Properties

Label 810.3.j.g.269.9
Level $810$
Weight $3$
Character 810.269
Analytic conductor $22.071$
Analytic rank $0$
Dimension $24$
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] = [810,3,Mod(269,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.269");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\), degree \(2\), not 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: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.9
Character \(\chi\) \(=\) 810.269
Dual form 810.3.j.g.539.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.51279 - 4.32272i) q^{5} +(5.12645 + 2.95976i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.51279 - 4.32272i) q^{5} +(5.12645 + 2.95976i) q^{7} -2.82843 q^{8} +(-7.07104 + 0.0209028i) q^{10} +(3.29935 + 1.90488i) q^{11} +(19.2513 - 11.1148i) q^{13} +(7.24989 - 4.18573i) q^{14} +(-2.00000 + 3.46410i) q^{16} -1.20411 q^{17} +29.3606 q^{19} +(-4.97438 + 8.67500i) q^{20} +(4.66598 - 2.69391i) q^{22} +(8.07107 + 13.9795i) q^{23} +(-12.3718 + 21.7242i) q^{25} -31.4373i q^{26} -11.8390i q^{28} +(-39.2196 - 22.6435i) q^{29} +(-21.8878 - 37.9108i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-0.851433 + 1.47473i) q^{34} +(-0.0874935 - 29.5974i) q^{35} -48.4190i q^{37} +(20.7611 - 35.9592i) q^{38} +(7.10724 + 12.2265i) q^{40} +(2.35652 - 1.36054i) q^{41} +(17.3080 + 9.99280i) q^{43} -7.61952i q^{44} +22.8284 q^{46} +(12.1492 - 21.0431i) q^{47} +(-6.97968 - 12.0892i) q^{49} +(17.8584 + 30.5136i) q^{50} +(-38.5027 - 22.2295i) q^{52} -10.8425 q^{53} +(-0.0563102 - 19.0487i) q^{55} +(-14.4998 - 8.37146i) q^{56} +(-55.4649 + 32.0227i) q^{58} +(-16.7913 + 9.69448i) q^{59} +(-9.19954 + 15.9341i) q^{61} -61.9081 q^{62} +8.00000 q^{64} +(-96.4205 - 55.2890i) q^{65} +(71.9917 - 41.5645i) q^{67} +(1.20411 + 2.08558i) q^{68} +(-36.3112 - 20.8214i) q^{70} -121.784i q^{71} +105.116i q^{73} +(-59.3009 - 34.2374i) q^{74} +(-29.3606 - 50.8540i) q^{76} +(11.2760 + 19.5305i) q^{77} +(-47.1052 + 81.5887i) q^{79} +(19.9999 - 0.0591221i) q^{80} -3.84818i q^{82} +(-47.3213 + 81.9629i) q^{83} +(3.02567 + 5.20502i) q^{85} +(24.4773 - 14.1320i) q^{86} +(-9.33197 - 5.38781i) q^{88} -132.665i q^{89} +131.588 q^{91} +(16.1421 - 27.9590i) q^{92} +(-17.1816 - 29.7595i) q^{94} +(-73.7770 - 126.918i) q^{95} +(103.065 + 59.5043i) q^{97} -19.7415 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −2.51279 4.32272i −0.502558 0.864544i
\(6\) 0 0
\(7\) 5.12645 + 2.95976i 0.732350 + 0.422822i 0.819281 0.573392i \(-0.194373\pi\)
−0.0869313 + 0.996214i \(0.527706\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) −7.07104 + 0.0209028i −0.707104 + 0.00209028i
\(11\) 3.29935 + 1.90488i 0.299941 + 0.173171i 0.642416 0.766356i \(-0.277932\pi\)
−0.342476 + 0.939527i \(0.611265\pi\)
\(12\) 0 0
\(13\) 19.2513 11.1148i 1.48087 0.854982i 0.481107 0.876662i \(-0.340235\pi\)
0.999765 + 0.0216805i \(0.00690166\pi\)
\(14\) 7.24989 4.18573i 0.517850 0.298981i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −1.20411 −0.0708299 −0.0354150 0.999373i \(-0.511275\pi\)
−0.0354150 + 0.999373i \(0.511275\pi\)
\(18\) 0 0
\(19\) 29.3606 1.54529 0.772647 0.634836i \(-0.218932\pi\)
0.772647 + 0.634836i \(0.218932\pi\)
\(20\) −4.97438 + 8.67500i −0.248719 + 0.433750i
\(21\) 0 0
\(22\) 4.66598 2.69391i 0.212090 0.122450i
\(23\) 8.07107 + 13.9795i 0.350916 + 0.607805i 0.986410 0.164301i \(-0.0525369\pi\)
−0.635494 + 0.772106i \(0.719204\pi\)
\(24\) 0 0
\(25\) −12.3718 + 21.7242i −0.494871 + 0.868966i
\(26\) 31.4373i 1.20913i
\(27\) 0 0
\(28\) 11.8390i 0.422822i
\(29\) −39.2196 22.6435i −1.35240 0.780809i −0.363815 0.931471i \(-0.618526\pi\)
−0.988585 + 0.150662i \(0.951859\pi\)
\(30\) 0 0
\(31\) −21.8878 37.9108i −0.706059 1.22293i −0.966308 0.257388i \(-0.917138\pi\)
0.260249 0.965541i \(-0.416195\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −0.851433 + 1.47473i −0.0250422 + 0.0433743i
\(35\) −0.0874935 29.5974i −0.00249981 0.845641i
\(36\) 0 0
\(37\) 48.4190i 1.30862i −0.756226 0.654311i \(-0.772959\pi\)
0.756226 0.654311i \(-0.227041\pi\)
\(38\) 20.7611 35.9592i 0.546344 0.946295i
\(39\) 0 0
\(40\) 7.10724 + 12.2265i 0.177681 + 0.305662i
\(41\) 2.35652 1.36054i 0.0574761 0.0331838i −0.470987 0.882140i \(-0.656102\pi\)
0.528463 + 0.848957i \(0.322769\pi\)
\(42\) 0 0
\(43\) 17.3080 + 9.99280i 0.402513 + 0.232391i 0.687568 0.726120i \(-0.258679\pi\)
−0.285055 + 0.958511i \(0.592012\pi\)
\(44\) 7.61952i 0.173171i
\(45\) 0 0
\(46\) 22.8284 0.496270
\(47\) 12.1492 21.0431i 0.258495 0.447726i −0.707344 0.706869i \(-0.750107\pi\)
0.965839 + 0.259143i \(0.0834402\pi\)
\(48\) 0 0
\(49\) −6.97968 12.0892i −0.142442 0.246717i
\(50\) 17.8584 + 30.5136i 0.357168 + 0.610271i
\(51\) 0 0
\(52\) −38.5027 22.2295i −0.740436 0.427491i
\(53\) −10.8425 −0.204576 −0.102288 0.994755i \(-0.532616\pi\)
−0.102288 + 0.994755i \(0.532616\pi\)
\(54\) 0 0
\(55\) −0.0563102 19.0487i −0.00102382 0.346340i
\(56\) −14.4998 8.37146i −0.258925 0.149490i
\(57\) 0 0
\(58\) −55.4649 + 32.0227i −0.956292 + 0.552115i
\(59\) −16.7913 + 9.69448i −0.284599 + 0.164313i −0.635504 0.772098i \(-0.719207\pi\)
0.350905 + 0.936411i \(0.385874\pi\)
\(60\) 0 0
\(61\) −9.19954 + 15.9341i −0.150812 + 0.261214i −0.931526 0.363674i \(-0.881522\pi\)
0.780714 + 0.624888i \(0.214856\pi\)
\(62\) −61.9081 −0.998518
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −96.4205 55.2890i −1.48339 0.850600i
\(66\) 0 0
\(67\) 71.9917 41.5645i 1.07450 0.620365i 0.145095 0.989418i \(-0.453651\pi\)
0.929408 + 0.369053i \(0.120318\pi\)
\(68\) 1.20411 + 2.08558i 0.0177075 + 0.0306703i
\(69\) 0 0
\(70\) −36.3112 20.8214i −0.518731 0.297448i
\(71\) 121.784i 1.71527i −0.514258 0.857635i \(-0.671933\pi\)
0.514258 0.857635i \(-0.328067\pi\)
\(72\) 0 0
\(73\) 105.116i 1.43994i 0.694003 + 0.719972i \(0.255845\pi\)
−0.694003 + 0.719972i \(0.744155\pi\)
\(74\) −59.3009 34.2374i −0.801364 0.462668i
\(75\) 0 0
\(76\) −29.3606 50.8540i −0.386324 0.669132i
\(77\) 11.2760 + 19.5305i 0.146441 + 0.253643i
\(78\) 0 0
\(79\) −47.1052 + 81.5887i −0.596269 + 1.03277i 0.397098 + 0.917776i \(0.370017\pi\)
−0.993366 + 0.114991i \(0.963316\pi\)
\(80\) 19.9999 0.0591221i 0.249999 0.000739026i
\(81\) 0 0
\(82\) 3.84818i 0.0469290i
\(83\) −47.3213 + 81.9629i −0.570136 + 0.987505i 0.426415 + 0.904528i \(0.359776\pi\)
−0.996551 + 0.0829774i \(0.973557\pi\)
\(84\) 0 0
\(85\) 3.02567 + 5.20502i 0.0355961 + 0.0612356i
\(86\) 24.4773 14.1320i 0.284619 0.164325i
\(87\) 0 0
\(88\) −9.33197 5.38781i −0.106045 0.0612251i
\(89\) 132.665i 1.49062i −0.666718 0.745310i \(-0.732302\pi\)
0.666718 0.745310i \(-0.267698\pi\)
\(90\) 0 0
\(91\) 131.588 1.44602
\(92\) 16.1421 27.9590i 0.175458 0.303902i
\(93\) 0 0
\(94\) −17.1816 29.7595i −0.182783 0.316590i
\(95\) −73.7770 126.918i −0.776600 1.33597i
\(96\) 0 0
\(97\) 103.065 + 59.5043i 1.06252 + 0.613447i 0.926129 0.377208i \(-0.123116\pi\)
0.136392 + 0.990655i \(0.456449\pi\)
\(98\) −19.7415 −0.201444
\(99\) 0 0
\(100\) 49.9991 0.295609i 0.499991 0.00295609i
\(101\) −20.6118 11.9002i −0.204077 0.117824i 0.394479 0.918905i \(-0.370925\pi\)
−0.598556 + 0.801081i \(0.704259\pi\)
\(102\) 0 0
\(103\) 3.57552 2.06432i 0.0347137 0.0200420i −0.482543 0.875872i \(-0.660287\pi\)
0.517256 + 0.855830i \(0.326953\pi\)
\(104\) −54.4510 + 31.4373i −0.523567 + 0.302282i
\(105\) 0 0
\(106\) −7.66683 + 13.2793i −0.0723285 + 0.125277i
\(107\) 117.008 1.09353 0.546765 0.837286i \(-0.315859\pi\)
0.546765 + 0.837286i \(0.315859\pi\)
\(108\) 0 0
\(109\) −84.3413 −0.773774 −0.386887 0.922127i \(-0.626450\pi\)
−0.386887 + 0.922127i \(0.626450\pi\)
\(110\) −23.3696 13.4005i −0.212451 0.121823i
\(111\) 0 0
\(112\) −20.5058 + 11.8390i −0.183087 + 0.105706i
\(113\) −40.0727 69.4080i −0.354626 0.614230i 0.632428 0.774619i \(-0.282058\pi\)
−0.987054 + 0.160389i \(0.948725\pi\)
\(114\) 0 0
\(115\) 40.1486 70.0165i 0.349118 0.608839i
\(116\) 90.5738i 0.780809i
\(117\) 0 0
\(118\) 27.4201i 0.232374i
\(119\) −6.17280 3.56387i −0.0518723 0.0299485i
\(120\) 0 0
\(121\) −53.2429 92.2194i −0.440024 0.762143i
\(122\) 13.0101 + 22.5342i 0.106640 + 0.184706i
\(123\) 0 0
\(124\) −43.7756 + 75.8216i −0.353029 + 0.611465i
\(125\) 124.995 1.10853i 0.999961 0.00886821i
\(126\) 0 0
\(127\) 91.3285i 0.719122i −0.933122 0.359561i \(-0.882926\pi\)
0.933122 0.359561i \(-0.117074\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −135.895 + 78.9953i −1.04534 + 0.607656i
\(131\) 197.410 113.974i 1.50694 0.870034i 0.506976 0.861960i \(-0.330763\pi\)
0.999967 0.00807357i \(-0.00256992\pi\)
\(132\) 0 0
\(133\) 150.516 + 86.9002i 1.13170 + 0.653385i
\(134\) 117.562i 0.877329i
\(135\) 0 0
\(136\) 3.40573 0.0250422
\(137\) −61.3594 + 106.278i −0.447879 + 0.775749i −0.998248 0.0591727i \(-0.981154\pi\)
0.550369 + 0.834922i \(0.314487\pi\)
\(138\) 0 0
\(139\) 19.2401 + 33.3249i 0.138418 + 0.239747i 0.926898 0.375313i \(-0.122465\pi\)
−0.788480 + 0.615061i \(0.789132\pi\)
\(140\) −51.1768 + 29.7490i −0.365548 + 0.212493i
\(141\) 0 0
\(142\) −149.155 86.1145i −1.05038 0.606440i
\(143\) 84.6891 0.592232
\(144\) 0 0
\(145\) 0.669364 + 226.434i 0.00461630 + 1.56161i
\(146\) 128.740 + 74.3281i 0.881782 + 0.509097i
\(147\) 0 0
\(148\) −83.8642 + 48.4190i −0.566650 + 0.327155i
\(149\) −6.49058 + 3.74734i −0.0435609 + 0.0251499i −0.521622 0.853177i \(-0.674673\pi\)
0.478061 + 0.878326i \(0.341340\pi\)
\(150\) 0 0
\(151\) −108.617 + 188.129i −0.719315 + 1.24589i 0.241957 + 0.970287i \(0.422211\pi\)
−0.961272 + 0.275603i \(0.911123\pi\)
\(152\) −83.0443 −0.546344
\(153\) 0 0
\(154\) 31.8932 0.207099
\(155\) −108.878 + 189.877i −0.702441 + 1.22501i
\(156\) 0 0
\(157\) 153.578 88.6685i 0.978206 0.564767i 0.0764777 0.997071i \(-0.475633\pi\)
0.901728 + 0.432304i \(0.142299\pi\)
\(158\) 66.6169 + 115.384i 0.421626 + 0.730277i
\(159\) 0 0
\(160\) 14.0697 24.5366i 0.0879354 0.153354i
\(161\) 95.5537i 0.593501i
\(162\) 0 0
\(163\) 42.6651i 0.261749i 0.991399 + 0.130875i \(0.0417785\pi\)
−0.991399 + 0.130875i \(0.958221\pi\)
\(164\) −4.71304 2.72108i −0.0287381 0.0165919i
\(165\) 0 0
\(166\) 66.9224 + 115.913i 0.403147 + 0.698271i
\(167\) 36.9936 + 64.0748i 0.221519 + 0.383681i 0.955269 0.295737i \(-0.0955653\pi\)
−0.733751 + 0.679419i \(0.762232\pi\)
\(168\) 0 0
\(169\) 162.576 281.590i 0.961987 1.66621i
\(170\) 8.51430 0.0251693i 0.0500841 0.000148054i
\(171\) 0 0
\(172\) 39.9712i 0.232391i
\(173\) 76.8727 133.147i 0.444351 0.769638i −0.553656 0.832745i \(-0.686768\pi\)
0.998007 + 0.0631075i \(0.0201011\pi\)
\(174\) 0 0
\(175\) −127.722 + 74.7503i −0.729837 + 0.427145i
\(176\) −13.1974 + 7.61952i −0.0749852 + 0.0432927i
\(177\) 0 0
\(178\) −162.481 93.8084i −0.912814 0.527014i
\(179\) 292.469i 1.63390i 0.576706 + 0.816951i \(0.304338\pi\)
−0.576706 + 0.816951i \(0.695662\pi\)
\(180\) 0 0
\(181\) 45.0019 0.248629 0.124315 0.992243i \(-0.460327\pi\)
0.124315 + 0.992243i \(0.460327\pi\)
\(182\) 93.0467 161.162i 0.511246 0.885504i
\(183\) 0 0
\(184\) −22.8284 39.5400i −0.124068 0.214891i
\(185\) −209.302 + 121.667i −1.13136 + 0.657658i
\(186\) 0 0
\(187\) −3.97277 2.29368i −0.0212448 0.0122657i
\(188\) −48.5970 −0.258495
\(189\) 0 0
\(190\) −207.610 + 0.613719i −1.09268 + 0.00323010i
\(191\) 163.433 + 94.3578i 0.855668 + 0.494020i 0.862559 0.505956i \(-0.168860\pi\)
−0.00689152 + 0.999976i \(0.502194\pi\)
\(192\) 0 0
\(193\) −78.7052 + 45.4405i −0.407799 + 0.235443i −0.689844 0.723958i \(-0.742321\pi\)
0.282045 + 0.959401i \(0.408987\pi\)
\(194\) 145.755 84.1518i 0.751316 0.433772i
\(195\) 0 0
\(196\) −13.9594 + 24.1783i −0.0712212 + 0.123359i
\(197\) −321.126 −1.63008 −0.815040 0.579405i \(-0.803285\pi\)
−0.815040 + 0.579405i \(0.803285\pi\)
\(198\) 0 0
\(199\) −22.7423 −0.114283 −0.0571414 0.998366i \(-0.518199\pi\)
−0.0571414 + 0.998366i \(0.518199\pi\)
\(200\) 34.9927 61.4452i 0.174963 0.307226i
\(201\) 0 0
\(202\) −29.1495 + 16.8295i −0.144304 + 0.0833142i
\(203\) −134.038 232.161i −0.660287 1.14365i
\(204\) 0 0
\(205\) −11.8027 6.76783i −0.0575740 0.0330138i
\(206\) 5.83879i 0.0283437i
\(207\) 0 0
\(208\) 88.9181i 0.427491i
\(209\) 96.8708 + 55.9284i 0.463497 + 0.267600i
\(210\) 0 0
\(211\) 39.9608 + 69.2142i 0.189388 + 0.328029i 0.945046 0.326937i \(-0.106016\pi\)
−0.755659 + 0.654966i \(0.772683\pi\)
\(212\) 10.8425 + 18.7798i 0.0511440 + 0.0885840i
\(213\) 0 0
\(214\) 82.7369 143.305i 0.386621 0.669647i
\(215\) −0.295398 99.9276i −0.00137394 0.464779i
\(216\) 0 0
\(217\) 259.131i 1.19415i
\(218\) −59.6383 + 103.297i −0.273570 + 0.473838i
\(219\) 0 0
\(220\) −32.9370 + 19.1462i −0.149714 + 0.0870284i
\(221\) −23.1807 + 13.3834i −0.104890 + 0.0605583i
\(222\) 0 0
\(223\) −56.8626 32.8297i −0.254989 0.147218i 0.367057 0.930198i \(-0.380365\pi\)
−0.622047 + 0.782980i \(0.713699\pi\)
\(224\) 33.4858i 0.149490i
\(225\) 0 0
\(226\) −113.343 −0.501516
\(227\) 183.852 318.441i 0.809921 1.40282i −0.102997 0.994682i \(-0.532843\pi\)
0.912918 0.408143i \(-0.133824\pi\)
\(228\) 0 0
\(229\) 149.821 + 259.497i 0.654238 + 1.13317i 0.982084 + 0.188443i \(0.0603440\pi\)
−0.327846 + 0.944731i \(0.606323\pi\)
\(230\) −57.3631 98.6809i −0.249405 0.429047i
\(231\) 0 0
\(232\) 110.930 + 64.0454i 0.478146 + 0.276058i
\(233\) 227.228 0.975229 0.487614 0.873059i \(-0.337867\pi\)
0.487614 + 0.873059i \(0.337867\pi\)
\(234\) 0 0
\(235\) −121.492 + 0.359144i −0.516987 + 0.00152827i
\(236\) 33.5827 + 19.3890i 0.142299 + 0.0821566i
\(237\) 0 0
\(238\) −8.72966 + 5.04007i −0.0366793 + 0.0211768i
\(239\) −164.387 + 94.9090i −0.687813 + 0.397109i −0.802792 0.596259i \(-0.796653\pi\)
0.114979 + 0.993368i \(0.463320\pi\)
\(240\) 0 0
\(241\) −45.4778 + 78.7699i −0.188705 + 0.326846i −0.944819 0.327594i \(-0.893762\pi\)
0.756114 + 0.654440i \(0.227096\pi\)
\(242\) −150.594 −0.622287
\(243\) 0 0
\(244\) 36.7982 0.150812
\(245\) −34.7195 + 60.5487i −0.141712 + 0.247137i
\(246\) 0 0
\(247\) 565.230 326.336i 2.28838 1.32120i
\(248\) 61.9081 + 107.228i 0.249629 + 0.432371i
\(249\) 0 0
\(250\) 87.0272 153.871i 0.348109 0.615484i
\(251\) 386.041i 1.53801i 0.639242 + 0.769005i \(0.279248\pi\)
−0.639242 + 0.769005i \(0.720752\pi\)
\(252\) 0 0
\(253\) 61.4977i 0.243074i
\(254\) −111.854 64.5790i −0.440371 0.254248i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 173.158 + 299.918i 0.673766 + 1.16700i 0.976828 + 0.214026i \(0.0686579\pi\)
−0.303062 + 0.952971i \(0.598009\pi\)
\(258\) 0 0
\(259\) 143.308 248.218i 0.553315 0.958369i
\(260\) 0.657128 + 222.294i 0.00252741 + 0.854978i
\(261\) 0 0
\(262\) 322.368i 1.23041i
\(263\) −216.736 + 375.397i −0.824090 + 1.42737i 0.0785228 + 0.996912i \(0.474980\pi\)
−0.902613 + 0.430453i \(0.858354\pi\)
\(264\) 0 0
\(265\) 27.2450 + 46.8692i 0.102811 + 0.176865i
\(266\) 212.861 122.895i 0.800230 0.462013i
\(267\) 0 0
\(268\) −143.983 83.1289i −0.537252 0.310182i
\(269\) 456.780i 1.69807i 0.528340 + 0.849033i \(0.322815\pi\)
−0.528340 + 0.849033i \(0.677185\pi\)
\(270\) 0 0
\(271\) −321.543 −1.18651 −0.593253 0.805016i \(-0.702156\pi\)
−0.593253 + 0.805016i \(0.702156\pi\)
\(272\) 2.40822 4.17116i 0.00885374 0.0153351i
\(273\) 0 0
\(274\) 86.7753 + 150.299i 0.316698 + 0.548537i
\(275\) −82.2007 + 48.1088i −0.298912 + 0.174941i
\(276\) 0 0
\(277\) 287.041 + 165.723i 1.03625 + 0.598278i 0.918768 0.394797i \(-0.129185\pi\)
0.117480 + 0.993075i \(0.462518\pi\)
\(278\) 54.4193 0.195753
\(279\) 0 0
\(280\) 0.247469 + 83.7142i 0.000883818 + 0.298979i
\(281\) 409.801 + 236.599i 1.45837 + 0.841989i 0.998931 0.0462214i \(-0.0147180\pi\)
0.459437 + 0.888211i \(0.348051\pi\)
\(282\) 0 0
\(283\) 26.3212 15.1965i 0.0930076 0.0536980i −0.452775 0.891625i \(-0.649566\pi\)
0.545782 + 0.837927i \(0.316233\pi\)
\(284\) −210.936 + 121.784i −0.742734 + 0.428818i
\(285\) 0 0
\(286\) 59.8842 103.723i 0.209385 0.362666i
\(287\) 16.1074 0.0561235
\(288\) 0 0
\(289\) −287.550 −0.994983
\(290\) 277.797 + 159.293i 0.957920 + 0.549286i
\(291\) 0 0
\(292\) 182.066 105.116i 0.623514 0.359986i
\(293\) −12.5081 21.6647i −0.0426898 0.0739409i 0.843891 0.536515i \(-0.180259\pi\)
−0.886581 + 0.462574i \(0.846926\pi\)
\(294\) 0 0
\(295\) 84.0996 + 48.2240i 0.285083 + 0.163471i
\(296\) 136.950i 0.462668i
\(297\) 0 0
\(298\) 10.5991i 0.0355674i
\(299\) 310.758 + 179.416i 1.03932 + 0.600054i
\(300\) 0 0
\(301\) 59.1525 + 102.455i 0.196520 + 0.340383i
\(302\) 153.607 + 266.055i 0.508632 + 0.880977i
\(303\) 0 0
\(304\) −58.7212 + 101.708i −0.193162 + 0.334566i
\(305\) 91.9950 0.271948i 0.301623 0.000891633i
\(306\) 0 0
\(307\) 596.302i 1.94235i −0.238365 0.971176i \(-0.576611\pi\)
0.238365 0.971176i \(-0.423389\pi\)
\(308\) 22.5519 39.0611i 0.0732205 0.126822i
\(309\) 0 0
\(310\) 155.562 + 267.611i 0.501813 + 0.863262i
\(311\) 47.0295 27.1525i 0.151220 0.0873070i −0.422481 0.906372i \(-0.638841\pi\)
0.573701 + 0.819065i \(0.305507\pi\)
\(312\) 0 0
\(313\) 139.802 + 80.7145i 0.446650 + 0.257874i 0.706415 0.707798i \(-0.250311\pi\)
−0.259764 + 0.965672i \(0.583645\pi\)
\(314\) 250.792i 0.798702i
\(315\) 0 0
\(316\) 188.421 0.596269
\(317\) 136.292 236.064i 0.429942 0.744682i −0.566926 0.823769i \(-0.691867\pi\)
0.996868 + 0.0790874i \(0.0252006\pi\)
\(318\) 0 0
\(319\) −86.2661 149.417i −0.270427 0.468393i
\(320\) −20.1023 34.5817i −0.0628197 0.108068i
\(321\) 0 0
\(322\) 117.029 + 67.5666i 0.363444 + 0.209834i
\(323\) −35.3533 −0.109453
\(324\) 0 0
\(325\) 3.28562 + 555.728i 0.0101096 + 1.70993i
\(326\) 52.2539 + 30.1688i 0.160288 + 0.0925423i
\(327\) 0 0
\(328\) −6.66525 + 3.84818i −0.0203209 + 0.0117323i
\(329\) 124.565 71.9177i 0.378617 0.218595i
\(330\) 0 0
\(331\) 264.356 457.879i 0.798660 1.38332i −0.121829 0.992551i \(-0.538876\pi\)
0.920489 0.390769i \(-0.127791\pi\)
\(332\) 189.285 0.570136
\(333\) 0 0
\(334\) 104.634 0.313274
\(335\) −360.571 206.757i −1.07633 0.617186i
\(336\) 0 0
\(337\) 337.626 194.929i 1.00186 0.578423i 0.0930609 0.995660i \(-0.470335\pi\)
0.908798 + 0.417237i \(0.137002\pi\)
\(338\) −229.917 398.228i −0.680228 1.17819i
\(339\) 0 0
\(340\) 5.98969 10.4456i 0.0176167 0.0307225i
\(341\) 166.775i 0.489075i
\(342\) 0 0
\(343\) 372.689i 1.08656i
\(344\) −48.9545 28.2639i −0.142310 0.0821625i
\(345\) 0 0
\(346\) −108.714 188.299i −0.314203 0.544216i
\(347\) −60.2010 104.271i −0.173490 0.300493i 0.766148 0.642664i \(-0.222171\pi\)
−0.939638 + 0.342171i \(0.888838\pi\)
\(348\) 0 0
\(349\) −274.137 + 474.820i −0.785494 + 1.36051i 0.143210 + 0.989692i \(0.454258\pi\)
−0.928704 + 0.370823i \(0.879076\pi\)
\(350\) 1.23734 + 209.283i 0.00353525 + 0.597951i
\(351\) 0 0
\(352\) 21.5513i 0.0612251i
\(353\) 146.668 254.036i 0.415489 0.719648i −0.579991 0.814623i \(-0.696944\pi\)
0.995480 + 0.0949749i \(0.0302771\pi\)
\(354\) 0 0
\(355\) −526.439 + 306.018i −1.48293 + 0.862023i
\(356\) −229.783 + 132.665i −0.645457 + 0.372655i
\(357\) 0 0
\(358\) 358.199 + 206.807i 1.00056 + 0.577672i
\(359\) 15.8718i 0.0442110i −0.999756 0.0221055i \(-0.992963\pi\)
0.999756 0.0221055i \(-0.00703698\pi\)
\(360\) 0 0
\(361\) 501.044 1.38793
\(362\) 31.8211 55.1158i 0.0879037 0.152254i
\(363\) 0 0
\(364\) −131.588 227.917i −0.361505 0.626146i
\(365\) 454.386 264.134i 1.24489 0.723655i
\(366\) 0 0
\(367\) −513.192 296.292i −1.39834 0.807334i −0.404125 0.914704i \(-0.632424\pi\)
−0.994219 + 0.107370i \(0.965757\pi\)
\(368\) −64.5686 −0.175458
\(369\) 0 0
\(370\) 1.01209 + 342.373i 0.00273539 + 0.925331i
\(371\) −55.5837 32.0913i −0.149821 0.0864993i
\(372\) 0 0
\(373\) −328.734 + 189.794i −0.881323 + 0.508832i −0.871094 0.491115i \(-0.836589\pi\)
−0.0102288 + 0.999948i \(0.503256\pi\)
\(374\) −5.61835 + 3.24376i −0.0150223 + 0.00867315i
\(375\) 0 0
\(376\) −34.3633 + 59.5189i −0.0913917 + 0.158295i
\(377\) −1006.71 −2.67031
\(378\) 0 0
\(379\) −493.432 −1.30193 −0.650966 0.759107i \(-0.725636\pi\)
−0.650966 + 0.759107i \(0.725636\pi\)
\(380\) −146.051 + 254.703i −0.384344 + 0.670271i
\(381\) 0 0
\(382\) 231.128 133.442i 0.605048 0.349325i
\(383\) 152.151 + 263.534i 0.397262 + 0.688078i 0.993387 0.114814i \(-0.0366271\pi\)
−0.596125 + 0.802892i \(0.703294\pi\)
\(384\) 0 0
\(385\) 56.0909 97.8189i 0.145691 0.254075i
\(386\) 128.525i 0.332967i
\(387\) 0 0
\(388\) 238.017i 0.613447i
\(389\) 391.427 + 225.990i 1.00624 + 0.580952i 0.910088 0.414414i \(-0.136014\pi\)
0.0961507 + 0.995367i \(0.469347\pi\)
\(390\) 0 0
\(391\) −9.71845 16.8328i −0.0248554 0.0430508i
\(392\) 19.7415 + 34.1933i 0.0503610 + 0.0872278i
\(393\) 0 0
\(394\) −227.070 + 393.297i −0.576320 + 0.998216i
\(395\) 471.050 1.39248i 1.19253 0.00352526i
\(396\) 0 0
\(397\) 316.160i 0.796373i 0.917304 + 0.398187i \(0.130360\pi\)
−0.917304 + 0.398187i \(0.869640\pi\)
\(398\) −16.0812 + 27.8535i −0.0404051 + 0.0699836i
\(399\) 0 0
\(400\) −50.5111 86.3054i −0.126278 0.215764i
\(401\) 66.1508 38.1922i 0.164964 0.0952423i −0.415245 0.909710i \(-0.636304\pi\)
0.580209 + 0.814467i \(0.302971\pi\)
\(402\) 0 0
\(403\) −842.739 486.556i −2.09116 1.20733i
\(404\) 47.6009i 0.117824i
\(405\) 0 0
\(406\) −379.117 −0.933787
\(407\) 92.2323 159.751i 0.226615 0.392509i
\(408\) 0 0
\(409\) 216.772 + 375.461i 0.530006 + 0.917997i 0.999387 + 0.0350014i \(0.0111436\pi\)
−0.469382 + 0.882995i \(0.655523\pi\)
\(410\) −16.6346 + 9.66967i −0.0405722 + 0.0235846i
\(411\) 0 0
\(412\) −7.15103 4.12865i −0.0173569 0.0100210i
\(413\) −114.773 −0.277901
\(414\) 0 0
\(415\) 473.211 1.39887i 1.14027 0.00337076i
\(416\) 108.902 + 62.8746i 0.261784 + 0.151141i
\(417\) 0 0
\(418\) 136.996 79.0947i 0.327742 0.189222i
\(419\) −137.665 + 79.4807i −0.328555 + 0.189691i −0.655200 0.755456i \(-0.727415\pi\)
0.326644 + 0.945147i \(0.394082\pi\)
\(420\) 0 0
\(421\) 16.0331 27.7702i 0.0380834 0.0659625i −0.846355 0.532619i \(-0.821208\pi\)
0.884439 + 0.466656i \(0.154541\pi\)
\(422\) 113.026 0.267835
\(423\) 0 0
\(424\) 30.6673 0.0723285
\(425\) 14.8970 26.1583i 0.0350517 0.0615488i
\(426\) 0 0
\(427\) −94.3220 + 54.4568i −0.220895 + 0.127534i
\(428\) −117.008 202.663i −0.273382 0.473512i
\(429\) 0 0
\(430\) −122.595 70.2977i −0.285104 0.163483i
\(431\) 636.866i 1.47765i −0.673898 0.738824i \(-0.735381\pi\)
0.673898 0.738824i \(-0.264619\pi\)
\(432\) 0 0
\(433\) 594.793i 1.37366i 0.726820 + 0.686828i \(0.240997\pi\)
−0.726820 + 0.686828i \(0.759003\pi\)
\(434\) −317.369 183.233i −0.731265 0.422196i
\(435\) 0 0
\(436\) 84.3413 + 146.083i 0.193443 + 0.335054i
\(437\) 236.971 + 410.447i 0.542269 + 0.939237i
\(438\) 0 0
\(439\) 253.860 439.699i 0.578269 1.00159i −0.417409 0.908719i \(-0.637062\pi\)
0.995678 0.0928725i \(-0.0296049\pi\)
\(440\) 0.159269 + 53.8779i 0.000361976 + 0.122450i
\(441\) 0 0
\(442\) 37.8539i 0.0856423i
\(443\) −340.505 + 589.771i −0.768633 + 1.33131i 0.169671 + 0.985501i \(0.445730\pi\)
−0.938304 + 0.345811i \(0.887604\pi\)
\(444\) 0 0
\(445\) −573.474 + 333.360i −1.28871 + 0.749123i
\(446\) −80.4159 + 46.4281i −0.180305 + 0.104099i
\(447\) 0 0
\(448\) 41.0116 + 23.6781i 0.0915437 + 0.0528528i
\(449\) 273.889i 0.609998i 0.952353 + 0.304999i \(0.0986561\pi\)
−0.952353 + 0.304999i \(0.901344\pi\)
\(450\) 0 0
\(451\) 10.3666 0.0229859
\(452\) −80.1454 + 138.816i −0.177313 + 0.307115i
\(453\) 0 0
\(454\) −260.006 450.344i −0.572701 0.991947i
\(455\) −330.653 568.818i −0.726710 1.25015i
\(456\) 0 0
\(457\) 176.210 + 101.735i 0.385580 + 0.222615i 0.680243 0.732987i \(-0.261874\pi\)
−0.294663 + 0.955601i \(0.595208\pi\)
\(458\) 423.757 0.925233
\(459\) 0 0
\(460\) −161.421 + 0.477178i −0.350915 + 0.00103734i
\(461\) −732.738 423.046i −1.58945 0.917671i −0.993397 0.114728i \(-0.963400\pi\)
−0.596056 0.802943i \(-0.703266\pi\)
\(462\) 0 0
\(463\) −380.771 + 219.838i −0.822400 + 0.474813i −0.851244 0.524771i \(-0.824151\pi\)
0.0288431 + 0.999584i \(0.490818\pi\)
\(464\) 156.878 90.5738i 0.338100 0.195202i
\(465\) 0 0
\(466\) 160.675 278.297i 0.344795 0.597203i
\(467\) 14.0853 0.0301612 0.0150806 0.999886i \(-0.495200\pi\)
0.0150806 + 0.999886i \(0.495200\pi\)
\(468\) 0 0
\(469\) 492.083 1.04922
\(470\) −85.4679 + 149.051i −0.181847 + 0.317129i
\(471\) 0 0
\(472\) 47.4931 27.4201i 0.100621 0.0580935i
\(473\) 38.0702 + 65.9395i 0.0804866 + 0.139407i
\(474\) 0 0
\(475\) −363.243 + 637.834i −0.764721 + 1.34281i
\(476\) 14.2555i 0.0299485i
\(477\) 0 0
\(478\) 268.443i 0.561597i
\(479\) −339.132 195.798i −0.708001 0.408765i 0.102319 0.994752i \(-0.467374\pi\)
−0.810320 + 0.585987i \(0.800707\pi\)
\(480\) 0 0
\(481\) −538.166 932.130i −1.11885 1.93790i
\(482\) 64.3154 + 111.397i 0.133434 + 0.231115i
\(483\) 0 0
\(484\) −106.486 + 184.439i −0.220012 + 0.381072i
\(485\) −1.75901 595.041i −0.00362682 1.22689i
\(486\) 0 0
\(487\) 881.169i 1.80938i −0.426069 0.904691i \(-0.640102\pi\)
0.426069 0.904691i \(-0.359898\pi\)
\(488\) 26.0202 45.0684i 0.0533202 0.0923532i
\(489\) 0 0
\(490\) 49.6062 + 85.3369i 0.101237 + 0.174157i
\(491\) −304.525 + 175.818i −0.620214 + 0.358081i −0.776952 0.629560i \(-0.783235\pi\)
0.156738 + 0.987640i \(0.449902\pi\)
\(492\) 0 0
\(493\) 47.2247 + 27.2652i 0.0957904 + 0.0553046i
\(494\) 923.017i 1.86846i
\(495\) 0 0
\(496\) 175.103 0.353029
\(497\) 360.452 624.321i 0.725255 1.25618i
\(498\) 0 0
\(499\) 240.926 + 417.296i 0.482817 + 0.836264i 0.999805 0.0197284i \(-0.00628015\pi\)
−0.516988 + 0.855993i \(0.672947\pi\)
\(500\) −126.915 215.389i −0.253830 0.430779i
\(501\) 0 0
\(502\) 472.801 + 272.972i 0.941835 + 0.543769i
\(503\) 670.477 1.33296 0.666478 0.745525i \(-0.267801\pi\)
0.666478 + 0.745525i \(0.267801\pi\)
\(504\) 0 0
\(505\) 0.351783 + 119.002i 0.000696600 + 0.235647i
\(506\) 75.3190 + 43.4854i 0.148852 + 0.0859396i
\(507\) 0 0
\(508\) −158.186 + 91.3285i −0.311389 + 0.179781i
\(509\) −9.57115 + 5.52591i −0.0188038 + 0.0108564i −0.509372 0.860546i \(-0.670122\pi\)
0.490569 + 0.871403i \(0.336789\pi\)
\(510\) 0 0
\(511\) −311.117 + 538.871i −0.608840 + 1.05454i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) 489.765 0.952849
\(515\) −17.9080 10.2687i −0.0347728 0.0199393i
\(516\) 0 0
\(517\) 80.1692 46.2857i 0.155066 0.0895275i
\(518\) −202.669 351.033i −0.391252 0.677669i
\(519\) 0 0
\(520\) 272.718 + 156.381i 0.524458 + 0.300733i
\(521\) 534.980i 1.02683i −0.858140 0.513416i \(-0.828380\pi\)
0.858140 0.513416i \(-0.171620\pi\)
\(522\) 0 0
\(523\) 615.393i 1.17666i 0.808621 + 0.588330i \(0.200214\pi\)
−0.808621 + 0.588330i \(0.799786\pi\)
\(524\) −394.819 227.949i −0.753472 0.435017i
\(525\) 0 0
\(526\) 306.511 + 530.892i 0.582720 + 1.00930i
\(527\) 26.3553 + 45.6488i 0.0500101 + 0.0866200i
\(528\) 0 0
\(529\) 134.216 232.468i 0.253716 0.439448i
\(530\) 76.6679 0.226639i 0.144656 0.000427621i
\(531\) 0 0
\(532\) 347.601i 0.653385i
\(533\) 30.2441 52.3843i 0.0567432 0.0982820i
\(534\) 0 0
\(535\) −294.016 505.791i −0.549562 0.945404i
\(536\) −203.623 + 117.562i −0.379894 + 0.219332i
\(537\) 0 0
\(538\) 559.439 + 322.992i 1.03985 + 0.600357i
\(539\) 53.1818i 0.0986675i
\(540\) 0 0
\(541\) −479.872 −0.887010 −0.443505 0.896272i \(-0.646265\pi\)
−0.443505 + 0.896272i \(0.646265\pi\)
\(542\) −227.365 + 393.808i −0.419493 + 0.726583i
\(543\) 0 0
\(544\) −3.40573 5.89890i −0.00626054 0.0108436i
\(545\) 211.932 + 364.584i 0.388866 + 0.668961i
\(546\) 0 0
\(547\) −307.990 177.818i −0.563053 0.325079i 0.191317 0.981528i \(-0.438724\pi\)
−0.754370 + 0.656449i \(0.772058\pi\)
\(548\) 245.438 0.447879
\(549\) 0 0
\(550\) 0.796343 + 134.693i 0.00144790 + 0.244896i
\(551\) −1151.51 664.825i −2.08986 1.20658i
\(552\) 0 0
\(553\) −482.965 + 278.840i −0.873355 + 0.504232i
\(554\) 405.937 234.368i 0.732738 0.423047i
\(555\) 0 0
\(556\) 38.4803 66.6498i 0.0692091 0.119874i
\(557\) 267.691 0.480595 0.240297 0.970699i \(-0.422755\pi\)
0.240297 + 0.970699i \(0.422755\pi\)
\(558\) 0 0
\(559\) 444.270 0.794759
\(560\) 102.704 + 58.8918i 0.183399 + 0.105164i
\(561\) 0 0
\(562\) 579.547 334.601i 1.03122 0.595376i
\(563\) −120.511 208.731i −0.214052 0.370749i 0.738927 0.673785i \(-0.235333\pi\)
−0.952979 + 0.303037i \(0.901999\pi\)
\(564\) 0 0
\(565\) −199.337 + 347.631i −0.352808 + 0.615275i
\(566\) 42.9823i 0.0759404i
\(567\) 0 0
\(568\) 344.458i 0.606440i
\(569\) −48.7478 28.1445i −0.0856727 0.0494632i 0.456552 0.889697i \(-0.349084\pi\)
−0.542224 + 0.840234i \(0.682418\pi\)
\(570\) 0 0
\(571\) 191.424 + 331.556i 0.335243 + 0.580658i 0.983531 0.180737i \(-0.0578482\pi\)
−0.648288 + 0.761395i \(0.724515\pi\)
\(572\) −84.6891 146.686i −0.148058 0.256444i
\(573\) 0 0
\(574\) 11.3897 19.7275i 0.0198427 0.0343685i
\(575\) −403.547 + 2.38588i −0.701820 + 0.00414936i
\(576\) 0 0
\(577\) 114.953i 0.199225i 0.995026 + 0.0996126i \(0.0317603\pi\)
−0.995026 + 0.0996126i \(0.968240\pi\)
\(578\) −203.329 + 352.176i −0.351780 + 0.609300i
\(579\) 0 0
\(580\) 391.525 227.593i 0.675043 0.392402i
\(581\) −485.181 + 280.119i −0.835079 + 0.482133i
\(582\) 0 0
\(583\) −35.7733 20.6537i −0.0613607 0.0354266i
\(584\) 297.313i 0.509097i
\(585\) 0 0
\(586\) −35.3783 −0.0603725
\(587\) −243.848 + 422.357i −0.415414 + 0.719518i −0.995472 0.0950571i \(-0.969697\pi\)
0.580058 + 0.814575i \(0.303030\pi\)
\(588\) 0 0
\(589\) −642.639 1113.08i −1.09107 1.88979i
\(590\) 118.529 68.9010i 0.200897 0.116781i
\(591\) 0 0
\(592\) 167.728 + 96.8380i 0.283325 + 0.163578i
\(593\) −631.323 −1.06463 −0.532313 0.846548i \(-0.678677\pi\)
−0.532313 + 0.846548i \(0.678677\pi\)
\(594\) 0 0
\(595\) 0.105352 + 35.6385i 0.000177062 + 0.0598967i
\(596\) 12.9812 + 7.49468i 0.0217805 + 0.0125750i
\(597\) 0 0
\(598\) 439.478 253.733i 0.734913 0.424302i
\(599\) 607.509 350.745i 1.01421 0.585552i 0.101785 0.994806i \(-0.467545\pi\)
0.912420 + 0.409255i \(0.134211\pi\)
\(600\) 0 0
\(601\) −200.165 + 346.696i −0.333053 + 0.576865i −0.983109 0.183022i \(-0.941412\pi\)
0.650056 + 0.759886i \(0.274745\pi\)
\(602\) 167.309 0.277921
\(603\) 0 0
\(604\) 434.466 0.719315
\(605\) −264.850 + 461.882i −0.437769 + 0.763441i
\(606\) 0 0
\(607\) 251.522 145.216i 0.414368 0.239236i −0.278297 0.960495i \(-0.589770\pi\)
0.692665 + 0.721259i \(0.256436\pi\)
\(608\) 83.0443 + 143.837i 0.136586 + 0.236574i
\(609\) 0 0
\(610\) 64.7172 112.863i 0.106094 0.185021i
\(611\) 540.144i 0.884033i
\(612\) 0 0
\(613\) 177.921i 0.290247i 0.989414 + 0.145123i \(0.0463579\pi\)
−0.989414 + 0.145123i \(0.953642\pi\)
\(614\) −730.318 421.649i −1.18944 0.686725i
\(615\) 0 0
\(616\) −31.8932 55.2407i −0.0517747 0.0896765i
\(617\) 232.716 + 403.076i 0.377173 + 0.653284i 0.990650 0.136429i \(-0.0435627\pi\)
−0.613476 + 0.789713i \(0.710229\pi\)
\(618\) 0 0
\(619\) −282.251 + 488.872i −0.455978 + 0.789778i −0.998744 0.0501067i \(-0.984044\pi\)
0.542766 + 0.839884i \(0.317377\pi\)
\(620\) 437.755 1.29405i 0.706056 0.00208718i
\(621\) 0 0
\(622\) 76.7988i 0.123471i
\(623\) 392.657 680.101i 0.630267 1.09166i
\(624\) 0 0
\(625\) −318.878 537.533i −0.510205 0.860053i
\(626\) 197.709 114.148i 0.315830 0.182344i
\(627\) 0 0
\(628\) −307.157 177.337i −0.489103 0.282384i
\(629\) 58.3017i 0.0926896i
\(630\) 0 0
\(631\) 696.074 1.10313 0.551564 0.834133i \(-0.314031\pi\)
0.551564 + 0.834133i \(0.314031\pi\)
\(632\) 133.234 230.768i 0.210813 0.365139i
\(633\) 0 0
\(634\) −192.745 333.845i −0.304015 0.526569i
\(635\) −394.787 + 229.489i −0.621712 + 0.361400i
\(636\) 0 0
\(637\) −268.736 155.155i −0.421878 0.243571i
\(638\) −243.997 −0.382441
\(639\) 0 0
\(640\) −56.5683 + 0.167222i −0.0883880 + 0.000261285i
\(641\) −282.197 162.927i −0.440245 0.254176i 0.263456 0.964671i \(-0.415138\pi\)
−0.703702 + 0.710495i \(0.748471\pi\)
\(642\) 0 0
\(643\) 93.9907 54.2656i 0.146175 0.0843944i −0.425129 0.905133i \(-0.639771\pi\)
0.571304 + 0.820739i \(0.306438\pi\)
\(644\) 165.504 95.5537i 0.256993 0.148375i
\(645\) 0 0
\(646\) −24.9986 + 43.2988i −0.0386975 + 0.0670260i
\(647\) −895.382 −1.38390 −0.691949 0.721946i \(-0.743248\pi\)
−0.691949 + 0.721946i \(0.743248\pi\)
\(648\) 0 0
\(649\) −73.8673 −0.113817
\(650\) 682.949 + 388.935i 1.05069 + 0.598362i
\(651\) 0 0
\(652\) 73.8981 42.6651i 0.113341 0.0654373i
\(653\) −46.6767 80.8464i −0.0714804 0.123808i 0.828070 0.560625i \(-0.189439\pi\)
−0.899550 + 0.436817i \(0.856106\pi\)
\(654\) 0 0
\(655\) −988.728 566.952i −1.50951 0.865575i
\(656\) 10.8843i 0.0165919i
\(657\) 0 0
\(658\) 203.414i 0.309140i
\(659\) 893.384 + 515.795i 1.35567 + 0.782694i 0.989036 0.147673i \(-0.0471783\pi\)
0.366630 + 0.930367i \(0.380512\pi\)
\(660\) 0 0
\(661\) 432.759 + 749.561i 0.654704 + 1.13398i 0.981968 + 0.189048i \(0.0605401\pi\)
−0.327264 + 0.944933i \(0.606127\pi\)
\(662\) −373.856 647.538i −0.564738 0.978155i
\(663\) 0 0
\(664\) 133.845 231.826i 0.201574 0.349136i
\(665\) −2.56886 868.998i −0.00386295 1.30676i
\(666\) 0 0
\(667\) 731.028i 1.09599i
\(668\) 73.9872 128.150i 0.110759 0.191841i
\(669\) 0 0
\(670\) −508.187 + 295.409i −0.758489 + 0.440908i
\(671\) −60.7050 + 35.0480i −0.0904694 + 0.0522326i
\(672\) 0 0
\(673\) 594.810 + 343.414i 0.883819 + 0.510273i 0.871916 0.489656i \(-0.162878\pi\)
0.0119032 + 0.999929i \(0.496211\pi\)
\(674\) 551.342i 0.818014i
\(675\) 0 0
\(676\) −650.303 −0.961987
\(677\) 390.040 675.569i 0.576130 0.997887i −0.419788 0.907622i \(-0.637895\pi\)
0.995918 0.0902643i \(-0.0287712\pi\)
\(678\) 0 0
\(679\) 352.237 + 610.092i 0.518758 + 0.898515i
\(680\) −8.55789 14.7220i −0.0125851 0.0216500i
\(681\) 0 0
\(682\) −204.256 117.927i −0.299496 0.172914i
\(683\) −285.666 −0.418252 −0.209126 0.977889i \(-0.567062\pi\)
−0.209126 + 0.977889i \(0.567062\pi\)
\(684\) 0 0
\(685\) 613.591 1.81385i 0.895754 0.00264795i
\(686\) −456.449 263.531i −0.665377 0.384156i
\(687\) 0 0
\(688\) −69.2322 + 39.9712i −0.100628 + 0.0580977i
\(689\) −208.733 + 120.512i −0.302951 + 0.174909i
\(690\) 0 0
\(691\) −32.8975 + 56.9801i −0.0476085 + 0.0824603i −0.888848 0.458203i \(-0.848493\pi\)
0.841239 + 0.540663i \(0.181827\pi\)
\(692\) −307.491 −0.444351
\(693\) 0 0
\(694\) −170.274 −0.245352
\(695\) 95.7077 166.908i 0.137709 0.240156i
\(696\) 0 0
\(697\) −2.83751 + 1.63824i −0.00407103 + 0.00235041i
\(698\) 387.689 + 671.496i 0.555428 + 0.962029i
\(699\) 0 0
\(700\) 257.193 + 146.470i 0.367418 + 0.209243i
\(701\) 736.516i 1.05067i 0.850897 + 0.525333i \(0.176059\pi\)
−0.850897 + 0.525333i \(0.823941\pi\)
\(702\) 0 0
\(703\) 1421.61i 2.02221i
\(704\) 26.3948 + 15.2390i 0.0374926 + 0.0216464i
\(705\) 0 0
\(706\) −207.419 359.261i −0.293795 0.508868i
\(707\) −70.4436 122.012i −0.0996373 0.172577i
\(708\) 0 0
\(709\) 291.126 504.245i 0.410615 0.711207i −0.584342 0.811508i \(-0.698647\pi\)
0.994957 + 0.100301i \(0.0319806\pi\)
\(710\) 2.54563 + 861.141i 0.00358540 + 1.21287i
\(711\) 0 0
\(712\) 375.234i 0.527014i
\(713\) 353.316 611.962i 0.495535 0.858292i
\(714\) 0 0
\(715\) −212.806 366.087i −0.297631 0.512010i
\(716\) 506.571 292.469i 0.707501 0.408476i
\(717\) 0 0
\(718\) −19.4389 11.2230i −0.0270736 0.0156310i
\(719\) 256.052i 0.356123i 0.984019 + 0.178061i \(0.0569826\pi\)
−0.984019 + 0.178061i \(0.943017\pi\)
\(720\) 0 0
\(721\) 24.4396 0.0338968
\(722\) 354.292 613.651i 0.490709 0.849932i
\(723\) 0 0
\(724\) −45.0019 77.9455i −0.0621573 0.107660i
\(725\) 977.127 571.873i 1.34776 0.788791i
\(726\) 0 0
\(727\) −64.1741 37.0509i −0.0882724 0.0509641i 0.455214 0.890382i \(-0.349563\pi\)
−0.543486 + 0.839418i \(0.682896\pi\)
\(728\) −372.187 −0.511246
\(729\) 0 0
\(730\) −2.19722 743.278i −0.00300989 1.01819i
\(731\) −20.8408 12.0324i −0.0285099 0.0164602i
\(732\) 0 0
\(733\) 202.116 116.692i 0.275738 0.159197i −0.355754 0.934579i \(-0.615776\pi\)
0.631492 + 0.775382i \(0.282443\pi\)
\(734\) −725.763 + 419.020i −0.988779 + 0.570872i
\(735\) 0 0
\(736\) −45.6569 + 79.0800i −0.0620338 + 0.107446i
\(737\) 316.701 0.429717
\(738\) 0 0
\(739\) −541.648 −0.732948 −0.366474 0.930428i \(-0.619435\pi\)
−0.366474 + 0.930428i \(0.619435\pi\)
\(740\) 420.035 + 240.854i 0.567614 + 0.325479i
\(741\) 0 0
\(742\) −78.6072 + 45.3839i −0.105940 + 0.0611643i
\(743\) 421.965 + 730.864i 0.567920 + 0.983667i 0.996771 + 0.0802915i \(0.0255851\pi\)
−0.428851 + 0.903375i \(0.641082\pi\)
\(744\) 0 0
\(745\) 32.5081 + 18.6407i 0.0436351 + 0.0250210i
\(746\) 536.820i 0.719597i
\(747\) 0 0
\(748\) 9.17473i 0.0122657i
\(749\) 599.834 + 346.314i 0.800846 + 0.462369i
\(750\) 0 0
\(751\) −50.8153 88.0147i −0.0676635 0.117197i 0.830209 0.557452i \(-0.188221\pi\)
−0.897872 + 0.440256i \(0.854888\pi\)
\(752\) 48.5970 + 84.1725i 0.0646237 + 0.111931i
\(753\) 0 0
\(754\) −711.849 + 1232.96i −0.944097 + 1.63522i
\(755\) 1086.16 3.21082i 1.43862 0.00425274i
\(756\) 0 0
\(757\) 456.777i 0.603404i 0.953402 + 0.301702i \(0.0975547\pi\)
−0.953402 + 0.301702i \(0.902445\pi\)
\(758\) −348.909 + 604.329i −0.460302 + 0.797267i
\(759\) 0 0
\(760\) 208.673 + 358.977i 0.274569 + 0.472338i
\(761\) −38.5440 + 22.2534i −0.0506492 + 0.0292423i −0.525111 0.851034i \(-0.675976\pi\)
0.474462 + 0.880276i \(0.342643\pi\)
\(762\) 0 0
\(763\) −432.372 249.630i −0.566673 0.327169i
\(764\) 377.431i 0.494020i
\(765\) 0 0
\(766\) 430.349 0.561813
\(767\) −215.504 + 373.263i −0.280970 + 0.486653i
\(768\) 0 0
\(769\) 125.075 + 216.637i 0.162647 + 0.281712i 0.935817 0.352486i \(-0.114664\pi\)
−0.773171 + 0.634198i \(0.781330\pi\)
\(770\) −80.1410 137.865i −0.104079 0.179046i
\(771\) 0 0
\(772\) 157.410 + 90.8810i 0.203900 + 0.117721i
\(773\) −1059.49 −1.37063 −0.685313 0.728249i \(-0.740334\pi\)
−0.685313 + 0.728249i \(0.740334\pi\)
\(774\) 0 0
\(775\) 1094.37 6.47024i 1.41209 0.00834869i
\(776\) −291.511 168.304i −0.375658 0.216886i
\(777\) 0 0
\(778\) 553.561 319.599i 0.711518 0.410795i
\(779\) 69.1888 39.9462i 0.0888175 0.0512788i
\(780\) 0 0
\(781\) 231.984 401.809i 0.297035 0.514480i
\(782\) −27.4879 −0.0351508
\(783\) 0 0
\(784\) 55.8374 0.0712212
\(785\) −769.199 441.070i −0.979871 0.561873i
\(786\) 0 0
\(787\) −707.755 + 408.623i −0.899308 + 0.519216i −0.876976 0.480535i \(-0.840443\pi\)
−0.0223324 + 0.999751i \(0.507109\pi\)
\(788\) 321.126 + 556.206i 0.407520 + 0.705845i
\(789\) 0 0
\(790\) 331.377 577.901i 0.419465 0.731520i
\(791\) 474.422i 0.599775i
\(792\) 0 0
\(793\) 409.003i 0.515767i
\(794\) 387.216 + 223.559i 0.487677 + 0.281561i
\(795\) 0 0
\(796\) 22.7423 + 39.3908i 0.0285707 + 0.0494859i
\(797\) 532.481 + 922.285i 0.668107 + 1.15720i 0.978433 + 0.206565i \(0.0662286\pi\)
−0.310326 + 0.950630i \(0.600438\pi\)
\(798\) 0 0
\(799\) −14.6290 + 25.3382i −0.0183092 + 0.0317124i
\(800\) −141.419 + 0.836109i −0.176774 + 0.00104514i
\(801\) 0 0
\(802\) 108.024i 0.134693i
\(803\) −200.233 + 346.814i −0.249356 + 0.431898i
\(804\) 0 0
\(805\) 413.051 240.106i 0.513107 0.298269i
\(806\) −1191.81 + 688.094i −1.47868 + 0.853714i
\(807\) 0 0
\(808\) 58.2990 + 33.6589i 0.0721522 + 0.0416571i
\(809\) 417.926i 0.516595i 0.966065 + 0.258298i \(0.0831615\pi\)
−0.966065 + 0.258298i \(0.916838\pi\)
\(810\) 0 0
\(811\) −993.633 −1.22519 −0.612597 0.790395i \(-0.709875\pi\)
−0.612597 + 0.790395i \(0.709875\pi\)
\(812\) −268.077 + 464.322i −0.330144 + 0.571825i
\(813\) 0 0
\(814\) −130.436 225.922i −0.160241 0.277546i
\(815\) 184.429 107.208i 0.226294 0.131544i
\(816\) 0 0
\(817\) 508.174 + 293.394i 0.622000 + 0.359112i
\(818\) 613.125 0.749541
\(819\) 0 0
\(820\) 0.0804378 + 27.2106i 9.80949e−5 + 0.0331837i
\(821\) −581.144 335.524i −0.707849 0.408677i 0.102415 0.994742i \(-0.467343\pi\)
−0.810264 + 0.586065i \(0.800676\pi\)
\(822\) 0 0
\(823\) 595.952 344.073i 0.724122 0.418072i −0.0921460 0.995746i \(-0.529373\pi\)
0.816268 + 0.577674i \(0.196039\pi\)
\(824\) −10.1131 + 5.83879i −0.0122732 + 0.00708591i
\(825\) 0 0
\(826\) −81.1569 + 140.568i −0.0982529 + 0.170179i
\(827\) 904.043 1.09316 0.546580 0.837407i \(-0.315930\pi\)
0.546580 + 0.837407i \(0.315930\pi\)
\(828\) 0 0
\(829\) −1539.16 −1.85664 −0.928321 0.371779i \(-0.878748\pi\)
−0.928321 + 0.371779i \(0.878748\pi\)
\(830\) 332.897 580.552i 0.401081 0.699460i
\(831\) 0 0
\(832\) 154.011 88.9181i 0.185109 0.106873i
\(833\) 8.40429 + 14.5567i 0.0100892 + 0.0174750i
\(834\) 0 0
\(835\) 184.020 320.919i 0.220383 0.384334i
\(836\) 223.714i 0.267600i
\(837\) 0 0
\(838\) 224.805i 0.268264i
\(839\) 767.579 + 443.162i 0.914874 + 0.528203i 0.881996 0.471257i \(-0.156199\pi\)
0.0328778 + 0.999459i \(0.489533\pi\)
\(840\) 0 0
\(841\) 604.952 + 1047.81i 0.719325 + 1.24591i
\(842\) −22.6743 39.2730i −0.0269291 0.0466425i
\(843\) 0 0
\(844\) 79.9216 138.428i 0.0946939 0.164015i
\(845\) −1625.75 + 4.80591i −1.92397 + 0.00568747i
\(846\) 0 0
\(847\) 630.344i 0.744208i
\(848\) 21.6851 37.5596i 0.0255720 0.0442920i
\(849\) 0 0
\(850\) −21.5034 36.7417i −0.0252982 0.0432255i
\(851\) 676.874 390.793i 0.795386 0.459216i
\(852\) 0 0
\(853\) 893.181 + 515.678i 1.04711 + 0.604547i 0.921838 0.387576i \(-0.126688\pi\)
0.125268 + 0.992123i \(0.460021\pi\)
\(854\) 154.027i 0.180360i
\(855\) 0 0
\(856\) −330.948 −0.386621
\(857\) −271.764 + 470.710i −0.317111 + 0.549253i −0.979884 0.199568i \(-0.936046\pi\)
0.662773 + 0.748821i \(0.269380\pi\)
\(858\) 0 0
\(859\) −181.682 314.682i −0.211504 0.366335i 0.740682 0.671856i \(-0.234503\pi\)
−0.952185 + 0.305521i \(0.901169\pi\)
\(860\) −172.784 + 100.439i −0.200912 + 0.116790i
\(861\) 0 0
\(862\) −779.999 450.332i −0.904871 0.522427i
\(863\) 693.976 0.804144 0.402072 0.915608i \(-0.368290\pi\)
0.402072 + 0.915608i \(0.368290\pi\)
\(864\) 0 0
\(865\) −768.723 + 2.27244i −0.888697 + 0.00262709i
\(866\) 728.470 + 420.582i 0.841189 + 0.485661i
\(867\) 0 0
\(868\) −448.827 + 259.131i −0.517082 + 0.298538i
\(869\) −310.833 + 179.460i −0.357691 + 0.206513i
\(870\) 0 0
\(871\) 923.958 1600.34i 1.06080 1.83736i
\(872\) 238.553 0.273570
\(873\) 0 0
\(874\) 670.256 0.766884
\(875\) 644.062 + 364.272i 0.736071 + 0.416311i
\(876\) 0 0
\(877\) 383.390 221.350i 0.437161 0.252395i −0.265232 0.964185i \(-0.585449\pi\)
0.702392 + 0.711790i \(0.252115\pi\)
\(878\) −359.012 621.828i −0.408898 0.708232i
\(879\) 0 0
\(880\) 66.0993 + 37.9024i 0.0751128 + 0.0430709i
\(881\) 1448.18i 1.64379i 0.569642 + 0.821893i \(0.307082\pi\)
−0.569642 + 0.821893i \(0.692918\pi\)
\(882\) 0 0
\(883\) 672.798i 0.761946i 0.924586 + 0.380973i \(0.124411\pi\)
−0.924586 + 0.380973i \(0.875589\pi\)
\(884\) 46.3614 + 26.7668i 0.0524450 + 0.0302791i
\(885\) 0 0
\(886\) 481.546 + 834.063i 0.543506 + 0.941380i
\(887\) −444.968 770.707i −0.501655 0.868891i −0.999998 0.00191164i \(-0.999392\pi\)
0.498344 0.866980i \(-0.333942\pi\)
\(888\) 0 0
\(889\) 270.310 468.191i 0.304061 0.526649i
\(890\) 2.77307 + 938.080i 0.00311581 + 1.05402i
\(891\) 0 0
\(892\) 131.319i 0.147218i
\(893\) 356.709 617.838i 0.399450 0.691868i
\(894\) 0 0
\(895\) 1264.26 734.912i 1.41258 0.821131i
\(896\) 57.9992 33.4858i 0.0647312 0.0373726i
\(897\) 0 0
\(898\) 335.444 + 193.669i 0.373546 + 0.215667i
\(899\) 1982.46i 2.20519i
\(900\) 0 0
\(901\) 13.0556 0.0144901
\(902\) 7.33032 12.6965i 0.00812674 0.0140759i
\(903\) 0 0
\(904\) 113.343 + 196.315i 0.125379 + 0.217163i
\(905\) −113.080 194.530i −0.124951 0.214951i
\(906\) 0 0
\(907\) 261.396 + 150.917i 0.288199 + 0.166392i 0.637129 0.770757i \(-0.280122\pi\)
−0.348930 + 0.937149i \(0.613455\pi\)
\(908\) −735.409 −0.809921
\(909\) 0 0
\(910\) −930.463 + 2.75056i −1.02249 + 0.00302259i
\(911\) 1186.55 + 685.053i 1.30247 + 0.751979i 0.980827 0.194883i \(-0.0624326\pi\)
0.321640 + 0.946862i \(0.395766\pi\)
\(912\) 0 0
\(913\) −312.259 + 180.283i −0.342014 + 0.197462i
\(914\) 249.198 143.875i 0.272646 0.157412i
\(915\) 0 0
\(916\) 299.641 518.994i 0.327119 0.566587i
\(917\) 1349.35 1.47148
\(918\) 0 0
\(919\) −228.522 −0.248664 −0.124332 0.992241i \(-0.539679\pi\)
−0.124332 + 0.992241i \(0.539679\pi\)
\(920\) −113.557 + 198.037i −0.123432 + 0.215257i
\(921\) 0 0
\(922\) −1036.25 + 598.278i −1.12391 + 0.648891i
\(923\) −1353.60 2344.51i −1.46652 2.54010i
\(924\) 0 0
\(925\) 1051.86 + 599.029i 1.13715 + 0.647599i
\(926\) 621.797i 0.671487i
\(927\) 0 0
\(928\) 256.181i 0.276058i
\(929\) 273.889 + 158.130i 0.294821 + 0.170215i 0.640114 0.768280i \(-0.278887\pi\)
−0.345293 + 0.938495i \(0.612220\pi\)
\(930\) 0 0
\(931\) −204.927 354.945i −0.220115 0.381251i
\(932\) −227.228 393.571i −0.243807 0.422286i
\(933\) 0 0
\(934\) 9.95981 17.2509i 0.0106636 0.0184699i
\(935\) 0.0678036 + 22.9367i 7.25172e−5 + 0.0245313i
\(936\) 0 0
\(937\) 1277.28i 1.36315i 0.731746 + 0.681577i \(0.238706\pi\)
−0.731746 + 0.681577i \(0.761294\pi\)
\(938\) 347.955 602.676i 0.370954 0.642512i
\(939\) 0 0
\(940\) 122.114 + 210.071i 0.129909 + 0.223480i
\(941\) −1393.26 + 804.397i −1.48061 + 0.854832i −0.999759 0.0219687i \(-0.993007\pi\)
−0.480854 + 0.876801i \(0.659673\pi\)
\(942\) 0 0
\(943\) 38.0393 + 21.9620i 0.0403386 + 0.0232895i
\(944\) 77.5558i 0.0821566i
\(945\) 0 0
\(946\) 107.679 0.113825
\(947\) −793.212 + 1373.88i −0.837605 + 1.45077i 0.0542864 + 0.998525i \(0.482712\pi\)
−0.891892 + 0.452249i \(0.850622\pi\)
\(948\) 0 0
\(949\) 1168.34 + 2023.62i 1.23113 + 2.13237i
\(950\) 524.333 + 895.896i 0.551929 + 0.943049i
\(951\) 0 0
\(952\) 17.4593 + 10.0801i 0.0183396 + 0.0105884i
\(953\) 985.215 1.03380 0.516902 0.856045i \(-0.327085\pi\)
0.516902 + 0.856045i \(0.327085\pi\)
\(954\) 0 0
\(955\) −2.78931 943.574i −0.00292075 0.988035i
\(956\) 328.774 + 189.818i 0.343906 + 0.198554i
\(957\) 0 0
\(958\) −479.606 + 276.901i −0.500632 + 0.289040i
\(959\) −629.112 + 363.218i −0.656008 + 0.378746i
\(960\) 0 0
\(961\) −477.654 + 827.320i −0.497038 + 0.860895i
\(962\) −1522.16 −1.58229
\(963\) 0 0
\(964\) 181.911 0.188705
\(965\) 394.196 + 226.038i 0.408493 + 0.234236i
\(966\) 0 0
\(967\) −361.961 + 208.979i −0.374314 + 0.216110i −0.675341 0.737505i \(-0.736004\pi\)
0.301028 + 0.953615i \(0.402670\pi\)
\(968\) 150.594 + 260.836i 0.155572 + 0.269458i
\(969\) 0 0
\(970\) −730.017 418.603i −0.752595 0.431549i
\(971\) 685.151i 0.705613i −0.935696 0.352807i \(-0.885227\pi\)
0.935696 0.352807i \(-0.114773\pi\)
\(972\) 0 0
\(973\) 227.785i 0.234105i
\(974\) −1079.21 623.080i −1.10802 0.639713i
\(975\) 0 0
\(976\) −36.7982 63.7363i −0.0377030 0.0653036i
\(977\) −730.930 1266.01i −0.748137 1.29581i −0.948715 0.316133i \(-0.897615\pi\)
0.200578 0.979678i \(-0.435718\pi\)
\(978\) 0 0
\(979\) 252.711 437.708i 0.258132 0.447097i
\(980\) 139.593 0.412653i 0.142442 0.000421074i
\(981\) 0 0
\(982\) 497.287i 0.506402i
\(983\) −407.208 + 705.306i −0.414251 + 0.717503i −0.995349 0.0963298i \(-0.969290\pi\)
0.581099 + 0.813833i \(0.302623\pi\)
\(984\) 0 0
\(985\) 806.921 + 1388.14i 0.819209 + 1.40927i
\(986\) 66.7858 38.5588i 0.0677341 0.0391063i
\(987\) 0 0
\(988\) −1130.46 652.672i −1.14419 0.660599i
\(989\) 322.610i 0.326199i
\(990\) 0 0
\(991\) −594.842 −0.600244 −0.300122 0.953901i \(-0.597027\pi\)
−0.300122 + 0.953901i \(0.597027\pi\)
\(992\) 123.816 214.456i 0.124815 0.216185i
\(993\) 0 0
\(994\) −509.756 882.923i −0.512833 0.888252i
\(995\) 57.1465 + 98.3084i 0.0574337 + 0.0988024i
\(996\) 0 0
\(997\) −297.131 171.549i −0.298026 0.172065i 0.343530 0.939142i \(-0.388377\pi\)
−0.641556 + 0.767077i \(0.721711\pi\)
\(998\) 681.441 0.682807
\(999\) 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 810.3.j.g.269.9 24
3.2 odd 2 inner 810.3.j.g.269.2 24
5.4 even 2 810.3.j.h.269.2 24
9.2 odd 6 810.3.b.c.809.14 yes 24
9.4 even 3 810.3.j.h.539.8 24
9.5 odd 6 810.3.j.h.539.2 24
9.7 even 3 810.3.b.c.809.11 24
15.14 odd 2 810.3.j.h.269.9 24
45.4 even 6 inner 810.3.j.g.539.2 24
45.14 odd 6 inner 810.3.j.g.539.8 24
45.29 odd 6 810.3.b.c.809.12 yes 24
45.34 even 6 810.3.b.c.809.13 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
810.3.b.c.809.11 24 9.7 even 3
810.3.b.c.809.12 yes 24 45.29 odd 6
810.3.b.c.809.13 yes 24 45.34 even 6
810.3.b.c.809.14 yes 24 9.2 odd 6
810.3.j.g.269.2 24 3.2 odd 2 inner
810.3.j.g.269.9 24 1.1 even 1 trivial
810.3.j.g.539.2 24 45.4 even 6 inner
810.3.j.g.539.8 24 45.14 odd 6 inner
810.3.j.h.269.2 24 5.4 even 2
810.3.j.h.269.9 24 15.14 odd 2
810.3.j.h.539.2 24 9.5 odd 6
810.3.j.h.539.8 24 9.4 even 3