Properties

Label 1134.2.f.o.379.1
Level $1134$
Weight $2$
Character 1134.379
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(379,1134)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.o.757.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +3.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +4.00000 q^{26} +1.00000 q^{28} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -3.00000 q^{35} -7.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(4.50000 + 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +3.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.00000 + 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} +12.0000 q^{53} -9.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} +9.00000 q^{71} +2.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-1.50000 - 2.59808i) q^{77} +(5.00000 - 8.66025i) q^{79} -3.00000 q^{80} +9.00000 q^{82} +(-9.00000 - 15.5885i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +15.0000 q^{89} -4.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{94} +(-10.5000 - 18.1865i) q^{95} +(-4.00000 + 6.92820i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 3 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 3 q^{5} - q^{7} - 2 q^{8} + 6 q^{10} - 3 q^{11} + 4 q^{13} + q^{14} - q^{16} - 12 q^{17} - 14 q^{19} + 3 q^{20} + 3 q^{22} + 3 q^{23} - 4 q^{25} + 8 q^{26} + 2 q^{28} - 5 q^{31} + q^{32} - 6 q^{34} - 6 q^{35} - 14 q^{37} - 7 q^{38} - 3 q^{40} + 9 q^{41} + 10 q^{43} + 6 q^{44} + 6 q^{46} - 6 q^{47} - q^{49} + 4 q^{50} + 4 q^{52} + 24 q^{53} - 18 q^{55} + q^{56} + 6 q^{59} - 8 q^{61} - 10 q^{62} + 2 q^{64} - 12 q^{65} + 4 q^{67} + 6 q^{68} - 3 q^{70} + 18 q^{71} + 4 q^{73} - 7 q^{74} + 7 q^{76} - 3 q^{77} + 10 q^{79} - 6 q^{80} + 18 q^{82} - 18 q^{85} - 10 q^{86} + 3 q^{88} + 30 q^{89} - 8 q^{91} + 3 q^{92} + 6 q^{94} - 21 q^{95} - 8 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 3.00000 0.948683
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) −3.50000 + 6.06218i −0.567775 + 0.983415i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0 0
\(58\) 0 0
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −5.00000 −0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) 0 0
\(70\) −1.50000 + 2.59808i −0.179284 + 0.310530i
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) −1.50000 2.59808i −0.170941 0.296078i
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) −3.00000 −0.335410
\(81\) 0 0
\(82\) 9.00000 0.993884
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) −9.00000 15.5885i −0.976187 1.69081i
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) −10.5000 18.1865i −1.07728 1.86590i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i \(-0.245892\pi\)
−0.962505 + 0.271263i \(0.912559\pi\)
\(104\) −2.00000 3.46410i −0.196116 0.339683i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) −4.50000 + 7.79423i −0.429058 + 0.743151i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) 9.00000 + 15.5885i 0.846649 + 1.46644i 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 4.00000 + 6.92820i 0.362143 + 0.627250i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 3.50000 6.06218i 0.303488 0.525657i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 0 0
\(142\) 4.50000 7.79423i 0.377632 0.654077i
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 7.00000 0.567775
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) 7.50000 12.9904i 0.602414 1.04341i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −5.00000 8.66025i −0.397779 0.688973i
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) 9.00000 + 15.5885i 0.696441 + 1.20627i 0.969693 + 0.244328i \(0.0785675\pi\)
−0.273252 + 0.961943i \(0.588099\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) −18.0000 −1.38054
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 0 0
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) 7.50000 12.9904i 0.562149 0.973670i
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −2.00000 + 3.46410i −0.148250 + 0.256776i
\(183\) 0 0
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) −10.5000 18.1865i −0.771975 1.33710i
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) −21.0000 −1.52350
\(191\) −7.50000 + 12.9904i −0.542681 + 0.939951i 0.456068 + 0.889945i \(0.349257\pi\)
−0.998749 + 0.0500060i \(0.984076\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 4.00000 + 6.92820i 0.287183 + 0.497416i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 0 0
\(202\) −3.00000 5.19615i −0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −13.5000 + 23.3827i −0.942881 + 1.63312i
\(206\) −5.00000 −0.348367
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 10.5000 18.1865i 0.726300 1.25799i
\(210\) 0 0
\(211\) −7.00000 12.1244i −0.481900 0.834675i 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 30.0000 2.04598
\(216\) 0 0
\(217\) 5.00000 0.339422
\(218\) 5.50000 9.52628i 0.372507 0.645201i
\(219\) 0 0
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) −12.0000 20.7846i −0.807207 1.39812i
\(222\) 0 0
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 18.0000 1.19734
\(227\) 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) 0 0
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) 4.50000 + 7.79423i 0.296721 + 0.513936i
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −18.0000 −1.17419
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 0 0
\(238\) −3.00000 5.19615i −0.194461 0.336817i
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) 2.00000 0.128565
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 1.50000 2.59808i 0.0958315 0.165985i
\(246\) 0 0
\(247\) −14.0000 24.2487i −0.890799 1.54291i
\(248\) 2.50000 + 4.33013i 0.158750 + 0.274963i
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 10.0000 17.3205i 0.627456 1.08679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 0 0
\(259\) 3.50000 6.06218i 0.217479 0.376685i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −6.00000 −0.370681
\(263\) 7.50000 12.9904i 0.462470 0.801021i −0.536614 0.843828i \(-0.680297\pi\)
0.999083 + 0.0428069i \(0.0136300\pi\)
\(264\) 0 0
\(265\) 18.0000 + 31.1769i 1.10573 + 1.91518i
\(266\) −3.50000 6.06218i −0.214599 0.371696i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −15.0000 −0.914566 −0.457283 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 3.00000 5.19615i 0.181902 0.315063i
\(273\) 0 0
\(274\) 6.00000 + 10.3923i 0.362473 + 0.627822i
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) −9.00000 + 15.5885i −0.536895 + 0.929929i 0.462174 + 0.886789i \(0.347070\pi\)
−0.999069 + 0.0431402i \(0.986264\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −4.50000 7.79423i −0.267026 0.462502i
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) −9.00000 −0.531253
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −9.00000 15.5885i −0.525786 0.910687i −0.999549 0.0300351i \(-0.990438\pi\)
0.473763 0.880652i \(-0.342895\pi\)
\(294\) 0 0
\(295\) −9.00000 + 15.5885i −0.524000 + 0.907595i
\(296\) 7.00000 0.406867
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) 5.00000 + 8.66025i 0.288195 + 0.499169i
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) −24.0000 −1.37424
\(306\) 0 0
\(307\) 29.0000 1.65512 0.827559 0.561379i \(-0.189729\pi\)
0.827559 + 0.561379i \(0.189729\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) 0 0
\(310\) −7.50000 12.9904i −0.425971 0.737804i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 0 0
\(313\) 14.0000 24.2487i 0.791327 1.37062i −0.133819 0.991006i \(-0.542724\pi\)
0.925146 0.379612i \(-0.123943\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i \(-0.514426\pi\)
0.887788 0.460252i \(-0.152241\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 0 0
\(322\) −1.50000 + 2.59808i −0.0835917 + 0.144785i
\(323\) 42.0000 2.33694
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) 0 0
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 18.0000 0.984916
\(335\) −6.00000 + 10.3923i −0.327815 + 0.567792i
\(336\) 0 0
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) 1.50000 + 2.59808i 0.0815892 + 0.141317i
\(339\) 0 0
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −5.00000 + 8.66025i −0.269582 + 0.466930i
\(345\) 0 0
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) −1.50000 2.59808i −0.0805242 0.139472i 0.822951 0.568112i \(-0.192326\pi\)
−0.903475 + 0.428640i \(0.858993\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) −3.00000 −0.159901
\(353\) −10.5000 + 18.1865i −0.558859 + 0.967972i 0.438733 + 0.898617i \(0.355427\pi\)
−0.997592 + 0.0693543i \(0.977906\pi\)
\(354\) 0 0
\(355\) 13.5000 + 23.3827i 0.716506 + 1.24102i
\(356\) −7.50000 12.9904i −0.397499 0.688489i
\(357\) 0 0
\(358\) −12.0000 + 20.7846i −0.634220 + 1.09850i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 0 0
\(364\) 2.00000 + 3.46410i 0.104828 + 0.181568i
\(365\) 3.00000 + 5.19615i 0.157027 + 0.271979i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) −21.0000 −1.09174
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 0 0
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) −10.5000 + 18.1865i −0.538639 + 0.932949i
\(381\) 0 0
\(382\) 7.50000 + 12.9904i 0.383733 + 0.664646i
\(383\) 15.0000 + 25.9808i 0.766464 + 1.32755i 0.939469 + 0.342634i \(0.111319\pi\)
−0.173005 + 0.984921i \(0.555348\pi\)
\(384\) 0 0
\(385\) 4.50000 7.79423i 0.229341 0.397231i
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) −6.00000 + 10.3923i −0.304212 + 0.526911i −0.977086 0.212847i \(-0.931726\pi\)
0.672874 + 0.739758i \(0.265060\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 30.0000 1.50946
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −3.50000 + 6.06218i −0.175439 + 0.303870i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) 10.5000 18.1865i 0.520466 0.901473i
\(408\) 0 0
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) 13.5000 + 23.3827i 0.666717 + 1.15479i
\(411\) 0 0
\(412\) −2.50000 + 4.33013i −0.123166 + 0.213330i
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) 0 0
\(418\) −10.5000 18.1865i −0.513572 0.889532i
\(419\) −9.00000 15.5885i −0.439679 0.761546i 0.557986 0.829851i \(-0.311574\pi\)
−0.997665 + 0.0683046i \(0.978241\pi\)
\(420\) 0 0
\(421\) −8.50000 + 14.7224i −0.414265 + 0.717527i −0.995351 0.0963145i \(-0.969295\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(422\) −14.0000 −0.681509
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) 12.0000 20.7846i 0.582086 1.00820i
\(426\) 0 0
\(427\) −4.00000 6.92820i −0.193574 0.335279i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) 15.0000 25.9808i 0.723364 1.25290i
\(431\) 3.00000 0.144505 0.0722525 0.997386i \(-0.476981\pi\)
0.0722525 + 0.997386i \(0.476981\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 2.50000 4.33013i 0.120004 0.207853i
\(435\) 0 0
\(436\) −5.50000 9.52628i −0.263402 0.456226i
\(437\) −10.5000 18.1865i −0.502283 0.869980i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 1.50000 2.59808i 0.0712672 0.123438i −0.828190 0.560448i \(-0.810629\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(444\) 0 0
\(445\) 22.5000 + 38.9711i 1.06660 + 1.84741i
\(446\) −0.500000 0.866025i −0.0236757 0.0410075i
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −27.0000 −1.27138
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 0 0
\(454\) −3.00000 5.19615i −0.140797 0.243868i
\(455\) −6.00000 10.3923i −0.281284 0.487199i
\(456\) 0 0
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) 4.00000 0.186908
\(459\) 0 0
\(460\) 9.00000 0.419627
\(461\) −13.5000 + 23.3827i −0.628758 + 1.08904i 0.359044 + 0.933321i \(0.383103\pi\)
−0.987801 + 0.155719i \(0.950230\pi\)
\(462\) 0 0
\(463\) −7.00000 12.1244i −0.325318 0.563467i 0.656259 0.754536i \(-0.272138\pi\)
−0.981577 + 0.191069i \(0.938805\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) −9.00000 + 15.5885i −0.415139 + 0.719042i
\(471\) 0 0
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) −6.00000 −0.275010
\(477\) 0 0
\(478\) 0 0
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) −14.0000 24.2487i −0.638345 1.10565i
\(482\) 13.0000 + 22.5167i 0.592134 + 1.02561i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −24.0000 −1.08978
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 4.00000 6.92820i 0.181071 0.313625i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −28.0000 −1.25978
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) −4.50000 + 7.79423i −0.201853 + 0.349619i
\(498\) 0 0
\(499\) 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) −4.50000 + 7.79423i −0.200049 + 0.346496i
\(507\) 0 0
\(508\) −10.0000 17.3205i −0.443678 0.768473i
\(509\) 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 21.0000 0.926270
\(515\) 7.50000 12.9904i 0.330489 0.572425i
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) −3.50000 6.06218i −0.153781 0.266357i
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) −15.0000 −0.657162 −0.328581 0.944476i \(-0.606570\pi\)
−0.328581 + 0.944476i \(0.606570\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) −3.00000 + 5.19615i −0.131056 + 0.226995i
\(525\) 0 0
\(526\) −7.50000 12.9904i −0.327016 0.566408i
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 36.0000 1.56374
\(531\) 0 0
\(532\) −7.00000 −0.303488
\(533\) −18.0000 + 31.1769i −0.779667 + 1.35042i
\(534\) 0 0
\(535\) −18.0000 31.1769i −0.778208 1.34790i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 0 0
\(538\) −7.50000 + 12.9904i −0.323348 + 0.560055i
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) −7.00000 −0.300954 −0.150477 0.988614i \(-0.548081\pi\)
−0.150477 + 0.988614i \(0.548081\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) 16.5000 + 28.5788i 0.706782 + 1.22418i
\(546\) 0 0
\(547\) 14.0000 24.2487i 0.598597 1.03680i −0.394432 0.918925i \(-0.629059\pi\)
0.993028 0.117875i \(-0.0376081\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) −12.0000 −0.511682
\(551\) 0 0
\(552\) 0 0
\(553\) 5.00000 + 8.66025i 0.212622 + 0.368271i
\(554\) 8.50000 + 14.7224i 0.361130 + 0.625496i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 1.50000 2.59808i 0.0633866 0.109789i
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 0 0
\(565\) −27.0000 + 46.7654i −1.13590 + 1.96743i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −9.00000 −0.377632
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −7.00000 12.1244i −0.292941 0.507388i 0.681563 0.731760i \(-0.261301\pi\)
−0.974504 + 0.224371i \(0.927967\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 0 0
\(574\) −4.50000 + 7.79423i −0.187826 + 0.325325i
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 0 0
\(589\) 17.5000 + 30.3109i 0.721075 + 1.24894i
\(590\) 9.00000 + 15.5885i 0.370524 + 0.641767i
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 33.0000 1.35515 0.677574 0.735455i \(-0.263031\pi\)
0.677574 + 0.735455i \(0.263031\pi\)
\(594\) 0 0
\(595\) 18.0000 0.737928
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) 16.5000 + 28.5788i 0.674172 + 1.16770i 0.976710 + 0.214563i \(0.0688326\pi\)
−0.302539 + 0.953137i \(0.597834\pi\)
\(600\) 0 0
\(601\) 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i \(-0.639861\pi\)
0.996456 0.0841128i \(-0.0268056\pi\)
\(602\) 10.0000 0.407570
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 0 0
\(607\) 2.00000 + 3.46410i 0.0811775 + 0.140604i 0.903756 0.428048i \(-0.140799\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 29.0000 1.17130 0.585649 0.810564i \(-0.300840\pi\)
0.585649 + 0.810564i \(0.300840\pi\)
\(614\) 14.5000 25.1147i 0.585172 1.01355i
\(615\) 0 0
\(616\) 1.50000 + 2.59808i 0.0604367 + 0.104679i
\(617\) −9.00000 15.5885i −0.362326 0.627568i 0.626017 0.779809i \(-0.284684\pi\)
−0.988343 + 0.152242i \(0.951351\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) −15.0000 −0.602414
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) −7.50000 + 12.9904i −0.300481 + 0.520449i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −14.0000 24.2487i −0.559553 0.969173i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −5.00000 + 8.66025i −0.198889 + 0.344486i
\(633\) 0 0
\(634\) −15.0000 25.9808i −0.595726 1.03183i
\(635\) 30.0000 + 51.9615i 1.19051 + 2.06203i
\(636\) 0 0
\(637\) 2.00000 3.46410i 0.0792429 0.137253i
\(638\) 0 0
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) 3.00000 5.19615i 0.118493 0.205236i −0.800678 0.599095i \(-0.795527\pi\)
0.919171 + 0.393860i \(0.128860\pi\)
\(642\) 0 0
\(643\) −2.50000 4.33013i −0.0985904 0.170764i 0.812511 0.582946i \(-0.198100\pi\)
−0.911101 + 0.412182i \(0.864767\pi\)
\(644\) 1.50000 + 2.59808i 0.0591083 + 0.102379i
\(645\) 0 0
\(646\) 21.0000 36.3731i 0.826234 1.43108i
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) −8.00000 + 13.8564i −0.313786 + 0.543493i
\(651\) 0 0
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) 9.00000 15.5885i 0.351659 0.609091i
\(656\) −9.00000 −0.351391
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 4.50000 7.79423i 0.175295 0.303620i −0.764968 0.644068i \(-0.777245\pi\)
0.940263 + 0.340448i \(0.110579\pi\)
\(660\) 0 0
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) −14.0000 24.2487i −0.544125 0.942453i
\(663\) 0 0
\(664\) 0 0
\(665\) 21.0000 0.814345
\(666\) 0 0
\(667\) 0 0
\(668\) 9.00000 15.5885i 0.348220 0.603136i
\(669\) 0 0
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) 0 0
\(673\) 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i \(-0.486405\pi\)
0.843886 0.536522i \(-0.180262\pi\)
\(674\) 13.0000 0.500741
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −7.50000 + 12.9904i −0.288248 + 0.499261i −0.973392 0.229147i \(-0.926406\pi\)
0.685143 + 0.728408i \(0.259740\pi\)
\(678\) 0 0
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) 9.00000 + 15.5885i 0.345134 + 0.597790i
\(681\) 0 0
\(682\) 7.50000 12.9904i 0.287190 0.497427i
\(683\) −15.0000 −0.573959 −0.286980 0.957937i \(-0.592651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) 24.0000 + 41.5692i 0.914327 + 1.58366i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) −21.0000 −0.798300
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 0 0
\(697\) −27.0000 46.7654i −1.02270 1.77136i
\(698\) −5.00000 8.66025i −0.189253 0.327795i
\(699\) 0 0
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 49.0000 1.84807
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 10.5000 + 18.1865i 0.395173 + 0.684459i
\(707\) 3.00000 + 5.19615i 0.112827 + 0.195421i
\(708\) 0 0
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 27.0000 1.01329
\(711\) 0 0
\(712\) −15.0000 −0.562149
\(713\) 7.50000 12.9904i 0.280877 0.486494i
\(714\) 0 0
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) 12.0000 + 20.7846i 0.448461 + 0.776757i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) 5.00000 0.186210
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 4.00000 0.148250
\(729\) 0 0
\(730\) 6.00000 0.222070
\(731\) −30.0000 + 51.9615i −1.10959 + 1.92187i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 8.50000 + 14.7224i 0.313741 + 0.543415i
\(735\) 0 0
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) −10.5000 + 18.1865i −0.385988 + 0.668550i
\(741\) 0 0
\(742\) 6.00000 + 10.3923i 0.220267 + 0.381514i
\(743\) −4.50000 7.79423i −0.165089 0.285943i 0.771598 0.636111i \(-0.219458\pi\)
−0.936687 + 0.350168i \(0.886124\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 13.0000 0.475964
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) 6.00000 10.3923i 0.219235 0.379727i
\(750\) 0 0
\(751\) 11.0000 + 19.0526i 0.401396 + 0.695238i 0.993895 0.110333i \(-0.0351919\pi\)
−0.592499 + 0.805571i \(0.701859\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) 0 0
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 1.00000 1.73205i 0.0363216 0.0629109i
\(759\) 0 0
\(760\) 10.5000 + 18.1865i 0.380875 + 0.659695i
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 0 0
\(763\) −5.50000 + 9.52628i −0.199113 + 0.344874i
\(764\) 15.0000 0.542681
\(765\) 0 0
\(766\) 30.0000 1.08394
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0 0
\(769\) 2.00000 + 3.46410i 0.0721218 + 0.124919i 0.899831 0.436239i \(-0.143690\pi\)
−0.827709 + 0.561157i \(0.810356\pi\)
\(770\) −4.50000 7.79423i −0.162169 0.280885i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 39.0000 1.40273 0.701366 0.712801i \(-0.252574\pi\)
0.701366 + 0.712801i \(0.252574\pi\)
\(774\) 0 0
\(775\) 20.0000 0.718421
\(776\) 4.00000 6.92820i 0.143592 0.248708i
\(777\) 0 0
\(778\) 6.00000 + 10.3923i 0.215110 + 0.372582i
\(779\) −31.5000 54.5596i −1.12860 1.95480i
\(780\) 0 0
\(781\) −13.5000 + 23.3827i −0.483068 + 0.836698i
\(782\) −18.0000 −0.643679
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −6.00000 + 10.3923i −0.214149 + 0.370917i
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 9.00000 + 15.5885i 0.320612 + 0.555316i
\(789\) 0 0
\(790\) 15.0000 25.9808i 0.533676 0.924354i
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) 1.00000 1.73205i 0.0354887 0.0614682i
\(795\) 0 0
\(796\) 3.50000 + 6.06218i 0.124054 + 0.214868i
\(797\) −13.5000 23.3827i −0.478195 0.828257i 0.521493 0.853256i \(-0.325375\pi\)
−0.999687 + 0.0249984i \(0.992042\pi\)
\(798\) 0 0
\(799\) 18.0000 31.1769i 0.636794 1.10296i
\(800\) −4.00000 −0.141421
\(801\) 0 0
\(802\) −24.0000 −0.847469
\(803\) −3.00000 + 5.19615i −0.105868 + 0.183368i
\(804\) 0 0
\(805\) −4.50000 7.79423i −0.158604 0.274710i
\(806\) −10.0000 17.3205i −0.352235 0.610089i
\(807\) 0 0
\(808\) −3.00000 + 5.19615i −0.105540 + 0.182800i
\(809\) −24.0000 −0.843795 −0.421898 0.906644i \(-0.638636\pi\)
−0.421898 + 0.906644i \(0.638636\pi\)
\(810\) 0 0
\(811\) −25.0000 −0.877869 −0.438934 0.898519i \(-0.644644\pi\)
−0.438934 + 0.898519i \(0.644644\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −10.5000 18.1865i −0.368025 0.637438i
\(815\) −24.0000 41.5692i −0.840683 1.45611i
\(816\) 0 0
\(817\) −35.0000 + 60.6218i −1.22449 + 2.12089i
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 27.0000 0.942881
\(821\) 15.0000 25.9808i 0.523504 0.906735i −0.476122 0.879379i \(-0.657958\pi\)
0.999626 0.0273557i \(-0.00870868\pi\)
\(822\) 0 0
\(823\) −7.00000 12.1244i −0.244005 0.422628i 0.717847 0.696201i \(-0.245128\pi\)
−0.961851 + 0.273573i \(0.911795\pi\)
\(824\) 2.50000 + 4.33013i 0.0870916 + 0.150847i
\(825\) 0 0
\(826\) −3.00000 + 5.19615i −0.104383 + 0.180797i
\(827\) 9.00000 0.312961 0.156480 0.987681i \(-0.449985\pi\)
0.156480 + 0.987681i \(0.449985\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 2.00000 + 3.46410i 0.0693375 + 0.120096i
\(833\) 3.00000 + 5.19615i 0.103944 + 0.180036i
\(834\) 0 0
\(835\) −27.0000 + 46.7654i −0.934374 + 1.61838i
\(836\) −21.0000 −0.726300
\(837\) 0 0
\(838\) −18.0000 −0.621800
\(839\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(840\) 0 0
\(841\) 14.5000 + 25.1147i 0.500000 + 0.866025i
\(842\) 8.50000 + 14.7224i 0.292929 + 0.507369i
\(843\) 0 0
\(844\) −7.00000 + 12.1244i −0.240950 + 0.417338i
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) −6.00000 + 10.3923i −0.206041 + 0.356873i
\(849\) 0 0
\(850\) −12.0000 20.7846i −0.411597 0.712906i
\(851\) −10.5000 18.1865i −0.359935 0.623426i
\(852\) 0 0
\(853\) −4.00000 + 6.92820i −0.136957 + 0.237217i −0.926343 0.376680i \(-0.877066\pi\)
0.789386 + 0.613897i \(0.210399\pi\)
\(854\) −8.00000 −0.273754
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −1.50000 + 2.59808i −0.0512390 + 0.0887486i −0.890507 0.454969i \(-0.849650\pi\)
0.839268 + 0.543718i \(0.182984\pi\)
\(858\) 0 0
\(859\) 15.5000 + 26.8468i 0.528853 + 0.916001i 0.999434 + 0.0336436i \(0.0107111\pi\)
−0.470581 + 0.882357i \(0.655956\pi\)
\(860\) −15.0000 25.9808i −0.511496 0.885937i
\(861\) 0 0
\(862\) 1.50000 2.59808i 0.0510902 0.0884908i
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 63.0000 2.14206
\(866\) −8.00000 + 13.8564i −0.271851 + 0.470860i
\(867\) 0 0
\(868\) −2.50000 4.33013i −0.0848555 0.146974i
\(869\) 15.0000 + 25.9808i 0.508840 + 0.881337i
\(870\) 0 0
\(871\) −8.00000 + 13.8564i −0.271070 + 0.469506i
\(872\) −11.0000 −0.372507
\(873\) 0 0
\(874\) −21.0000 −0.710336
\(875\) −1.50000 + 2.59808i −0.0507093 + 0.0878310i
\(876\) 0 0
\(877\) −7.00000 12.1244i −0.236373 0.409410i 0.723298 0.690536i \(-0.242625\pi\)
−0.959671 + 0.281126i \(0.909292\pi\)
\(878\) 4.00000 + 6.92820i 0.134993 + 0.233816i
\(879\) 0 0
\(880\) 4.50000 7.79423i 0.151695 0.262743i
\(881\) 9.00000 0.303218 0.151609 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) 0 0
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) −12.0000 + 20.7846i −0.403604 + 0.699062i
\(885\) 0 0
\(886\) −1.50000 2.59808i −0.0503935 0.0872841i
\(887\) −12.0000 20.7846i −0.402921 0.697879i 0.591156 0.806557i \(-0.298672\pi\)
−0.994077 + 0.108678i \(0.965338\pi\)
\(888\) 0 0
\(889\) −10.0000 + 17.3205i −0.335389 + 0.580911i
\(890\) 45.0000 1.50840
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) 21.0000 36.3731i 0.702738 1.21718i
\(894\) 0 0
\(895\) −36.0000 62.3538i −1.20335 2.08426i
\(896\) 0.500000 + 0.866025i 0.0167038 + 0.0289319i
\(897\) 0 0
\(898\) 9.00000 15.5885i 0.300334 0.520194i
\(899\) 0 0
\(900\) 0 0
\(901\) −72.0000 −2.39867
\(902\) −13.5000 + 23.3827i −0.449501 + 0.778558i
\(903\) 0 0
\(904\) −9.00000 15.5885i −0.299336 0.518464i
\(905\) 3.00000 + 5.19615i 0.0997234 + 0.172726i
\(906\) 0 0
\(907\) 23.0000 39.8372i 0.763702 1.32277i −0.177227 0.984170i \(-0.556713\pi\)
0.940930 0.338602i \(-0.109954\pi\)
\(908\) −6.00000 −0.199117
\(909\) 0 0
\(910\) −12.0000 −0.397796
\(911\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −9.50000 16.4545i −0.314232 0.544266i
\(915\) 0 0
\(916\) 2.00000 3.46410i 0.0660819 0.114457i
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) −52.0000 −1.71532 −0.857661 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) 4.50000 7.79423i 0.148361 0.256968i
\(921\) 0 0
\(922\) 13.5000 + 23.3827i 0.444599 + 0.770068i
\(923\) 18.0000 + 31.1769i 0.592477 + 1.02620i
\(924\) 0 0
\(925\) 14.0000 24.2487i 0.460317 0.797293i
\(926\) −14.0000 −0.460069
\(927\) 0 0
\(928\) 0 0
\(929\) −3.00000 + 5.19615i −0.0984268 + 0.170480i −0.911034 0.412332i \(-0.864714\pi\)
0.812607 + 0.582812i \(0.198048\pi\)
\(930\) 0 0
\(931\) 3.50000 + 6.06218i 0.114708 + 0.198680i
\(932\) −3.00000 5.19615i −0.0982683 0.170206i
\(933\) 0 0
\(934\) 3.00000 5.19615i 0.0981630 0.170023i
\(935\) 54.0000 1.76599
\(936\) 0 0
\(937\) 20.0000 0.653372 0.326686 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(938\) −2.00000 + 3.46410i −0.0653023 + 0.113107i
\(939\) 0 0
\(940\) 9.00000 + 15.5885i 0.293548 + 0.508439i
\(941\) 7.50000 + 12.9904i 0.244493 + 0.423474i 0.961989 0.273088i \(-0.0880451\pi\)
−0.717496 + 0.696563i \(0.754712\pi\)
\(942\) 0 0
\(943\) −13.5000 + 23.3827i −0.439620 + 0.761445i
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 30.0000 0.975384
\(947\) 19.5000 33.7750i 0.633665 1.09754i −0.353131 0.935574i \(-0.614883\pi\)
0.986796 0.161966i \(-0.0517835\pi\)
\(948\) 0 0
\(949\) 4.00000 + 6.92820i 0.129845 + 0.224899i
\(950\) −14.0000 24.2487i −0.454220 0.786732i
\(951\) 0 0
\(952\) −3.00000 + 5.19615i −0.0972306 + 0.168408i
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) −45.0000 −1.45617
\(956\) 0 0
\(957\) 0 0
\(958\) −12.0000 20.7846i −0.387702 0.671520i
\(959\) −6.00000 10.3923i −0.193750 0.335585i
\(960\) 0 0
\(961\) 3.00000 5.19615i 0.0967742 0.167618i
\(962\) −28.0000 −0.902756
\(963\) 0 0
\(964\) 26.0000 0.837404
\(965\) 21.0000 36.3731i 0.676014 1.17089i
\(966\) 0 0
\(967\) 29.0000 + 50.2295i 0.932577 + 1.61527i 0.778898 + 0.627150i \(0.215779\pi\)
0.153679 + 0.988121i \(0.450888\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 0 0
\(970\) −12.0000 + 20.7846i −0.385297 + 0.667354i
\(971\) −48.0000 −1.54039 −0.770197 0.637806i \(-0.779842\pi\)
−0.770197 + 0.637806i \(0.779842\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 1.00000 1.73205i 0.0320421 0.0554985i
\(975\) 0 0
\(976\) −4.00000 6.92820i −0.128037 0.221766i
\(977\) −6.00000 10.3923i −0.191957 0.332479i 0.753942 0.656941i \(-0.228150\pi\)
−0.945899 + 0.324462i \(0.894817\pi\)
\(978\) 0 0
\(979\) −22.5000 + 38.9711i −0.719103 + 1.24552i
\(980\) −3.00000 −0.0958315
\(981\) 0 0
\(982\) 9.00000 0.287202
\(983\) 3.00000 5.19615i 0.0956851 0.165732i −0.814209 0.580572i \(-0.802829\pi\)
0.909894 + 0.414840i \(0.136162\pi\)
\(984\) 0 0
\(985\) −27.0000 46.7654i −0.860292 1.49007i
\(986\) 0 0
\(987\) 0 0
\(988\) −14.0000 + 24.2487i −0.445399 + 0.771454i
\(989\) 30.0000 0.953945
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 2.50000 4.33013i 0.0793751 0.137482i
\(993\) 0 0
\(994\) 4.50000 + 7.79423i 0.142731 + 0.247218i
\(995\) −10.5000 18.1865i −0.332872 0.576552i
\(996\) 0 0
\(997\) 5.00000 8.66025i 0.158352 0.274273i −0.775923 0.630828i \(-0.782715\pi\)
0.934274 + 0.356555i \(0.116049\pi\)
\(998\) 22.0000 0.696398
\(999\) 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.f.o.379.1 2
3.2 odd 2 1134.2.f.b.379.1 2
9.2 odd 6 378.2.a.g.1.1 yes 1
9.4 even 3 inner 1134.2.f.o.757.1 2
9.5 odd 6 1134.2.f.b.757.1 2
9.7 even 3 378.2.a.b.1.1 1
36.7 odd 6 3024.2.a.c.1.1 1
36.11 even 6 3024.2.a.bb.1.1 1
45.29 odd 6 9450.2.a.h.1.1 1
45.34 even 6 9450.2.a.cu.1.1 1
63.20 even 6 2646.2.a.q.1.1 1
63.34 odd 6 2646.2.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.a.b.1.1 1 9.7 even 3
378.2.a.g.1.1 yes 1 9.2 odd 6
1134.2.f.b.379.1 2 3.2 odd 2
1134.2.f.b.757.1 2 9.5 odd 6
1134.2.f.o.379.1 2 1.1 even 1 trivial
1134.2.f.o.757.1 2 9.4 even 3 inner
2646.2.a.n.1.1 1 63.34 odd 6
2646.2.a.q.1.1 1 63.20 even 6
3024.2.a.c.1.1 1 36.7 odd 6
3024.2.a.bb.1.1 1 36.11 even 6
9450.2.a.h.1.1 1 45.29 odd 6
9450.2.a.cu.1.1 1 45.34 even 6