Properties

Label 1170.2.bs.h.901.3
Level $1170$
Weight $2$
Character 1170.901
Analytic conductor $9.342$
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] = [1170,2,Mod(361,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1170.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.3
Root \(1.35234 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 1170.901
Dual form 1170.2.bs.h.361.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(-3.34233 - 1.35234i) q^{13} -2.70469 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.34233 + 3.08440i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-3.95042 + 6.84233i) q^{23} -1.00000 q^{25} +(-2.21837 - 2.84233i) q^{26} +(-2.34233 - 1.35234i) q^{28} +(1.24573 - 2.15767i) q^{29} +0.972638i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.35234 + 2.34233i) q^{35} +(-1.50000 - 0.866025i) q^{37} -6.16879 q^{38} +1.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(-4.84233 - 8.38716i) q^{43} -3.00000i q^{44} +(-6.84233 + 3.95042i) q^{46} +3.00000i q^{47} +(0.157671 - 0.273094i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-0.500000 - 3.57071i) q^{52} +2.70469 q^{53} +(-1.50000 + 2.59808i) q^{55} +(-1.35234 - 2.34233i) q^{56} +(2.15767 - 1.24573i) q^{58} +(6.65511 - 3.84233i) q^{59} +(-6.68466 - 11.5782i) q^{61} +(-0.486319 + 0.842329i) q^{62} -1.00000 q^{64} +(-1.35234 + 3.34233i) q^{65} +(-1.68466 - 0.972638i) q^{67} +2.70469i q^{70} +(-5.19615 + 3.00000i) q^{71} +6.92820i q^{73} +(-0.866025 - 1.50000i) q^{74} +(-5.34233 - 3.08440i) q^{76} +8.11407 q^{77} +5.68466 q^{79} +(0.866025 + 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} +15.3693i q^{83} -9.68466i q^{86} +(1.50000 - 2.59808i) q^{88} +(-4.05703 - 2.34233i) q^{89} +(9.65767 - 1.35234i) q^{91} -7.90084 q^{92} +(-1.50000 + 2.59808i) q^{94} +(3.08440 + 5.34233i) q^{95} +(-7.68466 + 4.43674i) q^{97} +(0.273094 - 0.157671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 6 q^{7} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 18 q^{19} - 12 q^{22} - 8 q^{25} + 6 q^{28} - 12 q^{37} + 8 q^{40} - 14 q^{43} - 30 q^{46} + 26 q^{49} - 4 q^{52} - 12 q^{55} + 42 q^{58} - 4 q^{61} - 8 q^{64} + 36 q^{67} - 18 q^{76} - 4 q^{79} + 24 q^{82} + 12 q^{88} + 102 q^{91} - 12 q^{94} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.34233 + 1.35234i −0.885317 + 0.511138i −0.872408 0.488779i \(-0.837443\pi\)
−0.0129093 + 0.999917i \(0.504109\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 0 0
\(13\) −3.34233 1.35234i −0.926995 0.375073i
\(14\) −2.70469 −0.722858
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −5.34233 + 3.08440i −1.22561 + 0.707609i −0.966109 0.258133i \(-0.916893\pi\)
−0.259505 + 0.965742i \(0.583559\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −3.95042 + 6.84233i −0.823720 + 1.42672i 0.0791743 + 0.996861i \(0.474772\pi\)
−0.902894 + 0.429863i \(0.858562\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −2.21837 2.84233i −0.435058 0.557427i
\(27\) 0 0
\(28\) −2.34233 1.35234i −0.442659 0.255569i
\(29\) 1.24573 2.15767i 0.231327 0.400669i −0.726872 0.686773i \(-0.759027\pi\)
0.958199 + 0.286103i \(0.0923601\pi\)
\(30\) 0 0
\(31\) 0.972638i 0.174691i 0.996178 + 0.0873455i \(0.0278384\pi\)
−0.996178 + 0.0873455i \(0.972162\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.35234 + 2.34233i 0.228588 + 0.395926i
\(36\) 0 0
\(37\) −1.50000 0.866025i −0.246598 0.142374i 0.371607 0.928390i \(-0.378807\pi\)
−0.618206 + 0.786016i \(0.712140\pi\)
\(38\) −6.16879 −1.00071
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 5.19615 + 3.00000i 0.811503 + 0.468521i 0.847477 0.530831i \(-0.178120\pi\)
−0.0359748 + 0.999353i \(0.511454\pi\)
\(42\) 0 0
\(43\) −4.84233 8.38716i −0.738448 1.27903i −0.953194 0.302360i \(-0.902226\pi\)
0.214746 0.976670i \(-0.431108\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) −6.84233 + 3.95042i −1.00885 + 0.582458i
\(47\) 3.00000i 0.437595i 0.975770 + 0.218797i \(0.0702134\pi\)
−0.975770 + 0.218797i \(0.929787\pi\)
\(48\) 0 0
\(49\) 0.157671 0.273094i 0.0225244 0.0390134i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 0 0
\(52\) −0.500000 3.57071i −0.0693375 0.495169i
\(53\) 2.70469 0.371518 0.185759 0.982595i \(-0.440526\pi\)
0.185759 + 0.982595i \(0.440526\pi\)
\(54\) 0 0
\(55\) −1.50000 + 2.59808i −0.202260 + 0.350325i
\(56\) −1.35234 2.34233i −0.180715 0.313007i
\(57\) 0 0
\(58\) 2.15767 1.24573i 0.283316 0.163573i
\(59\) 6.65511 3.84233i 0.866421 0.500229i 0.000264050 1.00000i \(-0.499916\pi\)
0.866157 + 0.499771i \(0.166583\pi\)
\(60\) 0 0
\(61\) −6.68466 11.5782i −0.855883 1.48243i −0.875824 0.482631i \(-0.839681\pi\)
0.0199408 0.999801i \(-0.493652\pi\)
\(62\) −0.486319 + 0.842329i −0.0617626 + 0.106976i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.35234 + 3.34233i −0.167738 + 0.414565i
\(66\) 0 0
\(67\) −1.68466 0.972638i −0.205814 0.118827i 0.393551 0.919303i \(-0.371247\pi\)
−0.599364 + 0.800476i \(0.704580\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 2.70469i 0.323272i
\(71\) −5.19615 + 3.00000i −0.616670 + 0.356034i −0.775571 0.631260i \(-0.782538\pi\)
0.158901 + 0.987294i \(0.449205\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −0.866025 1.50000i −0.100673 0.174371i
\(75\) 0 0
\(76\) −5.34233 3.08440i −0.612807 0.353804i
\(77\) 8.11407 0.924684
\(78\) 0 0
\(79\) 5.68466 0.639574 0.319787 0.947489i \(-0.396389\pi\)
0.319787 + 0.947489i \(0.396389\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) 15.3693i 1.68700i 0.537128 + 0.843501i \(0.319509\pi\)
−0.537128 + 0.843501i \(0.680491\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 9.68466i 1.04432i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −4.05703 2.34233i −0.430045 0.248286i 0.269321 0.963050i \(-0.413201\pi\)
−0.699366 + 0.714764i \(0.746534\pi\)
\(90\) 0 0
\(91\) 9.65767 1.35234i 1.01240 0.141764i
\(92\) −7.90084 −0.823720
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 3.08440 + 5.34233i 0.316452 + 0.548111i
\(96\) 0 0
\(97\) −7.68466 + 4.43674i −0.780259 + 0.450483i −0.836522 0.547933i \(-0.815415\pi\)
0.0562632 + 0.998416i \(0.482081\pi\)
\(98\) 0.273094 0.157671i 0.0275866 0.0159272i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 5.40938 9.36932i 0.538253 0.932282i −0.460745 0.887533i \(-0.652418\pi\)
0.998998 0.0447493i \(-0.0142489\pi\)
\(102\) 0 0
\(103\) −14.6847 −1.44692 −0.723461 0.690365i \(-0.757450\pi\)
−0.723461 + 0.690365i \(0.757450\pi\)
\(104\) 1.35234 3.34233i 0.132608 0.327742i
\(105\) 0 0
\(106\) 2.34233 + 1.35234i 0.227507 + 0.131351i
\(107\) 2.70469 4.68466i 0.261472 0.452883i −0.705161 0.709047i \(-0.749125\pi\)
0.966633 + 0.256164i \(0.0824587\pi\)
\(108\) 0 0
\(109\) 12.3376i 1.18173i 0.806772 + 0.590863i \(0.201213\pi\)
−0.806772 + 0.590863i \(0.798787\pi\)
\(110\) −2.59808 + 1.50000i −0.247717 + 0.143019i
\(111\) 0 0
\(112\) 2.70469i 0.255569i
\(113\) −1.24573 2.15767i −0.117189 0.202977i 0.801464 0.598043i \(-0.204055\pi\)
−0.918653 + 0.395067i \(0.870722\pi\)
\(114\) 0 0
\(115\) 6.84233 + 3.95042i 0.638050 + 0.368379i
\(116\) 2.49146 0.231327
\(117\) 0 0
\(118\) 7.68466 0.707430
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 13.3693i 1.21040i
\(123\) 0 0
\(124\) −0.842329 + 0.486319i −0.0756434 + 0.0436727i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −1.34233 + 2.32498i −0.119112 + 0.206309i −0.919416 0.393286i \(-0.871338\pi\)
0.800304 + 0.599595i \(0.204672\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.84233 + 2.21837i −0.249289 + 0.194564i
\(131\) 20.9978 1.83459 0.917295 0.398209i \(-0.130368\pi\)
0.917295 + 0.398209i \(0.130368\pi\)
\(132\) 0 0
\(133\) 8.34233 14.4493i 0.723372 1.25292i
\(134\) −0.972638 1.68466i −0.0840231 0.145532i
\(135\) 0 0
\(136\) 0 0
\(137\) 17.0474 9.84233i 1.45646 0.840887i 0.457624 0.889146i \(-0.348701\pi\)
0.998835 + 0.0482589i \(0.0153672\pi\)
\(138\) 0 0
\(139\) −4.65767 8.06732i −0.395058 0.684261i 0.598050 0.801459i \(-0.295942\pi\)
−0.993109 + 0.117197i \(0.962609\pi\)
\(140\) −1.35234 + 2.34233i −0.114294 + 0.197963i
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) 6.65511 + 8.52699i 0.556528 + 0.713063i
\(144\) 0 0
\(145\) −2.15767 1.24573i −0.179185 0.103452i
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) 0 0
\(148\) 1.73205i 0.142374i
\(149\) −8.93335 + 5.15767i −0.731848 + 0.422533i −0.819098 0.573654i \(-0.805526\pi\)
0.0872496 + 0.996186i \(0.472192\pi\)
\(150\) 0 0
\(151\) 14.2829i 1.16232i −0.813788 0.581161i \(-0.802599\pi\)
0.813788 0.581161i \(-0.197401\pi\)
\(152\) −3.08440 5.34233i −0.250177 0.433320i
\(153\) 0 0
\(154\) 7.02699 + 4.05703i 0.566251 + 0.326925i
\(155\) 0.972638 0.0781242
\(156\) 0 0
\(157\) 8.36932 0.667944 0.333972 0.942583i \(-0.391611\pi\)
0.333972 + 0.942583i \(0.391611\pi\)
\(158\) 4.92306 + 2.84233i 0.391658 + 0.226124i
\(159\) 0 0
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 21.3693i 1.68414i
\(162\) 0 0
\(163\) −15.8423 + 9.14657i −1.24087 + 0.716415i −0.969271 0.245996i \(-0.920885\pi\)
−0.271596 + 0.962411i \(0.587552\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 0 0
\(166\) −7.68466 + 13.3102i −0.596445 + 1.03307i
\(167\) 5.51599 + 3.18466i 0.426840 + 0.246436i 0.698000 0.716098i \(-0.254074\pi\)
−0.271159 + 0.962534i \(0.587407\pi\)
\(168\) 0 0
\(169\) 9.34233 + 9.03996i 0.718641 + 0.695382i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.84233 8.38716i 0.369224 0.639515i
\(173\) 4.05703 + 7.02699i 0.308451 + 0.534252i 0.978024 0.208494i \(-0.0668562\pi\)
−0.669573 + 0.742746i \(0.733523\pi\)
\(174\) 0 0
\(175\) 2.34233 1.35234i 0.177063 0.102228i
\(176\) 2.59808 1.50000i 0.195837 0.113067i
\(177\) 0 0
\(178\) −2.34233 4.05703i −0.175565 0.304087i
\(179\) −6.44188 + 11.1577i −0.481489 + 0.833963i −0.999774 0.0212443i \(-0.993237\pi\)
0.518285 + 0.855208i \(0.326571\pi\)
\(180\) 0 0
\(181\) 5.36932 0.399098 0.199549 0.979888i \(-0.436052\pi\)
0.199549 + 0.979888i \(0.436052\pi\)
\(182\) 9.03996 + 3.65767i 0.670086 + 0.271125i
\(183\) 0 0
\(184\) −6.84233 3.95042i −0.504423 0.291229i
\(185\) −0.866025 + 1.50000i −0.0636715 + 0.110282i
\(186\) 0 0
\(187\) 0 0
\(188\) −2.59808 + 1.50000i −0.189484 + 0.109399i
\(189\) 0 0
\(190\) 6.16879i 0.447531i
\(191\) −10.6055 18.3693i −0.767389 1.32916i −0.938974 0.343988i \(-0.888222\pi\)
0.171585 0.985169i \(-0.445111\pi\)
\(192\) 0 0
\(193\) 13.6847 + 7.90084i 0.985043 + 0.568715i 0.903789 0.427978i \(-0.140774\pi\)
0.0812543 + 0.996693i \(0.474107\pi\)
\(194\) −8.87348 −0.637079
\(195\) 0 0
\(196\) 0.315342 0.0225244
\(197\) −17.3673 10.0270i −1.23737 0.714393i −0.268811 0.963193i \(-0.586631\pi\)
−0.968555 + 0.248800i \(0.919964\pi\)
\(198\) 0 0
\(199\) 8.68466 + 15.0423i 0.615639 + 1.06632i 0.990272 + 0.139145i \(0.0444354\pi\)
−0.374633 + 0.927173i \(0.622231\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 9.36932 5.40938i 0.659223 0.380602i
\(203\) 6.73863i 0.472959i
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) −12.7173 7.34233i −0.886055 0.511564i
\(207\) 0 0
\(208\) 2.84233 2.21837i 0.197080 0.153816i
\(209\) 18.5064 1.28011
\(210\) 0 0
\(211\) 3.34233 5.78908i 0.230095 0.398537i −0.727741 0.685853i \(-0.759429\pi\)
0.957836 + 0.287316i \(0.0927628\pi\)
\(212\) 1.35234 + 2.34233i 0.0928794 + 0.160872i
\(213\) 0 0
\(214\) 4.68466 2.70469i 0.320237 0.184889i
\(215\) −8.38716 + 4.84233i −0.572000 + 0.330244i
\(216\) 0 0
\(217\) −1.31534 2.27824i −0.0892912 0.154657i
\(218\) −6.16879 + 10.6847i −0.417803 + 0.723656i
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) 0 0
\(223\) 6.65767 + 3.84381i 0.445831 + 0.257400i 0.706068 0.708144i \(-0.250467\pi\)
−0.260237 + 0.965545i \(0.583801\pi\)
\(224\) 1.35234 2.34233i 0.0903573 0.156503i
\(225\) 0 0
\(226\) 2.49146i 0.165730i
\(227\) −2.91791 + 1.68466i −0.193669 + 0.111815i −0.593699 0.804687i \(-0.702333\pi\)
0.400030 + 0.916502i \(0.369000\pi\)
\(228\) 0 0
\(229\) 26.1940i 1.73095i 0.500954 + 0.865474i \(0.332982\pi\)
−0.500954 + 0.865474i \(0.667018\pi\)
\(230\) 3.95042 + 6.84233i 0.260483 + 0.451170i
\(231\) 0 0
\(232\) 2.15767 + 1.24573i 0.141658 + 0.0817863i
\(233\) 12.8838 0.844044 0.422022 0.906586i \(-0.361321\pi\)
0.422022 + 0.906586i \(0.361321\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) 6.65511 + 3.84233i 0.433211 + 0.250114i
\(237\) 0 0
\(238\) 0 0
\(239\) 24.7386i 1.60021i 0.599861 + 0.800105i \(0.295223\pi\)
−0.599861 + 0.800105i \(0.704777\pi\)
\(240\) 0 0
\(241\) −5.81534 + 3.35749i −0.374599 + 0.216275i −0.675466 0.737391i \(-0.736057\pi\)
0.300867 + 0.953666i \(0.402724\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 6.68466 11.5782i 0.427941 0.741216i
\(245\) −0.273094 0.157671i −0.0174473 0.0100732i
\(246\) 0 0
\(247\) 22.0270 3.08440i 1.40154 0.196255i
\(248\) −0.972638 −0.0617626
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −2.59808 4.50000i −0.163989 0.284037i 0.772307 0.635250i \(-0.219103\pi\)
−0.936296 + 0.351212i \(0.885770\pi\)
\(252\) 0 0
\(253\) 20.5270 11.8513i 1.29052 0.745082i
\(254\) −2.32498 + 1.34233i −0.145882 + 0.0842252i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.6380 + 20.1577i −0.725961 + 1.25740i 0.232617 + 0.972569i \(0.425271\pi\)
−0.958577 + 0.284832i \(0.908062\pi\)
\(258\) 0 0
\(259\) 4.68466 0.291091
\(260\) −3.57071 + 0.500000i −0.221446 + 0.0310087i
\(261\) 0 0
\(262\) 18.1847 + 10.4989i 1.12345 + 0.648625i
\(263\) −15.9083 + 27.5540i −0.980947 + 1.69905i −0.322228 + 0.946662i \(0.604432\pi\)
−0.658719 + 0.752389i \(0.728901\pi\)
\(264\) 0 0
\(265\) 2.70469i 0.166148i
\(266\) 14.4493 8.34233i 0.885946 0.511501i
\(267\) 0 0
\(268\) 1.94528i 0.118827i
\(269\) −5.40938 9.36932i −0.329816 0.571257i 0.652659 0.757651i \(-0.273653\pi\)
−0.982475 + 0.186394i \(0.940320\pi\)
\(270\) 0 0
\(271\) 11.5270 + 6.65511i 0.700215 + 0.404269i 0.807427 0.589967i \(-0.200859\pi\)
−0.107213 + 0.994236i \(0.534193\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 19.6847 1.18919
\(275\) 2.59808 + 1.50000i 0.156670 + 0.0904534i
\(276\) 0 0
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 9.31534i 0.558697i
\(279\) 0 0
\(280\) −2.34233 + 1.35234i −0.139981 + 0.0808180i
\(281\) 24.7386i 1.47578i −0.674919 0.737892i \(-0.735822\pi\)
0.674919 0.737892i \(-0.264178\pi\)
\(282\) 0 0
\(283\) 6.52699 11.3051i 0.387989 0.672017i −0.604190 0.796840i \(-0.706503\pi\)
0.992179 + 0.124824i \(0.0398365\pi\)
\(284\) −5.19615 3.00000i −0.308335 0.178017i
\(285\) 0 0
\(286\) 1.50000 + 10.7121i 0.0886969 + 0.633422i
\(287\) −16.2281 −0.957916
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −1.24573 2.15767i −0.0731519 0.126703i
\(291\) 0 0
\(292\) −6.00000 + 3.46410i −0.351123 + 0.202721i
\(293\) −19.6455 + 11.3423i −1.14770 + 0.662626i −0.948326 0.317297i \(-0.897225\pi\)
−0.199376 + 0.979923i \(0.563891\pi\)
\(294\) 0 0
\(295\) −3.84233 6.65511i −0.223709 0.387475i
\(296\) 0.866025 1.50000i 0.0503367 0.0871857i
\(297\) 0 0
\(298\) −10.3153 −0.597552
\(299\) 22.4568 17.5270i 1.29871 1.01361i
\(300\) 0 0
\(301\) 22.6847 + 13.0970i 1.30752 + 0.754898i
\(302\) 7.14143 12.3693i 0.410943 0.711774i
\(303\) 0 0
\(304\) 6.16879i 0.353804i
\(305\) −11.5782 + 6.68466i −0.662964 + 0.382762i
\(306\) 0 0
\(307\) 14.2829i 0.815166i 0.913168 + 0.407583i \(0.133628\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 4.05703 + 7.02699i 0.231171 + 0.400400i
\(309\) 0 0
\(310\) 0.842329 + 0.486319i 0.0478411 + 0.0276211i
\(311\) 4.98293 0.282556 0.141278 0.989970i \(-0.454879\pi\)
0.141278 + 0.989970i \(0.454879\pi\)
\(312\) 0 0
\(313\) −5.36932 −0.303492 −0.151746 0.988420i \(-0.548490\pi\)
−0.151746 + 0.988420i \(0.548490\pi\)
\(314\) 7.24804 + 4.18466i 0.409031 + 0.236154i
\(315\) 0 0
\(316\) 2.84233 + 4.92306i 0.159894 + 0.276944i
\(317\) 29.4233i 1.65258i −0.563247 0.826288i \(-0.690448\pi\)
0.563247 0.826288i \(-0.309552\pi\)
\(318\) 0 0
\(319\) −6.47301 + 3.73720i −0.362419 + 0.209243i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) 10.6847 18.5064i 0.595433 1.03132i
\(323\) 0 0
\(324\) 0 0
\(325\) 3.34233 + 1.35234i 0.185399 + 0.0750146i
\(326\) −18.2931 −1.01316
\(327\) 0 0
\(328\) −3.00000 + 5.19615i −0.165647 + 0.286910i
\(329\) −4.05703 7.02699i −0.223671 0.387410i
\(330\) 0 0
\(331\) 8.05398 4.64996i 0.442687 0.255585i −0.262050 0.965054i \(-0.584399\pi\)
0.704737 + 0.709469i \(0.251065\pi\)
\(332\) −13.3102 + 7.68466i −0.730493 + 0.421750i
\(333\) 0 0
\(334\) 3.18466 + 5.51599i 0.174257 + 0.301822i
\(335\) −0.972638 + 1.68466i −0.0531409 + 0.0920427i
\(336\) 0 0
\(337\) −29.3693 −1.59985 −0.799924 0.600101i \(-0.795127\pi\)
−0.799924 + 0.600101i \(0.795127\pi\)
\(338\) 3.57071 + 12.5000i 0.194221 + 0.679910i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.45896 2.52699i 0.0790070 0.136844i
\(342\) 0 0
\(343\) 18.0799i 0.976224i
\(344\) 8.38716 4.84233i 0.452205 0.261081i
\(345\) 0 0
\(346\) 8.11407i 0.436215i
\(347\) −2.49146 4.31534i −0.133749 0.231660i 0.791370 0.611337i \(-0.209368\pi\)
−0.925119 + 0.379678i \(0.876035\pi\)
\(348\) 0 0
\(349\) −29.0540 16.7743i −1.55522 0.897909i −0.997703 0.0677460i \(-0.978419\pi\)
−0.557521 0.830163i \(-0.688247\pi\)
\(350\) 2.70469 0.144572
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 13.3102 + 7.68466i 0.708431 + 0.409013i 0.810480 0.585766i \(-0.199206\pi\)
−0.102049 + 0.994779i \(0.532540\pi\)
\(354\) 0 0
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) 4.68466i 0.248286i
\(357\) 0 0
\(358\) −11.1577 + 6.44188i −0.589701 + 0.340464i
\(359\) 2.63068i 0.138842i −0.997587 0.0694211i \(-0.977885\pi\)
0.997587 0.0694211i \(-0.0221152\pi\)
\(360\) 0 0
\(361\) 9.52699 16.5012i 0.501420 0.868486i
\(362\) 4.64996 + 2.68466i 0.244397 + 0.141103i
\(363\) 0 0
\(364\) 6.00000 + 7.68762i 0.314485 + 0.402941i
\(365\) 6.92820 0.362639
\(366\) 0 0
\(367\) −11.6847 + 20.2384i −0.609934 + 1.05644i 0.381317 + 0.924445i \(0.375471\pi\)
−0.991251 + 0.131992i \(0.957863\pi\)
\(368\) −3.95042 6.84233i −0.205930 0.356681i
\(369\) 0 0
\(370\) −1.50000 + 0.866025i −0.0779813 + 0.0450225i
\(371\) −6.33527 + 3.65767i −0.328911 + 0.189897i
\(372\) 0 0
\(373\) 0.526988 + 0.912769i 0.0272864 + 0.0472614i 0.879346 0.476183i \(-0.157980\pi\)
−0.852060 + 0.523445i \(0.824647\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) −7.08156 + 5.52699i −0.364719 + 0.284654i
\(378\) 0 0
\(379\) −0.288354 0.166481i −0.0148117 0.00855157i 0.492576 0.870270i \(-0.336055\pi\)
−0.507388 + 0.861718i \(0.669389\pi\)
\(380\) −3.08440 + 5.34233i −0.158226 + 0.274056i
\(381\) 0 0
\(382\) 21.2111i 1.08525i
\(383\) −6.65511 + 3.84233i −0.340060 + 0.196334i −0.660299 0.751003i \(-0.729570\pi\)
0.320238 + 0.947337i \(0.396237\pi\)
\(384\) 0 0
\(385\) 8.11407i 0.413531i
\(386\) 7.90084 + 13.6847i 0.402142 + 0.696531i
\(387\) 0 0
\(388\) −7.68466 4.43674i −0.390129 0.225241i
\(389\) −24.1290 −1.22339 −0.611694 0.791095i \(-0.709512\pi\)
−0.611694 + 0.791095i \(0.709512\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.273094 + 0.157671i 0.0137933 + 0.00796358i
\(393\) 0 0
\(394\) −10.0270 17.3673i −0.505152 0.874950i
\(395\) 5.68466i 0.286026i
\(396\) 0 0
\(397\) −30.1847 + 17.4271i −1.51492 + 0.874642i −0.515078 + 0.857143i \(0.672237\pi\)
−0.999847 + 0.0174986i \(0.994430\pi\)
\(398\) 17.3693i 0.870645i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −1.77879 1.02699i −0.0888288 0.0512853i 0.454928 0.890528i \(-0.349665\pi\)
−0.543756 + 0.839243i \(0.682998\pi\)
\(402\) 0 0
\(403\) 1.31534 3.25088i 0.0655218 0.161938i
\(404\) 10.8188 0.538253
\(405\) 0 0
\(406\) −3.36932 + 5.83583i −0.167216 + 0.289627i
\(407\) 2.59808 + 4.50000i 0.128782 + 0.223057i
\(408\) 0 0
\(409\) −11.7116 + 6.76172i −0.579104 + 0.334346i −0.760777 0.649013i \(-0.775182\pi\)
0.181673 + 0.983359i \(0.441849\pi\)
\(410\) 5.19615 3.00000i 0.256620 0.148159i
\(411\) 0 0
\(412\) −7.34233 12.7173i −0.361731 0.626536i
\(413\) −10.3923 + 18.0000i −0.511372 + 0.885722i
\(414\) 0 0
\(415\) 15.3693 0.754450
\(416\) 3.57071 0.500000i 0.175069 0.0245145i
\(417\) 0 0
\(418\) 16.0270 + 9.25319i 0.783906 + 0.452588i
\(419\) −0.213225 + 0.369317i −0.0104167 + 0.0180423i −0.871187 0.490952i \(-0.836649\pi\)
0.860770 + 0.508994i \(0.169982\pi\)
\(420\) 0 0
\(421\) 26.6204i 1.29740i −0.761044 0.648700i \(-0.775313\pi\)
0.761044 0.648700i \(-0.224687\pi\)
\(422\) 5.78908 3.34233i 0.281808 0.162702i
\(423\) 0 0
\(424\) 2.70469i 0.131351i
\(425\) 0 0
\(426\) 0 0
\(427\) 31.3153 + 18.0799i 1.51546 + 0.874949i
\(428\) 5.40938 0.261472
\(429\) 0 0
\(430\) −9.68466 −0.467036
\(431\) −2.91791 1.68466i −0.140551 0.0811471i 0.428076 0.903743i \(-0.359192\pi\)
−0.568627 + 0.822596i \(0.692525\pi\)
\(432\) 0 0
\(433\) 17.6847 + 30.6307i 0.849870 + 1.47202i 0.881323 + 0.472514i \(0.156653\pi\)
−0.0314530 + 0.999505i \(0.510013\pi\)
\(434\) 2.63068i 0.126277i
\(435\) 0 0
\(436\) −10.6847 + 6.16879i −0.511702 + 0.295431i
\(437\) 48.7386i 2.33149i
\(438\) 0 0
\(439\) 3.31534 5.74234i 0.158233 0.274067i −0.775999 0.630734i \(-0.782754\pi\)
0.934231 + 0.356667i \(0.116087\pi\)
\(440\) −2.59808 1.50000i −0.123858 0.0715097i
\(441\) 0 0
\(442\) 0 0
\(443\) −10.3923 −0.493753 −0.246877 0.969047i \(-0.579404\pi\)
−0.246877 + 0.969047i \(0.579404\pi\)
\(444\) 0 0
\(445\) −2.34233 + 4.05703i −0.111037 + 0.192322i
\(446\) 3.84381 + 6.65767i 0.182010 + 0.315250i
\(447\) 0 0
\(448\) 2.34233 1.35234i 0.110665 0.0638923i
\(449\) 24.8416 14.3423i 1.17235 0.676856i 0.218117 0.975923i \(-0.430008\pi\)
0.954232 + 0.299066i \(0.0966751\pi\)
\(450\) 0 0
\(451\) −9.00000 15.5885i −0.423793 0.734032i
\(452\) 1.24573 2.15767i 0.0585943 0.101488i
\(453\) 0 0
\(454\) −3.36932 −0.158130
\(455\) −1.35234 9.65767i −0.0633989 0.452759i
\(456\) 0 0
\(457\) −3.00000 1.73205i −0.140334 0.0810219i 0.428189 0.903689i \(-0.359152\pi\)
−0.568523 + 0.822667i \(0.692485\pi\)
\(458\) −13.0970 + 22.6847i −0.611982 + 1.05998i
\(459\) 0 0
\(460\) 7.90084i 0.368379i
\(461\) −3.73720 + 2.15767i −0.174059 + 0.100493i −0.584498 0.811395i \(-0.698709\pi\)
0.410440 + 0.911888i \(0.365375\pi\)
\(462\) 0 0
\(463\) 30.0845i 1.39815i 0.715050 + 0.699074i \(0.246404\pi\)
−0.715050 + 0.699074i \(0.753596\pi\)
\(464\) 1.24573 + 2.15767i 0.0578316 + 0.100167i
\(465\) 0 0
\(466\) 11.1577 + 6.44188i 0.516869 + 0.298415i
\(467\) 21.6375 1.00126 0.500632 0.865660i \(-0.333101\pi\)
0.500632 + 0.865660i \(0.333101\pi\)
\(468\) 0 0
\(469\) 5.26137 0.242947
\(470\) 2.59808 + 1.50000i 0.119840 + 0.0691898i
\(471\) 0 0
\(472\) 3.84233 + 6.65511i 0.176858 + 0.306326i
\(473\) 29.0540i 1.33590i
\(474\) 0 0
\(475\) 5.34233 3.08440i 0.245123 0.141522i
\(476\) 0 0
\(477\) 0 0
\(478\) −12.3693 + 21.4243i −0.565759 + 0.979924i
\(479\) −23.7025 13.6847i −1.08300 0.625268i −0.151293 0.988489i \(-0.548344\pi\)
−0.931703 + 0.363221i \(0.881677\pi\)
\(480\) 0 0
\(481\) 3.84233 + 4.92306i 0.175195 + 0.224472i
\(482\) −6.71498 −0.305859
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 4.43674 + 7.68466i 0.201462 + 0.348942i
\(486\) 0 0
\(487\) −17.3423 + 10.0126i −0.785856 + 0.453714i −0.838502 0.544899i \(-0.816568\pi\)
0.0526457 + 0.998613i \(0.483235\pi\)
\(488\) 11.5782 6.68466i 0.524119 0.302600i
\(489\) 0 0
\(490\) −0.157671 0.273094i −0.00712284 0.0123371i
\(491\) −6.54850 + 11.3423i −0.295530 + 0.511872i −0.975108 0.221731i \(-0.928829\pi\)
0.679578 + 0.733603i \(0.262163\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 20.6181 + 8.34233i 0.927653 + 0.375339i
\(495\) 0 0
\(496\) −0.842329 0.486319i −0.0378217 0.0218364i
\(497\) 8.11407 14.0540i 0.363966 0.630407i
\(498\) 0 0
\(499\) 32.0298i 1.43385i −0.697150 0.716926i \(-0.745549\pi\)
0.697150 0.716926i \(-0.254451\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 5.19615i 0.231916i
\(503\) −14.2361 24.6577i −0.634757 1.09943i −0.986567 0.163360i \(-0.947767\pi\)
0.351810 0.936072i \(-0.385566\pi\)
\(504\) 0 0
\(505\) −9.36932 5.40938i −0.416929 0.240714i
\(506\) 23.7025 1.05371
\(507\) 0 0
\(508\) −2.68466 −0.119112
\(509\) −8.93335 5.15767i −0.395964 0.228610i 0.288777 0.957396i \(-0.406751\pi\)
−0.684741 + 0.728787i \(0.740085\pi\)
\(510\) 0 0
\(511\) −9.36932 16.2281i −0.414474 0.717890i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −20.1577 + 11.6380i −0.889117 + 0.513332i
\(515\) 14.6847i 0.647083i
\(516\) 0 0
\(517\) 4.50000 7.79423i 0.197910 0.342790i
\(518\) 4.05703 + 2.34233i 0.178256 + 0.102916i
\(519\) 0 0
\(520\) −3.34233 1.35234i −0.146571 0.0593042i
\(521\) 13.0970 0.573790 0.286895 0.957962i \(-0.407377\pi\)
0.286895 + 0.957962i \(0.407377\pi\)
\(522\) 0 0
\(523\) −0.526988 + 0.912769i −0.0230436 + 0.0399126i −0.877317 0.479911i \(-0.840669\pi\)
0.854274 + 0.519824i \(0.174002\pi\)
\(524\) 10.4989 + 18.1847i 0.458647 + 0.794400i
\(525\) 0 0
\(526\) −27.5540 + 15.9083i −1.20141 + 0.693635i
\(527\) 0 0
\(528\) 0 0
\(529\) −19.7116 34.1416i −0.857028 1.48442i
\(530\) 1.35234 2.34233i 0.0587421 0.101744i
\(531\) 0 0
\(532\) 16.6847 0.723372
\(533\) −13.3102 17.0540i −0.576530 0.738690i
\(534\) 0 0
\(535\) −4.68466 2.70469i −0.202535 0.116934i
\(536\) 0.972638 1.68466i 0.0420116 0.0727662i
\(537\) 0 0
\(538\) 10.8188i 0.466430i
\(539\) −0.819281 + 0.473012i −0.0352889 + 0.0203741i
\(540\) 0 0
\(541\) 40.0504i 1.72190i 0.508689 + 0.860950i \(0.330130\pi\)
−0.508689 + 0.860950i \(0.669870\pi\)
\(542\) 6.65511 + 11.5270i 0.285861 + 0.495127i
\(543\) 0 0
\(544\) 0 0
\(545\) 12.3376 0.528484
\(546\) 0 0
\(547\) −32.1080 −1.37284 −0.686418 0.727207i \(-0.740818\pi\)
−0.686418 + 0.727207i \(0.740818\pi\)
\(548\) 17.0474 + 9.84233i 0.728229 + 0.420443i
\(549\) 0 0
\(550\) 1.50000 + 2.59808i 0.0639602 + 0.110782i
\(551\) 15.3693i 0.654755i
\(552\) 0 0
\(553\) −13.3153 + 7.68762i −0.566226 + 0.326911i
\(554\) 1.00000i 0.0424859i
\(555\) 0 0
\(556\) 4.65767 8.06732i 0.197529 0.342131i
\(557\) 1.13912 + 0.657671i 0.0482660 + 0.0278664i 0.523939 0.851756i \(-0.324462\pi\)
−0.475673 + 0.879622i \(0.657795\pi\)
\(558\) 0 0
\(559\) 4.84233 + 34.5811i 0.204809 + 1.46263i
\(560\) −2.70469 −0.114294
\(561\) 0 0
\(562\) 12.3693 21.4243i 0.521768 0.903729i
\(563\) 12.8838 + 22.3153i 0.542986 + 0.940480i 0.998731 + 0.0503689i \(0.0160397\pi\)
−0.455745 + 0.890111i \(0.650627\pi\)
\(564\) 0 0
\(565\) −2.15767 + 1.24573i −0.0907739 + 0.0524083i
\(566\) 11.3051 6.52699i 0.475188 0.274350i
\(567\) 0 0
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) 14.6626 25.3963i 0.614687 1.06467i −0.375753 0.926720i \(-0.622616\pi\)
0.990439 0.137949i \(-0.0440509\pi\)
\(570\) 0 0
\(571\) −40.0540 −1.67621 −0.838103 0.545511i \(-0.816335\pi\)
−0.838103 + 0.545511i \(0.816335\pi\)
\(572\) −4.05703 + 10.0270i −0.169633 + 0.419249i
\(573\) 0 0
\(574\) −14.0540 8.11407i −0.586602 0.338675i
\(575\) 3.95042 6.84233i 0.164744 0.285345i
\(576\) 0 0
\(577\) 29.2316i 1.21693i −0.793581 0.608465i \(-0.791786\pi\)
0.793581 0.608465i \(-0.208214\pi\)
\(578\) 14.7224 8.50000i 0.612372 0.353553i
\(579\) 0 0
\(580\) 2.49146i 0.103452i
\(581\) −20.7846 36.0000i −0.862291 1.49353i
\(582\) 0 0
\(583\) −7.02699 4.05703i −0.291028 0.168025i
\(584\) −6.92820 −0.286691
\(585\) 0 0
\(586\) −22.6847 −0.937095
\(587\) −8.11407 4.68466i −0.334903 0.193357i 0.323113 0.946361i \(-0.395271\pi\)
−0.658016 + 0.753004i \(0.728604\pi\)
\(588\) 0 0
\(589\) −3.00000 5.19615i −0.123613 0.214104i
\(590\) 7.68466i 0.316372i
\(591\) 0 0
\(592\) 1.50000 0.866025i 0.0616496 0.0355934i
\(593\) 38.4233i 1.57786i −0.614486 0.788928i \(-0.710637\pi\)
0.614486 0.788928i \(-0.289363\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.93335 5.15767i −0.365924 0.211266i
\(597\) 0 0
\(598\) 28.2116 3.95042i 1.15366 0.161545i
\(599\) −0.426450 −0.0174243 −0.00871215 0.999962i \(-0.502773\pi\)
−0.00871215 + 0.999962i \(0.502773\pi\)
\(600\) 0 0
\(601\) 17.5000 30.3109i 0.713840 1.23641i −0.249565 0.968358i \(-0.580288\pi\)
0.963405 0.268049i \(-0.0863789\pi\)
\(602\) 13.0970 + 22.6847i 0.533794 + 0.924558i
\(603\) 0 0
\(604\) 12.3693 7.14143i 0.503300 0.290581i
\(605\) −1.73205 + 1.00000i −0.0704179 + 0.0406558i
\(606\) 0 0
\(607\) −2.97301 5.14941i −0.120671 0.209008i 0.799362 0.600850i \(-0.205171\pi\)
−0.920032 + 0.391842i \(0.871838\pi\)
\(608\) 3.08440 5.34233i 0.125089 0.216660i
\(609\) 0 0
\(610\) −13.3693 −0.541308
\(611\) 4.05703 10.0270i 0.164130 0.405649i
\(612\) 0 0
\(613\) −10.5000 6.06218i −0.424091 0.244849i 0.272735 0.962089i \(-0.412072\pi\)
−0.696826 + 0.717240i \(0.745405\pi\)
\(614\) −7.14143 + 12.3693i −0.288205 + 0.499185i
\(615\) 0 0
\(616\) 8.11407i 0.326925i
\(617\) −11.8513 + 6.84233i −0.477114 + 0.275462i −0.719213 0.694790i \(-0.755497\pi\)
0.242099 + 0.970252i \(0.422164\pi\)
\(618\) 0 0
\(619\) 3.13114i 0.125851i −0.998018 0.0629256i \(-0.979957\pi\)
0.998018 0.0629256i \(-0.0200431\pi\)
\(620\) 0.486319 + 0.842329i 0.0195310 + 0.0338288i
\(621\) 0 0
\(622\) 4.31534 + 2.49146i 0.173029 + 0.0998986i
\(623\) 12.6705 0.507635
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −4.64996 2.68466i −0.185850 0.107301i
\(627\) 0 0
\(628\) 4.18466 + 7.24804i 0.166986 + 0.289228i
\(629\) 0 0
\(630\) 0 0
\(631\) −19.6847 + 11.3649i −0.783634 + 0.452431i −0.837717 0.546105i \(-0.816110\pi\)
0.0540827 + 0.998536i \(0.482777\pi\)
\(632\) 5.68466i 0.226124i
\(633\) 0 0
\(634\) 14.7116 25.4813i 0.584274 1.01199i
\(635\) 2.32498 + 1.34233i 0.0922641 + 0.0532687i
\(636\) 0 0
\(637\) −0.896305 + 0.699544i −0.0355129 + 0.0277170i
\(638\) −7.47439 −0.295914
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −19.8587 34.3963i −0.784372 1.35857i −0.929373 0.369141i \(-0.879652\pi\)
0.145001 0.989431i \(-0.453681\pi\)
\(642\) 0 0
\(643\) −29.0540 + 16.7743i −1.14578 + 0.661515i −0.947855 0.318703i \(-0.896753\pi\)
−0.197922 + 0.980218i \(0.563419\pi\)
\(644\) 18.5064 10.6847i 0.729253 0.421035i
\(645\) 0 0
\(646\) 0 0
\(647\) −17.3673 + 30.0810i −0.682777 + 1.18260i 0.291353 + 0.956616i \(0.405895\pi\)
−0.974130 + 0.225989i \(0.927439\pi\)
\(648\) 0 0
\(649\) −23.0540 −0.904948
\(650\) 2.21837 + 2.84233i 0.0870116 + 0.111485i
\(651\) 0 0
\(652\) −15.8423 9.14657i −0.620433 0.358207i
\(653\) 11.5314 19.9730i 0.451259 0.781604i −0.547205 0.836999i \(-0.684308\pi\)
0.998465 + 0.0553942i \(0.0176416\pi\)
\(654\) 0 0
\(655\) 20.9978i 0.820453i
\(656\) −5.19615 + 3.00000i −0.202876 + 0.117130i
\(657\) 0 0
\(658\) 8.11407i 0.316319i
\(659\) 16.8342 + 29.1577i 0.655767 + 1.13582i 0.981701 + 0.190429i \(0.0609879\pi\)
−0.325934 + 0.945393i \(0.605679\pi\)
\(660\) 0 0
\(661\) 9.00000 + 5.19615i 0.350059 + 0.202107i 0.664711 0.747100i \(-0.268554\pi\)
−0.314652 + 0.949207i \(0.601888\pi\)
\(662\) 9.29993 0.361452
\(663\) 0 0
\(664\) −15.3693 −0.596445
\(665\) −14.4493 8.34233i −0.560321 0.323502i
\(666\) 0 0
\(667\) 9.84233 + 17.0474i 0.381097 + 0.660079i
\(668\) 6.36932i 0.246436i
\(669\) 0 0
\(670\) −1.68466 + 0.972638i −0.0650840 + 0.0375763i
\(671\) 40.1080i 1.54835i
\(672\) 0 0
\(673\) −16.0000 + 27.7128i −0.616755 + 1.06825i 0.373319 + 0.927703i \(0.378220\pi\)
−0.990074 + 0.140548i \(0.955114\pi\)
\(674\) −25.4346 14.6847i −0.979703 0.565632i
\(675\) 0 0
\(676\) −3.15767 + 12.6107i −0.121449 + 0.485026i
\(677\) 36.5863 1.40613 0.703063 0.711128i \(-0.251815\pi\)
0.703063 + 0.711128i \(0.251815\pi\)
\(678\) 0 0
\(679\) 12.0000 20.7846i 0.460518 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.52699 1.45896i 0.0967634 0.0558664i
\(683\) −2.27824 + 1.31534i −0.0871744 + 0.0503301i −0.542954 0.839763i \(-0.682694\pi\)
0.455779 + 0.890093i \(0.349361\pi\)
\(684\) 0 0
\(685\) −9.84233 17.0474i −0.376056 0.651348i
\(686\) 9.03996 15.6577i 0.345147 0.597813i
\(687\) 0 0
\(688\) 9.68466 0.369224
\(689\) −9.03996 3.65767i −0.344395 0.139346i
\(690\) 0 0
\(691\) −4.02699 2.32498i −0.153194 0.0884465i 0.421444 0.906855i \(-0.361524\pi\)
−0.574637 + 0.818408i \(0.694857\pi\)
\(692\) −4.05703 + 7.02699i −0.154225 + 0.267126i
\(693\) 0 0
\(694\) 4.98293i 0.189149i
\(695\) −8.06732 + 4.65767i −0.306011 + 0.176676i
\(696\) 0 0
\(697\) 0 0
\(698\) −16.7743 29.0540i −0.634917 1.09971i
\(699\) 0 0
\(700\) 2.34233 + 1.35234i 0.0885317 + 0.0511138i
\(701\) 23.2761 0.879125 0.439563 0.898212i \(-0.355133\pi\)
0.439563 + 0.898212i \(0.355133\pi\)
\(702\) 0 0
\(703\) 10.6847 0.402980
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 7.68466 + 13.3102i 0.289216 + 0.500937i
\(707\) 29.2614i 1.10049i
\(708\) 0 0
\(709\) −27.3693 + 15.8017i −1.02788 + 0.593445i −0.916376 0.400320i \(-0.868899\pi\)
−0.111501 + 0.993764i \(0.535566\pi\)
\(710\) 6.00000i 0.225176i
\(711\) 0 0
\(712\) 2.34233 4.05703i 0.0877825 0.152044i
\(713\) −6.65511 3.84233i −0.249236 0.143896i
\(714\) 0 0
\(715\) 8.52699 6.65511i 0.318891 0.248887i
\(716\) −12.8838 −0.481489
\(717\) 0 0
\(718\) 1.31534 2.27824i 0.0490881 0.0850231i
\(719\) 4.98293 + 8.63068i 0.185832 + 0.321870i 0.943857 0.330356i \(-0.107169\pi\)
−0.758025 + 0.652226i \(0.773835\pi\)
\(720\) 0 0
\(721\) 34.3963 19.8587i 1.28099 0.739577i
\(722\) 16.5012 9.52699i 0.614112 0.354558i
\(723\) 0 0
\(724\) 2.68466 + 4.64996i 0.0997745 + 0.172815i
\(725\) −1.24573 + 2.15767i −0.0462653 + 0.0801339i
\(726\) 0 0
\(727\) −36.6847 −1.36056 −0.680279 0.732953i \(-0.738142\pi\)
−0.680279 + 0.732953i \(0.738142\pi\)
\(728\) 1.35234 + 9.65767i 0.0501212 + 0.357937i
\(729\) 0 0
\(730\) 6.00000 + 3.46410i 0.222070 + 0.128212i
\(731\) 0 0
\(732\) 0 0
\(733\) 26.5269i 0.979795i −0.871780 0.489898i \(-0.837034\pi\)
0.871780 0.489898i \(-0.162966\pi\)
\(734\) −20.2384 + 11.6847i −0.747014 + 0.431289i
\(735\) 0 0
\(736\) 7.90084i 0.291229i
\(737\) 2.91791 + 5.05398i 0.107483 + 0.186166i
\(738\) 0 0
\(739\) 1.97301 + 1.13912i 0.0725784 + 0.0419032i 0.535850 0.844313i \(-0.319991\pi\)
−0.463272 + 0.886216i \(0.653325\pi\)
\(740\) −1.73205 −0.0636715
\(741\) 0 0
\(742\) −7.31534 −0.268555
\(743\) −17.0474 9.84233i −0.625409 0.361080i 0.153563 0.988139i \(-0.450925\pi\)
−0.778972 + 0.627059i \(0.784259\pi\)
\(744\) 0 0
\(745\) 5.15767 + 8.93335i 0.188962 + 0.327293i
\(746\) 1.05398i 0.0385888i
\(747\) 0 0
\(748\) 0 0
\(749\) 14.6307i 0.534594i
\(750\) 0 0
\(751\) 17.8423 30.9038i 0.651076 1.12770i −0.331786 0.943355i \(-0.607651\pi\)
0.982862 0.184342i \(-0.0590154\pi\)
\(752\) −2.59808 1.50000i −0.0947421 0.0546994i
\(753\) 0 0
\(754\) −8.89630 + 1.24573i −0.323984 + 0.0453669i
\(755\) −14.2829 −0.519806
\(756\) 0 0
\(757\) −18.0270 + 31.2237i −0.655202 + 1.13484i 0.326641 + 0.945148i \(0.394083\pi\)
−0.981843 + 0.189695i \(0.939250\pi\)
\(758\) −0.166481 0.288354i −0.00604687 0.0104735i
\(759\) 0 0
\(760\) −5.34233 + 3.08440i −0.193787 + 0.111883i
\(761\) −12.1711 + 7.02699i −0.441202 + 0.254728i −0.704107 0.710094i \(-0.748653\pi\)
0.262905 + 0.964822i \(0.415319\pi\)
\(762\) 0 0
\(763\) −16.6847 28.8987i −0.604025 1.04620i
\(764\) 10.6055 18.3693i 0.383695 0.664579i
\(765\) 0 0
\(766\) −7.68466 −0.277658
\(767\) −27.4397 + 3.84233i −0.990791 + 0.138738i
\(768\) 0 0
\(769\) −19.2116 11.0918i −0.692790 0.399982i 0.111867 0.993723i \(-0.464317\pi\)
−0.804656 + 0.593741i \(0.797650\pi\)
\(770\) 4.05703 7.02699i 0.146205 0.253235i
\(771\) 0 0
\(772\) 15.8017i 0.568715i
\(773\) 35.2339 20.3423i 1.26728 0.731663i 0.292805 0.956172i \(-0.405411\pi\)
0.974472 + 0.224509i \(0.0720780\pi\)
\(774\) 0 0
\(775\) 0.972638i 0.0349382i
\(776\) −4.43674 7.68466i −0.159270 0.275863i
\(777\) 0 0
\(778\) −20.8963 12.0645i −0.749169 0.432533i
\(779\) −37.0127 −1.32612
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 0.157671 + 0.273094i 0.00563110 + 0.00975335i
\(785\) 8.36932i 0.298714i
\(786\) 0 0
\(787\) 3.84233 2.21837i 0.136964 0.0790763i −0.429952 0.902852i \(-0.641470\pi\)
0.566916 + 0.823775i \(0.308136\pi\)
\(788\) 20.0540i 0.714393i
\(789\) 0 0
\(790\) 2.84233 4.92306i 0.101126 0.175155i
\(791\) 5.83583 + 3.36932i 0.207498 + 0.119799i
\(792\) 0 0
\(793\) 6.68466 + 47.7380i 0.237379 + 1.69523i
\(794\) −34.8542 −1.23693
\(795\) 0 0
\(796\) −8.68466 + 15.0423i −0.307820 + 0.533159i
\(797\) 10.8188 + 18.7386i 0.383220 + 0.663756i 0.991521 0.129950i \(-0.0414818\pi\)
−0.608301 + 0.793707i \(0.708148\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.866025 0.500000i 0.0306186 0.0176777i
\(801\) 0 0
\(802\) −1.02699 1.77879i −0.0362642 0.0628114i
\(803\) 10.3923 18.0000i 0.366736 0.635206i
\(804\) 0 0
\(805\) −21.3693 −0.753169
\(806\) 2.76456 2.15767i 0.0973774 0.0760007i
\(807\) 0 0
\(808\) 9.36932 + 5.40938i 0.329611 + 0.190301i
\(809\) 10.3923 18.0000i 0.365374 0.632846i −0.623462 0.781854i \(-0.714274\pi\)
0.988836 + 0.149007i \(0.0476078\pi\)
\(810\) 0 0
\(811\) 27.3799i 0.961437i 0.876875 + 0.480718i \(0.159624\pi\)
−0.876875 + 0.480718i \(0.840376\pi\)
\(812\) −5.83583 + 3.36932i −0.204797 + 0.118240i
\(813\) 0 0
\(814\) 5.19615i 0.182125i
\(815\) 9.14657 + 15.8423i 0.320390 + 0.554933i
\(816\) 0 0
\(817\) 51.7386 + 29.8713i 1.81011 + 1.04506i
\(818\) −13.5234 −0.472836
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 35.5538 + 20.5270i 1.24084 + 0.716397i 0.969264 0.246022i \(-0.0791234\pi\)
0.271571 + 0.962418i \(0.412457\pi\)
\(822\) 0 0
\(823\) 5.65767 + 9.79937i 0.197214 + 0.341585i 0.947624 0.319388i \(-0.103477\pi\)
−0.750410 + 0.660973i \(0.770144\pi\)
\(824\) 14.6847i 0.511564i
\(825\) 0 0
\(826\) −18.0000 + 10.3923i −0.626300 + 0.361595i
\(827\) 14.6307i 0.508759i −0.967105 0.254379i \(-0.918129\pi\)
0.967105 0.254379i \(-0.0818712\pi\)
\(828\) 0 0
\(829\) −17.3693 + 30.0845i −0.603261 + 1.04488i 0.389062 + 0.921211i \(0.372799\pi\)
−0.992324 + 0.123668i \(0.960534\pi\)
\(830\) 13.3102 + 7.68466i 0.462004 + 0.266738i
\(831\) 0 0
\(832\) 3.34233 + 1.35234i 0.115874 + 0.0468841i
\(833\) 0 0
\(834\) 0 0
\(835\) 3.18466 5.51599i 0.110210 0.190889i
\(836\) 9.25319 + 16.0270i 0.320028 + 0.554305i
\(837\) 0 0
\(838\) −0.369317 + 0.213225i −0.0127578 + 0.00736574i
\(839\) −42.2089 + 24.3693i −1.45721 + 0.841322i −0.998873 0.0474549i \(-0.984889\pi\)
−0.458340 + 0.888777i \(0.651556\pi\)
\(840\) 0 0
\(841\) 11.3963 + 19.7390i 0.392976 + 0.680654i
\(842\) 13.3102 23.0540i 0.458700 0.794492i
\(843\) 0 0
\(844\) 6.68466 0.230095
\(845\) 9.03996 9.34233i 0.310984 0.321386i
\(846\) 0 0
\(847\) 4.68466 + 2.70469i 0.160967 + 0.0929342i
\(848\) −1.35234 + 2.34233i −0.0464397 + 0.0804359i
\(849\) 0 0
\(850\) 0 0
\(851\) 11.8513 6.84233i 0.406256 0.234552i
\(852\) 0 0
\(853\) 2.49146i 0.0853061i 0.999090 + 0.0426530i \(0.0135810\pi\)
−0.999090 + 0.0426530i \(0.986419\pi\)
\(854\) 18.0799 + 31.3153i 0.618682 + 1.07159i
\(855\) 0 0
\(856\) 4.68466 + 2.70469i 0.160118 + 0.0924444i
\(857\) −12.8838 −0.440101 −0.220051 0.975488i \(-0.570622\pi\)
−0.220051 + 0.975488i \(0.570622\pi\)
\(858\) 0 0
\(859\) 18.0540 0.615994 0.307997 0.951387i \(-0.400341\pi\)
0.307997 + 0.951387i \(0.400341\pi\)
\(860\) −8.38716 4.84233i −0.286000 0.165122i
\(861\) 0 0
\(862\) −1.68466 2.91791i −0.0573797 0.0993845i
\(863\) 28.3153i 0.963865i 0.876208 + 0.481933i \(0.160065\pi\)
−0.876208 + 0.481933i \(0.839935\pi\)
\(864\) 0 0
\(865\) 7.02699 4.05703i 0.238925 0.137943i
\(866\) 35.3693i 1.20190i
\(867\) 0 0
\(868\) 1.31534 2.27824i 0.0446456 0.0773285i
\(869\) −14.7692 8.52699i −0.501010 0.289258i
\(870\) 0 0
\(871\) 4.31534 + 5.52911i 0.146220 + 0.187347i
\(872\) −12.3376 −0.417803
\(873\) 0 0
\(874\) 24.3693 42.2089i 0.824304 1.42774i
\(875\) −1.35234 2.34233i −0.0457176 0.0791852i
\(876\) 0 0
\(877\) −9.84233 + 5.68247i −0.332352 + 0.191883i −0.656885 0.753991i \(-0.728126\pi\)
0.324533 + 0.945874i \(0.394793\pi\)
\(878\) 5.74234 3.31534i 0.193795 0.111887i
\(879\) 0 0
\(880\) −1.50000 2.59808i −0.0505650 0.0875811i
\(881\) −17.1540 + 29.7116i −0.577934 + 1.00101i 0.417782 + 0.908547i \(0.362808\pi\)
−0.995716 + 0.0924636i \(0.970526\pi\)
\(882\) 0 0
\(883\) 14.3153 0.481750 0.240875 0.970556i \(-0.422566\pi\)
0.240875 + 0.970556i \(0.422566\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −9.00000 5.19615i −0.302361 0.174568i
\(887\) 23.3827 40.5000i 0.785114 1.35986i −0.143817 0.989604i \(-0.545938\pi\)
0.928931 0.370253i \(-0.120729\pi\)
\(888\) 0 0
\(889\) 7.26117i 0.243532i
\(890\) −4.05703 + 2.34233i −0.135992 + 0.0785151i
\(891\) 0 0
\(892\) 7.68762i 0.257400i
\(893\) −9.25319 16.0270i −0.309646 0.536323i
\(894\) 0 0
\(895\) 11.1577 + 6.44188i 0.372960 + 0.215328i
\(896\) 2.70469 0.0903573
\(897\) 0 0
\(898\) 28.6847 0.957219
\(899\) 2.09863 + 1.21165i 0.0699933 + 0.0404107i
\(900\) 0 0
\(901\) 0 0
\(902\) 18.0000i 0.599334i
\(903\) 0 0
\(904\) 2.15767 1.24573i 0.0717631 0.0414324i
\(905\) 5.36932i 0.178482i
\(906\) 0 0
\(907\) 15.1577 26.2539i 0.503302 0.871745i −0.496691 0.867928i \(-0.665452\pi\)
0.999993 0.00381726i \(-0.00121507\pi\)
\(908\) −2.91791 1.68466i −0.0968344 0.0559074i
\(909\) 0 0
\(910\) 3.65767 9.03996i 0.121251 0.299672i
\(911\) −37.4392 −1.24042 −0.620208 0.784437i \(-0.712952\pi\)
−0.620208 + 0.784437i \(0.712952\pi\)
\(912\) 0 0
\(913\) 23.0540 39.9307i 0.762975 1.32151i
\(914\) −1.73205 3.00000i −0.0572911 0.0992312i
\(915\) 0 0
\(916\) −22.6847 + 13.0970i −0.749522 + 0.432737i
\(917\) −49.1838 + 28.3963i −1.62419 + 0.937729i
\(918\) 0 0
\(919\) −0.684658 1.18586i −0.0225848 0.0391180i 0.854512 0.519431i \(-0.173856\pi\)
−0.877097 + 0.480313i \(0.840523\pi\)
\(920\) −3.95042 + 6.84233i −0.130242 + 0.225585i
\(921\) 0 0
\(922\) −4.31534 −0.142118
\(923\) 21.4243 3.00000i 0.705189 0.0987462i
\(924\) 0 0
\(925\) 1.50000 + 0.866025i 0.0493197 + 0.0284747i
\(926\) −15.0423 + 26.0540i −0.494320 + 0.856187i
\(927\) 0 0
\(928\) 2.49146i 0.0817863i
\(929\) −39.2910 + 22.6847i −1.28910 + 0.744260i −0.978493 0.206280i \(-0.933864\pi\)
−0.310602 + 0.950540i \(0.600531\pi\)
\(930\) 0 0
\(931\) 1.94528i 0.0637538i
\(932\) 6.44188 + 11.1577i 0.211011 + 0.365482i
\(933\) 0 0
\(934\) 18.7386 + 10.8188i 0.613147 + 0.354000i
\(935\) 0 0
\(936\) 0 0
\(937\) 28.7386 0.938850 0.469425 0.882972i \(-0.344461\pi\)
0.469425 + 0.882972i \(0.344461\pi\)
\(938\) 4.55648 + 2.63068i 0.148774 + 0.0858948i
\(939\) 0 0
\(940\) 1.50000 + 2.59808i 0.0489246 + 0.0847399i
\(941\) 27.3693i 0.892214i 0.894980 + 0.446107i \(0.147190\pi\)
−0.894980 + 0.446107i \(0.852810\pi\)
\(942\) 0 0
\(943\) −41.0540 + 23.7025i −1.33690 + 0.771860i
\(944\) 7.68466i 0.250114i
\(945\) 0 0
\(946\) −14.5270 + 25.1615i −0.472313 + 0.818070i
\(947\) 31.8166 + 18.3693i 1.03390 + 0.596923i 0.918100 0.396350i \(-0.129723\pi\)
0.115801 + 0.993272i \(0.463057\pi\)
\(948\) 0 0
\(949\) 9.36932 23.1563i 0.304141 0.751686i
\(950\) 6.16879 0.200142
\(951\) 0 0
\(952\) 0 0
\(953\) −25.1615 43.5810i −0.815060 1.41173i −0.909285 0.416175i \(-0.863370\pi\)
0.0942243 0.995551i \(-0.469963\pi\)
\(954\) 0 0
\(955\) −18.3693 + 10.6055i −0.594417 + 0.343187i
\(956\) −21.4243 + 12.3693i −0.692911 + 0.400052i
\(957\) 0 0
\(958\) −13.6847 23.7025i −0.442131 0.765794i
\(959\) −26.6204 + 46.1080i −0.859619 + 1.48890i
\(960\) 0 0
\(961\) 30.0540 0.969483
\(962\) 0.866025 + 6.18466i 0.0279218 + 0.199401i
\(963\) 0 0
\(964\) −5.81534 3.35749i −0.187300 0.108137i
\(965\) 7.90084 13.6847i 0.254337 0.440525i
\(966\) 0 0
\(967\) 4.64996i 0.149533i 0.997201 + 0.0747664i \(0.0238211\pi\)
−0.997201 + 0.0747664i \(0.976179\pi\)
\(968\) 1.73205 1.00000i 0.0556702 0.0321412i
\(969\) 0 0
\(970\) 8.87348i 0.284910i
\(971\) −1.13912 1.97301i −0.0365561 0.0633170i 0.847169 0.531324i \(-0.178305\pi\)
−0.883725 + 0.468007i \(0.844972\pi\)
\(972\) 0 0
\(973\) 21.8196 + 12.5976i 0.699504 + 0.403859i
\(974\) −20.0252 −0.641649
\(975\) 0 0
\(976\) 13.3693 0.427941
\(977\) 25.8012 + 14.8963i 0.825452 + 0.476575i 0.852293 0.523065i \(-0.175211\pi\)
−0.0268408 + 0.999640i \(0.508545\pi\)
\(978\) 0 0
\(979\) 7.02699 + 12.1711i 0.224583 + 0.388990i
\(980\) 0.315342i 0.0100732i
\(981\) 0 0
\(982\) −11.3423 + 6.54850i −0.361948 + 0.208971i
\(983\) 33.0000i 1.05254i −0.850319 0.526268i \(-0.823591\pi\)
0.850319 0.526268i \(-0.176409\pi\)
\(984\) 0 0
\(985\) −10.0270 + 17.3673i −0.319486 + 0.553367i
\(986\) 0 0
\(987\) 0 0
\(988\) 13.6847 + 17.5337i 0.435367 + 0.557822i
\(989\) 76.5169 2.43310
\(990\) 0 0
\(991\) 25.8963 44.8537i 0.822623 1.42483i −0.0810991 0.996706i \(-0.525843\pi\)
0.903722 0.428119i \(-0.140824\pi\)
\(992\) −0.486319 0.842329i −0.0154406 0.0267440i
\(993\) 0 0
\(994\) 14.0540 8.11407i 0.445765 0.257363i
\(995\) 15.0423 8.68466i 0.476872 0.275322i
\(996\) 0 0
\(997\) −24.7116 42.8018i −0.782626 1.35555i −0.930407 0.366527i \(-0.880547\pi\)
0.147782 0.989020i \(-0.452787\pi\)
\(998\) 16.0149 27.7386i 0.506943 0.878051i
\(999\) 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 1170.2.bs.h.901.3 yes 8
3.2 odd 2 inner 1170.2.bs.h.901.1 yes 8
13.10 even 6 inner 1170.2.bs.h.361.3 yes 8
39.23 odd 6 inner 1170.2.bs.h.361.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.bs.h.361.1 8 39.23 odd 6 inner
1170.2.bs.h.361.3 yes 8 13.10 even 6 inner
1170.2.bs.h.901.1 yes 8 3.2 odd 2 inner
1170.2.bs.h.901.3 yes 8 1.1 even 1 trivial