Properties

Label 864.2.bk.a.397.22
Level $864$
Weight $2$
Character 864.397
Analytic conductor $6.899$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(37,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bk (of order \(24\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 397.22
Character \(\chi\) \(=\) 864.397
Dual form 864.2.bk.a.37.22

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0671528 - 1.41262i) q^{2} +(-1.99098 + 0.189722i) q^{4} +(-3.52114 - 2.70187i) q^{5} +(-0.323768 - 1.20832i) q^{7} +(0.401705 + 2.79976i) q^{8} +O(q^{10})\) \(q+(-0.0671528 - 1.41262i) q^{2} +(-1.99098 + 0.189722i) q^{4} +(-3.52114 - 2.70187i) q^{5} +(-0.323768 - 1.20832i) q^{7} +(0.401705 + 2.79976i) q^{8} +(-3.58025 + 5.15547i) q^{10} +(-4.12219 - 0.542697i) q^{11} +(0.0124827 + 0.0948153i) q^{13} +(-1.68515 + 0.538502i) q^{14} +(3.92801 - 0.755467i) q^{16} -2.57648i q^{17} +(3.07003 + 1.27165i) q^{19} +(7.52313 + 4.71133i) q^{20} +(-0.489807 + 5.85953i) q^{22} +(0.135966 - 0.507432i) q^{23} +(3.80426 + 14.1977i) q^{25} +(0.133100 - 0.0240004i) q^{26} +(0.873860 + 2.34431i) q^{28} +(3.35182 + 4.36818i) q^{29} +(-1.95771 - 3.39085i) q^{31} +(-1.33096 - 5.49805i) q^{32} +(-3.63958 + 0.173018i) q^{34} +(-2.12468 + 5.12943i) q^{35} +(-0.306228 + 0.126844i) q^{37} +(1.59019 - 4.42217i) q^{38} +(6.15011 - 10.9437i) q^{40} +(-2.08827 + 7.79353i) q^{41} +(-9.26024 - 1.21913i) q^{43} +(8.31017 + 0.298427i) q^{44} +(-0.725938 - 0.157993i) q^{46} +(5.21248 + 3.00942i) q^{47} +(4.70697 - 2.71757i) q^{49} +(19.8004 - 6.32738i) q^{50} +(-0.0428413 - 0.186407i) q^{52} +(-0.848306 - 2.04799i) q^{53} +(13.0485 + 13.0485i) q^{55} +(3.25294 - 1.39186i) q^{56} +(5.94549 - 5.02818i) q^{58} +(7.35945 + 5.64710i) q^{59} +(-8.27002 - 10.7777i) q^{61} +(-4.65851 + 2.99320i) q^{62} +(-7.67727 + 2.24935i) q^{64} +(0.212225 - 0.367585i) q^{65} +(-12.2722 + 1.61567i) q^{67} +(0.488816 + 5.12972i) q^{68} +(7.38861 + 2.65691i) q^{70} +(-1.60783 + 1.60783i) q^{71} +(7.47247 + 7.47247i) q^{73} +(0.199746 + 0.424065i) q^{74} +(-6.35362 - 1.94937i) q^{76} +(0.678883 + 5.15662i) q^{77} +(1.18365 + 0.683378i) q^{79} +(-15.8723 - 7.95285i) q^{80} +(11.1495 + 2.42657i) q^{82} +(-9.75274 + 7.48354i) q^{83} +(-6.96130 + 9.07215i) q^{85} +(-1.10032 + 13.1631i) q^{86} +(-0.136487 - 11.7591i) q^{88} +(1.96743 - 1.96743i) q^{89} +(0.110526 - 0.0457812i) q^{91} +(-0.174435 + 1.03608i) q^{92} +(3.90114 - 7.56533i) q^{94} +(-7.37418 - 12.7724i) q^{95} +(-5.86403 + 10.1568i) q^{97} +(-4.15498 - 6.46666i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0671528 1.41262i −0.0474842 0.998872i
\(3\) 0 0
\(4\) −1.99098 + 0.189722i −0.995491 + 0.0948612i
\(5\) −3.52114 2.70187i −1.57470 1.20831i −0.862092 0.506751i \(-0.830846\pi\)
−0.712610 0.701560i \(-0.752487\pi\)
\(6\) 0 0
\(7\) −0.323768 1.20832i −0.122373 0.456701i 0.877360 0.479833i \(-0.159303\pi\)
−0.999732 + 0.0231321i \(0.992636\pi\)
\(8\) 0.401705 + 2.79976i 0.142024 + 0.989863i
\(9\) 0 0
\(10\) −3.58025 + 5.15547i −1.13218 + 1.63030i
\(11\) −4.12219 0.542697i −1.24289 0.163629i −0.519741 0.854324i \(-0.673972\pi\)
−0.723147 + 0.690695i \(0.757305\pi\)
\(12\) 0 0
\(13\) 0.0124827 + 0.0948153i 0.00346207 + 0.0262970i 0.993089 0.117366i \(-0.0374451\pi\)
−0.989627 + 0.143663i \(0.954112\pi\)
\(14\) −1.68515 + 0.538502i −0.450375 + 0.143921i
\(15\) 0 0
\(16\) 3.92801 0.755467i 0.982003 0.188867i
\(17\) 2.57648i 0.624888i −0.949936 0.312444i \(-0.898852\pi\)
0.949936 0.312444i \(-0.101148\pi\)
\(18\) 0 0
\(19\) 3.07003 + 1.27165i 0.704312 + 0.291736i 0.705949 0.708263i \(-0.250521\pi\)
−0.00163643 + 0.999999i \(0.500521\pi\)
\(20\) 7.52313 + 4.71133i 1.68222 + 1.05348i
\(21\) 0 0
\(22\) −0.489807 + 5.85953i −0.104427 + 1.24926i
\(23\) 0.135966 0.507432i 0.0283509 0.105807i −0.950301 0.311334i \(-0.899224\pi\)
0.978651 + 0.205527i \(0.0658909\pi\)
\(24\) 0 0
\(25\) 3.80426 + 14.1977i 0.760851 + 2.83954i
\(26\) 0.133100 0.0240004i 0.0261030 0.00470686i
\(27\) 0 0
\(28\) 0.873860 + 2.34431i 0.165144 + 0.443033i
\(29\) 3.35182 + 4.36818i 0.622418 + 0.811151i 0.993058 0.117626i \(-0.0375283\pi\)
−0.370640 + 0.928777i \(0.620862\pi\)
\(30\) 0 0
\(31\) −1.95771 3.39085i −0.351615 0.609014i 0.634918 0.772580i \(-0.281034\pi\)
−0.986533 + 0.163565i \(0.947701\pi\)
\(32\) −1.33096 5.49805i −0.235283 0.971927i
\(33\) 0 0
\(34\) −3.63958 + 0.173018i −0.624183 + 0.0296723i
\(35\) −2.12468 + 5.12943i −0.359137 + 0.867033i
\(36\) 0 0
\(37\) −0.306228 + 0.126844i −0.0503435 + 0.0208530i −0.407713 0.913110i \(-0.633674\pi\)
0.357370 + 0.933963i \(0.383674\pi\)
\(38\) 1.59019 4.42217i 0.257963 0.717371i
\(39\) 0 0
\(40\) 6.15011 10.9437i 0.972417 1.73035i
\(41\) −2.08827 + 7.79353i −0.326133 + 1.21715i 0.587035 + 0.809562i \(0.300295\pi\)
−0.913168 + 0.407584i \(0.866371\pi\)
\(42\) 0 0
\(43\) −9.26024 1.21913i −1.41217 0.185916i −0.614458 0.788950i \(-0.710625\pi\)
−0.797716 + 0.603033i \(0.793959\pi\)
\(44\) 8.31017 + 0.298427i 1.25280 + 0.0449895i
\(45\) 0 0
\(46\) −0.725938 0.157993i −0.107034 0.0232947i
\(47\) 5.21248 + 3.00942i 0.760318 + 0.438970i 0.829410 0.558641i \(-0.188677\pi\)
−0.0690921 + 0.997610i \(0.522010\pi\)
\(48\) 0 0
\(49\) 4.70697 2.71757i 0.672425 0.388224i
\(50\) 19.8004 6.32738i 2.80020 0.894826i
\(51\) 0 0
\(52\) −0.0428413 0.186407i −0.00594103 0.0258500i
\(53\) −0.848306 2.04799i −0.116524 0.281313i 0.854848 0.518879i \(-0.173650\pi\)
−0.971371 + 0.237566i \(0.923650\pi\)
\(54\) 0 0
\(55\) 13.0485 + 13.0485i 1.75946 + 1.75946i
\(56\) 3.25294 1.39186i 0.434692 0.185995i
\(57\) 0 0
\(58\) 5.94549 5.02818i 0.780681 0.660233i
\(59\) 7.35945 + 5.64710i 0.958119 + 0.735190i 0.964306 0.264791i \(-0.0853028\pi\)
−0.00618735 + 0.999981i \(0.501970\pi\)
\(60\) 0 0
\(61\) −8.27002 10.7777i −1.05887 1.37994i −0.921032 0.389487i \(-0.872652\pi\)
−0.137835 0.990455i \(-0.544014\pi\)
\(62\) −4.65851 + 2.99320i −0.591631 + 0.380137i
\(63\) 0 0
\(64\) −7.67727 + 2.24935i −0.959658 + 0.281169i
\(65\) 0.212225 0.367585i 0.0263233 0.0455933i
\(66\) 0 0
\(67\) −12.2722 + 1.61567i −1.49929 + 0.197385i −0.835066 0.550149i \(-0.814571\pi\)
−0.664223 + 0.747535i \(0.731237\pi\)
\(68\) 0.488816 + 5.12972i 0.0592776 + 0.622070i
\(69\) 0 0
\(70\) 7.38861 + 2.65691i 0.883108 + 0.317561i
\(71\) −1.60783 + 1.60783i −0.190815 + 0.190815i −0.796048 0.605233i \(-0.793080\pi\)
0.605233 + 0.796048i \(0.293080\pi\)
\(72\) 0 0
\(73\) 7.47247 + 7.47247i 0.874587 + 0.874587i 0.992968 0.118381i \(-0.0377706\pi\)
−0.118381 + 0.992968i \(0.537771\pi\)
\(74\) 0.199746 + 0.424065i 0.0232200 + 0.0492965i
\(75\) 0 0
\(76\) −6.35362 1.94937i −0.728811 0.223608i
\(77\) 0.678883 + 5.15662i 0.0773658 + 0.587652i
\(78\) 0 0
\(79\) 1.18365 + 0.683378i 0.133171 + 0.0768861i 0.565105 0.825019i \(-0.308836\pi\)
−0.431935 + 0.901905i \(0.642169\pi\)
\(80\) −15.8723 7.95285i −1.77457 0.889156i
\(81\) 0 0
\(82\) 11.1495 + 2.42657i 1.23126 + 0.267970i
\(83\) −9.75274 + 7.48354i −1.07050 + 0.821425i −0.984590 0.174878i \(-0.944047\pi\)
−0.0859118 + 0.996303i \(0.527380\pi\)
\(84\) 0 0
\(85\) −6.96130 + 9.07215i −0.755059 + 0.984013i
\(86\) −1.10032 + 13.1631i −0.118651 + 1.41941i
\(87\) 0 0
\(88\) −0.136487 11.7591i −0.0145496 1.25353i
\(89\) 1.96743 1.96743i 0.208547 0.208547i −0.595103 0.803650i \(-0.702889\pi\)
0.803650 + 0.595103i \(0.202889\pi\)
\(90\) 0 0
\(91\) 0.110526 0.0457812i 0.0115862 0.00479917i
\(92\) −0.174435 + 1.03608i −0.0181861 + 0.108019i
\(93\) 0 0
\(94\) 3.90114 7.56533i 0.402371 0.780304i
\(95\) −7.37418 12.7724i −0.756575 1.31043i
\(96\) 0 0
\(97\) −5.86403 + 10.1568i −0.595402 + 1.03127i 0.398088 + 0.917347i \(0.369674\pi\)
−0.993490 + 0.113919i \(0.963660\pi\)
\(98\) −4.15498 6.46666i −0.419716 0.653232i
\(99\) 0 0
\(100\) −10.2678 27.5456i −1.02678 2.75456i
\(101\) 1.23206 9.35843i 0.122595 0.931199i −0.814020 0.580837i \(-0.802725\pi\)
0.936614 0.350362i \(-0.113941\pi\)
\(102\) 0 0
\(103\) −5.39206 1.44480i −0.531296 0.142360i −0.0168091 0.999859i \(-0.505351\pi\)
−0.514486 + 0.857499i \(0.672017\pi\)
\(104\) −0.260445 + 0.0730362i −0.0255388 + 0.00716179i
\(105\) 0 0
\(106\) −2.83606 + 1.33586i −0.275463 + 0.129750i
\(107\) 2.57893 + 6.22609i 0.249315 + 0.601899i 0.998146 0.0608614i \(-0.0193848\pi\)
−0.748831 + 0.662760i \(0.769385\pi\)
\(108\) 0 0
\(109\) −1.85281 0.767459i −0.177467 0.0735093i 0.292181 0.956363i \(-0.405619\pi\)
−0.469648 + 0.882854i \(0.655619\pi\)
\(110\) 17.5563 19.3088i 1.67393 1.84102i
\(111\) 0 0
\(112\) −2.18461 4.50169i −0.206426 0.425370i
\(113\) 0.627382 0.362219i 0.0590191 0.0340747i −0.470200 0.882560i \(-0.655818\pi\)
0.529219 + 0.848485i \(0.322485\pi\)
\(114\) 0 0
\(115\) −1.84977 + 1.41938i −0.172492 + 0.132358i
\(116\) −7.50216 8.06105i −0.696558 0.748450i
\(117\) 0 0
\(118\) 7.48299 10.7753i 0.688865 0.991948i
\(119\) −3.11321 + 0.834181i −0.285387 + 0.0764692i
\(120\) 0 0
\(121\) 6.07276 + 1.62719i 0.552069 + 0.147926i
\(122\) −14.6694 + 12.4061i −1.32811 + 1.12320i
\(123\) 0 0
\(124\) 4.54108 + 6.37969i 0.407801 + 0.572913i
\(125\) 16.4726 39.7684i 1.47335 3.55699i
\(126\) 0 0
\(127\) −1.41741 −0.125775 −0.0628875 0.998021i \(-0.520031\pi\)
−0.0628875 + 0.998021i \(0.520031\pi\)
\(128\) 3.69303 + 10.6940i 0.326421 + 0.945225i
\(129\) 0 0
\(130\) −0.533508 0.275109i −0.0467918 0.0241286i
\(131\) −18.4301 + 2.42637i −1.61025 + 0.211993i −0.881293 0.472570i \(-0.843326\pi\)
−0.728954 + 0.684563i \(0.759993\pi\)
\(132\) 0 0
\(133\) 0.542577 4.12128i 0.0470474 0.357361i
\(134\) 3.10643 + 17.2275i 0.268355 + 1.48823i
\(135\) 0 0
\(136\) 7.21351 1.03499i 0.618554 0.0887492i
\(137\) −3.55457 + 0.952444i −0.303687 + 0.0813728i −0.407445 0.913230i \(-0.633580\pi\)
0.103757 + 0.994603i \(0.466913\pi\)
\(138\) 0 0
\(139\) −2.34586 + 3.05719i −0.198974 + 0.259307i −0.882174 0.470923i \(-0.843921\pi\)
0.683201 + 0.730231i \(0.260587\pi\)
\(140\) 3.25703 10.6157i 0.275269 0.897191i
\(141\) 0 0
\(142\) 2.37923 + 2.16329i 0.199660 + 0.181539i
\(143\) 0.397621i 0.0332507i
\(144\) 0 0
\(145\) 24.4372i 2.02940i
\(146\) 10.0540 11.0575i 0.832071 0.915129i
\(147\) 0 0
\(148\) 0.585628 0.310641i 0.0481383 0.0255346i
\(149\) 1.07625 1.40260i 0.0881698 0.114905i −0.747185 0.664616i \(-0.768595\pi\)
0.835355 + 0.549711i \(0.185262\pi\)
\(150\) 0 0
\(151\) −8.89127 + 2.38241i −0.723561 + 0.193878i −0.601760 0.798677i \(-0.705534\pi\)
−0.121801 + 0.992555i \(0.538867\pi\)
\(152\) −2.32705 + 9.10615i −0.188749 + 0.738606i
\(153\) 0 0
\(154\) 7.23875 1.30528i 0.583315 0.105183i
\(155\) −2.26826 + 17.2291i −0.182191 + 1.38388i
\(156\) 0 0
\(157\) 5.33732 0.702672i 0.425965 0.0560793i 0.0855034 0.996338i \(-0.472750\pi\)
0.340461 + 0.940259i \(0.389417\pi\)
\(158\) 0.885868 1.71793i 0.0704758 0.136671i
\(159\) 0 0
\(160\) −10.1685 + 22.9555i −0.803889 + 1.81479i
\(161\) −0.657161 −0.0517915
\(162\) 0 0
\(163\) −4.49655 + 10.8556i −0.352197 + 0.850279i 0.644151 + 0.764898i \(0.277211\pi\)
−0.996348 + 0.0853808i \(0.972789\pi\)
\(164\) 2.67910 15.9130i 0.209203 1.24259i
\(165\) 0 0
\(166\) 11.2263 + 13.2744i 0.871330 + 1.03029i
\(167\) 6.04195 + 1.61893i 0.467540 + 0.125277i 0.484895 0.874572i \(-0.338858\pi\)
−0.0173550 + 0.999849i \(0.505525\pi\)
\(168\) 0 0
\(169\) 12.5482 3.36228i 0.965246 0.258637i
\(170\) 13.2830 + 9.22444i 1.01876 + 0.707483i
\(171\) 0 0
\(172\) 18.6683 + 0.670397i 1.42344 + 0.0511173i
\(173\) −4.59054 + 3.52245i −0.349012 + 0.267807i −0.768358 0.640020i \(-0.778926\pi\)
0.419346 + 0.907827i \(0.362259\pi\)
\(174\) 0 0
\(175\) 15.9236 9.19350i 1.20371 0.694963i
\(176\) −16.6020 + 0.982463i −1.25142 + 0.0740559i
\(177\) 0 0
\(178\) −2.91135 2.64711i −0.218215 0.198409i
\(179\) −11.1115 4.60252i −0.830510 0.344009i −0.0734055 0.997302i \(-0.523387\pi\)
−0.757105 + 0.653294i \(0.773387\pi\)
\(180\) 0 0
\(181\) −6.51362 15.7253i −0.484153 1.16885i −0.957619 0.288037i \(-0.906997\pi\)
0.473466 0.880812i \(-0.343003\pi\)
\(182\) −0.0720934 0.153056i −0.00534392 0.0113453i
\(183\) 0 0
\(184\) 1.47530 + 0.176834i 0.108761 + 0.0130363i
\(185\) 1.42098 + 0.380752i 0.104473 + 0.0279934i
\(186\) 0 0
\(187\) −1.39825 + 10.6207i −0.102250 + 0.776665i
\(188\) −10.9489 5.00278i −0.798530 0.364865i
\(189\) 0 0
\(190\) −17.5474 + 11.2746i −1.27302 + 0.817946i
\(191\) −0.532783 + 0.922808i −0.0385509 + 0.0667720i −0.884657 0.466242i \(-0.845607\pi\)
0.846106 + 0.533014i \(0.178941\pi\)
\(192\) 0 0
\(193\) −7.00284 12.1293i −0.504076 0.873084i −0.999989 0.00471241i \(-0.998500\pi\)
0.495913 0.868372i \(-0.334833\pi\)
\(194\) 14.7415 + 7.60157i 1.05837 + 0.545761i
\(195\) 0 0
\(196\) −8.85591 + 6.30365i −0.632565 + 0.450261i
\(197\) −6.33207 + 2.62283i −0.451141 + 0.186869i −0.596673 0.802485i \(-0.703511\pi\)
0.145531 + 0.989354i \(0.453511\pi\)
\(198\) 0 0
\(199\) −6.36707 + 6.36707i −0.451350 + 0.451350i −0.895802 0.444453i \(-0.853398\pi\)
0.444453 + 0.895802i \(0.353398\pi\)
\(200\) −38.2219 + 16.3543i −2.70269 + 1.15642i
\(201\) 0 0
\(202\) −13.3026 1.11199i −0.935970 0.0782392i
\(203\) 4.19294 5.46434i 0.294287 0.383522i
\(204\) 0 0
\(205\) 28.4102 21.7999i 1.98425 1.52257i
\(206\) −1.67886 + 7.71395i −0.116971 + 0.537456i
\(207\) 0 0
\(208\) 0.120662 + 0.363005i 0.00836640 + 0.0251699i
\(209\) −11.9651 6.90806i −0.827644 0.477841i
\(210\) 0 0
\(211\) 0.477969 + 3.63053i 0.0329047 + 0.249936i 0.999990 0.00451706i \(-0.00143783\pi\)
−0.967085 + 0.254453i \(0.918104\pi\)
\(212\) 2.07751 + 3.91657i 0.142684 + 0.268991i
\(213\) 0 0
\(214\) 8.62191 4.06115i 0.589382 0.277614i
\(215\) 29.3127 + 29.3127i 1.99911 + 1.99911i
\(216\) 0 0
\(217\) −3.46338 + 3.46338i −0.235110 + 0.235110i
\(218\) −0.959706 + 2.66885i −0.0649995 + 0.180757i
\(219\) 0 0
\(220\) −28.4550 23.5038i −1.91843 1.58462i
\(221\) 0.244290 0.0321613i 0.0164327 0.00216341i
\(222\) 0 0
\(223\) −7.22965 + 12.5221i −0.484133 + 0.838543i −0.999834 0.0182256i \(-0.994198\pi\)
0.515701 + 0.856769i \(0.327532\pi\)
\(224\) −6.21247 + 3.38832i −0.415088 + 0.226392i
\(225\) 0 0
\(226\) −0.553808 0.861927i −0.0368387 0.0573345i
\(227\) −0.903483 1.17744i −0.0599663 0.0781496i 0.762407 0.647097i \(-0.224017\pi\)
−0.822374 + 0.568948i \(0.807351\pi\)
\(228\) 0 0
\(229\) 12.8674 + 9.87348i 0.850300 + 0.652458i 0.939120 0.343589i \(-0.111643\pi\)
−0.0888198 + 0.996048i \(0.528310\pi\)
\(230\) 2.12926 + 2.51770i 0.140399 + 0.166012i
\(231\) 0 0
\(232\) −10.8834 + 11.1390i −0.714530 + 0.731312i
\(233\) −13.0471 13.0471i −0.854741 0.854741i 0.135972 0.990713i \(-0.456584\pi\)
−0.990713 + 0.135972i \(0.956584\pi\)
\(234\) 0 0
\(235\) −10.2228 24.6800i −0.666862 1.60995i
\(236\) −15.7239 9.84702i −1.02354 0.640987i
\(237\) 0 0
\(238\) 1.38744 + 4.34175i 0.0899343 + 0.281434i
\(239\) −17.5726 + 10.1456i −1.13668 + 0.656262i −0.945606 0.325314i \(-0.894530\pi\)
−0.191073 + 0.981576i \(0.561197\pi\)
\(240\) 0 0
\(241\) 6.95525 + 4.01561i 0.448027 + 0.258668i 0.706997 0.707217i \(-0.250050\pi\)
−0.258970 + 0.965885i \(0.583383\pi\)
\(242\) 1.89080 8.68776i 0.121545 0.558470i
\(243\) 0 0
\(244\) 18.5102 + 19.8892i 1.18500 + 1.27327i
\(245\) −23.9164 3.14866i −1.52796 0.201160i
\(246\) 0 0
\(247\) −0.0822494 + 0.306959i −0.00523340 + 0.0195313i
\(248\) 8.70713 6.84322i 0.552903 0.434545i
\(249\) 0 0
\(250\) −57.2837 20.5989i −3.62294 1.30279i
\(251\) 6.63225 2.74717i 0.418624 0.173400i −0.163421 0.986556i \(-0.552253\pi\)
0.582045 + 0.813157i \(0.302253\pi\)
\(252\) 0 0
\(253\) −0.835860 + 2.01794i −0.0525500 + 0.126867i
\(254\) 0.0951831 + 2.00226i 0.00597232 + 0.125633i
\(255\) 0 0
\(256\) 14.8585 5.93497i 0.928659 0.370936i
\(257\) −12.6692 21.9436i −0.790280 1.36881i −0.925793 0.378030i \(-0.876602\pi\)
0.135513 0.990776i \(-0.456732\pi\)
\(258\) 0 0
\(259\) 0.252414 + 0.328952i 0.0156842 + 0.0204401i
\(260\) −0.352797 + 0.772118i −0.0218795 + 0.0478847i
\(261\) 0 0
\(262\) 4.66517 + 25.8718i 0.288215 + 1.59836i
\(263\) −4.97778 18.5773i −0.306943 1.14553i −0.931260 0.364356i \(-0.881289\pi\)
0.624317 0.781171i \(-0.285378\pi\)
\(264\) 0 0
\(265\) −2.54640 + 9.50328i −0.156424 + 0.583782i
\(266\) −5.85824 0.489699i −0.359192 0.0300254i
\(267\) 0 0
\(268\) 24.1272 5.54508i 1.47380 0.338719i
\(269\) 19.0648 + 7.89688i 1.16240 + 0.481482i 0.878673 0.477424i \(-0.158429\pi\)
0.283726 + 0.958905i \(0.408429\pi\)
\(270\) 0 0
\(271\) 16.3373i 0.992423i 0.868202 + 0.496211i \(0.165276\pi\)
−0.868202 + 0.496211i \(0.834724\pi\)
\(272\) −1.94645 10.1204i −0.118021 0.613642i
\(273\) 0 0
\(274\) 1.58414 + 4.95729i 0.0957014 + 0.299481i
\(275\) −7.97684 60.5901i −0.481022 3.65372i
\(276\) 0 0
\(277\) −21.9179 2.88554i −1.31692 0.173376i −0.560877 0.827899i \(-0.689536\pi\)
−0.756041 + 0.654524i \(0.772869\pi\)
\(278\) 4.47617 + 3.10851i 0.268463 + 0.186436i
\(279\) 0 0
\(280\) −15.2147 3.88807i −0.909250 0.232357i
\(281\) 3.35403 + 12.5174i 0.200085 + 0.746726i 0.990892 + 0.134660i \(0.0429943\pi\)
−0.790807 + 0.612065i \(0.790339\pi\)
\(282\) 0 0
\(283\) −7.92178 6.07859i −0.470901 0.361335i 0.345884 0.938277i \(-0.387579\pi\)
−0.816785 + 0.576942i \(0.804246\pi\)
\(284\) 2.89613 3.50621i 0.171853 0.208055i
\(285\) 0 0
\(286\) −0.561687 + 0.0267013i −0.0332132 + 0.00157888i
\(287\) 10.0932 0.595782
\(288\) 0 0
\(289\) 10.3618 0.609515
\(290\) −34.5204 + 1.64102i −2.02711 + 0.0963642i
\(291\) 0 0
\(292\) −16.2952 13.4599i −0.953607 0.787678i
\(293\) 11.0944 + 8.51304i 0.648142 + 0.497337i 0.879728 0.475478i \(-0.157725\pi\)
−0.231586 + 0.972815i \(0.574391\pi\)
\(294\) 0 0
\(295\) −10.6559 39.7685i −0.620413 2.31541i
\(296\) −0.478144 0.806409i −0.0277916 0.0468715i
\(297\) 0 0
\(298\) −2.05361 1.42614i −0.118962 0.0826142i
\(299\) 0.0498095 + 0.00655755i 0.00288056 + 0.000379233i
\(300\) 0 0
\(301\) 1.52507 + 11.5840i 0.0879034 + 0.667693i
\(302\) 3.96251 + 12.4000i 0.228017 + 0.713539i
\(303\) 0 0
\(304\) 13.0198 + 2.67574i 0.746736 + 0.153464i
\(305\) 60.2943i 3.45244i
\(306\) 0 0
\(307\) 11.3201 + 4.68895i 0.646074 + 0.267613i 0.681565 0.731757i \(-0.261300\pi\)
−0.0354914 + 0.999370i \(0.511300\pi\)
\(308\) −2.32997 10.1379i −0.132762 0.577663i
\(309\) 0 0
\(310\) 24.4905 + 2.04720i 1.39097 + 0.116273i
\(311\) −6.51148 + 24.3012i −0.369232 + 1.37799i 0.492360 + 0.870392i \(0.336134\pi\)
−0.861592 + 0.507601i \(0.830532\pi\)
\(312\) 0 0
\(313\) 1.18723 + 4.43079i 0.0671061 + 0.250443i 0.991328 0.131413i \(-0.0419515\pi\)
−0.924222 + 0.381857i \(0.875285\pi\)
\(314\) −1.35102 7.49241i −0.0762426 0.422821i
\(315\) 0 0
\(316\) −2.48627 1.13603i −0.139864 0.0639066i
\(317\) 15.3647 + 20.0237i 0.862968 + 1.12464i 0.991131 + 0.132889i \(0.0424252\pi\)
−0.128163 + 0.991753i \(0.540908\pi\)
\(318\) 0 0
\(319\) −11.4463 19.8255i −0.640868 1.11002i
\(320\) 33.1102 + 12.8227i 1.85092 + 0.716808i
\(321\) 0 0
\(322\) 0.0441301 + 0.928317i 0.00245928 + 0.0517331i
\(323\) 3.27637 7.90986i 0.182302 0.440116i
\(324\) 0 0
\(325\) −1.29867 + 0.537927i −0.0720372 + 0.0298388i
\(326\) 15.6368 + 5.62292i 0.866043 + 0.311425i
\(327\) 0 0
\(328\) −22.6589 2.71595i −1.25113 0.149963i
\(329\) 1.94871 7.27268i 0.107436 0.400956i
\(330\) 0 0
\(331\) 9.19754 + 1.21088i 0.505542 + 0.0665559i 0.378984 0.925403i \(-0.376274\pi\)
0.126558 + 0.991959i \(0.459607\pi\)
\(332\) 17.9977 16.7499i 0.987753 0.919270i
\(333\) 0 0
\(334\) 1.88120 8.64368i 0.102935 0.472961i
\(335\) 47.5775 + 27.4689i 2.59944 + 1.50079i
\(336\) 0 0
\(337\) 9.87204 5.69962i 0.537764 0.310478i −0.206408 0.978466i \(-0.566177\pi\)
0.744172 + 0.667988i \(0.232844\pi\)
\(338\) −5.59227 17.5000i −0.304179 0.951876i
\(339\) 0 0
\(340\) 12.1386 19.3832i 0.658310 1.05120i
\(341\) 6.22984 + 15.0402i 0.337365 + 0.814471i
\(342\) 0 0
\(343\) −10.9995 10.9995i −0.593917 0.593917i
\(344\) −0.306610 26.4162i −0.0165313 1.42426i
\(345\) 0 0
\(346\) 5.28414 + 6.24814i 0.284077 + 0.335902i
\(347\) 14.6438 + 11.2366i 0.786123 + 0.603213i 0.921856 0.387532i \(-0.126672\pi\)
−0.135733 + 0.990745i \(0.543339\pi\)
\(348\) 0 0
\(349\) 12.9141 + 16.8300i 0.691278 + 0.900891i 0.998715 0.0506774i \(-0.0161380\pi\)
−0.307437 + 0.951568i \(0.599471\pi\)
\(350\) −14.0562 21.8766i −0.751337 1.16935i
\(351\) 0 0
\(352\) 2.50271 + 23.3863i 0.133395 + 1.24649i
\(353\) −1.81403 + 3.14198i −0.0965508 + 0.167231i −0.910255 0.414049i \(-0.864114\pi\)
0.813704 + 0.581280i \(0.197448\pi\)
\(354\) 0 0
\(355\) 10.0056 1.31726i 0.531040 0.0699128i
\(356\) −3.54385 + 4.29038i −0.187824 + 0.227390i
\(357\) 0 0
\(358\) −5.75544 + 16.0053i −0.304184 + 0.845908i
\(359\) −1.72433 + 1.72433i −0.0910068 + 0.0910068i −0.751145 0.660138i \(-0.770498\pi\)
0.660138 + 0.751145i \(0.270498\pi\)
\(360\) 0 0
\(361\) −5.62705 5.62705i −0.296161 0.296161i
\(362\) −21.7764 + 10.2573i −1.14454 + 0.539109i
\(363\) 0 0
\(364\) −0.211368 + 0.112119i −0.0110787 + 0.00587661i
\(365\) −6.12201 46.5013i −0.320440 2.43399i
\(366\) 0 0
\(367\) −0.658261 0.380047i −0.0343610 0.0198383i 0.482721 0.875774i \(-0.339648\pi\)
−0.517082 + 0.855936i \(0.672982\pi\)
\(368\) 0.150728 2.09592i 0.00785722 0.109257i
\(369\) 0 0
\(370\) 0.442434 2.03288i 0.0230010 0.105684i
\(371\) −2.19997 + 1.68810i −0.114217 + 0.0876416i
\(372\) 0 0
\(373\) 8.43765 10.9962i 0.436885 0.569360i −0.522075 0.852899i \(-0.674842\pi\)
0.958961 + 0.283539i \(0.0915087\pi\)
\(374\) 15.0969 + 1.26198i 0.780645 + 0.0652553i
\(375\) 0 0
\(376\) −6.33177 + 15.8026i −0.326536 + 0.814955i
\(377\) −0.372331 + 0.372331i −0.0191760 + 0.0191760i
\(378\) 0 0
\(379\) −17.3658 + 7.19316i −0.892023 + 0.369488i −0.781148 0.624346i \(-0.785365\pi\)
−0.110875 + 0.993834i \(0.535365\pi\)
\(380\) 17.1051 + 24.0307i 0.877471 + 1.23275i
\(381\) 0 0
\(382\) 1.33935 + 0.690651i 0.0685273 + 0.0353368i
\(383\) 8.70697 + 15.0809i 0.444905 + 0.770599i 0.998046 0.0624894i \(-0.0199040\pi\)
−0.553140 + 0.833088i \(0.686571\pi\)
\(384\) 0 0
\(385\) 11.5421 19.9915i 0.588238 1.01886i
\(386\) −16.6638 + 10.7069i −0.848164 + 0.544965i
\(387\) 0 0
\(388\) 9.74819 21.3345i 0.494890 1.08310i
\(389\) −2.11221 + 16.0439i −0.107094 + 0.813456i 0.850630 + 0.525765i \(0.176221\pi\)
−0.957723 + 0.287691i \(0.907112\pi\)
\(390\) 0 0
\(391\) −1.30739 0.350314i −0.0661175 0.0177161i
\(392\) 9.49935 + 12.0867i 0.479790 + 0.610471i
\(393\) 0 0
\(394\) 4.13027 + 8.76867i 0.208080 + 0.441759i
\(395\) −2.32139 5.60433i −0.116802 0.281984i
\(396\) 0 0
\(397\) −30.8435 12.7758i −1.54799 0.641198i −0.565038 0.825065i \(-0.691138\pi\)
−0.982951 + 0.183867i \(0.941138\pi\)
\(398\) 9.42181 + 8.56668i 0.472273 + 0.429409i
\(399\) 0 0
\(400\) 25.6691 + 52.8947i 1.28345 + 2.64473i
\(401\) −9.16260 + 5.29003i −0.457558 + 0.264171i −0.711017 0.703175i \(-0.751765\pi\)
0.253459 + 0.967346i \(0.418432\pi\)
\(402\) 0 0
\(403\) 0.297067 0.227947i 0.0147980 0.0113549i
\(404\) −0.677506 + 18.8662i −0.0337072 + 0.938629i
\(405\) 0 0
\(406\) −8.00060 5.55608i −0.397063 0.275743i
\(407\) 1.33117 0.356685i 0.0659835 0.0176802i
\(408\) 0 0
\(409\) 25.9225 + 6.94590i 1.28178 + 0.343453i 0.834534 0.550957i \(-0.185737\pi\)
0.447249 + 0.894409i \(0.352404\pi\)
\(410\) −32.7028 38.6688i −1.61507 1.90972i
\(411\) 0 0
\(412\) 11.0096 + 1.85357i 0.542404 + 0.0913189i
\(413\) 4.44074 10.7209i 0.218515 0.527541i
\(414\) 0 0
\(415\) 54.5603 2.67826
\(416\) 0.504685 0.194826i 0.0247442 0.00955213i
\(417\) 0 0
\(418\) −8.95497 + 17.3660i −0.438002 + 0.849401i
\(419\) 17.9185 2.35902i 0.875378 0.115246i 0.320571 0.947225i \(-0.396125\pi\)
0.554807 + 0.831979i \(0.312792\pi\)
\(420\) 0 0
\(421\) −1.02970 + 7.82137i −0.0501846 + 0.381190i 0.947860 + 0.318687i \(0.103242\pi\)
−0.998045 + 0.0625034i \(0.980092\pi\)
\(422\) 5.09646 0.918988i 0.248092 0.0447356i
\(423\) 0 0
\(424\) 5.39311 3.19774i 0.261912 0.155296i
\(425\) 36.5800 9.80159i 1.77439 0.475447i
\(426\) 0 0
\(427\) −10.3453 + 13.4823i −0.500645 + 0.652453i
\(428\) −6.31583 11.9068i −0.305287 0.575535i
\(429\) 0 0
\(430\) 39.4392 43.3761i 1.90193 2.09178i
\(431\) 38.9561i 1.87645i −0.346025 0.938225i \(-0.612469\pi\)
0.346025 0.938225i \(-0.387531\pi\)
\(432\) 0 0
\(433\) 5.62134i 0.270145i 0.990836 + 0.135072i \(0.0431267\pi\)
−0.990836 + 0.135072i \(0.956873\pi\)
\(434\) 5.12501 + 4.65986i 0.246008 + 0.223680i
\(435\) 0 0
\(436\) 3.83452 + 1.17648i 0.183640 + 0.0563430i
\(437\) 1.06269 1.38493i 0.0508355 0.0662501i
\(438\) 0 0
\(439\) 10.4146 2.79058i 0.497062 0.133187i −0.00157424 0.999999i \(-0.500501\pi\)
0.498636 + 0.866811i \(0.333834\pi\)
\(440\) −31.2910 + 41.7743i −1.49174 + 1.99151i
\(441\) 0 0
\(442\) −0.0618364 0.342928i −0.00294126 0.0163114i
\(443\) 5.18080 39.3521i 0.246147 1.86967i −0.207145 0.978310i \(-0.566417\pi\)
0.453292 0.891362i \(-0.350249\pi\)
\(444\) 0 0
\(445\) −12.2433 + 1.61186i −0.580389 + 0.0764097i
\(446\) 18.1745 + 9.37184i 0.860586 + 0.443769i
\(447\) 0 0
\(448\) 5.20358 + 8.54831i 0.245846 + 0.403870i
\(449\) −23.0258 −1.08665 −0.543327 0.839521i \(-0.682836\pi\)
−0.543327 + 0.839521i \(0.682836\pi\)
\(450\) 0 0
\(451\) 12.8378 30.9931i 0.604507 1.45941i
\(452\) −1.18038 + 0.840200i −0.0555206 + 0.0395197i
\(453\) 0 0
\(454\) −1.60260 + 1.35534i −0.0752140 + 0.0636095i
\(455\) −0.512871 0.137423i −0.0240437 0.00644250i
\(456\) 0 0
\(457\) −7.66319 + 2.05335i −0.358469 + 0.0960515i −0.433559 0.901125i \(-0.642742\pi\)
0.0750898 + 0.997177i \(0.476076\pi\)
\(458\) 13.0834 18.8397i 0.611346 0.880322i
\(459\) 0 0
\(460\) 3.41357 3.17690i 0.159158 0.148124i
\(461\) 1.96944 1.51121i 0.0917261 0.0703839i −0.561880 0.827219i \(-0.689922\pi\)
0.653606 + 0.756835i \(0.273255\pi\)
\(462\) 0 0
\(463\) 18.1636 10.4867i 0.844133 0.487360i −0.0145342 0.999894i \(-0.504627\pi\)
0.858667 + 0.512534i \(0.171293\pi\)
\(464\) 16.4660 + 14.6261i 0.764416 + 0.678998i
\(465\) 0 0
\(466\) −17.5544 + 19.3067i −0.813190 + 0.894363i
\(467\) 2.29510 + 0.950660i 0.106204 + 0.0439913i 0.435153 0.900357i \(-0.356694\pi\)
−0.328949 + 0.944348i \(0.606694\pi\)
\(468\) 0 0
\(469\) 5.92559 + 14.3056i 0.273618 + 0.660573i
\(470\) −34.1770 + 16.0982i −1.57647 + 0.742557i
\(471\) 0 0
\(472\) −12.8542 + 22.8731i −0.591662 + 1.05282i
\(473\) 37.5109 + 10.0510i 1.72475 + 0.462146i
\(474\) 0 0
\(475\) −6.37526 + 48.4249i −0.292517 + 2.22189i
\(476\) 6.04007 2.25148i 0.276846 0.103197i
\(477\) 0 0
\(478\) 15.5119 + 24.1421i 0.709496 + 1.10424i
\(479\) 9.96920 17.2672i 0.455504 0.788957i −0.543213 0.839595i \(-0.682792\pi\)
0.998717 + 0.0506384i \(0.0161256\pi\)
\(480\) 0 0
\(481\) −0.0158492 0.0274517i −0.000722664 0.00125169i
\(482\) 5.20547 10.0948i 0.237102 0.459804i
\(483\) 0 0
\(484\) −12.3995 2.08757i −0.563612 0.0948894i
\(485\) 48.0904 19.9197i 2.18367 0.904506i
\(486\) 0 0
\(487\) −21.1033 + 21.1033i −0.956283 + 0.956283i −0.999084 0.0428006i \(-0.986372\pi\)
0.0428006 + 0.999084i \(0.486372\pi\)
\(488\) 26.8528 27.4835i 1.21557 1.24412i
\(489\) 0 0
\(490\) −2.84180 + 33.9962i −0.128379 + 1.53579i
\(491\) −7.97841 + 10.3977i −0.360061 + 0.469240i −0.937898 0.346912i \(-0.887230\pi\)
0.577837 + 0.816152i \(0.303897\pi\)
\(492\) 0 0
\(493\) 11.2545 8.63590i 0.506879 0.388942i
\(494\) 0.439139 + 0.0955739i 0.0197578 + 0.00430007i
\(495\) 0 0
\(496\) −10.2516 11.8403i −0.460309 0.531645i
\(497\) 2.46334 + 1.42221i 0.110496 + 0.0637948i
\(498\) 0 0
\(499\) −2.80424 21.3003i −0.125535 0.953532i −0.932053 0.362322i \(-0.881984\pi\)
0.806518 0.591209i \(-0.201349\pi\)
\(500\) −25.2517 + 82.3033i −1.12929 + 3.68071i
\(501\) 0 0
\(502\) −4.32608 9.18436i −0.193082 0.409918i
\(503\) −29.1393 29.1393i −1.29926 1.29926i −0.928882 0.370377i \(-0.879229\pi\)
−0.370377 0.928882i \(-0.620771\pi\)
\(504\) 0 0
\(505\) −29.6235 + 29.6235i −1.31823 + 1.31823i
\(506\) 2.90671 + 1.04524i 0.129219 + 0.0464666i
\(507\) 0 0
\(508\) 2.82204 0.268915i 0.125208 0.0119312i
\(509\) −19.4327 + 2.55836i −0.861340 + 0.113398i −0.548238 0.836322i \(-0.684701\pi\)
−0.313101 + 0.949720i \(0.601368\pi\)
\(510\) 0 0
\(511\) 6.60977 11.4485i 0.292399 0.506450i
\(512\) −9.38164 20.5909i −0.414614 0.909998i
\(513\) 0 0
\(514\) −30.1472 + 19.3703i −1.32974 + 0.854385i
\(515\) 15.0826 + 19.6560i 0.664617 + 0.866145i
\(516\) 0 0
\(517\) −19.8536 15.2342i −0.873161 0.670000i
\(518\) 0.447734 0.378655i 0.0196723 0.0166371i
\(519\) 0 0
\(520\) 1.11440 + 0.446518i 0.0488696 + 0.0195811i
\(521\) 2.53175 + 2.53175i 0.110918 + 0.110918i 0.760388 0.649469i \(-0.225009\pi\)
−0.649469 + 0.760388i \(0.725009\pi\)
\(522\) 0 0
\(523\) 10.0621 + 24.2921i 0.439986 + 1.06222i 0.975953 + 0.217982i \(0.0699473\pi\)
−0.535967 + 0.844239i \(0.680053\pi\)
\(524\) 36.2337 8.32746i 1.58288 0.363787i
\(525\) 0 0
\(526\) −25.9084 + 8.27922i −1.12966 + 0.360991i
\(527\) −8.73645 + 5.04399i −0.380566 + 0.219720i
\(528\) 0 0
\(529\) 19.6796 + 11.3620i 0.855634 + 0.494001i
\(530\) 13.5955 + 2.95891i 0.590551 + 0.128527i
\(531\) 0 0
\(532\) −0.298361 + 8.30834i −0.0129356 + 0.360212i
\(533\) −0.765013 0.100716i −0.0331364 0.00436249i
\(534\) 0 0
\(535\) 7.74129 28.8909i 0.334685 1.24906i
\(536\) −9.45328 33.7102i −0.408320 1.45606i
\(537\) 0 0
\(538\) 9.87503 27.4615i 0.425743 1.18395i
\(539\) −20.8779 + 8.64789i −0.899273 + 0.372491i
\(540\) 0 0
\(541\) 4.84101 11.6872i 0.208131 0.502473i −0.784998 0.619499i \(-0.787336\pi\)
0.993129 + 0.117025i \(0.0373359\pi\)
\(542\) 23.0784 1.09710i 0.991303 0.0471244i
\(543\) 0 0
\(544\) −14.1656 + 3.42920i −0.607345 + 0.147026i
\(545\) 4.45044 + 7.70838i 0.190636 + 0.330191i
\(546\) 0 0
\(547\) −21.7870 28.3933i −0.931544 1.21401i −0.976608 0.215027i \(-0.931016\pi\)
0.0450643 0.998984i \(-0.485651\pi\)
\(548\) 6.89638 2.57068i 0.294599 0.109814i
\(549\) 0 0
\(550\) −85.0550 + 15.3370i −3.62676 + 0.653973i
\(551\) 4.73540 + 17.6728i 0.201735 + 0.752885i
\(552\) 0 0
\(553\) 0.442512 1.65148i 0.0188175 0.0702279i
\(554\) −2.60433 + 31.1554i −0.110647 + 1.32366i
\(555\) 0 0
\(556\) 4.09055 6.53187i 0.173478 0.277013i
\(557\) −8.33216 3.45129i −0.353045 0.146236i 0.199111 0.979977i \(-0.436195\pi\)
−0.552156 + 0.833741i \(0.686195\pi\)
\(558\) 0 0
\(559\) 0.893231i 0.0377796i
\(560\) −4.47065 + 21.7536i −0.188919 + 0.919258i
\(561\) 0 0
\(562\) 17.4571 5.57854i 0.736382 0.235316i
\(563\) −2.21051 16.7905i −0.0931620 0.707636i −0.972743 0.231886i \(-0.925510\pi\)
0.879581 0.475749i \(-0.157823\pi\)
\(564\) 0 0
\(565\) −3.18777 0.419678i −0.134110 0.0176560i
\(566\) −8.05477 + 11.5986i −0.338567 + 0.487527i
\(567\) 0 0
\(568\) −5.14742 3.85567i −0.215981 0.161780i
\(569\) −2.22261 8.29489i −0.0931766 0.347740i 0.903560 0.428461i \(-0.140944\pi\)
−0.996737 + 0.0807216i \(0.974278\pi\)
\(570\) 0 0
\(571\) 31.8168 + 24.4139i 1.33149 + 1.02169i 0.996847 + 0.0793466i \(0.0252834\pi\)
0.334646 + 0.942344i \(0.391383\pi\)
\(572\) 0.0754376 + 0.791656i 0.00315421 + 0.0331008i
\(573\) 0 0
\(574\) −0.677785 14.2578i −0.0282902 0.595109i
\(575\) 7.72161 0.322013
\(576\) 0 0
\(577\) −25.1637 −1.04758 −0.523790 0.851847i \(-0.675482\pi\)
−0.523790 + 0.851847i \(0.675482\pi\)
\(578\) −0.695820 14.6372i −0.0289423 0.608828i
\(579\) 0 0
\(580\) 4.63628 + 48.6539i 0.192511 + 2.02024i
\(581\) 12.2001 + 9.36148i 0.506146 + 0.388379i
\(582\) 0 0
\(583\) 2.38544 + 8.90259i 0.0987949 + 0.368707i
\(584\) −17.9194 + 23.9228i −0.741509 + 0.989934i
\(585\) 0 0
\(586\) 11.2807 16.2438i 0.465999 0.671027i
\(587\) −12.4858 1.64378i −0.515343 0.0678462i −0.131631 0.991299i \(-0.542021\pi\)
−0.383713 + 0.923453i \(0.625355\pi\)
\(588\) 0 0
\(589\) −1.69825 12.8995i −0.0699753 0.531515i
\(590\) −55.4621 + 17.7233i −2.28334 + 0.729658i
\(591\) 0 0
\(592\) −1.10704 + 0.729588i −0.0454990 + 0.0299859i
\(593\) 2.54265i 0.104414i 0.998636 + 0.0522070i \(0.0166255\pi\)
−0.998636 + 0.0522070i \(0.983374\pi\)
\(594\) 0 0
\(595\) 13.2159 + 5.47420i 0.541798 + 0.224420i
\(596\) −1.87669 + 2.99673i −0.0768722 + 0.122751i
\(597\) 0 0
\(598\) 0.00591847 0.0708022i 0.000242024 0.00289532i
\(599\) 1.63697 6.10924i 0.0668846 0.249617i −0.924386 0.381458i \(-0.875422\pi\)
0.991271 + 0.131841i \(0.0420888\pi\)
\(600\) 0 0
\(601\) 0.899964 + 3.35871i 0.0367103 + 0.137005i 0.981849 0.189665i \(-0.0607402\pi\)
−0.945139 + 0.326670i \(0.894074\pi\)
\(602\) 16.2614 2.93224i 0.662765 0.119509i
\(603\) 0 0
\(604\) 17.2503 6.43020i 0.701907 0.261641i
\(605\) −16.9866 22.1374i −0.690603 0.900011i
\(606\) 0 0
\(607\) −14.8432 25.7092i −0.602468 1.04351i −0.992446 0.122681i \(-0.960851\pi\)
0.389978 0.920824i \(-0.372483\pi\)
\(608\) 2.90548 18.5717i 0.117833 0.753181i
\(609\) 0 0
\(610\) 85.1728 4.04893i 3.44855 0.163936i
\(611\) −0.220274 + 0.531788i −0.00891132 + 0.0215138i
\(612\) 0 0
\(613\) 33.6841 13.9524i 1.36049 0.563533i 0.421297 0.906923i \(-0.361575\pi\)
0.939193 + 0.343390i \(0.111575\pi\)
\(614\) 5.86352 16.3059i 0.236632 0.658052i
\(615\) 0 0
\(616\) −14.1646 + 3.97215i −0.570707 + 0.160042i
\(617\) 3.98938 14.8886i 0.160606 0.599391i −0.837953 0.545742i \(-0.816248\pi\)
0.998560 0.0536496i \(-0.0170854\pi\)
\(618\) 0 0
\(619\) −32.3309 4.25644i −1.29949 0.171081i −0.551154 0.834404i \(-0.685812\pi\)
−0.748333 + 0.663323i \(0.769146\pi\)
\(620\) 1.24731 34.7332i 0.0500930 1.39492i
\(621\) 0 0
\(622\) 34.7655 + 7.56634i 1.39397 + 0.303383i
\(623\) −3.01427 1.74029i −0.120764 0.0697232i
\(624\) 0 0
\(625\) −101.805 + 58.7770i −4.07219 + 2.35108i
\(626\) 6.17929 1.97464i 0.246974 0.0789225i
\(627\) 0 0
\(628\) −10.4932 + 2.41162i −0.418724 + 0.0962339i
\(629\) 0.326810 + 0.788989i 0.0130308 + 0.0314590i
\(630\) 0 0
\(631\) −12.7370 12.7370i −0.507050 0.507050i 0.406569 0.913620i \(-0.366725\pi\)
−0.913620 + 0.406569i \(0.866725\pi\)
\(632\) −1.43782 + 3.58844i −0.0571932 + 0.142740i
\(633\) 0 0
\(634\) 27.2540 23.0491i 1.08240 0.915397i
\(635\) 4.99091 + 3.82966i 0.198058 + 0.151975i
\(636\) 0 0
\(637\) 0.316423 + 0.412370i 0.0125371 + 0.0163387i
\(638\) −27.2372 + 17.5005i −1.07833 + 0.692853i
\(639\) 0 0
\(640\) 15.8901 47.6331i 0.628111 1.88287i
\(641\) −9.54719 + 16.5362i −0.377091 + 0.653141i −0.990638 0.136518i \(-0.956409\pi\)
0.613546 + 0.789659i \(0.289742\pi\)
\(642\) 0 0
\(643\) 24.4855 3.22358i 0.965615 0.127126i 0.368804 0.929507i \(-0.379767\pi\)
0.596811 + 0.802382i \(0.296434\pi\)
\(644\) 1.30839 0.124678i 0.0515580 0.00491300i
\(645\) 0 0
\(646\) −11.3936 4.09709i −0.448276 0.161198i
\(647\) −23.5792 + 23.5792i −0.926995 + 0.926995i −0.997511 0.0705153i \(-0.977536\pi\)
0.0705153 + 0.997511i \(0.477536\pi\)
\(648\) 0 0
\(649\) −27.2724 27.2724i −1.07053 1.07053i
\(650\) 0.847094 + 1.79840i 0.0332258 + 0.0705391i
\(651\) 0 0
\(652\) 6.89299 22.4665i 0.269950 0.879854i
\(653\) −4.96094 37.6821i −0.194137 1.47461i −0.759897 0.650044i \(-0.774750\pi\)
0.565760 0.824570i \(-0.308583\pi\)
\(654\) 0 0
\(655\) 71.4508 + 41.2521i 2.79181 + 1.61185i
\(656\) −2.31499 + 32.1907i −0.0903852 + 1.25684i
\(657\) 0 0
\(658\) −10.4044 2.26440i −0.405605 0.0882756i
\(659\) −28.1403 + 21.5928i −1.09619 + 0.841136i −0.988223 0.153018i \(-0.951101\pi\)
−0.107967 + 0.994155i \(0.534434\pi\)
\(660\) 0 0
\(661\) −27.4498 + 35.7732i −1.06767 + 1.39142i −0.152525 + 0.988300i \(0.548740\pi\)
−0.915148 + 0.403118i \(0.867926\pi\)
\(662\) 1.09287 13.0739i 0.0424756 0.508133i
\(663\) 0 0
\(664\) −24.8698 24.2991i −0.965136 0.942988i
\(665\) −13.0457 + 13.0457i −0.505889 + 0.505889i
\(666\) 0 0
\(667\) 2.67229 1.10690i 0.103471 0.0428593i
\(668\) −12.3365 2.07698i −0.477315 0.0803606i
\(669\) 0 0
\(670\) 35.6081 69.0535i 1.37566 2.66777i
\(671\) 28.2416 + 48.9158i 1.09025 + 1.88837i
\(672\) 0 0
\(673\) 10.1138 17.5177i 0.389859 0.675256i −0.602571 0.798065i \(-0.705857\pi\)
0.992430 + 0.122809i \(0.0391903\pi\)
\(674\) −8.71433 13.5627i −0.335663 0.522415i
\(675\) 0 0
\(676\) −24.3453 + 9.07491i −0.936359 + 0.349035i
\(677\) 3.22554 24.5004i 0.123967 0.941626i −0.810540 0.585683i \(-0.800826\pi\)
0.934508 0.355943i \(-0.115840\pi\)
\(678\) 0 0
\(679\) 14.1712 + 3.79716i 0.543841 + 0.145722i
\(680\) −28.1962 15.8456i −1.08127 0.607652i
\(681\) 0 0
\(682\) 20.8277 9.81038i 0.797533 0.375659i
\(683\) −1.02439 2.47310i −0.0391973 0.0946307i 0.903068 0.429497i \(-0.141309\pi\)
−0.942266 + 0.334866i \(0.891309\pi\)
\(684\) 0 0
\(685\) 15.0895 + 6.25029i 0.576541 + 0.238811i
\(686\) −14.7995 + 16.2767i −0.565046 + 0.621449i
\(687\) 0 0
\(688\) −37.2954 + 2.20704i −1.42187 + 0.0841426i
\(689\) 0.183592 0.105997i 0.00699429 0.00403815i
\(690\) 0 0
\(691\) −4.20272 + 3.22486i −0.159879 + 0.122679i −0.685603 0.727976i \(-0.740461\pi\)
0.525724 + 0.850655i \(0.323795\pi\)
\(692\) 8.47139 7.88405i 0.322034 0.299707i
\(693\) 0 0
\(694\) 14.8897 21.4407i 0.565204 0.813879i
\(695\) 16.5202 4.42658i 0.626648 0.167910i
\(696\) 0 0
\(697\) 20.0799 + 5.38039i 0.760580 + 0.203797i
\(698\) 22.9072 19.3729i 0.867050 0.733276i
\(699\) 0 0
\(700\) −29.9594 + 21.3252i −1.13236 + 0.806015i
\(701\) −12.4676 + 30.0995i −0.470895 + 1.13684i 0.492873 + 0.870101i \(0.335947\pi\)
−0.963768 + 0.266740i \(0.914053\pi\)
\(702\) 0 0
\(703\) −1.10143 −0.0415411
\(704\) 32.8679 5.10584i 1.23875 0.192433i
\(705\) 0 0
\(706\) 4.56024 + 2.35153i 0.171627 + 0.0885011i
\(707\) −11.7069 + 1.54124i −0.440282 + 0.0579642i
\(708\) 0 0
\(709\) 2.21164 16.7991i 0.0830598 0.630902i −0.898392 0.439194i \(-0.855264\pi\)
0.981452 0.191708i \(-0.0614026\pi\)
\(710\) −2.53268 14.0456i −0.0950499 0.527122i
\(711\) 0 0
\(712\) 6.29865 + 4.71800i 0.236052 + 0.176814i
\(713\) −1.98681 + 0.532363i −0.0744065 + 0.0199372i
\(714\) 0 0
\(715\) −1.07432 + 1.40008i −0.0401773 + 0.0523600i
\(716\) 22.9959 + 7.05544i 0.859398 + 0.263674i
\(717\) 0 0
\(718\) 2.55162 + 2.32003i 0.0952255 + 0.0865827i
\(719\) 33.2500i 1.24002i −0.784596 0.620008i \(-0.787129\pi\)
0.784596 0.620008i \(-0.212871\pi\)
\(720\) 0 0
\(721\) 6.98310i 0.260064i
\(722\) −7.57101 + 8.32675i −0.281764 + 0.309890i
\(723\) 0 0
\(724\) 15.9519 + 30.0729i 0.592849 + 1.11765i
\(725\) −49.2669 + 64.2058i −1.82973 + 2.38454i
\(726\) 0 0
\(727\) −21.8441 + 5.85311i −0.810153 + 0.217080i −0.640037 0.768344i \(-0.721081\pi\)
−0.170116 + 0.985424i \(0.554414\pi\)
\(728\) 0.172575 + 0.291054i 0.00639605 + 0.0107872i
\(729\) 0 0
\(730\) −65.2774 + 11.7707i −2.41603 + 0.435655i
\(731\) −3.14107 + 23.8588i −0.116177 + 0.882451i
\(732\) 0 0
\(733\) −22.9125 + 3.01649i −0.846293 + 0.111417i −0.541188 0.840902i \(-0.682025\pi\)
−0.305106 + 0.952319i \(0.598692\pi\)
\(734\) −0.492658 + 0.955393i −0.0181843 + 0.0352642i
\(735\) 0 0
\(736\) −2.97085 0.0721739i −0.109507 0.00266037i
\(737\) 51.4652 1.89575
\(738\) 0 0
\(739\) −10.7055 + 25.8453i −0.393807 + 0.950734i 0.595296 + 0.803507i \(0.297035\pi\)
−0.989103 + 0.147227i \(0.952965\pi\)
\(740\) −2.90139 0.488477i −0.106657 0.0179568i
\(741\) 0 0
\(742\) 2.53237 + 2.99436i 0.0929662 + 0.109926i
\(743\) −47.9896 12.8588i −1.76057 0.471742i −0.773737 0.633507i \(-0.781615\pi\)
−0.986829 + 0.161765i \(0.948281\pi\)
\(744\) 0 0
\(745\) −7.57925 + 2.03086i −0.277682 + 0.0744048i
\(746\) −16.1000 11.1808i −0.589463 0.409357i
\(747\) 0 0
\(748\) 0.768891 21.4110i 0.0281134 0.782863i
\(749\) 6.68812 5.13198i 0.244379 0.187518i
\(750\) 0 0
\(751\) −6.98357 + 4.03197i −0.254834 + 0.147129i −0.621976 0.783036i \(-0.713670\pi\)
0.367142 + 0.930165i \(0.380336\pi\)
\(752\) 22.7482 + 7.88319i 0.829541 + 0.287471i
\(753\) 0 0
\(754\) 0.550964 + 0.500958i 0.0200649 + 0.0182438i
\(755\) 37.7444 + 15.6342i 1.37366 + 0.568988i
\(756\) 0 0
\(757\) −17.1892 41.4984i −0.624752 1.50828i −0.846064 0.533081i \(-0.821034\pi\)
0.221312 0.975203i \(-0.428966\pi\)
\(758\) 11.3274 + 24.0482i 0.411428 + 0.873472i
\(759\) 0 0
\(760\) 32.7975 25.7767i 1.18969 0.935017i
\(761\) 42.8027 + 11.4690i 1.55160 + 0.415749i 0.929991 0.367581i \(-0.119814\pi\)
0.621606 + 0.783330i \(0.286481\pi\)
\(762\) 0 0
\(763\) −0.327454 + 2.48726i −0.0118546 + 0.0900450i
\(764\) 0.885684 1.93837i 0.0320429 0.0701279i
\(765\) 0 0
\(766\) 20.7189 13.3123i 0.748604 0.480995i
\(767\) −0.443566 + 0.768279i −0.0160162 + 0.0277410i
\(768\) 0 0
\(769\) 15.6506 + 27.1076i 0.564374 + 0.977524i 0.997108 + 0.0760022i \(0.0242156\pi\)
−0.432734 + 0.901522i \(0.642451\pi\)
\(770\) −29.0154 14.9621i −1.04564 0.539195i
\(771\) 0 0
\(772\) 16.2437 + 22.8206i 0.584624 + 0.821330i
\(773\) −32.9033 + 13.6290i −1.18345 + 0.490200i −0.885616 0.464418i \(-0.846263\pi\)
−0.297832 + 0.954618i \(0.596263\pi\)
\(774\) 0 0
\(775\) 40.6946 40.6946i 1.46179 1.46179i
\(776\) −30.7921 12.3378i −1.10537 0.442901i
\(777\) 0 0
\(778\) 22.8057 + 1.90636i 0.817624 + 0.0683464i
\(779\) −16.3217 + 21.2708i −0.584784 + 0.762106i
\(780\) 0 0
\(781\) 7.50037 5.75523i 0.268384 0.205938i
\(782\) −0.407065 + 1.87036i −0.0145566 + 0.0668841i
\(783\) 0 0
\(784\) 16.4360 14.2306i 0.587000 0.508236i
\(785\) −20.6920 11.9465i −0.738529 0.426390i
\(786\) 0 0
\(787\) −0.192434 1.46168i −0.00685953 0.0521033i 0.987673 0.156533i \(-0.0500317\pi\)
−0.994532 + 0.104429i \(0.966698\pi\)
\(788\) 12.1094 6.42334i 0.431380 0.228822i
\(789\) 0 0
\(790\) −7.76088 + 3.65558i −0.276120 + 0.130060i
\(791\) −0.640802 0.640802i −0.0227843 0.0227843i
\(792\) 0 0
\(793\) 0.918658 0.918658i 0.0326225 0.0326225i
\(794\) −15.9761 + 44.4280i −0.566970 + 1.57669i
\(795\) 0 0
\(796\) 11.4687 13.8847i 0.406499 0.492130i
\(797\) −34.2921 + 4.51465i −1.21469 + 0.159917i −0.710513 0.703684i \(-0.751537\pi\)
−0.504177 + 0.863601i \(0.668204\pi\)
\(798\) 0 0
\(799\) 7.75372 13.4298i 0.274307 0.475113i
\(800\) 72.9962 39.8126i 2.58081 1.40759i
\(801\) 0 0
\(802\) 8.08808 + 12.5880i 0.285600 + 0.444498i
\(803\) −26.7477 34.8582i −0.943905 1.23012i
\(804\) 0 0
\(805\) 2.31396 + 1.77556i 0.0815562 + 0.0625803i
\(806\) −0.341952 0.404335i −0.0120447 0.0142421i
\(807\) 0 0
\(808\) 26.6962 0.309861i 0.939171 0.0109009i
\(809\) 1.44428 + 1.44428i 0.0507784 + 0.0507784i 0.732040 0.681262i \(-0.238568\pi\)
−0.681262 + 0.732040i \(0.738568\pi\)
\(810\) 0 0
\(811\) 0.0225622 + 0.0544699i 0.000792266 + 0.00191270i 0.924275 0.381727i \(-0.124671\pi\)
−0.923483 + 0.383640i \(0.874671\pi\)
\(812\) −7.31135 + 11.6749i −0.256578 + 0.409709i
\(813\) 0 0
\(814\) −0.593251 1.85648i −0.0207934 0.0650695i
\(815\) 45.1635 26.0751i 1.58201 0.913372i
\(816\) 0 0
\(817\) −26.8789 15.5185i −0.940373 0.542925i
\(818\) 8.07114 37.0850i 0.282201 1.29665i
\(819\) 0 0
\(820\) −52.4282 + 48.7932i −1.83087 + 1.70393i
\(821\) 6.98686 + 0.919838i 0.243843 + 0.0321026i 0.251457 0.967868i \(-0.419090\pi\)
−0.00761391 + 0.999971i \(0.502424\pi\)
\(822\) 0 0
\(823\) −10.4669 + 39.0630i −0.364853 + 1.36165i 0.502766 + 0.864422i \(0.332316\pi\)
−0.867620 + 0.497229i \(0.834351\pi\)
\(824\) 1.87906 15.6768i 0.0654603 0.546128i
\(825\) 0 0
\(826\) −15.4428 5.55314i −0.537322 0.193218i
\(827\) −2.55963 + 1.06023i −0.0890070 + 0.0368679i −0.426743 0.904373i \(-0.640339\pi\)
0.337736 + 0.941241i \(0.390339\pi\)
\(828\) 0 0
\(829\) −20.2938 + 48.9935i −0.704832 + 1.70161i 0.00769626 + 0.999970i \(0.497550\pi\)
−0.712528 + 0.701644i \(0.752450\pi\)
\(830\) −3.66387 77.0729i −0.127175 2.67524i
\(831\) 0 0
\(832\) −0.309106 0.699844i −0.0107163 0.0242627i
\(833\) −7.00177 12.1274i −0.242597 0.420190i
\(834\) 0 0
\(835\) −16.9004 22.0250i −0.584862 0.762208i
\(836\) 25.1329 + 11.4838i 0.869241 + 0.397175i
\(837\) 0 0
\(838\) −4.53567 25.1536i −0.156682 0.868918i
\(839\) −8.93815 33.3576i −0.308579 1.15163i −0.929820 0.368014i \(-0.880038\pi\)
0.621241 0.783620i \(-0.286629\pi\)
\(840\) 0 0
\(841\) −0.340538 + 1.27091i −0.0117427 + 0.0438244i
\(842\) 11.1178 + 0.929350i 0.383143 + 0.0320275i
\(843\) 0 0
\(844\) −1.64042 7.13764i −0.0564656 0.245688i
\(845\) −53.2684 22.0645i −1.83249 0.759042i
\(846\) 0 0
\(847\) 7.86465i 0.270233i
\(848\) −4.87935 7.40366i −0.167557 0.254243i
\(849\) 0 0
\(850\) −16.3024 51.0154i −0.559166 1.74981i
\(851\) 0.0227280 + 0.172636i 0.000779105 + 0.00591789i
\(852\) 0 0
\(853\) −35.2308 4.63822i −1.20628 0.158810i −0.499545 0.866288i \(-0.666499\pi\)
−0.706735 + 0.707478i \(0.749833\pi\)
\(854\) 19.7400 + 13.7086i 0.675490 + 0.469099i
\(855\) 0 0
\(856\) −16.3956 + 9.72143i −0.560389 + 0.332272i
\(857\) 5.29457 + 19.7596i 0.180859 + 0.674976i 0.995479 + 0.0949805i \(0.0302789\pi\)
−0.814620 + 0.579995i \(0.803054\pi\)
\(858\) 0 0
\(859\) 18.1488 + 13.9261i 0.619229 + 0.475151i 0.870104 0.492869i \(-0.164052\pi\)
−0.250875 + 0.968019i \(0.580718\pi\)
\(860\) −63.9223 52.7997i −2.17973 1.80046i
\(861\) 0 0
\(862\) −55.0301 + 2.61601i −1.87433 + 0.0891017i
\(863\) −37.7370 −1.28458 −0.642290 0.766461i \(-0.722016\pi\)
−0.642290 + 0.766461i \(0.722016\pi\)
\(864\) 0 0
\(865\) 25.6811 0.873185
\(866\) 7.94081 0.377489i 0.269840 0.0128276i
\(867\) 0 0
\(868\) 6.23844 7.55260i 0.211747 0.256352i
\(869\) −4.50835 3.45938i −0.152935 0.117351i
\(870\) 0 0
\(871\) −0.306380 1.14343i −0.0103813 0.0387435i
\(872\) 1.40442 5.49571i 0.0475595 0.186108i
\(873\) 0 0
\(874\) −2.02774 1.40818i −0.0685893 0.0476323i
\(875\) −53.3861 7.02841i −1.80478 0.237604i
\(876\) 0 0
\(877\) −1.64843 12.5211i −0.0556635 0.422806i −0.996476 0.0838787i \(-0.973269\pi\)
0.940812 0.338928i \(-0.110064\pi\)
\(878\) −4.64140 14.5245i −0.156640 0.490177i
\(879\) 0 0
\(880\) 61.1125 + 41.3970i 2.06010 + 1.39549i
\(881\) 13.4697i 0.453805i −0.973917 0.226903i \(-0.927140\pi\)
0.973917 0.226903i \(-0.0728599\pi\)
\(882\) 0 0
\(883\) 3.92492 + 1.62576i 0.132084 + 0.0547111i 0.447747 0.894161i \(-0.352227\pi\)
−0.315662 + 0.948872i \(0.602227\pi\)
\(884\) −0.480274 + 0.110380i −0.0161534 + 0.00371248i
\(885\) 0 0
\(886\) −55.9373 4.67589i −1.87925 0.157090i
\(887\) 2.27256 8.48131i 0.0763051 0.284775i −0.917221 0.398379i \(-0.869573\pi\)
0.993526 + 0.113604i \(0.0362396\pi\)
\(888\) 0 0
\(889\) 0.458912 + 1.71268i 0.0153914 + 0.0574416i
\(890\) 3.09912 + 17.1869i 0.103883 + 0.576107i
\(891\) 0 0
\(892\) 12.0184 26.3029i 0.402405 0.880687i
\(893\) 12.1755 + 15.8674i 0.407438 + 0.530983i
\(894\) 0 0
\(895\) 26.6897 + 46.2278i 0.892137 + 1.54523i
\(896\) 11.7261 7.92472i 0.391740 0.264746i
\(897\) 0 0
\(898\) 1.54625 + 32.5267i 0.0515989 + 1.08543i
\(899\) 8.24995 19.9171i 0.275151 0.664274i
\(900\) 0 0
\(901\) −5.27661 + 2.18564i −0.175789 + 0.0728143i
\(902\) −44.6436 16.0536i −1.48647 0.534527i
\(903\) 0 0
\(904\) 1.26615 + 1.61101i 0.0421114 + 0.0535814i
\(905\) −19.5522 + 72.9698i −0.649937 + 2.42560i
\(906\) 0 0
\(907\) −12.8882 1.69677i −0.427946 0.0563402i −0.0865229 0.996250i \(-0.527576\pi\)
−0.341423 + 0.939910i \(0.610909\pi\)
\(908\) 2.02220 + 2.17285i 0.0671092 + 0.0721087i
\(909\) 0 0
\(910\) −0.159686 + 0.733719i −0.00529354 + 0.0243225i
\(911\) −40.1326 23.1706i −1.32965 0.767675i −0.344407 0.938821i \(-0.611920\pi\)
−0.985246 + 0.171145i \(0.945253\pi\)
\(912\) 0 0
\(913\) 44.2639 25.5558i 1.46492 0.845773i
\(914\) 3.41520 + 10.6873i 0.112965 + 0.353504i
\(915\) 0 0
\(916\) −27.4919 17.2167i −0.908359 0.568855i
\(917\) 8.89890 + 21.4839i 0.293868 + 0.709459i
\(918\) 0 0
\(919\) −15.2252 15.2252i −0.502234 0.502234i 0.409898 0.912131i \(-0.365564\pi\)
−0.912131 + 0.409898i \(0.865564\pi\)
\(920\) −4.71697 4.60873i −0.155514 0.151945i
\(921\) 0 0
\(922\) −2.26701 2.68059i −0.0746600 0.0882805i
\(923\) −0.172517 0.132377i −0.00567848 0.00435725i
\(924\) 0 0
\(925\) −2.96585 3.86518i −0.0975167 0.127086i
\(926\) −16.0335 24.9540i −0.526893 0.820039i
\(927\) 0 0
\(928\) 19.5553 24.2424i 0.641935 0.795795i
\(929\) 28.1355 48.7321i 0.923096 1.59885i 0.128501 0.991709i \(-0.458983\pi\)
0.794595 0.607140i \(-0.207683\pi\)
\(930\) 0 0
\(931\) 17.9063 2.35741i 0.586856 0.0772610i
\(932\) 28.4518 + 23.5011i 0.931968 + 0.769805i
\(933\) 0 0
\(934\) 1.18880 3.30593i 0.0388986 0.108173i
\(935\) 33.6192 33.6192i 1.09947 1.09947i
\(936\) 0 0
\(937\) −6.58034 6.58034i −0.214970 0.214970i 0.591405 0.806375i \(-0.298574\pi\)
−0.806375 + 0.591405i \(0.798574\pi\)
\(938\) 19.8105 9.33125i 0.646835 0.304676i
\(939\) 0 0
\(940\) 25.0358 + 47.1980i 0.816576 + 1.53943i
\(941\) 2.70922 + 20.5785i 0.0883180 + 0.670841i 0.977141 + 0.212591i \(0.0681903\pi\)
−0.888823 + 0.458250i \(0.848476\pi\)
\(942\) 0 0
\(943\) 3.67075 + 2.11931i 0.119536 + 0.0690143i
\(944\) 33.1742 + 16.6221i 1.07973 + 0.541002i
\(945\) 0 0
\(946\) 11.6793 53.6635i 0.379726 1.74475i
\(947\) 15.2792 11.7242i 0.496508 0.380984i −0.329936 0.944003i \(-0.607027\pi\)
0.826444 + 0.563019i \(0.190360\pi\)
\(948\) 0 0
\(949\) −0.615228 + 0.801781i −0.0199712 + 0.0260269i
\(950\) 68.8340 + 5.75394i 2.23327 + 0.186683i
\(951\) 0 0
\(952\) −3.58609 8.38112i −0.116226 0.271634i
\(953\) −21.2848 + 21.2848i −0.689482 + 0.689482i −0.962117 0.272635i \(-0.912105\pi\)
0.272635 + 0.962117i \(0.412105\pi\)
\(954\) 0 0
\(955\) 4.36931 1.80983i 0.141388 0.0585646i
\(956\) 33.0619 23.5336i 1.06930 0.761130i
\(957\) 0 0
\(958\) −25.0614 12.9231i −0.809696 0.417528i
\(959\) 2.30171 + 3.98668i 0.0743261 + 0.128737i
\(960\) 0 0
\(961\) 7.83476 13.5702i 0.252734 0.437749i
\(962\) −0.0377145 + 0.0242324i −0.00121596 + 0.000781284i
\(963\) 0 0
\(964\) −14.6096 6.67544i −0.470544 0.215002i
\(965\) −8.11370 + 61.6296i −0.261189 + 1.98393i
\(966\) 0 0
\(967\) 26.4432 + 7.08544i 0.850357 + 0.227852i 0.657575 0.753389i \(-0.271582\pi\)
0.192782 + 0.981242i \(0.438249\pi\)
\(968\) −2.11628 + 17.6559i −0.0680197 + 0.567482i
\(969\) 0 0
\(970\) −31.3683 66.5957i −1.00718 2.13826i
\(971\) 6.85568 + 16.5511i 0.220009 + 0.531149i 0.994891 0.100957i \(-0.0321905\pi\)
−0.774882 + 0.632107i \(0.782191\pi\)
\(972\) 0 0
\(973\) 4.45357 + 1.84473i 0.142775 + 0.0591393i
\(974\) 31.2281 + 28.3938i 1.00061 + 0.909796i
\(975\) 0 0
\(976\) −40.6269 36.0872i −1.30044 1.15512i
\(977\) −8.31807 + 4.80244i −0.266119 + 0.153644i −0.627122 0.778921i \(-0.715767\pi\)
0.361004 + 0.932564i \(0.382434\pi\)
\(978\) 0 0
\(979\) −9.17784 + 7.04240i −0.293325 + 0.225076i
\(980\) 48.2145 + 1.73143i 1.54016 + 0.0553087i
\(981\) 0 0
\(982\) 15.2237 + 10.5722i 0.485808 + 0.337373i
\(983\) −13.9877 + 3.74798i −0.446137 + 0.119542i −0.474891 0.880044i \(-0.657513\pi\)
0.0287541 + 0.999587i \(0.490846\pi\)
\(984\) 0 0
\(985\) 29.3827 + 7.87306i 0.936209 + 0.250857i
\(986\) −12.9550 15.3184i −0.412572 0.487838i
\(987\) 0 0
\(988\) 0.105520 0.626754i 0.00335704 0.0199397i
\(989\) −1.87771 + 4.53318i −0.0597076 + 0.144147i
\(990\) 0 0
\(991\) −19.4755 −0.618661 −0.309330 0.950955i \(-0.600105\pi\)
−0.309330 + 0.950955i \(0.600105\pi\)
\(992\) −16.0374 + 15.2767i −0.509188 + 0.485035i
\(993\) 0 0
\(994\) 1.84362 3.57526i 0.0584761 0.113400i
\(995\) 39.6223 5.21638i 1.25611 0.165370i
\(996\) 0 0
\(997\) −4.48752 + 34.0861i −0.142121 + 1.07952i 0.760578 + 0.649246i \(0.224916\pi\)
−0.902699 + 0.430272i \(0.858418\pi\)
\(998\) −29.9009 + 5.39169i −0.946495 + 0.170671i
\(999\) 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 864.2.bk.a.397.22 368
3.2 odd 2 288.2.bc.a.205.25 yes 368
9.4 even 3 inner 864.2.bk.a.685.39 368
9.5 odd 6 288.2.bc.a.13.8 368
32.5 even 8 inner 864.2.bk.a.613.39 368
96.5 odd 8 288.2.bc.a.133.8 yes 368
288.5 odd 24 288.2.bc.a.229.25 yes 368
288.229 even 24 inner 864.2.bk.a.37.22 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bc.a.13.8 368 9.5 odd 6
288.2.bc.a.133.8 yes 368 96.5 odd 8
288.2.bc.a.205.25 yes 368 3.2 odd 2
288.2.bc.a.229.25 yes 368 288.5 odd 24
864.2.bk.a.37.22 368 288.229 even 24 inner
864.2.bk.a.397.22 368 1.1 even 1 trivial
864.2.bk.a.613.39 368 32.5 even 8 inner
864.2.bk.a.685.39 368 9.4 even 3 inner