Properties

Label 690.3.f.a.229.36
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
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] = [690,3,Mod(229,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.229");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.f (of order \(2\), degree \(1\), 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: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.36
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.34

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.51156 - 2.15543i) q^{5} -2.44949 q^{6} +9.45027 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(4.51156 - 2.15543i) q^{5} -2.44949 q^{6} +9.45027 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(3.04824 + 6.38030i) q^{10} +0.168957i q^{11} -3.46410i q^{12} +0.410015i q^{13} +13.3647i q^{14} +(3.73331 + 7.81424i) q^{15} +4.00000 q^{16} +1.40721 q^{17} -4.24264i q^{18} -13.0341i q^{19} +(-9.02311 + 4.31086i) q^{20} +16.3683i q^{21} -0.238942 q^{22} +(19.0387 - 12.9045i) q^{23} +4.89898 q^{24} +(15.7083 - 19.4487i) q^{25} -0.579849 q^{26} -5.19615i q^{27} -18.9005 q^{28} +3.27423 q^{29} +(-11.0510 + 5.27970i) q^{30} +46.3652 q^{31} +5.65685i q^{32} -0.292643 q^{33} +1.99009i q^{34} +(42.6354 - 20.3694i) q^{35} +6.00000 q^{36} +8.23316 q^{37} +18.4330 q^{38} -0.710167 q^{39} +(-6.09647 - 12.7606i) q^{40} +22.2032 q^{41} -23.1483 q^{42} -27.5809 q^{43} -0.337915i q^{44} +(-13.5347 + 6.46628i) q^{45} +(18.2498 + 26.9248i) q^{46} +24.8110i q^{47} +6.92820i q^{48} +40.3076 q^{49} +(27.5046 + 22.2148i) q^{50} +2.43736i q^{51} -0.820030i q^{52} -5.90213 q^{53} +7.34847 q^{54} +(0.364176 + 0.762261i) q^{55} -26.7294i q^{56} +22.5757 q^{57} +4.63046i q^{58} -69.0614 q^{59} +(-7.46662 - 15.6285i) q^{60} +106.523i q^{61} +65.5703i q^{62} -28.3508 q^{63} -8.00000 q^{64} +(0.883758 + 1.84980i) q^{65} -0.413859i q^{66} +19.7414 q^{67} -2.81442 q^{68} +(22.3513 + 32.9760i) q^{69} +(28.8067 + 60.2956i) q^{70} +10.3118 q^{71} +8.48528i q^{72} -8.92696i q^{73} +11.6434i q^{74} +(33.6861 + 27.2075i) q^{75} +26.0681i q^{76} +1.59669i q^{77} -1.00433i q^{78} +84.6198i q^{79} +(18.0462 - 8.62171i) q^{80} +9.00000 q^{81} +31.4000i q^{82} -60.8352 q^{83} -32.7367i q^{84} +(6.34870 - 3.03314i) q^{85} -39.0053i q^{86} +5.67113i q^{87} +0.477884 q^{88} -9.16191i q^{89} +(-9.14471 - 19.1409i) q^{90} +3.87475i q^{91} +(-38.0774 + 25.8091i) q^{92} +80.3068i q^{93} -35.0880 q^{94} +(-28.0940 - 58.8039i) q^{95} -9.79796 q^{96} +86.3970 q^{97} +57.0036i q^{98} -0.506872i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) 4.51156 2.15543i 0.902311 0.431086i
\(6\) −2.44949 −0.408248
\(7\) 9.45027 1.35004 0.675019 0.737800i \(-0.264135\pi\)
0.675019 + 0.737800i \(0.264135\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) 3.04824 + 6.38030i 0.304824 + 0.638030i
\(11\) 0.168957i 0.0153598i 0.999971 + 0.00767988i \(0.00244461\pi\)
−0.999971 + 0.00767988i \(0.997555\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 0.410015i 0.0315396i 0.999876 + 0.0157698i \(0.00501989\pi\)
−0.999876 + 0.0157698i \(0.994980\pi\)
\(14\) 13.3647i 0.954621i
\(15\) 3.73331 + 7.81424i 0.248887 + 0.520950i
\(16\) 4.00000 0.250000
\(17\) 1.40721 0.0827770 0.0413885 0.999143i \(-0.486822\pi\)
0.0413885 + 0.999143i \(0.486822\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 13.0341i 0.686004i −0.939335 0.343002i \(-0.888556\pi\)
0.939335 0.343002i \(-0.111444\pi\)
\(20\) −9.02311 + 4.31086i −0.451156 + 0.215543i
\(21\) 16.3683i 0.779445i
\(22\) −0.238942 −0.0108610
\(23\) 19.0387 12.9045i 0.827771 0.561067i
\(24\) 4.89898 0.204124
\(25\) 15.7083 19.4487i 0.628330 0.777947i
\(26\) −0.579849 −0.0223019
\(27\) 5.19615i 0.192450i
\(28\) −18.9005 −0.675019
\(29\) 3.27423 0.112904 0.0564522 0.998405i \(-0.482021\pi\)
0.0564522 + 0.998405i \(0.482021\pi\)
\(30\) −11.0510 + 5.27970i −0.368367 + 0.175990i
\(31\) 46.3652 1.49565 0.747825 0.663896i \(-0.231098\pi\)
0.747825 + 0.663896i \(0.231098\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −0.292643 −0.00886796
\(34\) 1.99009i 0.0585322i
\(35\) 42.6354 20.3694i 1.21815 0.581982i
\(36\) 6.00000 0.166667
\(37\) 8.23316 0.222518 0.111259 0.993791i \(-0.464512\pi\)
0.111259 + 0.993791i \(0.464512\pi\)
\(38\) 18.4330 0.485078
\(39\) −0.710167 −0.0182094
\(40\) −6.09647 12.7606i −0.152412 0.319015i
\(41\) 22.2032 0.541541 0.270770 0.962644i \(-0.412722\pi\)
0.270770 + 0.962644i \(0.412722\pi\)
\(42\) −23.1483 −0.551151
\(43\) −27.5809 −0.641417 −0.320709 0.947178i \(-0.603921\pi\)
−0.320709 + 0.947178i \(0.603921\pi\)
\(44\) 0.337915i 0.00767988i
\(45\) −13.5347 + 6.46628i −0.300770 + 0.143695i
\(46\) 18.2498 + 26.9248i 0.396734 + 0.585322i
\(47\) 24.8110i 0.527893i 0.964537 + 0.263947i \(0.0850243\pi\)
−0.964537 + 0.263947i \(0.914976\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 40.3076 0.822604
\(50\) 27.5046 + 22.2148i 0.550091 + 0.444297i
\(51\) 2.43736i 0.0477913i
\(52\) 0.820030i 0.0157698i
\(53\) −5.90213 −0.111361 −0.0556805 0.998449i \(-0.517733\pi\)
−0.0556805 + 0.998449i \(0.517733\pi\)
\(54\) 7.34847 0.136083
\(55\) 0.364176 + 0.762261i 0.00662137 + 0.0138593i
\(56\) 26.7294i 0.477311i
\(57\) 22.5757 0.396064
\(58\) 4.63046i 0.0798355i
\(59\) −69.0614 −1.17053 −0.585266 0.810841i \(-0.699010\pi\)
−0.585266 + 0.810841i \(0.699010\pi\)
\(60\) −7.46662 15.6285i −0.124444 0.260475i
\(61\) 106.523i 1.74628i 0.487468 + 0.873141i \(0.337921\pi\)
−0.487468 + 0.873141i \(0.662079\pi\)
\(62\) 65.5703i 1.05758i
\(63\) −28.3508 −0.450013
\(64\) −8.00000 −0.125000
\(65\) 0.883758 + 1.84980i 0.0135963 + 0.0284585i
\(66\) 0.413859i 0.00627060i
\(67\) 19.7414 0.294648 0.147324 0.989088i \(-0.452934\pi\)
0.147324 + 0.989088i \(0.452934\pi\)
\(68\) −2.81442 −0.0413885
\(69\) 22.3513 + 32.9760i 0.323932 + 0.477914i
\(70\) 28.8067 + 60.2956i 0.411524 + 0.861365i
\(71\) 10.3118 0.145237 0.0726185 0.997360i \(-0.476864\pi\)
0.0726185 + 0.997360i \(0.476864\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 8.92696i 0.122287i −0.998129 0.0611436i \(-0.980525\pi\)
0.998129 0.0611436i \(-0.0194748\pi\)
\(74\) 11.6434i 0.157344i
\(75\) 33.6861 + 27.2075i 0.449148 + 0.362767i
\(76\) 26.0681i 0.343002i
\(77\) 1.59669i 0.0207363i
\(78\) 1.00433i 0.0128760i
\(79\) 84.6198i 1.07114i 0.844492 + 0.535568i \(0.179903\pi\)
−0.844492 + 0.535568i \(0.820097\pi\)
\(80\) 18.0462 8.62171i 0.225578 0.107771i
\(81\) 9.00000 0.111111
\(82\) 31.4000i 0.382927i
\(83\) −60.8352 −0.732955 −0.366477 0.930427i \(-0.619436\pi\)
−0.366477 + 0.930427i \(0.619436\pi\)
\(84\) 32.7367i 0.389723i
\(85\) 6.34870 3.03314i 0.0746906 0.0356840i
\(86\) 39.0053i 0.453551i
\(87\) 5.67113i 0.0651854i
\(88\) 0.477884 0.00543050
\(89\) 9.16191i 0.102943i −0.998674 0.0514714i \(-0.983609\pi\)
0.998674 0.0514714i \(-0.0163911\pi\)
\(90\) −9.14471 19.1409i −0.101608 0.212677i
\(91\) 3.87475i 0.0425797i
\(92\) −38.0774 + 25.8091i −0.413885 + 0.280533i
\(93\) 80.3068i 0.863514i
\(94\) −35.0880 −0.373277
\(95\) −28.0940 58.8039i −0.295726 0.618989i
\(96\) −9.79796 −0.102062
\(97\) 86.3970 0.890691 0.445345 0.895359i \(-0.353081\pi\)
0.445345 + 0.895359i \(0.353081\pi\)
\(98\) 57.0036i 0.581669i
\(99\) 0.506872i 0.00511992i
\(100\) −31.4165 + 38.8973i −0.314165 + 0.388973i
\(101\) −64.2539 −0.636177 −0.318088 0.948061i \(-0.603041\pi\)
−0.318088 + 0.948061i \(0.603041\pi\)
\(102\) −3.44694 −0.0337936
\(103\) −74.5544 −0.723829 −0.361915 0.932211i \(-0.617877\pi\)
−0.361915 + 0.932211i \(0.617877\pi\)
\(104\) 1.15970 0.0111509
\(105\) 35.2808 + 73.8467i 0.336008 + 0.703302i
\(106\) 8.34687i 0.0787441i
\(107\) 49.4322 0.461983 0.230992 0.972956i \(-0.425803\pi\)
0.230992 + 0.972956i \(0.425803\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 90.4875i 0.830161i 0.909785 + 0.415080i \(0.136247\pi\)
−0.909785 + 0.415080i \(0.863753\pi\)
\(110\) −1.07800 + 0.515022i −0.00979999 + 0.00468202i
\(111\) 14.2602i 0.128471i
\(112\) 37.8011 0.337510
\(113\) −100.086 −0.885713 −0.442856 0.896593i \(-0.646035\pi\)
−0.442856 + 0.896593i \(0.646035\pi\)
\(114\) 31.9268i 0.280060i
\(115\) 58.0795 99.2561i 0.505039 0.863097i
\(116\) −6.54846 −0.0564522
\(117\) 1.23004i 0.0105132i
\(118\) 97.6676i 0.827691i
\(119\) 13.2985 0.111752
\(120\) 22.1020 10.5594i 0.184183 0.0879950i
\(121\) 120.971 0.999764
\(122\) −150.647 −1.23481
\(123\) 38.4570i 0.312659i
\(124\) −92.7303 −0.747825
\(125\) 28.9485 121.602i 0.231588 0.972814i
\(126\) 40.0941i 0.318207i
\(127\) 158.414i 1.24735i −0.781683 0.623676i \(-0.785638\pi\)
0.781683 0.623676i \(-0.214362\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 47.7716i 0.370322i
\(130\) −2.61602 + 1.24982i −0.0201232 + 0.00961402i
\(131\) −228.138 −1.74151 −0.870757 0.491713i \(-0.836371\pi\)
−0.870757 + 0.491713i \(0.836371\pi\)
\(132\) 0.585286 0.00443398
\(133\) 123.175i 0.926131i
\(134\) 27.9185i 0.208347i
\(135\) −11.1999 23.4427i −0.0829625 0.173650i
\(136\) 3.98019i 0.0292661i
\(137\) −19.1955 −0.140113 −0.0700564 0.997543i \(-0.522318\pi\)
−0.0700564 + 0.997543i \(0.522318\pi\)
\(138\) −46.6352 + 31.6095i −0.337936 + 0.229055i
\(139\) 226.280 1.62791 0.813956 0.580926i \(-0.197310\pi\)
0.813956 + 0.580926i \(0.197310\pi\)
\(140\) −85.2708 + 40.7388i −0.609077 + 0.290991i
\(141\) −42.9739 −0.304779
\(142\) 14.5831i 0.102698i
\(143\) −0.0692751 −0.000484441
\(144\) −12.0000 −0.0833333
\(145\) 14.7719 7.05737i 0.101875 0.0486715i
\(146\) 12.6246 0.0864701
\(147\) 69.8148i 0.474931i
\(148\) −16.4663 −0.111259
\(149\) 138.045i 0.926474i 0.886235 + 0.463237i \(0.153312\pi\)
−0.886235 + 0.463237i \(0.846688\pi\)
\(150\) −38.4772 + 47.6393i −0.256515 + 0.317595i
\(151\) −111.059 −0.735490 −0.367745 0.929927i \(-0.619870\pi\)
−0.367745 + 0.929927i \(0.619870\pi\)
\(152\) −36.8659 −0.242539
\(153\) −4.22163 −0.0275923
\(154\) −2.25807 −0.0146628
\(155\) 209.179 99.9368i 1.34954 0.644754i
\(156\) 1.42033 0.00910470
\(157\) 208.561 1.32842 0.664208 0.747548i \(-0.268769\pi\)
0.664208 + 0.747548i \(0.268769\pi\)
\(158\) −119.670 −0.757408
\(159\) 10.2228i 0.0642943i
\(160\) 12.1929 + 25.5212i 0.0762059 + 0.159508i
\(161\) 179.921 121.951i 1.11752 0.757462i
\(162\) 12.7279i 0.0785674i
\(163\) 128.025i 0.785427i −0.919661 0.392713i \(-0.871536\pi\)
0.919661 0.392713i \(-0.128464\pi\)
\(164\) −44.4063 −0.270770
\(165\) −1.32027 + 0.630771i −0.00800166 + 0.00382285i
\(166\) 86.0340i 0.518277i
\(167\) 313.129i 1.87503i 0.347950 + 0.937513i \(0.386878\pi\)
−0.347950 + 0.937513i \(0.613122\pi\)
\(168\) 46.2967 0.275575
\(169\) 168.832 0.999005
\(170\) 4.28950 + 8.97842i 0.0252324 + 0.0528142i
\(171\) 39.1022i 0.228668i
\(172\) 55.1619 0.320709
\(173\) 271.648i 1.57022i −0.619355 0.785111i \(-0.712606\pi\)
0.619355 0.785111i \(-0.287394\pi\)
\(174\) −8.02019 −0.0460931
\(175\) 148.447 183.795i 0.848270 1.05026i
\(176\) 0.675830i 0.00383994i
\(177\) 119.618i 0.675807i
\(178\) 12.9569 0.0727916
\(179\) −237.537 −1.32702 −0.663510 0.748167i \(-0.730934\pi\)
−0.663510 + 0.748167i \(0.730934\pi\)
\(180\) 27.0693 12.9326i 0.150385 0.0718476i
\(181\) 40.7017i 0.224871i 0.993659 + 0.112436i \(0.0358652\pi\)
−0.993659 + 0.112436i \(0.964135\pi\)
\(182\) −5.47973 −0.0301084
\(183\) −184.504 −1.00822
\(184\) −36.4995 53.8496i −0.198367 0.292661i
\(185\) 37.1443 17.7460i 0.200780 0.0959242i
\(186\) −113.571 −0.610597
\(187\) 0.237758i 0.00127143i
\(188\) 49.6220i 0.263947i
\(189\) 49.1050i 0.259815i
\(190\) 83.1613 39.7309i 0.437691 0.209110i
\(191\) 202.716i 1.06134i 0.847578 + 0.530671i \(0.178060\pi\)
−0.847578 + 0.530671i \(0.821940\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 185.008i 0.958589i −0.877654 0.479294i \(-0.840893\pi\)
0.877654 0.479294i \(-0.159107\pi\)
\(194\) 122.184i 0.629813i
\(195\) −3.20396 + 1.53071i −0.0164305 + 0.00784981i
\(196\) −80.6152 −0.411302
\(197\) 54.1067i 0.274653i −0.990526 0.137327i \(-0.956149\pi\)
0.990526 0.137327i \(-0.0438510\pi\)
\(198\) 0.716826 0.00362033
\(199\) 40.4530i 0.203281i −0.994821 0.101641i \(-0.967591\pi\)
0.994821 0.101641i \(-0.0324092\pi\)
\(200\) −55.0091 44.4297i −0.275046 0.222148i
\(201\) 34.1931i 0.170115i
\(202\) 90.8687i 0.449845i
\(203\) 30.9424 0.152425
\(204\) 4.87471i 0.0238957i
\(205\) 100.171 47.8573i 0.488638 0.233450i
\(206\) 105.436i 0.511824i
\(207\) −57.1162 + 38.7136i −0.275924 + 0.187022i
\(208\) 1.64006i 0.00788490i
\(209\) 2.20220 0.0105369
\(210\) −104.435 + 49.8946i −0.497310 + 0.237593i
\(211\) −93.1211 −0.441332 −0.220666 0.975349i \(-0.570823\pi\)
−0.220666 + 0.975349i \(0.570823\pi\)
\(212\) 11.8043 0.0556805
\(213\) 17.8606i 0.0838526i
\(214\) 69.9077i 0.326672i
\(215\) −124.433 + 59.4487i −0.578758 + 0.276506i
\(216\) −14.6969 −0.0680414
\(217\) 438.163 2.01919
\(218\) −127.969 −0.587012
\(219\) 15.4620 0.0706025
\(220\) −0.728351 1.52452i −0.00331069 0.00692964i
\(221\) 0.576976i 0.00261075i
\(222\) −20.1670 −0.0908425
\(223\) 326.830i 1.46560i −0.680441 0.732802i \(-0.738212\pi\)
0.680441 0.732802i \(-0.261788\pi\)
\(224\) 53.4588i 0.238655i
\(225\) −47.1248 + 58.3460i −0.209443 + 0.259316i
\(226\) 141.542i 0.626293i
\(227\) −130.957 −0.576902 −0.288451 0.957495i \(-0.593140\pi\)
−0.288451 + 0.957495i \(0.593140\pi\)
\(228\) −45.1513 −0.198032
\(229\) 169.709i 0.741088i 0.928815 + 0.370544i \(0.120829\pi\)
−0.928815 + 0.370544i \(0.879171\pi\)
\(230\) 140.369 + 82.1368i 0.610302 + 0.357116i
\(231\) −2.76555 −0.0119721
\(232\) 9.26092i 0.0399178i
\(233\) 63.2641i 0.271520i −0.990742 0.135760i \(-0.956652\pi\)
0.990742 0.135760i \(-0.0433476\pi\)
\(234\) 1.73955 0.00743396
\(235\) 53.4783 + 111.936i 0.227567 + 0.476324i
\(236\) 138.123 0.585266
\(237\) −146.566 −0.618421
\(238\) 18.8069i 0.0790207i
\(239\) −415.109 −1.73686 −0.868429 0.495814i \(-0.834870\pi\)
−0.868429 + 0.495814i \(0.834870\pi\)
\(240\) 14.9332 + 31.2570i 0.0622219 + 0.130237i
\(241\) 112.766i 0.467910i 0.972247 + 0.233955i \(0.0751669\pi\)
−0.972247 + 0.233955i \(0.924833\pi\)
\(242\) 171.079i 0.706940i
\(243\) 15.5885i 0.0641500i
\(244\) 213.046i 0.873141i
\(245\) 181.850 86.8801i 0.742245 0.354613i
\(246\) −54.3864 −0.221083
\(247\) 5.34416 0.0216363
\(248\) 131.141i 0.528792i
\(249\) 105.370i 0.423172i
\(250\) 171.971 + 40.9393i 0.687883 + 0.163757i
\(251\) 361.428i 1.43995i −0.693998 0.719977i \(-0.744152\pi\)
0.693998 0.719977i \(-0.255848\pi\)
\(252\) 56.7016 0.225006
\(253\) 2.18032 + 3.21673i 0.00861785 + 0.0127144i
\(254\) 224.031 0.882011
\(255\) 5.25355 + 10.9963i 0.0206021 + 0.0431226i
\(256\) 16.0000 0.0625000
\(257\) 139.253i 0.541840i −0.962602 0.270920i \(-0.912672\pi\)
0.962602 0.270920i \(-0.0873279\pi\)
\(258\) 67.5592 0.261858
\(259\) 77.8055 0.300408
\(260\) −1.76752 3.69961i −0.00679814 0.0142293i
\(261\) −9.82269 −0.0376348
\(262\) 322.636i 1.23144i
\(263\) −10.0975 −0.0383934 −0.0191967 0.999816i \(-0.506111\pi\)
−0.0191967 + 0.999816i \(0.506111\pi\)
\(264\) 0.827719i 0.00313530i
\(265\) −26.6278 + 12.7216i −0.100482 + 0.0480061i
\(266\) 174.196 0.654874
\(267\) 15.8689 0.0594341
\(268\) −39.4828 −0.147324
\(269\) −182.893 −0.679900 −0.339950 0.940444i \(-0.610410\pi\)
−0.339950 + 0.940444i \(0.610410\pi\)
\(270\) 33.1530 15.8391i 0.122789 0.0586633i
\(271\) −132.990 −0.490739 −0.245369 0.969430i \(-0.578909\pi\)
−0.245369 + 0.969430i \(0.578909\pi\)
\(272\) 5.62883 0.0206942
\(273\) −6.71127 −0.0245834
\(274\) 27.1465i 0.0990747i
\(275\) 3.28600 + 2.65403i 0.0119491 + 0.00965101i
\(276\) −44.7026 65.9521i −0.161966 0.238957i
\(277\) 76.3745i 0.275720i −0.990452 0.137860i \(-0.955978\pi\)
0.990452 0.137860i \(-0.0440225\pi\)
\(278\) 320.008i 1.15111i
\(279\) −139.096 −0.498550
\(280\) −57.6133 120.591i −0.205762 0.430683i
\(281\) 389.767i 1.38707i −0.720423 0.693535i \(-0.756052\pi\)
0.720423 0.693535i \(-0.243948\pi\)
\(282\) 60.7743i 0.215512i
\(283\) −95.1971 −0.336385 −0.168193 0.985754i \(-0.553793\pi\)
−0.168193 + 0.985754i \(0.553793\pi\)
\(284\) −20.6237 −0.0726185
\(285\) 101.851 48.6602i 0.357373 0.170738i
\(286\) 0.0979697i 0.000342551i
\(287\) 209.826 0.731101
\(288\) 16.9706i 0.0589256i
\(289\) −287.020 −0.993148
\(290\) 9.98062 + 20.8906i 0.0344159 + 0.0720365i
\(291\) 149.644i 0.514240i
\(292\) 17.8539i 0.0611436i
\(293\) −197.320 −0.673448 −0.336724 0.941603i \(-0.609319\pi\)
−0.336724 + 0.941603i \(0.609319\pi\)
\(294\) −98.7331 −0.335827
\(295\) −311.574 + 148.857i −1.05618 + 0.504600i
\(296\) 23.2869i 0.0786719i
\(297\) 0.877928 0.00295599
\(298\) −195.225 −0.655116
\(299\) 5.29105 + 7.80616i 0.0176958 + 0.0261076i
\(300\) −67.3722 54.4150i −0.224574 0.181383i
\(301\) −260.647 −0.865938
\(302\) 157.061i 0.520070i
\(303\) 111.291i 0.367297i
\(304\) 52.1363i 0.171501i
\(305\) 229.603 + 480.585i 0.752797 + 1.57569i
\(306\) 5.97028i 0.0195107i
\(307\) 238.130i 0.775669i 0.921729 + 0.387835i \(0.126777\pi\)
−0.921729 + 0.387835i \(0.873223\pi\)
\(308\) 3.19339i 0.0103681i
\(309\) 129.132i 0.417903i
\(310\) 141.332 + 295.824i 0.455910 + 0.954270i
\(311\) 48.8991 0.157232 0.0786158 0.996905i \(-0.474950\pi\)
0.0786158 + 0.996905i \(0.474950\pi\)
\(312\) 2.00865i 0.00643800i
\(313\) −386.351 −1.23435 −0.617175 0.786826i \(-0.711723\pi\)
−0.617175 + 0.786826i \(0.711723\pi\)
\(314\) 294.950i 0.939332i
\(315\) −127.906 + 61.1081i −0.406052 + 0.193994i
\(316\) 169.240i 0.535568i
\(317\) 326.284i 1.02929i −0.857404 0.514644i \(-0.827924\pi\)
0.857404 0.514644i \(-0.172076\pi\)
\(318\) 14.4572 0.0454629
\(319\) 0.553205i 0.00173419i
\(320\) −36.0924 + 17.2434i −0.112789 + 0.0538857i
\(321\) 85.6191i 0.266726i
\(322\) 172.465 + 254.447i 0.535606 + 0.790208i
\(323\) 18.3417i 0.0567853i
\(324\) −18.0000 −0.0555556
\(325\) 7.97424 + 6.44062i 0.0245361 + 0.0198173i
\(326\) 181.054 0.555381
\(327\) −156.729 −0.479294
\(328\) 62.8000i 0.191464i
\(329\) 234.471i 0.712677i
\(330\) −0.892044 1.86715i −0.00270316 0.00565803i
\(331\) −45.7276 −0.138150 −0.0690750 0.997611i \(-0.522005\pi\)
−0.0690750 + 0.997611i \(0.522005\pi\)
\(332\) 121.670 0.366477
\(333\) −24.6995 −0.0741726
\(334\) −442.832 −1.32584
\(335\) 89.0644 42.5512i 0.265864 0.127018i
\(336\) 65.4734i 0.194861i
\(337\) 547.693 1.62520 0.812602 0.582820i \(-0.198051\pi\)
0.812602 + 0.582820i \(0.198051\pi\)
\(338\) 238.764i 0.706403i
\(339\) 173.353i 0.511366i
\(340\) −12.6974 + 6.06627i −0.0373453 + 0.0178420i
\(341\) 7.83374i 0.0229728i
\(342\) −55.2989 −0.161693
\(343\) −82.1455 −0.239491
\(344\) 78.0107i 0.226775i
\(345\) 171.917 + 100.597i 0.498309 + 0.291584i
\(346\) 384.169 1.11031
\(347\) 430.247i 1.23991i 0.784639 + 0.619953i \(0.212848\pi\)
−0.784639 + 0.619953i \(0.787152\pi\)
\(348\) 11.3423i 0.0325927i
\(349\) −32.7928 −0.0939623 −0.0469811 0.998896i \(-0.514960\pi\)
−0.0469811 + 0.998896i \(0.514960\pi\)
\(350\) 259.926 + 209.936i 0.742645 + 0.599818i
\(351\) 2.13050 0.00606980
\(352\) −0.955767 −0.00271525
\(353\) 228.526i 0.647383i −0.946163 0.323692i \(-0.895076\pi\)
0.946163 0.323692i \(-0.104924\pi\)
\(354\) 169.165 0.477868
\(355\) 46.5224 22.2264i 0.131049 0.0626096i
\(356\) 18.3238i 0.0514714i
\(357\) 23.0337i 0.0645201i
\(358\) 335.928i 0.938345i
\(359\) 687.674i 1.91553i −0.287559 0.957763i \(-0.592844\pi\)
0.287559 0.957763i \(-0.407156\pi\)
\(360\) 18.2894 + 38.2818i 0.0508039 + 0.106338i
\(361\) 191.113 0.529399
\(362\) −57.5609 −0.159008
\(363\) 209.529i 0.577214i
\(364\) 7.74950i 0.0212898i
\(365\) −19.2414 40.2745i −0.0527162 0.110341i
\(366\) 260.927i 0.712917i
\(367\) −595.848 −1.62356 −0.811782 0.583960i \(-0.801502\pi\)
−0.811782 + 0.583960i \(0.801502\pi\)
\(368\) 76.1549 51.6181i 0.206943 0.140267i
\(369\) −66.6095 −0.180514
\(370\) 25.0966 + 52.5300i 0.0678287 + 0.141973i
\(371\) −55.7767 −0.150342
\(372\) 160.614i 0.431757i
\(373\) 79.0781 0.212006 0.106003 0.994366i \(-0.466195\pi\)
0.106003 + 0.994366i \(0.466195\pi\)
\(374\) −0.336241 −0.000899040
\(375\) 210.620 + 50.1402i 0.561654 + 0.133707i
\(376\) 70.1761 0.186639
\(377\) 1.34248i 0.00356096i
\(378\) 69.4450 0.183717
\(379\) 397.595i 1.04906i −0.851391 0.524532i \(-0.824240\pi\)
0.851391 0.524532i \(-0.175760\pi\)
\(380\) 56.1880 + 117.608i 0.147863 + 0.309494i
\(381\) 274.381 0.720159
\(382\) −286.684 −0.750482
\(383\) −37.8458 −0.0988140 −0.0494070 0.998779i \(-0.515733\pi\)
−0.0494070 + 0.998779i \(0.515733\pi\)
\(384\) 19.5959 0.0510310
\(385\) 3.44156 + 7.20357i 0.00893911 + 0.0187106i
\(386\) 261.640 0.677825
\(387\) 82.7428 0.213806
\(388\) −172.794 −0.445345
\(389\) 223.018i 0.573310i 0.958034 + 0.286655i \(0.0925433\pi\)
−0.958034 + 0.286655i \(0.907457\pi\)
\(390\) −2.16476 4.53108i −0.00555065 0.0116181i
\(391\) 26.7915 18.1594i 0.0685203 0.0464434i
\(392\) 114.007i 0.290834i
\(393\) 395.147i 1.00546i
\(394\) 76.5184 0.194209
\(395\) 182.392 + 381.767i 0.461752 + 0.966499i
\(396\) 1.01374i 0.00255996i
\(397\) 95.2611i 0.239952i −0.992777 0.119976i \(-0.961718\pi\)
0.992777 0.119976i \(-0.0382818\pi\)
\(398\) 57.2091 0.143742
\(399\) 213.346 0.534702
\(400\) 62.8330 77.7947i 0.157083 0.194487i
\(401\) 91.8537i 0.229062i 0.993420 + 0.114531i \(0.0365365\pi\)
−0.993420 + 0.114531i \(0.963464\pi\)
\(402\) −48.3563 −0.120289
\(403\) 19.0104i 0.0471722i
\(404\) 128.508 0.318088
\(405\) 40.6040 19.3989i 0.100257 0.0478984i
\(406\) 43.7591i 0.107781i
\(407\) 1.39105i 0.00341782i
\(408\) 6.89389 0.0168968
\(409\) 89.3154 0.218375 0.109188 0.994021i \(-0.465175\pi\)
0.109188 + 0.994021i \(0.465175\pi\)
\(410\) 67.6805 + 141.663i 0.165074 + 0.345519i
\(411\) 33.2475i 0.0808942i
\(412\) 149.109 0.361915
\(413\) −652.649 −1.58026
\(414\) −54.7493 80.7745i −0.132245 0.195107i
\(415\) −274.462 + 131.126i −0.661353 + 0.315966i
\(416\) −2.31939 −0.00557547
\(417\) 391.928i 0.939876i
\(418\) 3.11438i 0.00745068i
\(419\) 9.33638i 0.0222825i 0.999938 + 0.0111413i \(0.00354645\pi\)
−0.999938 + 0.0111413i \(0.996454\pi\)
\(420\) −70.5616 147.693i −0.168004 0.351651i
\(421\) 737.189i 1.75104i 0.483179 + 0.875522i \(0.339482\pi\)
−0.483179 + 0.875522i \(0.660518\pi\)
\(422\) 131.693i 0.312069i
\(423\) 74.4330i 0.175964i
\(424\) 16.6937i 0.0393720i
\(425\) 22.1048 27.3683i 0.0520113 0.0643961i
\(426\) −25.2587 −0.0592928
\(427\) 1006.67i 2.35755i
\(428\) −98.8644 −0.230992
\(429\) 0.119988i 0.000279692i
\(430\) −84.0732 175.975i −0.195519 0.409244i
\(431\) 280.844i 0.651611i 0.945437 + 0.325805i \(0.105635\pi\)
−0.945437 + 0.325805i \(0.894365\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) −145.165 −0.335254 −0.167627 0.985851i \(-0.553610\pi\)
−0.167627 + 0.985851i \(0.553610\pi\)
\(434\) 619.657i 1.42778i
\(435\) 12.2237 + 25.5856i 0.0281005 + 0.0588175i
\(436\) 180.975i 0.415080i
\(437\) −168.199 248.152i −0.384894 0.567854i
\(438\) 21.8665i 0.0499235i
\(439\) 345.256 0.786460 0.393230 0.919440i \(-0.371358\pi\)
0.393230 + 0.919440i \(0.371358\pi\)
\(440\) 2.15600 1.03004i 0.00490000 0.00234101i
\(441\) −120.923 −0.274201
\(442\) −0.815968 −0.00184608
\(443\) 78.3990i 0.176973i 0.996077 + 0.0884864i \(0.0282030\pi\)
−0.996077 + 0.0884864i \(0.971797\pi\)
\(444\) 28.5205i 0.0642353i
\(445\) −19.7478 41.3345i −0.0443772 0.0928865i
\(446\) 462.207 1.03634
\(447\) −239.100 −0.534900
\(448\) −75.6022 −0.168755
\(449\) 56.5141 0.125867 0.0629333 0.998018i \(-0.479954\pi\)
0.0629333 + 0.998018i \(0.479954\pi\)
\(450\) −82.5137 66.6445i −0.183364 0.148099i
\(451\) 3.75139i 0.00831794i
\(452\) 200.171 0.442856
\(453\) 192.360i 0.424635i
\(454\) 185.201i 0.407931i
\(455\) 8.35175 + 17.4812i 0.0183555 + 0.0384201i
\(456\) 63.8536i 0.140030i
\(457\) −312.960 −0.684813 −0.342407 0.939552i \(-0.611242\pi\)
−0.342407 + 0.939552i \(0.611242\pi\)
\(458\) −240.005 −0.524029
\(459\) 7.31207i 0.0159304i
\(460\) −116.159 + 198.512i −0.252519 + 0.431548i
\(461\) 101.113 0.219335 0.109667 0.993968i \(-0.465021\pi\)
0.109667 + 0.993968i \(0.465021\pi\)
\(462\) 3.91108i 0.00846555i
\(463\) 674.719i 1.45728i 0.684899 + 0.728638i \(0.259846\pi\)
−0.684899 + 0.728638i \(0.740154\pi\)
\(464\) 13.0969 0.0282261
\(465\) 173.096 + 362.309i 0.372249 + 0.779158i
\(466\) 89.4690 0.191994
\(467\) −205.659 −0.440384 −0.220192 0.975457i \(-0.570668\pi\)
−0.220192 + 0.975457i \(0.570668\pi\)
\(468\) 2.46009i 0.00525660i
\(469\) 186.561 0.397786
\(470\) −158.302 + 75.6298i −0.336812 + 0.160914i
\(471\) 361.239i 0.766961i
\(472\) 195.335i 0.413846i
\(473\) 4.66000i 0.00985202i
\(474\) 207.275i 0.437290i
\(475\) −253.495 204.743i −0.533674 0.431037i
\(476\) −26.5970 −0.0558761
\(477\) 17.7064 0.0371203
\(478\) 587.053i 1.22814i
\(479\) 647.140i 1.35102i 0.737349 + 0.675512i \(0.236077\pi\)
−0.737349 + 0.675512i \(0.763923\pi\)
\(480\) −44.2040 + 21.1188i −0.0920917 + 0.0439975i
\(481\) 3.37572i 0.00701812i
\(482\) −159.476 −0.330862
\(483\) 211.226 + 311.632i 0.437321 + 0.645202i
\(484\) −241.943 −0.499882
\(485\) 389.785 186.223i 0.803680 0.383964i
\(486\) −22.0454 −0.0453609
\(487\) 605.672i 1.24368i 0.783144 + 0.621840i \(0.213615\pi\)
−0.783144 + 0.621840i \(0.786385\pi\)
\(488\) 301.293 0.617404
\(489\) 221.745 0.453466
\(490\) 122.867 + 257.175i 0.250749 + 0.524846i
\(491\) −276.372 −0.562876 −0.281438 0.959579i \(-0.590811\pi\)
−0.281438 + 0.959579i \(0.590811\pi\)
\(492\) 76.9140i 0.156329i
\(493\) 4.60752 0.00934589
\(494\) 7.55779i 0.0152992i
\(495\) −1.09253 2.28678i −0.00220712 0.00461976i
\(496\) 185.461 0.373913
\(497\) 97.4496 0.196076
\(498\) 149.015 0.299228
\(499\) 836.089 1.67553 0.837765 0.546031i \(-0.183862\pi\)
0.837765 + 0.546031i \(0.183862\pi\)
\(500\) −57.8969 + 243.204i −0.115794 + 0.486407i
\(501\) −542.356 −1.08255
\(502\) 511.137 1.01820
\(503\) −395.531 −0.786343 −0.393172 0.919465i \(-0.628622\pi\)
−0.393172 + 0.919465i \(0.628622\pi\)
\(504\) 80.1882i 0.159104i
\(505\) −289.885 + 138.495i −0.574029 + 0.274247i
\(506\) −4.54915 + 3.08343i −0.00899041 + 0.00609374i
\(507\) 292.425i 0.576776i
\(508\) 316.827i 0.623676i
\(509\) −7.74137 −0.0152090 −0.00760449 0.999971i \(-0.502421\pi\)
−0.00760449 + 0.999971i \(0.502421\pi\)
\(510\) −15.5511 + 7.42964i −0.0304923 + 0.0145679i
\(511\) 84.3622i 0.165092i
\(512\) 22.6274i 0.0441942i
\(513\) −67.7270 −0.132021
\(514\) 196.933 0.383139
\(515\) −336.356 + 160.697i −0.653119 + 0.312032i
\(516\) 95.5432i 0.185161i
\(517\) −4.19200 −0.00810832
\(518\) 110.034i 0.212420i
\(519\) 470.509 0.906568
\(520\) 5.23204 2.49964i 0.0100616 0.00480701i
\(521\) 186.274i 0.357531i 0.983892 + 0.178765i \(0.0572103\pi\)
−0.983892 + 0.178765i \(0.942790\pi\)
\(522\) 13.8914i 0.0266118i
\(523\) 561.122 1.07289 0.536445 0.843935i \(-0.319767\pi\)
0.536445 + 0.843935i \(0.319767\pi\)
\(524\) 456.277 0.870757
\(525\) 318.343 + 257.118i 0.606367 + 0.489749i
\(526\) 14.2800i 0.0271482i
\(527\) 65.2455 0.123805
\(528\) −1.17057 −0.00221699
\(529\) 195.946 491.372i 0.370408 0.928869i
\(530\) −17.9911 37.6574i −0.0339454 0.0710516i
\(531\) 207.184 0.390177
\(532\) 246.351i 0.463066i
\(533\) 9.10363i 0.0170800i
\(534\) 22.4420i 0.0420262i
\(535\) 223.016 106.548i 0.416853 0.199154i
\(536\) 55.8371i 0.104174i
\(537\) 411.425i 0.766155i
\(538\) 258.650i 0.480762i
\(539\) 6.81027i 0.0126350i
\(540\) 22.3999 + 46.8855i 0.0414812 + 0.0868249i
\(541\) −284.239 −0.525396 −0.262698 0.964878i \(-0.584612\pi\)
−0.262698 + 0.964878i \(0.584612\pi\)
\(542\) 188.077i 0.347005i
\(543\) −70.4974 −0.129830
\(544\) 7.96037i 0.0146330i
\(545\) 195.039 + 408.239i 0.357870 + 0.749063i
\(546\) 9.49116i 0.0173831i
\(547\) 588.955i 1.07670i 0.842721 + 0.538351i \(0.180952\pi\)
−0.842721 + 0.538351i \(0.819048\pi\)
\(548\) 38.3909 0.0700564
\(549\) 319.570i 0.582094i
\(550\) −3.75336 + 4.64710i −0.00682429 + 0.00844927i
\(551\) 42.6765i 0.0774529i
\(552\) 93.2703 63.2190i 0.168968 0.114527i
\(553\) 799.680i 1.44608i
\(554\) 108.010 0.194964
\(555\) 30.7369 + 64.3359i 0.0553819 + 0.115921i
\(556\) −452.560 −0.813956
\(557\) 29.3491 0.0526914 0.0263457 0.999653i \(-0.491613\pi\)
0.0263457 + 0.999653i \(0.491613\pi\)
\(558\) 196.711i 0.352528i
\(559\) 11.3086i 0.0202301i
\(560\) 170.542 81.4775i 0.304539 0.145496i
\(561\) −0.411809 −0.000734063
\(562\) 551.213 0.980807
\(563\) −335.437 −0.595802 −0.297901 0.954597i \(-0.596287\pi\)
−0.297901 + 0.954597i \(0.596287\pi\)
\(564\) 85.9478 0.152390
\(565\) −451.541 + 215.727i −0.799188 + 0.381818i
\(566\) 134.629i 0.237860i
\(567\) 85.0524 0.150004
\(568\) 29.1663i 0.0513490i
\(569\) 874.221i 1.53642i 0.640200 + 0.768208i \(0.278851\pi\)
−0.640200 + 0.768208i \(0.721149\pi\)
\(570\) 68.8160 + 144.040i 0.120730 + 0.252701i
\(571\) 296.172i 0.518689i 0.965785 + 0.259345i \(0.0835066\pi\)
−0.965785 + 0.259345i \(0.916493\pi\)
\(572\) 0.138550 0.000242220
\(573\) −351.115 −0.612766
\(574\) 296.739i 0.516966i
\(575\) 48.0892 572.986i 0.0836335 0.996497i
\(576\) 24.0000 0.0416667
\(577\) 309.659i 0.536670i −0.963326 0.268335i \(-0.913527\pi\)
0.963326 0.268335i \(-0.0864734\pi\)
\(578\) 405.907i 0.702262i
\(579\) 320.443 0.553442
\(580\) −29.5437 + 14.1147i −0.0509375 + 0.0243357i
\(581\) −574.909 −0.989517
\(582\) −211.629 −0.363623
\(583\) 0.997208i 0.00171048i
\(584\) −25.2493 −0.0432350
\(585\) −2.65127 5.54941i −0.00453209 0.00948618i
\(586\) 279.053i 0.476200i
\(587\) 892.095i 1.51975i −0.650068 0.759876i \(-0.725260\pi\)
0.650068 0.759876i \(-0.274740\pi\)
\(588\) 139.630i 0.237465i
\(589\) 604.327i 1.02602i
\(590\) −210.515 440.633i −0.356806 0.746835i
\(591\) 93.7156 0.158571
\(592\) 32.9326 0.0556294
\(593\) 109.141i 0.184049i −0.995757 0.0920244i \(-0.970666\pi\)
0.995757 0.0920244i \(-0.0293338\pi\)
\(594\) 1.24158i 0.00209020i
\(595\) 59.9969 28.6640i 0.100835 0.0481747i
\(596\) 276.089i 0.463237i
\(597\) 70.0666 0.117364
\(598\) −11.0396 + 7.48268i −0.0184608 + 0.0125128i
\(599\) −184.005 −0.307187 −0.153594 0.988134i \(-0.549085\pi\)
−0.153594 + 0.988134i \(0.549085\pi\)
\(600\) 76.9544 95.2786i 0.128257 0.158798i
\(601\) 819.863 1.36417 0.682083 0.731275i \(-0.261074\pi\)
0.682083 + 0.731275i \(0.261074\pi\)
\(602\) 368.611i 0.612311i
\(603\) −59.2242 −0.0982159
\(604\) 222.118 0.367745
\(605\) 545.769 260.745i 0.902098 0.430984i
\(606\) 157.389 0.259718
\(607\) 51.0051i 0.0840281i −0.999117 0.0420141i \(-0.986623\pi\)
0.999117 0.0420141i \(-0.0133774\pi\)
\(608\) 73.7318 0.121269
\(609\) 53.5937i 0.0880028i
\(610\) −679.650 + 324.708i −1.11418 + 0.532308i
\(611\) −10.1729 −0.0166496
\(612\) 8.44325 0.0137962
\(613\) −290.239 −0.473474 −0.236737 0.971574i \(-0.576078\pi\)
−0.236737 + 0.971574i \(0.576078\pi\)
\(614\) −336.767 −0.548481
\(615\) 82.8913 + 173.501i 0.134783 + 0.282115i
\(616\) 4.51613 0.00733138
\(617\) 901.299 1.46078 0.730388 0.683032i \(-0.239339\pi\)
0.730388 + 0.683032i \(0.239339\pi\)
\(618\) 182.620 0.295502
\(619\) 898.463i 1.45147i −0.687972 0.725737i \(-0.741499\pi\)
0.687972 0.725737i \(-0.258501\pi\)
\(620\) −418.358 + 199.874i −0.674771 + 0.322377i
\(621\) −67.0539 98.9281i −0.107977 0.159305i
\(622\) 69.1537i 0.111180i
\(623\) 86.5826i 0.138977i
\(624\) −2.84067 −0.00455235
\(625\) −131.501 611.009i −0.210402 0.977615i
\(626\) 546.383i 0.872817i
\(627\) 3.81433i 0.00608346i
\(628\) −417.123 −0.664208
\(629\) 11.5858 0.0184193
\(630\) −86.4200 180.887i −0.137175 0.287122i
\(631\) 234.478i 0.371598i 0.982588 + 0.185799i \(0.0594874\pi\)
−0.982588 + 0.185799i \(0.940513\pi\)
\(632\) 239.341 0.378704
\(633\) 161.290i 0.254803i
\(634\) 461.435 0.727816
\(635\) −341.449 714.692i −0.537716 1.12550i
\(636\) 20.4456i 0.0321471i
\(637\) 16.5267i 0.0259446i
\(638\) −0.782350 −0.00122625
\(639\) −30.9355 −0.0484123
\(640\) −24.3859 51.0424i −0.0381029 0.0797538i
\(641\) 859.266i 1.34051i 0.742132 + 0.670254i \(0.233815\pi\)
−0.742132 + 0.670254i \(0.766185\pi\)
\(642\) −121.084 −0.188604
\(643\) −1213.71 −1.88758 −0.943789 0.330548i \(-0.892766\pi\)
−0.943789 + 0.330548i \(0.892766\pi\)
\(644\) −359.842 + 243.903i −0.558761 + 0.378731i
\(645\) −102.968 215.524i −0.159641 0.334146i
\(646\) 25.9390 0.0401533
\(647\) 514.525i 0.795247i −0.917549 0.397624i \(-0.869835\pi\)
0.917549 0.397624i \(-0.130165\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 11.6684i 0.0179791i
\(650\) −9.10841 + 11.2773i −0.0140129 + 0.0173497i
\(651\) 758.921i 1.16578i
\(652\) 256.049i 0.392713i
\(653\) 129.367i 0.198111i 0.995082 + 0.0990556i \(0.0315822\pi\)
−0.995082 + 0.0990556i \(0.968418\pi\)
\(654\) 221.648i 0.338912i
\(655\) −1029.26 + 491.736i −1.57139 + 0.750742i
\(656\) 88.8127 0.135385
\(657\) 26.7809i 0.0407624i
\(658\) −331.591 −0.503938
\(659\) 871.444i 1.32237i −0.750221 0.661187i \(-0.770053\pi\)
0.750221 0.661187i \(-0.229947\pi\)
\(660\) 2.64055 1.26154i 0.00400083 0.00191143i
\(661\) 35.3844i 0.0535317i 0.999642 + 0.0267658i \(0.00852085\pi\)
−0.999642 + 0.0267658i \(0.991479\pi\)
\(662\) 64.6686i 0.0976867i
\(663\) −0.999353 −0.00150732
\(664\) 172.068i 0.259139i
\(665\) −265.496 555.713i −0.399242 0.835659i
\(666\) 34.9303i 0.0524479i
\(667\) 62.3372 42.2524i 0.0934590 0.0633469i
\(668\) 626.259i 0.937513i
\(669\) 566.086 0.846167
\(670\) 60.1764 + 125.956i 0.0898156 + 0.187994i
\(671\) −17.9979 −0.0268225
\(672\) −92.5934 −0.137788
\(673\) 1068.82i 1.58815i −0.607822 0.794074i \(-0.707956\pi\)
0.607822 0.794074i \(-0.292044\pi\)
\(674\) 774.555i 1.14919i
\(675\) −101.058 81.6225i −0.149716 0.120922i
\(676\) −337.664 −0.499503
\(677\) 870.438 1.28573 0.642864 0.765980i \(-0.277746\pi\)
0.642864 + 0.765980i \(0.277746\pi\)
\(678\) 245.158 0.361591
\(679\) 816.475 1.20247
\(680\) −8.57901 17.9568i −0.0126162 0.0264071i
\(681\) 226.824i 0.333074i
\(682\) −11.0786 −0.0162443
\(683\) 711.510i 1.04174i 0.853635 + 0.520871i \(0.174393\pi\)
−0.853635 + 0.520871i \(0.825607\pi\)
\(684\) 78.2044i 0.114334i
\(685\) −86.6013 + 41.3744i −0.126425 + 0.0604006i
\(686\) 116.171i 0.169346i
\(687\) −293.945 −0.427868
\(688\) −110.324 −0.160354
\(689\) 2.41996i 0.00351228i
\(690\) −142.265 + 243.127i −0.206181 + 0.352358i
\(691\) −958.657 −1.38735 −0.693674 0.720289i \(-0.744009\pi\)
−0.693674 + 0.720289i \(0.744009\pi\)
\(692\) 543.297i 0.785111i
\(693\) 4.79008i 0.00691209i
\(694\) −608.461 −0.876745
\(695\) 1020.87 487.730i 1.46888 0.701770i
\(696\) 16.0404 0.0230465
\(697\) 31.2445 0.0448271
\(698\) 46.3761i 0.0664413i
\(699\) 109.577 0.156762
\(700\) −296.895 + 367.590i −0.424135 + 0.525129i
\(701\) 94.5797i 0.134921i −0.997722 0.0674606i \(-0.978510\pi\)
0.997722 0.0674606i \(-0.0214897\pi\)
\(702\) 3.01298i 0.00429200i
\(703\) 107.312i 0.152648i
\(704\) 1.35166i 0.00191997i
\(705\) −193.879 + 92.6272i −0.275006 + 0.131386i
\(706\) 323.185 0.457769
\(707\) −607.216 −0.858863
\(708\) 239.236i 0.337904i
\(709\) 340.569i 0.480352i −0.970729 0.240176i \(-0.922795\pi\)
0.970729 0.240176i \(-0.0772051\pi\)
\(710\) 31.4329 + 65.7926i 0.0442717 + 0.0926656i
\(711\) 253.859i 0.357046i
\(712\) −25.9138 −0.0363958
\(713\) 882.734 598.321i 1.23806 0.839160i
\(714\) −32.5745 −0.0456226
\(715\) −0.312538 + 0.149317i −0.000437116 + 0.000208836i
\(716\) 475.073 0.663510
\(717\) 718.990i 1.00277i
\(718\) 972.518 1.35448
\(719\) −1054.77 −1.46700 −0.733499 0.679690i \(-0.762114\pi\)
−0.733499 + 0.679690i \(0.762114\pi\)
\(720\) −54.1387 + 25.8651i −0.0751926 + 0.0359238i
\(721\) −704.559 −0.977197
\(722\) 270.275i 0.374342i
\(723\) −195.317 −0.270148
\(724\) 81.4034i 0.112436i
\(725\) 51.4324 63.6794i 0.0709413 0.0878337i
\(726\) −296.318 −0.408152
\(727\) −230.764 −0.317419 −0.158709 0.987325i \(-0.550733\pi\)
−0.158709 + 0.987325i \(0.550733\pi\)
\(728\) 10.9595 0.0150542
\(729\) −27.0000 −0.0370370
\(730\) 56.9567 27.2115i 0.0780229 0.0372760i
\(731\) −38.8121 −0.0530946
\(732\) 369.007 0.504108
\(733\) 220.528 0.300857 0.150428 0.988621i \(-0.451935\pi\)
0.150428 + 0.988621i \(0.451935\pi\)
\(734\) 842.657i 1.14803i
\(735\) 150.481 + 314.973i 0.204736 + 0.428535i
\(736\) 72.9991 + 107.699i 0.0991835 + 0.146331i
\(737\) 3.33545i 0.00452572i
\(738\) 94.2001i 0.127642i
\(739\) −839.593 −1.13612 −0.568060 0.822987i \(-0.692306\pi\)
−0.568060 + 0.822987i \(0.692306\pi\)
\(740\) −74.2887 + 35.4920i −0.100390 + 0.0479621i
\(741\) 9.25636i 0.0124917i
\(742\) 78.8802i 0.106308i
\(743\) 1143.07 1.53846 0.769229 0.638973i \(-0.220640\pi\)
0.769229 + 0.638973i \(0.220640\pi\)
\(744\) 227.142 0.305298
\(745\) 297.545 + 622.796i 0.399390 + 0.835967i
\(746\) 111.833i 0.149911i
\(747\) 182.506 0.244318
\(748\) 0.475517i 0.000635717i
\(749\) 467.148 0.623695
\(750\) −70.9090 + 297.862i −0.0945453 + 0.397150i
\(751\) 672.056i 0.894881i 0.894314 + 0.447441i \(0.147664\pi\)
−0.894314 + 0.447441i \(0.852336\pi\)
\(752\) 99.2440i 0.131973i
\(753\) 626.012 0.831357
\(754\) −1.89856 −0.00251798
\(755\) −501.049 + 239.380i −0.663641 + 0.317059i
\(756\) 98.2101i 0.129908i
\(757\) −236.448 −0.312349 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(758\) 562.284 0.741800
\(759\) −5.57155 + 3.77642i −0.00734064 + 0.00497552i
\(760\) −166.323 + 79.4618i −0.218846 + 0.104555i
\(761\) 251.349 0.330288 0.165144 0.986269i \(-0.447191\pi\)
0.165144 + 0.986269i \(0.447191\pi\)
\(762\) 388.033i 0.509229i
\(763\) 855.131i 1.12075i
\(764\) 405.433i 0.530671i
\(765\) −19.0461 + 9.09941i −0.0248969 + 0.0118947i
\(766\) 53.5220i 0.0698721i
\(767\) 28.3162i 0.0369181i
\(768\) 27.7128i 0.0360844i
\(769\) 770.703i 1.00221i 0.865385 + 0.501107i \(0.167074\pi\)
−0.865385 + 0.501107i \(0.832926\pi\)
\(770\) −10.1874 + 4.86710i −0.0132304 + 0.00632091i
\(771\) 241.193 0.312831
\(772\) 370.015i 0.479294i
\(773\) 552.417 0.714640 0.357320 0.933982i \(-0.383691\pi\)
0.357320 + 0.933982i \(0.383691\pi\)
\(774\) 117.016i 0.151184i
\(775\) 728.316 901.741i 0.939763 1.16354i
\(776\) 244.368i 0.314907i
\(777\) 134.763i 0.173440i
\(778\) −315.394 −0.405391
\(779\) 289.398i 0.371499i
\(780\) 6.40791 3.06143i 0.00821527 0.00392491i
\(781\) 1.74226i 0.00223081i
\(782\) 25.6812 + 37.8888i 0.0328404 + 0.0484512i
\(783\) 17.0134i 0.0217285i
\(784\) 161.230 0.205651
\(785\) 940.936 449.539i 1.19864 0.572661i
\(786\) 558.823 0.710970
\(787\) −805.038 −1.02292 −0.511460 0.859307i \(-0.670895\pi\)
−0.511460 + 0.859307i \(0.670895\pi\)
\(788\) 108.213i 0.137327i
\(789\) 17.4893i 0.0221664i
\(790\) −539.900 + 257.941i −0.683418 + 0.326508i
\(791\) −945.835 −1.19575
\(792\) −1.43365 −0.00181017
\(793\) −43.6761 −0.0550770
\(794\) 134.719 0.169672
\(795\) −22.0345 46.1207i −0.0277163 0.0580134i
\(796\) 80.9059i 0.101641i
\(797\) 1385.63 1.73855 0.869276 0.494327i \(-0.164585\pi\)
0.869276 + 0.494327i \(0.164585\pi\)
\(798\) 301.717i 0.378092i
\(799\) 34.9142i 0.0436974i
\(800\) 110.018 + 88.8593i 0.137523 + 0.111074i
\(801\) 27.4857i 0.0343143i
\(802\) −129.901 −0.161971
\(803\) 1.50828 0.00187830
\(804\) 68.3862i 0.0850575i
\(805\) 548.867 937.997i 0.681822 1.16521i
\(806\) −26.8848 −0.0333558
\(807\) 316.780i 0.392540i
\(808\) 181.737i 0.224922i
\(809\) −802.124 −0.991500 −0.495750 0.868465i \(-0.665107\pi\)
−0.495750 + 0.868465i \(0.665107\pi\)
\(810\) 27.4341 + 57.4227i 0.0338693 + 0.0708922i
\(811\) −995.142 −1.22706 −0.613528 0.789673i \(-0.710250\pi\)
−0.613528 + 0.789673i \(0.710250\pi\)
\(812\) −61.8847 −0.0762127
\(813\) 230.346i 0.283328i
\(814\) −1.96725 −0.00241676
\(815\) −275.948 577.590i −0.338586 0.708699i
\(816\) 9.74943i 0.0119478i
\(817\) 359.492i 0.440015i
\(818\) 126.311i 0.154415i
\(819\) 11.6243i 0.0141932i
\(820\) −200.342 + 95.7147i −0.244319 + 0.116725i
\(821\) −414.760 −0.505189 −0.252595 0.967572i \(-0.581284\pi\)
−0.252595 + 0.967572i \(0.581284\pi\)
\(822\) 47.0191 0.0572008
\(823\) 804.054i 0.976979i 0.872570 + 0.488489i \(0.162452\pi\)
−0.872570 + 0.488489i \(0.837548\pi\)
\(824\) 210.872i 0.255912i
\(825\) −4.59691 + 5.69151i −0.00557201 + 0.00689880i
\(826\) 922.985i 1.11742i
\(827\) −1317.07 −1.59259 −0.796296 0.604907i \(-0.793210\pi\)
−0.796296 + 0.604907i \(0.793210\pi\)
\(828\) 114.232 77.4272i 0.137962 0.0935111i
\(829\) −921.119 −1.11112 −0.555560 0.831476i \(-0.687496\pi\)
−0.555560 + 0.831476i \(0.687496\pi\)
\(830\) −185.440 388.147i −0.223422 0.467647i
\(831\) 132.285 0.159187
\(832\) 3.28012i 0.00394245i
\(833\) 56.7212 0.0680927
\(834\) −554.270 −0.664592
\(835\) 674.928 + 1412.70i 0.808297 + 1.69186i
\(836\) −4.40440 −0.00526843
\(837\) 240.920i 0.287838i
\(838\) −13.2036 −0.0157561
\(839\) 703.790i 0.838844i 0.907791 + 0.419422i \(0.137767\pi\)
−0.907791 + 0.419422i \(0.862233\pi\)
\(840\) 208.870 99.7892i 0.248655 0.118797i
\(841\) −830.279 −0.987253
\(842\) −1042.54 −1.23817
\(843\) 675.096 0.800825
\(844\) 186.242 0.220666
\(845\) 761.694 363.905i 0.901413 0.430657i
\(846\) 105.264 0.124426
\(847\) 1143.21 1.34972
\(848\) −23.6085 −0.0278402
\(849\) 164.886i 0.194212i
\(850\) 38.7047 + 31.2609i 0.0455349 + 0.0367775i
\(851\) 156.749 106.245i 0.184194 0.124847i
\(852\) 35.7212i 0.0419263i
\(853\) 272.939i 0.319976i 0.987119 + 0.159988i \(0.0511455\pi\)
−0.987119 + 0.159988i \(0.948854\pi\)
\(854\) −1423.65 −1.66704
\(855\) 84.2820 + 176.412i 0.0985754 + 0.206330i
\(856\) 139.815i 0.163336i
\(857\) 66.8210i 0.0779708i 0.999240 + 0.0389854i \(0.0124126\pi\)
−0.999240 + 0.0389854i \(0.987587\pi\)
\(858\) 0.169689 0.000197772
\(859\) −1370.46 −1.59541 −0.797704 0.603049i \(-0.793952\pi\)
−0.797704 + 0.603049i \(0.793952\pi\)
\(860\) 248.866 118.897i 0.289379 0.138253i
\(861\) 363.429i 0.422101i
\(862\) −397.174 −0.460758
\(863\) 1271.82i 1.47372i −0.676044 0.736861i \(-0.736307\pi\)
0.676044 0.736861i \(-0.263693\pi\)
\(864\) 29.3939 0.0340207
\(865\) −585.518 1225.56i −0.676900 1.41683i
\(866\) 205.294i 0.237060i
\(867\) 497.133i 0.573394i
\(868\) −876.327 −1.00959
\(869\) −14.2971 −0.0164524
\(870\) −36.1835 + 17.2869i −0.0415903 + 0.0198701i
\(871\) 8.09427i 0.00929307i
\(872\) 255.937 0.293506
\(873\) −259.191 −0.296897
\(874\) 350.940 237.869i 0.401533 0.272161i
\(875\) 273.571 1149.17i 0.312652 1.31334i
\(876\) −30.9239 −0.0353013
\(877\) 419.885i 0.478774i −0.970924 0.239387i \(-0.923054\pi\)
0.970924 0.239387i \(-0.0769465\pi\)
\(878\) 488.266i 0.556111i
\(879\) 341.769i 0.388815i
\(880\) 1.45670 + 3.04904i 0.00165534 + 0.00346482i
\(881\) 723.901i 0.821681i 0.911707 + 0.410841i \(0.134765\pi\)
−0.911707 + 0.410841i \(0.865235\pi\)
\(882\) 171.011i 0.193890i
\(883\) 1279.17i 1.44867i 0.689449 + 0.724334i \(0.257853\pi\)
−0.689449 + 0.724334i \(0.742147\pi\)
\(884\) 1.15395i 0.00130538i
\(885\) −257.828 539.663i −0.291331 0.609788i
\(886\) −110.873 −0.125139
\(887\) 29.8132i 0.0336112i 0.999859 + 0.0168056i \(0.00534965\pi\)
−0.999859 + 0.0168056i \(0.994650\pi\)
\(888\) 40.3341 0.0454212
\(889\) 1497.05i 1.68397i
\(890\) 58.4558 27.9277i 0.0656807 0.0313794i
\(891\) 1.52062i 0.00170664i
\(892\) 653.660i 0.732802i
\(893\) 323.388 0.362137
\(894\) 338.139i 0.378231i
\(895\) −1071.66 + 511.993i −1.19738 + 0.572059i
\(896\) 106.918i 0.119328i
\(897\) −13.5207 + 9.16437i −0.0150732 + 0.0102167i
\(898\) 79.9231i 0.0890012i
\(899\) 151.810 0.168866
\(900\) 94.2496 116.692i 0.104722 0.129658i
\(901\) −8.30553 −0.00921812
\(902\) −5.30527 −0.00588167
\(903\) 451.454i 0.499950i
\(904\) 283.085i 0.313147i
\(905\) 87.7296 + 183.628i 0.0969388 + 0.202904i
\(906\) 272.038 0.300262
\(907\) 981.810 1.08248 0.541240 0.840868i \(-0.317955\pi\)
0.541240 + 0.840868i \(0.317955\pi\)
\(908\) 261.913 0.288451
\(909\) 192.762 0.212059
\(910\) −24.7221 + 11.8112i −0.0271671 + 0.0129793i
\(911\) 336.604i 0.369488i −0.982787 0.184744i \(-0.940854\pi\)
0.982787 0.184744i \(-0.0591456\pi\)
\(912\) 90.3027 0.0990161
\(913\) 10.2786i 0.0112580i
\(914\) 442.592i 0.484236i
\(915\) −832.398 + 397.684i −0.909725 + 0.434628i
\(916\) 339.419i 0.370544i
\(917\) −2155.97 −2.35111
\(918\) 10.3408 0.0112645
\(919\) 765.748i 0.833240i −0.909081 0.416620i \(-0.863215\pi\)
0.909081 0.416620i \(-0.136785\pi\)
\(920\) −280.739 164.274i −0.305151 0.178558i
\(921\) −412.454 −0.447833
\(922\) 142.996i 0.155093i
\(923\) 4.22800i 0.00458072i
\(924\) 5.53111 0.00598605
\(925\) 129.329 160.124i 0.139815 0.173107i
\(926\) −954.197 −1.03045
\(927\) 223.663 0.241276
\(928\) 18.5218i 0.0199589i
\(929\) 655.769 0.705887 0.352944 0.935645i \(-0.385181\pi\)
0.352944 + 0.935645i \(0.385181\pi\)
\(930\) −512.382 + 244.794i −0.550948 + 0.263220i
\(931\) 525.372i 0.564309i
\(932\) 126.528i 0.135760i
\(933\) 84.6956i 0.0907778i
\(934\) 290.846i 0.311398i
\(935\) 0.512471 + 1.07266i 0.000548097 + 0.00114723i
\(936\) −3.47909 −0.00371698
\(937\) −1549.41 −1.65359 −0.826795 0.562503i \(-0.809838\pi\)
−0.826795 + 0.562503i \(0.809838\pi\)
\(938\) 263.838i 0.281277i
\(939\) 669.180i 0.712652i
\(940\) −106.957 223.872i −0.113784 0.238162i
\(941\) 1106.87i 1.17627i −0.808762 0.588136i \(-0.799862\pi\)
0.808762 0.588136i \(-0.200138\pi\)
\(942\) −510.869 −0.542324
\(943\) 422.720 286.522i 0.448271 0.303840i
\(944\) −276.246 −0.292633
\(945\) −105.842 221.540i −0.112003 0.234434i
\(946\) 6.59024 0.00696643
\(947\) 739.050i 0.780411i −0.920728 0.390206i \(-0.872404\pi\)
0.920728 0.390206i \(-0.127596\pi\)
\(948\) 293.132 0.309211
\(949\) 3.66019 0.00385689
\(950\) 289.550 358.496i 0.304789 0.377365i
\(951\) 565.141 0.594259
\(952\) 37.6138i 0.0395103i
\(953\) −89.7360 −0.0941616 −0.0470808 0.998891i \(-0.514992\pi\)
−0.0470808 + 0.998891i \(0.514992\pi\)
\(954\) 25.0406i 0.0262480i
\(955\) 436.941 + 914.566i 0.457529 + 0.957661i
\(956\) 830.218 0.868429
\(957\) −0.958180 −0.00100123
\(958\) −915.195 −0.955318
\(959\) −181.402 −0.189158
\(960\) −29.8665 62.5139i −0.0311109 0.0651187i
\(961\) 1188.73 1.23697
\(962\) −4.77398 −0.00496256
\(963\) −148.297 −0.153994
\(964\) 225.533i 0.233955i
\(965\) −398.771 834.672i −0.413234 0.864945i
\(966\) −440.715 + 298.719i −0.456227 + 0.309232i
\(967\) 1704.43i 1.76260i −0.472560 0.881299i \(-0.656670\pi\)
0.472560 0.881299i \(-0.343330\pi\)
\(968\) 342.159i 0.353470i
\(969\) 31.7687 0.0327850
\(970\) 263.358 + 551.239i 0.271503 + 0.568288i
\(971\) 141.413i 0.145637i 0.997345 + 0.0728184i \(0.0231994\pi\)
−0.997345 + 0.0728184i \(0.976801\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 2138.41 2.19774
\(974\) −856.550 −0.879414
\(975\) −11.1555 + 13.8118i −0.0114415 + 0.0141659i
\(976\) 426.093i 0.436570i
\(977\) −689.166 −0.705390 −0.352695 0.935738i \(-0.614735\pi\)
−0.352695 + 0.935738i \(0.614735\pi\)
\(978\) 313.595i 0.320649i
\(979\) 1.54797 0.00158118
\(980\) −363.700 + 173.760i −0.371122 + 0.177306i
\(981\) 271.463i 0.276720i
\(982\) 390.849i 0.398014i
\(983\) 166.044 0.168915 0.0844577 0.996427i \(-0.473084\pi\)
0.0844577 + 0.996427i \(0.473084\pi\)
\(984\) 108.773 0.110542
\(985\) −116.623 244.105i −0.118399 0.247823i
\(986\) 6.51602i 0.00660854i
\(987\) −406.115 −0.411464
\(988\) −10.6883 −0.0108181
\(989\) −525.106 + 355.919i −0.530946 + 0.359878i
\(990\) 3.23400 1.54507i 0.00326666 0.00156067i
\(991\) −694.830 −0.701141 −0.350570 0.936536i \(-0.614012\pi\)
−0.350570 + 0.936536i \(0.614012\pi\)
\(992\) 262.281i 0.264396i
\(993\) 79.2026i 0.0797609i
\(994\) 137.815i 0.138646i
\(995\) −87.1935 182.506i −0.0876316 0.183423i
\(996\) 210.739i 0.211586i
\(997\) 302.519i 0.303429i −0.988424 0.151714i \(-0.951521\pi\)
0.988424 0.151714i \(-0.0484794\pi\)
\(998\) 1182.41i 1.18478i
\(999\) 42.7807i 0.0428236i
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 690.3.f.a.229.36 yes 48
5.4 even 2 inner 690.3.f.a.229.33 48
23.22 odd 2 inner 690.3.f.a.229.35 yes 48
115.114 odd 2 inner 690.3.f.a.229.34 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.3.f.a.229.33 48 5.4 even 2 inner
690.3.f.a.229.34 yes 48 115.114 odd 2 inner
690.3.f.a.229.35 yes 48 23.22 odd 2 inner
690.3.f.a.229.36 yes 48 1.1 even 1 trivial