Properties

Label 25.4.e.a.9.2
Level $25$
Weight $4$
Character 25.9
Analytic conductor $1.475$
Analytic rank $0$
Dimension $24$
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] = [25,4,Mod(4,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\), 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: \(1.47504775014\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.2
Character \(\chi\) \(=\) 25.9
Dual form 25.4.e.a.14.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.23725 + 3.07931i) q^{2} +(8.89950 - 2.89162i) q^{3} +(-2.00472 - 6.16988i) q^{4} +(-3.48187 + 10.6243i) q^{5} +(-11.0062 + 33.8735i) q^{6} -4.54748i q^{7} +(-5.47554 - 1.77911i) q^{8} +(48.9961 - 35.5978i) q^{9} +O(q^{10})\) \(q+(-2.23725 + 3.07931i) q^{2} +(8.89950 - 2.89162i) q^{3} +(-2.00472 - 6.16988i) q^{4} +(-3.48187 + 10.6243i) q^{5} +(-11.0062 + 33.8735i) q^{6} -4.54748i q^{7} +(-5.47554 - 1.77911i) q^{8} +(48.9961 - 35.5978i) q^{9} +(-24.9258 - 34.4910i) q^{10} +(10.9297 + 7.94089i) q^{11} +(-35.6819 - 49.1119i) q^{12} +(-40.2463 - 55.3943i) q^{13} +(14.0031 + 10.1738i) q^{14} +(-0.265365 + 104.620i) q^{15} +(59.7159 - 43.3861i) q^{16} +(-35.1667 - 11.4264i) q^{17} +230.515i q^{18} +(0.479342 - 1.47526i) q^{19} +(72.5311 + 0.183974i) q^{20} +(-13.1496 - 40.4703i) q^{21} +(-48.9049 + 15.8902i) q^{22} +(0.969915 - 1.33497i) q^{23} -53.8741 q^{24} +(-100.753 - 73.9852i) q^{25} +260.617 q^{26} +(184.600 - 254.080i) q^{27} +(-28.0574 + 9.11640i) q^{28} +(49.0853 + 151.069i) q^{29} +(-321.562 - 234.877i) q^{30} +(-83.6862 + 257.560i) q^{31} +234.890i q^{32} +(120.231 + 39.0654i) q^{33} +(113.862 - 82.7254i) q^{34} +(48.3140 + 15.8338i) q^{35} +(-317.857 - 230.937i) q^{36} +(81.9442 + 112.787i) q^{37} +(3.47038 + 4.77657i) q^{38} +(-518.351 - 376.604i) q^{39} +(37.9670 - 51.9793i) q^{40} +(80.5761 - 58.5420i) q^{41} +(154.039 + 50.0504i) q^{42} -135.690i q^{43} +(27.0834 - 83.3542i) q^{44} +(207.604 + 644.498i) q^{45} +(1.94085 + 5.97333i) q^{46} +(-171.103 + 55.5946i) q^{47} +(405.985 - 558.790i) q^{48} +322.320 q^{49} +(453.233 - 144.726i) q^{50} -346.007 q^{51} +(-261.094 + 359.365i) q^{52} +(-303.428 + 98.5897i) q^{53} +(369.395 + 1136.88i) q^{54} +(-122.423 + 88.4716i) q^{55} +(-8.09047 + 24.8999i) q^{56} -14.5152i q^{57} +(-575.004 - 186.830i) q^{58} +(-119.049 + 86.4944i) q^{59} +(646.022 - 208.095i) q^{60} +(180.319 + 131.009i) q^{61} +(-605.879 - 833.920i) q^{62} +(-161.880 - 222.809i) q^{63} +(-245.572 - 178.418i) q^{64} +(728.660 - 234.714i) q^{65} +(-389.280 + 282.829i) q^{66} +(842.149 + 273.631i) q^{67} +239.881i q^{68} +(4.77152 - 14.6852i) q^{69} +(-156.847 + 113.349i) q^{70} +(-163.685 - 503.769i) q^{71} +(-331.612 + 107.747i) q^{72} +(-210.474 + 289.693i) q^{73} -530.633 q^{74} +(-1110.59 - 367.091i) q^{75} -10.0631 q^{76} +(36.1110 - 49.7026i) q^{77} +(2319.36 - 753.605i) q^{78} +(-243.724 - 750.104i) q^{79} +(253.026 + 785.506i) q^{80} +(402.844 - 1239.83i) q^{81} +379.091i q^{82} +(-855.369 - 277.926i) q^{83} +(-223.336 + 162.263i) q^{84} +(243.843 - 333.838i) q^{85} +(417.832 + 303.573i) q^{86} +(873.669 + 1202.50i) q^{87} +(-45.7183 - 62.9258i) q^{88} +(68.1097 + 49.4846i) q^{89} +(-2449.07 - 802.624i) q^{90} +(-251.904 + 183.019i) q^{91} +(-10.1810 - 3.30802i) q^{92} +2534.14i q^{93} +(211.606 - 651.256i) q^{94} +(14.0047 + 10.2294i) q^{95} +(679.214 + 2090.40i) q^{96} +(851.962 - 276.819i) q^{97} +(-721.110 + 992.523i) q^{98} +818.191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23725 + 3.07931i −0.790986 + 1.08870i 0.202999 + 0.979179i \(0.434931\pi\)
−0.993985 + 0.109520i \(0.965069\pi\)
\(3\) 8.89950 2.89162i 1.71271 0.556493i 0.721928 0.691968i \(-0.243256\pi\)
0.990781 + 0.135475i \(0.0432561\pi\)
\(4\) −2.00472 6.16988i −0.250589 0.771235i
\(5\) −3.48187 + 10.6243i −0.311428 + 0.950270i
\(6\) −11.0062 + 33.8735i −0.748876 + 2.30480i
\(7\) 4.54748i 0.245541i −0.992435 0.122770i \(-0.960822\pi\)
0.992435 0.122770i \(-0.0391779\pi\)
\(8\) −5.47554 1.77911i −0.241987 0.0786263i
\(9\) 48.9961 35.5978i 1.81467 1.31844i
\(10\) −24.9258 34.4910i −0.788222 1.09070i
\(11\) 10.9297 + 7.94089i 0.299584 + 0.217661i 0.727414 0.686198i \(-0.240722\pi\)
−0.427830 + 0.903859i \(0.640722\pi\)
\(12\) −35.6819 49.1119i −0.858373 1.18145i
\(13\) −40.2463 55.3943i −0.858639 1.18182i −0.981892 0.189440i \(-0.939333\pi\)
0.123253 0.992375i \(-0.460667\pi\)
\(14\) 14.0031 + 10.1738i 0.267320 + 0.194219i
\(15\) −0.265365 + 104.620i −0.00456780 + 1.80084i
\(16\) 59.7159 43.3861i 0.933060 0.677908i
\(17\) −35.1667 11.4264i −0.501716 0.163017i 0.0472154 0.998885i \(-0.484965\pi\)
−0.548932 + 0.835867i \(0.684965\pi\)
\(18\) 230.515i 3.01849i
\(19\) 0.479342 1.47526i 0.00578782 0.0178131i −0.948121 0.317910i \(-0.897019\pi\)
0.953909 + 0.300097i \(0.0970190\pi\)
\(20\) 72.5311 + 0.183974i 0.810922 + 0.00205689i
\(21\) −13.1496 40.4703i −0.136642 0.420540i
\(22\) −48.9049 + 15.8902i −0.473934 + 0.153991i
\(23\) 0.969915 1.33497i 0.00879310 0.0121027i −0.804598 0.593820i \(-0.797619\pi\)
0.813391 + 0.581717i \(0.197619\pi\)
\(24\) −53.8741 −0.458208
\(25\) −100.753 73.9852i −0.806025 0.591882i
\(26\) 260.617 1.96581
\(27\) 184.600 254.080i 1.31579 1.81103i
\(28\) −28.0574 + 9.11640i −0.189370 + 0.0615299i
\(29\) 49.0853 + 151.069i 0.314307 + 0.967339i 0.976039 + 0.217597i \(0.0698220\pi\)
−0.661731 + 0.749741i \(0.730178\pi\)
\(30\) −321.562 234.877i −1.95696 1.42941i
\(31\) −83.6862 + 257.560i −0.484855 + 1.49223i 0.347337 + 0.937741i \(0.387086\pi\)
−0.832191 + 0.554489i \(0.812914\pi\)
\(32\) 234.890i 1.29760i
\(33\) 120.231 + 39.0654i 0.634228 + 0.206073i
\(34\) 113.862 82.7254i 0.574328 0.417273i
\(35\) 48.3140 + 15.8338i 0.233330 + 0.0764684i
\(36\) −317.857 230.937i −1.47156 1.06915i
\(37\) 81.9442 + 112.787i 0.364096 + 0.501135i 0.951284 0.308315i \(-0.0997652\pi\)
−0.587188 + 0.809450i \(0.699765\pi\)
\(38\) 3.47038 + 4.77657i 0.0148150 + 0.0203911i
\(39\) −518.351 376.604i −2.12827 1.54628i
\(40\) 37.9670 51.9793i 0.150078 0.205466i
\(41\) 80.5761 58.5420i 0.306924 0.222993i −0.423652 0.905825i \(-0.639252\pi\)
0.730575 + 0.682832i \(0.239252\pi\)
\(42\) 154.039 + 50.0504i 0.565923 + 0.183880i
\(43\) 135.690i 0.481223i −0.970622 0.240611i \(-0.922652\pi\)
0.970622 0.240611i \(-0.0773479\pi\)
\(44\) 27.0834 83.3542i 0.0927949 0.285593i
\(45\) 207.604 + 644.498i 0.687729 + 2.13502i
\(46\) 1.94085 + 5.97333i 0.00622094 + 0.0191461i
\(47\) −171.103 + 55.5946i −0.531019 + 0.172539i −0.562240 0.826974i \(-0.690060\pi\)
0.0312212 + 0.999512i \(0.490060\pi\)
\(48\) 405.985 558.790i 1.22081 1.68030i
\(49\) 322.320 0.939710
\(50\) 453.233 144.726i 1.28194 0.409348i
\(51\) −346.007 −0.950012
\(52\) −261.094 + 359.365i −0.696292 + 0.958363i
\(53\) −303.428 + 98.5897i −0.786397 + 0.255516i −0.674569 0.738212i \(-0.735670\pi\)
−0.111828 + 0.993728i \(0.535670\pi\)
\(54\) 369.395 + 1136.88i 0.930894 + 2.86500i
\(55\) −122.423 + 88.4716i −0.300136 + 0.216900i
\(56\) −8.09047 + 24.8999i −0.0193060 + 0.0594177i
\(57\) 14.5152i 0.0337295i
\(58\) −575.004 186.830i −1.30175 0.422965i
\(59\) −119.049 + 86.4944i −0.262693 + 0.190858i −0.711334 0.702855i \(-0.751908\pi\)
0.448640 + 0.893712i \(0.351908\pi\)
\(60\) 646.022 208.095i 1.39002 0.447749i
\(61\) 180.319 + 131.009i 0.378483 + 0.274984i 0.760720 0.649080i \(-0.224846\pi\)
−0.382237 + 0.924064i \(0.624846\pi\)
\(62\) −605.879 833.920i −1.24108 1.70819i
\(63\) −161.880 222.809i −0.323730 0.445576i
\(64\) −245.572 178.418i −0.479633 0.348474i
\(65\) 728.660 234.714i 1.39045 0.447888i
\(66\) −389.280 + 282.829i −0.726017 + 0.527482i
\(67\) 842.149 + 273.631i 1.53560 + 0.498945i 0.950157 0.311772i \(-0.100922\pi\)
0.585439 + 0.810717i \(0.300922\pi\)
\(68\) 239.881i 0.427792i
\(69\) 4.77152 14.6852i 0.00832498 0.0256216i
\(70\) −156.847 + 113.349i −0.267812 + 0.193541i
\(71\) −163.685 503.769i −0.273603 0.842062i −0.989586 0.143945i \(-0.954021\pi\)
0.715983 0.698118i \(-0.245979\pi\)
\(72\) −331.612 + 107.747i −0.542790 + 0.176363i
\(73\) −210.474 + 289.693i −0.337454 + 0.464466i −0.943696 0.330815i \(-0.892676\pi\)
0.606242 + 0.795281i \(0.292676\pi\)
\(74\) −530.633 −0.833580
\(75\) −1110.59 367.091i −1.70986 0.565174i
\(76\) −10.0631 −0.0151884
\(77\) 36.1110 49.7026i 0.0534446 0.0735602i
\(78\) 2319.36 753.605i 3.36687 1.09396i
\(79\) −243.724 750.104i −0.347102 1.06827i −0.960449 0.278456i \(-0.910177\pi\)
0.613347 0.789813i \(-0.289823\pi\)
\(80\) 253.026 + 785.506i 0.353614 + 1.09778i
\(81\) 402.844 1239.83i 0.552598 1.70072i
\(82\) 379.091i 0.510532i
\(83\) −855.369 277.926i −1.13119 0.367546i −0.317163 0.948371i \(-0.602730\pi\)
−0.814029 + 0.580825i \(0.802730\pi\)
\(84\) −223.336 + 162.263i −0.290094 + 0.210766i
\(85\) 243.843 333.838i 0.311159 0.425997i
\(86\) 417.832 + 303.573i 0.523907 + 0.380640i
\(87\) 873.669 + 1202.50i 1.07663 + 1.48186i
\(88\) −45.7183 62.9258i −0.0553816 0.0762263i
\(89\) 68.1097 + 49.4846i 0.0811192 + 0.0589366i 0.627606 0.778531i \(-0.284035\pi\)
−0.546486 + 0.837468i \(0.684035\pi\)
\(90\) −2449.07 802.624i −2.86838 0.940044i
\(91\) −251.904 + 183.019i −0.290184 + 0.210831i
\(92\) −10.1810 3.30802i −0.0115375 0.00374875i
\(93\) 2534.14i 2.82557i
\(94\) 211.606 651.256i 0.232186 0.714595i
\(95\) 14.0047 + 10.2294i 0.0151247 + 0.0110475i
\(96\) 679.214 + 2090.40i 0.722104 + 2.22241i
\(97\) 851.962 276.819i 0.891790 0.289760i 0.172946 0.984931i \(-0.444672\pi\)
0.718844 + 0.695171i \(0.244672\pi\)
\(98\) −721.110 + 992.523i −0.743297 + 1.02306i
\(99\) 818.191 0.830619
\(100\) −254.499 + 769.954i −0.254499 + 0.769954i
\(101\) −818.982 −0.806849 −0.403425 0.915013i \(-0.632180\pi\)
−0.403425 + 0.915013i \(0.632180\pi\)
\(102\) 774.102 1065.46i 0.751446 1.03428i
\(103\) 894.397 290.607i 0.855607 0.278004i 0.151814 0.988409i \(-0.451488\pi\)
0.703793 + 0.710405i \(0.251488\pi\)
\(104\) 121.818 + 374.916i 0.114858 + 0.353496i
\(105\) 475.755 + 1.20674i 0.442180 + 0.00112158i
\(106\) 375.255 1154.92i 0.343849 1.05826i
\(107\) 1461.83i 1.32075i −0.750937 0.660374i \(-0.770398\pi\)
0.750937 0.660374i \(-0.229602\pi\)
\(108\) −1937.72 629.602i −1.72645 0.560958i
\(109\) 289.623 210.424i 0.254504 0.184908i −0.453217 0.891400i \(-0.649724\pi\)
0.707720 + 0.706493i \(0.249724\pi\)
\(110\) 1.45825 574.909i 0.00126398 0.498322i
\(111\) 1055.40 + 766.791i 0.902468 + 0.655681i
\(112\) −197.297 271.557i −0.166454 0.229104i
\(113\) 509.732 + 701.585i 0.424350 + 0.584067i 0.966645 0.256121i \(-0.0824445\pi\)
−0.542295 + 0.840188i \(0.682444\pi\)
\(114\) 44.6967 + 32.4740i 0.0367213 + 0.0266796i
\(115\) 10.8061 + 14.9529i 0.00876238 + 0.0121249i
\(116\) 833.676 605.701i 0.667283 0.484810i
\(117\) −3943.82 1281.43i −3.11630 1.01255i
\(118\) 560.099i 0.436960i
\(119\) −51.9611 + 159.920i −0.0400275 + 0.123192i
\(120\) 187.583 572.376i 0.142699 0.435421i
\(121\) −354.901 1092.27i −0.266642 0.820641i
\(122\) −806.836 + 262.157i −0.598750 + 0.194546i
\(123\) 547.806 753.990i 0.401577 0.552723i
\(124\) 1756.88 1.27236
\(125\) 1136.85 812.828i 0.813466 0.581612i
\(126\) 1048.26 0.741163
\(127\) −1375.95 + 1893.83i −0.961384 + 1.32323i −0.0151035 + 0.999886i \(0.504808\pi\)
−0.946281 + 0.323346i \(0.895192\pi\)
\(128\) −688.341 + 223.656i −0.475323 + 0.154442i
\(129\) −392.365 1207.58i −0.267797 0.824194i
\(130\) −907.435 + 2768.88i −0.612210 + 1.86805i
\(131\) −470.086 + 1446.78i −0.313524 + 0.964926i 0.662834 + 0.748766i \(0.269353\pi\)
−0.976358 + 0.216160i \(0.930647\pi\)
\(132\) 820.125i 0.540778i
\(133\) −6.70873 2.17980i −0.00437384 0.00142115i
\(134\) −2726.69 + 1981.06i −1.75784 + 1.27714i
\(135\) 2056.68 + 2845.93i 1.31119 + 1.81436i
\(136\) 172.228 + 125.131i 0.108591 + 0.0788962i
\(137\) −1017.81 1400.90i −0.634727 0.873626i 0.363594 0.931558i \(-0.381550\pi\)
−0.998321 + 0.0579314i \(0.981550\pi\)
\(138\) 34.5452 + 47.5474i 0.0213093 + 0.0293298i
\(139\) 1132.98 + 823.160i 0.691355 + 0.502299i 0.877105 0.480298i \(-0.159472\pi\)
−0.185750 + 0.982597i \(0.559472\pi\)
\(140\) 0.836616 329.834i 0.000505050 0.199114i
\(141\) −1361.97 + 989.528i −0.813464 + 0.591017i
\(142\) 1917.46 + 623.021i 1.13317 + 0.368189i
\(143\) 925.034i 0.540946i
\(144\) 1381.40 4251.50i 0.799419 2.46036i
\(145\) −1775.92 4.50458i −1.01712 0.00257990i
\(146\) −421.171 1296.23i −0.238742 0.734772i
\(147\) 2868.49 932.029i 1.60945 0.522942i
\(148\) 531.604 731.691i 0.295254 0.406382i
\(149\) 3308.53 1.81910 0.909549 0.415596i \(-0.136427\pi\)
0.909549 + 0.415596i \(0.136427\pi\)
\(150\) 3615.05 2598.57i 1.96778 1.41448i
\(151\) −2045.43 −1.10235 −0.551173 0.834391i \(-0.685820\pi\)
−0.551173 + 0.834391i \(0.685820\pi\)
\(152\) −5.24931 + 7.22506i −0.00280116 + 0.00385546i
\(153\) −2129.78 + 692.009i −1.12538 + 0.365657i
\(154\) 72.2602 + 222.394i 0.0378110 + 0.116370i
\(155\) −2445.02 1785.90i −1.26702 0.925465i
\(156\) −1284.46 + 3953.15i −0.659223 + 2.02888i
\(157\) 2310.21i 1.17436i 0.809457 + 0.587180i \(0.199762\pi\)
−0.809457 + 0.587180i \(0.800238\pi\)
\(158\) 2855.07 + 927.668i 1.43758 + 0.467097i
\(159\) −2415.27 + 1754.80i −1.20468 + 0.875248i
\(160\) −2495.55 817.858i −1.23307 0.404109i
\(161\) −6.07077 4.41067i −0.00297170 0.00215907i
\(162\) 2916.54 + 4014.27i 1.41448 + 1.94686i
\(163\) −1074.35 1478.72i −0.516257 0.710567i 0.468702 0.883357i \(-0.344722\pi\)
−0.984959 + 0.172790i \(0.944722\pi\)
\(164\) −522.729 379.785i −0.248892 0.180831i
\(165\) −833.673 + 1141.35i −0.393341 + 0.538510i
\(166\) 2769.49 2012.15i 1.29490 0.940803i
\(167\) 1439.88 + 467.846i 0.667194 + 0.216784i 0.622980 0.782238i \(-0.285922\pi\)
0.0442138 + 0.999022i \(0.485922\pi\)
\(168\) 244.991i 0.112509i
\(169\) −769.851 + 2369.36i −0.350410 + 1.07845i
\(170\) 482.450 + 1497.75i 0.217660 + 0.675717i
\(171\) −29.0302 89.3457i −0.0129824 0.0399558i
\(172\) −837.193 + 272.020i −0.371136 + 0.120589i
\(173\) 2433.94 3350.03i 1.06965 1.47224i 0.199211 0.979957i \(-0.436162\pi\)
0.870434 0.492284i \(-0.163838\pi\)
\(174\) −5657.49 −2.46490
\(175\) −336.446 + 458.173i −0.145331 + 0.197912i
\(176\) 997.201 0.427084
\(177\) −809.370 + 1114.00i −0.343706 + 0.473071i
\(178\) −304.756 + 99.0213i −0.128328 + 0.0416964i
\(179\) −315.055 969.640i −0.131555 0.404884i 0.863483 0.504377i \(-0.168278\pi\)
−0.995038 + 0.0994931i \(0.968278\pi\)
\(180\) 3560.29 2572.93i 1.47427 1.06542i
\(181\) 1009.18 3105.94i 0.414430 1.27549i −0.498329 0.866988i \(-0.666053\pi\)
0.912759 0.408497i \(-0.133947\pi\)
\(182\) 1185.15i 0.482688i
\(183\) 1983.58 + 644.503i 0.801258 + 0.260345i
\(184\) −7.68588 + 5.58412i −0.00307940 + 0.00223732i
\(185\) −1483.60 + 477.894i −0.589603 + 0.189922i
\(186\) −7803.40 5669.50i −3.07620 2.23499i
\(187\) −293.626 404.142i −0.114824 0.158041i
\(188\) 686.024 + 944.232i 0.266135 + 0.366304i
\(189\) −1155.43 839.466i −0.444682 0.323080i
\(190\) −62.8313 + 20.2391i −0.0239909 + 0.00772788i
\(191\) −279.890 + 203.352i −0.106032 + 0.0770367i −0.639538 0.768760i \(-0.720874\pi\)
0.533506 + 0.845796i \(0.320874\pi\)
\(192\) −2701.39 877.733i −1.01539 0.329922i
\(193\) 1401.94i 0.522869i 0.965221 + 0.261434i \(0.0841955\pi\)
−0.965221 + 0.261434i \(0.915805\pi\)
\(194\) −1053.64 + 3242.76i −0.389932 + 1.20009i
\(195\) 5806.00 4195.85i 2.13219 1.54088i
\(196\) −646.161 1988.68i −0.235481 0.724737i
\(197\) 1371.47 445.616i 0.496004 0.161162i −0.0503235 0.998733i \(-0.516025\pi\)
0.546328 + 0.837571i \(0.316025\pi\)
\(198\) −1830.49 + 2519.46i −0.657008 + 0.904294i
\(199\) −180.474 −0.0642886 −0.0321443 0.999483i \(-0.510234\pi\)
−0.0321443 + 0.999483i \(0.510234\pi\)
\(200\) 420.050 + 584.360i 0.148510 + 0.206602i
\(201\) 8285.94 2.90769
\(202\) 1832.26 2521.90i 0.638206 0.878416i
\(203\) 686.984 223.214i 0.237521 0.0771753i
\(204\) 693.645 + 2134.82i 0.238063 + 0.732682i
\(205\) 341.414 + 1059.90i 0.116319 + 0.361107i
\(206\) −1106.12 + 3404.28i −0.374111 + 1.15140i
\(207\) 99.9353i 0.0335555i
\(208\) −4806.68 1561.79i −1.60232 0.520627i
\(209\) 16.9540 12.3178i 0.00561115 0.00407674i
\(210\) −1068.10 + 1462.30i −0.350980 + 0.480514i
\(211\) 1753.92 + 1274.30i 0.572250 + 0.415764i 0.835922 0.548848i \(-0.184934\pi\)
−0.263672 + 0.964612i \(0.584934\pi\)
\(212\) 1216.57 + 1674.47i 0.394125 + 0.542467i
\(213\) −2913.42 4009.98i −0.937203 1.28995i
\(214\) 4501.41 + 3270.46i 1.43790 + 1.04469i
\(215\) 1441.62 + 472.457i 0.457291 + 0.149866i
\(216\) −1462.82 + 1062.80i −0.460799 + 0.334790i
\(217\) 1171.25 + 380.562i 0.366403 + 0.119052i
\(218\) 1362.61i 0.423337i
\(219\) −1035.43 + 3186.73i −0.319489 + 0.983286i
\(220\) 791.282 + 577.972i 0.242492 + 0.177122i
\(221\) 782.375 + 2407.90i 0.238137 + 0.732909i
\(222\) −4722.37 + 1534.39i −1.42768 + 0.463881i
\(223\) −1321.79 + 1819.29i −0.396923 + 0.546318i −0.959969 0.280108i \(-0.909630\pi\)
0.563045 + 0.826426i \(0.309630\pi\)
\(224\) 1068.16 0.318613
\(225\) −7570.22 38.4037i −2.24303 0.0113789i
\(226\) −3300.79 −0.971528
\(227\) −624.114 + 859.019i −0.182484 + 0.251168i −0.890452 0.455076i \(-0.849612\pi\)
0.707968 + 0.706244i \(0.249612\pi\)
\(228\) −89.5569 + 29.0988i −0.0260134 + 0.00845226i
\(229\) −809.805 2492.32i −0.233683 0.719203i −0.997293 0.0735253i \(-0.976575\pi\)
0.763610 0.645678i \(-0.223425\pi\)
\(230\) −70.2205 0.178113i −0.0201313 5.10627e-5i
\(231\) 177.649 546.748i 0.0505993 0.155729i
\(232\) 914.513i 0.258796i
\(233\) 5838.56 + 1897.06i 1.64162 + 0.533393i 0.976899 0.213702i \(-0.0685521\pi\)
0.664717 + 0.747095i \(0.268552\pi\)
\(234\) 12769.2 9277.37i 3.56730 2.59180i
\(235\) 5.10194 2011.43i 0.00141623 0.558345i
\(236\) 772.320 + 561.123i 0.213024 + 0.154771i
\(237\) −4338.03 5970.79i −1.18897 1.63648i
\(238\) −376.192 517.784i −0.102458 0.141021i
\(239\) −1098.55 798.145i −0.297320 0.216016i 0.429117 0.903249i \(-0.358825\pi\)
−0.726437 + 0.687234i \(0.758825\pi\)
\(240\) 4523.19 + 6258.96i 1.21654 + 1.68339i
\(241\) −1999.56 + 1452.77i −0.534452 + 0.388302i −0.822021 0.569458i \(-0.807153\pi\)
0.287568 + 0.957760i \(0.407153\pi\)
\(242\) 4157.44 + 1350.84i 1.10434 + 0.358822i
\(243\) 3719.06i 0.981801i
\(244\) 446.824 1375.18i 0.117233 0.360808i
\(245\) −1122.28 + 3424.44i −0.292652 + 0.892978i
\(246\) 1096.19 + 3373.72i 0.284107 + 0.874393i
\(247\) −101.013 + 32.8211i −0.0260214 + 0.00845488i
\(248\) 916.455 1261.39i 0.234657 0.322978i
\(249\) −8416.01 −2.14194
\(250\) −40.4770 + 5319.22i −0.0102399 + 1.34567i
\(251\) −5820.65 −1.46373 −0.731865 0.681450i \(-0.761350\pi\)
−0.731865 + 0.681450i \(0.761350\pi\)
\(252\) −1050.18 + 1445.45i −0.262520 + 0.361328i
\(253\) 21.2018 6.88887i 0.00526855 0.00171186i
\(254\) −2753.35 8473.94i −0.680160 2.09332i
\(255\) 1204.75 3676.09i 0.295861 0.902768i
\(256\) 1601.69 4929.48i 0.391037 1.20349i
\(257\) 3408.82i 0.827378i 0.910418 + 0.413689i \(0.135760\pi\)
−0.910418 + 0.413689i \(0.864240\pi\)
\(258\) 4596.31 + 1493.43i 1.10912 + 0.360376i
\(259\) 512.894 372.640i 0.123049 0.0894004i
\(260\) −2908.91 4025.21i −0.693859 0.960126i
\(261\) 7782.71 + 5654.47i 1.84574 + 1.34101i
\(262\) −3403.37 4684.33i −0.802522 1.10458i
\(263\) 1808.74 + 2489.52i 0.424075 + 0.583690i 0.966581 0.256363i \(-0.0825241\pi\)
−0.542505 + 0.840052i \(0.682524\pi\)
\(264\) −588.827 427.808i −0.137272 0.0997340i
\(265\) 9.04762 3567.00i 0.00209732 0.826864i
\(266\) 21.7214 15.7815i 0.00500685 0.00363769i
\(267\) 749.232 + 243.440i 0.171731 + 0.0557989i
\(268\) 5744.51i 1.30934i
\(269\) 2239.41 6892.21i 0.507582 1.56218i −0.288805 0.957388i \(-0.593258\pi\)
0.796387 0.604788i \(-0.206742\pi\)
\(270\) −13364.8 33.8995i −3.01243 0.00764096i
\(271\) 347.203 + 1068.58i 0.0778268 + 0.239526i 0.982399 0.186794i \(-0.0598097\pi\)
−0.904572 + 0.426320i \(0.859810\pi\)
\(272\) −2595.75 + 843.412i −0.578642 + 0.188012i
\(273\) −1712.60 + 2357.19i −0.379675 + 0.522578i
\(274\) 6590.89 1.45318
\(275\) −513.692 1608.71i −0.112643 0.352759i
\(276\) −100.172 −0.0218465
\(277\) 580.951 799.610i 0.126014 0.173444i −0.741348 0.671120i \(-0.765813\pi\)
0.867363 + 0.497677i \(0.165813\pi\)
\(278\) −5069.52 + 1647.19i −1.09370 + 0.355366i
\(279\) 5068.25 + 15598.5i 1.08756 + 3.34715i
\(280\) −236.375 172.654i −0.0504504 0.0368502i
\(281\) −1539.49 + 4738.07i −0.326827 + 1.00587i 0.643782 + 0.765209i \(0.277365\pi\)
−0.970609 + 0.240662i \(0.922635\pi\)
\(282\) 6407.74i 1.35310i
\(283\) −3972.03 1290.59i −0.834320 0.271087i −0.139456 0.990228i \(-0.544535\pi\)
−0.694864 + 0.719141i \(0.744535\pi\)
\(284\) −2780.06 + 2019.83i −0.580866 + 0.422024i
\(285\) 154.214 + 50.5400i 0.0320521 + 0.0105043i
\(286\) 2848.46 + 2069.53i 0.588927 + 0.427881i
\(287\) −266.218 366.418i −0.0547539 0.0753623i
\(288\) 8361.56 + 11508.7i 1.71080 + 2.35471i
\(289\) −2868.57 2084.13i −0.583872 0.424208i
\(290\) 3987.04 5458.52i 0.807334 1.10529i
\(291\) 6781.57 4927.10i 1.36613 0.992549i
\(292\) 2209.31 + 717.849i 0.442775 + 0.143866i
\(293\) 4398.00i 0.876908i −0.898754 0.438454i \(-0.855526\pi\)
0.898754 0.438454i \(-0.144474\pi\)
\(294\) −3547.52 + 10918.1i −0.703726 + 2.16585i
\(295\) −504.431 1565.98i −0.0995563 0.309068i
\(296\) −248.029 763.355i −0.0487040 0.149896i
\(297\) 4035.25 1311.13i 0.788380 0.256160i
\(298\) −7402.01 + 10188.0i −1.43888 + 1.98045i
\(299\) −112.985 −0.0218532
\(300\) −38.4945 + 7588.11i −0.00740826 + 1.46033i
\(301\) −617.049 −0.118160
\(302\) 4576.12 6298.49i 0.871941 1.20012i
\(303\) −7288.53 + 2368.19i −1.38190 + 0.449006i
\(304\) −35.3816 108.893i −0.00667525 0.0205443i
\(305\) −2019.74 + 1459.61i −0.379179 + 0.274023i
\(306\) 2633.94 8106.45i 0.492067 1.51443i
\(307\) 7522.88i 1.39855i 0.714855 + 0.699273i \(0.246493\pi\)
−0.714855 + 0.699273i \(0.753507\pi\)
\(308\) −379.051 123.161i −0.0701249 0.0227849i
\(309\) 7119.36 5172.51i 1.31070 0.952279i
\(310\) 10969.4 3533.45i 2.00975 0.647376i
\(311\) −1641.91 1192.92i −0.299371 0.217506i 0.427951 0.903802i \(-0.359235\pi\)
−0.727322 + 0.686296i \(0.759235\pi\)
\(312\) 2168.23 + 2984.31i 0.393436 + 0.541518i
\(313\) 5314.68 + 7315.03i 0.959756 + 1.32099i 0.947055 + 0.321071i \(0.104043\pi\)
0.0127008 + 0.999919i \(0.495957\pi\)
\(314\) −7113.83 5168.50i −1.27852 0.928902i
\(315\) 2930.84 944.076i 0.524236 0.168866i
\(316\) −4139.46 + 3007.49i −0.736907 + 0.535394i
\(317\) −5959.78 1936.45i −1.05595 0.343098i −0.270946 0.962594i \(-0.587337\pi\)
−0.784999 + 0.619497i \(0.787337\pi\)
\(318\) 11363.3i 2.00384i
\(319\) −663.135 + 2040.92i −0.116390 + 0.358212i
\(320\) 2750.63 1987.81i 0.480515 0.347256i
\(321\) −4227.05 13009.5i −0.734987 2.26206i
\(322\) 27.1636 8.82599i 0.00470115 0.00152749i
\(323\) −33.7138 + 46.4030i −0.00580769 + 0.00799360i
\(324\) −8457.16 −1.45013
\(325\) −43.4186 + 8558.77i −0.00741056 + 1.46079i
\(326\) 6957.03 1.18195
\(327\) 1969.04 2710.15i 0.332991 0.458322i
\(328\) −545.350 + 177.195i −0.0918047 + 0.0298291i
\(329\) 252.815 + 778.086i 0.0423653 + 0.130387i
\(330\) −1649.44 5120.62i −0.275148 0.854184i
\(331\) 3252.86 10011.3i 0.540161 1.66244i −0.192064 0.981382i \(-0.561518\pi\)
0.732225 0.681063i \(-0.238482\pi\)
\(332\) 5834.68i 0.964518i
\(333\) 8029.89 + 2609.07i 1.32143 + 0.429358i
\(334\) −4662.01 + 3387.15i −0.763754 + 0.554900i
\(335\) −5839.41 + 7994.53i −0.952361 + 1.30384i
\(336\) −2541.09 1846.21i −0.412582 0.299759i
\(337\) 2314.77 + 3186.01i 0.374166 + 0.514995i 0.954027 0.299720i \(-0.0968934\pi\)
−0.579862 + 0.814715i \(0.696893\pi\)
\(338\) −5573.63 7671.44i −0.896939 1.23453i
\(339\) 6565.07 + 4769.81i 1.05182 + 0.764190i
\(340\) −2548.58 835.235i −0.406517 0.133226i
\(341\) −2959.92 + 2150.51i −0.470055 + 0.341515i
\(342\) 340.070 + 110.496i 0.0537687 + 0.0174705i
\(343\) 3025.53i 0.476278i
\(344\) −241.408 + 742.977i −0.0378368 + 0.116450i
\(345\) 139.407 + 101.826i 0.0217548 + 0.0158903i
\(346\) 4870.44 + 14989.7i 0.756752 + 2.32904i
\(347\) −10402.1 + 3379.85i −1.60926 + 0.522881i −0.969374 0.245588i \(-0.921019\pi\)
−0.639887 + 0.768469i \(0.721019\pi\)
\(348\) 5667.84 7801.11i 0.873069 1.20168i
\(349\) −2825.77 −0.433410 −0.216705 0.976237i \(-0.569531\pi\)
−0.216705 + 0.976237i \(0.569531\pi\)
\(350\) −658.140 2061.07i −0.100512 0.314768i
\(351\) −21504.1 −3.27009
\(352\) −1865.24 + 2567.28i −0.282436 + 0.388740i
\(353\) 1655.37 537.863i 0.249593 0.0810978i −0.181548 0.983382i \(-0.558111\pi\)
0.431142 + 0.902284i \(0.358111\pi\)
\(354\) −1619.59 4984.60i −0.243165 0.748385i
\(355\) 5922.14 + 15.0214i 0.885394 + 0.00224578i
\(356\) 168.773 519.431i 0.0251263 0.0773309i
\(357\) 1573.46i 0.233267i
\(358\) 3690.67 + 1199.17i 0.544855 + 0.177034i
\(359\) 3465.00 2517.47i 0.509403 0.370103i −0.303194 0.952929i \(-0.598053\pi\)
0.812597 + 0.582826i \(0.198053\pi\)
\(360\) 9.88803 3898.33i 0.00144762 0.570722i
\(361\) 5547.10 + 4030.20i 0.808733 + 0.587579i
\(362\) 7306.36 + 10056.3i 1.06081 + 1.46008i
\(363\) −6316.88 8694.44i −0.913362 1.25713i
\(364\) 1634.20 + 1187.32i 0.235317 + 0.170968i
\(365\) −2344.95 3244.83i −0.336275 0.465320i
\(366\) −6422.37 + 4666.13i −0.917221 + 0.666400i
\(367\) −2436.81 791.768i −0.346596 0.112616i 0.130546 0.991442i \(-0.458327\pi\)
−0.477141 + 0.878827i \(0.658327\pi\)
\(368\) 121.800i 0.0172534i
\(369\) 1863.95 5736.66i 0.262963 0.809318i
\(370\) 1847.60 5637.63i 0.259600 0.792125i
\(371\) 448.335 + 1379.83i 0.0627396 + 0.193093i
\(372\) 15635.3 5080.23i 2.17918 0.708059i
\(373\) 4827.71 6644.77i 0.670159 0.922394i −0.329605 0.944119i \(-0.606916\pi\)
0.999764 + 0.0217245i \(0.00691567\pi\)
\(374\) 1901.39 0.262884
\(375\) 7767.03 10521.1i 1.06957 1.44882i
\(376\) 1035.79 0.142066
\(377\) 6392.86 8799.01i 0.873339 1.20205i
\(378\) 5169.94 1679.82i 0.703474 0.228573i
\(379\) −3809.61 11724.8i −0.516324 1.58908i −0.780860 0.624706i \(-0.785219\pi\)
0.264536 0.964376i \(-0.414781\pi\)
\(380\) 35.0386 106.914i 0.00473011 0.0144331i
\(381\) −6769.01 + 20832.9i −0.910202 + 2.80131i
\(382\) 1316.81i 0.176372i
\(383\) −10243.5 3328.32i −1.36663 0.444044i −0.468378 0.883528i \(-0.655161\pi\)
−0.898251 + 0.439484i \(0.855161\pi\)
\(384\) −5479.16 + 3980.84i −0.728144 + 0.529028i
\(385\) 402.323 + 556.714i 0.0532579 + 0.0736955i
\(386\) −4316.99 3136.48i −0.569247 0.413582i
\(387\) −4830.27 6648.29i −0.634461 0.873260i
\(388\) −3415.88 4701.56i −0.446946 0.615169i
\(389\) 11921.6 + 8661.52i 1.55385 + 1.12894i 0.940835 + 0.338866i \(0.110043\pi\)
0.613014 + 0.790072i \(0.289957\pi\)
\(390\) −69.1587 + 27265.6i −0.00897945 + 3.54012i
\(391\) −49.3626 + 35.8640i −0.00638459 + 0.00463868i
\(392\) −1764.88 573.444i −0.227397 0.0738859i
\(393\) 14234.9i 1.82711i
\(394\) −1696.12 + 5220.12i −0.216876 + 0.667476i
\(395\) 8817.97 + 22.3666i 1.12324 + 0.00284908i
\(396\) −1640.24 5048.14i −0.208144 0.640602i
\(397\) −7758.71 + 2520.96i −0.980853 + 0.318699i −0.755189 0.655507i \(-0.772455\pi\)
−0.225664 + 0.974205i \(0.572455\pi\)
\(398\) 403.764 555.733i 0.0508514 0.0699910i
\(399\) −66.0075 −0.00828197
\(400\) −9226.49 46.8059i −1.15331 0.00585074i
\(401\) 9316.46 1.16020 0.580102 0.814544i \(-0.303013\pi\)
0.580102 + 0.814544i \(0.303013\pi\)
\(402\) −18537.7 + 25514.9i −2.29994 + 3.16560i
\(403\) 17635.4 5730.09i 2.17986 0.708278i
\(404\) 1641.83 + 5053.02i 0.202188 + 0.622270i
\(405\) 11769.7 + 8596.87i 1.44405 + 1.05477i
\(406\) −849.606 + 2614.82i −0.103855 + 0.319634i
\(407\) 1883.43i 0.229382i
\(408\) 1894.57 + 615.584i 0.229890 + 0.0746959i
\(409\) −2665.27 + 1936.43i −0.322223 + 0.234109i −0.737124 0.675758i \(-0.763816\pi\)
0.414900 + 0.909867i \(0.363816\pi\)
\(410\) −4027.59 1319.95i −0.485143 0.158994i
\(411\) −13108.9 9524.16i −1.57327 1.14305i
\(412\) −3586.02 4935.74i −0.428812 0.590209i
\(413\) 393.332 + 541.374i 0.0468634 + 0.0645019i
\(414\) 307.731 + 223.580i 0.0365318 + 0.0265419i
\(415\) 5931.07 8120.02i 0.701553 0.960473i
\(416\) 13011.6 9453.46i 1.53352 1.11417i
\(417\) 12463.2 + 4049.55i 1.46361 + 0.475557i
\(418\) 79.7644i 0.00933350i
\(419\) −1477.55 + 4547.42i −0.172274 + 0.530205i −0.999498 0.0316665i \(-0.989919\pi\)
0.827224 + 0.561872i \(0.189919\pi\)
\(420\) −946.308 2937.77i −0.109941 0.341306i
\(421\) −3954.74 12171.4i −0.457820 1.40902i −0.867793 0.496926i \(-0.834462\pi\)
0.409973 0.912098i \(-0.365538\pi\)
\(422\) −7847.90 + 2549.94i −0.905284 + 0.294145i
\(423\) −6404.32 + 8814.79i −0.736144 + 1.01321i
\(424\) 1836.83 0.210388
\(425\) 2697.77 + 3753.06i 0.307909 + 0.428353i
\(426\) 18866.0 2.14568
\(427\) 595.762 819.997i 0.0675198 0.0929331i
\(428\) −9019.29 + 2930.54i −1.01861 + 0.330965i
\(429\) −2674.85 8232.34i −0.301032 0.926483i
\(430\) −4680.10 + 3382.18i −0.524870 + 0.379310i
\(431\) −1927.52 + 5932.28i −0.215418 + 0.662989i 0.783706 + 0.621132i \(0.213327\pi\)
−0.999124 + 0.0418561i \(0.986673\pi\)
\(432\) 23181.7i 2.58178i
\(433\) −7246.14 2354.41i −0.804220 0.261307i −0.122072 0.992521i \(-0.538954\pi\)
−0.682148 + 0.731214i \(0.738954\pi\)
\(434\) −3792.24 + 2755.22i −0.419431 + 0.304735i
\(435\) −15817.8 + 5095.19i −1.74346 + 0.561600i
\(436\) −1878.90 1365.10i −0.206383 0.149946i
\(437\) −1.50452 2.07079i −0.000164693 0.000226680i
\(438\) −7496.41 10317.9i −0.817791 1.12559i
\(439\) −3502.24 2544.52i −0.380758 0.276637i 0.380900 0.924616i \(-0.375614\pi\)
−0.761658 + 0.647980i \(0.775614\pi\)
\(440\) 827.730 266.627i 0.0896829 0.0288885i
\(441\) 15792.4 11473.9i 1.70526 1.23895i
\(442\) −9165.03 2977.90i −0.986281 0.320462i
\(443\) 11381.7i 1.22067i 0.792142 + 0.610337i \(0.208966\pi\)
−0.792142 + 0.610337i \(0.791034\pi\)
\(444\) 2615.24 8048.88i 0.279535 0.860322i
\(445\) −762.890 + 551.321i −0.0812685 + 0.0587306i
\(446\) −2644.98 8140.42i −0.280815 0.864260i
\(447\) 29444.3 9567.03i 3.11559 1.01232i
\(448\) −811.354 + 1116.73i −0.0855645 + 0.117769i
\(449\) 1364.74 0.143443 0.0717216 0.997425i \(-0.477151\pi\)
0.0717216 + 0.997425i \(0.477151\pi\)
\(450\) 17054.7 23225.1i 1.78659 2.43298i
\(451\) 1345.55 0.140486
\(452\) 3306.83 4551.46i 0.344116 0.473634i
\(453\) −18203.3 + 5914.60i −1.88800 + 0.613448i
\(454\) −1248.89 3843.68i −0.129104 0.397341i
\(455\) −1067.36 3313.57i −0.109975 0.341412i
\(456\) −25.8241 + 79.4784i −0.00265203 + 0.00816210i
\(457\) 6981.47i 0.714615i −0.933987 0.357308i \(-0.883695\pi\)
0.933987 0.357308i \(-0.116305\pi\)
\(458\) 9486.36 + 3082.31i 0.967836 + 0.314469i
\(459\) −9394.99 + 6825.86i −0.955383 + 0.694126i
\(460\) 70.5946 96.6486i 0.00715541 0.00979623i
\(461\) −3680.64 2674.14i −0.371854 0.270168i 0.386125 0.922446i \(-0.373813\pi\)
−0.757979 + 0.652279i \(0.773813\pi\)
\(462\) 1286.16 + 1770.24i 0.129518 + 0.178267i
\(463\) 8763.10 + 12061.4i 0.879602 + 1.21067i 0.976531 + 0.215377i \(0.0690980\pi\)
−0.0969290 + 0.995291i \(0.530902\pi\)
\(464\) 9485.47 + 6891.60i 0.949034 + 0.689514i
\(465\) −26923.6 8823.56i −2.68506 0.879963i
\(466\) −18903.9 + 13734.5i −1.87920 + 1.36532i
\(467\) −869.570 282.541i −0.0861647 0.0279966i 0.265617 0.964079i \(-0.414424\pi\)
−0.351782 + 0.936082i \(0.614424\pi\)
\(468\) 26901.8i 2.65713i
\(469\) 1244.33 3829.66i 0.122511 0.377051i
\(470\) 6182.38 + 4515.77i 0.606749 + 0.443185i
\(471\) 6680.24 + 20559.7i 0.653523 + 2.01134i
\(472\) 805.742 261.802i 0.0785748 0.0255305i
\(473\) 1077.50 1483.05i 0.104743 0.144167i
\(474\) 28091.1 2.72209
\(475\) −157.443 + 113.173i −0.0152084 + 0.0109321i
\(476\) 1090.85 0.105040
\(477\) −11357.2 + 15631.9i −1.09017 + 1.50049i
\(478\) 4915.47 1597.13i 0.470352 0.152827i
\(479\) 657.165 + 2022.55i 0.0626861 + 0.192928i 0.977495 0.210959i \(-0.0676588\pi\)
−0.914809 + 0.403887i \(0.867659\pi\)
\(480\) −24574.1 62.3317i −2.33677 0.00592717i
\(481\) 2949.78 9078.48i 0.279622 0.860588i
\(482\) 9407.45i 0.889000i
\(483\) −66.7808 21.6984i −0.00629116 0.00204412i
\(484\) −6027.72 + 4379.39i −0.566089 + 0.411288i
\(485\) −25.4038 + 10015.4i −0.00237841 + 0.937680i
\(486\) 11452.1 + 8320.45i 1.06889 + 0.776591i
\(487\) 4438.11 + 6108.54i 0.412957 + 0.568386i 0.963937 0.266132i \(-0.0857458\pi\)
−0.550980 + 0.834519i \(0.685746\pi\)
\(488\) −754.263 1038.15i −0.0699670 0.0963013i
\(489\) −13837.1 10053.3i −1.27962 0.929701i
\(490\) −8034.09 11117.2i −0.740700 1.02494i
\(491\) 4878.03 3544.10i 0.448355 0.325749i −0.340591 0.940212i \(-0.610627\pi\)
0.788946 + 0.614463i \(0.210627\pi\)
\(492\) −5750.22 1868.36i −0.526910 0.171204i
\(493\) 5873.47i 0.536567i
\(494\) 124.925 384.478i 0.0113778 0.0350172i
\(495\) −2848.84 + 8692.73i −0.258678 + 0.789312i
\(496\) 6177.12 + 19011.2i 0.559195 + 1.72103i
\(497\) −2290.88 + 744.352i −0.206761 + 0.0671806i
\(498\) 18828.7 25915.5i 1.69424 2.33193i
\(499\) −11459.3 −1.02803 −0.514015 0.857781i \(-0.671842\pi\)
−0.514015 + 0.857781i \(0.671842\pi\)
\(500\) −7294.12 5384.76i −0.652406 0.481628i
\(501\) 14167.1 1.26335
\(502\) 13022.2 17923.6i 1.15779 1.59356i
\(503\) −3983.21 + 1294.22i −0.353087 + 0.114725i −0.480190 0.877165i \(-0.659432\pi\)
0.127103 + 0.991890i \(0.459432\pi\)
\(504\) 489.979 + 1508.00i 0.0433044 + 0.133277i
\(505\) 2851.59 8701.14i 0.251276 0.766724i
\(506\) −26.2206 + 80.6988i −0.00230366 + 0.00708992i
\(507\) 23312.2i 2.04207i
\(508\) 14443.1 + 4692.85i 1.26144 + 0.409865i
\(509\) −475.177 + 345.236i −0.0413789 + 0.0300635i −0.608282 0.793721i \(-0.708141\pi\)
0.566904 + 0.823784i \(0.308141\pi\)
\(510\) 8624.48 + 11934.1i 0.748820 + 1.03618i
\(511\) 1317.37 + 957.128i 0.114045 + 0.0828588i
\(512\) 8192.67 + 11276.2i 0.707165 + 0.973329i
\(513\) −286.349 394.125i −0.0246445 0.0339202i
\(514\) −10496.8 7626.36i −0.900766 0.654445i
\(515\) −26.6691 + 10514.2i −0.00228191 + 0.899636i
\(516\) −6664.01 + 4841.69i −0.568540 + 0.413069i
\(517\) −2311.57 751.075i −0.196640 0.0638922i
\(518\) 2413.05i 0.204678i
\(519\) 11973.8 36851.6i 1.01270 3.11677i
\(520\) −4407.39 11.1793i −0.371686 0.000942775i
\(521\) −5184.62 15956.6i −0.435974 1.34179i −0.892086 0.451866i \(-0.850758\pi\)
0.456112 0.889922i \(-0.349242\pi\)
\(522\) −34823.7 + 11314.9i −2.91991 + 0.948735i
\(523\) −4307.32 + 5928.52i −0.360127 + 0.495672i −0.950184 0.311690i \(-0.899105\pi\)
0.590057 + 0.807361i \(0.299105\pi\)
\(524\) 9868.82 0.822751
\(525\) −1669.34 + 5050.38i −0.138773 + 0.419841i
\(526\) −11712.6 −0.970900
\(527\) 5885.94 8101.30i 0.486519 0.669636i
\(528\) 8874.59 2883.53i 0.731471 0.237669i
\(529\) 3758.97 + 11568.9i 0.308948 + 0.950844i
\(530\) 10963.6 + 8008.11i 0.898547 + 0.656321i
\(531\) −2753.95 + 8475.78i −0.225068 + 0.692688i
\(532\) 45.7619i 0.00372938i
\(533\) −6485.78 2107.36i −0.527074 0.171257i
\(534\) −2425.85 + 1762.48i −0.196585 + 0.142828i
\(535\) 15530.9 + 5089.89i 1.25507 + 0.411318i
\(536\) −4124.40 2996.55i −0.332364 0.241476i
\(537\) −5607.66 7718.28i −0.450630 0.620239i
\(538\) 16213.1 + 22315.4i 1.29925 + 1.78826i
\(539\) 3522.87 + 2559.51i 0.281522 + 0.204538i
\(540\) 13436.0 18394.8i 1.07073 1.46590i
\(541\) −15024.3 + 10915.8i −1.19398 + 0.867481i −0.993680 0.112253i \(-0.964193\pi\)
−0.200305 + 0.979734i \(0.564193\pi\)
\(542\) −4067.26 1321.53i −0.322332 0.104732i
\(543\) 30559.5i 2.41516i
\(544\) 2683.94 8260.31i 0.211531 0.651026i
\(545\) 1227.18 + 3809.73i 0.0964525 + 0.299433i
\(546\) −3427.00 10547.2i −0.268612 0.826703i
\(547\) 22929.1 7450.13i 1.79228 0.582348i 0.792658 0.609667i \(-0.208697\pi\)
0.999627 + 0.0273186i \(0.00869687\pi\)
\(548\) −6602.95 + 9088.18i −0.514715 + 0.708445i
\(549\) 13498.6 1.04937
\(550\) 6102.95 + 2017.26i 0.473147 + 0.156393i
\(551\) 246.395 0.0190504
\(552\) −52.2533 + 71.9205i −0.00402907 + 0.00554554i
\(553\) −3411.08 + 1108.33i −0.262304 + 0.0852277i
\(554\) 1162.51 + 3577.85i 0.0891525 + 0.274383i
\(555\) −11821.4 + 8543.03i −0.904128 + 0.653390i
\(556\) 2807.49 8640.57i 0.214144 0.659068i
\(557\) 20922.4i 1.59158i −0.605571 0.795791i \(-0.707055\pi\)
0.605571 0.795791i \(-0.292945\pi\)
\(558\) −59371.4 19290.9i −4.50428 1.46353i
\(559\) −7516.46 + 5461.03i −0.568717 + 0.413197i
\(560\) 3572.08 1150.63i 0.269550 0.0868267i
\(561\) −3781.75 2747.60i −0.284609 0.206780i
\(562\) −11145.8 15340.8i −0.836575 1.15145i
\(563\) −8798.28 12109.8i −0.658621 0.906514i 0.340814 0.940131i \(-0.389297\pi\)
−0.999435 + 0.0336170i \(0.989297\pi\)
\(564\) 8835.63 + 6419.46i 0.659658 + 0.479270i
\(565\) −9228.70 + 2972.73i −0.687176 + 0.221352i
\(566\) 12860.5 9343.72i 0.955067 0.693897i
\(567\) −5638.08 1831.92i −0.417596 0.135685i
\(568\) 3049.62i 0.225280i
\(569\) −4983.24 + 15336.8i −0.367150 + 1.12997i 0.581474 + 0.813565i \(0.302476\pi\)
−0.948624 + 0.316406i \(0.897524\pi\)
\(570\) −500.643 + 361.802i −0.0367888 + 0.0265863i
\(571\) 6394.11 + 19679.0i 0.468625 + 1.44228i 0.854365 + 0.519673i \(0.173946\pi\)
−0.385740 + 0.922608i \(0.626054\pi\)
\(572\) −5707.35 + 1854.43i −0.417196 + 0.135555i
\(573\) −1902.86 + 2619.06i −0.138732 + 0.190948i
\(574\) 1723.91 0.125356
\(575\) −196.490 + 62.7434i −0.0142508 + 0.00455057i
\(576\) −18383.4 −1.32982
\(577\) −5635.91 + 7757.16i −0.406631 + 0.559679i −0.962393 0.271662i \(-0.912427\pi\)
0.555762 + 0.831342i \(0.312427\pi\)
\(578\) 12835.4 4170.47i 0.923670 0.300119i
\(579\) 4053.87 + 12476.5i 0.290973 + 0.895522i
\(580\) 3532.42 + 10966.2i 0.252889 + 0.785082i
\(581\) −1263.86 + 3889.77i −0.0902477 + 0.277754i
\(582\) 31905.7i 2.27239i
\(583\) −4099.27 1331.93i −0.291208 0.0946192i
\(584\) 1667.86 1211.77i 0.118179 0.0858619i
\(585\) 27346.2 37438.7i 1.93269 2.64599i
\(586\) 13542.8 + 9839.41i 0.954689 + 0.693622i
\(587\) −183.186 252.133i −0.0128805 0.0177285i 0.802528 0.596614i \(-0.203488\pi\)
−0.815409 + 0.578886i \(0.803488\pi\)
\(588\) −11501.0 15829.8i −0.806622 1.11022i
\(589\) 339.854 + 246.919i 0.0237750 + 0.0172735i
\(590\) 5950.68 + 1950.19i 0.415230 + 0.136082i
\(591\) 10916.8 7931.52i 0.759826 0.552046i
\(592\) 9786.74 + 3179.90i 0.679447 + 0.220766i
\(593\) 17122.1i 1.18570i 0.805312 + 0.592852i \(0.201998\pi\)
−0.805312 + 0.592852i \(0.798002\pi\)
\(594\) −4990.47 + 15359.1i −0.344716 + 1.06093i
\(595\) −1518.12 1108.87i −0.104600 0.0764023i
\(596\) −6632.67 20413.3i −0.455847 1.40295i
\(597\) −1606.12 + 521.861i −0.110108 + 0.0357762i
\(598\) 252.776 347.917i 0.0172856 0.0237916i
\(599\) −3330.47 −0.227178 −0.113589 0.993528i \(-0.536235\pi\)
−0.113589 + 0.993528i \(0.536235\pi\)
\(600\) 5427.98 + 3985.88i 0.369327 + 0.271205i
\(601\) −24046.3 −1.63206 −0.816031 0.578008i \(-0.803830\pi\)
−0.816031 + 0.578008i \(0.803830\pi\)
\(602\) 1380.49 1900.08i 0.0934628 0.128640i
\(603\) 51002.7 16571.8i 3.44443 1.11916i
\(604\) 4100.50 + 12620.0i 0.276236 + 0.850168i
\(605\) 12840.4 + 32.5694i 0.862870 + 0.00218865i
\(606\) 9013.86 27741.8i 0.604230 1.85963i
\(607\) 4926.48i 0.329423i 0.986342 + 0.164711i \(0.0526692\pi\)
−0.986342 + 0.164711i \(0.947331\pi\)
\(608\) 346.525 + 112.593i 0.0231142 + 0.00751026i
\(609\) 5468.36 3972.99i 0.363857 0.264358i
\(610\) 24.0582 9484.89i 0.00159687 0.629561i
\(611\) 9965.87 + 7240.63i 0.659863 + 0.479418i
\(612\) 8539.22 + 11753.2i 0.564015 + 0.776301i
\(613\) −3091.89 4255.63i −0.203720 0.280397i 0.694917 0.719090i \(-0.255441\pi\)
−0.898637 + 0.438694i \(0.855441\pi\)
\(614\) −23165.3 16830.5i −1.52260 1.10623i
\(615\) 6103.25 + 8445.37i 0.400174 + 0.553740i
\(616\) −286.154 + 207.903i −0.0187167 + 0.0135985i
\(617\) −2343.34 761.398i −0.152900 0.0496803i 0.231567 0.972819i \(-0.425615\pi\)
−0.384467 + 0.923139i \(0.625615\pi\)
\(618\) 33494.9i 2.18020i
\(619\) −7700.18 + 23698.7i −0.499994 + 1.53882i 0.309033 + 0.951051i \(0.399995\pi\)
−0.809027 + 0.587772i \(0.800005\pi\)
\(620\) −6117.24 + 18665.7i −0.396249 + 1.20908i
\(621\) −160.144 492.873i −0.0103484 0.0318491i
\(622\) 7346.73 2387.10i 0.473597 0.153881i
\(623\) 225.030 309.727i 0.0144713 0.0199181i
\(624\) −47293.2 −3.03404
\(625\) 4677.37 + 14908.5i 0.299352 + 0.954143i
\(626\) −34415.5 −2.19731
\(627\) 115.263 158.647i 0.00734159 0.0101048i
\(628\) 14253.7 4631.30i 0.905707 0.294282i
\(629\) −1592.97 4902.65i −0.100979 0.310781i
\(630\) −3649.92 + 11137.1i −0.230819 + 0.704305i
\(631\) 2274.53 7000.28i 0.143498 0.441643i −0.853316 0.521394i \(-0.825412\pi\)
0.996815 + 0.0797506i \(0.0254124\pi\)
\(632\) 4540.84i 0.285799i
\(633\) 19293.8 + 6268.93i 1.21147 + 0.393630i
\(634\) 19296.4 14019.7i 1.20877 0.878221i
\(635\) −15329.8 21212.6i −0.958025 1.32567i
\(636\) 15668.8 + 11384.1i 0.976901 + 0.709760i
\(637\) −12972.2 17854.7i −0.806872 1.11056i
\(638\) −4801.02 6608.04i −0.297922 0.410054i
\(639\) −25953.0 18855.9i −1.60670 1.16734i
\(640\) 20.5250 8091.91i 0.00126769 0.499783i
\(641\) −1818.04 + 1320.88i −0.112025 + 0.0813910i −0.642387 0.766380i \(-0.722056\pi\)
0.530362 + 0.847771i \(0.322056\pi\)
\(642\) 49517.2 + 16089.1i 3.04406 + 0.989076i
\(643\) 9835.59i 0.603231i −0.953430 0.301616i \(-0.902474\pi\)
0.953430 0.301616i \(-0.0975259\pi\)
\(644\) −15.0431 + 46.2981i −0.000920471 + 0.00283292i
\(645\) 14195.9 + 36.0075i 0.866606 + 0.00219813i
\(646\) −67.4631 207.630i −0.00410882 0.0126457i
\(647\) −3444.98 + 1119.34i −0.209329 + 0.0680152i −0.411805 0.911272i \(-0.635101\pi\)
0.202475 + 0.979287i \(0.435101\pi\)
\(648\) −4411.57 + 6072.01i −0.267443 + 0.368104i
\(649\) −1988.02 −0.120241
\(650\) −26257.9 19281.8i −1.58449 1.16353i
\(651\) 11524.0 0.693793
\(652\) −6969.76 + 9593.05i −0.418646 + 0.576216i
\(653\) 7770.32 2524.73i 0.465660 0.151302i −0.0667838 0.997767i \(-0.521274\pi\)
0.532444 + 0.846465i \(0.321274\pi\)
\(654\) 3940.15 + 12126.5i 0.235584 + 0.725053i
\(655\) −13734.3 10031.8i −0.819300 0.598437i
\(656\) 2271.76 6991.77i 0.135210 0.416132i
\(657\) 21686.2i 1.28776i
\(658\) −2961.58 962.274i −0.175462 0.0570112i
\(659\) 11651.6 8465.38i 0.688743 0.500401i −0.187503 0.982264i \(-0.560040\pi\)
0.876247 + 0.481863i \(0.160040\pi\)
\(660\) 8713.29 + 2855.57i 0.513885 + 0.168414i
\(661\) −6900.20 5013.29i −0.406032 0.294999i 0.365962 0.930630i \(-0.380740\pi\)
−0.771993 + 0.635631i \(0.780740\pi\)
\(662\) 23550.3 + 32414.2i 1.38264 + 1.90304i
\(663\) 13925.5 + 19166.8i 0.815718 + 1.12274i
\(664\) 4189.14 + 3043.59i 0.244835 + 0.177883i
\(665\) 46.5179 63.6860i 0.00271261 0.00371374i
\(666\) −25999.0 + 18889.4i −1.51267 + 1.09902i
\(667\) 249.282 + 80.9966i 0.0144711 + 0.00470195i
\(668\) 9821.79i 0.568887i
\(669\) −6502.60 + 20012.9i −0.375792 + 1.15657i
\(670\) −11553.4 35867.0i −0.666190 2.06816i
\(671\) 930.500 + 2863.79i 0.0535344 + 0.164762i
\(672\) 9506.07 3088.71i 0.545692 0.177306i
\(673\) 5322.13 7325.28i 0.304834 0.419567i −0.628928 0.777464i \(-0.716506\pi\)
0.933761 + 0.357896i \(0.116506\pi\)
\(674\) −14989.4 −0.856634
\(675\) −37397.2 + 11941.7i −2.13247 + 0.680943i
\(676\) 16162.0 0.919548
\(677\) 772.758 1063.61i 0.0438693 0.0603809i −0.786519 0.617566i \(-0.788119\pi\)
0.830388 + 0.557185i \(0.188119\pi\)
\(678\) −29375.4 + 9544.64i −1.66394 + 0.540649i
\(679\) −1258.83 3874.28i −0.0711479 0.218971i
\(680\) −1929.11 + 1394.12i −0.108791 + 0.0786205i
\(681\) −3070.34 + 9449.54i −0.172769 + 0.531729i
\(682\) 13925.7i 0.781881i
\(683\) −27438.1 8915.17i −1.53717 0.499458i −0.586578 0.809893i \(-0.699525\pi\)
−0.950595 + 0.310435i \(0.899525\pi\)
\(684\) −493.055 + 358.225i −0.0275620 + 0.0200250i
\(685\) 18427.5 5935.83i 1.02785 0.331089i
\(686\) 9316.54 + 6768.86i 0.518523 + 0.376729i
\(687\) −14413.7 19838.8i −0.800463 1.10174i
\(688\) −5887.07 8102.86i −0.326225 0.449010i
\(689\) 17673.2 + 12840.3i 0.977204 + 0.709980i
\(690\) −625.442 + 201.466i −0.0345075 + 0.0111155i
\(691\) 9161.32 6656.09i 0.504360 0.366439i −0.306320 0.951929i \(-0.599098\pi\)
0.810680 + 0.585489i \(0.199098\pi\)
\(692\) −25548.6 8301.24i −1.40349 0.456020i
\(693\) 3720.71i 0.203951i
\(694\) 12864.5 39592.8i 0.703644 2.16559i
\(695\) −12690.4 + 9171.05i −0.692627 + 0.500543i
\(696\) −2644.42 8138.70i −0.144018 0.443242i
\(697\) −3502.52 + 1138.04i −0.190340 + 0.0618454i
\(698\) 6321.95 8701.42i 0.342821 0.471853i
\(699\) 57445.8 3.10844
\(700\) 3501.35 + 1157.33i 0.189055 + 0.0624898i
\(701\) 10002.6 0.538934 0.269467 0.963010i \(-0.413152\pi\)
0.269467 + 0.963010i \(0.413152\pi\)
\(702\) 48109.9 66217.6i 2.58660 3.56015i
\(703\) 205.669 66.8259i 0.0110341 0.00358519i
\(704\) −1267.23 3900.12i −0.0678414 0.208794i
\(705\) −5770.88 17915.4i −0.308289 0.957070i
\(706\) −2047.23 + 6300.72i −0.109134 + 0.335879i
\(707\) 3724.30i 0.198114i
\(708\) 8495.82 + 2760.46i 0.450978 + 0.146532i
\(709\) −5513.27 + 4005.63i −0.292038 + 0.212178i −0.724151 0.689641i \(-0.757768\pi\)
0.432113 + 0.901820i \(0.357768\pi\)
\(710\) −13295.6 + 18202.5i −0.702779 + 0.962151i
\(711\) −38643.5 28076.2i −2.03832 1.48093i
\(712\) −284.899 392.129i −0.0149958 0.0206400i
\(713\) 262.667 + 361.530i 0.0137966 + 0.0189894i
\(714\) −4845.16 3520.21i −0.253957 0.184511i
\(715\) 9827.88 + 3220.85i 0.514044 + 0.168466i
\(716\) −5350.96 + 3887.70i −0.279295 + 0.202919i
\(717\) −12084.5 3926.49i −0.629434 0.204515i
\(718\) 16302.0i 0.847332i
\(719\) 1873.76 5766.85i 0.0971900 0.299120i −0.890628 0.454732i \(-0.849735\pi\)
0.987818 + 0.155612i \(0.0497350\pi\)
\(720\) 40359.5 + 29479.6i 2.08904 + 1.52589i
\(721\) −1321.53 4067.25i −0.0682612 0.210087i
\(722\) −24820.5 + 8064.66i −1.27939 + 0.415700i
\(723\) −13594.2 + 18710.9i −0.699274 + 0.962468i
\(724\) −21186.4 −1.08755
\(725\) 6231.38 18852.3i 0.319211 0.965732i
\(726\) 40905.3 2.09110
\(727\) −18958.7 + 26094.4i −0.967179 + 1.33121i −0.0237200 + 0.999719i \(0.507551\pi\)
−0.943459 + 0.331489i \(0.892449\pi\)
\(728\) 1704.92 553.963i 0.0867976 0.0282023i
\(729\) 122.673 + 377.549i 0.00623244 + 0.0191815i
\(730\) 15238.0 + 38.6510i 0.772583 + 0.00195964i
\(731\) −1550.44 + 4771.78i −0.0784477 + 0.241437i
\(732\) 13530.5i 0.683198i
\(733\) −6353.12 2064.25i −0.320134 0.104018i 0.144542 0.989499i \(-0.453829\pi\)
−0.464676 + 0.885481i \(0.653829\pi\)
\(734\) 7889.85 5732.31i 0.396757 0.288261i
\(735\) −85.5327 + 33721.0i −0.00429241 + 1.69227i
\(736\) 313.572 + 227.824i 0.0157044 + 0.0114099i
\(737\) 7031.57 + 9678.12i 0.351440 + 0.483715i
\(738\) 13494.8 + 18574.0i 0.673103 + 0.926447i
\(739\) −6279.12 4562.05i −0.312559 0.227088i 0.420435 0.907323i \(-0.361878\pi\)
−0.732994 + 0.680235i \(0.761878\pi\)
\(740\) 5922.75 + 8195.60i 0.294222 + 0.407130i
\(741\) −804.058 + 584.182i −0.0398621 + 0.0289615i
\(742\) −5251.96 1706.47i −0.259846 0.0844290i
\(743\) 5076.22i 0.250644i 0.992116 + 0.125322i \(0.0399964\pi\)
−0.992116 + 0.125322i \(0.960004\pi\)
\(744\) 4508.52 13875.8i 0.222164 0.683752i
\(745\) −11519.9 + 35151.0i −0.566519 + 1.72863i
\(746\) 9660.50 + 29732.0i 0.474124 + 1.45920i
\(747\) −51803.3 + 16831.9i −2.53733 + 0.824427i
\(748\) −1904.87 + 2621.83i −0.0931135 + 0.128160i
\(749\) −6647.62 −0.324297
\(750\) 15020.9 + 47455.4i 0.731316 + 2.31043i
\(751\) 13122.4 0.637607 0.318804 0.947821i \(-0.396719\pi\)
0.318804 + 0.947821i \(0.396719\pi\)
\(752\) −7805.51 + 10743.4i −0.378508 + 0.520971i
\(753\) −51800.8 + 16831.1i −2.50694 + 0.814555i
\(754\) 12792.5 + 39371.1i 0.617870 + 1.90161i
\(755\) 7121.91 21731.3i 0.343302 1.04753i
\(756\) −2863.10 + 8811.73i −0.137738 + 0.423915i
\(757\) 1050.93i 0.0504578i 0.999682 + 0.0252289i \(0.00803146\pi\)
−0.999682 + 0.0252289i \(0.991969\pi\)
\(758\) 44627.3 + 14500.3i 2.13844 + 0.694820i
\(759\) 168.765 122.615i 0.00807086 0.00586382i
\(760\) −58.4840 80.9272i −0.00279137 0.00386255i
\(761\) 16194.4 + 11765.9i 0.771414 + 0.560465i 0.902390 0.430920i \(-0.141811\pi\)
−0.130976 + 0.991386i \(0.541811\pi\)
\(762\) −49006.9 67452.2i −2.32983 3.20674i
\(763\) −956.898 1317.06i −0.0454024 0.0624910i
\(764\) 1815.76 + 1319.22i 0.0859839 + 0.0624710i
\(765\) 63.5059 25037.0i 0.00300139 1.18329i
\(766\) 33166.2 24096.6i 1.56441 1.13661i
\(767\) 9582.59 + 3113.57i 0.451118 + 0.146577i
\(768\) 48501.4i 2.27883i
\(769\) −8811.20 + 27118.1i −0.413186 + 1.27166i 0.500677 + 0.865634i \(0.333084\pi\)
−0.913863 + 0.406022i \(0.866916\pi\)
\(770\) −2614.39 6.63135i −0.122358 0.000310360i
\(771\) 9857.01 + 30336.8i 0.460430 + 1.41706i
\(772\) 8649.78 2810.49i 0.403255 0.131025i
\(773\) 16706.1 22994.0i 0.777333 1.06991i −0.218239 0.975895i \(-0.570031\pi\)
0.995571 0.0940111i \(-0.0299689\pi\)
\(774\) 31278.6 1.45257
\(775\) 27487.3 19758.4i 1.27403 0.915797i
\(776\) −5157.44 −0.238584
\(777\) 3486.97 4799.40i 0.160997 0.221593i
\(778\) −53343.0 + 17332.2i −2.45815 + 0.798700i
\(779\) −47.7413 146.933i −0.00219578 0.00675790i
\(780\) −37527.3 27410.8i −1.72268 1.25829i
\(781\) 2211.35 6805.85i 0.101317 0.311821i
\(782\) 232.239i 0.0106200i
\(783\) 47444.8 + 15415.8i 2.16544 + 0.703595i
\(784\) 19247.6 13984.2i 0.876806 0.637037i
\(785\) −24544.4 8043.84i −1.11596 0.365729i
\(786\) −43833.6 31846.9i −1.98917 1.44522i
\(787\) 9361.97 + 12885.6i 0.424038 + 0.583638i 0.966572 0.256396i \(-0.0825350\pi\)
−0.542534 + 0.840034i \(0.682535\pi\)
\(788\) −5498.80 7568.44i −0.248587 0.342151i
\(789\) 23295.6 + 16925.3i 1.05114 + 0.763696i
\(790\) −19796.9 + 27103.2i −0.891570 + 1.22062i
\(791\) 3190.45 2317.99i 0.143412 0.104195i
\(792\) −4480.03 1455.65i −0.200999 0.0653085i
\(793\) 15261.3i 0.683409i
\(794\) 9595.35 29531.5i 0.428875 1.31994i
\(795\) −10233.9 31770.6i −0.456552 1.41734i
\(796\) 361.798 + 1113.50i 0.0161100 + 0.0495816i
\(797\) 30886.1 10035.5i 1.37270 0.446018i 0.472438 0.881364i \(-0.343374\pi\)
0.900263 + 0.435346i \(0.143374\pi\)
\(798\) 147.675 203.257i 0.00655093 0.00901658i
\(799\) 6652.36 0.294548
\(800\) 17378.4 23665.9i 0.768024 1.04590i
\(801\) 5098.65 0.224909
\(802\) −20843.2 + 28688.2i −0.917705 + 1.26311i
\(803\) −4600.84 + 1494.90i −0.202192 + 0.0656962i
\(804\) −16611.0 51123.3i −0.728636 2.24251i
\(805\) 67.9981 49.1405i 0.00297717 0.00215152i
\(806\) −21810.0 + 67124.4i −0.953134 + 2.93344i
\(807\) 67812.7i 2.95802i
\(808\) 4484.37 + 1457.06i 0.195247 + 0.0634396i
\(809\) 13221.5 9605.98i 0.574590 0.417464i −0.262180 0.965019i \(-0.584441\pi\)
0.836770 + 0.547555i \(0.184441\pi\)
\(810\) −52804.0 + 17009.1i −2.29055 + 0.737827i
\(811\) 22556.4 + 16388.2i 0.976649 + 0.709577i 0.956957 0.290229i \(-0.0937314\pi\)
0.0196920 + 0.999806i \(0.493731\pi\)
\(812\) −2754.41 3791.12i −0.119041 0.163845i
\(813\) 6179.86 + 8505.85i 0.266589 + 0.366929i
\(814\) −5799.66 4213.70i −0.249727 0.181438i
\(815\) 19451.2 6265.58i 0.836007 0.269293i
\(816\) −20662.1 + 15011.9i −0.886418 + 0.644021i
\(817\) −200.179 65.0421i −0.00857206 0.00278523i
\(818\) 12539.5i 0.535981i
\(819\) −5827.26 + 17934.5i −0.248621 + 0.765178i
\(820\) 5855.04 4231.29i 0.249350 0.180199i
\(821\) −5333.37 16414.4i −0.226719 0.697768i −0.998113 0.0614103i \(-0.980440\pi\)
0.771394 0.636358i \(-0.219560\pi\)
\(822\) 58655.6 19058.4i 2.48887 0.808682i
\(823\) −8240.74 + 11342.4i −0.349033 + 0.480403i −0.947052 0.321079i \(-0.895955\pi\)
0.598019 + 0.801482i \(0.295955\pi\)
\(824\) −5414.33 −0.228904
\(825\) −9223.37 12831.3i −0.389232 0.541488i
\(826\) −2547.04 −0.107291
\(827\) −2417.01 + 3326.73i −0.101630 + 0.139881i −0.856803 0.515644i \(-0.827553\pi\)
0.755173 + 0.655525i \(0.227553\pi\)
\(828\) −616.589 + 200.342i −0.0258792 + 0.00840865i
\(829\) −6945.37 21375.6i −0.290980 0.895545i −0.984542 0.175148i \(-0.943960\pi\)
0.693562 0.720397i \(-0.256040\pi\)
\(830\) 11734.8 + 36430.1i 0.490747 + 1.52350i
\(831\) 2858.00 8796.02i 0.119306 0.367185i
\(832\) 20784.0i 0.866051i
\(833\) −11334.9 3682.95i −0.471468 0.153189i
\(834\) −40353.1 + 29318.3i −1.67544 + 1.21728i
\(835\) −9984.04 + 13668.8i −0.413787 + 0.566501i
\(836\) −109.987 79.9103i −0.00455022 0.00330593i
\(837\) 49992.4 + 68808.6i 2.06450 + 2.84155i
\(838\) −10697.3 14723.5i −0.440967 0.606940i
\(839\) −35978.0 26139.6i −1.48045 1.07561i −0.977411 0.211349i \(-0.932214\pi\)
−0.503041 0.864263i \(-0.667786\pi\)
\(840\) −2602.87 853.029i −0.106914 0.0350384i
\(841\) −681.377 + 495.050i −0.0279379 + 0.0202981i
\(842\) 46327.3 + 15052.6i 1.89613 + 0.616091i
\(843\) 46618.1i 1.90464i
\(844\) 4346.15 13376.1i 0.177252 0.545525i
\(845\) −22492.3 16429.0i −0.915691 0.668844i
\(846\) −12815.4 39441.7i −0.520806 1.60288i
\(847\) −4967.09 + 1613.91i −0.201501 + 0.0654716i
\(848\) −13842.0 + 19051.9i −0.560539 + 0.771516i
\(849\) −39080.9 −1.57980
\(850\) −17592.4 89.2461i −0.709899 0.00360131i
\(851\) 230.046 0.00926660
\(852\) −18900.5 + 26014.3i −0.760001 + 1.04605i
\(853\) 21281.6 6914.82i 0.854243 0.277560i 0.151021 0.988531i \(-0.451744\pi\)
0.703222 + 0.710970i \(0.251744\pi\)
\(854\) 1192.15 + 3669.07i 0.0477689 + 0.147018i
\(855\) 1050.32 + 2.66411i 0.0420118 + 0.000106562i
\(856\) −2600.75 + 8004.28i −0.103846 + 0.319604i
\(857\) 3861.39i 0.153912i −0.997034 0.0769561i \(-0.975480\pi\)
0.997034 0.0769561i \(-0.0245201\pi\)
\(858\) 31334.2 + 10181.1i 1.24677 + 0.405101i
\(859\) −8636.63 + 6274.88i −0.343048 + 0.249239i −0.745947 0.666006i \(-0.768003\pi\)
0.402899 + 0.915245i \(0.368003\pi\)
\(860\) 24.9634 9841.76i 0.000989821 0.390234i
\(861\) −3428.75 2491.13i −0.135716 0.0986035i
\(862\) −13955.0 19207.4i −0.551402 0.758940i
\(863\) 10062.6 + 13849.9i 0.396910 + 0.546300i 0.959965 0.280119i \(-0.0903741\pi\)
−0.563055 + 0.826419i \(0.690374\pi\)
\(864\) 59681.0 + 43360.8i 2.34999 + 1.70737i
\(865\) 27117.1 + 37523.3i 1.06591 + 1.47495i
\(866\) 23461.4 17045.7i 0.920612 0.668863i
\(867\) −31555.3 10252.9i −1.23607 0.401624i
\(868\) 7989.38i 0.312416i
\(869\) 3292.67 10133.8i 0.128534 0.395587i
\(870\) 19698.7 60107.0i 0.767640 2.34232i
\(871\) −18735.8 57662.9i −0.728862 2.24321i
\(872\) −1960.21 + 636.911i −0.0761251 + 0.0247346i
\(873\) 31888.7 43891.0i 1.23627 1.70159i
\(874\) 9.74257 0.000377057
\(875\) −3696.32 5169.82i −0.142810 0.199739i
\(876\) 21737.5 0.838405
\(877\) −2401.56 + 3305.47i −0.0924686 + 0.127272i −0.852745 0.522328i \(-0.825064\pi\)
0.760276 + 0.649600i \(0.225064\pi\)
\(878\) 15670.7 5091.73i 0.602348 0.195715i
\(879\) −12717.4 39140.0i −0.487993 1.50189i
\(880\) −3472.13 + 10594.6i −0.133006 + 0.405845i
\(881\) −4274.26 + 13154.8i −0.163454 + 0.503061i −0.998919 0.0464832i \(-0.985199\pi\)
0.835465 + 0.549544i \(0.185199\pi\)
\(882\) 74299.7i 2.83651i
\(883\) −8800.43 2859.43i −0.335400 0.108978i 0.136475 0.990643i \(-0.456423\pi\)
−0.471875 + 0.881666i \(0.656423\pi\)
\(884\) 13288.0 9654.31i 0.505571 0.367319i
\(885\) −9017.41 12477.8i −0.342505 0.473941i
\(886\) −35047.6 25463.6i −1.32895 0.965536i
\(887\) 7113.58 + 9791.01i 0.269279 + 0.370631i 0.922146 0.386841i \(-0.126434\pi\)
−0.652867 + 0.757473i \(0.726434\pi\)
\(888\) −4414.67 6076.27i −0.166832 0.229624i
\(889\) 8612.17 + 6257.10i 0.324907 + 0.236059i
\(890\) 9.08723 3582.61i 0.000342252 0.134932i
\(891\) 14248.3 10352.0i 0.535730 0.389231i
\(892\) 13874.6 + 4508.15i 0.520804 + 0.169220i
\(893\) 279.070i 0.0104577i
\(894\) −36414.3 + 112072.i −1.36228 + 4.19266i
\(895\) 11398.8 + 28.9127i 0.425719 + 0.00107983i
\(896\) 1017.07 + 3130.22i 0.0379218 + 0.116711i
\(897\) −1005.51 + 326.711i −0.0374282 + 0.0121612i
\(898\) −3053.26 + 4202.45i −0.113462 + 0.156167i
\(899\) −43017.1 −1.59588
\(900\) 14939.2 + 46784.3i 0.553303 + 1.73275i
\(901\) 11797.1 0.436202
\(902\) −3010.32 + 4143.35i −0.111123 + 0.152947i
\(903\) −5491.42 + 1784.27i −0.202373 + 0.0657551i
\(904\) −1542.86 4748.43i −0.0567640 0.174702i
\(905\) 29484.7 + 21536.4i 1.08299 + 0.791043i
\(906\) 22512.3 69285.8i 0.825521 2.54069i
\(907\) 31373.4i 1.14855i −0.818661 0.574276i \(-0.805283\pi\)
0.818661 0.574276i \(-0.194717\pi\)
\(908\) 6551.22 + 2128.62i 0.239438 + 0.0777981i
\(909\) −40126.9 + 29153.9i −1.46417 + 1.06378i
\(910\) 12591.4 + 4126.54i 0.458683 + 0.150323i
\(911\) 30121.2 + 21884.3i 1.09545 + 0.795894i 0.980312 0.197455i \(-0.0632675\pi\)
0.115143 + 0.993349i \(0.463267\pi\)
\(912\) −629.757 866.786i −0.0228655 0.0314717i
\(913\) −7141.94 9830.04i −0.258887 0.356327i
\(914\) 21498.1 + 15619.3i 0.778001 + 0.565251i
\(915\) −13754.0 + 18830.1i −0.496932 + 0.680333i
\(916\) −13753.9 + 9992.80i −0.496116 + 0.360449i
\(917\) 6579.18 + 2137.71i 0.236929 + 0.0769829i
\(918\) 44201.2i 1.58917i
\(919\) 4895.23 15066.0i 0.175712 0.540784i −0.823954 0.566657i \(-0.808236\pi\)
0.999665 + 0.0258726i \(0.00823644\pi\)
\(920\) −32.5663 101.101i −0.00116704 0.00362303i
\(921\) 21753.3 + 66949.9i 0.778281 + 2.39530i
\(922\) 16469.0 5351.11i 0.588263 0.191138i
\(923\) −21318.2 + 29342.0i −0.760236 + 1.04638i
\(924\) −3729.50 −0.132783
\(925\) 88.4033 17426.2i 0.00314236 0.619429i
\(926\) −56745.9 −2.01381
\(927\) 33477.0 46077.1i 1.18612 1.63255i
\(928\) −35484.6 + 11529.7i −1.25522 + 0.407844i
\(929\) −1483.77 4566.57i −0.0524014 0.161275i 0.921431 0.388542i \(-0.127021\pi\)
−0.973833 + 0.227267i \(0.927021\pi\)
\(930\) 87405.1 63165.4i 3.08186 2.22718i
\(931\) 154.502 475.508i 0.00543887 0.0167391i
\(932\) 39826.3i 1.39973i
\(933\) −18061.7 5868.60i −0.633776 0.205926i
\(934\) 2815.47 2045.56i 0.0986350 0.0716625i
\(935\) 5316.10 1712.41i 0.185941 0.0598950i
\(936\) 19314.8 + 14033.0i 0.674490 + 0.490046i
\(937\) 11639.9 + 16021.0i 0.405826 + 0.558572i 0.962194 0.272364i \(-0.0878055\pi\)
−0.556368 + 0.830936i \(0.687805\pi\)
\(938\) 9008.81 + 12399.6i 0.313591 + 0.431621i
\(939\) 68450.3 + 49732.1i 2.37890 + 1.72838i
\(940\) −12420.5 + 4000.86i −0.430970 + 0.138823i
\(941\) −25056.5 + 18204.6i −0.868034 + 0.630664i −0.930059 0.367411i \(-0.880244\pi\)
0.0620245 + 0.998075i \(0.480244\pi\)
\(942\) −78254.8 25426.5i −2.70667 0.879449i
\(943\) 164.348i 0.00567540i
\(944\) −3356.48 + 10330.2i −0.115725 + 0.356164i
\(945\) 12941.8 9352.72i 0.445500 0.321951i
\(946\) 2156.14 + 6635.91i 0.0741037 + 0.228068i
\(947\) −27273.4 + 8861.67i −0.935868 + 0.304082i −0.736960 0.675936i \(-0.763739\pi\)
−0.198908 + 0.980018i \(0.563739\pi\)
\(948\) −28142.5 + 38734.9i −0.964164 + 1.32706i
\(949\) 24518.1 0.838665
\(950\) 3.74393 738.011i 0.000127862 0.0252045i
\(951\) −58638.5 −1.99946
\(952\) 569.030 783.203i 0.0193722 0.0266636i
\(953\) 15746.8 5116.43i 0.535244 0.173911i −0.0289084 0.999582i \(-0.509203\pi\)
0.564152 + 0.825671i \(0.309203\pi\)
\(954\) −22726.4 69944.7i −0.771273 2.37373i
\(955\) −1185.94 3681.69i −0.0401843 0.124750i
\(956\) −2722.17 + 8377.99i −0.0920935 + 0.283435i
\(957\) 20080.7i 0.678283i
\(958\) −7698.28 2501.32i −0.259624 0.0843571i
\(959\) −6370.55 + 4628.48i −0.214511 + 0.155851i
\(960\) 18731.2 25644.3i 0.629737 0.862151i
\(961\) −35232.2 25597.7i −1.18265 0.859243i
\(962\) 21356.0 + 29394.1i 0.715744 + 0.985138i
\(963\) −52037.7 71623.7i −1.74132 2.39672i
\(964\) 12971.9 + 9424.67i 0.433401 + 0.314884i
\(965\) −14894.7 4881.37i −0.496866 0.162836i
\(966\) 216.221 157.094i 0.00720165 0.00523231i
\(967\) −27650.9 8984.32i −0.919537 0.298776i −0.189260 0.981927i \(-0.560609\pi\)
−0.730277 + 0.683151i \(0.760609\pi\)
\(968\) 6612.19i 0.219550i
\(969\) −165.856 + 510.451i −0.00549850 + 0.0169226i
\(970\) −30783.6 22485.1i −1.01897 0.744281i
\(971\) −12264.1 37745.1i −0.405329 1.24747i −0.920620 0.390459i \(-0.872316\pi\)
0.515292 0.857015i \(-0.327684\pi\)
\(972\) −22946.1 + 7455.65i −0.757199 + 0.246029i
\(973\) 3743.30 5152.21i 0.123335 0.169756i
\(974\) −28739.2 −0.945445
\(975\) 24362.3 + 76294.3i 0.800225 + 2.50602i
\(976\) 16451.9 0.539561
\(977\) 22975.6 31623.2i 0.752359 1.03553i −0.245452 0.969409i \(-0.578936\pi\)
0.997811 0.0661250i \(-0.0210636\pi\)
\(978\) 61914.1 20117.1i 2.02433 0.657744i
\(979\) 351.467 + 1081.70i 0.0114739 + 0.0353130i
\(980\) 23378.2 + 59.2984i 0.762031 + 0.00193288i
\(981\) 6699.81 20619.9i 0.218051 0.671093i
\(982\) 22950.0i 0.745787i
\(983\) 19288.8 + 6267.32i 0.625858 + 0.203354i 0.604739 0.796423i \(-0.293277\pi\)
0.0211186 + 0.999777i \(0.493277\pi\)
\(984\) −4340.96 + 3153.89i −0.140635 + 0.102177i
\(985\) −40.8944 + 16122.5i −0.00132285 + 0.521528i
\(986\) 18086.2 + 13140.4i 0.584160 + 0.424417i
\(987\) 4499.86 + 6193.53i 0.145119 + 0.199739i
\(988\) 405.004 + 557.440i 0.0130414 + 0.0179499i
\(989\) −181.143 131.608i −0.00582408 0.00423144i
\(990\) −20394.0 28220.2i −0.654712 0.905957i
\(991\) −4373.55 + 3177.57i −0.140192 + 0.101855i −0.655671 0.755047i \(-0.727614\pi\)
0.515479 + 0.856902i \(0.327614\pi\)
\(992\) −60498.3 19657.1i −1.93631 0.629146i
\(993\) 98501.3i 3.14788i
\(994\) 2833.18 8719.62i 0.0904053 0.278239i
\(995\) 628.387 1917.41i 0.0200213 0.0610915i
\(996\) 16871.7 + 51925.7i 0.536747 + 1.65194i
\(997\) 49634.9 16127.4i 1.57668 0.512295i 0.615484 0.788150i \(-0.288961\pi\)
0.961199 + 0.275854i \(0.0889608\pi\)
\(998\) 25637.2 35286.6i 0.813157 1.11922i
\(999\) 43783.8 1.38664
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 25.4.e.a.9.2 24
3.2 odd 2 225.4.m.a.109.5 24
5.2 odd 4 125.4.d.b.76.3 48
5.3 odd 4 125.4.d.b.76.10 48
5.4 even 2 125.4.e.a.49.5 24
25.2 odd 20 125.4.d.b.51.3 48
25.8 odd 20 625.4.a.g.1.4 24
25.11 even 5 125.4.e.a.74.5 24
25.14 even 10 inner 25.4.e.a.14.2 yes 24
25.17 odd 20 625.4.a.g.1.21 24
25.23 odd 20 125.4.d.b.51.10 48
75.14 odd 10 225.4.m.a.64.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.4.e.a.9.2 24 1.1 even 1 trivial
25.4.e.a.14.2 yes 24 25.14 even 10 inner
125.4.d.b.51.3 48 25.2 odd 20
125.4.d.b.51.10 48 25.23 odd 20
125.4.d.b.76.3 48 5.2 odd 4
125.4.d.b.76.10 48 5.3 odd 4
125.4.e.a.49.5 24 5.4 even 2
125.4.e.a.74.5 24 25.11 even 5
225.4.m.a.64.5 24 75.14 odd 10
225.4.m.a.109.5 24 3.2 odd 2
625.4.a.g.1.4 24 25.8 odd 20
625.4.a.g.1.21 24 25.17 odd 20