Properties

Label 1638.2.x.b.307.4
Level $1638$
Weight $2$
Character 1638.307
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
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] = [1638,2,Mod(307,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.x (of order \(4\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.7442857984.4
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.4
Root \(2.73923i\) of defining polynomial
Character \(\chi\) \(=\) 1638.307
Dual form 1638.2.x.b.811.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.0951965 - 0.0951965i) q^{5} +(-0.0951965 + 2.64404i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.0951965 - 0.0951965i) q^{5} +(-0.0951965 + 2.64404i) q^{7} +(-0.707107 + 0.707107i) q^{8} +0.134628 q^{10} +(3.64404 - 3.64404i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(-1.93693 + 1.80230i) q^{14} -1.00000 q^{16} +5.98188 q^{17} +(4.19288 - 4.19288i) q^{19} +(0.0951965 + 0.0951965i) q^{20} +5.15345 q^{22} +4.69380i q^{23} +4.98188i q^{25} +(0.707107 - 3.53553i) q^{26} +(-2.64404 - 0.0951965i) q^{28} +4.59428 q^{29} +(0.739235 - 0.739235i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.22982 + 4.22982i) q^{34} +(0.242641 + 0.260765i) q^{35} +(-4.83443 + 4.83443i) q^{37} +5.92963 q^{38} +0.134628i q^{40} +(3.04544 - 3.04544i) q^{41} +8.78467i q^{43} +(3.64404 + 3.64404i) q^{44} +(-3.31902 + 3.31902i) q^{46} +(3.28808 + 3.28808i) q^{47} +(-6.98188 - 0.503406i) q^{49} +(-3.52272 + 3.52272i) q^{50} +(3.00000 - 2.00000i) q^{52} -1.09768 q^{53} -0.693799i q^{55} +(-1.80230 - 1.93693i) q^{56} +(3.24864 + 3.24864i) q^{58} +(1.30620 + 1.30620i) q^{59} +5.98188i q^{61} +1.04544 q^{62} -1.00000i q^{64} +(-0.475982 - 0.0951965i) q^{65} +(-0.0454356 - 0.0454356i) q^{67} +5.98188i q^{68} +(-0.0128161 + 0.355962i) q^{70} +(-8.69380 - 8.69380i) q^{71} +(4.83443 + 4.83443i) q^{73} -6.83692 q^{74} +(4.19288 + 4.19288i) q^{76} +(9.28808 + 9.98188i) q^{77} -11.5780 q^{79} +(-0.0951965 + 0.0951965i) q^{80} +4.30690 q^{82} +(-1.28808 + 1.28808i) q^{83} +(0.569453 - 0.569453i) q^{85} +(-6.21170 + 6.21170i) q^{86} +5.15345i q^{88} +(-9.21770 - 9.21770i) q^{89} +(8.12251 - 5.00249i) q^{91} -4.69380 q^{92} +4.65004i q^{94} -0.798295i q^{95} +(9.97506 - 9.97506i) q^{97} +(-4.58097 - 5.29289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{5} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{16} - 12 q^{17} - 4 q^{19} - 4 q^{20} + 4 q^{22} + 12 q^{29} - 20 q^{31} + 24 q^{34} - 32 q^{35} - 8 q^{37} + 12 q^{38} + 16 q^{41} + 8 q^{44} - 20 q^{46} - 16 q^{47} + 4 q^{49} - 24 q^{50} + 24 q^{52} + 24 q^{53} - 4 q^{56} - 16 q^{58} + 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} + 8 q^{73} + 4 q^{74} - 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} - 40 q^{82} + 32 q^{83} + 20 q^{85} + 20 q^{86} + 4 q^{89} - 8 q^{91} - 20 q^{92} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0.0951965 0.0951965i 0.0425731 0.0425731i −0.685500 0.728073i \(-0.740416\pi\)
0.728073 + 0.685500i \(0.240416\pi\)
\(6\) 0 0
\(7\) −0.0951965 + 2.64404i −0.0359809 + 0.999352i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0.134628 0.0425731
\(11\) 3.64404 3.64404i 1.09872 1.09872i 0.104158 0.994561i \(-0.466785\pi\)
0.994561 0.104158i \(-0.0332148\pi\)
\(12\) 0 0
\(13\) −2.00000 3.00000i −0.554700 0.832050i
\(14\) −1.93693 + 1.80230i −0.517667 + 0.481686i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 5.98188 1.45082 0.725409 0.688318i \(-0.241651\pi\)
0.725409 + 0.688318i \(0.241651\pi\)
\(18\) 0 0
\(19\) 4.19288 4.19288i 0.961913 0.961913i −0.0373882 0.999301i \(-0.511904\pi\)
0.999301 + 0.0373882i \(0.0119038\pi\)
\(20\) 0.0951965 + 0.0951965i 0.0212866 + 0.0212866i
\(21\) 0 0
\(22\) 5.15345 1.09872
\(23\) 4.69380i 0.978725i 0.872081 + 0.489362i \(0.162770\pi\)
−0.872081 + 0.489362i \(0.837230\pi\)
\(24\) 0 0
\(25\) 4.98188i 0.996375i
\(26\) 0.707107 3.53553i 0.138675 0.693375i
\(27\) 0 0
\(28\) −2.64404 0.0951965i −0.499676 0.0179904i
\(29\) 4.59428 0.853136 0.426568 0.904456i \(-0.359723\pi\)
0.426568 + 0.904456i \(0.359723\pi\)
\(30\) 0 0
\(31\) 0.739235 0.739235i 0.132770 0.132770i −0.637598 0.770369i \(-0.720072\pi\)
0.770369 + 0.637598i \(0.220072\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 4.22982 + 4.22982i 0.725409 + 0.725409i
\(35\) 0.242641 + 0.260765i 0.0410138 + 0.0440774i
\(36\) 0 0
\(37\) −4.83443 + 4.83443i −0.794776 + 0.794776i −0.982266 0.187491i \(-0.939965\pi\)
0.187491 + 0.982266i \(0.439965\pi\)
\(38\) 5.92963 0.961913
\(39\) 0 0
\(40\) 0.134628i 0.0212866i
\(41\) 3.04544 3.04544i 0.475617 0.475617i −0.428110 0.903727i \(-0.640820\pi\)
0.903727 + 0.428110i \(0.140820\pi\)
\(42\) 0 0
\(43\) 8.78467i 1.33965i 0.742519 + 0.669825i \(0.233631\pi\)
−0.742519 + 0.669825i \(0.766369\pi\)
\(44\) 3.64404 + 3.64404i 0.549359 + 0.549359i
\(45\) 0 0
\(46\) −3.31902 + 3.31902i −0.489362 + 0.489362i
\(47\) 3.28808 + 3.28808i 0.479615 + 0.479615i 0.905009 0.425393i \(-0.139864\pi\)
−0.425393 + 0.905009i \(0.639864\pi\)
\(48\) 0 0
\(49\) −6.98188 0.503406i −0.997411 0.0719152i
\(50\) −3.52272 + 3.52272i −0.498188 + 0.498188i
\(51\) 0 0
\(52\) 3.00000 2.00000i 0.416025 0.277350i
\(53\) −1.09768 −0.150778 −0.0753892 0.997154i \(-0.524020\pi\)
−0.0753892 + 0.997154i \(0.524020\pi\)
\(54\) 0 0
\(55\) 0.693799i 0.0935518i
\(56\) −1.80230 1.93693i −0.240843 0.258833i
\(57\) 0 0
\(58\) 3.24864 + 3.24864i 0.426568 + 0.426568i
\(59\) 1.30620 + 1.30620i 0.170053 + 0.170053i 0.787003 0.616950i \(-0.211632\pi\)
−0.616950 + 0.787003i \(0.711632\pi\)
\(60\) 0 0
\(61\) 5.98188i 0.765901i 0.923769 + 0.382950i \(0.125092\pi\)
−0.923769 + 0.382950i \(0.874908\pi\)
\(62\) 1.04544 0.132770
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.475982 0.0951965i −0.0590383 0.0118077i
\(66\) 0 0
\(67\) −0.0454356 0.0454356i −0.00555084 0.00555084i 0.704326 0.709877i \(-0.251249\pi\)
−0.709877 + 0.704326i \(0.751249\pi\)
\(68\) 5.98188i 0.725409i
\(69\) 0 0
\(70\) −0.0128161 + 0.355962i −0.00153182 + 0.0425456i
\(71\) −8.69380 8.69380i −1.03176 1.03176i −0.999479 0.0322854i \(-0.989721\pi\)
−0.0322854 0.999479i \(-0.510279\pi\)
\(72\) 0 0
\(73\) 4.83443 + 4.83443i 0.565827 + 0.565827i 0.930957 0.365129i \(-0.118975\pi\)
−0.365129 + 0.930957i \(0.618975\pi\)
\(74\) −6.83692 −0.794776
\(75\) 0 0
\(76\) 4.19288 + 4.19288i 0.480956 + 0.480956i
\(77\) 9.28808 + 9.98188i 1.05847 + 1.13754i
\(78\) 0 0
\(79\) −11.5780 −1.30263 −0.651313 0.758809i \(-0.725781\pi\)
−0.651313 + 0.758809i \(0.725781\pi\)
\(80\) −0.0951965 + 0.0951965i −0.0106433 + 0.0106433i
\(81\) 0 0
\(82\) 4.30690 0.475617
\(83\) −1.28808 + 1.28808i −0.141385 + 0.141385i −0.774257 0.632872i \(-0.781876\pi\)
0.632872 + 0.774257i \(0.281876\pi\)
\(84\) 0 0
\(85\) 0.569453 0.569453i 0.0617659 0.0617659i
\(86\) −6.21170 + 6.21170i −0.669825 + 0.669825i
\(87\) 0 0
\(88\) 5.15345i 0.549359i
\(89\) −9.21770 9.21770i −0.977075 0.977075i 0.0226684 0.999743i \(-0.492784\pi\)
−0.999743 + 0.0226684i \(0.992784\pi\)
\(90\) 0 0
\(91\) 8.12251 5.00249i 0.851470 0.524403i
\(92\) −4.69380 −0.489362
\(93\) 0 0
\(94\) 4.65004i 0.479615i
\(95\) 0.798295i 0.0819033i
\(96\) 0 0
\(97\) 9.97506 9.97506i 1.01281 1.01281i 0.0128974 0.999917i \(-0.495895\pi\)
0.999917 0.0128974i \(-0.00410548\pi\)
\(98\) −4.58097 5.29289i −0.462748 0.534663i
\(99\) 0 0
\(100\) −4.98188 −0.498188
\(101\) −3.09271 −0.307736 −0.153868 0.988091i \(-0.549173\pi\)
−0.153868 + 0.988091i \(0.549173\pi\)
\(102\) 0 0
\(103\) 8.31301 0.819106 0.409553 0.912286i \(-0.365685\pi\)
0.409553 + 0.912286i \(0.365685\pi\)
\(104\) 3.53553 + 0.707107i 0.346688 + 0.0693375i
\(105\) 0 0
\(106\) −0.776179 0.776179i −0.0753892 0.0753892i
\(107\) 18.9569 1.83264 0.916318 0.400451i \(-0.131147\pi\)
0.916318 + 0.400451i \(0.131147\pi\)
\(108\) 0 0
\(109\) 11.3197 + 11.3197i 1.08423 + 1.08423i 0.996110 + 0.0881221i \(0.0280866\pi\)
0.0881221 + 0.996110i \(0.471913\pi\)
\(110\) 0.490590 0.490590i 0.0467759 0.0467759i
\(111\) 0 0
\(112\) 0.0951965 2.64404i 0.00899522 0.249838i
\(113\) 0.716898 0.0674400 0.0337200 0.999431i \(-0.489265\pi\)
0.0337200 + 0.999431i \(0.489265\pi\)
\(114\) 0 0
\(115\) 0.446833 + 0.446833i 0.0416674 + 0.0416674i
\(116\) 4.59428i 0.426568i
\(117\) 0 0
\(118\) 1.84725i 0.170053i
\(119\) −0.569453 + 15.8163i −0.0522017 + 1.44988i
\(120\) 0 0
\(121\) 15.5580i 1.41437i
\(122\) −4.22982 + 4.22982i −0.382950 + 0.382950i
\(123\) 0 0
\(124\) 0.739235 + 0.739235i 0.0663852 + 0.0663852i
\(125\) 0.950239 + 0.950239i 0.0849920 + 0.0849920i
\(126\) 0 0
\(127\) 2.28126i 0.202429i −0.994865 0.101215i \(-0.967727\pi\)
0.994865 0.101215i \(-0.0322729\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) −0.269256 0.403884i −0.0236153 0.0354230i
\(131\) 7.79148i 0.680745i −0.940291 0.340372i \(-0.889447\pi\)
0.940291 0.340372i \(-0.110553\pi\)
\(132\) 0 0
\(133\) 10.6870 + 11.4853i 0.926679 + 0.995900i
\(134\) 0.0642556i 0.00555084i
\(135\) 0 0
\(136\) −4.22982 + 4.22982i −0.362704 + 0.362704i
\(137\) −1.90480 + 1.90480i −0.162738 + 0.162738i −0.783779 0.621040i \(-0.786710\pi\)
0.621040 + 0.783779i \(0.286710\pi\)
\(138\) 0 0
\(139\) 0.716898i 0.0608065i −0.999538 0.0304032i \(-0.990321\pi\)
0.999538 0.0304032i \(-0.00967914\pi\)
\(140\) −0.260765 + 0.242641i −0.0220387 + 0.0205069i
\(141\) 0 0
\(142\) 12.2949i 1.03176i
\(143\) −18.2202 3.64404i −1.52365 0.304730i
\(144\) 0 0
\(145\) 0.437359 0.437359i 0.0363207 0.0363207i
\(146\) 6.83692i 0.565827i
\(147\) 0 0
\(148\) −4.83443 4.83443i −0.397388 0.397388i
\(149\) 8.22452 + 8.22452i 0.673779 + 0.673779i 0.958585 0.284806i \(-0.0919293\pi\)
−0.284806 + 0.958585i \(0.591929\pi\)
\(150\) 0 0
\(151\) 13.6713 13.6713i 1.11256 1.11256i 0.119755 0.992803i \(-0.461789\pi\)
0.992803 0.119755i \(-0.0382110\pi\)
\(152\) 5.92963i 0.480956i
\(153\) 0 0
\(154\) −0.490590 + 13.6259i −0.0395329 + 1.09801i
\(155\) 0.140745i 0.0113049i
\(156\) 0 0
\(157\) 12.3627i 0.986648i −0.869846 0.493324i \(-0.835782\pi\)
0.869846 0.493324i \(-0.164218\pi\)
\(158\) −8.18688 8.18688i −0.651313 0.651313i
\(159\) 0 0
\(160\) −0.134628 −0.0106433
\(161\) −12.4106 0.446833i −0.978091 0.0352154i
\(162\) 0 0
\(163\) 8.72111 8.72111i 0.683090 0.683090i −0.277605 0.960695i \(-0.589541\pi\)
0.960695 + 0.277605i \(0.0895407\pi\)
\(164\) 3.04544 + 3.04544i 0.237809 + 0.237809i
\(165\) 0 0
\(166\) −1.82161 −0.141385
\(167\) −13.3129 13.3129i −1.03018 1.03018i −0.999530 0.0306531i \(-0.990241\pi\)
−0.0306531 0.999530i \(-0.509759\pi\)
\(168\) 0 0
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 0.805329 0.0617659
\(171\) 0 0
\(172\) −8.78467 −0.669825
\(173\) 9.58296 0.728579 0.364290 0.931286i \(-0.381312\pi\)
0.364290 + 0.931286i \(0.381312\pi\)
\(174\) 0 0
\(175\) −13.1723 0.474257i −0.995730 0.0358504i
\(176\) −3.64404 + 3.64404i −0.274680 + 0.274680i
\(177\) 0 0
\(178\) 13.0358i 0.977075i
\(179\) 6.90729i 0.516275i −0.966108 0.258138i \(-0.916891\pi\)
0.966108 0.258138i \(-0.0831088\pi\)
\(180\) 0 0
\(181\) −22.3445 −1.66086 −0.830428 0.557126i \(-0.811904\pi\)
−0.830428 + 0.557126i \(0.811904\pi\)
\(182\) 9.28077 + 2.20619i 0.687937 + 0.163534i
\(183\) 0 0
\(184\) −3.31902 3.31902i −0.244681 0.244681i
\(185\) 0.920441i 0.0676722i
\(186\) 0 0
\(187\) 21.7982 21.7982i 1.59404 1.59404i
\(188\) −3.28808 + 3.28808i −0.239808 + 0.239808i
\(189\) 0 0
\(190\) 0.564480 0.564480i 0.0409516 0.0409516i
\(191\) −12.0315 −0.870570 −0.435285 0.900293i \(-0.643352\pi\)
−0.435285 + 0.900293i \(0.643352\pi\)
\(192\) 0 0
\(193\) −14.2700 + 14.2700i −1.02717 + 1.02717i −0.0275533 + 0.999620i \(0.508772\pi\)
−0.999620 + 0.0275533i \(0.991228\pi\)
\(194\) 14.1069 1.01281
\(195\) 0 0
\(196\) 0.503406 6.98188i 0.0359576 0.498705i
\(197\) 5.54884 + 5.54884i 0.395339 + 0.395339i 0.876585 0.481247i \(-0.159816\pi\)
−0.481247 + 0.876585i \(0.659816\pi\)
\(198\) 0 0
\(199\) −9.16546 −0.649722 −0.324861 0.945762i \(-0.605318\pi\)
−0.324861 + 0.945762i \(0.605318\pi\)
\(200\) −3.52272 3.52272i −0.249094 0.249094i
\(201\) 0 0
\(202\) −2.18688 2.18688i −0.153868 0.153868i
\(203\) −0.437359 + 12.1474i −0.0306966 + 0.852583i
\(204\) 0 0
\(205\) 0.579829i 0.0404970i
\(206\) 5.87819 + 5.87819i 0.409553 + 0.409553i
\(207\) 0 0
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) 30.5580i 2.11374i
\(210\) 0 0
\(211\) 0.784670 0.0540189 0.0270095 0.999635i \(-0.491402\pi\)
0.0270095 + 0.999635i \(0.491402\pi\)
\(212\) 1.09768i 0.0753892i
\(213\) 0 0
\(214\) 13.4046 + 13.4046i 0.916318 + 0.916318i
\(215\) 0.836269 + 0.836269i 0.0570331 + 0.0570331i
\(216\) 0 0
\(217\) 1.88419 + 2.02494i 0.127907 + 0.137462i
\(218\) 16.0085i 1.08423i
\(219\) 0 0
\(220\) 0.693799 0.0467759
\(221\) −11.9638 17.9456i −0.804769 1.20715i
\(222\) 0 0
\(223\) −19.2064 + 19.2064i −1.28616 + 1.28616i −0.349052 + 0.937104i \(0.613496\pi\)
−0.937104 + 0.349052i \(0.886504\pi\)
\(224\) 1.93693 1.80230i 0.129417 0.120421i
\(225\) 0 0
\(226\) 0.506923 + 0.506923i 0.0337200 + 0.0337200i
\(227\) −11.9819 + 11.9819i −0.795265 + 0.795265i −0.982345 0.187080i \(-0.940098\pi\)
0.187080 + 0.982345i \(0.440098\pi\)
\(228\) 0 0
\(229\) 8.98188 + 8.98188i 0.593539 + 0.593539i 0.938586 0.345047i \(-0.112137\pi\)
−0.345047 + 0.938586i \(0.612137\pi\)
\(230\) 0.631917i 0.0416674i
\(231\) 0 0
\(232\) −3.24864 + 3.24864i −0.213284 + 0.213284i
\(233\) 13.1473i 0.861310i −0.902517 0.430655i \(-0.858283\pi\)
0.902517 0.430655i \(-0.141717\pi\)
\(234\) 0 0
\(235\) 0.626026 0.0408375
\(236\) −1.30620 + 1.30620i −0.0850264 + 0.0850264i
\(237\) 0 0
\(238\) −11.5865 + 10.7812i −0.751040 + 0.698838i
\(239\) −17.4834 17.4834i −1.13091 1.13091i −0.990026 0.140884i \(-0.955006\pi\)
−0.140884 0.990026i \(-0.544994\pi\)
\(240\) 0 0
\(241\) 5.69380 + 5.69380i 0.366770 + 0.366770i 0.866298 0.499528i \(-0.166493\pi\)
−0.499528 + 0.866298i \(0.666493\pi\)
\(242\) 11.0012 11.0012i 0.707183 0.707183i
\(243\) 0 0
\(244\) −5.98188 −0.382950
\(245\) −0.712572 + 0.616727i −0.0455246 + 0.0394013i
\(246\) 0 0
\(247\) −20.9644 4.19288i −1.33393 0.266787i
\(248\) 1.04544i 0.0663852i
\(249\) 0 0
\(250\) 1.34384i 0.0849920i
\(251\) −12.4585 −0.786374 −0.393187 0.919459i \(-0.628627\pi\)
−0.393187 + 0.919459i \(0.628627\pi\)
\(252\) 0 0
\(253\) 17.1044 + 17.1044i 1.07534 + 1.07534i
\(254\) 1.61310 1.61310i 0.101215 0.101215i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 31.6738 1.97576 0.987880 0.155221i \(-0.0496089\pi\)
0.987880 + 0.155221i \(0.0496089\pi\)
\(258\) 0 0
\(259\) −12.3222 13.2426i −0.765664 0.822858i
\(260\) 0.0951965 0.475982i 0.00590383 0.0295192i
\(261\) 0 0
\(262\) 5.50941 5.50941i 0.340372 0.340372i
\(263\) −23.4422 −1.44551 −0.722755 0.691105i \(-0.757124\pi\)
−0.722755 + 0.691105i \(0.757124\pi\)
\(264\) 0 0
\(265\) −0.104496 + 0.104496i −0.00641911 + 0.00641911i
\(266\) −0.564480 + 15.6782i −0.0346105 + 0.961290i
\(267\) 0 0
\(268\) 0.0454356 0.0454356i 0.00277542 0.00277542i
\(269\) 16.2813i 0.992686i −0.868126 0.496343i \(-0.834676\pi\)
0.868126 0.496343i \(-0.165324\pi\)
\(270\) 0 0
\(271\) 10.1499 + 10.1499i 0.616564 + 0.616564i 0.944649 0.328084i \(-0.106403\pi\)
−0.328084 + 0.944649i \(0.606403\pi\)
\(272\) −5.98188 −0.362704
\(273\) 0 0
\(274\) −2.69380 −0.162738
\(275\) 18.1541 + 18.1541i 1.09474 + 1.09474i
\(276\) 0 0
\(277\) 1.09271i 0.0656546i −0.999461 0.0328273i \(-0.989549\pi\)
0.999461 0.0328273i \(-0.0104511\pi\)
\(278\) 0.506923 0.506923i 0.0304032 0.0304032i
\(279\) 0 0
\(280\) −0.355962 0.0128161i −0.0212728 0.000765910i
\(281\) 22.6284 22.6284i 1.34990 1.34990i 0.464130 0.885767i \(-0.346367\pi\)
0.885767 0.464130i \(-0.153633\pi\)
\(282\) 0 0
\(283\) −30.7167 −1.82592 −0.912958 0.408053i \(-0.866208\pi\)
−0.912958 + 0.408053i \(0.866208\pi\)
\(284\) 8.69380 8.69380i 0.515882 0.515882i
\(285\) 0 0
\(286\) −10.3069 15.4603i −0.609460 0.914189i
\(287\) 7.76233 + 8.34216i 0.458196 + 0.492422i
\(288\) 0 0
\(289\) 18.7828 1.10487
\(290\) 0.618519 0.0363207
\(291\) 0 0
\(292\) −4.83443 + 4.83443i −0.282914 + 0.282914i
\(293\) 15.5804 + 15.5804i 0.910215 + 0.910215i 0.996289 0.0860741i \(-0.0274322\pi\)
−0.0860741 + 0.996289i \(0.527432\pi\)
\(294\) 0 0
\(295\) 0.248691 0.0144794
\(296\) 6.83692i 0.397388i
\(297\) 0 0
\(298\) 11.6312i 0.673779i
\(299\) 14.0814 9.38760i 0.814348 0.542899i
\(300\) 0 0
\(301\) −23.2270 0.836269i −1.33878 0.0482018i
\(302\) 19.3342 1.11256
\(303\) 0 0
\(304\) −4.19288 + 4.19288i −0.240478 + 0.240478i
\(305\) 0.569453 + 0.569453i 0.0326068 + 0.0326068i
\(306\) 0 0
\(307\) −23.5058 23.5058i −1.34155 1.34155i −0.894522 0.447024i \(-0.852484\pi\)
−0.447024 0.894522i \(-0.647516\pi\)
\(308\) −9.98188 + 9.28808i −0.568770 + 0.529237i
\(309\) 0 0
\(310\) 0.0995218 0.0995218i 0.00565246 0.00565246i
\(311\) −33.9687 −1.92619 −0.963095 0.269162i \(-0.913253\pi\)
−0.963095 + 0.269162i \(0.913253\pi\)
\(312\) 0 0
\(313\) 29.8779i 1.68880i −0.535716 0.844398i \(-0.679958\pi\)
0.535716 0.844398i \(-0.320042\pi\)
\(314\) 8.74172 8.74172i 0.493324 0.493324i
\(315\) 0 0
\(316\) 11.5780i 0.651313i
\(317\) −15.1450 15.1450i −0.850626 0.850626i 0.139585 0.990210i \(-0.455423\pi\)
−0.990210 + 0.139585i \(0.955423\pi\)
\(318\) 0 0
\(319\) 16.7417 16.7417i 0.937356 0.937356i
\(320\) −0.0951965 0.0951965i −0.00532164 0.00532164i
\(321\) 0 0
\(322\) −8.45965 9.09157i −0.471438 0.506653i
\(323\) 25.0813 25.0813i 1.39556 1.39556i
\(324\) 0 0
\(325\) 14.9456 9.96375i 0.829034 0.552689i
\(326\) 12.3335 0.683090
\(327\) 0 0
\(328\) 4.30690i 0.237809i
\(329\) −9.00681 + 8.38079i −0.496562 + 0.462048i
\(330\) 0 0
\(331\) 10.2408 + 10.2408i 0.562885 + 0.562885i 0.930126 0.367241i \(-0.119697\pi\)
−0.367241 + 0.930126i \(0.619697\pi\)
\(332\) −1.28808 1.28808i −0.0706924 0.0706924i
\(333\) 0 0
\(334\) 18.8273i 1.03018i
\(335\) −0.00865061 −0.000472633
\(336\) 0 0
\(337\) 4.59428i 0.250266i 0.992140 + 0.125133i \(0.0399358\pi\)
−0.992140 + 0.125133i \(0.960064\pi\)
\(338\) −12.0208 + 4.94975i −0.653846 + 0.269231i
\(339\) 0 0
\(340\) 0.569453 + 0.569453i 0.0308829 + 0.0308829i
\(341\) 5.38760i 0.291755i
\(342\) 0 0
\(343\) 1.99567 18.4124i 0.107756 0.994177i
\(344\) −6.21170 6.21170i −0.334912 0.334912i
\(345\) 0 0
\(346\) 6.77618 + 6.77618i 0.364290 + 0.364290i
\(347\) 12.2500 0.657614 0.328807 0.944397i \(-0.393353\pi\)
0.328807 + 0.944397i \(0.393353\pi\)
\(348\) 0 0
\(349\) 1.38576 + 1.38576i 0.0741780 + 0.0741780i 0.743222 0.669044i \(-0.233296\pi\)
−0.669044 + 0.743222i \(0.733296\pi\)
\(350\) −8.97885 9.64955i −0.479940 0.515790i
\(351\) 0 0
\(352\) −5.15345 −0.274680
\(353\) 4.31041 4.31041i 0.229420 0.229420i −0.583030 0.812450i \(-0.698133\pi\)
0.812450 + 0.583030i \(0.198133\pi\)
\(354\) 0 0
\(355\) −1.65524 −0.0878509
\(356\) 9.21770 9.21770i 0.488537 0.488537i
\(357\) 0 0
\(358\) 4.88419 4.88419i 0.258138 0.258138i
\(359\) −0.213491 + 0.213491i −0.0112676 + 0.0112676i −0.712718 0.701451i \(-0.752536\pi\)
0.701451 + 0.712718i \(0.252536\pi\)
\(360\) 0 0
\(361\) 16.1605i 0.850552i
\(362\) −15.8000 15.8000i −0.830428 0.830428i
\(363\) 0 0
\(364\) 5.00249 + 8.12251i 0.262202 + 0.425735i
\(365\) 0.920441 0.0481781
\(366\) 0 0
\(367\) 1.09768i 0.0572986i −0.999590 0.0286493i \(-0.990879\pi\)
0.999590 0.0286493i \(-0.00912060\pi\)
\(368\) 4.69380i 0.244681i
\(369\) 0 0
\(370\) −0.650850 + 0.650850i −0.0338361 + 0.0338361i
\(371\) 0.104496 2.90232i 0.00542514 0.150681i
\(372\) 0 0
\(373\) 21.0565 1.09026 0.545131 0.838351i \(-0.316480\pi\)
0.545131 + 0.838351i \(0.316480\pi\)
\(374\) 30.8273 1.59404
\(375\) 0 0
\(376\) −4.65004 −0.239808
\(377\) −9.18855 13.7828i −0.473235 0.709852i
\(378\) 0 0
\(379\) −7.22452 7.22452i −0.371098 0.371098i 0.496779 0.867877i \(-0.334516\pi\)
−0.867877 + 0.496779i \(0.834516\pi\)
\(380\) 0.798295 0.0409516
\(381\) 0 0
\(382\) −8.50757 8.50757i −0.435285 0.435285i
\(383\) 5.97518 5.97518i 0.305317 0.305317i −0.537773 0.843090i \(-0.680734\pi\)
0.843090 + 0.537773i \(0.180734\pi\)
\(384\) 0 0
\(385\) 1.83443 + 0.0660472i 0.0934913 + 0.00336608i
\(386\) −20.1808 −1.02717
\(387\) 0 0
\(388\) 9.97506 + 9.97506i 0.506407 + 0.506407i
\(389\) 25.0614i 1.27067i 0.772239 + 0.635333i \(0.219137\pi\)
−0.772239 + 0.635333i \(0.780863\pi\)
\(390\) 0 0
\(391\) 28.0777i 1.41995i
\(392\) 5.29289 4.58097i 0.267331 0.231374i
\(393\) 0 0
\(394\) 7.84725i 0.395339i
\(395\) −1.10218 + 1.10218i −0.0554569 + 0.0554569i
\(396\) 0 0
\(397\) −7.28624 7.28624i −0.365686 0.365686i 0.500215 0.865901i \(-0.333254\pi\)
−0.865901 + 0.500215i \(0.833254\pi\)
\(398\) −6.48096 6.48096i −0.324861 0.324861i
\(399\) 0 0
\(400\) 4.98188i 0.249094i
\(401\) −11.1450 + 11.1450i −0.556553 + 0.556553i −0.928324 0.371772i \(-0.878750\pi\)
0.371772 + 0.928324i \(0.378750\pi\)
\(402\) 0 0
\(403\) −3.69617 0.739235i −0.184119 0.0368239i
\(404\) 3.09271i 0.153868i
\(405\) 0 0
\(406\) −8.89880 + 8.28028i −0.441640 + 0.410943i
\(407\) 35.2337i 1.74647i
\(408\) 0 0
\(409\) −14.6028 + 14.6028i −0.722063 + 0.722063i −0.969025 0.246962i \(-0.920568\pi\)
0.246962 + 0.969025i \(0.420568\pi\)
\(410\) 0.410001 0.410001i 0.0202485 0.0202485i
\(411\) 0 0
\(412\) 8.31301i 0.409553i
\(413\) −3.57799 + 3.32930i −0.176061 + 0.163824i
\(414\) 0 0
\(415\) 0.245241i 0.0120384i
\(416\) −0.707107 + 3.53553i −0.0346688 + 0.173344i
\(417\) 0 0
\(418\) 21.6078 21.6078i 1.05687 1.05687i
\(419\) 16.5630i 0.809156i 0.914504 + 0.404578i \(0.132582\pi\)
−0.914504 + 0.404578i \(0.867418\pi\)
\(420\) 0 0
\(421\) −12.1655 12.1655i −0.592908 0.592908i 0.345508 0.938416i \(-0.387707\pi\)
−0.938416 + 0.345508i \(0.887707\pi\)
\(422\) 0.554846 + 0.554846i 0.0270095 + 0.0270095i
\(423\) 0 0
\(424\) 0.776179 0.776179i 0.0376946 0.0376946i
\(425\) 29.8010i 1.44556i
\(426\) 0 0
\(427\) −15.8163 0.569453i −0.765405 0.0275578i
\(428\) 18.9569i 0.916318i
\(429\) 0 0
\(430\) 1.18266i 0.0570331i
\(431\) −5.80961 5.80961i −0.279839 0.279839i 0.553206 0.833045i \(-0.313404\pi\)
−0.833045 + 0.553206i \(0.813404\pi\)
\(432\) 0 0
\(433\) −30.1229 −1.44761 −0.723806 0.690003i \(-0.757609\pi\)
−0.723806 + 0.690003i \(0.757609\pi\)
\(434\) −0.0995218 + 2.76417i −0.00477720 + 0.132684i
\(435\) 0 0
\(436\) −11.3197 + 11.3197i −0.542116 + 0.542116i
\(437\) 19.6805 + 19.6805i 0.941448 + 0.941448i
\(438\) 0 0
\(439\) 8.65755 0.413202 0.206601 0.978425i \(-0.433760\pi\)
0.206601 + 0.978425i \(0.433760\pi\)
\(440\) 0.490590 + 0.490590i 0.0233880 + 0.0233880i
\(441\) 0 0
\(442\) 4.22982 21.1491i 0.201192 1.00596i
\(443\) −15.3839 −0.730912 −0.365456 0.930829i \(-0.619087\pi\)
−0.365456 + 0.930829i \(0.619087\pi\)
\(444\) 0 0
\(445\) −1.75499 −0.0831943
\(446\) −27.1619 −1.28616
\(447\) 0 0
\(448\) 2.64404 + 0.0951965i 0.124919 + 0.00449761i
\(449\) −2.29056 + 2.29056i −0.108098 + 0.108098i −0.759087 0.650989i \(-0.774354\pi\)
0.650989 + 0.759087i \(0.274354\pi\)
\(450\) 0 0
\(451\) 22.1954i 1.04514i
\(452\) 0.716898i 0.0337200i
\(453\) 0 0
\(454\) −16.9449 −0.795265
\(455\) 0.297015 1.24945i 0.0139243 0.0585753i
\(456\) 0 0
\(457\) 9.79829 + 9.79829i 0.458345 + 0.458345i 0.898112 0.439767i \(-0.144939\pi\)
−0.439767 + 0.898112i \(0.644939\pi\)
\(458\) 12.7023i 0.593539i
\(459\) 0 0
\(460\) −0.446833 + 0.446833i −0.0208337 + 0.0208337i
\(461\) −7.71441 + 7.71441i −0.359296 + 0.359296i −0.863553 0.504257i \(-0.831766\pi\)
0.504257 + 0.863553i \(0.331766\pi\)
\(462\) 0 0
\(463\) 10.0521 10.0521i 0.467162 0.467162i −0.433832 0.900994i \(-0.642839\pi\)
0.900994 + 0.433832i \(0.142839\pi\)
\(464\) −4.59428 −0.213284
\(465\) 0 0
\(466\) 9.29657 9.29657i 0.430655 0.430655i
\(467\) −9.63711 −0.445952 −0.222976 0.974824i \(-0.571577\pi\)
−0.222976 + 0.974824i \(0.571577\pi\)
\(468\) 0 0
\(469\) 0.124459 0.115808i 0.00574697 0.00534752i
\(470\) 0.442668 + 0.442668i 0.0204187 + 0.0204187i
\(471\) 0 0
\(472\) −1.84725 −0.0850264
\(473\) 32.0117 + 32.0117i 1.47190 + 1.47190i
\(474\) 0 0
\(475\) 20.8884 + 20.8884i 0.958426 + 0.958426i
\(476\) −15.8163 0.569453i −0.724939 0.0261008i
\(477\) 0 0
\(478\) 24.7253i 1.13091i
\(479\) 10.2288 + 10.2288i 0.467368 + 0.467368i 0.901061 0.433693i \(-0.142790\pi\)
−0.433693 + 0.901061i \(0.642790\pi\)
\(480\) 0 0
\(481\) 24.1722 + 4.83443i 1.10216 + 0.220431i
\(482\) 8.05225i 0.366770i
\(483\) 0 0
\(484\) 15.5580 0.707183
\(485\) 1.89918i 0.0862374i
\(486\) 0 0
\(487\) 1.05675 + 1.05675i 0.0478858 + 0.0478858i 0.730644 0.682758i \(-0.239220\pi\)
−0.682758 + 0.730644i \(0.739220\pi\)
\(488\) −4.22982 4.22982i −0.191475 0.191475i
\(489\) 0 0
\(490\) −0.939957 0.0677726i −0.0424629 0.00306165i
\(491\) 1.19721i 0.0540291i 0.999635 + 0.0270146i \(0.00860005\pi\)
−0.999635 + 0.0270146i \(0.991400\pi\)
\(492\) 0 0
\(493\) 27.4824 1.23774
\(494\) −11.8593 17.7889i −0.533573 0.800360i
\(495\) 0 0
\(496\) −0.739235 + 0.739235i −0.0331926 + 0.0331926i
\(497\) 23.8144 22.1591i 1.06822 0.993972i
\(498\) 0 0
\(499\) −4.14128 4.14128i −0.185389 0.185389i 0.608310 0.793699i \(-0.291848\pi\)
−0.793699 + 0.608310i \(0.791848\pi\)
\(500\) −0.950239 + 0.950239i −0.0424960 + 0.0424960i
\(501\) 0 0
\(502\) −8.80949 8.80949i −0.393187 0.393187i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) 0 0
\(505\) −0.294415 + 0.294415i −0.0131013 + 0.0131013i
\(506\) 24.1892i 1.07534i
\(507\) 0 0
\(508\) 2.28126 0.101215
\(509\) 7.43292 7.43292i 0.329458 0.329458i −0.522922 0.852380i \(-0.675158\pi\)
0.852380 + 0.522922i \(0.175158\pi\)
\(510\) 0 0
\(511\) −13.2426 + 12.3222i −0.585820 + 0.545102i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 22.3968 + 22.3968i 0.987880 + 0.987880i
\(515\) 0.791369 0.791369i 0.0348719 0.0348719i
\(516\) 0 0
\(517\) 23.9638 1.05392
\(518\) 0.650850 18.0771i 0.0285967 0.794261i
\(519\) 0 0
\(520\) 0.403884 0.269256i 0.0177115 0.0118077i
\(521\) 32.0002i 1.40196i −0.713183 0.700978i \(-0.752747\pi\)
0.713183 0.700978i \(-0.247253\pi\)
\(522\) 0 0
\(523\) 1.89550i 0.0828846i 0.999141 + 0.0414423i \(0.0131953\pi\)
−0.999141 + 0.0414423i \(0.986805\pi\)
\(524\) 7.79148 0.340372
\(525\) 0 0
\(526\) −16.5762 16.5762i −0.722755 0.722755i
\(527\) 4.42201 4.42201i 0.192626 0.192626i
\(528\) 0 0
\(529\) 0.968251 0.0420979
\(530\) −0.147779 −0.00641911
\(531\) 0 0
\(532\) −11.4853 + 10.6870i −0.497950 + 0.463340i
\(533\) −15.2272 3.04544i −0.659562 0.131912i
\(534\) 0 0
\(535\) 1.80463 1.80463i 0.0780211 0.0780211i
\(536\) 0.0642556 0.00277542
\(537\) 0 0
\(538\) 11.5126 11.5126i 0.496343 0.496343i
\(539\) −27.2767 + 23.6078i −1.17489 + 1.01686i
\(540\) 0 0
\(541\) −4.11753 + 4.11753i −0.177027 + 0.177027i −0.790058 0.613032i \(-0.789950\pi\)
0.613032 + 0.790058i \(0.289950\pi\)
\(542\) 14.3542i 0.616564i
\(543\) 0 0
\(544\) −4.22982 4.22982i −0.181352 0.181352i
\(545\) 2.15519 0.0923183
\(546\) 0 0
\(547\) −44.5000 −1.90268 −0.951341 0.308141i \(-0.900293\pi\)
−0.951341 + 0.308141i \(0.900293\pi\)
\(548\) −1.90480 1.90480i −0.0813692 0.0813692i
\(549\) 0 0
\(550\) 25.6738i 1.09474i
\(551\) 19.2633 19.2633i 0.820642 0.820642i
\(552\) 0 0
\(553\) 1.10218 30.6126i 0.0468696 1.30178i
\(554\) 0.772662 0.772662i 0.0328273 0.0328273i
\(555\) 0 0
\(556\) 0.716898 0.0304032
\(557\) 9.50762 9.50762i 0.402851 0.402851i −0.476386 0.879236i \(-0.658053\pi\)
0.879236 + 0.476386i \(0.158053\pi\)
\(558\) 0 0
\(559\) 26.3540 17.5693i 1.11466 0.743104i
\(560\) −0.242641 0.260765i −0.0102534 0.0110194i
\(561\) 0 0
\(562\) 32.0014 1.34990
\(563\) 16.3640 0.689659 0.344829 0.938665i \(-0.387937\pi\)
0.344829 + 0.938665i \(0.387937\pi\)
\(564\) 0 0
\(565\) 0.0682461 0.0682461i 0.00287114 0.00287114i
\(566\) −21.7200 21.7200i −0.912958 0.912958i
\(567\) 0 0
\(568\) 12.2949 0.515882
\(569\) 26.8760i 1.12670i −0.826218 0.563351i \(-0.809512\pi\)
0.826218 0.563351i \(-0.190488\pi\)
\(570\) 0 0
\(571\) 26.1591i 1.09472i 0.836896 + 0.547362i \(0.184368\pi\)
−0.836896 + 0.547362i \(0.815632\pi\)
\(572\) 3.64404 18.2202i 0.152365 0.761824i
\(573\) 0 0
\(574\) −0.410001 + 11.3876i −0.0171131 + 0.475309i
\(575\) −23.3839 −0.975177
\(576\) 0 0
\(577\) −3.83454 + 3.83454i −0.159634 + 0.159634i −0.782405 0.622770i \(-0.786007\pi\)
0.622770 + 0.782405i \(0.286007\pi\)
\(578\) 13.2815 + 13.2815i 0.552436 + 0.552436i
\(579\) 0 0
\(580\) 0.437359 + 0.437359i 0.0181603 + 0.0181603i
\(581\) −3.28310 3.52834i −0.136206 0.146380i
\(582\) 0 0
\(583\) −4.00000 + 4.00000i −0.165663 + 0.165663i
\(584\) −6.83692 −0.282914
\(585\) 0 0
\(586\) 22.0340i 0.910215i
\(587\) −15.5599 + 15.5599i −0.642224 + 0.642224i −0.951102 0.308877i \(-0.900047\pi\)
0.308877 + 0.951102i \(0.400047\pi\)
\(588\) 0 0
\(589\) 6.19904i 0.255427i
\(590\) 0.175851 + 0.175851i 0.00723969 + 0.00723969i
\(591\) 0 0
\(592\) 4.83443 4.83443i 0.198694 0.198694i
\(593\) −0.351637 0.351637i −0.0144400 0.0144400i 0.699850 0.714290i \(-0.253250\pi\)
−0.714290 + 0.699850i \(0.753250\pi\)
\(594\) 0 0
\(595\) 1.45145 + 1.55987i 0.0595035 + 0.0639483i
\(596\) −8.22452 + 8.22452i −0.336889 + 0.336889i
\(597\) 0 0
\(598\) 16.5951 + 3.31902i 0.678624 + 0.135725i
\(599\) −34.9302 −1.42721 −0.713604 0.700549i \(-0.752938\pi\)
−0.713604 + 0.700549i \(0.752938\pi\)
\(600\) 0 0
\(601\) 0.993188i 0.0405130i 0.999795 + 0.0202565i \(0.00644828\pi\)
−0.999795 + 0.0202565i \(0.993552\pi\)
\(602\) −15.8326 17.0153i −0.645290 0.693492i
\(603\) 0 0
\(604\) 13.6713 + 13.6713i 0.556279 + 0.556279i
\(605\) −1.48107 1.48107i −0.0602140 0.0602140i
\(606\) 0 0
\(607\) 20.6029i 0.836247i −0.908390 0.418124i \(-0.862688\pi\)
0.908390 0.418124i \(-0.137312\pi\)
\(608\) −5.92963 −0.240478
\(609\) 0 0
\(610\) 0.805329i 0.0326068i
\(611\) 3.28808 16.4404i 0.133021 0.665107i
\(612\) 0 0
\(613\) −30.3315 30.3315i −1.22508 1.22508i −0.965804 0.259274i \(-0.916517\pi\)
−0.259274 0.965804i \(-0.583483\pi\)
\(614\) 33.2422i 1.34155i
\(615\) 0 0
\(616\) −13.6259 0.490590i −0.549004 0.0197664i
\(617\) 22.7622 + 22.7622i 0.916372 + 0.916372i 0.996763 0.0803909i \(-0.0256169\pi\)
−0.0803909 + 0.996763i \(0.525617\pi\)
\(618\) 0 0
\(619\) 9.96126 + 9.96126i 0.400377 + 0.400377i 0.878366 0.477989i \(-0.158634\pi\)
−0.477989 + 0.878366i \(0.658634\pi\)
\(620\) 0.140745 0.00565246
\(621\) 0 0
\(622\) −24.0195 24.0195i −0.963095 0.963095i
\(623\) 25.2495 23.4945i 1.01160 0.941286i
\(624\) 0 0
\(625\) −24.7285 −0.989138
\(626\) 21.1268 21.1268i 0.844398 0.844398i
\(627\) 0 0
\(628\) 12.3627 0.493324
\(629\) −28.9190 + 28.9190i −1.15307 + 1.15307i
\(630\) 0 0
\(631\) 8.24750 8.24750i 0.328328 0.328328i −0.523623 0.851950i \(-0.675420\pi\)
0.851950 + 0.523623i \(0.175420\pi\)
\(632\) 8.18688 8.18688i 0.325656 0.325656i
\(633\) 0 0
\(634\) 21.4182i 0.850626i
\(635\) −0.217168 0.217168i −0.00861806 0.00861806i
\(636\) 0 0
\(637\) 12.4535 + 21.9524i 0.493427 + 0.869787i
\(638\) 23.6764 0.937356
\(639\) 0 0
\(640\) 0.134628i 0.00532164i
\(641\) 27.4472i 1.08410i 0.840347 + 0.542049i \(0.182351\pi\)
−0.840347 + 0.542049i \(0.817649\pi\)
\(642\) 0 0
\(643\) −27.7346 + 27.7346i −1.09375 + 1.09375i −0.0986217 + 0.995125i \(0.531443\pi\)
−0.995125 + 0.0986217i \(0.968557\pi\)
\(644\) 0.446833 12.4106i 0.0176077 0.489046i
\(645\) 0 0
\(646\) 35.4703 1.39556
\(647\) −14.6620 −0.576425 −0.288212 0.957567i \(-0.593061\pi\)
−0.288212 + 0.957567i \(0.593061\pi\)
\(648\) 0 0
\(649\) 9.51969 0.373681
\(650\) 17.6136 + 3.52272i 0.690862 + 0.138172i
\(651\) 0 0
\(652\) 8.72111 + 8.72111i 0.341545 + 0.341545i
\(653\) −15.7965 −0.618163 −0.309082 0.951036i \(-0.600022\pi\)
−0.309082 + 0.951036i \(0.600022\pi\)
\(654\) 0 0
\(655\) −0.741721 0.741721i −0.0289815 0.0289815i
\(656\) −3.04544 + 3.04544i −0.118904 + 0.118904i
\(657\) 0 0
\(658\) −12.2949 0.442668i −0.479305 0.0172570i
\(659\) −8.06825 −0.314294 −0.157147 0.987575i \(-0.550230\pi\)
−0.157147 + 0.987575i \(0.550230\pi\)
\(660\) 0 0
\(661\) −30.7552 30.7552i −1.19624 1.19624i −0.975284 0.220956i \(-0.929082\pi\)
−0.220956 0.975284i \(-0.570918\pi\)
\(662\) 14.4827i 0.562885i
\(663\) 0 0
\(664\) 1.82161i 0.0706924i
\(665\) 2.11072 + 0.0759948i 0.0818503 + 0.00294695i
\(666\) 0 0
\(667\) 21.5646i 0.834985i
\(668\) 13.3129 13.3129i 0.515092 0.515092i
\(669\) 0 0
\(670\) −0.00611691 0.00611691i −0.000236317 0.000236317i
\(671\) 21.7982 + 21.7982i 0.841509 + 0.841509i
\(672\) 0 0
\(673\) 43.5286i 1.67790i 0.544206 + 0.838952i \(0.316831\pi\)
−0.544206 + 0.838952i \(0.683169\pi\)
\(674\) −3.24864 + 3.24864i −0.125133 + 0.125133i
\(675\) 0 0
\(676\) −12.0000 5.00000i −0.461538 0.192308i
\(677\) 13.3826i 0.514336i 0.966367 + 0.257168i \(0.0827894\pi\)
−0.966367 + 0.257168i \(0.917211\pi\)
\(678\) 0 0
\(679\) 25.4249 + 27.3240i 0.975716 + 1.04860i
\(680\) 0.805329i 0.0308829i
\(681\) 0 0
\(682\) 3.80961 3.80961i 0.145877 0.145877i
\(683\) −11.4536 + 11.4536i −0.438262 + 0.438262i −0.891427 0.453165i \(-0.850295\pi\)
0.453165 + 0.891427i \(0.350295\pi\)
\(684\) 0 0
\(685\) 0.362661i 0.0138566i
\(686\) 14.4307 11.6084i 0.550967 0.443211i
\(687\) 0 0
\(688\) 8.78467i 0.334912i
\(689\) 2.19537 + 3.29305i 0.0836368 + 0.125455i
\(690\) 0 0
\(691\) 1.55068 1.55068i 0.0589907 0.0589907i −0.676996 0.735987i \(-0.736719\pi\)
0.735987 + 0.676996i \(0.236719\pi\)
\(692\) 9.58296i 0.364290i
\(693\) 0 0
\(694\) 8.66205 + 8.66205i 0.328807 + 0.328807i
\(695\) −0.0682461 0.0682461i −0.00258872 0.00258872i
\(696\) 0 0
\(697\) 18.2174 18.2174i 0.690034 0.690034i
\(698\) 1.95976i 0.0741780i
\(699\) 0 0
\(700\) 0.474257 13.1723i 0.0179252 0.497865i
\(701\) 8.43541i 0.318601i −0.987230 0.159300i \(-0.949076\pi\)
0.987230 0.159300i \(-0.0509239\pi\)
\(702\) 0 0
\(703\) 40.5404i 1.52901i
\(704\) −3.64404 3.64404i −0.137340 0.137340i
\(705\) 0 0
\(706\) 6.09584 0.229420
\(707\) 0.294415 8.17724i 0.0110726 0.307537i
\(708\) 0 0
\(709\) −19.8616 + 19.8616i −0.745917 + 0.745917i −0.973710 0.227793i \(-0.926849\pi\)
0.227793 + 0.973710i \(0.426849\pi\)
\(710\) −1.17043 1.17043i −0.0439254 0.0439254i
\(711\) 0 0
\(712\) 13.0358 0.488537
\(713\) 3.46982 + 3.46982i 0.129946 + 0.129946i
\(714\) 0 0
\(715\) −2.08140 + 1.38760i −0.0778398 + 0.0518932i
\(716\) 6.90729 0.258138
\(717\) 0 0
\(718\) −0.301922 −0.0112676
\(719\) 3.21983 0.120079 0.0600397 0.998196i \(-0.480877\pi\)
0.0600397 + 0.998196i \(0.480877\pi\)
\(720\) 0 0
\(721\) −0.791369 + 21.9799i −0.0294721 + 0.818575i
\(722\) 11.4272 11.4272i 0.425276 0.425276i
\(723\) 0 0
\(724\) 22.3445i 0.830428i
\(725\) 22.8881i 0.850043i
\(726\) 0 0
\(727\) −13.4007 −0.497006 −0.248503 0.968631i \(-0.579939\pi\)
−0.248503 + 0.968631i \(0.579939\pi\)
\(728\) −2.20619 + 9.28077i −0.0817668 + 0.343968i
\(729\) 0 0
\(730\) 0.650850 + 0.650850i 0.0240891 + 0.0240891i
\(731\) 52.5488i 1.94359i
\(732\) 0 0
\(733\) 28.6644 28.6644i 1.05874 1.05874i 0.0605789 0.998163i \(-0.480705\pi\)
0.998163 0.0605789i \(-0.0192947\pi\)
\(734\) 0.776179 0.776179i 0.0286493 0.0286493i
\(735\) 0 0
\(736\) 3.31902 3.31902i 0.122341 0.122341i
\(737\) −0.331138 −0.0121976
\(738\) 0 0
\(739\) 5.76417 5.76417i 0.212038 0.212038i −0.593094 0.805133i \(-0.702094\pi\)
0.805133 + 0.593094i \(0.202094\pi\)
\(740\) −0.920441 −0.0338361
\(741\) 0 0
\(742\) 2.12614 1.97836i 0.0780530 0.0726278i
\(743\) −15.4107 15.4107i −0.565364 0.565364i 0.365462 0.930826i \(-0.380911\pi\)
−0.930826 + 0.365462i \(0.880911\pi\)
\(744\) 0 0
\(745\) 1.56589 0.0573698
\(746\) 14.8892 + 14.8892i 0.545131 + 0.545131i
\(747\) 0 0
\(748\) 21.7982 + 21.7982i 0.797020 + 0.797020i
\(749\) −1.80463 + 50.1229i −0.0659399 + 1.83145i
\(750\) 0 0
\(751\) 4.11812i 0.150272i −0.997173 0.0751362i \(-0.976061\pi\)
0.997173 0.0751362i \(-0.0239391\pi\)
\(752\) −3.28808 3.28808i −0.119904 0.119904i
\(753\) 0 0
\(754\) 3.24864 16.2432i 0.118309 0.591543i
\(755\) 2.60293i 0.0947302i
\(756\) 0 0
\(757\) −18.1229 −0.658687 −0.329343 0.944210i \(-0.606827\pi\)
−0.329343 + 0.944210i \(0.606827\pi\)
\(758\) 10.2170i 0.371098i
\(759\) 0 0
\(760\) 0.564480 + 0.564480i 0.0204758 + 0.0204758i
\(761\) 21.1268 + 21.1268i 0.765847 + 0.765847i 0.977372 0.211525i \(-0.0678431\pi\)
−0.211525 + 0.977372i \(0.567843\pi\)
\(762\) 0 0
\(763\) −31.0073 + 28.8522i −1.12254 + 1.04452i
\(764\) 12.0315i 0.435285i
\(765\) 0 0
\(766\) 8.45018 0.305317
\(767\) 1.30620 6.53100i 0.0471642 0.235821i
\(768\) 0 0
\(769\) 2.12748 2.12748i 0.0767189 0.0767189i −0.667706 0.744425i \(-0.732724\pi\)
0.744425 + 0.667706i \(0.232724\pi\)
\(770\) 1.25044 + 1.34384i 0.0450626 + 0.0484287i
\(771\) 0 0
\(772\) −14.2700 14.2700i −0.513587 0.513587i
\(773\) 3.62354 3.62354i 0.130330 0.130330i −0.638933 0.769263i \(-0.720624\pi\)
0.769263 + 0.638933i \(0.220624\pi\)
\(774\) 0 0
\(775\) 3.68277 + 3.68277i 0.132289 + 0.132289i
\(776\) 14.1069i 0.506407i
\(777\) 0 0
\(778\) −17.7211 + 17.7211i −0.635333 + 0.635333i
\(779\) 25.5383i 0.915004i
\(780\) 0 0
\(781\) −63.3611 −2.26724
\(782\) −19.8539 + 19.8539i −0.709976 + 0.709976i
\(783\) 0 0
\(784\) 6.98188 + 0.503406i 0.249353 + 0.0179788i
\(785\) −1.17688 1.17688i −0.0420047 0.0420047i
\(786\) 0 0
\(787\) −1.94787 1.94787i −0.0694339 0.0694339i 0.671537 0.740971i \(-0.265634\pi\)
−0.740971 + 0.671537i \(0.765634\pi\)
\(788\) −5.54884 + 5.54884i −0.197669 + 0.197669i
\(789\) 0 0
\(790\) −1.55872 −0.0554569
\(791\) −0.0682461 + 1.89550i −0.00242655 + 0.0673964i
\(792\) 0 0
\(793\) 17.9456 11.9638i 0.637268 0.424845i
\(794\) 10.3043i 0.365686i
\(795\) 0 0
\(796\) 9.16546i 0.324861i
\(797\) 37.8727 1.34152 0.670759 0.741675i \(-0.265968\pi\)
0.670759 + 0.741675i \(0.265968\pi\)
\(798\) 0 0
\(799\) 19.6689 + 19.6689i 0.695834 + 0.695834i
\(800\) 3.52272 3.52272i 0.124547 0.124547i
\(801\) 0 0
\(802\) −15.7613 −0.556553
\(803\) 35.2337 1.24337
\(804\) 0 0
\(805\) −1.22398 + 1.13891i −0.0431396 + 0.0401412i
\(806\) −2.09087 3.13631i −0.0736478 0.110472i
\(807\) 0 0
\(808\) 2.18688 2.18688i 0.0769340 0.0769340i
\(809\) 30.9619 1.08856 0.544281 0.838903i \(-0.316802\pi\)
0.544281 + 0.838903i \(0.316802\pi\)
\(810\) 0 0
\(811\) −10.3882 + 10.3882i −0.364781 + 0.364781i −0.865569 0.500789i \(-0.833043\pi\)
0.500789 + 0.865569i \(0.333043\pi\)
\(812\) −12.1474 0.437359i −0.426292 0.0153483i
\(813\) 0 0
\(814\) −24.9140 + 24.9140i −0.873235 + 0.873235i
\(815\) 1.66044i 0.0581626i
\(816\) 0 0
\(817\) 36.8331 + 36.8331i 1.28863 + 1.28863i
\(818\) −20.6515 −0.722063
\(819\) 0 0
\(820\) 0.579829 0.0202485
\(821\) 28.9593 + 28.9593i 1.01069 + 1.01069i 0.999942 + 0.0107447i \(0.00342021\pi\)
0.0107447 + 0.999942i \(0.496580\pi\)
\(822\) 0 0
\(823\) 1.99480i 0.0695344i 0.999395 + 0.0347672i \(0.0110690\pi\)
−0.999395 + 0.0347672i \(0.988931\pi\)
\(824\) −5.87819 + 5.87819i −0.204776 + 0.204776i
\(825\) 0 0
\(826\) −4.88419 0.175851i −0.169943 0.00611865i
\(827\) 25.3675 25.3675i 0.882115 0.882115i −0.111634 0.993749i \(-0.535608\pi\)
0.993749 + 0.111634i \(0.0356085\pi\)
\(828\) 0 0
\(829\) 25.3522 0.880517 0.440259 0.897871i \(-0.354887\pi\)
0.440259 + 0.897871i \(0.354887\pi\)
\(830\) −0.173411 + 0.173411i −0.00601919 + 0.00601919i
\(831\) 0 0
\(832\) −3.00000 + 2.00000i −0.104006 + 0.0693375i
\(833\) −41.7647 3.01131i −1.44706 0.104336i
\(834\) 0 0
\(835\) −2.53468 −0.0877163
\(836\) 30.5580 1.05687
\(837\) 0 0
\(838\) −11.7118 + 11.7118i −0.404578 + 0.404578i
\(839\) −34.3545 34.3545i −1.18605 1.18605i −0.978151 0.207898i \(-0.933338\pi\)
−0.207898 0.978151i \(-0.566662\pi\)
\(840\) 0 0
\(841\) −7.89262 −0.272159
\(842\) 17.2046i 0.592908i
\(843\) 0 0
\(844\) 0.784670i 0.0270095i
\(845\) 0.666375 + 1.61834i 0.0229240 + 0.0556726i
\(846\) 0 0
\(847\) 41.1360 + 1.48107i 1.41345 + 0.0508901i
\(848\) 1.09768 0.0376946
\(849\) 0 0
\(850\) −21.0725 + 21.0725i −0.722779 + 0.722779i
\(851\) −22.6918 22.6918i −0.777867 0.777867i
\(852\) 0 0
\(853\) 15.6489 + 15.6489i 0.535808 + 0.535808i 0.922295 0.386487i \(-0.126312\pi\)
−0.386487 + 0.922295i \(0.626312\pi\)
\(854\) −10.7812 11.5865i −0.368923 0.396481i
\(855\) 0 0
\(856\) −13.4046 + 13.4046i −0.458159 + 0.458159i
\(857\) −44.8434 −1.53182 −0.765911 0.642946i \(-0.777712\pi\)
−0.765911 + 0.642946i \(0.777712\pi\)
\(858\) 0 0
\(859\) 55.8416i 1.90529i −0.304083 0.952645i \(-0.598350\pi\)
0.304083 0.952645i \(-0.401650\pi\)
\(860\) −0.836269 + 0.836269i −0.0285166 + 0.0285166i
\(861\) 0 0
\(862\) 8.21603i 0.279839i
\(863\) −28.7122 28.7122i −0.977374 0.977374i 0.0223760 0.999750i \(-0.492877\pi\)
−0.999750 + 0.0223760i \(0.992877\pi\)
\(864\) 0 0
\(865\) 0.912264 0.912264i 0.0310179 0.0310179i
\(866\) −21.3001 21.3001i −0.723806 0.723806i
\(867\) 0 0
\(868\) −2.02494 + 1.88419i −0.0687308 + 0.0639536i
\(869\) −42.1906 + 42.1906i −1.43122 + 1.43122i
\(870\) 0 0
\(871\) −0.0454356 + 0.227178i −0.00153953 + 0.00769763i
\(872\) −16.0085 −0.542116
\(873\) 0 0
\(874\) 27.8325i 0.941448i
\(875\) −2.60293 + 2.42201i −0.0879950 + 0.0818789i
\(876\) 0 0
\(877\) 25.4259 + 25.4259i 0.858573 + 0.858573i 0.991170 0.132597i \(-0.0423317\pi\)
−0.132597 + 0.991170i \(0.542332\pi\)
\(878\) 6.12181 + 6.12181i 0.206601 + 0.206601i
\(879\) 0 0
\(880\) 0.693799i 0.0233880i
\(881\) −32.2182 −1.08546 −0.542730 0.839907i \(-0.682609\pi\)
−0.542730 + 0.839907i \(0.682609\pi\)
\(882\) 0 0
\(883\) 16.0777i 0.541058i 0.962712 + 0.270529i \(0.0871987\pi\)
−0.962712 + 0.270529i \(0.912801\pi\)
\(884\) 17.9456 11.9638i 0.603577 0.402384i
\(885\) 0 0
\(886\) −10.8781 10.8781i −0.365456 0.365456i
\(887\) 48.6804i 1.63453i 0.576263 + 0.817264i \(0.304510\pi\)
−0.576263 + 0.817264i \(0.695490\pi\)
\(888\) 0 0
\(889\) 6.03175 + 0.217168i 0.202298 + 0.00728359i
\(890\) −1.24096 1.24096i −0.0415971 0.0415971i
\(891\) 0 0
\(892\) −19.2064 19.2064i −0.643078 0.643078i
\(893\) 27.5730 0.922696
\(894\) 0 0
\(895\) −0.657550 0.657550i −0.0219795 0.0219795i
\(896\) 1.80230 + 1.93693i 0.0602107 + 0.0647083i
\(897\) 0 0
\(898\) −3.23935 −0.108098
\(899\) 3.39625 3.39625i 0.113271 0.113271i
\(900\) 0 0
\(901\) −6.56620 −0.218752
\(902\) 15.6945 15.6945i 0.522569 0.522569i
\(903\) 0 0
\(904\) −0.506923 + 0.506923i −0.0168600 + 0.0168600i
\(905\) −2.12712 + 2.12712i −0.0707079 + 0.0707079i
\(906\) 0 0
\(907\) 9.60559i 0.318948i 0.987202 + 0.159474i \(0.0509799\pi\)
−0.987202 + 0.159474i \(0.949020\pi\)
\(908\) −11.9819 11.9819i −0.397632 0.397632i
\(909\) 0 0
\(910\) 1.09352 0.673475i 0.0362498 0.0223255i
\(911\) 20.1412 0.667308 0.333654 0.942696i \(-0.391718\pi\)
0.333654 + 0.942696i \(0.391718\pi\)
\(912\) 0 0
\(913\) 9.38760i 0.310684i
\(914\) 13.8569i 0.458345i
\(915\) 0 0
\(916\) −8.98188 + 8.98188i −0.296770 + 0.296770i
\(917\) 20.6010 + 0.741721i 0.680304 + 0.0244938i
\(918\) 0 0
\(919\) −48.6806 −1.60583 −0.802913 0.596096i \(-0.796718\pi\)
−0.802913 + 0.596096i \(0.796718\pi\)
\(920\) −0.631917 −0.0208337
\(921\) 0 0
\(922\) −10.9098 −0.359296
\(923\) −8.69380 + 43.4690i −0.286160 + 1.43080i
\(924\) 0 0
\(925\) −24.0845 24.0845i −0.791895 0.791895i
\(926\) 14.2159 0.467162
\(927\) 0 0
\(928\) −3.24864 3.24864i −0.106642 0.106642i
\(929\) 35.6667 35.6667i 1.17019 1.17019i 0.188023 0.982165i \(-0.439792\pi\)
0.982165 0.188023i \(-0.0602080\pi\)
\(930\) 0 0
\(931\) −31.3849 + 27.1634i −1.02860 + 0.890246i
\(932\) 13.1473 0.430655
\(933\) 0 0
\(934\) −6.81447 6.81447i −0.222976 0.222976i
\(935\) 4.15022i 0.135727i
\(936\) 0 0
\(937\) 38.9567i 1.27266i −0.771417 0.636330i \(-0.780452\pi\)
0.771417 0.636330i \(-0.219548\pi\)
\(938\) 0.169894 + 0.00611691i 0.00554724 + 0.000199724i
\(939\) 0 0
\(940\) 0.626026i 0.0204187i
\(941\) 23.3041 23.3041i 0.759691 0.759691i −0.216575 0.976266i \(-0.569489\pi\)
0.976266 + 0.216575i \(0.0694885\pi\)
\(942\) 0 0
\(943\) 14.2947 + 14.2947i 0.465498 + 0.465498i
\(944\) −1.30620 1.30620i −0.0425132 0.0425132i
\(945\) 0 0
\(946\) 45.2713i 1.47190i
\(947\) −5.45365 + 5.45365i −0.177220 + 0.177220i −0.790143 0.612923i \(-0.789994\pi\)
0.612923 + 0.790143i \(0.289994\pi\)
\(948\) 0 0
\(949\) 4.83443 24.1722i 0.156932 0.784661i
\(950\) 29.5407i 0.958426i
\(951\) 0 0
\(952\) −10.7812 11.5865i −0.349419 0.375520i
\(953\) 5.73711i 0.185843i 0.995673 + 0.0929216i \(0.0296206\pi\)
−0.995673 + 0.0929216i \(0.970379\pi\)
\(954\) 0 0
\(955\) −1.14536 + 1.14536i −0.0370629 + 0.0370629i
\(956\) 17.4834 17.4834i 0.565455 0.565455i
\(957\) 0 0
\(958\) 14.4658i 0.467368i
\(959\) −4.85504 5.21770i −0.156778 0.168488i
\(960\) 0 0
\(961\) 29.9071i 0.964744i
\(962\) 13.6738 + 20.5108i 0.440862 + 0.661293i
\(963\) 0 0
\(964\) −5.69380 + 5.69380i −0.183385 + 0.183385i
\(965\) 2.71690i 0.0874600i
\(966\) 0 0
\(967\) 13.7260 + 13.7260i 0.441397 + 0.441397i 0.892481 0.451084i \(-0.148963\pi\)
−0.451084 + 0.892481i \(0.648963\pi\)
\(968\) 11.0012 + 11.0012i 0.353592 + 0.353592i
\(969\) 0 0
\(970\) 1.34292 1.34292i 0.0431187 0.0431187i
\(971\) 43.6460i 1.40067i −0.713816 0.700334i \(-0.753035\pi\)
0.713816 0.700334i \(-0.246965\pi\)
\(972\) 0 0
\(973\) 1.89550 + 0.0682461i 0.0607671 + 0.00218787i
\(974\) 1.49447i 0.0478858i
\(975\) 0 0
\(976\) 5.98188i 0.191475i
\(977\) 34.3951 + 34.3951i 1.10040 + 1.10040i 0.994363 + 0.106033i \(0.0338148\pi\)
0.106033 + 0.994363i \(0.466185\pi\)
\(978\) 0 0
\(979\) −67.1793 −2.14706
\(980\) −0.616727 0.712572i −0.0197006 0.0227623i
\(981\) 0 0
\(982\) −0.846552 + 0.846552i −0.0270146 + 0.0270146i
\(983\) −34.2785 34.2785i −1.09331 1.09331i −0.995172 0.0981415i \(-0.968710\pi\)
−0.0981415 0.995172i \(-0.531290\pi\)
\(984\) 0 0
\(985\) 1.05646 0.0336616
\(986\) 19.4330 + 19.4330i 0.618872 + 0.618872i
\(987\) 0 0
\(988\) 4.19288 20.9644i 0.133393 0.666966i
\(989\) −41.2335 −1.31115
\(990\) 0 0
\(991\) 56.0596 1.78079 0.890396 0.455187i \(-0.150428\pi\)
0.890396 + 0.455187i \(0.150428\pi\)
\(992\) −1.04544 −0.0331926
\(993\) 0 0
\(994\) 32.5082 + 1.17043i 1.03110 + 0.0371238i
\(995\) −0.872519 + 0.872519i −0.0276607 + 0.0276607i
\(996\) 0 0
\(997\) 12.1817i 0.385800i 0.981218 + 0.192900i \(0.0617892\pi\)
−0.981218 + 0.192900i \(0.938211\pi\)
\(998\) 5.85666i 0.185389i
\(999\) 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 1638.2.x.b.307.4 8
3.2 odd 2 546.2.o.d.307.1 yes 8
7.6 odd 2 1638.2.x.d.307.3 8
13.5 odd 4 1638.2.x.d.811.3 8
21.20 even 2 546.2.o.a.307.2 yes 8
39.5 even 4 546.2.o.a.265.2 8
91.83 even 4 inner 1638.2.x.b.811.4 8
273.83 odd 4 546.2.o.d.265.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.o.a.265.2 8 39.5 even 4
546.2.o.a.307.2 yes 8 21.20 even 2
546.2.o.d.265.1 yes 8 273.83 odd 4
546.2.o.d.307.1 yes 8 3.2 odd 2
1638.2.x.b.307.4 8 1.1 even 1 trivial
1638.2.x.b.811.4 8 91.83 even 4 inner
1638.2.x.d.307.3 8 7.6 odd 2
1638.2.x.d.811.3 8 13.5 odd 4