Properties

Label 25.4.e.a.4.3
Level $25$
Weight $4$
Character 25.4
Analytic conductor $1.475$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,4,Mod(4,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.47504775014\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 4.3
Character \(\chi\) \(=\) 25.4
Dual form 25.4.e.a.19.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.48841 - 0.483614i) q^{2} +(-4.16357 + 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(-5.33345 + 9.82621i) q^{5} +(8.96855 - 6.51603i) q^{6} +1.18261i q^{7} +(12.4652 + 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +O(q^{10})\) \(q+(-1.48841 - 0.483614i) q^{2} +(-4.16357 + 5.73067i) q^{3} +(-4.49065 - 3.26265i) q^{4} +(-5.33345 + 9.82621i) q^{5} +(8.96855 - 6.51603i) q^{6} +1.18261i q^{7} +(12.4652 + 17.1569i) q^{8} +(-7.16175 - 22.0416i) q^{9} +(12.6905 - 12.0461i) q^{10} +(7.19826 - 22.1540i) q^{11} +(37.3943 - 12.1501i) q^{12} +(-34.0413 + 11.0607i) q^{13} +(0.571929 - 1.76022i) q^{14} +(-34.1045 - 71.4764i) q^{15} +(3.46617 + 10.6678i) q^{16} +(76.1834 + 104.857i) q^{17} +36.2705i q^{18} +(-85.6642 + 62.2387i) q^{19} +(56.0101 - 26.7249i) q^{20} +(-6.77717 - 4.92390i) q^{21} +(-21.4280 + 29.4931i) q^{22} +(-71.8250 - 23.3374i) q^{23} -150.220 q^{24} +(-68.1086 - 104.815i) q^{25} +56.0166 q^{26} +(-25.7621 - 8.37062i) q^{27} +(3.85845 - 5.31070i) q^{28} +(216.865 + 157.562i) q^{29} +(16.1946 + 122.880i) q^{30} +(192.656 - 139.973i) q^{31} -187.211i q^{32} +(96.9866 + 133.491i) q^{33} +(-62.6817 - 192.914i) q^{34} +(-11.6206 - 6.30741i) q^{35} +(-39.7531 + 122.347i) q^{36} +(-166.220 + 54.0080i) q^{37} +(157.603 - 51.2084i) q^{38} +(78.3483 - 241.131i) q^{39} +(-235.069 + 30.9802i) q^{40} +(6.36260 + 19.5821i) q^{41} +(7.70595 + 10.6063i) q^{42} -131.925i q^{43} +(-104.605 + 76.0003i) q^{44} +(254.782 + 47.1850i) q^{45} +(95.6189 + 69.4712i) q^{46} +(-101.704 + 139.984i) q^{47} +(-75.5651 - 24.5526i) q^{48} +341.601 q^{49} +(50.6836 + 188.946i) q^{50} -918.098 q^{51} +(188.955 + 61.3951i) q^{52} +(-19.3553 + 26.6403i) q^{53} +(34.2965 + 24.9179i) q^{54} +(179.298 + 188.889i) q^{55} +(-20.2899 + 14.7415i) q^{56} -750.049i q^{57} +(-246.586 - 339.396i) q^{58} +(148.786 + 457.918i) q^{59} +(-80.0508 + 432.246i) q^{60} +(-174.560 + 537.239i) q^{61} +(-354.445 + 115.166i) q^{62} +(26.0667 - 8.46959i) q^{63} +(-62.8084 + 193.304i) q^{64} +(72.8730 - 393.488i) q^{65} +(-79.7980 - 245.593i) q^{66} +(198.345 + 272.998i) q^{67} -719.437i q^{68} +(432.787 - 314.438i) q^{69} +(14.2459 + 15.0079i) q^{70} +(-170.875 - 124.148i) q^{71} +(288.892 - 397.626i) q^{72} +(452.871 + 147.147i) q^{73} +273.522 q^{74} +(884.236 + 46.0977i) q^{75} +587.751 q^{76} +(26.1996 + 8.51277i) q^{77} +(-233.229 + 321.013i) q^{78} +(-792.426 - 575.731i) q^{79} +(-123.310 - 22.8367i) q^{80} +(661.474 - 480.589i) q^{81} -32.2232i q^{82} +(126.573 + 174.213i) q^{83} +(14.3689 + 44.2230i) q^{84} +(-1436.67 + 189.342i) q^{85} +(-63.8008 + 196.359i) q^{86} +(-1805.87 + 586.763i) q^{87} +(469.820 - 152.654i) q^{88} +(-120.001 + 369.326i) q^{89} +(-356.402 - 193.447i) q^{90} +(-13.0805 - 40.2577i) q^{91} +(246.399 + 339.139i) q^{92} +1686.84i q^{93} +(219.076 - 159.168i) q^{94} +(-154.684 - 1173.70i) q^{95} +(1072.84 + 779.466i) q^{96} +(325.030 - 447.366i) q^{97} +(-508.444 - 165.203i) q^{98} -539.861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.48841 0.483614i −0.526233 0.170984i 0.0338391 0.999427i \(-0.489227\pi\)
−0.560072 + 0.828444i \(0.689227\pi\)
\(3\) −4.16357 + 5.73067i −0.801280 + 1.10287i 0.191330 + 0.981526i \(0.438720\pi\)
−0.992611 + 0.121342i \(0.961280\pi\)
\(4\) −4.49065 3.26265i −0.561331 0.407831i
\(5\) −5.33345 + 9.82621i −0.477038 + 0.878883i
\(6\) 8.96855 6.51603i 0.610232 0.443360i
\(7\) 1.18261i 0.0638552i 0.999490 + 0.0319276i \(0.0101646\pi\)
−0.999490 + 0.0319276i \(0.989835\pi\)
\(8\) 12.4652 + 17.1569i 0.550889 + 0.758233i
\(9\) −7.16175 22.0416i −0.265250 0.816356i
\(10\) 12.6905 12.0461i 0.401308 0.380931i
\(11\) 7.19826 22.1540i 0.197305 0.607243i −0.802637 0.596468i \(-0.796570\pi\)
0.999942 0.0107749i \(-0.00342983\pi\)
\(12\) 37.3943 12.1501i 0.899567 0.292287i
\(13\) −34.0413 + 11.0607i −0.726258 + 0.235976i −0.648734 0.761015i \(-0.724701\pi\)
−0.0775239 + 0.996990i \(0.524701\pi\)
\(14\) 0.571929 1.76022i 0.0109182 0.0336027i
\(15\) −34.1045 71.4764i −0.587050 1.23034i
\(16\) 3.46617 + 10.6678i 0.0541589 + 0.166684i
\(17\) 76.1834 + 104.857i 1.08689 + 1.49598i 0.851699 + 0.524032i \(0.175573\pi\)
0.235194 + 0.971948i \(0.424427\pi\)
\(18\) 36.2705i 0.474947i
\(19\) −85.6642 + 62.2387i −1.03435 + 0.751502i −0.969175 0.246372i \(-0.920762\pi\)
−0.0651781 + 0.997874i \(0.520762\pi\)
\(20\) 56.0101 26.7249i 0.626212 0.298793i
\(21\) −6.77717 4.92390i −0.0704238 0.0511659i
\(22\) −21.4280 + 29.4931i −0.207657 + 0.285816i
\(23\) −71.8250 23.3374i −0.651154 0.211573i −0.0352312 0.999379i \(-0.511217\pi\)
−0.615923 + 0.787806i \(0.711217\pi\)
\(24\) −150.220 −1.27765
\(25\) −68.1086 104.815i −0.544869 0.838521i
\(26\) 56.0166 0.422529
\(27\) −25.7621 8.37062i −0.183627 0.0596640i
\(28\) 3.85845 5.31070i 0.0260421 0.0358439i
\(29\) 216.865 + 157.562i 1.38865 + 1.00891i 0.996012 + 0.0892210i \(0.0284377\pi\)
0.392639 + 0.919693i \(0.371562\pi\)
\(30\) 16.1946 + 122.880i 0.0985570 + 0.747822i
\(31\) 192.656 139.973i 1.11620 0.810964i 0.132568 0.991174i \(-0.457678\pi\)
0.983628 + 0.180210i \(0.0576776\pi\)
\(32\) 187.211i 1.03420i
\(33\) 96.9866 + 133.491i 0.511612 + 0.704174i
\(34\) −62.6817 192.914i −0.316171 0.973075i
\(35\) −11.6206 6.30741i −0.0561212 0.0304614i
\(36\) −39.7531 + 122.347i −0.184042 + 0.566423i
\(37\) −166.220 + 54.0080i −0.738550 + 0.239969i −0.654047 0.756454i \(-0.726930\pi\)
−0.0845026 + 0.996423i \(0.526930\pi\)
\(38\) 157.603 51.2084i 0.672806 0.218608i
\(39\) 78.3483 241.131i 0.321687 0.990049i
\(40\) −235.069 + 30.9802i −0.929193 + 0.122460i
\(41\) 6.36260 + 19.5821i 0.0242359 + 0.0745903i 0.962443 0.271484i \(-0.0875144\pi\)
−0.938207 + 0.346074i \(0.887514\pi\)
\(42\) 7.70595 + 10.6063i 0.0283108 + 0.0389665i
\(43\) 131.925i 0.467869i −0.972252 0.233934i \(-0.924840\pi\)
0.972252 0.233934i \(-0.0751601\pi\)
\(44\) −104.605 + 76.0003i −0.358406 + 0.260397i
\(45\) 254.782 + 47.1850i 0.844015 + 0.156309i
\(46\) 95.6189 + 69.4712i 0.306483 + 0.222673i
\(47\) −101.704 + 139.984i −0.315640 + 0.434441i −0.937130 0.348981i \(-0.886528\pi\)
0.621490 + 0.783422i \(0.286528\pi\)
\(48\) −75.5651 24.5526i −0.227227 0.0738304i
\(49\) 341.601 0.995923
\(50\) 50.6836 + 188.946i 0.143355 + 0.534421i
\(51\) −918.098 −2.52077
\(52\) 188.955 + 61.3951i 0.503909 + 0.163730i
\(53\) −19.3553 + 26.6403i −0.0501633 + 0.0690438i −0.833362 0.552728i \(-0.813587\pi\)
0.783198 + 0.621772i \(0.213587\pi\)
\(54\) 34.2965 + 24.9179i 0.0864290 + 0.0627943i
\(55\) 179.298 + 188.889i 0.439573 + 0.463086i
\(56\) −20.2899 + 14.7415i −0.0484171 + 0.0351771i
\(57\) 750.049i 1.74292i
\(58\) −246.586 339.396i −0.558246 0.768360i
\(59\) 148.786 + 457.918i 0.328311 + 1.01044i 0.969924 + 0.243409i \(0.0782656\pi\)
−0.641613 + 0.767029i \(0.721734\pi\)
\(60\) −80.0508 + 432.246i −0.172242 + 0.930046i
\(61\) −174.560 + 537.239i −0.366395 + 1.12765i 0.582709 + 0.812681i \(0.301993\pi\)
−0.949103 + 0.314965i \(0.898007\pi\)
\(62\) −354.445 + 115.166i −0.726041 + 0.235905i
\(63\) 26.0667 8.46959i 0.0521285 0.0169376i
\(64\) −62.8084 + 193.304i −0.122673 + 0.377548i
\(65\) 72.8730 393.488i 0.139058 0.750865i
\(66\) −79.7980 245.593i −0.148825 0.458037i
\(67\) 198.345 + 272.998i 0.361667 + 0.497791i 0.950612 0.310381i \(-0.100457\pi\)
−0.588946 + 0.808173i \(0.700457\pi\)
\(68\) 719.437i 1.28301i
\(69\) 432.787 314.438i 0.755094 0.548608i
\(70\) 14.2459 + 15.0079i 0.0243244 + 0.0256256i
\(71\) −170.875 124.148i −0.285622 0.207517i 0.435744 0.900071i \(-0.356485\pi\)
−0.721366 + 0.692554i \(0.756485\pi\)
\(72\) 288.892 397.626i 0.472865 0.650842i
\(73\) 452.871 + 147.147i 0.726090 + 0.235921i 0.648662 0.761077i \(-0.275329\pi\)
0.0774284 + 0.996998i \(0.475329\pi\)
\(74\) 273.522 0.429680
\(75\) 884.236 + 46.0977i 1.36137 + 0.0709721i
\(76\) 587.751 0.887100
\(77\) 26.1996 + 8.51277i 0.0387756 + 0.0125990i
\(78\) −233.229 + 321.013i −0.338564 + 0.465994i
\(79\) −792.426 575.731i −1.12854 0.819934i −0.143060 0.989714i \(-0.545694\pi\)
−0.985482 + 0.169780i \(0.945694\pi\)
\(80\) −123.310 22.8367i −0.172331 0.0319153i
\(81\) 661.474 480.589i 0.907372 0.659244i
\(82\) 32.2232i 0.0433958i
\(83\) 126.573 + 174.213i 0.167388 + 0.230389i 0.884468 0.466602i \(-0.154522\pi\)
−0.717080 + 0.696991i \(0.754522\pi\)
\(84\) 14.3689 + 44.2230i 0.0186640 + 0.0574420i
\(85\) −1436.67 + 189.342i −1.83328 + 0.241612i
\(86\) −63.8008 + 196.359i −0.0799978 + 0.246208i
\(87\) −1805.87 + 586.763i −2.22540 + 0.723075i
\(88\) 469.820 152.654i 0.569125 0.184920i
\(89\) −120.001 + 369.326i −0.142922 + 0.439870i −0.996738 0.0807057i \(-0.974283\pi\)
0.853816 + 0.520576i \(0.174283\pi\)
\(90\) −356.402 193.447i −0.417422 0.226568i
\(91\) −13.0805 40.2577i −0.0150683 0.0463753i
\(92\) 246.399 + 339.139i 0.279227 + 0.384323i
\(93\) 1686.84i 1.88083i
\(94\) 219.076 159.168i 0.240382 0.174648i
\(95\) −154.684 1173.70i −0.167056 1.26757i
\(96\) 1072.84 + 779.466i 1.14059 + 0.828686i
\(97\) 325.030 447.366i 0.340225 0.468280i −0.604282 0.796770i \(-0.706540\pi\)
0.944507 + 0.328491i \(0.106540\pi\)
\(98\) −508.444 165.203i −0.524087 0.170286i
\(99\) −539.861 −0.548062
\(100\) −36.1230 + 692.902i −0.0361230 + 0.692902i
\(101\) −637.953 −0.628502 −0.314251 0.949340i \(-0.601753\pi\)
−0.314251 + 0.949340i \(0.601753\pi\)
\(102\) 1366.51 + 444.006i 1.32651 + 0.431011i
\(103\) 328.881 452.666i 0.314618 0.433034i −0.622197 0.782861i \(-0.713760\pi\)
0.936814 + 0.349827i \(0.113760\pi\)
\(104\) −614.098 446.168i −0.579012 0.420677i
\(105\) 84.5290 40.3325i 0.0785636 0.0374862i
\(106\) 41.6922 30.2912i 0.0382029 0.0277560i
\(107\) 347.014i 0.313524i 0.987636 + 0.156762i \(0.0501056\pi\)
−0.987636 + 0.156762i \(0.949894\pi\)
\(108\) 88.3783 + 121.642i 0.0787426 + 0.108380i
\(109\) 44.4432 + 136.782i 0.0390540 + 0.120196i 0.968683 0.248301i \(-0.0798724\pi\)
−0.929629 + 0.368497i \(0.879872\pi\)
\(110\) −175.520 367.855i −0.152138 0.318851i
\(111\) 382.566 1177.42i 0.327131 1.00681i
\(112\) −12.6159 + 4.09914i −0.0106436 + 0.00345832i
\(113\) −1243.62 + 404.077i −1.03531 + 0.336393i −0.776888 0.629639i \(-0.783203\pi\)
−0.258423 + 0.966032i \(0.583203\pi\)
\(114\) −362.734 + 1116.38i −0.298010 + 0.917182i
\(115\) 612.393 581.299i 0.496573 0.471360i
\(116\) −459.797 1415.11i −0.368027 1.13267i
\(117\) 487.591 + 671.111i 0.385280 + 0.530293i
\(118\) 753.525i 0.587861i
\(119\) −124.006 + 90.0955i −0.0955260 + 0.0694037i
\(120\) 801.191 1476.09i 0.609487 1.12290i
\(121\) 637.818 + 463.402i 0.479202 + 0.348161i
\(122\) 519.633 715.214i 0.385618 0.530758i
\(123\) −138.709 45.0694i −0.101683 0.0330388i
\(124\) −1321.83 −0.957292
\(125\) 1393.19 110.223i 0.996885 0.0788691i
\(126\) −42.8940 −0.0303278
\(127\) 1927.43 + 626.261i 1.34671 + 0.437572i 0.891584 0.452855i \(-0.149594\pi\)
0.455125 + 0.890427i \(0.349594\pi\)
\(128\) −693.348 + 954.311i −0.478780 + 0.658984i
\(129\) 756.018 + 549.279i 0.515997 + 0.374894i
\(130\) −298.762 + 550.431i −0.201563 + 0.371353i
\(131\) 546.263 396.883i 0.364330 0.264701i −0.390526 0.920592i \(-0.627707\pi\)
0.754856 + 0.655891i \(0.227707\pi\)
\(132\) 915.892i 0.603926i
\(133\) −73.6043 101.308i −0.0479873 0.0660488i
\(134\) −163.193 502.256i −0.105207 0.323793i
\(135\) 219.652 208.500i 0.140035 0.132924i
\(136\) −849.384 + 2614.13i −0.535545 + 1.64824i
\(137\) −94.5956 + 30.7360i −0.0589916 + 0.0191675i −0.338364 0.941015i \(-0.609874\pi\)
0.279373 + 0.960183i \(0.409874\pi\)
\(138\) −796.233 + 258.712i −0.491158 + 0.159587i
\(139\) 550.842 1695.32i 0.336128 1.03450i −0.630035 0.776566i \(-0.716960\pi\)
0.966164 0.257930i \(-0.0830403\pi\)
\(140\) 31.6052 + 66.2383i 0.0190795 + 0.0399869i
\(141\) −378.748 1165.67i −0.226215 0.696218i
\(142\) 194.293 + 267.421i 0.114822 + 0.158039i
\(143\) 833.768i 0.487575i
\(144\) 210.311 152.800i 0.121708 0.0884258i
\(145\) −2704.88 + 1290.61i −1.54916 + 0.739170i
\(146\) −602.897 438.030i −0.341754 0.248299i
\(147\) −1422.28 + 1957.60i −0.798013 + 1.09837i
\(148\) 922.643 + 299.785i 0.512438 + 0.166501i
\(149\) 918.569 0.505048 0.252524 0.967591i \(-0.418739\pi\)
0.252524 + 0.967591i \(0.418739\pi\)
\(150\) −1293.81 496.242i −0.704263 0.270120i
\(151\) 96.9677 0.0522591 0.0261295 0.999659i \(-0.491682\pi\)
0.0261295 + 0.999659i \(0.491682\pi\)
\(152\) −2135.64 693.912i −1.13963 0.370287i
\(153\) 1765.62 2430.17i 0.932953 1.28410i
\(154\) −34.8789 25.3410i −0.0182508 0.0132600i
\(155\) 347.881 + 2639.62i 0.180274 + 1.36787i
\(156\) −1138.56 + 827.213i −0.584345 + 0.424552i
\(157\) 3116.13i 1.58404i −0.610497 0.792019i \(-0.709030\pi\)
0.610497 0.792019i \(-0.290970\pi\)
\(158\) 901.024 + 1240.15i 0.453681 + 0.624439i
\(159\) −72.0793 221.837i −0.0359513 0.110647i
\(160\) 1839.57 + 998.479i 0.908943 + 0.493354i
\(161\) 27.5991 84.9412i 0.0135100 0.0415796i
\(162\) −1216.97 + 395.416i −0.590209 + 0.191770i
\(163\) 708.216 230.113i 0.340317 0.110576i −0.133872 0.990999i \(-0.542741\pi\)
0.474190 + 0.880423i \(0.342741\pi\)
\(164\) 35.3172 108.695i 0.0168159 0.0517540i
\(165\) −1828.98 + 241.045i −0.862944 + 0.113729i
\(166\) −104.141 320.513i −0.0486922 0.149859i
\(167\) 127.395 + 175.344i 0.0590307 + 0.0812488i 0.837512 0.546419i \(-0.184009\pi\)
−0.778481 + 0.627668i \(0.784009\pi\)
\(168\) 177.652i 0.0815843i
\(169\) −740.939 + 538.324i −0.337250 + 0.245027i
\(170\) 2229.93 + 412.976i 1.00604 + 0.186317i
\(171\) 1985.35 + 1442.44i 0.887855 + 0.645064i
\(172\) −430.424 + 592.428i −0.190811 + 0.262629i
\(173\) −16.8682 5.48081i −0.00741309 0.00240866i 0.305308 0.952254i \(-0.401241\pi\)
−0.312721 + 0.949845i \(0.601241\pi\)
\(174\) 2971.64 1.29471
\(175\) 123.956 80.5462i 0.0535439 0.0347927i
\(176\) 261.284 0.111903
\(177\) −3243.66 1053.93i −1.37745 0.447560i
\(178\) 357.222 491.674i 0.150421 0.207037i
\(179\) 2206.88 + 1603.39i 0.921509 + 0.669515i 0.943899 0.330234i \(-0.107128\pi\)
−0.0223903 + 0.999749i \(0.507128\pi\)
\(180\) −990.189 1043.16i −0.410024 0.431957i
\(181\) −1252.23 + 909.799i −0.514241 + 0.373618i −0.814430 0.580262i \(-0.802950\pi\)
0.300189 + 0.953880i \(0.402950\pi\)
\(182\) 66.2460i 0.0269807i
\(183\) −2351.95 3237.18i −0.950060 1.30765i
\(184\) −494.916 1523.20i −0.198292 0.610280i
\(185\) 355.830 1921.36i 0.141412 0.763573i
\(186\) 815.779 2510.71i 0.321590 0.989753i
\(187\) 2871.40 932.973i 1.12287 0.364844i
\(188\) 913.435 296.793i 0.354357 0.115138i
\(189\) 9.89922 30.4667i 0.00380985 0.0117255i
\(190\) −337.385 + 1821.76i −0.128823 + 0.695601i
\(191\) 994.375 + 3060.37i 0.376704 + 1.15938i 0.942322 + 0.334708i \(0.108638\pi\)
−0.565618 + 0.824667i \(0.691362\pi\)
\(192\) −846.256 1164.77i −0.318090 0.437813i
\(193\) 2386.85i 0.890205i −0.895480 0.445102i \(-0.853167\pi\)
0.895480 0.445102i \(-0.146833\pi\)
\(194\) −700.132 + 508.676i −0.259106 + 0.188251i
\(195\) 1951.54 + 2055.93i 0.716680 + 0.755016i
\(196\) −1534.01 1114.52i −0.559042 0.406168i
\(197\) 726.915 1000.51i 0.262896 0.361846i −0.657079 0.753822i \(-0.728208\pi\)
0.919976 + 0.391976i \(0.128208\pi\)
\(198\) 803.536 + 261.085i 0.288408 + 0.0937095i
\(199\) −2580.97 −0.919396 −0.459698 0.888075i \(-0.652042\pi\)
−0.459698 + 0.888075i \(0.652042\pi\)
\(200\) 949.312 2475.07i 0.335632 0.875069i
\(201\) −2390.28 −0.838794
\(202\) 949.537 + 308.523i 0.330738 + 0.107463i
\(203\) −186.335 + 256.468i −0.0644243 + 0.0886725i
\(204\) 4122.86 + 2995.43i 1.41499 + 1.02805i
\(205\) −226.352 41.9198i −0.0771176 0.0142820i
\(206\) −708.427 + 514.702i −0.239604 + 0.174083i
\(207\) 1750.27i 0.587693i
\(208\) −235.986 324.807i −0.0786667 0.108275i
\(209\) 762.201 + 2345.81i 0.252261 + 0.776379i
\(210\) −145.319 + 19.1519i −0.0477523 + 0.00629337i
\(211\) −888.596 + 2734.82i −0.289922 + 0.892287i 0.694958 + 0.719050i \(0.255423\pi\)
−0.984880 + 0.173237i \(0.944577\pi\)
\(212\) 173.836 56.4826i 0.0563164 0.0182983i
\(213\) 1422.90 462.330i 0.457727 0.148724i
\(214\) 167.821 516.500i 0.0536075 0.164987i
\(215\) 1296.32 + 703.615i 0.411202 + 0.223191i
\(216\) −177.516 546.338i −0.0559187 0.172100i
\(217\) 165.534 + 227.838i 0.0517843 + 0.0712749i
\(218\) 225.082i 0.0699287i
\(219\) −2728.81 + 1982.60i −0.841991 + 0.611742i
\(220\) −188.887 1433.22i −0.0578852 0.439216i
\(221\) −3753.18 2726.84i −1.14238 0.829988i
\(222\) −1138.83 + 1567.47i −0.344294 + 0.473880i
\(223\) −3938.36 1279.65i −1.18266 0.384268i −0.349303 0.937010i \(-0.613582\pi\)
−0.833353 + 0.552742i \(0.813582\pi\)
\(224\) 221.398 0.0660392
\(225\) −1822.52 + 2251.88i −0.540005 + 0.667225i
\(226\) 2046.44 0.602332
\(227\) −2216.13 720.064i −0.647972 0.210539i −0.0334522 0.999440i \(-0.510650\pi\)
−0.614520 + 0.788901i \(0.710650\pi\)
\(228\) −2447.14 + 3368.20i −0.710816 + 0.978354i
\(229\) −4250.24 3087.98i −1.22648 0.891088i −0.229857 0.973224i \(-0.573826\pi\)
−0.996621 + 0.0821360i \(0.973826\pi\)
\(230\) −1192.62 + 569.050i −0.341908 + 0.163139i
\(231\) −157.868 + 114.698i −0.0449651 + 0.0326691i
\(232\) 5684.76i 1.60872i
\(233\) 2231.74 + 3071.72i 0.627493 + 0.863671i 0.997872 0.0652105i \(-0.0207719\pi\)
−0.370378 + 0.928881i \(0.620772\pi\)
\(234\) −401.177 1234.70i −0.112076 0.344934i
\(235\) −833.075 1745.96i −0.231250 0.484655i
\(236\) 825.876 2541.78i 0.227796 0.701085i
\(237\) 6598.65 2144.03i 1.80856 0.587636i
\(238\) 228.143 74.1283i 0.0621359 0.0201892i
\(239\) 2008.57 6181.73i 0.543613 1.67307i −0.180653 0.983547i \(-0.557821\pi\)
0.724266 0.689521i \(-0.242179\pi\)
\(240\) 644.282 611.568i 0.173284 0.164486i
\(241\) 952.246 + 2930.71i 0.254521 + 0.783335i 0.993924 + 0.110071i \(0.0351080\pi\)
−0.739403 + 0.673263i \(0.764892\pi\)
\(242\) −725.228 998.191i −0.192642 0.265149i
\(243\) 5060.28i 1.33587i
\(244\) 2536.71 1843.03i 0.665558 0.483556i
\(245\) −1821.91 + 3356.65i −0.475093 + 0.875299i
\(246\) 184.661 + 134.164i 0.0478599 + 0.0347722i
\(247\) 2227.72 3066.19i 0.573872 0.789867i
\(248\) 4802.99 + 1560.59i 1.22980 + 0.399586i
\(249\) −1525.35 −0.388213
\(250\) −2126.94 509.709i −0.538079 0.128947i
\(251\) 7819.56 1.96640 0.983199 0.182536i \(-0.0584305\pi\)
0.983199 + 0.182536i \(0.0584305\pi\)
\(252\) −144.690 47.0125i −0.0361690 0.0117520i
\(253\) −1034.03 + 1423.22i −0.256952 + 0.353664i
\(254\) −2565.95 1864.27i −0.633866 0.460530i
\(255\) 4896.63 9021.42i 1.20251 2.21546i
\(256\) 2808.98 2040.85i 0.685787 0.498253i
\(257\) 2384.26i 0.578700i 0.957223 + 0.289350i \(0.0934392\pi\)
−0.957223 + 0.289350i \(0.906561\pi\)
\(258\) −859.627 1183.17i −0.207434 0.285509i
\(259\) −63.8706 196.574i −0.0153233 0.0471602i
\(260\) −1611.06 + 1529.26i −0.384284 + 0.364772i
\(261\) 1919.78 5908.48i 0.455293 1.40125i
\(262\) −1005.00 + 326.545i −0.236982 + 0.0770001i
\(263\) −2942.84 + 956.186i −0.689974 + 0.224186i −0.632957 0.774187i \(-0.718159\pi\)
−0.0570172 + 0.998373i \(0.518159\pi\)
\(264\) −1081.32 + 3327.97i −0.252086 + 0.775842i
\(265\) −158.542 332.273i −0.0367516 0.0770241i
\(266\) 60.5597 + 186.384i 0.0139592 + 0.0429621i
\(267\) −1616.85 2225.40i −0.370597 0.510084i
\(268\) 1873.07i 0.426924i
\(269\) −1193.33 + 867.006i −0.270478 + 0.196514i −0.714754 0.699376i \(-0.753461\pi\)
0.444275 + 0.895890i \(0.353461\pi\)
\(270\) −427.767 + 204.106i −0.0964187 + 0.0460056i
\(271\) 245.587 + 178.429i 0.0550492 + 0.0399956i 0.614970 0.788551i \(-0.289168\pi\)
−0.559920 + 0.828546i \(0.689168\pi\)
\(272\) −854.530 + 1176.16i −0.190491 + 0.262188i
\(273\) 285.165 + 92.6559i 0.0632198 + 0.0205413i
\(274\) 155.662 0.0343206
\(275\) −2812.34 + 754.390i −0.616692 + 0.165423i
\(276\) −2969.40 −0.647597
\(277\) 4610.31 + 1497.98i 1.00002 + 0.324927i 0.762875 0.646546i \(-0.223787\pi\)
0.237148 + 0.971473i \(0.423787\pi\)
\(278\) −1639.76 + 2256.94i −0.353764 + 0.486914i
\(279\) −4464.99 3244.00i −0.958107 0.696105i
\(280\) −36.6377 277.996i −0.00781971 0.0593338i
\(281\) 1203.90 874.687i 0.255583 0.185692i −0.452614 0.891706i \(-0.649509\pi\)
0.708198 + 0.706014i \(0.249509\pi\)
\(282\) 1918.16i 0.405052i
\(283\) 1574.63 + 2167.29i 0.330749 + 0.455237i 0.941711 0.336423i \(-0.109217\pi\)
−0.610962 + 0.791660i \(0.709217\pi\)
\(284\) 362.289 + 1115.01i 0.0756969 + 0.232971i
\(285\) 7370.13 + 4000.35i 1.53182 + 0.831439i
\(286\) 403.222 1240.99i 0.0833672 0.256578i
\(287\) −23.1580 + 7.52450i −0.00476298 + 0.00154759i
\(288\) −4126.42 + 1340.76i −0.844277 + 0.274322i
\(289\) −3672.97 + 11304.2i −0.747603 + 2.30088i
\(290\) 4650.13 612.850i 0.941603 0.124096i
\(291\) 1210.42 + 3725.28i 0.243835 + 0.750447i
\(292\) −1553.60 2138.34i −0.311361 0.428552i
\(293\) 3929.37i 0.783468i −0.920078 0.391734i \(-0.871875\pi\)
0.920078 0.391734i \(-0.128125\pi\)
\(294\) 3063.67 2225.89i 0.607744 0.441552i
\(295\) −5293.14 980.274i −1.04467 0.193470i
\(296\) −2998.57 2178.59i −0.588811 0.427796i
\(297\) −370.885 + 510.480i −0.0724611 + 0.0997341i
\(298\) −1367.21 444.233i −0.265773 0.0863549i
\(299\) 2703.14 0.522832
\(300\) −3820.39 3091.96i −0.735235 0.595048i
\(301\) 156.016 0.0298758
\(302\) −144.328 46.8950i −0.0275005 0.00893544i
\(303\) 2656.16 3655.90i 0.503606 0.693154i
\(304\) −960.875 698.116i −0.181283 0.131710i
\(305\) −4348.02 4580.60i −0.816285 0.859948i
\(306\) −3803.23 + 2763.21i −0.710511 + 0.516216i
\(307\) 8263.41i 1.53621i 0.640322 + 0.768107i \(0.278801\pi\)
−0.640322 + 0.768107i \(0.721199\pi\)
\(308\) −89.8790 123.708i −0.0166277 0.0228861i
\(309\) 1224.76 + 3769.42i 0.225483 + 0.693964i
\(310\) 758.768 4097.08i 0.139017 0.750641i
\(311\) −1483.86 + 4566.84i −0.270552 + 0.832675i 0.719810 + 0.694172i \(0.244229\pi\)
−0.990362 + 0.138503i \(0.955771\pi\)
\(312\) 5113.68 1661.54i 0.927902 0.301494i
\(313\) 9805.98 3186.15i 1.77082 0.575374i 0.772593 0.634902i \(-0.218959\pi\)
0.998227 + 0.0595277i \(0.0189595\pi\)
\(314\) −1507.00 + 4638.08i −0.270844 + 0.833573i
\(315\) −55.8016 + 301.309i −0.00998115 + 0.0538947i
\(316\) 1680.10 + 5170.81i 0.299091 + 0.920509i
\(317\) −1928.95 2654.97i −0.341768 0.470403i 0.603189 0.797598i \(-0.293896\pi\)
−0.944957 + 0.327195i \(0.893896\pi\)
\(318\) 365.044i 0.0643731i
\(319\) 5051.67 3670.26i 0.886644 0.644185i
\(320\) −1564.46 1648.15i −0.273301 0.287920i
\(321\) −1988.62 1444.82i −0.345776 0.251221i
\(322\) −82.1576 + 113.080i −0.0142188 + 0.0195705i
\(323\) −13052.4 4240.97i −2.24846 0.730570i
\(324\) −4538.44 −0.778196
\(325\) 3477.83 + 2814.72i 0.593586 + 0.480407i
\(326\) −1165.40 −0.197993
\(327\) −968.896 314.813i −0.163853 0.0532392i
\(328\) −256.656 + 353.256i −0.0432056 + 0.0594674i
\(329\) −165.547 120.277i −0.0277413 0.0201552i
\(330\) 2838.85 + 525.747i 0.473556 + 0.0877012i
\(331\) 290.415 210.999i 0.0482255 0.0350379i −0.563411 0.826177i \(-0.690511\pi\)
0.611637 + 0.791139i \(0.290511\pi\)
\(332\) 1195.29i 0.197591i
\(333\) 2380.85 + 3276.95i 0.391801 + 0.539267i
\(334\) −104.817 322.595i −0.0171717 0.0528491i
\(335\) −3740.40 + 492.954i −0.610029 + 0.0803969i
\(336\) 29.0362 89.3644i 0.00471445 0.0145096i
\(337\) −1246.37 + 404.970i −0.201466 + 0.0654603i −0.408012 0.912977i \(-0.633778\pi\)
0.206546 + 0.978437i \(0.433778\pi\)
\(338\) 1363.16 442.919i 0.219368 0.0712769i
\(339\) 2862.28 8809.19i 0.458577 1.41136i
\(340\) 7069.34 + 3837.08i 1.12761 + 0.612044i
\(341\) −1714.17 5275.67i −0.272221 0.837810i
\(342\) −2257.43 3107.09i −0.356923 0.491263i
\(343\) 809.619i 0.127450i
\(344\) 2263.42 1644.47i 0.354754 0.257744i
\(345\) 781.487 + 5929.70i 0.121953 + 0.925346i
\(346\) 22.4562 + 16.3154i 0.00348917 + 0.00253503i
\(347\) −2278.45 + 3136.01i −0.352488 + 0.485158i −0.948037 0.318161i \(-0.896935\pi\)
0.595549 + 0.803319i \(0.296935\pi\)
\(348\) 10023.9 + 3256.97i 1.54408 + 0.501701i
\(349\) 7122.39 1.09242 0.546208 0.837650i \(-0.316071\pi\)
0.546208 + 0.837650i \(0.316071\pi\)
\(350\) −223.451 + 59.9391i −0.0341256 + 0.00915394i
\(351\) 969.561 0.147440
\(352\) −4147.46 1347.59i −0.628012 0.204054i
\(353\) 6423.28 8840.89i 0.968490 1.33301i 0.0256839 0.999670i \(-0.491824\pi\)
0.942806 0.333342i \(-0.108176\pi\)
\(354\) 4318.20 + 3137.36i 0.648333 + 0.471042i
\(355\) 2131.26 1016.92i 0.318635 0.152035i
\(356\) 1743.86 1266.99i 0.259619 0.188624i
\(357\) 1085.76i 0.160964i
\(358\) −2509.33 3453.79i −0.370452 0.509884i
\(359\) −603.519 1857.44i −0.0887256 0.273069i 0.896842 0.442351i \(-0.145855\pi\)
−0.985568 + 0.169281i \(0.945855\pi\)
\(360\) 2366.36 + 4959.43i 0.346439 + 0.726069i
\(361\) 1345.15 4139.96i 0.196115 0.603581i
\(362\) 2303.83 748.559i 0.334493 0.108683i
\(363\) −5311.21 + 1725.72i −0.767950 + 0.249522i
\(364\) −72.6067 + 223.460i −0.0104550 + 0.0321772i
\(365\) −3861.26 + 3665.21i −0.553719 + 0.525604i
\(366\) 1935.12 + 5955.69i 0.276367 + 0.850571i
\(367\) −6175.15 8499.37i −0.878312 1.20889i −0.976886 0.213763i \(-0.931428\pi\)
0.0985740 0.995130i \(-0.468572\pi\)
\(368\) 847.104i 0.119995i
\(369\) 386.053 280.484i 0.0544637 0.0395702i
\(370\) −1458.82 + 2687.69i −0.204974 + 0.377638i
\(371\) −31.5051 22.8898i −0.00440880 0.00320318i
\(372\) 5503.56 7574.99i 0.767059 1.05577i
\(373\) −859.018 279.112i −0.119245 0.0387450i 0.248787 0.968558i \(-0.419968\pi\)
−0.368032 + 0.929813i \(0.619968\pi\)
\(374\) −4725.02 −0.653275
\(375\) −5169.00 + 8442.83i −0.711802 + 1.16263i
\(376\) −3669.44 −0.503290
\(377\) −9125.12 2964.93i −1.24660 0.405044i
\(378\) −29.4682 + 40.5595i −0.00400974 + 0.00551893i
\(379\) 7139.52 + 5187.17i 0.967632 + 0.703026i 0.954911 0.296893i \(-0.0959505\pi\)
0.0127216 + 0.999919i \(0.495950\pi\)
\(380\) −3134.74 + 5775.36i −0.423181 + 0.779657i
\(381\) −11613.9 + 8438.00i −1.56168 + 1.13462i
\(382\) 5035.99i 0.674512i
\(383\) 3587.32 + 4937.52i 0.478599 + 0.658734i 0.978235 0.207501i \(-0.0665330\pi\)
−0.499636 + 0.866235i \(0.666533\pi\)
\(384\) −2582.04 7946.69i −0.343135 1.05606i
\(385\) −223.382 + 212.040i −0.0295705 + 0.0280690i
\(386\) −1154.32 + 3552.62i −0.152210 + 0.468455i
\(387\) −2907.84 + 944.813i −0.381947 + 0.124102i
\(388\) −2919.19 + 948.504i −0.381958 + 0.124106i
\(389\) 2180.80 6711.81i 0.284244 0.874812i −0.702380 0.711802i \(-0.747879\pi\)
0.986624 0.163011i \(-0.0521205\pi\)
\(390\) −1910.42 4003.86i −0.248046 0.519855i
\(391\) −3024.78 9309.30i −0.391226 1.20407i
\(392\) 4258.13 + 5860.81i 0.548642 + 0.755141i
\(393\) 4782.90i 0.613907i
\(394\) −1565.81 + 1137.63i −0.200214 + 0.145464i
\(395\) 9883.61 4715.90i 1.25898 0.600716i
\(396\) 2424.33 + 1761.38i 0.307644 + 0.223516i
\(397\) −2498.77 + 3439.26i −0.315893 + 0.434789i −0.937208 0.348772i \(-0.886599\pi\)
0.621315 + 0.783561i \(0.286599\pi\)
\(398\) 3841.54 + 1248.19i 0.483817 + 0.157202i
\(399\) 887.018 0.111294
\(400\) 882.068 1089.87i 0.110258 0.136234i
\(401\) 7335.40 0.913497 0.456749 0.889596i \(-0.349014\pi\)
0.456749 + 0.889596i \(0.349014\pi\)
\(402\) 3557.73 + 1155.98i 0.441401 + 0.143420i
\(403\) −5010.07 + 6895.77i −0.619279 + 0.852365i
\(404\) 2864.82 + 2081.41i 0.352798 + 0.256322i
\(405\) 1194.43 + 9062.98i 0.146547 + 1.11196i
\(406\) 401.375 291.616i 0.0490638 0.0356469i
\(407\) 4071.19i 0.495826i
\(408\) −11444.3 15751.7i −1.38867 1.91133i
\(409\) 2850.25 + 8772.17i 0.344586 + 1.06053i 0.961805 + 0.273736i \(0.0882594\pi\)
−0.617219 + 0.786792i \(0.711741\pi\)
\(410\) 316.632 + 171.861i 0.0381399 + 0.0207015i
\(411\) 217.718 670.067i 0.0261295 0.0804185i
\(412\) −2953.78 + 959.742i −0.353210 + 0.114765i
\(413\) −541.540 + 175.957i −0.0645216 + 0.0209643i
\(414\) 846.458 2605.13i 0.100486 0.309264i
\(415\) −2386.92 + 314.577i −0.282336 + 0.0372096i
\(416\) 2070.68 + 6372.89i 0.244047 + 0.751098i
\(417\) 7421.83 + 10215.3i 0.871580 + 1.19963i
\(418\) 3860.15i 0.451689i
\(419\) −13028.6 + 9465.86i −1.51907 + 1.10367i −0.557124 + 0.830429i \(0.688095\pi\)
−0.961946 + 0.273240i \(0.911905\pi\)
\(420\) −511.180 94.6692i −0.0593882 0.0109985i
\(421\) −7316.13 5315.48i −0.846950 0.615346i 0.0773531 0.997004i \(-0.475353\pi\)
−0.924304 + 0.381658i \(0.875353\pi\)
\(422\) 2645.19 3640.80i 0.305133 0.419979i
\(423\) 3813.84 + 1239.19i 0.438382 + 0.142439i
\(424\) −698.330 −0.0799857
\(425\) 5801.90 15126.9i 0.662197 1.72650i
\(426\) −2341.46 −0.266300
\(427\) −635.347 206.437i −0.0720060 0.0233962i
\(428\) 1132.18 1558.32i 0.127865 0.175991i
\(429\) −4778.05 3471.45i −0.537730 0.390684i
\(430\) −1589.18 1674.19i −0.178226 0.187759i
\(431\) −4692.76 + 3409.49i −0.524460 + 0.381043i −0.818282 0.574818i \(-0.805073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(432\) 303.838i 0.0338390i
\(433\) 2478.33 + 3411.13i 0.275060 + 0.378587i 0.924090 0.382176i \(-0.124825\pi\)
−0.649030 + 0.760763i \(0.724825\pi\)
\(434\) −136.197 419.172i −0.0150638 0.0463615i
\(435\) 3865.86 20874.3i 0.426101 2.30080i
\(436\) 246.693 759.243i 0.0270974 0.0833971i
\(437\) 7605.32 2471.12i 0.832521 0.270502i
\(438\) 5020.41 1631.23i 0.547681 0.177952i
\(439\) 1064.67 3276.71i 0.115749 0.356239i −0.876354 0.481668i \(-0.840031\pi\)
0.992102 + 0.125430i \(0.0400310\pi\)
\(440\) −1005.75 + 5430.72i −0.108972 + 0.588408i
\(441\) −2446.46 7529.44i −0.264168 0.813027i
\(442\) 4267.53 + 5873.76i 0.459244 + 0.632095i
\(443\) 6083.40i 0.652441i −0.945294 0.326220i \(-0.894225\pi\)
0.945294 0.326220i \(-0.105775\pi\)
\(444\) −5559.46 + 4039.18i −0.594235 + 0.431737i
\(445\) −2989.05 3148.94i −0.318415 0.335447i
\(446\) 5243.05 + 3809.30i 0.556649 + 0.404429i
\(447\) −3824.53 + 5264.02i −0.404685 + 0.557001i
\(448\) −228.605 74.2781i −0.0241084 0.00783328i
\(449\) 11313.0 1.18907 0.594534 0.804070i \(-0.297337\pi\)
0.594534 + 0.804070i \(0.297337\pi\)
\(450\) 3801.70 2470.33i 0.398253 0.258784i
\(451\) 479.620 0.0500763
\(452\) 6903.03 + 2242.93i 0.718343 + 0.233404i
\(453\) −403.732 + 555.690i −0.0418742 + 0.0576348i
\(454\) 2950.28 + 2143.50i 0.304986 + 0.221585i
\(455\) 465.345 + 86.1806i 0.0479466 + 0.00887958i
\(456\) 12868.5 9349.50i 1.32154 0.960154i
\(457\) 16237.9i 1.66209i −0.556206 0.831045i \(-0.687743\pi\)
0.556206 0.831045i \(-0.312257\pi\)
\(458\) 4832.71 + 6651.66i 0.493052 + 0.678628i
\(459\) −1084.92 3339.05i −0.110327 0.339550i
\(460\) −4646.61 + 612.386i −0.470977 + 0.0620710i
\(461\) −1865.25 + 5740.66i −0.188446 + 0.579976i −0.999991 0.00431376i \(-0.998627\pi\)
0.811545 + 0.584290i \(0.198627\pi\)
\(462\) 290.442 94.3703i 0.0292480 0.00950325i
\(463\) 978.735 318.010i 0.0982412 0.0319205i −0.259484 0.965747i \(-0.583552\pi\)
0.357725 + 0.933827i \(0.383552\pi\)
\(464\) −929.142 + 2859.60i −0.0929619 + 0.286107i
\(465\) −16575.2 8996.66i −1.65303 0.897226i
\(466\) −1836.22 5651.29i −0.182534 0.561783i
\(467\) 4995.54 + 6875.76i 0.495002 + 0.681311i 0.981301 0.192481i \(-0.0616534\pi\)
−0.486299 + 0.873792i \(0.661653\pi\)
\(468\) 4604.56i 0.454799i
\(469\) −322.851 + 234.565i −0.0317865 + 0.0230943i
\(470\) 395.586 + 3001.60i 0.0388235 + 0.294582i
\(471\) 17857.5 + 12974.2i 1.74698 + 1.26926i
\(472\) −6001.78 + 8260.74i −0.585284 + 0.805575i
\(473\) −2922.66 949.630i −0.284110 0.0923130i
\(474\) −10858.4 −1.05220
\(475\) 12358.0 + 4739.92i 1.19374 + 0.457857i
\(476\) 850.817 0.0819267
\(477\) 725.812 + 235.831i 0.0696701 + 0.0226372i
\(478\) −5979.15 + 8229.60i −0.572134 + 0.787475i
\(479\) −2456.46 1784.72i −0.234318 0.170242i 0.464430 0.885610i \(-0.346259\pi\)
−0.698748 + 0.715368i \(0.746259\pi\)
\(480\) −13381.1 + 6384.73i −1.27242 + 0.607128i
\(481\) 5060.97 3677.01i 0.479751 0.348559i
\(482\) 4822.62i 0.455736i
\(483\) 371.859 + 511.820i 0.0350314 + 0.0482166i
\(484\) −1352.30 4161.95i −0.127000 0.390867i
\(485\) 2662.38 + 5579.82i 0.249262 + 0.522405i
\(486\) 2447.23 7531.79i 0.228412 0.702981i
\(487\) −12099.9 + 3931.48i −1.12587 + 0.365816i −0.812004 0.583652i \(-0.801623\pi\)
−0.313863 + 0.949468i \(0.601623\pi\)
\(488\) −11393.3 + 3701.89i −1.05686 + 0.343395i
\(489\) −1630.01 + 5016.64i −0.150739 + 0.463927i
\(490\) 4335.08 4114.97i 0.399671 0.379378i
\(491\) −2121.17 6528.30i −0.194964 0.600037i −0.999977 0.00678001i \(-0.997842\pi\)
0.805013 0.593257i \(-0.202158\pi\)
\(492\) 475.850 + 654.951i 0.0436036 + 0.0600152i
\(493\) 34743.5i 3.17398i
\(494\) −4798.62 + 3486.40i −0.437045 + 0.317531i
\(495\) 2879.32 5304.79i 0.261446 0.481682i
\(496\) 2160.98 + 1570.04i 0.195627 + 0.142131i
\(497\) 146.819 202.080i 0.0132510 0.0182384i
\(498\) 2270.35 + 737.681i 0.204291 + 0.0663781i
\(499\) −10000.2 −0.897134 −0.448567 0.893749i \(-0.648065\pi\)
−0.448567 + 0.893749i \(0.648065\pi\)
\(500\) −6615.94 4050.51i −0.591748 0.362289i
\(501\) −1535.26 −0.136907
\(502\) −11638.7 3781.65i −1.03478 0.336222i
\(503\) 1995.92 2747.15i 0.176926 0.243518i −0.711339 0.702849i \(-0.751911\pi\)
0.888265 + 0.459331i \(0.151911\pi\)
\(504\) 470.238 + 341.648i 0.0415596 + 0.0301948i
\(505\) 3402.49 6268.66i 0.299819 0.552379i
\(506\) 2227.35 1618.27i 0.195688 0.142175i
\(507\) 6487.43i 0.568278i
\(508\) −6612.16 9100.86i −0.577494 0.794853i
\(509\) −2003.56 6166.33i −0.174472 0.536970i 0.825137 0.564933i \(-0.191098\pi\)
−0.999609 + 0.0279631i \(0.991098\pi\)
\(510\) −11651.1 + 11059.5i −1.01161 + 0.960242i
\(511\) −174.018 + 535.572i −0.0150648 + 0.0463646i
\(512\) 3806.98 1236.96i 0.328606 0.106770i
\(513\) 2727.87 886.338i 0.234773 0.0762822i
\(514\) 1153.06 3548.76i 0.0989482 0.304531i
\(515\) 2693.92 + 5645.93i 0.230502 + 0.483086i
\(516\) −1602.91 4933.24i −0.136752 0.420879i
\(517\) 2369.10 + 3260.79i 0.201534 + 0.277388i
\(518\) 323.471i 0.0274373i
\(519\) 101.641 73.8462i 0.00859639 0.00624565i
\(520\) 7659.40 3654.64i 0.645936 0.308205i
\(521\) 5997.28 + 4357.28i 0.504310 + 0.366403i 0.810661 0.585516i \(-0.199108\pi\)
−0.306351 + 0.951919i \(0.599108\pi\)
\(522\) −5714.85 + 7865.82i −0.479180 + 0.659535i
\(523\) 8183.77 + 2659.07i 0.684228 + 0.222319i 0.630446 0.776233i \(-0.282872\pi\)
0.0537826 + 0.998553i \(0.482872\pi\)
\(524\) −3747.96 −0.312463
\(525\) −54.5158 + 1045.71i −0.00453193 + 0.0869305i
\(526\) 4842.58 0.401419
\(527\) 29354.4 + 9537.83i 2.42637 + 0.788376i
\(528\) −1087.87 + 1497.33i −0.0896661 + 0.123415i
\(529\) −5229.11 3799.17i −0.429778 0.312252i
\(530\) 75.2839 + 571.233i 0.00617005 + 0.0468166i
\(531\) 9027.67 6558.98i 0.737792 0.536037i
\(532\) 695.082i 0.0566459i
\(533\) −433.182 596.224i −0.0352030 0.0484528i
\(534\) 1330.30 + 4094.25i 0.107805 + 0.331789i
\(535\) −3409.83 1850.78i −0.275551 0.149563i
\(536\) −2211.38 + 6805.94i −0.178204 + 0.548455i
\(537\) −18377.0 + 5971.06i −1.47677 + 0.479833i
\(538\) 2195.47 713.350i 0.175935 0.0571649i
\(539\) 2458.94 7567.83i 0.196501 0.604767i
\(540\) −1666.64 + 219.650i −0.132816 + 0.0175041i
\(541\) −1851.10 5697.10i −0.147107 0.452749i 0.850169 0.526510i \(-0.176500\pi\)
−0.997276 + 0.0737611i \(0.976500\pi\)
\(542\) −279.243 384.346i −0.0221301 0.0304595i
\(543\) 10964.1i 0.866512i
\(544\) 19630.4 14262.3i 1.54715 1.12407i
\(545\) −1581.09 292.813i −0.124268 0.0230142i
\(546\) −379.634 275.820i −0.0297561 0.0216191i
\(547\) 12795.7 17611.8i 1.00019 1.37665i 0.0749850 0.997185i \(-0.476109\pi\)
0.925207 0.379462i \(-0.123891\pi\)
\(548\) 525.076 + 170.608i 0.0409309 + 0.0132993i
\(549\) 13091.8 1.01775
\(550\) 4550.75 + 237.243i 0.352808 + 0.0183929i
\(551\) −28384.0 −2.19456
\(552\) 10789.5 + 3505.74i 0.831945 + 0.270315i
\(553\) 680.867 937.134i 0.0523570 0.0720632i
\(554\) −6137.59 4459.22i −0.470688 0.341975i
\(555\) 9529.14 + 10038.9i 0.728810 + 0.767794i
\(556\) −8004.86 + 5815.87i −0.610579 + 0.443611i
\(557\) 10736.7i 0.816749i −0.912814 0.408375i \(-0.866096\pi\)
0.912814 0.408375i \(-0.133904\pi\)
\(558\) 5076.89 + 6987.74i 0.385165 + 0.530134i
\(559\) 1459.18 + 4490.89i 0.110406 + 0.339794i
\(560\) 27.0070 145.829i 0.00203796 0.0110043i
\(561\) −6608.71 + 20339.5i −0.497362 + 1.53072i
\(562\) −2214.92 + 719.670i −0.166247 + 0.0540168i
\(563\) −5145.09 + 1671.74i −0.385151 + 0.125143i −0.495191 0.868784i \(-0.664902\pi\)
0.110040 + 0.993927i \(0.464902\pi\)
\(564\) −2102.33 + 6470.31i −0.156958 + 0.483066i
\(565\) 2662.25 14375.2i 0.198233 1.07039i
\(566\) −1295.56 3987.34i −0.0962131 0.296114i
\(567\) 568.351 + 782.268i 0.0420961 + 0.0579404i
\(568\) 4479.21i 0.330887i
\(569\) 3521.64 2558.62i 0.259464 0.188511i −0.450447 0.892803i \(-0.648735\pi\)
0.709911 + 0.704292i \(0.248735\pi\)
\(570\) −9035.17 9518.47i −0.663933 0.699447i
\(571\) −14846.9 10786.9i −1.08813 0.790575i −0.109050 0.994036i \(-0.534781\pi\)
−0.979083 + 0.203461i \(0.934781\pi\)
\(572\) 2720.29 3744.16i 0.198848 0.273691i
\(573\) −21678.1 7043.65i −1.58048 0.513530i
\(574\) 38.1076 0.00277105
\(575\) 2445.79 + 9117.82i 0.177385 + 0.661286i
\(576\) 4710.56 0.340752
\(577\) 817.930 + 265.761i 0.0590136 + 0.0191747i 0.338375 0.941011i \(-0.390123\pi\)
−0.279361 + 0.960186i \(0.590123\pi\)
\(578\) 10933.8 15049.1i 0.786827 1.08297i
\(579\) 13678.3 + 9937.84i 0.981778 + 0.713303i
\(580\) 16357.5 + 3029.36i 1.17105 + 0.216874i
\(581\) −206.026 + 149.687i −0.0147116 + 0.0106886i
\(582\) 6130.13i 0.436602i
\(583\) 450.863 + 620.560i 0.0320289 + 0.0440840i
\(584\) 3120.55 + 9604.06i 0.221112 + 0.680512i
\(585\) −9195.01 + 1211.83i −0.649858 + 0.0856461i
\(586\) −1900.30 + 5848.52i −0.133960 + 0.412287i
\(587\) −19306.5 + 6273.05i −1.35752 + 0.441084i −0.895214 0.445637i \(-0.852977\pi\)
−0.462304 + 0.886721i \(0.652977\pi\)
\(588\) 12773.9 4150.51i 0.895899 0.291095i
\(589\) −7792.01 + 23981.4i −0.545101 + 1.67765i
\(590\) 7404.30 + 4018.89i 0.516661 + 0.280432i
\(591\) 2707.04 + 8331.42i 0.188414 + 0.579880i
\(592\) −1152.29 1585.99i −0.0799980 0.110108i
\(593\) 20628.0i 1.42848i −0.699900 0.714241i \(-0.746772\pi\)
0.699900 0.714241i \(-0.253228\pi\)
\(594\) 798.905 580.439i 0.0551843 0.0400937i
\(595\) −223.918 1699.03i −0.0154281 0.117064i
\(596\) −4124.97 2996.97i −0.283499 0.205974i
\(597\) 10746.0 14790.7i 0.736694 1.01397i
\(598\) −4023.39 1307.28i −0.275132 0.0893957i
\(599\) 2506.63 0.170982 0.0854909 0.996339i \(-0.472754\pi\)
0.0854909 + 0.996339i \(0.472754\pi\)
\(600\) 10231.3 + 15745.3i 0.696150 + 1.07133i
\(601\) −1595.54 −0.108292 −0.0541459 0.998533i \(-0.517244\pi\)
−0.0541459 + 0.998533i \(0.517244\pi\)
\(602\) −232.216 75.4517i −0.0157217 0.00510827i
\(603\) 4596.82 6326.98i 0.310443 0.427288i
\(604\) −435.448 316.371i −0.0293346 0.0213129i
\(605\) −7955.25 + 3795.80i −0.534590 + 0.255076i
\(606\) −5721.51 + 4156.92i −0.383532 + 0.278652i
\(607\) 26119.6i 1.74656i 0.487222 + 0.873278i \(0.338010\pi\)
−0.487222 + 0.873278i \(0.661990\pi\)
\(608\) 11651.7 + 16037.3i 0.777205 + 1.06973i
\(609\) −693.914 2135.65i −0.0461721 0.142103i
\(610\) 4256.40 + 8920.58i 0.282519 + 0.592104i
\(611\) 1913.82 5890.15i 0.126719 0.390000i
\(612\) −15857.6 + 5152.43i −1.04739 + 0.340318i
\(613\) −6416.22 + 2084.75i −0.422754 + 0.137361i −0.512665 0.858589i \(-0.671342\pi\)
0.0899108 + 0.995950i \(0.471342\pi\)
\(614\) 3996.30 12299.4i 0.262667 0.808406i
\(615\) 1182.66 1122.61i 0.0775439 0.0736066i
\(616\) 180.531 + 555.616i 0.0118081 + 0.0363416i
\(617\) −3731.74 5136.30i −0.243491 0.335137i 0.669727 0.742607i \(-0.266411\pi\)
−0.913219 + 0.407470i \(0.866411\pi\)
\(618\) 6202.76i 0.403741i
\(619\) 4852.37 3525.45i 0.315078 0.228918i −0.418994 0.907989i \(-0.637617\pi\)
0.734072 + 0.679071i \(0.237617\pi\)
\(620\) 7049.94 12988.6i 0.456665 0.841347i
\(621\) 1655.02 + 1202.44i 0.106946 + 0.0777009i
\(622\) 4417.18 6079.73i 0.284747 0.391921i
\(623\) −436.770 141.915i −0.0280880 0.00912633i
\(624\) 2843.90 0.182448
\(625\) −6347.43 + 14277.6i −0.406236 + 0.913768i
\(626\) −16136.2 −1.03024
\(627\) −16616.6 5399.05i −1.05838 0.343887i
\(628\) −10166.8 + 13993.4i −0.646019 + 0.889169i
\(629\) −18326.3 13314.8i −1.16171 0.844034i
\(630\) 228.773 421.485i 0.0144675 0.0266546i
\(631\) 14269.4 10367.4i 0.900250 0.654070i −0.0382803 0.999267i \(-0.512188\pi\)
0.938530 + 0.345197i \(0.112188\pi\)
\(632\) 20772.1i 1.30739i
\(633\) −11972.6 16478.9i −0.751766 1.03472i
\(634\) 1587.09 + 4884.55i 0.0994184 + 0.305978i
\(635\) −16433.6 + 15599.2i −1.02701 + 0.974861i
\(636\) −400.094 + 1231.36i −0.0249446 + 0.0767716i
\(637\) −11628.6 + 3778.35i −0.723297 + 0.235013i
\(638\) −9293.96 + 3019.79i −0.576726 + 0.187390i
\(639\) −1512.66 + 4655.48i −0.0936461 + 0.288213i
\(640\) −5679.32 11902.7i −0.350773 0.735152i
\(641\) 8585.30 + 26422.8i 0.529015 + 1.62814i 0.756236 + 0.654299i \(0.227036\pi\)
−0.227221 + 0.973843i \(0.572964\pi\)
\(642\) 2261.15 + 3112.21i 0.139004 + 0.191323i
\(643\) 7215.33i 0.442527i 0.975214 + 0.221263i \(0.0710181\pi\)
−0.975214 + 0.221263i \(0.928982\pi\)
\(644\) −401.071 + 291.395i −0.0245410 + 0.0178301i
\(645\) −9429.51 + 4499.23i −0.575638 + 0.274662i
\(646\) 17376.3 + 12624.6i 1.05830 + 0.768900i
\(647\) −10027.9 + 13802.3i −0.609334 + 0.838676i −0.996522 0.0833244i \(-0.973446\pi\)
0.387189 + 0.922001i \(0.373446\pi\)
\(648\) 16490.8 + 5358.18i 0.999721 + 0.324829i
\(649\) 11215.7 0.678359
\(650\) −3815.21 5871.39i −0.230223 0.354300i
\(651\) −1994.88 −0.120100
\(652\) −3931.13 1277.30i −0.236127 0.0767223i
\(653\) 5562.33 7655.89i 0.333340 0.458803i −0.609142 0.793061i \(-0.708486\pi\)
0.942481 + 0.334259i \(0.108486\pi\)
\(654\) 1289.87 + 937.144i 0.0771221 + 0.0560325i
\(655\) 986.390 + 7484.44i 0.0588419 + 0.446475i
\(656\) −186.843 + 135.749i −0.0111204 + 0.00807946i
\(657\) 11035.8i 0.655326i
\(658\) 188.234 + 259.082i 0.0111522 + 0.0153497i
\(659\) 4965.73 + 15282.9i 0.293531 + 0.903397i 0.983711 + 0.179759i \(0.0575317\pi\)
−0.690179 + 0.723638i \(0.742468\pi\)
\(660\) 8999.74 + 4884.87i 0.530780 + 0.288096i
\(661\) 4844.24 14909.0i 0.285051 0.877298i −0.701332 0.712835i \(-0.747411\pi\)
0.986383 0.164463i \(-0.0525891\pi\)
\(662\) −534.299 + 173.604i −0.0313688 + 0.0101923i
\(663\) 31253.3 10154.8i 1.83073 0.594841i
\(664\) −1411.19 + 4343.19i −0.0824769 + 0.253838i
\(665\) 1388.04 182.932i 0.0809409 0.0106674i
\(666\) −1958.90 6028.87i −0.113973 0.350772i
\(667\) −11899.3 16377.9i −0.690767 0.950759i
\(668\) 1203.06i 0.0696821i
\(669\) 23730.9 17241.5i 1.37144 0.996406i
\(670\) 5805.65 + 1075.19i 0.334764 + 0.0619974i
\(671\) 10645.5 + 7734.38i 0.612464 + 0.444981i
\(672\) −921.807 + 1268.76i −0.0529159 + 0.0728325i
\(673\) 8548.51 + 2777.58i 0.489630 + 0.159090i 0.543418 0.839462i \(-0.317130\pi\)
−0.0537886 + 0.998552i \(0.517130\pi\)
\(674\) 2050.96 0.117211
\(675\) 877.255 + 3270.37i 0.0500230 + 0.186484i
\(676\) 5083.66 0.289239
\(677\) −5438.99 1767.23i −0.308770 0.100325i 0.150533 0.988605i \(-0.451901\pi\)
−0.459303 + 0.888279i \(0.651901\pi\)
\(678\) −8520.50 + 11727.5i −0.482637 + 0.664293i
\(679\) 529.061 + 384.386i 0.0299021 + 0.0217251i
\(680\) −21156.9 22288.6i −1.19313 1.25695i
\(681\) 13353.5 9701.86i 0.751404 0.545927i
\(682\) 8681.36i 0.487429i
\(683\) 4557.14 + 6272.37i 0.255306 + 0.351399i 0.917361 0.398057i \(-0.130315\pi\)
−0.662054 + 0.749456i \(0.730315\pi\)
\(684\) −4209.32 12955.0i −0.235303 0.724189i
\(685\) 202.503 1093.44i 0.0112952 0.0609903i
\(686\) 391.544 1205.05i 0.0217918 0.0670684i
\(687\) 35392.3 11499.7i 1.96551 0.638631i
\(688\) 1407.34 457.274i 0.0779862 0.0253392i
\(689\) 364.219 1120.95i 0.0201388 0.0619809i
\(690\) 1704.51 9203.77i 0.0940431 0.507800i
\(691\) −3235.80 9958.77i −0.178141 0.548262i 0.821622 0.570033i \(-0.193070\pi\)
−0.999763 + 0.0217707i \(0.993070\pi\)
\(692\) 57.8672 + 79.6473i 0.00317887 + 0.00437534i
\(693\) 638.448i 0.0349966i
\(694\) 4907.89 3565.79i 0.268445 0.195037i
\(695\) 13720.7 + 14454.6i 0.748855 + 0.788911i
\(696\) −32577.5 23668.9i −1.77421 1.28904i
\(697\) −1568.60 + 2158.99i −0.0852439 + 0.117328i
\(698\) −10601.1 3444.49i −0.574865 0.186785i
\(699\) −26895.0 −1.45531
\(700\) −819.436 42.7195i −0.0442454 0.00230664i
\(701\) 8823.63 0.475412 0.237706 0.971337i \(-0.423605\pi\)
0.237706 + 0.971337i \(0.423605\pi\)
\(702\) −1443.11 468.894i −0.0775877 0.0252098i
\(703\) 10877.7 14971.8i 0.583584 0.803234i
\(704\) 3830.35 + 2782.91i 0.205059 + 0.148984i
\(705\) 13474.1 + 2495.37i 0.719807 + 0.133306i
\(706\) −13836.1 + 10052.5i −0.737575 + 0.535879i
\(707\) 754.452i 0.0401331i
\(708\) 11127.5 + 15315.7i 0.590675 + 0.812995i
\(709\) −7039.37 21665.0i −0.372876 1.14759i −0.944900 0.327358i \(-0.893842\pi\)
0.572024 0.820237i \(-0.306158\pi\)
\(710\) −3663.99 + 482.885i −0.193672 + 0.0255244i
\(711\) −7014.88 + 21589.6i −0.370012 + 1.13878i
\(712\) −7832.30 + 2544.87i −0.412258 + 0.133951i
\(713\) −17104.1 + 5557.47i −0.898394 + 0.291906i
\(714\) −525.087 + 1616.05i −0.0275223 + 0.0847048i
\(715\) −8192.77 4446.86i −0.428521 0.232592i
\(716\) −4679.02 14400.6i −0.244222 0.751639i
\(717\) 27062.7 + 37248.5i 1.40959 + 1.94013i
\(718\) 3056.51i 0.158869i
\(719\) −20157.2 + 14645.1i −1.04553 + 0.759624i −0.971358 0.237621i \(-0.923632\pi\)
−0.0741754 + 0.997245i \(0.523632\pi\)
\(720\) 379.760 + 2881.51i 0.0196567 + 0.149149i
\(721\) 535.330 + 388.940i 0.0276515 + 0.0200900i
\(722\) −4004.29 + 5511.43i −0.206405 + 0.284092i
\(723\) −20759.7 6745.23i −1.06786 0.346968i
\(724\) 8591.68 0.441032
\(725\) 1744.47 33462.1i 0.0893629 1.71414i
\(726\) 8739.84 0.446785
\(727\) 33574.1 + 10908.9i 1.71278 + 0.556518i 0.990793 0.135384i \(-0.0432268\pi\)
0.721992 + 0.691902i \(0.243227\pi\)
\(728\) 527.645 726.241i 0.0268624 0.0369729i
\(729\) −11139.0 8092.96i −0.565920 0.411165i
\(730\) 7519.69 3587.98i 0.381255 0.181914i
\(731\) 13833.3 10050.5i 0.699922 0.508523i
\(732\) 22210.6i 1.12149i
\(733\) −8613.37 11855.3i −0.434027 0.597388i 0.534844 0.844951i \(-0.320370\pi\)
−0.968872 + 0.247563i \(0.920370\pi\)
\(734\) 5080.76 + 15637.0i 0.255496 + 0.786336i
\(735\) −11650.1 24416.4i −0.584656 1.22532i
\(736\) −4369.00 + 13446.4i −0.218809 + 0.673425i
\(737\) 7475.73 2429.01i 0.373639 0.121403i
\(738\) −710.251 + 230.775i −0.0354264 + 0.0115108i
\(739\) −2051.60 + 6314.18i −0.102124 + 0.314304i −0.989045 0.147617i \(-0.952840\pi\)
0.886921 + 0.461921i \(0.152840\pi\)
\(740\) −7866.62 + 7467.19i −0.390787 + 0.370945i
\(741\) 8296.05 + 25532.6i 0.411286 + 1.26581i
\(742\) 35.8228 + 49.3058i 0.00177237 + 0.00243945i
\(743\) 15188.5i 0.749950i 0.927035 + 0.374975i \(0.122349\pi\)
−0.927035 + 0.374975i \(0.877651\pi\)
\(744\) −28940.8 + 21026.7i −1.42611 + 1.03613i
\(745\) −4899.14 + 9026.05i −0.240927 + 0.443878i
\(746\) 1143.59 + 830.867i 0.0561258 + 0.0407778i
\(747\) 2933.44 4037.54i 0.143680 0.197759i
\(748\) −15938.4 5178.70i −0.779098 0.253144i
\(749\) −410.384 −0.0200201
\(750\) 11776.7 10066.6i 0.573364 0.490107i
\(751\) −9087.13 −0.441537 −0.220768 0.975326i \(-0.570856\pi\)
−0.220768 + 0.975326i \(0.570856\pi\)
\(752\) −1845.84 599.749i −0.0895090 0.0290832i
\(753\) −32557.3 + 44811.3i −1.57564 + 2.16868i
\(754\) 12148.1 + 8826.08i 0.586745 + 0.426295i
\(755\) −517.172 + 952.825i −0.0249296 + 0.0459296i
\(756\) −143.856 + 104.517i −0.00692062 + 0.00502812i
\(757\) 13103.6i 0.629140i −0.949234 0.314570i \(-0.898140\pi\)
0.949234 0.314570i \(-0.101860\pi\)
\(758\) −8117.96 11173.4i −0.388994 0.535405i
\(759\) −3850.74 11851.4i −0.184154 0.566769i
\(760\) 18208.9 17284.3i 0.869085 0.824957i
\(761\) 9148.33 28155.7i 0.435777 1.34119i −0.456510 0.889718i \(-0.650901\pi\)
0.892288 0.451467i \(-0.149099\pi\)
\(762\) 21367.0 6942.57i 1.01581 0.330056i
\(763\) −161.760 + 52.5592i −0.00767513 + 0.00249380i
\(764\) 5519.52 16987.3i 0.261373 0.804425i
\(765\) 14462.5 + 30310.5i 0.683519 + 1.43252i
\(766\) −2951.55 9083.94i −0.139222 0.428480i
\(767\) −10129.8 13942.4i −0.476877 0.656365i
\(768\) 24594.6i 1.15557i
\(769\) −29802.3 + 21652.6i −1.39753 + 1.01536i −0.402534 + 0.915405i \(0.631870\pi\)
−0.994992 + 0.0999568i \(0.968130\pi\)
\(770\) 435.031 207.572i 0.0203603 0.00971479i
\(771\) −13663.4 9927.04i −0.638230 0.463701i
\(772\) −7787.46 + 10718.5i −0.363053 + 0.499699i
\(773\) 28237.4 + 9174.90i 1.31388 + 0.426906i 0.880389 0.474252i \(-0.157281\pi\)
0.433492 + 0.901158i \(0.357281\pi\)
\(774\) 4784.98 0.222213
\(775\) −27792.8 10659.9i −1.28819 0.494085i
\(776\) 11727.0 0.542491
\(777\) 1392.43 + 452.427i 0.0642897 + 0.0208890i
\(778\) −6491.85 + 8935.27i −0.299157 + 0.411754i
\(779\) −1763.81 1281.48i −0.0811232 0.0589395i
\(780\) −2055.91 15599.6i −0.0943760 0.716098i
\(781\) −3980.38 + 2891.92i −0.182368 + 0.132498i
\(782\) 15318.9i 0.700515i
\(783\) −4268.02 5874.42i −0.194798 0.268116i
\(784\) 1184.05 + 3644.13i 0.0539381 + 0.166004i
\(785\) 30619.7 + 16619.7i 1.39218 + 0.755647i
\(786\) 2313.08 7118.93i 0.104968 0.323058i
\(787\) 28425.6 9236.05i 1.28750 0.418335i 0.416286 0.909234i \(-0.363332\pi\)
0.871216 + 0.490899i \(0.163332\pi\)
\(788\) −6528.64 + 2121.28i −0.295144 + 0.0958980i
\(789\) 6773.14 20845.6i 0.305615 0.940586i
\(790\) −16991.6 + 2239.35i −0.765231 + 0.100851i
\(791\) −477.867 1470.72i −0.0214804 0.0661099i
\(792\) −6729.47 9262.32i −0.301921 0.415558i
\(793\) 20219.1i 0.905423i
\(794\) 5382.47 3910.59i 0.240575 0.174788i
\(795\) 2564.25 + 474.892i 0.114396 + 0.0211858i
\(796\) 11590.2 + 8420.78i 0.516086 + 0.374958i
\(797\) −6471.90 + 8907.81i −0.287637 + 0.395898i −0.928245 0.371970i \(-0.878682\pi\)
0.640608 + 0.767868i \(0.278682\pi\)
\(798\) −1320.25 428.975i −0.0585668 0.0190295i
\(799\) −22426.5 −0.992982
\(800\) −19622.5 + 12750.7i −0.867201 + 0.563505i
\(801\) 8999.95 0.397001
\(802\) −10918.1 3547.50i −0.480712 0.156193i
\(803\) 6519.77 8973.70i 0.286523 0.394365i
\(804\) 10733.9 + 7798.65i 0.470841 + 0.342086i
\(805\) 687.452 + 724.224i 0.0300987 + 0.0317088i
\(806\) 10792.0 7840.81i 0.471626 0.342656i
\(807\) 10448.4i 0.455765i
\(808\) −7952.20 10945.3i −0.346234 0.476551i
\(809\) −2620.85 8066.15i −0.113899 0.350545i 0.877817 0.478996i \(-0.158999\pi\)
−0.991716 + 0.128452i \(0.958999\pi\)
\(810\) 2605.19 14067.1i 0.113008 0.610206i
\(811\) 10024.8 30853.2i 0.434055 1.33588i −0.459997 0.887921i \(-0.652149\pi\)
0.894052 0.447964i \(-0.147851\pi\)
\(812\) 1673.53 543.762i 0.0723268 0.0235004i
\(813\) −2045.04 + 664.473i −0.0882197 + 0.0286643i
\(814\) 1968.89 6059.61i 0.0847781 0.260920i
\(815\) −1516.09 + 8186.37i −0.0651613 + 0.351848i
\(816\) −3182.28 9794.06i −0.136522 0.420172i
\(817\) 8210.83 + 11301.2i 0.351604 + 0.483942i
\(818\) 14435.0i 0.617003i
\(819\) −793.665 + 576.632i −0.0338619 + 0.0246021i
\(820\) 879.698 + 926.753i 0.0374639 + 0.0394678i
\(821\) 20550.8 + 14931.0i 0.873601 + 0.634709i 0.931551 0.363611i \(-0.118456\pi\)
−0.0579495 + 0.998320i \(0.518456\pi\)
\(822\) −648.108 + 892.045i −0.0275005 + 0.0378511i
\(823\) 40857.0 + 13275.2i 1.73048 + 0.562267i 0.993519 0.113667i \(-0.0362596\pi\)
0.736962 + 0.675934i \(0.236260\pi\)
\(824\) 11865.9 0.501660
\(825\) 7386.21 19257.5i 0.311703 0.812680i
\(826\) 891.130 0.0375380
\(827\) −29110.9 9458.71i −1.22405 0.397717i −0.375492 0.926826i \(-0.622526\pi\)
−0.848554 + 0.529109i \(0.822526\pi\)
\(828\) 5710.53 7859.87i 0.239679 0.329890i
\(829\) 17898.0 + 13003.6i 0.749846 + 0.544795i 0.895779 0.444499i \(-0.146618\pi\)
−0.145933 + 0.989294i \(0.546618\pi\)
\(830\) 3704.85 + 686.129i 0.154937 + 0.0286938i
\(831\) −27779.8 + 20183.2i −1.15965 + 0.842536i
\(832\) 7275.04i 0.303145i
\(833\) 26024.4 + 35819.4i 1.08246 + 1.48988i
\(834\) −6106.49 18793.8i −0.253538 0.780309i
\(835\) −2402.43 + 316.620i −0.0995681 + 0.0131223i
\(836\) 4230.78 13021.0i 0.175030 0.538686i
\(837\) −6134.90 + 1993.35i −0.253349 + 0.0823181i
\(838\) 23969.8 7788.26i 0.988094 0.321051i
\(839\) 10771.3 33150.6i 0.443226 1.36411i −0.441192 0.897413i \(-0.645444\pi\)
0.884418 0.466696i \(-0.154556\pi\)
\(840\) 1745.65 + 947.500i 0.0717031 + 0.0389189i
\(841\) 14668.2 + 45144.1i 0.601427 + 1.85100i
\(842\) 8318.77 + 11449.8i 0.340479 + 0.468630i
\(843\) 10541.0i 0.430666i
\(844\) 12913.1 9381.93i 0.526644 0.382629i
\(845\) −1337.92 10151.7i −0.0544684 0.413291i
\(846\) −5077.28 3688.86i −0.206336 0.149912i
\(847\) −548.026 + 754.293i −0.0222319 + 0.0305995i
\(848\) −351.281 114.138i −0.0142253 0.00462207i
\(849\) −18976.1 −0.767089
\(850\) −15951.2 + 19709.1i −0.643672 + 0.795315i
\(851\) 13199.1 0.531681
\(852\) −7898.18 2566.27i −0.317591 0.103191i
\(853\) 14739.6 20287.3i 0.591646 0.814331i −0.403265 0.915083i \(-0.632125\pi\)
0.994912 + 0.100752i \(0.0321249\pi\)
\(854\) 845.822 + 614.526i 0.0338916 + 0.0246237i
\(855\) −24762.4 + 11815.2i −0.990477 + 0.472600i
\(856\) −5953.67 + 4325.59i −0.237725 + 0.172717i
\(857\) 45770.6i 1.82438i 0.409767 + 0.912190i \(0.365610\pi\)
−0.409767 + 0.912190i \(0.634390\pi\)
\(858\) 5432.86 + 7477.69i 0.216171 + 0.297534i
\(859\) 2248.85 + 6921.23i 0.0893243 + 0.274912i 0.985733 0.168316i \(-0.0538330\pi\)
−0.896409 + 0.443228i \(0.853833\pi\)
\(860\) −3525.67 7389.12i −0.139796 0.292985i
\(861\) 53.2997 164.040i 0.00210970 0.00649298i
\(862\) 8633.64 2805.24i 0.341140 0.110843i
\(863\) −44371.3 + 14417.1i −1.75019 + 0.568672i −0.996111 0.0881101i \(-0.971917\pi\)
−0.754081 + 0.656782i \(0.771917\pi\)
\(864\) −1567.07 + 4822.94i −0.0617046 + 0.189907i
\(865\) 143.821 136.519i 0.00565326 0.00536621i
\(866\) −2039.10 6275.72i −0.0800133 0.246256i
\(867\) −49488.2 68114.7i −1.93853 2.66816i
\(868\) 1563.22i 0.0611280i
\(869\) −18458.8 + 13411.1i −0.720567 + 0.523522i
\(870\) −15849.1 + 29200.0i −0.617627 + 1.13790i
\(871\) −9771.46 7099.38i −0.380130 0.276181i
\(872\) −1792.76 + 2467.52i −0.0696221 + 0.0958266i
\(873\) −12188.5 3960.27i −0.472528 0.153534i
\(874\) −12514.9 −0.484352
\(875\) 130.351 + 1647.61i 0.00503620 + 0.0636562i
\(876\) 18722.7 0.722123
\(877\) −33210.6 10790.8i −1.27873 0.415484i −0.410595 0.911818i \(-0.634679\pi\)
−0.868132 + 0.496334i \(0.834679\pi\)
\(878\) −3169.33 + 4362.20i −0.121822 + 0.167673i
\(879\) 22517.9 + 16360.2i 0.864062 + 0.627778i
\(880\) −1393.54 + 2567.43i −0.0533823 + 0.0983500i
\(881\) −27671.6 + 20104.6i −1.05821 + 0.768833i −0.973756 0.227594i \(-0.926914\pi\)
−0.0844522 + 0.996428i \(0.526914\pi\)
\(882\) 12390.1i 0.473010i
\(883\) −27589.2 37973.3i −1.05147 1.44723i −0.887525 0.460760i \(-0.847577\pi\)
−0.163948 0.986469i \(-0.552423\pi\)
\(884\) 7957.47 + 24490.6i 0.302759 + 0.931796i
\(885\) 27656.0 26251.8i 1.05045 0.997111i
\(886\) −2942.02 + 9054.61i −0.111557 + 0.343336i
\(887\) 23565.0 7656.74i 0.892036 0.289840i 0.173090 0.984906i \(-0.444625\pi\)
0.718946 + 0.695066i \(0.244625\pi\)
\(888\) 24969.5 8113.08i 0.943606 0.306596i
\(889\) −740.625 + 2279.41i −0.0279413 + 0.0859943i
\(890\) 2926.07 + 6132.46i 0.110204 + 0.230967i
\(891\) −5885.49 18113.7i −0.221292 0.681068i
\(892\) 13510.7 + 18595.9i 0.507145 + 0.698025i
\(893\) 18321.5i 0.686569i
\(894\) 8238.23 5985.43i 0.308197 0.223918i
\(895\) −27525.6 + 13133.7i −1.02802 + 0.490514i
\(896\) −1128.58 819.963i −0.0420795 0.0305726i
\(897\) −11254.7 + 15490.8i −0.418935 + 0.576615i
\(898\) −16838.3 5471.11i −0.625727 0.203311i
\(899\) 63834.9 2.36820
\(900\) 15531.4 4166.19i 0.575236 0.154303i
\(901\) −4267.98 −0.157810
\(902\) −713.872 231.951i −0.0263518 0.00856223i
\(903\) −649.585 + 894.077i −0.0239389 + 0.0329491i
\(904\) −22434.7 16299.7i −0.825405 0.599692i
\(905\) −2261.16 17157.0i −0.0830536 0.630187i
\(906\) 869.659 631.845i 0.0318902 0.0231696i
\(907\) 5545.03i 0.202999i 0.994836 + 0.101499i \(0.0323640\pi\)
−0.994836 + 0.101499i \(0.967636\pi\)
\(908\) 7602.54 + 10464.0i 0.277863 + 0.382445i
\(909\) 4568.86 + 14061.5i 0.166710 + 0.513081i
\(910\) −650.947 353.320i −0.0237128 0.0128708i
\(911\) −11280.5 + 34717.8i −0.410252 + 1.26263i 0.506177 + 0.862429i \(0.331058\pi\)
−0.916429 + 0.400196i \(0.868942\pi\)
\(912\) 8001.35 2599.79i 0.290516 0.0943945i
\(913\) 4770.61 1550.06i 0.172929 0.0561880i
\(914\) −7852.86 + 24168.6i −0.284190 + 0.874646i
\(915\) 44353.2 5845.39i 1.60248 0.211194i
\(916\) 9011.33 + 27734.0i 0.325047 + 1.00039i
\(917\) 469.359 + 646.018i 0.0169025 + 0.0232643i
\(918\) 5494.57i 0.197547i
\(919\) 11538.5 8383.20i 0.414167 0.300910i −0.361120 0.932519i \(-0.617605\pi\)
0.775287 + 0.631610i \(0.217605\pi\)
\(920\) 17606.8 + 3260.74i 0.630957 + 0.116851i
\(921\) −47354.8 34405.3i −1.69424 1.23094i
\(922\) 5552.53 7642.40i 0.198333 0.272982i
\(923\) 7189.98 + 2336.17i 0.256404 + 0.0833108i
\(924\) 1083.15 0.0385638
\(925\) 16981.8 + 13743.9i 0.603632 + 0.488538i
\(926\) −1610.56 −0.0571557
\(927\) −12332.9 4007.19i −0.436963 0.141978i
\(928\) 29497.3 40599.5i 1.04342 1.43615i
\(929\) −2382.32 1730.86i −0.0841350 0.0611276i 0.544923 0.838486i \(-0.316559\pi\)
−0.629058 + 0.777359i \(0.716559\pi\)
\(930\) 20319.8 + 21406.8i 0.716466 + 0.754790i
\(931\) −29263.0 + 21260.8i −1.03014 + 0.748438i
\(932\) 21075.4i 0.740716i
\(933\) −19992.9 27517.9i −0.701542 0.965589i
\(934\) −4110.20 12649.9i −0.143993 0.443166i
\(935\) −6146.86 + 33190.9i −0.214999 + 1.16092i
\(936\) −5436.25 + 16731.0i −0.189839 + 0.584264i
\(937\) 27716.1 9005.50i 0.966323 0.313978i 0.216993 0.976173i \(-0.430375\pi\)
0.749331 + 0.662196i \(0.230375\pi\)
\(938\) 593.975 192.994i 0.0206759 0.00671800i
\(939\) −22569.1 + 69460.6i −0.784361 + 2.41402i
\(940\) −1955.41 + 10558.5i −0.0678494 + 0.366363i
\(941\) −10416.1 32057.5i −0.360845 1.11057i −0.952542 0.304406i \(-0.901542\pi\)
0.591697 0.806160i \(-0.298458\pi\)
\(942\) −20304.8 27947.1i −0.702299 0.966631i
\(943\) 1554.97i 0.0536975i
\(944\) −4369.24 + 3174.44i −0.150643 + 0.109448i
\(945\) 246.575 + 259.764i 0.00848791 + 0.00894193i
\(946\) 3890.87 + 2826.88i 0.133724 + 0.0971563i
\(947\) 14117.7 19431.3i 0.484438 0.666772i −0.494912 0.868943i \(-0.664800\pi\)
0.979350 + 0.202171i \(0.0647998\pi\)
\(948\) −36627.4 11901.0i −1.25486 0.407727i
\(949\) −17043.9 −0.583000
\(950\) −16101.5 13031.5i −0.549898 0.445049i
\(951\) 23246.0 0.792644
\(952\) −3091.51 1004.49i −0.105248 0.0341973i
\(953\) 21529.5 29632.9i 0.731805 1.00724i −0.267244 0.963629i \(-0.586113\pi\)
0.999048 0.0436139i \(-0.0138871\pi\)
\(954\) −966.256 702.026i −0.0327921 0.0238249i
\(955\) −35375.3 6551.40i −1.19866 0.221988i
\(956\) −29188.6 + 21206.7i −0.987475 + 0.717443i
\(957\) 44230.9i 1.49402i
\(958\) 2793.11 + 3844.38i 0.0941975 + 0.129652i
\(959\) −36.3488 111.870i −0.00122395 0.00376692i
\(960\) 15958.8 2103.24i 0.536528 0.0707100i
\(961\) 8318.09 25600.4i 0.279215 0.859335i
\(962\) −9311.06 + 3025.35i −0.312059 + 0.101394i
\(963\) 7648.74 2485.23i 0.255947 0.0831623i
\(964\) 5285.67 16267.6i 0.176598 0.543512i
\(965\) 23453.7 + 12730.2i 0.782385 + 0.424662i
\(966\) −305.956 941.636i −0.0101905 0.0313630i
\(967\) 4694.17 + 6460.97i 0.156106 + 0.214861i 0.879905 0.475149i \(-0.157606\pi\)
−0.723799 + 0.690010i \(0.757606\pi\)
\(968\) 16719.3i 0.555145i
\(969\) 78648.2 57141.2i 2.60737 1.89437i
\(970\) −1264.23 9592.64i −0.0418475 0.317527i
\(971\) −3656.19 2656.38i −0.120837 0.0877932i 0.525725 0.850654i \(-0.323794\pi\)
−0.646562 + 0.762861i \(0.723794\pi\)
\(972\) 16509.9 22723.9i 0.544810 0.749867i
\(973\) 2004.91 + 651.434i 0.0660579 + 0.0214635i
\(974\) 19910.9 0.655017
\(975\) −30610.4 + 8211.04i −1.00545 + 0.269706i
\(976\) −6336.20 −0.207804
\(977\) 1677.36 + 545.007i 0.0549267 + 0.0178468i 0.336352 0.941737i \(-0.390807\pi\)
−0.281425 + 0.959583i \(0.590807\pi\)
\(978\) 4852.24 6678.54i 0.158648 0.218360i
\(979\) 7318.23 + 5317.00i 0.238909 + 0.173577i
\(980\) 19133.1 9129.25i 0.623658 0.297575i
\(981\) 2696.61 1959.20i 0.0877635 0.0637639i
\(982\) 10742.6i 0.349095i
\(983\) 18302.6 + 25191.3i 0.593857 + 0.817374i 0.995129 0.0985849i \(-0.0314316\pi\)
−0.401271 + 0.915959i \(0.631432\pi\)
\(984\) −955.789 2941.62i −0.0309649 0.0953001i
\(985\) 5954.28 + 12479.0i 0.192608 + 0.403669i
\(986\) 16802.5 51712.7i 0.542697 1.67025i
\(987\) 1378.53 447.912i 0.0444571 0.0144450i
\(988\) −20007.8 + 6500.93i −0.644264 + 0.209334i
\(989\) −3078.78 + 9475.50i −0.0989883 + 0.304655i
\(990\) −6851.09 + 6503.23i −0.219941 + 0.208774i
\(991\) 4516.20 + 13899.4i 0.144765 + 0.445540i 0.996981 0.0776501i \(-0.0247417\pi\)
−0.852216 + 0.523190i \(0.824742\pi\)
\(992\) −26204.4 36067.3i −0.838701 1.15437i
\(993\) 2542.78i 0.0812616i
\(994\) −316.256 + 229.774i −0.0100916 + 0.00733197i
\(995\) 13765.5 25361.1i 0.438587 0.808041i
\(996\) 6849.81 + 4976.68i 0.217916 + 0.158325i
\(997\) 7437.62 10237.0i 0.236261 0.325185i −0.674380 0.738385i \(-0.735589\pi\)
0.910640 + 0.413200i \(0.135589\pi\)
\(998\) 14884.4 + 4836.23i 0.472102 + 0.153395i
\(999\) 4734.25 0.149935
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 25.4.e.a.4.3 24
3.2 odd 2 225.4.m.a.154.4 24
5.2 odd 4 125.4.d.b.101.8 48
5.3 odd 4 125.4.d.b.101.5 48
5.4 even 2 125.4.e.a.24.4 24
25.6 even 5 125.4.e.a.99.4 24
25.8 odd 20 125.4.d.b.26.5 48
25.12 odd 20 625.4.a.g.1.16 24
25.13 odd 20 625.4.a.g.1.9 24
25.17 odd 20 125.4.d.b.26.8 48
25.19 even 10 inner 25.4.e.a.19.3 yes 24
75.44 odd 10 225.4.m.a.19.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.4.e.a.4.3 24 1.1 even 1 trivial
25.4.e.a.19.3 yes 24 25.19 even 10 inner
125.4.d.b.26.5 48 25.8 odd 20
125.4.d.b.26.8 48 25.17 odd 20
125.4.d.b.101.5 48 5.3 odd 4
125.4.d.b.101.8 48 5.2 odd 4
125.4.e.a.24.4 24 5.4 even 2
125.4.e.a.99.4 24 25.6 even 5
225.4.m.a.19.4 24 75.44 odd 10
225.4.m.a.154.4 24 3.2 odd 2
625.4.a.g.1.9 24 25.13 odd 20
625.4.a.g.1.16 24 25.12 odd 20