Properties

Label 525.2.r.h.424.4
Level $525$
Weight $2$
Character 525.424
Analytic conductor $4.192$
Analytic rank $0$
Dimension $16$
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] = [525,2,Mod(424,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.424");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (of order \(6\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 15x^{14} + 158x^{12} - 843x^{10} + 3258x^{8} - 4947x^{6} + 5489x^{4} - 1296x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 424.4
Root \(-0.427967 + 0.247087i\) of defining polynomial
Character \(\chi\) \(=\) 525.424
Dual form 525.2.r.h.499.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.427967 + 0.247087i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.427967 + 0.247087i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.66927 + 4.62330i) q^{11} +(1.52056 - 0.877896i) q^{12} -5.09433i q^{13} +(-1.26162 - 0.343173i) q^{14} +(-1.29720 - 2.24681i) q^{16} +(-0.303270 - 0.175093i) q^{17} +(-0.427967 - 0.247087i) q^{18} +(1.38372 + 2.39668i) q^{19} +(-0.675093 - 2.55817i) q^{21} -2.63816i q^{22} +(-6.50522 + 3.75579i) q^{23} +(-0.928006 + 1.60735i) q^{24} +(1.25874 + 2.18020i) q^{26} -1.00000i q^{27} +(-4.49162 + 1.18532i) q^{28} -4.00000 q^{29} +(-3.05882 + 5.29802i) q^{31} +(4.32502 + 2.49705i) q^{32} +(4.62330 - 2.66927i) q^{33} +0.173053 q^{34} -1.75579 q^{36} +(-3.05121 + 1.76162i) q^{37} +(-1.18437 - 0.683799i) q^{38} +(-2.54716 + 4.41182i) q^{39} -7.86177 q^{41} +(0.921008 + 0.928006i) q^{42} -1.41726i q^{43} +(-4.68668 - 8.11757i) q^{44} +(1.85601 - 3.21471i) q^{46} +(-7.66443 + 4.42506i) q^{47} +2.59439i q^{48} +(-0.0529894 + 6.99980i) q^{49} +(0.175093 + 0.303270i) q^{51} +(7.74623 + 4.47229i) q^{52} +(-5.47924 - 3.16344i) q^{53} +(0.247087 + 0.427967i) q^{54} +(3.48540 - 3.45911i) q^{56} -2.76745i q^{57} +(1.71187 - 0.988347i) q^{58} +(6.42506 - 11.1285i) q^{59} +(2.50000 + 4.33013i) q^{61} -3.02317i q^{62} +(-0.694439 + 2.55299i) q^{63} +2.72083 q^{64} +(-1.31908 + 2.28471i) q^{66} +(-3.25261 - 1.87790i) q^{67} +(0.532479 - 0.307427i) q^{68} +7.51159 q^{69} +15.4883 q^{71} +(1.60735 - 0.928006i) q^{72} +(6.64853 + 3.83853i) q^{73} +(0.870545 - 1.50783i) q^{74} -4.85906 q^{76} +(-13.6569 + 3.60401i) q^{77} -2.51748i q^{78} +(1.18092 + 2.04541i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.36458 - 1.94254i) q^{82} +6.87342i q^{83} +(4.48252 + 1.21929i) q^{84} +(0.350186 + 0.606540i) q^{86} +(3.46410 + 2.00000i) q^{87} +(8.58091 + 4.95419i) q^{88} +(-2.17509 - 3.76737i) q^{89} +(9.56662 - 9.49447i) q^{91} -13.1888i q^{92} +(5.29802 - 3.05882i) q^{93} +(2.18675 - 3.78756i) q^{94} +(-2.49705 - 4.32502i) q^{96} +5.49993i q^{97} +(-1.70688 - 3.00877i) q^{98} -5.33853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.427967 + 0.247087i −0.302618 + 0.174717i −0.643618 0.765347i \(-0.722568\pi\)
0.341000 + 0.940063i \(0.389234\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.877896 + 1.52056i −0.438948 + 0.760281i
\(5\) 0 0
\(6\) 0.494173 0.201745
\(7\) 1.86373 + 1.87790i 0.704425 + 0.709778i
\(8\) 1.85601i 0.656200i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.66927 + 4.62330i −0.804814 + 1.39398i 0.111602 + 0.993753i \(0.464402\pi\)
−0.916416 + 0.400226i \(0.868932\pi\)
\(12\) 1.52056 0.877896i 0.438948 0.253427i
\(13\) 5.09433i 1.41291i −0.707757 0.706456i \(-0.750293\pi\)
0.707757 0.706456i \(-0.249707\pi\)
\(14\) −1.26162 0.343173i −0.337182 0.0917169i
\(15\) 0 0
\(16\) −1.29720 2.24681i −0.324299 0.561703i
\(17\) −0.303270 0.175093i −0.0735538 0.0424663i 0.462772 0.886477i \(-0.346855\pi\)
−0.536326 + 0.844011i \(0.680188\pi\)
\(18\) −0.427967 0.247087i −0.100873 0.0582389i
\(19\) 1.38372 + 2.39668i 0.317448 + 0.549836i 0.979955 0.199220i \(-0.0638408\pi\)
−0.662507 + 0.749056i \(0.730507\pi\)
\(20\) 0 0
\(21\) −0.675093 2.55817i −0.147317 0.558239i
\(22\) 2.63816i 0.562458i
\(23\) −6.50522 + 3.75579i −1.35643 + 0.783137i −0.989141 0.146969i \(-0.953048\pi\)
−0.367292 + 0.930106i \(0.619715\pi\)
\(24\) −0.928006 + 1.60735i −0.189429 + 0.328100i
\(25\) 0 0
\(26\) 1.25874 + 2.18020i 0.246859 + 0.427573i
\(27\) 1.00000i 0.192450i
\(28\) −4.49162 + 1.18532i −0.848837 + 0.224005i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −3.05882 + 5.29802i −0.549380 + 0.951553i 0.448938 + 0.893563i \(0.351803\pi\)
−0.998317 + 0.0579902i \(0.981531\pi\)
\(32\) 4.32502 + 2.49705i 0.764563 + 0.441421i
\(33\) 4.62330 2.66927i 0.804814 0.464660i
\(34\) 0.173053 0.0296783
\(35\) 0 0
\(36\) −1.75579 −0.292632
\(37\) −3.05121 + 1.76162i −0.501617 + 0.289608i −0.729381 0.684108i \(-0.760192\pi\)
0.227764 + 0.973716i \(0.426858\pi\)
\(38\) −1.18437 0.683799i −0.192131 0.110927i
\(39\) −2.54716 + 4.41182i −0.407872 + 0.706456i
\(40\) 0 0
\(41\) −7.86177 −1.22780 −0.613901 0.789383i \(-0.710401\pi\)
−0.613901 + 0.789383i \(0.710401\pi\)
\(42\) 0.921008 + 0.928006i 0.142115 + 0.143194i
\(43\) 1.41726i 0.216130i −0.994144 0.108065i \(-0.965535\pi\)
0.994144 0.108065i \(-0.0344655\pi\)
\(44\) −4.68668 8.11757i −0.706543 1.22377i
\(45\) 0 0
\(46\) 1.85601 3.21471i 0.273654 0.473983i
\(47\) −7.66443 + 4.42506i −1.11797 + 0.645461i −0.940882 0.338734i \(-0.890001\pi\)
−0.177089 + 0.984195i \(0.556668\pi\)
\(48\) 2.59439i 0.374468i
\(49\) −0.0529894 + 6.99980i −0.00756991 + 0.999971i
\(50\) 0 0
\(51\) 0.175093 + 0.303270i 0.0245179 + 0.0424663i
\(52\) 7.74623 + 4.47229i 1.07421 + 0.620195i
\(53\) −5.47924 3.16344i −0.752631 0.434532i 0.0740126 0.997257i \(-0.476419\pi\)
−0.826644 + 0.562725i \(0.809753\pi\)
\(54\) 0.247087 + 0.427967i 0.0336242 + 0.0582389i
\(55\) 0 0
\(56\) 3.48540 3.45911i 0.465756 0.462244i
\(57\) 2.76745i 0.366557i
\(58\) 1.71187 0.988347i 0.224779 0.129776i
\(59\) 6.42506 11.1285i 0.836471 1.44881i −0.0563553 0.998411i \(-0.517948\pi\)
0.892827 0.450400i \(-0.148719\pi\)
\(60\) 0 0
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) 3.02317i 0.383943i
\(63\) −0.694439 + 2.55299i −0.0874911 + 0.321646i
\(64\) 2.72083 0.340104
\(65\) 0 0
\(66\) −1.31908 + 2.28471i −0.162368 + 0.281229i
\(67\) −3.25261 1.87790i −0.397370 0.229422i 0.287979 0.957637i \(-0.407017\pi\)
−0.685348 + 0.728215i \(0.740350\pi\)
\(68\) 0.532479 0.307427i 0.0645726 0.0372810i
\(69\) 7.51159 0.904289
\(70\) 0 0
\(71\) 15.4883 1.83812 0.919060 0.394117i \(-0.128950\pi\)
0.919060 + 0.394117i \(0.128950\pi\)
\(72\) 1.60735 0.928006i 0.189429 0.109367i
\(73\) 6.64853 + 3.83853i 0.778152 + 0.449266i 0.835775 0.549072i \(-0.185019\pi\)
−0.0576229 + 0.998338i \(0.518352\pi\)
\(74\) 0.870545 1.50783i 0.101199 0.175282i
\(75\) 0 0
\(76\) −4.85906 −0.557373
\(77\) −13.6569 + 3.60401i −1.55635 + 0.410715i
\(78\) 2.51748i 0.285048i
\(79\) 1.18092 + 2.04541i 0.132864 + 0.230127i 0.924779 0.380504i \(-0.124249\pi\)
−0.791916 + 0.610631i \(0.790916\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.36458 1.94254i 0.371555 0.214518i
\(83\) 6.87342i 0.754456i 0.926120 + 0.377228i \(0.123123\pi\)
−0.926120 + 0.377228i \(0.876877\pi\)
\(84\) 4.48252 + 1.21929i 0.489083 + 0.133036i
\(85\) 0 0
\(86\) 0.350186 + 0.606540i 0.0377615 + 0.0654049i
\(87\) 3.46410 + 2.00000i 0.371391 + 0.214423i
\(88\) 8.58091 + 4.95419i 0.914728 + 0.528119i
\(89\) −2.17509 3.76737i −0.230559 0.399341i 0.727413 0.686199i \(-0.240722\pi\)
−0.957973 + 0.286859i \(0.907389\pi\)
\(90\) 0 0
\(91\) 9.56662 9.49447i 1.00285 0.995291i
\(92\) 13.1888i 1.37503i
\(93\) 5.29802 3.05882i 0.549380 0.317184i
\(94\) 2.18675 3.78756i 0.225546 0.390657i
\(95\) 0 0
\(96\) −2.49705 4.32502i −0.254854 0.441421i
\(97\) 5.49993i 0.558433i 0.960228 + 0.279217i \(0.0900748\pi\)
−0.960228 + 0.279217i \(0.909925\pi\)
\(98\) −1.70688 3.00877i −0.172421 0.303932i
\(99\) −5.33853 −0.536543
\(100\) 0 0
\(101\) −0.824907 + 1.42878i −0.0820813 + 0.142169i −0.904144 0.427228i \(-0.859490\pi\)
0.822062 + 0.569397i \(0.192823\pi\)
\(102\) −0.149868 0.0865263i −0.0148391 0.00856738i
\(103\) 8.80003 5.08070i 0.867093 0.500616i 0.000711688 1.00000i \(-0.499773\pi\)
0.866381 + 0.499384i \(0.166440\pi\)
\(104\) −9.45513 −0.927152
\(105\) 0 0
\(106\) 3.12658 0.303680
\(107\) −4.64349 + 2.68092i −0.448903 + 0.259174i −0.707367 0.706847i \(-0.750117\pi\)
0.258464 + 0.966021i \(0.416784\pi\)
\(108\) 1.52056 + 0.877896i 0.146316 + 0.0844756i
\(109\) −0.0529894 + 0.0917803i −0.00507546 + 0.00879096i −0.868552 0.495598i \(-0.834949\pi\)
0.863477 + 0.504389i \(0.168282\pi\)
\(110\) 0 0
\(111\) 3.52324 0.334411
\(112\) 1.80165 6.62346i 0.170240 0.625858i
\(113\) 4.67707i 0.439981i 0.975502 + 0.219991i \(0.0706027\pi\)
−0.975502 + 0.219991i \(0.929397\pi\)
\(114\) 0.683799 + 1.18437i 0.0640436 + 0.110927i
\(115\) 0 0
\(116\) 3.51159 6.08224i 0.326043 0.564722i
\(117\) 4.41182 2.54716i 0.407872 0.235485i
\(118\) 6.35019i 0.584582i
\(119\) −0.236408 0.895837i −0.0216715 0.0821212i
\(120\) 0 0
\(121\) −8.74997 15.1554i −0.795451 1.37776i
\(122\) −2.13983 1.23543i −0.193731 0.111851i
\(123\) 6.80849 + 3.93089i 0.613901 + 0.354436i
\(124\) −5.37065 9.30223i −0.482298 0.835365i
\(125\) 0 0
\(126\) −0.333613 1.26418i −0.0297206 0.112622i
\(127\) 17.5388i 1.55632i −0.628066 0.778160i \(-0.716153\pi\)
0.628066 0.778160i \(-0.283847\pi\)
\(128\) −9.81447 + 5.66639i −0.867485 + 0.500843i
\(129\) −0.708630 + 1.22738i −0.0623914 + 0.108065i
\(130\) 0 0
\(131\) 4.51159 + 7.81430i 0.394179 + 0.682738i 0.992996 0.118148i \(-0.0376956\pi\)
−0.598817 + 0.800886i \(0.704362\pi\)
\(132\) 9.37336i 0.815846i
\(133\) −1.92182 + 7.06526i −0.166643 + 0.612636i
\(134\) 1.85601 0.160335
\(135\) 0 0
\(136\) −0.324975 + 0.562873i −0.0278664 + 0.0482660i
\(137\) 0.722715 + 0.417260i 0.0617457 + 0.0356489i 0.530555 0.847650i \(-0.321984\pi\)
−0.468809 + 0.883299i \(0.655317\pi\)
\(138\) −3.21471 + 1.85601i −0.273654 + 0.157994i
\(139\) 14.3152 1.21420 0.607101 0.794625i \(-0.292332\pi\)
0.607101 + 0.794625i \(0.292332\pi\)
\(140\) 0 0
\(141\) 8.85012 0.745314
\(142\) −6.62847 + 3.82695i −0.556249 + 0.321150i
\(143\) 23.5526 + 13.5981i 1.96957 + 1.13713i
\(144\) 1.29720 2.24681i 0.108100 0.187234i
\(145\) 0 0
\(146\) −3.79380 −0.313977
\(147\) 3.54579 6.03551i 0.292452 0.497800i
\(148\) 6.18608i 0.508492i
\(149\) 9.69833 + 16.7980i 0.794518 + 1.37615i 0.923145 + 0.384453i \(0.125610\pi\)
−0.128626 + 0.991693i \(0.541057\pi\)
\(150\) 0 0
\(151\) −9.26359 + 16.0450i −0.753860 + 1.30572i 0.192078 + 0.981380i \(0.438477\pi\)
−0.945939 + 0.324345i \(0.894856\pi\)
\(152\) 4.44827 2.56821i 0.360802 0.208309i
\(153\) 0.350186i 0.0283109i
\(154\) 4.95419 4.91683i 0.399220 0.396209i
\(155\) 0 0
\(156\) −4.47229 7.74623i −0.358070 0.620195i
\(157\) 4.15654 + 2.39978i 0.331728 + 0.191523i 0.656608 0.754232i \(-0.271991\pi\)
−0.324880 + 0.945755i \(0.605324\pi\)
\(158\) −1.01079 0.583579i −0.0804140 0.0464271i
\(159\) 3.16344 + 5.47924i 0.250877 + 0.434532i
\(160\) 0 0
\(161\) −19.1770 5.21634i −1.51136 0.411105i
\(162\) 0.494173i 0.0388259i
\(163\) −0.716157 + 0.413474i −0.0560938 + 0.0323858i −0.527785 0.849378i \(-0.676977\pi\)
0.471691 + 0.881764i \(0.343644\pi\)
\(164\) 6.90182 11.9543i 0.538942 0.933474i
\(165\) 0 0
\(166\) −1.69833 2.94160i −0.131816 0.228312i
\(167\) 4.61485i 0.357108i 0.983930 + 0.178554i \(0.0571419\pi\)
−0.983930 + 0.178554i \(0.942858\pi\)
\(168\) −4.74800 + 1.25298i −0.366316 + 0.0966696i
\(169\) −12.9522 −0.996319
\(170\) 0 0
\(171\) −1.38372 + 2.39668i −0.105816 + 0.183279i
\(172\) 2.15503 + 1.24421i 0.164320 + 0.0948699i
\(173\) 10.9787 6.33853i 0.834692 0.481910i −0.0207644 0.999784i \(-0.506610\pi\)
0.855456 + 0.517875i \(0.173277\pi\)
\(174\) −1.97669 −0.149853
\(175\) 0 0
\(176\) 13.8503 1.04400
\(177\) −11.1285 + 6.42506i −0.836471 + 0.482937i
\(178\) 1.86173 + 1.07487i 0.139543 + 0.0805651i
\(179\) 6.52324 11.2986i 0.487570 0.844496i −0.512328 0.858790i \(-0.671217\pi\)
0.999898 + 0.0142942i \(0.00455015\pi\)
\(180\) 0 0
\(181\) 15.0594 1.11935 0.559677 0.828711i \(-0.310925\pi\)
0.559677 + 0.828711i \(0.310925\pi\)
\(182\) −1.74824 + 6.42710i −0.129588 + 0.476408i
\(183\) 5.00000i 0.369611i
\(184\) 6.97080 + 12.0738i 0.513894 + 0.890091i
\(185\) 0 0
\(186\) −1.51159 + 2.61814i −0.110835 + 0.191972i
\(187\) 1.61902 0.934740i 0.118394 0.0683549i
\(188\) 15.5390i 1.13330i
\(189\) 1.87790 1.86373i 0.136597 0.135567i
\(190\) 0 0
\(191\) −4.76359 8.25078i −0.344681 0.597006i 0.640614 0.767863i \(-0.278680\pi\)
−0.985296 + 0.170857i \(0.945346\pi\)
\(192\) −2.35631 1.36042i −0.170052 0.0981796i
\(193\) −13.0822 7.55299i −0.941675 0.543676i −0.0511897 0.998689i \(-0.516301\pi\)
−0.890485 + 0.455013i \(0.849635\pi\)
\(194\) −1.35896 2.35379i −0.0975676 0.168992i
\(195\) 0 0
\(196\) −10.5971 6.22567i −0.756936 0.444691i
\(197\) 16.8890i 1.20329i 0.798762 + 0.601647i \(0.205488\pi\)
−0.798762 + 0.601647i \(0.794512\pi\)
\(198\) 2.28471 1.31908i 0.162368 0.0937430i
\(199\) −12.6138 + 21.8477i −0.894167 + 1.54874i −0.0593348 + 0.998238i \(0.518898\pi\)
−0.834832 + 0.550505i \(0.814435\pi\)
\(200\) 0 0
\(201\) 1.87790 + 3.25261i 0.132457 + 0.229422i
\(202\) 0.815294i 0.0573639i
\(203\) −7.45494 7.51159i −0.523234 0.527210i
\(204\) −0.614854 −0.0430484
\(205\) 0 0
\(206\) −2.51075 + 4.34874i −0.174932 + 0.302991i
\(207\) −6.50522 3.75579i −0.452144 0.261046i
\(208\) −11.4460 + 6.60834i −0.793636 + 0.458206i
\(209\) −14.7741 −1.02195
\(210\) 0 0
\(211\) 20.3967 1.40416 0.702082 0.712096i \(-0.252254\pi\)
0.702082 + 0.712096i \(0.252254\pi\)
\(212\) 9.62041 5.55434i 0.660732 0.381474i
\(213\) −13.4132 7.74414i −0.919060 0.530620i
\(214\) 1.32484 2.29469i 0.0905641 0.156862i
\(215\) 0 0
\(216\) −1.85601 −0.126286
\(217\) −15.6500 + 4.12997i −1.06239 + 0.280361i
\(218\) 0.0523719i 0.00354707i
\(219\) −3.83853 6.64853i −0.259384 0.449266i
\(220\) 0 0
\(221\) −0.891981 + 1.54496i −0.0600011 + 0.103925i
\(222\) −1.50783 + 0.870545i −0.101199 + 0.0584272i
\(223\) 22.5738i 1.51165i 0.654772 + 0.755827i \(0.272765\pi\)
−0.654772 + 0.755827i \(0.727235\pi\)
\(224\) 3.37149 + 12.7758i 0.225267 + 0.853618i
\(225\) 0 0
\(226\) −1.15564 2.00163i −0.0768721 0.133146i
\(227\) 12.2675 + 7.08267i 0.814226 + 0.470093i 0.848421 0.529322i \(-0.177554\pi\)
−0.0341954 + 0.999415i \(0.510887\pi\)
\(228\) 4.20807 + 2.42953i 0.278686 + 0.160900i
\(229\) −8.90311 15.4206i −0.588334 1.01902i −0.994451 0.105203i \(-0.966451\pi\)
0.406117 0.913821i \(-0.366883\pi\)
\(230\) 0 0
\(231\) 13.6292 + 3.70728i 0.896737 + 0.243921i
\(232\) 7.42405i 0.487413i
\(233\) −11.8211 + 6.82491i −0.774425 + 0.447115i −0.834451 0.551082i \(-0.814215\pi\)
0.0600258 + 0.998197i \(0.480882\pi\)
\(234\) −1.25874 + 2.18020i −0.0822864 + 0.142524i
\(235\) 0 0
\(236\) 11.2811 + 19.5394i 0.734335 + 1.27191i
\(237\) 2.36184i 0.153418i
\(238\) 0.322524 + 0.324975i 0.0209061 + 0.0210650i
\(239\) 7.53489 0.487392 0.243696 0.969852i \(-0.421640\pi\)
0.243696 + 0.969852i \(0.421640\pi\)
\(240\) 0 0
\(241\) −14.2616 + 24.7017i −0.918667 + 1.59118i −0.117226 + 0.993105i \(0.537400\pi\)
−0.801442 + 0.598073i \(0.795933\pi\)
\(242\) 7.48939 + 4.32400i 0.481436 + 0.277957i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −8.77896 −0.562016
\(245\) 0 0
\(246\) −3.88508 −0.247704
\(247\) 12.2095 7.04914i 0.776869 0.448526i
\(248\) 9.83320 + 5.67720i 0.624409 + 0.360503i
\(249\) 3.43671 5.95256i 0.217793 0.377228i
\(250\) 0 0
\(251\) −22.8501 −1.44229 −0.721143 0.692786i \(-0.756383\pi\)
−0.721143 + 0.692786i \(0.756383\pi\)
\(252\) −3.27233 3.29720i −0.206137 0.207704i
\(253\) 40.1008i 2.52112i
\(254\) 4.33361 + 7.50604i 0.271915 + 0.470971i
\(255\) 0 0
\(256\) 0.0793447 0.137429i 0.00495904 0.00858931i
\(257\) 21.7702 12.5690i 1.35799 0.784036i 0.368637 0.929574i \(-0.379825\pi\)
0.989353 + 0.145538i \(0.0464913\pi\)
\(258\) 0.700372i 0.0436033i
\(259\) −8.99479 2.44667i −0.558909 0.152029i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) −3.86162 2.22951i −0.238571 0.137739i
\(263\) −11.7417 6.77910i −0.724027 0.418017i 0.0922061 0.995740i \(-0.470608\pi\)
−0.816233 + 0.577723i \(0.803941\pi\)
\(264\) −4.95419 8.58091i −0.304909 0.528119i
\(265\) 0 0
\(266\) −0.923256 3.49855i −0.0566085 0.214510i
\(267\) 4.35019i 0.266227i
\(268\) 5.71091 3.29720i 0.348849 0.201408i
\(269\) −4.51363 + 7.81783i −0.275201 + 0.476661i −0.970186 0.242363i \(-0.922078\pi\)
0.694985 + 0.719024i \(0.255411\pi\)
\(270\) 0 0
\(271\) −2.38819 4.13647i −0.145072 0.251273i 0.784328 0.620347i \(-0.213008\pi\)
−0.929400 + 0.369074i \(0.879675\pi\)
\(272\) 0.908520i 0.0550871i
\(273\) −13.0322 + 3.43914i −0.788743 + 0.208146i
\(274\) −0.412397 −0.0249138
\(275\) 0 0
\(276\) −6.59439 + 11.4218i −0.396936 + 0.687513i
\(277\) −1.62009 0.935357i −0.0973416 0.0562002i 0.450539 0.892757i \(-0.351232\pi\)
−0.547881 + 0.836557i \(0.684565\pi\)
\(278\) −6.12644 + 3.53710i −0.367439 + 0.212141i
\(279\) −6.11763 −0.366253
\(280\) 0 0
\(281\) 0.972748 0.0580293 0.0290147 0.999579i \(-0.490763\pi\)
0.0290147 + 0.999579i \(0.490763\pi\)
\(282\) −3.78756 + 2.18675i −0.225546 + 0.130219i
\(283\) −20.9402 12.0899i −1.24477 0.718667i −0.274707 0.961528i \(-0.588581\pi\)
−0.970061 + 0.242861i \(0.921914\pi\)
\(284\) −13.5971 + 23.5509i −0.806840 + 1.39749i
\(285\) 0 0
\(286\) −13.4396 −0.794703
\(287\) −14.6523 14.7636i −0.864895 0.871467i
\(288\) 4.99411i 0.294280i
\(289\) −8.43868 14.6162i −0.496393 0.859778i
\(290\) 0 0
\(291\) 2.74997 4.76308i 0.161206 0.279217i
\(292\) −11.6734 + 6.73967i −0.683137 + 0.394409i
\(293\) 15.5349i 0.907558i −0.891114 0.453779i \(-0.850076\pi\)
0.891114 0.453779i \(-0.149924\pi\)
\(294\) −0.0261859 + 3.45911i −0.00152719 + 0.201740i
\(295\) 0 0
\(296\) 3.26959 + 5.66309i 0.190041 + 0.329161i
\(297\) 4.62330 + 2.66927i 0.268271 + 0.154887i
\(298\) −8.30113 4.79266i −0.480871 0.277631i
\(299\) 19.1332 + 33.1397i 1.10650 + 1.91652i
\(300\) 0 0
\(301\) 2.66147 2.64140i 0.153404 0.152248i
\(302\) 9.15564i 0.526848i
\(303\) 1.42878 0.824907i 0.0820813 0.0473897i
\(304\) 3.58992 6.21793i 0.205896 0.356623i
\(305\) 0 0
\(306\) 0.0865263 + 0.149868i 0.00494638 + 0.00856738i
\(307\) 3.39395i 0.193703i −0.995299 0.0968516i \(-0.969123\pi\)
0.995299 0.0968516i \(-0.0308772\pi\)
\(308\) 6.50922 23.9301i 0.370897 1.36354i
\(309\) −10.1614 −0.578062
\(310\) 0 0
\(311\) 1.23255 2.13485i 0.0698917 0.121056i −0.828962 0.559305i \(-0.811068\pi\)
0.898853 + 0.438249i \(0.144401\pi\)
\(312\) 8.18839 + 4.72757i 0.463576 + 0.267646i
\(313\) 0.411818 0.237763i 0.0232773 0.0134392i −0.488316 0.872667i \(-0.662389\pi\)
0.511594 + 0.859228i \(0.329055\pi\)
\(314\) −2.37181 −0.133849
\(315\) 0 0
\(316\) −4.14690 −0.233281
\(317\) 12.3837 7.14975i 0.695539 0.401570i −0.110145 0.993916i \(-0.535131\pi\)
0.805684 + 0.592346i \(0.201798\pi\)
\(318\) −2.70769 1.56329i −0.151840 0.0876648i
\(319\) 10.6771 18.4932i 0.597801 1.03542i
\(320\) 0 0
\(321\) 5.36184 0.299269
\(322\) 9.49600 2.50596i 0.529192 0.139652i
\(323\) 0.969121i 0.0539233i
\(324\) −0.877896 1.52056i −0.0487720 0.0844756i
\(325\) 0 0
\(326\) 0.204328 0.353906i 0.0113167 0.0196010i
\(327\) 0.0917803 0.0529894i 0.00507546 0.00293032i
\(328\) 14.5915i 0.805683i
\(329\) −22.5943 6.14587i −1.24566 0.338833i
\(330\) 0 0
\(331\) 9.79273 + 16.9615i 0.538257 + 0.932288i 0.998998 + 0.0447537i \(0.0142503\pi\)
−0.460741 + 0.887535i \(0.652416\pi\)
\(332\) −10.4515 6.03415i −0.573598 0.331167i
\(333\) −3.05121 1.76162i −0.167206 0.0965361i
\(334\) −1.14027 1.97500i −0.0623927 0.108067i
\(335\) 0 0
\(336\) −4.87200 + 4.83526i −0.265789 + 0.263785i
\(337\) 4.38230i 0.238719i 0.992851 + 0.119360i \(0.0380841\pi\)
−0.992851 + 0.119360i \(0.961916\pi\)
\(338\) 5.54309 3.20030i 0.301504 0.174074i
\(339\) 2.33853 4.05046i 0.127012 0.219991i
\(340\) 0 0
\(341\) −16.3296 28.2837i −0.884297 1.53165i
\(342\) 1.36760i 0.0739512i
\(343\) −13.2437 + 12.9463i −0.715090 + 0.699032i
\(344\) −2.63045 −0.141824
\(345\) 0 0
\(346\) −3.13233 + 5.42536i −0.168395 + 0.291669i
\(347\) 8.31134 + 4.79855i 0.446176 + 0.257600i 0.706214 0.707999i \(-0.250402\pi\)
−0.260038 + 0.965598i \(0.583735\pi\)
\(348\) −6.08224 + 3.51159i −0.326043 + 0.188241i
\(349\) 19.9007 1.06526 0.532629 0.846349i \(-0.321204\pi\)
0.532629 + 0.846349i \(0.321204\pi\)
\(350\) 0 0
\(351\) −5.09433 −0.271915
\(352\) −23.0893 + 13.3306i −1.23066 + 0.710523i
\(353\) 23.7262 + 13.6983i 1.26282 + 0.729089i 0.973619 0.228180i \(-0.0732775\pi\)
0.289200 + 0.957269i \(0.406611\pi\)
\(354\) 3.17509 5.49942i 0.168754 0.292291i
\(355\) 0 0
\(356\) 7.63802 0.404815
\(357\) −0.243183 + 0.894021i −0.0128706 + 0.0473166i
\(358\) 6.44722i 0.340746i
\(359\) 12.7752 + 22.1274i 0.674252 + 1.16784i 0.976687 + 0.214668i \(0.0688670\pi\)
−0.302435 + 0.953170i \(0.597800\pi\)
\(360\) 0 0
\(361\) 5.67062 9.82180i 0.298454 0.516937i
\(362\) −6.44491 + 3.72097i −0.338737 + 0.195570i
\(363\) 17.4999i 0.918508i
\(364\) 6.03842 + 22.8818i 0.316499 + 1.19933i
\(365\) 0 0
\(366\) 1.23543 + 2.13983i 0.0645771 + 0.111851i
\(367\) 19.2876 + 11.1357i 1.00681 + 0.581280i 0.910255 0.414048i \(-0.135885\pi\)
0.0965519 + 0.995328i \(0.469219\pi\)
\(368\) 16.8771 + 9.74400i 0.879780 + 0.507941i
\(369\) −3.93089 6.80849i −0.204634 0.354436i
\(370\) 0 0
\(371\) −4.27123 16.1853i −0.221751 0.840296i
\(372\) 10.7413i 0.556910i
\(373\) 4.58540 2.64738i 0.237423 0.137076i −0.376569 0.926389i \(-0.622896\pi\)
0.613992 + 0.789312i \(0.289563\pi\)
\(374\) −0.461924 + 0.800075i −0.0238855 + 0.0413709i
\(375\) 0 0
\(376\) 8.21297 + 14.2253i 0.423551 + 0.733612i
\(377\) 20.3773i 1.04948i
\(378\) −0.343173 + 1.26162i −0.0176509 + 0.0648907i
\(379\) −3.10203 −0.159341 −0.0796704 0.996821i \(-0.525387\pi\)
−0.0796704 + 0.996821i \(0.525387\pi\)
\(380\) 0 0
\(381\) −8.76942 + 15.1891i −0.449271 + 0.778160i
\(382\) 4.07732 + 2.35404i 0.208614 + 0.120443i
\(383\) −18.7171 + 10.8064i −0.956402 + 0.552179i −0.895064 0.445938i \(-0.852870\pi\)
−0.0613379 + 0.998117i \(0.519537\pi\)
\(384\) 11.3328 0.578323
\(385\) 0 0
\(386\) 7.46497 0.379957
\(387\) 1.22738 0.708630i 0.0623914 0.0360217i
\(388\) −8.36298 4.82837i −0.424566 0.245123i
\(389\) −6.43082 + 11.1385i −0.326055 + 0.564745i −0.981725 0.190303i \(-0.939053\pi\)
0.655670 + 0.755048i \(0.272386\pi\)
\(390\) 0 0
\(391\) 2.63045 0.133028
\(392\) 12.9917 + 0.0983489i 0.656181 + 0.00496737i
\(393\) 9.02317i 0.455159i
\(394\) −4.17305 7.22794i −0.210235 0.364138i
\(395\) 0 0
\(396\) 4.68668 8.11757i 0.235514 0.407923i
\(397\) 6.05797 3.49757i 0.304041 0.175538i −0.340216 0.940347i \(-0.610500\pi\)
0.644257 + 0.764809i \(0.277167\pi\)
\(398\) 12.4668i 0.624904i
\(399\) 5.19698 5.15778i 0.260174 0.258212i
\(400\) 0 0
\(401\) 1.58070 + 2.73785i 0.0789364 + 0.136722i 0.902791 0.430079i \(-0.141514\pi\)
−0.823855 + 0.566801i \(0.808181\pi\)
\(402\) −1.60735 0.928006i −0.0801675 0.0462847i
\(403\) 26.9899 + 15.5826i 1.34446 + 0.776225i
\(404\) −1.44837 2.50864i −0.0720589 0.124810i
\(405\) 0 0
\(406\) 5.04648 + 1.37269i 0.250452 + 0.0681256i
\(407\) 18.8089i 0.932324i
\(408\) 0.562873 0.324975i 0.0278664 0.0160887i
\(409\) 1.24753 2.16079i 0.0616866 0.106844i −0.833533 0.552470i \(-0.813685\pi\)
0.895219 + 0.445626i \(0.147019\pi\)
\(410\) 0 0
\(411\) −0.417260 0.722715i −0.0205819 0.0356489i
\(412\) 17.8413i 0.878978i
\(413\) 32.8728 8.67503i 1.61757 0.426870i
\(414\) 3.71203 0.182436
\(415\) 0 0
\(416\) 12.7208 22.0331i 0.623688 1.08026i
\(417\) −12.3973 7.15761i −0.607101 0.350510i
\(418\) 6.32282 3.65048i 0.309259 0.178551i
\(419\) 32.6748 1.59627 0.798134 0.602480i \(-0.205821\pi\)
0.798134 + 0.602480i \(0.205821\pi\)
\(420\) 0 0
\(421\) −26.8774 −1.30992 −0.654961 0.755662i \(-0.727315\pi\)
−0.654961 + 0.755662i \(0.727315\pi\)
\(422\) −8.72909 + 5.03974i −0.424926 + 0.245331i
\(423\) −7.66443 4.42506i −0.372657 0.215154i
\(424\) −5.87138 + 10.1695i −0.285140 + 0.493876i
\(425\) 0 0
\(426\) 7.65389 0.370832
\(427\) −3.47219 + 12.7649i −0.168031 + 0.617739i
\(428\) 9.41428i 0.455056i
\(429\) −13.5981 23.5526i −0.656523 1.13713i
\(430\) 0 0
\(431\) −7.09433 + 12.2877i −0.341722 + 0.591879i −0.984753 0.173961i \(-0.944343\pi\)
0.643031 + 0.765840i \(0.277677\pi\)
\(432\) −2.24681 + 1.29720i −0.108100 + 0.0624114i
\(433\) 29.9717i 1.44035i −0.693794 0.720174i \(-0.744062\pi\)
0.693794 0.720174i \(-0.255938\pi\)
\(434\) 5.67720 5.63439i 0.272514 0.270459i
\(435\) 0 0
\(436\) −0.0930383 0.161147i −0.00445573 0.00771755i
\(437\) −18.0029 10.3940i −0.861193 0.497210i
\(438\) 3.28553 + 1.89690i 0.156989 + 0.0906374i
\(439\) −1.03693 1.79602i −0.0494901 0.0857193i 0.840219 0.542247i \(-0.182426\pi\)
−0.889709 + 0.456528i \(0.849093\pi\)
\(440\) 0 0
\(441\) −6.08850 + 3.45401i −0.289929 + 0.164477i
\(442\) 0.881586i 0.0419328i
\(443\) −27.7800 + 16.0388i −1.31987 + 0.762025i −0.983707 0.179780i \(-0.942461\pi\)
−0.336159 + 0.941805i \(0.609128\pi\)
\(444\) −3.09304 + 5.35730i −0.146789 + 0.254246i
\(445\) 0 0
\(446\) −5.57768 9.66083i −0.264111 0.457454i
\(447\) 19.3967i 0.917431i
\(448\) 5.07091 + 5.10944i 0.239578 + 0.241398i
\(449\) 4.46103 0.210529 0.105264 0.994444i \(-0.466431\pi\)
0.105264 + 0.994444i \(0.466431\pi\)
\(450\) 0 0
\(451\) 20.9852 36.3474i 0.988153 1.71153i
\(452\) −7.11176 4.10598i −0.334509 0.193129i
\(453\) 16.0450 9.26359i 0.753860 0.435242i
\(454\) −7.00014 −0.328533
\(455\) 0 0
\(456\) −5.13641 −0.240535
\(457\) −1.96607 + 1.13511i −0.0919689 + 0.0530983i −0.545279 0.838255i \(-0.683576\pi\)
0.453310 + 0.891353i \(0.350243\pi\)
\(458\) 7.62047 + 4.39968i 0.356081 + 0.205583i
\(459\) −0.175093 + 0.303270i −0.00817264 + 0.0141554i
\(460\) 0 0
\(461\) 4.33096 0.201713 0.100856 0.994901i \(-0.467842\pi\)
0.100856 + 0.994901i \(0.467842\pi\)
\(462\) −6.74887 + 1.78100i −0.313986 + 0.0828598i
\(463\) 41.7856i 1.94194i 0.239196 + 0.970971i \(0.423116\pi\)
−0.239196 + 0.970971i \(0.576884\pi\)
\(464\) 5.18879 + 8.98724i 0.240883 + 0.417222i
\(465\) 0 0
\(466\) 3.37269 5.84167i 0.156237 0.270610i
\(467\) 33.2357 19.1887i 1.53797 0.887945i 0.539008 0.842301i \(-0.318799\pi\)
0.998958 0.0456441i \(-0.0145340\pi\)
\(468\) 8.94458i 0.413463i
\(469\) −2.53551 9.60797i −0.117079 0.443655i
\(470\) 0 0
\(471\) −2.39978 4.15654i −0.110576 0.191523i
\(472\) −20.6547 11.9250i −0.950709 0.548892i
\(473\) 6.55242 + 3.78304i 0.301281 + 0.173945i
\(474\) 0.583579 + 1.01079i 0.0268047 + 0.0464271i
\(475\) 0 0
\(476\) 1.56972 + 0.426979i 0.0719478 + 0.0195705i
\(477\) 6.32688i 0.289688i
\(478\) −3.22468 + 1.86177i −0.147494 + 0.0851554i
\(479\) 19.0193 32.9424i 0.869015 1.50518i 0.00600999 0.999982i \(-0.498087\pi\)
0.863005 0.505196i \(-0.168580\pi\)
\(480\) 0 0
\(481\) 8.97426 + 15.5439i 0.409191 + 0.708740i
\(482\) 14.0954i 0.642026i
\(483\) 13.9996 + 14.1060i 0.637004 + 0.641844i
\(484\) 30.7263 1.39665
\(485\) 0 0
\(486\) −0.247087 + 0.427967i −0.0112081 + 0.0194130i
\(487\) −19.5572 11.2914i −0.886223 0.511661i −0.0135175 0.999909i \(-0.504303\pi\)
−0.872705 + 0.488248i \(0.837636\pi\)
\(488\) 8.03677 4.64003i 0.363808 0.210044i
\(489\) 0.826947 0.0373959
\(490\) 0 0
\(491\) −0.134148 −0.00605400 −0.00302700 0.999995i \(-0.500964\pi\)
−0.00302700 + 0.999995i \(0.500964\pi\)
\(492\) −11.9543 + 6.90182i −0.538942 + 0.311158i
\(493\) 1.21308 + 0.700372i 0.0546344 + 0.0315432i
\(494\) −3.48349 + 6.03359i −0.156730 + 0.271464i
\(495\) 0 0
\(496\) 15.8715 0.712653
\(497\) 28.8660 + 29.0854i 1.29482 + 1.30466i
\(498\) 3.39666i 0.152208i
\(499\) −7.77768 13.4713i −0.348177 0.603060i 0.637749 0.770244i \(-0.279866\pi\)
−0.985926 + 0.167185i \(0.946532\pi\)
\(500\) 0 0
\(501\) 2.30743 3.99658i 0.103088 0.178554i
\(502\) 9.77909 5.64596i 0.436462 0.251992i
\(503\) 4.39272i 0.195862i −0.995193 0.0979308i \(-0.968778\pi\)
0.995193 0.0979308i \(-0.0312224\pi\)
\(504\) 4.73838 + 1.28889i 0.211064 + 0.0574116i
\(505\) 0 0
\(506\) 9.90838 + 17.1618i 0.440481 + 0.762936i
\(507\) 11.2169 + 6.47608i 0.498160 + 0.287613i
\(508\) 26.6689 + 15.3973i 1.18324 + 0.683144i
\(509\) 1.04377 + 1.80786i 0.0462642 + 0.0801319i 0.888230 0.459399i \(-0.151935\pi\)
−0.841966 + 0.539531i \(0.818602\pi\)
\(510\) 0 0
\(511\) 5.18273 + 19.6393i 0.229271 + 0.868790i
\(512\) 22.5871i 0.998219i
\(513\) 2.39668 1.38372i 0.105816 0.0610929i
\(514\) −6.21129 + 10.7583i −0.273968 + 0.474527i
\(515\) 0 0
\(516\) −1.24421 2.15503i −0.0547732 0.0948699i
\(517\) 47.2466i 2.07791i
\(518\) 4.45401 1.17540i 0.195698 0.0516440i
\(519\) −12.6771 −0.556461
\(520\) 0 0
\(521\) 18.3501 31.7832i 0.803930 1.39245i −0.113081 0.993586i \(-0.536072\pi\)
0.917011 0.398862i \(-0.130595\pi\)
\(522\) 1.71187 + 0.988347i 0.0749264 + 0.0432588i
\(523\) −10.9371 + 6.31454i −0.478246 + 0.276116i −0.719685 0.694300i \(-0.755714\pi\)
0.241439 + 0.970416i \(0.422381\pi\)
\(524\) −15.8428 −0.692097
\(525\) 0 0
\(526\) 6.70010 0.292138
\(527\) 1.85529 1.07115i 0.0808179 0.0466602i
\(528\) −11.9947 6.92513i −0.522001 0.301377i
\(529\) 16.7120 28.9460i 0.726607 1.25852i
\(530\) 0 0
\(531\) 12.8501 0.557648
\(532\) −9.05600 9.12481i −0.392627 0.395611i
\(533\) 40.0504i 1.73478i
\(534\) −1.07487 1.86173i −0.0465143 0.0805651i
\(535\) 0 0
\(536\) −3.48540 + 6.03689i −0.150546 + 0.260754i
\(537\) −11.2986 + 6.52324i −0.487570 + 0.281499i
\(538\) 4.46103i 0.192329i
\(539\) −32.2208 18.9293i −1.38785 0.815343i
\(540\) 0 0
\(541\) −19.4206 33.6374i −0.834956 1.44619i −0.894066 0.447935i \(-0.852160\pi\)
0.0591098 0.998251i \(-0.481174\pi\)
\(542\) 2.04414 + 1.18018i 0.0878031 + 0.0506932i
\(543\) −13.0418 7.52968i −0.559677 0.323130i
\(544\) −0.874433 1.51456i −0.0374910 0.0649363i
\(545\) 0 0
\(546\) 4.72757 4.69191i 0.202321 0.200795i
\(547\) 18.6010i 0.795323i 0.917532 + 0.397662i \(0.130178\pi\)
−0.917532 + 0.397662i \(0.869822\pi\)
\(548\) −1.26894 + 0.732622i −0.0542064 + 0.0312961i
\(549\) −2.50000 + 4.33013i −0.106697 + 0.184805i
\(550\) 0 0
\(551\) −5.53489 9.58671i −0.235794 0.408408i
\(552\) 13.9416i 0.593394i
\(553\) −1.64015 + 6.02975i −0.0697464 + 0.256411i
\(554\) 0.924457 0.0392764
\(555\) 0 0
\(556\) −12.5673 + 21.7672i −0.532972 + 0.923134i
\(557\) 4.47344 + 2.58274i 0.189546 + 0.109434i 0.591770 0.806107i \(-0.298429\pi\)
−0.402224 + 0.915541i \(0.631763\pi\)
\(558\) 2.61814 1.51159i 0.110835 0.0639905i
\(559\) −7.21998 −0.305373
\(560\) 0 0
\(561\) −1.86948 −0.0789295
\(562\) −0.416304 + 0.240353i −0.0175607 + 0.0101387i
\(563\) 10.9450 + 6.31908i 0.461275 + 0.266317i 0.712580 0.701590i \(-0.247526\pi\)
−0.251305 + 0.967908i \(0.580860\pi\)
\(564\) −7.76949 + 13.4571i −0.327154 + 0.566648i
\(565\) 0 0
\(566\) 11.9490 0.502253
\(567\) −2.55817 + 0.675093i −0.107433 + 0.0283512i
\(568\) 28.7464i 1.20617i
\(569\) −4.39870 7.61878i −0.184403 0.319396i 0.758972 0.651123i \(-0.225702\pi\)
−0.943375 + 0.331727i \(0.892369\pi\)
\(570\) 0 0
\(571\) 19.9516 34.5572i 0.834950 1.44618i −0.0591220 0.998251i \(-0.518830\pi\)
0.894072 0.447924i \(-0.147837\pi\)
\(572\) −41.3535 + 23.8755i −1.72908 + 0.998283i
\(573\) 9.52718i 0.398004i
\(574\) 9.91856 + 2.69795i 0.413993 + 0.112610i
\(575\) 0 0
\(576\) 1.36042 + 2.35631i 0.0566840 + 0.0981796i
\(577\) −2.35289 1.35844i −0.0979523 0.0565528i 0.450224 0.892916i \(-0.351344\pi\)
−0.548176 + 0.836363i \(0.684678\pi\)
\(578\) 7.22295 + 4.17017i 0.300435 + 0.173456i
\(579\) 7.55299 + 13.0822i 0.313892 + 0.543676i
\(580\) 0 0
\(581\) −12.9076 + 12.8102i −0.535497 + 0.531458i
\(582\) 2.71792i 0.112661i
\(583\) 29.2511 16.8881i 1.21146 0.699435i
\(584\) 7.12437 12.3398i 0.294808 0.510623i
\(585\) 0 0
\(586\) 3.83846 + 6.64842i 0.158566 + 0.274644i
\(587\) 9.02317i 0.372426i 0.982509 + 0.186213i \(0.0596215\pi\)
−0.982509 + 0.186213i \(0.940379\pi\)
\(588\) 6.06452 + 10.6901i 0.250097 + 0.440854i
\(589\) −16.9302 −0.697597
\(590\) 0 0
\(591\) 8.44451 14.6263i 0.347361 0.601647i
\(592\) 7.91605 + 4.57033i 0.325348 + 0.187840i
\(593\) 9.06305 5.23255i 0.372175 0.214875i −0.302233 0.953234i \(-0.597732\pi\)
0.674408 + 0.738359i \(0.264399\pi\)
\(594\) −2.63816 −0.108245
\(595\) 0 0
\(596\) −34.0565 −1.39501
\(597\) 21.8477 12.6138i 0.894167 0.516248i
\(598\) −16.3768 9.45513i −0.669696 0.386649i
\(599\) 4.81915 8.34701i 0.196905 0.341050i −0.750618 0.660736i \(-0.770244\pi\)
0.947523 + 0.319686i \(0.103578\pi\)
\(600\) 0 0
\(601\) −7.19544 −0.293508 −0.146754 0.989173i \(-0.546883\pi\)
−0.146754 + 0.989173i \(0.546883\pi\)
\(602\) −0.486366 + 1.78804i −0.0198228 + 0.0728752i
\(603\) 3.75579i 0.152948i
\(604\) −16.2649 28.1717i −0.661811 1.14629i
\(605\) 0 0
\(606\) −0.407647 + 0.706065i −0.0165595 + 0.0286819i
\(607\) −34.0681 + 19.6692i −1.38278 + 0.798348i −0.992488 0.122343i \(-0.960959\pi\)
−0.390292 + 0.920691i \(0.627626\pi\)
\(608\) 13.8209i 0.560512i
\(609\) 2.70037 + 10.2327i 0.109425 + 0.414650i
\(610\) 0 0
\(611\) 22.5427 + 39.0451i 0.911980 + 1.57960i
\(612\) 0.532479 + 0.307427i 0.0215242 + 0.0124270i
\(613\) −16.9277 9.77320i −0.683703 0.394736i 0.117546 0.993067i \(-0.462497\pi\)
−0.801249 + 0.598331i \(0.795831\pi\)
\(614\) 0.838601 + 1.45250i 0.0338432 + 0.0586181i
\(615\) 0 0
\(616\) 6.68908 + 25.3474i 0.269511 + 1.02127i
\(617\) 35.9588i 1.44765i 0.689985 + 0.723824i \(0.257617\pi\)
−0.689985 + 0.723824i \(0.742383\pi\)
\(618\) 4.34874 2.51075i 0.174932 0.100997i
\(619\) 4.27972 7.41269i 0.172016 0.297941i −0.767108 0.641518i \(-0.778305\pi\)
0.939125 + 0.343577i \(0.111638\pi\)
\(620\) 0 0
\(621\) 3.75579 + 6.50522i 0.150715 + 0.261046i
\(622\) 1.21819i 0.0488450i
\(623\) 3.02094 11.1060i 0.121031 0.444952i
\(624\) 13.2167 0.529091
\(625\) 0 0
\(626\) −0.117496 + 0.203509i −0.00469609 + 0.00813387i
\(627\) 12.7947 + 7.38705i 0.510973 + 0.295010i
\(628\) −7.29802 + 4.21352i −0.291223 + 0.168138i
\(629\) 1.23379 0.0491944
\(630\) 0 0
\(631\) −17.5192 −0.697427 −0.348713 0.937229i \(-0.613381\pi\)
−0.348713 + 0.937229i \(0.613381\pi\)
\(632\) 3.79631 2.19180i 0.151009 0.0871852i
\(633\) −17.6640 10.1983i −0.702082 0.405347i
\(634\) −3.53321 + 6.11971i −0.140322 + 0.243045i
\(635\) 0 0
\(636\) −11.1087 −0.440488
\(637\) 35.6593 + 0.269945i 1.41287 + 0.0106956i
\(638\) 10.5526i 0.417783i
\(639\) 7.74414 + 13.4132i 0.306353 + 0.530620i
\(640\) 0 0
\(641\) −8.14094 + 14.1005i −0.321548 + 0.556937i −0.980808 0.194978i \(-0.937536\pi\)
0.659260 + 0.751915i \(0.270870\pi\)
\(642\) −2.29469 + 1.32484i −0.0905641 + 0.0522872i
\(643\) 15.7544i 0.621294i 0.950525 + 0.310647i \(0.100546\pi\)
−0.950525 + 0.310647i \(0.899454\pi\)
\(644\) 24.7672 24.5804i 0.975963 0.968603i
\(645\) 0 0
\(646\) 0.239457 + 0.414751i 0.00942131 + 0.0163182i
\(647\) −39.3517 22.7197i −1.54707 0.893203i −0.998363 0.0571903i \(-0.981786\pi\)
−0.548710 0.836013i \(-0.684881\pi\)
\(648\) 1.60735 + 0.928006i 0.0631428 + 0.0364555i
\(649\) 34.3004 + 59.4100i 1.34641 + 2.33205i
\(650\) 0 0
\(651\) 15.6182 + 4.24832i 0.612127 + 0.166505i
\(652\) 1.45195i 0.0568627i
\(653\) −16.5943 + 9.58070i −0.649384 + 0.374922i −0.788220 0.615394i \(-0.788997\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(654\) −0.0261859 + 0.0453554i −0.00102395 + 0.00177354i
\(655\) 0 0
\(656\) 10.1983 + 17.6639i 0.398175 + 0.689660i
\(657\) 7.67707i 0.299511i
\(658\) 11.1882 2.95251i 0.436160 0.115101i
\(659\) 8.76258 0.341342 0.170671 0.985328i \(-0.445407\pi\)
0.170671 + 0.985328i \(0.445407\pi\)
\(660\) 0 0
\(661\) 4.53801 7.86006i 0.176508 0.305721i −0.764174 0.645010i \(-0.776853\pi\)
0.940682 + 0.339289i \(0.110186\pi\)
\(662\) −8.38192 4.83930i −0.325773 0.188085i
\(663\) 1.54496 0.891981i 0.0600011 0.0346417i
\(664\) 12.7572 0.495074
\(665\) 0 0
\(666\) 1.74109 0.0674659
\(667\) 26.0209 15.0232i 1.00753 0.581699i
\(668\) −7.01717 4.05136i −0.271502 0.156752i
\(669\) 11.2869 19.5495i 0.436377 0.755827i
\(670\) 0 0
\(671\) −26.6927 −1.03046
\(672\) 3.46810 12.7499i 0.133785 0.491838i
\(673\) 18.3460i 0.707185i 0.935400 + 0.353593i \(0.115040\pi\)
−0.935400 + 0.353593i \(0.884960\pi\)
\(674\) −1.08281 1.87548i −0.0417082 0.0722407i
\(675\) 0 0
\(676\) 11.3706 19.6945i 0.437333 0.757482i
\(677\) −1.55532 + 0.897966i −0.0597759 + 0.0345116i −0.529590 0.848254i \(-0.677654\pi\)
0.469814 + 0.882765i \(0.344321\pi\)
\(678\) 2.31128i 0.0887642i
\(679\) −10.3283 + 10.2504i −0.396364 + 0.393375i
\(680\) 0 0
\(681\) −7.08267 12.2675i −0.271409 0.470093i
\(682\) 13.9770 + 8.06965i 0.535209 + 0.309003i
\(683\) −38.4454 22.1965i −1.47107 0.849324i −0.471599 0.881813i \(-0.656323\pi\)
−0.999472 + 0.0324893i \(0.989657\pi\)
\(684\) −2.42953 4.20807i −0.0928954 0.160900i
\(685\) 0 0
\(686\) 2.46900 8.81290i 0.0942667 0.336478i
\(687\) 17.8062i 0.679349i
\(688\) −3.18431 + 1.83846i −0.121401 + 0.0700908i
\(689\) −16.1156 + 27.9130i −0.613955 + 1.06340i
\(690\) 0 0
\(691\) −21.5962 37.4058i −0.821559 1.42298i −0.904521 0.426430i \(-0.859771\pi\)
0.0829614 0.996553i \(-0.473562\pi\)
\(692\) 22.2583i 0.846134i
\(693\) −9.94961 10.0252i −0.377954 0.380826i
\(694\) −4.74263 −0.180028
\(695\) 0 0
\(696\) 3.71203 6.42942i 0.140704 0.243706i
\(697\) 2.38424 + 1.37654i 0.0903095 + 0.0521402i
\(698\) −8.51683 + 4.91719i −0.322367 + 0.186118i
\(699\) 13.6498 0.516283
\(700\) 0 0
\(701\) −9.69616 −0.366219 −0.183109 0.983093i \(-0.558616\pi\)
−0.183109 + 0.983093i \(0.558616\pi\)
\(702\) 2.18020 1.25874i 0.0822864 0.0475081i
\(703\) −8.44407 4.87519i −0.318474 0.183871i
\(704\) −7.26263 + 12.5792i −0.273721 + 0.474098i
\(705\) 0 0
\(706\) −13.5387 −0.509536
\(707\) −4.22051 + 1.11378i −0.158729 + 0.0418879i
\(708\) 22.5621i 0.847937i
\(709\) 9.07685 + 15.7216i 0.340888 + 0.590435i 0.984598 0.174834i \(-0.0559389\pi\)
−0.643710 + 0.765270i \(0.722606\pi\)
\(710\) 0 0
\(711\) −1.18092 + 2.04541i −0.0442879 + 0.0767090i
\(712\) −6.99229 + 4.03700i −0.262047 + 0.151293i
\(713\) 45.9531i 1.72096i
\(714\) −0.116827 0.442699i −0.00437213 0.0165676i
\(715\) 0 0
\(716\) 11.4535 + 19.8380i 0.428036 + 0.741380i
\(717\) −6.52541 3.76745i −0.243696 0.140698i
\(718\) −10.9348 6.31319i −0.408082 0.235606i
\(719\) −17.5904 30.4675i −0.656011 1.13624i −0.981639 0.190747i \(-0.938909\pi\)
0.325628 0.945498i \(-0.394424\pi\)
\(720\) 0 0
\(721\) 25.9419 + 7.05647i 0.966128 + 0.262797i
\(722\) 5.60454i 0.208579i
\(723\) 24.7017 14.2616i 0.918667 0.530393i
\(724\) −13.2206 + 22.8987i −0.491338 + 0.851023i
\(725\) 0 0
\(726\) −4.32400 7.48939i −0.160479 0.277957i
\(727\) 4.79075i 0.177679i −0.996046 0.0888396i \(-0.971684\pi\)
0.996046 0.0888396i \(-0.0283158\pi\)
\(728\) −17.6219 17.7558i −0.653109 0.658072i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −0.248152 + 0.429812i −0.00917825 + 0.0158972i
\(732\) 7.60281 + 4.38948i 0.281008 + 0.162240i
\(733\) 10.4999 6.06214i 0.387824 0.223910i −0.293393 0.955992i \(-0.594784\pi\)
0.681217 + 0.732082i \(0.261451\pi\)
\(734\) −11.0060 −0.406237
\(735\) 0 0
\(736\) −37.5136 −1.38277
\(737\) 17.3642 10.0252i 0.639618 0.369283i
\(738\) 3.36458 + 1.94254i 0.123852 + 0.0715058i
\(739\) −16.4581 + 28.5063i −0.605422 + 1.04862i 0.386562 + 0.922263i \(0.373662\pi\)
−0.991985 + 0.126359i \(0.959671\pi\)
\(740\) 0 0
\(741\) −14.0983 −0.517913
\(742\) 5.82711 + 5.87138i 0.213920 + 0.215545i
\(743\) 38.8112i 1.42385i 0.702258 + 0.711923i \(0.252175\pi\)
−0.702258 + 0.711923i \(0.747825\pi\)
\(744\) −5.67720 9.83320i −0.208136 0.360503i
\(745\) 0 0
\(746\) −1.30827 + 2.26598i −0.0478990 + 0.0829635i
\(747\) −5.95256 + 3.43671i −0.217793 + 0.125743i
\(748\) 3.28242i 0.120017i
\(749\) −13.6887 3.72347i −0.500175 0.136053i
\(750\) 0 0
\(751\) 15.0341 + 26.0398i 0.548602 + 0.950206i 0.998371 + 0.0570610i \(0.0181729\pi\)
−0.449769 + 0.893145i \(0.648494\pi\)
\(752\) 19.8845 + 11.4803i 0.725115 + 0.418645i
\(753\) 19.7888 + 11.4251i 0.721143 + 0.416352i
\(754\) −5.03496 8.72081i −0.183362 0.317593i
\(755\) 0 0
\(756\) 1.18532 + 4.49162i 0.0431098 + 0.163359i
\(757\) 7.17713i 0.260857i 0.991458 + 0.130429i \(0.0416354\pi\)
−0.991458 + 0.130429i \(0.958365\pi\)
\(758\) 1.32757 0.766471i 0.0482194 0.0278395i
\(759\) −20.0504 + 34.7284i −0.727784 + 1.26056i
\(760\) 0 0
\(761\) 3.80431 + 6.58926i 0.137906 + 0.238860i 0.926704 0.375792i \(-0.122629\pi\)
−0.788798 + 0.614653i \(0.789296\pi\)
\(762\) 8.66723i 0.313980i
\(763\) −0.271112 + 0.0715455i −0.00981491 + 0.00259012i
\(764\) 16.7278 0.605189
\(765\) 0 0
\(766\) 5.34021 9.24952i 0.192950 0.334199i
\(767\) −56.6923 32.7313i −2.04704 1.18186i
\(768\) −0.137429 + 0.0793447i −0.00495904 + 0.00286310i
\(769\) −50.2712 −1.81283 −0.906413 0.422393i \(-0.861190\pi\)
−0.906413 + 0.422393i \(0.861190\pi\)
\(770\) 0 0
\(771\) −25.1381 −0.905326
\(772\) 22.9696 13.2615i 0.826693 0.477291i
\(773\) −23.4701 13.5505i −0.844162 0.487377i 0.0145147 0.999895i \(-0.495380\pi\)
−0.858677 + 0.512517i \(0.828713\pi\)
\(774\) −0.350186 + 0.606540i −0.0125872 + 0.0218016i
\(775\) 0 0
\(776\) 10.2079 0.366444
\(777\) 6.56638 + 6.61628i 0.235568 + 0.237358i
\(778\) 6.35588i 0.227869i
\(779\) −10.8785 18.8421i −0.389763 0.675090i
\(780\) 0 0
\(781\) −41.3423 + 71.6070i −1.47935 + 2.56230i
\(782\) −1.12575 + 0.649950i −0.0402566 + 0.0232422i
\(783\) 4.00000i 0.142948i
\(784\) 15.7960 8.96106i 0.564141 0.320038i
\(785\) 0 0
\(786\) 2.22951 + 3.86162i 0.0795238 + 0.137739i
\(787\) 29.7480 + 17.1750i 1.06040 + 0.612224i 0.925543 0.378641i \(-0.123609\pi\)
0.134859 + 0.990865i \(0.456942\pi\)
\(788\) −25.6808 14.8268i −0.914840 0.528183i
\(789\) 6.77910 + 11.7417i 0.241342 + 0.418017i
\(790\) 0 0
\(791\) −8.78304 + 8.71681i −0.312289 + 0.309934i
\(792\) 9.90838i 0.352079i
\(793\) 22.0591 12.7358i 0.783341 0.452262i
\(794\) −1.72841 + 2.99369i −0.0613388 + 0.106242i
\(795\) 0 0
\(796\) −22.1472 38.3600i −0.784986 1.35964i
\(797\) 16.5581i 0.586517i 0.956033 + 0.293258i \(0.0947396\pi\)
−0.956033 + 0.293258i \(0.905260\pi\)
\(798\) −0.949713 + 3.49146i −0.0336195 + 0.123596i
\(799\) 3.09919 0.109641
\(800\) 0 0
\(801\) 2.17509 3.76737i 0.0768531 0.133114i
\(802\) −1.35297 0.781140i −0.0477752 0.0275830i
\(803\) −35.4934 + 20.4921i −1.25254 + 0.723152i
\(804\) −6.59439 −0.232566
\(805\) 0 0
\(806\) −15.4010 −0.542478
\(807\) 7.81783 4.51363i 0.275201 0.158887i
\(808\) 2.65184 + 1.53104i 0.0932912 + 0.0538617i
\(809\) −4.27903 + 7.41150i −0.150443 + 0.260574i −0.931390 0.364022i \(-0.881403\pi\)
0.780948 + 0.624597i \(0.214737\pi\)
\(810\) 0 0
\(811\) 21.4277 0.752429 0.376215 0.926533i \(-0.377226\pi\)
0.376215 + 0.926533i \(0.377226\pi\)
\(812\) 17.9665 4.74129i 0.630500 0.166387i
\(813\) 4.77639i 0.167515i
\(814\) 4.64743 + 8.04959i 0.162893 + 0.282138i
\(815\) 0 0
\(816\) 0.454260 0.786802i 0.0159023 0.0275436i
\(817\) 3.39672 1.96110i 0.118836 0.0686100i
\(818\) 1.23300i 0.0431107i
\(819\) 13.0058 + 3.53770i 0.454458 + 0.123617i
\(820\) 0 0
\(821\) 7.56010 + 13.0945i 0.263849 + 0.457001i 0.967262 0.253782i \(-0.0816745\pi\)
−0.703412 + 0.710782i \(0.748341\pi\)
\(822\) 0.357147 + 0.206199i 0.0124569 + 0.00719201i
\(823\) −21.3946 12.3522i −0.745768 0.430569i 0.0783949 0.996922i \(-0.475020\pi\)
−0.824163 + 0.566353i \(0.808354\pi\)
\(824\) −9.42984 16.3330i −0.328504 0.568986i
\(825\) 0 0
\(826\) −11.9250 + 11.8351i −0.414924 + 0.411794i
\(827\) 28.8578i 1.00348i 0.865017 + 0.501742i \(0.167307\pi\)
−0.865017 + 0.501742i \(0.832693\pi\)
\(828\) 11.4218 6.59439i 0.396936 0.229171i
\(829\) −0.434740 + 0.752992i −0.0150991 + 0.0261525i −0.873476 0.486867i \(-0.838140\pi\)
0.858377 + 0.513019i \(0.171473\pi\)
\(830\) 0 0
\(831\) 0.935357 + 1.62009i 0.0324472 + 0.0562002i
\(832\) 13.8608i 0.480537i
\(833\) 1.24169 2.11355i 0.0430219 0.0732302i
\(834\) 7.07420 0.244960
\(835\) 0 0
\(836\) 12.9701 22.4649i 0.448581 0.776966i
\(837\) 5.29802 + 3.05882i 0.183127 + 0.105728i
\(838\) −13.9837 + 8.07350i −0.483059 + 0.278895i
\(839\) −21.7235 −0.749980 −0.374990 0.927029i \(-0.622354\pi\)
−0.374990 + 0.927029i \(0.622354\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 11.5026 6.64104i 0.396406 0.228865i
\(843\) −0.842425 0.486374i −0.0290147 0.0167516i
\(844\) −17.9062 + 31.0144i −0.616355 + 1.06756i
\(845\) 0 0
\(846\) 4.37349 0.150364
\(847\) 12.1526 44.6771i 0.417569 1.53512i
\(848\) 16.4144i 0.563673i
\(849\) 12.0899 + 20.9402i 0.414923 + 0.718667i
\(850\) 0 0
\(851\) 13.2326 22.9195i 0.453606 0.785669i
\(852\) 23.5509 13.5971i 0.806840 0.465829i
\(853\) 0.670546i 0.0229591i −0.999934 0.0114795i \(-0.996346\pi\)
0.999934 0.0114795i \(-0.00365413\pi\)
\(854\) −1.66806 6.32090i −0.0570800 0.216297i
\(855\) 0 0
\(856\) 4.97582 + 8.61837i 0.170070 + 0.294570i
\(857\) −21.2076 12.2442i −0.724437 0.418254i 0.0919463 0.995764i \(-0.470691\pi\)
−0.816384 + 0.577510i \(0.804025\pi\)
\(858\) 11.6391 + 6.71982i 0.397352 + 0.229411i
\(859\) 4.79970 + 8.31332i 0.163764 + 0.283647i 0.936215 0.351426i \(-0.114303\pi\)
−0.772452 + 0.635073i \(0.780970\pi\)
\(860\) 0 0
\(861\) 5.30743 + 20.1118i 0.180877 + 0.685407i
\(862\) 7.01165i 0.238818i
\(863\) 25.5511 14.7519i 0.869770 0.502162i 0.00249807 0.999997i \(-0.499205\pi\)
0.867272 + 0.497835i \(0.165872\pi\)
\(864\) 2.49705 4.32502i 0.0849515 0.147140i
\(865\) 0 0
\(866\) 7.40561 + 12.8269i 0.251653 + 0.435875i
\(867\) 16.8774i 0.573186i
\(868\) 7.45917 27.4224i 0.253181 0.930777i
\(869\) −12.6088 −0.427723
\(870\) 0 0
\(871\) −9.56662 + 16.5699i −0.324152 + 0.561448i
\(872\) 0.170345 + 0.0983489i 0.00576862 + 0.00333052i
\(873\) −4.76308 + 2.74997i −0.161206 + 0.0930722i
\(874\) 10.2728 0.347484
\(875\) 0 0
\(876\) 13.4793 0.455425
\(877\) −4.59656 + 2.65383i −0.155215 + 0.0896134i −0.575596 0.817734i \(-0.695230\pi\)
0.420381 + 0.907348i \(0.361896\pi\)
\(878\) 0.887545 + 0.512424i 0.0299532 + 0.0172935i
\(879\) −7.76745 + 13.4536i −0.261989 + 0.453779i
\(880\) 0 0
\(881\) 49.2817 1.66034 0.830172 0.557507i \(-0.188242\pi\)
0.830172 + 0.557507i \(0.188242\pi\)
\(882\) 1.75223 2.98259i 0.0590008 0.100429i
\(883\) 6.02862i 0.202879i 0.994842 + 0.101440i \(0.0323449\pi\)
−0.994842 + 0.101440i \(0.967655\pi\)
\(884\) −1.56613 2.71262i −0.0526748 0.0912354i
\(885\) 0 0
\(886\) 7.92593 13.7281i 0.266277 0.461205i
\(887\) 6.91509 3.99243i 0.232186 0.134053i −0.379394 0.925235i \(-0.623868\pi\)
0.611580 + 0.791183i \(0.290534\pi\)
\(888\) 6.53918i 0.219440i
\(889\) 32.9361 32.6877i 1.10464 1.09631i
\(890\) 0 0
\(891\) −2.66927 4.62330i −0.0894238 0.154887i
\(892\) −34.3248 19.8175i −1.14928 0.663537i
\(893\) −21.2109 12.2461i −0.709795 0.409801i
\(894\) 4.79266 + 8.30113i 0.160290 + 0.277631i
\(895\) 0 0
\(896\) −28.9325 7.86992i −0.966565 0.262916i
\(897\) 38.2665i 1.27768i
\(898\) −1.90917 + 1.10226i −0.0637099 + 0.0367829i
\(899\) 12.2353 21.1921i 0.408069 0.706796i
\(900\) 0 0
\(901\) 1.10779 + 1.91875i 0.0369059 + 0.0639229i
\(902\) 20.7406i 0.690587i
\(903\) −3.62560 + 0.956782i −0.120652 + 0.0318397i
\(904\) 8.68069 0.288716
\(905\) 0 0
\(906\) −4.57782 + 7.92902i −0.152088 + 0.263424i
\(907\) −2.19198 1.26554i −0.0727836 0.0420216i 0.463167 0.886271i \(-0.346713\pi\)
−0.535950 + 0.844250i \(0.680047\pi\)
\(908\) −21.5393 + 12.4357i −0.714806 + 0.412693i
\(909\) −1.64981 −0.0547209
\(910\) 0 0
\(911\) 1.41047 0.0467309 0.0233655 0.999727i \(-0.492562\pi\)
0.0233655 + 0.999727i \(0.492562\pi\)
\(912\) −6.21793 + 3.58992i −0.205896 + 0.118874i
\(913\) −31.7779 18.3470i −1.05170 0.607197i
\(914\) 0.560942 0.971580i 0.0185543 0.0321370i
\(915\) 0 0
\(916\) 31.2640 1.03299
\(917\) −6.26604 + 23.0361i −0.206923 + 0.760718i
\(918\) 0.173053i 0.00571159i
\(919\) 23.3418 + 40.4292i 0.769975 + 1.33364i 0.937576 + 0.347780i \(0.113065\pi\)
−0.167601 + 0.985855i \(0.553602\pi\)
\(920\) 0 0
\(921\) −1.69698 + 2.93925i −0.0559173 + 0.0968516i
\(922\) −1.85351 + 1.07012i −0.0610420 + 0.0352426i
\(923\) 78.9023i 2.59710i
\(924\) −17.6022 + 17.4694i −0.579070 + 0.574703i
\(925\) 0 0
\(926\) −10.3247 17.8829i −0.339290 0.587667i
\(927\) 8.80003 + 5.08070i 0.289031 + 0.166872i
\(928\) −17.3001 9.98821i −0.567903 0.327879i
\(929\) −8.91923 15.4486i −0.292631 0.506851i 0.681800 0.731538i \(-0.261197\pi\)
−0.974431 + 0.224687i \(0.927864\pi\)
\(930\) 0 0
\(931\) −16.8496 + 9.55878i −0.552223 + 0.313277i
\(932\) 23.9662i 0.785040i
\(933\) −2.13485 + 1.23255i −0.0698917 + 0.0403520i
\(934\) −9.48252 + 16.4242i −0.310278 + 0.537416i
\(935\) 0 0
\(936\) −4.72757 8.18839i −0.154525 0.267646i
\(937\) 0.343849i 0.0112330i −0.999984 0.00561652i \(-0.998212\pi\)
0.999984 0.00561652i \(-0.00178780\pi\)
\(938\) 3.45911 + 3.48540i 0.112944 + 0.113802i
\(939\) −0.475526 −0.0155182
\(940\) 0 0
\(941\) 23.0737 39.9649i 0.752182 1.30282i −0.194581 0.980886i \(-0.562335\pi\)
0.946763 0.321931i \(-0.104332\pi\)
\(942\) 2.05405 + 1.18591i 0.0669246 + 0.0386389i
\(943\) 51.1426 29.5272i 1.66543 0.961537i
\(944\) −33.3383 −1.08507
\(945\) 0 0
\(946\) −3.73896 −0.121564
\(947\) −23.9558 + 13.8309i −0.778459 + 0.449444i −0.835884 0.548906i \(-0.815044\pi\)
0.0574248 + 0.998350i \(0.481711\pi\)
\(948\) 3.59132 + 2.07345i 0.116641 + 0.0673425i
\(949\) 19.5547 33.8698i 0.634774 1.09946i
\(950\) 0 0
\(951\) −14.2995 −0.463693
\(952\) −1.66268 + 0.438777i −0.0538879 + 0.0142208i
\(953\) 4.24907i 0.137641i −0.997629 0.0688204i \(-0.978076\pi\)
0.997629 0.0688204i \(-0.0219236\pi\)
\(954\) 1.56329 + 2.70769i 0.0506133 + 0.0876648i
\(955\) 0 0
\(956\) −6.61485 + 11.4573i −0.213940 + 0.370554i
\(957\) −18.4932 + 10.6771i −0.597801 + 0.345141i
\(958\) 18.7977i 0.607325i
\(959\) 0.563379 + 2.13485i 0.0181924 + 0.0689378i
\(960\) 0 0
\(961\) −3.21271 5.56458i −0.103636 0.179503i
\(962\) −7.68137 4.43484i −0.247657 0.142985i
\(963\) −4.64349 2.68092i −0.149634 0.0863914i
\(964\) −25.0403 43.3711i −0.806495 1.39689i
\(965\) 0 0
\(966\) −9.47676 2.57777i −0.304910 0.0829385i
\(967\) 59.6146i 1.91708i 0.284965 + 0.958538i \(0.408018\pi\)
−0.284965 + 0.958538i \(0.591982\pi\)
\(968\) −28.1286 + 16.2400i −0.904087 + 0.521975i
\(969\) −0.484560 + 0.839283i −0.0155663 + 0.0269617i
\(970\) 0 0
\(971\) 0.475617 + 0.823793i 0.0152633 + 0.0264368i 0.873556 0.486723i \(-0.161808\pi\)
−0.858293 + 0.513160i \(0.828475\pi\)
\(972\) 1.75579i 0.0563171i
\(973\) 26.6798 + 26.8825i 0.855314 + 0.861814i
\(974\) 11.1598 0.357583
\(975\) 0 0
\(976\) 6.48598 11.2341i 0.207611 0.359593i
\(977\) 19.9624 + 11.5253i 0.638653 + 0.368726i 0.784095 0.620640i \(-0.213127\pi\)
−0.145443 + 0.989367i \(0.546461\pi\)
\(978\) −0.353906 + 0.204328i −0.0113167 + 0.00653368i
\(979\) 23.2236 0.742230
\(980\) 0 0
\(981\) −0.105979 −0.00338364
\(982\) 0.0574108 0.0331461i 0.00183205 0.00105774i
\(983\) 27.5698 + 15.9174i 0.879339 + 0.507687i 0.870441 0.492274i \(-0.163834\pi\)
0.00889883 + 0.999960i \(0.497167\pi\)
\(984\) 7.29577 12.6367i 0.232581 0.402842i
\(985\) 0 0
\(986\) −0.692210 −0.0220445
\(987\) 16.4943 + 16.6196i 0.525018 + 0.529008i
\(988\) 24.7536i 0.787518i
\(989\) 5.32293 + 9.21959i 0.169259 + 0.293166i
\(990\) 0 0
\(991\) 4.05306 7.02010i 0.128750 0.223001i −0.794443 0.607339i \(-0.792237\pi\)
0.923192 + 0.384338i \(0.125570\pi\)
\(992\) −26.4589 + 15.2760i −0.840071 + 0.485015i
\(993\) 19.5855i 0.621525i
\(994\) −19.5403 5.31516i −0.619781 0.168587i
\(995\) 0 0
\(996\) 6.03415 + 10.4515i 0.191199 + 0.331167i
\(997\) −24.4625 14.1235i −0.774737 0.447294i 0.0598251 0.998209i \(-0.480946\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(998\) 6.65717 + 3.84352i 0.210729 + 0.121665i
\(999\) 1.76162 + 3.05121i 0.0557352 + 0.0965361i
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 525.2.r.h.424.4 16
5.2 odd 4 525.2.i.j.151.2 yes 8
5.3 odd 4 525.2.i.i.151.3 8
5.4 even 2 inner 525.2.r.h.424.5 16
7.2 even 3 inner 525.2.r.h.499.5 16
35.2 odd 12 525.2.i.j.226.2 yes 8
35.3 even 12 3675.2.a.bx.1.2 4
35.9 even 6 inner 525.2.r.h.499.4 16
35.17 even 12 3675.2.a.bq.1.3 4
35.18 odd 12 3675.2.a.bw.1.2 4
35.23 odd 12 525.2.i.i.226.3 yes 8
35.32 odd 12 3675.2.a.br.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.i.i.151.3 8 5.3 odd 4
525.2.i.i.226.3 yes 8 35.23 odd 12
525.2.i.j.151.2 yes 8 5.2 odd 4
525.2.i.j.226.2 yes 8 35.2 odd 12
525.2.r.h.424.4 16 1.1 even 1 trivial
525.2.r.h.424.5 16 5.4 even 2 inner
525.2.r.h.499.4 16 35.9 even 6 inner
525.2.r.h.499.5 16 7.2 even 3 inner
3675.2.a.bq.1.3 4 35.17 even 12
3675.2.a.br.1.3 4 35.32 odd 12
3675.2.a.bw.1.2 4 35.18 odd 12
3675.2.a.bx.1.2 4 35.3 even 12