Properties

Label 125.2.h.a.104.9
Level $125$
Weight $2$
Character 125.104
Analytic conductor $0.998$
Analytic rank $0$
Dimension $240$
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] = [125,2,Mod(4,125)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(125, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("125.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.h (of order \(50\), degree \(20\), 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: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{50})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 104.9
Character \(\chi\) \(=\) 125.104
Dual form 125.2.h.a.119.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.292102 + 1.13766i) q^{2} +(-1.81873 + 0.346941i) q^{3} +(0.543663 - 0.298881i) q^{4} +(-1.30981 + 1.81229i) q^{5} +(-0.925956 - 1.96776i) q^{6} +(-2.46333 + 3.39049i) q^{7} +(2.10692 + 2.24364i) q^{8} +(0.398083 - 0.157612i) q^{9} +O(q^{10})\) \(q+(0.292102 + 1.13766i) q^{2} +(-1.81873 + 0.346941i) q^{3} +(0.543663 - 0.298881i) q^{4} +(-1.30981 + 1.81229i) q^{5} +(-0.925956 - 1.96776i) q^{6} +(-2.46333 + 3.39049i) q^{7} +(2.10692 + 2.24364i) q^{8} +(0.398083 - 0.157612i) q^{9} +(-2.44437 - 0.960749i) q^{10} +(4.17884 - 1.07295i) q^{11} +(-0.885083 + 0.732204i) q^{12} +(-1.05707 - 2.66985i) q^{13} +(-4.57677 - 1.81207i) q^{14} +(1.75344 - 3.75049i) q^{15} +(-1.27221 + 2.00468i) q^{16} +(1.93058 - 3.51171i) q^{17} +(0.295590 + 0.406845i) q^{18} +(-1.10541 + 5.79476i) q^{19} +(-0.170437 + 1.37675i) q^{20} +(3.30384 - 7.02102i) q^{21} +(2.44130 + 4.44070i) q^{22} +(6.70653 + 0.421939i) q^{23} +(-4.61033 - 3.34960i) q^{24} +(-1.56879 - 4.74752i) q^{25} +(2.72861 - 1.98245i) q^{26} +(4.02056 - 2.55153i) q^{27} +(-0.325870 + 2.57953i) q^{28} +(-0.601399 - 0.0759744i) q^{29} +(4.77897 + 0.899290i) q^{30} +(2.52023 + 1.38551i) q^{31} +(3.20211 + 1.04043i) q^{32} +(-7.22794 + 3.40121i) q^{33} +(4.55906 + 1.17057i) q^{34} +(-2.91804 - 8.90518i) q^{35} +(0.169316 - 0.204668i) q^{36} +(0.0253252 + 0.0160719i) q^{37} +(-6.91536 + 0.435078i) q^{38} +(2.84880 + 4.48899i) q^{39} +(-6.82579 + 0.879600i) q^{40} +(0.0832323 + 1.32294i) q^{41} +(8.95260 + 1.70780i) q^{42} +(-6.36064 + 2.06670i) q^{43} +(1.95120 - 1.83230i) q^{44} +(-0.235775 + 0.927884i) q^{45} +(1.47897 + 7.75301i) q^{46} +(-4.69280 + 4.99733i) q^{47} +(1.61830 - 4.08736i) q^{48} +(-3.26428 - 10.0464i) q^{49} +(4.94282 - 3.17151i) q^{50} +(-2.29284 + 7.05665i) q^{51} +(-1.37266 - 1.13556i) q^{52} +(3.82658 + 1.80065i) q^{53} +(4.07719 + 3.82873i) q^{54} +(-3.52901 + 8.97863i) q^{55} +(-12.7971 + 1.61665i) q^{56} -10.9226i q^{57} +(-0.0892367 - 0.706381i) q^{58} +(-3.79114 - 4.58270i) q^{59} +(-0.167674 - 2.56308i) q^{60} +(0.679080 - 10.7937i) q^{61} +(-0.840074 + 3.27187i) q^{62} +(-0.446229 + 1.73795i) q^{63} +(-0.546480 + 8.68605i) q^{64} +(6.22309 + 1.58128i) q^{65} +(-5.98072 - 7.22945i) q^{66} +(-1.61633 - 12.7946i) q^{67} -2.48620i q^{68} +(-12.3438 + 1.55938i) q^{69} +(9.27871 - 5.92097i) q^{70} +(8.88891 + 8.34724i) q^{71} +(1.19235 + 0.561079i) q^{72} +(2.89550 + 2.39537i) q^{73} +(-0.0108868 + 0.0335061i) q^{74} +(4.50031 + 8.09017i) q^{75} +(1.13097 + 3.48078i) q^{76} +(-6.65608 + 16.8114i) q^{77} +(-4.27481 + 4.55221i) q^{78} +(0.862662 + 4.52223i) q^{79} +(-1.96671 - 4.93137i) q^{80} +(-7.36341 + 6.91470i) q^{81} +(-1.48074 + 0.481123i) q^{82} +(3.02244 + 0.576561i) q^{83} +(-0.302275 - 4.80453i) q^{84} +(3.83554 + 8.09844i) q^{85} +(-4.20916 - 6.63257i) q^{86} +(1.12014 - 0.0704734i) q^{87} +(11.2118 + 7.11521i) q^{88} +(1.53623 - 1.85698i) q^{89} +(-1.12449 + 0.00280482i) q^{90} +(11.6560 + 2.99275i) q^{91} +(3.77220 - 1.77506i) q^{92} +(-5.06430 - 1.64549i) q^{93} +(-7.05604 - 3.87909i) q^{94} +(-9.05390 - 9.59336i) q^{95} +(-6.18474 - 0.781315i) q^{96} +(0.116535 - 0.922473i) q^{97} +(10.4759 - 6.64822i) q^{98} +(1.49442 - 1.08576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{21}{50}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.292102 + 1.13766i 0.206547 + 0.804448i 0.984392 + 0.175991i \(0.0563131\pi\)
−0.777845 + 0.628457i \(0.783687\pi\)
\(3\) −1.81873 + 0.346941i −1.05004 + 0.200307i −0.683392 0.730051i \(-0.739496\pi\)
−0.366652 + 0.930358i \(0.619496\pi\)
\(4\) 0.543663 0.298881i 0.271832 0.149441i
\(5\) −1.30981 + 1.81229i −0.585765 + 0.810481i
\(6\) −0.925956 1.96776i −0.378020 0.803334i
\(7\) −2.46333 + 3.39049i −0.931053 + 1.28148i 0.0283944 + 0.999597i \(0.490961\pi\)
−0.959447 + 0.281888i \(0.909039\pi\)
\(8\) 2.10692 + 2.24364i 0.744908 + 0.793246i
\(9\) 0.398083 0.157612i 0.132694 0.0525374i
\(10\) −2.44437 0.960749i −0.772978 0.303815i
\(11\) 4.17884 1.07295i 1.25997 0.323505i 0.441086 0.897465i \(-0.354593\pi\)
0.818883 + 0.573960i \(0.194593\pi\)
\(12\) −0.885083 + 0.732204i −0.255501 + 0.211369i
\(13\) −1.05707 2.66985i −0.293178 0.740482i −0.999470 0.0325616i \(-0.989633\pi\)
0.706292 0.707920i \(-0.250367\pi\)
\(14\) −4.57677 1.81207i −1.22319 0.484297i
\(15\) 1.75344 3.75049i 0.452735 0.968373i
\(16\) −1.27221 + 2.00468i −0.318053 + 0.501171i
\(17\) 1.93058 3.51171i 0.468234 0.851714i −0.531755 0.846898i \(-0.678467\pi\)
0.999988 0.00481559i \(-0.00153286\pi\)
\(18\) 0.295590 + 0.406845i 0.0696712 + 0.0958942i
\(19\) −1.10541 + 5.79476i −0.253598 + 1.32941i 0.596428 + 0.802667i \(0.296586\pi\)
−0.850026 + 0.526741i \(0.823414\pi\)
\(20\) −0.170437 + 1.37675i −0.0381108 + 0.307852i
\(21\) 3.30384 7.02102i 0.720957 1.53211i
\(22\) 2.44130 + 4.44070i 0.520486 + 0.946761i
\(23\) 6.70653 + 0.421939i 1.39841 + 0.0879803i 0.744009 0.668170i \(-0.232922\pi\)
0.654399 + 0.756150i \(0.272922\pi\)
\(24\) −4.61033 3.34960i −0.941079 0.683734i
\(25\) −1.56879 4.74752i −0.313758 0.949503i
\(26\) 2.72861 1.98245i 0.535124 0.388791i
\(27\) 4.02056 2.55153i 0.773758 0.491041i
\(28\) −0.325870 + 2.57953i −0.0615837 + 0.487485i
\(29\) −0.601399 0.0759744i −0.111677 0.0141081i 0.0692960 0.997596i \(-0.477925\pi\)
−0.180973 + 0.983488i \(0.557925\pi\)
\(30\) 4.77897 + 0.899290i 0.872517 + 0.164187i
\(31\) 2.52023 + 1.38551i 0.452646 + 0.248844i 0.691732 0.722154i \(-0.256848\pi\)
−0.239086 + 0.970998i \(0.576848\pi\)
\(32\) 3.20211 + 1.04043i 0.566058 + 0.183924i
\(33\) −7.22794 + 3.40121i −1.25822 + 0.592075i
\(34\) 4.55906 + 1.17057i 0.781872 + 0.200751i
\(35\) −2.91804 8.90518i −0.493240 1.50525i
\(36\) 0.169316 0.204668i 0.0282193 0.0341113i
\(37\) 0.0253252 + 0.0160719i 0.00416344 + 0.00264220i 0.537907 0.843004i \(-0.319215\pi\)
−0.533743 + 0.845646i \(0.679215\pi\)
\(38\) −6.91536 + 0.435078i −1.12182 + 0.0705789i
\(39\) 2.84880 + 4.48899i 0.456173 + 0.718814i
\(40\) −6.82579 + 0.879600i −1.07925 + 0.139077i
\(41\) 0.0832323 + 1.32294i 0.0129987 + 0.206608i 0.999165 + 0.0408509i \(0.0130069\pi\)
−0.986167 + 0.165757i \(0.946993\pi\)
\(42\) 8.95260 + 1.70780i 1.38142 + 0.263519i
\(43\) −6.36064 + 2.06670i −0.969989 + 0.315168i −0.750811 0.660517i \(-0.770337\pi\)
−0.219177 + 0.975685i \(0.570337\pi\)
\(44\) 1.95120 1.83230i 0.294155 0.276230i
\(45\) −0.235775 + 0.927884i −0.0351472 + 0.138321i
\(46\) 1.47897 + 7.75301i 0.218061 + 1.14312i
\(47\) −4.69280 + 4.99733i −0.684515 + 0.728935i −0.973573 0.228377i \(-0.926658\pi\)
0.289057 + 0.957312i \(0.406658\pi\)
\(48\) 1.61830 4.08736i 0.233582 0.589960i
\(49\) −3.26428 10.0464i −0.466326 1.43520i
\(50\) 4.94282 3.17151i 0.699020 0.448519i
\(51\) −2.29284 + 7.05665i −0.321062 + 0.988128i
\(52\) −1.37266 1.13556i −0.190353 0.157474i
\(53\) 3.82658 + 1.80065i 0.525621 + 0.247338i 0.670234 0.742150i \(-0.266194\pi\)
−0.144613 + 0.989488i \(0.546194\pi\)
\(54\) 4.07719 + 3.82873i 0.554835 + 0.521025i
\(55\) −3.52901 + 8.97863i −0.475852 + 1.21068i
\(56\) −12.7971 + 1.61665i −1.71008 + 0.216034i
\(57\) 10.9226i 1.44674i
\(58\) −0.0892367 0.706381i −0.0117173 0.0927524i
\(59\) −3.79114 4.58270i −0.493564 0.596616i 0.463643 0.886022i \(-0.346542\pi\)
−0.957206 + 0.289406i \(0.906542\pi\)
\(60\) −0.167674 2.56308i −0.0216467 0.330892i
\(61\) 0.679080 10.7937i 0.0869472 1.38199i −0.676655 0.736300i \(-0.736571\pi\)
0.763603 0.645687i \(-0.223429\pi\)
\(62\) −0.840074 + 3.27187i −0.106689 + 0.415528i
\(63\) −0.446229 + 1.73795i −0.0562196 + 0.218961i
\(64\) −0.546480 + 8.68605i −0.0683100 + 1.08576i
\(65\) 6.22309 + 1.58128i 0.771880 + 0.196134i
\(66\) −5.98072 7.22945i −0.736176 0.889884i
\(67\) −1.61633 12.7946i −0.197466 1.56311i −0.709852 0.704351i \(-0.751238\pi\)
0.512386 0.858755i \(-0.328762\pi\)
\(68\) 2.48620i 0.301496i
\(69\) −12.3438 + 1.55938i −1.48601 + 0.187727i
\(70\) 9.27871 5.92097i 1.10902 0.707691i
\(71\) 8.88891 + 8.34724i 1.05492 + 0.990635i 0.999969 0.00785387i \(-0.00249999\pi\)
0.0549502 + 0.998489i \(0.482500\pi\)
\(72\) 1.19235 + 0.561079i 0.140520 + 0.0661237i
\(73\) 2.89550 + 2.39537i 0.338893 + 0.280357i 0.791266 0.611472i \(-0.209422\pi\)
−0.452373 + 0.891829i \(0.649422\pi\)
\(74\) −0.0108868 + 0.0335061i −0.00126556 + 0.00389501i
\(75\) 4.50031 + 8.09017i 0.519651 + 0.934173i
\(76\) 1.13097 + 3.48078i 0.129732 + 0.399273i
\(77\) −6.65608 + 16.8114i −0.758531 + 1.91583i
\(78\) −4.27481 + 4.55221i −0.484027 + 0.515436i
\(79\) 0.862662 + 4.52223i 0.0970570 + 0.508791i 0.997302 + 0.0734072i \(0.0233873\pi\)
−0.900245 + 0.435384i \(0.856613\pi\)
\(80\) −1.96671 4.93137i −0.219885 0.551344i
\(81\) −7.36341 + 6.91470i −0.818157 + 0.768300i
\(82\) −1.48074 + 0.481123i −0.163521 + 0.0531312i
\(83\) 3.02244 + 0.576561i 0.331756 + 0.0632858i 0.350568 0.936537i \(-0.385988\pi\)
−0.0188122 + 0.999823i \(0.505988\pi\)
\(84\) −0.302275 4.80453i −0.0329809 0.524217i
\(85\) 3.83554 + 8.09844i 0.416023 + 0.878399i
\(86\) −4.20916 6.63257i −0.453885 0.715208i
\(87\) 1.12014 0.0704734i 0.120092 0.00755554i
\(88\) 11.2118 + 7.11521i 1.19518 + 0.758484i
\(89\) 1.53623 1.85698i 0.162840 0.196839i −0.682782 0.730622i \(-0.739230\pi\)
0.845621 + 0.533783i \(0.179230\pi\)
\(90\) −1.12449 + 0.00280482i −0.118531 + 0.000295654i
\(91\) 11.6560 + 2.99275i 1.22188 + 0.313726i
\(92\) 3.77220 1.77506i 0.393279 0.185063i
\(93\) −5.06430 1.64549i −0.525143 0.170629i
\(94\) −7.05604 3.87909i −0.727775 0.400098i
\(95\) −9.05390 9.59336i −0.928910 0.984258i
\(96\) −6.18474 0.781315i −0.631228 0.0797426i
\(97\) 0.116535 0.922473i 0.0118324 0.0936629i −0.985093 0.172025i \(-0.944969\pi\)
0.996925 + 0.0783621i \(0.0249690\pi\)
\(98\) 10.4759 6.64822i 1.05823 0.671572i
\(99\) 1.49442 1.08576i 0.150195 0.109123i
\(100\) −2.27184 2.11217i −0.227184 0.211217i
\(101\) −4.82403 3.50486i −0.480009 0.348747i 0.321320 0.946971i \(-0.395873\pi\)
−0.801329 + 0.598224i \(0.795873\pi\)
\(102\) −8.69782 0.547220i −0.861212 0.0541829i
\(103\) 5.90308 + 10.7377i 0.581648 + 1.05801i 0.989441 + 0.144939i \(0.0462986\pi\)
−0.407793 + 0.913075i \(0.633701\pi\)
\(104\) 3.76302 7.99682i 0.368994 0.784153i
\(105\) 8.39671 + 15.1837i 0.819435 + 1.48178i
\(106\) −0.930781 + 4.87932i −0.0904054 + 0.473922i
\(107\) −7.52111 10.3519i −0.727093 1.00076i −0.999258 0.0385073i \(-0.987740\pi\)
0.272165 0.962251i \(-0.412260\pi\)
\(108\) 1.42323 2.58884i 0.136950 0.249112i
\(109\) 0.151464 0.238668i 0.0145076 0.0228603i −0.836997 0.547208i \(-0.815691\pi\)
0.851504 + 0.524348i \(0.175691\pi\)
\(110\) −11.2455 1.39215i −1.07221 0.132736i
\(111\) −0.0516357 0.0204440i −0.00490105 0.00194046i
\(112\) −3.66298 9.25162i −0.346119 0.874196i
\(113\) 10.7461 8.88997i 1.01091 0.836298i 0.0243513 0.999703i \(-0.492248\pi\)
0.986559 + 0.163406i \(0.0522480\pi\)
\(114\) 12.4262 3.19051i 1.16382 0.298819i
\(115\) −9.54896 + 11.6015i −0.890445 + 1.08185i
\(116\) −0.349666 + 0.138443i −0.0324657 + 0.0128541i
\(117\) −0.841600 0.896213i −0.0778060 0.0828550i
\(118\) 4.10616 5.65164i 0.378002 0.520276i
\(119\) 7.15075 + 15.1961i 0.655508 + 1.39303i
\(120\) 12.1091 3.96791i 1.10540 0.362219i
\(121\) 6.67216 3.66805i 0.606560 0.333459i
\(122\) 12.4779 2.38029i 1.12970 0.215501i
\(123\) −0.610359 2.37719i −0.0550343 0.214344i
\(124\) 1.78426 0.160231
\(125\) 10.6587 + 3.37525i 0.953342 + 0.301892i
\(126\) −2.10754 −0.187755
\(127\) −4.02178 15.6638i −0.356875 1.38994i −0.853102 0.521744i \(-0.825282\pi\)
0.496227 0.868193i \(-0.334718\pi\)
\(128\) −3.42688 + 0.653713i −0.302897 + 0.0577806i
\(129\) 10.8513 5.96553i 0.955401 0.525236i
\(130\) 0.0188112 + 7.54167i 0.00164985 + 0.661448i
\(131\) −6.71425 14.2685i −0.586627 1.24665i −0.949195 0.314688i \(-0.898100\pi\)
0.362568 0.931957i \(-0.381900\pi\)
\(132\) −2.91301 + 4.00941i −0.253545 + 0.348975i
\(133\) −16.9241 18.0223i −1.46750 1.56273i
\(134\) 14.0838 5.57616i 1.21665 0.481707i
\(135\) −0.642074 + 10.6284i −0.0552609 + 0.914751i
\(136\) 11.9466 3.06736i 1.02441 0.263024i
\(137\) −0.756930 + 0.626187i −0.0646689 + 0.0534987i −0.669197 0.743085i \(-0.733362\pi\)
0.604528 + 0.796584i \(0.293362\pi\)
\(138\) −5.37968 13.5875i −0.457949 1.15665i
\(139\) 9.11799 + 3.61007i 0.773378 + 0.306202i 0.721466 0.692450i \(-0.243469\pi\)
0.0519118 + 0.998652i \(0.483469\pi\)
\(140\) −4.24803 3.96927i −0.359024 0.335464i
\(141\) 6.80116 10.7169i 0.572761 0.902527i
\(142\) −6.89987 + 12.5508i −0.579024 + 1.05324i
\(143\) −7.28192 10.0227i −0.608944 0.838140i
\(144\) −0.190483 + 0.998546i −0.0158736 + 0.0832121i
\(145\) 0.925407 0.990398i 0.0768509 0.0822480i
\(146\) −1.87934 + 3.99379i −0.155535 + 0.330529i
\(147\) 9.42237 + 17.1392i 0.777144 + 1.41362i
\(148\) 0.0185720 + 0.00116845i 0.00152661 + 9.60459e-5i
\(149\) 1.86592 + 1.35567i 0.152862 + 0.111061i 0.661587 0.749868i \(-0.269883\pi\)
−0.508725 + 0.860929i \(0.669883\pi\)
\(150\) −7.88933 + 7.48299i −0.644161 + 0.610983i
\(151\) −6.26338 + 4.55061i −0.509707 + 0.370324i −0.812712 0.582665i \(-0.802010\pi\)
0.303006 + 0.952989i \(0.402010\pi\)
\(152\) −15.3303 + 9.72893i −1.24346 + 0.789121i
\(153\) 0.215042 1.70223i 0.0173851 0.137617i
\(154\) −21.0699 2.66174i −1.69786 0.214490i
\(155\) −5.81196 + 2.75263i −0.466828 + 0.221096i
\(156\) 2.89046 + 1.58905i 0.231422 + 0.127226i
\(157\) −7.02035 2.28105i −0.560285 0.182048i 0.0151645 0.999885i \(-0.495173\pi\)
−0.575449 + 0.817837i \(0.695173\pi\)
\(158\) −4.89278 + 2.30237i −0.389249 + 0.183167i
\(159\) −7.58424 1.94730i −0.601469 0.154431i
\(160\) −6.07972 + 4.44039i −0.480644 + 0.351043i
\(161\) −17.9510 + 21.6990i −1.41474 + 1.71012i
\(162\) −10.0175 6.35727i −0.787046 0.499474i
\(163\) −12.3896 + 0.779485i −0.970426 + 0.0610540i −0.540083 0.841612i \(-0.681607\pi\)
−0.430342 + 0.902666i \(0.641607\pi\)
\(164\) 0.440652 + 0.694357i 0.0344092 + 0.0542202i
\(165\) 3.30326 17.5541i 0.257159 1.36658i
\(166\) 0.226929 + 3.60693i 0.0176131 + 0.279952i
\(167\) 15.7842 + 3.01100i 1.22142 + 0.232998i 0.757474 0.652866i \(-0.226433\pi\)
0.463945 + 0.885864i \(0.346433\pi\)
\(168\) 22.7136 7.38008i 1.75239 0.569386i
\(169\) 3.46590 3.25470i 0.266608 0.250362i
\(170\) −8.09291 + 6.72911i −0.620698 + 0.516099i
\(171\) 0.473280 + 2.48102i 0.0361926 + 0.189728i
\(172\) −2.84035 + 3.02467i −0.216575 + 0.230629i
\(173\) 1.15568 2.91892i 0.0878648 0.221921i −0.879199 0.476454i \(-0.841922\pi\)
0.967064 + 0.254533i \(0.0819218\pi\)
\(174\) 0.407370 + 1.25376i 0.0308827 + 0.0950471i
\(175\) 19.9608 + 6.37576i 1.50890 + 0.481962i
\(176\) −3.16546 + 9.74227i −0.238605 + 0.734351i
\(177\) 8.48498 + 7.01939i 0.637770 + 0.527609i
\(178\) 2.56135 + 1.20528i 0.191981 + 0.0903394i
\(179\) 1.16189 + 1.09109i 0.0868440 + 0.0815519i 0.726754 0.686898i \(-0.241028\pi\)
−0.639910 + 0.768450i \(0.721028\pi\)
\(180\) 0.149145 + 0.574925i 0.0111166 + 0.0428524i
\(181\) 4.82589 0.609652i 0.358706 0.0453151i 0.0560847 0.998426i \(-0.482138\pi\)
0.302621 + 0.953111i \(0.402138\pi\)
\(182\) 14.1348i 1.04774i
\(183\) 2.50970 + 19.8664i 0.185523 + 1.46856i
\(184\) 13.1834 + 15.9360i 0.971895 + 1.17482i
\(185\) −0.0622981 + 0.0248455i −0.00458025 + 0.00182668i
\(186\) 0.392720 6.24211i 0.0287956 0.457694i
\(187\) 4.29971 16.7463i 0.314426 1.22461i
\(188\) −1.05770 + 4.11945i −0.0771404 + 0.300442i
\(189\) −1.25307 + 19.9169i −0.0911472 + 1.44874i
\(190\) 8.26933 13.1025i 0.599920 0.950556i
\(191\) 1.56664 + 1.89374i 0.113358 + 0.137026i 0.824140 0.566386i \(-0.191659\pi\)
−0.710782 + 0.703412i \(0.751659\pi\)
\(192\) −2.01965 15.9872i −0.145756 1.15377i
\(193\) 0.332654i 0.0239449i −0.999928 0.0119725i \(-0.996189\pi\)
0.999928 0.0119725i \(-0.00381105\pi\)
\(194\) 1.08350 0.136878i 0.0777909 0.00982728i
\(195\) −11.8667 0.716880i −0.849795 0.0513369i
\(196\) −4.77736 4.48624i −0.341240 0.320446i
\(197\) −13.8135 6.50016i −0.984174 0.463117i −0.134779 0.990876i \(-0.543033\pi\)
−0.849394 + 0.527759i \(0.823033\pi\)
\(198\) 1.67175 + 1.38299i 0.118806 + 0.0982848i
\(199\) 1.48770 4.57867i 0.105460 0.324574i −0.884378 0.466772i \(-0.845417\pi\)
0.989838 + 0.142198i \(0.0454170\pi\)
\(200\) 7.34641 13.5224i 0.519469 0.956179i
\(201\) 7.37864 + 22.7091i 0.520449 + 1.60178i
\(202\) 2.57824 6.51189i 0.181404 0.458175i
\(203\) 1.73904 1.85189i 0.122057 0.129977i
\(204\) 0.862566 + 4.52173i 0.0603917 + 0.316584i
\(205\) −2.50657 1.58196i −0.175066 0.110489i
\(206\) −10.4915 + 9.85220i −0.730979 + 0.686435i
\(207\) 2.73626 0.889064i 0.190183 0.0617942i
\(208\) 6.69701 + 1.27752i 0.464354 + 0.0885802i
\(209\) 1.59812 + 25.4014i 0.110544 + 1.75705i
\(210\) −14.8212 + 13.9878i −1.02276 + 0.965251i
\(211\) −10.9834 17.3071i −0.756129 1.19147i −0.976387 0.216027i \(-0.930690\pi\)
0.220258 0.975442i \(-0.429310\pi\)
\(212\) 2.61855 0.164745i 0.179843 0.0113148i
\(213\) −19.0625 12.0975i −1.30614 0.828904i
\(214\) 9.58005 11.5803i 0.654879 0.791612i
\(215\) 4.58579 14.2343i 0.312748 0.970772i
\(216\) 14.1957 + 3.64484i 0.965895 + 0.248000i
\(217\) −10.9057 + 5.13183i −0.740327 + 0.348371i
\(218\) 0.315766 + 0.102599i 0.0213864 + 0.00694886i
\(219\) −6.09719 3.35196i −0.412010 0.226504i
\(220\) 0.764953 + 5.93611i 0.0515731 + 0.400212i
\(221\) −11.4165 1.44224i −0.767955 0.0970152i
\(222\) 0.00817549 0.0647157i 0.000548703 0.00434343i
\(223\) −10.2364 + 6.49624i −0.685482 + 0.435020i −0.832435 0.554123i \(-0.813054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(224\) −11.4154 + 8.29380i −0.762726 + 0.554153i
\(225\) −1.37277 1.64264i −0.0915183 0.109510i
\(226\) 13.2527 + 9.62867i 0.881559 + 0.640490i
\(227\) 22.0743 + 1.38880i 1.46512 + 0.0921776i 0.775204 0.631711i \(-0.217647\pi\)
0.689917 + 0.723888i \(0.257647\pi\)
\(228\) −3.26457 5.93822i −0.216201 0.393268i
\(229\) 10.7465 22.8375i 0.710149 1.50914i −0.144259 0.989540i \(-0.546080\pi\)
0.854408 0.519603i \(-0.173920\pi\)
\(230\) −15.9879 7.47466i −1.05421 0.492865i
\(231\) 6.27307 32.8846i 0.412738 2.16365i
\(232\) −1.09664 1.50939i −0.0719979 0.0990966i
\(233\) −0.157801 + 0.287038i −0.0103379 + 0.0188045i −0.881425 0.472324i \(-0.843415\pi\)
0.871087 + 0.491128i \(0.163415\pi\)
\(234\) 0.773754 1.21924i 0.0505819 0.0797043i
\(235\) −2.90992 15.0503i −0.189822 0.981771i
\(236\) −3.43078 1.35834i −0.223325 0.0884206i
\(237\) −3.13790 7.92543i −0.203828 0.514812i
\(238\) −15.1993 + 12.5739i −0.985223 + 0.815047i
\(239\) −14.1833 + 3.64165i −0.917441 + 0.235559i −0.677752 0.735291i \(-0.737046\pi\)
−0.239689 + 0.970850i \(0.577046\pi\)
\(240\) 5.28781 + 8.28650i 0.341327 + 0.534891i
\(241\) −15.0561 + 5.96114i −0.969850 + 0.383991i −0.799017 0.601309i \(-0.794646\pi\)
−0.170834 + 0.985300i \(0.554646\pi\)
\(242\) 6.12195 + 6.51922i 0.393534 + 0.419071i
\(243\) 2.59623 3.57340i 0.166548 0.229234i
\(244\) −2.85683 6.07108i −0.182890 0.388661i
\(245\) 22.4826 + 7.24310i 1.43636 + 0.462745i
\(246\) 2.52615 1.38876i 0.161062 0.0885444i
\(247\) 16.6396 3.17417i 1.05875 0.201968i
\(248\) 2.20133 + 8.57362i 0.139785 + 0.544426i
\(249\) −5.69704 −0.361035
\(250\) −0.726472 + 13.1119i −0.0459461 + 0.829269i
\(251\) −6.28616 −0.396779 −0.198390 0.980123i \(-0.563571\pi\)
−0.198390 + 0.980123i \(0.563571\pi\)
\(252\) 0.276842 + 1.07823i 0.0174394 + 0.0679220i
\(253\) 28.4783 5.43252i 1.79041 0.341539i
\(254\) 16.6453 9.15085i 1.04442 0.574175i
\(255\) −9.78549 13.3982i −0.612791 0.839026i
\(256\) 5.66660 + 12.0421i 0.354162 + 0.752633i
\(257\) −8.43041 + 11.6035i −0.525875 + 0.723804i −0.986495 0.163793i \(-0.947627\pi\)
0.460620 + 0.887597i \(0.347627\pi\)
\(258\) 9.95643 + 10.6025i 0.619860 + 0.660084i
\(259\) −0.116876 + 0.0462745i −0.00726232 + 0.00287535i
\(260\) 3.85588 1.00028i 0.239132 0.0620348i
\(261\) −0.251381 + 0.0645437i −0.0155601 + 0.00399516i
\(262\) 14.2715 11.8064i 0.881695 0.729402i
\(263\) 5.73994 + 14.4974i 0.353940 + 0.893950i 0.992260 + 0.124179i \(0.0396296\pi\)
−0.638320 + 0.769771i \(0.720370\pi\)
\(264\) −22.8598 9.05083i −1.40692 0.557040i
\(265\) −8.27540 + 4.57636i −0.508354 + 0.281123i
\(266\) 15.5597 24.5182i 0.954028 1.50331i
\(267\) −2.14972 + 3.91032i −0.131561 + 0.239308i
\(268\) −4.70280 6.47285i −0.287269 0.395392i
\(269\) 1.87273 9.81719i 0.114182 0.598565i −0.878493 0.477755i \(-0.841451\pi\)
0.992676 0.120810i \(-0.0385492\pi\)
\(270\) −12.2791 + 2.37412i −0.747283 + 0.144485i
\(271\) 8.09173 17.1958i 0.491538 1.04457i −0.493102 0.869972i \(-0.664137\pi\)
0.984640 0.174599i \(-0.0558630\pi\)
\(272\) 4.58376 + 8.33782i 0.277931 + 0.505555i
\(273\) −22.2374 1.39906i −1.34587 0.0846750i
\(274\) −0.933489 0.678219i −0.0563941 0.0409727i
\(275\) −11.6495 18.1559i −0.702494 1.09484i
\(276\) −6.24478 + 4.53710i −0.375891 + 0.273101i
\(277\) −11.1195 + 7.05667i −0.668108 + 0.423994i −0.826159 0.563436i \(-0.809479\pi\)
0.158051 + 0.987431i \(0.449479\pi\)
\(278\) −1.44365 + 11.4277i −0.0865846 + 0.685388i
\(279\) 1.22163 + 0.154328i 0.0731371 + 0.00923937i
\(280\) 13.8319 25.3095i 0.826616 1.51253i
\(281\) 0.688148 + 0.378313i 0.0410515 + 0.0225682i 0.502147 0.864782i \(-0.332544\pi\)
−0.461096 + 0.887350i \(0.652544\pi\)
\(282\) 14.1789 + 4.60699i 0.844339 + 0.274342i
\(283\) −9.30279 + 4.37756i −0.552994 + 0.260219i −0.681910 0.731437i \(-0.738850\pi\)
0.128916 + 0.991656i \(0.458850\pi\)
\(284\) 7.32741 + 1.88136i 0.434802 + 0.111638i
\(285\) 19.7949 + 14.3066i 1.17255 + 0.847447i
\(286\) 9.27538 11.2120i 0.548464 0.662980i
\(287\) −4.69044 2.97664i −0.276868 0.175706i
\(288\) 1.43869 0.0905147i 0.0847756 0.00533363i
\(289\) 0.504098 + 0.794331i 0.0296528 + 0.0467254i
\(290\) 1.39705 + 0.763503i 0.0820376 + 0.0448345i
\(291\) 0.108097 + 1.71816i 0.00633679 + 0.100720i
\(292\) 2.29011 + 0.436862i 0.134019 + 0.0255654i
\(293\) 7.78550 2.52966i 0.454834 0.147784i −0.0726356 0.997359i \(-0.523141\pi\)
0.527469 + 0.849574i \(0.323141\pi\)
\(294\) −16.7463 + 15.7259i −0.976666 + 0.917151i
\(295\) 13.2708 0.868168i 0.772658 0.0505467i
\(296\) 0.0172987 + 0.0906827i 0.00100546 + 0.00527083i
\(297\) 14.0637 14.9763i 0.816056 0.869012i
\(298\) −0.997256 + 2.51878i −0.0577695 + 0.145909i
\(299\) −5.96274 18.3514i −0.344834 1.06129i
\(300\) 4.86466 + 3.05327i 0.280861 + 0.176281i
\(301\) 8.66127 26.6566i 0.499227 1.53646i
\(302\) −7.00660 5.79636i −0.403185 0.333543i
\(303\) 9.98959 + 4.70074i 0.573887 + 0.270051i
\(304\) −10.2103 9.58814i −0.585603 0.549918i
\(305\) 18.6718 + 15.3683i 1.06914 + 0.879989i
\(306\) 1.99938 0.252580i 0.114297 0.0144391i
\(307\) 9.55170i 0.545144i 0.962135 + 0.272572i \(0.0878743\pi\)
−0.962135 + 0.272572i \(0.912126\pi\)
\(308\) 1.40593 + 11.1291i 0.0801104 + 0.634139i
\(309\) −14.4615 17.4809i −0.822683 0.994453i
\(310\) −4.82924 5.80799i −0.274282 0.329872i
\(311\) −1.92568 + 30.6078i −0.109195 + 1.73561i 0.438327 + 0.898815i \(0.355571\pi\)
−0.547522 + 0.836791i \(0.684429\pi\)
\(312\) −4.06949 + 15.8496i −0.230389 + 0.897308i
\(313\) 0.843290 3.28440i 0.0476655 0.185645i −0.940292 0.340368i \(-0.889448\pi\)
0.987958 + 0.154723i \(0.0494484\pi\)
\(314\) 0.544406 8.65308i 0.0307226 0.488322i
\(315\) −2.56519 3.08508i −0.144532 0.173825i
\(316\) 1.82061 + 2.20074i 0.102417 + 0.123801i
\(317\) 3.74193 + 29.6205i 0.210168 + 1.66365i 0.645786 + 0.763519i \(0.276530\pi\)
−0.435618 + 0.900132i \(0.643470\pi\)
\(318\) 9.19710i 0.515748i
\(319\) −2.59467 + 0.327783i −0.145274 + 0.0183523i
\(320\) −15.0258 12.3675i −0.839970 0.691362i
\(321\) 17.2704 + 16.2180i 0.963939 + 0.905199i
\(322\) −29.9297 14.0838i −1.66792 0.784861i
\(323\) 18.2154 + 15.0691i 1.01353 + 0.838467i
\(324\) −1.93654 + 5.96006i −0.107586 + 0.331114i
\(325\) −11.0168 + 9.20686i −0.611103 + 0.510705i
\(326\) −4.50580 13.8674i −0.249553 0.768047i
\(327\) −0.192667 + 0.486622i −0.0106545 + 0.0269103i
\(328\) −2.79283 + 2.97407i −0.154209 + 0.164215i
\(329\) −5.38344 28.2210i −0.296799 1.55587i
\(330\) 20.9355 1.36958i 1.15246 0.0753931i
\(331\) 6.78679 6.37322i 0.373036 0.350304i −0.475242 0.879855i \(-0.657640\pi\)
0.848278 + 0.529551i \(0.177640\pi\)
\(332\) 1.81551 0.589896i 0.0996393 0.0323748i
\(333\) 0.0126147 + 0.00240637i 0.000691279 + 0.000131868i
\(334\) 1.18510 + 18.8366i 0.0648457 + 1.03069i
\(335\) 25.3046 + 13.8292i 1.38254 + 0.755571i
\(336\) 9.87173 + 15.5554i 0.538547 + 0.848615i
\(337\) 12.3018 0.773963i 0.670121 0.0421604i 0.275914 0.961182i \(-0.411019\pi\)
0.394207 + 0.919022i \(0.371019\pi\)
\(338\) 4.71514 + 2.99232i 0.256470 + 0.162761i
\(339\) −16.4600 + 19.8967i −0.893985 + 1.08064i
\(340\) 4.50572 + 3.25645i 0.244357 + 0.176606i
\(341\) 12.0182 + 3.08575i 0.650822 + 0.167103i
\(342\) −2.68431 + 1.26314i −0.145151 + 0.0683029i
\(343\) 14.2030 + 4.61483i 0.766889 + 0.249177i
\(344\) −18.0383 9.91662i −0.972558 0.534668i
\(345\) 13.3419 24.4129i 0.718306 1.31435i
\(346\) 3.65831 + 0.462153i 0.196672 + 0.0248455i
\(347\) 1.89365 14.9898i 0.101656 0.804693i −0.856039 0.516910i \(-0.827082\pi\)
0.957696 0.287782i \(-0.0929180\pi\)
\(348\) 0.587917 0.373103i 0.0315157 0.0200004i
\(349\) −27.7971 + 20.1957i −1.48794 + 1.08105i −0.513055 + 0.858356i \(0.671486\pi\)
−0.974888 + 0.222697i \(0.928514\pi\)
\(350\) −1.42286 + 24.5711i −0.0760549 + 1.31338i
\(351\) −11.0622 8.03715i −0.590456 0.428991i
\(352\) 14.4974 + 0.912102i 0.772716 + 0.0486152i
\(353\) −2.86039 5.20302i −0.152243 0.276929i 0.789177 0.614166i \(-0.210508\pi\)
−0.941420 + 0.337237i \(0.890508\pi\)
\(354\) −5.50721 + 11.7034i −0.292705 + 0.622029i
\(355\) −26.7704 + 5.17597i −1.42083 + 0.274712i
\(356\) 0.280173 1.46872i 0.0148492 0.0778420i
\(357\) −18.2774 25.1567i −0.967345 1.33144i
\(358\) −0.901900 + 1.64055i −0.0476669 + 0.0867058i
\(359\) 4.36629 6.88017i 0.230444 0.363122i −0.709354 0.704853i \(-0.751013\pi\)
0.939798 + 0.341731i \(0.111013\pi\)
\(360\) −2.57859 + 1.42598i −0.135904 + 0.0751558i
\(361\) −14.6915 5.81678i −0.773237 0.306146i
\(362\) 2.10323 + 5.31215i 0.110543 + 0.279201i
\(363\) −10.8623 + 8.98605i −0.570121 + 0.471645i
\(364\) 7.23141 1.85671i 0.379029 0.0973181i
\(365\) −8.13366 + 2.11001i −0.425735 + 0.110443i
\(366\) −21.8681 + 8.65819i −1.14306 + 0.452571i
\(367\) 4.48819 + 4.77944i 0.234282 + 0.249485i 0.835357 0.549708i \(-0.185261\pi\)
−0.601075 + 0.799192i \(0.705261\pi\)
\(368\) −9.37797 + 12.9077i −0.488860 + 0.672858i
\(369\) 0.241645 + 0.513521i 0.0125795 + 0.0267328i
\(370\) −0.0464632 0.0636167i −0.00241550 0.00330728i
\(371\) −15.5312 + 8.53837i −0.806341 + 0.443290i
\(372\) −3.24508 + 0.619032i −0.168250 + 0.0320953i
\(373\) −0.688846 2.68288i −0.0356671 0.138914i 0.948256 0.317507i \(-0.102846\pi\)
−0.983923 + 0.178593i \(0.942846\pi\)
\(374\) 20.3076 1.05008
\(375\) −20.5563 2.44073i −1.06152 0.126039i
\(376\) −21.0995 −1.08813
\(377\) 0.432879 + 1.68595i 0.0222944 + 0.0868310i
\(378\) −23.0248 + 4.39221i −1.18427 + 0.225911i
\(379\) −30.0173 + 16.5021i −1.54188 + 0.847657i −0.541909 + 0.840437i \(0.682298\pi\)
−0.999974 + 0.00722050i \(0.997702\pi\)
\(380\) −7.78955 2.50951i −0.399595 0.128735i
\(381\) 12.7490 + 27.0929i 0.653149 + 1.38801i
\(382\) −1.69682 + 2.33547i −0.0868167 + 0.119493i
\(383\) −10.4936 11.1746i −0.536199 0.570994i 0.402636 0.915360i \(-0.368094\pi\)
−0.938836 + 0.344366i \(0.888094\pi\)
\(384\) 6.00578 2.37786i 0.306481 0.121344i
\(385\) −21.7488 34.0825i −1.10842 1.73700i
\(386\) 0.378447 0.0971687i 0.0192625 0.00494576i
\(387\) −2.20633 + 1.82523i −0.112154 + 0.0927817i
\(388\) −0.212354 0.536345i −0.0107806 0.0272288i
\(389\) 8.57826 + 3.39637i 0.434935 + 0.172203i 0.575381 0.817885i \(-0.304854\pi\)
−0.140446 + 0.990088i \(0.544854\pi\)
\(390\) −2.65073 13.7097i −0.134225 0.694219i
\(391\) 14.4292 22.7368i 0.729716 1.14985i
\(392\) 15.6630 28.4909i 0.791100 1.43901i
\(393\) 17.1617 + 23.6211i 0.865696 + 1.19153i
\(394\) 3.36002 17.6138i 0.169275 0.887372i
\(395\) −9.32552 4.35988i −0.469218 0.219369i
\(396\) 0.487947 1.03694i 0.0245203 0.0521082i
\(397\) 15.1641 + 27.5834i 0.761064 + 1.38437i 0.917927 + 0.396750i \(0.129862\pi\)
−0.156862 + 0.987620i \(0.550138\pi\)
\(398\) 5.64354 + 0.355062i 0.282885 + 0.0177976i
\(399\) 37.0330 + 26.9060i 1.85397 + 1.34699i
\(400\) 11.5131 + 2.89492i 0.575654 + 0.144746i
\(401\) 30.2876 22.0052i 1.51249 1.09889i 0.547434 0.836849i \(-0.315605\pi\)
0.965057 0.262040i \(-0.0843951\pi\)
\(402\) −23.6800 + 15.0278i −1.18105 + 0.749517i
\(403\) 1.03504 8.19319i 0.0515590 0.408132i
\(404\) −3.67019 0.463652i −0.182599 0.0230676i
\(405\) −2.88677 22.4016i −0.143445 1.11314i
\(406\) 2.61480 + 1.43750i 0.129770 + 0.0713418i
\(407\) 0.123074 + 0.0399893i 0.00610057 + 0.00198219i
\(408\) −20.6634 + 9.72346i −1.02299 + 0.481383i
\(409\) −23.8269 6.11771i −1.17817 0.302501i −0.391675 0.920104i \(-0.628104\pi\)
−0.786490 + 0.617602i \(0.788104\pi\)
\(410\) 1.06756 3.31372i 0.0527231 0.163653i
\(411\) 1.15940 1.40148i 0.0571890 0.0691297i
\(412\) 6.41858 + 4.07335i 0.316221 + 0.200680i
\(413\) 24.8764 1.56509i 1.22409 0.0770131i
\(414\) 1.81072 + 2.85324i 0.0889920 + 0.140229i
\(415\) −5.00372 + 4.72235i −0.245623 + 0.231811i
\(416\) −0.607060 9.64894i −0.0297636 0.473078i
\(417\) −17.8357 3.40233i −0.873416 0.166613i
\(418\) −28.4314 + 9.23792i −1.39063 + 0.451842i
\(419\) 24.4048 22.9176i 1.19225 1.11960i 0.202135 0.979358i \(-0.435212\pi\)
0.990117 0.140242i \(-0.0447879\pi\)
\(420\) 9.10312 + 5.74522i 0.444187 + 0.280338i
\(421\) 7.18989 + 37.6907i 0.350414 + 1.83693i 0.523498 + 0.852027i \(0.324627\pi\)
−0.173085 + 0.984907i \(0.555373\pi\)
\(422\) 16.4813 17.5508i 0.802298 0.854361i
\(423\) −1.08048 + 2.72899i −0.0525350 + 0.132688i
\(424\) 4.02227 + 12.3793i 0.195339 + 0.601191i
\(425\) −19.7006 3.65632i −0.955617 0.177358i
\(426\) 8.19460 25.2204i 0.397030 1.22193i
\(427\) 34.9230 + 28.8908i 1.69004 + 1.39812i
\(428\) −7.18295 3.38004i −0.347201 0.163380i
\(429\) 16.7211 + 15.7022i 0.807304 + 0.758109i
\(430\) 17.5333 + 1.05920i 0.845533 + 0.0510794i
\(431\) −11.6224 + 1.46826i −0.559833 + 0.0707234i −0.400158 0.916446i \(-0.631045\pi\)
−0.159675 + 0.987170i \(0.551045\pi\)
\(432\) 11.3060i 0.543962i
\(433\) −1.59145 12.5976i −0.0764803 0.605404i −0.983049 0.183345i \(-0.941308\pi\)
0.906568 0.422059i \(-0.138692\pi\)
\(434\) −9.02386 10.9080i −0.433159 0.523600i
\(435\) −1.33946 + 2.12233i −0.0642220 + 0.101758i
\(436\) 0.0110116 0.175025i 0.000527361 0.00838217i
\(437\) −9.85849 + 38.3963i −0.471595 + 1.83674i
\(438\) 2.03239 7.91565i 0.0971116 0.378225i
\(439\) 0.295159 4.69143i 0.0140872 0.223910i −0.984684 0.174349i \(-0.944218\pi\)
0.998771 0.0495606i \(-0.0157821\pi\)
\(440\) −27.5802 + 10.9994i −1.31483 + 0.524376i
\(441\) −2.88289 3.48482i −0.137281 0.165944i
\(442\) −1.69400 13.4094i −0.0805751 0.637818i
\(443\) 0.650810i 0.0309209i 0.999880 + 0.0154605i \(0.00492141\pi\)
−0.999880 + 0.0154605i \(0.995079\pi\)
\(444\) −0.0341828 + 0.00431829i −0.00162224 + 0.000204937i
\(445\) 1.35322 + 5.21638i 0.0641486 + 0.247280i
\(446\) −10.3806 9.74803i −0.491536 0.461583i
\(447\) −3.86395 1.81824i −0.182758 0.0859996i
\(448\) −28.1038 23.2495i −1.32778 1.09843i
\(449\) 1.72315 5.30330i 0.0813203 0.250278i −0.902128 0.431469i \(-0.857995\pi\)
0.983448 + 0.181191i \(0.0579953\pi\)
\(450\) 1.46778 2.04157i 0.0691920 0.0962406i
\(451\) 1.76726 + 5.43905i 0.0832168 + 0.256115i
\(452\) 3.18523 8.04497i 0.149820 0.378403i
\(453\) 9.81261 10.4494i 0.461036 0.490954i
\(454\) 4.86796 + 25.5187i 0.228465 + 1.19765i
\(455\) −20.6909 + 17.2041i −0.970004 + 0.806541i
\(456\) 24.5064 23.0130i 1.14762 1.07768i
\(457\) 37.3366 12.1314i 1.74653 0.567483i 0.750863 0.660457i \(-0.229638\pi\)
0.995668 + 0.0929748i \(0.0296376\pi\)
\(458\) 29.1204 + 5.55501i 1.36071 + 0.259569i
\(459\) −1.19821 19.0450i −0.0559275 0.888942i
\(460\) −1.72394 + 9.16132i −0.0803793 + 0.427149i
\(461\) −9.30153 14.6569i −0.433215 0.682638i 0.555656 0.831412i \(-0.312467\pi\)
−0.988871 + 0.148774i \(0.952467\pi\)
\(462\) 39.2439 2.46902i 1.82579 0.114869i
\(463\) −24.7433 15.7026i −1.14992 0.729761i −0.182566 0.983194i \(-0.558440\pi\)
−0.967353 + 0.253433i \(0.918440\pi\)
\(464\) 0.917411 1.10896i 0.0425897 0.0514821i
\(465\) 9.61538 7.02270i 0.445903 0.325670i
\(466\) −0.372646 0.0956794i −0.0172625 0.00443226i
\(467\) −27.9505 + 13.1525i −1.29339 + 0.608625i −0.944492 0.328535i \(-0.893445\pi\)
−0.348902 + 0.937159i \(0.613445\pi\)
\(468\) −0.725409 0.235700i −0.0335320 0.0108952i
\(469\) 47.3614 + 26.0372i 2.18695 + 1.20228i
\(470\) 16.2721 7.70671i 0.750577 0.355484i
\(471\) 13.5595 + 1.71297i 0.624789 + 0.0789293i
\(472\) 2.29431 18.1613i 0.105604 0.835942i
\(473\) −24.3627 + 15.4610i −1.12020 + 0.710899i
\(474\) 8.09987 5.88490i 0.372039 0.270302i
\(475\) 29.2448 3.84280i 1.34185 0.176320i
\(476\) 8.42944 + 6.12434i 0.386363 + 0.280709i
\(477\) 1.80710 + 0.113693i 0.0827414 + 0.00520565i
\(478\) −8.28593 15.0721i −0.378990 0.689380i
\(479\) −12.7539 + 27.1035i −0.582742 + 1.23839i 0.368410 + 0.929664i \(0.379902\pi\)
−0.951151 + 0.308725i \(0.900098\pi\)
\(480\) 9.51682 10.1852i 0.434381 0.464887i
\(481\) 0.0161390 0.0846034i 0.000735874 0.00385758i
\(482\) −11.1797 15.3875i −0.509221 0.700882i
\(483\) 25.1197 45.6926i 1.14299 2.07909i
\(484\) 2.53110 3.98837i 0.115050 0.181290i
\(485\) 1.51915 + 1.41946i 0.0689810 + 0.0644544i
\(486\) 4.82369 + 1.90983i 0.218807 + 0.0866317i
\(487\) −6.16305 15.5661i −0.279275 0.705367i −0.999927 0.0120707i \(-0.996158\pi\)
0.720653 0.693296i \(-0.243842\pi\)
\(488\) 25.6478 21.2177i 1.16102 0.960482i
\(489\) 22.2628 5.71613i 1.00676 0.258492i
\(490\) −1.67298 + 27.6933i −0.0755775 + 1.25106i
\(491\) −39.3455 + 15.5780i −1.77564 + 0.703025i −0.778481 + 0.627668i \(0.784010\pi\)
−0.997157 + 0.0753571i \(0.975990\pi\)
\(492\) −1.04233 1.10997i −0.0469918 0.0500412i
\(493\) −1.42785 + 1.96526i −0.0643070 + 0.0885110i
\(494\) 8.47159 + 18.0030i 0.381155 + 0.809995i
\(495\) 0.0103026 + 4.13046i 0.000463068 + 0.185650i
\(496\) −5.98375 + 3.28960i −0.268679 + 0.147707i
\(497\) −50.1976 + 9.57570i −2.25167 + 0.429529i
\(498\) −1.66412 6.48130i −0.0745708 0.290434i
\(499\) −7.04602 −0.315423 −0.157712 0.987485i \(-0.550412\pi\)
−0.157712 + 0.987485i \(0.550412\pi\)
\(500\) 6.80354 1.35068i 0.304264 0.0604044i
\(501\) −29.7519 −1.32922
\(502\) −1.83620 7.15152i −0.0819536 0.319188i
\(503\) −11.7346 + 2.23849i −0.523219 + 0.0998094i −0.442223 0.896905i \(-0.645810\pi\)
−0.0809961 + 0.996714i \(0.525810\pi\)
\(504\) −4.83949 + 2.66053i −0.215568 + 0.118510i
\(505\) 12.6704 4.15183i 0.563825 0.184754i
\(506\) 14.4989 + 30.8118i 0.644555 + 1.36975i
\(507\) −5.17436 + 7.12189i −0.229801 + 0.316294i
\(508\) −6.86811 7.31380i −0.304723 0.324497i
\(509\) 31.2031 12.3542i 1.38305 0.547589i 0.445453 0.895306i \(-0.353043\pi\)
0.937600 + 0.347716i \(0.113043\pi\)
\(510\) 12.3842 15.0462i 0.548383 0.666257i
\(511\) −15.2541 + 3.91658i −0.674800 + 0.173259i
\(512\) −17.4208 + 14.4117i −0.769898 + 0.636915i
\(513\) 10.3411 + 26.1187i 0.456571 + 1.15317i
\(514\) −15.6634 6.20156i −0.690881 0.273539i
\(515\) −27.1917 3.36622i −1.19821 0.148334i
\(516\) 4.11645 6.48649i 0.181217 0.285552i
\(517\) −14.2486 + 25.9182i −0.626654 + 1.13988i
\(518\) −0.0867843 0.119448i −0.00381308 0.00524826i
\(519\) −1.08918 + 5.70968i −0.0478096 + 0.250627i
\(520\) 9.56371 + 17.2940i 0.419397 + 0.758393i
\(521\) −5.96452 + 12.6753i −0.261310 + 0.555313i −0.991828 0.127581i \(-0.959279\pi\)
0.730518 + 0.682894i \(0.239279\pi\)
\(522\) −0.146858 0.267133i −0.00642779 0.0116921i
\(523\) 43.4241 + 2.73202i 1.89880 + 0.119463i 0.968763 0.247990i \(-0.0797700\pi\)
0.930042 + 0.367453i \(0.119770\pi\)
\(524\) −7.91488 5.75050i −0.345763 0.251212i
\(525\) −38.5154 4.67055i −1.68095 0.203839i
\(526\) −14.8165 + 10.7648i −0.646031 + 0.469369i
\(527\) 9.73098 6.17547i 0.423888 0.269008i
\(528\) 2.37711 18.8168i 0.103451 0.818896i
\(529\) 21.9808 + 2.77683i 0.955689 + 0.120732i
\(530\) −7.62360 8.07784i −0.331148 0.350879i
\(531\) −2.23147 1.22676i −0.0968377 0.0532370i
\(532\) −14.5875 4.73977i −0.632449 0.205495i
\(533\) 3.44406 1.62065i 0.149179 0.0701983i
\(534\) −5.07656 1.30344i −0.219684 0.0564053i
\(535\) 28.6119 0.0713669i 1.23700 0.00308546i
\(536\) 25.3009 30.5836i 1.09283 1.32101i
\(537\) −2.49172 1.58129i −0.107525 0.0682377i
\(538\) 11.7157 0.737088i 0.505098 0.0317781i
\(539\) −24.4202 38.4801i −1.05185 1.65745i
\(540\) 2.82757 + 5.97020i 0.121679 + 0.256916i
\(541\) 2.38981 + 37.9849i 0.102746 + 1.63310i 0.625224 + 0.780445i \(0.285007\pi\)
−0.522479 + 0.852652i \(0.674993\pi\)
\(542\) 21.9266 + 4.18273i 0.941829 + 0.179663i
\(543\) −8.56549 + 2.78309i −0.367580 + 0.119434i
\(544\) 9.83560 9.23624i 0.421698 0.396001i
\(545\) 0.234147 + 0.587106i 0.0100298 + 0.0251489i
\(546\) −4.90393 25.7073i −0.209869 1.10017i
\(547\) −17.6460 + 18.7911i −0.754488 + 0.803448i −0.985531 0.169495i \(-0.945786\pi\)
0.231043 + 0.972944i \(0.425786\pi\)
\(548\) −0.224359 + 0.566667i −0.00958416 + 0.0242068i
\(549\) −1.43088 4.40380i −0.0610686 0.187950i
\(550\) 17.2524 18.5566i 0.735646 0.791257i
\(551\) 1.10504 3.40098i 0.0470765 0.144887i
\(552\) −29.5060 24.4094i −1.25586 1.03894i
\(553\) −17.4576 8.21492i −0.742373 0.349334i
\(554\) −11.2761 10.5890i −0.479077 0.449884i
\(555\) 0.104684 0.0668011i 0.00444357 0.00283555i
\(556\) 6.03610 0.762537i 0.255988 0.0323388i
\(557\) 26.2392i 1.11179i −0.831253 0.555894i \(-0.812376\pi\)
0.831253 0.555894i \(-0.187624\pi\)
\(558\) 0.181268 + 1.43488i 0.00767368 + 0.0607434i
\(559\) 12.2414 + 14.7973i 0.517755 + 0.625859i
\(560\) 21.5644 + 5.47950i 0.911263 + 0.231551i
\(561\) −2.01004 + 31.9487i −0.0848641 + 1.34888i
\(562\) −0.229382 + 0.893385i −0.00967591 + 0.0376852i
\(563\) 7.98040 31.0816i 0.336334 1.30993i −0.545396 0.838178i \(-0.683621\pi\)
0.881730 0.471755i \(-0.156379\pi\)
\(564\) 0.494455 7.85914i 0.0208203 0.330929i
\(565\) 2.03580 + 31.1193i 0.0856467 + 1.30920i
\(566\) −7.69754 9.30473i −0.323552 0.391107i
\(567\) −5.30568 41.9988i −0.222818 1.76378i
\(568\) 37.5305i 1.57474i
\(569\) −7.07257 + 0.893474i −0.296498 + 0.0374564i −0.272175 0.962248i \(-0.587743\pi\)
−0.0243227 + 0.999704i \(0.507743\pi\)
\(570\) −10.4939 + 26.6989i −0.439540 + 1.11829i
\(571\) −19.6719 18.4731i −0.823243 0.773077i 0.153350 0.988172i \(-0.450994\pi\)
−0.976593 + 0.215095i \(0.930994\pi\)
\(572\) −6.95451 3.27254i −0.290783 0.136832i
\(573\) −3.50631 2.90067i −0.146478 0.121177i
\(574\) 2.01633 6.20562i 0.0841598 0.259017i
\(575\) −8.51796 32.5013i −0.355223 1.35540i
\(576\) 1.15148 + 3.54390i 0.0479784 + 0.147662i
\(577\) 11.6417 29.4035i 0.484650 1.22408i −0.457595 0.889160i \(-0.651289\pi\)
0.942245 0.334924i \(-0.108711\pi\)
\(578\) −0.756432 + 0.805518i −0.0314634 + 0.0335052i
\(579\) 0.115411 + 0.605007i 0.00479633 + 0.0251432i
\(580\) 0.207099 0.815030i 0.00859930 0.0338423i
\(581\) −9.40011 + 8.82729i −0.389982 + 0.366218i
\(582\) −1.92311 + 0.624856i −0.0797154 + 0.0259011i
\(583\) 17.9227 + 3.41893i 0.742282 + 0.141598i
\(584\) 0.726243 + 11.5433i 0.0300522 + 0.477665i
\(585\) 2.72654 0.351353i 0.112728 0.0145267i
\(586\) 5.15206 + 8.11834i 0.212829 + 0.335366i
\(587\) 15.0295 0.945576i 0.620334 0.0390281i 0.250486 0.968120i \(-0.419410\pi\)
0.369848 + 0.929092i \(0.379410\pi\)
\(588\) 10.2452 + 6.50180i 0.422505 + 0.268130i
\(589\) −10.8145 + 13.0725i −0.445606 + 0.538645i
\(590\) 4.86412 + 14.8441i 0.200253 + 0.611123i
\(591\) 27.3783 + 7.02955i 1.12619 + 0.289157i
\(592\) −0.0644380 + 0.0303222i −0.00264838 + 0.00124623i
\(593\) −23.2363 7.54993i −0.954200 0.310039i −0.209779 0.977749i \(-0.567275\pi\)
−0.744421 + 0.667710i \(0.767275\pi\)
\(594\) 21.1460 + 11.6251i 0.867629 + 0.476983i
\(595\) −36.9059 6.94482i −1.51299 0.284710i
\(596\) 1.41962 + 0.179339i 0.0581498 + 0.00734603i
\(597\) −1.11720 + 8.84352i −0.0457238 + 0.361941i
\(598\) 19.1360 12.1441i 0.782528 0.496607i
\(599\) 23.7091 17.2257i 0.968727 0.703821i 0.0135659 0.999908i \(-0.495682\pi\)
0.955161 + 0.296087i \(0.0956817\pi\)
\(600\) −8.66965 + 27.1424i −0.353937 + 1.10808i
\(601\) 7.65177 + 5.55934i 0.312122 + 0.226770i 0.732807 0.680437i \(-0.238210\pi\)
−0.420684 + 0.907207i \(0.638210\pi\)
\(602\) 32.8562 + 2.06714i 1.33912 + 0.0842502i
\(603\) −2.66001 4.83855i −0.108324 0.197041i
\(604\) −2.04508 + 4.34601i −0.0832130 + 0.176837i
\(605\) −2.09170 + 16.8963i −0.0850397 + 0.686934i
\(606\) −2.42988 + 12.7379i −0.0987070 + 0.517440i
\(607\) 14.0688 + 19.3641i 0.571036 + 0.785964i 0.992677 0.120799i \(-0.0385457\pi\)
−0.421641 + 0.906763i \(0.638546\pi\)
\(608\) −9.56867 + 17.4053i −0.388061 + 0.705880i
\(609\) −2.52035 + 3.97143i −0.102130 + 0.160930i
\(610\) −12.0299 + 25.7313i −0.487077 + 1.04183i
\(611\) 18.3027 + 7.24655i 0.740448 + 0.293164i
\(612\) −0.391855 0.989714i −0.0158398 0.0400068i
\(613\) −31.3595 + 25.9428i −1.26660 + 1.04782i −0.270218 + 0.962799i \(0.587096\pi\)
−0.996379 + 0.0850216i \(0.972904\pi\)
\(614\) −10.8666 + 2.79007i −0.438540 + 0.112598i
\(615\) 5.10762 + 2.00753i 0.205959 + 0.0809513i
\(616\) −51.7424 + 20.4863i −2.08476 + 0.825416i
\(617\) −2.33924 2.49104i −0.0941744 0.100286i 0.680155 0.733068i \(-0.261913\pi\)
−0.774329 + 0.632783i \(0.781913\pi\)
\(618\) 15.6631 21.5584i 0.630063 0.867208i
\(619\) −6.92172 14.7094i −0.278207 0.591221i 0.716073 0.698026i \(-0.245938\pi\)
−0.994280 + 0.106805i \(0.965938\pi\)
\(620\) −2.33704 + 3.23359i −0.0938577 + 0.129864i
\(621\) 28.0406 15.4154i 1.12523 0.618601i
\(622\) −35.3838 + 6.74981i −1.41876 + 0.270643i
\(623\) 2.51183 + 9.78291i 0.100634 + 0.391944i
\(624\) −12.6233 −0.505335
\(625\) −20.0778 + 14.8957i −0.803112 + 0.595828i
\(626\) 3.98286 0.159187
\(627\) −11.7194 45.6439i −0.468026 1.82284i
\(628\) −4.49847 + 0.858129i −0.179509 + 0.0342431i
\(629\) 0.105332 0.0579067i 0.00419986 0.00230889i
\(630\) 2.76048 3.81947i 0.109980 0.152171i
\(631\) −20.6803 43.9479i −0.823270 1.74954i −0.642915 0.765937i \(-0.722275\pi\)
−0.180355 0.983602i \(-0.557725\pi\)
\(632\) −8.32870 + 11.4635i −0.331298 + 0.455992i
\(633\) 25.9804 + 27.6663i 1.03263 + 1.09964i
\(634\) −32.6050 + 12.9092i −1.29491 + 0.512692i
\(635\) 33.6551 + 13.2280i 1.33556 + 0.524937i
\(636\) −4.70528 + 1.20811i −0.186577 + 0.0479047i
\(637\) −23.3718 + 19.3349i −0.926026 + 0.766075i
\(638\) −1.13081 2.85611i −0.0447694 0.113075i
\(639\) 4.85415 + 1.92189i 0.192027 + 0.0760289i
\(640\) 3.30386 7.06675i 0.130596 0.279338i
\(641\) −3.88435 + 6.12075i −0.153423 + 0.241755i −0.912342 0.409430i \(-0.865728\pi\)
0.758919 + 0.651185i \(0.225728\pi\)
\(642\) −13.4058 + 24.3851i −0.529087 + 0.962405i
\(643\) 15.7879 + 21.7302i 0.622614 + 0.856955i 0.997540 0.0700996i \(-0.0223317\pi\)
−0.374926 + 0.927055i \(0.622332\pi\)
\(644\) −3.27386 + 17.1622i −0.129008 + 0.676285i
\(645\) −3.40184 + 27.4794i −0.133947 + 1.08200i
\(646\) −11.8228 + 25.1247i −0.465161 + 0.988517i
\(647\) −5.97764 10.8733i −0.235005 0.427473i 0.732339 0.680941i \(-0.238429\pi\)
−0.967344 + 0.253468i \(0.918429\pi\)
\(648\) −31.0282 1.95213i −1.21890 0.0766869i
\(649\) −20.7595 15.0827i −0.814883 0.592047i
\(650\) −13.6923 9.84407i −0.537057 0.386116i
\(651\) 18.0541 13.1171i 0.707595 0.514098i
\(652\) −6.50278 + 4.12679i −0.254668 + 0.161618i
\(653\) 3.00472 23.7848i 0.117584 0.930772i −0.817397 0.576075i \(-0.804584\pi\)
0.934981 0.354698i \(-0.115416\pi\)
\(654\) −0.609890 0.0770470i −0.0238486 0.00301278i
\(655\) 34.6531 + 6.52089i 1.35401 + 0.254792i
\(656\) −2.75796 1.51620i −0.107680 0.0591978i
\(657\) 1.53019 + 0.497189i 0.0596984 + 0.0193972i
\(658\) 30.5334 14.3679i 1.19032 0.560120i
\(659\) −5.77285 1.48222i −0.224878 0.0577390i 0.134569 0.990904i \(-0.457035\pi\)
−0.359448 + 0.933165i \(0.617035\pi\)
\(660\) −3.45073 10.5308i −0.134319 0.409910i
\(661\) −5.19478 + 6.27941i −0.202054 + 0.244241i −0.861801 0.507247i \(-0.830663\pi\)
0.659747 + 0.751488i \(0.270663\pi\)
\(662\) 9.23301 + 5.85944i 0.358851 + 0.227734i
\(663\) 21.2638 1.33781i 0.825819 0.0519562i
\(664\) 5.07444 + 7.99604i 0.196926 + 0.310306i
\(665\) 54.8290 7.06549i 2.12618 0.273988i
\(666\) 0.000947124 0.0150541i 3.67003e−5 0.000583335i
\(667\) −4.00124 0.763278i −0.154929 0.0295542i
\(668\) 9.48123 3.08064i 0.366840 0.119193i
\(669\) 16.3635 15.3663i 0.632649 0.594097i
\(670\) −8.34146 + 32.8276i −0.322259 + 1.26824i
\(671\) −8.74324 45.8336i −0.337529 1.76939i
\(672\) 17.8841 19.0447i 0.689895 0.734664i
\(673\) −0.0269045 + 0.0679530i −0.00103709 + 0.00261940i −0.930294 0.366814i \(-0.880448\pi\)
0.929257 + 0.369434i \(0.120448\pi\)
\(674\) 4.47388 + 13.7692i 0.172327 + 0.530369i
\(675\) −18.4208 15.0849i −0.709018 0.580617i
\(676\) 0.911515 2.80536i 0.0350583 0.107898i
\(677\) 1.72419 + 1.42637i 0.0662658 + 0.0548199i 0.669967 0.742391i \(-0.266308\pi\)
−0.603701 + 0.797210i \(0.706308\pi\)
\(678\) −27.4437 12.9140i −1.05397 0.495961i
\(679\) 2.84057 + 2.66747i 0.109011 + 0.102368i
\(680\) −10.0888 + 25.6683i −0.386888 + 0.984335i
\(681\) −40.6290 + 5.13264i −1.55691 + 0.196683i
\(682\) 14.5740i 0.558067i
\(683\) 3.86144 + 30.5665i 0.147754 + 1.16959i 0.875316 + 0.483551i \(0.160653\pi\)
−0.727562 + 0.686042i \(0.759347\pi\)
\(684\) 0.998835 + 1.20738i 0.0381914 + 0.0461655i
\(685\) −0.143397 2.19196i −0.00547890 0.0837506i
\(686\) −1.10140 + 17.5062i −0.0420515 + 0.668390i
\(687\) −11.6217 + 45.2636i −0.443396 + 1.72691i
\(688\) 3.94900 15.3803i 0.150554 0.586370i
\(689\) 0.762512 12.1198i 0.0290494 0.461727i
\(690\) 31.6709 + 8.04755i 1.20569 + 0.306365i
\(691\) −9.77263 11.8131i −0.371769 0.449391i 0.551139 0.834414i \(-0.314194\pi\)
−0.922907 + 0.385023i \(0.874194\pi\)
\(692\) −0.244109 1.93232i −0.00927962 0.0734558i
\(693\) 7.74139i 0.294071i
\(694\) 17.6064 2.22421i 0.668330 0.0844298i
\(695\) −18.4853 + 11.7959i −0.701189 + 0.447445i
\(696\) 2.51816 + 2.36471i 0.0954507 + 0.0896342i
\(697\) 4.80646 + 2.26175i 0.182058 + 0.0856698i
\(698\) −31.0955 25.7244i −1.17698 0.973684i
\(699\) 0.187411 0.576793i 0.00708855 0.0218163i
\(700\) 12.7576 2.49966i 0.482191 0.0944783i
\(701\) −0.682588 2.10079i −0.0257810 0.0793458i 0.937338 0.348421i \(-0.113282\pi\)
−0.963119 + 0.269075i \(0.913282\pi\)
\(702\) 5.91227 14.9327i 0.223144 0.563598i
\(703\) −0.121127 + 0.128987i −0.00456840 + 0.00486485i
\(704\) 7.03600 + 36.8840i 0.265179 + 1.39012i
\(705\) 10.5139 + 26.3628i 0.395977 + 0.992881i
\(706\) 5.08376 4.77396i 0.191330 0.179671i
\(707\) 23.7664 7.72217i 0.893827 0.290422i
\(708\) 6.71094 + 1.28018i 0.252212 + 0.0481121i
\(709\) −2.24150 35.6277i −0.0841814 1.33803i −0.782685 0.622419i \(-0.786150\pi\)
0.698503 0.715607i \(-0.253850\pi\)
\(710\) −13.7082 28.9438i −0.514459 1.08624i
\(711\) 1.05617 + 1.66426i 0.0396095 + 0.0624145i
\(712\) 7.40309 0.465763i 0.277442 0.0174552i
\(713\) 16.3174 + 10.3553i 0.611090 + 0.387809i
\(714\) 23.2810 28.1419i 0.871269 1.05318i
\(715\) 27.7020 0.0690972i 1.03599 0.00258409i
\(716\) 0.957786 + 0.245918i 0.0357941 + 0.00919037i
\(717\) 24.5322 11.5440i 0.916170 0.431117i
\(718\) 9.10271 + 2.95765i 0.339710 + 0.110379i
\(719\) −10.6800 5.87137i −0.398296 0.218965i 0.270000 0.962860i \(-0.412976\pi\)
−0.668296 + 0.743895i \(0.732976\pi\)
\(720\) −1.56016 1.65312i −0.0581436 0.0616080i
\(721\) −50.9472 6.43613i −1.89737 0.239694i
\(722\) 2.32611 18.4131i 0.0865688 0.685263i
\(723\) 25.3149 16.0653i 0.941470 0.597475i
\(724\) 2.44145 1.77382i 0.0907357 0.0659233i
\(725\) 0.582778 + 2.97434i 0.0216438 + 0.110464i
\(726\) −13.3960 9.73274i −0.497171 0.361216i
\(727\) 1.52158 + 0.0957296i 0.0564322 + 0.00355042i 0.0909815 0.995853i \(-0.471000\pi\)
−0.0345493 + 0.999403i \(0.511000\pi\)
\(728\) 17.8436 + 32.4573i 0.661327 + 1.20295i
\(729\) 9.42048 20.0195i 0.348907 0.741465i
\(730\) −4.77633 8.63702i −0.176780 0.319670i
\(731\) −5.02207 + 26.3266i −0.185748 + 0.973725i
\(732\) 7.30212 + 10.0505i 0.269894 + 0.371477i
\(733\) 16.2151 29.4952i 0.598919 1.08943i −0.386980 0.922088i \(-0.626482\pi\)
0.985899 0.167342i \(-0.0535183\pi\)
\(734\) −4.12637 + 6.50212i −0.152307 + 0.239998i
\(735\) −43.4028 5.37309i −1.60093 0.198189i
\(736\) 21.0360 + 8.32876i 0.775399 + 0.307002i
\(737\) −20.4823 51.7323i −0.754474 1.90558i
\(738\) −0.513628 + 0.424910i −0.0189069 + 0.0156412i
\(739\) −16.4745 + 4.22994i −0.606026 + 0.155601i −0.539220 0.842165i \(-0.681281\pi\)
−0.0668058 + 0.997766i \(0.521281\pi\)
\(740\) −0.0264433 + 0.0321273i −0.000972077 + 0.00118102i
\(741\) −29.1617 + 11.5459i −1.07128 + 0.424150i
\(742\) −14.2505 15.1752i −0.523151 0.557100i
\(743\) −19.3130 + 26.5821i −0.708526 + 0.975202i 0.291302 + 0.956631i \(0.405912\pi\)
−0.999828 + 0.0185708i \(0.994088\pi\)
\(744\) −6.97817 14.8294i −0.255832 0.543671i
\(745\) −4.90087 + 1.60592i −0.179554 + 0.0588362i
\(746\) 2.85099 1.56735i 0.104382 0.0573846i
\(747\) 1.29406 0.246854i 0.0473470 0.00903192i
\(748\) −2.66756 10.3894i −0.0975355 0.379876i
\(749\) 53.6251 1.95942
\(750\) −3.22780 24.0991i −0.117863 0.879973i
\(751\) 23.9734 0.874801 0.437401 0.899267i \(-0.355899\pi\)
0.437401 + 0.899267i \(0.355899\pi\)
\(752\) −4.04782 15.7652i −0.147609 0.574899i
\(753\) 11.4328 2.18093i 0.416636 0.0794775i
\(754\) −1.79160 + 0.984940i −0.0652462 + 0.0358694i
\(755\) −0.0431802 17.3115i −0.00157149 0.630030i
\(756\) 5.27156 + 11.2026i 0.191725 + 0.407436i
\(757\) 7.79679 10.7314i 0.283379 0.390038i −0.643470 0.765471i \(-0.722506\pi\)
0.926850 + 0.375433i \(0.122506\pi\)
\(758\) −27.5419 29.3292i −1.00037 1.06528i
\(759\) −49.9095 + 19.7606i −1.81160 + 0.717263i
\(760\) 2.44822 40.5261i 0.0888062 1.47004i
\(761\) 49.0814 12.6020i 1.77920 0.456820i 0.791235 0.611512i \(-0.209438\pi\)
0.987963 + 0.154691i \(0.0494383\pi\)
\(762\) −27.0986 + 22.4179i −0.981677 + 0.812114i
\(763\) 0.436097 + 1.10146i 0.0157878 + 0.0398754i
\(764\) 1.41773 + 0.561318i 0.0512916 + 0.0203078i
\(765\) 2.80327 + 2.61932i 0.101353 + 0.0947018i
\(766\) 9.64768 15.2023i 0.348585 0.549282i
\(767\) −8.22761 + 14.9660i −0.297082 + 0.540390i
\(768\) −14.4839 19.9354i −0.522644 0.719357i
\(769\) 4.27577 22.4144i 0.154188 0.808284i −0.818203 0.574929i \(-0.805030\pi\)
0.972392 0.233355i \(-0.0749703\pi\)
\(770\) 32.4214 34.6983i 1.16839 1.25044i
\(771\) 11.3069 24.0284i 0.407209 0.865363i
\(772\) −0.0994240 0.180852i −0.00357835 0.00650899i
\(773\) −28.5591 1.79678i −1.02720 0.0646258i −0.459761 0.888043i \(-0.652065\pi\)
−0.567437 + 0.823417i \(0.692065\pi\)
\(774\) −2.72097 1.97690i −0.0978031 0.0710581i
\(775\) 2.62401 14.1384i 0.0942572 0.507865i
\(776\) 2.31523 1.68211i 0.0831118 0.0603843i
\(777\) 0.196511 0.124710i 0.00704980 0.00447394i
\(778\) −1.35820 + 10.7512i −0.0486937 + 0.385451i
\(779\) −7.75811 0.980078i −0.277963 0.0351149i
\(780\) −6.66578 + 3.15701i −0.238673 + 0.113039i
\(781\) 46.1015 + 25.3445i 1.64964 + 0.906898i
\(782\) 30.0815 + 9.77409i 1.07571 + 0.349521i
\(783\) −2.61181 + 1.22903i −0.0933386 + 0.0439218i
\(784\) 24.2927 + 6.23732i 0.867598 + 0.222761i
\(785\) 13.3293 9.73516i 0.475742 0.347463i
\(786\) −21.8599 + 26.4240i −0.779715 + 0.942514i
\(787\) −12.0838 7.66864i −0.430742 0.273357i 0.302730 0.953076i \(-0.402102\pi\)
−0.733473 + 0.679719i \(0.762102\pi\)
\(788\) −9.45269 + 0.594713i −0.336738 + 0.0211858i
\(789\) −15.4692 24.3755i −0.550717 0.867791i
\(790\) 2.23606 11.8828i 0.0795556 0.422771i
\(791\) 3.67004 + 58.3336i 0.130492 + 2.07410i
\(792\) 5.58466 + 1.06533i 0.198442 + 0.0378549i
\(793\) −29.5352 + 9.59658i −1.04883 + 0.340785i
\(794\) −26.9511 + 25.3088i −0.956459 + 0.898175i
\(795\) 13.4630 11.1942i 0.477483 0.397019i
\(796\) −0.559672 2.93390i −0.0198371 0.103989i
\(797\) 22.3011 23.7482i 0.789944 0.841205i −0.200417 0.979711i \(-0.564230\pi\)
0.990362 + 0.138505i \(0.0442298\pi\)
\(798\) −19.7926 + 49.9903i −0.700649 + 1.76964i
\(799\) 8.48933 + 26.1275i 0.300331 + 0.924323i
\(800\) −0.0839802 16.8343i −0.00296915 0.595182i
\(801\) 0.318863 0.981359i 0.0112665 0.0346746i
\(802\) 33.8816 + 28.0293i 1.19640 + 0.989748i
\(803\) 14.6700 + 6.90316i 0.517692 + 0.243607i
\(804\) 10.7988 + 10.1408i 0.380845 + 0.357638i
\(805\) −15.8125 60.9541i −0.557318 2.14835i
\(806\) 9.62341 1.21572i 0.338970 0.0428219i
\(807\) 18.5046i 0.651391i
\(808\) −2.30018 18.2078i −0.0809202 0.640549i
\(809\) −3.19679 3.86425i −0.112393 0.135860i 0.711316 0.702872i \(-0.248099\pi\)
−0.823710 + 0.567012i \(0.808099\pi\)
\(810\) 24.6422 9.82771i 0.865839 0.345310i
\(811\) 0.878695 13.9665i 0.0308552 0.490429i −0.952006 0.306080i \(-0.900982\pi\)
0.982861 0.184349i \(-0.0590175\pi\)
\(812\) 0.391956 1.52657i 0.0137550 0.0535721i
\(813\) −8.75075 + 34.0819i −0.306902 + 1.19530i
\(814\) −0.00954402 + 0.151698i −0.000334518 + 0.00531701i
\(815\) 14.8153 23.4745i 0.518959 0.822274i
\(816\) −11.2294 13.5740i −0.393106 0.475184i
\(817\) −4.94490 39.1429i −0.173000 1.36944i
\(818\) 28.8940i 1.01025i
\(819\) 5.11175 0.645764i 0.178619 0.0225648i
\(820\) −1.83555 0.110887i −0.0641001 0.00387234i
\(821\) 4.38256 + 4.11550i 0.152952 + 0.143632i 0.757246 0.653130i \(-0.226545\pi\)
−0.604293 + 0.796762i \(0.706545\pi\)
\(822\) 1.93307 + 0.909632i 0.0674235 + 0.0317271i
\(823\) 38.3408 + 31.7183i 1.33648 + 1.10563i 0.985579 + 0.169215i \(0.0541231\pi\)
0.350896 + 0.936414i \(0.385877\pi\)
\(824\) −11.6541 + 35.8678i −0.405991 + 1.24951i
\(825\) 27.4864 + 28.9790i 0.956954 + 1.00892i
\(826\) 9.04699 + 27.8438i 0.314785 + 0.968809i
\(827\) 2.08223 5.25912i 0.0724063 0.182878i −0.889066 0.457779i \(-0.848645\pi\)
0.961472 + 0.274901i \(0.0886452\pi\)
\(828\) 1.22188 1.30117i 0.0424632 0.0452187i
\(829\) −4.49764 23.5774i −0.156209 0.818879i −0.970992 0.239112i \(-0.923144\pi\)
0.814783 0.579767i \(-0.196856\pi\)
\(830\) −6.83403 4.31314i −0.237213 0.149711i
\(831\) 17.7752 16.6920i 0.616615 0.579040i
\(832\) 23.7681 7.72271i 0.824010 0.267737i
\(833\) −41.5820 7.93220i −1.44073 0.274834i
\(834\) −1.33912 21.2848i −0.0463701 0.737031i
\(835\) −26.1311 + 24.6617i −0.904305 + 0.853454i
\(836\) 8.46086 + 13.3322i 0.292625 + 0.461103i
\(837\) 13.6679 0.859910i 0.472431 0.0297228i
\(838\) 33.2012 + 21.0701i 1.14692 + 0.727855i
\(839\) 17.4019 21.0353i 0.600782 0.726220i −0.379198 0.925315i \(-0.623800\pi\)
0.979980 + 0.199095i \(0.0638002\pi\)
\(840\) −16.3756 + 50.8301i −0.565013 + 1.75380i
\(841\) −27.7330 7.12062i −0.956310 0.245539i
\(842\) −40.7791 + 19.1892i −1.40534 + 0.661303i
\(843\) −1.38281 0.449302i −0.0476264 0.0154748i
\(844\) −11.1440 6.12649i −0.383594 0.210882i
\(845\) 1.35878 + 10.5443i 0.0467434 + 0.362734i
\(846\) −3.42028 0.432082i −0.117592 0.0148553i
\(847\) −3.99928 + 31.6575i −0.137417 + 1.08777i
\(848\) −8.47795 + 5.38027i −0.291134 + 0.184759i
\(849\) 15.4005 11.1891i 0.528544 0.384010i
\(850\) −1.59491 23.4806i −0.0547049 0.805377i
\(851\) 0.163063 + 0.118472i 0.00558972 + 0.00406117i
\(852\) −13.9793 0.879503i −0.478923 0.0301313i
\(853\) −8.50453 15.4697i −0.291189 0.529672i 0.689735 0.724062i \(-0.257727\pi\)
−0.980924 + 0.194390i \(0.937727\pi\)
\(854\) −22.6669 + 48.1696i −0.775645 + 1.64833i
\(855\) −5.11623 2.39195i −0.174971 0.0818029i
\(856\) 7.37962 38.6853i 0.252230 1.32224i
\(857\) 8.16423 + 11.2371i 0.278885 + 0.383852i 0.925364 0.379080i \(-0.123759\pi\)
−0.646479 + 0.762932i \(0.723759\pi\)
\(858\) −12.9795 + 23.6096i −0.443113 + 0.806019i
\(859\) −23.9127 + 37.6805i −0.815892 + 1.28564i 0.139477 + 0.990225i \(0.455458\pi\)
−0.955369 + 0.295415i \(0.904542\pi\)
\(860\) −1.76125 9.10928i −0.0600580 0.310624i
\(861\) 9.56337 + 3.78640i 0.325919 + 0.129040i
\(862\) −5.06531 12.7935i −0.172525 0.435749i
\(863\) 16.4419 13.6019i 0.559690 0.463016i −0.314052 0.949406i \(-0.601687\pi\)
0.873742 + 0.486390i \(0.161687\pi\)
\(864\) 15.5290 3.98716i 0.528306 0.135646i
\(865\) 3.77620 + 5.91766i 0.128395 + 0.201206i
\(866\) 13.8670 5.49033i 0.471219 0.186569i
\(867\) −1.19240 1.26978i −0.0404962 0.0431241i
\(868\) −4.39522 + 6.04950i −0.149183 + 0.205333i
\(869\) 8.45704 + 17.9721i 0.286885 + 0.609662i
\(870\) −2.80575 0.903912i −0.0951238 0.0306455i
\(871\) −32.4510 + 17.8401i −1.09956 + 0.604488i
\(872\) 0.854607 0.163025i 0.0289406 0.00552072i
\(873\) −0.0990022 0.385588i −0.00335072 0.0130502i
\(874\) −46.5616 −1.57497
\(875\) −37.6997 + 27.8238i −1.27448 + 0.940616i
\(876\) −4.31666 −0.145846
\(877\) 5.96671 + 23.2388i 0.201482 + 0.784719i 0.986296 + 0.164988i \(0.0527584\pi\)
−0.784814 + 0.619731i \(0.787242\pi\)
\(878\) 5.42347 1.03458i 0.183033 0.0349155i
\(879\) −13.2821 + 7.30188i −0.447993 + 0.246286i
\(880\) −13.5097 18.4973i −0.455411 0.623542i
\(881\) −11.3400 24.0988i −0.382056 0.811910i −0.999677 0.0254337i \(-0.991903\pi\)
0.617621 0.786476i \(-0.288097\pi\)
\(882\) 3.12245 4.29768i 0.105138 0.144710i
\(883\) −20.2226 21.5349i −0.680545 0.724707i 0.292258 0.956339i \(-0.405593\pi\)
−0.972803 + 0.231633i \(0.925593\pi\)
\(884\) −6.63777 + 2.62808i −0.223252 + 0.0883919i
\(885\) −23.8349 + 6.18317i −0.801201 + 0.207845i
\(886\) −0.740402 + 0.190103i −0.0248743 + 0.00638663i
\(887\) −9.92013 + 8.20664i −0.333085 + 0.275552i −0.788899 0.614523i \(-0.789348\pi\)
0.455813 + 0.890075i \(0.349348\pi\)
\(888\) −0.0629232 0.158926i −0.00211156 0.00533320i
\(889\) 63.0149 + 24.9494i 2.11345 + 0.836775i
\(890\) −5.53919 + 3.06321i −0.185674 + 0.102679i
\(891\) −23.3515 + 36.7960i −0.782303 + 1.23271i
\(892\) −3.62357 + 6.59125i −0.121326 + 0.220691i
\(893\) −23.7708 32.7177i −0.795460 1.09486i
\(894\) 0.939870 4.92697i 0.0314340 0.164783i
\(895\) −3.49923 + 0.676565i −0.116966 + 0.0226151i
\(896\) 6.22516 13.2291i 0.207968 0.441954i
\(897\) 17.2115 + 31.3076i 0.574674 + 1.04533i
\(898\) 6.53669 + 0.411254i 0.218132 + 0.0137237i
\(899\) −1.41040 1.02471i −0.0470394 0.0341761i
\(900\) −1.23728 0.482749i −0.0412428 0.0160916i
\(901\) 13.7109 9.96153i 0.456775 0.331867i
\(902\) −5.67158 + 3.59930i −0.188843 + 0.119843i
\(903\) −6.50422 + 51.4862i −0.216447 + 1.71335i
\(904\) 42.5871 + 5.38000i 1.41643 + 0.178936i
\(905\) −5.21614 + 9.54445i −0.173390 + 0.317268i
\(906\) 14.7541 + 8.11114i 0.490173 + 0.269475i
\(907\) 37.7097 + 12.2526i 1.25213 + 0.406841i 0.858683 0.512506i \(-0.171283\pi\)
0.393446 + 0.919348i \(0.371283\pi\)
\(908\) 12.4161 5.84256i 0.412042 0.193892i
\(909\) −2.47277 0.634900i −0.0820167 0.0210583i
\(910\) −25.6163 18.5139i −0.849172 0.613729i
\(911\) 5.08613 6.14808i 0.168511 0.203695i −0.679497 0.733678i \(-0.737802\pi\)
0.848008 + 0.529984i \(0.177802\pi\)
\(912\) 21.8964 + 13.8959i 0.725061 + 0.460138i
\(913\) 13.2489 0.833552i 0.438476 0.0275865i
\(914\) 24.7075 + 38.9328i 0.817252 + 1.28778i
\(915\) −39.2908 21.4729i −1.29892 0.709871i
\(916\) −0.983220 15.6278i −0.0324865 0.516358i
\(917\) 64.9167 + 12.3835i 2.14374 + 0.408940i
\(918\) 21.3167 6.92622i 0.703556 0.228599i
\(919\) −15.5418 + 14.5947i −0.512676 + 0.481435i −0.897165 0.441695i \(-0.854377\pi\)
0.384489 + 0.923129i \(0.374377\pi\)
\(920\) −46.1485 + 3.01900i −1.52147 + 0.0995334i
\(921\) −3.31388 17.3720i −0.109196 0.572426i
\(922\) 13.9576 14.8633i 0.459668 0.489496i
\(923\) 12.8897 32.5556i 0.424269 1.07158i
\(924\) −6.41816 19.7531i −0.211142 0.649828i
\(925\) 0.0365715 0.145445i 0.00120247 0.00478221i
\(926\) 10.6367 32.7363i 0.349542 1.07578i
\(927\) 4.04230 + 3.34408i 0.132767 + 0.109834i
\(928\) −1.84670 0.868991i −0.0606209 0.0285260i
\(929\) −21.4040 20.0997i −0.702242 0.659449i 0.248784 0.968559i \(-0.419969\pi\)
−0.951026 + 0.309110i \(0.899969\pi\)
\(930\) 10.7981 + 8.88771i 0.354084 + 0.291439i
\(931\) 61.8249 7.81030i 2.02623 0.255972i
\(932\) 0.203216i 0.00665656i
\(933\) −7.11681 56.3354i −0.232994 1.84434i
\(934\) −23.1275 27.9563i −0.756754 0.914758i
\(935\) 24.7173 + 29.7268i 0.808342 + 0.972170i
\(936\) 0.237597 3.77650i 0.00776610 0.123439i
\(937\) −7.16178 + 27.8933i −0.233965 + 0.911234i 0.737749 + 0.675075i \(0.235889\pi\)
−0.971714 + 0.236159i \(0.924111\pi\)
\(938\) −15.7871 + 61.4868i −0.515468 + 2.00761i
\(939\) −0.394224 + 6.26600i −0.0128650 + 0.204483i
\(940\) −6.08026 7.31256i −0.198316 0.238509i
\(941\) −11.5042 13.9062i −0.375026 0.453328i 0.548907 0.835883i \(-0.315044\pi\)
−0.923933 + 0.382555i \(0.875044\pi\)
\(942\) 2.01198 + 15.9265i 0.0655540 + 0.518913i
\(943\) 8.90745i 0.290066i
\(944\) 14.0100 1.76987i 0.455986 0.0576044i
\(945\) −34.4540 28.3584i −1.12079 0.922497i
\(946\) −24.7058 23.2003i −0.803255 0.754306i
\(947\) 11.0677 + 5.20808i 0.359653 + 0.169240i 0.597112 0.802158i \(-0.296315\pi\)
−0.237459 + 0.971397i \(0.576315\pi\)
\(948\) −4.07472 3.37090i −0.132341 0.109482i
\(949\) 3.33452 10.2626i 0.108243 0.333138i
\(950\) 12.9143 + 32.1482i 0.418994 + 1.04303i
\(951\) −17.0821 52.5734i −0.553926 1.70481i
\(952\) −19.0286 + 48.0607i −0.616719 + 1.55765i
\(953\) −5.73043 + 6.10228i −0.185627 + 0.197672i −0.815051 0.579390i \(-0.803291\pi\)
0.629424 + 0.777062i \(0.283291\pi\)
\(954\) 0.398513 + 2.08908i 0.0129023 + 0.0676364i
\(955\) −5.48401 + 0.358760i −0.177458 + 0.0116092i
\(956\) −6.62252 + 6.21896i −0.214187 + 0.201135i
\(957\) 4.60529 1.49635i 0.148868 0.0483701i
\(958\) −34.5600 6.59267i −1.11658 0.213000i
\(959\) −0.258508 4.10887i −0.00834766 0.132682i
\(960\) 31.6187 + 17.2800i 1.02049 + 0.557709i
\(961\) −12.1787 19.1906i −0.392862 0.619051i
\(962\) 0.100964 0.00635213i 0.00325522 0.000204801i
\(963\) −4.62561 2.93550i −0.149058 0.0945953i
\(964\) −6.40379 + 7.74085i −0.206252 + 0.249316i
\(965\) 0.602865 + 0.435714i 0.0194069 + 0.0140261i
\(966\) 59.3203 + 15.2309i 1.90860 + 0.490045i
\(967\) −45.0734 + 21.2099i −1.44946 + 0.682066i −0.979652 0.200701i \(-0.935678\pi\)
−0.469811 + 0.882767i \(0.655678\pi\)
\(968\) 22.2875 + 7.24164i 0.716347 + 0.232755i
\(969\) −38.3570 21.0869i −1.23220 0.677410i
\(970\) −1.17112 + 2.14290i −0.0376024 + 0.0688045i
\(971\) 21.5104 + 2.71739i 0.690300 + 0.0872052i 0.462654 0.886539i \(-0.346897\pi\)
0.227646 + 0.973744i \(0.426897\pi\)
\(972\) 0.343451 2.71869i 0.0110162 0.0872021i
\(973\) −34.7006 + 22.0216i −1.11245 + 0.705982i
\(974\) 15.9087 11.5584i 0.509748 0.370354i
\(975\) 16.8424 20.5670i 0.539388 0.658671i
\(976\) 20.7739 + 15.0931i 0.664957 + 0.483120i
\(977\) −55.3264 3.48084i −1.77005 0.111362i −0.856003 0.516971i \(-0.827059\pi\)
−0.914047 + 0.405609i \(0.867059\pi\)
\(978\) 13.0060 + 23.6579i 0.415887 + 0.756496i
\(979\) 4.42721 9.40831i 0.141494 0.300691i
\(980\) 14.3878 2.78183i 0.459602 0.0888624i
\(981\) 0.0226780 0.118882i 0.000724053 0.00379562i
\(982\) −29.2154 40.2115i −0.932300 1.28320i
\(983\) 1.04143 1.89435i 0.0332164 0.0604204i −0.859178 0.511678i \(-0.829024\pi\)
0.892394 + 0.451257i \(0.149024\pi\)
\(984\) 4.04759 6.37798i 0.129032 0.203322i
\(985\) 29.8733 16.5202i 0.951842 0.526376i
\(986\) −2.65288 1.05035i −0.0844850 0.0334500i
\(987\) 19.5821 + 49.4586i 0.623304 + 1.57429i
\(988\) 8.09764 6.69895i 0.257620 0.213122i
\(989\) −43.5298 + 11.1766i −1.38417 + 0.355394i
\(990\) −4.69605 + 1.21823i −0.149250 + 0.0387180i
\(991\) 47.9707 18.9929i 1.52384 0.603330i 0.550936 0.834547i \(-0.314271\pi\)
0.972902 + 0.231217i \(0.0742708\pi\)
\(992\) 6.62852 + 7.05866i 0.210456 + 0.224113i
\(993\) −10.1322 + 13.9458i −0.321536 + 0.442557i
\(994\) −25.5567 54.3108i −0.810610 1.72263i
\(995\) 6.34928 + 8.69335i 0.201286 + 0.275598i
\(996\) −3.09727 + 1.70274i −0.0981408 + 0.0539534i
\(997\) −16.3502 + 3.11896i −0.517816 + 0.0987786i −0.439663 0.898163i \(-0.644902\pi\)
−0.0781525 + 0.996941i \(0.524902\pi\)
\(998\) −2.05816 8.01599i −0.0651498 0.253742i
\(999\) 0.142829 0.00451892
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 125.2.h.a.104.9 240
5.2 odd 4 625.2.g.b.351.8 480
5.3 odd 4 625.2.g.b.351.17 480
5.4 even 2 625.2.h.a.274.4 240
125.6 even 25 625.2.h.a.349.4 240
125.33 odd 100 625.2.g.b.276.17 480
125.92 odd 100 625.2.g.b.276.8 480
125.119 even 50 inner 125.2.h.a.119.9 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
125.2.h.a.104.9 240 1.1 even 1 trivial
125.2.h.a.119.9 yes 240 125.119 even 50 inner
625.2.g.b.276.8 480 125.92 odd 100
625.2.g.b.276.17 480 125.33 odd 100
625.2.g.b.351.8 480 5.2 odd 4
625.2.g.b.351.17 480 5.3 odd 4
625.2.h.a.274.4 240 5.4 even 2
625.2.h.a.349.4 240 125.6 even 25