Properties

Label 100.4.e.e.43.6
Level $100$
Weight $4$
Character 100.43
Analytic conductor $5.900$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [100,4,Mod(7,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.e (of order \(4\), 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: \(5.90019100057\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.6
Root \(1.13579 + 1.64620i\) of defining polynomial
Character \(\chi\) \(=\) 100.43
Dual form 100.4.e.e.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.78199 - 0.510409i) q^{2} +(-4.02923 + 4.02923i) q^{3} +(7.47897 - 2.83991i) q^{4} +(-9.15273 + 13.2658i) q^{6} +(14.4440 + 14.4440i) q^{7} +(19.3569 - 11.7179i) q^{8} -5.46937i q^{9} +O(q^{10})\) \(q+(2.78199 - 0.510409i) q^{2} +(-4.02923 + 4.02923i) q^{3} +(7.47897 - 2.83991i) q^{4} +(-9.15273 + 13.2658i) q^{6} +(14.4440 + 14.4440i) q^{7} +(19.3569 - 11.7179i) q^{8} -5.46937i q^{9} +47.0607i q^{11} +(-18.6918 + 41.5771i) q^{12} +(8.79525 + 8.79525i) q^{13} +(47.5554 + 32.8107i) q^{14} +(47.8698 - 42.4791i) q^{16} +(26.4898 - 26.4898i) q^{17} +(-2.79162 - 15.2157i) q^{18} -49.8054 q^{19} -116.396 q^{21} +(24.0202 + 130.922i) q^{22} +(41.2762 - 41.2762i) q^{23} +(-30.7792 + 125.208i) q^{24} +(28.9575 + 19.9791i) q^{26} +(-86.7518 - 86.7518i) q^{27} +(149.046 + 67.0065i) q^{28} -247.406i q^{29} -62.3240i q^{31} +(111.492 - 142.610i) q^{32} +(-189.618 - 189.618i) q^{33} +(60.1738 - 87.2150i) q^{34} +(-15.5325 - 40.9052i) q^{36} +(73.2182 - 73.2182i) q^{37} +(-138.558 + 25.4211i) q^{38} -70.8761 q^{39} +118.624 q^{41} +(-323.814 + 59.4097i) q^{42} +(-245.335 + 245.335i) q^{43} +(133.648 + 351.965i) q^{44} +(93.7624 - 135.898i) q^{46} +(-125.525 - 125.525i) q^{47} +(-21.7203 + 364.037i) q^{48} +74.2578i q^{49} +213.467i q^{51} +(90.7571 + 40.8017i) q^{52} +(326.574 + 326.574i) q^{53} +(-285.622 - 197.064i) q^{54} +(448.845 + 110.337i) q^{56} +(200.677 - 200.677i) q^{57} +(-126.278 - 688.282i) q^{58} -365.123 q^{59} -268.160 q^{61} +(-31.8107 - 173.385i) q^{62} +(78.9995 - 78.9995i) q^{63} +(237.380 - 453.646i) q^{64} +(-624.299 - 430.733i) q^{66} +(112.617 + 112.617i) q^{67} +(122.888 - 273.345i) q^{68} +332.623i q^{69} -559.873i q^{71} +(-64.0897 - 105.870i) q^{72} +(-215.825 - 215.825i) q^{73} +(166.321 - 241.064i) q^{74} +(-372.493 + 141.443i) q^{76} +(-679.744 + 679.744i) q^{77} +(-197.177 + 36.1758i) q^{78} +1172.36 q^{79} +846.759 q^{81} +(330.012 - 60.5470i) q^{82} +(592.561 - 592.561i) q^{83} +(-870.524 + 330.555i) q^{84} +(-557.299 + 807.742i) q^{86} +(996.857 + 996.857i) q^{87} +(551.454 + 910.949i) q^{88} +552.071i q^{89} +254.077i q^{91} +(191.483 - 425.924i) q^{92} +(251.118 + 251.118i) q^{93} +(-413.277 - 285.139i) q^{94} +(125.382 + 1023.83i) q^{96} +(-460.651 + 460.651i) q^{97} +(37.9019 + 206.585i) q^{98} +257.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78199 0.510409i 0.983583 0.180457i
\(3\) −4.02923 + 4.02923i −0.775425 + 0.775425i −0.979049 0.203624i \(-0.934728\pi\)
0.203624 + 0.979049i \(0.434728\pi\)
\(4\) 7.47897 2.83991i 0.934871 0.354989i
\(5\) 0 0
\(6\) −9.15273 + 13.2658i −0.622764 + 0.902626i
\(7\) 14.4440 + 14.4440i 0.779902 + 0.779902i 0.979814 0.199912i \(-0.0640655\pi\)
−0.199912 + 0.979814i \(0.564066\pi\)
\(8\) 19.3569 11.7179i 0.855463 0.517864i
\(9\) 5.46937i 0.202569i
\(10\) 0 0
\(11\) 47.0607i 1.28994i 0.764209 + 0.644969i \(0.223130\pi\)
−0.764209 + 0.644969i \(0.776870\pi\)
\(12\) −18.6918 + 41.5771i −0.449655 + 1.00019i
\(13\) 8.79525 + 8.79525i 0.187643 + 0.187643i 0.794676 0.607033i \(-0.207640\pi\)
−0.607033 + 0.794676i \(0.707640\pi\)
\(14\) 47.5554 + 32.8107i 0.907837 + 0.626360i
\(15\) 0 0
\(16\) 47.8698 42.4791i 0.747966 0.663737i
\(17\) 26.4898 26.4898i 0.377925 0.377925i −0.492428 0.870353i \(-0.663891\pi\)
0.870353 + 0.492428i \(0.163891\pi\)
\(18\) −2.79162 15.2157i −0.0365550 0.199244i
\(19\) −49.8054 −0.601376 −0.300688 0.953723i \(-0.597216\pi\)
−0.300688 + 0.953723i \(0.597216\pi\)
\(20\) 0 0
\(21\) −116.396 −1.20951
\(22\) 24.0202 + 130.922i 0.232778 + 1.26876i
\(23\) 41.2762 41.2762i 0.374204 0.374204i −0.494802 0.869006i \(-0.664759\pi\)
0.869006 + 0.494802i \(0.164759\pi\)
\(24\) −30.7792 + 125.208i −0.261782 + 1.06491i
\(25\) 0 0
\(26\) 28.9575 + 19.9791i 0.218424 + 0.150701i
\(27\) −86.7518 86.7518i −0.618348 0.618348i
\(28\) 149.046 + 67.0065i 1.00596 + 0.452251i
\(29\) 247.406i 1.58421i −0.610382 0.792107i \(-0.708984\pi\)
0.610382 0.792107i \(-0.291016\pi\)
\(30\) 0 0
\(31\) 62.3240i 0.361088i −0.983567 0.180544i \(-0.942214\pi\)
0.983567 0.180544i \(-0.0577858\pi\)
\(32\) 111.492 142.610i 0.615911 0.787816i
\(33\) −189.618 189.618i −1.00025 1.00025i
\(34\) 60.1738 87.2150i 0.303521 0.439919i
\(35\) 0 0
\(36\) −15.5325 40.9052i −0.0719098 0.189376i
\(37\) 73.2182 73.2182i 0.325324 0.325324i −0.525481 0.850805i \(-0.676115\pi\)
0.850805 + 0.525481i \(0.176115\pi\)
\(38\) −138.558 + 25.4211i −0.591503 + 0.108522i
\(39\) −70.8761 −0.291007
\(40\) 0 0
\(41\) 118.624 0.451854 0.225927 0.974144i \(-0.427459\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(42\) −323.814 + 59.4097i −1.18966 + 0.218265i
\(43\) −245.335 + 245.335i −0.870076 + 0.870076i −0.992480 0.122404i \(-0.960940\pi\)
0.122404 + 0.992480i \(0.460940\pi\)
\(44\) 133.648 + 351.965i 0.457913 + 1.20593i
\(45\) 0 0
\(46\) 93.7624 135.898i 0.300533 0.435588i
\(47\) −125.525 125.525i −0.389567 0.389567i 0.484966 0.874533i \(-0.338832\pi\)
−0.874533 + 0.484966i \(0.838832\pi\)
\(48\) −21.7203 + 364.037i −0.0653138 + 1.09467i
\(49\) 74.2578i 0.216495i
\(50\) 0 0
\(51\) 213.467i 0.586105i
\(52\) 90.7571 + 40.8017i 0.242033 + 0.108811i
\(53\) 326.574 + 326.574i 0.846385 + 0.846385i 0.989680 0.143295i \(-0.0457699\pi\)
−0.143295 + 0.989680i \(0.545770\pi\)
\(54\) −285.622 197.064i −0.719782 0.496611i
\(55\) 0 0
\(56\) 448.845 + 110.337i 1.07106 + 0.263294i
\(57\) 200.677 200.677i 0.466322 0.466322i
\(58\) −126.278 688.282i −0.285882 1.55821i
\(59\) −365.123 −0.805677 −0.402839 0.915271i \(-0.631976\pi\)
−0.402839 + 0.915271i \(0.631976\pi\)
\(60\) 0 0
\(61\) −268.160 −0.562858 −0.281429 0.959582i \(-0.590808\pi\)
−0.281429 + 0.959582i \(0.590808\pi\)
\(62\) −31.8107 173.385i −0.0651608 0.355160i
\(63\) 78.9995 78.9995i 0.157984 0.157984i
\(64\) 237.380 453.646i 0.463633 0.886027i
\(65\) 0 0
\(66\) −624.299 430.733i −1.16433 0.803328i
\(67\) 112.617 + 112.617i 0.205349 + 0.205349i 0.802287 0.596938i \(-0.203616\pi\)
−0.596938 + 0.802287i \(0.703616\pi\)
\(68\) 122.888 273.345i 0.219152 0.487469i
\(69\) 332.623i 0.580334i
\(70\) 0 0
\(71\) 559.873i 0.935841i −0.883771 0.467921i \(-0.845003\pi\)
0.883771 0.467921i \(-0.154997\pi\)
\(72\) −64.0897 105.870i −0.104903 0.173290i
\(73\) −215.825 215.825i −0.346033 0.346033i 0.512597 0.858629i \(-0.328684\pi\)
−0.858629 + 0.512597i \(0.828684\pi\)
\(74\) 166.321 241.064i 0.261276 0.378690i
\(75\) 0 0
\(76\) −372.493 + 141.443i −0.562209 + 0.213482i
\(77\) −679.744 + 679.744i −1.00603 + 1.00603i
\(78\) −197.177 + 36.1758i −0.286229 + 0.0525142i
\(79\) 1172.36 1.66963 0.834816 0.550528i \(-0.185574\pi\)
0.834816 + 0.550528i \(0.185574\pi\)
\(80\) 0 0
\(81\) 846.759 1.16153
\(82\) 330.012 60.5470i 0.444436 0.0815402i
\(83\) 592.561 592.561i 0.783639 0.783639i −0.196804 0.980443i \(-0.563056\pi\)
0.980443 + 0.196804i \(0.0630562\pi\)
\(84\) −870.524 + 330.555i −1.13074 + 0.429363i
\(85\) 0 0
\(86\) −557.299 + 807.742i −0.698781 + 1.01280i
\(87\) 996.857 + 996.857i 1.22844 + 1.22844i
\(88\) 551.454 + 910.949i 0.668013 + 1.10349i
\(89\) 552.071i 0.657522i 0.944413 + 0.328761i \(0.106631\pi\)
−0.944413 + 0.328761i \(0.893369\pi\)
\(90\) 0 0
\(91\) 254.077i 0.292687i
\(92\) 191.483 425.924i 0.216994 0.482670i
\(93\) 251.118 + 251.118i 0.279997 + 0.279997i
\(94\) −413.277 285.139i −0.453471 0.312871i
\(95\) 0 0
\(96\) 125.382 + 1023.83i 0.133299 + 1.08849i
\(97\) −460.651 + 460.651i −0.482186 + 0.482186i −0.905829 0.423643i \(-0.860751\pi\)
0.423643 + 0.905829i \(0.360751\pi\)
\(98\) 37.9019 + 206.585i 0.0390680 + 0.212941i
\(99\) 257.392 0.261302
\(100\) 0 0
\(101\) −5.97644 −0.00588790 −0.00294395 0.999996i \(-0.500937\pi\)
−0.00294395 + 0.999996i \(0.500937\pi\)
\(102\) 108.955 + 593.863i 0.105767 + 0.576483i
\(103\) 137.824 137.824i 0.131847 0.131847i −0.638104 0.769951i \(-0.720281\pi\)
0.769951 + 0.638104i \(0.220281\pi\)
\(104\) 273.311 + 67.1867i 0.257696 + 0.0633481i
\(105\) 0 0
\(106\) 1075.21 + 741.840i 0.985225 + 0.679754i
\(107\) −723.943 723.943i −0.654077 0.654077i 0.299895 0.953972i \(-0.403048\pi\)
−0.953972 + 0.299895i \(0.903048\pi\)
\(108\) −895.181 402.447i −0.797582 0.358569i
\(109\) 896.758i 0.788017i 0.919107 + 0.394009i \(0.128912\pi\)
−0.919107 + 0.394009i \(0.871088\pi\)
\(110\) 0 0
\(111\) 590.026i 0.504530i
\(112\) 1305.00 + 77.8631i 1.10099 + 0.0656908i
\(113\) 525.727 + 525.727i 0.437665 + 0.437665i 0.891226 0.453560i \(-0.149846\pi\)
−0.453560 + 0.891226i \(0.649846\pi\)
\(114\) 455.855 660.710i 0.374515 0.542817i
\(115\) 0 0
\(116\) −702.611 1850.34i −0.562378 1.48103i
\(117\) 48.1045 48.1045i 0.0380108 0.0380108i
\(118\) −1015.77 + 186.362i −0.792450 + 0.145390i
\(119\) 765.237 0.589488
\(120\) 0 0
\(121\) −883.705 −0.663941
\(122\) −746.019 + 136.871i −0.553618 + 0.101572i
\(123\) −477.965 + 477.965i −0.350379 + 0.350379i
\(124\) −176.995 466.119i −0.128182 0.337571i
\(125\) 0 0
\(126\) 179.454 260.098i 0.126881 0.183900i
\(127\) 75.4237 + 75.4237i 0.0526990 + 0.0526990i 0.732965 0.680266i \(-0.238136\pi\)
−0.680266 + 0.732965i \(0.738136\pi\)
\(128\) 428.844 1383.20i 0.296132 0.955147i
\(129\) 1977.02i 1.34936i
\(130\) 0 0
\(131\) 1374.47i 0.916701i −0.888771 0.458351i \(-0.848440\pi\)
0.888771 0.458351i \(-0.151560\pi\)
\(132\) −1956.65 879.649i −1.29018 0.580028i
\(133\) −719.389 719.389i −0.469014 0.469014i
\(134\) 370.782 + 255.820i 0.239035 + 0.164922i
\(135\) 0 0
\(136\) 202.355 823.166i 0.127587 0.519014i
\(137\) 2002.37 2002.37i 1.24871 1.24871i 0.292424 0.956289i \(-0.405538\pi\)
0.956289 0.292424i \(-0.0944618\pi\)
\(138\) 169.774 + 925.354i 0.104725 + 0.570807i
\(139\) −2575.00 −1.57129 −0.785643 0.618679i \(-0.787668\pi\)
−0.785643 + 0.618679i \(0.787668\pi\)
\(140\) 0 0
\(141\) 1011.53 0.604160
\(142\) −285.764 1557.56i −0.168879 0.920477i
\(143\) −413.910 + 413.910i −0.242048 + 0.242048i
\(144\) −232.334 261.818i −0.134453 0.151515i
\(145\) 0 0
\(146\) −710.582 490.264i −0.402796 0.277908i
\(147\) −299.202 299.202i −0.167876 0.167876i
\(148\) 339.663 755.529i 0.188650 0.419623i
\(149\) 1322.91i 0.727364i 0.931523 + 0.363682i \(0.118481\pi\)
−0.931523 + 0.363682i \(0.881519\pi\)
\(150\) 0 0
\(151\) 57.2419i 0.0308495i −0.999881 0.0154248i \(-0.995090\pi\)
0.999881 0.0154248i \(-0.00491005\pi\)
\(152\) −964.079 + 583.616i −0.514455 + 0.311431i
\(153\) −144.882 144.882i −0.0765559 0.0765559i
\(154\) −1544.09 + 2237.99i −0.807966 + 1.17105i
\(155\) 0 0
\(156\) −530.080 + 201.282i −0.272054 + 0.103304i
\(157\) −1622.22 + 1622.22i −0.824634 + 0.824634i −0.986769 0.162134i \(-0.948162\pi\)
0.162134 + 0.986769i \(0.448162\pi\)
\(158\) 3261.50 598.384i 1.64222 0.301297i
\(159\) −2631.68 −1.31262
\(160\) 0 0
\(161\) 1192.39 0.583685
\(162\) 2355.68 432.193i 1.14247 0.209607i
\(163\) −1696.16 + 1696.16i −0.815052 + 0.815052i −0.985386 0.170334i \(-0.945515\pi\)
0.170334 + 0.985386i \(0.445515\pi\)
\(164\) 887.188 336.882i 0.422425 0.160403i
\(165\) 0 0
\(166\) 1346.05 1950.95i 0.629361 0.912187i
\(167\) −2015.29 2015.29i −0.933819 0.933819i 0.0641235 0.997942i \(-0.479575\pi\)
−0.997942 + 0.0641235i \(0.979575\pi\)
\(168\) −2253.07 + 1363.92i −1.03469 + 0.626363i
\(169\) 2042.29i 0.929580i
\(170\) 0 0
\(171\) 272.404i 0.121820i
\(172\) −1138.12 + 2531.58i −0.504542 + 1.12228i
\(173\) −317.896 317.896i −0.139706 0.139706i 0.633795 0.773501i \(-0.281496\pi\)
−0.773501 + 0.633795i \(0.781496\pi\)
\(174\) 3282.05 + 2264.44i 1.42995 + 0.986592i
\(175\) 0 0
\(176\) 1999.10 + 2252.79i 0.856179 + 0.964830i
\(177\) 1471.16 1471.16i 0.624743 0.624743i
\(178\) 281.782 + 1535.86i 0.118654 + 0.646727i
\(179\) 3518.04 1.46900 0.734499 0.678610i \(-0.237417\pi\)
0.734499 + 0.678610i \(0.237417\pi\)
\(180\) 0 0
\(181\) −4769.86 −1.95879 −0.979395 0.201955i \(-0.935271\pi\)
−0.979395 + 0.201955i \(0.935271\pi\)
\(182\) 129.683 + 706.840i 0.0528174 + 0.287882i
\(183\) 1080.48 1080.48i 0.436455 0.436455i
\(184\) 315.308 1282.65i 0.126331 0.513904i
\(185\) 0 0
\(186\) 826.781 + 570.435i 0.325927 + 0.224873i
\(187\) 1246.63 + 1246.63i 0.487499 + 0.487499i
\(188\) −1295.27 582.316i −0.502486 0.225903i
\(189\) 2506.09i 0.964502i
\(190\) 0 0
\(191\) 1728.42i 0.654787i 0.944888 + 0.327393i \(0.106170\pi\)
−0.944888 + 0.327393i \(0.893830\pi\)
\(192\) 871.385 + 2784.30i 0.327536 + 1.04656i
\(193\) −1439.32 1439.32i −0.536813 0.536813i 0.385779 0.922591i \(-0.373933\pi\)
−0.922591 + 0.385779i \(0.873933\pi\)
\(194\) −1046.41 + 1516.65i −0.387256 + 0.561283i
\(195\) 0 0
\(196\) 210.885 + 555.372i 0.0768533 + 0.202395i
\(197\) 658.673 658.673i 0.238216 0.238216i −0.577895 0.816111i \(-0.696126\pi\)
0.816111 + 0.577895i \(0.196126\pi\)
\(198\) 716.063 131.375i 0.257012 0.0471537i
\(199\) −658.733 −0.234655 −0.117327 0.993093i \(-0.537433\pi\)
−0.117327 + 0.993093i \(0.537433\pi\)
\(200\) 0 0
\(201\) −907.523 −0.318466
\(202\) −16.6264 + 3.05043i −0.00579124 + 0.00106251i
\(203\) 3573.53 3573.53i 1.23553 1.23553i
\(204\) 606.226 + 1596.51i 0.208060 + 0.547932i
\(205\) 0 0
\(206\) 313.080 453.773i 0.105890 0.153475i
\(207\) −225.755 225.755i −0.0758022 0.0758022i
\(208\) 794.642 + 47.4125i 0.264897 + 0.0158051i
\(209\) 2343.87i 0.775738i
\(210\) 0 0
\(211\) 5821.53i 1.89939i 0.313182 + 0.949693i \(0.398605\pi\)
−0.313182 + 0.949693i \(0.601395\pi\)
\(212\) 3369.88 + 1515.00i 1.09172 + 0.490803i
\(213\) 2255.86 + 2255.86i 0.725675 + 0.725675i
\(214\) −2383.51 1644.50i −0.761371 0.525306i
\(215\) 0 0
\(216\) −2695.80 662.695i −0.849194 0.208753i
\(217\) 900.208 900.208i 0.281613 0.281613i
\(218\) 457.714 + 2494.77i 0.142203 + 0.775080i
\(219\) 1739.22 0.536645
\(220\) 0 0
\(221\) 465.969 0.141830
\(222\) 301.155 + 1641.45i 0.0910458 + 0.496247i
\(223\) −2315.57 + 2315.57i −0.695347 + 0.695347i −0.963403 0.268056i \(-0.913619\pi\)
0.268056 + 0.963403i \(0.413619\pi\)
\(224\) 3670.24 449.469i 1.09477 0.134069i
\(225\) 0 0
\(226\) 1730.90 + 1194.23i 0.509460 + 0.351501i
\(227\) 2970.19 + 2970.19i 0.868450 + 0.868450i 0.992301 0.123851i \(-0.0395243\pi\)
−0.123851 + 0.992301i \(0.539524\pi\)
\(228\) 930.954 2070.76i 0.270412 0.601490i
\(229\) 4981.25i 1.43742i 0.695308 + 0.718712i \(0.255268\pi\)
−0.695308 + 0.718712i \(0.744732\pi\)
\(230\) 0 0
\(231\) 5477.69i 1.56020i
\(232\) −2899.09 4789.02i −0.820408 1.35524i
\(233\) −1649.04 1649.04i −0.463659 0.463659i 0.436194 0.899853i \(-0.356326\pi\)
−0.899853 + 0.436194i \(0.856326\pi\)
\(234\) 109.273 158.379i 0.0305274 0.0442460i
\(235\) 0 0
\(236\) −2730.74 + 1036.92i −0.753204 + 0.286006i
\(237\) −4723.71 + 4723.71i −1.29468 + 1.29468i
\(238\) 2128.88 390.584i 0.579811 0.106377i
\(239\) −3574.98 −0.967558 −0.483779 0.875190i \(-0.660736\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(240\) 0 0
\(241\) 5135.22 1.37257 0.686283 0.727334i \(-0.259241\pi\)
0.686283 + 0.727334i \(0.259241\pi\)
\(242\) −2458.46 + 451.051i −0.653041 + 0.119813i
\(243\) −1069.49 + 1069.49i −0.282336 + 0.282336i
\(244\) −2005.56 + 761.549i −0.526200 + 0.199808i
\(245\) 0 0
\(246\) −1085.74 + 1573.65i −0.281399 + 0.407855i
\(247\) −438.051 438.051i −0.112844 0.112844i
\(248\) −730.309 1206.40i −0.186995 0.308897i
\(249\) 4775.13i 1.21531i
\(250\) 0 0
\(251\) 6648.06i 1.67180i −0.548882 0.835900i \(-0.684946\pi\)
0.548882 0.835900i \(-0.315054\pi\)
\(252\) 366.483 815.186i 0.0916122 0.203777i
\(253\) 1942.49 + 1942.49i 0.482700 + 0.482700i
\(254\) 248.325 + 171.331i 0.0613437 + 0.0423239i
\(255\) 0 0
\(256\) 487.044 4066.94i 0.118907 0.992905i
\(257\) 448.260 448.260i 0.108800 0.108800i −0.650611 0.759411i \(-0.725487\pi\)
0.759411 + 0.650611i \(0.225487\pi\)
\(258\) −1009.09 5500.06i −0.243501 1.32721i
\(259\) 2115.13 0.507442
\(260\) 0 0
\(261\) −1353.16 −0.320913
\(262\) −701.541 3823.76i −0.165425 0.901652i
\(263\) 145.529 145.529i 0.0341205 0.0341205i −0.689841 0.723961i \(-0.742319\pi\)
0.723961 + 0.689841i \(0.242319\pi\)
\(264\) −5892.35 1448.49i −1.37367 0.337683i
\(265\) 0 0
\(266\) −2368.52 1634.15i −0.545951 0.376678i
\(267\) −2224.42 2224.42i −0.509859 0.509859i
\(268\) 1162.09 + 522.439i 0.264872 + 0.119078i
\(269\) 2764.90i 0.626687i −0.949640 0.313344i \(-0.898551\pi\)
0.949640 0.313344i \(-0.101449\pi\)
\(270\) 0 0
\(271\) 6372.29i 1.42837i 0.699955 + 0.714187i \(0.253203\pi\)
−0.699955 + 0.714187i \(0.746797\pi\)
\(272\) 142.798 2393.33i 0.0318324 0.533517i
\(273\) −1023.73 1023.73i −0.226957 0.226957i
\(274\) 4548.54 6592.59i 1.00287 1.45355i
\(275\) 0 0
\(276\) 944.618 + 2487.67i 0.206012 + 0.542538i
\(277\) 387.343 387.343i 0.0840187 0.0840187i −0.663848 0.747867i \(-0.731078\pi\)
0.747867 + 0.663848i \(0.231078\pi\)
\(278\) −7163.64 + 1314.30i −1.54549 + 0.283549i
\(279\) −340.873 −0.0731453
\(280\) 0 0
\(281\) 5284.49 1.12187 0.560936 0.827859i \(-0.310441\pi\)
0.560936 + 0.827859i \(0.310441\pi\)
\(282\) 2814.08 516.296i 0.594241 0.109025i
\(283\) 341.577 341.577i 0.0717479 0.0717479i −0.670322 0.742070i \(-0.733844\pi\)
0.742070 + 0.670322i \(0.233844\pi\)
\(284\) −1589.99 4187.27i −0.332213 0.874890i
\(285\) 0 0
\(286\) −940.232 + 1362.76i −0.194395 + 0.281754i
\(287\) 1713.41 + 1713.41i 0.352402 + 0.352402i
\(288\) −779.986 609.790i −0.159587 0.124765i
\(289\) 3509.58i 0.714346i
\(290\) 0 0
\(291\) 3712.13i 0.747798i
\(292\) −2227.07 1001.22i −0.446333 0.200658i
\(293\) 6655.74 + 6655.74i 1.32707 + 1.32707i 0.907912 + 0.419161i \(0.137676\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(294\) −985.092 679.662i −0.195414 0.134825i
\(295\) 0 0
\(296\) 559.312 2275.24i 0.109829 0.446777i
\(297\) 4082.60 4082.60i 0.797631 0.797631i
\(298\) 675.227 + 3680.33i 0.131258 + 0.715423i
\(299\) 726.069 0.140434
\(300\) 0 0
\(301\) −7087.24 −1.35715
\(302\) −29.2168 159.247i −0.00556701 0.0303431i
\(303\) 24.0804 24.0804i 0.00456563 0.00456563i
\(304\) −2384.18 + 2115.69i −0.449809 + 0.399155i
\(305\) 0 0
\(306\) −477.011 329.113i −0.0891141 0.0614840i
\(307\) 535.672 + 535.672i 0.0995844 + 0.0995844i 0.755144 0.655559i \(-0.227567\pi\)
−0.655559 + 0.755144i \(0.727567\pi\)
\(308\) −3153.37 + 7014.19i −0.583376 + 1.29763i
\(309\) 1110.65i 0.204475i
\(310\) 0 0
\(311\) 3579.61i 0.652672i 0.945254 + 0.326336i \(0.105814\pi\)
−0.945254 + 0.326336i \(0.894186\pi\)
\(312\) −1371.94 + 830.522i −0.248945 + 0.150702i
\(313\) −6740.52 6740.52i −1.21724 1.21724i −0.968594 0.248648i \(-0.920014\pi\)
−0.248648 0.968594i \(-0.579986\pi\)
\(314\) −3685.02 + 5341.01i −0.662285 + 0.959907i
\(315\) 0 0
\(316\) 8768.05 3329.40i 1.56089 0.592701i
\(317\) −4163.19 + 4163.19i −0.737628 + 0.737628i −0.972118 0.234490i \(-0.924658\pi\)
0.234490 + 0.972118i \(0.424658\pi\)
\(318\) −7321.32 + 1343.23i −1.29107 + 0.236871i
\(319\) 11643.1 2.04354
\(320\) 0 0
\(321\) 5833.86 1.01438
\(322\) 3317.21 608.605i 0.574102 0.105330i
\(323\) −1319.33 + 1319.33i −0.227275 + 0.227275i
\(324\) 6332.88 2404.72i 1.08588 0.412332i
\(325\) 0 0
\(326\) −3852.97 + 5584.44i −0.654590 + 0.948753i
\(327\) −3613.24 3613.24i −0.611049 0.611049i
\(328\) 2296.20 1390.03i 0.386544 0.233999i
\(329\) 3626.15i 0.607648i
\(330\) 0 0
\(331\) 8821.65i 1.46490i −0.680821 0.732450i \(-0.738377\pi\)
0.680821 0.732450i \(-0.261623\pi\)
\(332\) 2748.93 6114.57i 0.454418 1.01078i
\(333\) −400.457 400.457i −0.0659007 0.0659007i
\(334\) −6635.14 4577.90i −1.08700 0.749974i
\(335\) 0 0
\(336\) −5571.87 + 4944.42i −0.904674 + 0.802798i
\(337\) −3165.30 + 3165.30i −0.511647 + 0.511647i −0.915031 0.403384i \(-0.867834\pi\)
0.403384 + 0.915031i \(0.367834\pi\)
\(338\) −1042.40 5681.63i −0.167749 0.914319i
\(339\) −4236.55 −0.678754
\(340\) 0 0
\(341\) 2933.01 0.465781
\(342\) 139.038 + 757.826i 0.0219833 + 0.119820i
\(343\) 3881.71 3881.71i 0.611057 0.611057i
\(344\) −1874.11 + 7623.75i −0.293736 + 1.19490i
\(345\) 0 0
\(346\) −1046.64 722.128i −0.162624 0.112202i
\(347\) −856.765 856.765i −0.132546 0.132546i 0.637721 0.770267i \(-0.279877\pi\)
−0.770267 + 0.637721i \(0.779877\pi\)
\(348\) 10286.4 + 4624.47i 1.58451 + 0.712350i
\(349\) 3731.17i 0.572278i 0.958188 + 0.286139i \(0.0923720\pi\)
−0.958188 + 0.286139i \(0.907628\pi\)
\(350\) 0 0
\(351\) 1526.01i 0.232058i
\(352\) 6711.31 + 5246.88i 1.01623 + 0.794487i
\(353\) 1774.39 + 1774.39i 0.267539 + 0.267539i 0.828108 0.560569i \(-0.189417\pi\)
−0.560569 + 0.828108i \(0.689417\pi\)
\(354\) 3341.87 4843.66i 0.501747 0.727225i
\(355\) 0 0
\(356\) 1567.83 + 4128.92i 0.233413 + 0.614698i
\(357\) −3083.31 + 3083.31i −0.457104 + 0.457104i
\(358\) 9787.16 1795.64i 1.44488 0.265091i
\(359\) −10477.6 −1.54036 −0.770178 0.637829i \(-0.779832\pi\)
−0.770178 + 0.637829i \(0.779832\pi\)
\(360\) 0 0
\(361\) −4378.42 −0.638347
\(362\) −13269.7 + 2434.58i −1.92663 + 0.353477i
\(363\) 3560.65 3560.65i 0.514837 0.514837i
\(364\) 721.555 + 1900.23i 0.103901 + 0.273624i
\(365\) 0 0
\(366\) 2454.39 3557.37i 0.350528 0.508051i
\(367\) 5250.87 + 5250.87i 0.746848 + 0.746848i 0.973886 0.227038i \(-0.0729040\pi\)
−0.227038 + 0.973886i \(0.572904\pi\)
\(368\) 222.507 3729.27i 0.0315190 0.528265i
\(369\) 648.801i 0.0915317i
\(370\) 0 0
\(371\) 9434.06i 1.32019i
\(372\) 2591.25 + 1164.95i 0.361156 + 0.162365i
\(373\) −3349.09 3349.09i −0.464904 0.464904i 0.435355 0.900259i \(-0.356623\pi\)
−0.900259 + 0.435355i \(0.856623\pi\)
\(374\) 4104.40 + 2831.82i 0.567469 + 0.391523i
\(375\) 0 0
\(376\) −3900.66 958.879i −0.535003 0.131517i
\(377\) 2176.00 2176.00i 0.297267 0.297267i
\(378\) −1279.13 6971.91i −0.174051 0.948668i
\(379\) 1701.61 0.230622 0.115311 0.993329i \(-0.463213\pi\)
0.115311 + 0.993329i \(0.463213\pi\)
\(380\) 0 0
\(381\) −607.798 −0.0817282
\(382\) 882.202 + 4808.46i 0.118161 + 0.644037i
\(383\) −5674.07 + 5674.07i −0.757001 + 0.757001i −0.975775 0.218775i \(-0.929794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(384\) 3845.32 + 7301.14i 0.511017 + 0.970273i
\(385\) 0 0
\(386\) −4738.83 3269.55i −0.624871 0.431128i
\(387\) 1341.83 + 1341.83i 0.176251 + 0.176251i
\(388\) −2136.99 + 4753.40i −0.279611 + 0.621951i
\(389\) 2301.42i 0.299965i −0.988689 0.149983i \(-0.952078\pi\)
0.988689 0.149983i \(-0.0479218\pi\)
\(390\) 0 0
\(391\) 2186.80i 0.282842i
\(392\) 870.148 + 1437.40i 0.112115 + 0.185203i
\(393\) 5538.05 + 5538.05i 0.710833 + 0.710833i
\(394\) 1496.23 2168.62i 0.191317 0.277293i
\(395\) 0 0
\(396\) 1925.03 730.970i 0.244283 0.0927592i
\(397\) 7499.18 7499.18i 0.948043 0.948043i −0.0506721 0.998715i \(-0.516136\pi\)
0.998715 + 0.0506721i \(0.0161363\pi\)
\(398\) −1832.59 + 336.223i −0.230803 + 0.0423451i
\(399\) 5797.16 0.727371
\(400\) 0 0
\(401\) −9495.99 −1.18256 −0.591280 0.806466i \(-0.701377\pi\)
−0.591280 + 0.806466i \(0.701377\pi\)
\(402\) −2524.72 + 463.208i −0.313238 + 0.0574694i
\(403\) 548.155 548.155i 0.0677557 0.0677557i
\(404\) −44.6976 + 16.9725i −0.00550442 + 0.00209014i
\(405\) 0 0
\(406\) 8117.58 11765.5i 0.992288 1.43821i
\(407\) 3445.70 + 3445.70i 0.419648 + 0.419648i
\(408\) 2501.39 + 4132.06i 0.303523 + 0.501391i
\(409\) 10456.4i 1.26415i −0.774909 0.632073i \(-0.782204\pi\)
0.774909 0.632073i \(-0.217796\pi\)
\(410\) 0 0
\(411\) 16136.0i 1.93657i
\(412\) 639.375 1422.19i 0.0764557 0.170064i
\(413\) −5273.83 5273.83i −0.628349 0.628349i
\(414\) −743.276 512.821i −0.0882368 0.0608787i
\(415\) 0 0
\(416\) 2234.89 273.691i 0.263400 0.0322568i
\(417\) 10375.3 10375.3i 1.21842 1.21842i
\(418\) −1196.33 6520.64i −0.139987 0.763002i
\(419\) −8542.91 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(420\) 0 0
\(421\) −3112.71 −0.360342 −0.180171 0.983635i \(-0.557665\pi\)
−0.180171 + 0.983635i \(0.557665\pi\)
\(422\) 2971.36 + 16195.4i 0.342757 + 1.86820i
\(423\) −686.540 + 686.540i −0.0789142 + 0.0789142i
\(424\) 10148.2 + 2494.69i 1.16236 + 0.285738i
\(425\) 0 0
\(426\) 7427.19 + 5124.37i 0.844714 + 0.582808i
\(427\) −3873.30 3873.30i −0.438974 0.438974i
\(428\) −7470.28 3358.41i −0.843667 0.379287i
\(429\) 3335.48i 0.375381i
\(430\) 0 0
\(431\) 1474.93i 0.164837i −0.996598 0.0824187i \(-0.973736\pi\)
0.996598 0.0824187i \(-0.0262645\pi\)
\(432\) −7837.94 467.653i −0.872924 0.0520832i
\(433\) 6196.57 + 6196.57i 0.687733 + 0.687733i 0.961730 0.273998i \(-0.0883460\pi\)
−0.273998 + 0.961730i \(0.588346\pi\)
\(434\) 2044.90 2963.85i 0.226171 0.327809i
\(435\) 0 0
\(436\) 2546.71 + 6706.82i 0.279737 + 0.736694i
\(437\) −2055.78 + 2055.78i −0.225037 + 0.225037i
\(438\) 4838.48 887.711i 0.527835 0.0968413i
\(439\) −4661.49 −0.506790 −0.253395 0.967363i \(-0.581547\pi\)
−0.253395 + 0.967363i \(0.581547\pi\)
\(440\) 0 0
\(441\) 406.144 0.0438553
\(442\) 1296.32 237.835i 0.139502 0.0255942i
\(443\) −5250.61 + 5250.61i −0.563124 + 0.563124i −0.930194 0.367069i \(-0.880361\pi\)
0.367069 + 0.930194i \(0.380361\pi\)
\(444\) 1675.62 + 4412.78i 0.179102 + 0.471670i
\(445\) 0 0
\(446\) −5260.02 + 7623.80i −0.558451 + 0.809411i
\(447\) −5330.32 5330.32i −0.564017 0.564017i
\(448\) 9981.17 3123.74i 1.05260 0.329427i
\(449\) 2992.06i 0.314485i 0.987560 + 0.157243i \(0.0502605\pi\)
−0.987560 + 0.157243i \(0.949740\pi\)
\(450\) 0 0
\(451\) 5582.54i 0.582864i
\(452\) 5424.91 + 2438.88i 0.564527 + 0.253794i
\(453\) 230.641 + 230.641i 0.0239215 + 0.0239215i
\(454\) 9779.05 + 6747.03i 1.01091 + 0.697475i
\(455\) 0 0
\(456\) 1532.97 6236.02i 0.157430 0.640413i
\(457\) −13147.8 + 13147.8i −1.34579 + 1.34579i −0.455619 + 0.890175i \(0.650582\pi\)
−0.890175 + 0.455619i \(0.849418\pi\)
\(458\) 2542.47 + 13857.8i 0.259393 + 1.41383i
\(459\) −4596.08 −0.467378
\(460\) 0 0
\(461\) 3239.67 0.327302 0.163651 0.986518i \(-0.447673\pi\)
0.163651 + 0.986518i \(0.447673\pi\)
\(462\) −2795.86 15238.9i −0.281548 1.53458i
\(463\) 1552.82 1552.82i 0.155865 0.155865i −0.624867 0.780732i \(-0.714847\pi\)
0.780732 + 0.624867i \(0.214847\pi\)
\(464\) −10509.6 11843.3i −1.05150 1.18494i
\(465\) 0 0
\(466\) −5429.32 3745.94i −0.539717 0.372377i
\(467\) −6322.16 6322.16i −0.626456 0.626456i 0.320719 0.947174i \(-0.396076\pi\)
−0.947174 + 0.320719i \(0.896076\pi\)
\(468\) 223.159 496.384i 0.0220418 0.0490285i
\(469\) 3253.29i 0.320305i
\(470\) 0 0
\(471\) 13072.6i 1.27888i
\(472\) −7067.65 + 4278.49i −0.689227 + 0.417232i
\(473\) −11545.6 11545.6i −1.12234 1.12234i
\(474\) −10730.3 + 15552.4i −1.03979 + 1.50705i
\(475\) 0 0
\(476\) 5723.18 2173.20i 0.551095 0.209262i
\(477\) 1786.15 1786.15i 0.171451 0.171451i
\(478\) −9945.57 + 1824.70i −0.951673 + 0.174602i
\(479\) 7141.64 0.681232 0.340616 0.940203i \(-0.389364\pi\)
0.340616 + 0.940203i \(0.389364\pi\)
\(480\) 0 0
\(481\) 1287.94 0.122090
\(482\) 14286.1 2621.06i 1.35003 0.247689i
\(483\) −4804.40 + 4804.40i −0.452604 + 0.452604i
\(484\) −6609.20 + 2509.64i −0.620699 + 0.235691i
\(485\) 0 0
\(486\) −2429.43 + 3521.18i −0.226751 + 0.328650i
\(487\) −3827.76 3827.76i −0.356165 0.356165i 0.506232 0.862397i \(-0.331038\pi\)
−0.862397 + 0.506232i \(0.831038\pi\)
\(488\) −5190.75 + 3142.28i −0.481504 + 0.291484i
\(489\) 13668.4i 1.26402i
\(490\) 0 0
\(491\) 14943.2i 1.37348i −0.726904 0.686739i \(-0.759041\pi\)
0.726904 0.686739i \(-0.240959\pi\)
\(492\) −2217.31 + 4932.06i −0.203179 + 0.451940i
\(493\) −6553.74 6553.74i −0.598713 0.598713i
\(494\) −1442.24 995.069i −0.131355 0.0906281i
\(495\) 0 0
\(496\) −2647.47 2983.44i −0.239667 0.270082i
\(497\) 8086.80 8086.80i 0.729865 0.729865i
\(498\) 2437.27 + 13284.4i 0.219311 + 1.19536i
\(499\) 2324.51 0.208535 0.104268 0.994549i \(-0.466750\pi\)
0.104268 + 0.994549i \(0.466750\pi\)
\(500\) 0 0
\(501\) 16240.1 1.44821
\(502\) −3393.23 18494.8i −0.301688 1.64435i
\(503\) 4791.06 4791.06i 0.424697 0.424697i −0.462120 0.886817i \(-0.652911\pi\)
0.886817 + 0.462120i \(0.152911\pi\)
\(504\) 603.476 2454.90i 0.0533352 0.216964i
\(505\) 0 0
\(506\) 6395.44 + 4412.52i 0.561882 + 0.387669i
\(507\) 8228.84 + 8228.84i 0.720820 + 0.720820i
\(508\) 778.287 + 349.895i 0.0679742 + 0.0305592i
\(509\) 3391.52i 0.295337i 0.989037 + 0.147668i \(0.0471768\pi\)
−0.989037 + 0.147668i \(0.952823\pi\)
\(510\) 0 0
\(511\) 6234.74i 0.539743i
\(512\) −720.851 11562.8i −0.0622215 0.998062i
\(513\) 4320.71 + 4320.71i 0.371860 + 0.371860i
\(514\) 1018.26 1475.85i 0.0873804 0.126648i
\(515\) 0 0
\(516\) −5614.56 14786.1i −0.479007 1.26148i
\(517\) 5907.27 5907.27i 0.502517 0.502517i
\(518\) 5884.27 1079.58i 0.499112 0.0915714i
\(519\) 2561.75 0.216664
\(520\) 0 0
\(521\) −10835.4 −0.911146 −0.455573 0.890198i \(-0.650566\pi\)
−0.455573 + 0.890198i \(0.650566\pi\)
\(522\) −3764.47 + 690.663i −0.315645 + 0.0579109i
\(523\) −1210.80 + 1210.80i −0.101233 + 0.101233i −0.755909 0.654676i \(-0.772805\pi\)
0.654676 + 0.755909i \(0.272805\pi\)
\(524\) −3903.36 10279.6i −0.325418 0.856997i
\(525\) 0 0
\(526\) 330.581 479.139i 0.0274030 0.0397176i
\(527\) −1650.95 1650.95i −0.136464 0.136464i
\(528\) −17131.8 1022.17i −1.41206 0.0842507i
\(529\) 8759.55i 0.719943i
\(530\) 0 0
\(531\) 1996.99i 0.163205i
\(532\) −7423.28 3337.29i −0.604963 0.271973i
\(533\) 1043.33 + 1043.33i 0.0847874 + 0.0847874i
\(534\) −7323.69 5052.96i −0.593496 0.409481i
\(535\) 0 0
\(536\) 3499.57 + 860.282i 0.282012 + 0.0693256i
\(537\) −14175.0 + 14175.0i −1.13910 + 1.13910i
\(538\) −1411.23 7691.93i −0.113090 0.616399i
\(539\) −3494.62 −0.279265
\(540\) 0 0
\(541\) −7014.81 −0.557468 −0.278734 0.960368i \(-0.589915\pi\)
−0.278734 + 0.960368i \(0.589915\pi\)
\(542\) 3252.47 + 17727.7i 0.257760 + 1.40492i
\(543\) 19218.9 19218.9i 1.51890 1.51890i
\(544\) −824.311 6731.10i −0.0649670 0.530503i
\(545\) 0 0
\(546\) −3370.55 2325.50i −0.264187 0.182275i
\(547\) −10104.9 10104.9i −0.789860 0.789860i 0.191611 0.981471i \(-0.438629\pi\)
−0.981471 + 0.191611i \(0.938629\pi\)
\(548\) 9289.09 20662.2i 0.724106 1.61066i
\(549\) 1466.67i 0.114018i
\(550\) 0 0
\(551\) 12322.2i 0.952708i
\(552\) 3897.65 + 6438.55i 0.300535 + 0.496454i
\(553\) 16933.6 + 16933.6i 1.30215 + 1.30215i
\(554\) 879.882 1275.29i 0.0674776 0.0978011i
\(555\) 0 0
\(556\) −19258.4 + 7312.77i −1.46895 + 0.557789i
\(557\) −1950.22 + 1950.22i −0.148355 + 0.148355i −0.777383 0.629028i \(-0.783453\pi\)
0.629028 + 0.777383i \(0.283453\pi\)
\(558\) −948.307 + 173.985i −0.0719445 + 0.0131996i
\(559\) −4315.57 −0.326528
\(560\) 0 0
\(561\) −10045.9 −0.756039
\(562\) 14701.4 2697.25i 1.10346 0.202450i
\(563\) −4425.60 + 4425.60i −0.331291 + 0.331291i −0.853077 0.521786i \(-0.825266\pi\)
0.521786 + 0.853077i \(0.325266\pi\)
\(564\) 7565.23 2872.66i 0.564811 0.214470i
\(565\) 0 0
\(566\) 775.921 1124.61i 0.0576226 0.0835174i
\(567\) 12230.6 + 12230.6i 0.905884 + 0.905884i
\(568\) −6560.56 10837.4i −0.484639 0.800577i
\(569\) 14666.9i 1.08061i 0.841469 + 0.540305i \(0.181691\pi\)
−0.841469 + 0.540305i \(0.818309\pi\)
\(570\) 0 0
\(571\) 664.054i 0.0486686i 0.999704 + 0.0243343i \(0.00774662\pi\)
−0.999704 + 0.0243343i \(0.992253\pi\)
\(572\) −1920.15 + 4271.09i −0.140359 + 0.312208i
\(573\) −6964.21 6964.21i −0.507738 0.507738i
\(574\) 5641.23 + 3892.15i 0.410210 + 0.283023i
\(575\) 0 0
\(576\) −2481.16 1298.32i −0.179482 0.0939178i
\(577\) −583.058 + 583.058i −0.0420676 + 0.0420676i −0.727828 0.685760i \(-0.759470\pi\)
0.685760 + 0.727828i \(0.259470\pi\)
\(578\) 1791.32 + 9763.63i 0.128909 + 0.702619i
\(579\) 11598.7 0.832516
\(580\) 0 0
\(581\) 17117.9 1.22232
\(582\) −1894.71 10327.1i −0.134945 0.735521i
\(583\) −15368.8 + 15368.8i −1.09178 + 1.09178i
\(584\) −6706.72 1648.68i −0.475216 0.116820i
\(585\) 0 0
\(586\) 21913.4 + 15119.1i 1.54477 + 1.06581i
\(587\) 6911.99 + 6911.99i 0.486011 + 0.486011i 0.907045 0.421034i \(-0.138333\pi\)
−0.421034 + 0.907045i \(0.638333\pi\)
\(588\) −3087.43 1388.01i −0.216536 0.0973482i
\(589\) 3104.07i 0.217150i
\(590\) 0 0
\(591\) 5307.89i 0.369437i
\(592\) 394.697 6615.19i 0.0274019 0.459261i
\(593\) 11384.8 + 11384.8i 0.788396 + 0.788396i 0.981231 0.192835i \(-0.0617682\pi\)
−0.192835 + 0.981231i \(0.561768\pi\)
\(594\) 9273.96 13441.6i 0.640598 0.928474i
\(595\) 0 0
\(596\) 3756.95 + 9894.02i 0.258206 + 0.679991i
\(597\) 2654.19 2654.19i 0.181957 0.181957i
\(598\) 2019.92 370.592i 0.138128 0.0253422i
\(599\) 25321.6 1.72723 0.863616 0.504151i \(-0.168194\pi\)
0.863616 + 0.504151i \(0.168194\pi\)
\(600\) 0 0
\(601\) 27777.8 1.88533 0.942663 0.333746i \(-0.108313\pi\)
0.942663 + 0.333746i \(0.108313\pi\)
\(602\) −19716.6 + 3617.39i −1.33487 + 0.244907i
\(603\) 615.947 615.947i 0.0415975 0.0415975i
\(604\) −162.562 428.110i −0.0109512 0.0288403i
\(605\) 0 0
\(606\) 54.7007 79.2825i 0.00366677 0.00531457i
\(607\) 19575.7 + 19575.7i 1.30898 + 1.30898i 0.922150 + 0.386833i \(0.126431\pi\)
0.386833 + 0.922150i \(0.373569\pi\)
\(608\) −5552.89 + 7102.74i −0.370394 + 0.473773i
\(609\) 28797.2i 1.91613i
\(610\) 0 0
\(611\) 2208.04i 0.146199i
\(612\) −1495.02 672.118i −0.0987463 0.0443934i
\(613\) 12841.3 + 12841.3i 0.846091 + 0.846091i 0.989643 0.143552i \(-0.0458525\pi\)
−0.143552 + 0.989643i \(0.545853\pi\)
\(614\) 1763.65 + 1216.82i 0.115920 + 0.0799788i
\(615\) 0 0
\(616\) −5192.55 + 21122.9i −0.339633 + 1.38160i
\(617\) −15254.6 + 15254.6i −0.995346 + 0.995346i −0.999989 0.00464336i \(-0.998522\pi\)
0.00464336 + 0.999989i \(0.498522\pi\)
\(618\) 566.887 + 3089.83i 0.0368989 + 0.201118i
\(619\) −13042.3 −0.846874 −0.423437 0.905926i \(-0.639176\pi\)
−0.423437 + 0.905926i \(0.639176\pi\)
\(620\) 0 0
\(621\) −7161.58 −0.462776
\(622\) 1827.07 + 9958.45i 0.117779 + 0.641957i
\(623\) −7974.11 + 7974.11i −0.512803 + 0.512803i
\(624\) −3392.83 + 3010.76i −0.217663 + 0.193152i
\(625\) 0 0
\(626\) −22192.5 15311.7i −1.41692 0.977599i
\(627\) 9444.01 + 9444.01i 0.601527 + 0.601527i
\(628\) −7525.59 + 16739.5i −0.478191 + 1.06366i
\(629\) 3879.07i 0.245896i
\(630\) 0 0
\(631\) 6843.39i 0.431745i 0.976422 + 0.215872i \(0.0692595\pi\)
−0.976422 + 0.215872i \(0.930740\pi\)
\(632\) 22693.3 13737.7i 1.42831 0.864644i
\(633\) −23456.3 23456.3i −1.47283 1.47283i
\(634\) −9457.04 + 13706.9i −0.592409 + 0.858629i
\(635\) 0 0
\(636\) −19682.3 + 7473.74i −1.22713 + 0.465964i
\(637\) −653.116 + 653.116i −0.0406239 + 0.0406239i
\(638\) 32391.0 5942.74i 2.00999 0.368770i
\(639\) −3062.15 −0.189573
\(640\) 0 0
\(641\) −2449.97 −0.150964 −0.0754820 0.997147i \(-0.524050\pi\)
−0.0754820 + 0.997147i \(0.524050\pi\)
\(642\) 16229.8 2977.66i 0.997723 0.183051i
\(643\) 22279.7 22279.7i 1.36645 1.36645i 0.500999 0.865448i \(-0.332966\pi\)
0.865448 0.500999i \(-0.167034\pi\)
\(644\) 8917.82 3386.27i 0.545670 0.207201i
\(645\) 0 0
\(646\) −2996.98 + 4343.78i −0.182530 + 0.264557i
\(647\) −5040.77 5040.77i −0.306295 0.306295i 0.537175 0.843471i \(-0.319491\pi\)
−0.843471 + 0.537175i \(0.819491\pi\)
\(648\) 16390.6 9922.27i 0.993650 0.601518i
\(649\) 17182.9i 1.03927i
\(650\) 0 0
\(651\) 7254.29i 0.436740i
\(652\) −7868.58 + 17502.5i −0.472634 + 1.05130i
\(653\) 4532.72 + 4532.72i 0.271637 + 0.271637i 0.829759 0.558122i \(-0.188478\pi\)
−0.558122 + 0.829759i \(0.688478\pi\)
\(654\) −11896.3 8207.79i −0.711285 0.490749i
\(655\) 0 0
\(656\) 5678.53 5039.06i 0.337972 0.299912i
\(657\) −1180.43 + 1180.43i −0.0700956 + 0.0700956i
\(658\) −1850.82 10087.9i −0.109654 0.597672i
\(659\) 12951.7 0.765595 0.382797 0.923832i \(-0.374961\pi\)
0.382797 + 0.923832i \(0.374961\pi\)
\(660\) 0 0
\(661\) 6827.08 0.401729 0.200864 0.979619i \(-0.435625\pi\)
0.200864 + 0.979619i \(0.435625\pi\)
\(662\) −4502.65 24541.8i −0.264351 1.44085i
\(663\) −1877.49 + 1877.49i −0.109979 + 0.109979i
\(664\) 4526.56 18413.8i 0.264555 1.07619i
\(665\) 0 0
\(666\) −1318.47 909.673i −0.0767110 0.0529266i
\(667\) −10212.0 10212.0i −0.592819 0.592819i
\(668\) −20795.5 9349.04i −1.20449 0.541505i
\(669\) 18660.0i 1.07838i
\(670\) 0 0
\(671\) 12619.8i 0.726052i
\(672\) −12977.2 + 16599.3i −0.744952 + 0.952873i
\(673\) −9731.89 9731.89i −0.557410 0.557410i 0.371159 0.928569i \(-0.378960\pi\)
−0.928569 + 0.371159i \(0.878960\pi\)
\(674\) −7190.25 + 10421.5i −0.410917 + 0.595578i
\(675\) 0 0
\(676\) −5799.91 15274.2i −0.329990 0.869037i
\(677\) 7885.88 7885.88i 0.447679 0.447679i −0.446903 0.894582i \(-0.647473\pi\)
0.894582 + 0.446903i \(0.147473\pi\)
\(678\) −11786.0 + 2162.37i −0.667611 + 0.122486i
\(679\) −13307.3 −0.752115
\(680\) 0 0
\(681\) −23935.1 −1.34684
\(682\) 8159.61 1497.03i 0.458134 0.0840534i
\(683\) 15861.8 15861.8i 0.888629 0.888629i −0.105763 0.994391i \(-0.533728\pi\)
0.994391 + 0.105763i \(0.0337284\pi\)
\(684\) 773.603 + 2037.30i 0.0432448 + 0.113886i
\(685\) 0 0
\(686\) 8817.63 12780.1i 0.490756 0.711295i
\(687\) −20070.6 20070.6i −1.11462 1.11462i
\(688\) −1322.53 + 22165.8i −0.0732861 + 1.22829i
\(689\) 5744.60i 0.317637i
\(690\) 0 0
\(691\) 30100.7i 1.65714i −0.559883 0.828572i \(-0.689154\pi\)
0.559883 0.828572i \(-0.310846\pi\)
\(692\) −3280.33 1474.74i −0.180201 0.0810132i
\(693\) 3717.77 + 3717.77i 0.203790 + 0.203790i
\(694\) −2820.81 1946.21i −0.154289 0.106451i
\(695\) 0 0
\(696\) 30977.2 + 7614.96i 1.68705 + 0.414719i
\(697\) 3142.34 3142.34i 0.170767 0.170767i
\(698\) 1904.43 + 10380.1i 0.103272 + 0.562883i
\(699\) 13288.8 0.719066
\(700\) 0 0
\(701\) −20267.4 −1.09199 −0.545997 0.837787i \(-0.683849\pi\)
−0.545997 + 0.837787i \(0.683849\pi\)
\(702\) −778.888 4245.34i −0.0418764 0.228248i
\(703\) −3646.66 + 3646.66i −0.195642 + 0.195642i
\(704\) 21348.9 + 11171.3i 1.14292 + 0.598058i
\(705\) 0 0
\(706\) 5842.01 + 4030.68i 0.311426 + 0.214868i
\(707\) −86.3236 86.3236i −0.00459199 0.00459199i
\(708\) 6824.81 15180.8i 0.362277 0.805830i
\(709\) 18499.1i 0.979900i −0.871750 0.489950i \(-0.837015\pi\)
0.871750 0.489950i \(-0.162985\pi\)
\(710\) 0 0
\(711\) 6412.08i 0.338216i
\(712\) 6469.13 + 10686.4i 0.340507 + 0.562485i
\(713\) −2572.50 2572.50i −0.135120 0.135120i
\(714\) −7004.00 + 10151.5i −0.367112 + 0.532088i
\(715\) 0 0
\(716\) 26311.3 9990.91i 1.37332 0.521478i
\(717\) 14404.4 14404.4i 0.750269 0.750269i
\(718\) −29148.7 + 5347.87i −1.51507 + 0.277968i
\(719\) −25990.9 −1.34812 −0.674060 0.738676i \(-0.735451\pi\)
−0.674060 + 0.738676i \(0.735451\pi\)
\(720\) 0 0
\(721\) 3981.47 0.205656
\(722\) −12180.7 + 2234.79i −0.627867 + 0.115194i
\(723\) −20691.0 + 20691.0i −1.06432 + 1.06432i
\(724\) −35673.6 + 13546.0i −1.83122 + 0.695348i
\(725\) 0 0
\(726\) 8088.31 11723.1i 0.413479 0.599290i
\(727\) −23543.5 23543.5i −1.20107 1.20107i −0.973841 0.227232i \(-0.927033\pi\)
−0.227232 0.973841i \(-0.572967\pi\)
\(728\) 2977.26 + 4918.15i 0.151572 + 0.250383i
\(729\) 14244.1i 0.723674i
\(730\) 0 0
\(731\) 12997.8i 0.657646i
\(732\) 5012.40 11149.3i 0.253092 0.562965i
\(733\) −16546.7 16546.7i −0.833789 0.833789i 0.154244 0.988033i \(-0.450706\pi\)
−0.988033 + 0.154244i \(0.950706\pi\)
\(734\) 17288.0 + 11927.8i 0.869361 + 0.599813i
\(735\) 0 0
\(736\) −1284.44 10488.4i −0.0643274 0.525280i
\(737\) −5299.85 + 5299.85i −0.264888 + 0.264888i
\(738\) −331.154 1804.96i −0.0165175 0.0900291i
\(739\) −8124.95 −0.404440 −0.202220 0.979340i \(-0.564816\pi\)
−0.202220 + 0.979340i \(0.564816\pi\)
\(740\) 0 0
\(741\) 3530.01 0.175004
\(742\) 4815.23 + 26245.5i 0.238238 + 1.29852i
\(743\) 5222.62 5222.62i 0.257873 0.257873i −0.566316 0.824188i \(-0.691632\pi\)
0.824188 + 0.566316i \(0.191632\pi\)
\(744\) 7803.45 + 1918.28i 0.384527 + 0.0945264i
\(745\) 0 0
\(746\) −11026.5 7607.73i −0.541167 0.373376i
\(747\) −3240.94 3240.94i −0.158741 0.158741i
\(748\) 12863.8 + 5783.17i 0.628806 + 0.282692i
\(749\) 20913.3i 1.02023i
\(750\) 0 0
\(751\) 27086.9i 1.31613i 0.752961 + 0.658066i \(0.228625\pi\)
−0.752961 + 0.658066i \(0.771375\pi\)
\(752\) −11341.0 676.664i −0.549953 0.0328130i
\(753\) 26786.5 + 26786.5i 1.29636 + 1.29636i
\(754\) 4942.97 7164.27i 0.238743 0.346031i
\(755\) 0 0
\(756\) −7117.05 18742.9i −0.342387 0.901685i
\(757\) 11094.6 11094.6i 0.532684 0.532684i −0.388686 0.921370i \(-0.627071\pi\)
0.921370 + 0.388686i \(0.127071\pi\)
\(758\) 4733.87 868.517i 0.226836 0.0416174i
\(759\) −15653.4 −0.748595
\(760\) 0 0
\(761\) −8006.53 −0.381388 −0.190694 0.981649i \(-0.561074\pi\)
−0.190694 + 0.981649i \(0.561074\pi\)
\(762\) −1690.89 + 310.226i −0.0803865 + 0.0147484i
\(763\) −12952.8 + 12952.8i −0.614576 + 0.614576i
\(764\) 4908.56 + 12926.8i 0.232442 + 0.612141i
\(765\) 0 0
\(766\) −12889.1 + 18681.3i −0.607967 + 0.881179i
\(767\) −3211.35 3211.35i −0.151180 0.151180i
\(768\) 14424.2 + 18349.0i 0.677720 + 0.862128i
\(769\) 5515.54i 0.258642i 0.991603 + 0.129321i \(0.0412797\pi\)
−0.991603 + 0.129321i \(0.958720\pi\)
\(770\) 0 0
\(771\) 3612.28i 0.168733i
\(772\) −14852.2 6677.11i −0.692413 0.311288i
\(773\) −7904.07 7904.07i −0.367774 0.367774i 0.498891 0.866665i \(-0.333741\pi\)
−0.866665 + 0.498891i \(0.833741\pi\)
\(774\) 4417.84 + 3048.08i 0.205163 + 0.141551i
\(775\) 0 0
\(776\) −3518.90 + 14314.7i −0.162785 + 0.662199i
\(777\) −8522.33 + 8522.33i −0.393484 + 0.393484i
\(778\) −1174.66 6402.52i −0.0541308 0.295041i
\(779\) −5908.13 −0.271734
\(780\) 0 0
\(781\) 26348.0 1.20718
\(782\) −1116.16 6083.65i −0.0510407 0.278198i
\(783\) −21463.0 + 21463.0i −0.979596 + 0.979596i
\(784\) 3154.41 + 3554.71i 0.143696 + 0.161931i
\(785\) 0 0
\(786\) 18233.5 + 12580.1i 0.827438 + 0.570889i
\(787\) 27606.7 + 27606.7i 1.25041 + 1.25041i 0.955537 + 0.294870i \(0.0952765\pi\)
0.294870 + 0.955537i \(0.404724\pi\)
\(788\) 3055.62 6796.76i 0.138137 0.307265i
\(789\) 1172.74i 0.0529158i
\(790\) 0 0
\(791\) 15187.2i 0.682673i
\(792\) 4982.32 3016.10i 0.223534 0.135319i
\(793\) −2358.53 2358.53i −0.105617 0.105617i
\(794\) 17035.0 24690.3i 0.761398 1.10356i
\(795\) 0 0
\(796\) −4926.64 + 1870.74i −0.219372 + 0.0832998i
\(797\) 19000.5 19000.5i 0.844456 0.844456i −0.144979 0.989435i \(-0.546311\pi\)
0.989435 + 0.144979i \(0.0463113\pi\)
\(798\) 16127.7 2958.92i 0.715430 0.131259i
\(799\) −6650.24 −0.294454
\(800\) 0 0
\(801\) 3019.48 0.133194
\(802\) −26417.8 + 4846.84i −1.16315 + 0.213401i
\(803\) 10156.9 10156.9i 0.446361 0.446361i
\(804\) −6787.33 + 2577.28i −0.297725 + 0.113052i
\(805\) 0 0
\(806\) 1245.18 1804.75i 0.0544164 0.0788704i
\(807\) 11140.4 + 11140.4i 0.485949 + 0.485949i
\(808\) −115.685 + 70.0315i −0.00503688 + 0.00304913i
\(809\) 33025.1i 1.43523i −0.696440 0.717615i \(-0.745234\pi\)
0.696440 0.717615i \(-0.254766\pi\)
\(810\) 0 0
\(811\) 19125.0i 0.828075i −0.910260 0.414037i \(-0.864118\pi\)
0.910260 0.414037i \(-0.135882\pi\)
\(812\) 16577.8 36874.9i 0.716463 1.59366i
\(813\) −25675.4 25675.4i −1.10760 1.10760i
\(814\) 11344.6 + 7827.19i 0.488487 + 0.337030i
\(815\) 0 0
\(816\) 9067.89 + 10218.6i 0.389019 + 0.438387i
\(817\) 12219.0 12219.0i 0.523243 0.523243i
\(818\) −5337.04 29089.6i −0.228124 1.24339i
\(819\) 1389.64 0.0592894
\(820\) 0 0
\(821\) 8022.85 0.341047 0.170523 0.985354i \(-0.445454\pi\)
0.170523 + 0.985354i \(0.445454\pi\)
\(822\) 8235.95 + 44890.2i 0.349467 + 1.90477i
\(823\) 941.682 941.682i 0.0398845 0.0398845i −0.686883 0.726768i \(-0.741022\pi\)
0.726768 + 0.686883i \(0.241022\pi\)
\(824\) 1052.84 4282.87i 0.0445113 0.181069i
\(825\) 0 0
\(826\) −17363.6 11980.0i −0.731424 0.504644i
\(827\) 413.194 + 413.194i 0.0173739 + 0.0173739i 0.715740 0.698366i \(-0.246089\pi\)
−0.698366 + 0.715740i \(0.746089\pi\)
\(828\) −2329.54 1047.29i −0.0977741 0.0439563i
\(829\) 13830.1i 0.579418i −0.957115 0.289709i \(-0.906441\pi\)
0.957115 0.289709i \(-0.0935585\pi\)
\(830\) 0 0
\(831\) 3121.39i 0.130301i
\(832\) 6077.75 1902.11i 0.253255 0.0792595i
\(833\) 1967.07 + 1967.07i 0.0818188 + 0.0818188i
\(834\) 23568.3 34159.6i 0.978542 1.41828i
\(835\) 0 0
\(836\) −6656.39 17529.8i −0.275378 0.725214i
\(837\) −5406.72 + 5406.72i −0.223278 + 0.223278i
\(838\) −23766.3 + 4360.38i −0.979705 + 0.179745i
\(839\) 29230.2 1.20279 0.601393 0.798954i \(-0.294613\pi\)
0.601393 + 0.798954i \(0.294613\pi\)
\(840\) 0 0
\(841\) −36820.9 −1.50973
\(842\) −8659.53 + 1588.75i −0.354426 + 0.0650262i
\(843\) −21292.4 + 21292.4i −0.869929 + 0.869929i
\(844\) 16532.6 + 43539.0i 0.674260 + 1.77568i
\(845\) 0 0
\(846\) −1559.53 + 2260.37i −0.0633781 + 0.0918593i
\(847\) −12764.2 12764.2i −0.517809 0.517809i
\(848\) 29505.6 + 1760.46i 1.19484 + 0.0712906i
\(849\) 2752.59i 0.111270i
\(850\) 0 0
\(851\) 6044.34i 0.243475i
\(852\) 23277.9 + 10465.0i 0.936018 + 0.420806i
\(853\) 20858.3 + 20858.3i 0.837251 + 0.837251i 0.988496 0.151245i \(-0.0483283\pi\)
−0.151245 + 0.988496i \(0.548328\pi\)
\(854\) −12752.5 8798.52i −0.510984 0.352552i
\(855\) 0 0
\(856\) −22496.4 5530.18i −0.898261 0.220815i
\(857\) −24905.5 + 24905.5i −0.992714 + 0.992714i −0.999974 0.00725972i \(-0.997689\pi\)
0.00725972 + 0.999974i \(0.497689\pi\)
\(858\) −1702.46 9279.27i −0.0677400 0.369218i
\(859\) 26939.2 1.07003 0.535013 0.844844i \(-0.320307\pi\)
0.535013 + 0.844844i \(0.320307\pi\)
\(860\) 0 0
\(861\) −13807.4 −0.546523
\(862\) −752.818 4103.25i −0.0297460 0.162131i
\(863\) 17233.1 17233.1i 0.679747 0.679747i −0.280196 0.959943i \(-0.590399\pi\)
0.959943 + 0.280196i \(0.0903995\pi\)
\(864\) −22043.8 + 2699.55i −0.867992 + 0.106297i
\(865\) 0 0
\(866\) 20401.6 + 14076.0i 0.800548 + 0.552336i
\(867\) −14140.9 14140.9i −0.553922 0.553922i
\(868\) 4176.12 9289.13i 0.163303 0.363241i
\(869\) 55172.1i 2.15372i
\(870\) 0 0
\(871\) 1981.00i 0.0770649i
\(872\) 10508.2 + 17358.5i 0.408086 + 0.674119i
\(873\) 2519.47 + 2519.47i 0.0976760 + 0.0976760i
\(874\) −4669.87 + 6768.45i −0.180733 + 0.261952i
\(875\) 0 0
\(876\) 13007.5 4939.21i 0.501694 0.190503i
\(877\) −8676.94 + 8676.94i −0.334093 + 0.334093i −0.854138 0.520046i \(-0.825915\pi\)
0.520046 + 0.854138i \(0.325915\pi\)
\(878\) −12968.2 + 2379.26i −0.498470 + 0.0914536i
\(879\) −53635.0 −2.05809
\(880\) 0 0
\(881\) −9480.93 −0.362566 −0.181283 0.983431i \(-0.558025\pi\)
−0.181283 + 0.983431i \(0.558025\pi\)
\(882\) 1129.89 207.299i 0.0431353 0.00791398i
\(883\) 27861.7 27861.7i 1.06186 1.06186i 0.0639013 0.997956i \(-0.479646\pi\)
0.997956 0.0639013i \(-0.0203543\pi\)
\(884\) 3484.96 1323.31i 0.132593 0.0503480i
\(885\) 0 0
\(886\) −11927.2 + 17287.1i −0.452260 + 0.655499i
\(887\) 27498.7 + 27498.7i 1.04094 + 1.04094i 0.999125 + 0.0418178i \(0.0133149\pi\)
0.0418178 + 0.999125i \(0.486685\pi\)
\(888\) 6913.88 + 11421.1i 0.261278 + 0.431606i
\(889\) 2178.84i 0.0822001i
\(890\) 0 0
\(891\) 39849.0i 1.49831i
\(892\) −10742.1 + 23894.1i −0.403219 + 0.896899i
\(893\) 6251.80 + 6251.80i 0.234276 + 0.234276i
\(894\) −17549.5 12108.3i −0.656538 0.452976i
\(895\) 0 0
\(896\) 26173.2 13784.7i 0.975875 0.513968i
\(897\) −2925.50 + 2925.50i −0.108896 + 0.108896i
\(898\) 1527.17 + 8323.88i 0.0567510 + 0.309322i
\(899\) −15419.4 −0.572040
\(900\) 0 0
\(901\) 17301.8 0.639739
\(902\) 2849.38 + 15530.6i 0.105182 + 0.573295i
\(903\) 28556.1 28556.1i 1.05237 1.05237i
\(904\) 16336.9 + 4016.01i 0.601058 + 0.147755i
\(905\) 0 0
\(906\) 759.362 + 523.920i 0.0278456 + 0.0192120i
\(907\) 1450.80 + 1450.80i 0.0531127 + 0.0531127i 0.733164 0.680052i \(-0.238043\pi\)
−0.680052 + 0.733164i \(0.738043\pi\)
\(908\) 30649.0 + 13778.9i 1.12018 + 0.503599i
\(909\) 32.6873i 0.00119271i
\(910\) 0 0
\(911\) 20370.8i 0.740850i −0.928862 0.370425i \(-0.879212\pi\)
0.928862 0.370425i \(-0.120788\pi\)
\(912\) 1081.79 18131.0i 0.0392781 0.658308i
\(913\) 27886.3 + 27886.3i 1.01085 + 1.01085i
\(914\) −29866.3 + 43287.8i −1.08084 + 1.56656i
\(915\) 0 0
\(916\) 14146.3 + 37254.6i 0.510269 + 1.34381i
\(917\) 19852.8 19852.8i 0.714937 0.714937i
\(918\) −12786.2 + 2345.88i −0.459705 + 0.0843415i
\(919\) 21825.1 0.783399 0.391699 0.920093i \(-0.371887\pi\)
0.391699 + 0.920093i \(0.371887\pi\)
\(920\) 0 0
\(921\) −4316.69 −0.154440
\(922\) 9012.73 1653.56i 0.321929 0.0590639i
\(923\) 4924.22 4924.22i 0.175604 0.175604i
\(924\) −15556.1 40967.4i −0.553852 1.45858i
\(925\) 0 0
\(926\) 3527.35 5112.49i 0.125179 0.181433i
\(927\) −753.812 753.812i −0.0267081 0.0267081i
\(928\) −35282.6 27583.8i −1.24807 0.975735i
\(929\) 9339.19i 0.329827i 0.986308 + 0.164913i \(0.0527345\pi\)
−0.986308 + 0.164913i \(0.947266\pi\)
\(930\) 0 0
\(931\) 3698.44i 0.130195i
\(932\) −17016.3 7650.01i −0.598055 0.268867i
\(933\) −14423.1 14423.1i −0.506099 0.506099i
\(934\) −20815.1 14361.3i −0.729219 0.503123i
\(935\) 0 0
\(936\) 367.469 1494.84i 0.0128324 0.0522012i
\(937\) −431.639 + 431.639i −0.0150491 + 0.0150491i −0.714591 0.699542i \(-0.753387\pi\)
0.699542 + 0.714591i \(0.253387\pi\)
\(938\) 1660.51 + 9050.63i 0.0578012 + 0.315047i
\(939\) 54318.2 1.88776
\(940\) 0 0
\(941\) 21225.1 0.735300 0.367650 0.929964i \(-0.380162\pi\)
0.367650 + 0.929964i \(0.380162\pi\)
\(942\) −6672.38 36367.9i −0.230783 1.25789i
\(943\) 4896.37 4896.37i 0.169086 0.169086i
\(944\) −17478.4 + 15510.1i −0.602619 + 0.534758i
\(945\) 0 0
\(946\) −38012.9 26226.9i −1.30645 0.901384i
\(947\) −11052.1 11052.1i −0.379244 0.379244i 0.491585 0.870830i \(-0.336418\pi\)
−0.870830 + 0.491585i \(0.836418\pi\)
\(948\) −21913.6 + 48743.4i −0.750759 + 1.66995i
\(949\) 3796.47i 0.129861i
\(950\) 0 0
\(951\) 33548.9i 1.14395i
\(952\) 14812.6 8966.99i 0.504285 0.305275i
\(953\) −22553.2 22553.2i −0.766600 0.766600i 0.210906 0.977506i \(-0.432359\pi\)
−0.977506 + 0.210906i \(0.932359\pi\)
\(954\) 4057.40 5880.74i 0.137697 0.199576i
\(955\) 0 0
\(956\) −26737.2 + 10152.6i −0.904541 + 0.343472i
\(957\) −46912.7 + 46912.7i −1.58461 + 1.58461i
\(958\) 19868.0 3645.16i 0.670048 0.122933i
\(959\) 57844.3 1.94775
\(960\) 0 0
\(961\) 25906.7 0.869616
\(962\) 3583.05 657.379i 0.120086 0.0220320i
\(963\) −3959.51 + 3959.51i −0.132496 + 0.132496i
\(964\) 38406.1 14583.6i 1.28317 0.487246i
\(965\) 0 0
\(966\) −10913.6 + 15818.0i −0.363498 + 0.526849i
\(967\) 18695.9 + 18695.9i 0.621739 + 0.621739i 0.945976 0.324237i \(-0.105108\pi\)
−0.324237 + 0.945976i \(0.605108\pi\)
\(968\) −17105.8 + 10355.2i −0.567976 + 0.343831i
\(969\) 10631.8i 0.352469i
\(970\) 0 0
\(971\) 11285.7i 0.372993i 0.982456 + 0.186496i \(0.0597133\pi\)
−0.982456 + 0.186496i \(0.940287\pi\)
\(972\) −4961.41 + 11035.9i −0.163721 + 0.364173i
\(973\) −37193.3 37193.3i −1.22545 1.22545i
\(974\) −12602.5 8695.07i −0.414590 0.286045i
\(975\) 0 0
\(976\) −12836.8 + 11391.2i −0.420999 + 0.373590i
\(977\) −9765.98 + 9765.98i −0.319797 + 0.319797i −0.848689 0.528892i \(-0.822608\pi\)
0.528892 + 0.848689i \(0.322608\pi\)
\(978\) −6976.49 38025.5i −0.228102 1.24327i
\(979\) −25980.8 −0.848162
\(980\) 0 0
\(981\) 4904.70 0.159628
\(982\) −7627.15 41571.9i −0.247854 1.35093i
\(983\) −33483.4 + 33483.4i −1.08642 + 1.08642i −0.0905295 + 0.995894i \(0.528856\pi\)
−0.995894 + 0.0905295i \(0.971144\pi\)
\(984\) −3651.16 + 14852.7i −0.118287 + 0.481185i
\(985\) 0 0
\(986\) −21577.5 14887.4i −0.696926 0.480842i
\(987\) 14610.6 + 14610.6i 0.471186 + 0.471186i
\(988\) −4520.19 2032.14i −0.145553 0.0654363i
\(989\) 20253.0i 0.651171i
\(990\) 0 0
\(991\) 35651.6i 1.14280i −0.820673 0.571398i \(-0.806401\pi\)
0.820673 0.571398i \(-0.193599\pi\)
\(992\) −8888.02 6948.62i −0.284471 0.222398i
\(993\) 35544.4 + 35544.4i 1.13592 + 1.13592i
\(994\) 18369.8 26625.0i 0.586173 0.849591i
\(995\) 0 0
\(996\) 13560.9 + 35713.0i 0.431420 + 1.13616i
\(997\) 19421.9 19421.9i 0.616949 0.616949i −0.327799 0.944748i \(-0.606307\pi\)
0.944748 + 0.327799i \(0.106307\pi\)
\(998\) 6466.76 1186.45i 0.205112 0.0376316i
\(999\) −12703.6 −0.402327
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 100.4.e.e.43.6 12
4.3 odd 2 inner 100.4.e.e.43.3 12
5.2 odd 4 inner 100.4.e.e.7.3 12
5.3 odd 4 20.4.e.b.7.4 yes 12
5.4 even 2 20.4.e.b.3.1 12
15.8 even 4 180.4.k.e.127.3 12
15.14 odd 2 180.4.k.e.163.6 12
20.3 even 4 20.4.e.b.7.1 yes 12
20.7 even 4 inner 100.4.e.e.7.6 12
20.19 odd 2 20.4.e.b.3.4 yes 12
40.3 even 4 320.4.n.k.127.2 12
40.13 odd 4 320.4.n.k.127.5 12
40.19 odd 2 320.4.n.k.63.5 12
40.29 even 2 320.4.n.k.63.2 12
60.23 odd 4 180.4.k.e.127.6 12
60.59 even 2 180.4.k.e.163.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.4.e.b.3.1 12 5.4 even 2
20.4.e.b.3.4 yes 12 20.19 odd 2
20.4.e.b.7.1 yes 12 20.3 even 4
20.4.e.b.7.4 yes 12 5.3 odd 4
100.4.e.e.7.3 12 5.2 odd 4 inner
100.4.e.e.7.6 12 20.7 even 4 inner
100.4.e.e.43.3 12 4.3 odd 2 inner
100.4.e.e.43.6 12 1.1 even 1 trivial
180.4.k.e.127.3 12 15.8 even 4
180.4.k.e.127.6 12 60.23 odd 4
180.4.k.e.163.3 12 60.59 even 2
180.4.k.e.163.6 12 15.14 odd 2
320.4.n.k.63.2 12 40.29 even 2
320.4.n.k.63.5 12 40.19 odd 2
320.4.n.k.127.2 12 40.3 even 4
320.4.n.k.127.5 12 40.13 odd 4