Properties

Label 60.3.l.a.47.3
Level $60$
Weight $3$
Character 60.47
Analytic conductor $1.635$
Analytic rank $0$
Dimension $40$
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] = [60,3,Mod(23,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.3
Character \(\chi\) \(=\) 60.47
Dual form 60.3.l.a.23.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.81610 + 0.837725i) q^{2} +(2.69303 - 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.21472 - 3.82956i) q^{5} +(-3.78336 + 4.65685i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-2.16636 + 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +O(q^{10})\) \(q+(-1.81610 + 0.837725i) q^{2} +(2.69303 - 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.21472 - 3.82956i) q^{5} +(-3.78336 + 4.65685i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-2.16636 + 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +(9.04638 + 4.26182i) q^{10} +16.8337 q^{11} +(2.96979 - 11.6267i) q^{12} +(-8.64592 + 8.64592i) q^{13} +(-3.46580 + 9.40093i) q^{14} +(-13.7199 - 6.06335i) q^{15} +(-2.51707 - 15.8008i) q^{16} +(-9.72710 + 9.72710i) q^{17} +(-4.03246 + 17.5425i) q^{18} -4.78419 q^{19} +(-19.9993 - 0.161503i) q^{20} +(4.85684 - 14.2228i) q^{21} +(-30.5716 + 14.1020i) q^{22} +(-13.5716 + 13.5716i) q^{23} +(4.34655 + 23.6031i) q^{24} +(-4.33113 + 24.6220i) q^{25} +(8.45895 - 22.9448i) q^{26} +(5.41182 - 26.4521i) q^{27} +(-1.58116 - 19.9764i) q^{28} +14.8741 q^{29} +(29.9961 - 0.481867i) q^{30} +14.0641i q^{31} +(17.8080 + 26.5872i) q^{32} +(45.3336 - 22.2536i) q^{33} +(9.51674 - 25.8140i) q^{34} +(-24.9537 - 2.17802i) q^{35} +(-7.37245 - 35.2370i) q^{36} +(-10.1182 - 10.1182i) q^{37} +(8.68857 - 4.00784i) q^{38} +(-11.8540 + 34.7134i) q^{39} +(36.4561 - 16.4607i) q^{40} +6.08509i q^{41} +(3.09427 + 29.8987i) q^{42} +(57.2366 + 57.2366i) q^{43} +(43.7075 - 51.2213i) q^{44} +(-44.9636 + 1.80856i) q^{45} +(13.2781 - 36.0167i) q^{46} +(-17.6247 - 17.6247i) q^{47} +(-27.6667 - 39.2244i) q^{48} +23.9027i q^{49} +(-12.7607 - 48.3442i) q^{50} +(-13.3364 + 39.0543i) q^{51} +(3.85911 + 48.7562i) q^{52} +(-16.2015 - 16.2015i) q^{53} +(12.3312 + 52.5732i) q^{54} +(-54.1156 - 64.4657i) q^{55} +(19.6063 + 34.9546i) q^{56} +(-12.8840 + 6.32456i) q^{57} +(-27.0128 + 12.4604i) q^{58} -4.37150i q^{59} +(-54.0723 + 26.0036i) q^{60} +8.52269 q^{61} +(-11.7818 - 25.5418i) q^{62} +(-5.72249 - 44.7229i) q^{63} +(-54.6137 - 33.3667i) q^{64} +(60.9043 + 5.31588i) q^{65} +(-63.6878 + 78.3919i) q^{66} +(53.9714 - 53.9714i) q^{67} +(4.34170 + 54.8532i) q^{68} +(-18.6074 + 54.4900i) q^{69} +(47.1431 - 16.9489i) q^{70} +36.6679 q^{71} +(42.9080 + 57.8178i) q^{72} +(-12.6800 + 12.6800i) q^{73} +(26.8519 + 9.89937i) q^{74} +(20.8857 + 72.0332i) q^{75} +(-12.4218 + 14.5573i) q^{76} +(59.6318 - 59.6318i) q^{77} +(-7.55214 - 72.9733i) q^{78} -88.4346 q^{79} +(-52.4184 + 60.4344i) q^{80} +(-20.3947 - 78.3904i) q^{81} +(-5.09763 - 11.0511i) q^{82} +(63.7372 - 63.7372i) q^{83} +(-30.6663 - 51.7068i) q^{84} +(68.5205 + 5.98063i) q^{85} +(-151.896 - 55.9988i) q^{86} +(40.0563 - 19.6631i) q^{87} +(-36.4679 + 129.638i) q^{88} -115.022 q^{89} +(80.1434 - 40.9517i) q^{90} +61.2548i q^{91} +(6.05770 + 76.5332i) q^{92} +(18.5923 + 37.8749i) q^{93} +(46.7728 + 17.2435i) q^{94} +(15.3798 + 18.3214i) q^{95} +(83.1047 + 48.0583i) q^{96} +(-85.3544 - 85.3544i) q^{97} +(-20.0239 - 43.4096i) q^{98} +(92.6658 - 119.859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81610 + 0.837725i −0.908050 + 0.418863i
\(3\) 2.69303 1.32197i 0.897676 0.440657i
\(4\) 2.59643 3.04278i 0.649108 0.760696i
\(5\) −3.21472 3.82956i −0.642944 0.765913i
\(6\) −3.78336 + 4.65685i −0.630559 + 0.776141i
\(7\) 3.54241 3.54241i 0.506059 0.506059i −0.407256 0.913314i \(-0.633514\pi\)
0.913314 + 0.407256i \(0.133514\pi\)
\(8\) −2.16636 + 7.70110i −0.270795 + 0.962637i
\(9\) 5.50478 7.12021i 0.611643 0.791134i
\(10\) 9.04638 + 4.26182i 0.904638 + 0.426182i
\(11\) 16.8337 1.53034 0.765168 0.643831i \(-0.222656\pi\)
0.765168 + 0.643831i \(0.222656\pi\)
\(12\) 2.96979 11.6267i 0.247483 0.968892i
\(13\) −8.64592 + 8.64592i −0.665071 + 0.665071i −0.956571 0.291500i \(-0.905846\pi\)
0.291500 + 0.956571i \(0.405846\pi\)
\(14\) −3.46580 + 9.40093i −0.247557 + 0.671495i
\(15\) −13.7199 6.06335i −0.914660 0.404223i
\(16\) −2.51707 15.8008i −0.157317 0.987548i
\(17\) −9.72710 + 9.72710i −0.572182 + 0.572182i −0.932738 0.360556i \(-0.882587\pi\)
0.360556 + 0.932738i \(0.382587\pi\)
\(18\) −4.03246 + 17.5425i −0.224025 + 0.974583i
\(19\) −4.78419 −0.251800 −0.125900 0.992043i \(-0.540182\pi\)
−0.125900 + 0.992043i \(0.540182\pi\)
\(20\) −19.9993 0.161503i −0.999967 0.00807515i
\(21\) 4.85684 14.2228i 0.231278 0.677275i
\(22\) −30.5716 + 14.1020i −1.38962 + 0.641000i
\(23\) −13.5716 + 13.5716i −0.590070 + 0.590070i −0.937650 0.347580i \(-0.887003\pi\)
0.347580 + 0.937650i \(0.387003\pi\)
\(24\) 4.34655 + 23.6031i 0.181106 + 0.983464i
\(25\) −4.33113 + 24.6220i −0.173245 + 0.984879i
\(26\) 8.45895 22.9448i 0.325344 0.882491i
\(27\) 5.41182 26.4521i 0.200438 0.979706i
\(28\) −1.58116 19.9764i −0.0564699 0.713444i
\(29\) 14.8741 0.512899 0.256449 0.966558i \(-0.417447\pi\)
0.256449 + 0.966558i \(0.417447\pi\)
\(30\) 29.9961 0.481867i 0.999871 0.0160622i
\(31\) 14.0641i 0.453680i 0.973932 + 0.226840i \(0.0728395\pi\)
−0.973932 + 0.226840i \(0.927161\pi\)
\(32\) 17.8080 + 26.5872i 0.556498 + 0.830849i
\(33\) 45.3336 22.2536i 1.37374 0.674353i
\(34\) 9.51674 25.8140i 0.279904 0.759235i
\(35\) −24.9537 2.17802i −0.712964 0.0622292i
\(36\) −7.37245 35.2370i −0.204790 0.978806i
\(37\) −10.1182 10.1182i −0.273465 0.273465i 0.557029 0.830493i \(-0.311941\pi\)
−0.830493 + 0.557029i \(0.811941\pi\)
\(38\) 8.68857 4.00784i 0.228647 0.105469i
\(39\) −11.8540 + 34.7134i −0.303950 + 0.890086i
\(40\) 36.4561 16.4607i 0.911402 0.411516i
\(41\) 6.08509i 0.148417i 0.997243 + 0.0742084i \(0.0236430\pi\)
−0.997243 + 0.0742084i \(0.976357\pi\)
\(42\) 3.09427 + 29.8987i 0.0736730 + 0.711873i
\(43\) 57.2366 + 57.2366i 1.33108 + 1.33108i 0.904401 + 0.426683i \(0.140318\pi\)
0.426683 + 0.904401i \(0.359682\pi\)
\(44\) 43.7075 51.2213i 0.993353 1.16412i
\(45\) −44.9636 + 1.80856i −0.999192 + 0.0401903i
\(46\) 13.2781 36.0167i 0.288654 0.782971i
\(47\) −17.6247 17.6247i −0.374993 0.374993i 0.494299 0.869292i \(-0.335425\pi\)
−0.869292 + 0.494299i \(0.835425\pi\)
\(48\) −27.6667 39.2244i −0.576390 0.817175i
\(49\) 23.9027i 0.487809i
\(50\) −12.7607 48.3442i −0.255214 0.966885i
\(51\) −13.3364 + 39.0543i −0.261498 + 0.765770i
\(52\) 3.85911 + 48.7562i 0.0742137 + 0.937620i
\(53\) −16.2015 16.2015i −0.305688 0.305688i 0.537546 0.843234i \(-0.319351\pi\)
−0.843234 + 0.537546i \(0.819351\pi\)
\(54\) 12.3312 + 52.5732i 0.228355 + 0.973578i
\(55\) −54.1156 64.4657i −0.983920 1.17210i
\(56\) 19.6063 + 34.9546i 0.350112 + 0.624189i
\(57\) −12.8840 + 6.32456i −0.226034 + 0.110957i
\(58\) −27.0128 + 12.4604i −0.465738 + 0.214834i
\(59\) 4.37150i 0.0740931i −0.999314 0.0370466i \(-0.988205\pi\)
0.999314 0.0370466i \(-0.0117950\pi\)
\(60\) −54.0723 + 26.0036i −0.901205 + 0.433394i
\(61\) 8.52269 0.139716 0.0698582 0.997557i \(-0.477745\pi\)
0.0698582 + 0.997557i \(0.477745\pi\)
\(62\) −11.7818 25.5418i −0.190030 0.411964i
\(63\) −5.72249 44.7229i −0.0908332 0.709887i
\(64\) −54.6137 33.3667i −0.853340 0.521355i
\(65\) 60.9043 + 5.31588i 0.936990 + 0.0817828i
\(66\) −63.6878 + 78.3919i −0.964967 + 1.18776i
\(67\) 53.9714 53.9714i 0.805543 0.805543i −0.178413 0.983956i \(-0.557096\pi\)
0.983956 + 0.178413i \(0.0570963\pi\)
\(68\) 4.34170 + 54.8532i 0.0638485 + 0.806665i
\(69\) −18.6074 + 54.4900i −0.269673 + 0.789710i
\(70\) 47.1431 16.9489i 0.673472 0.242127i
\(71\) 36.6679 0.516449 0.258225 0.966085i \(-0.416863\pi\)
0.258225 + 0.966085i \(0.416863\pi\)
\(72\) 42.9080 + 57.8178i 0.595945 + 0.803025i
\(73\) −12.6800 + 12.6800i −0.173699 + 0.173699i −0.788602 0.614903i \(-0.789195\pi\)
0.614903 + 0.788602i \(0.289195\pi\)
\(74\) 26.8519 + 9.89937i 0.362863 + 0.133775i
\(75\) 20.8857 + 72.0332i 0.278476 + 0.960443i
\(76\) −12.4218 + 14.5573i −0.163445 + 0.191543i
\(77\) 59.6318 59.6318i 0.774439 0.774439i
\(78\) −7.55214 72.9733i −0.0968223 0.935555i
\(79\) −88.4346 −1.11943 −0.559713 0.828687i \(-0.689088\pi\)
−0.559713 + 0.828687i \(0.689088\pi\)
\(80\) −52.4184 + 60.4344i −0.655230 + 0.755430i
\(81\) −20.3947 78.3904i −0.251786 0.967783i
\(82\) −5.09763 11.0511i −0.0621663 0.134770i
\(83\) 63.7372 63.7372i 0.767918 0.767918i −0.209822 0.977740i \(-0.567288\pi\)
0.977740 + 0.209822i \(0.0672884\pi\)
\(84\) −30.6663 51.7068i −0.365076 0.615557i
\(85\) 68.5205 + 5.98063i 0.806123 + 0.0703604i
\(86\) −151.896 55.9988i −1.76623 0.651149i
\(87\) 40.0563 19.6631i 0.460417 0.226013i
\(88\) −36.4679 + 129.638i −0.414408 + 1.47316i
\(89\) −115.022 −1.29238 −0.646190 0.763177i \(-0.723639\pi\)
−0.646190 + 0.763177i \(0.723639\pi\)
\(90\) 80.1434 40.9517i 0.890482 0.455019i
\(91\) 61.2548i 0.673130i
\(92\) 6.05770 + 76.5332i 0.0658445 + 0.831883i
\(93\) 18.5923 + 37.8749i 0.199917 + 0.407258i
\(94\) 46.7728 + 17.2435i 0.497583 + 0.183442i
\(95\) 15.3798 + 18.3214i 0.161893 + 0.192857i
\(96\) 83.1047 + 48.0583i 0.865674 + 0.500607i
\(97\) −85.3544 85.3544i −0.879942 0.879942i 0.113586 0.993528i \(-0.463766\pi\)
−0.993528 + 0.113586i \(0.963766\pi\)
\(98\) −20.0239 43.4096i −0.204325 0.442955i
\(99\) 92.6658 119.859i 0.936018 1.21070i
\(100\) 63.6739 + 77.1080i 0.636739 + 0.771080i
\(101\) 158.917i 1.57343i 0.617313 + 0.786717i \(0.288221\pi\)
−0.617313 + 0.786717i \(0.711779\pi\)
\(102\) −8.49654 82.0987i −0.0832994 0.804889i
\(103\) −28.6266 28.6266i −0.277928 0.277928i 0.554353 0.832282i \(-0.312966\pi\)
−0.832282 + 0.554353i \(0.812966\pi\)
\(104\) −47.8529 85.3133i −0.460124 0.820320i
\(105\) −70.0804 + 27.1227i −0.667432 + 0.258311i
\(106\) 42.9959 + 15.8511i 0.405622 + 0.149539i
\(107\) 28.1808 + 28.1808i 0.263372 + 0.263372i 0.826423 0.563050i \(-0.190372\pi\)
−0.563050 + 0.826423i \(0.690372\pi\)
\(108\) −66.4365 85.1480i −0.615153 0.788408i
\(109\) 159.944i 1.46737i −0.679489 0.733686i \(-0.737798\pi\)
0.679489 0.733686i \(-0.262202\pi\)
\(110\) 152.284 + 71.7421i 1.38440 + 0.652201i
\(111\) −40.6245 13.8726i −0.365986 0.124978i
\(112\) −64.8893 47.0563i −0.579369 0.420146i
\(113\) −101.260 101.260i −0.896110 0.896110i 0.0989792 0.995089i \(-0.468442\pi\)
−0.995089 + 0.0989792i \(0.968442\pi\)
\(114\) 18.1003 22.2793i 0.158775 0.195432i
\(115\) 95.6023 + 8.34440i 0.831324 + 0.0725600i
\(116\) 38.6195 45.2586i 0.332927 0.390160i
\(117\) 13.9668 + 109.155i 0.119375 + 0.932946i
\(118\) 3.66211 + 7.93907i 0.0310348 + 0.0672803i
\(119\) 68.9147i 0.579115i
\(120\) 76.4167 92.5229i 0.636806 0.771024i
\(121\) 162.373 1.34193
\(122\) −15.4781 + 7.13968i −0.126869 + 0.0585219i
\(123\) 8.04432 + 16.3873i 0.0654009 + 0.133230i
\(124\) 42.7940 + 36.5165i 0.345113 + 0.294488i
\(125\) 108.215 62.5665i 0.865718 0.500532i
\(126\) 47.8581 + 76.4273i 0.379826 + 0.606566i
\(127\) −94.0845 + 94.0845i −0.740823 + 0.740823i −0.972736 0.231914i \(-0.925501\pi\)
0.231914 + 0.972736i \(0.425501\pi\)
\(128\) 127.136 + 14.8460i 0.993251 + 0.115985i
\(129\) 229.805 + 78.4746i 1.78143 + 0.608330i
\(130\) −115.062 + 41.3669i −0.885089 + 0.318207i
\(131\) −145.148 −1.10800 −0.554002 0.832515i \(-0.686900\pi\)
−0.554002 + 0.832515i \(0.686900\pi\)
\(132\) 49.9925 195.720i 0.378731 1.48273i
\(133\) −16.9476 + 16.9476i −0.127425 + 0.127425i
\(134\) −52.8042 + 143.231i −0.394061 + 1.06888i
\(135\) −118.697 + 64.3111i −0.879240 + 0.476379i
\(136\) −53.8369 95.9817i −0.395859 0.705748i
\(137\) −60.1022 + 60.1022i −0.438702 + 0.438702i −0.891575 0.452873i \(-0.850399\pi\)
0.452873 + 0.891575i \(0.350399\pi\)
\(138\) −11.8547 114.547i −0.0859035 0.830051i
\(139\) 12.5985 0.0906366 0.0453183 0.998973i \(-0.485570\pi\)
0.0453183 + 0.998973i \(0.485570\pi\)
\(140\) −71.4180 + 70.2738i −0.510129 + 0.501956i
\(141\) −70.7630 24.1644i −0.501865 0.171379i
\(142\) −66.5925 + 30.7176i −0.468961 + 0.216321i
\(143\) −145.543 + 145.543i −1.01778 + 1.01778i
\(144\) −126.361 69.0578i −0.877505 0.479568i
\(145\) −47.8160 56.9612i −0.329765 0.392836i
\(146\) 12.4058 33.6506i 0.0849713 0.230483i
\(147\) 31.5986 + 64.3705i 0.214957 + 0.437895i
\(148\) −57.0587 + 4.51626i −0.385531 + 0.0305153i
\(149\) −25.9233 −0.173982 −0.0869911 0.996209i \(-0.527725\pi\)
−0.0869911 + 0.996209i \(0.527725\pi\)
\(150\) −98.2746 113.323i −0.655164 0.755487i
\(151\) 200.379i 1.32701i −0.748171 0.663506i \(-0.769068\pi\)
0.748171 0.663506i \(-0.230932\pi\)
\(152\) 10.3643 36.8435i 0.0681862 0.242392i
\(153\) 15.7134 + 122.805i 0.102702 + 0.802644i
\(154\) −58.3422 + 158.252i −0.378846 + 1.02761i
\(155\) 53.8593 45.2121i 0.347479 0.291691i
\(156\) 74.8470 + 126.200i 0.479789 + 0.808976i
\(157\) 139.992 + 139.992i 0.891666 + 0.891666i 0.994680 0.103014i \(-0.0328486\pi\)
−0.103014 + 0.994680i \(0.532849\pi\)
\(158\) 160.606 74.0839i 1.01649 0.468885i
\(159\) −65.0489 22.2131i −0.409113 0.139705i
\(160\) 44.5696 153.667i 0.278560 0.960419i
\(161\) 96.1524i 0.597220i
\(162\) 102.708 + 125.280i 0.634003 + 0.773331i
\(163\) −58.6324 58.6324i −0.359708 0.359708i 0.503997 0.863705i \(-0.331862\pi\)
−0.863705 + 0.503997i \(0.831862\pi\)
\(164\) 18.5156 + 15.7995i 0.112900 + 0.0963386i
\(165\) −230.957 102.069i −1.39974 0.618597i
\(166\) −62.3588 + 169.147i −0.375655 + 1.01896i
\(167\) −84.2556 84.2556i −0.504524 0.504524i 0.408316 0.912841i \(-0.366116\pi\)
−0.912841 + 0.408316i \(0.866116\pi\)
\(168\) 99.0092 + 68.2147i 0.589341 + 0.406040i
\(169\) 19.4961i 0.115361i
\(170\) −129.450 + 46.5399i −0.761471 + 0.273764i
\(171\) −26.3359 + 34.0644i −0.154011 + 0.199207i
\(172\) 322.770 25.5476i 1.87657 0.148533i
\(173\) 51.2341 + 51.2341i 0.296151 + 0.296151i 0.839504 0.543353i \(-0.182846\pi\)
−0.543353 + 0.839504i \(0.682846\pi\)
\(174\) −56.2739 + 69.2663i −0.323413 + 0.398082i
\(175\) 71.8785 + 102.564i 0.410734 + 0.586078i
\(176\) −42.3716 265.985i −0.240747 1.51128i
\(177\) −5.77899 11.7726i −0.0326497 0.0665116i
\(178\) 208.891 96.3566i 1.17354 0.541329i
\(179\) 27.2276i 0.152109i 0.997104 + 0.0760547i \(0.0242324\pi\)
−0.997104 + 0.0760547i \(0.975768\pi\)
\(180\) −111.242 + 141.510i −0.618011 + 0.786169i
\(181\) −276.624 −1.52831 −0.764155 0.645033i \(-0.776844\pi\)
−0.764155 + 0.645033i \(0.776844\pi\)
\(182\) −51.3147 111.245i −0.281949 0.611235i
\(183\) 22.9518 11.2668i 0.125420 0.0615670i
\(184\) −75.1152 133.917i −0.408235 0.727811i
\(185\) −6.22109 + 71.2754i −0.0336275 + 0.385272i
\(186\) −65.4943 53.2094i −0.352120 0.286072i
\(187\) −163.743 + 163.743i −0.875630 + 0.875630i
\(188\) −99.3894 + 7.86679i −0.528667 + 0.0418446i
\(189\) −74.5332 112.875i −0.394356 0.597222i
\(190\) −43.2796 20.3893i −0.227787 0.107312i
\(191\) 340.010 1.78016 0.890078 0.455807i \(-0.150649\pi\)
0.890078 + 0.455807i \(0.150649\pi\)
\(192\) −191.186 17.6597i −0.995761 0.0919779i
\(193\) 100.981 100.981i 0.523220 0.523220i −0.395322 0.918542i \(-0.629367\pi\)
0.918542 + 0.395322i \(0.129367\pi\)
\(194\) 226.515 + 83.5085i 1.16761 + 0.430456i
\(195\) 171.044 66.1980i 0.877151 0.339477i
\(196\) 72.7306 + 62.0617i 0.371075 + 0.316641i
\(197\) 225.584 225.584i 1.14510 1.14510i 0.157595 0.987504i \(-0.449626\pi\)
0.987504 0.157595i \(-0.0503741\pi\)
\(198\) −67.8811 + 295.305i −0.342834 + 1.49144i
\(199\) 286.672 1.44056 0.720281 0.693682i \(-0.244013\pi\)
0.720281 + 0.693682i \(0.244013\pi\)
\(200\) −180.233 86.6945i −0.901167 0.433473i
\(201\) 73.9977 216.695i 0.368148 1.07808i
\(202\) −133.129 288.609i −0.659053 1.42876i
\(203\) 52.6900 52.6900i 0.259557 0.259557i
\(204\) 84.2067 + 141.982i 0.412778 + 0.695988i
\(205\) 23.3032 19.5619i 0.113674 0.0954238i
\(206\) 75.9701 + 28.0076i 0.368787 + 0.135959i
\(207\) 21.9239 + 171.341i 0.105912 + 0.827736i
\(208\) 158.375 + 114.850i 0.761416 + 0.552163i
\(209\) −80.5356 −0.385338
\(210\) 104.552 107.966i 0.497865 0.514122i
\(211\) 183.842i 0.871288i −0.900119 0.435644i \(-0.856521\pi\)
0.900119 0.435644i \(-0.143479\pi\)
\(212\) −91.3637 + 7.23155i −0.430961 + 0.0341111i
\(213\) 98.7476 48.4739i 0.463604 0.227577i
\(214\) −74.7870 27.5714i −0.349472 0.128838i
\(215\) 35.1915 403.191i 0.163681 1.87531i
\(216\) 191.986 + 98.9818i 0.888824 + 0.458249i
\(217\) 49.8207 + 49.8207i 0.229589 + 0.229589i
\(218\) 133.989 + 290.473i 0.614627 + 1.33245i
\(219\) −17.3850 + 50.9103i −0.0793836 + 0.232467i
\(220\) −336.663 2.71869i −1.53029 0.0123577i
\(221\) 168.199i 0.761083i
\(222\) 85.3995 8.83816i 0.384683 0.0398115i
\(223\) −7.02165 7.02165i −0.0314872 0.0314872i 0.691188 0.722675i \(-0.257088\pi\)
−0.722675 + 0.691188i \(0.757088\pi\)
\(224\) 157.266 + 31.0995i 0.702079 + 0.138837i
\(225\) 151.472 + 166.377i 0.673207 + 0.739454i
\(226\) 268.727 + 99.0706i 1.18906 + 0.438366i
\(227\) 36.6684 + 36.6684i 0.161535 + 0.161535i 0.783246 0.621711i \(-0.213562\pi\)
−0.621711 + 0.783246i \(0.713562\pi\)
\(228\) −14.2081 + 55.6244i −0.0623160 + 0.243967i
\(229\) 270.126i 1.17959i 0.807554 + 0.589794i \(0.200791\pi\)
−0.807554 + 0.589794i \(0.799209\pi\)
\(230\) −180.613 + 64.9342i −0.785276 + 0.282322i
\(231\) 81.7585 239.422i 0.353933 1.03646i
\(232\) −32.2226 + 114.547i −0.138891 + 0.493735i
\(233\) −55.2135 55.2135i −0.236968 0.236968i 0.578625 0.815593i \(-0.303589\pi\)
−0.815593 + 0.578625i \(0.803589\pi\)
\(234\) −116.807 186.535i −0.499174 0.797160i
\(235\) −10.8364 + 124.153i −0.0461123 + 0.528312i
\(236\) −13.3015 11.3503i −0.0563624 0.0480945i
\(237\) −238.157 + 116.908i −1.00488 + 0.493283i
\(238\) −57.7316 125.156i −0.242570 0.525865i
\(239\) 46.1374i 0.193044i 0.995331 + 0.0965218i \(0.0307718\pi\)
−0.995331 + 0.0965218i \(0.969228\pi\)
\(240\) −61.2716 + 232.047i −0.255298 + 0.966862i
\(241\) −212.165 −0.880351 −0.440176 0.897912i \(-0.645084\pi\)
−0.440176 + 0.897912i \(0.645084\pi\)
\(242\) −294.885 + 136.024i −1.21853 + 0.562082i
\(243\) −158.553 184.146i −0.652483 0.757803i
\(244\) 22.1286 25.9327i 0.0906910 0.106282i
\(245\) 91.5368 76.8404i 0.373620 0.313634i
\(246\) −28.3373 23.0221i −0.115192 0.0935856i
\(247\) 41.3638 41.3638i 0.167465 0.167465i
\(248\) −108.309 30.4679i −0.436729 0.122855i
\(249\) 87.3872 255.905i 0.350953 1.02773i
\(250\) −144.115 + 204.281i −0.576461 + 0.817125i
\(251\) −159.687 −0.636203 −0.318101 0.948057i \(-0.603045\pi\)
−0.318101 + 0.948057i \(0.603045\pi\)
\(252\) −150.940 98.7077i −0.598969 0.391697i
\(253\) −228.460 + 228.460i −0.903004 + 0.903004i
\(254\) 92.0498 249.684i 0.362401 0.983007i
\(255\) 192.434 74.4761i 0.754642 0.292063i
\(256\) −243.329 + 79.5433i −0.950503 + 0.310716i
\(257\) −98.0877 + 98.0877i −0.381664 + 0.381664i −0.871701 0.490037i \(-0.836983\pi\)
0.490037 + 0.871701i \(0.336983\pi\)
\(258\) −483.089 + 49.9957i −1.87244 + 0.193782i
\(259\) −71.6855 −0.276778
\(260\) 174.309 171.516i 0.670420 0.659679i
\(261\) 81.8785 105.906i 0.313711 0.405772i
\(262\) 263.604 121.595i 1.00612 0.464101i
\(263\) −141.919 + 141.919i −0.539614 + 0.539614i −0.923416 0.383802i \(-0.874615\pi\)
0.383802 + 0.923416i \(0.374615\pi\)
\(264\) 73.1685 + 397.328i 0.277153 + 1.50503i
\(265\) −9.96136 + 114.128i −0.0375900 + 0.430671i
\(266\) 16.5811 44.9759i 0.0623348 0.169082i
\(267\) −309.757 + 152.055i −1.16014 + 0.569496i
\(268\) −24.0902 304.356i −0.0898887 1.13566i
\(269\) −0.543377 −0.00201999 −0.00100999 0.999999i \(-0.500321\pi\)
−0.00100999 + 0.999999i \(0.500321\pi\)
\(270\) 161.691 216.231i 0.598856 0.800856i
\(271\) 362.830i 1.33886i 0.742877 + 0.669428i \(0.233461\pi\)
−0.742877 + 0.669428i \(0.766539\pi\)
\(272\) 178.179 + 129.212i 0.655071 + 0.475044i
\(273\) 80.9771 + 164.961i 0.296619 + 0.604252i
\(274\) 58.8025 159.501i 0.214608 0.582120i
\(275\) −72.9088 + 414.478i −0.265123 + 1.50719i
\(276\) 117.488 + 198.098i 0.425682 + 0.717746i
\(277\) −79.2266 79.2266i −0.286016 0.286016i 0.549486 0.835503i \(-0.314823\pi\)
−0.835503 + 0.549486i \(0.814823\pi\)
\(278\) −22.8801 + 10.5541i −0.0823025 + 0.0379643i
\(279\) 100.139 + 77.4197i 0.358922 + 0.277490i
\(280\) 70.8321 187.453i 0.252972 0.669474i
\(281\) 318.753i 1.13435i 0.823597 + 0.567176i \(0.191964\pi\)
−0.823597 + 0.567176i \(0.808036\pi\)
\(282\) 148.756 15.3950i 0.527503 0.0545922i
\(283\) −223.036 223.036i −0.788112 0.788112i 0.193072 0.981185i \(-0.438155\pi\)
−0.981185 + 0.193072i \(0.938155\pi\)
\(284\) 95.2057 111.572i 0.335231 0.392861i
\(285\) 65.6387 + 29.0082i 0.230311 + 0.101783i
\(286\) 142.395 386.245i 0.497885 1.35051i
\(287\) 21.5559 + 21.5559i 0.0751076 + 0.0751076i
\(288\) 287.335 + 19.5603i 0.997691 + 0.0679176i
\(289\) 99.7672i 0.345215i
\(290\) 134.556 + 63.3905i 0.463988 + 0.218588i
\(291\) −342.698 117.026i −1.17765 0.402150i
\(292\) 5.65974 + 71.5054i 0.0193827 + 0.244881i
\(293\) 75.3066 + 75.3066i 0.257019 + 0.257019i 0.823841 0.566822i \(-0.191827\pi\)
−0.566822 + 0.823841i \(0.691827\pi\)
\(294\) −111.311 90.4323i −0.378609 0.307593i
\(295\) −16.7409 + 14.0531i −0.0567489 + 0.0476378i
\(296\) 99.8408 56.0015i 0.337300 0.189194i
\(297\) 91.1009 445.286i 0.306737 1.49928i
\(298\) 47.0794 21.7166i 0.157984 0.0728746i
\(299\) 234.678i 0.784876i
\(300\) 273.410 + 123.479i 0.911366 + 0.411596i
\(301\) 405.511 1.34721
\(302\) 167.862 + 363.908i 0.555836 + 1.20499i
\(303\) 210.084 + 427.967i 0.693345 + 1.41243i
\(304\) 12.0421 + 75.5939i 0.0396123 + 0.248664i
\(305\) −27.3981 32.6382i −0.0898298 0.107011i
\(306\) −131.413 209.862i −0.429456 0.685823i
\(307\) 330.497 330.497i 1.07654 1.07654i 0.0797218 0.996817i \(-0.474597\pi\)
0.996817 0.0797218i \(-0.0254032\pi\)
\(308\) −26.6167 336.277i −0.0864179 1.09181i
\(309\) −114.936 39.2487i −0.371961 0.127018i
\(310\) −59.9385 + 127.229i −0.193350 + 0.410416i
\(311\) −26.5302 −0.0853063 −0.0426531 0.999090i \(-0.513581\pi\)
−0.0426531 + 0.999090i \(0.513581\pi\)
\(312\) −241.651 166.491i −0.774522 0.533624i
\(313\) 131.851 131.851i 0.421248 0.421248i −0.464385 0.885633i \(-0.653725\pi\)
0.885633 + 0.464385i \(0.153725\pi\)
\(314\) −371.513 136.964i −1.18316 0.436191i
\(315\) −152.873 + 165.686i −0.485311 + 0.525988i
\(316\) −229.614 + 269.087i −0.726628 + 0.851542i
\(317\) −66.6091 + 66.6091i −0.210123 + 0.210123i −0.804320 0.594197i \(-0.797470\pi\)
0.594197 + 0.804320i \(0.297470\pi\)
\(318\) 136.744 14.1519i 0.430012 0.0445027i
\(319\) 250.385 0.784907
\(320\) 47.7879 + 316.412i 0.149337 + 0.988786i
\(321\) 113.146 + 38.6375i 0.352480 + 0.120366i
\(322\) −80.5492 174.622i −0.250153 0.542305i
\(323\) 46.5363 46.5363i 0.144075 0.144075i
\(324\) −291.479 141.479i −0.899625 0.436663i
\(325\) −175.433 250.326i −0.539794 0.770234i
\(326\) 155.600 + 57.3644i 0.477301 + 0.175965i
\(327\) −211.441 430.732i −0.646608 1.31722i
\(328\) −46.8619 13.1825i −0.142872 0.0401906i
\(329\) −124.868 −0.379537
\(330\) 504.945 8.11159i 1.53014 0.0245806i
\(331\) 284.948i 0.860871i 0.902621 + 0.430436i \(0.141640\pi\)
−0.902621 + 0.430436i \(0.858360\pi\)
\(332\) −28.4491 359.428i −0.0856902 1.08261i
\(333\) −127.742 + 16.3452i −0.383610 + 0.0490845i
\(334\) 223.599 + 82.4335i 0.669460 + 0.246807i
\(335\) −380.190 33.1839i −1.13489 0.0990564i
\(336\) −236.956 40.9421i −0.705225 0.121852i
\(337\) 294.164 + 294.164i 0.872889 + 0.872889i 0.992786 0.119897i \(-0.0382564\pi\)
−0.119897 + 0.992786i \(0.538256\pi\)
\(338\) −16.3324 35.4068i −0.0483206 0.104754i
\(339\) −406.561 138.834i −1.19929 0.409539i
\(340\) 196.107 192.965i 0.576784 0.567543i
\(341\) 236.750i 0.694283i
\(342\) 19.2921 83.9267i 0.0564095 0.245400i
\(343\) 258.251 + 258.251i 0.752919 + 0.752919i
\(344\) −564.780 + 316.789i −1.64180 + 0.920899i
\(345\) 268.490 103.912i 0.778233 0.301193i
\(346\) −135.966 50.1262i −0.392966 0.144873i
\(347\) 274.053 + 274.053i 0.789779 + 0.789779i 0.981458 0.191679i \(-0.0613932\pi\)
−0.191679 + 0.981458i \(0.561393\pi\)
\(348\) 44.1729 172.936i 0.126934 0.496944i
\(349\) 129.175i 0.370128i −0.982726 0.185064i \(-0.940751\pi\)
0.982726 0.185064i \(-0.0592492\pi\)
\(350\) −216.459 126.051i −0.618453 0.360147i
\(351\) 181.912 + 275.493i 0.518269 + 0.784880i
\(352\) 299.773 + 447.560i 0.851629 + 1.27148i
\(353\) −381.746 381.746i −1.08143 1.08143i −0.996376 0.0850569i \(-0.972893\pi\)
−0.0850569 0.996376i \(-0.527107\pi\)
\(354\) 20.3574 + 16.5389i 0.0575067 + 0.0467201i
\(355\) −117.877 140.422i −0.332048 0.395555i
\(356\) −298.646 + 349.986i −0.838894 + 0.983108i
\(357\) 91.1033 + 185.589i 0.255191 + 0.519858i
\(358\) −22.8092 49.4480i −0.0637129 0.138123i
\(359\) 209.720i 0.584178i 0.956391 + 0.292089i \(0.0943503\pi\)
−0.956391 + 0.292089i \(0.905650\pi\)
\(360\) 83.4797 350.187i 0.231888 0.972742i
\(361\) −338.112 −0.936597
\(362\) 502.377 231.735i 1.38778 0.640151i
\(363\) 437.275 214.652i 1.20461 0.591329i
\(364\) 186.385 + 159.044i 0.512047 + 0.436934i
\(365\) 89.3217 + 7.79621i 0.244717 + 0.0213595i
\(366\) −32.2444 + 39.6889i −0.0880994 + 0.108440i
\(367\) 4.27652 4.27652i 0.0116527 0.0116527i −0.701256 0.712909i \(-0.747377\pi\)
0.712909 + 0.701256i \(0.247377\pi\)
\(368\) 248.602 + 180.281i 0.675550 + 0.489894i
\(369\) 43.3271 + 33.4971i 0.117418 + 0.0907781i
\(370\) −48.4111 134.655i −0.130841 0.363932i
\(371\) −114.785 −0.309393
\(372\) 163.519 + 41.7674i 0.439567 + 0.112278i
\(373\) 363.822 363.822i 0.975394 0.975394i −0.0243109 0.999704i \(-0.507739\pi\)
0.999704 + 0.0243109i \(0.00773917\pi\)
\(374\) 160.202 434.545i 0.428347 1.16188i
\(375\) 208.714 311.550i 0.556571 0.830800i
\(376\) 173.911 97.5478i 0.462529 0.259436i
\(377\) −128.600 + 128.600i −0.341114 + 0.341114i
\(378\) 229.918 + 142.554i 0.608248 + 0.377127i
\(379\) −732.379 −1.93240 −0.966199 0.257796i \(-0.917004\pi\)
−0.966199 + 0.257796i \(0.917004\pi\)
\(380\) 95.6807 + 0.772662i 0.251791 + 0.00203332i
\(381\) −128.995 + 377.749i −0.338570 + 0.991467i
\(382\) −617.492 + 284.835i −1.61647 + 0.745641i
\(383\) 343.246 343.246i 0.896203 0.896203i −0.0988948 0.995098i \(-0.531531\pi\)
0.995098 + 0.0988948i \(0.0315307\pi\)
\(384\) 362.007 128.090i 0.942727 0.333567i
\(385\) −420.064 36.6642i −1.09107 0.0952316i
\(386\) −98.7977 + 267.987i −0.255952 + 0.694267i
\(387\) 722.612 92.4613i 1.86721 0.238918i
\(388\) −481.332 + 38.0980i −1.24055 + 0.0981907i
\(389\) 600.575 1.54389 0.771947 0.635687i \(-0.219283\pi\)
0.771947 + 0.635687i \(0.219283\pi\)
\(390\) −255.178 + 263.510i −0.654303 + 0.675668i
\(391\) 264.025i 0.675255i
\(392\) −184.077 51.7819i −0.469583 0.132097i
\(393\) −390.889 + 191.882i −0.994628 + 0.488250i
\(394\) −220.706 + 598.662i −0.560168 + 1.51945i
\(395\) 284.293 + 338.666i 0.719728 + 0.857382i
\(396\) −124.105 593.169i −0.313398 1.49790i
\(397\) −295.285 295.285i −0.743792 0.743792i 0.229513 0.973306i \(-0.426287\pi\)
−0.973306 + 0.229513i \(0.926287\pi\)
\(398\) −520.625 + 240.152i −1.30810 + 0.603398i
\(399\) −23.2361 + 68.0445i −0.0582357 + 0.170537i
\(400\) 399.948 + 6.45991i 0.999870 + 0.0161498i
\(401\) 300.412i 0.749157i −0.927195 0.374578i \(-0.877787\pi\)
0.927195 0.374578i \(-0.122213\pi\)
\(402\) 47.1436 + 455.529i 0.117273 + 1.13316i
\(403\) −121.597 121.597i −0.301729 0.301729i
\(404\) 483.550 + 412.617i 1.19691 + 1.02133i
\(405\) −234.638 + 330.106i −0.579353 + 0.815077i
\(406\) −51.5506 + 139.830i −0.126972 + 0.344409i
\(407\) −170.326 170.326i −0.418492 0.418492i
\(408\) −271.869 187.311i −0.666346 0.459094i
\(409\) 53.8159i 0.131579i 0.997834 + 0.0657896i \(0.0209566\pi\)
−0.997834 + 0.0657896i \(0.979043\pi\)
\(410\) −25.9335 + 55.0480i −0.0632525 + 0.134263i
\(411\) −82.4035 + 241.310i −0.200495 + 0.587130i
\(412\) −161.432 + 12.7775i −0.391825 + 0.0310134i
\(413\) −15.4856 15.4856i −0.0374955 0.0374955i
\(414\) −183.353 292.807i −0.442881 0.707263i
\(415\) −448.983 39.1883i −1.08189 0.0944297i
\(416\) −383.837 75.9043i −0.922684 0.182462i
\(417\) 33.9281 16.6548i 0.0813623 0.0399397i
\(418\) 146.261 67.4667i 0.349906 0.161404i
\(419\) 582.593i 1.39044i −0.718799 0.695218i \(-0.755308\pi\)
0.718799 0.695218i \(-0.244692\pi\)
\(420\) −99.4307 + 283.662i −0.236740 + 0.675385i
\(421\) 486.678 1.15600 0.578002 0.816035i \(-0.303833\pi\)
0.578002 + 0.816035i \(0.303833\pi\)
\(422\) 154.009 + 333.875i 0.364950 + 0.791173i
\(423\) −222.511 + 28.4713i −0.526032 + 0.0673080i
\(424\) 159.868 89.6709i 0.377046 0.211488i
\(425\) −197.371 281.630i −0.464402 0.662658i
\(426\) −138.728 + 170.757i −0.325652 + 0.400837i
\(427\) 30.1909 30.1909i 0.0707046 0.0707046i
\(428\) 158.918 12.5785i 0.371304 0.0293891i
\(429\) −199.547 + 584.354i −0.465145 + 1.36213i
\(430\) 273.852 + 761.716i 0.636865 + 1.77143i
\(431\) 554.639 1.28686 0.643432 0.765503i \(-0.277510\pi\)
0.643432 + 0.765503i \(0.277510\pi\)
\(432\) −431.585 18.9292i −0.999040 0.0438177i
\(433\) 152.907 152.907i 0.353135 0.353135i −0.508140 0.861275i \(-0.669667\pi\)
0.861275 + 0.508140i \(0.169667\pi\)
\(434\) −132.216 48.7433i −0.304644 0.112312i
\(435\) −204.071 90.1867i −0.469128 0.207326i
\(436\) −486.674 415.283i −1.11622 0.952483i
\(437\) 64.9292 64.9292i 0.148579 0.148579i
\(438\) −11.0759 107.022i −0.0252874 0.244342i
\(439\) 218.824 0.498461 0.249231 0.968444i \(-0.419822\pi\)
0.249231 + 0.968444i \(0.419822\pi\)
\(440\) 613.690 277.093i 1.39475 0.629758i
\(441\) 170.192 + 131.579i 0.385923 + 0.298365i
\(442\) 140.905 + 305.467i 0.318789 + 0.691101i
\(443\) −39.9964 + 39.9964i −0.0902853 + 0.0902853i −0.750807 0.660522i \(-0.770335\pi\)
0.660522 + 0.750807i \(0.270335\pi\)
\(444\) −147.690 + 87.5923i −0.332635 + 0.197280i
\(445\) 369.763 + 440.483i 0.830928 + 0.989850i
\(446\) 18.6342 + 6.86980i 0.0417808 + 0.0154031i
\(447\) −69.8122 + 34.2699i −0.156180 + 0.0766665i
\(448\) −311.663 + 75.2655i −0.695676 + 0.168003i
\(449\) −236.471 −0.526660 −0.263330 0.964706i \(-0.584821\pi\)
−0.263330 + 0.964706i \(0.584821\pi\)
\(450\) −414.466 175.266i −0.921035 0.389480i
\(451\) 102.435i 0.227128i
\(452\) −571.030 + 45.1977i −1.26334 + 0.0999949i
\(453\) −264.895 539.626i −0.584757 1.19123i
\(454\) −97.3115 35.8754i −0.214343 0.0790208i
\(455\) 234.579 196.917i 0.515559 0.432785i
\(456\) −20.7947 112.922i −0.0456025 0.247636i
\(457\) −242.806 242.806i −0.531304 0.531304i 0.389657 0.920960i \(-0.372594\pi\)
−0.920960 + 0.389657i \(0.872594\pi\)
\(458\) −226.291 490.575i −0.494085 1.07112i
\(459\) 204.661 + 309.943i 0.445884 + 0.675257i
\(460\) 273.615 269.231i 0.594815 0.585286i
\(461\) 640.776i 1.38997i −0.719024 0.694985i \(-0.755411\pi\)
0.719024 0.694985i \(-0.244589\pi\)
\(462\) 52.0879 + 503.305i 0.112744 + 1.08940i
\(463\) 162.780 + 162.780i 0.351577 + 0.351577i 0.860696 0.509119i \(-0.170029\pi\)
−0.509119 + 0.860696i \(0.670029\pi\)
\(464\) −37.4391 235.022i −0.0806876 0.506512i
\(465\) 85.2754 192.958i 0.183388 0.414963i
\(466\) 146.527 + 54.0195i 0.314436 + 0.115922i
\(467\) −424.962 424.962i −0.909984 0.909984i 0.0862867 0.996270i \(-0.472500\pi\)
−0.996270 + 0.0862867i \(0.972500\pi\)
\(468\) 368.398 + 240.915i 0.787175 + 0.514775i
\(469\) 382.377i 0.815304i
\(470\) −84.3263 234.553i −0.179418 0.499048i
\(471\) 562.066 + 191.936i 1.19335 + 0.407508i
\(472\) 33.6653 + 9.47025i 0.0713248 + 0.0200641i
\(473\) 963.503 + 963.503i 2.03700 + 2.03700i
\(474\) 334.579 411.826i 0.705864 0.868832i
\(475\) 20.7209 117.796i 0.0436230 0.247992i
\(476\) 209.693 + 178.932i 0.440531 + 0.375909i
\(477\) −204.544 + 26.1723i −0.428813 + 0.0548685i
\(478\) −38.6505 83.7902i −0.0808588 0.175293i
\(479\) 439.071i 0.916641i 0.888787 + 0.458321i \(0.151549\pi\)
−0.888787 + 0.458321i \(0.848451\pi\)
\(480\) −83.1162 472.749i −0.173159 0.984894i
\(481\) 174.962 0.363747
\(482\) 385.312 177.736i 0.799403 0.368746i
\(483\) 127.111 + 258.941i 0.263169 + 0.536109i
\(484\) 421.591 494.066i 0.871055 1.02080i
\(485\) −52.4795 + 601.261i −0.108205 + 1.23971i
\(486\) 442.213 + 201.604i 0.909902 + 0.414823i
\(487\) 308.231 308.231i 0.632918 0.632918i −0.315881 0.948799i \(-0.602300\pi\)
0.948799 + 0.315881i \(0.102300\pi\)
\(488\) −18.4633 + 65.6341i −0.0378345 + 0.134496i
\(489\) −235.409 80.3883i −0.481409 0.164393i
\(490\) −101.869 + 216.233i −0.207895 + 0.441291i
\(491\) −751.660 −1.53088 −0.765438 0.643509i \(-0.777478\pi\)
−0.765438 + 0.643509i \(0.777478\pi\)
\(492\) 70.7496 + 18.0714i 0.143800 + 0.0367306i
\(493\) −144.681 + 144.681i −0.293472 + 0.293472i
\(494\) −40.4692 + 109.772i −0.0819215 + 0.222211i
\(495\) −756.904 + 30.4448i −1.52910 + 0.0615046i
\(496\) 222.223 35.4003i 0.448031 0.0713715i
\(497\) 129.893 129.893i 0.261353 0.261353i
\(498\) 55.6739 + 537.955i 0.111795 + 1.08023i
\(499\) 304.485 0.610191 0.305096 0.952322i \(-0.401312\pi\)
0.305096 + 0.952322i \(0.401312\pi\)
\(500\) 90.5962 491.724i 0.181192 0.983448i
\(501\) −338.286 115.519i −0.675221 0.230577i
\(502\) 290.007 133.774i 0.577704 0.266481i
\(503\) −230.058 + 230.058i −0.457372 + 0.457372i −0.897792 0.440420i \(-0.854830\pi\)
0.440420 + 0.897792i \(0.354830\pi\)
\(504\) 356.812 + 52.8166i 0.707961 + 0.104795i
\(505\) 608.582 510.874i 1.20511 1.01163i
\(506\) 223.519 606.293i 0.441738 1.19821i
\(507\) 25.7733 + 52.5035i 0.0508348 + 0.103557i
\(508\) 41.9947 + 530.563i 0.0826667 + 1.04442i
\(509\) −98.9386 −0.194378 −0.0971892 0.995266i \(-0.530985\pi\)
−0.0971892 + 0.995266i \(0.530985\pi\)
\(510\) −287.088 + 296.462i −0.562918 + 0.581299i
\(511\) 89.8357i 0.175804i
\(512\) 375.274 348.301i 0.732956 0.680276i
\(513\) −25.8912 + 126.552i −0.0504702 + 0.246690i
\(514\) 95.9665 260.307i 0.186705 0.506435i
\(515\) −17.6009 + 201.654i −0.0341764 + 0.391562i
\(516\) 835.454 495.493i 1.61910 0.960257i
\(517\) −296.688 296.688i −0.573865 0.573865i
\(518\) 130.188 60.0528i 0.251328 0.115932i
\(519\) 205.705 + 70.2448i 0.396349 + 0.135346i
\(520\) −172.879 + 457.514i −0.332460 + 0.879835i
\(521\) 485.997i 0.932816i −0.884570 0.466408i \(-0.845548\pi\)
0.884570 0.466408i \(-0.154452\pi\)
\(522\) −59.9791 + 260.928i −0.114902 + 0.499863i
\(523\) 303.922 + 303.922i 0.581112 + 0.581112i 0.935209 0.354096i \(-0.115212\pi\)
−0.354096 + 0.935209i \(0.615212\pi\)
\(524\) −376.868 + 441.655i −0.719214 + 0.842854i
\(525\) 329.157 + 181.186i 0.626966 + 0.345115i
\(526\) 138.849 376.627i 0.263972 0.716021i
\(527\) −136.803 136.803i −0.259588 0.259588i
\(528\) −465.733 660.291i −0.882069 1.25055i
\(529\) 160.623i 0.303636i
\(530\) −77.5170 215.613i −0.146259 0.406816i
\(531\) −31.1260 24.0641i −0.0586176 0.0453185i
\(532\) 7.56456 + 95.5710i 0.0142191 + 0.179645i
\(533\) −52.6112 52.6112i −0.0987077 0.0987077i
\(534\) 435.168 535.639i 0.814922 1.00307i
\(535\) 17.3268 198.514i 0.0323865 0.371054i
\(536\) 298.717 + 532.560i 0.557308 + 0.993583i
\(537\) 35.9941 + 73.3246i 0.0670281 + 0.136545i
\(538\) 0.986826 0.455200i 0.00183425 0.000846097i
\(539\) 402.370i 0.746512i
\(540\) −112.505 + 528.150i −0.208343 + 0.978056i
\(541\) −388.275 −0.717700 −0.358850 0.933395i \(-0.616831\pi\)
−0.358850 + 0.933395i \(0.616831\pi\)
\(542\) −303.952 658.936i −0.560797 1.21575i
\(543\) −744.956 + 365.689i −1.37193 + 0.673460i
\(544\) −431.835 85.3962i −0.793815 0.156978i
\(545\) −612.514 + 514.174i −1.12388 + 0.943439i
\(546\) −285.254 231.749i −0.522444 0.424448i
\(547\) −169.325 + 169.325i −0.309551 + 0.309551i −0.844735 0.535184i \(-0.820242\pi\)
0.535184 + 0.844735i \(0.320242\pi\)
\(548\) 26.8267 + 338.929i 0.0489538 + 0.618484i
\(549\) 46.9156 60.6834i 0.0854565 0.110534i
\(550\) −214.809 813.812i −0.390563 1.47966i
\(551\) −71.1604 −0.129148
\(552\) −379.322 261.343i −0.687177 0.473447i
\(553\) −313.272 + 313.272i −0.566495 + 0.566495i
\(554\) 210.253 + 77.5132i 0.379519 + 0.139916i
\(555\) 77.4705 + 200.171i 0.139586 + 0.360668i
\(556\) 32.7111 38.3345i 0.0588330 0.0689469i
\(557\) −310.481 + 310.481i −0.557417 + 0.557417i −0.928571 0.371155i \(-0.878962\pi\)
0.371155 + 0.928571i \(0.378962\pi\)
\(558\) −246.719 56.7128i −0.442149 0.101636i
\(559\) −989.727 −1.77053
\(560\) 28.3959 + 399.771i 0.0507069 + 0.713876i
\(561\) −224.501 + 657.427i −0.400179 + 1.17188i
\(562\) −267.027 578.887i −0.475137 1.03005i
\(563\) 234.187 234.187i 0.415962 0.415962i −0.467847 0.883809i \(-0.654970\pi\)
0.883809 + 0.467847i \(0.154970\pi\)
\(564\) −257.259 + 152.575i −0.456132 + 0.270524i
\(565\) −62.2592 + 713.308i −0.110193 + 1.26249i
\(566\) 591.898 + 218.212i 1.04576 + 0.385534i
\(567\) −349.937 205.445i −0.617173 0.362336i
\(568\) −79.4360 + 282.383i −0.139852 + 0.497153i
\(569\) 386.708 0.679627 0.339813 0.940493i \(-0.389636\pi\)
0.339813 + 0.940493i \(0.389636\pi\)
\(570\) −143.507 + 2.30534i −0.251767 + 0.00404446i
\(571\) 556.152i 0.973996i 0.873403 + 0.486998i \(0.161908\pi\)
−0.873403 + 0.486998i \(0.838092\pi\)
\(572\) 64.9631 + 820.747i 0.113572 + 1.43487i
\(573\) 915.656 449.483i 1.59800 0.784439i
\(574\) −57.2055 21.0897i −0.0996612 0.0367417i
\(575\) −275.379 392.940i −0.478920 0.683374i
\(576\) −538.215 + 205.184i −0.934401 + 0.356223i
\(577\) 695.792 + 695.792i 1.20588 + 1.20588i 0.972350 + 0.233530i \(0.0750277\pi\)
0.233530 + 0.972350i \(0.424972\pi\)
\(578\) −83.5775 181.187i −0.144598 0.313473i
\(579\) 138.451 405.440i 0.239121 0.700242i
\(580\) −297.472 2.40221i −0.512882 0.00414174i
\(581\) 451.566i 0.777223i
\(582\) 720.408 74.5563i 1.23781 0.128104i
\(583\) −272.731 272.731i −0.467806 0.467806i
\(584\) −70.1805 125.120i −0.120172 0.214246i
\(585\) 373.115 404.389i 0.637804 0.691263i
\(586\) −199.850 73.6780i −0.341042 0.125730i
\(587\) 241.691 + 241.691i 0.411740 + 0.411740i 0.882344 0.470604i \(-0.155964\pi\)
−0.470604 + 0.882344i \(0.655964\pi\)
\(588\) 277.909 + 70.9859i 0.472635 + 0.120724i
\(589\) 67.2853i 0.114236i
\(590\) 18.6305 39.5462i 0.0315771 0.0670274i
\(591\) 309.289 905.721i 0.523331 1.53252i
\(592\) −134.407 + 185.343i −0.227039 + 0.313080i
\(593\) 109.471 + 109.471i 0.184605 + 0.184605i 0.793359 0.608754i \(-0.208330\pi\)
−0.608754 + 0.793359i \(0.708330\pi\)
\(594\) 207.579 + 885.001i 0.349459 + 1.48990i
\(595\) 263.913 221.542i 0.443552 0.372339i
\(596\) −67.3082 + 78.8791i −0.112933 + 0.132348i
\(597\) 772.015 378.972i 1.29316 0.634794i
\(598\) 196.596 + 426.199i 0.328755 + 0.712707i
\(599\) 527.412i 0.880487i 0.897878 + 0.440243i \(0.145108\pi\)
−0.897878 + 0.440243i \(0.854892\pi\)
\(600\) −599.981 + 4.79255i −0.999968 + 0.00798759i
\(601\) −133.338 −0.221861 −0.110930 0.993828i \(-0.535383\pi\)
−0.110930 + 0.993828i \(0.535383\pi\)
\(602\) −736.448 + 339.707i −1.22334 + 0.564297i
\(603\) −87.1866 681.388i −0.144588 1.13000i
\(604\) −609.710 520.270i −1.00945 0.861375i
\(605\) −521.984 621.818i −0.862783 1.02780i
\(606\) −740.052 601.239i −1.22121 0.992144i
\(607\) −401.515 + 401.515i −0.661475 + 0.661475i −0.955728 0.294253i \(-0.904929\pi\)
0.294253 + 0.955728i \(0.404929\pi\)
\(608\) −85.1967 127.198i −0.140126 0.209207i
\(609\) 72.2410 211.550i 0.118622 0.347373i
\(610\) 77.0995 + 36.3222i 0.126393 + 0.0595445i
\(611\) 304.763 0.498794
\(612\) 414.466 + 271.041i 0.677233 + 0.442878i
\(613\) −604.618 + 604.618i −0.986326 + 0.986326i −0.999908 0.0135821i \(-0.995677\pi\)
0.0135821 + 0.999908i \(0.495677\pi\)
\(614\) −323.350 + 877.082i −0.526629 + 1.42847i
\(615\) 36.8960 83.4869i 0.0599935 0.135751i
\(616\) 330.046 + 588.414i 0.535789 + 0.955218i
\(617\) −51.5846 + 51.5846i −0.0836055 + 0.0836055i −0.747673 0.664067i \(-0.768829\pi\)
0.664067 + 0.747673i \(0.268829\pi\)
\(618\) 241.615 25.0051i 0.390962 0.0404614i
\(619\) 1063.63 1.71831 0.859155 0.511716i \(-0.170990\pi\)
0.859155 + 0.511716i \(0.170990\pi\)
\(620\) 2.27139 281.272i 0.00366354 0.453665i
\(621\) 285.550 + 432.444i 0.459823 + 0.696367i
\(622\) 48.1816 22.2251i 0.0774623 0.0357316i
\(623\) −407.454 + 407.454i −0.654020 + 0.654020i
\(624\) 578.335 + 99.9270i 0.926819 + 0.160139i
\(625\) −587.483 213.282i −0.939972 0.341251i
\(626\) −128.999 + 349.908i −0.206069 + 0.558959i
\(627\) −216.884 + 106.466i −0.345908 + 0.169802i
\(628\) 789.443 62.4854i 1.25707 0.0994990i
\(629\) 196.841 0.312943
\(630\) 138.833 428.968i 0.220370 0.680902i
\(631\) 834.260i 1.32212i −0.750331 0.661062i \(-0.770106\pi\)
0.750331 0.661062i \(-0.229894\pi\)
\(632\) 191.581 681.043i 0.303135 1.07760i
\(633\) −243.034 495.091i −0.383939 0.782134i
\(634\) 65.1686 176.769i 0.102790 0.278815i
\(635\) 662.758 + 57.8471i 1.04371 + 0.0910978i
\(636\) −236.485 + 140.255i −0.371832 + 0.220527i
\(637\) −206.661 206.661i −0.324428 0.324428i
\(638\) −454.725 + 209.754i −0.712735 + 0.328768i
\(639\) 201.849 261.083i 0.315882 0.408581i
\(640\) −351.854 534.602i −0.549771 0.835315i
\(641\) 104.566i 0.163130i 0.996668 + 0.0815648i \(0.0259918\pi\)
−0.996668 + 0.0815648i \(0.974008\pi\)
\(642\) −237.852 + 24.6157i −0.370486 + 0.0383423i
\(643\) 357.160 + 357.160i 0.555459 + 0.555459i 0.928011 0.372552i \(-0.121517\pi\)
−0.372552 + 0.928011i \(0.621517\pi\)
\(644\) 292.571 + 249.653i 0.454303 + 0.387660i
\(645\) −438.235 1132.33i −0.679435 1.75554i
\(646\) −45.5299 + 123.499i −0.0704797 + 0.191175i
\(647\) 428.808 + 428.808i 0.662764 + 0.662764i 0.956031 0.293266i \(-0.0947423\pi\)
−0.293266 + 0.956031i \(0.594742\pi\)
\(648\) 647.874 + 12.7606i 0.999806 + 0.0196923i
\(649\) 73.5884i 0.113387i
\(650\) 528.308 + 307.653i 0.812782 + 0.473312i
\(651\) 200.030 + 68.3070i 0.307266 + 0.104926i
\(652\) −330.641 + 26.1706i −0.507118 + 0.0401390i
\(653\) −216.356 216.356i −0.331327 0.331327i 0.521763 0.853090i \(-0.325274\pi\)
−0.853090 + 0.521763i \(0.825274\pi\)
\(654\) 744.833 + 605.123i 1.13889 + 0.925265i
\(655\) 466.612 + 555.855i 0.712385 + 0.848634i
\(656\) 96.1491 15.3166i 0.146569 0.0233485i
\(657\) 20.4836 + 160.085i 0.0311775 + 0.243661i
\(658\) 226.772 104.605i 0.344638 0.158974i
\(659\) 862.678i 1.30907i −0.756031 0.654535i \(-0.772864\pi\)
0.756031 0.654535i \(-0.227136\pi\)
\(660\) −910.236 + 437.737i −1.37915 + 0.663238i
\(661\) 56.1770 0.0849879 0.0424939 0.999097i \(-0.486470\pi\)
0.0424939 + 0.999097i \(0.486470\pi\)
\(662\) −238.708 517.494i −0.360587 0.781714i
\(663\) −222.355 452.966i −0.335377 0.683206i
\(664\) 352.768 + 628.924i 0.531277 + 0.947175i
\(665\) 119.384 + 10.4201i 0.179524 + 0.0156693i
\(666\) 218.299 136.697i 0.327777 0.205251i
\(667\) −201.865 + 201.865i −0.302646 + 0.302646i
\(668\) −475.135 + 37.6075i −0.711281 + 0.0562987i
\(669\) −28.1919 9.62707i −0.0421404 0.0143902i
\(670\) 718.261 258.229i 1.07203 0.385417i
\(671\) 143.468 0.213813
\(672\) 464.633 124.149i 0.691419 0.184745i
\(673\) 236.472 236.472i 0.351371 0.351371i −0.509249 0.860619i \(-0.670077\pi\)
0.860619 + 0.509249i \(0.170077\pi\)
\(674\) −780.659 287.802i −1.15825 0.427006i
\(675\) 627.863 + 247.817i 0.930167 + 0.367136i
\(676\) 59.3223 + 50.6203i 0.0877550 + 0.0748820i
\(677\) −754.987 + 754.987i −1.11520 + 1.11520i −0.122759 + 0.992437i \(0.539174\pi\)
−0.992437 + 0.122759i \(0.960826\pi\)
\(678\) 854.659 88.4502i 1.26056 0.130458i
\(679\) −604.720 −0.890604
\(680\) −194.498 + 514.726i −0.286026 + 0.756950i
\(681\) 147.224 + 50.2744i 0.216187 + 0.0738244i
\(682\) −198.332 429.962i −0.290809 0.630443i
\(683\) 848.561 848.561i 1.24240 1.24240i 0.283401 0.959002i \(-0.408537\pi\)
0.959002 0.283401i \(-0.0914626\pi\)
\(684\) 35.2712 + 168.581i 0.0515661 + 0.246463i
\(685\) 423.377 + 36.9534i 0.618069 + 0.0539466i
\(686\) −685.353 252.666i −0.999057 0.368318i
\(687\) 357.098 + 727.455i 0.519794 + 1.05889i
\(688\) 760.314 1048.45i 1.10511 1.52391i
\(689\) 280.154 0.406609
\(690\) −400.556 + 413.635i −0.580516 + 0.599471i
\(691\) 973.366i 1.40863i −0.709886 0.704317i \(-0.751253\pi\)
0.709886 0.704317i \(-0.248747\pi\)
\(692\) 288.920 22.8684i 0.417515 0.0330468i
\(693\) −96.3306 752.851i −0.139005 1.08637i
\(694\) −727.289 268.127i −1.04797 0.386350i
\(695\) −40.5006 48.2467i −0.0582743 0.0694197i
\(696\) 64.6509 + 351.074i 0.0928892 + 0.504417i
\(697\) −59.1903 59.1903i −0.0849215 0.0849215i
\(698\) 108.213 + 234.594i 0.155033 + 0.336094i
\(699\) −221.682 75.7008i −0.317142 0.108299i
\(700\) 498.707 + 47.5892i 0.712438 + 0.0679845i
\(701\) 8.02635i 0.0114499i −0.999984 0.00572493i \(-0.998178\pi\)
0.999984 0.00572493i \(-0.00182231\pi\)
\(702\) −561.158 347.930i −0.799371 0.495626i
\(703\) 48.4074 + 48.4074i 0.0688583 + 0.0688583i
\(704\) −919.350 561.685i −1.30590 0.797848i
\(705\) 134.944 + 348.673i 0.191410 + 0.494572i
\(706\) 1013.09 + 373.490i 1.43497 + 0.529023i
\(707\) 562.949 + 562.949i 0.796250 + 0.796250i
\(708\) −50.8261 12.9824i −0.0717883 0.0183368i
\(709\) 378.225i 0.533463i 0.963771 + 0.266731i \(0.0859437\pi\)
−0.963771 + 0.266731i \(0.914056\pi\)
\(710\) 331.712 + 156.272i 0.467199 + 0.220101i
\(711\) −486.813 + 629.673i −0.684688 + 0.885615i
\(712\) 249.179 885.794i 0.349970 1.24409i
\(713\) −190.872 190.872i −0.267703 0.267703i
\(714\) −320.925 260.729i −0.449475 0.365166i
\(715\) 1025.24 + 89.4858i 1.43391 + 0.125155i
\(716\) 82.8476 + 70.6946i 0.115709 + 0.0987354i
\(717\) 60.9924 + 124.249i 0.0850660 + 0.173291i
\(718\) −175.688 380.872i −0.244690 0.530463i
\(719\) 901.949i 1.25445i −0.778838 0.627225i \(-0.784191\pi\)
0.778838 0.627225i \(-0.215809\pi\)
\(720\) 141.753 + 705.908i 0.196880 + 0.980428i
\(721\) −202.815 −0.281296
\(722\) 614.044 283.245i 0.850477 0.392305i
\(723\) −571.365 + 280.476i −0.790270 + 0.387933i
\(724\) −718.236 + 841.707i −0.992038 + 1.16258i
\(725\) −64.4215 + 366.229i −0.0888572 + 0.505143i
\(726\) −614.315 + 756.146i −0.846163 + 1.04152i
\(727\) −647.476 + 647.476i −0.890613 + 0.890613i −0.994581 0.103967i \(-0.966846\pi\)
0.103967 + 0.994581i \(0.466846\pi\)
\(728\) −471.729 132.700i −0.647979 0.182280i
\(729\) −670.424 286.308i −0.919649 0.392740i
\(730\) −168.748 + 60.6683i −0.231162 + 0.0831073i
\(731\) −1113.49 −1.52325
\(732\) 25.3106 99.0909i 0.0345773 0.135370i
\(733\) −664.993 + 664.993i −0.907221 + 0.907221i −0.996047 0.0888262i \(-0.971688\pi\)
0.0888262 + 0.996047i \(0.471688\pi\)
\(734\) −4.18404 + 11.3491i −0.00570033 + 0.0154620i
\(735\) 144.930 327.942i 0.197184 0.446180i
\(736\) −602.513 119.148i −0.818631 0.161886i
\(737\) 908.537 908.537i 1.23275 1.23275i
\(738\) −106.748 24.5379i −0.144645 0.0332492i
\(739\) 605.307 0.819090 0.409545 0.912290i \(-0.365687\pi\)
0.409545 + 0.912290i \(0.365687\pi\)
\(740\) 200.723 + 203.991i 0.271247 + 0.275664i
\(741\) 56.7120 166.075i 0.0765344 0.224123i
\(742\) 208.460 96.1580i 0.280944 0.129593i
\(743\) −149.548 + 149.548i −0.201275 + 0.201275i −0.800546 0.599271i \(-0.795457\pi\)
0.599271 + 0.800546i \(0.295457\pi\)
\(744\) −331.956 + 61.1303i −0.446178 + 0.0821643i
\(745\) 83.3363 + 99.2751i 0.111861 + 0.133255i
\(746\) −355.954 + 965.519i −0.477150 + 1.29426i
\(747\) −102.963 804.681i −0.137835 1.07722i
\(748\) 73.0868 + 923.382i 0.0977096 + 1.23447i
\(749\) 199.656 0.266564
\(750\) −118.052 + 740.651i −0.157403 + 0.987534i
\(751\) 988.027i 1.31562i −0.753186 0.657808i \(-0.771484\pi\)
0.753186 0.657808i \(-0.228516\pi\)
\(752\) −234.121 + 322.846i −0.311331 + 0.429316i
\(753\) −430.041 + 211.101i −0.571103 + 0.280347i
\(754\) 125.819 341.282i 0.166869 0.452629i
\(755\) −767.364 + 644.162i −1.01638 + 0.853195i
\(756\) −536.975 66.2839i −0.710284 0.0876771i
\(757\) 590.607 + 590.607i 0.780195 + 0.780195i 0.979863 0.199669i \(-0.0639866\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(758\) 1330.07 613.532i 1.75471 0.809410i
\(759\) −313.231 + 917.267i −0.412690 + 1.20852i
\(760\) −174.413 + 78.7509i −0.229491 + 0.103620i
\(761\) 354.692i 0.466087i 0.972466 + 0.233043i \(0.0748684\pi\)
−0.972466 + 0.233043i \(0.925132\pi\)
\(762\) −82.1820 794.092i −0.107850 1.04212i
\(763\) −566.586 566.586i −0.742576 0.742576i
\(764\) 882.813 1034.58i 1.15551 1.35416i
\(765\) 419.774 454.958i 0.548724 0.594716i
\(766\) −335.823 + 910.914i −0.438411 + 1.18918i
\(767\) 37.7956 + 37.7956i 0.0492772 + 0.0492772i
\(768\) −550.137 + 535.886i −0.716324 + 0.697768i
\(769\) 262.078i 0.340804i −0.985375 0.170402i \(-0.945493\pi\)
0.985375 0.170402i \(-0.0545067\pi\)
\(770\) 793.592 285.312i 1.03064 0.370535i
\(771\) −134.484 + 393.822i −0.174428 + 0.510794i
\(772\) −45.0732 569.456i −0.0583849 0.737638i
\(773\) 616.984 + 616.984i 0.798168 + 0.798168i 0.982806 0.184639i \(-0.0591115\pi\)
−0.184639 + 0.982806i \(0.559112\pi\)
\(774\) −1234.88 + 773.269i −1.59545 + 0.999056i
\(775\) −346.285 60.9133i −0.446820 0.0785978i
\(776\) 842.231 472.413i 1.08535 0.608780i
\(777\) −193.051 + 94.7662i −0.248457 + 0.121964i
\(778\) −1090.70 + 503.117i −1.40193 + 0.646679i
\(779\) 29.1122i 0.0373713i
\(780\) 242.679 692.330i 0.311127 0.887603i
\(781\) 617.256 0.790340
\(782\) 221.180 + 479.495i 0.282839 + 0.613165i
\(783\) 80.4958 393.450i 0.102804 0.502490i
\(784\) 377.681 60.1647i 0.481735 0.0767407i
\(785\) 86.0727 986.141i 0.109647 1.25623i
\(786\) 549.148 675.934i 0.698662 0.859967i
\(787\) −471.258 + 471.258i −0.598803 + 0.598803i −0.939994 0.341191i \(-0.889170\pi\)
0.341191 + 0.939994i \(0.389170\pi\)
\(788\) −100.690 1272.12i −0.127779 1.61437i
\(789\) −194.578 + 569.802i −0.246614 + 0.722183i
\(790\) −800.012 376.892i −1.01267 0.477078i
\(791\) −717.412 −0.906969
\(792\) 722.300 + 973.287i 0.911995 + 1.22890i
\(793\) −73.6865 + 73.6865i −0.0929212 + 0.0929212i
\(794\) 783.636 + 288.900i 0.986947 + 0.363853i
\(795\) 124.048 + 320.518i 0.156035 + 0.403168i
\(796\) 744.324 872.281i 0.935081 1.09583i
\(797\) 485.701 485.701i 0.609411 0.609411i −0.333381 0.942792i \(-0.608189\pi\)
0.942792 + 0.333381i \(0.108189\pi\)
\(798\) −14.8036 143.041i −0.0185508 0.179249i
\(799\) 342.874 0.429129
\(800\) −731.757 + 323.315i −0.914696 + 0.404143i
\(801\) −633.170 + 818.979i −0.790474 + 1.02245i
\(802\) 251.663 + 545.578i 0.313794 + 0.680271i
\(803\) −213.451 + 213.451i −0.265818 + 0.265818i
\(804\) −467.226 787.793i −0.581127 0.979842i
\(805\) 368.222 309.103i 0.457418 0.383979i
\(806\) 322.697 + 118.967i 0.400368 + 0.147602i
\(807\) −1.46333 + 0.718328i −0.00181329 + 0.000890122i
\(808\) −1223.83 344.272i −1.51465 0.426079i
\(809\) 183.688 0.227056 0.113528 0.993535i \(-0.463785\pi\)
0.113528 + 0.993535i \(0.463785\pi\)
\(810\) 149.587 796.068i 0.184676 0.982800i
\(811\) 1332.68i 1.64325i 0.570027 + 0.821626i \(0.306933\pi\)
−0.570027 + 0.821626i \(0.693067\pi\)
\(812\) −23.5182 297.131i −0.0289634 0.365924i
\(813\) 479.651 + 977.111i 0.589977 + 1.20186i
\(814\) 452.016 + 166.643i 0.555303 + 0.204721i
\(815\) −36.0497 + 413.023i −0.0442327 + 0.506777i
\(816\) 650.656 + 112.423i 0.797373 + 0.137773i
\(817\) −273.831 273.831i −0.335166 0.335166i
\(818\) −45.0829 97.7350i −0.0551136 0.119480i
\(819\) 436.147 + 337.194i 0.532536 + 0.411715i
\(820\) 0.982761 121.698i 0.00119849 0.148412i
\(821\) 1157.86i 1.41030i 0.709057 + 0.705152i \(0.249121\pi\)
−0.709057 + 0.705152i \(0.750879\pi\)
\(822\) −52.4988 507.275i −0.0638672 0.617123i
\(823\) −420.085 420.085i −0.510432 0.510432i 0.404227 0.914659i \(-0.367541\pi\)
−0.914659 + 0.404227i \(0.867541\pi\)
\(824\) 282.472 158.441i 0.342806 0.192282i
\(825\) 351.583 + 1212.58i 0.426162 + 1.46980i
\(826\) 41.0961 + 15.1507i 0.0497532 + 0.0183423i
\(827\) −450.627 450.627i −0.544893 0.544893i 0.380066 0.924959i \(-0.375901\pi\)
−0.924959 + 0.380066i \(0.875901\pi\)
\(828\) 578.279 + 378.167i 0.698404 + 0.456723i
\(829\) 1059.56i 1.27812i −0.769155 0.639062i \(-0.779323\pi\)
0.769155 0.639062i \(-0.220677\pi\)
\(830\) 848.227 304.954i 1.02196 0.367415i
\(831\) −318.094 108.624i −0.382785 0.130715i
\(832\) 760.672 183.700i 0.914270 0.220793i
\(833\) −232.504 232.504i −0.279116 0.279116i
\(834\) −47.6646 + 58.6692i −0.0571517 + 0.0703468i
\(835\) −51.8039 + 593.520i −0.0620406 + 0.710803i
\(836\) −209.105 + 245.052i −0.250126 + 0.293125i
\(837\) 372.024 + 76.1123i 0.444473 + 0.0909346i
\(838\) 488.053 + 1058.05i 0.582402 + 1.26259i
\(839\) 425.692i 0.507380i −0.967286 0.253690i \(-0.918356\pi\)
0.967286 0.253690i \(-0.0816443\pi\)
\(840\) −57.0546 598.453i −0.0679221 0.712444i
\(841\) −619.762 −0.736935
\(842\) −883.855 + 407.702i −1.04971 + 0.484207i
\(843\) 421.382 + 858.410i 0.499860 + 1.01828i
\(844\) −559.391 477.333i −0.662786 0.565560i
\(845\) 74.6615 62.6745i 0.0883568 0.0741710i
\(846\) 380.252 238.110i 0.449470 0.281454i
\(847\) 575.192 575.192i 0.679093 0.679093i
\(848\) −215.216 + 296.776i −0.253792 + 0.349972i
\(849\) −895.488 305.794i −1.05476 0.360182i
\(850\) 594.373 + 346.125i 0.699263 + 0.407205i
\(851\) 274.640 0.322726
\(852\) 108.896 426.327i 0.127812 0.500384i
\(853\) 533.860 533.860i 0.625861 0.625861i −0.321163 0.947024i \(-0.604074\pi\)
0.947024 + 0.321163i \(0.104074\pi\)
\(854\) −29.5380 + 80.1213i −0.0345878 + 0.0938188i
\(855\) 215.115 8.65251i 0.251596 0.0101199i
\(856\) −278.073 + 155.973i −0.324852 + 0.182212i
\(857\) −575.339 + 575.339i −0.671340 + 0.671340i −0.958025 0.286685i \(-0.907447\pi\)
0.286685 + 0.958025i \(0.407447\pi\)
\(858\) −127.130 1228.41i −0.148171 1.43171i
\(859\) −730.948 −0.850929 −0.425465 0.904975i \(-0.639889\pi\)
−0.425465 + 0.904975i \(0.639889\pi\)
\(860\) −1135.45 1153.94i −1.32029 1.34179i
\(861\) 86.5468 + 29.5543i 0.100519 + 0.0343256i
\(862\) −1007.28 + 464.635i −1.16854 + 0.539019i
\(863\) −503.710 + 503.710i −0.583673 + 0.583673i −0.935911 0.352238i \(-0.885421\pi\)
0.352238 + 0.935911i \(0.385421\pi\)
\(864\) 799.659 327.172i 0.925531 0.378672i
\(865\) 31.5009 360.908i 0.0364172 0.417235i
\(866\) −149.601 + 405.789i −0.172749 + 0.468579i
\(867\) 131.889 + 268.676i 0.152122 + 0.309891i
\(868\) 280.950 22.2375i 0.323675 0.0256193i
\(869\) −1488.68 −1.71310
\(870\) 446.164 7.16732i 0.512833 0.00823830i
\(871\) 933.264i 1.07149i
\(872\) 1231.74 + 346.496i 1.41255 + 0.397358i
\(873\) −1077.60 + 137.883i −1.23436 + 0.157942i
\(874\) −63.5250 + 172.311i −0.0726831 + 0.197152i
\(875\) 161.705 604.977i 0.184806 0.691402i
\(876\) 109.770 + 185.084i 0.125308 + 0.211283i
\(877\) −1002.77 1002.77i −1.14341 1.14341i −0.987822 0.155586i \(-0.950273\pi\)
−0.155586 0.987822i \(-0.549727\pi\)
\(878\) −397.407 + 183.315i −0.452627 + 0.208787i
\(879\) 302.356 + 103.249i 0.343977 + 0.117462i
\(880\) −882.395 + 1017.33i −1.00272 + 1.15606i
\(881\) 1337.17i 1.51779i −0.651213 0.758895i \(-0.725739\pi\)
0.651213 0.758895i \(-0.274261\pi\)
\(882\) −419.312 96.3865i −0.475411 0.109282i
\(883\) 29.5709 + 29.5709i 0.0334891 + 0.0334891i 0.723653 0.690164i \(-0.242462\pi\)
−0.690164 + 0.723653i \(0.742462\pi\)
\(884\) −511.795 436.719i −0.578953 0.494026i
\(885\) −26.5059 + 59.9765i −0.0299502 + 0.0677701i
\(886\) 39.1314 106.143i 0.0441664 0.119801i
\(887\) −815.068 815.068i −0.918904 0.918904i 0.0780457 0.996950i \(-0.475132\pi\)
−0.996950 + 0.0780457i \(0.975132\pi\)
\(888\) 194.842 282.800i 0.219416 0.318469i
\(889\) 666.572i 0.749799i
\(890\) −1040.53 490.202i −1.16914 0.550788i
\(891\) −343.318 1319.60i −0.385318 1.48103i
\(892\) −39.5966 + 3.13412i −0.0443908 + 0.00351359i
\(893\) 84.3198 + 84.3198i 0.0944231 + 0.0944231i
\(894\) 98.0772 120.721i 0.109706 0.135035i
\(895\) 104.270 87.5291i 0.116502 0.0977978i
\(896\) 502.959 397.778i 0.561338 0.443948i
\(897\) −310.238 631.994i −0.345861 0.704564i
\(898\) 429.454 198.097i 0.478234 0.220598i
\(899\) 209.190i 0.232692i
\(900\) 899.536 28.9083i 0.999484 0.0321203i
\(901\) 315.187 0.349819
\(902\) −85.8120 186.031i −0.0951352 0.206243i
\(903\) 1092.05 536.074i 1.20936 0.593659i
\(904\) 999.183 560.449i 1.10529 0.619966i
\(905\) 889.269 + 1059.35i 0.982618 + 1.17055i
\(906\) 933.134 + 758.104i 1.02995 + 0.836760i
\(907\) 551.789 551.789i 0.608367 0.608367i −0.334152 0.942519i \(-0.608450\pi\)
0.942519 + 0.334152i \(0.108450\pi\)
\(908\) 206.781 16.3670i 0.227733 0.0180253i
\(909\) 1131.52 + 874.803i 1.24480 + 0.962380i
\(910\) −261.057 + 554.134i −0.286875 + 0.608938i
\(911\) 1547.30 1.69846 0.849231 0.528022i \(-0.177066\pi\)
0.849231 + 0.528022i \(0.177066\pi\)
\(912\) 132.363 + 187.657i 0.145135 + 0.205764i
\(913\) 1072.93 1072.93i 1.17517 1.17517i
\(914\) 644.364 + 237.555i 0.704993 + 0.259907i
\(915\) −116.931 51.6761i −0.127793 0.0564766i
\(916\) 821.934 + 701.363i 0.897307 + 0.765680i
\(917\) −514.175 + 514.175i −0.560715 + 0.560715i
\(918\) −631.331 391.438i −0.687725 0.426403i
\(919\) 1012.94 1.10222 0.551109 0.834433i \(-0.314205\pi\)
0.551109 + 0.834433i \(0.314205\pi\)
\(920\) −271.370 + 718.165i −0.294968 + 0.780614i
\(921\) 453.130 1326.95i 0.491998 1.44077i
\(922\) 536.794 + 1163.71i 0.582207 + 1.26216i
\(923\) −317.028 + 317.028i −0.343475 + 0.343475i
\(924\) −516.228 870.416i −0.558688 0.942008i
\(925\) 292.953 205.307i 0.316706 0.221953i
\(926\) −431.990 159.260i −0.466512 0.171987i
\(927\) −361.411 + 46.2441i −0.389872 + 0.0498858i
\(928\) 264.877 + 395.459i 0.285427 + 0.426141i
\(929\) 1529.05 1.64591 0.822955 0.568106i \(-0.192324\pi\)
0.822955 + 0.568106i \(0.192324\pi\)
\(930\) 6.77702 + 421.868i 0.00728711 + 0.453622i
\(931\) 114.355i 0.122830i
\(932\) −311.361 + 24.6446i −0.334079 + 0.0264427i
\(933\) −71.4467 + 35.0722i −0.0765773 + 0.0375908i
\(934\) 1127.78 + 415.772i 1.20747 + 0.445152i
\(935\) 1153.45 + 100.676i 1.23364 + 0.107675i
\(936\) −870.868 128.909i −0.930414 0.137723i
\(937\) 662.561 + 662.561i 0.707109 + 0.707109i 0.965926 0.258818i \(-0.0833328\pi\)
−0.258818 + 0.965926i \(0.583333\pi\)
\(938\) 320.327 + 694.435i 0.341500 + 0.740336i
\(939\) 180.774 529.380i 0.192518 0.563769i
\(940\) 349.636 + 355.328i 0.371953 + 0.378009i
\(941\) 961.186i 1.02145i −0.859744 0.510726i \(-0.829377\pi\)
0.859744 0.510726i \(-0.170623\pi\)
\(942\) −1181.56 + 122.281i −1.25431 + 0.129811i
\(943\) −82.5844 82.5844i −0.0875763 0.0875763i
\(944\) −69.0730 + 11.0034i −0.0731706 + 0.0116561i
\(945\) −192.658 + 648.291i −0.203871 + 0.686023i
\(946\) −2556.97 942.667i −2.70293 0.996476i
\(947\) 1259.29 + 1259.29i 1.32977 + 1.32977i 0.905568 + 0.424202i \(0.139445\pi\)
0.424202 + 0.905568i \(0.360555\pi\)
\(948\) −262.632 + 1028.20i −0.277038 + 1.08460i
\(949\) 219.261i 0.231044i
\(950\) 61.0496 + 231.288i 0.0642627 + 0.243461i
\(951\) −91.3247 + 267.435i −0.0960302 + 0.281215i
\(952\) −530.719 149.294i −0.557478 0.156822i
\(953\) 62.1880 + 62.1880i 0.0652550 + 0.0652550i 0.738981 0.673726i \(-0.235307\pi\)
−0.673726 + 0.738981i \(0.735307\pi\)
\(954\) 349.546 218.883i 0.366401 0.229437i
\(955\) −1093.04 1302.09i −1.14454 1.36345i
\(956\) 140.386 + 119.793i 0.146848 + 0.125306i
\(957\) 674.295 331.002i 0.704592 0.345875i
\(958\) −367.821 797.397i −0.383947 0.832356i
\(959\) 425.813i 0.444018i
\(960\) 546.981 + 788.931i 0.569772 + 0.821803i
\(961\) 763.202 0.794174
\(962\) −317.749 + 146.570i −0.330300 + 0.152360i
\(963\) 355.783 45.5240i 0.369453 0.0472731i
\(964\) −550.871 + 645.571i −0.571443 + 0.669680i
\(965\) −711.342 62.0877i −0.737142 0.0643396i
\(966\) −447.767 363.779i −0.463527 0.376582i
\(967\) −1.17333 + 1.17333i −0.00121337 + 0.00121337i −0.707713 0.706500i \(-0.750273\pi\)
0.706500 + 0.707713i \(0.250273\pi\)
\(968\) −351.759 + 1250.45i −0.363387 + 1.29179i
\(969\) 63.8038 186.843i 0.0658450 0.192821i
\(970\) −408.383 1135.91i −0.421014 1.17104i
\(971\) 570.125 0.587153 0.293576 0.955936i \(-0.405154\pi\)
0.293576 + 0.955936i \(0.405154\pi\)
\(972\) −971.990 + 4.32014i −0.999990 + 0.00444459i
\(973\) 44.6290 44.6290i 0.0458674 0.0458674i
\(974\) −301.565 + 817.991i −0.309615 + 0.839827i
\(975\) −803.370 442.218i −0.823969 0.453557i
\(976\) −21.4522 134.665i −0.0219797 0.137977i
\(977\) 430.216 430.216i 0.440344 0.440344i −0.451784 0.892128i \(-0.649212\pi\)
0.892128 + 0.451784i \(0.149212\pi\)
\(978\) 494.869 51.2149i 0.506001 0.0523670i
\(979\) −1936.24 −1.97777
\(980\) 3.86035 478.038i 0.00393914 0.487794i
\(981\) −1138.83 880.455i −1.16089 0.897507i
\(982\) 1365.09 629.685i 1.39011 0.641227i
\(983\) 876.585 876.585i 0.891745 0.891745i −0.102942 0.994687i \(-0.532826\pi\)
0.994687 + 0.102942i \(0.0328257\pi\)
\(984\) −143.627 + 26.4492i −0.145963 + 0.0268792i
\(985\) −1589.08 138.699i −1.61328 0.140811i
\(986\) 141.553 383.959i 0.143563 0.389411i
\(987\) −336.272 + 165.071i −0.340701 + 0.167246i
\(988\) −18.4627 233.259i −0.0186870 0.236092i
\(989\) −1553.59 −1.57086
\(990\) 1349.11 689.368i 1.36274 0.696331i
\(991\) 183.991i 0.185662i 0.995682 + 0.0928310i \(0.0295916\pi\)
−0.995682 + 0.0928310i \(0.970408\pi\)
\(992\) −373.924 + 250.453i −0.376939 + 0.252472i
\(993\) 376.693 + 767.373i 0.379349 + 0.772783i
\(994\) −127.084 + 344.712i −0.127851 + 0.346793i
\(995\) −921.571 1097.83i −0.926202 1.10335i
\(996\) −551.768 930.340i −0.553983 0.934076i
\(997\) 276.341 + 276.341i 0.277172 + 0.277172i 0.831979 0.554807i \(-0.187208\pi\)
−0.554807 + 0.831979i \(0.687208\pi\)
\(998\) −552.976 + 255.075i −0.554084 + 0.255586i
\(999\) −322.405 + 212.889i −0.322728 + 0.213102i
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 60.3.l.a.47.3 yes 40
3.2 odd 2 inner 60.3.l.a.47.18 yes 40
4.3 odd 2 inner 60.3.l.a.47.8 yes 40
5.2 odd 4 300.3.l.g.143.8 40
5.3 odd 4 inner 60.3.l.a.23.13 yes 40
5.4 even 2 300.3.l.g.107.18 40
12.11 even 2 inner 60.3.l.a.47.13 yes 40
15.2 even 4 300.3.l.g.143.13 40
15.8 even 4 inner 60.3.l.a.23.8 yes 40
15.14 odd 2 300.3.l.g.107.3 40
20.3 even 4 inner 60.3.l.a.23.18 yes 40
20.7 even 4 300.3.l.g.143.3 40
20.19 odd 2 300.3.l.g.107.13 40
60.23 odd 4 inner 60.3.l.a.23.3 40
60.47 odd 4 300.3.l.g.143.18 40
60.59 even 2 300.3.l.g.107.8 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.l.a.23.3 40 60.23 odd 4 inner
60.3.l.a.23.8 yes 40 15.8 even 4 inner
60.3.l.a.23.13 yes 40 5.3 odd 4 inner
60.3.l.a.23.18 yes 40 20.3 even 4 inner
60.3.l.a.47.3 yes 40 1.1 even 1 trivial
60.3.l.a.47.8 yes 40 4.3 odd 2 inner
60.3.l.a.47.13 yes 40 12.11 even 2 inner
60.3.l.a.47.18 yes 40 3.2 odd 2 inner
300.3.l.g.107.3 40 15.14 odd 2
300.3.l.g.107.8 40 60.59 even 2
300.3.l.g.107.13 40 20.19 odd 2
300.3.l.g.107.18 40 5.4 even 2
300.3.l.g.143.3 40 20.7 even 4
300.3.l.g.143.8 40 5.2 odd 4
300.3.l.g.143.13 40 15.2 even 4
300.3.l.g.143.18 40 60.47 odd 4