Properties

Label 75.4.g.a.61.7
Level $75$
Weight $4$
Character 75.61
Analytic conductor $4.425$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,4,Mod(16,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 75.g (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.42514325043\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.7
Character \(\chi\) \(=\) 75.61
Dual form 75.4.g.a.16.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.67736 - 2.67176i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(3.91255 - 12.0416i) q^{4} +(6.73234 - 8.92612i) q^{5} +(4.21388 + 12.9690i) q^{6} +9.62995 q^{7} +(-6.54736 - 20.1507i) q^{8} +(-7.28115 - 5.29007i) q^{9} +O(q^{10})\) \(q+(3.67736 - 2.67176i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(3.91255 - 12.0416i) q^{4} +(6.73234 - 8.92612i) q^{5} +(4.21388 + 12.9690i) q^{6} +9.62995 q^{7} +(-6.54736 - 20.1507i) q^{8} +(-7.28115 - 5.29007i) q^{9} +(0.908811 - 50.8118i) q^{10} +(-4.49599 + 3.26653i) q^{11} +(30.7296 + 22.3263i) q^{12} +(-39.0421 - 28.3657i) q^{13} +(35.4128 - 25.7289i) q^{14} +(19.2265 + 27.4835i) q^{15} +(4.03070 + 2.92847i) q^{16} +(29.0298 + 89.3445i) q^{17} -40.9092 q^{18} +(14.5147 + 44.6717i) q^{19} +(-81.1441 - 115.992i) q^{20} +(-8.92746 + 27.4759i) q^{21} +(-7.80600 + 24.0244i) q^{22} +(-143.830 + 104.499i) q^{23} +63.5631 q^{24} +(-34.3512 - 120.187i) q^{25} -219.358 q^{26} +(21.8435 - 15.8702i) q^{27} +(37.6777 - 115.960i) q^{28} +(-20.1011 + 61.8649i) q^{29} +(144.132 + 49.6981i) q^{30} +(37.2519 + 114.650i) q^{31} +192.148 q^{32} +(-5.15194 - 15.8561i) q^{33} +(345.460 + 250.991i) q^{34} +(64.8321 - 85.9581i) q^{35} +(-92.1887 + 66.9790i) q^{36} +(-6.32796 - 4.59753i) q^{37} +(172.728 + 125.494i) q^{38} +(117.126 - 85.0971i) q^{39} +(-223.947 - 77.2189i) q^{40} +(-390.226 - 283.516i) q^{41} +(40.5795 + 124.891i) q^{42} +421.245 q^{43} +(21.7434 + 66.9193i) q^{44} +(-96.2390 + 29.3779i) q^{45} +(-249.720 + 768.558i) q^{46} +(134.747 - 414.710i) q^{47} +(-12.0921 + 8.78542i) q^{48} -250.264 q^{49} +(-447.433 - 350.194i) q^{50} -281.827 q^{51} +(-494.322 + 359.146i) q^{52} +(4.44871 - 13.6917i) q^{53} +(37.9249 - 116.721i) q^{54} +(-1.11112 + 62.1231i) q^{55} +(-63.0508 - 194.050i) q^{56} -140.912 q^{57} +(91.3691 + 281.205i) q^{58} +(-430.331 - 312.654i) q^{59} +(406.170 - 123.987i) q^{60} +(380.377 - 276.360i) q^{61} +(443.305 + 322.080i) q^{62} +(-70.1172 - 50.9431i) q^{63} +(674.352 - 489.946i) q^{64} +(-516.040 + 157.526i) q^{65} +(-61.3091 - 44.5437i) q^{66} +(81.8767 + 251.990i) q^{67} +1189.43 q^{68} +(-164.814 - 507.247i) q^{69} +(8.75181 - 489.315i) q^{70} +(60.2024 - 185.284i) q^{71} +(-58.9262 + 181.356i) q^{72} +(-66.1027 + 48.0264i) q^{73} -35.5537 q^{74} +(374.760 + 13.4101i) q^{75} +594.708 q^{76} +(-43.2962 + 31.4565i) q^{77} +(203.356 - 625.866i) q^{78} +(379.401 - 1167.67i) q^{79} +(53.2759 - 16.2630i) q^{80} +(25.0304 + 77.0356i) q^{81} -2192.49 q^{82} +(329.978 + 1015.57i) q^{83} +(295.924 + 215.002i) q^{84} +(992.937 + 342.374i) q^{85} +(1549.07 - 1125.46i) q^{86} +(-157.876 - 114.704i) q^{87} +(95.2597 + 69.2102i) q^{88} +(-941.245 + 683.855i) q^{89} +(-275.415 + 365.160i) q^{90} +(-375.973 - 273.160i) q^{91} +(695.587 + 2140.80i) q^{92} -361.649 q^{93} +(-612.490 - 1885.05i) q^{94} +(496.463 + 171.185i) q^{95} +(-178.131 + 548.231i) q^{96} +(351.696 - 1082.41i) q^{97} +(-920.311 + 668.645i) q^{98} +50.0161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{2} + 21 q^{3} - 18 q^{4} + 15 q^{5} + 12 q^{6} + 58 q^{7} - 111 q^{8} - 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{2} + 21 q^{3} - 18 q^{4} + 15 q^{5} + 12 q^{6} + 58 q^{7} - 111 q^{8} - 63 q^{9} - 155 q^{10} + 65 q^{11} + 84 q^{12} - 100 q^{13} - 108 q^{14} - 75 q^{15} + 46 q^{16} + 72 q^{17} + 144 q^{18} + 146 q^{19} + 265 q^{20} + 81 q^{21} - 901 q^{22} - 464 q^{23} - 702 q^{24} + 95 q^{25} - 114 q^{26} + 189 q^{27} - 66 q^{28} + 372 q^{29} - 135 q^{30} + 149 q^{31} + 2968 q^{32} + 210 q^{33} + 734 q^{34} + 650 q^{35} - 252 q^{36} - 72 q^{37} + 568 q^{38} + 300 q^{39} + 1080 q^{40} - 1306 q^{41} + 339 q^{42} + 928 q^{43} - 2297 q^{44} - 270 q^{45} - 186 q^{46} - 1416 q^{47} - 138 q^{48} + 498 q^{49} - 2315 q^{50} - 756 q^{51} - 2018 q^{52} + 56 q^{53} + 108 q^{54} - 1520 q^{55} - 300 q^{56} + 792 q^{57} - 979 q^{58} + 419 q^{59} + 1245 q^{60} + 1292 q^{61} + 501 q^{62} - 18 q^{63} + 259 q^{64} + 1000 q^{65} - 1842 q^{66} + 1772 q^{67} + 1218 q^{68} - 468 q^{69} - 5030 q^{70} + 2506 q^{71} - 999 q^{72} - 2234 q^{73} + 1882 q^{74} - 765 q^{75} + 2576 q^{76} - 999 q^{77} + 432 q^{78} + 1500 q^{79} + 730 q^{80} - 567 q^{81} + 3956 q^{82} - 953 q^{83} + 3618 q^{84} + 4370 q^{85} - 10 q^{86} - 36 q^{87} + 8439 q^{88} - 774 q^{89} - 5896 q^{91} + 2663 q^{92} - 42 q^{93} - 7295 q^{94} - 5340 q^{95} + 4461 q^{96} - 3753 q^{97} - 9855 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.67736 2.67176i 1.30014 0.944610i 0.300186 0.953881i \(-0.402951\pi\)
0.999957 + 0.00927105i \(0.00295111\pi\)
\(3\) −0.927051 + 2.85317i −0.178411 + 0.549093i
\(4\) 3.91255 12.0416i 0.489069 1.50520i
\(5\) 6.73234 8.92612i 0.602159 0.798376i
\(6\) 4.21388 + 12.9690i 0.286718 + 0.882428i
\(7\) 9.62995 0.519969 0.259984 0.965613i \(-0.416283\pi\)
0.259984 + 0.965613i \(0.416283\pi\)
\(8\) −6.54736 20.1507i −0.289355 0.890544i
\(9\) −7.28115 5.29007i −0.269672 0.195928i
\(10\) 0.908811 50.8118i 0.0287391 1.60681i
\(11\) −4.49599 + 3.26653i −0.123236 + 0.0895359i −0.647696 0.761899i \(-0.724267\pi\)
0.524460 + 0.851435i \(0.324267\pi\)
\(12\) 30.7296 + 22.3263i 0.739239 + 0.537088i
\(13\) −39.0421 28.3657i −0.832948 0.605172i 0.0874441 0.996169i \(-0.472130\pi\)
−0.920392 + 0.390998i \(0.872130\pi\)
\(14\) 35.4128 25.7289i 0.676034 0.491167i
\(15\) 19.2265 + 27.4835i 0.330951 + 0.473080i
\(16\) 4.03070 + 2.92847i 0.0629797 + 0.0457574i
\(17\) 29.0298 + 89.3445i 0.414162 + 1.27466i 0.912998 + 0.407963i \(0.133761\pi\)
−0.498836 + 0.866696i \(0.666239\pi\)
\(18\) −40.9092 −0.535689
\(19\) 14.5147 + 44.6717i 0.175258 + 0.539389i 0.999645 0.0266373i \(-0.00847993\pi\)
−0.824387 + 0.566027i \(0.808480\pi\)
\(20\) −81.1441 115.992i −0.907218 1.29683i
\(21\) −8.92746 + 27.4759i −0.0927681 + 0.285511i
\(22\) −7.80600 + 24.0244i −0.0756475 + 0.232819i
\(23\) −143.830 + 104.499i −1.30394 + 0.947368i −0.999986 0.00531897i \(-0.998307\pi\)
−0.303954 + 0.952687i \(0.598307\pi\)
\(24\) 63.5631 0.540615
\(25\) −34.3512 120.187i −0.274809 0.961499i
\(26\) −219.358 −1.65460
\(27\) 21.8435 15.8702i 0.155695 0.113119i
\(28\) 37.6777 115.960i 0.254300 0.782656i
\(29\) −20.1011 + 61.8649i −0.128713 + 0.396139i −0.994559 0.104172i \(-0.966781\pi\)
0.865846 + 0.500311i \(0.166781\pi\)
\(30\) 144.132 + 49.6981i 0.877160 + 0.302453i
\(31\) 37.2519 + 114.650i 0.215827 + 0.664248i 0.999094 + 0.0425619i \(0.0135520\pi\)
−0.783267 + 0.621686i \(0.786448\pi\)
\(32\) 192.148 1.06148
\(33\) −5.15194 15.8561i −0.0271769 0.0836420i
\(34\) 345.460 + 250.991i 1.74253 + 1.26602i
\(35\) 64.8321 85.9581i 0.313104 0.415131i
\(36\) −92.1887 + 66.9790i −0.426800 + 0.310088i
\(37\) −6.32796 4.59753i −0.0281165 0.0204278i 0.573638 0.819109i \(-0.305532\pi\)
−0.601755 + 0.798681i \(0.705532\pi\)
\(38\) 172.728 + 125.494i 0.737373 + 0.535733i
\(39\) 117.126 85.0971i 0.480903 0.349396i
\(40\) −223.947 77.2189i −0.885227 0.305234i
\(41\) −390.226 283.516i −1.48641 1.07994i −0.975418 0.220361i \(-0.929277\pi\)
−0.510996 0.859583i \(-0.670723\pi\)
\(42\) 40.5795 + 124.891i 0.149084 + 0.458835i
\(43\) 421.245 1.49394 0.746968 0.664861i \(-0.231509\pi\)
0.746968 + 0.664861i \(0.231509\pi\)
\(44\) 21.7434 + 66.9193i 0.0744987 + 0.229283i
\(45\) −96.2390 + 29.3779i −0.318810 + 0.0973199i
\(46\) −249.720 + 768.558i −0.800416 + 2.46343i
\(47\) 134.747 414.710i 0.418190 1.28706i −0.491177 0.871060i \(-0.663433\pi\)
0.909366 0.415996i \(-0.136567\pi\)
\(48\) −12.0921 + 8.78542i −0.0363613 + 0.0264181i
\(49\) −250.264 −0.729633
\(50\) −447.433 350.194i −1.26553 0.990499i
\(51\) −281.827 −0.773797
\(52\) −494.322 + 359.146i −1.31827 + 0.957781i
\(53\) 4.44871 13.6917i 0.0115298 0.0354849i −0.945126 0.326706i \(-0.894061\pi\)
0.956656 + 0.291221i \(0.0940614\pi\)
\(54\) 37.9249 116.721i 0.0955728 0.294143i
\(55\) −1.11112 + 62.1231i −0.00272407 + 0.152303i
\(56\) −63.0508 194.050i −0.150456 0.463055i
\(57\) −140.912 −0.327443
\(58\) 91.3691 + 281.205i 0.206851 + 0.636621i
\(59\) −430.331 312.654i −0.949564 0.689899i 0.00113944 0.999999i \(-0.499637\pi\)
−0.950704 + 0.310100i \(0.899637\pi\)
\(60\) 406.170 123.987i 0.873938 0.266778i
\(61\) 380.377 276.360i 0.798399 0.580071i −0.112045 0.993703i \(-0.535740\pi\)
0.910444 + 0.413632i \(0.135740\pi\)
\(62\) 443.305 + 322.080i 0.908061 + 0.659745i
\(63\) −70.1172 50.9431i −0.140221 0.101877i
\(64\) 674.352 489.946i 1.31709 0.956925i
\(65\) −516.040 + 157.526i −0.984722 + 0.300596i
\(66\) −61.3091 44.5437i −0.114343 0.0830750i
\(67\) 81.8767 + 251.990i 0.149296 + 0.459486i 0.997538 0.0701225i \(-0.0223390\pi\)
−0.848242 + 0.529608i \(0.822339\pi\)
\(68\) 1189.43 2.12117
\(69\) −164.814 507.247i −0.287555 0.885005i
\(70\) 8.75181 489.315i 0.0149434 0.835490i
\(71\) 60.2024 185.284i 0.100630 0.309707i −0.888050 0.459747i \(-0.847940\pi\)
0.988680 + 0.150040i \(0.0479403\pi\)
\(72\) −58.9262 + 181.356i −0.0964517 + 0.296848i
\(73\) −66.1027 + 48.0264i −0.105983 + 0.0770009i −0.639514 0.768779i \(-0.720865\pi\)
0.533532 + 0.845780i \(0.320865\pi\)
\(74\) −35.5537 −0.0558518
\(75\) 374.760 + 13.4101i 0.576981 + 0.0206462i
\(76\) 594.708 0.897602
\(77\) −43.2962 + 31.4565i −0.0640786 + 0.0465559i
\(78\) 203.356 625.866i 0.295199 0.908530i
\(79\) 379.401 1167.67i 0.540328 1.66296i −0.191519 0.981489i \(-0.561341\pi\)
0.731847 0.681469i \(-0.238659\pi\)
\(80\) 53.2759 16.2630i 0.0744554 0.0227282i
\(81\) 25.0304 + 77.0356i 0.0343352 + 0.105673i
\(82\) −2192.49 −2.95268
\(83\) 329.978 + 1015.57i 0.436383 + 1.34305i 0.891662 + 0.452701i \(0.149540\pi\)
−0.455279 + 0.890349i \(0.650460\pi\)
\(84\) 295.924 + 215.002i 0.384381 + 0.279269i
\(85\) 992.937 + 342.374i 1.26705 + 0.436891i
\(86\) 1549.07 1125.46i 1.94233 1.41119i
\(87\) −157.876 114.704i −0.194553 0.141351i
\(88\) 95.2597 + 69.2102i 0.115394 + 0.0838390i
\(89\) −941.245 + 683.855i −1.12103 + 0.814477i −0.984365 0.176140i \(-0.943639\pi\)
−0.136666 + 0.990617i \(0.543639\pi\)
\(90\) −275.415 + 365.160i −0.322570 + 0.427681i
\(91\) −375.973 273.160i −0.433107 0.314670i
\(92\) 695.587 + 2140.80i 0.788261 + 2.42602i
\(93\) −361.649 −0.403240
\(94\) −612.490 1885.05i −0.672059 2.06838i
\(95\) 496.463 + 171.185i 0.536169 + 0.184876i
\(96\) −178.131 + 548.231i −0.189379 + 0.582850i
\(97\) 351.696 1082.41i 0.368137 1.13301i −0.579856 0.814719i \(-0.696891\pi\)
0.947993 0.318291i \(-0.103109\pi\)
\(98\) −920.311 + 668.645i −0.948627 + 0.689218i
\(99\) 50.0161 0.0507759
\(100\) −1581.65 56.5963i −1.58165 0.0565963i
\(101\) −1277.88 −1.25895 −0.629476 0.777020i \(-0.716730\pi\)
−0.629476 + 0.777020i \(0.716730\pi\)
\(102\) −1036.38 + 752.974i −1.00605 + 0.730936i
\(103\) −159.139 + 489.781i −0.152238 + 0.468539i −0.997871 0.0652256i \(-0.979223\pi\)
0.845633 + 0.533765i \(0.179223\pi\)
\(104\) −315.967 + 972.445i −0.297914 + 0.916886i
\(105\) 185.150 + 264.665i 0.172084 + 0.245987i
\(106\) −20.2215 62.2352i −0.0185291 0.0570266i
\(107\) −330.363 −0.298480 −0.149240 0.988801i \(-0.547683\pi\)
−0.149240 + 0.988801i \(0.547683\pi\)
\(108\) −105.639 325.123i −0.0941213 0.289676i
\(109\) 152.898 + 111.087i 0.134357 + 0.0976162i 0.652934 0.757415i \(-0.273538\pi\)
−0.518577 + 0.855031i \(0.673538\pi\)
\(110\) 161.892 + 231.418i 0.140325 + 0.200589i
\(111\) 18.9839 13.7926i 0.0162331 0.0117940i
\(112\) 38.8154 + 28.2011i 0.0327474 + 0.0237924i
\(113\) 1675.54 + 1217.35i 1.39488 + 1.01344i 0.995310 + 0.0967367i \(0.0308405\pi\)
0.399570 + 0.916703i \(0.369160\pi\)
\(114\) −518.184 + 376.483i −0.425723 + 0.309306i
\(115\) −35.5457 + 1987.36i −0.0288231 + 1.61150i
\(116\) 666.306 + 484.099i 0.533318 + 0.387478i
\(117\) 134.215 + 413.070i 0.106053 + 0.326396i
\(118\) −2417.82 −1.88625
\(119\) 279.555 + 860.383i 0.215351 + 0.662783i
\(120\) 427.929 567.372i 0.325536 0.431614i
\(121\) −401.758 + 1236.48i −0.301847 + 0.928988i
\(122\) 660.417 2032.55i 0.490093 1.50835i
\(123\) 1170.68 850.547i 0.858182 0.623506i
\(124\) 1526.31 1.10538
\(125\) −1304.07 502.520i −0.933117 0.359574i
\(126\) −393.954 −0.278541
\(127\) 2243.28 1629.84i 1.56739 1.13878i 0.637795 0.770206i \(-0.279847\pi\)
0.929599 0.368573i \(-0.120153\pi\)
\(128\) 695.804 2141.46i 0.480476 1.47875i
\(129\) −390.515 + 1201.88i −0.266535 + 0.820309i
\(130\) −1476.79 + 1958.02i −0.996334 + 1.32100i
\(131\) −551.639 1697.77i −0.367915 1.13233i −0.948135 0.317867i \(-0.897033\pi\)
0.580220 0.814460i \(-0.302967\pi\)
\(132\) −211.089 −0.139189
\(133\) 139.776 + 430.187i 0.0911288 + 0.280465i
\(134\) 974.348 + 707.905i 0.628141 + 0.456371i
\(135\) 5.39832 301.821i 0.00344158 0.192419i
\(136\) 1610.29 1169.94i 1.01530 0.737659i
\(137\) 490.996 + 356.730i 0.306194 + 0.222463i 0.730262 0.683167i \(-0.239398\pi\)
−0.424067 + 0.905631i \(0.639398\pi\)
\(138\) −1961.32 1424.98i −1.20985 0.879005i
\(139\) −271.154 + 197.005i −0.165460 + 0.120214i −0.667434 0.744669i \(-0.732607\pi\)
0.501974 + 0.864883i \(0.332607\pi\)
\(140\) −781.413 1117.00i −0.471725 0.674311i
\(141\) 1058.32 + 768.914i 0.632103 + 0.459250i
\(142\) −273.648 842.202i −0.161719 0.497719i
\(143\) 268.190 0.156833
\(144\) −13.8563 42.6453i −0.00801870 0.0246790i
\(145\) 416.886 + 595.921i 0.238762 + 0.341300i
\(146\) −114.768 + 353.221i −0.0650569 + 0.200225i
\(147\) 232.008 714.046i 0.130175 0.400636i
\(148\) −80.1201 + 58.2107i −0.0444989 + 0.0323303i
\(149\) 1749.73 0.962037 0.481019 0.876710i \(-0.340267\pi\)
0.481019 + 0.876710i \(0.340267\pi\)
\(150\) 1413.96 951.955i 0.769661 0.518179i
\(151\) −1852.06 −0.998136 −0.499068 0.866563i \(-0.666324\pi\)
−0.499068 + 0.866563i \(0.666324\pi\)
\(152\) 805.134 584.964i 0.429638 0.312150i
\(153\) 261.268 804.100i 0.138054 0.424887i
\(154\) −75.1714 + 231.354i −0.0393343 + 0.121059i
\(155\) 1274.17 + 439.345i 0.660282 + 0.227671i
\(156\) −566.443 1743.33i −0.290716 0.894733i
\(157\) 515.248 0.261919 0.130960 0.991388i \(-0.458194\pi\)
0.130960 + 0.991388i \(0.458194\pi\)
\(158\) −1724.55 5307.63i −0.868342 2.67248i
\(159\) 34.9406 + 25.3858i 0.0174275 + 0.0126618i
\(160\) 1293.61 1715.14i 0.639179 0.847459i
\(161\) −1385.08 + 1006.32i −0.678008 + 0.492601i
\(162\) 297.866 + 216.412i 0.144460 + 0.104957i
\(163\) 825.151 + 599.507i 0.396508 + 0.288080i 0.768117 0.640309i \(-0.221194\pi\)
−0.371609 + 0.928389i \(0.621194\pi\)
\(164\) −4940.76 + 3589.67i −2.35249 + 1.70918i
\(165\) −176.218 60.7615i −0.0831426 0.0286683i
\(166\) 3926.80 + 2852.99i 1.83602 + 1.33395i
\(167\) 56.6060 + 174.215i 0.0262294 + 0.0807257i 0.963314 0.268376i \(-0.0864869\pi\)
−0.937085 + 0.349101i \(0.886487\pi\)
\(168\) 612.110 0.281103
\(169\) 40.7582 + 125.441i 0.0185517 + 0.0570964i
\(170\) 4566.13 1393.86i 2.06004 0.628846i
\(171\) 130.633 402.046i 0.0584194 0.179796i
\(172\) 1648.14 5072.46i 0.730637 2.24867i
\(173\) −3203.39 + 2327.40i −1.40780 + 1.02283i −0.414160 + 0.910204i \(0.635925\pi\)
−0.993638 + 0.112621i \(0.964075\pi\)
\(174\) −887.030 −0.386469
\(175\) −330.800 1157.40i −0.142892 0.499949i
\(176\) −27.6879 −0.0118583
\(177\) 1290.99 937.961i 0.548231 0.398313i
\(178\) −1634.20 + 5029.56i −0.688139 + 2.11787i
\(179\) −283.506 + 872.543i −0.118381 + 0.364340i −0.992637 0.121125i \(-0.961350\pi\)
0.874256 + 0.485465i \(0.161350\pi\)
\(180\) −22.7832 + 1273.81i −0.00943423 + 0.527469i
\(181\) −297.258 914.867i −0.122072 0.375699i 0.871284 0.490779i \(-0.163288\pi\)
−0.993356 + 0.115080i \(0.963288\pi\)
\(182\) −2112.41 −0.860341
\(183\) 435.874 + 1341.48i 0.176070 + 0.541886i
\(184\) 3047.43 + 2214.08i 1.22097 + 0.887090i
\(185\) −83.6401 + 25.5320i −0.0332397 + 0.0101467i
\(186\) −1329.91 + 966.240i −0.524269 + 0.380904i
\(187\) −422.364 306.865i −0.165167 0.120001i
\(188\) −4466.56 3245.15i −1.73275 1.25892i
\(189\) 210.351 152.829i 0.0809567 0.0588185i
\(190\) 2283.04 696.920i 0.871732 0.266105i
\(191\) 2389.63 + 1736.17i 0.905274 + 0.657720i 0.939815 0.341683i \(-0.110997\pi\)
−0.0345412 + 0.999403i \(0.510997\pi\)
\(192\) 772.739 + 2378.25i 0.290456 + 0.893933i
\(193\) −3932.89 −1.46682 −0.733408 0.679789i \(-0.762071\pi\)
−0.733408 + 0.679789i \(0.762071\pi\)
\(194\) −1598.62 4920.05i −0.591620 1.82082i
\(195\) 28.9462 1618.39i 0.0106302 0.594333i
\(196\) −979.171 + 3013.58i −0.356841 + 1.09824i
\(197\) 876.736 2698.32i 0.317080 0.975873i −0.657809 0.753185i \(-0.728517\pi\)
0.974890 0.222689i \(-0.0714833\pi\)
\(198\) 183.927 133.631i 0.0660159 0.0479634i
\(199\) −1133.25 −0.403689 −0.201845 0.979418i \(-0.564694\pi\)
−0.201845 + 0.979418i \(0.564694\pi\)
\(200\) −2196.95 + 1479.11i −0.776739 + 0.522944i
\(201\) −794.875 −0.278936
\(202\) −4699.24 + 3414.20i −1.63682 + 1.18922i
\(203\) −193.573 + 595.756i −0.0669269 + 0.205980i
\(204\) −1102.66 + 3393.65i −0.378440 + 1.16472i
\(205\) −5157.83 + 1574.48i −1.75726 + 0.536421i
\(206\) 723.363 + 2226.28i 0.244656 + 0.752973i
\(207\) 1600.05 0.537253
\(208\) −74.2985 228.667i −0.0247677 0.0762270i
\(209\) −211.179 153.431i −0.0698928 0.0507801i
\(210\) 1387.98 + 478.590i 0.456095 + 0.157266i
\(211\) 2469.17 1793.96i 0.805614 0.585313i −0.106942 0.994265i \(-0.534106\pi\)
0.912556 + 0.408953i \(0.134106\pi\)
\(212\) −147.464 107.139i −0.0477730 0.0347091i
\(213\) 472.836 + 343.535i 0.152104 + 0.110510i
\(214\) −1214.86 + 882.650i −0.388067 + 0.281947i
\(215\) 2835.96 3760.08i 0.899586 1.19272i
\(216\) −462.813 336.253i −0.145789 0.105922i
\(217\) 358.734 + 1104.07i 0.112223 + 0.345388i
\(218\) 859.057 0.266893
\(219\) −75.7470 233.125i −0.0233722 0.0719321i
\(220\) 743.714 + 256.440i 0.227914 + 0.0785870i
\(221\) 1400.94 4311.64i 0.426413 1.31236i
\(222\) 32.9601 101.441i 0.00996458 0.0306678i
\(223\) 4172.02 3031.15i 1.25282 0.910228i 0.254439 0.967089i \(-0.418109\pi\)
0.998382 + 0.0568608i \(0.0181091\pi\)
\(224\) 1850.38 0.551935
\(225\) −385.683 + 1056.82i −0.114276 + 0.313133i
\(226\) 9414.03 2.77085
\(227\) −1446.95 + 1051.27i −0.423072 + 0.307380i −0.778873 0.627182i \(-0.784208\pi\)
0.355801 + 0.934562i \(0.384208\pi\)
\(228\) −551.325 + 1696.80i −0.160142 + 0.492867i
\(229\) −390.744 + 1202.59i −0.112756 + 0.347027i −0.991472 0.130317i \(-0.958400\pi\)
0.878717 + 0.477344i \(0.158400\pi\)
\(230\) 5179.04 + 7403.22i 1.48476 + 2.12241i
\(231\) −49.6130 152.693i −0.0141311 0.0434912i
\(232\) 1378.23 0.390023
\(233\) −1342.37 4131.40i −0.377432 1.16162i −0.941823 0.336109i \(-0.890889\pi\)
0.564391 0.825508i \(-0.309111\pi\)
\(234\) 1597.18 + 1160.42i 0.446201 + 0.324184i
\(235\) −2794.58 3994.74i −0.775738 1.10889i
\(236\) −5448.54 + 3958.60i −1.50284 + 1.09188i
\(237\) 2979.85 + 2164.99i 0.816718 + 0.593380i
\(238\) 3326.76 + 2417.03i 0.906058 + 0.658290i
\(239\) −329.291 + 239.244i −0.0891216 + 0.0647506i −0.631454 0.775414i \(-0.717541\pi\)
0.542332 + 0.840164i \(0.317541\pi\)
\(240\) −2.98840 + 167.082i −0.000803752 + 0.0449379i
\(241\) −1381.89 1004.00i −0.369358 0.268354i 0.387587 0.921833i \(-0.373309\pi\)
−0.756945 + 0.653479i \(0.773309\pi\)
\(242\) 1826.18 + 5620.40i 0.485087 + 1.49295i
\(243\) −243.000 −0.0641500
\(244\) −1839.57 5661.63i −0.482650 1.48544i
\(245\) −1684.86 + 2233.89i −0.439355 + 0.582521i
\(246\) 2032.55 6255.53i 0.526790 1.62129i
\(247\) 700.461 2155.80i 0.180442 0.555344i
\(248\) 2066.37 1501.30i 0.529091 0.384407i
\(249\) −3203.50 −0.815315
\(250\) −6138.15 + 1636.22i −1.55284 + 0.413933i
\(251\) −5706.80 −1.43510 −0.717549 0.696508i \(-0.754736\pi\)
−0.717549 + 0.696508i \(0.754736\pi\)
\(252\) −887.773 + 645.005i −0.221922 + 0.161236i
\(253\) 305.310 939.649i 0.0758684 0.233499i
\(254\) 3894.82 11987.0i 0.962136 2.96115i
\(255\) −1897.36 + 2515.62i −0.465949 + 0.617781i
\(256\) −1102.12 3391.97i −0.269072 0.828117i
\(257\) −6301.59 −1.52950 −0.764751 0.644326i \(-0.777138\pi\)
−0.764751 + 0.644326i \(0.777138\pi\)
\(258\) 1775.07 + 5463.12i 0.428338 + 1.31829i
\(259\) −60.9380 44.2740i −0.0146197 0.0106218i
\(260\) −122.165 + 6830.28i −0.0291399 + 1.62921i
\(261\) 473.629 344.112i 0.112325 0.0816091i
\(262\) −6564.61 4769.47i −1.54795 1.12465i
\(263\) 4016.60 + 2918.23i 0.941726 + 0.684204i 0.948836 0.315771i \(-0.102263\pi\)
−0.00710931 + 0.999975i \(0.502263\pi\)
\(264\) −285.779 + 207.631i −0.0666230 + 0.0484045i
\(265\) −92.2636 131.887i −0.0213876 0.0305726i
\(266\) 1663.36 + 1208.50i 0.383411 + 0.278564i
\(267\) −1078.57 3319.50i −0.247219 0.760862i
\(268\) 3354.71 0.764633
\(269\) 1917.12 + 5900.28i 0.434530 + 1.33735i 0.893567 + 0.448930i \(0.148195\pi\)
−0.459037 + 0.888417i \(0.651805\pi\)
\(270\) −786.541 1124.33i −0.177287 0.253424i
\(271\) 421.312 1296.66i 0.0944386 0.290652i −0.892668 0.450714i \(-0.851169\pi\)
0.987107 + 0.160062i \(0.0511694\pi\)
\(272\) −144.633 + 445.134i −0.0322413 + 0.0992286i
\(273\) 1127.92 819.481i 0.250054 0.181675i
\(274\) 2758.67 0.608238
\(275\) 547.038 + 428.152i 0.119955 + 0.0938856i
\(276\) −6752.90 −1.47274
\(277\) −1694.73 + 1231.29i −0.367604 + 0.267080i −0.756216 0.654321i \(-0.772954\pi\)
0.388613 + 0.921401i \(0.372954\pi\)
\(278\) −470.781 + 1448.91i −0.101567 + 0.312590i
\(279\) 335.267 1031.85i 0.0719424 0.221416i
\(280\) −2156.60 743.614i −0.460290 0.158712i
\(281\) −737.828 2270.80i −0.156637 0.482081i 0.841686 0.539968i \(-0.181564\pi\)
−0.998323 + 0.0578873i \(0.981564\pi\)
\(282\) 5946.18 1.25564
\(283\) 773.293 + 2379.95i 0.162429 + 0.499906i 0.998838 0.0482007i \(-0.0153487\pi\)
−0.836408 + 0.548107i \(0.815349\pi\)
\(284\) −1995.57 1449.87i −0.416955 0.302936i
\(285\) −948.667 + 1257.80i −0.197173 + 0.261423i
\(286\) 986.232 716.539i 0.203906 0.148146i
\(287\) −3757.85 2730.24i −0.772889 0.561537i
\(288\) −1399.06 1016.48i −0.286251 0.207974i
\(289\) −3165.00 + 2299.51i −0.644210 + 0.468046i
\(290\) 3125.20 + 1077.60i 0.632820 + 0.218202i
\(291\) 2762.25 + 2006.90i 0.556448 + 0.404283i
\(292\) 319.685 + 983.888i 0.0640689 + 0.197184i
\(293\) 4049.95 0.807510 0.403755 0.914867i \(-0.367705\pi\)
0.403755 + 0.914867i \(0.367705\pi\)
\(294\) −1054.58 3245.67i −0.209199 0.643848i
\(295\) −5687.92 + 1736.29i −1.12259 + 0.342681i
\(296\) −51.2121 + 157.615i −0.0100562 + 0.0309499i
\(297\) −46.3675 + 142.705i −0.00905897 + 0.0278807i
\(298\) 6434.39 4674.86i 1.25079 0.908749i
\(299\) 8579.59 1.65943
\(300\) 1627.75 4460.24i 0.313260 0.858374i
\(301\) 4056.57 0.776799
\(302\) −6810.70 + 4948.26i −1.29772 + 0.942849i
\(303\) 1184.66 3646.02i 0.224611 0.691281i
\(304\) −72.3155 + 222.564i −0.0136434 + 0.0419899i
\(305\) 94.0053 5255.85i 0.0176483 0.986718i
\(306\) −1187.59 3655.01i −0.221862 0.682821i
\(307\) 5937.18 1.10375 0.551877 0.833925i \(-0.313912\pi\)
0.551877 + 0.833925i \(0.313912\pi\)
\(308\) 209.388 + 644.430i 0.0387370 + 0.119220i
\(309\) −1249.90 908.104i −0.230111 0.167185i
\(310\) 5859.40 1788.64i 1.07352 0.327703i
\(311\) 333.441 242.259i 0.0607965 0.0441713i −0.556972 0.830531i \(-0.688037\pi\)
0.617768 + 0.786360i \(0.288037\pi\)
\(312\) −2481.63 1803.01i −0.450304 0.327165i
\(313\) 3197.33 + 2323.00i 0.577393 + 0.419500i 0.837783 0.546003i \(-0.183851\pi\)
−0.260390 + 0.965503i \(0.583851\pi\)
\(314\) 1894.75 1376.62i 0.340532 0.247411i
\(315\) −926.777 + 282.908i −0.165771 + 0.0506033i
\(316\) −12576.2 9137.18i −2.23883 1.62660i
\(317\) 315.053 + 969.635i 0.0558207 + 0.171798i 0.975080 0.221855i \(-0.0712111\pi\)
−0.919259 + 0.393653i \(0.871211\pi\)
\(318\) 196.314 0.0346187
\(319\) −111.709 343.805i −0.0196066 0.0603429i
\(320\) 166.657 9317.83i 0.0291138 1.62776i
\(321\) 306.263 942.581i 0.0532522 0.163893i
\(322\) −2404.79 + 7401.18i −0.416191 + 1.28091i
\(323\) −3569.81 + 2593.62i −0.614952 + 0.446789i
\(324\) 1025.56 0.175851
\(325\) −2068.06 + 5666.76i −0.352970 + 0.967185i
\(326\) 4636.12 0.787641
\(327\) −458.693 + 333.260i −0.0775712 + 0.0563588i
\(328\) −3158.09 + 9719.60i −0.531635 + 1.63620i
\(329\) 1297.61 3993.64i 0.217446 0.669229i
\(330\) −810.356 + 247.369i −0.135178 + 0.0412643i
\(331\) 1115.39 + 3432.83i 0.185219 + 0.570047i 0.999952 0.00978995i \(-0.00311629\pi\)
−0.814733 + 0.579837i \(0.803116\pi\)
\(332\) 13520.1 2.23498
\(333\) 21.7536 + 66.9507i 0.00357985 + 0.0110176i
\(334\) 673.622 + 489.415i 0.110356 + 0.0801784i
\(335\) 2800.52 + 965.645i 0.456742 + 0.157489i
\(336\) −116.446 + 84.6032i −0.0189067 + 0.0137366i
\(337\) 783.872 + 569.517i 0.126707 + 0.0920580i 0.649334 0.760504i \(-0.275048\pi\)
−0.522627 + 0.852562i \(0.675048\pi\)
\(338\) 485.030 + 352.395i 0.0780538 + 0.0567094i
\(339\) −5026.62 + 3652.05i −0.805334 + 0.585110i
\(340\) 8007.65 10617.0i 1.27728 1.69349i
\(341\) −541.990 393.779i −0.0860716 0.0625347i
\(342\) −593.786 1827.49i −0.0938838 0.288945i
\(343\) −5713.10 −0.899355
\(344\) −2758.04 8488.38i −0.432278 1.33041i
\(345\) −5637.33 1943.80i −0.879721 0.303336i
\(346\) −5561.77 + 17117.4i −0.864169 + 2.65964i
\(347\) −2913.92 + 8968.11i −0.450799 + 1.38742i 0.425198 + 0.905100i \(0.360204\pi\)
−0.875997 + 0.482316i \(0.839796\pi\)
\(348\) −1998.92 + 1452.30i −0.307912 + 0.223711i
\(349\) 8291.60 1.27175 0.635873 0.771794i \(-0.280640\pi\)
0.635873 + 0.771794i \(0.280640\pi\)
\(350\) −4308.76 3372.35i −0.658037 0.515028i
\(351\) −1302.98 −0.198143
\(352\) −863.896 + 627.657i −0.130812 + 0.0950404i
\(353\) 3508.98 10799.5i 0.529076 1.62833i −0.227035 0.973887i \(-0.572903\pi\)
0.756112 0.654443i \(-0.227097\pi\)
\(354\) 2241.44 6898.44i 0.336529 1.03573i
\(355\) −1248.56 1784.77i −0.186667 0.266833i
\(356\) 4552.03 + 14009.7i 0.677689 + 2.08571i
\(357\) −2713.98 −0.402350
\(358\) 1288.67 + 3966.12i 0.190247 + 0.585519i
\(359\) 5106.43 + 3710.04i 0.750716 + 0.545427i 0.896049 0.443956i \(-0.146425\pi\)
−0.145333 + 0.989383i \(0.546425\pi\)
\(360\) 1222.10 + 1746.94i 0.178917 + 0.255754i
\(361\) 3764.16 2734.82i 0.548792 0.398720i
\(362\) −3537.43 2570.09i −0.513600 0.373152i
\(363\) −3155.45 2292.57i −0.456248 0.331484i
\(364\) −4760.30 + 3458.56i −0.685460 + 0.498016i
\(365\) −16.3364 + 913.371i −0.00234270 + 0.130981i
\(366\) 5186.98 + 3768.56i 0.740786 + 0.538213i
\(367\) 1979.71 + 6092.93i 0.281581 + 0.866617i 0.987403 + 0.158227i \(0.0505779\pi\)
−0.705822 + 0.708389i \(0.749422\pi\)
\(368\) −885.757 −0.125471
\(369\) 1341.48 + 4128.64i 0.189253 + 0.582462i
\(370\) −239.360 + 317.357i −0.0336317 + 0.0445908i
\(371\) 42.8408 131.851i 0.00599511 0.0184510i
\(372\) −1414.97 + 4354.83i −0.197212 + 0.606956i
\(373\) −1659.80 + 1205.91i −0.230405 + 0.167399i −0.696998 0.717073i \(-0.745481\pi\)
0.466593 + 0.884472i \(0.345481\pi\)
\(374\) −2373.05 −0.328095
\(375\) 2642.71 3254.87i 0.363918 0.448216i
\(376\) −9238.93 −1.26719
\(377\) 2539.63 1845.15i 0.346944 0.252069i
\(378\) 365.215 1124.02i 0.0496948 0.152945i
\(379\) −548.565 + 1688.31i −0.0743480 + 0.228819i −0.981324 0.192363i \(-0.938385\pi\)
0.906976 + 0.421183i \(0.138385\pi\)
\(380\) 4003.78 5308.44i 0.540499 0.716624i
\(381\) 2570.57 + 7911.41i 0.345655 + 1.06382i
\(382\) 13426.1 1.79827
\(383\) 3419.50 + 10524.1i 0.456209 + 1.40407i 0.869710 + 0.493563i \(0.164306\pi\)
−0.413501 + 0.910504i \(0.635694\pi\)
\(384\) 5464.92 + 3970.49i 0.726251 + 0.527652i
\(385\) −10.7001 + 598.242i −0.00141643 + 0.0791929i
\(386\) −14462.6 + 10507.7i −1.90707 + 1.38557i
\(387\) −3067.15 2228.41i −0.402873 0.292704i
\(388\) −11657.9 8469.96i −1.52536 1.10824i
\(389\) −7939.29 + 5768.23i −1.03480 + 0.751828i −0.969264 0.246022i \(-0.920876\pi\)
−0.0655378 + 0.997850i \(0.520876\pi\)
\(390\) −4217.49 6028.72i −0.547592 0.782760i
\(391\) −13511.7 9816.84i −1.74761 1.26972i
\(392\) 1638.57 + 5043.00i 0.211123 + 0.649770i
\(393\) 5355.42 0.687393
\(394\) −3985.17 12265.1i −0.509569 1.56829i
\(395\) −7868.55 11247.8i −1.00230 1.43275i
\(396\) 195.691 602.274i 0.0248329 0.0764278i
\(397\) −824.666 + 2538.06i −0.104254 + 0.320861i −0.989555 0.144158i \(-0.953953\pi\)
0.885301 + 0.465019i \(0.153953\pi\)
\(398\) −4167.38 + 3027.78i −0.524854 + 0.381329i
\(399\) −1356.97 −0.170260
\(400\) 213.506 585.035i 0.0266883 0.0731294i
\(401\) 7824.21 0.974371 0.487185 0.873299i \(-0.338024\pi\)
0.487185 + 0.873299i \(0.338024\pi\)
\(402\) −2923.04 + 2123.72i −0.362657 + 0.263486i
\(403\) 1797.73 5532.84i 0.222211 0.683896i
\(404\) −4999.78 + 15387.7i −0.615714 + 1.89497i
\(405\) 856.142 + 295.206i 0.105042 + 0.0362195i
\(406\) 879.880 + 2707.99i 0.107556 + 0.331023i
\(407\) 43.4684 0.00529398
\(408\) 1845.22 + 5679.01i 0.223902 + 0.689100i
\(409\) −1645.97 1195.86i −0.198992 0.144576i 0.483827 0.875164i \(-0.339246\pi\)
−0.682819 + 0.730587i \(0.739246\pi\)
\(410\) −14760.6 + 19570.4i −1.77798 + 2.35735i
\(411\) −1472.99 + 1070.19i −0.176781 + 0.128439i
\(412\) 5275.10 + 3832.59i 0.630790 + 0.458296i
\(413\) −4144.06 3010.84i −0.493744 0.358726i
\(414\) 5883.97 4274.95i 0.698506 0.507494i
\(415\) 11286.6 + 3891.73i 1.33503 + 0.460331i
\(416\) −7501.86 5450.42i −0.884156 0.642377i
\(417\) −310.714 956.280i −0.0364886 0.112300i
\(418\) −1186.51 −0.138838
\(419\) 1669.11 + 5137.00i 0.194610 + 0.598947i 0.999981 + 0.00617611i \(0.00196593\pi\)
−0.805371 + 0.592771i \(0.798034\pi\)
\(420\) 3911.39 1193.99i 0.454420 0.138716i
\(421\) −1827.80 + 5625.37i −0.211594 + 0.651221i 0.787783 + 0.615952i \(0.211229\pi\)
−0.999378 + 0.0352685i \(0.988771\pi\)
\(422\) 4287.00 13194.0i 0.494521 1.52198i
\(423\) −3174.96 + 2306.74i −0.364945 + 0.265148i
\(424\) −305.025 −0.0349371
\(425\) 9740.87 6558.10i 1.11177 0.748505i
\(426\) 2656.63 0.302146
\(427\) 3663.02 2661.34i 0.415142 0.301619i
\(428\) −1292.56 + 3978.09i −0.145977 + 0.449272i
\(429\) −248.626 + 765.192i −0.0279808 + 0.0861161i
\(430\) 382.832 21404.2i 0.0429344 2.40047i
\(431\) 225.406 + 693.727i 0.0251912 + 0.0775305i 0.962862 0.269995i \(-0.0870220\pi\)
−0.937671 + 0.347525i \(0.887022\pi\)
\(432\) 134.520 0.0149817
\(433\) −5283.48 16260.9i −0.586393 1.80473i −0.593604 0.804757i \(-0.702295\pi\)
0.00721121 0.999974i \(-0.497705\pi\)
\(434\) 4269.01 + 3101.61i 0.472163 + 0.343047i
\(435\) −2086.74 + 636.997i −0.230003 + 0.0702108i
\(436\) 1935.88 1406.50i 0.212642 0.154493i
\(437\) −6755.78 4908.36i −0.739526 0.537297i
\(438\) −901.403 654.908i −0.0983350 0.0714445i
\(439\) 8738.54 6348.92i 0.950040 0.690245i −0.000776050 1.00000i \(-0.500247\pi\)
0.950816 + 0.309755i \(0.100247\pi\)
\(440\) 1259.10 384.352i 0.136421 0.0416438i
\(441\) 1822.21 + 1323.91i 0.196762 + 0.142956i
\(442\) −6367.92 19598.4i −0.685273 2.10905i
\(443\) 9357.79 1.00362 0.501808 0.864979i \(-0.332668\pi\)
0.501808 + 0.864979i \(0.332668\pi\)
\(444\) −91.8095 282.560i −0.00981325 0.0302021i
\(445\) −232.616 + 13005.6i −0.0247799 + 1.38545i
\(446\) 7243.52 22293.3i 0.769037 2.36685i
\(447\) −1622.09 + 4992.28i −0.171638 + 0.528248i
\(448\) 6493.98 4718.15i 0.684848 0.497571i
\(449\) 3875.68 0.407360 0.203680 0.979038i \(-0.434710\pi\)
0.203680 + 0.979038i \(0.434710\pi\)
\(450\) 1405.28 + 4916.77i 0.147212 + 0.515064i
\(451\) 2680.56 0.279873
\(452\) 21214.5 15413.2i 2.20762 1.60393i
\(453\) 1716.96 5284.24i 0.178079 0.548069i
\(454\) −2512.21 + 7731.80i −0.259700 + 0.799276i
\(455\) −4969.44 + 1516.97i −0.512024 + 0.156300i
\(456\) 922.601 + 2839.47i 0.0947473 + 0.291602i
\(457\) 13179.1 1.34899 0.674497 0.738277i \(-0.264360\pi\)
0.674497 + 0.738277i \(0.264360\pi\)
\(458\) 1776.11 + 5466.32i 0.181206 + 0.557695i
\(459\) 2052.03 + 1490.88i 0.208672 + 0.151609i
\(460\) 23791.9 + 8203.69i 2.41153 + 0.831519i
\(461\) 11024.5 8009.76i 1.11380 0.809223i 0.130542 0.991443i \(-0.458328\pi\)
0.983258 + 0.182220i \(0.0583282\pi\)
\(462\) −590.404 428.954i −0.0594547 0.0431964i
\(463\) 5883.71 + 4274.77i 0.590582 + 0.429083i 0.842523 0.538660i \(-0.181069\pi\)
−0.251942 + 0.967742i \(0.581069\pi\)
\(464\) −262.191 + 190.493i −0.0262326 + 0.0190591i
\(465\) −2434.75 + 3228.12i −0.242814 + 0.321937i
\(466\) −15974.5 11606.1i −1.58799 1.15374i
\(467\) −399.983 1231.02i −0.0396338 0.121980i 0.929282 0.369371i \(-0.120427\pi\)
−0.968916 + 0.247391i \(0.920427\pi\)
\(468\) 5499.15 0.543158
\(469\) 788.468 + 2426.66i 0.0776292 + 0.238918i
\(470\) −20949.7 7223.64i −2.05603 0.708940i
\(471\) −477.661 + 1470.09i −0.0467292 + 0.143818i
\(472\) −3482.66 + 10718.5i −0.339624 + 1.04525i
\(473\) −1893.91 + 1376.01i −0.184106 + 0.133761i
\(474\) 16742.3 1.62236
\(475\) 4870.38 3279.01i 0.470460 0.316740i
\(476\) 11454.2 1.10294
\(477\) −104.822 + 76.1575i −0.0100618 + 0.00731030i
\(478\) −571.720 + 1759.57i −0.0547068 + 0.168370i
\(479\) −1286.67 + 3959.96i −0.122734 + 0.377735i −0.993481 0.113995i \(-0.963635\pi\)
0.870748 + 0.491730i \(0.163635\pi\)
\(480\) 3694.34 + 5280.90i 0.351297 + 0.502164i
\(481\) 116.644 + 358.994i 0.0110572 + 0.0340306i
\(482\) −7764.15 −0.733708
\(483\) −1587.16 4884.76i −0.149520 0.460175i
\(484\) 13317.3 + 9675.61i 1.25069 + 0.908679i
\(485\) −7293.97 10426.4i −0.682891 0.976164i
\(486\) −893.599 + 649.237i −0.0834042 + 0.0605967i
\(487\) −3269.87 2375.70i −0.304255 0.221054i 0.425173 0.905112i \(-0.360213\pi\)
−0.729427 + 0.684058i \(0.760213\pi\)
\(488\) −8059.33 5855.44i −0.747599 0.543163i
\(489\) −2475.45 + 1798.52i −0.228924 + 0.166323i
\(490\) −227.443 + 12716.4i −0.0209690 + 1.17238i
\(491\) −6716.60 4879.90i −0.617344 0.448527i 0.234649 0.972080i \(-0.424606\pi\)
−0.851993 + 0.523553i \(0.824606\pi\)
\(492\) −5661.60 17424.6i −0.518790 1.59667i
\(493\) −6110.82 −0.558251
\(494\) −3183.92 9799.11i −0.289983 0.892475i
\(495\) 336.726 446.450i 0.0305751 0.0405382i
\(496\) −185.597 + 571.209i −0.0168015 + 0.0517098i
\(497\) 579.746 1784.28i 0.0523243 0.161038i
\(498\) −11780.4 + 8558.97i −1.06003 + 0.770154i
\(499\) −5737.93 −0.514760 −0.257380 0.966310i \(-0.582859\pi\)
−0.257380 + 0.966310i \(0.582859\pi\)
\(500\) −11153.4 + 13736.9i −0.997588 + 1.22867i
\(501\) −549.542 −0.0490055
\(502\) −20986.0 + 15247.2i −1.86583 + 1.35561i
\(503\) −700.467 + 2155.82i −0.0620920 + 0.191100i −0.977291 0.211904i \(-0.932034\pi\)
0.915199 + 0.403003i \(0.132034\pi\)
\(504\) −567.457 + 1746.45i −0.0501519 + 0.154352i
\(505\) −8603.14 + 11406.5i −0.758089 + 1.00512i
\(506\) −1387.78 4271.14i −0.121925 0.375248i
\(507\) −395.689 −0.0346611
\(508\) −10848.9 33389.5i −0.947525 2.91618i
\(509\) −5626.05 4087.57i −0.489922 0.355949i 0.315232 0.949015i \(-0.397918\pi\)
−0.805154 + 0.593065i \(0.797918\pi\)
\(510\) −256.128 + 14320.1i −0.0222383 + 1.24334i
\(511\) −636.566 + 462.492i −0.0551077 + 0.0400381i
\(512\) 1457.70 + 1059.08i 0.125824 + 0.0914165i
\(513\) 1026.00 + 745.433i 0.0883022 + 0.0641553i
\(514\) −23173.2 + 16836.3i −1.98857 + 1.44478i
\(515\) 3300.46 + 4717.87i 0.282399 + 0.403678i
\(516\) 12944.7 + 9404.85i 1.10437 + 0.802375i
\(517\) 748.838 + 2304.69i 0.0637019 + 0.196054i
\(518\) −342.380 −0.0290412
\(519\) −3670.76 11297.4i −0.310459 0.955495i
\(520\) 6552.97 + 9367.19i 0.552628 + 0.789959i
\(521\) 4158.12 12797.4i 0.349656 1.07613i −0.609388 0.792872i \(-0.708585\pi\)
0.959044 0.283258i \(-0.0914153\pi\)
\(522\) 822.322 2530.85i 0.0689503 0.212207i
\(523\) −15776.8 + 11462.5i −1.31906 + 0.958356i −0.319121 + 0.947714i \(0.603388\pi\)
−0.999943 + 0.0106422i \(0.996612\pi\)
\(524\) −22602.2 −1.88431
\(525\) 3608.92 + 129.139i 0.300012 + 0.0107354i
\(526\) 22567.3 1.87069
\(527\) −9161.89 + 6656.51i −0.757302 + 0.550212i
\(528\) 25.6681 78.9983i 0.00211565 0.00651129i
\(529\) 6007.29 18488.5i 0.493736 1.51956i
\(530\) −691.657 238.490i −0.0566861 0.0195459i
\(531\) 1479.35 + 4552.96i 0.120900 + 0.372093i
\(532\) 5727.01 0.466725
\(533\) 7193.09 + 22138.1i 0.584554 + 1.79907i
\(534\) −12835.2 9325.32i −1.04014 0.755704i
\(535\) −2224.11 + 2948.86i −0.179732 + 0.238299i
\(536\) 4541.71 3299.74i 0.365992 0.265909i
\(537\) −2226.69 1617.78i −0.178936 0.130005i
\(538\) 22814.1 + 16575.4i 1.82822 + 1.32828i
\(539\) 1125.18 817.494i 0.0899167 0.0653283i
\(540\) −3613.28 1245.89i −0.287946 0.0992866i
\(541\) 13978.5 + 10156.0i 1.11087 + 0.807096i 0.982801 0.184669i \(-0.0591213\pi\)
0.128072 + 0.991765i \(0.459121\pi\)
\(542\) −1915.06 5893.94i −0.151769 0.467097i
\(543\) 2885.84 0.228073
\(544\) 5578.02 + 17167.4i 0.439624 + 1.35302i
\(545\) 2020.93 616.909i 0.158839 0.0484871i
\(546\) 1958.31 6027.06i 0.153494 0.472407i
\(547\) −7017.43 + 21597.4i −0.548526 + 1.68819i 0.163929 + 0.986472i \(0.447583\pi\)
−0.712455 + 0.701718i \(0.752417\pi\)
\(548\) 6216.64 4516.65i 0.484602 0.352084i
\(549\) −4231.55 −0.328959
\(550\) 3155.57 + 112.916i 0.244644 + 0.00875413i
\(551\) −3055.38 −0.236231
\(552\) −9142.28 + 6642.25i −0.704930 + 0.512161i
\(553\) 3653.61 11244.7i 0.280953 0.864686i
\(554\) −2942.41 + 9055.80i −0.225651 + 0.694484i
\(555\) 4.69162 262.309i 0.000358825 0.0200620i
\(556\) 1311.35 + 4035.91i 0.100024 + 0.307843i
\(557\) 7542.26 0.573745 0.286872 0.957969i \(-0.407384\pi\)
0.286872 + 0.957969i \(0.407384\pi\)
\(558\) −1523.95 4690.23i −0.115616 0.355830i
\(559\) −16446.3 11948.9i −1.24437 0.904087i
\(560\) 513.045 156.612i 0.0387145 0.0118180i
\(561\) 1267.09 920.595i 0.0953594 0.0692827i
\(562\) −8780.29 6379.26i −0.659029 0.478813i
\(563\) 9453.57 + 6868.42i 0.707674 + 0.514155i 0.882422 0.470458i \(-0.155911\pi\)
−0.174749 + 0.984613i \(0.555911\pi\)
\(564\) 13399.7 9735.44i 1.00040 0.726837i
\(565\) 22146.5 6760.44i 1.64905 0.503387i
\(566\) 9202.34 + 6685.89i 0.683398 + 0.496517i
\(567\) 241.041 + 741.849i 0.0178532 + 0.0549466i
\(568\) −4127.77 −0.304925
\(569\) −5612.42 17273.3i −0.413506 1.27264i −0.913580 0.406659i \(-0.866694\pi\)
0.500074 0.865983i \(-0.333306\pi\)
\(570\) −128.062 + 7159.98i −0.00941042 + 0.526138i
\(571\) −1636.40 + 5036.33i −0.119932 + 0.369114i −0.992944 0.118586i \(-0.962164\pi\)
0.873011 + 0.487700i \(0.162164\pi\)
\(572\) 1049.31 3229.44i 0.0767023 0.236066i
\(573\) −7168.88 + 5208.50i −0.522660 + 0.379735i
\(574\) −21113.5 −1.53530
\(575\) 17500.1 + 13696.9i 1.26923 + 0.993391i
\(576\) −7501.91 −0.542673
\(577\) 5077.07 3688.71i 0.366311 0.266140i −0.389369 0.921082i \(-0.627307\pi\)
0.755679 + 0.654942i \(0.227307\pi\)
\(578\) −5495.12 + 16912.3i −0.395445 + 1.21705i
\(579\) 3645.99 11221.2i 0.261696 0.805418i
\(580\) 8806.93 2688.40i 0.630496 0.192465i
\(581\) 3177.67 + 9779.88i 0.226906 + 0.698344i
\(582\) 15519.7 1.10535
\(583\) 24.7230 + 76.0896i 0.00175630 + 0.00540533i
\(584\) 1400.56 + 1017.57i 0.0992393 + 0.0721016i
\(585\) 4590.69 + 1582.91i 0.324447 + 0.111873i
\(586\) 14893.1 10820.5i 1.04988 0.762781i
\(587\) −761.336 553.143i −0.0535327 0.0388938i 0.560697 0.828021i \(-0.310533\pi\)
−0.614230 + 0.789127i \(0.710533\pi\)
\(588\) −7690.51 5587.48i −0.539373 0.391877i
\(589\) −4580.90 + 3328.22i −0.320463 + 0.232830i
\(590\) −16277.6 + 21581.7i −1.13583 + 1.50594i
\(591\) 6885.97 + 5002.95i 0.479274 + 0.348213i
\(592\) −12.0424 37.0625i −0.000836043 0.00257308i
\(593\) −17718.9 −1.22703 −0.613516 0.789682i \(-0.710245\pi\)
−0.613516 + 0.789682i \(0.710245\pi\)
\(594\) 210.762 + 648.659i 0.0145584 + 0.0448060i
\(595\) 9561.94 + 3297.05i 0.658826 + 0.227169i
\(596\) 6845.91 21069.5i 0.470502 1.44806i
\(597\) 1050.58 3233.36i 0.0720226 0.221663i
\(598\) 31550.3 22922.6i 2.15750 1.56752i
\(599\) −7231.26 −0.493258 −0.246629 0.969110i \(-0.579323\pi\)
−0.246629 + 0.969110i \(0.579323\pi\)
\(600\) −2183.47 7639.48i −0.148566 0.519801i
\(601\) −5488.00 −0.372479 −0.186240 0.982504i \(-0.559630\pi\)
−0.186240 + 0.982504i \(0.559630\pi\)
\(602\) 14917.5 10838.2i 1.00995 0.733772i
\(603\) 736.890 2267.91i 0.0497653 0.153162i
\(604\) −7246.28 + 22301.8i −0.488157 + 1.50239i
\(605\) 8332.23 + 11910.6i 0.559923 + 0.800386i
\(606\) −5384.85 16572.9i −0.360964 1.11093i
\(607\) −23649.8 −1.58141 −0.790704 0.612198i \(-0.790285\pi\)
−0.790704 + 0.612198i \(0.790285\pi\)
\(608\) 2788.98 + 8583.59i 0.186033 + 0.572550i
\(609\) −1520.34 1104.59i −0.101162 0.0734981i
\(610\) −13696.7 19578.8i −0.909118 1.29955i
\(611\) −17024.4 + 12368.9i −1.12722 + 0.818974i
\(612\) −8660.42 6292.17i −0.572021 0.415598i
\(613\) −3762.55 2733.65i −0.247909 0.180116i 0.456891 0.889523i \(-0.348963\pi\)
−0.704799 + 0.709407i \(0.748963\pi\)
\(614\) 21833.1 15862.7i 1.43504 1.04262i
\(615\) 289.317 16175.8i 0.0189698 1.06060i
\(616\) 917.346 + 666.491i 0.0600015 + 0.0435936i
\(617\) −1505.87 4634.58i −0.0982560 0.302401i 0.889833 0.456287i \(-0.150821\pi\)
−0.988089 + 0.153886i \(0.950821\pi\)
\(618\) −7022.56 −0.457102
\(619\) 3764.65 + 11586.4i 0.244449 + 0.752338i 0.995727 + 0.0923509i \(0.0294382\pi\)
−0.751277 + 0.659987i \(0.770562\pi\)
\(620\) 10275.7 13624.1i 0.665614 0.882509i
\(621\) −1483.33 + 4565.22i −0.0958518 + 0.295002i
\(622\) 578.925 1781.75i 0.0373196 0.114858i
\(623\) −9064.15 + 6585.49i −0.582901 + 0.423502i
\(624\) 721.305 0.0462745
\(625\) −13265.0 + 8257.15i −0.848960 + 0.528458i
\(626\) 17964.2 1.14696
\(627\) 633.538 460.293i 0.0403526 0.0293179i
\(628\) 2015.94 6204.41i 0.128096 0.394240i
\(629\) 227.065 698.834i 0.0143937 0.0442994i
\(630\) −2652.23 + 3516.48i −0.167726 + 0.222381i
\(631\) −3757.85 11565.5i −0.237080 0.729659i −0.996839 0.0794528i \(-0.974683\pi\)
0.759758 0.650206i \(-0.225317\pi\)
\(632\) −26013.5 −1.63728
\(633\) 2829.41 + 8708.04i 0.177661 + 0.546783i
\(634\) 3749.19 + 2723.95i 0.234857 + 0.170634i
\(635\) 554.398 30996.4i 0.0346466 1.93710i
\(636\) 442.393 321.417i 0.0275818 0.0200393i
\(637\) 9770.82 + 7098.92i 0.607746 + 0.441553i
\(638\) −1329.36 965.835i −0.0824919 0.0599338i
\(639\) −1418.51 + 1030.61i −0.0878174 + 0.0638031i
\(640\) −14430.6 20627.9i −0.891279 1.27405i
\(641\) 8768.13 + 6370.42i 0.540281 + 0.392537i 0.824190 0.566314i \(-0.191631\pi\)
−0.283908 + 0.958851i \(0.591631\pi\)
\(642\) −1392.11 4284.47i −0.0855797 0.263387i
\(643\) −15336.9 −0.940632 −0.470316 0.882498i \(-0.655860\pi\)
−0.470316 + 0.882498i \(0.655860\pi\)
\(644\) 6698.47 + 20615.8i 0.409871 + 1.26145i
\(645\) 8099.06 + 11577.3i 0.494419 + 0.706751i
\(646\) −6197.96 + 19075.4i −0.377485 + 1.16178i
\(647\) 2347.69 7225.46i 0.142654 0.439045i −0.854048 0.520195i \(-0.825859\pi\)
0.996702 + 0.0811500i \(0.0258593\pi\)
\(648\) 1388.44 1008.76i 0.0841713 0.0611540i
\(649\) 2956.05 0.178791
\(650\) 7535.21 + 26364.1i 0.454700 + 1.59090i
\(651\) −3482.67 −0.209672
\(652\) 10447.5 7590.53i 0.627538 0.455933i
\(653\) 5843.81 17985.4i 0.350208 1.07783i −0.608528 0.793533i \(-0.708240\pi\)
0.958736 0.284298i \(-0.0917605\pi\)
\(654\) −796.389 + 2451.03i −0.0476166 + 0.146549i
\(655\) −18868.3 6505.97i −1.12557 0.388106i
\(656\) −742.614 2285.53i −0.0441985 0.136029i
\(657\) 735.367 0.0436673
\(658\) −5898.25 18152.9i −0.349449 1.07549i
\(659\) 10574.2 + 7682.64i 0.625059 + 0.454132i 0.854685 0.519147i \(-0.173750\pi\)
−0.229626 + 0.973279i \(0.573750\pi\)
\(660\) −1421.13 + 1884.21i −0.0838140 + 0.111125i
\(661\) −3910.79 + 2841.36i −0.230124 + 0.167195i −0.696872 0.717195i \(-0.745426\pi\)
0.466748 + 0.884390i \(0.345426\pi\)
\(662\) 13273.4 + 9643.70i 0.779284 + 0.566183i
\(663\) 11003.1 + 7994.22i 0.644533 + 0.468280i
\(664\) 18303.9 13298.6i 1.06977 0.777237i
\(665\) 4780.92 + 1648.50i 0.278791 + 0.0961297i
\(666\) 258.872 + 188.081i 0.0150617 + 0.0109430i
\(667\) −3573.65 10998.6i −0.207455 0.638480i
\(668\) 2319.30 0.134336
\(669\) 4780.71 + 14713.5i 0.276282 + 0.850310i
\(670\) 12878.5 3931.29i 0.742596 0.226685i
\(671\) −807.434 + 2485.03i −0.0464540 + 0.142971i
\(672\) −1715.39 + 5279.44i −0.0984714 + 0.303064i
\(673\) −13291.3 + 9656.72i −0.761283 + 0.553104i −0.899304 0.437325i \(-0.855926\pi\)
0.138021 + 0.990429i \(0.455926\pi\)
\(674\) 4404.19 0.251696
\(675\) −2657.75 2080.15i −0.151551 0.118615i
\(676\) 1669.98 0.0950146
\(677\) 17003.8 12354.0i 0.965304 0.701334i 0.0109275 0.999940i \(-0.496522\pi\)
0.954377 + 0.298606i \(0.0965216\pi\)
\(678\) −8727.28 + 26859.8i −0.494350 + 1.52145i
\(679\) 3386.81 10423.5i 0.191420 0.589129i
\(680\) 397.961 22250.0i 0.0224428 1.25478i
\(681\) −1658.06 5102.97i −0.0932993 0.287146i
\(682\) −3045.18 −0.170976
\(683\) −2500.26 7695.01i −0.140073 0.431100i 0.856272 0.516526i \(-0.172775\pi\)
−0.996345 + 0.0854256i \(0.972775\pi\)
\(684\) −4330.16 3146.05i −0.242058 0.175866i
\(685\) 6489.77 1981.06i 0.361987 0.110500i
\(686\) −21009.1 + 15264.0i −1.16929 + 0.849539i
\(687\) −3068.94 2229.72i −0.170433 0.123827i
\(688\) 1697.91 + 1233.60i 0.0940875 + 0.0683586i
\(689\) −562.062 + 408.362i −0.0310782 + 0.0225796i
\(690\) −25923.9 + 7913.52i −1.43030 + 0.436612i
\(691\) −24064.9 17484.2i −1.32485 0.962561i −0.999858 0.0168450i \(-0.994638\pi\)
−0.324994 0.945716i \(-0.605362\pi\)
\(692\) 15492.2 + 47680.0i 0.851045 + 2.61925i
\(693\) 481.653 0.0264019
\(694\) 13245.1 + 40764.3i 0.724464 + 2.22967i
\(695\) −67.0120 + 3746.65i −0.00365743 + 0.204487i
\(696\) −1277.69 + 3932.33i −0.0695844 + 0.214159i
\(697\) 14002.4 43094.9i 0.760944 2.34194i
\(698\) 30491.2 22153.2i 1.65345 1.20130i
\(699\) 13032.0 0.705173
\(700\) −15231.2 545.020i −0.822407 0.0294283i
\(701\) −24612.8 −1.32612 −0.663061 0.748565i \(-0.730743\pi\)
−0.663061 + 0.748565i \(0.730743\pi\)
\(702\) −4791.54 + 3481.26i −0.257614 + 0.187168i
\(703\) 113.531 349.413i 0.00609091 0.0187459i
\(704\) −1431.46 + 4405.58i −0.0766338 + 0.235855i
\(705\) 13988.4 4270.09i 0.747281 0.228115i
\(706\) −15949.9 49088.9i −0.850260 2.61683i
\(707\) −12306.0 −0.654615
\(708\) −6243.47 19215.4i −0.331418 1.02000i
\(709\) −21821.6 15854.3i −1.15589 0.839805i −0.166639 0.986018i \(-0.553291\pi\)
−0.989253 + 0.146213i \(0.953291\pi\)
\(710\) −9359.89 3227.38i −0.494747 0.170593i
\(711\) −8939.55 + 6494.97i −0.471532 + 0.342588i
\(712\) 19942.8 + 14489.3i 1.04970 + 0.762654i
\(713\) −17338.7 12597.3i −0.910713 0.661671i
\(714\) −9980.28 + 7251.10i −0.523113 + 0.380064i
\(715\) 1805.55 2393.90i 0.0944386 0.125212i
\(716\) 9397.57 + 6827.74i 0.490508 + 0.356375i
\(717\) −377.334 1161.31i −0.0196538 0.0604882i
\(718\) 28690.5 1.49125
\(719\) −1029.02 3167.00i −0.0533742 0.164269i 0.920816 0.389997i \(-0.127524\pi\)
−0.974190 + 0.225728i \(0.927524\pi\)
\(720\) −473.943 163.420i −0.0245317 0.00845875i
\(721\) −1532.51 + 4716.57i −0.0791588 + 0.243626i
\(722\) 6535.39 20113.9i 0.336873 1.03679i
\(723\) 4145.66 3012.00i 0.213249 0.154934i
\(724\) −12179.5 −0.625203
\(725\) 8125.88 + 290.770i 0.416259 + 0.0148950i
\(726\) −17728.9 −0.906310
\(727\) −8000.88 + 5812.98i −0.408165 + 0.296550i −0.772859 0.634578i \(-0.781174\pi\)
0.364693 + 0.931128i \(0.381174\pi\)
\(728\) −3042.74 + 9364.60i −0.154906 + 0.476752i
\(729\) 225.273 693.320i 0.0114451 0.0352243i
\(730\) 2380.23 + 3402.44i 0.120680 + 0.172507i
\(731\) 12228.6 + 37635.9i 0.618731 + 1.90426i
\(732\) 17859.0 0.901757
\(733\) 3623.64 + 11152.4i 0.182595 + 0.561970i 0.999899 0.0142375i \(-0.00453208\pi\)
−0.817304 + 0.576207i \(0.804532\pi\)
\(734\) 23559.0 + 17116.6i 1.18471 + 0.860742i
\(735\) −4811.70 6878.13i −0.241473 0.345175i
\(736\) −27636.7 + 20079.2i −1.38410 + 1.00561i
\(737\) −1191.25 865.494i −0.0595390 0.0432576i
\(738\) 15963.8 + 11598.4i 0.796255 + 0.578513i
\(739\) 23869.9 17342.5i 1.18819 0.863267i 0.195114 0.980781i \(-0.437492\pi\)
0.993071 + 0.117513i \(0.0374923\pi\)
\(740\) −19.8006 + 1107.06i −0.000983629 + 0.0549948i
\(741\) 5501.49 + 3997.07i 0.272743 + 0.198159i
\(742\) −194.732 599.322i −0.00963453 0.0296520i
\(743\) −18171.7 −0.897249 −0.448625 0.893720i \(-0.648086\pi\)
−0.448625 + 0.893720i \(0.648086\pi\)
\(744\) 2367.85 + 7287.49i 0.116679 + 0.359102i
\(745\) 11779.8 15618.3i 0.579299 0.768068i
\(746\) −2881.76 + 8869.15i −0.141433 + 0.435285i
\(747\) 2969.80 9140.12i 0.145461 0.447683i
\(748\) −5347.66 + 3885.31i −0.261404 + 0.189921i
\(749\) −3181.38 −0.155200
\(750\) 1021.98 19030.0i 0.0497564 0.926505i
\(751\) −31181.1 −1.51507 −0.757534 0.652796i \(-0.773596\pi\)
−0.757534 + 0.652796i \(0.773596\pi\)
\(752\) 1757.59 1276.97i 0.0852298 0.0619231i
\(753\) 5290.49 16282.5i 0.256037 0.788002i
\(754\) 4409.35 13570.6i 0.212969 0.655453i
\(755\) −12468.7 + 16531.7i −0.601037 + 0.796888i
\(756\) −1017.30 3130.92i −0.0489401 0.150622i
\(757\) 23324.8 1.11989 0.559943 0.828531i \(-0.310823\pi\)
0.559943 + 0.828531i \(0.310823\pi\)
\(758\) 2493.48 + 7674.15i 0.119482 + 0.367728i
\(759\) 2397.94 + 1742.20i 0.114677 + 0.0833176i
\(760\) 198.978 11124.9i 0.00949697 0.530977i
\(761\) −5535.02 + 4021.43i −0.263659 + 0.191559i −0.711758 0.702424i \(-0.752101\pi\)
0.448100 + 0.893984i \(0.352101\pi\)
\(762\) 30590.3 + 22225.2i 1.45429 + 1.05660i
\(763\) 1472.40 + 1069.76i 0.0698615 + 0.0507574i
\(764\) 30255.7 21982.1i 1.43274 1.04095i
\(765\) −5418.55 7745.58i −0.256089 0.366068i
\(766\) 40692.6 + 29564.9i 1.91943 + 1.39455i
\(767\) 7932.36 + 24413.3i 0.373430 + 1.14930i
\(768\) 10699.6 0.502719
\(769\) −2150.40 6618.26i −0.100839 0.310352i 0.887892 0.460052i \(-0.152169\pi\)
−0.988731 + 0.149700i \(0.952169\pi\)
\(770\) 1559.01 + 2228.54i 0.0729648 + 0.104300i
\(771\) 5841.89 17979.5i 0.272880 0.839839i
\(772\) −15387.6 + 47358.2i −0.717374 + 2.20785i
\(773\) 19308.2 14028.2i 0.898405 0.652729i −0.0396508 0.999214i \(-0.512625\pi\)
0.938056 + 0.346484i \(0.112625\pi\)
\(774\) −17232.8 −0.800284
\(775\) 12499.8 8415.56i 0.579362 0.390059i
\(776\) −24114.0 −1.11552
\(777\) 182.814 132.822i 0.00844069 0.00613252i
\(778\) −13784.3 + 42423.7i −0.635207 + 1.95497i
\(779\) 7001.11 21547.2i 0.322004 0.991025i
\(780\) −19374.7 6680.57i −0.889391 0.306670i
\(781\) 334.566 + 1029.69i 0.0153287 + 0.0471768i
\(782\) −75915.7 −3.47153
\(783\) 542.731 + 1670.35i 0.0247709 + 0.0762370i
\(784\) −1008.74 732.892i −0.0459520 0.0333861i
\(785\) 3468.83 4599.17i 0.157717 0.209110i
\(786\) 19693.8 14308.4i 0.893709 0.649318i
\(787\) 33192.1 + 24115.5i 1.50339 + 1.09228i 0.969005 + 0.247039i \(0.0794577\pi\)
0.534388 + 0.845240i \(0.320542\pi\)
\(788\) −29061.7 21114.6i −1.31381 0.954538i
\(789\) −12049.8 + 8754.69i −0.543706 + 0.395025i
\(790\) −58986.8 20339.2i −2.65653 0.915995i
\(791\) 16135.4 + 11723.0i 0.725294 + 0.526957i
\(792\) −327.474 1007.86i −0.0146923 0.0452181i
\(793\) −22689.9 −1.01607
\(794\) 3748.49 + 11536.7i 0.167543 + 0.515644i
\(795\) 461.829 140.978i 0.0206030 0.00628927i
\(796\) −4433.91 + 13646.2i −0.197432 + 0.607633i
\(797\) −1082.46 + 3331.47i −0.0481088 + 0.148064i −0.972225 0.234048i \(-0.924803\pi\)
0.924116 + 0.382111i \(0.124803\pi\)
\(798\) −4990.09 + 3625.51i −0.221362 + 0.160829i
\(799\) 40963.7 1.81376
\(800\) −6600.51 23093.8i −0.291704 1.02061i
\(801\) 10471.0 0.461890
\(802\) 28772.5 20904.4i 1.26682 0.920400i
\(803\) 140.317 431.853i 0.00616649 0.0189785i
\(804\) −3109.99 + 9571.57i −0.136419 + 0.419855i
\(805\) −342.303 + 19138.2i −0.0149871 + 0.837930i
\(806\) −8171.51 25149.3i −0.357108 1.09907i
\(807\) −18611.8 −0.811852
\(808\) 8366.76 + 25750.2i 0.364284 + 1.12115i
\(809\) −31071.6 22574.8i −1.35033 0.981074i −0.998995 0.0448251i \(-0.985727\pi\)
−0.351338 0.936249i \(-0.614273\pi\)
\(810\) 3937.06 1201.83i 0.170783 0.0521332i
\(811\) 30978.5 22507.2i 1.34131 0.974520i 0.341917 0.939730i \(-0.388924\pi\)
0.999395 0.0347900i \(-0.0110762\pi\)
\(812\) 6416.49 + 4661.85i 0.277309 + 0.201477i
\(813\) 3309.02 + 2404.15i 0.142746 + 0.103711i
\(814\) 159.849 116.137i 0.00688293 0.00500074i
\(815\) 10906.5 3329.31i 0.468757 0.143093i
\(816\) −1135.96 825.323i −0.0487335 0.0354070i
\(817\) 6114.25 + 18817.7i 0.261824 + 0.805813i
\(818\) −9247.87 −0.395286
\(819\) 1292.48 + 3977.85i 0.0551440 + 0.169716i
\(820\) −1221.04 + 68268.7i −0.0520008 + 2.90737i
\(821\) −11356.6 + 34952.0i −0.482762 + 1.48579i 0.352434 + 0.935837i \(0.385354\pi\)
−0.835196 + 0.549953i \(0.814646\pi\)
\(822\) −2557.42 + 7870.94i −0.108516 + 0.333979i
\(823\) −21125.5 + 15348.6i −0.894761 + 0.650082i −0.937115 0.349020i \(-0.886514\pi\)
0.0423536 + 0.999103i \(0.486514\pi\)
\(824\) 10911.4 0.461305
\(825\) −1728.72 + 1163.87i −0.0729532 + 0.0491162i
\(826\) −23283.5 −0.980793
\(827\) −24442.5 + 17758.5i −1.02775 + 0.746705i −0.967857 0.251500i \(-0.919076\pi\)
−0.0598941 + 0.998205i \(0.519076\pi\)
\(828\) 6260.29 19267.2i 0.262754 0.808672i
\(829\) −4787.44 + 14734.2i −0.200572 + 0.617299i 0.799294 + 0.600941i \(0.205207\pi\)
−0.999866 + 0.0163581i \(0.994793\pi\)
\(830\) 51902.7 15843.8i 2.17057 0.662587i
\(831\) −1941.98 5976.81i −0.0810669 0.249498i
\(832\) −40225.8 −1.67618
\(833\) −7265.11 22359.7i −0.302186 0.930033i
\(834\) −3697.56 2686.43i −0.153520 0.111539i
\(835\) 1936.16 + 667.605i 0.0802437 + 0.0276688i
\(836\) −2673.80 + 1942.63i −0.110616 + 0.0803676i
\(837\) 2633.22 + 1913.15i 0.108743 + 0.0790061i
\(838\) 19862.7 + 14431.1i 0.818791 + 0.594887i
\(839\) 5434.83 3948.64i 0.223637 0.162482i −0.470325 0.882493i \(-0.655863\pi\)
0.693962 + 0.720011i \(0.255863\pi\)
\(840\) 4120.93 5463.76i 0.169269 0.224426i
\(841\) 16307.9 + 11848.4i 0.668658 + 0.485808i
\(842\) 8308.18 + 25570.0i 0.340046 + 1.04655i
\(843\) 7162.98 0.292653
\(844\) −11941.3 36751.6i −0.487011 1.49887i
\(845\) 1394.10 + 480.698i 0.0567555 + 0.0195698i
\(846\) −5512.41 + 16965.4i −0.224020 + 0.689461i
\(847\) −3868.91 + 11907.3i −0.156951 + 0.483045i
\(848\) 58.0272 42.1592i 0.00234984 0.00170726i
\(849\) −7507.29 −0.303474
\(850\) 18299.0 50141.7i 0.738413 2.02335i
\(851\) 1390.59 0.0560149
\(852\) 5986.71 4349.60i 0.240729 0.174900i
\(853\) −6181.47 + 19024.6i −0.248124 + 0.763646i 0.746983 + 0.664843i \(0.231501\pi\)
−0.995107 + 0.0988032i \(0.968499\pi\)
\(854\) 6359.78 19573.4i 0.254833 0.784295i
\(855\) −2709.24 3872.75i −0.108367 0.154907i
\(856\) 2163.00 + 6657.04i 0.0863668 + 0.265810i
\(857\) −48267.5 −1.92391 −0.961953 0.273214i \(-0.911913\pi\)
−0.961953 + 0.273214i \(0.911913\pi\)
\(858\) 1130.12 + 3478.15i 0.0449670 + 0.138394i
\(859\) −1154.15 838.539i −0.0458429 0.0333068i 0.564628 0.825346i \(-0.309020\pi\)
−0.610471 + 0.792039i \(0.709020\pi\)
\(860\) −34181.5 48861.0i −1.35532 1.93738i
\(861\) 11273.6 8190.72i 0.446228 0.324203i
\(862\) 2682.37 + 1948.86i 0.105988 + 0.0770050i
\(863\) 18910.4 + 13739.2i 0.745905 + 0.541932i 0.894555 0.446958i \(-0.147493\pi\)
−0.148650 + 0.988890i \(0.547493\pi\)
\(864\) 4197.18 3049.43i 0.165267 0.120074i
\(865\) −791.675 + 44262.7i −0.0311188 + 1.73986i
\(866\) −62874.5 45681.0i −2.46716 1.79250i
\(867\) −3626.77 11162.1i −0.142066 0.437236i
\(868\) 14698.3 0.574763
\(869\) 2108.46 + 6489.18i 0.0823068 + 0.253314i
\(870\) −5971.79 + 7917.73i −0.232716 + 0.308547i
\(871\) 3951.26 12160.7i 0.153712 0.473077i
\(872\) 1237.40 3808.32i 0.0480546 0.147897i
\(873\) −8286.76 + 6020.69i −0.321265 + 0.233413i
\(874\) −37957.4 −1.46903
\(875\) −12558.1 4839.24i −0.485191 0.186967i
\(876\) −3103.56 −0.119703
\(877\) −9849.32 + 7155.95i −0.379234 + 0.275529i −0.761029 0.648717i \(-0.775306\pi\)
0.381796 + 0.924247i \(0.375306\pi\)
\(878\) 15172.0 46694.5i 0.583177 1.79483i
\(879\) −3754.51 + 11555.2i −0.144069 + 0.443398i
\(880\) −186.404 + 247.146i −0.00714056 + 0.00946736i
\(881\) 5210.38 + 16035.9i 0.199253 + 0.613239i 0.999901 + 0.0141028i \(0.00448922\pi\)
−0.800647 + 0.599136i \(0.795511\pi\)
\(882\) 10238.1 0.390856
\(883\) 7204.01 + 22171.7i 0.274557 + 0.845001i 0.989336 + 0.145650i \(0.0465274\pi\)
−0.714779 + 0.699351i \(0.753473\pi\)
\(884\) −46437.8 33739.0i −1.76682 1.28367i
\(885\) 319.052 17838.2i 0.0121184 0.677543i
\(886\) 34412.0 25001.8i 1.30484 0.948025i
\(887\) 8788.66 + 6385.33i 0.332688 + 0.241712i 0.741570 0.670875i \(-0.234081\pi\)
−0.408882 + 0.912587i \(0.634081\pi\)
\(888\) −402.225 292.234i −0.0152002 0.0110436i
\(889\) 21602.7 15695.3i 0.814996 0.592129i
\(890\) 33892.4 + 48447.8i 1.27649 + 1.82469i
\(891\) −364.175 264.589i −0.0136928 0.00994843i
\(892\) −20176.6 62097.3i −0.757358 2.33091i
\(893\) 20481.6 0.767515
\(894\) 7373.16 + 22692.2i 0.275834 + 0.848929i
\(895\) 5879.76 + 8404.87i 0.219596 + 0.313904i
\(896\) 6700.56 20622.2i 0.249833 0.768906i
\(897\) −7953.72 + 24479.0i −0.296061 + 0.911183i
\(898\) 14252.3 10354.9i 0.529627 0.384796i
\(899\) −7841.60 −0.290914
\(900\) 11216.8 + 8779.11i 0.415438 + 0.325152i
\(901\) 1352.42 0.0500064
\(902\) 9857.39 7161.81i 0.363875 0.264371i
\(903\) −3760.64 + 11574.1i −0.138590 + 0.426535i
\(904\) 13560.1 41733.7i 0.498896 1.53545i
\(905\) −10167.5 3505.83i −0.373456 0.128771i
\(906\) −7804.36 24019.4i −0.286184 0.880784i
\(907\) 21465.3 0.785825 0.392913 0.919576i \(-0.371468\pi\)
0.392913 + 0.919576i \(0.371468\pi\)
\(908\) 6997.70 + 21536.7i 0.255757 + 0.787138i
\(909\) 9304.46 + 6760.09i 0.339504 + 0.246664i
\(910\) −14221.5 + 18855.6i −0.518062 + 0.686876i
\(911\) 29140.5 21171.8i 1.05979 0.769981i 0.0857393 0.996318i \(-0.472675\pi\)
0.974049 + 0.226336i \(0.0726748\pi\)
\(912\) −567.973 412.657i −0.0206222 0.0149829i
\(913\) −4800.96 3488.10i −0.174029 0.126440i
\(914\) 48464.2 35211.3i 1.75389 1.27427i
\(915\) 14908.7 + 5140.65i 0.538651 + 0.185732i
\(916\) 12952.3 + 9410.36i 0.467199 + 0.339440i
\(917\) −5312.26 16349.4i −0.191304 0.588774i
\(918\) 11529.3 0.414514
\(919\) 3005.90 + 9251.22i 0.107895 + 0.332067i 0.990399 0.138238i \(-0.0441439\pi\)
−0.882504 + 0.470305i \(0.844144\pi\)
\(920\) 40279.5 12295.7i 1.44345 0.440628i
\(921\) −5504.07 + 16939.8i −0.196922 + 0.606064i
\(922\) 19140.9 58909.6i 0.683700 2.10421i
\(923\) −7606.14 + 5526.18i −0.271245 + 0.197071i
\(924\) −2032.78 −0.0723740
\(925\) −335.192 + 918.472i −0.0119147 + 0.0326477i
\(926\) 33057.7 1.17316
\(927\) 3749.69 2724.31i 0.132854 0.0965244i
\(928\) −3862.40 + 11887.2i −0.136626 + 0.420493i
\(929\) −5837.99 + 17967.5i −0.206177 + 0.634547i 0.793486 + 0.608588i \(0.208264\pi\)
−0.999663 + 0.0259588i \(0.991736\pi\)
\(930\) −328.671 + 18376.0i −0.0115888 + 0.647929i
\(931\) −3632.51 11179.7i −0.127874 0.393556i
\(932\) −55000.7 −1.93305
\(933\) 382.090 + 1175.95i 0.0134073 + 0.0412636i
\(934\) −4759.87 3458.25i −0.166753 0.121153i
\(935\) −5582.61 + 1704.15i −0.195263 + 0.0596059i
\(936\) 7444.90 5409.04i 0.259983 0.188889i
\(937\) −29538.6 21461.0i −1.02986 0.748240i −0.0615828 0.998102i \(-0.519615\pi\)
−0.968282 + 0.249862i \(0.919615\pi\)
\(938\) 9382.92 + 6817.09i 0.326613 + 0.237298i
\(939\) −9592.00 + 6969.00i −0.333358 + 0.242199i
\(940\) −59037.0 + 18021.6i −2.04848 + 0.625319i
\(941\) 14935.2 + 10851.1i 0.517401 + 0.375914i 0.815624 0.578582i \(-0.196394\pi\)
−0.298223 + 0.954496i \(0.596394\pi\)
\(942\) 2171.19 + 6682.25i 0.0750970 + 0.231125i
\(943\) 85753.1 2.96130
\(944\) −818.936 2520.43i −0.0282353 0.0868992i
\(945\) 51.9856 2906.52i 0.00178951 0.100052i
\(946\) −3288.24 + 10120.1i −0.113012 + 0.347817i
\(947\) 1026.02 3157.77i 0.0352072 0.108357i −0.931908 0.362694i \(-0.881857\pi\)
0.967116 + 0.254337i \(0.0818572\pi\)
\(948\) 37728.7 27411.5i 1.29259 0.939119i
\(949\) 3943.09 0.134877
\(950\) 9149.41 25070.6i 0.312470 0.856208i
\(951\) −3058.60 −0.104292
\(952\) 15507.0 11266.5i 0.527924 0.383559i
\(953\) 7939.69 24435.8i 0.269876 0.830593i −0.720654 0.693295i \(-0.756158\pi\)
0.990530 0.137298i \(-0.0438417\pi\)
\(954\) −181.993 + 560.117i −0.00617636 + 0.0190089i
\(955\) 31585.0 9641.63i 1.07023 0.326697i
\(956\) 1592.51 + 4901.24i 0.0538760 + 0.165813i
\(957\) 1084.49 0.0366319
\(958\) 5848.51 + 17999.9i 0.197241 + 0.607045i
\(959\) 4728.27 + 3435.29i 0.159211 + 0.115674i
\(960\) 26430.9 + 9113.61i 0.888596 + 0.306396i
\(961\) 12344.6 8968.87i 0.414373 0.301060i
\(962\) 1388.09 + 1008.51i 0.0465216 + 0.0337999i
\(963\) 2405.42 + 1747.64i 0.0804918 + 0.0584807i
\(964\) −17496.5 + 12711.9i −0.584568 + 0.424713i
\(965\) −26477.5 + 35105.4i −0.883256 + 1.17107i
\(966\) −18887.4 13722.5i −0.629083 0.457055i
\(967\) 7324.06 + 22541.2i 0.243564 + 0.749612i 0.995869 + 0.0907977i \(0.0289417\pi\)
−0.752306 + 0.658814i \(0.771058\pi\)
\(968\) 27546.5 0.914646
\(969\) −4090.64 12589.7i −0.135614 0.417378i
\(970\) −54679.4 18854.0i −1.80995 0.624088i
\(971\) 2678.45 8243.43i 0.0885228 0.272445i −0.896989 0.442053i \(-0.854250\pi\)
0.985512 + 0.169608i \(0.0542502\pi\)
\(972\) −950.750 + 2926.11i −0.0313738 + 0.0965586i
\(973\) −2611.20 + 1897.14i −0.0860340 + 0.0625074i
\(974\) −18371.8 −0.604384
\(975\) −14251.0 11153.9i −0.468100 0.366370i
\(976\) 2342.50 0.0768255
\(977\) 33990.8 24695.8i 1.11306 0.808688i 0.129920 0.991524i \(-0.458528\pi\)
0.983143 + 0.182836i \(0.0585278\pi\)
\(978\) −4297.92 + 13227.6i −0.140524 + 0.432488i
\(979\) 1998.00 6149.21i 0.0652261 0.200745i
\(980\) 20307.4 + 29028.6i 0.661936 + 0.946210i
\(981\) −525.615 1617.68i −0.0171066 0.0526488i
\(982\) −37737.3 −1.22632
\(983\) −1249.89 3846.78i −0.0405548 0.124815i 0.928729 0.370758i \(-0.120902\pi\)
−0.969284 + 0.245944i \(0.920902\pi\)
\(984\) −24804.0 18021.1i −0.803579 0.583834i
\(985\) −18183.0 25991.8i −0.588181 0.840780i
\(986\) −22471.7 + 16326.6i −0.725806 + 0.527329i
\(987\) 10191.6 + 7404.61i 0.328674 + 0.238796i
\(988\) −23218.6 16869.3i −0.747655 0.543203i
\(989\) −60587.6 + 44019.5i −1.94800 + 1.41531i
\(990\) 45.4552 2541.41i 0.00145925 0.0815871i
\(991\) −10409.7 7563.08i −0.333678 0.242431i 0.408312 0.912843i \(-0.366118\pi\)
−0.741990 + 0.670411i \(0.766118\pi\)
\(992\) 7157.89 + 22029.7i 0.229096 + 0.705085i
\(993\) −10828.5 −0.346054
\(994\) −2635.22 8110.37i −0.0840886 0.258798i
\(995\) −7629.44 + 10115.5i −0.243085 + 0.322296i
\(996\) −12533.8 + 38575.2i −0.398745 + 1.22721i
\(997\) 2451.22 7544.06i 0.0778644 0.239642i −0.904546 0.426376i \(-0.859790\pi\)
0.982411 + 0.186734i \(0.0597902\pi\)
\(998\) −21100.4 + 15330.4i −0.669261 + 0.486247i
\(999\) −211.188 −0.00668839
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 75.4.g.a.61.7 yes 28
3.2 odd 2 225.4.h.c.136.1 28
25.4 even 10 1875.4.a.e.1.14 14
25.16 even 5 inner 75.4.g.a.16.7 28
25.21 even 5 1875.4.a.h.1.1 14
75.41 odd 10 225.4.h.c.91.1 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.4.g.a.16.7 28 25.16 even 5 inner
75.4.g.a.61.7 yes 28 1.1 even 1 trivial
225.4.h.c.91.1 28 75.41 odd 10
225.4.h.c.136.1 28 3.2 odd 2
1875.4.a.e.1.14 14 25.4 even 10
1875.4.a.h.1.1 14 25.21 even 5