Properties

Label 441.2.h.h.373.5
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(214,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.5
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.h.214.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.10281 q^{2} +(-1.22001 - 1.22947i) q^{3} -0.783802 q^{4} +(-0.0527330 - 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +O(q^{10})\) \(q-1.10281 q^{2} +(-1.22001 - 1.22947i) q^{3} -0.783802 q^{4} +(-0.0527330 - 0.0913363i) q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 + 2.99991i) q^{9} +(0.0581547 + 0.100727i) q^{10} +(-1.66866 + 2.89020i) q^{11} +(0.956244 + 0.963657i) q^{12} +(-1.23997 + 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} -1.81805 q^{16} +(-0.806594 - 1.39706i) q^{17} +(0.0255511 - 3.30834i) q^{18} +(3.84133 - 6.65338i) q^{19} +(0.0413323 + 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +(0.948593 + 1.64301i) q^{23} +(-3.74544 - 3.77448i) q^{24} +(2.49444 - 4.32049i) q^{25} +(1.36746 - 2.36851i) q^{26} +(3.71655 - 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(0.0528911 - 0.194387i) q^{30} +9.26162 q^{31} -4.13506 q^{32} +(5.58917 - 1.47451i) q^{33} +(0.889523 + 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} +(0.991268 - 1.71693i) q^{37} +(-4.23627 + 7.33744i) q^{38} +(4.15329 - 1.09570i) q^{39} +(-0.161891 - 0.280404i) q^{40} +(3.74268 - 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(1.30790 - 2.26534i) q^{44} +(0.275223 - 0.156078i) q^{45} +(-1.04612 - 1.81194i) q^{46} -3.19560 q^{47} +(2.21803 + 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(-0.733589 + 2.69610i) q^{51} +(0.971894 - 1.68337i) q^{52} +(4.98839 + 8.64015i) q^{53} +(-4.09866 + 4.00478i) q^{54} +0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +(-5.12280 - 8.87296i) q^{58} +4.45986 q^{59} +(0.0375913 - 0.138156i) q^{60} -5.67100 q^{61} -10.2138 q^{62} +8.19630 q^{64} +0.261550 q^{65} +(-6.16381 + 1.62610i) q^{66} +9.97141 q^{67} +(0.632210 + 1.09502i) q^{68} +(0.862736 - 3.17075i) q^{69} +3.29042 q^{71} +(-0.0711292 + 9.20977i) q^{72} +(2.36189 + 4.09091i) q^{73} +(-1.09318 + 1.89345i) q^{74} +(-8.35513 + 2.20421i) q^{75} +(-3.01084 + 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +7.69409 q^{79} +(0.0958713 + 0.166054i) q^{80} +(-8.99893 - 0.139010i) q^{81} +(-4.12748 + 7.14901i) q^{82} +(-0.584428 - 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +(4.16189 + 7.20860i) q^{86} +(4.22477 - 15.5270i) q^{87} +(-5.12280 + 8.87296i) q^{88} +(-3.01477 + 5.22173i) q^{89} +(-0.303519 + 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(-11.2992 - 11.3868i) q^{93} +3.52415 q^{94} -0.810260 q^{95} +(5.04480 + 5.08391i) q^{96} +(-1.90127 - 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10281 −0.779807 −0.389903 0.920856i \(-0.627492\pi\)
−0.389903 + 0.920856i \(0.627492\pi\)
\(3\) −1.22001 1.22947i −0.704371 0.709832i
\(4\) −0.783802 −0.391901
\(5\) −0.0527330 0.0913363i −0.0235829 0.0408468i 0.853993 0.520284i \(-0.174174\pi\)
−0.877576 + 0.479438i \(0.840841\pi\)
\(6\) 1.34544 + 1.35587i 0.549273 + 0.553532i
\(7\) 0 0
\(8\) 3.07001 1.08541
\(9\) −0.0231690 + 2.99991i −0.00772300 + 0.999970i
\(10\) 0.0581547 + 0.100727i 0.0183901 + 0.0318527i
\(11\) −1.66866 + 2.89020i −0.503119 + 0.871428i 0.496874 + 0.867822i \(0.334481\pi\)
−0.999994 + 0.00360543i \(0.998852\pi\)
\(12\) 0.956244 + 0.963657i 0.276044 + 0.278184i
\(13\) −1.23997 + 2.14770i −0.343907 + 0.595664i −0.985155 0.171670i \(-0.945084\pi\)
0.641248 + 0.767334i \(0.278417\pi\)
\(14\) 0 0
\(15\) −0.0479602 + 0.176264i −0.0123833 + 0.0455113i
\(16\) −1.81805 −0.454512
\(17\) −0.806594 1.39706i −0.195628 0.338837i 0.751478 0.659758i \(-0.229341\pi\)
−0.947106 + 0.320921i \(0.896008\pi\)
\(18\) 0.0255511 3.30834i 0.00602245 0.779784i
\(19\) 3.84133 6.65338i 0.881262 1.52639i 0.0313221 0.999509i \(-0.490028\pi\)
0.849939 0.526880i \(-0.176638\pi\)
\(20\) 0.0413323 + 0.0715896i 0.00924218 + 0.0160079i
\(21\) 0 0
\(22\) 1.84022 3.18735i 0.392336 0.679546i
\(23\) 0.948593 + 1.64301i 0.197795 + 0.342592i 0.947813 0.318826i \(-0.103289\pi\)
−0.750018 + 0.661417i \(0.769955\pi\)
\(24\) −3.74544 3.77448i −0.764534 0.770462i
\(25\) 2.49444 4.32049i 0.498888 0.864099i
\(26\) 1.36746 2.36851i 0.268181 0.464503i
\(27\) 3.71655 3.63142i 0.715251 0.698868i
\(28\) 0 0
\(29\) 4.64521 + 8.04574i 0.862594 + 1.49406i 0.869416 + 0.494080i \(0.164495\pi\)
−0.00682200 + 0.999977i \(0.502172\pi\)
\(30\) 0.0528911 0.194387i 0.00965655 0.0354900i
\(31\) 9.26162 1.66344 0.831718 0.555199i \(-0.187358\pi\)
0.831718 + 0.555199i \(0.187358\pi\)
\(32\) −4.13506 −0.730982
\(33\) 5.58917 1.47451i 0.972950 0.256678i
\(34\) 0.889523 + 1.54070i 0.152552 + 0.264228i
\(35\) 0 0
\(36\) 0.0181599 2.35134i 0.00302665 0.391889i
\(37\) 0.991268 1.71693i 0.162963 0.282261i −0.772967 0.634447i \(-0.781228\pi\)
0.935930 + 0.352186i \(0.114561\pi\)
\(38\) −4.23627 + 7.33744i −0.687214 + 1.19029i
\(39\) 4.15329 1.09570i 0.665059 0.175452i
\(40\) −0.161891 0.280404i −0.0255973 0.0443357i
\(41\) 3.74268 6.48252i 0.584509 1.01240i −0.410427 0.911893i \(-0.634621\pi\)
0.994936 0.100506i \(-0.0320462\pi\)
\(42\) 0 0
\(43\) −3.77388 6.53655i −0.575512 0.996815i −0.995986 0.0895108i \(-0.971470\pi\)
0.420474 0.907304i \(-0.361864\pi\)
\(44\) 1.30790 2.26534i 0.197173 0.341514i
\(45\) 0.275223 0.156078i 0.0410278 0.0232668i
\(46\) −1.04612 1.81194i −0.154242 0.267155i
\(47\) −3.19560 −0.466127 −0.233063 0.972462i \(-0.574875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(48\) 2.21803 + 2.23523i 0.320145 + 0.322627i
\(49\) 0 0
\(50\) −2.75090 + 4.76470i −0.389036 + 0.673830i
\(51\) −0.733589 + 2.69610i −0.102723 + 0.377530i
\(52\) 0.971894 1.68337i 0.134777 0.233441i
\(53\) 4.98839 + 8.64015i 0.685209 + 1.18682i 0.973371 + 0.229234i \(0.0736223\pi\)
−0.288163 + 0.957581i \(0.593044\pi\)
\(54\) −4.09866 + 4.00478i −0.557757 + 0.544982i
\(55\) 0.351974 0.0474601
\(56\) 0 0
\(57\) −12.8665 + 3.39438i −1.70422 + 0.449597i
\(58\) −5.12280 8.87296i −0.672657 1.16508i
\(59\) 4.45986 0.580625 0.290312 0.956932i \(-0.406241\pi\)
0.290312 + 0.956932i \(0.406241\pi\)
\(60\) 0.0375913 0.138156i 0.00485301 0.0178359i
\(61\) −5.67100 −0.726097 −0.363048 0.931770i \(-0.618264\pi\)
−0.363048 + 0.931770i \(0.618264\pi\)
\(62\) −10.2138 −1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) 0.261550 0.0324413
\(66\) −6.16381 + 1.62610i −0.758713 + 0.200160i
\(67\) 9.97141 1.21820 0.609101 0.793093i \(-0.291530\pi\)
0.609101 + 0.793093i \(0.291530\pi\)
\(68\) 0.632210 + 1.09502i 0.0766667 + 0.132791i
\(69\) 0.862736 3.17075i 0.103861 0.381713i
\(70\) 0 0
\(71\) 3.29042 0.390502 0.195251 0.980753i \(-0.437448\pi\)
0.195251 + 0.980753i \(0.437448\pi\)
\(72\) −0.0711292 + 9.20977i −0.00838265 + 1.08538i
\(73\) 2.36189 + 4.09091i 0.276438 + 0.478805i 0.970497 0.241113i \(-0.0775125\pi\)
−0.694059 + 0.719919i \(0.744179\pi\)
\(74\) −1.09318 + 1.89345i −0.127080 + 0.220109i
\(75\) −8.35513 + 2.20421i −0.964767 + 0.254520i
\(76\) −3.01084 + 5.21493i −0.345367 + 0.598194i
\(77\) 0 0
\(78\) −4.58031 + 1.20835i −0.518618 + 0.136819i
\(79\) 7.69409 0.865653 0.432827 0.901477i \(-0.357516\pi\)
0.432827 + 0.901477i \(0.357516\pi\)
\(80\) 0.0958713 + 0.166054i 0.0107187 + 0.0185654i
\(81\) −8.99893 0.139010i −0.999881 0.0154455i
\(82\) −4.12748 + 7.14901i −0.455804 + 0.789476i
\(83\) −0.584428 1.01226i −0.0641493 0.111110i 0.832167 0.554525i \(-0.187100\pi\)
−0.896316 + 0.443415i \(0.853767\pi\)
\(84\) 0 0
\(85\) −0.0850683 + 0.147343i −0.00922695 + 0.0159815i
\(86\) 4.16189 + 7.20860i 0.448788 + 0.777323i
\(87\) 4.22477 15.5270i 0.452943 1.66467i
\(88\) −5.12280 + 8.87296i −0.546093 + 0.945860i
\(89\) −3.01477 + 5.22173i −0.319565 + 0.553503i −0.980397 0.197031i \(-0.936870\pi\)
0.660832 + 0.750534i \(0.270203\pi\)
\(90\) −0.303519 + 0.172125i −0.0319937 + 0.0181436i
\(91\) 0 0
\(92\) −0.743509 1.28780i −0.0775162 0.134262i
\(93\) −11.2992 11.3868i −1.17168 1.18076i
\(94\) 3.52415 0.363489
\(95\) −0.810260 −0.0831309
\(96\) 5.04480 + 5.08391i 0.514883 + 0.518875i
\(97\) −1.90127 3.29310i −0.193045 0.334364i 0.753213 0.657777i \(-0.228503\pi\)
−0.946258 + 0.323413i \(0.895170\pi\)
\(98\) 0 0
\(99\) −8.63168 5.07279i −0.867516 0.509834i
\(100\) −1.95515 + 3.38641i −0.195515 + 0.338641i
\(101\) −8.73512 + 15.1297i −0.869177 + 1.50546i −0.00633771 + 0.999980i \(0.502017\pi\)
−0.862839 + 0.505479i \(0.831316\pi\)
\(102\) 0.809012 2.97330i 0.0801041 0.294400i
\(103\) 4.36602 + 7.56217i 0.430197 + 0.745123i 0.996890 0.0788062i \(-0.0251108\pi\)
−0.566693 + 0.823929i \(0.691777\pi\)
\(104\) −3.80674 + 6.59346i −0.373281 + 0.646542i
\(105\) 0 0
\(106\) −5.50127 9.52848i −0.534330 0.925487i
\(107\) 9.07316 15.7152i 0.877135 1.51924i 0.0226645 0.999743i \(-0.492785\pi\)
0.854471 0.519500i \(-0.173882\pi\)
\(108\) −2.91304 + 2.84632i −0.280308 + 0.273887i
\(109\) 2.11124 + 3.65678i 0.202220 + 0.350256i 0.949243 0.314542i \(-0.101851\pi\)
−0.747023 + 0.664798i \(0.768518\pi\)
\(110\) −0.388161 −0.0370097
\(111\) −3.32025 + 0.875932i −0.315145 + 0.0831398i
\(112\) 0 0
\(113\) 1.02824 1.78096i 0.0967285 0.167539i −0.813600 0.581425i \(-0.802495\pi\)
0.910329 + 0.413886i \(0.135829\pi\)
\(114\) 14.1894 3.74337i 1.32896 0.350599i
\(115\) 0.100044 0.173282i 0.00932919 0.0161586i
\(116\) −3.64093 6.30627i −0.338052 0.585523i
\(117\) −6.41417 3.76957i −0.592990 0.348497i
\(118\) −4.91840 −0.452775
\(119\) 0 0
\(120\) −0.147238 + 0.541134i −0.0134410 + 0.0493986i
\(121\) −0.0688352 0.119226i −0.00625774 0.0108387i
\(122\) 6.25405 0.566215
\(123\) −12.5361 + 3.30721i −1.13034 + 0.298201i
\(124\) −7.25928 −0.651902
\(125\) −1.05349 −0.0942268
\(126\) 0 0
\(127\) 0.317159 0.0281433 0.0140717 0.999901i \(-0.495521\pi\)
0.0140717 + 0.999901i \(0.495521\pi\)
\(128\) −0.768871 −0.0679592
\(129\) −3.43231 + 12.6145i −0.302198 + 1.11064i
\(130\) −0.288441 −0.0252980
\(131\) 7.47816 + 12.9525i 0.653370 + 1.13167i 0.982300 + 0.187315i \(0.0599786\pi\)
−0.328930 + 0.944354i \(0.606688\pi\)
\(132\) −4.38081 + 1.15572i −0.381300 + 0.100593i
\(133\) 0 0
\(134\) −10.9966 −0.949962
\(135\) −0.527666 0.147960i −0.0454143 0.0127344i
\(136\) −2.47625 4.28900i −0.212337 0.367779i
\(137\) 7.62367 13.2046i 0.651334 1.12814i −0.331466 0.943467i \(-0.607543\pi\)
0.982799 0.184676i \(-0.0591235\pi\)
\(138\) −0.951437 + 3.49674i −0.0809917 + 0.297663i
\(139\) −4.05943 + 7.03114i −0.344316 + 0.596374i −0.985229 0.171240i \(-0.945223\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(140\) 0 0
\(141\) 3.89866 + 3.92888i 0.328326 + 0.330872i
\(142\) −3.62872 −0.304516
\(143\) −4.13818 7.16754i −0.346052 0.599380i
\(144\) 0.0421224 5.45399i 0.00351020 0.454499i
\(145\) 0.489912 0.848553i 0.0406850 0.0704685i
\(146\) −2.60473 4.51152i −0.215569 0.373376i
\(147\) 0 0
\(148\) −0.776958 + 1.34573i −0.0638656 + 0.110618i
\(149\) 5.57430 + 9.65497i 0.456664 + 0.790966i 0.998782 0.0493365i \(-0.0157107\pi\)
−0.542118 + 0.840303i \(0.682377\pi\)
\(150\) 9.21415 2.43083i 0.752332 0.198476i
\(151\) 5.63676 9.76315i 0.458713 0.794514i −0.540180 0.841549i \(-0.681644\pi\)
0.998893 + 0.0470354i \(0.0149774\pi\)
\(152\) 11.7929 20.4260i 0.956534 1.65677i
\(153\) 4.20975 2.38734i 0.340338 0.193005i
\(154\) 0 0
\(155\) −0.488393 0.845922i −0.0392287 0.0679461i
\(156\) −3.25536 + 0.858812i −0.260637 + 0.0687600i
\(157\) −12.2064 −0.974173 −0.487087 0.873354i \(-0.661940\pi\)
−0.487087 + 0.873354i \(0.661940\pi\)
\(158\) −8.48515 −0.675042
\(159\) 4.53689 16.6741i 0.359799 1.32234i
\(160\) 0.218054 + 0.377681i 0.0172387 + 0.0298583i
\(161\) 0 0
\(162\) 9.92414 + 0.153302i 0.779714 + 0.0120445i
\(163\) −4.48132 + 7.76187i −0.351004 + 0.607957i −0.986426 0.164209i \(-0.947493\pi\)
0.635422 + 0.772165i \(0.280826\pi\)
\(164\) −2.93352 + 5.08101i −0.229070 + 0.396760i
\(165\) −0.429410 0.432739i −0.0334295 0.0336887i
\(166\) 0.644515 + 1.11633i 0.0500240 + 0.0866442i
\(167\) 8.70833 15.0833i 0.673871 1.16718i −0.302927 0.953014i \(-0.597964\pi\)
0.976798 0.214165i \(-0.0687030\pi\)
\(168\) 0 0
\(169\) 3.42493 + 5.93216i 0.263456 + 0.456320i
\(170\) 0.0938145 0.162491i 0.00719524 0.0124625i
\(171\) 19.8705 + 11.6778i 1.51954 + 0.893024i
\(172\) 2.95798 + 5.12337i 0.225544 + 0.390653i
\(173\) −2.82933 −0.215110 −0.107555 0.994199i \(-0.534302\pi\)
−0.107555 + 0.994199i \(0.534302\pi\)
\(174\) −4.65914 + 17.1234i −0.353208 + 1.29812i
\(175\) 0 0
\(176\) 3.03370 5.25453i 0.228674 0.396075i
\(177\) −5.44106 5.48325i −0.408975 0.412146i
\(178\) 3.32473 5.75860i 0.249199 0.431625i
\(179\) 5.08135 + 8.80115i 0.379798 + 0.657829i 0.991033 0.133620i \(-0.0426603\pi\)
−0.611235 + 0.791449i \(0.709327\pi\)
\(180\) −0.215720 + 0.122334i −0.0160788 + 0.00911827i
\(181\) 17.0870 1.27006 0.635032 0.772486i \(-0.280987\pi\)
0.635032 + 0.772486i \(0.280987\pi\)
\(182\) 0 0
\(183\) 6.91865 + 6.97229i 0.511441 + 0.515407i
\(184\) 2.91220 + 5.04407i 0.214690 + 0.371854i
\(185\) −0.209090 −0.0153726
\(186\) 12.4609 + 12.5576i 0.913681 + 0.920765i
\(187\) 5.38371 0.393696
\(188\) 2.50472 0.182676
\(189\) 0 0
\(190\) 0.893566 0.0648261
\(191\) −22.4000 −1.62081 −0.810404 0.585872i \(-0.800752\pi\)
−0.810404 + 0.585872i \(0.800752\pi\)
\(192\) −9.99954 10.0771i −0.721654 0.727249i
\(193\) −0.256786 −0.0184839 −0.00924194 0.999957i \(-0.502942\pi\)
−0.00924194 + 0.999957i \(0.502942\pi\)
\(194\) 2.09675 + 3.63168i 0.150538 + 0.260739i
\(195\) −0.319093 0.321567i −0.0228507 0.0230279i
\(196\) 0 0
\(197\) −0.763370 −0.0543878 −0.0271939 0.999630i \(-0.508657\pi\)
−0.0271939 + 0.999630i \(0.508657\pi\)
\(198\) 9.51913 + 5.59434i 0.676495 + 0.397572i
\(199\) −2.51561 4.35716i −0.178327 0.308871i 0.762981 0.646421i \(-0.223735\pi\)
−0.941307 + 0.337550i \(0.890402\pi\)
\(200\) 7.65796 13.2640i 0.541500 0.937905i
\(201\) −12.1652 12.2595i −0.858066 0.864719i
\(202\) 9.63321 16.6852i 0.677790 1.17397i
\(203\) 0 0
\(204\) 0.574988 2.11321i 0.0402572 0.147954i
\(205\) −0.789452 −0.0551377
\(206\) −4.81491 8.33966i −0.335470 0.581052i
\(207\) −4.95087 + 2.80763i −0.344109 + 0.195144i
\(208\) 2.25433 3.90462i 0.156310 0.270737i
\(209\) 12.8197 + 22.2044i 0.886759 + 1.53591i
\(210\) 0 0
\(211\) −3.60537 + 6.24468i −0.248204 + 0.429901i −0.963027 0.269403i \(-0.913174\pi\)
0.714824 + 0.699305i \(0.246507\pi\)
\(212\) −3.90991 6.77217i −0.268534 0.465114i
\(213\) −4.01434 4.04546i −0.275058 0.277190i
\(214\) −10.0060 + 17.3309i −0.683996 + 1.18472i
\(215\) −0.398017 + 0.689385i −0.0271445 + 0.0470157i
\(216\) 11.4099 11.1485i 0.776343 0.758561i
\(217\) 0 0
\(218\) −2.32831 4.03274i −0.157693 0.273132i
\(219\) 2.14812 7.89480i 0.145156 0.533481i
\(220\) −0.275878 −0.0185997
\(221\) 4.00062 0.269111
\(222\) 3.66162 0.965990i 0.245752 0.0648330i
\(223\) −5.59106 9.68400i −0.374405 0.648488i 0.615833 0.787877i \(-0.288820\pi\)
−0.990238 + 0.139388i \(0.955486\pi\)
\(224\) 0 0
\(225\) 12.9033 + 7.58319i 0.860220 + 0.505546i
\(226\) −1.13395 + 1.96407i −0.0754295 + 0.130648i
\(227\) 11.8853 20.5860i 0.788857 1.36634i −0.137811 0.990459i \(-0.544007\pi\)
0.926668 0.375881i \(-0.122660\pi\)
\(228\) 10.0848 2.66052i 0.667884 0.176198i
\(229\) −0.952737 1.65019i −0.0629586 0.109048i 0.832828 0.553532i \(-0.186720\pi\)
−0.895787 + 0.444484i \(0.853387\pi\)
\(230\) −0.110330 + 0.191098i −0.00727497 + 0.0126006i
\(231\) 0 0
\(232\) 14.2609 + 24.7006i 0.936272 + 1.62167i
\(233\) −3.27092 + 5.66540i −0.214285 + 0.371153i −0.953051 0.302809i \(-0.902075\pi\)
0.738766 + 0.673962i \(0.235409\pi\)
\(234\) 7.07363 + 4.15713i 0.462418 + 0.271760i
\(235\) 0.168514 + 0.291875i 0.0109926 + 0.0190398i
\(236\) −3.49565 −0.227547
\(237\) −9.38684 9.45962i −0.609741 0.614468i
\(238\) 0 0
\(239\) 10.6735 18.4870i 0.690409 1.19582i −0.281295 0.959621i \(-0.590764\pi\)
0.971704 0.236202i \(-0.0759028\pi\)
\(240\) 0.0871940 0.320457i 0.00562835 0.0206854i
\(241\) −10.0331 + 17.3778i −0.646288 + 1.11940i 0.337715 + 0.941248i \(0.390346\pi\)
−0.984003 + 0.178155i \(0.942987\pi\)
\(242\) 0.0759124 + 0.131484i 0.00487983 + 0.00845212i
\(243\) 10.8078 + 11.2335i 0.693323 + 0.720627i
\(244\) 4.44494 0.284558
\(245\) 0 0
\(246\) 13.8250 3.64724i 0.881451 0.232540i
\(247\) 9.52629 + 16.5000i 0.606144 + 1.04987i
\(248\) 28.4333 1.80552
\(249\) −0.531531 + 1.95349i −0.0336844 + 0.123798i
\(250\) 1.16180 0.0734787
\(251\) 6.81467 0.430138 0.215069 0.976599i \(-0.431002\pi\)
0.215069 + 0.976599i \(0.431002\pi\)
\(252\) 0 0
\(253\) −6.33151 −0.398059
\(254\) −0.349767 −0.0219464
\(255\) 0.284936 0.0751704i 0.0178434 0.00470735i
\(256\) −15.5447 −0.971542
\(257\) −7.19415 12.4606i −0.448759 0.777273i 0.549546 0.835463i \(-0.314801\pi\)
−0.998306 + 0.0581897i \(0.981467\pi\)
\(258\) 3.78519 13.9114i 0.235656 0.866088i
\(259\) 0 0
\(260\) −0.205004 −0.0127138
\(261\) −24.2441 + 13.7488i −1.50067 + 0.851030i
\(262\) −8.24701 14.2842i −0.509502 0.882484i
\(263\) 0.769503 1.33282i 0.0474496 0.0821851i −0.841325 0.540529i \(-0.818224\pi\)
0.888775 + 0.458344i \(0.151557\pi\)
\(264\) 17.1588 4.52675i 1.05605 0.278602i
\(265\) 0.526106 0.911243i 0.0323185 0.0559772i
\(266\) 0 0
\(267\) 10.0980 2.66399i 0.617986 0.163034i
\(268\) −7.81562 −0.477415
\(269\) −13.1285 22.7393i −0.800461 1.38644i −0.919313 0.393527i \(-0.871255\pi\)
0.118852 0.992912i \(-0.462079\pi\)
\(270\) 0.581917 + 0.163172i 0.0354144 + 0.00993035i
\(271\) 8.96673 15.5308i 0.544690 0.943431i −0.453936 0.891034i \(-0.649981\pi\)
0.998626 0.0523969i \(-0.0166861\pi\)
\(272\) 1.46643 + 2.53993i 0.0889152 + 0.154006i
\(273\) 0 0
\(274\) −8.40748 + 14.5622i −0.507915 + 0.879734i
\(275\) 8.32473 + 14.4188i 0.502000 + 0.869489i
\(276\) −0.676214 + 2.48524i −0.0407033 + 0.149594i
\(277\) 9.43563 16.3430i 0.566932 0.981955i −0.429935 0.902860i \(-0.641463\pi\)
0.996867 0.0790954i \(-0.0252032\pi\)
\(278\) 4.47680 7.75404i 0.268500 0.465056i
\(279\) −0.214582 + 27.7840i −0.0128467 + 1.66339i
\(280\) 0 0
\(281\) −2.49578 4.32283i −0.148886 0.257878i 0.781930 0.623366i \(-0.214235\pi\)
−0.930816 + 0.365488i \(0.880902\pi\)
\(282\) −4.29949 4.33282i −0.256031 0.258016i
\(283\) −15.3927 −0.915000 −0.457500 0.889210i \(-0.651255\pi\)
−0.457500 + 0.889210i \(0.651255\pi\)
\(284\) −2.57904 −0.153038
\(285\) 0.988522 + 0.996187i 0.0585550 + 0.0590090i
\(286\) 4.56364 + 7.90446i 0.269854 + 0.467401i
\(287\) 0 0
\(288\) 0.0958052 12.4048i 0.00564537 0.730960i
\(289\) 7.19881 12.4687i 0.423460 0.733454i
\(290\) −0.540282 + 0.935796i −0.0317265 + 0.0549518i
\(291\) −1.72919 + 6.35516i −0.101367 + 0.372546i
\(292\) −1.85126 3.20647i −0.108337 0.187644i
\(293\) −12.9013 + 22.3456i −0.753700 + 1.30545i 0.192318 + 0.981333i \(0.438399\pi\)
−0.946018 + 0.324114i \(0.894934\pi\)
\(294\) 0 0
\(295\) −0.235182 0.407347i −0.0136928 0.0237167i
\(296\) 3.04321 5.27099i 0.176883 0.306370i
\(297\) 4.29389 + 16.8012i 0.249157 + 0.974903i
\(298\) −6.14741 10.6476i −0.356110 0.616801i
\(299\) −4.70492 −0.272093
\(300\) 6.54877 1.72766i 0.378093 0.0997465i
\(301\) 0 0
\(302\) −6.21629 + 10.7669i −0.357707 + 0.619567i
\(303\) 29.2583 7.71877i 1.68085 0.443432i
\(304\) −6.98373 + 12.0962i −0.400544 + 0.693763i
\(305\) 0.299049 + 0.517968i 0.0171235 + 0.0296588i
\(306\) −4.64257 + 2.63279i −0.265398 + 0.150507i
\(307\) −22.2914 −1.27224 −0.636120 0.771590i \(-0.719462\pi\)
−0.636120 + 0.771590i \(0.719462\pi\)
\(308\) 0 0
\(309\) 3.97085 14.5938i 0.225894 0.830210i
\(310\) 0.538607 + 0.932894i 0.0305908 + 0.0529848i
\(311\) −1.30986 −0.0742755 −0.0371377 0.999310i \(-0.511824\pi\)
−0.0371377 + 0.999310i \(0.511824\pi\)
\(312\) 12.7507 3.36382i 0.721865 0.190439i
\(313\) 21.5770 1.21960 0.609802 0.792554i \(-0.291249\pi\)
0.609802 + 0.792554i \(0.291249\pi\)
\(314\) 13.4613 0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) −24.7819 −1.39189 −0.695946 0.718094i \(-0.745015\pi\)
−0.695946 + 0.718094i \(0.745015\pi\)
\(318\) −5.00335 + 18.3884i −0.280574 + 1.03117i
\(319\) −31.0051 −1.73595
\(320\) −0.432216 0.748620i −0.0241616 0.0418491i
\(321\) −30.3906 + 8.01748i −1.69624 + 0.447492i
\(322\) 0 0
\(323\) −12.3936 −0.689597
\(324\) 7.05338 + 0.108956i 0.391854 + 0.00605312i
\(325\) 6.18608 + 10.7146i 0.343142 + 0.594339i
\(326\) 4.94206 8.55990i 0.273715 0.474089i
\(327\) 1.92015 7.05699i 0.106185 0.390252i
\(328\) 11.4901 19.9014i 0.634434 1.09887i
\(329\) 0 0
\(330\) 0.473559 + 0.477231i 0.0260686 + 0.0262707i
\(331\) 13.8451 0.760996 0.380498 0.924782i \(-0.375753\pi\)
0.380498 + 0.924782i \(0.375753\pi\)
\(332\) 0.458076 + 0.793410i 0.0251402 + 0.0435440i
\(333\) 5.12766 + 3.01349i 0.280994 + 0.165139i
\(334\) −9.60367 + 16.6340i −0.525489 + 0.910174i
\(335\) −0.525823 0.910752i −0.0287288 0.0497597i
\(336\) 0 0
\(337\) 1.69444 2.93485i 0.0923018 0.159871i −0.816178 0.577801i \(-0.803911\pi\)
0.908479 + 0.417930i \(0.137244\pi\)
\(338\) −3.77706 6.54206i −0.205445 0.355841i
\(339\) −3.44408 + 0.908600i −0.187057 + 0.0493484i
\(340\) 0.0666767 0.115487i 0.00361605 0.00626319i
\(341\) −15.4545 + 26.7679i −0.836906 + 1.44956i
\(342\) −21.9135 12.8784i −1.18495 0.696386i
\(343\) 0 0
\(344\) −11.5859 20.0673i −0.624668 1.08196i
\(345\) −0.335099 + 0.0884040i −0.0180411 + 0.00475951i
\(346\) 3.12022 0.167744
\(347\) −14.5148 −0.779195 −0.389597 0.920985i \(-0.627386\pi\)
−0.389597 + 0.920985i \(0.627386\pi\)
\(348\) −3.31139 + 12.1701i −0.177509 + 0.652385i
\(349\) 7.86412 + 13.6211i 0.420957 + 0.729119i 0.996033 0.0889810i \(-0.0283610\pi\)
−0.575076 + 0.818100i \(0.695028\pi\)
\(350\) 0 0
\(351\) 3.19077 + 12.4849i 0.170311 + 0.666395i
\(352\) 6.90000 11.9511i 0.367771 0.636998i
\(353\) 2.07211 3.58900i 0.110287 0.191023i −0.805599 0.592462i \(-0.798156\pi\)
0.915886 + 0.401438i \(0.131490\pi\)
\(354\) 6.00048 + 6.04700i 0.318922 + 0.321394i
\(355\) −0.173514 0.300535i −0.00920917 0.0159508i
\(356\) 2.36298 4.09281i 0.125238 0.216918i
\(357\) 0 0
\(358\) −5.60378 9.70603i −0.296169 0.512979i
\(359\) −3.96994 + 6.87614i −0.209525 + 0.362909i −0.951565 0.307447i \(-0.900525\pi\)
0.742040 + 0.670356i \(0.233859\pi\)
\(360\) 0.844937 0.479163i 0.0445321 0.0252541i
\(361\) −20.0116 34.6612i −1.05324 1.82427i
\(362\) −18.8437 −0.990405
\(363\) −0.0626049 + 0.230087i −0.00328590 + 0.0120764i
\(364\) 0 0
\(365\) 0.249099 0.431453i 0.0130385 0.0225833i
\(366\) −7.62998 7.68914i −0.398826 0.401918i
\(367\) 6.57455 11.3875i 0.343189 0.594420i −0.641834 0.766843i \(-0.721826\pi\)
0.985023 + 0.172423i \(0.0551596\pi\)
\(368\) −1.72459 2.98708i −0.0899004 0.155712i
\(369\) 19.3603 + 11.3779i 1.00785 + 0.592310i
\(370\) 0.230588 0.0119877
\(371\) 0 0
\(372\) 8.85636 + 8.92503i 0.459181 + 0.462741i
\(373\) −3.90543 6.76441i −0.202216 0.350248i 0.747026 0.664794i \(-0.231481\pi\)
−0.949242 + 0.314547i \(0.898147\pi\)
\(374\) −5.93723 −0.307007
\(375\) 1.28526 + 1.29523i 0.0663706 + 0.0668852i
\(376\) −9.81055 −0.505940
\(377\) −23.0398 −1.18661
\(378\) 0 0
\(379\) −31.6147 −1.62394 −0.811968 0.583702i \(-0.801604\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(380\) 0.635084 0.0325791
\(381\) −0.386936 0.389936i −0.0198233 0.0199770i
\(382\) 24.7030 1.26392
\(383\) 5.36593 + 9.29407i 0.274186 + 0.474905i 0.969930 0.243386i \(-0.0782582\pi\)
−0.695743 + 0.718291i \(0.744925\pi\)
\(384\) 0.938027 + 0.945300i 0.0478685 + 0.0482396i
\(385\) 0 0
\(386\) 0.283187 0.0144139
\(387\) 19.6965 11.1699i 1.00123 0.567796i
\(388\) 1.49022 + 2.58114i 0.0756546 + 0.131038i
\(389\) −12.0734 + 20.9118i −0.612147 + 1.06027i 0.378731 + 0.925507i \(0.376361\pi\)
−0.990878 + 0.134763i \(0.956973\pi\)
\(390\) 0.351900 + 0.354628i 0.0178192 + 0.0179573i
\(391\) 1.53026 2.65049i 0.0773885 0.134041i
\(392\) 0 0
\(393\) 6.80131 24.9963i 0.343081 1.26090i
\(394\) 0.841854 0.0424120
\(395\) −0.405733 0.702750i −0.0204146 0.0353592i
\(396\) 6.76553 + 3.97606i 0.339981 + 0.199805i
\(397\) −12.0285 + 20.8339i −0.603691 + 1.04562i 0.388566 + 0.921421i \(0.372971\pi\)
−0.992257 + 0.124203i \(0.960363\pi\)
\(398\) 2.77424 + 4.80513i 0.139060 + 0.240860i
\(399\) 0 0
\(400\) −4.53501 + 7.85487i −0.226751 + 0.392744i
\(401\) 0.781158 + 1.35301i 0.0390092 + 0.0675659i 0.884871 0.465836i \(-0.154247\pi\)
−0.845862 + 0.533402i \(0.820913\pi\)
\(402\) 13.4159 + 13.5199i 0.669126 + 0.674314i
\(403\) −11.4842 + 19.8911i −0.572067 + 0.990849i
\(404\) 6.84661 11.8587i 0.340631 0.589991i
\(405\) 0.461844 + 0.829259i 0.0229492 + 0.0412062i
\(406\) 0 0
\(407\) 3.30817 + 5.72992i 0.163980 + 0.284022i
\(408\) −2.25213 + 8.27708i −0.111497 + 0.409776i
\(409\) −22.3456 −1.10492 −0.552460 0.833539i \(-0.686311\pi\)
−0.552460 + 0.833539i \(0.686311\pi\)
\(410\) 0.870619 0.0429968
\(411\) −25.5355 + 6.73664i −1.25957 + 0.332294i
\(412\) −3.42210 5.92725i −0.168595 0.292014i
\(413\) 0 0
\(414\) 5.45988 3.09629i 0.268339 0.152174i
\(415\) −0.0616373 + 0.106759i −0.00302566 + 0.00524059i
\(416\) 5.12736 8.88086i 0.251390 0.435420i
\(417\) 13.5971 3.58711i 0.665852 0.175661i
\(418\) −14.1378 24.4873i −0.691501 1.19771i
\(419\) 2.98648 5.17273i 0.145899 0.252704i −0.783809 0.621002i \(-0.786726\pi\)
0.929708 + 0.368298i \(0.120059\pi\)
\(420\) 0 0
\(421\) 7.31594 + 12.6716i 0.356557 + 0.617575i 0.987383 0.158349i \(-0.0506172\pi\)
−0.630826 + 0.775924i \(0.717284\pi\)
\(422\) 3.97605 6.88672i 0.193551 0.335240i
\(423\) 0.0740389 9.58652i 0.00359989 0.466113i
\(424\) 15.3144 + 26.5254i 0.743735 + 1.28819i
\(425\) −8.04799 −0.390385
\(426\) 4.42707 + 4.46139i 0.214492 + 0.216155i
\(427\) 0 0
\(428\) −7.11156 + 12.3176i −0.343750 + 0.595393i
\(429\) −3.76363 + 13.8322i −0.181710 + 0.667825i
\(430\) 0.438938 0.760263i 0.0211675 0.0366631i
\(431\) 9.70169 + 16.8038i 0.467314 + 0.809411i 0.999303 0.0373401i \(-0.0118885\pi\)
−0.531989 + 0.846751i \(0.678555\pi\)
\(432\) −6.75688 + 6.60211i −0.325090 + 0.317644i
\(433\) 1.35217 0.0649810 0.0324905 0.999472i \(-0.489656\pi\)
0.0324905 + 0.999472i \(0.489656\pi\)
\(434\) 0 0
\(435\) −1.64096 + 0.432910i −0.0786781 + 0.0207564i
\(436\) −1.65480 2.86619i −0.0792503 0.137266i
\(437\) 14.5754 0.697238
\(438\) −2.36897 + 8.70650i −0.113194 + 0.416013i
\(439\) 17.3412 0.827650 0.413825 0.910356i \(-0.364193\pi\)
0.413825 + 0.910356i \(0.364193\pi\)
\(440\) 1.08056 0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) 19.6100 0.931698 0.465849 0.884864i \(-0.345749\pi\)
0.465849 + 0.884864i \(0.345749\pi\)
\(444\) 2.60242 0.686557i 0.123506 0.0325826i
\(445\) 0.635912 0.0301451
\(446\) 6.16590 + 10.6796i 0.291964 + 0.505696i
\(447\) 5.06977 18.6325i 0.239792 0.881289i
\(448\) 0 0
\(449\) −17.7345 −0.836942 −0.418471 0.908230i \(-0.637434\pi\)
−0.418471 + 0.908230i \(0.637434\pi\)
\(450\) −14.2299 8.36285i −0.670806 0.394228i
\(451\) 12.4905 + 21.6342i 0.588155 + 1.01871i
\(452\) −0.805935 + 1.39592i −0.0379080 + 0.0656586i
\(453\) −18.8803 + 4.98091i −0.887075 + 0.234023i
\(454\) −13.1073 + 22.7025i −0.615156 + 1.06548i
\(455\) 0 0
\(456\) −39.5005 + 10.4208i −1.84978 + 0.487999i
\(457\) 0.485451 0.0227084 0.0113542 0.999936i \(-0.496386\pi\)
0.0113542 + 0.999936i \(0.496386\pi\)
\(458\) 1.05069 + 1.81985i 0.0490956 + 0.0850361i
\(459\) −8.07107 2.26317i −0.376725 0.105636i
\(460\) −0.0784150 + 0.135819i −0.00365612 + 0.00633259i
\(461\) 3.99687 + 6.92279i 0.186153 + 0.322426i 0.943964 0.330047i \(-0.107065\pi\)
−0.757811 + 0.652474i \(0.773731\pi\)
\(462\) 0 0
\(463\) 5.24280 9.08080i 0.243654 0.422021i −0.718098 0.695942i \(-0.754987\pi\)
0.961752 + 0.273921i \(0.0883206\pi\)
\(464\) −8.44523 14.6276i −0.392060 0.679068i
\(465\) −0.444189 + 1.63249i −0.0205988 + 0.0757050i
\(466\) 3.60721 6.24788i 0.167101 0.289427i
\(467\) −10.9489 + 18.9640i −0.506653 + 0.877549i 0.493317 + 0.869849i \(0.335784\pi\)
−0.999970 + 0.00769944i \(0.997549\pi\)
\(468\) 5.02744 + 2.95460i 0.232394 + 0.136576i
\(469\) 0 0
\(470\) −0.185839 0.321883i −0.00857213 0.0148474i
\(471\) 14.8918 + 15.0073i 0.686179 + 0.691499i
\(472\) 13.6918 0.630218
\(473\) 25.1893 1.15820
\(474\) 10.3519 + 10.4322i 0.475480 + 0.479167i
\(475\) −19.1639 33.1929i −0.879301 1.52299i
\(476\) 0 0
\(477\) −26.0353 + 14.7645i −1.19207 + 0.676022i
\(478\) −11.7708 + 20.3877i −0.538386 + 0.932512i
\(479\) −2.00085 + 3.46557i −0.0914210 + 0.158346i −0.908109 0.418733i \(-0.862474\pi\)
0.816688 + 0.577079i \(0.195808\pi\)
\(480\) 0.198318 0.728864i 0.00905194 0.0332679i
\(481\) 2.45829 + 4.25789i 0.112088 + 0.194143i
\(482\) 11.0646 19.1645i 0.503980 0.872918i
\(483\) 0 0
\(484\) 0.0539532 + 0.0934496i 0.00245242 + 0.00424771i
\(485\) −0.200520 + 0.347311i −0.00910514 + 0.0157706i
\(486\) −11.9190 12.3884i −0.540658 0.561950i
\(487\) 13.2377 + 22.9284i 0.599859 + 1.03899i 0.992841 + 0.119440i \(0.0381100\pi\)
−0.392982 + 0.919546i \(0.628557\pi\)
\(488\) −17.4100 −0.788116
\(489\) 15.0102 3.95991i 0.678784 0.179073i
\(490\) 0 0
\(491\) 14.2149 24.6210i 0.641511 1.11113i −0.343584 0.939122i \(-0.611641\pi\)
0.985096 0.172008i \(-0.0550255\pi\)
\(492\) 9.82584 2.59220i 0.442983 0.116865i
\(493\) 7.49360 12.9793i 0.337495 0.584558i
\(494\) −10.5057 18.1965i −0.472675 0.818697i
\(495\) −0.00815487 + 1.05589i −0.000366534 + 0.0474587i
\(496\) −16.8381 −0.756052
\(497\) 0 0
\(498\) 0.586179 2.15434i 0.0262673 0.0965383i
\(499\) 3.71559 + 6.43559i 0.166333 + 0.288097i 0.937128 0.348986i \(-0.113474\pi\)
−0.770795 + 0.637083i \(0.780141\pi\)
\(500\) 0.825726 0.0369276
\(501\) −29.1686 + 7.69510i −1.30316 + 0.343792i
\(502\) −7.51531 −0.335425
\(503\) −10.1610 −0.453057 −0.226529 0.974004i \(-0.572738\pi\)
−0.226529 + 0.974004i \(0.572738\pi\)
\(504\) 0 0
\(505\) 1.84252 0.0819910
\(506\) 6.98247 0.310409
\(507\) 3.11494 11.4481i 0.138339 0.508428i
\(508\) −0.248590 −0.0110294
\(509\) −14.4532 25.0336i −0.640625 1.10960i −0.985293 0.170871i \(-0.945342\pi\)
0.344668 0.938725i \(-0.387991\pi\)
\(510\) −0.314232 + 0.0828990i −0.0139144 + 0.00367083i
\(511\) 0 0
\(512\) 18.6806 0.825575
\(513\) −9.88474 38.6771i −0.436422 1.70764i
\(514\) 7.93381 + 13.7418i 0.349945 + 0.606123i
\(515\) 0.460467 0.797553i 0.0202906 0.0351444i
\(516\) 2.69025 9.88727i 0.118432 0.435263i
\(517\) 5.33237 9.23593i 0.234517 0.406196i
\(518\) 0 0
\(519\) 3.45180 + 3.47856i 0.151517 + 0.152692i
\(520\) 0.802963 0.0352123
\(521\) 16.8995 + 29.2708i 0.740381 + 1.28238i 0.952322 + 0.305095i \(0.0986883\pi\)
−0.211941 + 0.977283i \(0.567978\pi\)
\(522\) 26.7368 15.1624i 1.17024 0.663639i
\(523\) −7.18895 + 12.4516i −0.314351 + 0.544471i −0.979299 0.202418i \(-0.935120\pi\)
0.664949 + 0.746889i \(0.268453\pi\)
\(524\) −5.86140 10.1522i −0.256056 0.443502i
\(525\) 0 0
\(526\) −0.848618 + 1.46985i −0.0370015 + 0.0640885i
\(527\) −7.47036 12.9390i −0.325414 0.563634i
\(528\) −10.1614 + 2.68072i −0.442218 + 0.116664i
\(529\) 9.70034 16.8015i 0.421754 0.730499i
\(530\) −0.580197 + 1.00493i −0.0252022 + 0.0436514i
\(531\) −0.103331 + 13.3792i −0.00448416 + 0.580607i
\(532\) 0 0
\(533\) 9.28166 + 16.0763i 0.402033 + 0.696342i
\(534\) −11.1362 + 2.93789i −0.481910 + 0.127135i
\(535\) −1.91382 −0.0827417
\(536\) 30.6124 1.32225
\(537\) 4.62143 16.9848i 0.199429 0.732948i
\(538\) 14.4783 + 25.0772i 0.624205 + 1.08116i
\(539\) 0 0
\(540\) 0.413586 + 0.115971i 0.0177979 + 0.00499062i
\(541\) 12.5882 21.8034i 0.541210 0.937403i −0.457625 0.889145i \(-0.651300\pi\)
0.998835 0.0482577i \(-0.0153669\pi\)
\(542\) −9.88863 + 17.1276i −0.424753 + 0.735694i
\(543\) −20.8462 21.0078i −0.894596 0.901532i
\(544\) 3.33531 + 5.77693i 0.143000 + 0.247684i
\(545\) 0.222664 0.385666i 0.00953789 0.0165201i
\(546\) 0 0
\(547\) 1.59011 + 2.75416i 0.0679883 + 0.117759i 0.898016 0.439963i \(-0.145009\pi\)
−0.830027 + 0.557723i \(0.811675\pi\)
\(548\) −5.97545 + 10.3498i −0.255258 + 0.442121i
\(549\) 0.131391 17.0125i 0.00560764 0.726075i
\(550\) −9.18062 15.9013i −0.391463 0.678034i
\(551\) 71.3752 3.04068
\(552\) 2.64861 9.73424i 0.112732 0.414317i
\(553\) 0 0
\(554\) −10.4057 + 18.0233i −0.442098 + 0.765736i
\(555\) 0.255092 + 0.257069i 0.0108280 + 0.0109120i
\(556\) 3.18179 5.51102i 0.134938 0.233719i
\(557\) −10.0229 17.3602i −0.424686 0.735577i 0.571705 0.820459i \(-0.306282\pi\)
−0.996391 + 0.0848820i \(0.972949\pi\)
\(558\) 0.236644 30.6406i 0.0100180 1.29712i
\(559\) 18.7181 0.791689
\(560\) 0 0
\(561\) −6.56817 6.61909i −0.277308 0.279458i
\(562\) 2.75238 + 4.76727i 0.116102 + 0.201095i
\(563\) −39.8013 −1.67743 −0.838713 0.544574i \(-0.816691\pi\)
−0.838713 + 0.544574i \(0.816691\pi\)
\(564\) −3.05578 3.07947i −0.128671 0.129669i
\(565\) −0.216888 −0.00912457
\(566\) 16.9753 0.713523
\(567\) 0 0
\(568\) 10.1017 0.423856
\(569\) 13.8159 0.579194 0.289597 0.957149i \(-0.406479\pi\)
0.289597 + 0.957149i \(0.406479\pi\)
\(570\) −1.09016 1.09861i −0.0456616 0.0460156i
\(571\) 10.4387 0.436846 0.218423 0.975854i \(-0.429909\pi\)
0.218423 + 0.975854i \(0.429909\pi\)
\(572\) 3.24352 + 5.61793i 0.135618 + 0.234898i
\(573\) 27.3281 + 27.5400i 1.14165 + 1.15050i
\(574\) 0 0
\(575\) 9.46483 0.394711
\(576\) −0.189900 + 24.5882i −0.00791250 + 1.02451i
\(577\) −12.7461 22.0769i −0.530628 0.919075i −0.999361 0.0357353i \(-0.988623\pi\)
0.468733 0.883340i \(-0.344711\pi\)
\(578\) −7.93895 + 13.7507i −0.330217 + 0.571952i
\(579\) 0.313281 + 0.315710i 0.0130195 + 0.0131204i
\(580\) −0.383994 + 0.665098i −0.0159445 + 0.0276167i
\(581\) 0 0
\(582\) 1.90697 7.00855i 0.0790466 0.290514i
\(583\) −33.2957 −1.37897
\(584\) 7.25104 + 12.5592i 0.300050 + 0.519702i
\(585\) −0.00605986 + 0.784628i −0.000250544 + 0.0324404i
\(586\) 14.2277 24.6431i 0.587740 1.01800i
\(587\) −17.5168 30.3401i −0.722998 1.25227i −0.959793 0.280709i \(-0.909430\pi\)
0.236795 0.971560i \(-0.423903\pi\)
\(588\) 0 0
\(589\) 35.5769 61.6210i 1.46592 2.53905i
\(590\) 0.259362 + 0.449228i 0.0106778 + 0.0184944i
\(591\) 0.931316 + 0.938536i 0.0383092 + 0.0386062i
\(592\) −1.80217 + 3.12146i −0.0740689 + 0.128291i
\(593\) 18.0646 31.2888i 0.741824 1.28488i −0.209840 0.977736i \(-0.567294\pi\)
0.951664 0.307141i \(-0.0993724\pi\)
\(594\) −4.73536 18.5286i −0.194294 0.760236i
\(595\) 0 0
\(596\) −4.36915 7.56759i −0.178967 0.309980i
\(597\) −2.28792 + 8.40861i −0.0936383 + 0.344142i
\(598\) 5.18865 0.212180
\(599\) −40.9484 −1.67310 −0.836552 0.547887i \(-0.815432\pi\)
−0.836552 + 0.547887i \(0.815432\pi\)
\(600\) −25.6504 + 6.76694i −1.04717 + 0.276259i
\(601\) 12.8547 + 22.2650i 0.524354 + 0.908207i 0.999598 + 0.0283533i \(0.00902635\pi\)
−0.475244 + 0.879854i \(0.657640\pi\)
\(602\) 0 0
\(603\) −0.231028 + 29.9133i −0.00940817 + 1.21817i
\(604\) −4.41810 + 7.65238i −0.179770 + 0.311371i
\(605\) −0.00725978 + 0.0125743i −0.000295152 + 0.000511218i
\(606\) −32.2665 + 8.51236i −1.31074 + 0.345791i
\(607\) −3.42258 5.92808i −0.138918 0.240613i 0.788169 0.615459i \(-0.211029\pi\)
−0.927087 + 0.374845i \(0.877696\pi\)
\(608\) −15.8841 + 27.5121i −0.644187 + 1.11576i
\(609\) 0 0
\(610\) −0.329795 0.571222i −0.0133530 0.0231281i
\(611\) 3.96246 6.86319i 0.160304 0.277655i
\(612\) −3.29961 + 1.87120i −0.133379 + 0.0756389i
\(613\) 14.5648 + 25.2271i 0.588269 + 1.01891i 0.994459 + 0.105123i \(0.0335235\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(614\) 24.5833 0.992101
\(615\) 0.963137 + 0.970604i 0.0388374 + 0.0391385i
\(616\) 0 0
\(617\) −10.3395 + 17.9085i −0.416252 + 0.720969i −0.995559 0.0941404i \(-0.969990\pi\)
0.579307 + 0.815109i \(0.303323\pi\)
\(618\) −4.37911 + 16.0942i −0.176154 + 0.647404i
\(619\) 4.43178 7.67606i 0.178128 0.308527i −0.763111 0.646267i \(-0.776329\pi\)
0.941239 + 0.337740i \(0.109663\pi\)
\(620\) 0.382804 + 0.663035i 0.0153738 + 0.0266281i
\(621\) 9.49197 + 2.66159i 0.380900 + 0.106806i
\(622\) 1.44453 0.0579205
\(623\) 0 0
\(624\) −7.55090 + 1.99204i −0.302278 + 0.0797453i
\(625\) −12.4166 21.5062i −0.496666 0.860250i
\(626\) −23.7954 −0.951055
\(627\) 11.6594 42.8509i 0.465632 1.71130i
\(628\) 9.56737 0.381779
\(629\) −3.19820 −0.127521
\(630\) 0 0
\(631\) 26.4661 1.05360 0.526799 0.849990i \(-0.323392\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(632\) 23.6210 0.939592
\(633\) 12.0762 3.18588i 0.479985 0.126627i
\(634\) 27.3299 1.08541
\(635\) −0.0167248 0.0289681i −0.000663702 0.00114957i
\(636\) −3.55603 + 13.0692i −0.141006 + 0.518227i
\(637\) 0 0
\(638\) 34.1928 1.35371
\(639\) −0.0762358 + 9.87098i −0.00301584 + 0.390490i
\(640\) 0.0405449 + 0.0702258i 0.00160268 + 0.00277592i
\(641\) 8.26595 14.3171i 0.326486 0.565489i −0.655326 0.755346i \(-0.727469\pi\)
0.981812 + 0.189856i \(0.0608022\pi\)
\(642\) 33.5151 8.84178i 1.32274 0.348957i
\(643\) −15.4460 + 26.7532i −0.609130 + 1.05504i 0.382254 + 0.924057i \(0.375148\pi\)
−0.991384 + 0.130987i \(0.958185\pi\)
\(644\) 0 0
\(645\) 1.33316 0.351706i 0.0524930 0.0138484i
\(646\) 13.6678 0.537752
\(647\) 0.649903 + 1.12567i 0.0255503 + 0.0442545i 0.878518 0.477710i \(-0.158533\pi\)
−0.852968 + 0.521964i \(0.825200\pi\)
\(648\) −27.6268 0.426762i −1.08528 0.0167648i
\(649\) −7.44198 + 12.8899i −0.292123 + 0.505972i
\(650\) −6.82209 11.8162i −0.267584 0.463470i
\(651\) 0 0
\(652\) 3.51247 6.08377i 0.137559 0.238259i
\(653\) 22.4435 + 38.8733i 0.878281 + 1.52123i 0.853226 + 0.521542i \(0.174643\pi\)
0.0250558 + 0.999686i \(0.492024\pi\)
\(654\) −2.11757 + 7.78254i −0.0828035 + 0.304321i
\(655\) 0.788692 1.36605i 0.0308167 0.0533762i
\(656\) −6.80438 + 11.7855i −0.265667 + 0.460148i
\(657\) −12.3271 + 6.99068i −0.480926 + 0.272732i
\(658\) 0 0
\(659\) 8.96167 + 15.5221i 0.349097 + 0.604654i 0.986089 0.166216i \(-0.0531549\pi\)
−0.636992 + 0.770870i \(0.719822\pi\)
\(660\) 0.336572 + 0.339182i 0.0131011 + 0.0132026i
\(661\) 33.0256 1.28455 0.642274 0.766475i \(-0.277991\pi\)
0.642274 + 0.766475i \(0.277991\pi\)
\(662\) −15.2686 −0.593430
\(663\) −4.88078 4.91862i −0.189554 0.191023i
\(664\) −1.79420 3.10765i −0.0696285 0.120600i
\(665\) 0 0
\(666\) −5.65485 3.32332i −0.219121 0.128776i
\(667\) −8.81283 + 15.2643i −0.341234 + 0.591035i
\(668\) −6.82561 + 11.8223i −0.264091 + 0.457419i
\(669\) −5.08501 + 18.6885i −0.196598 + 0.722541i
\(670\) 0.579885 + 1.00439i 0.0224029 + 0.0388030i
\(671\) 9.46295 16.3903i 0.365313 0.632741i
\(672\) 0 0
\(673\) −10.6758 18.4909i −0.411520 0.712774i 0.583536 0.812087i \(-0.301669\pi\)
−0.995056 + 0.0993135i \(0.968335\pi\)
\(674\) −1.86865 + 3.23659i −0.0719776 + 0.124669i
\(675\) −6.41884 25.1157i −0.247061 0.966704i
\(676\) −2.68447 4.64964i −0.103249 0.178832i
\(677\) 8.30167 0.319059 0.159530 0.987193i \(-0.449002\pi\)
0.159530 + 0.987193i \(0.449002\pi\)
\(678\) 3.79818 1.00202i 0.145868 0.0384822i
\(679\) 0 0
\(680\) −0.261161 + 0.452344i −0.0100151 + 0.0173466i
\(681\) −39.8099 + 10.5024i −1.52552 + 0.402454i
\(682\) 17.0434 29.5200i 0.652625 1.13038i
\(683\) −1.24728 2.16036i −0.0477259 0.0826637i 0.841176 0.540762i \(-0.181864\pi\)
−0.888902 + 0.458098i \(0.848531\pi\)
\(684\) −15.5746 9.15308i −0.595509 0.349977i
\(685\) −1.60808 −0.0614414
\(686\) 0 0
\(687\) −0.866505 + 3.18460i −0.0330592 + 0.121500i
\(688\) 6.86110 + 11.8838i 0.261577 + 0.453065i
\(689\) −24.7419 −0.942591
\(690\) 0.369552 0.0974932i 0.0140686 0.00371150i
\(691\) −16.8691 −0.641731 −0.320865 0.947125i \(-0.603974\pi\)
−0.320865 + 0.947125i \(0.603974\pi\)
\(692\) 2.21763 0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) 0.856265 0.0324800
\(696\) 12.9701 47.6681i 0.491631 1.80685i
\(697\) −12.0753 −0.457385
\(698\) −8.67266 15.0215i −0.328265 0.568572i
\(699\) 10.9559 2.89034i 0.414392 0.109323i
\(700\) 0 0
\(701\) 16.4806 0.622465 0.311232 0.950334i \(-0.399258\pi\)
0.311232 + 0.950334i \(0.399258\pi\)
\(702\) −3.51883 13.7685i −0.132810 0.519659i
\(703\) −7.61558 13.1906i −0.287227 0.497492i
\(704\) −13.6768 + 23.6889i −0.515464 + 0.892811i
\(705\) 0.153262 0.563271i 0.00577217 0.0212140i
\(706\) −2.28515 + 3.95800i −0.0860029 + 0.148961i
\(707\) 0 0
\(708\) 4.26472 + 4.29778i 0.160278 + 0.161520i
\(709\) −29.4925 −1.10761 −0.553807 0.832645i \(-0.686825\pi\)
−0.553807 + 0.832645i \(0.686825\pi\)
\(710\) 0.191354 + 0.331434i 0.00718138 + 0.0124385i
\(711\) −0.178264 + 23.0816i −0.00668544 + 0.865627i
\(712\) −9.25539 + 16.0308i −0.346860 + 0.600780i
\(713\) 8.78551 + 15.2169i 0.329020 + 0.569879i
\(714\) 0 0
\(715\) −0.436438 + 0.755933i −0.0163219 + 0.0282703i
\(716\) −3.98277 6.89836i −0.148843 0.257804i
\(717\) −35.7508 + 9.43158i −1.33514 + 0.352229i
\(718\) 4.37810 7.58310i 0.163389 0.282999i
\(719\) 0.217311 0.376394i 0.00810433 0.0140371i −0.861945 0.507002i \(-0.830754\pi\)
0.870049 + 0.492965i \(0.164087\pi\)
\(720\) −0.500368 + 0.283758i −0.0186476 + 0.0105750i
\(721\) 0 0
\(722\) 22.0691 + 38.2248i 0.821327 + 1.42258i
\(723\) 33.6058 8.86571i 1.24981 0.329719i
\(724\) −13.3928 −0.497740
\(725\) 46.3488 1.72135
\(726\) 0.0690415 0.253743i 0.00256237 0.00941729i
\(727\) 13.5839 + 23.5280i 0.503799 + 0.872605i 0.999990 + 0.00439187i \(0.00139798\pi\)
−0.496192 + 0.868213i \(0.665269\pi\)
\(728\) 0 0
\(729\) 0.625513 26.9928i 0.0231672 0.999732i
\(730\) −0.274710 + 0.475812i −0.0101675 + 0.0176106i
\(731\) −6.08798 + 10.5447i −0.225172 + 0.390009i
\(732\) −5.42285 5.46490i −0.200434 0.201988i
\(733\) 2.83307 + 4.90702i 0.104642 + 0.181245i 0.913592 0.406632i \(-0.133297\pi\)
−0.808950 + 0.587878i \(0.799964\pi\)
\(734\) −7.25050 + 12.5582i −0.267621 + 0.463533i
\(735\) 0 0
\(736\) −3.92249 6.79395i −0.144585 0.250428i
\(737\) −16.6389 + 28.8194i −0.612901 + 1.06158i
\(738\) −21.3508 12.5477i −0.785932 0.461888i
\(739\) 6.80540 + 11.7873i 0.250341 + 0.433603i 0.963620 0.267278i \(-0.0861241\pi\)
−0.713279 + 0.700880i \(0.752791\pi\)
\(740\) 0.163885 0.00602455
\(741\) 8.66407 31.8424i 0.318282 1.16976i
\(742\) 0 0
\(743\) −6.33421 + 10.9712i −0.232380 + 0.402493i −0.958508 0.285066i \(-0.907985\pi\)
0.726128 + 0.687559i \(0.241318\pi\)
\(744\) −34.6888 34.9578i −1.27175 1.28161i
\(745\) 0.587900 1.01827i 0.0215390 0.0373066i
\(746\) 4.30696 + 7.45988i 0.157689 + 0.273126i
\(747\) 3.05022 1.72978i 0.111602 0.0632892i
\(748\) −4.21977 −0.154290
\(749\) 0 0
\(750\) −1.41740 1.42839i −0.0517563 0.0521576i
\(751\) 3.57269 + 6.18808i 0.130369 + 0.225806i 0.923819 0.382830i \(-0.125050\pi\)
−0.793450 + 0.608636i \(0.791717\pi\)
\(752\) 5.80977 0.211860
\(753\) −8.31394 8.37840i −0.302977 0.305326i
\(754\) 25.4086 0.925325
\(755\) −1.18897 −0.0432712
\(756\) 0 0
\(757\) 37.6446 1.36822 0.684108 0.729381i \(-0.260192\pi\)
0.684108 + 0.729381i \(0.260192\pi\)
\(758\) 34.8651 1.26636
\(759\) 7.72448 + 7.78437i 0.280381 + 0.282555i
\(760\) −2.48751 −0.0902315
\(761\) −5.02358 8.70109i −0.182104 0.315414i 0.760493 0.649347i \(-0.224958\pi\)
−0.942597 + 0.333933i \(0.891624\pi\)
\(762\) 0.426718 + 0.430027i 0.0154584 + 0.0155782i
\(763\) 0 0
\(764\) 17.5572 0.635196
\(765\) −0.440044 0.258611i −0.0159098 0.00935010i
\(766\) −5.91762 10.2496i −0.213812 0.370334i
\(767\) −5.53011 + 9.57843i −0.199681 + 0.345857i
\(768\) 18.9646 + 19.1116i 0.684326 + 0.689632i
\(769\) 16.1463 27.9663i 0.582252 1.00849i −0.412960 0.910749i \(-0.635505\pi\)
0.995212 0.0977407i \(-0.0311616\pi\)
\(770\) 0 0
\(771\) −6.54301 + 24.0470i −0.235641 + 0.866032i
\(772\) 0.201270 0.00724385
\(773\) 24.2939 + 42.0783i 0.873792 + 1.51345i 0.858044 + 0.513576i \(0.171679\pi\)
0.0157473 + 0.999876i \(0.494987\pi\)
\(774\) −21.7216 + 12.3183i −0.780766 + 0.442771i
\(775\) 23.1025 40.0148i 0.829867 1.43737i
\(776\) −5.83694 10.1099i −0.209534 0.362923i
\(777\) 0 0
\(778\) 13.3147 23.0618i 0.477356 0.826806i
\(779\) −28.7538 49.8030i −1.03021 1.78438i
\(780\) 0.250106 + 0.252045i 0.00895522 + 0.00902466i
\(781\) −5.49059 + 9.50998i −0.196469 + 0.340294i
\(782\) −1.68759 + 2.92299i −0.0603481 + 0.104526i
\(783\) 46.4817 + 13.0337i 1.66112 + 0.465786i
\(784\) 0 0
\(785\) 0.643678 + 1.11488i 0.0229739 + 0.0397919i
\(786\) −7.50057 + 27.5663i −0.267537 + 0.983257i
\(787\) 48.9551 1.74506 0.872531 0.488560i \(-0.162478\pi\)
0.872531 + 0.488560i \(0.162478\pi\)
\(788\) 0.598331 0.0213147
\(789\) −2.57745 + 0.679970i −0.0917597 + 0.0242076i
\(790\) 0.447448 + 0.775003i 0.0159195 + 0.0275734i
\(791\) 0 0
\(792\) −26.4994 15.5735i −0.941615 0.553381i
\(793\) 7.03188 12.1796i 0.249710 0.432510i
\(794\) 13.2652 22.9759i 0.470763 0.815385i
\(795\) −1.76219 + 0.464893i −0.0624986 + 0.0164880i
\(796\) 1.97174 + 3.41515i 0.0698864 + 0.121047i
\(797\) 1.44417 2.50137i 0.0511550 0.0886030i −0.839314 0.543647i \(-0.817043\pi\)
0.890469 + 0.455044i \(0.150376\pi\)
\(798\) 0 0
\(799\) 2.57755 + 4.46445i 0.0911873 + 0.157941i
\(800\) −10.3147 + 17.8655i −0.364678 + 0.631641i
\(801\) −15.5949 9.16502i −0.551018 0.323830i
\(802\) −0.861472 1.49211i −0.0304196 0.0526883i
\(803\) −15.7647 −0.556326
\(804\) 9.53510 + 9.60903i 0.336277 + 0.338884i
\(805\) 0 0
\(806\) 12.6649 21.9362i 0.446102 0.772671i
\(807\) −11.9403 + 43.8832i −0.420317 + 1.54476i
\(808\) −26.8169 + 46.4483i −0.943417 + 1.63405i
\(809\) −5.84869 10.1302i −0.205629 0.356160i 0.744704 0.667395i \(-0.232591\pi\)
−0.950333 + 0.311235i \(0.899257\pi\)
\(810\) −0.509328 0.914518i −0.0178960 0.0321329i
\(811\) −17.1780 −0.603199 −0.301600 0.953435i \(-0.597521\pi\)
−0.301600 + 0.953435i \(0.597521\pi\)
\(812\) 0 0
\(813\) −30.0341 + 7.92343i −1.05334 + 0.277887i
\(814\) −3.64830 6.31904i −0.127873 0.221482i
\(815\) 0.945254 0.0331108
\(816\) 1.33370 4.90165i 0.0466889 0.171592i
\(817\) −57.9869 −2.02870
\(818\) 24.6431 0.861624
\(819\) 0 0
\(820\) 0.618775 0.0216085
\(821\) 34.0137 1.18709 0.593543 0.804803i \(-0.297729\pi\)
0.593543 + 0.804803i \(0.297729\pi\)
\(822\) 28.1609 7.42925i 0.982224 0.259125i
\(823\) 43.3780 1.51206 0.756031 0.654536i \(-0.227136\pi\)
0.756031 + 0.654536i \(0.227136\pi\)
\(824\) 13.4037 + 23.2160i 0.466942 + 0.808767i
\(825\) 7.57125 27.8260i 0.263597 0.968779i
\(826\) 0 0
\(827\) −34.0909 −1.18546 −0.592728 0.805403i \(-0.701949\pi\)
−0.592728 + 0.805403i \(0.701949\pi\)
\(828\) 3.88050 2.20062i 0.134857 0.0764770i
\(829\) 8.45833 + 14.6503i 0.293770 + 0.508824i 0.974698 0.223526i \(-0.0717567\pi\)
−0.680928 + 0.732350i \(0.738423\pi\)
\(830\) 0.0679744 0.117735i 0.00235943 0.00408665i
\(831\) −31.6047 + 8.33778i −1.09635 + 0.289234i
\(832\) −10.1632 + 17.6032i −0.352345 + 0.610280i
\(833\) 0 0
\(834\) −14.9950 + 3.95591i −0.519236 + 0.136982i
\(835\) −1.83687 −0.0635674
\(836\) −10.0481 17.4039i −0.347522 0.601926i
\(837\) 34.4213 33.6329i 1.18977 1.16252i
\(838\) −3.29353 + 5.70456i −0.113773 + 0.197061i
\(839\) −8.16244 14.1378i −0.281799 0.488089i 0.690029 0.723782i \(-0.257598\pi\)
−0.971828 + 0.235692i \(0.924264\pi\)
\(840\) 0 0
\(841\) −28.6560 + 49.6336i −0.988138 + 1.71150i
\(842\) −8.06812 13.9744i −0.278046 0.481589i
\(843\) −2.26989 + 8.34235i −0.0781792 + 0.287326i
\(844\) 2.82590 4.89459i 0.0972713 0.168479i
\(845\) 0.361214 0.625641i 0.0124261 0.0215227i
\(846\) −0.0816511 + 10.5721i −0.00280722 + 0.363478i
\(847\) 0 0
\(848\) −9.06915 15.7082i −0.311436 0.539423i
\(849\) 18.7792 + 18.9248i 0.644499 + 0.649496i
\(850\) 8.87544 0.304425
\(851\) 3.76124 0.128934
\(852\) 3.14645 + 3.17084i 0.107796 + 0.108631i
\(853\) −14.4524 25.0323i −0.494841 0.857089i 0.505142 0.863036i \(-0.331440\pi\)
−0.999982 + 0.00594733i \(0.998107\pi\)
\(854\) 0 0
\(855\) 0.0187729 2.43071i 0.000642020 0.0831285i
\(856\) 27.8547 48.2458i 0.952055 1.64901i
\(857\) 14.5284 25.1639i 0.496280 0.859582i −0.503711 0.863872i \(-0.668032\pi\)
0.999991 + 0.00429061i \(0.00136575\pi\)
\(858\) 4.15059 15.2543i 0.141699 0.520774i
\(859\) 6.29820 + 10.9088i 0.214892 + 0.372203i 0.953239 0.302217i \(-0.0977268\pi\)
−0.738347 + 0.674421i \(0.764393\pi\)
\(860\) 0.311966 0.540341i 0.0106380 0.0184255i
\(861\) 0 0
\(862\) −10.6992 18.5315i −0.364415 0.631185i
\(863\) 7.33309 12.7013i 0.249621 0.432357i −0.713799 0.700350i \(-0.753027\pi\)
0.963421 + 0.267993i \(0.0863605\pi\)
\(864\) −15.3682 + 15.0162i −0.522836 + 0.510860i
\(865\) 0.149199 + 0.258420i 0.00507292 + 0.00878655i
\(866\) −1.49119 −0.0506726
\(867\) −24.1124 + 6.36122i −0.818901 + 0.216038i
\(868\) 0 0
\(869\) −12.8388 + 22.2375i −0.435527 + 0.754354i
\(870\) 1.80968 0.477419i 0.0613538 0.0161860i
\(871\) −12.3643 + 21.4156i −0.418948 + 0.725639i
\(872\) 6.48154 + 11.2264i 0.219493 + 0.380172i
\(873\) 9.92307 5.62736i 0.335845 0.190457i
\(874\) −16.0740 −0.543711
\(875\) 0 0
\(876\) −1.68370 + 6.18797i −0.0568869 + 0.209072i
\(877\) −16.5951 28.7435i −0.560376 0.970600i −0.997463 0.0711811i \(-0.977323\pi\)
0.437087 0.899419i \(-0.356010\pi\)
\(878\) −19.1241 −0.645407
\(879\) 43.2128 11.4002i 1.45753 0.384518i
\(880\) −0.639905 −0.0215712
\(881\) −31.7179 −1.06860 −0.534301 0.845294i \(-0.679425\pi\)
−0.534301 + 0.845294i \(0.679425\pi\)
\(882\) 0 0
\(883\) −39.5231 −1.33006 −0.665029 0.746818i \(-0.731581\pi\)
−0.665029 + 0.746818i \(0.731581\pi\)
\(884\) −3.13569 −0.105465
\(885\) −0.213896 + 0.786115i −0.00719003 + 0.0264250i
\(886\) −21.6262 −0.726545
\(887\) −24.9513 43.2169i −0.837782 1.45108i −0.891745 0.452538i \(-0.850519\pi\)
0.0539627 0.998543i \(-0.482815\pi\)
\(888\) −10.1932 + 2.68912i −0.342062 + 0.0902411i
\(889\) 0 0
\(890\) −0.701292 −0.0235074
\(891\) 15.4179 25.7767i 0.516519 0.863553i
\(892\) 4.38228 + 7.59034i 0.146730 + 0.254143i
\(893\) −12.2754 + 21.2616i −0.410779 + 0.711491i
\(894\) −5.59101 + 20.5482i −0.186991 + 0.687235i
\(895\) 0.535910 0.928223i 0.0179135 0.0310271i
\(896\) 0 0
\(897\) 5.74003 + 5.78454i 0.191654 + 0.193140i
\(898\) 19.5578 0.652653
\(899\) 43.0222 + 74.5166i 1.43487 + 2.48527i
\(900\) −10.1136 5.94372i −0.337121 0.198124i
\(901\) 8.04721 13.9382i 0.268092 0.464348i
\(902\) −13.7747 23.8585i −0.458648 0.794401i
\(903\) 0 0
\(904\) 3.15671 5.46757i 0.104990 0.181849i
\(905\) −0.901048 1.56066i −0.0299518 0.0518781i
\(906\) 20.8215 5.49301i 0.691747 0.182493i
\(907\) 6.96080 12.0565i 0.231129 0.400328i −0.727011 0.686625i \(-0.759091\pi\)
0.958141 + 0.286298i \(0.0924246\pi\)
\(908\) −9.31574 + 16.1353i −0.309154 + 0.535470i
\(909\) −45.1853 26.5551i −1.49870 0.880778i
\(910\) 0 0
\(911\) 2.70428 + 4.68394i 0.0895967 + 0.155186i 0.907341 0.420396i \(-0.138109\pi\)
−0.817744 + 0.575582i \(0.804776\pi\)
\(912\) 23.3920 6.17116i 0.774587 0.204347i
\(913\) 3.90084 0.129099
\(914\) −0.535362 −0.0177082
\(915\) 0.271982 0.999594i 0.00899144 0.0330456i
\(916\) 0.746758 + 1.29342i 0.0246736 + 0.0427359i
\(917\) 0 0
\(918\) 8.90089 + 2.49585i 0.293773 + 0.0823754i
\(919\) −17.0142 + 29.4694i −0.561245 + 0.972105i 0.436143 + 0.899877i \(0.356344\pi\)
−0.997388 + 0.0722280i \(0.976989\pi\)
\(920\) 0.307138 0.531978i 0.0101260 0.0175388i
\(921\) 27.1957 + 27.4065i 0.896129 + 0.903076i
\(922\) −4.40781 7.63455i −0.145163 0.251430i
\(923\) −4.08004 + 7.06683i −0.134296 + 0.232608i
\(924\) 0 0
\(925\) −4.94531 8.56554i −0.162601 0.281633i
\(926\) −5.78184 + 10.0144i −0.190003 + 0.329095i
\(927\) −22.7870 + 12.9225i −0.748423 + 0.424429i
\(928\) −19.2082 33.2696i −0.630541 1.09213i
\(929\) 10.6329 0.348855 0.174427 0.984670i \(-0.444193\pi\)
0.174427 + 0.984670i \(0.444193\pi\)
\(930\) 0.489857 1.80033i 0.0160631 0.0590353i
\(931\) 0 0
\(932\) 2.56375 4.44055i 0.0839785 0.145455i
\(933\) 1.59804 + 1.61043i 0.0523175 + 0.0527231i
\(934\) 12.0746 20.9137i 0.395092 0.684319i
\(935\) −0.283900 0.491729i −0.00928451 0.0160812i
\(936\) −19.6916 11.5726i −0.643640 0.378263i
\(937\) 52.6692 1.72063 0.860314 0.509765i \(-0.170268\pi\)
0.860314 + 0.509765i \(0.170268\pi\)
\(938\) 0 0
\(939\) −26.3241 26.5282i −0.859053 0.865714i
\(940\) −0.132082 0.228772i −0.00430802 0.00746172i
\(941\) −34.3656 −1.12029 −0.560143 0.828396i \(-0.689254\pi\)
−0.560143 + 0.828396i \(0.689254\pi\)
\(942\) −16.4229 16.5502i −0.535087 0.539236i
\(943\) 14.2011 0.462453
\(944\) −8.10825 −0.263901
\(945\) 0 0
\(946\) −27.7791 −0.903175
\(947\) −40.5840 −1.31880 −0.659401 0.751791i \(-0.729190\pi\)
−0.659401 + 0.751791i \(0.729190\pi\)
\(948\) 7.35743 + 7.41447i 0.238958 + 0.240811i
\(949\) −11.7147 −0.380276
\(950\) 21.1342 + 36.6056i 0.685685 + 1.18764i
\(951\) 30.2341 + 30.4685i 0.980408 + 0.988009i
\(952\) 0 0
\(953\) −22.6904 −0.735013 −0.367507 0.930021i \(-0.619789\pi\)
−0.367507 + 0.930021i \(0.619789\pi\)
\(954\) 28.7120 16.2825i 0.929586 0.527167i
\(955\) 1.18122 + 2.04593i 0.0382234 + 0.0662049i
\(956\) −8.36589 + 14.4901i −0.270572 + 0.468645i
\(957\) 37.8264 + 38.1197i 1.22275 + 1.23223i
\(958\) 2.20656 3.82187i 0.0712907 0.123479i
\(959\) 0 0
\(960\) −0.393096 + 1.44472i −0.0126871 + 0.0466280i
\(961\) 54.7775 1.76702
\(962\) −2.71104 4.69566i −0.0874074 0.151394i
\(963\) 46.9339 + 27.5828i 1.51242 + 0.888842i
\(964\) 7.86395 13.6208i 0.253281 0.438695i
\(965\) 0.0135411 + 0.0234539i 0.000435904 + 0.000755008i
\(966\) 0 0
\(967\) −12.1388 + 21.0250i −0.390357 + 0.676118i −0.992497 0.122273i \(-0.960982\pi\)
0.602139 + 0.798391i \(0.294315\pi\)
\(968\) −0.211325 0.366026i −0.00679224 0.0117645i
\(969\) 15.1202 + 15.2375i 0.485732 + 0.489498i
\(970\) 0.221136 0.383019i 0.00710025 0.0122980i
\(971\) −22.7886 + 39.4709i −0.731319 + 1.26668i 0.225000 + 0.974359i \(0.427762\pi\)
−0.956319 + 0.292324i \(0.905572\pi\)
\(972\) −8.47121 8.80481i −0.271714 0.282414i
\(973\) 0 0
\(974\) −14.5988 25.2858i −0.467774 0.810209i
\(975\) 5.62617 20.6774i 0.180182 0.662208i
\(976\) 10.3102 0.330020
\(977\) −14.6896 −0.469963 −0.234981 0.972000i \(-0.575503\pi\)
−0.234981 + 0.972000i \(0.575503\pi\)
\(978\) −16.5534 + 4.36704i −0.529321 + 0.139643i
\(979\) −10.0612 17.4266i −0.321558 0.556956i
\(980\) 0 0
\(981\) −11.0189 + 6.24881i −0.351807 + 0.199509i
\(982\) −15.6764 + 27.1524i −0.500255 + 0.866467i
\(983\) 22.2955 38.6169i 0.711115 1.23169i −0.253324 0.967381i \(-0.581524\pi\)
0.964439 0.264305i \(-0.0851427\pi\)
\(984\) −38.4861 + 10.1532i −1.22689 + 0.323672i
\(985\) 0.0402548 + 0.0697234i 0.00128262 + 0.00222157i
\(986\) −8.26404 + 14.3137i −0.263181 + 0.455842i
\(987\) 0 0
\(988\) −7.46673 12.9328i −0.237548 0.411446i
\(989\) 7.15976 12.4011i 0.227667 0.394331i
\(990\) 0.00899330 1.16445i 0.000285826 0.0370086i
\(991\) −12.0915 20.9430i −0.384098 0.665277i 0.607546 0.794285i \(-0.292154\pi\)
−0.991644 + 0.129007i \(0.958821\pi\)
\(992\) −38.2973 −1.21594
\(993\) −16.8911 17.0221i −0.536024 0.540179i
\(994\) 0 0
\(995\) −0.265311 + 0.459532i −0.00841093 + 0.0145682i
\(996\) 0.416615 1.53115i 0.0132010 0.0485165i
\(997\) 5.43262 9.40957i 0.172053 0.298004i −0.767085 0.641546i \(-0.778293\pi\)
0.939137 + 0.343542i \(0.111627\pi\)
\(998\) −4.09760 7.09726i −0.129707 0.224660i
\(999\) −2.55079 9.98076i −0.0807034 0.315777i
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 441.2.h.h.373.5 24
3.2 odd 2 1323.2.h.h.226.8 24
7.2 even 3 441.2.f.h.148.8 yes 24
7.3 odd 6 441.2.g.h.67.8 24
7.4 even 3 441.2.g.h.67.7 24
7.5 odd 6 441.2.f.h.148.7 24
7.6 odd 2 inner 441.2.h.h.373.6 24
9.2 odd 6 1323.2.g.h.667.5 24
9.7 even 3 441.2.g.h.79.7 24
21.2 odd 6 1323.2.f.h.442.5 24
21.5 even 6 1323.2.f.h.442.6 24
21.11 odd 6 1323.2.g.h.361.5 24
21.17 even 6 1323.2.g.h.361.6 24
21.20 even 2 1323.2.h.h.226.7 24
63.2 odd 6 1323.2.f.h.883.5 24
63.5 even 6 3969.2.a.bi.1.8 12
63.11 odd 6 1323.2.h.h.802.8 24
63.16 even 3 441.2.f.h.295.8 yes 24
63.20 even 6 1323.2.g.h.667.6 24
63.23 odd 6 3969.2.a.bi.1.7 12
63.25 even 3 inner 441.2.h.h.214.5 24
63.34 odd 6 441.2.g.h.79.8 24
63.38 even 6 1323.2.h.h.802.7 24
63.40 odd 6 3969.2.a.bh.1.5 12
63.47 even 6 1323.2.f.h.883.6 24
63.52 odd 6 inner 441.2.h.h.214.6 24
63.58 even 3 3969.2.a.bh.1.6 12
63.61 odd 6 441.2.f.h.295.7 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.h.148.7 24 7.5 odd 6
441.2.f.h.148.8 yes 24 7.2 even 3
441.2.f.h.295.7 yes 24 63.61 odd 6
441.2.f.h.295.8 yes 24 63.16 even 3
441.2.g.h.67.7 24 7.4 even 3
441.2.g.h.67.8 24 7.3 odd 6
441.2.g.h.79.7 24 9.7 even 3
441.2.g.h.79.8 24 63.34 odd 6
441.2.h.h.214.5 24 63.25 even 3 inner
441.2.h.h.214.6 24 63.52 odd 6 inner
441.2.h.h.373.5 24 1.1 even 1 trivial
441.2.h.h.373.6 24 7.6 odd 2 inner
1323.2.f.h.442.5 24 21.2 odd 6
1323.2.f.h.442.6 24 21.5 even 6
1323.2.f.h.883.5 24 63.2 odd 6
1323.2.f.h.883.6 24 63.47 even 6
1323.2.g.h.361.5 24 21.11 odd 6
1323.2.g.h.361.6 24 21.17 even 6
1323.2.g.h.667.5 24 9.2 odd 6
1323.2.g.h.667.6 24 63.20 even 6
1323.2.h.h.226.7 24 21.20 even 2
1323.2.h.h.226.8 24 3.2 odd 2
1323.2.h.h.802.7 24 63.38 even 6
1323.2.h.h.802.8 24 63.11 odd 6
3969.2.a.bh.1.5 12 63.40 odd 6
3969.2.a.bh.1.6 12 63.58 even 3
3969.2.a.bi.1.7 12 63.23 odd 6
3969.2.a.bi.1.8 12 63.5 even 6