Properties

Label 450.2.l.c.289.4
Level $450$
Weight $2$
Character 450.289
Analytic conductor $3.593$
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] = [450,2,Mod(19,450)]
 
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, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), 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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + 6259 x^{8} - 11958 x^{7} - 15752 x^{6} + 14670 x^{5} + 18271 x^{4} + \cdots + 11105 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.4
Root \(2.17199 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 450.289
Dual form 450.2.l.c.109.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.53938 - 1.62182i) q^{5} +4.63137i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.53938 - 1.62182i) q^{5} +4.63137i q^{7} +(-0.951057 + 0.309017i) q^{8} +(2.21691 + 0.292102i) q^{10} +(-2.05464 + 1.49278i) q^{11} +(0.0846260 - 0.116478i) q^{13} +(-3.74686 + 2.72225i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(7.12436 - 2.31485i) q^{17} +(2.08298 + 6.41074i) q^{19} +(1.06675 + 1.96521i) q^{20} +(-2.41537 - 0.784803i) q^{22} +(-0.985910 - 1.35699i) q^{23} +(-0.260613 - 4.99320i) q^{25} +0.143974 q^{26} +(-4.40469 - 1.43117i) q^{28} +(-0.696812 + 2.14457i) q^{29} +(0.310207 + 0.954718i) q^{31} -1.00000i q^{32} +(6.06035 + 4.40310i) q^{34} +(7.51126 + 7.12944i) q^{35} +(-0.0523017 + 0.0719871i) q^{37} +(-3.96205 + 5.45330i) q^{38} +(-0.962868 + 2.01814i) q^{40} +(2.48680 + 1.80677i) q^{41} -9.02860i q^{43} +(-0.784803 - 2.41537i) q^{44} +(0.518324 - 1.59524i) q^{46} +(-10.3526 - 3.36376i) q^{47} -14.4496 q^{49} +(3.88640 - 3.14577i) q^{50} +(0.0846260 + 0.116478i) q^{52} +(-4.72205 - 1.53429i) q^{53} +(-0.741845 + 5.63022i) q^{55} +(-1.43117 - 4.40469i) q^{56} +(-2.14457 + 0.696812i) q^{58} +(-4.25029 - 3.08802i) q^{59} +(11.0841 - 8.05305i) q^{61} +(-0.590048 + 0.812131i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-0.0586344 - 0.316552i) q^{65} +(7.27491 - 2.36376i) q^{67} +7.49100i q^{68} +(-1.35283 + 10.2673i) q^{70} +(3.17196 - 9.76228i) q^{71} +(1.15547 + 1.59036i) q^{73} -0.0889810 q^{74} -6.74065 q^{76} +(-6.91363 - 9.51580i) q^{77} +(-0.230908 + 0.710661i) q^{79} +(-2.19867 + 0.407256i) q^{80} +3.07386i q^{82} +(2.95072 - 0.958745i) q^{83} +(7.21284 - 15.1179i) q^{85} +(7.30429 - 5.30688i) q^{86} +(1.49278 - 2.05464i) q^{88} +(-0.593709 + 0.431355i) q^{89} +(0.539451 + 0.391934i) q^{91} +(1.59524 - 0.518324i) q^{92} +(-3.36376 - 10.3526i) q^{94} +(13.6036 + 6.49035i) q^{95} +(-8.67406 - 2.81837i) q^{97} +(-8.49326 - 11.6900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.809017i 0.415627 + 0.572061i
\(3\) 0 0
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 1.53938 1.62182i 0.688432 0.725301i
\(6\) 0 0
\(7\) 4.63137i 1.75049i 0.483677 + 0.875247i \(0.339301\pi\)
−0.483677 + 0.875247i \(0.660699\pi\)
\(8\) −0.951057 + 0.309017i −0.336249 + 0.109254i
\(9\) 0 0
\(10\) 2.21691 + 0.292102i 0.701048 + 0.0923709i
\(11\) −2.05464 + 1.49278i −0.619497 + 0.450091i −0.852746 0.522326i \(-0.825064\pi\)
0.233249 + 0.972417i \(0.425064\pi\)
\(12\) 0 0
\(13\) 0.0846260 0.116478i 0.0234710 0.0323051i −0.797120 0.603821i \(-0.793644\pi\)
0.820591 + 0.571516i \(0.193644\pi\)
\(14\) −3.74686 + 2.72225i −1.00139 + 0.727552i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 7.12436 2.31485i 1.72791 0.561433i 0.734767 0.678320i \(-0.237292\pi\)
0.993145 + 0.116887i \(0.0372915\pi\)
\(18\) 0 0
\(19\) 2.08298 + 6.41074i 0.477867 + 1.47072i 0.842051 + 0.539397i \(0.181348\pi\)
−0.364184 + 0.931327i \(0.618652\pi\)
\(20\) 1.06675 + 1.96521i 0.238532 + 0.439434i
\(21\) 0 0
\(22\) −2.41537 0.784803i −0.514959 0.167320i
\(23\) −0.985910 1.35699i −0.205576 0.282952i 0.693763 0.720204i \(-0.255952\pi\)
−0.899339 + 0.437252i \(0.855952\pi\)
\(24\) 0 0
\(25\) −0.260613 4.99320i −0.0521225 0.998641i
\(26\) 0.143974 0.0282357
\(27\) 0 0
\(28\) −4.40469 1.43117i −0.832409 0.270466i
\(29\) −0.696812 + 2.14457i −0.129395 + 0.398236i −0.994676 0.103050i \(-0.967140\pi\)
0.865281 + 0.501287i \(0.167140\pi\)
\(30\) 0 0
\(31\) 0.310207 + 0.954718i 0.0557148 + 0.171472i 0.975042 0.222023i \(-0.0712659\pi\)
−0.919327 + 0.393495i \(0.871266\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 6.06035 + 4.40310i 1.03934 + 0.755125i
\(35\) 7.51126 + 7.12944i 1.26963 + 1.20510i
\(36\) 0 0
\(37\) −0.0523017 + 0.0719871i −0.00859835 + 0.0118346i −0.813295 0.581852i \(-0.802328\pi\)
0.804696 + 0.593687i \(0.202328\pi\)
\(38\) −3.96205 + 5.45330i −0.642730 + 0.884642i
\(39\) 0 0
\(40\) −0.962868 + 2.01814i −0.152243 + 0.319096i
\(41\) 2.48680 + 1.80677i 0.388373 + 0.282170i 0.764789 0.644281i \(-0.222843\pi\)
−0.376415 + 0.926451i \(0.622843\pi\)
\(42\) 0 0
\(43\) 9.02860i 1.37685i −0.725308 0.688424i \(-0.758303\pi\)
0.725308 0.688424i \(-0.241697\pi\)
\(44\) −0.784803 2.41537i −0.118313 0.364131i
\(45\) 0 0
\(46\) 0.518324 1.59524i 0.0764226 0.235205i
\(47\) −10.3526 3.36376i −1.51008 0.490655i −0.567141 0.823620i \(-0.691951\pi\)
−0.942939 + 0.332965i \(0.891951\pi\)
\(48\) 0 0
\(49\) −14.4496 −2.06423
\(50\) 3.88640 3.14577i 0.549620 0.444879i
\(51\) 0 0
\(52\) 0.0846260 + 0.116478i 0.0117355 + 0.0161525i
\(53\) −4.72205 1.53429i −0.648624 0.210751i −0.0338165 0.999428i \(-0.510766\pi\)
−0.614807 + 0.788677i \(0.710766\pi\)
\(54\) 0 0
\(55\) −0.741845 + 5.63022i −0.100030 + 0.759179i
\(56\) −1.43117 4.40469i −0.191248 0.588602i
\(57\) 0 0
\(58\) −2.14457 + 0.696812i −0.281596 + 0.0914959i
\(59\) −4.25029 3.08802i −0.553341 0.402026i 0.275675 0.961251i \(-0.411099\pi\)
−0.829016 + 0.559225i \(0.811099\pi\)
\(60\) 0 0
\(61\) 11.0841 8.05305i 1.41917 1.03109i 0.427263 0.904127i \(-0.359478\pi\)
0.991908 0.126960i \(-0.0405221\pi\)
\(62\) −0.590048 + 0.812131i −0.0749362 + 0.103141i
\(63\) 0 0
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) −0.0586344 0.316552i −0.00727270 0.0392634i
\(66\) 0 0
\(67\) 7.27491 2.36376i 0.888771 0.288779i 0.171177 0.985240i \(-0.445243\pi\)
0.717595 + 0.696461i \(0.245243\pi\)
\(68\) 7.49100i 0.908417i
\(69\) 0 0
\(70\) −1.35283 + 10.2673i −0.161695 + 1.22718i
\(71\) 3.17196 9.76228i 0.376442 1.15857i −0.566059 0.824365i \(-0.691532\pi\)
0.942501 0.334204i \(-0.108468\pi\)
\(72\) 0 0
\(73\) 1.15547 + 1.59036i 0.135237 + 0.186138i 0.871264 0.490814i \(-0.163301\pi\)
−0.736027 + 0.676952i \(0.763301\pi\)
\(74\) −0.0889810 −0.0103438
\(75\) 0 0
\(76\) −6.74065 −0.773206
\(77\) −6.91363 9.51580i −0.787881 1.08443i
\(78\) 0 0
\(79\) −0.230908 + 0.710661i −0.0259792 + 0.0799556i −0.963205 0.268766i \(-0.913384\pi\)
0.937226 + 0.348722i \(0.113384\pi\)
\(80\) −2.19867 + 0.407256i −0.245819 + 0.0455326i
\(81\) 0 0
\(82\) 3.07386i 0.339451i
\(83\) 2.95072 0.958745i 0.323883 0.105236i −0.142563 0.989786i \(-0.545534\pi\)
0.466446 + 0.884550i \(0.345534\pi\)
\(84\) 0 0
\(85\) 7.21284 15.1179i 0.782343 1.63976i
\(86\) 7.30429 5.30688i 0.787642 0.572255i
\(87\) 0 0
\(88\) 1.49278 2.05464i 0.159131 0.219025i
\(89\) −0.593709 + 0.431355i −0.0629331 + 0.0457236i −0.618807 0.785543i \(-0.712384\pi\)
0.555874 + 0.831267i \(0.312384\pi\)
\(90\) 0 0
\(91\) 0.539451 + 0.391934i 0.0565498 + 0.0410859i
\(92\) 1.59524 0.518324i 0.166315 0.0540390i
\(93\) 0 0
\(94\) −3.36376 10.3526i −0.346945 1.06779i
\(95\) 13.6036 + 6.49035i 1.39570 + 0.665896i
\(96\) 0 0
\(97\) −8.67406 2.81837i −0.880717 0.286162i −0.166462 0.986048i \(-0.553234\pi\)
−0.714255 + 0.699886i \(0.753234\pi\)
\(98\) −8.49326 11.6900i −0.857948 1.18086i
\(99\) 0 0
\(100\) 4.82935 + 1.29513i 0.482935 + 0.129513i
\(101\) 2.88013 0.286583 0.143292 0.989680i \(-0.454231\pi\)
0.143292 + 0.989680i \(0.454231\pi\)
\(102\) 0 0
\(103\) 10.6246 + 3.45214i 1.04687 + 0.340149i 0.781440 0.623981i \(-0.214486\pi\)
0.265432 + 0.964130i \(0.414486\pi\)
\(104\) −0.0444905 + 0.136928i −0.00436265 + 0.0134269i
\(105\) 0 0
\(106\) −1.53429 4.72205i −0.149023 0.458646i
\(107\) 14.0538i 1.35863i −0.733846 0.679316i \(-0.762277\pi\)
0.733846 0.679316i \(-0.237723\pi\)
\(108\) 0 0
\(109\) 5.43552 + 3.94914i 0.520628 + 0.378259i 0.816841 0.576863i \(-0.195724\pi\)
−0.296212 + 0.955122i \(0.595724\pi\)
\(110\) −4.99099 + 2.70920i −0.475872 + 0.258312i
\(111\) 0 0
\(112\) 2.72225 3.74686i 0.257229 0.354045i
\(113\) 0.586387 0.807092i 0.0551626 0.0759248i −0.780545 0.625100i \(-0.785058\pi\)
0.835707 + 0.549175i \(0.185058\pi\)
\(114\) 0 0
\(115\) −3.71849 0.489952i −0.346751 0.0456883i
\(116\) −1.82428 1.32542i −0.169380 0.123062i
\(117\) 0 0
\(118\) 5.25365i 0.483638i
\(119\) 10.7209 + 32.9956i 0.982784 + 3.02470i
\(120\) 0 0
\(121\) −1.40604 + 4.32736i −0.127822 + 0.393396i
\(122\) 13.0301 + 4.23374i 1.17969 + 0.383305i
\(123\) 0 0
\(124\) −1.00385 −0.0901484
\(125\) −8.49927 7.26377i −0.760198 0.649692i
\(126\) 0 0
\(127\) −6.77227 9.32123i −0.600942 0.827125i 0.394852 0.918745i \(-0.370796\pi\)
−0.995794 + 0.0916192i \(0.970796\pi\)
\(128\) 0.951057 + 0.309017i 0.0840623 + 0.0273135i
\(129\) 0 0
\(130\) 0.221631 0.233501i 0.0194383 0.0204794i
\(131\) 0.551316 + 1.69677i 0.0481687 + 0.148248i 0.972248 0.233953i \(-0.0751662\pi\)
−0.924079 + 0.382201i \(0.875166\pi\)
\(132\) 0 0
\(133\) −29.6905 + 9.64703i −2.57449 + 0.836504i
\(134\) 6.18841 + 4.49614i 0.534597 + 0.388407i
\(135\) 0 0
\(136\) −6.06035 + 4.40310i −0.519670 + 0.377563i
\(137\) −9.41828 + 12.9632i −0.804658 + 1.10752i 0.187467 + 0.982271i \(0.439972\pi\)
−0.992126 + 0.125246i \(0.960028\pi\)
\(138\) 0 0
\(139\) −2.99660 + 2.17716i −0.254168 + 0.184664i −0.707572 0.706641i \(-0.750210\pi\)
0.453404 + 0.891305i \(0.350210\pi\)
\(140\) −9.10161 + 4.94051i −0.769226 + 0.417549i
\(141\) 0 0
\(142\) 9.76228 3.17196i 0.819232 0.266185i
\(143\) 0.365648i 0.0305770i
\(144\) 0 0
\(145\) 2.40545 + 4.43141i 0.199762 + 0.368009i
\(146\) −0.607465 + 1.86958i −0.0502741 + 0.154728i
\(147\) 0 0
\(148\) −0.0523017 0.0719871i −0.00429918 0.00591731i
\(149\) 1.88534 0.154453 0.0772267 0.997014i \(-0.475393\pi\)
0.0772267 + 0.997014i \(0.475393\pi\)
\(150\) 0 0
\(151\) −6.15090 −0.500553 −0.250276 0.968174i \(-0.580522\pi\)
−0.250276 + 0.968174i \(0.580522\pi\)
\(152\) −3.96205 5.45330i −0.321365 0.442321i
\(153\) 0 0
\(154\) 3.63471 11.1865i 0.292893 0.901433i
\(155\) 2.02591 + 0.966575i 0.162725 + 0.0776371i
\(156\) 0 0
\(157\) 23.4830i 1.87414i −0.349137 0.937072i \(-0.613525\pi\)
0.349137 0.937072i \(-0.386475\pi\)
\(158\) −0.710661 + 0.230908i −0.0565372 + 0.0183700i
\(159\) 0 0
\(160\) −1.62182 1.53938i −0.128216 0.121699i
\(161\) 6.28472 4.56611i 0.495305 0.359860i
\(162\) 0 0
\(163\) 9.27366 12.7641i 0.726369 0.999762i −0.272919 0.962037i \(-0.587989\pi\)
0.999288 0.0377245i \(-0.0120109\pi\)
\(164\) −2.48680 + 1.80677i −0.194187 + 0.141085i
\(165\) 0 0
\(166\) 2.51003 + 1.82364i 0.194816 + 0.141542i
\(167\) −3.84208 + 1.24837i −0.297309 + 0.0966016i −0.453873 0.891066i \(-0.649958\pi\)
0.156564 + 0.987668i \(0.449958\pi\)
\(168\) 0 0
\(169\) 4.01082 + 12.3440i 0.308524 + 0.949540i
\(170\) 16.4702 3.05076i 1.26321 0.233982i
\(171\) 0 0
\(172\) 8.58671 + 2.78999i 0.654730 + 0.212735i
\(173\) −11.8495 16.3094i −0.900899 1.23998i −0.970180 0.242384i \(-0.922070\pi\)
0.0692809 0.997597i \(-0.477930\pi\)
\(174\) 0 0
\(175\) 23.1254 1.20699i 1.74811 0.0912402i
\(176\) 2.53967 0.191435
\(177\) 0 0
\(178\) −0.697947 0.226777i −0.0523134 0.0169976i
\(179\) −2.39818 + 7.38084i −0.179248 + 0.551670i −0.999802 0.0198998i \(-0.993665\pi\)
0.820554 + 0.571570i \(0.193665\pi\)
\(180\) 0 0
\(181\) 3.64358 + 11.2138i 0.270825 + 0.833515i 0.990294 + 0.138990i \(0.0443855\pi\)
−0.719469 + 0.694525i \(0.755615\pi\)
\(182\) 0.666798i 0.0494264i
\(183\) 0 0
\(184\) 1.35699 + 0.985910i 0.100039 + 0.0726822i
\(185\) 0.0362381 + 0.195640i 0.00266427 + 0.0143837i
\(186\) 0 0
\(187\) −11.1824 + 15.3913i −0.817741 + 1.12552i
\(188\) 6.39825 8.80644i 0.466641 0.642276i
\(189\) 0 0
\(190\) 2.74517 + 14.8205i 0.199156 + 1.07519i
\(191\) 3.95155 + 2.87097i 0.285924 + 0.207736i 0.721497 0.692417i \(-0.243454\pi\)
−0.435573 + 0.900153i \(0.643454\pi\)
\(192\) 0 0
\(193\) 18.7342i 1.34852i 0.738496 + 0.674258i \(0.235536\pi\)
−0.738496 + 0.674258i \(0.764464\pi\)
\(194\) −2.81837 8.67406i −0.202347 0.622761i
\(195\) 0 0
\(196\) 4.46517 13.7424i 0.318941 0.981598i
\(197\) 1.19314 + 0.387674i 0.0850075 + 0.0276206i 0.351212 0.936296i \(-0.385770\pi\)
−0.266204 + 0.963917i \(0.585770\pi\)
\(198\) 0 0
\(199\) −19.3703 −1.37312 −0.686562 0.727071i \(-0.740881\pi\)
−0.686562 + 0.727071i \(0.740881\pi\)
\(200\) 1.79084 + 4.66828i 0.126632 + 0.330098i
\(201\) 0 0
\(202\) 1.69290 + 2.33007i 0.119112 + 0.163943i
\(203\) −9.93229 3.22720i −0.697110 0.226505i
\(204\) 0 0
\(205\) 6.75839 1.25185i 0.472027 0.0874328i
\(206\) 3.45214 + 10.6246i 0.240522 + 0.740250i
\(207\) 0 0
\(208\) −0.136928 + 0.0444905i −0.00949423 + 0.00308486i
\(209\) −13.8496 10.0623i −0.957997 0.696026i
\(210\) 0 0
\(211\) 1.01062 0.734260i 0.0695741 0.0505485i −0.552455 0.833543i \(-0.686309\pi\)
0.622029 + 0.782994i \(0.286309\pi\)
\(212\) 2.91839 4.01682i 0.200436 0.275876i
\(213\) 0 0
\(214\) 11.3698 8.26061i 0.777221 0.564684i
\(215\) −14.6428 13.8985i −0.998629 0.947867i
\(216\) 0 0
\(217\) −4.42165 + 1.43668i −0.300161 + 0.0975283i
\(218\) 6.71867i 0.455046i
\(219\) 0 0
\(220\) −5.12542 2.44537i −0.345556 0.164867i
\(221\) 0.333278 1.02573i 0.0224187 0.0689978i
\(222\) 0 0
\(223\) 12.8640 + 17.7058i 0.861437 + 1.18567i 0.981225 + 0.192867i \(0.0617787\pi\)
−0.119788 + 0.992800i \(0.538221\pi\)
\(224\) 4.63137 0.309446
\(225\) 0 0
\(226\) 0.997621 0.0663607
\(227\) 8.52486 + 11.7335i 0.565815 + 0.778777i 0.992051 0.125835i \(-0.0401609\pi\)
−0.426237 + 0.904612i \(0.640161\pi\)
\(228\) 0 0
\(229\) −1.45262 + 4.47071i −0.0959920 + 0.295433i −0.987511 0.157550i \(-0.949640\pi\)
0.891519 + 0.452983i \(0.149640\pi\)
\(230\) −1.78929 3.29630i −0.117982 0.217352i
\(231\) 0 0
\(232\) 2.25493i 0.148044i
\(233\) 11.2403 3.65218i 0.736374 0.239262i 0.0832661 0.996527i \(-0.473465\pi\)
0.653108 + 0.757265i \(0.273465\pi\)
\(234\) 0 0
\(235\) −21.3920 + 11.6119i −1.39546 + 0.757480i
\(236\) 4.25029 3.08802i 0.276671 0.201013i
\(237\) 0 0
\(238\) −20.3924 + 28.0677i −1.32184 + 1.81936i
\(239\) −7.85849 + 5.70953i −0.508324 + 0.369319i −0.812187 0.583397i \(-0.801723\pi\)
0.303864 + 0.952716i \(0.401723\pi\)
\(240\) 0 0
\(241\) −5.40451 3.92661i −0.348135 0.252935i 0.399951 0.916537i \(-0.369027\pi\)
−0.748086 + 0.663601i \(0.769027\pi\)
\(242\) −4.32736 + 1.40604i −0.278173 + 0.0903839i
\(243\) 0 0
\(244\) 4.23374 + 13.0301i 0.271037 + 0.834168i
\(245\) −22.2434 + 23.4347i −1.42108 + 1.49719i
\(246\) 0 0
\(247\) 0.922982 + 0.299895i 0.0587279 + 0.0190819i
\(248\) −0.590048 0.812131i −0.0374681 0.0515704i
\(249\) 0 0
\(250\) 0.880772 11.1456i 0.0557049 0.704909i
\(251\) 19.6023 1.23729 0.618644 0.785672i \(-0.287683\pi\)
0.618644 + 0.785672i \(0.287683\pi\)
\(252\) 0 0
\(253\) 4.05138 + 1.31637i 0.254708 + 0.0827597i
\(254\) 3.56039 10.9578i 0.223399 0.687551i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 9.46931i 0.590679i −0.955392 0.295340i \(-0.904567\pi\)
0.955392 0.295340i \(-0.0954328\pi\)
\(258\) 0 0
\(259\) −0.333399 0.242229i −0.0207164 0.0150514i
\(260\) 0.319178 + 0.0420552i 0.0197946 + 0.00260815i
\(261\) 0 0
\(262\) −1.04866 + 1.44336i −0.0647867 + 0.0891713i
\(263\) −12.4296 + 17.1079i −0.766441 + 1.05492i 0.230210 + 0.973141i \(0.426059\pi\)
−0.996651 + 0.0817747i \(0.973941\pi\)
\(264\) 0 0
\(265\) −9.75738 + 5.29647i −0.599391 + 0.325360i
\(266\) −25.2563 18.3497i −1.54856 1.12509i
\(267\) 0 0
\(268\) 7.64929i 0.467255i
\(269\) −0.603355 1.85694i −0.0367872 0.113219i 0.930977 0.365079i \(-0.118958\pi\)
−0.967764 + 0.251859i \(0.918958\pi\)
\(270\) 0 0
\(271\) −4.91521 + 15.1274i −0.298577 + 0.918927i 0.683419 + 0.730027i \(0.260492\pi\)
−0.981996 + 0.188900i \(0.939508\pi\)
\(272\) −7.12436 2.31485i −0.431978 0.140358i
\(273\) 0 0
\(274\) −16.0233 −0.968006
\(275\) 7.98924 + 9.87020i 0.481769 + 0.595195i
\(276\) 0 0
\(277\) 1.16998 + 1.61033i 0.0702970 + 0.0967555i 0.842718 0.538356i \(-0.180954\pi\)
−0.772421 + 0.635111i \(0.780954\pi\)
\(278\) −3.52272 1.14460i −0.211278 0.0686485i
\(279\) 0 0
\(280\) −9.34675 4.45940i −0.558575 0.266500i
\(281\) 7.78302 + 23.9537i 0.464296 + 1.42896i 0.859866 + 0.510521i \(0.170547\pi\)
−0.395569 + 0.918436i \(0.629453\pi\)
\(282\) 0 0
\(283\) 10.7090 3.47958i 0.636586 0.206839i 0.0270957 0.999633i \(-0.491374\pi\)
0.609490 + 0.792794i \(0.291374\pi\)
\(284\) 8.30429 + 6.03342i 0.492769 + 0.358018i
\(285\) 0 0
\(286\) −0.295815 + 0.214922i −0.0174919 + 0.0127086i
\(287\) −8.36781 + 11.5173i −0.493936 + 0.679845i
\(288\) 0 0
\(289\) 31.6448 22.9913i 1.86146 1.35243i
\(290\) −2.17120 + 4.55077i −0.127497 + 0.267230i
\(291\) 0 0
\(292\) −1.86958 + 0.607465i −0.109409 + 0.0355492i
\(293\) 20.0482i 1.17123i 0.810591 + 0.585613i \(0.199146\pi\)
−0.810591 + 0.585613i \(0.800854\pi\)
\(294\) 0 0
\(295\) −11.5510 + 2.13958i −0.672527 + 0.124571i
\(296\) 0.0274966 0.0846260i 0.00159821 0.00491878i
\(297\) 0 0
\(298\) 1.10818 + 1.52528i 0.0641950 + 0.0883569i
\(299\) −0.241492 −0.0139659
\(300\) 0 0
\(301\) 41.8148 2.41016
\(302\) −3.61541 4.97618i −0.208043 0.286347i
\(303\) 0 0
\(304\) 2.08298 6.41074i 0.119467 0.367681i
\(305\) 4.00200 30.3731i 0.229154 1.73916i
\(306\) 0 0
\(307\) 14.4493i 0.824668i −0.911033 0.412334i \(-0.864714\pi\)
0.911033 0.412334i \(-0.135286\pi\)
\(308\) 11.1865 3.63471i 0.637410 0.207107i
\(309\) 0 0
\(310\) 0.408824 + 2.20713i 0.0232196 + 0.125357i
\(311\) −19.0778 + 13.8608i −1.08180 + 0.785977i −0.977997 0.208621i \(-0.933103\pi\)
−0.103807 + 0.994597i \(0.533103\pi\)
\(312\) 0 0
\(313\) 16.1598 22.2420i 0.913405 1.25719i −0.0525858 0.998616i \(-0.516746\pi\)
0.965991 0.258577i \(-0.0832537\pi\)
\(314\) 18.9981 13.8029i 1.07213 0.778945i
\(315\) 0 0
\(316\) −0.604525 0.439213i −0.0340072 0.0247077i
\(317\) 5.74985 1.86824i 0.322944 0.104931i −0.143059 0.989714i \(-0.545694\pi\)
0.466002 + 0.884783i \(0.345694\pi\)
\(318\) 0 0
\(319\) −1.76968 5.44650i −0.0990829 0.304946i
\(320\) 0.292102 2.21691i 0.0163290 0.123929i
\(321\) 0 0
\(322\) 7.38813 + 2.40055i 0.411724 + 0.133777i
\(323\) 29.6798 + 40.8507i 1.65143 + 2.27299i
\(324\) 0 0
\(325\) −0.603651 0.392199i −0.0334845 0.0217553i
\(326\) 15.7773 0.873824
\(327\) 0 0
\(328\) −2.92341 0.949874i −0.161418 0.0524480i
\(329\) 15.5788 47.9467i 0.858888 2.64339i
\(330\) 0 0
\(331\) 5.23211 + 16.1028i 0.287583 + 0.885089i 0.985613 + 0.169020i \(0.0540603\pi\)
−0.698030 + 0.716069i \(0.745940\pi\)
\(332\) 3.10257i 0.170275i
\(333\) 0 0
\(334\) −3.26827 2.37454i −0.178832 0.129929i
\(335\) 7.36525 15.4373i 0.402407 0.843432i
\(336\) 0 0
\(337\) −13.3205 + 18.3341i −0.725616 + 0.998724i 0.273703 + 0.961814i \(0.411751\pi\)
−0.999319 + 0.0369100i \(0.988249\pi\)
\(338\) −7.62902 + 10.5005i −0.414964 + 0.571149i
\(339\) 0 0
\(340\) 12.1491 + 11.5315i 0.658876 + 0.625384i
\(341\) −2.06255 1.49853i −0.111693 0.0811500i
\(342\) 0 0
\(343\) 34.5018i 1.86292i
\(344\) 2.78999 + 8.58671i 0.150426 + 0.462964i
\(345\) 0 0
\(346\) 6.22964 19.1729i 0.334908 1.03074i
\(347\) 9.75025 + 3.16805i 0.523421 + 0.170070i 0.558797 0.829304i \(-0.311263\pi\)
−0.0353763 + 0.999374i \(0.511263\pi\)
\(348\) 0 0
\(349\) −1.38746 −0.0742691 −0.0371346 0.999310i \(-0.511823\pi\)
−0.0371346 + 0.999310i \(0.511823\pi\)
\(350\) 14.5692 + 17.9994i 0.778758 + 0.962107i
\(351\) 0 0
\(352\) 1.49278 + 2.05464i 0.0795656 + 0.109513i
\(353\) 12.2858 + 3.99189i 0.653906 + 0.212467i 0.617136 0.786857i \(-0.288293\pi\)
0.0367706 + 0.999324i \(0.488293\pi\)
\(354\) 0 0
\(355\) −10.9498 20.1722i −0.581156 1.07063i
\(356\) −0.226777 0.697947i −0.0120191 0.0369911i
\(357\) 0 0
\(358\) −7.38084 + 2.39818i −0.390089 + 0.126748i
\(359\) −7.98876 5.80417i −0.421630 0.306332i 0.356663 0.934233i \(-0.383914\pi\)
−0.778294 + 0.627901i \(0.783914\pi\)
\(360\) 0 0
\(361\) −21.3875 + 15.5389i −1.12566 + 0.817837i
\(362\) −6.93051 + 9.53902i −0.364259 + 0.501360i
\(363\) 0 0
\(364\) −0.539451 + 0.391934i −0.0282749 + 0.0205429i
\(365\) 4.35799 + 0.574214i 0.228108 + 0.0300557i
\(366\) 0 0
\(367\) −5.05886 + 1.64372i −0.264070 + 0.0858016i −0.438060 0.898946i \(-0.644334\pi\)
0.173989 + 0.984748i \(0.444334\pi\)
\(368\) 1.67733i 0.0874369i
\(369\) 0 0
\(370\) −0.136976 + 0.144311i −0.00712103 + 0.00750239i
\(371\) 7.10585 21.8696i 0.368918 1.13541i
\(372\) 0 0
\(373\) −5.69246 7.83499i −0.294744 0.405681i 0.635804 0.771851i \(-0.280669\pi\)
−0.930548 + 0.366170i \(0.880669\pi\)
\(374\) −19.0247 −0.983744
\(375\) 0 0
\(376\) 10.8854 0.561369
\(377\) 0.190826 + 0.262649i 0.00982803 + 0.0135271i
\(378\) 0 0
\(379\) 6.95968 21.4197i 0.357495 1.10026i −0.597054 0.802201i \(-0.703662\pi\)
0.954549 0.298055i \(-0.0963379\pi\)
\(380\) −10.3764 + 10.9321i −0.532300 + 0.560807i
\(381\) 0 0
\(382\) 4.88438i 0.249907i
\(383\) 6.85864 2.22851i 0.350460 0.113871i −0.128497 0.991710i \(-0.541015\pi\)
0.478957 + 0.877839i \(0.341015\pi\)
\(384\) 0 0
\(385\) −26.0756 3.43576i −1.32894 0.175102i
\(386\) −15.1563 + 11.0117i −0.771434 + 0.560479i
\(387\) 0 0
\(388\) 5.36086 7.37859i 0.272157 0.374591i
\(389\) −10.7139 + 7.78411i −0.543217 + 0.394670i −0.825278 0.564726i \(-0.808982\pi\)
0.282062 + 0.959396i \(0.408982\pi\)
\(390\) 0 0
\(391\) −10.1652 7.38545i −0.514076 0.373498i
\(392\) 13.7424 4.46517i 0.694095 0.225525i
\(393\) 0 0
\(394\) 0.387674 + 1.19314i 0.0195307 + 0.0601094i
\(395\) 0.797111 + 1.46847i 0.0401070 + 0.0738867i
\(396\) 0 0
\(397\) −27.8304 9.04265i −1.39677 0.453838i −0.488624 0.872494i \(-0.662501\pi\)
−0.908144 + 0.418657i \(0.862501\pi\)
\(398\) −11.3856 15.6709i −0.570707 0.785511i
\(399\) 0 0
\(400\) −2.72409 + 4.19277i −0.136205 + 0.209639i
\(401\) −27.4005 −1.36832 −0.684158 0.729334i \(-0.739830\pi\)
−0.684158 + 0.729334i \(0.739830\pi\)
\(402\) 0 0
\(403\) 0.137455 + 0.0446618i 0.00684711 + 0.00222476i
\(404\) −0.890008 + 2.73916i −0.0442796 + 0.136279i
\(405\) 0 0
\(406\) −3.22720 9.93229i −0.160163 0.492931i
\(407\) 0.225983i 0.0112016i
\(408\) 0 0
\(409\) 8.09226 + 5.87937i 0.400137 + 0.290716i 0.769597 0.638530i \(-0.220457\pi\)
−0.369460 + 0.929247i \(0.620457\pi\)
\(410\) 4.98525 + 4.73184i 0.246204 + 0.233689i
\(411\) 0 0
\(412\) −6.56635 + 9.03781i −0.323501 + 0.445261i
\(413\) 14.3018 19.6847i 0.703744 0.968620i
\(414\) 0 0
\(415\) 2.98736 6.26141i 0.146644 0.307360i
\(416\) −0.116478 0.0846260i −0.00571079 0.00414913i
\(417\) 0 0
\(418\) 17.1191i 0.837320i
\(419\) −2.48795 7.65713i −0.121544 0.374075i 0.871711 0.490020i \(-0.163010\pi\)
−0.993256 + 0.115945i \(0.963010\pi\)
\(420\) 0 0
\(421\) 3.10662 9.56120i 0.151408 0.465984i −0.846372 0.532593i \(-0.821218\pi\)
0.997779 + 0.0666083i \(0.0212178\pi\)
\(422\) 1.18806 + 0.386023i 0.0578337 + 0.0187913i
\(423\) 0 0
\(424\) 4.96506 0.241125
\(425\) −13.4152 34.9701i −0.650733 1.69630i
\(426\) 0 0
\(427\) 37.2967 + 51.3345i 1.80491 + 2.48425i
\(428\) 13.3660 + 4.34286i 0.646068 + 0.209920i
\(429\) 0 0
\(430\) 2.63727 20.0156i 0.127181 0.965236i
\(431\) −7.09793 21.8452i −0.341895 1.05225i −0.963225 0.268697i \(-0.913407\pi\)
0.621329 0.783549i \(-0.286593\pi\)
\(432\) 0 0
\(433\) 17.1156 5.56121i 0.822525 0.267254i 0.132631 0.991165i \(-0.457657\pi\)
0.689893 + 0.723911i \(0.257657\pi\)
\(434\) −3.76128 2.73273i −0.180547 0.131175i
\(435\) 0 0
\(436\) −5.43552 + 3.94914i −0.260314 + 0.189129i
\(437\) 6.64567 9.14699i 0.317906 0.437560i
\(438\) 0 0
\(439\) −21.1610 + 15.3743i −1.00996 + 0.733777i −0.964200 0.265176i \(-0.914570\pi\)
−0.0457572 + 0.998953i \(0.514570\pi\)
\(440\) −1.03430 5.58390i −0.0493082 0.266202i
\(441\) 0 0
\(442\) 1.02573 0.333278i 0.0487888 0.0158524i
\(443\) 40.5689i 1.92749i −0.266833 0.963743i \(-0.585977\pi\)
0.266833 0.963743i \(-0.414023\pi\)
\(444\) 0 0
\(445\) −0.214364 + 1.62691i −0.0101618 + 0.0771230i
\(446\) −6.76301 + 20.8144i −0.320238 + 0.985590i
\(447\) 0 0
\(448\) 2.72225 + 3.74686i 0.128614 + 0.177022i
\(449\) −23.1589 −1.09294 −0.546468 0.837480i \(-0.684028\pi\)
−0.546468 + 0.837480i \(0.684028\pi\)
\(450\) 0 0
\(451\) −7.80660 −0.367598
\(452\) 0.586387 + 0.807092i 0.0275813 + 0.0379624i
\(453\) 0 0
\(454\) −4.48178 + 13.7935i −0.210340 + 0.647361i
\(455\) 1.46607 0.271558i 0.0687303 0.0127308i
\(456\) 0 0
\(457\) 38.3997i 1.79626i −0.439728 0.898131i \(-0.644925\pi\)
0.439728 0.898131i \(-0.355075\pi\)
\(458\) −4.47071 + 1.45262i −0.208903 + 0.0678766i
\(459\) 0 0
\(460\) 1.61505 3.38509i 0.0753020 0.157830i
\(461\) −26.3670 + 19.1567i −1.22803 + 0.892217i −0.996741 0.0806677i \(-0.974295\pi\)
−0.231290 + 0.972885i \(0.574295\pi\)
\(462\) 0 0
\(463\) 1.49167 2.05311i 0.0693238 0.0954160i −0.772947 0.634470i \(-0.781218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(464\) 1.82428 1.32542i 0.0846900 0.0615309i
\(465\) 0 0
\(466\) 9.56154 + 6.94686i 0.442930 + 0.321807i
\(467\) 1.42329 0.462456i 0.0658622 0.0213999i −0.275901 0.961186i \(-0.588976\pi\)
0.341763 + 0.939786i \(0.388976\pi\)
\(468\) 0 0
\(469\) 10.9475 + 33.6928i 0.505506 + 1.55579i
\(470\) −21.9682 10.4812i −1.01332 0.483460i
\(471\) 0 0
\(472\) 4.99652 + 1.62347i 0.229983 + 0.0747262i
\(473\) 13.4777 + 18.5505i 0.619707 + 0.852954i
\(474\) 0 0
\(475\) 31.4673 12.0714i 1.44382 0.553876i
\(476\) −34.6936 −1.59018
\(477\) 0 0
\(478\) −9.23821 3.00168i −0.422546 0.137294i
\(479\) 7.50880 23.1097i 0.343086 1.05591i −0.619514 0.784985i \(-0.712670\pi\)
0.962600 0.270925i \(-0.0873295\pi\)
\(480\) 0 0
\(481\) 0.00395881 + 0.0121840i 0.000180506 + 0.000555541i
\(482\) 6.68035i 0.304281i
\(483\) 0 0
\(484\) −3.68107 2.67445i −0.167321 0.121566i
\(485\) −17.9236 + 9.72923i −0.813868 + 0.441782i
\(486\) 0 0
\(487\) −5.87877 + 8.09143i −0.266392 + 0.366658i −0.921168 0.389166i \(-0.872763\pi\)
0.654775 + 0.755824i \(0.272763\pi\)
\(488\) −8.05305 + 11.0841i −0.364545 + 0.501753i
\(489\) 0 0
\(490\) −32.0334 4.22076i −1.44712 0.190674i
\(491\) 3.38163 + 2.45690i 0.152611 + 0.110878i 0.661470 0.749971i \(-0.269933\pi\)
−0.508860 + 0.860850i \(0.669933\pi\)
\(492\) 0 0
\(493\) 16.8917i 0.760764i
\(494\) 0.299895 + 0.922982i 0.0134929 + 0.0415269i
\(495\) 0 0
\(496\) 0.310207 0.954718i 0.0139287 0.0428681i
\(497\) 45.2127 + 14.6905i 2.02807 + 0.658959i
\(498\) 0 0
\(499\) −1.70548 −0.0763476 −0.0381738 0.999271i \(-0.512154\pi\)
−0.0381738 + 0.999271i \(0.512154\pi\)
\(500\) 9.53468 5.83866i 0.426404 0.261113i
\(501\) 0 0
\(502\) 11.5220 + 15.8586i 0.514250 + 0.707804i
\(503\) −29.4265 9.56125i −1.31206 0.426315i −0.432301 0.901729i \(-0.642298\pi\)
−0.879762 + 0.475414i \(0.842298\pi\)
\(504\) 0 0
\(505\) 4.43361 4.67105i 0.197293 0.207859i
\(506\) 1.31637 + 4.05138i 0.0585199 + 0.180106i
\(507\) 0 0
\(508\) 10.9578 3.56039i 0.486172 0.157967i
\(509\) 29.2182 + 21.2283i 1.29507 + 0.940926i 0.999895 0.0145162i \(-0.00462080\pi\)
0.295179 + 0.955442i \(0.404621\pi\)
\(510\) 0 0
\(511\) −7.36556 + 5.35139i −0.325833 + 0.236732i
\(512\) −0.587785 + 0.809017i −0.0259767 + 0.0357538i
\(513\) 0 0
\(514\) 7.66083 5.56592i 0.337905 0.245502i
\(515\) 21.9540 11.9170i 0.967410 0.525127i
\(516\) 0 0
\(517\) 26.2922 8.54286i 1.15633 0.375714i
\(518\) 0.412104i 0.0181068i
\(519\) 0 0
\(520\) 0.153584 + 0.282940i 0.00673513 + 0.0124077i
\(521\) −1.38131 + 4.25122i −0.0605161 + 0.186249i −0.976744 0.214407i \(-0.931218\pi\)
0.916228 + 0.400657i \(0.131218\pi\)
\(522\) 0 0
\(523\) −18.0150 24.7955i −0.787741 1.08423i −0.994386 0.105817i \(-0.966254\pi\)
0.206644 0.978416i \(-0.433746\pi\)
\(524\) −1.78409 −0.0779385
\(525\) 0 0
\(526\) −21.1465 −0.922030
\(527\) 4.42005 + 6.08368i 0.192540 + 0.265009i
\(528\) 0 0
\(529\) 6.23799 19.1986i 0.271217 0.834720i
\(530\) −10.0202 4.78070i −0.435249 0.207660i
\(531\) 0 0
\(532\) 31.2184i 1.35349i
\(533\) 0.420896 0.136757i 0.0182310 0.00592362i
\(534\) 0 0
\(535\) −22.7928 21.6341i −0.985417 0.935326i
\(536\) −6.18841 + 4.49614i −0.267298 + 0.194204i
\(537\) 0 0
\(538\) 1.14765 1.57960i 0.0494787 0.0681016i
\(539\) 29.6887 21.5701i 1.27878 0.929090i
\(540\) 0 0
\(541\) −11.9065 8.65055i −0.511899 0.371916i 0.301645 0.953420i \(-0.402464\pi\)
−0.813543 + 0.581504i \(0.802464\pi\)
\(542\) −15.1274 + 4.91521i −0.649780 + 0.211126i
\(543\) 0 0
\(544\) −2.31485 7.12436i −0.0992482 0.305455i
\(545\) 14.7721 2.73622i 0.632769 0.117207i
\(546\) 0 0
\(547\) 10.1457 + 3.29653i 0.433798 + 0.140950i 0.517773 0.855518i \(-0.326761\pi\)
−0.0839742 + 0.996468i \(0.526761\pi\)
\(548\) −9.41828 12.9632i −0.402329 0.553759i
\(549\) 0 0
\(550\) −3.28920 + 12.2650i −0.140252 + 0.522981i
\(551\) −15.1997 −0.647529
\(552\) 0 0
\(553\) −3.29134 1.06942i −0.139962 0.0454764i
\(554\) −0.615092 + 1.89306i −0.0261328 + 0.0804284i
\(555\) 0 0
\(556\) −1.14460 3.52272i −0.0485418 0.149396i
\(557\) 16.1652i 0.684942i 0.939528 + 0.342471i \(0.111264\pi\)
−0.939528 + 0.342471i \(0.888736\pi\)
\(558\) 0 0
\(559\) −1.05163 0.764054i −0.0444792 0.0323160i
\(560\) −1.88615 10.1828i −0.0797045 0.430304i
\(561\) 0 0
\(562\) −14.8042 + 20.3762i −0.624477 + 0.859519i
\(563\) 25.5559 35.1746i 1.07705 1.48243i 0.214326 0.976762i \(-0.431245\pi\)
0.862726 0.505672i \(-0.168755\pi\)
\(564\) 0 0
\(565\) −0.406287 2.19344i −0.0170926 0.0922786i
\(566\) 9.10965 + 6.61855i 0.382907 + 0.278198i
\(567\) 0 0
\(568\) 10.2647i 0.430696i
\(569\) 3.71683 + 11.4392i 0.155818 + 0.479558i 0.998243 0.0592558i \(-0.0188728\pi\)
−0.842425 + 0.538813i \(0.818873\pi\)
\(570\) 0 0
\(571\) 5.80332 17.8608i 0.242861 0.747450i −0.753120 0.657884i \(-0.771452\pi\)
0.995981 0.0895664i \(-0.0285481\pi\)
\(572\) −0.347752 0.112991i −0.0145402 0.00472441i
\(573\) 0 0
\(574\) −14.2362 −0.594206
\(575\) −6.51878 + 5.27650i −0.271852 + 0.220045i
\(576\) 0 0
\(577\) −12.4817 17.1796i −0.519619 0.715195i 0.465885 0.884845i \(-0.345736\pi\)
−0.985504 + 0.169651i \(0.945736\pi\)
\(578\) 37.2007 + 12.0872i 1.54734 + 0.502762i
\(579\) 0 0
\(580\) −4.95785 + 0.918335i −0.205863 + 0.0381318i
\(581\) 4.44031 + 13.6659i 0.184215 + 0.566955i
\(582\) 0 0
\(583\) 11.9925 3.89659i 0.496678 0.161380i
\(584\) −1.59036 1.15547i −0.0658097 0.0478135i
\(585\) 0 0
\(586\) −16.2193 + 11.7840i −0.670013 + 0.486793i
\(587\) −19.1781 + 26.3964i −0.791566 + 1.08950i 0.202345 + 0.979314i \(0.435144\pi\)
−0.993911 + 0.110183i \(0.964856\pi\)
\(588\) 0 0
\(589\) −5.47429 + 3.97731i −0.225564 + 0.163882i
\(590\) −8.52049 8.08737i −0.350783 0.332952i
\(591\) 0 0
\(592\) 0.0846260 0.0274966i 0.00347811 0.00113011i
\(593\) 0.911868i 0.0374460i 0.999825 + 0.0187230i \(0.00596006\pi\)
−0.999825 + 0.0187230i \(0.994040\pi\)
\(594\) 0 0
\(595\) 70.0165 + 33.4053i 2.87040 + 1.36949i
\(596\) −0.582604 + 1.79307i −0.0238644 + 0.0734470i
\(597\) 0 0
\(598\) −0.141946 0.195371i −0.00580459 0.00798933i
\(599\) −35.5516 −1.45260 −0.726300 0.687378i \(-0.758762\pi\)
−0.726300 + 0.687378i \(0.758762\pi\)
\(600\) 0 0
\(601\) −42.8608 −1.74833 −0.874164 0.485630i \(-0.838590\pi\)
−0.874164 + 0.485630i \(0.838590\pi\)
\(602\) 24.5781 + 33.8289i 1.00173 + 1.37876i
\(603\) 0 0
\(604\) 1.90073 5.84985i 0.0773397 0.238027i
\(605\) 4.85377 + 8.94180i 0.197334 + 0.363536i
\(606\) 0 0
\(607\) 47.7389i 1.93766i 0.247724 + 0.968831i \(0.420317\pi\)
−0.247724 + 0.968831i \(0.579683\pi\)
\(608\) 6.41074 2.08298i 0.259990 0.0844758i
\(609\) 0 0
\(610\) 26.9247 14.6152i 1.09015 0.591752i
\(611\) −1.26790 + 0.921184i −0.0512938 + 0.0372671i
\(612\) 0 0
\(613\) −14.4025 + 19.8234i −0.581713 + 0.800660i −0.993882 0.110448i \(-0.964771\pi\)
0.412169 + 0.911108i \(0.364771\pi\)
\(614\) 11.6898 8.49311i 0.471761 0.342754i
\(615\) 0 0
\(616\) 9.51580 + 6.91363i 0.383402 + 0.278558i
\(617\) 2.49230 0.809796i 0.100336 0.0326012i −0.258419 0.966033i \(-0.583201\pi\)
0.358755 + 0.933432i \(0.383201\pi\)
\(618\) 0 0
\(619\) 2.08751 + 6.42470i 0.0839041 + 0.258230i 0.984204 0.177041i \(-0.0566525\pi\)
−0.900299 + 0.435271i \(0.856652\pi\)
\(620\) −1.54531 + 1.62807i −0.0620610 + 0.0653847i
\(621\) 0 0
\(622\) −22.4273 7.28708i −0.899254 0.292185i
\(623\) −1.99777 2.74969i −0.0800388 0.110164i
\(624\) 0 0
\(625\) −24.8642 + 2.60258i −0.994566 + 0.104103i
\(626\) 27.4927 1.09883
\(627\) 0 0
\(628\) 22.3336 + 7.25663i 0.891208 + 0.289571i
\(629\) −0.205977 + 0.633933i −0.00821285 + 0.0252766i
\(630\) 0 0
\(631\) −9.31855 28.6796i −0.370966 1.14172i −0.946160 0.323699i \(-0.895074\pi\)
0.575194 0.818017i \(-0.304926\pi\)
\(632\) 0.747233i 0.0297234i
\(633\) 0 0
\(634\) 4.89111 + 3.55360i 0.194251 + 0.141132i
\(635\) −25.5425 3.36551i −1.01362 0.133556i
\(636\) 0 0
\(637\) −1.22281 + 1.68305i −0.0484495 + 0.0666850i
\(638\) 3.36612 4.63307i 0.133266 0.183425i
\(639\) 0 0
\(640\) 1.96521 1.06675i 0.0776817 0.0421670i
\(641\) 16.6059 + 12.0649i 0.655892 + 0.476534i 0.865273 0.501301i \(-0.167145\pi\)
−0.209381 + 0.977834i \(0.567145\pi\)
\(642\) 0 0
\(643\) 33.4413i 1.31880i 0.751793 + 0.659399i \(0.229189\pi\)
−0.751793 + 0.659399i \(0.770811\pi\)
\(644\) 2.40055 + 7.38813i 0.0945949 + 0.291133i
\(645\) 0 0
\(646\) −15.6036 + 48.0228i −0.613914 + 1.88943i
\(647\) −17.2006 5.58881i −0.676224 0.219719i −0.0492828 0.998785i \(-0.515694\pi\)
−0.626942 + 0.779066i \(0.715694\pi\)
\(648\) 0 0
\(649\) 13.3426 0.523742
\(650\) −0.0375215 0.718893i −0.00147172 0.0281973i
\(651\) 0 0
\(652\) 9.27366 + 12.7641i 0.363185 + 0.499881i
\(653\) 29.4770 + 9.57766i 1.15352 + 0.374803i 0.822470 0.568809i \(-0.192596\pi\)
0.331055 + 0.943612i \(0.392596\pi\)
\(654\) 0 0
\(655\) 3.60055 + 1.71785i 0.140685 + 0.0671218i
\(656\) −0.949874 2.92341i −0.0370864 0.114140i
\(657\) 0 0
\(658\) 47.9467 15.5788i 1.86916 0.607326i
\(659\) 17.4953 + 12.7110i 0.681519 + 0.495152i 0.873861 0.486176i \(-0.161608\pi\)
−0.192343 + 0.981328i \(0.561608\pi\)
\(660\) 0 0
\(661\) 29.7396 21.6071i 1.15674 0.840418i 0.167374 0.985893i \(-0.446471\pi\)
0.989362 + 0.145476i \(0.0464713\pi\)
\(662\) −9.95207 + 13.6978i −0.386798 + 0.532382i
\(663\) 0 0
\(664\) −2.51003 + 1.82364i −0.0974080 + 0.0707710i
\(665\) −30.0592 + 63.0032i −1.16565 + 2.44316i
\(666\) 0 0
\(667\) 3.59715 1.16878i 0.139282 0.0452555i
\(668\) 4.03980i 0.156305i
\(669\) 0 0
\(670\) 16.8183 3.11522i 0.649746 0.120351i
\(671\) −10.7523 + 33.0923i −0.415089 + 1.27751i
\(672\) 0 0
\(673\) 18.1235 + 24.9448i 0.698608 + 0.961552i 0.999968 + 0.00804101i \(0.00255956\pi\)
−0.301360 + 0.953511i \(0.597440\pi\)
\(674\) −22.6622 −0.872917
\(675\) 0 0
\(676\) −12.9793 −0.499203
\(677\) −15.1708 20.8808i −0.583061 0.802515i 0.410966 0.911651i \(-0.365192\pi\)
−0.994027 + 0.109136i \(0.965192\pi\)
\(678\) 0 0
\(679\) 13.0529 40.1728i 0.500925 1.54169i
\(680\) −2.18814 + 16.6068i −0.0839113 + 0.636844i
\(681\) 0 0
\(682\) 2.54945i 0.0976235i
\(683\) −19.8582 + 6.45234i −0.759855 + 0.246892i −0.663216 0.748428i \(-0.730809\pi\)
−0.0966385 + 0.995320i \(0.530809\pi\)
\(684\) 0 0
\(685\) 6.52560 + 35.2300i 0.249331 + 1.34607i
\(686\) 27.9126 20.2797i 1.06571 0.774281i
\(687\) 0 0
\(688\) −5.30688 + 7.30429i −0.202323 + 0.278473i
\(689\) −0.578318 + 0.420173i −0.0220322 + 0.0160073i
\(690\) 0 0
\(691\) −16.7033 12.1357i −0.635424 0.461662i 0.222851 0.974852i \(-0.428464\pi\)
−0.858275 + 0.513190i \(0.828464\pi\)
\(692\) 19.1729 6.22964i 0.728843 0.236815i
\(693\) 0 0
\(694\) 3.16805 + 9.75025i 0.120258 + 0.370115i
\(695\) −1.08195 + 8.21143i −0.0410406 + 0.311477i
\(696\) 0 0
\(697\) 21.8993 + 7.11551i 0.829494 + 0.269519i
\(698\) −0.815529 1.12248i −0.0308682 0.0424865i
\(699\) 0 0
\(700\) −5.99821 + 22.3665i −0.226711 + 0.845375i
\(701\) 12.3050 0.464752 0.232376 0.972626i \(-0.425350\pi\)
0.232376 + 0.972626i \(0.425350\pi\)
\(702\) 0 0
\(703\) −0.570434 0.185345i −0.0215143 0.00699043i
\(704\) −0.784803 + 2.41537i −0.0295784 + 0.0910328i
\(705\) 0 0
\(706\) 3.99189 + 12.2858i 0.150237 + 0.462382i
\(707\) 13.3389i 0.501662i
\(708\) 0 0
\(709\) −19.9814 14.5173i −0.750417 0.545210i 0.145539 0.989353i \(-0.453508\pi\)
−0.895956 + 0.444143i \(0.853508\pi\)
\(710\) 9.88352 20.7155i 0.370922 0.777440i
\(711\) 0 0
\(712\) 0.431355 0.593709i 0.0161657 0.0222502i
\(713\) 0.989705 1.36221i 0.0370648 0.0510153i
\(714\) 0 0
\(715\) 0.593016 + 0.562871i 0.0221775 + 0.0210502i
\(716\) −6.27852 4.56161i −0.234639 0.170475i
\(717\) 0 0
\(718\) 9.87465i 0.368519i
\(719\) −6.49650 19.9942i −0.242279 0.745657i −0.996072 0.0885457i \(-0.971778\pi\)
0.753793 0.657111i \(-0.228222\pi\)
\(720\) 0 0
\(721\) −15.9881 + 49.2064i −0.595429 + 1.83254i
\(722\) −25.1425 8.16929i −0.935706 0.304029i
\(723\) 0 0
\(724\) −11.7909 −0.438205
\(725\) 10.8899 + 2.92042i 0.404439 + 0.108462i
\(726\) 0 0
\(727\) −5.09683 7.01519i −0.189031 0.260179i 0.703974 0.710226i \(-0.251407\pi\)
−0.893005 + 0.450047i \(0.851407\pi\)
\(728\) −0.634163 0.206052i −0.0235036 0.00763680i
\(729\) 0 0
\(730\) 2.09701 + 3.86320i 0.0776139 + 0.142983i
\(731\) −20.8998 64.3230i −0.773008 2.37907i
\(732\) 0 0
\(733\) −32.2766 + 10.4873i −1.19216 + 0.387357i −0.836872 0.547398i \(-0.815618\pi\)
−0.355291 + 0.934756i \(0.615618\pi\)
\(734\) −4.30332 3.12654i −0.158838 0.115403i
\(735\) 0 0
\(736\) −1.35699 + 0.985910i −0.0500193 + 0.0363411i
\(737\) −11.4187 + 15.7165i −0.420614 + 0.578926i
\(738\) 0 0
\(739\) −13.2781 + 9.64708i −0.488442 + 0.354874i −0.804585 0.593838i \(-0.797612\pi\)
0.316143 + 0.948712i \(0.397612\pi\)
\(740\) −0.197263 0.0259916i −0.00725152 0.000955469i
\(741\) 0 0
\(742\) 21.8696 7.10585i 0.802857 0.260864i
\(743\) 3.98742i 0.146284i −0.997322 0.0731422i \(-0.976697\pi\)
0.997322 0.0731422i \(-0.0233027\pi\)
\(744\) 0 0
\(745\) 2.90226 3.05769i 0.106331 0.112025i
\(746\) 2.99270 9.21059i 0.109571 0.337224i
\(747\) 0 0
\(748\) −11.1824 15.3913i −0.408870 0.562762i
\(749\) 65.0883 2.37828
\(750\) 0 0
\(751\) 37.5827 1.37141 0.685706 0.727879i \(-0.259494\pi\)
0.685706 + 0.727879i \(0.259494\pi\)
\(752\) 6.39825 + 8.80644i 0.233320 + 0.321138i
\(753\) 0 0
\(754\) −0.100323 + 0.308763i −0.00365355 + 0.0112445i
\(755\) −9.46858 + 9.97566i −0.344597 + 0.363051i
\(756\) 0 0
\(757\) 31.2749i 1.13671i 0.822785 + 0.568353i \(0.192419\pi\)
−0.822785 + 0.568353i \(0.807581\pi\)
\(758\) 21.4197 6.95968i 0.777999 0.252787i
\(759\) 0 0
\(760\) −14.9434 1.96896i −0.542054 0.0714217i
\(761\) 24.2292 17.6035i 0.878306 0.638127i −0.0544967 0.998514i \(-0.517355\pi\)
0.932803 + 0.360387i \(0.117355\pi\)
\(762\) 0 0
\(763\) −18.2899 + 25.1739i −0.662139 + 0.911357i
\(764\) −3.95155 + 2.87097i −0.142962 + 0.103868i
\(765\) 0 0
\(766\) 5.83431 + 4.23887i 0.210802 + 0.153157i
\(767\) −0.719370 + 0.233738i −0.0259750 + 0.00843978i
\(768\) 0 0
\(769\) 11.4039 + 35.0975i 0.411234 + 1.26565i 0.915576 + 0.402145i \(0.131735\pi\)
−0.504342 + 0.863504i \(0.668265\pi\)
\(770\) −12.5473 23.1151i −0.452173 0.833011i
\(771\) 0 0
\(772\) −17.8173 5.78918i −0.641257 0.208357i
\(773\) 26.0028 + 35.7898i 0.935256 + 1.28727i 0.957774 + 0.287523i \(0.0928319\pi\)
−0.0225174 + 0.999746i \(0.507168\pi\)
\(774\) 0 0
\(775\) 4.68626 1.79774i 0.168335 0.0645766i
\(776\) 9.12044 0.327405
\(777\) 0 0
\(778\) −12.5950 4.09235i −0.451551 0.146718i
\(779\) −6.40277 + 19.7057i −0.229403 + 0.706030i
\(780\) 0 0
\(781\) 8.05574 + 24.7930i 0.288257 + 0.887164i
\(782\) 12.5649i 0.449319i
\(783\) 0 0
\(784\) 11.6900 + 8.49326i 0.417499 + 0.303331i
\(785\) −38.0852 36.1492i −1.35932 1.29022i
\(786\) 0 0
\(787\) 23.5408 32.4011i 0.839138 1.15497i −0.147015 0.989134i \(-0.546966\pi\)
0.986153 0.165840i \(-0.0530336\pi\)
\(788\) −0.737399 + 1.01494i −0.0262688 + 0.0361559i
\(789\) 0 0
\(790\) −0.719487 + 1.50802i −0.0255982 + 0.0536530i
\(791\) 3.73794 + 2.71577i 0.132906 + 0.0965618i
\(792\) 0 0
\(793\) 1.97254i 0.0700471i
\(794\) −9.04265 27.8304i −0.320912 0.987664i
\(795\) 0 0
\(796\) 5.98575 18.4222i 0.212159 0.652959i
\(797\) −42.3012 13.7445i −1.49838 0.486854i −0.558838 0.829277i \(-0.688753\pi\)
−0.939546 + 0.342423i \(0.888753\pi\)
\(798\) 0 0
\(799\) −81.5422 −2.88476
\(800\) −4.99320 + 0.260613i −0.176536 + 0.00921405i
\(801\) 0 0
\(802\) −16.1056 22.1675i −0.568709 0.782761i
\(803\) −4.74813 1.54276i −0.167558 0.0544429i
\(804\) 0 0
\(805\) 2.26915 17.2217i 0.0799770 0.606985i
\(806\) 0.0446618 + 0.137455i 0.00157314 + 0.00484164i
\(807\) 0 0
\(808\) −2.73916 + 0.890008i −0.0963635 + 0.0313104i
\(809\) 27.7120 + 20.1339i 0.974301 + 0.707871i 0.956428 0.291969i \(-0.0943105\pi\)
0.0178730 + 0.999840i \(0.494311\pi\)
\(810\) 0 0
\(811\) −8.61506 + 6.25921i −0.302516 + 0.219790i −0.728678 0.684856i \(-0.759865\pi\)
0.426163 + 0.904646i \(0.359865\pi\)
\(812\) 6.13849 8.44891i 0.215419 0.296499i
\(813\) 0 0
\(814\) 0.182824 0.132829i 0.00640798 0.00465567i
\(815\) −6.42540 34.6890i −0.225072 1.21510i
\(816\) 0 0
\(817\) 57.8800 18.8063i 2.02496 0.657951i
\(818\) 10.0026i 0.349732i
\(819\) 0 0
\(820\) −0.897881 + 6.81446i −0.0313554 + 0.237971i
\(821\) 4.55450 14.0173i 0.158953 0.489208i −0.839587 0.543226i \(-0.817203\pi\)
0.998540 + 0.0540178i \(0.0172028\pi\)
\(822\) 0 0
\(823\) 1.66495 + 2.29161i 0.0580365 + 0.0798805i 0.837049 0.547128i \(-0.184279\pi\)
−0.779012 + 0.627009i \(0.784279\pi\)
\(824\) −11.1713 −0.389172
\(825\) 0 0
\(826\) 24.3316 0.846605
\(827\) 12.8205 + 17.6459i 0.445813 + 0.613609i 0.971492 0.237074i \(-0.0761884\pi\)
−0.525678 + 0.850683i \(0.676188\pi\)
\(828\) 0 0
\(829\) 12.5472 38.6164i 0.435784 1.34120i −0.456497 0.889725i \(-0.650896\pi\)
0.892281 0.451480i \(-0.149104\pi\)
\(830\) 6.82151 1.26354i 0.236778 0.0438581i
\(831\) 0 0
\(832\) 0.143974i 0.00499141i
\(833\) −102.944 + 33.4486i −3.56680 + 1.15892i
\(834\) 0 0
\(835\) −3.88979 + 8.15288i −0.134612 + 0.282142i
\(836\) 13.8496 10.0623i 0.478999 0.348013i
\(837\) 0 0
\(838\) 4.73236 6.51354i 0.163477 0.225007i
\(839\) −23.3715 + 16.9804i −0.806875 + 0.586229i −0.912923 0.408132i \(-0.866180\pi\)
0.106048 + 0.994361i \(0.466180\pi\)
\(840\) 0 0
\(841\) 19.3479 + 14.0571i 0.667168 + 0.484726i
\(842\) 9.56120 3.10662i 0.329501 0.107061i
\(843\) 0 0
\(844\) 0.386023 + 1.18806i 0.0132875 + 0.0408946i
\(845\) 26.1940 + 12.4973i 0.901100 + 0.429921i
\(846\) 0 0
\(847\) −20.0416 6.51191i −0.688637 0.223752i
\(848\) 2.91839 + 4.01682i 0.100218 + 0.137938i
\(849\) 0 0
\(850\) 20.4062 31.4080i 0.699926 1.07729i
\(851\) 0.149251 0.00511624
\(852\) 0 0
\(853\) −23.5949 7.66646i −0.807875 0.262495i −0.124178 0.992260i \(-0.539629\pi\)
−0.683698 + 0.729765i \(0.739629\pi\)
\(854\) −19.6080 + 60.3473i −0.670973 + 2.06504i
\(855\) 0 0
\(856\) 4.34286 + 13.3660i 0.148436 + 0.456839i
\(857\) 20.0312i 0.684251i 0.939654 + 0.342126i \(0.111147\pi\)
−0.939654 + 0.342126i \(0.888853\pi\)
\(858\) 0 0
\(859\) −25.7151 18.6831i −0.877387 0.637459i 0.0551721 0.998477i \(-0.482429\pi\)
−0.932559 + 0.361018i \(0.882429\pi\)
\(860\) 17.7431 9.63125i 0.605034 0.328423i
\(861\) 0 0
\(862\) 13.5011 18.5826i 0.459848 0.632927i
\(863\) 14.0480 19.3354i 0.478199 0.658184i −0.499959 0.866049i \(-0.666652\pi\)
0.978157 + 0.207865i \(0.0666515\pi\)
\(864\) 0 0
\(865\) −44.6918 5.88865i −1.51957 0.200220i
\(866\) 14.5594 + 10.5780i 0.494749 + 0.359456i
\(867\) 0 0
\(868\) 4.64920i 0.157804i
\(869\) −0.586431 1.80485i −0.0198933 0.0612253i
\(870\) 0 0
\(871\) 0.340321 1.04740i 0.0115313 0.0354898i
\(872\) −6.38984 2.07618i −0.216387 0.0703085i
\(873\) 0 0
\(874\) 11.3063 0.382441
\(875\) 33.6412 39.3633i 1.13728 1.33072i
\(876\) 0 0
\(877\) 2.76512 + 3.80586i 0.0933715 + 0.128515i 0.853147 0.521671i \(-0.174691\pi\)
−0.759775 + 0.650186i \(0.774691\pi\)
\(878\) −24.8762 8.08277i −0.839531 0.272780i
\(879\) 0 0
\(880\) 3.90953 4.11890i 0.131790 0.138848i
\(881\) 13.7902 + 42.4420i 0.464605 + 1.42991i 0.859478 + 0.511172i \(0.170789\pi\)
−0.394873 + 0.918736i \(0.629211\pi\)
\(882\) 0 0
\(883\) 30.6286 9.95182i 1.03073 0.334905i 0.255653 0.966769i \(-0.417710\pi\)
0.775080 + 0.631863i \(0.217710\pi\)
\(884\) 0.872534 + 0.633933i 0.0293465 + 0.0213215i
\(885\) 0 0
\(886\) 32.8209 23.8458i 1.10264 0.801115i
\(887\) 25.2895 34.8080i 0.849137 1.16874i −0.134915 0.990857i \(-0.543076\pi\)
0.984052 0.177880i \(-0.0569239\pi\)
\(888\) 0 0
\(889\) 43.1701 31.3649i 1.44788 1.05194i
\(890\) −1.44220 + 0.782850i −0.0483426 + 0.0262412i
\(891\) 0 0
\(892\) −20.8144 + 6.76301i −0.696917 + 0.226442i
\(893\) 73.3744i 2.45538i
\(894\) 0 0
\(895\) 8.27869 + 15.2513i 0.276726 + 0.509796i
\(896\) −1.43117 + 4.40469i −0.0478121 + 0.147151i
\(897\) 0 0
\(898\) −13.6125 18.7360i −0.454254 0.625227i
\(899\) −2.26361 −0.0754957
\(900\) 0 0
\(901\) −37.1933 −1.23909
\(902\) −4.58860 6.31567i −0.152784 0.210289i
\(903\) 0 0
\(904\) −0.308282 + 0.948794i −0.0102533 + 0.0315564i
\(905\) 23.7956 + 11.3531i 0.790994 + 0.377388i
\(906\) 0 0
\(907\) 39.3398i 1.30626i 0.757247 + 0.653129i \(0.226544\pi\)
−0.757247 + 0.653129i \(0.773456\pi\)
\(908\) −13.7935 + 4.48178i −0.457754 + 0.148733i
\(909\) 0 0
\(910\) 1.08143 + 1.02646i 0.0358490 + 0.0340267i
\(911\) −11.0045 + 7.99523i −0.364595 + 0.264894i −0.754966 0.655764i \(-0.772347\pi\)
0.390371 + 0.920658i \(0.372347\pi\)
\(912\) 0 0
\(913\) −4.63146 + 6.37465i −0.153279 + 0.210970i
\(914\) 31.0660 22.5708i 1.02757 0.746575i
\(915\) 0 0
\(916\) −3.80302 2.76305i −0.125655 0.0912938i
\(917\) −7.85839 + 2.55335i −0.259507 + 0.0843189i
\(918\) 0 0
\(919\) 4.38951 + 13.5095i 0.144797 + 0.445638i 0.996985 0.0775974i \(-0.0247249\pi\)
−0.852188 + 0.523235i \(0.824725\pi\)
\(920\) 3.68789 0.683103i 0.121586 0.0225212i
\(921\) 0 0
\(922\) −30.9962 10.0713i −1.02081 0.331680i
\(923\) −0.868657 1.19560i −0.0285922 0.0393538i
\(924\) 0 0
\(925\) 0.373077 + 0.242392i 0.0122667 + 0.00796981i
\(926\) 2.53778 0.0833966
\(927\) 0 0
\(928\) 2.14457 + 0.696812i 0.0703989 + 0.0228740i
\(929\) 2.50600 7.71269i 0.0822193 0.253045i −0.901493 0.432793i \(-0.857528\pi\)
0.983713 + 0.179748i \(0.0575282\pi\)
\(930\) 0 0
\(931\) −30.0981 92.6326i −0.986427 3.03591i
\(932\) 11.8187i 0.387135i
\(933\) 0 0
\(934\) 1.21073 + 0.879644i 0.0396161 + 0.0287828i
\(935\) 7.74793 + 41.8290i 0.253384 + 1.36795i
\(936\) 0 0
\(937\) 6.18675 8.51533i 0.202112 0.278184i −0.695914 0.718125i \(-0.745001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(938\) −20.8233 + 28.6608i −0.679904 + 0.935808i
\(939\) 0 0
\(940\) −4.43313 23.9333i −0.144593 0.780618i
\(941\) −40.0792 29.1193i −1.30655 0.949261i −0.306549 0.951855i \(-0.599174\pi\)
−0.999997 + 0.00259412i \(0.999174\pi\)
\(942\) 0 0
\(943\) 5.15587i 0.167898i
\(944\) 1.62347 + 4.99652i 0.0528394 + 0.162623i
\(945\) 0 0
\(946\) −7.08567 + 21.8074i −0.230375 + 0.709021i
\(947\) −10.0635 3.26983i −0.327020 0.106255i 0.140906 0.990023i \(-0.454999\pi\)
−0.467926 + 0.883768i \(0.654999\pi\)
\(948\) 0 0
\(949\) 0.283024 0.00918735
\(950\) 28.2620 + 18.3621i 0.916940 + 0.595747i
\(951\) 0 0
\(952\) −20.3924 28.0677i −0.660921 0.909680i
\(953\) −24.7411 8.03886i −0.801442 0.260404i −0.120473 0.992717i \(-0.538441\pi\)
−0.680969 + 0.732312i \(0.738441\pi\)
\(954\) 0 0
\(955\) 10.7391 1.98919i 0.347510 0.0643688i
\(956\) −3.00168 9.23821i −0.0970812 0.298785i
\(957\) 0 0
\(958\) 23.1097 7.50880i 0.746641 0.242598i
\(959\) −60.0372 43.6196i −1.93870 1.40855i
\(960\) 0 0
\(961\) 24.2643 17.6290i 0.782718 0.568678i
\(962\) −0.00753010 + 0.0103643i −0.000242780 + 0.000334158i
\(963\) 0 0
\(964\) 5.40451 3.92661i 0.174068 0.126468i
\(965\) 30.3835 + 28.8390i 0.978079 + 0.928361i
\(966\) 0 0
\(967\) −28.1049 + 9.13183i −0.903793 + 0.293660i −0.723802 0.690008i \(-0.757607\pi\)
−0.179991 + 0.983668i \(0.557607\pi\)
\(968\) 4.55005i 0.146244i
\(969\) 0 0
\(970\) −18.4063 8.78178i −0.590991 0.281966i
\(971\) −11.0850 + 34.1161i −0.355734 + 1.09484i 0.599849 + 0.800114i \(0.295227\pi\)
−0.955583 + 0.294723i \(0.904773\pi\)
\(972\) 0 0
\(973\) −10.0832 13.8784i −0.323253 0.444920i
\(974\) −10.0016 −0.320470
\(975\) 0 0
\(976\) −13.7007 −0.438548
\(977\) 12.7115 + 17.4959i 0.406677 + 0.559743i 0.962404 0.271622i \(-0.0875599\pi\)
−0.555727 + 0.831365i \(0.687560\pi\)
\(978\) 0 0
\(979\) 0.575939 1.77256i 0.0184071 0.0566512i
\(980\) −15.4141 28.3965i −0.492385 0.907092i
\(981\) 0 0
\(982\) 4.17992i 0.133387i
\(983\) 13.9026 4.51722i 0.443424 0.144077i −0.0787911 0.996891i \(-0.525106\pi\)
0.522215 + 0.852814i \(0.325106\pi\)
\(984\) 0 0
\(985\) 2.46543 1.33828i 0.0785552 0.0426411i
\(986\) −13.6657 + 9.92869i −0.435204 + 0.316194i
\(987\) 0 0
\(988\) −0.570434 + 0.785135i −0.0181479 + 0.0249785i
\(989\) −12.2517 + 8.90139i −0.389582 + 0.283048i
\(990\) 0 0
\(991\) 10.5772 + 7.68477i 0.335995 + 0.244115i 0.742970 0.669325i \(-0.233416\pi\)
−0.406975 + 0.913439i \(0.633416\pi\)
\(992\) 0.954718 0.310207i 0.0303123 0.00984907i
\(993\) 0 0
\(994\) 14.6905 + 45.2127i 0.465955 + 1.43406i
\(995\) −29.8183 + 31.4152i −0.945302 + 0.995928i
\(996\) 0 0
\(997\) −11.5998 3.76901i −0.367370 0.119366i 0.119514 0.992833i \(-0.461866\pi\)
−0.486884 + 0.873467i \(0.661866\pi\)
\(998\) −1.00245 1.37976i −0.0317321 0.0436755i
\(999\) 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.l.c.289.4 16
3.2 odd 2 150.2.h.b.139.1 yes 16
15.2 even 4 750.2.g.g.301.1 16
15.8 even 4 750.2.g.f.301.4 16
15.14 odd 2 750.2.h.d.199.3 16
25.9 even 10 inner 450.2.l.c.109.4 16
75.29 odd 10 3750.2.c.k.1249.1 16
75.38 even 20 750.2.g.f.451.4 16
75.41 odd 10 750.2.h.d.49.4 16
75.47 even 20 3750.2.a.u.1.1 8
75.53 even 20 3750.2.a.v.1.8 8
75.59 odd 10 150.2.h.b.109.1 16
75.62 even 20 750.2.g.g.451.1 16
75.71 odd 10 3750.2.c.k.1249.16 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.b.109.1 16 75.59 odd 10
150.2.h.b.139.1 yes 16 3.2 odd 2
450.2.l.c.109.4 16 25.9 even 10 inner
450.2.l.c.289.4 16 1.1 even 1 trivial
750.2.g.f.301.4 16 15.8 even 4
750.2.g.f.451.4 16 75.38 even 20
750.2.g.g.301.1 16 15.2 even 4
750.2.g.g.451.1 16 75.62 even 20
750.2.h.d.49.4 16 75.41 odd 10
750.2.h.d.199.3 16 15.14 odd 2
3750.2.a.u.1.1 8 75.47 even 20
3750.2.a.v.1.8 8 75.53 even 20
3750.2.c.k.1249.1 16 75.29 odd 10
3750.2.c.k.1249.16 16 75.71 odd 10