Properties

Label 45.4.j.a.4.2
Level $45$
Weight $4$
Character 45.4
Analytic conductor $2.655$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,4,Mod(4,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Character \(\chi\) \(=\) 45.4
Dual form 45.4.j.a.34.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.35066 + 2.51186i) q^{2} +(-1.99648 - 4.79730i) q^{3} +(8.61884 - 14.9283i) q^{4} +(5.42265 + 9.77726i) q^{5} +(20.7361 + 15.8565i) q^{6} +(-4.66092 + 2.69099i) q^{7} +46.4074i q^{8} +(-19.0281 + 19.1554i) q^{9} +O(q^{10})\) \(q+(-4.35066 + 2.51186i) q^{2} +(-1.99648 - 4.79730i) q^{3} +(8.61884 - 14.9283i) q^{4} +(5.42265 + 9.77726i) q^{5} +(20.7361 + 15.8565i) q^{6} +(-4.66092 + 2.69099i) q^{7} +46.4074i q^{8} +(-19.0281 + 19.1554i) q^{9} +(-48.1512 - 28.9166i) q^{10} +(19.5509 + 33.8631i) q^{11} +(-88.8227 - 11.5431i) q^{12} +(75.0212 + 43.3135i) q^{13} +(13.5187 - 23.4151i) q^{14} +(36.0782 - 45.5342i) q^{15} +(-47.6180 - 82.4768i) q^{16} +15.4194i q^{17} +(34.6693 - 131.135i) q^{18} +26.8412 q^{19} +(192.694 + 3.31781i) q^{20} +(22.2149 + 16.9873i) q^{21} +(-170.119 - 98.2180i) q^{22} +(-96.2486 - 55.5692i) q^{23} +(222.630 - 92.6515i) q^{24} +(-66.1897 + 106.037i) q^{25} -435.189 q^{26} +(129.884 + 53.0401i) q^{27} +92.7727i q^{28} +(24.6174 + 42.6385i) q^{29} +(-42.5887 + 288.727i) q^{30} +(89.9383 - 155.778i) q^{31} +(92.8196 + 53.5894i) q^{32} +(123.419 - 161.398i) q^{33} +(-38.7312 - 67.0844i) q^{34} +(-51.5851 - 30.9788i) q^{35} +(121.957 + 449.154i) q^{36} +293.496i q^{37} +(-116.777 + 67.4211i) q^{38} +(58.0094 - 446.374i) q^{39} +(-453.737 + 251.651i) q^{40} +(-13.8016 + 23.9051i) q^{41} +(-139.319 - 18.1055i) q^{42} +(-52.3971 + 30.2515i) q^{43} +674.023 q^{44} +(-290.471 - 82.1697i) q^{45} +558.327 q^{46} +(83.3420 - 48.1175i) q^{47} +(-300.597 + 393.101i) q^{48} +(-157.017 + 271.962i) q^{49} +(21.6181 - 627.592i) q^{50} +(73.9713 - 30.7845i) q^{51} +(1293.19 - 746.625i) q^{52} -251.203i q^{53} +(-698.309 + 95.4892i) q^{54} +(-225.071 + 374.782i) q^{55} +(-124.882 - 216.301i) q^{56} +(-53.5879 - 128.765i) q^{57} +(-214.204 - 123.671i) q^{58} +(-38.4231 + 66.5508i) q^{59} +(-368.794 - 931.037i) q^{60} +(-245.045 - 424.431i) q^{61} +903.648i q^{62} +(37.1417 - 140.486i) q^{63} +223.452 q^{64} +(-16.6735 + 968.377i) q^{65} +(-131.542 + 1012.20i) q^{66} +(206.738 + 119.360i) q^{67} +(230.184 + 132.897i) q^{68} +(-74.4232 + 572.676i) q^{69} +(302.243 + 5.20402i) q^{70} -640.447 q^{71} +(-888.954 - 883.046i) q^{72} -769.257i q^{73} +(-737.219 - 1276.90i) q^{74} +(640.839 + 105.830i) q^{75} +(231.340 - 400.692i) q^{76} +(-182.250 - 105.222i) q^{77} +(868.847 + 2087.73i) q^{78} +(331.176 + 573.613i) q^{79} +(548.181 - 912.817i) q^{80} +(-4.86094 - 728.984i) q^{81} -138.670i q^{82} +(1127.69 - 651.071i) q^{83} +(445.058 - 185.219i) q^{84} +(-150.759 + 83.6139i) q^{85} +(151.975 - 263.228i) q^{86} +(155.402 - 203.224i) q^{87} +(-1571.50 + 907.306i) q^{88} +995.544 q^{89} +(1470.14 - 372.128i) q^{90} -466.224 q^{91} +(-1659.10 + 957.883i) q^{92} +(-926.872 - 120.453i) q^{93} +(-241.729 + 418.686i) q^{94} +(145.550 + 262.433i) q^{95} +(71.7718 - 552.274i) q^{96} +(-705.677 + 407.423i) q^{97} -1577.62i q^{98} +(-1020.68 - 269.846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9} - 20 q^{10} + 90 q^{11} - 102 q^{14} - 87 q^{15} - 146 q^{16} - 8 q^{19} - 6 q^{20} + 30 q^{21} + 462 q^{24} + 71 q^{25} - 936 q^{26} - 516 q^{29} - 66 q^{30} - 38 q^{31} + 212 q^{34} - 534 q^{35} + 864 q^{36} + 330 q^{39} + 44 q^{40} + 576 q^{41} + 3288 q^{44} + 1053 q^{45} - 580 q^{46} - 4 q^{49} + 558 q^{50} + 1260 q^{51} - 3726 q^{54} + 30 q^{55} + 2430 q^{56} - 2202 q^{59} - 5052 q^{60} - 20 q^{61} + 644 q^{64} + 339 q^{65} - 5052 q^{66} + 1452 q^{69} + 636 q^{70} - 5904 q^{71} - 4080 q^{74} + 2283 q^{75} + 396 q^{76} - 218 q^{79} + 2532 q^{80} + 198 q^{81} + 4662 q^{84} - 704 q^{85} + 6108 q^{86} + 8148 q^{89} + 6408 q^{90} - 1884 q^{91} - 1078 q^{94} - 1692 q^{95} + 11874 q^{96} - 1602 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.35066 + 2.51186i −1.53819 + 0.888075i −0.539246 + 0.842148i \(0.681291\pi\)
−0.998945 + 0.0459269i \(0.985376\pi\)
\(3\) −1.99648 4.79730i −0.384223 0.923240i
\(4\) 8.61884 14.9283i 1.07735 1.86603i
\(5\) 5.42265 + 9.77726i 0.485017 + 0.874505i
\(6\) 20.7361 + 15.8565i 1.41092 + 1.07890i
\(7\) −4.66092 + 2.69099i −0.251666 + 0.145300i −0.620527 0.784185i \(-0.713081\pi\)
0.368861 + 0.929485i \(0.379748\pi\)
\(8\) 46.4074i 2.05094i
\(9\) −19.0281 + 19.1554i −0.704745 + 0.709460i
\(10\) −48.1512 28.9166i −1.52267 0.914424i
\(11\) 19.5509 + 33.8631i 0.535892 + 0.928192i 0.999120 + 0.0419529i \(0.0133580\pi\)
−0.463227 + 0.886239i \(0.653309\pi\)
\(12\) −88.8227 11.5431i −2.13674 0.277684i
\(13\) 75.0212 + 43.3135i 1.60055 + 0.924078i 0.991377 + 0.131040i \(0.0418318\pi\)
0.609173 + 0.793037i \(0.291502\pi\)
\(14\) 13.5187 23.4151i 0.258074 0.446997i
\(15\) 36.0782 45.5342i 0.621023 0.783792i
\(16\) −47.6180 82.4768i −0.744031 1.28870i
\(17\) 15.4194i 0.219985i 0.993932 + 0.109993i \(0.0350827\pi\)
−0.993932 + 0.109993i \(0.964917\pi\)
\(18\) 34.6693 131.135i 0.453979 1.71715i
\(19\) 26.8412 0.324094 0.162047 0.986783i \(-0.448190\pi\)
0.162047 + 0.986783i \(0.448190\pi\)
\(20\) 192.694 + 3.31781i 2.15439 + 0.0370942i
\(21\) 22.2149 + 16.9873i 0.230842 + 0.176521i
\(22\) −170.119 98.2180i −1.64861 0.951825i
\(23\) −96.2486 55.5692i −0.872575 0.503781i −0.00437188 0.999990i \(-0.501392\pi\)
−0.868203 + 0.496209i \(0.834725\pi\)
\(24\) 222.630 92.6515i 1.89351 0.788017i
\(25\) −66.1897 + 106.037i −0.529517 + 0.848299i
\(26\) −435.189 −3.28260
\(27\) 129.884 + 53.0401i 0.925782 + 0.378058i
\(28\) 92.7727i 0.626157i
\(29\) 24.6174 + 42.6385i 0.157632 + 0.273027i 0.934014 0.357236i \(-0.116281\pi\)
−0.776382 + 0.630262i \(0.782947\pi\)
\(30\) −42.5887 + 288.727i −0.259187 + 1.75714i
\(31\) 89.9383 155.778i 0.521077 0.902532i −0.478622 0.878021i \(-0.658864\pi\)
0.999700 0.0245112i \(-0.00780295\pi\)
\(32\) 92.8196 + 53.5894i 0.512761 + 0.296043i
\(33\) 123.419 161.398i 0.651043 0.851390i
\(34\) −38.7312 67.0844i −0.195363 0.338379i
\(35\) −51.5851 30.9788i −0.249128 0.149611i
\(36\) 121.957 + 449.154i 0.564616 + 2.07942i
\(37\) 293.496i 1.30407i 0.758191 + 0.652033i \(0.226084\pi\)
−0.758191 + 0.652033i \(0.773916\pi\)
\(38\) −116.777 + 67.4211i −0.498518 + 0.287820i
\(39\) 58.0094 446.374i 0.238178 1.83274i
\(40\) −453.737 + 251.651i −1.79355 + 0.994739i
\(41\) −13.8016 + 23.9051i −0.0525719 + 0.0910571i −0.891114 0.453780i \(-0.850075\pi\)
0.838542 + 0.544837i \(0.183409\pi\)
\(42\) −139.319 18.1055i −0.511844 0.0665177i
\(43\) −52.3971 + 30.2515i −0.185825 + 0.107286i −0.590027 0.807384i \(-0.700883\pi\)
0.404201 + 0.914670i \(0.367549\pi\)
\(44\) 674.023 2.30938
\(45\) −290.471 82.1697i −0.962240 0.272203i
\(46\) 558.327 1.78958
\(47\) 83.3420 48.1175i 0.258653 0.149333i −0.365067 0.930981i \(-0.618954\pi\)
0.623720 + 0.781648i \(0.285621\pi\)
\(48\) −300.597 + 393.101i −0.903906 + 1.18207i
\(49\) −157.017 + 271.962i −0.457776 + 0.792891i
\(50\) 21.6181 627.592i 0.0611453 1.77510i
\(51\) 73.9713 30.7845i 0.203099 0.0845233i
\(52\) 1293.19 746.625i 3.44872 1.99112i
\(53\) 251.203i 0.651046i −0.945534 0.325523i \(-0.894460\pi\)
0.945534 0.325523i \(-0.105540\pi\)
\(54\) −698.309 + 95.4892i −1.75977 + 0.240638i
\(55\) −225.071 + 374.782i −0.551792 + 0.918829i
\(56\) −124.882 216.301i −0.298000 0.516152i
\(57\) −53.5879 128.765i −0.124524 0.299217i
\(58\) −214.204 123.671i −0.484937 0.279978i
\(59\) −38.4231 + 66.5508i −0.0847841 + 0.146850i −0.905299 0.424774i \(-0.860353\pi\)
0.820515 + 0.571625i \(0.193687\pi\)
\(60\) −368.794 931.037i −0.793519 2.00327i
\(61\) −245.045 424.431i −0.514342 0.890866i −0.999862 0.0166406i \(-0.994703\pi\)
0.485520 0.874226i \(-0.338630\pi\)
\(62\) 903.648i 1.85102i
\(63\) 37.1417 140.486i 0.0742763 0.280946i
\(64\) 223.452 0.436430
\(65\) −16.6735 + 968.377i −0.0318168 + 1.84788i
\(66\) −131.542 + 1012.20i −0.245330 + 1.88778i
\(67\) 206.738 + 119.360i 0.376972 + 0.217645i 0.676500 0.736443i \(-0.263496\pi\)
−0.299528 + 0.954087i \(0.596829\pi\)
\(68\) 230.184 + 132.897i 0.410499 + 0.237002i
\(69\) −74.4232 + 572.676i −0.129848 + 0.999161i
\(70\) 302.243 + 5.20402i 0.516071 + 0.00888570i
\(71\) −640.447 −1.07052 −0.535261 0.844687i \(-0.679787\pi\)
−0.535261 + 0.844687i \(0.679787\pi\)
\(72\) −888.954 883.046i −1.45506 1.44539i
\(73\) 769.257i 1.23335i −0.787217 0.616676i \(-0.788479\pi\)
0.787217 0.616676i \(-0.211521\pi\)
\(74\) −737.219 1276.90i −1.15811 2.00590i
\(75\) 640.839 + 105.830i 0.986637 + 0.162936i
\(76\) 231.340 400.692i 0.349164 0.604770i
\(77\) −182.250 105.222i −0.269732 0.155730i
\(78\) 868.847 + 2087.73i 1.26125 + 3.03063i
\(79\) 331.176 + 573.613i 0.471648 + 0.816918i 0.999474 0.0324343i \(-0.0103260\pi\)
−0.527826 + 0.849353i \(0.676993\pi\)
\(80\) 548.181 912.817i 0.766106 1.27570i
\(81\) −4.86094 728.984i −0.00666796 0.999978i
\(82\) 138.670i 0.186751i
\(83\) 1127.69 651.071i 1.49132 0.861016i 0.491373 0.870949i \(-0.336495\pi\)
0.999951 + 0.00993336i \(0.00316194\pi\)
\(84\) 445.058 185.219i 0.578093 0.240584i
\(85\) −150.759 + 83.6139i −0.192378 + 0.106696i
\(86\) 151.975 263.228i 0.190557 0.330054i
\(87\) 155.402 203.224i 0.191503 0.250436i
\(88\) −1571.50 + 907.306i −1.90366 + 1.09908i
\(89\) 995.544 1.18570 0.592851 0.805312i \(-0.298002\pi\)
0.592851 + 0.805312i \(0.298002\pi\)
\(90\) 1470.14 372.128i 1.72185 0.435841i
\(91\) −466.224 −0.537073
\(92\) −1659.10 + 957.883i −1.88015 + 1.08550i
\(93\) −926.872 120.453i −1.03346 0.134306i
\(94\) −241.729 + 418.686i −0.265238 + 0.459406i
\(95\) 145.550 + 262.433i 0.157191 + 0.283422i
\(96\) 71.7718 552.274i 0.0763040 0.587148i
\(97\) −705.677 + 407.423i −0.738667 + 0.426470i −0.821584 0.570087i \(-0.806910\pi\)
0.0829175 + 0.996556i \(0.473576\pi\)
\(98\) 1577.62i 1.62616i
\(99\) −1020.68 269.846i −1.03618 0.273945i
\(100\) 1012.48 + 1902.02i 1.01248 + 1.90202i
\(101\) 326.302 + 565.172i 0.321468 + 0.556799i 0.980791 0.195061i \(-0.0624904\pi\)
−0.659323 + 0.751860i \(0.729157\pi\)
\(102\) −244.498 + 319.738i −0.237342 + 0.310380i
\(103\) 133.329 + 76.9776i 0.127547 + 0.0736391i 0.562416 0.826855i \(-0.309872\pi\)
−0.434869 + 0.900494i \(0.643205\pi\)
\(104\) −2010.07 + 3481.54i −1.89523 + 3.28263i
\(105\) −45.6259 + 309.317i −0.0424060 + 0.287488i
\(106\) 630.987 + 1092.90i 0.578178 + 1.00143i
\(107\) 348.878i 0.315209i 0.987502 + 0.157604i \(0.0503770\pi\)
−0.987502 + 0.157604i \(0.949623\pi\)
\(108\) 1911.24 1481.79i 1.70286 1.32024i
\(109\) −1125.26 −0.988815 −0.494407 0.869230i \(-0.664615\pi\)
−0.494407 + 0.869230i \(0.664615\pi\)
\(110\) 37.8089 2195.90i 0.0327721 1.90337i
\(111\) 1407.99 585.959i 1.20397 0.501052i
\(112\) 443.888 + 256.279i 0.374495 + 0.216215i
\(113\) 304.907 + 176.038i 0.253834 + 0.146551i 0.621518 0.783400i \(-0.286516\pi\)
−0.367685 + 0.929951i \(0.619849\pi\)
\(114\) 556.582 + 425.608i 0.457269 + 0.349665i
\(115\) 21.3913 1242.38i 0.0173456 1.00741i
\(116\) 848.692 0.679303
\(117\) −2257.20 + 612.889i −1.78358 + 0.484287i
\(118\) 386.053i 0.301179i
\(119\) −41.4933 71.8685i −0.0319637 0.0553628i
\(120\) 2113.12 + 1674.30i 1.60751 + 1.27368i
\(121\) −98.9741 + 171.428i −0.0743607 + 0.128797i
\(122\) 2132.22 + 1231.04i 1.58231 + 0.913549i
\(123\) 142.234 + 18.4843i 0.104267 + 0.0135502i
\(124\) −1550.33 2685.24i −1.12277 1.94469i
\(125\) −1395.68 72.1493i −0.998666 0.0516259i
\(126\) 191.291 + 704.503i 0.135250 + 0.498112i
\(127\) 1502.08i 1.04951i −0.851252 0.524757i \(-0.824156\pi\)
0.851252 0.524757i \(-0.175844\pi\)
\(128\) −1714.72 + 989.995i −1.18407 + 0.683625i
\(129\) 249.735 + 190.968i 0.170449 + 0.130340i
\(130\) −2359.88 4254.96i −1.59212 2.87065i
\(131\) 787.356 1363.74i 0.525127 0.909546i −0.474445 0.880285i \(-0.657351\pi\)
0.999572 0.0292609i \(-0.00931535\pi\)
\(132\) −1345.68 3233.49i −0.887318 2.13212i
\(133\) −125.105 + 72.2292i −0.0815635 + 0.0470907i
\(134\) −1199.26 −0.773140
\(135\) 185.727 + 1557.52i 0.118406 + 0.992965i
\(136\) −715.573 −0.451175
\(137\) 772.753 446.149i 0.481903 0.278227i −0.239306 0.970944i \(-0.576920\pi\)
0.721209 + 0.692717i \(0.243587\pi\)
\(138\) −1114.69 2678.46i −0.687599 1.65221i
\(139\) 326.353 565.260i 0.199143 0.344926i −0.749108 0.662448i \(-0.769517\pi\)
0.948251 + 0.317522i \(0.102851\pi\)
\(140\) −907.063 + 503.074i −0.547577 + 0.303697i
\(141\) −397.225 303.751i −0.237251 0.181421i
\(142\) 2786.37 1608.71i 1.64667 0.950704i
\(143\) 3387.27i 1.98082i
\(144\) 2485.96 + 657.235i 1.43863 + 0.380345i
\(145\) −283.397 + 471.905i −0.162309 + 0.270273i
\(146\) 1932.26 + 3346.78i 1.09531 + 1.89713i
\(147\) 1618.16 + 210.292i 0.907917 + 0.117990i
\(148\) 4381.38 + 2529.59i 2.43343 + 1.40494i
\(149\) 1718.93 2977.27i 0.945101 1.63696i 0.189551 0.981871i \(-0.439297\pi\)
0.755550 0.655092i \(-0.227370\pi\)
\(150\) −3053.90 + 1149.27i −1.66233 + 0.625581i
\(151\) −835.459 1447.06i −0.450256 0.779867i 0.548145 0.836383i \(-0.315334\pi\)
−0.998402 + 0.0565162i \(0.982001\pi\)
\(152\) 1245.63i 0.664696i
\(153\) −295.365 293.402i −0.156071 0.155033i
\(154\) 1057.21 0.553199
\(155\) 2010.78 + 34.6216i 1.04200 + 0.0179411i
\(156\) −6163.61 4713.20i −3.16336 2.41896i
\(157\) 576.864 + 333.052i 0.293240 + 0.169302i 0.639402 0.768872i \(-0.279182\pi\)
−0.346162 + 0.938175i \(0.612515\pi\)
\(158\) −2881.67 1663.73i −1.45097 0.837718i
\(159\) −1205.10 + 501.523i −0.601072 + 0.250147i
\(160\) −20.6292 + 1198.12i −0.0101930 + 0.591998i
\(161\) 598.143 0.292797
\(162\) 1852.25 + 3159.35i 0.898312 + 1.53224i
\(163\) 889.255i 0.427312i −0.976909 0.213656i \(-0.931463\pi\)
0.976909 0.213656i \(-0.0685371\pi\)
\(164\) 237.907 + 412.067i 0.113277 + 0.196202i
\(165\) 2247.29 + 331.487i 1.06031 + 0.156401i
\(166\) −3270.79 + 5665.18i −1.52929 + 2.64881i
\(167\) −349.755 201.931i −0.162065 0.0935683i 0.416774 0.909010i \(-0.363161\pi\)
−0.578839 + 0.815442i \(0.696494\pi\)
\(168\) −788.338 + 1030.94i −0.362033 + 0.473443i
\(169\) 2653.62 + 4596.21i 1.20784 + 2.09204i
\(170\) 445.876 742.461i 0.201160 0.334966i
\(171\) −510.737 + 514.154i −0.228404 + 0.229932i
\(172\) 1042.93i 0.462342i
\(173\) −204.435 + 118.031i −0.0898435 + 0.0518712i −0.544249 0.838924i \(-0.683185\pi\)
0.454405 + 0.890795i \(0.349852\pi\)
\(174\) −165.631 + 1274.50i −0.0721634 + 0.555287i
\(175\) 23.1598 672.348i 0.0100041 0.290427i
\(176\) 1861.95 3224.99i 0.797441 1.38121i
\(177\) 395.975 + 51.4597i 0.168154 + 0.0218528i
\(178\) −4331.28 + 2500.66i −1.82384 + 1.05299i
\(179\) −2404.31 −1.00395 −0.501973 0.864883i \(-0.667392\pi\)
−0.501973 + 0.864883i \(0.667392\pi\)
\(180\) −3730.17 + 3628.01i −1.54461 + 1.50231i
\(181\) −1218.41 −0.500354 −0.250177 0.968200i \(-0.580489\pi\)
−0.250177 + 0.968200i \(0.580489\pi\)
\(182\) 2028.38 1171.09i 0.826120 0.476961i
\(183\) −1546.89 + 2022.93i −0.624862 + 0.817153i
\(184\) 2578.82 4466.65i 1.03322 1.78960i
\(185\) −2869.59 + 1591.53i −1.14041 + 0.632494i
\(186\) 4335.07 1804.12i 1.70894 0.711205i
\(187\) −522.148 + 301.462i −0.204188 + 0.117888i
\(188\) 1658.87i 0.643539i
\(189\) −748.108 + 102.299i −0.287920 + 0.0393712i
\(190\) −1292.43 776.156i −0.493490 0.296359i
\(191\) −87.9715 152.371i −0.0333267 0.0577235i 0.848881 0.528584i \(-0.177277\pi\)
−0.882208 + 0.470861i \(0.843944\pi\)
\(192\) −446.118 1071.97i −0.167686 0.402930i
\(193\) 1918.47 + 1107.63i 0.715516 + 0.413103i 0.813100 0.582124i \(-0.197778\pi\)
−0.0975842 + 0.995227i \(0.531112\pi\)
\(194\) 2046.78 3545.12i 0.757474 1.31198i
\(195\) 4678.88 1853.36i 1.71826 0.680624i
\(196\) 2706.61 + 4687.99i 0.986374 + 1.70845i
\(197\) 1054.08i 0.381218i −0.981666 0.190609i \(-0.938954\pi\)
0.981666 0.190609i \(-0.0610462\pi\)
\(198\) 5118.44 1389.79i 1.83713 0.498829i
\(199\) 3484.04 1.24109 0.620546 0.784170i \(-0.286911\pi\)
0.620546 + 0.784170i \(0.286911\pi\)
\(200\) −4920.92 3071.69i −1.73981 1.08601i
\(201\) 159.858 1230.09i 0.0560972 0.431660i
\(202\) −2839.26 1639.25i −0.988958 0.570975i
\(203\) −229.479 132.490i −0.0793414 0.0458078i
\(204\) 177.988 1369.59i 0.0610864 0.470051i
\(205\) −308.567 5.31290i −0.105128 0.00181009i
\(206\) −773.426 −0.261588
\(207\) 2895.88 786.307i 0.972356 0.264020i
\(208\) 8250.01i 2.75017i
\(209\) 524.768 + 908.926i 0.173679 + 0.300822i
\(210\) −578.458 1460.34i −0.190083 0.479872i
\(211\) 2098.45 3634.62i 0.684660 1.18587i −0.288884 0.957364i \(-0.593284\pi\)
0.973544 0.228501i \(-0.0733825\pi\)
\(212\) −3750.03 2165.08i −1.21487 0.701408i
\(213\) 1278.64 + 3072.41i 0.411319 + 0.988349i
\(214\) −876.331 1517.85i −0.279929 0.484851i
\(215\) −579.908 348.257i −0.183951 0.110469i
\(216\) −2461.45 + 6027.56i −0.775374 + 1.89872i
\(217\) 968.091i 0.302849i
\(218\) 4895.65 2826.50i 1.52099 0.878142i
\(219\) −3690.35 + 1535.81i −1.13868 + 0.473882i
\(220\) 3655.00 + 6590.10i 1.12009 + 2.01957i
\(221\) −667.867 + 1156.78i −0.203283 + 0.352097i
\(222\) −4653.83 + 6085.97i −1.40696 + 1.83993i
\(223\) −2628.00 + 1517.28i −0.789166 + 0.455625i −0.839669 0.543098i \(-0.817251\pi\)
0.0505026 + 0.998724i \(0.483918\pi\)
\(224\) −576.834 −0.172059
\(225\) −771.727 3285.58i −0.228660 0.973506i
\(226\) −1768.73 −0.520593
\(227\) −2802.60 + 1618.08i −0.819450 + 0.473109i −0.850227 0.526417i \(-0.823535\pi\)
0.0307770 + 0.999526i \(0.490202\pi\)
\(228\) −2384.10 309.831i −0.692505 0.0899958i
\(229\) −1487.28 + 2576.04i −0.429180 + 0.743361i −0.996801 0.0799288i \(-0.974531\pi\)
0.567621 + 0.823290i \(0.307864\pi\)
\(230\) 3027.61 + 5458.91i 0.867978 + 1.56500i
\(231\) −140.923 + 1084.38i −0.0401388 + 0.308862i
\(232\) −1978.74 + 1142.43i −0.559961 + 0.323293i
\(233\) 2927.42i 0.823097i −0.911388 0.411549i \(-0.864988\pi\)
0.911388 0.411549i \(-0.135012\pi\)
\(234\) 8280.84 8336.24i 2.31340 2.32888i
\(235\) 922.392 + 553.932i 0.256044 + 0.153764i
\(236\) 662.325 + 1147.18i 0.182685 + 0.316420i
\(237\) 2090.61 2733.96i 0.572994 0.749323i
\(238\) 361.047 + 208.450i 0.0983327 + 0.0567724i
\(239\) 1439.35 2493.02i 0.389555 0.674729i −0.602835 0.797866i \(-0.705962\pi\)
0.992390 + 0.123137i \(0.0392955\pi\)
\(240\) −5473.49 807.367i −1.47213 0.217147i
\(241\) 558.792 + 967.856i 0.149357 + 0.258693i 0.930990 0.365045i \(-0.118946\pi\)
−0.781633 + 0.623738i \(0.785613\pi\)
\(242\) 994.435i 0.264152i
\(243\) −3487.45 + 1478.72i −0.920658 + 0.390371i
\(244\) −8448.03 −2.21651
\(245\) −3510.49 60.4435i −0.915416 0.0157616i
\(246\) −665.243 + 276.853i −0.172416 + 0.0717540i
\(247\) 2013.66 + 1162.59i 0.518729 + 0.299488i
\(248\) 7229.24 + 4173.80i 1.85104 + 1.06870i
\(249\) −5374.79 4110.00i −1.36793 1.04603i
\(250\) 6253.35 3191.85i 1.58199 0.807480i
\(251\) −4612.00 −1.15979 −0.579894 0.814692i \(-0.696906\pi\)
−0.579894 + 0.814692i \(0.696906\pi\)
\(252\) −1777.10 1765.29i −0.444233 0.441281i
\(253\) 4345.71i 1.07989i
\(254\) 3773.02 + 6535.06i 0.932048 + 1.61435i
\(255\) 702.109 + 556.303i 0.172423 + 0.136616i
\(256\) 4079.64 7066.14i 0.996006 1.72513i
\(257\) −3280.26 1893.86i −0.796176 0.459672i 0.0459562 0.998943i \(-0.485367\pi\)
−0.842132 + 0.539271i \(0.818700\pi\)
\(258\) −1566.20 203.538i −0.377935 0.0491153i
\(259\) −789.793 1367.96i −0.189480 0.328189i
\(260\) 14312.5 + 8595.18i 3.41393 + 2.05020i
\(261\) −1285.18 339.775i −0.304792 0.0805807i
\(262\) 7910.89i 1.86541i
\(263\) −4321.08 + 2494.78i −1.01312 + 0.584923i −0.912102 0.409962i \(-0.865542\pi\)
−0.101013 + 0.994885i \(0.532209\pi\)
\(264\) 7490.08 + 5727.53i 1.74615 + 1.33525i
\(265\) 2456.08 1362.19i 0.569343 0.315768i
\(266\) 362.859 628.490i 0.0836402 0.144869i
\(267\) −1987.59 4775.92i −0.455574 1.09469i
\(268\) 3563.69 2057.50i 0.812265 0.468961i
\(269\) 5845.57 1.32495 0.662473 0.749086i \(-0.269507\pi\)
0.662473 + 0.749086i \(0.269507\pi\)
\(270\) −4720.31 6309.74i −1.06396 1.42222i
\(271\) 2766.09 0.620030 0.310015 0.950732i \(-0.399666\pi\)
0.310015 + 0.950732i \(0.399666\pi\)
\(272\) 1271.74 734.239i 0.283495 0.163676i
\(273\) 930.808 + 2236.62i 0.206356 + 0.495847i
\(274\) −2241.32 + 3882.09i −0.494173 + 0.855933i
\(275\) −4884.82 168.263i −1.07115 0.0368970i
\(276\) 7907.62 + 6046.81i 1.72457 + 1.31875i
\(277\) −1640.08 + 946.900i −0.355750 + 0.205393i −0.667215 0.744865i \(-0.732514\pi\)
0.311465 + 0.950258i \(0.399180\pi\)
\(278\) 3279.01i 0.707417i
\(279\) 1272.63 + 4686.96i 0.273084 + 1.00574i
\(280\) 1437.65 2393.93i 0.306842 0.510945i
\(281\) −2242.19 3883.58i −0.476006 0.824467i 0.523616 0.851954i \(-0.324583\pi\)
−0.999622 + 0.0274877i \(0.991249\pi\)
\(282\) 2491.17 + 323.745i 0.526053 + 0.0683642i
\(283\) −5020.91 2898.82i −1.05464 0.608894i −0.130692 0.991423i \(-0.541720\pi\)
−0.923944 + 0.382529i \(0.875053\pi\)
\(284\) −5519.91 + 9560.76i −1.15333 + 1.99763i
\(285\) 968.381 1222.19i 0.201270 0.254022i
\(286\) −8508.34 14736.9i −1.75912 3.04689i
\(287\) 148.560i 0.0305547i
\(288\) −2792.71 + 758.293i −0.571396 + 0.155149i
\(289\) 4675.24 0.951607
\(290\) 47.6068 2764.95i 0.00963989 0.559874i
\(291\) 3363.40 + 2571.93i 0.677547 + 0.518108i
\(292\) −11483.7 6630.10i −2.30148 1.32876i
\(293\) 6850.49 + 3955.13i 1.36590 + 0.788605i 0.990402 0.138217i \(-0.0441370\pi\)
0.375502 + 0.926822i \(0.377470\pi\)
\(294\) −7568.30 + 3149.68i −1.50133 + 0.624807i
\(295\) −859.039 14.7909i −0.169543 0.00291919i
\(296\) −13620.4 −2.67456
\(297\) 743.235 + 5435.25i 0.145208 + 1.06190i
\(298\) 17270.8i 3.35728i
\(299\) −4813.79 8337.74i −0.931066 1.61265i
\(300\) 7103.14 8654.49i 1.36700 1.66556i
\(301\) 162.813 282.000i 0.0311773 0.0540007i
\(302\) 7269.60 + 4197.11i 1.38516 + 0.799723i
\(303\) 2059.84 2693.72i 0.390544 0.510727i
\(304\) −1278.12 2213.77i −0.241136 0.417660i
\(305\) 2820.98 4697.42i 0.529602 0.881880i
\(306\) 2022.01 + 534.578i 0.377748 + 0.0998686i
\(307\) 4426.37i 0.822887i −0.911435 0.411443i \(-0.865025\pi\)
0.911435 0.411443i \(-0.134975\pi\)
\(308\) −3141.57 + 1813.79i −0.581194 + 0.335552i
\(309\) 103.095 793.304i 0.0189802 0.146050i
\(310\) −8835.20 + 4900.17i −1.61873 + 0.897777i
\(311\) −4848.62 + 8398.06i −0.884052 + 1.53122i −0.0372549 + 0.999306i \(0.511861\pi\)
−0.846797 + 0.531917i \(0.821472\pi\)
\(312\) 20715.1 + 2692.07i 3.75884 + 0.488488i
\(313\) 3917.11 2261.55i 0.707375 0.408403i −0.102713 0.994711i \(-0.532752\pi\)
0.810088 + 0.586308i \(0.199419\pi\)
\(314\) −3346.32 −0.601413
\(315\) 1574.98 398.666i 0.281714 0.0713088i
\(316\) 11417.4 2.03253
\(317\) 4609.17 2661.10i 0.816646 0.471491i −0.0326127 0.999468i \(-0.510383\pi\)
0.849258 + 0.527977i \(0.177049\pi\)
\(318\) 3983.22 5208.99i 0.702415 0.918571i
\(319\) −962.583 + 1667.24i −0.168948 + 0.292626i
\(320\) 1211.70 + 2184.75i 0.211676 + 0.381660i
\(321\) 1673.67 696.528i 0.291013 0.121110i
\(322\) −2602.32 + 1502.45i −0.450378 + 0.260026i
\(323\) 413.874i 0.0712958i
\(324\) −10924.4 6210.43i −1.87318 1.06489i
\(325\) −9558.48 + 5088.15i −1.63141 + 0.868430i
\(326\) 2233.68 + 3868.85i 0.379485 + 0.657287i
\(327\) 2246.57 + 5398.23i 0.379925 + 0.912914i
\(328\) −1109.37 640.496i −0.186752 0.107822i
\(329\) −258.967 + 448.544i −0.0433961 + 0.0751643i
\(330\) −10609.8 + 4202.68i −1.76986 + 0.701061i
\(331\) 3916.56 + 6783.67i 0.650373 + 1.12648i 0.983032 + 0.183432i \(0.0587207\pi\)
−0.332660 + 0.943047i \(0.607946\pi\)
\(332\) 22445.9i 3.71048i
\(333\) −5622.04 5584.68i −0.925183 0.919034i
\(334\) 2028.89 0.332383
\(335\) −45.9476 + 2668.59i −0.00749369 + 0.435225i
\(336\) 343.232 2641.12i 0.0557286 0.428824i
\(337\) 8597.97 + 4964.04i 1.38980 + 0.802399i 0.993292 0.115633i \(-0.0368897\pi\)
0.396505 + 0.918033i \(0.370223\pi\)
\(338\) −23090.0 13331.0i −3.71578 2.14530i
\(339\) 235.766 1814.19i 0.0377730 0.290658i
\(340\) −51.1585 + 2971.23i −0.00816018 + 0.473934i
\(341\) 7033.49 1.11696
\(342\) 930.563 3519.81i 0.147132 0.556519i
\(343\) 3536.14i 0.556658i
\(344\) −1403.89 2431.62i −0.220037 0.381116i
\(345\) −6002.77 + 2377.77i −0.936749 + 0.371057i
\(346\) 592.952 1027.02i 0.0921310 0.159576i
\(347\) 3499.03 + 2020.17i 0.541320 + 0.312531i 0.745614 0.666379i \(-0.232157\pi\)
−0.204294 + 0.978910i \(0.565490\pi\)
\(348\) −1694.40 4071.43i −0.261004 0.627160i
\(349\) 2399.86 + 4156.68i 0.368085 + 0.637541i 0.989266 0.146125i \(-0.0466803\pi\)
−0.621181 + 0.783667i \(0.713347\pi\)
\(350\) 1588.08 + 2983.33i 0.242533 + 0.455617i
\(351\) 7446.67 + 9604.85i 1.13240 + 1.46060i
\(352\) 4190.88i 0.634588i
\(353\) 2762.17 1594.74i 0.416474 0.240451i −0.277094 0.960843i \(-0.589371\pi\)
0.693568 + 0.720391i \(0.256038\pi\)
\(354\) −1852.01 + 770.748i −0.278060 + 0.115720i
\(355\) −3472.92 6261.82i −0.519221 0.936177i
\(356\) 8580.43 14861.7i 1.27742 2.21256i
\(357\) −261.934 + 342.540i −0.0388320 + 0.0507819i
\(358\) 10460.3 6039.27i 1.54426 0.891579i
\(359\) 1159.83 0.170511 0.0852554 0.996359i \(-0.472829\pi\)
0.0852554 + 0.996359i \(0.472829\pi\)
\(360\) 3813.28 13480.0i 0.558271 1.97349i
\(361\) −6138.55 −0.894963
\(362\) 5300.91 3060.48i 0.769640 0.444352i
\(363\) 1019.99 + 132.555i 0.147481 + 0.0191662i
\(364\) −4018.31 + 6959.92i −0.578618 + 1.00220i
\(365\) 7521.23 4171.41i 1.07857 0.598197i
\(366\) 1648.72 12686.6i 0.235464 1.81186i
\(367\) −10284.2 + 5937.58i −1.46275 + 0.844520i −0.999138 0.0415170i \(-0.986781\pi\)
−0.463614 + 0.886037i \(0.653448\pi\)
\(368\) 10584.4i 1.49932i
\(369\) −195.293 719.244i −0.0275516 0.101470i
\(370\) 8486.91 14132.2i 1.19247 1.98567i
\(371\) 675.985 + 1170.84i 0.0945968 + 0.163846i
\(372\) −9786.72 + 12798.4i −1.36403 + 1.78378i
\(373\) 2289.13 + 1321.63i 0.317766 + 0.183462i 0.650396 0.759595i \(-0.274603\pi\)
−0.332631 + 0.943057i \(0.607936\pi\)
\(374\) 1514.46 2623.12i 0.209387 0.362669i
\(375\) 2440.32 + 6839.53i 0.336048 + 0.941845i
\(376\) 2233.01 + 3867.69i 0.306273 + 0.530480i
\(377\) 4265.06i 0.582657i
\(378\) 2997.80 2324.21i 0.407911 0.316255i
\(379\) −10452.7 −1.41667 −0.708335 0.705876i \(-0.750553\pi\)
−0.708335 + 0.705876i \(0.750553\pi\)
\(380\) 5172.14 + 89.0539i 0.698225 + 0.0120220i
\(381\) −7205.94 + 2998.88i −0.968954 + 0.403248i
\(382\) 765.468 + 441.943i 0.102526 + 0.0591932i
\(383\) 9422.23 + 5439.92i 1.25706 + 0.725763i 0.972502 0.232896i \(-0.0748203\pi\)
0.284557 + 0.958659i \(0.408154\pi\)
\(384\) 8172.71 + 6249.52i 1.08610 + 0.830520i
\(385\) 40.5052 2352.49i 0.00536191 0.311413i
\(386\) −11128.8 −1.46747
\(387\) 417.539 1579.32i 0.0548442 0.207445i
\(388\) 14046.1i 1.83784i
\(389\) 838.831 + 1452.90i 0.109333 + 0.189370i 0.915500 0.402318i \(-0.131795\pi\)
−0.806167 + 0.591687i \(0.798462\pi\)
\(390\) −15700.8 + 19816.0i −2.03857 + 2.57288i
\(391\) 856.841 1484.09i 0.110824 0.191953i
\(392\) −12621.0 7286.76i −1.62617 0.938870i
\(393\) −8114.21 1054.50i −1.04150 0.135350i
\(394\) 2647.69 + 4585.93i 0.338550 + 0.586385i
\(395\) −3812.52 + 6348.50i −0.485642 + 0.808678i
\(396\) −12825.4 + 12911.2i −1.62753 + 1.63842i
\(397\) 13147.5i 1.66210i −0.556199 0.831049i \(-0.687741\pi\)
0.556199 0.831049i \(-0.312259\pi\)
\(398\) −15157.9 + 8751.41i −1.90904 + 1.10218i
\(399\) 596.274 + 455.960i 0.0748146 + 0.0572094i
\(400\) 11897.4 + 409.821i 1.48718 + 0.0512277i
\(401\) 3260.95 5648.14i 0.406095 0.703378i −0.588353 0.808604i \(-0.700223\pi\)
0.994448 + 0.105226i \(0.0335568\pi\)
\(402\) 2394.31 + 5753.23i 0.297058 + 0.713794i
\(403\) 13494.6 7791.09i 1.66802 0.963032i
\(404\) 11249.4 1.38534
\(405\) 7101.11 4000.55i 0.871251 0.490837i
\(406\) 1331.18 0.162723
\(407\) −9938.69 + 5738.10i −1.21042 + 0.698838i
\(408\) 1428.63 + 3432.82i 0.173352 + 0.416543i
\(409\) 2821.34 4886.70i 0.341091 0.590786i −0.643545 0.765408i \(-0.722537\pi\)
0.984636 + 0.174622i \(0.0558704\pi\)
\(410\) 1355.82 751.961i 0.163315 0.0905774i
\(411\) −3683.10 2816.40i −0.442029 0.338011i
\(412\) 2298.28 1326.91i 0.274826 0.158671i
\(413\) 413.584i 0.0492764i
\(414\) −10623.9 + 10695.0i −1.26120 + 1.26964i
\(415\) 12480.8 + 7495.17i 1.47628 + 0.886562i
\(416\) 4642.30 + 8040.69i 0.547133 + 0.947662i
\(417\) −3363.28 437.082i −0.394965 0.0513285i
\(418\) −4566.18 2636.29i −0.534304 0.308481i
\(419\) −4810.87 + 8332.66i −0.560922 + 0.971545i 0.436495 + 0.899707i \(0.356220\pi\)
−0.997416 + 0.0718380i \(0.977114\pi\)
\(420\) 4224.33 + 3347.07i 0.490777 + 0.388858i
\(421\) −5015.14 8686.47i −0.580577 1.00559i −0.995411 0.0956916i \(-0.969494\pi\)
0.414834 0.909897i \(-0.363840\pi\)
\(422\) 21084.0i 2.43212i
\(423\) −664.130 + 2512.04i −0.0763383 + 0.288746i
\(424\) 11657.7 1.33525
\(425\) −1635.03 1020.60i −0.186613 0.116486i
\(426\) −13280.4 10155.3i −1.51042 1.15499i
\(427\) 2284.28 + 1318.83i 0.258885 + 0.149467i
\(428\) 5208.14 + 3006.92i 0.588189 + 0.339591i
\(429\) 16249.7 6762.62i 1.82878 0.761078i
\(430\) 3397.76 + 58.5025i 0.381057 + 0.00656103i
\(431\) 3867.23 0.432200 0.216100 0.976371i \(-0.430666\pi\)
0.216100 + 0.976371i \(0.430666\pi\)
\(432\) −1810.22 13238.0i −0.201607 1.47434i
\(433\) 2345.27i 0.260292i −0.991495 0.130146i \(-0.958455\pi\)
0.991495 0.130146i \(-0.0415446\pi\)
\(434\) −2431.70 4211.83i −0.268953 0.465840i
\(435\) 2829.66 + 417.389i 0.311889 + 0.0460053i
\(436\) −9698.47 + 16798.2i −1.06530 + 1.84516i
\(437\) −2583.42 1491.54i −0.282796 0.163273i
\(438\) 12197.8 15951.4i 1.33067 1.74016i
\(439\) −7058.94 12226.4i −0.767437 1.32924i −0.938949 0.344057i \(-0.888199\pi\)
0.171512 0.985182i \(-0.445135\pi\)
\(440\) −17392.7 10445.0i −1.88446 1.13169i
\(441\) −2221.80 8182.65i −0.239909 0.883560i
\(442\) 6710.34i 0.722123i
\(443\) 15412.3 8898.31i 1.65296 0.954337i 0.677115 0.735877i \(-0.263230\pi\)
0.975846 0.218460i \(-0.0701033\pi\)
\(444\) 3387.86 26069.1i 0.362119 2.78645i
\(445\) 5398.49 + 9733.70i 0.575086 + 1.03690i
\(446\) 7622.37 13202.3i 0.809259 1.40168i
\(447\) −17714.7 2302.14i −1.87444 0.243596i
\(448\) −1041.49 + 601.307i −0.109835 + 0.0634131i
\(449\) 11518.0 1.21062 0.605310 0.795990i \(-0.293049\pi\)
0.605310 + 0.795990i \(0.293049\pi\)
\(450\) 11610.4 + 12356.0i 1.21627 + 1.29437i
\(451\) −1079.33 −0.112691
\(452\) 5255.88 3034.49i 0.546938 0.315775i
\(453\) −5273.99 + 6896.97i −0.547006 + 0.715338i
\(454\) 8128.77 14079.4i 0.840313 1.45547i
\(455\) −2528.17 4558.40i −0.260489 0.469673i
\(456\) 5975.65 2486.87i 0.613674 0.255392i
\(457\) −8537.03 + 4928.86i −0.873841 + 0.504512i −0.868623 0.495474i \(-0.834994\pi\)
−0.00521822 + 0.999986i \(0.501661\pi\)
\(458\) 14943.3i 1.52458i
\(459\) −817.845 + 2002.72i −0.0831672 + 0.203658i
\(460\) −18362.2 11027.2i −1.86118 1.11771i
\(461\) 8040.79 + 13927.1i 0.812358 + 1.40704i 0.911210 + 0.411943i \(0.135150\pi\)
−0.0988520 + 0.995102i \(0.531517\pi\)
\(462\) −2110.71 5071.77i −0.212552 0.510736i
\(463\) −16364.2 9447.88i −1.64257 0.948338i −0.979916 0.199411i \(-0.936097\pi\)
−0.662653 0.748927i \(-0.730569\pi\)
\(464\) 2344.46 4060.72i 0.234566 0.406281i
\(465\) −3848.40 9715.44i −0.383796 0.968910i
\(466\) 7353.25 + 12736.2i 0.730972 + 1.26608i
\(467\) 10368.7i 1.02742i −0.857963 0.513712i \(-0.828270\pi\)
0.857963 0.513712i \(-0.171730\pi\)
\(468\) −10305.1 + 38978.5i −1.01785 + 3.84996i
\(469\) −1284.79 −0.126495
\(470\) −5404.41 93.0531i −0.530398 0.00913238i
\(471\) 446.054 3432.32i 0.0436371 0.335781i
\(472\) −3088.45 1783.12i −0.301181 0.173887i
\(473\) −2048.82 1182.89i −0.199165 0.114988i
\(474\) −2228.22 + 17145.8i −0.215919 + 1.66146i
\(475\) −1776.61 + 2846.17i −0.171613 + 0.274929i
\(476\) −1430.50 −0.137745
\(477\) 4811.91 + 4779.93i 0.461892 + 0.458822i
\(478\) 14461.7i 1.38382i
\(479\) −4777.01 8274.02i −0.455672 0.789248i 0.543054 0.839698i \(-0.317268\pi\)
−0.998727 + 0.0504500i \(0.983934\pi\)
\(480\) 5788.92 2293.06i 0.550472 0.218048i
\(481\) −12712.3 + 22018.4i −1.20506 + 2.08722i
\(482\) −4862.23 2807.21i −0.459478 0.265280i
\(483\) −1194.18 2869.47i −0.112499 0.270322i
\(484\) 1706.08 + 2955.02i 0.160226 + 0.277519i
\(485\) −7810.13 4690.28i −0.731216 0.439123i
\(486\) 11458.4 15193.4i 1.06947 1.41808i
\(487\) 17514.2i 1.62966i 0.579699 + 0.814831i \(0.303170\pi\)
−0.579699 + 0.814831i \(0.696830\pi\)
\(488\) 19696.8 11371.9i 1.82711 1.05488i
\(489\) −4266.02 + 1775.38i −0.394511 + 0.164183i
\(490\) 15424.8 8554.88i 1.42208 0.788714i
\(491\) 1933.27 3348.52i 0.177693 0.307773i −0.763397 0.645929i \(-0.776470\pi\)
0.941090 + 0.338157i \(0.109803\pi\)
\(492\) 1501.83 1964.00i 0.137618 0.179967i
\(493\) −657.459 + 379.584i −0.0600618 + 0.0346767i
\(494\) −11681.0 −1.06387
\(495\) −2896.43 11442.7i −0.263000 1.03902i
\(496\) −17130.7 −1.55079
\(497\) 2985.08 1723.43i 0.269414 0.155546i
\(498\) 33707.6 + 4380.54i 3.03308 + 0.394170i
\(499\) 2427.98 4205.39i 0.217818 0.377272i −0.736322 0.676631i \(-0.763439\pi\)
0.954141 + 0.299358i \(0.0967726\pi\)
\(500\) −13106.2 + 20213.2i −1.17225 + 1.80793i
\(501\) −270.445 + 2081.03i −0.0241169 + 0.185576i
\(502\) 20065.2 11584.7i 1.78398 1.02998i
\(503\) 5481.79i 0.485927i 0.970035 + 0.242963i \(0.0781195\pi\)
−0.970035 + 0.242963i \(0.921881\pi\)
\(504\) 6519.61 + 1723.65i 0.576203 + 0.152336i
\(505\) −3756.41 + 6255.07i −0.331006 + 0.551182i
\(506\) 10915.8 + 18906.7i 0.959023 + 1.66108i
\(507\) 16751.5 21906.5i 1.46738 1.91894i
\(508\) −22423.5 12946.2i −1.95843 1.13070i
\(509\) −10213.5 + 17690.4i −0.889405 + 1.54049i −0.0488251 + 0.998807i \(0.515548\pi\)
−0.840580 + 0.541687i \(0.817786\pi\)
\(510\) −4451.99 656.691i −0.386544 0.0570172i
\(511\) 2070.06 + 3585.45i 0.179206 + 0.310393i
\(512\) 25150.0i 2.17086i
\(513\) 3486.23 + 1423.66i 0.300040 + 0.122526i
\(514\) 19028.4 1.63289
\(515\) −29.6324 + 1721.02i −0.00253546 + 0.147256i
\(516\) 5003.25 2082.19i 0.426852 0.177642i
\(517\) 3258.82 + 1881.48i 0.277220 + 0.160053i
\(518\) 6872.25 + 3967.69i 0.582914 + 0.336545i
\(519\) 974.380 + 745.091i 0.0824095 + 0.0630170i
\(520\) −44939.8 773.773i −3.78989 0.0652542i
\(521\) −5768.55 −0.485076 −0.242538 0.970142i \(-0.577980\pi\)
−0.242538 + 0.970142i \(0.577980\pi\)
\(522\) 6444.86 1749.94i 0.540390 0.146730i
\(523\) 1753.72i 0.146625i 0.997309 + 0.0733126i \(0.0233571\pi\)
−0.997309 + 0.0733126i \(0.976643\pi\)
\(524\) −13572.2 23507.7i −1.13149 1.95981i
\(525\) −3271.69 + 1231.23i −0.271978 + 0.102353i
\(526\) 12533.1 21707.9i 1.03891 1.79945i
\(527\) 2401.99 + 1386.79i 0.198544 + 0.114629i
\(528\) −19188.6 2493.69i −1.58158 0.205538i
\(529\) 92.3641 + 159.979i 0.00759136 + 0.0131486i
\(530\) −7263.96 + 12095.7i −0.595332 + 0.991332i
\(531\) −543.689 2002.35i −0.0444333 0.163643i
\(532\) 2490.13i 0.202934i
\(533\) −2070.82 + 1195.59i −0.168288 + 0.0971610i
\(534\) 20643.7 + 15785.9i 1.67293 + 1.27926i
\(535\) −3411.07 + 1891.84i −0.275651 + 0.152881i
\(536\) −5539.21 + 9594.19i −0.446376 + 0.773145i
\(537\) 4800.15 + 11534.2i 0.385739 + 0.926883i
\(538\) −25432.1 + 14683.2i −2.03802 + 1.17665i
\(539\) −12279.3 −0.981274
\(540\) 24851.9 + 10651.5i 1.98047 + 0.848826i
\(541\) 7146.18 0.567908 0.283954 0.958838i \(-0.408354\pi\)
0.283954 + 0.958838i \(0.408354\pi\)
\(542\) −12034.3 + 6948.03i −0.953725 + 0.550633i
\(543\) 2432.54 + 5845.10i 0.192247 + 0.461947i
\(544\) −826.315 + 1431.22i −0.0651250 + 0.112800i
\(545\) −6101.92 11002.0i −0.479592 0.864723i
\(546\) −9667.69 7392.71i −0.757764 0.579448i
\(547\) 6415.42 3703.95i 0.501469 0.289523i −0.227851 0.973696i \(-0.573170\pi\)
0.729320 + 0.684173i \(0.239837\pi\)
\(548\) 15381.1i 1.19900i
\(549\) 12792.9 + 3382.18i 0.994514 + 0.262929i
\(550\) 21674.9 11537.9i 1.68040 0.894506i
\(551\) 660.759 + 1144.47i 0.0510876 + 0.0884863i
\(552\) −26576.4 3453.79i −2.04922 0.266310i
\(553\) −3087.17 1782.38i −0.237396 0.137061i
\(554\) 4756.95 8239.29i 0.364808 0.631866i
\(555\) 13364.1 + 10588.8i 1.02212 + 0.809855i
\(556\) −5625.57 9743.77i −0.429096 0.743216i
\(557\) 11116.3i 0.845626i −0.906217 0.422813i \(-0.861043\pi\)
0.906217 0.422813i \(-0.138957\pi\)
\(558\) −17309.8 17194.7i −1.31323 1.30450i
\(559\) −5241.20 −0.396564
\(560\) −98.6541 + 5729.72i −0.00744446 + 0.432366i
\(561\) 2488.66 + 1903.04i 0.187293 + 0.143220i
\(562\) 19510.0 + 11264.1i 1.46438 + 0.845458i
\(563\) −9705.19 5603.29i −0.726509 0.419450i 0.0906344 0.995884i \(-0.471111\pi\)
−0.817144 + 0.576434i \(0.804444\pi\)
\(564\) −7958.09 + 3311.90i −0.594142 + 0.247263i
\(565\) −67.7656 + 3935.75i −0.00504588 + 0.293059i
\(566\) 29125.7 2.16298
\(567\) 1984.34 + 3384.66i 0.146974 + 0.250692i
\(568\) 29721.5i 2.19557i
\(569\) 7936.88 + 13747.1i 0.584765 + 1.01284i 0.994905 + 0.100820i \(0.0321465\pi\)
−0.410140 + 0.912023i \(0.634520\pi\)
\(570\) −1143.13 + 7749.77i −0.0840008 + 0.569478i
\(571\) 1194.23 2068.46i 0.0875250 0.151598i −0.818939 0.573880i \(-0.805438\pi\)
0.906464 + 0.422282i \(0.138771\pi\)
\(572\) 50566.1 + 29194.3i 3.69628 + 2.13405i
\(573\) −555.336 + 726.231i −0.0404878 + 0.0529472i
\(574\) 373.160 + 646.332i 0.0271348 + 0.0469989i
\(575\) 12263.1 6527.85i 0.889401 0.473444i
\(576\) −4251.88 + 4280.32i −0.307572 + 0.309630i
\(577\) 10429.0i 0.752455i −0.926527 0.376227i \(-0.877221\pi\)
0.926527 0.376227i \(-0.122779\pi\)
\(578\) −20340.4 + 11743.5i −1.46375 + 0.845098i
\(579\) 1483.44 11414.8i 0.106476 0.819317i
\(580\) 4602.17 + 8297.89i 0.329473 + 0.594053i
\(581\) −3504.05 + 6069.19i −0.250211 + 0.433377i
\(582\) −21093.3 2741.23i −1.50231 0.195236i
\(583\) 8506.54 4911.25i 0.604296 0.348891i
\(584\) 35699.2 2.52953
\(585\) −18232.4 18745.8i −1.28858 1.32486i
\(586\) −39738.9 −2.80136
\(587\) −2726.29 + 1574.02i −0.191697 + 0.110676i −0.592777 0.805367i \(-0.701968\pi\)
0.401080 + 0.916043i \(0.368635\pi\)
\(588\) 17086.0 22343.9i 1.19832 1.56709i
\(589\) 2414.05 4181.25i 0.168878 0.292505i
\(590\) 3774.54 2093.43i 0.263382 0.146077i
\(591\) −5056.72 + 2104.44i −0.351955 + 0.146473i
\(592\) 24206.6 13975.7i 1.68055 0.970265i
\(593\) 12123.4i 0.839542i 0.907630 + 0.419771i \(0.137890\pi\)
−0.907630 + 0.419771i \(0.862110\pi\)
\(594\) −16886.1 21780.0i −1.16641 1.50445i
\(595\) 477.673 795.409i 0.0329121 0.0548043i
\(596\) −29630.3 51321.2i −2.03642 3.52718i
\(597\) −6955.83 16714.0i −0.476856 1.14583i
\(598\) 41886.4 + 24183.1i 2.86432 + 1.65371i
\(599\) −7921.39 + 13720.3i −0.540333 + 0.935884i 0.458552 + 0.888668i \(0.348368\pi\)
−0.998885 + 0.0472161i \(0.984965\pi\)
\(600\) −4911.28 + 29739.7i −0.334171 + 2.02353i
\(601\) 12845.1 + 22248.3i 0.871815 + 1.51003i 0.860118 + 0.510096i \(0.170390\pi\)
0.0116971 + 0.999932i \(0.496277\pi\)
\(602\) 1635.85i 0.110751i
\(603\) −6220.24 + 1688.96i −0.420079 + 0.114062i
\(604\) −28802.8 −1.94034
\(605\) −2212.80 38.0999i −0.148699 0.00256030i
\(606\) −2195.43 + 16893.5i −0.147167 + 1.13243i
\(607\) 12577.5 + 7261.64i 0.841031 + 0.485570i 0.857615 0.514293i \(-0.171946\pi\)
−0.0165834 + 0.999862i \(0.505279\pi\)
\(608\) 2491.39 + 1438.40i 0.166183 + 0.0959456i
\(609\) −177.443 + 1365.39i −0.0118068 + 0.0908516i
\(610\) −473.886 + 27522.8i −0.0314543 + 1.82683i
\(611\) 8336.56 0.551982
\(612\) −6925.68 + 1880.50i −0.457441 + 0.124207i
\(613\) 26426.7i 1.74121i 0.491981 + 0.870606i \(0.336273\pi\)
−0.491981 + 0.870606i \(0.663727\pi\)
\(614\) 11118.4 + 19257.6i 0.730785 + 1.26576i
\(615\) 590.561 + 1490.90i 0.0387215 + 0.0977540i
\(616\) 4883.09 8457.77i 0.319392 0.553203i
\(617\) −3254.33 1878.89i −0.212341 0.122595i 0.390058 0.920790i \(-0.372455\pi\)
−0.602399 + 0.798195i \(0.705788\pi\)
\(618\) 1544.13 + 3710.36i 0.100508 + 0.241509i
\(619\) −11740.3 20334.7i −0.762327 1.32039i −0.941648 0.336599i \(-0.890723\pi\)
0.179321 0.983791i \(-0.442610\pi\)
\(620\) 17847.4 29719.1i 1.15608 1.92508i
\(621\) −9553.72 12322.6i −0.617355 0.796276i
\(622\) 48716.1i 3.14042i
\(623\) −4640.16 + 2679.00i −0.298401 + 0.172282i
\(624\) −39577.8 + 16471.0i −2.53907 + 1.05668i
\(625\) −6862.86 14037.2i −0.439223 0.898378i
\(626\) −11361.4 + 19678.5i −0.725385 + 1.25640i
\(627\) 3312.70 4332.12i 0.210999 0.275930i
\(628\) 9943.79 5741.05i 0.631848 0.364797i
\(629\) −4525.52 −0.286875
\(630\) −5850.81 + 5690.58i −0.370003 + 0.359870i
\(631\) 8654.12 0.545983 0.272991 0.962016i \(-0.411987\pi\)
0.272991 + 0.962016i \(0.411987\pi\)
\(632\) −26619.9 + 15369.0i −1.67545 + 0.967320i
\(633\) −21625.9 2810.43i −1.35790 0.176469i
\(634\) −13368.6 + 23155.1i −0.837438 + 1.45049i
\(635\) 14686.3 8145.28i 0.917806 0.509032i
\(636\) −2899.67 + 22312.6i −0.180785 + 1.39112i
\(637\) −23559.2 + 13601.9i −1.46539 + 0.846041i
\(638\) 9671.48i 0.600153i
\(639\) 12186.5 12268.0i 0.754446 0.759493i
\(640\) −18977.8 11396.9i −1.17213 0.703908i
\(641\) −9588.81 16608.3i −0.590850 1.02338i −0.994118 0.108301i \(-0.965459\pi\)
0.403268 0.915082i \(-0.367874\pi\)
\(642\) −5532.00 + 7234.38i −0.340079 + 0.444732i
\(643\) 8517.85 + 4917.78i 0.522413 + 0.301615i 0.737921 0.674887i \(-0.235808\pi\)
−0.215509 + 0.976502i \(0.569141\pi\)
\(644\) 5155.30 8929.24i 0.315446 0.546369i
\(645\) −512.917 + 3477.28i −0.0313117 + 0.212276i
\(646\) −1039.59 1800.62i −0.0633160 0.109667i
\(647\) 7621.18i 0.463090i 0.972824 + 0.231545i \(0.0743781\pi\)
−0.972824 + 0.231545i \(0.925622\pi\)
\(648\) 33830.2 225.584i 2.05089 0.0136756i
\(649\) −3004.82 −0.181741
\(650\) 28805.0 46146.3i 1.73819 2.78463i
\(651\) 4644.22 1932.77i 0.279603 0.116362i
\(652\) −13275.0 7664.34i −0.797378 0.460366i
\(653\) −3807.33 2198.16i −0.228166 0.131731i 0.381560 0.924344i \(-0.375387\pi\)
−0.609726 + 0.792613i \(0.708720\pi\)
\(654\) −23333.6 17842.8i −1.39513 1.06683i
\(655\) 17603.2 + 303.091i 1.05010 + 0.0180806i
\(656\) 2628.82 0.156460
\(657\) 14735.4 + 14637.5i 0.875015 + 0.869199i
\(658\) 2601.95i 0.154156i
\(659\) 5410.13 + 9370.61i 0.319801 + 0.553911i 0.980446 0.196787i \(-0.0630507\pi\)
−0.660646 + 0.750698i \(0.729717\pi\)
\(660\) 24317.6 30691.1i 1.43418 1.81008i
\(661\) 14457.8 25041.6i 0.850744 1.47353i −0.0297946 0.999556i \(-0.509485\pi\)
0.880538 0.473975i \(-0.157181\pi\)
\(662\) −34079.2 19675.6i −2.00080 1.15516i
\(663\) 6882.80 + 894.468i 0.403176 + 0.0523956i
\(664\) 30214.5 + 52333.1i 1.76589 + 3.05861i
\(665\) −1384.60 831.507i −0.0807407 0.0484879i
\(666\) 38487.5 + 10175.3i 2.23928 + 0.592018i
\(667\) 5471.87i 0.317649i
\(668\) −6028.96 + 3480.82i −0.349203 + 0.201612i
\(669\) 12525.6 + 9578.10i 0.723868 + 0.553529i
\(670\) −6503.20 11725.5i −0.374986 0.676114i
\(671\) 9581.71 16596.0i 0.551264 0.954817i
\(672\) 1151.64 + 2767.24i 0.0661092 + 0.158852i
\(673\) −4383.09 + 2530.58i −0.251049 + 0.144943i −0.620244 0.784409i \(-0.712967\pi\)
0.369196 + 0.929352i \(0.379633\pi\)
\(674\) −49875.8 −2.85036
\(675\) −14221.2 + 10261.8i −0.810924 + 0.585152i
\(676\) 91484.6 5.20509
\(677\) 10443.6 6029.63i 0.592882 0.342300i −0.173354 0.984860i \(-0.555461\pi\)
0.766236 + 0.642559i \(0.222127\pi\)
\(678\) 3531.23 + 8485.12i 0.200024 + 0.480633i
\(679\) 2192.74 3797.94i 0.123932 0.214656i
\(680\) −3880.30 6996.34i −0.218828 0.394555i
\(681\) 13357.8 + 10214.4i 0.751645 + 0.574769i
\(682\) −30600.3 + 17667.1i −1.71810 + 0.991948i
\(683\) 6110.33i 0.342321i 0.985243 + 0.171160i \(0.0547516\pi\)
−0.985243 + 0.171160i \(0.945248\pi\)
\(684\) 3273.47 + 12055.8i 0.182989 + 0.673927i
\(685\) 8552.49 + 5136.10i 0.477042 + 0.286482i
\(686\) 8882.27 + 15384.6i 0.494354 + 0.856246i
\(687\) 15327.4 + 1991.90i 0.851202 + 0.110620i
\(688\) 4990.09 + 2881.03i 0.276520 + 0.159649i
\(689\) 10880.5 18845.6i 0.601617 1.04203i
\(690\) 20143.4 25423.0i 1.11137 1.40266i
\(691\) −13604.9 23564.3i −0.748991 1.29729i −0.948307 0.317356i \(-0.897205\pi\)
0.199315 0.979935i \(-0.436128\pi\)
\(692\) 4069.15i 0.223535i
\(693\) 5483.46 1488.90i 0.300576 0.0816143i
\(694\) −20297.5 −1.11020
\(695\) 7296.40 + 125.629i 0.398228 + 0.00685667i
\(696\) 9431.09 + 7211.79i 0.513627 + 0.392762i
\(697\) −368.601 212.812i −0.0200312 0.0115650i
\(698\) −20882.0 12056.2i −1.13237 0.653774i
\(699\) −14043.7 + 5844.54i −0.759916 + 0.316253i
\(700\) −9837.37 6140.59i −0.531168 0.331561i
\(701\) −30424.7 −1.63927 −0.819633 0.572888i \(-0.805823\pi\)
−0.819633 + 0.572888i \(0.805823\pi\)
\(702\) −56524.0 23082.5i −3.03897 1.24102i
\(703\) 7877.77i 0.422640i
\(704\) 4368.69 + 7566.79i 0.233879 + 0.405091i
\(705\) 815.836 5530.91i 0.0435832 0.295469i
\(706\) −8011.51 + 13876.3i −0.427078 + 0.739721i
\(707\) −3041.74 1756.15i −0.161805 0.0934183i
\(708\) 4181.05 5467.69i 0.221940 0.290238i
\(709\) 923.205 + 1599.04i 0.0489022 + 0.0847012i 0.889440 0.457051i \(-0.151094\pi\)
−0.840538 + 0.541752i \(0.817761\pi\)
\(710\) 30838.3 + 18519.6i 1.63006 + 0.978911i
\(711\) −17289.5 4570.97i −0.911963 0.241104i
\(712\) 46200.6i 2.43180i
\(713\) −17312.9 + 9995.59i −0.909358 + 0.525018i
\(714\) 279.176 2148.22i 0.0146329 0.112598i
\(715\) −33118.2 + 18368.0i −1.73224 + 0.960733i
\(716\) −20722.3 + 35892.1i −1.08161 + 1.87340i
\(717\) −14833.4 1927.70i −0.772613 0.100406i
\(718\) −5046.02 + 2913.32i −0.262278 + 0.151426i
\(719\) −13301.3 −0.689923 −0.344961 0.938617i \(-0.612108\pi\)
−0.344961 + 0.938617i \(0.612108\pi\)
\(720\) 7054.53 + 27869.8i 0.365149 + 1.44257i
\(721\) −828.583 −0.0427989
\(722\) 26706.8 15419.2i 1.37662 0.794794i
\(723\) 3527.47 4613.00i 0.181450 0.237288i
\(724\) −10501.3 + 18188.8i −0.539058 + 0.933676i
\(725\) −6150.70 211.868i −0.315077 0.0108532i
\(726\) −4770.60 + 1985.37i −0.243875 + 0.101493i
\(727\) 22443.2 12957.6i 1.14494 0.661031i 0.197290 0.980345i \(-0.436786\pi\)
0.947649 + 0.319314i \(0.103452\pi\)
\(728\) 21636.3i 1.10150i
\(729\) 14056.5 + 13778.1i 0.714144 + 0.699999i
\(730\) −22244.3 + 37040.6i −1.12781 + 1.87799i
\(731\) −466.459 807.931i −0.0236014 0.0408788i
\(732\) 16866.3 + 40527.7i 0.851636 + 2.04638i
\(733\) −19267.1 11123.9i −0.970871 0.560532i −0.0713691 0.997450i \(-0.522737\pi\)
−0.899502 + 0.436918i \(0.856070\pi\)
\(734\) 29828.7 51664.8i 1.49999 2.59807i
\(735\) 6718.66 + 16961.5i 0.337172 + 0.851205i
\(736\) −5955.84 10315.8i −0.298282 0.516639i
\(737\) 9334.41i 0.466536i
\(738\) 2656.29 + 2638.64i 0.132492 + 0.131612i
\(739\) 23675.6 1.17851 0.589256 0.807947i \(-0.299421\pi\)
0.589256 + 0.807947i \(0.299421\pi\)
\(740\) −973.763 + 56555.0i −0.0483733 + 2.80947i
\(741\) 1557.04 11981.2i 0.0771920 0.593981i
\(742\) −5881.96 3395.95i −0.291016 0.168018i
\(743\) 29059.6 + 16777.6i 1.43485 + 0.828411i 0.997485 0.0708729i \(-0.0225785\pi\)
0.437365 + 0.899284i \(0.355912\pi\)
\(744\) 5589.93 43013.7i 0.275453 2.11957i
\(745\) 38430.7 + 661.699i 1.88992 + 0.0325406i
\(746\) −13279.0 −0.651713
\(747\) −8986.24 + 33990.0i −0.440147 + 1.66483i
\(748\) 10393.0i 0.508030i
\(749\) −938.826 1626.09i −0.0457997 0.0793274i
\(750\) −27796.9 23626.7i −1.35333 1.15030i
\(751\) −10944.9 + 18957.1i −0.531804 + 0.921111i 0.467507 + 0.883989i \(0.345152\pi\)
−0.999311 + 0.0371219i \(0.988181\pi\)
\(752\) −7937.16 4582.52i −0.384891 0.222217i
\(753\) 9207.77 + 22125.1i 0.445617 + 1.07076i
\(754\) −10713.2 18555.8i −0.517444 0.896238i
\(755\) 9617.86 16015.4i 0.463615 0.772000i
\(756\) −4920.67 + 12049.6i −0.236724 + 0.579684i
\(757\) 24362.3i 1.16970i −0.811141 0.584851i \(-0.801153\pi\)
0.811141 0.584851i \(-0.198847\pi\)
\(758\) 45476.1 26255.6i 2.17911 1.25811i
\(759\) −20847.6 + 8676.12i −0.996998 + 0.414919i
\(760\) −12178.8 + 6754.61i −0.581280 + 0.322389i
\(761\) 13842.7 23976.2i 0.659391 1.14210i −0.321383 0.946949i \(-0.604148\pi\)
0.980774 0.195149i \(-0.0625189\pi\)
\(762\) 23817.9 31147.4i 1.13232 1.48078i
\(763\) 5244.77 3028.07i 0.248851 0.143674i
\(764\) −3032.85 −0.143619
\(765\) 1267.00 4478.87i 0.0598806 0.211678i
\(766\) −54657.2 −2.57813
\(767\) −5765.10 + 3328.48i −0.271402 + 0.156694i
\(768\) −42043.3 5463.82i −1.97540 0.256717i
\(769\) −3498.05 + 6058.81i −0.164035 + 0.284117i −0.936312 0.351169i \(-0.885784\pi\)
0.772277 + 0.635286i \(0.219118\pi\)
\(770\) 5732.90 + 10336.6i 0.268311 + 0.483775i
\(771\) −2536.43 + 19517.5i −0.118479 + 0.911679i
\(772\) 33070.0 19093.0i 1.54173 0.890117i
\(773\) 19650.7i 0.914342i 0.889379 + 0.457171i \(0.151137\pi\)
−0.889379 + 0.457171i \(0.848863\pi\)
\(774\) 2150.45 + 7919.88i 0.0998661 + 0.367796i
\(775\) 10565.3 + 19847.7i 0.489698 + 0.919936i
\(776\) −18907.4 32748.7i −0.874662 1.51496i
\(777\) −4985.71 + 6519.98i −0.230195 + 0.301034i
\(778\) −7298.94 4214.04i −0.336349 0.194191i
\(779\) −370.451 + 641.639i −0.0170382 + 0.0295111i
\(780\) 12659.1 85821.3i 0.581112 3.93961i
\(781\) −12521.3 21687.5i −0.573684 0.993651i
\(782\) 8609.05i 0.393681i
\(783\) 935.840 + 6843.75i 0.0427129 + 0.312357i
\(784\) 29907.4 1.36240
\(785\) −128.208 + 7446.18i −0.00582923 + 0.338555i
\(786\) 37950.9 15794.0i 1.72222 0.716732i
\(787\) 1137.06 + 656.480i 0.0515016 + 0.0297344i 0.525530 0.850775i \(-0.323867\pi\)
−0.474028 + 0.880510i \(0.657201\pi\)
\(788\) −15735.5 9084.91i −0.711364 0.410706i
\(789\) 20595.2 + 15748.7i 0.929287 + 0.710609i
\(790\) 640.451 37196.7i 0.0288433 1.67519i
\(791\) −1894.86 −0.0851752
\(792\) 12522.9 47367.1i 0.561844 2.12515i
\(793\) 42455.1i 1.90117i
\(794\) 33024.6 + 57200.2i 1.47607 + 2.55662i
\(795\) −11438.4 9062.97i −0.510285 0.404315i
\(796\) 30028.4 52010.7i 1.33710 2.31592i
\(797\) 2071.21 + 1195.82i 0.0920529 + 0.0531468i 0.545320 0.838228i \(-0.316408\pi\)
−0.453267 + 0.891375i \(0.649742\pi\)
\(798\) −3739.49 485.973i −0.165885 0.0215580i
\(799\) 741.942 + 1285.08i 0.0328511 + 0.0568997i
\(800\) −11826.2 + 6295.29i −0.522648 + 0.278215i
\(801\) −18943.3 + 19070.1i −0.835618 + 0.841209i
\(802\) 32764.2i 1.44257i
\(803\) 26049.4 15039.7i 1.14479 0.660944i
\(804\) −16985.3 12988.3i −0.745055 0.569730i
\(805\) 3243.52 + 5848.20i 0.142011 + 0.256052i
\(806\) −39140.2 + 67792.8i −1.71049 + 2.96265i
\(807\) −11670.6 28042.9i −0.509075 1.22324i
\(808\) −26228.2 + 15142.8i −1.14196 + 0.659311i
\(809\) 7059.58 0.306801 0.153400 0.988164i \(-0.450978\pi\)
0.153400 + 0.988164i \(0.450978\pi\)
\(810\) −20845.7 + 35242.0i −0.904251 + 1.52874i
\(811\) 12699.2 0.549849 0.274925 0.961466i \(-0.411347\pi\)
0.274925 + 0.961466i \(0.411347\pi\)
\(812\) −3955.69 + 2283.82i −0.170958 + 0.0987024i
\(813\) −5522.45 13269.8i −0.238230 0.572437i
\(814\) 28826.6 49929.1i 1.24124 2.14989i
\(815\) 8694.48 4822.12i 0.373686 0.207253i
\(816\) −6061.37 4635.02i −0.260037 0.198846i
\(817\) −1406.40 + 811.986i −0.0602249 + 0.0347708i
\(818\) 28347.1i 1.21166i
\(819\) 8871.38 8930.73i 0.378499 0.381032i
\(820\) −2738.80 + 4560.58i −0.116638 + 0.194222i
\(821\) −812.003 1406.43i −0.0345178 0.0597865i 0.848250 0.529595i \(-0.177656\pi\)
−0.882768 + 0.469809i \(0.844323\pi\)
\(822\) 23098.3 + 3001.78i 0.980104 + 0.127371i
\(823\) −18317.9 10575.8i −0.775846 0.447935i 0.0591102 0.998251i \(-0.481174\pi\)
−0.834956 + 0.550317i \(0.814507\pi\)
\(824\) −3572.33 + 6187.46i −0.151029 + 0.261590i
\(825\) 8945.25 + 23769.9i 0.377495 + 1.00310i
\(826\) 1038.86 + 1799.36i 0.0437611 + 0.0757965i
\(827\) 18269.2i 0.768178i 0.923296 + 0.384089i \(0.125484\pi\)
−0.923296 + 0.384089i \(0.874516\pi\)
\(828\) 13220.9 50007.5i 0.554903 2.09889i
\(829\) −19893.4 −0.833446 −0.416723 0.909034i \(-0.636821\pi\)
−0.416723 + 0.909034i \(0.636821\pi\)
\(830\) −73126.3 1259.09i −3.05813 0.0526549i
\(831\) 7816.95 + 5977.48i 0.326314 + 0.249526i
\(832\) 16763.7 + 9678.50i 0.698528 + 0.403295i
\(833\) −4193.48 2421.11i −0.174424 0.100704i
\(834\) 15730.4 6546.48i 0.653116 0.271806i
\(835\) 77.7331 4514.65i 0.00322164 0.187109i
\(836\) 18091.6 0.748457
\(837\) 19944.0 15462.6i 0.823613 0.638550i
\(838\) 48336.8i 1.99256i
\(839\) −5852.88 10137.5i −0.240839 0.417145i 0.720115 0.693855i \(-0.244089\pi\)
−0.960954 + 0.276710i \(0.910756\pi\)
\(840\) −14354.6 2117.38i −0.589621 0.0869720i
\(841\) 10982.5 19022.2i 0.450304 0.779950i
\(842\) 43638.3 + 25194.6i 1.78608 + 1.03119i
\(843\) −14154.2 + 18509.9i −0.578288 + 0.756247i
\(844\) −36172.4 62652.4i −1.47524 2.55519i
\(845\) −30548.7 + 50868.8i −1.24368 + 2.07094i
\(846\) −3420.47 12597.2i −0.139005 0.511940i
\(847\) 1065.35i 0.0432183i
\(848\) −20718.5 + 11961.8i −0.839003 + 0.484399i
\(849\) −3882.36 + 29874.2i −0.156940 + 1.20763i
\(850\) 9677.07 + 333.338i 0.390495 + 0.0134511i
\(851\) 16309.3 28248.6i 0.656964 1.13790i
\(852\) 56886.2 + 7392.76i 2.28743 + 0.297267i
\(853\) 916.495 529.139i 0.0367880 0.0212396i −0.481493 0.876450i \(-0.659905\pi\)
0.518281 + 0.855210i \(0.326572\pi\)
\(854\) −13250.8 −0.530953
\(855\) −7796.57 2205.53i −0.311856 0.0882193i
\(856\) −16190.5 −0.646473
\(857\) 20815.2 12017.7i 0.829678 0.479015i −0.0240642 0.999710i \(-0.507661\pi\)
0.853742 + 0.520695i \(0.174327\pi\)
\(858\) −53710.4 + 70238.9i −2.13711 + 2.79477i
\(859\) −17547.1 + 30392.5i −0.696973 + 1.20719i 0.272538 + 0.962145i \(0.412137\pi\)
−0.969511 + 0.245047i \(0.921196\pi\)
\(860\) −10197.0 + 5655.45i −0.404320 + 0.224244i
\(861\) −712.684 + 296.596i −0.0282093 + 0.0117398i
\(862\) −16825.0 + 9713.93i −0.664805 + 0.383826i
\(863\) 41958.9i 1.65504i −0.561439 0.827518i \(-0.689752\pi\)
0.561439 0.827518i \(-0.310248\pi\)
\(864\) 9213.36 + 11883.6i 0.362783 + 0.467924i
\(865\) −2262.60 1358.78i −0.0889372 0.0534102i
\(866\) 5890.98 + 10203.5i 0.231159 + 0.400379i
\(867\) −9334.04 22428.5i −0.365629 0.878562i
\(868\) 14451.9 + 8343.81i 0.565127 + 0.326276i
\(869\) −12949.6 + 22429.3i −0.505505 + 0.875560i
\(870\) −13359.3 + 5291.78i −0.520602 + 0.206216i
\(871\) 10339.8 + 17909.1i 0.402241 + 0.696703i
\(872\) 52220.6i 2.02800i
\(873\) 5623.36 21270.1i 0.218009 0.824607i
\(874\) 14986.1 0.579993
\(875\) 6699.31 3419.47i 0.258832 0.132113i
\(876\) −8879.63 + 68327.5i −0.342483 + 2.63535i
\(877\) −16983.7 9805.55i −0.653933 0.377548i 0.136028 0.990705i \(-0.456566\pi\)
−0.789961 + 0.613157i \(0.789899\pi\)
\(878\) 61422.1 + 35462.1i 2.36093 + 1.36308i
\(879\) 5297.07 40760.2i 0.203260 1.56406i
\(880\) 41628.2 + 716.754i 1.59465 + 0.0274566i
\(881\) 10465.2 0.400204 0.200102 0.979775i \(-0.435873\pi\)
0.200102 + 0.979775i \(0.435873\pi\)
\(882\) 30219.9 + 30019.1i 1.15369 + 1.14603i
\(883\) 10812.2i 0.412074i 0.978544 + 0.206037i \(0.0660567\pi\)
−0.978544 + 0.206037i \(0.933943\pi\)
\(884\) 11512.5 + 19940.2i 0.438016 + 0.758667i
\(885\) 1644.10 + 4150.60i 0.0624472 + 0.157651i
\(886\) −44702.5 + 77427.1i −1.69505 + 2.93591i
\(887\) −31177.4 18000.3i −1.18020 0.681387i −0.224137 0.974558i \(-0.571956\pi\)
−0.956060 + 0.293171i \(0.905289\pi\)
\(888\) 27192.8 + 65341.0i 1.02763 + 2.46926i
\(889\) 4042.09 + 7001.10i 0.152494 + 0.264127i
\(890\) −47936.7 28787.8i −1.80544 1.08423i
\(891\) 24590.6 14416.9i 0.924598 0.542069i
\(892\) 52308.7i 1.96348i
\(893\) 2237.00 1291.53i 0.0838278 0.0483980i
\(894\) 82853.1 34480.8i 3.09958 1.28994i
\(895\) −13037.7 23507.5i −0.486931 0.877955i
\(896\) 5328.13 9228.58i 0.198661 0.344091i
\(897\) −30387.9 + 39739.3i −1.13113 + 1.47922i
\(898\) −50110.9 + 28931.6i −1.86216 + 1.07512i
\(899\) 8856.18 0.328554
\(900\) −55699.5 16797.4i −2.06294 0.622125i
\(901\) 3873.40 0.143220
\(902\) 4695.81 2711.13i 0.173341 0.100078i
\(903\) −1677.89 218.054i −0.0618347 0.00803585i
\(904\) −8169.47 + 14149.9i −0.300567 + 0.520597i
\(905\) −6607.04 11912.8i −0.242680 0.437562i
\(906\) 5621.14 43253.9i 0.206126 1.58611i
\(907\) −4513.41 + 2605.82i −0.165232 + 0.0953968i −0.580336 0.814377i \(-0.697079\pi\)
0.415104 + 0.909774i \(0.363745\pi\)
\(908\) 55783.9i 2.03883i
\(909\) −17035.0 4503.70i −0.621580 0.164333i
\(910\) 22449.3 + 13481.6i 0.817787 + 0.491112i
\(911\) 8366.56 + 14491.3i 0.304277 + 0.527024i 0.977100 0.212780i \(-0.0682517\pi\)
−0.672823 + 0.739804i \(0.734918\pi\)
\(912\) −8068.38 + 10551.3i −0.292950 + 0.383101i
\(913\) 44094.6 + 25458.0i 1.59838 + 0.922823i
\(914\) 24761.1 42887.6i 0.896090 1.55207i
\(915\) −28166.9 4154.76i −1.01767 0.150112i
\(916\) 25637.2 + 44405.0i 0.924758 + 1.60173i
\(917\) 8475.05i 0.305203i
\(918\) −1472.38 10767.5i −0.0529367 0.387124i
\(919\) −16722.8 −0.600255 −0.300127 0.953899i \(-0.597029\pi\)
−0.300127 + 0.953899i \(0.597029\pi\)
\(920\) 57655.6 + 992.713i 2.06614 + 0.0355748i
\(921\) −21234.6 + 8837.16i −0.759722 + 0.316172i
\(922\) −69965.5 40394.6i −2.49912 1.44287i
\(923\) −48047.1 27740.0i −1.71342 0.989246i
\(924\) 14973.4 + 11449.9i 0.533104 + 0.407655i
\(925\) −31121.5 19426.4i −1.10624 0.690525i
\(926\) 94926.8 3.36878
\(927\) −4011.54 + 1089.24i −0.142132 + 0.0385925i
\(928\) 5276.93i 0.186663i
\(929\) −17672.3 30609.2i −0.624120 1.08101i −0.988710 0.149840i \(-0.952124\pi\)
0.364590 0.931168i \(-0.381209\pi\)
\(930\) 41146.9 + 32602.0i 1.45082 + 1.14953i
\(931\) −4214.52 + 7299.77i −0.148362 + 0.256971i
\(932\) −43701.3 25230.9i −1.53593 0.886767i
\(933\) 49968.2 + 6493.71i 1.75336 + 0.227861i
\(934\) 26044.7 + 45110.8i 0.912430 + 1.58037i
\(935\) −5778.90 3470.45i −0.202129 0.121386i
\(936\) −28442.6 104751.i −0.993242 3.65800i
\(937\) 2015.96i 0.0702867i −0.999382 0.0351433i \(-0.988811\pi\)
0.999382 0.0351433i \(-0.0111888\pi\)
\(938\) 5589.68 3227.21i 0.194573 0.112337i
\(939\) −18669.8 14276.4i −0.648844 0.496159i
\(940\) 16219.2 8995.47i 0.562778 0.312128i
\(941\) −19940.2 + 34537.4i −0.690787 + 1.19648i 0.280794 + 0.959768i \(0.409402\pi\)
−0.971580 + 0.236710i \(0.923931\pi\)
\(942\) 6680.86 + 16053.3i 0.231077 + 0.555249i
\(943\) 2656.77 1533.89i 0.0917458 0.0529694i
\(944\) 7318.52 0.252328
\(945\) −5056.93 6759.71i −0.174076 0.232692i
\(946\) 11885.0 0.408471
\(947\) −30319.7 + 17505.1i −1.04040 + 0.600675i −0.919947 0.392044i \(-0.871768\pi\)
−0.120453 + 0.992719i \(0.538435\pi\)
\(948\) −22794.6 54772.7i −0.780944 1.87651i
\(949\) 33319.2 57710.6i 1.13971 1.97404i
\(950\) 580.256 16845.3i 0.0198168 0.575298i
\(951\) −21968.2 16798.7i −0.749073 0.572803i
\(952\) 3335.23 1925.60i 0.113546 0.0655556i
\(953\) 49213.8i 1.67281i −0.548109 0.836407i \(-0.684652\pi\)
0.548109 0.836407i \(-0.315348\pi\)
\(954\) −32941.5 8709.04i −1.11795 0.295561i
\(955\) 1012.73 1686.38i 0.0343155 0.0571412i
\(956\) −24811.0 42973.9i −0.839378 1.45384i
\(957\) 9920.04 + 1289.18i 0.335078 + 0.0435457i
\(958\) 41566.3 + 23998.3i 1.40182 + 0.809342i
\(959\) −2401.16 + 4158.94i −0.0808525 + 0.140041i
\(960\) 8061.75 10174.7i 0.271033 0.342070i
\(961\) −1282.29 2220.98i −0.0430427 0.0745522i
\(962\) 127726.i 4.28073i
\(963\) −6682.91 6638.49i −0.223628 0.222142i
\(964\) 19264.5 0.643640
\(965\) −426.381 + 24763.7i −0.0142235 + 0.826084i
\(966\) 12403.2 + 9484.49i 0.413112 + 0.315899i
\(967\) −1055.98 609.670i −0.0351169 0.0202747i 0.482339 0.875985i \(-0.339787\pi\)
−0.517456 + 0.855710i \(0.673121\pi\)
\(968\) −7955.54 4593.13i −0.264154 0.152509i
\(969\) 1985.48 826.291i 0.0658232 0.0273935i
\(970\) 45760.5 + 787.904i 1.51472 + 0.0260805i
\(971\) −1660.33 −0.0548740 −0.0274370 0.999624i \(-0.508735\pi\)
−0.0274370 + 0.999624i \(0.508735\pi\)
\(972\) −7982.99 + 64806.4i −0.263431 + 2.13855i
\(973\) 3512.85i 0.115742i
\(974\) −43993.2 76198.5i −1.44726 2.50673i
\(975\) 43492.7 + 35696.5i 1.42860 + 1.17252i
\(976\) −23337.1 + 40421.1i −0.765373 + 1.32566i
\(977\) 40969.7 + 23653.9i 1.34159 + 0.774569i 0.987041 0.160467i \(-0.0512999\pi\)
0.354552 + 0.935036i \(0.384633\pi\)
\(978\) 14100.5 18439.7i 0.461027 0.602901i
\(979\) 19463.8 + 33712.2i 0.635408 + 1.10056i
\(980\) −31158.7 + 51884.6i −1.01564 + 1.69122i
\(981\) 21411.7 21554.9i 0.696863 0.701525i
\(982\) 19424.4i 0.631218i
\(983\) −35682.9 + 20601.5i −1.15779 + 0.668450i −0.950773 0.309888i \(-0.899709\pi\)
−0.207016 + 0.978338i \(0.566375\pi\)
\(984\) −857.810 + 6600.72i −0.0277906 + 0.213845i
\(985\) 10306.0 5715.89i 0.333377 0.184897i
\(986\) 1906.92 3302.89i 0.0615910 0.106679i
\(987\) 2668.82 + 346.832i 0.0860685 + 0.0111852i
\(988\) 34710.8 20040.3i 1.11771 0.645310i
\(989\) 6724.20 0.216195
\(990\) 41343.9 + 42508.0i 1.32727 + 1.36464i
\(991\) −29805.3 −0.955395 −0.477698 0.878524i \(-0.658529\pi\)
−0.477698 + 0.878524i \(0.658529\pi\)
\(992\) 16696.1 9639.48i 0.534376 0.308522i
\(993\) 24724.0 32332.4i 0.790122 1.03327i
\(994\) −8658.04 + 14996.2i −0.276274 + 0.478520i
\(995\) 18892.8 + 34064.4i 0.601950 + 1.08534i
\(996\) −107680. + 44812.8i −3.42566 + 1.42565i
\(997\) −34496.2 + 19916.4i −1.09579 + 0.632657i −0.935113 0.354350i \(-0.884702\pi\)
−0.160680 + 0.987006i \(0.551369\pi\)
\(998\) 24395.0i 0.773756i
\(999\) −15567.1 + 38120.3i −0.493013 + 1.20728i
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 45.4.j.a.4.2 32
3.2 odd 2 135.4.j.a.64.15 32
5.2 odd 4 225.4.e.g.76.2 32
5.3 odd 4 225.4.e.g.76.15 32
5.4 even 2 inner 45.4.j.a.4.15 yes 32
9.2 odd 6 135.4.j.a.19.2 32
9.4 even 3 405.4.b.e.244.2 16
9.5 odd 6 405.4.b.f.244.15 16
9.7 even 3 inner 45.4.j.a.34.15 yes 32
15.14 odd 2 135.4.j.a.64.2 32
45.4 even 6 405.4.b.e.244.15 16
45.7 odd 12 225.4.e.g.151.2 32
45.13 odd 12 2025.4.a.bk.1.2 16
45.14 odd 6 405.4.b.f.244.2 16
45.22 odd 12 2025.4.a.bk.1.15 16
45.23 even 12 2025.4.a.bl.1.15 16
45.29 odd 6 135.4.j.a.19.15 32
45.32 even 12 2025.4.a.bl.1.2 16
45.34 even 6 inner 45.4.j.a.34.2 yes 32
45.43 odd 12 225.4.e.g.151.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.j.a.4.2 32 1.1 even 1 trivial
45.4.j.a.4.15 yes 32 5.4 even 2 inner
45.4.j.a.34.2 yes 32 45.34 even 6 inner
45.4.j.a.34.15 yes 32 9.7 even 3 inner
135.4.j.a.19.2 32 9.2 odd 6
135.4.j.a.19.15 32 45.29 odd 6
135.4.j.a.64.2 32 15.14 odd 2
135.4.j.a.64.15 32 3.2 odd 2
225.4.e.g.76.2 32 5.2 odd 4
225.4.e.g.76.15 32 5.3 odd 4
225.4.e.g.151.2 32 45.7 odd 12
225.4.e.g.151.15 32 45.43 odd 12
405.4.b.e.244.2 16 9.4 even 3
405.4.b.e.244.15 16 45.4 even 6
405.4.b.f.244.2 16 45.14 odd 6
405.4.b.f.244.15 16 9.5 odd 6
2025.4.a.bk.1.2 16 45.13 odd 12
2025.4.a.bk.1.15 16 45.22 odd 12
2025.4.a.bl.1.2 16 45.32 even 12
2025.4.a.bl.1.15 16 45.23 even 12