Properties

Label 69.2.e.a.58.1
Level $69$
Weight $2$
Character 69.58
Analytic conductor $0.551$
Analytic rank $0$
Dimension $10$
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] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 58.1
Root \(-0.841254 + 0.540641i\) of defining polynomial
Character \(\chi\) \(=\) 69.58
Dual form 69.2.e.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.402869 + 0.258908i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.735560 + 1.61065i) q^{4} +(3.37102 - 0.989821i) q^{5} +(0.198939 + 0.435615i) q^{6} +(0.527646 + 0.608936i) q^{7} +(-0.256983 - 1.78736i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(q+(-0.402869 + 0.258908i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.735560 + 1.61065i) q^{4} +(3.37102 - 0.989821i) q^{5} +(0.198939 + 0.435615i) q^{6} +(0.527646 + 0.608936i) q^{7} +(-0.256983 - 1.78736i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-1.10181 + 1.27155i) q^{10} +(-2.98325 - 1.91722i) q^{11} +(1.48958 + 0.957293i) q^{12} +(-4.32972 + 4.99677i) q^{13} +(-0.370231 - 0.108710i) q^{14} +(-0.500000 - 3.47758i) q^{15} +(-1.75278 - 2.02282i) q^{16} +(0.387956 + 0.849505i) q^{17} +(0.459493 - 0.134919i) q^{18} +(1.55773 - 3.41095i) q^{19} +(-0.885331 + 6.15762i) q^{20} +(0.677830 - 0.435615i) q^{21} +1.69824 q^{22} +(-4.71737 - 0.863983i) q^{23} -1.80574 q^{24} +(6.17778 - 3.97022i) q^{25} +(0.450608 - 3.13404i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.36890 + 0.401945i) q^{28} +(0.657326 + 1.43934i) q^{29} +(1.10181 + 1.27155i) q^{30} +(-0.0804100 - 0.559264i) q^{31} +(4.69505 + 1.37859i) q^{32} +(-2.32227 + 2.68004i) q^{33} +(-0.376239 - 0.241794i) q^{34} +(2.38145 + 1.53046i) q^{35} +(1.15954 - 1.33818i) q^{36} +(7.84580 + 2.30374i) q^{37} +(0.255563 + 1.77748i) q^{38} +(4.32972 + 4.99677i) q^{39} +(-2.63546 - 5.77086i) q^{40} +(3.65843 - 1.07421i) q^{41} +(-0.160293 + 0.350992i) q^{42} +(-0.975753 + 6.78651i) q^{43} +(5.28234 - 3.39475i) q^{44} -3.51334 q^{45} +(2.12417 - 0.873293i) q^{46} -5.69427 q^{47} +(-2.25168 + 1.44706i) q^{48} +(0.903811 - 6.28614i) q^{49} +(-1.46091 + 3.19895i) q^{50} +(0.896070 - 0.263110i) q^{51} +(-4.86328 - 10.6491i) q^{52} +(-4.57100 - 5.27521i) q^{53} +(-0.0681534 - 0.474017i) q^{54} +(-11.9543 - 3.51011i) q^{55} +(0.952791 - 1.09958i) q^{56} +(-3.15455 - 2.02730i) q^{57} +(-0.637474 - 0.409680i) q^{58} +(-0.663766 + 0.766027i) q^{59} +(5.96894 + 1.75264i) q^{60} +(1.74697 + 12.1505i) q^{61} +(0.177193 + 0.204491i) q^{62} +(-0.334716 - 0.732925i) q^{63} +(2.88789 - 0.847960i) q^{64} +(-9.64969 + 21.1299i) q^{65} +(0.241685 - 1.68096i) q^{66} +(2.09309 - 1.34515i) q^{67} -1.65362 q^{68} +(-1.52654 + 4.54639i) q^{69} -1.35566 q^{70} +(11.1508 - 7.16620i) q^{71} +(-0.256983 + 1.78736i) q^{72} +(2.78441 - 6.09701i) q^{73} +(-3.75729 + 1.10324i) q^{74} +(-3.05062 - 6.67992i) q^{75} +(4.34805 + 5.01792i) q^{76} +(-0.406637 - 2.82823i) q^{77} +(-3.03802 - 0.892042i) q^{78} +(-0.940694 + 1.08562i) q^{79} +(-7.91090 - 5.08403i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-1.19575 + 1.37997i) q^{82} +(1.68020 + 0.493351i) q^{83} +(0.203039 + 1.41217i) q^{84} +(2.14867 + 2.47969i) q^{85} +(-1.36398 - 2.98671i) q^{86} +(1.51824 - 0.445795i) q^{87} +(-2.66011 + 5.82484i) q^{88} +(0.667422 - 4.64202i) q^{89} +(1.41542 - 0.909632i) q^{90} -5.32728 q^{91} +(4.86148 - 6.96252i) q^{92} -0.565015 q^{93} +(2.29404 - 1.47429i) q^{94} +(1.87491 - 13.0403i) q^{95} +(2.03274 - 4.45107i) q^{96} +(-0.762432 + 0.223870i) q^{97} +(1.26342 + 2.76650i) q^{98} +(2.32227 + 2.68004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{10}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.402869 + 0.258908i −0.284871 + 0.183076i −0.675271 0.737570i \(-0.735973\pi\)
0.390399 + 0.920646i \(0.372337\pi\)
\(3\) 0.142315 0.989821i 0.0821655 0.571474i
\(4\) −0.735560 + 1.61065i −0.367780 + 0.805326i
\(5\) 3.37102 0.989821i 1.50757 0.442662i 0.579468 0.814995i \(-0.303260\pi\)
0.928099 + 0.372333i \(0.121442\pi\)
\(6\) 0.198939 + 0.435615i 0.0812164 + 0.177839i
\(7\) 0.527646 + 0.608936i 0.199432 + 0.230156i 0.846652 0.532146i \(-0.178614\pi\)
−0.647221 + 0.762302i \(0.724069\pi\)
\(8\) −0.256983 1.78736i −0.0908573 0.631927i
\(9\) −0.959493 0.281733i −0.319831 0.0939109i
\(10\) −1.10181 + 1.27155i −0.348422 + 0.402101i
\(11\) −2.98325 1.91722i −0.899485 0.578064i 0.00715262 0.999974i \(-0.497723\pi\)
−0.906637 + 0.421911i \(0.861360\pi\)
\(12\) 1.48958 + 0.957293i 0.430004 + 0.276347i
\(13\) −4.32972 + 4.99677i −1.20085 + 1.38585i −0.298747 + 0.954332i \(0.596569\pi\)
−0.902103 + 0.431522i \(0.857977\pi\)
\(14\) −0.370231 0.108710i −0.0989484 0.0290539i
\(15\) −0.500000 3.47758i −0.129099 0.897906i
\(16\) −1.75278 2.02282i −0.438196 0.505705i
\(17\) 0.387956 + 0.849505i 0.0940931 + 0.206035i 0.950826 0.309725i \(-0.100237\pi\)
−0.856733 + 0.515760i \(0.827510\pi\)
\(18\) 0.459493 0.134919i 0.108304 0.0318008i
\(19\) 1.55773 3.41095i 0.357368 0.782526i −0.642500 0.766285i \(-0.722103\pi\)
0.999868 0.0162408i \(-0.00516984\pi\)
\(20\) −0.885331 + 6.15762i −0.197966 + 1.37688i
\(21\) 0.677830 0.435615i 0.147915 0.0950590i
\(22\) 1.69824 0.362067
\(23\) −4.71737 0.863983i −0.983639 0.180153i
\(24\) −1.80574 −0.368595
\(25\) 6.17778 3.97022i 1.23556 0.794043i
\(26\) 0.450608 3.13404i 0.0883714 0.614637i
\(27\) −0.415415 + 0.909632i −0.0799467 + 0.175059i
\(28\) −1.36890 + 0.401945i −0.258698 + 0.0759605i
\(29\) 0.657326 + 1.43934i 0.122062 + 0.267279i 0.960793 0.277268i \(-0.0894289\pi\)
−0.838730 + 0.544547i \(0.816702\pi\)
\(30\) 1.10181 + 1.27155i 0.201162 + 0.232153i
\(31\) −0.0804100 0.559264i −0.0144421 0.100447i 0.981325 0.192355i \(-0.0616125\pi\)
−0.995767 + 0.0919082i \(0.970703\pi\)
\(32\) 4.69505 + 1.37859i 0.829976 + 0.243703i
\(33\) −2.32227 + 2.68004i −0.404255 + 0.466535i
\(34\) −0.376239 0.241794i −0.0645245 0.0414674i
\(35\) 2.38145 + 1.53046i 0.402538 + 0.258695i
\(36\) 1.15954 1.33818i 0.193256 0.223030i
\(37\) 7.84580 + 2.30374i 1.28984 + 0.378732i 0.853521 0.521059i \(-0.174463\pi\)
0.436321 + 0.899791i \(0.356281\pi\)
\(38\) 0.255563 + 1.77748i 0.0414577 + 0.288345i
\(39\) 4.32972 + 4.99677i 0.693311 + 0.800123i
\(40\) −2.63546 5.77086i −0.416703 0.912453i
\(41\) 3.65843 1.07421i 0.571351 0.167764i 0.0167200 0.999860i \(-0.494678\pi\)
0.554631 + 0.832096i \(0.312859\pi\)
\(42\) −0.160293 + 0.350992i −0.0247337 + 0.0541592i
\(43\) −0.975753 + 6.78651i −0.148801 + 1.03493i 0.769386 + 0.638785i \(0.220562\pi\)
−0.918187 + 0.396148i \(0.870347\pi\)
\(44\) 5.28234 3.39475i 0.796342 0.511778i
\(45\) −3.51334 −0.523737
\(46\) 2.12417 0.873293i 0.313192 0.128760i
\(47\) −5.69427 −0.830594 −0.415297 0.909686i \(-0.636322\pi\)
−0.415297 + 0.909686i \(0.636322\pi\)
\(48\) −2.25168 + 1.44706i −0.325002 + 0.208866i
\(49\) 0.903811 6.28614i 0.129116 0.898021i
\(50\) −1.46091 + 3.19895i −0.206604 + 0.452401i
\(51\) 0.896070 0.263110i 0.125475 0.0368427i
\(52\) −4.86328 10.6491i −0.674416 1.47676i
\(53\) −4.57100 5.27521i −0.627875 0.724606i 0.349308 0.937008i \(-0.386417\pi\)
−0.977182 + 0.212402i \(0.931871\pi\)
\(54\) −0.0681534 0.474017i −0.00927450 0.0645055i
\(55\) −11.9543 3.51011i −1.61192 0.473302i
\(56\) 0.952791 1.09958i 0.127322 0.146938i
\(57\) −3.15455 2.02730i −0.417830 0.268523i
\(58\) −0.637474 0.409680i −0.0837044 0.0537936i
\(59\) −0.663766 + 0.766027i −0.0864150 + 0.0997282i −0.797310 0.603570i \(-0.793745\pi\)
0.710895 + 0.703298i \(0.248290\pi\)
\(60\) 5.96894 + 1.75264i 0.770587 + 0.226265i
\(61\) 1.74697 + 12.1505i 0.223677 + 1.55571i 0.723958 + 0.689844i \(0.242321\pi\)
−0.500281 + 0.865863i \(0.666770\pi\)
\(62\) 0.177193 + 0.204491i 0.0225035 + 0.0259704i
\(63\) −0.334716 0.732925i −0.0421702 0.0923399i
\(64\) 2.88789 0.847960i 0.360986 0.105995i
\(65\) −9.64969 + 21.1299i −1.19690 + 2.62084i
\(66\) 0.241685 1.68096i 0.0297494 0.206912i
\(67\) 2.09309 1.34515i 0.255712 0.164336i −0.406504 0.913649i \(-0.633252\pi\)
0.662216 + 0.749313i \(0.269616\pi\)
\(68\) −1.65362 −0.200531
\(69\) −1.52654 + 4.54639i −0.183774 + 0.547321i
\(70\) −1.35566 −0.162032
\(71\) 11.1508 7.16620i 1.32336 0.850471i 0.327813 0.944743i \(-0.393689\pi\)
0.995547 + 0.0942715i \(0.0300522\pi\)
\(72\) −0.256983 + 1.78736i −0.0302858 + 0.210642i
\(73\) 2.78441 6.09701i 0.325891 0.713601i −0.673789 0.738924i \(-0.735334\pi\)
0.999679 + 0.0253229i \(0.00806139\pi\)
\(74\) −3.75729 + 1.10324i −0.436776 + 0.128249i
\(75\) −3.05062 6.67992i −0.352255 0.771330i
\(76\) 4.34805 + 5.01792i 0.498756 + 0.575595i
\(77\) −0.406637 2.82823i −0.0463406 0.322306i
\(78\) −3.03802 0.892042i −0.343988 0.101004i
\(79\) −0.940694 + 1.08562i −0.105836 + 0.122142i −0.806196 0.591648i \(-0.798477\pi\)
0.700360 + 0.713790i \(0.253023\pi\)
\(80\) −7.91090 5.08403i −0.884465 0.568411i
\(81\) 0.841254 + 0.540641i 0.0934726 + 0.0600712i
\(82\) −1.19575 + 1.37997i −0.132048 + 0.152392i
\(83\) 1.68020 + 0.493351i 0.184426 + 0.0541523i 0.372641 0.927975i \(-0.378452\pi\)
−0.188216 + 0.982128i \(0.560270\pi\)
\(84\) 0.203039 + 1.41217i 0.0221534 + 0.154080i
\(85\) 2.14867 + 2.47969i 0.233055 + 0.268960i
\(86\) −1.36398 2.98671i −0.147082 0.322065i
\(87\) 1.51824 0.445795i 0.162772 0.0477943i
\(88\) −2.66011 + 5.82484i −0.283569 + 0.620930i
\(89\) 0.667422 4.64202i 0.0707466 0.492053i −0.923385 0.383875i \(-0.874589\pi\)
0.994132 0.108178i \(-0.0345016\pi\)
\(90\) 1.41542 0.909632i 0.149198 0.0958836i
\(91\) −5.32728 −0.558450
\(92\) 4.86148 6.96252i 0.506844 0.725893i
\(93\) −0.565015 −0.0585893
\(94\) 2.29404 1.47429i 0.236613 0.152062i
\(95\) 1.87491 13.0403i 0.192362 1.33790i
\(96\) 2.03274 4.45107i 0.207465 0.454285i
\(97\) −0.762432 + 0.223870i −0.0774132 + 0.0227306i −0.320210 0.947347i \(-0.603753\pi\)
0.242797 + 0.970077i \(0.421935\pi\)
\(98\) 1.26342 + 2.76650i 0.127624 + 0.279458i
\(99\) 2.32227 + 2.68004i 0.233397 + 0.269354i
\(100\) 1.85051 + 12.8706i 0.185051 + 1.28706i
\(101\) 12.0847 + 3.54840i 1.20248 + 0.353079i 0.820800 0.571216i \(-0.193528\pi\)
0.381678 + 0.924295i \(0.375346\pi\)
\(102\) −0.292878 + 0.337999i −0.0289992 + 0.0334669i
\(103\) 8.91245 + 5.72768i 0.878169 + 0.564365i 0.900241 0.435391i \(-0.143390\pi\)
−0.0220720 + 0.999756i \(0.507026\pi\)
\(104\) 10.0437 + 6.45468i 0.984864 + 0.632934i
\(105\) 1.85380 2.13940i 0.180912 0.208784i
\(106\) 3.20731 + 0.941751i 0.311521 + 0.0914709i
\(107\) 0.913569 + 6.35401i 0.0883181 + 0.614266i 0.985124 + 0.171842i \(0.0549720\pi\)
−0.896806 + 0.442423i \(0.854119\pi\)
\(108\) −1.15954 1.33818i −0.111577 0.128766i
\(109\) −0.487454 1.06738i −0.0466896 0.102236i 0.884850 0.465877i \(-0.154261\pi\)
−0.931539 + 0.363641i \(0.881534\pi\)
\(110\) 5.72482 1.68096i 0.545840 0.160273i
\(111\) 3.39686 7.43809i 0.322416 0.705992i
\(112\) 0.306919 2.13467i 0.0290011 0.201707i
\(113\) −14.5204 + 9.33173i −1.36597 + 0.877855i −0.998635 0.0522342i \(-0.983366\pi\)
−0.367334 + 0.930089i \(0.619729\pi\)
\(114\) 1.79575 0.168188
\(115\) −16.7575 + 1.75684i −1.56265 + 0.163826i
\(116\) −2.80178 −0.260139
\(117\) 5.56209 3.57454i 0.514216 0.330466i
\(118\) 0.0690802 0.480463i 0.00635934 0.0442302i
\(119\) −0.312591 + 0.684478i −0.0286552 + 0.0627460i
\(120\) −6.08718 + 1.78736i −0.555681 + 0.163163i
\(121\) 0.654502 + 1.43316i 0.0595002 + 0.130287i
\(122\) −3.84966 4.44274i −0.348531 0.402227i
\(123\) −0.542629 3.77407i −0.0489272 0.340296i
\(124\) 0.959925 + 0.281859i 0.0862038 + 0.0253117i
\(125\) 5.39189 6.22257i 0.482265 0.556563i
\(126\) 0.324607 + 0.208612i 0.0289183 + 0.0185847i
\(127\) 7.96136 + 5.11646i 0.706457 + 0.454012i 0.843902 0.536497i \(-0.180253\pi\)
−0.137445 + 0.990509i \(0.543889\pi\)
\(128\) −7.35271 + 8.48548i −0.649894 + 0.750018i
\(129\) 6.57857 + 1.93164i 0.579211 + 0.170072i
\(130\) −1.58314 11.0110i −0.138850 0.965725i
\(131\) −8.83379 10.1947i −0.771812 0.890718i 0.224678 0.974433i \(-0.427867\pi\)
−0.996490 + 0.0837147i \(0.973322\pi\)
\(132\) −2.60844 5.71169i −0.227036 0.497139i
\(133\) 2.89898 0.851218i 0.251374 0.0738100i
\(134\) −0.494973 + 1.08384i −0.0427591 + 0.0936294i
\(135\) −0.500000 + 3.47758i −0.0430331 + 0.299302i
\(136\) 1.41867 0.911725i 0.121650 0.0781797i
\(137\) −0.768502 −0.0656576 −0.0328288 0.999461i \(-0.510452\pi\)
−0.0328288 + 0.999461i \(0.510452\pi\)
\(138\) −0.562102 2.22683i −0.0478493 0.189561i
\(139\) −14.8410 −1.25879 −0.629397 0.777084i \(-0.716698\pi\)
−0.629397 + 0.777084i \(0.716698\pi\)
\(140\) −4.21674 + 2.70993i −0.356379 + 0.229031i
\(141\) −0.810379 + 5.63631i −0.0682462 + 0.474663i
\(142\) −2.63693 + 5.77408i −0.221287 + 0.484550i
\(143\) 22.4966 6.60559i 1.88126 0.552387i
\(144\) 1.11189 + 2.43470i 0.0926574 + 0.202891i
\(145\) 3.64055 + 4.20142i 0.302331 + 0.348909i
\(146\) 0.456813 + 3.17721i 0.0378061 + 0.262947i
\(147\) −6.09353 1.78922i −0.502586 0.147573i
\(148\) −9.48157 + 10.9423i −0.779381 + 0.899453i
\(149\) −7.81799 5.02432i −0.640475 0.411608i 0.179700 0.983722i \(-0.442487\pi\)
−0.820175 + 0.572113i \(0.806124\pi\)
\(150\) 2.95848 + 1.90130i 0.241559 + 0.155241i
\(151\) 5.52469 6.37583i 0.449593 0.518857i −0.485031 0.874497i \(-0.661192\pi\)
0.934623 + 0.355640i \(0.115737\pi\)
\(152\) −6.49691 1.90766i −0.526969 0.154732i
\(153\) −0.132908 0.924394i −0.0107450 0.0747328i
\(154\) 0.896073 + 1.03412i 0.0722076 + 0.0833320i
\(155\) −0.824635 1.80570i −0.0662363 0.145037i
\(156\) −11.2328 + 3.29825i −0.899346 + 0.264072i
\(157\) 3.89922 8.53811i 0.311192 0.681415i −0.687819 0.725882i \(-0.741432\pi\)
0.999011 + 0.0444670i \(0.0141590\pi\)
\(158\) 0.0979009 0.680916i 0.00778858 0.0541707i
\(159\) −5.87204 + 3.77373i −0.465683 + 0.299276i
\(160\) 17.1917 1.35912
\(161\) −1.96299 3.32845i −0.154705 0.262319i
\(162\) −0.478891 −0.0376253
\(163\) −14.3998 + 9.25418i −1.12788 + 0.724843i −0.965116 0.261822i \(-0.915677\pi\)
−0.162762 + 0.986665i \(0.552040\pi\)
\(164\) −0.960814 + 6.68261i −0.0750270 + 0.521824i
\(165\) −5.17565 + 11.3331i −0.402924 + 0.882281i
\(166\) −0.804632 + 0.236261i −0.0624516 + 0.0183374i
\(167\) 4.44222 + 9.72711i 0.343750 + 0.752707i 0.999998 0.00183806i \(-0.000585072\pi\)
−0.656249 + 0.754545i \(0.727858\pi\)
\(168\) −0.952791 1.09958i −0.0735094 0.0848344i
\(169\) −4.37109 30.4016i −0.336237 2.33858i
\(170\) −1.50764 0.442684i −0.115631 0.0339523i
\(171\) −2.45561 + 2.83392i −0.187785 + 0.216715i
\(172\) −10.2130 6.56348i −0.778732 0.500461i
\(173\) −20.3079 13.0511i −1.54398 0.992255i −0.986815 0.161852i \(-0.948253\pi\)
−0.557164 0.830403i \(-0.688110\pi\)
\(174\) −0.496232 + 0.572682i −0.0376192 + 0.0434149i
\(175\) 5.67729 + 1.66700i 0.429163 + 0.126014i
\(176\) 1.35080 + 9.39505i 0.101821 + 0.708179i
\(177\) 0.663766 + 0.766027i 0.0498917 + 0.0575781i
\(178\) 0.932974 + 2.04293i 0.0699293 + 0.153124i
\(179\) −2.50104 + 0.734371i −0.186936 + 0.0548894i −0.373861 0.927485i \(-0.621966\pi\)
0.186925 + 0.982374i \(0.440148\pi\)
\(180\) 2.58427 5.65876i 0.192620 0.421779i
\(181\) 1.42736 9.92752i 0.106095 0.737907i −0.865440 0.501012i \(-0.832961\pi\)
0.971535 0.236895i \(-0.0761296\pi\)
\(182\) 2.14620 1.37928i 0.159087 0.102239i
\(183\) 12.2754 0.907424
\(184\) −0.331964 + 8.65365i −0.0244727 + 0.637956i
\(185\) 28.7287 2.11217
\(186\) 0.227627 0.146287i 0.0166904 0.0107263i
\(187\) 0.471317 3.27808i 0.0344661 0.239717i
\(188\) 4.18848 9.17148i 0.305476 0.668899i
\(189\) −0.773100 + 0.227003i −0.0562348 + 0.0165120i
\(190\) 2.62089 + 5.73895i 0.190139 + 0.416347i
\(191\) 16.4041 + 18.9313i 1.18696 + 1.36982i 0.912938 + 0.408097i \(0.133808\pi\)
0.274019 + 0.961724i \(0.411647\pi\)
\(192\) −0.428340 2.97917i −0.0309128 0.215003i
\(193\) 0.0958162 + 0.0281342i 0.00689700 + 0.00202514i 0.285179 0.958474i \(-0.407947\pi\)
−0.278282 + 0.960499i \(0.589765\pi\)
\(194\) 0.249198 0.287590i 0.0178914 0.0206478i
\(195\) 19.5415 + 12.5586i 1.39940 + 0.899337i
\(196\) 9.45998 + 6.07956i 0.675713 + 0.434254i
\(197\) −10.8572 + 12.5299i −0.773543 + 0.892716i −0.996625 0.0820836i \(-0.973843\pi\)
0.223083 + 0.974800i \(0.428388\pi\)
\(198\) −1.62945 0.478451i −0.115800 0.0340020i
\(199\) −2.85274 19.8412i −0.202225 1.40651i −0.797662 0.603104i \(-0.793930\pi\)
0.595437 0.803402i \(-0.296979\pi\)
\(200\) −8.68379 10.0216i −0.614036 0.708636i
\(201\) −1.03358 2.26322i −0.0729031 0.159636i
\(202\) −5.78728 + 1.69930i −0.407192 + 0.119562i
\(203\) −0.529632 + 1.15973i −0.0371729 + 0.0813973i
\(204\) −0.235335 + 1.63679i −0.0164767 + 0.114598i
\(205\) 11.2694 7.24239i 0.787087 0.505830i
\(206\) −5.07349 −0.353487
\(207\) 4.28287 + 2.15802i 0.297680 + 0.149993i
\(208\) 17.6966 1.22704
\(209\) −11.1867 + 7.18922i −0.773797 + 0.497289i
\(210\) −0.192931 + 1.34186i −0.0133135 + 0.0925972i
\(211\) −0.964715 + 2.11243i −0.0664137 + 0.145426i −0.939928 0.341373i \(-0.889108\pi\)
0.873514 + 0.486799i \(0.161835\pi\)
\(212\) 11.8588 3.48205i 0.814464 0.239148i
\(213\) −5.50633 12.0572i −0.377287 0.826144i
\(214\) −2.01316 2.32331i −0.137616 0.158818i
\(215\) 3.42815 + 23.8433i 0.233798 + 1.62610i
\(216\) 1.73259 + 0.508735i 0.117888 + 0.0346150i
\(217\) 0.298128 0.344058i 0.0202382 0.0233562i
\(218\) 0.472733 + 0.303807i 0.0320175 + 0.0205764i
\(219\) −5.63869 3.62377i −0.381027 0.244871i
\(220\) 14.4467 16.6724i 0.973995 1.12405i
\(221\) −5.92452 1.73960i −0.398526 0.117018i
\(222\) 0.557292 + 3.87605i 0.0374030 + 0.260144i
\(223\) 3.01311 + 3.47732i 0.201773 + 0.232858i 0.847614 0.530614i \(-0.178038\pi\)
−0.645841 + 0.763472i \(0.723493\pi\)
\(224\) 1.63785 + 3.58640i 0.109434 + 0.239626i
\(225\) −7.04607 + 2.06891i −0.469738 + 0.137928i
\(226\) 3.43378 7.51893i 0.228412 0.500152i
\(227\) −1.24145 + 8.63450i −0.0823981 + 0.573092i 0.906239 + 0.422767i \(0.138941\pi\)
−0.988637 + 0.150325i \(0.951968\pi\)
\(228\) 5.58564 3.58967i 0.369918 0.237732i
\(229\) −9.31081 −0.615276 −0.307638 0.951503i \(-0.599539\pi\)
−0.307638 + 0.951503i \(0.599539\pi\)
\(230\) 6.29623 5.04644i 0.415161 0.332752i
\(231\) −2.85731 −0.187997
\(232\) 2.40370 1.54476i 0.157811 0.101419i
\(233\) 0.419991 2.92111i 0.0275146 0.191368i −0.971429 0.237332i \(-0.923727\pi\)
0.998943 + 0.0459644i \(0.0146361\pi\)
\(234\) −1.31532 + 2.88014i −0.0859850 + 0.188281i
\(235\) −19.1955 + 5.63631i −1.25218 + 0.367672i
\(236\) −0.745563 1.63255i −0.0485320 0.106270i
\(237\) 0.940694 + 1.08562i 0.0611046 + 0.0705185i
\(238\) −0.0512839 0.356688i −0.00332424 0.0231206i
\(239\) 15.7671 + 4.62963i 1.01989 + 0.299466i 0.748592 0.663031i \(-0.230730\pi\)
0.271294 + 0.962496i \(0.412548\pi\)
\(240\) −6.15812 + 7.10685i −0.397505 + 0.458745i
\(241\) −1.11201 0.714643i −0.0716306 0.0460342i 0.504335 0.863508i \(-0.331738\pi\)
−0.575966 + 0.817474i \(0.695374\pi\)
\(242\) −0.634735 0.407920i −0.0408023 0.0262221i
\(243\) 0.654861 0.755750i 0.0420093 0.0484814i
\(244\) −20.8552 6.12363i −1.33511 0.392025i
\(245\) −3.17539 22.0853i −0.202868 1.41098i
\(246\) 1.19575 + 1.37997i 0.0762380 + 0.0879834i
\(247\) 10.2992 + 22.5521i 0.655322 + 1.43496i
\(248\) −0.978940 + 0.287443i −0.0621628 + 0.0182526i
\(249\) 0.727446 1.59288i 0.0461000 0.100945i
\(250\) −0.561150 + 3.90288i −0.0354902 + 0.246840i
\(251\) −15.7308 + 10.1096i −0.992920 + 0.638111i −0.932919 0.360087i \(-0.882747\pi\)
−0.0600015 + 0.998198i \(0.519111\pi\)
\(252\) 1.42669 0.0898731
\(253\) 12.4166 + 11.6217i 0.780628 + 0.730651i
\(254\) −4.53208 −0.284368
\(255\) 2.76024 1.77390i 0.172853 0.111086i
\(256\) −0.0914606 + 0.636123i −0.00571629 + 0.0397577i
\(257\) 2.62732 5.75302i 0.163888 0.358864i −0.809816 0.586685i \(-0.800433\pi\)
0.973703 + 0.227821i \(0.0731601\pi\)
\(258\) −3.15042 + 0.925047i −0.196137 + 0.0575909i
\(259\) 2.73698 + 5.99315i 0.170068 + 0.372396i
\(260\) −26.9349 31.0846i −1.67043 1.92778i
\(261\) −0.225190 1.56623i −0.0139389 0.0969471i
\(262\) 6.19836 + 1.82000i 0.382936 + 0.112440i
\(263\) 15.9658 18.4255i 0.984491 1.13616i −0.00619241 0.999981i \(-0.501971\pi\)
0.990684 0.136183i \(-0.0434834\pi\)
\(264\) 5.38698 + 3.46200i 0.331545 + 0.213071i
\(265\) −20.6305 13.2584i −1.26732 0.814456i
\(266\) −0.947523 + 1.09350i −0.0580964 + 0.0670468i
\(267\) −4.49979 1.32126i −0.275383 0.0808596i
\(268\) 0.626972 + 4.36068i 0.0382984 + 0.266371i
\(269\) 8.87170 + 10.2385i 0.540917 + 0.624252i 0.958743 0.284276i \(-0.0917531\pi\)
−0.417825 + 0.908527i \(0.637208\pi\)
\(270\) −0.698939 1.53046i −0.0425361 0.0931410i
\(271\) −10.6726 + 3.13375i −0.648312 + 0.190362i −0.589324 0.807897i \(-0.700606\pi\)
−0.0589883 + 0.998259i \(0.518787\pi\)
\(272\) 1.03839 2.27376i 0.0629618 0.137867i
\(273\) −0.758150 + 5.27305i −0.0458854 + 0.319140i
\(274\) 0.309606 0.198972i 0.0187040 0.0120203i
\(275\) −26.0417 −1.57037
\(276\) −6.19979 5.80287i −0.373184 0.349292i
\(277\) −14.7239 −0.884673 −0.442337 0.896849i \(-0.645850\pi\)
−0.442337 + 0.896849i \(0.645850\pi\)
\(278\) 5.97896 3.84245i 0.358594 0.230455i
\(279\) −0.0804100 + 0.559264i −0.00481402 + 0.0334822i
\(280\) 2.12349 4.64980i 0.126903 0.277879i
\(281\) −20.2215 + 5.93758i −1.20632 + 0.354206i −0.822264 0.569106i \(-0.807289\pi\)
−0.384051 + 0.923312i \(0.625471\pi\)
\(282\) −1.13281 2.48051i −0.0674579 0.147712i
\(283\) 3.85528 + 4.44924i 0.229173 + 0.264480i 0.858677 0.512518i \(-0.171287\pi\)
−0.629504 + 0.776998i \(0.716742\pi\)
\(284\) 3.34015 + 23.2313i 0.198201 + 1.37852i
\(285\) −12.6407 3.71165i −0.748771 0.219859i
\(286\) −7.35293 + 8.48574i −0.434788 + 0.501772i
\(287\) 2.58449 + 1.66095i 0.152557 + 0.0980426i
\(288\) −4.11648 2.64550i −0.242566 0.155887i
\(289\) 10.5615 12.1886i 0.621264 0.716977i
\(290\) −2.55445 0.750054i −0.150002 0.0440447i
\(291\) 0.113086 + 0.786531i 0.00662923 + 0.0461073i
\(292\) 7.77206 + 8.96944i 0.454825 + 0.524897i
\(293\) −0.0808672 0.177074i −0.00472431 0.0103448i 0.907255 0.420581i \(-0.138174\pi\)
−0.911979 + 0.410236i \(0.865446\pi\)
\(294\) 2.91814 0.856844i 0.170189 0.0499721i
\(295\) −1.47934 + 3.23930i −0.0861305 + 0.188600i
\(296\) 2.10136 14.6153i 0.122139 0.849496i
\(297\) 2.98325 1.91722i 0.173106 0.111248i
\(298\) 4.45047 0.257809
\(299\) 24.7420 19.8308i 1.43087 1.14684i
\(300\) 13.0029 0.750725
\(301\) −4.64740 + 2.98671i −0.267872 + 0.172151i
\(302\) −0.574971 + 3.99901i −0.0330859 + 0.230117i
\(303\) 5.23212 11.4568i 0.300578 0.658173i
\(304\) −9.63010 + 2.82765i −0.552324 + 0.162177i
\(305\) 17.9159 + 39.2303i 1.02586 + 2.24632i
\(306\) 0.292878 + 0.337999i 0.0167427 + 0.0193221i
\(307\) 1.84026 + 12.7993i 0.105029 + 0.730492i 0.972483 + 0.232975i \(0.0748459\pi\)
−0.867454 + 0.497518i \(0.834245\pi\)
\(308\) 4.85439 + 1.42538i 0.276605 + 0.0812185i
\(309\) 6.93775 8.00660i 0.394675 0.455479i
\(310\) 0.799730 + 0.513955i 0.0454216 + 0.0291907i
\(311\) −25.2289 16.2136i −1.43060 0.919391i −0.999857 0.0169172i \(-0.994615\pi\)
−0.430744 0.902474i \(-0.641749\pi\)
\(312\) 7.81835 9.02285i 0.442627 0.510819i
\(313\) 1.46922 + 0.431401i 0.0830451 + 0.0243843i 0.322991 0.946402i \(-0.395312\pi\)
−0.239946 + 0.970786i \(0.577130\pi\)
\(314\) 0.639710 + 4.44928i 0.0361009 + 0.251087i
\(315\) −1.85380 2.13940i −0.104450 0.120541i
\(316\) −1.05662 2.31367i −0.0594393 0.130154i
\(317\) 20.3746 5.98254i 1.14435 0.336013i 0.346020 0.938227i \(-0.387533\pi\)
0.798334 + 0.602215i \(0.205715\pi\)
\(318\) 1.38861 3.04064i 0.0778696 0.170511i
\(319\) 0.798568 5.55416i 0.0447112 0.310973i
\(320\) 8.89580 5.71698i 0.497290 0.319589i
\(321\) 6.41935 0.358293
\(322\) 1.65259 + 0.832697i 0.0920953 + 0.0464044i
\(323\) 3.50195 0.194854
\(324\) −1.48958 + 0.957293i −0.0827542 + 0.0531829i
\(325\) −6.90982 + 48.0589i −0.383288 + 2.66583i
\(326\) 3.40525 7.45645i 0.188599 0.412974i
\(327\) −1.12588 + 0.330589i −0.0622615 + 0.0182816i
\(328\) −2.86016 6.26287i −0.157926 0.345809i
\(329\) −3.00456 3.46745i −0.165647 0.191167i
\(330\) −0.849122 5.90578i −0.0467427 0.325102i
\(331\) 0.778568 + 0.228608i 0.0427940 + 0.0125654i 0.303059 0.952972i \(-0.401992\pi\)
−0.260266 + 0.965537i \(0.583810\pi\)
\(332\) −2.03050 + 2.34332i −0.111438 + 0.128607i
\(333\) −6.87896 4.42084i −0.376964 0.242260i
\(334\) −4.30806 2.76862i −0.235727 0.151492i
\(335\) 5.72441 6.60632i 0.312758 0.360942i
\(336\) −2.06926 0.607589i −0.112887 0.0331467i
\(337\) 2.55623 + 17.7790i 0.139247 + 0.968483i 0.932906 + 0.360120i \(0.117264\pi\)
−0.793659 + 0.608363i \(0.791827\pi\)
\(338\) 9.63219 + 11.1161i 0.523922 + 0.604639i
\(339\) 7.17027 + 15.7007i 0.389435 + 0.852745i
\(340\) −5.57439 + 1.63679i −0.302314 + 0.0887674i
\(341\) −0.832348 + 1.82259i −0.0450742 + 0.0986987i
\(342\) 0.255563 1.77748i 0.0138192 0.0961149i
\(343\) 9.04957 5.81580i 0.488631 0.314024i
\(344\) 12.3807 0.667521
\(345\) −0.645886 + 16.8370i −0.0347733 + 0.906473i
\(346\) 11.5604 0.621493
\(347\) −3.92153 + 2.52021i −0.210519 + 0.135292i −0.641651 0.766996i \(-0.721750\pi\)
0.431133 + 0.902288i \(0.358114\pi\)
\(348\) −0.398735 + 2.77326i −0.0213744 + 0.148663i
\(349\) −6.62642 + 14.5098i −0.354704 + 0.776694i 0.645215 + 0.764001i \(0.276768\pi\)
−0.999919 + 0.0126928i \(0.995960\pi\)
\(350\) −2.71881 + 0.798313i −0.145326 + 0.0426716i
\(351\) −2.74659 6.01419i −0.146602 0.321014i
\(352\) −11.3635 13.1141i −0.605675 0.698986i
\(353\) −3.97269 27.6307i −0.211445 1.47063i −0.768336 0.640047i \(-0.778915\pi\)
0.556891 0.830586i \(-0.311994\pi\)
\(354\) −0.465741 0.136754i −0.0247539 0.00726839i
\(355\) 30.4964 35.1947i 1.61858 1.86794i
\(356\) 6.98575 + 4.48947i 0.370244 + 0.237941i
\(357\) 0.633025 + 0.406821i 0.0335032 + 0.0215312i
\(358\) 0.817456 0.943394i 0.0432039 0.0498599i
\(359\) −31.6936 9.30607i −1.67272 0.491156i −0.698286 0.715819i \(-0.746054\pi\)
−0.974436 + 0.224663i \(0.927872\pi\)
\(360\) 0.902869 + 6.27959i 0.0475854 + 0.330964i
\(361\) 3.23428 + 3.73256i 0.170225 + 0.196450i
\(362\) 1.99528 + 4.36905i 0.104869 + 0.229632i
\(363\) 1.51172 0.443880i 0.0793445 0.0232977i
\(364\) 3.91853 8.58039i 0.205387 0.449734i
\(365\) 3.35136 23.3092i 0.175418 1.22006i
\(366\) −4.94538 + 3.17820i −0.258499 + 0.166127i
\(367\) −13.3155 −0.695066 −0.347533 0.937668i \(-0.612981\pi\)
−0.347533 + 0.937668i \(0.612981\pi\)
\(368\) 6.52083 + 11.0568i 0.339922 + 0.576373i
\(369\) −3.81288 −0.198491
\(370\) −11.5739 + 7.43809i −0.601698 + 0.386688i
\(371\) 0.800398 5.56689i 0.0415546 0.289019i
\(372\) 0.415602 0.910042i 0.0215480 0.0471835i
\(373\) 23.7335 6.96879i 1.22888 0.360830i 0.398050 0.917364i \(-0.369687\pi\)
0.830825 + 0.556533i \(0.187869\pi\)
\(374\) 0.658844 + 1.44267i 0.0340680 + 0.0745985i
\(375\) −5.39189 6.22257i −0.278436 0.321332i
\(376\) 1.46333 + 10.1777i 0.0754656 + 0.524875i
\(377\) −10.0381 2.94745i −0.516988 0.151801i
\(378\) 0.252685 0.291614i 0.0129967 0.0149990i
\(379\) 32.2149 + 20.7033i 1.65477 + 1.06345i 0.925152 + 0.379597i \(0.123938\pi\)
0.729616 + 0.683857i \(0.239699\pi\)
\(380\) 19.6242 + 12.6117i 1.00670 + 0.646968i
\(381\) 6.19740 7.15218i 0.317502 0.366417i
\(382\) −11.5102 3.37969i −0.588911 0.172920i
\(383\) 2.38718 + 16.6032i 0.121979 + 0.848383i 0.955309 + 0.295608i \(0.0955221\pi\)
−0.833330 + 0.552775i \(0.813569\pi\)
\(384\) 7.35271 + 8.48548i 0.375216 + 0.433023i
\(385\) −4.17022 9.13151i −0.212534 0.465385i
\(386\) −0.0458856 + 0.0134732i −0.00233551 + 0.000685768i
\(387\) 2.84821 6.23671i 0.144783 0.317030i
\(388\) 0.200237 1.39268i 0.0101655 0.0707027i
\(389\) 1.65871 1.06599i 0.0841000 0.0540478i −0.497915 0.867226i \(-0.665901\pi\)
0.582015 + 0.813178i \(0.302264\pi\)
\(390\) −11.1242 −0.563295
\(391\) −1.09617 4.34261i −0.0554358 0.219615i
\(392\) −11.4679 −0.579214
\(393\) −11.3482 + 7.29301i −0.572438 + 0.367884i
\(394\) 1.12994 7.85891i 0.0569256 0.395926i
\(395\) −2.09653 + 4.59076i −0.105488 + 0.230986i
\(396\) −6.02478 + 1.76903i −0.302756 + 0.0888973i
\(397\) −12.0830 26.4580i −0.606426 1.32789i −0.924992 0.379988i \(-0.875928\pi\)
0.318565 0.947901i \(-0.396799\pi\)
\(398\) 6.28633 + 7.25481i 0.315105 + 0.363651i
\(399\) −0.429986 2.99062i −0.0215262 0.149718i
\(400\) −18.8593 5.53760i −0.942967 0.276880i
\(401\) 5.76326 6.65116i 0.287803 0.332143i −0.593376 0.804926i \(-0.702205\pi\)
0.881179 + 0.472783i \(0.156751\pi\)
\(402\) 1.00236 + 0.644181i 0.0499934 + 0.0321288i
\(403\) 3.14266 + 2.01967i 0.156547 + 0.100607i
\(404\) −14.6043 + 16.8543i −0.726591 + 0.838531i
\(405\) 3.37102 + 0.989821i 0.167507 + 0.0491846i
\(406\) −0.0868920 0.604347i −0.00431238 0.0299932i
\(407\) −18.9892 21.9148i −0.941262 1.08627i
\(408\) −0.700547 1.53398i −0.0346822 0.0759435i
\(409\) −6.24249 + 1.83296i −0.308671 + 0.0906340i −0.432400 0.901682i \(-0.642333\pi\)
0.123729 + 0.992316i \(0.460515\pi\)
\(410\) −2.66497 + 5.83547i −0.131613 + 0.288193i
\(411\) −0.109369 + 0.760680i −0.00539479 + 0.0375216i
\(412\) −15.7809 + 10.1418i −0.777471 + 0.499650i
\(413\) −0.816695 −0.0401869
\(414\) −2.28416 + 0.239469i −0.112261 + 0.0117693i
\(415\) 6.15231 0.302005
\(416\) −27.2168 + 17.4912i −1.33441 + 0.857575i
\(417\) −2.11209 + 14.6899i −0.103429 + 0.719367i
\(418\) 2.64541 5.79263i 0.129391 0.283327i
\(419\) −8.92579 + 2.62085i −0.436054 + 0.128037i −0.492389 0.870375i \(-0.663876\pi\)
0.0563359 + 0.998412i \(0.482058\pi\)
\(420\) 2.08225 + 4.55948i 0.101603 + 0.222480i
\(421\) 3.18611 + 3.67697i 0.155282 + 0.179205i 0.828060 0.560640i \(-0.189445\pi\)
−0.672778 + 0.739844i \(0.734899\pi\)
\(422\) −0.158272 1.10081i −0.00770456 0.0535864i
\(423\) 5.46361 + 1.60426i 0.265650 + 0.0780018i
\(424\) −8.25402 + 9.52565i −0.400851 + 0.462607i
\(425\) 5.76942 + 3.70778i 0.279858 + 0.179854i
\(426\) 5.34003 + 3.43183i 0.258725 + 0.166273i
\(427\) −6.47707 + 7.47494i −0.313447 + 0.361738i
\(428\) −10.9061 3.20232i −0.527166 0.154790i
\(429\) −3.33676 23.2077i −0.161100 1.12048i
\(430\) −7.55432 8.71815i −0.364302 0.420427i
\(431\) 13.7691 + 30.1501i 0.663234 + 1.45228i 0.879478 + 0.475940i \(0.157892\pi\)
−0.216244 + 0.976339i \(0.569381\pi\)
\(432\) 2.56815 0.754078i 0.123560 0.0362806i
\(433\) 12.7795 27.9833i 0.614145 1.34479i −0.305557 0.952174i \(-0.598843\pi\)
0.919702 0.392617i \(-0.128430\pi\)
\(434\) −0.0310271 + 0.215798i −0.00148935 + 0.0103586i
\(435\) 4.67676 3.00557i 0.224234 0.144106i
\(436\) 2.07772 0.0995048
\(437\) −10.2954 + 14.7449i −0.492495 + 0.705342i
\(438\) 3.20988 0.153374
\(439\) 26.1267 16.7906i 1.24696 0.801371i 0.260514 0.965470i \(-0.416108\pi\)
0.986444 + 0.164099i \(0.0524716\pi\)
\(440\) −3.20175 + 22.2687i −0.152638 + 1.06162i
\(441\) −2.63821 + 5.77688i −0.125629 + 0.275089i
\(442\) 2.83720 0.833078i 0.134952 0.0396255i
\(443\) −1.34137 2.93720i −0.0637305 0.139550i 0.875087 0.483966i \(-0.160804\pi\)
−0.938817 + 0.344416i \(0.888077\pi\)
\(444\) 9.48157 + 10.9423i 0.449976 + 0.519300i
\(445\) −2.34488 16.3090i −0.111158 0.773120i
\(446\) −2.11420 0.620784i −0.100110 0.0293950i
\(447\) −6.08579 + 7.02338i −0.287848 + 0.332195i
\(448\) 2.04014 + 1.31112i 0.0963874 + 0.0619444i
\(449\) 17.6082 + 11.3161i 0.830982 + 0.534040i 0.885590 0.464468i \(-0.153754\pi\)
−0.0546076 + 0.998508i \(0.517391\pi\)
\(450\) 2.30299 2.65779i 0.108564 0.125289i
\(451\) −12.9735 3.80937i −0.610900 0.179376i
\(452\) −4.34950 30.2514i −0.204583 1.42291i
\(453\) −5.52469 6.37583i −0.259572 0.299562i
\(454\) −1.73540 3.79999i −0.0814463 0.178343i
\(455\) −17.9584 + 5.27305i −0.841901 + 0.247205i
\(456\) −2.81285 + 6.15929i −0.131724 + 0.288435i
\(457\) 0.0771726 0.536747i 0.00360998 0.0251080i −0.987937 0.154857i \(-0.950508\pi\)
0.991547 + 0.129749i \(0.0414173\pi\)
\(458\) 3.75104 2.41065i 0.175275 0.112642i
\(459\) −0.933899 −0.0435907
\(460\) 9.49651 28.2828i 0.442777 1.31869i
\(461\) 2.74045 0.127636 0.0638178 0.997962i \(-0.479672\pi\)
0.0638178 + 0.997962i \(0.479672\pi\)
\(462\) 1.15112 0.739781i 0.0535550 0.0344177i
\(463\) −1.60699 + 11.1768i −0.0746831 + 0.519432i 0.917799 + 0.397045i \(0.129964\pi\)
−0.992482 + 0.122388i \(0.960945\pi\)
\(464\) 1.75938 3.85251i 0.0816772 0.178848i
\(465\) −1.90468 + 0.559264i −0.0883273 + 0.0259352i
\(466\) 0.587097 + 1.28556i 0.0271967 + 0.0595525i
\(467\) 3.78682 + 4.37023i 0.175233 + 0.202230i 0.836571 0.547858i \(-0.184557\pi\)
−0.661338 + 0.750088i \(0.730011\pi\)
\(468\) 1.66609 + 11.5879i 0.0770148 + 0.535650i
\(469\) 1.92352 + 0.564798i 0.0888201 + 0.0260799i
\(470\) 6.27399 7.24057i 0.289398 0.333983i
\(471\) −7.89629 5.07463i −0.363842 0.233827i
\(472\) 1.53974 + 0.989532i 0.0708723 + 0.0455469i
\(473\) 15.9222 18.3751i 0.732101 0.844890i
\(474\) −0.660052 0.193809i −0.0303172 0.00890193i
\(475\) −3.91891 27.2566i −0.179812 1.25062i
\(476\) −0.872527 1.00695i −0.0399922 0.0461535i
\(477\) 2.89964 + 6.34933i 0.132765 + 0.290716i
\(478\) −7.55071 + 2.21709i −0.345361 + 0.101407i
\(479\) 3.47182 7.60222i 0.158631 0.347354i −0.813582 0.581450i \(-0.802486\pi\)
0.972214 + 0.234096i \(0.0752129\pi\)
\(480\) 2.44663 17.0167i 0.111673 0.776703i
\(481\) −45.4814 + 29.2291i −2.07377 + 1.33273i
\(482\) 0.633020 0.0288333
\(483\) −3.57394 + 1.46932i −0.162620 + 0.0668564i
\(484\) −2.78974 −0.126807
\(485\) −2.34858 + 1.50934i −0.106644 + 0.0685357i
\(486\) −0.0681534 + 0.474017i −0.00309150 + 0.0215018i
\(487\) −1.44084 + 3.15501i −0.0652909 + 0.142967i −0.939464 0.342647i \(-0.888677\pi\)
0.874173 + 0.485614i \(0.161404\pi\)
\(488\) 21.2683 6.24493i 0.962770 0.282695i
\(489\) 7.11068 + 15.5702i 0.321556 + 0.704110i
\(490\) 6.99735 + 8.07537i 0.316108 + 0.364808i
\(491\) −0.0523189 0.363886i −0.00236112 0.0164219i 0.988607 0.150521i \(-0.0480951\pi\)
−0.990968 + 0.134099i \(0.957186\pi\)
\(492\) 6.47785 + 1.90207i 0.292044 + 0.0857519i
\(493\) −0.967715 + 1.11680i −0.0435837 + 0.0502983i
\(494\) −9.98815 6.41900i −0.449388 0.288804i
\(495\) 10.4812 + 6.73584i 0.471094 + 0.302754i
\(496\) −0.990348 + 1.14292i −0.0444679 + 0.0513187i
\(497\) 10.2474 + 3.00892i 0.459661 + 0.134969i
\(498\) 0.119345 + 0.830066i 0.00534800 + 0.0371961i
\(499\) −8.88893 10.2584i −0.397923 0.459228i 0.521063 0.853518i \(-0.325536\pi\)
−0.918986 + 0.394291i \(0.870990\pi\)
\(500\) 6.05633 + 13.2615i 0.270847 + 0.593073i
\(501\) 10.2603 3.01270i 0.458396 0.134597i
\(502\) 3.72001 8.14567i 0.166032 0.363559i
\(503\) 2.38681 16.6006i 0.106423 0.740186i −0.864818 0.502086i \(-0.832566\pi\)
0.971241 0.238100i \(-0.0765247\pi\)
\(504\) −1.22398 + 0.786607i −0.0545206 + 0.0350382i
\(505\) 44.2502 1.96911
\(506\) −8.01124 1.46726i −0.356143 0.0652275i
\(507\) −30.7142 −1.36407
\(508\) −14.0969 + 9.05952i −0.625449 + 0.401951i
\(509\) −0.426906 + 2.96920i −0.0189223 + 0.131607i −0.997093 0.0761963i \(-0.975722\pi\)
0.978171 + 0.207804i \(0.0666315\pi\)
\(510\) −0.652738 + 1.42930i −0.0289037 + 0.0632904i
\(511\) 5.18188 1.52154i 0.229233 0.0673088i
\(512\) −9.45633 20.7065i −0.417915 0.915105i
\(513\) 2.45561 + 2.83392i 0.108418 + 0.125121i
\(514\) 0.431040 + 2.99795i 0.0190124 + 0.132234i
\(515\) 35.7134 + 10.4864i 1.57372 + 0.462086i
\(516\) −7.95013 + 9.17494i −0.349985 + 0.403904i
\(517\) 16.9874 + 10.9172i 0.747107 + 0.480137i
\(518\) −2.65432 1.70583i −0.116624 0.0749498i
\(519\) −15.8083 + 18.2438i −0.693909 + 0.800814i
\(520\) 40.2465 + 11.8174i 1.76492 + 0.518228i
\(521\) 1.30671 + 9.08839i 0.0572482 + 0.398170i 0.998218 + 0.0596783i \(0.0190075\pi\)
−0.940970 + 0.338491i \(0.890083\pi\)
\(522\) 0.496232 + 0.572682i 0.0217195 + 0.0250656i
\(523\) −3.03941 6.65538i −0.132904 0.291019i 0.831466 0.555575i \(-0.187502\pi\)
−0.964370 + 0.264556i \(0.914775\pi\)
\(524\) 22.9180 6.72932i 1.00118 0.293972i
\(525\) 2.45800 5.38226i 0.107276 0.234901i
\(526\) −1.66161 + 11.5567i −0.0724495 + 0.503897i
\(527\) 0.443901 0.285278i 0.0193367 0.0124269i
\(528\) 9.49167 0.413072
\(529\) 21.5071 + 8.15145i 0.935090 + 0.354411i
\(530\) 11.7441 0.510130
\(531\) 0.852693 0.547993i 0.0370037 0.0237809i
\(532\) −0.761360 + 5.29537i −0.0330091 + 0.229584i
\(533\) −10.4724 + 22.9314i −0.453610 + 0.993268i
\(534\) 2.15491 0.632739i 0.0932521 0.0273813i
\(535\) 9.36900 + 20.5153i 0.405057 + 0.886952i
\(536\) −2.94216 3.39543i −0.127082 0.146660i
\(537\) 0.370961 + 2.58009i 0.0160082 + 0.111339i
\(538\) −6.22496 1.82781i −0.268377 0.0788027i
\(539\) −14.7482 + 17.0204i −0.635251 + 0.733119i
\(540\) −5.23338 3.36329i −0.225209 0.144733i
\(541\) 0.558457 + 0.358898i 0.0240099 + 0.0154303i 0.552591 0.833453i \(-0.313639\pi\)
−0.528581 + 0.848883i \(0.677276\pi\)
\(542\) 3.48829 4.02570i 0.149835 0.172919i
\(543\) −9.62333 2.82567i −0.412977 0.121261i
\(544\) 0.650353 + 4.52330i 0.0278836 + 0.193935i
\(545\) −2.69973 3.11565i −0.115644 0.133460i
\(546\) −1.05980 2.32064i −0.0453553 0.0993143i
\(547\) 17.4721 5.13026i 0.747052 0.219354i 0.114018 0.993479i \(-0.463628\pi\)
0.633033 + 0.774124i \(0.281810\pi\)
\(548\) 0.565279 1.23779i 0.0241475 0.0528757i
\(549\) 1.74697 12.1505i 0.0745590 0.518569i
\(550\) 10.4914 6.74240i 0.447354 0.287497i
\(551\) 5.93346 0.252774
\(552\) 8.51833 + 1.56013i 0.362564 + 0.0664035i
\(553\) −1.15743 −0.0492188
\(554\) 5.93180 3.81214i 0.252018 0.161962i
\(555\) 4.08851 28.4362i 0.173548 1.20705i
\(556\) 10.9164 23.9036i 0.462959 1.01374i
\(557\) 24.4462 7.17805i 1.03582 0.304144i 0.280744 0.959783i \(-0.409419\pi\)
0.755075 + 0.655639i \(0.227601\pi\)
\(558\) −0.112403 0.246129i −0.00475841 0.0104195i
\(559\) −29.6859 34.2593i −1.25558 1.44901i
\(560\) −1.07831 7.49980i −0.0455669 0.316924i
\(561\) −3.17764 0.933040i −0.134160 0.0393930i
\(562\) 6.60934 7.62759i 0.278798 0.321750i
\(563\) −17.8550 11.4747i −0.752499 0.483602i 0.107305 0.994226i \(-0.465778\pi\)
−0.859804 + 0.510624i \(0.829414\pi\)
\(564\) −8.48205 5.45108i −0.357159 0.229532i
\(565\) −39.7120 + 45.8301i −1.67070 + 1.92809i
\(566\) −2.70512 0.794295i −0.113705 0.0333867i
\(567\) 0.114669 + 0.797537i 0.00481562 + 0.0334934i
\(568\) −15.6741 18.0889i −0.657672 0.758994i
\(569\) −13.9743 30.5994i −0.585833 1.28279i −0.937928 0.346831i \(-0.887258\pi\)
0.352095 0.935964i \(-0.385469\pi\)
\(570\) 6.05353 1.77748i 0.253554 0.0744503i
\(571\) −5.34091 + 11.6950i −0.223510 + 0.489419i −0.987853 0.155391i \(-0.950336\pi\)
0.764343 + 0.644810i \(0.223064\pi\)
\(572\) −5.90827 + 41.0929i −0.247037 + 1.71818i
\(573\) 21.0732 13.5429i 0.880344 0.565763i
\(574\) −1.47124 −0.0614085
\(575\) −32.5730 + 13.3915i −1.35839 + 0.558463i
\(576\) −3.00980 −0.125409
\(577\) −9.24070 + 5.93864i −0.384695 + 0.247229i −0.718667 0.695354i \(-0.755247\pi\)
0.333972 + 0.942583i \(0.391611\pi\)
\(578\) −1.09917 + 7.64487i −0.0457193 + 0.317985i
\(579\) 0.0414839 0.0908370i 0.00172401 0.00377506i
\(580\) −9.44487 + 2.77326i −0.392177 + 0.115154i
\(581\) 0.586131 + 1.28345i 0.0243168 + 0.0532464i
\(582\) −0.249198 0.287590i −0.0103296 0.0119210i
\(583\) 3.52270 + 24.5009i 0.145895 + 1.01472i
\(584\) −11.6131 3.40991i −0.480553 0.141103i
\(585\) 15.2118 17.5553i 0.628930 0.725824i
\(586\) 0.0784249 + 0.0504006i 0.00323970 + 0.00208203i
\(587\) −11.4406 7.35242i −0.472204 0.303467i 0.282810 0.959176i \(-0.408733\pi\)
−0.755014 + 0.655709i \(0.772370\pi\)
\(588\) 7.36398 8.49848i 0.303685 0.350471i
\(589\) −2.03288 0.596907i −0.0837633 0.0245951i
\(590\) −0.242702 1.68803i −0.00999188 0.0694950i
\(591\) 10.8572 + 12.5299i 0.446605 + 0.515410i
\(592\) −9.09195 19.9086i −0.373677 0.818238i
\(593\) −41.1409 + 12.0800i −1.68945 + 0.496068i −0.978339 0.207009i \(-0.933627\pi\)
−0.711113 + 0.703077i \(0.751809\pi\)
\(594\) −0.705476 + 1.54478i −0.0289461 + 0.0633830i
\(595\) −0.376239 + 2.61680i −0.0154243 + 0.107278i
\(596\) 13.8430 8.89638i 0.567033 0.364410i
\(597\) −20.0452 −0.820397
\(598\) −4.83344 + 14.3951i −0.197654 + 0.588660i
\(599\) −14.6628 −0.599106 −0.299553 0.954080i \(-0.596838\pi\)
−0.299553 + 0.954080i \(0.596838\pi\)
\(600\) −11.1554 + 7.16917i −0.455419 + 0.292680i
\(601\) 4.44759 30.9337i 0.181421 1.26181i −0.671985 0.740564i \(-0.734558\pi\)
0.853406 0.521246i \(-0.174533\pi\)
\(602\) 1.09901 2.40650i 0.0447924 0.0980817i
\(603\) −2.38728 + 0.700969i −0.0972176 + 0.0285457i
\(604\) 6.20550 + 13.5881i 0.252498 + 0.552894i
\(605\) 3.62491 + 4.18337i 0.147374 + 0.170078i
\(606\) 0.858387 + 5.97021i 0.0348696 + 0.242523i
\(607\) −3.74039 1.09828i −0.151818 0.0445777i 0.204941 0.978774i \(-0.434300\pi\)
−0.356758 + 0.934197i \(0.616118\pi\)
\(608\) 12.0159 13.8671i 0.487311 0.562386i
\(609\) 1.07255 + 0.689289i 0.0434621 + 0.0279314i
\(610\) −17.3748 11.1661i −0.703485 0.452102i
\(611\) 24.6546 28.4529i 0.997419 1.15108i
\(612\) 1.58664 + 0.465879i 0.0641360 + 0.0188320i
\(613\) 4.96719 + 34.5476i 0.200623 + 1.39536i 0.802442 + 0.596731i \(0.203534\pi\)
−0.601819 + 0.798633i \(0.705557\pi\)
\(614\) −4.05522 4.67997i −0.163655 0.188868i
\(615\) −5.56487 12.1854i −0.224397 0.491362i
\(616\) −4.95055 + 1.45361i −0.199464 + 0.0585678i
\(617\) −6.31092 + 13.8190i −0.254068 + 0.556332i −0.993091 0.117349i \(-0.962560\pi\)
0.739023 + 0.673681i \(0.235288\pi\)
\(618\) −0.722033 + 5.02185i −0.0290444 + 0.202009i
\(619\) −4.17467 + 2.68290i −0.167794 + 0.107835i −0.621843 0.783142i \(-0.713616\pi\)
0.454048 + 0.890977i \(0.349979\pi\)
\(620\) 3.51492 0.141163
\(621\) 2.74557 3.93215i 0.110176 0.157792i
\(622\) 14.3618 0.575856
\(623\) 3.17886 2.04293i 0.127358 0.0818482i
\(624\) 2.51849 17.5165i 0.100820 0.701221i
\(625\) −3.23614 + 7.08616i −0.129446 + 0.283447i
\(626\) −0.703596 + 0.206594i −0.0281214 + 0.00825718i
\(627\) 5.52402 + 12.0959i 0.220608 + 0.483065i
\(628\) 10.8838 + 12.5606i 0.434311 + 0.501222i
\(629\) 1.08679 + 7.55879i 0.0433332 + 0.301389i
\(630\) 1.30075 + 0.381934i 0.0518230 + 0.0152166i
\(631\) −24.0121 + 27.7114i −0.955905 + 1.10317i 0.0386804 + 0.999252i \(0.487685\pi\)
−0.994585 + 0.103922i \(0.966861\pi\)
\(632\) 2.18213 + 1.40237i 0.0868006 + 0.0557833i
\(633\) 1.95364 + 1.25553i 0.0776500 + 0.0499027i
\(634\) −6.65939 + 7.68534i −0.264478 + 0.305224i
\(635\) 31.9023 + 9.36737i 1.26600 + 0.371733i
\(636\) −1.75893 12.2336i −0.0697460 0.485094i
\(637\) 27.4972 + 31.7334i 1.08948 + 1.25732i
\(638\) 1.11630 + 2.44436i 0.0441947 + 0.0967730i
\(639\) −12.7181 + 3.73437i −0.503120 + 0.147729i
\(640\) −16.3870 + 35.8826i −0.647755 + 1.41838i
\(641\) −1.95454 + 13.5941i −0.0771997 + 0.536936i 0.914118 + 0.405448i \(0.132884\pi\)
−0.991318 + 0.131488i \(0.958025\pi\)
\(642\) −2.58616 + 1.66202i −0.102068 + 0.0655948i
\(643\) −34.2265 −1.34976 −0.674880 0.737927i \(-0.735805\pi\)
−0.674880 + 0.737927i \(0.735805\pi\)
\(644\) 6.80487 0.713416i 0.268150 0.0281125i
\(645\) 24.0885 0.948483
\(646\) −1.41083 + 0.906684i −0.0555083 + 0.0356730i
\(647\) 5.48316 38.1362i 0.215565 1.49929i −0.538576 0.842577i \(-0.681038\pi\)
0.754141 0.656712i \(-0.228053\pi\)
\(648\) 0.750131 1.64256i 0.0294679 0.0645257i
\(649\) 3.44882 1.01267i 0.135378 0.0397506i
\(650\) −9.65908 21.1504i −0.378860 0.829588i
\(651\) −0.298128 0.344058i −0.0116846 0.0134847i
\(652\) −4.31336 30.0000i −0.168924 1.17489i
\(653\) −19.8816 5.83777i −0.778027 0.228449i −0.131475 0.991319i \(-0.541971\pi\)
−0.646552 + 0.762870i \(0.723790\pi\)
\(654\) 0.367991 0.424685i 0.0143896 0.0166065i
\(655\) −39.8699 25.6228i −1.55785 1.00117i
\(656\) −8.58537 5.51748i −0.335203 0.215422i
\(657\) −4.38935 + 5.06558i −0.171245 + 0.197627i
\(658\) 2.10819 + 0.619022i 0.0821860 + 0.0241320i
\(659\) 2.25543 + 15.6869i 0.0878592 + 0.611074i 0.985414 + 0.170172i \(0.0544324\pi\)
−0.897555 + 0.440902i \(0.854659\pi\)
\(660\) −14.4467 16.6724i −0.562336 0.648970i
\(661\) −0.0565318 0.123787i −0.00219883 0.00481477i 0.908529 0.417821i \(-0.137206\pi\)
−0.910728 + 0.413006i \(0.864479\pi\)
\(662\) −0.372850 + 0.109479i −0.0144912 + 0.00425500i
\(663\) −2.56504 + 5.61665i −0.0996178 + 0.218132i
\(664\) 0.450011 3.12990i 0.0174638 0.121464i
\(665\) 8.92998 5.73895i 0.346290 0.222547i
\(666\) 3.91591 0.151738
\(667\) −1.85728 7.35782i −0.0719141 0.284896i
\(668\) −18.9345 −0.732598
\(669\) 3.87074 2.48757i 0.149651 0.0961750i
\(670\) −0.595757 + 4.14358i −0.0230161 + 0.160080i
\(671\) 18.0834 39.5972i 0.698104 1.52863i
\(672\) 3.78298 1.11078i 0.145932 0.0428494i
\(673\) −8.57511 18.7769i −0.330546 0.723795i 0.669269 0.743020i \(-0.266607\pi\)
−0.999815 + 0.0192250i \(0.993880\pi\)
\(674\) −5.63295 6.50077i −0.216973 0.250400i
\(675\) 1.04509 + 7.26879i 0.0402257 + 0.279776i
\(676\) 52.1815 + 15.3219i 2.00698 + 0.589303i
\(677\) −18.5314 + 21.3864i −0.712220 + 0.821945i −0.990349 0.138599i \(-0.955740\pi\)
0.278129 + 0.960544i \(0.410286\pi\)
\(678\) −6.95372 4.46888i −0.267056 0.171626i
\(679\) −0.538617 0.346148i −0.0206702 0.0132839i
\(680\) 3.87993 4.47767i 0.148788 0.171711i
\(681\) 8.36993 + 2.45763i 0.320736 + 0.0941767i
\(682\) −0.136556 0.949767i −0.00522899 0.0363684i
\(683\) 12.7796 + 14.7484i 0.488997 + 0.564332i 0.945597 0.325340i \(-0.105479\pi\)
−0.456601 + 0.889672i \(0.650933\pi\)
\(684\) −2.75821 6.03965i −0.105463 0.230932i
\(685\) −2.59064 + 0.760680i −0.0989832 + 0.0290641i
\(686\) −2.14003 + 4.68601i −0.0817068 + 0.178913i
\(687\) −1.32507 + 9.21604i −0.0505545 + 0.351614i
\(688\) 15.4382 9.92150i 0.588574 0.378254i
\(689\) 46.1502 1.75818
\(690\) −4.09903 6.95033i −0.156047 0.264594i
\(691\) 18.2405 0.693902 0.346951 0.937883i \(-0.387217\pi\)
0.346951 + 0.937883i \(0.387217\pi\)
\(692\) 35.9584 23.1091i 1.36693 0.878474i
\(693\) −0.406637 + 2.82823i −0.0154469 + 0.107435i
\(694\) 0.927358 2.03063i 0.0352020 0.0770817i
\(695\) −50.0292 + 14.6899i −1.89772 + 0.557220i
\(696\) −1.18696 2.59908i −0.0449915 0.0985177i
\(697\) 2.33186 + 2.69111i 0.0883254 + 0.101933i
\(698\) −1.08714 7.56120i −0.0411487 0.286196i
\(699\) −2.83160 0.831433i −0.107101 0.0314477i
\(700\) −6.86095 + 7.91796i −0.259319 + 0.299271i
\(701\) 21.0479 + 13.5267i 0.794970 + 0.510896i 0.873971 0.485979i \(-0.161537\pi\)
−0.0790011 + 0.996875i \(0.525173\pi\)
\(702\) 2.66364 + 1.71182i 0.100533 + 0.0646083i
\(703\) 20.0796 23.1731i 0.757315 0.873989i
\(704\) −10.2410 3.00704i −0.385973 0.113332i
\(705\) 2.84713 + 19.8023i 0.107229 + 0.745796i
\(706\) 8.75429 + 10.1030i 0.329472 + 0.380231i
\(707\) 4.21572 + 9.23114i 0.158549 + 0.347173i
\(708\) −1.72204 + 0.505637i −0.0647183 + 0.0190030i
\(709\) −13.2237 + 28.9559i −0.496626 + 1.08746i 0.480925 + 0.876762i \(0.340301\pi\)
−0.977551 + 0.210698i \(0.932426\pi\)
\(710\) −3.17385 + 22.0746i −0.119113 + 0.828447i
\(711\) 1.20844 0.776619i 0.0453202 0.0291255i
\(712\) −8.46847 −0.317369
\(713\) −0.103871 + 2.70772i −0.00389001 + 0.101405i
\(714\) −0.360355 −0.0134860
\(715\) 69.2981 44.5352i 2.59160 1.66552i
\(716\) 0.656847 4.56847i 0.0245475 0.170732i
\(717\) 6.82639 14.9477i 0.254936 0.558232i
\(718\) 15.1778 4.45660i 0.566430 0.166319i
\(719\) −0.758817 1.66158i −0.0282991 0.0619664i 0.894955 0.446157i \(-0.147208\pi\)
−0.923254 + 0.384191i \(0.874480\pi\)
\(720\) 6.15812 + 7.10685i 0.229499 + 0.264857i
\(721\) 1.21483 + 8.44930i 0.0452425 + 0.314668i
\(722\) −2.26938 0.666350i −0.0844576 0.0247990i
\(723\) −0.865624 + 0.998983i −0.0321929 + 0.0371526i
\(724\) 14.9399 + 9.60127i 0.555236 + 0.356828i
\(725\) 9.77531 + 6.28221i 0.363046 + 0.233315i
\(726\) −0.494100 + 0.570221i −0.0183378 + 0.0211629i
\(727\) 35.9742 + 10.5630i 1.33421 + 0.391759i 0.869600 0.493757i \(-0.164377\pi\)
0.464609 + 0.885516i \(0.346195\pi\)
\(728\) 1.36902 + 9.52175i 0.0507393 + 0.352900i
\(729\) −0.654861 0.755750i −0.0242541 0.0279907i
\(730\) 4.68479 + 10.2583i 0.173392 + 0.379675i
\(731\) −6.14372 + 1.80396i −0.227234 + 0.0667218i
\(732\) −9.02930 + 19.7714i −0.333732 + 0.730772i
\(733\) 0.471638 3.28031i 0.0174203 0.121161i −0.979256 0.202629i \(-0.935052\pi\)
0.996676 + 0.0814675i \(0.0259607\pi\)
\(734\) 5.36442 3.44751i 0.198004 0.127250i
\(735\) −22.3125 −0.823007
\(736\) −20.9572 10.5598i −0.772493 0.389238i
\(737\) −8.82318 −0.325006
\(738\) 1.53609 0.987186i 0.0565443 0.0363388i
\(739\) 0.762673 5.30451i 0.0280554 0.195129i −0.970974 0.239187i \(-0.923119\pi\)
0.999029 + 0.0440571i \(0.0140284\pi\)
\(740\) −21.1317 + 46.2719i −0.776815 + 1.70099i
\(741\) 23.7883 6.98487i 0.873884 0.256596i
\(742\) 1.11886 + 2.44996i 0.0410746 + 0.0899408i
\(743\) 16.8909 + 19.4931i 0.619665 + 0.715132i 0.975643 0.219362i \(-0.0703977\pi\)
−0.355978 + 0.934494i \(0.615852\pi\)
\(744\) 0.145199 + 1.00988i 0.00532327 + 0.0370241i
\(745\) −31.3278 9.19867i −1.14776 0.337013i
\(746\) −7.75723 + 8.95231i −0.284012 + 0.327768i
\(747\) −1.47314 0.946733i −0.0538996 0.0346391i
\(748\) 4.93317 + 3.17036i 0.180375 + 0.115920i
\(749\) −3.38715 + 3.90898i −0.123764 + 0.142831i
\(750\) 3.78330 + 1.11088i 0.138147 + 0.0405635i
\(751\) −5.51058 38.3269i −0.201084 1.39857i −0.801075 0.598564i \(-0.795738\pi\)
0.599991 0.800007i \(-0.295171\pi\)
\(752\) 9.98081 + 11.5185i 0.363963 + 0.420036i
\(753\) 7.76795 + 17.0094i 0.283080 + 0.619858i
\(754\) 4.80716 1.41151i 0.175066 0.0514041i
\(755\) 12.3129 26.9615i 0.448113 0.981230i
\(756\) 0.203039 1.41217i 0.00738447 0.0513601i
\(757\) 21.7825 13.9987i 0.791697 0.508793i −0.0811996 0.996698i \(-0.525875\pi\)
0.872897 + 0.487905i \(0.162239\pi\)
\(758\) −18.3386 −0.666089
\(759\) 13.2705 10.6363i 0.481688 0.386074i
\(760\) −23.7895 −0.862934
\(761\) 25.7260 16.5331i 0.932568 0.599325i 0.0162899 0.999867i \(-0.494815\pi\)
0.916278 + 0.400542i \(0.131178\pi\)
\(762\) −0.644982 + 4.48595i −0.0233652 + 0.162509i
\(763\) 0.392760 0.860025i 0.0142189 0.0311350i
\(764\) −42.5579 + 12.4961i −1.53969 + 0.452094i
\(765\) −1.36302 2.98460i −0.0492801 0.107908i
\(766\) −5.26042 6.07085i −0.190067 0.219349i
\(767\) −0.953734 6.63337i −0.0344374 0.239517i
\(768\) 0.616632 + 0.181059i 0.0222508 + 0.00653342i
\(769\) 9.90083 11.4262i 0.357033 0.412038i −0.548610 0.836078i \(-0.684843\pi\)
0.905643 + 0.424040i \(0.139388\pi\)
\(770\) 4.04428 + 2.59910i 0.145746 + 0.0936651i
\(771\) −5.32056 3.41931i −0.191615 0.123144i
\(772\) −0.115793 + 0.133632i −0.00416748 + 0.00480953i
\(773\) 24.1446 + 7.08951i 0.868423 + 0.254992i 0.685444 0.728125i \(-0.259608\pi\)
0.182978 + 0.983117i \(0.441426\pi\)
\(774\) 0.467280 + 3.25000i 0.0167960 + 0.116819i
\(775\) −2.71715 3.13576i −0.0976030 0.112640i
\(776\) 0.596068 + 1.30521i 0.0213976 + 0.0468542i
\(777\) 6.32166 1.85621i 0.226788 0.0665911i
\(778\) −0.392250 + 0.858908i −0.0140628 + 0.0307933i
\(779\) 2.03476 14.1521i 0.0729029 0.507051i
\(780\) −34.6014 + 22.2370i −1.23893 + 0.796212i
\(781\) −47.0049 −1.68197
\(782\) 1.56595 + 1.46570i 0.0559983 + 0.0524132i
\(783\) −1.58233 −0.0565480
\(784\) −14.2999 + 9.19000i −0.510711 + 0.328214i
\(785\) 4.69317 32.6417i 0.167506 1.16503i
\(786\) 2.68360 5.87626i 0.0957208 0.209599i
\(787\) −21.0701 + 6.18675i −0.751070 + 0.220534i −0.634792 0.772683i \(-0.718914\pi\)
−0.116277 + 0.993217i \(0.537096\pi\)
\(788\) −12.1951 26.7036i −0.434434 0.951277i
\(789\) −15.9658 18.4255i −0.568396 0.655964i
\(790\) −0.343959 2.39229i −0.0122375 0.0851137i
\(791\) −13.3441 3.91818i −0.474461 0.139314i
\(792\) 4.19341 4.83945i 0.149006 0.171962i
\(793\) −68.2769 43.8789i −2.42458 1.55819i
\(794\) 11.7180 + 7.53073i 0.415858 + 0.267256i
\(795\) −16.0595 + 18.5336i −0.569570 + 0.657319i
\(796\) 34.0556 + 9.99964i 1.20707 + 0.354428i
\(797\) 0.684007 + 4.75737i 0.0242288 + 0.168515i 0.998343 0.0575409i \(-0.0183260\pi\)
−0.974114 + 0.226056i \(0.927417\pi\)
\(798\) 0.947523 + 1.09350i 0.0335420 + 0.0387095i
\(799\) −2.20912 4.83731i −0.0781532 0.171132i
\(800\) 34.4783 10.1237i 1.21899 0.357928i
\(801\) −1.94819 + 4.26595i −0.0688361 + 0.150730i
\(802\) −0.599800 + 4.17170i −0.0211797 + 0.147308i
\(803\) −19.9959 + 12.8506i −0.705641 + 0.453488i
\(804\) 4.40553 0.155371
\(805\) −9.91185 9.27728i −0.349347 0.326981i
\(806\) −1.78899 −0.0630145
\(807\) 11.3969 7.32431i 0.401188 0.257828i
\(808\) 3.23669 22.5117i 0.113866 0.791957i
\(809\) −12.2663 + 26.8594i −0.431260 + 0.944327i 0.561861 + 0.827232i \(0.310086\pi\)
−0.993121 + 0.117095i \(0.962642\pi\)
\(810\) −1.61435 + 0.474017i −0.0567226 + 0.0166553i
\(811\) −9.34727 20.4677i −0.328227 0.718717i 0.671525 0.740982i \(-0.265640\pi\)
−0.999752 + 0.0222649i \(0.992912\pi\)
\(812\) −1.47835 1.70611i −0.0518799 0.0598726i
\(813\) 1.58299 + 11.0099i 0.0555177 + 0.386134i
\(814\) 13.3241 + 3.91231i 0.467009 + 0.137126i
\(815\) −39.3820 + 45.4493i −1.37949 + 1.59202i
\(816\) −2.10284 1.35141i −0.0736141 0.0473089i
\(817\) 21.6285 + 13.8998i 0.756685 + 0.486292i
\(818\) 2.04034 2.35467i 0.0713387 0.0823292i
\(819\) 5.11148 + 1.50087i 0.178610 + 0.0524445i
\(820\) 3.37566 + 23.4783i 0.117883 + 0.819896i
\(821\) 12.2433 + 14.1296i 0.427296 + 0.493125i 0.928046 0.372467i \(-0.121488\pi\)
−0.500750 + 0.865592i \(0.666942\pi\)
\(822\) −0.152885 0.334771i −0.00533247 0.0116765i
\(823\) 39.1112 11.4841i 1.36333 0.400310i 0.483396 0.875402i \(-0.339403\pi\)
0.879936 + 0.475092i \(0.157585\pi\)
\(824\) 7.94707 17.4017i 0.276849 0.606215i
\(825\) −3.70611 + 25.7766i −0.129030 + 0.897426i
\(826\) 0.329021 0.211449i 0.0114481 0.00735726i
\(827\) 23.5429 0.818666 0.409333 0.912385i \(-0.365761\pi\)
0.409333 + 0.912385i \(0.365761\pi\)
\(828\) −6.62613 + 5.31085i −0.230274 + 0.184565i
\(829\) −10.5885 −0.367752 −0.183876 0.982949i \(-0.558865\pi\)
−0.183876 + 0.982949i \(0.558865\pi\)
\(830\) −2.47858 + 1.59288i −0.0860327 + 0.0552898i
\(831\) −2.09543 + 14.5740i −0.0726896 + 0.505567i
\(832\) −8.26669 + 18.1015i −0.286596 + 0.627558i
\(833\) 5.69075 1.67095i 0.197173 0.0578951i
\(834\) −2.95244 6.46494i −0.102235 0.223863i
\(835\) 24.6029 + 28.3933i 0.851420 + 0.982591i
\(836\) −3.35088 23.3059i −0.115893 0.806052i
\(837\) 0.542128 + 0.159183i 0.0187387 + 0.00550217i
\(838\) 2.91737 3.36682i 0.100779 0.116305i
\(839\) 33.0705 + 21.2531i 1.14172 + 0.733740i 0.967974 0.251051i \(-0.0807760\pi\)
0.173747 + 0.984790i \(0.444412\pi\)
\(840\) −4.30027 2.76361i −0.148373 0.0953537i
\(841\) 17.3513 20.0245i 0.598322 0.690500i
\(842\) −2.23558 0.656427i −0.0770433 0.0226220i
\(843\) 2.99932 + 20.8607i 0.103302 + 0.718481i
\(844\) −2.69278 3.10764i −0.0926894 0.106969i
\(845\) −44.8272 98.1578i −1.54210 3.37673i
\(846\) −2.61648 + 0.768267i −0.0899563 + 0.0264136i
\(847\) −0.527357 + 1.15475i −0.0181202 + 0.0396777i
\(848\) −2.65883 + 18.4926i −0.0913048 + 0.635039i
\(849\) 4.95261 3.18285i 0.169973 0.109235i
\(850\) −3.28430 −0.112650
\(851\) −35.0211 17.6462i −1.20051 0.604904i
\(852\) 23.4702 0.804074
\(853\) −34.9175 + 22.4401i −1.19555 + 0.768335i −0.978181 0.207754i \(-0.933385\pi\)
−0.217372 + 0.976089i \(0.569748\pi\)
\(854\) 0.674089 4.68839i 0.0230668 0.160433i
\(855\) −5.47283 + 11.9838i −0.187167 + 0.409838i
\(856\) 11.1221 3.26575i 0.380147 0.111621i
\(857\) 4.65231 + 10.1871i 0.158920 + 0.347986i 0.972296 0.233752i \(-0.0751003\pi\)
−0.813376 + 0.581738i \(0.802373\pi\)
\(858\) 7.35293 + 8.48574i 0.251025 + 0.289698i
\(859\) −0.286639 1.99362i −0.00978001 0.0680215i 0.984347 0.176242i \(-0.0563940\pi\)
−0.994127 + 0.108220i \(0.965485\pi\)
\(860\) −40.9248 12.0166i −1.39553 0.409763i
\(861\) 2.01185 2.32180i 0.0685637 0.0791268i
\(862\) −13.3533 8.58161i −0.454814 0.292291i
\(863\) 18.5634 + 11.9299i 0.631904 + 0.406100i 0.817014 0.576618i \(-0.195628\pi\)
−0.185110 + 0.982718i \(0.559264\pi\)
\(864\) −3.20441 + 3.69808i −0.109016 + 0.125811i
\(865\) −81.3765 23.8943i −2.76688 0.812431i
\(866\) 2.09662 + 14.5823i 0.0712461 + 0.495528i
\(867\) −10.5615 12.1886i −0.358687 0.413947i
\(868\) 0.334867 + 0.733255i 0.0113661 + 0.0248883i
\(869\) 4.88770 1.43516i 0.165804 0.0486844i
\(870\) −1.10596 + 2.42170i −0.0374954 + 0.0821034i
\(871\) −2.34112 + 16.2828i −0.0793258 + 0.551723i
\(872\) −1.78252 + 1.14555i −0.0603636 + 0.0387933i
\(873\) 0.794619 0.0268938
\(874\) 0.330128 8.60581i 0.0111668 0.291096i
\(875\) 6.63416 0.224275
\(876\) 9.98422 6.41647i 0.337336 0.216792i
\(877\) 7.99011 55.5724i 0.269807 1.87655i −0.180355 0.983602i \(-0.557725\pi\)
0.450162 0.892947i \(-0.351366\pi\)
\(878\) −6.17841 + 13.5288i −0.208511 + 0.456576i
\(879\) −0.186781 + 0.0548438i −0.00629996 + 0.00184983i
\(880\) 13.8530 + 30.3339i 0.466985 + 1.02255i
\(881\) 26.6917 + 30.8039i 0.899267 + 1.03781i 0.999084 + 0.0428034i \(0.0136289\pi\)
−0.0998167 + 0.995006i \(0.531826\pi\)
\(882\) −0.432827 3.01038i −0.0145741 0.101365i
\(883\) 7.31464 + 2.14777i 0.246157 + 0.0722783i 0.402484 0.915427i \(-0.368147\pi\)
−0.156326 + 0.987705i \(0.549965\pi\)
\(884\) 7.15972 8.26276i 0.240808 0.277907i
\(885\) 2.99580 + 1.92528i 0.100703 + 0.0647177i
\(886\) 1.30086 + 0.836013i 0.0437033 + 0.0280864i
\(887\) −26.3936 + 30.4598i −0.886210 + 1.02274i 0.113364 + 0.993554i \(0.463837\pi\)
−0.999574 + 0.0291872i \(0.990708\pi\)
\(888\) −14.1675 4.15994i −0.475429 0.139599i
\(889\) 1.08519 + 7.54764i 0.0363960 + 0.253140i
\(890\) 5.16721 + 5.96328i 0.173205 + 0.199890i
\(891\) −1.47314 3.22574i −0.0493522 0.108066i
\(892\) −7.81707 + 2.29530i −0.261735 + 0.0768523i
\(893\) −8.87013 + 19.4229i −0.296828 + 0.649962i
\(894\) 0.633367 4.40517i 0.0211830 0.147331i
\(895\) −7.70415 + 4.95116i −0.257521 + 0.165499i
\(896\) −9.04675 −0.302231
\(897\) −16.1078 27.3124i −0.537823 0.911934i
\(898\) −10.0236 −0.334493
\(899\) 0.752116 0.483356i 0.0250845 0.0161208i
\(900\) 1.85051 12.8706i 0.0616837 0.429019i
\(901\) 2.70797 5.92963i 0.0902156 0.197545i
\(902\) 6.21291 1.82428i 0.206867 0.0607417i
\(903\) 2.29491 + 5.02515i 0.0763698 + 0.167227i
\(904\) 20.4107 + 23.5551i 0.678848 + 0.783433i
\(905\) −5.01480 34.8787i −0.166698 1.15941i
\(906\) 3.87648 + 1.13824i 0.128787 + 0.0378154i
\(907\) 12.7271 14.6878i 0.422595 0.487701i −0.504031 0.863686i \(-0.668150\pi\)
0.926626 + 0.375985i \(0.122696\pi\)
\(908\) −12.9940 8.35074i −0.431221 0.277129i
\(909\) −10.5955 6.80933i −0.351432 0.225851i
\(910\) 5.86963 6.77392i 0.194577 0.224553i
\(911\) 45.9029 + 13.4783i 1.52083 + 0.446556i 0.932230 0.361867i \(-0.117860\pi\)
0.588602 + 0.808423i \(0.299679\pi\)
\(912\) 1.42837 + 9.93450i 0.0472979 + 0.328964i
\(913\) −4.06659 4.69310i −0.134585 0.155319i
\(914\) 0.107878 + 0.236219i 0.00356828 + 0.00781344i
\(915\) 41.3807 12.1505i 1.36800 0.401682i
\(916\) 6.84866 14.9965i 0.226286 0.495498i
\(917\) 1.54683 10.7584i 0.0510808 0.355275i
\(918\) 0.376239 0.241794i 0.0124177 0.00798040i
\(919\) 50.2660 1.65812 0.829061 0.559158i \(-0.188876\pi\)
0.829061 + 0.559158i \(0.188876\pi\)
\(920\) 7.44651 + 29.5002i 0.245504 + 0.972594i
\(921\) 12.9309 0.426087
\(922\) −1.10404 + 0.709526i −0.0363597 + 0.0233670i
\(923\) −12.4722 + 86.7457i −0.410526 + 2.85527i
\(924\) 2.10172 4.60213i 0.0691416 0.151399i
\(925\) 57.6159 16.9176i 1.89440 0.556246i
\(926\) −2.24637 4.91887i −0.0738204 0.161644i
\(927\) −6.93775 8.00660i −0.227866 0.262971i
\(928\) 1.10191 + 7.66397i 0.0361721 + 0.251582i
\(929\) −45.0030 13.2141i −1.47650 0.433540i −0.558295 0.829643i \(-0.688544\pi\)
−0.918206 + 0.396103i \(0.870362\pi\)
\(930\) 0.622537 0.718447i 0.0204138 0.0235588i
\(931\) −20.0338 12.8750i −0.656583 0.421960i
\(932\) 4.39595 + 2.82511i 0.143994 + 0.0925395i
\(933\) −19.6391 + 22.6647i −0.642954 + 0.742008i
\(934\) −2.65708 0.780190i −0.0869424 0.0255286i
\(935\) −1.65590 11.5170i −0.0541536 0.376647i
\(936\) −7.81835 9.02285i −0.255551 0.294921i
\(937\) 0.316944 + 0.694011i 0.0103541 + 0.0226724i 0.914738 0.404047i \(-0.132397\pi\)
−0.904384 + 0.426719i \(0.859669\pi\)
\(938\) −0.921159 + 0.270477i −0.0300769 + 0.00883138i
\(939\) 0.636102 1.39287i 0.0207584 0.0454546i
\(940\) 5.04131 35.0631i 0.164430 1.14363i
\(941\) 27.2858 17.5355i 0.889492 0.571642i −0.0141648 0.999900i \(-0.504509\pi\)
0.903656 + 0.428258i \(0.140873\pi\)
\(942\) 4.49503 0.146456
\(943\) −18.1863 + 1.90663i −0.592226 + 0.0620884i
\(944\) 2.71297 0.0882997
\(945\) −2.38145 + 1.53046i −0.0774684 + 0.0497859i
\(946\) −1.65707 + 11.5252i −0.0538759 + 0.374715i
\(947\) 13.0693 28.6178i 0.424696 0.929954i −0.569462 0.822018i \(-0.692848\pi\)
0.994158 0.107937i \(-0.0344243\pi\)
\(948\) −2.44049 + 0.716593i −0.0792634 + 0.0232738i
\(949\) 18.4096 + 40.3114i 0.597602 + 1.30856i
\(950\) 8.63577 + 9.96622i 0.280182 + 0.323347i
\(951\) −3.02203 21.0187i −0.0979960 0.681577i
\(952\) 1.30374 + 0.382812i 0.0422544 + 0.0124070i
\(953\) 3.07721 3.55129i 0.0996808 0.115038i −0.703717 0.710480i \(-0.748478\pi\)
0.803398 + 0.595442i \(0.203023\pi\)
\(954\) −2.81207 1.80721i −0.0910441 0.0585105i
\(955\) 74.0371 + 47.5808i 2.39578 + 1.53968i
\(956\) −19.0543 + 21.9899i −0.616261 + 0.711203i
\(957\) −5.38398 1.58088i −0.174039 0.0511026i
\(958\) 0.569590 + 3.96158i 0.0184026 + 0.127993i
\(959\) −0.405497 0.467969i −0.0130942 0.0151115i
\(960\) −4.39279 9.61886i −0.141777 0.310448i
\(961\) 29.4380 8.64377i 0.949612 0.278831i
\(962\) 10.7554 23.5510i 0.346768 0.759315i
\(963\) 0.913569 6.35401i 0.0294394 0.204755i
\(964\) 1.96899 1.26539i 0.0634168 0.0407555i
\(965\) 0.350846 0.0112941
\(966\) 1.05941 1.51727i 0.0340859 0.0488172i
\(967\) −26.0335 −0.837180 −0.418590 0.908175i \(-0.637476\pi\)
−0.418590 + 0.908175i \(0.637476\pi\)
\(968\) 2.39337 1.53813i 0.0769259 0.0494373i
\(969\) 0.498380 3.46631i 0.0160103 0.111354i
\(970\) 0.555390 1.21613i 0.0178325 0.0390477i
\(971\) 1.29473 0.380168i 0.0415500 0.0122002i −0.260892 0.965368i \(-0.584016\pi\)
0.302442 + 0.953168i \(0.402198\pi\)
\(972\) 0.735560 + 1.61065i 0.0235931 + 0.0516617i
\(973\) −7.83078 9.03720i −0.251043 0.289719i
\(974\) −0.236386 1.64410i −0.00757430 0.0526804i
\(975\) 46.5863 + 13.6790i 1.49196 + 0.438078i
\(976\) 21.5161 24.8309i 0.688714 0.794818i
\(977\) −10.8844 6.99500i −0.348224 0.223790i 0.354823 0.934934i \(-0.384541\pi\)
−0.703047 + 0.711144i \(0.748178\pi\)
\(978\) −6.89593 4.43175i −0.220508 0.141712i
\(979\) −10.8909 + 12.5687i −0.348074 + 0.401698i
\(980\) 37.9075 + 11.1306i 1.21091 + 0.355555i
\(981\) 0.166994 + 1.16147i 0.00533172 + 0.0370829i
\(982\) 0.115291 + 0.133053i 0.00367907 + 0.00424588i
\(983\) 4.04926 + 8.86663i 0.129151 + 0.282802i 0.963150 0.268964i \(-0.0866814\pi\)
−0.833999 + 0.551766i \(0.813954\pi\)
\(984\) −6.60617 + 1.93975i −0.210597 + 0.0618369i
\(985\) −24.1975 + 52.9851i −0.770996 + 1.68825i
\(986\) 0.100713 0.700475i 0.00320736 0.0223077i
\(987\) −3.85975 + 2.48051i −0.122857 + 0.0789555i
\(988\) −43.8993 −1.39662
\(989\) 10.4664 31.1714i 0.332813 0.991193i
\(990\) −5.96651 −0.189628
\(991\) −17.6477 + 11.3415i −0.560598 + 0.360274i −0.790047 0.613046i \(-0.789944\pi\)
0.229449 + 0.973321i \(0.426308\pi\)
\(992\) 0.393467 2.73662i 0.0124926 0.0868879i
\(993\) 0.337083 0.738109i 0.0106970 0.0234232i
\(994\) −4.90742 + 1.44095i −0.155654 + 0.0457041i
\(995\) −29.2559 64.0615i −0.927474 2.03088i
\(996\) 2.03050 + 2.34332i 0.0643389 + 0.0742511i
\(997\) 1.29155 + 8.98293i 0.0409038 + 0.284492i 0.999999 + 0.00140859i \(0.000448368\pi\)
−0.959095 + 0.283084i \(0.908643\pi\)
\(998\) 6.23705 + 1.83136i 0.197430 + 0.0579708i
\(999\) −5.35482 + 6.17979i −0.169419 + 0.195520i
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 69.2.e.a.58.1 yes 10
3.2 odd 2 207.2.i.b.127.1 10
23.2 even 11 inner 69.2.e.a.25.1 10
23.5 odd 22 1587.2.a.p.1.3 5
23.18 even 11 1587.2.a.o.1.3 5
69.2 odd 22 207.2.i.b.163.1 10
69.5 even 22 4761.2.a.bq.1.3 5
69.41 odd 22 4761.2.a.br.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.a.25.1 10 23.2 even 11 inner
69.2.e.a.58.1 yes 10 1.1 even 1 trivial
207.2.i.b.127.1 10 3.2 odd 2
207.2.i.b.163.1 10 69.2 odd 22
1587.2.a.o.1.3 5 23.18 even 11
1587.2.a.p.1.3 5 23.5 odd 22
4761.2.a.bq.1.3 5 69.5 even 22
4761.2.a.br.1.3 5 69.41 odd 22