Properties

Label 324.3.j.a.199.33
Level $324$
Weight $3$
Character 324.199
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), 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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.33
Character \(\chi\) \(=\) 324.199
Dual form 324.3.j.a.127.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.97098 + 0.339470i) q^{2} +(3.76952 + 1.33818i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(-5.65258 + 0.996703i) q^{7} +(6.97538 + 3.91715i) q^{8} +O(q^{10})\) \(q+(1.97098 + 0.339470i) q^{2} +(3.76952 + 1.33818i) q^{4} +(-7.18780 + 2.61614i) q^{5} +(-5.65258 + 0.996703i) q^{7} +(6.97538 + 3.91715i) q^{8} +(-15.0551 + 2.71633i) q^{10} +(-2.01574 + 5.53819i) q^{11} +(8.25839 + 6.92961i) q^{13} +(-11.4795 + 0.0456012i) q^{14} +(12.4186 + 10.0886i) q^{16} +(-10.4844 + 18.1596i) q^{17} +(-21.5373 + 12.4346i) q^{19} +(-30.5954 + 0.243079i) q^{20} +(-5.85302 + 10.2314i) q^{22} +(-20.5338 - 3.62067i) q^{23} +(25.6691 - 21.5389i) q^{25} +(13.9247 + 16.4616i) q^{26} +(-22.6413 - 3.80705i) q^{28} +(30.1767 - 25.3212i) q^{29} +(-10.3697 - 1.82845i) q^{31} +(21.0520 + 24.1001i) q^{32} +(-26.8292 + 32.2330i) q^{34} +(38.0221 - 21.9521i) q^{35} +(-1.83871 + 3.18474i) q^{37} +(-46.6707 + 17.1970i) q^{38} +(-60.3854 - 9.90710i) q^{40} +(51.1323 + 42.9051i) q^{41} +(28.3547 - 77.9040i) q^{43} +(-15.0094 + 18.1789i) q^{44} +(-39.2427 - 14.1069i) q^{46} +(33.3947 - 5.88839i) q^{47} +(-15.0867 + 5.49110i) q^{49} +(57.9051 - 33.7389i) q^{50} +(21.8571 + 37.1725i) q^{52} +43.9772 q^{53} -45.0808i q^{55} +(-43.3331 - 15.1896i) q^{56} +(68.0734 - 39.6636i) q^{58} +(9.37752 + 25.7645i) q^{59} +(-1.47945 - 8.39040i) q^{61} +(-19.8177 - 7.12403i) q^{62} +(33.3118 + 54.6473i) q^{64} +(-77.4885 - 28.2035i) q^{65} +(-31.0935 + 37.0558i) q^{67} +(-63.8219 + 54.4228i) q^{68} +(82.3928 - 30.3597i) q^{70} +(-24.2168 - 13.9816i) q^{71} +(43.5064 + 75.3554i) q^{73} +(-4.70519 + 5.65288i) q^{74} +(-97.8249 + 18.0517i) q^{76} +(5.87418 - 33.3142i) q^{77} +(-11.6931 - 13.9353i) q^{79} +(-115.655 - 40.0257i) q^{80} +(86.2157 + 101.923i) q^{82} +(-8.95501 - 10.6722i) q^{83} +(27.8519 - 157.956i) q^{85} +(82.3326 - 143.922i) q^{86} +(-35.7545 + 30.7350i) q^{88} +(81.2903 + 140.799i) q^{89} +(-53.5880 - 30.9390i) q^{91} +(-72.5576 - 41.1261i) q^{92} +(67.8193 - 0.269406i) q^{94} +(122.275 - 145.722i) q^{95} +(39.6511 + 14.4318i) q^{97} +(-31.5996 + 5.70138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97098 + 0.339470i 0.985490 + 0.169735i
\(3\) 0 0
\(4\) 3.76952 + 1.33818i 0.942380 + 0.334544i
\(5\) −7.18780 + 2.61614i −1.43756 + 0.523229i −0.939088 0.343677i \(-0.888327\pi\)
−0.498471 + 0.866906i \(0.666105\pi\)
\(6\) 0 0
\(7\) −5.65258 + 0.996703i −0.807512 + 0.142386i −0.562139 0.827043i \(-0.690021\pi\)
−0.245373 + 0.969429i \(0.578910\pi\)
\(8\) 6.97538 + 3.91715i 0.871922 + 0.489644i
\(9\) 0 0
\(10\) −15.0551 + 2.71633i −1.50551 + 0.271633i
\(11\) −2.01574 + 5.53819i −0.183249 + 0.503472i −0.996970 0.0777831i \(-0.975216\pi\)
0.813722 + 0.581255i \(0.197438\pi\)
\(12\) 0 0
\(13\) 8.25839 + 6.92961i 0.635261 + 0.533047i 0.902559 0.430567i \(-0.141686\pi\)
−0.267298 + 0.963614i \(0.586131\pi\)
\(14\) −11.4795 + 0.0456012i −0.819962 + 0.00325723i
\(15\) 0 0
\(16\) 12.4186 + 10.0886i 0.776161 + 0.630535i
\(17\) −10.4844 + 18.1596i −0.616731 + 1.06821i 0.373347 + 0.927692i \(0.378210\pi\)
−0.990078 + 0.140518i \(0.955123\pi\)
\(18\) 0 0
\(19\) −21.5373 + 12.4346i −1.13354 + 0.654450i −0.944823 0.327581i \(-0.893767\pi\)
−0.188718 + 0.982031i \(0.560433\pi\)
\(20\) −30.5954 + 0.243079i −1.52977 + 0.0121540i
\(21\) 0 0
\(22\) −5.85302 + 10.2314i −0.266046 + 0.465063i
\(23\) −20.5338 3.62067i −0.892776 0.157420i −0.291603 0.956539i \(-0.594189\pi\)
−0.601173 + 0.799119i \(0.705300\pi\)
\(24\) 0 0
\(25\) 25.6691 21.5389i 1.02676 0.861557i
\(26\) 13.9247 + 16.4616i 0.535566 + 0.633138i
\(27\) 0 0
\(28\) −22.6413 3.80705i −0.808617 0.135966i
\(29\) 30.1767 25.3212i 1.04058 0.873146i 0.0485038 0.998823i \(-0.484555\pi\)
0.992071 + 0.125677i \(0.0401102\pi\)
\(30\) 0 0
\(31\) −10.3697 1.82845i −0.334505 0.0589823i 0.00387293 0.999993i \(-0.498767\pi\)
−0.338378 + 0.941010i \(0.609878\pi\)
\(32\) 21.0520 + 24.1001i 0.657875 + 0.753127i
\(33\) 0 0
\(34\) −26.8292 + 32.2330i −0.789094 + 0.948029i
\(35\) 38.0221 21.9521i 1.08635 0.627202i
\(36\) 0 0
\(37\) −1.83871 + 3.18474i −0.0496950 + 0.0860742i −0.889803 0.456345i \(-0.849158\pi\)
0.840108 + 0.542419i \(0.182492\pi\)
\(38\) −46.6707 + 17.1970i −1.22818 + 0.452553i
\(39\) 0 0
\(40\) −60.3854 9.90710i −1.50964 0.247678i
\(41\) 51.1323 + 42.9051i 1.24713 + 1.04647i 0.996932 + 0.0782699i \(0.0249396\pi\)
0.250196 + 0.968195i \(0.419505\pi\)
\(42\) 0 0
\(43\) 28.3547 77.9040i 0.659412 1.81172i 0.0798268 0.996809i \(-0.474563\pi\)
0.579585 0.814912i \(-0.303215\pi\)
\(44\) −15.0094 + 18.1789i −0.341123 + 0.413157i
\(45\) 0 0
\(46\) −39.2427 14.1069i −0.853102 0.306671i
\(47\) 33.3947 5.88839i 0.710526 0.125285i 0.193308 0.981138i \(-0.438078\pi\)
0.517219 + 0.855853i \(0.326967\pi\)
\(48\) 0 0
\(49\) −15.0867 + 5.49110i −0.307891 + 0.112063i
\(50\) 57.9051 33.7389i 1.15810 0.674778i
\(51\) 0 0
\(52\) 21.8571 + 37.1725i 0.420330 + 0.714855i
\(53\) 43.9772 0.829758 0.414879 0.909877i \(-0.363824\pi\)
0.414879 + 0.909877i \(0.363824\pi\)
\(54\) 0 0
\(55\) 45.0808i 0.819651i
\(56\) −43.3331 15.1896i −0.773806 0.271244i
\(57\) 0 0
\(58\) 68.0734 39.6636i 1.17368 0.683855i
\(59\) 9.37752 + 25.7645i 0.158941 + 0.436687i 0.993444 0.114316i \(-0.0364676\pi\)
−0.834503 + 0.551003i \(0.814245\pi\)
\(60\) 0 0
\(61\) −1.47945 8.39040i −0.0242533 0.137548i 0.970277 0.241998i \(-0.0778028\pi\)
−0.994530 + 0.104450i \(0.966692\pi\)
\(62\) −19.8177 7.12403i −0.319640 0.114904i
\(63\) 0 0
\(64\) 33.3118 + 54.6473i 0.520497 + 0.853863i
\(65\) −77.4885 28.2035i −1.19213 0.433900i
\(66\) 0 0
\(67\) −31.0935 + 37.0558i −0.464083 + 0.553072i −0.946431 0.322908i \(-0.895340\pi\)
0.482348 + 0.875980i \(0.339784\pi\)
\(68\) −63.8219 + 54.4228i −0.938558 + 0.800336i
\(69\) 0 0
\(70\) 82.3928 30.3597i 1.17704 0.433710i
\(71\) −24.2168 13.9816i −0.341082 0.196924i 0.319668 0.947530i \(-0.396429\pi\)
−0.660751 + 0.750606i \(0.729762\pi\)
\(72\) 0 0
\(73\) 43.5064 + 75.3554i 0.595979 + 1.03227i 0.993408 + 0.114633i \(0.0365691\pi\)
−0.397429 + 0.917633i \(0.630098\pi\)
\(74\) −4.70519 + 5.65288i −0.0635837 + 0.0763903i
\(75\) 0 0
\(76\) −97.8249 + 18.0517i −1.28717 + 0.237522i
\(77\) 5.87418 33.3142i 0.0762881 0.432651i
\(78\) 0 0
\(79\) −11.6931 13.9353i −0.148014 0.176396i 0.686943 0.726711i \(-0.258952\pi\)
−0.834957 + 0.550315i \(0.814508\pi\)
\(80\) −115.655 40.0257i −1.44569 0.500321i
\(81\) 0 0
\(82\) 86.2157 + 101.923i 1.05141 + 1.24296i
\(83\) −8.95501 10.6722i −0.107892 0.128580i 0.709396 0.704810i \(-0.248968\pi\)
−0.817288 + 0.576230i \(0.804523\pi\)
\(84\) 0 0
\(85\) 27.8519 157.956i 0.327669 1.85831i
\(86\) 82.3326 143.922i 0.957356 1.67351i
\(87\) 0 0
\(88\) −35.7545 + 30.7350i −0.406301 + 0.349262i
\(89\) 81.2903 + 140.799i 0.913374 + 1.58201i 0.809264 + 0.587445i \(0.199866\pi\)
0.104110 + 0.994566i \(0.466801\pi\)
\(90\) 0 0
\(91\) −53.5880 30.9390i −0.588879 0.339989i
\(92\) −72.5576 41.1261i −0.788670 0.447022i
\(93\) 0 0
\(94\) 67.8193 0.269406i 0.721482 0.00286602i
\(95\) 122.275 145.722i 1.28711 1.53391i
\(96\) 0 0
\(97\) 39.6511 + 14.4318i 0.408775 + 0.148782i 0.538219 0.842805i \(-0.319097\pi\)
−0.129445 + 0.991587i \(0.541319\pi\)
\(98\) −31.5996 + 5.70138i −0.322445 + 0.0581774i
\(99\) 0 0
\(100\) 125.583 46.8417i 1.25583 0.468417i
\(101\) −19.0016 107.763i −0.188134 1.06696i −0.921862 0.387519i \(-0.873332\pi\)
0.733728 0.679444i \(-0.237779\pi\)
\(102\) 0 0
\(103\) −0.336017 0.923198i −0.00326230 0.00896309i 0.938051 0.346498i \(-0.112629\pi\)
−0.941313 + 0.337535i \(0.890407\pi\)
\(104\) 30.4610 + 80.6860i 0.292895 + 0.775827i
\(105\) 0 0
\(106\) 86.6781 + 14.9289i 0.817718 + 0.140839i
\(107\) 129.179i 1.20728i 0.797258 + 0.603639i \(0.206283\pi\)
−0.797258 + 0.603639i \(0.793717\pi\)
\(108\) 0 0
\(109\) −160.479 −1.47229 −0.736144 0.676825i \(-0.763355\pi\)
−0.736144 + 0.676825i \(0.763355\pi\)
\(110\) 15.3036 88.8534i 0.139123 0.807758i
\(111\) 0 0
\(112\) −80.2523 44.6488i −0.716538 0.398650i
\(113\) −61.3383 + 22.3253i −0.542817 + 0.197569i −0.598852 0.800860i \(-0.704376\pi\)
0.0560354 + 0.998429i \(0.482154\pi\)
\(114\) 0 0
\(115\) 157.065 27.6948i 1.36578 0.240825i
\(116\) 147.636 55.0673i 1.27272 0.474718i
\(117\) 0 0
\(118\) 9.73662 + 53.9647i 0.0825138 + 0.457328i
\(119\) 41.1644 113.098i 0.345919 0.950405i
\(120\) 0 0
\(121\) 66.0830 + 55.4502i 0.546141 + 0.458267i
\(122\) −0.0676881 17.0395i −0.000554820 0.139668i
\(123\) 0 0
\(124\) −36.6419 20.7688i −0.295499 0.167490i
\(125\) −32.5416 + 56.3637i −0.260333 + 0.450909i
\(126\) 0 0
\(127\) 42.9918 24.8213i 0.338518 0.195443i −0.321099 0.947046i \(-0.604052\pi\)
0.659616 + 0.751602i \(0.270719\pi\)
\(128\) 47.1058 + 119.017i 0.368014 + 0.929820i
\(129\) 0 0
\(130\) −143.154 81.8935i −1.10118 0.629950i
\(131\) −170.857 30.1266i −1.30425 0.229974i −0.522002 0.852944i \(-0.674815\pi\)
−0.782246 + 0.622970i \(0.785926\pi\)
\(132\) 0 0
\(133\) 109.348 91.7536i 0.822163 0.689877i
\(134\) −73.8641 + 62.4810i −0.551224 + 0.466276i
\(135\) 0 0
\(136\) −144.267 + 85.6007i −1.06078 + 0.629417i
\(137\) −38.4087 + 32.2287i −0.280356 + 0.235246i −0.772112 0.635487i \(-0.780800\pi\)
0.491756 + 0.870733i \(0.336355\pi\)
\(138\) 0 0
\(139\) 183.877 + 32.4224i 1.32285 + 0.233255i 0.790081 0.613003i \(-0.210039\pi\)
0.532773 + 0.846258i \(0.321150\pi\)
\(140\) 172.701 31.8685i 1.23358 0.227632i
\(141\) 0 0
\(142\) −42.9846 35.7783i −0.302708 0.251960i
\(143\) −55.0242 + 31.7682i −0.384785 + 0.222156i
\(144\) 0 0
\(145\) −150.660 + 260.950i −1.03903 + 1.79966i
\(146\) 60.1695 + 163.293i 0.412120 + 1.11845i
\(147\) 0 0
\(148\) −11.1928 + 9.54444i −0.0756271 + 0.0644895i
\(149\) −29.7807 24.9890i −0.199871 0.167711i 0.537359 0.843354i \(-0.319422\pi\)
−0.737230 + 0.675642i \(0.763866\pi\)
\(150\) 0 0
\(151\) −97.1070 + 266.799i −0.643093 + 1.76688i −0.00130597 + 0.999999i \(0.500416\pi\)
−0.641787 + 0.766883i \(0.721807\pi\)
\(152\) −198.939 + 2.37090i −1.30881 + 0.0155980i
\(153\) 0 0
\(154\) 22.8870 63.6674i 0.148617 0.413425i
\(155\) 79.3185 13.9860i 0.511732 0.0902322i
\(156\) 0 0
\(157\) 137.397 50.0085i 0.875141 0.318525i 0.134894 0.990860i \(-0.456931\pi\)
0.740247 + 0.672335i \(0.234708\pi\)
\(158\) −18.3162 31.4356i −0.115925 0.198959i
\(159\) 0 0
\(160\) −214.367 118.151i −1.33979 0.738446i
\(161\) 119.678 0.743341
\(162\) 0 0
\(163\) 55.1271i 0.338203i −0.985599 0.169102i \(-0.945913\pi\)
0.985599 0.169102i \(-0.0540866\pi\)
\(164\) 135.330 + 230.155i 0.825181 + 1.40339i
\(165\) 0 0
\(166\) −14.0273 24.0746i −0.0845016 0.145028i
\(167\) −58.1117 159.661i −0.347974 0.956051i −0.983007 0.183566i \(-0.941236\pi\)
0.635033 0.772485i \(-0.280986\pi\)
\(168\) 0 0
\(169\) −9.16507 51.9777i −0.0542312 0.307560i
\(170\) 108.517 301.873i 0.638334 1.77572i
\(171\) 0 0
\(172\) 211.133 255.717i 1.22752 1.48673i
\(173\) −87.8563 31.9771i −0.507840 0.184839i 0.0753771 0.997155i \(-0.475984\pi\)
−0.583217 + 0.812317i \(0.698206\pi\)
\(174\) 0 0
\(175\) −123.629 + 147.335i −0.706450 + 0.841914i
\(176\) −80.9049 + 48.4405i −0.459687 + 0.275230i
\(177\) 0 0
\(178\) 112.425 + 305.107i 0.631599 + 1.71409i
\(179\) −130.749 75.4882i −0.730444 0.421722i 0.0881407 0.996108i \(-0.471908\pi\)
−0.818585 + 0.574386i \(0.805241\pi\)
\(180\) 0 0
\(181\) 9.82485 + 17.0171i 0.0542809 + 0.0940173i 0.891889 0.452254i \(-0.149380\pi\)
−0.837608 + 0.546272i \(0.816047\pi\)
\(182\) −95.1179 79.1717i −0.522626 0.435009i
\(183\) 0 0
\(184\) −129.049 105.690i −0.701351 0.574401i
\(185\) 4.88455 27.7016i 0.0264029 0.149739i
\(186\) 0 0
\(187\) −79.4372 94.6696i −0.424798 0.506255i
\(188\) 133.762 + 22.4916i 0.711499 + 0.119636i
\(189\) 0 0
\(190\) 290.470 245.706i 1.52879 1.29319i
\(191\) 161.522 + 192.495i 0.845667 + 1.00783i 0.999804 + 0.0197775i \(0.00629580\pi\)
−0.154137 + 0.988049i \(0.549260\pi\)
\(192\) 0 0
\(193\) 2.54996 14.4615i 0.0132122 0.0749303i −0.977489 0.210988i \(-0.932332\pi\)
0.990701 + 0.136057i \(0.0434431\pi\)
\(194\) 73.2524 + 41.9052i 0.377590 + 0.216006i
\(195\) 0 0
\(196\) −64.2176 + 0.510206i −0.327641 + 0.00260309i
\(197\) −104.711 181.365i −0.531528 0.920634i −0.999323 0.0367968i \(-0.988285\pi\)
0.467794 0.883837i \(-0.345049\pi\)
\(198\) 0 0
\(199\) 4.56353 + 2.63476i 0.0229323 + 0.0132400i 0.511422 0.859330i \(-0.329119\pi\)
−0.488490 + 0.872569i \(0.662452\pi\)
\(200\) 263.423 49.6924i 1.31711 0.248462i
\(201\) 0 0
\(202\) −0.869361 218.850i −0.00430377 1.08341i
\(203\) −145.338 + 173.208i −0.715953 + 0.853239i
\(204\) 0 0
\(205\) −479.774 174.623i −2.34036 0.851822i
\(206\) −0.348884 1.93367i −0.00169361 0.00938676i
\(207\) 0 0
\(208\) 32.6476 + 169.371i 0.156960 + 0.814284i
\(209\) −25.4514 144.342i −0.121777 0.690633i
\(210\) 0 0
\(211\) 30.7845 + 84.5797i 0.145898 + 0.400852i 0.991019 0.133724i \(-0.0426936\pi\)
−0.845120 + 0.534576i \(0.820471\pi\)
\(212\) 165.773 + 58.8491i 0.781947 + 0.277590i
\(213\) 0 0
\(214\) −43.8522 + 254.609i −0.204917 + 1.18976i
\(215\) 634.138i 2.94948i
\(216\) 0 0
\(217\) 60.4378 0.278515
\(218\) −316.302 54.4779i −1.45092 0.249898i
\(219\) 0 0
\(220\) 60.3260 169.933i 0.274209 0.772423i
\(221\) −212.423 + 77.3157i −0.961191 + 0.349845i
\(222\) 0 0
\(223\) 233.603 41.1905i 1.04755 0.184711i 0.376722 0.926326i \(-0.377051\pi\)
0.670825 + 0.741616i \(0.265940\pi\)
\(224\) −143.019 115.245i −0.638477 0.514487i
\(225\) 0 0
\(226\) −128.475 + 23.1802i −0.568475 + 0.102567i
\(227\) −92.2846 + 253.550i −0.406540 + 1.11696i 0.552456 + 0.833542i \(0.313691\pi\)
−0.958996 + 0.283418i \(0.908532\pi\)
\(228\) 0 0
\(229\) 132.829 + 111.457i 0.580039 + 0.486710i 0.884960 0.465667i \(-0.154186\pi\)
−0.304921 + 0.952378i \(0.598630\pi\)
\(230\) 318.974 1.26710i 1.38684 0.00550911i
\(231\) 0 0
\(232\) 309.681 58.4186i 1.33483 0.251804i
\(233\) 85.3765 147.877i 0.366423 0.634663i −0.622580 0.782556i \(-0.713916\pi\)
0.989003 + 0.147893i \(0.0472490\pi\)
\(234\) 0 0
\(235\) −224.630 + 129.690i −0.955871 + 0.551872i
\(236\) 0.871312 + 109.669i 0.00369200 + 0.464698i
\(237\) 0 0
\(238\) 119.528 208.940i 0.502217 0.877900i
\(239\) −126.129 22.2400i −0.527738 0.0930544i −0.0965700 0.995326i \(-0.530787\pi\)
−0.431168 + 0.902272i \(0.641898\pi\)
\(240\) 0 0
\(241\) −126.565 + 106.201i −0.525167 + 0.440668i −0.866429 0.499301i \(-0.833590\pi\)
0.341261 + 0.939968i \(0.389146\pi\)
\(242\) 111.425 + 131.724i 0.460432 + 0.544316i
\(243\) 0 0
\(244\) 5.65099 33.6076i 0.0231598 0.137736i
\(245\) 94.0744 78.9378i 0.383977 0.322195i
\(246\) 0 0
\(247\) −264.030 46.5556i −1.06895 0.188484i
\(248\) −65.1700 53.3737i −0.262782 0.215217i
\(249\) 0 0
\(250\) −83.2725 + 100.045i −0.333090 + 0.400179i
\(251\) 114.384 66.0395i 0.455712 0.263106i −0.254527 0.967066i \(-0.581920\pi\)
0.710240 + 0.703960i \(0.248587\pi\)
\(252\) 0 0
\(253\) 61.4428 106.422i 0.242857 0.420640i
\(254\) 93.1620 34.3279i 0.366779 0.135149i
\(255\) 0 0
\(256\) 52.4420 + 250.571i 0.204852 + 0.978793i
\(257\) −7.69515 6.45700i −0.0299422 0.0251245i 0.627694 0.778460i \(-0.283999\pi\)
−0.657636 + 0.753336i \(0.728443\pi\)
\(258\) 0 0
\(259\) 7.21923 19.8347i 0.0278735 0.0765818i
\(260\) −254.353 210.007i −0.978281 0.807718i
\(261\) 0 0
\(262\) −326.528 117.380i −1.24629 0.448013i
\(263\) 97.1175 17.1244i 0.369268 0.0651119i 0.0140650 0.999901i \(-0.495523\pi\)
0.355203 + 0.934789i \(0.384412\pi\)
\(264\) 0 0
\(265\) −316.099 + 115.051i −1.19283 + 0.434153i
\(266\) 246.670 143.724i 0.927329 0.540317i
\(267\) 0 0
\(268\) −166.795 + 98.0742i −0.622369 + 0.365948i
\(269\) −39.0655 −0.145225 −0.0726125 0.997360i \(-0.523134\pi\)
−0.0726125 + 0.997360i \(0.523134\pi\)
\(270\) 0 0
\(271\) 286.162i 1.05595i 0.849260 + 0.527975i \(0.177049\pi\)
−0.849260 + 0.527975i \(0.822951\pi\)
\(272\) −313.405 + 119.743i −1.15223 + 0.440232i
\(273\) 0 0
\(274\) −86.6435 + 50.4836i −0.316217 + 0.184247i
\(275\) 67.5445 + 185.577i 0.245616 + 0.674826i
\(276\) 0 0
\(277\) 11.2278 + 63.6758i 0.0405334 + 0.229877i 0.998344 0.0575231i \(-0.0183203\pi\)
−0.957811 + 0.287400i \(0.907209\pi\)
\(278\) 351.411 + 126.324i 1.26407 + 0.454405i
\(279\) 0 0
\(280\) 351.208 4.18561i 1.25431 0.0149486i
\(281\) 370.748 + 134.941i 1.31939 + 0.480219i 0.903263 0.429088i \(-0.141165\pi\)
0.416127 + 0.909307i \(0.363387\pi\)
\(282\) 0 0
\(283\) −31.3644 + 37.3786i −0.110828 + 0.132080i −0.818607 0.574355i \(-0.805253\pi\)
0.707778 + 0.706435i \(0.249698\pi\)
\(284\) −72.5761 85.1103i −0.255550 0.299684i
\(285\) 0 0
\(286\) −119.236 + 43.9355i −0.416909 + 0.153621i
\(287\) −331.793 191.561i −1.15607 0.667459i
\(288\) 0 0
\(289\) −75.3464 130.504i −0.260714 0.451570i
\(290\) −385.532 + 463.184i −1.32942 + 1.59718i
\(291\) 0 0
\(292\) 63.1598 + 342.273i 0.216301 + 1.17217i
\(293\) −95.7393 + 542.964i −0.326755 + 1.85312i 0.170287 + 0.985395i \(0.445531\pi\)
−0.497042 + 0.867727i \(0.665580\pi\)
\(294\) 0 0
\(295\) −134.807 160.657i −0.456974 0.544600i
\(296\) −25.3009 + 15.0123i −0.0854759 + 0.0507172i
\(297\) 0 0
\(298\) −50.2142 59.3625i −0.168504 0.199203i
\(299\) −144.487 172.192i −0.483233 0.575894i
\(300\) 0 0
\(301\) −82.6303 + 468.620i −0.274519 + 1.55688i
\(302\) −281.966 + 492.891i −0.933663 + 1.63209i
\(303\) 0 0
\(304\) −392.909 62.8607i −1.29246 0.206778i
\(305\) 32.5845 + 56.4380i 0.106834 + 0.185043i
\(306\) 0 0
\(307\) −256.843 148.288i −0.836622 0.483024i 0.0194923 0.999810i \(-0.493795\pi\)
−0.856115 + 0.516786i \(0.827128\pi\)
\(308\) 66.7230 117.718i 0.216633 0.382200i
\(309\) 0 0
\(310\) 161.083 0.639888i 0.519623 0.00206416i
\(311\) −96.9784 + 115.574i −0.311828 + 0.371622i −0.899082 0.437781i \(-0.855765\pi\)
0.587254 + 0.809403i \(0.300209\pi\)
\(312\) 0 0
\(313\) −290.511 105.737i −0.928150 0.337819i −0.166674 0.986012i \(-0.553303\pi\)
−0.761476 + 0.648193i \(0.775525\pi\)
\(314\) 287.783 51.9235i 0.916507 0.165362i
\(315\) 0 0
\(316\) −25.4295 68.1767i −0.0804730 0.215749i
\(317\) −26.3539 149.461i −0.0831355 0.471485i −0.997743 0.0671428i \(-0.978612\pi\)
0.914608 0.404342i \(-0.132499\pi\)
\(318\) 0 0
\(319\) 79.4056 + 218.165i 0.248920 + 0.683903i
\(320\) −382.404 305.645i −1.19501 0.955140i
\(321\) 0 0
\(322\) 235.883 + 40.6270i 0.732555 + 0.126171i
\(323\) 521.477i 1.61448i
\(324\) 0 0
\(325\) 361.242 1.11151
\(326\) 18.7140 108.654i 0.0574049 0.333296i
\(327\) 0 0
\(328\) 188.601 + 499.572i 0.575004 + 1.52309i
\(329\) −182.898 + 66.5693i −0.555920 + 0.202338i
\(330\) 0 0
\(331\) 569.180 100.362i 1.71958 0.303208i 0.775114 0.631822i \(-0.217692\pi\)
0.944464 + 0.328614i \(0.106581\pi\)
\(332\) −19.4749 52.2123i −0.0586592 0.157266i
\(333\) 0 0
\(334\) −60.3370 334.415i −0.180650 1.00124i
\(335\) 126.551 347.695i 0.377763 1.03790i
\(336\) 0 0
\(337\) 340.126 + 285.400i 1.00928 + 0.846883i 0.988242 0.152896i \(-0.0488599\pi\)
0.0210336 + 0.999779i \(0.493304\pi\)
\(338\) −0.419321 105.558i −0.00124059 0.312302i
\(339\) 0 0
\(340\) 316.361 558.148i 0.930474 1.64161i
\(341\) 31.0288 53.7435i 0.0909936 0.157606i
\(342\) 0 0
\(343\) 323.375 186.700i 0.942783 0.544316i
\(344\) 502.947 432.340i 1.46205 1.25680i
\(345\) 0 0
\(346\) −162.308 92.8507i −0.469097 0.268355i
\(347\) 539.222 + 95.0793i 1.55395 + 0.274004i 0.883673 0.468105i \(-0.155063\pi\)
0.670280 + 0.742108i \(0.266174\pi\)
\(348\) 0 0
\(349\) 308.273 258.672i 0.883305 0.741181i −0.0835512 0.996503i \(-0.526626\pi\)
0.966856 + 0.255323i \(0.0821818\pi\)
\(350\) −293.685 + 248.426i −0.839101 + 0.709789i
\(351\) 0 0
\(352\) −175.906 + 68.0106i −0.499733 + 0.193212i
\(353\) 87.4208 73.3547i 0.247651 0.207804i −0.510509 0.859872i \(-0.670543\pi\)
0.758160 + 0.652069i \(0.226099\pi\)
\(354\) 0 0
\(355\) 210.644 + 37.1421i 0.593362 + 0.104626i
\(356\) 118.012 + 639.525i 0.331494 + 1.79642i
\(357\) 0 0
\(358\) −232.079 193.171i −0.648264 0.539584i
\(359\) 441.999 255.188i 1.23120 0.710831i 0.263916 0.964546i \(-0.414986\pi\)
0.967279 + 0.253715i \(0.0816524\pi\)
\(360\) 0 0
\(361\) 128.736 222.978i 0.356610 0.617667i
\(362\) 13.5878 + 36.8757i 0.0375353 + 0.101866i
\(363\) 0 0
\(364\) −160.599 188.335i −0.441206 0.517405i
\(365\) −509.856 427.820i −1.39687 1.17211i
\(366\) 0 0
\(367\) 18.6859 51.3391i 0.0509152 0.139888i −0.911628 0.411016i \(-0.865174\pi\)
0.962544 + 0.271127i \(0.0873964\pi\)
\(368\) −218.474 252.120i −0.593678 0.685110i
\(369\) 0 0
\(370\) 19.0312 52.9412i 0.0514357 0.143084i
\(371\) −248.585 + 43.8322i −0.670039 + 0.118146i
\(372\) 0 0
\(373\) 620.992 226.023i 1.66486 0.605959i 0.673744 0.738965i \(-0.264685\pi\)
0.991115 + 0.133006i \(0.0424629\pi\)
\(374\) −124.432 213.558i −0.332705 0.571012i
\(375\) 0 0
\(376\) 256.007 + 89.7386i 0.680869 + 0.238666i
\(377\) 424.677 1.12646
\(378\) 0 0
\(379\) 294.012i 0.775757i −0.921711 0.387878i \(-0.873208\pi\)
0.921711 0.387878i \(-0.126792\pi\)
\(380\) 655.919 385.676i 1.72610 1.01494i
\(381\) 0 0
\(382\) 253.011 + 434.236i 0.662333 + 1.13674i
\(383\) −178.617 490.746i −0.466362 1.28132i −0.920624 0.390451i \(-0.872319\pi\)
0.454261 0.890869i \(-0.349903\pi\)
\(384\) 0 0
\(385\) 44.9322 + 254.823i 0.116707 + 0.661878i
\(386\) 9.93517 27.6378i 0.0257388 0.0716004i
\(387\) 0 0
\(388\) 130.153 + 107.461i 0.335447 + 0.276962i
\(389\) −101.361 36.8924i −0.260568 0.0948391i 0.208433 0.978037i \(-0.433164\pi\)
−0.469001 + 0.883198i \(0.655386\pi\)
\(390\) 0 0
\(391\) 281.035 334.925i 0.718760 0.856585i
\(392\) −126.745 20.7943i −0.323329 0.0530467i
\(393\) 0 0
\(394\) −144.816 393.013i −0.367552 0.997494i
\(395\) 120.504 + 69.5731i 0.305074 + 0.176134i
\(396\) 0 0
\(397\) −197.478 342.043i −0.497427 0.861568i 0.502569 0.864537i \(-0.332388\pi\)
−0.999996 + 0.00296877i \(0.999055\pi\)
\(398\) 8.10021 + 6.74223i 0.0203523 + 0.0169403i
\(399\) 0 0
\(400\) 536.070 8.51864i 1.34018 0.0212966i
\(401\) −5.45754 + 30.9512i −0.0136098 + 0.0771851i −0.990856 0.134922i \(-0.956922\pi\)
0.977246 + 0.212107i \(0.0680326\pi\)
\(402\) 0 0
\(403\) −72.9663 86.9578i −0.181058 0.215776i
\(404\) 72.5792 431.643i 0.179652 1.06842i
\(405\) 0 0
\(406\) −345.258 + 292.051i −0.850388 + 0.719336i
\(407\) −13.9314 16.6027i −0.0342294 0.0407930i
\(408\) 0 0
\(409\) 36.6237 207.703i 0.0895445 0.507832i −0.906739 0.421693i \(-0.861436\pi\)
0.996283 0.0861391i \(-0.0274529\pi\)
\(410\) −886.346 507.048i −2.16182 1.23670i
\(411\) 0 0
\(412\) −0.0312210 3.92966i −7.57791e−5 0.00953802i
\(413\) −78.6867 136.289i −0.190525 0.329999i
\(414\) 0 0
\(415\) 92.2867 + 53.2817i 0.222378 + 0.128390i
\(416\) 6.85149 + 344.910i 0.0164699 + 0.829110i
\(417\) 0 0
\(418\) −1.16446 293.136i −0.00278578 0.701282i
\(419\) −26.3541 + 31.4075i −0.0628975 + 0.0749583i −0.796576 0.604539i \(-0.793357\pi\)
0.733678 + 0.679497i \(0.237802\pi\)
\(420\) 0 0
\(421\) 180.665 + 65.7568i 0.429134 + 0.156192i 0.547551 0.836772i \(-0.315560\pi\)
−0.118418 + 0.992964i \(0.537782\pi\)
\(422\) 31.9634 + 177.155i 0.0757426 + 0.419799i
\(423\) 0 0
\(424\) 306.757 + 172.265i 0.723484 + 0.406286i
\(425\) 122.012 + 691.962i 0.287086 + 1.62815i
\(426\) 0 0
\(427\) 16.7255 + 45.9529i 0.0391697 + 0.107618i
\(428\) −172.864 + 486.942i −0.403887 + 1.13771i
\(429\) 0 0
\(430\) −215.270 + 1249.87i −0.500629 + 2.90668i
\(431\) 427.089i 0.990927i 0.868629 + 0.495463i \(0.165002\pi\)
−0.868629 + 0.495463i \(0.834998\pi\)
\(432\) 0 0
\(433\) −265.388 −0.612906 −0.306453 0.951886i \(-0.599142\pi\)
−0.306453 + 0.951886i \(0.599142\pi\)
\(434\) 119.122 + 20.5168i 0.274474 + 0.0472737i
\(435\) 0 0
\(436\) −604.930 214.750i −1.38746 0.492545i
\(437\) 487.265 177.350i 1.11502 0.405835i
\(438\) 0 0
\(439\) −553.109 + 97.5280i −1.25993 + 0.222159i −0.763437 0.645882i \(-0.776490\pi\)
−0.496492 + 0.868041i \(0.665379\pi\)
\(440\) 176.589 314.456i 0.401338 0.714672i
\(441\) 0 0
\(442\) −444.928 + 80.2765i −1.00662 + 0.181621i
\(443\) 111.741 307.006i 0.252237 0.693016i −0.747354 0.664426i \(-0.768676\pi\)
0.999591 0.0285901i \(-0.00910175\pi\)
\(444\) 0 0
\(445\) −952.648 799.367i −2.14078 1.79633i
\(446\) 474.410 1.88455i 1.06370 0.00422545i
\(447\) 0 0
\(448\) −242.765 275.696i −0.541886 0.615393i
\(449\) −97.3394 + 168.597i −0.216791 + 0.375494i −0.953825 0.300362i \(-0.902892\pi\)
0.737034 + 0.675856i \(0.236226\pi\)
\(450\) 0 0
\(451\) −340.686 + 196.695i −0.755400 + 0.436131i
\(452\) −261.091 + 2.07436i −0.577635 + 0.00458928i
\(453\) 0 0
\(454\) −267.964 + 468.414i −0.590228 + 1.03175i
\(455\) 466.120 + 82.1896i 1.02444 + 0.180636i
\(456\) 0 0
\(457\) 237.405 199.206i 0.519486 0.435900i −0.344967 0.938615i \(-0.612110\pi\)
0.864452 + 0.502715i \(0.167665\pi\)
\(458\) 223.967 + 264.770i 0.489010 + 0.578101i
\(459\) 0 0
\(460\) 629.121 + 105.785i 1.36765 + 0.229966i
\(461\) −308.002 + 258.445i −0.668118 + 0.560617i −0.912508 0.409060i \(-0.865857\pi\)
0.244390 + 0.969677i \(0.421412\pi\)
\(462\) 0 0
\(463\) 66.1231 + 11.6593i 0.142814 + 0.0251820i 0.244598 0.969624i \(-0.421344\pi\)
−0.101784 + 0.994807i \(0.532455\pi\)
\(464\) 630.206 10.0145i 1.35820 0.0215831i
\(465\) 0 0
\(466\) 218.475 262.479i 0.468830 0.563259i
\(467\) 309.740 178.828i 0.663254 0.382930i −0.130261 0.991480i \(-0.541582\pi\)
0.793516 + 0.608550i \(0.208248\pi\)
\(468\) 0 0
\(469\) 138.825 240.452i 0.296002 0.512691i
\(470\) −486.766 + 179.361i −1.03567 + 0.381620i
\(471\) 0 0
\(472\) −35.5118 + 216.450i −0.0752369 + 0.458581i
\(473\) 374.291 + 314.068i 0.791313 + 0.663991i
\(474\) 0 0
\(475\) −285.015 + 783.074i −0.600033 + 1.64858i
\(476\) 306.515 371.241i 0.643940 0.779918i
\(477\) 0 0
\(478\) −241.049 86.6517i −0.504286 0.181280i
\(479\) −7.06355 + 1.24549i −0.0147464 + 0.00260020i −0.181017 0.983480i \(-0.557939\pi\)
0.166270 + 0.986080i \(0.446828\pi\)
\(480\) 0 0
\(481\) −37.2539 + 13.5593i −0.0774508 + 0.0281898i
\(482\) −285.510 + 166.355i −0.592344 + 0.345134i
\(483\) 0 0
\(484\) 174.899 + 297.452i 0.361362 + 0.614569i
\(485\) −322.760 −0.665485
\(486\) 0 0
\(487\) 432.322i 0.887725i −0.896095 0.443862i \(-0.853608\pi\)
0.896095 0.443862i \(-0.146392\pi\)
\(488\) 22.5467 64.3215i 0.0462023 0.131806i
\(489\) 0 0
\(490\) 212.216 123.649i 0.433093 0.252346i
\(491\) −61.1331 167.962i −0.124507 0.342081i 0.861742 0.507347i \(-0.169374\pi\)
−0.986249 + 0.165266i \(0.947152\pi\)
\(492\) 0 0
\(493\) 143.437 + 813.474i 0.290948 + 1.65005i
\(494\) −504.593 181.390i −1.02144 0.367187i
\(495\) 0 0
\(496\) −110.330 127.322i −0.222440 0.256697i
\(497\) 150.823 + 54.8951i 0.303467 + 0.110453i
\(498\) 0 0
\(499\) 413.773 493.116i 0.829205 0.988208i −0.170791 0.985307i \(-0.554632\pi\)
0.999996 0.00290072i \(-0.000923328\pi\)
\(500\) −198.091 + 168.918i −0.396181 + 0.337835i
\(501\) 0 0
\(502\) 247.866 91.3327i 0.493758 0.181938i
\(503\) −306.467 176.939i −0.609279 0.351767i 0.163404 0.986559i \(-0.447752\pi\)
−0.772683 + 0.634792i \(0.781086\pi\)
\(504\) 0 0
\(505\) 418.503 + 724.869i 0.828719 + 1.43538i
\(506\) 157.229 188.898i 0.310730 0.373315i
\(507\) 0 0
\(508\) 195.274 36.0339i 0.384397 0.0709329i
\(509\) 94.0125 533.171i 0.184700 1.04749i −0.741639 0.670799i \(-0.765951\pi\)
0.926340 0.376689i \(-0.122937\pi\)
\(510\) 0 0
\(511\) −321.031 382.589i −0.628240 0.748707i
\(512\) 18.3009 + 511.673i 0.0357439 + 0.999361i
\(513\) 0 0
\(514\) −12.9750 15.3389i −0.0252432 0.0298422i
\(515\) 4.83044 + 5.75669i 0.00937949 + 0.0111780i
\(516\) 0 0
\(517\) −34.7039 + 196.816i −0.0671256 + 0.380688i
\(518\) 20.9622 36.6430i 0.0404676 0.0707395i
\(519\) 0 0
\(520\) −430.034 500.264i −0.826988 0.962047i
\(521\) −3.55297 6.15392i −0.00681952 0.0118118i 0.862596 0.505894i \(-0.168837\pi\)
−0.869415 + 0.494082i \(0.835504\pi\)
\(522\) 0 0
\(523\) 26.6849 + 15.4065i 0.0510227 + 0.0294580i 0.525294 0.850921i \(-0.323955\pi\)
−0.474272 + 0.880379i \(0.657289\pi\)
\(524\) −603.733 342.199i −1.15216 0.653051i
\(525\) 0 0
\(526\) 197.230 0.783478i 0.374962 0.00148950i
\(527\) 141.924 169.138i 0.269305 0.320945i
\(528\) 0 0
\(529\) −88.5681 32.2361i −0.167425 0.0609379i
\(530\) −662.081 + 119.456i −1.24921 + 0.225389i
\(531\) 0 0
\(532\) 534.971 199.541i 1.00558 0.375077i
\(533\) 124.955 + 708.653i 0.234437 + 1.32956i
\(534\) 0 0
\(535\) −337.950 928.510i −0.631682 1.73553i
\(536\) −362.043 + 136.680i −0.675453 + 0.255001i
\(537\) 0 0
\(538\) −76.9973 13.2616i −0.143118 0.0246497i
\(539\) 94.6215i 0.175550i
\(540\) 0 0
\(541\) 74.8336 0.138325 0.0691623 0.997605i \(-0.477967\pi\)
0.0691623 + 0.997605i \(0.477967\pi\)
\(542\) −97.1434 + 564.020i −0.179231 + 1.04063i
\(543\) 0 0
\(544\) −658.365 + 129.620i −1.21023 + 0.238271i
\(545\) 1153.49 419.837i 2.11650 0.770343i
\(546\) 0 0
\(547\) −290.555 + 51.2327i −0.531179 + 0.0936612i −0.432804 0.901488i \(-0.642476\pi\)
−0.0983754 + 0.995149i \(0.531365\pi\)
\(548\) −187.910 + 70.0893i −0.342902 + 0.127900i
\(549\) 0 0
\(550\) 70.1311 + 388.698i 0.127511 + 0.706723i
\(551\) −335.065 + 920.584i −0.608104 + 1.67075i
\(552\) 0 0
\(553\) 79.9854 + 67.1157i 0.144639 + 0.121367i
\(554\) 0.513694 + 129.315i 0.000927245 + 0.233421i
\(555\) 0 0
\(556\) 649.740 + 368.276i 1.16860 + 0.662367i
\(557\) 73.4754 127.263i 0.131913 0.228480i −0.792501 0.609870i \(-0.791221\pi\)
0.924414 + 0.381391i \(0.124555\pi\)
\(558\) 0 0
\(559\) 774.009 446.874i 1.38463 0.799417i
\(560\) 693.645 + 110.975i 1.23865 + 0.198169i
\(561\) 0 0
\(562\) 684.929 + 391.825i 1.21874 + 0.697197i
\(563\) −286.120 50.4507i −0.508207 0.0896105i −0.0863350 0.996266i \(-0.527516\pi\)
−0.421871 + 0.906656i \(0.638627\pi\)
\(564\) 0 0
\(565\) 382.481 320.939i 0.676957 0.568034i
\(566\) −74.5075 + 63.0253i −0.131639 + 0.111352i
\(567\) 0 0
\(568\) −114.154 192.388i −0.200975 0.338711i
\(569\) 37.1059 31.1355i 0.0652125 0.0547198i −0.609599 0.792710i \(-0.708669\pi\)
0.674811 + 0.737990i \(0.264225\pi\)
\(570\) 0 0
\(571\) −860.734 151.771i −1.50741 0.265798i −0.641941 0.766754i \(-0.721871\pi\)
−0.865473 + 0.500956i \(0.832982\pi\)
\(572\) −249.926 + 46.1190i −0.436934 + 0.0806277i
\(573\) 0 0
\(574\) −588.928 490.196i −1.02601 0.854000i
\(575\) −605.070 + 349.337i −1.05230 + 0.607543i
\(576\) 0 0
\(577\) −92.1639 + 159.633i −0.159730 + 0.276660i −0.934771 0.355251i \(-0.884396\pi\)
0.775042 + 0.631910i \(0.217729\pi\)
\(578\) −104.204 282.798i −0.180284 0.489270i
\(579\) 0 0
\(580\) −917.113 + 782.049i −1.58123 + 1.34836i
\(581\) 61.2559 + 51.3998i 0.105432 + 0.0884678i
\(582\) 0 0
\(583\) −88.6464 + 243.554i −0.152052 + 0.417760i
\(584\) 8.29539 + 696.054i 0.0142044 + 1.19187i
\(585\) 0 0
\(586\) −373.020 + 1037.67i −0.636553 + 1.77077i
\(587\) 624.158 110.056i 1.06330 0.187489i 0.385481 0.922716i \(-0.374035\pi\)
0.677821 + 0.735227i \(0.262924\pi\)
\(588\) 0 0
\(589\) 246.070 89.5623i 0.417777 0.152058i
\(590\) −211.164 362.415i −0.357906 0.614263i
\(591\) 0 0
\(592\) −54.9637 + 21.0000i −0.0928441 + 0.0354730i
\(593\) −445.495 −0.751256 −0.375628 0.926771i \(-0.622573\pi\)
−0.375628 + 0.926771i \(0.622573\pi\)
\(594\) 0 0
\(595\) 920.619i 1.54726i
\(596\) −78.8194 134.048i −0.132247 0.224913i
\(597\) 0 0
\(598\) −226.326 388.437i −0.378472 0.649559i
\(599\) 304.954 + 837.855i 0.509105 + 1.39876i 0.882162 + 0.470947i \(0.156088\pi\)
−0.373056 + 0.927809i \(0.621690\pi\)
\(600\) 0 0
\(601\) 174.212 + 988.005i 0.289870 + 1.64393i 0.687352 + 0.726325i \(0.258773\pi\)
−0.397482 + 0.917610i \(0.630116\pi\)
\(602\) −321.945 + 895.590i −0.534792 + 1.48769i
\(603\) 0 0
\(604\) −723.071 + 875.759i −1.19714 + 1.44993i
\(605\) −620.057 225.682i −1.02489 0.373029i
\(606\) 0 0
\(607\) −522.302 + 622.455i −0.860464 + 1.02546i 0.138918 + 0.990304i \(0.455638\pi\)
−0.999382 + 0.0351573i \(0.988807\pi\)
\(608\) −753.077 257.278i −1.23861 0.423154i
\(609\) 0 0
\(610\) 45.0644 + 122.300i 0.0738761 + 0.200491i
\(611\) 316.591 + 182.784i 0.518152 + 0.299155i
\(612\) 0 0
\(613\) −176.799 306.225i −0.288416 0.499551i 0.685016 0.728528i \(-0.259795\pi\)
−0.973432 + 0.228977i \(0.926462\pi\)
\(614\) −455.893 379.464i −0.742497 0.618019i
\(615\) 0 0
\(616\) 171.471 209.369i 0.278363 0.339884i
\(617\) −14.8981 + 84.4914i −0.0241460 + 0.136939i −0.994498 0.104758i \(-0.966593\pi\)
0.970352 + 0.241697i \(0.0777042\pi\)
\(618\) 0 0
\(619\) −409.962 488.574i −0.662298 0.789296i 0.325416 0.945571i \(-0.394496\pi\)
−0.987714 + 0.156275i \(0.950051\pi\)
\(620\) 317.709 + 53.4216i 0.512433 + 0.0861638i
\(621\) 0 0
\(622\) −230.376 + 194.874i −0.370380 + 0.313302i
\(623\) −599.835 714.855i −0.962817 1.14744i
\(624\) 0 0
\(625\) −59.0210 + 334.725i −0.0944335 + 0.535559i
\(626\) −536.697 307.026i −0.857343 0.490457i
\(627\) 0 0
\(628\) 584.841 4.64654i 0.931276 0.00739894i
\(629\) −38.5557 66.7804i −0.0612968 0.106169i
\(630\) 0 0
\(631\) 1010.86 + 583.618i 1.60199 + 0.924909i 0.991089 + 0.133203i \(0.0425262\pi\)
0.610901 + 0.791707i \(0.290807\pi\)
\(632\) −26.9771 143.007i −0.0426852 0.226277i
\(633\) 0 0
\(634\) −1.20575 303.530i −0.00190181 0.478754i
\(635\) −244.080 + 290.883i −0.384378 + 0.458084i
\(636\) 0 0
\(637\) −162.643 59.1971i −0.255326 0.0929312i
\(638\) 82.4464 + 456.955i 0.129226 + 0.716230i
\(639\) 0 0
\(640\) −649.953 732.234i −1.01555 1.14412i
\(641\) −80.0762 454.134i −0.124924 0.708478i −0.981353 0.192214i \(-0.938433\pi\)
0.856429 0.516264i \(-0.172678\pi\)
\(642\) 0 0
\(643\) −27.9088 76.6788i −0.0434040 0.119252i 0.916097 0.400957i \(-0.131322\pi\)
−0.959501 + 0.281705i \(0.909100\pi\)
\(644\) 451.128 + 160.150i 0.700510 + 0.248680i
\(645\) 0 0
\(646\) 177.025 1027.82i 0.274033 1.59105i
\(647\) 360.614i 0.557363i −0.960384 0.278682i \(-0.910103\pi\)
0.960384 0.278682i \(-0.0898974\pi\)
\(648\) 0 0
\(649\) −161.591 −0.248985
\(650\) 712.000 + 122.631i 1.09538 + 0.188662i
\(651\) 0 0
\(652\) 73.7698 207.803i 0.113144 0.318716i
\(653\) −114.976 + 41.8479i −0.176074 + 0.0640857i −0.428553 0.903517i \(-0.640976\pi\)
0.252479 + 0.967602i \(0.418754\pi\)
\(654\) 0 0
\(655\) 1306.90 230.441i 1.99526 0.351819i
\(656\) 202.140 + 1048.67i 0.308140 + 1.59858i
\(657\) 0 0
\(658\) −383.086 + 69.1185i −0.582197 + 0.105043i
\(659\) −19.5137 + 53.6136i −0.0296111 + 0.0813560i −0.953617 0.301022i \(-0.902672\pi\)
0.924006 + 0.382378i \(0.124895\pi\)
\(660\) 0 0
\(661\) −716.089 600.870i −1.08334 0.909031i −0.0871475 0.996195i \(-0.527775\pi\)
−0.996194 + 0.0871639i \(0.972220\pi\)
\(662\) 1155.91 4.59176i 1.74609 0.00693620i
\(663\) 0 0
\(664\) −20.6601 109.521i −0.0311146 0.164941i
\(665\) −545.928 + 945.575i −0.820945 + 1.42192i
\(666\) 0 0
\(667\) −711.323 + 410.682i −1.06645 + 0.615716i
\(668\) −5.39945 679.607i −0.00808300 1.01738i
\(669\) 0 0
\(670\) 367.461 642.340i 0.548449 0.958716i
\(671\) 49.4498 + 8.71934i 0.0736957 + 0.0129945i
\(672\) 0 0
\(673\) 48.9893 41.1069i 0.0727924 0.0610801i −0.605666 0.795719i \(-0.707093\pi\)
0.678458 + 0.734639i \(0.262649\pi\)
\(674\) 573.497 + 677.979i 0.850886 + 1.00590i
\(675\) 0 0
\(676\) 35.0073 208.195i 0.0517860 0.307981i
\(677\) 453.503 380.534i 0.669872 0.562089i −0.243156 0.969987i \(-0.578183\pi\)
0.913028 + 0.407898i \(0.133738\pi\)
\(678\) 0 0
\(679\) −238.516 42.0567i −0.351275 0.0619392i
\(680\) 813.015 992.702i 1.19561 1.45986i
\(681\) 0 0
\(682\) 79.4014 95.3940i 0.116424 0.139874i
\(683\) −187.818 + 108.437i −0.274990 + 0.158766i −0.631153 0.775658i \(-0.717418\pi\)
0.356163 + 0.934424i \(0.384085\pi\)
\(684\) 0 0
\(685\) 191.759 332.136i 0.279940 0.484870i
\(686\) 700.744 258.207i 1.02149 0.376395i
\(687\) 0 0
\(688\) 1138.06 681.398i 1.65416 0.990404i
\(689\) 363.181 + 304.745i 0.527112 + 0.442300i
\(690\) 0 0
\(691\) −444.760 + 1221.97i −0.643647 + 1.76841i −0.00369336 + 0.999993i \(0.501176\pi\)
−0.639954 + 0.768413i \(0.721047\pi\)
\(692\) −288.385 238.105i −0.416741 0.344083i
\(693\) 0 0
\(694\) 1030.52 + 370.449i 1.48490 + 0.533788i
\(695\) −1406.49 + 248.002i −2.02373 + 0.356838i
\(696\) 0 0
\(697\) −1315.23 + 478.704i −1.88699 + 0.686807i
\(698\) 695.412 405.188i 0.996292 0.580498i
\(699\) 0 0
\(700\) −663.181 + 389.945i −0.947401 + 0.557065i
\(701\) −937.091 −1.33679 −0.668396 0.743806i \(-0.733019\pi\)
−0.668396 + 0.743806i \(0.733019\pi\)
\(702\) 0 0
\(703\) 91.4543i 0.130092i
\(704\) −369.795 + 74.3327i −0.525277 + 0.105586i
\(705\) 0 0
\(706\) 197.206 114.904i 0.279329 0.162754i
\(707\) 214.816 + 590.201i 0.303841 + 0.834797i
\(708\) 0 0
\(709\) −223.970 1270.20i −0.315896 1.79153i −0.567152 0.823613i \(-0.691955\pi\)
0.251256 0.967921i \(-0.419156\pi\)
\(710\) 402.566 + 144.713i 0.566994 + 0.203822i
\(711\) 0 0
\(712\) 15.4996 + 1300.55i 0.0217692 + 1.82662i
\(713\) 206.309 + 75.0903i 0.289353 + 0.105316i
\(714\) 0 0
\(715\) 312.393 372.295i 0.436913 0.520692i
\(716\) −391.846 459.520i −0.547271 0.641788i
\(717\) 0 0
\(718\) 957.800 352.926i 1.33398 0.491540i
\(719\) 843.005 + 486.709i 1.17247 + 0.676925i 0.954260 0.298977i \(-0.0966453\pi\)
0.218209 + 0.975902i \(0.429979\pi\)
\(720\) 0 0
\(721\) 2.81952 + 4.88354i 0.00391056 + 0.00677329i
\(722\) 329.431 395.783i 0.456276 0.548176i
\(723\) 0 0
\(724\) 14.2631 + 77.2938i 0.0197004 + 0.106759i
\(725\) 229.216 1299.95i 0.316159 1.79303i
\(726\) 0 0
\(727\) −632.891 754.250i −0.870551 1.03748i −0.998952 0.0457605i \(-0.985429\pi\)
0.128401 0.991722i \(-0.459016\pi\)
\(728\) −252.603 425.724i −0.346983 0.584785i
\(729\) 0 0
\(730\) −859.684 1016.30i −1.17765 1.39220i
\(731\) 1117.42 + 1331.69i 1.52862 + 1.82173i
\(732\) 0 0
\(733\) 102.753 582.739i 0.140181 0.795006i −0.830930 0.556377i \(-0.812191\pi\)
0.971111 0.238629i \(-0.0766979\pi\)
\(734\) 54.2576 94.8449i 0.0739204 0.129217i
\(735\) 0 0
\(736\) −345.020 571.089i −0.468777 0.775937i
\(737\) −142.546 246.897i −0.193414 0.335002i
\(738\) 0 0
\(739\) 722.804 + 417.311i 0.978084 + 0.564697i 0.901691 0.432380i \(-0.142326\pi\)
0.0763932 + 0.997078i \(0.475660\pi\)
\(740\) 55.4820 97.8855i 0.0749757 0.132278i
\(741\) 0 0
\(742\) −504.835 + 2.00541i −0.680370 + 0.00270271i
\(743\) 374.265 446.031i 0.503721 0.600311i −0.452931 0.891546i \(-0.649622\pi\)
0.956652 + 0.291234i \(0.0940660\pi\)
\(744\) 0 0
\(745\) 279.433 + 101.705i 0.375077 + 0.136517i
\(746\) 1300.69 234.678i 1.74355 0.314582i
\(747\) 0 0
\(748\) −172.756 463.160i −0.230957 0.619198i
\(749\) −128.753 730.193i −0.171900 0.974891i
\(750\) 0 0
\(751\) 383.766 + 1054.39i 0.511006 + 1.40398i 0.880190 + 0.474622i \(0.157415\pi\)
−0.369183 + 0.929357i \(0.620362\pi\)
\(752\) 474.121 + 263.779i 0.630479 + 0.350770i
\(753\) 0 0
\(754\) 837.030 + 144.165i 1.11012 + 0.191200i
\(755\) 2171.74i 2.87648i
\(756\) 0 0
\(757\) 84.4056 0.111500 0.0557501 0.998445i \(-0.482245\pi\)
0.0557501 + 0.998445i \(0.482245\pi\)
\(758\) 99.8080 579.491i 0.131673 0.764500i
\(759\) 0 0
\(760\) 1423.73 537.494i 1.87333 0.707229i
\(761\) −1003.11 + 365.103i −1.31815 + 0.479768i −0.902865 0.429924i \(-0.858540\pi\)
−0.415285 + 0.909691i \(0.636318\pi\)
\(762\) 0 0
\(763\) 907.123 159.950i 1.18889 0.209633i
\(764\) 351.270 + 941.759i 0.459778 + 1.23267i
\(765\) 0 0
\(766\) −185.457 1027.88i −0.242111 1.34189i
\(767\) −101.095 + 277.756i −0.131806 + 0.362133i
\(768\) 0 0
\(769\) 121.602 + 102.037i 0.158131 + 0.132687i 0.718420 0.695610i \(-0.244866\pi\)
−0.560289 + 0.828297i \(0.689310\pi\)
\(770\) 2.05574 + 517.504i 0.00266979 + 0.672083i
\(771\) 0 0
\(772\) 28.9642 51.1008i 0.0375184 0.0661927i
\(773\) 371.280 643.076i 0.480310 0.831922i −0.519434 0.854510i \(-0.673857\pi\)
0.999745 + 0.0225883i \(0.00719069\pi\)
\(774\) 0 0
\(775\) −305.563 + 176.417i −0.394274 + 0.227634i
\(776\) 220.050 + 255.987i 0.283570 + 0.329880i
\(777\) 0 0
\(778\) −187.257 107.123i −0.240690 0.137690i
\(779\) −1634.76 288.252i −2.09853 0.370028i
\(780\) 0 0
\(781\) 126.247 105.934i 0.161649 0.135639i
\(782\) 667.612 564.727i 0.853723 0.722157i
\(783\) 0 0
\(784\) −242.752 84.0112i −0.309633 0.107157i
\(785\) −856.753 + 718.901i −1.09141 + 0.915798i
\(786\) 0 0
\(787\) 754.529 + 133.044i 0.958741 + 0.169052i 0.631058 0.775736i \(-0.282621\pi\)
0.327683 + 0.944788i \(0.393732\pi\)
\(788\) −152.013 823.781i −0.192909 1.04541i
\(789\) 0 0
\(790\) 213.893 + 178.035i 0.270751 + 0.225360i
\(791\) 324.468 187.332i 0.410200 0.236829i
\(792\) 0 0
\(793\) 45.9243 79.5432i 0.0579121 0.100307i
\(794\) −273.113 741.197i −0.343971 0.933498i
\(795\) 0 0
\(796\) 13.6766 + 16.0386i 0.0171816 + 0.0201490i
\(797\) 772.076 + 647.848i 0.968727 + 0.812859i 0.982351 0.187048i \(-0.0598921\pi\)
−0.0136233 + 0.999907i \(0.504337\pi\)
\(798\) 0 0
\(799\) −243.194 + 668.170i −0.304373 + 0.836258i
\(800\) 1059.48 + 165.189i 1.32434 + 0.206487i
\(801\) 0 0
\(802\) −21.2637 + 59.1516i −0.0265133 + 0.0737551i
\(803\) −505.030 + 89.0504i −0.628929 + 0.110897i
\(804\) 0 0
\(805\) −860.221 + 313.095i −1.06860 + 0.388937i
\(806\) −114.295 196.162i −0.141806 0.243377i
\(807\) 0 0
\(808\) 289.582 826.121i 0.358393 1.02243i
\(809\) −909.106 −1.12374 −0.561870 0.827226i \(-0.689918\pi\)
−0.561870 + 0.827226i \(0.689918\pi\)
\(810\) 0 0
\(811\) 241.760i 0.298101i −0.988830 0.149051i \(-0.952378\pi\)
0.988830 0.149051i \(-0.0476217\pi\)
\(812\) −779.638 + 458.421i −0.960145 + 0.564558i
\(813\) 0 0
\(814\) −21.8223 37.4529i −0.0268087 0.0460110i
\(815\) 144.220 + 396.243i 0.176958 + 0.486187i
\(816\) 0 0
\(817\) 358.018 + 2030.42i 0.438210 + 2.48521i
\(818\) 142.694 396.946i 0.174442 0.485265i
\(819\) 0 0
\(820\) −1574.84 1300.27i −1.92054 1.58569i
\(821\) −381.889 138.996i −0.465151 0.169301i 0.0988038 0.995107i \(-0.468498\pi\)
−0.563954 + 0.825806i \(0.690721\pi\)
\(822\) 0 0
\(823\) 30.4525 36.2919i 0.0370019 0.0440971i −0.747226 0.664570i \(-0.768615\pi\)
0.784228 + 0.620473i \(0.213059\pi\)
\(824\) 1.27247 7.75589i 0.00154425 0.00941248i
\(825\) 0 0
\(826\) −108.824 295.335i −0.131748 0.357549i
\(827\) −310.818 179.451i −0.375839 0.216991i 0.300168 0.953886i \(-0.402957\pi\)
−0.676006 + 0.736896i \(0.736291\pi\)
\(828\) 0 0
\(829\) 95.4686 + 165.356i 0.115161 + 0.199465i 0.917844 0.396941i \(-0.129928\pi\)
−0.802683 + 0.596406i \(0.796595\pi\)
\(830\) 163.808 + 136.346i 0.197359 + 0.164272i
\(831\) 0 0
\(832\) −103.582 + 682.136i −0.124498 + 0.819875i
\(833\) 58.4592 331.538i 0.0701791 0.398005i
\(834\) 0 0
\(835\) 835.390 + 995.579i 1.00047 + 1.19231i
\(836\) 97.2155 578.160i 0.116287 0.691579i
\(837\) 0 0
\(838\) −62.6052 + 52.9572i −0.0747079 + 0.0631948i
\(839\) −826.157 984.575i −0.984692 1.17351i −0.984832 0.173511i \(-0.944489\pi\)
0.000139714 1.00000i \(-0.499956\pi\)
\(840\) 0 0
\(841\) 123.429 699.998i 0.146764 0.832340i
\(842\) 333.765 + 190.936i 0.396396 + 0.226764i
\(843\) 0 0
\(844\) 2.86034 + 360.020i 0.00338903 + 0.426564i
\(845\) 201.858 + 349.628i 0.238885 + 0.413761i
\(846\) 0 0
\(847\) −428.807 247.572i −0.506266 0.292293i
\(848\) 546.134 + 443.666i 0.644026 + 0.523191i
\(849\) 0 0
\(850\) 5.58229 + 1405.26i 0.00656740 + 1.65325i
\(851\) 49.2868 58.7377i 0.0579163 0.0690219i
\(852\) 0 0
\(853\) 508.554 + 185.098i 0.596194 + 0.216997i 0.622452 0.782658i \(-0.286137\pi\)
−0.0262574 + 0.999655i \(0.508359\pi\)
\(854\) 17.3660 + 96.2499i 0.0203349 + 0.112705i
\(855\) 0 0
\(856\) −506.013 + 901.070i −0.591136 + 1.05265i
\(857\) −27.5580 156.289i −0.0321563 0.182367i 0.964499 0.264086i \(-0.0850703\pi\)
−0.996655 + 0.0817185i \(0.973959\pi\)
\(858\) 0 0
\(859\) −360.358 990.074i −0.419508 1.15259i −0.951985 0.306145i \(-0.900961\pi\)
0.532477 0.846445i \(-0.321261\pi\)
\(860\) −848.587 + 2390.40i −0.986730 + 2.77953i
\(861\) 0 0
\(862\) −144.984 + 841.785i −0.168195 + 0.976548i
\(863\) 251.308i 0.291203i 0.989343 + 0.145601i \(0.0465117\pi\)
−0.989343 + 0.145601i \(0.953488\pi\)
\(864\) 0 0
\(865\) 715.149 0.826762
\(866\) −523.075 90.0912i −0.604013 0.104031i
\(867\) 0 0
\(868\) 227.822 + 80.8763i 0.262467 + 0.0931755i
\(869\) 100.746 36.6686i 0.115934 0.0421964i
\(870\) 0 0
\(871\) −513.565 + 90.5554i −0.589627 + 0.103967i
\(872\) −1119.40 628.622i −1.28372 0.720897i
\(873\) 0 0
\(874\) 1020.59 184.141i 1.16773 0.210688i
\(875\) 127.766 351.035i 0.146018 0.401182i
\(876\) 0 0
\(877\) −153.816 129.067i −0.175389 0.147168i 0.550868 0.834593i \(-0.314297\pi\)
−0.726256 + 0.687424i \(0.758741\pi\)
\(878\) −1123.27 + 4.46211i −1.27936 + 0.00508213i
\(879\) 0 0
\(880\) 454.801 559.840i 0.516819 0.636181i
\(881\) 402.080 696.424i 0.456391 0.790492i −0.542376 0.840136i \(-0.682475\pi\)
0.998767 + 0.0496435i \(0.0158085\pi\)
\(882\) 0 0
\(883\) 1490.79 860.707i 1.68832 0.974753i 0.732518 0.680747i \(-0.238345\pi\)
0.955804 0.294006i \(-0.0949885\pi\)
\(884\) −904.195 + 7.18379i −1.02285 + 0.00812646i
\(885\) 0 0
\(886\) 324.459 567.170i 0.366206 0.640147i
\(887\) 1284.01 + 226.405i 1.44759 + 0.255248i 0.841546 0.540186i \(-0.181646\pi\)
0.606040 + 0.795434i \(0.292757\pi\)
\(888\) 0 0
\(889\) −218.275 + 183.154i −0.245529 + 0.206023i
\(890\) −1606.29 1898.93i −1.80482 2.13363i
\(891\) 0 0
\(892\) 935.692 + 157.333i 1.04898 + 0.176383i
\(893\) −646.012 + 542.069i −0.723418 + 0.607020i
\(894\) 0 0
\(895\) 1137.29 + 200.535i 1.27071 + 0.224061i
\(896\) −384.894 625.803i −0.429569 0.698440i
\(897\) 0 0
\(898\) −249.087 + 299.257i −0.277380 + 0.333248i
\(899\) −359.221 + 207.396i −0.399578 + 0.230696i
\(900\) 0 0
\(901\) −461.075 + 798.606i −0.511737 + 0.886355i
\(902\) −738.256 + 272.029i −0.818466 + 0.301584i
\(903\) 0 0
\(904\) −515.309 84.5440i −0.570032 0.0935221i
\(905\) −115.138 96.6125i −0.127225 0.106754i
\(906\) 0 0
\(907\) 329.124 904.260i 0.362871 0.996979i −0.615139 0.788419i \(-0.710900\pi\)
0.978010 0.208560i \(-0.0668776\pi\)
\(908\) −687.163 + 832.269i −0.756787 + 0.916596i
\(909\) 0 0
\(910\) 890.813 + 320.228i 0.978915 + 0.351899i
\(911\) −145.176 + 25.5984i −0.159359 + 0.0280992i −0.252758 0.967529i \(-0.581338\pi\)
0.0933996 + 0.995629i \(0.470227\pi\)
\(912\) 0 0
\(913\) 77.1554 28.0823i 0.0845076 0.0307582i
\(914\) 535.545 312.040i 0.585935 0.341400i
\(915\) 0 0
\(916\) 351.553 + 597.886i 0.383791 + 0.652714i
\(917\) 995.808 1.08594
\(918\) 0 0
\(919\) 1373.16i 1.49419i 0.664720 + 0.747093i \(0.268551\pi\)
−0.664720 + 0.747093i \(0.731449\pi\)
\(920\) 1204.07 + 422.067i 1.30878 + 0.458768i
\(921\) 0 0
\(922\) −694.800 + 404.832i −0.753579 + 0.439080i
\(923\) −103.105 283.279i −0.111706 0.306911i
\(924\) 0 0
\(925\) 21.3979 + 121.353i 0.0231328 + 0.131193i
\(926\) 126.369 + 45.4270i 0.136468 + 0.0490572i
\(927\) 0 0
\(928\) 1245.52 + 194.197i 1.34216 + 0.209264i
\(929\) 1478.64 + 538.182i 1.59165 + 0.579313i 0.977695 0.210029i \(-0.0673557\pi\)
0.613954 + 0.789342i \(0.289578\pi\)
\(930\) 0 0
\(931\) 256.647 305.860i 0.275668 0.328528i
\(932\) 519.713 443.175i 0.557632 0.475509i
\(933\) 0 0
\(934\) 671.198 247.320i 0.718627 0.264796i
\(935\) 818.648 + 472.647i 0.875559 + 0.505504i
\(936\) 0 0
\(937\) −829.427 1436.61i −0.885195 1.53320i −0.845491 0.533990i \(-0.820692\pi\)
−0.0397040 0.999211i \(-0.512641\pi\)
\(938\) 355.248 426.799i 0.378729 0.455010i
\(939\) 0 0
\(940\) −1020.29 + 188.275i −1.08542 + 0.200293i
\(941\) 48.3337 274.114i 0.0513642 0.291301i −0.948295 0.317389i \(-0.897194\pi\)
0.999660 + 0.0260881i \(0.00830503\pi\)
\(942\) 0 0
\(943\) −894.597 1066.14i −0.948671 1.13058i
\(944\) −143.471 + 414.564i −0.151982 + 0.439157i
\(945\) 0 0
\(946\) 631.104 + 746.081i 0.667129 + 0.788670i
\(947\) 84.4477 + 100.641i 0.0891739 + 0.106273i 0.808786 0.588103i \(-0.200125\pi\)
−0.719612 + 0.694376i \(0.755680\pi\)
\(948\) 0 0
\(949\) −162.890 + 923.797i −0.171644 + 0.973442i
\(950\) −827.589 + 1446.67i −0.871147 + 1.52281i
\(951\) 0 0
\(952\) 730.160 627.656i 0.766975 0.659302i
\(953\) −107.243 185.750i −0.112532 0.194911i 0.804258 0.594280i \(-0.202563\pi\)
−0.916791 + 0.399368i \(0.869229\pi\)
\(954\) 0 0
\(955\) −1664.58 961.048i −1.74302 1.00633i
\(956\) −445.686 252.617i −0.466199 0.264244i
\(957\) 0 0
\(958\) −14.3449 + 0.0569839i −0.0149738 + 5.94822e-5i
\(959\) 184.986 220.458i 0.192895 0.229883i
\(960\) 0 0
\(961\) −798.858 290.761i −0.831278 0.302560i
\(962\) −78.0295 + 14.0785i −0.0811118 + 0.0146347i
\(963\) 0 0
\(964\) −619.206 + 230.960i −0.642330 + 0.239585i
\(965\) 19.5049 + 110.618i 0.0202123 + 0.114630i
\(966\) 0 0
\(967\) 551.943 + 1516.45i 0.570779 + 1.56820i 0.803277 + 0.595605i \(0.203088\pi\)
−0.232499 + 0.972597i \(0.574690\pi\)
\(968\) 243.747 + 645.644i 0.251805 + 0.666987i
\(969\) 0 0
\(970\) −636.154 109.567i −0.655828 0.112956i
\(971\) 981.080i 1.01038i 0.863008 + 0.505190i \(0.168578\pi\)
−0.863008 + 0.505190i \(0.831422\pi\)
\(972\) 0 0
\(973\) −1071.69 −1.10143
\(974\) 146.760 852.098i 0.150678 0.874844i
\(975\) 0 0
\(976\) 66.2743 119.122i 0.0679040 0.122052i
\(977\) −109.248 + 39.7629i −0.111820 + 0.0406990i −0.397324 0.917678i \(-0.630061\pi\)
0.285504 + 0.958377i \(0.407839\pi\)
\(978\) 0 0
\(979\) −943.631 + 166.388i −0.963872 + 0.169957i
\(980\) 460.248 171.670i 0.469641 0.175173i
\(981\) 0 0
\(982\) −63.4741 351.802i −0.0646376 0.358250i
\(983\) 318.542 875.187i 0.324051 0.890322i −0.665534 0.746368i \(-0.731796\pi\)
0.989584 0.143954i \(-0.0459818\pi\)
\(984\) 0 0
\(985\) 1227.12 + 1029.67i 1.24581 + 1.04536i
\(986\) 6.56256 + 1652.03i 0.00665574 + 1.67549i
\(987\) 0 0
\(988\) −932.967 528.810i −0.944298 0.535233i
\(989\) −864.296 + 1497.00i −0.873909 + 1.51365i
\(990\) 0 0
\(991\) −509.689 + 294.269i −0.514318 + 0.296941i −0.734607 0.678493i \(-0.762633\pi\)
0.220289 + 0.975435i \(0.429300\pi\)
\(992\) −174.236 288.402i −0.175641 0.290728i
\(993\) 0 0
\(994\) 278.634 + 159.397i 0.280316 + 0.160359i
\(995\) −39.6946 6.99924i −0.0398941 0.00703441i
\(996\) 0 0
\(997\) −89.4084 + 75.0226i −0.0896774 + 0.0752483i −0.686524 0.727107i \(-0.740864\pi\)
0.596847 + 0.802355i \(0.296420\pi\)
\(998\) 982.937 831.458i 0.984906 0.833124i
\(999\) 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 324.3.j.a.199.33 204
3.2 odd 2 108.3.j.a.103.2 yes 204
4.3 odd 2 inner 324.3.j.a.199.17 204
12.11 even 2 108.3.j.a.103.18 yes 204
27.11 odd 18 108.3.j.a.43.18 yes 204
27.16 even 9 inner 324.3.j.a.127.17 204
108.11 even 18 108.3.j.a.43.2 204
108.43 odd 18 inner 324.3.j.a.127.33 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.43.2 204 108.11 even 18
108.3.j.a.43.18 yes 204 27.11 odd 18
108.3.j.a.103.2 yes 204 3.2 odd 2
108.3.j.a.103.18 yes 204 12.11 even 2
324.3.j.a.127.17 204 27.16 even 9 inner
324.3.j.a.127.33 204 108.43 odd 18 inner
324.3.j.a.199.17 204 4.3 odd 2 inner
324.3.j.a.199.33 204 1.1 even 1 trivial