + 0.0390937i
\(166\) 7.11686 + 4.10892i 0.552375 + 0.318914i
\(167\) 6.20475 10.7469i 0.480138 0.831624i −0.519602 0.854408i \(-0.673920\pi\)
0.999740 + 0.0227845i \(0.00725316\pi\)
\(168\) 2.44175 + 5.02357i 0.188385 + 0.387577i
\(169\) −1.51961 2.63204i −0.116893 0.202465i
\(170\) 5.16633i 0.396239i
\(171\) 11.9396 8.56060i 0.913045 0.654646i
\(172\) −2.32037 −0.176927
\(173\) 6.14289 + 10.6398i 0.467035 + 0.808929i 0.999291 0.0376549i \(-0.0119888\pi\)
−0.532255 + 0.846584i \(0.678655\pi\)
\(174\) −0.197125 0.305643i −0.0149440 0.0231707i
\(175\) 0.317742 2.62660i 0.0240190 0.198552i
\(176\) −2.68768 1.55173i −0.202591 0.116966i
\(177\) −14.3642 22.2717i −1.07968 1.67404i
\(178\) −17.5525 + 10.1340i −1.31562 + 0.759572i
\(179\) 4.60808i 0.344424i 0.985060 + 0.172212i \(0.0550914\pi\)
−0.985060 + 0.172212i \(0.944909\pi\)
\(180\) −1.64858 + 3.64105i −0.122878 + 0.271388i
\(181\) 16.3361i 1.21425i 0.794605 + 0.607127i \(0.207678\pi\)
−0.794605 + 0.607127i \(0.792322\pi\)
\(182\) −12.1899 9.15163i −0.903575 0.678364i
\(183\) 0.880266 + 17.8699i 0.0650711 + 1.32098i
\(184\) 2.69530 4.66840i 0.198700 0.344159i
\(185\) 5.39002 9.33580i 0.396282 0.686381i
\(186\) 0.454755 0.885621i 0.0333442 0.0649369i
\(187\) 1.55566 0.898163i 0.113761 0.0656802i
\(188\) 10.5274 0.767788
\(189\) −12.0889 6.54662i −0.879339 0.476197i
\(190\) 8.93953 0.648542
\(191\) −21.0061 + 12.1279i −1.51995 + 0.877543i −0.520225 + 0.854029i \(0.674152\pi\)
−0.999724 + 0.0235140i \(0.992515\pi\)
\(192\) 1.63329 3.18078i 0.117872 0.229553i
\(193\) 6.56678 11.3740i 0.472687 0.818718i −0.526825 0.849974i \(-0.676618\pi\)
0.999511 + 0.0312564i \(0.00995083\pi\)
\(194\) 0.281339 0.487293i 0.0201990 0.0349856i
\(195\) 0.268951 + 5.45985i 0.0192600 + 0.390988i
\(196\) 9.05705 + 2.22382i 0.646932 + 0.158844i
\(197\) 3.76813i 0.268468i 0.990950 + 0.134234i \(0.0428573\pi\)
−0.990950 + 0.134234i \(0.957143\pi\)
\(198\) 3.45908 0.341616i 0.245826 0.0242776i
\(199\) 18.8678i 1.33750i −0.743487 0.668751i \(-0.766829\pi\)
0.743487 0.668751i \(-0.233171\pi\)
\(200\) 1.05557 0.609434i 0.0746401 0.0430935i
\(201\) 4.51709 + 7.00376i 0.318611 + 0.494007i
\(202\) 3.11887 + 1.80068i 0.219443 + 0.126695i
\(203\) 0.302136 + 0.0365495i 0.0212058 + 0.00256528i
\(204\) 3.53975 + 5.48839i 0.247832 + 0.384264i
\(205\) 1.11318 + 1.92808i 0.0777477 + 0.134663i
\(206\) −29.3611 −2.04568
\(207\) 1.30398 + 13.2037i 0.0906332 + 0.917718i
\(208\) 15.4319i 1.07001i
\(209\) −1.55413 2.69184i −0.107502 0.186198i
\(210\) −3.65693 7.52363i −0.252352 0.519180i
\(211\) 12.9903 22.4999i 0.894292 1.54896i 0.0596142 0.998221i \(-0.481013\pi\)
0.834678 0.550738i \(-0.185654\pi\)
\(212\) −9.96389 5.75265i −0.684323 0.395094i
\(213\) −19.9909 10.2651i −1.36976 0.703351i
\(214\) −9.19701 15.9297i −0.628695 1.08893i
\(215\) −1.74163 −0.118778
\(216\) −0.931799 6.26450i −0.0634009 0.426245i
\(217\) 0.326876 + 0.766262i 0.0221898 + 0.0520172i
\(218\) −22.5292 + 13.0072i −1.52587 + 0.880961i
\(219\) −9.95310 5.11079i −0.672568 0.345355i
\(220\) 0.732329 + 0.422810i 0.0493736 + 0.0285059i
\(221\) 7.73548 + 4.46608i 0.520345 + 0.300421i
\(222\) −1.67695 34.0429i −0.112549 2.28481i
\(223\) 20.0761 11.5909i 1.34440 0.776187i 0.356946 0.934125i \(-0.383818\pi\)
0.987449 + 0.157938i \(0.0504846\pi\)
\(224\) 6.73536 + 15.7890i 0.450025 + 1.05495i
\(225\) −1.23740 + 2.73292i −0.0824931 + 0.182195i
\(226\) 0.370693 0.0246582
\(227\) −9.75293 16.8926i −0.647325 1.12120i −0.983759 0.179493i \(-0.942554\pi\)
0.336434 0.941707i \(-0.390779\pi\)
\(228\) 9.49681 6.12499i 0.628942 0.405638i
\(229\) 19.9441 + 11.5147i 1.31794 + 0.760913i 0.983397 0.181467i \(-0.0580845\pi\)
0.334544 + 0.942380i \(0.391418\pi\)
\(230\) −4.03666 + 6.99171i −0.266170 + 0.461019i
\(231\) −1.62973 + 2.40914i −0.107228 + 0.158510i
\(232\) 0.0701026 + 0.121421i 0.00460246 + 0.00797170i
\(233\) 18.2501i 1.19560i 0.801644 + 0.597801i \(0.203959\pi\)
−0.801644 + 0.597801i \(0.796041\pi\)
\(234\) 10.0712 + 14.0464i 0.658373 + 0.918243i
\(235\) 7.90169 0.515449
\(236\) −10.1927 17.6543i −0.663488 1.14920i
\(237\) 22.5577 1.11119i 1.46528 0.0721793i
\(238\) −13.5699 1.64156i −0.879605 0.106406i
\(239\) −16.0585 9.27139i −1.03874 0.599716i −0.119263 0.992863i \(-0.538053\pi\)
−0.919476 + 0.393146i \(0.871387\pi\)
\(240\) 3.86852 7.53383i 0.249712 0.486306i
\(241\) −6.19724 + 3.57798i −0.399200 + 0.230478i −0.686139 0.727471i \(-0.740696\pi\)
0.286939 + 0.957949i \(0.407362\pi\)
\(242\) 19.3446i 1.24352i
\(243\) 10.8483 + 11.1944i 0.695919 + 0.718120i
\(244\) 13.7622i 0.881033i
\(245\) 6.79808 + 1.66916i 0.434313 + 0.106639i
\(246\) 6.26196 + 3.21543i 0.399248 + 0.205008i
\(247\) 7.72787 13.3851i 0.491713 0.851671i
\(248\) −0.191893 + 0.332368i −0.0121852 + 0.0211054i
\(249\) 7.78790 0.383631i 0.493538 0.0243116i
\(250\) −1.58089 + 0.912729i −0.0999844 + 0.0577260i
\(251\) 29.5574 1.86564 0.932822 0.360338i \(-0.117339\pi\)
0.932822 + 0.360338i \(0.117339\pi\)
\(252\) −9.03978 5.48707i −0.569453 0.345653i
\(253\) 2.80709 0.176480
\(254\) 7.27633 4.20099i 0.456558 0.263594i
\(255\) 2.65688 + 4.11950i 0.166380 + 0.257973i
\(256\) −10.4684 + 18.1317i −0.654272 + 1.13323i
\(257\) 4.33852 7.51453i 0.270629 0.468744i −0.698394 0.715714i \(-0.746102\pi\)
0.969023 + 0.246970i \(0.0794349\pi\)
\(258\) −4.62768 + 2.98463i −0.288107 + 0.185815i
\(259\) 22.8088 + 17.1238i 1.41727 + 1.06402i
\(260\) 4.20482i 0.260772i
\(261\) −0.314365 0.142337i −0.0194587 0.00881041i
\(262\) 2.75768i 0.170370i
\(263\) −5.81261 + 3.35591i −0.358421 + 0.206934i −0.668388 0.743813i \(-0.733015\pi\)
0.309967 + 0.950747i \(0.399682\pi\)
\(264\) −1.33834 + 0.0659263i −0.0823691 + 0.00405749i
\(265\) −7.47874 4.31785i −0.459415 0.265244i
\(266\) −2.84046 + 23.4806i −0.174160 + 1.43969i
\(267\) −8.78437 + 17.1073i −0.537595 + 1.04695i
\(268\) 3.20529 + 5.55172i 0.195794 + 0.339125i
\(269\) −7.10403 −0.433140 −0.216570 0.976267i \(-0.569487\pi\)
−0.216570 + 0.976267i \(0.569487\pi\)
\(270\) 1.39552 + 9.38214i 0.0849289 + 0.570979i
\(271\) 24.9418i 1.51511i 0.652773 + 0.757554i \(0.273606\pi\)
−0.652773 + 0.757554i \(0.726394\pi\)
\(272\) −6.91913 11.9843i −0.419534 0.726654i
\(273\) −14.4263 1.02839i −0.873121 0.0622413i
\(274\) 11.5115 19.9386i 0.695437 1.20453i
\(275\) 0.549675 + 0.317355i 0.0331466 + 0.0191372i
\(276\) 0.502121 + 10.1933i 0.0302241 + 0.613565i
\(277\) −3.69399 6.39818i −0.221950 0.384429i 0.733450 0.679744i \(-0.237909\pi\)
−0.955400 + 0.295314i \(0.904576\pi\)
\(278\) 10.2596 0.615330
\(279\) −0.0928376 0.940039i −0.00555804 0.0562787i
\(280\) 1.26534 + 2.96621i 0.0756186 + 0.177265i
\(281\) −4.56414 + 2.63511i −0.272274 + 0.157197i −0.629921 0.776660i \(-0.716913\pi\)
0.357647 + 0.933857i \(0.383579\pi\)
\(282\) 20.9955 13.5411i 1.25026 0.806361i
\(283\) 19.8282 + 11.4478i 1.17867 + 0.680503i 0.955706 0.294325i \(-0.0950947\pi\)
0.222960 + 0.974828i \(0.428428\pi\)
\(284\) −14.9699 8.64289i −0.888302 0.512861i
\(285\) 7.12816 4.59733i 0.422236 0.272322i
\(286\) 3.16683 1.82837i 0.187258 0.108114i
\(287\) −5.41800 + 2.31124i −0.319815 + 0.136428i
\(288\) −1.91294 19.3697i −0.112721 1.14137i
\(289\) −8.99023 −0.528837
\(290\) −0.104990 0.181849i −0.00616525 0.0106785i
\(291\) −0.0262673 0.533240i −0.00153982 0.0312591i
\(292\) −7.45325 4.30313i −0.436168 0.251822i
\(293\) −12.2600 + 21.2349i −0.716236 + 1.24056i 0.246244 + 0.969208i \(0.420803\pi\)
−0.962481 + 0.271350i \(0.912530\pi\)
\(294\) 20.9235 7.21474i 1.22029 0.420772i
\(295\) −7.65048 13.2510i −0.445428 0.771504i
\(296\) 13.1395i 0.763715i
\(297\) 2.58250 2.05129i 0.149852 0.119028i
\(298\) −22.8667 −1.32463
\(299\) 6.97907 + 12.0881i 0.403610 + 0.699073i
\(300\) −1.05408 + 2.05279i −0.0608573 + 0.118518i
\(301\) 0.553390 4.57458i 0.0318969 0.263674i
\(302\) −14.0607 8.11798i −0.809105 0.467137i
\(303\) 3.41294 0.168121i 0.196069 0.00965830i
\(304\) −20.7370 + 11.9725i −1.18935 + 0.686670i
\(305\) 10.3297i 0.591475i
\(306\) 14.1192 + 6.39279i 0.807138 + 0.365452i
\(307\) 23.9095i 1.36459i 0.731078 + 0.682294i \(0.239017\pi\)
−0.731078 + 0.682294i \(0.760983\pi\)
\(308\) −1.34325 + 1.78919i −0.0765385 + 0.101949i
\(309\) −23.4118 + 15.0995i −1.33185 + 0.858981i
\(310\) 0.287392 0.497777i 0.0163227 0.0282718i
\(311\) −11.9796 + 20.7493i −0.679303 + 1.17659i 0.295889 + 0.955222i \(0.404384\pi\)
−0.975191 + 0.221364i \(0.928949\pi\)
\(312\) −3.61132 5.59935i −0.204451 0.317001i
\(313\) 20.2952 11.7174i 1.14715 0.662307i 0.198959 0.980008i \(-0.436244\pi\)
0.948191 + 0.317701i \(0.102911\pi\)
\(314\) 3.10707 0.175342
\(315\) −6.78512 4.11851i −0.382298 0.232052i
\(316\) 17.3724 0.977274
\(317\) 0.0621219 0.0358661i 0.00348911 0.00201444i −0.498254 0.867031i \(-0.666025\pi\)
0.501744 + 0.865016i \(0.332692\pi\)
\(318\) −27.2712 + 1.34337i −1.52929 + 0.0753326i
\(319\) −0.0365051 + 0.0632286i −0.00204389 + 0.00354012i
\(320\) 1.03219 1.78781i 0.0577012 0.0999414i
\(321\) −15.5256 7.97220i −0.866556 0.444965i
\(322\) −17.0818 12.8243i −0.951932 0.714668i
\(323\) 13.8597i 0.771173i
\(324\) 7.91077 + 9.01085i 0.439487 + 0.500603i
\(325\) 3.15607i 0.175067i
\(326\) 29.8711 17.2461i 1.65441 0.955171i
\(327\) −11.2750 + 21.9577i −0.623509 + 1.21426i
\(328\) −2.35007 1.35682i −0.129761 0.0749176i
\(329\) −2.51070 + 20.7546i −0.138419 + 1.14424i
\(330\) 2.00439 0.0987357i 0.110338 0.00543522i
\(331\) 5.30278 + 9.18468i 0.291467 + 0.504836i 0.974157 0.225873i \(-0.0725233\pi\)
−0.682690 + 0.730708i \(0.739190\pi\)
\(332\) 5.99772 0.329168
\(333\) −18.8444 26.2826i −1.03267 1.44028i
\(334\) 22.6530i 1.23952i
\(335\) 2.40584 + 4.16704i 0.131445 + 0.227669i
\(336\) 18.5592 + 12.5549i 1.01249 + 0.684925i
\(337\) −7.49923 + 12.9890i −0.408509 + 0.707558i −0.994723 0.102598i \(-0.967284\pi\)
0.586214 + 0.810156i \(0.300618\pi\)
\(338\) −4.80468 2.77398i −0.261340 0.150885i
\(339\) 0.295582 0.190636i 0.0160538 0.0103539i
\(340\) 1.88530 + 3.26543i 0.102245 + 0.177093i
\(341\) −0.199852 −0.0108226
\(342\) 11.0617 24.4310i 0.598150 1.32108i
\(343\) −6.54426 + 17.3255i −0.353357 + 0.935489i
\(344\) 1.83842 1.06141i 0.0991208 0.0572274i
\(345\) 0.376884 + 7.65095i 0.0202908 + 0.411913i
\(346\) 19.4225 + 11.2136i 1.04416 + 0.602846i
\(347\) 8.94211 + 5.16273i 0.480037 + 0.277150i 0.720432 0.693525i \(-0.243944\pi\)
−0.240395 + 0.970675i \(0.577277\pi\)
\(348\) −0.236131 0.121250i −0.0126579 0.00649968i
\(349\) −11.0162 + 6.36020i −0.589683 + 0.340454i −0.764972 0.644063i \(-0.777247\pi\)
0.175289 + 0.984517i \(0.443914\pi\)
\(350\) −1.89506 4.44239i −0.101295 0.237456i
\(351\) 15.2541 + 6.02098i 0.814206 + 0.321376i
\(352\) −4.11799 −0.219489
\(353\) 2.64706 + 4.58484i 0.140889 + 0.244027i 0.927832 0.372999i \(-0.121671\pi\)
−0.786943 + 0.617026i \(0.788337\pi\)
\(354\) −43.0363 22.0986i −2.28735 1.17452i
\(355\) −11.2362 6.48722i −0.596356 0.344306i
\(356\) −7.39618 + 12.8106i −0.391997 + 0.678959i
\(357\) −11.6645 + 5.66964i −0.617350 + 0.300069i
\(358\) 4.20592 + 7.28488i 0.222290 + 0.385018i
\(359\) 28.3441i 1.49594i 0.663730 + 0.747972i \(0.268972\pi\)
−0.663730 + 0.747972i \(0.731028\pi\)
\(360\) −0.359375 3.63890i −0.0189407 0.191787i
\(361\) −4.98204 −0.262212
\(362\) 14.9104 + 25.8256i 0.783675 + 1.35736i
\(363\) 9.94835 + 15.4249i 0.522153 + 0.809599i
\(364\) −11.0444 1.33605i −0.578883 0.0700278i
\(365\) −5.59429 3.22987i −0.292819 0.169059i
\(366\) 17.7019 + 27.4469i 0.925295 + 1.43467i
\(367\) 16.6696 9.62420i 0.870146 0.502379i 0.00274922 0.999996i \(-0.499125\pi\)
0.867397 + 0.497617i \(0.165792\pi\)
\(368\) 21.6248i 1.12727i
\(369\) 6.64673 0.656426i 0.346015 0.0341722i
\(370\) 19.6785i 1.02304i
\(371\) 13.7176 18.2717i 0.712182 0.948620i
\(372\) −0.0357487 0.725716i −0.00185348 0.0376266i
\(373\) −0.291671 + 0.505190i −0.0151022 + 0.0261577i −0.873478 0.486864i \(-0.838141\pi\)
0.858376 + 0.513022i \(0.171474\pi\)
\(374\) 1.63956 2.83980i 0.0847796 0.146843i
\(375\) −0.791176 + 1.54079i −0.0408562 + 0.0795662i
\(376\) −8.34079 + 4.81556i −0.430143 + 0.248343i
\(377\) −0.363040 −0.0186975
\(378\) −25.0866 + 0.684392i −1.29031 + 0.0352013i
\(379\) −13.7533 −0.706458 −0.353229 0.935537i \(-0.614916\pi\)
−0.353229 + 0.935537i \(0.614916\pi\)
\(380\) 5.65033 3.26222i 0.289856 0.167348i
\(381\) 3.64153 7.09176i 0.186561 0.363322i
\(382\) −22.1389 + 38.3458i −1.13273 + 1.96194i
\(383\) 17.9867 31.1539i 0.919078 1.59189i 0.118260 0.992983i \(-0.462268\pi\)
0.800818 0.598907i \(-0.204398\pi\)
\(384\) 0.784640 + 15.9286i 0.0400410 + 0.812853i
\(385\) −1.00822 + 1.34294i −0.0513836 + 0.0684426i
\(386\) 23.9747i 1.22028i
\(387\) −2.15509 + 4.75975i −0.109549 + 0.241952i
\(388\) 0.410666i 0.0208484i
\(389\) 1.51792 0.876372i 0.0769616 0.0444338i −0.461025 0.887387i \(-0.652518\pi\)
0.537987 + 0.842953i \(0.319185\pi\)
\(390\) 5.40855 + 8.38596i 0.273873 + 0.424640i
\(391\) 10.8398 + 6.25836i 0.548193 + 0.316499i
\(392\) −8.19310 + 2.38106i −0.413814 + 0.120262i
\(393\) −1.41819 2.19890i −0.0715381 0.110920i
\(394\) 3.43928 + 5.95700i 0.173268 + 0.300109i
\(395\) 13.0395 0.656087
\(396\) 2.06169 1.47821i 0.103604 0.0742830i
\(397\) 5.19511i 0.260735i 0.991466 + 0.130367i \(0.0416157\pi\)
−0.991466 + 0.130367i \(0.958384\pi\)
\(398\) −17.2212 29.8279i −0.863219 1.49514i
\(399\) 9.81044 + 20.1836i 0.491136 + 1.01044i
\(400\) 2.44479 4.23450i 0.122240 0.211725i
\(401\) 24.3757 + 14.0733i 1.21726 + 0.702788i 0.964332 0.264696i \(-0.0852717\pi\)
0.252932 + 0.967484i \(0.418605\pi\)
\(402\) 13.5336 + 6.94931i 0.674993 + 0.346600i
\(403\) −0.496877 0.860617i −0.0247512 0.0428704i
\(404\) 2.62842 0.130769
\(405\) 5.93770 + 6.76341i 0.295047 + 0.336076i
\(406\) 0.511004 0.217987i 0.0253607 0.0108185i
\(407\) −5.92552 + 3.42110i −0.293717 + 0.169578i
\(408\) −5.31509 2.72923i −0.263136 0.135117i
\(409\) −30.3765 17.5379i −1.50202 0.867193i −0.999997 0.00234081i \(-0.999255\pi\)
−0.502026 0.864853i \(-0.667412\pi\)
\(410\) 3.51963 + 2.03206i 0.173822 + 0.100356i
\(411\) −1.07478 21.8186i −0.0530149 1.07623i
\(412\) −18.5580 + 10.7145i −0.914287 + 0.527864i
\(413\) 37.2360 15.8844i 1.83227 0.781619i
\(414\) 14.1128 + 19.6834i 0.693607 + 0.967386i
\(415\) 4.50180 0.220985
\(416\) −10.2383 17.7332i −0.501972 0.869442i
\(417\) 8.18075 5.27620i 0.400613 0.258376i
\(418\) −4.91383 2.83700i −0.240344 0.138762i
\(419\) −5.42356 + 9.39389i −0.264958 + 0.458921i −0.967553 0.252669i \(-0.918692\pi\)
0.702594 + 0.711591i \(0.252025\pi\)
\(420\) −5.05694 3.42091i −0.246753 0.166923i
\(421\) 10.3703 + 17.9619i 0.505417 + 0.875408i 0.999980 + 0.00626646i \(0.00199469\pi\)
−0.494563 + 0.869142i \(0.664672\pi\)
\(422\) 47.4266i 2.30869i
\(423\) 9.77752 21.5947i 0.475399 1.04997i
\(424\) 10.5258 0.511177
\(425\) 1.41508 + 2.45099i 0.0686413 + 0.118890i
\(426\) −40.9727 + 2.01831i −1.98514 + 0.0977874i
\(427\) −27.1319 3.28217i −1.31301 0.158835i
\(428\) −11.6261 6.71236i −0.561971 0.324454i
\(429\) 1.58488 3.08650i 0.0765185 0.149017i
\(430\) −2.75334 + 1.58964i −0.132778 + 0.0766592i
\(431\) 10.0323i 0.483240i 0.970371 + 0.241620i \(0.0776787\pi\)
−0.970371 + 0.241620i \(0.922321\pi\)
\(432\) −15.8025 19.8947i −0.760296 0.957183i
\(433\) 11.9241i 0.573034i −0.958075 0.286517i \(-0.907503\pi\)
0.958075 0.286517i \(-0.0924975\pi\)
\(434\) 1.21615 + 0.913028i 0.0583769 + 0.0438267i
\(435\) −0.177236 0.0910083i −0.00849781 0.00436352i
\(436\) −9.49322 + 16.4427i −0.454643 + 0.787465i
\(437\) 10.8291 18.7566i 0.518028 0.897251i
\(438\) −20.3995 + 1.00488i −0.974728 + 0.0480149i
\(439\) 21.8143 12.5945i 1.04114 0.601103i 0.120985 0.992654i \(-0.461395\pi\)
0.920156 + 0.391552i \(0.128062\pi\)
\(440\) −0.773627 −0.0368812
\(441\) 12.9736 16.5132i 0.617791 0.786343i
\(442\) 16.3053 0.775564
\(443\) 19.2098 11.0908i 0.912687 0.526940i 0.0313921 0.999507i \(-0.490006\pi\)
0.881295 + 0.472567i \(0.156673\pi\)
\(444\) −13.4829 20.9053i −0.639870 0.992120i
\(445\) −5.55146 + 9.61541i −0.263165 + 0.455814i
\(446\) 21.1588 36.6481i 1.00190 1.73534i
\(447\) −18.2333 + 11.7596i −0.862406 + 0.556211i
\(448\) 4.36788 + 3.27921i 0.206363 + 0.154928i
\(449\) 24.3237i 1.14791i −0.818888 0.573954i \(-0.805409\pi\)
0.818888 0.573954i \(-0.194591\pi\)
\(450\) 0.538224 + 5.44986i 0.0253721 + 0.256909i
\(451\) 1.41309i 0.0665398i
\(452\) 0.234301 0.135274i 0.0110206 0.00636274i
\(453\) −15.3865 + 0.757937i −0.722922 + 0.0356110i
\(454\) −30.8367 17.8036i −1.44724 0.835563i
\(455\) −8.28974 1.00282i −0.388629 0.0470127i
\(456\) −4.72251 + 9.19694i −0.221152 + 0.430686i
\(457\) −6.84087 11.8487i −0.320002 0.554261i 0.660486 0.750839i \(-0.270350\pi\)
−0.980488 + 0.196578i \(0.937017\pi\)
\(458\) 42.0392 1.96436
\(459\) 14.5459 2.16359i 0.678944 0.100988i
\(460\) 5.89225i 0.274728i
\(461\) 13.9624 + 24.1836i 0.650293 + 1.12634i 0.983052 + 0.183329i \(0.0586872\pi\)
−0.332759 + 0.943012i \(0.607979\pi\)
\(462\) −0.377537 + 5.29610i −0.0175646 + 0.246397i
\(463\) 5.19491 8.99785i 0.241428 0.418165i −0.719693 0.694292i \(-0.755718\pi\)
0.961121 + 0.276127i \(0.0890509\pi\)
\(464\) 0.487091 + 0.281222i 0.0226126 + 0.0130554i
\(465\) −0.0268324 0.544712i −0.00124432 0.0252604i
\(466\) 16.6574 + 28.8514i 0.771638 + 1.33652i
\(467\) −13.3976 −0.619968 −0.309984 0.950742i \(-0.600324\pi\)
−0.309984 + 0.950742i \(0.600324\pi\)
\(468\) 11.4914 + 5.20302i 0.531191 + 0.240510i
\(469\) −11.7096 + 4.99514i −0.540698 + 0.230654i
\(470\) 12.4917 7.21210i 0.576200 0.332669i
\(471\) 2.47750 1.59787i 0.114157 0.0736259i
\(472\) 16.1512 + 9.32493i 0.743421 + 0.429214i
\(473\) 0.957332 + 0.552716i 0.0440182 + 0.0254139i
\(474\) 34.6470 22.3457i 1.59139 1.02637i
\(475\) 4.24105 2.44857i 0.194593 0.112348i
\(476\) −9.17604 + 3.91437i −0.420583 + 0.179415i
\(477\) −21.0545 + 15.0959i −0.964020 + 0.691194i
\(478\) −33.8491 −1.54822
\(479\) 3.08962 + 5.35139i 0.141169 + 0.244511i 0.927937 0.372737i \(-0.121581\pi\)
−0.786768 + 0.617248i \(0.788247\pi\)
\(480\) −0.552888 11.2239i −0.0252358 0.512299i
\(481\) −29.4644 17.0113i −1.34346 0.775648i
\(482\) −6.53145 + 11.3128i −0.297499 + 0.515284i
\(483\) −20.2157 1.44110i −0.919848 0.0655723i
\(484\) 7.05926 + 12.2270i 0.320875 + 0.555773i
\(485\) 0.308239i 0.0139964i
\(486\) 27.3674 + 7.79556i 1.24141 + 0.353614i
\(487\) 11.0928 0.502665 0.251332 0.967901i \(-0.419131\pi\)
0.251332 + 0.967901i \(0.419131\pi\)
\(488\) −6.29525 10.9037i −0.284973 0.493587i
\(489\) 14.9493 29.1134i 0.676032 1.31655i
\(490\) 12.2705 3.56604i 0.554326 0.161097i
\(491\) −0.777992 0.449174i −0.0351103 0.0202709i 0.482342 0.875983i \(-0.339786\pi\)
−0.517452 + 0.855712i \(0.673120\pi\)
\(492\) 5.13132 0.252768i 0.231338 0.0113957i
\(493\) −0.281935 + 0.162775i −0.0126977 + 0.00733102i
\(494\) 28.2138i 1.26940i
\(495\) 1.54747 1.10952i 0.0695536 0.0498694i
\(496\) 1.53959i 0.0691294i
\(497\) 20.6096 27.4518i 0.924465 1.23138i
\(498\) 11.9617 7.71472i 0.536016 0.345705i
\(499\) 17.0653 29.5579i 0.763946 1.32319i −0.176857 0.984237i \(-0.556593\pi\)
0.940802 0.338956i \(-0.110074\pi\)
\(500\) −0.666147 + 1.15380i −0.0297910 + 0.0515996i
\(501\) −11.6498 18.0630i −0.520473 0.806994i
\(502\) 46.7270 26.9778i 2.08553 1.20408i
\(503\) −39.5756 −1.76459 −0.882294 0.470698i \(-0.844002\pi\)
−0.882294 + 0.470698i \(0.844002\pi\)
\(504\) 9.67213 + 0.212294i 0.430831 + 0.00945635i
\(505\) 1.97285 0.0877908
\(506\) 4.43770 2.56211i 0.197280 0.113900i
\(507\) −5.25770 + 0.258994i −0.233503 + 0.0115023i
\(508\) 3.06606 5.31057i 0.136034 0.235618i
\(509\) −4.36091 + 7.55332i −0.193294 + 0.334795i −0.946340 0.323173i \(-0.895250\pi\)
0.753046 + 0.657968i \(0.228584\pi\)
\(510\) 7.96023 + 4.08747i 0.352485 + 0.180996i
\(511\) 10.2611 13.6677i 0.453925 0.604624i
\(512\) 19.8040i 0.875222i
\(513\) −3.74377 25.1694i −0.165291 1.11126i
\(514\) 15.8396i 0.698653i
\(515\) −13.9294 + 8.04212i −0.613801 + 0.354378i
\(516\) −1.83582 + 3.57521i −0.0808175 + 0.157390i
\(517\) −4.34336 2.50764i −0.191021 0.110286i
\(518\) 51.6876 + 6.25269i 2.27102 + 0.274727i
\(519\) 21.2538 1.04696i 0.932939 0.0459564i
\(520\) −1.92342 3.33145i −0.0843474 0.146094i
\(521\) −17.4216 −0.763256 −0.381628 0.924316i \(-0.624636\pi\)
−0.381628 + 0.924316i \(0.624636\pi\)
\(522\) −0.626893 + 0.0619115i −0.0274383 + 0.00270979i
\(523\) 13.2690i 0.580215i 0.956994 + 0.290107i \(0.0936910\pi\)
−0.956994 + 0.290107i \(0.906309\pi\)
\(524\) −1.00633 1.74302i −0.0439619 0.0761442i
\(525\) −3.79566 2.56768i −0.165656 0.112063i
\(526\) −6.12607 + 10.6107i −0.267109 + 0.462647i
\(527\) −0.771744 0.445566i −0.0336177 0.0194092i
\(528\) −4.51732 + 2.91346i −0.196591 + 0.126792i
\(529\) −1.72016 2.97941i −0.0747897 0.129540i
\(530\) −15.7641 −0.684749
\(531\) −45.6807 + 4.51139i −1.98237 + 0.195778i
\(532\) 6.77321 + 15.8777i 0.293656 + 0.688386i
\(533\) 6.08516 3.51327i 0.263577 0.152176i
\(534\) 1.72717 + 35.0625i 0.0747422 + 1.51730i
\(535\) −8.72641 5.03820i −0.377276 0.217820i
\(536\) −5.07906 2.93240i −0.219382 0.126660i
\(537\) 7.10009 + 3.64580i 0.306391 + 0.157328i
\(538\) −11.2307 + 6.48405i −0.484190 + 0.279547i
\(539\) −3.20702 3.07490i −0.138136 0.132445i
\(540\) 4.30579 + 5.42083i 0.185292 + 0.233275i
\(541\) −2.60119 −0.111834 −0.0559170 0.998435i \(-0.517808\pi\)
−0.0559170 + 0.998435i \(0.517808\pi\)
\(542\) 22.7651 + 39.4303i 0.977845 + 1.69368i
\(543\) 25.1705 + 12.9247i 1.08017 + 0.554654i
\(544\) −15.9020 9.18100i −0.681791 0.393632i
\(545\) −7.12547 + 12.3417i −0.305221 + 0.528659i
\(546\) −23.7451 + 11.5415i −1.01620 + 0.493932i
\(547\) −0.836471 1.44881i −0.0357649 0.0619467i 0.847589 0.530653i \(-0.178053\pi\)
−0.883354 + 0.468707i \(0.844720\pi\)
\(548\) 16.8032i 0.717797i
\(549\) 28.2302 + 12.7819i 1.20483 + 0.545518i
\(550\) 1.15864 0.0494044
\(551\) 0.281657 + 0.487845i 0.0119990 + 0.0207829i
\(552\) −5.06057 7.84643i −0.215392 0.333966i
\(553\) −4.14318 + 34.2495i −0.176186 + 1.45644i
\(554\) −11.6796 6.74322i −0.496219 0.286492i
\(555\) −10.1201 15.6912i −0.429573 0.666053i
\(556\) 6.48470 3.74394i 0.275012 0.158778i
\(557\) 14.5888i 0.618147i 0.951038 + 0.309073i \(0.100019\pi\)
−0.951038 + 0.309073i \(0.899981\pi\)
\(558\) −1.00477 1.40137i −0.0425352 0.0593245i
\(559\) 5.49672i 0.232486i
\(560\) 10.3455 + 7.76697i 0.437179 + 0.328214i
\(561\) −0.153078 3.10756i −0.00646295 0.131201i
\(562\) −4.81028 + 8.33165i −0.202909 + 0.351450i
\(563\) 6.16179 10.6725i 0.259688 0.449793i −0.706470 0.707743i \(-0.749713\pi\)
0.966158 + 0.257950i \(0.0830468\pi\)
\(564\) 8.32901 16.2205i 0.350715 0.683006i
\(565\) 0.175863 0.101534i 0.00739860 0.00427158i
\(566\) 41.7951 1.75678
\(567\) −19.6514 + 13.4470i −0.825283 + 0.564719i
\(568\) 15.8141 0.663546
\(569\) 21.4923 12.4086i 0.901004 0.520195i 0.0234780 0.999724i \(-0.492526\pi\)
0.877526 + 0.479530i \(0.159193\pi\)
\(570\) 7.07275 13.7740i 0.296245 0.576928i
\(571\) 14.8775 25.7686i 0.622605 1.07838i −0.366393 0.930460i \(-0.619407\pi\)
0.988999 0.147924i \(-0.0472592\pi\)
\(572\) 1.33442 2.31128i 0.0557949 0.0966395i
\(573\) 2.06701 + 41.9613i 0.0863505 + 1.75296i
\(574\) −6.45574 + 8.59899i −0.269457 + 0.358915i
\(575\) 4.42263i 0.184436i
\(576\) −3.60870 5.03312i −0.150363 0.209713i
\(577\) 37.2085i 1.54901i −0.632568 0.774505i \(-0.717999\pi\)
0.632568 0.774505i \(-0.282001\pi\)
\(578\) −14.2126 + 8.20564i −0.591166 + 0.341310i
\(579\) −12.3295 19.1169i −0.512395 0.794470i
\(580\) −0.132721 0.0766264i −0.00551093 0.00318174i
\(581\) −1.43041 + 11.8244i −0.0593434 + 0.490560i
\(582\) −0.528229 0.819020i −0.0218958 0.0339495i
\(583\) 2.74058 + 4.74683i 0.113503 + 0.196594i
\(584\) 7.87356 0.325810
\(585\) 8.62529 + 3.90531i 0.356612 + 0.161465i
\(586\) 44.7602i 1.84903i
\(587\) −8.94805 15.4985i −0.369326 0.639691i 0.620135 0.784495i \(-0.287078\pi\)
−0.989460 + 0.144805i \(0.953745\pi\)
\(588\) 10.5922 12.1956i 0.436813 0.502938i
\(589\) −0.770984 + 1.33538i −0.0317678 + 0.0550235i
\(590\) −24.1892 13.9656i −0.995853 0.574956i
\(591\) 5.80590 + 2.98125i 0.238823 + 0.122632i
\(592\) 26.3550 + 45.6481i 1.08318 + 1.87613i
\(593\) −19.2039 −0.788610 −0.394305 0.918980i \(-0.629015\pi\)
−0.394305 + 0.918980i \(0.629015\pi\)
\(594\) 2.21038 5.60000i 0.0906931 0.229771i
\(595\) −6.88739 + 2.93806i −0.282356 + 0.120449i
\(596\) −14.4531 + 8.34452i −0.592023 + 0.341805i
\(597\) −29.0713 14.9277i −1.18981 0.610952i
\(598\) 22.0663 + 12.7400i 0.902359 + 0.520977i
\(599\) −11.0142 6.35908i −0.450030 0.259825i 0.257813 0.966195i \(-0.416998\pi\)
−0.707843 + 0.706370i \(0.750331\pi\)
\(600\) −0.103868 2.10858i −0.00424041 0.0860826i
\(601\) −26.1187 + 15.0797i −1.06541 + 0.615112i −0.926922 0.375253i \(-0.877556\pi\)
−0.138483 + 0.990365i \(0.544223\pi\)
\(602\) −3.30050 7.73701i −0.134518 0.315337i
\(603\) 14.3651 1.41869i 0.584994 0.0577736i
\(604\) −11.8497 −0.482156
\(605\) 5.29857 + 9.17740i 0.215418 + 0.373114i
\(606\) 5.24205 3.38087i 0.212944 0.137339i
\(607\) −12.2648 7.08106i −0.497811 0.287411i 0.229998 0.973191i \(-0.426128\pi\)
−0.727809 + 0.685780i \(0.759461\pi\)
\(608\) −15.8863 + 27.5159i −0.644275 + 1.11592i
\(609\) 0.295358 0.436611i 0.0119685 0.0176924i
\(610\) 9.42819 + 16.3301i 0.381736 + 0.661187i
\(611\) 24.9383i 1.00890i
\(612\) 11.2570 1.11174i 0.455039 0.0449393i
\(613\) −15.2883 −0.617488 −0.308744 0.951145i \(-0.599909\pi\)
−0.308744 + 0.951145i \(0.599909\pi\)
\(614\) 21.8229 + 37.7983i 0.880700 + 1.52542i
\(615\) 3.85149 0.189724i 0.155307 0.00765040i
\(616\) 0.245814 2.03201i 0.00990411 0.0818721i
\(617\) 8.33983 + 4.81500i 0.335749 + 0.193845i 0.658391 0.752677i \(-0.271238\pi\)
−0.322642 + 0.946521i \(0.604571\pi\)
\(618\) −23.2298 + 45.2393i −0.934439 + 1.81979i
\(619\) 0.588045 0.339508i 0.0236355 0.0136460i −0.488136 0.872768i \(-0.662323\pi\)
0.511771 + 0.859122i \(0.328990\pi\)
\(620\) 0.419501i 0.0168476i
\(621\) 21.3758 + 8.43726i 0.857780 + 0.338575i
\(622\) 43.7366i 1.75368i
\(623\) −23.4919 17.6367i −0.941185 0.706599i
\(624\) −23.7773 12.2093i −0.951853 0.488764i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 21.3896 37.0479i 0.854902 1.48073i
\(627\) −5.37716 + 0.264878i −0.214743 + 0.0105782i
\(628\) 1.96386 1.13383i 0.0783664 0.0452449i
\(629\) −30.5092 −1.21648
\(630\) −14.4856 0.317946i −0.577121 0.0126673i
\(631\) −18.5432 −0.738192 −0.369096 0.929391i \(-0.620333\pi\)
−0.369096 + 0.929391i \(0.620333\pi\)
\(632\) −13.7641 + 7.94669i −0.547505 + 0.316102i
\(633\) −24.3901 37.8168i −0.969418 1.50308i
\(634\) 0.0654720 0.113401i 0.00260023 0.00450372i
\(635\) 2.30134 3.98603i 0.0913258 0.158181i
\(636\) −16.7468 + 10.8009i −0.664055 + 0.428284i
\(637\) 5.26799 21.4552i 0.208725 0.850087i
\(638\) 0.133277i 0.00527648i
\(639\) −31.6327 + 22.6804i −1.25137 + 0.897221i
\(640\) 9.20753i 0.363960i
\(641\) −25.0099 + 14.4395i −0.987831 + 0.570325i −0.904625 0.426208i \(-0.859849\pi\)
−0.0832059 + 0.996532i \(0.526516\pi\)
\(642\) −31.8208 + 1.56749i −1.25587 + 0.0618638i
\(643\) −3.83286 2.21290i −0.151153 0.0872683i 0.422516 0.906356i \(-0.361147\pi\)
−0.573669 + 0.819087i \(0.694480\pi\)
\(644\) −15.4766 1.87221i −0.609863 0.0737755i
\(645\) −1.37794 + 2.68350i −0.0542563 + 0.105663i
\(646\) −12.6501 21.9107i −0.497713 0.862063i
\(647\) 7.06316 0.277681 0.138841 0.990315i \(-0.455662\pi\)
0.138841 + 0.990315i \(0.455662\pi\)
\(648\) −10.3895 3.52062i −0.408139 0.138303i
\(649\) 9.71167i 0.381216i
\(650\) 2.88064 + 4.98941i 0.112988 + 0.195701i
\(651\) 1.43927 + 0.102600i 0.0564093 + 0.00402119i
\(652\) 12.5869 21.8011i 0.492941 0.853799i
\(653\) 40.1784 + 23.1970i 1.57230 + 0.907768i 0.995886 + 0.0906102i \(0.0288817\pi\)
0.576414 + 0.817158i \(0.304452\pi\)
\(654\) 2.21688 + 45.0038i 0.0866869 + 1.75979i
\(655\) −0.755338 1.30828i −0.0295135 0.0511189i
\(656\) −10.8859 −0.425025
\(657\) −15.7493 + 11.2921i −0.614439 + 0.440548i
\(658\) 14.9742 + 35.1024i 0.583754 + 1.36843i
\(659\) −17.1849 + 9.92173i −0.669431 + 0.386496i −0.795861 0.605480i \(-0.792981\pi\)
0.126430 + 0.991975i \(0.459648\pi\)
\(660\) 1.23086 0.793849i 0.0479113 0.0309005i
\(661\) 3.50683 + 2.02467i 0.136400 + 0.0787505i 0.566647 0.823961i \(-0.308240\pi\)
−0.430247 + 0.902711i \(0.641574\pi\)
\(662\) 16.7662 + 9.67999i 0.651638 + 0.376224i
\(663\) 13.0014 8.38531i 0.504934 0.325658i
\(664\) −4.75196 + 2.74355i −0.184412 + 0.106470i
\(665\) 5.08387 + 11.9176i 0.197144 + 0.462144i
\(666\) −53.7798 24.3501i −2.08393 0.943548i
\(667\) −0.508732 −0.0196982
\(668\) −8.26656 14.3181i −0.319843 0.553984i
\(669\) −1.97550 40.1036i −0.0763771 1.55049i
\(670\) 7.60674 + 4.39176i 0.293874 + 0.169668i
\(671\) 3.27817 5.67796i 0.126552 0.219195i
\(672\) 29.6564 + 2.11409i 1.14402 + 0.0815527i
\(673\) 2.08333 + 3.60844i 0.0803066 + 0.139095i 0.903382 0.428838i \(-0.141077\pi\)
−0.823075 + 0.567933i \(0.807743\pi\)
\(674\) 27.3790i 1.05460i
\(675\) 3.23186 + 4.06879i 0.124394 + 0.156608i
\(676\) −4.04913 −0.155736
\(677\) 10.5329 + 18.2435i 0.404812 + 0.701155i 0.994300 0.106622i \(-0.0340035\pi\)
−0.589487 + 0.807778i \(0.700670\pi\)
\(678\) 0.293284 0.571161i 0.0112635 0.0219353i
\(679\) 0.809622 + 0.0979405i 0.0310705 + 0.00375861i
\(680\) −2.98743 1.72479i −0.114563 0.0661427i
\(681\) −33.7442 + 1.66224i −1.29308 + 0.0636970i
\(682\) −0.315944 + 0.182410i −0.0120981 + 0.00698485i
\(683\) 14.6226i 0.559518i 0.960070 + 0.279759i \(0.0902546\pi\)
−0.960070 + 0.279759i \(0.909745\pi\)
\(684\) −1.92369 19.4786i −0.0735541 0.744781i
\(685\) 12.6122i 0.481888i
\(686\) 5.46770 + 33.3629i 0.208758 + 1.27380i
\(687\) 33.5210 21.6195i 1.27891 0.824835i
\(688\) 4.25793 7.37495i 0.162332 0.281167i
\(689\) −13.6274 + 23.6034i −0.519164 + 0.899219i
\(690\) 7.57905 + 11.7513i 0.288530 + 0.447365i
\(691\) 9.11482 5.26245i 0.346744 0.200193i −0.316506 0.948590i \(-0.602510\pi\)
0.663250 + 0.748398i \(0.269176\pi\)
\(692\) 16.3683 0.622229
\(693\) 2.42258 + 4.41713i 0.0920262 + 0.167793i
\(694\) 18.8487 0.715486
\(695\) 4.86731 2.81014i 0.184628 0.106595i
\(696\) 0.242549 0.0119479i 0.00919378 0.000452884i
\(697\) 3.15046 5.45676i 0.119332 0.206690i
\(698\) −11.6103 + 20.1096i −0.439455 + 0.761159i
\(699\) 28.1196 + 14.4390i 1.06358 + 0.546134i
\(700\) −2.81891 2.11631i −0.106545 0.0799892i
\(701\) 22.2426i 0.840090i 0.907503 + 0.420045i \(0.137986\pi\)
−0.907503 + 0.420045i \(0.862014\pi\)
\(702\) 29.6107 4.40437i 1.11758 0.166232i
\(703\) 52.7915i 1.99107i
\(704\) −1.13474 + 0.655141i −0.0427670 + 0.0246916i
\(705\) 6.25163 12.1749i 0.235450 0.458532i
\(706\) 8.36944 + 4.83210i 0.314988 + 0.181858i
\(707\) −0.626858 + 5.18190i −0.0235754 + 0.194885i
\(708\) −35.2658 + 1.73719i −1.32537 + 0.0652874i
\(709\) 12.3741 + 21.4326i 0.464721 + 0.804920i 0.999189 0.0402687i \(-0.0128214\pi\)
−0.534468 + 0.845189i \(0.679488\pi\)
\(710\) −23.6843 −0.888856
\(711\) 16.1350 35.6358i 0.605109 1.33645i
\(712\) 13.5330i 0.507170i
\(713\) −0.696279 1.20599i −0.0260758 0.0451647i
\(714\) −13.2655 + 19.6096i −0.496448 + 0.733871i
\(715\) 1.00159 1.73481i 0.0374575 0.0648783i
\(716\) 5.31680 + 3.06966i 0.198698 + 0.114719i
\(717\) −26.9904 + 17.4075i −1.00798 + 0.650096i
\(718\) 25.8705 + 44.8090i 0.965477 + 1.67226i
\(719\) −26.6502 −0.993885 −0.496942 0.867784i \(-0.665544\pi\)
−0.496942 + 0.867784i \(0.665544\pi\)
\(720\) −8.54738 11.9212i −0.318542 0.444276i
\(721\) −16.6975 39.1422i −0.621848 1.45773i
\(722\) −7.87606 + 4.54725i −0.293117 + 0.169231i
\(723\) 0.609811 + 12.3795i 0.0226791 + 0.460398i
\(724\) 18.8486 + 10.8823i 0.700503 + 0.404436i
\(725\) −0.0996181 0.0575146i −0.00369973 0.00213604i
\(726\) 29.8061 + 15.3050i 1.10621 + 0.568022i
\(727\) −17.4130 + 10.0534i −0.645811 + 0.372859i −0.786850 0.617145i \(-0.788289\pi\)
0.141038 + 0.990004i \(0.454956\pi\)
\(728\) 9.36156 3.99351i 0.346962 0.148009i
\(729\) 25.8311 7.85825i 0.956709 0.291046i
\(730\) −11.7920 −0.436440
\(731\) 2.46455 + 4.26872i 0.0911545 + 0.157884i
\(732\) 21.2046 + 10.8883i 0.783746 + 0.402443i
\(733\) 2.85584 + 1.64882i 0.105483 + 0.0609005i 0.551813 0.833968i \(-0.313936\pi\)
−0.446331 + 0.894868i \(0.647269\pi\)
\(734\) 17.5686 30.4296i 0.648467 1.12318i
\(735\) 7.95031 9.15383i 0.293252 0.337644i
\(736\) −14.3470 24.8497i −0.528837 0.915972i
\(737\) 3.05402i 0.112496i
\(738\) 9.90862 7.10440i 0.364742 0.261517i
\(739\) 44.1618 1.62452 0.812259 0.583296i \(-0.198237\pi\)
0.812259 + 0.583296i \(0.198237\pi\)
\(740\) −7.18110 12.4380i −0.263983 0.457231i
\(741\) −14.5095 22.4970i −0.533019 0.826447i
\(742\) 5.00892 41.4061i 0.183883 1.52006i
\(743\) 15.6185 + 9.01733i 0.572986 + 0.330814i 0.758341 0.651858i \(-0.226010\pi\)
−0.185355 + 0.982672i \(0.559343\pi\)
\(744\) 0.360289 + 0.558629i 0.0132088 + 0.0204803i
\(745\) −10.8483 + 6.26327i −0.397451 + 0.229468i
\(746\) 1.06487i 0.0389876i
\(747\) 5.57051 12.3031i 0.203814 0.450145i
\(748\) 2.39324i 0.0875054i
\(749\) 16.0061 21.3200i 0.584849 0.779015i
\(750\) 0.155560 + 3.15796i 0.00568026 + 0.115312i
\(751\) 13.9337 24.1338i 0.508447 0.880655i −0.491505 0.870874i \(-0.663553\pi\)
0.999952 0.00978101i \(-0.00311344\pi\)
\(752\) −19.3180 + 33.4597i −0.704454 + 1.22015i
\(753\) 23.3851 45.5417i 0.852200 1.65963i
\(754\) −0.573927 + 0.331357i −0.0209012 + 0.0120673i
\(755\) −8.89418 −0.323692
\(756\) −15.6065 + 9.58718i −0.567603 + 0.348683i
\(757\) −15.4396 −0.561162 −0.280581 0.959830i \(-0.590527\pi\)
−0.280581 + 0.959830i \(0.590527\pi\)
\(758\) −21.7424 + 12.5530i −0.789721 + 0.455946i
\(759\) 2.22090 4.32514i 0.0806136 0.156993i
\(760\) −2.98449 + 5.16928i −0.108259 + 0.187510i
\(761\) 25.1763 43.6066i 0.912639 1.58074i 0.102318 0.994752i \(-0.467374\pi\)
0.810321 0.585986i \(-0.199293\pi\)
\(762\) −0.715994 14.5350i −0.0259377 0.526549i
\(763\) −30.1526 22.6372i −1.09160 0.819523i
\(764\) 32.3158i 1.16915i
\(765\) 8.44936 0.834453i 0.305487 0.0301697i
\(766\) 65.6680i 2.37268i
\(767\) −41.8212 + 24.1455i −1.51007 + 0.871842i
\(768\) 19.6549 + 30.4750i 0.709235 + 1.09967i
\(769\) 28.8897 + 16.6795i 1.04179 + 0.601478i 0.920340 0.391120i \(-0.127912\pi\)
0.121450 + 0.992598i \(0.461245\pi\)
\(770\) −0.368147 + 3.04328i −0.0132671 + 0.109672i
\(771\) −8.14580 12.6301i −0.293364 0.454861i
\(772\) −8.74888 15.1535i −0.314879 0.545387i
\(773\) −5.27400 −0.189693 −0.0948463 0.995492i \(-0.530236\pi\)
−0.0948463 + 0.995492i \(0.530236\pi\)
\(774\) 0.937390 + 9.49166i 0.0336938 + 0.341171i
\(775\) 0.314871i 0.0113105i
\(776\) 0.187852 + 0.325368i 0.00674348 + 0.0116800i
\(777\) 44.4300 21.5956i 1.59392 0.774739i
\(778\) 1.59978 2.77090i 0.0573549 0.0993415i
\(779\) −9.44209 5.45139i −0.338298 0.195316i
\(780\) 6.47875 + 3.32675i 0.231976 + 0.119117i
\(781\) 4.11750 + 7.13173i 0.147336 + 0.255193i
\(782\) 22.8488 0.817070
\(783\) −0.468030 + 0.371758i −0.0167260 + 0.0132856i
\(784\) −23.6879 + 24.7057i −0.845998 + 0.882347i
\(785\) 1.47404 0.851038i 0.0526108 0.0303748i
\(786\) −4.24900 2.18181i −0.151557 0.0778225i
\(787\) −9.49824 5.48381i −0.338576 0.195477i 0.321066 0.947057i \(-0.395959\pi\)
−0.659642 + 0.751580i \(0.729292\pi\)
\(788\) 4.34767 + 2.51013i 0.154879 + 0.0894196i
\(789\) 0.571962 + 11.6111i 0.0203624 + 0.413367i
\(790\) 20.6140 11.9015i 0.733413 0.423436i
\(791\) 0.210812 + 0.494183i 0.00749559 + 0.0175711i
\(792\) −0.957283 + 2.11426i −0.0340156 + 0.0751270i
\(793\) 32.6012 1.15770
\(794\) 4.74172 + 8.21290i 0.168277 + 0.291465i
\(795\) −12.5699 + 8.10700i −0.445809 + 0.287526i
\(796\) −21.7697 12.5687i −0.771606 0.445487i
\(797\) 25.1385 43.5412i 0.890452 1.54231i 0.0511176 0.998693i \(-0.483722\pi\)
0.839334 0.543615i \(-0.182945\pi\)
\(798\) 33.9314 + 22.9539i 1.20116 + 0.812558i
\(799\) −11.1815 19.3669i −0.395573 0.685153i
\(800\) 6.48799i 0.229385i
\(801\) 19.4088 + 27.0698i 0.685776 + 0.956463i
\(802\) 51.3805 1.81431
\(803\) 2.05003 + 3.55075i 0.0723439 + 0.125303i
\(804\) 11.0900 0.546291i 0.391114 0.0192662i
\(805\) −11.6165 1.40525i −0.409428 0.0495287i
\(806\) −1.57102 0.907028i −0.0553368 0.0319487i
\(807\) −5.62054 + 10.9458i −0.197852 + 0.385312i
\(808\) −2.08249 + 1.20232i −0.0732616 + 0.0422976i
\(809\) 35.3803i 1.24391i 0.783055 + 0.621953i \(0.213661\pi\)
−0.783055 + 0.621953i \(0.786339\pi\)
\(810\) 15.5600 + 5.27271i 0.546724 + 0.185264i
\(811\) 3.52553i 0.123798i −0.998082 0.0618991i \(-0.980284\pi\)
0.998082 0.0618991i \(-0.0197157\pi\)
\(812\) 0.243438 0.324257i 0.00854299 0.0113792i
\(813\) 38.4301 + 19.7334i 1.34780 + 0.692079i
\(814\) −6.24507 + 10.8168i −0.218890 + 0.379128i
\(815\) 9.44753 16.3636i 0.330933 0.573192i
\(816\) −23.9396 + 1.17926i −0.838052 + 0.0412823i
\(817\) 7.38636 4.26452i 0.258416 0.149197i
\(818\) −64.0294 −2.23873
\(819\) −12.9983 + 21.4143i −0.454198 + 0.748277i
\(820\) 2.96616 0.103583
\(821\) −6.40672 + 3.69892i −0.223596 + 0.129093i −0.607614 0.794232i \(-0.707873\pi\)
0.384018 + 0.923326i \(0.374540\pi\)
\(822\) −21.6135 33.5118i −0.753858 1.16886i
\(823\) −0.413321 + 0.715893i −0.0144075 + 0.0249545i −0.873139 0.487471i \(-0.837920\pi\)
0.858732 + 0.512425i \(0.171253\pi\)
\(824\) 9.80227 16.9780i 0.341478 0.591458i
\(825\) 0.923868 0.595851i 0.0321649 0.0207449i
\(826\) 44.3681 59.0979i 1.54376 2.05628i
\(827\) 4.54802i 0.158150i 0.996869 + 0.0790750i \(0.0251967\pi\)
−0.996869 + 0.0790750i \(0.974803\pi\)
\(828\) 16.1030 + 7.29105i 0.559619 + 0.253381i
\(829\) 5.00576i 0.173857i 0.996215 + 0.0869286i \(0.0277052\pi\)
−0.996215 + 0.0869286i \(0.972295\pi\)
\(830\) 7.11686 4.10892i 0.247030 0.142623i
\(831\) −12.7809 + 0.629583i −0.443363 + 0.0218400i
\(832\) −5.64244 3.25766i −0.195616 0.112939i
\(833\) −5.52872 19.0240i −0.191559 0.659142i
\(834\) 8.11715 15.8079i 0.281074 0.547383i
\(835\) −6.20475 10.7469i −0.214724 0.371913i
\(836\) −4.14113 −0.143224
\(837\) −1.52186 0.600693i −0.0526030 0.0207630i
\(838\) 19.8010i 0.684013i
\(839\) 7.84346 + 13.5853i 0.270786 + 0.469016i 0.969063 0.246812i \(-0.0793829\pi\)
−0.698277 + 0.715828i \(0.746050\pi\)
\(840\) 5.57141 + 0.397164i 0.192232 + 0.0137035i
\(841\) −14.4934 + 25.1033i −0.499772 + 0.865630i
\(842\) 32.7886 + 18.9305i 1.12997 + 0.652389i
\(843\) 0.449113 + 9.11723i 0.0154683 + 0.314014i
\(844\) −17.3070 29.9765i −0.595730 1.03184i
\(845\) −3.03922 −0.104552
\(846\) −4.25288 43.0631i −0.146217 1.48054i
\(847\) −25.7889 + 11.0012i −0.886119 + 0.378006i
\(848\) 36.5679 21.1125i 1.25575 0.725006i
\(849\) 33.3264 21.4939i 1.14376 0.737669i
\(850\) 4.47417 + 2.58316i 0.153463 + 0.0886018i
\(851\) −41.2888 23.8381i −1.41536 0.817159i
\(852\) −25.1608 + 16.2275i −0.861993 + 0.555945i
\(853\) 20.9096 12.0722i 0.715931 0.413343i −0.0973224 0.995253i \(-0.531028\pi\)
0.813253 + 0.581910i \(0.197694\pi\)
\(854\) −45.8884 + 19.5754i −1.57027 + 0.669855i
\(855\) −1.44389 14.6203i −0.0493801 0.500004i
\(856\) 12.2818 0.419783
\(857\) −16.3837 28.3774i −0.559657 0.969354i −0.997525 0.0703148i \(-0.977600\pi\)
0.437868 0.899039i \(-0.355734\pi\)
\(858\) −0.311617 6.32598i −0.0106384 0.215965i
\(859\) −17.9251 10.3490i −0.611595 0.353105i 0.161994 0.986792i \(-0.448207\pi\)
−0.773589 + 0.633687i \(0.781541\pi\)
\(860\) −1.16018 + 2.00950i −0.0395620 + 0.0685234i
\(861\) −0.725450 + 10.1766i −0.0247233 + 0.346818i
\(862\) 9.15679 + 15.8600i 0.311881 + 0.540194i
\(863\) 21.0272i 0.715774i −0.933765 0.357887i \(-0.883497\pi\)
0.933765 0.357887i \(-0.116503\pi\)
\(864\) −31.3582 12.3774i −1.06683 0.421089i
\(865\) 12.2858 0.417729
\(866\) −10.8834 18.8507i −0.369834 0.640572i
\(867\) −7.11286 + 13.8521i −0.241565 + 0.470441i
\(868\) 1.10186 + 0.133293i 0.0373996 + 0.00452425i
\(869\) −7.16747 4.13814i −0.243140 0.140377i
\(870\) −0.363257 + 0.0178940i −0.0123156 + 0.000606662i
\(871\) 13.1515 7.59300i 0.445620 0.257279i
\(872\) 17.3700i 0.588222i
\(873\) −0.842394 0.381414i −0.0285107 0.0129089i
\(874\) 39.5363i 1.33733i
\(875\) −2.11583 1.58847i −0.0715282 0.0537002i
\(876\) −12.5271 + 8.07936i −0.423250 + 0.272976i
\(877\) −1.25552 + 2.17463i −0.0423960 + 0.0734320i −0.886445 0.462834i \(-0.846832\pi\)
0.844049 + 0.536266i \(0.180166\pi\)
\(878\) 22.9907 39.8211i 0.775900 1.34390i
\(879\) 23.0188 + 35.6907i 0.776405 + 1.20382i
\(880\) −2.68768 + 1.55173i −0.0906016 + 0.0523089i
\(881\) 24.5031 0.825531 0.412766 0.910837i \(-0.364563\pi\)
0.412766 + 0.910837i \(0.364563\pi\)
\(882\) 5.43781 37.9470i 0.183100 1.27774i
\(883\) −40.4938 −1.36273 −0.681363 0.731945i \(-0.738613\pi\)
−0.681363 + 0.731945i \(0.738613\pi\)
\(884\) 10.3059 5.95014i 0.346626 0.200125i
\(885\) −26.4700 + 1.30391i −0.889778 + 0.0438303i
\(886\) 20.2458 35.0667i 0.680171 1.17809i
\(887\) −12.4282 + 21.5262i −0.417297 + 0.722779i −0.995667 0.0929957i \(-0.970356\pi\)
0.578370 + 0.815775i \(0.303689\pi\)
\(888\) 20.2452 + 10.3956i 0.679383 + 0.348854i
\(889\) 9.73849 + 7.31123i 0.326619 + 0.245211i
\(890\) 20.2679i 0.679382i
\(891\) −1.11740 5.60203i −0.0374345 0.187675i
\(892\) 30.8851i 1.03411i
\(893\) −33.5115 + 19.3479i −1.12142 + 0.647452i
\(894\) −18.0916 + 35.2328i −0.605072 + 1.17836i
\(895\) 3.99071 + 2.30404i 0.133395 + 0.0770155i
\(896\) −24.1845 2.92562i −0.807948 0.0977380i
\(897\) 24.1469 1.18947i 0.806242 0.0397154i
\(898\) −22.2010 38.4532i −0.740856 1.28320i
\(899\) 0.0362193 0.00120798
\(900\) 2.32896 + 3.24824i 0.0776319 + 0.108275i
\(901\) 24.4404i 0.814227i
\(902\) −1.28977 2.23394i −0.0429445 0.0743821i
\(903\) −6.61065 4.47196i −0.219989 0.148817i
\(904\) −0.123757 + 0.214353i −0.00411610 + 0.00712929i
\(905\) 14.1475 + 8.16805i 0.470278 + 0.271515i
\(906\) −23.6326 + 15.2419i −0.785142 + 0.506379i
\(907\) 7.71147 + 13.3567i 0.256055 + 0.443500i 0.965182 0.261581i \(-0.0842438\pi\)
−0.709127 + 0.705081i \(0.750911\pi\)
\(908\) −25.9876 −0.862428
\(909\) 2.44120 5.39165i 0.0809695 0.178830i
\(910\) −14.0205 + 5.98094i −0.464775 + 0.198266i
\(911\) −22.9764 + 13.2654i −0.761243 + 0.439504i −0.829742 0.558148i \(-0.811512\pi\)
0.0684992 + 0.997651i \(0.478179\pi\)
\(912\) 2.04052 + 41.4237i 0.0675685 + 1.37168i
\(913\) −2.47453 1.42867i −0.0818948 0.0472820i
\(914\) −21.6294 12.4877i −0.715436 0.413057i
\(915\) 15.9159 + 8.17259i 0.526163 + 0.270178i
\(916\) 26.5714 15.3410i 0.877943 0.506881i
\(917\) 3.67634 1.56828i 0.121404 0.0517891i
\(918\) 21.0207 16.6969i 0.693787 0.551078i
\(919\) −14.6707 −0.483943 −0.241972 0.970283i \(-0.577794\pi\)
−0.241972 + 0.970283i \(0.577794\pi\)
\(920\) −2.69530 4.66840i −0.0888615 0.153913i
\(921\) 36.8396 + 18.9166i 1.21390 + 0.623324i
\(922\) 44.1461 + 25.4877i 1.45387 + 0.839394i
\(923\) −20.4741 + 35.4622i −0.673914 + 1.16725i
\(924\) 1.69403 + 3.48523i 0.0557295 + 0.114656i
\(925\) −5.39002 9.33580i −0.177223 0.306959i
\(926\) 18.9662i 0.623267i
\(927\) 4.74233 + 48.0191i 0.155759 + 1.57715i
\(928\) 0.746307 0.0244987
\(929\) 5.60554 + 9.70909i 0.183912 + 0.318545i 0.943209 0.332199i \(-0.107791\pi\)
−0.759297 + 0.650744i \(0.774457\pi\)
\(930\) −0.539593 0.836640i −0.0176940 0.0274345i
\(931\) −32.9181 + 9.56659i −1.07885 + 0.313532i
\(932\) 21.0570 + 12.1572i 0.689744 + 0.398224i
\(933\) 22.4924 + 34.8745i 0.736368 + 1.14174i
\(934\) −21.1802 + 12.2284i −0.693037 + 0.400125i
\(935\) 1.79633i 0.0587462i
\(936\) −11.4846 + 1.13421i −0.375387 + 0.0370729i
\(937\) 9.04669i 0.295543i −0.989022 0.147771i \(-0.952790\pi\)
0.989022 0.147771i \(-0.0472099\pi\)
\(938\) −13.9524 + 18.5845i −0.455561 + 0.606804i
\(939\) −1.99705 40.5411i −0.0651713 1.32301i
\(940\) 5.26369 9.11698i 0.171683 0.297363i
\(941\) −25.3643 + 43.9322i −0.826851 + 1.43215i 0.0736454 + 0.997284i \(0.476537\pi\)
−0.900496 + 0.434863i \(0.856797\pi\)
\(942\) 2.45824 4.78734i 0.0800937 0.155980i
\(943\) 8.52719 4.92317i 0.277683 0.160321i
\(944\) 74.8153 2.43503
\(945\) −11.7140 + 7.19599i −0.381056 + 0.234086i
\(946\) 2.01792 0.0656082
\(947\) −7.30505 + 4.21757i −0.237382 + 0.137053i −0.613973 0.789327i \(-0.710430\pi\)
0.376591 + 0.926380i \(0.377096\pi\)
\(948\) 13.7446 26.7673i 0.446405 0.869361i
\(949\) −10.1937 + 17.6560i −0.330901 + 0.573137i
\(950\) 4.46977 7.74186i 0.145018 0.251179i
\(951\) −0.00611281 0.124093i −0.000198222 0.00402400i
\(952\) 5.47957 7.29874i 0.177594 0.236554i
\(953\) 7.58700i 0.245767i 0.992421 + 0.122884i \(0.0392142\pi\)
−0.992421 + 0.122884i \(0.960786\pi\)
\(954\) −19.5065 + 43.0821i −0.631545 + 1.39483i
\(955\) 24.2558i 0.784898i
\(956\) −21.3947 + 12.3522i −0.691953 + 0.399500i
\(957\) 0.0685402 + 0.106272i 0.00221559 + 0.00343528i
\(958\) 9.76873 + 5.63998i 0.315613 + 0.182219i
\(959\) 33.1273 + 4.00743i 1.06974 + 0.129407i
\(960\) −1.93799 3.00486i −0.0625484 0.0969814i
\(961\) −15.4504 26.7609i −0.498401 0.863256i
\(962\) −62.1068 −2.00240
\(963\) −24.5670 + 17.6143i −0.791661 + 0.567614i
\(964\) 9.53385i 0.307065i
\(965\) −6.56678 11.3740i −0.211392 0.366142i
\(966\) −33.2743 + 16.1733i −1.07058 + 0.520366i
\(967\) 10.2508 17.7549i 0.329643 0.570958i −0.652798 0.757532i \(-0.726405\pi\)
0.982441 + 0.186574i \(0.0597383\pi\)
\(968\) −11.1860 6.45826i −0.359533 0.207576i
\(969\) −21.3549 10.9654i −0.686018 0.352261i
\(970\) −0.281339 0.487293i −0.00903325 0.0156460i
\(971\) 14.4194 0.462741 0.231370 0.972866i \(-0.425679\pi\)
0.231370 + 0.972866i \(0.425679\pi\)
\(972\) 20.1427 5.05968i 0.646076 0.162289i
\(973\) 5.83458 + 13.6774i 0.187048 + 0.438477i
\(974\) 17.5366 10.1248i 0.561909 0.324418i
\(975\) 4.86285 + 2.49701i 0.155736 + 0.0799683i
\(976\) −43.7410 25.2539i −1.40012 0.808357i
\(977\) −7.27578 4.20067i −0.232773 0.134391i 0.379078 0.925365i \(-0.376241\pi\)
−0.611851 + 0.790973i \(0.709575\pi\)
\(978\) −2.93932 59.6698i −0.0939892 1.90803i
\(979\) 6.10300 3.52357i 0.195053 0.112614i
\(980\) 6.45440 6.73172i 0.206178 0.215037i
\(981\) 24.9118 + 34.7449i 0.795372 + 1.10932i
\(982\) −1.63990 −0.0523312
\(983\) −1.36690 2.36754i −0.0435973 0.0755127i 0.843403 0.537281i \(-0.180549\pi\)
−0.887001 + 0.461768i \(0.847215\pi\)
\(984\) −3.94989 + 2.54749i −0.125918 + 0.0812112i
\(985\) 3.26329 + 1.88406i 0.103977 + 0.0600312i
\(986\) −0.297139 + 0.514660i −0.00946283 + 0.0163901i
\(987\) 29.9921 + 20.2890i 0.954660 + 0.645806i
\(988\) −10.2958 17.8328i −0.327553 0.567338i
\(989\) 7.70261i 0.244929i
\(990\) 1.43369 3.16646i 0.0455657 0.100637i
\(991\) −42.1641 −1.33939 −0.669693 0.742638i \(-0.733574\pi\)
−0.669693 + 0.742638i \(0.733574\pi\)
\(992\) 1.02144 + 1.76918i 0.0324307 + 0.0561716i
\(993\) 18.3471 0.903775i 0.582228 0.0286804i
\(994\) 7.52549 62.2092i 0.238694 1.97316i
\(995\) −16.3400 9.43389i −0.518012 0.299075i
\(996\) 4.74526 9.24124i 0.150359 0.292820i
\(997\) −27.5027 + 15.8787i −0.871019 + 0.502883i −0.867687 0.497111i \(-0.834394\pi\)
−0.00333236 + 0.999994i \(0.501061\pi\)
\(998\) 62.3038i 1.97219i
\(999\) −55.4052 + 8.24112i −1.75294 + 0.260738i
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 315.2.bl.i.41.9 24
3.2 odd 2 945.2.bl.i.881.4 24
7.6 odd 2 315.2.bl.j.41.9 yes 24
9.2 odd 6 315.2.bl.j.146.9 yes 24
9.7 even 3 945.2.bl.j.251.4 24
21.20 even 2 945.2.bl.j.881.4 24
63.20 even 6 inner 315.2.bl.i.146.9 yes 24
63.34 odd 6 945.2.bl.i.251.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bl.i.41.9 24 1.1 even 1 trivial
315.2.bl.i.146.9 yes 24 63.20 even 6 inner
315.2.bl.j.41.9 yes 24 7.6 odd 2
315.2.bl.j.146.9 yes 24 9.2 odd 6
945.2.bl.i.251.4 24 63.34 odd 6
945.2.bl.i.881.4 24 3.2 odd 2
945.2.bl.j.251.4 24 9.7 even 3
945.2.bl.j.881.4 24 21.20 even 2