Properties

Label 460.2.w.a.3.15
Level $460$
Weight $2$
Character 460.3
Analytic conductor $3.673$
Analytic rank $0$
Dimension $1360$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(3,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([22, 33, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.w (of order \(44\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(1360\)
Relative dimension: \(68\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 3.15
Character \(\chi\) \(=\) 460.3
Dual form 460.2.w.a.307.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11682 + 0.867590i) q^{2} +(-0.106315 - 0.285041i) q^{3} +(0.494574 - 1.93788i) q^{4} +(1.46736 - 1.68726i) q^{5} +(0.366034 + 0.226102i) q^{6} +(3.49451 + 0.760183i) q^{7} +(1.12894 + 2.59336i) q^{8} +(2.19730 - 1.90397i) q^{9} +O(q^{10})\) \(q+(-1.11682 + 0.867590i) q^{2} +(-0.106315 - 0.285041i) q^{3} +(0.494574 - 1.93788i) q^{4} +(1.46736 - 1.68726i) q^{5} +(0.366034 + 0.226102i) q^{6} +(3.49451 + 0.760183i) q^{7} +(1.12894 + 2.59336i) q^{8} +(2.19730 - 1.90397i) q^{9} +(-0.174928 + 3.15744i) q^{10} +(-3.73251 - 0.536654i) q^{11} +(-0.604958 + 0.0650518i) q^{12} +(-0.800200 - 3.67846i) q^{13} +(-4.56226 + 2.18281i) q^{14} +(-0.636941 - 0.238878i) q^{15} +(-3.51079 - 1.91686i) q^{16} +(-4.73719 + 2.58670i) q^{17} +(-0.802123 + 4.03276i) q^{18} +(2.41530 - 0.709197i) q^{19} +(-2.54400 - 3.67805i) q^{20} +(-0.154834 - 1.07690i) q^{21} +(4.63414 - 2.63894i) q^{22} +(4.63283 + 1.23971i) q^{23} +(0.619190 - 0.597506i) q^{24} +(-0.693700 - 4.95164i) q^{25} +(4.08507 + 3.41393i) q^{26} +(-1.57735 - 0.861296i) q^{27} +(3.20144 - 6.39598i) q^{28} +(1.80808 - 6.15776i) q^{29} +(0.918597 - 0.285821i) q^{30} +(-5.95584 + 2.71994i) q^{31} +(5.58397 - 0.905145i) q^{32} +(0.243853 + 1.12097i) q^{33} +(3.04639 - 6.99882i) q^{34} +(6.41033 - 4.78068i) q^{35} +(-2.60295 - 5.19978i) q^{36} +(10.4317 + 0.746087i) q^{37} +(-2.08217 + 2.88754i) q^{38} +(-0.963439 + 0.619165i) q^{39} +(6.03223 + 1.90058i) q^{40} +(-4.73240 + 5.46148i) q^{41} +(1.10723 + 1.06837i) q^{42} +(1.57981 + 4.23562i) q^{43} +(-2.88598 + 6.96776i) q^{44} +(0.0117366 - 6.50124i) q^{45} +(-6.24960 + 2.63486i) q^{46} +(-2.61367 - 2.61367i) q^{47} +(-0.173134 + 1.20451i) q^{48} +(5.26626 + 2.40502i) q^{49} +(5.07074 + 4.92825i) q^{50} +(1.24095 + 1.07529i) q^{51} +(-7.52419 - 0.268577i) q^{52} +(10.3454 + 2.25050i) q^{53} +(2.50886 - 0.406577i) q^{54} +(-6.38242 + 5.51025i) q^{55} +(1.97366 + 9.92070i) q^{56} +(-0.458933 - 0.613062i) q^{57} +(3.32311 + 8.44578i) q^{58} +(-1.68231 - 1.08116i) q^{59} +(-0.777932 + 1.11618i) q^{60} +(-0.467700 - 1.02412i) q^{61} +(4.29181 - 8.20492i) q^{62} +(9.12586 - 4.98309i) q^{63} +(-5.45099 + 5.85548i) q^{64} +(-7.38070 - 4.04748i) q^{65} +(-1.24488 - 1.04036i) q^{66} +(8.40339 - 11.2256i) q^{67} +(2.66983 + 10.4594i) q^{68} +(-0.139170 - 1.45235i) q^{69} +(-3.01151 + 10.9007i) q^{70} +(-4.19127 + 0.602614i) q^{71} +(7.41830 + 3.54892i) q^{72} +(5.00399 + 2.73238i) q^{73} +(-12.2976 + 8.21716i) q^{74} +(-1.33767 + 0.724167i) q^{75} +(-0.179794 - 5.03133i) q^{76} +(-12.6353 - 4.71273i) q^{77} +(0.538807 - 1.52737i) q^{78} +(-3.50409 - 2.25194i) q^{79} +(-8.38584 + 3.11090i) q^{80} +(1.16351 - 8.09239i) q^{81} +(0.546913 - 10.2053i) q^{82} +(-14.7120 - 1.05222i) q^{83} +(-2.16348 - 0.232555i) q^{84} +(-2.58673 + 11.7885i) q^{85} +(-5.43914 - 3.35980i) q^{86} +(-1.94744 + 0.139284i) q^{87} +(-2.82204 - 10.2856i) q^{88} +(8.03445 + 3.66921i) q^{89} +(5.62731 + 7.27090i) q^{90} -13.4627i q^{91} +(4.69370 - 8.36476i) q^{92} +(1.40849 + 1.40849i) q^{93} +(5.18659 + 0.651405i) q^{94} +(2.34752 - 5.11589i) q^{95} +(-0.851663 - 1.49543i) q^{96} +(0.323748 + 4.52658i) q^{97} +(-7.96804 + 1.88298i) q^{98} +(-9.22323 + 5.92741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{8}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11682 + 0.867590i −0.789711 + 0.613479i
\(3\) −0.106315 0.285041i −0.0613809 0.164569i 0.902639 0.430398i \(-0.141627\pi\)
−0.964020 + 0.265830i \(0.914354\pi\)
\(4\) 0.494574 1.93788i 0.247287 0.968942i
\(5\) 1.46736 1.68726i 0.656224 0.754566i
\(6\) 0.366034 + 0.226102i 0.149433 + 0.0923058i
\(7\) 3.49451 + 0.760183i 1.32080 + 0.287322i 0.817069 0.576539i \(-0.195597\pi\)
0.503729 + 0.863861i \(0.331961\pi\)
\(8\) 1.12894 + 2.59336i 0.399140 + 0.916890i
\(9\) 2.19730 1.90397i 0.732434 0.634658i
\(10\) −0.174928 + 3.15744i −0.0553170 + 0.998469i
\(11\) −3.73251 0.536654i −1.12539 0.161807i −0.445615 0.895225i \(-0.647015\pi\)
−0.679779 + 0.733417i \(0.737924\pi\)
\(12\) −0.604958 + 0.0650518i −0.174636 + 0.0187788i
\(13\) −0.800200 3.67846i −0.221935 1.02022i −0.944396 0.328809i \(-0.893353\pi\)
0.722461 0.691412i \(-0.243011\pi\)
\(14\) −4.56226 + 2.18281i −1.21932 + 0.583381i
\(15\) −0.636941 0.238878i −0.164458 0.0616779i
\(16\) −3.51079 1.91686i −0.877698 0.479214i
\(17\) −4.73719 + 2.58670i −1.14894 + 0.627367i −0.936797 0.349872i \(-0.886225\pi\)
−0.212140 + 0.977239i \(0.568043\pi\)
\(18\) −0.802123 + 4.03276i −0.189062 + 0.950529i
\(19\) 2.41530 0.709197i 0.554108 0.162701i 0.00732216 0.999973i \(-0.497669\pi\)
0.546786 + 0.837272i \(0.315851\pi\)
\(20\) −2.54400 3.67805i −0.568855 0.822438i
\(21\) −0.154834 1.07690i −0.0337876 0.234998i
\(22\) 4.63414 2.63894i 0.988001 0.562624i
\(23\) 4.63283 + 1.23971i 0.966012 + 0.258498i
\(24\) 0.619190 0.597506i 0.126392 0.121965i
\(25\) −0.693700 4.95164i −0.138740 0.990329i
\(26\) 4.08507 + 3.41393i 0.801149 + 0.669527i
\(27\) −1.57735 0.861296i −0.303560 0.165757i
\(28\) 3.20144 6.39598i 0.605015 1.20873i
\(29\) 1.80808 6.15776i 0.335752 1.14347i −0.602674 0.797987i \(-0.705898\pi\)
0.938426 0.345479i \(-0.112284\pi\)
\(30\) 0.918597 0.285821i 0.167712 0.0521835i
\(31\) −5.95584 + 2.71994i −1.06970 + 0.488516i −0.870868 0.491517i \(-0.836442\pi\)
−0.198833 + 0.980033i \(0.563715\pi\)
\(32\) 5.58397 0.905145i 0.987116 0.160009i
\(33\) 0.243853 + 1.12097i 0.0424493 + 0.195136i
\(34\) 3.04639 6.99882i 0.522452 1.20029i
\(35\) 6.41033 4.78068i 1.08354 0.808082i
\(36\) −2.60295 5.19978i −0.433825 0.866629i
\(37\) 10.4317 + 0.746087i 1.71495 + 0.122656i 0.893921 0.448225i \(-0.147944\pi\)
0.821033 + 0.570881i \(0.193398\pi\)
\(38\) −2.08217 + 2.88754i −0.337772 + 0.468420i
\(39\) −0.963439 + 0.619165i −0.154274 + 0.0991457i
\(40\) 6.03223 + 1.90058i 0.953779 + 0.300508i
\(41\) −4.73240 + 5.46148i −0.739077 + 0.852940i −0.993462 0.114163i \(-0.963582\pi\)
0.254385 + 0.967103i \(0.418127\pi\)
\(42\) 1.10723 + 1.06837i 0.170849 + 0.164853i
\(43\) 1.57981 + 4.23562i 0.240918 + 0.645926i 0.999987 0.00508379i \(-0.00161823\pi\)
−0.759069 + 0.651010i \(0.774346\pi\)
\(44\) −2.88598 + 6.96776i −0.435077 + 1.05043i
\(45\) 0.0117366 6.50124i 0.00174959 0.969148i
\(46\) −6.24960 + 2.63486i −0.921453 + 0.388489i
\(47\) −2.61367 2.61367i −0.381243 0.381243i 0.490307 0.871550i \(-0.336885\pi\)
−0.871550 + 0.490307i \(0.836885\pi\)
\(48\) −0.173134 + 1.20451i −0.0249897 + 0.173856i
\(49\) 5.26626 + 2.40502i 0.752324 + 0.343575i
\(50\) 5.07074 + 4.92825i 0.717110 + 0.696960i
\(51\) 1.24095 + 1.07529i 0.173768 + 0.150571i
\(52\) −7.52419 0.268577i −1.04342 0.0372450i
\(53\) 10.3454 + 2.25050i 1.42105 + 0.309131i 0.856448 0.516233i \(-0.172666\pi\)
0.564602 + 0.825363i \(0.309030\pi\)
\(54\) 2.50886 0.406577i 0.341413 0.0553281i
\(55\) −6.38242 + 5.51025i −0.860605 + 0.743002i
\(56\) 1.97366 + 9.92070i 0.263741 + 1.32571i
\(57\) −0.458933 0.613062i −0.0607871 0.0812021i
\(58\) 3.32311 + 8.44578i 0.436345 + 1.10898i
\(59\) −1.68231 1.08116i −0.219018 0.140755i 0.426531 0.904473i \(-0.359735\pi\)
−0.645550 + 0.763718i \(0.723372\pi\)
\(60\) −0.777932 + 1.11618i −0.100431 + 0.144098i
\(61\) −0.467700 1.02412i −0.0598828 0.131125i 0.877325 0.479897i \(-0.159326\pi\)
−0.937208 + 0.348772i \(0.886599\pi\)
\(62\) 4.29181 8.20492i 0.545060 1.04203i
\(63\) 9.12586 4.98309i 1.14975 0.627811i
\(64\) −5.45099 + 5.85548i −0.681374 + 0.731935i
\(65\) −7.38070 4.04748i −0.915464 0.502029i
\(66\) −1.24488 1.04036i −0.153235 0.128060i
\(67\) 8.40339 11.2256i 1.02664 1.37143i 0.100204 0.994967i \(-0.468050\pi\)
0.926433 0.376460i \(-0.122859\pi\)
\(68\) 2.66983 + 10.4594i 0.323765 + 1.26839i
\(69\) −0.139170 1.45235i −0.0167541 0.174842i
\(70\) −3.01151 + 10.9007i −0.359945 + 1.30288i
\(71\) −4.19127 + 0.602614i −0.497412 + 0.0715171i −0.386455 0.922308i \(-0.626301\pi\)
−0.110957 + 0.993825i \(0.535392\pi\)
\(72\) 7.41830 + 3.54892i 0.874255 + 0.418244i
\(73\) 5.00399 + 2.73238i 0.585672 + 0.319801i 0.744623 0.667485i \(-0.232629\pi\)
−0.158951 + 0.987287i \(0.550811\pi\)
\(74\) −12.2976 + 8.21716i −1.42956 + 0.955225i
\(75\) −1.33767 + 0.724167i −0.154461 + 0.0836196i
\(76\) −0.179794 5.03133i −0.0206238 0.577133i
\(77\) −12.6353 4.71273i −1.43993 0.537065i
\(78\) 0.538807 1.52737i 0.0610079 0.172940i
\(79\) −3.50409 2.25194i −0.394240 0.253363i 0.328469 0.944515i \(-0.393467\pi\)
−0.722710 + 0.691152i \(0.757104\pi\)
\(80\) −8.38584 + 3.11090i −0.937565 + 0.347809i
\(81\) 1.16351 8.09239i 0.129279 0.899154i
\(82\) 0.546913 10.2053i 0.0603964 1.12698i
\(83\) −14.7120 1.05222i −1.61485 0.115496i −0.765540 0.643389i \(-0.777528\pi\)
−0.849311 + 0.527892i \(0.822983\pi\)
\(84\) −2.16348 0.232555i −0.236055 0.0253738i
\(85\) −2.58673 + 11.7885i −0.280570 + 1.27864i
\(86\) −5.43914 3.35980i −0.586518 0.362297i
\(87\) −1.94744 + 0.139284i −0.208787 + 0.0149328i
\(88\) −2.82204 10.2856i −0.300830 1.09645i
\(89\) 8.03445 + 3.66921i 0.851650 + 0.388935i 0.792911 0.609338i \(-0.208565\pi\)
0.0587391 + 0.998273i \(0.481292\pi\)
\(90\) 5.62731 + 7.27090i 0.593170 + 0.766420i
\(91\) 13.4627i 1.41127i
\(92\) 4.69370 8.36476i 0.489352 0.872086i
\(93\) 1.40849 + 1.40849i 0.146054 + 0.146054i
\(94\) 5.18659 + 0.651405i 0.534956 + 0.0671873i
\(95\) 2.34752 5.11589i 0.240851 0.524880i
\(96\) −0.851663 1.49543i −0.0869224 0.152627i
\(97\) 0.323748 + 4.52658i 0.0328716 + 0.459605i 0.987055 + 0.160382i \(0.0512727\pi\)
−0.954183 + 0.299222i \(0.903273\pi\)
\(98\) −7.96804 + 1.88298i −0.804894 + 0.190210i
\(99\) −9.22323 + 5.92741i −0.926969 + 0.595727i
\(100\) −9.93880 1.10465i −0.993880 0.110465i
\(101\) 8.48439 + 9.79151i 0.844228 + 0.974291i 0.999909 0.0135161i \(-0.00430244\pi\)
−0.155680 + 0.987807i \(0.549757\pi\)
\(102\) −2.31883 0.124269i −0.229598 0.0123044i
\(103\) 5.69491 + 7.60751i 0.561136 + 0.749590i 0.987954 0.154747i \(-0.0494564\pi\)
−0.426818 + 0.904338i \(0.640365\pi\)
\(104\) 8.63618 6.22796i 0.846847 0.610702i
\(105\) −2.04420 1.31895i −0.199494 0.128716i
\(106\) −13.5065 + 6.46216i −1.31186 + 0.627661i
\(107\) −6.31994 + 16.9444i −0.610971 + 1.63808i 0.149542 + 0.988755i \(0.452220\pi\)
−0.760513 + 0.649322i \(0.775053\pi\)
\(108\) −2.44921 + 2.63074i −0.235675 + 0.253143i
\(109\) 0.132242 0.450375i 0.0126665 0.0431381i −0.952917 0.303230i \(-0.901935\pi\)
0.965584 + 0.260092i \(0.0837530\pi\)
\(110\) 2.34737 11.6913i 0.223813 1.11472i
\(111\) −0.896375 3.05277i −0.0850801 0.289756i
\(112\) −10.8113 9.36731i −1.02157 0.885128i
\(113\) −1.81362 + 2.42272i −0.170611 + 0.227910i −0.877695 0.479220i \(-0.840920\pi\)
0.707083 + 0.707130i \(0.250011\pi\)
\(114\) 1.04443 + 0.286515i 0.0978200 + 0.0268346i
\(115\) 8.88975 5.99769i 0.828974 0.559287i
\(116\) −11.0388 6.54932i −1.02493 0.608089i
\(117\) −8.76197 6.55913i −0.810045 0.606392i
\(118\) 2.81684 0.252100i 0.259311 0.0232077i
\(119\) −18.5205 + 5.43811i −1.69777 + 0.498511i
\(120\) −0.0995732 1.92149i −0.00908974 0.175408i
\(121\) 3.08920 + 0.907072i 0.280837 + 0.0824611i
\(122\) 1.41085 + 0.737986i 0.127733 + 0.0668141i
\(123\) 2.05987 + 0.768293i 0.185732 + 0.0692746i
\(124\) 2.32533 + 12.8869i 0.208820 + 1.15728i
\(125\) −9.37263 6.09540i −0.838313 0.545189i
\(126\) −5.86866 + 13.4827i −0.522821 + 1.20114i
\(127\) −10.6323 + 7.95925i −0.943465 + 0.706269i −0.955912 0.293653i \(-0.905129\pi\)
0.0124469 + 0.999923i \(0.496038\pi\)
\(128\) 1.00762 11.2687i 0.0890621 0.996026i
\(129\) 1.03937 0.900619i 0.0915114 0.0792951i
\(130\) 11.7545 1.88312i 1.03094 0.165160i
\(131\) 5.00499 + 7.78791i 0.437288 + 0.680433i 0.988033 0.154240i \(-0.0492929\pi\)
−0.550746 + 0.834673i \(0.685657\pi\)
\(132\) 2.29292 + 0.0818462i 0.199573 + 0.00712380i
\(133\) 8.97940 0.642220i 0.778613 0.0556875i
\(134\) 0.354158 + 19.8277i 0.0305946 + 1.71285i
\(135\) −3.76777 + 1.39756i −0.324278 + 0.120283i
\(136\) −12.0562 9.36499i −1.03381 0.803041i
\(137\) −2.93560 + 2.93560i −0.250805 + 0.250805i −0.821301 0.570495i \(-0.806751\pi\)
0.570495 + 0.821301i \(0.306751\pi\)
\(138\) 1.41547 + 1.50127i 0.120493 + 0.127796i
\(139\) 11.0285 0.935427 0.467713 0.883880i \(-0.345078\pi\)
0.467713 + 0.883880i \(0.345078\pi\)
\(140\) −6.09402 14.7869i −0.515039 1.24972i
\(141\) −0.467132 + 1.02288i −0.0393396 + 0.0861417i
\(142\) 4.15807 4.30932i 0.348938 0.361630i
\(143\) 1.01269 + 14.1593i 0.0846857 + 1.18406i
\(144\) −11.3639 + 2.47254i −0.946993 + 0.206045i
\(145\) −7.73663 12.0864i −0.642492 1.00372i
\(146\) −7.95914 + 1.28983i −0.658703 + 0.106747i
\(147\) 0.125648 1.75679i 0.0103633 0.144898i
\(148\) 6.60506 19.8463i 0.542933 1.63136i
\(149\) −12.3693 1.77843i −1.01333 0.145695i −0.384407 0.923164i \(-0.625594\pi\)
−0.628921 + 0.777469i \(0.716503\pi\)
\(150\) 0.865659 1.96931i 0.0706808 0.160794i
\(151\) 5.68374 8.84407i 0.462536 0.719720i −0.529132 0.848539i \(-0.677482\pi\)
0.991668 + 0.128820i \(0.0411188\pi\)
\(152\) 4.56593 + 5.46310i 0.370346 + 0.443116i
\(153\) −5.48403 + 14.7033i −0.443357 + 1.18869i
\(154\) 18.2001 5.69901i 1.46661 0.459239i
\(155\) −4.15012 + 14.0402i −0.333346 + 1.12774i
\(156\) 0.723377 + 2.17326i 0.0579165 + 0.174000i
\(157\) −5.32722 + 9.75608i −0.425159 + 0.778620i −0.999191 0.0402124i \(-0.987197\pi\)
0.574032 + 0.818833i \(0.305378\pi\)
\(158\) 5.86719 0.525099i 0.466769 0.0417747i
\(159\) −0.458384 3.18813i −0.0363522 0.252835i
\(160\) 6.66649 10.7498i 0.527032 0.849845i
\(161\) 15.2470 + 7.85398i 1.20164 + 0.618980i
\(162\) 5.72145 + 10.0472i 0.449519 + 0.789382i
\(163\) −6.53983 4.89566i −0.512239 0.383457i 0.311660 0.950194i \(-0.399115\pi\)
−0.823899 + 0.566736i \(0.808206\pi\)
\(164\) 8.24320 + 11.8720i 0.643686 + 0.927044i
\(165\) 2.24919 + 1.23343i 0.175100 + 0.0960224i
\(166\) 17.3435 11.5888i 1.34612 0.899468i
\(167\) 9.96455 + 18.2487i 0.771080 + 1.41213i 0.906879 + 0.421391i \(0.138458\pi\)
−0.135799 + 0.990736i \(0.543360\pi\)
\(168\) 2.61798 1.61729i 0.201981 0.124777i
\(169\) −1.06553 + 0.486610i −0.0819636 + 0.0374315i
\(170\) −7.33868 15.4099i −0.562851 1.18188i
\(171\) 3.95686 6.15699i 0.302589 0.470837i
\(172\) 8.98948 0.966650i 0.685441 0.0737063i
\(173\) −10.3564 + 7.75269i −0.787381 + 0.589426i −0.915493 0.402334i \(-0.868199\pi\)
0.128112 + 0.991760i \(0.459108\pi\)
\(174\) 2.05410 1.84513i 0.155721 0.139879i
\(175\) 1.34002 17.8309i 0.101296 1.34789i
\(176\) 12.0754 + 9.03876i 0.910216 + 0.681322i
\(177\) −0.129319 + 0.594471i −0.00972023 + 0.0446832i
\(178\) −12.1564 + 2.87276i −0.911161 + 0.215323i
\(179\) 4.68355 5.40511i 0.350065 0.403997i −0.553222 0.833034i \(-0.686602\pi\)
0.903287 + 0.429038i \(0.141147\pi\)
\(180\) −12.5929 3.23809i −0.938616 0.241353i
\(181\) −2.51926 + 5.51641i −0.187255 + 0.410032i −0.979855 0.199711i \(-0.936000\pi\)
0.792600 + 0.609742i \(0.208727\pi\)
\(182\) 11.6801 + 15.0354i 0.865787 + 1.11450i
\(183\) −0.242193 + 0.242193i −0.0179034 + 0.0179034i
\(184\) 2.01517 + 13.4141i 0.148560 + 0.988903i
\(185\) 16.5659 16.5061i 1.21795 1.21356i
\(186\) −2.79502 0.351038i −0.204941 0.0257393i
\(187\) 19.0698 7.11265i 1.39452 0.520129i
\(188\) −6.35764 + 3.77234i −0.463679 + 0.275126i
\(189\) −4.85730 4.20888i −0.353317 0.306151i
\(190\) 1.81674 + 7.75022i 0.131800 + 0.562260i
\(191\) −8.35288 12.9973i −0.604393 0.940454i −0.999759 0.0219305i \(-0.993019\pi\)
0.395366 0.918523i \(-0.370618\pi\)
\(192\) 2.24858 + 0.931233i 0.162277 + 0.0672060i
\(193\) −0.602954 + 8.43040i −0.0434016 + 0.606834i 0.928483 + 0.371375i \(0.121114\pi\)
−0.971884 + 0.235458i \(0.924341\pi\)
\(194\) −4.28879 4.77450i −0.307917 0.342789i
\(195\) −0.369021 + 2.53411i −0.0264261 + 0.181472i
\(196\) 7.26522 9.01595i 0.518944 0.643996i
\(197\) −8.33475 + 1.81311i −0.593826 + 0.129179i −0.499428 0.866355i \(-0.666456\pi\)
−0.0943985 + 0.995534i \(0.530093\pi\)
\(198\) 5.15813 14.6218i 0.366572 1.03913i
\(199\) −0.273343 0.598537i −0.0193767 0.0424292i 0.899696 0.436517i \(-0.143788\pi\)
−0.919073 + 0.394087i \(0.871061\pi\)
\(200\) 12.0582 7.38912i 0.852646 0.522489i
\(201\) −4.09317 1.20186i −0.288710 0.0847728i
\(202\) −17.9706 3.57438i −1.26440 0.251492i
\(203\) 10.9994 20.1438i 0.772004 1.41382i
\(204\) 2.69753 1.87301i 0.188865 0.131137i
\(205\) 2.27080 + 15.9988i 0.158600 + 1.11740i
\(206\) −12.9604 3.55537i −0.902993 0.247714i
\(207\) 12.5401 6.09676i 0.871598 0.423754i
\(208\) −4.24174 + 14.4482i −0.294112 + 1.00180i
\(209\) −9.39573 + 1.35090i −0.649916 + 0.0934438i
\(210\) 3.42732 0.300501i 0.236507 0.0207365i
\(211\) 1.51254 + 5.15125i 0.104128 + 0.354627i 0.995031 0.0995668i \(-0.0317457\pi\)
−0.890903 + 0.454193i \(0.849928\pi\)
\(212\) 9.47779 18.9352i 0.650937 1.30047i
\(213\) 0.617364 + 1.13062i 0.0423011 + 0.0774687i
\(214\) −7.64257 24.4070i −0.522435 1.66843i
\(215\) 9.46475 + 3.54965i 0.645490 + 0.242084i
\(216\) 0.452921 5.06297i 0.0308173 0.344492i
\(217\) −22.8804 + 4.97732i −1.55322 + 0.337883i
\(218\) 0.243050 + 0.617720i 0.0164615 + 0.0418373i
\(219\) 0.246844 1.71683i 0.0166801 0.116013i
\(220\) 7.52165 + 15.0936i 0.507110 + 1.01761i
\(221\) 13.3058 + 15.3557i 0.895043 + 1.03293i
\(222\) 3.64964 + 2.63171i 0.244948 + 0.176629i
\(223\) −3.75535 + 17.2631i −0.251477 + 1.15602i 0.662120 + 0.749398i \(0.269657\pi\)
−0.913596 + 0.406622i \(0.866707\pi\)
\(224\) 20.2013 + 1.08181i 1.34976 + 0.0722811i
\(225\) −10.9521 9.55948i −0.730138 0.637298i
\(226\) −0.0764346 4.27922i −0.00508436 0.284650i
\(227\) 11.9454 4.45540i 0.792844 0.295715i 0.0797780 0.996813i \(-0.474579\pi\)
0.713066 + 0.701097i \(0.247306\pi\)
\(228\) −1.41502 + 0.586154i −0.0937120 + 0.0388190i
\(229\) 0.0730179i 0.00482516i −0.999997 0.00241258i \(-0.999232\pi\)
0.999997 0.00241258i \(-0.000767949\pi\)
\(230\) −4.72472 + 14.4110i −0.311539 + 0.950233i
\(231\) 4.10262i 0.269933i
\(232\) 18.0105 2.26273i 1.18244 0.148556i
\(233\) 6.25526 2.33309i 0.409796 0.152846i −0.136108 0.990694i \(-0.543459\pi\)
0.545903 + 0.837848i \(0.316187\pi\)
\(234\) 15.4762 0.276432i 1.01171 0.0180710i
\(235\) −8.24514 + 0.574745i −0.537854 + 0.0374922i
\(236\) −2.92718 + 2.72541i −0.190543 + 0.177409i
\(237\) −0.269359 + 1.23822i −0.0174967 + 0.0804313i
\(238\) 15.9660 22.1416i 1.03492 1.43523i
\(239\) 9.42269 + 10.8744i 0.609503 + 0.703404i 0.973678 0.227926i \(-0.0731945\pi\)
−0.364175 + 0.931330i \(0.618649\pi\)
\(240\) 1.77827 + 2.05957i 0.114787 + 0.132945i
\(241\) −2.37992 + 16.5527i −0.153304 + 1.06625i 0.757328 + 0.653035i \(0.226505\pi\)
−0.910632 + 0.413219i \(0.864404\pi\)
\(242\) −4.23705 + 1.66713i −0.272368 + 0.107167i
\(243\) −7.69869 + 1.67475i −0.493871 + 0.107435i
\(244\) −2.21594 + 0.399845i −0.141861 + 0.0255974i
\(245\) 11.7854 5.35653i 0.752943 0.342216i
\(246\) −2.96707 + 0.929080i −0.189173 + 0.0592360i
\(247\) −4.54148 8.31709i −0.288967 0.529204i
\(248\) −13.7776 12.3750i −0.874876 0.785811i
\(249\) 1.26418 + 4.30539i 0.0801140 + 0.272843i
\(250\) 15.7558 1.32414i 0.996487 0.0837457i
\(251\) −4.15249 + 0.597037i −0.262103 + 0.0376847i −0.272113 0.962265i \(-0.587723\pi\)
0.0100107 + 0.999950i \(0.496813\pi\)
\(252\) −5.14325 20.1494i −0.323994 1.26929i
\(253\) −16.6268 7.11346i −1.04532 0.447220i
\(254\) 4.96901 18.1135i 0.311784 1.13654i
\(255\) 3.63522 0.515969i 0.227646 0.0323112i
\(256\) 8.65132 + 13.4594i 0.540708 + 0.841211i
\(257\) 5.07062 9.28615i 0.316297 0.579254i −0.670366 0.742030i \(-0.733863\pi\)
0.986663 + 0.162776i \(0.0520449\pi\)
\(258\) −0.379421 + 1.90758i −0.0236217 + 0.118761i
\(259\) 35.8863 + 10.5372i 2.22987 + 0.654748i
\(260\) −11.4939 + 12.3012i −0.712819 + 0.762886i
\(261\) −7.75131 16.9730i −0.479794 1.05060i
\(262\) −12.3464 4.35542i −0.762762 0.269079i
\(263\) −2.27280 + 0.494416i −0.140147 + 0.0304870i −0.282091 0.959388i \(-0.591028\pi\)
0.141945 + 0.989875i \(0.454664\pi\)
\(264\) −2.63179 + 1.89791i −0.161975 + 0.116808i
\(265\) 18.9776 14.1531i 1.16579 0.869418i
\(266\) −9.47120 + 8.50769i −0.580716 + 0.521640i
\(267\) 0.191695 2.68024i 0.0117315 0.164028i
\(268\) −17.5978 21.8367i −1.07496 1.33389i
\(269\) 5.81472 + 9.04788i 0.354530 + 0.551659i 0.972014 0.234925i \(-0.0754843\pi\)
−0.617484 + 0.786583i \(0.711848\pi\)
\(270\) 2.99541 4.82970i 0.182295 0.293926i
\(271\) 5.68144 + 4.92299i 0.345123 + 0.299051i 0.810123 0.586260i \(-0.199400\pi\)
−0.465000 + 0.885311i \(0.653946\pi\)
\(272\) 21.5896 0.000858085i 1.30906 5.20290e-5i
\(273\) −3.83742 + 1.43128i −0.232251 + 0.0866253i
\(274\) 0.731640 5.82544i 0.0442000 0.351927i
\(275\) −0.0680754 + 18.8543i −0.00410510 + 1.13696i
\(276\) −2.88331 0.448599i −0.173555 0.0270025i
\(277\) −19.1989 + 19.1989i −1.15355 + 1.15355i −0.167711 + 0.985836i \(0.553638\pi\)
−0.985836 + 0.167711i \(0.946362\pi\)
\(278\) −12.3169 + 9.56823i −0.738717 + 0.573865i
\(279\) −7.90809 + 17.3163i −0.473445 + 1.03670i
\(280\) 19.6349 + 11.2272i 1.17341 + 0.670952i
\(281\) 14.8498 17.1376i 0.885867 1.02234i −0.113717 0.993513i \(-0.536276\pi\)
0.999584 0.0288317i \(-0.00917870\pi\)
\(282\) −0.365735 1.54765i −0.0217792 0.0921610i
\(283\) 6.00546 27.6067i 0.356988 1.64105i −0.352127 0.935952i \(-0.614541\pi\)
0.709115 0.705093i \(-0.249095\pi\)
\(284\) −0.905100 + 8.42024i −0.0537078 + 0.499649i
\(285\) −1.70782 0.125245i −0.101162 0.00741886i
\(286\) −13.4155 14.9348i −0.793274 0.883113i
\(287\) −20.6891 + 15.4877i −1.22124 + 0.914209i
\(288\) 10.5463 12.6206i 0.621447 0.743677i
\(289\) 6.55904 10.2061i 0.385826 0.600357i
\(290\) 19.1264 + 6.78606i 1.12314 + 0.398491i
\(291\) 1.25584 0.573524i 0.0736188 0.0336206i
\(292\) 7.76989 8.34578i 0.454698 0.488400i
\(293\) 3.36376 + 6.16027i 0.196513 + 0.359887i 0.957291 0.289125i \(-0.0933643\pi\)
−0.760778 + 0.649012i \(0.775182\pi\)
\(294\) 1.38385 + 2.07103i 0.0807077 + 0.120785i
\(295\) −4.29275 + 1.25205i −0.249934 + 0.0728973i
\(296\) 9.84183 + 27.8953i 0.572045 + 1.62138i
\(297\) 5.42524 + 4.06128i 0.314804 + 0.235660i
\(298\) 15.3572 8.74526i 0.889618 0.506599i
\(299\) 0.853042 18.0337i 0.0493327 1.04292i
\(300\) 0.741773 + 2.95041i 0.0428263 + 0.170342i
\(301\) 2.30079 + 16.0023i 0.132615 + 0.922360i
\(302\) 1.32531 + 14.8084i 0.0762633 + 0.852127i
\(303\) 1.88897 3.45938i 0.108518 0.198736i
\(304\) −9.83905 2.13995i −0.564308 0.122734i
\(305\) −2.41424 0.713622i −0.138239 0.0408619i
\(306\) −6.63172 21.1788i −0.379110 1.21071i
\(307\) 0.326200 0.874576i 0.0186172 0.0499147i −0.927309 0.374298i \(-0.877884\pi\)
0.945926 + 0.324383i \(0.105157\pi\)
\(308\) −15.3818 + 22.1550i −0.876461 + 1.26240i
\(309\) 1.56300 2.43208i 0.0889160 0.138356i
\(310\) −7.54620 19.2810i −0.428595 1.09509i
\(311\) −13.0089 1.87040i −0.737667 0.106060i −0.236768 0.971566i \(-0.576088\pi\)
−0.500899 + 0.865506i \(0.666997\pi\)
\(312\) −2.69338 1.79954i −0.152483 0.101879i
\(313\) −1.08310 + 15.1437i −0.0612204 + 0.855974i 0.870355 + 0.492425i \(0.163889\pi\)
−0.931575 + 0.363548i \(0.881565\pi\)
\(314\) −2.51473 15.5176i −0.141914 0.875711i
\(315\) 4.98315 22.7097i 0.280769 1.27955i
\(316\) −6.09703 + 5.67676i −0.342985 + 0.319343i
\(317\) −1.65670 23.1637i −0.0930495 1.30100i −0.802672 0.596420i \(-0.796589\pi\)
0.709623 0.704582i \(-0.248865\pi\)
\(318\) 3.27792 + 3.16288i 0.183817 + 0.177365i
\(319\) −10.0533 + 22.0136i −0.562874 + 1.23252i
\(320\) 1.88115 + 17.7894i 0.105159 + 0.994455i
\(321\) 5.50176 0.307078
\(322\) −23.8422 + 4.45670i −1.32868 + 0.248362i
\(323\) −9.60726 + 9.60726i −0.534562 + 0.534562i
\(324\) −15.1067 6.25704i −0.839259 0.347613i
\(325\) −17.6593 + 6.51405i −0.979563 + 0.361335i
\(326\) 11.5512 0.206326i 0.639764 0.0114273i
\(327\) −0.142435 + 0.0101871i −0.00787666 + 0.000563350i
\(328\) −19.5062 6.10713i −1.07705 0.337210i
\(329\) −7.14662 11.1204i −0.394006 0.613085i
\(330\) −3.58206 + 0.573860i −0.197186 + 0.0315900i
\(331\) 1.77479 1.53787i 0.0975513 0.0845287i −0.604720 0.796438i \(-0.706715\pi\)
0.702271 + 0.711910i \(0.252169\pi\)
\(332\) −9.31526 + 27.9897i −0.511241 + 1.53614i
\(333\) 24.3420 18.2222i 1.33394 0.998571i
\(334\) −26.9610 11.7354i −1.47524 0.642131i
\(335\) −6.60973 30.6507i −0.361128 1.67463i
\(336\) −1.52067 + 4.07756i −0.0829591 + 0.222449i
\(337\) 23.8104 + 8.88084i 1.29704 + 0.483770i 0.900743 0.434353i \(-0.143023\pi\)
0.396295 + 0.918123i \(0.370296\pi\)
\(338\) 0.767824 1.46790i 0.0417641 0.0798430i
\(339\) 0.883390 + 0.259387i 0.0479792 + 0.0140880i
\(340\) 21.5654 + 10.8431i 1.16955 + 0.588048i
\(341\) 23.6899 6.95598i 1.28288 0.376688i
\(342\) 0.922647 + 10.3092i 0.0498910 + 0.557457i
\(343\) −3.46572 2.59441i −0.187131 0.140085i
\(344\) −9.20098 + 8.87876i −0.496083 + 0.478711i
\(345\) −2.65470 1.89630i −0.142924 0.102094i
\(346\) 4.84006 17.6435i 0.260203 0.948518i
\(347\) −12.3388 + 16.4827i −0.662382 + 0.884839i −0.998373 0.0570262i \(-0.981838\pi\)
0.335990 + 0.941865i \(0.390929\pi\)
\(348\) −0.693238 + 3.84280i −0.0371615 + 0.205996i
\(349\) −5.52014 18.7999i −0.295486 1.00633i −0.964719 0.263281i \(-0.915195\pi\)
0.669233 0.743053i \(-0.266623\pi\)
\(350\) 13.9733 + 21.0765i 0.746907 + 1.12659i
\(351\) −1.90605 + 6.49141i −0.101737 + 0.346486i
\(352\) −21.3280 + 0.381804i −1.13678 + 0.0203502i
\(353\) 4.11715 11.0385i 0.219134 0.587521i −0.780141 0.625604i \(-0.784852\pi\)
0.999275 + 0.0380833i \(0.0121252\pi\)
\(354\) −0.371331 0.776114i −0.0197360 0.0412500i
\(355\) −5.13334 + 7.95602i −0.272450 + 0.422262i
\(356\) 11.0841 13.7551i 0.587458 0.729021i
\(357\) 3.51909 + 4.70095i 0.186250 + 0.248801i
\(358\) −0.541267 + 10.0999i −0.0286069 + 0.533798i
\(359\) −15.6354 18.0443i −0.825207 0.952340i 0.174269 0.984698i \(-0.444244\pi\)
−0.999476 + 0.0323585i \(0.989698\pi\)
\(360\) 16.8733 7.30907i 0.889300 0.385222i
\(361\) −10.6531 + 6.84633i −0.560689 + 0.360333i
\(362\) −1.97242 8.34653i −0.103668 0.438684i
\(363\) −0.0698754 0.976985i −0.00366751 0.0512784i
\(364\) −26.0891 6.65830i −1.36744 0.348990i
\(365\) 11.9529 4.43364i 0.625643 0.232067i
\(366\) 0.0603617 0.480610i 0.00315516 0.0251219i
\(367\) −5.34779 5.34779i −0.279153 0.279153i 0.553618 0.832771i \(-0.313247\pi\)
−0.832771 + 0.553618i \(0.813247\pi\)
\(368\) −13.8886 13.2328i −0.723991 0.689810i
\(369\) 21.0109i 1.09378i
\(370\) −4.18051 + 32.8068i −0.217334 + 1.70554i
\(371\) 34.4413 + 15.7288i 1.78810 + 0.816599i
\(372\) 3.42609 2.03289i 0.177635 0.105400i
\(373\) 4.93744 0.353133i 0.255651 0.0182845i 0.0570746 0.998370i \(-0.481823\pi\)
0.198577 + 0.980085i \(0.436368\pi\)
\(374\) −15.1266 + 24.4883i −0.782179 + 1.26626i
\(375\) −0.740990 + 3.31962i −0.0382646 + 0.171424i
\(376\) 3.82750 9.72885i 0.197388 0.501727i
\(377\) −24.0979 1.72351i −1.24110 0.0887655i
\(378\) 9.07631 + 0.486410i 0.466835 + 0.0250182i
\(379\) 4.05310 28.1899i 0.208194 1.44802i −0.570852 0.821053i \(-0.693387\pi\)
0.779046 0.626967i \(-0.215704\pi\)
\(380\) −8.75299 7.07942i −0.449019 0.363166i
\(381\) 3.39909 + 2.18446i 0.174140 + 0.111913i
\(382\) 20.6050 + 7.26881i 1.05424 + 0.371905i
\(383\) 15.2839 + 5.70060i 0.780971 + 0.291287i 0.708154 0.706058i \(-0.249528\pi\)
0.0728173 + 0.997345i \(0.476801\pi\)
\(384\) −3.31918 + 0.910822i −0.169381 + 0.0464802i
\(385\) −26.4922 + 14.4038i −1.35017 + 0.734086i
\(386\) −6.64074 9.93836i −0.338005 0.505849i
\(387\) 11.5358 + 6.29904i 0.586399 + 0.320198i
\(388\) 8.93211 + 1.61135i 0.453459 + 0.0818037i
\(389\) −17.5157 + 2.51838i −0.888084 + 0.127687i −0.571233 0.820788i \(-0.693535\pi\)
−0.316851 + 0.948475i \(0.602626\pi\)
\(390\) −1.78644 3.15031i −0.0904600 0.159522i
\(391\) −25.1534 + 6.11099i −1.27206 + 0.309046i
\(392\) −0.291790 + 16.3724i −0.0147376 + 0.826932i
\(393\) 1.68777 2.25460i 0.0851368 0.113729i
\(394\) 7.73538 9.25607i 0.389703 0.466314i
\(395\) −8.94137 + 2.60790i −0.449889 + 0.131218i
\(396\) 6.92506 + 20.8051i 0.347997 + 1.04550i
\(397\) −20.5893 + 11.2426i −1.03335 + 0.564250i −0.904081 0.427360i \(-0.859444\pi\)
−0.129265 + 0.991610i \(0.541262\pi\)
\(398\) 0.824559 + 0.431309i 0.0413314 + 0.0216196i
\(399\) −1.13770 2.49122i −0.0569564 0.124717i
\(400\) −7.05615 + 18.7139i −0.352808 + 0.935696i
\(401\) −21.5340 13.8390i −1.07536 0.691089i −0.121875 0.992545i \(-0.538891\pi\)
−0.953480 + 0.301457i \(0.902527\pi\)
\(402\) 5.61405 2.20893i 0.280004 0.110171i
\(403\) 14.7711 + 19.7318i 0.735799 + 0.982912i
\(404\) 23.1710 11.5991i 1.15280 0.577079i
\(405\) −11.9467 13.8376i −0.593635 0.687596i
\(406\) 5.19228 + 32.0400i 0.257689 + 1.59012i
\(407\) −38.5359 8.38296i −1.91015 0.415528i
\(408\) −1.38765 + 4.43216i −0.0686990 + 0.219425i
\(409\) −2.73257 2.36779i −0.135117 0.117079i 0.584681 0.811264i \(-0.301220\pi\)
−0.719797 + 0.694184i \(0.755765\pi\)
\(410\) −16.4165 15.8976i −0.810751 0.785127i
\(411\) 1.14887 + 0.524669i 0.0566693 + 0.0258800i
\(412\) 17.5590 7.27360i 0.865071 0.358344i
\(413\) −5.05697 5.05697i −0.248837 0.248837i
\(414\) −8.71556 + 17.6887i −0.428346 + 0.869351i
\(415\) −23.3632 + 23.2790i −1.14685 + 1.14272i
\(416\) −7.79783 19.8161i −0.382320 0.971565i
\(417\) −1.17250 3.14358i −0.0574173 0.153942i
\(418\) 9.32131 9.66036i 0.455920 0.472504i
\(419\) 17.7804 20.5197i 0.868629 1.00245i −0.131310 0.991341i \(-0.541918\pi\)
0.999938 0.0111095i \(-0.00353634\pi\)
\(420\) −3.56699 + 3.30911i −0.174051 + 0.161468i
\(421\) 4.04349 2.59859i 0.197068 0.126648i −0.438386 0.898787i \(-0.644450\pi\)
0.635453 + 0.772139i \(0.280813\pi\)
\(422\) −6.15841 4.44075i −0.299787 0.216172i
\(423\) −10.7194 0.766665i −0.521194 0.0372766i
\(424\) 5.84297 + 29.3700i 0.283760 + 1.42633i
\(425\) 16.0946 + 21.6625i 0.780703 + 1.05078i
\(426\) −1.67040 0.727078i −0.0809310 0.0352270i
\(427\) −0.855861 3.93433i −0.0414180 0.190395i
\(428\) 29.7106 + 20.6276i 1.43612 + 0.997072i
\(429\) 3.92832 1.79400i 0.189661 0.0866154i
\(430\) −13.6501 + 4.24721i −0.658264 + 0.204819i
\(431\) −1.17819 + 4.01254i −0.0567513 + 0.193277i −0.982990 0.183661i \(-0.941205\pi\)
0.926238 + 0.376939i \(0.123023\pi\)
\(432\) 3.88675 + 6.04738i 0.187002 + 0.290955i
\(433\) −21.0584 11.4988i −1.01200 0.552595i −0.114415 0.993433i \(-0.536499\pi\)
−0.897587 + 0.440838i \(0.854681\pi\)
\(434\) 21.2350 25.4096i 1.01931 1.21970i
\(435\) −2.62259 + 3.49022i −0.125744 + 0.167343i
\(436\) −0.807371 0.479014i −0.0386661 0.0229406i
\(437\) 12.0689 0.291308i 0.577333 0.0139351i
\(438\) 1.21383 + 2.13155i 0.0579990 + 0.101850i
\(439\) 0.967964 + 6.73234i 0.0461984 + 0.321317i 0.999795 + 0.0202308i \(0.00644009\pi\)
−0.953597 + 0.301086i \(0.902651\pi\)
\(440\) −21.4954 10.3311i −1.02475 0.492518i
\(441\) 16.1507 4.74227i 0.769080 0.225822i
\(442\) −28.1826 5.60557i −1.34051 0.266630i
\(443\) −0.304725 + 0.166392i −0.0144779 + 0.00790554i −0.486472 0.873696i \(-0.661716\pi\)
0.471994 + 0.881602i \(0.343534\pi\)
\(444\) −6.35924 + 0.227247i −0.301796 + 0.0107847i
\(445\) 17.9804 8.17215i 0.852350 0.387397i
\(446\) −10.7832 22.5378i −0.510600 1.06720i
\(447\) 0.808110 + 3.71482i 0.0382223 + 0.175705i
\(448\) −23.4998 + 16.3183i −1.11026 + 0.770965i
\(449\) −0.248293 0.0356992i −0.0117177 0.00168475i 0.136453 0.990646i \(-0.456430\pi\)
−0.148171 + 0.988962i \(0.547339\pi\)
\(450\) 20.5252 + 1.17430i 0.967567 + 0.0553573i
\(451\) 20.5947 17.8454i 0.969765 0.840306i
\(452\) 3.79798 + 4.71281i 0.178642 + 0.221672i
\(453\) −3.12519 0.679843i −0.146834 0.0319418i
\(454\) −9.47539 + 15.3396i −0.444702 + 0.719923i
\(455\) −22.7151 19.7546i −1.06490 0.926112i
\(456\) 1.07178 1.88229i 0.0501908 0.0881461i
\(457\) 11.7770 + 31.5754i 0.550906 + 1.47704i 0.852051 + 0.523458i \(0.175358\pi\)
−0.301145 + 0.953578i \(0.597369\pi\)
\(458\) 0.0633496 + 0.0815479i 0.00296013 + 0.00381048i
\(459\) 9.70010 0.452762
\(460\) −7.22618 20.1936i −0.336922 0.941532i
\(461\) −12.6013 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(462\) −3.55939 4.58189i −0.165598 0.213169i
\(463\) −5.18274 13.8955i −0.240862 0.645777i 0.759124 0.650946i \(-0.225627\pi\)
−0.999987 + 0.00516900i \(0.998355\pi\)
\(464\) −18.1513 + 18.1528i −0.842654 + 0.842721i
\(465\) 4.44325 0.309726i 0.206051 0.0143632i
\(466\) −4.96183 + 8.03265i −0.229852 + 0.372105i
\(467\) 12.0550 + 2.62239i 0.557837 + 0.121350i 0.482640 0.875819i \(-0.339678\pi\)
0.0751966 + 0.997169i \(0.476042\pi\)
\(468\) −17.0443 + 13.7357i −0.787872 + 0.634933i
\(469\) 37.8992 32.8398i 1.75002 1.51640i
\(470\) 8.70970 7.79529i 0.401748 0.359570i
\(471\) 3.34725 + 0.481262i 0.154233 + 0.0221754i
\(472\) 0.904596 5.58339i 0.0416374 0.256997i
\(473\) −3.62358 16.6573i −0.166612 0.765904i
\(474\) −0.773445 1.61657i −0.0355255 0.0742513i
\(475\) −5.18719 11.4677i −0.238004 0.526176i
\(476\) 1.37866 + 38.5801i 0.0631908 + 1.76832i
\(477\) 27.0169 14.7523i 1.23702 0.675463i
\(478\) −19.9579 3.96968i −0.912855 0.181569i
\(479\) −26.1136 + 7.66763i −1.19316 + 0.350343i −0.817233 0.576307i \(-0.804493\pi\)
−0.375925 + 0.926650i \(0.622675\pi\)
\(480\) −3.77288 0.757361i −0.172208 0.0345686i
\(481\) −5.60296 38.9694i −0.255473 1.77685i
\(482\) −11.7030 20.5512i −0.533058 0.936081i
\(483\) 0.617721 5.18103i 0.0281073 0.235745i
\(484\) 3.28564 5.53790i 0.149347 0.251723i
\(485\) 8.11258 + 6.09589i 0.368373 + 0.276800i
\(486\) 7.14505 8.54969i 0.324106 0.387822i
\(487\) −7.27422 3.97203i −0.329626 0.179990i 0.305910 0.952060i \(-0.401039\pi\)
−0.635537 + 0.772071i \(0.719221\pi\)
\(488\) 2.12790 2.36908i 0.0963256 0.107243i
\(489\) −0.700182 + 2.38460i −0.0316633 + 0.107835i
\(490\) −8.51492 + 16.2072i −0.384665 + 0.732166i
\(491\) 15.4224 7.04319i 0.696005 0.317855i −0.0358097 0.999359i \(-0.511401\pi\)
0.731814 + 0.681504i \(0.238674\pi\)
\(492\) 2.50762 3.61182i 0.113052 0.162833i
\(493\) 7.36305 + 33.8474i 0.331615 + 1.52441i
\(494\) 12.2878 + 5.34856i 0.552856 + 0.240643i
\(495\) −3.53272 + 24.2596i −0.158784 + 1.09039i
\(496\) 26.1235 + 1.86734i 1.17298 + 0.0838462i
\(497\) −15.1045 1.08030i −0.677530 0.0484579i
\(498\) −5.14717 3.71156i −0.230650 0.166319i
\(499\) −31.4504 + 20.2120i −1.40791 + 0.904812i −0.999966 0.00819361i \(-0.997392\pi\)
−0.407948 + 0.913005i \(0.633755\pi\)
\(500\) −16.4476 + 15.1484i −0.735561 + 0.677459i
\(501\) 4.14225 4.78042i 0.185062 0.213573i
\(502\) 4.11960 4.26944i 0.183867 0.190554i
\(503\) −4.60444 12.3450i −0.205302 0.550436i 0.792966 0.609266i \(-0.208536\pi\)
−0.998268 + 0.0588300i \(0.981263\pi\)
\(504\) 23.2255 + 18.0410i 1.03454 + 0.803609i
\(505\) 28.9705 + 0.0523002i 1.28917 + 0.00232733i
\(506\) 24.7407 6.48077i 1.09986 0.288106i
\(507\) 0.251985 + 0.251985i 0.0111910 + 0.0111910i
\(508\) 10.1656 + 24.5406i 0.451027 + 1.08881i
\(509\) 38.5836 + 17.6205i 1.71019 + 0.781016i 0.996773 + 0.0802728i \(0.0255792\pi\)
0.713414 + 0.700743i \(0.247148\pi\)
\(510\) −3.61223 + 3.73012i −0.159952 + 0.165173i
\(511\) 15.4093 + 13.3523i 0.681669 + 0.590670i
\(512\) −21.3392 7.52589i −0.943068 0.332601i
\(513\) −4.42060 0.961642i −0.195174 0.0424575i
\(514\) 2.39360 + 14.7702i 0.105577 + 0.651485i
\(515\) 21.1923 + 1.55417i 0.933846 + 0.0684847i
\(516\) −1.23125 2.45960i −0.0542028 0.108278i
\(517\) 8.35291 + 11.1582i 0.367361 + 0.490736i
\(518\) −49.2205 + 19.3665i −2.16262 + 0.850914i
\(519\) 3.31087 + 2.12777i 0.145331 + 0.0933987i
\(520\) 2.16420 23.7102i 0.0949066 1.03976i
\(521\) 11.6649 + 25.5427i 0.511051 + 1.11904i 0.972718 + 0.231991i \(0.0745242\pi\)
−0.461667 + 0.887053i \(0.652749\pi\)
\(522\) 23.3824 + 12.2308i 1.02342 + 0.535329i
\(523\) 1.53780 0.839700i 0.0672431 0.0367175i −0.445276 0.895394i \(-0.646894\pi\)
0.512519 + 0.858676i \(0.328713\pi\)
\(524\) 17.5674 5.84738i 0.767436 0.255444i
\(525\) −5.22500 + 1.51373i −0.228038 + 0.0660645i
\(526\) 2.10935 2.52403i 0.0919722 0.110053i
\(527\) 21.1783 28.2909i 0.922540 1.23237i
\(528\) 1.29263 4.40293i 0.0562544 0.191613i
\(529\) 19.9262 + 11.4868i 0.866358 + 0.499424i
\(530\) −8.91552 + 32.2713i −0.387265 + 1.40177i
\(531\) −5.75504 + 0.827450i −0.249748 + 0.0359083i
\(532\) 3.19644 17.7187i 0.138583 0.768202i
\(533\) 23.8767 + 13.0377i 1.03422 + 0.564724i
\(534\) 2.11126 + 3.15966i 0.0913632 + 0.136732i
\(535\) 19.3160 + 35.5270i 0.835104 + 1.53596i
\(536\) 38.5989 + 9.11995i 1.66722 + 0.393922i
\(537\) −2.03861 0.760362i −0.0879725 0.0328120i
\(538\) −14.3438 5.06006i −0.618407 0.218155i
\(539\) −18.3657 11.8029i −0.791067 0.508388i
\(540\) 0.844872 + 7.99270i 0.0363575 + 0.343951i
\(541\) 3.51054 24.4163i 0.150930 1.04974i −0.763736 0.645529i \(-0.776637\pi\)
0.914666 0.404211i \(-0.132454\pi\)
\(542\) −10.6163 0.568939i −0.456009 0.0244380i
\(543\) 1.84024 + 0.131617i 0.0789723 + 0.00564821i
\(544\) −24.1110 + 18.7319i −1.03375 + 0.803124i
\(545\) −0.565853 0.883990i −0.0242385 0.0378660i
\(546\) 3.04394 4.92780i 0.130269 0.210890i
\(547\) −4.39039 + 0.314007i −0.187720 + 0.0134260i −0.164882 0.986313i \(-0.552724\pi\)
−0.0228372 + 0.999739i \(0.507270\pi\)
\(548\) 4.23698 + 7.14073i 0.180995 + 0.305037i
\(549\) −2.97757 1.35981i −0.127080 0.0580354i
\(550\) −16.2818 21.1160i −0.694259 0.900388i
\(551\) 16.1551i 0.688231i
\(552\) 3.60934 2.00053i 0.153624 0.0851481i
\(553\) −10.5332 10.5332i −0.447916 0.447916i
\(554\) 4.78493 38.0984i 0.203292 1.61865i
\(555\) −6.46613 2.96710i −0.274472 0.125946i
\(556\) 5.45442 21.3720i 0.231319 0.906374i
\(557\) −2.40051 33.5636i −0.101713 1.42213i −0.750352 0.661038i \(-0.770116\pi\)
0.648639 0.761096i \(-0.275338\pi\)
\(558\) −6.19154 26.2002i −0.262109 1.10914i
\(559\) 14.3164 9.20059i 0.605519 0.389144i
\(560\) −31.6692 + 4.49629i −1.33827 + 0.190003i
\(561\) −4.05480 4.67949i −0.171194 0.197568i
\(562\) −1.71616 + 32.0232i −0.0723919 + 1.35082i
\(563\) −6.57319 8.78075i −0.277027 0.370065i 0.640351 0.768083i \(-0.278789\pi\)
−0.917378 + 0.398018i \(0.869698\pi\)
\(564\) 1.75118 + 1.41114i 0.0737381 + 0.0594195i
\(565\) 1.42652 + 6.61506i 0.0600140 + 0.278298i
\(566\) 17.2442 + 36.0420i 0.724830 + 1.51496i
\(567\) 10.2176 27.3944i 0.429098 1.15046i
\(568\) −6.29448 10.1891i −0.264111 0.427527i
\(569\) 8.29960 28.2658i 0.347937 1.18497i −0.580744 0.814086i \(-0.697238\pi\)
0.928681 0.370879i \(-0.120944\pi\)
\(570\) 2.01599 1.34181i 0.0844403 0.0562022i
\(571\) 11.1004 + 37.8046i 0.464539 + 1.58207i 0.775305 + 0.631587i \(0.217596\pi\)
−0.310766 + 0.950486i \(0.600586\pi\)
\(572\) 27.9400 + 5.04035i 1.16823 + 0.210748i
\(573\) −2.81674 + 3.76272i −0.117671 + 0.157190i
\(574\) 9.66907 35.2467i 0.403579 1.47117i
\(575\) 2.92482 23.8001i 0.121973 0.992533i
\(576\) −0.828803 + 23.2448i −0.0345335 + 0.968534i
\(577\) 21.6244 + 16.1879i 0.900237 + 0.673909i 0.945694 0.325057i \(-0.105384\pi\)
−0.0454572 + 0.998966i \(0.514474\pi\)
\(578\) 1.52942 + 17.0889i 0.0636153 + 0.710805i
\(579\) 2.46711 0.724410i 0.102530 0.0301055i
\(580\) −27.2483 + 9.01510i −1.13142 + 0.374332i
\(581\) −50.6113 14.8608i −2.09971 0.616530i
\(582\) −0.904967 + 1.73008i −0.0375121 + 0.0717142i
\(583\) −37.4066 13.9519i −1.54922 0.577830i
\(584\) −1.43685 + 16.0618i −0.0594572 + 0.664642i
\(585\) −23.9239 + 5.15912i −0.989133 + 0.213303i
\(586\) −9.10131 3.96155i −0.375972 0.163650i
\(587\) −14.3599 + 10.7497i −0.592698 + 0.443688i −0.853052 0.521825i \(-0.825251\pi\)
0.260355 + 0.965513i \(0.416160\pi\)
\(588\) −3.34232 1.11236i −0.137835 0.0458728i
\(589\) −12.4562 + 10.7933i −0.513248 + 0.444732i
\(590\) 3.70796 5.12267i 0.152654 0.210897i
\(591\) 1.40292 + 2.18299i 0.0577084 + 0.0897961i
\(592\) −35.1932 22.6153i −1.44643 0.929485i
\(593\) 28.6609 2.04987i 1.17696 0.0841780i 0.530881 0.847446i \(-0.321861\pi\)
0.646081 + 0.763268i \(0.276407\pi\)
\(594\) −9.58255 + 0.171162i −0.393177 + 0.00702284i
\(595\) −18.0008 + 39.2286i −0.737959 + 1.60822i
\(596\) −9.56391 + 23.0906i −0.391753 + 0.945829i
\(597\) −0.141547 + 0.141547i −0.00579315 + 0.00579315i
\(598\) 14.6932 + 20.8805i 0.600848 + 0.853866i
\(599\) 22.9162 0.936332 0.468166 0.883640i \(-0.344915\pi\)
0.468166 + 0.883640i \(0.344915\pi\)
\(600\) −3.38817 2.65152i −0.138322 0.108248i
\(601\) −11.0038 + 24.0949i −0.448852 + 0.982850i 0.541036 + 0.841000i \(0.318032\pi\)
−0.989888 + 0.141850i \(0.954695\pi\)
\(602\) −16.4530 15.8756i −0.670576 0.647041i
\(603\) −2.90848 40.6659i −0.118443 1.65604i
\(604\) −14.3277 15.3885i −0.582988 0.626148i
\(605\) 6.06344 3.88129i 0.246514 0.157797i
\(606\) 0.891692 + 5.50236i 0.0362225 + 0.223518i
\(607\) −1.54401 + 21.5881i −0.0626696 + 0.876235i 0.864748 + 0.502207i \(0.167478\pi\)
−0.927417 + 0.374028i \(0.877976\pi\)
\(608\) 12.8450 6.14633i 0.520935 0.249267i
\(609\) −6.91122 0.993683i −0.280057 0.0402661i
\(610\) 3.31540 1.29758i 0.134237 0.0525377i
\(611\) −7.52282 + 11.7057i −0.304341 + 0.473563i
\(612\) 25.7809 + 17.8993i 1.04213 + 0.723535i
\(613\) 2.35223 6.30658i 0.0950057 0.254720i −0.880750 0.473581i \(-0.842961\pi\)
0.975756 + 0.218860i \(0.0702340\pi\)
\(614\) 0.394467 + 1.25975i 0.0159194 + 0.0508394i
\(615\) 4.31889 2.34818i 0.174154 0.0946877i
\(616\) −2.04271 38.0883i −0.0823032 1.53462i
\(617\) 4.05097 7.41879i 0.163086 0.298669i −0.783338 0.621596i \(-0.786485\pi\)
0.946424 + 0.322926i \(0.104667\pi\)
\(618\) 0.364455 + 4.07223i 0.0146605 + 0.163809i
\(619\) −5.09057 35.4057i −0.204607 1.42308i −0.790389 0.612606i \(-0.790121\pi\)
0.585781 0.810469i \(-0.300788\pi\)
\(620\) 25.1557 + 14.9864i 1.01028 + 0.601867i
\(621\) −6.23982 5.94569i −0.250395 0.238592i
\(622\) 16.1513 9.19750i 0.647610 0.368786i
\(623\) 25.2871 + 18.9297i 1.01311 + 0.758403i
\(624\) 4.56929 0.326984i 0.182918 0.0130898i
\(625\) −24.0376 + 6.86992i −0.961502 + 0.274797i
\(626\) −11.9289 17.8525i −0.476775 0.713529i
\(627\) 1.38397 + 2.53455i 0.0552704 + 0.101220i
\(628\) 16.2715 + 15.1487i 0.649302 + 0.604497i
\(629\) −51.3466 + 23.4492i −2.04732 + 0.934981i
\(630\) 14.1374 + 29.6860i 0.563249 + 1.18272i
\(631\) −7.07036 + 11.0017i −0.281466 + 0.437970i −0.952985 0.303017i \(-0.902006\pi\)
0.671519 + 0.740988i \(0.265642\pi\)
\(632\) 1.88418 11.6296i 0.0749488 0.462602i
\(633\) 1.30751 0.978791i 0.0519689 0.0389035i
\(634\) 21.9468 + 24.4323i 0.871619 + 0.970332i
\(635\) −2.17211 + 29.6186i −0.0861977 + 1.17538i
\(636\) −6.40493 0.688472i −0.253972 0.0272997i
\(637\) 4.63271 21.2962i 0.183555 0.843788i
\(638\) −7.87107 33.3073i −0.311619 1.31865i
\(639\) −8.06213 + 9.30419i −0.318933 + 0.368068i
\(640\) −17.5348 18.2355i −0.693123 0.720819i
\(641\) 14.3083 31.3307i 0.565143 1.23749i −0.384201 0.923250i \(-0.625523\pi\)
0.949343 0.314241i \(-0.101750\pi\)
\(642\) −6.14447 + 4.77327i −0.242503 + 0.188386i
\(643\) −8.82714 + 8.82714i −0.348109 + 0.348109i −0.859405 0.511296i \(-0.829166\pi\)
0.511296 + 0.859405i \(0.329166\pi\)
\(644\) 22.7609 25.6626i 0.896905 1.01125i
\(645\) 0.00555167 3.07522i 0.000218597 0.121087i
\(646\) 2.39442 19.0648i 0.0942071 0.750093i
\(647\) 7.60011 2.83469i 0.298791 0.111443i −0.195598 0.980684i \(-0.562665\pi\)
0.494389 + 0.869241i \(0.335392\pi\)
\(648\) 22.3000 6.11842i 0.876026 0.240354i
\(649\) 5.69904 + 4.93824i 0.223707 + 0.193843i
\(650\) 14.0708 22.5961i 0.551901 0.886291i
\(651\) 3.85127 + 5.99269i 0.150943 + 0.234872i
\(652\) −12.7216 + 10.2522i −0.498218 + 0.401506i
\(653\) 0.786788 11.0007i 0.0307894 0.430492i −0.958556 0.284904i \(-0.908038\pi\)
0.989345 0.145588i \(-0.0465073\pi\)
\(654\) 0.150236 0.134952i 0.00587468 0.00527705i
\(655\) 20.4844 + 2.98296i 0.800390 + 0.116554i
\(656\) 27.0834 10.1028i 1.05743 0.394448i
\(657\) 16.1977 3.52358i 0.631931 0.137468i
\(658\) 17.6294 + 6.21910i 0.687265 + 0.242446i
\(659\) −12.0744 26.4393i −0.470353 1.02993i −0.985004 0.172529i \(-0.944806\pi\)
0.514652 0.857399i \(-0.327921\pi\)
\(660\) 3.50264 3.74866i 0.136340 0.145916i
\(661\) −1.83638 0.539209i −0.0714268 0.0209728i 0.245824 0.969314i \(-0.420941\pi\)
−0.317251 + 0.948342i \(0.602760\pi\)
\(662\) −0.647886 + 3.25731i −0.0251808 + 0.126599i
\(663\) 2.96240 5.42523i 0.115050 0.210698i
\(664\) −13.8802 39.3413i −0.538654 1.52674i
\(665\) 12.0924 16.0930i 0.468925 0.624059i
\(666\) −11.3763 + 41.4699i −0.440821 + 1.60692i
\(667\) 16.0104 26.2863i 0.619924 1.01781i
\(668\) 40.2921 10.2848i 1.55895 0.397931i
\(669\) 5.31993 0.764891i 0.205681 0.0295724i
\(670\) 33.9742 + 28.4968i 1.31254 + 1.10093i
\(671\) 1.19610 + 4.07353i 0.0461748 + 0.157257i
\(672\) −1.83934 5.87321i −0.0709540 0.226564i
\(673\) 2.27753 + 4.17099i 0.0877925 + 0.160780i 0.917886 0.396844i \(-0.129895\pi\)
−0.830093 + 0.557624i \(0.811713\pi\)
\(674\) −34.2969 + 10.7394i −1.32107 + 0.413667i
\(675\) −3.17063 + 8.40794i −0.122037 + 0.323622i
\(676\) 0.416011 + 2.30553i 0.0160004 + 0.0886743i
\(677\) 26.1320 5.68466i 1.00433 0.218479i 0.319819 0.947479i \(-0.396378\pi\)
0.684514 + 0.728999i \(0.260014\pi\)
\(678\) −1.21163 + 0.476732i −0.0465323 + 0.0183088i
\(679\) −2.30969 + 16.0643i −0.0886379 + 0.616490i
\(680\) −33.4920 + 6.60019i −1.28436 + 0.253106i
\(681\) −2.53995 2.93125i −0.0973310 0.112326i
\(682\) −20.4224 + 28.3217i −0.782015 + 1.08449i
\(683\) 2.76186 12.6961i 0.105680 0.485801i −0.893635 0.448794i \(-0.851854\pi\)
0.999315 0.0370075i \(-0.0117825\pi\)
\(684\) −9.97458 10.7130i −0.381388 0.409623i
\(685\) 0.645538 + 9.26071i 0.0246647 + 0.353834i
\(686\) 6.12147 0.109340i 0.233719 0.00417464i
\(687\) −0.0208131 + 0.00776289i −0.000794070 + 0.000296173i
\(688\) 2.57271 17.8987i 0.0980837 0.682380i
\(689\) 39.8560i 1.51839i
\(690\) 4.61004 0.185363i 0.175501 0.00705666i
\(691\) 43.5107i 1.65523i −0.561299 0.827613i \(-0.689698\pi\)
0.561299 0.827613i \(-0.310302\pi\)
\(692\) 9.90181 + 23.9038i 0.376411 + 0.908684i
\(693\) −36.7365 + 13.7020i −1.39551 + 0.520497i
\(694\) −0.520015 29.1133i −0.0197395 1.10513i
\(695\) 16.1828 18.6080i 0.613849 0.705841i
\(696\) −2.55975 4.89316i −0.0970272 0.185475i
\(697\) 8.29106 38.1134i 0.314046 1.44365i
\(698\) 22.4756 + 16.2069i 0.850714 + 0.613439i
\(699\) −1.33005 1.53496i −0.0503073 0.0580577i
\(700\) −33.8915 11.4155i −1.28098 0.431465i
\(701\) −1.42450 + 9.90762i −0.0538026 + 0.374206i 0.945076 + 0.326852i \(0.105988\pi\)
−0.998878 + 0.0473536i \(0.984921\pi\)
\(702\) −3.50317 8.90341i −0.132219 0.336038i
\(703\) 25.7247 5.59607i 0.970226 0.211060i
\(704\) 23.4883 18.9303i 0.885247 0.713464i
\(705\) 1.04041 + 2.28910i 0.0391840 + 0.0862125i
\(706\) 4.97879 + 15.9000i 0.187379 + 0.598406i
\(707\) 22.2054 + 40.6662i 0.835120 + 1.52941i
\(708\) 1.08806 + 0.544616i 0.0408917 + 0.0204679i
\(709\) −4.57053 15.5658i −0.171650 0.584586i −0.999713 0.0239514i \(-0.992375\pi\)
0.828063 0.560635i \(-0.189443\pi\)
\(710\) −1.16955 13.3391i −0.0438922 0.500607i
\(711\) −11.9872 + 1.72350i −0.449554 + 0.0646361i
\(712\) −0.445168 + 24.9785i −0.0166834 + 0.936109i
\(713\) −30.9643 + 5.21750i −1.15962 + 0.195397i
\(714\) −8.00869 2.19699i −0.299718 0.0822203i
\(715\) 25.3764 + 19.0682i 0.949025 + 0.713108i
\(716\) −8.15811 11.7494i −0.304883 0.439096i
\(717\) 2.09787 3.84196i 0.0783464 0.143481i
\(718\) 33.1170 + 6.58704i 1.23592 + 0.245826i
\(719\) 50.0901 + 14.7078i 1.86805 + 0.548508i 0.998506 + 0.0546441i \(0.0174024\pi\)
0.869539 + 0.493864i \(0.164416\pi\)
\(720\) −12.5032 + 22.8020i −0.465965 + 0.849781i
\(721\) 14.1178 + 30.9137i 0.525774 + 1.15128i
\(722\) 5.95778 16.8886i 0.221726 0.628530i
\(723\) 4.97123 1.08142i 0.184882 0.0402186i
\(724\) 9.44421 + 7.61032i 0.350991 + 0.282835i
\(725\) −31.7453 4.68133i −1.17899 0.173860i
\(726\) 0.925661 + 1.03049i 0.0343545 + 0.0382452i
\(727\) 0.256902 3.59196i 0.00952798 0.133219i −0.990462 0.137789i \(-0.956000\pi\)
0.999990 + 0.00457068i \(0.00145490\pi\)
\(728\) 34.9136 15.1986i 1.29398 0.563296i
\(729\) −11.9643 18.6169i −0.443124 0.689514i
\(730\) −9.50266 + 15.3218i −0.351709 + 0.567085i
\(731\) −18.4401 15.9785i −0.682033 0.590985i
\(732\) 0.349559 + 0.589124i 0.0129201 + 0.0217747i
\(733\) −34.7298 + 12.9536i −1.28278 + 0.478450i −0.896135 0.443781i \(-0.853637\pi\)
−0.386640 + 0.922231i \(0.626364\pi\)
\(734\) 10.6122 + 1.33283i 0.391704 + 0.0491957i
\(735\) −2.77980 2.78985i −0.102534 0.102905i
\(736\) 26.9917 + 2.72913i 0.994927 + 0.100597i
\(737\) −37.3900 + 37.3900i −1.37728 + 1.37728i
\(738\) −18.2289 23.4654i −0.671013 0.863773i
\(739\) 10.2884 22.5285i 0.378465 0.828724i −0.620542 0.784173i \(-0.713087\pi\)
0.999007 0.0445503i \(-0.0141855\pi\)
\(740\) −23.7940 40.2662i −0.874683 1.48022i
\(741\) −1.88789 + 2.17874i −0.0693533 + 0.0800379i
\(742\) −52.1109 + 12.3147i −1.91305 + 0.452086i
\(743\) −3.66871 + 16.8648i −0.134592 + 0.618708i 0.859589 + 0.510986i \(0.170719\pi\)
−0.994181 + 0.107723i \(0.965644\pi\)
\(744\) −2.06262 + 5.24282i −0.0756192 + 0.192211i
\(745\) −21.1508 + 18.2606i −0.774907 + 0.669015i
\(746\) −5.20786 + 4.67806i −0.190673 + 0.171276i
\(747\) −34.3301 + 25.6992i −1.25607 + 0.940285i
\(748\) −4.35208 40.4727i −0.159128 1.47983i
\(749\) −34.9659 + 54.4080i −1.27763 + 1.98803i
\(750\) −2.05251 4.35029i −0.0749472 0.158850i
\(751\) 22.2991 10.1837i 0.813706 0.371607i 0.0353070 0.999377i \(-0.488759\pi\)
0.778400 + 0.627769i \(0.216032\pi\)
\(752\) 4.16602 + 14.1861i 0.151919 + 0.517313i
\(753\) 0.611651 + 1.12016i 0.0222898 + 0.0408207i
\(754\) 28.4083 18.9822i 1.03457 0.691292i
\(755\) −6.58215 22.5674i −0.239549 0.821311i
\(756\) −10.5586 + 7.33129i −0.384013 + 0.266636i
\(757\) 6.86685 + 5.14046i 0.249580 + 0.186833i 0.716742 0.697339i \(-0.245633\pi\)
−0.467162 + 0.884172i \(0.654724\pi\)
\(758\) 19.9307 + 34.9995i 0.723916 + 1.27124i
\(759\) −0.259956 + 5.49559i −0.00943580 + 0.199477i
\(760\) 15.9175 + 0.312429i 0.577390 + 0.0113330i
\(761\) −1.80613 12.5619i −0.0654722 0.455369i −0.996015 0.0891858i \(-0.971574\pi\)
0.930543 0.366183i \(-0.119336\pi\)
\(762\) −5.69138 + 0.509365i −0.206177 + 0.0184523i
\(763\) 0.804488 1.47331i 0.0291244 0.0533374i
\(764\) −29.3184 + 9.75876i −1.06070 + 0.353060i
\(765\) 16.7612 + 30.8280i 0.606001 + 1.11459i
\(766\) −22.0152 + 6.89362i −0.795440 + 0.249077i
\(767\) −2.63080 + 7.05346i −0.0949928 + 0.254686i
\(768\) 2.91671 3.89691i 0.105248 0.140618i
\(769\) 0.366577 0.570405i 0.0132191 0.0205693i −0.834581 0.550885i \(-0.814290\pi\)
0.847800 + 0.530316i \(0.177927\pi\)
\(770\) 17.0904 39.0708i 0.615896 1.40801i
\(771\) −3.18602 0.458080i −0.114742 0.0164974i
\(772\) 16.0389 + 5.33792i 0.577254 + 0.192116i
\(773\) 1.45046 20.2801i 0.0521696 0.729426i −0.902298 0.431112i \(-0.858121\pi\)
0.954468 0.298314i \(-0.0964242\pi\)
\(774\) −18.3484 + 2.97348i −0.659521 + 0.106879i
\(775\) 17.5998 + 27.6044i 0.632202 + 0.991579i
\(776\) −11.3735 + 5.94983i −0.408287 + 0.213586i
\(777\) −0.811720 11.3493i −0.0291203 0.407155i
\(778\) 17.3770 18.0091i 0.622996 0.645657i
\(779\) −7.55691 + 16.5473i −0.270755 + 0.592870i
\(780\) 4.72831 + 1.96843i 0.169301 + 0.0704810i
\(781\) 15.9673 0.571357
\(782\) 22.7899 28.6477i 0.814966 1.02444i
\(783\) −8.15562 + 8.15562i −0.291458 + 0.291458i
\(784\) −13.8787 18.5382i −0.495667 0.662079i
\(785\) 8.64410 + 23.3041i 0.308521 + 0.831760i
\(786\) 0.0711306 + 3.98227i 0.00253714 + 0.142043i
\(787\) −31.6050 + 2.26043i −1.12660 + 0.0805757i −0.622172 0.782881i \(-0.713749\pi\)
−0.504423 + 0.863456i \(0.668295\pi\)
\(788\) −0.608550 + 17.0485i −0.0216787 + 0.607328i
\(789\) 0.382561 + 0.595277i 0.0136195 + 0.0211924i
\(790\) 7.72332 10.6700i 0.274783 0.379622i
\(791\) −8.17943 + 7.08752i −0.290827 + 0.252003i
\(792\) −25.7843 17.2274i −0.916207 0.612150i
\(793\) −3.39293 + 2.53991i −0.120486 + 0.0901950i
\(794\) 13.2406 30.4190i 0.469890 1.07953i
\(795\) −6.05182 3.90472i −0.214636 0.138486i
\(796\) −1.29508 + 0.233685i −0.0459030 + 0.00828276i
\(797\) 2.95340 + 1.10156i 0.104615 + 0.0390194i 0.401227 0.915979i \(-0.368584\pi\)
−0.296612 + 0.954998i \(0.595857\pi\)
\(798\) 3.43197 + 1.79519i 0.121490 + 0.0635490i
\(799\) 19.1422 + 5.62067i 0.677203 + 0.198845i
\(800\) −8.35556 27.0219i −0.295414 0.955369i
\(801\) 24.6402 7.23501i 0.870618 0.255637i
\(802\) 36.0562 3.22694i 1.27319 0.113947i
\(803\) −17.2111 12.8841i −0.607366 0.454668i
\(804\) −4.35345 + 7.33767i −0.153534 + 0.258780i
\(805\) 35.6246 14.2011i 1.25560 0.500523i
\(806\) −33.6158 9.22167i −1.18406 0.324820i
\(807\) 1.96083 2.61936i 0.0690244 0.0922058i
\(808\) −15.8145 + 33.0571i −0.556353 + 1.16294i
\(809\) 3.94592 + 13.4386i 0.138731 + 0.472475i 0.999322 0.0368221i \(-0.0117235\pi\)
−0.860591 + 0.509297i \(0.829905\pi\)
\(810\) 25.3477 + 5.08929i 0.890626 + 0.178819i
\(811\) −3.26758 + 11.1283i −0.114740 + 0.390769i −0.996759 0.0804449i \(-0.974366\pi\)
0.882019 + 0.471214i \(0.156184\pi\)
\(812\) −33.5964 31.2781i −1.17900 1.09765i
\(813\) 0.799235 2.14283i 0.0280304 0.0751524i
\(814\) 50.3106 24.0711i 1.76339 0.843690i
\(815\) −17.8565 + 3.85071i −0.625488 + 0.134884i
\(816\) −2.29554 6.15384i −0.0803601 0.215427i
\(817\) 6.81960 + 9.10992i 0.238587 + 0.318716i
\(818\) 5.10606 + 0.273639i 0.178529 + 0.00956758i
\(819\) −25.6326 29.5816i −0.895676 1.03367i
\(820\) 32.1268 + 3.51203i 1.12192 + 0.122645i
\(821\) −12.1404 + 7.80216i −0.423703 + 0.272297i −0.735068 0.677993i \(-0.762850\pi\)
0.311366 + 0.950290i \(0.399214\pi\)
\(822\) −1.73827 + 0.410783i −0.0606292 + 0.0143277i
\(823\) 2.05011 + 28.6643i 0.0714623 + 0.999173i 0.899053 + 0.437841i \(0.144257\pi\)
−0.827590 + 0.561332i \(0.810289\pi\)
\(824\) −13.2998 + 23.3573i −0.463320 + 0.813692i
\(825\) 5.38150 1.98509i 0.187360 0.0691120i
\(826\) 10.0351 + 1.26035i 0.349166 + 0.0438531i
\(827\) −18.7849 18.7849i −0.653213 0.653213i 0.300552 0.953765i \(-0.402829\pi\)
−0.953765 + 0.300552i \(0.902829\pi\)
\(828\) −5.61280 27.3166i −0.195058 0.949317i
\(829\) 18.5976i 0.645920i 0.946413 + 0.322960i \(0.104678\pi\)
−0.946413 + 0.322960i \(0.895322\pi\)
\(830\) 5.89586 46.2681i 0.204648 1.60599i
\(831\) 7.51359 + 3.43134i 0.260644 + 0.119032i
\(832\) 25.9010 + 15.3657i 0.897957 + 0.532710i
\(833\) −31.1684 + 2.22921i −1.07992 + 0.0772374i
\(834\) 4.03681 + 2.49357i 0.139783 + 0.0863453i
\(835\) 45.4119 + 9.96466i 1.57154 + 0.344841i
\(836\) −2.02900 + 18.8760i −0.0701743 + 0.652839i
\(837\) 11.7371 + 0.839454i 0.405693 + 0.0290158i
\(838\) −2.05484 + 38.3429i −0.0709832 + 1.32453i
\(839\) −3.11339 + 21.6541i −0.107486 + 0.747582i 0.862787 + 0.505568i \(0.168717\pi\)
−0.970273 + 0.242014i \(0.922192\pi\)
\(840\) 1.11273 6.79036i 0.0383928 0.234290i
\(841\) −10.2524 6.58884i −0.353532 0.227202i
\(842\) −2.26134 + 6.41025i −0.0779308 + 0.220912i
\(843\) −6.46369 2.41083i −0.222621 0.0830334i
\(844\) 10.7306 0.383458i 0.369362 0.0131992i
\(845\) −0.742475 + 2.51185i −0.0255419 + 0.0864104i
\(846\) 12.6368 8.44381i 0.434461 0.290304i
\(847\) 10.1057 + 5.51813i 0.347236 + 0.189605i
\(848\) −32.0067 27.7317i −1.09911 0.952311i
\(849\) −8.50750 + 1.22319i −0.291977 + 0.0419799i
\(850\) −36.7689 10.2296i −1.26116 0.350871i
\(851\) 47.4031 + 16.3887i 1.62496 + 0.561799i
\(852\) 2.49634 0.637206i 0.0855232 0.0218303i
\(853\) 16.4634 21.9926i 0.563698 0.753012i −0.424628 0.905368i \(-0.639595\pi\)
0.988326 + 0.152356i \(0.0486860\pi\)
\(854\) 4.36923 + 3.65140i 0.149512 + 0.124948i
\(855\) −4.58231 15.7108i −0.156712 0.537298i
\(856\) −51.0777 + 2.73935i −1.74580 + 0.0936290i
\(857\) 37.0653 20.2392i 1.26613 0.691357i 0.301120 0.953586i \(-0.402640\pi\)
0.965005 + 0.262230i \(0.0844578\pi\)
\(858\) −2.83077 + 5.41176i −0.0966409 + 0.184754i
\(859\) −4.95027 10.8396i −0.168901 0.369842i 0.806187 0.591661i \(-0.201528\pi\)
−0.975088 + 0.221820i \(0.928800\pi\)
\(860\) 11.5598 16.5860i 0.394187 0.565579i
\(861\) 6.61419 + 4.25068i 0.225411 + 0.144863i
\(862\) −2.16542 5.50347i −0.0737544 0.187449i
\(863\) 28.6365 + 38.2538i 0.974796 + 1.30218i 0.953178 + 0.302409i \(0.0977909\pi\)
0.0216183 + 0.999766i \(0.493118\pi\)
\(864\) −9.58745 3.38172i −0.326172 0.115049i
\(865\) −2.11574 + 28.8499i −0.0719374 + 0.980927i
\(866\) 33.4946 5.42802i 1.13819 0.184452i
\(867\) −3.60647 0.784541i −0.122482 0.0266444i
\(868\) −1.67058 + 46.8012i −0.0567031 + 1.58854i
\(869\) 11.8705 + 10.2859i 0.402680 + 0.348924i
\(870\) −0.0991181 6.17328i −0.00336042 0.209294i
\(871\) −48.0173 21.9288i −1.62701 0.743029i
\(872\) 1.31728 0.165495i 0.0446086 0.00560437i
\(873\) 9.32987 + 9.32987i 0.315768 + 0.315768i
\(874\) −13.2260 + 10.7962i −0.447377 + 0.365186i
\(875\) −28.1191 28.4253i −0.950598 0.960951i
\(876\) −3.20495 1.32746i −0.108285 0.0448506i
\(877\) 8.33139 + 22.3373i 0.281331 + 0.754278i 0.998361 + 0.0572351i \(0.0182285\pi\)
−0.717030 + 0.697043i \(0.754499\pi\)
\(878\) −6.92195 6.67901i −0.233605 0.225406i
\(879\) 1.39831 1.61374i 0.0471639 0.0544301i
\(880\) 32.9697 7.11118i 1.11141 0.239718i
\(881\) −15.8882 + 10.2107i −0.535287 + 0.344008i −0.780193 0.625539i \(-0.784879\pi\)
0.244906 + 0.969547i \(0.421243\pi\)
\(882\) −13.9231 + 19.3084i −0.468814 + 0.650149i
\(883\) 2.82637 + 0.202146i 0.0951150 + 0.00680276i 0.118816 0.992916i \(-0.462090\pi\)
−0.0237005 + 0.999719i \(0.507545\pi\)
\(884\) 36.3382 18.1905i 1.22219 0.611813i
\(885\) 0.813270 + 1.09050i 0.0273378 + 0.0366567i
\(886\) 0.195963 0.450207i 0.00658349 0.0151250i
\(887\) −10.5468 48.4830i −0.354128 1.62790i −0.717713 0.696339i \(-0.754811\pi\)
0.363586 0.931561i \(-0.381552\pi\)
\(888\) 6.90497 5.77101i 0.231716 0.193662i
\(889\) −43.2052 + 19.7311i −1.44905 + 0.661761i
\(890\) −12.9907 + 24.7264i −0.435451 + 0.828831i
\(891\) −8.68562 + 29.5805i −0.290979 + 0.990984i
\(892\) 31.5965 + 15.8153i 1.05793 + 0.529536i
\(893\) −8.16641 4.45920i −0.273278 0.149221i
\(894\) −4.12546 3.44768i −0.137976 0.115308i
\(895\) −2.24736 15.8336i −0.0751211 0.529259i
\(896\) 12.0875 38.6127i 0.403813 1.28996i
\(897\) −5.23104 + 1.67410i −0.174659 + 0.0558965i
\(898\) 0.308271 0.175547i 0.0102871 0.00585809i
\(899\) 5.98010 + 41.5925i 0.199447 + 1.38719i
\(900\) −23.9418 + 16.4960i −0.798059 + 0.549866i
\(901\) −54.8295 + 16.0994i −1.82664 + 0.536349i
\(902\) −7.51806 + 37.7978i −0.250324 + 1.25853i
\(903\) 4.31672 2.35711i 0.143651 0.0784396i
\(904\) −8.33045 1.96827i −0.277066 0.0654638i
\(905\) 5.61096 + 12.3452i 0.186515 + 0.410369i
\(906\) 4.08010 1.95212i 0.135552 0.0648549i
\(907\) −0.370862 1.70483i −0.0123143 0.0566078i 0.970580 0.240780i \(-0.0774032\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(908\) −2.72617 25.3523i −0.0904710 0.841346i
\(909\) 37.2855 + 5.36085i 1.23668 + 0.177808i
\(910\) 42.5076 + 2.35500i 1.40911 + 0.0780674i
\(911\) 9.25626 8.02059i 0.306673 0.265734i −0.487903 0.872898i \(-0.662238\pi\)
0.794577 + 0.607164i \(0.207693\pi\)
\(912\) 0.436065 + 3.03204i 0.0144396 + 0.100401i
\(913\) 54.3480 + 11.8227i 1.79866 + 0.391274i
\(914\) −40.5474 25.0464i −1.34119 0.828463i
\(915\) 0.0532581 + 0.764027i 0.00176066 + 0.0252580i
\(916\) −0.141500 0.0361128i −0.00467530 0.00119320i
\(917\) 11.5697 + 31.0196i 0.382066 + 1.02436i
\(918\) −10.8333 + 8.41571i −0.357551 + 0.277760i
\(919\) 42.8821 1.41455 0.707276 0.706938i \(-0.249924\pi\)
0.707276 + 0.706938i \(0.249924\pi\)
\(920\) 25.5901 + 16.2833i 0.843682 + 0.536844i
\(921\) −0.283970 −0.00935713
\(922\) 14.0734 10.9328i 0.463484 0.360052i
\(923\) 5.57054 + 14.9352i 0.183357 + 0.491598i
\(924\) 7.95040 + 2.02905i 0.261549 + 0.0667509i
\(925\) −3.54209 52.1714i −0.116463 1.71539i
\(926\) 17.8437 + 11.0222i 0.586382 + 0.362213i
\(927\) 26.9979 + 5.87304i 0.886729 + 0.192896i
\(928\) 4.52260 36.0213i 0.148462 1.18246i
\(929\) −32.6968 + 28.3319i −1.07275 + 0.929540i −0.997710 0.0676408i \(-0.978453\pi\)
−0.0750366 + 0.997181i \(0.523907\pi\)
\(930\) −4.69360 + 4.20083i −0.153909 + 0.137751i
\(931\) 14.4253 + 2.07404i 0.472769 + 0.0679739i
\(932\) −1.42757 13.2759i −0.0467616 0.434865i
\(933\) 0.849899 + 3.90692i 0.0278244 + 0.127907i
\(934\) −15.7384 + 7.53001i −0.514975 + 0.246390i
\(935\) 15.9813 42.6125i 0.522645 1.39358i
\(936\) 7.11843 30.1278i 0.232673 0.984757i
\(937\) −10.2828 + 5.61485i −0.335926 + 0.183429i −0.638354 0.769743i \(-0.720384\pi\)
0.302429 + 0.953172i \(0.402203\pi\)
\(938\) −13.8351 + 69.5572i −0.451731 + 2.27112i
\(939\) 4.43173 1.30127i 0.144624 0.0424655i
\(940\) −2.96405 + 16.2624i −0.0966766 + 0.530421i
\(941\) 5.10601 + 35.5131i 0.166451 + 1.15769i 0.886147 + 0.463404i \(0.153372\pi\)
−0.719696 + 0.694289i \(0.755719\pi\)
\(942\) −4.15581 + 2.36656i −0.135404 + 0.0771066i
\(943\) −28.6951 + 19.4353i −0.934440 + 0.632901i
\(944\) 3.83383 + 7.02047i 0.124780 + 0.228497i
\(945\) −14.2289 + 2.01959i −0.462866 + 0.0656974i
\(946\) 18.4986 + 15.4594i 0.601441 + 0.502630i
\(947\) 8.14682 + 4.44850i 0.264736 + 0.144557i 0.606135 0.795362i \(-0.292719\pi\)
−0.341399 + 0.939918i \(0.610901\pi\)
\(948\) 2.26632 + 1.13438i 0.0736065 + 0.0368430i
\(949\) 6.04677 20.5934i 0.196286 0.668490i
\(950\) 15.7425 + 8.30706i 0.510753 + 0.269517i
\(951\) −6.42647 + 2.93487i −0.208393 + 0.0951697i
\(952\) −35.0115 41.8910i −1.13473 1.35769i
\(953\) −1.43569 6.59974i −0.0465064 0.213786i 0.948029 0.318183i \(-0.103073\pi\)
−0.994536 + 0.104396i \(0.966709\pi\)
\(954\) −17.3740 + 39.9153i −0.562505 + 1.29231i
\(955\) −34.1866 4.97830i −1.10625 0.161094i
\(956\) 25.7335 12.8819i 0.832280 0.416631i
\(957\) 7.34358 + 0.525223i 0.237384 + 0.0169781i
\(958\) 22.5118 31.2192i 0.727323 1.00865i
\(959\) −12.4901 + 8.02688i −0.403325 + 0.259201i
\(960\) 4.87071 2.42748i 0.157201 0.0783465i
\(961\) 7.77328 8.97085i 0.250751 0.289382i
\(962\) 40.0670 + 38.6608i 1.29181 + 1.24647i
\(963\) 18.3749 + 49.2650i 0.592123 + 1.58754i
\(964\) 30.9002 + 12.7986i 0.995228 + 0.412214i
\(965\) 13.3395 + 13.3878i 0.429415 + 0.430968i
\(966\) 3.80513 + 6.32221i 0.122428 + 0.203414i
\(967\) −10.2641 10.2641i −0.330071 0.330071i 0.522542 0.852613i \(-0.324984\pi\)
−0.852613 + 0.522542i \(0.824984\pi\)
\(968\) 1.13516 + 9.03543i 0.0364854 + 0.290410i
\(969\) 3.75986 + 1.71707i 0.120784 + 0.0551603i
\(970\) −14.3490 + 0.230388i −0.460719 + 0.00739730i
\(971\) 4.44109 + 3.84823i 0.142521 + 0.123496i 0.723204 0.690635i \(-0.242669\pi\)
−0.580682 + 0.814130i \(0.697214\pi\)
\(972\) −0.562108 + 15.7474i −0.0180296 + 0.505100i
\(973\) 38.5392 + 8.38369i 1.23551 + 0.268769i
\(974\) 11.5701 1.87501i 0.370730 0.0600790i
\(975\) 3.73422 + 4.34109i 0.119591 + 0.139026i
\(976\) −0.321094 + 4.49198i −0.0102780 + 0.143785i
\(977\) −32.1291 42.9195i −1.02790 1.37312i −0.925660 0.378357i \(-0.876489\pi\)
−0.102242 0.994760i \(-0.532602\pi\)
\(978\) −1.28688 3.27064i −0.0411499 0.104584i
\(979\) −28.0196 18.0071i −0.895509 0.575509i
\(980\) −4.55156 25.4880i −0.145394 0.814183i
\(981\) −0.566927 1.24140i −0.0181006 0.0396347i
\(982\) −11.1135 + 21.2463i −0.354646 + 0.677998i
\(983\) 51.8049 28.2876i 1.65232 0.902234i 0.664379 0.747396i \(-0.268696\pi\)
0.987940 0.154839i \(-0.0494859\pi\)
\(984\) 0.333013 + 6.20934i 0.0106161 + 0.197946i
\(985\) −9.17090 + 16.7234i −0.292209 + 0.532852i
\(986\) −37.5889 31.4134i −1.19707 1.00041i
\(987\) −2.40997 + 3.21934i −0.0767101 + 0.102473i
\(988\) −18.3637 + 4.68743i −0.584226 + 0.149127i
\(989\) 2.06802 + 21.5814i 0.0657591 + 0.686249i
\(990\) −17.1020 30.1586i −0.543538 0.958504i
\(991\) −41.7706 + 6.00571i −1.32689 + 0.190778i −0.769058 0.639178i \(-0.779275\pi\)
−0.557829 + 0.829956i \(0.688365\pi\)
\(992\) −30.7953 + 20.5790i −0.977752 + 0.653383i
\(993\) −0.627042 0.342391i −0.0198986 0.0108654i
\(994\) 17.8063 11.8980i 0.564781 0.377383i
\(995\) −1.41098 0.417070i −0.0447311 0.0132220i
\(996\) 8.96858 0.320492i 0.284180 0.0101552i
\(997\) −19.9000 7.42233i −0.630240 0.235068i 0.0139862 0.999902i \(-0.495548\pi\)
−0.644227 + 0.764835i \(0.722821\pi\)
\(998\) 17.5888 49.8592i 0.556763 1.57827i
\(999\) −15.8117 10.1616i −0.500261 0.321498i
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 460.2.w.a.3.15 1360
4.3 odd 2 inner 460.2.w.a.3.42 yes 1360
5.2 odd 4 inner 460.2.w.a.187.21 yes 1360
20.7 even 4 inner 460.2.w.a.187.61 yes 1360
23.8 even 11 inner 460.2.w.a.123.61 yes 1360
92.31 odd 22 inner 460.2.w.a.123.21 yes 1360
115.77 odd 44 inner 460.2.w.a.307.42 yes 1360
460.307 even 44 inner 460.2.w.a.307.15 yes 1360
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.w.a.3.15 1360 1.1 even 1 trivial
460.2.w.a.3.42 yes 1360 4.3 odd 2 inner
460.2.w.a.123.21 yes 1360 92.31 odd 22 inner
460.2.w.a.123.61 yes 1360 23.8 even 11 inner
460.2.w.a.187.21 yes 1360 5.2 odd 4 inner
460.2.w.a.187.61 yes 1360 20.7 even 4 inner
460.2.w.a.307.15 yes 1360 460.307 even 44 inner
460.2.w.a.307.42 yes 1360 115.77 odd 44 inner