Properties

Label 287.2.e.d.165.11
Level $287$
Weight $2$
Character 287.165
Analytic conductor $2.292$
Analytic rank $0$
Dimension $34$
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] = [287,2,Mod(165,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.11
Character \(\chi\) \(=\) 287.165
Dual form 287.2.e.d.247.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.451240 + 0.781570i) q^{2} +(1.66259 - 2.87969i) q^{3} +(0.592766 - 1.02670i) q^{4} +(0.469181 + 0.812645i) q^{5} +3.00091 q^{6} +(1.14720 + 2.38410i) q^{7} +2.87488 q^{8} +(-4.02843 - 6.97744i) q^{9} +O(q^{10})\) \(q+(0.451240 + 0.781570i) q^{2} +(1.66259 - 2.87969i) q^{3} +(0.592766 - 1.02670i) q^{4} +(0.469181 + 0.812645i) q^{5} +3.00091 q^{6} +(1.14720 + 2.38410i) q^{7} +2.87488 q^{8} +(-4.02843 - 6.97744i) q^{9} +(-0.423426 + 0.733395i) q^{10} +(-2.73018 + 4.72882i) q^{11} +(-1.97106 - 3.41397i) q^{12} -2.52551 q^{13} +(-1.34568 + 1.97242i) q^{14} +3.12023 q^{15} +(0.111726 + 0.193516i) q^{16} +(-3.35567 + 5.81218i) q^{17} +(3.63557 - 6.29699i) q^{18} +(-0.428704 - 0.742537i) q^{19} +1.11246 q^{20} +(8.77281 + 0.660185i) q^{21} -4.92787 q^{22} +(-2.38342 - 4.12820i) q^{23} +(4.77975 - 8.27876i) q^{24} +(2.05974 - 3.56757i) q^{25} +(-1.13961 - 1.97386i) q^{26} -16.8150 q^{27} +(3.12778 + 0.235376i) q^{28} +3.28519 q^{29} +(1.40797 + 2.43867i) q^{30} +(-0.0596187 + 0.103263i) q^{31} +(2.77404 - 4.80479i) q^{32} +(9.07836 + 15.7242i) q^{33} -6.05684 q^{34} +(-1.39918 + 2.05084i) q^{35} -9.55165 q^{36} +(1.90949 + 3.30733i) q^{37} +(0.386896 - 0.670124i) q^{38} +(-4.19889 + 7.27268i) q^{39} +(1.34884 + 2.33625i) q^{40} +1.00000 q^{41} +(3.44266 + 7.15446i) q^{42} +1.64508 q^{43} +(3.23672 + 5.60616i) q^{44} +(3.78012 - 6.54736i) q^{45} +(2.15098 - 3.72561i) q^{46} +(-2.36841 - 4.10220i) q^{47} +0.743022 q^{48} +(-4.36784 + 5.47009i) q^{49} +3.71774 q^{50} +(11.1582 + 19.3266i) q^{51} +(-1.49703 + 2.59294i) q^{52} +(-1.12195 + 1.94328i) q^{53} +(-7.58758 - 13.1421i) q^{54} -5.12380 q^{55} +(3.29807 + 6.85398i) q^{56} -2.85104 q^{57} +(1.48241 + 2.56761i) q^{58} +(-2.22327 + 3.85081i) q^{59} +(1.84956 - 3.20354i) q^{60} +(-5.98023 - 10.3581i) q^{61} -0.107609 q^{62} +(12.0135 - 17.6087i) q^{63} +5.45394 q^{64} +(-1.18492 - 2.05234i) q^{65} +(-8.19303 + 14.1907i) q^{66} +(5.86555 - 10.1594i) q^{67} +(3.97825 + 6.89053i) q^{68} -15.8506 q^{69} +(-2.23424 - 0.168135i) q^{70} +9.78432 q^{71} +(-11.5812 - 20.0593i) q^{72} +(1.85766 - 3.21756i) q^{73} +(-1.72327 + 2.98479i) q^{74} +(-6.84901 - 11.8628i) q^{75} -1.01648 q^{76} +(-14.4060 - 1.08411i) q^{77} -7.57881 q^{78} +(1.40646 + 2.43606i) q^{79} +(-0.104840 + 0.181588i) q^{80} +(-15.8711 + 27.4896i) q^{81} +(0.451240 + 0.781570i) q^{82} +3.41464 q^{83} +(5.87803 - 8.61571i) q^{84} -6.29766 q^{85} +(0.742326 + 1.28575i) q^{86} +(5.46194 - 9.46036i) q^{87} +(-7.84894 + 13.5948i) q^{88} +(7.12084 + 12.3337i) q^{89} +6.82296 q^{90} +(-2.89727 - 6.02105i) q^{91} -5.65123 q^{92} +(0.198243 + 0.343367i) q^{93} +(2.13744 - 3.70215i) q^{94} +(0.402280 - 0.696769i) q^{95} +(-9.22421 - 15.9768i) q^{96} -8.40546 q^{97} +(-6.24621 - 0.945452i) q^{98} +43.9934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.451240 + 0.781570i 0.319075 + 0.552653i 0.980295 0.197538i \(-0.0632946\pi\)
−0.661221 + 0.750191i \(0.729961\pi\)
\(3\) 1.66259 2.87969i 0.959898 1.66259i 0.237159 0.971471i \(-0.423784\pi\)
0.722739 0.691121i \(-0.242883\pi\)
\(4\) 0.592766 1.02670i 0.296383 0.513350i
\(5\) 0.469181 + 0.812645i 0.209824 + 0.363426i 0.951659 0.307157i \(-0.0993775\pi\)
−0.741835 + 0.670583i \(0.766044\pi\)
\(6\) 3.00091 1.22512
\(7\) 1.14720 + 2.38410i 0.433602 + 0.901104i
\(8\) 2.87488 1.01642
\(9\) −4.02843 6.97744i −1.34281 2.32581i
\(10\) −0.423426 + 0.733395i −0.133899 + 0.231920i
\(11\) −2.73018 + 4.72882i −0.823181 + 1.42579i 0.0801202 + 0.996785i \(0.474470\pi\)
−0.903301 + 0.429006i \(0.858864\pi\)
\(12\) −1.97106 3.41397i −0.568995 0.985528i
\(13\) −2.52551 −0.700449 −0.350225 0.936666i \(-0.613895\pi\)
−0.350225 + 0.936666i \(0.613895\pi\)
\(14\) −1.34568 + 1.97242i −0.359647 + 0.527151i
\(15\) 3.12023 0.805639
\(16\) 0.111726 + 0.193516i 0.0279316 + 0.0483790i
\(17\) −3.35567 + 5.81218i −0.813868 + 1.40966i 0.0962691 + 0.995355i \(0.469309\pi\)
−0.910138 + 0.414306i \(0.864024\pi\)
\(18\) 3.63557 6.29699i 0.856912 1.48422i
\(19\) −0.428704 0.742537i −0.0983514 0.170350i 0.812651 0.582751i \(-0.198024\pi\)
−0.911002 + 0.412401i \(0.864690\pi\)
\(20\) 1.11246 0.248753
\(21\) 8.77281 + 0.660185i 1.91438 + 0.144064i
\(22\) −4.92787 −1.05062
\(23\) −2.38342 4.12820i −0.496977 0.860789i 0.503017 0.864276i \(-0.332223\pi\)
−0.999994 + 0.00348754i \(0.998890\pi\)
\(24\) 4.77975 8.27876i 0.975662 1.68990i
\(25\) 2.05974 3.56757i 0.411948 0.713514i
\(26\) −1.13961 1.97386i −0.223496 0.387106i
\(27\) −16.8150 −3.23604
\(28\) 3.12778 + 0.235376i 0.591094 + 0.0444819i
\(29\) 3.28519 0.610045 0.305023 0.952345i \(-0.401336\pi\)
0.305023 + 0.952345i \(0.401336\pi\)
\(30\) 1.40797 + 2.43867i 0.257059 + 0.445239i
\(31\) −0.0596187 + 0.103263i −0.0107078 + 0.0185465i −0.871330 0.490698i \(-0.836742\pi\)
0.860622 + 0.509245i \(0.170075\pi\)
\(32\) 2.77404 4.80479i 0.490386 0.849374i
\(33\) 9.07836 + 15.7242i 1.58034 + 2.73723i
\(34\) −6.05684 −1.03874
\(35\) −1.39918 + 2.05084i −0.236504 + 0.346656i
\(36\) −9.55165 −1.59194
\(37\) 1.90949 + 3.30733i 0.313917 + 0.543721i 0.979207 0.202865i \(-0.0650252\pi\)
−0.665289 + 0.746586i \(0.731692\pi\)
\(38\) 0.386896 0.670124i 0.0627629 0.108709i
\(39\) −4.19889 + 7.27268i −0.672360 + 1.16456i
\(40\) 1.34884 + 2.33625i 0.213270 + 0.369394i
\(41\) 1.00000 0.156174
\(42\) 3.44266 + 7.15446i 0.531213 + 1.10396i
\(43\) 1.64508 0.250873 0.125436 0.992102i \(-0.459967\pi\)
0.125436 + 0.992102i \(0.459967\pi\)
\(44\) 3.23672 + 5.60616i 0.487954 + 0.845160i
\(45\) 3.78012 6.54736i 0.563507 0.976023i
\(46\) 2.15098 3.72561i 0.317145 0.549312i
\(47\) −2.36841 4.10220i −0.345468 0.598367i 0.639971 0.768399i \(-0.278946\pi\)
−0.985439 + 0.170032i \(0.945613\pi\)
\(48\) 0.743022 0.107246
\(49\) −4.36784 + 5.47009i −0.623978 + 0.781442i
\(50\) 3.71774 0.525768
\(51\) 11.1582 + 19.3266i 1.56246 + 2.70626i
\(52\) −1.49703 + 2.59294i −0.207601 + 0.359576i
\(53\) −1.12195 + 1.94328i −0.154112 + 0.266930i −0.932735 0.360562i \(-0.882585\pi\)
0.778623 + 0.627492i \(0.215918\pi\)
\(54\) −7.58758 13.1421i −1.03254 1.78841i
\(55\) −5.12380 −0.690893
\(56\) 3.29807 + 6.85398i 0.440723 + 0.915902i
\(57\) −2.85104 −0.377629
\(58\) 1.48241 + 2.56761i 0.194650 + 0.337144i
\(59\) −2.22327 + 3.85081i −0.289445 + 0.501333i −0.973677 0.227931i \(-0.926804\pi\)
0.684233 + 0.729264i \(0.260137\pi\)
\(60\) 1.84956 3.20354i 0.238778 0.413575i
\(61\) −5.98023 10.3581i −0.765690 1.32621i −0.939881 0.341501i \(-0.889065\pi\)
0.174192 0.984712i \(-0.444269\pi\)
\(62\) −0.107609 −0.0136664
\(63\) 12.0135 17.6087i 1.51355 2.21849i
\(64\) 5.45394 0.681743
\(65\) −1.18492 2.05234i −0.146971 0.254561i
\(66\) −8.19303 + 14.1907i −1.00849 + 1.74676i
\(67\) 5.86555 10.1594i 0.716591 1.24117i −0.245751 0.969333i \(-0.579035\pi\)
0.962343 0.271840i \(-0.0876320\pi\)
\(68\) 3.97825 + 6.89053i 0.482433 + 0.835599i
\(69\) −15.8506 −1.90819
\(70\) −2.23424 0.168135i −0.267043 0.0200959i
\(71\) 9.78432 1.16119 0.580593 0.814194i \(-0.302821\pi\)
0.580593 + 0.814194i \(0.302821\pi\)
\(72\) −11.5812 20.0593i −1.36486 2.36401i
\(73\) 1.85766 3.21756i 0.217422 0.376587i −0.736597 0.676332i \(-0.763568\pi\)
0.954019 + 0.299745i \(0.0969018\pi\)
\(74\) −1.72327 + 2.98479i −0.200326 + 0.346975i
\(75\) −6.84901 11.8628i −0.790856 1.36980i
\(76\) −1.01648 −0.116599
\(77\) −14.4060 1.08411i −1.64172 0.123545i
\(78\) −7.57881 −0.858132
\(79\) 1.40646 + 2.43606i 0.158239 + 0.274078i 0.934234 0.356661i \(-0.116085\pi\)
−0.775995 + 0.630739i \(0.782752\pi\)
\(80\) −0.104840 + 0.181588i −0.0117214 + 0.0203021i
\(81\) −15.8711 + 27.4896i −1.76346 + 3.05440i
\(82\) 0.451240 + 0.781570i 0.0498311 + 0.0863100i
\(83\) 3.41464 0.374805 0.187403 0.982283i \(-0.439993\pi\)
0.187403 + 0.982283i \(0.439993\pi\)
\(84\) 5.87803 8.61571i 0.641346 0.940051i
\(85\) −6.29766 −0.683077
\(86\) 0.742326 + 1.28575i 0.0800470 + 0.138646i
\(87\) 5.46194 9.46036i 0.585581 1.01426i
\(88\) −7.84894 + 13.5948i −0.836700 + 1.44921i
\(89\) 7.12084 + 12.3337i 0.754808 + 1.30737i 0.945470 + 0.325710i \(0.105603\pi\)
−0.190662 + 0.981656i \(0.561063\pi\)
\(90\) 6.82296 0.719203
\(91\) −2.89727 6.02105i −0.303717 0.631178i
\(92\) −5.65123 −0.589181
\(93\) 0.198243 + 0.343367i 0.0205569 + 0.0356055i
\(94\) 2.13744 3.70215i 0.220460 0.381848i
\(95\) 0.402280 0.696769i 0.0412730 0.0714869i
\(96\) −9.22421 15.9768i −0.941442 1.63063i
\(97\) −8.40546 −0.853446 −0.426723 0.904382i \(-0.640332\pi\)
−0.426723 + 0.904382i \(0.640332\pi\)
\(98\) −6.24621 0.945452i −0.630962 0.0955051i
\(99\) 43.9934 4.42150
\(100\) −2.44188 4.22947i −0.244188 0.422947i
\(101\) 3.13654 5.43266i 0.312098 0.540569i −0.666718 0.745310i \(-0.732302\pi\)
0.978816 + 0.204740i \(0.0656350\pi\)
\(102\) −10.0700 + 17.4418i −0.997083 + 1.72700i
\(103\) −4.37283 7.57396i −0.430867 0.746284i 0.566081 0.824350i \(-0.308459\pi\)
−0.996948 + 0.0780655i \(0.975126\pi\)
\(104\) −7.26051 −0.711952
\(105\) 3.57954 + 7.43892i 0.349327 + 0.725965i
\(106\) −2.02508 −0.196693
\(107\) 5.26144 + 9.11308i 0.508643 + 0.880995i 0.999950 + 0.0100084i \(0.00318583\pi\)
−0.491307 + 0.870986i \(0.663481\pi\)
\(108\) −9.96733 + 17.2639i −0.959107 + 1.66122i
\(109\) 1.62426 2.81330i 0.155576 0.269466i −0.777693 0.628645i \(-0.783610\pi\)
0.933269 + 0.359179i \(0.116943\pi\)
\(110\) −2.31206 4.00461i −0.220446 0.381824i
\(111\) 12.6988 1.20531
\(112\) −0.333188 + 0.488369i −0.0314833 + 0.0461465i
\(113\) 4.20493 0.395566 0.197783 0.980246i \(-0.436626\pi\)
0.197783 + 0.980246i \(0.436626\pi\)
\(114\) −1.28650 2.22829i −0.120492 0.208698i
\(115\) 2.23651 3.87374i 0.208555 0.361228i
\(116\) 1.94735 3.37291i 0.180807 0.313167i
\(117\) 10.1738 + 17.6216i 0.940569 + 1.62911i
\(118\) −4.01291 −0.369418
\(119\) −17.7064 1.33247i −1.62315 0.122148i
\(120\) 8.97026 0.818869
\(121\) −9.40780 16.2948i −0.855255 1.48134i
\(122\) 5.39703 9.34793i 0.488624 0.846322i
\(123\) 1.66259 2.87969i 0.149911 0.259653i
\(124\) 0.0706799 + 0.122421i 0.00634724 + 0.0109937i
\(125\) 8.55737 0.765394
\(126\) 19.1834 + 1.44362i 1.70899 + 0.128608i
\(127\) 6.36861 0.565123 0.282561 0.959249i \(-0.408816\pi\)
0.282561 + 0.959249i \(0.408816\pi\)
\(128\) −3.08706 5.34694i −0.272860 0.472607i
\(129\) 2.73510 4.73733i 0.240812 0.417099i
\(130\) 1.06936 1.85219i 0.0937895 0.162448i
\(131\) −3.25353 5.63527i −0.284262 0.492356i 0.688168 0.725551i \(-0.258415\pi\)
−0.972430 + 0.233195i \(0.925082\pi\)
\(132\) 21.5254 1.87354
\(133\) 1.27847 1.87391i 0.110857 0.162489i
\(134\) 10.5871 0.914584
\(135\) −7.88926 13.6646i −0.678999 1.17606i
\(136\) −9.64712 + 16.7093i −0.827234 + 1.43281i
\(137\) −6.63174 + 11.4865i −0.566588 + 0.981359i 0.430312 + 0.902680i \(0.358403\pi\)
−0.996900 + 0.0786787i \(0.974930\pi\)
\(138\) −7.15242 12.3883i −0.608854 1.05457i
\(139\) 5.17790 0.439184 0.219592 0.975592i \(-0.429527\pi\)
0.219592 + 0.975592i \(0.429527\pi\)
\(140\) 1.27622 + 2.65221i 0.107860 + 0.224152i
\(141\) −15.7508 −1.32645
\(142\) 4.41507 + 7.64713i 0.370505 + 0.641733i
\(143\) 6.89509 11.9427i 0.576597 0.998695i
\(144\) 0.900163 1.55913i 0.0750136 0.129927i
\(145\) 1.54135 + 2.66970i 0.128002 + 0.221706i
\(146\) 3.35299 0.277496
\(147\) 8.49026 + 21.6726i 0.700265 + 1.78753i
\(148\) 4.52751 0.372159
\(149\) −1.83789 3.18332i −0.150566 0.260788i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(150\) 6.18109 10.7060i 0.504684 0.874138i
\(151\) −7.13336 + 12.3553i −0.580505 + 1.00546i 0.414915 + 0.909860i \(0.363811\pi\)
−0.995420 + 0.0956032i \(0.969522\pi\)
\(152\) −1.23247 2.13470i −0.0999666 0.173147i
\(153\) 54.0722 4.37148
\(154\) −5.65327 11.7485i −0.455554 0.946722i
\(155\) −0.111888 −0.00898705
\(156\) 4.97791 + 8.62199i 0.398552 + 0.690312i
\(157\) −4.52471 + 7.83702i −0.361111 + 0.625462i −0.988144 0.153530i \(-0.950936\pi\)
0.627033 + 0.778993i \(0.284269\pi\)
\(158\) −1.26930 + 2.19849i −0.100980 + 0.174903i
\(159\) 3.73070 + 6.46176i 0.295864 + 0.512451i
\(160\) 5.20612 0.411580
\(161\) 7.10776 10.4182i 0.560170 0.821068i
\(162\) −28.6468 −2.25070
\(163\) 4.44632 + 7.70125i 0.348263 + 0.603209i 0.985941 0.167094i \(-0.0534384\pi\)
−0.637678 + 0.770303i \(0.720105\pi\)
\(164\) 0.592766 1.02670i 0.0462872 0.0801718i
\(165\) −8.51879 + 14.7550i −0.663187 + 1.14867i
\(166\) 1.54082 + 2.66878i 0.119591 + 0.207137i
\(167\) 7.46298 0.577503 0.288751 0.957404i \(-0.406760\pi\)
0.288751 + 0.957404i \(0.406760\pi\)
\(168\) 25.2207 + 1.89795i 1.94582 + 0.146430i
\(169\) −6.62182 −0.509371
\(170\) −2.84175 4.92206i −0.217952 0.377505i
\(171\) −3.45400 + 5.98251i −0.264134 + 0.457494i
\(172\) 0.975148 1.68901i 0.0743543 0.128785i
\(173\) 7.51035 + 13.0083i 0.571001 + 0.989003i 0.996463 + 0.0840268i \(0.0267781\pi\)
−0.425462 + 0.904976i \(0.639889\pi\)
\(174\) 9.85857 0.747377
\(175\) 10.8684 + 0.817884i 0.821572 + 0.0618262i
\(176\) −1.22013 −0.0919711
\(177\) 7.39278 + 12.8047i 0.555675 + 0.962457i
\(178\) −6.42641 + 11.1309i −0.481680 + 0.834294i
\(179\) 8.95967 15.5186i 0.669677 1.15991i −0.308317 0.951284i \(-0.599766\pi\)
0.977994 0.208631i \(-0.0669008\pi\)
\(180\) −4.48145 7.76210i −0.334028 0.578553i
\(181\) −24.9578 −1.85510 −0.927548 0.373705i \(-0.878087\pi\)
−0.927548 + 0.373705i \(0.878087\pi\)
\(182\) 3.39851 4.98136i 0.251914 0.369243i
\(183\) −39.7707 −2.93994
\(184\) −6.85203 11.8681i −0.505138 0.874925i
\(185\) −1.79179 + 3.10347i −0.131735 + 0.228171i
\(186\) −0.178910 + 0.309882i −0.0131183 + 0.0227216i
\(187\) −18.3232 31.7366i −1.33992 2.32081i
\(188\) −5.61564 −0.409563
\(189\) −19.2902 40.0885i −1.40316 2.91601i
\(190\) 0.726098 0.0526767
\(191\) −8.15068 14.1174i −0.589762 1.02150i −0.994263 0.106961i \(-0.965888\pi\)
0.404501 0.914538i \(-0.367445\pi\)
\(192\) 9.06768 15.7057i 0.654403 1.13346i
\(193\) 4.87475 8.44331i 0.350892 0.607763i −0.635514 0.772089i \(-0.719212\pi\)
0.986406 + 0.164326i \(0.0525450\pi\)
\(194\) −3.79288 6.56946i −0.272313 0.471660i
\(195\) −7.88015 −0.564309
\(196\) 3.02704 + 7.72695i 0.216217 + 0.551925i
\(197\) −24.4370 −1.74106 −0.870531 0.492114i \(-0.836224\pi\)
−0.870531 + 0.492114i \(0.836224\pi\)
\(198\) 19.8515 + 34.3839i 1.41079 + 2.44356i
\(199\) 2.46523 4.26990i 0.174756 0.302685i −0.765321 0.643649i \(-0.777420\pi\)
0.940077 + 0.340963i \(0.110753\pi\)
\(200\) 5.92149 10.2563i 0.418713 0.725232i
\(201\) −19.5040 33.7820i −1.37571 2.38280i
\(202\) 5.66133 0.398330
\(203\) 3.76879 + 7.83223i 0.264517 + 0.549714i
\(204\) 26.4568 1.85235
\(205\) 0.469181 + 0.812645i 0.0327690 + 0.0567576i
\(206\) 3.94638 6.83534i 0.274958 0.476241i
\(207\) −19.2028 + 33.2603i −1.33469 + 2.31175i
\(208\) −0.282166 0.488725i −0.0195647 0.0338870i
\(209\) 4.68176 0.323844
\(210\) −4.19881 + 6.15440i −0.289745 + 0.424694i
\(211\) 27.1561 1.86950 0.934751 0.355303i \(-0.115622\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(212\) 1.33011 + 2.30382i 0.0913523 + 0.158227i
\(213\) 16.2673 28.1759i 1.11462 1.93058i
\(214\) −4.74834 + 8.22436i −0.324590 + 0.562206i
\(215\) 0.771841 + 1.33687i 0.0526391 + 0.0911736i
\(216\) −48.3409 −3.28918
\(217\) −0.314583 0.0236735i −0.0213553 0.00160706i
\(218\) 2.93172 0.198561
\(219\) −6.17705 10.6990i −0.417407 0.722970i
\(220\) −3.03721 + 5.26061i −0.204769 + 0.354670i
\(221\) 8.47475 14.6787i 0.570073 0.987396i
\(222\) 5.73019 + 9.92498i 0.384585 + 0.666121i
\(223\) −8.74237 −0.585432 −0.292716 0.956199i \(-0.594559\pi\)
−0.292716 + 0.956199i \(0.594559\pi\)
\(224\) 14.6375 + 1.10152i 0.978008 + 0.0735985i
\(225\) −33.1900 −2.21267
\(226\) 1.89743 + 3.28644i 0.126215 + 0.218611i
\(227\) −7.34492 + 12.7218i −0.487500 + 0.844374i −0.999897 0.0143744i \(-0.995424\pi\)
0.512397 + 0.858749i \(0.328758\pi\)
\(228\) −1.69000 + 2.92716i −0.111923 + 0.193856i
\(229\) 2.65206 + 4.59350i 0.175253 + 0.303547i 0.940249 0.340488i \(-0.110592\pi\)
−0.764996 + 0.644035i \(0.777259\pi\)
\(230\) 4.03680 0.266179
\(231\) −27.0733 + 39.6826i −1.78129 + 2.61092i
\(232\) 9.44453 0.620064
\(233\) 2.21282 + 3.83271i 0.144967 + 0.251089i 0.929360 0.369174i \(-0.120359\pi\)
−0.784394 + 0.620263i \(0.787026\pi\)
\(234\) −9.18165 + 15.9031i −0.600223 + 1.03962i
\(235\) 2.22242 3.84935i 0.144975 0.251104i
\(236\) 2.63575 + 4.56526i 0.171573 + 0.297173i
\(237\) 9.35347 0.607573
\(238\) −6.94843 14.4401i −0.450400 0.936012i
\(239\) −0.685835 −0.0443630 −0.0221815 0.999754i \(-0.507061\pi\)
−0.0221815 + 0.999754i \(0.507061\pi\)
\(240\) 0.348612 + 0.603813i 0.0225028 + 0.0389760i
\(241\) −4.43393 + 7.67979i −0.285614 + 0.494699i −0.972758 0.231823i \(-0.925531\pi\)
0.687144 + 0.726522i \(0.258864\pi\)
\(242\) 8.49034 14.7057i 0.545780 0.945319i
\(243\) 27.5520 + 47.7215i 1.76746 + 3.06134i
\(244\) −14.1795 −0.907749
\(245\) −6.49456 0.983044i −0.414922 0.0628044i
\(246\) 3.00091 0.191331
\(247\) 1.08269 + 1.87528i 0.0688902 + 0.119321i
\(248\) −0.171396 + 0.296867i −0.0108837 + 0.0188511i
\(249\) 5.67715 9.83312i 0.359775 0.623149i
\(250\) 3.86142 + 6.68818i 0.244218 + 0.422998i
\(251\) 3.42941 0.216463 0.108231 0.994126i \(-0.465481\pi\)
0.108231 + 0.994126i \(0.465481\pi\)
\(252\) −10.9577 22.7721i −0.690270 1.43451i
\(253\) 26.0287 1.63641
\(254\) 2.87377 + 4.97751i 0.180316 + 0.312317i
\(255\) −10.4704 + 18.1353i −0.655684 + 1.13568i
\(256\) 8.23994 14.2720i 0.514997 0.892000i
\(257\) −7.61522 13.1899i −0.475024 0.822766i 0.524567 0.851369i \(-0.324227\pi\)
−0.999591 + 0.0286035i \(0.990894\pi\)
\(258\) 4.93674 0.307348
\(259\) −5.69442 + 8.34658i −0.353834 + 0.518631i
\(260\) −2.80952 −0.174239
\(261\) −13.2342 22.9222i −0.819174 1.41885i
\(262\) 2.93624 5.08572i 0.181402 0.314197i
\(263\) 6.13704 10.6297i 0.378426 0.655453i −0.612408 0.790542i \(-0.709799\pi\)
0.990833 + 0.135089i \(0.0431322\pi\)
\(264\) 26.0992 + 45.2051i 1.60629 + 2.78218i
\(265\) −2.10560 −0.129346
\(266\) 2.04149 + 0.153629i 0.125172 + 0.00941962i
\(267\) 47.3562 2.89815
\(268\) −6.95380 12.0443i −0.424771 0.735724i
\(269\) −6.41499 + 11.1111i −0.391129 + 0.677455i −0.992599 0.121440i \(-0.961249\pi\)
0.601470 + 0.798896i \(0.294582\pi\)
\(270\) 7.11989 12.3320i 0.433303 0.750503i
\(271\) −8.98588 15.5640i −0.545854 0.945446i −0.998553 0.0537828i \(-0.982872\pi\)
0.452699 0.891663i \(-0.350461\pi\)
\(272\) −1.49967 −0.0909306
\(273\) −22.1558 1.66730i −1.34093 0.100910i
\(274\) −11.9700 −0.723135
\(275\) 11.2469 + 19.4802i 0.678215 + 1.17470i
\(276\) −9.39569 + 16.2738i −0.565554 + 0.979568i
\(277\) 0.417368 0.722903i 0.0250772 0.0434350i −0.853214 0.521560i \(-0.825350\pi\)
0.878292 + 0.478125i \(0.158684\pi\)
\(278\) 2.33647 + 4.04689i 0.140132 + 0.242717i
\(279\) 0.960678 0.0575143
\(280\) −4.02247 + 5.89592i −0.240388 + 0.352349i
\(281\) 5.96703 0.355963 0.177982 0.984034i \(-0.443043\pi\)
0.177982 + 0.984034i \(0.443043\pi\)
\(282\) −7.10737 12.3103i −0.423238 0.733069i
\(283\) −9.20789 + 15.9485i −0.547352 + 0.948042i 0.451103 + 0.892472i \(0.351031\pi\)
−0.998455 + 0.0555695i \(0.982303\pi\)
\(284\) 5.79981 10.0456i 0.344156 0.596095i
\(285\) −1.33765 2.31688i −0.0792358 0.137240i
\(286\) 12.4454 0.735909
\(287\) 1.14720 + 2.38410i 0.0677173 + 0.140729i
\(288\) −44.7001 −2.63398
\(289\) −14.0210 24.2851i −0.824764 1.42853i
\(290\) −1.39104 + 2.40935i −0.0816845 + 0.141482i
\(291\) −13.9749 + 24.2052i −0.819221 + 1.41893i
\(292\) −2.20231 3.81452i −0.128881 0.223228i
\(293\) −18.3646 −1.07287 −0.536435 0.843941i \(-0.680229\pi\)
−0.536435 + 0.843941i \(0.680229\pi\)
\(294\) −13.1075 + 16.4153i −0.764445 + 0.957357i
\(295\) −4.17246 −0.242930
\(296\) 5.48953 + 9.50815i 0.319073 + 0.552650i
\(297\) 45.9079 79.5149i 2.66385 4.61392i
\(298\) 1.65866 2.87288i 0.0960835 0.166422i
\(299\) 6.01933 + 10.4258i 0.348107 + 0.602939i
\(300\) −16.2394 −0.937584
\(301\) 1.88724 + 3.92203i 0.108779 + 0.226062i
\(302\) −12.8754 −0.740897
\(303\) −10.4296 18.0646i −0.599164 1.03778i
\(304\) 0.0957951 0.165922i 0.00549423 0.00951628i
\(305\) 5.61162 9.71960i 0.321320 0.556543i
\(306\) 24.3995 + 42.2612i 1.39483 + 2.41591i
\(307\) 16.8758 0.963153 0.481577 0.876404i \(-0.340064\pi\)
0.481577 + 0.876404i \(0.340064\pi\)
\(308\) −9.65246 + 14.1481i −0.550000 + 0.806161i
\(309\) −29.0809 −1.65436
\(310\) −0.0504882 0.0874482i −0.00286754 0.00496672i
\(311\) −5.22685 + 9.05317i −0.296387 + 0.513358i −0.975307 0.220855i \(-0.929115\pi\)
0.678919 + 0.734213i \(0.262449\pi\)
\(312\) −12.0713 + 20.9081i −0.683401 + 1.18369i
\(313\) 3.13464 + 5.42936i 0.177180 + 0.306886i 0.940914 0.338646i \(-0.109969\pi\)
−0.763733 + 0.645532i \(0.776636\pi\)
\(314\) −8.16691 −0.460885
\(315\) 19.9461 + 1.50102i 1.12384 + 0.0845727i
\(316\) 3.33480 0.187597
\(317\) 13.0875 + 22.6682i 0.735066 + 1.27317i 0.954694 + 0.297589i \(0.0961824\pi\)
−0.219628 + 0.975584i \(0.570484\pi\)
\(318\) −3.36688 + 5.83160i −0.188805 + 0.327020i
\(319\) −8.96918 + 15.5351i −0.502178 + 0.869798i
\(320\) 2.55889 + 4.43212i 0.143046 + 0.247763i
\(321\) 34.9905 1.95298
\(322\) 11.3498 + 0.854116i 0.632502 + 0.0475980i
\(323\) 5.75435 0.320181
\(324\) 18.8157 + 32.5898i 1.04532 + 1.81055i
\(325\) −5.20188 + 9.00992i −0.288548 + 0.499781i
\(326\) −4.01271 + 6.95022i −0.222244 + 0.384937i
\(327\) −5.40097 9.35475i −0.298674 0.517319i
\(328\) 2.87488 0.158738
\(329\) 7.06300 10.3526i 0.389396 0.570756i
\(330\) −15.3761 −0.846424
\(331\) −3.67575 6.36658i −0.202037 0.349939i 0.747147 0.664658i \(-0.231423\pi\)
−0.949185 + 0.314719i \(0.898090\pi\)
\(332\) 2.02408 3.50581i 0.111086 0.192406i
\(333\) 15.3844 26.6466i 0.843062 1.46023i
\(334\) 3.36759 + 5.83284i 0.184266 + 0.319159i
\(335\) 11.0080 0.601432
\(336\) 0.852398 + 1.77144i 0.0465021 + 0.0966398i
\(337\) −1.58075 −0.0861092 −0.0430546 0.999073i \(-0.513709\pi\)
−0.0430546 + 0.999073i \(0.513709\pi\)
\(338\) −2.98803 5.17542i −0.162527 0.281506i
\(339\) 6.99108 12.1089i 0.379703 0.657665i
\(340\) −3.73303 + 6.46581i −0.202452 + 0.350658i
\(341\) −0.325540 0.563852i −0.0176290 0.0305343i
\(342\) −6.23433 −0.337114
\(343\) −18.0521 4.13805i −0.974719 0.223434i
\(344\) 4.72940 0.254992
\(345\) −7.43680 12.8809i −0.400384 0.693485i
\(346\) −6.77793 + 11.7397i −0.364384 + 0.631131i
\(347\) −10.9417 + 18.9516i −0.587382 + 1.01737i 0.407192 + 0.913342i \(0.366508\pi\)
−0.994574 + 0.104032i \(0.966825\pi\)
\(348\) −6.47530 11.2155i −0.347113 0.601217i
\(349\) 5.31231 0.284362 0.142181 0.989841i \(-0.454589\pi\)
0.142181 + 0.989841i \(0.454589\pi\)
\(350\) 4.26501 + 8.86346i 0.227974 + 0.473772i
\(351\) 42.4663 2.26668
\(352\) 15.1473 + 26.2359i 0.807354 + 1.39838i
\(353\) −12.7642 + 22.1083i −0.679371 + 1.17671i 0.295799 + 0.955250i \(0.404414\pi\)
−0.975170 + 0.221456i \(0.928919\pi\)
\(354\) −6.67183 + 11.5559i −0.354604 + 0.614191i
\(355\) 4.59062 + 7.95118i 0.243645 + 0.422005i
\(356\) 16.8840 0.894848
\(357\) −33.2757 + 48.7738i −1.76114 + 2.58138i
\(358\) 16.1718 0.854708
\(359\) −10.1139 17.5178i −0.533792 0.924555i −0.999221 0.0394699i \(-0.987433\pi\)
0.465428 0.885086i \(-0.345900\pi\)
\(360\) 10.8674 18.8228i 0.572761 0.992051i
\(361\) 9.13243 15.8178i 0.480654 0.832517i
\(362\) −11.2619 19.5062i −0.591914 1.02522i
\(363\) −62.5653 −3.28383
\(364\) −7.89922 0.594444i −0.414032 0.0311573i
\(365\) 3.48631 0.182482
\(366\) −17.9461 31.0836i −0.938059 1.62477i
\(367\) 16.3207 28.2683i 0.851934 1.47559i −0.0275261 0.999621i \(-0.508763\pi\)
0.879460 0.475972i \(-0.157904\pi\)
\(368\) 0.532581 0.922457i 0.0277627 0.0480864i
\(369\) −4.02843 6.97744i −0.209711 0.363231i
\(370\) −3.23410 −0.168133
\(371\) −5.92008 0.445507i −0.307355 0.0231296i
\(372\) 0.470047 0.0243708
\(373\) 4.42301 + 7.66089i 0.229015 + 0.396666i 0.957516 0.288379i \(-0.0931162\pi\)
−0.728501 + 0.685044i \(0.759783\pi\)
\(374\) 16.5363 28.6417i 0.855070 1.48103i
\(375\) 14.2274 24.6426i 0.734701 1.27254i
\(376\) −6.80887 11.7933i −0.351141 0.608194i
\(377\) −8.29678 −0.427306
\(378\) 22.6275 33.1662i 1.16383 1.70588i
\(379\) 10.5565 0.542252 0.271126 0.962544i \(-0.412604\pi\)
0.271126 + 0.962544i \(0.412604\pi\)
\(380\) −0.476915 0.826041i −0.0244652 0.0423750i
\(381\) 10.5884 18.3397i 0.542460 0.939569i
\(382\) 7.35582 12.7406i 0.376356 0.651868i
\(383\) −12.4272 21.5245i −0.634998 1.09985i −0.986516 0.163668i \(-0.947667\pi\)
0.351517 0.936181i \(-0.385666\pi\)
\(384\) −20.5301 −1.04767
\(385\) −5.87805 12.2156i −0.299573 0.622567i
\(386\) 8.79872 0.447843
\(387\) −6.62709 11.4785i −0.336874 0.583482i
\(388\) −4.98247 + 8.62989i −0.252947 + 0.438116i
\(389\) −3.62123 + 6.27215i −0.183604 + 0.318011i −0.943105 0.332495i \(-0.892110\pi\)
0.759501 + 0.650506i \(0.225443\pi\)
\(390\) −3.55583 6.15889i −0.180057 0.311867i
\(391\) 31.9918 1.61789
\(392\) −12.5570 + 15.7258i −0.634225 + 0.794275i
\(393\) −21.6372 −1.09145
\(394\) −11.0269 19.0992i −0.555528 0.962203i
\(395\) −1.31977 + 2.28590i −0.0664047 + 0.115016i
\(396\) 26.0778 45.1680i 1.31046 2.26978i
\(397\) 17.3510 + 30.0527i 0.870819 + 1.50830i 0.861151 + 0.508350i \(0.169744\pi\)
0.00966877 + 0.999953i \(0.496922\pi\)
\(398\) 4.44964 0.223040
\(399\) −3.27073 6.79716i −0.163741 0.340284i
\(400\) 0.920509 0.0460254
\(401\) −9.38251 16.2510i −0.468540 0.811535i 0.530813 0.847489i \(-0.321887\pi\)
−0.999353 + 0.0359533i \(0.988553\pi\)
\(402\) 17.6020 30.4875i 0.877908 1.52058i
\(403\) 0.150567 0.260790i 0.00750030 0.0129909i
\(404\) −3.71847 6.44058i −0.185001 0.320431i
\(405\) −29.7858 −1.48007
\(406\) −4.42080 + 6.47978i −0.219401 + 0.321586i
\(407\) −20.8530 −1.03364
\(408\) 32.0785 + 55.5615i 1.58812 + 2.75070i
\(409\) −14.8238 + 25.6755i −0.732989 + 1.26957i 0.222611 + 0.974907i \(0.428542\pi\)
−0.955600 + 0.294667i \(0.904791\pi\)
\(410\) −0.423426 + 0.733395i −0.0209115 + 0.0362198i
\(411\) 22.0518 + 38.1948i 1.08773 + 1.88401i
\(412\) −10.3682 −0.510807
\(413\) −11.7313 0.882819i −0.577257 0.0434407i
\(414\) −34.6603 −1.70346
\(415\) 1.60208 + 2.77489i 0.0786432 + 0.136214i
\(416\) −7.00587 + 12.1345i −0.343491 + 0.594944i
\(417\) 8.60874 14.9108i 0.421572 0.730184i
\(418\) 2.11260 + 3.65912i 0.103330 + 0.178974i
\(419\) −8.62323 −0.421273 −0.210636 0.977564i \(-0.567554\pi\)
−0.210636 + 0.977564i \(0.567554\pi\)
\(420\) 9.75937 + 0.734427i 0.476209 + 0.0358364i
\(421\) 11.6599 0.568267 0.284134 0.958785i \(-0.408294\pi\)
0.284134 + 0.958785i \(0.408294\pi\)
\(422\) 12.2539 + 21.2244i 0.596511 + 1.03319i
\(423\) −19.0819 + 33.0508i −0.927793 + 1.60699i
\(424\) −3.22547 + 5.58669i −0.156643 + 0.271313i
\(425\) 13.8236 + 23.9432i 0.670542 + 1.16141i
\(426\) 29.3619 1.42259
\(427\) 17.8341 26.1403i 0.863051 1.26502i
\(428\) 12.4752 0.603012
\(429\) −22.9275 39.7115i −1.10695 1.91729i
\(430\) −0.696570 + 1.20649i −0.0335916 + 0.0581823i
\(431\) 14.2606 24.7001i 0.686910 1.18976i −0.285923 0.958253i \(-0.592300\pi\)
0.972833 0.231510i \(-0.0743665\pi\)
\(432\) −1.87868 3.25396i −0.0903878 0.156556i
\(433\) −6.13071 −0.294623 −0.147312 0.989090i \(-0.547062\pi\)
−0.147312 + 0.989090i \(0.547062\pi\)
\(434\) −0.123450 0.256551i −0.00592578 0.0123148i
\(435\) 10.2506 0.491476
\(436\) −1.92561 3.33526i −0.0922201 0.159730i
\(437\) −2.04356 + 3.53955i −0.0977568 + 0.169320i
\(438\) 5.57466 9.65560i 0.266368 0.461362i
\(439\) −11.6640 20.2026i −0.556692 0.964219i −0.997770 0.0667500i \(-0.978737\pi\)
0.441078 0.897469i \(-0.354596\pi\)
\(440\) −14.7303 −0.702239
\(441\) 55.7628 + 8.44049i 2.65537 + 0.401928i
\(442\) 15.2966 0.727584
\(443\) 11.1142 + 19.2504i 0.528053 + 0.914615i 0.999465 + 0.0327020i \(0.0104112\pi\)
−0.471412 + 0.881913i \(0.656255\pi\)
\(444\) 7.52740 13.0378i 0.357235 0.618749i
\(445\) −6.68193 + 11.5734i −0.316754 + 0.548634i
\(446\) −3.94490 6.83277i −0.186797 0.323541i
\(447\) −12.2227 −0.578112
\(448\) 6.25679 + 13.0027i 0.295605 + 0.614321i
\(449\) −11.6146 −0.548126 −0.274063 0.961712i \(-0.588368\pi\)
−0.274063 + 0.961712i \(0.588368\pi\)
\(450\) −14.9766 25.9403i −0.706006 1.22284i
\(451\) −2.73018 + 4.72882i −0.128559 + 0.222671i
\(452\) 2.49254 4.31720i 0.117239 0.203064i
\(453\) 23.7197 + 41.0838i 1.11445 + 1.93028i
\(454\) −13.2573 −0.622195
\(455\) 3.53363 5.17942i 0.165659 0.242815i
\(456\) −8.19639 −0.383831
\(457\) 1.71196 + 2.96521i 0.0800823 + 0.138707i 0.903285 0.429041i \(-0.141148\pi\)
−0.823203 + 0.567747i \(0.807815\pi\)
\(458\) −2.39343 + 4.14554i −0.111838 + 0.193708i
\(459\) 56.4254 97.7316i 2.63371 4.56172i
\(460\) −2.65145 4.59244i −0.123624 0.214124i
\(461\) 9.15435 0.426360 0.213180 0.977013i \(-0.431618\pi\)
0.213180 + 0.977013i \(0.431618\pi\)
\(462\) −43.2312 3.25330i −2.01130 0.151357i
\(463\) 4.14841 0.192793 0.0963965 0.995343i \(-0.469268\pi\)
0.0963965 + 0.995343i \(0.469268\pi\)
\(464\) 0.367043 + 0.635737i 0.0170395 + 0.0295134i
\(465\) −0.186024 + 0.322203i −0.00862665 + 0.0149418i
\(466\) −1.99702 + 3.45894i −0.0925103 + 0.160233i
\(467\) 1.67482 + 2.90087i 0.0775014 + 0.134236i 0.902171 0.431378i \(-0.141972\pi\)
−0.824670 + 0.565614i \(0.808639\pi\)
\(468\) 24.1227 1.11507
\(469\) 30.9501 + 2.32910i 1.42914 + 0.107548i
\(470\) 4.01138 0.185031
\(471\) 15.0455 + 26.0595i 0.693259 + 1.20076i
\(472\) −6.39162 + 11.0706i −0.294198 + 0.509566i
\(473\) −4.49137 + 7.77929i −0.206514 + 0.357692i
\(474\) 4.22066 + 7.31039i 0.193861 + 0.335777i
\(475\) −3.53207 −0.162063
\(476\) −11.8638 + 17.3894i −0.543777 + 0.797040i
\(477\) 18.0788 0.827772
\(478\) −0.309476 0.536028i −0.0141551 0.0245174i
\(479\) 1.01960 1.76600i 0.0465866 0.0806904i −0.841792 0.539802i \(-0.818499\pi\)
0.888378 + 0.459112i \(0.151832\pi\)
\(480\) 8.65565 14.9920i 0.395074 0.684289i
\(481\) −4.82242 8.35267i −0.219883 0.380849i
\(482\) −8.00306 −0.364529
\(483\) −18.1839 37.7894i −0.827395 1.71948i
\(484\) −22.3065 −1.01393
\(485\) −3.94368 6.83066i −0.179073 0.310164i
\(486\) −24.8651 + 43.0677i −1.12791 + 1.95359i
\(487\) −13.4602 + 23.3138i −0.609941 + 1.05645i 0.381309 + 0.924448i \(0.375474\pi\)
−0.991250 + 0.132001i \(0.957860\pi\)
\(488\) −17.1924 29.7781i −0.778264 1.34799i
\(489\) 29.5697 1.33719
\(490\) −2.16228 5.51954i −0.0976820 0.249347i
\(491\) −29.1260 −1.31444 −0.657218 0.753700i \(-0.728267\pi\)
−0.657218 + 0.753700i \(0.728267\pi\)
\(492\) −1.97106 3.41397i −0.0888620 0.153914i
\(493\) −11.0240 + 19.0942i −0.496497 + 0.859957i
\(494\) −0.977109 + 1.69240i −0.0439622 + 0.0761448i
\(495\) 20.6408 + 35.7510i 0.927737 + 1.60689i
\(496\) −0.0266439 −0.00119635
\(497\) 11.2246 + 23.3268i 0.503493 + 1.04635i
\(498\) 10.2470 0.459180
\(499\) 9.99956 + 17.3197i 0.447642 + 0.775338i 0.998232 0.0594374i \(-0.0189307\pi\)
−0.550590 + 0.834776i \(0.685597\pi\)
\(500\) 5.07251 8.78585i 0.226850 0.392915i
\(501\) 12.4079 21.4911i 0.554344 0.960151i
\(502\) 1.54749 + 2.68033i 0.0690677 + 0.119629i
\(503\) 41.5151 1.85107 0.925534 0.378663i \(-0.123616\pi\)
0.925534 + 0.378663i \(0.123616\pi\)
\(504\) 34.5372 50.6228i 1.53841 2.25492i
\(505\) 5.88643 0.261943
\(506\) 11.7452 + 20.3432i 0.522136 + 0.904366i
\(507\) −11.0094 + 19.0688i −0.488944 + 0.846876i
\(508\) 3.77509 6.53865i 0.167493 0.290106i
\(509\) −14.5064 25.1258i −0.642985 1.11368i −0.984763 0.173902i \(-0.944363\pi\)
0.341778 0.939781i \(-0.388971\pi\)
\(510\) −18.8987 −0.836848
\(511\) 9.80209 + 0.737642i 0.433619 + 0.0326313i
\(512\) 2.52453 0.111570
\(513\) 7.20864 + 12.4857i 0.318269 + 0.551259i
\(514\) 6.87257 11.9036i 0.303136 0.525047i
\(515\) 4.10329 7.10711i 0.180813 0.313177i
\(516\) −3.24255 5.61625i −0.142745 0.247242i
\(517\) 25.8647 1.13753
\(518\) −9.09298 0.684279i −0.399523 0.0300655i
\(519\) 49.9466 2.19241
\(520\) −3.40649 5.90022i −0.149385 0.258742i
\(521\) −5.67389 + 9.82747i −0.248578 + 0.430549i −0.963131 0.269031i \(-0.913296\pi\)
0.714554 + 0.699581i \(0.246630\pi\)
\(522\) 11.9436 20.6868i 0.522755 0.905439i
\(523\) 12.6105 + 21.8421i 0.551420 + 0.955088i 0.998172 + 0.0604303i \(0.0192473\pi\)
−0.446752 + 0.894658i \(0.647419\pi\)
\(524\) −7.71432 −0.337002
\(525\) 20.4249 29.9378i 0.891418 1.30659i
\(526\) 11.0771 0.482984
\(527\) −0.400121 0.693030i −0.0174295 0.0301889i
\(528\) −2.02859 + 3.51361i −0.0882829 + 0.152910i
\(529\) 0.138653 0.240154i 0.00602839 0.0104415i
\(530\) −0.950128 1.64567i −0.0412709 0.0714833i
\(531\) 35.8251 1.55468
\(532\) −1.16612 2.42340i −0.0505575 0.105068i
\(533\) −2.52551 −0.109392
\(534\) 21.3690 + 37.0122i 0.924727 + 1.60167i
\(535\) −4.93713 + 8.55137i −0.213451 + 0.369708i
\(536\) 16.8627 29.2071i 0.728359 1.26156i
\(537\) −29.7925 51.6022i −1.28564 2.22680i
\(538\) −11.5788 −0.499197
\(539\) −13.9421 35.5891i −0.600527 1.53293i
\(540\) −18.7059 −0.804975
\(541\) 17.6271 + 30.5310i 0.757848 + 1.31263i 0.943946 + 0.330100i \(0.107083\pi\)
−0.186098 + 0.982531i \(0.559584\pi\)
\(542\) 8.10957 14.0462i 0.348336 0.603336i
\(543\) −41.4946 + 71.8707i −1.78070 + 3.08427i
\(544\) 18.6175 + 32.2465i 0.798220 + 1.38256i
\(545\) 3.04829 0.130574
\(546\) −8.69445 18.0686i −0.372088 0.773266i
\(547\) 31.7557 1.35778 0.678889 0.734241i \(-0.262462\pi\)
0.678889 + 0.734241i \(0.262462\pi\)
\(548\) 7.86214 + 13.6176i 0.335854 + 0.581716i
\(549\) −48.1818 + 83.4533i −2.05635 + 3.56170i
\(550\) −10.1501 + 17.5805i −0.432802 + 0.749636i
\(551\) −1.40838 2.43938i −0.0599988 0.103921i
\(552\) −45.5685 −1.93952
\(553\) −4.19431 + 6.14779i −0.178360 + 0.261431i
\(554\) 0.753332 0.0320060
\(555\) 5.95803 + 10.3196i 0.252904 + 0.438043i
\(556\) 3.06928 5.31615i 0.130167 0.225455i
\(557\) −17.2338 + 29.8498i −0.730219 + 1.26478i 0.226571 + 0.973995i \(0.427249\pi\)
−0.956790 + 0.290781i \(0.906085\pi\)
\(558\) 0.433496 + 0.750837i 0.0183514 + 0.0317855i
\(559\) −4.15466 −0.175723
\(560\) −0.553196 0.0416299i −0.0233768 0.00175919i
\(561\) −121.856 −5.14476
\(562\) 2.69256 + 4.66365i 0.113579 + 0.196724i
\(563\) −6.13481 + 10.6258i −0.258552 + 0.447824i −0.965854 0.259086i \(-0.916579\pi\)
0.707303 + 0.706911i \(0.249912\pi\)
\(564\) −9.33652 + 16.1713i −0.393138 + 0.680936i
\(565\) 1.97287 + 3.41711i 0.0829993 + 0.143759i
\(566\) −16.6199 −0.698584
\(567\) −83.7454 6.30214i −3.51698 0.264665i
\(568\) 28.1287 1.18025
\(569\) 6.70388 + 11.6115i 0.281041 + 0.486778i 0.971642 0.236459i \(-0.0759868\pi\)
−0.690600 + 0.723237i \(0.742653\pi\)
\(570\) 1.20720 2.09094i 0.0505642 0.0875798i
\(571\) −5.21373 + 9.03045i −0.218188 + 0.377912i −0.954254 0.298997i \(-0.903348\pi\)
0.736066 + 0.676910i \(0.236681\pi\)
\(572\) −8.17435 14.1584i −0.341787 0.591992i
\(573\) −54.2050 −2.26445
\(574\) −1.34568 + 1.97242i −0.0561674 + 0.0823272i
\(575\) −19.6369 −0.818914
\(576\) −21.9708 38.0545i −0.915450 1.58561i
\(577\) −0.701313 + 1.21471i −0.0291960 + 0.0505690i −0.880254 0.474502i \(-0.842628\pi\)
0.851058 + 0.525071i \(0.175961\pi\)
\(578\) 12.6536 21.9168i 0.526322 0.911617i
\(579\) −16.2094 28.0756i −0.673641 1.16678i
\(580\) 3.65464 0.151751
\(581\) 3.91729 + 8.14084i 0.162517 + 0.337739i
\(582\) −25.2240 −1.04557
\(583\) −6.12627 10.6110i −0.253724 0.439463i
\(584\) 5.34054 9.25008i 0.220993 0.382771i
\(585\) −9.54672 + 16.5354i −0.394708 + 0.683655i
\(586\) −8.28683 14.3532i −0.342326 0.592926i
\(587\) 40.2338 1.66063 0.830313 0.557298i \(-0.188162\pi\)
0.830313 + 0.557298i \(0.188162\pi\)
\(588\) 27.2840 + 4.12982i 1.12517 + 0.170311i
\(589\) 0.102235 0.00421253
\(590\) −1.88278 3.26107i −0.0775128 0.134256i
\(591\) −40.6287 + 70.3710i −1.67124 + 2.89467i
\(592\) −0.426680 + 0.739031i −0.0175364 + 0.0303740i
\(593\) −7.62087 13.1997i −0.312952 0.542048i 0.666048 0.745909i \(-0.267984\pi\)
−0.979000 + 0.203861i \(0.934651\pi\)
\(594\) 82.8619 3.39986
\(595\) −7.22470 15.0142i −0.296184 0.615523i
\(596\) −4.35776 −0.178501
\(597\) −8.19734 14.1982i −0.335495 0.581094i
\(598\) −5.43232 + 9.40906i −0.222144 + 0.384765i
\(599\) 1.35851 2.35301i 0.0555071 0.0961412i −0.836937 0.547300i \(-0.815656\pi\)
0.892444 + 0.451159i \(0.148989\pi\)
\(600\) −19.6901 34.1042i −0.803843 1.39230i
\(601\) 22.9588 0.936511 0.468255 0.883593i \(-0.344883\pi\)
0.468255 + 0.883593i \(0.344883\pi\)
\(602\) −2.21374 + 3.24479i −0.0902255 + 0.132248i
\(603\) −94.5158 −3.84898
\(604\) 8.45682 + 14.6476i 0.344103 + 0.596004i
\(605\) 8.82792 15.2904i 0.358906 0.621643i
\(606\) 9.41249 16.3029i 0.382356 0.662260i
\(607\) 22.1303 + 38.3308i 0.898241 + 1.55580i 0.829741 + 0.558149i \(0.188488\pi\)
0.0685005 + 0.997651i \(0.478179\pi\)
\(608\) −4.75698 −0.192921
\(609\) 28.8204 + 2.16884i 1.16786 + 0.0878856i
\(610\) 10.1287 0.410100
\(611\) 5.98142 + 10.3601i 0.241982 + 0.419126i
\(612\) 32.0521 55.5159i 1.29563 2.24410i
\(613\) −10.5460 + 18.2661i −0.425947 + 0.737762i −0.996508 0.0834931i \(-0.973392\pi\)
0.570561 + 0.821255i \(0.306726\pi\)
\(614\) 7.61503 + 13.1896i 0.307318 + 0.532290i
\(615\) 3.12023 0.125820
\(616\) −41.4156 3.11667i −1.66868 0.125574i
\(617\) −22.5480 −0.907750 −0.453875 0.891065i \(-0.649959\pi\)
−0.453875 + 0.891065i \(0.649959\pi\)
\(618\) −13.1225 22.7288i −0.527863 0.914285i
\(619\) 16.8984 29.2689i 0.679205 1.17642i −0.296015 0.955183i \(-0.595658\pi\)
0.975221 0.221235i \(-0.0710088\pi\)
\(620\) −0.0663233 + 0.114875i −0.00266361 + 0.00461350i
\(621\) 40.0771 + 69.4155i 1.60824 + 2.78555i
\(622\) −9.43424 −0.378279
\(623\) −21.2356 + 31.1260i −0.850786 + 1.24704i
\(624\) −1.87651 −0.0751203
\(625\) −6.28374 10.8838i −0.251350 0.435350i
\(626\) −2.82895 + 4.89988i −0.113068 + 0.195839i
\(627\) 7.78386 13.4820i 0.310857 0.538421i
\(628\) 5.36418 + 9.29103i 0.214054 + 0.370753i
\(629\) −25.6304 −1.02195
\(630\) 7.82733 + 16.2666i 0.311848 + 0.648077i
\(631\) 34.1027 1.35761 0.678803 0.734321i \(-0.262499\pi\)
0.678803 + 0.734321i \(0.262499\pi\)
\(632\) 4.04339 + 7.00336i 0.160838 + 0.278579i
\(633\) 45.1495 78.2012i 1.79453 3.10822i
\(634\) −11.8112 + 20.4576i −0.469082 + 0.812474i
\(635\) 2.98803 + 5.17542i 0.118576 + 0.205380i
\(636\) 8.84572 0.350756
\(637\) 11.0310 13.8148i 0.437065 0.547360i
\(638\) −16.1890 −0.640929
\(639\) −39.4154 68.2695i −1.55925 2.70070i
\(640\) 2.89678 5.01736i 0.114505 0.198329i
\(641\) −5.54119 + 9.59763i −0.218864 + 0.379084i −0.954461 0.298336i \(-0.903568\pi\)
0.735597 + 0.677419i \(0.236902\pi\)
\(642\) 15.7891 + 27.3475i 0.623146 + 1.07932i
\(643\) 33.9767 1.33991 0.669954 0.742402i \(-0.266314\pi\)
0.669954 + 0.742402i \(0.266314\pi\)
\(644\) −6.48312 13.4731i −0.255471 0.530914i
\(645\) 5.13302 0.202113
\(646\) 2.59659 + 4.49743i 0.102161 + 0.176949i
\(647\) −3.94631 + 6.83520i −0.155145 + 0.268720i −0.933112 0.359586i \(-0.882918\pi\)
0.777967 + 0.628306i \(0.216251\pi\)
\(648\) −45.6276 + 79.0293i −1.79242 + 3.10456i
\(649\) −12.1399 21.0268i −0.476531 0.825376i
\(650\) −9.38918 −0.368274
\(651\) −0.591196 + 0.866544i −0.0231708 + 0.0339625i
\(652\) 10.5425 0.412876
\(653\) −17.1684 29.7366i −0.671852 1.16368i −0.977378 0.211499i \(-0.932166\pi\)
0.305526 0.952184i \(-0.401168\pi\)
\(654\) 4.87426 8.44247i 0.190599 0.330127i
\(655\) 3.05299 5.28793i 0.119290 0.206616i
\(656\) 0.111726 + 0.193516i 0.00436218 + 0.00755552i
\(657\) −29.9337 −1.16783
\(658\) 11.2784 + 0.848737i 0.439676 + 0.0330872i
\(659\) −23.9977 −0.934819 −0.467409 0.884041i \(-0.654813\pi\)
−0.467409 + 0.884041i \(0.654813\pi\)
\(660\) 10.0993 + 17.4925i 0.393114 + 0.680894i
\(661\) 4.77778 8.27535i 0.185834 0.321874i −0.758023 0.652228i \(-0.773835\pi\)
0.943857 + 0.330354i \(0.107168\pi\)
\(662\) 3.31729 5.74571i 0.128930 0.223313i
\(663\) −28.1801 48.8094i −1.09442 1.89560i
\(664\) 9.81667 0.380961
\(665\) 2.12266 + 0.159738i 0.0823133 + 0.00619436i
\(666\) 27.7683 1.07600
\(667\) −7.82999 13.5619i −0.303178 0.525120i
\(668\) 4.42380 7.66224i 0.171162 0.296461i
\(669\) −14.5350 + 25.1754i −0.561955 + 0.973335i
\(670\) 4.96725 + 8.60354i 0.191902 + 0.332384i
\(671\) 65.3085 2.52120
\(672\) 27.5082 40.3201i 1.06115 1.55538i
\(673\) 3.20764 0.123645 0.0618227 0.998087i \(-0.480309\pi\)
0.0618227 + 0.998087i \(0.480309\pi\)
\(674\) −0.713299 1.23547i −0.0274753 0.0475885i
\(675\) −34.6344 + 59.9886i −1.33308 + 2.30896i
\(676\) −3.92519 + 6.79863i −0.150969 + 0.261486i
\(677\) −0.812181 1.40674i −0.0312147 0.0540654i 0.849996 0.526789i \(-0.176604\pi\)
−0.881211 + 0.472724i \(0.843271\pi\)
\(678\) 12.6186 0.484615
\(679\) −9.64279 20.0394i −0.370056 0.769043i
\(680\) −18.1050 −0.694294
\(681\) 24.4232 + 42.3023i 0.935900 + 1.62103i
\(682\) 0.293793 0.508865i 0.0112499 0.0194854i
\(683\) −18.8633 + 32.6723i −0.721786 + 1.25017i 0.238498 + 0.971143i \(0.423345\pi\)
−0.960283 + 0.279026i \(0.909988\pi\)
\(684\) 4.09483 + 7.09245i 0.156570 + 0.271187i
\(685\) −12.4459 −0.475535
\(686\) −4.91162 15.9762i −0.187527 0.609974i
\(687\) 17.6372 0.672900
\(688\) 0.183799 + 0.318349i 0.00700727 + 0.0121369i
\(689\) 2.83350 4.90776i 0.107948 0.186971i
\(690\) 6.71156 11.6248i 0.255505 0.442547i
\(691\) −19.4756 33.7327i −0.740886 1.28325i −0.952092 0.305811i \(-0.901073\pi\)
0.211206 0.977442i \(-0.432261\pi\)
\(692\) 17.8075 0.676940
\(693\) 50.4694 + 104.884i 1.91717 + 3.98423i
\(694\) −19.7493 −0.749674
\(695\) 2.42937 + 4.20780i 0.0921514 + 0.159611i
\(696\) 15.7024 27.1973i 0.595198 1.03091i
\(697\) −3.35567 + 5.81218i −0.127105 + 0.220152i
\(698\) 2.39713 + 4.15194i 0.0907325 + 0.157153i
\(699\) 14.7161 0.556613
\(700\) 7.28212 10.6738i 0.275238 0.403430i
\(701\) −8.29770 −0.313400 −0.156700 0.987646i \(-0.550086\pi\)
−0.156700 + 0.987646i \(0.550086\pi\)
\(702\) 19.1625 + 33.1904i 0.723241 + 1.25269i
\(703\) 1.63721 2.83573i 0.0617485 0.106951i
\(704\) −14.8903 + 25.7907i −0.561198 + 0.972023i
\(705\) −7.38996 12.7998i −0.278322 0.482068i
\(706\) −23.0389 −0.867081
\(707\) 16.5502 + 1.24546i 0.622436 + 0.0468405i
\(708\) 17.5287 0.658770
\(709\) −10.9637 18.9897i −0.411751 0.713174i 0.583330 0.812235i \(-0.301749\pi\)
−0.995081 + 0.0990614i \(0.968416\pi\)
\(710\) −4.14294 + 7.17578i −0.155482 + 0.269302i
\(711\) 11.3316 19.6270i 0.424969 0.736068i
\(712\) 20.4715 + 35.4577i 0.767203 + 1.32884i
\(713\) 0.568385 0.0212862
\(714\) −53.1354 3.99863i −1.98854 0.149645i
\(715\) 12.9402 0.483935
\(716\) −10.6220 18.3978i −0.396962 0.687557i
\(717\) −1.14026 + 1.97500i −0.0425840 + 0.0737576i
\(718\) 9.12760 15.8095i 0.340639 0.590004i
\(719\) 6.07991 + 10.5307i 0.226742 + 0.392729i 0.956841 0.290613i \(-0.0938591\pi\)
−0.730098 + 0.683342i \(0.760526\pi\)
\(720\) 1.68936 0.0629586
\(721\) 13.0405 19.1141i 0.485655 0.711847i
\(722\) 16.4836 0.613458
\(723\) 14.7436 + 25.5367i 0.548322 + 0.949721i
\(724\) −14.7941 + 25.6241i −0.549818 + 0.952313i
\(725\) 6.76664 11.7202i 0.251307 0.435276i
\(726\) −28.2320 48.8992i −1.04779 1.81482i
\(727\) 5.65386 0.209690 0.104845 0.994489i \(-0.466565\pi\)
0.104845 + 0.994489i \(0.466565\pi\)
\(728\) −8.32929 17.3098i −0.308704 0.641543i
\(729\) 88.0044 3.25942
\(730\) 1.57316 + 2.72480i 0.0582253 + 0.100849i
\(731\) −5.52034 + 9.56151i −0.204177 + 0.353645i
\(732\) −23.5747 + 40.8326i −0.871346 + 1.50922i
\(733\) 12.1627 + 21.0663i 0.449238 + 0.778103i 0.998337 0.0576548i \(-0.0183623\pi\)
−0.549099 + 0.835757i \(0.685029\pi\)
\(734\) 29.4582 1.08732
\(735\) −13.6287 + 17.0679i −0.502701 + 0.629560i
\(736\) −26.4468 −0.974843
\(737\) 32.0281 + 55.4742i 1.17977 + 2.04342i
\(738\) 3.63557 6.29699i 0.133827 0.231795i
\(739\) 19.3662 33.5433i 0.712398 1.23391i −0.251556 0.967843i \(-0.580942\pi\)
0.963955 0.266067i \(-0.0857242\pi\)
\(740\) 2.12422 + 3.67926i 0.0780879 + 0.135252i
\(741\) 7.20032 0.264510
\(742\) −2.32318 4.82798i −0.0852865 0.177241i
\(743\) −5.26170 −0.193033 −0.0965165 0.995331i \(-0.530770\pi\)
−0.0965165 + 0.995331i \(0.530770\pi\)
\(744\) 0.569925 + 0.987138i 0.0208945 + 0.0361903i
\(745\) 1.72461 2.98711i 0.0631847 0.109439i
\(746\) −3.99168 + 6.91379i −0.146146 + 0.253132i
\(747\) −13.7556 23.8254i −0.503292 0.871727i
\(748\) −43.4454 −1.58852
\(749\) −15.6905 + 22.9983i −0.573319 + 0.840341i
\(750\) 25.6799 0.937697
\(751\) −26.1615 45.3130i −0.954646 1.65350i −0.735176 0.677876i \(-0.762901\pi\)
−0.219470 0.975619i \(-0.570433\pi\)
\(752\) 0.529227 0.916648i 0.0192989 0.0334267i
\(753\) 5.70171 9.87566i 0.207782 0.359889i
\(754\) −3.74383 6.48451i −0.136342 0.236152i
\(755\) −13.3873 −0.487215
\(756\) −52.5935 3.95784i −1.91281 0.143945i
\(757\) 21.9399 0.797421 0.398710 0.917077i \(-0.369458\pi\)
0.398710 + 0.917077i \(0.369458\pi\)
\(758\) 4.76352 + 8.25066i 0.173019 + 0.299677i
\(759\) 43.2750 74.9546i 1.57078 2.72068i
\(760\) 1.15650 2.00312i 0.0419508 0.0726609i
\(761\) 4.90915 + 8.50290i 0.177957 + 0.308230i 0.941181 0.337904i \(-0.109718\pi\)
−0.763224 + 0.646134i \(0.776385\pi\)
\(762\) 19.1116 0.692341
\(763\) 8.57055 + 0.644964i 0.310275 + 0.0233493i
\(764\) −19.3258 −0.699182
\(765\) 25.3696 + 43.9415i 0.917241 + 1.58871i
\(766\) 11.2153 19.4254i 0.405224 0.701868i
\(767\) 5.61487 9.72525i 0.202741 0.351158i
\(768\) −27.3993 47.4570i −0.988688 1.71246i
\(769\) 3.37717 0.121784 0.0608920 0.998144i \(-0.480605\pi\)
0.0608920 + 0.998144i \(0.480605\pi\)
\(770\) 6.89497 10.1063i 0.248477 0.364205i
\(771\) −50.6440 −1.82390
\(772\) −5.77917 10.0098i −0.207997 0.360261i
\(773\) 19.1751 33.2123i 0.689681 1.19456i −0.282261 0.959338i \(-0.591084\pi\)
0.971941 0.235224i \(-0.0755824\pi\)
\(774\) 5.98081 10.3591i 0.214976 0.372349i
\(775\) 0.245598 + 0.425388i 0.00882214 + 0.0152804i
\(776\) −24.1647 −0.867461
\(777\) 14.5681 + 30.2751i 0.522628 + 1.08611i
\(778\) −6.53617 −0.234333
\(779\) −0.428704 0.742537i −0.0153599 0.0266042i
\(780\) −4.67108 + 8.09055i −0.167252 + 0.289688i
\(781\) −26.7130 + 46.2683i −0.955866 + 1.65561i
\(782\) 14.4360 + 25.0038i 0.516229 + 0.894135i
\(783\) −55.2404 −1.97413
\(784\) −1.54655 0.234093i −0.0552340 0.00836046i
\(785\) −8.49162 −0.303079
\(786\) −9.76354 16.9110i −0.348254 0.603194i
\(787\) 8.63054 14.9485i 0.307645 0.532858i −0.670201 0.742179i \(-0.733792\pi\)
0.977847 + 0.209322i \(0.0671256\pi\)
\(788\) −14.4854 + 25.0894i −0.516021 + 0.893774i
\(789\) −20.4068 35.3456i −0.726500 1.25834i
\(790\) −2.38213 −0.0847522
\(791\) 4.82391 + 10.0250i 0.171519 + 0.356446i
\(792\) 126.475 4.49411
\(793\) 15.1031 + 26.1593i 0.536327 + 0.928945i
\(794\) −15.6589 + 27.1220i −0.555713 + 0.962522i
\(795\) −3.50075 + 6.06347i −0.124159 + 0.215049i
\(796\) −2.92261 5.06210i −0.103589 0.179422i
\(797\) 19.8669 0.703722 0.351861 0.936052i \(-0.385549\pi\)
0.351861 + 0.936052i \(0.385549\pi\)
\(798\) 3.83657 5.62345i 0.135813 0.199068i
\(799\) 31.7903 1.12466
\(800\) −11.4276 19.7932i −0.404027 0.699796i
\(801\) 57.3716 99.3705i 2.02712 3.51108i
\(802\) 8.46752 14.6662i 0.298999 0.517881i
\(803\) 10.1435 + 17.5690i 0.357956 + 0.619998i
\(804\) −46.2453 −1.63095
\(805\) 11.8011 + 0.888076i 0.415935 + 0.0313006i
\(806\) 0.271768 0.00957262
\(807\) 21.3310 + 36.9464i 0.750888 + 1.30058i
\(808\) 9.01718 15.6182i 0.317223 0.549447i
\(809\) 15.4400 26.7429i 0.542842 0.940230i −0.455897 0.890032i \(-0.650682\pi\)
0.998739 0.0501976i \(-0.0159851\pi\)
\(810\) −13.4405 23.2797i −0.472251 0.817964i
\(811\) 22.6923 0.796834 0.398417 0.917204i \(-0.369560\pi\)
0.398417 + 0.917204i \(0.369560\pi\)
\(812\) 10.2754 + 0.773257i 0.360594 + 0.0271360i
\(813\) −59.7594 −2.09586
\(814\) −9.40969 16.2981i −0.329809 0.571247i
\(815\) −4.17226 + 7.22656i −0.146148 + 0.253135i
\(816\) −2.49333 + 4.31858i −0.0872841 + 0.151180i
\(817\) −0.705253 1.22153i −0.0246737 0.0427361i
\(818\) −26.7563 −0.935512
\(819\) −30.3401 + 44.4709i −1.06017 + 1.55394i
\(820\) 1.11246 0.0388487
\(821\) −15.1960 26.3203i −0.530345 0.918585i −0.999373 0.0354016i \(-0.988729\pi\)
0.469028 0.883183i \(-0.344604\pi\)
\(822\) −19.9013 + 34.4700i −0.694136 + 1.20228i
\(823\) 25.5427 44.2413i 0.890364 1.54216i 0.0509246 0.998703i \(-0.483783\pi\)
0.839439 0.543453i \(-0.182883\pi\)
\(824\) −12.5713 21.7742i −0.437943 0.758540i
\(825\) 74.7962 2.60407
\(826\) −4.60362 9.56716i −0.160181 0.332884i
\(827\) −53.5924 −1.86359 −0.931794 0.362987i \(-0.881757\pi\)
−0.931794 + 0.362987i \(0.881757\pi\)
\(828\) 22.7656 + 39.4311i 0.791158 + 1.37033i
\(829\) 2.19046 3.79400i 0.0760780 0.131771i −0.825477 0.564436i \(-0.809094\pi\)
0.901555 + 0.432665i \(0.142427\pi\)
\(830\) −1.44585 + 2.50428i −0.0501861 + 0.0869249i
\(831\) −1.38783 2.40378i −0.0481431 0.0833864i
\(832\) −13.7740 −0.477526
\(833\) −17.1362 43.7425i −0.593733 1.51559i
\(834\) 15.5384 0.538051
\(835\) 3.50149 + 6.06475i 0.121174 + 0.209879i
\(836\) 2.77519 4.80677i 0.0959819 0.166245i
\(837\) 1.00249 1.73636i 0.0346510 0.0600173i
\(838\) −3.89114 6.73966i −0.134417 0.232818i
\(839\) −5.15856 −0.178093 −0.0890466 0.996027i \(-0.528382\pi\)
−0.0890466 + 0.996027i \(0.528382\pi\)
\(840\) 10.2907 + 21.3860i 0.355064 + 0.737886i
\(841\) −18.2075 −0.627845
\(842\) 5.26140 + 9.11301i 0.181320 + 0.314055i
\(843\) 9.92073 17.1832i 0.341688 0.591821i
\(844\) 16.0972 27.8812i 0.554088 0.959709i
\(845\) −3.10683 5.38119i −0.106878 0.185119i
\(846\) −34.4420 −1.18414
\(847\) 28.0557 41.1226i 0.964005 1.41299i
\(848\) −0.501407 −0.0172184
\(849\) 30.6179 + 53.0318i 1.05080 + 1.82005i
\(850\) −12.4755 + 21.6082i −0.427906 + 0.741155i
\(851\) 9.10220 15.7655i 0.312019 0.540433i
\(852\) −19.2854 33.4034i −0.660708 1.14438i
\(853\) 16.7568 0.573744 0.286872 0.957969i \(-0.407385\pi\)
0.286872 + 0.957969i \(0.407385\pi\)
\(854\) 28.4779 + 2.14306i 0.974493 + 0.0733340i
\(855\) −6.48221 −0.221687
\(856\) 15.1260 + 26.1990i 0.516995 + 0.895462i
\(857\) 16.1055 27.8955i 0.550152 0.952891i −0.448111 0.893978i \(-0.647903\pi\)
0.998263 0.0589134i \(-0.0187636\pi\)
\(858\) 20.6915 35.8388i 0.706398 1.22352i
\(859\) 12.5182 + 21.6822i 0.427117 + 0.739788i 0.996616 0.0822040i \(-0.0261959\pi\)
−0.569498 + 0.821992i \(0.692863\pi\)
\(860\) 1.83008 0.0624053
\(861\) 8.77281 + 0.660185i 0.298976 + 0.0224990i
\(862\) 25.7398 0.876702
\(863\) −2.62143 4.54045i −0.0892346 0.154559i 0.817953 0.575285i \(-0.195109\pi\)
−0.907188 + 0.420726i \(0.861775\pi\)
\(864\) −46.6455 + 80.7923i −1.58691 + 2.74861i
\(865\) −7.04742 + 12.2065i −0.239620 + 0.415033i
\(866\) −2.76642 4.79158i −0.0940067 0.162824i
\(867\) −93.2447 −3.16676
\(868\) −0.210780 + 0.308950i −0.00715433 + 0.0104864i
\(869\) −15.3596 −0.521037
\(870\) 4.62545 + 8.01152i 0.156818 + 0.271616i
\(871\) −14.8135 + 25.6577i −0.501936 + 0.869378i
\(872\) 4.66955 8.08790i 0.158131 0.273891i
\(873\) 33.8608 + 58.6486i 1.14601 + 1.98495i
\(874\) −3.68854 −0.124767
\(875\) 9.81705 + 20.4016i 0.331877 + 0.689700i
\(876\) −14.6462 −0.494849
\(877\) −24.8866 43.1048i −0.840361 1.45555i −0.889590 0.456760i \(-0.849010\pi\)
0.0492296 0.998787i \(-0.484323\pi\)
\(878\) 10.5265 18.2325i 0.355253 0.615316i
\(879\) −30.5328 + 52.8844i −1.02985 + 1.78375i
\(880\) −0.572464 0.991536i −0.0192977 0.0334247i
\(881\) 4.99315 0.168223 0.0841117 0.996456i \(-0.473195\pi\)
0.0841117 + 0.996456i \(0.473195\pi\)
\(882\) 18.5655 + 47.3912i 0.625134 + 1.59574i
\(883\) −44.6535 −1.50271 −0.751354 0.659899i \(-0.770599\pi\)
−0.751354 + 0.659899i \(0.770599\pi\)
\(884\) −10.0471 17.4021i −0.337920 0.585295i
\(885\) −6.93710 + 12.0154i −0.233188 + 0.403893i
\(886\) −10.0304 + 17.3731i −0.336977 + 0.583661i
\(887\) −18.2060 31.5337i −0.611297 1.05880i −0.991022 0.133698i \(-0.957315\pi\)
0.379725 0.925099i \(-0.376019\pi\)
\(888\) 36.5074 1.22511
\(889\) 7.30610 + 15.1834i 0.245039 + 0.509235i
\(890\) −12.0606 −0.404272
\(891\) −86.6623 150.103i −2.90330 5.02866i
\(892\) −5.18218 + 8.97579i −0.173512 + 0.300532i
\(893\) −2.03069 + 3.51726i −0.0679545 + 0.117701i
\(894\) −5.51535 9.55286i −0.184461 0.319495i
\(895\) 16.8148 0.562057
\(896\) 9.20614 13.4939i 0.307555 0.450799i
\(897\) 40.0308 1.33659
\(898\) −5.24096 9.07761i −0.174893 0.302924i
\(899\) −0.195859 + 0.339238i −0.00653227 + 0.0113142i
\(900\) −19.6739 + 34.0762i −0.655797 + 1.13587i
\(901\) −7.52980 13.0420i −0.250854 0.434492i
\(902\) −4.92787 −0.164080
\(903\) 14.4320 + 1.08606i 0.480266 + 0.0361417i
\(904\) 12.0886 0.402062
\(905\) −11.7097 20.2818i −0.389244 0.674190i
\(906\) −21.4066 + 37.0773i −0.711186 + 1.23181i
\(907\) 1.10496 1.91385i 0.0366896 0.0635482i −0.847098 0.531437i \(-0.821652\pi\)
0.883787 + 0.467889i \(0.154985\pi\)
\(908\) 8.70764 + 15.0821i 0.288973 + 0.500516i
\(909\) −50.5413 −1.67635
\(910\) 5.64259 + 0.424625i 0.187050 + 0.0140762i
\(911\) 46.7251 1.54807 0.774035 0.633142i \(-0.218235\pi\)
0.774035 + 0.633142i \(0.218235\pi\)
\(912\) −0.318536 0.551721i −0.0105478 0.0182693i
\(913\) −9.32259 + 16.1472i −0.308533 + 0.534394i
\(914\) −1.54501 + 2.67604i −0.0511045 + 0.0885155i
\(915\) −18.6597 32.3195i −0.616869 1.06845i
\(916\) 6.28820 0.207768
\(917\) 9.70259 14.2215i 0.320408 0.469637i
\(918\) 101.845 3.36140
\(919\) −12.4561 21.5747i −0.410890 0.711682i 0.584097 0.811684i \(-0.301449\pi\)
−0.994987 + 0.100001i \(0.968115\pi\)
\(920\) 6.42968 11.1365i 0.211980 0.367161i
\(921\) 28.0576 48.5972i 0.924529 1.60133i
\(922\) 4.13080 + 7.15476i 0.136041 + 0.235630i
\(923\) −24.7104 −0.813352
\(924\) 24.6940 + 51.3186i 0.812373 + 1.68826i
\(925\) 15.7322 0.517270
\(926\) 1.87193 + 3.24227i 0.0615153 + 0.106548i
\(927\) −35.2312 + 61.0222i −1.15714 + 2.00423i
\(928\) 9.11328 15.7847i 0.299158 0.518157i
\(929\) 0.553073 + 0.957951i 0.0181458 + 0.0314294i 0.874956 0.484203i \(-0.160890\pi\)
−0.856810 + 0.515632i \(0.827557\pi\)
\(930\) −0.335765 −0.0110102
\(931\) 5.93426 + 0.898235i 0.194488 + 0.0294385i
\(932\) 5.24673 0.171862
\(933\) 17.3802 + 30.1034i 0.569003 + 0.985543i
\(934\) −1.51149 + 2.61798i −0.0494575 + 0.0856629i
\(935\) 17.1938 29.7805i 0.562296 0.973925i
\(936\) 29.2484 + 50.6598i 0.956015 + 1.65587i
\(937\) −4.28847 −0.140098 −0.0700491 0.997544i \(-0.522316\pi\)
−0.0700491 + 0.997544i \(0.522316\pi\)
\(938\) 12.1455 + 25.2406i 0.396566 + 0.824136i
\(939\) 20.8465 0.680301
\(940\) −2.63475 4.56352i −0.0859361 0.148846i
\(941\) 10.4732 18.1402i 0.341418 0.591353i −0.643278 0.765632i \(-0.722426\pi\)
0.984696 + 0.174279i \(0.0557595\pi\)
\(942\) −13.5782 + 23.5182i −0.442403 + 0.766264i
\(943\) −2.38342 4.12820i −0.0776147 0.134433i
\(944\) −0.993591 −0.0323386
\(945\) 23.5271 34.4849i 0.765338 1.12179i
\(946\) −8.10674 −0.263573
\(947\) −3.75616 6.50585i −0.122059 0.211412i 0.798521 0.601967i \(-0.205616\pi\)
−0.920579 + 0.390556i \(0.872283\pi\)
\(948\) 5.54442 9.60321i 0.180074 0.311898i
\(949\) −4.69152 + 8.12596i −0.152293 + 0.263780i
\(950\) −1.59381 2.76056i −0.0517101 0.0895645i
\(951\) 87.0366 2.82236
\(952\) −50.9038 3.83069i −1.64980 0.124153i
\(953\) −30.4377 −0.985974 −0.492987 0.870037i \(-0.664095\pi\)
−0.492987 + 0.870037i \(0.664095\pi\)
\(954\) 8.15787 + 14.1299i 0.264121 + 0.457471i
\(955\) 7.64828 13.2472i 0.247493 0.428670i
\(956\) −0.406540 + 0.704147i −0.0131484 + 0.0227737i
\(957\) 29.8242 + 51.6570i 0.964079 + 1.66983i
\(958\) 1.84033 0.0594585
\(959\) −34.9929 2.63334i −1.12998 0.0850350i
\(960\) 17.0175 0.549238
\(961\) 15.4929 + 26.8345i 0.499771 + 0.865628i
\(962\) 4.35213 7.53811i 0.140318 0.243038i
\(963\) 42.3906 73.4227i 1.36602 2.36601i
\(964\) 5.25656 + 9.10463i 0.169302 + 0.293240i
\(965\) 9.14856 0.294503
\(966\) 21.3298 31.2640i 0.686274 1.00590i
\(967\) 43.8093 1.40881 0.704405 0.709798i \(-0.251214\pi\)
0.704405 + 0.709798i \(0.251214\pi\)
\(968\) −27.0463 46.8455i −0.869300 1.50567i
\(969\) 9.56714 16.5708i 0.307341 0.532330i
\(970\) 3.55909 6.16453i 0.114276 0.197931i
\(971\) −3.58123 6.20287i −0.114927 0.199060i 0.802823 0.596217i \(-0.203330\pi\)
−0.917751 + 0.397157i \(0.869997\pi\)
\(972\) 65.3276 2.09538
\(973\) 5.94011 + 12.3446i 0.190431 + 0.395751i
\(974\) −24.2951 −0.778467
\(975\) 17.2972 + 29.9597i 0.553954 + 0.959477i
\(976\) 1.33630 2.31454i 0.0427739 0.0740865i
\(977\) −21.0133 + 36.3961i −0.672276 + 1.16442i 0.304982 + 0.952358i \(0.401350\pi\)
−0.977257 + 0.212057i \(0.931984\pi\)
\(978\) 13.3430 + 23.1108i 0.426662 + 0.739001i
\(979\) −77.7648 −2.48537
\(980\) −4.85904 + 6.08525i −0.155216 + 0.194386i
\(981\) −26.1729 −0.835635
\(982\) −13.1428 22.7640i −0.419403 0.726428i
\(983\) −6.60637 + 11.4426i −0.210710 + 0.364961i −0.951937 0.306294i \(-0.900911\pi\)
0.741227 + 0.671255i \(0.234244\pi\)
\(984\) 4.77975 8.27876i 0.152373 0.263917i
\(985\) −11.4654 19.8586i −0.365317 0.632747i
\(986\) −19.8979 −0.633678
\(987\) −18.0694 37.5514i −0.575154 1.19527i
\(988\) 2.56714 0.0816715
\(989\) −3.92091 6.79122i −0.124678 0.215948i
\(990\) −18.6279 + 32.2645i −0.592035 + 1.02543i
\(991\) −13.3185 + 23.0683i −0.423075 + 0.732788i −0.996239 0.0866534i \(-0.972383\pi\)
0.573163 + 0.819441i \(0.305716\pi\)
\(992\) 0.330770 + 0.572910i 0.0105020 + 0.0181899i
\(993\) −24.4451 −0.775741
\(994\) −13.1665 + 19.2988i −0.417617 + 0.612121i
\(995\) 4.62656 0.146672
\(996\) −6.73044 11.6575i −0.213262 0.369381i
\(997\) −27.7880 + 48.1302i −0.880054 + 1.52430i −0.0287743 + 0.999586i \(0.509160\pi\)
−0.851280 + 0.524712i \(0.824173\pi\)
\(998\) −9.02439 + 15.6307i −0.285662 + 0.494781i
\(999\) −32.1079 55.6125i −1.01585 1.75950i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 287.2.e.d.165.11 34
7.2 even 3 inner 287.2.e.d.247.11 yes 34
7.3 odd 6 2009.2.a.r.1.7 17
7.4 even 3 2009.2.a.s.1.7 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.e.d.165.11 34 1.1 even 1 trivial
287.2.e.d.247.11 yes 34 7.2 even 3 inner
2009.2.a.r.1.7 17 7.3 odd 6
2009.2.a.s.1.7 17 7.4 even 3