Properties

Label 126.3.r.a.11.5
Level $126$
Weight $3$
Character 126.11
Analytic conductor $3.433$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,3,Mod(11,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.r (of order \(6\), 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: \(3.43325133094\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.5
Character \(\chi\) \(=\) 126.11
Dual form 126.3.r.a.23.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(0.146807 + 2.99641i) q^{3} -2.00000 q^{4} +(2.36201 + 1.36371i) q^{5} +(4.23756 - 0.207617i) q^{6} +(-2.54299 + 6.52175i) q^{7} +2.82843i q^{8} +(-8.95690 + 0.879787i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(0.146807 + 2.99641i) q^{3} -2.00000 q^{4} +(2.36201 + 1.36371i) q^{5} +(4.23756 - 0.207617i) q^{6} +(-2.54299 + 6.52175i) q^{7} +2.82843i q^{8} +(-8.95690 + 0.879787i) q^{9} +(1.92857 - 3.34039i) q^{10} +(-2.52158 + 1.45583i) q^{11} +(-0.293614 - 5.99281i) q^{12} +(10.4745 + 18.1424i) q^{13} +(9.22314 + 3.59634i) q^{14} +(-3.73946 + 7.27775i) q^{15} +4.00000 q^{16} +(24.7647 + 14.2979i) q^{17} +(1.24421 + 12.6670i) q^{18} +(-17.7418 - 30.7298i) q^{19} +(-4.72402 - 2.72742i) q^{20} +(-19.9151 - 6.66240i) q^{21} +(2.05886 + 3.56605i) q^{22} +(13.6186 + 7.86269i) q^{23} +(-8.47512 + 0.415233i) q^{24} +(-8.78060 - 15.2084i) q^{25} +(25.6572 - 14.8132i) q^{26} +(-3.95113 - 26.7093i) q^{27} +(5.08599 - 13.0435i) q^{28} +(18.1582 + 10.4836i) q^{29} +(10.2923 + 5.28840i) q^{30} -12.4651 q^{31} -5.65685i q^{32} +(-4.73245 - 7.34194i) q^{33} +(20.2203 - 35.0226i) q^{34} +(-14.9003 + 11.9365i) q^{35} +(17.9138 - 1.75957i) q^{36} +(-5.80585 - 10.0560i) q^{37} +(-43.4585 + 25.0908i) q^{38} +(-52.8242 + 34.0493i) q^{39} +(-3.85715 + 6.68078i) q^{40} +(26.4059 - 15.2455i) q^{41} +(-9.42206 + 28.1642i) q^{42} +(-12.6505 + 21.9113i) q^{43} +(5.04315 - 2.91167i) q^{44} +(-22.3561 - 10.1365i) q^{45} +(11.1195 - 19.2596i) q^{46} -84.6070i q^{47} +(0.587228 + 11.9856i) q^{48} +(-36.0664 - 33.1695i) q^{49} +(-21.5080 + 12.4176i) q^{50} +(-39.2067 + 76.3041i) q^{51} +(-20.9490 - 36.2847i) q^{52} +(15.1905 + 8.77025i) q^{53} +(-37.7727 + 5.58775i) q^{54} -7.94133 q^{55} +(-18.4463 - 7.19267i) q^{56} +(89.4743 - 57.6731i) q^{57} +(14.8261 - 25.6795i) q^{58} +43.1446i q^{59} +(7.47893 - 14.5555i) q^{60} +30.2949 q^{61} +17.6283i q^{62} +(17.0396 - 60.6519i) q^{63} -8.00000 q^{64} +57.1367i q^{65} +(-10.3831 + 6.69270i) q^{66} +86.4501 q^{67} +(-49.5294 - 28.5958i) q^{68} +(-21.5605 + 41.9611i) q^{69} +(16.8808 + 21.0723i) q^{70} +1.24828i q^{71} +(-2.48841 - 25.3339i) q^{72} +(-6.48414 + 11.2309i) q^{73} +(-14.2214 + 8.21071i) q^{74} +(44.2816 - 28.5429i) q^{75} +(35.4837 + 61.4596i) q^{76} +(-3.08222 - 20.1473i) q^{77} +(48.1530 + 74.7047i) q^{78} +103.529 q^{79} +(9.44805 + 5.45483i) q^{80} +(79.4519 - 15.7603i) q^{81} +(-21.5604 - 37.3436i) q^{82} +(35.2944 + 20.3772i) q^{83} +(39.8303 + 13.3248i) q^{84} +(38.9964 + 67.5437i) q^{85} +(30.9872 + 17.8905i) q^{86} +(-28.7475 + 55.9484i) q^{87} +(-4.11772 - 7.13210i) q^{88} +(15.5031 - 8.95074i) q^{89} +(-14.3352 + 31.6163i) q^{90} +(-144.957 + 22.1761i) q^{91} +(-27.2372 - 15.7254i) q^{92} +(-1.82997 - 37.3505i) q^{93} -119.652 q^{94} -96.7788i q^{95} +(16.9502 - 0.830466i) q^{96} +(-2.62198 + 4.54141i) q^{97} +(-46.9088 + 51.0055i) q^{98} +(21.3047 - 15.2582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27} - 4 q^{28} + 36 q^{29} + 76 q^{30} + 16 q^{31} - 40 q^{33} - 90 q^{35} + 40 q^{36} + 22 q^{37} + 46 q^{39} + 72 q^{41} + 120 q^{42} + 16 q^{43} + 72 q^{44} + 464 q^{45} - 12 q^{46} + 2 q^{49} - 288 q^{50} - 286 q^{51} - 20 q^{52} - 72 q^{53} - 160 q^{54} - 24 q^{55} - 72 q^{56} - 282 q^{57} - 24 q^{58} - 20 q^{60} + 124 q^{61} + 66 q^{63} - 256 q^{64} - 16 q^{66} - 140 q^{67} + 108 q^{68} + 218 q^{69} + 72 q^{70} + 196 q^{73} + 216 q^{74} + 658 q^{75} - 56 q^{76} + 486 q^{77} + 32 q^{78} + 76 q^{79} - 380 q^{81} - 56 q^{84} + 60 q^{85} - 144 q^{86} - 740 q^{87} - 486 q^{89} + 296 q^{90} - 122 q^{91} + 252 q^{92} + 238 q^{93} - 336 q^{94} + 32 q^{96} - 38 q^{97} + 288 q^{98} + 394 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 0.146807 + 2.99641i 0.0489357 + 0.998802i
\(4\) −2.00000 −0.500000
\(5\) 2.36201 + 1.36371i 0.472402 + 0.272742i 0.717245 0.696821i \(-0.245403\pi\)
−0.244842 + 0.969563i \(0.578736\pi\)
\(6\) 4.23756 0.207617i 0.706260 0.0346028i
\(7\) −2.54299 + 6.52175i −0.363285 + 0.931678i
\(8\) 2.82843i 0.353553i
\(9\) −8.95690 + 0.879787i −0.995211 + 0.0977541i
\(10\) 1.92857 3.34039i 0.192857 0.334039i
\(11\) −2.52158 + 1.45583i −0.229234 + 0.132348i −0.610219 0.792233i \(-0.708918\pi\)
0.380984 + 0.924581i \(0.375585\pi\)
\(12\) −0.293614 5.99281i −0.0244678 0.499401i
\(13\) 10.4745 + 18.1424i 0.805731 + 1.39557i 0.915796 + 0.401643i \(0.131561\pi\)
−0.110065 + 0.993924i \(0.535106\pi\)
\(14\) 9.22314 + 3.59634i 0.658796 + 0.256881i
\(15\) −3.73946 + 7.27775i −0.249298 + 0.485183i
\(16\) 4.00000 0.250000
\(17\) 24.7647 + 14.2979i 1.45675 + 0.841053i 0.998850 0.0479514i \(-0.0152693\pi\)
0.457898 + 0.889005i \(0.348603\pi\)
\(18\) 1.24421 + 12.6670i 0.0691226 + 0.703720i
\(19\) −17.7418 30.7298i −0.933782 1.61736i −0.776792 0.629757i \(-0.783155\pi\)
−0.156989 0.987600i \(-0.550179\pi\)
\(20\) −4.72402 2.72742i −0.236201 0.136371i
\(21\) −19.9151 6.66240i −0.948339 0.317257i
\(22\) 2.05886 + 3.56605i 0.0935845 + 0.162093i
\(23\) 13.6186 + 7.86269i 0.592112 + 0.341856i 0.765932 0.642921i \(-0.222278\pi\)
−0.173820 + 0.984777i \(0.555611\pi\)
\(24\) −8.47512 + 0.415233i −0.353130 + 0.0173014i
\(25\) −8.78060 15.2084i −0.351224 0.608338i
\(26\) 25.6572 14.8132i 0.986815 0.569738i
\(27\) −3.95113 26.7093i −0.146338 0.989235i
\(28\) 5.08599 13.0435i 0.181642 0.465839i
\(29\) 18.1582 + 10.4836i 0.626144 + 0.361505i 0.779257 0.626704i \(-0.215597\pi\)
−0.153113 + 0.988209i \(0.548930\pi\)
\(30\) 10.2923 + 5.28840i 0.343076 + 0.176280i
\(31\) −12.4651 −0.402101 −0.201050 0.979581i \(-0.564435\pi\)
−0.201050 + 0.979581i \(0.564435\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −4.73245 7.34194i −0.143408 0.222483i
\(34\) 20.2203 35.0226i 0.594715 1.03008i
\(35\) −14.9003 + 11.9365i −0.425724 + 0.341044i
\(36\) 17.9138 1.75957i 0.497605 0.0488771i
\(37\) −5.80585 10.0560i −0.156915 0.271785i 0.776840 0.629698i \(-0.216821\pi\)
−0.933755 + 0.357914i \(0.883488\pi\)
\(38\) −43.4585 + 25.0908i −1.14364 + 0.660283i
\(39\) −52.8242 + 34.0493i −1.35447 + 0.873059i
\(40\) −3.85715 + 6.68078i −0.0964287 + 0.167019i
\(41\) 26.4059 15.2455i 0.644047 0.371841i −0.142125 0.989849i \(-0.545393\pi\)
0.786172 + 0.618008i \(0.212060\pi\)
\(42\) −9.42206 + 28.1642i −0.224335 + 0.670577i
\(43\) −12.6505 + 21.9113i −0.294197 + 0.509564i −0.974798 0.223090i \(-0.928386\pi\)
0.680601 + 0.732655i \(0.261719\pi\)
\(44\) 5.04315 2.91167i 0.114617 0.0661742i
\(45\) −22.3561 10.1365i −0.496802 0.225256i
\(46\) 11.1195 19.2596i 0.241729 0.418687i
\(47\) 84.6070i 1.80015i −0.435736 0.900075i \(-0.643512\pi\)
0.435736 0.900075i \(-0.356488\pi\)
\(48\) 0.587228 + 11.9856i 0.0122339 + 0.249700i
\(49\) −36.0664 33.1695i −0.736048 0.676929i
\(50\) −21.5080 + 12.4176i −0.430160 + 0.248353i
\(51\) −39.2067 + 76.3041i −0.768759 + 1.49616i
\(52\) −20.9490 36.2847i −0.402866 0.697784i
\(53\) 15.1905 + 8.77025i 0.286614 + 0.165476i 0.636414 0.771348i \(-0.280417\pi\)
−0.349800 + 0.936824i \(0.613750\pi\)
\(54\) −37.7727 + 5.58775i −0.699494 + 0.103477i
\(55\) −7.94133 −0.144388
\(56\) −18.4463 7.19267i −0.329398 0.128441i
\(57\) 89.4743 57.6731i 1.56972 1.01181i
\(58\) 14.8261 25.6795i 0.255622 0.442751i
\(59\) 43.1446i 0.731264i 0.930760 + 0.365632i \(0.119147\pi\)
−0.930760 + 0.365632i \(0.880853\pi\)
\(60\) 7.47893 14.5555i 0.124649 0.242592i
\(61\) 30.2949 0.496637 0.248319 0.968678i \(-0.420122\pi\)
0.248319 + 0.968678i \(0.420122\pi\)
\(62\) 17.6283i 0.284328i
\(63\) 17.0396 60.6519i 0.270470 0.962729i
\(64\) −8.00000 −0.125000
\(65\) 57.1367i 0.879026i
\(66\) −10.3831 + 6.69270i −0.157319 + 0.101405i
\(67\) 86.4501 1.29030 0.645150 0.764056i \(-0.276795\pi\)
0.645150 + 0.764056i \(0.276795\pi\)
\(68\) −49.5294 28.5958i −0.728374 0.420527i
\(69\) −21.5605 + 41.9611i −0.312471 + 0.608132i
\(70\) 16.8808 + 21.0723i 0.241155 + 0.301032i
\(71\) 1.24828i 0.0175814i 0.999961 + 0.00879071i \(0.00279821\pi\)
−0.999961 + 0.00879071i \(0.997202\pi\)
\(72\) −2.48841 25.3339i −0.0345613 0.351860i
\(73\) −6.48414 + 11.2309i −0.0888239 + 0.153848i −0.907014 0.421100i \(-0.861644\pi\)
0.818190 + 0.574947i \(0.194978\pi\)
\(74\) −14.2214 + 8.21071i −0.192181 + 0.110956i
\(75\) 44.2816 28.5429i 0.590422 0.380573i
\(76\) 35.4837 + 61.4596i 0.466891 + 0.808679i
\(77\) −3.08222 20.1473i −0.0400288 0.261653i
\(78\) 48.1530 + 74.7047i 0.617346 + 0.957752i
\(79\) 103.529 1.31049 0.655247 0.755415i \(-0.272565\pi\)
0.655247 + 0.755415i \(0.272565\pi\)
\(80\) 9.44805 + 5.45483i 0.118101 + 0.0681854i
\(81\) 79.4519 15.7603i 0.980888 0.194572i
\(82\) −21.5604 37.3436i −0.262931 0.455410i
\(83\) 35.2944 + 20.3772i 0.425234 + 0.245509i 0.697314 0.716766i \(-0.254378\pi\)
−0.272080 + 0.962275i \(0.587712\pi\)
\(84\) 39.8303 + 13.3248i 0.474170 + 0.158629i
\(85\) 38.9964 + 67.5437i 0.458781 + 0.794631i
\(86\) 30.9872 + 17.8905i 0.360316 + 0.208029i
\(87\) −28.7475 + 55.9484i −0.330431 + 0.643085i
\(88\) −4.11772 7.13210i −0.0467923 0.0810466i
\(89\) 15.5031 8.95074i 0.174193 0.100570i −0.410369 0.911920i \(-0.634600\pi\)
0.584561 + 0.811350i \(0.301267\pi\)
\(90\) −14.3352 + 31.6163i −0.159280 + 0.351292i
\(91\) −144.957 + 22.1761i −1.59293 + 0.243693i
\(92\) −27.2372 15.7254i −0.296056 0.170928i
\(93\) −1.82997 37.3505i −0.0196771 0.401619i
\(94\) −119.652 −1.27290
\(95\) 96.7788i 1.01872i
\(96\) 16.9502 0.830466i 0.176565 0.00865069i
\(97\) −2.62198 + 4.54141i −0.0270307 + 0.0468186i −0.879224 0.476408i \(-0.841939\pi\)
0.852194 + 0.523227i \(0.175272\pi\)
\(98\) −46.9088 + 51.0055i −0.478661 + 0.520465i
\(99\) 21.3047 15.2582i 0.215199 0.154123i
\(100\) 17.5612 + 30.4169i 0.175612 + 0.304169i
\(101\) 155.079 89.5347i 1.53543 0.886482i 0.536334 0.844006i \(-0.319809\pi\)
0.999097 0.0424762i \(-0.0135247\pi\)
\(102\) 107.910 + 55.4467i 1.05794 + 0.543595i
\(103\) −76.1322 + 131.865i −0.739148 + 1.28024i 0.213732 + 0.976892i \(0.431438\pi\)
−0.952880 + 0.303349i \(0.901895\pi\)
\(104\) −51.3144 + 29.6264i −0.493407 + 0.284869i
\(105\) −37.9542 42.8951i −0.361469 0.408525i
\(106\) 12.4030 21.4826i 0.117010 0.202666i
\(107\) −129.207 + 74.5978i −1.20754 + 0.697175i −0.962222 0.272267i \(-0.912227\pi\)
−0.245321 + 0.969442i \(0.578893\pi\)
\(108\) 7.90227 + 53.4187i 0.0731692 + 0.494617i
\(109\) −11.0071 + 19.0649i −0.100983 + 0.174907i −0.912090 0.409990i \(-0.865532\pi\)
0.811107 + 0.584898i \(0.198865\pi\)
\(110\) 11.2307i 0.102098i
\(111\) 29.2796 18.8730i 0.263780 0.170027i
\(112\) −10.1720 + 26.0870i −0.0908212 + 0.232920i
\(113\) 13.7209 7.92175i 0.121424 0.0701040i −0.438058 0.898947i \(-0.644334\pi\)
0.559482 + 0.828843i \(0.311000\pi\)
\(114\) −81.5621 126.536i −0.715457 1.10996i
\(115\) 21.4448 + 37.1436i 0.186477 + 0.322987i
\(116\) −36.3164 20.9673i −0.313072 0.180752i
\(117\) −109.780 153.284i −0.938294 1.31012i
\(118\) 61.0156 0.517082
\(119\) −156.224 + 125.150i −1.31281 + 1.05168i
\(120\) −20.5846 10.5768i −0.171538 0.0881400i
\(121\) −56.2611 + 97.4471i −0.464968 + 0.805348i
\(122\) 42.8434i 0.351176i
\(123\) 49.5582 + 76.8848i 0.402912 + 0.625079i
\(124\) 24.9302 0.201050
\(125\) 116.082i 0.928657i
\(126\) −85.7747 24.0976i −0.680752 0.191251i
\(127\) −86.5080 −0.681166 −0.340583 0.940215i \(-0.610624\pi\)
−0.340583 + 0.940215i \(0.610624\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −67.5122 34.6892i −0.523350 0.268909i
\(130\) 80.8035 0.621565
\(131\) 87.6284 + 50.5923i 0.668919 + 0.386200i 0.795667 0.605734i \(-0.207121\pi\)
−0.126748 + 0.991935i \(0.540454\pi\)
\(132\) 9.46490 + 14.6839i 0.0717038 + 0.111242i
\(133\) 245.529 37.5622i 1.84608 0.282422i
\(134\) 122.259i 0.912380i
\(135\) 27.0911 68.4760i 0.200675 0.507229i
\(136\) −40.4406 + 70.0452i −0.297357 + 0.515038i
\(137\) 35.2605 20.3576i 0.257376 0.148596i −0.365761 0.930709i \(-0.619191\pi\)
0.623137 + 0.782113i \(0.285858\pi\)
\(138\) 59.3420 + 30.4912i 0.430014 + 0.220951i
\(139\) −22.3342 38.6840i −0.160678 0.278302i 0.774434 0.632655i \(-0.218035\pi\)
−0.935112 + 0.354352i \(0.884701\pi\)
\(140\) 29.8007 23.8731i 0.212862 0.170522i
\(141\) 253.517 12.4209i 1.79799 0.0880915i
\(142\) 1.76534 0.0124319
\(143\) −52.8245 30.4983i −0.369402 0.213275i
\(144\) −35.8276 + 3.51915i −0.248803 + 0.0244385i
\(145\) 28.5932 + 49.5249i 0.197195 + 0.341551i
\(146\) 15.8828 + 9.16996i 0.108787 + 0.0628080i
\(147\) 94.0946 112.939i 0.640099 0.768292i
\(148\) 11.6117 + 20.1121i 0.0784574 + 0.135892i
\(149\) −54.3567 31.3829i −0.364810 0.210623i 0.306379 0.951910i \(-0.400883\pi\)
−0.671189 + 0.741286i \(0.734216\pi\)
\(150\) −40.3658 62.6237i −0.269105 0.417491i
\(151\) −94.8677 164.316i −0.628263 1.08818i −0.987900 0.155091i \(-0.950433\pi\)
0.359637 0.933092i \(-0.382900\pi\)
\(152\) 86.9170 50.1815i 0.571822 0.330142i
\(153\) −234.394 106.277i −1.53199 0.694622i
\(154\) −28.4925 + 4.35892i −0.185016 + 0.0283047i
\(155\) −29.4428 16.9988i −0.189953 0.109670i
\(156\) 105.648 68.0986i 0.677233 0.436529i
\(157\) −86.0225 −0.547914 −0.273957 0.961742i \(-0.588333\pi\)
−0.273957 + 0.961742i \(0.588333\pi\)
\(158\) 146.412i 0.926659i
\(159\) −24.0492 + 46.8045i −0.151253 + 0.294368i
\(160\) 7.71430 13.3616i 0.0482144 0.0835097i
\(161\) −85.9105 + 68.8222i −0.533606 + 0.427467i
\(162\) −22.2885 112.362i −0.137583 0.693593i
\(163\) 36.5758 + 63.3511i 0.224391 + 0.388657i 0.956137 0.292921i \(-0.0946273\pi\)
−0.731745 + 0.681578i \(0.761294\pi\)
\(164\) −52.8119 + 30.4909i −0.322024 + 0.185920i
\(165\) −1.16584 23.7954i −0.00706571 0.144215i
\(166\) 28.8177 49.9138i 0.173601 0.300686i
\(167\) −72.8922 + 42.0843i −0.436480 + 0.252002i −0.702103 0.712075i \(-0.747756\pi\)
0.265623 + 0.964077i \(0.414422\pi\)
\(168\) 18.8441 56.3285i 0.112167 0.335289i
\(169\) −134.930 + 233.706i −0.798405 + 1.38288i
\(170\) 95.5212 55.1492i 0.561889 0.324407i
\(171\) 185.948 + 259.634i 1.08741 + 1.51833i
\(172\) 25.3009 43.8225i 0.147099 0.254782i
\(173\) 236.832i 1.36897i −0.729026 0.684486i \(-0.760027\pi\)
0.729026 0.684486i \(-0.239973\pi\)
\(174\) 79.1229 + 40.6551i 0.454729 + 0.233650i
\(175\) 121.515 18.5899i 0.694369 0.106228i
\(176\) −10.0863 + 5.82333i −0.0573086 + 0.0330871i
\(177\) −129.279 + 6.33393i −0.730388 + 0.0357849i
\(178\) −12.6583 21.9247i −0.0711138 0.123173i
\(179\) −166.309 96.0186i −0.929101 0.536417i −0.0425737 0.999093i \(-0.513556\pi\)
−0.886527 + 0.462677i \(0.846889\pi\)
\(180\) 44.7121 + 20.2731i 0.248401 + 0.112628i
\(181\) −45.1148 −0.249253 −0.124626 0.992204i \(-0.539773\pi\)
−0.124626 + 0.992204i \(0.539773\pi\)
\(182\) 31.3618 + 205.000i 0.172317 + 1.12637i
\(183\) 4.44750 + 90.7758i 0.0243033 + 0.496042i
\(184\) −22.2391 + 38.5192i −0.120864 + 0.209343i
\(185\) 31.6699i 0.171189i
\(186\) −52.8217 + 2.58796i −0.283987 + 0.0139138i
\(187\) −83.2615 −0.445249
\(188\) 169.214i 0.900075i
\(189\) 184.239 + 42.1534i 0.974811 + 0.223034i
\(190\) −136.866 −0.720347
\(191\) 87.2707i 0.456915i 0.973554 + 0.228457i \(0.0733681\pi\)
−0.973554 + 0.228457i \(0.926632\pi\)
\(192\) −1.17446 23.9712i −0.00611696 0.124850i
\(193\) −158.035 −0.818832 −0.409416 0.912348i \(-0.634268\pi\)
−0.409416 + 0.912348i \(0.634268\pi\)
\(194\) 6.42252 + 3.70804i 0.0331058 + 0.0191136i
\(195\) −171.205 + 8.38807i −0.877973 + 0.0430157i
\(196\) 72.1327 + 66.3391i 0.368024 + 0.338465i
\(197\) 72.5385i 0.368216i −0.982906 0.184108i \(-0.941060\pi\)
0.982906 0.184108i \(-0.0589396\pi\)
\(198\) −21.5783 30.1294i −0.108982 0.152169i
\(199\) 156.303 270.725i 0.785442 1.36043i −0.143292 0.989680i \(-0.545769\pi\)
0.928735 0.370745i \(-0.120898\pi\)
\(200\) 43.0160 24.8353i 0.215080 0.124176i
\(201\) 12.6915 + 259.040i 0.0631417 + 1.28875i
\(202\) −126.621 219.314i −0.626837 1.08571i
\(203\) −114.548 + 91.7632i −0.564275 + 0.452036i
\(204\) 78.4134 152.608i 0.384379 0.748080i
\(205\) 83.1615 0.405666
\(206\) 186.485 + 107.667i 0.905267 + 0.522656i
\(207\) −128.898 58.4439i −0.622694 0.282338i
\(208\) 41.8980 + 72.5695i 0.201433 + 0.348892i
\(209\) 89.4749 + 51.6583i 0.428109 + 0.247169i
\(210\) −60.6628 + 53.6753i −0.288871 + 0.255597i
\(211\) 91.2819 + 158.105i 0.432616 + 0.749312i 0.997098 0.0761331i \(-0.0242574\pi\)
−0.564482 + 0.825445i \(0.690924\pi\)
\(212\) −30.3810 17.5405i −0.143307 0.0827382i
\(213\) −3.74035 + 0.183256i −0.0175604 + 0.000860359i
\(214\) 105.497 + 182.726i 0.492977 + 0.853862i
\(215\) −59.7611 + 34.5031i −0.277959 + 0.160480i
\(216\) 75.5454 11.1755i 0.349747 0.0517384i
\(217\) 31.6987 81.2943i 0.146077 0.374628i
\(218\) 26.9619 + 15.5664i 0.123678 + 0.0714057i
\(219\) −34.6042 17.7804i −0.158010 0.0811888i
\(220\) 15.8827 0.0721939
\(221\) 599.054i 2.71065i
\(222\) −26.6904 41.4076i −0.120227 0.186521i
\(223\) 125.388 217.179i 0.562279 0.973896i −0.435018 0.900422i \(-0.643258\pi\)
0.997297 0.0734742i \(-0.0234087\pi\)
\(224\) 36.8926 + 14.3853i 0.164699 + 0.0642203i
\(225\) 92.0271 + 128.495i 0.409009 + 0.571091i
\(226\) −11.2030 19.4042i −0.0495710 0.0858595i
\(227\) 351.333 202.842i 1.54772 0.893578i 0.549407 0.835555i \(-0.314854\pi\)
0.998315 0.0580230i \(-0.0184797\pi\)
\(228\) −178.949 + 115.346i −0.784862 + 0.505905i
\(229\) −54.8376 + 94.9815i −0.239465 + 0.414766i −0.960561 0.278069i \(-0.910306\pi\)
0.721096 + 0.692836i \(0.243639\pi\)
\(230\) 52.5289 30.3276i 0.228387 0.131859i
\(231\) 59.9169 12.1933i 0.259380 0.0527850i
\(232\) −29.6522 + 51.3591i −0.127811 + 0.221375i
\(233\) −59.9074 + 34.5876i −0.257113 + 0.148445i −0.623017 0.782208i \(-0.714093\pi\)
0.365904 + 0.930653i \(0.380760\pi\)
\(234\) −216.776 + 155.253i −0.926394 + 0.663474i
\(235\) 115.379 199.843i 0.490976 0.850395i
\(236\) 86.2891i 0.365632i
\(237\) 15.1988 + 310.215i 0.0641299 + 1.30892i
\(238\) 176.988 + 220.934i 0.743648 + 0.928294i
\(239\) −206.558 + 119.256i −0.864260 + 0.498981i −0.865437 0.501018i \(-0.832959\pi\)
0.00117636 + 0.999999i \(0.499626\pi\)
\(240\) −14.9579 + 29.1110i −0.0623244 + 0.121296i
\(241\) −140.911 244.065i −0.584693 1.01272i −0.994914 0.100732i \(-0.967881\pi\)
0.410220 0.911987i \(-0.365452\pi\)
\(242\) 137.811 + 79.5652i 0.569467 + 0.328782i
\(243\) 58.8884 + 235.757i 0.242339 + 0.970192i
\(244\) −60.5898 −0.248319
\(245\) −39.9556 127.531i −0.163084 0.520534i
\(246\) 108.731 70.0859i 0.441998 0.284902i
\(247\) 371.674 643.758i 1.50475 2.60631i
\(248\) 35.2567i 0.142164i
\(249\) −55.8770 + 108.748i −0.224405 + 0.436738i
\(250\) −164.165 −0.656660
\(251\) 222.540i 0.886615i −0.896370 0.443308i \(-0.853805\pi\)
0.896370 0.443308i \(-0.146195\pi\)
\(252\) −34.0792 + 121.304i −0.135235 + 0.481364i
\(253\) −45.7871 −0.180977
\(254\) 122.341i 0.481657i
\(255\) −196.663 + 126.765i −0.771229 + 0.497117i
\(256\) 16.0000 0.0625000
\(257\) 291.865 + 168.508i 1.13566 + 0.655674i 0.945353 0.326050i \(-0.105718\pi\)
0.190309 + 0.981724i \(0.439051\pi\)
\(258\) −49.0580 + 95.4767i −0.190147 + 0.370065i
\(259\) 80.3471 12.2919i 0.310220 0.0474589i
\(260\) 114.273i 0.439513i
\(261\) −171.864 77.9255i −0.658484 0.298565i
\(262\) 71.5483 123.925i 0.273085 0.472997i
\(263\) −141.259 + 81.5557i −0.537105 + 0.310098i −0.743905 0.668285i \(-0.767029\pi\)
0.206800 + 0.978383i \(0.433695\pi\)
\(264\) 20.7661 13.3854i 0.0786596 0.0507023i
\(265\) 23.9201 + 41.4309i 0.0902646 + 0.156343i
\(266\) −53.1209 347.231i −0.199703 1.30538i
\(267\) 29.0960 + 45.1396i 0.108974 + 0.169062i
\(268\) −172.900 −0.645150
\(269\) 430.483 + 248.539i 1.60031 + 0.923938i 0.991425 + 0.130677i \(0.0417152\pi\)
0.608882 + 0.793261i \(0.291618\pi\)
\(270\) −96.8396 38.3126i −0.358665 0.141899i
\(271\) −86.2128 149.325i −0.318129 0.551015i 0.661969 0.749531i \(-0.269721\pi\)
−0.980098 + 0.198516i \(0.936388\pi\)
\(272\) 99.0588 + 57.1916i 0.364187 + 0.210263i
\(273\) −87.7293 431.093i −0.321353 1.57910i
\(274\) −28.7901 49.8659i −0.105073 0.181992i
\(275\) 44.2819 + 25.5662i 0.161025 + 0.0929679i
\(276\) 43.1210 83.9222i 0.156236 0.304066i
\(277\) −44.6018 77.2526i −0.161017 0.278890i 0.774216 0.632921i \(-0.218144\pi\)
−0.935234 + 0.354031i \(0.884811\pi\)
\(278\) −54.7075 + 31.5854i −0.196790 + 0.113616i
\(279\) 111.649 10.9666i 0.400175 0.0393070i
\(280\) −33.7616 42.1445i −0.120577 0.150516i
\(281\) −406.825 234.881i −1.44778 0.835874i −0.449428 0.893317i \(-0.648372\pi\)
−0.998349 + 0.0574426i \(0.981705\pi\)
\(282\) −17.5658 358.527i −0.0622901 1.27137i
\(283\) −47.4160 −0.167548 −0.0837738 0.996485i \(-0.526697\pi\)
−0.0837738 + 0.996485i \(0.526697\pi\)
\(284\) 2.49656i 0.00879071i
\(285\) 289.989 14.2078i 1.01750 0.0498520i
\(286\) −43.1311 + 74.7052i −0.150808 + 0.261207i
\(287\) 32.2770 + 210.982i 0.112463 + 0.735129i
\(288\) 4.97683 + 50.6679i 0.0172806 + 0.175930i
\(289\) 264.360 + 457.886i 0.914742 + 1.58438i
\(290\) 70.0388 40.4369i 0.241513 0.139438i
\(291\) −13.9928 7.18981i −0.0480853 0.0247073i
\(292\) 12.9683 22.4617i 0.0444119 0.0769238i
\(293\) 80.5230 46.4900i 0.274823 0.158669i −0.356255 0.934389i \(-0.615946\pi\)
0.631077 + 0.775720i \(0.282613\pi\)
\(294\) −159.720 133.070i −0.543265 0.452618i
\(295\) −58.8366 + 101.908i −0.199446 + 0.345451i
\(296\) 28.4427 16.4214i 0.0960903 0.0554778i
\(297\) 48.8474 + 61.5975i 0.164469 + 0.207399i
\(298\) −44.3821 + 76.8720i −0.148933 + 0.257960i
\(299\) 329.431i 1.10178i
\(300\) −88.5632 + 57.0859i −0.295211 + 0.190286i
\(301\) −110.730 138.223i −0.367872 0.459214i
\(302\) −232.378 + 134.163i −0.769462 + 0.444249i
\(303\) 291.049 + 451.534i 0.960557 + 1.49021i
\(304\) −70.9674 122.919i −0.233445 0.404339i
\(305\) 71.5569 + 41.3134i 0.234613 + 0.135454i
\(306\) −150.299 + 331.483i −0.491172 + 1.08328i
\(307\) 202.315 0.659008 0.329504 0.944154i \(-0.393119\pi\)
0.329504 + 0.944154i \(0.393119\pi\)
\(308\) 6.16444 + 40.2945i 0.0200144 + 0.130826i
\(309\) −406.297 208.764i −1.31488 0.675613i
\(310\) −24.0399 + 41.6383i −0.0775481 + 0.134317i
\(311\) 297.017i 0.955037i −0.878622 0.477519i \(-0.841536\pi\)
0.878622 0.477519i \(-0.158464\pi\)
\(312\) −96.3059 149.409i −0.308673 0.478876i
\(313\) −378.321 −1.20869 −0.604347 0.796721i \(-0.706566\pi\)
−0.604347 + 0.796721i \(0.706566\pi\)
\(314\) 121.654i 0.387434i
\(315\) 122.959 120.023i 0.390347 0.381027i
\(316\) −207.058 −0.655247
\(317\) 258.230i 0.814607i −0.913293 0.407304i \(-0.866469\pi\)
0.913293 0.407304i \(-0.133531\pi\)
\(318\) 66.1916 + 34.0106i 0.208150 + 0.106952i
\(319\) −61.0497 −0.191378
\(320\) −18.8961 10.9097i −0.0590503 0.0340927i
\(321\) −242.494 376.205i −0.755432 1.17198i
\(322\) 97.3293 + 121.496i 0.302265 + 0.377316i
\(323\) 1014.69i 3.14144i
\(324\) −158.904 + 31.5206i −0.490444 + 0.0972859i
\(325\) 183.945 318.602i 0.565984 0.980313i
\(326\) 89.5920 51.7260i 0.274822 0.158669i
\(327\) −58.7421 30.1830i −0.179640 0.0923026i
\(328\) 43.1207 + 74.6873i 0.131466 + 0.227705i
\(329\) 551.785 + 215.155i 1.67716 + 0.653967i
\(330\) −33.6518 + 1.64875i −0.101975 + 0.00499621i
\(331\) −381.770 −1.15338 −0.576692 0.816961i \(-0.695657\pi\)
−0.576692 + 0.816961i \(0.695657\pi\)
\(332\) −70.5888 40.7544i −0.212617 0.122754i
\(333\) 60.8496 + 84.9629i 0.182731 + 0.255144i
\(334\) 59.5162 + 103.085i 0.178192 + 0.308638i
\(335\) 204.196 + 117.893i 0.609541 + 0.351919i
\(336\) −79.6605 26.6496i −0.237085 0.0793143i
\(337\) −121.433 210.329i −0.360337 0.624122i 0.627679 0.778472i \(-0.284005\pi\)
−0.988016 + 0.154350i \(0.950672\pi\)
\(338\) 330.511 + 190.820i 0.977842 + 0.564558i
\(339\) 25.7511 + 39.9503i 0.0759619 + 0.117848i
\(340\) −77.9927 135.087i −0.229390 0.397316i
\(341\) 31.4318 18.1471i 0.0921752 0.0532174i
\(342\) 367.179 262.970i 1.07362 0.768917i
\(343\) 308.040 150.866i 0.898075 0.439842i
\(344\) −61.9744 35.7809i −0.180158 0.104014i
\(345\) −108.149 + 69.7104i −0.313475 + 0.202059i
\(346\) −334.931 −0.968009
\(347\) 242.378i 0.698495i −0.937031 0.349247i \(-0.886437\pi\)
0.937031 0.349247i \(-0.113563\pi\)
\(348\) 57.4949 111.897i 0.165215 0.321542i
\(349\) −2.46388 + 4.26756i −0.00705982 + 0.0122280i −0.869534 0.493874i \(-0.835581\pi\)
0.862474 + 0.506102i \(0.168914\pi\)
\(350\) −26.2900 171.848i −0.0751144 0.490993i
\(351\) 443.185 351.450i 1.26263 1.00128i
\(352\) 8.23544 + 14.2642i 0.0233961 + 0.0405233i
\(353\) −530.683 + 306.390i −1.50335 + 0.867960i −0.503359 + 0.864078i \(0.667903\pi\)
−0.999992 + 0.00388263i \(0.998764\pi\)
\(354\) 8.95753 + 182.828i 0.0253037 + 0.516462i
\(355\) −1.70229 + 2.94845i −0.00479518 + 0.00830550i
\(356\) −31.0063 + 17.9015i −0.0870963 + 0.0502850i
\(357\) −397.934 449.737i −1.11466 1.25977i
\(358\) −135.791 + 235.196i −0.379304 + 0.656973i
\(359\) −461.352 + 266.362i −1.28510 + 0.741955i −0.977777 0.209649i \(-0.932768\pi\)
−0.307327 + 0.951604i \(0.599435\pi\)
\(360\) 28.6704 63.2325i 0.0796401 0.175646i
\(361\) −449.046 + 777.771i −1.24390 + 2.15449i
\(362\) 63.8019i 0.176248i
\(363\) −300.251 154.275i −0.827136 0.425000i
\(364\) 289.913 44.3522i 0.796465 0.121847i
\(365\) −30.6313 + 17.6850i −0.0839212 + 0.0484520i
\(366\) 128.376 6.28972i 0.350755 0.0171850i
\(367\) 185.198 + 320.773i 0.504628 + 0.874041i 0.999986 + 0.00535178i \(0.00170353\pi\)
−0.495358 + 0.868689i \(0.664963\pi\)
\(368\) 54.4743 + 31.4508i 0.148028 + 0.0854641i
\(369\) −223.102 + 159.784i −0.604614 + 0.433018i
\(370\) −44.7881 −0.121049
\(371\) −95.8268 + 76.7660i −0.258293 + 0.206917i
\(372\) 3.65993 + 74.7011i 0.00983853 + 0.200809i
\(373\) 209.212 362.366i 0.560891 0.971492i −0.436528 0.899691i \(-0.643792\pi\)
0.997419 0.0718011i \(-0.0228747\pi\)
\(374\) 117.750i 0.314838i
\(375\) 347.829 17.0417i 0.927544 0.0454445i
\(376\) 239.305 0.636449
\(377\) 439.243i 1.16510i
\(378\) 59.6139 260.554i 0.157709 0.689295i
\(379\) 241.600 0.637468 0.318734 0.947844i \(-0.396742\pi\)
0.318734 + 0.947844i \(0.396742\pi\)
\(380\) 193.558i 0.509362i
\(381\) −12.7000 259.213i −0.0333333 0.680350i
\(382\) 123.419 0.323087
\(383\) −145.452 83.9766i −0.379770 0.219260i 0.297948 0.954582i \(-0.403698\pi\)
−0.677718 + 0.735322i \(0.737031\pi\)
\(384\) −33.9005 + 1.66093i −0.0882825 + 0.00432534i
\(385\) 20.1948 51.7913i 0.0524539 0.134523i
\(386\) 223.495i 0.579002i
\(387\) 94.0317 207.387i 0.242976 0.535883i
\(388\) 5.24396 9.08281i 0.0135154 0.0234093i
\(389\) 436.463 251.992i 1.12201 0.647795i 0.180099 0.983648i \(-0.442358\pi\)
0.941914 + 0.335854i \(0.109025\pi\)
\(390\) 11.8625 + 242.120i 0.0304167 + 0.620820i
\(391\) 224.840 + 389.435i 0.575039 + 0.995997i
\(392\) 93.8176 102.011i 0.239331 0.260232i
\(393\) −138.730 + 269.997i −0.353004 + 0.687016i
\(394\) −102.585 −0.260368
\(395\) 244.537 + 141.183i 0.619080 + 0.357426i
\(396\) −42.6094 + 30.5164i −0.107599 + 0.0770616i
\(397\) 170.757 + 295.760i 0.430118 + 0.744986i 0.996883 0.0788933i \(-0.0251386\pi\)
−0.566765 + 0.823879i \(0.691805\pi\)
\(398\) −382.863 221.046i −0.961966 0.555391i
\(399\) 148.597 + 730.191i 0.372423 + 1.83005i
\(400\) −35.1224 60.8338i −0.0878060 0.152084i
\(401\) −589.296 340.230i −1.46957 0.848455i −0.470150 0.882587i \(-0.655800\pi\)
−0.999417 + 0.0341316i \(0.989133\pi\)
\(402\) 366.337 17.9485i 0.911287 0.0446479i
\(403\) −130.566 226.147i −0.323985 0.561158i
\(404\) −310.157 + 179.069i −0.767716 + 0.443241i
\(405\) 209.159 + 71.1232i 0.516442 + 0.175613i
\(406\) 129.773 + 161.995i 0.319638 + 0.399002i
\(407\) 29.2798 + 16.9047i 0.0719405 + 0.0415349i
\(408\) −215.821 110.893i −0.528972 0.271797i
\(409\) −257.554 −0.629717 −0.314858 0.949139i \(-0.601957\pi\)
−0.314858 + 0.949139i \(0.601957\pi\)
\(410\) 117.608i 0.286849i
\(411\) 66.1763 + 102.666i 0.161013 + 0.249796i
\(412\) 152.264 263.730i 0.369574 0.640121i
\(413\) −281.378 109.716i −0.681303 0.265657i
\(414\) −82.6521 + 182.289i −0.199643 + 0.440311i
\(415\) 55.5772 + 96.2625i 0.133921 + 0.231958i
\(416\) 102.629 59.2527i 0.246704 0.142434i
\(417\) 112.634 72.6015i 0.270106 0.174104i
\(418\) 73.0559 126.537i 0.174775 0.302719i
\(419\) 187.674 108.354i 0.447909 0.258600i −0.259038 0.965867i \(-0.583405\pi\)
0.706947 + 0.707267i \(0.250072\pi\)
\(420\) 75.9084 + 85.7902i 0.180734 + 0.204262i
\(421\) −395.045 + 684.238i −0.938349 + 1.62527i −0.169799 + 0.985479i \(0.554312\pi\)
−0.768550 + 0.639790i \(0.779021\pi\)
\(422\) 223.594 129.092i 0.529844 0.305905i
\(423\) 74.4361 + 757.816i 0.175972 + 1.79153i
\(424\) −24.8060 + 42.9653i −0.0585048 + 0.101333i
\(425\) 502.177i 1.18159i
\(426\) 0.259164 + 5.28966i 0.000608365 + 0.0124170i
\(427\) −77.0397 + 197.576i −0.180421 + 0.462706i
\(428\) 258.414 149.196i 0.603771 0.348588i
\(429\) 83.6301 162.761i 0.194942 0.379397i
\(430\) 48.7948 + 84.5150i 0.113476 + 0.196547i
\(431\) 478.460 + 276.239i 1.11012 + 0.640925i 0.938859 0.344301i \(-0.111884\pi\)
0.171256 + 0.985227i \(0.445218\pi\)
\(432\) −15.8045 106.837i −0.0365846 0.247309i
\(433\) −351.734 −0.812319 −0.406160 0.913802i \(-0.633132\pi\)
−0.406160 + 0.913802i \(0.633132\pi\)
\(434\) −114.968 44.8288i −0.264902 0.103292i
\(435\) −144.199 + 92.9475i −0.331492 + 0.213672i
\(436\) 22.0143 38.1298i 0.0504914 0.0874537i
\(437\) 557.995i 1.27688i
\(438\) −25.1452 + 48.9377i −0.0574092 + 0.111730i
\(439\) 47.2343 0.107595 0.0537976 0.998552i \(-0.482867\pi\)
0.0537976 + 0.998552i \(0.482867\pi\)
\(440\) 22.4615i 0.0510488i
\(441\) 352.225 + 265.365i 0.798696 + 0.601735i
\(442\) 847.190 1.91672
\(443\) 512.244i 1.15631i 0.815928 + 0.578154i \(0.196227\pi\)
−0.815928 + 0.578154i \(0.803773\pi\)
\(444\) −58.5592 + 37.7460i −0.131890 + 0.0850134i
\(445\) 48.8248 0.109719
\(446\) −307.137 177.326i −0.688648 0.397591i
\(447\) 86.0559 167.482i 0.192519 0.374680i
\(448\) 20.3440 52.1740i 0.0454106 0.116460i
\(449\) 560.296i 1.24787i 0.781475 + 0.623937i \(0.214468\pi\)
−0.781475 + 0.623937i \(0.785532\pi\)
\(450\) 181.720 130.146i 0.403822 0.289213i
\(451\) −44.3897 + 76.8853i −0.0984251 + 0.170477i
\(452\) −27.4417 + 15.8435i −0.0607118 + 0.0350520i
\(453\) 478.429 308.385i 1.05614 0.680761i
\(454\) −286.862 496.860i −0.631855 1.09440i
\(455\) −372.631 145.298i −0.818969 0.319337i
\(456\) 163.124 + 253.071i 0.357729 + 0.554981i
\(457\) 669.482 1.46495 0.732475 0.680794i \(-0.238365\pi\)
0.732475 + 0.680794i \(0.238365\pi\)
\(458\) 134.324 + 77.5520i 0.293284 + 0.169328i
\(459\) 284.039 717.942i 0.618821 1.56414i
\(460\) −42.8897 74.2871i −0.0932385 0.161494i
\(461\) 80.8290 + 46.6667i 0.175334 + 0.101229i 0.585099 0.810962i \(-0.301056\pi\)
−0.409765 + 0.912191i \(0.634389\pi\)
\(462\) −17.2440 84.7353i −0.0373246 0.183410i
\(463\) −208.033 360.324i −0.449316 0.778238i 0.549026 0.835805i \(-0.314999\pi\)
−0.998342 + 0.0575676i \(0.981666\pi\)
\(464\) 72.6327 + 41.9345i 0.156536 + 0.0903761i
\(465\) 46.6129 90.7180i 0.100243 0.195092i
\(466\) 48.9142 + 84.7219i 0.104966 + 0.181807i
\(467\) −646.848 + 373.458i −1.38511 + 0.799696i −0.992760 0.120119i \(-0.961672\pi\)
−0.392354 + 0.919814i \(0.628339\pi\)
\(468\) 219.561 + 306.568i 0.469147 + 0.655060i
\(469\) −219.842 + 563.806i −0.468746 + 1.20214i
\(470\) −282.620 163.171i −0.601320 0.347172i
\(471\) −12.6287 257.758i −0.0268126 0.547258i
\(472\) −122.031 −0.258541
\(473\) 73.6679i 0.155746i
\(474\) 438.710 21.4943i 0.925549 0.0453467i
\(475\) −311.568 + 539.652i −0.655933 + 1.13611i
\(476\) 312.448 250.299i 0.656403 0.525839i
\(477\) −143.776 65.1898i −0.301417 0.136666i
\(478\) 168.654 + 292.117i 0.352833 + 0.611124i
\(479\) −9.52571 + 5.49967i −0.0198867 + 0.0114816i −0.509910 0.860228i \(-0.670321\pi\)
0.490024 + 0.871709i \(0.336988\pi\)
\(480\) 41.1692 + 21.1536i 0.0857691 + 0.0440700i
\(481\) 121.627 210.664i 0.252862 0.437970i
\(482\) −345.160 + 199.278i −0.716100 + 0.413441i
\(483\) −218.831 247.319i −0.453067 0.512048i
\(484\) 112.522 194.894i 0.232484 0.402674i
\(485\) −12.3863 + 7.15124i −0.0255388 + 0.0147448i
\(486\) 333.410 83.2808i 0.686029 0.171360i
\(487\) −207.376 + 359.187i −0.425824 + 0.737549i −0.996497 0.0836282i \(-0.973349\pi\)
0.570673 + 0.821178i \(0.306683\pi\)
\(488\) 85.6869i 0.175588i
\(489\) −184.456 + 118.896i −0.377211 + 0.243142i
\(490\) −180.356 + 56.5058i −0.368073 + 0.115318i
\(491\) 49.0458 28.3166i 0.0998896 0.0576713i −0.449223 0.893420i \(-0.648299\pi\)
0.549113 + 0.835748i \(0.314966\pi\)
\(492\) −99.1164 153.770i −0.201456 0.312540i
\(493\) 299.788 + 519.248i 0.608089 + 1.05324i
\(494\) −910.412 525.627i −1.84294 1.06402i
\(495\) 71.1296 6.98668i 0.143696 0.0141145i
\(496\) −49.8605 −0.100525
\(497\) −8.14097 3.17437i −0.0163802 0.00638706i
\(498\) 153.793 + 79.0220i 0.308821 + 0.158679i
\(499\) 223.211 386.613i 0.447317 0.774775i −0.550894 0.834575i \(-0.685713\pi\)
0.998210 + 0.0598003i \(0.0190464\pi\)
\(500\) 232.164i 0.464328i
\(501\) −136.803 212.236i −0.273059 0.423625i
\(502\) −314.720 −0.626932
\(503\) 198.013i 0.393663i −0.980437 0.196832i \(-0.936935\pi\)
0.980437 0.196832i \(-0.0630652\pi\)
\(504\) 171.549 + 48.1952i 0.340376 + 0.0956255i
\(505\) 488.397 0.967122
\(506\) 64.7527i 0.127970i
\(507\) −720.088 369.997i −1.42029 0.729776i
\(508\) 173.016 0.340583
\(509\) 592.816 + 342.262i 1.16467 + 0.672421i 0.952418 0.304794i \(-0.0985878\pi\)
0.212249 + 0.977216i \(0.431921\pi\)
\(510\) 179.272 + 278.124i 0.351515 + 0.545341i
\(511\) −56.7557 70.8480i −0.111068 0.138646i
\(512\) 22.6274i 0.0441942i
\(513\) −750.672 + 595.290i −1.46330 + 1.16041i
\(514\) 238.307 412.759i 0.463632 0.803034i
\(515\) −359.650 + 207.644i −0.698350 + 0.403193i
\(516\) 135.024 + 69.3784i 0.261675 + 0.134454i
\(517\) 123.174 + 213.343i 0.238247 + 0.412656i
\(518\) −17.3833 113.628i −0.0335585 0.219359i
\(519\) 709.645 34.7686i 1.36733 0.0669916i
\(520\) −161.607 −0.310783
\(521\) −818.004 472.275i −1.57006 0.906477i −0.996160 0.0875552i \(-0.972095\pi\)
−0.573905 0.818922i \(-0.694572\pi\)
\(522\) −110.203 + 243.053i −0.211117 + 0.465618i
\(523\) −129.056 223.531i −0.246761 0.427402i 0.715864 0.698239i \(-0.246033\pi\)
−0.962625 + 0.270837i \(0.912700\pi\)
\(524\) −175.257 101.185i −0.334459 0.193100i
\(525\) 73.5420 + 361.378i 0.140080 + 0.688339i
\(526\) 115.337 + 199.770i 0.219272 + 0.379791i
\(527\) −308.695 178.225i −0.585759 0.338188i
\(528\) −18.9298 29.3678i −0.0358519 0.0556208i
\(529\) −140.856 243.970i −0.266269 0.461191i
\(530\) 58.5921 33.8282i 0.110551 0.0638267i
\(531\) −37.9580 386.441i −0.0714841 0.727762i
\(532\) −491.059 + 75.1244i −0.923042 + 0.141211i
\(533\) 553.178 + 319.378i 1.03786 + 0.599207i
\(534\) 63.8371 41.1480i 0.119545 0.0770561i
\(535\) −406.918 −0.760595
\(536\) 244.518i 0.456190i
\(537\) 263.295 512.426i 0.490308 0.954238i
\(538\) 351.488 608.794i 0.653323 1.13159i
\(539\) 139.233 + 31.1329i 0.258318 + 0.0577605i
\(540\) −54.1822 + 136.952i −0.100337 + 0.253615i
\(541\) −388.642 673.147i −0.718377 1.24426i −0.961643 0.274305i \(-0.911552\pi\)
0.243266 0.969960i \(-0.421781\pi\)
\(542\) −211.177 + 121.923i −0.389626 + 0.224951i
\(543\) −6.62317 135.182i −0.0121974 0.248954i
\(544\) 80.8812 140.090i 0.148679 0.257519i
\(545\) −51.9979 + 30.0210i −0.0954091 + 0.0550845i
\(546\) −609.658 + 124.068i −1.11659 + 0.227231i
\(547\) 201.360 348.766i 0.368118 0.637598i −0.621154 0.783689i \(-0.713336\pi\)
0.989271 + 0.146090i \(0.0466691\pi\)
\(548\) −70.5210 + 40.7153i −0.128688 + 0.0742980i
\(549\) −271.348 + 26.6530i −0.494259 + 0.0485483i
\(550\) 36.1560 62.6241i 0.0657382 0.113862i
\(551\) 743.996i 1.35026i
\(552\) −118.684 60.9824i −0.215007 0.110475i
\(553\) −263.274 + 675.190i −0.476083 + 1.22096i
\(554\) −109.252 + 63.0765i −0.197205 + 0.113857i
\(555\) 94.8960 4.64937i 0.170984 0.00837725i
\(556\) 44.6685 + 77.3681i 0.0803390 + 0.139151i
\(557\) 155.838 + 89.9733i 0.279782 + 0.161532i 0.633325 0.773886i \(-0.281690\pi\)
−0.353543 + 0.935418i \(0.615023\pi\)
\(558\) −15.5092 157.895i −0.0277942 0.282966i
\(559\) −530.030 −0.948175
\(560\) −59.6014 + 47.7462i −0.106431 + 0.0852610i
\(561\) −12.2234 249.485i −0.0217885 0.444715i
\(562\) −332.171 + 575.338i −0.591052 + 1.02373i
\(563\) 9.40822i 0.0167109i 0.999965 + 0.00835544i \(0.00265965\pi\)
−0.999965 + 0.00835544i \(0.997340\pi\)
\(564\) −507.034 + 24.8418i −0.898996 + 0.0440458i
\(565\) 43.2118 0.0764811
\(566\) 67.0563i 0.118474i
\(567\) −99.2610 + 558.244i −0.175064 + 0.984557i
\(568\) −3.53067 −0.00621597
\(569\) 33.0375i 0.0580624i −0.999579 0.0290312i \(-0.990758\pi\)
0.999579 0.0290312i \(-0.00924221\pi\)
\(570\) −20.0929 410.106i −0.0352507 0.719484i
\(571\) −410.353 −0.718657 −0.359329 0.933211i \(-0.616994\pi\)
−0.359329 + 0.933211i \(0.616994\pi\)
\(572\) 105.649 + 60.9965i 0.184701 + 0.106637i
\(573\) −261.498 + 12.8120i −0.456367 + 0.0223594i
\(574\) 298.374 45.6465i 0.519815 0.0795236i
\(575\) 276.157i 0.480272i
\(576\) 71.6552 7.03830i 0.124401 0.0122193i
\(577\) 205.506 355.947i 0.356163 0.616892i −0.631154 0.775658i \(-0.717418\pi\)
0.987316 + 0.158766i \(0.0507516\pi\)
\(578\) 647.548 373.862i 1.12033 0.646820i
\(579\) −23.2006 473.536i −0.0400701 0.817851i
\(580\) −57.1865 99.0499i −0.0985973 0.170776i
\(581\) −222.648 + 178.362i −0.383216 + 0.306991i
\(582\) −10.1679 + 19.7888i −0.0174707 + 0.0340014i
\(583\) −51.0721 −0.0876022
\(584\) −31.7657 18.3399i −0.0543933 0.0314040i
\(585\) −50.2681 511.767i −0.0859284 0.874816i
\(586\) −65.7468 113.877i −0.112196 0.194329i
\(587\) 474.540 + 273.976i 0.808416 + 0.466739i 0.846406 0.532539i \(-0.178762\pi\)
−0.0379895 + 0.999278i \(0.512095\pi\)
\(588\) −188.189 + 225.878i −0.320050 + 0.384146i
\(589\) 221.154 + 383.050i 0.375474 + 0.650340i
\(590\) 144.120 + 83.2075i 0.244271 + 0.141030i
\(591\) 217.355 10.6492i 0.367775 0.0180189i
\(592\) −23.2234 40.2241i −0.0392287 0.0679461i
\(593\) 347.401 200.572i 0.585837 0.338233i −0.177613 0.984100i \(-0.556837\pi\)
0.763450 + 0.645867i \(0.223504\pi\)
\(594\) 87.1120 69.0807i 0.146653 0.116297i
\(595\) −539.670 + 82.5612i −0.907009 + 0.138758i
\(596\) 108.713 + 62.7657i 0.182405 + 0.105312i
\(597\) 834.147 + 428.603i 1.39723 + 0.717928i
\(598\) 465.886 0.779074
\(599\) 245.708i 0.410197i 0.978741 + 0.205098i \(0.0657515\pi\)
−0.978741 + 0.205098i \(0.934249\pi\)
\(600\) 80.7316 + 125.247i 0.134553 + 0.208746i
\(601\) 243.356 421.505i 0.404919 0.701340i −0.589393 0.807846i \(-0.700633\pi\)
0.994312 + 0.106507i \(0.0339665\pi\)
\(602\) −195.477 + 156.595i −0.324713 + 0.260125i
\(603\) −774.324 + 76.0577i −1.28412 + 0.126132i
\(604\) 189.735 + 328.631i 0.314132 + 0.544092i
\(605\) −265.779 + 153.447i −0.439304 + 0.253632i
\(606\) 638.566 411.605i 1.05374 0.679217i
\(607\) 265.813 460.402i 0.437913 0.758487i −0.559616 0.828752i \(-0.689051\pi\)
0.997528 + 0.0702653i \(0.0223846\pi\)
\(608\) −173.834 + 100.363i −0.285911 + 0.165071i
\(609\) −291.776 329.760i −0.479107 0.541478i
\(610\) 58.4259 101.197i 0.0957802 0.165896i
\(611\) 1534.97 886.216i 2.51223 1.45044i
\(612\) 468.788 + 212.554i 0.765993 + 0.347311i
\(613\) 417.393 722.946i 0.680902 1.17936i −0.293803 0.955866i \(-0.594921\pi\)
0.974706 0.223492i \(-0.0717456\pi\)
\(614\) 286.117i 0.465989i
\(615\) 12.2087 + 249.186i 0.0198515 + 0.405180i
\(616\) 56.9851 8.71783i 0.0925082 0.0141523i
\(617\) 739.602 427.009i 1.19871 0.692073i 0.238439 0.971157i \(-0.423364\pi\)
0.960267 + 0.279084i \(0.0900308\pi\)
\(618\) −295.237 + 574.591i −0.477730 + 0.929759i
\(619\) 383.189 + 663.703i 0.619045 + 1.07222i 0.989660 + 0.143431i \(0.0458136\pi\)
−0.370615 + 0.928787i \(0.620853\pi\)
\(620\) 58.8855 + 33.9976i 0.0949766 + 0.0548348i
\(621\) 156.198 394.810i 0.251527 0.635765i
\(622\) −420.045 −0.675313
\(623\) 18.9501 + 123.869i 0.0304174 + 0.198827i
\(624\) −211.297 + 136.197i −0.338617 + 0.218265i
\(625\) −61.2128 + 106.024i −0.0979405 + 0.169638i
\(626\) 535.027i 0.854676i
\(627\) −141.654 + 275.687i −0.225923 + 0.439692i
\(628\) 172.045 0.273957
\(629\) 332.046i 0.527895i
\(630\) −169.739 173.891i −0.269427 0.276017i
\(631\) 414.115 0.656283 0.328142 0.944629i \(-0.393578\pi\)
0.328142 + 0.944629i \(0.393578\pi\)
\(632\) 292.824i 0.463330i
\(633\) −460.346 + 296.729i −0.727244 + 0.468765i
\(634\) −365.193 −0.576014
\(635\) −204.333 117.972i −0.321784 0.185782i
\(636\) 48.0983 93.6090i 0.0756263 0.147184i
\(637\) 223.997 1001.76i 0.351643 1.57263i
\(638\) 86.3373i 0.135325i
\(639\) −1.09822 11.1807i −0.00171866 0.0174972i
\(640\) −15.4286 + 26.7231i −0.0241072 + 0.0417549i
\(641\) 443.256 255.914i 0.691507 0.399242i −0.112669 0.993633i \(-0.535940\pi\)
0.804176 + 0.594391i \(0.202607\pi\)
\(642\) −532.035 + 342.938i −0.828715 + 0.534171i
\(643\) 474.057 + 821.091i 0.737258 + 1.27697i 0.953725 + 0.300679i \(0.0972132\pi\)
−0.216467 + 0.976290i \(0.569453\pi\)
\(644\) 171.821 137.644i 0.266803 0.213733i
\(645\) −112.159 174.003i −0.173889 0.269773i
\(646\) −1434.98 −2.22133
\(647\) −118.963 68.6832i −0.183868 0.106156i 0.405241 0.914210i \(-0.367188\pi\)
−0.589109 + 0.808054i \(0.700521\pi\)
\(648\) 44.5769 + 224.724i 0.0687915 + 0.346796i
\(649\) −62.8113 108.792i −0.0967817 0.167631i
\(650\) −450.571 260.137i −0.693186 0.400211i
\(651\) 248.244 + 83.0476i 0.381328 + 0.127569i
\(652\) −73.1516 126.702i −0.112196 0.194329i
\(653\) 126.996 + 73.3211i 0.194481 + 0.112283i 0.594078 0.804407i \(-0.297517\pi\)
−0.399598 + 0.916691i \(0.630850\pi\)
\(654\) −42.6852 + 83.0739i −0.0652678 + 0.127024i
\(655\) 137.986 + 238.999i 0.210666 + 0.364884i
\(656\) 105.624 60.9819i 0.161012 0.0929602i
\(657\) 48.1970 106.298i 0.0733593 0.161794i
\(658\) 304.275 780.343i 0.462424 1.18593i
\(659\) 736.802 + 425.393i 1.11806 + 0.645513i 0.940905 0.338670i \(-0.109977\pi\)
0.177155 + 0.984183i \(0.443310\pi\)
\(660\) 2.33169 + 47.5909i 0.00353286 + 0.0721074i
\(661\) −280.785 −0.424788 −0.212394 0.977184i \(-0.568126\pi\)
−0.212394 + 0.977184i \(0.568126\pi\)
\(662\) 539.905i 0.815566i
\(663\) −1795.01 + 87.9453i −2.70740 + 0.132648i
\(664\) −57.6355 + 99.8276i −0.0868004 + 0.150343i
\(665\) 631.167 + 246.108i 0.949123 + 0.370087i
\(666\) 120.156 86.0543i 0.180414 0.129211i
\(667\) 164.859 + 285.544i 0.247165 + 0.428103i
\(668\) 145.784 84.1686i 0.218240 0.126001i
\(669\) 669.164 + 343.831i 1.00024 + 0.513947i
\(670\) 166.725 288.777i 0.248844 0.431010i
\(671\) −76.3909 + 44.1043i −0.113846 + 0.0657292i
\(672\) −37.6883 + 112.657i −0.0560837 + 0.167644i
\(673\) −182.652 + 316.362i −0.271400 + 0.470078i −0.969220 0.246194i \(-0.920820\pi\)
0.697821 + 0.716272i \(0.254153\pi\)
\(674\) −297.450 + 171.733i −0.441321 + 0.254797i
\(675\) −371.514 + 294.615i −0.550391 + 0.436466i
\(676\) 269.861 467.413i 0.399202 0.691439i
\(677\) 942.705i 1.39247i 0.717812 + 0.696237i \(0.245144\pi\)
−0.717812 + 0.696237i \(0.754856\pi\)
\(678\) 56.4983 36.4175i 0.0833308 0.0537132i
\(679\) −22.9502 28.6487i −0.0338000 0.0421925i
\(680\) −191.042 + 110.298i −0.280945 + 0.162203i
\(681\) 659.376 + 1022.96i 0.968246 + 1.50214i
\(682\) −25.6639 44.4512i −0.0376304 0.0651777i
\(683\) 730.079 + 421.511i 1.06893 + 0.617147i 0.927889 0.372857i \(-0.121622\pi\)
0.141041 + 0.990004i \(0.454955\pi\)
\(684\) −371.895 519.269i −0.543706 0.759165i
\(685\) 111.048 0.162113
\(686\) −213.356 435.634i −0.311015 0.635035i
\(687\) −292.654 150.372i −0.425988 0.218882i
\(688\) −50.6019 + 87.6450i −0.0735493 + 0.127391i
\(689\) 367.456i 0.533318i
\(690\) 98.5854 + 152.946i 0.142877 + 0.221660i
\(691\) −749.201 −1.08423 −0.542113 0.840305i \(-0.682376\pi\)
−0.542113 + 0.840305i \(0.682376\pi\)
\(692\) 473.664i 0.684486i
\(693\) 45.3324 + 177.745i 0.0654147 + 0.256487i
\(694\) −342.774 −0.493910
\(695\) 121.830i 0.175294i
\(696\) −158.246 81.3101i −0.227365 0.116825i
\(697\) 871.914 1.25095
\(698\) 6.03525 + 3.48445i 0.00864648 + 0.00499205i
\(699\) −112.433 174.429i −0.160849 0.249541i
\(700\) −243.029 + 37.1797i −0.347185 + 0.0531139i
\(701\) 849.790i 1.21225i 0.795368 + 0.606127i \(0.207278\pi\)
−0.795368 + 0.606127i \(0.792722\pi\)
\(702\) −497.025 626.758i −0.708013 0.892817i
\(703\) −206.013 + 356.825i −0.293048 + 0.507575i
\(704\) 20.1726 11.6467i 0.0286543 0.0165436i
\(705\) 615.749 + 316.385i 0.873402 + 0.448773i
\(706\) 433.301 + 750.499i 0.613741 + 1.06303i
\(707\) 189.558 + 1239.07i 0.268117 + 1.75257i
\(708\) 258.557 12.6679i 0.365194 0.0178925i
\(709\) −875.721 −1.23515 −0.617575 0.786512i \(-0.711885\pi\)
−0.617575 + 0.786512i \(0.711885\pi\)
\(710\) 4.16974 + 2.40740i 0.00587288 + 0.00339071i
\(711\) −927.299 + 91.0835i −1.30422 + 0.128106i
\(712\) 25.3165 + 43.8495i 0.0355569 + 0.0615863i
\(713\) −169.757 98.0094i −0.238089 0.137461i
\(714\) −636.024 + 562.763i −0.890791 + 0.788184i
\(715\) −83.1815 144.075i −0.116338 0.201503i
\(716\) 332.618 + 192.037i 0.464550 + 0.268208i
\(717\) −387.665 601.425i −0.540676 0.838807i
\(718\) 376.693 + 652.451i 0.524641 + 0.908706i
\(719\) 32.2621 18.6266i 0.0448708 0.0259062i −0.477397 0.878688i \(-0.658420\pi\)
0.522268 + 0.852782i \(0.325086\pi\)
\(720\) −89.4243 40.5461i −0.124200 0.0563140i
\(721\) −666.385 831.847i −0.924252 1.15374i
\(722\) 1099.93 + 635.048i 1.52346 + 0.879567i
\(723\) 710.632 458.057i 0.982893 0.633551i
\(724\) 90.2296 0.124626
\(725\) 368.210i 0.507876i
\(726\) −218.178 + 424.618i −0.300521 + 0.584874i
\(727\) 92.7399 160.630i 0.127565 0.220949i −0.795168 0.606390i \(-0.792617\pi\)
0.922733 + 0.385440i \(0.125950\pi\)
\(728\) −62.7235 409.999i −0.0861587 0.563186i
\(729\) −697.777 + 211.064i −0.957170 + 0.289526i
\(730\) 25.0103 + 43.3191i 0.0342607 + 0.0593413i
\(731\) −626.570 + 361.751i −0.857142 + 0.494871i
\(732\) −8.89500 181.552i −0.0121516 0.248021i
\(733\) 315.666 546.749i 0.430649 0.745906i −0.566280 0.824213i \(-0.691618\pi\)
0.996929 + 0.0783065i \(0.0249513\pi\)
\(734\) 453.641 261.910i 0.618040 0.356826i
\(735\) 376.268 138.446i 0.511930 0.188361i
\(736\) 44.4781 77.0384i 0.0604322 0.104672i
\(737\) −217.991 + 125.857i −0.295781 + 0.170769i
\(738\) 225.968 + 315.514i 0.306190 + 0.427526i
\(739\) 245.760 425.669i 0.332558 0.576007i −0.650455 0.759545i \(-0.725422\pi\)
0.983013 + 0.183538i \(0.0587550\pi\)
\(740\) 63.3399i 0.0855944i
\(741\) 1983.53 + 1019.18i 2.67682 + 1.37541i
\(742\) 108.564 + 135.520i 0.146312 + 0.182641i
\(743\) −487.432 + 281.419i −0.656032 + 0.378760i −0.790764 0.612122i \(-0.790316\pi\)
0.134731 + 0.990882i \(0.456983\pi\)
\(744\) 105.643 5.17593i 0.141994 0.00695689i
\(745\) −85.5942 148.253i −0.114891 0.198998i
\(746\) −512.464 295.871i −0.686948 0.396610i
\(747\) −334.056 151.465i −0.447196 0.202765i
\(748\) 166.523 0.222624
\(749\) −157.935 1032.36i −0.210861 1.37831i
\(750\) −24.1006 491.905i −0.0321341 0.655873i
\(751\) 32.3457 56.0244i 0.0430702 0.0745997i −0.843687 0.536836i \(-0.819619\pi\)
0.886757 + 0.462236i \(0.152953\pi\)
\(752\) 338.428i 0.450037i
\(753\) 666.821 32.6705i 0.885553 0.0433871i
\(754\) 621.184 0.823851
\(755\) 517.488i 0.685414i
\(756\) −368.478 84.3068i −0.487405 0.111517i
\(757\) −629.889 −0.832086 −0.416043 0.909345i \(-0.636583\pi\)
−0.416043 + 0.909345i \(0.636583\pi\)
\(758\) 341.674i 0.450758i
\(759\) −6.72187 137.197i −0.00885622 0.180760i
\(760\) 273.732 0.360174
\(761\) 412.140 + 237.949i 0.541577 + 0.312680i 0.745718 0.666262i \(-0.232107\pi\)
−0.204141 + 0.978942i \(0.565440\pi\)
\(762\) −366.583 + 17.9605i −0.481080 + 0.0235702i
\(763\) −96.3454 120.268i −0.126272 0.157625i
\(764\) 174.541i 0.228457i
\(765\) −408.710 570.673i −0.534262 0.745978i
\(766\) −118.761 + 205.700i −0.155040 + 0.268538i
\(767\) −782.745 + 451.918i −1.02053 + 0.589202i
\(768\) 2.34891 + 47.9425i 0.00305848 + 0.0624251i
\(769\) 424.359 + 735.011i 0.551832 + 0.955801i 0.998142 + 0.0609226i \(0.0194043\pi\)
−0.446311 + 0.894878i \(0.647262\pi\)
\(770\) −73.2440 28.5597i −0.0951221 0.0370905i
\(771\) −462.071 + 899.284i −0.599314 + 1.16639i
\(772\) 316.069 0.409416
\(773\) −45.6733 26.3695i −0.0590857 0.0341132i 0.470166 0.882578i \(-0.344194\pi\)
−0.529252 + 0.848465i \(0.677527\pi\)
\(774\) −293.289 132.981i −0.378926 0.171810i
\(775\) 109.451 + 189.575i 0.141227 + 0.244613i
\(776\) −12.8450 7.41609i −0.0165529 0.00955681i
\(777\) 48.6269 + 238.948i 0.0625829 + 0.307526i
\(778\) −356.371 617.252i −0.458060 0.793383i
\(779\) −936.980 540.966i −1.20280 0.694436i
\(780\) 342.409 16.7761i 0.438986 0.0215079i
\(781\) −1.81729 3.14764i −0.00232687 0.00403026i
\(782\) 550.744 317.972i 0.704276 0.406614i
\(783\) 208.265 526.415i 0.265984 0.672305i
\(784\) −144.265 132.678i −0.184012 0.169232i
\(785\) −203.186 117.310i −0.258836 0.149439i
\(786\) 381.834 + 196.195i 0.485794 + 0.249611i
\(787\) −312.691 −0.397320 −0.198660 0.980068i \(-0.563659\pi\)
−0.198660 + 0.980068i \(0.563659\pi\)
\(788\) 145.077i 0.184108i
\(789\) −265.112 411.295i −0.336010 0.521287i
\(790\) 199.663 345.827i 0.252739 0.437756i
\(791\) 16.7715 + 109.629i 0.0212030 + 0.138595i
\(792\) 43.1567 + 60.2587i 0.0544908 + 0.0760843i
\(793\) 317.324 + 549.621i 0.400156 + 0.693091i
\(794\) 418.267 241.487i 0.526785 0.304139i
\(795\) −120.632 + 77.7568i −0.151738 + 0.0978072i
\(796\) −312.606 + 541.449i −0.392721 + 0.680213i
\(797\) 406.221 234.532i 0.509688 0.294269i −0.223017 0.974814i \(-0.571591\pi\)
0.732705 + 0.680546i \(0.238257\pi\)
\(798\) 1032.65 210.148i 1.29404 0.263343i
\(799\) 1209.70 2095.27i 1.51402 2.62236i
\(800\) −86.0319 + 49.6706i −0.107540 + 0.0620882i
\(801\) −130.985 + 93.8103i −0.163527 + 0.117116i
\(802\) −481.159 + 833.391i −0.599948 + 1.03914i
\(803\) 37.7593i 0.0470228i
\(804\) −25.3830 518.079i −0.0315709 0.644377i
\(805\) −296.775 + 45.4020i −0.368665 + 0.0564000i
\(806\) −319.820 + 184.648i −0.396799 + 0.229092i
\(807\) −681.527 + 1326.39i −0.844519 + 1.64360i
\(808\) 253.242 + 438.629i 0.313419 + 0.542857i
\(809\) −476.849 275.309i −0.589430 0.340308i 0.175442 0.984490i \(-0.443865\pi\)
−0.764872 + 0.644182i \(0.777198\pi\)
\(810\) 100.583 295.795i 0.124177 0.365180i
\(811\) −848.334 −1.04604 −0.523018 0.852322i \(-0.675194\pi\)
−0.523018 + 0.852322i \(0.675194\pi\)
\(812\) 229.095 183.526i 0.282137 0.226018i
\(813\) 434.782 280.251i 0.534787 0.344712i
\(814\) 23.9069 41.4079i 0.0293696 0.0508696i
\(815\) 199.515i 0.244803i
\(816\) −156.827 + 305.217i −0.192190 + 0.374040i
\(817\) 897.771 1.09886
\(818\) 364.237i 0.445277i
\(819\) 1278.85 326.160i 1.56148 0.398242i
\(820\) −166.323 −0.202833
\(821\) 1379.51i 1.68028i −0.542373 0.840138i \(-0.682474\pi\)
0.542373 0.840138i \(-0.317526\pi\)
\(822\) 145.192 93.5874i 0.176632 0.113853i
\(823\) −103.993 −0.126359 −0.0631794 0.998002i \(-0.520124\pi\)
−0.0631794 + 0.998002i \(0.520124\pi\)
\(824\) −372.970 215.334i −0.452634 0.261328i
\(825\) −70.1057 + 136.440i −0.0849767 + 0.165382i
\(826\) −155.162 + 397.929i −0.187848 + 0.481754i
\(827\) 445.099i 0.538209i 0.963111 + 0.269104i \(0.0867277\pi\)
−0.963111 + 0.269104i \(0.913272\pi\)
\(828\) 257.796 + 116.888i 0.311347 + 0.141169i
\(829\) 370.808 642.258i 0.447295 0.774738i −0.550914 0.834562i \(-0.685721\pi\)
0.998209 + 0.0598243i \(0.0190541\pi\)
\(830\) 136.136 78.5980i 0.164019 0.0946964i
\(831\) 224.932 144.986i 0.270677 0.174472i
\(832\) −83.7960 145.139i −0.100716 0.174446i
\(833\) −418.918 1337.11i −0.502903 1.60517i
\(834\) −102.674 159.289i −0.123110 0.190994i
\(835\) −229.563 −0.274926
\(836\) −178.950 103.317i −0.214055 0.123585i
\(837\) 49.2513 + 332.935i 0.0588427 + 0.397772i
\(838\) −153.235 265.411i −0.182858 0.316720i
\(839\) 290.739 + 167.858i 0.346531 + 0.200069i 0.663156 0.748481i \(-0.269217\pi\)
−0.316626 + 0.948551i \(0.602550\pi\)
\(840\) 121.326 107.351i 0.144435 0.127798i
\(841\) −200.687 347.600i −0.238629 0.413317i
\(842\) 967.659 + 558.678i 1.14924 + 0.663513i
\(843\) 644.073 1253.50i 0.764025 1.48695i
\(844\) −182.564 316.210i −0.216308 0.374656i
\(845\) −637.415 + 368.012i −0.754337 + 0.435517i
\(846\) 1071.71 105.269i 1.26680 0.124431i
\(847\) −492.454 614.728i −0.581409 0.725771i
\(848\) 60.7621 + 35.0810i 0.0716534 + 0.0413691i
\(849\) −6.96100 142.077i −0.00819905 0.167347i
\(850\) −710.185 −0.835512
\(851\) 182.599i 0.214569i
\(852\) 7.48071 0.366513i 0.00878018 0.000430179i
\(853\) 346.509 600.172i 0.406224 0.703601i −0.588239 0.808687i \(-0.700179\pi\)
0.994463 + 0.105086i \(0.0335119\pi\)
\(854\) 279.414 + 108.951i 0.327183 + 0.127577i
\(855\) 85.1448 + 866.838i 0.0995845 + 1.01385i
\(856\) −210.994 365.453i −0.246489 0.426931i
\(857\) −735.467 + 424.622i −0.858188 + 0.495475i −0.863405 0.504511i \(-0.831673\pi\)
0.00521719 + 0.999986i \(0.498339\pi\)
\(858\) −230.179 118.271i −0.268274 0.137845i
\(859\) −730.939 + 1266.02i −0.850919 + 1.47383i 0.0294619 + 0.999566i \(0.490621\pi\)
−0.880380 + 0.474268i \(0.842713\pi\)
\(860\) 119.522 69.0062i 0.138979 0.0802398i
\(861\) −627.449 + 127.689i −0.728745 + 0.148303i
\(862\) 390.661 676.644i 0.453203 0.784970i
\(863\) 262.264 151.418i 0.303898 0.175455i −0.340295 0.940319i \(-0.610527\pi\)
0.644193 + 0.764863i \(0.277194\pi\)
\(864\) −151.091 + 22.3510i −0.174874 + 0.0258692i
\(865\) 322.970 559.400i 0.373376 0.646706i
\(866\) 497.427i 0.574396i
\(867\) −1333.20 + 859.352i −1.53772 + 0.991179i
\(868\) −63.3974 + 162.589i −0.0730385 + 0.187314i
\(869\) −261.056 + 150.721i −0.300410 + 0.173442i
\(870\) 131.448 + 203.928i 0.151089 + 0.234400i
\(871\) 905.522 + 1568.41i 1.03963 + 1.80070i
\(872\) −53.9237 31.1329i −0.0618391 0.0357028i
\(873\) 19.4893 42.9837i 0.0223246 0.0492368i
\(874\) −789.124 −0.902888
\(875\) 757.058 + 295.196i 0.865209 + 0.337367i
\(876\) 69.2083 + 35.5607i 0.0790049 + 0.0405944i
\(877\) 155.891 270.011i 0.177754 0.307880i −0.763357 0.645977i \(-0.776450\pi\)
0.941111 + 0.338098i \(0.109783\pi\)
\(878\) 66.7994i 0.0760813i
\(879\) 151.124 + 234.455i 0.171927 + 0.266729i
\(880\) −31.7653 −0.0360969
\(881\) 1088.82i 1.23589i −0.786220 0.617947i \(-0.787965\pi\)
0.786220 0.617947i \(-0.212035\pi\)
\(882\) 375.283 498.121i 0.425491 0.564763i
\(883\) 877.900 0.994224 0.497112 0.867686i \(-0.334394\pi\)
0.497112 + 0.867686i \(0.334394\pi\)
\(884\) 1198.11i 1.35533i
\(885\) −313.995 161.338i −0.354797 0.182302i
\(886\) 724.422 0.817633
\(887\) −1311.60 757.255i −1.47870 0.853726i −0.478987 0.877822i \(-0.658996\pi\)
−0.999710 + 0.0240962i \(0.992329\pi\)
\(888\) 53.3808 + 82.8152i 0.0601136 + 0.0932604i
\(889\) 219.989 564.184i 0.247457 0.634627i
\(890\) 69.0487i 0.0775828i
\(891\) −177.400 + 155.410i −0.199102 + 0.174422i
\(892\) −250.776 + 434.358i −0.281140 + 0.486948i
\(893\) −2599.96 + 1501.08i −2.91148 + 1.68095i
\(894\) −236.855 121.701i −0.264939 0.136131i
\(895\) −261.883 453.594i −0.292606 0.506809i
\(896\) −73.7851 28.7707i −0.0823495 0.0321102i
\(897\) −987.110 + 48.3628i −1.10046 + 0.0539162i
\(898\) 792.378 0.882380
\(899\) −226.344 130.680i −0.251773 0.145361i
\(900\) −184.054 256.991i −0.204505 0.285545i
\(901\) 250.793 + 434.385i 0.278349 + 0.482115i
\(902\) 108.732 + 62.7766i 0.120546 + 0.0695971i
\(903\) 397.917 352.083i 0.440662 0.389904i
\(904\) 22.4061 + 38.8085i 0.0247855 + 0.0429297i
\(905\) −106.562 61.5234i −0.117748 0.0679817i
\(906\) −436.122 676.601i −0.481371 0.746800i
\(907\) 183.872 + 318.475i 0.202725 + 0.351131i 0.949406 0.314052i \(-0.101687\pi\)
−0.746680 + 0.665183i \(0.768353\pi\)
\(908\) −702.666 + 405.684i −0.773861 + 0.446789i
\(909\) −1310.25 + 938.389i −1.44142 + 1.03233i
\(910\) −205.483 + 526.980i −0.225805 + 0.579099i
\(911\) −742.768 428.837i −0.815333 0.470733i 0.0334717 0.999440i \(-0.489344\pi\)
−0.848804 + 0.528707i \(0.822677\pi\)
\(912\) 357.897 230.693i 0.392431 0.252952i
\(913\) −118.663 −0.129971
\(914\) 946.791i 1.03588i
\(915\) −113.287 + 220.479i −0.123810 + 0.240960i
\(916\) 109.675 189.963i 0.119733 0.207383i
\(917\) −552.788 + 442.834i −0.602823 + 0.482916i
\(918\) −1015.32 401.692i −1.10602 0.437573i
\(919\) −52.7068 91.2909i −0.0573524 0.0993372i 0.835924 0.548846i \(-0.184933\pi\)
−0.893276 + 0.449508i \(0.851599\pi\)
\(920\) −105.058 + 60.6552i −0.114193 + 0.0659295i
\(921\) 29.7013 + 606.219i 0.0322490 + 0.658218i
\(922\) 65.9966 114.310i 0.0715798 0.123980i
\(923\) −22.6468 + 13.0751i −0.0245360 + 0.0141659i
\(924\) −119.834 + 24.3867i −0.129690 + 0.0263925i
\(925\) −101.958 + 176.596i −0.110225 + 0.190914i
\(926\) −509.575 + 294.203i −0.550297 + 0.317714i
\(927\) 565.895 1248.08i 0.610459 1.34636i
\(928\) 59.3044 102.718i 0.0639056 0.110688i
\(929\) 515.060i 0.554424i 0.960809 + 0.277212i \(0.0894105\pi\)
−0.960809 + 0.277212i \(0.910590\pi\)
\(930\) −128.295 65.9205i −0.137951 0.0708823i
\(931\) −379.409 + 1696.80i −0.407528 + 1.82256i
\(932\) 119.815 69.1752i 0.128557 0.0742223i
\(933\) 889.982 43.6041i 0.953893 0.0467354i
\(934\) 528.149 + 914.781i 0.565470 + 0.979423i
\(935\) −196.665 113.544i −0.210337 0.121438i
\(936\) 433.553 310.506i 0.463197 0.331737i
\(937\) 86.9061 0.0927493 0.0463746 0.998924i \(-0.485233\pi\)
0.0463746 + 0.998924i \(0.485233\pi\)
\(938\) 797.342 + 310.904i 0.850044 + 0.331454i
\(939\) −55.5403 1133.60i −0.0591483 1.20725i
\(940\) −230.759 + 399.686i −0.245488 + 0.425197i
\(941\) 677.244i 0.719707i −0.933009 0.359853i \(-0.882827\pi\)
0.933009 0.359853i \(-0.117173\pi\)
\(942\) −364.525 + 17.8597i −0.386970 + 0.0189593i
\(943\) 479.482 0.508465
\(944\) 172.578i 0.182816i
\(945\) 377.690 + 350.815i 0.399672 + 0.371233i
\(946\) −104.182 −0.110129
\(947\) 947.519i 1.00055i 0.865867 + 0.500274i \(0.166767\pi\)
−0.865867 + 0.500274i \(0.833233\pi\)
\(948\) −30.3976 620.430i −0.0320650 0.654462i
\(949\) −271.673 −0.286273
\(950\) 763.183 + 440.624i 0.803350 + 0.463815i
\(951\) 773.763 37.9101i 0.813631 0.0398634i
\(952\) −353.977 441.868i −0.371824 0.464147i
\(953\) 1873.88i 1.96630i 0.182805 + 0.983149i \(0.441482\pi\)
−0.182805 + 0.983149i \(0.558518\pi\)
\(954\) −92.1923 + 203.330i −0.0966376 + 0.213134i
\(955\) −119.012 + 206.134i −0.124620 + 0.215848i
\(956\) 413.116 238.513i 0.432130 0.249490i
\(957\) −8.96252 182.930i −0.00936523 0.191149i
\(958\) 7.77771 + 13.4714i 0.00811870 + 0.0140620i
\(959\) 43.1002 + 281.729i 0.0449429 + 0.293774i
\(960\) 29.9157 58.2220i 0.0311622 0.0606479i
\(961\) −805.621 −0.838315
\(962\) −297.924 172.006i −0.309692 0.178801i
\(963\) 1091.66 781.839i 1.13361 0.811878i
\(964\) 281.822 + 488.130i 0.292347 + 0.506359i
\(965\) −373.280 215.513i −0.386818 0.223330i
\(966\) −349.762 + 309.474i −0.362073 + 0.320367i
\(967\) −801.055 1387.47i −0.828392 1.43482i −0.899299 0.437334i \(-0.855923\pi\)
0.0709071 0.997483i \(-0.477411\pi\)
\(968\) −275.622 159.130i −0.284733 0.164391i
\(969\) 3040.41 148.963i 3.13768 0.153729i
\(970\) 10.1134 + 17.5169i 0.0104262 + 0.0180586i
\(971\) 1566.15 904.219i 1.61293 0.931225i 0.624242 0.781231i \(-0.285408\pi\)
0.988687 0.149994i \(-0.0479253\pi\)
\(972\) −117.777 471.513i −0.121170 0.485096i
\(973\) 309.083 47.2850i 0.317660 0.0485971i
\(974\) 507.966 + 293.275i 0.521526 + 0.301103i
\(975\) 981.665 + 504.400i 1.00684 + 0.517334i
\(976\) 121.180 0.124159
\(977\) 36.3348i 0.0371902i 0.999827 + 0.0185951i \(0.00591934\pi\)
−0.999827 + 0.0185951i \(0.994081\pi\)
\(978\) 168.145 + 260.860i 0.171927 + 0.266728i
\(979\) −26.0616 + 45.1400i −0.0266206 + 0.0461082i
\(980\) 79.9112 + 255.062i 0.0815421 + 0.260267i
\(981\) 81.8167 180.446i 0.0834013 0.183941i
\(982\) −40.0457 69.3613i −0.0407798 0.0706326i
\(983\) 677.386 391.089i 0.689101 0.397853i −0.114174 0.993461i \(-0.536422\pi\)
0.803275 + 0.595608i \(0.203089\pi\)
\(984\) −217.463 + 140.172i −0.220999 + 0.142451i
\(985\) 98.9214 171.337i 0.100428 0.173946i
\(986\) 734.328 423.964i 0.744754 0.429984i
\(987\) −563.686 + 1684.96i −0.571111 + 1.70715i
\(988\) −743.348 + 1287.52i −0.752377 + 1.30315i
\(989\) −344.563 + 198.934i −0.348395 + 0.201146i
\(990\) −9.88065 100.593i −0.00998046 0.101609i
\(991\) −716.282 + 1240.64i −0.722787 + 1.25190i 0.237091 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280417i \(0.909527\pi\)
\(992\) 70.5133i 0.0710820i
\(993\) −56.0466 1143.94i −0.0564417 1.15200i
\(994\) −4.48924 + 11.5131i −0.00451634 + 0.0115826i
\(995\) 738.379 426.303i 0.742090 0.428446i
\(996\) 111.754 217.496i 0.112203 0.218369i
\(997\) 213.563 + 369.901i 0.214205 + 0.371014i 0.953026 0.302887i \(-0.0979505\pi\)
−0.738821 + 0.673902i \(0.764617\pi\)
\(998\) −546.753 315.668i −0.547849 0.316301i
\(999\) −245.650 + 194.803i −0.245896 + 0.194998i
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 126.3.r.a.11.5 yes 32
3.2 odd 2 378.3.r.a.305.11 32
7.2 even 3 126.3.i.a.65.2 32
9.4 even 3 378.3.i.a.179.11 32
9.5 odd 6 126.3.i.a.95.2 yes 32
21.2 odd 6 378.3.i.a.359.14 32
63.23 odd 6 inner 126.3.r.a.23.13 yes 32
63.58 even 3 378.3.r.a.233.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.i.a.65.2 32 7.2 even 3
126.3.i.a.95.2 yes 32 9.5 odd 6
126.3.r.a.11.5 yes 32 1.1 even 1 trivial
126.3.r.a.23.13 yes 32 63.23 odd 6 inner
378.3.i.a.179.11 32 9.4 even 3
378.3.i.a.359.14 32 21.2 odd 6
378.3.r.a.233.3 32 63.58 even 3
378.3.r.a.305.11 32 3.2 odd 2