Properties

Label 23.4.c.a.2.1
Level $23$
Weight $4$
Character 23.2
Analytic conductor $1.357$
Analytic rank $0$
Dimension $50$
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] = [23,4,Mod(2,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\), degree \(10\), 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: \(1.35704393013\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 2.1
Character \(\chi\) \(=\) 23.2
Dual form 23.4.c.a.12.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.24175 - 2.08335i) q^{2} +(1.21610 + 8.45817i) q^{3} +(2.84529 + 6.23031i) q^{4} +(12.7969 + 3.75752i) q^{5} +(13.6790 - 29.9528i) q^{6} +(-11.3462 + 13.0942i) q^{7} +(-0.631070 + 4.38919i) q^{8} +(-44.1554 + 12.9652i) q^{9} +O(q^{10})\) \(q+(-3.24175 - 2.08335i) q^{2} +(1.21610 + 8.45817i) q^{3} +(2.84529 + 6.23031i) q^{4} +(12.7969 + 3.75752i) q^{5} +(13.6790 - 29.9528i) q^{6} +(-11.3462 + 13.0942i) q^{7} +(-0.631070 + 4.38919i) q^{8} +(-44.1554 + 12.9652i) q^{9} +(-33.6563 - 38.8414i) q^{10} +(45.2432 - 29.0760i) q^{11} +(-49.2369 + 31.6426i) q^{12} +(-27.2602 - 31.4600i) q^{13} +(64.0613 - 18.8101i) q^{14} +(-16.2194 + 112.808i) q^{15} +(47.0725 - 54.3245i) q^{16} +(14.8231 - 32.4581i) q^{17} +(170.152 + 49.9611i) q^{18} +(8.29844 + 18.1710i) q^{19} +(13.0005 + 90.4202i) q^{20} +(-124.551 - 80.0442i) q^{21} -207.242 q^{22} +(89.7322 + 64.1492i) q^{23} -37.8919 q^{24} +(44.4861 + 28.5895i) q^{25} +(22.8288 + 158.778i) q^{26} +(-67.5152 - 147.838i) q^{27} +(-113.864 - 33.4335i) q^{28} +(77.8452 - 170.457i) q^{29} +(287.598 - 331.905i) q^{30} +(-0.302527 + 2.10412i) q^{31} +(-231.736 + 68.0439i) q^{32} +(300.950 + 347.315i) q^{33} +(-115.674 + 74.3393i) q^{34} +(-194.398 + 124.932i) q^{35} +(-206.412 - 238.212i) q^{36} +(99.0257 - 29.0766i) q^{37} +(10.9551 - 76.1945i) q^{38} +(232.943 - 268.830i) q^{39} +(-24.5682 + 53.7969i) q^{40} +(-457.540 - 134.346i) q^{41} +(237.004 + 518.966i) q^{42} +(1.21166 + 8.42730i) q^{43} +(309.883 + 199.149i) q^{44} -613.771 q^{45} +(-157.244 - 394.899i) q^{46} +239.887 q^{47} +(516.731 + 332.083i) q^{48} +(6.09187 + 42.3699i) q^{49} +(-84.6511 - 185.360i) q^{50} +(292.562 + 85.9041i) q^{51} +(118.442 - 259.353i) q^{52} +(49.4924 - 57.1173i) q^{53} +(-89.1296 + 619.910i) q^{54} +(688.228 - 202.082i) q^{55} +(-50.3127 - 58.0639i) q^{56} +(-143.602 + 92.2874i) q^{57} +(-607.476 + 390.401i) q^{58} +(136.622 + 157.670i) q^{59} +(-748.979 + 219.920i) q^{60} +(-45.8150 + 318.650i) q^{61} +(5.36433 - 6.19077i) q^{62} +(331.227 - 725.286i) q^{63} +(341.231 + 100.194i) q^{64} +(-230.636 - 505.023i) q^{65} +(-252.028 - 1752.89i) q^{66} +(-583.925 - 375.266i) q^{67} +244.400 q^{68} +(-433.462 + 836.982i) q^{69} +890.468 q^{70} +(76.1783 + 48.9568i) q^{71} +(-29.0415 - 201.988i) q^{72} +(44.1089 + 96.5851i) q^{73} +(-381.593 - 112.046i) q^{74} +(-187.715 + 411.039i) q^{75} +(-89.5998 + 103.404i) q^{76} +(-132.610 + 922.326i) q^{77} +(-1315.21 + 386.180i) q^{78} +(-373.412 - 430.940i) q^{79} +(806.510 - 518.312i) q^{80} +(123.050 - 79.0792i) q^{81} +(1203.34 + 1388.73i) q^{82} +(-713.068 + 209.376i) q^{83} +(144.316 - 1003.74i) q^{84} +(311.653 - 359.666i) q^{85} +(13.6291 - 29.8435i) q^{86} +(1536.42 + 451.134i) q^{87} +(99.0685 + 216.930i) q^{88} +(-79.7950 - 554.987i) q^{89} +(1989.69 + 1278.70i) q^{90} +721.244 q^{91} +(-144.356 + 741.583i) q^{92} -18.1649 q^{93} +(-777.655 - 499.768i) q^{94} +(37.9165 + 263.715i) q^{95} +(-857.342 - 1877.32i) q^{96} +(-538.454 - 158.104i) q^{97} +(68.5229 - 150.044i) q^{98} +(-1620.75 + 1870.45i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9} + 47 q^{10} - 53 q^{11} + 36 q^{12} - 65 q^{13} + 117 q^{14} - 425 q^{15} - 499 q^{16} - 117 q^{17} + 24 q^{18} + 73 q^{19} + 529 q^{20} + 429 q^{21} + 310 q^{22} + 542 q^{23} + 1606 q^{24} + 246 q^{25} + 324 q^{26} + 65 q^{27} - 677 q^{28} - 497 q^{29} - 1041 q^{30} - 471 q^{31} - 915 q^{32} - 391 q^{33} - 2751 q^{34} - 737 q^{35} - 1865 q^{36} - 1071 q^{37} - 1504 q^{38} + 127 q^{39} + 1479 q^{40} + 569 q^{41} + 3059 q^{42} + 1615 q^{43} + 2518 q^{44} + 2768 q^{45} + 4041 q^{46} + 2904 q^{47} + 2702 q^{48} + 1226 q^{49} + 1322 q^{50} + 589 q^{51} - 2156 q^{52} + 391 q^{53} - 5862 q^{54} - 3323 q^{55} - 7028 q^{56} - 7623 q^{57} - 5639 q^{58} - 2445 q^{59} - 3157 q^{60} - 1059 q^{61} + 1468 q^{62} + 3155 q^{63} + 4570 q^{64} + 2641 q^{65} + 5206 q^{66} + 27 q^{67} + 8350 q^{68} + 4005 q^{69} + 9702 q^{70} + 3465 q^{71} + 5629 q^{72} + 435 q^{73} - 994 q^{74} - 7819 q^{75} - 3598 q^{76} - 5931 q^{77} - 8996 q^{78} - 2559 q^{79} - 14052 q^{80} - 4788 q^{81} - 3822 q^{82} - 3967 q^{83} - 8427 q^{84} + 299 q^{85} + 721 q^{86} + 8363 q^{87} + 5825 q^{88} + 3717 q^{89} + 16742 q^{90} + 7238 q^{91} + 9550 q^{92} + 12750 q^{93} + 6035 q^{94} + 4551 q^{95} + 2493 q^{96} - 2419 q^{97} - 5687 q^{98} - 755 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.24175 2.08335i −1.14613 0.736574i −0.177266 0.984163i \(-0.556725\pi\)
−0.968865 + 0.247589i \(0.920362\pi\)
\(3\) 1.21610 + 8.45817i 0.234039 + 1.62778i 0.680343 + 0.732894i \(0.261831\pi\)
−0.446304 + 0.894881i \(0.647260\pi\)
\(4\) 2.84529 + 6.23031i 0.355661 + 0.778789i
\(5\) 12.7969 + 3.75752i 1.14459 + 0.336083i 0.798428 0.602090i \(-0.205665\pi\)
0.346166 + 0.938173i \(0.387484\pi\)
\(6\) 13.6790 29.9528i 0.930738 2.03803i
\(7\) −11.3462 + 13.0942i −0.612637 + 0.707021i −0.974291 0.225291i \(-0.927667\pi\)
0.361654 + 0.932312i \(0.382212\pi\)
\(8\) −0.631070 + 4.38919i −0.0278896 + 0.193977i
\(9\) −44.1554 + 12.9652i −1.63539 + 0.480193i
\(10\) −33.6563 38.8414i −1.06430 1.22827i
\(11\) 45.2432 29.0760i 1.24012 0.796977i 0.254685 0.967024i \(-0.418028\pi\)
0.985436 + 0.170047i \(0.0543919\pi\)
\(12\) −49.2369 + 31.6426i −1.18446 + 0.761203i
\(13\) −27.2602 31.4600i −0.581587 0.671187i 0.386358 0.922349i \(-0.373733\pi\)
−0.967945 + 0.251162i \(0.919187\pi\)
\(14\) 64.0613 18.8101i 1.22294 0.359086i
\(15\) −16.2194 + 112.808i −0.279188 + 1.94180i
\(16\) 47.0725 54.3245i 0.735508 0.848821i
\(17\) 14.8231 32.4581i 0.211478 0.463073i −0.773932 0.633269i \(-0.781713\pi\)
0.985410 + 0.170196i \(0.0544400\pi\)
\(18\) 170.152 + 49.9611i 2.22806 + 0.654219i
\(19\) 8.29844 + 18.1710i 0.100200 + 0.219406i 0.953092 0.302680i \(-0.0978812\pi\)
−0.852893 + 0.522086i \(0.825154\pi\)
\(20\) 13.0005 + 90.4202i 0.145350 + 1.01093i
\(21\) −124.551 80.0442i −1.29425 0.831765i
\(22\) −207.242 −2.00837
\(23\) 89.7322 + 64.1492i 0.813499 + 0.581567i
\(24\) −37.8919 −0.322277
\(25\) 44.4861 + 28.5895i 0.355889 + 0.228716i
\(26\) 22.8288 + 158.778i 0.172196 + 1.19765i
\(27\) −67.5152 147.838i −0.481233 1.05375i
\(28\) −113.864 33.4335i −0.768511 0.225655i
\(29\) 77.8452 170.457i 0.498465 1.09149i −0.478500 0.878087i \(-0.658819\pi\)
0.976965 0.213399i \(-0.0684533\pi\)
\(30\) 287.598 331.905i 1.75026 2.01991i
\(31\) −0.302527 + 2.10412i −0.00175276 + 0.0121907i −0.990679 0.136217i \(-0.956506\pi\)
0.988926 + 0.148407i \(0.0474147\pi\)
\(32\) −231.736 + 68.0439i −1.28017 + 0.375893i
\(33\) 300.950 + 347.315i 1.58754 + 1.83211i
\(34\) −115.674 + 74.3393i −0.583470 + 0.374973i
\(35\) −194.398 + 124.932i −0.938838 + 0.603355i
\(36\) −206.412 238.212i −0.955612 1.10283i
\(37\) 99.0257 29.0766i 0.439993 0.129194i −0.0542307 0.998528i \(-0.517271\pi\)
0.494223 + 0.869335i \(0.335452\pi\)
\(38\) 10.9551 76.1945i 0.0467672 0.325273i
\(39\) 232.943 268.830i 0.956428 1.10378i
\(40\) −24.5682 + 53.7969i −0.0971145 + 0.212651i
\(41\) −457.540 134.346i −1.74282 0.511739i −0.753497 0.657451i \(-0.771635\pi\)
−0.989327 + 0.145711i \(0.953453\pi\)
\(42\) 237.004 + 518.966i 0.870726 + 1.90662i
\(43\) 1.21166 + 8.42730i 0.00429714 + 0.0298872i 0.991857 0.127355i \(-0.0406487\pi\)
−0.987560 + 0.157242i \(0.949740\pi\)
\(44\) 309.883 + 199.149i 1.06174 + 0.682339i
\(45\) −613.771 −2.03324
\(46\) −157.244 394.899i −0.504009 1.26575i
\(47\) 239.887 0.744493 0.372246 0.928134i \(-0.378588\pi\)
0.372246 + 0.928134i \(0.378588\pi\)
\(48\) 516.731 + 332.083i 1.55383 + 0.998584i
\(49\) 6.09187 + 42.3699i 0.0177606 + 0.123527i
\(50\) −84.6511 185.360i −0.239429 0.524277i
\(51\) 292.562 + 85.9041i 0.803273 + 0.235862i
\(52\) 118.442 259.353i 0.315865 0.691649i
\(53\) 49.4924 57.1173i 0.128270 0.148031i −0.687981 0.725728i \(-0.741503\pi\)
0.816251 + 0.577697i \(0.196048\pi\)
\(54\) −89.1296 + 619.910i −0.224611 + 1.56220i
\(55\) 688.228 202.082i 1.68728 0.495432i
\(56\) −50.3127 58.0639i −0.120059 0.138556i
\(57\) −143.602 + 92.2874i −0.333694 + 0.214452i
\(58\) −607.476 + 390.401i −1.37527 + 0.883830i
\(59\) 136.622 + 157.670i 0.301469 + 0.347913i 0.886191 0.463320i \(-0.153342\pi\)
−0.584722 + 0.811234i \(0.698797\pi\)
\(60\) −748.979 + 219.920i −1.61155 + 0.473193i
\(61\) −45.8150 + 318.650i −0.0961641 + 0.668836i 0.883535 + 0.468364i \(0.155157\pi\)
−0.979699 + 0.200472i \(0.935753\pi\)
\(62\) 5.36433 6.19077i 0.0109882 0.0126811i
\(63\) 331.227 725.286i 0.662392 1.45044i
\(64\) 341.231 + 100.194i 0.666466 + 0.195692i
\(65\) −230.636 505.023i −0.440106 0.963698i
\(66\) −252.028 1752.89i −0.470037 3.26918i
\(67\) −583.925 375.266i −1.06474 0.684269i −0.113759 0.993508i \(-0.536289\pi\)
−0.950984 + 0.309240i \(0.899926\pi\)
\(68\) 244.400 0.435851
\(69\) −433.462 + 836.982i −0.756270 + 1.46030i
\(70\) 890.468 1.52045
\(71\) 76.1783 + 48.9568i 0.127334 + 0.0818325i 0.602757 0.797925i \(-0.294069\pi\)
−0.475423 + 0.879757i \(0.657705\pi\)
\(72\) −29.0415 201.988i −0.0475358 0.330619i
\(73\) 44.1089 + 96.5851i 0.0707200 + 0.154855i 0.941691 0.336480i \(-0.109236\pi\)
−0.870971 + 0.491335i \(0.836509\pi\)
\(74\) −381.593 112.046i −0.599450 0.176014i
\(75\) −187.715 + 411.039i −0.289007 + 0.632836i
\(76\) −89.5998 + 103.404i −0.135234 + 0.156069i
\(77\) −132.610 + 922.326i −0.196264 + 1.36505i
\(78\) −1315.21 + 386.180i −1.90921 + 0.560593i
\(79\) −373.412 430.940i −0.531799 0.613728i 0.424747 0.905312i \(-0.360363\pi\)
−0.956545 + 0.291584i \(0.905818\pi\)
\(80\) 806.510 518.312i 1.12713 0.724364i
\(81\) 123.050 79.0792i 0.168792 0.108476i
\(82\) 1203.34 + 1388.73i 1.62057 + 1.87024i
\(83\) −713.068 + 209.376i −0.943005 + 0.276891i −0.716872 0.697205i \(-0.754427\pi\)
−0.226133 + 0.974096i \(0.572608\pi\)
\(84\) 144.316 1003.74i 0.187455 1.30378i
\(85\) 311.653 359.666i 0.397688 0.458956i
\(86\) 13.6291 29.8435i 0.0170891 0.0374199i
\(87\) 1536.42 + 451.134i 1.89335 + 0.555939i
\(88\) 99.0685 + 216.930i 0.120008 + 0.262782i
\(89\) −79.7950 554.987i −0.0950366 0.660994i −0.980534 0.196350i \(-0.937091\pi\)
0.885497 0.464644i \(-0.153818\pi\)
\(90\) 1989.69 + 1278.70i 2.33036 + 1.49763i
\(91\) 721.244 0.830845
\(92\) −144.356 + 741.583i −0.163588 + 0.840384i
\(93\) −18.1649 −0.0202539
\(94\) −777.655 499.768i −0.853287 0.548374i
\(95\) 37.9165 + 263.715i 0.0409490 + 0.284807i
\(96\) −857.342 1877.32i −0.911480 1.99586i
\(97\) −538.454 158.104i −0.563626 0.165495i −0.0125062 0.999922i \(-0.503981\pi\)
−0.551119 + 0.834426i \(0.685799\pi\)
\(98\) 68.5229 150.044i 0.0706312 0.154661i
\(99\) −1620.75 + 1870.45i −1.64537 + 1.89886i
\(100\) −51.5457 + 358.508i −0.0515457 + 0.358508i
\(101\) 1467.28 430.833i 1.44555 0.424450i 0.537479 0.843277i \(-0.319377\pi\)
0.908066 + 0.418827i \(0.137559\pi\)
\(102\) −769.446 887.988i −0.746926 0.861999i
\(103\) −1591.23 + 1022.62i −1.52222 + 0.978270i −0.530807 + 0.847493i \(0.678111\pi\)
−0.991412 + 0.130777i \(0.958253\pi\)
\(104\) 155.287 99.7969i 0.146415 0.0940951i
\(105\) −1293.11 1492.32i −1.20185 1.38701i
\(106\) −279.437 + 82.0501i −0.256050 + 0.0751831i
\(107\) 98.6006 685.782i 0.0890848 0.619599i −0.895548 0.444964i \(-0.853216\pi\)
0.984633 0.174635i \(-0.0558744\pi\)
\(108\) 728.974 841.281i 0.649496 0.749558i
\(109\) 124.876 273.441i 0.109734 0.240283i −0.846796 0.531917i \(-0.821472\pi\)
0.956530 + 0.291634i \(0.0941989\pi\)
\(110\) −2652.07 778.718i −2.29877 0.674980i
\(111\) 366.360 + 802.216i 0.313273 + 0.685973i
\(112\) 177.243 + 1232.75i 0.149535 + 1.04004i
\(113\) 369.752 + 237.625i 0.307817 + 0.197822i 0.685424 0.728144i \(-0.259617\pi\)
−0.377607 + 0.925966i \(0.623253\pi\)
\(114\) 657.788 0.540417
\(115\) 907.256 + 1158.09i 0.735670 + 0.939061i
\(116\) 1283.49 1.02732
\(117\) 1611.57 + 1035.69i 1.27342 + 0.818376i
\(118\) −114.413 795.757i −0.0892588 0.620809i
\(119\) 256.827 + 562.373i 0.197843 + 0.433215i
\(120\) −484.901 142.380i −0.368877 0.108312i
\(121\) 648.612 1420.26i 0.487312 1.06706i
\(122\) 812.380 937.536i 0.602864 0.695742i
\(123\) 579.906 4033.33i 0.425108 2.95669i
\(124\) −13.9701 + 4.10200i −0.0101174 + 0.00297073i
\(125\) −629.890 726.931i −0.450712 0.520150i
\(126\) −2584.78 + 1661.13i −1.82754 + 1.17449i
\(127\) 1267.62 814.647i 0.885691 0.569199i −0.0168236 0.999858i \(-0.505355\pi\)
0.902515 + 0.430659i \(0.141719\pi\)
\(128\) 367.849 + 424.521i 0.254012 + 0.293146i
\(129\) −69.8060 + 20.4969i −0.0476440 + 0.0139895i
\(130\) −304.472 + 2117.65i −0.205415 + 1.42870i
\(131\) −1741.65 + 2009.97i −1.16159 + 1.34055i −0.231673 + 0.972794i \(0.574420\pi\)
−0.929921 + 0.367758i \(0.880125\pi\)
\(132\) −1307.59 + 2863.22i −0.862206 + 1.88797i
\(133\) −332.091 97.5107i −0.216511 0.0635733i
\(134\) 1111.13 + 2433.03i 0.716321 + 1.56852i
\(135\) −308.485 2145.56i −0.196668 1.36785i
\(136\) 133.110 + 85.5447i 0.0839272 + 0.0539368i
\(137\) −437.110 −0.272590 −0.136295 0.990668i \(-0.543519\pi\)
−0.136295 + 0.990668i \(0.543519\pi\)
\(138\) 3148.90 1810.24i 1.94241 1.11665i
\(139\) −2.56348 −0.00156425 −0.000782127 1.00000i \(-0.500249\pi\)
−0.000782127 1.00000i \(0.500249\pi\)
\(140\) −1331.49 855.694i −0.803794 0.516567i
\(141\) 291.727 + 2029.01i 0.174240 + 1.21187i
\(142\) −144.957 317.412i −0.0856657 0.187582i
\(143\) −2148.07 630.731i −1.25616 0.368842i
\(144\) −1374.18 + 3009.03i −0.795241 + 1.74133i
\(145\) 1636.68 1888.83i 0.937370 1.08178i
\(146\) 58.2300 404.999i 0.0330079 0.229575i
\(147\) −350.964 + 103.052i −0.196918 + 0.0578204i
\(148\) 462.913 + 534.230i 0.257103 + 0.296712i
\(149\) 2034.14 1307.26i 1.11841 0.718760i 0.155303 0.987867i \(-0.450365\pi\)
0.963110 + 0.269106i \(0.0867284\pi\)
\(150\) 1464.86 941.410i 0.797370 0.512439i
\(151\) 84.3251 + 97.3163i 0.0454455 + 0.0524470i 0.778017 0.628243i \(-0.216226\pi\)
−0.732572 + 0.680690i \(0.761680\pi\)
\(152\) −84.9930 + 24.9562i −0.0453542 + 0.0133172i
\(153\) −233.695 + 1625.38i −0.123484 + 0.858853i
\(154\) 2351.41 2713.68i 1.23040 1.41996i
\(155\) −11.7777 + 25.7896i −0.00610328 + 0.0133643i
\(156\) 2337.69 + 686.407i 1.19977 + 0.352285i
\(157\) −830.268 1818.03i −0.422055 0.924171i −0.994550 0.104263i \(-0.966752\pi\)
0.572495 0.819908i \(-0.305976\pi\)
\(158\) 312.710 + 2174.95i 0.157455 + 1.09512i
\(159\) 543.296 + 349.155i 0.270982 + 0.174150i
\(160\) −3221.19 −1.59161
\(161\) −1858.10 + 447.123i −0.909559 + 0.218871i
\(162\) −563.645 −0.273359
\(163\) −2359.29 1516.22i −1.13370 0.728587i −0.167373 0.985894i \(-0.553529\pi\)
−0.966330 + 0.257307i \(0.917165\pi\)
\(164\) −464.817 3232.87i −0.221318 1.53930i
\(165\) 2546.20 + 5575.40i 1.20134 + 2.63057i
\(166\) 2747.79 + 806.824i 1.28476 + 0.377239i
\(167\) 388.976 851.738i 0.180239 0.394667i −0.797850 0.602856i \(-0.794029\pi\)
0.978089 + 0.208188i \(0.0667567\pi\)
\(168\) 429.929 496.165i 0.197439 0.227857i
\(169\) 66.0550 459.423i 0.0300660 0.209114i
\(170\) −1759.61 + 516.668i −0.793858 + 0.233098i
\(171\) −602.012 694.759i −0.269222 0.310699i
\(172\) −49.0572 + 31.5271i −0.0217475 + 0.0139763i
\(173\) −1505.56 + 967.563i −0.661650 + 0.425216i −0.827906 0.560866i \(-0.810468\pi\)
0.166257 + 0.986082i \(0.446832\pi\)
\(174\) −4040.83 4663.36i −1.76054 2.03177i
\(175\) −879.105 + 258.129i −0.379738 + 0.111501i
\(176\) 550.167 3826.50i 0.235627 1.63882i
\(177\) −1167.45 + 1347.31i −0.495770 + 0.572149i
\(178\) −897.554 + 1965.37i −0.377947 + 0.827587i
\(179\) 4347.88 + 1276.65i 1.81551 + 0.533082i 0.999019 0.0442784i \(-0.0140989\pi\)
0.816490 + 0.577360i \(0.195917\pi\)
\(180\) −1746.36 3823.99i −0.723143 1.58346i
\(181\) 321.559 + 2236.49i 0.132051 + 0.918437i 0.942875 + 0.333146i \(0.108110\pi\)
−0.810824 + 0.585290i \(0.800981\pi\)
\(182\) −2338.09 1502.60i −0.952258 0.611979i
\(183\) −2750.92 −1.11122
\(184\) −338.190 + 353.369i −0.135498 + 0.141580i
\(185\) 1376.48 0.547033
\(186\) 58.8861 + 37.8438i 0.0232137 + 0.0149185i
\(187\) −273.107 1899.50i −0.106800 0.742810i
\(188\) 682.549 + 1494.57i 0.264787 + 0.579803i
\(189\) 2701.86 + 793.336i 1.03985 + 0.305327i
\(190\) 426.494 933.892i 0.162848 0.356588i
\(191\) −1965.04 + 2267.78i −0.744425 + 0.859113i −0.994016 0.109239i \(-0.965159\pi\)
0.249590 + 0.968352i \(0.419704\pi\)
\(192\) −432.490 + 3008.03i −0.162564 + 1.13066i
\(193\) −675.793 + 198.431i −0.252045 + 0.0740070i −0.405314 0.914177i \(-0.632838\pi\)
0.153270 + 0.988184i \(0.451020\pi\)
\(194\) 1416.15 + 1634.32i 0.524089 + 0.604831i
\(195\) 3991.09 2564.92i 1.46568 0.941937i
\(196\) −246.645 + 158.509i −0.0898851 + 0.0577656i
\(197\) 3060.96 + 3532.53i 1.10703 + 1.27758i 0.957378 + 0.288837i \(0.0932685\pi\)
0.149648 + 0.988739i \(0.452186\pi\)
\(198\) 9150.87 2686.94i 3.28447 0.964406i
\(199\) −622.170 + 4327.29i −0.221630 + 1.54147i 0.510241 + 0.860031i \(0.329556\pi\)
−0.731872 + 0.681442i \(0.761353\pi\)
\(200\) −153.559 + 177.216i −0.0542912 + 0.0626553i
\(201\) 2463.95 5395.30i 0.864645 1.89331i
\(202\) −5654.14 1660.20i −1.96942 0.578275i
\(203\) 1348.75 + 2953.36i 0.466325 + 1.02111i
\(204\) 297.215 + 2067.18i 0.102006 + 0.709467i
\(205\) −5350.31 3438.44i −1.82284 1.17147i
\(206\) 7288.84 2.46523
\(207\) −4793.87 1669.14i −1.60965 0.560450i
\(208\) −2992.26 −0.997480
\(209\) 903.789 + 580.830i 0.299122 + 0.192234i
\(210\) 1082.90 + 7531.73i 0.355844 + 2.47495i
\(211\) −202.422 443.243i −0.0660442 0.144617i 0.873731 0.486409i \(-0.161693\pi\)
−0.939776 + 0.341792i \(0.888966\pi\)
\(212\) 496.679 + 145.838i 0.160906 + 0.0472462i
\(213\) −321.445 + 703.866i −0.103404 + 0.226423i
\(214\) −1748.36 + 2017.71i −0.558483 + 0.644524i
\(215\) −16.1602 + 112.397i −0.00512612 + 0.0356529i
\(216\) 691.494 203.041i 0.217825 0.0639592i
\(217\) −24.1193 27.8351i −0.00754527 0.00870771i
\(218\) −974.490 + 626.266i −0.302756 + 0.194569i
\(219\) −763.292 + 490.538i −0.235518 + 0.151358i
\(220\) 3217.24 + 3712.89i 0.985938 + 1.13783i
\(221\) −1425.21 + 418.480i −0.433802 + 0.127376i
\(222\) 483.647 3363.84i 0.146217 1.01696i
\(223\) 832.410 960.653i 0.249966 0.288476i −0.616875 0.787061i \(-0.711602\pi\)
0.866840 + 0.498586i \(0.166147\pi\)
\(224\) 1738.34 3806.44i 0.518518 1.13540i
\(225\) −2334.97 685.610i −0.691844 0.203144i
\(226\) −703.588 1540.64i −0.207088 0.453460i
\(227\) −220.228 1531.72i −0.0643923 0.447858i −0.996355 0.0853040i \(-0.972814\pi\)
0.931963 0.362554i \(-0.118095\pi\)
\(228\) −983.568 632.101i −0.285695 0.183605i
\(229\) −102.367 −0.0295398 −0.0147699 0.999891i \(-0.504702\pi\)
−0.0147699 + 0.999891i \(0.504702\pi\)
\(230\) −528.406 5644.35i −0.151487 1.61816i
\(231\) −7962.45 −2.26793
\(232\) 699.043 + 449.247i 0.197821 + 0.127132i
\(233\) −77.2406 537.220i −0.0217176 0.151049i 0.976077 0.217425i \(-0.0697656\pi\)
−0.997795 + 0.0663754i \(0.978857\pi\)
\(234\) −3066.60 6714.93i −0.856710 1.87593i
\(235\) 3069.83 + 901.382i 0.852142 + 0.250211i
\(236\) −593.605 + 1299.81i −0.163731 + 0.358520i
\(237\) 3190.86 3682.45i 0.874551 1.00929i
\(238\) 339.048 2358.13i 0.0923412 0.642247i
\(239\) 465.626 136.720i 0.126020 0.0370028i −0.218114 0.975923i \(-0.569991\pi\)
0.344134 + 0.938920i \(0.388172\pi\)
\(240\) 5364.77 + 6191.28i 1.44289 + 1.66519i
\(241\) 3236.62 2080.05i 0.865099 0.555965i −0.0311512 0.999515i \(-0.509917\pi\)
0.896250 + 0.443550i \(0.146281\pi\)
\(242\) −5061.54 + 3252.85i −1.34450 + 0.864055i
\(243\) −2055.13 2371.75i −0.542538 0.626122i
\(244\) −2115.65 + 621.211i −0.555084 + 0.162987i
\(245\) −81.2485 + 565.096i −0.0211868 + 0.147358i
\(246\) −10282.7 + 11866.9i −2.66505 + 3.07564i
\(247\) 345.444 756.416i 0.0889881 0.194857i
\(248\) −9.04447 2.65570i −0.00231583 0.000679988i
\(249\) −2638.10 5776.63i −0.671416 1.47020i
\(250\) 527.495 + 3668.81i 0.133447 + 0.928143i
\(251\) 2816.17 + 1809.84i 0.708187 + 0.455124i 0.844510 0.535540i \(-0.179892\pi\)
−0.136323 + 0.990664i \(0.543528\pi\)
\(252\) 5461.19 1.36517
\(253\) 5924.98 + 293.258i 1.47233 + 0.0728734i
\(254\) −5806.49 −1.43438
\(255\) 3421.12 + 2198.62i 0.840152 + 0.539933i
\(256\) −712.950 4958.68i −0.174060 1.21062i
\(257\) −2604.97 5704.09i −0.632271 1.38448i −0.906249 0.422744i \(-0.861067\pi\)
0.273978 0.961736i \(-0.411660\pi\)
\(258\) 268.996 + 78.9843i 0.0649106 + 0.0190595i
\(259\) −742.831 + 1626.57i −0.178213 + 0.390233i
\(260\) 2490.22 2873.87i 0.593989 0.685500i
\(261\) −1227.27 + 8535.88i −0.291059 + 2.02436i
\(262\) 9833.47 2887.37i 2.31876 0.680848i
\(263\) 1812.02 + 2091.18i 0.424843 + 0.490295i 0.927306 0.374303i \(-0.122118\pi\)
−0.502463 + 0.864599i \(0.667573\pi\)
\(264\) −1714.35 + 1101.75i −0.399663 + 0.256848i
\(265\) 847.971 544.958i 0.196568 0.126326i
\(266\) 873.407 + 1007.97i 0.201323 + 0.232340i
\(267\) 4597.13 1349.84i 1.05371 0.309396i
\(268\) 676.588 4705.77i 0.154213 1.07258i
\(269\) 1103.48 1273.48i 0.250113 0.288645i −0.616785 0.787132i \(-0.711565\pi\)
0.866898 + 0.498486i \(0.166111\pi\)
\(270\) −3469.91 + 7598.04i −0.782119 + 1.71260i
\(271\) −1188.51 348.979i −0.266410 0.0782250i 0.145800 0.989314i \(-0.453425\pi\)
−0.412209 + 0.911089i \(0.635243\pi\)
\(272\) −1065.51 2333.14i −0.237522 0.520101i
\(273\) 877.105 + 6100.40i 0.194450 + 1.35243i
\(274\) 1417.00 + 910.650i 0.312424 + 0.200782i
\(275\) 2843.96 0.623627
\(276\) −6447.98 319.145i −1.40624 0.0696023i
\(277\) 1842.26 0.399605 0.199802 0.979836i \(-0.435970\pi\)
0.199802 + 0.979836i \(0.435970\pi\)
\(278\) 8.31015 + 5.34061i 0.00179284 + 0.00115219i
\(279\) −13.9222 96.8307i −0.00298745 0.0207782i
\(280\) −425.672 932.092i −0.0908528 0.198940i
\(281\) −8411.91 2469.96i −1.78581 0.524361i −0.789780 0.613390i \(-0.789805\pi\)
−0.996029 + 0.0890297i \(0.971623\pi\)
\(282\) 3281.42 7185.30i 0.692928 1.51730i
\(283\) −5821.38 + 6718.23i −1.22277 + 1.41116i −0.340618 + 0.940202i \(0.610636\pi\)
−0.882157 + 0.470956i \(0.843909\pi\)
\(284\) −88.2671 + 613.911i −0.0184426 + 0.128271i
\(285\) −2184.44 + 641.409i −0.454018 + 0.133312i
\(286\) 5649.48 + 6519.85i 1.16804 + 1.34800i
\(287\) 6950.50 4466.81i 1.42953 0.918703i
\(288\) 9350.21 6009.02i 1.91308 1.22946i
\(289\) 2383.53 + 2750.74i 0.485147 + 0.559890i
\(290\) −9240.77 + 2713.34i −1.87116 + 0.549423i
\(291\) 682.458 4746.60i 0.137479 0.956188i
\(292\) −476.253 + 549.625i −0.0954472 + 0.110152i
\(293\) −1670.17 + 3657.15i −0.333011 + 0.729192i −0.999872 0.0159901i \(-0.994910\pi\)
0.666862 + 0.745182i \(0.267637\pi\)
\(294\) 1352.43 + 397.109i 0.268283 + 0.0787751i
\(295\) 1155.89 + 2531.06i 0.228131 + 0.499538i
\(296\) 65.1304 + 452.992i 0.0127893 + 0.0889514i
\(297\) −7353.13 4725.57i −1.43661 0.923250i
\(298\) −9317.67 −1.81127
\(299\) −427.988 4571.70i −0.0827799 0.884242i
\(300\) −3095.01 −0.595634
\(301\) −124.097 79.7520i −0.0237635 0.0152719i
\(302\) −70.6172 491.153i −0.0134555 0.0935851i
\(303\) 5428.42 + 11886.6i 1.02922 + 2.25369i
\(304\) 1377.76 + 404.547i 0.259934 + 0.0763236i
\(305\) −1783.63 + 3905.60i −0.334853 + 0.733227i
\(306\) 4143.82 4782.22i 0.774138 0.893403i
\(307\) −1333.59 + 9275.32i −0.247922 + 1.72433i 0.362264 + 0.932075i \(0.382004\pi\)
−0.610186 + 0.792258i \(0.708905\pi\)
\(308\) −6123.69 + 1798.08i −1.13289 + 0.332646i
\(309\) −10584.6 12215.3i −1.94866 2.24888i
\(310\) 91.9090 59.0663i 0.0168390 0.0108218i
\(311\) 5508.58 3540.15i 1.00438 0.645477i 0.0684489 0.997655i \(-0.478195\pi\)
0.935933 + 0.352177i \(0.114559\pi\)
\(312\) 1032.94 + 1192.08i 0.187432 + 0.216309i
\(313\) 8744.45 2567.60i 1.57912 0.463673i 0.629483 0.777014i \(-0.283267\pi\)
0.949641 + 0.313341i \(0.101448\pi\)
\(314\) −1096.07 + 7623.34i −0.196990 + 1.37010i
\(315\) 6963.97 8036.85i 1.24564 1.43754i
\(316\) 1622.43 3552.62i 0.288825 0.632438i
\(317\) −4985.48 1463.87i −0.883320 0.259366i −0.191549 0.981483i \(-0.561351\pi\)
−0.691771 + 0.722117i \(0.743169\pi\)
\(318\) −1033.82 2263.74i −0.182307 0.399197i
\(319\) −1434.25 9975.45i −0.251733 1.75084i
\(320\) 3990.23 + 2564.36i 0.697064 + 0.447976i
\(321\) 5920.37 1.02942
\(322\) 6955.01 + 2421.61i 1.20369 + 0.419103i
\(323\) 712.806 0.122791
\(324\) 842.800 + 541.634i 0.144513 + 0.0928728i
\(325\) −313.277 2178.89i −0.0534692 0.371887i
\(326\) 4489.40 + 9830.42i 0.762715 + 1.67011i
\(327\) 2464.67 + 723.693i 0.416809 + 0.122386i
\(328\) 878.410 1923.45i 0.147872 0.323795i
\(329\) −2721.81 + 3141.13i −0.456104 + 0.526372i
\(330\) 3361.34 23378.7i 0.560715 3.89986i
\(331\) −2745.78 + 806.235i −0.455957 + 0.133881i −0.501643 0.865075i \(-0.667271\pi\)
0.0456856 + 0.998956i \(0.485453\pi\)
\(332\) −3333.36 3846.90i −0.551030 0.635922i
\(333\) −3995.54 + 2567.78i −0.657520 + 0.422562i
\(334\) −3035.43 + 1950.75i −0.497279 + 0.319582i
\(335\) −6062.39 6996.37i −0.988727 1.14105i
\(336\) −10211.3 + 2998.31i −1.65795 + 0.486819i
\(337\) −1601.88 + 11141.3i −0.258932 + 1.80091i 0.281541 + 0.959549i \(0.409154\pi\)
−0.540473 + 0.841361i \(0.681755\pi\)
\(338\) −1171.27 + 1351.72i −0.188487 + 0.217526i
\(339\) −1560.22 + 3416.40i −0.249969 + 0.547355i
\(340\) 3127.57 + 918.339i 0.498872 + 0.146482i
\(341\) 47.4922 + 103.993i 0.00754208 + 0.0165148i
\(342\) 504.149 + 3506.43i 0.0797113 + 0.554404i
\(343\) −5623.37 3613.92i −0.885229 0.568902i
\(344\) −37.7536 −0.00591727
\(345\) −8691.96 + 9082.08i −1.35640 + 1.41728i
\(346\) 6896.40 1.07154
\(347\) −7456.51 4792.01i −1.15356 0.741350i −0.183218 0.983072i \(-0.558652\pi\)
−0.970346 + 0.241722i \(0.922288\pi\)
\(348\) 1560.86 + 10856.0i 0.240433 + 1.67225i
\(349\) 484.545 + 1061.01i 0.0743183 + 0.162734i 0.943145 0.332382i \(-0.107852\pi\)
−0.868826 + 0.495117i \(0.835125\pi\)
\(350\) 3387.61 + 994.692i 0.517358 + 0.151910i
\(351\) −2810.49 + 6154.12i −0.427387 + 0.935847i
\(352\) −8506.04 + 9816.50i −1.28799 + 1.48642i
\(353\) 1126.71 7836.42i 0.169883 1.18156i −0.709241 0.704966i \(-0.750962\pi\)
0.879124 0.476594i \(-0.158129\pi\)
\(354\) 6591.51 1935.44i 0.989647 0.290587i
\(355\) 790.894 + 912.740i 0.118243 + 0.136460i
\(356\) 3230.70 2076.24i 0.480974 0.309103i
\(357\) −4444.32 + 2856.19i −0.658874 + 0.423433i
\(358\) −11435.0 13196.7i −1.68816 1.94824i
\(359\) 2012.00 590.776i 0.295792 0.0868523i −0.130470 0.991452i \(-0.541649\pi\)
0.426261 + 0.904600i \(0.359830\pi\)
\(360\) 387.333 2693.96i 0.0567062 0.394400i
\(361\) 4230.37 4882.10i 0.616761 0.711781i
\(362\) 3616.97 7920.06i 0.525148 1.14991i
\(363\) 12801.6 + 3758.89i 1.85099 + 0.543500i
\(364\) 2052.15 + 4493.57i 0.295499 + 0.647053i
\(365\) 201.539 + 1401.73i 0.0289015 + 0.201014i
\(366\) 8917.78 + 5731.11i 1.27361 + 0.818497i
\(367\) 6556.23 0.932514 0.466257 0.884649i \(-0.345602\pi\)
0.466257 + 0.884649i \(0.345602\pi\)
\(368\) 7708.80 1855.00i 1.09198 0.262768i
\(369\) 21944.7 3.09592
\(370\) −4462.21 2867.69i −0.626971 0.402930i
\(371\) 186.355 + 1296.13i 0.0260784 + 0.181379i
\(372\) −51.6845 113.173i −0.00720353 0.0157735i
\(373\) 7087.92 + 2081.20i 0.983911 + 0.288902i 0.733838 0.679325i \(-0.237727\pi\)
0.250073 + 0.968227i \(0.419545\pi\)
\(374\) −3071.98 + 6726.69i −0.424728 + 0.930024i
\(375\) 5382.50 6211.73i 0.741203 0.855394i
\(376\) −151.386 + 1052.91i −0.0207636 + 0.144414i
\(377\) −7484.66 + 2197.69i −1.02249 + 0.300231i
\(378\) −7105.95 8200.70i −0.966906 1.11587i
\(379\) −10833.7 + 6962.37i −1.46831 + 0.943622i −0.470170 + 0.882576i \(0.655807\pi\)
−0.998135 + 0.0610467i \(0.980556\pi\)
\(380\) −1535.15 + 986.578i −0.207240 + 0.133185i
\(381\) 8431.98 + 9731.02i 1.13381 + 1.30849i
\(382\) 11094.7 3257.71i 1.48601 0.436332i
\(383\) −1006.90 + 7003.15i −0.134335 + 0.934319i 0.805477 + 0.592627i \(0.201909\pi\)
−0.939812 + 0.341692i \(0.889000\pi\)
\(384\) −3143.33 + 3627.59i −0.417727 + 0.482083i
\(385\) −5162.67 + 11304.7i −0.683413 + 1.49647i
\(386\) 2604.15 + 764.648i 0.343388 + 0.100828i
\(387\) −162.763 356.401i −0.0213791 0.0468137i
\(388\) −547.017 3804.59i −0.0715737 0.497806i
\(389\) 11720.3 + 7532.15i 1.52761 + 0.981735i 0.990391 + 0.138292i \(0.0441613\pi\)
0.537219 + 0.843443i \(0.319475\pi\)
\(390\) −18281.7 −2.37367
\(391\) 3412.27 1961.65i 0.441345 0.253720i
\(392\) −189.814 −0.0244568
\(393\) −19118.7 12286.9i −2.45398 1.57707i
\(394\) −2563.37 17828.6i −0.327768 2.27968i
\(395\) −3159.26 6917.82i −0.402430 0.881198i
\(396\) −16265.0 4775.84i −2.06401 0.606047i
\(397\) −1251.21 + 2739.76i −0.158177 + 0.346359i −0.972083 0.234637i \(-0.924610\pi\)
0.813906 + 0.580997i \(0.197337\pi\)
\(398\) 11032.2 12731.8i 1.38943 1.60348i
\(399\) 420.906 2927.47i 0.0528112 0.367310i
\(400\) 3647.19 1070.91i 0.455898 0.133864i
\(401\) −4482.45 5173.02i −0.558212 0.644211i 0.404565 0.914509i \(-0.367423\pi\)
−0.962776 + 0.270299i \(0.912878\pi\)
\(402\) −19227.8 + 12356.9i −2.38556 + 1.53310i
\(403\) 74.4427 47.8414i 0.00920162 0.00591352i
\(404\) 6859.07 + 7915.78i 0.844681 + 0.974814i
\(405\) 1871.80 549.610i 0.229656 0.0674330i
\(406\) 1780.55 12384.0i 0.217653 1.51381i
\(407\) 3634.81 4194.79i 0.442680 0.510880i
\(408\) −561.676 + 1229.90i −0.0681547 + 0.149238i
\(409\) −6416.45 1884.04i −0.775728 0.227774i −0.130176 0.991491i \(-0.541554\pi\)
−0.645552 + 0.763717i \(0.723373\pi\)
\(410\) 10180.9 + 22293.1i 1.22634 + 2.68531i
\(411\) −531.569 3697.15i −0.0637966 0.443715i
\(412\) −10898.8 7004.20i −1.30326 0.837554i
\(413\) −3614.70 −0.430673
\(414\) 12063.1 + 15398.2i 1.43205 + 1.82797i
\(415\) −9911.83 −1.17242
\(416\) 8457.85 + 5435.53i 0.996828 + 0.640622i
\(417\) −3.11745 21.6823i −0.000366096 0.00254625i
\(418\) −1719.79 3765.81i −0.201238 0.440650i
\(419\) −3914.17 1149.30i −0.456371 0.134003i 0.0454639 0.998966i \(-0.485523\pi\)
−0.501835 + 0.864963i \(0.667342\pi\)
\(420\) 5618.39 12302.5i 0.652736 1.42929i
\(421\) −4454.26 + 5140.49i −0.515647 + 0.595088i −0.952536 0.304427i \(-0.901535\pi\)
0.436889 + 0.899516i \(0.356080\pi\)
\(422\) −267.226 + 1858.60i −0.0308255 + 0.214396i
\(423\) −10592.3 + 3110.19i −1.21753 + 0.357500i
\(424\) 219.465 + 253.277i 0.0251372 + 0.0290099i
\(425\) 1587.38 1020.15i 0.181175 0.116434i
\(426\) 2508.44 1612.08i 0.285292 0.183346i
\(427\) −3652.65 4215.38i −0.413967 0.477744i
\(428\) 4553.18 1336.94i 0.514221 0.150989i
\(429\) 2722.55 18935.8i 0.306401 2.13107i
\(430\) 286.548 330.694i 0.0321362 0.0370872i
\(431\) 6137.37 13439.0i 0.685908 1.50193i −0.170351 0.985384i \(-0.554490\pi\)
0.856259 0.516547i \(-0.172783\pi\)
\(432\) −11209.3 3291.35i −1.24840 0.366563i
\(433\) −1023.71 2241.62i −0.113618 0.248788i 0.844277 0.535907i \(-0.180030\pi\)
−0.957895 + 0.287118i \(0.907303\pi\)
\(434\) 20.1985 + 140.483i 0.00223400 + 0.0155378i
\(435\) 17966.4 + 11546.3i 1.98028 + 1.27265i
\(436\) 2058.93 0.226158
\(437\) −421.021 + 2162.87i −0.0460873 + 0.236760i
\(438\) 3496.36 0.381421
\(439\) 12933.1 + 8311.58i 1.40606 + 0.903622i 0.999948 0.0101993i \(-0.00324659\pi\)
0.406116 + 0.913822i \(0.366883\pi\)
\(440\) 452.656 + 3148.29i 0.0490444 + 0.341111i
\(441\) −818.324 1791.88i −0.0883623 0.193487i
\(442\) 5492.02 + 1612.60i 0.591016 + 0.173538i
\(443\) −71.5364 + 156.643i −0.00767223 + 0.0167998i −0.913429 0.406997i \(-0.866576\pi\)
0.905757 + 0.423797i \(0.139303\pi\)
\(444\) −3955.66 + 4565.07i −0.422809 + 0.487948i
\(445\) 1064.24 7401.97i 0.113371 0.788510i
\(446\) −4699.84 + 1380.00i −0.498977 + 0.146513i
\(447\) 13530.8 + 15615.4i 1.43173 + 1.65231i
\(448\) −5183.63 + 3331.32i −0.546660 + 0.351317i
\(449\) 9187.70 5904.58i 0.965689 0.620611i 0.0401224 0.999195i \(-0.487225\pi\)
0.925567 + 0.378584i \(0.123589\pi\)
\(450\) 6141.03 + 7087.13i 0.643314 + 0.742423i
\(451\) −24606.8 + 7225.22i −2.56916 + 0.754373i
\(452\) −428.428 + 2979.78i −0.0445831 + 0.310082i
\(453\) −720.570 + 831.582i −0.0747358 + 0.0862498i
\(454\) −2477.18 + 5424.26i −0.256079 + 0.560734i
\(455\) 9229.72 + 2710.09i 0.950980 + 0.279233i
\(456\) −314.444 688.536i −0.0322921 0.0707098i
\(457\) 6.66914 + 46.3849i 0.000682646 + 0.00474791i 0.990160 0.139940i \(-0.0446911\pi\)
−0.989477 + 0.144688i \(0.953782\pi\)
\(458\) 331.849 + 213.266i 0.0338565 + 0.0217582i
\(459\) −5799.31 −0.589735
\(460\) −4633.83 + 8947.58i −0.469681 + 0.906919i
\(461\) 527.073 0.0532500 0.0266250 0.999645i \(-0.491524\pi\)
0.0266250 + 0.999645i \(0.491524\pi\)
\(462\) 25812.3 + 16588.5i 2.59934 + 1.67050i
\(463\) −652.623 4539.09i −0.0655075 0.455614i −0.996004 0.0893127i \(-0.971533\pi\)
0.930496 0.366302i \(-0.119376\pi\)
\(464\) −5595.64 12252.7i −0.559852 1.22590i
\(465\) −232.456 68.2551i −0.0231825 0.00680700i
\(466\) −868.820 + 1902.45i −0.0863677 + 0.189119i
\(467\) −1791.34 + 2067.32i −0.177502 + 0.204849i −0.837528 0.546395i \(-0.816000\pi\)
0.660026 + 0.751243i \(0.270545\pi\)
\(468\) −1867.31 + 12987.4i −0.184437 + 1.28279i
\(469\) 11539.1 3388.20i 1.13609 0.333587i
\(470\) −8073.71 9317.56i −0.792367 0.914441i
\(471\) 14367.5 9233.46i 1.40557 0.903302i
\(472\) −778.261 + 500.158i −0.0758949 + 0.0487747i
\(473\) 299.852 + 346.047i 0.0291484 + 0.0336391i
\(474\) −18015.8 + 5289.91i −1.74576 + 0.512602i
\(475\) −150.336 + 1045.61i −0.0145218 + 0.101002i
\(476\) −2773.01 + 3200.22i −0.267018 + 0.308156i
\(477\) −1444.82 + 3163.72i −0.138687 + 0.303683i
\(478\) −1794.28 526.847i −0.171691 0.0504130i
\(479\) 2336.86 + 5117.01i 0.222910 + 0.488105i 0.987736 0.156132i \(-0.0499024\pi\)
−0.764826 + 0.644237i \(0.777175\pi\)
\(480\) −3917.30 27245.4i −0.372499 2.59079i
\(481\) −3614.22 2322.72i −0.342607 0.220180i
\(482\) −14825.8 −1.40103
\(483\) −6041.48 15172.4i −0.569145 1.42933i
\(484\) 10694.2 1.00434
\(485\) −6296.48 4046.50i −0.589502 0.378850i
\(486\) 1721.05 + 11970.2i 0.160634 + 1.11724i
\(487\) −2780.44 6088.32i −0.258714 0.566506i 0.735049 0.678014i \(-0.237159\pi\)
−0.993764 + 0.111508i \(0.964432\pi\)
\(488\) −1369.70 402.181i −0.127057 0.0373072i
\(489\) 9955.33 21799.1i 0.920645 2.01593i
\(490\) 1440.68 1662.63i 0.132823 0.153286i
\(491\) −497.765 + 3462.03i −0.0457511 + 0.318206i 0.954075 + 0.299567i \(0.0968423\pi\)
−0.999826 + 0.0186388i \(0.994067\pi\)
\(492\) 26778.9 7863.00i 2.45383 0.720511i
\(493\) −4378.81 5053.41i −0.400023 0.461651i
\(494\) −2695.72 + 1732.43i −0.245518 + 0.157785i
\(495\) −27769.0 + 17846.0i −2.52146 + 1.62044i
\(496\) 100.065 + 115.481i 0.00905855 + 0.0104541i
\(497\) −1505.39 + 442.021i −0.135867 + 0.0398941i
\(498\) −3482.66 + 24222.4i −0.313377 + 2.17959i
\(499\) 1863.92 2151.08i 0.167215 0.192977i −0.665957 0.745990i \(-0.731977\pi\)
0.833172 + 0.553013i \(0.186522\pi\)
\(500\) 2736.79 5992.74i 0.244786 0.536007i
\(501\) 7677.18 + 2254.22i 0.684613 + 0.201020i
\(502\) −5358.78 11734.1i −0.476443 1.04326i
\(503\) 1138.76 + 7920.22i 0.100944 + 0.702078i 0.975954 + 0.217975i \(0.0699450\pi\)
−0.875011 + 0.484103i \(0.839146\pi\)
\(504\) 2974.39 + 1911.52i 0.262876 + 0.168940i
\(505\) 20395.6 1.79721
\(506\) −18596.3 13294.4i −1.63381 1.16800i
\(507\) 3966.21 0.347427
\(508\) 8682.24 + 5579.74i 0.758292 + 0.487324i
\(509\) 1719.11 + 11956.7i 0.149702 + 1.04120i 0.916707 + 0.399559i \(0.130837\pi\)
−0.767005 + 0.641641i \(0.778254\pi\)
\(510\) −6509.92 14254.7i −0.565224 1.23767i
\(511\) −1765.17 518.302i −0.152812 0.0448695i
\(512\) −6152.66 + 13472.4i −0.531077 + 1.16290i
\(513\) 2126.09 2453.64i 0.182981 0.211171i
\(514\) −3438.93 + 23918.3i −0.295106 + 2.05251i
\(515\) −24205.4 + 7107.35i −2.07110 + 0.608130i
\(516\) −326.320 376.594i −0.0278400 0.0321291i
\(517\) 10853.3 6974.97i 0.923261 0.593344i
\(518\) 5796.78 3725.37i 0.491691 0.315991i
\(519\) −10014.7 11557.6i −0.847008 0.977500i
\(520\) 2362.19 693.601i 0.199209 0.0584931i
\(521\) 633.895 4408.84i 0.0533041 0.370738i −0.945657 0.325166i \(-0.894580\pi\)
0.998961 0.0455722i \(-0.0145111\pi\)
\(522\) 21761.7 25114.4i 1.82468 2.10580i
\(523\) −132.252 + 289.591i −0.0110573 + 0.0242121i −0.915080 0.403272i \(-0.867873\pi\)
0.904023 + 0.427484i \(0.140600\pi\)
\(524\) −17478.3 5132.08i −1.45714 0.427855i
\(525\) −3252.38 7121.71i −0.270372 0.592032i
\(526\) −1517.46 10554.1i −0.125788 0.874871i
\(527\) 63.8114 + 41.0091i 0.00527451 + 0.00338972i
\(528\) 33034.2 2.72278
\(529\) 3936.75 + 11512.5i 0.323560 + 0.946208i
\(530\) −3884.25 −0.318341
\(531\) −8076.82 5190.66i −0.660083 0.424210i
\(532\) −337.372 2346.48i −0.0274943 0.191227i
\(533\) 8246.14 + 18056.5i 0.670131 + 1.46738i
\(534\) −17714.9 5201.57i −1.43558 0.421524i
\(535\) 3838.63 8405.42i 0.310202 0.679249i
\(536\) 2015.61 2326.14i 0.162427 0.187451i
\(537\) −5510.69 + 38327.7i −0.442838 + 3.08000i
\(538\) −6230.31 + 1829.38i −0.499271 + 0.146599i
\(539\) 1507.56 + 1739.82i 0.120474 + 0.139034i
\(540\) 12489.8 8026.69i 0.995323 0.639655i
\(541\) −11321.2 + 7275.70i −0.899698 + 0.578201i −0.906701 0.421774i \(-0.861407\pi\)
0.00700233 + 0.999975i \(0.497771\pi\)
\(542\) 3125.82 + 3607.39i 0.247722 + 0.285887i
\(543\) −18525.6 + 5439.60i −1.46410 + 0.429900i
\(544\) −1226.48 + 8530.34i −0.0966633 + 0.672308i
\(545\) 2625.50 3029.98i 0.206356 0.238147i
\(546\) 9865.89 21603.3i 0.773299 1.69329i
\(547\) 7179.24 + 2108.01i 0.561174 + 0.164775i 0.550004 0.835162i \(-0.314626\pi\)
0.0111698 + 0.999938i \(0.496444\pi\)
\(548\) −1243.70 2723.33i −0.0969495 0.212290i
\(549\) −2108.39 14664.1i −0.163905 1.13998i
\(550\) −9219.42 5924.96i −0.714759 0.459347i
\(551\) 3743.38 0.289425
\(552\) −3400.13 2430.74i −0.262172 0.187426i
\(553\) 9879.62 0.759718
\(554\) −5972.14 3838.06i −0.458000 0.294338i
\(555\) 1673.94 + 11642.5i 0.128027 + 0.890446i
\(556\) −7.29383 15.9713i −0.000556344 0.00121822i
\(557\) −3823.17 1122.58i −0.290831 0.0853957i 0.133063 0.991108i \(-0.457519\pi\)
−0.423894 + 0.905712i \(0.639337\pi\)
\(558\) −156.600 + 342.906i −0.0118806 + 0.0260150i
\(559\) 232.093 267.849i 0.0175608 0.0202662i
\(560\) −2363.93 + 16441.5i −0.178382 + 1.24068i
\(561\) 15734.2 4619.98i 1.18413 0.347693i
\(562\) 22123.5 + 25531.9i 1.66054 + 1.91637i
\(563\) 5386.70 3461.82i 0.403237 0.259145i −0.323266 0.946308i \(-0.604781\pi\)
0.726503 + 0.687163i \(0.241144\pi\)
\(564\) −11811.3 + 7590.66i −0.881818 + 0.566710i
\(565\) 3838.81 + 4430.23i 0.285841 + 0.329878i
\(566\) 32867.9 9650.88i 2.44088 0.716708i
\(567\) −360.666 + 2508.48i −0.0267135 + 0.185796i
\(568\) −262.955 + 303.466i −0.0194249 + 0.0224175i
\(569\) −9673.05 + 21181.0i −0.712680 + 1.56055i 0.111206 + 0.993797i \(0.464529\pi\)
−0.823886 + 0.566755i \(0.808199\pi\)
\(570\) 8417.68 + 2471.65i 0.618558 + 0.181625i
\(571\) −8699.16 19048.5i −0.637563 1.39607i −0.902030 0.431673i \(-0.857923\pi\)
0.264467 0.964395i \(-0.414804\pi\)
\(572\) −2182.23 15177.8i −0.159517 1.10947i
\(573\) −21570.9 13862.8i −1.57267 1.01069i
\(574\) −31837.7 −2.31512
\(575\) 2157.85 + 5419.15i 0.156502 + 0.393034i
\(576\) −16366.2 −1.18390
\(577\) 9983.85 + 6416.23i 0.720335 + 0.462931i 0.848753 0.528789i \(-0.177354\pi\)
−0.128419 + 0.991720i \(0.540990\pi\)
\(578\) −1996.06 13882.9i −0.143642 0.999054i
\(579\) −2500.19 5474.66i −0.179455 0.392952i
\(580\) 16424.8 + 4822.75i 1.17587 + 0.345265i
\(581\) 5349.00 11712.7i 0.381952 0.836358i
\(582\) −12101.2 + 13965.5i −0.861872 + 0.994654i
\(583\) 578.450 4023.21i 0.0410926 0.285805i
\(584\) −451.766 + 132.650i −0.0320106 + 0.00939917i
\(585\) 16731.6 + 19309.2i 1.18250 + 1.36468i
\(586\) 13033.4 8376.04i 0.918777 0.590462i
\(587\) 4627.33 2973.81i 0.325367 0.209101i −0.367752 0.929924i \(-0.619872\pi\)
0.693119 + 0.720823i \(0.256236\pi\)
\(588\) −1640.64 1893.40i −0.115066 0.132793i
\(589\) −40.7446 + 11.9637i −0.00285034 + 0.000836936i
\(590\) 1525.94 10613.2i 0.106478 0.740572i
\(591\) −26156.3 + 30186.0i −1.82052 + 2.10099i
\(592\) 3081.82 6748.24i 0.213956 0.468498i
\(593\) 536.249 + 157.457i 0.0371351 + 0.0109038i 0.300247 0.953861i \(-0.402931\pi\)
−0.263112 + 0.964765i \(0.584749\pi\)
\(594\) 13992.0 + 30638.2i 0.966496 + 2.11633i
\(595\) 1173.47 + 8161.69i 0.0808533 + 0.562347i
\(596\) 13932.4 + 8953.81i 0.957539 + 0.615373i
\(597\) −37357.5 −2.56104
\(598\) −8137.00 + 15712.0i −0.556433 + 1.07443i
\(599\) 856.240 0.0584057 0.0292029 0.999574i \(-0.490703\pi\)
0.0292029 + 0.999574i \(0.490703\pi\)
\(600\) −1685.67 1083.31i −0.114695 0.0737100i
\(601\) 3056.66 + 21259.5i 0.207461 + 1.44292i 0.781404 + 0.624025i \(0.214504\pi\)
−0.573944 + 0.818895i \(0.694587\pi\)
\(602\) 236.139 + 517.072i 0.0159872 + 0.0350071i
\(603\) 30648.8 + 8999.31i 2.06985 + 0.607762i
\(604\) −366.382 + 802.265i −0.0246819 + 0.0540458i
\(605\) 13636.9 15737.8i 0.916396 1.05758i
\(606\) 7166.29 49842.6i 0.480380 3.34112i
\(607\) 4410.48 1295.03i 0.294919 0.0865960i −0.130926 0.991392i \(-0.541795\pi\)
0.425845 + 0.904796i \(0.359977\pi\)
\(608\) −3159.48 3646.23i −0.210746 0.243214i
\(609\) −23339.8 + 14999.6i −1.55300 + 0.998052i
\(610\) 13918.8 8945.07i 0.923861 0.593730i
\(611\) −6539.39 7546.86i −0.432987 0.499694i
\(612\) −10791.6 + 3168.69i −0.712784 + 0.209292i
\(613\) 2750.77 19132.0i 0.181244 1.26058i −0.672582 0.740023i \(-0.734815\pi\)
0.853826 0.520558i \(-0.174276\pi\)
\(614\) 23646.9 27289.9i 1.55425 1.79370i
\(615\) 22576.4 49435.3i 1.48027 3.24134i
\(616\) −3964.57 1164.10i −0.259314 0.0761414i
\(617\) 3164.01 + 6928.22i 0.206448 + 0.452058i 0.984326 0.176357i \(-0.0564314\pi\)
−0.777878 + 0.628415i \(0.783704\pi\)
\(618\) 8863.97 + 61650.2i 0.576960 + 4.01284i
\(619\) 9597.89 + 6168.19i 0.623218 + 0.400518i 0.813793 0.581155i \(-0.197399\pi\)
−0.190575 + 0.981673i \(0.561035\pi\)
\(620\) −194.188 −0.0125787
\(621\) 3425.38 17596.8i 0.221346 1.13710i
\(622\) −25232.8 −1.62660
\(623\) 8172.48 + 5252.13i 0.525559 + 0.337756i
\(624\) −3638.89 25309.0i −0.233449 1.62367i
\(625\) −8075.14 17682.1i −0.516809 1.13165i
\(626\) −33696.5 9894.20i −2.15141 0.631712i
\(627\) −3813.66 + 8350.75i −0.242907 + 0.531893i
\(628\) 8964.56 10345.7i 0.569626 0.657383i
\(629\) 524.099 3645.19i 0.0332229 0.231070i
\(630\) −39319.0 + 11545.1i −2.48652 + 0.730107i
\(631\) −16928.1 19536.1i −1.06799 1.23252i −0.971463 0.237190i \(-0.923774\pi\)
−0.0965219 0.995331i \(-0.530772\pi\)
\(632\) 2127.13 1367.02i 0.133881 0.0860398i
\(633\) 3502.86 2251.15i 0.219947 0.141351i
\(634\) 13111.9 + 15132.0i 0.821359 + 0.947898i
\(635\) 19282.7 5661.90i 1.20505 0.353836i
\(636\) −629.511 + 4378.35i −0.0392480 + 0.272976i
\(637\) 1166.89 1346.66i 0.0725807 0.0837626i
\(638\) −16132.8 + 35326.0i −1.00110 + 2.19211i
\(639\) −3998.42 1174.04i −0.247535 0.0726829i
\(640\) 3112.20 + 6814.77i 0.192220 + 0.420902i
\(641\) 2891.91 + 20113.7i 0.178196 + 1.23938i 0.860934 + 0.508716i \(0.169880\pi\)
−0.682739 + 0.730663i \(0.739211\pi\)
\(642\) −19192.3 12334.2i −1.17985 0.758241i
\(643\) −4432.19 −0.271833 −0.135917 0.990720i \(-0.543398\pi\)
−0.135917 + 0.990720i \(0.543398\pi\)
\(644\) −8072.55 10304.4i −0.493949 0.630511i
\(645\) −970.321 −0.0592347
\(646\) −2310.74 1485.02i −0.140735 0.0904448i
\(647\) −3146.42 21883.8i −0.191188 1.32974i −0.828870 0.559441i \(-0.811016\pi\)
0.637682 0.770300i \(-0.279893\pi\)
\(648\) 269.440 + 589.992i 0.0163343 + 0.0357671i
\(649\) 10765.6 + 3161.07i 0.651137 + 0.191191i
\(650\) −3523.82 + 7716.08i −0.212639 + 0.465615i
\(651\) 206.103 237.855i 0.0124083 0.0143199i
\(652\) 2733.68 19013.2i 0.164201 1.14205i
\(653\) 6058.51 1778.94i 0.363075 0.106608i −0.0951066 0.995467i \(-0.530319\pi\)
0.458181 + 0.888859i \(0.348501\pi\)
\(654\) −6482.14 7480.79i −0.387572 0.447282i
\(655\) −29840.4 + 19177.2i −1.78009 + 1.14399i
\(656\) −28835.9 + 18531.7i −1.71624 + 1.10296i
\(657\) −3199.89 3692.87i −0.190015 0.219289i
\(658\) 15367.5 4512.30i 0.910467 0.267337i
\(659\) 1542.91 10731.2i 0.0912037 0.634336i −0.892029 0.451979i \(-0.850718\pi\)
0.983232 0.182357i \(-0.0583727\pi\)
\(660\) −27491.8 + 31727.2i −1.62139 + 1.87118i
\(661\) −8445.88 + 18493.9i −0.496984 + 1.08824i 0.480454 + 0.877020i \(0.340472\pi\)
−0.977438 + 0.211223i \(0.932255\pi\)
\(662\) 10580.8 + 3106.81i 0.621201 + 0.182401i
\(663\) −5272.78 11545.8i −0.308865 0.676321i
\(664\) −468.993 3261.92i −0.0274103 0.190643i
\(665\) −3883.35 2495.68i −0.226451 0.145531i
\(666\) 18302.1 1.06485
\(667\) 17919.9 10301.8i 1.04027 0.598032i
\(668\) 6413.34 0.371467
\(669\) 9137.66 + 5872.42i 0.528075 + 0.339373i
\(670\) 5076.89 + 35310.5i 0.292742 + 2.03607i
\(671\) 7192.27 + 15748.9i 0.413792 + 0.906078i
\(672\) 34309.6 + 10074.2i 1.96952 + 0.578304i
\(673\) −1906.21 + 4174.03i −0.109181 + 0.239074i −0.956334 0.292275i \(-0.905588\pi\)
0.847153 + 0.531350i \(0.178315\pi\)
\(674\) 28404.1 32780.1i 1.62327 1.87336i
\(675\) 1223.11 8506.95i 0.0697448 0.485085i
\(676\) 3050.29 895.647i 0.173549 0.0509585i
\(677\) −4259.03 4915.19i −0.241784 0.279034i 0.621868 0.783122i \(-0.286374\pi\)
−0.863652 + 0.504088i \(0.831829\pi\)
\(678\) 12175.4 7824.64i 0.689664 0.443220i
\(679\) 8179.65 5256.74i 0.462307 0.297106i
\(680\) 1381.97 + 1594.88i 0.0779354 + 0.0899422i
\(681\) 12687.7 3725.45i 0.713942 0.209632i
\(682\) 62.6965 436.063i 0.00352019 0.0244835i
\(683\) −8953.78 + 10333.2i −0.501620 + 0.578901i −0.948933 0.315477i \(-0.897836\pi\)
0.447313 + 0.894378i \(0.352381\pi\)
\(684\) 2615.67 5727.51i 0.146217 0.320171i
\(685\) −5593.67 1642.45i −0.312004 0.0916128i
\(686\) 10700.5 + 23430.9i 0.595550 + 1.30407i
\(687\) −124.489 865.839i −0.00691346 0.0480842i
\(688\) 514.845 + 330.871i 0.0285295 + 0.0183348i
\(689\) −3146.09 −0.173957
\(690\) 47098.3 11333.5i 2.59855 0.625300i
\(691\) 7900.25 0.434934 0.217467 0.976068i \(-0.430220\pi\)
0.217467 + 0.976068i \(0.430220\pi\)
\(692\) −10312.0 6627.09i −0.566477 0.364052i
\(693\) −6102.67 42445.0i −0.334518 2.32663i
\(694\) 14188.7 + 31069.0i 0.776076 + 1.69937i
\(695\) −32.8047 9.63232i −0.00179043 0.000525719i
\(696\) −2949.70 + 6458.95i −0.160644 + 0.351761i
\(697\) −11142.8 + 12859.5i −0.605542 + 0.698833i
\(698\) 639.668 4448.99i 0.0346874 0.241256i
\(699\) 4449.97 1306.63i 0.240791 0.0707027i
\(700\) −4109.53 4742.65i −0.221894 0.256079i
\(701\) −18188.7 + 11689.1i −0.979995 + 0.629805i −0.929462 0.368918i \(-0.879728\pi\)
−0.0505330 + 0.998722i \(0.516092\pi\)
\(702\) 21932.1 14094.9i 1.17916 0.757802i
\(703\) 1350.11 + 1558.11i 0.0724330 + 0.0835921i
\(704\) 18351.6 5388.52i 0.982461 0.288476i
\(705\) −3890.82 + 27061.3i −0.207854 + 1.44565i
\(706\) −19978.5 + 23056.4i −1.06501 + 1.22909i
\(707\) −11006.7 + 24101.2i −0.585499 + 1.28206i
\(708\) −11715.9 3440.11i −0.621909 0.182609i
\(709\) −11037.2 24168.0i −0.584640 1.28018i −0.938627 0.344933i \(-0.887902\pi\)
0.353987 0.935250i \(-0.384826\pi\)
\(710\) −662.326 4606.58i −0.0350094 0.243496i
\(711\) 22075.4 + 14187.0i 1.16440 + 0.748317i
\(712\) 2486.30 0.130868
\(713\) −162.124 + 169.401i −0.00851557 + 0.00889777i
\(714\) 20357.8 1.06705
\(715\) −25118.8 16142.9i −1.31383 0.844348i
\(716\) 4417.03 + 30721.1i 0.230548 + 1.60349i
\(717\) 1722.65 + 3772.07i 0.0897259 + 0.196472i
\(718\) −7753.18 2276.54i −0.402989 0.118328i
\(719\) 1486.93 3255.93i 0.0771255 0.168881i −0.867141 0.498062i \(-0.834045\pi\)
0.944267 + 0.329181i \(0.106772\pi\)
\(720\) −28891.7 + 33342.9i −1.49546 + 1.72585i
\(721\) 4663.99 32438.7i 0.240910 1.67556i
\(722\) −23884.9 + 7013.24i −1.23117 + 0.361504i
\(723\) 21529.4 + 24846.3i 1.10745 + 1.27807i
\(724\) −13019.1 + 8366.87i −0.668303 + 0.429492i
\(725\) 8336.32 5357.43i 0.427039 0.274441i
\(726\) −33668.5 38855.5i −1.72115 1.98631i
\(727\) 18599.9 5461.42i 0.948874 0.278615i 0.229556 0.973295i \(-0.426273\pi\)
0.719318 + 0.694681i \(0.244454\pi\)
\(728\) −455.155 + 3165.67i −0.0231719 + 0.161164i
\(729\) 20147.6 23251.6i 1.02360 1.18130i
\(730\) 2266.96 4963.95i 0.114937 0.251677i
\(731\) 291.495 + 85.5905i 0.0147487 + 0.00433062i
\(732\) −7827.15 17139.1i −0.395218 0.865407i
\(733\) −2179.55 15159.1i −0.109828 0.763867i −0.968080 0.250640i \(-0.919359\pi\)
0.858253 0.513227i \(-0.171550\pi\)
\(734\) −21253.7 13658.9i −1.06878 0.686865i
\(735\) −4878.48 −0.244824
\(736\) −25159.2 8759.98i −1.26003 0.438719i
\(737\) −37329.9 −1.86576
\(738\) −71139.2 45718.4i −3.54833 2.28038i
\(739\) 4519.76 + 31435.6i 0.224982 + 1.56479i 0.718797 + 0.695220i \(0.244693\pi\)
−0.493815 + 0.869567i \(0.664398\pi\)
\(740\) 3916.49 + 8575.92i 0.194558 + 0.426023i
\(741\) 6817.99 + 2001.94i 0.338010 + 0.0992485i
\(742\) 2096.17 4589.96i 0.103710 0.227093i
\(743\) −18412.5 + 21249.2i −0.909138 + 1.04920i 0.0894455 + 0.995992i \(0.471491\pi\)
−0.998583 + 0.0532094i \(0.983055\pi\)
\(744\) 11.4633 79.7293i 0.000564874 0.00392879i
\(745\) 30942.9 9085.66i 1.52169 0.446809i
\(746\) −18641.4 21513.3i −0.914893 1.05584i
\(747\) 28771.2 18490.1i 1.40922 0.905648i
\(748\) 11057.4 7106.18i 0.540508 0.347363i
\(749\) 7861.03 + 9072.11i 0.383492 + 0.442574i
\(750\) −30389.9 + 8923.28i −1.47958 + 0.434443i
\(751\) −2695.05 + 18744.5i −0.130951 + 0.910782i 0.813368 + 0.581749i \(0.197632\pi\)
−0.944319 + 0.329032i \(0.893278\pi\)
\(752\) 11292.1 13031.8i 0.547580 0.631941i
\(753\) −11883.2 + 26020.6i −0.575097 + 1.25929i
\(754\) 28841.9 + 8468.76i 1.39305 + 0.409037i
\(755\) 713.435 + 1562.21i 0.0343902 + 0.0753039i
\(756\) 2744.82 + 19090.7i 0.132048 + 0.918414i
\(757\) −16197.1 10409.3i −0.777669 0.499777i 0.0905903 0.995888i \(-0.471125\pi\)
−0.868259 + 0.496111i \(0.834761\pi\)
\(758\) 49625.0 2.37792
\(759\) 4724.94 + 50471.1i 0.225961 + 2.41368i
\(760\) −1181.42 −0.0563878
\(761\) 15297.2 + 9830.90i 0.728676 + 0.468292i 0.851645 0.524119i \(-0.175605\pi\)
−0.122969 + 0.992410i \(0.539242\pi\)
\(762\) −7061.27 49112.2i −0.335699 2.33484i
\(763\) 2163.62 + 4737.67i 0.102658 + 0.224791i
\(764\) −19720.1 5790.33i −0.933831 0.274197i
\(765\) −9098.00 + 19921.8i −0.429986 + 0.941537i
\(766\) 17854.1 20604.7i 0.842161 0.971905i
\(767\) 1235.95 8596.25i 0.0581848 0.404684i
\(768\) 41074.3 12060.5i 1.92987 0.566662i
\(769\) −6961.08 8033.52i −0.326428 0.376718i 0.568687 0.822554i \(-0.307452\pi\)
−0.895114 + 0.445836i \(0.852906\pi\)
\(770\) 40287.6 25891.3i 1.88554 1.21176i
\(771\) 45078.3 28970.0i 2.10565 1.35322i
\(772\) −3159.11 3645.81i −0.147278 0.169968i
\(773\) 2189.60 642.924i 0.101881 0.0299151i −0.230394 0.973097i \(-0.574002\pi\)
0.332276 + 0.943182i \(0.392183\pi\)
\(774\) −214.870 + 1494.46i −0.00997849 + 0.0694019i
\(775\) −73.6141 + 84.9552i −0.00341200 + 0.00393765i
\(776\) 1033.75 2263.60i 0.0478215 0.104715i
\(777\) −14661.2 4304.91i −0.676920 0.198762i
\(778\) −22302.0 48834.7i −1.02772 2.25040i
\(779\) −1355.66 9428.85i −0.0623513 0.433663i
\(780\) 27336.1 + 17567.8i 1.25486 + 0.806447i
\(781\) 4870.02 0.223128
\(782\) −15148.5 749.779i −0.692724 0.0342865i
\(783\) −30455.7 −1.39004
\(784\) 2588.49 + 1663.52i 0.117916 + 0.0757798i
\(785\) −3793.59 26385.0i −0.172483 1.19965i
\(786\) 36380.3 + 79661.8i 1.65095 + 3.61507i
\(787\) −28363.4 8328.23i −1.28468 0.377217i −0.433056 0.901367i \(-0.642565\pi\)
−0.851626 + 0.524150i \(0.824383\pi\)
\(788\) −13299.5 + 29121.8i −0.601236 + 1.31652i
\(789\) −15484.0 + 17869.4i −0.698661 + 0.806298i
\(790\) −4170.67 + 29007.7i −0.187830 + 1.30639i
\(791\) −7306.79 + 2145.47i −0.328444 + 0.0964400i
\(792\) −7186.95 8294.18i −0.322446 0.372122i
\(793\) 11273.7 7245.15i 0.504842 0.324442i
\(794\) 9763.96 6274.92i 0.436411 0.280464i
\(795\) 5640.57 + 6509.56i 0.251636 + 0.290403i
\(796\) −28730.6 + 8436.07i −1.27931 + 0.375639i
\(797\) −3757.65 + 26135.0i −0.167005 + 1.16154i 0.718028 + 0.696014i \(0.245045\pi\)
−0.885033 + 0.465529i \(0.845864\pi\)
\(798\) −7463.39 + 8613.22i −0.331079 + 0.382086i
\(799\) 3555.88 7786.28i 0.157444 0.344755i
\(800\) −12254.4 3598.22i −0.541573 0.159020i
\(801\) 10718.9 + 23471.1i 0.472826 + 1.03534i
\(802\) 3753.78 + 26108.1i 0.165275 + 1.14951i
\(803\) 4803.94 + 3087.30i 0.211117 + 0.135677i
\(804\) 40625.0 1.78201
\(805\) −25458.1 1260.06i −1.11463 0.0551691i
\(806\) −340.995 −0.0149020
\(807\) 12113.3 + 7784.73i 0.528386 + 0.339573i
\(808\) 965.049 + 6712.06i 0.0420177 + 0.292240i
\(809\) −12052.9 26392.1i −0.523802 1.14697i −0.967980 0.251028i \(-0.919231\pi\)
0.444178 0.895939i \(-0.353496\pi\)
\(810\) −7212.94 2117.91i −0.312885 0.0918713i
\(811\) −1255.42 + 2748.99i −0.0543574 + 0.119026i −0.934862 0.355012i \(-0.884477\pi\)
0.880504 + 0.474038i \(0.157204\pi\)
\(812\) −14562.8 + 16806.3i −0.629375 + 0.726338i
\(813\) 1506.37 10477.0i 0.0649824 0.451963i
\(814\) −20522.3 + 6025.90i −0.883670 + 0.259469i
\(815\) −24494.4 28268.1i −1.05276 1.21495i
\(816\) 18438.3 11849.6i 0.791018 0.508357i
\(817\) −143.078 + 91.9506i −0.00612688 + 0.00393751i
\(818\) 16875.4 + 19475.3i 0.721314 + 0.832440i
\(819\) −31846.8 + 9351.07i −1.35875 + 0.398966i
\(820\) 6199.35 43117.5i 0.264013 1.83625i
\(821\) −1355.56 + 1564.40i −0.0576242 + 0.0665019i −0.783830 0.620976i \(-0.786737\pi\)
0.726206 + 0.687478i \(0.241282\pi\)
\(822\) −5979.22 + 13092.7i −0.253710 + 0.555546i
\(823\) −19199.5 5637.49i −0.813188 0.238774i −0.151408 0.988471i \(-0.548381\pi\)
−0.661780 + 0.749698i \(0.730199\pi\)
\(824\) −3484.30 7629.55i −0.147307 0.322558i
\(825\) 3458.55 + 24054.7i 0.145953 + 1.01512i
\(826\) 11718.0 + 7530.68i 0.493608 + 0.317222i
\(827\) 30354.5 1.27634 0.638168 0.769897i \(-0.279693\pi\)
0.638168 + 0.769897i \(0.279693\pi\)
\(828\) −3240.69 34616.5i −0.136017 1.45291i
\(829\) 41580.9 1.74205 0.871027 0.491234i \(-0.163454\pi\)
0.871027 + 0.491234i \(0.163454\pi\)
\(830\) 32131.7 + 20649.8i 1.34374 + 0.863571i
\(831\) 2240.37 + 15582.1i 0.0935230 + 0.650467i
\(832\) −6149.92 13466.4i −0.256262 0.561136i
\(833\) 1465.55 + 430.323i 0.0609582 + 0.0178989i
\(834\) −35.0658 + 76.7833i −0.00145591 + 0.00318800i
\(835\) 8178.13 9438.06i 0.338941 0.391159i
\(836\) −1047.21 + 7283.52i −0.0433237 + 0.301323i
\(837\) 331.494 97.3353i 0.0136895 0.00401959i
\(838\) 10294.4 + 11880.3i 0.424359 + 0.489736i
\(839\) −9214.55 + 5921.83i −0.379167 + 0.243676i −0.716317 0.697775i \(-0.754174\pi\)
0.337150 + 0.941451i \(0.390537\pi\)
\(840\) 7366.13 4733.93i 0.302566 0.194448i
\(841\) −7024.37 8106.56i −0.288014 0.332386i
\(842\) 25149.0 7384.41i 1.02933 0.302237i
\(843\) 10661.6 74153.0i 0.435593 3.02962i
\(844\) 2185.59 2522.31i 0.0891366 0.102869i
\(845\) 2571.59 5631.01i 0.104693 0.229246i
\(846\) 40817.3 + 11985.0i 1.65878 + 0.487061i
\(847\) 11237.9 + 24607.6i 0.455891 + 0.998263i
\(848\) −773.140 5377.31i −0.0313087 0.217756i
\(849\) −63903.3 41068.2i −2.58322 1.66014i
\(850\) −7271.23 −0.293413
\(851\) 10751.0 + 3743.32i 0.433068 + 0.150786i
\(852\) −5299.91 −0.213112
\(853\) −2178.81 1400.23i −0.0874572 0.0562053i 0.496181 0.868219i \(-0.334735\pi\)
−0.583639 + 0.812014i \(0.698371\pi\)
\(854\) 3058.87 + 21274.9i 0.122567 + 0.852475i
\(855\) −5093.34 11152.9i −0.203729 0.446105i
\(856\) 2947.80 + 865.553i 0.117703 + 0.0345607i
\(857\) −5877.54 + 12870.0i −0.234274 + 0.512989i −0.989858 0.142064i \(-0.954626\pi\)
0.755583 + 0.655053i \(0.227354\pi\)
\(858\) −48275.6 + 55713.0i −1.92087 + 2.21680i
\(859\) 2261.85 15731.5i 0.0898409 0.624857i −0.894300 0.447468i \(-0.852326\pi\)
0.984141 0.177389i \(-0.0567651\pi\)
\(860\) −746.246 + 219.118i −0.0295893 + 0.00868819i
\(861\) 46233.6 + 53356.4i 1.83001 + 2.11194i
\(862\) −47893.8 + 30779.5i −1.89242 + 1.21619i
\(863\) 19389.4 12460.8i 0.764802 0.491508i −0.0991565 0.995072i \(-0.531614\pi\)
0.863958 + 0.503564i \(0.167978\pi\)
\(864\) 25705.2 + 29665.4i 1.01216 + 1.16810i
\(865\) −22902.2 + 6724.68i −0.900228 + 0.264331i
\(866\) −1351.45 + 9399.52i −0.0530301 + 0.368832i
\(867\) −20367.6 + 23505.5i −0.797831 + 0.920747i
\(868\) 104.795 229.470i 0.00409791 0.00897317i
\(869\) −29424.4 8639.77i −1.14862 0.337266i
\(870\) −34187.6 74860.3i −1.33226 2.91724i
\(871\) 4112.08 + 28600.1i 0.159968 + 1.11260i
\(872\) 1121.38 + 720.666i 0.0435489 + 0.0279872i
\(873\) 25825.5 1.00121
\(874\) 5870.84 6134.34i 0.227213 0.237411i
\(875\) 16665.4 0.643880
\(876\) −5227.99 3359.83i −0.201641 0.129587i
\(877\) −2812.94 19564.4i −0.108308 0.753300i −0.969513 0.245041i \(-0.921199\pi\)
0.861204 0.508259i \(-0.169711\pi\)
\(878\) −24609.9 53888.1i −0.945949 2.07134i
\(879\) −32963.9 9679.08i −1.26490 0.371407i
\(880\) 21418.6 46900.2i 0.820478 1.79660i
\(881\) 13712.9 15825.6i 0.524404 0.605195i −0.430324 0.902675i \(-0.641601\pi\)
0.954728 + 0.297480i \(0.0961461\pi\)
\(882\) −1080.30 + 7513.67i −0.0412423 + 0.286846i
\(883\) 32469.9 9534.02i 1.23748 0.363358i 0.403415 0.915017i \(-0.367823\pi\)
0.834070 + 0.551659i \(0.186005\pi\)
\(884\) −6662.40 7688.83i −0.253485 0.292538i
\(885\) −20002.4 + 12854.8i −0.759744 + 0.488258i
\(886\) 558.245 358.762i 0.0211677 0.0136037i
\(887\) 18451.1 + 21293.7i 0.698451 + 0.806056i 0.988542 0.150943i \(-0.0482311\pi\)
−0.290091 + 0.956999i \(0.593686\pi\)
\(888\) −3752.28 + 1101.77i −0.141800 + 0.0416362i
\(889\) −3715.46 + 25841.6i −0.140171 + 0.974914i
\(890\) −18870.9 + 21778.1i −0.710733 + 0.820230i
\(891\) 3267.85 7155.59i 0.122870 0.269047i
\(892\) 8353.61 + 2452.84i 0.313565 + 0.0920709i
\(893\) 1990.69 + 4359.00i 0.0745979 + 0.163347i
\(894\) −11331.2 78810.4i −0.423907 2.94834i
\(895\) 50842.6 + 32674.5i 1.89886 + 1.22032i
\(896\) −9732.45 −0.362878
\(897\) 38147.7 9179.65i 1.41997 0.341694i
\(898\) −42085.5 −1.56393
\(899\) 335.112 + 215.364i 0.0124323 + 0.00798975i
\(900\) −2372.11 16498.4i −0.0878558 0.611051i
\(901\) −1120.29 2453.09i −0.0414230 0.0907038i
\(902\) 94821.8 + 27842.2i 3.50024 + 1.02776i
\(903\) 523.642 1146.62i 0.0192976 0.0422558i
\(904\) −1276.32 + 1472.95i −0.0469577 + 0.0541921i
\(905\) −4288.69 + 29828.5i −0.157526 + 1.09562i
\(906\) 4068.38 1194.58i 0.149186 0.0438051i
\(907\) −16214.6 18712.6i −0.593602 0.685053i 0.376870 0.926266i \(-0.377000\pi\)
−0.970472 + 0.241213i \(0.922455\pi\)
\(908\) 8916.48 5730.27i 0.325885 0.209434i
\(909\) −59202.6 + 38047.2i −2.16021 + 1.38828i
\(910\) −24274.4 28014.1i −0.884272 1.02050i
\(911\) 7559.21 2219.58i 0.274915 0.0807224i −0.141369 0.989957i \(-0.545150\pi\)
0.416284 + 0.909235i \(0.363332\pi\)
\(912\) −1746.23 + 12145.3i −0.0634030 + 0.440977i
\(913\) −26173.6 + 30206.0i −0.948764 + 1.09493i
\(914\) 75.0161 164.262i 0.00271478 0.00594455i
\(915\) −35203.3 10336.6i −1.27190 0.373463i
\(916\) −291.264 637.780i −0.0105062 0.0230053i
\(917\) −6557.89 45611.1i −0.236162 1.64254i
\(918\) 18799.9 + 12082.0i 0.675914 + 0.434384i
\(919\) 9064.56 0.325367 0.162684 0.986678i \(-0.447985\pi\)
0.162684 + 0.986678i \(0.447985\pi\)
\(920\) −5655.59 + 3251.29i −0.202673 + 0.116513i
\(921\) −80074.0 −2.86485
\(922\) −1708.64 1098.08i −0.0610315 0.0392226i
\(923\) −536.458 3731.15i −0.0191308 0.133058i
\(924\) −22655.5 49608.6i −0.806613 1.76624i
\(925\) 5236.56 + 1537.59i 0.186137 + 0.0546548i
\(926\) −7340.86 + 16074.2i −0.260513 + 0.570445i
\(927\) 57002.9 65784.9i 2.01966 2.33081i
\(928\) −6440.98 + 44798.0i −0.227840 + 1.58466i
\(929\) −3145.85 + 923.704i −0.111100 + 0.0326219i −0.336810 0.941573i \(-0.609348\pi\)
0.225710 + 0.974195i \(0.427530\pi\)
\(930\) 611.364 + 705.551i 0.0215564 + 0.0248774i
\(931\) −719.352 + 462.300i −0.0253231 + 0.0162742i
\(932\) 3127.28 2009.78i 0.109911 0.0706357i
\(933\) 36642.2 + 42287.3i 1.28576 + 1.48384i
\(934\) 10114.0 2969.75i 0.354327 0.104040i
\(935\) 3642.49 25334.1i 0.127403 0.886109i
\(936\) −5562.87 + 6419.90i −0.194261 + 0.224189i
\(937\) 18056.7 39538.7i 0.629549 1.37852i −0.278817 0.960344i \(-0.589942\pi\)
0.908366 0.418176i \(-0.137330\pi\)
\(938\) −44465.8 13056.3i −1.54782 0.454482i
\(939\) 32351.4 + 70839.6i 1.12433 + 2.46194i
\(940\) 3118.65 + 21690.7i 0.108212 + 0.752629i
\(941\) 418.834 + 269.169i 0.0145097 + 0.00932481i 0.547876 0.836560i \(-0.315437\pi\)
−0.533366 + 0.845885i \(0.679073\pi\)
\(942\) −65812.5 −2.27631
\(943\) −32437.9 41406.0i −1.12017 1.42987i
\(944\) 14996.5 0.517049
\(945\) 31594.5 + 20304.6i 1.08759 + 0.698950i
\(946\) −251.108 1746.49i −0.00863026 0.0600248i
\(947\) 2792.75 + 6115.26i 0.0958311 + 0.209841i 0.951476 0.307722i \(-0.0995666\pi\)
−0.855645 + 0.517563i \(0.826839\pi\)
\(948\) 32021.7 + 9402.42i 1.09706 + 0.322127i
\(949\) 1836.15 4020.60i 0.0628070 0.137528i
\(950\) 2665.71 3076.40i 0.0910391 0.105065i
\(951\) 6318.80 43948.2i 0.215459 1.49855i
\(952\) −2630.43 + 772.365i −0.0895513 + 0.0262946i
\(953\) 16476.4 + 19014.8i 0.560044 + 0.646326i 0.963194 0.268809i \(-0.0866299\pi\)
−0.403149 + 0.915134i \(0.632084\pi\)
\(954\) 11274.9 7245.91i 0.382639 0.245907i
\(955\) −33667.7 + 21636.9i −1.14080 + 0.733146i
\(956\) 2176.65 + 2511.98i 0.0736379 + 0.0849826i
\(957\) 82629.8 24262.3i 2.79106 0.819529i
\(958\) 3084.99 21456.6i 0.104041 0.723622i
\(959\) 4959.53 5723.60i 0.166999 0.192727i
\(960\) −16837.3 + 36868.5i −0.566064 + 1.23951i
\(961\) 28579.9 + 8391.82i 0.959347 + 0.281690i
\(962\) 6877.36 + 15059.3i 0.230494 + 0.504711i
\(963\) 4537.55 + 31559.4i 0.151839 + 1.05606i
\(964\) 22168.4 + 14246.8i 0.740661 + 0.475994i
\(965\) −9393.69 −0.313361
\(966\) −12024.4 + 61771.6i −0.400495 + 2.05742i
\(967\) −12375.4 −0.411548 −0.205774 0.978599i \(-0.565971\pi\)
−0.205774 + 0.978599i \(0.565971\pi\)
\(968\) 5824.48 + 3743.17i 0.193394 + 0.124287i
\(969\) 866.844 + 6029.03i 0.0287379 + 0.199877i
\(970\) 11981.3 + 26235.5i 0.396596 + 0.868424i
\(971\) −51591.9 15148.7i −1.70511 0.500666i −0.723301 0.690533i \(-0.757376\pi\)
−0.981810 + 0.189868i \(0.939194\pi\)
\(972\) 8929.29 19552.4i 0.294657 0.645210i
\(973\) 29.0857 33.5667i 0.000958319 0.00110596i
\(974\) −3670.58 + 25529.4i −0.120753 + 0.839852i
\(975\) 18048.5 5299.50i 0.592834 0.174072i
\(976\) 15153.9 + 17488.6i 0.496993 + 0.573560i
\(977\) 23111.7 14853.0i 0.756814 0.486375i −0.104452 0.994530i \(-0.533309\pi\)
0.861266 + 0.508155i \(0.169672\pi\)
\(978\) −77687.8 + 49926.9i −2.54006 + 1.63240i
\(979\) −19747.0 22789.2i −0.644654 0.743970i
\(980\) −3751.90 + 1101.66i −0.122296 + 0.0359093i
\(981\) −1968.75 + 13692.9i −0.0640747 + 0.445649i
\(982\) 8826.24 10186.0i 0.286819 0.331007i
\(983\) 14035.9 30734.3i 0.455417 0.997223i −0.533092 0.846057i \(-0.678970\pi\)
0.988508 0.151166i \(-0.0483027\pi\)
\(984\) 17337.1 + 5090.63i 0.561673 + 0.164922i
\(985\) 25897.3 + 56707.2i 0.837723 + 1.83436i
\(986\) 3666.99 + 25504.5i 0.118439 + 0.823760i
\(987\) −29878.2 19201.6i −0.963561 0.619243i
\(988\) 5695.59 0.183402
\(989\) −431.880 + 833.928i −0.0138857 + 0.0268123i
\(990\) 127199. 4.08350
\(991\) −9325.92 5993.41i −0.298938 0.192116i 0.382570 0.923927i \(-0.375039\pi\)
−0.681508 + 0.731811i \(0.738676\pi\)
\(992\) −73.0663 508.187i −0.00233856 0.0162651i
\(993\) −10158.4 22243.8i −0.324640 0.710863i
\(994\) 5800.96 + 1703.32i 0.185106 + 0.0543520i
\(995\) −24221.8 + 53038.2i −0.771740 + 1.68987i
\(996\) 28484.0 32872.3i 0.906176 1.04578i
\(997\) 2946.24 20491.6i 0.0935892 0.650927i −0.887989 0.459865i \(-0.847898\pi\)
0.981578 0.191062i \(-0.0611931\pi\)
\(998\) −10523.8 + 3090.06i −0.333792 + 0.0980102i
\(999\) −10984.3 12676.6i −0.347877 0.401472i
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 23.4.c.a.2.1 50
3.2 odd 2 207.4.i.a.163.5 50
23.9 even 11 529.4.a.n.1.4 25
23.12 even 11 inner 23.4.c.a.12.1 yes 50
23.14 odd 22 529.4.a.m.1.4 25
69.35 odd 22 207.4.i.a.127.5 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.4.c.a.2.1 50 1.1 even 1 trivial
23.4.c.a.12.1 yes 50 23.12 even 11 inner
207.4.i.a.127.5 50 69.35 odd 22
207.4.i.a.163.5 50 3.2 odd 2
529.4.a.m.1.4 25 23.14 odd 22
529.4.a.n.1.4 25 23.9 even 11