Properties

Label 450.2.h.g.361.3
Level $450$
Weight $2$
Character 450.361
Analytic conductor $3.593$
Analytic rank $0$
Dimension $12$
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] = [450,2,Mod(91,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} - 3250 x^{3} + 3750 x^{2} - 3125 x + 15625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.3
Root \(-1.38239 - 1.75756i\) of defining polynomial
Character \(\chi\) \(=\) 450.361
Dual form 450.2.h.g.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(1.38239 + 1.75756i) q^{5} -0.447412 q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.15144 + 0.609344i) q^{10} +(4.42816 - 3.21725i) q^{11} +(-0.573372 - 0.416579i) q^{13} +(-0.361964 + 0.262982i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.133697 + 0.411479i) q^{17} +(2.49304 + 7.67280i) q^{19} +(2.09872 - 0.771616i) q^{20} +(1.69141 - 5.20561i) q^{22} +(4.65186 - 3.37978i) q^{23} +(-1.17800 + 4.85925i) q^{25} -0.708727 q^{26} +(-0.138258 + 0.425514i) q^{28} +(1.03259 - 3.17797i) q^{29} +(-0.407310 - 1.25357i) q^{31} -1.00000 q^{32} +(0.350025 + 0.254308i) q^{34} +(-0.618497 - 0.786351i) q^{35} +(-8.14595 - 5.91838i) q^{37} +(6.52687 + 4.74205i) q^{38} +(1.24435 - 1.85784i) q^{40} +(-4.80242 - 3.48916i) q^{41} -7.09283 q^{43} +(-1.69141 - 5.20561i) q^{44} +(1.77685 - 5.46859i) q^{46} +(-2.83769 + 8.73350i) q^{47} -6.79982 q^{49} +(1.90317 + 4.62363i) q^{50} +(-0.573372 + 0.416579i) q^{52} +(-0.210809 + 0.648802i) q^{53} +(11.7759 + 3.33525i) q^{55} +(0.138258 + 0.425514i) q^{56} +(-1.03259 - 3.17797i) q^{58} +(2.75539 + 2.00191i) q^{59} +(4.91755 - 3.57281i) q^{61} +(-1.06635 - 0.774750i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-0.0604623 - 1.58361i) q^{65} +(0.528998 + 1.62809i) q^{67} +0.432654 q^{68} +(-0.962580 - 0.272628i) q^{70} +(0.558490 - 1.71886i) q^{71} +(-10.0932 + 7.33316i) q^{73} -10.0689 q^{74} +8.06766 q^{76} +(-1.98121 + 1.43943i) q^{77} +(-2.72171 + 8.37656i) q^{79} +(-0.0853112 - 2.23444i) q^{80} -5.93612 q^{82} +(-0.545222 - 1.67802i) q^{83} +(-0.538374 + 0.803804i) q^{85} +(-5.73822 + 4.16906i) q^{86} +(-4.42816 - 3.21725i) q^{88} +(-11.2689 + 8.18730i) q^{89} +(0.256533 + 0.186382i) q^{91} +(-1.77685 - 5.46859i) q^{92} +(2.83769 + 8.73350i) q^{94} +(-10.0390 + 14.9885i) q^{95} +(4.04585 - 12.4519i) q^{97} +(-5.50117 + 3.99684i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) 0 0
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 1.38239 + 1.75756i 0.618223 + 0.786003i
\(6\) 0 0
\(7\) −0.447412 −0.169106 −0.0845529 0.996419i \(-0.526946\pi\)
−0.0845529 + 0.996419i \(0.526946\pi\)
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0 0
\(10\) 2.15144 + 0.609344i 0.680345 + 0.192692i
\(11\) 4.42816 3.21725i 1.33514 0.970036i 0.335532 0.942029i \(-0.391084\pi\)
0.999608 0.0280073i \(-0.00891617\pi\)
\(12\) 0 0
\(13\) −0.573372 0.416579i −0.159025 0.115538i 0.505427 0.862869i \(-0.331335\pi\)
−0.664452 + 0.747331i \(0.731335\pi\)
\(14\) −0.361964 + 0.262982i −0.0967389 + 0.0702849i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 0.133697 + 0.411479i 0.0324264 + 0.0997982i 0.965960 0.258692i \(-0.0832916\pi\)
−0.933533 + 0.358490i \(0.883292\pi\)
\(18\) 0 0
\(19\) 2.49304 + 7.67280i 0.571944 + 1.76026i 0.646358 + 0.763034i \(0.276291\pi\)
−0.0744148 + 0.997227i \(0.523709\pi\)
\(20\) 2.09872 0.771616i 0.469287 0.172539i
\(21\) 0 0
\(22\) 1.69141 5.20561i 0.360609 1.10984i
\(23\) 4.65186 3.37978i 0.969981 0.704732i 0.0145336 0.999894i \(-0.495374\pi\)
0.955447 + 0.295162i \(0.0953737\pi\)
\(24\) 0 0
\(25\) −1.17800 + 4.85925i −0.235600 + 0.971850i
\(26\) −0.708727 −0.138993
\(27\) 0 0
\(28\) −0.138258 + 0.425514i −0.0261283 + 0.0804145i
\(29\) 1.03259 3.17797i 0.191746 0.590135i −0.808253 0.588836i \(-0.799587\pi\)
0.999999 0.00129904i \(-0.000413496\pi\)
\(30\) 0 0
\(31\) −0.407310 1.25357i −0.0731550 0.225148i 0.907793 0.419419i \(-0.137766\pi\)
−0.980948 + 0.194271i \(0.937766\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0.350025 + 0.254308i 0.0600287 + 0.0436134i
\(35\) −0.618497 0.786351i −0.104545 0.132918i
\(36\) 0 0
\(37\) −8.14595 5.91838i −1.33919 0.972976i −0.999473 0.0324464i \(-0.989670\pi\)
−0.339713 0.940529i \(-0.610330\pi\)
\(38\) 6.52687 + 4.74205i 1.05880 + 0.769262i
\(39\) 0 0
\(40\) 1.24435 1.85784i 0.196749 0.293751i
\(41\) −4.80242 3.48916i −0.750012 0.544916i 0.145819 0.989311i \(-0.453418\pi\)
−0.895831 + 0.444396i \(0.853418\pi\)
\(42\) 0 0
\(43\) −7.09283 −1.08165 −0.540823 0.841136i \(-0.681887\pi\)
−0.540823 + 0.841136i \(0.681887\pi\)
\(44\) −1.69141 5.20561i −0.254989 0.784776i
\(45\) 0 0
\(46\) 1.77685 5.46859i 0.261983 0.806300i
\(47\) −2.83769 + 8.73350i −0.413919 + 1.27391i 0.499295 + 0.866432i \(0.333592\pi\)
−0.913214 + 0.407480i \(0.866408\pi\)
\(48\) 0 0
\(49\) −6.79982 −0.971403
\(50\) 1.90317 + 4.62363i 0.269149 + 0.653880i
\(51\) 0 0
\(52\) −0.573372 + 0.416579i −0.0795124 + 0.0577691i
\(53\) −0.210809 + 0.648802i −0.0289568 + 0.0891198i −0.964490 0.264118i \(-0.914919\pi\)
0.935534 + 0.353238i \(0.114919\pi\)
\(54\) 0 0
\(55\) 11.7759 + 3.33525i 1.58787 + 0.449725i
\(56\) 0.138258 + 0.425514i 0.0184755 + 0.0568617i
\(57\) 0 0
\(58\) −1.03259 3.17797i −0.135585 0.417288i
\(59\) 2.75539 + 2.00191i 0.358721 + 0.260626i 0.752518 0.658571i \(-0.228839\pi\)
−0.393798 + 0.919197i \(0.628839\pi\)
\(60\) 0 0
\(61\) 4.91755 3.57281i 0.629628 0.457451i −0.226644 0.973978i \(-0.572775\pi\)
0.856271 + 0.516527i \(0.172775\pi\)
\(62\) −1.06635 0.774750i −0.135427 0.0983933i
\(63\) 0 0
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −0.0604623 1.58361i −0.00749943 0.196422i
\(66\) 0 0
\(67\) 0.528998 + 1.62809i 0.0646274 + 0.198903i 0.978156 0.207871i \(-0.0666536\pi\)
−0.913529 + 0.406774i \(0.866654\pi\)
\(68\) 0.432654 0.0524670
\(69\) 0 0
\(70\) −0.962580 0.272628i −0.115050 0.0325852i
\(71\) 0.558490 1.71886i 0.0662806 0.203991i −0.912431 0.409230i \(-0.865797\pi\)
0.978712 + 0.205240i \(0.0657973\pi\)
\(72\) 0 0
\(73\) −10.0932 + 7.33316i −1.18132 + 0.858281i −0.992320 0.123695i \(-0.960525\pi\)
−0.189003 + 0.981977i \(0.560525\pi\)
\(74\) −10.0689 −1.17049
\(75\) 0 0
\(76\) 8.06766 0.925424
\(77\) −1.98121 + 1.43943i −0.225780 + 0.164039i
\(78\) 0 0
\(79\) −2.72171 + 8.37656i −0.306216 + 0.942436i 0.673004 + 0.739638i \(0.265003\pi\)
−0.979221 + 0.202798i \(0.934997\pi\)
\(80\) −0.0853112 2.23444i −0.00953808 0.249818i
\(81\) 0 0
\(82\) −5.93612 −0.655534
\(83\) −0.545222 1.67802i −0.0598459 0.184187i 0.916664 0.399658i \(-0.130871\pi\)
−0.976510 + 0.215471i \(0.930871\pi\)
\(84\) 0 0
\(85\) −0.538374 + 0.803804i −0.0583949 + 0.0871848i
\(86\) −5.73822 + 4.16906i −0.618768 + 0.449561i
\(87\) 0 0
\(88\) −4.42816 3.21725i −0.472043 0.342960i
\(89\) −11.2689 + 8.18730i −1.19450 + 0.867852i −0.993732 0.111787i \(-0.964342\pi\)
−0.200764 + 0.979640i \(0.564342\pi\)
\(90\) 0 0
\(91\) 0.256533 + 0.186382i 0.0268920 + 0.0195382i
\(92\) −1.77685 5.46859i −0.185250 0.570140i
\(93\) 0 0
\(94\) 2.83769 + 8.73350i 0.292685 + 0.900792i
\(95\) −10.0390 + 14.9885i −1.02998 + 1.53778i
\(96\) 0 0
\(97\) 4.04585 12.4519i 0.410794 1.26429i −0.505165 0.863023i \(-0.668568\pi\)
0.915959 0.401272i \(-0.131432\pi\)
\(98\) −5.50117 + 3.99684i −0.555702 + 0.403741i
\(99\) 0 0
\(100\) 4.25740 + 2.62194i 0.425740 + 0.262194i
\(101\) 11.9062 1.18471 0.592354 0.805678i \(-0.298199\pi\)
0.592354 + 0.805678i \(0.298199\pi\)
\(102\) 0 0
\(103\) −1.66263 + 5.11705i −0.163824 + 0.504198i −0.998948 0.0458642i \(-0.985396\pi\)
0.835124 + 0.550062i \(0.185396\pi\)
\(104\) −0.219009 + 0.674039i −0.0214756 + 0.0660950i
\(105\) 0 0
\(106\) 0.210809 + 0.648802i 0.0204755 + 0.0630172i
\(107\) −13.9215 −1.34584 −0.672921 0.739715i \(-0.734960\pi\)
−0.672921 + 0.739715i \(0.734960\pi\)
\(108\) 0 0
\(109\) 5.60018 + 4.06877i 0.536400 + 0.389718i 0.822746 0.568409i \(-0.192441\pi\)
−0.286346 + 0.958126i \(0.592441\pi\)
\(110\) 11.4873 4.22344i 1.09527 0.402689i
\(111\) 0 0
\(112\) 0.361964 + 0.262982i 0.0342024 + 0.0248495i
\(113\) −11.1677 8.11381i −1.05057 0.763283i −0.0782487 0.996934i \(-0.524933\pi\)
−0.972321 + 0.233651i \(0.924933\pi\)
\(114\) 0 0
\(115\) 12.3708 + 3.50374i 1.15359 + 0.326726i
\(116\) −2.70335 1.96410i −0.250999 0.182362i
\(117\) 0 0
\(118\) 3.40584 0.313533
\(119\) −0.0598178 0.184100i −0.00548349 0.0168764i
\(120\) 0 0
\(121\) 5.85873 18.0313i 0.532612 1.63921i
\(122\) 1.87834 5.78092i 0.170057 0.523380i
\(123\) 0 0
\(124\) −1.31808 −0.118367
\(125\) −10.1689 + 4.64697i −0.909530 + 0.415638i
\(126\) 0 0
\(127\) 8.62222 6.26441i 0.765098 0.555876i −0.135372 0.990795i \(-0.543223\pi\)
0.900470 + 0.434919i \(0.143223\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) −0.979736 1.24563i −0.0859285 0.109249i
\(131\) −3.01855 9.29014i −0.263732 0.811683i −0.991983 0.126373i \(-0.959666\pi\)
0.728251 0.685311i \(-0.240334\pi\)
\(132\) 0 0
\(133\) −1.11542 3.43290i −0.0967189 0.297670i
\(134\) 1.38494 + 1.00621i 0.119640 + 0.0869237i
\(135\) 0 0
\(136\) 0.350025 0.254308i 0.0300144 0.0218067i
\(137\) 12.7881 + 9.29107i 1.09256 + 0.793790i 0.979829 0.199836i \(-0.0640409\pi\)
0.112729 + 0.993626i \(0.464041\pi\)
\(138\) 0 0
\(139\) −8.10149 + 5.88608i −0.687159 + 0.499251i −0.875725 0.482810i \(-0.839616\pi\)
0.188566 + 0.982061i \(0.439616\pi\)
\(140\) −0.938990 + 0.345230i −0.0793591 + 0.0291772i
\(141\) 0 0
\(142\) −0.558490 1.71886i −0.0468674 0.144243i
\(143\) −3.87922 −0.324397
\(144\) 0 0
\(145\) 7.01290 2.57837i 0.582390 0.214122i
\(146\) −3.85527 + 11.8653i −0.319064 + 0.981979i
\(147\) 0 0
\(148\) −8.14595 + 5.91838i −0.669593 + 0.486488i
\(149\) 15.8758 1.30060 0.650299 0.759678i \(-0.274644\pi\)
0.650299 + 0.759678i \(0.274644\pi\)
\(150\) 0 0
\(151\) 17.9787 1.46308 0.731541 0.681797i \(-0.238801\pi\)
0.731541 + 0.681797i \(0.238801\pi\)
\(152\) 6.52687 4.74205i 0.529399 0.384631i
\(153\) 0 0
\(154\) −0.756755 + 2.32905i −0.0609810 + 0.187680i
\(155\) 1.64016 2.44879i 0.131741 0.196692i
\(156\) 0 0
\(157\) −20.7997 −1.66000 −0.830000 0.557763i \(-0.811660\pi\)
−0.830000 + 0.557763i \(0.811660\pi\)
\(158\) 2.72171 + 8.37656i 0.216528 + 0.666403i
\(159\) 0 0
\(160\) −1.38239 1.75756i −0.109287 0.138947i
\(161\) −2.08130 + 1.51215i −0.164029 + 0.119174i
\(162\) 0 0
\(163\) −4.54778 3.30416i −0.356210 0.258802i 0.395260 0.918569i \(-0.370655\pi\)
−0.751469 + 0.659768i \(0.770655\pi\)
\(164\) −4.80242 + 3.48916i −0.375006 + 0.272458i
\(165\) 0 0
\(166\) −1.42741 1.03707i −0.110788 0.0804925i
\(167\) 0.628797 + 1.93524i 0.0486578 + 0.149753i 0.972433 0.233181i \(-0.0749135\pi\)
−0.923776 + 0.382934i \(0.874914\pi\)
\(168\) 0 0
\(169\) −3.86200 11.8860i −0.297077 0.914310i
\(170\) 0.0369102 + 0.966740i 0.00283088 + 0.0741455i
\(171\) 0 0
\(172\) −2.19180 + 6.74568i −0.167124 + 0.514353i
\(173\) 3.75509 2.72823i 0.285494 0.207424i −0.435816 0.900036i \(-0.643540\pi\)
0.721310 + 0.692612i \(0.243540\pi\)
\(174\) 0 0
\(175\) 0.527051 2.17409i 0.0398413 0.164345i
\(176\) −5.47350 −0.412581
\(177\) 0 0
\(178\) −4.30432 + 13.2473i −0.322622 + 0.992930i
\(179\) 5.14952 15.8486i 0.384893 1.18458i −0.551664 0.834066i \(-0.686007\pi\)
0.936558 0.350514i \(-0.113993\pi\)
\(180\) 0 0
\(181\) 2.03554 + 6.26475i 0.151301 + 0.465655i 0.997767 0.0667863i \(-0.0212746\pi\)
−0.846467 + 0.532442i \(0.821275\pi\)
\(182\) 0.317093 0.0235045
\(183\) 0 0
\(184\) −4.65186 3.37978i −0.342940 0.249160i
\(185\) −0.858994 22.4985i −0.0631545 1.65412i
\(186\) 0 0
\(187\) 1.91586 + 1.39195i 0.140102 + 0.101790i
\(188\) 7.42916 + 5.39760i 0.541827 + 0.393661i
\(189\) 0 0
\(190\) 0.688261 + 18.0267i 0.0499317 + 1.30779i
\(191\) 7.30988 + 5.31094i 0.528924 + 0.384286i 0.819955 0.572428i \(-0.193998\pi\)
−0.291031 + 0.956714i \(0.593998\pi\)
\(192\) 0 0
\(193\) −16.1970 −1.16589 −0.582944 0.812512i \(-0.698099\pi\)
−0.582944 + 0.812512i \(0.698099\pi\)
\(194\) −4.04585 12.4519i −0.290475 0.893991i
\(195\) 0 0
\(196\) −2.10126 + 6.46702i −0.150090 + 0.461930i
\(197\) −2.93651 + 9.03765i −0.209218 + 0.643906i 0.790296 + 0.612725i \(0.209927\pi\)
−0.999514 + 0.0311807i \(0.990073\pi\)
\(198\) 0 0
\(199\) 17.2676 1.22407 0.612033 0.790832i \(-0.290352\pi\)
0.612033 + 0.790832i \(0.290352\pi\)
\(200\) 4.98544 0.381245i 0.352524 0.0269581i
\(201\) 0 0
\(202\) 9.63228 6.99826i 0.677725 0.492396i
\(203\) −0.461991 + 1.42186i −0.0324254 + 0.0997952i
\(204\) 0 0
\(205\) −0.506417 13.2639i −0.0353697 0.926391i
\(206\) 1.66263 + 5.11705i 0.115841 + 0.356521i
\(207\) 0 0
\(208\) 0.219009 + 0.674039i 0.0151855 + 0.0467362i
\(209\) 35.7249 + 25.9556i 2.47114 + 1.79539i
\(210\) 0 0
\(211\) −1.18538 + 0.861229i −0.0816049 + 0.0592894i −0.627840 0.778343i \(-0.716061\pi\)
0.546235 + 0.837632i \(0.316061\pi\)
\(212\) 0.551904 + 0.400982i 0.0379049 + 0.0275395i
\(213\) 0 0
\(214\) −11.2627 + 8.18285i −0.769904 + 0.559368i
\(215\) −9.80505 12.4660i −0.668699 0.850177i
\(216\) 0 0
\(217\) 0.182235 + 0.560863i 0.0123709 + 0.0380738i
\(218\) 6.92221 0.468831
\(219\) 0 0
\(220\) 6.81097 10.1689i 0.459196 0.685589i
\(221\) 0.0947550 0.291626i 0.00637391 0.0196169i
\(222\) 0 0
\(223\) 13.5522 9.84622i 0.907520 0.659352i −0.0328667 0.999460i \(-0.510464\pi\)
0.940386 + 0.340108i \(0.110464\pi\)
\(224\) 0.447412 0.0298940
\(225\) 0 0
\(226\) −13.8040 −0.918231
\(227\) 17.3999 12.6418i 1.15487 0.839064i 0.165752 0.986167i \(-0.446995\pi\)
0.989121 + 0.147103i \(0.0469949\pi\)
\(228\) 0 0
\(229\) −5.13908 + 15.8165i −0.339600 + 1.04518i 0.624812 + 0.780775i \(0.285176\pi\)
−0.964412 + 0.264406i \(0.914824\pi\)
\(230\) 12.0677 4.43681i 0.795718 0.292554i
\(231\) 0 0
\(232\) −3.34152 −0.219381
\(233\) −6.74920 20.7719i −0.442155 1.36081i −0.885574 0.464498i \(-0.846235\pi\)
0.443420 0.896314i \(-0.353765\pi\)
\(234\) 0 0
\(235\) −19.2724 + 7.08571i −1.25719 + 0.462221i
\(236\) 2.75539 2.00191i 0.179360 0.130313i
\(237\) 0 0
\(238\) −0.156605 0.113780i −0.0101512 0.00737528i
\(239\) −5.25729 + 3.81964i −0.340066 + 0.247072i −0.744690 0.667411i \(-0.767402\pi\)
0.404624 + 0.914483i \(0.367402\pi\)
\(240\) 0 0
\(241\) −16.3804 11.9011i −1.05515 0.766614i −0.0819684 0.996635i \(-0.526121\pi\)
−0.973186 + 0.230021i \(0.926121\pi\)
\(242\) −5.85873 18.0313i −0.376614 1.15910i
\(243\) 0 0
\(244\) −1.87834 5.78092i −0.120248 0.370086i
\(245\) −9.40000 11.9511i −0.600544 0.763525i
\(246\) 0 0
\(247\) 1.76689 5.43792i 0.112424 0.346007i
\(248\) −1.06635 + 0.774750i −0.0677134 + 0.0491967i
\(249\) 0 0
\(250\) −5.49536 + 9.73658i −0.347557 + 0.615796i
\(251\) 2.36756 0.149439 0.0747196 0.997205i \(-0.476194\pi\)
0.0747196 + 0.997205i \(0.476194\pi\)
\(252\) 0 0
\(253\) 9.72562 29.9324i 0.611444 1.88183i
\(254\) 3.29339 10.1360i 0.206646 0.635991i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 13.0993 0.817115 0.408557 0.912733i \(-0.366032\pi\)
0.408557 + 0.912733i \(0.366032\pi\)
\(258\) 0 0
\(259\) 3.64459 + 2.64795i 0.226464 + 0.164536i
\(260\) −1.52478 0.431859i −0.0945631 0.0267827i
\(261\) 0 0
\(262\) −7.90267 5.74162i −0.488228 0.354719i
\(263\) 5.88793 + 4.27783i 0.363065 + 0.263782i 0.754330 0.656496i \(-0.227962\pi\)
−0.391264 + 0.920278i \(0.627962\pi\)
\(264\) 0 0
\(265\) −1.43172 + 0.526389i −0.0879501 + 0.0323358i
\(266\) −2.92020 2.12165i −0.179049 0.130087i
\(267\) 0 0
\(268\) 1.71187 0.104569
\(269\) −0.236058 0.726511i −0.0143927 0.0442962i 0.943602 0.331081i \(-0.107413\pi\)
−0.957995 + 0.286785i \(0.907413\pi\)
\(270\) 0 0
\(271\) 0.744584 2.29159i 0.0452303 0.139204i −0.925891 0.377791i \(-0.876684\pi\)
0.971121 + 0.238586i \(0.0766839\pi\)
\(272\) 0.133697 0.411479i 0.00810660 0.0249496i
\(273\) 0 0
\(274\) 15.8069 0.954931
\(275\) 10.4170 + 25.3074i 0.628170 + 1.52610i
\(276\) 0 0
\(277\) 8.52655 6.19490i 0.512311 0.372215i −0.301389 0.953501i \(-0.597450\pi\)
0.813699 + 0.581286i \(0.197450\pi\)
\(278\) −3.09449 + 9.52387i −0.185595 + 0.571204i
\(279\) 0 0
\(280\) −0.556738 + 0.831221i −0.0332715 + 0.0496750i
\(281\) 5.62518 + 17.3125i 0.335570 + 1.03278i 0.966440 + 0.256891i \(0.0826980\pi\)
−0.630870 + 0.775888i \(0.717302\pi\)
\(282\) 0 0
\(283\) 8.09320 + 24.9083i 0.481091 + 1.48064i 0.837564 + 0.546339i \(0.183979\pi\)
−0.356473 + 0.934305i \(0.616021\pi\)
\(284\) −1.46215 1.06231i −0.0867624 0.0630366i
\(285\) 0 0
\(286\) −3.13835 + 2.28015i −0.185575 + 0.134828i
\(287\) 2.14866 + 1.56109i 0.126831 + 0.0921483i
\(288\) 0 0
\(289\) 13.6018 9.88232i 0.800109 0.581313i
\(290\) 4.15803 6.20802i 0.244168 0.364548i
\(291\) 0 0
\(292\) 3.85527 + 11.8653i 0.225613 + 0.694364i
\(293\) −23.8637 −1.39413 −0.697067 0.717006i \(-0.745512\pi\)
−0.697067 + 0.717006i \(0.745512\pi\)
\(294\) 0 0
\(295\) 0.290557 + 7.61015i 0.0169169 + 0.443080i
\(296\) −3.11148 + 9.57614i −0.180851 + 0.556602i
\(297\) 0 0
\(298\) 12.8438 9.33157i 0.744022 0.540563i
\(299\) −4.07519 −0.235675
\(300\) 0 0
\(301\) 3.17341 0.182913
\(302\) 14.5450 10.5676i 0.836973 0.608097i
\(303\) 0 0
\(304\) 2.49304 7.67280i 0.142986 0.440065i
\(305\) 13.0774 + 3.70385i 0.748808 + 0.212082i
\(306\) 0 0
\(307\) −18.8333 −1.07487 −0.537436 0.843304i \(-0.680607\pi\)
−0.537436 + 0.843304i \(0.680607\pi\)
\(308\) 0.756755 + 2.32905i 0.0431201 + 0.132710i
\(309\) 0 0
\(310\) −0.112447 2.94518i −0.00638657 0.167275i
\(311\) 24.9160 18.1025i 1.41285 1.02650i 0.419955 0.907545i \(-0.362046\pi\)
0.992900 0.118954i \(-0.0379542\pi\)
\(312\) 0 0
\(313\) 13.8105 + 10.0339i 0.780616 + 0.567151i 0.905164 0.425063i \(-0.139748\pi\)
−0.124548 + 0.992214i \(0.539748\pi\)
\(314\) −16.8273 + 12.2258i −0.949622 + 0.689941i
\(315\) 0 0
\(316\) 7.12553 + 5.17700i 0.400842 + 0.291229i
\(317\) −8.42991 25.9446i −0.473471 1.45719i −0.848009 0.529982i \(-0.822199\pi\)
0.374538 0.927212i \(-0.377801\pi\)
\(318\) 0 0
\(319\) −5.65186 17.3946i −0.316444 0.973913i
\(320\) −2.15144 0.609344i −0.120269 0.0340634i
\(321\) 0 0
\(322\) −0.794985 + 2.44671i −0.0443028 + 0.136350i
\(323\) −2.82388 + 2.05167i −0.157125 + 0.114158i
\(324\) 0 0
\(325\) 2.69970 2.29543i 0.149752 0.127327i
\(326\) −5.62137 −0.311339
\(327\) 0 0
\(328\) −1.83436 + 5.64558i −0.101286 + 0.311725i
\(329\) 1.26961 3.90747i 0.0699961 0.215426i
\(330\) 0 0
\(331\) 3.85194 + 11.8551i 0.211722 + 0.651613i 0.999370 + 0.0354879i \(0.0112985\pi\)
−0.787648 + 0.616125i \(0.788701\pi\)
\(332\) −1.76437 −0.0968327
\(333\) 0 0
\(334\) 1.64621 + 1.19604i 0.0900768 + 0.0654446i
\(335\) −2.13018 + 3.18040i −0.116384 + 0.173764i
\(336\) 0 0
\(337\) 25.2892 + 18.3737i 1.37759 + 1.00088i 0.997101 + 0.0760905i \(0.0242438\pi\)
0.380487 + 0.924786i \(0.375756\pi\)
\(338\) −10.1109 7.34597i −0.549958 0.399568i
\(339\) 0 0
\(340\) 0.598096 + 0.760414i 0.0324363 + 0.0412392i
\(341\) −5.83668 4.24060i −0.316074 0.229641i
\(342\) 0 0
\(343\) 6.17420 0.333376
\(344\) 2.19180 + 6.74568i 0.118174 + 0.363703i
\(345\) 0 0
\(346\) 1.43432 4.41438i 0.0771094 0.237318i
\(347\) −8.23487 + 25.3443i −0.442071 + 1.36056i 0.443593 + 0.896228i \(0.353704\pi\)
−0.885664 + 0.464327i \(0.846296\pi\)
\(348\) 0 0
\(349\) −17.1736 −0.919283 −0.459642 0.888104i \(-0.652022\pi\)
−0.459642 + 0.888104i \(0.652022\pi\)
\(350\) −0.851502 2.06867i −0.0455147 0.110575i
\(351\) 0 0
\(352\) −4.42816 + 3.21725i −0.236022 + 0.171480i
\(353\) 1.75506 5.40152i 0.0934124 0.287494i −0.893424 0.449214i \(-0.851704\pi\)
0.986837 + 0.161720i \(0.0517041\pi\)
\(354\) 0 0
\(355\) 3.79303 1.39455i 0.201313 0.0740150i
\(356\) 4.30432 + 13.2473i 0.228128 + 0.702107i
\(357\) 0 0
\(358\) −5.14952 15.8486i −0.272161 0.837625i
\(359\) 24.1874 + 17.5731i 1.27656 + 0.927475i 0.999443 0.0333611i \(-0.0106211\pi\)
0.277117 + 0.960836i \(0.410621\pi\)
\(360\) 0 0
\(361\) −37.2853 + 27.0893i −1.96238 + 1.42576i
\(362\) 5.32912 + 3.87183i 0.280092 + 0.203499i
\(363\) 0 0
\(364\) 0.256533 0.186382i 0.0134460 0.00976909i
\(365\) −26.8412 7.60213i −1.40493 0.397913i
\(366\) 0 0
\(367\) 8.81431 + 27.1277i 0.460103 + 1.41605i 0.865038 + 0.501706i \(0.167294\pi\)
−0.404935 + 0.914346i \(0.632706\pi\)
\(368\) −5.75002 −0.299741
\(369\) 0 0
\(370\) −13.9192 17.6967i −0.723625 0.920009i
\(371\) 0.0943182 0.290282i 0.00489676 0.0150707i
\(372\) 0 0
\(373\) 2.60399 1.89191i 0.134830 0.0979595i −0.518326 0.855183i \(-0.673445\pi\)
0.653156 + 0.757224i \(0.273445\pi\)
\(374\) 2.36813 0.122453
\(375\) 0 0
\(376\) 9.18295 0.473574
\(377\) −1.91593 + 1.39201i −0.0986756 + 0.0716920i
\(378\) 0 0
\(379\) 6.54435 20.1414i 0.336161 1.03460i −0.629987 0.776606i \(-0.716940\pi\)
0.966147 0.257990i \(-0.0830603\pi\)
\(380\) 11.1526 + 14.1794i 0.572119 + 0.727386i
\(381\) 0 0
\(382\) 9.03551 0.462297
\(383\) 1.68003 + 5.17061i 0.0858456 + 0.264206i 0.984760 0.173919i \(-0.0556430\pi\)
−0.898914 + 0.438124i \(0.855643\pi\)
\(384\) 0 0
\(385\) −5.26869 1.49223i −0.268517 0.0760510i
\(386\) −13.1037 + 9.52038i −0.666960 + 0.484575i
\(387\) 0 0
\(388\) −10.5922 7.69567i −0.537737 0.390689i
\(389\) −21.4966 + 15.6182i −1.08992 + 0.791873i −0.979386 0.201999i \(-0.935256\pi\)
−0.110534 + 0.993872i \(0.535256\pi\)
\(390\) 0 0
\(391\) 2.01265 + 1.46227i 0.101784 + 0.0739504i
\(392\) 2.10126 + 6.46702i 0.106130 + 0.326634i
\(393\) 0 0
\(394\) 2.93651 + 9.03765i 0.147939 + 0.455310i
\(395\) −18.4847 + 6.79611i −0.930067 + 0.341949i
\(396\) 0 0
\(397\) 0.315674 0.971546i 0.0158432 0.0487605i −0.942822 0.333296i \(-0.891839\pi\)
0.958666 + 0.284535i \(0.0918393\pi\)
\(398\) 13.9698 10.1496i 0.700241 0.508755i
\(399\) 0 0
\(400\) 3.80922 3.23880i 0.190461 0.161940i
\(401\) −22.2689 −1.11205 −0.556027 0.831164i \(-0.687675\pi\)
−0.556027 + 0.831164i \(0.687675\pi\)
\(402\) 0 0
\(403\) −0.288672 + 0.888440i −0.0143798 + 0.0442563i
\(404\) 3.67921 11.3234i 0.183047 0.563362i
\(405\) 0 0
\(406\) 0.461991 + 1.42186i 0.0229282 + 0.0705658i
\(407\) −55.1124 −2.73182
\(408\) 0 0
\(409\) −2.27376 1.65198i −0.112430 0.0816852i 0.530150 0.847904i \(-0.322136\pi\)
−0.642580 + 0.766219i \(0.722136\pi\)
\(410\) −8.20602 10.4331i −0.405267 0.515252i
\(411\) 0 0
\(412\) 4.35282 + 3.16251i 0.214448 + 0.155806i
\(413\) −1.23279 0.895676i −0.0606617 0.0440733i
\(414\) 0 0
\(415\) 2.19550 3.27793i 0.107773 0.160907i
\(416\) 0.573372 + 0.416579i 0.0281119 + 0.0204245i
\(417\) 0 0
\(418\) 44.1584 2.15986
\(419\) −11.9334 36.7271i −0.582983 1.79424i −0.607222 0.794532i \(-0.707716\pi\)
0.0242384 0.999706i \(-0.492284\pi\)
\(420\) 0 0
\(421\) −6.31871 + 19.4470i −0.307955 + 0.947788i 0.670603 + 0.741816i \(0.266035\pi\)
−0.978558 + 0.205971i \(0.933965\pi\)
\(422\) −0.452775 + 1.39350i −0.0220407 + 0.0678344i
\(423\) 0 0
\(424\) 0.682191 0.0331301
\(425\) −2.15697 + 0.164947i −0.104629 + 0.00800112i
\(426\) 0 0
\(427\) −2.20017 + 1.59852i −0.106474 + 0.0773576i
\(428\) −4.30198 + 13.2401i −0.207944 + 0.639985i
\(429\) 0 0
\(430\) −15.2598 4.32197i −0.735893 0.208424i
\(431\) −6.40476 19.7118i −0.308506 0.949485i −0.978345 0.206979i \(-0.933637\pi\)
0.669839 0.742506i \(-0.266363\pi\)
\(432\) 0 0
\(433\) 0.302540 + 0.931123i 0.0145392 + 0.0447469i 0.958063 0.286558i \(-0.0925111\pi\)
−0.943524 + 0.331305i \(0.892511\pi\)
\(434\) 0.477098 + 0.346632i 0.0229014 + 0.0166389i
\(435\) 0 0
\(436\) 5.60018 4.06877i 0.268200 0.194859i
\(437\) 37.5297 + 27.2669i 1.79529 + 1.30435i
\(438\) 0 0
\(439\) 24.2110 17.5904i 1.15553 0.839542i 0.166324 0.986071i \(-0.446810\pi\)
0.989206 + 0.146529i \(0.0468103\pi\)
\(440\) −0.466951 12.2302i −0.0222610 0.583053i
\(441\) 0 0
\(442\) −0.0947550 0.291626i −0.00450704 0.0138712i
\(443\) 24.4581 1.16204 0.581020 0.813889i \(-0.302654\pi\)
0.581020 + 0.813889i \(0.302654\pi\)
\(444\) 0 0
\(445\) −29.9676 8.48760i −1.42060 0.402351i
\(446\) 5.17646 15.9315i 0.245113 0.754379i
\(447\) 0 0
\(448\) 0.361964 0.262982i 0.0171012 0.0124247i
\(449\) −14.0251 −0.661886 −0.330943 0.943651i \(-0.607367\pi\)
−0.330943 + 0.943651i \(0.607367\pi\)
\(450\) 0 0
\(451\) −32.4914 −1.52996
\(452\) −11.1677 + 8.11381i −0.525285 + 0.381642i
\(453\) 0 0
\(454\) 6.64618 20.4548i 0.311921 0.959993i
\(455\) 0.0270515 + 0.708525i 0.00126820 + 0.0332161i
\(456\) 0 0
\(457\) 17.2858 0.808595 0.404298 0.914627i \(-0.367516\pi\)
0.404298 + 0.914627i \(0.367516\pi\)
\(458\) 5.13908 + 15.8165i 0.240133 + 0.739055i
\(459\) 0 0
\(460\) 7.15505 10.6826i 0.333606 0.498081i
\(461\) −29.2840 + 21.2761i −1.36389 + 0.990925i −0.365705 + 0.930731i \(0.619172\pi\)
−0.998187 + 0.0601941i \(0.980828\pi\)
\(462\) 0 0
\(463\) 15.6981 + 11.4054i 0.729554 + 0.530052i 0.889422 0.457086i \(-0.151107\pi\)
−0.159868 + 0.987138i \(0.551107\pi\)
\(464\) −2.70335 + 1.96410i −0.125500 + 0.0911808i
\(465\) 0 0
\(466\) −17.6696 12.8377i −0.818530 0.594697i
\(467\) 2.20831 + 6.79649i 0.102189 + 0.314504i 0.989060 0.147512i \(-0.0471264\pi\)
−0.886872 + 0.462016i \(0.847126\pi\)
\(468\) 0 0
\(469\) −0.236680 0.728426i −0.0109289 0.0336356i
\(470\) −11.4268 + 17.0605i −0.527080 + 0.786942i
\(471\) 0 0
\(472\) 1.05246 3.23915i 0.0484436 0.149094i
\(473\) −31.4082 + 22.8194i −1.44415 + 1.04924i
\(474\) 0 0
\(475\) −40.2209 + 3.07576i −1.84546 + 0.141125i
\(476\) −0.193575 −0.00887247
\(477\) 0 0
\(478\) −2.00811 + 6.18031i −0.0918486 + 0.282681i
\(479\) 5.88784 18.1209i 0.269022 0.827965i −0.721717 0.692188i \(-0.756647\pi\)
0.990739 0.135777i \(-0.0433531\pi\)
\(480\) 0 0
\(481\) 2.20519 + 6.78687i 0.100548 + 0.309455i
\(482\) −20.2473 −0.922239
\(483\) 0 0
\(484\) −15.3384 11.1440i −0.697198 0.506544i
\(485\) 27.4778 10.1025i 1.24770 0.458731i
\(486\) 0 0
\(487\) −20.0136 14.5407i −0.906903 0.658904i 0.0333265 0.999445i \(-0.489390\pi\)
−0.940230 + 0.340541i \(0.889390\pi\)
\(488\) −4.91755 3.57281i −0.222607 0.161733i
\(489\) 0 0
\(490\) −14.6294 4.14343i −0.660890 0.187181i
\(491\) 8.43327 + 6.12713i 0.380588 + 0.276513i 0.761588 0.648062i \(-0.224420\pi\)
−0.381000 + 0.924575i \(0.624420\pi\)
\(492\) 0 0
\(493\) 1.44572 0.0651120
\(494\) −1.76689 5.43792i −0.0794960 0.244664i
\(495\) 0 0
\(496\) −0.407310 + 1.25357i −0.0182888 + 0.0562870i
\(497\) −0.249875 + 0.769036i −0.0112084 + 0.0344960i
\(498\) 0 0
\(499\) −43.6293 −1.95311 −0.976557 0.215259i \(-0.930940\pi\)
−0.976557 + 0.215259i \(0.930940\pi\)
\(500\) 1.27718 + 11.1072i 0.0571174 + 0.496727i
\(501\) 0 0
\(502\) 1.91540 1.39162i 0.0854884 0.0621110i
\(503\) 8.61533 26.5153i 0.384139 1.18226i −0.552965 0.833205i \(-0.686504\pi\)
0.937103 0.349052i \(-0.113496\pi\)
\(504\) 0 0
\(505\) 16.4589 + 20.9257i 0.732413 + 0.931183i
\(506\) −9.72562 29.9324i −0.432357 1.33066i
\(507\) 0 0
\(508\) −3.29339 10.1360i −0.146121 0.449713i
\(509\) 21.3896 + 15.5405i 0.948078 + 0.688819i 0.950352 0.311178i \(-0.100724\pi\)
−0.00227352 + 0.999997i \(0.500724\pi\)
\(510\) 0 0
\(511\) 4.51583 3.28094i 0.199768 0.145140i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) 10.5976 7.69960i 0.467440 0.339615i
\(515\) −11.2919 + 4.15159i −0.497580 + 0.182941i
\(516\) 0 0
\(517\) 15.5321 + 47.8029i 0.683101 + 2.10237i
\(518\) 4.50497 0.197937
\(519\) 0 0
\(520\) −1.48742 + 0.546865i −0.0652275 + 0.0239816i
\(521\) 3.63782 11.1961i 0.159376 0.490509i −0.839202 0.543820i \(-0.816977\pi\)
0.998578 + 0.0533110i \(0.0169775\pi\)
\(522\) 0 0
\(523\) 4.22035 3.06626i 0.184543 0.134078i −0.491678 0.870777i \(-0.663616\pi\)
0.676221 + 0.736699i \(0.263616\pi\)
\(524\) −9.76823 −0.426727
\(525\) 0 0
\(526\) 7.27788 0.317331
\(527\) 0.461361 0.335199i 0.0200972 0.0146015i
\(528\) 0 0
\(529\) 3.10956 9.57023i 0.135198 0.416097i
\(530\) −0.848886 + 1.26740i −0.0368732 + 0.0550525i
\(531\) 0 0
\(532\) −3.60957 −0.156495
\(533\) 1.30006 + 4.00118i 0.0563119 + 0.173310i
\(534\) 0 0
\(535\) −19.2449 24.4678i −0.832030 1.05783i
\(536\) 1.38494 1.00621i 0.0598201 0.0434619i
\(537\) 0 0
\(538\) −0.618008 0.449009i −0.0266442 0.0193581i
\(539\) −30.1107 + 21.8767i −1.29696 + 0.942296i
\(540\) 0 0
\(541\) 9.91189 + 7.20141i 0.426145 + 0.309613i 0.780106 0.625648i \(-0.215165\pi\)
−0.353960 + 0.935260i \(0.615165\pi\)
\(542\) −0.744584 2.29159i −0.0319826 0.0984324i
\(543\) 0 0
\(544\) −0.133697 0.411479i −0.00573223 0.0176420i
\(545\) 0.590541 + 15.4673i 0.0252960 + 0.662544i
\(546\) 0 0
\(547\) −10.7782 + 33.1719i −0.460842 + 1.41833i 0.403295 + 0.915070i \(0.367865\pi\)
−0.864137 + 0.503256i \(0.832135\pi\)
\(548\) 12.7881 9.29107i 0.546279 0.396895i
\(549\) 0 0
\(550\) 23.3029 + 14.3512i 0.993639 + 0.611936i
\(551\) 26.9582 1.14846
\(552\) 0 0
\(553\) 1.21772 3.74777i 0.0517829 0.159371i
\(554\) 3.25685 10.0236i 0.138370 0.425860i
\(555\) 0 0
\(556\) 3.09449 + 9.52387i 0.131236 + 0.403902i
\(557\) 9.78468 0.414590 0.207295 0.978278i \(-0.433534\pi\)
0.207295 + 0.978278i \(0.433534\pi\)
\(558\) 0 0
\(559\) 4.06683 + 2.95472i 0.172009 + 0.124972i
\(560\) 0.0381692 + 0.999715i 0.00161294 + 0.0422456i
\(561\) 0 0
\(562\) 14.7269 + 10.6997i 0.621218 + 0.451341i
\(563\) 15.8610 + 11.5237i 0.668460 + 0.485665i 0.869510 0.493916i \(-0.164435\pi\)
−0.201049 + 0.979581i \(0.564435\pi\)
\(564\) 0 0
\(565\) −1.17764 30.8443i −0.0495436 1.29763i
\(566\) 21.1883 + 15.3942i 0.890609 + 0.647065i
\(567\) 0 0
\(568\) −1.80731 −0.0758331
\(569\) −4.27880 13.1688i −0.179377 0.552064i 0.820430 0.571747i \(-0.193734\pi\)
−0.999806 + 0.0196831i \(0.993734\pi\)
\(570\) 0 0
\(571\) −6.28381 + 19.3396i −0.262969 + 0.809336i 0.729185 + 0.684317i \(0.239899\pi\)
−0.992154 + 0.125020i \(0.960101\pi\)
\(572\) −1.19874 + 3.68936i −0.0501220 + 0.154260i
\(573\) 0 0
\(574\) 2.65589 0.110855
\(575\) 10.9433 + 26.5860i 0.456366 + 1.10871i
\(576\) 0 0
\(577\) −25.3717 + 18.4337i −1.05624 + 0.767403i −0.973389 0.229159i \(-0.926402\pi\)
−0.0828507 + 0.996562i \(0.526402\pi\)
\(578\) 5.19544 15.9899i 0.216102 0.665094i
\(579\) 0 0
\(580\) −0.285069 7.46642i −0.0118368 0.310026i
\(581\) 0.243939 + 0.750766i 0.0101203 + 0.0311470i
\(582\) 0 0
\(583\) 1.15386 + 3.55122i 0.0477881 + 0.147077i
\(584\) 10.0932 + 7.33316i 0.417661 + 0.303448i
\(585\) 0 0
\(586\) −19.3062 + 14.0267i −0.797530 + 0.579439i
\(587\) −18.9945 13.8003i −0.783985 0.569598i 0.122187 0.992507i \(-0.461009\pi\)
−0.906172 + 0.422909i \(0.861009\pi\)
\(588\) 0 0
\(589\) 8.60296 6.25042i 0.354479 0.257544i
\(590\) 4.70820 + 5.98596i 0.193834 + 0.246438i
\(591\) 0 0
\(592\) 3.11148 + 9.57614i 0.127881 + 0.393577i
\(593\) 21.9658 0.902025 0.451013 0.892518i \(-0.351063\pi\)
0.451013 + 0.892518i \(0.351063\pi\)
\(594\) 0 0
\(595\) 0.240875 0.359631i 0.00987491 0.0147434i
\(596\) 4.90590 15.0988i 0.200953 0.618471i
\(597\) 0 0
\(598\) −3.29690 + 2.39534i −0.134820 + 0.0979527i
\(599\) −19.6941 −0.804680 −0.402340 0.915490i \(-0.631803\pi\)
−0.402340 + 0.915490i \(0.631803\pi\)
\(600\) 0 0
\(601\) 13.4764 0.549715 0.274857 0.961485i \(-0.411369\pi\)
0.274857 + 0.961485i \(0.411369\pi\)
\(602\) 2.56735 1.86529i 0.104637 0.0760234i
\(603\) 0 0
\(604\) 5.55571 17.0987i 0.226059 0.695737i
\(605\) 39.7901 14.6293i 1.61770 0.594764i
\(606\) 0 0
\(607\) 46.7224 1.89641 0.948203 0.317666i \(-0.102899\pi\)
0.948203 + 0.317666i \(0.102899\pi\)
\(608\) −2.49304 7.67280i −0.101106 0.311173i
\(609\) 0 0
\(610\) 12.7569 4.69021i 0.516511 0.189901i
\(611\) 5.26525 3.82543i 0.213009 0.154760i
\(612\) 0 0
\(613\) 20.9461 + 15.2182i 0.846006 + 0.614659i 0.924042 0.382291i \(-0.124865\pi\)
−0.0780360 + 0.996951i \(0.524865\pi\)
\(614\) −15.2364 + 11.0699i −0.614893 + 0.446746i
\(615\) 0 0
\(616\) 1.98121 + 1.43943i 0.0798252 + 0.0579964i
\(617\) −11.0219 33.9219i −0.443725 1.36565i −0.883876 0.467722i \(-0.845075\pi\)
0.440150 0.897924i \(-0.354925\pi\)
\(618\) 0 0
\(619\) −3.57307 10.9968i −0.143614 0.441998i 0.853216 0.521557i \(-0.174649\pi\)
−0.996830 + 0.0795594i \(0.974649\pi\)
\(620\) −1.82210 2.31660i −0.0731774 0.0930370i
\(621\) 0 0
\(622\) 9.51705 29.2905i 0.381599 1.17444i
\(623\) 5.04182 3.66309i 0.201996 0.146759i
\(624\) 0 0
\(625\) −22.2246 11.4484i −0.888985 0.457936i
\(626\) 17.0707 0.682283
\(627\) 0 0
\(628\) −6.42747 + 19.7817i −0.256484 + 0.789377i
\(629\) 1.34619 4.14316i 0.0536762 0.165198i
\(630\) 0 0
\(631\) −0.207791 0.639515i −0.00827202 0.0254587i 0.946835 0.321719i \(-0.104261\pi\)
−0.955107 + 0.296260i \(0.904261\pi\)
\(632\) 8.80763 0.350349
\(633\) 0 0
\(634\) −22.0698 16.0346i −0.876504 0.636817i
\(635\) 22.9293 + 6.49417i 0.909921 + 0.257713i
\(636\) 0 0
\(637\) 3.89883 + 2.83266i 0.154477 + 0.112234i
\(638\) −14.7968 10.7505i −0.585810 0.425616i
\(639\) 0 0
\(640\) −2.09872 + 0.771616i −0.0829590 + 0.0305008i
\(641\) 3.29243 + 2.39209i 0.130043 + 0.0944820i 0.650905 0.759159i \(-0.274389\pi\)
−0.520862 + 0.853641i \(0.674389\pi\)
\(642\) 0 0
\(643\) −23.9998 −0.946458 −0.473229 0.880939i \(-0.656912\pi\)
−0.473229 + 0.880939i \(0.656912\pi\)
\(644\) 0.794985 + 2.44671i 0.0313268 + 0.0964140i
\(645\) 0 0
\(646\) −1.07863 + 3.31967i −0.0424380 + 0.130611i
\(647\) −5.10597 + 15.7146i −0.200737 + 0.617804i 0.799125 + 0.601165i \(0.205297\pi\)
−0.999862 + 0.0166387i \(0.994703\pi\)
\(648\) 0 0
\(649\) 18.6419 0.731759
\(650\) 0.834881 3.44388i 0.0327467 0.135080i
\(651\) 0 0
\(652\) −4.54778 + 3.30416i −0.178105 + 0.129401i
\(653\) 7.91588 24.3626i 0.309772 0.953381i −0.668081 0.744089i \(-0.732884\pi\)
0.977853 0.209292i \(-0.0671160\pi\)
\(654\) 0 0
\(655\) 12.1551 18.1479i 0.474940 0.709095i
\(656\) 1.83436 + 5.64558i 0.0716198 + 0.220423i
\(657\) 0 0
\(658\) −1.26961 3.90747i −0.0494947 0.152329i
\(659\) −12.5375 9.10904i −0.488392 0.354838i 0.316173 0.948701i \(-0.397602\pi\)
−0.804566 + 0.593864i \(0.797602\pi\)
\(660\) 0 0
\(661\) 12.2492 8.89955i 0.476438 0.346152i −0.323507 0.946226i \(-0.604862\pi\)
0.799945 + 0.600073i \(0.204862\pi\)
\(662\) 10.0845 + 7.32683i 0.391946 + 0.284765i
\(663\) 0 0
\(664\) −1.42741 + 1.03707i −0.0553942 + 0.0402463i
\(665\) 4.49157 6.70601i 0.174176 0.260048i
\(666\) 0 0
\(667\) −5.93739 18.2734i −0.229897 0.707549i
\(668\) 2.03483 0.0787300
\(669\) 0 0
\(670\) 0.146042 + 3.82508i 0.00564210 + 0.147776i
\(671\) 10.2811 31.6419i 0.396897 1.22152i
\(672\) 0 0
\(673\) 22.8814 16.6243i 0.882012 0.640819i −0.0517712 0.998659i \(-0.516487\pi\)
0.933783 + 0.357840i \(0.116487\pi\)
\(674\) 31.2591 1.20406
\(675\) 0 0
\(676\) −12.4977 −0.480681
\(677\) 32.8594 23.8737i 1.26289 0.917542i 0.263992 0.964525i \(-0.414961\pi\)
0.998896 + 0.0469832i \(0.0149607\pi\)
\(678\) 0 0
\(679\) −1.81016 + 5.57111i −0.0694677 + 0.213799i
\(680\) 0.930830 + 0.263635i 0.0356957 + 0.0101100i
\(681\) 0 0
\(682\) −7.21453 −0.276259
\(683\) 10.4076 + 32.0312i 0.398235 + 1.22564i 0.926414 + 0.376507i \(0.122875\pi\)
−0.528179 + 0.849133i \(0.677125\pi\)
\(684\) 0 0
\(685\) 1.34851 + 35.3196i 0.0515238 + 1.34949i
\(686\) 4.99503 3.62910i 0.190711 0.138560i
\(687\) 0 0
\(688\) 5.73822 + 4.16906i 0.218768 + 0.158944i
\(689\) 0.391149 0.284186i 0.0149016 0.0108266i
\(690\) 0 0
\(691\) −9.02540 6.55734i −0.343342 0.249453i 0.402728 0.915320i \(-0.368062\pi\)
−0.746071 + 0.665867i \(0.768062\pi\)
\(692\) −1.43432 4.41438i −0.0545246 0.167809i
\(693\) 0 0
\(694\) 8.23487 + 25.3443i 0.312592 + 0.962058i
\(695\) −21.5445 6.10197i −0.817230 0.231461i
\(696\) 0 0
\(697\) 0.793644 2.44258i 0.0300614 0.0925195i
\(698\) −13.8938 + 10.0944i −0.525886 + 0.382079i
\(699\) 0 0
\(700\) −1.90481 1.17309i −0.0719951 0.0443384i
\(701\) −11.1999 −0.423014 −0.211507 0.977377i \(-0.567837\pi\)
−0.211507 + 0.977377i \(0.567837\pi\)
\(702\) 0 0
\(703\) 25.1023 77.2570i 0.946753 2.91380i
\(704\) −1.69141 + 5.20561i −0.0637473 + 0.196194i
\(705\) 0 0
\(706\) −1.75506 5.40152i −0.0660526 0.203289i
\(707\) −5.32695 −0.200341
\(708\) 0 0
\(709\) 10.8595 + 7.88987i 0.407836 + 0.296310i 0.772725 0.634741i \(-0.218893\pi\)
−0.364889 + 0.931051i \(0.618893\pi\)
\(710\) 2.24893 3.35770i 0.0844009 0.126012i
\(711\) 0 0
\(712\) 11.2689 + 8.18730i 0.422318 + 0.306832i
\(713\) −6.13154 4.45483i −0.229628 0.166835i
\(714\) 0 0
\(715\) −5.36259 6.81794i −0.200550 0.254977i
\(716\) −13.4816 9.79497i −0.503832 0.366055i
\(717\) 0 0
\(718\) 29.8972 1.11575
\(719\) −13.5053 41.5652i −0.503664 1.55012i −0.803004 0.595973i \(-0.796766\pi\)
0.299340 0.954147i \(-0.403234\pi\)
\(720\) 0 0
\(721\) 0.743880 2.28943i 0.0277035 0.0852627i
\(722\) −14.2417 + 43.8315i −0.530022 + 1.63124i
\(723\) 0 0
\(724\) 6.58715 0.244809
\(725\) 14.2262 + 8.76125i 0.528347 + 0.325385i
\(726\) 0 0
\(727\) 15.3509 11.1531i 0.569334 0.413646i −0.265529 0.964103i \(-0.585547\pi\)
0.834863 + 0.550457i \(0.185547\pi\)
\(728\) 0.0979870 0.301573i 0.00363164 0.0111770i
\(729\) 0 0
\(730\) −26.1834 + 9.62661i −0.969091 + 0.356297i
\(731\) −0.948293 2.91855i −0.0350739 0.107946i
\(732\) 0 0
\(733\) 13.8676 + 42.6802i 0.512213 + 1.57643i 0.788297 + 0.615295i \(0.210963\pi\)
−0.276085 + 0.961133i \(0.589037\pi\)
\(734\) 23.0762 + 16.7658i 0.851757 + 0.618837i
\(735\) 0 0
\(736\) −4.65186 + 3.37978i −0.171470 + 0.124580i
\(737\) 7.58045 + 5.50752i 0.279230 + 0.202872i
\(738\) 0 0
\(739\) 5.55621 4.03683i 0.204389 0.148497i −0.480883 0.876785i \(-0.659684\pi\)
0.685271 + 0.728288i \(0.259684\pi\)
\(740\) −21.6628 6.13546i −0.796339 0.225544i
\(741\) 0 0
\(742\) −0.0943182 0.290282i −0.00346253 0.0106566i
\(743\) 35.5994 1.30602 0.653008 0.757351i \(-0.273507\pi\)
0.653008 + 0.757351i \(0.273507\pi\)
\(744\) 0 0
\(745\) 21.9466 + 27.9026i 0.804060 + 1.02227i
\(746\) 0.994637 3.06118i 0.0364162 0.112078i
\(747\) 0 0
\(748\) 1.91586 1.39195i 0.0700508 0.0508949i
\(749\) 6.22864 0.227589
\(750\) 0 0
\(751\) −20.1261 −0.734414 −0.367207 0.930139i \(-0.619686\pi\)
−0.367207 + 0.930139i \(0.619686\pi\)
\(752\) 7.42916 5.39760i 0.270914 0.196830i
\(753\) 0 0
\(754\) −0.731821 + 2.25231i −0.0266514 + 0.0820245i
\(755\) 24.8535 + 31.5985i 0.904512 + 1.14999i
\(756\) 0 0
\(757\) −20.7503 −0.754183 −0.377091 0.926176i \(-0.623076\pi\)
−0.377091 + 0.926176i \(0.623076\pi\)
\(758\) −6.54435 20.1414i −0.237702 0.731570i
\(759\) 0 0
\(760\) 17.3571 + 4.91598i 0.629608 + 0.178321i
\(761\) −6.20460 + 4.50791i −0.224917 + 0.163412i −0.694537 0.719457i \(-0.744391\pi\)
0.469620 + 0.882868i \(0.344391\pi\)
\(762\) 0 0
\(763\) −2.50559 1.82042i −0.0907083 0.0659035i
\(764\) 7.30988 5.31094i 0.264462 0.192143i
\(765\) 0 0
\(766\) 4.39838 + 3.19561i 0.158920 + 0.115462i
\(767\) −0.745909 2.29567i −0.0269332 0.0828919i
\(768\) 0 0
\(769\) −0.130256 0.400887i −0.00469715 0.0144563i 0.948680 0.316236i \(-0.102419\pi\)
−0.953378 + 0.301780i \(0.902419\pi\)
\(770\) −5.13957 + 1.88962i −0.185217 + 0.0680971i
\(771\) 0 0
\(772\) −5.00516 + 15.4043i −0.180140 + 0.554413i
\(773\) 30.4631 22.1327i 1.09568 0.796059i 0.115332 0.993327i \(-0.463207\pi\)
0.980350 + 0.197268i \(0.0632069\pi\)
\(774\) 0 0
\(775\) 6.57123 0.502513i 0.236046 0.0180508i
\(776\) −13.0927 −0.469999
\(777\) 0 0
\(778\) −8.21096 + 25.2707i −0.294377 + 0.906000i
\(779\) 14.7990 45.5466i 0.530229 1.63188i
\(780\) 0 0
\(781\) −3.05690 9.40816i −0.109384 0.336651i
\(782\) 2.48777 0.0889625
\(783\) 0 0
\(784\) 5.50117 + 3.99684i 0.196470 + 0.142744i
\(785\) −28.7533 36.5567i −1.02625 1.30476i
\(786\) 0 0
\(787\) −3.58854 2.60723i −0.127918 0.0929377i 0.521987 0.852954i \(-0.325191\pi\)
−0.649904 + 0.760016i \(0.725191\pi\)
\(788\) 7.68788 + 5.58557i 0.273870 + 0.198978i
\(789\) 0 0
\(790\) −10.9598 + 16.3632i −0.389932 + 0.582177i
\(791\) 4.99656 + 3.63021i 0.177657 + 0.129076i
\(792\) 0 0
\(793\) −4.30794 −0.152980
\(794\) −0.315674 0.971546i −0.0112029 0.0344789i
\(795\) 0 0
\(796\) 5.33598 16.4224i 0.189129 0.582078i
\(797\) −3.51514 + 10.8185i −0.124513 + 0.383211i −0.993812 0.111075i \(-0.964571\pi\)
0.869299 + 0.494286i \(0.164571\pi\)
\(798\) 0 0
\(799\) −3.97304 −0.140556
\(800\) 1.17800 4.85925i 0.0416486 0.171800i
\(801\) 0 0
\(802\) −18.0159 + 13.0893i −0.636163 + 0.462200i
\(803\) −21.1018 + 64.9448i −0.744668 + 2.29185i
\(804\) 0 0
\(805\) −5.53485 1.56761i −0.195078 0.0552512i
\(806\) 0.288672 + 0.888440i 0.0101680 + 0.0312940i
\(807\) 0 0
\(808\) −3.67921 11.3234i −0.129434 0.398357i
\(809\) 15.2356 + 11.0693i 0.535655 + 0.389176i 0.822469 0.568810i \(-0.192596\pi\)
−0.286814 + 0.957986i \(0.592596\pi\)
\(810\) 0 0
\(811\) −3.52006 + 2.55748i −0.123606 + 0.0898051i −0.647871 0.761750i \(-0.724340\pi\)
0.524265 + 0.851555i \(0.324340\pi\)
\(812\) 1.20951 + 0.878759i 0.0424454 + 0.0308384i
\(813\) 0 0
\(814\) −44.5869 + 32.3943i −1.56277 + 1.13542i
\(815\) −0.479565 12.5606i −0.0167984 0.439979i
\(816\) 0 0
\(817\) −17.6827 54.4219i −0.618641 1.90398i
\(818\) −2.81052 −0.0982674
\(819\) 0 0
\(820\) −12.7712 3.61714i −0.445990 0.126316i
\(821\) −14.6214 + 45.0000i −0.510290 + 1.57051i 0.281402 + 0.959590i \(0.409201\pi\)
−0.791692 + 0.610921i \(0.790799\pi\)
\(822\) 0 0
\(823\) −29.8018 + 21.6523i −1.03882 + 0.754750i −0.970056 0.242882i \(-0.921907\pi\)
−0.0687689 + 0.997633i \(0.521907\pi\)
\(824\) 5.38038 0.187434
\(825\) 0 0
\(826\) −1.52381 −0.0530203
\(827\) 4.98478 3.62165i 0.173338 0.125937i −0.497734 0.867330i \(-0.665834\pi\)
0.671072 + 0.741393i \(0.265834\pi\)
\(828\) 0 0
\(829\) 3.41535 10.5114i 0.118620 0.365074i −0.874065 0.485809i \(-0.838525\pi\)
0.992685 + 0.120735i \(0.0385250\pi\)
\(830\) −0.150521 3.94239i −0.00522466 0.136842i
\(831\) 0 0
\(832\) 0.708727 0.0245707
\(833\) −0.909119 2.79798i −0.0314991 0.0969443i
\(834\) 0 0
\(835\) −2.53205 + 3.78040i −0.0876251 + 0.130826i
\(836\) 35.7249 25.9556i 1.23557 0.897695i
\(837\) 0 0
\(838\) −31.2420 22.6986i −1.07924 0.784111i
\(839\) −23.7557 + 17.2596i −0.820139 + 0.595866i −0.916752 0.399456i \(-0.869199\pi\)
0.0966132 + 0.995322i \(0.469199\pi\)
\(840\) 0 0
\(841\) 14.4282 + 10.4827i 0.497525 + 0.361473i
\(842\) 6.31871 + 19.4470i 0.217757 + 0.670187i
\(843\) 0 0
\(844\) 0.452775 + 1.39350i 0.0155852 + 0.0479662i
\(845\) 15.5516 23.2188i 0.534990 0.798751i
\(846\) 0 0
\(847\) −2.62127 + 8.06742i −0.0900677 + 0.277200i
\(848\) 0.551904 0.400982i 0.0189525 0.0137698i
\(849\) 0 0
\(850\) −1.64807 + 1.40128i −0.0565285 + 0.0480636i
\(851\) −57.8967 −1.98467
\(852\) 0 0
\(853\) −8.97089 + 27.6096i −0.307157 + 0.945333i 0.671706 + 0.740818i \(0.265562\pi\)
−0.978863 + 0.204515i \(0.934438\pi\)
\(854\) −0.840390 + 2.58645i −0.0287575 + 0.0885066i
\(855\) 0 0
\(856\) 4.30198 + 13.2401i 0.147039 + 0.452538i
\(857\) −11.5950 −0.396076 −0.198038 0.980194i \(-0.563457\pi\)
−0.198038 + 0.980194i \(0.563457\pi\)
\(858\) 0 0
\(859\) −2.87734 2.09051i −0.0981737 0.0713274i 0.537615 0.843190i \(-0.319325\pi\)
−0.635789 + 0.771863i \(0.719325\pi\)
\(860\) −14.8858 + 5.47294i −0.507603 + 0.186626i
\(861\) 0 0
\(862\) −16.7679 12.1826i −0.571116 0.414940i
\(863\) 14.3646 + 10.4365i 0.488975 + 0.355261i 0.804790 0.593559i \(-0.202278\pi\)
−0.315815 + 0.948821i \(0.602278\pi\)
\(864\) 0 0
\(865\) 9.98602 + 2.82830i 0.339535 + 0.0961651i
\(866\) 0.792061 + 0.575466i 0.0269153 + 0.0195551i
\(867\) 0 0
\(868\) 0.589726 0.0200166
\(869\) 14.8973 + 45.8491i 0.505356 + 1.55533i
\(870\) 0 0
\(871\) 0.374915 1.15387i 0.0127035 0.0390974i
\(872\) 2.13908 6.58341i 0.0724384 0.222942i
\(873\) 0 0
\(874\) 46.3892 1.56914
\(875\) 4.54967 2.07911i 0.153807 0.0702867i
\(876\) 0 0
\(877\) 19.1476 13.9115i 0.646568 0.469759i −0.215532 0.976497i \(-0.569149\pi\)
0.862100 + 0.506737i \(0.169149\pi\)
\(878\) 9.24780 28.4618i 0.312098 0.960539i
\(879\) 0 0
\(880\) −7.56651 9.61999i −0.255067 0.324290i
\(881\) 8.46021 + 26.0378i 0.285032 + 0.877237i 0.986389 + 0.164427i \(0.0525776\pi\)
−0.701358 + 0.712810i \(0.747422\pi\)
\(882\) 0 0
\(883\) −14.2222 43.7714i −0.478615 1.47303i −0.841020 0.541005i \(-0.818044\pi\)
0.362404 0.932021i \(-0.381956\pi\)
\(884\) −0.248072 0.180235i −0.00834356 0.00606195i
\(885\) 0 0
\(886\) 19.7870 14.3761i 0.664758 0.482975i
\(887\) −5.80575 4.21812i −0.194938 0.141631i 0.486035 0.873939i \(-0.338443\pi\)
−0.680973 + 0.732309i \(0.738443\pi\)
\(888\) 0 0
\(889\) −3.85768 + 2.80277i −0.129382 + 0.0940018i
\(890\) −29.2332 + 10.7479i −0.979898 + 0.360270i
\(891\) 0 0
\(892\) −5.17646 15.9315i −0.173321 0.533427i
\(893\) −74.0849 −2.47916
\(894\) 0 0
\(895\) 34.9734 12.8584i 1.16903 0.429808i
\(896\) 0.138258 0.425514i 0.00461887 0.0142154i
\(897\) 0 0
\(898\) −11.3466 + 8.24376i −0.378640 + 0.275098i
\(899\) −4.40440 −0.146895
\(900\) 0 0
\(901\) −0.295153 −0.00983296
\(902\) −26.2861 + 19.0979i −0.875230 + 0.635892i
\(903\) 0 0
\(904\) −4.26568 + 13.1284i −0.141875 + 0.436645i
\(905\) −8.19674 + 12.2379i −0.272469 + 0.406802i
\(906\) 0 0
\(907\) −5.56195 −0.184682 −0.0923408 0.995727i \(-0.529435\pi\)
−0.0923408 + 0.995727i \(0.529435\pi\)
\(908\) −6.64618 20.4548i −0.220561 0.678817i
\(909\) 0 0
\(910\) 0.438345 + 0.557308i 0.0145310 + 0.0184746i
\(911\) −8.66550 + 6.29585i −0.287101 + 0.208591i −0.722009 0.691884i \(-0.756781\pi\)
0.434908 + 0.900475i \(0.356781\pi\)
\(912\) 0 0
\(913\) −7.81293 5.67643i −0.258570 0.187862i
\(914\) 13.9845 10.1603i 0.462566 0.336074i
\(915\) 0 0
\(916\) 13.4543 + 9.77511i 0.444542 + 0.322979i
\(917\) 1.35053 + 4.15652i 0.0445986 + 0.137260i
\(918\) 0 0
\(919\) −7.39033 22.7451i −0.243785 0.750292i −0.995834 0.0911851i \(-0.970935\pi\)
0.752049 0.659107i \(-0.229065\pi\)
\(920\) −0.490541 12.8481i −0.0161727 0.423589i
\(921\) 0 0
\(922\) −11.1855 + 34.4254i −0.368374 + 1.13374i
\(923\) −1.03626 + 0.752888i −0.0341090 + 0.0247816i
\(924\) 0 0
\(925\) 38.3548 32.6114i 1.26110 1.07225i
\(926\) 19.4040 0.637654
\(927\) 0 0
\(928\) −1.03259 + 3.17797i −0.0338963 + 0.104322i
\(929\) −6.00826 + 18.4915i −0.197124 + 0.606687i 0.802821 + 0.596220i \(0.203332\pi\)
−0.999945 + 0.0104663i \(0.996668\pi\)
\(930\) 0 0
\(931\) −16.9523 52.1737i −0.555588 1.70992i
\(932\) −21.8409 −0.715421
\(933\) 0 0
\(934\) 5.78144 + 4.20046i 0.189175 + 0.137443i
\(935\) 0.202028 + 5.29145i 0.00660703 + 0.173049i
\(936\) 0 0
\(937\) 13.3009 + 9.66370i 0.434523 + 0.315699i 0.783455 0.621449i \(-0.213456\pi\)
−0.348932 + 0.937148i \(0.613456\pi\)
\(938\) −0.619637 0.450192i −0.0202318 0.0146993i
\(939\) 0 0
\(940\) 0.783408 + 20.5187i 0.0255519 + 0.669248i
\(941\) −5.92599 4.30548i −0.193182 0.140355i 0.486990 0.873408i \(-0.338095\pi\)
−0.680172 + 0.733053i \(0.738095\pi\)
\(942\) 0 0
\(943\) −34.1328 −1.11152
\(944\) −1.05246 3.23915i −0.0342548 0.105425i
\(945\) 0 0
\(946\) −11.9969 + 36.9225i −0.390051 + 1.20045i
\(947\) 13.0142 40.0535i 0.422903 1.30156i −0.482085 0.876125i \(-0.660120\pi\)
0.904988 0.425438i \(-0.139880\pi\)
\(948\) 0 0
\(949\) 8.84201 0.287024
\(950\) −30.7315 + 26.1296i −0.997061 + 0.847755i
\(951\) 0 0
\(952\) −0.156605 + 0.113780i −0.00507560 + 0.00368764i
\(953\) −11.4876 + 35.3551i −0.372119 + 1.14526i 0.573283 + 0.819357i \(0.305669\pi\)
−0.945402 + 0.325907i \(0.894331\pi\)
\(954\) 0 0
\(955\) 0.770830 + 20.1893i 0.0249435 + 0.653310i
\(956\) 2.00811 + 6.18031i 0.0649468 + 0.199886i
\(957\) 0 0
\(958\) −5.88784 18.1209i −0.190227 0.585460i
\(959\) −5.72153 4.15693i −0.184758 0.134234i
\(960\) 0 0
\(961\) 23.6740 17.2002i 0.763677 0.554844i
\(962\) 5.77325 + 4.19451i 0.186137 + 0.135237i
\(963\) 0 0
\(964\) −16.3804 + 11.9011i −0.527577 + 0.383307i
\(965\) −22.3906 28.4672i −0.720779 0.916391i
\(966\) 0 0
\(967\) −18.0263 55.4791i −0.579685 1.78409i −0.619639 0.784887i \(-0.712721\pi\)
0.0399536 0.999202i \(-0.487279\pi\)
\(968\) −18.9593 −0.609374
\(969\) 0 0
\(970\) 16.2919 24.3241i 0.523101 0.781001i
\(971\) −1.77798 + 5.47205i −0.0570579 + 0.175606i −0.975524 0.219894i \(-0.929429\pi\)
0.918466 + 0.395500i \(0.129429\pi\)
\(972\) 0 0
\(973\) 3.62470 2.63350i 0.116203 0.0844261i
\(974\) −24.7382 −0.792663
\(975\) 0 0
\(976\) −6.07842 −0.194566
\(977\) 38.3212 27.8420i 1.22600 0.890744i 0.229420 0.973327i \(-0.426317\pi\)
0.996584 + 0.0825830i \(0.0263170\pi\)
\(978\) 0 0
\(979\) −23.5597 + 72.5093i −0.752972 + 2.31741i
\(980\) −14.2709 + 5.24685i −0.455867 + 0.167604i
\(981\) 0 0
\(982\) 10.4241 0.332646
\(983\) −2.26705 6.97726i −0.0723077 0.222540i 0.908371 0.418165i \(-0.137327\pi\)
−0.980679 + 0.195625i \(0.937327\pi\)
\(984\) 0 0
\(985\) −19.9436 + 7.33247i −0.635455 + 0.233632i
\(986\) 1.16961 0.849774i 0.0372481 0.0270623i
\(987\) 0 0
\(988\) −4.62577 3.36082i −0.147165 0.106922i
\(989\) −32.9949 + 23.9722i −1.04918 + 0.762271i
\(990\) 0 0
\(991\) 0.714712 + 0.519269i 0.0227036 + 0.0164951i 0.599079 0.800690i \(-0.295533\pi\)
−0.576376 + 0.817185i \(0.695533\pi\)
\(992\) 0.407310 + 1.25357i 0.0129321 + 0.0398009i
\(993\) 0 0
\(994\) 0.249875 + 0.769036i 0.00792555 + 0.0243923i
\(995\) 23.8705 + 30.3487i 0.756746 + 0.962119i
\(996\) 0 0
\(997\) 8.50456 26.1743i 0.269342 0.828950i −0.721319 0.692603i \(-0.756464\pi\)
0.990661 0.136347i \(-0.0435361\pi\)
\(998\) −35.2968 + 25.6446i −1.11730 + 0.811767i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 450.2.h.g.361.3 yes 12
3.2 odd 2 450.2.h.f.361.1 yes 12
25.16 even 5 inner 450.2.h.g.91.3 yes 12
75.41 odd 10 450.2.h.f.91.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.h.f.91.1 12 75.41 odd 10
450.2.h.f.361.1 yes 12 3.2 odd 2
450.2.h.g.91.3 yes 12 25.16 even 5 inner
450.2.h.g.361.3 yes 12 1.1 even 1 trivial