Properties

Label 693.2.m.i.379.3
Level $693$
Weight $2$
Character 693.379
Analytic conductor $5.534$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (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: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 379.3
Root \(0.435488 + 1.34029i\) of defining polynomial
Character \(\chi\) \(=\) 693.379
Dual form 693.2.m.i.64.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.435488 + 1.34029i) q^{2} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(2.29616 + 1.66826i) q^{8} +O(q^{10})\) \(q+(0.435488 + 1.34029i) q^{2} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(2.29616 + 1.66826i) q^{8} +2.58091 q^{10} +(2.26009 + 2.42734i) q^{11} +(-1.43602 - 4.41961i) q^{13} +(-1.14012 - 0.828347i) q^{14} +(-1.22738 + 3.77748i) q^{16} +(1.69039 - 5.20248i) q^{17} +(4.69325 + 3.40985i) q^{19} +(-0.00790293 - 0.0243227i) q^{20} +(-2.26911 + 4.08626i) q^{22} +0.719682 q^{23} +(1.33166 + 0.967509i) q^{25} +(5.29821 - 3.84937i) q^{26} +(-0.00431527 + 0.0132810i) q^{28} +(-0.948551 + 0.689163i) q^{29} +(-0.404153 - 1.24385i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(0.565930 + 1.74175i) q^{35} +(-1.69468 + 1.23126i) q^{37} +(-2.52634 + 7.77528i) q^{38} +(4.20516 - 3.05523i) q^{40} +(-0.741582 - 0.538791i) q^{41} +8.02379 q^{43} +(0.0454574 + 0.00887181i) q^{44} +(0.313413 + 0.964586i) q^{46} +(4.83455 + 3.51251i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.716823 + 2.20615i) q^{50} +(-0.0525003 - 0.0381437i) q^{52} +(-3.13496 - 9.64840i) q^{53} +(5.50688 - 2.56282i) q^{55} -2.83822 q^{56} +(-1.33676 - 0.971215i) q^{58} +(-6.21390 + 4.51466i) q^{59} +(-1.93943 + 5.96895i) q^{61} +(1.49113 - 1.08337i) q^{62} +(2.48916 + 7.66083i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(-0.0236055 - 0.0726501i) q^{68} +(-2.08800 + 1.51702i) q^{70} +(-4.29593 + 13.2215i) q^{71} +(-4.86593 + 3.53531i) q^{73} +(-2.38826 - 1.73517i) q^{74} +0.0810106 q^{76} +(-3.25521 - 0.635311i) q^{77} +(-4.83332 - 14.8754i) q^{79} +(5.88482 + 4.27557i) q^{80} +(0.399188 - 1.22857i) q^{82} +(1.35217 - 4.16157i) q^{83} +(-8.10479 - 5.88848i) q^{85} +(3.49426 + 10.7542i) q^{86} +(1.14011 + 9.34400i) q^{88} -15.3437 q^{89} +(3.75955 + 2.73147i) q^{91} +(0.00813063 - 0.00590725i) q^{92} +(-2.60240 + 8.00937i) q^{94} +(8.59515 - 6.24474i) q^{95} +(0.745114 + 2.29323i) q^{97} +1.40927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.435488 + 1.34029i 0.307936 + 0.947730i 0.978565 + 0.205937i \(0.0660243\pi\)
−0.670629 + 0.741793i \(0.733976\pi\)
\(3\) 0 0
\(4\) 0.0112975 0.00820814i 0.00564876 0.00410407i
\(5\) 0.565930 1.74175i 0.253091 0.778935i −0.741108 0.671385i \(-0.765700\pi\)
0.994200 0.107550i \(-0.0343005\pi\)
\(6\) 0 0
\(7\) −0.809017 + 0.587785i −0.305780 + 0.222162i
\(8\) 2.29616 + 1.66826i 0.811817 + 0.589819i
\(9\) 0 0
\(10\) 2.58091 0.816157
\(11\) 2.26009 + 2.42734i 0.681444 + 0.731871i
\(12\) 0 0
\(13\) −1.43602 4.41961i −0.398280 1.22578i −0.926377 0.376596i \(-0.877094\pi\)
0.528097 0.849184i \(-0.322906\pi\)
\(14\) −1.14012 0.828347i −0.304710 0.221385i
\(15\) 0 0
\(16\) −1.22738 + 3.77748i −0.306844 + 0.944370i
\(17\) 1.69039 5.20248i 0.409980 1.26179i −0.506685 0.862131i \(-0.669129\pi\)
0.916665 0.399656i \(-0.130871\pi\)
\(18\) 0 0
\(19\) 4.69325 + 3.40985i 1.07671 + 0.782272i 0.977106 0.212755i \(-0.0682437\pi\)
0.0995999 + 0.995028i \(0.468244\pi\)
\(20\) −0.00790293 0.0243227i −0.00176715 0.00543873i
\(21\) 0 0
\(22\) −2.26911 + 4.08626i −0.483775 + 0.871194i
\(23\) 0.719682 0.150064 0.0750321 0.997181i \(-0.476094\pi\)
0.0750321 + 0.997181i \(0.476094\pi\)
\(24\) 0 0
\(25\) 1.33166 + 0.967509i 0.266332 + 0.193502i
\(26\) 5.29821 3.84937i 1.03906 0.754924i
\(27\) 0 0
\(28\) −0.00431527 + 0.0132810i −0.000815510 + 0.00250988i
\(29\) −0.948551 + 0.689163i −0.176142 + 0.127974i −0.672363 0.740222i \(-0.734720\pi\)
0.496221 + 0.868196i \(0.334720\pi\)
\(30\) 0 0
\(31\) −0.404153 1.24385i −0.0725879 0.223403i 0.908180 0.418580i \(-0.137472\pi\)
−0.980768 + 0.195177i \(0.937472\pi\)
\(32\) 0.0789938 0.0139643
\(33\) 0 0
\(34\) 7.70900 1.32208
\(35\) 0.565930 + 1.74175i 0.0956595 + 0.294410i
\(36\) 0 0
\(37\) −1.69468 + 1.23126i −0.278604 + 0.202417i −0.718308 0.695725i \(-0.755083\pi\)
0.439705 + 0.898142i \(0.355083\pi\)
\(38\) −2.52634 + 7.77528i −0.409827 + 1.26132i
\(39\) 0 0
\(40\) 4.20516 3.05523i 0.664895 0.483074i
\(41\) −0.741582 0.538791i −0.115816 0.0841449i 0.528370 0.849014i \(-0.322803\pi\)
−0.644185 + 0.764869i \(0.722803\pi\)
\(42\) 0 0
\(43\) 8.02379 1.22362 0.611808 0.791006i \(-0.290442\pi\)
0.611808 + 0.791006i \(0.290442\pi\)
\(44\) 0.0454574 + 0.00887181i 0.00685296 + 0.00133748i
\(45\) 0 0
\(46\) 0.313413 + 0.964586i 0.0462102 + 0.142220i
\(47\) 4.83455 + 3.51251i 0.705192 + 0.512352i 0.881619 0.471962i \(-0.156454\pi\)
−0.176427 + 0.984314i \(0.556454\pi\)
\(48\) 0 0
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −0.716823 + 2.20615i −0.101374 + 0.311997i
\(51\) 0 0
\(52\) −0.0525003 0.0381437i −0.00728048 0.00528958i
\(53\) −3.13496 9.64840i −0.430619 1.32531i −0.897510 0.440995i \(-0.854626\pi\)
0.466890 0.884315i \(-0.345374\pi\)
\(54\) 0 0
\(55\) 5.50688 2.56282i 0.742547 0.345570i
\(56\) −2.83822 −0.379272
\(57\) 0 0
\(58\) −1.33676 0.971215i −0.175526 0.127527i
\(59\) −6.21390 + 4.51466i −0.808981 + 0.587759i −0.913535 0.406760i \(-0.866659\pi\)
0.104554 + 0.994519i \(0.466659\pi\)
\(60\) 0 0
\(61\) −1.93943 + 5.96895i −0.248318 + 0.764246i 0.746754 + 0.665100i \(0.231611\pi\)
−0.995073 + 0.0991458i \(0.968389\pi\)
\(62\) 1.49113 1.08337i 0.189373 0.137588i
\(63\) 0 0
\(64\) 2.48916 + 7.66083i 0.311144 + 0.957604i
\(65\) −8.51056 −1.05560
\(66\) 0 0
\(67\) −15.4673 −1.88963 −0.944814 0.327608i \(-0.893758\pi\)
−0.944814 + 0.327608i \(0.893758\pi\)
\(68\) −0.0236055 0.0726501i −0.00286258 0.00881012i
\(69\) 0 0
\(70\) −2.08800 + 1.51702i −0.249564 + 0.181319i
\(71\) −4.29593 + 13.2215i −0.509833 + 1.56910i 0.282659 + 0.959221i \(0.408784\pi\)
−0.792491 + 0.609883i \(0.791216\pi\)
\(72\) 0 0
\(73\) −4.86593 + 3.53531i −0.569514 + 0.413776i −0.834929 0.550358i \(-0.814491\pi\)
0.265414 + 0.964134i \(0.414491\pi\)
\(74\) −2.38826 1.73517i −0.277629 0.201709i
\(75\) 0 0
\(76\) 0.0810106 0.00929255
\(77\) −3.25521 0.635311i −0.370965 0.0724004i
\(78\) 0 0
\(79\) −4.83332 14.8754i −0.543791 1.67362i −0.723848 0.689959i \(-0.757628\pi\)
0.180058 0.983656i \(-0.442372\pi\)
\(80\) 5.88482 + 4.27557i 0.657943 + 0.478024i
\(81\) 0 0
\(82\) 0.399188 1.22857i 0.0440829 0.135673i
\(83\) 1.35217 4.16157i 0.148420 0.456791i −0.849015 0.528370i \(-0.822804\pi\)
0.997435 + 0.0715783i \(0.0228036\pi\)
\(84\) 0 0
\(85\) −8.10479 5.88848i −0.879088 0.638695i
\(86\) 3.49426 + 10.7542i 0.376796 + 1.15966i
\(87\) 0 0
\(88\) 1.14011 + 9.34400i 0.121536 + 0.996073i
\(89\) −15.3437 −1.62643 −0.813215 0.581963i \(-0.802285\pi\)
−0.813215 + 0.581963i \(0.802285\pi\)
\(90\) 0 0
\(91\) 3.75955 + 2.73147i 0.394108 + 0.286336i
\(92\) 0.00813063 0.00590725i 0.000847677 0.000615873i
\(93\) 0 0
\(94\) −2.60240 + 8.00937i −0.268417 + 0.826104i
\(95\) 8.59515 6.24474i 0.881844 0.640697i
\(96\) 0 0
\(97\) 0.745114 + 2.29323i 0.0756549 + 0.232842i 0.981731 0.190272i \(-0.0609370\pi\)
−0.906077 + 0.423114i \(0.860937\pi\)
\(98\) 1.40927 0.142358
\(99\) 0 0
\(100\) 0.0229859 0.00229859
\(101\) −3.67603 11.3136i −0.365778 1.12575i −0.949492 0.313790i \(-0.898401\pi\)
0.583714 0.811959i \(-0.301599\pi\)
\(102\) 0 0
\(103\) −0.320625 + 0.232947i −0.0315921 + 0.0229530i −0.603469 0.797386i \(-0.706215\pi\)
0.571877 + 0.820339i \(0.306215\pi\)
\(104\) 4.07573 12.5438i 0.399658 1.23002i
\(105\) 0 0
\(106\) 11.5665 8.40352i 1.12343 0.816222i
\(107\) −2.64496 1.92168i −0.255698 0.185776i 0.452550 0.891739i \(-0.350514\pi\)
−0.708248 + 0.705963i \(0.750514\pi\)
\(108\) 0 0
\(109\) −2.84638 −0.272634 −0.136317 0.990665i \(-0.543527\pi\)
−0.136317 + 0.990665i \(0.543527\pi\)
\(110\) 5.83310 + 6.26476i 0.556165 + 0.597321i
\(111\) 0 0
\(112\) −1.22738 3.77748i −0.115976 0.356938i
\(113\) 11.7668 + 8.54906i 1.10692 + 0.804228i 0.982177 0.187961i \(-0.0601878\pi\)
0.124748 + 0.992188i \(0.460188\pi\)
\(114\) 0 0
\(115\) 0.407290 1.25351i 0.0379799 0.116890i
\(116\) −0.00505954 + 0.0155717i −0.000469767 + 0.00144579i
\(117\) 0 0
\(118\) −8.75705 6.36237i −0.806152 0.585704i
\(119\) 1.69039 + 5.20248i 0.154958 + 0.476911i
\(120\) 0 0
\(121\) −0.783964 + 10.9720i −0.0712695 + 0.997457i
\(122\) −8.84474 −0.800765
\(123\) 0 0
\(124\) −0.0147756 0.0107351i −0.00132689 0.000964044i
\(125\) 9.84690 7.15419i 0.880734 0.639890i
\(126\) 0 0
\(127\) 1.55524 4.78655i 0.138006 0.424737i −0.858040 0.513583i \(-0.828318\pi\)
0.996045 + 0.0888458i \(0.0283178\pi\)
\(128\) −9.05595 + 6.57953i −0.800440 + 0.581554i
\(129\) 0 0
\(130\) −3.70624 11.4066i −0.325059 1.00043i
\(131\) 0.180053 0.0157313 0.00786565 0.999969i \(-0.497496\pi\)
0.00786565 + 0.999969i \(0.497496\pi\)
\(132\) 0 0
\(133\) −5.80118 −0.503026
\(134\) −6.73581 20.7307i −0.581885 1.79086i
\(135\) 0 0
\(136\) 12.5605 9.12574i 1.07705 0.782526i
\(137\) −2.57224 + 7.91655i −0.219762 + 0.676357i 0.779020 + 0.627000i \(0.215717\pi\)
−0.998781 + 0.0493570i \(0.984283\pi\)
\(138\) 0 0
\(139\) 5.63172 4.09169i 0.477677 0.347052i −0.322749 0.946485i \(-0.604607\pi\)
0.800425 + 0.599432i \(0.204607\pi\)
\(140\) 0.0206901 + 0.0150323i 0.00174864 + 0.00127046i
\(141\) 0 0
\(142\) −19.5915 −1.64408
\(143\) 7.48237 13.4744i 0.625707 1.12679i
\(144\) 0 0
\(145\) 0.663538 + 2.04216i 0.0551038 + 0.169592i
\(146\) −6.85740 4.98219i −0.567523 0.412329i
\(147\) 0 0
\(148\) −0.00903937 + 0.0278203i −0.000743031 + 0.00228682i
\(149\) 0.993277 3.05699i 0.0813724 0.250439i −0.902091 0.431546i \(-0.857968\pi\)
0.983463 + 0.181108i \(0.0579682\pi\)
\(150\) 0 0
\(151\) −18.0144 13.0882i −1.46599 1.06510i −0.981752 0.190168i \(-0.939097\pi\)
−0.484239 0.874936i \(-0.660903\pi\)
\(152\) 5.08796 + 15.6591i 0.412688 + 1.27012i
\(153\) 0 0
\(154\) −0.566100 4.63960i −0.0456177 0.373870i
\(155\) −2.39521 −0.192388
\(156\) 0 0
\(157\) −10.7233 7.79096i −0.855816 0.621786i 0.0709277 0.997481i \(-0.477404\pi\)
−0.926743 + 0.375695i \(0.877404\pi\)
\(158\) 17.8326 12.9561i 1.41868 1.03073i
\(159\) 0 0
\(160\) 0.0447049 0.137588i 0.00353423 0.0108773i
\(161\) −0.582235 + 0.423019i −0.0458866 + 0.0333385i
\(162\) 0 0
\(163\) 4.23920 + 13.0469i 0.332040 + 1.02191i 0.968162 + 0.250325i \(0.0805375\pi\)
−0.636122 + 0.771589i \(0.719462\pi\)
\(164\) −0.0128005 −0.000999552
\(165\) 0 0
\(166\) 6.16657 0.478619
\(167\) −2.87651 8.85300i −0.222591 0.685066i −0.998527 0.0542539i \(-0.982722\pi\)
0.775936 0.630812i \(-0.217278\pi\)
\(168\) 0 0
\(169\) −6.95361 + 5.05209i −0.534893 + 0.388623i
\(170\) 4.36275 13.4272i 0.334608 1.02982i
\(171\) 0 0
\(172\) 0.0906490 0.0658604i 0.00691192 0.00502181i
\(173\) 8.49927 + 6.17508i 0.646188 + 0.469483i 0.861970 0.506959i \(-0.169230\pi\)
−0.215783 + 0.976441i \(0.569230\pi\)
\(174\) 0 0
\(175\) −1.64602 −0.124428
\(176\) −11.9432 + 5.55819i −0.900254 + 0.418964i
\(177\) 0 0
\(178\) −6.68200 20.5651i −0.500837 1.54142i
\(179\) −6.73370 4.89232i −0.503300 0.365669i 0.306976 0.951717i \(-0.400683\pi\)
−0.810276 + 0.586048i \(0.800683\pi\)
\(180\) 0 0
\(181\) −4.57437 + 14.0785i −0.340010 + 1.04644i 0.624191 + 0.781272i \(0.285429\pi\)
−0.964201 + 0.265172i \(0.914571\pi\)
\(182\) −2.02374 + 6.22842i −0.150009 + 0.461681i
\(183\) 0 0
\(184\) 1.65251 + 1.20062i 0.121825 + 0.0885107i
\(185\) 1.18547 + 3.64852i 0.0871578 + 0.268244i
\(186\) 0 0
\(187\) 16.4486 7.65494i 1.20284 0.559785i
\(188\) 0.0834496 0.00608619
\(189\) 0 0
\(190\) 12.1129 + 8.80052i 0.878760 + 0.638457i
\(191\) −7.77203 + 5.64671i −0.562364 + 0.408582i −0.832324 0.554290i \(-0.812990\pi\)
0.269959 + 0.962872i \(0.412990\pi\)
\(192\) 0 0
\(193\) −0.459758 + 1.41499i −0.0330941 + 0.101853i −0.966239 0.257647i \(-0.917053\pi\)
0.933145 + 0.359500i \(0.117053\pi\)
\(194\) −2.74911 + 1.99734i −0.197374 + 0.143401i
\(195\) 0 0
\(196\) −0.00431527 0.0132810i −0.000308234 0.000948646i
\(197\) 14.0434 1.00055 0.500274 0.865867i \(-0.333233\pi\)
0.500274 + 0.865867i \(0.333233\pi\)
\(198\) 0 0
\(199\) −4.28729 −0.303918 −0.151959 0.988387i \(-0.548558\pi\)
−0.151959 + 0.988387i \(0.548558\pi\)
\(200\) 1.44366 + 4.44312i 0.102082 + 0.314176i
\(201\) 0 0
\(202\) 13.5627 9.85391i 0.954271 0.693318i
\(203\) 0.362314 1.11509i 0.0254295 0.0782639i
\(204\) 0 0
\(205\) −1.35812 + 0.986734i −0.0948554 + 0.0689165i
\(206\) −0.451846 0.328285i −0.0314816 0.0228727i
\(207\) 0 0
\(208\) 18.4575 1.27980
\(209\) 2.33032 + 19.0987i 0.161192 + 1.32108i
\(210\) 0 0
\(211\) −0.449704 1.38405i −0.0309589 0.0952816i 0.934383 0.356270i \(-0.115952\pi\)
−0.965342 + 0.260988i \(0.915952\pi\)
\(212\) −0.114613 0.0832710i −0.00787163 0.00571907i
\(213\) 0 0
\(214\) 1.42376 4.38189i 0.0973264 0.299540i
\(215\) 4.54090 13.9755i 0.309687 0.953118i
\(216\) 0 0
\(217\) 1.05809 + 0.768744i 0.0718275 + 0.0521857i
\(218\) −1.23957 3.81499i −0.0839540 0.258384i
\(219\) 0 0
\(220\) 0.0411782 0.0741547i 0.00277623 0.00499951i
\(221\) −25.4204 −1.70996
\(222\) 0 0
\(223\) 3.92893 + 2.85453i 0.263101 + 0.191154i 0.711513 0.702673i \(-0.248010\pi\)
−0.448412 + 0.893827i \(0.648010\pi\)
\(224\) −0.0639073 + 0.0464314i −0.00426999 + 0.00310233i
\(225\) 0 0
\(226\) −6.33396 + 19.4939i −0.421329 + 1.29672i
\(227\) 0.321296 0.233435i 0.0213252 0.0154936i −0.577072 0.816694i \(-0.695805\pi\)
0.598397 + 0.801200i \(0.295805\pi\)
\(228\) 0 0
\(229\) 0.676634 + 2.08246i 0.0447132 + 0.137613i 0.970921 0.239401i \(-0.0769509\pi\)
−0.926208 + 0.377014i \(0.876951\pi\)
\(230\) 1.85744 0.122476
\(231\) 0 0
\(232\) −3.32773 −0.218476
\(233\) 0.389410 + 1.19848i 0.0255111 + 0.0785150i 0.963001 0.269496i \(-0.0868571\pi\)
−0.937490 + 0.348011i \(0.886857\pi\)
\(234\) 0 0
\(235\) 8.85393 6.43276i 0.577567 0.419627i
\(236\) −0.0331448 + 0.102009i −0.00215754 + 0.00664023i
\(237\) 0 0
\(238\) −6.23671 + 4.53123i −0.404266 + 0.293716i
\(239\) −9.02997 6.56066i −0.584100 0.424374i 0.256100 0.966650i \(-0.417562\pi\)
−0.840200 + 0.542277i \(0.817562\pi\)
\(240\) 0 0
\(241\) −21.4843 −1.38392 −0.691962 0.721934i \(-0.743254\pi\)
−0.691962 + 0.721934i \(0.743254\pi\)
\(242\) −15.0471 + 3.72744i −0.967267 + 0.239609i
\(243\) 0 0
\(244\) 0.0270832 + 0.0833535i 0.00173382 + 0.00533616i
\(245\) −1.48162 1.07646i −0.0946574 0.0687726i
\(246\) 0 0
\(247\) 8.33060 25.6390i 0.530063 1.63137i
\(248\) 1.14707 3.53032i 0.0728391 0.224176i
\(249\) 0 0
\(250\) 13.8769 + 10.0822i 0.877653 + 0.637652i
\(251\) 0.130968 + 0.403077i 0.00826660 + 0.0254420i 0.955105 0.296268i \(-0.0957423\pi\)
−0.946838 + 0.321710i \(0.895742\pi\)
\(252\) 0 0
\(253\) 1.62655 + 1.74691i 0.102260 + 0.109828i
\(254\) 7.09267 0.445033
\(255\) 0 0
\(256\) 0.271127 + 0.196986i 0.0169455 + 0.0123116i
\(257\) 14.1093 10.2510i 0.880115 0.639441i −0.0531672 0.998586i \(-0.516932\pi\)
0.933282 + 0.359145i \(0.116932\pi\)
\(258\) 0 0
\(259\) 0.647310 1.99221i 0.0402219 0.123790i
\(260\) −0.0961483 + 0.0698558i −0.00596286 + 0.00433227i
\(261\) 0 0
\(262\) 0.0784109 + 0.241324i 0.00484424 + 0.0149090i
\(263\) −1.51519 −0.0934307 −0.0467153 0.998908i \(-0.514875\pi\)
−0.0467153 + 0.998908i \(0.514875\pi\)
\(264\) 0 0
\(265\) −18.5793 −1.14132
\(266\) −2.52634 7.77528i −0.154900 0.476733i
\(267\) 0 0
\(268\) −0.174742 + 0.126957i −0.0106741 + 0.00775516i
\(269\) 0.627622 1.93162i 0.0382668 0.117773i −0.930098 0.367311i \(-0.880279\pi\)
0.968365 + 0.249538i \(0.0802786\pi\)
\(270\) 0 0
\(271\) −6.15212 + 4.46978i −0.373715 + 0.271520i −0.758750 0.651382i \(-0.774189\pi\)
0.385035 + 0.922902i \(0.374189\pi\)
\(272\) 17.5775 + 12.7708i 1.06579 + 0.774344i
\(273\) 0 0
\(274\) −11.7307 −0.708676
\(275\) 0.661205 + 5.41905i 0.0398722 + 0.326781i
\(276\) 0 0
\(277\) 4.45813 + 13.7207i 0.267863 + 0.824398i 0.991020 + 0.133714i \(0.0426903\pi\)
−0.723157 + 0.690684i \(0.757310\pi\)
\(278\) 7.93661 + 5.76628i 0.476006 + 0.345839i
\(279\) 0 0
\(280\) −1.60623 + 4.94347i −0.0959906 + 0.295429i
\(281\) −5.48494 + 16.8809i −0.327204 + 1.00703i 0.643232 + 0.765672i \(0.277593\pi\)
−0.970436 + 0.241359i \(0.922407\pi\)
\(282\) 0 0
\(283\) 25.1897 + 18.3014i 1.49737 + 1.08790i 0.971414 + 0.237392i \(0.0762924\pi\)
0.525956 + 0.850512i \(0.323708\pi\)
\(284\) 0.0599905 + 0.184632i 0.00355978 + 0.0109559i
\(285\) 0 0
\(286\) 21.3182 + 4.16062i 1.26057 + 0.246022i
\(287\) 0.916645 0.0541079
\(288\) 0 0
\(289\) −10.4551 7.59609i −0.615007 0.446829i
\(290\) −2.44813 + 1.77867i −0.143759 + 0.104447i
\(291\) 0 0
\(292\) −0.0259547 + 0.0798805i −0.00151889 + 0.00467465i
\(293\) −19.4409 + 14.1247i −1.13575 + 0.825171i −0.986522 0.163632i \(-0.947679\pi\)
−0.149229 + 0.988803i \(0.547679\pi\)
\(294\) 0 0
\(295\) 4.34679 + 13.3781i 0.253080 + 0.778901i
\(296\) −5.94532 −0.345565
\(297\) 0 0
\(298\) 4.52983 0.262406
\(299\) −1.03348 3.18072i −0.0597676 0.183946i
\(300\) 0 0
\(301\) −6.49138 + 4.71627i −0.374157 + 0.271841i
\(302\) 9.69701 29.8443i 0.558000 1.71735i
\(303\) 0 0
\(304\) −18.6410 + 13.5435i −1.06914 + 0.776772i
\(305\) 9.29885 + 6.75601i 0.532450 + 0.386848i
\(306\) 0 0
\(307\) −5.46298 −0.311789 −0.155894 0.987774i \(-0.549826\pi\)
−0.155894 + 0.987774i \(0.549826\pi\)
\(308\) −0.0419905 + 0.0195417i −0.00239263 + 0.00111349i
\(309\) 0 0
\(310\) −1.04308 3.21028i −0.0592431 0.182332i
\(311\) 11.2360 + 8.16342i 0.637134 + 0.462905i 0.858864 0.512203i \(-0.171170\pi\)
−0.221730 + 0.975108i \(0.571170\pi\)
\(312\) 0 0
\(313\) 8.48207 26.1051i 0.479435 1.47555i −0.360447 0.932780i \(-0.617376\pi\)
0.839882 0.542770i \(-0.182624\pi\)
\(314\) 5.77229 17.7653i 0.325749 1.00255i
\(315\) 0 0
\(316\) −0.176704 0.128383i −0.00994038 0.00722211i
\(317\) −2.41828 7.44269i −0.135824 0.418023i 0.859893 0.510474i \(-0.170530\pi\)
−0.995717 + 0.0924507i \(0.970530\pi\)
\(318\) 0 0
\(319\) −3.81665 0.744885i −0.213691 0.0417056i
\(320\) 14.7520 0.824659
\(321\) 0 0
\(322\) −0.820525 0.596147i −0.0457261 0.0332220i
\(323\) 25.6731 18.6526i 1.42849 1.03786i
\(324\) 0 0
\(325\) 2.36372 7.27479i 0.131116 0.403533i
\(326\) −15.6406 + 11.3635i −0.866252 + 0.629369i
\(327\) 0 0
\(328\) −0.803950 2.47430i −0.0443907 0.136621i
\(329\) −5.97584 −0.329458
\(330\) 0 0
\(331\) −28.1462 −1.54705 −0.773527 0.633764i \(-0.781509\pi\)
−0.773527 + 0.633764i \(0.781509\pi\)
\(332\) −0.0188825 0.0581143i −0.00103631 0.00318943i
\(333\) 0 0
\(334\) 10.6129 7.71075i 0.580714 0.421913i
\(335\) −8.75338 + 26.9401i −0.478248 + 1.47190i
\(336\) 0 0
\(337\) 20.2084 14.6823i 1.10082 0.799793i 0.119628 0.992819i \(-0.461830\pi\)
0.981194 + 0.193025i \(0.0618300\pi\)
\(338\) −9.79950 7.11975i −0.533022 0.387263i
\(339\) 0 0
\(340\) −0.139898 −0.00758701
\(341\) 2.10583 3.79224i 0.114037 0.205361i
\(342\) 0 0
\(343\) 0.309017 + 0.951057i 0.0166853 + 0.0513522i
\(344\) 18.4239 + 13.3858i 0.993352 + 0.721713i
\(345\) 0 0
\(346\) −4.57509 + 14.0807i −0.245959 + 0.756983i
\(347\) −6.38096 + 19.6386i −0.342548 + 1.05425i 0.620335 + 0.784337i \(0.286997\pi\)
−0.962883 + 0.269918i \(0.913003\pi\)
\(348\) 0 0
\(349\) 4.85185 + 3.52507i 0.259713 + 0.188693i 0.710021 0.704181i \(-0.248686\pi\)
−0.450307 + 0.892874i \(0.648686\pi\)
\(350\) −0.716823 2.20615i −0.0383158 0.117924i
\(351\) 0 0
\(352\) 0.178533 + 0.191745i 0.00951585 + 0.0102200i
\(353\) −24.0382 −1.27942 −0.639712 0.768615i \(-0.720946\pi\)
−0.639712 + 0.768615i \(0.720946\pi\)
\(354\) 0 0
\(355\) 20.5974 + 14.9649i 1.09320 + 0.794253i
\(356\) −0.173346 + 0.125943i −0.00918732 + 0.00667498i
\(357\) 0 0
\(358\) 3.62470 11.1557i 0.191571 0.589596i
\(359\) −8.85883 + 6.43632i −0.467551 + 0.339696i −0.796486 0.604657i \(-0.793310\pi\)
0.328935 + 0.944353i \(0.393310\pi\)
\(360\) 0 0
\(361\) 4.52822 + 13.9364i 0.238328 + 0.733497i
\(362\) −20.8613 −1.09645
\(363\) 0 0
\(364\) 0.0648939 0.00340136
\(365\) 3.40385 + 10.4760i 0.178166 + 0.548338i
\(366\) 0 0
\(367\) −8.58995 + 6.24096i −0.448392 + 0.325776i −0.788960 0.614444i \(-0.789380\pi\)
0.340569 + 0.940220i \(0.389380\pi\)
\(368\) −0.883322 + 2.71859i −0.0460463 + 0.141716i
\(369\) 0 0
\(370\) −4.37382 + 3.17777i −0.227384 + 0.165204i
\(371\) 8.20742 + 5.96304i 0.426108 + 0.309586i
\(372\) 0 0
\(373\) 36.6036 1.89526 0.947631 0.319367i \(-0.103470\pi\)
0.947631 + 0.319367i \(0.103470\pi\)
\(374\) 17.4230 + 18.7124i 0.900924 + 0.967593i
\(375\) 0 0
\(376\) 5.24115 + 16.1306i 0.270292 + 0.831872i
\(377\) 4.40797 + 3.20258i 0.227022 + 0.164941i
\(378\) 0 0
\(379\) −3.91147 + 12.0383i −0.200919 + 0.618364i 0.798938 + 0.601414i \(0.205396\pi\)
−0.999856 + 0.0169501i \(0.994604\pi\)
\(380\) 0.0458463 0.141100i 0.00235187 0.00723830i
\(381\) 0 0
\(382\) −10.9529 7.95773i −0.560398 0.407153i
\(383\) 4.77984 + 14.7108i 0.244238 + 0.751688i 0.995761 + 0.0919809i \(0.0293199\pi\)
−0.751522 + 0.659708i \(0.770680\pi\)
\(384\) 0 0
\(385\) −2.94877 + 5.31022i −0.150283 + 0.270634i
\(386\) −2.09672 −0.106720
\(387\) 0 0
\(388\) 0.0272411 + 0.0197918i 0.00138296 + 0.00100478i
\(389\) −10.2850 + 7.47249i −0.521470 + 0.378870i −0.817157 0.576415i \(-0.804451\pi\)
0.295687 + 0.955285i \(0.404451\pi\)
\(390\) 0 0
\(391\) 1.21654 3.74414i 0.0615232 0.189349i
\(392\) 2.29616 1.66826i 0.115974 0.0842599i
\(393\) 0 0
\(394\) 6.11571 + 18.8222i 0.308105 + 0.948250i
\(395\) −28.6446 −1.44127
\(396\) 0 0
\(397\) −18.9574 −0.951445 −0.475722 0.879596i \(-0.657813\pi\)
−0.475722 + 0.879596i \(0.657813\pi\)
\(398\) −1.86706 5.74622i −0.0935873 0.288032i
\(399\) 0 0
\(400\) −5.28919 + 3.84282i −0.264460 + 0.192141i
\(401\) 2.68291 8.25715i 0.133978 0.412343i −0.861451 0.507840i \(-0.830444\pi\)
0.995430 + 0.0954974i \(0.0304442\pi\)
\(402\) 0 0
\(403\) −4.91698 + 3.57240i −0.244932 + 0.177954i
\(404\) −0.134394 0.0976429i −0.00668635 0.00485792i
\(405\) 0 0
\(406\) 1.65233 0.0820037
\(407\) −6.81881 1.33081i −0.337996 0.0659658i
\(408\) 0 0
\(409\) 1.76574 + 5.43440i 0.0873104 + 0.268714i 0.985173 0.171561i \(-0.0548811\pi\)
−0.897863 + 0.440275i \(0.854881\pi\)
\(410\) −1.91396 1.39057i −0.0945237 0.0686755i
\(411\) 0 0
\(412\) −0.00171020 + 0.00526346i −8.42556e−5 + 0.000259312i
\(413\) 2.37350 7.30488i 0.116792 0.359450i
\(414\) 0 0
\(415\) −6.48318 4.71031i −0.318247 0.231220i
\(416\) −0.113437 0.349122i −0.00556169 0.0171171i
\(417\) 0 0
\(418\) −24.5830 + 11.4406i −1.20239 + 0.559576i
\(419\) 27.1909 1.32836 0.664181 0.747571i \(-0.268780\pi\)
0.664181 + 0.747571i \(0.268780\pi\)
\(420\) 0 0
\(421\) 19.3881 + 14.0863i 0.944921 + 0.686525i 0.949600 0.313464i \(-0.101490\pi\)
−0.00467947 + 0.999989i \(0.501490\pi\)
\(422\) 1.65919 1.20547i 0.0807679 0.0586813i
\(423\) 0 0
\(424\) 8.89768 27.3842i 0.432110 1.32990i
\(425\) 7.28447 5.29248i 0.353349 0.256723i
\(426\) 0 0
\(427\) −1.93943 5.96895i −0.0938555 0.288858i
\(428\) −0.0456549 −0.00220681
\(429\) 0 0
\(430\) 20.7087 0.998663
\(431\) −5.09049 15.6669i −0.245200 0.754649i −0.995603 0.0936683i \(-0.970141\pi\)
0.750403 0.660980i \(-0.229859\pi\)
\(432\) 0 0
\(433\) −16.2539 + 11.8092i −0.781113 + 0.567512i −0.905313 0.424745i \(-0.860364\pi\)
0.124200 + 0.992257i \(0.460364\pi\)
\(434\) −0.569559 + 1.75292i −0.0273397 + 0.0841430i
\(435\) 0 0
\(436\) −0.0321571 + 0.0233635i −0.00154005 + 0.00111891i
\(437\) 3.37765 + 2.45401i 0.161575 + 0.117391i
\(438\) 0 0
\(439\) 26.7682 1.27758 0.638788 0.769383i \(-0.279436\pi\)
0.638788 + 0.769383i \(0.279436\pi\)
\(440\) 16.9201 + 3.30226i 0.806636 + 0.157429i
\(441\) 0 0
\(442\) −11.0703 34.0708i −0.526559 1.62058i
\(443\) 21.2086 + 15.4090i 1.00765 + 0.732103i 0.963716 0.266931i \(-0.0860097\pi\)
0.0439378 + 0.999034i \(0.486010\pi\)
\(444\) 0 0
\(445\) −8.68346 + 26.7249i −0.411635 + 1.26688i
\(446\) −2.11491 + 6.50903i −0.100144 + 0.308212i
\(447\) 0 0
\(448\) −6.51669 4.73465i −0.307885 0.223691i
\(449\) −3.01211 9.27033i −0.142150 0.437494i 0.854483 0.519479i \(-0.173874\pi\)
−0.996634 + 0.0819851i \(0.973874\pi\)
\(450\) 0 0
\(451\) −0.368215 3.01779i −0.0173386 0.142102i
\(452\) 0.203107 0.00955336
\(453\) 0 0
\(454\) 0.452792 + 0.328973i 0.0212506 + 0.0154395i
\(455\) 6.88518 5.00238i 0.322782 0.234515i
\(456\) 0 0
\(457\) 3.67276 11.3036i 0.171805 0.528760i −0.827669 0.561217i \(-0.810333\pi\)
0.999473 + 0.0324572i \(0.0103333\pi\)
\(458\) −2.49645 + 1.81378i −0.116651 + 0.0847522i
\(459\) 0 0
\(460\) −0.00568760 0.0175046i −0.000265186 0.000816158i
\(461\) −9.14737 −0.426035 −0.213018 0.977048i \(-0.568329\pi\)
−0.213018 + 0.977048i \(0.568329\pi\)
\(462\) 0 0
\(463\) 38.9342 1.80943 0.904713 0.426021i \(-0.140085\pi\)
0.904713 + 0.426021i \(0.140085\pi\)
\(464\) −1.43907 4.42899i −0.0668070 0.205611i
\(465\) 0 0
\(466\) −1.43673 + 1.04385i −0.0665553 + 0.0483552i
\(467\) 6.42243 19.7662i 0.297195 0.914671i −0.685281 0.728279i \(-0.740320\pi\)
0.982475 0.186392i \(-0.0596795\pi\)
\(468\) 0 0
\(469\) 12.5133 9.09143i 0.577810 0.419803i
\(470\) 12.4776 + 9.06548i 0.575547 + 0.418159i
\(471\) 0 0
\(472\) −21.7998 −1.00342
\(473\) 18.1345 + 19.4765i 0.833826 + 0.895529i
\(474\) 0 0
\(475\) 2.95076 + 9.08152i 0.135390 + 0.416689i
\(476\) 0.0617999 + 0.0449003i 0.00283259 + 0.00205800i
\(477\) 0 0
\(478\) 4.86076 14.9599i 0.222326 0.684249i
\(479\) 7.58214 23.3354i 0.346437 1.06622i −0.614374 0.789015i \(-0.710591\pi\)
0.960810 0.277207i \(-0.0894088\pi\)
\(480\) 0 0
\(481\) 7.87527 + 5.72172i 0.359081 + 0.260888i
\(482\) −9.35614 28.7952i −0.426161 1.31159i
\(483\) 0 0
\(484\) 0.0812030 + 0.130392i 0.00369105 + 0.00592690i
\(485\) 4.41591 0.200516
\(486\) 0 0
\(487\) 10.0086 + 7.27168i 0.453533 + 0.329511i 0.790989 0.611830i \(-0.209566\pi\)
−0.337456 + 0.941341i \(0.609566\pi\)
\(488\) −14.4110 + 10.4702i −0.652356 + 0.473964i
\(489\) 0 0
\(490\) 0.797546 2.45459i 0.0360295 0.110887i
\(491\) 13.3691 9.71320i 0.603338 0.438350i −0.243724 0.969845i \(-0.578369\pi\)
0.847062 + 0.531494i \(0.178369\pi\)
\(492\) 0 0
\(493\) 1.98194 + 6.09977i 0.0892620 + 0.274720i
\(494\) 37.9916 1.70932
\(495\) 0 0
\(496\) 5.19468 0.233248
\(497\) −4.29593 13.2215i −0.192699 0.593065i
\(498\) 0 0
\(499\) 11.1167 8.07673i 0.497650 0.361564i −0.310469 0.950584i \(-0.600486\pi\)
0.808119 + 0.589020i \(0.200486\pi\)
\(500\) 0.0525231 0.161649i 0.00234890 0.00722918i
\(501\) 0 0
\(502\) −0.483206 + 0.351070i −0.0215665 + 0.0156690i
\(503\) −18.2812 13.2820i −0.815117 0.592217i 0.100193 0.994968i \(-0.468054\pi\)
−0.915310 + 0.402751i \(0.868054\pi\)
\(504\) 0 0
\(505\) −21.7859 −0.969461
\(506\) −1.63304 + 2.94081i −0.0725973 + 0.130735i
\(507\) 0 0
\(508\) −0.0217182 0.0668418i −0.000963590 0.00296563i
\(509\) −17.3644 12.6160i −0.769664 0.559194i 0.132195 0.991224i \(-0.457798\pi\)
−0.901859 + 0.432030i \(0.857798\pi\)
\(510\) 0 0
\(511\) 1.85862 5.72025i 0.0822206 0.253049i
\(512\) −7.06408 + 21.7410i −0.312191 + 0.960825i
\(513\) 0 0
\(514\) 19.8838 + 14.4464i 0.877037 + 0.637204i
\(515\) 0.224286 + 0.690280i 0.00988321 + 0.0304174i
\(516\) 0 0
\(517\) 2.40048 + 19.6737i 0.105573 + 0.865248i
\(518\) 2.95205 0.129706
\(519\) 0 0
\(520\) −19.5416 14.1978i −0.856957 0.622616i
\(521\) 28.0822 20.4029i 1.23031 0.893869i 0.233393 0.972383i \(-0.425017\pi\)
0.996913 + 0.0785132i \(0.0250173\pi\)
\(522\) 0 0
\(523\) 6.09633 18.7626i 0.266574 0.820430i −0.724753 0.689009i \(-0.758046\pi\)
0.991327 0.131421i \(-0.0419540\pi\)
\(524\) 0.00203415 0.00147790i 8.88624e−5 6.45623e-5i
\(525\) 0 0
\(526\) −0.659847 2.03080i −0.0287707 0.0885471i
\(527\) −7.15430 −0.311646
\(528\) 0 0
\(529\) −22.4821 −0.977481
\(530\) −8.09105 24.9017i −0.351453 1.08166i
\(531\) 0 0
\(532\) −0.0655390 + 0.0476168i −0.00284147 + 0.00206445i
\(533\) −1.31632 + 4.05122i −0.0570162 + 0.175478i
\(534\) 0 0
\(535\) −4.84395 + 3.51933i −0.209422 + 0.152154i
\(536\) −35.5154 25.8034i −1.53403 1.11454i
\(537\) 0 0
\(538\) 2.86226 0.123401
\(539\) 3.00695 1.39939i 0.129518 0.0602758i
\(540\) 0 0
\(541\) −1.71487 5.27782i −0.0737279 0.226911i 0.907401 0.420266i \(-0.138063\pi\)
−0.981129 + 0.193355i \(0.938063\pi\)
\(542\) −8.66998 6.29911i −0.372408 0.270570i
\(543\) 0 0
\(544\) 0.133530 0.410964i 0.00572506 0.0176199i
\(545\) −1.61085 + 4.95770i −0.0690014 + 0.212364i
\(546\) 0 0
\(547\) 6.83353 + 4.96485i 0.292181 + 0.212282i 0.724213 0.689576i \(-0.242203\pi\)
−0.432032 + 0.901858i \(0.642203\pi\)
\(548\) 0.0359201 + 0.110551i 0.00153443 + 0.00472250i
\(549\) 0 0
\(550\) −6.97518 + 3.24614i −0.297422 + 0.138416i
\(551\) −6.80173 −0.289763
\(552\) 0 0
\(553\) 12.6538 + 9.19351i 0.538094 + 0.390948i
\(554\) −16.4483 + 11.9504i −0.698822 + 0.507724i
\(555\) 0 0
\(556\) 0.0300394 0.0924519i 0.00127396 0.00392083i
\(557\) −9.85665 + 7.16128i −0.417640 + 0.303433i −0.776687 0.629886i \(-0.783102\pi\)
0.359048 + 0.933319i \(0.383102\pi\)
\(558\) 0 0
\(559\) −11.5223 35.4620i −0.487342 1.49988i
\(560\) −7.27404 −0.307384
\(561\) 0 0
\(562\) −25.0140 −1.05515
\(563\) 8.45270 + 26.0147i 0.356239 + 1.09639i 0.955288 + 0.295678i \(0.0955456\pi\)
−0.599049 + 0.800713i \(0.704454\pi\)
\(564\) 0 0
\(565\) 21.5495 15.6566i 0.906594 0.658679i
\(566\) −13.5594 + 41.7316i −0.569944 + 1.75411i
\(567\) 0 0
\(568\) −31.9211 + 23.1920i −1.33938 + 0.973115i
\(569\) 5.77253 + 4.19399i 0.241997 + 0.175821i 0.702173 0.712007i \(-0.252214\pi\)
−0.460176 + 0.887828i \(0.652214\pi\)
\(570\) 0 0
\(571\) 32.4839 1.35941 0.679705 0.733486i \(-0.262108\pi\)
0.679705 + 0.733486i \(0.262108\pi\)
\(572\) −0.0260678 0.213644i −0.00108995 0.00893291i
\(573\) 0 0
\(574\) 0.399188 + 1.22857i 0.0166618 + 0.0512797i
\(575\) 0.958373 + 0.696299i 0.0399669 + 0.0290377i
\(576\) 0 0
\(577\) 10.7482 33.0795i 0.447453 1.37712i −0.432317 0.901721i \(-0.642304\pi\)
0.879771 0.475398i \(-0.157696\pi\)
\(578\) 5.62791 17.3209i 0.234090 0.720456i
\(579\) 0 0
\(580\) 0.0242587 + 0.0176249i 0.00100729 + 0.000731836i
\(581\) 1.35217 + 4.16157i 0.0560977 + 0.172651i
\(582\) 0 0
\(583\) 16.3347 29.4159i 0.676513 1.21828i
\(584\) −17.0708 −0.706395
\(585\) 0 0
\(586\) −27.3975 19.9054i −1.13178 0.822285i
\(587\) −11.7105 + 8.50816i −0.483343 + 0.351169i −0.802618 0.596493i \(-0.796560\pi\)
0.319276 + 0.947662i \(0.396560\pi\)
\(588\) 0 0
\(589\) 2.34456 7.21581i 0.0966059 0.297322i
\(590\) −16.0375 + 11.6520i −0.660255 + 0.479704i
\(591\) 0 0
\(592\) −2.57103 7.91283i −0.105669 0.325215i
\(593\) 15.0291 0.617169 0.308585 0.951197i \(-0.400145\pi\)
0.308585 + 0.951197i \(0.400145\pi\)
\(594\) 0 0
\(595\) 10.0181 0.410701
\(596\) −0.0138706 0.0426894i −0.000568163 0.00174863i
\(597\) 0 0
\(598\) 3.81303 2.77033i 0.155926 0.113287i
\(599\) −0.544010 + 1.67429i −0.0222276 + 0.0684097i −0.961555 0.274612i \(-0.911451\pi\)
0.939327 + 0.343022i \(0.111451\pi\)
\(600\) 0 0
\(601\) −18.9605 + 13.7756i −0.773415 + 0.561919i −0.902995 0.429650i \(-0.858637\pi\)
0.129581 + 0.991569i \(0.458637\pi\)
\(602\) −9.14810 6.64648i −0.372849 0.270890i
\(603\) 0 0
\(604\) −0.310948 −0.0126523
\(605\) 18.6669 + 7.57487i 0.758917 + 0.307962i
\(606\) 0 0
\(607\) −7.81149 24.0413i −0.317059 0.975806i −0.974899 0.222649i \(-0.928530\pi\)
0.657840 0.753158i \(-0.271470\pi\)
\(608\) 0.370738 + 0.269357i 0.0150354 + 0.0109239i
\(609\) 0 0
\(610\) −5.00550 + 15.4053i −0.202667 + 0.623744i
\(611\) 8.58142 26.4109i 0.347167 1.06847i
\(612\) 0 0
\(613\) −0.939222 0.682385i −0.0379348 0.0275613i 0.568656 0.822575i \(-0.307463\pi\)
−0.606591 + 0.795014i \(0.707463\pi\)
\(614\) −2.37906 7.32199i −0.0960110 0.295492i
\(615\) 0 0
\(616\) −6.41463 6.88931i −0.258453 0.277578i
\(617\) −12.9711 −0.522197 −0.261098 0.965312i \(-0.584085\pi\)
−0.261098 + 0.965312i \(0.584085\pi\)
\(618\) 0 0
\(619\) −37.0465 26.9158i −1.48902 1.08184i −0.974507 0.224358i \(-0.927971\pi\)
−0.514517 0.857480i \(-0.672029\pi\)
\(620\) −0.0270599 + 0.0196602i −0.00108675 + 0.000789572i
\(621\) 0 0
\(622\) −6.04824 + 18.6146i −0.242512 + 0.746377i
\(623\) 12.4133 9.01881i 0.497329 0.361331i
\(624\) 0 0
\(625\) −4.34493 13.3723i −0.173797 0.534893i
\(626\) 38.6824 1.54606
\(627\) 0 0
\(628\) −0.185097 −0.00738615
\(629\) 3.54092 + 10.8978i 0.141186 + 0.434525i
\(630\) 0 0
\(631\) 10.2103 7.41824i 0.406467 0.295316i −0.365703 0.930732i \(-0.619171\pi\)
0.772170 + 0.635416i \(0.219171\pi\)
\(632\) 13.7180 42.2196i 0.545672 1.67941i
\(633\) 0 0
\(634\) 8.92225 6.48240i 0.354348 0.257449i
\(635\) −7.45682 5.41770i −0.295915 0.214995i
\(636\) 0 0
\(637\) −4.64706 −0.184123
\(638\) −0.663738 5.43981i −0.0262776 0.215364i
\(639\) 0 0
\(640\) 6.33488 + 19.4968i 0.250408 + 0.770678i
\(641\) 22.6175 + 16.4326i 0.893336 + 0.649047i 0.936746 0.350011i \(-0.113822\pi\)
−0.0434095 + 0.999057i \(0.513822\pi\)
\(642\) 0 0
\(643\) −15.3575 + 47.2657i −0.605642 + 1.86398i −0.113330 + 0.993557i \(0.536152\pi\)
−0.492313 + 0.870418i \(0.663848\pi\)
\(644\) −0.00310563 + 0.00955813i −0.000122379 + 0.000376643i
\(645\) 0 0
\(646\) 36.1802 + 26.2865i 1.42349 + 1.03423i
\(647\) 3.40125 + 10.4680i 0.133717 + 0.411539i 0.995388 0.0959281i \(-0.0305819\pi\)
−0.861671 + 0.507467i \(0.830582\pi\)
\(648\) 0 0
\(649\) −25.0026 4.87970i −0.981439 0.191545i
\(650\) 10.7797 0.422816
\(651\) 0 0
\(652\) 0.154983 + 0.112602i 0.00606962 + 0.00440984i
\(653\) 23.4100 17.0084i 0.916106 0.665590i −0.0264458 0.999650i \(-0.508419\pi\)
0.942552 + 0.334060i \(0.108419\pi\)
\(654\) 0 0
\(655\) 0.101897 0.313608i 0.00398146 0.0122537i
\(656\) 2.94547 2.14001i 0.115001 0.0835533i
\(657\) 0 0
\(658\) −2.60240 8.00937i −0.101452 0.312238i
\(659\) −10.8405 −0.422288 −0.211144 0.977455i \(-0.567719\pi\)
−0.211144 + 0.977455i \(0.567719\pi\)
\(660\) 0 0
\(661\) 20.3444 0.791305 0.395652 0.918400i \(-0.370519\pi\)
0.395652 + 0.918400i \(0.370519\pi\)
\(662\) −12.2573 37.7241i −0.476394 1.46619i
\(663\) 0 0
\(664\) 10.0474 7.29986i 0.389915 0.283289i
\(665\) −3.28306 + 10.1042i −0.127311 + 0.391824i
\(666\) 0 0
\(667\) −0.682656 + 0.495978i −0.0264325 + 0.0192044i
\(668\) −0.105164 0.0764062i −0.00406892 0.00295625i
\(669\) 0 0
\(670\) −39.9197 −1.54223
\(671\) −18.8720 + 8.78272i −0.728544 + 0.339053i
\(672\) 0 0
\(673\) −3.73255 11.4876i −0.143879 0.442815i 0.852986 0.521934i \(-0.174789\pi\)
−0.996865 + 0.0791188i \(0.974789\pi\)
\(674\) 28.4790 + 20.6912i 1.09697 + 0.796996i
\(675\) 0 0
\(676\) −0.0370903 + 0.114152i −0.00142655 + 0.00439047i
\(677\) −1.04951 + 3.23007i −0.0403361 + 0.124142i −0.969197 0.246287i \(-0.920789\pi\)
0.928861 + 0.370429i \(0.120789\pi\)
\(678\) 0 0
\(679\) −1.95073 1.41729i −0.0748623 0.0543906i
\(680\) −8.78642 27.0418i −0.336944 1.03701i
\(681\) 0 0
\(682\) 5.99978 + 1.17096i 0.229743 + 0.0448384i
\(683\) 4.75643 0.182000 0.0909999 0.995851i \(-0.470994\pi\)
0.0909999 + 0.995851i \(0.470994\pi\)
\(684\) 0 0
\(685\) 12.3330 + 8.96042i 0.471218 + 0.342360i
\(686\) −1.14012 + 0.828347i −0.0435300 + 0.0316264i
\(687\) 0 0
\(688\) −9.84822 + 30.3097i −0.375460 + 1.15555i
\(689\) −38.1404 + 27.7106i −1.45303 + 1.05569i
\(690\) 0 0
\(691\) 2.04998 + 6.30920i 0.0779850 + 0.240013i 0.982447 0.186540i \(-0.0597275\pi\)
−0.904462 + 0.426554i \(0.859728\pi\)
\(692\) 0.146707 0.00557695
\(693\) 0 0
\(694\) −29.1003 −1.10463
\(695\) −3.93955 12.1247i −0.149435 0.459915i
\(696\) 0 0
\(697\) −4.05661 + 2.94730i −0.153655 + 0.111637i
\(698\) −2.61171 + 8.03802i −0.0988547 + 0.304244i
\(699\) 0 0
\(700\) −0.0185960 + 0.0135108i −0.000702863 + 0.000510660i
\(701\) 2.45134 + 1.78101i 0.0925860 + 0.0672677i 0.633115 0.774058i \(-0.281776\pi\)
−0.540529 + 0.841325i \(0.681776\pi\)
\(702\) 0 0
\(703\) −12.1519 −0.458319
\(704\) −12.9697 + 23.3562i −0.488815 + 0.880270i
\(705\) 0 0
\(706\) −10.4683 32.2182i −0.393981 1.21255i
\(707\) 9.62396 + 6.99222i 0.361946 + 0.262969i
\(708\) 0 0
\(709\) −4.22026 + 12.9886i −0.158495 + 0.487798i −0.998498 0.0547836i \(-0.982553\pi\)
0.840003 + 0.542582i \(0.182553\pi\)
\(710\) −11.0874 + 34.1236i −0.416103 + 1.28063i
\(711\) 0 0
\(712\) −35.2317 25.5973i −1.32036 0.959300i
\(713\) −0.290862 0.895180i −0.0108928 0.0335247i
\(714\) 0 0
\(715\) −19.2346 20.6580i −0.719335 0.772566i
\(716\) −0.116231 −0.00434376
\(717\) 0 0
\(718\) −12.4845 9.07050i −0.465916 0.338508i
\(719\) −1.53737 + 1.11696i −0.0573341 + 0.0416557i −0.616083 0.787681i \(-0.711281\pi\)
0.558749 + 0.829337i \(0.311281\pi\)
\(720\) 0 0
\(721\) 0.122468 0.376917i 0.00456094 0.0140371i
\(722\) −16.7069 + 12.1383i −0.621768 + 0.451741i
\(723\) 0 0
\(724\) 0.0638788 + 0.196599i 0.00237404 + 0.00730654i
\(725\) −1.92992 −0.0716754
\(726\) 0 0
\(727\) −13.8211 −0.512595 −0.256298 0.966598i \(-0.582503\pi\)
−0.256298 + 0.966598i \(0.582503\pi\)
\(728\) 4.07573 + 12.5438i 0.151057 + 0.464905i
\(729\) 0 0
\(730\) −12.5586 + 9.12432i −0.464813 + 0.337706i
\(731\) 13.5633 41.7436i 0.501658 1.54394i
\(732\) 0 0
\(733\) −39.1357 + 28.4337i −1.44551 + 1.05022i −0.458655 + 0.888615i \(0.651669\pi\)
−0.986855 + 0.161610i \(0.948331\pi\)
\(734\) −12.1055 8.79519i −0.446824 0.324636i
\(735\) 0 0
\(736\) 0.0568504 0.00209553
\(737\) −34.9575 37.5443i −1.28767 1.38296i
\(738\) 0 0
\(739\) 7.17170 + 22.0722i 0.263815 + 0.811939i 0.991964 + 0.126520i \(0.0403809\pi\)
−0.728149 + 0.685419i \(0.759619\pi\)
\(740\) 0.0433404 + 0.0314887i 0.00159323 + 0.00115755i
\(741\) 0 0
\(742\) −4.41799 + 13.5972i −0.162190 + 0.499168i
\(743\) 13.8536 42.6369i 0.508238 1.56420i −0.287019 0.957925i \(-0.592664\pi\)
0.795257 0.606272i \(-0.207336\pi\)
\(744\) 0 0
\(745\) −4.76240 3.46009i −0.174481 0.126768i
\(746\) 15.9404 + 49.0596i 0.583620 + 1.79620i
\(747\) 0 0
\(748\) 0.122996 0.221495i 0.00449718 0.00809864i
\(749\) 3.26935 0.119460
\(750\) 0 0
\(751\) 33.3199 + 24.2083i 1.21586 + 0.883373i 0.995750 0.0921022i \(-0.0293587\pi\)
0.220109 + 0.975475i \(0.429359\pi\)
\(752\) −19.2022 + 13.9512i −0.700234 + 0.508750i
\(753\) 0 0
\(754\) −2.37278 + 7.30266i −0.0864115 + 0.265947i
\(755\) −32.9913 + 23.9696i −1.20068 + 0.872343i
\(756\) 0 0
\(757\) −6.76401 20.8175i −0.245842 0.756624i −0.995497 0.0947948i \(-0.969781\pi\)
0.749655 0.661829i \(-0.230219\pi\)
\(758\) −17.8382 −0.647912
\(759\) 0 0
\(760\) 30.1537 1.09379
\(761\) 11.0367 + 33.9673i 0.400078 + 1.23131i 0.924935 + 0.380124i \(0.124119\pi\)
−0.524857 + 0.851190i \(0.675881\pi\)
\(762\) 0 0
\(763\) 2.30277 1.67306i 0.0833660 0.0605690i
\(764\) −0.0414558 + 0.127588i −0.00149982 + 0.00461596i
\(765\) 0 0
\(766\) −17.6353 + 12.8128i −0.637188 + 0.462944i
\(767\) 28.8764 + 20.9799i 1.04266 + 0.757540i
\(768\) 0 0
\(769\) 5.30246 0.191212 0.0956058 0.995419i \(-0.469521\pi\)
0.0956058 + 0.995419i \(0.469521\pi\)
\(770\) −8.40141 1.63968i −0.302766 0.0590900i
\(771\) 0 0
\(772\) 0.00642030 + 0.0197596i 0.000231072 + 0.000711165i
\(773\) −40.3628 29.3253i −1.45175 1.05476i −0.985418 0.170149i \(-0.945575\pi\)
−0.466332 0.884610i \(-0.654425\pi\)
\(774\) 0 0
\(775\) 0.665245 2.04741i 0.0238963 0.0735452i
\(776\) −2.11479 + 6.50867i −0.0759167 + 0.233648i
\(777\) 0 0
\(778\) −14.4943 10.5307i −0.519646 0.377545i
\(779\) −1.64324 5.05736i −0.0588750 0.181199i
\(780\) 0 0
\(781\) −41.8023 + 19.4541i −1.49580 + 0.696124i
\(782\) 5.54803 0.198397
\(783\) 0 0
\(784\) 3.21332 + 2.33461i 0.114761 + 0.0833789i
\(785\) −19.6386 + 14.2683i −0.700931 + 0.509256i
\(786\) 0 0
\(787\) 11.0804 34.1020i 0.394974 1.21560i −0.534008 0.845479i \(-0.679315\pi\)
0.928982 0.370125i \(-0.120685\pi\)
\(788\) 0.158655 0.115270i 0.00565186 0.00410632i
\(789\) 0 0
\(790\) −12.4744 38.3922i −0.443818 1.36593i
\(791\) −14.5445 −0.517144
\(792\) 0 0
\(793\) 29.1655 1.03570
\(794\) −8.25571 25.4085i −0.292984 0.901713i
\(795\) 0 0
\(796\) −0.0484357 + 0.0351906i −0.00171676 + 0.00124730i
\(797\) −4.55530 + 14.0198i −0.161357 + 0.496606i −0.998749 0.0499962i \(-0.984079\pi\)
0.837392 + 0.546602i \(0.184079\pi\)
\(798\) 0 0
\(799\) 26.4460 19.2142i 0.935593 0.679748i
\(800\) 0.105193 + 0.0764272i 0.00371913 + 0.00270211i
\(801\) 0 0
\(802\) 12.2354 0.432046
\(803\) −19.5789 3.82116i −0.690923 0.134846i
\(804\) 0 0
\(805\) 0.407290 + 1.25351i 0.0143551 + 0.0441804i
\(806\) −6.92934 5.03446i −0.244076 0.177331i
\(807\) 0 0
\(808\) 10.4334 32.1106i 0.367044 1.12965i
\(809\) 8.33599 25.6556i 0.293078 0.902001i −0.690782 0.723063i \(-0.742734\pi\)
0.983860 0.178938i \(-0.0572663\pi\)
\(810\) 0 0
\(811\) −1.18472 0.860750i −0.0416012 0.0302250i 0.566790 0.823862i \(-0.308185\pi\)
−0.608392 + 0.793637i \(0.708185\pi\)
\(812\) −0.00505954 0.0155717i −0.000177555 0.000546459i
\(813\) 0 0
\(814\) −1.18583 9.71876i −0.0415634 0.340642i
\(815\) 25.1236 0.880041
\(816\) 0 0
\(817\) 37.6577 + 27.3599i 1.31747 + 0.957201i
\(818\) −6.51473 + 4.73323i −0.227782 + 0.165493i
\(819\) 0 0
\(820\) −0.00724418 + 0.0222953i −0.000252978 + 0.000778586i
\(821\) 24.7791 18.0031i 0.864797 0.628312i −0.0643886 0.997925i \(-0.520510\pi\)
0.929186 + 0.369613i \(0.120510\pi\)
\(822\) 0 0
\(823\) −7.58137 23.3330i −0.264270 0.813339i −0.991861 0.127328i \(-0.959360\pi\)
0.727591 0.686011i \(-0.240640\pi\)
\(824\) −1.12482 −0.0391851
\(825\) 0 0
\(826\) 10.8243 0.376626
\(827\) 2.02927 + 6.24545i 0.0705646 + 0.217176i 0.980119 0.198408i \(-0.0635772\pi\)
−0.909555 + 0.415584i \(0.863577\pi\)
\(828\) 0 0
\(829\) 16.0543 11.6642i 0.557590 0.405113i −0.272986 0.962018i \(-0.588011\pi\)
0.830576 + 0.556905i \(0.188011\pi\)
\(830\) 3.48985 10.7406i 0.121134 0.372813i
\(831\) 0 0
\(832\) 30.2834 22.0022i 1.04989 0.762789i
\(833\) −4.42550 3.21531i −0.153334 0.111404i
\(834\) 0 0
\(835\) −17.0476 −0.589958
\(836\) 0.183091 + 0.196640i 0.00633235 + 0.00680095i
\(837\) 0 0
\(838\) 11.8413 + 36.4438i 0.409051 + 1.25893i
\(839\) −6.44019 4.67907i −0.222340 0.161539i 0.471039 0.882112i \(-0.343879\pi\)
−0.693379 + 0.720573i \(0.743879\pi\)
\(840\) 0 0
\(841\) −8.53669 + 26.2732i −0.294369 + 0.905973i
\(842\) −10.4365 + 32.1202i −0.359665 + 1.10694i
\(843\) 0 0
\(844\) −0.0164410 0.0119451i −0.000565922 0.000411166i
\(845\) 4.86424 + 14.9706i 0.167335 + 0.515004i
\(846\) 0 0
\(847\) −5.81496 9.33736i −0.199804 0.320835i
\(848\) 40.2944 1.38372
\(849\) 0 0
\(850\) 10.2658 + 7.45852i 0.352113 + 0.255825i
\(851\) −1.21963 + 0.886114i −0.0418084 + 0.0303756i
\(852\) 0 0
\(853\) 10.5292 32.4055i 0.360513 1.10954i −0.592231 0.805768i \(-0.701753\pi\)
0.952744 0.303776i \(-0.0982473\pi\)
\(854\) 7.15554 5.19881i 0.244858 0.177900i
\(855\) 0 0
\(856\) −2.86741 8.82497i −0.0980060 0.301631i
\(857\) −24.8539 −0.848992 −0.424496 0.905430i \(-0.639549\pi\)
−0.424496 + 0.905430i \(0.639549\pi\)
\(858\) 0 0
\(859\) 2.05654 0.0701683 0.0350841 0.999384i \(-0.488830\pi\)
0.0350841 + 0.999384i \(0.488830\pi\)
\(860\) −0.0634115 0.195160i −0.00216231 0.00665491i
\(861\) 0 0
\(862\) 18.7814 13.6455i 0.639697 0.464767i
\(863\) 0.0801824 0.246776i 0.00272944 0.00840035i −0.949683 0.313214i \(-0.898594\pi\)
0.952412 + 0.304814i \(0.0985942\pi\)
\(864\) 0 0
\(865\) 15.5655 11.3090i 0.529241 0.384516i
\(866\) −22.9061 16.6423i −0.778381 0.565527i
\(867\) 0 0
\(868\) 0.0182637 0.000619910
\(869\) 25.1840 45.3519i 0.854307 1.53846i
\(870\) 0 0
\(871\) 22.2113 + 68.3593i 0.752601 + 2.31627i
\(872\) −6.53577 4.74851i −0.221329 0.160805i
\(873\) 0 0
\(874\) −1.81816 + 5.59573i −0.0615003 + 0.189278i
\(875\) −3.76118 + 11.5757i −0.127151 + 0.391331i
\(876\) 0 0
\(877\) −15.0420 10.9287i −0.507934 0.369035i 0.304106 0.952638i \(-0.401642\pi\)
−0.812039 + 0.583603i \(0.801642\pi\)
\(878\) 11.6572 + 35.8772i 0.393412 + 1.21080i
\(879\) 0 0
\(880\) 2.92197 + 23.9477i 0.0984996 + 0.807275i
\(881\) −6.45292 −0.217404 −0.108702 0.994074i \(-0.534670\pi\)
−0.108702 + 0.994074i \(0.534670\pi\)
\(882\) 0 0
\(883\) 0.225301 + 0.163691i 0.00758198 + 0.00550863i 0.591570 0.806254i \(-0.298508\pi\)
−0.583988 + 0.811762i \(0.698508\pi\)
\(884\) −0.287188 + 0.208654i −0.00965917 + 0.00701779i
\(885\) 0 0
\(886\) −11.4165 + 35.1362i −0.383543 + 1.18042i
\(887\) 24.7211 17.9609i 0.830054 0.603069i −0.0895209 0.995985i \(-0.528534\pi\)
0.919575 + 0.392916i \(0.128534\pi\)
\(888\) 0 0
\(889\) 1.55524 + 4.78655i 0.0521612 + 0.160536i
\(890\) −39.6008 −1.32742
\(891\) 0 0
\(892\) 0.0678176 0.00227070
\(893\) 10.7127 + 32.9702i 0.358485 + 1.10330i
\(894\) 0 0
\(895\) −12.3320 + 8.95972i −0.412213 + 0.299491i
\(896\) 3.45907 10.6459i 0.115559 0.355655i
\(897\) 0 0
\(898\) 11.1132 8.07423i 0.370853 0.269441i
\(899\) 1.24058 + 0.901332i 0.0413756 + 0.0300611i
\(900\) 0 0
\(901\) −55.4949 −1.84880
\(902\) 3.88437 1.80773i 0.129335 0.0601907i
\(903\) 0 0
\(904\) 12.7564 + 39.2601i 0.424271 + 1.30577i
\(905\) 21.9324 + 15.9348i 0.729058 + 0.529692i
\(906\) 0 0
\(907\) 9.86836 30.3717i 0.327674 1.00848i −0.642546 0.766247i \(-0.722122\pi\)
0.970219 0.242228i \(-0.0778782\pi\)
\(908\) 0.00171378 0.00527448i 5.68739e−5 0.000175040i
\(909\) 0 0
\(910\) 9.70307 + 7.04969i 0.321654 + 0.233695i
\(911\) −0.865378 2.66336i −0.0286713 0.0882411i 0.935697 0.352805i \(-0.114772\pi\)
−0.964368 + 0.264564i \(0.914772\pi\)
\(912\) 0 0
\(913\) 13.1576 6.12334i 0.435452 0.202653i
\(914\) 16.7496 0.554027
\(915\) 0 0
\(916\) 0.0247374 + 0.0179728i 0.000817348 + 0.000593838i
\(917\) −0.145666 + 0.105832i −0.00481031 + 0.00349490i
\(918\) 0 0
\(919\) −4.89293 + 15.0589i −0.161403 + 0.496747i −0.998753 0.0499194i \(-0.984104\pi\)
0.837350 + 0.546667i \(0.184104\pi\)
\(920\) 3.02638 2.19880i 0.0997769 0.0724922i
\(921\) 0 0
\(922\) −3.98356 12.2602i −0.131192 0.403767i
\(923\) 64.6030 2.12643
\(924\) 0 0
\(925\) −3.44799 −0.113369
\(926\) 16.9554 + 52.1833i 0.557188 + 1.71485i
\(927\) 0 0
\(928\) −0.0749296 + 0.0544396i −0.00245969 + 0.00178707i
\(929\) 8.49282 26.1382i 0.278640 0.857567i −0.709593 0.704612i \(-0.751121\pi\)
0.988233 0.152955i \(-0.0488790\pi\)
\(930\) 0 0
\(931\) 4.69325 3.40985i 0.153815 0.111753i
\(932\) 0.0142366 + 0.0103435i 0.000466337 + 0.000338814i
\(933\) 0 0
\(934\) 29.2894 0.958379
\(935\) −4.02424 32.9816i −0.131607 1.07861i
\(936\) 0 0
\(937\) −3.80357 11.7062i −0.124257 0.382425i 0.869508 0.493919i \(-0.164436\pi\)
−0.993765 + 0.111495i \(0.964436\pi\)
\(938\) 17.6346 + 12.8123i 0.575789 + 0.418335i
\(939\) 0 0
\(940\) 0.0472266 0.145349i 0.00154036 0.00474075i
\(941\) −0.451208 + 1.38867i −0.0147089 + 0.0452695i −0.958142 0.286295i \(-0.907576\pi\)
0.943433 + 0.331564i \(0.107576\pi\)
\(942\) 0 0
\(943\) −0.533703 0.387758i −0.0173798 0.0126271i
\(944\) −9.42725 29.0141i −0.306831 0.944328i
\(945\) 0 0
\(946\) −18.2068 + 32.7873i −0.591955 + 1.06601i
\(947\) −11.0714 −0.359771 −0.179885 0.983688i \(-0.557573\pi\)
−0.179885 + 0.983688i \(0.557573\pi\)
\(948\) 0 0
\(949\) 22.6123 + 16.4288i 0.734025 + 0.533301i
\(950\) −10.8869 + 7.90978i −0.353217 + 0.256627i
\(951\) 0 0
\(952\) −4.79769 + 14.7658i −0.155494 + 0.478561i
\(953\) −11.9924 + 8.71296i −0.388471 + 0.282240i −0.764828 0.644234i \(-0.777176\pi\)
0.376358 + 0.926474i \(0.377176\pi\)
\(954\) 0 0
\(955\) 5.43675 + 16.7326i 0.175929 + 0.541454i
\(956\) −0.155867 −0.00504110
\(957\) 0 0
\(958\) 34.5782 1.11717
\(959\) −2.57224 7.91655i −0.0830621 0.255639i
\(960\) 0 0
\(961\) 23.6957 17.2159i 0.764377 0.555353i
\(962\) −4.23920 + 13.0469i −0.136677 + 0.420649i
\(963\) 0 0
\(964\) −0.242719 + 0.176346i −0.00781746 + 0.00567972i
\(965\) 2.20437 + 1.60157i 0.0709612 + 0.0515563i
\(966\) 0 0
\(967\) 16.5193 0.531224 0.265612 0.964080i \(-0.414426\pi\)
0.265612 + 0.964080i \(0.414426\pi\)
\(968\) −20.1043 + 23.8857i −0.646177 + 0.767716i
\(969\) 0 0
\(970\) 1.92308 + 5.91862i 0.0617462 + 0.190035i
\(971\) 33.0073 + 23.9812i 1.05926 + 0.769595i 0.973951 0.226760i \(-0.0728134\pi\)
0.0853055 + 0.996355i \(0.472813\pi\)
\(972\) 0 0
\(973\) −2.15113 + 6.62049i −0.0689620 + 0.212243i
\(974\) −5.38755 + 16.5812i −0.172628 + 0.531296i
\(975\) 0 0
\(976\) −20.1672 14.6523i −0.645535 0.469009i
\(977\) −15.1772 46.7107i −0.485562 1.49441i −0.831165 0.556025i \(-0.812326\pi\)
0.345603 0.938381i \(-0.387674\pi\)
\(978\) 0 0
\(979\) −34.6782 37.2444i −1.10832 1.19034i
\(980\) −0.0255744 −0.000816945
\(981\) 0 0
\(982\) 18.8406 + 13.6885i 0.601228 + 0.436817i
\(983\) 0.895411 0.650554i 0.0285592 0.0207495i −0.573414 0.819266i \(-0.694381\pi\)
0.601973 + 0.798516i \(0.294381\pi\)
\(984\) 0 0
\(985\) 7.94756 24.4601i 0.253230 0.779362i
\(986\) −7.31238 + 5.31275i −0.232874 + 0.169193i
\(987\) 0 0
\(988\) −0.116333 0.358036i −0.00370104 0.0113906i
\(989\) 5.77458 0.183621
\(990\) 0 0
\(991\) 41.7851 1.32735 0.663674 0.748022i \(-0.268996\pi\)
0.663674 + 0.748022i \(0.268996\pi\)
\(992\) −0.0319255 0.0982567i −0.00101364 0.00311965i
\(993\) 0 0
\(994\) 15.8499 11.5156i 0.502727 0.365253i
\(995\) −2.42630 + 7.46739i −0.0769189 + 0.236732i
\(996\) 0 0
\(997\) −35.7541 + 25.9769i −1.13234 + 0.822695i −0.986034 0.166543i \(-0.946739\pi\)
−0.146309 + 0.989239i \(0.546739\pi\)
\(998\) 15.6664 + 11.3823i 0.495910 + 0.360300i
\(999\) 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 693.2.m.i.379.3 16
3.2 odd 2 77.2.f.b.71.2 yes 16
11.3 even 5 7623.2.a.ct.1.6 8
11.8 odd 10 7623.2.a.cw.1.3 8
11.9 even 5 inner 693.2.m.i.64.3 16
21.2 odd 6 539.2.q.g.214.2 32
21.5 even 6 539.2.q.f.214.2 32
21.11 odd 6 539.2.q.g.324.3 32
21.17 even 6 539.2.q.f.324.3 32
21.20 even 2 539.2.f.e.148.2 16
33.2 even 10 847.2.f.x.372.3 16
33.5 odd 10 847.2.f.w.323.3 16
33.8 even 10 847.2.a.o.1.6 8
33.14 odd 10 847.2.a.p.1.3 8
33.17 even 10 847.2.f.v.323.2 16
33.20 odd 10 77.2.f.b.64.2 16
33.26 odd 10 847.2.f.w.729.3 16
33.29 even 10 847.2.f.v.729.2 16
33.32 even 2 847.2.f.x.148.3 16
231.20 even 10 539.2.f.e.295.2 16
231.41 odd 10 5929.2.a.bs.1.6 8
231.53 odd 30 539.2.q.g.471.2 32
231.86 odd 30 539.2.q.g.361.3 32
231.146 even 10 5929.2.a.bt.1.3 8
231.152 even 30 539.2.q.f.361.3 32
231.185 even 30 539.2.q.f.471.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.2 16 33.20 odd 10
77.2.f.b.71.2 yes 16 3.2 odd 2
539.2.f.e.148.2 16 21.20 even 2
539.2.f.e.295.2 16 231.20 even 10
539.2.q.f.214.2 32 21.5 even 6
539.2.q.f.324.3 32 21.17 even 6
539.2.q.f.361.3 32 231.152 even 30
539.2.q.f.471.2 32 231.185 even 30
539.2.q.g.214.2 32 21.2 odd 6
539.2.q.g.324.3 32 21.11 odd 6
539.2.q.g.361.3 32 231.86 odd 30
539.2.q.g.471.2 32 231.53 odd 30
693.2.m.i.64.3 16 11.9 even 5 inner
693.2.m.i.379.3 16 1.1 even 1 trivial
847.2.a.o.1.6 8 33.8 even 10
847.2.a.p.1.3 8 33.14 odd 10
847.2.f.v.323.2 16 33.17 even 10
847.2.f.v.729.2 16 33.29 even 10
847.2.f.w.323.3 16 33.5 odd 10
847.2.f.w.729.3 16 33.26 odd 10
847.2.f.x.148.3 16 33.32 even 2
847.2.f.x.372.3 16 33.2 even 10
5929.2.a.bs.1.6 8 231.41 odd 10
5929.2.a.bt.1.3 8 231.146 even 10
7623.2.a.ct.1.6 8 11.3 even 5
7623.2.a.cw.1.3 8 11.8 odd 10