Properties

Label 74.4.e.a.11.1
Level $74$
Weight $4$
Character 74.11
Analytic conductor $4.366$
Analytic rank $0$
Dimension $20$
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] = [74,4,Mod(11,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + 109290291168 x^{8} + 1091662316544 x^{6} + \cdots + 1118416232704 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-6.77277i\) of defining polynomial
Character \(\chi\) \(=\) 74.11
Dual form 74.4.e.a.27.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(-3.38639 + 5.86539i) q^{3} +(2.00000 - 3.46410i) q^{4} +(14.5934 + 8.42549i) q^{5} -13.5455i q^{6} +(-7.56088 + 13.0958i) q^{7} +8.00000i q^{8} +(-9.43523 - 16.3423i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(-3.38639 + 5.86539i) q^{3} +(2.00000 - 3.46410i) q^{4} +(14.5934 + 8.42549i) q^{5} -13.5455i q^{6} +(-7.56088 + 13.0958i) q^{7} +8.00000i q^{8} +(-9.43523 - 16.3423i) q^{9} -33.7019 q^{10} -16.4204 q^{11} +(13.5455 + 23.4616i) q^{12} +(-75.3996 - 43.5320i) q^{13} -30.2435i q^{14} +(-98.8376 + 57.0639i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-1.45821 + 0.841898i) q^{17} +(32.6846 + 18.8705i) q^{18} +(108.417 + 62.5948i) q^{19} +(58.3735 - 33.7019i) q^{20} +(-51.2081 - 88.6951i) q^{21} +(28.4409 - 16.4204i) q^{22} +85.4461i q^{23} +(-46.9232 - 27.0911i) q^{24} +(79.4776 + 137.659i) q^{25} +174.128 q^{26} -55.0595 q^{27} +(30.2435 + 52.3833i) q^{28} -151.487i q^{29} +(114.128 - 197.675i) q^{30} +88.7582i q^{31} +(27.7128 + 16.0000i) q^{32} +(55.6057 - 96.3119i) q^{33} +(1.68380 - 2.91642i) q^{34} +(-220.677 + 127.408i) q^{35} -75.4819 q^{36} +(112.519 + 194.917i) q^{37} -250.379 q^{38} +(510.665 - 294.832i) q^{39} +(-67.4039 + 116.747i) q^{40} +(217.078 - 375.990i) q^{41} +(177.390 + 102.416i) q^{42} +215.822i q^{43} +(-32.8407 + 56.8818i) q^{44} -317.986i q^{45} +(-85.4461 - 147.997i) q^{46} -101.825 q^{47} +108.364 q^{48} +(57.1662 + 99.0148i) q^{49} +(-275.319 - 158.955i) q^{50} -11.4040i q^{51} +(-301.599 + 174.128i) q^{52} +(249.053 + 431.373i) q^{53} +(95.3658 - 55.0595i) q^{54} +(-239.628 - 138.350i) q^{55} +(-104.767 - 60.4870i) q^{56} +(-734.287 + 423.941i) q^{57} +(151.487 + 262.384i) q^{58} +(-577.395 + 333.359i) q^{59} +456.511i q^{60} +(660.867 + 381.552i) q^{61} +(-88.7582 - 153.734i) q^{62} +285.355 q^{63} -64.0000 q^{64} +(-733.557 - 1270.56i) q^{65} +222.423i q^{66} +(87.8771 - 152.208i) q^{67} +6.73518i q^{68} +(-501.175 - 289.353i) q^{69} +(254.816 - 441.355i) q^{70} +(214.143 - 370.906i) q^{71} +(130.738 - 75.4819i) q^{72} +162.065 q^{73} +(-389.805 - 225.087i) q^{74} -1076.57 q^{75} +(433.670 - 250.379i) q^{76} +(124.152 - 215.038i) q^{77} +(-589.665 + 1021.33i) q^{78} +(476.666 + 275.203i) q^{79} -269.616i q^{80} +(441.204 - 764.188i) q^{81} +868.312i q^{82} +(407.247 + 705.373i) q^{83} -409.665 q^{84} -28.3736 q^{85} +(-215.822 - 373.815i) q^{86} +(888.534 + 512.995i) q^{87} -131.363i q^{88} +(-290.566 + 167.758i) q^{89} +(317.986 + 550.767i) q^{90} +(1140.18 - 658.280i) q^{91} +(295.994 + 170.892i) q^{92} +(-520.602 - 300.570i) q^{93} +(176.367 - 101.825i) q^{94} +(1054.78 + 1826.94i) q^{95} +(-187.693 + 108.364i) q^{96} +1088.06i q^{97} +(-198.030 - 114.332i) q^{98} +(154.930 + 268.347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9} - 16 q^{10} - 16 q^{11} + 8 q^{12} - 150 q^{13} + 198 q^{15} - 160 q^{16} + 90 q^{17} + 162 q^{19} - 72 q^{20} - 30 q^{21} + 532 q^{25} + 528 q^{26} - 644 q^{27} + 8 q^{28} + 312 q^{30} - 596 q^{33} - 488 q^{34} - 342 q^{35} - 608 q^{36} - 112 q^{37} + 144 q^{38} + 1146 q^{39} - 32 q^{40} - 498 q^{41} - 120 q^{42} - 32 q^{44} + 424 q^{47} + 64 q^{48} + 84 q^{49} + 1008 q^{50} - 600 q^{52} - 142 q^{53} + 1080 q^{54} - 540 q^{55} + 138 q^{57} + 224 q^{58} + 1590 q^{59} - 1542 q^{61} + 8 q^{62} + 1864 q^{63} - 1280 q^{64} - 694 q^{65} + 62 q^{67} + 708 q^{69} - 368 q^{70} - 178 q^{71} - 528 q^{73} - 560 q^{74} - 7224 q^{75} + 648 q^{76} + 3468 q^{77} - 1736 q^{78} - 3474 q^{79} + 2414 q^{81} + 938 q^{83} - 240 q^{84} - 1100 q^{85} - 2120 q^{86} + 9420 q^{87} + 510 q^{89} + 2504 q^{90} + 666 q^{91} + 1344 q^{92} + 1728 q^{93} + 264 q^{94} + 4126 q^{95} - 816 q^{98} + 2312 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −0.612372 + 0.353553i
\(3\) −3.38639 + 5.86539i −0.651710 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 14.5934 + 8.42549i 1.30527 + 0.753598i 0.981303 0.192470i \(-0.0616497\pi\)
0.323968 + 0.946068i \(0.394983\pi\)
\(6\) 13.5455i 0.921658i
\(7\) −7.56088 + 13.0958i −0.408249 + 0.707108i −0.994694 0.102881i \(-0.967194\pi\)
0.586445 + 0.809989i \(0.300527\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −9.43523 16.3423i −0.349453 0.605271i
\(10\) −33.7019 −1.06575
\(11\) −16.4204 −0.450084 −0.225042 0.974349i \(-0.572252\pi\)
−0.225042 + 0.974349i \(0.572252\pi\)
\(12\) 13.5455 + 23.4616i 0.325855 + 0.564398i
\(13\) −75.3996 43.5320i −1.60862 0.928739i −0.989679 0.143304i \(-0.954227\pi\)
−0.618944 0.785435i \(-0.712439\pi\)
\(14\) 30.2435i 0.577351i
\(15\) −98.8376 + 57.0639i −1.70132 + 0.982256i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −1.45821 + 0.841898i −0.0208040 + 0.0120112i −0.510366 0.859957i \(-0.670490\pi\)
0.489562 + 0.871969i \(0.337157\pi\)
\(18\) 32.6846 + 18.8705i 0.427991 + 0.247101i
\(19\) 108.417 + 62.5948i 1.30909 + 0.755802i 0.981944 0.189173i \(-0.0605806\pi\)
0.327143 + 0.944975i \(0.393914\pi\)
\(20\) 58.3735 33.7019i 0.652635 0.376799i
\(21\) −51.2081 88.6951i −0.532120 0.921660i
\(22\) 28.4409 16.4204i 0.275619 0.159129i
\(23\) 85.4461i 0.774641i 0.921945 + 0.387320i \(0.126599\pi\)
−0.921945 + 0.387320i \(0.873401\pi\)
\(24\) −46.9232 27.0911i −0.399090 0.230414i
\(25\) 79.4776 + 137.659i 0.635821 + 1.10127i
\(26\) 174.128 1.31344
\(27\) −55.0595 −0.392452
\(28\) 30.2435 + 52.3833i 0.204125 + 0.353554i
\(29\) 151.487i 0.970018i −0.874509 0.485009i \(-0.838816\pi\)
0.874509 0.485009i \(-0.161184\pi\)
\(30\) 114.128 197.675i 0.694560 1.20301i
\(31\) 88.7582i 0.514240i 0.966379 + 0.257120i \(0.0827736\pi\)
−0.966379 + 0.257120i \(0.917226\pi\)
\(32\) 27.7128 + 16.0000i 0.153093 + 0.0883883i
\(33\) 55.6057 96.3119i 0.293324 0.508053i
\(34\) 1.68380 2.91642i 0.00849320 0.0147106i
\(35\) −220.677 + 127.408i −1.06575 + 0.615312i
\(36\) −75.4819 −0.349453
\(37\) 112.519 + 194.917i 0.499945 + 0.866057i
\(38\) −250.379 −1.06887
\(39\) 510.665 294.832i 2.09671 1.21054i
\(40\) −67.4039 + 116.747i −0.266437 + 0.461483i
\(41\) 217.078 375.990i 0.826875 1.43219i −0.0736023 0.997288i \(-0.523450\pi\)
0.900478 0.434902i \(-0.143217\pi\)
\(42\) 177.390 + 102.416i 0.651712 + 0.376266i
\(43\) 215.822i 0.765408i 0.923871 + 0.382704i \(0.125007\pi\)
−0.923871 + 0.382704i \(0.874993\pi\)
\(44\) −32.8407 + 56.8818i −0.112521 + 0.194892i
\(45\) 317.986i 1.05339i
\(46\) −85.4461 147.997i −0.273877 0.474369i
\(47\) −101.825 −0.316016 −0.158008 0.987438i \(-0.550507\pi\)
−0.158008 + 0.987438i \(0.550507\pi\)
\(48\) 108.364 0.325855
\(49\) 57.1662 + 99.0148i 0.166665 + 0.288673i
\(50\) −275.319 158.955i −0.778719 0.449593i
\(51\) 11.4040i 0.0313113i
\(52\) −301.599 + 174.128i −0.804311 + 0.464369i
\(53\) 249.053 + 431.373i 0.645473 + 1.11799i 0.984192 + 0.177105i \(0.0566731\pi\)
−0.338719 + 0.940888i \(0.609994\pi\)
\(54\) 95.3658 55.0595i 0.240327 0.138753i
\(55\) −239.628 138.350i −0.587482 0.339183i
\(56\) −104.767 60.4870i −0.250000 0.144338i
\(57\) −734.287 + 423.941i −1.70629 + 0.985128i
\(58\) 151.487 + 262.384i 0.342953 + 0.594012i
\(59\) −577.395 + 333.359i −1.27407 + 0.735587i −0.975752 0.218878i \(-0.929760\pi\)
−0.298322 + 0.954465i \(0.596427\pi\)
\(60\) 456.511i 0.982256i
\(61\) 660.867 + 381.552i 1.38714 + 0.800864i 0.992992 0.118184i \(-0.0377071\pi\)
0.394146 + 0.919048i \(0.371040\pi\)
\(62\) −88.7582 153.734i −0.181811 0.314906i
\(63\) 285.355 0.570656
\(64\) −64.0000 −0.125000
\(65\) −733.557 1270.56i −1.39979 2.42451i
\(66\) 222.423i 0.414823i
\(67\) 87.8771 152.208i 0.160237 0.277539i −0.774717 0.632309i \(-0.782107\pi\)
0.934954 + 0.354770i \(0.115441\pi\)
\(68\) 6.73518i 0.0120112i
\(69\) −501.175 289.353i −0.874411 0.504842i
\(70\) 254.816 441.355i 0.435091 0.753600i
\(71\) 214.143 370.906i 0.357944 0.619978i −0.629673 0.776860i \(-0.716811\pi\)
0.987617 + 0.156883i \(0.0501444\pi\)
\(72\) 130.738 75.4819i 0.213995 0.123550i
\(73\) 162.065 0.259839 0.129920 0.991525i \(-0.458528\pi\)
0.129920 + 0.991525i \(0.458528\pi\)
\(74\) −389.805 225.087i −0.612350 0.353592i
\(75\) −1076.57 −1.65749
\(76\) 433.670 250.379i 0.654544 0.377901i
\(77\) 124.152 215.038i 0.183746 0.318258i
\(78\) −589.665 + 1021.33i −0.855979 + 1.48260i
\(79\) 476.666 + 275.203i 0.678849 + 0.391934i 0.799421 0.600771i \(-0.205140\pi\)
−0.120572 + 0.992705i \(0.538473\pi\)
\(80\) 269.616i 0.376799i
\(81\) 441.204 764.188i 0.605218 1.04827i
\(82\) 868.312i 1.16938i
\(83\) 407.247 + 705.373i 0.538568 + 0.932828i 0.998981 + 0.0451231i \(0.0143680\pi\)
−0.460413 + 0.887705i \(0.652299\pi\)
\(84\) −409.665 −0.532120
\(85\) −28.3736 −0.0362065
\(86\) −215.822 373.815i −0.270613 0.468715i
\(87\) 888.534 + 512.995i 1.09495 + 0.632171i
\(88\) 131.363i 0.159129i
\(89\) −290.566 + 167.758i −0.346066 + 0.199802i −0.662951 0.748662i \(-0.730696\pi\)
0.316885 + 0.948464i \(0.397363\pi\)
\(90\) 317.986 + 550.767i 0.372429 + 0.645067i
\(91\) 1140.18 658.280i 1.31344 0.758314i
\(92\) 295.994 + 170.892i 0.335429 + 0.193660i
\(93\) −520.602 300.570i −0.580472 0.335136i
\(94\) 176.367 101.825i 0.193519 0.111728i
\(95\) 1054.78 + 1826.94i 1.13914 + 1.97305i
\(96\) −187.693 + 108.364i −0.199545 + 0.115207i
\(97\) 1088.06i 1.13893i 0.822016 + 0.569465i \(0.192849\pi\)
−0.822016 + 0.569465i \(0.807151\pi\)
\(98\) −198.030 114.332i −0.204123 0.117850i
\(99\) 154.930 + 268.347i 0.157283 + 0.272423i
\(100\) 635.821 0.635821
\(101\) −689.403 −0.679189 −0.339595 0.940572i \(-0.610290\pi\)
−0.339595 + 0.940572i \(0.610290\pi\)
\(102\) 11.4040 + 19.7523i 0.0110702 + 0.0191742i
\(103\) 1060.53i 1.01453i −0.861790 0.507265i \(-0.830656\pi\)
0.861790 0.507265i \(-0.169344\pi\)
\(104\) 348.256 603.197i 0.328359 0.568734i
\(105\) 1725.81i 1.60402i
\(106\) −862.745 498.106i −0.790540 0.456418i
\(107\) 949.293 1644.22i 0.857679 1.48554i −0.0164583 0.999865i \(-0.505239\pi\)
0.874137 0.485679i \(-0.161428\pi\)
\(108\) −110.119 + 190.732i −0.0981130 + 0.169937i
\(109\) −367.930 + 212.424i −0.323314 + 0.186666i −0.652869 0.757471i \(-0.726435\pi\)
0.329555 + 0.944137i \(0.393101\pi\)
\(110\) 553.398 0.479677
\(111\) −1524.30 0.0966041i −1.30342 8.26059e-5i
\(112\) 241.948 0.204125
\(113\) 1803.46 1041.23i 1.50138 0.866820i 0.501378 0.865228i \(-0.332827\pi\)
0.999999 0.00159207i \(-0.000506773\pi\)
\(114\) 847.881 1468.57i 0.696591 1.20653i
\(115\) −719.925 + 1246.95i −0.583768 + 1.01112i
\(116\) −524.768 302.975i −0.420030 0.242504i
\(117\) 1642.94i 1.29820i
\(118\) 666.718 1154.79i 0.520139 0.900906i
\(119\) 25.4620i 0.0196142i
\(120\) −456.511 790.701i −0.347280 0.601506i
\(121\) −1061.37 −0.797424
\(122\) −1526.21 −1.13259
\(123\) 1470.22 + 2546.50i 1.07777 + 1.86675i
\(124\) 307.467 + 177.516i 0.222672 + 0.128560i
\(125\) 572.180i 0.409418i
\(126\) −494.249 + 285.355i −0.349454 + 0.201757i
\(127\) −515.369 892.645i −0.360091 0.623696i 0.627884 0.778307i \(-0.283921\pi\)
−0.987976 + 0.154610i \(0.950588\pi\)
\(128\) 110.851 64.0000i 0.0765466 0.0441942i
\(129\) −1265.88 730.857i −0.863989 0.498824i
\(130\) 2541.11 + 1467.11i 1.71439 + 0.989803i
\(131\) 314.224 181.417i 0.209571 0.120996i −0.391541 0.920161i \(-0.628058\pi\)
0.601112 + 0.799165i \(0.294724\pi\)
\(132\) −222.423 385.248i −0.146662 0.254026i
\(133\) −1639.46 + 946.544i −1.06887 + 0.617111i
\(134\) 351.508i 0.226610i
\(135\) −803.504 463.903i −0.512256 0.295751i
\(136\) −6.73518 11.6657i −0.00424660 0.00735532i
\(137\) −1378.59 −0.859715 −0.429857 0.902897i \(-0.641436\pi\)
−0.429857 + 0.902897i \(0.641436\pi\)
\(138\) 1157.41 0.713954
\(139\) 236.291 + 409.268i 0.144187 + 0.249739i 0.929069 0.369906i \(-0.120610\pi\)
−0.784883 + 0.619645i \(0.787277\pi\)
\(140\) 1019.27i 0.615312i
\(141\) 344.820 597.245i 0.205951 0.356717i
\(142\) 856.570i 0.506210i
\(143\) 1238.09 + 714.811i 0.724016 + 0.418011i
\(144\) −150.964 + 261.477i −0.0873633 + 0.151318i
\(145\) 1276.36 2210.71i 0.731004 1.26614i
\(146\) −280.704 + 162.065i −0.159118 + 0.0918670i
\(147\) −774.348 −0.434470
\(148\) 900.249 + 0.0570544i 0.500000 + 3.16881e-5i
\(149\) 1856.02 1.02048 0.510238 0.860033i \(-0.329557\pi\)
0.510238 + 0.860033i \(0.329557\pi\)
\(150\) 1864.67 1076.57i 1.01500 0.586010i
\(151\) −1191.56 + 2063.84i −0.642171 + 1.11227i 0.342776 + 0.939417i \(0.388633\pi\)
−0.984947 + 0.172856i \(0.944701\pi\)
\(152\) −500.759 + 867.339i −0.267216 + 0.462832i
\(153\) 27.5171 + 15.8870i 0.0145400 + 0.00839470i
\(154\) 496.609i 0.259857i
\(155\) −747.831 + 1295.28i −0.387530 + 0.671222i
\(156\) 2358.66i 1.21054i
\(157\) −597.821 1035.46i −0.303894 0.526360i 0.673121 0.739533i \(-0.264953\pi\)
−0.977014 + 0.213173i \(0.931620\pi\)
\(158\) −1100.81 −0.554278
\(159\) −3373.56 −1.68265
\(160\) 269.616 + 466.988i 0.133219 + 0.230741i
\(161\) −1118.99 646.047i −0.547755 0.316246i
\(162\) 1764.82i 0.855908i
\(163\) −825.839 + 476.798i −0.396839 + 0.229115i −0.685119 0.728431i \(-0.740250\pi\)
0.288280 + 0.957546i \(0.406916\pi\)
\(164\) −868.312 1503.96i −0.413438 0.716095i
\(165\) 1622.95 937.010i 0.765736 0.442098i
\(166\) −1410.75 814.494i −0.659609 0.380825i
\(167\) −2066.79 1193.26i −0.957684 0.552919i −0.0622245 0.998062i \(-0.519819\pi\)
−0.895459 + 0.445143i \(0.853153\pi\)
\(168\) 709.561 409.665i 0.325856 0.188133i
\(169\) 2691.57 + 4661.94i 1.22511 + 2.12196i
\(170\) 49.1445 28.3736i 0.0221718 0.0128009i
\(171\) 2362.39i 1.05647i
\(172\) 747.629 + 431.644i 0.331431 + 0.191352i
\(173\) 2118.24 + 3668.90i 0.930907 + 1.61238i 0.781774 + 0.623561i \(0.214315\pi\)
0.149133 + 0.988817i \(0.452352\pi\)
\(174\) −2051.98 −0.894024
\(175\) −2403.68 −1.03829
\(176\) 131.363 + 227.527i 0.0562605 + 0.0974461i
\(177\) 4515.53i 1.91756i
\(178\) 335.516 581.132i 0.141281 0.244706i
\(179\) 3656.41i 1.52678i −0.645940 0.763388i \(-0.723534\pi\)
0.645940 0.763388i \(-0.276466\pi\)
\(180\) −1101.53 635.971i −0.456131 0.263347i
\(181\) −1233.96 + 2137.28i −0.506738 + 0.877696i 0.493231 + 0.869898i \(0.335816\pi\)
−0.999970 + 0.00779807i \(0.997518\pi\)
\(182\) −1316.56 + 2280.35i −0.536209 + 0.928741i
\(183\) −4475.91 + 2584.17i −1.80802 + 1.04386i
\(184\) −683.569 −0.273877
\(185\) −0.240355 + 3792.52i −9.55205e−5 + 1.50720i
\(186\) 1202.28 0.473953
\(187\) 23.9443 13.8243i 0.00936355 0.00540605i
\(188\) −203.651 + 352.733i −0.0790039 + 0.136839i
\(189\) 416.298 721.050i 0.160218 0.277506i
\(190\) −3653.88 2109.57i −1.39516 0.805495i
\(191\) 1201.72i 0.455253i −0.973749 0.227627i \(-0.926903\pi\)
0.973749 0.227627i \(-0.0730965\pi\)
\(192\) 216.729 375.385i 0.0814638 0.141099i
\(193\) 2844.06i 1.06073i −0.847771 0.530363i \(-0.822056\pi\)
0.847771 0.530363i \(-0.177944\pi\)
\(194\) −1088.06 1884.58i −0.402672 0.697449i
\(195\) 9936.43 3.64904
\(196\) 457.330 0.166665
\(197\) −648.159 1122.64i −0.234413 0.406016i 0.724689 0.689076i \(-0.241984\pi\)
−0.959102 + 0.283061i \(0.908650\pi\)
\(198\) −536.693 309.860i −0.192632 0.111216i
\(199\) 3721.05i 1.32552i −0.748833 0.662759i \(-0.769385\pi\)
0.748833 0.662759i \(-0.230615\pi\)
\(200\) −1101.27 + 635.821i −0.389359 + 0.224797i
\(201\) 595.171 + 1030.87i 0.208857 + 0.361750i
\(202\) 1194.08 689.403i 0.415917 0.240130i
\(203\) 1983.85 + 1145.38i 0.685907 + 0.396009i
\(204\) −39.5045 22.8079i −0.0135582 0.00782782i
\(205\) 6335.80 3657.98i 2.15859 1.24626i
\(206\) 1060.53 + 1836.88i 0.358691 + 0.621271i
\(207\) 1396.39 806.204i 0.468867 0.270701i
\(208\) 1393.02i 0.464369i
\(209\) −1780.25 1027.83i −0.589199 0.340174i
\(210\) 1725.81 + 2989.20i 0.567107 + 0.982258i
\(211\) 4602.50 1.50165 0.750827 0.660499i \(-0.229655\pi\)
0.750827 + 0.660499i \(0.229655\pi\)
\(212\) 1992.42 0.645473
\(213\) 1450.34 + 2512.06i 0.466552 + 0.808092i
\(214\) 3797.17i 1.21294i
\(215\) −1818.40 + 3149.57i −0.576810 + 0.999064i
\(216\) 440.476i 0.138753i
\(217\) −1162.36 671.090i −0.363623 0.209938i
\(218\) 424.849 735.859i 0.131993 0.228618i
\(219\) −548.814 + 950.574i −0.169340 + 0.293305i
\(220\) −958.514 + 553.398i −0.293741 + 0.169591i
\(221\) 146.598 0.0446210
\(222\) 2640.25 1524.13i 0.798208 0.460778i
\(223\) 2008.08 0.603009 0.301504 0.953465i \(-0.402511\pi\)
0.301504 + 0.953465i \(0.402511\pi\)
\(224\) −419.066 + 241.948i −0.125000 + 0.0721689i
\(225\) 1499.78 2597.70i 0.444379 0.769688i
\(226\) −2082.46 + 3606.93i −0.612935 + 1.06163i
\(227\) −2003.64 1156.80i −0.585842 0.338236i 0.177609 0.984101i \(-0.443164\pi\)
−0.763452 + 0.645865i \(0.776497\pi\)
\(228\) 3391.52i 0.985128i
\(229\) −525.797 + 910.708i −0.151728 + 0.262800i −0.931863 0.362811i \(-0.881817\pi\)
0.780135 + 0.625611i \(0.215150\pi\)
\(230\) 2879.70i 0.825573i
\(231\) 840.856 + 1456.41i 0.239499 + 0.414824i
\(232\) 1211.90 0.342953
\(233\) 2407.86 0.677014 0.338507 0.940964i \(-0.390078\pi\)
0.338507 + 0.940964i \(0.390078\pi\)
\(234\) −1642.94 2845.65i −0.458984 0.794984i
\(235\) −1485.97 857.927i −0.412486 0.238149i
\(236\) 2666.87i 0.735587i
\(237\) −3228.35 + 1863.89i −0.884827 + 0.510855i
\(238\) 25.4620 + 44.1014i 0.00693468 + 0.0120112i
\(239\) 5167.49 2983.45i 1.39857 0.807462i 0.404324 0.914616i \(-0.367507\pi\)
0.994242 + 0.107154i \(0.0341737\pi\)
\(240\) 1581.40 + 913.023i 0.425329 + 0.245564i
\(241\) −2047.85 1182.33i −0.547359 0.316018i 0.200697 0.979653i \(-0.435679\pi\)
−0.748056 + 0.663635i \(0.769013\pi\)
\(242\) 1838.35 1061.37i 0.488321 0.281932i
\(243\) 2244.87 + 3888.23i 0.592628 + 1.02646i
\(244\) 2643.47 1526.21i 0.693569 0.400432i
\(245\) 1926.61i 0.502395i
\(246\) −5092.99 2940.44i −1.31999 0.762096i
\(247\) −5449.76 9439.25i −1.40389 2.43160i
\(248\) −710.065 −0.181811
\(249\) −5516.39 −1.40396
\(250\) −572.180 991.044i −0.144751 0.250717i
\(251\) 374.640i 0.0942115i 0.998890 + 0.0471058i \(0.0149998\pi\)
−0.998890 + 0.0471058i \(0.985000\pi\)
\(252\) 570.709 988.497i 0.142664 0.247101i
\(253\) 1403.06i 0.348653i
\(254\) 1785.29 + 1030.74i 0.441020 + 0.254623i
\(255\) 96.0840 166.422i 0.0235961 0.0408697i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1375.99 794.430i 0.333977 0.192822i −0.323628 0.946184i \(-0.604903\pi\)
0.657605 + 0.753363i \(0.271569\pi\)
\(258\) 2923.43 0.705444
\(259\) −3403.34 0.215691i −0.816498 5.17466e-5i
\(260\) −5868.45 −1.39979
\(261\) −2475.65 + 1429.32i −0.587123 + 0.338976i
\(262\) −362.834 + 628.447i −0.0855571 + 0.148189i
\(263\) −1260.57 + 2183.37i −0.295552 + 0.511911i −0.975113 0.221708i \(-0.928837\pi\)
0.679561 + 0.733619i \(0.262170\pi\)
\(264\) 770.495 + 444.846i 0.179624 + 0.103706i
\(265\) 8393.57i 1.94571i
\(266\) 1893.09 3278.92i 0.436363 0.755803i
\(267\) 2272.38i 0.520851i
\(268\) −351.508 608.830i −0.0801186 0.138769i
\(269\) 2167.74 0.491336 0.245668 0.969354i \(-0.420993\pi\)
0.245668 + 0.969354i \(0.420993\pi\)
\(270\) 1855.61 0.418255
\(271\) −3647.17 6317.08i −0.817526 1.41600i −0.907500 0.420053i \(-0.862012\pi\)
0.0899734 0.995944i \(-0.471322\pi\)
\(272\) 23.3314 + 13.4704i 0.00520100 + 0.00300280i
\(273\) 8916.77i 1.97680i
\(274\) 2387.79 1378.59i 0.526466 0.303955i
\(275\) −1305.05 2260.42i −0.286173 0.495666i
\(276\) −2004.70 + 1157.41i −0.437206 + 0.252421i
\(277\) −1518.51 876.714i −0.329381 0.190168i 0.326185 0.945306i \(-0.394237\pi\)
−0.655566 + 0.755137i \(0.727570\pi\)
\(278\) −818.536 472.582i −0.176592 0.101955i
\(279\) 1450.51 837.454i 0.311254 0.179703i
\(280\) −1019.27 1765.42i −0.217546 0.376800i
\(281\) 3888.07 2244.78i 0.825419 0.476556i −0.0268626 0.999639i \(-0.508552\pi\)
0.852282 + 0.523083i \(0.175218\pi\)
\(282\) 1379.28i 0.291258i
\(283\) 6033.77 + 3483.60i 1.26739 + 0.731726i 0.974493 0.224419i \(-0.0720483\pi\)
0.292894 + 0.956145i \(0.405382\pi\)
\(284\) −856.570 1483.62i −0.178972 0.309989i
\(285\) −14287.6 −2.96956
\(286\) −2859.24 −0.591156
\(287\) 3282.60 + 5685.63i 0.675142 + 1.16938i
\(288\) 603.855i 0.123550i
\(289\) −2455.08 + 4252.33i −0.499711 + 0.865526i
\(290\) 5105.42i 1.03380i
\(291\) −6381.92 3684.60i −1.28562 0.742252i
\(292\) 324.130 561.409i 0.0649598 0.112514i
\(293\) −1063.94 + 1842.80i −0.212136 + 0.367431i −0.952383 0.304905i \(-0.901375\pi\)
0.740247 + 0.672336i \(0.234709\pi\)
\(294\) 1341.21 774.348i 0.266058 0.153608i
\(295\) −11234.8 −2.21735
\(296\) −1559.33 + 900.150i −0.306197 + 0.176757i
\(297\) 904.097 0.176636
\(298\) −3214.72 + 1856.02i −0.624911 + 0.360793i
\(299\) 3719.64 6442.60i 0.719439 1.24610i
\(300\) −2153.14 + 3729.34i −0.414371 + 0.717712i
\(301\) −2826.37 1631.80i −0.541226 0.312477i
\(302\) 4766.24i 0.908167i
\(303\) 2334.58 4043.62i 0.442635 0.766666i
\(304\) 2003.03i 0.377901i
\(305\) 6429.52 + 11136.3i 1.20706 + 2.09069i
\(306\) −63.5480 −0.0118719
\(307\) 7143.74 1.32806 0.664031 0.747705i \(-0.268844\pi\)
0.664031 + 0.747705i \(0.268844\pi\)
\(308\) −496.609 860.153i −0.0918732 0.159129i
\(309\) 6220.40 + 3591.35i 1.14520 + 0.661180i
\(310\) 2991.32i 0.548051i
\(311\) −758.571 + 437.961i −0.138311 + 0.0798536i −0.567559 0.823333i \(-0.692112\pi\)
0.429248 + 0.903187i \(0.358779\pi\)
\(312\) 2358.66 + 4085.32i 0.427990 + 0.741300i
\(313\) −3778.25 + 2181.37i −0.682298 + 0.393925i −0.800720 0.599038i \(-0.795550\pi\)
0.118422 + 0.992963i \(0.462216\pi\)
\(314\) 2070.91 + 1195.64i 0.372192 + 0.214885i
\(315\) 4164.29 + 2404.25i 0.744860 + 0.430045i
\(316\) 1906.66 1100.81i 0.339425 0.195967i
\(317\) −2890.51 5006.52i −0.512137 0.887047i −0.999901 0.0140719i \(-0.995521\pi\)
0.487764 0.872976i \(-0.337813\pi\)
\(318\) 5843.18 3373.56i 1.03041 0.594905i
\(319\) 2487.48i 0.436589i
\(320\) −933.976 539.231i −0.163159 0.0941998i
\(321\) 6429.35 + 11136.0i 1.11792 + 1.93629i
\(322\) 2584.19 0.447240
\(323\) −210.794 −0.0363123
\(324\) −1764.82 3056.75i −0.302609 0.524134i
\(325\) 13839.3i 2.36205i
\(326\) 953.597 1651.68i 0.162009 0.280607i
\(327\) 2877.40i 0.486608i
\(328\) 3007.92 + 1736.62i 0.506356 + 0.292345i
\(329\) 769.888 1333.49i 0.129013 0.223457i
\(330\) −1874.02 + 3245.90i −0.312610 + 0.541457i
\(331\) −6421.10 + 3707.22i −1.06627 + 0.615612i −0.927160 0.374665i \(-0.877758\pi\)
−0.139110 + 0.990277i \(0.544424\pi\)
\(332\) 3257.98 0.538568
\(333\) 2123.75 3677.90i 0.349491 0.605248i
\(334\) 4773.05 0.781946
\(335\) 2564.84 1480.81i 0.418306 0.241509i
\(336\) −819.330 + 1419.12i −0.133030 + 0.230415i
\(337\) 2407.08 4169.19i 0.389086 0.673917i −0.603241 0.797559i \(-0.706124\pi\)
0.992327 + 0.123642i \(0.0394575\pi\)
\(338\) −9323.87 5383.14i −1.50045 0.866285i
\(339\) 14104.0i 2.25966i
\(340\) −56.7472 + 98.2890i −0.00905162 + 0.0156779i
\(341\) 1457.44i 0.231451i
\(342\) 2362.39 + 4091.77i 0.373518 + 0.646953i
\(343\) −6915.67 −1.08866
\(344\) −1726.58 −0.270613
\(345\) −4875.89 8445.29i −0.760896 1.31791i
\(346\) −7337.81 4236.48i −1.14012 0.658251i
\(347\) 6483.43i 1.00302i −0.865151 0.501511i \(-0.832778\pi\)
0.865151 0.501511i \(-0.167222\pi\)
\(348\) 3554.13 2051.98i 0.547476 0.316085i
\(349\) 2174.66 + 3766.61i 0.333543 + 0.577714i 0.983204 0.182510i \(-0.0584223\pi\)
−0.649661 + 0.760224i \(0.725089\pi\)
\(350\) 4163.30 2403.68i 0.635822 0.367092i
\(351\) 4151.47 + 2396.85i 0.631307 + 0.364485i
\(352\) −455.054 262.726i −0.0689048 0.0397822i
\(353\) 5061.96 2922.52i 0.763232 0.440652i −0.0672230 0.997738i \(-0.521414\pi\)
0.830455 + 0.557086i \(0.188081\pi\)
\(354\) 4515.53 + 7821.13i 0.677959 + 1.17426i
\(355\) 6250.12 3608.51i 0.934429 0.539493i
\(356\) 1342.07i 0.199802i
\(357\) 149.344 + 86.2240i 0.0221405 + 0.0127828i
\(358\) 3656.41 + 6333.09i 0.539797 + 0.934956i
\(359\) −11195.2 −1.64585 −0.822924 0.568152i \(-0.807659\pi\)
−0.822924 + 0.568152i \(0.807659\pi\)
\(360\) 2543.89 0.372429
\(361\) 4406.72 + 7632.67i 0.642473 + 1.11280i
\(362\) 4935.84i 0.716636i
\(363\) 3594.22 6225.36i 0.519690 0.900129i
\(364\) 5266.24i 0.758314i
\(365\) 2365.07 + 1365.47i 0.339160 + 0.195814i
\(366\) 5168.33 8951.81i 0.738123 1.27847i
\(367\) −1259.14 + 2180.90i −0.179092 + 0.310196i −0.941570 0.336818i \(-0.890649\pi\)
0.762478 + 0.647014i \(0.223983\pi\)
\(368\) 1183.98 683.569i 0.167715 0.0968301i
\(369\) −8192.73 −1.15582
\(370\) −3792.10 6569.07i −0.532816 0.923000i
\(371\) −7532.24 −1.05406
\(372\) −2082.41 + 1202.28i −0.290236 + 0.167568i
\(373\) −1927.57 + 3338.66i −0.267576 + 0.463456i −0.968235 0.250040i \(-0.919556\pi\)
0.700659 + 0.713496i \(0.252889\pi\)
\(374\) −27.6485 + 47.8887i −0.00382265 + 0.00662103i
\(375\) −3356.06 1937.62i −0.462150 0.266822i
\(376\) 814.602i 0.111728i
\(377\) −6594.55 + 11422.1i −0.900893 + 1.56039i
\(378\) 1665.19i 0.226583i
\(379\) 27.2024 + 47.1159i 0.00368679 + 0.00638570i 0.867863 0.496804i \(-0.165493\pi\)
−0.864176 + 0.503189i \(0.832160\pi\)
\(380\) 8438.27 1.13914
\(381\) 6980.95 0.938701
\(382\) 1201.72 + 2081.44i 0.160956 + 0.278784i
\(383\) −799.417 461.544i −0.106654 0.0615765i 0.445724 0.895170i \(-0.352946\pi\)
−0.552378 + 0.833594i \(0.686279\pi\)
\(384\) 866.915i 0.115207i
\(385\) 3623.60 2092.09i 0.479678 0.276942i
\(386\) 2844.06 + 4926.06i 0.375023 + 0.649559i
\(387\) 3527.03 2036.33i 0.463279 0.267474i
\(388\) 3769.16 + 2176.13i 0.493171 + 0.284732i
\(389\) 427.934 + 247.068i 0.0557766 + 0.0322027i 0.527629 0.849475i \(-0.323081\pi\)
−0.471852 + 0.881678i \(0.656414\pi\)
\(390\) −17210.4 + 9936.43i −2.23457 + 1.29013i
\(391\) −71.9369 124.598i −0.00930436 0.0161156i
\(392\) −792.118 + 457.330i −0.102061 + 0.0589251i
\(393\) 2457.39i 0.315418i
\(394\) 2245.29 + 1296.32i 0.287096 + 0.165755i
\(395\) 4637.44 + 8032.28i 0.590722 + 1.02316i
\(396\) 1239.44 0.157283
\(397\) 4248.92 0.537147 0.268574 0.963259i \(-0.413448\pi\)
0.268574 + 0.963259i \(0.413448\pi\)
\(398\) 3721.05 + 6445.04i 0.468641 + 0.811710i
\(399\) 12821.5i 1.60871i
\(400\) 1271.64 2202.55i 0.158955 0.275319i
\(401\) 3788.88i 0.471839i −0.971773 0.235920i \(-0.924190\pi\)
0.971773 0.235920i \(-0.0758102\pi\)
\(402\) −2061.73 1190.34i −0.255796 0.147684i
\(403\) 3863.82 6692.33i 0.477595 0.827218i
\(404\) −1378.81 + 2388.16i −0.169797 + 0.294098i
\(405\) 12877.3 7434.72i 1.57995 0.912183i
\(406\) −4581.51 −0.560041
\(407\) −1847.60 3200.60i −0.225017 0.389798i
\(408\) 91.2318 0.0110702
\(409\) 9861.50 5693.54i 1.19222 0.688331i 0.233414 0.972377i \(-0.425010\pi\)
0.958811 + 0.284046i \(0.0916770\pi\)
\(410\) −7315.95 + 12671.6i −0.881242 + 1.52636i
\(411\) 4668.44 8085.97i 0.560285 0.970442i
\(412\) −3673.77 2121.05i −0.439305 0.253633i
\(413\) 10081.9i 1.20121i
\(414\) −1612.41 + 2792.77i −0.191414 + 0.331539i
\(415\) 13725.0i 1.62346i
\(416\) −1393.02 2412.79i −0.164179 0.284367i
\(417\) −3200.69 −0.375872
\(418\) 4111.32 0.481079
\(419\) 3468.14 + 6006.99i 0.404367 + 0.700384i 0.994248 0.107107i \(-0.0341586\pi\)
−0.589881 + 0.807490i \(0.700825\pi\)
\(420\) −5978.39 3451.63i −0.694561 0.401005i
\(421\) 9388.82i 1.08690i −0.839443 0.543448i \(-0.817118\pi\)
0.839443 0.543448i \(-0.182882\pi\)
\(422\) −7971.76 + 4602.50i −0.919571 + 0.530915i
\(423\) 960.745 + 1664.06i 0.110433 + 0.191275i
\(424\) −3450.98 + 1992.42i −0.395270 + 0.228209i
\(425\) −231.790 133.824i −0.0264552 0.0152739i
\(426\) −5024.12 2900.68i −0.571407 0.329902i
\(427\) −9993.48 + 5769.74i −1.13260 + 0.653904i
\(428\) −3797.17 6576.90i −0.428839 0.742772i
\(429\) −8385.30 + 4841.25i −0.943697 + 0.544844i
\(430\) 7273.62i 0.815733i
\(431\) −1038.51 599.585i −0.116063 0.0670093i 0.440844 0.897584i \(-0.354679\pi\)
−0.556908 + 0.830574i \(0.688012\pi\)
\(432\) 440.476 + 762.927i 0.0490565 + 0.0849683i
\(433\) 5267.93 0.584667 0.292333 0.956316i \(-0.405568\pi\)
0.292333 + 0.956316i \(0.405568\pi\)
\(434\) 2684.36 0.296897
\(435\) 8644.47 + 14972.7i 0.952806 + 1.65031i
\(436\) 1699.39i 0.186666i
\(437\) −5348.48 + 9263.84i −0.585475 + 1.01407i
\(438\) 2195.26i 0.239483i
\(439\) −13463.2 7772.98i −1.46370 0.845066i −0.464517 0.885564i \(-0.653772\pi\)
−0.999180 + 0.0404980i \(0.987106\pi\)
\(440\) 1106.80 1917.03i 0.119919 0.207706i
\(441\) 1078.75 1868.46i 0.116483 0.201755i
\(442\) −253.915 + 146.598i −0.0273247 + 0.0157759i
\(443\) −3079.97 −0.330324 −0.165162 0.986266i \(-0.552815\pi\)
−0.165162 + 0.986266i \(0.552815\pi\)
\(444\) −3048.93 + 5280.12i −0.325891 + 0.564377i
\(445\) −5653.78 −0.602281
\(446\) −3478.10 + 2008.08i −0.369266 + 0.213196i
\(447\) −6285.19 + 10886.3i −0.665055 + 1.15191i
\(448\) 483.896 838.133i 0.0510311 0.0883885i
\(449\) −2218.53 1280.87i −0.233183 0.134628i 0.378857 0.925455i \(-0.376317\pi\)
−0.612039 + 0.790827i \(0.709651\pi\)
\(450\) 5999.12i 0.628447i
\(451\) −3564.50 + 6173.89i −0.372163 + 0.644606i
\(452\) 8329.84i 0.866820i
\(453\) −8070.17 13977.9i −0.837019 1.44976i
\(454\) 4627.21 0.478338
\(455\) 22185.3 2.28586
\(456\) −3391.52 5874.29i −0.348295 0.603265i
\(457\) −12130.9 7003.77i −1.24170 0.716898i −0.272263 0.962223i \(-0.587772\pi\)
−0.969441 + 0.245325i \(0.921105\pi\)
\(458\) 2103.19i 0.214576i
\(459\) 80.2883 46.3545i 0.00816457 0.00471382i
\(460\) 2879.70 + 4987.79i 0.291884 + 0.505558i
\(461\) −102.193 + 59.0013i −0.0103245 + 0.00596088i −0.505153 0.863030i \(-0.668564\pi\)
0.494829 + 0.868990i \(0.335231\pi\)
\(462\) −2912.81 1681.71i −0.293325 0.169351i
\(463\) 10078.7 + 5818.94i 1.01166 + 0.584080i 0.911676 0.410909i \(-0.134789\pi\)
0.0999806 + 0.994989i \(0.468122\pi\)
\(464\) −2099.07 + 1211.90i −0.210015 + 0.121252i
\(465\) −5064.89 8772.65i −0.505115 0.874885i
\(466\) −4170.54 + 2407.86i −0.414585 + 0.239360i
\(467\) 5413.21i 0.536388i −0.963365 0.268194i \(-0.913573\pi\)
0.963365 0.268194i \(-0.0864269\pi\)
\(468\) 5691.31 + 3285.88i 0.562138 + 0.324551i
\(469\) 1328.86 + 2301.65i 0.130833 + 0.226610i
\(470\) 3431.71 0.336793
\(471\) 8097.82 0.792203
\(472\) −2666.87 4619.16i −0.260069 0.450453i
\(473\) 3543.87i 0.344498i
\(474\) 3727.78 6456.70i 0.361229 0.625667i
\(475\) 19899.6i 1.92222i
\(476\) −88.2028 50.9239i −0.00849321 0.00490356i
\(477\) 4699.75 8140.20i 0.451125 0.781372i
\(478\) −5966.91 + 10335.0i −0.570962 + 0.988935i
\(479\) −4700.30 + 2713.72i −0.448355 + 0.258858i −0.707135 0.707078i \(-0.750013\pi\)
0.258780 + 0.965936i \(0.416680\pi\)
\(480\) −3652.09 −0.347280
\(481\) 1.24185 19594.8i 0.000117720 1.85748i
\(482\) 4729.30 0.446917
\(483\) 7578.65 4375.53i 0.713955 0.412202i
\(484\) −2122.74 + 3676.70i −0.199356 + 0.345295i
\(485\) −9167.46 + 15878.5i −0.858295 + 1.48661i
\(486\) −7776.47 4489.74i −0.725818 0.419051i
\(487\) 13015.8i 1.21109i 0.795811 + 0.605545i \(0.207045\pi\)
−0.795811 + 0.605545i \(0.792955\pi\)
\(488\) −3052.42 + 5286.94i −0.283148 + 0.490427i
\(489\) 6458.49i 0.597266i
\(490\) −1926.61 3336.99i −0.177623 0.307653i
\(491\) −8167.85 −0.750733 −0.375367 0.926876i \(-0.622483\pi\)
−0.375367 + 0.926876i \(0.622483\pi\)
\(492\) 11761.8 1.07777
\(493\) 127.537 + 220.901i 0.0116511 + 0.0201802i
\(494\) 18878.5 + 10899.5i 1.71940 + 0.992697i
\(495\) 5221.44i 0.474114i
\(496\) 1229.87 710.065i 0.111336 0.0642800i
\(497\) 3238.21 + 5608.75i 0.292261 + 0.506211i
\(498\) 9554.66 5516.39i 0.859748 0.496376i
\(499\) 16660.1 + 9618.70i 1.49460 + 0.862910i 0.999981 0.00619792i \(-0.00197287\pi\)
0.494623 + 0.869108i \(0.335306\pi\)
\(500\) 1982.09 + 1144.36i 0.177283 + 0.102355i
\(501\) 13997.9 8081.70i 1.24827 0.720686i
\(502\) −374.640 648.896i −0.0333088 0.0576925i
\(503\) 6038.11 3486.10i 0.535240 0.309021i −0.207907 0.978149i \(-0.566665\pi\)
0.743148 + 0.669127i \(0.233332\pi\)
\(504\) 2282.84i 0.201757i
\(505\) −10060.7 5808.55i −0.886526 0.511836i
\(506\) 1403.06 + 2430.16i 0.123268 + 0.213506i
\(507\) −36458.8 −3.19367
\(508\) −4122.95 −0.360091
\(509\) 6493.86 + 11247.7i 0.565491 + 0.979460i 0.997004 + 0.0773529i \(0.0246468\pi\)
−0.431512 + 0.902107i \(0.642020\pi\)
\(510\) 384.336i 0.0333700i
\(511\) −1225.35 + 2122.37i −0.106079 + 0.183734i
\(512\) 512.000i 0.0441942i
\(513\) −5969.41 3446.44i −0.513754 0.296616i
\(514\) −1588.86 + 2751.99i −0.136346 + 0.236157i
\(515\) 8935.44 15476.6i 0.764549 1.32424i
\(516\) −5063.52 + 2923.43i −0.431994 + 0.249412i
\(517\) 1672.01 0.142234
\(518\) 5894.97 3402.96i 0.500019 0.288644i
\(519\) −28692.7 −2.42673
\(520\) 10164.5 5868.45i 0.857194 0.494901i
\(521\) 1407.68 2438.18i 0.118372 0.205026i −0.800751 0.598998i \(-0.795566\pi\)
0.919123 + 0.393972i \(0.128899\pi\)
\(522\) 2858.64 4951.31i 0.239692 0.415159i
\(523\) 2612.40 + 1508.27i 0.218417 + 0.126103i 0.605217 0.796060i \(-0.293086\pi\)
−0.386800 + 0.922164i \(0.626420\pi\)
\(524\) 1451.34i 0.120996i
\(525\) 8139.80 14098.6i 0.676667 1.17202i
\(526\) 5042.29i 0.417974i
\(527\) −74.7253 129.428i −0.00617663 0.0106982i
\(528\) −1779.38 −0.146662
\(529\) 4865.97 0.399932
\(530\) −8393.57 14538.1i −0.687912 1.19150i
\(531\) 10895.7 + 6290.64i 0.890458 + 0.514106i
\(532\) 7572.35i 0.617111i
\(533\) −32735.2 + 18899.7i −2.66026 + 1.53590i
\(534\) 2272.38 + 3935.87i 0.184149 + 0.318955i
\(535\) 27706.8 15996.5i 2.23901 1.29269i
\(536\) 1217.66 + 703.016i 0.0981248 + 0.0566524i
\(537\) 21446.3 + 12382.0i 1.72342 + 0.995016i
\(538\) −3754.63 + 2167.74i −0.300880 + 0.173713i
\(539\) −938.690 1625.86i −0.0750134 0.129927i
\(540\) −3214.01 + 1855.61i −0.256128 + 0.147876i
\(541\) 13211.4i 1.04991i 0.851130 + 0.524954i \(0.175918\pi\)
−0.851130 + 0.524954i \(0.824082\pi\)
\(542\) 12634.2 + 7294.33i 1.00126 + 0.578078i
\(543\) −8357.34 14475.3i −0.660493 1.14401i
\(544\) −53.8815 −0.00424660
\(545\) −7159.11 −0.562684
\(546\) −8916.77 15444.3i −0.698906 1.21054i
\(547\) 14450.3i 1.12952i 0.825255 + 0.564761i \(0.191031\pi\)
−0.825255 + 0.564761i \(0.808969\pi\)
\(548\) −2757.18 + 4775.58i −0.214929 + 0.372267i
\(549\) 14400.1i 1.11946i
\(550\) 4520.83 + 2610.10i 0.350489 + 0.202355i
\(551\) 9482.33 16423.9i 0.733141 1.26984i
\(552\) 2314.83 4009.40i 0.178488 0.309151i
\(553\) −7208.03 + 4161.56i −0.554279 + 0.320013i
\(554\) 3506.86 0.268939
\(555\) −22243.8 12844.3i −1.70125 0.982364i
\(556\) 1890.33 0.144187
\(557\) −12889.1 + 7441.53i −0.980484 + 0.566083i −0.902416 0.430866i \(-0.858208\pi\)
−0.0780675 + 0.996948i \(0.524875\pi\)
\(558\) −1674.91 + 2901.03i −0.127069 + 0.220090i
\(559\) 9395.16 16272.9i 0.710864 1.23125i
\(560\) 3530.84 + 2038.53i 0.266438 + 0.153828i
\(561\) 187.257i 0.0140927i
\(562\) −4489.55 + 7776.14i −0.336976 + 0.583659i
\(563\) 1078.27i 0.0807167i 0.999185 + 0.0403584i \(0.0128500\pi\)
−0.999185 + 0.0403584i \(0.987150\pi\)
\(564\) −1379.28 2388.98i −0.102975 0.178359i
\(565\) 35091.5 2.61294
\(566\) −13934.4 −1.03482
\(567\) 6671.78 + 11555.9i 0.494160 + 0.855909i
\(568\) 2967.25 + 1713.14i 0.219195 + 0.126552i
\(569\) 9857.95i 0.726304i −0.931730 0.363152i \(-0.881701\pi\)
0.931730 0.363152i \(-0.118299\pi\)
\(570\) 24746.9 14287.6i 1.81848 1.04990i
\(571\) −1583.74 2743.13i −0.116073 0.201044i 0.802135 0.597142i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(572\) 4952.36 2859.24i 0.362008 0.209005i
\(573\) 7048.56 + 4069.49i 0.513888 + 0.296693i
\(574\) −11371.3 6565.20i −0.826877 0.477398i
\(575\) −11762.4 + 6791.05i −0.853092 + 0.492533i
\(576\) 603.855 + 1045.91i 0.0436816 + 0.0756588i
\(577\) 6218.31 3590.14i 0.448651 0.259029i −0.258609 0.965982i \(-0.583264\pi\)
0.707260 + 0.706953i \(0.249931\pi\)
\(578\) 9820.33i 0.706699i
\(579\) 16681.6 + 9631.10i 1.19734 + 0.691286i
\(580\) −5105.42 8842.85i −0.365502 0.633068i
\(581\) −12316.6 −0.879480
\(582\) 14738.4 1.04970
\(583\) −4089.54 7083.29i −0.290517 0.503190i
\(584\) 1296.52i 0.0918670i
\(585\) −13842.6 + 23976.0i −0.978323 + 1.69451i
\(586\) 4255.76i 0.300006i
\(587\) 12557.9 + 7250.28i 0.882995 + 0.509798i 0.871645 0.490138i \(-0.163054\pi\)
0.0113504 + 0.999936i \(0.496387\pi\)
\(588\) −1548.70 + 2682.42i −0.108618 + 0.188131i
\(589\) −5555.80 + 9622.93i −0.388664 + 0.673185i
\(590\) 19459.3 11234.8i 1.35784 0.783951i
\(591\) 8779.67 0.611078
\(592\) 1800.70 3118.44i 0.125014 0.216498i
\(593\) 17193.2 1.19062 0.595311 0.803495i \(-0.297029\pi\)
0.595311 + 0.803495i \(0.297029\pi\)
\(594\) −1565.94 + 904.097i −0.108167 + 0.0624504i
\(595\) 214.529 371.576i 0.0147813 0.0256019i
\(596\) 3712.04 6429.43i 0.255119 0.441879i
\(597\) 21825.4 + 12600.9i 1.49624 + 0.863854i
\(598\) 14878.6i 1.01744i
\(599\) −345.402 + 598.254i −0.0235605 + 0.0408080i −0.877565 0.479457i \(-0.840834\pi\)
0.854005 + 0.520265i \(0.174167\pi\)
\(600\) 8612.55i 0.586010i
\(601\) 4310.22 + 7465.51i 0.292541 + 0.506697i 0.974410 0.224778i \(-0.0721657\pi\)
−0.681869 + 0.731475i \(0.738832\pi\)
\(602\) 6527.21 0.441909
\(603\) −3316.56 −0.223982
\(604\) 4766.24 + 8255.38i 0.321086 + 0.556137i
\(605\) −15489.0 8942.57i −1.04085 0.600938i
\(606\) 9338.34i 0.625980i
\(607\) −6586.57 + 3802.76i −0.440430 + 0.254282i −0.703780 0.710418i \(-0.748506\pi\)
0.263350 + 0.964700i \(0.415173\pi\)
\(608\) 2003.03 + 3469.36i 0.133608 + 0.231416i
\(609\) −13436.2 + 7757.39i −0.894026 + 0.516166i
\(610\) −22272.5 12859.0i −1.47834 0.853520i
\(611\) 7677.59 + 4432.66i 0.508350 + 0.293496i
\(612\) 110.068 63.5480i 0.00727002 0.00419735i
\(613\) −261.702 453.281i −0.0172432 0.0298660i 0.857275 0.514859i \(-0.172156\pi\)
−0.874518 + 0.484993i \(0.838822\pi\)
\(614\) −12373.3 + 7143.74i −0.813268 + 0.469541i
\(615\) 49549.3i 3.24881i
\(616\) 1720.31 + 993.219i 0.112521 + 0.0649642i
\(617\) −11965.5 20724.8i −0.780734 1.35227i −0.931515 0.363703i \(-0.881512\pi\)
0.150781 0.988567i \(-0.451821\pi\)
\(618\) −14365.4 −0.935050
\(619\) −6344.72 −0.411980 −0.205990 0.978554i \(-0.566041\pi\)
−0.205990 + 0.978554i \(0.566041\pi\)
\(620\) 2991.32 + 5181.12i 0.193765 + 0.335611i
\(621\) 4704.62i 0.304009i
\(622\) 875.922 1517.14i 0.0564651 0.0978003i
\(623\) 5073.60i 0.326275i
\(624\) −8170.64 4717.32i −0.524178 0.302634i
\(625\) 5113.81 8857.39i 0.327284 0.566873i
\(626\) 4362.75 7556.50i 0.278547 0.482458i
\(627\) 12057.2 6961.26i 0.767975 0.443390i
\(628\) −4782.57 −0.303894
\(629\) −328.176 189.500i −0.0208032 0.0120125i
\(630\) −9617.01 −0.608176
\(631\) −17527.7 + 10119.6i −1.10581 + 0.638439i −0.937741 0.347336i \(-0.887086\pi\)
−0.168069 + 0.985775i \(0.553753\pi\)
\(632\) −2201.63 + 3813.33i −0.138570 + 0.240010i
\(633\) −15585.8 + 26995.5i −0.978643 + 1.69506i
\(634\) 10013.0 + 5781.03i 0.627237 + 0.362136i
\(635\) 17368.9i 1.08546i
\(636\) −6747.12 + 11686.4i −0.420662 + 0.728607i
\(637\) 9954.24i 0.619154i
\(638\) −2487.48 4308.44i −0.154358 0.267355i
\(639\) −8081.94 −0.500339
\(640\) 2156.92 0.133219
\(641\) 6975.19 + 12081.4i 0.429803 + 0.744440i 0.996855 0.0792414i \(-0.0252498\pi\)
−0.567053 + 0.823681i \(0.691916\pi\)
\(642\) −22271.9 12858.7i −1.36916 0.790486i
\(643\) 9082.55i 0.557046i 0.960430 + 0.278523i \(0.0898449\pi\)
−0.960430 + 0.278523i \(0.910155\pi\)
\(644\) −4475.95 + 2584.19i −0.273877 + 0.158123i
\(645\) −12315.6 21331.3i −0.751826 1.30220i
\(646\) 365.106 210.794i 0.0222367 0.0128383i
\(647\) −26714.4 15423.6i −1.62327 0.937193i −0.986039 0.166516i \(-0.946748\pi\)
−0.637227 0.770676i \(-0.719919\pi\)
\(648\) 6113.50 + 3529.63i 0.370619 + 0.213977i
\(649\) 9481.03 5473.87i 0.573440 0.331076i
\(650\) 13839.3 + 23970.3i 0.835110 + 1.44645i
\(651\) 7872.41 4545.14i 0.473954 0.273638i
\(652\) 3814.39i 0.229115i
\(653\) −25950.6 14982.6i −1.55517 0.897879i −0.997707 0.0676776i \(-0.978441\pi\)
−0.557464 0.830201i \(-0.688226\pi\)
\(654\) 2877.40 + 4983.81i 0.172042 + 0.297985i
\(655\) 6114.11 0.364730
\(656\) −6946.50 −0.413438
\(657\) −1529.12 2648.51i −0.0908016 0.157273i
\(658\) 3079.55i 0.182452i
\(659\) 12415.0 21503.4i 0.733870 1.27110i −0.221347 0.975195i \(-0.571045\pi\)
0.955217 0.295905i \(-0.0956212\pi\)
\(660\) 7496.08i 0.442098i
\(661\) 23643.6 + 13650.6i 1.39127 + 0.803249i 0.993456 0.114219i \(-0.0364364\pi\)
0.397812 + 0.917467i \(0.369770\pi\)
\(662\) 7414.45 12842.2i 0.435303 0.753967i
\(663\) −496.438 + 859.855i −0.0290800 + 0.0503680i
\(664\) −5642.98 + 3257.98i −0.329804 + 0.190413i
\(665\) −31900.4 −1.86022
\(666\) −0.538321 + 8494.06i −3.13206e−5 + 0.494201i
\(667\) 12944.0 0.751415
\(668\) −8267.17 + 4773.05i −0.478842 + 0.276460i
\(669\) −6800.14 + 11778.2i −0.392987 + 0.680674i
\(670\) −2961.63 + 5129.69i −0.170773 + 0.295787i
\(671\) −10851.7 6265.22i −0.624329 0.360456i
\(672\) 3277.32i 0.188133i
\(673\) 6832.69 11834.6i 0.391354 0.677844i −0.601275 0.799042i \(-0.705340\pi\)
0.992628 + 0.121198i \(0.0386736\pi\)
\(674\) 9628.32i 0.550251i
\(675\) −4376.00 7579.45i −0.249529 0.432197i
\(676\) 21532.6 1.22511
\(677\) −25968.9 −1.47425 −0.737124 0.675758i \(-0.763816\pi\)
−0.737124 + 0.675758i \(0.763816\pi\)
\(678\) −14104.0 24428.9i −0.798912 1.38376i
\(679\) −14249.1 8226.72i −0.805346 0.464967i
\(680\) 226.989i 0.0128009i
\(681\) 13570.2 7834.76i 0.763599 0.440864i
\(682\) 1457.44 + 2524.36i 0.0818304 + 0.141734i
\(683\) 1939.61 1119.84i 0.108663 0.0627369i −0.444683 0.895688i \(-0.646684\pi\)
0.553347 + 0.832951i \(0.313350\pi\)
\(684\) −8183.55 4724.77i −0.457465 0.264117i
\(685\) −20118.3 11615.3i −1.12216 0.647880i
\(686\) 11978.3 6915.67i 0.666667 0.384900i
\(687\) −3561.11 6168.02i −0.197765 0.342539i
\(688\) 2990.52 1726.58i 0.165716 0.0956760i
\(689\) 43367.1i 2.39790i
\(690\) 16890.6 + 9751.78i 0.931903 + 0.538034i
\(691\) 2426.93 + 4203.57i 0.133611 + 0.231420i 0.925066 0.379807i \(-0.124010\pi\)
−0.791455 + 0.611227i \(0.790676\pi\)
\(692\) 16945.9 0.930907
\(693\) −4685.63 −0.256843
\(694\) 6483.43 + 11229.6i 0.354622 + 0.614224i
\(695\) 7963.47i 0.434635i
\(696\) −4103.96 + 7108.27i −0.223506 + 0.387124i
\(697\) 731.030i 0.0397270i
\(698\) −7533.23 4349.31i −0.408505 0.235851i
\(699\) −8153.95 + 14123.1i −0.441217 + 0.764210i
\(700\) −4807.37 + 8326.60i −0.259573 + 0.449594i
\(701\) 13809.4 7972.84i 0.744041 0.429572i −0.0794959 0.996835i \(-0.525331\pi\)
0.823537 + 0.567263i \(0.191998\pi\)
\(702\) −9587.40 −0.515460
\(703\) −1.78565 + 28175.5i −9.57998e−5 + 1.51160i
\(704\) 1050.90 0.0562605
\(705\) 10064.2 5810.55i 0.537643 0.310408i
\(706\) −5845.05 + 10123.9i −0.311588 + 0.539687i
\(707\) 5212.49 9028.30i 0.277278 0.480260i
\(708\) −15642.3 9031.06i −0.830327 0.479390i
\(709\) 22666.0i 1.20062i 0.799767 + 0.600311i \(0.204956\pi\)
−0.799767 + 0.600311i \(0.795044\pi\)
\(710\) −7217.02 + 12500.2i −0.381479 + 0.660741i
\(711\) 10386.4i 0.547850i
\(712\) −1342.07 2324.53i −0.0706405 0.122353i
\(713\) −7584.04 −0.398351
\(714\) −344.896 −0.0180776
\(715\) 12045.3 + 20863.0i 0.630024 + 1.09123i
\(716\) −12666.2 7312.82i −0.661114 0.381694i
\(717\) 40412.5i 2.10493i
\(718\) 19390.6 11195.2i 1.00787 0.581895i
\(719\) 4558.49 + 7895.54i 0.236444 + 0.409533i 0.959691 0.281056i \(-0.0906848\pi\)
−0.723248 + 0.690589i \(0.757351\pi\)
\(720\) −4406.14 + 2543.89i −0.228065 + 0.131674i
\(721\) 13888.5 + 8018.50i 0.717383 + 0.414181i
\(722\) −15265.3 8813.44i −0.786866 0.454297i
\(723\) 13869.6 8007.63i 0.713439 0.411904i
\(724\) 4935.84 + 8549.13i 0.253369 + 0.438848i
\(725\) 20853.7 12039.9i 1.06826 0.616758i
\(726\) 14376.9i 0.734952i
\(727\) −1259.67 727.271i −0.0642622 0.0371018i 0.467525 0.883980i \(-0.345146\pi\)
−0.531787 + 0.846878i \(0.678479\pi\)
\(728\) 5266.24 + 9121.40i 0.268104 + 0.464370i
\(729\) −6583.01 −0.334451
\(730\) −5461.90 −0.276923
\(731\) −181.700 314.714i −0.00919346 0.0159235i
\(732\) 20673.3i 1.04386i
\(733\) 3073.97 5324.27i 0.154897 0.268290i −0.778124 0.628110i \(-0.783829\pi\)
0.933022 + 0.359820i \(0.117162\pi\)
\(734\) 5036.57i 0.253274i
\(735\) −11300.3 6524.26i −0.567101 0.327416i
\(736\) −1367.14 + 2367.95i −0.0684692 + 0.118592i
\(737\) −1442.97 + 2499.30i −0.0721202 + 0.124916i
\(738\) 14190.2 8192.73i 0.707790 0.408643i
\(739\) 20606.1 1.02572 0.512860 0.858472i \(-0.328586\pi\)
0.512860 + 0.858472i \(0.328586\pi\)
\(740\) 13137.2 + 7585.87i 0.652611 + 0.376841i
\(741\) 73819.9 3.65971
\(742\) 13046.2 7532.24i 0.645474 0.372665i
\(743\) 13443.9 23285.5i 0.663806 1.14975i −0.315801 0.948825i \(-0.602273\pi\)
0.979608 0.200921i \(-0.0643933\pi\)
\(744\) 2404.56 4164.81i 0.118488 0.205228i
\(745\) 27085.6 + 15637.9i 1.33200 + 0.769029i
\(746\) 7710.30i 0.378410i
\(747\) 7684.94 13310.7i 0.376409 0.651959i
\(748\) 110.594i 0.00540605i
\(749\) 14355.0 + 24863.6i 0.700293 + 1.21294i
\(750\) 7750.49 0.377344
\(751\) −28416.5 −1.38074 −0.690369 0.723457i \(-0.742552\pi\)
−0.690369 + 0.723457i \(0.742552\pi\)
\(752\) 814.602 + 1410.93i 0.0395020 + 0.0684194i
\(753\) −2197.41 1268.68i −0.106346 0.0613986i
\(754\) 26378.2i 1.27406i
\(755\) −34777.8 + 20079.0i −1.67641 + 0.967878i
\(756\) −1665.19 2884.20i −0.0801091 0.138753i
\(757\) 2452.37 1415.87i 0.117745 0.0679799i −0.439971 0.898012i \(-0.645011\pi\)
0.557716 + 0.830032i \(0.311678\pi\)
\(758\) −94.2318 54.4047i −0.00451537 0.00260695i
\(759\) 8229.47 + 4751.29i 0.393559 + 0.227221i
\(760\) −14615.5 + 8438.27i −0.697579 + 0.402748i
\(761\) 16346.9 + 28313.7i 0.778680 + 1.34871i 0.932703 + 0.360646i \(0.117444\pi\)
−0.154023 + 0.988067i \(0.549223\pi\)
\(762\) −12091.4 + 6980.95i −0.574834 + 0.331881i
\(763\) 6424.46i 0.304824i
\(764\) −4162.88 2403.44i −0.197130 0.113813i
\(765\) 267.712 + 463.690i 0.0126525 + 0.0219147i
\(766\) 1846.18 0.0870823
\(767\) 58047.1 2.73267
\(768\) −866.915 1501.54i −0.0407319 0.0705497i
\(769\) 38366.0i 1.79911i −0.436809 0.899555i \(-0.643891\pi\)
0.436809 0.899555i \(-0.356109\pi\)
\(770\) −4184.18 + 7247.21i −0.195828 + 0.339183i
\(771\) 10761.0i 0.502656i
\(772\) −9852.12 5688.13i −0.459308 0.265182i
\(773\) −3972.86 + 6881.20i −0.184856 + 0.320181i −0.943528 0.331292i \(-0.892515\pi\)
0.758672 + 0.651473i \(0.225849\pi\)
\(774\) −4072.66 + 7054.05i −0.189133 + 0.327588i
\(775\) −12218.4 + 7054.29i −0.566319 + 0.326965i
\(776\) −8704.51 −0.402672
\(777\) 11526.3 19961.2i 0.532179 0.921626i
\(778\) −988.271 −0.0455414
\(779\) 47070.1 27175.9i 2.16490 1.24991i
\(780\) 19872.9 34420.8i 0.912259 1.58008i
\(781\) −3516.30 + 6090.41i −0.161105 + 0.279042i
\(782\) 249.197 + 143.874i 0.0113955 + 0.00657918i
\(783\) 8340.82i 0.380685i
\(784\) 914.659 1584.24i 0.0416663 0.0721682i
\(785\) 20147.7i 0.916056i
\(786\) −2457.39 4256.33i −0.111517 0.193153i
\(787\) −18768.7 −0.850106 −0.425053 0.905168i \(-0.639745\pi\)
−0.425053 + 0.905168i \(0.639745\pi\)
\(788\) −5185.27 −0.234413
\(789\) −8537.57 14787.5i −0.385229 0.667236i
\(790\) −16064.6 9274.88i −0.723483 0.417703i
\(791\) 31490.5i 1.41551i
\(792\) −2146.77 + 1239.44i −0.0963159 + 0.0556080i
\(793\) −33219.4 57537.8i −1.48759 2.57658i
\(794\) −7359.35 + 4248.92i −0.328934 + 0.189910i
\(795\) −49231.6 28423.9i −2.19631 1.26804i
\(796\) −12890.1 7442.09i −0.573966 0.331379i
\(797\) 19946.1 11515.9i 0.886484 0.511812i 0.0136929 0.999906i \(-0.495641\pi\)
0.872791 + 0.488095i \(0.162308\pi\)
\(798\) 12821.5 + 22207.4i 0.568765 + 0.985130i
\(799\) 148.483 85.7265i 0.00657439 0.00379573i
\(800\) 5086.57i 0.224797i
\(801\) 5483.11 + 3165.68i 0.241868 + 0.139643i
\(802\) 3788.88 + 6562.53i 0.166820 + 0.288941i
\(803\) −2661.16 −0.116949
\(804\) 4761.37 0.208857
\(805\) −10886.5 18856.0i −0.476646 0.825574i
\(806\) 15455.3i 0.675421i
\(807\) −7340.80 + 12714.6i −0.320209 + 0.554618i
\(808\) 5515.22i 0.240130i
\(809\) 2273.28 + 1312.48i 0.0987937 + 0.0570386i 0.548583 0.836096i \(-0.315168\pi\)
−0.449789 + 0.893135i \(0.648501\pi\)
\(810\) −14869.4 + 25754.6i −0.645011 + 1.11719i
\(811\) 5944.94 10296.9i 0.257405 0.445838i −0.708141 0.706071i \(-0.750466\pi\)
0.965546 + 0.260233i \(0.0837994\pi\)
\(812\) 7935.41 4581.51i 0.342954 0.198004i
\(813\) 49402.9 2.13116
\(814\) 6400.74 + 3696.01i 0.275609 + 0.159146i
\(815\) −16069.0 −0.690642
\(816\) −158.018 + 91.2318i −0.00677909 + 0.00391391i
\(817\) −13509.3 + 23398.9i −0.578497 + 1.00199i
\(818\) −11387.1 + 19723.0i −0.486724 + 0.843030i
\(819\) −21515.6 12422.1i −0.917970 0.529990i
\(820\) 29263.8i 1.24626i
\(821\) −7166.10 + 12412.0i −0.304627 + 0.527629i −0.977178 0.212421i \(-0.931865\pi\)
0.672551 + 0.740050i \(0.265198\pi\)
\(822\) 18673.8i 0.792363i
\(823\) −8584.24 14868.3i −0.363582 0.629742i 0.624966 0.780652i \(-0.285113\pi\)
−0.988548 + 0.150910i \(0.951780\pi\)
\(824\) 8484.20 0.358691
\(825\) 17677.6 0.746008
\(826\) 10081.9 + 17462.4i 0.424692 + 0.735588i
\(827\) −7620.91 4399.93i −0.320441 0.185007i 0.331148 0.943579i \(-0.392564\pi\)
−0.651589 + 0.758572i \(0.725897\pi\)
\(828\) 6449.63i 0.270701i
\(829\) −35843.6 + 20694.3i −1.50169 + 0.867001i −0.501692 + 0.865046i \(0.667289\pi\)
−0.999998 + 0.00195493i \(0.999378\pi\)
\(830\) −13725.0 23772.4i −0.573979 0.994161i
\(831\) 10284.6 5937.79i 0.429323 0.247870i
\(832\) 4825.58 + 2786.05i 0.201078 + 0.116092i
\(833\) −166.721 96.2562i −0.00693461 0.00400370i
\(834\) 5543.76 3200.69i 0.230173 0.132891i
\(835\) −20107.6 34827.5i −0.833358 1.44342i
\(836\) −7121.01 + 4111.32i −0.294600 + 0.170087i
\(837\) 4886.98i 0.201814i
\(838\) −12014.0 6936.28i −0.495246 0.285930i
\(839\) 6796.12 + 11771.2i 0.279652 + 0.484372i 0.971298 0.237865i \(-0.0764475\pi\)
−0.691646 + 0.722237i \(0.743114\pi\)
\(840\) 13806.5 0.567107
\(841\) 1440.55 0.0590657
\(842\) 9388.82 + 16261.9i 0.384276 + 0.665585i
\(843\) 30406.7i 1.24231i
\(844\) 9204.99 15943.5i 0.375413 0.650235i
\(845\) 90711.2i 3.69297i
\(846\) −3328.12 1921.49i −0.135252 0.0780877i
\(847\) 8024.90 13899.5i 0.325548 0.563865i
\(848\) 3984.85 6901.96i 0.161368 0.279498i
\(849\) −40865.4 + 23593.6i −1.65194 + 0.953747i
\(850\) 535.297 0.0216006
\(851\) −16654.9 + 9614.29i −0.670883 + 0.387278i
\(852\) 11602.7 0.466552
\(853\) −34986.4 + 20199.4i −1.40435 + 0.810802i −0.994835 0.101502i \(-0.967635\pi\)
−0.409514 + 0.912304i \(0.634302\pi\)
\(854\) 11539.5 19987.0i 0.462380 0.800866i
\(855\) 19904.3 34475.2i 0.796154 1.37898i
\(856\) 13153.8 + 7594.35i 0.525219 + 0.303235i
\(857\) 10500.4i 0.418539i −0.977858 0.209270i \(-0.932891\pi\)
0.977858 0.209270i \(-0.0671087\pi\)
\(858\) 9682.51 16770.6i 0.385263 0.667295i
\(859\) 30169.6i 1.19834i 0.800622 + 0.599169i \(0.204502\pi\)
−0.800622 + 0.599169i \(0.795498\pi\)
\(860\) 7273.62 + 12598.3i 0.288405 + 0.499532i
\(861\) −44464.6 −1.75999
\(862\) 2398.34 0.0947654
\(863\) 3487.86 + 6041.14i 0.137576 + 0.238288i 0.926579 0.376101i \(-0.122736\pi\)
−0.789003 + 0.614390i \(0.789402\pi\)
\(864\) −1525.85 880.952i −0.0600817 0.0346882i
\(865\) 71388.9i 2.80612i
\(866\) −9124.33 + 5267.93i −0.358034 + 0.206711i
\(867\) −16627.7 28800.1i −0.651334 1.12814i
\(868\) −4649.45 + 2684.36i −0.181812 + 0.104969i
\(869\) −7827.03 4518.94i −0.305539 0.176403i
\(870\) −29945.3 17288.9i −1.16694 0.673735i
\(871\) −13251.8 + 7650.93i −0.515522 + 0.297637i
\(872\) −1699.39 2943.44i −0.0659963 0.114309i
\(873\) 17781.5 10266.1i 0.689360 0.398002i
\(874\) 21393.9i 0.827987i
\(875\) −7493.16 4326.18i −0.289503 0.167145i
\(876\) 2195.26 + 3802.30i 0.0846699 + 0.146653i
\(877\) 21969.1 0.845887 0.422944 0.906156i \(-0.360997\pi\)
0.422944 + 0.906156i \(0.360997\pi\)
\(878\) 31091.9 1.19510
\(879\) −7205.82 12480.8i −0.276503 0.478917i
\(880\) 4427.18i 0.169591i
\(881\) −12876.9 + 22303.4i −0.492433 + 0.852919i −0.999962 0.00871576i \(-0.997226\pi\)
0.507529 + 0.861635i \(0.330559\pi\)
\(882\) 4315.01i 0.164732i
\(883\) 11974.9 + 6913.71i 0.456385 + 0.263494i 0.710523 0.703674i \(-0.248458\pi\)
−0.254138 + 0.967168i \(0.581792\pi\)
\(884\) 293.196 507.830i 0.0111553 0.0193215i
\(885\) 38045.5 65896.8i 1.44507 2.50293i
\(886\) 5334.66 3079.97i 0.202281 0.116787i
\(887\) 18967.7 0.718007 0.359004 0.933336i \(-0.383117\pi\)
0.359004 + 0.933336i \(0.383117\pi\)
\(888\) 0.772833 12194.4i 2.92056e−5 0.460829i
\(889\) 15586.6 0.588028
\(890\) 9792.63 5653.78i 0.368820 0.212938i
\(891\) −7244.73 + 12548.2i −0.272399 + 0.471809i
\(892\) 4016.16 6956.19i 0.150752 0.261111i
\(893\) −11039.6 6373.73i −0.413692 0.238845i
\(894\) 25140.8i 0.940529i
\(895\) 30807.0 53359.4i 1.15058 1.99286i
\(896\) 1935.59i 0.0721689i
\(897\) 25192.3 + 43634.3i 0.937732 + 1.62420i
\(898\) 5123.48 0.190393
\(899\) 13445.7 0.498822
\(900\) −5999.12 10390.8i −0.222190 0.384844i
\(901\) −726.343 419.355i −0.0268568 0.0155058i
\(902\) 14258.0i 0.526319i
\(903\) 19142.3 11051.8i 0.705445 0.407289i
\(904\) 8329.84 + 14427.7i 0.306467 + 0.530817i
\(905\) −36015.3 + 20793.4i −1.32286 + 0.763754i
\(906\) 27955.9 + 16140.3i 1.02514 + 0.591862i
\(907\) −28140.9 16247.1i −1.03021 0.594793i −0.113167 0.993576i \(-0.536099\pi\)
−0.917045 + 0.398783i \(0.869433\pi\)
\(908\) −8014.56 + 4627.21i −0.292921 + 0.169118i
\(909\) 6504.67 + 11266.4i 0.237345 + 0.411093i
\(910\) −38426.1 + 22185.3i −1.39980 + 0.808172i
\(911\) 3300.84i 0.120046i 0.998197 + 0.0600228i \(0.0191173\pi\)
−0.998197 + 0.0600228i \(0.980883\pi\)
\(912\) 11748.6 + 6783.05i 0.426573 + 0.246282i
\(913\) −6687.14 11582.5i −0.242401 0.419851i
\(914\) 28015.1 1.01385
\(915\) −87091.4 −3.14661
\(916\) 2103.19 + 3642.83i 0.0758639 + 0.131400i
\(917\) 5486.69i 0.197586i
\(918\) −92.7089 + 160.577i −0.00333317 + 0.00577322i
\(919\) 40530.5i 1.45482i −0.686203 0.727410i \(-0.740724\pi\)
0.686203 0.727410i \(-0.259276\pi\)
\(920\) −9975.57 5759.40i −0.357483 0.206393i
\(921\) −24191.5 + 41900.9i −0.865511 + 1.49911i
\(922\) 118.003 204.386i 0.00421498 0.00730055i
\(923\) −32292.6 + 18644.1i −1.15160 + 0.664874i
\(924\) 6726.85 0.239499
\(925\) −17889.4 + 30980.8i −0.635891 + 1.10123i
\(926\) −23275.8 −0.826014
\(927\) −17331.4 + 10006.3i −0.614066 + 0.354531i
\(928\) 2423.80 4198.14i 0.0857383 0.148503i
\(929\) −15798.2 + 27363.2i −0.557935 + 0.966371i 0.439734 + 0.898128i \(0.355073\pi\)
−0.997669 + 0.0682431i \(0.978261\pi\)
\(930\) 17545.3 + 10129.8i 0.618637 + 0.357170i
\(931\) 14313.2i 0.503864i
\(932\) 4815.72 8341.07i 0.169253 0.293156i
\(933\) 5932.42i 0.208166i
\(934\) 5413.21 + 9375.95i 0.189642 + 0.328469i
\(935\) 465.905 0.0162960
\(936\) −13143.5 −0.458984
\(937\) 151.865 + 263.039i 0.00529480 + 0.00917086i 0.868661 0.495408i \(-0.164981\pi\)
−0.863366 + 0.504578i \(0.831648\pi\)
\(938\) −4603.29 2657.71i −0.160237 0.0925132i
\(939\) 29547.9i 1.02690i
\(940\) −5943.89 + 3431.71i −0.206243 + 0.119074i
\(941\) 16266.0 + 28173.5i 0.563502 + 0.976015i 0.997187 + 0.0749502i \(0.0238798\pi\)
−0.433685 + 0.901065i \(0.642787\pi\)
\(942\) −14025.8 + 8097.82i −0.485123 + 0.280086i
\(943\) 32126.9 + 18548.5i 1.10943 + 0.640531i
\(944\) 9238.31 + 5333.74i 0.318518 + 0.183897i
\(945\) 12150.4 7015.03i 0.418256 0.241480i
\(946\) 3543.87 + 6138.17i 0.121798 + 0.210961i
\(947\) −14211.7 + 8205.12i −0.487664 + 0.281553i −0.723605 0.690214i \(-0.757516\pi\)
0.235941 + 0.971767i \(0.424183\pi\)
\(948\) 14911.1i 0.510855i
\(949\) −12219.6 7055.00i −0.417983 0.241323i
\(950\) −19899.6 34467.0i −0.679607 1.17711i
\(951\) 39153.6 1.33506
\(952\) 203.696 0.00693468
\(953\) −8490.84 14706.6i −0.288610 0.499887i 0.684868 0.728667i \(-0.259860\pi\)
−0.973478 + 0.228780i \(0.926526\pi\)
\(954\) 18799.0i 0.637987i
\(955\) 10125.1 17537.1i 0.343078 0.594229i
\(956\) 23867.6i 0.807462i
\(957\) −14590.0 8423.56i −0.492820 0.284530i
\(958\) 5427.44 9400.60i 0.183040 0.317035i
\(959\) 10423.4 18053.8i 0.350978 0.607911i
\(960\) 6325.61 3652.09i 0.212665 0.122782i
\(961\) 21913.0 0.735557
\(962\) 19592.7 + 33940.5i 0.656645 + 1.13751i
\(963\) −35827.2 −1.19887
\(964\) −8191.39 + 4729.30i −0.273680 + 0.158009i
\(965\) 23962.6 41504.5i 0.799362 1.38453i
\(966\) −8751.07 + 15157.3i −0.291471 + 0.504843i
\(967\) −481.795 278.165i −0.0160222 0.00925044i 0.491967 0.870614i \(-0.336278\pi\)
−0.507990 + 0.861363i \(0.669611\pi\)
\(968\) 8490.97i 0.281932i
\(969\) 713.829 1236.39i 0.0236651 0.0409892i
\(970\) 36669.9i 1.21381i
\(971\) 6766.45 + 11719.8i 0.223631 + 0.387340i 0.955908 0.293667i \(-0.0948756\pi\)
−0.732277 + 0.681007i \(0.761542\pi\)
\(972\) 17959.0 0.592628
\(973\) −7146.27 −0.235456
\(974\) −13015.8 22544.0i −0.428185 0.741638i
\(975\) 81172.9 + 46865.2i 2.66627 + 1.53937i
\(976\) 12209.7i 0.400432i
\(977\) 6481.97 3742.36i 0.212258 0.122547i −0.390102 0.920772i \(-0.627560\pi\)
0.602361 + 0.798224i \(0.294227\pi\)
\(978\) 6458.49 + 11186.4i 0.211166 + 0.365749i
\(979\) 4771.19 2754.65i 0.155759 0.0899275i
\(980\) 6673.98 + 3853.23i 0.217543 + 0.125599i
\(981\) 6943.01 + 4008.55i 0.225966 + 0.130462i
\(982\) 14147.1 8167.85i 0.459728 0.265424i
\(983\) −2587.38 4481.47i −0.0839517 0.145409i 0.820992 0.570939i \(-0.193421\pi\)
−0.904944 + 0.425531i \(0.860087\pi\)
\(984\) −20372.0 + 11761.8i −0.659995 + 0.381048i
\(985\) 21844.2i 0.706614i
\(986\) −441.801 255.074i −0.0142696 0.00823855i
\(987\) 5214.28 + 9031.40i 0.168158 + 0.291259i
\(988\) −43598.0 −1.40389
\(989\) −18441.1 −0.592916
\(990\) −5221.44 9043.80i −0.167624 0.290334i
\(991\) 52973.7i 1.69805i −0.528354 0.849024i \(-0.677191\pi\)
0.528354 0.849024i \(-0.322809\pi\)
\(992\) −1420.13 + 2459.74i −0.0454528 + 0.0787266i
\(993\) 50216.4i 1.60480i
\(994\) −11217.5 6476.43i −0.357945 0.206660i
\(995\) 31351.6 54302.6i 0.998908 1.73016i
\(996\) −11032.8 + 19109.3i −0.350991 + 0.607934i
\(997\) 16252.7 9383.50i 0.516277 0.298073i −0.219133 0.975695i \(-0.570323\pi\)
0.735410 + 0.677622i \(0.236990\pi\)
\(998\) −38474.8 −1.22034
\(999\) −6195.23 10732.0i −0.196204 0.339886i
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 74.4.e.a.11.1 20
3.2 odd 2 666.4.s.d.307.6 20
37.27 even 6 inner 74.4.e.a.27.1 yes 20
111.101 odd 6 666.4.s.d.397.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.e.a.11.1 20 1.1 even 1 trivial
74.4.e.a.27.1 yes 20 37.27 even 6 inner
666.4.s.d.307.6 20 3.2 odd 2
666.4.s.d.397.6 20 111.101 odd 6