Properties

Label 1134.3.q.c.1079.3
Level $1134$
Weight $3$
Character 1134.1079
Analytic conductor $30.899$
Analytic rank $0$
Dimension $8$
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] = [1134,3,Mod(701,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.701");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1134.q (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: \(30.8992619785\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12745506816.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1079.3
Root \(-1.00781 - 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1079
Dual form 1134.3.q.c.701.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 + 3.03455i) q^{5} +(1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 + 3.03455i) q^{5} +(1.32288 - 2.29129i) q^{7} +2.82843i q^{8} -8.58301 q^{10} +(10.5120 + 6.06910i) q^{11} +(9.29150 + 16.0934i) q^{13} +(3.24037 - 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} -10.9015i q^{17} +20.0000 q^{19} +(-10.5120 - 6.06910i) q^{20} +(8.58301 + 14.8662i) q^{22} +(-10.5120 + 6.06910i) q^{23} +(5.91699 - 10.2485i) q^{25} +26.2803i q^{26} +5.29150 q^{28} +(-36.2316 - 20.9183i) q^{29} +(-12.5830 - 21.7944i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(7.70850 - 13.3515i) q^{34} +16.0573i q^{35} +38.0000 q^{37} +(24.4949 + 14.1421i) q^{38} +(-8.58301 - 14.8662i) q^{40} +(-52.5103 + 30.3169i) q^{41} +(-41.7490 + 72.3114i) q^{43} +24.2764i q^{44} -17.1660 q^{46} +(14.6969 + 8.48528i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(14.4936 - 8.36789i) q^{50} +(-18.5830 + 32.1867i) q^{52} +94.0424i q^{53} -73.6680 q^{55} +(6.48074 + 3.74166i) q^{56} +(-29.5830 - 51.2393i) q^{58} +(-50.4179 + 29.1088i) q^{59} +(-7.83399 + 13.5689i) q^{61} -35.5901i q^{62} -8.00000 q^{64} +(-97.6722 - 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(18.8819 - 10.9015i) q^{68} +(-11.3542 + 19.6661i) q^{70} -12.1382i q^{71} -76.9150 q^{73} +(46.5403 + 26.8701i) q^{74} +(20.0000 + 34.6410i) q^{76} +(27.8121 - 16.0573i) q^{77} +(-16.8340 + 29.1573i) q^{79} -24.2764i q^{80} -85.7490 q^{82} +(52.4607 + 30.2882i) q^{83} +(33.0810 + 57.2980i) q^{85} +(-102.264 + 59.0420i) q^{86} +(-17.1660 + 29.7324i) q^{88} -4.77506i q^{89} +49.1660 q^{91} +(-21.0240 - 12.1382i) q^{92} +(12.0000 + 20.7846i) q^{94} +(-105.120 + 60.6910i) q^{95} +(94.2065 - 163.170i) q^{97} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −5.25600 + 3.03455i −1.05120 + 0.606910i −0.922985 0.384836i \(-0.874258\pi\)
−0.128214 + 0.991746i \(0.540925\pi\)
\(6\) 0 0
\(7\) 1.32288 2.29129i 0.188982 0.327327i
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −8.58301 −0.858301
\(11\) 10.5120 + 6.06910i 0.955636 + 0.551736i 0.894827 0.446413i \(-0.147299\pi\)
0.0608086 + 0.998149i \(0.480632\pi\)
\(12\) 0 0
\(13\) 9.29150 + 16.0934i 0.714731 + 1.23795i 0.963063 + 0.269275i \(0.0867842\pi\)
−0.248332 + 0.968675i \(0.579882\pi\)
\(14\) 3.24037 1.87083i 0.231455 0.133631i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 10.9015i 0.641262i −0.947204 0.320631i \(-0.896105\pi\)
0.947204 0.320631i \(-0.103895\pi\)
\(18\) 0 0
\(19\) 20.0000 1.05263 0.526316 0.850289i \(-0.323573\pi\)
0.526316 + 0.850289i \(0.323573\pi\)
\(20\) −10.5120 6.06910i −0.525600 0.303455i
\(21\) 0 0
\(22\) 8.58301 + 14.8662i 0.390137 + 0.675736i
\(23\) −10.5120 + 6.06910i −0.457043 + 0.263874i −0.710800 0.703394i \(-0.751667\pi\)
0.253757 + 0.967268i \(0.418334\pi\)
\(24\) 0 0
\(25\) 5.91699 10.2485i 0.236680 0.409941i
\(26\) 26.2803i 1.01078i
\(27\) 0 0
\(28\) 5.29150 0.188982
\(29\) −36.2316 20.9183i −1.24937 0.721322i −0.278384 0.960470i \(-0.589799\pi\)
−0.970983 + 0.239148i \(0.923132\pi\)
\(30\) 0 0
\(31\) −12.5830 21.7944i −0.405903 0.703045i 0.588523 0.808481i \(-0.299710\pi\)
−0.994426 + 0.105435i \(0.966376\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 7.70850 13.3515i 0.226721 0.392691i
\(35\) 16.0573i 0.458781i
\(36\) 0 0
\(37\) 38.0000 1.02703 0.513514 0.858082i \(-0.328344\pi\)
0.513514 + 0.858082i \(0.328344\pi\)
\(38\) 24.4949 + 14.1421i 0.644603 + 0.372161i
\(39\) 0 0
\(40\) −8.58301 14.8662i −0.214575 0.371655i
\(41\) −52.5103 + 30.3169i −1.28074 + 0.739435i −0.976984 0.213314i \(-0.931574\pi\)
−0.303756 + 0.952750i \(0.598241\pi\)
\(42\) 0 0
\(43\) −41.7490 + 72.3114i −0.970907 + 1.68166i −0.278079 + 0.960558i \(0.589698\pi\)
−0.692828 + 0.721103i \(0.743636\pi\)
\(44\) 24.2764i 0.551736i
\(45\) 0 0
\(46\) −17.1660 −0.373174
\(47\) 14.6969 + 8.48528i 0.312701 + 0.180538i 0.648134 0.761526i \(-0.275549\pi\)
−0.335434 + 0.942064i \(0.608883\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.0714286 0.123718i
\(50\) 14.4936 8.36789i 0.289872 0.167358i
\(51\) 0 0
\(52\) −18.5830 + 32.1867i −0.357365 + 0.618975i
\(53\) 94.0424i 1.77439i 0.461399 + 0.887193i \(0.347348\pi\)
−0.461399 + 0.887193i \(0.652652\pi\)
\(54\) 0 0
\(55\) −73.6680 −1.33942
\(56\) 6.48074 + 3.74166i 0.115728 + 0.0668153i
\(57\) 0 0
\(58\) −29.5830 51.2393i −0.510052 0.883436i
\(59\) −50.4179 + 29.1088i −0.854540 + 0.493369i −0.862180 0.506602i \(-0.830901\pi\)
0.00764008 + 0.999971i \(0.497568\pi\)
\(60\) 0 0
\(61\) −7.83399 + 13.5689i −0.128426 + 0.222440i −0.923067 0.384639i \(-0.874326\pi\)
0.794641 + 0.607080i \(0.207659\pi\)
\(62\) 35.5901i 0.574034i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −97.6722 56.3911i −1.50265 0.867555i
\(66\) 0 0
\(67\) 66.3320 + 114.890i 0.990030 + 1.71478i 0.617000 + 0.786964i \(0.288348\pi\)
0.373031 + 0.927819i \(0.378319\pi\)
\(68\) 18.8819 10.9015i 0.277675 0.160316i
\(69\) 0 0
\(70\) −11.3542 + 19.6661i −0.162204 + 0.280945i
\(71\) 12.1382i 0.170961i −0.996340 0.0854803i \(-0.972758\pi\)
0.996340 0.0854803i \(-0.0272425\pi\)
\(72\) 0 0
\(73\) −76.9150 −1.05363 −0.526815 0.849980i \(-0.676614\pi\)
−0.526815 + 0.849980i \(0.676614\pi\)
\(74\) 46.5403 + 26.8701i 0.628923 + 0.363109i
\(75\) 0 0
\(76\) 20.0000 + 34.6410i 0.263158 + 0.455803i
\(77\) 27.8121 16.0573i 0.361196 0.208537i
\(78\) 0 0
\(79\) −16.8340 + 29.1573i −0.213088 + 0.369080i −0.952680 0.303976i \(-0.901686\pi\)
0.739591 + 0.673056i \(0.235019\pi\)
\(80\) 24.2764i 0.303455i
\(81\) 0 0
\(82\) −85.7490 −1.04572
\(83\) 52.4607 + 30.2882i 0.632057 + 0.364918i 0.781548 0.623845i \(-0.214430\pi\)
−0.149491 + 0.988763i \(0.547764\pi\)
\(84\) 0 0
\(85\) 33.0810 + 57.2980i 0.389189 + 0.674095i
\(86\) −102.264 + 59.0420i −1.18911 + 0.686535i
\(87\) 0 0
\(88\) −17.1660 + 29.7324i −0.195068 + 0.337868i
\(89\) 4.77506i 0.0536523i −0.999640 0.0268262i \(-0.991460\pi\)
0.999640 0.0268262i \(-0.00854006\pi\)
\(90\) 0 0
\(91\) 49.1660 0.540286
\(92\) −21.0240 12.1382i −0.228522 0.131937i
\(93\) 0 0
\(94\) 12.0000 + 20.7846i 0.127660 + 0.221113i
\(95\) −105.120 + 60.6910i −1.10653 + 0.638853i
\(96\) 0 0
\(97\) 94.2065 163.170i 0.971201 1.68217i 0.279261 0.960215i \(-0.409910\pi\)
0.691940 0.721955i \(-0.256756\pi\)
\(98\) 9.89949i 0.101015i
\(99\) 0 0
\(100\) 23.6680 0.236680
\(101\) −92.4162 53.3565i −0.915012 0.528282i −0.0329716 0.999456i \(-0.510497\pi\)
−0.882040 + 0.471174i \(0.843830\pi\)
\(102\) 0 0
\(103\) −65.7490 113.881i −0.638340 1.10564i −0.985797 0.167941i \(-0.946288\pi\)
0.347457 0.937696i \(-0.387045\pi\)
\(104\) −45.5189 + 26.2803i −0.437682 + 0.252696i
\(105\) 0 0
\(106\) −66.4980 + 115.178i −0.627340 + 1.08658i
\(107\) 82.3793i 0.769900i 0.922937 + 0.384950i \(0.125781\pi\)
−0.922937 + 0.384950i \(0.874219\pi\)
\(108\) 0 0
\(109\) 33.8301 0.310367 0.155184 0.987886i \(-0.450403\pi\)
0.155184 + 0.987886i \(0.450403\pi\)
\(110\) −90.2245 52.0911i −0.820223 0.473556i
\(111\) 0 0
\(112\) 5.29150 + 9.16515i 0.0472456 + 0.0818317i
\(113\) −24.6982 + 14.2595i −0.218568 + 0.126190i −0.605287 0.796007i \(-0.706942\pi\)
0.386719 + 0.922198i \(0.373608\pi\)
\(114\) 0 0
\(115\) 36.8340 63.7983i 0.320296 0.554768i
\(116\) 83.6734i 0.721322i
\(117\) 0 0
\(118\) −82.3320 −0.697729
\(119\) −24.9784 14.4213i −0.209902 0.121187i
\(120\) 0 0
\(121\) 13.1680 + 22.8076i 0.108826 + 0.188493i
\(122\) −19.1893 + 11.0789i −0.157289 + 0.0908109i
\(123\) 0 0
\(124\) 25.1660 43.5888i 0.202952 0.351523i
\(125\) 79.9059i 0.639247i
\(126\) 0 0
\(127\) 129.668 1.02101 0.510504 0.859875i \(-0.329459\pi\)
0.510504 + 0.859875i \(0.329459\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −79.7490 138.129i −0.613454 1.06253i
\(131\) −128.187 + 74.0087i −0.978525 + 0.564952i −0.901824 0.432103i \(-0.857772\pi\)
−0.0767004 + 0.997054i \(0.524438\pi\)
\(132\) 0 0
\(133\) 26.4575 45.8258i 0.198929 0.344555i
\(134\) 187.615i 1.40011i
\(135\) 0 0
\(136\) 30.8340 0.226721
\(137\) 66.6469 + 38.4786i 0.486474 + 0.280866i 0.723111 0.690732i \(-0.242712\pi\)
−0.236637 + 0.971598i \(0.576045\pi\)
\(138\) 0 0
\(139\) −108.664 188.212i −0.781756 1.35404i −0.930918 0.365228i \(-0.880991\pi\)
0.149162 0.988813i \(-0.452342\pi\)
\(140\) −27.8121 + 16.0573i −0.198658 + 0.114695i
\(141\) 0 0
\(142\) 8.58301 14.8662i 0.0604437 0.104692i
\(143\) 225.564i 1.57737i
\(144\) 0 0
\(145\) 253.911 1.75111
\(146\) −94.2013 54.3871i −0.645214 0.372515i
\(147\) 0 0
\(148\) 38.0000 + 65.8179i 0.256757 + 0.444716i
\(149\) 140.231 80.9623i 0.941147 0.543371i 0.0508272 0.998707i \(-0.483814\pi\)
0.890320 + 0.455336i \(0.150481\pi\)
\(150\) 0 0
\(151\) 46.5830 80.6841i 0.308497 0.534332i −0.669537 0.742779i \(-0.733507\pi\)
0.978034 + 0.208447i \(0.0668408\pi\)
\(152\) 56.5685i 0.372161i
\(153\) 0 0
\(154\) 45.4170 0.294916
\(155\) 132.272 + 76.3675i 0.853371 + 0.492694i
\(156\) 0 0
\(157\) 92.4980 + 160.211i 0.589159 + 1.02045i 0.994343 + 0.106219i \(0.0338743\pi\)
−0.405183 + 0.914235i \(0.632792\pi\)
\(158\) −41.2347 + 23.8069i −0.260979 + 0.150676i
\(159\) 0 0
\(160\) 17.1660 29.7324i 0.107288 0.185828i
\(161\) 32.1147i 0.199470i
\(162\) 0 0
\(163\) 86.9961 0.533718 0.266859 0.963736i \(-0.414014\pi\)
0.266859 + 0.963736i \(0.414014\pi\)
\(164\) −105.021 60.6337i −0.640370 0.369718i
\(165\) 0 0
\(166\) 42.8340 + 74.1906i 0.258036 + 0.446932i
\(167\) 52.4607 30.2882i 0.314136 0.181366i −0.334640 0.942346i \(-0.608615\pi\)
0.648776 + 0.760980i \(0.275281\pi\)
\(168\) 0 0
\(169\) −88.1640 + 152.705i −0.521681 + 0.903578i
\(170\) 93.5673i 0.550396i
\(171\) 0 0
\(172\) −166.996 −0.970907
\(173\) −140.791 81.2858i −0.813822 0.469860i 0.0344594 0.999406i \(-0.489029\pi\)
−0.848281 + 0.529546i \(0.822362\pi\)
\(174\) 0 0
\(175\) −15.6549 27.1151i −0.0894566 0.154943i
\(176\) −42.0480 + 24.2764i −0.238909 + 0.137934i
\(177\) 0 0
\(178\) 3.37648 5.84823i 0.0189690 0.0328552i
\(179\) 223.091i 1.24632i 0.782095 + 0.623159i \(0.214151\pi\)
−0.782095 + 0.623159i \(0.785849\pi\)
\(180\) 0 0
\(181\) 188.915 1.04373 0.521865 0.853028i \(-0.325237\pi\)
0.521865 + 0.853028i \(0.325237\pi\)
\(182\) 60.2158 + 34.7656i 0.330856 + 0.191020i
\(183\) 0 0
\(184\) −17.1660 29.7324i −0.0932935 0.161589i
\(185\) −199.728 + 115.313i −1.07961 + 0.623313i
\(186\) 0 0
\(187\) 66.1621 114.596i 0.353808 0.612813i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) −171.660 −0.903474
\(191\) 197.486 + 114.019i 1.03396 + 0.596957i 0.918117 0.396310i \(-0.129709\pi\)
0.115844 + 0.993267i \(0.463043\pi\)
\(192\) 0 0
\(193\) −67.0000 116.047i −0.347150 0.601282i 0.638592 0.769546i \(-0.279517\pi\)
−0.985742 + 0.168264i \(0.946184\pi\)
\(194\) 230.758 133.228i 1.18947 0.686743i
\(195\) 0 0
\(196\) 7.00000 12.1244i 0.0357143 0.0618590i
\(197\) 188.560i 0.957157i −0.878045 0.478579i \(-0.841152\pi\)
0.878045 0.478579i \(-0.158848\pi\)
\(198\) 0 0
\(199\) 102.494 0.515046 0.257523 0.966272i \(-0.417094\pi\)
0.257523 + 0.966272i \(0.417094\pi\)
\(200\) 28.9872 + 16.7358i 0.144936 + 0.0836789i
\(201\) 0 0
\(202\) −75.4575 130.696i −0.373552 0.647011i
\(203\) −95.8599 + 55.3447i −0.472216 + 0.272634i
\(204\) 0 0
\(205\) 183.996 318.691i 0.897542 1.55459i
\(206\) 185.966i 0.902749i
\(207\) 0 0
\(208\) −74.3320 −0.357365
\(209\) 210.240 + 121.382i 1.00593 + 0.580775i
\(210\) 0 0
\(211\) 42.2510 + 73.1809i 0.200242 + 0.346829i 0.948606 0.316459i \(-0.102494\pi\)
−0.748365 + 0.663288i \(0.769161\pi\)
\(212\) −162.886 + 94.0424i −0.768331 + 0.443596i
\(213\) 0 0
\(214\) −58.2510 + 100.894i −0.272201 + 0.471466i
\(215\) 506.758i 2.35701i
\(216\) 0 0
\(217\) −66.5830 −0.306834
\(218\) 41.4332 + 23.9215i 0.190060 + 0.109731i
\(219\) 0 0
\(220\) −73.6680 127.597i −0.334854 0.579985i
\(221\) 175.441 101.291i 0.793851 0.458330i
\(222\) 0 0
\(223\) 79.2470 137.260i 0.355368 0.615515i −0.631813 0.775121i \(-0.717689\pi\)
0.987181 + 0.159606i \(0.0510222\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −40.3320 −0.178460
\(227\) −88.1816 50.9117i −0.388465 0.224281i 0.293030 0.956103i \(-0.405337\pi\)
−0.681495 + 0.731823i \(0.738670\pi\)
\(228\) 0 0
\(229\) 134.458 + 232.887i 0.587151 + 1.01697i 0.994604 + 0.103749i \(0.0330837\pi\)
−0.407453 + 0.913226i \(0.633583\pi\)
\(230\) 90.2245 52.0911i 0.392280 0.226483i
\(231\) 0 0
\(232\) 59.1660 102.479i 0.255026 0.441718i
\(233\) 26.2748i 0.112767i −0.998409 0.0563836i \(-0.982043\pi\)
0.998409 0.0563836i \(-0.0179570\pi\)
\(234\) 0 0
\(235\) −102.996 −0.438281
\(236\) −100.836 58.2175i −0.427270 0.246684i
\(237\) 0 0
\(238\) −20.3948 35.3248i −0.0856923 0.148423i
\(239\) 79.9110 46.1366i 0.334356 0.193040i −0.323418 0.946256i \(-0.604832\pi\)
0.657773 + 0.753216i \(0.271499\pi\)
\(240\) 0 0
\(241\) −171.624 + 297.261i −0.712131 + 1.23345i 0.251925 + 0.967747i \(0.418936\pi\)
−0.964056 + 0.265700i \(0.914397\pi\)
\(242\) 37.2447i 0.153904i
\(243\) 0 0
\(244\) −31.3360 −0.128426
\(245\) 36.7920 + 21.2419i 0.150171 + 0.0867014i
\(246\) 0 0
\(247\) 185.830 + 321.867i 0.752348 + 1.30311i
\(248\) 61.6439 35.5901i 0.248564 0.143509i
\(249\) 0 0
\(250\) 56.5020 97.8643i 0.226008 0.391457i
\(251\) 356.382i 1.41985i 0.704278 + 0.709924i \(0.251271\pi\)
−0.704278 + 0.709924i \(0.748729\pi\)
\(252\) 0 0
\(253\) −147.336 −0.582356
\(254\) 158.810 + 91.6891i 0.625237 + 0.360981i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −220.603 + 127.365i −0.858377 + 0.495584i −0.863469 0.504403i \(-0.831713\pi\)
0.00509129 + 0.999987i \(0.498379\pi\)
\(258\) 0 0
\(259\) 50.2693 87.0689i 0.194090 0.336174i
\(260\) 225.564i 0.867555i
\(261\) 0 0
\(262\) −209.328 −0.798962
\(263\) −226.880 130.989i −0.862663 0.498059i 0.00224015 0.999997i \(-0.499287\pi\)
−0.864903 + 0.501939i \(0.832620\pi\)
\(264\) 0 0
\(265\) −285.376 494.287i −1.07689 1.86523i
\(266\) 64.8074 37.4166i 0.243637 0.140664i
\(267\) 0 0
\(268\) −132.664 + 229.781i −0.495015 + 0.857391i
\(269\) 93.6246i 0.348047i 0.984742 + 0.174023i \(0.0556768\pi\)
−0.984742 + 0.174023i \(0.944323\pi\)
\(270\) 0 0
\(271\) 1.16601 0.00430262 0.00215131 0.999998i \(-0.499315\pi\)
0.00215131 + 0.999998i \(0.499315\pi\)
\(272\) 37.7638 + 21.8029i 0.138837 + 0.0801578i
\(273\) 0 0
\(274\) 54.4170 + 94.2530i 0.198602 + 0.343989i
\(275\) 124.399 71.8217i 0.452359 0.261170i
\(276\) 0 0
\(277\) −16.0000 + 27.7128i −0.0577617 + 0.100046i −0.893460 0.449142i \(-0.851730\pi\)
0.835699 + 0.549188i \(0.185063\pi\)
\(278\) 307.348i 1.10557i
\(279\) 0 0
\(280\) −45.4170 −0.162204
\(281\) −144.416 83.3785i −0.513935 0.296721i 0.220514 0.975384i \(-0.429226\pi\)
−0.734450 + 0.678663i \(0.762560\pi\)
\(282\) 0 0
\(283\) −8.16995 14.1508i −0.0288691 0.0500027i 0.851230 0.524793i \(-0.175857\pi\)
−0.880099 + 0.474790i \(0.842524\pi\)
\(284\) 21.0240 12.1382i 0.0740281 0.0427401i
\(285\) 0 0
\(286\) −159.498 + 276.259i −0.557685 + 0.965939i
\(287\) 160.422i 0.558961i
\(288\) 0 0
\(289\) 170.158 0.588782
\(290\) 310.976 + 179.542i 1.07233 + 0.619111i
\(291\) 0 0
\(292\) −76.9150 133.221i −0.263408 0.456235i
\(293\) 319.495 184.461i 1.09043 0.629558i 0.156737 0.987640i \(-0.449903\pi\)
0.933690 + 0.358082i \(0.116569\pi\)
\(294\) 0 0
\(295\) 176.664 305.991i 0.598861 1.03726i
\(296\) 107.480i 0.363109i
\(297\) 0 0
\(298\) 228.996 0.768443
\(299\) −195.344 112.782i −0.653326 0.377198i
\(300\) 0 0
\(301\) 110.458 + 191.318i 0.366968 + 0.635608i
\(302\) 114.105 65.8783i 0.377830 0.218140i
\(303\) 0 0
\(304\) −40.0000 + 69.2820i −0.131579 + 0.227901i
\(305\) 95.0906i 0.311772i
\(306\) 0 0
\(307\) −192.664 −0.627570 −0.313785 0.949494i \(-0.601597\pi\)
−0.313785 + 0.949494i \(0.601597\pi\)
\(308\) 55.6242 + 32.1147i 0.180598 + 0.104268i
\(309\) 0 0
\(310\) 108.000 + 187.061i 0.348387 + 0.603424i
\(311\) 113.688 65.6380i 0.365557 0.211055i −0.305959 0.952045i \(-0.598977\pi\)
0.671516 + 0.740990i \(0.265644\pi\)
\(312\) 0 0
\(313\) −21.6640 + 37.5232i −0.0692142 + 0.119882i −0.898556 0.438860i \(-0.855383\pi\)
0.829341 + 0.558742i \(0.188716\pi\)
\(314\) 261.624i 0.833197i
\(315\) 0 0
\(316\) −67.3360 −0.213088
\(317\) 218.000 + 125.862i 0.687696 + 0.397042i 0.802748 0.596318i \(-0.203370\pi\)
−0.115052 + 0.993359i \(0.536703\pi\)
\(318\) 0 0
\(319\) −253.911 439.787i −0.795960 1.37864i
\(320\) 42.0480 24.2764i 0.131400 0.0758638i
\(321\) 0 0
\(322\) −22.7085 + 39.3323i −0.0705233 + 0.122150i
\(323\) 218.029i 0.675013i
\(324\) 0 0
\(325\) 219.911 0.676650
\(326\) 106.548 + 61.5155i 0.326834 + 0.188698i
\(327\) 0 0
\(328\) −85.7490 148.522i −0.261430 0.452810i
\(329\) 38.8844 22.4499i 0.118190 0.0682369i
\(330\) 0 0
\(331\) −180.745 + 313.060i −0.546058 + 0.945800i 0.452482 + 0.891774i \(0.350539\pi\)
−0.998540 + 0.0540260i \(0.982795\pi\)
\(332\) 121.153i 0.364918i
\(333\) 0 0
\(334\) 85.6680 0.256491
\(335\) −697.282 402.576i −2.08144 1.20172i
\(336\) 0 0
\(337\) 149.417 + 258.798i 0.443374 + 0.767946i 0.997937 0.0641954i \(-0.0204481\pi\)
−0.554563 + 0.832141i \(0.687115\pi\)
\(338\) −215.957 + 124.683i −0.638926 + 0.368884i
\(339\) 0 0
\(340\) −66.1621 + 114.596i −0.194594 + 0.337047i
\(341\) 305.470i 0.895807i
\(342\) 0 0
\(343\) −18.5203 −0.0539949
\(344\) −204.528 118.084i −0.594557 0.343268i
\(345\) 0 0
\(346\) −114.956 199.109i −0.332241 0.575459i
\(347\) 178.505 103.060i 0.514425 0.297003i −0.220226 0.975449i \(-0.570679\pi\)
0.734651 + 0.678446i \(0.237346\pi\)
\(348\) 0 0
\(349\) −217.162 + 376.136i −0.622241 + 1.07775i 0.366827 + 0.930289i \(0.380444\pi\)
−0.989067 + 0.147464i \(0.952889\pi\)
\(350\) 44.2787i 0.126511i
\(351\) 0 0
\(352\) −68.6640 −0.195068
\(353\) 160.595 + 92.7197i 0.454944 + 0.262662i 0.709916 0.704286i \(-0.248733\pi\)
−0.254972 + 0.966948i \(0.582066\pi\)
\(354\) 0 0
\(355\) 36.8340 + 63.7983i 0.103758 + 0.179714i
\(356\) 8.27064 4.77506i 0.0232321 0.0134131i
\(357\) 0 0
\(358\) −157.749 + 273.229i −0.440640 + 0.763210i
\(359\) 516.767i 1.43946i −0.694254 0.719731i \(-0.744265\pi\)
0.694254 0.719731i \(-0.255735\pi\)
\(360\) 0 0
\(361\) 39.0000 0.108033
\(362\) 231.373 + 133.583i 0.639151 + 0.369014i
\(363\) 0 0
\(364\) 49.1660 + 85.1580i 0.135071 + 0.233951i
\(365\) 404.265 233.403i 1.10758 0.639459i
\(366\) 0 0
\(367\) 58.7451 101.749i 0.160068 0.277246i −0.774825 0.632176i \(-0.782162\pi\)
0.934893 + 0.354930i \(0.115495\pi\)
\(368\) 48.5528i 0.131937i
\(369\) 0 0
\(370\) −326.154 −0.881498
\(371\) 215.478 + 124.406i 0.580804 + 0.335327i
\(372\) 0 0
\(373\) 201.332 + 348.717i 0.539764 + 0.934899i 0.998916 + 0.0465413i \(0.0148199\pi\)
−0.459152 + 0.888358i \(0.651847\pi\)
\(374\) 162.063 93.5673i 0.433324 0.250180i
\(375\) 0 0
\(376\) −24.0000 + 41.5692i −0.0638298 + 0.110556i
\(377\) 777.451i 2.06221i
\(378\) 0 0
\(379\) 398.834 1.05233 0.526166 0.850382i \(-0.323629\pi\)
0.526166 + 0.850382i \(0.323629\pi\)
\(380\) −210.240 121.382i −0.553263 0.319426i
\(381\) 0 0
\(382\) 161.247 + 279.288i 0.422113 + 0.731121i
\(383\) 645.019 372.402i 1.68412 0.972329i 0.725255 0.688481i \(-0.241722\pi\)
0.958869 0.283849i \(-0.0916114\pi\)
\(384\) 0 0
\(385\) −97.4536 + 168.795i −0.253126 + 0.438427i
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) 376.826 0.971201
\(389\) 463.464 + 267.581i 1.19142 + 0.687869i 0.958630 0.284656i \(-0.0918795\pi\)
0.232795 + 0.972526i \(0.425213\pi\)
\(390\) 0 0
\(391\) 66.1621 + 114.596i 0.169212 + 0.293085i
\(392\) 17.1464 9.89949i 0.0437409 0.0252538i
\(393\) 0 0
\(394\) 133.332 230.938i 0.338406 0.586137i
\(395\) 204.334i 0.517302i
\(396\) 0 0
\(397\) −94.3241 −0.237592 −0.118796 0.992919i \(-0.537904\pi\)
−0.118796 + 0.992919i \(0.537904\pi\)
\(398\) 125.529 + 72.4743i 0.315400 + 0.182096i
\(399\) 0 0
\(400\) 23.6680 + 40.9941i 0.0591699 + 0.102485i
\(401\) −89.7138 + 51.7963i −0.223725 + 0.129168i −0.607674 0.794187i \(-0.707897\pi\)
0.383949 + 0.923354i \(0.374564\pi\)
\(402\) 0 0
\(403\) 233.830 405.006i 0.580223 1.00498i
\(404\) 213.426i 0.528282i
\(405\) 0 0
\(406\) −156.539 −0.385563
\(407\) 399.456 + 230.626i 0.981464 + 0.566648i
\(408\) 0 0
\(409\) 4.87844 + 8.44971i 0.0119277 + 0.0206594i 0.871928 0.489635i \(-0.162870\pi\)
−0.860000 + 0.510294i \(0.829537\pi\)
\(410\) 450.696 260.210i 1.09926 0.634658i
\(411\) 0 0
\(412\) 131.498 227.761i 0.319170 0.552819i
\(413\) 154.029i 0.372952i
\(414\) 0 0
\(415\) −367.644 −0.885890
\(416\) −91.0378 52.5607i −0.218841 0.126348i
\(417\) 0 0
\(418\) 171.660 + 297.324i 0.410670 + 0.711301i
\(419\) 293.939 169.706i 0.701525 0.405025i −0.106390 0.994324i \(-0.533929\pi\)
0.807915 + 0.589299i \(0.200596\pi\)
\(420\) 0 0
\(421\) 299.660 519.027i 0.711782 1.23284i −0.252406 0.967621i \(-0.581222\pi\)
0.964188 0.265221i \(-0.0854448\pi\)
\(422\) 119.504i 0.283184i
\(423\) 0 0
\(424\) −265.992 −0.627340
\(425\) −111.724 64.5039i −0.262880 0.151774i
\(426\) 0 0
\(427\) 20.7268 + 35.8998i 0.0485405 + 0.0840746i
\(428\) −142.685 + 82.3793i −0.333377 + 0.192475i
\(429\) 0 0
\(430\) 358.332 620.649i 0.833330 1.44337i
\(431\) 710.978i 1.64960i 0.565424 + 0.824800i \(0.308712\pi\)
−0.565424 + 0.824800i \(0.691288\pi\)
\(432\) 0 0
\(433\) 377.984 0.872943 0.436471 0.899718i \(-0.356228\pi\)
0.436471 + 0.899718i \(0.356228\pi\)
\(434\) −81.5472 47.0813i −0.187897 0.108482i
\(435\) 0 0
\(436\) 33.8301 + 58.5954i 0.0775919 + 0.134393i
\(437\) −210.240 + 121.382i −0.481098 + 0.277762i
\(438\) 0 0
\(439\) −264.073 + 457.388i −0.601533 + 1.04189i 0.391056 + 0.920367i \(0.372110\pi\)
−0.992589 + 0.121519i \(0.961223\pi\)
\(440\) 208.365i 0.473556i
\(441\) 0 0
\(442\) 286.494 0.648177
\(443\) −31.7345 18.3219i −0.0716354 0.0413587i 0.463754 0.885964i \(-0.346502\pi\)
−0.535390 + 0.844605i \(0.679835\pi\)
\(444\) 0 0
\(445\) 14.4902 + 25.0977i 0.0325622 + 0.0563993i
\(446\) 194.115 112.072i 0.435235 0.251283i
\(447\) 0 0
\(448\) −10.5830 + 18.3303i −0.0236228 + 0.0409159i
\(449\) 397.612i 0.885550i −0.896633 0.442775i \(-0.853994\pi\)
0.896633 0.442775i \(-0.146006\pi\)
\(450\) 0 0
\(451\) −735.984 −1.63189
\(452\) −49.3964 28.5190i −0.109284 0.0630952i
\(453\) 0 0
\(454\) −72.0000 124.708i −0.158590 0.274686i
\(455\) −258.416 + 149.197i −0.567948 + 0.327905i
\(456\) 0 0
\(457\) −172.162 + 298.193i −0.376722 + 0.652502i −0.990583 0.136912i \(-0.956282\pi\)
0.613861 + 0.789414i \(0.289616\pi\)
\(458\) 380.303i 0.830357i
\(459\) 0 0
\(460\) 147.336 0.320296
\(461\) 321.240 + 185.468i 0.696833 + 0.402317i 0.806167 0.591688i \(-0.201538\pi\)
−0.109334 + 0.994005i \(0.534872\pi\)
\(462\) 0 0
\(463\) −39.1660 67.8375i −0.0845918 0.146517i 0.820625 0.571467i \(-0.193625\pi\)
−0.905217 + 0.424949i \(0.860292\pi\)
\(464\) 144.927 83.6734i 0.312342 0.180331i
\(465\) 0 0
\(466\) 18.5791 32.1799i 0.0398692 0.0690556i
\(467\) 399.758i 0.856014i −0.903775 0.428007i \(-0.859216\pi\)
0.903775 0.428007i \(-0.140784\pi\)
\(468\) 0 0
\(469\) 350.996 0.748392
\(470\) −126.144 72.8292i −0.268391 0.154956i
\(471\) 0 0
\(472\) −82.3320 142.603i −0.174432 0.302126i
\(473\) −877.731 + 506.758i −1.85567 + 1.07137i
\(474\) 0 0
\(475\) 118.340 204.971i 0.249137 0.431517i
\(476\) 57.6851i 0.121187i
\(477\) 0 0
\(478\) 130.494 0.273000
\(479\) 609.100 + 351.664i 1.27161 + 0.734163i 0.975290 0.220927i \(-0.0709081\pi\)
0.296317 + 0.955090i \(0.404241\pi\)
\(480\) 0 0
\(481\) 353.077 + 611.547i 0.734048 + 1.27141i
\(482\) −420.390 + 242.712i −0.872179 + 0.503553i
\(483\) 0 0
\(484\) −26.3360 + 45.6152i −0.0544131 + 0.0942463i
\(485\) 1143.50i 2.35773i
\(486\) 0 0
\(487\) −82.5098 −0.169425 −0.0847124 0.996405i \(-0.526997\pi\)
−0.0847124 + 0.996405i \(0.526997\pi\)
\(488\) −38.3786 22.1579i −0.0786446 0.0454055i
\(489\) 0 0
\(490\) 30.0405 + 52.0317i 0.0613072 + 0.106187i
\(491\) −159.524 + 92.1014i −0.324897 + 0.187579i −0.653573 0.756863i \(-0.726731\pi\)
0.328676 + 0.944443i \(0.393397\pi\)
\(492\) 0 0
\(493\) −228.041 + 394.978i −0.462557 + 0.801172i
\(494\) 525.607i 1.06398i
\(495\) 0 0
\(496\) 100.664 0.202952
\(497\) −27.8121 16.0573i −0.0559600 0.0323085i
\(498\) 0 0
\(499\) −376.405 651.953i −0.754319 1.30652i −0.945712 0.325005i \(-0.894634\pi\)
0.191393 0.981513i \(-0.438699\pi\)
\(500\) 138.401 79.9059i 0.276802 0.159812i
\(501\) 0 0
\(502\) −252.000 + 436.477i −0.501992 + 0.869476i
\(503\) 662.540i 1.31718i −0.752504 0.658588i \(-0.771154\pi\)
0.752504 0.658588i \(-0.228846\pi\)
\(504\) 0 0
\(505\) 647.652 1.28248
\(506\) −180.449 104.182i −0.356618 0.205894i
\(507\) 0 0
\(508\) 129.668 + 224.592i 0.255252 + 0.442109i
\(509\) 821.958 474.557i 1.61485 0.932333i 0.626623 0.779322i \(-0.284437\pi\)
0.988225 0.153010i \(-0.0488968\pi\)
\(510\) 0 0
\(511\) −101.749 + 176.234i −0.199117 + 0.344882i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −360.243 −0.700862
\(515\) 691.153 + 399.037i 1.34204 + 0.774830i
\(516\) 0 0
\(517\) 102.996 + 178.394i 0.199219 + 0.345057i
\(518\) 123.134 71.0915i 0.237711 0.137242i
\(519\) 0 0
\(520\) 159.498 276.259i 0.306727 0.531267i
\(521\) 714.344i 1.37110i 0.728025 + 0.685551i \(0.240439\pi\)
−0.728025 + 0.685551i \(0.759561\pi\)
\(522\) 0 0
\(523\) −232.000 −0.443595 −0.221797 0.975093i \(-0.571192\pi\)
−0.221797 + 0.975093i \(0.571192\pi\)
\(524\) −256.373 148.017i −0.489262 0.282476i
\(525\) 0 0
\(526\) −185.247 320.857i −0.352181 0.609995i
\(527\) −237.591 + 137.173i −0.450837 + 0.260291i
\(528\) 0 0
\(529\) −190.832 + 330.531i −0.360741 + 0.624822i
\(530\) 807.167i 1.52296i
\(531\) 0 0
\(532\) 105.830 0.198929
\(533\) −975.800 563.378i −1.83077 1.05699i
\(534\) 0 0
\(535\) −249.984 432.985i −0.467260 0.809319i
\(536\) −324.959 + 187.615i −0.606267 + 0.350029i
\(537\) 0 0
\(538\) −66.2026 + 114.666i −0.123053 + 0.213134i
\(539\) 84.9674i 0.157639i
\(540\) 0 0
\(541\) 165.668 0.306225 0.153113 0.988209i \(-0.451070\pi\)
0.153113 + 0.988209i \(0.451070\pi\)
\(542\) 1.42807 + 0.824494i 0.00263481 + 0.00152121i
\(543\) 0 0
\(544\) 30.8340 + 53.4060i 0.0566801 + 0.0981729i
\(545\) −177.811 + 102.659i −0.326258 + 0.188365i
\(546\) 0 0
\(547\) −147.838 + 256.063i −0.270270 + 0.468122i −0.968931 0.247331i \(-0.920446\pi\)
0.698661 + 0.715453i \(0.253780\pi\)
\(548\) 153.915i 0.280866i
\(549\) 0 0
\(550\) 203.142 0.369350
\(551\) −724.633 418.367i −1.31512 0.759287i
\(552\) 0 0
\(553\) 44.5385 + 77.1430i 0.0805399 + 0.139499i
\(554\) −39.1918 + 22.6274i −0.0707434 + 0.0408437i
\(555\) 0 0
\(556\) 217.328 376.423i 0.390878 0.677020i
\(557\) 76.8426i 0.137958i 0.997618 + 0.0689790i \(0.0219742\pi\)
−0.997618 + 0.0689790i \(0.978026\pi\)
\(558\) 0 0
\(559\) −1551.64 −2.77575
\(560\) −55.6242 32.1147i −0.0993290 0.0573476i
\(561\) 0 0
\(562\) −117.915 204.235i −0.209813 0.363407i
\(563\) 880.170 508.167i 1.56336 0.902605i 0.566444 0.824100i \(-0.308319\pi\)
0.996914 0.0785049i \(-0.0250146\pi\)
\(564\) 0 0
\(565\) 86.5425 149.896i 0.153173 0.265303i
\(566\) 23.1081i 0.0408270i
\(567\) 0 0
\(568\) 34.3320 0.0604437
\(569\) 507.952 + 293.266i 0.892710 + 0.515406i 0.874828 0.484434i \(-0.160974\pi\)
0.0178822 + 0.999840i \(0.494308\pi\)
\(570\) 0 0
\(571\) −475.822 824.148i −0.833314 1.44334i −0.895396 0.445271i \(-0.853107\pi\)
0.0620822 0.998071i \(-0.480226\pi\)
\(572\) −390.689 + 225.564i −0.683022 + 0.394343i
\(573\) 0 0
\(574\) −113.435 + 196.476i −0.197622 + 0.342292i
\(575\) 143.643i 0.249815i
\(576\) 0 0
\(577\) −148.672 −0.257664 −0.128832 0.991666i \(-0.541123\pi\)
−0.128832 + 0.991666i \(0.541123\pi\)
\(578\) 208.400 + 120.320i 0.360554 + 0.208166i
\(579\) 0 0
\(580\) 253.911 + 439.787i 0.437778 + 0.758253i
\(581\) 138.798 80.1351i 0.238895 0.137926i
\(582\) 0 0
\(583\) −570.753 + 988.573i −0.978993 + 1.69567i
\(584\) 217.549i 0.372515i
\(585\) 0 0
\(586\) 521.733 0.890330
\(587\) −288.009 166.282i −0.490645 0.283274i 0.234197 0.972189i \(-0.424754\pi\)
−0.724842 + 0.688915i \(0.758087\pi\)
\(588\) 0 0
\(589\) −251.660 435.888i −0.427267 0.740048i
\(590\) 432.737 249.841i 0.733452 0.423459i
\(591\) 0 0
\(592\) −76.0000 + 131.636i −0.128378 + 0.222358i
\(593\) 217.251i 0.366359i 0.983079 + 0.183180i \(0.0586390\pi\)
−0.983079 + 0.183180i \(0.941361\pi\)
\(594\) 0 0
\(595\) 175.048 0.294199
\(596\) 280.462 + 161.925i 0.470573 + 0.271686i
\(597\) 0 0
\(598\) −159.498 276.259i −0.266719 0.461971i
\(599\) −149.111 + 86.0896i −0.248934 + 0.143722i −0.619276 0.785173i \(-0.712574\pi\)
0.370342 + 0.928895i \(0.379240\pi\)
\(600\) 0 0
\(601\) 209.000 361.999i 0.347754 0.602327i −0.638096 0.769957i \(-0.720278\pi\)
0.985850 + 0.167629i \(0.0536112\pi\)
\(602\) 312.421i 0.518972i
\(603\) 0 0
\(604\) 186.332 0.308497
\(605\) −138.422 79.9178i −0.228796 0.132096i
\(606\) 0 0
\(607\) −313.579 543.135i −0.516605 0.894786i −0.999814 0.0192808i \(-0.993862\pi\)
0.483209 0.875505i \(-0.339471\pi\)
\(608\) −97.9796 + 56.5685i −0.161151 + 0.0930404i
\(609\) 0 0
\(610\) 67.2392 116.462i 0.110228 0.190921i
\(611\) 315.364i 0.516144i
\(612\) 0 0
\(613\) −279.328 −0.455674 −0.227837 0.973699i \(-0.573165\pi\)
−0.227837 + 0.973699i \(0.573165\pi\)
\(614\) −235.964 136.234i −0.384307 0.221880i
\(615\) 0 0
\(616\) 45.4170 + 78.6645i 0.0737289 + 0.127702i
\(617\) 310.366 179.190i 0.503025 0.290422i −0.226937 0.973909i \(-0.572871\pi\)
0.729962 + 0.683488i \(0.239538\pi\)
\(618\) 0 0
\(619\) 491.822 851.861i 0.794543 1.37619i −0.128586 0.991698i \(-0.541044\pi\)
0.923129 0.384491i \(-0.125623\pi\)
\(620\) 305.470i 0.492694i
\(621\) 0 0
\(622\) 185.652 0.298476
\(623\) −10.9410 6.31681i −0.0175619 0.0101393i
\(624\) 0 0
\(625\) 390.403 + 676.198i 0.624645 + 1.08192i
\(626\) −53.0658 + 30.6376i −0.0847697 + 0.0489418i
\(627\) 0 0
\(628\) −184.996 + 320.423i −0.294580 + 0.510227i
\(629\) 414.256i 0.658594i
\(630\) 0 0
\(631\) −298.996 −0.473845 −0.236922 0.971529i \(-0.576139\pi\)
−0.236922 + 0.971529i \(0.576139\pi\)
\(632\) −82.4694 47.6137i −0.130490 0.0753382i
\(633\) 0 0
\(634\) 177.996 + 308.298i 0.280751 + 0.486275i
\(635\) −681.534 + 393.484i −1.07328 + 0.619660i
\(636\) 0 0
\(637\) 65.0405 112.653i 0.102104 0.176850i
\(638\) 718.169i 1.12566i
\(639\) 0 0
\(640\) 68.6640 0.107288
\(641\) 270.163 + 155.979i 0.421471 + 0.243336i 0.695706 0.718326i \(-0.255091\pi\)
−0.274236 + 0.961663i \(0.588425\pi\)
\(642\) 0 0
\(643\) 302.000 + 523.079i 0.469673 + 0.813498i 0.999399 0.0346710i \(-0.0110383\pi\)
−0.529725 + 0.848169i \(0.677705\pi\)
\(644\) −55.6242 + 32.1147i −0.0863730 + 0.0498675i
\(645\) 0 0
\(646\) 154.170 267.030i 0.238653 0.413359i
\(647\) 179.600i 0.277588i 0.990321 + 0.138794i \(0.0443226\pi\)
−0.990321 + 0.138794i \(0.955677\pi\)
\(648\) 0 0
\(649\) −706.656 −1.08884
\(650\) 269.335 + 155.501i 0.414362 + 0.239232i
\(651\) 0 0
\(652\) 86.9961 + 150.682i 0.133430 + 0.231107i
\(653\) 417.331 240.946i 0.639097 0.368983i −0.145169 0.989407i \(-0.546373\pi\)
0.784267 + 0.620424i \(0.213039\pi\)
\(654\) 0 0
\(655\) 449.166 777.978i 0.685750 1.18775i
\(656\) 242.535i 0.369718i
\(657\) 0 0
\(658\) 63.4980 0.0965016
\(659\) −759.857 438.704i −1.15305 0.665711i −0.203418 0.979092i \(-0.565205\pi\)
−0.949628 + 0.313380i \(0.898538\pi\)
\(660\) 0 0
\(661\) 260.822 + 451.757i 0.394587 + 0.683445i 0.993048 0.117707i \(-0.0375543\pi\)
−0.598461 + 0.801152i \(0.704221\pi\)
\(662\) −442.733 + 255.612i −0.668781 + 0.386121i
\(663\) 0 0
\(664\) −85.6680 + 148.381i −0.129018 + 0.223466i
\(665\) 321.147i 0.482927i
\(666\) 0 0
\(667\) 507.822 0.761353
\(668\) 104.921 + 60.5764i 0.157068 + 0.0906832i
\(669\) 0 0
\(670\) −569.328 986.105i −0.849743 1.47180i
\(671\) −164.702 + 95.0906i −0.245457 + 0.141715i
\(672\) 0 0
\(673\) 329.996 571.570i 0.490336 0.849287i −0.509602 0.860410i \(-0.670207\pi\)
0.999938 + 0.0111234i \(0.00354077\pi\)
\(674\) 422.615i 0.627025i
\(675\) 0 0
\(676\) −352.656 −0.521681
\(677\) −880.121 508.138i −1.30003 0.750573i −0.319622 0.947545i \(-0.603556\pi\)
−0.980409 + 0.196972i \(0.936889\pi\)
\(678\) 0 0
\(679\) −249.247 431.709i −0.367080 0.635801i
\(680\) −162.063 + 93.5673i −0.238328 + 0.137599i
\(681\) 0 0
\(682\) 216.000 374.123i 0.316716 0.548567i
\(683\) 235.114i 0.344238i −0.985076 0.172119i \(-0.944939\pi\)
0.985076 0.172119i \(-0.0550613\pi\)
\(684\) 0 0
\(685\) −467.061 −0.681841
\(686\) −22.6826 13.0958i −0.0330650 0.0190901i
\(687\) 0 0
\(688\) −166.996 289.246i −0.242727 0.420415i
\(689\) −1513.46 + 873.795i −2.19660 + 1.26821i
\(690\) 0 0
\(691\) 25.4902 44.1502i 0.0368888 0.0638933i −0.846992 0.531606i \(-0.821589\pi\)
0.883880 + 0.467713i \(0.154922\pi\)
\(692\) 325.143i 0.469860i
\(693\) 0 0
\(694\) 291.498 0.420026
\(695\) 1142.28 + 659.493i 1.64356 + 0.948911i
\(696\) 0 0
\(697\) 330.498 + 572.439i 0.474172 + 0.821290i
\(698\) −531.936 + 307.114i −0.762086 + 0.439991i
\(699\) 0 0
\(700\) 31.3098 54.2302i 0.0447283 0.0774716i
\(701\) 141.530i 0.201898i 0.994892 + 0.100949i \(0.0321879\pi\)
−0.994892 + 0.100949i \(0.967812\pi\)
\(702\) 0 0
\(703\) 760.000 1.08108
\(704\) −84.0959 48.5528i −0.119454 0.0689671i
\(705\) 0 0
\(706\) 131.125 + 227.116i 0.185730 + 0.321694i
\(707\) −244.510 + 141.168i −0.345842 + 0.199672i
\(708\) 0 0
\(709\) 27.7490 48.0627i 0.0391382 0.0677894i −0.845793 0.533512i \(-0.820872\pi\)
0.884931 + 0.465722i \(0.154205\pi\)
\(710\) 104.182i 0.146736i
\(711\) 0 0
\(712\) 13.5059 0.0189690
\(713\) 264.545 + 152.735i 0.371031 + 0.214215i
\(714\) 0 0
\(715\) −684.486 1185.56i −0.957323 1.65813i
\(716\) −386.405 + 223.091i −0.539671 + 0.311579i
\(717\) 0 0
\(718\) 365.409 632.907i 0.508926 0.881486i
\(719\) 1009.03i 1.40338i −0.712484 0.701688i \(-0.752430\pi\)
0.712484 0.701688i \(-0.247570\pi\)
\(720\) 0 0
\(721\) −347.911 −0.482540
\(722\) 47.7650 + 27.5772i 0.0661566 + 0.0381955i
\(723\) 0 0
\(724\) 188.915 + 327.210i 0.260932 + 0.451948i
\(725\) −428.765 + 247.547i −0.591400 + 0.341445i
\(726\) 0 0
\(727\) 182.591 316.257i 0.251157 0.435016i −0.712688 0.701481i \(-0.752522\pi\)
0.963845 + 0.266465i \(0.0858557\pi\)
\(728\) 139.062i 0.191020i
\(729\) 0 0
\(730\) 660.162 0.904332
\(731\) 788.300 + 455.125i 1.07839 + 0.622606i
\(732\) 0 0
\(733\) 176.539 + 305.774i 0.240844 + 0.417154i 0.960955 0.276705i \(-0.0892425\pi\)
−0.720111 + 0.693859i \(0.755909\pi\)
\(734\) 143.895 83.0781i 0.196043 0.113185i
\(735\) 0 0
\(736\) 34.3320 59.4648i 0.0466468 0.0807946i
\(737\) 1610.30i 2.18494i
\(738\) 0 0
\(739\) 329.684 0.446121 0.223061 0.974805i \(-0.428395\pi\)
0.223061 + 0.974805i \(0.428395\pi\)
\(740\) −399.456 230.626i −0.539805 0.311657i
\(741\) 0 0
\(742\) 175.937 + 304.732i 0.237112 + 0.410690i
\(743\) −97.0478 + 56.0306i −0.130616 + 0.0754112i −0.563884 0.825854i \(-0.690694\pi\)
0.433268 + 0.901265i \(0.357360\pi\)
\(744\) 0 0
\(745\) −491.369 + 851.075i −0.659555 + 1.14238i
\(746\) 569.453i 0.763342i
\(747\) 0 0
\(748\) 264.648 0.353808
\(749\) 188.755 + 108.978i 0.252009 + 0.145497i
\(750\) 0 0
\(751\) 72.4131 + 125.423i 0.0964222 + 0.167008i 0.910201 0.414166i \(-0.135927\pi\)
−0.813779 + 0.581174i \(0.802593\pi\)
\(752\) −58.7878 + 33.9411i −0.0781752 + 0.0451345i
\(753\) 0 0
\(754\) 549.741 952.180i 0.729100 1.26284i
\(755\) 565.434i 0.748919i
\(756\) 0 0
\(757\) 78.1699 0.103263 0.0516314 0.998666i \(-0.483558\pi\)
0.0516314 + 0.998666i \(0.483558\pi\)
\(758\) 488.470 + 282.018i 0.644419 + 0.372056i
\(759\) 0 0
\(760\) −171.660 297.324i −0.225869 0.391216i
\(761\) 1269.16 732.752i 1.66776 0.962880i 0.698915 0.715205i \(-0.253667\pi\)
0.968843 0.247676i \(-0.0796667\pi\)
\(762\) 0 0
\(763\) 44.7530 77.5144i 0.0586539 0.101592i
\(764\) 456.076i 0.596957i
\(765\) 0 0
\(766\) 1053.31 1.37508
\(767\) −936.915 540.928i −1.22153 0.705252i
\(768\) 0 0
\(769\) −364.660 631.610i −0.474200 0.821339i 0.525363 0.850878i \(-0.323929\pi\)
−0.999564 + 0.0295389i \(0.990596\pi\)
\(770\) −238.712 + 137.820i −0.310015 + 0.178987i
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) 434.559i 0.562172i −0.959683 0.281086i \(-0.909305\pi\)
0.959683 0.281086i \(-0.0906947\pi\)
\(774\) 0 0
\(775\) −297.814 −0.384277
\(776\) 461.516 + 266.456i 0.594737 + 0.343372i
\(777\) 0 0
\(778\) 378.417 + 655.437i 0.486397 + 0.842465i
\(779\) −1050.21 + 606.337i −1.34815 + 0.778353i
\(780\) 0 0
\(781\) 73.6680 127.597i 0.0943252 0.163376i
\(782\) 187.135i 0.239303i
\(783\) 0 0
\(784\) 28.0000 0.0357143
\(785\) −972.339 561.380i −1.23865 0.715134i
\(786\) 0 0
\(787\) 7.67585 + 13.2950i 0.00975331 + 0.0168932i 0.870861 0.491530i \(-0.163562\pi\)
−0.861108 + 0.508423i \(0.830229\pi\)
\(788\) 326.595 188.560i 0.414461 0.239289i
\(789\) 0 0
\(790\) 144.486 250.257i 0.182894 0.316782i
\(791\) 75.4543i 0.0953910i
\(792\) 0 0
\(793\) −291.158 −0.367160
\(794\) −115.523 66.6972i −0.145495 0.0840016i
\(795\) 0 0
\(796\) 102.494 + 177.525i 0.128761 + 0.223021i
\(797\) −903.684 + 521.742i −1.13386 + 0.654633i −0.944902 0.327353i \(-0.893843\pi\)
−0.188955 + 0.981986i \(0.560510\pi\)
\(798\) 0 0
\(799\) 92.5020 160.218i 0.115772 0.200523i
\(800\) 66.9432i 0.0836789i
\(801\) 0 0
\(802\) −146.502 −0.182671
\(803\) −808.530 466.805i −1.00689 0.581326i
\(804\) 0 0
\(805\) −97.4536 168.795i −0.121060 0.209683i
\(806\) 572.764 330.686i 0.710626 0.410280i
\(807\) 0 0
\(808\) 150.915 261.392i 0.186776 0.323506i
\(809\) 1041.31i 1.28716i 0.765378 + 0.643581i \(0.222552\pi\)
−0.765378 + 0.643581i \(0.777448\pi\)
\(810\) 0 0
\(811\) 502.316 0.619379 0.309689 0.950838i \(-0.399775\pi\)
0.309689 + 0.950838i \(0.399775\pi\)
\(812\) −191.720 110.689i −0.236108 0.136317i
\(813\) 0 0
\(814\) 326.154 + 564.916i 0.400681 + 0.694000i
\(815\) −457.251 + 263.994i −0.561044 + 0.323919i
\(816\) 0 0
\(817\) −834.980 + 1446.23i −1.02201 + 1.77017i
\(818\) 13.7983i 0.0168684i
\(819\) 0 0
\(820\) 735.984 0.897542
\(821\) 20.0170 + 11.5568i 0.0243813 + 0.0140765i 0.512141 0.858901i \(-0.328852\pi\)
−0.487760 + 0.872978i \(0.662186\pi\)
\(822\) 0 0
\(823\) 300.332 + 520.190i 0.364923 + 0.632066i 0.988764 0.149486i \(-0.0477618\pi\)
−0.623840 + 0.781552i \(0.714428\pi\)
\(824\) 322.103 185.966i 0.390902 0.225687i
\(825\) 0 0
\(826\) −108.915 + 188.646i −0.131858 + 0.228385i
\(827\) 1309.21i 1.58308i −0.611118 0.791540i \(-0.709280\pi\)
0.611118 0.791540i \(-0.290720\pi\)
\(828\) 0 0
\(829\) −621.919 −0.750204 −0.375102 0.926984i \(-0.622392\pi\)
−0.375102 + 0.926984i \(0.622392\pi\)
\(830\) −450.271 259.964i −0.542495 0.313209i
\(831\) 0 0
\(832\) −74.3320 128.747i −0.0893414 0.154744i
\(833\) −66.0866 + 38.1551i −0.0793357 + 0.0458045i
\(834\) 0 0
\(835\) −183.822 + 318.389i −0.220146 + 0.381305i
\(836\) 485.528i 0.580775i
\(837\) 0 0
\(838\) 480.000 0.572792
\(839\) −1030.83 595.149i −1.22864 0.709355i −0.261894 0.965097i \(-0.584347\pi\)
−0.966745 + 0.255741i \(0.917680\pi\)
\(840\) 0 0
\(841\) 454.654 + 787.484i 0.540611 + 0.936366i
\(842\) 734.014 423.783i 0.871751 0.503306i
\(843\) 0 0
\(844\) −84.5020 + 146.362i −0.100121 + 0.173414i
\(845\) 1070.15i 1.26645i
\(846\) 0 0
\(847\) 69.6784 0.0822649
\(848\) −325.772 188.085i −0.384166 0.221798i
\(849\) 0 0
\(850\) −91.2223 158.002i −0.107320 0.185884i
\(851\) −399.456 + 230.626i −0.469396 + 0.271006i
\(852\) 0 0
\(853\) −68.5059 + 118.656i −0.0803117 + 0.139104i −0.903384 0.428833i \(-0.858925\pi\)
0.823072 + 0.567937i \(0.192258\pi\)
\(854\) 58.6242i 0.0686466i
\(855\) 0 0
\(856\) −233.004 −0.272201
\(857\) −403.690 233.071i −0.471050 0.271961i 0.245629 0.969364i \(-0.421006\pi\)
−0.716679 + 0.697403i \(0.754339\pi\)
\(858\) 0 0
\(859\) −11.9921 20.7710i −0.0139606 0.0241804i 0.858961 0.512041i \(-0.171111\pi\)
−0.872921 + 0.487861i \(0.837777\pi\)
\(860\) 877.731 506.758i 1.02062 0.589253i
\(861\) 0 0
\(862\) −502.737 + 870.766i −0.583222 + 1.01017i
\(863\) 0.114603i 0.000132796i 1.00000 6.63982e-5i \(2.11352e-5\pi\)
−1.00000 6.63982e-5i \(0.999979\pi\)
\(864\) 0 0
\(865\) 986.664 1.14065
\(866\) 462.934 + 267.275i 0.534566 + 0.308632i
\(867\) 0 0
\(868\) −66.5830 115.325i −0.0767085 0.132863i
\(869\) −353.918 + 204.334i −0.407270 + 0.235137i
\(870\) 0 0
\(871\) −1232.65 + 2135.01i −1.41521 + 2.45122i
\(872\) 95.6858i 0.109731i
\(873\) 0 0
\(874\) −343.320 −0.392815
\(875\) −183.087 105.706i −0.209243 0.120806i
\(876\) 0 0
\(877\) −498.652 863.691i −0.568589 0.984824i −0.996706 0.0811012i \(-0.974156\pi\)
0.428117 0.903723i \(-0.359177\pi\)
\(878\) −646.845 + 373.456i −0.736725 + 0.425348i
\(879\) 0 0
\(880\) 147.336 255.193i 0.167427 0.289992i
\(881\) 935.649i 1.06203i 0.847362 + 0.531015i \(0.178189\pi\)
−0.847362 + 0.531015i \(0.821811\pi\)
\(882\) 0 0
\(883\) −1549.47 −1.75478 −0.877392 0.479774i \(-0.840719\pi\)
−0.877392 + 0.479774i \(0.840719\pi\)
\(884\) 350.882 + 202.582i 0.396926 + 0.229165i
\(885\) 0 0
\(886\) −25.9111 44.8793i −0.0292450 0.0506539i
\(887\) −774.654 + 447.246i −0.873341 + 0.504224i −0.868457 0.495764i \(-0.834888\pi\)
−0.00488401 + 0.999988i \(0.501555\pi\)
\(888\) 0 0
\(889\) 171.535 297.107i 0.192952 0.334203i
\(890\) 40.9844i 0.0460498i
\(891\) 0 0
\(892\) 316.988 0.355368
\(893\) 293.939 + 169.706i 0.329159 + 0.190040i
\(894\) 0 0
\(895\) −676.980 1172.56i −0.756403 1.31013i
\(896\) −25.9230 + 14.9666i −0.0289319 + 0.0167038i
\(897\) 0 0
\(898\) 281.154 486.973i 0.313089 0.542287i
\(899\) 1052.86i 1.17115i
\(900\) 0 0
\(901\) 1025.20 1.13785
\(902\) −901.393 520.419i −0.999327 0.576962i
\(903\) 0 0
\(904\) −40.3320 69.8571i −0.0446151 0.0772756i
\(905\) −992.937 + 573.272i −1.09717 + 0.633450i
\(906\) 0 0
\(907\) 67.9190 117.639i 0.0748831 0.129701i −0.826152 0.563447i \(-0.809475\pi\)
0.901035 + 0.433746i \(0.142808\pi\)
\(908\) 203.647i 0.224281i
\(909\) 0 0
\(910\) −421.992 −0.463728
\(911\) 1075.61 + 621.006i 1.18070 + 0.681675i 0.956175 0.292794i \(-0.0945851\pi\)
0.224521 + 0.974469i \(0.427918\pi\)
\(912\) 0 0
\(913\) 367.644 + 636.779i 0.402677 + 0.697458i
\(914\) −421.709 + 243.474i −0.461389 + 0.266383i
\(915\) 0 0
\(916\) −268.915 + 465.774i −0.293575 + 0.508487i
\(917\) 391.617i 0.427063i
\(918\) 0 0
\(919\) −388.162 −0.422374 −0.211187 0.977446i \(-0.567733\pi\)
−0.211187 + 0.977446i \(0.567733\pi\)
\(920\) 180.449 + 104.182i 0.196140 + 0.113242i
\(921\) 0 0
\(922\) 262.292 + 454.302i 0.284481 + 0.492736i
\(923\) 195.344 112.782i 0.211641 0.122191i
\(924\) 0 0
\(925\) 224.846 389.444i 0.243077 0.421021i
\(926\) 110.778i 0.119631i
\(927\) 0 0
\(928\) 236.664 0.255026
\(929\) 538.403 + 310.847i 0.579551 + 0.334604i 0.760955 0.648805i \(-0.224731\pi\)
−0.181404 + 0.983409i \(0.558064\pi\)
\(930\) 0 0
\(931\) −70.0000 121.244i −0.0751880 0.130229i
\(932\) 45.5092 26.2748i 0.0488297 0.0281918i
\(933\) 0 0
\(934\) 282.672 489.602i 0.302647 0.524199i
\(935\) 803.089i 0.858918i
\(936\) 0 0
\(937\) 1262.00 1.34685 0.673426 0.739255i \(-0.264822\pi\)
0.673426 + 0.739255i \(0.264822\pi\)
\(938\) 429.881 + 248.192i 0.458295 + 0.264597i
\(939\) 0 0
\(940\) −102.996 178.394i −0.109570 0.189781i
\(941\) 582.324 336.205i 0.618835 0.357285i −0.157580 0.987506i \(-0.550369\pi\)
0.776415 + 0.630222i \(0.217036\pi\)
\(942\) 0 0
\(943\) 367.992 637.381i 0.390236 0.675908i
\(944\) 232.870i 0.246684i
\(945\) 0 0
\(946\) −1433.33 −1.51515
\(947\) −1004.37 579.874i −1.06058 0.612327i −0.134989 0.990847i \(-0.543100\pi\)
−0.925593 + 0.378520i \(0.876433\pi\)
\(948\) 0 0
\(949\) −714.656 1237.82i −0.753062 1.30434i
\(950\) 289.872 167.358i 0.305129 0.176166i
\(951\) 0 0
\(952\) 40.7895 70.6495i 0.0428461 0.0742117i
\(953\) 163.104i 0.171148i −0.996332 0.0855740i \(-0.972728\pi\)
0.996332 0.0855740i \(-0.0272724\pi\)
\(954\) 0 0
\(955\) −1383.98 −1.44920
\(956\) 159.822 + 92.2733i 0.167178 + 0.0965201i
\(957\) 0 0
\(958\) 497.328 + 861.398i 0.519132 + 0.899162i
\(959\) 176.331 101.805i 0.183870 0.106157i
\(960\) 0 0
\(961\) 163.836 283.772i 0.170485 0.295288i
\(962\) 998.653i 1.03810i
\(963\) 0 0
\(964\) −686.494 −0.712131
\(965\) 704.303 + 406.630i 0.729848 + 0.421378i
\(966\) 0 0
\(967\) −443.506 768.175i −0.458641 0.794390i 0.540248 0.841506i \(-0.318330\pi\)
−0.998889 + 0.0471160i \(0.984997\pi\)
\(968\) −64.5097 + 37.2447i −0.0666422 + 0.0384759i
\(969\) 0 0
\(970\) −808.575 + 1400.49i −0.833583 + 1.44381i
\(971\) 1416.32i 1.45862i −0.684183 0.729310i \(-0.739841\pi\)
0.684183 0.729310i \(-0.260159\pi\)
\(972\) 0 0
\(973\) −574.996 −0.590952
\(974\) −101.054 58.3433i −0.103751 0.0599007i
\(975\) 0 0
\(976\) −31.3360 54.2755i −0.0321065 0.0556101i
\(977\) 293.627 169.525i 0.300539 0.173516i −0.342146 0.939647i \(-0.611154\pi\)
0.642685 + 0.766131i \(0.277820\pi\)
\(978\) 0 0
\(979\) 28.9803 50.1954i 0.0296020 0.0512721i
\(980\) 84.9674i 0.0867014i
\(981\) 0 0
\(982\) −260.502 −0.265277
\(983\) 422.523 + 243.943i 0.429830 + 0.248162i 0.699274 0.714854i \(-0.253507\pi\)
−0.269444 + 0.963016i \(0.586840\pi\)
\(984\) 0 0
\(985\) 572.195 + 991.070i 0.580908 + 1.00616i
\(986\) −558.583 + 322.498i −0.566514 + 0.327077i
\(987\) 0 0
\(988\) −371.660 + 643.734i −0.376174 + 0.651553i
\(989\) 1013.52i 1.02479i
\(990\) 0 0
\(991\) −937.474 −0.945988 −0.472994 0.881066i \(-0.656827\pi\)
−0.472994 + 0.881066i \(0.656827\pi\)
\(992\) 123.288 + 71.1802i 0.124282 + 0.0717543i
\(993\) 0 0
\(994\) −22.7085 39.3323i −0.0228456 0.0395697i
\(995\) −538.709 + 311.024i −0.541416 + 0.312586i
\(996\) 0 0
\(997\) −230.506 + 399.248i −0.231200 + 0.400449i −0.958161 0.286229i \(-0.907598\pi\)
0.726962 + 0.686678i \(0.240932\pi\)
\(998\) 1064.63i 1.06677i
\(999\) 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 1134.3.q.c.1079.3 8
3.2 odd 2 inner 1134.3.q.c.1079.2 8
9.2 odd 6 126.3.b.a.71.4 yes 4
9.4 even 3 inner 1134.3.q.c.701.2 8
9.5 odd 6 inner 1134.3.q.c.701.3 8
9.7 even 3 126.3.b.a.71.1 4
36.7 odd 6 1008.3.d.a.449.2 4
36.11 even 6 1008.3.d.a.449.3 4
45.2 even 12 3150.3.c.b.449.1 8
45.7 odd 12 3150.3.c.b.449.6 8
45.29 odd 6 3150.3.e.e.701.2 4
45.34 even 6 3150.3.e.e.701.4 4
45.38 even 12 3150.3.c.b.449.7 8
45.43 odd 12 3150.3.c.b.449.4 8
63.2 odd 6 882.3.s.e.557.4 8
63.11 odd 6 882.3.s.e.863.1 8
63.16 even 3 882.3.s.e.557.1 8
63.20 even 6 882.3.b.f.197.3 4
63.25 even 3 882.3.s.e.863.4 8
63.34 odd 6 882.3.b.f.197.2 4
63.38 even 6 882.3.s.i.863.2 8
63.47 even 6 882.3.s.i.557.3 8
63.52 odd 6 882.3.s.i.863.3 8
63.61 odd 6 882.3.s.i.557.2 8
72.11 even 6 4032.3.d.j.449.2 4
72.29 odd 6 4032.3.d.i.449.2 4
72.43 odd 6 4032.3.d.j.449.3 4
72.61 even 6 4032.3.d.i.449.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.b.a.71.1 4 9.7 even 3
126.3.b.a.71.4 yes 4 9.2 odd 6
882.3.b.f.197.2 4 63.34 odd 6
882.3.b.f.197.3 4 63.20 even 6
882.3.s.e.557.1 8 63.16 even 3
882.3.s.e.557.4 8 63.2 odd 6
882.3.s.e.863.1 8 63.11 odd 6
882.3.s.e.863.4 8 63.25 even 3
882.3.s.i.557.2 8 63.61 odd 6
882.3.s.i.557.3 8 63.47 even 6
882.3.s.i.863.2 8 63.38 even 6
882.3.s.i.863.3 8 63.52 odd 6
1008.3.d.a.449.2 4 36.7 odd 6
1008.3.d.a.449.3 4 36.11 even 6
1134.3.q.c.701.2 8 9.4 even 3 inner
1134.3.q.c.701.3 8 9.5 odd 6 inner
1134.3.q.c.1079.2 8 3.2 odd 2 inner
1134.3.q.c.1079.3 8 1.1 even 1 trivial
3150.3.c.b.449.1 8 45.2 even 12
3150.3.c.b.449.4 8 45.43 odd 12
3150.3.c.b.449.6 8 45.7 odd 12
3150.3.c.b.449.7 8 45.38 even 12
3150.3.e.e.701.2 4 45.29 odd 6
3150.3.e.e.701.4 4 45.34 even 6
4032.3.d.i.449.2 4 72.29 odd 6
4032.3.d.i.449.3 4 72.61 even 6
4032.3.d.j.449.2 4 72.11 even 6
4032.3.d.j.449.3 4 72.43 odd 6