Properties

Label 143.4.h.b.14.9
Level $143$
Weight $4$
Character 143.14
Analytic conductor $8.437$
Analytic rank $0$
Dimension $76$
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] = [143,4,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(19\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 14.9
Character \(\chi\) \(=\) 143.14
Dual form 143.4.h.b.92.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.471643 + 0.342668i) q^{2} +(-1.46721 - 4.51561i) q^{3} +(-2.36711 + 7.28522i) q^{4} +(1.58259 + 1.14982i) q^{5} +(2.23936 + 1.62699i) q^{6} +(-0.116501 + 0.358552i) q^{7} +(-2.82120 - 8.68275i) q^{8} +(3.60544 - 2.61951i) q^{9} +O(q^{10})\) \(q+(-0.471643 + 0.342668i) q^{2} +(-1.46721 - 4.51561i) q^{3} +(-2.36711 + 7.28522i) q^{4} +(1.58259 + 1.14982i) q^{5} +(2.23936 + 1.62699i) q^{6} +(-0.116501 + 0.358552i) q^{7} +(-2.82120 - 8.68275i) q^{8} +(3.60544 - 2.61951i) q^{9} -1.14042 q^{10} +(-24.8165 - 26.7421i) q^{11} +36.3702 q^{12} +(10.5172 - 7.64121i) q^{13} +(-0.0679178 - 0.209029i) q^{14} +(2.87013 - 8.83336i) q^{15} +(-45.2715 - 32.8917i) q^{16} +(-14.3293 - 10.4108i) q^{17} +(-0.802858 + 2.47094i) q^{18} +(-29.7701 - 91.6229i) q^{19} +(-12.1228 + 8.80775i) q^{20} +1.79001 q^{21} +(20.8682 + 4.10891i) q^{22} -133.927 q^{23} +(-35.0686 + 25.4788i) q^{24} +(-37.4446 - 115.243i) q^{25} +(-2.34197 + 7.20784i) q^{26} +(-120.831 - 87.7890i) q^{27} +(-2.33636 - 1.69746i) q^{28} +(-27.1309 + 83.5002i) q^{29} +(1.67324 + 5.14970i) q^{30} +(156.452 - 113.669i) q^{31} +105.660 q^{32} +(-84.3461 + 151.298i) q^{33} +10.3258 q^{34} +(-0.596641 + 0.433485i) q^{35} +(10.5492 + 32.4671i) q^{36} +(-0.594108 + 1.82848i) q^{37} +(45.4371 + 33.0120i) q^{38} +(-49.9357 - 36.2804i) q^{39} +(5.51878 - 16.9851i) q^{40} +(-61.9309 - 190.604i) q^{41} +(-0.844245 + 0.613380i) q^{42} +112.095 q^{43} +(253.566 - 117.492i) q^{44} +8.71788 q^{45} +(63.1656 - 45.8925i) q^{46} +(-20.1458 - 62.0023i) q^{47} +(-82.1031 + 252.687i) q^{48} +(277.378 + 201.527i) q^{49} +(57.1505 + 41.5223i) q^{50} +(-25.9872 + 79.9804i) q^{51} +(30.7724 + 94.7078i) q^{52} +(377.607 - 274.348i) q^{53} +87.0717 q^{54} +(-8.52567 - 70.8562i) q^{55} +3.44189 q^{56} +(-370.054 + 268.860i) q^{57} +(-15.8168 - 48.6792i) q^{58} +(-261.121 + 803.646i) q^{59} +(57.5591 + 41.8191i) q^{60} +(-60.8324 - 44.1973i) q^{61} +(-34.8386 + 107.222i) q^{62} +(0.519193 + 1.59791i) q^{63} +(312.339 - 226.927i) q^{64} +25.4304 q^{65} +(-12.0638 - 100.261i) q^{66} -459.767 q^{67} +(109.764 - 79.7484i) q^{68} +(196.499 + 604.761i) q^{69} +(0.132860 - 0.408900i) q^{70} +(-160.110 - 116.326i) q^{71} +(-32.9162 - 23.9150i) q^{72} +(-292.882 + 901.397i) q^{73} +(-0.346355 - 1.06597i) q^{74} +(-465.452 + 338.171i) q^{75} +737.962 q^{76} +(12.4796 - 5.78252i) q^{77} +35.9839 q^{78} +(120.266 - 87.3781i) q^{79} +(-33.8267 - 104.108i) q^{80} +(-181.953 + 559.993i) q^{81} +(94.5232 + 68.6751i) q^{82} +(-31.7830 - 23.0917i) q^{83} +(-4.23715 + 13.0406i) q^{84} +(-10.7068 - 32.9521i) q^{85} +(-52.8687 + 38.4113i) q^{86} +416.861 q^{87} +(-162.183 + 290.920i) q^{88} +480.228 q^{89} +(-4.11172 + 2.98734i) q^{90} +(1.51451 + 4.66117i) q^{91} +(317.020 - 975.686i) q^{92} +(-742.833 - 539.699i) q^{93} +(30.7478 + 22.3396i) q^{94} +(58.2358 - 179.231i) q^{95} +(-155.025 - 477.117i) q^{96} +(880.641 - 639.823i) q^{97} -199.880 q^{98} +(-159.526 - 31.4103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9} + 60 q^{10} - 47 q^{11} + 244 q^{12} + 247 q^{13} + 117 q^{14} - 2 q^{15} + 212 q^{16} - 344 q^{17} - 461 q^{18} - 59 q^{19} + 55 q^{20} - 296 q^{21} - 76 q^{22} + 1680 q^{23} + 784 q^{24} - 89 q^{25} + 13 q^{26} - 309 q^{27} - 654 q^{28} - 306 q^{29} + 606 q^{30} + 344 q^{31} - 2408 q^{32} + 1265 q^{33} - 116 q^{34} + 934 q^{35} - 3571 q^{36} + 188 q^{37} - 9 q^{38} + 91 q^{39} - 1803 q^{40} + 1518 q^{41} + 1734 q^{42} - 966 q^{43} + 1513 q^{44} + 2272 q^{45} - 165 q^{46} - 2146 q^{47} + 2320 q^{48} - 2085 q^{49} - 71 q^{50} - 501 q^{51} + 1924 q^{52} + 814 q^{53} - 6546 q^{54} - 1924 q^{55} + 6538 q^{56} - 1099 q^{57} - 4169 q^{58} - 41 q^{59} - 2812 q^{60} + 1788 q^{61} - 3931 q^{62} + 4980 q^{63} + 4256 q^{64} - 1352 q^{65} - 1543 q^{66} + 9878 q^{67} + 648 q^{68} - 2994 q^{69} + 6094 q^{70} - 612 q^{71} + 2965 q^{72} + 3436 q^{73} + 2616 q^{74} + 5089 q^{75} - 6632 q^{76} - 2604 q^{77} + 2704 q^{78} - 7688 q^{79} - 11093 q^{80} - 3972 q^{81} + 1076 q^{82} + 2007 q^{83} - 5729 q^{84} - 2128 q^{85} + 2433 q^{86} + 1812 q^{87} - 9006 q^{88} + 7454 q^{89} - 2204 q^{90} - 728 q^{91} + 2143 q^{92} - 8158 q^{93} + 4055 q^{94} + 824 q^{95} + 811 q^{96} + 5711 q^{97} - 4086 q^{98} - 11439 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.471643 + 0.342668i −0.166751 + 0.121152i −0.668031 0.744133i \(-0.732863\pi\)
0.501280 + 0.865285i \(0.332863\pi\)
\(3\) −1.46721 4.51561i −0.282365 0.869029i −0.987176 0.159635i \(-0.948968\pi\)
0.704811 0.709395i \(-0.251032\pi\)
\(4\) −2.36711 + 7.28522i −0.295889 + 0.910652i
\(5\) 1.58259 + 1.14982i 0.141551 + 0.102843i 0.656307 0.754494i \(-0.272118\pi\)
−0.514756 + 0.857337i \(0.672118\pi\)
\(6\) 2.23936 + 1.62699i 0.152369 + 0.110702i
\(7\) −0.116501 + 0.358552i −0.00629044 + 0.0193600i −0.954152 0.299321i \(-0.903240\pi\)
0.947862 + 0.318681i \(0.103240\pi\)
\(8\) −2.82120 8.68275i −0.124680 0.383727i
\(9\) 3.60544 2.61951i 0.133535 0.0970188i
\(10\) −1.14042 −0.0360633
\(11\) −24.8165 26.7421i −0.680223 0.733005i
\(12\) 36.3702 0.874932
\(13\) 10.5172 7.64121i 0.224381 0.163022i
\(14\) −0.0679178 0.209029i −0.00129656 0.00399039i
\(15\) 2.87013 8.83336i 0.0494044 0.152051i
\(16\) −45.2715 32.8917i −0.707367 0.513932i
\(17\) −14.3293 10.4108i −0.204433 0.148529i 0.480858 0.876798i \(-0.340325\pi\)
−0.685291 + 0.728269i \(0.740325\pi\)
\(18\) −0.802858 + 2.47094i −0.0105131 + 0.0323559i
\(19\) −29.7701 91.6229i −0.359459 1.10630i −0.953378 0.301777i \(-0.902420\pi\)
0.593919 0.804525i \(-0.297580\pi\)
\(20\) −12.1228 + 8.80775i −0.135537 + 0.0984736i
\(21\) 1.79001 0.0186006
\(22\) 20.8682 + 4.10891i 0.202233 + 0.0398192i
\(23\) −133.927 −1.21416 −0.607080 0.794641i \(-0.707659\pi\)
−0.607080 + 0.794641i \(0.707659\pi\)
\(24\) −35.0686 + 25.4788i −0.298265 + 0.216702i
\(25\) −37.4446 115.243i −0.299557 0.921942i
\(26\) −2.34197 + 7.20784i −0.0176653 + 0.0543682i
\(27\) −120.831 87.7890i −0.861258 0.625741i
\(28\) −2.33636 1.69746i −0.0157689 0.0114568i
\(29\) −27.1309 + 83.5002i −0.173727 + 0.534676i −0.999573 0.0292193i \(-0.990698\pi\)
0.825846 + 0.563895i \(0.190698\pi\)
\(30\) 1.67324 + 5.14970i 0.0101830 + 0.0313401i
\(31\) 156.452 113.669i 0.906439 0.658566i −0.0336730 0.999433i \(-0.510720\pi\)
0.940112 + 0.340867i \(0.110720\pi\)
\(32\) 105.660 0.583692
\(33\) −84.3461 + 151.298i −0.444932 + 0.798108i
\(34\) 10.3258 0.0520840
\(35\) −0.596641 + 0.433485i −0.00288145 + 0.00209350i
\(36\) 10.5492 + 32.4671i 0.0488389 + 0.150311i
\(37\) −0.594108 + 1.82848i −0.00263975 + 0.00812432i −0.952368 0.304952i \(-0.901360\pi\)
0.949728 + 0.313076i \(0.101360\pi\)
\(38\) 45.4371 + 33.0120i 0.193970 + 0.140928i
\(39\) −49.9357 36.2804i −0.205028 0.148962i
\(40\) 5.51878 16.9851i 0.0218149 0.0671393i
\(41\) −61.9309 190.604i −0.235902 0.726032i −0.997000 0.0773956i \(-0.975340\pi\)
0.761098 0.648637i \(-0.224660\pi\)
\(42\) −0.844245 + 0.613380i −0.00310166 + 0.00225349i
\(43\) 112.095 0.397542 0.198771 0.980046i \(-0.436305\pi\)
0.198771 + 0.980046i \(0.436305\pi\)
\(44\) 253.566 117.492i 0.868783 0.402558i
\(45\) 8.71788 0.0288796
\(46\) 63.1656 45.8925i 0.202462 0.147097i
\(47\) −20.1458 62.0023i −0.0625226 0.192425i 0.914916 0.403644i \(-0.132257\pi\)
−0.977439 + 0.211219i \(0.932257\pi\)
\(48\) −82.1031 + 252.687i −0.246887 + 0.759839i
\(49\) 277.378 + 201.527i 0.808682 + 0.587542i
\(50\) 57.1505 + 41.5223i 0.161646 + 0.117443i
\(51\) −25.9872 + 79.9804i −0.0713517 + 0.219598i
\(52\) 30.7724 + 94.7078i 0.0820648 + 0.252569i
\(53\) 377.607 274.348i 0.978648 0.711029i 0.0212418 0.999774i \(-0.493238\pi\)
0.957406 + 0.288745i \(0.0932380\pi\)
\(54\) 87.0717 0.219425
\(55\) −8.52567 70.8562i −0.0209018 0.173714i
\(56\) 3.44189 0.00821324
\(57\) −370.054 + 268.860i −0.859910 + 0.624761i
\(58\) −15.8168 48.6792i −0.0358078 0.110205i
\(59\) −261.121 + 803.646i −0.576186 + 1.77332i 0.0559173 + 0.998435i \(0.482192\pi\)
−0.632104 + 0.774884i \(0.717808\pi\)
\(60\) 57.5591 + 41.8191i 0.123847 + 0.0899804i
\(61\) −60.8324 44.1973i −0.127685 0.0927686i 0.522110 0.852878i \(-0.325145\pi\)
−0.649795 + 0.760110i \(0.725145\pi\)
\(62\) −34.8386 + 107.222i −0.0713631 + 0.219633i
\(63\) 0.519193 + 1.59791i 0.00103829 + 0.00319552i
\(64\) 312.339 226.927i 0.610036 0.443217i
\(65\) 25.4304 0.0485270
\(66\) −12.0638 100.261i −0.0224993 0.186990i
\(67\) −459.767 −0.838351 −0.419175 0.907905i \(-0.637681\pi\)
−0.419175 + 0.907905i \(0.637681\pi\)
\(68\) 109.764 79.7484i 0.195748 0.142219i
\(69\) 196.499 + 604.761i 0.342836 + 1.05514i
\(70\) 0.132860 0.408900i 0.000226854 0.000698184i
\(71\) −160.110 116.326i −0.267627 0.194442i 0.445876 0.895095i \(-0.352892\pi\)
−0.713503 + 0.700653i \(0.752892\pi\)
\(72\) −32.9162 23.9150i −0.0538779 0.0391446i
\(73\) −292.882 + 901.397i −0.469578 + 1.44521i 0.383554 + 0.923519i \(0.374700\pi\)
−0.853132 + 0.521695i \(0.825300\pi\)
\(74\) −0.346355 1.06597i −0.000544094 0.00167455i
\(75\) −465.452 + 338.171i −0.716610 + 0.520648i
\(76\) 737.962 1.11382
\(77\) 12.4796 5.78252i 0.0184699 0.00855817i
\(78\) 35.9839 0.0522356
\(79\) 120.266 87.3781i 0.171278 0.124440i −0.498844 0.866692i \(-0.666242\pi\)
0.670122 + 0.742251i \(0.266242\pi\)
\(80\) −33.8267 104.108i −0.0472742 0.145495i
\(81\) −181.953 + 559.993i −0.249592 + 0.768166i
\(82\) 94.5232 + 68.6751i 0.127297 + 0.0924866i
\(83\) −31.7830 23.0917i −0.0420318 0.0305379i 0.566571 0.824013i \(-0.308270\pi\)
−0.608603 + 0.793475i \(0.708270\pi\)
\(84\) −4.23715 + 13.0406i −0.00550371 + 0.0169387i
\(85\) −10.7068 32.9521i −0.0136625 0.0420489i
\(86\) −52.8687 + 38.4113i −0.0662904 + 0.0481628i
\(87\) 416.861 0.513704
\(88\) −162.183 + 290.920i −0.196463 + 0.352411i
\(89\) 480.228 0.571956 0.285978 0.958236i \(-0.407682\pi\)
0.285978 + 0.958236i \(0.407682\pi\)
\(90\) −4.11172 + 2.98734i −0.00481571 + 0.00349882i
\(91\) 1.51451 + 4.66117i 0.00174465 + 0.00536949i
\(92\) 317.020 975.686i 0.359256 1.10568i
\(93\) −742.833 539.699i −0.828260 0.601766i
\(94\) 30.7478 + 22.3396i 0.0337383 + 0.0245123i
\(95\) 58.2358 179.231i 0.0628933 0.193566i
\(96\) −155.025 477.117i −0.164814 0.507246i
\(97\) 880.641 639.823i 0.921810 0.669734i −0.0221640 0.999754i \(-0.507056\pi\)
0.943974 + 0.330020i \(0.107056\pi\)
\(98\) −199.880 −0.206030
\(99\) −159.526 31.4103i −0.161949 0.0318874i
\(100\) 928.204 0.928204
\(101\) −1460.88 + 1061.39i −1.43924 + 1.04567i −0.451036 + 0.892506i \(0.648946\pi\)
−0.988201 + 0.153162i \(0.951054\pi\)
\(102\) −15.1501 46.6272i −0.0147067 0.0452625i
\(103\) 293.084 902.019i 0.280373 0.862899i −0.707375 0.706839i \(-0.750121\pi\)
0.987748 0.156060i \(-0.0498793\pi\)
\(104\) −96.0178 69.7610i −0.0905319 0.0657753i
\(105\) 2.83285 + 2.05818i 0.00263293 + 0.00191293i
\(106\) −84.0854 + 258.788i −0.0770480 + 0.237129i
\(107\) −356.333 1096.68i −0.321944 0.990841i −0.972801 0.231641i \(-0.925591\pi\)
0.650858 0.759200i \(-0.274409\pi\)
\(108\) 925.583 672.475i 0.824669 0.599157i
\(109\) 1718.34 1.50998 0.754988 0.655738i \(-0.227643\pi\)
0.754988 + 0.655738i \(0.227643\pi\)
\(110\) 28.3012 + 30.4973i 0.0245311 + 0.0264346i
\(111\) 9.12837 0.00780565
\(112\) 17.0675 12.4003i 0.0143994 0.0104618i
\(113\) −357.776 1101.12i −0.297848 0.916681i −0.982250 0.187576i \(-0.939937\pi\)
0.684402 0.729104i \(-0.260063\pi\)
\(114\) 82.4035 253.612i 0.0676999 0.208359i
\(115\) −211.951 153.991i −0.171865 0.124867i
\(116\) −544.096 395.309i −0.435500 0.316409i
\(117\) 17.9030 55.0999i 0.0141465 0.0435383i
\(118\) −152.229 468.512i −0.118761 0.365508i
\(119\) 5.40220 3.92492i 0.00416150 0.00302351i
\(120\) −84.7951 −0.0645058
\(121\) −99.2846 + 1327.29i −0.0745940 + 0.997214i
\(122\) 43.8362 0.0325307
\(123\) −769.827 + 559.312i −0.564333 + 0.410012i
\(124\) 457.764 + 1408.85i 0.331520 + 1.02031i
\(125\) 148.810 457.991i 0.106480 0.327712i
\(126\) −0.792427 0.575732i −0.000560278 0.000407066i
\(127\) −1597.97 1161.00i −1.11651 0.811195i −0.132837 0.991138i \(-0.542409\pi\)
−0.983677 + 0.179943i \(0.942409\pi\)
\(128\) −330.756 + 1017.96i −0.228398 + 0.702938i
\(129\) −164.467 506.176i −0.112252 0.345475i
\(130\) −11.9941 + 8.71420i −0.00809191 + 0.00587912i
\(131\) −1661.77 −1.10832 −0.554158 0.832412i \(-0.686960\pi\)
−0.554158 + 0.832412i \(0.686960\pi\)
\(132\) −902.581 972.618i −0.595149 0.641330i
\(133\) 36.3198 0.0236791
\(134\) 216.846 157.548i 0.139796 0.101568i
\(135\) −90.2846 277.867i −0.0575590 0.177148i
\(136\) −49.9690 + 153.789i −0.0315059 + 0.0969652i
\(137\) −1648.61 1197.78i −1.02810 0.746960i −0.0601743 0.998188i \(-0.519166\pi\)
−0.967928 + 0.251228i \(0.919166\pi\)
\(138\) −299.910 217.897i −0.185000 0.134410i
\(139\) −381.605 + 1174.46i −0.232859 + 0.716665i 0.764540 + 0.644577i \(0.222966\pi\)
−0.997398 + 0.0720883i \(0.977034\pi\)
\(140\) −1.74572 5.37277i −0.00105386 0.00324344i
\(141\) −250.420 + 181.941i −0.149569 + 0.108668i
\(142\) 115.376 0.0681840
\(143\) −465.343 91.6251i −0.272125 0.0535810i
\(144\) −249.384 −0.144319
\(145\) −138.947 + 100.951i −0.0795787 + 0.0578173i
\(146\) −170.745 525.499i −0.0967873 0.297881i
\(147\) 503.045 1548.21i 0.282248 0.868669i
\(148\) −11.9145 8.65642i −0.00661736 0.00480779i
\(149\) 1224.27 + 889.488i 0.673131 + 0.489058i 0.871072 0.491156i \(-0.163425\pi\)
−0.197941 + 0.980214i \(0.563425\pi\)
\(150\) 103.647 318.991i 0.0564180 0.173637i
\(151\) 864.650 + 2661.12i 0.465988 + 1.43416i 0.857735 + 0.514091i \(0.171871\pi\)
−0.391747 + 0.920073i \(0.628129\pi\)
\(152\) −711.551 + 516.972i −0.379700 + 0.275868i
\(153\) −78.9347 −0.0417091
\(154\) −3.90441 + 7.00364i −0.00204303 + 0.00366474i
\(155\) 378.297 0.196036
\(156\) 382.514 277.913i 0.196318 0.142633i
\(157\) 386.587 + 1189.79i 0.196516 + 0.604814i 0.999956 + 0.00942768i \(0.00300097\pi\)
−0.803440 + 0.595386i \(0.796999\pi\)
\(158\) −26.7807 + 82.4224i −0.0134845 + 0.0415011i
\(159\) −1792.88 1302.60i −0.894241 0.649704i
\(160\) 167.215 + 121.489i 0.0826221 + 0.0600285i
\(161\) 15.6025 48.0197i 0.00763759 0.0235061i
\(162\) −106.075 326.466i −0.0514448 0.158331i
\(163\) 1738.58 1263.15i 0.835437 0.606981i −0.0856551 0.996325i \(-0.527298\pi\)
0.921092 + 0.389344i \(0.127298\pi\)
\(164\) 1535.19 0.730964
\(165\) −307.450 + 142.459i −0.145060 + 0.0672149i
\(166\) 22.9030 0.0107086
\(167\) 1236.23 898.172i 0.572828 0.416184i −0.263304 0.964713i \(-0.584812\pi\)
0.836131 + 0.548529i \(0.184812\pi\)
\(168\) −5.04997 15.5422i −0.00231913 0.00713754i
\(169\) 52.2239 160.729i 0.0237705 0.0731582i
\(170\) 16.3414 + 11.8727i 0.00737253 + 0.00535646i
\(171\) −347.341 252.358i −0.155332 0.112856i
\(172\) −265.341 + 816.635i −0.117628 + 0.362022i
\(173\) 319.230 + 982.490i 0.140293 + 0.431776i 0.996376 0.0850620i \(-0.0271088\pi\)
−0.856083 + 0.516838i \(0.827109\pi\)
\(174\) −196.610 + 142.845i −0.0856605 + 0.0622360i
\(175\) 45.6828 0.0197331
\(176\) 243.886 + 2026.91i 0.104452 + 0.868093i
\(177\) 4012.07 1.70376
\(178\) −226.496 + 164.559i −0.0953742 + 0.0692934i
\(179\) −636.935 1960.28i −0.265959 0.818539i −0.991471 0.130329i \(-0.958397\pi\)
0.725511 0.688210i \(-0.241603\pi\)
\(180\) −20.6362 + 63.5116i −0.00854517 + 0.0262993i
\(181\) −354.236 257.368i −0.145471 0.105691i 0.512670 0.858586i \(-0.328657\pi\)
−0.658140 + 0.752895i \(0.728657\pi\)
\(182\) −2.31154 1.67943i −0.000941445 0.000684000i
\(183\) −110.324 + 339.542i −0.0445649 + 0.137157i
\(184\) 377.834 + 1162.85i 0.151382 + 0.465906i
\(185\) −3.04264 + 2.21061i −0.00120919 + 0.000878525i
\(186\) 535.290 0.211018
\(187\) 77.1944 + 641.557i 0.0301872 + 0.250884i
\(188\) 499.387 0.193732
\(189\) 45.5538 33.0968i 0.0175320 0.0127378i
\(190\) 33.9504 + 104.489i 0.0129633 + 0.0398969i
\(191\) 1493.65 4596.99i 0.565848 1.74150i −0.0995698 0.995031i \(-0.531747\pi\)
0.665418 0.746471i \(-0.268253\pi\)
\(192\) −1482.98 1077.45i −0.557422 0.404990i
\(193\) 4183.16 + 3039.24i 1.56016 + 1.13352i 0.935880 + 0.352319i \(0.114607\pi\)
0.624278 + 0.781202i \(0.285393\pi\)
\(194\) −196.101 + 603.536i −0.0725732 + 0.223357i
\(195\) −37.3117 114.834i −0.0137023 0.0421714i
\(196\) −2124.75 + 1543.72i −0.774326 + 0.562581i
\(197\) −2271.17 −0.821391 −0.410695 0.911773i \(-0.634714\pi\)
−0.410695 + 0.911773i \(0.634714\pi\)
\(198\) 86.0024 39.8499i 0.0308683 0.0143031i
\(199\) 4426.57 1.57684 0.788421 0.615136i \(-0.210899\pi\)
0.788421 + 0.615136i \(0.210899\pi\)
\(200\) −894.985 + 650.244i −0.316425 + 0.229896i
\(201\) 674.575 + 2076.13i 0.236721 + 0.728551i
\(202\) 325.308 1001.19i 0.113310 0.348732i
\(203\) −26.7784 19.4556i −0.00925850 0.00672669i
\(204\) −521.160 378.645i −0.178865 0.129953i
\(205\) 121.148 372.856i 0.0412750 0.127031i
\(206\) 170.863 + 525.861i 0.0577892 + 0.177857i
\(207\) −482.865 + 350.822i −0.162133 + 0.117796i
\(208\) −727.463 −0.242502
\(209\) −1711.40 + 3069.87i −0.566413 + 1.01602i
\(210\) −2.04137 −0.000670798
\(211\) −980.664 + 712.494i −0.319961 + 0.232465i −0.736159 0.676809i \(-0.763362\pi\)
0.416198 + 0.909274i \(0.363362\pi\)
\(212\) 1104.84 + 3400.36i 0.357929 + 1.10159i
\(213\) −290.370 + 893.668i −0.0934077 + 0.287479i
\(214\) 543.859 + 395.137i 0.173726 + 0.126220i
\(215\) 177.400 + 128.888i 0.0562724 + 0.0408843i
\(216\) −421.361 + 1296.82i −0.132731 + 0.408506i
\(217\) 22.5295 + 69.3386i 0.00704793 + 0.0216913i
\(218\) −810.444 + 588.822i −0.251790 + 0.182936i
\(219\) 4500.08 1.38853
\(220\) 536.384 + 105.613i 0.164377 + 0.0323656i
\(221\) −230.256 −0.0700845
\(222\) −4.30533 + 3.12801i −0.00130160 + 0.000945667i
\(223\) −232.337 715.059i −0.0697687 0.214726i 0.910093 0.414405i \(-0.136010\pi\)
−0.979861 + 0.199679i \(0.936010\pi\)
\(224\) −12.3094 + 37.8844i −0.00367168 + 0.0113003i
\(225\) −436.883 317.414i −0.129447 0.0940487i
\(226\) 546.063 + 396.738i 0.160724 + 0.116773i
\(227\) −590.087 + 1816.10i −0.172535 + 0.531008i −0.999512 0.0312271i \(-0.990058\pi\)
0.826977 + 0.562235i \(0.190058\pi\)
\(228\) −1082.75 3332.35i −0.314502 0.967939i
\(229\) −332.331 + 241.452i −0.0958997 + 0.0696752i −0.634702 0.772757i \(-0.718877\pi\)
0.538802 + 0.842432i \(0.318877\pi\)
\(230\) 152.733 0.0437866
\(231\) −44.4218 47.8687i −0.0126525 0.0136343i
\(232\) 801.553 0.226830
\(233\) −3979.91 + 2891.57i −1.11902 + 0.813018i −0.984061 0.177832i \(-0.943092\pi\)
−0.134963 + 0.990851i \(0.543092\pi\)
\(234\) 10.4372 + 32.1222i 0.00291580 + 0.00897392i
\(235\) 39.4088 121.288i 0.0109394 0.0336679i
\(236\) −5236.64 3804.64i −1.44439 1.04941i
\(237\) −571.020 414.870i −0.156505 0.113708i
\(238\) −1.20296 + 3.70232i −0.000327631 + 0.00100834i
\(239\) 371.041 + 1141.95i 0.100421 + 0.309064i 0.988629 0.150378i \(-0.0480492\pi\)
−0.888207 + 0.459443i \(0.848049\pi\)
\(240\) −420.480 + 305.496i −0.113091 + 0.0821654i
\(241\) −1262.14 −0.337350 −0.168675 0.985672i \(-0.553949\pi\)
−0.168675 + 0.985672i \(0.553949\pi\)
\(242\) −407.994 660.029i −0.108375 0.175323i
\(243\) −1236.93 −0.326539
\(244\) 465.984 338.557i 0.122261 0.0888275i
\(245\) 207.256 + 637.867i 0.0540452 + 0.166334i
\(246\) 171.425 527.591i 0.0444294 0.136740i
\(247\) −1013.21 736.139i −0.261008 0.189633i
\(248\) −1428.34 1037.75i −0.365725 0.265715i
\(249\) −57.6408 + 177.400i −0.0146700 + 0.0451497i
\(250\) 86.7538 + 267.001i 0.0219472 + 0.0675465i
\(251\) 892.980 648.788i 0.224559 0.163152i −0.469817 0.882764i \(-0.655680\pi\)
0.694377 + 0.719612i \(0.255680\pi\)
\(252\) −12.8701 −0.00321723
\(253\) 3323.59 + 3581.49i 0.825899 + 0.889985i
\(254\) 1151.51 0.284457
\(255\) −133.090 + 96.6954i −0.0326839 + 0.0237463i
\(256\) 761.597 + 2343.95i 0.185937 + 0.572254i
\(257\) 2002.76 6163.85i 0.486103 1.49607i −0.344274 0.938869i \(-0.611875\pi\)
0.830377 0.557202i \(-0.188125\pi\)
\(258\) 251.020 + 182.377i 0.0605730 + 0.0440088i
\(259\) −0.586390 0.426037i −0.000140681 0.000102211i
\(260\) −60.1966 + 185.266i −0.0143586 + 0.0441912i
\(261\) 120.911 + 372.125i 0.0286750 + 0.0882527i
\(262\) 783.761 569.435i 0.184813 0.134274i
\(263\) 3139.44 0.736068 0.368034 0.929812i \(-0.380031\pi\)
0.368034 + 0.929812i \(0.380031\pi\)
\(264\) 1551.64 + 305.515i 0.361730 + 0.0712240i
\(265\) 913.046 0.211653
\(266\) −17.1300 + 12.4456i −0.00394852 + 0.00286877i
\(267\) −704.596 2168.52i −0.161500 0.497047i
\(268\) 1088.32 3349.50i 0.248059 0.763446i
\(269\) −798.887 580.426i −0.181074 0.131558i 0.493556 0.869714i \(-0.335697\pi\)
−0.674630 + 0.738156i \(0.735697\pi\)
\(270\) 137.798 + 100.116i 0.0310598 + 0.0225663i
\(271\) 470.445 1447.88i 0.105452 0.324548i −0.884384 0.466760i \(-0.845421\pi\)
0.989836 + 0.142212i \(0.0454213\pi\)
\(272\) 306.279 + 942.629i 0.0682753 + 0.210130i
\(273\) 18.8259 13.6778i 0.00417362 0.00303231i
\(274\) 1188.00 0.261932
\(275\) −2152.59 + 3861.27i −0.472023 + 0.846703i
\(276\) −4870.95 −1.06231
\(277\) 3068.20 2229.18i 0.665525 0.483532i −0.202999 0.979179i \(-0.565069\pi\)
0.868524 + 0.495647i \(0.165069\pi\)
\(278\) −222.469 684.690i −0.0479957 0.147716i
\(279\) 266.322 819.654i 0.0571479 0.175883i
\(280\) 5.44708 + 3.95754i 0.00116259 + 0.000844672i
\(281\) 3983.90 + 2894.47i 0.845763 + 0.614483i 0.923974 0.382454i \(-0.124921\pi\)
−0.0782117 + 0.996937i \(0.524921\pi\)
\(282\) 55.7634 171.622i 0.0117754 0.0362409i
\(283\) −2319.76 7139.48i −0.487263 1.49964i −0.828677 0.559727i \(-0.810906\pi\)
0.341414 0.939913i \(-0.389094\pi\)
\(284\) 1226.46 891.076i 0.256257 0.186182i
\(285\) −894.783 −0.185973
\(286\) 250.873 116.244i 0.0518685 0.0240337i
\(287\) 75.5563 0.0155399
\(288\) 380.949 276.776i 0.0779433 0.0566291i
\(289\) −1421.26 4374.18i −0.289285 0.890328i
\(290\) 30.9406 95.2255i 0.00626516 0.0192822i
\(291\) −4181.28 3037.88i −0.842305 0.611971i
\(292\) −5873.59 4267.41i −1.17714 0.855245i
\(293\) 459.482 1414.14i 0.0916151 0.281962i −0.894742 0.446584i \(-0.852640\pi\)
0.986357 + 0.164622i \(0.0526404\pi\)
\(294\) 293.266 + 902.580i 0.0581756 + 0.179046i
\(295\) −1337.29 + 971.599i −0.263933 + 0.191758i
\(296\) 17.5523 0.00344665
\(297\) 650.939 + 5409.90i 0.127176 + 1.05695i
\(298\) −882.220 −0.171495
\(299\) −1408.54 + 1023.36i −0.272434 + 0.197935i
\(300\) −1361.87 4191.40i −0.262092 0.806636i
\(301\) −13.0591 + 40.1918i −0.00250071 + 0.00769640i
\(302\) −1319.69 958.809i −0.251455 0.182693i
\(303\) 6936.25 + 5039.48i 1.31511 + 0.955480i
\(304\) −1665.89 + 5127.10i −0.314295 + 0.967300i
\(305\) −45.4537 139.892i −0.00853335 0.0262630i
\(306\) 37.2290 27.0484i 0.00695503 0.00505312i
\(307\) 8015.67 1.49016 0.745079 0.666976i \(-0.232412\pi\)
0.745079 + 0.666976i \(0.232412\pi\)
\(308\) 12.5864 + 104.604i 0.00232849 + 0.0193519i
\(309\) −4503.18 −0.829052
\(310\) −178.421 + 129.631i −0.0326892 + 0.0237501i
\(311\) −519.374 1598.47i −0.0946978 0.291450i 0.892477 0.451093i \(-0.148966\pi\)
−0.987175 + 0.159643i \(0.948966\pi\)
\(312\) −174.135 + 535.933i −0.0315976 + 0.0972475i
\(313\) −5282.94 3838.28i −0.954024 0.693139i −0.00226870 0.999997i \(-0.500722\pi\)
−0.951755 + 0.306859i \(0.900722\pi\)
\(314\) −590.035 428.686i −0.106043 0.0770450i
\(315\) −1.01564 + 3.12581i −0.000181666 + 0.000559109i
\(316\) 351.886 + 1082.99i 0.0626429 + 0.192795i
\(317\) 2870.41 2085.48i 0.508575 0.369501i −0.303708 0.952765i \(-0.598225\pi\)
0.812283 + 0.583264i \(0.198225\pi\)
\(318\) 1291.96 0.227828
\(319\) 2906.27 1346.64i 0.510093 0.236356i
\(320\) 755.227 0.131933
\(321\) −4429.36 + 3218.12i −0.770164 + 0.559557i
\(322\) 9.09601 + 27.9946i 0.00157423 + 0.00484497i
\(323\) −527.287 + 1622.82i −0.0908330 + 0.279555i
\(324\) −3648.97 2651.13i −0.625681 0.454584i
\(325\) −1274.41 925.911i −0.217512 0.158032i
\(326\) −387.147 + 1191.51i −0.0657732 + 0.202429i
\(327\) −2521.17 7759.37i −0.426364 1.31221i
\(328\) −1480.25 + 1075.46i −0.249186 + 0.181044i
\(329\) 24.5780 0.00411863
\(330\) 96.1901 172.543i 0.0160457 0.0287824i
\(331\) 9268.55 1.53911 0.769555 0.638581i \(-0.220478\pi\)
0.769555 + 0.638581i \(0.220478\pi\)
\(332\) 243.462 176.886i 0.0402462 0.0292406i
\(333\) 2.64769 + 8.14874i 0.000435713 + 0.00134099i
\(334\) −275.283 + 847.233i −0.0450982 + 0.138798i
\(335\) −727.621 528.648i −0.118669 0.0862183i
\(336\) −81.0365 58.8764i −0.0131574 0.00955944i
\(337\) −1183.95 + 3643.81i −0.191376 + 0.588994i 0.808624 + 0.588326i \(0.200213\pi\)
−1.00000 0.000668085i \(0.999787\pi\)
\(338\) 30.4456 + 93.7019i 0.00489947 + 0.0150790i
\(339\) −4447.31 + 3231.16i −0.712521 + 0.517677i
\(340\) 265.408 0.0423345
\(341\) −6922.34 1363.00i −1.09931 0.216453i
\(342\) 250.296 0.0395744
\(343\) −209.188 + 151.984i −0.0329303 + 0.0239253i
\(344\) −316.241 973.291i −0.0495657 0.152547i
\(345\) −384.388 + 1183.02i −0.0599848 + 0.184614i
\(346\) −487.231 353.994i −0.0757043 0.0550024i
\(347\) 1533.13 + 1113.89i 0.237184 + 0.172324i 0.700028 0.714116i \(-0.253171\pi\)
−0.462844 + 0.886440i \(0.653171\pi\)
\(348\) −986.757 + 3036.92i −0.151999 + 0.467805i
\(349\) −1861.55 5729.25i −0.285520 0.878739i −0.986242 0.165305i \(-0.947139\pi\)
0.700723 0.713434i \(-0.252861\pi\)
\(350\) −21.5460 + 15.6541i −0.00329051 + 0.00239070i
\(351\) −1941.62 −0.295260
\(352\) −2622.10 2825.56i −0.397041 0.427850i
\(353\) −1067.61 −0.160972 −0.0804858 0.996756i \(-0.525647\pi\)
−0.0804858 + 0.996756i \(0.525647\pi\)
\(354\) −1892.26 + 1374.81i −0.284104 + 0.206413i
\(355\) −119.633 368.193i −0.0178858 0.0550470i
\(356\) −1136.75 + 3498.57i −0.169235 + 0.520853i
\(357\) −25.6496 18.6355i −0.00380258 0.00276273i
\(358\) 972.133 + 706.296i 0.143516 + 0.104271i
\(359\) 2897.10 8916.35i 0.425914 1.31083i −0.476203 0.879335i \(-0.657987\pi\)
0.902117 0.431492i \(-0.142013\pi\)
\(360\) −24.5948 75.6951i −0.00360073 0.0110819i
\(361\) −1959.45 + 1423.63i −0.285676 + 0.207556i
\(362\) 255.265 0.0370619
\(363\) 6139.20 1499.09i 0.887671 0.216754i
\(364\) −37.5427 −0.00540596
\(365\) −1499.95 + 1089.78i −0.215099 + 0.156278i
\(366\) −64.3169 197.947i −0.00918551 0.0282701i
\(367\) 2168.39 6673.63i 0.308418 0.949212i −0.669962 0.742395i \(-0.733690\pi\)
0.978380 0.206817i \(-0.0663103\pi\)
\(368\) 6063.07 + 4405.08i 0.858857 + 0.623996i
\(369\) −722.576 524.982i −0.101940 0.0740637i
\(370\) 0.677534 2.08524i 9.51981e−5 0.000292990i
\(371\) 54.3764 + 167.353i 0.00760939 + 0.0234193i
\(372\) 5690.19 4134.17i 0.793072 0.576201i
\(373\) 3621.06 0.502658 0.251329 0.967902i \(-0.419132\pi\)
0.251329 + 0.967902i \(0.419132\pi\)
\(374\) −256.249 276.133i −0.0354287 0.0381778i
\(375\) −2286.45 −0.314857
\(376\) −481.515 + 349.841i −0.0660432 + 0.0479832i
\(377\) 352.701 + 1085.50i 0.0481831 + 0.148292i
\(378\) −10.1439 + 31.2197i −0.00138028 + 0.00424806i
\(379\) −292.533 212.538i −0.0396475 0.0288056i 0.567785 0.823177i \(-0.307800\pi\)
−0.607433 + 0.794371i \(0.707800\pi\)
\(380\) 1167.89 + 848.521i 0.157662 + 0.114548i
\(381\) −2898.04 + 8919.25i −0.389688 + 1.19934i
\(382\) 870.774 + 2679.97i 0.116630 + 0.358950i
\(383\) 4882.21 3547.13i 0.651355 0.473237i −0.212377 0.977188i \(-0.568121\pi\)
0.863733 + 0.503950i \(0.168121\pi\)
\(384\) 5082.01 0.675365
\(385\) 26.3988 + 5.19789i 0.00349457 + 0.000688075i
\(386\) −3014.41 −0.397486
\(387\) 404.151 293.633i 0.0530857 0.0385690i
\(388\) 2576.68 + 7930.19i 0.337142 + 1.03762i
\(389\) −1927.64 + 5932.65i −0.251247 + 0.773258i 0.743299 + 0.668959i \(0.233260\pi\)
−0.994546 + 0.104299i \(0.966740\pi\)
\(390\) 56.9477 + 41.3749i 0.00739400 + 0.00537205i
\(391\) 1919.08 + 1394.29i 0.248214 + 0.180338i
\(392\) 967.269 2976.95i 0.124629 0.383568i
\(393\) 2438.16 + 7503.89i 0.312949 + 0.963159i
\(394\) 1071.18 778.257i 0.136968 0.0995128i
\(395\) 290.799 0.0370423
\(396\) 606.446 1087.83i 0.0769572 0.138044i
\(397\) −3469.46 −0.438607 −0.219304 0.975657i \(-0.570379\pi\)
−0.219304 + 0.975657i \(0.570379\pi\)
\(398\) −2087.76 + 1516.85i −0.262940 + 0.191037i
\(399\) −53.2888 164.006i −0.00668615 0.0205779i
\(400\) −2095.35 + 6448.83i −0.261919 + 0.806103i
\(401\) 10108.4 + 7344.18i 1.25883 + 0.914591i 0.998700 0.0509831i \(-0.0162355\pi\)
0.260127 + 0.965574i \(0.416235\pi\)
\(402\) −1029.58 748.035i −0.127739 0.0928075i
\(403\) 776.871 2390.96i 0.0960266 0.295539i
\(404\) −4274.40 13155.3i −0.526385 1.62005i
\(405\) −931.845 + 677.025i −0.114330 + 0.0830658i
\(406\) 19.2967 0.00235881
\(407\) 63.6411 29.4887i 0.00775079 0.00359140i
\(408\) 767.764 0.0931618
\(409\) 3349.81 2433.78i 0.404982 0.294237i −0.366585 0.930384i \(-0.619473\pi\)
0.771567 + 0.636148i \(0.219473\pi\)
\(410\) 70.6274 + 217.369i 0.00850741 + 0.0261831i
\(411\) −2989.87 + 9201.86i −0.358830 + 1.10437i
\(412\) 5877.64 + 4270.36i 0.702842 + 0.510644i
\(413\) −257.728 187.250i −0.0307070 0.0223099i
\(414\) 107.524 330.925i 0.0127646 0.0392852i
\(415\) −23.7482 73.0893i −0.00280904 0.00864533i
\(416\) 1111.25 807.367i 0.130969 0.0951548i
\(417\) 5863.30 0.688554
\(418\) −244.778 2034.33i −0.0286423 0.238044i
\(419\) 2880.64 0.335867 0.167934 0.985798i \(-0.446291\pi\)
0.167934 + 0.985798i \(0.446291\pi\)
\(420\) −21.7000 + 15.7660i −0.00252107 + 0.00183167i
\(421\) 615.096 + 1893.07i 0.0712065 + 0.219151i 0.980326 0.197384i \(-0.0632445\pi\)
−0.909120 + 0.416535i \(0.863244\pi\)
\(422\) 218.374 672.085i 0.0251902 0.0775275i
\(423\) −235.050 170.774i −0.0270177 0.0196295i
\(424\) −3447.40 2504.68i −0.394859 0.286882i
\(425\) −663.218 + 2041.18i −0.0756960 + 0.232968i
\(426\) −169.281 520.992i −0.0192528 0.0592539i
\(427\) 22.9340 16.6625i 0.00259919 0.00188842i
\(428\) 8833.02 0.997571
\(429\) 269.012 + 2235.74i 0.0302751 + 0.251614i
\(430\) −127.835 −0.0143367
\(431\) −4011.29 + 2914.37i −0.448299 + 0.325708i −0.788924 0.614491i \(-0.789361\pi\)
0.340625 + 0.940199i \(0.389361\pi\)
\(432\) 2582.68 + 7948.68i 0.287637 + 0.885257i
\(433\) −291.171 + 896.133i −0.0323159 + 0.0994582i −0.965913 0.258865i \(-0.916651\pi\)
0.933598 + 0.358323i \(0.116651\pi\)
\(434\) −34.3860 24.9829i −0.00380318 0.00276317i
\(435\) 659.719 + 479.314i 0.0727152 + 0.0528307i
\(436\) −4067.51 + 12518.5i −0.446785 + 1.37506i
\(437\) 3987.01 + 12270.8i 0.436441 + 1.34323i
\(438\) −2122.43 + 1542.03i −0.231538 + 0.168222i
\(439\) −11859.6 −1.28935 −0.644676 0.764456i \(-0.723008\pi\)
−0.644676 + 0.764456i \(0.723008\pi\)
\(440\) −591.174 + 273.925i −0.0640525 + 0.0296793i
\(441\) 1527.97 0.164990
\(442\) 108.598 78.9014i 0.0116867 0.00849085i
\(443\) −2057.79 6333.22i −0.220696 0.679233i −0.998700 0.0509736i \(-0.983768\pi\)
0.778004 0.628260i \(-0.216232\pi\)
\(444\) −21.6079 + 66.5022i −0.00230960 + 0.00710823i
\(445\) 760.003 + 552.174i 0.0809609 + 0.0588215i
\(446\) 354.608 + 257.638i 0.0376484 + 0.0273532i
\(447\) 2220.31 6833.41i 0.234937 0.723063i
\(448\) 44.9776 + 138.427i 0.00474328 + 0.0145983i
\(449\) −1189.43 + 864.168i −0.125017 + 0.0908299i −0.648536 0.761184i \(-0.724619\pi\)
0.523520 + 0.852013i \(0.324619\pi\)
\(450\) 314.821 0.0329795
\(451\) −3560.25 + 6386.28i −0.371720 + 0.666781i
\(452\) 8868.82 0.922907
\(453\) 10747.9 7808.84i 1.11475 0.809915i
\(454\) −344.010 1058.75i −0.0355621 0.109449i
\(455\) −2.96265 + 9.11811i −0.000305256 + 0.000939481i
\(456\) 3378.44 + 2454.58i 0.346952 + 0.252075i
\(457\) 494.318 + 359.143i 0.0505978 + 0.0367615i 0.612797 0.790241i \(-0.290044\pi\)
−0.562199 + 0.827002i \(0.690044\pi\)
\(458\) 74.0033 227.759i 0.00755010 0.0232368i
\(459\) 817.468 + 2515.91i 0.0831289 + 0.255844i
\(460\) 1623.57 1179.59i 0.164564 0.119563i
\(461\) −14270.6 −1.44175 −0.720876 0.693064i \(-0.756260\pi\)
−0.720876 + 0.693064i \(0.756260\pi\)
\(462\) 37.3543 + 7.35499i 0.00376164 + 0.000740661i
\(463\) −5997.52 −0.602005 −0.301003 0.953623i \(-0.597321\pi\)
−0.301003 + 0.953623i \(0.597321\pi\)
\(464\) 3974.72 2887.80i 0.397676 0.288929i
\(465\) −555.042 1708.24i −0.0553536 0.170361i
\(466\) 886.244 2727.58i 0.0880997 0.271143i
\(467\) 489.854 + 355.900i 0.0485391 + 0.0352657i 0.611790 0.791020i \(-0.290450\pi\)
−0.563251 + 0.826286i \(0.690450\pi\)
\(468\) 359.036 + 260.855i 0.0354625 + 0.0257650i
\(469\) 53.5631 164.850i 0.00527359 0.0162304i
\(470\) 22.9747 + 70.7087i 0.00225477 + 0.00693947i
\(471\) 4805.43 3491.35i 0.470112 0.341556i
\(472\) 7714.53 0.752309
\(473\) −2781.80 2997.65i −0.270417 0.291400i
\(474\) 411.480 0.0398732
\(475\) −9444.14 + 6861.57i −0.912267 + 0.662801i
\(476\) 15.8063 + 48.6469i 0.00152202 + 0.00468430i
\(477\) 642.785 1978.29i 0.0617004 0.189894i
\(478\) −566.308 411.447i −0.0541890 0.0393706i
\(479\) 4159.65 + 3022.16i 0.396783 + 0.288280i 0.768229 0.640175i \(-0.221138\pi\)
−0.371446 + 0.928454i \(0.621138\pi\)
\(480\) 303.257 933.330i 0.0288369 0.0887510i
\(481\) 7.72341 + 23.7702i 0.000732136 + 0.00225328i
\(482\) 595.277 432.494i 0.0562534 0.0408705i
\(483\) −239.730 −0.0225841
\(484\) −9434.59 3865.16i −0.886044 0.362994i
\(485\) 2129.37 0.199360
\(486\) 583.388 423.856i 0.0544506 0.0395607i
\(487\) −1139.40 3506.72i −0.106019 0.326293i 0.883949 0.467583i \(-0.154875\pi\)
−0.989968 + 0.141290i \(0.954875\pi\)
\(488\) −212.134 + 652.881i −0.0196780 + 0.0605626i
\(489\) −8254.77 5997.44i −0.763382 0.554630i
\(490\) −316.328 229.825i −0.0291637 0.0211887i
\(491\) −3288.67 + 10121.5i −0.302272 + 0.930298i 0.678409 + 0.734685i \(0.262670\pi\)
−0.980681 + 0.195614i \(0.937330\pi\)
\(492\) −2252.44 6932.31i −0.206398 0.635229i
\(493\) 1258.07 914.044i 0.114931 0.0835020i
\(494\) 730.124 0.0664976
\(495\) −216.347 233.135i −0.0196446 0.0211689i
\(496\) −10821.6 −0.979644
\(497\) 60.3619 43.8555i 0.00544789 0.00395812i
\(498\) −33.6036 103.421i −0.00302372 0.00930605i
\(499\) 2302.24 7085.58i 0.206538 0.635660i −0.793108 0.609081i \(-0.791539\pi\)
0.999647 0.0265791i \(-0.00846137\pi\)
\(500\) 2984.32 + 2168.23i 0.266925 + 0.193933i
\(501\) −5869.60 4264.51i −0.523422 0.380288i
\(502\) −198.848 + 611.992i −0.0176794 + 0.0544115i
\(503\) −5573.34 17153.0i −0.494041 1.52050i −0.818445 0.574585i \(-0.805164\pi\)
0.324404 0.945919i \(-0.394836\pi\)
\(504\) 12.4095 9.01604i 0.00109675 0.000796838i
\(505\) −3532.37 −0.311265
\(506\) −2794.81 550.293i −0.245543 0.0483469i
\(507\) −802.411 −0.0702886
\(508\) 12240.7 8893.38i 1.06908 0.776732i
\(509\) 2207.11 + 6792.79i 0.192197 + 0.591523i 0.999998 + 0.00206686i \(0.000657902\pi\)
−0.807800 + 0.589456i \(0.799342\pi\)
\(510\) 29.6364 91.2113i 0.00257318 0.00791942i
\(511\) −289.077 210.027i −0.0250254 0.0181820i
\(512\) −8089.85 5877.62i −0.698289 0.507337i
\(513\) −4446.33 + 13684.4i −0.382671 + 1.17774i
\(514\) 1167.57 + 3593.42i 0.100193 + 0.308363i
\(515\) 1500.99 1090.53i 0.128430 0.0933098i
\(516\) 4076.91 0.347822
\(517\) −1158.13 + 2077.42i −0.0985191 + 0.176721i
\(518\) 0.422556 3.58418e−5
\(519\) 3968.16 2883.04i 0.335613 0.243837i
\(520\) −71.7441 220.806i −0.00605036 0.0186211i
\(521\) 725.702 2233.48i 0.0610241 0.187813i −0.915897 0.401413i \(-0.868519\pi\)
0.976921 + 0.213600i \(0.0685191\pi\)
\(522\) −184.542 134.078i −0.0154735 0.0112422i
\(523\) −12397.1 9007.02i −1.03650 0.753059i −0.0668976 0.997760i \(-0.521310\pi\)
−0.969599 + 0.244701i \(0.921310\pi\)
\(524\) 3933.59 12106.3i 0.327938 1.00929i
\(525\) −67.0263 206.286i −0.00557193 0.0171487i
\(526\) −1480.69 + 1075.79i −0.122740 + 0.0891758i
\(527\) −3425.24 −0.283123
\(528\) 8794.92 4075.20i 0.724904 0.335891i
\(529\) 5769.38 0.474183
\(530\) −430.631 + 312.872i −0.0352933 + 0.0256421i
\(531\) 1163.70 + 3581.51i 0.0951043 + 0.292701i
\(532\) −85.9730 + 264.598i −0.00700639 + 0.0215635i
\(533\) −2107.79 1531.40i −0.171291 0.124450i
\(534\) 1075.40 + 781.325i 0.0871483 + 0.0633169i
\(535\) 697.052 2145.31i 0.0563294 0.173364i
\(536\) 1297.09 + 3992.04i 0.104526 + 0.321698i
\(537\) −7917.35 + 5752.29i −0.636237 + 0.462253i
\(538\) 575.683 0.0461328
\(539\) −1494.28 12418.9i −0.119412 0.992427i
\(540\) 2238.04 0.178352
\(541\) −7948.83 + 5775.16i −0.631695 + 0.458953i −0.856987 0.515338i \(-0.827666\pi\)
0.225292 + 0.974291i \(0.427666\pi\)
\(542\) 274.261 + 844.089i 0.0217353 + 0.0668943i
\(543\) −642.433 + 1977.21i −0.0507725 + 0.156262i
\(544\) −1514.03 1100.01i −0.119326 0.0866955i
\(545\) 2719.43 + 1975.78i 0.213738 + 0.155290i
\(546\) −4.19215 + 12.9021i −0.000328585 + 0.00101128i
\(547\) 854.832 + 2630.90i 0.0668189 + 0.205648i 0.978891 0.204382i \(-0.0655184\pi\)
−0.912072 + 0.410029i \(0.865518\pi\)
\(548\) 12628.5 9175.18i 0.984425 0.715226i
\(549\) −335.103 −0.0260507
\(550\) −307.880 2558.76i −0.0238692 0.198375i
\(551\) 8458.22 0.653961
\(552\) 4696.63 3412.30i 0.362141 0.263111i
\(553\) 17.3186 + 53.3010i 0.00133175 + 0.00409872i
\(554\) −683.226 + 2102.75i −0.0523962 + 0.161259i
\(555\) 14.4464 + 10.4960i 0.00110490 + 0.000802754i
\(556\) −7652.90 5560.16i −0.583732 0.424106i
\(557\) 2725.88 8389.40i 0.207360 0.638187i −0.792249 0.610198i \(-0.791090\pi\)
0.999608 0.0279888i \(-0.00891027\pi\)
\(558\) 155.261 + 477.844i 0.0117791 + 0.0362522i
\(559\) 1178.93 856.539i 0.0892008 0.0648082i
\(560\) 41.2689 0.00311416
\(561\) 2783.76 1289.88i 0.209502 0.0970743i
\(562\) −2870.82 −0.215477
\(563\) −6503.65 + 4725.18i −0.486850 + 0.353717i −0.803971 0.594668i \(-0.797284\pi\)
0.317122 + 0.948385i \(0.397284\pi\)
\(564\) −732.706 2255.04i −0.0547030 0.168359i
\(565\) 699.877 2154.00i 0.0521133 0.160388i
\(566\) 3540.57 + 2572.38i 0.262935 + 0.191034i
\(567\) −179.589 130.479i −0.0133016 0.00966420i
\(568\) −558.333 + 1718.37i −0.0412449 + 0.126939i
\(569\) 874.480 + 2691.37i 0.0644290 + 0.198292i 0.978089 0.208187i \(-0.0667563\pi\)
−0.913660 + 0.406479i \(0.866756\pi\)
\(570\) 422.018 306.614i 0.0310112 0.0225309i
\(571\) −23770.3 −1.74213 −0.871066 0.491166i \(-0.836571\pi\)
−0.871066 + 0.491166i \(0.836571\pi\)
\(572\) 1769.03 3173.24i 0.129312 0.231957i
\(573\) −22949.7 −1.67319
\(574\) −35.6356 + 25.8908i −0.00259129 + 0.00188268i
\(575\) 5014.84 + 15434.1i 0.363710 + 1.11938i
\(576\) 531.681 1636.35i 0.0384607 0.118370i
\(577\) 7940.16 + 5768.87i 0.572883 + 0.416224i 0.836151 0.548499i \(-0.184801\pi\)
−0.263269 + 0.964723i \(0.584801\pi\)
\(578\) 2169.22 + 1576.03i 0.156103 + 0.113416i
\(579\) 7586.46 23348.7i 0.544529 1.67589i
\(580\) −406.546 1251.22i −0.0291050 0.0895760i
\(581\) 11.9823 8.70567i 0.000855612 0.000621638i
\(582\) 3013.05 0.214596
\(583\) −16707.5 3289.68i −1.18689 0.233696i
\(584\) 8652.88 0.613114
\(585\) 91.6878 66.6151i 0.00648004 0.00470803i
\(586\) 267.870 + 824.419i 0.0188833 + 0.0581168i
\(587\) −216.665 + 666.827i −0.0152346 + 0.0468874i −0.958385 0.285479i \(-0.907847\pi\)
0.943150 + 0.332367i \(0.107847\pi\)
\(588\) 10088.3 + 7329.58i 0.707542 + 0.514059i
\(589\) −15072.3 10950.6i −1.05440 0.766067i
\(590\) 297.787 916.495i 0.0207792 0.0639517i
\(591\) 3332.28 + 10255.7i 0.231932 + 0.713813i
\(592\) 87.0379 63.2367i 0.00604263 0.00439023i
\(593\) −15700.6 −1.08726 −0.543631 0.839324i \(-0.682951\pi\)
−0.543631 + 0.839324i \(0.682951\pi\)
\(594\) −2160.81 2328.48i −0.149258 0.160840i
\(595\) 13.0624 0.000900009
\(596\) −9378.11 + 6813.59i −0.644534 + 0.468281i
\(597\) −6494.71 19988.7i −0.445244 1.37032i
\(598\) 313.652 965.323i 0.0214485 0.0660117i
\(599\) 19638.4 + 14268.1i 1.33957 + 0.973256i 0.999460 + 0.0328707i \(0.0104650\pi\)
0.340112 + 0.940385i \(0.389535\pi\)
\(600\) 4249.38 + 3087.36i 0.289134 + 0.210068i
\(601\) 8163.21 25123.8i 0.554051 1.70519i −0.144386 0.989521i \(-0.546121\pi\)
0.698437 0.715671i \(-0.253879\pi\)
\(602\) −7.61322 23.4311i −0.000515435 0.00158635i
\(603\) −1657.66 + 1204.36i −0.111949 + 0.0813358i
\(604\) −21433.6 −1.44391
\(605\) −1683.27 + 1986.40i −0.113115 + 0.133485i
\(606\) −4998.30 −0.335053
\(607\) 22379.7 16259.8i 1.49648 1.08726i 0.524728 0.851270i \(-0.324167\pi\)
0.971756 0.235989i \(-0.0758329\pi\)
\(608\) −3145.49 9680.84i −0.209814 0.645740i
\(609\) −48.5645 + 149.466i −0.00323142 + 0.00994529i
\(610\) 69.3745 + 50.4036i 0.00460474 + 0.00334554i
\(611\) −685.650 498.154i −0.0453984 0.0329839i
\(612\) 186.847 575.056i 0.0123413 0.0379825i
\(613\) 8192.76 + 25214.7i 0.539808 + 1.66136i 0.733025 + 0.680202i \(0.238108\pi\)
−0.193217 + 0.981156i \(0.561892\pi\)
\(614\) −3780.53 + 2746.72i −0.248485 + 0.180535i
\(615\) −1861.42 −0.122049
\(616\) −85.4155 92.0434i −0.00558683 0.00602035i
\(617\) 20378.9 1.32970 0.664848 0.746979i \(-0.268496\pi\)
0.664848 + 0.746979i \(0.268496\pi\)
\(618\) 2123.89 1543.10i 0.138245 0.100441i
\(619\) 3472.05 + 10685.9i 0.225450 + 0.693864i 0.998246 + 0.0592089i \(0.0188578\pi\)
−0.772796 + 0.634655i \(0.781142\pi\)
\(620\) −895.471 + 2755.98i −0.0580048 + 0.178521i
\(621\) 16182.5 + 11757.3i 1.04570 + 0.759749i
\(622\) 792.704 + 575.933i 0.0511006 + 0.0371267i
\(623\) −55.9468 + 172.187i −0.00359785 + 0.0110731i
\(624\) 1067.34 + 3284.94i 0.0684741 + 0.210742i
\(625\) −11491.8 + 8349.28i −0.735475 + 0.534354i
\(626\) 3806.92 0.243059
\(627\) 16373.3 + 3223.88i 1.04288 + 0.205342i
\(628\) −9582.99 −0.608922
\(629\) 27.5491 20.0156i 0.00174635 0.00126880i
\(630\) −0.592099 1.82229i −3.74441e−5 0.000115241i
\(631\) −1908.02 + 5872.29i −0.120376 + 0.370479i −0.993030 0.117859i \(-0.962397\pi\)
0.872654 + 0.488338i \(0.162397\pi\)
\(632\) −1097.97 797.725i −0.0691061 0.0502085i
\(633\) 4656.19 + 3382.92i 0.292365 + 0.212415i
\(634\) −639.182 + 1967.20i −0.0400397 + 0.123229i
\(635\) −1194.00 3674.75i −0.0746180 0.229651i
\(636\) 13733.7 9978.09i 0.856250 0.622102i
\(637\) 4457.15 0.277235
\(638\) −909.268 + 1631.02i −0.0564236 + 0.101211i
\(639\) −881.984 −0.0546021
\(640\) −1693.92 + 1230.71i −0.104622 + 0.0760124i
\(641\) −2311.83 7115.08i −0.142452 0.438422i 0.854223 0.519908i \(-0.174034\pi\)
−0.996675 + 0.0814853i \(0.974034\pi\)
\(642\) 986.327 3035.60i 0.0606343 0.186613i
\(643\) −7465.77 5424.20i −0.457887 0.332674i 0.334815 0.942284i \(-0.391326\pi\)
−0.792702 + 0.609610i \(0.791326\pi\)
\(644\) 312.901 + 227.336i 0.0191460 + 0.0139104i
\(645\) 321.727 990.174i 0.0196403 0.0604466i
\(646\) −307.399 946.078i −0.0187221 0.0576206i
\(647\) −16098.2 + 11696.0i −0.978183 + 0.710691i −0.957302 0.289091i \(-0.906647\pi\)
−0.0208809 + 0.999782i \(0.506647\pi\)
\(648\) 5375.60 0.325885
\(649\) 27971.3 12960.8i 1.69179 0.783904i
\(650\) 918.345 0.0554161
\(651\) 280.051 203.469i 0.0168603 0.0122497i
\(652\) 5086.93 + 15656.0i 0.305552 + 0.940392i
\(653\) 1185.54 3648.73i 0.0710474 0.218661i −0.909228 0.416299i \(-0.863327\pi\)
0.980275 + 0.197638i \(0.0633269\pi\)
\(654\) 3847.98 + 2795.72i 0.230073 + 0.167158i
\(655\) −2629.89 1910.73i −0.156883 0.113982i
\(656\) −3465.57 + 10665.9i −0.206262 + 0.634809i
\(657\) 1305.25 + 4017.14i 0.0775077 + 0.238544i
\(658\) −11.5920 + 8.42211i −0.000686785 + 0.000498979i
\(659\) −31860.3 −1.88331 −0.941655 0.336581i \(-0.890729\pi\)
−0.941655 + 0.336581i \(0.890729\pi\)
\(660\) −310.081 2577.06i −0.0182877 0.151988i
\(661\) −32986.5 −1.94104 −0.970518 0.241028i \(-0.922515\pi\)
−0.970518 + 0.241028i \(0.922515\pi\)
\(662\) −4371.44 + 3176.04i −0.256648 + 0.186466i
\(663\) 337.834 + 1039.74i 0.0197894 + 0.0609055i
\(664\) −110.833 + 341.110i −0.00647767 + 0.0199362i
\(665\) 57.4792 + 41.7611i 0.00335180 + 0.00243523i
\(666\) −4.04108 2.93602i −0.000235118 0.000170823i
\(667\) 3633.55 11182.9i 0.210932 0.649182i
\(668\) 3617.09 + 11132.3i 0.209505 + 0.644791i
\(669\) −2888.04 + 2098.28i −0.166903 + 0.121262i
\(670\) 524.328 0.0302337
\(671\) 327.715 + 2723.61i 0.0188544 + 0.156697i
\(672\) 189.132 0.0108570
\(673\) 9751.55 7084.91i 0.558536 0.405800i −0.272387 0.962188i \(-0.587813\pi\)
0.830923 + 0.556388i \(0.187813\pi\)
\(674\) −690.219 2124.28i −0.0394455 0.121401i
\(675\) −5592.56 + 17212.1i −0.318900 + 0.981475i
\(676\) 1047.32 + 760.925i 0.0595882 + 0.0432934i
\(677\) 21331.1 + 15498.0i 1.21096 + 0.879815i 0.995318 0.0966568i \(-0.0308149\pi\)
0.215644 + 0.976472i \(0.430815\pi\)
\(678\) 990.324 3047.90i 0.0560961 0.172646i
\(679\) 126.815 + 390.295i 0.00716745 + 0.0220591i
\(680\) −255.909 + 185.929i −0.0144319 + 0.0104854i
\(681\) 9066.58 0.510179
\(682\) 3731.93 1729.22i 0.209535 0.0970898i
\(683\) −5126.89 −0.287226 −0.143613 0.989634i \(-0.545872\pi\)
−0.143613 + 0.989634i \(0.545872\pi\)
\(684\) 2660.68 1933.10i 0.148733 0.108061i
\(685\) −1231.83 3791.19i −0.0687094 0.211466i
\(686\) 46.5819 143.364i 0.00259257 0.00797912i
\(687\) 1577.90 + 1146.41i 0.0876285 + 0.0636659i
\(688\) −5074.70 3686.98i −0.281208 0.204310i
\(689\) 1875.03 5770.75i 0.103676 0.319083i
\(690\) −224.091 689.682i −0.0123638 0.0380518i
\(691\) −15212.2 + 11052.3i −0.837483 + 0.608467i −0.921666 0.387983i \(-0.873172\pi\)
0.0841833 + 0.996450i \(0.473172\pi\)
\(692\) −7913.30 −0.434709
\(693\) 29.8470 53.5389i 0.00163607 0.00293474i
\(694\) −1104.78 −0.0604280
\(695\) −1954.34 + 1419.91i −0.106665 + 0.0774967i
\(696\) −1176.05 3619.50i −0.0640488 0.197122i
\(697\) −1096.92 + 3375.97i −0.0596109 + 0.183463i
\(698\) 2841.22 + 2064.27i 0.154071 + 0.111939i
\(699\) 18896.6 + 13729.2i 1.02251 + 0.742897i
\(700\) −108.136 + 332.809i −0.00583881 + 0.0179700i
\(701\) 7452.55 + 22936.6i 0.401539 + 1.23581i 0.923750 + 0.382995i \(0.125107\pi\)
−0.522211 + 0.852816i \(0.674893\pi\)
\(702\) 915.752 665.333i 0.0492348 0.0357712i
\(703\) 185.217 0.00993684
\(704\) −13819.7 2721.07i −0.739841 0.145673i
\(705\) −605.510 −0.0323473
\(706\) 503.529 365.835i 0.0268421 0.0195020i
\(707\) −210.370 647.454i −0.0111907 0.0344413i
\(708\) −9497.02 + 29228.8i −0.504124 + 1.55153i
\(709\) −1465.57 1064.80i −0.0776315 0.0564026i 0.548293 0.836287i \(-0.315278\pi\)
−0.625924 + 0.779884i \(0.715278\pi\)
\(710\) 182.592 + 132.661i 0.00965151 + 0.00701223i
\(711\) 204.723 630.073i 0.0107985 0.0332343i
\(712\) −1354.82 4169.70i −0.0713117 0.219475i
\(713\) −20953.1 + 15223.3i −1.10056 + 0.799604i
\(714\) 18.4832 0.000968793
\(715\) −631.093 680.063i −0.0330091 0.0355705i
\(716\) 15788.8 0.824099
\(717\) 4612.19 3350.95i 0.240231 0.174538i
\(718\) 1688.96 + 5198.08i 0.0877874 + 0.270182i
\(719\) 4753.09 14628.5i 0.246537 0.758764i −0.748843 0.662748i \(-0.769390\pi\)
0.995380 0.0960158i \(-0.0306099\pi\)
\(720\) −394.671 286.746i −0.0204285 0.0148422i
\(721\) 289.276 + 210.171i 0.0149420 + 0.0108560i
\(722\) 436.330 1342.89i 0.0224910 0.0692203i
\(723\) 1851.82 + 5699.31i 0.0952557 + 0.293167i
\(724\) 2713.50 1971.47i 0.139291 0.101200i
\(725\) 10638.7 0.544981
\(726\) −2381.82 + 2810.74i −0.121760 + 0.143687i
\(727\) 17850.3 0.910636 0.455318 0.890329i \(-0.349526\pi\)
0.455318 + 0.890329i \(0.349526\pi\)
\(728\) 36.1991 26.3002i 0.00184289 0.00133894i
\(729\) 6727.56 + 20705.3i 0.341795 + 1.05194i
\(730\) 334.009 1027.97i 0.0169345 0.0521191i
\(731\) −1606.24 1167.00i −0.0812707 0.0590466i
\(732\) −2212.49 1607.47i −0.111716 0.0811662i
\(733\) 5042.11 15518.0i 0.254072 0.781953i −0.739939 0.672674i \(-0.765146\pi\)
0.994011 0.109279i \(-0.0348542\pi\)
\(734\) 1264.14 + 3890.61i 0.0635696 + 0.195647i
\(735\) 2576.27 1871.77i 0.129289 0.0939337i
\(736\) −14150.6 −0.708695
\(737\) 11409.8 + 12295.2i 0.570265 + 0.614516i
\(738\) 520.693 0.0259715
\(739\) 20559.0 14937.0i 1.02338 0.743527i 0.0564049 0.998408i \(-0.482036\pi\)
0.966972 + 0.254881i \(0.0820362\pi\)
\(740\) −8.90250 27.3991i −0.000442246 0.00136109i
\(741\) −1837.53 + 5655.32i −0.0910974 + 0.280369i
\(742\) −82.9929 60.2979i −0.00410616 0.00298330i
\(743\) 8852.49 + 6431.71i 0.437102 + 0.317573i 0.784482 0.620151i \(-0.212929\pi\)
−0.347381 + 0.937724i \(0.612929\pi\)
\(744\) −2590.40 + 7972.43i −0.127646 + 0.392854i
\(745\) 914.773 + 2815.38i 0.0449862 + 0.138453i
\(746\) −1707.85 + 1240.82i −0.0838186 + 0.0608978i
\(747\) −175.081 −0.00857546
\(748\) −4856.61 956.257i −0.237400 0.0467436i
\(749\) 434.729 0.0212078
\(750\) 1078.39 783.493i 0.0525028 0.0381455i
\(751\) −5615.57 17283.0i −0.272856 0.839765i −0.989779 0.142612i \(-0.954450\pi\)
0.716922 0.697153i \(-0.245550\pi\)
\(752\) −1127.33 + 3469.56i −0.0546669 + 0.168247i
\(753\) −4239.86 3080.44i −0.205191 0.149080i
\(754\) −538.317 391.110i −0.0260005 0.0188904i
\(755\) −1691.41 + 5205.64i −0.0815323 + 0.250931i
\(756\) 133.286 + 410.213i 0.00641214 + 0.0197345i
\(757\) 22063.5 16030.1i 1.05933 0.769648i 0.0853654 0.996350i \(-0.472794\pi\)
0.973964 + 0.226702i \(0.0727942\pi\)
\(758\) 210.801 0.0101011
\(759\) 11296.2 20262.8i 0.540219 0.969031i
\(760\) −1720.52 −0.0821180
\(761\) 21617.5 15706.1i 1.02974 0.748152i 0.0614862 0.998108i \(-0.480416\pi\)
0.968257 + 0.249955i \(0.0804160\pi\)
\(762\) −1689.51 5199.77i −0.0803207 0.247202i
\(763\) −200.188 + 616.115i −0.00949841 + 0.0292331i
\(764\) 29954.5 + 21763.2i 1.41847 + 1.03058i
\(765\) −124.921 90.7604i −0.00590396 0.00428948i
\(766\) −1087.17 + 3345.96i −0.0512806 + 0.157825i
\(767\) 3394.57 + 10447.4i 0.159805 + 0.491830i
\(768\) 9466.95 6878.14i 0.444804 0.323169i
\(769\) 31295.9 1.46757 0.733783 0.679384i \(-0.237753\pi\)
0.733783 + 0.679384i \(0.237753\pi\)
\(770\) −14.2320 + 6.59451i −0.000666084 + 0.000308636i
\(771\) −30772.0 −1.43739
\(772\) −32043.6 + 23281.0i −1.49388 + 1.08537i
\(773\) −11574.5 35622.7i −0.538559 1.65751i −0.735830 0.677166i \(-0.763208\pi\)
0.197271 0.980349i \(-0.436792\pi\)
\(774\) −89.9961 + 276.980i −0.00417939 + 0.0128628i
\(775\) −18957.8 13773.7i −0.878690 0.638405i
\(776\) −8039.88 5841.32i −0.371927 0.270220i
\(777\) −1.06346 + 3.27299i −4.91009e−5 + 0.000151117i
\(778\) −1123.78 3458.63i −0.0517858 0.159380i
\(779\) −15620.0 + 11348.6i −0.718414 + 0.521958i
\(780\) 924.910 0.0424578
\(781\) 862.538 + 7168.49i 0.0395186 + 0.328436i
\(782\) −1382.90 −0.0632383
\(783\) 10608.7 7707.64i 0.484192 0.351786i
\(784\) −5928.76 18246.8i −0.270078 0.831216i
\(785\) −756.236 + 2327.45i −0.0343837 + 0.105822i
\(786\) −3721.29 2703.67i −0.168873 0.122693i
\(787\) 8425.70 + 6121.63i 0.381631 + 0.277271i 0.762018 0.647556i \(-0.224209\pi\)
−0.380386 + 0.924828i \(0.624209\pi\)
\(788\) 5376.10 16545.9i 0.243040 0.748001i
\(789\) −4606.21 14176.5i −0.207840 0.639665i
\(790\) −137.153 + 99.6478i −0.00617684 + 0.00448773i
\(791\) 436.491 0.0196205
\(792\) 177.325 + 1473.74i 0.00795578 + 0.0661198i
\(793\) −977.508 −0.0437734
\(794\) 1636.35 1188.87i 0.0731382 0.0531380i
\(795\) −1339.63 4122.96i −0.0597632 0.183932i
\(796\) −10478.2 + 32248.6i −0.466570 + 1.43595i
\(797\) −15523.1 11278.2i −0.689907 0.501247i 0.186722 0.982413i \(-0.440214\pi\)
−0.876630 + 0.481166i \(0.840214\pi\)
\(798\) 81.3329 + 59.0918i 0.00360796 + 0.00262134i
\(799\) −356.821 + 1098.18i −0.0157990 + 0.0486244i
\(800\) −3956.38 12176.5i −0.174849 0.538130i
\(801\) 1731.43 1257.96i 0.0763761 0.0554905i
\(802\) −7284.17 −0.320715
\(803\) 31373.6 14537.2i 1.37877 0.638864i
\(804\) −16721.8 −0.733500
\(805\) 79.9062 58.0552i 0.00349854 0.00254184i
\(806\) 452.902 + 1393.89i 0.0197926 + 0.0609152i
\(807\) −1448.84 + 4459.07i −0.0631990 + 0.194506i
\(808\) 13337.2 + 9690.06i 0.580695 + 0.421900i
\(809\) 30264.8 + 21988.6i 1.31527 + 0.955599i 0.999978 + 0.00660398i \(0.00210213\pi\)
0.315291 + 0.948995i \(0.397898\pi\)
\(810\) 207.503 638.628i 0.00900112 0.0277026i
\(811\) 9145.74 + 28147.7i 0.395993 + 1.21874i 0.928185 + 0.372118i \(0.121368\pi\)
−0.532192 + 0.846623i \(0.678632\pi\)
\(812\) 205.126 149.033i 0.00886516 0.00644092i
\(813\) −7228.31 −0.311818
\(814\) −19.9110 + 35.7159i −0.000857348 + 0.00153789i
\(815\) 4203.85 0.180680
\(816\) 3807.17 2766.07i 0.163330 0.118666i
\(817\) −3337.07 10270.4i −0.142900 0.439801i
\(818\) −745.935 + 2295.75i −0.0318839 + 0.0981284i
\(819\) 17.6704 + 12.8383i 0.000753913 + 0.000547750i
\(820\) 2429.57 + 1765.18i 0.103469 + 0.0751743i
\(821\) 12366.4 38059.9i 0.525689 1.61790i −0.237262 0.971446i \(-0.576250\pi\)
0.762950 0.646457i \(-0.223750\pi\)
\(822\) −1743.04 5364.53i −0.0739605 0.227627i
\(823\) −20512.7 + 14903.4i −0.868808 + 0.631226i −0.930267 0.366884i \(-0.880425\pi\)
0.0614588 + 0.998110i \(0.480425\pi\)
\(824\) −8658.85 −0.366074
\(825\) 20594.3 + 4054.98i 0.869092 + 0.171123i
\(826\) 185.720 0.00782329
\(827\) −4981.09 + 3618.98i −0.209443 + 0.152169i −0.687562 0.726126i \(-0.741319\pi\)
0.478118 + 0.878295i \(0.341319\pi\)
\(828\) −1412.82 4348.21i −0.0592982 0.182501i
\(829\) 5192.54 15981.0i 0.217545 0.669533i −0.781419 0.624007i \(-0.785504\pi\)
0.998963 0.0455260i \(-0.0144964\pi\)
\(830\) 36.2461 + 26.3343i 0.00151581 + 0.00110130i
\(831\) −14567.8 10584.1i −0.608124 0.441828i
\(832\) 1550.94 4773.29i 0.0646262 0.198899i
\(833\) −1876.57 5775.47i −0.0780542 0.240226i
\(834\) −2765.38 + 2009.17i −0.114817 + 0.0834194i
\(835\) 2989.17 0.123886
\(836\) −18313.6 19734.7i −0.757643 0.816434i
\(837\) −28883.2 −1.19277
\(838\) −1358.63 + 987.104i −0.0560061 + 0.0406908i
\(839\) 7804.26 + 24019.0i 0.321136 + 0.988354i 0.973155 + 0.230152i \(0.0739222\pi\)
−0.652019 + 0.758203i \(0.726078\pi\)
\(840\) 9.87867 30.4034i 0.000405770 0.00124883i
\(841\) 13494.9 + 9804.62i 0.553319 + 0.402010i
\(842\) −938.801 682.079i −0.0384242 0.0279168i
\(843\) 7225.08 22236.5i 0.295190 0.908501i
\(844\) −2869.33 8830.90i −0.117022 0.360157i
\(845\) 267.457 194.319i 0.0108885 0.00791098i
\(846\) 169.378 0.00688338
\(847\) −464.336 190.229i −0.0188368 0.00771705i
\(848\) −26118.6 −1.05768
\(849\) −28835.5 + 20950.2i −1.16565 + 0.846891i
\(850\) −386.645 1189.97i −0.0156021 0.0480184i
\(851\) 79.5670 244.882i 0.00320508 0.00986422i
\(852\) −5823.22 4230.82i −0.234155 0.170124i
\(853\) −26409.4 19187.6i −1.06007 0.770187i −0.0859702 0.996298i \(-0.527399\pi\)
−0.974102 + 0.226110i \(0.927399\pi\)
\(854\) −5.10694 + 15.7175i −0.000204632 + 0.000629793i
\(855\) −259.532 798.757i −0.0103811 0.0319496i
\(856\) −8516.90 + 6187.89i −0.340072 + 0.247077i
\(857\) −38051.1 −1.51669 −0.758344 0.651855i \(-0.773991\pi\)
−0.758344 + 0.651855i \(0.773991\pi\)
\(858\) −892.995 962.288i −0.0355319 0.0382890i
\(859\) 8358.76 0.332011 0.166005 0.986125i \(-0.446913\pi\)
0.166005 + 0.986125i \(0.446913\pi\)
\(860\) −1358.90 + 987.302i −0.0538817 + 0.0391474i
\(861\) −110.857 341.183i −0.00438792 0.0135046i
\(862\) 893.232 2749.08i 0.0352942 0.108624i
\(863\) −12781.6 9286.40i −0.504162 0.366295i 0.306442 0.951889i \(-0.400861\pi\)
−0.810605 + 0.585594i \(0.800861\pi\)
\(864\) −12767.0 9275.75i −0.502710 0.365240i
\(865\) −624.473 + 1921.93i −0.0245465 + 0.0755464i
\(866\) −169.748 522.430i −0.00666081 0.0204999i
\(867\) −17666.8 + 12835.7i −0.692037 + 0.502794i
\(868\) −558.477 −0.0218386
\(869\) −5321.24 1047.74i −0.207723 0.0409002i
\(870\) −475.397 −0.0185258
\(871\) −4835.47 + 3513.18i −0.188110 + 0.136670i
\(872\) −4847.78 14919.9i −0.188264 0.579418i
\(873\) 1499.08 4613.69i 0.0581170 0.178866i
\(874\) −6085.25 4421.19i −0.235511 0.171109i
\(875\) 146.877 + 106.712i 0.00567469 + 0.00412290i
\(876\) −10652.2 + 32784.0i −0.410849 + 1.26446i
\(877\) −9504.02 29250.4i −0.365938 1.12624i −0.949391 0.314095i \(-0.898299\pi\)
0.583453 0.812147i \(-0.301701\pi\)
\(878\) 5593.47 4063.89i 0.215001 0.156207i
\(879\) −7059.86 −0.270902
\(880\) −1944.61 + 3488.19i −0.0744917 + 0.133621i
\(881\) 33588.3 1.28447 0.642235 0.766508i \(-0.278007\pi\)
0.642235 + 0.766508i \(0.278007\pi\)
\(882\) −720.656 + 523.587i −0.0275122 + 0.0199888i
\(883\) 6608.40 + 20338.6i 0.251858 + 0.775139i 0.994433 + 0.105376i \(0.0336045\pi\)
−0.742575 + 0.669763i \(0.766396\pi\)
\(884\) 545.041 1677.46i 0.0207372 0.0638226i
\(885\) 6349.45 + 4613.15i 0.241169 + 0.175219i
\(886\) 3140.73 + 2281.88i 0.119091 + 0.0865250i
\(887\) 11631.8 35799.0i 0.440313 1.35514i −0.447231 0.894419i \(-0.647590\pi\)
0.887543 0.460724i \(-0.152410\pi\)
\(888\) −25.7529 79.2594i −0.000973211 0.00299524i
\(889\) 602.442 437.700i 0.0227281 0.0165129i
\(890\) −547.662 −0.0206266
\(891\) 19490.8 9031.25i 0.732848 0.339572i
\(892\) 5759.33 0.216185
\(893\) −5081.09 + 3691.63i −0.190406 + 0.138338i
\(894\) 1294.40 + 3983.76i 0.0484242 + 0.149034i
\(895\) 1245.96 3834.68i 0.0465340 0.143217i
\(896\) −326.459 237.186i −0.0121721 0.00884357i
\(897\) 6687.73 + 4858.92i 0.248937 + 0.180863i
\(898\) 264.861 815.157i 0.00984244 0.0302919i
\(899\) 5246.71 + 16147.7i 0.194647 + 0.599062i
\(900\) 3346.58 2431.44i 0.123948 0.0900532i
\(901\) −8267.03 −0.305677
\(902\) −509.213 4232.03i −0.0187971 0.156221i
\(903\) 200.651 0.00739451
\(904\) −8551.41 + 6212.97i −0.314619 + 0.228584i
\(905\) −264.684 814.614i −0.00972198 0.0299212i
\(906\) −2393.35 + 7365.97i −0.0877634 + 0.270108i
\(907\) 16718.8 + 12146.9i 0.612059 + 0.444687i 0.850139 0.526559i \(-0.176518\pi\)
−0.238080 + 0.971246i \(0.576518\pi\)
\(908\) −11833.9 8597.82i −0.432513 0.314239i
\(909\) −2486.80 + 7653.57i −0.0907390 + 0.279266i
\(910\) −1.72718 5.31570i −6.29179e−5 0.000193641i
\(911\) −35252.2 + 25612.2i −1.28206 + 0.931472i −0.999613 0.0278107i \(-0.991146\pi\)
−0.282448 + 0.959283i \(0.591146\pi\)
\(912\) 25596.2 0.929358
\(913\) 171.221 + 1423.00i 0.00620655 + 0.0515821i
\(914\) −356.208 −0.0128909
\(915\) −565.008 + 410.502i −0.0204138 + 0.0148315i
\(916\) −972.370 2992.65i −0.0350742 0.107947i
\(917\) 193.597 595.830i 0.00697179 0.0214570i
\(918\) −1247.68 906.489i −0.0448578 0.0325911i
\(919\) 24694.5 + 17941.6i 0.886393 + 0.644002i 0.934935 0.354819i \(-0.115457\pi\)
−0.0485418 + 0.998821i \(0.515457\pi\)
\(920\) −739.112 + 2274.75i −0.0264868 + 0.0815179i
\(921\) −11760.7 36195.6i −0.420768 1.29499i
\(922\) 6730.62 4890.08i 0.240413 0.174671i
\(923\) −2572.78 −0.0917488
\(924\) 453.885 210.312i 0.0161599 0.00748782i
\(925\) 232.965 0.00828091
\(926\) 2828.69 2055.16i 0.100385 0.0729339i
\(927\) −1306.15 4019.91i −0.0462778 0.142428i
\(928\) −2866.64 + 8822.60i −0.101403 + 0.312086i
\(929\) 1519.84 + 1104.23i 0.0536752 + 0.0389973i 0.614299 0.789073i \(-0.289439\pi\)
−0.560624 + 0.828070i \(0.689439\pi\)
\(930\) 847.142 + 615.485i 0.0298698 + 0.0217017i
\(931\) 10206.9 31413.6i 0.359310 1.10584i
\(932\) −11644.9 35839.2i −0.409270 1.25960i
\(933\) −6456.03 + 4690.58i −0.226539 + 0.164590i
\(934\) −352.992 −0.0123664
\(935\) −615.505 + 1104.08i −0.0215285 + 0.0386173i
\(936\) −528.926 −0.0184706
\(937\) 35213.6 25584.2i 1.22772 0.891994i 0.231007 0.972952i \(-0.425798\pi\)
0.996718 + 0.0809577i \(0.0257979\pi\)
\(938\) 31.2264 + 96.1048i 0.00108697 + 0.00334535i
\(939\) −9580.99 + 29487.3i −0.332975 + 1.02479i
\(940\) 790.324 + 574.204i 0.0274229 + 0.0199239i
\(941\) 4981.23 + 3619.08i 0.172565 + 0.125376i 0.670715 0.741715i \(-0.265987\pi\)
−0.498150 + 0.867091i \(0.665987\pi\)
\(942\) −1070.07 + 3293.34i −0.0370115 + 0.113910i
\(943\) 8294.21 + 25527.0i 0.286423 + 0.881519i
\(944\) 38254.6 27793.6i 1.31894 0.958267i
\(945\) 110.148 0.00379166
\(946\) 2339.22 + 460.587i 0.0803958 + 0.0158298i
\(947\) −18413.6 −0.631849 −0.315924 0.948784i \(-0.602315\pi\)
−0.315924 + 0.948784i \(0.602315\pi\)
\(948\) 4374.09 3177.96i 0.149856 0.108877i
\(949\) 3807.46 + 11718.2i 0.130238 + 0.400830i
\(950\) 2103.02 6472.42i 0.0718220 0.221045i
\(951\) −13628.7 9901.82i −0.464711 0.337633i
\(952\) −49.3198 35.8329i −0.00167906 0.00121991i
\(953\) −5194.98 + 15988.5i −0.176581 + 0.543461i −0.999702 0.0244049i \(-0.992231\pi\)
0.823121 + 0.567866i \(0.192231\pi\)
\(954\) 374.732 + 1153.31i 0.0127174 + 0.0391402i
\(955\) 7649.54 5557.71i 0.259197 0.188318i
\(956\) −9197.63 −0.311164
\(957\) −10345.0 11147.8i −0.349433 0.376547i
\(958\) −2997.47 −0.101089
\(959\) 621.531 451.569i 0.0209283 0.0152053i
\(960\) −1108.08 3410.31i −0.0372532 0.114653i
\(961\) 2350.64 7234.54i 0.0789045 0.242843i
\(962\) −11.7880 8.56448i −0.000395073 0.000287037i
\(963\) −4157.49 3020.60i −0.139121 0.101077i
\(964\) 2987.62 9194.94i 0.0998181 0.307208i
\(965\) 3125.64 + 9619.73i 0.104267 + 0.320902i
\(966\) 113.067 82.1480i 0.00376591 0.00273610i
\(967\) 52939.1 1.76050 0.880252 0.474507i \(-0.157374\pi\)
0.880252 + 0.474507i \(0.157374\pi\)
\(968\) 11804.6 2882.49i 0.391958 0.0957093i
\(969\) 8101.68 0.268590
\(970\) −1004.30 + 729.668i −0.0332435 + 0.0241528i
\(971\) 14698.2 + 45236.5i 0.485776 + 1.49506i 0.830854 + 0.556490i \(0.187852\pi\)
−0.345079 + 0.938574i \(0.612148\pi\)
\(972\) 2927.94 9011.28i 0.0966192 0.297363i
\(973\) −376.648 273.650i −0.0124098 0.00901627i
\(974\) 1739.03 + 1263.48i 0.0572096 + 0.0415652i
\(975\) −2311.23 + 7113.23i −0.0759164 + 0.233647i
\(976\) 1300.25 + 4001.76i 0.0426434 + 0.131243i
\(977\) 38345.6 27859.7i 1.25566 0.912293i 0.257128 0.966377i \(-0.417224\pi\)
0.998536 + 0.0540841i \(0.0172239\pi\)
\(978\) 5948.44 0.194489
\(979\) −11917.6 12842.3i −0.389057 0.419247i
\(980\) −5137.60 −0.167464
\(981\) 6195.39 4501.21i 0.201634 0.146496i
\(982\) −1917.24 5900.65i −0.0623030 0.191749i
\(983\) −3657.85 + 11257.7i −0.118685 + 0.365274i −0.992698 0.120628i \(-0.961509\pi\)
0.874013 + 0.485903i \(0.161509\pi\)
\(984\) 7028.20 + 5106.28i 0.227694 + 0.165429i
\(985\) −3594.32 2611.43i −0.116269 0.0844740i
\(986\) −280.147 + 862.205i −0.00904838 + 0.0278481i
\(987\) −36.0611 110.985i −0.00116296 0.00357921i
\(988\) 7761.31 5638.92i 0.249919 0.181577i
\(989\) −15012.5 −0.482679
\(990\) 181.926 + 35.8210i 0.00584040 + 0.00114997i
\(991\) −6982.40 −0.223818 −0.111909 0.993718i \(-0.535696\pi\)
−0.111909 + 0.993718i \(0.535696\pi\)
\(992\) 16530.6 12010.2i 0.529081 0.384400i
\(993\) −13598.9 41853.1i −0.434590 1.33753i
\(994\) −13.4414 + 41.3682i −0.000428907 + 0.00132004i
\(995\) 7005.44 + 5089.75i 0.223203 + 0.162167i
\(996\) −1155.96 839.852i −0.0367750 0.0267186i
\(997\) −10380.4 + 31947.5i −0.329739 + 1.01483i 0.639516 + 0.768778i \(0.279135\pi\)
−0.969256 + 0.246056i \(0.920865\pi\)
\(998\) 1342.17 + 4130.77i 0.0425707 + 0.131019i
\(999\) 232.307 168.781i 0.00735723 0.00534534i
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 143.4.h.b.14.9 76
11.2 odd 10 1573.4.a.r.1.18 38
11.4 even 5 inner 143.4.h.b.92.9 yes 76
11.9 even 5 1573.4.a.q.1.21 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.h.b.14.9 76 1.1 even 1 trivial
143.4.h.b.92.9 yes 76 11.4 even 5 inner
1573.4.a.q.1.21 38 11.9 even 5
1573.4.a.r.1.18 38 11.2 odd 10