Properties

Label 1050.3.p.i.451.1
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,3,Mod(451,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.451");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.6104277578\)
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: \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + \cdots + 101626561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{4}\cdot 7 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.1
Root \(2.81422 - 4.87437i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.i.901.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.99242 + 0.325616i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.99242 + 0.325616i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.09582 + 10.5583i) q^{11} +(-3.00000 + 1.73205i) q^{12} -25.3938i q^{13} +(5.34319 + 8.33369i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(24.9196 + 14.3873i) q^{17} +(2.12132 - 3.67423i) q^{18} +(-13.9147 + 8.03365i) q^{19} +(-10.7706 - 5.56719i) q^{21} +17.2416 q^{22} +(-11.8709 - 20.5610i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-31.1010 + 17.9562i) q^{26} +5.19615i q^{27} +(6.42844 - 12.4368i) q^{28} +27.9121 q^{29} +(20.0480 + 11.5747i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-18.2875 + 10.5583i) q^{33} -40.6936i q^{34} -6.00000 q^{36} +(-14.5321 - 25.1703i) q^{37} +(19.6783 + 11.3613i) q^{38} +(21.9917 - 38.0908i) q^{39} -56.9065i q^{41} +(0.797593 + 17.1279i) q^{42} -7.83839 q^{43} +(-12.1916 - 21.1165i) q^{44} +(-16.7880 + 29.0777i) q^{46} +(19.7390 - 11.3963i) q^{47} -6.92820i q^{48} +(48.7879 - 4.55369i) q^{49} +(24.9196 + 43.1620i) q^{51} +(43.9834 + 25.3938i) q^{52} +(24.2781 - 42.0510i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-19.7776 + 0.920981i) q^{56} -27.8294 q^{57} +(-19.7368 - 34.1852i) q^{58} +(-62.3779 - 36.0139i) q^{59} +(99.2512 - 57.3027i) q^{61} -32.7382i q^{62} +(-11.3346 - 17.6784i) q^{63} +8.00000 q^{64} +(25.8624 + 14.9316i) q^{66} +(-35.2674 + 61.0850i) q^{67} +(-49.8392 + 28.7747i) q^{68} -41.1221i q^{69} +6.41501 q^{71} +(4.24264 + 7.34847i) q^{72} +(34.2569 + 19.7782i) q^{73} +(-20.5514 + 35.5961i) q^{74} -32.1346i q^{76} +(39.1866 - 75.8127i) q^{77} -62.2019 q^{78} +(27.3985 + 47.4555i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-69.6960 + 40.2390i) q^{82} -135.934i q^{83} +(20.4133 - 13.0881i) q^{84} +(5.54258 + 9.60002i) q^{86} +(41.8682 + 24.1726i) q^{87} +(-17.2416 + 29.8633i) q^{88} +(124.905 - 72.1140i) q^{89} +(8.26863 + 177.564i) q^{91} +47.4837 q^{92} +(20.0480 + 34.7241i) q^{93} +(-27.9152 - 16.1168i) q^{94} +(-8.48528 + 4.89898i) q^{96} +78.9980i q^{97} +(-40.0754 - 56.5328i) q^{98} -36.5749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −6.99242 + 0.325616i −0.998918 + 0.0465165i
\(8\) 2.82843 0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −6.09582 + 10.5583i −0.554165 + 0.959842i 0.443803 + 0.896125i \(0.353629\pi\)
−0.997968 + 0.0637178i \(0.979704\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 25.3938i 1.95337i −0.214672 0.976686i \(-0.568868\pi\)
0.214672 0.976686i \(-0.431132\pi\)
\(14\) 5.34319 + 8.33369i 0.381656 + 0.595263i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 24.9196 + 14.3873i 1.46586 + 0.846315i 0.999272 0.0381599i \(-0.0121496\pi\)
0.466588 + 0.884475i \(0.345483\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) −13.9147 + 8.03365i −0.732352 + 0.422824i −0.819282 0.573391i \(-0.805628\pi\)
0.0869298 + 0.996214i \(0.472294\pi\)
\(20\) 0 0
\(21\) −10.7706 5.56719i −0.512887 0.265104i
\(22\) 17.2416 0.783708
\(23\) −11.8709 20.5610i −0.516127 0.893958i −0.999825 0.0187231i \(-0.994040\pi\)
0.483698 0.875235i \(-0.339293\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −31.1010 + 17.9562i −1.19619 + 0.690621i
\(27\) 5.19615i 0.192450i
\(28\) 6.42844 12.4368i 0.229587 0.444173i
\(29\) 27.9121 0.962486 0.481243 0.876587i \(-0.340185\pi\)
0.481243 + 0.876587i \(0.340185\pi\)
\(30\) 0 0
\(31\) 20.0480 + 11.5747i 0.646709 + 0.373378i 0.787194 0.616705i \(-0.211533\pi\)
−0.140485 + 0.990083i \(0.544866\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) −18.2875 + 10.5583i −0.554165 + 0.319947i
\(34\) 40.6936i 1.19687i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −14.5321 25.1703i −0.392758 0.680277i 0.600054 0.799960i \(-0.295146\pi\)
−0.992812 + 0.119682i \(0.961812\pi\)
\(38\) 19.6783 + 11.3613i 0.517851 + 0.298982i
\(39\) 21.9917 38.0908i 0.563890 0.976686i
\(40\) 0 0
\(41\) 56.9065i 1.38796i −0.719992 0.693982i \(-0.755855\pi\)
0.719992 0.693982i \(-0.244145\pi\)
\(42\) 0.797593 + 17.1279i 0.0189903 + 0.407806i
\(43\) −7.83839 −0.182288 −0.0911440 0.995838i \(-0.529052\pi\)
−0.0911440 + 0.995838i \(0.529052\pi\)
\(44\) −12.1916 21.1165i −0.277083 0.479921i
\(45\) 0 0
\(46\) −16.7880 + 29.0777i −0.364957 + 0.632124i
\(47\) 19.7390 11.3963i 0.419979 0.242475i −0.275089 0.961419i \(-0.588707\pi\)
0.695068 + 0.718944i \(0.255374\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 48.7879 4.55369i 0.995672 0.0929324i
\(50\) 0 0
\(51\) 24.9196 + 43.1620i 0.488620 + 0.846315i
\(52\) 43.9834 + 25.3938i 0.845835 + 0.488343i
\(53\) 24.2781 42.0510i 0.458078 0.793414i −0.540781 0.841163i \(-0.681871\pi\)
0.998859 + 0.0477489i \(0.0152047\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −19.7776 + 0.920981i −0.353171 + 0.0164461i
\(57\) −27.8294 −0.488235
\(58\) −19.7368 34.1852i −0.340290 0.589400i
\(59\) −62.3779 36.0139i −1.05725 0.610405i −0.132581 0.991172i \(-0.542327\pi\)
−0.924671 + 0.380767i \(0.875660\pi\)
\(60\) 0 0
\(61\) 99.2512 57.3027i 1.62707 0.939388i 0.642107 0.766615i \(-0.278060\pi\)
0.984962 0.172773i \(-0.0552729\pi\)
\(62\) 32.7382i 0.528036i
\(63\) −11.3346 17.6784i −0.179914 0.280610i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 25.8624 + 14.9316i 0.391854 + 0.226237i
\(67\) −35.2674 + 61.0850i −0.526380 + 0.911716i 0.473148 + 0.880983i \(0.343118\pi\)
−0.999528 + 0.0307332i \(0.990216\pi\)
\(68\) −49.8392 + 28.7747i −0.732930 + 0.423157i
\(69\) 41.1221i 0.595972i
\(70\) 0 0
\(71\) 6.41501 0.0903522 0.0451761 0.998979i \(-0.485615\pi\)
0.0451761 + 0.998979i \(0.485615\pi\)
\(72\) 4.24264 + 7.34847i 0.0589256 + 0.102062i
\(73\) 34.2569 + 19.7782i 0.469272 + 0.270934i 0.715935 0.698167i \(-0.246001\pi\)
−0.246663 + 0.969101i \(0.579334\pi\)
\(74\) −20.5514 + 35.5961i −0.277722 + 0.481029i
\(75\) 0 0
\(76\) 32.1346i 0.422824i
\(77\) 39.1866 75.8127i 0.508917 0.984581i
\(78\) −62.2019 −0.797461
\(79\) 27.3985 + 47.4555i 0.346816 + 0.600703i 0.985682 0.168615i \(-0.0539295\pi\)
−0.638866 + 0.769318i \(0.720596\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −69.6960 + 40.2390i −0.849951 + 0.490719i
\(83\) 135.934i 1.63775i −0.573969 0.818877i \(-0.694597\pi\)
0.573969 0.818877i \(-0.305403\pi\)
\(84\) 20.4133 13.0881i 0.243015 0.155810i
\(85\) 0 0
\(86\) 5.54258 + 9.60002i 0.0644486 + 0.111628i
\(87\) 41.8682 + 24.1726i 0.481243 + 0.277846i
\(88\) −17.2416 + 29.8633i −0.195927 + 0.339356i
\(89\) 124.905 72.1140i 1.40343 0.810270i 0.408686 0.912675i \(-0.365987\pi\)
0.994743 + 0.102405i \(0.0326537\pi\)
\(90\) 0 0
\(91\) 8.26863 + 177.564i 0.0908641 + 1.95126i
\(92\) 47.4837 0.516127
\(93\) 20.0480 + 34.7241i 0.215570 + 0.373378i
\(94\) −27.9152 16.1168i −0.296970 0.171456i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 78.9980i 0.814412i 0.913336 + 0.407206i \(0.133497\pi\)
−0.913336 + 0.407206i \(0.866503\pi\)
\(98\) −40.0754 56.5328i −0.408933 0.576866i
\(99\) −36.5749 −0.369443
\(100\) 0 0
\(101\) −40.4728 23.3670i −0.400721 0.231356i 0.286074 0.958208i \(-0.407650\pi\)
−0.686795 + 0.726851i \(0.740983\pi\)
\(102\) 35.2417 61.0404i 0.345507 0.598435i
\(103\) 144.022 83.1514i 1.39828 0.807295i 0.404064 0.914731i \(-0.367597\pi\)
0.994212 + 0.107435i \(0.0342639\pi\)
\(104\) 71.8246i 0.690621i
\(105\) 0 0
\(106\) −68.6689 −0.647820
\(107\) −16.4908 28.5629i −0.154120 0.266943i 0.778618 0.627498i \(-0.215921\pi\)
−0.932738 + 0.360554i \(0.882587\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 75.8575 131.389i 0.695940 1.20540i −0.273923 0.961752i \(-0.588321\pi\)
0.969863 0.243652i \(-0.0783454\pi\)
\(110\) 0 0
\(111\) 50.3405i 0.453518i
\(112\) 15.1128 + 23.5712i 0.134936 + 0.210457i
\(113\) 42.1910 0.373372 0.186686 0.982420i \(-0.440225\pi\)
0.186686 + 0.982420i \(0.440225\pi\)
\(114\) 19.6783 + 34.0839i 0.172617 + 0.298982i
\(115\) 0 0
\(116\) −27.9121 + 48.3452i −0.240622 + 0.416769i
\(117\) 65.9751 38.0908i 0.563890 0.325562i
\(118\) 101.863i 0.863243i
\(119\) −178.933 92.4882i −1.50364 0.777212i
\(120\) 0 0
\(121\) −13.8180 23.9334i −0.114198 0.197797i
\(122\) −140.362 81.0383i −1.15051 0.664248i
\(123\) 49.2825 85.3598i 0.400671 0.693982i
\(124\) −40.0960 + 23.1494i −0.323354 + 0.186689i
\(125\) 0 0
\(126\) −13.6368 + 26.3825i −0.108228 + 0.209385i
\(127\) −49.3159 −0.388314 −0.194157 0.980970i \(-0.562197\pi\)
−0.194157 + 0.980970i \(0.562197\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) −11.7576 6.78824i −0.0911440 0.0526220i
\(130\) 0 0
\(131\) −12.6892 + 7.32612i −0.0968642 + 0.0559246i −0.547650 0.836708i \(-0.684477\pi\)
0.450785 + 0.892632i \(0.351144\pi\)
\(132\) 42.2331i 0.319947i
\(133\) 94.6815 60.7055i 0.711891 0.456433i
\(134\) 99.7514 0.744413
\(135\) 0 0
\(136\) 70.4833 + 40.6936i 0.518260 + 0.299217i
\(137\) −8.61062 + 14.9140i −0.0628512 + 0.108862i −0.895739 0.444581i \(-0.853353\pi\)
0.832888 + 0.553442i \(0.186686\pi\)
\(138\) −50.3641 + 29.0777i −0.364957 + 0.210708i
\(139\) 31.2612i 0.224901i −0.993657 0.112450i \(-0.964130\pi\)
0.993657 0.112450i \(-0.0358699\pi\)
\(140\) 0 0
\(141\) 39.4780 0.279986
\(142\) −4.53610 7.85675i −0.0319443 0.0553292i
\(143\) 268.115 + 154.796i 1.87493 + 1.08249i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 55.9412i 0.383159i
\(147\) 77.1255 + 35.4211i 0.524663 + 0.240960i
\(148\) 58.1282 0.392758
\(149\) 71.5886 + 123.995i 0.480460 + 0.832182i 0.999749 0.0224175i \(-0.00713631\pi\)
−0.519288 + 0.854599i \(0.673803\pi\)
\(150\) 0 0
\(151\) −23.1788 + 40.1468i −0.153502 + 0.265873i −0.932512 0.361138i \(-0.882388\pi\)
0.779011 + 0.627011i \(0.215722\pi\)
\(152\) −39.3567 + 22.7226i −0.258926 + 0.149491i
\(153\) 86.3241i 0.564210i
\(154\) −120.560 + 5.61413i −0.782860 + 0.0364554i
\(155\) 0 0
\(156\) 43.9834 + 76.1815i 0.281945 + 0.488343i
\(157\) −71.4553 41.2548i −0.455130 0.262769i 0.254865 0.966977i \(-0.417969\pi\)
−0.709994 + 0.704208i \(0.751302\pi\)
\(158\) 38.7473 67.1122i 0.245236 0.424761i
\(159\) 72.8344 42.0510i 0.458078 0.264471i
\(160\) 0 0
\(161\) 89.7015 + 139.906i 0.557152 + 0.868982i
\(162\) 12.7279 0.0785674
\(163\) −123.208 213.403i −0.755879 1.30922i −0.944936 0.327254i \(-0.893877\pi\)
0.189058 0.981966i \(-0.439457\pi\)
\(164\) 98.5650 + 56.9065i 0.601006 + 0.346991i
\(165\) 0 0
\(166\) −166.484 + 96.1195i −1.00292 + 0.579033i
\(167\) 287.387i 1.72088i −0.509549 0.860441i \(-0.670188\pi\)
0.509549 0.860441i \(-0.329812\pi\)
\(168\) −30.4639 15.7464i −0.181333 0.0937286i
\(169\) −475.847 −2.81566
\(170\) 0 0
\(171\) −41.7441 24.1010i −0.244117 0.140941i
\(172\) 7.83839 13.5765i 0.0455720 0.0789330i
\(173\) −236.901 + 136.775i −1.36937 + 0.790605i −0.990847 0.134988i \(-0.956900\pi\)
−0.378521 + 0.925593i \(0.623567\pi\)
\(174\) 68.3704i 0.392933i
\(175\) 0 0
\(176\) 48.7665 0.277083
\(177\) −62.3779 108.042i −0.352417 0.610405i
\(178\) −176.643 101.985i −0.992374 0.572948i
\(179\) 50.3990 87.2936i 0.281558 0.487674i −0.690210 0.723609i \(-0.742482\pi\)
0.971769 + 0.235935i \(0.0758153\pi\)
\(180\) 0 0
\(181\) 135.147i 0.746667i 0.927697 + 0.373333i \(0.121785\pi\)
−0.927697 + 0.373333i \(0.878215\pi\)
\(182\) 211.624 135.684i 1.16277 0.745516i
\(183\) 198.502 1.08471
\(184\) −33.5760 58.1554i −0.182478 0.316062i
\(185\) 0 0
\(186\) 28.3521 49.1073i 0.152431 0.264018i
\(187\) −303.811 + 175.405i −1.62466 + 0.937996i
\(188\) 45.5853i 0.242475i
\(189\) −1.69195 36.3337i −0.00895211 0.192242i
\(190\) 0 0
\(191\) −89.0902 154.309i −0.466441 0.807900i 0.532824 0.846226i \(-0.321131\pi\)
−0.999265 + 0.0383263i \(0.987797\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) 67.5577 117.013i 0.350040 0.606287i −0.636216 0.771511i \(-0.719501\pi\)
0.986256 + 0.165224i \(0.0528347\pi\)
\(194\) 96.7523 55.8600i 0.498723 0.287938i
\(195\) 0 0
\(196\) −40.9007 + 89.0569i −0.208677 + 0.454372i
\(197\) −64.7529 −0.328695 −0.164347 0.986403i \(-0.552552\pi\)
−0.164347 + 0.986403i \(0.552552\pi\)
\(198\) 25.8624 + 44.7949i 0.130618 + 0.226237i
\(199\) 116.757 + 67.4097i 0.586719 + 0.338742i 0.763799 0.645454i \(-0.223332\pi\)
−0.177080 + 0.984196i \(0.556665\pi\)
\(200\) 0 0
\(201\) −105.802 + 61.0850i −0.526380 + 0.303905i
\(202\) 66.0918i 0.327187i
\(203\) −195.173 + 9.08862i −0.961444 + 0.0447715i
\(204\) −99.6785 −0.488620
\(205\) 0 0
\(206\) −203.679 117.594i −0.988731 0.570844i
\(207\) 35.6128 61.6831i 0.172042 0.297986i
\(208\) −87.9668 + 50.7877i −0.422917 + 0.244172i
\(209\) 195.887i 0.937257i
\(210\) 0 0
\(211\) −116.352 −0.551432 −0.275716 0.961239i \(-0.588915\pi\)
−0.275716 + 0.961239i \(0.588915\pi\)
\(212\) 48.5563 + 84.1019i 0.229039 + 0.396707i
\(213\) 9.62251 + 5.55556i 0.0451761 + 0.0260824i
\(214\) −23.3215 + 40.3941i −0.108979 + 0.188757i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −143.953 74.4073i −0.663377 0.342891i
\(218\) −214.557 −0.984208
\(219\) 34.2569 + 59.3346i 0.156424 + 0.270934i
\(220\) 0 0
\(221\) 365.350 632.805i 1.65317 2.86337i
\(222\) −61.6543 + 35.5961i −0.277722 + 0.160343i
\(223\) 30.0511i 0.134758i −0.997727 0.0673791i \(-0.978536\pi\)
0.997727 0.0673791i \(-0.0214637\pi\)
\(224\) 18.1824 35.1767i 0.0811713 0.157039i
\(225\) 0 0
\(226\) −29.8335 51.6732i −0.132007 0.228642i
\(227\) −122.698 70.8400i −0.540522 0.312070i 0.204769 0.978810i \(-0.434356\pi\)
−0.745290 + 0.666740i \(0.767689\pi\)
\(228\) 27.8294 48.2019i 0.122059 0.211412i
\(229\) −188.648 + 108.916i −0.823792 + 0.475617i −0.851722 0.523993i \(-0.824442\pi\)
0.0279303 + 0.999610i \(0.491108\pi\)
\(230\) 0 0
\(231\) 124.436 79.7825i 0.538683 0.345379i
\(232\) 78.9473 0.340290
\(233\) −2.12597 3.68229i −0.00912435 0.0158038i 0.861427 0.507881i \(-0.169571\pi\)
−0.870552 + 0.492077i \(0.836238\pi\)
\(234\) −93.3029 53.8685i −0.398730 0.230207i
\(235\) 0 0
\(236\) 124.756 72.0278i 0.528626 0.305202i
\(237\) 94.9110i 0.400468i
\(238\) 13.2505 + 284.547i 0.0556742 + 1.19557i
\(239\) 261.513 1.09419 0.547097 0.837069i \(-0.315733\pi\)
0.547097 + 0.837069i \(0.315733\pi\)
\(240\) 0 0
\(241\) −86.5156 49.9498i −0.358986 0.207261i 0.309650 0.950851i \(-0.399788\pi\)
−0.668636 + 0.743590i \(0.733121\pi\)
\(242\) −19.5416 + 33.8470i −0.0807503 + 0.139864i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 229.211i 0.939388i
\(245\) 0 0
\(246\) −139.392 −0.566634
\(247\) 204.005 + 353.347i 0.825932 + 1.43056i
\(248\) 56.7042 + 32.7382i 0.228646 + 0.132009i
\(249\) 117.722 203.900i 0.472779 0.818877i
\(250\) 0 0
\(251\) 250.563i 0.998258i 0.866528 + 0.499129i \(0.166347\pi\)
−0.866528 + 0.499129i \(0.833653\pi\)
\(252\) 41.9545 1.95369i 0.166486 0.00775276i
\(253\) 289.452 1.14408
\(254\) 34.8716 + 60.3993i 0.137290 + 0.237793i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −151.261 + 87.3305i −0.588563 + 0.339807i −0.764529 0.644589i \(-0.777029\pi\)
0.175966 + 0.984396i \(0.443695\pi\)
\(258\) 19.2000i 0.0744188i
\(259\) 109.810 + 171.269i 0.423977 + 0.661271i
\(260\) 0 0
\(261\) 41.8682 + 72.5178i 0.160414 + 0.277846i
\(262\) 17.9452 + 10.3607i 0.0684933 + 0.0395446i
\(263\) 10.4417 18.0856i 0.0397023 0.0687664i −0.845491 0.533989i \(-0.820692\pi\)
0.885194 + 0.465223i \(0.154026\pi\)
\(264\) −51.7247 + 29.8633i −0.195927 + 0.113119i
\(265\) 0 0
\(266\) −141.299 73.0354i −0.531198 0.274569i
\(267\) 249.810 0.935619
\(268\) −70.5349 122.170i −0.263190 0.455858i
\(269\) 0.255741 + 0.147652i 0.000950712 + 0.000548894i 0.500475 0.865751i \(-0.333159\pi\)
−0.499525 + 0.866300i \(0.666492\pi\)
\(270\) 0 0
\(271\) 284.141 164.049i 1.04849 0.605346i 0.126264 0.991997i \(-0.459702\pi\)
0.922226 + 0.386651i \(0.126368\pi\)
\(272\) 115.099i 0.423157i
\(273\) −141.372 + 273.508i −0.517848 + 1.00186i
\(274\) 24.3545 0.0888851
\(275\) 0 0
\(276\) 71.2255 + 41.1221i 0.258064 + 0.148993i
\(277\) −251.485 + 435.585i −0.907888 + 1.57251i −0.0908951 + 0.995860i \(0.528973\pi\)
−0.816993 + 0.576648i \(0.804361\pi\)
\(278\) −38.2870 + 22.1050i −0.137723 + 0.0795144i
\(279\) 69.4482i 0.248918i
\(280\) 0 0
\(281\) 264.481 0.941213 0.470607 0.882343i \(-0.344035\pi\)
0.470607 + 0.882343i \(0.344035\pi\)
\(282\) −27.9152 48.3505i −0.0989900 0.171456i
\(283\) 399.801 + 230.825i 1.41272 + 0.815636i 0.995644 0.0932336i \(-0.0297203\pi\)
0.417079 + 0.908870i \(0.363054\pi\)
\(284\) −6.41501 + 11.1111i −0.0225881 + 0.0391237i
\(285\) 0 0
\(286\) 437.830i 1.53087i
\(287\) 18.5297 + 397.914i 0.0645633 + 1.38646i
\(288\) −16.9706 −0.0589256
\(289\) 269.492 + 466.773i 0.932497 + 1.61513i
\(290\) 0 0
\(291\) −68.4142 + 118.497i −0.235100 + 0.407206i
\(292\) −68.5137 + 39.5564i −0.234636 + 0.135467i
\(293\) 134.788i 0.460027i −0.973187 0.230014i \(-0.926123\pi\)
0.973187 0.230014i \(-0.0738771\pi\)
\(294\) −11.1542 119.506i −0.0379395 0.406482i
\(295\) 0 0
\(296\) −41.1029 71.1922i −0.138861 0.240514i
\(297\) −54.8624 31.6748i −0.184722 0.106649i
\(298\) 101.242 175.355i 0.339737 0.588441i
\(299\) −522.124 + 301.448i −1.74623 + 1.00819i
\(300\) 0 0
\(301\) 54.8093 2.55230i 0.182091 0.00847941i
\(302\) 65.5595 0.217084
\(303\) −40.4728 70.1010i −0.133574 0.231356i
\(304\) 55.6588 + 32.1346i 0.183088 + 0.105706i
\(305\) 0 0
\(306\) 105.725 61.0404i 0.345507 0.199478i
\(307\) 23.7237i 0.0772760i −0.999253 0.0386380i \(-0.987698\pi\)
0.999253 0.0386380i \(-0.0123019\pi\)
\(308\) 92.1249 + 143.686i 0.299107 + 0.466513i
\(309\) 288.045 0.932184
\(310\) 0 0
\(311\) 245.097 + 141.507i 0.788092 + 0.455005i 0.839290 0.543683i \(-0.182971\pi\)
−0.0511984 + 0.998689i \(0.516304\pi\)
\(312\) 62.2019 107.737i 0.199365 0.345311i
\(313\) −367.522 + 212.189i −1.17419 + 0.677920i −0.954664 0.297687i \(-0.903785\pi\)
−0.219528 + 0.975606i \(0.570452\pi\)
\(314\) 116.686i 0.371612i
\(315\) 0 0
\(316\) −109.594 −0.346816
\(317\) −14.0641 24.3597i −0.0443661 0.0768444i 0.842990 0.537930i \(-0.180793\pi\)
−0.887356 + 0.461085i \(0.847460\pi\)
\(318\) −103.003 59.4690i −0.323910 0.187010i
\(319\) −170.147 + 294.703i −0.533376 + 0.923835i
\(320\) 0 0
\(321\) 57.1258i 0.177962i
\(322\) 107.921 208.790i 0.335158 0.648416i
\(323\) −462.332 −1.43137
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −174.243 + 301.797i −0.534487 + 0.925758i
\(327\) 227.572 131.389i 0.695940 0.401801i
\(328\) 160.956i 0.490719i
\(329\) −134.313 + 86.1153i −0.408245 + 0.261749i
\(330\) 0 0
\(331\) −130.940 226.795i −0.395590 0.685182i 0.597586 0.801805i \(-0.296127\pi\)
−0.993176 + 0.116623i \(0.962793\pi\)
\(332\) 235.444 + 135.934i 0.709168 + 0.409438i
\(333\) 43.5962 75.5108i 0.130919 0.226759i
\(334\) −351.976 + 203.214i −1.05382 + 0.608424i
\(335\) 0 0
\(336\) 2.25593 + 48.4449i 0.00671408 + 0.144181i
\(337\) 539.998 1.60237 0.801185 0.598417i \(-0.204204\pi\)
0.801185 + 0.598417i \(0.204204\pi\)
\(338\) 336.475 + 582.791i 0.995487 + 1.72423i
\(339\) 63.2865 + 36.5385i 0.186686 + 0.107783i
\(340\) 0 0
\(341\) −244.418 + 141.115i −0.716767 + 0.413826i
\(342\) 68.1678i 0.199321i
\(343\) −339.663 + 47.7274i −0.990272 + 0.139147i
\(344\) −22.1703 −0.0644486
\(345\) 0 0
\(346\) 335.028 + 193.429i 0.968289 + 0.559042i
\(347\) −19.9273 + 34.5150i −0.0574273 + 0.0994670i −0.893310 0.449441i \(-0.851623\pi\)
0.835883 + 0.548908i \(0.184956\pi\)
\(348\) −83.7363 + 48.3452i −0.240622 + 0.138923i
\(349\) 326.000i 0.934099i 0.884231 + 0.467049i \(0.154683\pi\)
−0.884231 + 0.467049i \(0.845317\pi\)
\(350\) 0 0
\(351\) 131.950 0.375927
\(352\) −34.4832 59.7266i −0.0979635 0.169678i
\(353\) 126.505 + 73.0374i 0.358370 + 0.206905i 0.668365 0.743833i \(-0.266994\pi\)
−0.309996 + 0.950738i \(0.600328\pi\)
\(354\) −88.2156 + 152.794i −0.249197 + 0.431621i
\(355\) 0 0
\(356\) 288.456i 0.810270i
\(357\) −188.303 293.693i −0.527459 0.822670i
\(358\) −142.550 −0.398184
\(359\) −10.7785 18.6689i −0.0300237 0.0520026i 0.850623 0.525776i \(-0.176225\pi\)
−0.880647 + 0.473773i \(0.842892\pi\)
\(360\) 0 0
\(361\) −51.4209 + 89.0636i −0.142440 + 0.246714i
\(362\) 165.520 95.5632i 0.457238 0.263987i
\(363\) 47.8669i 0.131865i
\(364\) −315.819 163.243i −0.867635 0.448469i
\(365\) 0 0
\(366\) −140.362 243.115i −0.383504 0.664248i
\(367\) −176.974 102.176i −0.482217 0.278408i 0.239123 0.970989i \(-0.423140\pi\)
−0.721340 + 0.692581i \(0.756473\pi\)
\(368\) −47.4837 + 82.2442i −0.129032 + 0.223490i
\(369\) 147.847 85.3598i 0.400671 0.231327i
\(370\) 0 0
\(371\) −156.070 + 301.943i −0.420675 + 0.813864i
\(372\) −80.1919 −0.215570
\(373\) 281.632 + 487.800i 0.755045 + 1.30778i 0.945352 + 0.326051i \(0.105718\pi\)
−0.190308 + 0.981724i \(0.560949\pi\)
\(374\) 429.654 + 248.061i 1.14881 + 0.663264i
\(375\) 0 0
\(376\) 55.8304 32.2337i 0.148485 0.0857279i
\(377\) 708.795i 1.88009i
\(378\) −43.3031 + 27.7640i −0.114559 + 0.0734498i
\(379\) 300.642 0.793250 0.396625 0.917981i \(-0.370181\pi\)
0.396625 + 0.917981i \(0.370181\pi\)
\(380\) 0 0
\(381\) −73.9738 42.7088i −0.194157 0.112097i
\(382\) −125.993 + 218.226i −0.329824 + 0.571271i
\(383\) 9.34543 5.39559i 0.0244006 0.0140877i −0.487750 0.872983i \(-0.662182\pi\)
0.512151 + 0.858896i \(0.328849\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −191.082 −0.495031
\(387\) −11.7576 20.3647i −0.0303813 0.0526220i
\(388\) −136.828 78.9980i −0.352651 0.203603i
\(389\) 65.7124 113.817i 0.168927 0.292589i −0.769116 0.639109i \(-0.779303\pi\)
0.938043 + 0.346520i \(0.112637\pi\)
\(390\) 0 0
\(391\) 683.164i 1.74722i
\(392\) 137.993 12.8798i 0.352023 0.0328566i
\(393\) −25.3784 −0.0645761
\(394\) 45.7872 + 79.3058i 0.116211 + 0.201284i
\(395\) 0 0
\(396\) 36.5749 63.3496i 0.0923609 0.159974i
\(397\) 485.778 280.464i 1.22362 0.706459i 0.257935 0.966162i \(-0.416958\pi\)
0.965689 + 0.259703i \(0.0836247\pi\)
\(398\) 190.664i 0.479054i
\(399\) 194.595 9.06169i 0.487706 0.0227110i
\(400\) 0 0
\(401\) −170.877 295.967i −0.426126 0.738072i 0.570399 0.821368i \(-0.306789\pi\)
−0.996525 + 0.0832958i \(0.973455\pi\)
\(402\) 149.627 + 86.3872i 0.372207 + 0.214894i
\(403\) 293.926 509.095i 0.729345 1.26326i
\(404\) 80.9456 46.7340i 0.200360 0.115678i
\(405\) 0 0
\(406\) 149.140 + 232.611i 0.367339 + 0.572933i
\(407\) 354.339 0.870612
\(408\) 70.4833 + 122.081i 0.172753 + 0.299217i
\(409\) 19.6793 + 11.3619i 0.0481157 + 0.0277796i 0.523865 0.851801i \(-0.324490\pi\)
−0.475749 + 0.879581i \(0.657823\pi\)
\(410\) 0 0
\(411\) −25.8319 + 14.9140i −0.0628512 + 0.0362872i
\(412\) 332.606i 0.807295i
\(413\) 447.899 + 231.513i 1.08450 + 0.560564i
\(414\) −100.728 −0.243305
\(415\) 0 0
\(416\) 124.404 + 71.8246i 0.299048 + 0.172655i
\(417\) 27.0730 46.8918i 0.0649232 0.112450i
\(418\) −239.911 + 138.513i −0.573950 + 0.331370i
\(419\) 347.375i 0.829057i 0.910036 + 0.414529i \(0.136054\pi\)
−0.910036 + 0.414529i \(0.863946\pi\)
\(420\) 0 0
\(421\) −340.381 −0.808507 −0.404253 0.914647i \(-0.632469\pi\)
−0.404253 + 0.914647i \(0.632469\pi\)
\(422\) 82.2734 + 142.502i 0.194961 + 0.337682i
\(423\) 59.2170 + 34.1890i 0.139993 + 0.0808250i
\(424\) 68.6689 118.938i 0.161955 0.280514i
\(425\) 0 0
\(426\) 15.7135i 0.0368861i
\(427\) −675.348 + 433.002i −1.58161 + 1.01406i
\(428\) 65.9632 0.154120
\(429\) 268.115 + 464.389i 0.624976 + 1.08249i
\(430\) 0 0
\(431\) 21.7871 37.7363i 0.0505500 0.0875552i −0.839643 0.543138i \(-0.817236\pi\)
0.890193 + 0.455583i \(0.150569\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 304.620i 0.703509i 0.936092 + 0.351755i \(0.114415\pi\)
−0.936092 + 0.351755i \(0.885585\pi\)
\(434\) 10.6601 + 228.919i 0.0245624 + 0.527464i
\(435\) 0 0
\(436\) 151.715 + 262.778i 0.347970 + 0.602702i
\(437\) 330.360 + 190.734i 0.755974 + 0.436462i
\(438\) 48.4465 83.9118i 0.110608 0.191579i
\(439\) −539.136 + 311.270i −1.22810 + 0.709044i −0.966632 0.256168i \(-0.917540\pi\)
−0.261468 + 0.965212i \(0.584207\pi\)
\(440\) 0 0
\(441\) 85.0127 + 119.924i 0.192773 + 0.271937i
\(442\) −1033.37 −2.33793
\(443\) −42.8024 74.1360i −0.0966195 0.167350i 0.813664 0.581336i \(-0.197470\pi\)
−0.910283 + 0.413986i \(0.864136\pi\)
\(444\) 87.1923 + 50.3405i 0.196379 + 0.113380i
\(445\) 0 0
\(446\) −36.8049 + 21.2493i −0.0825222 + 0.0476442i
\(447\) 247.990i 0.554788i
\(448\) −55.9394 + 2.60493i −0.124865 + 0.00581457i
\(449\) −143.625 −0.319876 −0.159938 0.987127i \(-0.551129\pi\)
−0.159938 + 0.987127i \(0.551129\pi\)
\(450\) 0 0
\(451\) 600.834 + 346.892i 1.33223 + 0.769161i
\(452\) −42.1910 + 73.0769i −0.0933429 + 0.161675i
\(453\) −69.5363 + 40.1468i −0.153502 + 0.0886243i
\(454\) 200.366i 0.441334i
\(455\) 0 0
\(456\) −78.7134 −0.172617
\(457\) −11.7226 20.3041i −0.0256512 0.0444292i 0.852915 0.522050i \(-0.174833\pi\)
−0.878566 + 0.477621i \(0.841499\pi\)
\(458\) 266.789 + 154.031i 0.582509 + 0.336312i
\(459\) −74.7589 + 129.486i −0.162873 + 0.282105i
\(460\) 0 0
\(461\) 170.444i 0.369728i 0.982764 + 0.184864i \(0.0591844\pi\)
−0.982764 + 0.184864i \(0.940816\pi\)
\(462\) −185.703 95.9872i −0.401954 0.207764i
\(463\) −475.871 −1.02780 −0.513899 0.857850i \(-0.671800\pi\)
−0.513899 + 0.857850i \(0.671800\pi\)
\(464\) −55.8242 96.6904i −0.120311 0.208384i
\(465\) 0 0
\(466\) −3.00658 + 5.20755i −0.00645189 + 0.0111750i
\(467\) 188.847 109.031i 0.404384 0.233471i −0.283990 0.958827i \(-0.591658\pi\)
0.688374 + 0.725356i \(0.258325\pi\)
\(468\) 152.363i 0.325562i
\(469\) 226.715 438.616i 0.483400 0.935215i
\(470\) 0 0
\(471\) −71.4553 123.764i −0.151710 0.262769i
\(472\) −176.431 101.863i −0.373795 0.215811i
\(473\) 47.7814 82.7598i 0.101018 0.174968i
\(474\) 116.242 67.1122i 0.245236 0.141587i
\(475\) 0 0
\(476\) 339.128 217.433i 0.712453 0.456793i
\(477\) 145.669 0.305385
\(478\) −184.917 320.286i −0.386856 0.670055i
\(479\) −482.916 278.812i −1.00817 0.582070i −0.0975181 0.995234i \(-0.531090\pi\)
−0.910657 + 0.413164i \(0.864424\pi\)
\(480\) 0 0
\(481\) −639.170 + 369.025i −1.32883 + 0.767203i
\(482\) 141.279i 0.293111i
\(483\) 13.3900 + 287.543i 0.0277226 + 0.595327i
\(484\) 55.2719 0.114198
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) −258.122 + 447.080i −0.530024 + 0.918029i 0.469362 + 0.883006i \(0.344484\pi\)
−0.999386 + 0.0350234i \(0.988849\pi\)
\(488\) 280.725 162.077i 0.575256 0.332124i
\(489\) 426.806i 0.872813i
\(490\) 0 0
\(491\) 122.586 0.249666 0.124833 0.992178i \(-0.460161\pi\)
0.124833 + 0.992178i \(0.460161\pi\)
\(492\) 98.5650 + 170.720i 0.200335 + 0.346991i
\(493\) 695.559 + 401.581i 1.41087 + 0.814566i
\(494\) 288.507 499.709i 0.584022 1.01156i
\(495\) 0 0
\(496\) 92.5976i 0.186689i
\(497\) −44.8565 + 2.08883i −0.0902544 + 0.00420287i
\(498\) −332.968 −0.668610
\(499\) −187.525 324.802i −0.375801 0.650906i 0.614646 0.788803i \(-0.289299\pi\)
−0.990447 + 0.137897i \(0.955966\pi\)
\(500\) 0 0
\(501\) 248.885 431.081i 0.496776 0.860441i
\(502\) 306.875 177.175i 0.611306 0.352938i
\(503\) 303.836i 0.604048i 0.953300 + 0.302024i \(0.0976622\pi\)
−0.953300 + 0.302024i \(0.902338\pi\)
\(504\) −32.0591 50.0021i −0.0636094 0.0992106i
\(505\) 0 0
\(506\) −204.673 354.505i −0.404493 0.700602i
\(507\) −713.771 412.096i −1.40783 0.812812i
\(508\) 49.3159 85.4176i 0.0970784 0.168145i
\(509\) −161.864 + 93.4522i −0.318004 + 0.183600i −0.650503 0.759504i \(-0.725442\pi\)
0.332499 + 0.943104i \(0.392108\pi\)
\(510\) 0 0
\(511\) −245.978 127.143i −0.481367 0.248812i
\(512\) 22.6274 0.0441942
\(513\) −41.7441 72.3029i −0.0813725 0.140941i
\(514\) 213.915 + 123.504i 0.416177 + 0.240280i
\(515\) 0 0
\(516\) 23.5152 13.5765i 0.0455720 0.0263110i
\(517\) 277.880i 0.537485i
\(518\) 132.114 255.595i 0.255046 0.493427i
\(519\) −473.801 −0.912912
\(520\) 0 0
\(521\) 518.758 + 299.505i 0.995697 + 0.574866i 0.906972 0.421190i \(-0.138388\pi\)
0.0887246 + 0.996056i \(0.471721\pi\)
\(522\) 59.2105 102.556i 0.113430 0.196467i
\(523\) −132.497 + 76.4975i −0.253341 + 0.146267i −0.621293 0.783578i \(-0.713392\pi\)
0.367952 + 0.929845i \(0.380059\pi\)
\(524\) 29.3045i 0.0559246i
\(525\) 0 0
\(526\) −29.5336 −0.0561475
\(527\) 333.059 + 576.875i 0.631990 + 1.09464i
\(528\) 73.1498 + 42.2331i 0.138541 + 0.0799869i
\(529\) −17.3376 + 30.0295i −0.0327742 + 0.0567666i
\(530\) 0 0
\(531\) 216.083i 0.406937i
\(532\) 10.4635 + 224.699i 0.0196683 + 0.422366i
\(533\) −1445.07 −2.71121
\(534\) −176.643 305.954i −0.330791 0.572948i
\(535\) 0 0
\(536\) −99.7514 + 172.774i −0.186103 + 0.322340i
\(537\) 151.197 87.2936i 0.281558 0.162558i
\(538\) 0.417624i 0.000776253i
\(539\) −249.323 + 542.875i −0.462567 + 1.00719i
\(540\) 0 0
\(541\) −71.7086 124.203i −0.132548 0.229580i 0.792110 0.610378i \(-0.208983\pi\)
−0.924658 + 0.380798i \(0.875649\pi\)
\(542\) −401.836 232.000i −0.741394 0.428044i
\(543\) −117.040 + 202.720i −0.215544 + 0.373333i
\(544\) −140.967 + 81.3871i −0.259130 + 0.149609i
\(545\) 0 0
\(546\) 434.942 20.2539i 0.796598 0.0370951i
\(547\) 103.778 0.189721 0.0948607 0.995491i \(-0.469759\pi\)
0.0948607 + 0.995491i \(0.469759\pi\)
\(548\) −17.2212 29.8281i −0.0314256 0.0544308i
\(549\) 297.754 + 171.908i 0.542356 + 0.313129i
\(550\) 0 0
\(551\) −388.388 + 224.236i −0.704879 + 0.406962i
\(552\) 116.311i 0.210708i
\(553\) −207.034 322.908i −0.374383 0.583920i
\(554\) 711.307 1.28395
\(555\) 0 0
\(556\) 54.1460 + 31.2612i 0.0973848 + 0.0562251i
\(557\) 412.613 714.666i 0.740777 1.28306i −0.211366 0.977407i \(-0.567791\pi\)
0.952142 0.305656i \(-0.0988756\pi\)
\(558\) 85.0564 49.1073i 0.152431 0.0880059i
\(559\) 199.047i 0.356076i
\(560\) 0 0
\(561\) −607.622 −1.08310
\(562\) −187.016 323.922i −0.332769 0.576373i
\(563\) −331.959 191.657i −0.589626 0.340421i 0.175324 0.984511i \(-0.443903\pi\)
−0.764949 + 0.644090i \(0.777236\pi\)
\(564\) −39.4780 + 68.3780i −0.0699965 + 0.121238i
\(565\) 0 0
\(566\) 652.872i 1.15348i
\(567\) 28.9280 55.9658i 0.0510194 0.0987051i
\(568\) 18.1444 0.0319443
\(569\) −377.462 653.783i −0.663377 1.14900i −0.979723 0.200359i \(-0.935789\pi\)
0.316345 0.948644i \(-0.397544\pi\)
\(570\) 0 0
\(571\) 345.652 598.687i 0.605346 1.04849i −0.386651 0.922226i \(-0.626368\pi\)
0.991997 0.126263i \(-0.0402984\pi\)
\(572\) −536.230 + 309.592i −0.937465 + 0.541245i
\(573\) 308.618i 0.538600i
\(574\) 474.241 304.062i 0.826204 0.529725i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −338.973 195.706i −0.587476 0.339179i 0.176623 0.984279i \(-0.443483\pi\)
−0.764099 + 0.645099i \(0.776816\pi\)
\(578\) 381.119 660.117i 0.659375 1.14207i
\(579\) 202.673 117.013i 0.350040 0.202096i
\(580\) 0 0
\(581\) 44.2621 + 950.505i 0.0761826 + 1.63598i
\(582\) 193.505 0.332482
\(583\) 295.990 + 512.670i 0.507702 + 0.879365i
\(584\) 96.8930 + 55.9412i 0.165913 + 0.0957897i
\(585\) 0 0
\(586\) −165.081 + 95.3095i −0.281708 + 0.162644i
\(587\) 1027.13i 1.74979i 0.484312 + 0.874896i \(0.339070\pi\)
−0.484312 + 0.874896i \(0.660930\pi\)
\(588\) −138.477 + 98.1643i −0.235504 + 0.166946i
\(589\) −371.949 −0.631492
\(590\) 0 0
\(591\) −97.1294 56.0777i −0.164347 0.0948861i
\(592\) −58.1282 + 100.681i −0.0981896 + 0.170069i
\(593\) −116.894 + 67.4886i −0.197123 + 0.113809i −0.595313 0.803494i \(-0.702972\pi\)
0.398190 + 0.917303i \(0.369638\pi\)
\(594\) 89.5899i 0.150825i
\(595\) 0 0
\(596\) −286.354 −0.480460
\(597\) 116.757 + 202.229i 0.195573 + 0.338742i
\(598\) 738.394 + 426.312i 1.23477 + 0.712897i
\(599\) 380.159 658.455i 0.634656 1.09926i −0.351932 0.936026i \(-0.614475\pi\)
0.986588 0.163231i \(-0.0521917\pi\)
\(600\) 0 0
\(601\) 604.796i 1.00632i 0.864194 + 0.503158i \(0.167829\pi\)
−0.864194 + 0.503158i \(0.832171\pi\)
\(602\) −41.8820 65.3227i −0.0695714 0.108509i
\(603\) −211.605 −0.350920
\(604\) −46.3575 80.2936i −0.0767509 0.132936i
\(605\) 0 0
\(606\) −57.2372 + 99.1377i −0.0944508 + 0.163594i
\(607\) −11.2280 + 6.48250i −0.0184976 + 0.0106796i −0.509220 0.860636i \(-0.670066\pi\)
0.490723 + 0.871316i \(0.336733\pi\)
\(608\) 90.8904i 0.149491i
\(609\) −300.631 155.392i −0.493647 0.255159i
\(610\) 0 0
\(611\) −289.396 501.249i −0.473644 0.820375i
\(612\) −149.518 86.3241i −0.244310 0.141052i
\(613\) 566.514 981.231i 0.924167 1.60070i 0.131271 0.991347i \(-0.458094\pi\)
0.792896 0.609357i \(-0.208572\pi\)
\(614\) −29.0555 + 16.7752i −0.0473217 + 0.0273212i
\(615\) 0 0
\(616\) 110.836 214.431i 0.179929 0.348102i
\(617\) −19.5534 −0.0316910 −0.0158455 0.999874i \(-0.505044\pi\)
−0.0158455 + 0.999874i \(0.505044\pi\)
\(618\) −203.679 352.782i −0.329577 0.570844i
\(619\) 574.387 + 331.623i 0.927928 + 0.535739i 0.886156 0.463388i \(-0.153366\pi\)
0.0417724 + 0.999127i \(0.486700\pi\)
\(620\) 0 0
\(621\) 106.838 61.6831i 0.172042 0.0993287i
\(622\) 400.241i 0.643474i
\(623\) −849.908 + 544.923i −1.36422 + 0.874676i
\(624\) −175.934 −0.281945
\(625\) 0 0
\(626\) 519.754 + 300.080i 0.830279 + 0.479362i
\(627\) 169.643 293.830i 0.270563 0.468628i
\(628\) 142.911 82.5095i 0.227565 0.131385i
\(629\) 836.311i 1.32959i
\(630\) 0 0
\(631\) −303.828 −0.481503 −0.240752 0.970587i \(-0.577394\pi\)
−0.240752 + 0.970587i \(0.577394\pi\)
\(632\) 77.4945 + 134.224i 0.122618 + 0.212380i
\(633\) −174.528 100.764i −0.275716 0.159185i
\(634\) −19.8896 + 34.4498i −0.0313716 + 0.0543372i
\(635\) 0 0
\(636\) 168.204i 0.264471i
\(637\) −115.636 1238.91i −0.181532 1.94492i
\(638\) 481.249 0.754308
\(639\) 9.62251 + 16.6667i 0.0150587 + 0.0260824i
\(640\) 0 0
\(641\) 470.134 814.296i 0.733439 1.27035i −0.221967 0.975054i \(-0.571248\pi\)
0.955405 0.295298i \(-0.0954191\pi\)
\(642\) −69.9646 + 40.3941i −0.108979 + 0.0629191i
\(643\) 1143.40i 1.77823i −0.457681 0.889116i \(-0.651320\pi\)
0.457681 0.889116i \(-0.348680\pi\)
\(644\) −332.026 + 15.4614i −0.515568 + 0.0240084i
\(645\) 0 0
\(646\) 326.918 + 566.239i 0.506065 + 0.876530i
\(647\) −790.146 456.191i −1.22125 0.705087i −0.256063 0.966660i \(-0.582425\pi\)
−0.965184 + 0.261573i \(0.915759\pi\)
\(648\) −12.7279 + 22.0454i −0.0196419 + 0.0340207i
\(649\) 760.488 439.068i 1.17178 0.676530i
\(650\) 0 0
\(651\) −151.491 236.278i −0.232705 0.362946i
\(652\) 492.833 0.755879
\(653\) 109.628 + 189.881i 0.167884 + 0.290783i 0.937676 0.347512i \(-0.112973\pi\)
−0.769792 + 0.638295i \(0.779640\pi\)
\(654\) −321.836 185.812i −0.492104 0.284116i
\(655\) 0 0
\(656\) −197.130 + 113.813i −0.300503 + 0.173495i
\(657\) 118.669i 0.180623i
\(658\) 200.443 + 103.606i 0.304624 + 0.157456i
\(659\) 661.525 1.00383 0.501916 0.864916i \(-0.332629\pi\)
0.501916 + 0.864916i \(0.332629\pi\)
\(660\) 0 0
\(661\) −481.878 278.212i −0.729013 0.420896i 0.0890478 0.996027i \(-0.471618\pi\)
−0.818061 + 0.575131i \(0.804951\pi\)
\(662\) −185.178 + 320.737i −0.279724 + 0.484497i
\(663\) 1096.05 632.805i 1.65317 0.954457i
\(664\) 384.478i 0.579033i
\(665\) 0 0
\(666\) −123.309 −0.185148
\(667\) −331.342 573.902i −0.496765 0.860423i
\(668\) 497.770 + 287.387i 0.745164 + 0.430221i
\(669\) 26.0250 45.0766i 0.0389014 0.0673791i
\(670\) 0 0
\(671\) 1397.23i 2.08231i
\(672\) 57.7375 37.0187i 0.0859189 0.0550873i
\(673\) 153.903 0.228682 0.114341 0.993442i \(-0.463524\pi\)
0.114341 + 0.993442i \(0.463524\pi\)
\(674\) −381.837 661.360i −0.566523 0.981247i
\(675\) 0 0
\(676\) 475.847 824.191i 0.703916 1.21922i
\(677\) 362.794 209.459i 0.535886 0.309394i −0.207524 0.978230i \(-0.566541\pi\)
0.743410 + 0.668836i \(0.233207\pi\)
\(678\) 103.346i 0.152428i
\(679\) −25.7230 552.387i −0.0378836 0.813530i
\(680\) 0 0
\(681\) −122.698 212.520i −0.180174 0.312070i
\(682\) 345.659 + 199.566i 0.506831 + 0.292619i
\(683\) 614.628 1064.57i 0.899895 1.55866i 0.0722678 0.997385i \(-0.476976\pi\)
0.827627 0.561278i \(-0.189690\pi\)
\(684\) 83.4882 48.2019i 0.122059 0.0704706i
\(685\) 0 0
\(686\) 298.632 + 382.252i 0.435324 + 0.557219i
\(687\) −377.297 −0.549195
\(688\) 15.6768 + 27.1530i 0.0227860 + 0.0394665i
\(689\) −1067.84 616.515i −1.54983 0.894797i
\(690\) 0 0
\(691\) 314.293 181.457i 0.454838 0.262601i −0.255033 0.966932i \(-0.582086\pi\)
0.709871 + 0.704331i \(0.248753\pi\)
\(692\) 547.099i 0.790605i
\(693\) 255.747 11.9094i 0.369044 0.0171852i
\(694\) 56.3628 0.0812144
\(695\) 0 0
\(696\) 118.421 + 68.3704i 0.170145 + 0.0982333i
\(697\) 818.734 1418.09i 1.17465 2.03456i
\(698\) 399.267 230.517i 0.572016 0.330254i
\(699\) 7.36459i 0.0105359i
\(700\) 0 0
\(701\) −319.012 −0.455081 −0.227541 0.973769i \(-0.573068\pi\)
−0.227541 + 0.973769i \(0.573068\pi\)
\(702\) −93.3029 161.605i −0.132910 0.230207i
\(703\) 404.418 + 233.491i 0.575275 + 0.332135i
\(704\) −48.7665 + 84.4661i −0.0692707 + 0.119980i
\(705\) 0 0
\(706\) 206.581i 0.292608i
\(707\) 290.612 + 150.213i 0.411049 + 0.212466i
\(708\) 249.512 0.352417
\(709\) −565.639 979.716i −0.797799 1.38183i −0.921047 0.389452i \(-0.872664\pi\)
0.123248 0.992376i \(-0.460669\pi\)
\(710\) 0 0
\(711\) −82.1954 + 142.367i −0.115605 + 0.200234i
\(712\) 353.285 203.969i 0.496187 0.286474i
\(713\) 549.610i 0.770841i
\(714\) −226.549 + 438.295i −0.317295 + 0.613859i
\(715\) 0 0
\(716\) 100.798 + 174.587i 0.140779 + 0.243837i
\(717\) 392.269 + 226.477i 0.547097 + 0.315867i
\(718\) −15.2431 + 26.4018i −0.0212300 + 0.0367714i
\(719\) −243.094 + 140.350i −0.338100 + 0.195202i −0.659431 0.751765i \(-0.729203\pi\)
0.321332 + 0.946967i \(0.395870\pi\)
\(720\) 0 0
\(721\) −979.991 + 628.326i −1.35921 + 0.871464i
\(722\) 145.440 0.201441
\(723\) −86.5156 149.849i −0.119662 0.207261i
\(724\) −234.081 135.147i −0.323316 0.186667i
\(725\) 0 0
\(726\) −58.6247 + 33.8470i −0.0807503 + 0.0466212i
\(727\) 737.233i 1.01408i 0.861924 + 0.507038i \(0.169260\pi\)
−0.861924 + 0.507038i \(0.830740\pi\)
\(728\) 23.3872 + 502.228i 0.0321253 + 0.689874i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −195.330 112.774i −0.267209 0.154273i
\(732\) −198.502 + 343.816i −0.271178 + 0.469694i
\(733\) −1172.96 + 677.208i −1.60022 + 0.923886i −0.608775 + 0.793343i \(0.708339\pi\)
−0.991443 + 0.130543i \(0.958328\pi\)
\(734\) 288.997i 0.393728i
\(735\) 0 0
\(736\) 134.304 0.182478
\(737\) −429.968 744.726i −0.583403 1.01048i
\(738\) −209.088 120.717i −0.283317 0.163573i
\(739\) −2.66286 + 4.61222i −0.00360333 + 0.00624116i −0.867821 0.496876i \(-0.834480\pi\)
0.864218 + 0.503117i \(0.167814\pi\)
\(740\) 0 0
\(741\) 706.695i 0.953704i
\(742\) 480.162 22.3597i 0.647119 0.0301343i
\(743\) −58.3655 −0.0785539 −0.0392769 0.999228i \(-0.512505\pi\)
−0.0392769 + 0.999228i \(0.512505\pi\)
\(744\) 56.7042 + 98.2146i 0.0762154 + 0.132009i
\(745\) 0 0
\(746\) 398.287 689.854i 0.533897 0.924737i
\(747\) 353.166 203.900i 0.472779 0.272959i
\(748\) 701.621i 0.937996i
\(749\) 124.611 + 194.354i 0.166370 + 0.259485i
\(750\) 0 0
\(751\) −139.145 241.006i −0.185279 0.320913i 0.758391 0.651800i \(-0.225986\pi\)
−0.943671 + 0.330886i \(0.892652\pi\)
\(752\) −78.9561 45.5853i −0.104995 0.0606188i
\(753\) −216.994 + 375.844i −0.288172 + 0.499129i
\(754\) −868.094 + 501.194i −1.15132 + 0.664714i
\(755\) 0 0
\(756\) 64.6238 + 33.4032i 0.0854812 + 0.0441841i
\(757\) 59.2916 0.0783244 0.0391622 0.999233i \(-0.487531\pi\)
0.0391622 + 0.999233i \(0.487531\pi\)
\(758\) −212.586 368.209i −0.280456 0.485764i
\(759\) 434.178 + 250.673i 0.572039 + 0.330267i
\(760\) 0 0
\(761\) 788.790 455.408i 1.03652 0.598434i 0.117673 0.993052i \(-0.462457\pi\)
0.918845 + 0.394619i \(0.129123\pi\)
\(762\) 120.799i 0.158528i
\(763\) −487.645 + 943.428i −0.639115 + 1.23647i
\(764\) 356.361 0.466441
\(765\) 0 0
\(766\) −13.2164 7.63051i −0.0172538 0.00996150i
\(767\) −914.531 + 1584.01i −1.19235 + 2.06521i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 660.381i 0.858753i −0.903126 0.429376i \(-0.858733\pi\)
0.903126 0.429376i \(-0.141267\pi\)
\(770\) 0 0
\(771\) −302.522 −0.392376
\(772\) 135.115 + 234.027i 0.175020 + 0.303143i
\(773\) −1201.60 693.744i −1.55446 0.897469i −0.997770 0.0667508i \(-0.978737\pi\)
−0.556693 0.830718i \(-0.687930\pi\)
\(774\) −16.6277 + 28.8001i −0.0214829 + 0.0372094i
\(775\) 0 0
\(776\) 223.440i 0.287938i
\(777\) 16.3917 + 352.002i 0.0210961 + 0.453027i
\(778\) −185.863 −0.238898
\(779\) 457.167 + 791.837i 0.586864 + 1.01648i
\(780\) 0 0
\(781\) −39.1047 + 67.7314i −0.0500701 + 0.0867239i
\(782\) −836.702 + 483.070i −1.06995 + 0.617737i
\(783\) 145.036i 0.185231i
\(784\) −113.350 159.899i −0.144580 0.203953i
\(785\) 0 0
\(786\) 17.9452 + 31.0821i 0.0228311 + 0.0395446i
\(787\) 1188.71 + 686.304i 1.51044 + 0.872050i 0.999926 + 0.0121785i \(0.00387664\pi\)
0.510510 + 0.859872i \(0.329457\pi\)
\(788\) 64.7529 112.155i 0.0821737 0.142329i
\(789\) 31.3251 18.0856i 0.0397023 0.0229221i
\(790\) 0 0
\(791\) −295.017 + 13.7381i −0.372967 + 0.0173680i
\(792\) −103.449 −0.130618
\(793\) −1455.14 2520.37i −1.83498 3.17827i
\(794\) −686.995 396.636i −0.865232 0.499542i
\(795\) 0 0
\(796\) −233.514 + 134.819i −0.293359 + 0.169371i
\(797\) 64.7049i 0.0811855i −0.999176 0.0405928i \(-0.987075\pi\)
0.999176 0.0405928i \(-0.0129246\pi\)
\(798\) −148.698 231.921i −0.186338 0.290628i
\(799\) 655.852 0.820841
\(800\) 0 0
\(801\) 374.716 + 216.342i 0.467810 + 0.270090i
\(802\) −241.656 + 418.560i −0.301317 + 0.521896i
\(803\) −417.647 + 241.129i −0.520108 + 0.300285i
\(804\) 244.340i 0.303905i
\(805\) 0 0
\(806\) −831.349 −1.03145
\(807\) 0.255741 + 0.442957i 0.000316904 + 0.000548894i
\(808\) −114.474 66.0918i −0.141676 0.0817968i
\(809\) −268.427 + 464.929i −0.331801 + 0.574696i −0.982865 0.184327i \(-0.940990\pi\)
0.651064 + 0.759023i \(0.274323\pi\)
\(810\) 0 0
\(811\) 1472.44i 1.81559i 0.419418 + 0.907793i \(0.362234\pi\)
−0.419418 + 0.907793i \(0.637766\pi\)
\(812\) 179.431 347.139i 0.220974 0.427511i
\(813\) 568.281 0.698993
\(814\) −250.556 433.975i −0.307808 0.533139i
\(815\) 0 0
\(816\) 99.6785 172.648i 0.122155 0.211579i
\(817\) 109.069 62.9709i 0.133499 0.0770757i
\(818\) 32.1362i 0.0392863i
\(819\) −448.923 + 287.829i −0.548136 + 0.351440i
\(820\) 0 0
\(821\) 114.603 + 198.498i 0.139590 + 0.241776i 0.927341 0.374217i \(-0.122088\pi\)
−0.787752 + 0.615993i \(0.788755\pi\)
\(822\) 36.5318 + 21.0916i 0.0444425 + 0.0256589i
\(823\) −7.10905 + 12.3132i −0.00863797 + 0.0149614i −0.870312 0.492501i \(-0.836083\pi\)
0.861674 + 0.507462i \(0.169416\pi\)
\(824\) 407.357 235.188i 0.494365 0.285422i
\(825\) 0 0
\(826\) −33.1681 712.267i −0.0401551 0.862308i
\(827\) 136.480 0.165030 0.0825151 0.996590i \(-0.473705\pi\)
0.0825151 + 0.996590i \(0.473705\pi\)
\(828\) 71.2255 + 123.366i 0.0860212 + 0.148993i
\(829\) 254.554 + 146.967i 0.307061 + 0.177282i 0.645611 0.763667i \(-0.276603\pi\)
−0.338549 + 0.940949i \(0.609936\pi\)
\(830\) 0 0
\(831\) −754.455 + 435.585i −0.907888 + 0.524169i
\(832\) 203.151i 0.244172i
\(833\) 1281.29 + 588.453i 1.53817 + 0.706426i
\(834\) −76.5739 −0.0918153
\(835\) 0 0
\(836\) 339.286 + 195.887i 0.405844 + 0.234314i
\(837\) −60.1439 + 104.172i −0.0718565 + 0.124459i
\(838\) 425.446 245.631i 0.507692 0.293116i
\(839\) 658.476i 0.784834i −0.919787 0.392417i \(-0.871639\pi\)
0.919787 0.392417i \(-0.128361\pi\)
\(840\) 0 0
\(841\) −61.9146 −0.0736202
\(842\) 240.686 + 416.880i 0.285850 + 0.495107i
\(843\) 396.721 + 229.047i 0.470607 + 0.271705i
\(844\) 116.352 201.528i 0.137858 0.238777i
\(845\) 0 0
\(846\) 96.7010i 0.114304i
\(847\) 104.414 + 162.853i 0.123275 + 0.192271i
\(848\) −194.225 −0.229039
\(849\) 399.801 + 692.475i 0.470908 + 0.815636i
\(850\) 0 0
\(851\) −345.018 + 597.588i −0.405426 + 0.702219i
\(852\) −19.2450 + 11.1111i −0.0225881 + 0.0130412i
\(853\) 1026.25i 1.20310i 0.798834 + 0.601552i \(0.205451\pi\)
−0.798834 + 0.601552i \(0.794549\pi\)
\(854\) 1007.86 + 520.950i 1.18016 + 0.610011i
\(855\) 0 0
\(856\) −46.6431 80.7881i −0.0544896 0.0943787i
\(857\) −1405.85 811.667i −1.64043 0.947103i −0.980680 0.195619i \(-0.937328\pi\)
−0.659751 0.751484i \(-0.729338\pi\)
\(858\) 379.172 656.745i 0.441925 0.765437i
\(859\) 894.833 516.632i 1.04171 0.601434i 0.121396 0.992604i \(-0.461263\pi\)
0.920318 + 0.391170i \(0.127930\pi\)
\(860\) 0 0
\(861\) −316.809 + 612.919i −0.367955 + 0.711868i
\(862\) −61.6231 −0.0714885
\(863\) −141.684 245.403i −0.164176 0.284361i 0.772187 0.635396i \(-0.219163\pi\)
−0.936362 + 0.351035i \(0.885830\pi\)
\(864\) −25.4558 14.6969i −0.0294628 0.0170103i
\(865\) 0 0
\(866\) 373.081 215.399i 0.430810 0.248728i
\(867\) 933.547i 1.07675i
\(868\) 272.830 174.926i 0.314320 0.201528i
\(869\) −668.064 −0.768773
\(870\) 0 0
\(871\) 1551.18 + 895.575i 1.78092 + 1.02822i
\(872\) 214.557 371.624i 0.246052 0.426174i
\(873\) −205.243 + 118.497i −0.235100 + 0.135735i
\(874\) 539.476i 0.617250i
\(875\) 0 0
\(876\) −137.027 −0.156424
\(877\) −254.904 441.507i −0.290655 0.503429i 0.683310 0.730128i \(-0.260540\pi\)
−0.973965 + 0.226700i \(0.927206\pi\)
\(878\) 762.454 + 440.203i 0.868398 + 0.501370i
\(879\) 116.730 202.182i 0.132798 0.230014i
\(880\) 0 0
\(881\) 846.387i 0.960711i −0.877074 0.480356i \(-0.840508\pi\)
0.877074 0.480356i \(-0.159492\pi\)
\(882\) 86.7636 188.918i 0.0983714 0.214193i
\(883\) 350.886 0.397379 0.198690 0.980062i \(-0.436331\pi\)
0.198690 + 0.980062i \(0.436331\pi\)
\(884\) 730.700 + 1265.61i 0.826584 + 1.43169i
\(885\) 0 0
\(886\) −60.5318 + 104.844i −0.0683203 + 0.118334i
\(887\) −434.565 + 250.896i −0.489927 + 0.282859i −0.724544 0.689228i \(-0.757950\pi\)
0.234617 + 0.972088i \(0.424616\pi\)
\(888\) 142.384i 0.160343i
\(889\) 344.837 16.0580i 0.387893 0.0180630i
\(890\) 0 0
\(891\) −54.8624 95.0244i −0.0615739 0.106649i
\(892\) 52.0500 + 30.0511i 0.0583520 + 0.0336896i
\(893\) −183.108 + 317.153i −0.205048 + 0.355154i
\(894\) 303.725 175.355i 0.339737 0.196147i
\(895\) 0 0
\(896\) 42.7455 + 66.6695i 0.0477070 + 0.0744079i
\(897\) −1044.25 −1.16416
\(898\) 101.558 + 175.903i 0.113093 + 0.195883i
\(899\) 559.581 + 323.074i 0.622448 + 0.359371i
\(900\) 0 0
\(901\) 1210.00 698.596i 1.34296 0.775356i
\(902\) 981.158i 1.08776i
\(903\) 84.4243 + 43.6378i 0.0934932 + 0.0483254i
\(904\) 119.334 0.132007
\(905\) 0 0
\(906\) 98.3392 + 56.7762i 0.108542 + 0.0626668i
\(907\) 831.238 1439.75i 0.916470 1.58737i 0.111735 0.993738i \(-0.464359\pi\)
0.804735 0.593634i \(-0.202307\pi\)
\(908\) 245.397 141.680i 0.270261 0.156035i
\(909\) 140.202i 0.154238i
\(910\) 0 0
\(911\) −143.213 −0.157204 −0.0786019 0.996906i \(-0.525046\pi\)
−0.0786019 + 0.996906i \(0.525046\pi\)
\(912\) 55.6588 + 96.4038i 0.0610294 + 0.105706i
\(913\) 1435.22 + 828.626i 1.57199 + 0.907586i
\(914\) −16.5783 + 28.7144i −0.0181381 + 0.0314162i
\(915\) 0 0
\(916\) 435.665i 0.475617i
\(917\) 86.3428 55.3591i 0.0941579 0.0603698i
\(918\) 211.450 0.230338
\(919\) −435.504 754.315i −0.473889 0.820800i 0.525664 0.850692i \(-0.323817\pi\)
−0.999553 + 0.0298922i \(0.990484\pi\)
\(920\) 0 0
\(921\) 20.5453 35.5856i 0.0223077 0.0386380i
\(922\) 208.751 120.522i 0.226411 0.130718i
\(923\) 162.902i 0.176492i
\(924\) 13.7518 + 295.311i 0.0148828 + 0.319601i
\(925\) 0 0
\(926\) 336.492 + 582.820i 0.363382 + 0.629396i
\(927\) 432.067 + 249.454i 0.466092 + 0.269098i
\(928\) −78.9473 + 136.741i −0.0850726 + 0.147350i
\(929\) 1308.36 755.381i 1.40835 0.813112i 0.413123 0.910675i \(-0.364438\pi\)
0.995229 + 0.0975629i \(0.0311047\pi\)
\(930\) 0 0
\(931\) −642.287 + 455.309i −0.689889 + 0.489053i
\(932\) 8.50390 0.00912435
\(933\) 245.097 + 424.520i 0.262697 + 0.455005i
\(934\) −267.071 154.193i −0.285943 0.165089i
\(935\) 0 0
\(936\) 186.606 107.737i 0.199365 0.115104i
\(937\) 485.168i 0.517788i 0.965906 + 0.258894i \(0.0833581\pi\)
−0.965906 + 0.258894i \(0.916642\pi\)
\(938\) −697.504 + 32.4806i −0.743607 + 0.0346275i
\(939\) −735.044 −0.782794
\(940\) 0 0
\(941\) 215.272 + 124.288i 0.228770 + 0.132080i 0.610004 0.792398i \(-0.291168\pi\)
−0.381235 + 0.924478i \(0.624501\pi\)
\(942\) −101.053 + 175.029i −0.107275 + 0.185806i
\(943\) −1170.06 + 675.533i −1.24078 + 0.716366i
\(944\) 288.111i 0.305202i
\(945\) 0 0
\(946\) −135.146 −0.142861
\(947\) 681.531 + 1180.45i 0.719674 + 1.24651i 0.961129 + 0.276100i \(0.0890421\pi\)
−0.241455 + 0.970412i \(0.577625\pi\)
\(948\) −164.391 94.9110i −0.173408 0.100117i
\(949\) 502.244 869.913i 0.529235 0.916663i
\(950\) 0 0
\(951\) 48.7193i 0.0512296i
\(952\) −506.100 261.596i −0.531617 0.274786i
\(953\) −879.838 −0.923230 −0.461615 0.887080i \(-0.652730\pi\)
−0.461615 + 0.887080i \(0.652730\pi\)
\(954\) −103.003 178.407i −0.107970 0.187010i
\(955\) 0 0
\(956\) −261.513 + 452.953i −0.273549 + 0.473800i
\(957\) −510.441 + 294.703i −0.533376 + 0.307945i
\(958\) 788.598i 0.823171i
\(959\) 55.3528 107.089i 0.0577193 0.111667i
\(960\) 0 0
\(961\) −212.552 368.152i −0.221178 0.383092i
\(962\) 903.922 + 521.880i 0.939628 + 0.542495i
\(963\) 49.4724 85.6888i 0.0513732 0.0889811i
\(964\) 173.031 99.8996i 0.179493 0.103630i
\(965\) 0 0
\(966\) 342.699 219.723i 0.354760 0.227456i
\(967\) 186.884 0.193262 0.0966310 0.995320i \(-0.469193\pi\)
0.0966310 + 0.995320i \(0.469193\pi\)
\(968\) −39.0832 67.6940i −0.0403752 0.0699318i
\(969\) −693.498 400.391i −0.715684 0.413200i
\(970\) 0 0
\(971\) −159.547 + 92.1145i −0.164312 + 0.0948656i −0.579901 0.814687i \(-0.696909\pi\)
0.415589 + 0.909553i \(0.363575\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 10.1791 + 218.591i 0.0104616 + 0.224657i
\(974\) 730.079 0.749568
\(975\) 0 0
\(976\) −397.005 229.211i −0.406767 0.234847i
\(977\) −554.021 + 959.592i −0.567063 + 0.982183i 0.429791 + 0.902928i \(0.358587\pi\)
−0.996854 + 0.0792543i \(0.974746\pi\)
\(978\) −522.728 + 301.797i −0.534487 + 0.308586i
\(979\) 1758.38i 1.79609i
\(980\) 0 0
\(981\) 455.145 0.463960
\(982\) −86.6813 150.136i −0.0882702 0.152888i
\(983\) 1216.86 + 702.557i 1.23791 + 0.714707i 0.968666 0.248365i \(-0.0798934\pi\)
0.269242 + 0.963072i \(0.413227\pi\)
\(984\) 139.392 241.434i 0.141658 0.245360i
\(985\) 0 0
\(986\) 1135.84i 1.15197i
\(987\) −276.047 + 12.8547i −0.279683 + 0.0130240i
\(988\) −816.021 −0.825932
\(989\) 93.0489 + 161.165i 0.0940838 + 0.162958i
\(990\) 0 0
\(991\) −218.084 + 377.732i −0.220064 + 0.381162i −0.954827 0.297161i \(-0.903960\pi\)
0.734763 + 0.678324i \(0.237293\pi\)
\(992\) −113.408 + 65.4764i −0.114323 + 0.0660045i
\(993\) 453.591i 0.456788i
\(994\) 34.2766 + 53.4607i 0.0344835 + 0.0537834i
\(995\) 0 0
\(996\) 235.444 + 407.801i 0.236389 + 0.409438i
\(997\) 77.2090 + 44.5767i 0.0774414 + 0.0447108i 0.538221 0.842804i \(-0.319097\pi\)
−0.460779 + 0.887515i \(0.652430\pi\)
\(998\) −265.200 + 459.340i −0.265731 + 0.460260i
\(999\) 130.789 75.5108i 0.130919 0.0755864i
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 1050.3.p.i.451.1 16
5.2 odd 4 1050.3.q.e.199.9 32
5.3 odd 4 1050.3.q.e.199.8 32
5.4 even 2 210.3.o.b.31.6 16
7.5 odd 6 inner 1050.3.p.i.901.1 16
15.14 odd 2 630.3.v.c.451.4 16
35.4 even 6 1470.3.f.d.391.6 16
35.12 even 12 1050.3.q.e.649.8 32
35.19 odd 6 210.3.o.b.61.6 yes 16
35.24 odd 6 1470.3.f.d.391.4 16
35.33 even 12 1050.3.q.e.649.9 32
105.89 even 6 630.3.v.c.271.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.o.b.31.6 16 5.4 even 2
210.3.o.b.61.6 yes 16 35.19 odd 6
630.3.v.c.271.4 16 105.89 even 6
630.3.v.c.451.4 16 15.14 odd 2
1050.3.p.i.451.1 16 1.1 even 1 trivial
1050.3.p.i.901.1 16 7.5 odd 6 inner
1050.3.q.e.199.8 32 5.3 odd 4
1050.3.q.e.199.9 32 5.2 odd 4
1050.3.q.e.649.8 32 35.12 even 12
1050.3.q.e.649.9 32 35.33 even 12
1470.3.f.d.391.4 16 35.24 odd 6
1470.3.f.d.391.6 16 35.4 even 6