Properties

Label 1134.2.e.k.919.1
Level $1134$
Weight $2$
Character 1134.919
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(865,1134)]
 
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([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.865");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.e (of order \(3\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 919.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.919
Dual form 1134.2.e.k.865.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(2.50000 - 0.866025i) q^{14} +1.00000 q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(2.50000 - 0.866025i) q^{28} +(-4.50000 - 7.79423i) q^{29} -7.00000 q^{31} +1.00000 q^{32} +(-3.00000 - 5.19615i) q^{34} +(-6.00000 - 5.19615i) q^{35} +(5.00000 - 8.66025i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(2.00000 + 3.46410i) q^{43} +(1.50000 - 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +12.0000 q^{47} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(-4.50000 - 7.79423i) q^{58} -3.00000 q^{59} -4.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +2.00000 q^{67} +(-3.00000 - 5.19615i) q^{68} +(-6.00000 - 5.19615i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(5.00000 - 8.66025i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.50000 - 7.79423i) q^{77} +5.00000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{83} +(-9.00000 + 15.5885i) q^{85} +(2.00000 + 3.46410i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(3.00000 + 5.19615i) q^{92} +12.0000 q^{94} +6.00000 q^{95} +(6.50000 + 11.2583i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8} - 3 q^{10} + 3 q^{11} - 2 q^{13} + 5 q^{14} + 2 q^{16} - 6 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 5 q^{28} - 9 q^{29} - 14 q^{31} + 2 q^{32} - 6 q^{34} - 12 q^{35} + 10 q^{37} - 2 q^{38} - 3 q^{40} + 4 q^{43} + 3 q^{44} + 6 q^{46} + 24 q^{47} + 11 q^{49} - 4 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} + 5 q^{56} - 9 q^{58} - 6 q^{59} - 8 q^{61} - 14 q^{62} + 2 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} - 12 q^{70} - 2 q^{73} + 10 q^{74} - 2 q^{76} + 3 q^{77} + 10 q^{79} - 3 q^{80} - 9 q^{83} - 18 q^{85} + 4 q^{86} + 3 q^{88} + 6 q^{89} - 2 q^{91} + 6 q^{92} + 24 q^{94} + 12 q^{95} + 13 q^{97} + 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.50000 2.59808i −0.335410 0.580948i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −4.50000 7.79423i −0.835629 1.44735i −0.893517 0.449029i \(-0.851770\pi\)
0.0578882 0.998323i \(-0.481563\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.00000 5.19615i −0.514496 0.891133i
\(35\) −6.00000 5.19615i −1.01419 0.878310i
\(36\) 0 0
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 2.50000 0.866025i 0.334077 0.115728i
\(57\) 0 0
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) −7.00000 −0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) −6.00000 5.19615i −0.717137 0.621059i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 5.00000 8.66025i 0.581238 1.00673i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0 0
\(85\) −9.00000 + 15.5885i −0.976187 + 1.69081i
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.19615i −0.104828 + 0.544705i
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) 6.50000 + 11.2583i 0.659975 + 1.14311i 0.980622 + 0.195911i \(0.0627665\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 0 0
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) −9.00000 −0.858116
\(111\) 0 0
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) 0 0
\(115\) 9.00000 15.5885i 0.839254 1.45363i
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) −12.0000 10.3923i −1.10004 0.952661i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.00000 −0.362143
\(123\) 0 0
\(124\) −7.00000 −0.628619
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 6.00000 0.526235
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 0 0
\(133\) −1.00000 + 5.19615i −0.0867110 + 0.450564i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i \(-0.860365\pi\)
0.820495 + 0.571654i \(0.193698\pi\)
\(140\) −6.00000 5.19615i −0.507093 0.439155i
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) −13.5000 + 23.3827i −1.12111 + 1.94183i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) 5.00000 8.66025i 0.410997 0.711868i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 0 0
\(154\) 1.50000 7.79423i 0.120873 0.628077i
\(155\) 10.5000 + 18.1865i 0.843380 + 1.46078i
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 5.00000 0.397779
\(159\) 0 0
\(160\) −1.50000 2.59808i −0.118585 0.205396i
\(161\) 12.0000 + 10.3923i 0.945732 + 0.819028i
\(162\) 0 0
\(163\) 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i \(-0.705245\pi\)
0.992665 + 0.120900i \(0.0385779\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 9.00000 15.5885i 0.696441 1.20627i −0.273252 0.961943i \(-0.588099\pi\)
0.969693 0.244328i \(-0.0785675\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −9.00000 + 15.5885i −0.690268 + 1.19558i
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −2.00000 + 10.3923i −0.151186 + 0.785584i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) −1.00000 + 5.19615i −0.0741249 + 0.385164i
\(183\) 0 0
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) −30.0000 −2.20564
\(186\) 0 0
\(187\) −18.0000 −1.31629
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 6.50000 + 11.2583i 0.466673 + 0.808301i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) −18.0000 15.5885i −1.26335 1.09410i
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 3.00000 + 5.19615i 0.207514 + 0.359425i
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 0 0
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 6.00000 10.3923i 0.409197 0.708749i
\(216\) 0 0
\(217\) −17.5000 + 6.06218i −1.18798 + 0.411527i
\(218\) 5.00000 + 8.66025i 0.338643 + 0.586546i
\(219\) 0 0
\(220\) −9.00000 −0.606780
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) 2.50000 0.866025i 0.167038 0.0578638i
\(225\) 0 0
\(226\) 0 0
\(227\) −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i \(-0.999189\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(228\) 0 0
\(229\) −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i \(-0.936876\pi\)
0.319582 0.947559i \(-0.396457\pi\)
\(230\) 9.00000 15.5885i 0.593442 1.02787i
\(231\) 0 0
\(232\) −4.50000 7.79423i −0.295439 0.511716i
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 0 0
\(235\) −18.0000 31.1769i −1.17419 2.03376i
\(236\) −3.00000 −0.195283
\(237\) 0 0
\(238\) −12.0000 10.3923i −0.777844 0.673633i
\(239\) −9.00000 + 15.5885i −0.582162 + 1.00833i 0.413061 + 0.910703i \(0.364460\pi\)
−0.995223 + 0.0976302i \(0.968874\pi\)
\(240\) 0 0
\(241\) −11.5000 + 19.9186i −0.740780 + 1.28307i 0.211360 + 0.977408i \(0.432211\pi\)
−0.952141 + 0.305661i \(0.901123\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) −19.5000 7.79423i −1.24581 0.497955i
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) −7.00000 −0.444500
\(249\) 0 0
\(250\) −3.00000 −0.189737
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) −1.00000 −0.0627456
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 5.00000 25.9808i 0.310685 1.61437i
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) 4.50000 7.79423i 0.276433 0.478796i
\(266\) −1.00000 + 5.19615i −0.0613139 + 0.318597i
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) 9.50000 16.4545i 0.577084 0.999539i −0.418728 0.908112i \(-0.637524\pi\)
0.995812 0.0914269i \(-0.0291428\pi\)
\(272\) −3.00000 5.19615i −0.181902 0.315063i
\(273\) 0 0
\(274\) −3.00000 + 5.19615i −0.181237 + 0.313911i
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) 2.00000 3.46410i 0.120168 0.208138i −0.799666 0.600446i \(-0.794990\pi\)
0.919834 + 0.392308i \(0.128323\pi\)
\(278\) −1.00000 + 1.73205i −0.0599760 + 0.103882i
\(279\) 0 0
\(280\) −6.00000 5.19615i −0.358569 0.310530i
\(281\) 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i \(0.0137362\pi\)
−0.462174 + 0.886789i \(0.652930\pi\)
\(282\) 0 0
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 3.00000 + 5.19615i 0.177394 + 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −13.5000 + 23.3827i −0.792747 + 1.37308i
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) 0 0
\(295\) 4.50000 + 7.79423i 0.262000 + 0.453798i
\(296\) 5.00000 8.66025i 0.290619 0.503367i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) 8.00000 + 6.92820i 0.461112 + 0.399335i
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) 0 0
\(307\) 26.0000 1.48390 0.741949 0.670456i \(-0.233902\pi\)
0.741949 + 0.670456i \(0.233902\pi\)
\(308\) 1.50000 7.79423i 0.0854704 0.444117i
\(309\) 0 0
\(310\) 10.5000 + 18.1865i 0.596360 + 1.03293i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 17.0000 0.960897 0.480448 0.877023i \(-0.340474\pi\)
0.480448 + 0.877023i \(0.340474\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) 21.0000 1.17948 0.589739 0.807594i \(-0.299231\pi\)
0.589739 + 0.807594i \(0.299231\pi\)
\(318\) 0 0
\(319\) −27.0000 −1.51171
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) 12.0000 + 10.3923i 0.668734 + 0.579141i
\(323\) 12.0000 0.667698
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) 5.00000 8.66025i 0.276924 0.479647i
\(327\) 0 0
\(328\) 0 0
\(329\) 30.0000 10.3923i 1.65395 0.572946i
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) 0 0
\(334\) 9.00000 15.5885i 0.492458 0.852962i
\(335\) −3.00000 5.19615i −0.163908 0.283896i
\(336\) 0 0
\(337\) −2.50000 + 4.33013i −0.136184 + 0.235877i −0.926049 0.377403i \(-0.876817\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) −10.5000 + 18.1865i −0.568607 + 0.984856i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 0 0
\(349\) −7.00000 12.1244i −0.374701 0.649002i 0.615581 0.788074i \(-0.288921\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) −2.00000 + 10.3923i −0.106904 + 0.555492i
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) −15.0000 + 25.9808i −0.791670 + 1.37121i 0.133263 + 0.991081i \(0.457455\pi\)
−0.924932 + 0.380131i \(0.875879\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 20.0000 1.05118
\(363\) 0 0
\(364\) −1.00000 + 5.19615i −0.0524142 + 0.272352i
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) 18.5000 32.0429i 0.965692 1.67263i 0.257948 0.966159i \(-0.416954\pi\)
0.707744 0.706469i \(-0.249713\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 0 0
\(370\) −30.0000 −1.55963
\(371\) 6.00000 + 5.19615i 0.311504 + 0.269771i
\(372\) 0 0
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) −18.0000 −0.930758
\(375\) 0 0
\(376\) 12.0000 0.618853
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 6.00000 0.307794
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) −15.0000 25.9808i −0.766464 1.32755i −0.939469 0.342634i \(-0.888681\pi\)
0.173005 0.984921i \(-0.444652\pi\)
\(384\) 0 0
\(385\) −22.5000 + 7.79423i −1.14671 + 0.397231i
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) 6.50000 + 11.2583i 0.329988 + 0.571555i
\(389\) 15.0000 25.9808i 0.760530 1.31728i −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) 0 0
\(391\) 18.0000 31.1769i 0.910299 1.57668i
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) −7.50000 12.9904i −0.377366 0.653617i
\(396\) 0 0
\(397\) −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i \(-0.897673\pi\)
0.748017 + 0.663679i \(0.231006\pi\)
\(398\) −4.00000 6.92820i −0.200502 0.347279i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) 0 0
\(403\) 7.00000 12.1244i 0.348695 0.603957i
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) 0 0
\(406\) −18.0000 15.5885i −0.893325 0.773642i
\(407\) −15.0000 25.9808i −0.743522 1.28782i
\(408\) 0 0
\(409\) 11.0000 0.543915 0.271957 0.962309i \(-0.412329\pi\)
0.271957 + 0.962309i \(0.412329\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 + 13.8564i 0.394132 + 0.682656i
\(413\) −7.50000 + 2.59808i −0.369051 + 0.127843i
\(414\) 0 0
\(415\) −13.5000 + 23.3827i −0.662689 + 1.14781i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 3.00000 + 5.19615i 0.146735 + 0.254152i
\(419\) 18.0000 31.1769i 0.879358 1.52309i 0.0273103 0.999627i \(-0.491306\pi\)
0.852047 0.523465i \(-0.175361\pi\)
\(420\) 0 0
\(421\) −4.00000 6.92820i −0.194948 0.337660i 0.751935 0.659237i \(-0.229121\pi\)
−0.946883 + 0.321577i \(0.895787\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) 0 0
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 24.0000 1.16417
\(426\) 0 0
\(427\) −10.0000 + 3.46410i −0.483934 + 0.167640i
\(428\) −1.50000 + 2.59808i −0.0725052 + 0.125583i
\(429\) 0 0
\(430\) 6.00000 10.3923i 0.289346 0.501161i
\(431\) −12.0000 20.7846i −0.578020 1.00116i −0.995706 0.0925683i \(-0.970492\pi\)
0.417687 0.908591i \(-0.362841\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) −17.5000 + 6.06218i −0.840027 + 0.290994i
\(435\) 0 0
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) −12.0000 −0.574038
\(438\) 0 0
\(439\) −19.0000 −0.906821 −0.453410 0.891302i \(-0.649793\pi\)
−0.453410 + 0.891302i \(0.649793\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 0 0
\(445\) −18.0000 −0.853282
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −7.50000 + 12.9904i −0.351992 + 0.609669i
\(455\) 15.0000 5.19615i 0.703211 0.243599i
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) −10.0000 17.3205i −0.467269 0.809334i
\(459\) 0 0
\(460\) 9.00000 15.5885i 0.419627 0.726816i
\(461\) −9.00000 15.5885i −0.419172 0.726027i 0.576685 0.816967i \(-0.304346\pi\)
−0.995856 + 0.0909401i \(0.971013\pi\)
\(462\) 0 0
\(463\) 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i \(-0.803704\pi\)
0.908750 + 0.417340i \(0.137038\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 0 0
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) −18.0000 31.1769i −0.830278 1.43808i
\(471\) 0 0
\(472\) −3.00000 −0.138086
\(473\) 12.0000 0.551761
\(474\) 0 0
\(475\) −4.00000 6.92820i −0.183533 0.317888i
\(476\) −12.0000 10.3923i −0.550019 0.476331i
\(477\) 0 0
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) 10.0000 + 17.3205i 0.455961 + 0.789747i
\(482\) −11.5000 + 19.9186i −0.523811 + 0.907267i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 19.5000 33.7750i 0.885449 1.53364i
\(486\) 0 0
\(487\) −5.50000 9.52628i −0.249229 0.431677i 0.714083 0.700061i \(-0.246844\pi\)
−0.963312 + 0.268384i \(0.913510\pi\)
\(488\) −4.00000 −0.181071
\(489\) 0 0
\(490\) −19.5000 7.79423i −0.880920 0.352107i
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −27.0000 + 46.7654i −1.21602 + 2.10621i
\(494\) −2.00000 3.46410i −0.0899843 0.155857i
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) 0 0
\(498\) 0 0
\(499\) −19.0000 32.9090i −0.850557 1.47321i −0.880707 0.473662i \(-0.842932\pi\)
0.0301498 0.999545i \(-0.490402\pi\)
\(500\) −3.00000 −0.134164
\(501\) 0 0
\(502\) 9.00000 0.401690
\(503\) 18.0000 0.802580 0.401290 0.915951i \(-0.368562\pi\)
0.401290 + 0.915951i \(0.368562\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 18.0000 0.800198
\(507\) 0 0
\(508\) −1.00000 −0.0443678
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) −4.00000 3.46410i −0.176950 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 24.0000 41.5692i 1.05757 1.83176i
\(516\) 0 0
\(517\) 18.0000 31.1769i 0.791639 1.37116i
\(518\) 5.00000 25.9808i 0.219687 1.14153i
\(519\) 0 0
\(520\) 6.00000 0.263117
\(521\) −12.0000 20.7846i −0.525730 0.910590i −0.999551 0.0299693i \(-0.990459\pi\)
0.473821 0.880621i \(-0.342874\pi\)
\(522\) 0 0
\(523\) −13.0000 + 22.5167i −0.568450 + 0.984585i 0.428269 + 0.903651i \(0.359124\pi\)
−0.996719 + 0.0809336i \(0.974210\pi\)
\(524\) 7.50000 + 12.9904i 0.327639 + 0.567487i
\(525\) 0 0
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) 21.0000 + 36.3731i 0.914774 + 1.58444i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) −1.00000 + 5.19615i −0.0433555 + 0.225282i
\(533\) 0 0
\(534\) 0 0
\(535\) 9.00000 0.389104
\(536\) 2.00000 0.0863868
\(537\) 0 0
\(538\) 1.50000 + 2.59808i 0.0646696 + 0.112011i
\(539\) −3.00000 20.7846i −0.129219 0.895257i
\(540\) 0 0
\(541\) 8.00000 13.8564i 0.343947 0.595733i −0.641215 0.767361i \(-0.721569\pi\)
0.985162 + 0.171628i \(0.0549027\pi\)
\(542\) 9.50000 16.4545i 0.408060 0.706781i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) 15.0000 25.9808i 0.642529 1.11289i
\(546\) 0 0
\(547\) −7.00000 12.1244i −0.299298 0.518400i 0.676677 0.736280i \(-0.263419\pi\)
−0.975976 + 0.217880i \(0.930086\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) 0 0
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 18.0000 0.766826
\(552\) 0 0
\(553\) 12.5000 4.33013i 0.531554 0.184136i
\(554\) 2.00000 3.46410i 0.0849719 0.147176i
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −7.50000 12.9904i −0.317785 0.550420i 0.662240 0.749291i \(-0.269606\pi\)
−0.980026 + 0.198871i \(0.936272\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) −6.00000 5.19615i −0.253546 0.219578i
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) 0 0
\(575\) −24.0000 −1.00087
\(576\) 0 0
\(577\) 0.500000 + 0.866025i 0.0208153 + 0.0360531i 0.876245 0.481865i \(-0.160040\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) −13.5000 + 23.3827i −0.560557 + 0.970913i
\(581\) −18.0000 15.5885i −0.746766 0.646718i
\(582\) 0 0
\(583\) 9.00000 0.372742
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) −13.5000 23.3827i −0.557205 0.965107i −0.997728 0.0673658i \(-0.978541\pi\)
0.440524 0.897741i \(-0.354793\pi\)
\(588\) 0 0
\(589\) 7.00000 12.1244i 0.288430 0.499575i
\(590\) 4.50000 + 7.79423i 0.185262 + 0.320883i
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) −15.0000 + 25.9808i −0.615976 + 1.06690i 0.374236 + 0.927333i \(0.377905\pi\)
−0.990212 + 0.139569i \(0.955428\pi\)
\(594\) 0 0
\(595\) −9.00000 + 46.7654i −0.368964 + 1.91719i
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 0 0
\(598\) −12.0000 −0.490716
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −11.5000 19.9186i −0.469095 0.812496i 0.530281 0.847822i \(-0.322086\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 8.00000 + 6.92820i 0.326056 + 0.282372i
\(603\) 0 0
\(604\) −2.50000 + 4.33013i −0.101724 + 0.176190i
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) 6.50000 + 11.2583i 0.263827 + 0.456962i 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) −1.00000 + 1.73205i −0.0405554 + 0.0702439i
\(609\) 0 0
\(610\) 6.00000 + 10.3923i 0.242933 + 0.420772i
\(611\) −12.0000 + 20.7846i −0.485468 + 0.840855i
\(612\) 0 0
\(613\) −13.0000 22.5167i −0.525065 0.909439i −0.999574 0.0291886i \(-0.990708\pi\)
0.474509 0.880251i \(-0.342626\pi\)
\(614\) 26.0000 1.04927
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) −18.0000 + 31.1769i −0.724653 + 1.25514i 0.234464 + 0.972125i \(0.424666\pi\)
−0.959117 + 0.283011i \(0.908667\pi\)
\(618\) 0 0
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 10.5000 + 18.1865i 0.421690 + 0.730389i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 3.00000 15.5885i 0.120192 0.624538i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 17.0000 0.679457
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 5.00000 0.198889
\(633\) 0 0
\(634\) 21.0000 0.834017
\(635\) 1.50000 + 2.59808i 0.0595257 + 0.103102i
\(636\) 0 0
\(637\) 2.00000 + 13.8564i 0.0792429 + 0.549011i
\(638\) −27.0000 −1.06894
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 6.00000 10.3923i 0.236986 0.410471i −0.722862 0.690992i \(-0.757174\pi\)
0.959848 + 0.280521i \(0.0905072\pi\)
\(642\) 0 0
\(643\) −19.0000 + 32.9090i −0.749287 + 1.29780i 0.198878 + 0.980024i \(0.436270\pi\)
−0.948165 + 0.317779i \(0.897063\pi\)
\(644\) 12.0000 + 10.3923i 0.472866 + 0.409514i
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) 0 0
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) −4.00000 6.92820i −0.156893 0.271746i
\(651\) 0 0
\(652\) 5.00000 8.66025i 0.195815 0.339162i
\(653\) −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i \(-0.890346\pi\)
0.178154 0.984003i \(-0.442987\pi\)
\(654\) 0 0
\(655\) 22.5000 38.9711i 0.879148 1.52273i
\(656\) 0 0
\(657\) 0 0
\(658\) 30.0000 10.3923i 1.16952 0.405134i
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 8.00000 0.310929
\(663\) 0 0
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 15.0000 5.19615i 0.581675 0.201498i
\(666\) 0 0
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 9.00000 15.5885i 0.348220 0.603136i
\(669\) 0 0
\(670\) −3.00000 5.19615i −0.115900 0.200745i
\(671\) −6.00000 + 10.3923i −0.231627 + 0.401190i
\(672\) 0 0
\(673\) −8.50000 14.7224i −0.327651 0.567508i 0.654394 0.756153i \(-0.272924\pi\)
−0.982045 + 0.188645i \(0.939590\pi\)
\(674\) −2.50000 + 4.33013i −0.0962964 + 0.166790i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −33.0000 −1.26829 −0.634147 0.773213i \(-0.718648\pi\)
−0.634147 + 0.773213i \(0.718648\pi\)
\(678\) 0 0
\(679\) 26.0000 + 22.5167i 0.997788 + 0.864110i
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) 0 0
\(682\) −10.5000 + 18.1865i −0.402066 + 0.696398i
\(683\) −25.5000 44.1673i −0.975730 1.69001i −0.677503 0.735520i \(-0.736938\pi\)
−0.298227 0.954495i \(-0.596395\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 10.0000 15.5885i 0.381802 0.595170i
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 32.0000 1.21734 0.608669 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 6.00000 0.227593
\(696\) 0 0
\(697\) 0 0
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 0 0
\(700\) −2.00000 + 10.3923i −0.0755929 + 0.392792i
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) 10.0000 + 17.3205i 0.377157 + 0.653255i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) −3.00000 + 15.5885i −0.112827 + 0.586264i
\(708\) 0 0
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −21.0000 36.3731i −0.786456 1.36218i
\(714\) 0 0
\(715\) 9.00000 15.5885i 0.336581 0.582975i
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) −15.0000 + 25.9808i −0.559795 + 0.969593i
\(719\) 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i \(-0.546936\pi\)
0.930087 0.367338i \(-0.119731\pi\)
\(720\) 0 0
\(721\) 32.0000 + 27.7128i 1.19174 + 1.03208i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) 0 0
\(724\) 20.0000 0.743294
\(725\) 36.0000 1.33701
\(726\) 0 0
\(727\) 15.5000 + 26.8468i 0.574863 + 0.995692i 0.996056 + 0.0887213i \(0.0282781\pi\)
−0.421193 + 0.906971i \(0.638389\pi\)
\(728\) −1.00000 + 5.19615i −0.0370625 + 0.192582i
\(729\) 0 0
\(730\) −3.00000 + 5.19615i −0.111035 + 0.192318i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) −10.0000 17.3205i −0.369358 0.639748i 0.620107 0.784517i \(-0.287089\pi\)
−0.989465 + 0.144770i \(0.953756\pi\)
\(734\) 18.5000 32.0429i 0.682847 1.18273i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 3.00000 5.19615i 0.110506 0.191403i
\(738\) 0 0
\(739\) −13.0000 22.5167i −0.478213 0.828289i 0.521475 0.853266i \(-0.325382\pi\)
−0.999688 + 0.0249776i \(0.992049\pi\)
\(740\) −30.0000 −1.10282
\(741\) 0 0
\(742\) 6.00000 + 5.19615i 0.220267 + 0.190757i
\(743\) 27.0000 46.7654i 0.990534 1.71566i 0.376389 0.926462i \(-0.377166\pi\)
0.614145 0.789193i \(-0.289501\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 2.00000 + 3.46410i 0.0732252 + 0.126830i
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) −1.50000 + 7.79423i −0.0548088 + 0.284795i
\(750\) 0 0
\(751\) −11.5000 19.9186i −0.419641 0.726839i 0.576262 0.817265i \(-0.304511\pi\)
−0.995903 + 0.0904254i \(0.971177\pi\)
\(752\) 12.0000 0.437595
\(753\) 0 0
\(754\) 18.0000 0.655521
\(755\) 15.0000 0.545906
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −28.0000 −1.01701
\(759\) 0 0
\(760\) 6.00000 0.217643
\(761\) 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 0 0
\(763\) 20.0000 + 17.3205i 0.724049 + 0.627044i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −15.0000 25.9808i −0.541972 0.938723i
\(767\) 3.00000 5.19615i 0.108324 0.187622i
\(768\) 0 0
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) −22.5000 + 7.79423i −0.810844 + 0.280885i
\(771\) 0 0
\(772\) −7.00000 −0.251936
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) 0 0
\(775\) 14.0000 24.2487i 0.502895 0.871039i
\(776\) 6.50000 + 11.2583i 0.233336 + 0.404151i
\(777\) 0 0
\(778\) 15.0000 25.9808i 0.537776 0.931455i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 18.0000 31.1769i 0.643679 1.11488i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 6.00000 + 10.3923i 0.214149 + 0.370917i
\(786\) 0 0
\(787\) −16.0000 −0.570338 −0.285169 0.958477i \(-0.592050\pi\)
−0.285169 + 0.958477i \(0.592050\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) −7.50000 12.9904i −0.266838 0.462177i
\(791\) 0 0
\(792\) 0 0
\(793\) 4.00000 6.92820i 0.142044 0.246028i
\(794\) −4.00000 + 6.92820i −0.141955 + 0.245873i
\(795\) 0 0
\(796\) −4.00000 6.92820i −0.141776 0.245564i
\(797\) −13.5000 + 23.3827i −0.478195 + 0.828257i −0.999687 0.0249984i \(-0.992042\pi\)
0.521493 + 0.853256i \(0.325375\pi\)
\(798\) 0 0
\(799\) −36.0000 62.3538i −1.27359 2.20592i
\(800\) −2.00000 + 3.46410i −0.0707107 + 0.122474i
\(801\) 0 0
\(802\) 12.0000 + 20.7846i 0.423735 + 0.733930i
\(803\) −6.00000 −0.211735
\(804\) 0 0
\(805\) 9.00000 46.7654i 0.317208 1.64826i
\(806\) 7.00000 12.1244i 0.246564 0.427062i
\(807\) 0 0
\(808\) −3.00000 + 5.19615i −0.105540 + 0.182800i
\(809\) 6.00000 + 10.3923i 0.210949 + 0.365374i 0.952012 0.306062i \(-0.0990113\pi\)
−0.741063 + 0.671436i \(0.765678\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) −18.0000 15.5885i −0.631676 0.547048i
\(813\) 0 0
\(814\) −15.0000 25.9808i −0.525750 0.910625i
\(815\) −30.0000 −1.05085
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 11.0000 0.384606
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 −0.523504 −0.261752 0.965135i \(-0.584300\pi\)
−0.261752 + 0.965135i \(0.584300\pi\)
\(822\) 0 0
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 8.00000 + 13.8564i 0.278693 + 0.482711i
\(825\) 0 0
\(826\) −7.50000 + 2.59808i −0.260958 + 0.0903986i
\(827\) 9.00000 0.312961 0.156480 0.987681i \(-0.449985\pi\)
0.156480 + 0.987681i \(0.449985\pi\)
\(828\) 0 0
\(829\) −1.00000 1.73205i −0.0347314 0.0601566i 0.848137 0.529777i \(-0.177724\pi\)
−0.882869 + 0.469620i \(0.844391\pi\)
\(830\) −13.5000 + 23.3827i −0.468592 + 0.811625i
\(831\) 0 0
\(832\) −1.00000 + 1.73205i −0.0346688 + 0.0600481i
\(833\) −39.0000 15.5885i −1.35127 0.540108i
\(834\) 0 0
\(835\) −54.0000 −1.86875
\(836\) 3.00000 + 5.19615i 0.103757 + 0.179713i
\(837\) 0 0
\(838\) 18.0000 31.1769i 0.621800 1.07699i
\(839\) 27.0000 + 46.7654i 0.932144 + 1.61452i 0.779650 + 0.626215i \(0.215397\pi\)
0.152493 + 0.988304i \(0.451270\pi\)
\(840\) 0 0
\(841\) −26.0000 + 45.0333i −0.896552 + 1.55287i
\(842\) −4.00000 6.92820i −0.137849 0.238762i
\(843\) 0 0
\(844\) 8.00000 13.8564i 0.275371 0.476957i
\(845\) 13.5000 23.3827i 0.464414 0.804389i
\(846\) 0 0
\(847\) 4.00000 + 3.46410i 0.137442 + 0.119028i
\(848\) 1.50000 + 2.59808i 0.0515102 + 0.0892183i
\(849\) 0 0
\(850\) 24.0000 0.823193
\(851\) 60.0000 2.05677
\(852\) 0 0
\(853\) 23.0000 + 39.8372i 0.787505 + 1.36400i 0.927491 + 0.373845i \(0.121961\pi\)
−0.139986 + 0.990153i \(0.544706\pi\)
\(854\) −10.0000 + 3.46410i −0.342193 + 0.118539i
\(855\) 0 0
\(856\) −1.50000 + 2.59808i −0.0512689 + 0.0888004i
\(857\) 6.00000 10.3923i 0.204956 0.354994i −0.745163 0.666883i \(-0.767628\pi\)
0.950119 + 0.311888i \(0.100962\pi\)
\(858\) 0 0
\(859\) 8.00000 + 13.8564i 0.272956 + 0.472774i 0.969618 0.244626i \(-0.0786652\pi\)
−0.696661 + 0.717400i \(0.745332\pi\)
\(860\) 6.00000 10.3923i 0.204598 0.354375i
\(861\) 0 0
\(862\) −12.0000 20.7846i −0.408722 0.707927i
\(863\) 3.00000 5.19615i 0.102121 0.176879i −0.810437 0.585826i \(-0.800770\pi\)
0.912558 + 0.408946i \(0.134104\pi\)
\(864\) 0 0
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) 26.0000 0.883516
\(867\) 0 0
\(868\) −17.5000 + 6.06218i −0.593989 + 0.205764i
\(869\) 7.50000 12.9904i 0.254420 0.440668i
\(870\) 0 0
\(871\) −2.00000 + 3.46410i −0.0677674 + 0.117377i
\(872\) 5.00000 + 8.66025i 0.169321 + 0.293273i
\(873\) 0 0
\(874\) −12.0000 −0.405906
\(875\) −7.50000 + 2.59808i −0.253546 + 0.0878310i
\(876\) 0 0
\(877\) −28.0000 48.4974i −0.945493 1.63764i −0.754761 0.655999i \(-0.772247\pi\)
−0.190731 0.981642i \(-0.561086\pi\)
\(878\) −19.0000 −0.641219
\(879\) 0 0
\(880\) −9.00000 −0.303390
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) −15.0000 −0.503935
\(887\) 3.00000 + 5.19615i 0.100730 + 0.174470i 0.911986 0.410222i \(-0.134549\pi\)
−0.811256 + 0.584692i \(0.801215\pi\)
\(888\) 0 0
\(889\) −2.50000 + 0.866025i −0.0838473 + 0.0290456i
\(890\) −18.0000 −0.603361
\(891\) 0 0
\(892\) 0.500000 + 0.866025i 0.0167412 + 0.0289967i
\(893\) −12.0000 + 20.7846i −0.401565 + 0.695530i
\(894\) 0 0
\(895\) 18.0000 31.1769i 0.601674 1.04213i
\(896\) 2.50000 0.866025i 0.0835191 0.0289319i
\(897\) 0 0
\(898\) 18.0000 0.600668
\(899\) 31.5000 + 54.5596i 1.05058 + 1.81966i
\(900\) 0 0
\(901\) 9.00000 15.5885i 0.299833 0.519327i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −30.0000 51.9615i −0.997234 1.72726i
\(906\) 0 0
\(907\) −25.0000 + 43.3013i −0.830111 + 1.43780i 0.0678380 + 0.997696i \(0.478390\pi\)
−0.897949 + 0.440099i \(0.854943\pi\)
\(908\) −7.50000 + 12.9904i −0.248896 + 0.431101i
\(909\) 0 0
\(910\) 15.0000 5.19615i 0.497245 0.172251i
\(911\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(912\) 0 0
\(913\) −27.0000 −0.893570
\(914\) −13.0000 −0.430002
\(915\) 0 0
\(916\) −10.0000 17.3205i −0.330409 0.572286i
\(917\) 30.0000 + 25.9808i 0.990687 + 0.857960i
\(918\) 0 0
\(919\) 14.0000 24.2487i 0.461817 0.799891i −0.537234 0.843433i \(-0.680531\pi\)
0.999052 + 0.0435419i \(0.0138642\pi\)
\(920\) 9.00000 15.5885i 0.296721 0.513936i
\(921\) 0 0
\(922\) −9.00000 15.5885i −0.296399 0.513378i
\(923\) 0 0
\(924\) 0 0
\(925\) 20.0000 + 34.6410i 0.657596 + 1.13899i
\(926\) 2.00000 3.46410i 0.0657241 0.113837i
\(927\) 0 0
\(928\) −4.50000 7.79423i −0.147720 0.255858i
\(929\) −24.0000 −0.787414 −0.393707 0.919236i \(-0.628808\pi\)
−0.393707 + 0.919236i \(0.628808\pi\)
\(930\) 0 0
\(931\) 2.00000 + 13.8564i 0.0655474 + 0.454125i
\(932\) 3.00000 5.19615i 0.0982683 0.170206i
\(933\) 0 0
\(934\) −6.00000 + 10.3923i −0.196326 + 0.340047i
\(935\) 27.0000 + 46.7654i 0.882994 + 1.52939i
\(936\) 0 0
\(937\) −37.0000 −1.20874 −0.604369 0.796705i \(-0.706575\pi\)
−0.604369 + 0.796705i \(0.706575\pi\)
\(938\) 5.00000 1.73205i 0.163256 0.0565535i
\(939\) 0 0
\(940\) −18.0000 31.1769i −0.587095 1.01688i
\(941\) 15.0000 0.488986 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 4.00000 0.129845
\(950\) −4.00000 6.92820i −0.129777 0.224781i
\(951\) 0 0
\(952\) −12.0000 10.3923i −0.388922 0.336817i
\(953\) −36.0000 −1.16615 −0.583077 0.812417i \(-0.698151\pi\)
−0.583077 + 0.812417i \(0.698151\pi\)
\(954\) 0 0
\(955\) −18.0000 31.1769i −0.582466 1.00886i
\(956\) −9.00000 + 15.5885i −0.291081 + 0.504167i
\(957\) 0 0
\(958\) −12.0000 + 20.7846i −0.387702 + 0.671520i
\(959\) −3.00000 + 15.5885i −0.0968751 + 0.503378i
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 10.0000 + 17.3205i 0.322413 + 0.558436i
\(963\) 0 0
\(964\) −11.5000 + 19.9186i −0.370390 + 0.641534i
\(965\) 10.5000 + 18.1865i 0.338007 + 0.585445i
\(966\) 0 0
\(967\) −14.5000 + 25.1147i −0.466289 + 0.807635i −0.999259 0.0384986i \(-0.987742\pi\)
0.532970 + 0.846134i \(0.321076\pi\)
\(968\) 1.00000 + 1.73205i 0.0321412 + 0.0556702i
\(969\) 0 0
\(970\) 19.5000 33.7750i 0.626107 1.08445i
\(971\) −19.5000 + 33.7750i −0.625785 + 1.08389i 0.362604 + 0.931943i \(0.381888\pi\)
−0.988389 + 0.151948i \(0.951445\pi\)
\(972\) 0 0
\(973\) −1.00000 + 5.19615i −0.0320585 + 0.166581i
\(974\) −5.50000 9.52628i −0.176231 0.305242i
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) −12.0000 −0.383914 −0.191957 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) 0 0
\(979\) −9.00000 15.5885i −0.287641 0.498209i
\(980\) −19.5000 7.79423i −0.622905 0.248978i
\(981\) 0 0
\(982\) −4.50000 + 7.79423i −0.143601 + 0.248724i
\(983\) −12.0000 + 20.7846i −0.382741 + 0.662926i −0.991453 0.130465i \(-0.958353\pi\)
0.608712 + 0.793391i \(0.291686\pi\)
\(984\) 0 0
\(985\) 27.0000 + 46.7654i 0.860292 + 1.49007i
\(986\) −27.0000 + 46.7654i −0.859855 + 1.48931i
\(987\) 0 0
\(988\) −2.00000 3.46410i −0.0636285 0.110208i
\(989\) −12.0000 + 20.7846i −0.381578 + 0.660912i
\(990\) 0 0
\(991\) 9.50000 + 16.4545i 0.301777 + 0.522694i 0.976539 0.215342i \(-0.0690867\pi\)
−0.674761 + 0.738036i \(0.735753\pi\)
\(992\) −7.00000 −0.222250
\(993\) 0 0
\(994\) 0 0
\(995\) −12.0000 + 20.7846i −0.380426 + 0.658916i
\(996\) 0 0
\(997\) 11.0000 19.0526i 0.348373 0.603401i −0.637587 0.770378i \(-0.720067\pi\)
0.985961 + 0.166978i \(0.0534008\pi\)
\(998\) −19.0000 32.9090i −0.601434 1.04172i
\(999\) 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 1134.2.e.k.919.1 2
3.2 odd 2 1134.2.e.g.919.1 2
7.4 even 3 1134.2.h.f.109.1 2
9.2 odd 6 1134.2.h.j.541.1 2
9.4 even 3 126.2.g.a.37.1 2
9.5 odd 6 126.2.g.d.37.1 yes 2
9.7 even 3 1134.2.h.f.541.1 2
21.11 odd 6 1134.2.h.j.109.1 2
36.23 even 6 1008.2.s.o.289.1 2
36.31 odd 6 1008.2.s.b.289.1 2
63.4 even 3 126.2.g.a.109.1 yes 2
63.5 even 6 882.2.a.e.1.1 1
63.11 odd 6 1134.2.e.g.865.1 2
63.13 odd 6 882.2.g.e.667.1 2
63.23 odd 6 882.2.a.a.1.1 1
63.25 even 3 inner 1134.2.e.k.865.1 2
63.31 odd 6 882.2.g.e.361.1 2
63.32 odd 6 126.2.g.d.109.1 yes 2
63.40 odd 6 882.2.a.h.1.1 1
63.41 even 6 882.2.g.g.667.1 2
63.58 even 3 882.2.a.j.1.1 1
63.59 even 6 882.2.g.g.361.1 2
252.23 even 6 7056.2.a.e.1.1 1
252.67 odd 6 1008.2.s.b.865.1 2
252.95 even 6 1008.2.s.o.865.1 2
252.103 even 6 7056.2.a.h.1.1 1
252.131 odd 6 7056.2.a.bx.1.1 1
252.247 odd 6 7056.2.a.by.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.g.a.37.1 2 9.4 even 3
126.2.g.a.109.1 yes 2 63.4 even 3
126.2.g.d.37.1 yes 2 9.5 odd 6
126.2.g.d.109.1 yes 2 63.32 odd 6
882.2.a.a.1.1 1 63.23 odd 6
882.2.a.e.1.1 1 63.5 even 6
882.2.a.h.1.1 1 63.40 odd 6
882.2.a.j.1.1 1 63.58 even 3
882.2.g.e.361.1 2 63.31 odd 6
882.2.g.e.667.1 2 63.13 odd 6
882.2.g.g.361.1 2 63.59 even 6
882.2.g.g.667.1 2 63.41 even 6
1008.2.s.b.289.1 2 36.31 odd 6
1008.2.s.b.865.1 2 252.67 odd 6
1008.2.s.o.289.1 2 36.23 even 6
1008.2.s.o.865.1 2 252.95 even 6
1134.2.e.g.865.1 2 63.11 odd 6
1134.2.e.g.919.1 2 3.2 odd 2
1134.2.e.k.865.1 2 63.25 even 3 inner
1134.2.e.k.919.1 2 1.1 even 1 trivial
1134.2.h.f.109.1 2 7.4 even 3
1134.2.h.f.541.1 2 9.7 even 3
1134.2.h.j.109.1 2 21.11 odd 6
1134.2.h.j.541.1 2 9.2 odd 6
7056.2.a.e.1.1 1 252.23 even 6
7056.2.a.h.1.1 1 252.103 even 6
7056.2.a.bx.1.1 1 252.131 odd 6
7056.2.a.by.1.1 1 252.247 odd 6