Properties

Label 429.2.n.d.235.7
Level $429$
Weight $2$
Character 429.235
Analytic conductor $3.426$
Analytic rank $0$
Dimension $36$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), degree \(4\), 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: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 235.7
Character \(\chi\) \(=\) 429.235
Dual form 429.2.n.d.157.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.30744 + 0.949910i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.189034 + 0.581786i) q^{4} +(1.69854 - 1.23406i) q^{5} +(1.30744 - 0.949910i) q^{6} +(1.36281 + 4.19429i) q^{7} +(0.693300 - 2.13376i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.30744 + 0.949910i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.189034 + 0.581786i) q^{4} +(1.69854 - 1.23406i) q^{5} +(1.30744 - 0.949910i) q^{6} +(1.36281 + 4.19429i) q^{7} +(0.693300 - 2.13376i) q^{8} +(-0.809017 - 0.587785i) q^{9} +3.39298 q^{10} +(-3.28357 + 0.467064i) q^{11} +0.611726 q^{12} +(0.809017 + 0.587785i) q^{13} +(-2.20241 + 6.77832i) q^{14} +(-0.648783 - 1.99675i) q^{15} +(3.92312 - 2.85031i) q^{16} +(5.73404 - 4.16602i) q^{17} +(-0.499397 - 1.53699i) q^{18} +(0.292494 - 0.900203i) q^{19} +(1.03904 + 0.754906i) q^{20} +4.41014 q^{21} +(-4.73674 - 2.50844i) q^{22} -4.97977 q^{23} +(-1.81508 - 1.31874i) q^{24} +(-0.182961 + 0.563098i) q^{25} +(0.499397 + 1.53699i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.18256 + 1.58572i) q^{28} +(1.54168 + 4.74480i) q^{29} +(1.04849 - 3.22691i) q^{30} +(-6.38023 - 4.63551i) q^{31} +3.34965 q^{32} +(-0.570475 + 3.26719i) q^{33} +11.4543 q^{34} +(7.49077 + 5.44237i) q^{35} +(0.189034 - 0.581786i) q^{36} +(2.40088 + 7.38914i) q^{37} +(1.23753 - 0.899118i) q^{38} +(0.809017 - 0.587785i) q^{39} +(-1.45559 - 4.47984i) q^{40} +(-0.153644 + 0.472869i) q^{41} +(5.76598 + 4.18923i) q^{42} -11.1839 q^{43} +(-0.892438 - 1.82205i) q^{44} -2.09951 q^{45} +(-6.51075 - 4.73034i) q^{46} +(0.374620 - 1.15296i) q^{47} +(-1.49850 - 4.61190i) q^{48} +(-10.0717 + 7.31752i) q^{49} +(-0.774103 + 0.562419i) q^{50} +(-2.19021 - 6.74077i) q^{51} +(-0.189034 + 0.581786i) q^{52} +(-0.886832 - 0.644321i) q^{53} -1.61608 q^{54} +(-5.00088 + 4.84545i) q^{55} +9.89444 q^{56} +(-0.765759 - 0.556356i) q^{57} +(-2.49148 + 7.66799i) q^{58} +(-0.0285215 - 0.0877803i) q^{59} +(1.03904 - 0.754906i) q^{60} +(-7.82276 + 5.68357i) q^{61} +(-3.93845 - 12.1213i) q^{62} +(1.36281 - 4.19429i) q^{63} +(-3.46678 - 2.51876i) q^{64} +2.09951 q^{65} +(-3.84940 + 3.72976i) q^{66} +8.50741 q^{67} +(3.50766 + 2.54847i) q^{68} +(-1.53883 + 4.73604i) q^{69} +(4.62397 + 14.2311i) q^{70} +(-13.0623 + 9.49035i) q^{71} +(-1.81508 + 1.31874i) q^{72} +(-0.962901 - 2.96350i) q^{73} +(-3.88002 + 11.9415i) q^{74} +(0.478999 + 0.348013i) q^{75} +0.579017 q^{76} +(-6.43388 - 13.1357i) q^{77} +1.61608 q^{78} +(-1.97455 - 1.43459i) q^{79} +(3.14611 - 9.68272i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.650064 + 0.472299i) q^{82} +(11.1230 - 8.08132i) q^{83} +(0.833665 + 2.56576i) q^{84} +(4.59835 - 14.1523i) q^{85} +(-14.6222 - 10.6237i) q^{86} +4.98898 q^{87} +(-1.27990 + 7.33017i) q^{88} +7.34531 q^{89} +(-2.74498 - 1.99434i) q^{90} +(-1.36281 + 4.19429i) q^{91} +(-0.941345 - 2.89716i) q^{92} +(-6.38023 + 4.63551i) q^{93} +(1.58500 - 1.15157i) q^{94} +(-0.614092 - 1.88998i) q^{95} +(1.03510 - 3.18571i) q^{96} +(6.01556 + 4.37056i) q^{97} -20.1191 q^{98} +(2.93100 + 1.55217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30744 + 0.949910i 0.924499 + 0.671688i 0.944640 0.328109i \(-0.106411\pi\)
−0.0201407 + 0.999797i \(0.506411\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0.189034 + 0.581786i 0.0945169 + 0.290893i
\(5\) 1.69854 1.23406i 0.759608 0.551888i −0.139182 0.990267i \(-0.544447\pi\)
0.898790 + 0.438379i \(0.144447\pi\)
\(6\) 1.30744 0.949910i 0.533760 0.387799i
\(7\) 1.36281 + 4.19429i 0.515093 + 1.58529i 0.783113 + 0.621879i \(0.213630\pi\)
−0.268021 + 0.963413i \(0.586370\pi\)
\(8\) 0.693300 2.13376i 0.245119 0.754398i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 3.39298 1.07295
\(11\) −3.28357 + 0.467064i −0.990034 + 0.140825i
\(12\) 0.611726 0.176590
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i
\(14\) −2.20241 + 6.77832i −0.588619 + 1.81158i
\(15\) −0.648783 1.99675i −0.167515 0.515558i
\(16\) 3.92312 2.85031i 0.980780 0.712578i
\(17\) 5.73404 4.16602i 1.39071 1.01041i 0.394922 0.918715i \(-0.370772\pi\)
0.995787 0.0916944i \(-0.0292283\pi\)
\(18\) −0.499397 1.53699i −0.117709 0.362271i
\(19\) 0.292494 0.900203i 0.0671027 0.206521i −0.911883 0.410451i \(-0.865371\pi\)
0.978986 + 0.203930i \(0.0653714\pi\)
\(20\) 1.03904 + 0.754906i 0.232336 + 0.168802i
\(21\) 4.41014 0.962371
\(22\) −4.73674 2.50844i −1.00988 0.534801i
\(23\) −4.97977 −1.03835 −0.519177 0.854667i \(-0.673762\pi\)
−0.519177 + 0.854667i \(0.673762\pi\)
\(24\) −1.81508 1.31874i −0.370502 0.269186i
\(25\) −0.182961 + 0.563098i −0.0365923 + 0.112620i
\(26\) 0.499397 + 1.53699i 0.0979399 + 0.301428i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −2.18256 + 1.58572i −0.412466 + 0.299674i
\(29\) 1.54168 + 4.74480i 0.286282 + 0.881087i 0.986011 + 0.166678i \(0.0533041\pi\)
−0.699729 + 0.714409i \(0.746696\pi\)
\(30\) 1.04849 3.22691i 0.191427 0.589151i
\(31\) −6.38023 4.63551i −1.14592 0.832562i −0.157990 0.987441i \(-0.550501\pi\)
−0.987934 + 0.154878i \(0.950501\pi\)
\(32\) 3.34965 0.592140
\(33\) −0.570475 + 3.26719i −0.0993070 + 0.568746i
\(34\) 11.4543 1.96439
\(35\) 7.49077 + 5.44237i 1.26617 + 0.919928i
\(36\) 0.189034 0.581786i 0.0315056 0.0969644i
\(37\) 2.40088 + 7.38914i 0.394702 + 1.21477i 0.929193 + 0.369594i \(0.120503\pi\)
−0.534492 + 0.845174i \(0.679497\pi\)
\(38\) 1.23753 0.899118i 0.200754 0.145856i
\(39\) 0.809017 0.587785i 0.129546 0.0941210i
\(40\) −1.45559 4.47984i −0.230149 0.708325i
\(41\) −0.153644 + 0.472869i −0.0239952 + 0.0738497i −0.962337 0.271859i \(-0.912362\pi\)
0.938342 + 0.345709i \(0.112362\pi\)
\(42\) 5.76598 + 4.18923i 0.889711 + 0.646413i
\(43\) −11.1839 −1.70553 −0.852763 0.522298i \(-0.825075\pi\)
−0.852763 + 0.522298i \(0.825075\pi\)
\(44\) −0.892438 1.82205i −0.134540 0.274684i
\(45\) −2.09951 −0.312976
\(46\) −6.51075 4.73034i −0.959958 0.697450i
\(47\) 0.374620 1.15296i 0.0546439 0.168177i −0.920010 0.391895i \(-0.871820\pi\)
0.974654 + 0.223718i \(0.0718196\pi\)
\(48\) −1.49850 4.61190i −0.216290 0.665671i
\(49\) −10.0717 + 7.31752i −1.43881 + 1.04536i
\(50\) −0.774103 + 0.562419i −0.109475 + 0.0795380i
\(51\) −2.19021 6.74077i −0.306691 0.943896i
\(52\) −0.189034 + 0.581786i −0.0262143 + 0.0806792i
\(53\) −0.886832 0.644321i −0.121816 0.0885043i 0.525209 0.850973i \(-0.323987\pi\)
−0.647025 + 0.762469i \(0.723987\pi\)
\(54\) −1.61608 −0.219921
\(55\) −5.00088 + 4.84545i −0.674319 + 0.653360i
\(56\) 9.89444 1.32220
\(57\) −0.765759 0.556356i −0.101427 0.0736912i
\(58\) −2.49148 + 7.66799i −0.327147 + 1.00686i
\(59\) −0.0285215 0.0877803i −0.00371319 0.0114280i 0.949183 0.314725i \(-0.101912\pi\)
−0.952896 + 0.303297i \(0.901912\pi\)
\(60\) 1.03904 0.754906i 0.134139 0.0974579i
\(61\) −7.82276 + 5.68357i −1.00160 + 0.727706i −0.962431 0.271526i \(-0.912472\pi\)
−0.0391708 + 0.999233i \(0.512472\pi\)
\(62\) −3.93845 12.1213i −0.500183 1.53941i
\(63\) 1.36281 4.19429i 0.171698 0.528431i
\(64\) −3.46678 2.51876i −0.433347 0.314845i
\(65\) 2.09951 0.260412
\(66\) −3.84940 + 3.72976i −0.473829 + 0.459101i
\(67\) 8.50741 1.03935 0.519673 0.854365i \(-0.326054\pi\)
0.519673 + 0.854365i \(0.326054\pi\)
\(68\) 3.50766 + 2.54847i 0.425366 + 0.309047i
\(69\) −1.53883 + 4.73604i −0.185254 + 0.570153i
\(70\) 4.62397 + 14.2311i 0.552670 + 1.70094i
\(71\) −13.0623 + 9.49035i −1.55022 + 1.12630i −0.606718 + 0.794917i \(0.707514\pi\)
−0.943497 + 0.331380i \(0.892486\pi\)
\(72\) −1.81508 + 1.31874i −0.213910 + 0.155414i
\(73\) −0.962901 2.96350i −0.112699 0.346852i 0.878761 0.477262i \(-0.158371\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(74\) −3.88002 + 11.9415i −0.451043 + 1.38817i
\(75\) 0.478999 + 0.348013i 0.0553101 + 0.0401851i
\(76\) 0.579017 0.0664178
\(77\) −6.43388 13.1357i −0.733209 1.49696i
\(78\) 1.61608 0.182985
\(79\) −1.97455 1.43459i −0.222154 0.161404i 0.471142 0.882057i \(-0.343842\pi\)
−0.693296 + 0.720653i \(0.743842\pi\)
\(80\) 3.14611 9.68272i 0.351745 1.08256i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −0.650064 + 0.472299i −0.0717875 + 0.0521567i
\(83\) 11.1230 8.08132i 1.22091 0.887040i 0.224731 0.974421i \(-0.427850\pi\)
0.996175 + 0.0873803i \(0.0278495\pi\)
\(84\) 0.833665 + 2.56576i 0.0909603 + 0.279947i
\(85\) 4.59835 14.1523i 0.498762 1.53503i
\(86\) −14.6222 10.6237i −1.57676 1.14558i
\(87\) 4.98898 0.534874
\(88\) −1.27990 + 7.33017i −0.136438 + 0.781399i
\(89\) 7.34531 0.778601 0.389301 0.921111i \(-0.372717\pi\)
0.389301 + 0.921111i \(0.372717\pi\)
\(90\) −2.74498 1.99434i −0.289346 0.210222i
\(91\) −1.36281 + 4.19429i −0.142861 + 0.439681i
\(92\) −0.941345 2.89716i −0.0981420 0.302050i
\(93\) −6.38023 + 4.63551i −0.661599 + 0.480680i
\(94\) 1.58500 1.15157i 0.163480 0.118776i
\(95\) −0.614092 1.88998i −0.0630045 0.193908i
\(96\) 1.03510 3.18571i 0.105644 0.325140i
\(97\) 6.01556 + 4.37056i 0.610787 + 0.443763i 0.849691 0.527280i \(-0.176788\pi\)
−0.238904 + 0.971043i \(0.576788\pi\)
\(98\) −20.1191 −2.03234
\(99\) 2.93100 + 1.55217i 0.294577 + 0.155999i
\(100\) −0.362188 −0.0362188
\(101\) −6.34482 4.60978i −0.631333 0.458690i 0.225529 0.974237i \(-0.427589\pi\)
−0.856862 + 0.515546i \(0.827589\pi\)
\(102\) 3.53956 10.8936i 0.350469 1.07863i
\(103\) −3.60560 11.0969i −0.355270 1.09341i −0.955852 0.293847i \(-0.905064\pi\)
0.600582 0.799563i \(-0.294936\pi\)
\(104\) 1.81508 1.31874i 0.177984 0.129313i
\(105\) 7.49077 5.44237i 0.731025 0.531121i
\(106\) −0.547432 1.68482i −0.0531712 0.163644i
\(107\) 0.413186 1.27166i 0.0399442 0.122936i −0.929096 0.369839i \(-0.879413\pi\)
0.969040 + 0.246903i \(0.0794129\pi\)
\(108\) −0.494897 0.359564i −0.0476215 0.0345990i
\(109\) 3.08747 0.295726 0.147863 0.989008i \(-0.452761\pi\)
0.147863 + 0.989008i \(0.452761\pi\)
\(110\) −11.1411 + 1.58474i −1.06226 + 0.151099i
\(111\) 7.76940 0.737439
\(112\) 17.3015 + 12.5703i 1.63484 + 1.18778i
\(113\) 1.30386 4.01288i 0.122657 0.377500i −0.870810 0.491620i \(-0.836405\pi\)
0.993467 + 0.114120i \(0.0364048\pi\)
\(114\) −0.472694 1.45480i −0.0442719 0.136255i
\(115\) −8.45832 + 6.14533i −0.788743 + 0.573055i
\(116\) −2.46903 + 1.79385i −0.229244 + 0.166555i
\(117\) −0.309017 0.951057i −0.0285686 0.0879252i
\(118\) 0.0460932 0.141860i 0.00424322 0.0130593i
\(119\) 25.2879 + 18.3727i 2.31814 + 1.68423i
\(120\) −4.71038 −0.429997
\(121\) 10.5637 3.06728i 0.960337 0.278844i
\(122\) −15.6267 −1.41477
\(123\) 0.402246 + 0.292249i 0.0362693 + 0.0263512i
\(124\) 1.49080 4.58820i 0.133877 0.412033i
\(125\) 3.62804 + 11.1660i 0.324502 + 0.998715i
\(126\) 5.76598 4.18923i 0.513675 0.373207i
\(127\) −8.47569 + 6.15795i −0.752095 + 0.546429i −0.896476 0.443093i \(-0.853881\pi\)
0.144380 + 0.989522i \(0.453881\pi\)
\(128\) −4.21020 12.9577i −0.372133 1.14531i
\(129\) −3.45601 + 10.6365i −0.304285 + 0.936492i
\(130\) 2.74498 + 1.99434i 0.240750 + 0.174915i
\(131\) 1.45244 0.126901 0.0634503 0.997985i \(-0.479790\pi\)
0.0634503 + 0.997985i \(0.479790\pi\)
\(132\) −2.00865 + 0.285715i −0.174830 + 0.0248683i
\(133\) 4.17433 0.361960
\(134\) 11.1229 + 8.08127i 0.960874 + 0.698116i
\(135\) −0.648783 + 1.99675i −0.0558383 + 0.171853i
\(136\) −4.91388 15.1234i −0.421362 1.29682i
\(137\) 15.7711 11.4584i 1.34742 0.978958i 0.348285 0.937389i \(-0.386764\pi\)
0.999136 0.0415692i \(-0.0132357\pi\)
\(138\) −6.51075 + 4.73034i −0.554232 + 0.402673i
\(139\) 2.99391 + 9.21432i 0.253940 + 0.781548i 0.994037 + 0.109047i \(0.0347799\pi\)
−0.740096 + 0.672501i \(0.765220\pi\)
\(140\) −1.75028 + 5.38682i −0.147926 + 0.455269i
\(141\) −0.980767 0.712569i −0.0825955 0.0600092i
\(142\) −26.0932 −2.18969
\(143\) −2.93100 1.55217i −0.245103 0.129799i
\(144\) −4.84924 −0.404104
\(145\) 8.47395 + 6.15669i 0.703724 + 0.511285i
\(146\) 1.55613 4.78927i 0.128786 0.396363i
\(147\) 3.84705 + 11.8400i 0.317299 + 0.976546i
\(148\) −3.84505 + 2.79360i −0.316061 + 0.229632i
\(149\) 4.53248 3.29304i 0.371315 0.269776i −0.386441 0.922314i \(-0.626296\pi\)
0.757756 + 0.652538i \(0.226296\pi\)
\(150\) 0.295681 + 0.910013i 0.0241423 + 0.0743022i
\(151\) 1.18800 3.65628i 0.0966779 0.297544i −0.891009 0.453985i \(-0.850002\pi\)
0.987687 + 0.156441i \(0.0500021\pi\)
\(152\) −1.71803 1.24822i −0.139351 0.101244i
\(153\) −7.08766 −0.573004
\(154\) 4.06586 23.2858i 0.327637 1.87642i
\(155\) −16.5575 −1.32993
\(156\) 0.494897 + 0.359564i 0.0396235 + 0.0287881i
\(157\) −2.59264 + 7.97932i −0.206915 + 0.636819i 0.792714 + 0.609594i \(0.208667\pi\)
−0.999629 + 0.0272259i \(0.991333\pi\)
\(158\) −1.21887 3.75128i −0.0969678 0.298436i
\(159\) −0.886832 + 0.644321i −0.0703303 + 0.0510980i
\(160\) 5.68950 4.13366i 0.449794 0.326795i
\(161\) −6.78647 20.8866i −0.534849 1.64609i
\(162\) −0.499397 + 1.53699i −0.0392364 + 0.120757i
\(163\) −14.1203 10.2590i −1.10598 0.803545i −0.123958 0.992287i \(-0.539559\pi\)
−0.982027 + 0.188743i \(0.939559\pi\)
\(164\) −0.304152 −0.0237503
\(165\) 3.06294 + 6.25345i 0.238449 + 0.486830i
\(166\) 22.2192 1.72454
\(167\) 9.69746 + 7.04562i 0.750412 + 0.545206i 0.895954 0.444146i \(-0.146493\pi\)
−0.145543 + 0.989352i \(0.546493\pi\)
\(168\) 3.05755 9.41017i 0.235895 0.726010i
\(169\) 0.309017 + 0.951057i 0.0237705 + 0.0731582i
\(170\) 19.4555 14.1352i 1.49217 1.08412i
\(171\) −0.765759 + 0.556356i −0.0585590 + 0.0425456i
\(172\) −2.11413 6.50663i −0.161201 0.496126i
\(173\) 4.64048 14.2819i 0.352809 1.08584i −0.604459 0.796636i \(-0.706611\pi\)
0.957269 0.289200i \(-0.0933891\pi\)
\(174\) 6.52278 + 4.73908i 0.494491 + 0.359269i
\(175\) −2.61114 −0.197383
\(176\) −11.5506 + 11.1916i −0.870657 + 0.843596i
\(177\) −0.0922977 −0.00693752
\(178\) 9.60355 + 6.97738i 0.719816 + 0.522977i
\(179\) 2.94088 9.05110i 0.219812 0.676511i −0.778965 0.627067i \(-0.784255\pi\)
0.998777 0.0494439i \(-0.0157449\pi\)
\(180\) −0.396877 1.22146i −0.0295815 0.0910425i
\(181\) −11.4975 + 8.35344i −0.854604 + 0.620906i −0.926412 0.376512i \(-0.877123\pi\)
0.0718074 + 0.997419i \(0.477123\pi\)
\(182\) −5.76598 + 4.18923i −0.427403 + 0.310527i
\(183\) 2.98803 + 9.19621i 0.220881 + 0.679803i
\(184\) −3.45248 + 10.6256i −0.254520 + 0.783332i
\(185\) 13.1966 + 9.58790i 0.970234 + 0.704916i
\(186\) −12.7451 −0.934515
\(187\) −16.8823 + 16.3576i −1.23456 + 1.19619i
\(188\) 0.741593 0.0540862
\(189\) −3.56788 2.59221i −0.259525 0.188556i
\(190\) 0.992425 3.05437i 0.0719980 0.221587i
\(191\) 3.11863 + 9.59816i 0.225656 + 0.694498i 0.998224 + 0.0595665i \(0.0189719\pi\)
−0.772568 + 0.634932i \(0.781028\pi\)
\(192\) −3.46678 + 2.51876i −0.250193 + 0.181776i
\(193\) 7.65399 5.56095i 0.550946 0.400286i −0.277188 0.960816i \(-0.589402\pi\)
0.828134 + 0.560530i \(0.189402\pi\)
\(194\) 3.71334 + 11.4285i 0.266602 + 0.820517i
\(195\) 0.648783 1.99675i 0.0464603 0.142990i
\(196\) −6.16112 4.47632i −0.440080 0.319737i
\(197\) −15.5981 −1.11132 −0.555661 0.831409i \(-0.687535\pi\)
−0.555661 + 0.831409i \(0.687535\pi\)
\(198\) 2.35768 + 4.81356i 0.167553 + 0.342085i
\(199\) 7.17405 0.508555 0.254277 0.967131i \(-0.418162\pi\)
0.254277 + 0.967131i \(0.418162\pi\)
\(200\) 1.07467 + 0.780791i 0.0759904 + 0.0552103i
\(201\) 2.62893 8.09103i 0.185431 0.570697i
\(202\) −3.91659 12.0540i −0.275570 0.848118i
\(203\) −17.8000 + 12.9325i −1.24932 + 0.907683i
\(204\) 3.50766 2.54847i 0.245585 0.178428i
\(205\) 0.322577 + 0.992791i 0.0225298 + 0.0693395i
\(206\) 5.82695 17.9335i 0.405983 1.24949i
\(207\) 4.02872 + 2.92704i 0.280015 + 0.203443i
\(208\) 4.84924 0.336235
\(209\) −0.539972 + 3.09250i −0.0373506 + 0.213912i
\(210\) 14.9635 1.03258
\(211\) 23.1195 + 16.7973i 1.59161 + 1.15637i 0.901596 + 0.432580i \(0.142397\pi\)
0.690016 + 0.723794i \(0.257603\pi\)
\(212\) 0.207216 0.637745i 0.0142316 0.0438005i
\(213\) 4.98937 + 15.3557i 0.341866 + 1.05216i
\(214\) 1.74817 1.27012i 0.119503 0.0868238i
\(215\) −18.9962 + 13.8016i −1.29553 + 0.941259i
\(216\) 0.693300 + 2.13376i 0.0471731 + 0.145184i
\(217\) 10.7476 33.0779i 0.729598 2.24547i
\(218\) 4.03668 + 2.93282i 0.273398 + 0.198636i
\(219\) −3.11601 −0.210561
\(220\) −3.76435 1.99349i −0.253792 0.134401i
\(221\) 7.08766 0.476768
\(222\) 10.1580 + 7.38024i 0.681762 + 0.495329i
\(223\) 0.0619908 0.190788i 0.00415121 0.0127761i −0.948959 0.315398i \(-0.897862\pi\)
0.953111 + 0.302622i \(0.0978620\pi\)
\(224\) 4.56493 + 14.0494i 0.305007 + 0.938715i
\(225\) 0.478999 0.348013i 0.0319333 0.0232009i
\(226\) 5.51660 4.00805i 0.366959 0.266611i
\(227\) 0.471657 + 1.45161i 0.0313050 + 0.0963468i 0.965488 0.260447i \(-0.0838699\pi\)
−0.934183 + 0.356794i \(0.883870\pi\)
\(228\) 0.178926 0.550678i 0.0118497 0.0364695i
\(229\) −22.3704 16.2531i −1.47828 1.07403i −0.978106 0.208107i \(-0.933270\pi\)
−0.500173 0.865925i \(-0.666730\pi\)
\(230\) −16.8963 −1.11411
\(231\) −14.4810 + 2.05982i −0.952780 + 0.135526i
\(232\) 11.1931 0.734863
\(233\) 6.66133 + 4.83974i 0.436399 + 0.317062i 0.784202 0.620505i \(-0.213072\pi\)
−0.347804 + 0.937567i \(0.613072\pi\)
\(234\) 0.499397 1.53699i 0.0326466 0.100476i
\(235\) −0.786516 2.42065i −0.0513067 0.157906i
\(236\) 0.0456778 0.0331869i 0.00297337 0.00216028i
\(237\) −1.97455 + 1.43459i −0.128261 + 0.0931868i
\(238\) 15.6099 + 48.0425i 1.01184 + 3.11413i
\(239\) 9.18787 28.2774i 0.594314 1.82911i 0.0362025 0.999344i \(-0.488474\pi\)
0.558111 0.829766i \(-0.311526\pi\)
\(240\) −8.23661 5.98425i −0.531671 0.386282i
\(241\) 12.8808 0.829728 0.414864 0.909884i \(-0.363829\pi\)
0.414864 + 0.909884i \(0.363829\pi\)
\(242\) 16.7250 + 6.02429i 1.07513 + 0.387256i
\(243\) 1.00000 0.0641500
\(244\) −4.78539 3.47679i −0.306353 0.222578i
\(245\) −8.07690 + 24.8581i −0.516014 + 1.58813i
\(246\) 0.248302 + 0.764195i 0.0158312 + 0.0487233i
\(247\) 0.765759 0.556356i 0.0487241 0.0354001i
\(248\) −14.3145 + 10.4001i −0.908970 + 0.660406i
\(249\) −4.24860 13.0759i −0.269244 0.828649i
\(250\) −5.86322 + 18.0451i −0.370823 + 1.14127i
\(251\) 10.6204 + 7.71616i 0.670353 + 0.487040i 0.870143 0.492799i \(-0.164026\pi\)
−0.199790 + 0.979839i \(0.564026\pi\)
\(252\) 2.69780 0.169945
\(253\) 16.3514 2.32587i 1.02801 0.146226i
\(254\) −16.9309 −1.06234
\(255\) −12.0386 8.74659i −0.753889 0.547733i
\(256\) 4.15565 12.7898i 0.259728 0.799362i
\(257\) 8.32381 + 25.6181i 0.519225 + 1.59801i 0.775460 + 0.631396i \(0.217518\pi\)
−0.256235 + 0.966614i \(0.582482\pi\)
\(258\) −14.6222 + 10.6237i −0.910341 + 0.661401i
\(259\) −27.7203 + 20.1400i −1.72245 + 1.25144i
\(260\) 0.396877 + 1.22146i 0.0246133 + 0.0757519i
\(261\) 1.54168 4.74480i 0.0954275 0.293696i
\(262\) 1.89898 + 1.37969i 0.117320 + 0.0852376i
\(263\) 17.2319 1.06256 0.531282 0.847195i \(-0.321711\pi\)
0.531282 + 0.847195i \(0.321711\pi\)
\(264\) 6.57589 + 3.48240i 0.404718 + 0.214327i
\(265\) −2.30145 −0.141377
\(266\) 5.45768 + 3.96523i 0.334632 + 0.243124i
\(267\) 2.26983 6.98580i 0.138911 0.427524i
\(268\) 1.60819 + 4.94949i 0.0982357 + 0.302338i
\(269\) −1.33811 + 0.972196i −0.0815862 + 0.0592759i −0.627831 0.778350i \(-0.716057\pi\)
0.546244 + 0.837626i \(0.316057\pi\)
\(270\) −2.74498 + 1.99434i −0.167054 + 0.121372i
\(271\) 0.415173 + 1.27777i 0.0252199 + 0.0776190i 0.962874 0.269950i \(-0.0870072\pi\)
−0.937654 + 0.347569i \(0.887007\pi\)
\(272\) 10.6209 32.6876i 0.643984 1.98198i
\(273\) 3.56788 + 2.59221i 0.215938 + 0.156888i
\(274\) 31.5043 1.90324
\(275\) 0.337765 1.93443i 0.0203680 0.116650i
\(276\) −3.04626 −0.183363
\(277\) −10.5510 7.66576i −0.633949 0.460591i 0.223817 0.974631i \(-0.428148\pi\)
−0.857766 + 0.514040i \(0.828148\pi\)
\(278\) −4.83841 + 14.8911i −0.290189 + 0.893109i
\(279\) 2.43703 + 7.50042i 0.145901 + 0.449038i
\(280\) 16.8061 12.2103i 1.00435 0.729706i
\(281\) 18.8714 13.7109i 1.12578 0.817924i 0.140701 0.990052i \(-0.455064\pi\)
0.985075 + 0.172128i \(0.0550643\pi\)
\(282\) −0.605417 1.86328i −0.0360521 0.110957i
\(283\) 3.18956 9.81645i 0.189600 0.583527i −0.810398 0.585880i \(-0.800749\pi\)
0.999997 + 0.00235273i \(0.000748899\pi\)
\(284\) −7.99058 5.80549i −0.474154 0.344493i
\(285\) −1.98724 −0.117714
\(286\) −2.35768 4.81356i −0.139412 0.284632i
\(287\) −2.19274 −0.129433
\(288\) −2.70992 1.96887i −0.159684 0.116017i
\(289\) 10.2702 31.6083i 0.604128 1.85931i
\(290\) 5.23088 + 16.0990i 0.307168 + 0.945365i
\(291\) 6.01556 4.37056i 0.352638 0.256207i
\(292\) 1.54210 1.12040i 0.0902448 0.0655667i
\(293\) −0.629549 1.93755i −0.0367787 0.113193i 0.930982 0.365066i \(-0.118954\pi\)
−0.967760 + 0.251873i \(0.918954\pi\)
\(294\) −6.21715 + 19.1344i −0.362592 + 1.11594i
\(295\) −0.156771 0.113901i −0.00912755 0.00663156i
\(296\) 17.4312 1.01317
\(297\) 2.38193 2.30790i 0.138214 0.133918i
\(298\) 9.05403 0.524486
\(299\) −4.02872 2.92704i −0.232987 0.169275i
\(300\) −0.111922 + 0.344461i −0.00646184 + 0.0198875i
\(301\) −15.2415 46.9084i −0.878504 2.70376i
\(302\) 5.02637 3.65187i 0.289235 0.210142i
\(303\) −6.34482 + 4.60978i −0.364500 + 0.264825i
\(304\) −1.41837 4.36530i −0.0813493 0.250367i
\(305\) −6.27338 + 19.3075i −0.359213 + 1.10554i
\(306\) −9.26669 6.73264i −0.529741 0.384880i
\(307\) 26.8345 1.53153 0.765763 0.643123i \(-0.222362\pi\)
0.765763 + 0.643123i \(0.222362\pi\)
\(308\) 6.42597 6.22624i 0.366154 0.354773i
\(309\) −11.6680 −0.663768
\(310\) −21.6480 15.7282i −1.22952 0.893301i
\(311\) 4.93791 15.1973i 0.280003 0.861761i −0.707849 0.706364i \(-0.750334\pi\)
0.987852 0.155397i \(-0.0496657\pi\)
\(312\) −0.693300 2.13376i −0.0392504 0.120800i
\(313\) −5.37012 + 3.90162i −0.303537 + 0.220533i −0.729118 0.684387i \(-0.760070\pi\)
0.425581 + 0.904920i \(0.360070\pi\)
\(314\) −10.9694 + 7.96971i −0.619037 + 0.449757i
\(315\) −2.86122 8.80593i −0.161212 0.496158i
\(316\) 0.461370 1.41995i 0.0259541 0.0798785i
\(317\) −3.78387 2.74914i −0.212523 0.154407i 0.476431 0.879212i \(-0.341930\pi\)
−0.688955 + 0.724805i \(0.741930\pi\)
\(318\) −1.77153 −0.0993422
\(319\) −7.27834 14.8598i −0.407509 0.831991i
\(320\) −8.99675 −0.502933
\(321\) −1.08173 0.785926i −0.0603766 0.0438661i
\(322\) 10.9675 33.7545i 0.611195 1.88106i
\(323\) −2.07310 6.38034i −0.115350 0.355011i
\(324\) −0.494897 + 0.359564i −0.0274943 + 0.0199758i
\(325\) −0.478999 + 0.348013i −0.0265701 + 0.0193043i
\(326\) −8.71628 26.8260i −0.482750 1.48575i
\(327\) 0.954081 2.93636i 0.0527608 0.162381i
\(328\) 0.902466 + 0.655680i 0.0498304 + 0.0362039i
\(329\) 5.34639 0.294756
\(330\) −1.93561 + 11.0855i −0.106552 + 0.610237i
\(331\) 7.33259 0.403036 0.201518 0.979485i \(-0.435413\pi\)
0.201518 + 0.979485i \(0.435413\pi\)
\(332\) 6.80422 + 4.94356i 0.373430 + 0.271313i
\(333\) 2.40088 7.38914i 0.131567 0.404923i
\(334\) 5.98613 + 18.4234i 0.327547 + 1.00808i
\(335\) 14.4501 10.4986i 0.789495 0.573602i
\(336\) 17.3015 12.5703i 0.943874 0.685765i
\(337\) −9.70689 29.8747i −0.528768 1.62738i −0.756743 0.653713i \(-0.773210\pi\)
0.227975 0.973667i \(-0.426790\pi\)
\(338\) −0.499397 + 1.53699i −0.0271636 + 0.0836011i
\(339\) −3.41356 2.48010i −0.185399 0.134700i
\(340\) 9.10284 0.493671
\(341\) 23.1150 + 12.2411i 1.25175 + 0.662891i
\(342\) −1.52967 −0.0827151
\(343\) −19.4424 14.1258i −1.04979 0.762719i
\(344\) −7.75379 + 23.8637i −0.418056 + 1.28664i
\(345\) 3.23079 + 9.94335i 0.173940 + 0.535332i
\(346\) 19.6337 14.2647i 1.05551 0.766876i
\(347\) −21.9137 + 15.9212i −1.17639 + 0.854695i −0.991759 0.128114i \(-0.959108\pi\)
−0.184627 + 0.982809i \(0.559108\pi\)
\(348\) 0.943085 + 2.90252i 0.0505547 + 0.155591i
\(349\) −5.89468 + 18.1420i −0.315535 + 0.971117i 0.659998 + 0.751267i \(0.270557\pi\)
−0.975534 + 0.219850i \(0.929443\pi\)
\(350\) −3.41390 2.48034i −0.182481 0.132580i
\(351\) −1.00000 −0.0533761
\(352\) −10.9988 + 1.56450i −0.586239 + 0.0833882i
\(353\) 0.825609 0.0439427 0.0219714 0.999759i \(-0.493006\pi\)
0.0219714 + 0.999759i \(0.493006\pi\)
\(354\) −0.120674 0.0876745i −0.00641373 0.00465985i
\(355\) −10.4752 + 32.2394i −0.555967 + 1.71109i
\(356\) 1.38851 + 4.27340i 0.0735910 + 0.226490i
\(357\) 25.2879 18.3727i 1.33838 0.972388i
\(358\) 12.4428 9.04019i 0.657620 0.477789i
\(359\) 6.20649 + 19.1016i 0.327566 + 1.00814i 0.970269 + 0.242029i \(0.0778130\pi\)
−0.642703 + 0.766116i \(0.722187\pi\)
\(360\) −1.45559 + 4.47984i −0.0767162 + 0.236108i
\(361\) 14.6465 + 10.6413i 0.770869 + 0.560069i
\(362\) −22.9673 −1.20714
\(363\) 0.347208 10.9945i 0.0182237 0.577063i
\(364\) −2.69780 −0.141403
\(365\) −5.29266 3.84534i −0.277030 0.201274i
\(366\) −4.82890 + 14.8618i −0.252411 + 0.776841i
\(367\) 7.70602 + 23.7167i 0.402251 + 1.23800i 0.923169 + 0.384395i \(0.125590\pi\)
−0.520918 + 0.853607i \(0.674410\pi\)
\(368\) −19.5362 + 14.1939i −1.01840 + 0.739909i
\(369\) 0.402246 0.292249i 0.0209401 0.0152139i
\(370\) 8.14612 + 25.0712i 0.423497 + 1.30339i
\(371\) 1.49389 4.59771i 0.0775588 0.238701i
\(372\) −3.90296 2.83566i −0.202359 0.147022i
\(373\) −23.7393 −1.22917 −0.614587 0.788849i \(-0.710677\pi\)
−0.614587 + 0.788849i \(0.710677\pi\)
\(374\) −37.6109 + 5.34987i −1.94481 + 0.276635i
\(375\) 11.7406 0.606282
\(376\) −2.20042 1.59870i −0.113478 0.0824465i
\(377\) −1.54168 + 4.74480i −0.0794005 + 0.244370i
\(378\) −2.20241 6.77832i −0.113280 0.348639i
\(379\) 18.4708 13.4198i 0.948782 0.689330i −0.00173686 0.999998i \(-0.500553\pi\)
0.950518 + 0.310668i \(0.100553\pi\)
\(380\) 0.983481 0.714541i 0.0504515 0.0366552i
\(381\) 3.23742 + 9.96377i 0.165858 + 0.510459i
\(382\) −5.03997 + 15.5114i −0.257867 + 0.793634i
\(383\) 5.59079 + 4.06195i 0.285676 + 0.207556i 0.721389 0.692530i \(-0.243504\pi\)
−0.435713 + 0.900085i \(0.643504\pi\)
\(384\) −13.6245 −0.695272
\(385\) −27.1384 14.3717i −1.38310 0.732451i
\(386\) 15.2895 0.778217
\(387\) 9.04795 + 6.57372i 0.459933 + 0.334161i
\(388\) −1.40559 + 4.32595i −0.0713578 + 0.219617i
\(389\) −3.86991 11.9104i −0.196212 0.603880i −0.999960 0.00890978i \(-0.997164\pi\)
0.803748 0.594970i \(-0.202836\pi\)
\(390\) 2.74498 1.99434i 0.138997 0.100987i
\(391\) −28.5542 + 20.7458i −1.44405 + 1.04916i
\(392\) 8.63111 + 26.5638i 0.435937 + 1.34168i
\(393\) 0.448830 1.38136i 0.0226405 0.0696802i
\(394\) −20.3936 14.8168i −1.02742 0.746461i
\(395\) −5.12421 −0.257827
\(396\) −0.348975 + 1.99863i −0.0175366 + 0.100435i
\(397\) 14.6729 0.736409 0.368205 0.929745i \(-0.379973\pi\)
0.368205 + 0.929745i \(0.379973\pi\)
\(398\) 9.37963 + 6.81470i 0.470158 + 0.341590i
\(399\) 1.28994 3.97002i 0.0645776 0.198750i
\(400\) 0.887225 + 2.73060i 0.0443612 + 0.136530i
\(401\) −24.3143 + 17.6653i −1.21420 + 0.882165i −0.995605 0.0936512i \(-0.970146\pi\)
−0.218591 + 0.975817i \(0.570146\pi\)
\(402\) 11.1229 8.08127i 0.554761 0.403057i
\(403\) −2.43703 7.50042i −0.121397 0.373622i
\(404\) 1.48252 4.56273i 0.0737582 0.227004i
\(405\) 1.69854 + 1.23406i 0.0844009 + 0.0613209i
\(406\) −35.5572 −1.76467
\(407\) −11.3347 23.1414i −0.561838 1.14708i
\(408\) −15.9016 −0.787249
\(409\) −6.65695 4.83656i −0.329165 0.239153i 0.410911 0.911675i \(-0.365211\pi\)
−0.740076 + 0.672523i \(0.765211\pi\)
\(410\) −0.521312 + 1.60443i −0.0257458 + 0.0792373i
\(411\) −6.02404 18.5401i −0.297144 0.914516i
\(412\) 5.77444 4.19538i 0.284486 0.206691i
\(413\) 0.329307 0.239255i 0.0162041 0.0117730i
\(414\) 2.48688 + 7.65384i 0.122224 + 0.376166i
\(415\) 8.91997 27.4528i 0.437864 1.34761i
\(416\) 2.70992 + 1.96887i 0.132865 + 0.0965320i
\(417\) 9.68851 0.474448
\(418\) −3.64357 + 3.53033i −0.178213 + 0.172674i
\(419\) −31.4008 −1.53403 −0.767015 0.641630i \(-0.778259\pi\)
−0.767015 + 0.641630i \(0.778259\pi\)
\(420\) 4.58230 + 3.32924i 0.223593 + 0.162450i
\(421\) −2.30727 + 7.10106i −0.112450 + 0.346084i −0.991407 0.130817i \(-0.958240\pi\)
0.878957 + 0.476901i \(0.158240\pi\)
\(422\) 14.2714 + 43.9229i 0.694721 + 2.13813i
\(423\) −0.980767 + 0.712569i −0.0476865 + 0.0346463i
\(424\) −1.98967 + 1.44558i −0.0966267 + 0.0702034i
\(425\) 1.29677 + 3.99105i 0.0629026 + 0.193594i
\(426\) −8.06324 + 24.8161i −0.390665 + 1.20234i
\(427\) −34.4994 25.0653i −1.66955 1.21300i
\(428\) 0.817938 0.0395365
\(429\) −2.38193 + 2.30790i −0.115001 + 0.111426i
\(430\) −37.9466 −1.82995
\(431\) −26.1632 19.0087i −1.26024 0.915615i −0.261466 0.965213i \(-0.584206\pi\)
−0.998769 + 0.0495977i \(0.984206\pi\)
\(432\) −1.49850 + 4.61190i −0.0720965 + 0.221890i
\(433\) 5.68893 + 17.5087i 0.273393 + 0.841416i 0.989640 + 0.143570i \(0.0458581\pi\)
−0.716248 + 0.697846i \(0.754142\pi\)
\(434\) 45.4729 33.0380i 2.18277 1.58587i
\(435\) 8.47395 6.15669i 0.406295 0.295191i
\(436\) 0.583636 + 1.79625i 0.0279511 + 0.0860246i
\(437\) −1.45655 + 4.48281i −0.0696763 + 0.214442i
\(438\) −4.07400 2.95993i −0.194663 0.141431i
\(439\) 4.35766 0.207980 0.103990 0.994578i \(-0.466839\pi\)
0.103990 + 0.994578i \(0.466839\pi\)
\(440\) 6.87190 + 14.0300i 0.327605 + 0.668855i
\(441\) 12.4493 0.592824
\(442\) 9.26669 + 6.73264i 0.440771 + 0.320239i
\(443\) −3.68705 + 11.3476i −0.175177 + 0.539139i −0.999641 0.0267746i \(-0.991476\pi\)
0.824465 + 0.565913i \(0.191476\pi\)
\(444\) 1.46868 + 4.52013i 0.0697005 + 0.214516i
\(445\) 12.4763 9.06454i 0.591432 0.429701i
\(446\) 0.262281 0.190558i 0.0124193 0.00902318i
\(447\) −1.73125 5.32825i −0.0818854 0.252017i
\(448\) 5.83987 17.9733i 0.275908 0.849157i
\(449\) −17.9031 13.0074i −0.844899 0.613855i 0.0788355 0.996888i \(-0.474880\pi\)
−0.923735 + 0.383032i \(0.874880\pi\)
\(450\) 0.956844 0.0451061
\(451\) 0.283642 1.62446i 0.0133562 0.0764929i
\(452\) 2.58111 0.121405
\(453\) −3.11022 2.25971i −0.146131 0.106170i
\(454\) −0.762237 + 2.34592i −0.0357735 + 0.110100i
\(455\) 2.86122 + 8.80593i 0.134136 + 0.412829i
\(456\) −1.71803 + 1.24822i −0.0804541 + 0.0584534i
\(457\) 16.6608 12.1048i 0.779359 0.566237i −0.125428 0.992103i \(-0.540030\pi\)
0.904786 + 0.425866i \(0.140030\pi\)
\(458\) −13.8090 42.4998i −0.645253 1.98588i
\(459\) −2.19021 + 6.74077i −0.102230 + 0.314632i
\(460\) −5.17418 3.75926i −0.241247 0.175276i
\(461\) −4.11740 −0.191766 −0.0958831 0.995393i \(-0.530568\pi\)
−0.0958831 + 0.995393i \(0.530568\pi\)
\(462\) −20.8897 11.0626i −0.971876 0.514677i
\(463\) 13.5247 0.628546 0.314273 0.949333i \(-0.398239\pi\)
0.314273 + 0.949333i \(0.398239\pi\)
\(464\) 19.5724 + 14.2201i 0.908624 + 0.660154i
\(465\) −5.11656 + 15.7472i −0.237275 + 0.730257i
\(466\) 4.11197 + 12.6553i 0.190483 + 0.586247i
\(467\) −12.2634 + 8.90988i −0.567482 + 0.412300i −0.834190 0.551478i \(-0.814064\pi\)
0.266708 + 0.963778i \(0.414064\pi\)
\(468\) 0.494897 0.359564i 0.0228766 0.0166208i
\(469\) 11.5940 + 35.6825i 0.535359 + 1.64767i
\(470\) 1.27108 3.91197i 0.0586304 0.180446i
\(471\) 6.78762 + 4.93149i 0.312757 + 0.227231i
\(472\) −0.207076 −0.00953144
\(473\) 36.7231 5.22359i 1.68853 0.240181i
\(474\) −3.94433 −0.181169
\(475\) 0.453387 + 0.329405i 0.0208028 + 0.0151141i
\(476\) −5.90873 + 18.1852i −0.270826 + 0.833518i
\(477\) 0.338740 + 1.04253i 0.0155098 + 0.0477343i
\(478\) 38.8735 28.2433i 1.77803 1.29182i
\(479\) −0.383924 + 0.278937i −0.0175419 + 0.0127450i −0.596522 0.802597i \(-0.703451\pi\)
0.578980 + 0.815342i \(0.303451\pi\)
\(480\) −2.17320 6.68841i −0.0991923 0.305283i
\(481\) −2.40088 + 7.38914i −0.109471 + 0.336916i
\(482\) 16.8409 + 12.2356i 0.767082 + 0.557318i
\(483\) −21.9615 −0.999282
\(484\) 3.78140 + 5.56600i 0.171882 + 0.253000i
\(485\) 15.6112 0.708866
\(486\) 1.30744 + 0.949910i 0.0593066 + 0.0430888i
\(487\) 4.46306 13.7359i 0.202240 0.622432i −0.797575 0.603220i \(-0.793884\pi\)
0.999815 0.0192121i \(-0.00611578\pi\)
\(488\) 6.70384 + 20.6323i 0.303469 + 0.933980i
\(489\) −14.1203 + 10.2590i −0.638540 + 0.463927i
\(490\) −34.1730 + 24.8282i −1.54378 + 1.12162i
\(491\) −8.31046 25.5770i −0.375046 1.15427i −0.943448 0.331521i \(-0.892438\pi\)
0.568402 0.822751i \(-0.307562\pi\)
\(492\) −0.0939883 + 0.289266i −0.00423732 + 0.0130411i
\(493\) 28.6070 + 20.7842i 1.28839 + 0.936073i
\(494\) 1.52967 0.0688232
\(495\) 6.89388 0.980604i 0.309857 0.0440749i
\(496\) −38.2431 −1.71717
\(497\) −57.6067 41.8537i −2.58401 1.87740i
\(498\) 6.86610 21.1317i 0.307677 0.946933i
\(499\) −4.35334 13.3982i −0.194882 0.599786i −0.999978 0.00664097i \(-0.997886\pi\)
0.805096 0.593145i \(-0.202114\pi\)
\(500\) −5.81038 + 4.22149i −0.259848 + 0.188791i
\(501\) 9.69746 7.04562i 0.433250 0.314775i
\(502\) 6.55585 + 20.1768i 0.292602 + 0.900536i
\(503\) 3.59302 11.0582i 0.160205 0.493060i −0.838446 0.544984i \(-0.816536\pi\)
0.998651 + 0.0519248i \(0.0165356\pi\)
\(504\) −8.00477 5.81580i −0.356561 0.259056i
\(505\) −16.4656 −0.732712
\(506\) 23.5879 + 12.4915i 1.04861 + 0.555313i
\(507\) 1.00000 0.0444116
\(508\) −5.18480 3.76698i −0.230038 0.167133i
\(509\) −3.40327 + 10.4742i −0.150847 + 0.464261i −0.997717 0.0675407i \(-0.978485\pi\)
0.846869 + 0.531802i \(0.178485\pi\)
\(510\) −7.43133 22.8713i −0.329065 1.01276i
\(511\) 11.1175 8.07737i 0.491811 0.357322i
\(512\) −4.46249 + 3.24219i −0.197216 + 0.143286i
\(513\) 0.292494 + 0.900203i 0.0129139 + 0.0397449i
\(514\) −13.4520 + 41.4009i −0.593341 + 1.82612i
\(515\) −19.8185 14.3990i −0.873306 0.634494i
\(516\) −6.84147 −0.301179
\(517\) −0.691585 + 3.96080i −0.0304159 + 0.174196i
\(518\) −55.3737 −2.43298
\(519\) −12.1489 8.82672i −0.533279 0.387450i
\(520\) 1.45559 4.47984i 0.0638317 0.196454i
\(521\) −10.7307 33.0257i −0.470120 1.44688i −0.852427 0.522846i \(-0.824870\pi\)
0.382307 0.924035i \(-0.375130\pi\)
\(522\) 6.52278 4.73908i 0.285494 0.207424i
\(523\) −32.6239 + 23.7027i −1.42654 + 1.03645i −0.435898 + 0.899996i \(0.643569\pi\)
−0.990647 + 0.136449i \(0.956431\pi\)
\(524\) 0.274561 + 0.845012i 0.0119943 + 0.0369145i
\(525\) −0.806885 + 2.48334i −0.0352154 + 0.108382i
\(526\) 22.5296 + 16.3687i 0.982339 + 0.713711i
\(527\) −55.8962 −2.43488
\(528\) 7.07449 + 14.4436i 0.307877 + 0.628578i
\(529\) 1.79813 0.0781795
\(530\) −3.00900 2.18617i −0.130703 0.0949610i
\(531\) −0.0285215 + 0.0877803i −0.00123773 + 0.00380934i
\(532\) 0.789088 + 2.42856i 0.0342113 + 0.105292i
\(533\) −0.402246 + 0.292249i −0.0174232 + 0.0126587i
\(534\) 9.60355 6.97738i 0.415586 0.301941i
\(535\) −0.867486 2.66985i −0.0375047 0.115428i
\(536\) 5.89819 18.1528i 0.254763 0.784080i
\(537\) −7.69933 5.59389i −0.332251 0.241394i
\(538\) −2.67300 −0.115241
\(539\) 29.6534 28.7317i 1.27726 1.23756i
\(540\) −1.28432 −0.0552684
\(541\) −3.06411 2.22621i −0.131736 0.0957120i 0.519966 0.854187i \(-0.325945\pi\)
−0.651702 + 0.758475i \(0.725945\pi\)
\(542\) −0.670954 + 2.06498i −0.0288199 + 0.0886986i
\(543\) 4.39166 + 13.5162i 0.188464 + 0.580034i
\(544\) 19.2070 13.9547i 0.823494 0.598304i
\(545\) 5.24418 3.81012i 0.224636 0.163208i
\(546\) 2.20241 + 6.77832i 0.0942545 + 0.290085i
\(547\) −11.9571 + 36.8000i −0.511247 + 1.57346i 0.278762 + 0.960360i \(0.410076\pi\)
−0.790009 + 0.613096i \(0.789924\pi\)
\(548\) 9.64762 + 7.00941i 0.412126 + 0.299427i
\(549\) 9.66946 0.412683
\(550\) 2.27914 2.20830i 0.0971828 0.0941622i
\(551\) 4.72221 0.201173
\(552\) 9.03870 + 6.56700i 0.384713 + 0.279510i
\(553\) 3.32617 10.2369i 0.141443 0.435317i
\(554\) −6.51302 20.0450i −0.276712 0.851632i
\(555\) 13.1966 9.58790i 0.560165 0.406984i
\(556\) −4.79481 + 3.48363i −0.203345 + 0.147739i
\(557\) 4.36248 + 13.4263i 0.184844 + 0.568892i 0.999946 0.0104264i \(-0.00331889\pi\)
−0.815102 + 0.579318i \(0.803319\pi\)
\(558\) −3.93845 + 12.1213i −0.166728 + 0.513135i
\(559\) −9.04795 6.57372i −0.382687 0.278039i
\(560\) 44.8997 1.89736
\(561\) 10.3401 + 21.1108i 0.436559 + 0.891300i
\(562\) 37.6974 1.59017
\(563\) −16.1663 11.7455i −0.681329 0.495014i 0.192469 0.981303i \(-0.438350\pi\)
−0.873798 + 0.486289i \(0.838350\pi\)
\(564\) 0.229165 0.705297i 0.00964958 0.0296983i
\(565\) −2.73747 8.42507i −0.115166 0.354445i
\(566\) 13.4949 9.80462i 0.567233 0.412119i
\(567\) −3.56788 + 2.59221i −0.149837 + 0.108863i
\(568\) 11.1940 + 34.4516i 0.469689 + 1.44556i
\(569\) 0.624122 1.92085i 0.0261646 0.0805263i −0.937122 0.349003i \(-0.886520\pi\)
0.963286 + 0.268477i \(0.0865203\pi\)
\(570\) −2.59820 1.88770i −0.108827 0.0790672i
\(571\) 25.0318 1.04755 0.523774 0.851857i \(-0.324524\pi\)
0.523774 + 0.851857i \(0.324524\pi\)
\(572\) 0.348975 1.99863i 0.0145914 0.0835668i
\(573\) 10.0921 0.421604
\(574\) −2.86687 2.08290i −0.119661 0.0869387i
\(575\) 0.911106 2.80410i 0.0379958 0.116939i
\(576\) 1.32419 + 4.07544i 0.0551746 + 0.169810i
\(577\) −20.0401 + 14.5600i −0.834279 + 0.606139i −0.920767 0.390114i \(-0.872436\pi\)
0.0864876 + 0.996253i \(0.472436\pi\)
\(578\) 43.4527 31.5702i 1.80739 1.31315i
\(579\) −2.92357 8.99781i −0.121499 0.373936i
\(580\) −1.98001 + 6.09385i −0.0822155 + 0.253033i
\(581\) 49.0539 + 35.6397i 2.03510 + 1.47859i
\(582\) 12.0166 0.498105
\(583\) 3.21292 + 1.70147i 0.133065 + 0.0704676i
\(584\) −6.99098 −0.289289
\(585\) −1.69854 1.23406i −0.0702258 0.0510220i
\(586\) 1.01740 3.13125i 0.0420286 0.129351i
\(587\) −13.1771 40.5550i −0.543878 1.67389i −0.723642 0.690176i \(-0.757533\pi\)
0.179763 0.983710i \(-0.442467\pi\)
\(588\) −6.16112 + 4.47632i −0.254080 + 0.184600i
\(589\) −6.03908 + 4.38765i −0.248836 + 0.180790i
\(590\) −0.0967729 0.297837i −0.00398408 0.0122617i
\(591\) −4.82009 + 14.8347i −0.198272 + 0.610219i
\(592\) 30.4803 + 22.1452i 1.25273 + 0.910164i
\(593\) −22.8548 −0.938534 −0.469267 0.883056i \(-0.655482\pi\)
−0.469267 + 0.883056i \(0.655482\pi\)
\(594\) 5.30653 0.754815i 0.217729 0.0309704i
\(595\) 65.6254 2.69038
\(596\) 2.77264 + 2.01444i 0.113572 + 0.0825146i
\(597\) 2.21690 6.82292i 0.0907318 0.279244i
\(598\) −2.48688 7.65384i −0.101696 0.312989i
\(599\) 18.6876 13.5774i 0.763556 0.554756i −0.136443 0.990648i \(-0.543567\pi\)
0.899999 + 0.435892i \(0.143567\pi\)
\(600\) 1.07467 0.780791i 0.0438731 0.0318757i
\(601\) −4.12736 12.7027i −0.168359 0.518154i 0.830910 0.556408i \(-0.187821\pi\)
−0.999268 + 0.0382532i \(0.987821\pi\)
\(602\) 24.6315 75.8079i 1.00390 3.08970i
\(603\) −6.88264 5.00053i −0.280283 0.203637i
\(604\) 2.35175 0.0956912
\(605\) 14.1576 18.2461i 0.575589 0.741810i
\(606\) −12.6743 −0.514860
\(607\) 6.14272 + 4.46294i 0.249325 + 0.181145i 0.705428 0.708782i \(-0.250755\pi\)
−0.456103 + 0.889927i \(0.650755\pi\)
\(608\) 0.979752 3.01537i 0.0397342 0.122289i
\(609\) 6.79901 + 20.9252i 0.275510 + 0.847932i
\(610\) −26.5424 + 19.2842i −1.07467 + 0.780795i
\(611\) 0.980767 0.712569i 0.0396776 0.0288275i
\(612\) −1.33981 4.12350i −0.0541585 0.166683i
\(613\) −8.22487 + 25.3135i −0.332199 + 1.02240i 0.635886 + 0.771783i \(0.280635\pi\)
−0.968085 + 0.250621i \(0.919365\pi\)
\(614\) 35.0845 + 25.4904i 1.41589 + 1.02871i
\(615\) 1.04388 0.0420934
\(616\) −32.4891 + 4.62134i −1.30902 + 0.186199i
\(617\) −21.5936 −0.869326 −0.434663 0.900593i \(-0.643133\pi\)
−0.434663 + 0.900593i \(0.643133\pi\)
\(618\) −15.2552 11.0835i −0.613653 0.445845i
\(619\) 4.13104 12.7140i 0.166041 0.511020i −0.833071 0.553166i \(-0.813419\pi\)
0.999111 + 0.0421460i \(0.0134195\pi\)
\(620\) −3.12994 9.63295i −0.125701 0.386869i
\(621\) 4.02872 2.92704i 0.161667 0.117458i
\(622\) 20.8921 15.1790i 0.837697 0.608622i
\(623\) 10.0102 + 30.8084i 0.401052 + 1.23431i
\(624\) 1.49850 4.61190i 0.0599880 0.184624i
\(625\) 17.5468 + 12.7485i 0.701873 + 0.509941i
\(626\) −10.7273 −0.428749
\(627\) 2.77428 + 1.46918i 0.110794 + 0.0586733i
\(628\) −5.13236 −0.204803
\(629\) 44.5501 + 32.3675i 1.77633 + 1.29058i
\(630\) 4.62397 14.2311i 0.184223 0.566982i
\(631\) 11.5516 + 35.5522i 0.459862 + 1.41531i 0.865330 + 0.501202i \(0.167109\pi\)
−0.405468 + 0.914109i \(0.632891\pi\)
\(632\) −4.43003 + 3.21860i −0.176217 + 0.128029i
\(633\) 23.1195 16.7973i 0.918918 0.667633i
\(634\) −2.33574 7.18867i −0.0927641 0.285498i
\(635\) −6.79699 + 20.9190i −0.269730 + 0.830145i
\(636\) −0.542498 0.394148i −0.0215115 0.0156290i
\(637\) −12.4493 −0.493259
\(638\) 4.59952 26.3421i 0.182097 1.04289i
\(639\) 16.1459 0.638724
\(640\) −23.1417 16.8134i −0.914756 0.664609i
\(641\) 7.27351 22.3856i 0.287286 0.884177i −0.698418 0.715691i \(-0.746112\pi\)
0.985704 0.168486i \(-0.0538879\pi\)
\(642\) −0.667743 2.05510i −0.0263537 0.0811084i
\(643\) −32.1590 + 23.3649i −1.26823 + 0.921421i −0.999131 0.0416919i \(-0.986725\pi\)
−0.269097 + 0.963113i \(0.586725\pi\)
\(644\) 10.8687 7.89655i 0.428285 0.311168i
\(645\) 7.25591 + 22.3314i 0.285701 + 0.879298i
\(646\) 3.35030 10.3112i 0.131816 0.405687i
\(647\) 10.4115 + 7.56442i 0.409320 + 0.297388i 0.773326 0.634008i \(-0.218591\pi\)
−0.364007 + 0.931396i \(0.618591\pi\)
\(648\) 2.24357 0.0881356
\(649\) 0.134652 + 0.274912i 0.00528554 + 0.0107912i
\(650\) −0.956844 −0.0375305
\(651\) −28.1377 20.4432i −1.10280 0.801234i
\(652\) 3.29932 10.1543i 0.129211 0.397672i
\(653\) 11.0056 + 33.8718i 0.430683 + 1.32551i 0.897446 + 0.441123i \(0.145420\pi\)
−0.466764 + 0.884382i \(0.654580\pi\)
\(654\) 4.03668 2.93282i 0.157847 0.114682i
\(655\) 2.46703 1.79240i 0.0963948 0.0700349i
\(656\) 0.745059 + 2.29306i 0.0290897 + 0.0895288i
\(657\) −0.962901 + 2.96350i −0.0375663 + 0.115617i
\(658\) 6.99008 + 5.07859i 0.272502 + 0.197984i
\(659\) 27.4165 1.06800 0.533998 0.845486i \(-0.320689\pi\)
0.533998 + 0.845486i \(0.320689\pi\)
\(660\) −3.05917 + 2.96409i −0.119078 + 0.115377i
\(661\) 2.93350 0.114100 0.0570499 0.998371i \(-0.481831\pi\)
0.0570499 + 0.998371i \(0.481831\pi\)
\(662\) 9.58692 + 6.96530i 0.372606 + 0.270714i
\(663\) 2.19021 6.74077i 0.0850606 0.261790i
\(664\) −9.53202 29.3366i −0.369914 1.13848i
\(665\) 7.09024 5.15136i 0.274948 0.199761i
\(666\) 10.1580 7.38024i 0.393615 0.285978i
\(667\) −7.67721 23.6280i −0.297263 0.914880i
\(668\) −2.26589 + 6.97371i −0.0876701 + 0.269821i
\(669\) −0.162294 0.117913i −0.00627465 0.00455880i
\(670\) 28.8654 1.11517
\(671\) 23.0320 22.3161i 0.889141 0.861505i
\(672\) 14.7724 0.569858
\(673\) 2.21758 + 1.61116i 0.0854813 + 0.0621058i 0.629705 0.776834i \(-0.283176\pi\)
−0.544224 + 0.838940i \(0.683176\pi\)
\(674\) 15.6871 48.2801i 0.604246 1.85968i
\(675\) −0.182961 0.563098i −0.00704219 0.0216736i
\(676\) −0.494897 + 0.359564i −0.0190345 + 0.0138294i
\(677\) 18.7138 13.5964i 0.719230 0.522551i −0.166908 0.985972i \(-0.553378\pi\)
0.886138 + 0.463421i \(0.153378\pi\)
\(678\) −2.10715 6.48515i −0.0809248 0.249061i
\(679\) −10.1333 + 31.1872i −0.388882 + 1.19686i
\(680\) −27.0095 19.6236i −1.03577 0.752529i
\(681\) 1.52631 0.0584885
\(682\) 18.5936 + 37.9617i 0.711986 + 1.45363i
\(683\) 10.6098 0.405971 0.202986 0.979182i \(-0.434936\pi\)
0.202986 + 0.979182i \(0.434936\pi\)
\(684\) −0.468435 0.340338i −0.0179110 0.0130131i
\(685\) 12.6475 38.9250i 0.483237 1.48725i
\(686\) −12.0016 36.9371i −0.458223 1.41027i
\(687\) −22.3704 + 16.2531i −0.853485 + 0.620093i
\(688\) −43.8757 + 31.8776i −1.67275 + 1.21532i
\(689\) −0.338740 1.04253i −0.0129050 0.0397174i
\(690\) −5.22123 + 16.0693i −0.198769 + 0.611747i
\(691\) 0.460311 + 0.334435i 0.0175110 + 0.0127225i 0.596506 0.802608i \(-0.296555\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(692\) 9.18624 0.349208
\(693\) −2.51587 + 14.4088i −0.0955702 + 0.547344i
\(694\) −43.7745 −1.66166
\(695\) 16.4563 + 11.9562i 0.624222 + 0.453524i
\(696\) 3.45886 10.6453i 0.131108 0.403508i
\(697\) 1.08898 + 3.35153i 0.0412480 + 0.126948i
\(698\) −24.9402 + 18.1201i −0.944000 + 0.685856i
\(699\) 6.66133 4.83974i 0.251955 0.183056i
\(700\) −0.493593 1.51912i −0.0186561 0.0574174i
\(701\) 3.33374 10.2602i 0.125914 0.387523i −0.868153 0.496297i \(-0.834693\pi\)
0.994066 + 0.108774i \(0.0346926\pi\)
\(702\) −1.30744 0.949910i −0.0493461 0.0358520i
\(703\) 7.35397 0.277360
\(704\) 12.5598 + 6.65133i 0.473367 + 0.250681i
\(705\) −2.54522 −0.0958586
\(706\) 1.07943 + 0.784255i 0.0406250 + 0.0295158i
\(707\) 10.6880 32.8943i 0.401963 1.23712i
\(708\) −0.0174474 0.0536975i −0.000655713 0.00201808i
\(709\) −25.6535 + 18.6384i −0.963439 + 0.699979i −0.953947 0.299976i \(-0.903021\pi\)
−0.00949199 + 0.999955i \(0.503021\pi\)
\(710\) −44.3202 + 32.2005i −1.66331 + 1.20846i
\(711\) 0.754210 + 2.32122i 0.0282851 + 0.0870525i
\(712\) 5.09250 15.6731i 0.190850 0.587375i
\(713\) 31.7721 + 23.0838i 1.18987 + 0.864495i
\(714\) 50.5148 1.89047
\(715\) −6.89388 + 0.980604i −0.257816 + 0.0366725i
\(716\) 5.82173 0.217568
\(717\) −24.0542 17.4764i −0.898319 0.652667i
\(718\) −10.0302 + 30.8698i −0.374324 + 1.15205i
\(719\) 12.4350 + 38.2709i 0.463746 + 1.42726i 0.860553 + 0.509361i \(0.170118\pi\)
−0.396807 + 0.917902i \(0.629882\pi\)
\(720\) −8.23661 + 5.98425i −0.306960 + 0.223020i
\(721\) 41.6299 30.2459i 1.55038 1.12642i
\(722\) 9.04113 + 27.8257i 0.336476 + 1.03557i
\(723\) 3.98040 12.2504i 0.148033 0.455597i
\(724\) −7.03334 5.11002i −0.261392 0.189912i
\(725\) −2.95385 −0.109703
\(726\) 10.8978 14.0448i 0.404454 0.521253i
\(727\) 28.7502 1.06628 0.533142 0.846026i \(-0.321011\pi\)
0.533142 + 0.846026i \(0.321011\pi\)
\(728\) 8.00477 + 5.81580i 0.296676 + 0.215548i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −3.26710 10.0551i −0.120921 0.372156i
\(731\) −64.1288 + 46.5923i −2.37189 + 1.72328i
\(732\) −4.78539 + 3.47679i −0.176873 + 0.128506i
\(733\) 3.74810 + 11.5355i 0.138439 + 0.426072i 0.996109 0.0881288i \(-0.0280887\pi\)
−0.857670 + 0.514201i \(0.828089\pi\)
\(734\) −12.4536 + 38.3282i −0.459670 + 1.41472i
\(735\) 21.1456 + 15.3632i 0.779967 + 0.566679i
\(736\) −16.6805 −0.614851
\(737\) −27.9347 + 3.97351i −1.02899 + 0.146366i
\(738\) 0.803523 0.0295781
\(739\) 21.1216 + 15.3457i 0.776969 + 0.564501i 0.904068 0.427389i \(-0.140567\pi\)
−0.127099 + 0.991890i \(0.540567\pi\)
\(740\) −3.08350 + 9.49004i −0.113352 + 0.348861i
\(741\) −0.292494 0.900203i −0.0107450 0.0330698i
\(742\) 6.32058 4.59217i 0.232036 0.168584i
\(743\) −30.4945 + 22.1556i −1.11874 + 0.812810i −0.984017 0.178074i \(-0.943013\pi\)
−0.134719 + 0.990884i \(0.543013\pi\)
\(744\) 5.46765 + 16.8277i 0.200454 + 0.616933i
\(745\) 3.63478 11.1867i 0.133168 0.409849i
\(746\) −31.0377 22.5502i −1.13637 0.825621i
\(747\) −13.7488 −0.503041
\(748\) −12.7080 6.72977i −0.464649 0.246065i
\(749\) 5.89678 0.215464
\(750\) 15.3501 + 11.1525i 0.560507 + 0.407232i
\(751\) −7.21031 + 22.1910i −0.263108 + 0.809763i 0.729015 + 0.684497i \(0.239978\pi\)
−0.992123 + 0.125265i \(0.960022\pi\)
\(752\) −1.81662 5.59099i −0.0662454 0.203882i
\(753\) 10.6204 7.71616i 0.387028 0.281193i
\(754\) −6.52278 + 4.73908i −0.237546 + 0.172587i
\(755\) −2.49421 7.67638i −0.0907735 0.279372i
\(756\) 0.833665 2.56576i 0.0303201 0.0933157i
\(757\) −31.4875 22.8770i −1.14443 0.831480i −0.156703 0.987646i \(-0.550087\pi\)
−0.987731 + 0.156166i \(0.950087\pi\)
\(758\) 36.8971 1.34016
\(759\) 2.84084 16.2699i 0.103116 0.590559i
\(760\) −4.45852 −0.161727
\(761\) 3.01413 + 2.18989i 0.109262 + 0.0793835i 0.641075 0.767479i \(-0.278489\pi\)
−0.531813 + 0.846862i \(0.678489\pi\)
\(762\) −5.23195 + 16.1023i −0.189533 + 0.583324i
\(763\) 4.20763 + 12.9497i 0.152326 + 0.468812i
\(764\) −4.99455 + 3.62875i −0.180696 + 0.131284i
\(765\) −12.0386 + 8.74659i −0.435258 + 0.316234i
\(766\) 3.45113 + 10.6215i 0.124694 + 0.383770i
\(767\) 0.0285215 0.0877803i 0.00102985 0.00316956i
\(768\) −10.8796 7.90452i −0.392585 0.285230i
\(769\) 52.0029 1.87527 0.937636 0.347618i \(-0.113009\pi\)
0.937636 + 0.347618i \(0.113009\pi\)
\(770\) −21.8300 44.5692i −0.786699 1.60616i
\(771\) 26.9364 0.970092
\(772\) 4.68215 + 3.40178i 0.168514 + 0.122433i
\(773\) −3.93228 + 12.1023i −0.141434 + 0.435290i −0.996535 0.0831717i \(-0.973495\pi\)
0.855101 + 0.518461i \(0.173495\pi\)
\(774\) 5.58520 + 17.1895i 0.200756 + 0.617863i
\(775\) 3.77758 2.74457i 0.135695 0.0985880i
\(776\) 13.4963 9.80564i 0.484489 0.352002i
\(777\) 10.5882 + 32.5871i 0.379850 + 1.16906i
\(778\) 6.25411 19.2482i 0.224221 0.690080i
\(779\) 0.380738 + 0.276622i 0.0136414 + 0.00991102i
\(780\) 1.28432 0.0459861
\(781\) 38.4586 37.2632i 1.37616 1.33338i
\(782\) −57.0396 −2.03973
\(783\) −4.03617 2.93245i −0.144241 0.104797i
\(784\) −18.6553 + 57.4150i −0.666260 + 2.05054i
\(785\) 5.44326 + 16.7526i 0.194278 + 0.597927i
\(786\) 1.89898 1.37969i 0.0677345 0.0492120i
\(787\) 24.3861 17.7176i 0.869272 0.631563i −0.0611194 0.998130i \(-0.519467\pi\)
0.930392 + 0.366567i \(0.119467\pi\)
\(788\) −2.94858 9.07478i −0.105039 0.323276i
\(789\) 5.32495 16.3885i 0.189573 0.583446i
\(790\) −6.69959 4.86754i −0.238361 0.173179i
\(791\) 18.6081 0.661628
\(792\) 5.34402 5.17792i 0.189892 0.183990i
\(793\) −9.66946 −0.343373
\(794\) 19.1839 + 13.9379i 0.680810 + 0.494637i
\(795\) −0.711186 + 2.18880i −0.0252232 + 0.0776289i
\(796\) 1.35614 + 4.17376i 0.0480670 + 0.147935i
\(797\) −15.1658 + 11.0186i −0.537202 + 0.390300i −0.823045 0.567977i \(-0.807726\pi\)
0.285843 + 0.958276i \(0.407726\pi\)
\(798\) 5.45768 3.96523i 0.193200 0.140368i
\(799\) −2.65518 8.17180i −0.0939335 0.289098i
\(800\) −0.612857 + 1.88618i −0.0216678 + 0.0666865i
\(801\) −5.94248 4.31746i −0.209967 0.152550i
\(802\) −48.5699 −1.71506
\(803\) 4.54590 + 9.28114i 0.160421 + 0.327524i
\(804\) 5.20420 0.183538
\(805\) −37.3024 27.1017i −1.31474 0.955211i
\(806\) 3.93845 12.1213i 0.138726 0.426955i
\(807\) 0.511114 + 1.57305i 0.0179921 + 0.0553739i
\(808\) −14.2350 + 10.3424i −0.500787 + 0.363843i
\(809\) −10.0588 + 7.30814i −0.353648 + 0.256940i −0.750398 0.660986i \(-0.770138\pi\)
0.396750 + 0.917927i \(0.370138\pi\)
\(810\) 1.04849 + 3.22691i 0.0368401 + 0.113382i
\(811\) −8.36700 + 25.7510i −0.293805 + 0.904239i 0.689815 + 0.723985i \(0.257692\pi\)
−0.983620 + 0.180253i \(0.942308\pi\)
\(812\) −10.8888 7.91114i −0.382120 0.277627i
\(813\) 1.34353 0.0471195
\(814\) 7.16289 41.0229i 0.251059 1.43785i
\(815\) −36.6439 −1.28358
\(816\) −27.8058 20.2021i −0.973396 0.707214i
\(817\) −3.27121 + 10.0678i −0.114445 + 0.352226i
\(818\) −4.10926 12.6470i −0.143677 0.442193i
\(819\) 3.56788 2.59221i 0.124672 0.0905793i
\(820\) −0.516614 + 0.375342i −0.0180409 + 0.0131075i
\(821\) −9.34055 28.7473i −0.325987 1.00329i −0.970993 0.239108i \(-0.923145\pi\)
0.645006 0.764178i \(-0.276855\pi\)
\(822\) 9.73536 29.9623i 0.339560 1.04506i
\(823\) 23.8304 + 17.3138i 0.830674 + 0.603520i 0.919750 0.392505i \(-0.128391\pi\)
−0.0890759 + 0.996025i \(0.528391\pi\)
\(824\) −26.1779 −0.911949
\(825\) −1.73537 0.919004i −0.0604180 0.0319956i
\(826\) 0.657819 0.0228885
\(827\) −35.6492 25.9007i −1.23964 0.900654i −0.242069 0.970259i \(-0.577826\pi\)
−0.997575 + 0.0696051i \(0.977826\pi\)
\(828\) −0.941345 + 2.89716i −0.0327140 + 0.100683i
\(829\) −10.5238 32.3888i −0.365505 1.12491i −0.949664 0.313270i \(-0.898576\pi\)
0.584159 0.811639i \(-0.301424\pi\)
\(830\) 37.7400 27.4197i 1.30998 0.951753i
\(831\) −10.5510 + 7.66576i −0.366011 + 0.265922i
\(832\) −1.32419 4.07544i −0.0459081 0.141291i
\(833\) −27.2666 + 83.9179i −0.944731 + 2.90758i
\(834\) 12.6671 + 9.20321i 0.438627 + 0.318681i
\(835\) 25.1662 0.870912
\(836\) −1.90124 + 0.270438i −0.0657559 + 0.00935330i
\(837\) 7.88640 0.272594
\(838\) −41.0546 29.8279i −1.41821 1.03039i
\(839\) 0.667628 2.05475i 0.0230491 0.0709378i −0.938870 0.344271i \(-0.888126\pi\)
0.961919 + 0.273333i \(0.0881261\pi\)
\(840\) −6.41934 19.7567i −0.221488 0.681671i
\(841\) 3.32516 2.41587i 0.114661 0.0833058i
\(842\) −9.76198 + 7.09250i −0.336420 + 0.244424i
\(843\) −7.20825 22.1847i −0.248265 0.764082i
\(844\) −5.40207 + 16.6259i −0.185947 + 0.572286i
\(845\) 1.69854 + 1.23406i 0.0584314 + 0.0424529i
\(846\) −1.95917 −0.0673577
\(847\) 27.2613 + 40.1271i 0.936711 + 1.37878i
\(848\) −5.31566 −0.182541
\(849\) −8.35037 6.06690i −0.286584 0.208215i
\(850\) −2.09569 + 6.44986i −0.0718815 + 0.221228i
\(851\) −11.9558 36.7962i −0.409840 1.26136i
\(852\) −7.99058 + 5.80549i −0.273753 + 0.198893i
\(853\) 32.8705 23.8818i 1.12547 0.817699i 0.140437 0.990090i \(-0.455149\pi\)
0.985029 + 0.172391i \(0.0551492\pi\)
\(854\) −21.2961 65.5427i −0.728738 2.24283i
\(855\) −0.614092 + 1.88998i −0.0210015 + 0.0646360i
\(856\) −2.42694 1.76328i −0.0829512 0.0602676i
\(857\) 6.55009 0.223747 0.111873 0.993722i \(-0.464315\pi\)
0.111873 + 0.993722i \(0.464315\pi\)
\(858\) −5.30653 + 0.754815i −0.181162 + 0.0257690i
\(859\) −17.9430 −0.612207 −0.306103 0.951998i \(-0.599025\pi\)
−0.306103 + 0.951998i \(0.599025\pi\)
\(860\) −11.6205 8.44278i −0.396255 0.287896i
\(861\) −0.677593 + 2.08542i −0.0230923 + 0.0710708i
\(862\) −16.1502 49.7053i −0.550079 1.69297i
\(863\) 11.0397 8.02079i 0.375795 0.273031i −0.383815 0.923410i \(-0.625390\pi\)
0.759610 + 0.650379i \(0.225390\pi\)
\(864\) −2.70992 + 1.96887i −0.0921935 + 0.0669825i
\(865\) −9.74272 29.9850i −0.331262 1.01952i
\(866\) −9.19379 + 28.2956i −0.312418 + 0.961523i
\(867\) −26.8877 19.5350i −0.913153 0.663444i
\(868\) 21.2759 0.722151
\(869\) 7.15362 + 3.78835i 0.242670 + 0.128511i
\(870\) 16.9275 0.573895
\(871\) 6.88264 + 5.00053i 0.233209 + 0.169436i
\(872\) 2.14054 6.58791i 0.0724879 0.223095i
\(873\) −2.29774 7.07171i −0.0777667 0.239341i
\(874\) −6.16262 + 4.47740i −0.208454 + 0.151450i
\(875\) −41.8890 + 30.4341i −1.41611 + 1.02886i
\(876\) −0.589031 1.81285i −0.0199015 0.0612506i
\(877\) −14.0168 + 43.1392i −0.473313 + 1.45671i 0.374906 + 0.927063i \(0.377675\pi\)
−0.848219 + 0.529645i \(0.822325\pi\)
\(878\) 5.69738 + 4.13939i 0.192277 + 0.139698i
\(879\) −2.03726 −0.0687152
\(880\) −5.80802 + 33.2634i −0.195788 + 1.12131i
\(881\) −0.648468 −0.0218474 −0.0109237 0.999940i \(-0.503477\pi\)
−0.0109237 + 0.999940i \(0.503477\pi\)
\(882\) 16.2767 + 11.8257i 0.548065 + 0.398193i
\(883\) −16.6313 + 51.1859i −0.559688 + 1.72254i 0.123541 + 0.992340i \(0.460575\pi\)
−0.683229 + 0.730204i \(0.739425\pi\)
\(884\) 1.33981 + 4.12350i 0.0450626 + 0.138688i
\(885\) −0.156771 + 0.113901i −0.00526980 + 0.00382873i
\(886\) −15.5997 + 11.3339i −0.524084 + 0.380769i
\(887\) 0.227875 + 0.701327i 0.00765129 + 0.0235483i 0.954809 0.297219i \(-0.0960592\pi\)
−0.947158 + 0.320767i \(0.896059\pi\)
\(888\) 5.38653 16.5780i 0.180760 0.556322i
\(889\) −37.3789 27.1574i −1.25365 0.910829i
\(890\) 24.9225 0.835403
\(891\) −1.45888 2.97853i −0.0488745 0.0997846i
\(892\) 0.122716 0.00410884
\(893\) −0.928326 0.674468i −0.0310652 0.0225702i
\(894\) 2.79785 8.61089i 0.0935741 0.287991i
\(895\) −6.17440 19.0028i −0.206387 0.635195i
\(896\) 48.6105 35.3176i 1.62396 1.17988i
\(897\) −4.02872 + 2.92704i −0.134515 + 0.0977309i
\(898\) −11.0514 34.0127i −0.368790 1.13502i
\(899\) 12.1583 37.4194i 0.405502 1.24801i
\(900\) 0.293016 + 0.212889i 0.00976721 + 0.00709630i
\(901\) −7.76939 −0.258836
\(902\) 1.91394 1.85445i 0.0637271 0.0617464i
\(903\) −49.3224 −1.64135
\(904\) −7.65855 5.56426i −0.254720 0.185065i
\(905\) −9.22032 + 28.3772i −0.306494 + 0.943291i
\(906\) −1.91990 5.90886i −0.0637845 0.196309i
\(907\) −17.5533 + 12.7532i −0.582848 + 0.423464i −0.839750 0.542974i \(-0.817298\pi\)
0.256902 + 0.966438i \(0.417298\pi\)
\(908\) −0.755368 + 0.548807i −0.0250678 + 0.0182128i
\(909\) 2.42351 + 7.45878i 0.0803826 + 0.247392i
\(910\) −4.62397 + 14.2311i −0.153283 + 0.471757i
\(911\) −6.16070 4.47601i −0.204113 0.148297i 0.481033 0.876702i \(-0.340262\pi\)
−0.685146 + 0.728406i \(0.740262\pi\)
\(912\) −4.58995 −0.151989
\(913\) −32.7486 + 31.7308i −1.08382 + 1.05014i
\(914\) 33.2814 1.10085
\(915\) 16.4239 + 11.9327i 0.542958 + 0.394482i
\(916\) 5.22704 16.0872i 0.172706 0.531535i
\(917\) 1.97940 + 6.09197i 0.0653656 + 0.201175i
\(918\) −9.26669 + 6.73264i −0.305846 + 0.222210i
\(919\) 12.3268 8.95593i 0.406623 0.295429i −0.365610 0.930768i \(-0.619140\pi\)
0.772233 + 0.635339i \(0.219140\pi\)
\(920\) 7.24850 + 22.3086i 0.238976 + 0.735492i
\(921\) 8.29232 25.5211i 0.273241 0.840950i
\(922\) −5.38325 3.91116i −0.177288 0.128807i
\(923\) −16.1459 −0.531450
\(924\) −3.93577 8.03547i −0.129477 0.264348i
\(925\) −4.60008 −0.151250
\(926\) 17.6827 + 12.8472i 0.581090 + 0.422187i
\(927\) −3.60560 + 11.0969i −0.118423 + 0.364470i
\(928\) 5.16408 + 15.8934i 0.169519 + 0.521727i
\(929\) −34.1610 + 24.8194i −1.12079 + 0.814298i −0.984328 0.176348i \(-0.943572\pi\)
−0.136457 + 0.990646i \(0.543572\pi\)
\(930\) −21.6480 + 15.7282i −0.709865 + 0.515747i
\(931\) 3.64134 + 11.2069i 0.119340 + 0.367291i
\(932\) −1.55648 + 4.79035i −0.0509841 + 0.156913i
\(933\) −12.9276 9.39246i −0.423231 0.307495i
\(934\) −24.4972 −0.801574
\(935\) −8.48901 + 48.6178i −0.277620 + 1.58997i
\(936\) −2.24357 −0.0733333
\(937\) 10.3811 + 7.54231i 0.339136 + 0.246396i 0.744297 0.667849i \(-0.232785\pi\)
−0.405161 + 0.914245i \(0.632785\pi\)
\(938\) −18.7368 + 57.6660i −0.611778 + 1.88286i
\(939\) 2.05120 + 6.31296i 0.0669385 + 0.206016i
\(940\) 1.25962 0.915169i 0.0410843 0.0298495i
\(941\) 23.6940 17.2147i 0.772402 0.561183i −0.130287 0.991476i \(-0.541590\pi\)
0.902689 + 0.430293i \(0.141590\pi\)
\(942\) 4.18992 + 12.8953i 0.136515 + 0.420150i
\(943\) 0.765114 2.35478i 0.0249155 0.0766821i
\(944\) −0.362095 0.263077i −0.0117852 0.00856244i
\(945\) −9.25911 −0.301199
\(946\) 52.9751 + 28.0541i 1.72237 + 0.912118i
\(947\) −5.04354 −0.163893 −0.0819466 0.996637i \(-0.526114\pi\)
−0.0819466 + 0.996637i \(0.526114\pi\)
\(948\) −1.20788 0.877578i −0.0392302 0.0285024i
\(949\) 0.962901 2.96350i 0.0312571 0.0961994i
\(950\) 0.279871 + 0.861354i 0.00908021 + 0.0279460i
\(951\) −3.78387 + 2.74914i −0.122700 + 0.0891470i
\(952\) 56.7351 41.2205i 1.83879 1.33596i
\(953\) −4.58297 14.1049i −0.148457 0.456904i 0.848982 0.528421i \(-0.177216\pi\)
−0.997439 + 0.0715175i \(0.977216\pi\)
\(954\) −0.547432 + 1.68482i −0.0177237 + 0.0545481i
\(955\) 17.1418 + 12.4542i 0.554696 + 0.403010i
\(956\) 18.1882 0.588248
\(957\) −16.3817 + 2.33017i −0.529544 + 0.0753238i
\(958\) −0.766922 −0.0247781
\(959\) 69.5529 + 50.5332i 2.24598 + 1.63180i
\(960\) −2.78015 + 8.55641i −0.0897289 + 0.276157i
\(961\) 9.63990 + 29.6686i 0.310964 + 0.957050i
\(962\) −10.1580 + 7.38024i −0.327508 + 0.237948i
\(963\) −1.08173 + 0.785926i −0.0348584 + 0.0253261i
\(964\) 2.43491 + 7.49389i 0.0784233 + 0.241362i
\(965\) 6.13804 18.8909i 0.197591 0.608121i
\(966\) −28.7133 20.8614i −0.923835 0.671205i
\(967\) 27.0278 0.869156 0.434578 0.900634i \(-0.356898\pi\)
0.434578 + 0.900634i \(0.356898\pi\)
\(968\) 0.778984 24.6669i 0.0250375 0.792825i
\(969\) −6.70868 −0.215514
\(970\) 20.4106 + 14.8292i 0.655346 + 0.476137i
\(971\) 4.08660 12.5773i 0.131145 0.403624i −0.863825 0.503792i \(-0.831938\pi\)
0.994971 + 0.100168i \(0.0319379\pi\)
\(972\) 0.189034 + 0.581786i 0.00606326 + 0.0186608i
\(973\) −34.5674 + 25.1147i −1.10818 + 0.805139i
\(974\) 18.8830 13.7193i 0.605051 0.439595i
\(975\) 0.182961 + 0.563098i 0.00585946 + 0.0180336i
\(976\) −14.4897 + 44.5946i −0.463803 + 1.42744i
\(977\) −20.3209 14.7640i −0.650124 0.472343i 0.213190 0.977011i \(-0.431615\pi\)
−0.863313 + 0.504668i \(0.831615\pi\)
\(978\) −28.2065 −0.901944
\(979\) −24.1189 + 3.43073i −0.770842 + 0.109647i
\(980\) −15.9889 −0.510747
\(981\) −2.49782 1.81477i −0.0797491 0.0579411i
\(982\) 13.4304 41.3345i 0.428581 1.31904i
\(983\) −1.52431 4.69134i −0.0486179 0.149630i 0.923800 0.382875i \(-0.125066\pi\)
−0.972418 + 0.233244i \(0.925066\pi\)
\(984\) 0.902466 0.655680i 0.0287696 0.0209023i
\(985\) −26.4940 + 19.2490i −0.844169 + 0.613325i
\(986\) 17.6588 + 54.3481i 0.562370 + 1.73080i
\(987\) 1.65212 5.08472i 0.0525877 0.161848i
\(988\) 0.468435 + 0.340338i 0.0149029 + 0.0108276i
\(989\) 55.6932 1.77094
\(990\) 9.94481 + 5.26649i 0.316067 + 0.167380i
\(991\) 9.74941 0.309700 0.154850 0.987938i \(-0.450511\pi\)
0.154850 + 0.987938i \(0.450511\pi\)
\(992\) −21.3715 15.5273i −0.678547 0.492994i
\(993\) 2.26590 6.97371i 0.0719060 0.221304i
\(994\) −35.5600 109.442i −1.12789 3.47130i
\(995\) 12.1854 8.85319i 0.386302 0.280665i
\(996\) 6.80422 4.94356i 0.215600 0.156643i
\(997\) 1.45918 + 4.49089i 0.0462126 + 0.142228i 0.971500 0.237038i \(-0.0761766\pi\)
−0.925288 + 0.379266i \(0.876177\pi\)
\(998\) 7.03536 21.6526i 0.222700 0.685402i
\(999\) −6.28558 4.56674i −0.198867 0.144485i
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.n.d.235.7 yes 36
11.3 even 5 inner 429.2.n.d.157.7 36
11.5 even 5 4719.2.a.bq.1.5 18
11.6 odd 10 4719.2.a.br.1.14 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.d.157.7 36 11.3 even 5 inner
429.2.n.d.235.7 yes 36 1.1 even 1 trivial
4719.2.a.bq.1.5 18 11.5 even 5
4719.2.a.br.1.14 18 11.6 odd 10