Properties

Label 177.4.e.a.133.14
Level $177$
Weight $4$
Character 177.133
Analytic conductor $10.443$
Analytic rank $0$
Dimension $420$
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] = [177,4,Mod(4,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\), degree \(28\), 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: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(420\)
Relative dimension: \(15\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 133.14
Character \(\chi\) \(=\) 177.133
Dual form 177.4.e.a.4.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.44507 - 0.483430i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(11.7120 - 2.57800i) q^{4} +(8.85655 - 6.73258i) q^{5} +(-9.73839 - 9.22469i) q^{6} +(-9.70013 - 24.3455i) q^{7} +(16.9165 - 5.69982i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\) \(q+(4.44507 - 0.483430i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(11.7120 - 2.57800i) q^{4} +(8.85655 - 6.73258i) q^{5} +(-9.73839 - 9.22469i) q^{6} +(-9.70013 - 24.3455i) q^{7} +(16.9165 - 5.69982i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(36.1133 - 34.2083i) q^{10} +(1.10339 + 0.510481i) q^{11} +(-28.6411 - 21.7724i) q^{12} +(7.69977 + 46.9665i) q^{13} +(-54.8871 - 103.528i) q^{14} +(-32.5948 - 7.17465i) q^{15} +(-14.6323 + 6.76963i) q^{16} +(38.0786 - 95.5702i) q^{17} +(-2.17863 + 40.1825i) q^{18} +(41.8049 - 61.6577i) q^{19} +(86.3711 - 101.684i) q^{20} +(-36.8264 + 69.4620i) q^{21} +(5.15141 + 1.73571i) q^{22} +(4.13809 + 76.3226i) q^{23} +(-45.8870 - 27.6093i) q^{24} +(-0.330111 + 1.18895i) q^{25} +(56.9310 + 205.047i) q^{26} +(23.1351 - 13.9200i) q^{27} +(-176.370 - 260.127i) q^{28} +(272.492 + 29.6353i) q^{29} +(-148.354 - 16.1345i) q^{30} +(88.3519 + 130.309i) q^{31} +(-184.134 + 110.790i) q^{32} +(-0.975744 - 3.51431i) q^{33} +(123.061 - 443.224i) q^{34} +(-249.818 - 150.310i) q^{35} +(5.84327 + 107.773i) q^{36} +(32.6396 + 10.9975i) q^{37} +(156.019 - 294.282i) q^{38} +(92.4341 - 108.822i) q^{39} +(111.447 - 164.372i) q^{40} +(4.51531 - 83.2800i) q^{41} +(-130.116 + 326.567i) q^{42} +(-269.710 + 124.781i) q^{43} +(14.2388 + 3.13421i) q^{44} +(46.8995 + 88.4618i) q^{45} +(55.2907 + 337.259i) q^{46} +(-41.1233 - 31.2611i) q^{47} +(43.8969 + 20.3089i) q^{48} +(-249.594 + 236.428i) q^{49} +(-0.892591 + 5.44456i) q^{50} +(-292.475 + 98.5462i) q^{51} +(211.259 + 530.220i) q^{52} +(437.551 + 414.470i) q^{53} +(96.1080 - 73.0594i) q^{54} +(13.2090 - 2.90753i) q^{55} +(-302.857 - 356.550i) q^{56} +(-222.171 + 24.1626i) q^{57} +1225.57 q^{58} +(-361.767 + 272.953i) q^{59} -400.245 q^{60} +(-226.915 + 24.6785i) q^{61} +(455.726 + 536.522i) q^{62} +(230.347 - 50.7031i) q^{63} +(-662.251 + 503.430i) q^{64} +(384.399 + 364.122i) q^{65} +(-6.03618 - 15.1497i) q^{66} +(-275.393 + 92.7907i) q^{67} +(199.596 - 1217.48i) q^{68} +(166.474 - 157.692i) q^{69} +(-1183.12 - 547.370i) q^{70} +(96.3412 + 73.2367i) q^{71} +(25.9916 + 158.542i) q^{72} +(486.250 + 917.165i) q^{73} +(150.402 + 33.1059i) q^{74} +(3.35965 - 1.55434i) q^{75} +(330.665 - 829.906i) q^{76} +(1.72492 - 31.8142i) q^{77} +(358.268 - 528.406i) q^{78} +(507.083 - 596.984i) q^{79} +(-84.0148 + 158.469i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-20.1892 - 372.368i) q^{82} +(-841.508 - 506.319i) q^{83} +(-252.237 + 908.476i) q^{84} +(-306.188 - 1102.79i) q^{85} +(-1138.56 + 685.046i) q^{86} +(-461.463 - 680.606i) q^{87} +(21.5750 + 2.34643i) q^{88} +(350.472 + 38.1162i) q^{89} +(251.237 + 370.546i) q^{90} +(1068.73 - 643.036i) q^{91} +(245.225 + 883.220i) q^{92} +(126.357 - 455.097i) q^{93} +(-197.909 - 119.078i) q^{94} +(-44.8673 - 827.529i) q^{95} +(610.938 + 205.849i) q^{96} +(409.148 - 771.735i) q^{97} +(-995.166 + 1171.60i) q^{98} +(-6.14038 + 9.05638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{28}{29}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.44507 0.483430i 1.57157 0.170918i 0.719554 0.694436i \(-0.244346\pi\)
0.852015 + 0.523518i \(0.175381\pi\)
\(3\) −1.94216 2.28649i −0.373769 0.440034i
\(4\) 11.7120 2.57800i 1.46400 0.322250i
\(5\) 8.85655 6.73258i 0.792154 0.602180i −0.128881 0.991660i \(-0.541138\pi\)
0.921035 + 0.389480i \(0.127345\pi\)
\(6\) −9.73839 9.22469i −0.662613 0.627661i
\(7\) −9.70013 24.3455i −0.523758 1.31453i −0.918384 0.395691i \(-0.870505\pi\)
0.394626 0.918842i \(-0.370874\pi\)
\(8\) 16.9165 5.69982i 0.747609 0.251899i
\(9\) −1.45604 + 8.88144i −0.0539273 + 0.328942i
\(10\) 36.1133 34.2083i 1.14200 1.08176i
\(11\) 1.10339 + 0.510481i 0.0302440 + 0.0139923i 0.434953 0.900453i \(-0.356765\pi\)
−0.404709 + 0.914446i \(0.632627\pi\)
\(12\) −28.6411 21.7724i −0.688997 0.523762i
\(13\) 7.69977 + 46.9665i 0.164272 + 1.00201i 0.932324 + 0.361625i \(0.117778\pi\)
−0.768052 + 0.640388i \(0.778774\pi\)
\(14\) −54.8871 103.528i −1.04780 1.97636i
\(15\) −32.5948 7.17465i −0.561062 0.123499i
\(16\) −14.6323 + 6.76963i −0.228630 + 0.105775i
\(17\) 38.0786 95.5702i 0.543260 1.36348i −0.359423 0.933175i \(-0.617026\pi\)
0.902683 0.430306i \(-0.141594\pi\)
\(18\) −2.17863 + 40.1825i −0.0285282 + 0.526173i
\(19\) 41.8049 61.6577i 0.504774 0.744486i −0.486872 0.873473i \(-0.661862\pi\)
0.991646 + 0.128987i \(0.0411726\pi\)
\(20\) 86.3711 101.684i 0.965658 1.13686i
\(21\) −36.8264 + 69.4620i −0.382676 + 0.721803i
\(22\) 5.15141 + 1.73571i 0.0499220 + 0.0168207i
\(23\) 4.13809 + 76.3226i 0.0375153 + 0.691928i 0.955442 + 0.295179i \(0.0953792\pi\)
−0.917927 + 0.396750i \(0.870138\pi\)
\(24\) −45.8870 27.6093i −0.390277 0.234822i
\(25\) −0.330111 + 1.18895i −0.00264089 + 0.00951162i
\(26\) 56.9310 + 205.047i 0.429427 + 1.54666i
\(27\) 23.1351 13.9200i 0.164902 0.0992184i
\(28\) −176.370 260.127i −1.19039 1.75569i
\(29\) 272.492 + 29.6353i 1.74485 + 0.189764i 0.924261 0.381760i \(-0.124682\pi\)
0.820585 + 0.571524i \(0.193648\pi\)
\(30\) −148.354 16.1345i −0.902856 0.0981916i
\(31\) 88.3519 + 130.309i 0.511886 + 0.754975i 0.992538 0.121936i \(-0.0389103\pi\)
−0.480652 + 0.876911i \(0.659600\pi\)
\(32\) −184.134 + 110.790i −1.01721 + 0.612034i
\(33\) −0.975744 3.51431i −0.00514713 0.0185383i
\(34\) 123.061 443.224i 0.620727 2.23566i
\(35\) −249.818 150.310i −1.20648 0.725916i
\(36\) 5.84327 + 107.773i 0.0270522 + 0.498948i
\(37\) 32.6396 + 10.9975i 0.145025 + 0.0488645i 0.390878 0.920443i \(-0.372172\pi\)
−0.245853 + 0.969307i \(0.579068\pi\)
\(38\) 156.019 294.282i 0.666041 1.25629i
\(39\) 92.4341 108.822i 0.379521 0.446806i
\(40\) 111.447 164.372i 0.440533 0.649738i
\(41\) 4.51531 83.2800i 0.0171993 0.317223i −0.977256 0.212063i \(-0.931982\pi\)
0.994455 0.105160i \(-0.0335355\pi\)
\(42\) −130.116 + 326.567i −0.478032 + 1.19977i
\(43\) −269.710 + 124.781i −0.956520 + 0.442533i −0.835118 0.550070i \(-0.814601\pi\)
−0.121401 + 0.992603i \(0.538739\pi\)
\(44\) 14.2388 + 3.13421i 0.0487861 + 0.0107386i
\(45\) 46.8995 + 88.4618i 0.155364 + 0.293047i
\(46\) 55.2907 + 337.259i 0.177221 + 1.08100i
\(47\) −41.1233 31.2611i −0.127627 0.0970193i 0.539414 0.842041i \(-0.318646\pi\)
−0.667040 + 0.745022i \(0.732439\pi\)
\(48\) 43.8969 + 20.3089i 0.131999 + 0.0610695i
\(49\) −249.594 + 236.428i −0.727679 + 0.689294i
\(50\) −0.892591 + 5.44456i −0.00252463 + 0.0153995i
\(51\) −292.475 + 98.5462i −0.803032 + 0.270573i
\(52\) 211.259 + 530.220i 0.563392 + 1.41401i
\(53\) 437.551 + 414.470i 1.13400 + 1.07419i 0.996492 + 0.0836849i \(0.0266689\pi\)
0.137511 + 0.990500i \(0.456090\pi\)
\(54\) 96.1080 73.0594i 0.242197 0.184113i
\(55\) 13.2090 2.90753i 0.0323838 0.00712821i
\(56\) −302.857 356.550i −0.722695 0.850822i
\(57\) −222.171 + 24.1626i −0.516268 + 0.0561476i
\(58\) 1225.57 2.77458
\(59\) −361.767 + 272.953i −0.798273 + 0.602296i
\(60\) −400.245 −0.861191
\(61\) −226.915 + 24.6785i −0.476287 + 0.0517993i −0.343115 0.939294i \(-0.611482\pi\)
−0.133172 + 0.991093i \(0.542516\pi\)
\(62\) 455.726 + 536.522i 0.933504 + 1.09901i
\(63\) 230.347 50.7031i 0.460650 0.101397i
\(64\) −662.251 + 503.430i −1.29346 + 0.983262i
\(65\) 384.399 + 364.122i 0.733520 + 0.694827i
\(66\) −6.03618 15.1497i −0.0112576 0.0282545i
\(67\) −275.393 + 92.7907i −0.502158 + 0.169197i −0.558970 0.829188i \(-0.688803\pi\)
0.0568113 + 0.998385i \(0.481907\pi\)
\(68\) 199.596 1217.48i 0.355950 2.17120i
\(69\) 166.474 157.692i 0.290450 0.275129i
\(70\) −1183.12 547.370i −2.02014 0.934617i
\(71\) 96.3412 + 73.2367i 0.161037 + 0.122417i 0.682589 0.730802i \(-0.260854\pi\)
−0.521553 + 0.853219i \(0.674647\pi\)
\(72\) 25.9916 + 158.542i 0.0425436 + 0.259504i
\(73\) 486.250 + 917.165i 0.779607 + 1.47049i 0.879707 + 0.475517i \(0.157739\pi\)
−0.100100 + 0.994977i \(0.531916\pi\)
\(74\) 150.402 + 33.1059i 0.236268 + 0.0520065i
\(75\) 3.35965 1.55434i 0.00517252 0.00239306i
\(76\) 330.665 829.906i 0.499077 1.25259i
\(77\) 1.72492 31.8142i 0.00255289 0.0470853i
\(78\) 358.268 528.406i 0.520075 0.767054i
\(79\) 507.083 596.984i 0.722168 0.850202i −0.271514 0.962435i \(-0.587524\pi\)
0.993682 + 0.112233i \(0.0358002\pi\)
\(80\) −84.0148 + 158.469i −0.117414 + 0.221467i
\(81\) −76.7599 25.8634i −0.105295 0.0354779i
\(82\) −20.1892 372.368i −0.0271894 0.501478i
\(83\) −841.508 506.319i −1.11286 0.669587i −0.164373 0.986398i \(-0.552560\pi\)
−0.948489 + 0.316812i \(0.897388\pi\)
\(84\) −252.237 + 908.476i −0.327635 + 1.18003i
\(85\) −306.188 1102.79i −0.390715 1.40723i
\(86\) −1138.56 + 685.046i −1.42760 + 0.858959i
\(87\) −461.463 680.606i −0.568666 0.838720i
\(88\) 21.5750 + 2.34643i 0.0261353 + 0.00284239i
\(89\) 350.472 + 38.1162i 0.417416 + 0.0453967i 0.314417 0.949285i \(-0.398191\pi\)
0.102998 + 0.994682i \(0.467156\pi\)
\(90\) 251.237 + 370.546i 0.294252 + 0.433989i
\(91\) 1068.73 643.036i 1.23114 0.740752i
\(92\) 245.225 + 883.220i 0.277896 + 1.00089i
\(93\) 126.357 455.097i 0.140888 0.507434i
\(94\) −197.909 119.078i −0.217157 0.130659i
\(95\) −44.8673 827.529i −0.0484557 0.893712i
\(96\) 610.938 + 205.849i 0.649516 + 0.218848i
\(97\) 409.148 771.735i 0.428275 0.807813i −0.571644 0.820502i \(-0.693694\pi\)
0.999919 + 0.0126887i \(0.00403906\pi\)
\(98\) −995.166 + 1171.60i −1.02578 + 1.20765i
\(99\) −6.14038 + 9.05638i −0.00623365 + 0.00919394i
\(100\) −0.801132 + 14.7760i −0.000801132 + 0.0147760i
\(101\) −189.140 + 474.706i −0.186338 + 0.467674i −0.992234 0.124383i \(-0.960305\pi\)
0.805896 + 0.592057i \(0.201684\pi\)
\(102\) −1252.43 + 579.436i −1.21577 + 0.562477i
\(103\) 1489.56 + 327.876i 1.42495 + 0.313656i 0.859505 0.511127i \(-0.170772\pi\)
0.565449 + 0.824783i \(0.308703\pi\)
\(104\) 397.953 + 750.620i 0.375217 + 0.707734i
\(105\) 141.503 + 863.131i 0.131517 + 0.802218i
\(106\) 2145.31 + 1630.82i 1.96576 + 1.49433i
\(107\) −1042.68 482.396i −0.942055 0.435841i −0.112116 0.993695i \(-0.535763\pi\)
−0.829939 + 0.557854i \(0.811625\pi\)
\(108\) 235.072 222.672i 0.209443 0.198395i
\(109\) 261.702 1596.31i 0.229968 1.40274i −0.579211 0.815178i \(-0.696639\pi\)
0.809178 0.587563i \(-0.199913\pi\)
\(110\) 57.3096 19.3098i 0.0496750 0.0167375i
\(111\) −38.2455 95.9889i −0.0327036 0.0820798i
\(112\) 306.745 + 290.564i 0.258792 + 0.245141i
\(113\) −1776.65 + 1350.58i −1.47906 + 1.12435i −0.515486 + 0.856898i \(0.672389\pi\)
−0.963571 + 0.267453i \(0.913818\pi\)
\(114\) −975.885 + 214.809i −0.801755 + 0.176480i
\(115\) 550.497 + 648.095i 0.446383 + 0.525523i
\(116\) 3267.82 355.397i 2.61560 0.284464i
\(117\) −428.341 −0.338463
\(118\) −1476.13 + 1388.18i −1.15160 + 1.08299i
\(119\) −2696.07 −2.07688
\(120\) −592.282 + 64.4146i −0.450564 + 0.0490018i
\(121\) −860.714 1013.31i −0.646667 0.761316i
\(122\) −996.723 + 219.395i −0.739665 + 0.162812i
\(123\) −199.188 + 151.419i −0.146018 + 0.111000i
\(124\) 1370.71 + 1298.41i 0.992690 + 0.940326i
\(125\) 519.805 + 1304.61i 0.371942 + 0.933505i
\(126\) 999.396 336.736i 0.706613 0.238086i
\(127\) 143.867 877.551i 0.100521 0.613150i −0.887737 0.460352i \(-0.847723\pi\)
0.988257 0.152798i \(-0.0488284\pi\)
\(128\) −1452.28 + 1375.67i −1.00285 + 0.949946i
\(129\) 809.129 + 374.343i 0.552247 + 0.255497i
\(130\) 1884.71 + 1432.72i 1.27154 + 0.966597i
\(131\) −107.955 658.498i −0.0720007 0.439185i −0.998084 0.0618668i \(-0.980295\pi\)
0.926084 0.377318i \(-0.123154\pi\)
\(132\) −20.4878 38.6441i −0.0135093 0.0254813i
\(133\) −1906.60 419.674i −1.24303 0.273612i
\(134\) −1179.28 + 545.594i −0.760258 + 0.351733i
\(135\) 111.180 279.042i 0.0708807 0.177897i
\(136\) 99.4230 1833.75i 0.0626872 1.15620i
\(137\) 49.0505 72.3441i 0.0305888 0.0451151i −0.812087 0.583536i \(-0.801669\pi\)
0.842676 + 0.538421i \(0.180979\pi\)
\(138\) 663.754 781.431i 0.409438 0.482028i
\(139\) 302.199 570.008i 0.184404 0.347823i −0.774024 0.633156i \(-0.781759\pi\)
0.958429 + 0.285333i \(0.0921041\pi\)
\(140\) −3313.36 1116.40i −2.00021 0.673950i
\(141\) 8.38987 + 154.742i 0.00501102 + 0.0924229i
\(142\) 463.648 + 278.968i 0.274003 + 0.164862i
\(143\) −15.4797 + 55.7528i −0.00905228 + 0.0326034i
\(144\) −38.8188 139.813i −0.0224646 0.0809102i
\(145\) 2612.86 1572.11i 1.49646 0.900390i
\(146\) 2604.80 + 3841.79i 1.47654 + 2.17773i
\(147\) 1025.34 + 111.512i 0.575297 + 0.0625673i
\(148\) 410.625 + 44.6582i 0.228062 + 0.0248032i
\(149\) −794.997 1172.53i −0.437105 0.644682i 0.543789 0.839222i \(-0.316989\pi\)
−0.980895 + 0.194540i \(0.937679\pi\)
\(150\) 14.1825 8.53331i 0.00771996 0.00464494i
\(151\) −617.169 2222.84i −0.332613 1.19796i −0.921058 0.389426i \(-0.872674\pi\)
0.588445 0.808537i \(-0.299740\pi\)
\(152\) 355.754 1281.31i 0.189838 0.683736i
\(153\) 793.357 + 477.347i 0.419210 + 0.252230i
\(154\) −7.71258 142.250i −0.00403570 0.0744341i
\(155\) 1659.81 + 559.255i 0.860123 + 0.289809i
\(156\) 802.043 1512.81i 0.411633 0.776423i
\(157\) −1005.40 + 1183.65i −0.511082 + 0.601693i −0.955814 0.293971i \(-0.905023\pi\)
0.444732 + 0.895664i \(0.353299\pi\)
\(158\) 1965.42 2898.77i 0.989622 1.45958i
\(159\) 97.8870 1805.42i 0.0488235 0.900497i
\(160\) −884.893 + 2220.91i −0.437231 + 1.09737i
\(161\) 1817.97 841.083i 0.889914 0.411718i
\(162\) −353.706 77.8566i −0.171542 0.0377592i
\(163\) −782.046 1475.10i −0.375795 0.708824i 0.621414 0.783482i \(-0.286558\pi\)
−0.997209 + 0.0746577i \(0.976214\pi\)
\(164\) −161.813 987.014i −0.0770454 0.469956i
\(165\) −32.3021 24.5554i −0.0152407 0.0115857i
\(166\) −3985.33 1843.81i −1.86338 0.862093i
\(167\) 1704.39 1614.49i 0.789760 0.748100i −0.182196 0.983262i \(-0.558321\pi\)
0.971956 + 0.235162i \(0.0755620\pi\)
\(168\) −227.052 + 1384.96i −0.104270 + 0.636022i
\(169\) −64.5723 + 21.7569i −0.0293911 + 0.00990302i
\(170\) −1894.15 4753.96i −0.854556 2.14477i
\(171\) 486.739 + 461.064i 0.217672 + 0.206190i
\(172\) −2837.15 + 2156.74i −1.25774 + 0.956106i
\(173\) −3333.01 + 733.651i −1.46476 + 0.322419i −0.874592 0.484859i \(-0.838871\pi\)
−0.590171 + 0.807278i \(0.700940\pi\)
\(174\) −2380.26 2802.26i −1.03705 1.22091i
\(175\) 32.1477 3.49628i 0.0138865 0.00151025i
\(176\) −19.6009 −0.00839472
\(177\) 1326.71 + 297.058i 0.563400 + 0.126148i
\(178\) 1576.30 0.663757
\(179\) −2731.69 + 297.089i −1.14065 + 0.124053i −0.658881 0.752247i \(-0.728970\pi\)
−0.481766 + 0.876300i \(0.660004\pi\)
\(180\) 777.340 + 915.155i 0.321886 + 0.378954i
\(181\) 2693.94 592.981i 1.10629 0.243514i 0.375981 0.926627i \(-0.377306\pi\)
0.730312 + 0.683114i \(0.239375\pi\)
\(182\) 4439.73 3375.00i 1.80821 1.37457i
\(183\) 497.132 + 470.909i 0.200815 + 0.190222i
\(184\) 505.027 + 1267.52i 0.202343 + 0.507842i
\(185\) 363.116 122.348i 0.144307 0.0486227i
\(186\) 341.658 2084.02i 0.134686 0.821547i
\(187\) 90.8022 86.0124i 0.0355086 0.0336356i
\(188\) −562.226 260.114i −0.218109 0.100908i
\(189\) −563.302 428.211i −0.216795 0.164803i
\(190\) −599.491 3656.73i −0.228903 1.39625i
\(191\) 938.470 + 1770.14i 0.355525 + 0.670592i 0.995179 0.0980712i \(-0.0312673\pi\)
−0.639654 + 0.768663i \(0.720922\pi\)
\(192\) 2437.28 + 536.486i 0.916124 + 0.201654i
\(193\) −1604.13 + 742.149i −0.598279 + 0.276793i −0.695565 0.718463i \(-0.744846\pi\)
0.0972863 + 0.995256i \(0.468984\pi\)
\(194\) 1445.61 3628.21i 0.534994 1.34273i
\(195\) 85.9961 1586.11i 0.0315811 0.582479i
\(196\) −2313.73 + 3412.49i −0.843194 + 1.24362i
\(197\) −1944.63 + 2289.39i −0.703294 + 0.827982i −0.991571 0.129565i \(-0.958642\pi\)
0.288277 + 0.957547i \(0.406918\pi\)
\(198\) −22.9163 + 43.2247i −0.00822520 + 0.0155144i
\(199\) −608.015 204.864i −0.216588 0.0729770i 0.208916 0.977934i \(-0.433007\pi\)
−0.425504 + 0.904957i \(0.639903\pi\)
\(200\) 1.19250 + 21.9944i 0.000421614 + 0.00777621i
\(201\) 747.022 + 449.468i 0.262144 + 0.157727i
\(202\) −611.254 + 2201.54i −0.212909 + 0.766830i
\(203\) −1921.72 6921.43i −0.664427 2.39305i
\(204\) −3171.40 + 1908.17i −1.08844 + 0.654895i
\(205\) −520.699 767.973i −0.177401 0.261647i
\(206\) 6779.68 + 737.335i 2.29302 + 0.249381i
\(207\) −683.879 74.3764i −0.229628 0.0249735i
\(208\) −430.611 635.104i −0.143546 0.211714i
\(209\) 77.6020 46.6916i 0.0256835 0.0154532i
\(210\) 1046.25 + 3768.27i 0.343802 + 1.23826i
\(211\) 270.273 973.436i 0.0881818 0.317602i −0.906283 0.422671i \(-0.861093\pi\)
0.994465 + 0.105069i \(0.0335063\pi\)
\(212\) 6193.08 + 3726.25i 2.00633 + 1.20717i
\(213\) −19.6553 362.520i −0.00632280 0.116617i
\(214\) −4868.00 1640.22i −1.55500 0.523940i
\(215\) −1548.60 + 2920.97i −0.491226 + 0.926551i
\(216\) 312.023 367.342i 0.0982894 0.115715i
\(217\) 2315.42 3414.99i 0.724336 1.06832i
\(218\) 391.577 7222.22i 0.121656 2.24381i
\(219\) 1152.71 2893.08i 0.355676 0.892678i
\(220\) 147.208 68.1059i 0.0451127 0.0208713i
\(221\) 4781.79 + 1052.55i 1.45547 + 0.320373i
\(222\) −216.408 408.188i −0.0654249 0.123404i
\(223\) 690.282 + 4210.54i 0.207286 + 1.26439i 0.861375 + 0.507970i \(0.169604\pi\)
−0.654089 + 0.756418i \(0.726948\pi\)
\(224\) 4483.36 + 3408.16i 1.33731 + 1.01660i
\(225\) −10.0790 4.66302i −0.00298636 0.00138164i
\(226\) −7244.44 + 6862.30i −2.13227 + 2.01979i
\(227\) −1019.58 + 6219.18i −0.298115 + 1.81842i 0.234560 + 0.972102i \(0.424635\pi\)
−0.532675 + 0.846320i \(0.678813\pi\)
\(228\) −2539.77 + 855.749i −0.737721 + 0.248567i
\(229\) 1639.61 + 4115.10i 0.473136 + 1.18748i 0.951039 + 0.309069i \(0.100018\pi\)
−0.477903 + 0.878412i \(0.658603\pi\)
\(230\) 2760.30 + 2614.70i 0.791344 + 0.749601i
\(231\) −76.0928 + 57.8443i −0.0216733 + 0.0164756i
\(232\) 4778.52 1051.83i 1.35226 0.297656i
\(233\) 711.804 + 838.000i 0.200137 + 0.235619i 0.853070 0.521796i \(-0.174738\pi\)
−0.652934 + 0.757415i \(0.726462\pi\)
\(234\) −1904.01 + 207.073i −0.531918 + 0.0578496i
\(235\) −574.679 −0.159523
\(236\) −3533.34 + 4129.45i −0.974579 + 1.13900i
\(237\) −2349.83 −0.644042
\(238\) −11984.2 + 1303.36i −3.26396 + 0.354977i
\(239\) 1187.10 + 1397.57i 0.321286 + 0.378247i 0.898968 0.438015i \(-0.144318\pi\)
−0.577682 + 0.816262i \(0.696042\pi\)
\(240\) 525.506 115.673i 0.141339 0.0311110i
\(241\) −2282.61 + 1735.19i −0.610107 + 0.463791i −0.864035 0.503432i \(-0.832070\pi\)
0.253928 + 0.967223i \(0.418277\pi\)
\(242\) −4315.80 4088.14i −1.14641 1.08593i
\(243\) 89.9436 + 225.741i 0.0237444 + 0.0595939i
\(244\) −2594.00 + 874.021i −0.680590 + 0.229317i
\(245\) −618.773 + 3774.35i −0.161355 + 0.984221i
\(246\) −812.204 + 769.361i −0.210505 + 0.199401i
\(247\) 3217.73 + 1488.68i 0.828905 + 0.383492i
\(248\) 2237.34 + 1700.78i 0.572868 + 0.435483i
\(249\) 476.652 + 2907.45i 0.121312 + 0.739968i
\(250\) 2941.26 + 5547.81i 0.744087 + 1.40350i
\(251\) 5086.57 + 1119.64i 1.27913 + 0.281558i 0.802026 0.597289i \(-0.203756\pi\)
0.477104 + 0.878847i \(0.341687\pi\)
\(252\) 2567.10 1187.67i 0.641715 0.296889i
\(253\) −34.3953 + 86.3257i −0.00854709 + 0.0214516i
\(254\) 215.265 3970.32i 0.0531768 0.980788i
\(255\) −1926.85 + 2841.89i −0.473192 + 0.697905i
\(256\) −1482.06 + 1744.82i −0.361832 + 0.425981i
\(257\) 3374.21 6364.43i 0.818977 1.54476i −0.0194940 0.999810i \(-0.506206\pi\)
0.838472 0.544945i \(-0.183450\pi\)
\(258\) 3777.60 + 1272.82i 0.911564 + 0.307142i
\(259\) −48.8673 901.304i −0.0117238 0.216233i
\(260\) 5440.78 + 3273.61i 1.29778 + 0.780848i
\(261\) −659.963 + 2376.97i −0.156516 + 0.563720i
\(262\) −798.206 2874.88i −0.188219 0.677903i
\(263\) −3707.80 + 2230.91i −0.869327 + 0.523056i −0.878959 0.476897i \(-0.841761\pi\)
0.00963252 + 0.999954i \(0.496934\pi\)
\(264\) −36.5371 53.8882i −0.00851781 0.0125628i
\(265\) 6665.64 + 724.932i 1.54516 + 0.168046i
\(266\) −8677.85 943.773i −2.00027 0.217543i
\(267\) −593.521 875.378i −0.136041 0.200645i
\(268\) −2986.18 + 1796.73i −0.680634 + 0.409524i
\(269\) −352.182 1268.45i −0.0798250 0.287504i 0.912854 0.408286i \(-0.133873\pi\)
−0.992679 + 0.120783i \(0.961460\pi\)
\(270\) 359.307 1294.11i 0.0809880 0.291692i
\(271\) −5683.00 3419.35i −1.27387 0.766459i −0.292069 0.956397i \(-0.594344\pi\)
−0.981796 + 0.189938i \(0.939171\pi\)
\(272\) 89.7960 + 1656.19i 0.0200172 + 0.369196i
\(273\) −3545.94 1194.77i −0.786118 0.264874i
\(274\) 183.059 345.287i 0.0403614 0.0761297i
\(275\) −0.971177 + 1.14336i −0.000212961 + 0.000250717i
\(276\) 1543.20 2276.06i 0.336558 0.496386i
\(277\) 14.1939 261.792i 0.00307881 0.0567854i −0.996590 0.0825097i \(-0.973706\pi\)
0.999669 + 0.0257243i \(0.00818921\pi\)
\(278\) 1067.74 2679.82i 0.230355 0.578146i
\(279\) −1285.98 + 594.957i −0.275948 + 0.127667i
\(280\) −5082.77 1118.80i −1.08483 0.238790i
\(281\) 60.7840 + 114.651i 0.0129042 + 0.0243398i 0.889880 0.456194i \(-0.150788\pi\)
−0.876976 + 0.480534i \(0.840443\pi\)
\(282\) 112.101 + 683.783i 0.0236720 + 0.144393i
\(283\) 3091.89 + 2350.40i 0.649449 + 0.493698i 0.877265 0.480006i \(-0.159366\pi\)
−0.227817 + 0.973704i \(0.573159\pi\)
\(284\) 1317.15 + 609.378i 0.275206 + 0.127324i
\(285\) −1804.99 + 1709.78i −0.375153 + 0.355364i
\(286\) −41.8557 + 255.308i −0.00865377 + 0.0527857i
\(287\) −2071.29 + 697.900i −0.426009 + 0.143539i
\(288\) −715.868 1796.69i −0.146468 0.367608i
\(289\) −4116.86 3899.70i −0.837953 0.793751i
\(290\) 10854.4 8251.27i 2.19790 1.67080i
\(291\) −2559.19 + 563.321i −0.515541 + 0.113479i
\(292\) 8059.40 + 9488.26i 1.61521 + 1.90157i
\(293\) −6048.19 + 657.781i −1.20594 + 0.131153i −0.688930 0.724828i \(-0.741919\pi\)
−0.517006 + 0.855982i \(0.672954\pi\)
\(294\) 4611.62 0.914813
\(295\) −1366.34 + 4853.05i −0.269665 + 0.957815i
\(296\) 614.830 0.120731
\(297\) 32.6329 3.54904i 0.00637559 0.000693388i
\(298\) −4100.66 4827.67i −0.797130 0.938454i
\(299\) −3552.74 + 782.018i −0.687158 + 0.151255i
\(300\) 35.3410 26.8656i 0.00680139 0.00517028i
\(301\) 5654.07 + 5355.82i 1.08271 + 1.02560i
\(302\) −3817.95 9582.33i −0.727478 1.82583i
\(303\) 1452.75 489.489i 0.275440 0.0928065i
\(304\) −194.303 + 1185.20i −0.0366581 + 0.223604i
\(305\) −1843.54 + 1746.29i −0.346100 + 0.327843i
\(306\) 3757.29 + 1738.31i 0.701928 + 0.324746i
\(307\) 4623.25 + 3514.51i 0.859489 + 0.653366i 0.939169 0.343454i \(-0.111597\pi\)
−0.0796808 + 0.996820i \(0.525390\pi\)
\(308\) −61.8149 377.054i −0.0114358 0.0697553i
\(309\) −2143.27 4042.64i −0.394584 0.744264i
\(310\) 7648.33 + 1683.52i 1.40128 + 0.308444i
\(311\) −3077.16 + 1423.65i −0.561060 + 0.259574i −0.679857 0.733345i \(-0.737958\pi\)
0.118797 + 0.992919i \(0.462096\pi\)
\(312\) 943.393 2367.74i 0.171183 0.429637i
\(313\) −485.614 + 8956.63i −0.0876950 + 1.61744i 0.541850 + 0.840475i \(0.317724\pi\)
−0.629545 + 0.776964i \(0.716759\pi\)
\(314\) −3896.87 + 5747.46i −0.700361 + 1.03295i
\(315\) 1698.71 1999.88i 0.303847 0.357716i
\(316\) 4399.91 8299.12i 0.783274 1.47741i
\(317\) 6685.76 + 2252.70i 1.18457 + 0.399129i 0.841540 0.540194i \(-0.181649\pi\)
0.343033 + 0.939323i \(0.388546\pi\)
\(318\) −437.680 8072.54i −0.0771820 1.42354i
\(319\) 285.536 + 171.801i 0.0501158 + 0.0301537i
\(320\) −2475.88 + 8917.31i −0.432518 + 1.55779i
\(321\) 922.062 + 3320.97i 0.160326 + 0.577440i
\(322\) 7674.40 4617.53i 1.32819 0.799146i
\(323\) −4300.76 6343.14i −0.740869 1.09270i
\(324\) −965.686 105.025i −0.165584 0.0180083i
\(325\) −58.3827 6.34950i −0.00996459 0.00108371i
\(326\) −4189.35 6178.84i −0.711739 1.04974i
\(327\) −4158.21 + 2501.91i −0.703209 + 0.423107i
\(328\) −398.298 1434.54i −0.0670498 0.241491i
\(329\) −362.166 + 1304.40i −0.0606896 + 0.218584i
\(330\) −155.456 93.5347i −0.0259320 0.0156028i
\(331\) −576.098 10625.5i −0.0956653 1.76444i −0.515545 0.856862i \(-0.672411\pi\)
0.419880 0.907580i \(-0.362072\pi\)
\(332\) −11161.0 3760.58i −1.84500 0.621653i
\(333\) −145.198 + 273.873i −0.0238944 + 0.0450696i
\(334\) 6795.65 8000.46i 1.11330 1.31068i
\(335\) −1814.31 + 2675.91i −0.295900 + 0.436420i
\(336\) 68.6238 1265.69i 0.0111421 0.205503i
\(337\) 1598.56 4012.09i 0.258396 0.648524i −0.741349 0.671120i \(-0.765814\pi\)
0.999745 + 0.0225956i \(0.00719301\pi\)
\(338\) −276.510 + 127.927i −0.0444976 + 0.0205868i
\(339\) 6538.62 + 1439.26i 1.04758 + 0.230589i
\(340\) −6429.06 12126.5i −1.02548 1.93427i
\(341\) 30.9659 + 188.883i 0.00491758 + 0.0299959i
\(342\) 2386.48 + 1814.16i 0.377328 + 0.286837i
\(343\) 18.9175 + 8.75217i 0.00297799 + 0.00137776i
\(344\) −3851.30 + 3648.15i −0.603629 + 0.571788i
\(345\) 412.708 2517.41i 0.0644042 0.392848i
\(346\) −14460.8 + 4872.41i −2.24687 + 0.757059i
\(347\) 925.489 + 2322.80i 0.143178 + 0.359351i 0.983025 0.183474i \(-0.0587343\pi\)
−0.839846 + 0.542824i \(0.817355\pi\)
\(348\) −7159.24 6781.59i −1.10280 1.04463i
\(349\) 7512.74 5711.03i 1.15229 0.875945i 0.158511 0.987357i \(-0.449331\pi\)
0.993774 + 0.111413i \(0.0355375\pi\)
\(350\) 141.209 31.0824i 0.0215655 0.00474693i
\(351\) 831.907 + 979.396i 0.126507 + 0.148935i
\(352\) −259.727 + 28.2471i −0.0393282 + 0.00427720i
\(353\) −858.428 −0.129432 −0.0647160 0.997904i \(-0.520614\pi\)
−0.0647160 + 0.997904i \(0.520614\pi\)
\(354\) 6040.94 + 679.071i 0.906984 + 0.101955i
\(355\) 1346.32 0.201283
\(356\) 4202.99 457.102i 0.625724 0.0680516i
\(357\) 5236.20 + 6164.53i 0.776272 + 0.913898i
\(358\) −11998.9 + 2641.16i −1.77140 + 0.389915i
\(359\) −3161.21 + 2403.09i −0.464742 + 0.353288i −0.811191 0.584781i \(-0.801180\pi\)
0.346449 + 0.938069i \(0.387387\pi\)
\(360\) 1297.59 + 1229.14i 0.189969 + 0.179948i
\(361\) 484.763 + 1216.66i 0.0706755 + 0.177382i
\(362\) 11688.1 3938.18i 1.69700 0.571784i
\(363\) −645.278 + 3936.02i −0.0933012 + 0.569112i
\(364\) 10859.2 10286.4i 1.56368 1.48119i
\(365\) 10481.4 + 4849.20i 1.50307 + 0.695394i
\(366\) 2437.44 + 1852.89i 0.348107 + 0.264624i
\(367\) −1302.52 7945.01i −0.185261 1.13004i −0.901690 0.432384i \(-0.857673\pi\)
0.716428 0.697661i \(-0.245776\pi\)
\(368\) −577.225 1088.76i −0.0817661 0.154227i
\(369\) 733.072 + 161.361i 0.103421 + 0.0227646i
\(370\) 1554.93 719.386i 0.218478 0.101079i
\(371\) 5846.17 14672.8i 0.818109 2.05330i
\(372\) 306.650 5655.83i 0.0427394 0.788282i
\(373\) −4466.85 + 6588.11i −0.620066 + 0.914529i −0.999945 0.0105074i \(-0.996655\pi\)
0.379879 + 0.925036i \(0.375966\pi\)
\(374\) 362.041 426.228i 0.0500553 0.0589297i
\(375\) 1973.44 3722.29i 0.271754 0.512582i
\(376\) −873.844 294.432i −0.119854 0.0403835i
\(377\) 706.260 + 13026.2i 0.0964834 + 1.77953i
\(378\) −2710.93 1631.11i −0.368876 0.221945i
\(379\) 1255.88 4523.26i 0.170211 0.613046i −0.828389 0.560154i \(-0.810742\pi\)
0.998600 0.0528926i \(-0.0168441\pi\)
\(380\) −2658.85 9576.33i −0.358938 1.29278i
\(381\) −2285.92 + 1375.39i −0.307379 + 0.184944i
\(382\) 5027.30 + 7414.72i 0.673349 + 0.993115i
\(383\) 2573.99 + 279.938i 0.343407 + 0.0373477i 0.278197 0.960524i \(-0.410263\pi\)
0.0652091 + 0.997872i \(0.479229\pi\)
\(384\) 5966.00 + 648.841i 0.792841 + 0.0862267i
\(385\) −198.915 293.377i −0.0263315 0.0388361i
\(386\) −6771.69 + 4074.39i −0.892927 + 0.537256i
\(387\) −715.527 2577.10i −0.0939853 0.338504i
\(388\) 2802.40 10093.3i 0.366676 1.32065i
\(389\) −6297.81 3789.27i −0.820853 0.493891i 0.0421370 0.999112i \(-0.486583\pi\)
−0.862990 + 0.505221i \(0.831411\pi\)
\(390\) −384.513 7091.92i −0.0499245 0.920804i
\(391\) 7451.73 + 2510.78i 0.963812 + 0.324746i
\(392\) −2874.65 + 5422.16i −0.370387 + 0.698624i
\(393\) −1295.98 + 1525.75i −0.166345 + 0.195836i
\(394\) −7537.24 + 11116.6i −0.963758 + 1.42144i
\(395\) 471.765 8701.19i 0.0600939 1.10837i
\(396\) −48.5686 + 121.898i −0.00616329 + 0.0154687i
\(397\) −9918.63 + 4588.85i −1.25391 + 0.580120i −0.930553 0.366158i \(-0.880673\pi\)
−0.323356 + 0.946278i \(0.604811\pi\)
\(398\) −2801.70 616.702i −0.352856 0.0776695i
\(399\) 2743.34 + 5174.49i 0.344207 + 0.649244i
\(400\) −3.21848 19.6318i −0.000402310 0.00245398i
\(401\) 2304.97 + 1752.19i 0.287044 + 0.218205i 0.738780 0.673947i \(-0.235402\pi\)
−0.451737 + 0.892151i \(0.649195\pi\)
\(402\) 3537.85 + 1636.78i 0.438935 + 0.203073i
\(403\) −5439.88 + 5152.93i −0.672407 + 0.636937i
\(404\) −991.413 + 6047.35i −0.122091 + 0.744720i
\(405\) −853.956 + 287.731i −0.104774 + 0.0353024i
\(406\) −11888.2 29837.2i −1.45321 3.64728i
\(407\) 30.4000 + 28.7964i 0.00370239 + 0.00350709i
\(408\) −4385.94 + 3334.10i −0.532197 + 0.404566i
\(409\) −8236.49 + 1812.99i −0.995766 + 0.219185i −0.682820 0.730586i \(-0.739247\pi\)
−0.312946 + 0.949771i \(0.601316\pi\)
\(410\) −2685.80 3161.97i −0.323518 0.380875i
\(411\) −260.678 + 28.3504i −0.0312853 + 0.00340249i
\(412\) 18290.9 2.18720
\(413\) 10154.4 + 6159.73i 1.20984 + 0.733899i
\(414\) −3075.85 −0.365144
\(415\) −10861.7 + 1181.28i −1.28477 + 0.139727i
\(416\) −6621.21 7795.09i −0.780364 0.918716i
\(417\) −1890.23 + 416.072i −0.221979 + 0.0488612i
\(418\) 322.374 245.063i 0.0377221 0.0286756i
\(419\) 3942.98 + 3734.99i 0.459730 + 0.435480i 0.882184 0.470905i \(-0.156072\pi\)
−0.422454 + 0.906385i \(0.638831\pi\)
\(420\) 3882.43 + 9744.17i 0.451055 + 1.13206i
\(421\) 1248.51 420.671i 0.144533 0.0486989i −0.246105 0.969243i \(-0.579151\pi\)
0.390638 + 0.920544i \(0.372254\pi\)
\(422\) 730.794 4457.65i 0.0842998 0.514206i
\(423\) 337.521 319.717i 0.0387963 0.0367498i
\(424\) 9764.21 + 4517.40i 1.11838 + 0.517416i
\(425\) 101.058 + 76.8225i 0.0115342 + 0.00876809i
\(426\) −262.622 1601.92i −0.0298688 0.182191i
\(427\) 2801.92 + 5284.98i 0.317551 + 0.598965i
\(428\) −13455.5 2961.78i −1.51961 0.334493i
\(429\) 157.542 72.8867i 0.0177301 0.00820280i
\(430\) −5471.55 + 13732.6i −0.613632 + 1.54010i
\(431\) −477.478 + 8806.56i −0.0533626 + 0.984216i 0.842168 + 0.539216i \(0.181279\pi\)
−0.895530 + 0.445000i \(0.853204\pi\)
\(432\) −244.288 + 360.297i −0.0272067 + 0.0401269i
\(433\) 3879.75 4567.59i 0.430598 0.506939i −0.503481 0.864006i \(-0.667948\pi\)
0.934079 + 0.357068i \(0.116223\pi\)
\(434\) 8641.29 16299.2i 0.955749 1.80273i
\(435\) −8669.20 2920.99i −0.955532 0.321956i
\(436\) −1050.24 19370.6i −0.115361 2.12771i
\(437\) 4878.86 + 2935.51i 0.534068 + 0.321338i
\(438\) 3725.27 13417.2i 0.406394 1.46370i
\(439\) −3181.02 11457.0i −0.345836 1.24559i −0.908143 0.418659i \(-0.862500\pi\)
0.562308 0.826928i \(-0.309914\pi\)
\(440\) 206.878 124.474i 0.0224148 0.0134865i
\(441\) −1736.40 2561.00i −0.187496 0.276536i
\(442\) 21764.2 + 2367.00i 2.34213 + 0.254721i
\(443\) −7650.73 832.067i −0.820535 0.0892386i −0.311785 0.950153i \(-0.600927\pi\)
−0.508750 + 0.860914i \(0.669892\pi\)
\(444\) −695.389 1025.62i −0.0743282 0.109626i
\(445\) 3360.60 2022.00i 0.357995 0.215398i
\(446\) 5103.85 + 18382.4i 0.541871 + 1.95164i
\(447\) −1136.97 + 4095.00i −0.120306 + 0.433304i
\(448\) 18680.2 + 11239.5i 1.96999 + 1.18530i
\(449\) 1013.24 + 18688.0i 0.106498 + 1.96424i 0.233555 + 0.972344i \(0.424964\pi\)
−0.127057 + 0.991895i \(0.540553\pi\)
\(450\) −47.0559 15.8550i −0.00492941 0.00166091i
\(451\) 47.4950 89.5851i 0.00495887 0.00935343i
\(452\) −17326.3 + 20398.1i −1.80301 + 2.12267i
\(453\) −3883.86 + 5728.26i −0.402825 + 0.594122i
\(454\) −1525.58 + 28137.6i −0.157707 + 2.90873i
\(455\) 5136.01 12890.4i 0.529186 1.32816i
\(456\) −3620.63 + 1675.08i −0.371823 + 0.172024i
\(457\) −3718.10 818.417i −0.380581 0.0837722i 0.0205597 0.999789i \(-0.493455\pi\)
−0.401141 + 0.916016i \(0.631386\pi\)
\(458\) 9277.52 + 17499.3i 0.946529 + 1.78534i
\(459\) −449.378 2741.08i −0.0456975 0.278742i
\(460\) 8118.19 + 6171.29i 0.822853 + 0.625517i
\(461\) −13640.2 6310.65i −1.37807 0.637562i −0.415748 0.909480i \(-0.636480\pi\)
−0.962320 + 0.271918i \(0.912342\pi\)
\(462\) −310.274 + 293.907i −0.0312452 + 0.0295970i
\(463\) −335.207 + 2044.67i −0.0336466 + 0.205235i −0.998300 0.0582873i \(-0.981436\pi\)
0.964653 + 0.263523i \(0.0848843\pi\)
\(464\) −4187.81 + 1411.04i −0.418996 + 0.141176i
\(465\) −1944.89 4881.29i −0.193961 0.486806i
\(466\) 3569.13 + 3380.86i 0.354800 + 0.336085i
\(467\) 5307.71 4034.81i 0.525935 0.399805i −0.308237 0.951309i \(-0.599739\pi\)
0.834172 + 0.551504i \(0.185946\pi\)
\(468\) −5016.72 + 1104.26i −0.495509 + 0.109070i
\(469\) 4930.38 + 5804.50i 0.485424 + 0.571486i
\(470\) −2554.49 + 277.817i −0.250702 + 0.0272654i
\(471\) 4659.06 0.455792
\(472\) −4564.04 + 6679.41i −0.445078 + 0.651366i
\(473\) −361.292 −0.0351210
\(474\) −10445.2 + 1135.98i −1.01216 + 0.110079i
\(475\) 59.5077 + 70.0579i 0.00574822 + 0.00676732i
\(476\) −31576.3 + 6950.47i −3.04054 + 0.669274i
\(477\) −4318.18 + 3282.59i −0.414499 + 0.315094i
\(478\) 5952.38 + 5638.40i 0.569573 + 0.539528i
\(479\) −6912.00 17347.8i −0.659327 1.65479i −0.752060 0.659094i \(-0.770940\pi\)
0.0927338 0.995691i \(-0.470439\pi\)
\(480\) 6796.69 2290.07i 0.646303 0.217765i
\(481\) −265.199 + 1617.64i −0.0251394 + 0.153344i
\(482\) −9307.50 + 8816.54i −0.879554 + 0.833158i
\(483\) −5453.91 2523.25i −0.513792 0.237705i
\(484\) −12693.0 9648.95i −1.19205 0.906175i
\(485\) −1572.12 9589.53i −0.147189 0.897811i
\(486\) 508.936 + 959.954i 0.0475016 + 0.0895976i
\(487\) −11807.0 2598.93i −1.09862 0.241825i −0.371567 0.928406i \(-0.621180\pi\)
−0.727053 + 0.686581i \(0.759111\pi\)
\(488\) −3697.94 + 1710.85i −0.343028 + 0.158702i
\(489\) −1853.93 + 4653.01i −0.171447 + 0.430299i
\(490\) −925.853 + 17076.4i −0.0853588 + 1.57435i
\(491\) −9077.75 + 13388.7i −0.834365 + 1.23060i 0.136421 + 0.990651i \(0.456440\pi\)
−0.970786 + 0.239946i \(0.922870\pi\)
\(492\) −1942.53 + 2286.92i −0.178000 + 0.209558i
\(493\) 13208.4 24913.7i 1.20665 2.27597i
\(494\) 15022.7 + 5061.74i 1.36823 + 0.461009i
\(495\) 6.59019 + 121.549i 0.000598398 + 0.0110368i
\(496\) −2174.94 1308.62i −0.196890 0.118465i
\(497\) 848.461 3055.88i 0.0765768 0.275805i
\(498\) 3524.30 + 12693.4i 0.317124 + 1.14218i
\(499\) −10837.4 + 6520.63i −0.972239 + 0.584977i −0.910674 0.413126i \(-0.864437\pi\)
−0.0615655 + 0.998103i \(0.519609\pi\)
\(500\) 9451.24 + 13939.5i 0.845344 + 1.24679i
\(501\) −7001.70 761.481i −0.624377 0.0679051i
\(502\) 23151.4 + 2517.87i 2.05836 + 0.223861i
\(503\) −1257.29 1854.37i −0.111451 0.164378i 0.767873 0.640603i \(-0.221315\pi\)
−0.879324 + 0.476224i \(0.842005\pi\)
\(504\) 3607.65 2170.65i 0.318844 0.191842i
\(505\) 1520.87 + 5477.66i 0.134015 + 0.482679i
\(506\) −111.157 + 400.351i −0.00976588 + 0.0351735i
\(507\) 175.157 + 105.388i 0.0153432 + 0.00923167i
\(508\) −577.358 10648.7i −0.0504254 0.930042i
\(509\) 8764.04 + 2952.95i 0.763182 + 0.257146i 0.673862 0.738857i \(-0.264634\pi\)
0.0893196 + 0.996003i \(0.471531\pi\)
\(510\) −7191.12 + 13563.9i −0.624368 + 1.17768i
\(511\) 17612.1 20734.6i 1.52469 1.79500i
\(512\) 3236.38 4773.30i 0.279354 0.412016i
\(513\) 108.891 2008.38i 0.00937167 0.172850i
\(514\) 11921.8 29921.5i 1.02305 2.56767i
\(515\) 15399.8 7124.69i 1.31766 0.609615i
\(516\) 10441.6 + 2298.36i 0.890821 + 0.196085i
\(517\) −29.4167 55.4858i −0.00250241 0.00472004i
\(518\) −652.936 3982.73i −0.0553829 0.337821i
\(519\) 8150.72 + 6196.02i 0.689358 + 0.524036i
\(520\) 8578.10 + 3968.65i 0.723412 + 0.334686i
\(521\) 1107.63 1049.20i 0.0931402 0.0882271i −0.639713 0.768614i \(-0.720947\pi\)
0.732853 + 0.680387i \(0.238188\pi\)
\(522\) −1784.48 + 10884.9i −0.149626 + 0.912677i
\(523\) 14008.7 4720.07i 1.17123 0.394635i 0.334581 0.942367i \(-0.391405\pi\)
0.836654 + 0.547732i \(0.184509\pi\)
\(524\) −2961.98 7434.00i −0.246936 0.619763i
\(525\) −70.4302 66.7151i −0.00585491 0.00554606i
\(526\) −15402.9 + 11709.0i −1.27681 + 0.970603i
\(527\) 15818.0 3481.81i 1.30748 0.287799i
\(528\) 38.0680 + 44.8171i 0.00313768 + 0.00369396i
\(529\) 6287.67 683.825i 0.516780 0.0562032i
\(530\) 29979.7 2.45705
\(531\) −1897.47 3610.45i −0.155072 0.295066i
\(532\) −23412.0 −1.90796
\(533\) 3946.14 429.168i 0.320687 0.0348768i
\(534\) −3061.43 3604.19i −0.248092 0.292076i
\(535\) −12482.3 + 2747.57i −1.00871 + 0.222033i
\(536\) −4129.78 + 3139.38i −0.332798 + 0.252986i
\(537\) 5984.66 + 5668.97i 0.480925 + 0.455557i
\(538\) −2178.68 5468.07i −0.174590 0.438188i
\(539\) −396.090 + 133.458i −0.0316527 + 0.0106650i
\(540\) 582.772 3554.75i 0.0464417 0.283282i
\(541\) 11596.1 10984.4i 0.921545 0.872934i −0.0706660 0.997500i \(-0.522512\pi\)
0.992211 + 0.124566i \(0.0397538\pi\)
\(542\) −26914.3 12451.9i −2.13297 0.986817i
\(543\) −6587.91 5008.00i −0.520652 0.395789i
\(544\) 3576.63 + 21816.5i 0.281887 + 1.71944i
\(545\) −8429.50 15899.7i −0.662532 1.24967i
\(546\) −16339.6 3596.61i −1.28071 0.281906i
\(547\) 11128.9 5148.79i 0.869906 0.402461i 0.0664246 0.997791i \(-0.478841\pi\)
0.803481 + 0.595330i \(0.202979\pi\)
\(548\) 387.975 973.744i 0.0302436 0.0759056i
\(549\) 111.216 2051.27i 0.00864590 0.159464i
\(550\) −3.76422 + 5.55180i −0.000291830 + 0.000430418i
\(551\) 13218.8 15562.3i 1.02203 1.20323i
\(552\) 1917.33 3616.46i 0.147839 0.278853i
\(553\) −19452.6 6554.36i −1.49586 0.504014i
\(554\) −63.4651 1170.54i −0.00486710 0.0897684i
\(555\) −984.975 592.640i −0.0753331 0.0453264i
\(556\) 2069.87 7454.98i 0.157881 0.568636i
\(557\) −6062.98 21836.9i −0.461215 1.66115i −0.719051 0.694958i \(-0.755423\pi\)
0.257836 0.966189i \(-0.416991\pi\)
\(558\) −5428.64 + 3266.30i −0.411851 + 0.247802i
\(559\) −7937.23 11706.5i −0.600553 0.885749i
\(560\) 4672.95 + 508.214i 0.352622 + 0.0383499i
\(561\) −373.019 40.5682i −0.0280728 0.00305310i
\(562\) 325.615 + 480.245i 0.0244399 + 0.0360461i
\(563\) −4737.55 + 2850.49i −0.354643 + 0.213381i −0.681715 0.731618i \(-0.738766\pi\)
0.327072 + 0.944999i \(0.393938\pi\)
\(564\) 497.187 + 1790.70i 0.0371194 + 0.133692i
\(565\) −6642.16 + 23922.9i −0.494580 + 1.78132i
\(566\) 14879.9 + 8952.96i 1.10504 + 0.664878i
\(567\) 114.923 + 2119.64i 0.00851204 + 0.156995i
\(568\) 2047.19 + 689.778i 0.151229 + 0.0509550i
\(569\) 8523.13 16076.3i 0.627958 1.18445i −0.341658 0.939824i \(-0.610989\pi\)
0.969616 0.244630i \(-0.0786666\pi\)
\(570\) −7196.76 + 8472.68i −0.528841 + 0.622600i
\(571\) 14057.6 20733.4i 1.03028 1.51955i 0.186797 0.982399i \(-0.440189\pi\)
0.843485 0.537153i \(-0.180500\pi\)
\(572\) −37.5670 + 692.882i −0.00274607 + 0.0506483i
\(573\) 2224.75 5583.70i 0.162199 0.407089i
\(574\) −8869.65 + 4103.54i −0.644969 + 0.298394i
\(575\) −92.1099 20.2749i −0.00668043 0.00147047i
\(576\) −3506.92 6614.76i −0.253684 0.478498i
\(577\) 3669.57 + 22383.4i 0.264759 + 1.61496i 0.699656 + 0.714480i \(0.253337\pi\)
−0.434897 + 0.900480i \(0.643215\pi\)
\(578\) −20185.0 15344.2i −1.45257 1.10421i
\(579\) 4812.39 + 2226.45i 0.345416 + 0.159807i
\(580\) 26548.9 25148.4i 1.90066 1.80040i
\(581\) −4163.84 + 25398.3i −0.297324 + 1.81359i
\(582\) −11103.5 + 3741.19i −0.790813 + 0.266456i
\(583\) 271.208 + 680.682i 0.0192664 + 0.0483550i
\(584\) 13453.3 + 12743.6i 0.953256 + 0.902972i
\(585\) −3793.63 + 2883.84i −0.268115 + 0.203816i
\(586\) −26566.6 + 5847.76i −1.87279 + 0.412233i
\(587\) 13803.0 + 16250.2i 0.970549 + 1.14262i 0.989751 + 0.142804i \(0.0456117\pi\)
−0.0192016 + 0.999816i \(0.506112\pi\)
\(588\) 12296.2 1337.30i 0.862395 0.0937911i
\(589\) 11728.1 0.820455
\(590\) −3727.34 + 22232.7i −0.260089 + 1.55136i
\(591\) 9011.44 0.627210
\(592\) −552.041 + 60.0381i −0.0383256 + 0.00416816i
\(593\) −9156.20 10779.5i −0.634064 0.746478i 0.347486 0.937685i \(-0.387036\pi\)
−0.981550 + 0.191208i \(0.938760\pi\)
\(594\) 143.340 31.5514i 0.00990118 0.00217941i
\(595\) −23877.9 + 18151.5i −1.64521 + 1.25065i
\(596\) −12333.8 11683.2i −0.847670 0.802955i
\(597\) 712.442 + 1788.10i 0.0488414 + 0.122583i
\(598\) −15414.1 + 5193.63i −1.05406 + 0.355156i
\(599\) 1173.20 7156.20i 0.0800261 0.488137i −0.916155 0.400824i \(-0.868724\pi\)
0.996181 0.0873129i \(-0.0278280\pi\)
\(600\) 47.9739 45.4433i 0.00326421 0.00309203i
\(601\) −19172.7 8870.24i −1.30128 0.602038i −0.357906 0.933758i \(-0.616509\pi\)
−0.943378 + 0.331720i \(0.892371\pi\)
\(602\) 27721.9 + 21073.7i 1.87685 + 1.42674i
\(603\) −423.132 2580.99i −0.0285759 0.174305i
\(604\) −12958.8 24442.8i −0.872987 1.64663i
\(605\) −14445.2 3179.62i −0.970709 0.213669i
\(606\) 6220.94 2878.11i 0.417011 0.192930i
\(607\) −5725.32 + 14369.5i −0.382840 + 0.960855i 0.603682 + 0.797225i \(0.293700\pi\)
−0.986522 + 0.163630i \(0.947680\pi\)
\(608\) −866.674 + 15984.9i −0.0578096 + 1.06624i
\(609\) −12093.4 + 17836.5i −0.804682 + 1.18682i
\(610\) −7350.43 + 8653.60i −0.487886 + 0.574384i
\(611\) 1151.59 2172.12i 0.0762491 0.143821i
\(612\) 10522.4 + 3545.40i 0.695003 + 0.234174i
\(613\) 1248.21 + 23021.9i 0.0822428 + 1.51688i 0.690612 + 0.723226i \(0.257341\pi\)
−0.608369 + 0.793654i \(0.708176\pi\)
\(614\) 22249.7 + 13387.2i 1.46242 + 0.879908i
\(615\) −744.681 + 2682.10i −0.0488267 + 0.175858i
\(616\) −152.156 548.015i −0.00995216 0.0358444i
\(617\) 10503.6 6319.78i 0.685344 0.412358i −0.129859 0.991532i \(-0.541453\pi\)
0.815204 + 0.579174i \(0.196625\pi\)
\(618\) −11481.3 16933.7i −0.747324 1.10222i
\(619\) 13291.9 + 1445.58i 0.863082 + 0.0938658i 0.528942 0.848658i \(-0.322589\pi\)
0.334139 + 0.942524i \(0.391554\pi\)
\(620\) 20881.4 + 2270.99i 1.35261 + 0.147105i
\(621\) 1158.14 + 1708.13i 0.0748384 + 0.110378i
\(622\) −12990.0 + 7815.80i −0.837379 + 0.503834i
\(623\) −2471.67 8902.15i −0.158949 0.572484i
\(624\) −615.841 + 2218.06i −0.0395086 + 0.142297i
\(625\) 13254.9 + 7975.22i 0.848315 + 0.510414i
\(626\) 2171.32 + 40047.6i 0.138631 + 2.55691i
\(627\) −257.475 86.7535i −0.0163996 0.00552568i
\(628\) −8723.80 + 16454.8i −0.554327 + 1.04557i
\(629\) 2293.91 2700.60i 0.145412 0.171192i
\(630\) 6584.10 9710.82i 0.416376 0.614109i
\(631\) 1216.17 22430.9i 0.0767274 1.41515i −0.666196 0.745777i \(-0.732079\pi\)
0.742924 0.669376i \(-0.233439\pi\)
\(632\) 5175.34 12989.1i 0.325734 0.817532i
\(633\) −2750.66 + 1272.59i −0.172716 + 0.0799067i
\(634\) 30807.7 + 6781.29i 1.92986 + 0.424794i
\(635\) −4634.01 8740.67i −0.289598 0.546241i
\(636\) −3507.92 21397.4i −0.218708 1.33406i
\(637\) −13026.0 9902.11i −0.810219 0.615912i
\(638\) 1352.28 + 625.632i 0.0839143 + 0.0388229i
\(639\) −790.723 + 749.013i −0.0489523 + 0.0463701i
\(640\) −3600.36 + 21961.2i −0.222370 + 1.35640i
\(641\) −9606.52 + 3236.81i −0.591942 + 0.199449i −0.599300 0.800524i \(-0.704554\pi\)
0.00735804 + 0.999973i \(0.497658\pi\)
\(642\) 5704.09 + 14316.2i 0.350658 + 0.880085i
\(643\) 7045.59 + 6673.94i 0.432116 + 0.409322i 0.872598 0.488439i \(-0.162434\pi\)
−0.440481 + 0.897762i \(0.645192\pi\)
\(644\) 19123.7 14537.5i 1.17015 0.889528i
\(645\) 9686.39 2132.14i 0.591320 0.130159i
\(646\) −22183.6 26116.6i −1.35109 1.59063i
\(647\) 8333.19 906.289i 0.506355 0.0550694i 0.148623 0.988894i \(-0.452516\pi\)
0.357732 + 0.933824i \(0.383550\pi\)
\(648\) −1445.92 −0.0876562
\(649\) −538.507 + 116.497i −0.0325705 + 0.00704610i
\(650\) −262.585 −0.0158453
\(651\) −12305.2 + 1338.27i −0.740829 + 0.0805701i
\(652\) −12962.1 15260.2i −0.778581 0.916616i
\(653\) −1660.36 + 365.474i −0.0995024 + 0.0219021i −0.264443 0.964401i \(-0.585188\pi\)
0.164940 + 0.986304i \(0.447257\pi\)
\(654\) −17274.0 + 13131.4i −1.03282 + 0.785133i
\(655\) −5389.50 5105.20i −0.321504 0.304545i
\(656\) 497.705 + 1249.15i 0.0296221 + 0.0743460i
\(657\) −8853.74 + 2983.17i −0.525750 + 0.177146i
\(658\) −979.265 + 5973.25i −0.0580178 + 0.353893i
\(659\) −8756.21 + 8294.32i −0.517593 + 0.490290i −0.901318 0.433157i \(-0.857399\pi\)
0.383726 + 0.923447i \(0.374641\pi\)
\(660\) −441.625 204.318i −0.0260458 0.0120501i
\(661\) 18412.2 + 13996.6i 1.08344 + 0.823609i 0.985175 0.171551i \(-0.0548780\pi\)
0.0982640 + 0.995160i \(0.468671\pi\)
\(662\) −7697.48 46952.6i −0.451920 2.75659i
\(663\) −6880.36 12977.7i −0.403033 0.760201i
\(664\) −17121.3 3768.67i −1.00065 0.220260i
\(665\) −19711.4 + 9119.46i −1.14944 + 0.531785i
\(666\) −513.019 + 1287.58i −0.0298484 + 0.0749140i
\(667\) −1134.25 + 20919.9i −0.0658444 + 1.21443i
\(668\) 15799.7 23302.7i 0.915130 1.34972i
\(669\) 8286.70 9755.85i 0.478897 0.563801i
\(670\) −6771.13 + 12771.7i −0.390435 + 0.736438i
\(671\) −262.973 88.6059i −0.0151296 0.00509775i
\(672\) −914.683 16870.3i −0.0525070 0.968434i
\(673\) 1958.35 + 1178.30i 0.112167 + 0.0674889i 0.570532 0.821275i \(-0.306737\pi\)
−0.458365 + 0.888764i \(0.651565\pi\)
\(674\) 5166.16 18606.8i 0.295242 1.06336i
\(675\) 8.91300 + 32.1017i 0.000508239 + 0.00183051i
\(676\) −700.179 + 421.284i −0.0398372 + 0.0239693i
\(677\) −1589.27 2344.00i −0.0902226 0.133068i 0.779899 0.625905i \(-0.215270\pi\)
−0.870122 + 0.492837i \(0.835960\pi\)
\(678\) 29760.4 + 3236.64i 1.68575 + 0.183337i
\(679\) −22757.1 2474.98i −1.28621 0.139884i
\(680\) −11465.3 16910.1i −0.646581 0.953635i
\(681\) 16200.3 9747.38i 0.911594 0.548488i
\(682\) 228.957 + 824.630i 0.0128552 + 0.0463002i
\(683\) 7545.66 27177.0i 0.422733 1.52255i −0.379304 0.925272i \(-0.623836\pi\)
0.802037 0.597275i \(-0.203750\pi\)
\(684\) 6889.30 + 4145.15i 0.385115 + 0.231716i
\(685\) −52.6436 970.955i −0.00293637 0.0541581i
\(686\) 88.3207 + 29.7587i 0.00491560 + 0.00165626i
\(687\) 6224.74 11741.1i 0.345690 0.652040i
\(688\) 3101.76 3651.67i 0.171880 0.202353i
\(689\) −16097.2 + 23741.5i −0.890063 + 1.31274i
\(690\) 617.524 11389.6i 0.0340706 0.628396i
\(691\) −10710.0 + 26880.1i −0.589620 + 1.47984i 0.266901 + 0.963724i \(0.414000\pi\)
−0.856521 + 0.516112i \(0.827379\pi\)
\(692\) −37144.8 + 17185.0i −2.04051 + 0.944040i
\(693\) 280.044 + 61.6424i 0.0153507 + 0.00337894i
\(694\) 5236.78 + 9877.61i 0.286434 + 0.540272i
\(695\) −1161.18 7082.88i −0.0633756 0.386574i
\(696\) −11685.6 8883.20i −0.636413 0.483788i
\(697\) −7787.15 3602.72i −0.423184 0.195786i
\(698\) 30633.8 29017.8i 1.66118 1.57355i
\(699\) 533.640 3255.06i 0.0288757 0.176134i
\(700\) 367.500 123.825i 0.0198431 0.00668593i
\(701\) 5501.06 + 13806.6i 0.296394 + 0.743892i 0.999463 + 0.0327709i \(0.0104332\pi\)
−0.703069 + 0.711122i \(0.748188\pi\)
\(702\) 4171.35 + 3951.32i 0.224270 + 0.212440i
\(703\) 2042.58 1552.73i 0.109584 0.0833033i
\(704\) −987.710 + 217.411i −0.0528775 + 0.0116392i
\(705\) 1116.12 + 1314.00i 0.0596247 + 0.0701956i
\(706\) −3815.77 + 414.990i −0.203411 + 0.0221223i
\(707\) 13391.6 0.712369
\(708\) 16304.2 + 58.8714i 0.865467 + 0.00312503i
\(709\) 27996.0 1.48295 0.741474 0.670981i \(-0.234127\pi\)
0.741474 + 0.670981i \(0.234127\pi\)
\(710\) 5984.49 650.853i 0.316330 0.0344029i
\(711\) 4563.75 + 5372.86i 0.240723 + 0.283401i
\(712\) 6146.01 1352.84i 0.323499 0.0712075i
\(713\) −9579.93 + 7282.47i −0.503185 + 0.382512i
\(714\) 26255.4 + 24870.4i 1.37617 + 1.30357i
\(715\) 238.263 + 597.996i 0.0124623 + 0.0312780i
\(716\) −31227.5 + 10521.8i −1.62993 + 0.549186i
\(717\) 889.972 5428.59i 0.0463551 0.282754i
\(718\) −12890.1 + 12210.1i −0.669991 + 0.634649i
\(719\) −10159.4 4700.25i −0.526958 0.243797i 0.138327 0.990387i \(-0.455828\pi\)
−0.665284 + 0.746590i \(0.731690\pi\)
\(720\) −1285.10 976.908i −0.0665179 0.0505656i
\(721\) −6466.58 39444.4i −0.334020 2.03743i
\(722\) 2742.98 + 5173.81i 0.141389 + 0.266689i
\(723\) 8400.68 + 1849.13i 0.432123 + 0.0951174i
\(724\) 30022.7 13890.0i 1.54114 0.713006i
\(725\) −125.188 + 314.197i −0.00641290 + 0.0160952i
\(726\) −965.513 + 17807.8i −0.0493575 + 0.910346i
\(727\) 4132.28 6094.66i 0.210809 0.310919i −0.707554 0.706659i \(-0.750201\pi\)
0.918363 + 0.395740i \(0.129512\pi\)
\(728\) 14414.0 16969.5i 0.733817 0.863916i
\(729\) 341.470 644.080i 0.0173485 0.0327227i
\(730\) 48934.7 + 16488.0i 2.48103 + 0.835958i
\(731\) 1655.16 + 30527.7i 0.0837462 + 1.54461i
\(732\) 7036.40 + 4233.66i 0.355291 + 0.213771i
\(733\) 8288.68 29853.1i 0.417666 1.50430i −0.393413 0.919362i \(-0.628706\pi\)
0.811079 0.584936i \(-0.198881\pi\)
\(734\) −9630.64 34686.4i −0.484296 1.74428i
\(735\) 9831.74 5915.56i 0.493400 0.296869i
\(736\) −9217.74 13595.1i −0.461644 0.680875i
\(737\) −351.233 38.1989i −0.0175547 0.00190919i
\(738\) 3336.56 + 362.873i 0.166424 + 0.0180996i
\(739\) 2457.12 + 3623.98i 0.122309 + 0.180393i 0.883914 0.467649i \(-0.154899\pi\)
−0.761605 + 0.648041i \(0.775588\pi\)
\(740\) 3937.39 2369.05i 0.195596 0.117686i
\(741\) −2845.50 10248.6i −0.141069 0.508084i
\(742\) 18893.4 68047.8i 0.934768 3.36673i
\(743\) 16733.1 + 10068.0i 0.826217 + 0.497118i 0.864788 0.502138i \(-0.167453\pi\)
−0.0385708 + 0.999256i \(0.512280\pi\)
\(744\) −456.456 8418.83i −0.0224926 0.414851i
\(745\) −14935.1 5032.22i −0.734470 0.247472i
\(746\) −16670.6 + 31444.0i −0.818167 + 1.54323i
\(747\) 5722.11 6736.58i 0.280269 0.329958i
\(748\) 841.733 1241.46i 0.0411455 0.0606850i
\(749\) −1630.02 + 30063.9i −0.0795188 + 1.46664i
\(750\) 6972.59 17499.9i 0.339470 0.852007i
\(751\) −29991.1 + 13875.3i −1.45724 + 0.674192i −0.978967 0.204018i \(-0.934600\pi\)
−0.478275 + 0.878210i \(0.658738\pi\)
\(752\) 813.355 + 179.033i 0.0394415 + 0.00868173i
\(753\) −7318.89 13804.9i −0.354203 0.668098i
\(754\) 9436.63 + 57560.9i 0.455785 + 2.78017i
\(755\) −20431.4 15531.6i −0.984869 0.748678i
\(756\) −7701.30 3563.00i −0.370494 0.171409i
\(757\) −5771.54 + 5467.10i −0.277107 + 0.262490i −0.813613 0.581407i \(-0.802503\pi\)
0.536506 + 0.843897i \(0.319744\pi\)
\(758\) 3395.78 20713.4i 0.162718 0.992537i
\(759\) 264.184 89.0138i 0.0126341 0.00425691i
\(760\) −5475.76 13743.1i −0.261351 0.655941i
\(761\) 10709.5 + 10144.6i 0.510145 + 0.483235i 0.898929 0.438093i \(-0.144346\pi\)
−0.388784 + 0.921329i \(0.627105\pi\)
\(762\) −9496.17 + 7218.80i −0.451456 + 0.343188i
\(763\) −41401.5 + 9113.16i −1.96440 + 0.432396i
\(764\) 15554.8 + 18312.5i 0.736586 + 0.867176i
\(765\) 10240.2 1113.69i 0.483967 0.0526345i
\(766\) 11576.9 0.546071
\(767\) −15605.2 14889.3i −0.734642 0.700940i
\(768\) 6867.91 0.322688
\(769\) 29808.0 3241.81i 1.39779 0.152019i 0.622005 0.783013i \(-0.286318\pi\)
0.775788 + 0.630994i \(0.217353\pi\)
\(770\) −1026.02 1207.92i −0.0480196 0.0565331i
\(771\) −21105.4 + 4645.65i −0.985854 + 0.217003i
\(772\) −16874.3 + 12827.5i −0.786681 + 0.598019i
\(773\) 1347.57 + 1276.49i 0.0627022 + 0.0593947i 0.718409 0.695621i \(-0.244871\pi\)
−0.655707 + 0.755016i \(0.727629\pi\)
\(774\) −4426.42 11109.5i −0.205561 0.515919i
\(775\) −184.097 + 62.0297i −0.00853287 + 0.00287506i
\(776\) 2522.59 15387.1i 0.116695 0.711810i
\(777\) −1965.91 + 1862.21i −0.0907679 + 0.0859799i
\(778\) −29826.1 13799.0i −1.37444 0.635885i
\(779\) −4946.09 3759.92i −0.227487 0.172931i
\(780\) −3081.80 18798.1i −0.141469 0.862924i
\(781\) 68.9156 + 129.989i 0.00315748 + 0.00595565i
\(782\) 34337.3 + 7558.20i 1.57020 + 0.345628i
\(783\) 6716.67 3107.46i 0.306557 0.141828i
\(784\) 2051.61 5149.14i 0.0934587 0.234564i
\(785\) −935.378 + 17252.0i −0.0425288 + 0.784397i
\(786\) −5023.13 + 7408.56i −0.227950 + 0.336202i
\(787\) −8816.13 + 10379.1i −0.399315 + 0.470110i −0.924668 0.380774i \(-0.875657\pi\)
0.525353 + 0.850884i \(0.323933\pi\)
\(788\) −16873.4 + 31826.5i −0.762803 + 1.43880i
\(789\) 12302.1 + 4145.06i 0.555090 + 0.187032i
\(790\) −2109.39 38905.5i −0.0949985 1.75215i
\(791\) 50114.2 + 30152.7i 2.25266 + 1.35538i
\(792\) −52.2537 + 188.201i −0.00234439 + 0.00844372i
\(793\) −2906.26 10467.4i −0.130144 0.468736i
\(794\) −41870.6 + 25192.7i −1.87145 + 1.12601i
\(795\) −11288.2 16648.8i −0.503586 0.742733i
\(796\) −7649.19 831.899i −0.340601 0.0370426i
\(797\) −18943.0 2060.18i −0.841902 0.0915623i −0.323003 0.946398i \(-0.604692\pi\)
−0.518899 + 0.854836i \(0.673658\pi\)
\(798\) 14695.8 + 21674.7i 0.651913 + 0.961500i
\(799\) −4553.55 + 2739.78i −0.201618 + 0.121310i
\(800\) −70.9392 255.500i −0.00313510 0.0112916i
\(801\) −848.828 + 3057.20i −0.0374430 + 0.134858i
\(802\) 11092.8 + 6674.31i 0.488404 + 0.293863i
\(803\) 68.3265 + 1260.21i 0.00300273 + 0.0553821i
\(804\) 9907.82 + 3338.33i 0.434605 + 0.146435i
\(805\) 10438.3 19688.7i 0.457021 0.862032i
\(806\) −21689.6 + 25534.9i −0.947869 + 1.11592i
\(807\) −2216.29 + 3268.78i −0.0966754 + 0.142586i
\(808\) −493.844 + 9108.42i −0.0215017 + 0.396575i
\(809\) 12980.8 32579.3i 0.564128 1.41585i −0.319465 0.947598i \(-0.603503\pi\)
0.883593 0.468256i \(-0.155118\pi\)
\(810\) −3656.79 + 1691.81i −0.158625 + 0.0733880i
\(811\) 13403.0 + 2950.22i 0.580323 + 0.127739i 0.495425 0.868651i \(-0.335012\pi\)
0.0848984 + 0.996390i \(0.472943\pi\)
\(812\) −40350.6 76109.3i −1.74388 3.28930i
\(813\) 3219.00 + 19635.0i 0.138862 + 0.847023i
\(814\) 149.051 + 113.306i 0.00641799 + 0.00487883i
\(815\) −16857.4 7799.07i −0.724527 0.335202i
\(816\) 3612.46 3421.90i 0.154977 0.146802i
\(817\) −3581.49 + 21846.1i −0.153367 + 0.935495i
\(818\) −35735.3 + 12040.6i −1.52745 + 0.514659i
\(819\) 4154.97 + 10428.2i 0.177273 + 0.444921i
\(820\) −8078.25 7652.12i −0.344030 0.325883i
\(821\) 7815.53 5941.21i 0.332234 0.252558i −0.425736 0.904848i \(-0.639985\pi\)
0.757970 + 0.652290i \(0.226192\pi\)
\(822\) −1145.02 + 252.039i −0.0485855 + 0.0106945i
\(823\) 4839.60 + 5697.62i 0.204979 + 0.241320i 0.855040 0.518562i \(-0.173532\pi\)
−0.650061 + 0.759882i \(0.725257\pi\)
\(824\) 27066.8 2943.70i 1.14432 0.124452i
\(825\) 4.50045 0.000189922
\(826\) 48114.7 + 22471.5i 2.02678 + 0.946589i
\(827\) −32276.2 −1.35714 −0.678569 0.734537i \(-0.737400\pi\)
−0.678569 + 0.734537i \(0.737400\pi\)
\(828\) −8201.32 + 891.947i −0.344222 + 0.0374364i
\(829\) −6931.31 8160.17i −0.290391 0.341875i 0.597550 0.801831i \(-0.296141\pi\)
−0.887941 + 0.459957i \(0.847865\pi\)
\(830\) −47709.9 + 10501.7i −1.99522 + 0.439182i
\(831\) −626.151 + 475.987i −0.0261383 + 0.0198698i
\(832\) −28743.5 27227.3i −1.19772 1.13454i
\(833\) 13091.3 + 32856.6i 0.544520 + 1.36664i
\(834\) −8201.07 + 2763.26i −0.340504 + 0.114729i
\(835\) 4225.39 25773.7i 0.175121 1.06819i
\(836\) 788.502 746.909i 0.0326207 0.0309000i
\(837\) 3857.93 + 1784.87i 0.159319 + 0.0737086i
\(838\) 19332.4 + 14696.1i 0.796930 + 0.605810i
\(839\) 212.199 + 1294.36i 0.00873174 + 0.0532613i 0.990833 0.135092i \(-0.0431331\pi\)
−0.982101 + 0.188354i \(0.939685\pi\)
\(840\) 7313.42 + 13794.6i 0.300401 + 0.566617i
\(841\) 49555.0 + 10907.9i 2.03186 + 0.447246i
\(842\) 5346.34 2473.48i 0.218821 0.101237i
\(843\) 144.095 361.652i 0.00588719 0.0147757i
\(844\) 655.914 12097.6i 0.0267506 0.493385i
\(845\) −425.408 + 627.429i −0.0173189 + 0.0255435i
\(846\) 1345.74 1584.33i 0.0546899 0.0643859i
\(847\) −16320.5 + 30783.8i −0.662077 + 1.24881i
\(848\) −9208.18 3102.60i −0.372889 0.125641i
\(849\) −630.799 11634.4i −0.0254994 0.470309i
\(850\) 486.349 + 292.627i 0.0196255 + 0.0118082i
\(851\) −704.296 + 2536.64i −0.0283701 + 0.102180i
\(852\) −1164.78 4195.15i −0.0468364 0.168690i
\(853\) 29418.7 17700.6i 1.18086 0.710502i 0.216810 0.976214i \(-0.430435\pi\)
0.964052 + 0.265712i \(0.0856071\pi\)
\(854\) 15009.6 + 22137.5i 0.601427 + 0.887039i
\(855\) 7414.98 + 806.427i 0.296593 + 0.0322564i
\(856\) −20388.1 2217.33i −0.814076 0.0885361i
\(857\) −13418.1 19790.2i −0.534834 0.788822i 0.460257 0.887786i \(-0.347757\pi\)
−0.995091 + 0.0989643i \(0.968447\pi\)
\(858\) 665.049 400.147i 0.0264620 0.0159217i
\(859\) 9787.56 + 35251.6i 0.388763 + 1.40020i 0.856417 + 0.516285i \(0.172685\pi\)
−0.467654 + 0.883912i \(0.654901\pi\)
\(860\) −10606.9 + 38202.6i −0.420573 + 1.51477i
\(861\) 5618.52 + 3380.55i 0.222391 + 0.133808i
\(862\) 2134.94 + 39376.6i 0.0843576 + 1.55588i
\(863\) −33840.7 11402.3i −1.33482 0.449753i −0.440730 0.897640i \(-0.645280\pi\)
−0.894091 + 0.447886i \(0.852177\pi\)
\(864\) −2717.78 + 5126.28i −0.107015 + 0.201851i
\(865\) −24579.6 + 28937.4i −0.966164 + 1.13746i
\(866\) 15037.6 22178.9i 0.590069 0.870287i
\(867\) −921.007 + 16987.0i −0.0360773 + 0.665407i
\(868\) 18314.3 45965.4i 0.716160 1.79743i
\(869\) 864.257 399.848i 0.0337375 0.0156086i
\(870\) −39947.3 8793.06i −1.55671 0.342658i
\(871\) −6478.52 12219.8i −0.252028 0.475375i
\(872\) −4671.61 28495.6i −0.181423 1.10663i
\(873\) 6258.38 + 4757.50i 0.242628 + 0.184441i
\(874\) 23106.0 + 10690.0i 0.894247 + 0.413723i
\(875\) 26719.3 25309.8i 1.03232 0.977861i
\(876\) 6042.14 36855.4i 0.233042 1.42149i
\(877\) 14654.5 4937.66i 0.564248 0.190117i −0.0226993 0.999742i \(-0.507226\pi\)
0.586948 + 0.809625i \(0.300329\pi\)
\(878\) −19678.5 49389.4i −0.756399 1.89842i
\(879\) 13250.6 + 12551.6i 0.508453 + 0.481632i
\(880\) −173.596 + 131.964i −0.00664991 + 0.00505513i
\(881\) 12015.7 2644.86i 0.459500 0.101144i 0.0208126 0.999783i \(-0.493375\pi\)
0.438687 + 0.898640i \(0.355444\pi\)
\(882\) −8956.49 10544.4i −0.341928 0.402549i
\(883\) −21805.9 + 2371.54i −0.831062 + 0.0903835i −0.513752 0.857938i \(-0.671745\pi\)
−0.317310 + 0.948322i \(0.602779\pi\)
\(884\) 58717.7 2.23404
\(885\) 13750.1 6301.28i 0.522264 0.239339i
\(886\) −34410.3 −1.30478
\(887\) −20132.3 + 2189.52i −0.762094 + 0.0828827i −0.480908 0.876771i \(-0.659693\pi\)
−0.281185 + 0.959653i \(0.590728\pi\)
\(888\) −1194.10 1405.80i −0.0451253 0.0531256i
\(889\) −22759.9 + 5009.84i −0.858654 + 0.189004i
\(890\) 13960.6 10612.6i 0.525798 0.399701i
\(891\) −71.4931 67.7218i −0.00268811 0.00254631i
\(892\) 18939.3 + 47534.1i 0.710914 + 1.78426i
\(893\) −3646.65 + 1228.70i −0.136652 + 0.0460435i
\(894\) −3074.27 + 18752.2i −0.115010 + 0.701529i
\(895\) −22193.1 + 21022.5i −0.828866 + 0.785143i
\(896\) 47578.6 + 22012.2i 1.77398 + 0.820732i
\(897\) 8688.06 + 6604.49i 0.323396 + 0.245839i
\(898\) 13538.3 + 82579.8i 0.503094 + 3.06874i
\(899\) 20213.5 + 38126.6i 0.749896 + 1.41445i
\(900\) −130.066 28.6296i −0.00481725 0.00106036i
\(901\) 56272.3 26034.3i 2.08069 0.962630i
\(902\) 167.810 421.172i 0.00619454 0.0155471i
\(903\) 1264.91 23329.8i 0.0466151 0.859765i
\(904\) −22356.6 + 32973.6i −0.822534 + 1.21315i
\(905\) 19866.7 23388.9i 0.729716 0.859088i
\(906\) −14494.8 + 27340.1i −0.531520 + 1.00255i
\(907\) 3047.77 + 1026.91i 0.111576 + 0.0375944i 0.374536 0.927212i \(-0.377802\pi\)
−0.262960 + 0.964807i \(0.584699\pi\)
\(908\) 4091.72 + 75467.4i 0.149547 + 2.75823i
\(909\) −3940.68 2371.03i −0.143789 0.0865149i
\(910\) 16598.3 59781.7i 0.604646 2.17774i
\(911\) 12960.7 + 46680.1i 0.471357 + 1.69767i 0.691644 + 0.722239i \(0.256887\pi\)
−0.220287 + 0.975435i \(0.570699\pi\)
\(912\) 3087.31 1857.57i 0.112095 0.0674455i
\(913\) −670.043 988.239i −0.0242883 0.0358225i
\(914\) −16922.9 1840.47i −0.612428 0.0666055i
\(915\) 7573.31 + 823.647i 0.273624 + 0.0297584i
\(916\) 29811.7 + 43969.0i 1.07534 + 1.58600i
\(917\) −14984.3 + 9015.74i −0.539612 + 0.324674i
\(918\) −3322.64 11967.1i −0.119459 0.430253i
\(919\) −10634.7 + 38302.6i −0.381725 + 1.37485i 0.484324 + 0.874889i \(0.339066\pi\)
−0.866049 + 0.499960i \(0.833348\pi\)
\(920\) 13006.5 + 7825.74i 0.466099 + 0.280442i
\(921\) −943.223 17396.7i −0.0337462 0.622412i
\(922\) −63682.6 21457.2i −2.27470 0.766436i
\(923\) −2697.87 + 5088.71i −0.0962095 + 0.181470i
\(924\) −742.074 + 873.638i −0.0264204 + 0.0311045i
\(925\) −23.8502 + 35.1765i −0.000847774 + 0.00125037i
\(926\) −501.561 + 9250.75i −0.0177995 + 0.328292i
\(927\) −5080.86 + 12752.0i −0.180019 + 0.451813i
\(928\) −53458.5 + 24732.5i −1.89101 + 0.874876i
\(929\) 39278.2 + 8645.78i 1.38716 + 0.305338i 0.844924 0.534887i \(-0.179646\pi\)
0.542239 + 0.840224i \(0.317577\pi\)
\(930\) −11004.9 20757.5i −0.388027 0.731897i
\(931\) 4143.33 + 25273.2i 0.145856 + 0.889685i
\(932\) 10497.0 + 7979.61i 0.368927 + 0.280451i
\(933\) 9231.48 + 4270.94i 0.323928 + 0.149865i
\(934\) 21642.6 20500.9i 0.758208 0.718213i
\(935\) 225.109 1373.11i 0.00787365 0.0480271i
\(936\) −7246.02 + 2441.47i −0.253038 + 0.0852584i
\(937\) −16122.3 40463.8i −0.562104 1.41077i −0.885557 0.464530i \(-0.846223\pi\)
0.323454 0.946244i \(-0.395156\pi\)
\(938\) 24722.0 + 23417.9i 0.860555 + 0.815161i
\(939\) 21422.3 16284.8i 0.744507 0.565959i
\(940\) −6730.62 + 1481.52i −0.233541 + 0.0514063i
\(941\) 25795.9 + 30369.3i 0.893647 + 1.05208i 0.998341 + 0.0575777i \(0.0183377\pi\)
−0.104694 + 0.994504i \(0.533386\pi\)
\(942\) 20709.8 2252.33i 0.716309 0.0779033i
\(943\) 6374.83 0.220141
\(944\) 3445.70 6442.96i 0.118801 0.222140i
\(945\) −7871.88 −0.270976
\(946\) −1605.97 + 174.660i −0.0551951 + 0.00600283i
\(947\) −12284.4 14462.3i −0.421530 0.496264i 0.509875 0.860249i \(-0.329692\pi\)
−0.931405 + 0.363985i \(0.881416\pi\)
\(948\) −27521.2 + 6057.86i −0.942875 + 0.207542i
\(949\) −39332.0 + 29899.4i −1.34539 + 1.02274i
\(950\) 298.384 + 282.645i 0.0101904 + 0.00965284i
\(951\) −7834.05 19662.0i −0.267126 0.670435i
\(952\) −45608.0 + 15367.1i −1.55269 + 0.523163i
\(953\) 1606.19 9797.31i 0.0545955 0.333018i −0.945380 0.325971i \(-0.894309\pi\)
0.999975 0.00704654i \(-0.00224300\pi\)
\(954\) −17607.7 + 16678.9i −0.597558 + 0.566037i
\(955\) 20229.2 + 9359.04i 0.685447 + 0.317122i
\(956\) 17506.2 + 13307.9i 0.592252 + 0.450218i
\(957\) −161.735 986.540i −0.00546306 0.0333232i
\(958\) −39110.8 73770.8i −1.31901 2.48792i
\(959\) −2237.05 492.411i −0.0753264 0.0165806i
\(960\) 25197.9 11657.8i 0.847143 0.391930i
\(961\) 1852.33 4649.01i 0.0621776 0.156054i
\(962\) −396.811 + 7318.75i −0.0132991 + 0.245287i
\(963\) 5802.56 8558.13i 0.194169 0.286378i
\(964\) −22260.5 + 26207.1i −0.743737 + 0.875595i
\(965\) −9210.48 + 17372.8i −0.307250 + 0.579534i
\(966\) −25462.8 8579.42i −0.848088 0.285754i
\(967\) −1742.95 32146.8i −0.0579623 1.06905i −0.872398 0.488797i \(-0.837436\pi\)
0.814435 0.580254i \(-0.197047\pi\)
\(968\) −20335.9 12235.7i −0.675229 0.406272i
\(969\) −6150.76 + 22153.0i −0.203912 + 0.734425i
\(970\) −11624.1 41866.1i −0.384770 1.38581i
\(971\) −6660.84 + 4007.69i −0.220140 + 0.132454i −0.621353 0.783531i \(-0.713417\pi\)
0.401212 + 0.915985i \(0.368589\pi\)
\(972\) 1635.38 + 2412.00i 0.0539658 + 0.0795936i
\(973\) −16808.5 1828.03i −0.553808 0.0602303i
\(974\) −53739.5 5844.52i −1.76789 0.192270i
\(975\) 98.8705 + 145.823i 0.00324758 + 0.00478982i
\(976\) 3153.23 1897.23i 0.103414 0.0622223i
\(977\) −9420.16 33928.3i −0.308472 1.11102i −0.941535 0.336916i \(-0.890616\pi\)
0.633062 0.774101i \(-0.281798\pi\)
\(978\) −5991.43 + 21579.2i −0.195895 + 0.705548i
\(979\) 367.249 + 220.966i 0.0119891 + 0.00721360i
\(980\) 2483.22 + 45800.2i 0.0809423 + 1.49289i
\(981\) 13796.5 + 4648.58i 0.449019 + 0.151292i
\(982\) −33878.7 + 63902.1i −1.10093 + 2.07658i
\(983\) 15486.6 18232.2i 0.502487 0.591573i −0.451182 0.892432i \(-0.648998\pi\)
0.953669 + 0.300859i \(0.0972734\pi\)
\(984\) −2506.50 + 3696.81i −0.0812034 + 0.119766i
\(985\) −1809.19 + 33368.5i −0.0585233 + 1.07940i
\(986\) 46668.2 117128.i 1.50732 3.78309i
\(987\) 3685.89 1705.27i 0.118868 0.0549944i
\(988\) 41523.8 + 9140.08i 1.33709 + 0.294317i
\(989\) −10639.7 20068.6i −0.342085 0.645242i
\(990\) 88.0542 + 537.107i 0.00282682 + 0.0172428i
\(991\) −12396.1 9423.29i −0.397352 0.302059i 0.387349 0.921933i \(-0.373391\pi\)
−0.784702 + 0.619874i \(0.787184\pi\)
\(992\) −30705.6 14205.9i −0.982765 0.454675i
\(993\) −23176.2 + 21953.6i −0.740659 + 0.701589i
\(994\) 2294.16 13993.8i 0.0732056 0.446534i
\(995\) −6764.17 + 2279.12i −0.215516 + 0.0726159i
\(996\) 13077.9 + 32823.1i 0.416054 + 1.04422i
\(997\) −11907.6 11279.5i −0.378254 0.358301i 0.474828 0.880079i \(-0.342510\pi\)
−0.853081 + 0.521778i \(0.825269\pi\)
\(998\) −45020.6 + 34223.8i −1.42796 + 1.08551i
\(999\) 908.206 199.911i 0.0287631 0.00633125i
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 177.4.e.a.133.14 yes 420
59.4 even 29 inner 177.4.e.a.4.14 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.e.a.4.14 420 59.4 even 29 inner
177.4.e.a.133.14 yes 420 1.1 even 1 trivial