Properties

Label 441.2.bn.a.5.5
Level $441$
Weight $2$
Character 441.5
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
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] = [441,2,Mod(5,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([35, 29]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bn (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 441.5
Dual form 441.2.bn.a.353.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96009 + 1.56312i) q^{2} +(1.60753 + 0.644869i) q^{3} +(0.953564 - 4.17784i) q^{4} +(0.688287 + 0.469266i) q^{5} +(-4.15890 + 1.24876i) q^{6} +(1.84507 + 1.89623i) q^{7} +(2.48585 + 5.16192i) q^{8} +(2.16829 + 2.07329i) q^{9} +O(q^{10})\) \(q+(-1.96009 + 1.56312i) q^{2} +(1.60753 + 0.644869i) q^{3} +(0.953564 - 4.17784i) q^{4} +(0.688287 + 0.469266i) q^{5} +(-4.15890 + 1.24876i) q^{6} +(1.84507 + 1.89623i) q^{7} +(2.48585 + 5.16192i) q^{8} +(2.16829 + 2.07329i) q^{9} +(-2.08262 + 0.156071i) q^{10} +(0.172004 + 1.14117i) q^{11} +(4.22704 - 6.10106i) q^{12} +(-1.00260 - 6.65184i) q^{13} +(-6.58054 - 0.832715i) q^{14} +(0.803825 + 1.19821i) q^{15} +(-5.21935 - 2.51351i) q^{16} +(1.04713 - 0.971599i) q^{17} +(-7.49083 - 0.674536i) q^{18} +(4.95852 + 2.86280i) q^{19} +(2.61684 - 2.42807i) q^{20} +(1.74319 + 4.23808i) q^{21} +(-2.12093 - 1.96793i) q^{22} +(2.60794 + 8.45473i) q^{23} +(0.667310 + 9.90097i) q^{24} +(-1.57318 - 4.00839i) q^{25} +(12.3628 + 11.4710i) q^{26} +(2.14859 + 4.73113i) q^{27} +(9.68155 - 5.90024i) q^{28} +(-1.21411 - 1.30850i) q^{29} +(-3.44851 - 1.09213i) q^{30} +0.899146i q^{31} +(2.98800 - 0.681992i) q^{32} +(-0.459405 + 1.94539i) q^{33} +(-0.533752 + 3.54121i) q^{34} +(0.380102 + 2.17098i) q^{35} +(10.7295 - 7.08174i) q^{36} +(-4.78288 - 1.47532i) q^{37} +(-14.1940 + 2.13941i) q^{38} +(2.67785 - 11.3396i) q^{39} +(-0.711335 + 4.71940i) q^{40} +(0.248358 - 3.31411i) q^{41} +(-10.0414 - 5.58220i) q^{42} +(0.455407 + 6.07698i) q^{43} +(4.93165 + 0.369576i) q^{44} +(0.519481 + 2.44452i) q^{45} +(-18.3275 - 12.4955i) q^{46} +(-5.40911 - 6.78281i) q^{47} +(-6.76937 - 7.40633i) q^{48} +(-0.191401 + 6.99738i) q^{49} +(9.34915 + 5.39773i) q^{50} +(2.30985 - 0.886608i) q^{51} +(-28.7464 - 2.15424i) q^{52} +(1.78561 + 5.78880i) q^{53} +(-11.6067 - 5.91493i) q^{54} +(-0.417125 + 0.866169i) q^{55} +(-5.20162 + 14.2379i) q^{56} +(6.12483 + 7.79963i) q^{57} +(4.42511 + 0.666978i) q^{58} +(-5.41780 - 2.60908i) q^{59} +(5.77243 - 2.21568i) q^{60} +(-0.293062 + 0.0668894i) q^{61} +(-1.40547 - 1.76241i) q^{62} +(0.0692161 + 7.93695i) q^{63} +(2.43310 - 3.05101i) q^{64} +(2.43140 - 5.04886i) q^{65} +(-2.14039 - 4.53123i) q^{66} -3.71201 q^{67} +(-3.06067 - 5.30124i) q^{68} +(-1.25986 + 15.2730i) q^{69} +(-4.13853 - 3.66117i) q^{70} +(-13.2147 - 3.01617i) q^{71} +(-5.31210 + 16.3464i) q^{72} +(-0.722899 + 4.79612i) q^{73} +(11.6810 - 4.58444i) q^{74} +(0.0559597 - 7.45809i) q^{75} +(16.6886 - 17.9860i) q^{76} +(-1.84657 + 2.43171i) q^{77} +(12.4763 + 26.4123i) q^{78} +9.44511 q^{79} +(-2.41291 - 4.17928i) q^{80} +(0.402953 + 8.99097i) q^{81} +(4.69354 + 6.88415i) q^{82} +(8.13734 + 1.22651i) q^{83} +(19.3682 - 3.24147i) q^{84} +(1.17667 - 0.177354i) q^{85} +(-10.3917 - 11.1996i) q^{86} +(-1.10791 - 2.88640i) q^{87} +(-5.46306 + 3.72465i) q^{88} +(-6.26262 - 15.9569i) q^{89} +(-4.83930 - 3.97946i) q^{90} +(10.7636 - 14.1743i) q^{91} +(37.8093 - 2.83342i) q^{92} +(-0.579831 + 1.44540i) q^{93} +(21.2047 + 4.83982i) q^{94} +(2.06947 + 4.29730i) q^{95} +(5.24309 + 0.830548i) q^{96} +(-2.31392 + 1.33594i) q^{97} +(-10.5626 - 14.0147i) q^{98} +(-1.99302 + 2.83100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9} - 22 q^{10} - 18 q^{11} - 72 q^{12} - 4 q^{13} + 66 q^{14} - 10 q^{15} - 105 q^{16} - 9 q^{17} - 27 q^{18} - 36 q^{19} - 27 q^{20} - 11 q^{21} - 9 q^{22} - 27 q^{23} - 8 q^{24} + 38 q^{25} + 6 q^{26} - 29 q^{27} - 26 q^{28} + 3 q^{29} - 16 q^{30} - 21 q^{32} - 11 q^{33} - 13 q^{34} + 28 q^{36} - 13 q^{37} - 90 q^{38} - 15 q^{39} - 31 q^{40} - 27 q^{41} - 4 q^{42} - 9 q^{43} + 51 q^{44} - 11 q^{45} - 108 q^{46} + 75 q^{47} - 15 q^{48} - 13 q^{49} - 45 q^{50} - 38 q^{51} + 64 q^{52} - 12 q^{53} - 41 q^{54} + 14 q^{55} + 3 q^{56} - 7 q^{57} - 90 q^{58} + 15 q^{59} - 69 q^{60} - 56 q^{61} + 66 q^{62} + 13 q^{63} + 64 q^{64} - 21 q^{65} - 204 q^{66} - 26 q^{67} + 3 q^{68} + 58 q^{69} - 22 q^{70} - 63 q^{71} - 18 q^{72} - 22 q^{73} - 12 q^{74} + 118 q^{75} - 63 q^{76} - 69 q^{77} - 147 q^{78} - 2 q^{79} - 45 q^{80} + 29 q^{81} - 28 q^{82} - 51 q^{83} - 31 q^{84} - 10 q^{85} - 72 q^{86} - 67 q^{87} + 4 q^{88} + 132 q^{89} + 58 q^{90} - 13 q^{91} - 15 q^{92} + 217 q^{93} - 7 q^{94} - 21 q^{95} - 44 q^{96} + 3 q^{97} + 21 q^{98} - 148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96009 + 1.56312i −1.38599 + 1.10529i −0.404339 + 0.914609i \(0.632498\pi\)
−0.981652 + 0.190682i \(0.938930\pi\)
\(3\) 1.60753 + 0.644869i 0.928106 + 0.372315i
\(4\) 0.953564 4.17784i 0.476782 2.08892i
\(5\) 0.688287 + 0.469266i 0.307811 + 0.209862i 0.707366 0.706847i \(-0.249883\pi\)
−0.399555 + 0.916709i \(0.630835\pi\)
\(6\) −4.15890 + 1.24876i −1.69786 + 0.509802i
\(7\) 1.84507 + 1.89623i 0.697373 + 0.716709i
\(8\) 2.48585 + 5.16192i 0.878880 + 1.82501i
\(9\) 2.16829 + 2.07329i 0.722763 + 0.691096i
\(10\) −2.08262 + 0.156071i −0.658582 + 0.0493539i
\(11\) 0.172004 + 1.14117i 0.0518612 + 0.344076i 0.999681 + 0.0252690i \(0.00804421\pi\)
−0.947820 + 0.318807i \(0.896718\pi\)
\(12\) 4.22704 6.10106i 1.22024 1.76123i
\(13\) −1.00260 6.65184i −0.278072 1.84489i −0.495242 0.868755i \(-0.664921\pi\)
0.217170 0.976134i \(-0.430318\pi\)
\(14\) −6.58054 0.832715i −1.75872 0.222552i
\(15\) 0.803825 + 1.19821i 0.207547 + 0.309377i
\(16\) −5.21935 2.51351i −1.30484 0.628377i
\(17\) 1.04713 0.971599i 0.253967 0.235647i −0.542906 0.839793i \(-0.682676\pi\)
0.796874 + 0.604146i \(0.206486\pi\)
\(18\) −7.49083 0.674536i −1.76560 0.158990i
\(19\) 4.95852 + 2.86280i 1.13756 + 0.656772i 0.945826 0.324674i \(-0.105255\pi\)
0.191737 + 0.981446i \(0.438588\pi\)
\(20\) 2.61684 2.42807i 0.585144 0.542934i
\(21\) 1.74319 + 4.23808i 0.380394 + 0.924824i
\(22\) −2.12093 1.96793i −0.452184 0.419565i
\(23\) 2.60794 + 8.45473i 0.543793 + 1.76293i 0.640863 + 0.767656i \(0.278577\pi\)
−0.0970697 + 0.995278i \(0.530947\pi\)
\(24\) 0.667310 + 9.90097i 0.136214 + 2.02103i
\(25\) −1.57318 4.00839i −0.314635 0.801678i
\(26\) 12.3628 + 11.4710i 2.42454 + 2.24965i
\(27\) 2.14859 + 4.73113i 0.413495 + 0.910506i
\(28\) 9.68155 5.90024i 1.82964 1.11504i
\(29\) −1.21411 1.30850i −0.225455 0.242983i 0.610187 0.792258i \(-0.291094\pi\)
−0.835642 + 0.549275i \(0.814904\pi\)
\(30\) −3.44851 1.09213i −0.629609 0.199394i
\(31\) 0.899146i 0.161491i 0.996735 + 0.0807457i \(0.0257302\pi\)
−0.996735 + 0.0807457i \(0.974270\pi\)
\(32\) 2.98800 0.681992i 0.528209 0.120560i
\(33\) −0.459405 + 1.94539i −0.0799721 + 0.338648i
\(34\) −0.533752 + 3.54121i −0.0915377 + 0.607313i
\(35\) 0.380102 + 2.17098i 0.0642490 + 0.366963i
\(36\) 10.7295 7.08174i 1.78824 1.18029i
\(37\) −4.78288 1.47532i −0.786300 0.242541i −0.124498 0.992220i \(-0.539732\pi\)
−0.661802 + 0.749678i \(0.730208\pi\)
\(38\) −14.1940 + 2.13941i −2.30258 + 0.347058i
\(39\) 2.67785 11.3396i 0.428799 1.81578i
\(40\) −0.711335 + 4.71940i −0.112472 + 0.746203i
\(41\) 0.248358 3.31411i 0.0387870 0.517577i −0.943645 0.330958i \(-0.892628\pi\)
0.982432 0.186619i \(-0.0597528\pi\)
\(42\) −10.0414 5.58220i −1.54942 0.861352i
\(43\) 0.455407 + 6.07698i 0.0694489 + 0.926731i 0.917735 + 0.397193i \(0.130016\pi\)
−0.848286 + 0.529538i \(0.822365\pi\)
\(44\) 4.93165 + 0.369576i 0.743474 + 0.0557157i
\(45\) 0.519481 + 2.44452i 0.0774396 + 0.364408i
\(46\) −18.3275 12.4955i −2.70225 1.84236i
\(47\) −5.40911 6.78281i −0.789000 0.989375i −0.999930 0.0118733i \(-0.996221\pi\)
0.210930 0.977501i \(-0.432351\pi\)
\(48\) −6.76937 7.40633i −0.977075 1.06901i
\(49\) −0.191401 + 6.99738i −0.0273430 + 0.999626i
\(50\) 9.34915 + 5.39773i 1.32217 + 0.763355i
\(51\) 2.30985 0.886608i 0.323444 0.124150i
\(52\) −28.7464 2.15424i −3.98640 0.298740i
\(53\) 1.78561 + 5.78880i 0.245272 + 0.795152i 0.991574 + 0.129544i \(0.0413515\pi\)
−0.746302 + 0.665608i \(0.768172\pi\)
\(54\) −11.6067 5.91493i −1.57948 0.804921i
\(55\) −0.417125 + 0.866169i −0.0562451 + 0.116794i
\(56\) −5.20162 + 14.2379i −0.695096 + 1.90261i
\(57\) 6.12483 + 7.79963i 0.811253 + 1.03309i
\(58\) 4.42511 + 0.666978i 0.581046 + 0.0875785i
\(59\) −5.41780 2.60908i −0.705338 0.339673i 0.0465936 0.998914i \(-0.485163\pi\)
−0.751932 + 0.659241i \(0.770878\pi\)
\(60\) 5.77243 2.21568i 0.745218 0.286043i
\(61\) −0.293062 + 0.0668894i −0.0375227 + 0.00856431i −0.241241 0.970465i \(-0.577554\pi\)
0.203718 + 0.979030i \(0.434697\pi\)
\(62\) −1.40547 1.76241i −0.178495 0.223826i
\(63\) 0.0692161 + 7.93695i 0.00872041 + 0.999962i
\(64\) 2.43310 3.05101i 0.304138 0.381377i
\(65\) 2.43140 5.04886i 0.301579 0.626234i
\(66\) −2.14039 4.53123i −0.263464 0.557756i
\(67\) −3.71201 −0.453494 −0.226747 0.973954i \(-0.572809\pi\)
−0.226747 + 0.973954i \(0.572809\pi\)
\(68\) −3.06067 5.30124i −0.371161 0.642870i
\(69\) −1.25986 + 15.2730i −0.151669 + 1.83865i
\(70\) −4.13853 3.66117i −0.494649 0.437594i
\(71\) −13.2147 3.01617i −1.56830 0.357954i −0.651927 0.758282i \(-0.726039\pi\)
−0.916372 + 0.400327i \(0.868896\pi\)
\(72\) −5.31210 + 16.3464i −0.626037 + 1.92644i
\(73\) −0.722899 + 4.79612i −0.0846089 + 0.561343i 0.905857 + 0.423584i \(0.139228\pi\)
−0.990466 + 0.137759i \(0.956010\pi\)
\(74\) 11.6810 4.58444i 1.35788 0.532930i
\(75\) 0.0559597 7.45809i 0.00646167 0.861186i
\(76\) 16.6886 17.9860i 1.91431 2.06314i
\(77\) −1.84657 + 2.43171i −0.210436 + 0.277119i
\(78\) 12.4763 + 26.4123i 1.41266 + 2.99061i
\(79\) 9.44511 1.06266 0.531329 0.847165i \(-0.321693\pi\)
0.531329 + 0.847165i \(0.321693\pi\)
\(80\) −2.41291 4.17928i −0.269771 0.467258i
\(81\) 0.402953 + 8.99097i 0.0447725 + 0.998997i
\(82\) 4.69354 + 6.88415i 0.518314 + 0.760227i
\(83\) 8.13734 + 1.22651i 0.893189 + 0.134627i 0.579570 0.814922i \(-0.303220\pi\)
0.313619 + 0.949549i \(0.398459\pi\)
\(84\) 19.3682 3.24147i 2.11325 0.353673i
\(85\) 1.17667 0.177354i 0.127627 0.0192367i
\(86\) −10.3917 11.1996i −1.12056 1.20768i
\(87\) −1.10791 2.88640i −0.118780 0.309454i
\(88\) −5.46306 + 3.72465i −0.582364 + 0.397049i
\(89\) −6.26262 15.9569i −0.663836 1.69143i −0.720884 0.693056i \(-0.756264\pi\)
0.0570471 0.998371i \(-0.481831\pi\)
\(90\) −4.83930 3.97946i −0.510107 0.419472i
\(91\) 10.7636 14.1743i 1.12833 1.48587i
\(92\) 37.8093 2.83342i 3.94189 0.295404i
\(93\) −0.579831 + 1.44540i −0.0601257 + 0.149881i
\(94\) 21.2047 + 4.83982i 2.18709 + 0.499190i
\(95\) 2.06947 + 4.29730i 0.212323 + 0.440893i
\(96\) 5.24309 + 0.830548i 0.535120 + 0.0847674i
\(97\) −2.31392 + 1.33594i −0.234943 + 0.135644i −0.612850 0.790199i \(-0.709977\pi\)
0.377907 + 0.925843i \(0.376644\pi\)
\(98\) −10.5626 14.0147i −1.06698 1.41569i
\(99\) −1.99302 + 2.83100i −0.200306 + 0.284527i
\(100\) −18.2465 + 2.75022i −1.82465 + 0.275022i
\(101\) 0.224953 3.00178i 0.0223836 0.298689i −0.974765 0.223232i \(-0.928339\pi\)
0.997149 0.0754570i \(-0.0240416\pi\)
\(102\) −3.14164 + 5.34840i −0.311069 + 0.529570i
\(103\) −9.78875 + 14.3575i −0.964514 + 1.41468i −0.0552458 + 0.998473i \(0.517594\pi\)
−0.909269 + 0.416210i \(0.863358\pi\)
\(104\) 31.8439 21.7108i 3.12255 2.12892i
\(105\) −0.788974 + 3.73503i −0.0769959 + 0.364502i
\(106\) −12.5485 8.55543i −1.21882 0.830977i
\(107\) 2.02356 0.794188i 0.195625 0.0767771i −0.265506 0.964109i \(-0.585539\pi\)
0.461131 + 0.887332i \(0.347444\pi\)
\(108\) 21.8147 4.46500i 2.09912 0.429645i
\(109\) 4.36822 11.1300i 0.418400 1.06606i −0.553953 0.832548i \(-0.686881\pi\)
0.972353 0.233517i \(-0.0750235\pi\)
\(110\) −0.536322 2.34978i −0.0511363 0.224043i
\(111\) −6.73722 5.45595i −0.639468 0.517856i
\(112\) −4.86390 14.5347i −0.459595 1.37340i
\(113\) 8.37448 3.28674i 0.787805 0.309191i 0.0628821 0.998021i \(-0.479971\pi\)
0.724923 + 0.688830i \(0.241876\pi\)
\(114\) −24.1969 5.71413i −2.26625 0.535178i
\(115\) −2.17251 + 7.04310i −0.202587 + 0.656772i
\(116\) −6.62445 + 3.82463i −0.615064 + 0.355108i
\(117\) 11.6173 16.5018i 1.07402 1.52559i
\(118\) 14.6977 3.35465i 1.35303 0.308820i
\(119\) 3.77442 + 0.192939i 0.346000 + 0.0176867i
\(120\) −4.18688 + 7.12785i −0.382209 + 0.650681i
\(121\) 9.23861 2.84973i 0.839874 0.259067i
\(122\) 0.469871 0.589199i 0.0425401 0.0533436i
\(123\) 2.53641 5.16736i 0.228700 0.465925i
\(124\) 3.75649 + 0.857394i 0.337342 + 0.0769962i
\(125\) 1.72504 7.55791i 0.154293 0.676000i
\(126\) −12.5421 15.4489i −1.11734 1.37630i
\(127\) −1.63456 7.16148i −0.145044 0.635479i −0.994219 0.107368i \(-0.965758\pi\)
0.849175 0.528111i \(-0.177099\pi\)
\(128\) 15.9132i 1.40654i
\(129\) −3.18677 + 10.0626i −0.280580 + 0.885961i
\(130\) 3.12620 + 13.6968i 0.274186 + 1.20129i
\(131\) −0.519252 6.92893i −0.0453672 0.605384i −0.972838 0.231488i \(-0.925641\pi\)
0.927471 0.373896i \(-0.121978\pi\)
\(132\) 7.68943 + 3.77437i 0.669279 + 0.328517i
\(133\) 3.72030 + 14.6846i 0.322591 + 1.27332i
\(134\) 7.27587 5.80231i 0.628539 0.501243i
\(135\) −0.741315 + 4.26463i −0.0638022 + 0.367041i
\(136\) 7.61833 + 2.98997i 0.653266 + 0.256388i
\(137\) −1.53686 2.25416i −0.131303 0.192586i 0.754957 0.655774i \(-0.227658\pi\)
−0.886260 + 0.463188i \(0.846705\pi\)
\(138\) −21.4040 31.9057i −1.82203 2.71599i
\(139\) 22.1716 + 1.66153i 1.88057 + 0.140930i 0.965173 0.261614i \(-0.0842546\pi\)
0.915401 + 0.402543i \(0.131874\pi\)
\(140\) 9.43246 + 0.482165i 0.797189 + 0.0407504i
\(141\) −4.32127 14.3917i −0.363917 1.21200i
\(142\) 30.6166 14.7442i 2.56929 1.23731i
\(143\) 7.41844 2.28829i 0.620361 0.191356i
\(144\) −6.10584 16.2712i −0.508820 1.35594i
\(145\) −0.221622 1.47037i −0.0184047 0.122107i
\(146\) −6.07995 10.5308i −0.503181 0.871534i
\(147\) −4.82008 + 11.1251i −0.397553 + 0.917579i
\(148\) −10.7244 + 18.5753i −0.881543 + 1.52688i
\(149\) 5.77583 + 2.26684i 0.473174 + 0.185707i 0.589931 0.807453i \(-0.299155\pi\)
−0.116757 + 0.993160i \(0.537250\pi\)
\(150\) 11.5482 + 14.7060i 0.942905 + 1.20074i
\(151\) −6.45656 5.99081i −0.525427 0.487525i 0.372278 0.928121i \(-0.378577\pi\)
−0.897706 + 0.440596i \(0.854767\pi\)
\(152\) −2.45142 + 32.7120i −0.198837 + 2.65329i
\(153\) 4.28489 + 0.0643047i 0.346413 + 0.00519873i
\(154\) −0.181609 7.65276i −0.0146345 0.616677i
\(155\) −0.421939 + 0.618870i −0.0338909 + 0.0497089i
\(156\) −44.8213 22.0006i −3.58858 1.76146i
\(157\) 3.45765 7.17989i 0.275951 0.573018i −0.716225 0.697870i \(-0.754131\pi\)
0.992175 + 0.124852i \(0.0398457\pi\)
\(158\) −18.5132 + 14.7638i −1.47283 + 1.17455i
\(159\) −0.862601 + 10.4571i −0.0684087 + 0.829304i
\(160\) 2.37664 + 0.932761i 0.187890 + 0.0737412i
\(161\) −11.2203 + 20.5449i −0.884284 + 1.61916i
\(162\) −14.8438 16.9932i −1.16624 1.33511i
\(163\) −0.445752 + 0.303908i −0.0349140 + 0.0238039i −0.580651 0.814152i \(-0.697202\pi\)
0.545737 + 0.837956i \(0.316250\pi\)
\(164\) −13.6090 4.19781i −1.06268 0.327794i
\(165\) −1.22911 + 1.12340i −0.0956857 + 0.0874566i
\(166\) −17.8671 + 10.3156i −1.38675 + 0.800643i
\(167\) −0.132559 0.0408891i −0.0102577 0.00316410i 0.289622 0.957141i \(-0.406470\pi\)
−0.299880 + 0.953977i \(0.596947\pi\)
\(168\) −17.5433 + 19.5334i −1.35350 + 1.50703i
\(169\) −30.8193 + 9.50651i −2.37072 + 0.731270i
\(170\) −2.02914 + 2.18690i −0.155628 + 0.167727i
\(171\) 4.81609 + 16.4878i 0.368296 + 1.26086i
\(172\) 25.8229 + 3.89217i 1.96898 + 0.296775i
\(173\) 0.216552 0.948775i 0.0164641 0.0721340i −0.966028 0.258436i \(-0.916793\pi\)
0.982493 + 0.186302i \(0.0596502\pi\)
\(174\) 6.68337 + 3.92580i 0.506665 + 0.297614i
\(175\) 4.69821 10.3789i 0.355152 0.784570i
\(176\) 1.97060 6.38852i 0.148539 0.481552i
\(177\) −7.02676 7.68794i −0.528163 0.577861i
\(178\) 37.2178 + 21.4877i 2.78959 + 1.61057i
\(179\) −12.5663 13.5432i −0.939248 1.01227i −0.999900 0.0141096i \(-0.995509\pi\)
0.0606525 0.998159i \(-0.480682\pi\)
\(180\) 10.7082 + 0.160701i 0.798139 + 0.0119779i
\(181\) −7.59810 6.05928i −0.564763 0.450383i 0.299021 0.954247i \(-0.403340\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(182\) 1.05859 + 44.6076i 0.0784679 + 3.30654i
\(183\) −0.514240 0.0814598i −0.0380137 0.00602168i
\(184\) −37.1597 + 34.4791i −2.73945 + 2.54184i
\(185\) −2.59967 3.25989i −0.191132 0.239672i
\(186\) −1.12281 3.73946i −0.0823287 0.274190i
\(187\) 1.28887 + 1.02784i 0.0942517 + 0.0751632i
\(188\) −33.4954 + 16.1305i −2.44290 + 1.17644i
\(189\) −5.00702 + 12.8035i −0.364207 + 0.931318i
\(190\) −10.7735 5.18825i −0.781593 0.376395i
\(191\) −8.02776 16.6698i −0.580868 1.20619i −0.959780 0.280753i \(-0.909416\pi\)
0.378912 0.925433i \(-0.376298\pi\)
\(192\) 5.87878 3.33556i 0.424264 0.240723i
\(193\) −1.96076 + 0.944254i −0.141139 + 0.0679689i −0.503120 0.864216i \(-0.667815\pi\)
0.361981 + 0.932185i \(0.382100\pi\)
\(194\) 2.44725 6.23549i 0.175702 0.447682i
\(195\) 7.16440 6.54825i 0.513053 0.468930i
\(196\) 29.0514 + 7.47209i 2.07510 + 0.533721i
\(197\) 8.16946i 0.582050i 0.956715 + 0.291025i \(0.0939963\pi\)
−0.956715 + 0.291025i \(0.906004\pi\)
\(198\) −0.518691 8.66435i −0.0368618 0.615748i
\(199\) 12.5731 18.4413i 0.891281 1.30727i −0.0597629 0.998213i \(-0.519034\pi\)
0.951044 0.309056i \(-0.100013\pi\)
\(200\) 16.7803 18.0849i 1.18655 1.27879i
\(201\) −5.96716 2.39376i −0.420891 0.168843i
\(202\) 4.25121 + 6.23539i 0.299114 + 0.438720i
\(203\) 0.241097 4.71653i 0.0169217 0.331035i
\(204\) −1.50151 10.4956i −0.105127 0.734840i
\(205\) 1.72614 2.16451i 0.120559 0.151176i
\(206\) −3.25559 43.4428i −0.226828 3.02681i
\(207\) −11.8743 + 23.7393i −0.825323 + 1.65000i
\(208\) −11.4865 + 37.2384i −0.796447 + 2.58202i
\(209\) −2.41407 + 6.15094i −0.166984 + 0.425470i
\(210\) −4.29183 8.55424i −0.296165 0.590299i
\(211\) −1.08502 2.76459i −0.0746960 0.190322i 0.888649 0.458588i \(-0.151645\pi\)
−0.963345 + 0.268266i \(0.913549\pi\)
\(212\) 25.8873 1.93999i 1.77795 0.133239i
\(213\) −19.2980 13.3703i −1.32228 0.916121i
\(214\) −2.72494 + 4.71974i −0.186273 + 0.322635i
\(215\) −2.53827 + 4.39641i −0.173108 + 0.299833i
\(216\) −19.0806 + 22.8517i −1.29827 + 1.55486i
\(217\) −1.70499 + 1.65899i −0.115742 + 0.112620i
\(218\) 8.83547 + 28.6439i 0.598414 + 1.94001i
\(219\) −4.25495 + 7.24372i −0.287523 + 0.489485i
\(220\) 3.22096 + 2.56863i 0.217157 + 0.173177i
\(221\) −7.51278 5.99125i −0.505365 0.403015i
\(222\) 21.7338 + 0.163074i 1.45868 + 0.0109448i
\(223\) −1.62293 5.26142i −0.108680 0.352331i 0.884854 0.465868i \(-0.154258\pi\)
−0.993534 + 0.113538i \(0.963782\pi\)
\(224\) 6.80630 + 4.40762i 0.454765 + 0.294497i
\(225\) 4.89944 11.9530i 0.326630 0.796866i
\(226\) −11.2771 + 19.5326i −0.750145 + 1.29929i
\(227\) −2.98955 + 5.17805i −0.198423 + 0.343679i −0.948017 0.318219i \(-0.896915\pi\)
0.749594 + 0.661898i \(0.230249\pi\)
\(228\) 38.4260 18.1511i 2.54482 1.20208i
\(229\) 9.35276 0.700893i 0.618048 0.0463163i 0.237973 0.971272i \(-0.423517\pi\)
0.380075 + 0.924956i \(0.375898\pi\)
\(230\) −6.75088 17.2010i −0.445140 1.13420i
\(231\) −4.53654 + 2.71824i −0.298482 + 0.178847i
\(232\) 3.73628 9.51989i 0.245299 0.625011i
\(233\) 7.39788 23.9834i 0.484652 1.57120i −0.301688 0.953407i \(-0.597550\pi\)
0.786339 0.617795i \(-0.211974\pi\)
\(234\) 3.02343 + 50.5041i 0.197648 + 3.30156i
\(235\) −0.540077 7.20683i −0.0352308 0.470122i
\(236\) −16.0665 + 20.1468i −1.04584 + 1.31144i
\(237\) 15.1833 + 6.09086i 0.986260 + 0.395644i
\(238\) −7.69978 + 5.52168i −0.499102 + 0.357918i
\(239\) 3.73786 + 5.48243i 0.241782 + 0.354629i 0.927879 0.372881i \(-0.121630\pi\)
−0.686097 + 0.727510i \(0.740678\pi\)
\(240\) −1.18373 8.27432i −0.0764094 0.534105i
\(241\) 3.21324 3.46305i 0.206983 0.223074i −0.621025 0.783790i \(-0.713284\pi\)
0.828008 + 0.560716i \(0.189474\pi\)
\(242\) −13.6540 + 20.0268i −0.877713 + 1.28737i
\(243\) −5.15024 + 14.7131i −0.330388 + 0.943845i
\(244\) 1.28815i 0.0824652i
\(245\) −3.41537 + 4.72639i −0.218200 + 0.301958i
\(246\) 3.10561 + 14.0932i 0.198007 + 0.898548i
\(247\) 14.0715 35.8536i 0.895347 2.28131i
\(248\) −4.64132 + 2.23514i −0.294724 + 0.141932i
\(249\) 12.2901 + 7.21916i 0.778851 + 0.457496i
\(250\) 8.43266 + 17.5106i 0.533329 + 1.10747i
\(251\) 19.1020 + 9.19905i 1.20571 + 0.580639i 0.925298 0.379241i \(-0.123815\pi\)
0.280411 + 0.959880i \(0.409529\pi\)
\(252\) 33.2253 + 7.27922i 2.09300 + 0.458548i
\(253\) −9.19973 + 4.43035i −0.578382 + 0.278534i
\(254\) 14.3981 + 11.4821i 0.903419 + 0.720452i
\(255\) 2.00589 + 0.473694i 0.125614 + 0.0296639i
\(256\) −20.0079 25.0892i −1.25050 1.56807i
\(257\) −15.3205 + 14.2154i −0.955669 + 0.886732i −0.993646 0.112547i \(-0.964099\pi\)
0.0379771 + 0.999279i \(0.487909\pi\)
\(258\) −9.48265 24.7049i −0.590364 1.53806i
\(259\) −6.02721 11.7915i −0.374512 0.732690i
\(260\) −18.7748 14.9724i −1.16436 0.928550i
\(261\) 0.0803554 5.35442i 0.00497387 0.331430i
\(262\) 11.8485 + 12.7697i 0.732004 + 0.788912i
\(263\) −17.0640 9.85188i −1.05221 0.607493i −0.128942 0.991652i \(-0.541158\pi\)
−0.923267 + 0.384159i \(0.874491\pi\)
\(264\) −11.1839 + 2.46452i −0.688323 + 0.151681i
\(265\) −1.48747 + 4.82227i −0.0913749 + 0.296230i
\(266\) −30.2459 22.9678i −1.85449 1.40825i
\(267\) 0.222769 29.6897i 0.0136332 1.81698i
\(268\) −3.53964 + 15.5082i −0.216218 + 0.947313i
\(269\) 2.68739 + 0.405060i 0.163853 + 0.0246969i 0.230457 0.973083i \(-0.425978\pi\)
−0.0666032 + 0.997780i \(0.521216\pi\)
\(270\) −5.21308 9.51781i −0.317258 0.579235i
\(271\) −9.03397 + 9.73631i −0.548775 + 0.591439i −0.945145 0.326652i \(-0.894079\pi\)
0.396370 + 0.918091i \(0.370270\pi\)
\(272\) −7.90749 + 2.43914i −0.479462 + 0.147894i
\(273\) 26.4433 15.8445i 1.60042 0.958953i
\(274\) 6.53590 + 2.01606i 0.394848 + 0.121795i
\(275\) 4.30367 2.48472i 0.259521 0.149835i
\(276\) 62.6067 + 19.8272i 3.76848 + 1.19346i
\(277\) 5.63961 + 1.73959i 0.338851 + 0.104522i 0.459511 0.888172i \(-0.348025\pi\)
−0.120659 + 0.992694i \(0.538501\pi\)
\(278\) −46.0555 + 31.4001i −2.76223 + 1.88325i
\(279\) −1.86419 + 1.94961i −0.111606 + 0.116720i
\(280\) −10.2616 + 7.35879i −0.613245 + 0.439772i
\(281\) 3.78332 + 1.48484i 0.225694 + 0.0885782i 0.475493 0.879719i \(-0.342270\pi\)
−0.249800 + 0.968298i \(0.580365\pi\)
\(282\) 30.9660 + 21.4544i 1.84400 + 1.27759i
\(283\) −11.2209 + 8.94841i −0.667016 + 0.531927i −0.897425 0.441166i \(-0.854565\pi\)
0.230409 + 0.973094i \(0.425993\pi\)
\(284\) −25.2022 + 52.3328i −1.49547 + 3.10538i
\(285\) 0.555536 + 8.24256i 0.0329071 + 0.488247i
\(286\) −10.9639 + 16.0811i −0.648311 + 0.950898i
\(287\) 6.74256 5.64383i 0.398001 0.333145i
\(288\) 7.89281 + 4.71623i 0.465089 + 0.277907i
\(289\) −1.11793 + 14.9177i −0.0657603 + 0.877510i
\(290\) 2.73275 + 2.53563i 0.160473 + 0.148897i
\(291\) −4.58119 + 0.655389i −0.268554 + 0.0384196i
\(292\) 19.3481 + 7.59356i 1.13226 + 0.444379i
\(293\) 7.65065 13.2513i 0.446956 0.774150i −0.551230 0.834353i \(-0.685841\pi\)
0.998186 + 0.0602028i \(0.0191747\pi\)
\(294\) −7.94200 29.3404i −0.463187 1.71117i
\(295\) −2.50465 4.33818i −0.145826 0.252579i
\(296\) −4.27401 28.3562i −0.248422 1.64817i
\(297\) −5.02947 + 3.26568i −0.291839 + 0.189494i
\(298\) −14.8645 + 4.58508i −0.861075 + 0.265607i
\(299\) 53.6248 25.8243i 3.10120 1.49346i
\(300\) −31.1053 7.34556i −1.79587 0.424096i
\(301\) −10.6831 + 12.0760i −0.615764 + 0.696051i
\(302\) 22.0198 + 1.65015i 1.26709 + 0.0949556i
\(303\) 2.29737 4.68038i 0.131981 0.268881i
\(304\) −18.6846 27.4053i −1.07164 1.57180i
\(305\) −0.233099 0.0914848i −0.0133472 0.00523840i
\(306\) −8.49928 + 6.57175i −0.485872 + 0.375682i
\(307\) −8.47727 + 6.76040i −0.483823 + 0.385836i −0.834805 0.550546i \(-0.814419\pi\)
0.350981 + 0.936382i \(0.385848\pi\)
\(308\) 8.39845 + 10.0334i 0.478546 + 0.571709i
\(309\) −24.9944 + 16.7676i −1.42188 + 0.953873i
\(310\) −0.140330 1.87258i −0.00797023 0.106355i
\(311\) 2.63236 + 11.5331i 0.149268 + 0.653984i 0.993089 + 0.117361i \(0.0374433\pi\)
−0.843822 + 0.536624i \(0.819700\pi\)
\(312\) 65.1906 14.3656i 3.69069 0.813291i
\(313\) 22.3091i 1.26098i −0.776196 0.630492i \(-0.782853\pi\)
0.776196 0.630492i \(-0.217147\pi\)
\(314\) 4.44571 + 19.4779i 0.250886 + 1.09920i
\(315\) −3.67690 + 5.49538i −0.207170 + 0.309630i
\(316\) 9.00652 39.4601i 0.506656 2.21981i
\(317\) −23.7843 5.42862i −1.33586 0.304901i −0.505837 0.862629i \(-0.668816\pi\)
−0.830024 + 0.557728i \(0.811673\pi\)
\(318\) −14.6549 21.8452i −0.821809 1.22502i
\(319\) 1.28439 1.61058i 0.0719123 0.0901752i
\(320\) 3.10641 0.958200i 0.173653 0.0535650i
\(321\) 3.76507 + 0.0282502i 0.210146 + 0.00157677i
\(322\) −10.1213 57.8084i −0.564036 3.22153i
\(323\) 7.97374 1.81995i 0.443671 0.101265i
\(324\) 37.9471 + 6.89000i 2.10817 + 0.382778i
\(325\) −25.0859 + 14.4834i −1.39152 + 0.803392i
\(326\) 0.398668 1.29245i 0.0220802 0.0715822i
\(327\) 14.1995 15.0749i 0.785231 0.833645i
\(328\) 17.7245 6.95636i 0.978673 0.384101i
\(329\) 2.88158 22.7717i 0.158867 1.25545i
\(330\) 0.653148 4.12320i 0.0359546 0.226975i
\(331\) 4.03490 + 17.6781i 0.221778 + 0.971675i 0.956139 + 0.292915i \(0.0946252\pi\)
−0.734360 + 0.678760i \(0.762518\pi\)
\(332\) 12.8836 32.8269i 0.707080 1.80161i
\(333\) −7.31189 13.1152i −0.400689 0.718709i
\(334\) 0.323742 0.127059i 0.0177144 0.00695238i
\(335\) −2.55493 1.74192i −0.139591 0.0951713i
\(336\) 1.55414 26.5015i 0.0847852 1.44578i
\(337\) −25.4216 + 17.3321i −1.38480 + 0.944141i −0.385026 + 0.922906i \(0.625808\pi\)
−0.999775 + 0.0212353i \(0.993240\pi\)
\(338\) 45.5488 66.8078i 2.47753 3.63387i
\(339\) 15.5817 + 0.116913i 0.846283 + 0.00634985i
\(340\) 0.381071 5.08504i 0.0206665 0.275775i
\(341\) −1.02608 + 0.154657i −0.0555654 + 0.00837513i
\(342\) −35.2124 24.7895i −1.90407 1.34046i
\(343\) −13.6218 + 12.5478i −0.735509 + 0.677515i
\(344\) −30.2368 + 17.4572i −1.63026 + 0.941230i
\(345\) −8.03424 + 9.92099i −0.432549 + 0.534128i
\(346\) 1.05859 + 2.19818i 0.0569100 + 0.118175i
\(347\) 5.05250 + 1.15320i 0.271233 + 0.0619071i 0.355974 0.934496i \(-0.384149\pi\)
−0.0847412 + 0.996403i \(0.527006\pi\)
\(348\) −13.1154 + 1.87629i −0.703057 + 0.100580i
\(349\) −20.3593 + 1.52572i −1.08981 + 0.0816699i −0.607491 0.794327i \(-0.707824\pi\)
−0.482318 + 0.875996i \(0.660205\pi\)
\(350\) 7.01451 + 27.6874i 0.374941 + 1.47995i
\(351\) 29.3165 19.0355i 1.56480 1.01604i
\(352\) 1.29222 + 3.29252i 0.0688755 + 0.175492i
\(353\) 12.1058 8.25360i 0.644327 0.439295i −0.196570 0.980490i \(-0.562980\pi\)
0.840897 + 0.541195i \(0.182028\pi\)
\(354\) 25.7902 + 4.08538i 1.37073 + 0.217135i
\(355\) −7.68013 8.27721i −0.407619 0.439309i
\(356\) −72.6371 + 10.9483i −3.84976 + 0.580258i
\(357\) 5.94306 + 2.74416i 0.314540 + 0.145236i
\(358\) 45.8007 + 6.90334i 2.42064 + 0.364853i
\(359\) −12.0674 17.6997i −0.636896 0.934154i −0.999997 0.00240462i \(-0.999235\pi\)
0.363102 0.931750i \(-0.381718\pi\)
\(360\) −11.3271 + 8.75822i −0.596988 + 0.461599i
\(361\) 6.89130 + 11.9361i 0.362700 + 0.628215i
\(362\) 24.3643 1.28056
\(363\) 16.6890 + 1.37667i 0.875947 + 0.0722562i
\(364\) −48.9542 58.4845i −2.56590 3.06542i
\(365\) −2.74822 + 2.96187i −0.143848 + 0.155032i
\(366\) 1.13529 0.644149i 0.0593423 0.0336702i
\(367\) −31.8958 + 12.5182i −1.66495 + 0.653444i −0.995958 0.0898254i \(-0.971369\pi\)
−0.668992 + 0.743270i \(0.733274\pi\)
\(368\) 7.63928 50.6833i 0.398225 2.64205i
\(369\) 7.40961 6.67102i 0.385729 0.347280i
\(370\) 10.1912 + 2.32607i 0.529813 + 0.120926i
\(371\) −7.68233 + 14.0667i −0.398847 + 0.730306i
\(372\) 5.48575 + 3.80072i 0.284423 + 0.197058i
\(373\) 12.8921 + 22.3298i 0.667528 + 1.15619i 0.978593 + 0.205804i \(0.0659810\pi\)
−0.311065 + 0.950389i \(0.600686\pi\)
\(374\) −4.13294 −0.213709
\(375\) 7.64691 11.0371i 0.394885 0.569954i
\(376\) 21.5661 44.7824i 1.11219 2.30948i
\(377\) −7.48668 + 9.38800i −0.385584 + 0.483507i
\(378\) −10.1992 32.9225i −0.524589 1.69335i
\(379\) −15.6481 19.6221i −0.803789 1.00792i −0.999628 0.0272831i \(-0.991314\pi\)
0.195839 0.980636i \(-0.437257\pi\)
\(380\) 19.9268 4.54816i 1.02222 0.233315i
\(381\) 1.99061 12.5664i 0.101982 0.643794i
\(382\) 41.7920 + 20.1260i 2.13826 + 1.02973i
\(383\) 9.47923 + 1.42876i 0.484366 + 0.0730064i 0.386686 0.922211i \(-0.373620\pi\)
0.0976800 + 0.995218i \(0.468858\pi\)
\(384\) −10.2619 + 25.5808i −0.523675 + 1.30542i
\(385\) −2.41209 + 0.807180i −0.122931 + 0.0411377i
\(386\) 2.36729 4.91572i 0.120492 0.250204i
\(387\) −11.6119 + 14.1208i −0.590265 + 0.717802i
\(388\) 3.37487 + 10.9411i 0.171333 + 0.555449i
\(389\) −16.9489 1.27014i −0.859343 0.0643988i −0.362234 0.932087i \(-0.617986\pi\)
−0.497109 + 0.867688i \(0.665605\pi\)
\(390\) −3.80717 + 24.0339i −0.192784 + 1.21701i
\(391\) 10.9455 + 6.31937i 0.553536 + 0.319584i
\(392\) −36.5957 + 16.4064i −1.84836 + 0.828650i
\(393\) 3.63354 11.4733i 0.183288 0.578751i
\(394\) −12.7698 16.0129i −0.643335 0.806716i
\(395\) 6.50095 + 4.43227i 0.327098 + 0.223012i
\(396\) 9.92700 + 11.0261i 0.498850 + 0.554081i
\(397\) 27.8297 + 2.08555i 1.39673 + 0.104671i 0.751711 0.659492i \(-0.229229\pi\)
0.645023 + 0.764163i \(0.276848\pi\)
\(398\) 4.18161 + 55.7997i 0.209605 + 2.79699i
\(399\) −3.48916 + 26.0050i −0.174676 + 1.30188i
\(400\) −1.86415 + 24.8754i −0.0932077 + 1.24377i
\(401\) −3.09304 + 20.5210i −0.154459 + 1.02477i 0.768494 + 0.639857i \(0.221007\pi\)
−0.922953 + 0.384913i \(0.874232\pi\)
\(402\) 15.4379 4.63539i 0.769972 0.231192i
\(403\) 5.98098 0.901488i 0.297934 0.0449063i
\(404\) −12.3265 3.80221i −0.613264 0.189167i
\(405\) −3.94181 + 6.37746i −0.195870 + 0.316899i
\(406\) 6.89991 + 9.62167i 0.342437 + 0.477515i
\(407\) 0.860922 5.71185i 0.0426743 0.283126i
\(408\) 10.3185 + 9.71929i 0.510843 + 0.481176i
\(409\) 23.3181 5.32220i 1.15300 0.263166i 0.397055 0.917795i \(-0.370032\pi\)
0.755950 + 0.654629i \(0.227175\pi\)
\(410\) 6.94079i 0.342781i
\(411\) −1.01691 4.61470i −0.0501604 0.227626i
\(412\) 50.6489 + 54.5866i 2.49529 + 2.68929i
\(413\) −5.04883 15.0874i −0.248437 0.742401i
\(414\) −13.8326 65.0921i −0.679835 3.19910i
\(415\) 5.02527 + 4.66276i 0.246681 + 0.228886i
\(416\) −7.53228 19.1919i −0.369301 0.940962i
\(417\) 34.5700 + 16.9688i 1.69290 + 0.830964i
\(418\) −4.88286 15.8299i −0.238829 0.774263i
\(419\) 0.219673 + 0.203827i 0.0107317 + 0.00995758i 0.685520 0.728053i \(-0.259575\pi\)
−0.674789 + 0.738011i \(0.735765\pi\)
\(420\) 14.8520 + 6.85779i 0.724704 + 0.334626i
\(421\) −3.34072 + 3.09974i −0.162817 + 0.151072i −0.757374 0.652981i \(-0.773518\pi\)
0.594557 + 0.804053i \(0.297327\pi\)
\(422\) 6.44812 + 3.72282i 0.313890 + 0.181224i
\(423\) 2.33421 25.9217i 0.113493 1.26036i
\(424\) −25.4425 + 23.6072i −1.23560 + 1.14647i
\(425\) −5.54188 2.66883i −0.268820 0.129457i
\(426\) 58.7252 3.95799i 2.84524 0.191765i
\(427\) −0.667559 0.432298i −0.0323054 0.0209203i
\(428\) −1.38840 9.21141i −0.0671107 0.445250i
\(429\) 13.4010 + 1.10544i 0.647006 + 0.0533711i
\(430\) −1.89688 12.5850i −0.0914755 0.606901i
\(431\) 24.3695 1.82624i 1.17384 0.0879669i 0.526503 0.850174i \(-0.323503\pi\)
0.647334 + 0.762207i \(0.275884\pi\)
\(432\) 0.677506 30.0939i 0.0325965 1.44789i
\(433\) 3.49907 + 7.26589i 0.168155 + 0.349176i 0.967969 0.251071i \(-0.0807829\pi\)
−0.799814 + 0.600248i \(0.795069\pi\)
\(434\) 0.748732 5.91687i 0.0359403 0.284019i
\(435\) 0.591930 2.50657i 0.0283809 0.120181i
\(436\) −42.3341 28.8629i −2.02744 1.38228i
\(437\) −11.2727 + 49.3890i −0.539247 + 2.36260i
\(438\) −2.98272 20.8493i −0.142520 0.996218i
\(439\) 1.19432 0.952438i 0.0570018 0.0454574i −0.594574 0.804041i \(-0.702679\pi\)
0.651576 + 0.758583i \(0.274108\pi\)
\(440\) −5.50800 −0.262584
\(441\) −14.9226 + 14.7755i −0.710600 + 0.703596i
\(442\) 24.0907 1.14588
\(443\) −18.1322 + 14.4599i −0.861487 + 0.687013i −0.951073 0.308966i \(-0.900017\pi\)
0.0895861 + 0.995979i \(0.471446\pi\)
\(444\) −29.2184 + 22.9444i −1.38664 + 1.08889i
\(445\) 3.17755 13.9218i 0.150630 0.659954i
\(446\) 11.4053 + 7.77600i 0.540057 + 0.368204i
\(447\) 7.82298 + 7.36866i 0.370014 + 0.348526i
\(448\) 10.2747 1.01562i 0.485433 0.0479834i
\(449\) 7.71521 + 16.0208i 0.364103 + 0.756069i 0.999875 0.0158086i \(-0.00503225\pi\)
−0.635772 + 0.771877i \(0.719318\pi\)
\(450\) 9.08060 + 31.0873i 0.428063 + 1.46547i
\(451\) 3.82469 0.286621i 0.180097 0.0134964i
\(452\) −5.74586 38.1213i −0.270263 1.79308i
\(453\) −6.51581 13.7940i −0.306139 0.648100i
\(454\) −2.23412 14.8224i −0.104853 0.695652i
\(455\) 14.0599 4.70502i 0.659140 0.220575i
\(456\) −25.0357 + 51.0045i −1.17240 + 2.38851i
\(457\) −6.52434 3.14196i −0.305196 0.146975i 0.275017 0.961439i \(-0.411316\pi\)
−0.580213 + 0.814465i \(0.697031\pi\)
\(458\) −17.2367 + 15.9933i −0.805416 + 0.747317i
\(459\) 6.84662 + 2.86657i 0.319573 + 0.133800i
\(460\) 27.3533 + 15.7924i 1.27535 + 0.736325i
\(461\) −22.4653 + 20.8447i −1.04631 + 0.970837i −0.999606 0.0280719i \(-0.991063\pi\)
−0.0467073 + 0.998909i \(0.514873\pi\)
\(462\) 4.64308 12.4191i 0.216016 0.577791i
\(463\) −21.8033 20.2305i −1.01329 0.940193i −0.0150703 0.999886i \(-0.504797\pi\)
−0.998217 + 0.0596934i \(0.980988\pi\)
\(464\) 3.04795 + 9.88122i 0.141498 + 0.458724i
\(465\) −1.07737 + 0.722756i −0.0499618 + 0.0335170i
\(466\) 22.9883 + 58.5732i 1.06491 + 2.71335i
\(467\) 30.8136 + 28.5908i 1.42588 + 1.32302i 0.871170 + 0.490982i \(0.163362\pi\)
0.554712 + 0.832042i \(0.312828\pi\)
\(468\) −57.8640 64.2705i −2.67477 2.97090i
\(469\) −6.84894 7.03884i −0.316255 0.325023i
\(470\) 12.3237 + 13.2818i 0.568451 + 0.612644i
\(471\) 10.1884 9.31214i 0.469455 0.429081i
\(472\) 34.4520i 1.58578i
\(473\) −6.85655 + 1.56496i −0.315264 + 0.0719570i
\(474\) −39.2813 + 11.7946i −1.80425 + 0.541745i
\(475\) 3.67460 24.3794i 0.168602 1.11860i
\(476\) 4.40522 15.5849i 0.201913 0.714334i
\(477\) −8.13013 + 16.2539i −0.372253 + 0.744213i
\(478\) −15.8962 4.90333i −0.727076 0.224273i
\(479\) 9.02307 1.36001i 0.412275 0.0621404i 0.0603696 0.998176i \(-0.480772\pi\)
0.351905 + 0.936036i \(0.385534\pi\)
\(480\) 3.21900 + 3.03206i 0.146927 + 0.138394i
\(481\) −5.01828 + 33.2941i −0.228814 + 1.51808i
\(482\) −0.885077 + 11.8105i −0.0403142 + 0.537955i
\(483\) −31.2857 + 25.7908i −1.42355 + 1.17352i
\(484\) −3.09612 41.3148i −0.140733 1.87795i
\(485\) −2.21955 0.166332i −0.100785 0.00755276i
\(486\) −12.9034 36.8894i −0.585309 1.67334i
\(487\) −6.83637 4.66096i −0.309785 0.211208i 0.398440 0.917194i \(-0.369552\pi\)
−0.708226 + 0.705986i \(0.750504\pi\)
\(488\) −1.07378 1.34648i −0.0486079 0.0609524i
\(489\) −0.912539 + 0.201090i −0.0412665 + 0.00909359i
\(490\) −0.693471 14.6028i −0.0313278 0.659685i
\(491\) −26.8398 15.4960i −1.21127 0.699324i −0.248230 0.968701i \(-0.579849\pi\)
−0.963035 + 0.269377i \(0.913182\pi\)
\(492\) −19.1698 15.5241i −0.864239 0.699880i
\(493\) −2.54268 0.190548i −0.114517 0.00858183i
\(494\) 28.4620 + 92.2715i 1.28057 + 4.15149i
\(495\) −2.70027 + 1.01328i −0.121368 + 0.0455437i
\(496\) 2.26001 4.69296i 0.101478 0.210720i
\(497\) −18.6628 30.6233i −0.837140 1.37364i
\(498\) −35.3740 + 5.06063i −1.58515 + 0.226772i
\(499\) 10.2015 + 1.53762i 0.456680 + 0.0688335i 0.373354 0.927689i \(-0.378208\pi\)
0.0833261 + 0.996522i \(0.473446\pi\)
\(500\) −29.9308 14.4139i −1.33854 0.644609i
\(501\) −0.186725 0.151214i −0.00834224 0.00675573i
\(502\) −51.8208 + 11.8278i −2.31288 + 0.527899i
\(503\) 8.72340 + 10.9388i 0.388957 + 0.487737i 0.937303 0.348515i \(-0.113314\pi\)
−0.548346 + 0.836251i \(0.684742\pi\)
\(504\) −40.7978 + 20.0873i −1.81728 + 0.894761i
\(505\) 1.56347 1.96053i 0.0695734 0.0872422i
\(506\) 11.1071 23.0641i 0.493771 1.02533i
\(507\) −55.6734 4.59246i −2.47254 0.203958i
\(508\) −31.4782 −1.39662
\(509\) 3.46160 + 5.99567i 0.153433 + 0.265754i 0.932487 0.361203i \(-0.117634\pi\)
−0.779054 + 0.626956i \(0.784300\pi\)
\(510\) −4.67217 + 2.20697i −0.206887 + 0.0977261i
\(511\) −10.4284 + 7.47841i −0.461324 + 0.330826i
\(512\) 47.4062 + 10.8202i 2.09508 + 0.478188i
\(513\) −2.89049 + 29.6104i −0.127618 + 1.30733i
\(514\) 7.80928 51.8112i 0.344453 2.28529i
\(515\) −13.4749 + 5.28852i −0.593777 + 0.233040i
\(516\) 39.0011 + 22.9091i 1.71693 + 1.00852i
\(517\) 6.80996 7.33940i 0.299502 0.322786i
\(518\) 30.2454 + 13.6912i 1.32891 + 0.601556i
\(519\) 0.959948 1.38553i 0.0421370 0.0608182i
\(520\) 32.1059 1.40794
\(521\) 11.6063 + 20.1027i 0.508482 + 0.880716i 0.999952 + 0.00982161i \(0.00312637\pi\)
−0.491470 + 0.870894i \(0.663540\pi\)
\(522\) 8.21208 + 10.6207i 0.359433 + 0.464857i
\(523\) −9.16729 13.4459i −0.400857 0.587950i 0.571743 0.820433i \(-0.306267\pi\)
−0.972600 + 0.232483i \(0.925315\pi\)
\(524\) −29.4431 4.43783i −1.28623 0.193868i
\(525\) 14.2455 13.6546i 0.621726 0.595936i
\(526\) 48.8465 7.36242i 2.12981 0.321017i
\(527\) 0.873610 + 0.941527i 0.0380550 + 0.0410136i
\(528\) 7.28754 8.99894i 0.317149 0.391628i
\(529\) −45.6776 + 31.1425i −1.98598 + 1.35402i
\(530\) −4.62220 11.7772i −0.200776 0.511568i
\(531\) −6.33800 16.8899i −0.275046 0.732959i
\(532\) 64.8974 1.54009i 2.81366 0.0667714i
\(533\) −22.2939 + 1.67070i −0.965657 + 0.0723660i
\(534\) 45.9719 + 58.5426i 1.98940 + 2.53339i
\(535\) 1.76547 + 0.402958i 0.0763281 + 0.0174214i
\(536\) −9.22750 19.1611i −0.398567 0.827633i
\(537\) −11.4670 29.8747i −0.494839 1.28919i
\(538\) −5.90068 + 3.40676i −0.254396 + 0.146876i
\(539\) −8.01814 + 0.985156i −0.345366 + 0.0424337i
\(540\) 17.1100 + 7.16369i 0.736299 + 0.308276i
\(541\) −20.8110 + 3.13676i −0.894735 + 0.134860i −0.580284 0.814414i \(-0.697059\pi\)
−0.314451 + 0.949274i \(0.601820\pi\)
\(542\) 2.48838 33.2052i 0.106885 1.42628i
\(543\) −8.30672 14.6402i −0.356475 0.628273i
\(544\) 2.46622 3.61728i 0.105738 0.155089i
\(545\) 8.22954 5.61080i 0.352515 0.240340i
\(546\) −27.0643 + 72.3906i −1.15825 + 3.09803i
\(547\) 29.4620 + 20.0868i 1.25970 + 0.858851i 0.994438 0.105325i \(-0.0335883\pi\)
0.265265 + 0.964176i \(0.414541\pi\)
\(548\) −10.8830 + 4.27127i −0.464899 + 0.182460i
\(549\) −0.774124 0.462566i −0.0330388 0.0197418i
\(550\) −4.55165 + 11.5974i −0.194083 + 0.494516i
\(551\) −2.27422 9.96401i −0.0968850 0.424481i
\(552\) −81.9697 + 31.4630i −3.48886 + 1.33916i
\(553\) 17.4269 + 17.9101i 0.741069 + 0.761617i
\(554\) −13.7733 + 5.40563i −0.585172 + 0.229663i
\(555\) −2.07685 6.91680i −0.0881572 0.293602i
\(556\) 28.0837 91.0451i 1.19101 3.86117i
\(557\) 35.0916 20.2602i 1.48688 0.858450i 0.486992 0.873407i \(-0.338094\pi\)
0.999888 + 0.0149561i \(0.00476085\pi\)
\(558\) 0.606506 6.73535i 0.0256755 0.285130i
\(559\) 39.9665 9.12210i 1.69040 0.385824i
\(560\) 3.47289 12.2865i 0.146757 0.519200i
\(561\) 1.40908 + 2.48344i 0.0594912 + 0.104851i
\(562\) −9.73661 + 3.00335i −0.410714 + 0.126689i
\(563\) 13.6353 17.0981i 0.574658 0.720598i −0.406533 0.913636i \(-0.633263\pi\)
0.981191 + 0.193038i \(0.0618340\pi\)
\(564\) −64.2469 + 4.33014i −2.70528 + 0.182332i
\(565\) 7.30640 + 1.66764i 0.307382 + 0.0701580i
\(566\) 8.00662 35.0793i 0.336543 1.47449i
\(567\) −16.3055 + 17.3531i −0.684767 + 0.728762i
\(568\) −17.2806 75.7110i −0.725076 3.17677i
\(569\) 30.0707i 1.26063i −0.776340 0.630315i \(-0.782926\pi\)
0.776340 0.630315i \(-0.217074\pi\)
\(570\) −13.9730 15.2878i −0.585264 0.640334i
\(571\) −4.86505 21.3152i −0.203596 0.892012i −0.968725 0.248136i \(-0.920182\pi\)
0.765129 0.643877i \(-0.222675\pi\)
\(572\) −2.48613 33.1751i −0.103950 1.38712i
\(573\) −2.15500 31.9740i −0.0900265 1.33573i
\(574\) −4.39404 + 21.6018i −0.183404 + 0.901642i
\(575\) 29.7871 23.7544i 1.24221 0.990628i
\(576\) 11.6013 1.57096i 0.483387 0.0654565i
\(577\) 21.4568 + 8.42119i 0.893260 + 0.350579i 0.767173 0.641440i \(-0.221663\pi\)
0.126087 + 0.992019i \(0.459758\pi\)
\(578\) −21.1268 30.9874i −0.878761 1.28891i
\(579\) −3.76090 + 0.253479i −0.156298 + 0.0105342i
\(580\) −6.35428 0.476188i −0.263847 0.0197726i
\(581\) 12.6883 + 17.6933i 0.526398 + 0.734041i
\(582\) 7.95509 8.44556i 0.329749 0.350080i
\(583\) −6.29888 + 3.03338i −0.260873 + 0.125630i
\(584\) −26.5542 + 8.19088i −1.09882 + 0.338941i
\(585\) 15.7397 5.90639i 0.650758 0.244199i
\(586\) 5.71742 + 37.9326i 0.236184 + 1.56698i
\(587\) 21.6956 + 37.5779i 0.895474 + 1.55101i 0.833217 + 0.552945i \(0.186496\pi\)
0.0622561 + 0.998060i \(0.480170\pi\)
\(588\) 41.8824 + 30.7459i 1.72720 + 1.26794i
\(589\) −2.57408 + 4.45844i −0.106063 + 0.183707i
\(590\) 11.6904 + 4.58815i 0.481287 + 0.188891i
\(591\) −5.26823 + 13.1326i −0.216706 + 0.540205i
\(592\) 21.2553 + 19.7220i 0.873587 + 0.810570i
\(593\) 0.979320 13.0681i 0.0402159 0.536643i −0.940318 0.340296i \(-0.889473\pi\)
0.980534 0.196348i \(-0.0629081\pi\)
\(594\) 4.75355 14.2627i 0.195041 0.585204i
\(595\) 2.50734 + 1.90400i 0.102791 + 0.0780565i
\(596\) 14.9781 21.9689i 0.613528 0.899880i
\(597\) 32.1038 21.5369i 1.31392 0.881447i
\(598\) −64.7428 + 134.440i −2.64753 + 5.49765i
\(599\) 5.99247 4.77883i 0.244845 0.195258i −0.493376 0.869816i \(-0.664237\pi\)
0.738222 + 0.674558i \(0.235666\pi\)
\(600\) 38.6371 18.2508i 1.57735 0.745086i
\(601\) 8.79659 + 3.45241i 0.358821 + 0.140827i 0.537902 0.843008i \(-0.319217\pi\)
−0.179081 + 0.983834i \(0.557312\pi\)
\(602\) 2.06357 40.3690i 0.0841047 1.64532i
\(603\) −8.04871 7.69607i −0.327769 0.313408i
\(604\) −31.1854 + 21.2618i −1.26891 + 0.865132i
\(605\) 7.69610 + 2.37393i 0.312891 + 0.0965140i
\(606\) 2.81294 + 12.7650i 0.114268 + 0.518544i
\(607\) 4.77811 2.75865i 0.193938 0.111970i −0.399887 0.916564i \(-0.630951\pi\)
0.593825 + 0.804595i \(0.297617\pi\)
\(608\) 16.7685 + 5.17239i 0.680052 + 0.209768i
\(609\) 3.42911 7.42647i 0.138955 0.300936i
\(610\) 0.599897 0.185044i 0.0242891 0.00749220i
\(611\) −39.6950 + 42.7810i −1.60589 + 1.73073i
\(612\) 4.35458 17.8403i 0.176023 0.721150i
\(613\) −32.8880 4.95707i −1.32833 0.200214i −0.553749 0.832683i \(-0.686803\pi\)
−0.774586 + 0.632469i \(0.782042\pi\)
\(614\) 6.04889 26.5019i 0.244113 1.06953i
\(615\) 4.17064 2.36638i 0.168176 0.0954215i
\(616\) −17.1426 3.48698i −0.690693 0.140494i
\(617\) −10.8770 + 35.2622i −0.437890 + 1.41960i 0.420822 + 0.907143i \(0.361742\pi\)
−0.858711 + 0.512460i \(0.828734\pi\)
\(618\) 22.7815 71.9350i 0.916405 2.89365i
\(619\) −18.5138 10.6890i −0.744134 0.429626i 0.0794365 0.996840i \(-0.474688\pi\)
−0.823570 + 0.567214i \(0.808021\pi\)
\(620\) 2.18319 + 2.35292i 0.0876792 + 0.0944957i
\(621\) −34.3970 + 30.5042i −1.38031 + 1.22409i
\(622\) −23.1873 18.4913i −0.929726 0.741432i
\(623\) 18.7030 41.3171i 0.749320 1.65533i
\(624\) −42.4788 + 52.4544i −1.70051 + 2.09986i
\(625\) −11.0488 + 10.2518i −0.441952 + 0.410072i
\(626\) 34.8717 + 43.7277i 1.39375 + 1.74771i
\(627\) −7.84723 + 8.33105i −0.313388 + 0.332710i
\(628\) −26.6993 21.2920i −1.06542 0.849643i
\(629\) −6.44174 + 3.10218i −0.256849 + 0.123692i
\(630\) −1.38288 16.5188i −0.0550951 0.658127i
\(631\) −6.13206 2.95304i −0.244113 0.117559i 0.307827 0.951442i \(-0.400398\pi\)
−0.551941 + 0.833883i \(0.686112\pi\)
\(632\) 23.4791 + 48.7549i 0.933949 + 1.93936i
\(633\) 0.0385955 5.14385i 0.00153403 0.204450i
\(634\) 55.1049 26.5371i 2.18850 1.05392i
\(635\) 2.23559 5.69620i 0.0887168 0.226047i
\(636\) 42.8656 + 13.5753i 1.69973 + 0.538297i
\(637\) 46.7374 5.74243i 1.85180 0.227523i
\(638\) 5.16454i 0.204466i
\(639\) −22.3999 33.9379i −0.886128 1.34256i
\(640\) −7.46750 + 10.9528i −0.295179 + 0.432948i
\(641\) −1.47224 + 1.58669i −0.0581499 + 0.0626707i −0.761457 0.648216i \(-0.775516\pi\)
0.703307 + 0.710886i \(0.251706\pi\)
\(642\) −7.42403 + 5.82988i −0.293003 + 0.230087i
\(643\) 2.94034 + 4.31269i 0.115956 + 0.170076i 0.879829 0.475291i \(-0.157657\pi\)
−0.763873 + 0.645366i \(0.776705\pi\)
\(644\) 75.1338 + 66.4674i 2.96069 + 2.61918i
\(645\) −6.91544 + 5.43050i −0.272295 + 0.213826i
\(646\) −12.7844 + 16.0312i −0.502996 + 0.630737i
\(647\) −1.31398 17.5339i −0.0516580 0.689329i −0.961576 0.274540i \(-0.911475\pi\)
0.909918 0.414789i \(-0.136145\pi\)
\(648\) −45.4090 + 24.4302i −1.78383 + 0.959709i
\(649\) 2.04552 6.63142i 0.0802938 0.260306i
\(650\) 26.5314 67.6008i 1.04065 2.65152i
\(651\) −3.81065 + 1.56738i −0.149351 + 0.0614304i
\(652\) 0.844627 + 2.15207i 0.0330781 + 0.0842817i
\(653\) −1.13448 + 0.0850177i −0.0443957 + 0.00332700i −0.0969094 0.995293i \(-0.530896\pi\)
0.0525137 + 0.998620i \(0.483277\pi\)
\(654\) −4.26829 + 51.7436i −0.166903 + 2.02333i
\(655\) 2.89412 5.01276i 0.113083 0.195865i
\(656\) −9.62631 + 16.6733i −0.375844 + 0.650981i
\(657\) −11.5112 + 8.90060i −0.449094 + 0.347245i
\(658\) 29.9467 + 49.1388i 1.16745 + 1.91563i
\(659\) 11.8957 + 38.5649i 0.463390 + 1.50227i 0.822383 + 0.568934i \(0.192644\pi\)
−0.358993 + 0.933340i \(0.616880\pi\)
\(660\) 3.52135 + 6.20623i 0.137068 + 0.241577i
\(661\) −14.6884 11.7136i −0.571313 0.455607i 0.294727 0.955581i \(-0.404771\pi\)
−0.866040 + 0.499975i \(0.833343\pi\)
\(662\) −35.5417 28.3435i −1.38137 1.10160i
\(663\) −8.21344 14.4758i −0.318984 0.562195i
\(664\) 13.8971 + 45.0532i 0.539311 + 1.74840i
\(665\) −4.33035 + 11.8530i −0.167924 + 0.459641i
\(666\) 34.8325 + 14.2776i 1.34973 + 0.553246i
\(667\) 7.89671 13.6775i 0.305762 0.529595i
\(668\) −0.297232 + 0.514821i −0.0115002 + 0.0199190i
\(669\) 0.784015 9.50445i 0.0303118 0.367463i
\(670\) 7.73071 0.579337i 0.298663 0.0223817i
\(671\) −0.126740 0.322929i −0.00489275 0.0124665i
\(672\) 8.09898 + 11.4745i 0.312425 + 0.442640i
\(673\) −7.80883 + 19.8966i −0.301008 + 0.766956i 0.697712 + 0.716378i \(0.254202\pi\)
−0.998720 + 0.0505779i \(0.983894\pi\)
\(674\) 22.7363 73.7094i 0.875770 2.83918i
\(675\) 15.5841 16.0553i 0.599832 0.617968i
\(676\) 10.3284 + 137.823i 0.397247 + 5.30089i
\(677\) 4.68811 5.87870i 0.180179 0.225937i −0.683538 0.729915i \(-0.739559\pi\)
0.863716 + 0.503978i \(0.168131\pi\)
\(678\) −30.7243 + 24.1269i −1.17996 + 0.926588i
\(679\) −6.80261 1.92282i −0.261060 0.0737910i
\(680\) 3.84050 + 5.63298i 0.147277 + 0.216015i
\(681\) −8.14495 + 6.39599i −0.312115 + 0.245095i
\(682\) 1.76946 1.90703i 0.0677562 0.0730238i
\(683\) −22.4818 + 32.9747i −0.860241 + 1.26174i 0.103426 + 0.994637i \(0.467019\pi\)
−0.963667 + 0.267105i \(0.913933\pi\)
\(684\) 73.4759 4.39864i 2.80942 0.168186i
\(685\) 2.27271i 0.0868356i
\(686\) 7.08635 45.8872i 0.270558 1.75198i
\(687\) 15.4868 + 4.90460i 0.590858 + 0.187122i
\(688\) 12.8976 32.8626i 0.491717 1.25287i
\(689\) 36.7159 17.6814i 1.39876 0.673609i
\(690\) 0.240137 32.0045i 0.00914185 1.21839i
\(691\) −0.246820 0.512527i −0.00938948 0.0194974i 0.896221 0.443607i \(-0.146301\pi\)
−0.905611 + 0.424110i \(0.860587\pi\)
\(692\) −3.75733 1.80944i −0.142832 0.0687844i
\(693\) −9.04552 + 1.44418i −0.343611 + 0.0548597i
\(694\) −11.7059 + 5.63728i −0.444351 + 0.213988i
\(695\) 14.4807 + 11.5480i 0.549286 + 0.438041i
\(696\) 12.1453 12.8941i 0.460365 0.488748i
\(697\) −2.95992 3.71162i −0.112115 0.140588i
\(698\) 37.5211 34.8145i 1.42020 1.31775i
\(699\) 27.3584 33.7832i 1.03479 1.27780i
\(700\) −38.8812 29.5253i −1.46957 1.11595i
\(701\) −19.6933 15.7049i −0.743804 0.593164i 0.176531 0.984295i \(-0.443512\pi\)
−0.920335 + 0.391131i \(0.872084\pi\)
\(702\) −27.7083 + 83.1364i −1.04578 + 3.13778i
\(703\) −19.4924 21.0079i −0.735171 0.792326i
\(704\) 3.90023 + 2.25180i 0.146996 + 0.0848679i
\(705\) 3.77927 11.9335i 0.142336 0.449440i
\(706\) −10.8271 + 35.1006i −0.407483 + 1.32103i
\(707\) 6.10714 5.11195i 0.229683 0.192255i
\(708\) −38.8194 + 22.0257i −1.45892 + 0.827777i
\(709\) 10.8790 47.6642i 0.408571 1.79007i −0.182238 0.983254i \(-0.558334\pi\)
0.590809 0.806811i \(-0.298809\pi\)
\(710\) 27.9920 + 4.21911i 1.05052 + 0.158340i
\(711\) 20.4797 + 19.5824i 0.768050 + 0.734399i
\(712\) 66.8002 71.9935i 2.50344 2.69807i
\(713\) −7.60204 + 2.34492i −0.284699 + 0.0878179i
\(714\) −15.9384 + 3.91091i −0.596478 + 0.146362i
\(715\) 6.17983 + 1.90623i 0.231113 + 0.0712888i
\(716\) −68.5642 + 39.5855i −2.56236 + 1.47938i
\(717\) 2.47326 + 11.2236i 0.0923656 + 0.419152i
\(718\) 51.3199 + 15.8301i 1.91524 + 0.590774i
\(719\) 31.2935 21.3355i 1.16705 0.795681i 0.184711 0.982793i \(-0.440865\pi\)
0.982339 + 0.187112i \(0.0599128\pi\)
\(720\) 3.43297 14.0645i 0.127939 0.524154i
\(721\) −45.2861 + 7.92883i −1.68654 + 0.295285i
\(722\) −32.1650 12.6238i −1.19706 0.469811i
\(723\) 7.39857 3.49482i 0.275156 0.129974i
\(724\) −32.5600 + 25.9657i −1.21008 + 0.965008i
\(725\) −3.33497 + 6.92515i −0.123858 + 0.257193i
\(726\) −34.8638 + 23.3885i −1.29392 + 0.868030i
\(727\) −23.7625 + 34.8531i −0.881301 + 1.29263i 0.0740798 + 0.997252i \(0.476398\pi\)
−0.955380 + 0.295378i \(0.904554\pi\)
\(728\) 99.9232 + 20.3254i 3.70340 + 0.753311i
\(729\) −17.7672 + 20.3305i −0.658043 + 0.752980i
\(730\) 0.756989 10.1013i 0.0280174 0.373866i
\(731\) 6.38126 + 5.92094i 0.236019 + 0.218994i
\(732\) −0.830686 + 2.07073i −0.0307030 + 0.0765365i
\(733\) 25.9763 + 10.1950i 0.959457 + 0.376559i 0.792818 0.609459i \(-0.208613\pi\)
0.166639 + 0.986018i \(0.446708\pi\)
\(734\) 42.9512 74.3937i 1.58536 2.74592i
\(735\) −8.53820 + 5.39533i −0.314936 + 0.199010i
\(736\) 13.5586 + 23.4842i 0.499776 + 0.865637i
\(737\) −0.638481 4.23604i −0.0235187 0.156037i
\(738\) −4.09589 + 24.6579i −0.150772 + 0.907669i
\(739\) −35.5187 + 10.9561i −1.30658 + 0.403025i −0.868400 0.495864i \(-0.834852\pi\)
−0.438176 + 0.898889i \(0.644375\pi\)
\(740\) −16.0982 + 7.75249i −0.591782 + 0.284987i
\(741\) 45.7411 48.5613i 1.68034 1.78395i
\(742\) −6.92984 39.5803i −0.254403 1.45304i
\(743\) −4.14853 0.310889i −0.152195 0.0114054i −0.00158514 0.999999i \(-0.500505\pi\)
−0.150610 + 0.988593i \(0.548124\pi\)
\(744\) −8.90242 + 0.600010i −0.326378 + 0.0219974i
\(745\) 2.91167 + 4.27064i 0.106675 + 0.156464i
\(746\) −60.1737 23.6165i −2.20312 0.864660i
\(747\) 15.1012 + 19.5305i 0.552524 + 0.714583i
\(748\) 5.52318 4.40459i 0.201947 0.161048i
\(749\) 5.23958 + 2.37180i 0.191450 + 0.0866638i
\(750\) 2.26370 + 33.5867i 0.0826585 + 1.22641i
\(751\) −2.87161 38.3189i −0.104786 1.39828i −0.763463 0.645852i \(-0.776502\pi\)
0.658676 0.752426i \(-0.271117\pi\)
\(752\) 11.1834 + 48.9977i 0.407817 + 1.78676i
\(753\) 24.7748 + 27.1060i 0.902846 + 0.987798i
\(754\) 30.1039i 1.09632i
\(755\) −1.63268 7.15324i −0.0594193 0.260333i
\(756\) 48.7164 + 33.1275i 1.77180 + 1.20484i
\(757\) −9.29088 + 40.7060i −0.337683 + 1.47948i 0.466191 + 0.884684i \(0.345626\pi\)
−0.803873 + 0.594800i \(0.797231\pi\)
\(758\) 61.3433 + 14.0012i 2.22809 + 0.508546i
\(759\) −17.6458 + 1.18930i −0.640502 + 0.0431689i
\(760\) −17.0379 + 21.3648i −0.618029 + 0.774984i
\(761\) −10.9344 + 3.37282i −0.396373 + 0.122265i −0.486532 0.873663i \(-0.661738\pi\)
0.0901597 + 0.995927i \(0.471262\pi\)
\(762\) 15.7409 + 27.7427i 0.570233 + 1.00501i
\(763\) 29.1649 12.2526i 1.05584 0.443574i
\(764\) −77.2987 + 17.6429i −2.79657 + 0.638299i
\(765\) 2.91906 + 2.05502i 0.105539 + 0.0742992i
\(766\) −20.8134 + 12.0166i −0.752020 + 0.434179i
\(767\) −11.9233 + 38.6542i −0.430524 + 1.39572i
\(768\) −15.9841 53.2340i −0.576776 1.92092i
\(769\) 9.73580 3.82102i 0.351082 0.137789i −0.183245 0.983067i \(-0.558660\pi\)
0.534327 + 0.845278i \(0.320565\pi\)
\(770\) 3.46618 5.35252i 0.124912 0.192891i
\(771\) −33.7953 + 12.9719i −1.21711 + 0.467171i
\(772\) 2.07523 + 9.09216i 0.0746890 + 0.327234i
\(773\) 9.11812 23.2326i 0.327956 0.835618i −0.667864 0.744283i \(-0.732791\pi\)
0.995820 0.0913351i \(-0.0291134\pi\)
\(774\) 0.687766 45.8288i 0.0247212 1.64728i
\(775\) 3.60413 1.41452i 0.129464 0.0508109i
\(776\) −12.6481 8.62330i −0.454039 0.309559i
\(777\) −2.08491 22.8420i −0.0747959 0.819451i
\(778\) 35.2067 24.0035i 1.26222 0.860568i
\(779\) 10.7191 15.7221i 0.384053 0.563302i
\(780\) −20.5258 36.1759i −0.734941 1.29530i
\(781\) 1.16899 15.5991i 0.0418297 0.558179i
\(782\) −31.3320 + 4.72254i −1.12043 + 0.168878i
\(783\) 3.58207 8.55556i 0.128013 0.305751i
\(784\) 18.5870 36.0407i 0.663820 1.28717i
\(785\) 5.74913 3.31926i 0.205195 0.118470i
\(786\) 10.8121 + 28.1683i 0.385653 + 1.00473i
\(787\) −4.89541 10.1654i −0.174503 0.362359i 0.795313 0.606200i \(-0.207307\pi\)
−0.969815 + 0.243841i \(0.921592\pi\)
\(788\) 34.1307 + 7.79011i 1.21586 + 0.277511i
\(789\) −21.0776 26.8412i −0.750383 0.955571i
\(790\) −19.6706 + 1.47411i −0.699848 + 0.0524463i
\(791\) 21.6840 + 9.81568i 0.770993 + 0.349006i
\(792\) −19.5678 3.25038i −0.695310 0.115497i
\(793\) 0.738763 + 1.88234i 0.0262342 + 0.0668437i
\(794\) −57.8087 + 39.4133i −2.05155 + 1.39873i
\(795\) −5.50089 + 6.79271i −0.195096 + 0.240913i
\(796\) −65.0555 70.1132i −2.30583 2.48509i
\(797\) −13.6943 + 2.06409i −0.485077 + 0.0731137i −0.387028 0.922068i \(-0.626498\pi\)
−0.0980493 + 0.995182i \(0.531260\pi\)
\(798\) −33.8098 56.4260i −1.19685 1.99746i
\(799\) −12.2542 1.84703i −0.433524 0.0653432i
\(800\) −7.43434 10.9042i −0.262844 0.385521i
\(801\) 19.5041 47.5834i 0.689143 1.68128i
\(802\) −26.0141 45.0577i −0.918590 1.59104i
\(803\) −5.59754 −0.197533
\(804\) −15.6908 + 22.6472i −0.553372 + 0.798706i
\(805\) −17.3638 + 8.87545i −0.611993 + 0.312819i
\(806\) −10.3141 + 11.1160i −0.363299 + 0.391543i
\(807\) 4.05885 + 2.38416i 0.142878 + 0.0839264i
\(808\) 16.0542 6.30079i 0.564783 0.221661i
\(809\) 3.17531 21.0668i 0.111638 0.740670i −0.861044 0.508530i \(-0.830189\pi\)
0.972682 0.232140i \(-0.0745729\pi\)
\(810\) −2.24243 18.6619i −0.0787908 0.655712i
\(811\) 24.8357 + 5.66859i 0.872100 + 0.199051i 0.635073 0.772452i \(-0.280970\pi\)
0.237027 + 0.971503i \(0.423827\pi\)
\(812\) −19.4750 5.50478i −0.683438 0.193180i
\(813\) −20.8010 + 9.82566i −0.729523 + 0.344601i
\(814\) 7.24080 + 12.5414i 0.253790 + 0.439577i
\(815\) −0.449419 −0.0157425
\(816\) −14.2844 1.17831i −0.500055 0.0412492i
\(817\) −15.1391 + 31.4366i −0.529649 + 1.09983i
\(818\) −37.3862 + 46.8809i −1.30718 + 1.63915i
\(819\) 52.7260 8.41803i 1.84239 0.294150i
\(820\) −7.39698 9.27552i −0.258314 0.323915i
\(821\) −38.0017 + 8.67365i −1.32627 + 0.302713i −0.826251 0.563302i \(-0.809531\pi\)
−0.500019 + 0.866014i \(0.666674\pi\)
\(822\) 9.20655 + 7.45567i 0.321115 + 0.260046i
\(823\) 27.9565 + 13.4631i 0.974501 + 0.469295i 0.852210 0.523199i \(-0.175262\pi\)
0.122291 + 0.992494i \(0.460976\pi\)
\(824\) −98.4453 14.8382i −3.42951 0.516915i
\(825\) 8.52059 1.21896i 0.296649 0.0424388i
\(826\) 33.4795 + 21.6806i 1.16490 + 0.754365i
\(827\) −8.43466 + 17.5148i −0.293302 + 0.609048i −0.994596 0.103825i \(-0.966892\pi\)
0.701294 + 0.712872i \(0.252606\pi\)
\(828\) 87.8560 + 72.2459i 3.05321 + 2.51072i
\(829\) 3.63553 + 11.7861i 0.126267 + 0.409348i 0.996529 0.0832405i \(-0.0265270\pi\)
−0.870262 + 0.492588i \(0.836051\pi\)
\(830\) −17.1384 1.28435i −0.594883 0.0445803i
\(831\) 7.94402 + 6.43325i 0.275575 + 0.223167i
\(832\) −22.7343 13.1256i −0.788170 0.455050i
\(833\) 6.59823 + 7.51317i 0.228615 + 0.260316i
\(834\) −94.2845 + 20.7768i −3.26480 + 0.719441i
\(835\) −0.0720509 0.0903490i −0.00249342 0.00312666i
\(836\) 23.3957 + 15.9509i 0.809156 + 0.551673i
\(837\) −4.25398 + 1.93189i −0.147039 + 0.0667760i
\(838\) −0.749183 0.0561435i −0.0258801 0.00193944i
\(839\) 0.564461 + 7.53221i 0.0194874 + 0.260041i 0.998435 + 0.0559283i \(0.0178118\pi\)
−0.978947 + 0.204113i \(0.934569\pi\)
\(840\) −21.2412 + 5.21210i −0.732890 + 0.179835i
\(841\) 1.92906 25.7416i 0.0665194 0.887640i
\(842\) 1.70285 11.2977i 0.0586842 0.389344i
\(843\) 5.12425 + 4.82667i 0.176489 + 0.166239i
\(844\) −12.5847 + 1.89683i −0.433182 + 0.0652916i
\(845\) −25.6736 7.91926i −0.883199 0.272431i
\(846\) 35.9435 + 54.4575i 1.23576 + 1.87229i
\(847\) 22.4497 + 12.2606i 0.771380 + 0.421279i
\(848\) 5.23047 34.7019i 0.179615 1.19167i
\(849\) −23.8085 + 7.14877i −0.817106 + 0.245345i
\(850\) 15.0342 3.43147i 0.515670 0.117698i
\(851\) 44.2855i 1.51809i
\(852\) −74.2610 + 67.8744i −2.54414 + 2.32534i
\(853\) −29.6323 31.9360i −1.01459 1.09347i −0.995605 0.0936483i \(-0.970147\pi\)
−0.0189848 0.999820i \(-0.506043\pi\)
\(854\) 1.98421 0.196132i 0.0678981 0.00671149i
\(855\) −4.42233 + 13.6084i −0.151240 + 0.465397i
\(856\) 9.12979 + 8.47121i 0.312050 + 0.289540i
\(857\) −5.69784 14.5179i −0.194635 0.495921i 0.799924 0.600102i \(-0.204873\pi\)
−0.994558 + 0.104181i \(0.966778\pi\)
\(858\) −27.9951 + 18.7806i −0.955735 + 0.641158i
\(859\) 11.6270 + 37.6937i 0.396707 + 1.28609i 0.905185 + 0.425017i \(0.139732\pi\)
−0.508479 + 0.861075i \(0.669792\pi\)
\(860\) 15.9471 + 14.7967i 0.543791 + 0.504564i
\(861\) 14.4784 4.72455i 0.493422 0.161012i
\(862\) −44.9117 + 41.6719i −1.52970 + 1.41935i
\(863\) 13.9109 + 8.03147i 0.473533 + 0.273394i 0.717717 0.696334i \(-0.245187\pi\)
−0.244185 + 0.969729i \(0.578520\pi\)
\(864\) 9.64657 + 12.6713i 0.328183 + 0.431086i
\(865\) 0.594277 0.551409i 0.0202060 0.0187485i
\(866\) −18.2159 8.77233i −0.619002 0.298096i
\(867\) −11.4170 + 23.2597i −0.387743 + 0.789939i
\(868\) 5.30518 + 8.70513i 0.180070 + 0.295471i
\(869\) 1.62460 + 10.7785i 0.0551107 + 0.365636i
\(870\) 2.75783 + 5.83836i 0.0934993 + 0.197939i
\(871\) 3.72168 + 24.6917i 0.126104 + 0.836647i
\(872\) 68.3111 5.11921i 2.31331 0.173358i
\(873\) −7.78703 1.90071i −0.263551 0.0643294i
\(874\) −55.1053 114.427i −1.86396 3.87056i
\(875\) 17.5144 10.6738i 0.592095 0.360841i
\(876\) 26.2057 + 24.6838i 0.885409 + 0.833989i
\(877\) 3.17896 + 2.16738i 0.107346 + 0.0731871i 0.615803 0.787900i \(-0.288832\pi\)
−0.508457 + 0.861087i \(0.669784\pi\)
\(878\) −0.852198 + 3.73372i −0.0287603 + 0.126007i
\(879\) 20.8440 16.3682i 0.703051 0.552085i
\(880\) 4.35425 3.47240i 0.146782 0.117054i
\(881\) 22.9301 0.772535 0.386268 0.922387i \(-0.373764\pi\)
0.386268 + 0.922387i \(0.373764\pi\)
\(882\) 6.15374 52.2871i 0.207207 1.76060i
\(883\) 38.4505 1.29396 0.646982 0.762505i \(-0.276031\pi\)
0.646982 + 0.762505i \(0.276031\pi\)
\(884\) −32.1944 + 25.6741i −1.08281 + 0.863515i
\(885\) −1.22874 8.58892i −0.0413036 0.288713i
\(886\) 12.9381 56.6855i 0.434664 1.90439i
\(887\) −42.8288 29.2001i −1.43805 0.980445i −0.996534 0.0831913i \(-0.973489\pi\)
−0.441515 0.897254i \(-0.645559\pi\)
\(888\) 11.4154 48.3396i 0.383077 1.62217i
\(889\) 10.5640 16.3130i 0.354304 0.547120i
\(890\) 15.5331 + 32.2547i 0.520669 + 1.08118i
\(891\) −10.1909 + 2.00632i −0.341409 + 0.0672143i
\(892\) −23.5289 + 1.76325i −0.787806 + 0.0590379i
\(893\) −7.40334 49.1179i −0.247743 1.64367i
\(894\) −26.8518 2.21499i −0.898059 0.0740802i
\(895\) −2.29383 15.2186i −0.0766742 0.508700i
\(896\) −30.1751 + 29.3610i −1.00808 + 0.980881i
\(897\) 102.857 6.93239i 3.43428 0.231466i
\(898\) −40.1649 19.3424i −1.34032 0.645464i
\(899\) 1.17654 1.09167i 0.0392397 0.0364091i
\(900\) −45.2657 31.8670i −1.50886 1.06223i
\(901\) 7.49416 + 4.32675i 0.249667 + 0.144145i
\(902\) −7.04869 + 6.54023i −0.234696 + 0.217766i
\(903\) −24.9608 + 12.5234i −0.830645 + 0.416751i
\(904\) 37.7836 + 35.0580i 1.25666 + 1.16601i
\(905\) −2.38626 7.73606i −0.0793219 0.257155i
\(906\) 34.3332 + 16.8525i 1.14065 + 0.559887i
\(907\) −3.48154 8.87082i −0.115603 0.294551i 0.861348 0.508015i \(-0.169621\pi\)
−0.976951 + 0.213464i \(0.931525\pi\)
\(908\) 18.7823 + 17.4275i 0.623313 + 0.578350i
\(909\) 6.71132 6.04234i 0.222601 0.200412i
\(910\) −20.2042 + 31.1996i −0.669763 + 1.03426i
\(911\) 15.5665 + 16.7766i 0.515740 + 0.555835i 0.936196 0.351477i \(-0.114321\pi\)
−0.420457 + 0.907313i \(0.638130\pi\)
\(912\) −12.3632 56.1039i −0.409387 1.85778i
\(913\) 9.49707i 0.314307i
\(914\) 17.6995 4.03980i 0.585448 0.133625i
\(915\) −0.315718 0.297383i −0.0104373 0.00983117i
\(916\) 5.99024 39.7427i 0.197923 1.31313i
\(917\) 12.1808 13.7690i 0.402246 0.454693i
\(918\) −17.9007 + 5.08335i −0.590813 + 0.167775i
\(919\) −7.47379 2.30536i −0.246538 0.0760468i 0.169024 0.985612i \(-0.445939\pi\)
−0.415561 + 0.909565i \(0.636415\pi\)
\(920\) −41.7564 + 6.29376i −1.37667 + 0.207499i
\(921\) −17.9870 + 5.40080i −0.592692 + 0.177962i
\(922\) 11.4512 75.9734i 0.377124 2.50205i
\(923\) −6.81398 + 90.9263i −0.224285 + 2.99288i
\(924\) 7.03049 + 21.5449i 0.231286 + 0.708777i
\(925\) 1.61065 + 21.4926i 0.0529577 + 0.706672i
\(926\) 74.3592 + 5.57245i 2.44359 + 0.183122i
\(927\) −50.9920 + 10.8362i −1.67480 + 0.355908i
\(928\) −4.52016 3.08179i −0.148382 0.101165i
\(929\) −6.61934 8.30039i −0.217174 0.272327i 0.661296 0.750125i \(-0.270007\pi\)
−0.878470 + 0.477798i \(0.841435\pi\)
\(930\) 0.981983 3.10072i 0.0322005 0.101677i
\(931\) −20.9812 + 34.1487i −0.687631 + 1.11918i
\(932\) −93.1442 53.7768i −3.05104 1.76152i
\(933\) −3.20576 + 20.2374i −0.104952 + 0.662542i
\(934\) −105.088 7.87526i −3.43859 0.257686i
\(935\) 0.404783 + 1.31227i 0.0132378 + 0.0429159i
\(936\) 114.060 + 18.9463i 3.72816 + 0.619279i
\(937\) −4.28277 + 8.89326i −0.139912 + 0.290530i −0.959137 0.282942i \(-0.908690\pi\)
0.819225 + 0.573472i \(0.194404\pi\)
\(938\) 24.4271 + 3.09105i 0.797571 + 0.100926i
\(939\) 14.3864 35.8625i 0.469483 1.17033i
\(940\) −30.6240 4.61582i −0.998843 0.150551i
\(941\) −3.87556 1.86637i −0.126340 0.0608419i 0.369646 0.929173i \(-0.379479\pi\)
−0.495986 + 0.868331i \(0.665193\pi\)
\(942\) −5.41411 + 34.1782i −0.176401 + 1.11359i
\(943\) 28.6676 6.54319i 0.933545 0.213076i
\(944\) 21.7195 + 27.2354i 0.706910 + 0.886437i
\(945\) −9.45452 + 6.46285i −0.307555 + 0.210237i
\(946\) 10.9932 13.7850i 0.357420 0.448191i
\(947\) −13.4515 + 27.9324i −0.437116 + 0.907682i 0.559756 + 0.828657i \(0.310895\pi\)
−0.996873 + 0.0790244i \(0.974820\pi\)
\(948\) 39.9248 57.6252i 1.29670 1.87158i
\(949\) 32.6278 1.05914
\(950\) 30.9053 + 53.5296i 1.00270 + 1.73673i
\(951\) −34.7332 24.0644i −1.12630 0.780342i
\(952\) 8.38670 + 19.9629i 0.271814 + 0.647000i
\(953\) 45.4138 + 10.3654i 1.47110 + 0.335768i 0.881598 0.472001i \(-0.156468\pi\)
0.589498 + 0.807770i \(0.299325\pi\)
\(954\) −9.47092 44.5673i −0.306632 1.44292i
\(955\) 2.29718 15.2408i 0.0743349 0.493180i
\(956\) 26.4690 10.3883i 0.856068 0.335982i
\(957\) 3.10331 1.76079i 0.100316 0.0569181i
\(958\) −15.5602 + 16.7699i −0.502726 + 0.541810i
\(959\) 1.43879 7.07334i 0.0464610 0.228410i
\(960\) 5.61155 + 0.462892i 0.181112 + 0.0149398i
\(961\) 30.1915 0.973921
\(962\) −42.2063 73.1035i −1.36079 2.35695i
\(963\) 6.03424 + 2.47339i 0.194451 + 0.0797039i
\(964\) −11.4040 16.7266i −0.367298 0.538728i
\(965\) −1.79267 0.270202i −0.0577082 0.00869811i
\(966\) 21.0086 99.4554i 0.675940 3.19993i
\(967\) 4.49881 0.678086i 0.144672 0.0218058i −0.0763070 0.997084i \(-0.524313\pi\)
0.220979 + 0.975279i \(0.429075\pi\)
\(968\) 37.6759 + 40.6049i 1.21095 + 1.30509i
\(969\) 13.9916 + 2.21639i 0.449476 + 0.0712007i
\(970\) 4.61051 3.14339i 0.148035 0.100928i
\(971\) 2.86738 + 7.30595i 0.0920185 + 0.234459i 0.969472 0.245203i \(-0.0788545\pi\)
−0.877453 + 0.479662i \(0.840759\pi\)
\(972\) 56.5578 + 35.5467i 1.81409 + 1.14016i
\(973\) 37.7577 + 45.1083i 1.21046 + 1.44610i
\(974\) 20.6855 1.55016i 0.662806 0.0496704i
\(975\) −49.6661 + 7.10527i −1.59059 + 0.227551i
\(976\) 1.69772 + 0.387494i 0.0543427 + 0.0124034i
\(977\) 3.22201 + 6.69057i 0.103081 + 0.214050i 0.946130 0.323786i \(-0.104956\pi\)
−0.843049 + 0.537837i \(0.819242\pi\)
\(978\) 1.47433 1.82056i 0.0471439 0.0582151i
\(979\) 17.1324 9.89138i 0.547553 0.316130i
\(980\) 16.4893 + 18.7758i 0.526731 + 0.599770i
\(981\) 32.5474 15.0766i 1.03916 0.481358i
\(982\) 76.8305 11.5803i 2.45176 0.369543i
\(983\) −0.320184 + 4.27256i −0.0102123 + 0.136273i −0.999979 0.00641874i \(-0.997957\pi\)
0.989767 + 0.142692i \(0.0455759\pi\)
\(984\) 32.9786 + 0.247446i 1.05132 + 0.00788829i
\(985\) −3.83365 + 5.62293i −0.122150 + 0.179162i
\(986\) 5.28172 3.60102i 0.168204 0.114680i
\(987\) 19.3170 34.7479i 0.614867 1.10604i
\(988\) −136.372 92.9770i −4.33858 2.95799i
\(989\) −50.1915 + 19.6987i −1.59600 + 0.626383i
\(990\) 3.70887 6.20696i 0.117876 0.197270i
\(991\) 17.1865 43.7906i 0.545949 1.39105i −0.345708 0.938342i \(-0.612361\pi\)
0.891657 0.452712i \(-0.149544\pi\)
\(992\) 0.613210 + 2.68665i 0.0194694 + 0.0853012i
\(993\) −4.91382 + 31.0200i −0.155935 + 0.984389i
\(994\) 84.4484 + 30.8522i 2.67854 + 0.978571i
\(995\) 17.3077 6.79279i 0.548692 0.215346i
\(996\) 41.8798 44.4619i 1.32701 1.40883i
\(997\) −6.04723 + 19.6046i −0.191518 + 0.620885i 0.807981 + 0.589209i \(0.200561\pi\)
−0.999498 + 0.0316758i \(0.989916\pi\)
\(998\) −22.3992 + 12.9322i −0.709036 + 0.409362i
\(999\) −3.29648 25.7983i −0.104296 0.816221i
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 441.2.bn.a.5.5 yes 648
9.2 odd 6 441.2.bd.a.299.5 yes 648
49.10 odd 42 441.2.bd.a.59.5 648
441.353 even 42 inner 441.2.bn.a.353.5 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bd.a.59.5 648 49.10 odd 42
441.2.bd.a.299.5 yes 648 9.2 odd 6
441.2.bn.a.5.5 yes 648 1.1 even 1 trivial
441.2.bn.a.353.5 yes 648 441.353 even 42 inner