Properties

Label 126.4.g.e.109.2
Level $126$
Weight $4$
Character 126.109
Analytic conductor $7.434$
Analytic rank $0$
Dimension $4$
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] = [126,4,Mod(37,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), 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: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(3.72311 + 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.4.g.e.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} +(-12.3924 - 13.7633i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} +(-12.3924 - 13.7633i) q^{7} +8.00000 q^{8} +(10.4462 - 18.0934i) q^{10} +(-30.5618 + 52.9346i) q^{11} -59.2311 q^{13} +(-11.4462 + 35.2276i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-10.2311 + 17.7208i) q^{17} +(40.1693 + 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(79.1236 + 137.046i) q^{23} +(7.93822 - 13.7494i) q^{25} +(59.2311 + 102.591i) q^{26} +(72.4622 - 15.4022i) q^{28} -85.1236 q^{29} +(-121.747 + 210.872i) q^{31} +(-16.0000 + 27.7128i) q^{32} +40.9244 q^{34} +(59.7849 - 183.998i) q^{35} +(-145.185 - 251.468i) q^{37} +(80.3387 - 139.151i) q^{38} +(41.7849 + 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(-122.247 - 211.738i) q^{44} +(158.247 - 274.092i) q^{46} +(84.6453 + 146.610i) q^{47} +(-35.8547 + 341.121i) q^{49} -31.7529 q^{50} +(118.462 - 205.183i) q^{52} +(125.056 - 216.603i) q^{53} -638.510 q^{55} +(-99.1396 - 110.106i) q^{56} +(85.1236 + 147.438i) q^{58} +(402.610 - 697.341i) q^{59} +(-16.5858 - 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(-309.371 - 535.846i) q^{65} +(138.691 - 240.220i) q^{67} +(-40.9244 - 70.8832i) q^{68} +(-378.478 + 80.4472i) q^{70} -631.506 q^{71} +(384.142 - 665.353i) q^{73} +(-290.371 + 502.937i) q^{74} -321.355 q^{76} +(1107.29 - 235.359i) q^{77} +(209.365 + 362.631i) q^{79} +(83.5698 - 144.747i) q^{80} +(168.000 + 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(-7.62934 - 13.2144i) q^{86} +(-244.494 + 423.476i) q^{88} +(786.048 + 1361.48i) q^{89} +(734.018 + 815.213i) q^{91} -632.988 q^{92} +(169.291 - 293.220i) q^{94} +(-419.618 + 726.799i) q^{95} +1045.16 q^{97} +(626.693 - 279.019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8} + 14 q^{10} - 25 q^{11} - 98 q^{13} - 18 q^{14} - 32 q^{16} + 98 q^{17} + 119 q^{19} - 56 q^{20} + 100 q^{22} + 122 q^{23} + 129 q^{25} + 98 q^{26} + 12 q^{28} - 146 q^{29} - 98 q^{31} - 64 q^{32} - 392 q^{34} + 128 q^{35} - 289 q^{37} + 238 q^{38} + 56 q^{40} - 672 q^{41} + 614 q^{43} - 100 q^{44} + 244 q^{46} + 672 q^{47} + 190 q^{49} - 516 q^{50} + 196 q^{52} - 375 q^{53} - 1526 q^{55} + 48 q^{56} + 146 q^{58} + 763 q^{59} + 406 q^{61} + 392 q^{62} + 256 q^{64} - 654 q^{65} + 1041 q^{67} + 392 q^{68} - 986 q^{70} - 3304 q^{71} + 189 q^{73} - 578 q^{74} - 952 q^{76} + 3415 q^{77} - 524 q^{79} + 112 q^{80} + 672 q^{82} - 574 q^{83} - 1244 q^{85} - 614 q^{86} - 200 q^{88} + 2394 q^{89} + 1783 q^{91} - 976 q^{92} + 1344 q^{94} - 706 q^{95} - 126 q^{97} + 2090 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 5.22311 + 9.04669i 0.467169 + 0.809161i 0.999296 0.0375035i \(-0.0119405\pi\)
−0.532127 + 0.846664i \(0.678607\pi\)
\(6\) 0 0
\(7\) −12.3924 13.7633i −0.669129 0.743146i
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 10.4462 18.0934i 0.330339 0.572163i
\(11\) −30.5618 + 52.9346i −0.837702 + 1.45094i 0.0541093 + 0.998535i \(0.482768\pi\)
−0.891811 + 0.452407i \(0.850565\pi\)
\(12\) 0 0
\(13\) −59.2311 −1.26367 −0.631837 0.775102i \(-0.717699\pi\)
−0.631837 + 0.775102i \(0.717699\pi\)
\(14\) −11.4462 + 35.2276i −0.218509 + 0.672498i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −10.2311 + 17.7208i −0.145965 + 0.252819i −0.929733 0.368235i \(-0.879962\pi\)
0.783767 + 0.621054i \(0.213295\pi\)
\(18\) 0 0
\(19\) 40.1693 + 69.5753i 0.485025 + 0.840088i 0.999852 0.0172061i \(-0.00547713\pi\)
−0.514827 + 0.857294i \(0.672144\pi\)
\(20\) −41.7849 −0.467169
\(21\) 0 0
\(22\) 122.247 1.18469
\(23\) 79.1236 + 137.046i 0.717322 + 1.24244i 0.962057 + 0.272848i \(0.0879656\pi\)
−0.244735 + 0.969590i \(0.578701\pi\)
\(24\) 0 0
\(25\) 7.93822 13.7494i 0.0635058 0.109995i
\(26\) 59.2311 + 102.591i 0.446776 + 0.773839i
\(27\) 0 0
\(28\) 72.4622 15.4022i 0.489074 0.103955i
\(29\) −85.1236 −0.545071 −0.272535 0.962146i \(-0.587862\pi\)
−0.272535 + 0.962146i \(0.587862\pi\)
\(30\) 0 0
\(31\) −121.747 + 210.872i −0.705369 + 1.22173i 0.261190 + 0.965287i \(0.415885\pi\)
−0.966558 + 0.256447i \(0.917448\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 40.9244 0.206426
\(35\) 59.7849 183.998i 0.288728 0.888608i
\(36\) 0 0
\(37\) −145.185 251.468i −0.645090 1.11733i −0.984281 0.176611i \(-0.943487\pi\)
0.339191 0.940718i \(-0.389847\pi\)
\(38\) 80.3387 139.151i 0.342965 0.594032i
\(39\) 0 0
\(40\) 41.7849 + 72.3735i 0.165169 + 0.286082i
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 0 0
\(43\) 7.62934 0.0270573 0.0135286 0.999908i \(-0.495694\pi\)
0.0135286 + 0.999908i \(0.495694\pi\)
\(44\) −122.247 211.738i −0.418851 0.725471i
\(45\) 0 0
\(46\) 158.247 274.092i 0.507223 0.878536i
\(47\) 84.6453 + 146.610i 0.262698 + 0.455006i 0.966958 0.254936i \(-0.0820545\pi\)
−0.704260 + 0.709942i \(0.748721\pi\)
\(48\) 0 0
\(49\) −35.8547 + 341.121i −0.104533 + 0.994521i
\(50\) −31.7529 −0.0898107
\(51\) 0 0
\(52\) 118.462 205.183i 0.315918 0.547187i
\(53\) 125.056 216.603i 0.324109 0.561373i −0.657223 0.753696i \(-0.728269\pi\)
0.981332 + 0.192324i \(0.0616023\pi\)
\(54\) 0 0
\(55\) −638.510 −1.56539
\(56\) −99.1396 110.106i −0.236573 0.262742i
\(57\) 0 0
\(58\) 85.1236 + 147.438i 0.192712 + 0.333786i
\(59\) 402.610 697.341i 0.888395 1.53875i 0.0466235 0.998913i \(-0.485154\pi\)
0.841772 0.539833i \(-0.181513\pi\)
\(60\) 0 0
\(61\) −16.5858 28.7274i −0.0348130 0.0602978i 0.848094 0.529846i \(-0.177750\pi\)
−0.882907 + 0.469548i \(0.844417\pi\)
\(62\) 486.988 0.997542
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −309.371 535.846i −0.590349 1.02252i
\(66\) 0 0
\(67\) 138.691 240.220i 0.252893 0.438023i −0.711428 0.702759i \(-0.751951\pi\)
0.964321 + 0.264736i \(0.0852847\pi\)
\(68\) −40.9244 70.8832i −0.0729826 0.126410i
\(69\) 0 0
\(70\) −378.478 + 80.4472i −0.646240 + 0.137361i
\(71\) −631.506 −1.05558 −0.527788 0.849376i \(-0.676979\pi\)
−0.527788 + 0.849376i \(0.676979\pi\)
\(72\) 0 0
\(73\) 384.142 665.353i 0.615896 1.06676i −0.374331 0.927295i \(-0.622128\pi\)
0.990227 0.139468i \(-0.0445391\pi\)
\(74\) −290.371 + 502.937i −0.456147 + 0.790070i
\(75\) 0 0
\(76\) −321.355 −0.485025
\(77\) 1107.29 235.359i 1.63879 0.348333i
\(78\) 0 0
\(79\) 209.365 + 362.631i 0.298169 + 0.516445i 0.975717 0.219034i \(-0.0702906\pi\)
−0.677548 + 0.735479i \(0.736957\pi\)
\(80\) 83.5698 144.747i 0.116792 0.202290i
\(81\) 0 0
\(82\) 168.000 + 290.985i 0.226250 + 0.391876i
\(83\) −761.714 −1.00734 −0.503668 0.863897i \(-0.668017\pi\)
−0.503668 + 0.863897i \(0.668017\pi\)
\(84\) 0 0
\(85\) −213.753 −0.272762
\(86\) −7.62934 13.2144i −0.00956619 0.0165691i
\(87\) 0 0
\(88\) −244.494 + 423.476i −0.296172 + 0.512986i
\(89\) 786.048 + 1361.48i 0.936190 + 1.62153i 0.772498 + 0.635017i \(0.219007\pi\)
0.163692 + 0.986511i \(0.447660\pi\)
\(90\) 0 0
\(91\) 734.018 + 815.213i 0.845561 + 0.939094i
\(92\) −632.988 −0.717322
\(93\) 0 0
\(94\) 169.291 293.220i 0.185755 0.321738i
\(95\) −419.618 + 726.799i −0.453178 + 0.784927i
\(96\) 0 0
\(97\) 1045.16 1.09402 0.547012 0.837125i \(-0.315765\pi\)
0.547012 + 0.837125i \(0.315765\pi\)
\(98\) 626.693 279.019i 0.645975 0.287604i
\(99\) 0 0
\(100\) 31.7529 + 54.9976i 0.0317529 + 0.0549976i
\(101\) −487.961 + 845.173i −0.480732 + 0.832652i −0.999756 0.0221078i \(-0.992962\pi\)
0.519024 + 0.854760i \(0.326296\pi\)
\(102\) 0 0
\(103\) 321.572 + 556.979i 0.307626 + 0.532823i 0.977842 0.209342i \(-0.0671323\pi\)
−0.670217 + 0.742165i \(0.733799\pi\)
\(104\) −473.849 −0.446776
\(105\) 0 0
\(106\) −500.224 −0.458359
\(107\) 155.797 + 269.849i 0.140762 + 0.243806i 0.927784 0.373119i \(-0.121712\pi\)
−0.787022 + 0.616925i \(0.788378\pi\)
\(108\) 0 0
\(109\) 932.915 1615.86i 0.819790 1.41992i −0.0860476 0.996291i \(-0.527424\pi\)
0.905837 0.423626i \(-0.139243\pi\)
\(110\) 638.510 + 1105.93i 0.553451 + 0.958604i
\(111\) 0 0
\(112\) −91.5698 + 281.821i −0.0772547 + 0.237764i
\(113\) −1720.49 −1.43231 −0.716153 0.697944i \(-0.754099\pi\)
−0.716153 + 0.697944i \(0.754099\pi\)
\(114\) 0 0
\(115\) −826.542 + 1431.61i −0.670221 + 1.16086i
\(116\) 170.247 294.877i 0.136268 0.236022i
\(117\) 0 0
\(118\) −1610.44 −1.25638
\(119\) 370.684 78.7906i 0.285551 0.0606952i
\(120\) 0 0
\(121\) −1202.54 2082.87i −0.903489 1.56489i
\(122\) −33.1715 + 57.4548i −0.0246165 + 0.0426370i
\(123\) 0 0
\(124\) −486.988 843.489i −0.352684 0.610867i
\(125\) 1471.63 1.05301
\(126\) 0 0
\(127\) 142.236 0.0993808 0.0496904 0.998765i \(-0.484177\pi\)
0.0496904 + 0.998765i \(0.484177\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −618.741 + 1071.69i −0.417440 + 0.723027i
\(131\) 1243.26 + 2153.38i 0.829189 + 1.43620i 0.898676 + 0.438614i \(0.144530\pi\)
−0.0694870 + 0.997583i \(0.522136\pi\)
\(132\) 0 0
\(133\) 459.787 1415.07i 0.299764 0.922572i
\(134\) −554.764 −0.357644
\(135\) 0 0
\(136\) −81.8489 + 141.766i −0.0516065 + 0.0893851i
\(137\) −1298.61 + 2249.25i −0.809835 + 1.40268i 0.103143 + 0.994667i \(0.467110\pi\)
−0.912978 + 0.408009i \(0.866223\pi\)
\(138\) 0 0
\(139\) 1600.52 0.976651 0.488325 0.872662i \(-0.337608\pi\)
0.488325 + 0.872662i \(0.337608\pi\)
\(140\) 517.817 + 575.096i 0.312597 + 0.347175i
\(141\) 0 0
\(142\) 631.506 + 1093.80i 0.373203 + 0.646406i
\(143\) 1810.21 3135.37i 1.05858 1.83352i
\(144\) 0 0
\(145\) −444.610 770.087i −0.254640 0.441050i
\(146\) −1536.57 −0.871008
\(147\) 0 0
\(148\) 1161.48 0.645090
\(149\) −1468.85 2544.13i −0.807605 1.39881i −0.914518 0.404545i \(-0.867430\pi\)
0.106913 0.994268i \(-0.465903\pi\)
\(150\) 0 0
\(151\) −911.662 + 1579.05i −0.491325 + 0.850999i −0.999950 0.00998867i \(-0.996820\pi\)
0.508625 + 0.860988i \(0.330154\pi\)
\(152\) 321.355 + 556.603i 0.171482 + 0.297016i
\(153\) 0 0
\(154\) −1514.94 1682.52i −0.792710 0.880398i
\(155\) −2543.59 −1.31811
\(156\) 0 0
\(157\) −316.824 + 548.755i −0.161053 + 0.278952i −0.935247 0.353997i \(-0.884822\pi\)
0.774194 + 0.632949i \(0.218156\pi\)
\(158\) 418.730 725.261i 0.210838 0.365182i
\(159\) 0 0
\(160\) −334.279 −0.165169
\(161\) 905.666 2787.33i 0.443332 1.36443i
\(162\) 0 0
\(163\) 672.853 + 1165.42i 0.323325 + 0.560015i 0.981172 0.193137i \(-0.0618660\pi\)
−0.657847 + 0.753151i \(0.728533\pi\)
\(164\) 336.000 581.969i 0.159983 0.277098i
\(165\) 0 0
\(166\) 761.714 + 1319.33i 0.356147 + 0.616865i
\(167\) 387.922 0.179750 0.0898751 0.995953i \(-0.471353\pi\)
0.0898751 + 0.995953i \(0.471353\pi\)
\(168\) 0 0
\(169\) 1311.32 0.596870
\(170\) 213.753 + 370.231i 0.0964359 + 0.167032i
\(171\) 0 0
\(172\) −15.2587 + 26.4288i −0.00676432 + 0.0117161i
\(173\) 311.330 + 539.239i 0.136821 + 0.236980i 0.926291 0.376808i \(-0.122978\pi\)
−0.789471 + 0.613788i \(0.789645\pi\)
\(174\) 0 0
\(175\) −287.611 + 61.1329i −0.124236 + 0.0264069i
\(176\) 977.977 0.418851
\(177\) 0 0
\(178\) 1572.10 2722.95i 0.661986 1.14659i
\(179\) 224.965 389.651i 0.0939368 0.162703i −0.815228 0.579141i \(-0.803388\pi\)
0.909164 + 0.416437i \(0.136721\pi\)
\(180\) 0 0
\(181\) 184.353 0.0757063 0.0378532 0.999283i \(-0.487948\pi\)
0.0378532 + 0.999283i \(0.487948\pi\)
\(182\) 677.972 2086.57i 0.276125 0.849818i
\(183\) 0 0
\(184\) 632.988 + 1096.37i 0.253612 + 0.439268i
\(185\) 1516.64 2626.89i 0.602732 1.04396i
\(186\) 0 0
\(187\) −625.362 1083.16i −0.244551 0.423574i
\(188\) −677.163 −0.262698
\(189\) 0 0
\(190\) 1678.47 0.640890
\(191\) −175.483 303.945i −0.0664789 0.115145i 0.830870 0.556466i \(-0.187843\pi\)
−0.897349 + 0.441321i \(0.854510\pi\)
\(192\) 0 0
\(193\) −764.129 + 1323.51i −0.284991 + 0.493619i −0.972607 0.232456i \(-0.925324\pi\)
0.687616 + 0.726074i \(0.258657\pi\)
\(194\) −1045.16 1810.28i −0.386796 0.669950i
\(195\) 0 0
\(196\) −1109.97 806.446i −0.404507 0.293894i
\(197\) 2874.65 1.03965 0.519823 0.854274i \(-0.325998\pi\)
0.519823 + 0.854274i \(0.325998\pi\)
\(198\) 0 0
\(199\) −2474.35 + 4285.70i −0.881418 + 1.52666i −0.0316529 + 0.999499i \(0.510077\pi\)
−0.849765 + 0.527162i \(0.823256\pi\)
\(200\) 63.5058 109.995i 0.0224527 0.0388892i
\(201\) 0 0
\(202\) 1951.84 0.679858
\(203\) 1054.89 + 1171.58i 0.364723 + 0.405067i
\(204\) 0 0
\(205\) −877.483 1519.84i −0.298956 0.517808i
\(206\) 643.144 1113.96i 0.217524 0.376763i
\(207\) 0 0
\(208\) 473.849 + 820.730i 0.157959 + 0.273593i
\(209\) −4910.58 −1.62523
\(210\) 0 0
\(211\) −5280.90 −1.72299 −0.861497 0.507762i \(-0.830473\pi\)
−0.861497 + 0.507762i \(0.830473\pi\)
\(212\) 500.224 + 866.413i 0.162054 + 0.280686i
\(213\) 0 0
\(214\) 311.595 539.698i 0.0995335 0.172397i
\(215\) 39.8489 + 69.0203i 0.0126403 + 0.0218937i
\(216\) 0 0
\(217\) 4411.03 937.585i 1.37991 0.293306i
\(218\) −3731.66 −1.15936
\(219\) 0 0
\(220\) 1277.02 2211.86i 0.391349 0.677836i
\(221\) 606.000 1049.62i 0.184452 0.319481i
\(222\) 0 0
\(223\) 3996.57 1.20013 0.600067 0.799950i \(-0.295141\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(224\) 579.698 123.217i 0.172914 0.0367536i
\(225\) 0 0
\(226\) 1720.49 + 2979.98i 0.506396 + 0.877104i
\(227\) −269.296 + 466.434i −0.0787392 + 0.136380i −0.902706 0.430257i \(-0.858423\pi\)
0.823967 + 0.566638i \(0.191756\pi\)
\(228\) 0 0
\(229\) −2085.80 3612.72i −0.601895 1.04251i −0.992534 0.121968i \(-0.961079\pi\)
0.390639 0.920544i \(-0.372254\pi\)
\(230\) 3306.17 0.947836
\(231\) 0 0
\(232\) −680.988 −0.192712
\(233\) 769.865 + 1333.45i 0.216461 + 0.374922i 0.953724 0.300684i \(-0.0972151\pi\)
−0.737262 + 0.675607i \(0.763882\pi\)
\(234\) 0 0
\(235\) −884.224 + 1531.52i −0.245449 + 0.425129i
\(236\) 1610.44 + 2789.36i 0.444198 + 0.769373i
\(237\) 0 0
\(238\) −507.154 563.254i −0.138126 0.153405i
\(239\) −3132.67 −0.847848 −0.423924 0.905698i \(-0.639348\pi\)
−0.423924 + 0.905698i \(0.639348\pi\)
\(240\) 0 0
\(241\) −1303.35 + 2257.46i −0.348365 + 0.603386i −0.985959 0.166987i \(-0.946596\pi\)
0.637594 + 0.770372i \(0.279930\pi\)
\(242\) −2405.09 + 4165.74i −0.638863 + 1.10654i
\(243\) 0 0
\(244\) 132.686 0.0348130
\(245\) −3273.29 + 1457.35i −0.853562 + 0.380026i
\(246\) 0 0
\(247\) −2379.27 4121.02i −0.612913 1.06160i
\(248\) −973.977 + 1686.98i −0.249385 + 0.431948i
\(249\) 0 0
\(250\) −1471.63 2548.93i −0.372295 0.644834i
\(251\) 3426.24 0.861603 0.430801 0.902447i \(-0.358231\pi\)
0.430801 + 0.902447i \(0.358231\pi\)
\(252\) 0 0
\(253\) −9672.63 −2.40361
\(254\) −142.236 246.359i −0.0351364 0.0608581i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2928.72 + 5072.69i 0.710850 + 1.23123i 0.964538 + 0.263943i \(0.0850230\pi\)
−0.253688 + 0.967286i \(0.581644\pi\)
\(258\) 0 0
\(259\) −1661.82 + 5114.53i −0.398690 + 1.22703i
\(260\) 2474.97 0.590349
\(261\) 0 0
\(262\) 2486.51 4306.76i 0.586325 1.01554i
\(263\) −542.965 + 940.443i −0.127303 + 0.220495i −0.922631 0.385684i \(-0.873965\pi\)
0.795328 + 0.606180i \(0.207299\pi\)
\(264\) 0 0
\(265\) 2612.73 0.605654
\(266\) −2910.76 + 618.695i −0.670940 + 0.142611i
\(267\) 0 0
\(268\) 554.764 + 960.880i 0.126446 + 0.219012i
\(269\) −2789.73 + 4831.95i −0.632315 + 1.09520i 0.354763 + 0.934956i \(0.384562\pi\)
−0.987077 + 0.160245i \(0.948772\pi\)
\(270\) 0 0
\(271\) 280.164 + 485.258i 0.0627997 + 0.108772i 0.895716 0.444627i \(-0.146664\pi\)
−0.832916 + 0.553399i \(0.813330\pi\)
\(272\) 327.396 0.0729826
\(273\) 0 0
\(274\) 5194.42 1.14528
\(275\) 485.212 + 840.413i 0.106398 + 0.184286i
\(276\) 0 0
\(277\) 2254.04 3904.11i 0.488924 0.846842i −0.510994 0.859584i \(-0.670723\pi\)
0.999919 + 0.0127421i \(0.00405606\pi\)
\(278\) −1600.52 2772.19i −0.345298 0.598074i
\(279\) 0 0
\(280\) 478.279 1471.98i 0.102081 0.314170i
\(281\) 4329.75 0.919186 0.459593 0.888130i \(-0.347995\pi\)
0.459593 + 0.888130i \(0.347995\pi\)
\(282\) 0 0
\(283\) 435.526 754.353i 0.0914817 0.158451i −0.816653 0.577129i \(-0.804173\pi\)
0.908135 + 0.418678i \(0.137506\pi\)
\(284\) 1263.01 2187.60i 0.263894 0.457078i
\(285\) 0 0
\(286\) −7240.83 −1.49706
\(287\) 2081.93 + 2312.23i 0.428197 + 0.475563i
\(288\) 0 0
\(289\) 2247.15 + 3892.18i 0.457388 + 0.792220i
\(290\) −889.220 + 1540.17i −0.180058 + 0.311869i
\(291\) 0 0
\(292\) 1536.57 + 2661.41i 0.307948 + 0.533381i
\(293\) −1651.91 −0.329372 −0.164686 0.986346i \(-0.552661\pi\)
−0.164686 + 0.986346i \(0.552661\pi\)
\(294\) 0 0
\(295\) 8411.50 1.66012
\(296\) −1161.48 2011.75i −0.228074 0.395035i
\(297\) 0 0
\(298\) −2937.71 + 5088.26i −0.571063 + 0.989110i
\(299\) −4686.58 8117.39i −0.906460 1.57004i
\(300\) 0 0
\(301\) −94.5461 105.005i −0.0181048 0.0201075i
\(302\) 3646.65 0.694838
\(303\) 0 0
\(304\) 642.709 1113.21i 0.121256 0.210022i
\(305\) 173.259 300.093i 0.0325271 0.0563386i
\(306\) 0 0
\(307\) 1016.42 0.188958 0.0944791 0.995527i \(-0.469881\pi\)
0.0944791 + 0.995527i \(0.469881\pi\)
\(308\) −1399.27 + 4306.47i −0.258866 + 0.796701i
\(309\) 0 0
\(310\) 2543.59 + 4405.64i 0.466021 + 0.807172i
\(311\) −4596.53 + 7961.42i −0.838087 + 1.45161i 0.0534049 + 0.998573i \(0.482993\pi\)
−0.891492 + 0.453037i \(0.850341\pi\)
\(312\) 0 0
\(313\) 3346.30 + 5795.97i 0.604295 + 1.04667i 0.992162 + 0.124954i \(0.0398784\pi\)
−0.387868 + 0.921715i \(0.626788\pi\)
\(314\) 1267.30 0.227763
\(315\) 0 0
\(316\) −1674.92 −0.298169
\(317\) 3526.25 + 6107.64i 0.624775 + 1.08214i 0.988584 + 0.150669i \(0.0481426\pi\)
−0.363809 + 0.931473i \(0.618524\pi\)
\(318\) 0 0
\(319\) 2601.53 4505.98i 0.456607 0.790866i
\(320\) 334.279 + 578.988i 0.0583962 + 0.101145i
\(321\) 0 0
\(322\) −5733.47 + 1218.67i −0.992279 + 0.210913i
\(323\) −1643.91 −0.283187
\(324\) 0 0
\(325\) −470.190 + 814.393i −0.0802506 + 0.138998i
\(326\) 1345.71 2330.83i 0.228625 0.395990i
\(327\) 0 0
\(328\) −1344.00 −0.226250
\(329\) 968.869 2981.85i 0.162357 0.499680i
\(330\) 0 0
\(331\) −1570.19 2719.64i −0.260741 0.451616i 0.705698 0.708513i \(-0.250633\pi\)
−0.966439 + 0.256896i \(0.917300\pi\)
\(332\) 1523.43 2638.65i 0.251834 0.436190i
\(333\) 0 0
\(334\) −387.922 671.900i −0.0635513 0.110074i
\(335\) 2897.60 0.472575
\(336\) 0 0
\(337\) 2743.87 0.443526 0.221763 0.975101i \(-0.428819\pi\)
0.221763 + 0.975101i \(0.428819\pi\)
\(338\) −1311.32 2271.28i −0.211026 0.365507i
\(339\) 0 0
\(340\) 427.506 740.462i 0.0681905 0.118109i
\(341\) −7441.62 12889.3i −1.18178 2.04690i
\(342\) 0 0
\(343\) 5139.26 3733.84i 0.809021 0.587780i
\(344\) 61.0347 0.00956619
\(345\) 0 0
\(346\) 622.660 1078.48i 0.0967468 0.167570i
\(347\) 5218.45 9038.62i 0.807323 1.39832i −0.107389 0.994217i \(-0.534249\pi\)
0.914712 0.404107i \(-0.132418\pi\)
\(348\) 0 0
\(349\) −2257.01 −0.346175 −0.173087 0.984906i \(-0.555374\pi\)
−0.173087 + 0.984906i \(0.555374\pi\)
\(350\) 393.496 + 437.023i 0.0600950 + 0.0667425i
\(351\) 0 0
\(352\) −977.977 1693.91i −0.148086 0.256493i
\(353\) 2808.22 4863.98i 0.423418 0.733381i −0.572854 0.819658i \(-0.694164\pi\)
0.996271 + 0.0862770i \(0.0274970\pi\)
\(354\) 0 0
\(355\) −3298.42 5713.04i −0.493133 0.854131i
\(356\) −6288.38 −0.936190
\(357\) 0 0
\(358\) −899.861 −0.132847
\(359\) −397.795 689.002i −0.0584815 0.101293i 0.835302 0.549791i \(-0.185293\pi\)
−0.893784 + 0.448498i \(0.851959\pi\)
\(360\) 0 0
\(361\) 202.349 350.479i 0.0295013 0.0510977i
\(362\) −184.353 319.309i −0.0267662 0.0463605i
\(363\) 0 0
\(364\) −4292.02 + 912.287i −0.618030 + 0.131365i
\(365\) 8025.66 1.15091
\(366\) 0 0
\(367\) −4096.99 + 7096.19i −0.582727 + 1.00931i 0.412427 + 0.910990i \(0.364681\pi\)
−0.995155 + 0.0983227i \(0.968652\pi\)
\(368\) 1265.98 2192.74i 0.179330 0.310609i
\(369\) 0 0
\(370\) −6066.55 −0.852392
\(371\) −4530.92 + 963.067i −0.634053 + 0.134771i
\(372\) 0 0
\(373\) −7038.69 12191.4i −0.977076 1.69235i −0.672906 0.739728i \(-0.734954\pi\)
−0.304170 0.952618i \(-0.598379\pi\)
\(374\) −1250.72 + 2166.32i −0.172923 + 0.299512i
\(375\) 0 0
\(376\) 677.163 + 1172.88i 0.0928777 + 0.160869i
\(377\) 5041.96 0.688791
\(378\) 0 0
\(379\) 6221.22 0.843173 0.421587 0.906788i \(-0.361473\pi\)
0.421587 + 0.906788i \(0.361473\pi\)
\(380\) −1678.47 2907.20i −0.226589 0.392463i
\(381\) 0 0
\(382\) −350.965 + 607.890i −0.0470077 + 0.0814197i
\(383\) −5350.71 9267.70i −0.713860 1.23644i −0.963397 0.268077i \(-0.913612\pi\)
0.249537 0.968365i \(-0.419722\pi\)
\(384\) 0 0
\(385\) 7912.70 + 8787.98i 1.04745 + 1.16332i
\(386\) 3056.52 0.403038
\(387\) 0 0
\(388\) −2090.33 + 3620.56i −0.273506 + 0.473726i
\(389\) 2110.81 3656.03i 0.275121 0.476524i −0.695044 0.718967i \(-0.744615\pi\)
0.970166 + 0.242443i \(0.0779487\pi\)
\(390\) 0 0
\(391\) −3238.09 −0.418816
\(392\) −286.837 + 2728.97i −0.0369578 + 0.351616i
\(393\) 0 0
\(394\) −2874.65 4979.04i −0.367570 0.636651i
\(395\) −2187.07 + 3788.12i −0.278591 + 0.482534i
\(396\) 0 0
\(397\) 6037.87 + 10457.9i 0.763305 + 1.32208i 0.941138 + 0.338023i \(0.109758\pi\)
−0.177833 + 0.984061i \(0.556909\pi\)
\(398\) 9897.41 1.24651
\(399\) 0 0
\(400\) −254.023 −0.0317529
\(401\) −2753.19 4768.66i −0.342862 0.593855i 0.642101 0.766620i \(-0.278063\pi\)
−0.984963 + 0.172766i \(0.944730\pi\)
\(402\) 0 0
\(403\) 7211.22 12490.2i 0.891356 1.54387i
\(404\) −1951.84 3380.69i −0.240366 0.416326i
\(405\) 0 0
\(406\) 974.343 2998.70i 0.119103 0.366559i
\(407\) 17748.5 2.16157
\(408\) 0 0
\(409\) −714.089 + 1236.84i −0.0863311 + 0.149530i −0.905958 0.423368i \(-0.860848\pi\)
0.819627 + 0.572898i \(0.194181\pi\)
\(410\) −1754.97 + 3039.69i −0.211394 + 0.366145i
\(411\) 0 0
\(412\) −2572.58 −0.307626
\(413\) −14587.0 + 3100.53i −1.73796 + 0.369412i
\(414\) 0 0
\(415\) −3978.52 6890.99i −0.470597 0.815097i
\(416\) 947.698 1641.46i 0.111694 0.193460i
\(417\) 0 0
\(418\) 4910.58 + 8505.38i 0.574604 + 0.995244i
\(419\) −264.960 −0.0308929 −0.0154465 0.999881i \(-0.504917\pi\)
−0.0154465 + 0.999881i \(0.504917\pi\)
\(420\) 0 0
\(421\) −281.066 −0.0325375 −0.0162688 0.999868i \(-0.505179\pi\)
−0.0162688 + 0.999868i \(0.505179\pi\)
\(422\) 5280.90 + 9146.78i 0.609171 + 1.05511i
\(423\) 0 0
\(424\) 1000.45 1732.83i 0.114590 0.198475i
\(425\) 162.434 + 281.343i 0.0185393 + 0.0321110i
\(426\) 0 0
\(427\) −189.844 + 584.277i −0.0215157 + 0.0662181i
\(428\) −1246.38 −0.140762
\(429\) 0 0
\(430\) 79.6978 138.041i 0.00893806 0.0154812i
\(431\) −893.189 + 1547.05i −0.0998223 + 0.172897i −0.911611 0.411054i \(-0.865161\pi\)
0.811789 + 0.583951i \(0.198494\pi\)
\(432\) 0 0
\(433\) 184.621 0.0204904 0.0102452 0.999948i \(-0.496739\pi\)
0.0102452 + 0.999948i \(0.496739\pi\)
\(434\) −6034.98 6702.55i −0.667484 0.741319i
\(435\) 0 0
\(436\) 3731.66 + 6463.43i 0.409895 + 0.709959i
\(437\) −6356.68 + 11010.1i −0.695838 + 1.20523i
\(438\) 0 0
\(439\) −5637.32 9764.12i −0.612881 1.06154i −0.990752 0.135682i \(-0.956677\pi\)
0.377872 0.925858i \(-0.376656\pi\)
\(440\) −5108.08 −0.553451
\(441\) 0 0
\(442\) −2424.00 −0.260855
\(443\) 3984.92 + 6902.09i 0.427380 + 0.740244i 0.996639 0.0819142i \(-0.0261033\pi\)
−0.569259 + 0.822158i \(0.692770\pi\)
\(444\) 0 0
\(445\) −8211.23 + 14222.3i −0.874718 + 1.51506i
\(446\) −3996.57 6922.25i −0.424311 0.734929i
\(447\) 0 0
\(448\) −793.116 880.849i −0.0836411 0.0928933i
\(449\) −8850.37 −0.930233 −0.465117 0.885249i \(-0.653988\pi\)
−0.465117 + 0.885249i \(0.653988\pi\)
\(450\) 0 0
\(451\) 5134.38 8893.00i 0.536072 0.928504i
\(452\) 3440.99 5959.97i 0.358076 0.620206i
\(453\) 0 0
\(454\) 1077.18 0.111354
\(455\) −3541.13 + 10898.4i −0.364858 + 1.12291i
\(456\) 0 0
\(457\) 6513.65 + 11282.0i 0.666730 + 1.15481i 0.978813 + 0.204756i \(0.0656400\pi\)
−0.312083 + 0.950055i \(0.601027\pi\)
\(458\) −4171.61 + 7225.44i −0.425604 + 0.737167i
\(459\) 0 0
\(460\) −3306.17 5726.45i −0.335111 0.580429i
\(461\) −1261.05 −0.127403 −0.0637016 0.997969i \(-0.520291\pi\)
−0.0637016 + 0.997969i \(0.520291\pi\)
\(462\) 0 0
\(463\) −4005.47 −0.402052 −0.201026 0.979586i \(-0.564427\pi\)
−0.201026 + 0.979586i \(0.564427\pi\)
\(464\) 680.988 + 1179.51i 0.0681338 + 0.118011i
\(465\) 0 0
\(466\) 1539.73 2666.89i 0.153061 0.265110i
\(467\) 8548.91 + 14807.1i 0.847101 + 1.46722i 0.883784 + 0.467895i \(0.154988\pi\)
−0.0366825 + 0.999327i \(0.511679\pi\)
\(468\) 0 0
\(469\) −5024.93 + 1068.07i −0.494733 + 0.105158i
\(470\) 3536.90 0.347117
\(471\) 0 0
\(472\) 3220.88 5578.72i 0.314095 0.544029i
\(473\) −233.166 + 403.856i −0.0226659 + 0.0392586i
\(474\) 0 0
\(475\) 1275.49 0.123208
\(476\) −468.430 + 1441.67i −0.0451060 + 0.138821i
\(477\) 0 0
\(478\) 3132.67 + 5425.95i 0.299760 + 0.519199i
\(479\) 5844.26 10122.6i 0.557477 0.965578i −0.440230 0.897885i \(-0.645103\pi\)
0.997706 0.0676925i \(-0.0215637\pi\)
\(480\) 0 0
\(481\) 8599.49 + 14894.8i 0.815183 + 1.41194i
\(482\) 5213.39 0.492662
\(483\) 0 0
\(484\) 9620.36 0.903489
\(485\) 5459.01 + 9455.28i 0.511095 + 0.885242i
\(486\) 0 0
\(487\) 4812.40 8335.31i 0.447783 0.775583i −0.550458 0.834863i \(-0.685547\pi\)
0.998241 + 0.0592793i \(0.0188803\pi\)
\(488\) −132.686 229.819i −0.0123082 0.0213185i
\(489\) 0 0
\(490\) 5797.49 + 4212.16i 0.534497 + 0.388338i
\(491\) 6320.63 0.580949 0.290475 0.956883i \(-0.406187\pi\)
0.290475 + 0.956883i \(0.406187\pi\)
\(492\) 0 0
\(493\) 870.908 1508.46i 0.0795613 0.137804i
\(494\) −4758.55 + 8242.05i −0.433395 + 0.750662i
\(495\) 0 0
\(496\) 3895.91 0.352684
\(497\) 7825.90 + 8691.58i 0.706317 + 0.784448i
\(498\) 0 0
\(499\) 7527.29 + 13037.6i 0.675286 + 1.16963i 0.976385 + 0.216037i \(0.0693130\pi\)
−0.301100 + 0.953593i \(0.597354\pi\)
\(500\) −2943.25 + 5097.86i −0.263253 + 0.455967i
\(501\) 0 0
\(502\) −3426.24 5934.42i −0.304623 0.527622i
\(503\) −16559.1 −1.46786 −0.733930 0.679225i \(-0.762316\pi\)
−0.733930 + 0.679225i \(0.762316\pi\)
\(504\) 0 0
\(505\) −10194.7 −0.898333
\(506\) 9672.63 + 16753.5i 0.849804 + 1.47190i
\(507\) 0 0
\(508\) −284.471 + 492.718i −0.0248452 + 0.0430332i
\(509\) −6669.48 11551.9i −0.580785 1.00595i −0.995387 0.0959462i \(-0.969412\pi\)
0.414601 0.910003i \(-0.363921\pi\)
\(510\) 0 0
\(511\) −13917.9 + 2958.31i −1.20487 + 0.256101i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 5857.44 10145.4i 0.502647 0.870610i
\(515\) −3359.21 + 5818.33i −0.287426 + 0.497837i
\(516\) 0 0
\(517\) −10347.6 −0.880250
\(518\) 10520.5 2236.17i 0.892359 0.189675i
\(519\) 0 0
\(520\) −2474.97 4286.77i −0.208720 0.361514i
\(521\) −3591.35 + 6220.40i −0.301996 + 0.523072i −0.976588 0.215118i \(-0.930986\pi\)
0.674592 + 0.738191i \(0.264320\pi\)
\(522\) 0 0
\(523\) −4815.07 8339.94i −0.402578 0.697285i 0.591459 0.806335i \(-0.298552\pi\)
−0.994036 + 0.109050i \(0.965219\pi\)
\(524\) −9946.04 −0.829189
\(525\) 0 0
\(526\) 2171.86 0.180034
\(527\) −2491.22 4314.91i −0.205919 0.356661i
\(528\) 0 0
\(529\) −6437.57 + 11150.2i −0.529101 + 0.916430i
\(530\) −2612.73 4525.37i −0.214131 0.370886i
\(531\) 0 0
\(532\) 3982.37 + 4422.89i 0.324544 + 0.360445i
\(533\) 9950.83 0.808664
\(534\) 0 0
\(535\) −1627.49 + 2818.90i −0.131519 + 0.227798i
\(536\) 1109.53 1921.76i 0.0894111 0.154865i
\(537\) 0 0
\(538\) 11158.9 0.894228
\(539\) −16961.3 12323.2i −1.35543 0.984783i
\(540\) 0 0
\(541\) −7774.74 13466.2i −0.617860 1.07016i −0.989875 0.141938i \(-0.954667\pi\)
0.372016 0.928227i \(-0.378667\pi\)
\(542\) 560.327 970.515i 0.0444061 0.0769136i
\(543\) 0 0
\(544\) −327.396 567.066i −0.0258032 0.0446925i
\(545\) 19490.9 1.53192
\(546\) 0 0
\(547\) −5917.38 −0.462539 −0.231270 0.972890i \(-0.574288\pi\)
−0.231270 + 0.972890i \(0.574288\pi\)
\(548\) −5194.42 8997.01i −0.404918 0.701338i
\(549\) 0 0
\(550\) 970.425 1680.83i 0.0752346 0.130310i
\(551\) −3419.36 5922.50i −0.264373 0.457907i
\(552\) 0 0
\(553\) 2396.44 7375.42i 0.184280 0.567152i
\(554\) −9016.15 −0.691444
\(555\) 0 0
\(556\) −3201.04 + 5544.37i −0.244163 + 0.422902i
\(557\) 1065.93 1846.25i 0.0810862 0.140445i −0.822631 0.568576i \(-0.807494\pi\)
0.903717 + 0.428131i \(0.140828\pi\)
\(558\) 0 0
\(559\) −451.894 −0.0341916
\(560\) −3027.83 + 643.578i −0.228480 + 0.0485645i
\(561\) 0 0
\(562\) −4329.75 7499.35i −0.324981 0.562884i
\(563\) −3687.95 + 6387.72i −0.276072 + 0.478171i −0.970405 0.241483i \(-0.922366\pi\)
0.694333 + 0.719654i \(0.255700\pi\)
\(564\) 0 0
\(565\) −8986.33 15564.8i −0.669129 1.15897i
\(566\) −1742.10 −0.129375
\(567\) 0 0
\(568\) −5052.05 −0.373203
\(569\) −6350.42 10999.3i −0.467880 0.810391i 0.531447 0.847092i \(-0.321649\pi\)
−0.999326 + 0.0367005i \(0.988315\pi\)
\(570\) 0 0
\(571\) 3845.06 6659.84i 0.281805 0.488101i −0.690024 0.723786i \(-0.742400\pi\)
0.971829 + 0.235686i \(0.0757335\pi\)
\(572\) 7240.83 + 12541.5i 0.529291 + 0.916759i
\(573\) 0 0
\(574\) 1922.97 5918.24i 0.139831 0.430353i
\(575\) 2512.40 0.182216
\(576\) 0 0
\(577\) −1547.43 + 2680.23i −0.111647 + 0.193379i −0.916435 0.400185i \(-0.868946\pi\)
0.804787 + 0.593563i \(0.202279\pi\)
\(578\) 4494.30 7784.35i 0.323422 0.560184i
\(579\) 0 0
\(580\) 3556.88 0.254640
\(581\) 9439.50 + 10483.7i 0.674038 + 0.748598i
\(582\) 0 0
\(583\) 7643.87 + 13239.6i 0.543013 + 0.940526i
\(584\) 3073.13 5322.82i 0.217752 0.377158i
\(585\) 0 0
\(586\) 1651.91 + 2861.20i 0.116450 + 0.201698i
\(587\) 9967.83 0.700880 0.350440 0.936585i \(-0.386032\pi\)
0.350440 + 0.936585i \(0.386032\pi\)
\(588\) 0 0
\(589\) −19562.0 −1.36849
\(590\) −8411.50 14569.1i −0.586942 1.01661i
\(591\) 0 0
\(592\) −2322.97 + 4023.49i −0.161272 + 0.279332i
\(593\) 884.864 + 1532.63i 0.0612766 + 0.106134i 0.895036 0.445993i \(-0.147149\pi\)
−0.833760 + 0.552127i \(0.813816\pi\)
\(594\) 0 0
\(595\) 2648.92 + 2941.94i 0.182513 + 0.202702i
\(596\) 11750.8 0.807605
\(597\) 0 0
\(598\) −9373.15 + 16234.8i −0.640964 + 1.11018i
\(599\) −3173.66 + 5496.95i −0.216481 + 0.374957i −0.953730 0.300665i \(-0.902791\pi\)
0.737248 + 0.675622i \(0.236125\pi\)
\(600\) 0 0
\(601\) 22005.7 1.49356 0.746781 0.665070i \(-0.231599\pi\)
0.746781 + 0.665070i \(0.231599\pi\)
\(602\) −87.3271 + 268.763i −0.00591227 + 0.0181960i
\(603\) 0 0
\(604\) −3646.65 6316.18i −0.245662 0.425500i
\(605\) 12562.0 21758.1i 0.844165 1.46214i
\(606\) 0 0
\(607\) −8853.55 15334.8i −0.592017 1.02540i −0.993960 0.109740i \(-0.964998\pi\)
0.401943 0.915665i \(-0.368335\pi\)
\(608\) −2570.84 −0.171482
\(609\) 0 0
\(610\) −693.035 −0.0460003
\(611\) −5013.64 8683.87i −0.331964 0.574979i
\(612\) 0 0
\(613\) −7923.32 + 13723.6i −0.522055 + 0.904226i 0.477616 + 0.878569i \(0.341501\pi\)
−0.999671 + 0.0256570i \(0.991832\pi\)
\(614\) −1016.42 1760.49i −0.0668068 0.115713i
\(615\) 0 0
\(616\) 8858.30 1882.87i 0.579401 0.123154i
\(617\) −29473.4 −1.92311 −0.961553 0.274621i \(-0.911448\pi\)
−0.961553 + 0.274621i \(0.911448\pi\)
\(618\) 0 0
\(619\) −5763.74 + 9983.08i −0.374255 + 0.648229i −0.990215 0.139548i \(-0.955435\pi\)
0.615960 + 0.787778i \(0.288768\pi\)
\(620\) 5087.19 8811.27i 0.329527 0.570757i
\(621\) 0 0
\(622\) 18386.1 1.18523
\(623\) 8997.28 27690.6i 0.578601 1.78074i
\(624\) 0 0
\(625\) 6694.19 + 11594.7i 0.428428 + 0.742059i
\(626\) 6692.61 11591.9i 0.427301 0.740107i
\(627\) 0 0
\(628\) −1267.30 2195.02i −0.0805265 0.139476i
\(629\) 5941.63 0.376643
\(630\) 0 0
\(631\) 25846.1 1.63062 0.815308 0.579027i \(-0.196568\pi\)
0.815308 + 0.579027i \(0.196568\pi\)
\(632\) 1674.92 + 2901.04i 0.105419 + 0.182591i
\(633\) 0 0
\(634\) 7052.49 12215.3i 0.441783 0.765190i
\(635\) 742.912 + 1286.76i 0.0464277 + 0.0804151i
\(636\) 0 0
\(637\) 2123.71 20205.0i 0.132095 1.25675i
\(638\) −10406.1 −0.645739
\(639\) 0 0
\(640\) 668.558 1157.98i 0.0412923 0.0715204i
\(641\) 2767.39 4793.26i 0.170523 0.295355i −0.768080 0.640354i \(-0.778788\pi\)
0.938603 + 0.344999i \(0.112121\pi\)
\(642\) 0 0
\(643\) 1634.56 0.100250 0.0501251 0.998743i \(-0.484038\pi\)
0.0501251 + 0.998743i \(0.484038\pi\)
\(644\) 7844.27 + 8711.98i 0.479981 + 0.533075i
\(645\) 0 0
\(646\) 1643.91 + 2847.33i 0.100122 + 0.173416i
\(647\) 3769.00 6528.10i 0.229018 0.396671i −0.728499 0.685047i \(-0.759782\pi\)
0.957517 + 0.288375i \(0.0931151\pi\)
\(648\) 0 0
\(649\) 24608.9 + 42623.9i 1.48842 + 2.57802i
\(650\) 1880.76 0.113491
\(651\) 0 0
\(652\) −5382.83 −0.323325
\(653\) −6656.09 11528.7i −0.398887 0.690892i 0.594702 0.803946i \(-0.297270\pi\)
−0.993589 + 0.113054i \(0.963937\pi\)
\(654\) 0 0
\(655\) −12987.3 + 22494.7i −0.774743 + 1.34189i
\(656\) 1344.00 + 2327.88i 0.0799914 + 0.138549i
\(657\) 0 0
\(658\) −6133.59 + 1303.72i −0.363392 + 0.0772407i
\(659\) −10962.0 −0.647981 −0.323991 0.946060i \(-0.605025\pi\)
−0.323991 + 0.946060i \(0.605025\pi\)
\(660\) 0 0
\(661\) 11816.3 20466.4i 0.695309 1.20431i −0.274767 0.961511i \(-0.588601\pi\)
0.970076 0.242800i \(-0.0780659\pi\)
\(662\) −3140.37 + 5439.28i −0.184372 + 0.319341i
\(663\) 0 0
\(664\) −6093.71 −0.356147
\(665\) 15203.2 3231.51i 0.886550 0.188440i
\(666\) 0 0
\(667\) −6735.28 11665.8i −0.390991 0.677216i
\(668\) −775.843 + 1343.80i −0.0449376 + 0.0778341i
\(669\) 0 0
\(670\) −2897.60 5018.78i −0.167080 0.289392i
\(671\) 2027.56 0.116652
\(672\) 0 0
\(673\) 23483.0 1.34503 0.672513 0.740085i \(-0.265215\pi\)
0.672513 + 0.740085i \(0.265215\pi\)
\(674\) −2743.87 4752.53i −0.156810 0.271603i
\(675\) 0 0
\(676\) −2622.65 + 4542.56i −0.149218 + 0.258452i
\(677\) 12336.2 + 21367.0i 0.700325 + 1.21300i 0.968352 + 0.249587i \(0.0802948\pi\)
−0.268028 + 0.963411i \(0.586372\pi\)
\(678\) 0 0
\(679\) −12952.1 14384.9i −0.732044 0.813020i
\(680\) −1710.02 −0.0964359
\(681\) 0 0
\(682\) −14883.2 + 25778.5i −0.835643 + 1.44738i
\(683\) 4469.73 7741.80i 0.250409 0.433721i −0.713229 0.700931i \(-0.752768\pi\)
0.963638 + 0.267209i \(0.0861016\pi\)
\(684\) 0 0
\(685\) −27131.1 −1.51332
\(686\) −11606.5 5167.62i −0.645972 0.287610i
\(687\) 0 0
\(688\) −61.0347 105.715i −0.00338216 0.00585807i
\(689\) −7407.21 + 12829.7i −0.409568 + 0.709392i
\(690\) 0 0
\(691\) −7555.03 13085.7i −0.415929 0.720410i 0.579597 0.814904i \(-0.303210\pi\)
−0.995525 + 0.0944937i \(0.969877\pi\)
\(692\) −2490.64 −0.136821
\(693\) 0 0
\(694\) −20873.8 −1.14173
\(695\) 8359.70 + 14479.4i 0.456261 + 0.790268i
\(696\) 0 0
\(697\) 1718.83 2977.09i 0.0934077 0.161787i
\(698\) 2257.01 + 3909.26i 0.122391 + 0.211988i
\(699\) 0 0
\(700\) 363.451 1118.58i 0.0196245 0.0603975i
\(701\) −18353.3 −0.988865 −0.494432 0.869216i \(-0.664624\pi\)
−0.494432 + 0.869216i \(0.664624\pi\)
\(702\) 0 0
\(703\) 11664.0 20202.6i 0.625769 1.08386i
\(704\) −1955.95 + 3387.81i −0.104713 + 0.181368i
\(705\) 0 0
\(706\) −11232.9 −0.598803
\(707\) 17679.4 3757.83i 0.940454 0.199898i
\(708\) 0 0
\(709\) 5036.85 + 8724.07i 0.266802 + 0.462115i 0.968034 0.250818i \(-0.0806997\pi\)
−0.701232 + 0.712933i \(0.747366\pi\)
\(710\) −6596.85 + 11426.1i −0.348698 + 0.603962i
\(711\) 0 0
\(712\) 6288.38 + 10891.8i 0.330993 + 0.573297i
\(713\) −38532.3 −2.02391
\(714\) 0 0
\(715\) 37819.7 1.97815
\(716\) 899.861 + 1558.61i 0.0469684 + 0.0813517i
\(717\) 0 0
\(718\) −795.591 + 1378.00i −0.0413526 + 0.0716249i
\(719\) 9944.63 + 17224.6i 0.515817 + 0.893420i 0.999831 + 0.0183607i \(0.00584472\pi\)
−0.484015 + 0.875060i \(0.660822\pi\)
\(720\) 0 0
\(721\) 3680.78 11328.2i 0.190124 0.585138i
\(722\) −809.397 −0.0417211
\(723\) 0 0
\(724\) −368.706 + 638.617i −0.0189266 + 0.0327818i
\(725\) −675.730 + 1170.40i −0.0346151 + 0.0599552i
\(726\) 0 0
\(727\) 13403.5 0.683780 0.341890 0.939740i \(-0.388933\pi\)
0.341890 + 0.939740i \(0.388933\pi\)
\(728\) 5872.15 + 6521.71i 0.298951 + 0.332020i
\(729\) 0 0
\(730\) −8025.66 13900.9i −0.406908 0.704786i
\(731\) −78.0566 + 135.198i −0.00394942 + 0.00684060i
\(732\) 0 0
\(733\) −6627.50 11479.2i −0.333960 0.578435i 0.649325 0.760511i \(-0.275052\pi\)
−0.983284 + 0.182076i \(0.941718\pi\)
\(734\) 16387.9 0.824101
\(735\) 0 0
\(736\) −5063.91 −0.253612
\(737\) 8477.29 + 14683.1i 0.423698 + 0.733866i
\(738\) 0 0
\(739\) −7710.19 + 13354.4i −0.383794 + 0.664751i −0.991601 0.129334i \(-0.958716\pi\)
0.607807 + 0.794085i \(0.292049\pi\)
\(740\) 6066.55 + 10507.6i 0.301366 + 0.521981i
\(741\) 0 0
\(742\) 6199.00 + 6884.71i 0.306701 + 0.340628i
\(743\) −943.019 −0.0465626 −0.0232813 0.999729i \(-0.507411\pi\)
−0.0232813 + 0.999729i \(0.507411\pi\)
\(744\) 0 0
\(745\) 15344.0 26576.5i 0.754576 1.30696i
\(746\) −14077.4 + 24382.7i −0.690897 + 1.19667i
\(747\) 0 0
\(748\) 5002.89 0.244551
\(749\) 1783.29 5488.37i 0.0869960 0.267744i
\(750\) 0 0
\(751\) 14297.9 + 24764.7i 0.694726 + 1.20330i 0.970273 + 0.242013i \(0.0778076\pi\)
−0.275547 + 0.961287i \(0.588859\pi\)
\(752\) 1354.33 2345.76i 0.0656744 0.113751i
\(753\) 0 0
\(754\) −5041.96 8732.94i −0.243524 0.421797i
\(755\) −19046.9 −0.918127
\(756\) 0 0
\(757\) −28984.4 −1.39162 −0.695810 0.718226i \(-0.744955\pi\)
−0.695810 + 0.718226i \(0.744955\pi\)
\(758\) −6221.22 10775.5i −0.298107 0.516336i
\(759\) 0 0
\(760\) −3356.94 + 5814.39i −0.160222 + 0.277513i
\(761\) 4465.05 + 7733.70i 0.212691 + 0.368392i 0.952556 0.304364i \(-0.0984438\pi\)
−0.739865 + 0.672756i \(0.765110\pi\)
\(762\) 0 0
\(763\) −33800.5 + 7184.46i −1.60375 + 0.340884i
\(764\) 1403.86 0.0664789
\(765\) 0 0
\(766\) −10701.4 + 18535.4i −0.504776 + 0.874297i
\(767\) −23847.0 + 41304.3i −1.12264 + 1.94447i
\(768\) 0 0
\(769\) 2373.15 0.111285 0.0556424 0.998451i \(-0.482279\pi\)
0.0556424 + 0.998451i \(0.482279\pi\)
\(770\) 7308.53 22493.2i 0.342053 1.05272i
\(771\) 0 0
\(772\) −3056.52 5294.04i −0.142495 0.246809i
\(773\) 13988.5 24228.8i 0.650881 1.12736i −0.332029 0.943269i \(-0.607733\pi\)
0.982909 0.184089i \(-0.0589336\pi\)
\(774\) 0 0
\(775\) 1932.91 + 3347.90i 0.0895900 + 0.155174i
\(776\) 8361.32 0.386796
\(777\) 0 0
\(778\) −8443.23 −0.389080
\(779\) −6748.45 11688.7i −0.310383 0.537599i
\(780\) 0 0
\(781\) 19299.9 33428.5i 0.884259 1.53158i
\(782\) 3238.09 + 5608.53i 0.148074 + 0.256471i
\(783\) 0 0
\(784\) 5013.55 2232.15i 0.228387 0.101683i
\(785\) −6619.23 −0.300956
\(786\) 0 0
\(787\) −17180.5 + 29757.4i −0.778167 + 1.34782i 0.154831 + 0.987941i \(0.450517\pi\)
−0.932997 + 0.359883i \(0.882817\pi\)
\(788\) −5749.30 + 9958.08i −0.259911 + 0.450180i
\(789\) 0 0
\(790\) 8748.29 0.393987
\(791\) 21321.1 + 23679.6i 0.958397 + 1.06441i
\(792\) 0 0
\(793\) 982.394 + 1701.56i 0.0439922 + 0.0761968i
\(794\) 12075.7 20915.8i 0.539738 0.934854i
\(795\) 0 0
\(796\) −9897.41 17142.8i −0.440709 0.763330i
\(797\) 10399.5 0.462196 0.231098 0.972930i \(-0.425768\pi\)
0.231098 + 0.972930i \(0.425768\pi\)
\(798\) 0 0
\(799\) −3464.06 −0.153379
\(800\) 254.023 + 439.981i 0.0112263 + 0.0194446i
\(801\) 0 0
\(802\) −5506.38 + 9537.33i −0.242440 + 0.419919i
\(803\) 23480.1 + 40668.7i 1.03187 + 1.78726i
\(804\) 0 0
\(805\) 29946.5 6365.27i 1.31115 0.278691i
\(806\) −28844.9 −1.26057
\(807\) 0 0
\(808\) −3903.69 + 6761.38i −0.169964 + 0.294387i
\(809\) −8971.53 + 15539.1i −0.389891 + 0.675312i −0.992435 0.122775i \(-0.960821\pi\)
0.602543 + 0.798086i \(0.294154\pi\)
\(810\) 0 0
\(811\) −571.663 −0.0247519 −0.0123760 0.999923i \(-0.503939\pi\)
−0.0123760 + 0.999923i \(0.503939\pi\)
\(812\) −6168.24 + 1311.09i −0.266580 + 0.0566627i
\(813\) 0 0
\(814\) −17748.5 30741.3i −0.764231 1.32369i
\(815\) −7028.78 + 12174.2i −0.302095 + 0.523244i
\(816\) 0 0
\(817\) 306.465 + 530.814i 0.0131235 + 0.0227305i
\(818\) 2856.36 0.122091
\(819\) 0 0
\(820\) 7019.86 0.298956
\(821\) 6947.84 + 12034.0i 0.295349 + 0.511559i 0.975066 0.221915i \(-0.0712308\pi\)
−0.679717 + 0.733474i \(0.737897\pi\)
\(822\) 0 0
\(823\) 10814.6 18731.5i 0.458049 0.793364i −0.540809 0.841145i \(-0.681882\pi\)
0.998858 + 0.0477816i \(0.0152152\pi\)
\(824\) 2572.58 + 4455.83i 0.108762 + 0.188381i
\(825\) 0 0
\(826\) 19957.3 + 22164.9i 0.840681 + 0.933675i
\(827\) −4700.10 −0.197628 −0.0988140 0.995106i \(-0.531505\pi\)
−0.0988140 + 0.995106i \(0.531505\pi\)
\(828\) 0 0
\(829\) 19055.4 33004.9i 0.798337 1.38276i −0.122361 0.992486i \(-0.539047\pi\)
0.920698 0.390275i \(-0.127620\pi\)
\(830\) −7957.03 + 13782.0i −0.332762 + 0.576361i
\(831\) 0 0
\(832\) −3790.79 −0.157959
\(833\) −5678.10 4125.42i −0.236176 0.171593i
\(834\) 0 0
\(835\) 2026.16 + 3509.41i 0.0839738 + 0.145447i
\(836\) 9821.17 17010.8i 0.406307 0.703744i
\(837\) 0 0
\(838\) 264.960 + 458.924i 0.0109223 + 0.0189180i
\(839\) −20080.2 −0.826277 −0.413138 0.910668i \(-0.635567\pi\)
−0.413138 + 0.910668i \(0.635567\pi\)
\(840\) 0 0
\(841\) −17143.0 −0.702898
\(842\) 281.066 + 486.820i 0.0115038 + 0.0199251i
\(843\) 0 0
\(844\) 10561.8 18293.6i 0.430749 0.746079i
\(845\) 6849.19 + 11863.1i 0.278840 + 0.482964i
\(846\) 0 0
\(847\) −13764.6 + 42362.8i −0.558391 + 1.71854i
\(848\) −4001.79 −0.162054
\(849\) 0 0
\(850\) 324.867 562.687i 0.0131092 0.0227059i
\(851\) 22975.2 39794.1i 0.925474 1.60297i
\(852\) 0 0
\(853\) −34906.8 −1.40116 −0.700578 0.713576i \(-0.747074\pi\)
−0.700578 + 0.713576i \(0.747074\pi\)
\(854\) 1201.84 255.457i 0.0481571 0.0102360i
\(855\) 0 0
\(856\) 1246.38 + 2158.79i 0.0497668 + 0.0861985i
\(857\) 24023.4 41609.7i 0.957553 1.65853i 0.229139 0.973394i \(-0.426409\pi\)
0.728414 0.685137i \(-0.240258\pi\)
\(858\) 0 0
\(859\) 17603.1 + 30489.5i 0.699198 + 1.21105i 0.968745 + 0.248059i \(0.0797926\pi\)
−0.269547 + 0.962987i \(0.586874\pi\)
\(860\) −318.791 −0.0126403
\(861\) 0 0
\(862\) 3572.76 0.141170
\(863\) −17928.8 31053.7i −0.707190 1.22489i −0.965895 0.258933i \(-0.916629\pi\)
0.258705 0.965956i \(-0.416704\pi\)
\(864\) 0 0
\(865\) −3252.22 + 5633.01i −0.127837 + 0.221420i
\(866\) −184.621 319.773i −0.00724444 0.0125477i
\(867\) 0 0
\(868\) −5574.18 + 17155.4i −0.217972 + 0.670845i
\(869\) −25594.3 −0.999109
\(870\) 0 0
\(871\) −8214.83 + 14228.5i −0.319574 + 0.553518i
\(872\) 7463.32 12926.9i 0.289839 0.502017i
\(873\) 0 0
\(874\) 25426.7 0.984064
\(875\) −18237.1 20254.4i −0.704600 0.782541i
\(876\) 0 0
\(877\) −3683.09 6379.30i −0.141812 0.245625i 0.786367 0.617760i \(-0.211959\pi\)
−0.928179 + 0.372134i \(0.878626\pi\)
\(878\) −11274.6 + 19528.2i −0.433372 + 0.750622i
\(879\) 0 0
\(880\) 5108.08 + 8847.46i 0.195674 + 0.338918i
\(881\) −3628.00 −0.138741 −0.0693703 0.997591i \(-0.522099\pi\)
−0.0693703 + 0.997591i \(0.522099\pi\)
\(882\) 0 0
\(883\) 25123.0 0.957483 0.478741 0.877956i \(-0.341093\pi\)
0.478741 + 0.877956i \(0.341093\pi\)
\(884\) 2424.00 + 4198.49i 0.0922262 + 0.159740i
\(885\) 0 0
\(886\) 7969.84 13804.2i 0.302203 0.523431i
\(887\) −7887.38 13661.3i −0.298571 0.517140i 0.677238 0.735764i \(-0.263177\pi\)
−0.975809 + 0.218624i \(0.929843\pi\)
\(888\) 0 0
\(889\) −1762.65 1957.62i −0.0664986 0.0738545i
\(890\) 32844.9 1.23704
\(891\) 0 0
\(892\) −7993.13 + 13844.5i −0.300033 + 0.519673i
\(893\) −6800.29 + 11778.5i −0.254830 + 0.441378i
\(894\) 0 0
\(895\) 4700.07 0.175538
\(896\) −732.558 + 2254.57i −0.0273137 + 0.0840623i
\(897\) 0 0
\(898\) 8850.37 + 15329.3i 0.328887 + 0.569649i
\(899\) 10363.5 17950.2i 0.384476 0.665931i
\(900\) 0 0
\(901\) 2558.92 + 4432.19i 0.0946172 + 0.163882i
\(902\) −20537.5 −0.758120
\(903\) 0 0
\(904\) −13764.0 −0.506396
\(905\) 962.896 + 1667.78i 0.0353677 + 0.0612586i
\(906\) 0 0
\(907\) 2556.99 4428.84i 0.0936092 0.162136i −0.815418 0.578872i \(-0.803493\pi\)
0.909027 + 0.416737i \(0.136826\pi\)
\(908\) −1077.18 1865.74i −0.0393696 0.0681902i
\(909\) 0 0
\(910\) 22417.7 4764.98i 0.816636 0.173580i
\(911\) −10279.1 −0.373834 −0.186917 0.982376i \(-0.559850\pi\)
−0.186917 + 0.982376i \(0.559850\pi\)
\(912\) 0 0
\(913\) 23279.3 40321.0i 0.843848 1.46159i
\(914\) 13027.3 22563.9i 0.471449 0.816574i
\(915\) 0 0
\(916\) 16686.4 0.601895
\(917\) 14230.6 43796.9i 0.512470 1.57721i
\(918\) 0 0
\(919\) 19461.0 + 33707.4i 0.698540 + 1.20991i 0.968973 + 0.247168i \(0.0794999\pi\)
−0.270433 + 0.962739i \(0.587167\pi\)
\(920\) −6612.34 + 11452.9i −0.236959 + 0.410425i
\(921\) 0 0
\(922\) 1261.05 + 2184.20i 0.0450439 + 0.0780182i
\(923\) 37404.8 1.33390
\(924\) 0 0
\(925\) −4610.05 −0.163868
\(926\) 4005.47 + 6937.67i 0.142147 + 0.246205i
\(927\) 0 0
\(928\) 1361.98 2359.01i 0.0481779 0.0834466i
\(929\) −7483.82 12962.4i −0.264302 0.457784i 0.703079 0.711112i \(-0.251808\pi\)
−0.967380 + 0.253328i \(0.918475\pi\)
\(930\) 0 0
\(931\) −25173.9 + 11208.0i −0.886187 + 0.394551i
\(932\) −6158.92 −0.216461
\(933\) 0 0
\(934\) 17097.8 29614.3i 0.598991 1.03748i
\(935\) 6532.67 11314.9i 0.228493 0.395762i
\(936\) 0 0
\(937\) −22353.0 −0.779339 −0.389669 0.920955i \(-0.627411\pi\)
−0.389669 + 0.920955i \(0.627411\pi\)
\(938\) 6874.89 + 7635.37i 0.239310 + 0.265782i
\(939\) 0 0
\(940\) −3536.90 6126.08i −0.122724 0.212565i
\(941\) −6690.77 + 11588.7i −0.231788 + 0.401469i −0.958334 0.285649i \(-0.907791\pi\)
0.726546 + 0.687118i \(0.241124\pi\)
\(942\) 0 0
\(943\) −13292.8 23023.7i −0.459037 0.795075i
\(944\) −12883.5 −0.444198
\(945\) 0 0
\(946\) 932.665 0.0320545
\(947\) −316.888 548.867i −0.0108738 0.0188340i 0.860537 0.509387i \(-0.170128\pi\)
−0.871411 + 0.490553i \(0.836795\pi\)
\(948\) 0 0
\(949\) −22753.1 + 39409.6i −0.778291 + 1.34804i
\(950\) −1275.49 2209.22i −0.0435605 0.0754489i
\(951\) 0 0
\(952\) 2965.48 630.325i 0.100958 0.0214590i
\(953\) 49340.0 1.67710 0.838551 0.544823i \(-0.183403\pi\)
0.838551 + 0.544823i \(0.183403\pi\)
\(954\) 0 0
\(955\) 1833.13 3175.08i 0.0621138 0.107584i
\(956\) 6265.34 10851.9i 0.211962 0.367129i
\(957\) 0 0
\(958\) −23377.1 −0.788391
\(959\) 47049.9 10000.7i 1.58428 0.336745i
\(960\) 0 0
\(961\) −14749.2 25546.4i −0.495090 0.857520i
\(962\) 17199.0 29789.5i 0.576421 0.998391i
\(963\) 0 0
\(964\) −5213.39 9029.85i −0.174182 0.301693i
\(965\) −15964.5 −0.532556
\(966\) 0 0
\(967\) −3340.71 −0.111096 −0.0555480 0.998456i \(-0.517691\pi\)
−0.0555480 + 0.998456i \(0.517691\pi\)
\(968\) −9620.36 16662.9i −0.319432 0.553272i
\(969\) 0 0
\(970\) 10918.0 18910.6i 0.361398 0.625960i
\(971\) −2435.20 4217.89i −0.0804833 0.139401i 0.822974 0.568079i \(-0.192313\pi\)
−0.903458 + 0.428677i \(0.858980\pi\)
\(972\) 0 0
\(973\) −19834.4 22028.4i −0.653506 0.725794i
\(974\) −19249.6 −0.633261
\(975\) 0 0
\(976\) −265.372 + 459.638i −0.00870324 + 0.0150745i
\(977\) −3420.67 + 5924.78i −0.112013 + 0.194013i −0.916582 0.399847i \(-0.869063\pi\)
0.804569 + 0.593860i \(0.202397\pi\)
\(978\) 0 0
\(979\) −96092.1 −3.13699
\(980\) 1498.18 14253.7i 0.0488344 0.464610i
\(981\) 0 0
\(982\) −6320.63 10947.7i −0.205397 0.355757i
\(983\) 5344.94 9257.71i 0.173425 0.300382i −0.766190 0.642614i \(-0.777850\pi\)
0.939615 + 0.342233i \(0.111183\pi\)
\(984\) 0 0
\(985\) 15014.6 + 26006.1i 0.485691 + 0.841241i
\(986\) −3483.63 −0.112517
\(987\) 0 0
\(988\) 19034.2 0.612913
\(989\) 603.660 + 1045.57i 0.0194088 + 0.0336170i
\(990\) 0 0
\(991\) −3732.84 + 6465.48i −0.119655 + 0.207248i −0.919631 0.392784i \(-0.871512\pi\)
0.799976 + 0.600032i \(0.204845\pi\)
\(992\) −3895.91 6747.91i −0.124693 0.215974i
\(993\) 0 0
\(994\) 7228.36 22246.4i 0.230653 0.709873i
\(995\) −51695.3 −1.64709
\(996\) 0 0
\(997\) 8677.41 15029.7i 0.275643 0.477428i −0.694654 0.719344i \(-0.744443\pi\)
0.970297 + 0.241916i \(0.0777759\pi\)
\(998\) 15054.6 26075.3i 0.477499 0.827053i
\(999\) 0 0
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 126.4.g.e.109.2 yes 4
3.2 odd 2 126.4.g.f.109.1 yes 4
7.2 even 3 inner 126.4.g.e.37.2 4
7.3 odd 6 882.4.a.bh.1.2 2
7.4 even 3 882.4.a.bd.1.1 2
7.5 odd 6 882.4.g.z.667.1 4
7.6 odd 2 882.4.g.z.361.1 4
21.2 odd 6 126.4.g.f.37.1 yes 4
21.5 even 6 882.4.g.bj.667.2 4
21.11 odd 6 882.4.a.ba.1.2 2
21.17 even 6 882.4.a.u.1.1 2
21.20 even 2 882.4.g.bj.361.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.4.g.e.37.2 4 7.2 even 3 inner
126.4.g.e.109.2 yes 4 1.1 even 1 trivial
126.4.g.f.37.1 yes 4 21.2 odd 6
126.4.g.f.109.1 yes 4 3.2 odd 2
882.4.a.u.1.1 2 21.17 even 6
882.4.a.ba.1.2 2 21.11 odd 6
882.4.a.bd.1.1 2 7.4 even 3
882.4.a.bh.1.2 2 7.3 odd 6
882.4.g.z.361.1 4 7.6 odd 2
882.4.g.z.667.1 4 7.5 odd 6
882.4.g.bj.361.2 4 21.20 even 2
882.4.g.bj.667.2 4 21.5 even 6