Properties

Label 151.2.k.a.39.2
Level $151$
Weight $2$
Character 151.39
Analytic conductor $1.206$
Analytic rank $0$
Dimension $480$
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] = [151,2,Mod(5,151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(151, base_ring=CyclotomicField(150))
 
chi = DirichletCharacter(H, H._module([112]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("151.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 151.k (of order \(75\), degree \(40\), 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: \(1.20574107052\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(12\) over \(\Q(\zeta_{75})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{75}]$

Embedding invariants

Embedding label 39.2
Character \(\chi\) \(=\) 151.39
Dual form 151.2.k.a.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.92072 + 0.408262i) q^{2} +(-0.835538 + 0.330813i) q^{3} +(1.69541 - 0.754845i) q^{4} +(1.68742 + 0.509462i) q^{5} +(1.46978 - 0.976519i) q^{6} +(-0.0413232 - 1.97275i) q^{7} +(0.228987 - 0.166369i) q^{8} +(-1.59822 + 1.50083i) q^{9} +O(q^{10})\) \(q+(-1.92072 + 0.408262i) q^{2} +(-0.835538 + 0.330813i) q^{3} +(1.69541 - 0.754845i) q^{4} +(1.68742 + 0.509462i) q^{5} +(1.46978 - 0.976519i) q^{6} +(-0.0413232 - 1.97275i) q^{7} +(0.228987 - 0.166369i) q^{8} +(-1.59822 + 1.50083i) q^{9} +(-3.44906 - 0.289626i) q^{10} +(0.750541 + 5.08265i) q^{11} +(-1.16687 + 1.19156i) q^{12} +(1.39184 + 2.66235i) q^{13} +(0.884771 + 3.77224i) q^{14} +(-1.57844 + 0.132545i) q^{15} +(-2.85552 + 3.17138i) q^{16} +(4.64631 + 2.81390i) q^{17} +(2.45701 - 3.53517i) q^{18} +(-1.04580 - 0.759819i) q^{19} +(3.24544 - 0.409994i) q^{20} +(0.687139 + 1.63464i) q^{21} +(-3.51664 - 9.45595i) q^{22} +(-0.537816 + 5.11698i) q^{23} +(-0.136290 + 0.214759i) q^{24} +(-1.57677 - 1.04760i) q^{25} +(-3.76028 - 4.54539i) q^{26} +(1.98675 - 4.22206i) q^{27} +(-1.55918 - 3.31343i) q^{28} +(2.23273 - 2.69891i) q^{29} +(2.97763 - 0.899001i) q^{30} +(-2.73280 + 2.35889i) q^{31} +(3.90687 - 6.76689i) q^{32} +(-2.30851 - 3.99846i) q^{33} +(-10.0731 - 3.50782i) q^{34} +(0.935313 - 3.34991i) q^{35} +(-1.57674 + 3.75093i) q^{36} +(8.55111 + 0.358398i) q^{37} +(2.31890 + 1.03244i) q^{38} +(-2.04367 - 1.76405i) q^{39} +(0.471156 - 0.164074i) q^{40} +(0.386191 + 6.13833i) q^{41} +(-1.98716 - 2.85915i) q^{42} +(0.248600 - 11.8680i) q^{43} +(5.10909 + 8.05064i) q^{44} +(-3.46148 + 1.71830i) q^{45} +(-1.05607 - 10.0479i) q^{46} +(-0.684325 - 0.339702i) q^{47} +(1.33676 - 3.59445i) q^{48} +(3.10382 - 0.130089i) q^{49} +(3.45623 + 1.36842i) q^{50} +(-4.81304 - 0.814065i) q^{51} +(4.36940 + 3.46314i) q^{52} +(-0.464729 + 0.119322i) q^{53} +(-2.09229 + 8.92053i) q^{54} +(-1.32294 + 8.95894i) q^{55} +(-0.337667 - 0.444860i) q^{56} +(1.12516 + 0.288893i) q^{57} +(-3.18660 + 6.09541i) q^{58} +(-0.747995 - 2.30209i) q^{59} +(-2.57605 + 1.41620i) q^{60} +(-7.92028 + 6.27754i) q^{61} +(4.28591 - 5.64647i) q^{62} +(3.02680 + 3.09087i) q^{63} +(-2.10388 + 6.47508i) q^{64} +(0.992256 + 5.20159i) q^{65} +(6.06643 + 6.73746i) q^{66} +(-8.73531 - 8.20301i) q^{67} +(10.0015 + 1.26348i) q^{68} +(-1.24340 - 4.45334i) q^{69} +(-0.428833 + 6.81611i) q^{70} +(0.467736 - 0.283271i) q^{71} +(-0.116281 + 0.609564i) q^{72} +(7.63410 + 4.19688i) q^{73} +(-16.5706 + 2.80271i) q^{74} +(1.66401 + 0.353696i) q^{75} +(-2.34661 - 0.498787i) q^{76} +(9.99579 - 1.69066i) q^{77} +(4.64553 + 2.55390i) q^{78} +(0.643822 - 3.37503i) q^{79} +(-6.43416 + 3.89667i) q^{80} +(0.149700 - 2.37941i) q^{81} +(-3.24782 - 11.6324i) q^{82} +(-7.04704 - 0.890248i) q^{83} +(2.39888 + 2.25270i) q^{84} +(6.40669 + 7.11536i) q^{85} +(4.36778 + 22.8967i) q^{86} +(-0.972699 + 2.99366i) q^{87} +(1.01746 + 1.03899i) q^{88} +(4.40501 - 5.80339i) q^{89} +(5.94704 - 4.71357i) q^{90} +(5.19463 - 2.85577i) q^{91} +(2.95071 + 9.08134i) q^{92} +(1.50301 - 2.87499i) q^{93} +(1.45309 + 0.373089i) q^{94} +(-1.37761 - 1.81493i) q^{95} +(-1.02576 + 6.94644i) q^{96} +(1.18957 - 5.07177i) q^{97} +(-5.90847 + 1.51704i) q^{98} +(-8.82772 - 6.99676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\) \(6\)
\(\chi(n)\) \(e\left(\frac{61}{75}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92072 + 0.408262i −1.35816 + 0.288685i −0.828720 0.559664i \(-0.810930\pi\)
−0.529437 + 0.848349i \(0.677597\pi\)
\(3\) −0.835538 + 0.330813i −0.482398 + 0.190995i −0.596721 0.802449i \(-0.703530\pi\)
0.114323 + 0.993444i \(0.463530\pi\)
\(4\) 1.69541 0.754845i 0.847705 0.377423i
\(5\) 1.68742 + 0.509462i 0.754638 + 0.227838i 0.642953 0.765905i \(-0.277709\pi\)
0.111684 + 0.993744i \(0.464376\pi\)
\(6\) 1.46978 0.976519i 0.600035 0.398662i
\(7\) −0.0413232 1.97275i −0.0156187 0.745630i −0.935479 0.353383i \(-0.885031\pi\)
0.919860 0.392247i \(-0.128302\pi\)
\(8\) 0.228987 0.166369i 0.0809591 0.0588203i
\(9\) −1.59822 + 1.50083i −0.532740 + 0.500276i
\(10\) −3.44906 0.289626i −1.09069 0.0915878i
\(11\) 0.750541 + 5.08265i 0.226297 + 1.53248i 0.738878 + 0.673839i \(0.235356\pi\)
−0.512582 + 0.858638i \(0.671311\pi\)
\(12\) −1.16687 + 1.19156i −0.336845 + 0.343975i
\(13\) 1.39184 + 2.66235i 0.386027 + 0.738402i 0.998648 0.0519749i \(-0.0165516\pi\)
−0.612621 + 0.790377i \(0.709885\pi\)
\(14\) 0.884771 + 3.77224i 0.236465 + 1.00817i
\(15\) −1.57844 + 0.132545i −0.407552 + 0.0342231i
\(16\) −2.85552 + 3.17138i −0.713880 + 0.792844i
\(17\) 4.64631 + 2.81390i 1.12689 + 0.682472i 0.953204 0.302329i \(-0.0977640\pi\)
0.173691 + 0.984800i \(0.444431\pi\)
\(18\) 2.45701 3.53517i 0.579122 0.833247i
\(19\) −1.04580 0.759819i −0.239923 0.174314i 0.461326 0.887231i \(-0.347374\pi\)
−0.701249 + 0.712916i \(0.747374\pi\)
\(20\) 3.24544 0.409994i 0.725701 0.0916774i
\(21\) 0.687139 + 1.63464i 0.149946 + 0.356707i
\(22\) −3.51664 9.45595i −0.749749 2.01602i
\(23\) −0.537816 + 5.11698i −0.112142 + 1.06696i 0.783257 + 0.621699i \(0.213557\pi\)
−0.895399 + 0.445265i \(0.853110\pi\)
\(24\) −0.136290 + 0.214759i −0.0278202 + 0.0438376i
\(25\) −1.57677 1.04760i −0.315354 0.209521i
\(26\) −3.76028 4.54539i −0.737451 0.891425i
\(27\) 1.98675 4.22206i 0.382350 0.812536i
\(28\) −1.55918 3.31343i −0.294658 0.626179i
\(29\) 2.23273 2.69891i 0.414608 0.501176i −0.521322 0.853360i \(-0.674561\pi\)
0.935931 + 0.352184i \(0.114561\pi\)
\(30\) 2.97763 0.899001i 0.543639 0.164134i
\(31\) −2.73280 + 2.35889i −0.490825 + 0.423669i −0.863543 0.504276i \(-0.831759\pi\)
0.372717 + 0.927945i \(0.378426\pi\)
\(32\) 3.90687 6.76689i 0.690643 1.19623i
\(33\) −2.30851 3.99846i −0.401860 0.696042i
\(34\) −10.0731 3.50782i −1.72752 0.601586i
\(35\) 0.935313 3.34991i 0.158097 0.566239i
\(36\) −1.57674 + 3.75093i −0.262791 + 0.625155i
\(37\) 8.55111 + 0.358398i 1.40579 + 0.0589202i 0.732657 0.680598i \(-0.238280\pi\)
0.673137 + 0.739518i \(0.264946\pi\)
\(38\) 2.31890 + 1.03244i 0.376175 + 0.167484i
\(39\) −2.04367 1.76405i −0.327250 0.282474i
\(40\) 0.471156 0.164074i 0.0744963 0.0259424i
\(41\) 0.386191 + 6.13833i 0.0603129 + 0.958647i 0.905546 + 0.424249i \(0.139462\pi\)
−0.845233 + 0.534398i \(0.820538\pi\)
\(42\) −1.98716 2.85915i −0.306626 0.441177i
\(43\) 0.248600 11.8680i 0.0379111 1.80986i −0.406092 0.913832i \(-0.633109\pi\)
0.444003 0.896025i \(-0.353558\pi\)
\(44\) 5.10909 + 8.05064i 0.770224 + 1.21368i
\(45\) −3.46148 + 1.71830i −0.516008 + 0.256148i
\(46\) −1.05607 10.0479i −0.155710 1.48148i
\(47\) −0.684325 0.339702i −0.0998191 0.0495506i 0.394035 0.919095i \(-0.371079\pi\)
−0.493854 + 0.869545i \(0.664412\pi\)
\(48\) 1.33676 3.59445i 0.192945 0.518814i
\(49\) 3.10382 0.130089i 0.443403 0.0185841i
\(50\) 3.45623 + 1.36842i 0.488785 + 0.193524i
\(51\) −4.81304 0.814065i −0.673960 0.113992i
\(52\) 4.36940 + 3.46314i 0.605927 + 0.480251i
\(53\) −0.464729 + 0.119322i −0.0638354 + 0.0163902i −0.280473 0.959862i \(-0.590491\pi\)
0.216637 + 0.976252i \(0.430491\pi\)
\(54\) −2.09229 + 8.92053i −0.284725 + 1.21393i
\(55\) −1.32294 + 8.95894i −0.178385 + 1.20802i
\(56\) −0.337667 0.444860i −0.0451226 0.0594469i
\(57\) 1.12516 + 0.288893i 0.149032 + 0.0382648i
\(58\) −3.18660 + 6.09541i −0.418421 + 0.800366i
\(59\) −0.747995 2.30209i −0.0973807 0.299707i 0.890486 0.455010i \(-0.150364\pi\)
−0.987867 + 0.155303i \(0.950364\pi\)
\(60\) −2.57605 + 1.41620i −0.332567 + 0.182830i
\(61\) −7.92028 + 6.27754i −1.01409 + 0.803756i −0.980667 0.195685i \(-0.937307\pi\)
−0.0334214 + 0.999441i \(0.510640\pi\)
\(62\) 4.28591 5.64647i 0.544311 0.717103i
\(63\) 3.02680 + 3.09087i 0.381342 + 0.389413i
\(64\) −2.10388 + 6.47508i −0.262985 + 0.809385i
\(65\) 0.992256 + 5.20159i 0.123074 + 0.645177i
\(66\) 6.06643 + 6.73746i 0.746726 + 0.829323i
\(67\) −8.73531 8.20301i −1.06719 1.00216i −0.999990 0.00441692i \(-0.998594\pi\)
−0.0671981 0.997740i \(-0.521406\pi\)
\(68\) 10.0015 + 1.26348i 1.21285 + 0.153219i
\(69\) −1.24340 4.45334i −0.149687 0.536120i
\(70\) −0.428833 + 6.81611i −0.0512554 + 0.814681i
\(71\) 0.467736 0.283271i 0.0555100 0.0336181i −0.489999 0.871723i \(-0.663003\pi\)
0.545509 + 0.838105i \(0.316336\pi\)
\(72\) −0.116281 + 0.609564i −0.0137038 + 0.0718378i
\(73\) 7.63410 + 4.19688i 0.893504 + 0.491208i 0.861198 0.508270i \(-0.169715\pi\)
0.0323062 + 0.999478i \(0.489715\pi\)
\(74\) −16.5706 + 2.80271i −1.92630 + 0.325809i
\(75\) 1.66401 + 0.353696i 0.192143 + 0.0408413i
\(76\) −2.34661 0.498787i −0.269174 0.0572147i
\(77\) 9.99579 1.69066i 1.13913 0.192669i
\(78\) 4.64553 + 2.55390i 0.526002 + 0.289172i
\(79\) 0.643822 3.37503i 0.0724357 0.379721i −0.927546 0.373708i \(-0.878086\pi\)
0.999982 0.00601268i \(-0.00191391\pi\)
\(80\) −6.43416 + 3.89667i −0.719361 + 0.435661i
\(81\) 0.149700 2.37941i 0.0166333 0.264378i
\(82\) −3.24782 11.6324i −0.358661 1.28458i
\(83\) −7.04704 0.890248i −0.773513 0.0977175i −0.271339 0.962484i \(-0.587466\pi\)
−0.502174 + 0.864766i \(0.667466\pi\)
\(84\) 2.39888 + 2.25270i 0.261739 + 0.245790i
\(85\) 6.40669 + 7.11536i 0.694904 + 0.771769i
\(86\) 4.36778 + 22.8967i 0.470990 + 2.46901i
\(87\) −0.972699 + 2.99366i −0.104284 + 0.320954i
\(88\) 1.01746 + 1.03899i 0.108461 + 0.110757i
\(89\) 4.40501 5.80339i 0.466930 0.615158i −0.501283 0.865283i \(-0.667139\pi\)
0.968213 + 0.250126i \(0.0804719\pi\)
\(90\) 5.94704 4.71357i 0.626873 0.496853i
\(91\) 5.19463 2.85577i 0.544545 0.299366i
\(92\) 2.95071 + 9.08134i 0.307632 + 0.946795i
\(93\) 1.50301 2.87499i 0.155854 0.298122i
\(94\) 1.45309 + 0.373089i 0.149874 + 0.0384812i
\(95\) −1.37761 1.81493i −0.141339 0.186208i
\(96\) −1.02576 + 6.94644i −0.104691 + 0.708968i
\(97\) 1.18957 5.07177i 0.120783 0.514960i −0.878523 0.477701i \(-0.841470\pi\)
0.999306 0.0372599i \(-0.0118629\pi\)
\(98\) −5.90847 + 1.51704i −0.596846 + 0.153244i
\(99\) −8.82772 6.99676i −0.887219 0.703201i
\(100\) −3.46405 0.585900i −0.346405 0.0585900i
\(101\) −16.6544 6.59396i −1.65718 0.656124i −0.661583 0.749872i \(-0.730115\pi\)
−0.995596 + 0.0937477i \(0.970115\pi\)
\(102\) 9.57687 0.401390i 0.948251 0.0397435i
\(103\) 3.27723 8.81220i 0.322915 0.868291i −0.669214 0.743070i \(-0.733369\pi\)
0.992129 0.125222i \(-0.0399642\pi\)
\(104\) 0.761645 + 0.378084i 0.0746854 + 0.0370742i
\(105\) 0.326705 + 3.10839i 0.0318832 + 0.303348i
\(106\) 0.843901 0.418916i 0.0819669 0.0406887i
\(107\) 2.48593 + 3.91720i 0.240324 + 0.378690i 0.942985 0.332834i \(-0.108005\pi\)
−0.702661 + 0.711525i \(0.748005\pi\)
\(108\) 0.181355 8.65781i 0.0174509 0.833099i
\(109\) 7.49789 + 10.7880i 0.718167 + 1.03331i 0.997327 + 0.0730626i \(0.0232773\pi\)
−0.279160 + 0.960245i \(0.590056\pi\)
\(110\) −1.11659 17.7478i −0.106463 1.69218i
\(111\) −7.26334 + 2.52936i −0.689406 + 0.240076i
\(112\) 6.37434 + 5.50218i 0.602318 + 0.519907i
\(113\) −8.99977 4.00696i −0.846627 0.376943i −0.0628789 0.998021i \(-0.520028\pi\)
−0.783748 + 0.621078i \(0.786695\pi\)
\(114\) −2.27907 0.0955214i −0.213455 0.00894640i
\(115\) −3.51443 + 8.36050i −0.327722 + 0.779620i
\(116\) 1.74814 6.26113i 0.162311 0.581332i
\(117\) −6.22019 2.16610i −0.575057 0.200256i
\(118\) 2.37655 + 4.11631i 0.218779 + 0.378937i
\(119\) 5.35913 9.28228i 0.491271 0.850906i
\(120\) −0.339391 + 0.292954i −0.0309820 + 0.0267430i
\(121\) −14.7395 + 4.45012i −1.33996 + 0.404557i
\(122\) 12.6498 15.2910i 1.14526 1.38438i
\(123\) −2.35332 5.00105i −0.212191 0.450930i
\(124\) −2.85262 + 6.06212i −0.256173 + 0.544395i
\(125\) −7.74474 9.36178i −0.692711 0.837343i
\(126\) −7.07554 4.70098i −0.630339 0.418796i
\(127\) 2.04691 3.22541i 0.181634 0.286209i −0.741295 0.671179i \(-0.765788\pi\)
0.922929 + 0.384970i \(0.125788\pi\)
\(128\) −0.236074 + 2.24610i −0.0208662 + 0.198529i
\(129\) 3.71838 + 9.99843i 0.327385 + 0.880312i
\(130\) −4.02946 9.58571i −0.353407 0.840722i
\(131\) 11.7013 1.47821i 1.02234 0.129152i 0.403756 0.914867i \(-0.367705\pi\)
0.618589 + 0.785715i \(0.287705\pi\)
\(132\) −6.93209 5.03646i −0.603361 0.438367i
\(133\) −1.45572 + 2.09450i −0.126227 + 0.181616i
\(134\) 20.1271 + 12.1894i 1.73872 + 1.05300i
\(135\) 5.50347 6.11222i 0.473663 0.526056i
\(136\) 1.53209 0.128653i 0.131376 0.0110319i
\(137\) −2.40843 10.2684i −0.205766 0.877288i −0.972048 0.234783i \(-0.924562\pi\)
0.766282 0.642505i \(-0.222105\pi\)
\(138\) 4.20635 + 8.04601i 0.358069 + 0.684922i
\(139\) 10.3125 10.5308i 0.874694 0.893208i −0.120341 0.992733i \(-0.538399\pi\)
0.995035 + 0.0995245i \(0.0317322\pi\)
\(140\) −0.942928 6.38549i −0.0796919 0.539673i
\(141\) 0.684157 + 0.0574503i 0.0576164 + 0.00483819i
\(142\) −0.782743 + 0.735044i −0.0656863 + 0.0616835i
\(143\) −12.4871 + 9.07244i −1.04423 + 0.758675i
\(144\) −0.195943 9.35420i −0.0163286 0.779517i
\(145\) 5.14256 3.41671i 0.427066 0.283742i
\(146\) −16.3764 4.94433i −1.35532 0.409196i
\(147\) −2.55032 + 1.13548i −0.210347 + 0.0936526i
\(148\) 14.7682 5.84713i 1.21394 0.480631i
\(149\) 5.07298 1.07829i 0.415595 0.0883374i 0.00463137 0.999989i \(-0.498526\pi\)
0.410963 + 0.911652i \(0.365192\pi\)
\(150\) −3.34051 −0.272751
\(151\) 9.72492 + 7.51172i 0.791403 + 0.611295i
\(152\) −0.365885 −0.0296772
\(153\) −11.6490 + 2.47607i −0.941766 + 0.200179i
\(154\) −18.5089 + 7.32820i −1.49149 + 0.590523i
\(155\) −5.81315 + 2.58818i −0.466923 + 0.207888i
\(156\) −4.79645 1.44813i −0.384023 0.115943i
\(157\) 6.12638 4.07035i 0.488938 0.324850i −0.284549 0.958661i \(-0.591844\pi\)
0.773487 + 0.633812i \(0.218511\pi\)
\(158\) 0.141295 + 6.74536i 0.0112408 + 0.536632i
\(159\) 0.348825 0.253436i 0.0276636 0.0200988i
\(160\) 10.0400 9.42820i 0.793732 0.745364i
\(161\) 10.1167 + 0.849527i 0.797311 + 0.0669521i
\(162\) 0.683890 + 4.63130i 0.0537315 + 0.363869i
\(163\) −14.2855 + 14.5878i −1.11892 + 1.14261i −0.130411 + 0.991460i \(0.541630\pi\)
−0.988511 + 0.151146i \(0.951703\pi\)
\(164\) 5.28824 + 10.1155i 0.412942 + 0.789886i
\(165\) −1.85837 7.92318i −0.144674 0.616819i
\(166\) 13.8989 1.16712i 1.07876 0.0905862i
\(167\) 1.57381 1.74790i 0.121785 0.135256i −0.679169 0.733982i \(-0.737660\pi\)
0.800954 + 0.598726i \(0.204326\pi\)
\(168\) 0.429299 + 0.259992i 0.0331211 + 0.0200589i
\(169\) 2.26841 3.26382i 0.174493 0.251063i
\(170\) −15.2104 11.0510i −1.16659 0.847574i
\(171\) 2.81178 0.355210i 0.215022 0.0271636i
\(172\) −8.53705 20.3088i −0.650944 1.54853i
\(173\) 7.83174 + 21.0589i 0.595436 + 1.60108i 0.785195 + 0.619249i \(0.212563\pi\)
−0.189758 + 0.981831i \(0.560770\pi\)
\(174\) 0.646087 6.14711i 0.0489798 0.466011i
\(175\) −2.00150 + 3.15386i −0.151299 + 0.238410i
\(176\) −18.2622 12.1334i −1.37656 0.914587i
\(177\) 1.38654 + 1.67604i 0.104219 + 0.125979i
\(178\) −6.09150 + 12.9451i −0.456577 + 0.970276i
\(179\) 9.28081 + 19.7227i 0.693680 + 1.47415i 0.871660 + 0.490111i \(0.163044\pi\)
−0.177980 + 0.984034i \(0.556956\pi\)
\(180\) −4.57159 + 5.52610i −0.340746 + 0.411891i
\(181\) 10.0955 3.04802i 0.750394 0.226557i 0.109289 0.994010i \(-0.465143\pi\)
0.641106 + 0.767453i \(0.278476\pi\)
\(182\) −8.81154 + 7.60592i −0.653155 + 0.563788i
\(183\) 4.54100 7.86525i 0.335681 0.581416i
\(184\) 0.728153 + 1.26120i 0.0536801 + 0.0929767i
\(185\) 14.2467 + 4.96124i 1.04744 + 0.364757i
\(186\) −1.71311 + 6.13567i −0.125611 + 0.449889i
\(187\) −10.8148 + 25.7275i −0.790860 + 1.88138i
\(188\) −1.41663 0.0593746i −0.103319 0.00433033i
\(189\) −8.41118 3.74490i −0.611823 0.272401i
\(190\) 3.38697 + 2.92355i 0.245717 + 0.212097i
\(191\) −5.12880 + 1.78604i −0.371107 + 0.129233i −0.508010 0.861351i \(-0.669619\pi\)
0.136903 + 0.990584i \(0.456285\pi\)
\(192\) −0.384167 6.10616i −0.0277249 0.440674i
\(193\) 2.08297 + 2.99700i 0.149935 + 0.215728i 0.889002 0.457904i \(-0.151400\pi\)
−0.739066 + 0.673633i \(0.764733\pi\)
\(194\) −0.214228 + 10.2271i −0.0153807 + 0.734265i
\(195\) −2.54982 4.01787i −0.182596 0.287726i
\(196\) 5.16405 2.56346i 0.368861 0.183104i
\(197\) −2.42995 23.1195i −0.173127 1.64719i −0.644024 0.765005i \(-0.722736\pi\)
0.470897 0.882188i \(-0.343930\pi\)
\(198\) 19.8121 + 9.83482i 1.40799 + 0.698930i
\(199\) −4.62582 + 12.4385i −0.327916 + 0.881739i 0.663164 + 0.748474i \(0.269213\pi\)
−0.991080 + 0.133266i \(0.957454\pi\)
\(200\) −0.535348 + 0.0224377i −0.0378548 + 0.00158659i
\(201\) 10.0123 + 3.96417i 0.706216 + 0.279611i
\(202\) 34.6807 + 5.86579i 2.44012 + 0.412716i
\(203\) −5.41655 4.29310i −0.380167 0.301317i
\(204\) −8.77457 + 2.25293i −0.614342 + 0.157736i
\(205\) −2.47558 + 10.5547i −0.172902 + 0.737172i
\(206\) −2.69696 + 18.2638i −0.187906 + 1.27250i
\(207\) −6.82015 8.98522i −0.474034 0.624516i
\(208\) −12.4177 3.18833i −0.861015 0.221071i
\(209\) 3.07698 5.88571i 0.212839 0.407123i
\(210\) −1.89655 5.83698i −0.130874 0.402790i
\(211\) 4.44494 2.44363i 0.306002 0.168226i −0.321353 0.946960i \(-0.604138\pi\)
0.627355 + 0.778733i \(0.284138\pi\)
\(212\) −0.697836 + 0.553098i −0.0479276 + 0.0379869i
\(213\) −0.297101 + 0.391417i −0.0203571 + 0.0268194i
\(214\) −6.37404 6.50895i −0.435720 0.444943i
\(215\) 6.46581 19.8997i 0.440964 1.35715i
\(216\) −0.247479 1.29733i −0.0168388 0.0882722i
\(217\) 4.76643 + 5.29366i 0.323566 + 0.359357i
\(218\) −18.8057 17.6597i −1.27368 1.19607i
\(219\) −7.76696 0.981195i −0.524843 0.0663030i
\(220\) 4.51969 + 16.1877i 0.304717 + 1.09137i
\(221\) −1.02466 + 16.2866i −0.0689264 + 1.09555i
\(222\) 12.9182 7.82355i 0.867014 0.525083i
\(223\) 4.49532 23.5653i 0.301029 1.57805i −0.434575 0.900636i \(-0.643102\pi\)
0.735604 0.677412i \(-0.236898\pi\)
\(224\) −13.5108 7.42765i −0.902731 0.496281i
\(225\) 4.09230 0.692160i 0.272820 0.0461440i
\(226\) 18.9220 + 4.02199i 1.25867 + 0.267539i
\(227\) −25.2388 5.36468i −1.67516 0.356066i −0.730195 0.683238i \(-0.760571\pi\)
−0.944965 + 0.327172i \(0.893904\pi\)
\(228\) 2.12568 0.359532i 0.140777 0.0238106i
\(229\) −16.1530 8.88018i −1.06742 0.586819i −0.151614 0.988440i \(-0.548447\pi\)
−0.915806 + 0.401621i \(0.868447\pi\)
\(230\) 3.33697 17.4930i 0.220033 1.15345i
\(231\) −7.79257 + 4.71935i −0.512713 + 0.310510i
\(232\) 0.0622524 0.989474i 0.00408707 0.0649621i
\(233\) 3.42507 + 12.2672i 0.224384 + 0.803653i 0.987531 + 0.157428i \(0.0503201\pi\)
−0.763147 + 0.646226i \(0.776347\pi\)
\(234\) 12.8316 + 1.62101i 0.838828 + 0.105969i
\(235\) −0.981679 0.921858i −0.0640377 0.0601354i
\(236\) −3.00588 3.33837i −0.195666 0.217309i
\(237\) 0.578567 + 3.03295i 0.0375820 + 0.197011i
\(238\) −6.50380 + 20.0166i −0.421579 + 1.29749i
\(239\) 11.1187 + 11.3541i 0.719210 + 0.734433i 0.972486 0.232961i \(-0.0748415\pi\)
−0.253276 + 0.967394i \(0.581508\pi\)
\(240\) 4.08692 5.38432i 0.263809 0.347556i
\(241\) 17.9796 14.2504i 1.15816 0.917950i 0.160554 0.987027i \(-0.448672\pi\)
0.997611 + 0.0690769i \(0.0220054\pi\)
\(242\) 26.4937 14.5651i 1.70308 0.936277i
\(243\) 4.98782 + 15.3509i 0.319969 + 0.984763i
\(244\) −8.68956 + 16.6216i −0.556292 + 1.06409i
\(245\) 5.30372 + 1.36177i 0.338843 + 0.0870000i
\(246\) 6.56181 + 8.64487i 0.418366 + 0.551177i
\(247\) 0.567312 3.84183i 0.0360972 0.244450i
\(248\) −0.233330 + 0.994807i −0.0148165 + 0.0631703i
\(249\) 6.18258 1.58742i 0.391805 0.100598i
\(250\) 18.6976 + 14.8195i 1.18254 + 0.937268i
\(251\) −0.828351 0.140105i −0.0522850 0.00884335i 0.140568 0.990071i \(-0.455107\pi\)
−0.192853 + 0.981228i \(0.561774\pi\)
\(252\) 7.46480 + 2.95552i 0.470238 + 0.186181i
\(253\) −26.4115 + 1.10697i −1.66047 + 0.0695945i
\(254\) −2.61473 + 7.03080i −0.164063 + 0.441151i
\(255\) −7.70689 3.82573i −0.482624 0.239577i
\(256\) −1.88689 17.9525i −0.117930 1.12203i
\(257\) 23.3398 11.5860i 1.45589 0.722712i 0.468868 0.883268i \(-0.344662\pi\)
0.987027 + 0.160556i \(0.0513288\pi\)
\(258\) −11.2240 17.6861i −0.698774 1.10109i
\(259\) 0.353670 16.8840i 0.0219760 1.04912i
\(260\) 5.60867 + 8.06982i 0.347835 + 0.500469i
\(261\) 0.482204 + 7.66441i 0.0298477 + 0.474415i
\(262\) −21.8714 + 7.61643i −1.35122 + 0.470545i
\(263\) 7.96371 + 6.87409i 0.491063 + 0.423874i 0.863626 0.504133i \(-0.168188\pi\)
−0.372563 + 0.928007i \(0.621521\pi\)
\(264\) −1.19384 0.531531i −0.0734757 0.0327135i
\(265\) −0.844983 0.0354153i −0.0519069 0.00217554i
\(266\) 1.94092 4.61728i 0.119006 0.283103i
\(267\) −1.76072 + 6.30618i −0.107754 + 0.385932i
\(268\) −21.0019 7.31365i −1.28290 0.446752i
\(269\) −12.1680 21.0756i −0.741898 1.28500i −0.951630 0.307246i \(-0.900593\pi\)
0.209733 0.977759i \(-0.432741\pi\)
\(270\) −8.07525 + 13.9867i −0.491444 + 0.851206i
\(271\) −12.8466 + 11.0889i −0.780374 + 0.673601i −0.950119 0.311887i \(-0.899039\pi\)
0.169745 + 0.985488i \(0.445706\pi\)
\(272\) −22.1916 + 6.70003i −1.34556 + 0.406249i
\(273\) −3.39558 + 4.10456i −0.205510 + 0.248419i
\(274\) 8.81813 + 18.7395i 0.532723 + 1.13209i
\(275\) 4.14117 8.80044i 0.249722 0.530686i
\(276\) −5.46965 6.61167i −0.329234 0.397976i
\(277\) −19.1540 12.7259i −1.15085 0.764623i −0.175324 0.984511i \(-0.556097\pi\)
−0.975525 + 0.219888i \(0.929431\pi\)
\(278\) −15.5081 + 24.4369i −0.930116 + 1.46563i
\(279\) 0.827326 7.87148i 0.0495307 0.471253i
\(280\) −0.343147 0.922694i −0.0205069 0.0551415i
\(281\) 8.28696 + 19.7139i 0.494358 + 1.17603i 0.957157 + 0.289569i \(0.0935119\pi\)
−0.462799 + 0.886463i \(0.653155\pi\)
\(282\) −1.33753 + 0.168970i −0.0796489 + 0.0100620i
\(283\) 20.4307 + 14.8438i 1.21448 + 0.882372i 0.995630 0.0933863i \(-0.0297692\pi\)
0.218851 + 0.975758i \(0.429769\pi\)
\(284\) 0.579178 0.833329i 0.0343679 0.0494490i
\(285\) 1.75144 + 1.06071i 0.103747 + 0.0628312i
\(286\) 20.2804 22.5237i 1.19921 1.33185i
\(287\) 12.0934 1.01552i 0.713854 0.0599440i
\(288\) 3.91191 + 16.6785i 0.230512 + 0.982791i
\(289\) 5.79407 + 11.0830i 0.340828 + 0.651943i
\(290\) −8.48252 + 8.66206i −0.498111 + 0.508654i
\(291\) 0.683874 + 4.63118i 0.0400894 + 0.271485i
\(292\) 16.1109 + 1.35287i 0.942821 + 0.0791709i
\(293\) 1.49357 1.40256i 0.0872554 0.0819382i −0.639692 0.768631i \(-0.720938\pi\)
0.726948 + 0.686693i \(0.240938\pi\)
\(294\) 4.43489 3.22214i 0.258648 0.187919i
\(295\) −0.0893531 4.26567i −0.00520234 0.248357i
\(296\) 2.01772 1.34057i 0.117278 0.0779191i
\(297\) 22.9504 + 6.92914i 1.33172 + 0.402069i
\(298\) −9.30356 + 4.14221i −0.538941 + 0.239952i
\(299\) −14.3717 + 5.69016i −0.831138 + 0.329071i
\(300\) 3.08817 0.656410i 0.178295 0.0378978i
\(301\) −23.4229 −1.35008
\(302\) −21.7456 10.4576i −1.25132 0.601768i
\(303\) 16.0968 0.924736
\(304\) 5.39598 1.14695i 0.309480 0.0657821i
\(305\) −16.5630 + 6.55776i −0.948396 + 0.375496i
\(306\) 21.3636 9.51170i 1.22128 0.543748i
\(307\) −18.3460 5.53898i −1.04706 0.316126i −0.281548 0.959547i \(-0.590848\pi\)
−0.765513 + 0.643421i \(0.777515\pi\)
\(308\) 15.6708 10.4116i 0.892926 0.593258i
\(309\) 0.176941 + 8.44707i 0.0100658 + 0.480537i
\(310\) 10.1088 7.34447i 0.574141 0.417138i
\(311\) −0.496652 + 0.466387i −0.0281625 + 0.0264464i −0.698501 0.715609i \(-0.746149\pi\)
0.670338 + 0.742056i \(0.266149\pi\)
\(312\) −0.761458 0.0639414i −0.0431091 0.00361997i
\(313\) −1.92566 13.0405i −0.108845 0.737095i −0.972481 0.232980i \(-0.925152\pi\)
0.863637 0.504114i \(-0.168181\pi\)
\(314\) −10.1053 + 10.3192i −0.570275 + 0.582346i
\(315\) 3.53281 + 6.75764i 0.199051 + 0.380750i
\(316\) −1.45609 6.20805i −0.0819112 0.349230i
\(317\) 4.55822 0.382764i 0.256015 0.0214982i 0.0450230 0.998986i \(-0.485664\pi\)
0.210992 + 0.977488i \(0.432331\pi\)
\(318\) −0.566528 + 0.629194i −0.0317693 + 0.0352834i
\(319\) 15.3934 + 9.32257i 0.861865 + 0.521964i
\(320\) −6.84894 + 9.85433i −0.382867 + 0.550874i
\(321\) −3.37295 2.45059i −0.188260 0.136779i
\(322\) −19.7783 + 2.49858i −1.10220 + 0.139240i
\(323\) −2.72105 6.47313i −0.151403 0.360175i
\(324\) −1.54228 4.14707i −0.0856823 0.230393i
\(325\) 0.594470 5.65600i 0.0329752 0.313738i
\(326\) 21.4827 33.8514i 1.18982 1.87485i
\(327\) −9.83359 6.53342i −0.543799 0.361299i
\(328\) 1.10966 + 1.34135i 0.0612707 + 0.0740636i
\(329\) −0.641869 + 1.36404i −0.0353874 + 0.0752020i
\(330\) 6.80414 + 14.4595i 0.374556 + 0.795972i
\(331\) 22.5034 27.2019i 1.23690 1.49515i 0.431847 0.901947i \(-0.357862\pi\)
0.805051 0.593206i \(-0.202138\pi\)
\(332\) −12.6196 + 3.81009i −0.692592 + 0.209106i
\(333\) −14.2044 + 12.2610i −0.778399 + 0.671896i
\(334\) −2.30926 + 3.99975i −0.126357 + 0.218857i
\(335\) −10.5610 18.2922i −0.577011 0.999412i
\(336\) −7.14619 2.48857i −0.389857 0.135762i
\(337\) −5.36172 + 19.2035i −0.292072 + 1.04608i 0.662735 + 0.748854i \(0.269396\pi\)
−0.954806 + 0.297229i \(0.903938\pi\)
\(338\) −3.02450 + 7.19500i −0.164511 + 0.391357i
\(339\) 8.84520 + 0.370724i 0.480405 + 0.0201350i
\(340\) 16.2330 + 7.22738i 0.880356 + 0.391960i
\(341\) −14.0405 12.1194i −0.760335 0.656303i
\(342\) −5.25563 + 1.83020i −0.284192 + 0.0989660i
\(343\) −1.25217 19.9027i −0.0676110 1.07465i
\(344\) −1.91754 2.75898i −0.103387 0.148754i
\(345\) 0.170679 8.14813i 0.00918905 0.438680i
\(346\) −23.6402 37.2510i −1.27090 2.00262i
\(347\) 16.5162 8.19871i 0.886636 0.440130i 0.0569605 0.998376i \(-0.481859\pi\)
0.829675 + 0.558247i \(0.188526\pi\)
\(348\) 0.610626 + 5.80972i 0.0327330 + 0.311434i
\(349\) −9.60735 4.76913i −0.514269 0.255286i 0.168785 0.985653i \(-0.446016\pi\)
−0.683055 + 0.730367i \(0.739349\pi\)
\(350\) 2.55673 6.87484i 0.136663 0.367476i
\(351\) 14.0058 0.587018i 0.747576 0.0313327i
\(352\) 37.3260 + 14.7784i 1.98948 + 0.787692i
\(353\) 18.8562 + 3.18928i 1.00361 + 0.169748i 0.645362 0.763877i \(-0.276707\pi\)
0.358251 + 0.933625i \(0.383373\pi\)
\(354\) −3.34742 2.65314i −0.177914 0.141013i
\(355\) 0.933583 0.239703i 0.0495495 0.0127221i
\(356\) 3.08764 13.1642i 0.163645 0.697702i
\(357\) −1.40706 + 9.52857i −0.0744693 + 0.504305i
\(358\) −25.8779 34.0929i −1.36769 1.80186i
\(359\) −7.55957 1.94097i −0.398979 0.102440i 0.0438687 0.999037i \(-0.486032\pi\)
−0.442847 + 0.896597i \(0.646032\pi\)
\(360\) −0.506764 + 0.969351i −0.0267088 + 0.0510893i
\(361\) −5.35495 16.4808i −0.281839 0.867412i
\(362\) −18.1463 + 9.97602i −0.953749 + 0.524328i
\(363\) 10.8433 8.59427i 0.569124 0.451082i
\(364\) 6.65136 8.76285i 0.348626 0.459298i
\(365\) 10.7438 + 10.9712i 0.562356 + 0.574259i
\(366\) −5.51093 + 16.9609i −0.288061 + 0.886560i
\(367\) 3.02140 + 15.8387i 0.157716 + 0.826775i 0.969924 + 0.243408i \(0.0782653\pi\)
−0.812208 + 0.583368i \(0.801735\pi\)
\(368\) −14.6921 16.3172i −0.765880 0.850595i
\(369\) −9.82980 9.23080i −0.511719 0.480536i
\(370\) −29.3895 3.71276i −1.52789 0.193017i
\(371\) 0.254597 + 0.911864i 0.0132180 + 0.0473416i
\(372\) 0.378043 6.00882i 0.0196006 0.311543i
\(373\) 2.37021 1.43545i 0.122725 0.0743248i −0.455330 0.890323i \(-0.650479\pi\)
0.578055 + 0.815998i \(0.303812\pi\)
\(374\) 10.2688 53.8307i 0.530985 2.78352i
\(375\) 9.56802 + 5.26006i 0.494091 + 0.271629i
\(376\) −0.213217 + 0.0360630i −0.0109958 + 0.00185981i
\(377\) 10.2930 + 2.18786i 0.530119 + 0.112680i
\(378\) 17.6844 + 3.75894i 0.909590 + 0.193339i
\(379\) 10.3641 1.75295i 0.532366 0.0900430i 0.105606 0.994408i \(-0.466322\pi\)
0.426760 + 0.904365i \(0.359655\pi\)
\(380\) −3.70560 2.03717i −0.190093 0.104505i
\(381\) −0.643261 + 3.37209i −0.0329553 + 0.172758i
\(382\) 9.12183 5.52438i 0.466713 0.282652i
\(383\) −0.217474 + 3.45665i −0.0111124 + 0.176626i 0.988556 + 0.150857i \(0.0482034\pi\)
−0.999668 + 0.0257690i \(0.991797\pi\)
\(384\) −0.545788 1.95479i −0.0278521 0.0997552i
\(385\) 17.7284 + 2.23962i 0.903525 + 0.114142i
\(386\) −5.22436 4.90600i −0.265913 0.249709i
\(387\) 17.4146 + 19.3408i 0.885232 + 0.983149i
\(388\) −1.81159 9.49668i −0.0919694 0.482121i
\(389\) −7.10475 + 21.8662i −0.360225 + 1.10866i 0.592692 + 0.805429i \(0.298065\pi\)
−0.952917 + 0.303230i \(0.901935\pi\)
\(390\) 6.53784 + 6.67623i 0.331057 + 0.338064i
\(391\) −16.8975 + 22.2617i −0.854545 + 1.12582i
\(392\) 0.689092 0.546167i 0.0348044 0.0275856i
\(393\) −9.28784 + 5.10603i −0.468510 + 0.257565i
\(394\) 14.1061 + 43.4140i 0.710654 + 2.18717i
\(395\) 2.80585 5.36710i 0.141178 0.270048i
\(396\) −20.2481 5.19882i −1.01750 0.261251i
\(397\) −7.79280 10.2666i −0.391109 0.515268i 0.558159 0.829734i \(-0.311508\pi\)
−0.949269 + 0.314466i \(0.898174\pi\)
\(398\) 3.80677 25.7794i 0.190816 1.29220i
\(399\) 0.523418 2.23161i 0.0262037 0.111720i
\(400\) 7.82484 2.00908i 0.391242 0.100454i
\(401\) 3.50286 + 2.77634i 0.174925 + 0.138644i 0.704730 0.709476i \(-0.251068\pi\)
−0.529805 + 0.848119i \(0.677735\pi\)
\(402\) −20.8494 3.52641i −1.03987 0.175881i
\(403\) −10.0838 3.99246i −0.502310 0.198878i
\(404\) −33.2135 + 1.39206i −1.65244 + 0.0692576i
\(405\) 1.46482 3.93879i 0.0727877 0.195720i
\(406\) 12.1564 + 6.03449i 0.603312 + 0.299487i
\(407\) 4.59635 + 43.7313i 0.227832 + 2.16768i
\(408\) −1.23756 + 0.614329i −0.0612683 + 0.0304138i
\(409\) −13.6677 21.5369i −0.675825 1.06493i −0.993176 0.116622i \(-0.962793\pi\)
0.317351 0.948308i \(-0.397207\pi\)
\(410\) 0.445823 21.2834i 0.0220176 1.05111i
\(411\) 5.40925 + 7.78289i 0.266819 + 0.383902i
\(412\) −1.09560 17.4141i −0.0539764 0.857930i
\(413\) −4.51055 + 1.57074i −0.221950 + 0.0772910i
\(414\) 16.7680 + 14.4737i 0.824100 + 0.711344i
\(415\) −11.4378 5.09243i −0.561458 0.249977i
\(416\) 23.4535 + 0.982995i 1.14990 + 0.0481953i
\(417\) −5.13276 + 12.2104i −0.251352 + 0.597944i
\(418\) −3.50711 + 12.5610i −0.171538 + 0.614381i
\(419\) −8.66849 3.01869i −0.423483 0.147472i 0.108752 0.994069i \(-0.465315\pi\)
−0.532235 + 0.846596i \(0.678648\pi\)
\(420\) 2.90026 + 5.02339i 0.141518 + 0.245116i
\(421\) 1.27249 2.20401i 0.0620173 0.107417i −0.833350 0.552746i \(-0.813580\pi\)
0.895367 + 0.445329i \(0.146913\pi\)
\(422\) −7.53986 + 6.50823i −0.367034 + 0.316816i
\(423\) 1.60354 0.484136i 0.0779666 0.0235395i
\(424\) −0.0865654 + 0.104640i −0.00420399 + 0.00508175i
\(425\) −4.37830 9.30436i −0.212379 0.451328i
\(426\) 0.410849 0.873098i 0.0199057 0.0423018i
\(427\) 12.7113 + 15.3653i 0.615144 + 0.743581i
\(428\) 7.17156 + 4.76477i 0.346650 + 0.230314i
\(429\) 7.43220 11.7113i 0.358830 0.565425i
\(430\) −4.29473 + 40.8616i −0.207110 + 1.97052i
\(431\) 9.91997 + 26.6740i 0.477828 + 1.28484i 0.921405 + 0.388605i \(0.127043\pi\)
−0.443577 + 0.896236i \(0.646291\pi\)
\(432\) 7.71654 + 18.3569i 0.371262 + 0.883198i
\(433\) 27.1442 3.42911i 1.30447 0.164792i 0.557791 0.829981i \(-0.311649\pi\)
0.746675 + 0.665189i \(0.231649\pi\)
\(434\) −11.3162 8.22169i −0.543195 0.394654i
\(435\) −3.16651 + 4.55601i −0.151823 + 0.218444i
\(436\) 20.8553 + 12.6304i 0.998787 + 0.604887i
\(437\) 4.45042 4.94269i 0.212893 0.236441i
\(438\) 15.3188 1.28635i 0.731959 0.0614643i
\(439\) 6.68907 + 28.5190i 0.319252 + 1.36114i 0.855817 + 0.517278i \(0.173055\pi\)
−0.536566 + 0.843859i \(0.680279\pi\)
\(440\) 1.18755 + 2.27158i 0.0566143 + 0.108293i
\(441\) −4.76534 + 4.86621i −0.226921 + 0.231724i
\(442\) −4.68110 31.7003i −0.222657 1.50783i
\(443\) −12.4268 1.04351i −0.590416 0.0495786i −0.215286 0.976551i \(-0.569068\pi\)
−0.375130 + 0.926972i \(0.622402\pi\)
\(444\) −10.4051 + 9.77100i −0.493802 + 0.463711i
\(445\) 10.3897 7.54857i 0.492520 0.357836i
\(446\) 0.986555 + 47.0976i 0.0467147 + 2.23014i
\(447\) −3.88195 + 2.57916i −0.183610 + 0.121990i
\(448\) 12.8607 + 3.88286i 0.607609 + 0.183448i
\(449\) −29.1341 + 12.9713i −1.37492 + 0.612154i −0.955325 0.295557i \(-0.904495\pi\)
−0.419596 + 0.907711i \(0.637828\pi\)
\(450\) −7.57759 + 3.00018i −0.357211 + 0.141430i
\(451\) −30.9092 + 6.56994i −1.45546 + 0.309367i
\(452\) −18.2829 −0.859957
\(453\) −10.6105 3.05920i −0.498525 0.143734i
\(454\) 50.6670 2.37792
\(455\) 10.2204 2.17242i 0.479141 0.101845i
\(456\) 0.305711 0.121039i 0.0143162 0.00566819i
\(457\) −26.3436 + 11.7289i −1.23230 + 0.548655i −0.916448 0.400153i \(-0.868957\pi\)
−0.315852 + 0.948809i \(0.602290\pi\)
\(458\) 34.6509 + 10.4617i 1.61913 + 0.488844i
\(459\) 21.1115 14.0265i 0.985401 0.654699i
\(460\) 0.352482 + 16.8273i 0.0164346 + 0.784578i
\(461\) −22.9909 + 16.7038i −1.07079 + 0.777975i −0.976054 0.217527i \(-0.930201\pi\)
−0.0947370 + 0.995502i \(0.530201\pi\)
\(462\) 13.0406 12.2460i 0.606705 0.569734i
\(463\) 0.294460 + 0.0247265i 0.0136847 + 0.00114914i 0.0905182 0.995895i \(-0.471148\pi\)
−0.0768335 + 0.997044i \(0.524481\pi\)
\(464\) 2.18365 + 14.7876i 0.101373 + 0.686499i
\(465\) 4.00090 4.08558i 0.185537 0.189464i
\(466\) −11.5869 22.1636i −0.536751 1.02671i
\(467\) 0.454926 + 1.93959i 0.0210515 + 0.0897534i 0.983070 0.183231i \(-0.0586558\pi\)
−0.962018 + 0.272985i \(0.911989\pi\)
\(468\) −12.1808 + 1.02285i −0.563060 + 0.0472814i
\(469\) −15.8215 + 17.5716i −0.730570 + 0.811380i
\(470\) 2.26189 + 1.36985i 0.104333 + 0.0631866i
\(471\) −3.77229 + 5.42762i −0.173818 + 0.250091i
\(472\) −0.554278 0.402706i −0.0255127 0.0185361i
\(473\) 60.5076 7.64389i 2.78214 0.351467i
\(474\) −2.34951 5.58926i −0.107916 0.256723i
\(475\) 0.852998 + 2.29364i 0.0391382 + 0.105240i
\(476\) 2.07923 19.7826i 0.0953015 0.906734i
\(477\) 0.563657 0.888181i 0.0258081 0.0406670i
\(478\) −25.9914 17.2687i −1.18882 0.789850i
\(479\) −13.8776 16.7751i −0.634082 0.766474i 0.351405 0.936224i \(-0.385704\pi\)
−0.985487 + 0.169750i \(0.945704\pi\)
\(480\) −5.26984 + 11.1990i −0.240534 + 0.511161i
\(481\) 10.9476 + 23.2648i 0.499168 + 1.06079i
\(482\) −28.7158 + 34.7115i −1.30797 + 1.58107i
\(483\) −8.73396 + 2.63694i −0.397409 + 0.119985i
\(484\) −21.6304 + 18.6708i −0.983199 + 0.848675i
\(485\) 4.59119 7.95217i 0.208475 0.361089i
\(486\) −15.8474 27.4486i −0.718854 1.24509i
\(487\) −6.06309 2.11139i −0.274745 0.0956763i 0.187996 0.982170i \(-0.439801\pi\)
−0.462741 + 0.886493i \(0.653134\pi\)
\(488\) −0.769255 + 2.75516i −0.0348226 + 0.124720i
\(489\) 7.11020 16.9145i 0.321534 0.764899i
\(490\) −10.7429 0.450263i −0.485317 0.0203408i
\(491\) 38.6405 + 17.2038i 1.74382 + 0.776399i 0.993302 + 0.115548i \(0.0368625\pi\)
0.750518 + 0.660850i \(0.229804\pi\)
\(492\) −7.76486 6.70244i −0.350067 0.302170i
\(493\) 17.9684 6.25728i 0.809258 0.281813i
\(494\) 0.478825 + 7.61070i 0.0215433 + 0.342422i
\(495\) −11.3315 16.3039i −0.509312 0.732804i
\(496\) 0.322638 15.4026i 0.0144869 0.691597i
\(497\) −0.578152 0.911021i −0.0259336 0.0408649i
\(498\) −11.2269 + 5.57310i −0.503091 + 0.249737i
\(499\) 1.09662 + 10.4337i 0.0490916 + 0.467075i 0.991259 + 0.131932i \(0.0421180\pi\)
−0.942167 + 0.335143i \(0.891215\pi\)
\(500\) −20.1972 10.0260i −0.903247 0.448376i
\(501\) −0.736753 + 1.98107i −0.0329157 + 0.0885077i
\(502\) 1.64823 0.0690814i 0.0735642 0.00308325i
\(503\) 17.4629 + 6.91404i 0.778631 + 0.308282i 0.723615 0.690204i \(-0.242479\pi\)
0.0550156 + 0.998485i \(0.482479\pi\)
\(504\) 1.20732 + 0.204203i 0.0537785 + 0.00909595i
\(505\) −24.7437 19.6116i −1.10108 0.872705i
\(506\) 50.2772 12.9090i 2.23509 0.573874i
\(507\) −0.815632 + 3.47747i −0.0362235 + 0.154440i
\(508\) 1.03566 7.01349i 0.0459501 0.311173i
\(509\) −17.8636 23.5345i −0.791791 1.04315i −0.997910 0.0646193i \(-0.979417\pi\)
0.206119 0.978527i \(-0.433917\pi\)
\(510\) 16.3647 + 4.20174i 0.724641 + 0.186056i
\(511\) 7.96394 15.2336i 0.352304 0.673895i
\(512\) 9.55771 + 29.4156i 0.422395 + 1.30000i
\(513\) −5.28575 + 2.90586i −0.233371 + 0.128297i
\(514\) −40.0991 + 31.7822i −1.76870 + 1.40185i
\(515\) 10.0195 13.2003i 0.441514 0.581673i
\(516\) 13.8514 + 14.1446i 0.609776 + 0.622683i
\(517\) 1.21297 3.73315i 0.0533465 0.164184i
\(518\) 6.21381 + 32.5739i 0.273019 + 1.43122i
\(519\) −13.5103 15.0047i −0.593035 0.658632i
\(520\) 1.09260 + 1.02602i 0.0479135 + 0.0449938i
\(521\) 9.84722 + 1.24399i 0.431414 + 0.0545003i 0.338042 0.941131i \(-0.390235\pi\)
0.0933723 + 0.995631i \(0.470235\pi\)
\(522\) −4.05527 14.5243i −0.177494 0.635713i
\(523\) 0.238314 3.78790i 0.0104208 0.165633i −0.989374 0.145391i \(-0.953556\pi\)
0.999795 0.0202427i \(-0.00644389\pi\)
\(524\) 18.7226 11.3388i 0.817902 0.495339i
\(525\) 0.628993 3.29730i 0.0274515 0.143906i
\(526\) −18.1025 9.95194i −0.789307 0.433925i
\(527\) −19.3351 + 3.27029i −0.842250 + 0.142456i
\(528\) 19.2726 + 4.09652i 0.838733 + 0.178278i
\(529\) −3.39681 0.722014i −0.147687 0.0313919i
\(530\) 1.63744 0.276952i 0.0711258 0.0120300i
\(531\) 4.65051 + 2.55664i 0.201815 + 0.110949i
\(532\) −0.887012 + 4.64988i −0.0384569 + 0.201598i
\(533\) −15.8048 + 9.57176i −0.684584 + 0.414599i
\(534\) 0.807275 12.8313i 0.0349342 0.555263i
\(535\) 2.19915 + 7.87646i 0.0950774 + 0.340529i
\(536\) −3.36500 0.425098i −0.145346 0.0183614i
\(537\) −14.2790 13.4089i −0.616184 0.578635i
\(538\) 31.9758 + 35.5127i 1.37857 + 1.53106i
\(539\) 2.99074 + 15.6780i 0.128820 + 0.675299i
\(540\) 4.71685 14.5170i 0.202981 0.624711i
\(541\) −30.0258 30.6614i −1.29091 1.31824i −0.921201 0.389088i \(-0.872790\pi\)
−0.369711 0.929147i \(-0.620543\pi\)
\(542\) 20.1476 26.5434i 0.865412 1.14014i
\(543\) −7.42687 + 5.88646i −0.318717 + 0.252612i
\(544\) 37.1939 20.4475i 1.59467 0.876680i
\(545\) 7.15599 + 22.0239i 0.306529 + 0.943398i
\(546\) 4.84624 9.27000i 0.207400 0.396720i
\(547\) 29.5436 + 7.58550i 1.26319 + 0.324333i 0.820140 0.572163i \(-0.193896\pi\)
0.443053 + 0.896496i \(0.353896\pi\)
\(548\) −11.8343 15.5911i −0.505537 0.666021i
\(549\) 3.23684 21.9199i 0.138145 0.935517i
\(550\) −4.36116 + 18.5939i −0.185960 + 0.792846i
\(551\) −4.38568 + 1.12605i −0.186836 + 0.0479714i
\(552\) −1.02562 0.812896i −0.0436532 0.0345991i
\(553\) −6.68471 1.13063i −0.284263 0.0480794i
\(554\) 41.9849 + 16.6230i 1.78377 + 0.706244i
\(555\) −13.5449 + 0.567701i −0.574950 + 0.0240975i
\(556\) 9.53480 25.6383i 0.404366 1.08731i
\(557\) −0.221098 0.109754i −0.00936820 0.00465042i 0.439945 0.898025i \(-0.354998\pi\)
−0.449313 + 0.893374i \(0.648331\pi\)
\(558\) 1.62457 + 15.4567i 0.0687733 + 0.654335i
\(559\) 31.9428 15.8565i 1.35104 0.670660i
\(560\) 7.95304 + 12.5320i 0.336077 + 0.529573i
\(561\) 0.525225 25.0740i 0.0221750 1.05862i
\(562\) −23.9654 34.4817i −1.01092 1.45452i
\(563\) −2.80763 44.6260i −0.118327 1.88076i −0.393443 0.919349i \(-0.628716\pi\)
0.275116 0.961411i \(-0.411284\pi\)
\(564\) 1.20329 0.419031i 0.0506678 0.0176444i
\(565\) −13.1450 11.3465i −0.553015 0.477349i
\(566\) −45.3019 20.1697i −1.90418 0.847797i
\(567\) −4.70016 0.196995i −0.197388 0.00827302i
\(568\) 0.0599780 0.142682i 0.00251662 0.00598681i
\(569\) 4.03104 14.4375i 0.168990 0.605253i −0.829890 0.557927i \(-0.811597\pi\)
0.998880 0.0473259i \(-0.0150699\pi\)
\(570\) −3.79709 1.32229i −0.159043 0.0553845i
\(571\) −6.07462 10.5216i −0.254215 0.440313i 0.710467 0.703731i \(-0.248484\pi\)
−0.964682 + 0.263417i \(0.915150\pi\)
\(572\) −14.3225 + 24.8074i −0.598855 + 1.03725i
\(573\) 3.69446 3.18897i 0.154338 0.133221i
\(574\) −22.8136 + 6.88782i −0.952220 + 0.287492i
\(575\) 6.20857 7.50487i 0.258915 0.312975i
\(576\) −6.35552 13.5062i −0.264813 0.562757i
\(577\) −7.84755 + 16.6769i −0.326698 + 0.694268i −0.998938 0.0460644i \(-0.985332\pi\)
0.672241 + 0.740333i \(0.265332\pi\)
\(578\) −15.6536 18.9220i −0.651104 0.787049i
\(579\) −2.73184 1.81503i −0.113531 0.0754301i
\(580\) 6.13966 9.67455i 0.254935 0.401714i
\(581\) −1.46503 + 13.9388i −0.0607798 + 0.578281i
\(582\) −3.20427 8.61602i −0.132821 0.357146i
\(583\) −0.955271 2.27250i −0.0395633 0.0941173i
\(584\) 2.44634 0.309045i 0.101230 0.0127884i
\(585\) −9.39253 6.82407i −0.388333 0.282141i
\(586\) −2.29613 + 3.30369i −0.0948521 + 0.136474i
\(587\) −30.1857 18.2811i −1.24590 0.754542i −0.267957 0.963431i \(-0.586349\pi\)
−0.977939 + 0.208889i \(0.933015\pi\)
\(588\) −3.46673 + 3.85020i −0.142966 + 0.158780i
\(589\) 4.65029 0.390496i 0.191612 0.0160901i
\(590\) 1.91314 + 8.15670i 0.0787626 + 0.335806i
\(591\) 9.67853 + 18.5133i 0.398122 + 0.761536i
\(592\) −25.5545 + 26.0954i −1.05028 + 1.07251i
\(593\) −3.71790 25.1776i −0.152676 1.03392i −0.919791 0.392410i \(-0.871642\pi\)
0.767115 0.641510i \(-0.221692\pi\)
\(594\) −46.9103 3.93917i −1.92475 0.161626i
\(595\) 13.7721 12.9328i 0.564600 0.530195i
\(596\) 7.78683 5.65747i 0.318961 0.231739i
\(597\) −0.249753 11.9231i −0.0102217 0.487979i
\(598\) 25.2810 16.7967i 1.03382 0.686867i
\(599\) −3.14008 0.948047i −0.128300 0.0387362i 0.224232 0.974536i \(-0.428013\pi\)
−0.352532 + 0.935800i \(0.614679\pi\)
\(600\) 0.439881 0.195848i 0.0179581 0.00799545i
\(601\) −7.88754 + 3.12290i −0.321739 + 0.127386i −0.523442 0.852061i \(-0.675352\pi\)
0.201703 + 0.979447i \(0.435352\pi\)
\(602\) 44.9890 9.56271i 1.83361 0.389747i
\(603\) 26.2723 1.06989
\(604\) 22.1579 + 5.39463i 0.901593 + 0.219504i
\(605\) −27.1389 −1.10336
\(606\) −30.9175 + 6.57171i −1.25594 + 0.266958i
\(607\) 9.72713 3.85124i 0.394812 0.156317i −0.162326 0.986737i \(-0.551900\pi\)
0.557138 + 0.830420i \(0.311900\pi\)
\(608\) −9.22742 + 4.10831i −0.374221 + 0.166614i
\(609\) 5.94594 + 1.79519i 0.240942 + 0.0727446i
\(610\) 29.1357 19.3577i 1.17967 0.783771i
\(611\) −0.0480675 2.29472i −0.00194460 0.0928345i
\(612\) −17.8808 + 12.9911i −0.722788 + 0.525136i
\(613\) 11.3234 10.6333i 0.457347 0.429477i −0.421321 0.906912i \(-0.638433\pi\)
0.878667 + 0.477435i \(0.158433\pi\)
\(614\) 37.4989 + 3.14887i 1.51333 + 0.127078i
\(615\) −1.42319 9.63781i −0.0573885 0.388634i
\(616\) 2.00763 2.05013i 0.0808899 0.0826020i
\(617\) −7.36053 14.0794i −0.296324 0.566815i 0.691503 0.722374i \(-0.256949\pi\)
−0.987827 + 0.155559i \(0.950282\pi\)
\(618\) −3.78848 16.1522i −0.152395 0.649739i
\(619\) −21.3508 + 1.79287i −0.858160 + 0.0720617i −0.504603 0.863351i \(-0.668361\pi\)
−0.353557 + 0.935413i \(0.615028\pi\)
\(620\) −7.90199 + 8.77605i −0.317352 + 0.352455i
\(621\) 20.5357 + 12.4369i 0.824069 + 0.499074i
\(622\) 0.763522 1.09856i 0.0306145 0.0440484i
\(623\) −11.6307 8.45017i −0.465973 0.338549i
\(624\) 11.4302 1.44397i 0.457575 0.0578052i
\(625\) −4.63121 11.0172i −0.185248 0.440689i
\(626\) 9.02262 + 24.2611i 0.360616 + 0.969668i
\(627\) −0.623861 + 5.93564i −0.0249146 + 0.237047i
\(628\) 7.31423 11.5254i 0.291870 0.459913i
\(629\) 38.7226 + 25.7272i 1.54397 + 1.02581i
\(630\) −9.54444 11.5373i −0.380260 0.459655i
\(631\) −7.48746 + 15.9117i −0.298071 + 0.633433i −0.996622 0.0821271i \(-0.973829\pi\)
0.698551 + 0.715561i \(0.253829\pi\)
\(632\) −0.414074 0.879951i −0.0164710 0.0350026i
\(633\) −2.90553 + 3.51218i −0.115484 + 0.139597i
\(634\) −8.59881 + 2.59613i −0.341502 + 0.103106i
\(635\) 5.09722 4.39980i 0.202277 0.174601i
\(636\) 0.400097 0.692988i 0.0158649 0.0274788i
\(637\) 4.66636 + 8.08238i 0.184888 + 0.320235i
\(638\) −33.3725 11.6215i −1.32123 0.460101i
\(639\) −0.322404 + 1.15472i −0.0127541 + 0.0456800i
\(640\) −1.54266 + 3.66984i −0.0609789 + 0.145063i
\(641\) 36.5718 + 1.53281i 1.44450 + 0.0605425i 0.751185 0.660092i \(-0.229483\pi\)
0.693315 + 0.720634i \(0.256149\pi\)
\(642\) 7.47899 + 3.32986i 0.295172 + 0.131419i
\(643\) 1.74907 + 1.50976i 0.0689766 + 0.0595390i 0.687230 0.726439i \(-0.258826\pi\)
−0.618254 + 0.785979i \(0.712160\pi\)
\(644\) 17.7933 6.19628i 0.701154 0.244168i
\(645\) 1.18065 + 18.7659i 0.0464881 + 0.738908i
\(646\) 7.86913 + 11.3222i 0.309607 + 0.445466i
\(647\) −0.566975 + 27.0671i −0.0222901 + 1.06412i 0.835303 + 0.549789i \(0.185292\pi\)
−0.857594 + 0.514328i \(0.828041\pi\)
\(648\) −0.361580 0.569758i −0.0142042 0.0223822i
\(649\) 11.1393 5.52961i 0.437257 0.217056i
\(650\) 1.16732 + 11.1063i 0.0457861 + 0.435625i
\(651\) −5.73374 2.84625i −0.224723 0.111553i
\(652\) −13.2081 + 35.5156i −0.517271 + 1.39090i
\(653\) −49.0549 + 2.05601i −1.91967 + 0.0804579i −0.971461 0.237198i \(-0.923771\pi\)
−0.948206 + 0.317656i \(0.897104\pi\)
\(654\) 21.5550 + 8.53421i 0.842865 + 0.333714i
\(655\) 20.4981 + 3.46699i 0.800925 + 0.135466i
\(656\) −20.5697 16.3034i −0.803114 0.636540i
\(657\) −18.4998 + 4.74993i −0.721745 + 0.185313i
\(658\) 0.675966 2.88200i 0.0263519 0.112352i
\(659\) −4.21121 + 28.5182i −0.164045 + 1.11091i 0.736591 + 0.676339i \(0.236434\pi\)
−0.900636 + 0.434574i \(0.856899\pi\)
\(660\) −9.13147 12.0303i −0.355442 0.468277i
\(661\) −26.7282 6.86263i −1.03960 0.266925i −0.309959 0.950750i \(-0.600315\pi\)
−0.729646 + 0.683825i \(0.760315\pi\)
\(662\) −32.1173 + 61.4347i −1.24827 + 2.38773i
\(663\) −4.53166 13.9470i −0.175995 0.541657i
\(664\) −1.76179 + 0.968553i −0.0683707 + 0.0375871i
\(665\) −3.52348 + 2.79267i −0.136635 + 0.108295i
\(666\) 22.2771 29.3490i 0.863221 1.13725i
\(667\) 12.6095 + 12.8764i 0.488241 + 0.498575i
\(668\) 1.34887 4.15138i 0.0521892 0.160622i
\(669\) 4.03969 + 21.1768i 0.156183 + 0.818742i
\(670\) 27.7528 + 30.8227i 1.07219 + 1.19078i
\(671\) −37.8510 35.5445i −1.46122 1.37218i
\(672\) 13.7460 + 1.73652i 0.530263 + 0.0669878i
\(673\) 1.77356 + 6.35218i 0.0683658 + 0.244859i 0.989533 0.144309i \(-0.0460960\pi\)
−0.921167 + 0.389168i \(0.872763\pi\)
\(674\) 2.45831 39.0737i 0.0946904 1.50506i
\(675\) −7.55569 + 4.57589i −0.290819 + 0.176126i
\(676\) 1.38221 7.24581i 0.0531620 0.278685i
\(677\) −20.1986 11.1043i −0.776294 0.426771i 0.0437708 0.999042i \(-0.486063\pi\)
−0.820065 + 0.572270i \(0.806063\pi\)
\(678\) −17.1405 + 2.89911i −0.658279 + 0.111339i
\(679\) −10.0545 2.13715i −0.385856 0.0820163i
\(680\) 2.65082 + 0.563450i 0.101654 + 0.0216073i
\(681\) 22.8627 3.86694i 0.876101 0.148181i
\(682\) 31.9158 + 17.5459i 1.22212 + 0.671866i
\(683\) −1.79467 + 9.40799i −0.0686712 + 0.359987i −0.999991 0.00421522i \(-0.998658\pi\)
0.931320 + 0.364202i \(0.118658\pi\)
\(684\) 4.49898 2.72468i 0.172023 0.104181i
\(685\) 1.16733 18.5541i 0.0446012 0.708916i
\(686\) 10.5306 + 37.7164i 0.402061 + 1.44002i
\(687\) 16.4341 + 2.07611i 0.627000 + 0.0792086i
\(688\) 36.9281 + 34.6778i 1.40787 + 1.32208i
\(689\) −0.964505 1.07119i −0.0367447 0.0408092i
\(690\) 2.99875 + 15.7200i 0.114160 + 0.598450i
\(691\) 3.14464 9.67821i 0.119628 0.368176i −0.873256 0.487261i \(-0.837996\pi\)
0.992884 + 0.119085i \(0.0379960\pi\)
\(692\) 29.1742 + 29.7917i 1.10904 + 1.13251i
\(693\) −13.4381 + 17.7040i −0.510470 + 0.672520i
\(694\) −28.3758 + 22.4904i −1.07713 + 0.853724i
\(695\) 22.7665 12.5160i 0.863584 0.474759i
\(696\) 0.275316 + 0.847336i 0.0104358 + 0.0321182i
\(697\) −15.4783 + 29.6073i −0.586283 + 1.12146i
\(698\) 20.4001 + 5.23786i 0.772156 + 0.198256i
\(699\) −6.91994 9.11668i −0.261736 0.344824i
\(700\) −1.01269 + 6.85792i −0.0382760 + 0.259205i
\(701\) 0.447796 1.90919i 0.0169130 0.0721090i −0.964455 0.264249i \(-0.914876\pi\)
0.981368 + 0.192140i \(0.0615427\pi\)
\(702\) −26.6617 + 6.84555i −1.00628 + 0.258369i
\(703\) −8.67044 6.87211i −0.327012 0.259186i
\(704\) −34.4896 5.83348i −1.29988 0.219858i
\(705\) 1.12519 + 0.445495i 0.0423772 + 0.0167783i
\(706\) −37.5195 + 1.57253i −1.41207 + 0.0591831i
\(707\) −12.3200 + 33.1276i −0.463342 + 1.24589i
\(708\) 3.61590 + 1.79495i 0.135894 + 0.0674584i
\(709\) 1.16234 + 11.0590i 0.0436527 + 0.415328i 0.994426 + 0.105440i \(0.0336250\pi\)
−0.950773 + 0.309888i \(0.899708\pi\)
\(710\) −1.69529 + 0.841551i −0.0636232 + 0.0315828i
\(711\) 4.03638 + 6.36031i 0.151376 + 0.238530i
\(712\) 0.0431876 2.06176i 0.00161853 0.0772676i
\(713\) −10.6006 15.2523i −0.396997 0.571204i
\(714\) −1.18759 18.8762i −0.0444444 0.706424i
\(715\) −25.6931 + 8.94729i −0.960868 + 0.334610i
\(716\) 30.6224 + 26.4325i 1.14441 + 0.987830i
\(717\) −13.0462 5.80853i −0.487218 0.216924i
\(718\) 15.3123 + 0.641774i 0.571449 + 0.0239508i
\(719\) 5.61292 13.3526i 0.209327 0.497968i −0.782939 0.622098i \(-0.786281\pi\)
0.992266 + 0.124130i \(0.0396139\pi\)
\(720\) 4.43498 15.8843i 0.165282 0.591973i
\(721\) −17.5197 6.10100i −0.652468 0.227213i
\(722\) 17.0139 + 29.4689i 0.633191 + 1.09672i
\(723\) −10.3084 + 17.8546i −0.383373 + 0.664021i
\(724\) 14.8153 12.7882i 0.550605 0.475270i
\(725\) −6.34790 + 1.91654i −0.235755 + 0.0711786i
\(726\) −17.3182 + 20.9341i −0.642739 + 0.776938i
\(727\) 8.55861 + 18.1880i 0.317421 + 0.674555i 0.998327 0.0578162i \(-0.0184137\pi\)
−0.680906 + 0.732371i \(0.738414\pi\)
\(728\) 0.714391 1.51816i 0.0264771 0.0562667i
\(729\) −4.68673 5.66528i −0.173583 0.209825i
\(730\) −25.1150 16.6863i −0.929547 0.617589i
\(731\) 34.5505 54.4430i 1.27790 2.01365i
\(732\) 1.76182 16.7626i 0.0651187 0.619563i
\(733\) −8.70055 23.3951i −0.321362 0.864117i −0.992440 0.122730i \(-0.960835\pi\)
0.671078 0.741387i \(-0.265832\pi\)
\(734\) −12.2696 29.1883i −0.452881 1.07736i
\(735\) −4.88195 + 0.616734i −0.180074 + 0.0227486i
\(736\) 32.5249 + 23.6307i 1.19888 + 0.871039i
\(737\) 35.1368 50.5552i 1.29428 1.86223i
\(738\) 22.6489 + 13.7167i 0.833718 + 0.504918i
\(739\) 17.9419 19.9265i 0.660004 0.733008i −0.316480 0.948599i \(-0.602501\pi\)
0.976484 + 0.215591i \(0.0691677\pi\)
\(740\) 27.8990 2.34275i 1.02559 0.0861211i
\(741\) 0.796916 + 3.39767i 0.0292754 + 0.124816i
\(742\) −0.861290 1.64750i −0.0316190 0.0604815i
\(743\) 23.8591 24.3641i 0.875304 0.893831i −0.119787 0.992800i \(-0.538221\pi\)
0.995091 + 0.0989688i \(0.0315544\pi\)
\(744\) −0.134139 0.908388i −0.00491777 0.0333031i
\(745\) 9.10960 + 0.764955i 0.333750 + 0.0280258i
\(746\) −3.96648 + 3.72477i −0.145223 + 0.136374i
\(747\) 12.5988 9.15359i 0.460967 0.334912i
\(748\) 1.08468 + 51.7822i 0.0396599 + 1.89334i
\(749\) 7.62494 5.06600i 0.278609 0.185108i
\(750\) −20.5250 6.19687i −0.749467 0.226278i
\(751\) −26.4944 + 11.7961i −0.966795 + 0.430445i −0.828527 0.559950i \(-0.810820\pi\)
−0.138269 + 0.990395i \(0.544154\pi\)
\(752\) 3.03143 1.20023i 0.110545 0.0437678i
\(753\) 0.738467 0.156966i 0.0269112 0.00572016i
\(754\) −20.6633 −0.752514
\(755\) 12.5831 + 17.6299i 0.457946 + 0.641618i
\(756\) −17.0872 −0.621456
\(757\) −1.80663 + 0.384012i −0.0656632 + 0.0139571i −0.240626 0.970618i \(-0.577353\pi\)
0.174963 + 0.984575i \(0.444019\pi\)
\(758\) −19.1908 + 7.59819i −0.697043 + 0.275979i
\(759\) 21.7016 9.66216i 0.787717 0.350714i
\(760\) −0.617402 0.186405i −0.0223955 0.00676161i
\(761\) 25.1118 16.6843i 0.910303 0.604804i −0.00830844 0.999965i \(-0.502645\pi\)
0.918612 + 0.395161i \(0.129311\pi\)
\(762\) −0.141172 6.73948i −0.00511412 0.244146i
\(763\) 20.9723 15.2373i 0.759248 0.551626i
\(764\) −7.34723 + 6.89951i −0.265814 + 0.249616i
\(765\) −20.9182 1.75655i −0.756300 0.0635083i
\(766\) −0.993512 6.72805i −0.0358970 0.243094i
\(767\) 5.08788 5.19557i 0.183713 0.187601i
\(768\) 7.51548 + 14.3758i 0.271192 + 0.518742i
\(769\) 7.02752 + 29.9620i 0.253419 + 1.08046i 0.936653 + 0.350258i \(0.113906\pi\)
−0.683235 + 0.730199i \(0.739427\pi\)
\(770\) −34.9658 + 2.93616i −1.26008 + 0.105812i
\(771\) −15.6685 + 17.4016i −0.564286 + 0.626703i
\(772\) 5.79375 + 3.50882i 0.208522 + 0.126285i
\(773\) 0.781449 1.12436i 0.0281068 0.0404403i −0.806847 0.590761i \(-0.798828\pi\)
0.834954 + 0.550320i \(0.185494\pi\)
\(774\) −41.3447 30.0387i −1.48610 1.07972i
\(775\) 6.78017 0.856535i 0.243551 0.0307676i
\(776\) −0.571388 1.35928i −0.0205116 0.0487952i
\(777\) 5.28995 + 14.2242i 0.189776 + 0.510292i
\(778\) 4.71912 44.8995i 0.169189 1.60972i
\(779\) 4.26014 6.71291i 0.152635 0.240515i
\(780\) −7.35586 4.88722i −0.263382 0.174991i
\(781\) 1.79082 + 2.16473i 0.0640807 + 0.0774602i
\(782\) 23.3669 49.6571i 0.835598 1.77574i
\(783\) −6.95909 14.7888i −0.248697 0.528509i
\(784\) −8.45046 + 10.2149i −0.301802 + 0.364816i
\(785\) 12.4115 3.74724i 0.442984 0.133745i
\(786\) 15.7548 13.5992i 0.561954 0.485066i
\(787\) 10.6981 18.5297i 0.381347 0.660513i −0.609908 0.792472i \(-0.708794\pi\)
0.991255 + 0.131959i \(0.0421269\pi\)
\(788\) −21.5714 37.3627i −0.768448 1.33099i
\(789\) −8.92801 3.10906i −0.317846 0.110686i
\(790\) −3.19808 + 11.4542i −0.113783 + 0.407524i
\(791\) −7.53283 + 17.9199i −0.267837 + 0.637158i
\(792\) −3.18548 0.133511i −0.113191 0.00474411i
\(793\) −27.7367 12.3492i −0.984961 0.438533i
\(794\) 19.1593 + 16.5379i 0.679938 + 0.586907i
\(795\) 0.717731 0.249941i 0.0254553 0.00886448i
\(796\) 1.54645 + 24.5801i 0.0548124 + 0.871218i
\(797\) −1.92501 2.76972i −0.0681872 0.0981085i 0.785589 0.618749i \(-0.212360\pi\)
−0.853776 + 0.520640i \(0.825693\pi\)
\(798\) −0.0942614 + 4.49999i −0.00333682 + 0.159298i
\(799\) −2.22370 3.50398i −0.0786687 0.123962i
\(800\) −13.2492 + 6.57698i −0.468432 + 0.232531i
\(801\) 1.66971 + 15.8862i 0.0589964 + 0.561313i
\(802\) −7.86151 3.90249i −0.277599 0.137802i
\(803\) −15.6016 + 41.9514i −0.550568 + 1.48043i
\(804\) 19.9674 0.836880i 0.704194 0.0295145i
\(805\) 16.6384 + 6.58761i 0.586427 + 0.232183i
\(806\) 20.9982 + 3.55157i 0.739628 + 0.125099i
\(807\) 17.1389 + 13.5842i 0.603319 + 0.478185i
\(808\) −4.91068 + 1.26085i −0.172757 + 0.0443565i
\(809\) −3.42688 + 14.6106i −0.120483 + 0.513680i 0.878848 + 0.477101i \(0.158313\pi\)
−0.999331 + 0.0365786i \(0.988354\pi\)
\(810\) −1.20546 + 8.16336i −0.0423556 + 0.286831i
\(811\) 21.3468 + 28.1234i 0.749589 + 0.987547i 0.999813 + 0.0193590i \(0.00616254\pi\)
−0.250224 + 0.968188i \(0.580504\pi\)
\(812\) −12.4239 3.18991i −0.435993 0.111944i
\(813\) 7.06546 13.5150i 0.247796 0.473991i
\(814\) −26.6822 82.1193i −0.935209 2.87828i
\(815\) −31.5375 + 17.3379i −1.10471 + 0.607320i
\(816\) 16.3254 12.9394i 0.571505 0.452969i
\(817\) −9.27754 + 12.2227i −0.324580 + 0.427618i
\(818\) 35.0446 + 35.7864i 1.22531 + 1.25124i
\(819\) −4.01614 + 12.3604i −0.140335 + 0.431907i
\(820\) 3.77004 + 19.7632i 0.131655 + 0.690162i
\(821\) 33.7636 + 37.4982i 1.17836 + 1.30870i 0.941445 + 0.337166i \(0.109468\pi\)
0.236911 + 0.971531i \(0.423865\pi\)
\(822\) −13.5671 12.7404i −0.473208 0.444372i
\(823\) −17.3856 2.19631i −0.606024 0.0765586i −0.183667 0.982988i \(-0.558797\pi\)
−0.422356 + 0.906430i \(0.638797\pi\)
\(824\) −0.715632 2.56311i −0.0249302 0.0892901i
\(825\) −0.548808 + 8.72305i −0.0191070 + 0.303698i
\(826\) 8.02224 4.85844i 0.279129 0.169047i
\(827\) −2.34462 + 12.2909i −0.0815304 + 0.427397i 0.917995 + 0.396592i \(0.129807\pi\)
−0.999525 + 0.0308053i \(0.990193\pi\)
\(828\) −18.3454 10.0855i −0.637547 0.350494i
\(829\) −9.40240 + 1.59030i −0.326559 + 0.0552333i −0.327746 0.944766i \(-0.606289\pi\)
0.00118679 + 0.999999i \(0.499622\pi\)
\(830\) 24.0479 + 5.11153i 0.834713 + 0.177424i
\(831\) 20.2137 + 4.29656i 0.701206 + 0.149046i
\(832\) −20.1672 + 3.41102i −0.699170 + 0.118256i
\(833\) 14.7874 + 8.12941i 0.512351 + 0.281668i
\(834\) 4.87359 25.5482i 0.168759 0.884663i
\(835\) 3.54617 2.14764i 0.122720 0.0743221i
\(836\) 0.773935 12.3013i 0.0267671 0.425451i
\(837\) 4.52998 + 16.2246i 0.156579 + 0.560803i
\(838\) 17.8822 + 2.25905i 0.617730 + 0.0780374i
\(839\) 3.36354 + 3.15858i 0.116122 + 0.109046i 0.740434 0.672130i \(-0.234620\pi\)
−0.624311 + 0.781176i \(0.714620\pi\)
\(840\) 0.591951 + 0.657428i 0.0204243 + 0.0226834i
\(841\) 3.13503 + 16.4344i 0.108105 + 0.566704i
\(842\) −1.54428 + 4.75281i −0.0532194 + 0.163793i
\(843\) −13.4457 13.7303i −0.463094 0.472896i
\(844\) 5.69143 7.49819i 0.195907 0.258098i
\(845\) 5.49056 4.35177i 0.188881 0.149705i
\(846\) −2.88230 + 1.58456i −0.0990953 + 0.0544781i
\(847\) 9.38807 + 28.8935i 0.322578 + 0.992793i
\(848\) 0.948628 1.81456i 0.0325760 0.0623122i
\(849\) −21.9812 5.64380i −0.754392 0.193695i
\(850\) 12.2081 + 16.0836i 0.418735 + 0.551663i
\(851\) −6.43284 + 43.5631i −0.220515 + 1.49332i
\(852\) −0.208250 + 0.887877i −0.00713452 + 0.0304182i
\(853\) 26.2460 6.73883i 0.898646 0.230733i 0.229011 0.973424i \(-0.426451\pi\)
0.669635 + 0.742691i \(0.266451\pi\)
\(854\) −30.6880 24.3230i −1.05012 0.832317i
\(855\) 4.92562 + 0.833106i 0.168453 + 0.0284916i
\(856\) 1.22095 + 0.483407i 0.0417311 + 0.0165225i
\(857\) −6.62318 + 0.277594i −0.226244 + 0.00948242i −0.154728 0.987957i \(-0.549450\pi\)
−0.0715154 + 0.997439i \(0.522784\pi\)
\(858\) −9.49393 + 25.5284i −0.324117 + 0.871525i
\(859\) −31.3748 15.5746i −1.07050 0.531398i −0.178731 0.983898i \(-0.557199\pi\)
−0.891765 + 0.452500i \(0.850532\pi\)
\(860\) −4.05900 38.6188i −0.138411 1.31689i
\(861\) −9.76859 + 4.84917i −0.332913 + 0.165259i
\(862\) −29.9435 47.1834i −1.01988 1.60707i
\(863\) −0.739345 + 35.2960i −0.0251676 + 1.20149i 0.786583 + 0.617484i \(0.211848\pi\)
−0.811751 + 0.584004i \(0.801485\pi\)
\(864\) −20.8083 29.9392i −0.707912 1.01855i
\(865\) 2.48672 + 39.5252i 0.0845509 + 1.34390i
\(866\) −50.7365 + 17.6683i −1.72410 + 0.600394i
\(867\) −8.50758 7.34354i −0.288932 0.249400i
\(868\) 12.0769 + 5.37700i 0.409918 + 0.182507i
\(869\) 17.6373 + 0.739224i 0.598306 + 0.0250764i
\(870\) 4.22194 10.0436i 0.143137 0.340510i
\(871\) 9.68107 34.6737i 0.328031 1.17487i
\(872\) 3.51171 + 1.22291i 0.118922 + 0.0414129i
\(873\) 5.71066 + 9.89115i 0.193276 + 0.334765i
\(874\) −6.53011 + 11.3105i −0.220884 + 0.382583i
\(875\) −18.1484 + 15.6653i −0.613529 + 0.529584i
\(876\) −13.9088 + 4.19932i −0.469936 + 0.141882i
\(877\) 14.8840 17.9917i 0.502597 0.607535i −0.456809 0.889565i \(-0.651008\pi\)
0.959406 + 0.282030i \(0.0910077\pi\)
\(878\) −24.4911 52.0462i −0.826534 1.75647i
\(879\) −0.783951 + 1.66598i −0.0264420 + 0.0561922i
\(880\) −24.6345 29.7780i −0.830429 1.00382i
\(881\) 6.30172 + 4.18685i 0.212310 + 0.141059i 0.655034 0.755600i \(-0.272654\pi\)
−0.442724 + 0.896658i \(0.645988\pi\)
\(882\) 7.16622 11.2922i 0.241299 0.380227i
\(883\) −0.244458 + 2.32586i −0.00822666 + 0.0782714i −0.997865 0.0653118i \(-0.979196\pi\)
0.989638 + 0.143583i \(0.0458625\pi\)
\(884\) 10.5566 + 28.3859i 0.355057 + 0.954720i
\(885\) 1.48580 + 3.53457i 0.0499445 + 0.118813i
\(886\) 24.2945 3.06911i 0.816190 0.103109i
\(887\) −35.3162 25.6587i −1.18580 0.861535i −0.192987 0.981201i \(-0.561817\pi\)
−0.992814 + 0.119666i \(0.961817\pi\)
\(888\) −1.24240 + 1.78758i −0.0416923 + 0.0599874i
\(889\) −6.44752 3.90475i −0.216243 0.130961i
\(890\) −16.8740 + 18.7404i −0.565617 + 0.628181i
\(891\) 12.2060 1.02497i 0.408918 0.0343378i
\(892\) −10.1667 43.3461i −0.340407 1.45133i
\(893\) 0.457556 + 0.875223i 0.0153115 + 0.0292882i
\(894\) 6.40318 6.53871i 0.214154 0.218687i
\(895\) 5.61264 + 38.0087i 0.187610 + 1.27049i
\(896\) 4.44074 + 0.372900i 0.148355 + 0.0124577i
\(897\) 10.1257 9.50869i 0.338088 0.317486i
\(898\) 50.6628 36.8087i 1.69064 1.22832i
\(899\) 0.264820 + 12.6424i 0.00883223 + 0.421646i
\(900\) 6.41565 4.26254i 0.213855 0.142085i
\(901\) −2.49503 0.753295i −0.0831216 0.0250959i
\(902\) 56.6857 25.2381i 1.88743 0.840337i
\(903\) 19.5708 7.74861i 0.651274 0.257858i
\(904\) −2.72746 + 0.579740i −0.0907141 + 0.0192819i
\(905\) 18.5882 0.617894
\(906\) 21.6288 + 1.54400i 0.718569 + 0.0512958i
\(907\) 49.6432 1.64837 0.824187 0.566317i \(-0.191632\pi\)
0.824187 + 0.566317i \(0.191632\pi\)
\(908\) −46.8397 + 9.95608i −1.55443 + 0.330404i
\(909\) 36.5139 14.4569i 1.21109 0.479504i
\(910\) −18.7437 + 8.34524i −0.621348 + 0.276642i
\(911\) −18.6942 5.64411i −0.619366 0.186998i −0.0361919 0.999345i \(-0.511523\pi\)
−0.583174 + 0.812347i \(0.698189\pi\)
\(912\) −4.12912 + 2.74338i −0.136729 + 0.0908423i
\(913\) −0.764269 36.4858i −0.0252936 1.20750i
\(914\) 45.8102 33.2831i 1.51527 1.10091i
\(915\) 11.6696 10.9585i 0.385786 0.362277i
\(916\) −34.0891 2.86254i −1.12634 0.0945811i
\(917\) −3.39968 23.0226i −0.112267 0.760274i
\(918\) −34.8229 + 35.5600i −1.14933 + 1.17365i
\(919\) 8.34182 + 15.9564i 0.275171 + 0.526354i 0.983809 0.179218i \(-0.0573568\pi\)
−0.708638 + 0.705572i \(0.750690\pi\)
\(920\) 0.586167 + 2.49914i 0.0193254 + 0.0823941i
\(921\) 17.1611 1.44106i 0.565479 0.0474846i
\(922\) 37.3395 41.4698i 1.22971 1.36573i
\(923\) 1.40518 + 0.851007i 0.0462520 + 0.0280112i
\(924\) −9.64922 + 13.8834i −0.317436 + 0.456731i
\(925\) −13.1077 9.52328i −0.430978 0.313124i
\(926\) −0.575671 + 0.0727242i −0.0189177 + 0.00238987i
\(927\) 7.98786 + 19.0024i 0.262356 + 0.624120i
\(928\) −9.54026 25.6530i −0.313174 0.842100i
\(929\) 2.96247 28.1861i 0.0971956 0.924755i −0.831903 0.554922i \(-0.812748\pi\)
0.929098 0.369833i \(-0.120585\pi\)
\(930\) −6.01663 + 9.48070i −0.197293 + 0.310884i
\(931\) −3.34482 2.22229i −0.109622 0.0728327i
\(932\) 15.0668 + 18.2126i 0.493528 + 0.596573i
\(933\) 0.260684 0.553983i 0.00853443 0.0181366i
\(934\) −1.66565 3.53968i −0.0545016 0.115822i
\(935\) −31.3564 + 37.9034i −1.02546 + 1.23957i
\(936\) −1.78471 + 0.538837i −0.0583352 + 0.0176124i
\(937\) −31.2552 + 26.9788i −1.02106 + 0.881358i −0.992984 0.118248i \(-0.962272\pi\)
−0.0280788 + 0.999606i \(0.508939\pi\)
\(938\) 23.2149 40.2095i 0.757995 1.31289i
\(939\) 5.92294 + 10.2588i 0.193288 + 0.334784i
\(940\) −2.36021 0.821912i −0.0769815 0.0268078i
\(941\) −7.89354 + 28.2715i −0.257322 + 0.921624i 0.717114 + 0.696956i \(0.245463\pi\)
−0.974436 + 0.224667i \(0.927870\pi\)
\(942\) 5.02964 11.9650i 0.163875 0.389842i
\(943\) −31.6174 1.32516i −1.02960 0.0431532i
\(944\) 9.43672 + 4.20150i 0.307139 + 0.136747i
\(945\) −12.2853 10.6044i −0.399641 0.344961i
\(946\) −113.098 + 39.3848i −3.67712 + 1.28051i
\(947\) −0.635634 10.1031i −0.0206553 0.328307i −0.994762 0.102218i \(-0.967406\pi\)
0.974107 0.226089i \(-0.0725940\pi\)
\(948\) 3.27032 + 4.70537i 0.106215 + 0.152823i
\(949\) −0.548100 + 26.1660i −0.0177921 + 0.849384i
\(950\) −2.57478 4.05721i −0.0835369 0.131633i
\(951\) −3.68194 + 1.82773i −0.119395 + 0.0592683i
\(952\) −0.317112 3.01711i −0.0102776 0.0977853i
\(953\) 29.5450 + 14.6662i 0.957055 + 0.475086i 0.854392 0.519630i \(-0.173930\pi\)
0.102664 + 0.994716i \(0.467263\pi\)
\(954\) −0.720018 + 1.93607i −0.0233115 + 0.0626826i
\(955\) −9.56436 + 0.400865i −0.309495 + 0.0129717i
\(956\) 27.4213 + 10.8569i 0.886869 + 0.351136i
\(957\) −15.9458 2.69703i −0.515454 0.0871825i
\(958\) 33.5036 + 26.5546i 1.08245 + 0.857941i
\(959\) −20.1575 + 5.17556i −0.650919 + 0.167127i
\(960\) 2.46261 10.4994i 0.0794803 0.338866i
\(961\) −2.62474 + 17.7747i −0.0846691 + 0.573378i
\(962\) −30.5255 40.2158i −0.984181 1.29661i
\(963\) −9.85212 2.52959i −0.317480 0.0815150i
\(964\) 19.7259 37.7321i 0.635327 1.21527i
\(965\) 1.98798 + 6.11839i 0.0639955 + 0.196958i
\(966\) 15.6990 8.63057i 0.505106 0.277684i
\(967\) 43.0956 34.1572i 1.38586 1.09842i 0.402772 0.915300i \(-0.368047\pi\)
0.983090 0.183121i \(-0.0586199\pi\)
\(968\) −2.63480 + 3.47122i −0.0846856 + 0.111569i
\(969\) 4.41494 + 4.50839i 0.141828 + 0.144830i
\(970\) −5.57183 + 17.1483i −0.178901 + 0.550600i
\(971\) 2.56859 + 13.4650i 0.0824300 + 0.432113i 0.999447 + 0.0332641i \(0.0105903\pi\)
−0.917017 + 0.398849i \(0.869410\pi\)
\(972\) 20.0440 + 22.2611i 0.642911 + 0.714025i
\(973\) −21.2007 19.9088i −0.679664 0.638247i
\(974\) 12.5075 + 1.58007i 0.400767 + 0.0506286i
\(975\) 1.37438 + 4.92246i 0.0440152 + 0.157645i
\(976\) 2.70809 43.0438i 0.0866838 1.37780i
\(977\) −4.76760 + 2.88736i −0.152529 + 0.0923749i −0.592228 0.805770i \(-0.701752\pi\)
0.439699 + 0.898145i \(0.355085\pi\)
\(978\) −6.75117 + 35.3909i −0.215879 + 1.13168i
\(979\) 32.8027 + 18.0335i 1.04838 + 0.576352i
\(980\) 10.0199 1.69474i 0.320074 0.0541365i
\(981\) −28.1743 5.98863i −0.899535 0.191202i
\(982\) −81.2413 17.2684i −2.59251 0.551056i
\(983\) −29.4697 + 4.98443i −0.939938 + 0.158979i −0.616575 0.787296i \(-0.711480\pi\)
−0.323363 + 0.946275i \(0.604814\pi\)
\(984\) −1.37090 0.753658i −0.0437026 0.0240257i
\(985\) 7.67814 40.2502i 0.244646 1.28248i
\(986\) −31.9578 + 19.3543i −1.01774 + 0.616368i
\(987\) 0.0850635 1.35205i 0.00270760 0.0430361i
\(988\) −1.93816 6.94171i −0.0616611 0.220845i
\(989\) 60.5947 + 7.65489i 1.92680 + 0.243411i
\(990\) 28.4209 + 26.6890i 0.903276 + 0.848232i
\(991\) −10.8436 12.0431i −0.344459 0.382560i 0.545876 0.837866i \(-0.316197\pi\)
−0.890335 + 0.455305i \(0.849530\pi\)
\(992\) 5.28566 + 27.7084i 0.167820 + 0.879743i
\(993\) −9.80368 + 30.1726i −0.311111 + 0.957500i
\(994\) 1.48240 + 1.51378i 0.0470190 + 0.0480143i
\(995\) −14.1426 + 18.6322i −0.448352 + 0.590682i
\(996\) 9.28375 7.35821i 0.294167 0.233154i
\(997\) 24.1711 13.2882i 0.765506 0.420840i −0.0506175 0.998718i \(-0.516119\pi\)
0.816123 + 0.577878i \(0.196119\pi\)
\(998\) −6.36598 19.5925i −0.201512 0.620189i
\(999\) 18.5021 35.3913i 0.585381 1.11973i
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 151.2.k.a.39.2 yes 480
151.31 even 75 inner 151.2.k.a.31.2 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
151.2.k.a.31.2 480 151.31 even 75 inner
151.2.k.a.39.2 yes 480 1.1 even 1 trivial