Properties

Label 225.3.r.b.208.1
Level $225$
Weight $3$
Character 225.208
Analytic conductor $6.131$
Analytic rank $0$
Dimension $80$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,3,Mod(28,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 225.r (of order \(20\), degree \(8\), 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: \(6.13080594811\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 208.1
Character \(\chi\) \(=\) 225.208
Dual form 225.3.r.b.172.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.93190 - 1.49388i) q^{2} +(4.01322 + 5.52372i) q^{4} +(0.890939 - 4.91998i) q^{5} +(4.34391 - 4.34391i) q^{7} +(-1.45557 - 9.19012i) q^{8} +O(q^{10})\) \(q+(-2.93190 - 1.49388i) q^{2} +(4.01322 + 5.52372i) q^{4} +(0.890939 - 4.91998i) q^{5} +(4.34391 - 4.34391i) q^{7} +(-1.45557 - 9.19012i) q^{8} +(-9.96199 + 13.0939i) q^{10} +(4.51369 + 13.8917i) q^{11} +(6.86423 - 3.49750i) q^{13} +(-19.2252 + 6.24664i) q^{14} +(-1.02182 + 3.14483i) q^{16} +(25.6357 - 4.06030i) q^{17} +(-1.24222 + 1.70977i) q^{19} +(30.7522 - 14.8237i) q^{20} +(7.51883 - 47.4720i) q^{22} +(2.15443 - 4.22830i) q^{23} +(-23.4125 - 8.76681i) q^{25} -25.3501 q^{26} +(41.4277 + 6.56150i) q^{28} +(-32.6254 - 44.9050i) q^{29} +(27.1558 + 19.7298i) q^{31} +(-18.6237 + 18.6237i) q^{32} +(-81.2269 - 26.3922i) q^{34} +(-17.5018 - 25.2421i) q^{35} +(-18.7363 - 36.7721i) q^{37} +(6.19627 - 3.15716i) q^{38} +(-46.5120 - 1.02645i) q^{40} +(1.20677 - 3.71404i) q^{41} +(-32.8976 - 32.8976i) q^{43} +(-58.6196 + 80.6829i) q^{44} +(-12.6331 + 9.17851i) q^{46} +(12.8776 - 81.3060i) q^{47} +11.2608i q^{49} +(55.5464 + 60.6787i) q^{50} +(46.8669 + 23.8799i) q^{52} +(81.1884 + 12.8590i) q^{53} +(72.3684 - 9.83061i) q^{55} +(-46.2440 - 33.5982i) q^{56} +(28.5718 + 180.395i) q^{58} +(10.7101 + 3.47991i) q^{59} +(-9.84864 - 30.3110i) q^{61} +(-50.1440 - 98.4132i) q^{62} +(95.0038 - 30.8686i) q^{64} +(-11.0920 - 36.8880i) q^{65} +(-0.351533 + 0.0556774i) q^{67} +(125.310 + 125.310i) q^{68} +(13.6049 + 100.153i) q^{70} +(-88.5525 + 64.3371i) q^{71} +(-20.1163 + 39.4805i) q^{73} +135.802i q^{74} -14.4296 q^{76} +(79.9515 + 40.7373i) q^{77} +(33.1447 + 45.6197i) q^{79} +(14.5621 + 7.82918i) q^{80} +(-9.08644 + 9.08644i) q^{82} +(2.71085 + 17.1156i) q^{83} +(2.86327 - 129.745i) q^{85} +(47.3074 + 145.597i) q^{86} +(121.097 - 61.7018i) q^{88} +(85.2857 - 27.7110i) q^{89} +(14.6248 - 45.0105i) q^{91} +(32.0022 - 5.06865i) q^{92} +(-159.217 + 219.143i) q^{94} +(7.30531 + 7.63503i) q^{95} +(1.37908 - 8.70714i) q^{97} +(16.8223 - 33.0156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.93190 1.49388i −1.46595 0.746939i −0.474850 0.880066i \(-0.657498\pi\)
−0.991099 + 0.133128i \(0.957498\pi\)
\(3\) 0 0
\(4\) 4.01322 + 5.52372i 1.00331 + 1.38093i
\(5\) 0.890939 4.91998i 0.178188 0.983996i
\(6\) 0 0
\(7\) 4.34391 4.34391i 0.620559 0.620559i −0.325115 0.945674i \(-0.605403\pi\)
0.945674 + 0.325115i \(0.105403\pi\)
\(8\) −1.45557 9.19012i −0.181946 1.14876i
\(9\) 0 0
\(10\) −9.96199 + 13.0939i −0.996199 + 1.30939i
\(11\) 4.51369 + 13.8917i 0.410336 + 1.26288i 0.916357 + 0.400362i \(0.131116\pi\)
−0.506021 + 0.862521i \(0.668884\pi\)
\(12\) 0 0
\(13\) 6.86423 3.49750i 0.528018 0.269039i −0.169595 0.985514i \(-0.554246\pi\)
0.697612 + 0.716475i \(0.254246\pi\)
\(14\) −19.2252 + 6.24664i −1.37323 + 0.446189i
\(15\) 0 0
\(16\) −1.02182 + 3.14483i −0.0638636 + 0.196552i
\(17\) 25.6357 4.06030i 1.50798 0.238841i 0.652945 0.757405i \(-0.273533\pi\)
0.855039 + 0.518564i \(0.173533\pi\)
\(18\) 0 0
\(19\) −1.24222 + 1.70977i −0.0653802 + 0.0899881i −0.840455 0.541881i \(-0.817712\pi\)
0.775075 + 0.631870i \(0.217712\pi\)
\(20\) 30.7522 14.8237i 1.53761 0.741184i
\(21\) 0 0
\(22\) 7.51883 47.4720i 0.341765 2.15782i
\(23\) 2.15443 4.22830i 0.0936708 0.183839i −0.839417 0.543488i \(-0.817103\pi\)
0.933088 + 0.359649i \(0.117103\pi\)
\(24\) 0 0
\(25\) −23.4125 8.76681i −0.936498 0.350672i
\(26\) −25.3501 −0.975003
\(27\) 0 0
\(28\) 41.4277 + 6.56150i 1.47956 + 0.234339i
\(29\) −32.6254 44.9050i −1.12501 1.54845i −0.797208 0.603704i \(-0.793691\pi\)
−0.327806 0.944745i \(-0.606309\pi\)
\(30\) 0 0
\(31\) 27.1558 + 19.7298i 0.875993 + 0.636446i 0.932188 0.361974i \(-0.117897\pi\)
−0.0561957 + 0.998420i \(0.517897\pi\)
\(32\) −18.6237 + 18.6237i −0.581992 + 0.581992i
\(33\) 0 0
\(34\) −81.2269 26.3922i −2.38903 0.776242i
\(35\) −17.5018 25.2421i −0.500052 0.721204i
\(36\) 0 0
\(37\) −18.7363 36.7721i −0.506388 0.993842i −0.992763 0.120092i \(-0.961681\pi\)
0.486375 0.873750i \(-0.338319\pi\)
\(38\) 6.19627 3.15716i 0.163060 0.0830831i
\(39\) 0 0
\(40\) −46.5120 1.02645i −1.16280 0.0256613i
\(41\) 1.20677 3.71404i 0.0294333 0.0905864i −0.935261 0.353960i \(-0.884835\pi\)
0.964694 + 0.263373i \(0.0848350\pi\)
\(42\) 0 0
\(43\) −32.8976 32.8976i −0.765060 0.765060i 0.212172 0.977232i \(-0.431946\pi\)
−0.977232 + 0.212172i \(0.931946\pi\)
\(44\) −58.6196 + 80.6829i −1.33226 + 1.83370i
\(45\) 0 0
\(46\) −12.6331 + 9.17851i −0.274633 + 0.199533i
\(47\) 12.8776 81.3060i 0.273991 1.72991i −0.339846 0.940481i \(-0.610375\pi\)
0.613837 0.789433i \(-0.289625\pi\)
\(48\) 0 0
\(49\) 11.2608i 0.229813i
\(50\) 55.5464 + 60.6787i 1.11093 + 1.21357i
\(51\) 0 0
\(52\) 46.8669 + 23.8799i 0.901287 + 0.459229i
\(53\) 81.1884 + 12.8590i 1.53186 + 0.242622i 0.864697 0.502293i \(-0.167510\pi\)
0.667159 + 0.744916i \(0.267510\pi\)
\(54\) 0 0
\(55\) 72.3684 9.83061i 1.31579 0.178738i
\(56\) −46.2440 33.5982i −0.825785 0.599968i
\(57\) 0 0
\(58\) 28.5718 + 180.395i 0.492618 + 3.11026i
\(59\) 10.7101 + 3.47991i 0.181526 + 0.0589815i 0.398370 0.917225i \(-0.369576\pi\)
−0.216843 + 0.976206i \(0.569576\pi\)
\(60\) 0 0
\(61\) −9.84864 30.3110i −0.161453 0.496902i 0.837304 0.546737i \(-0.184130\pi\)
−0.998757 + 0.0498356i \(0.984130\pi\)
\(62\) −50.1440 98.4132i −0.808775 1.58731i
\(63\) 0 0
\(64\) 95.0038 30.8686i 1.48443 0.482322i
\(65\) −11.0920 36.8880i −0.170647 0.567507i
\(66\) 0 0
\(67\) −0.351533 + 0.0556774i −0.00524677 + 0.000831006i −0.159057 0.987269i \(-0.550845\pi\)
0.153811 + 0.988100i \(0.450845\pi\)
\(68\) 125.310 + 125.310i 1.84279 + 1.84279i
\(69\) 0 0
\(70\) 13.6049 + 100.153i 0.194356 + 1.43076i
\(71\) −88.5525 + 64.3371i −1.24722 + 0.906157i −0.998057 0.0623051i \(-0.980155\pi\)
−0.249161 + 0.968462i \(0.580155\pi\)
\(72\) 0 0
\(73\) −20.1163 + 39.4805i −0.275566 + 0.540828i −0.986764 0.162163i \(-0.948153\pi\)
0.711198 + 0.702992i \(0.248153\pi\)
\(74\) 135.802i 1.83516i
\(75\) 0 0
\(76\) −14.4296 −0.189864
\(77\) 79.9515 + 40.7373i 1.03833 + 0.529056i
\(78\) 0 0
\(79\) 33.1447 + 45.6197i 0.419553 + 0.577465i 0.965516 0.260344i \(-0.0838361\pi\)
−0.545963 + 0.837809i \(0.683836\pi\)
\(80\) 14.5621 + 7.82918i 0.182027 + 0.0978648i
\(81\) 0 0
\(82\) −9.08644 + 9.08644i −0.110810 + 0.110810i
\(83\) 2.71085 + 17.1156i 0.0326608 + 0.206212i 0.998622 0.0524736i \(-0.0167105\pi\)
−0.965961 + 0.258686i \(0.916711\pi\)
\(84\) 0 0
\(85\) 2.86327 129.745i 0.0336855 1.52641i
\(86\) 47.3074 + 145.597i 0.550087 + 1.69299i
\(87\) 0 0
\(88\) 121.097 61.7018i 1.37610 0.701156i
\(89\) 85.2857 27.7110i 0.958267 0.311360i 0.212196 0.977227i \(-0.431938\pi\)
0.746070 + 0.665867i \(0.231938\pi\)
\(90\) 0 0
\(91\) 14.6248 45.0105i 0.160712 0.494621i
\(92\) 32.0022 5.06865i 0.347850 0.0550940i
\(93\) 0 0
\(94\) −159.217 + 219.143i −1.69380 + 2.33131i
\(95\) 7.30531 + 7.63503i 0.0768981 + 0.0803687i
\(96\) 0 0
\(97\) 1.37908 8.70714i 0.0142173 0.0897643i −0.979559 0.201155i \(-0.935531\pi\)
0.993777 + 0.111391i \(0.0355305\pi\)
\(98\) 16.8223 33.0156i 0.171656 0.336894i
\(99\) 0 0
\(100\) −45.5339 164.507i −0.455339 1.64507i
\(101\) −4.54639 −0.0450138 −0.0225069 0.999747i \(-0.507165\pi\)
−0.0225069 + 0.999747i \(0.507165\pi\)
\(102\) 0 0
\(103\) 98.1209 + 15.5408i 0.952630 + 0.150882i 0.613357 0.789806i \(-0.289819\pi\)
0.339273 + 0.940688i \(0.389819\pi\)
\(104\) −42.1338 57.9922i −0.405133 0.557618i
\(105\) 0 0
\(106\) −218.826 158.987i −2.06440 1.49987i
\(107\) −58.0204 + 58.0204i −0.542247 + 0.542247i −0.924187 0.381940i \(-0.875256\pi\)
0.381940 + 0.924187i \(0.375256\pi\)
\(108\) 0 0
\(109\) 77.8317 + 25.2890i 0.714052 + 0.232010i 0.643442 0.765494i \(-0.277506\pi\)
0.0706096 + 0.997504i \(0.477506\pi\)
\(110\) −226.863 79.2872i −2.06239 0.720793i
\(111\) 0 0
\(112\) 9.22219 + 18.0996i 0.0823410 + 0.161603i
\(113\) −168.661 + 85.9369i −1.49257 + 0.760504i −0.994310 0.106523i \(-0.966028\pi\)
−0.498262 + 0.867027i \(0.666028\pi\)
\(114\) 0 0
\(115\) −18.8837 14.3669i −0.164206 0.124930i
\(116\) 117.110 360.428i 1.00957 3.10713i
\(117\) 0 0
\(118\) −26.2022 26.2022i −0.222053 0.222053i
\(119\) 93.7218 128.997i 0.787578 1.08401i
\(120\) 0 0
\(121\) −74.7153 + 54.2839i −0.617482 + 0.448627i
\(122\) −16.4057 + 103.581i −0.134473 + 0.849028i
\(123\) 0 0
\(124\) 229.181i 1.84823i
\(125\) −63.9916 + 107.378i −0.511933 + 0.859025i
\(126\) 0 0
\(127\) −99.6529 50.7757i −0.784668 0.399808i 0.0152756 0.999883i \(-0.495137\pi\)
−0.799944 + 0.600075i \(0.795137\pi\)
\(128\) −220.601 34.9397i −1.72344 0.272967i
\(129\) 0 0
\(130\) −22.5854 + 124.722i −0.173734 + 0.959399i
\(131\) 84.3598 + 61.2910i 0.643968 + 0.467870i 0.861211 0.508247i \(-0.169706\pi\)
−0.217243 + 0.976118i \(0.569706\pi\)
\(132\) 0 0
\(133\) 2.03100 + 12.8232i 0.0152707 + 0.0964152i
\(134\) 1.11384 + 0.361907i 0.00831221 + 0.00270080i
\(135\) 0 0
\(136\) −74.6293 229.685i −0.548745 1.68886i
\(137\) −69.3960 136.197i −0.506540 0.994141i −0.992738 0.120293i \(-0.961617\pi\)
0.486198 0.873849i \(-0.338383\pi\)
\(138\) 0 0
\(139\) 149.736 48.6523i 1.07724 0.350016i 0.283937 0.958843i \(-0.408359\pi\)
0.793303 + 0.608827i \(0.208359\pi\)
\(140\) 69.1920 197.977i 0.494228 1.41412i
\(141\) 0 0
\(142\) 355.739 56.3435i 2.50520 0.396785i
\(143\) 79.5693 + 79.5693i 0.556429 + 0.556429i
\(144\) 0 0
\(145\) −249.999 + 120.509i −1.72413 + 0.831095i
\(146\) 117.958 85.7015i 0.807931 0.586996i
\(147\) 0 0
\(148\) 127.926 251.069i 0.864365 1.69641i
\(149\) 80.4685i 0.540057i −0.962852 0.270028i \(-0.912967\pi\)
0.962852 0.270028i \(-0.0870331\pi\)
\(150\) 0 0
\(151\) 187.435 1.24129 0.620647 0.784090i \(-0.286870\pi\)
0.620647 + 0.784090i \(0.286870\pi\)
\(152\) 17.5212 + 8.92749i 0.115271 + 0.0587335i
\(153\) 0 0
\(154\) −173.553 238.875i −1.12697 1.55114i
\(155\) 121.265 116.028i 0.782352 0.748567i
\(156\) 0 0
\(157\) −90.0864 + 90.0864i −0.573798 + 0.573798i −0.933188 0.359389i \(-0.882985\pi\)
0.359389 + 0.933188i \(0.382985\pi\)
\(158\) −29.0266 183.267i −0.183712 1.15991i
\(159\) 0 0
\(160\) 75.0358 + 108.221i 0.468974 + 0.676382i
\(161\) −9.00873 27.7260i −0.0559549 0.172211i
\(162\) 0 0
\(163\) −30.5160 + 15.5487i −0.187215 + 0.0953908i −0.545086 0.838380i \(-0.683503\pi\)
0.357871 + 0.933771i \(0.383503\pi\)
\(164\) 25.3584 8.23943i 0.154624 0.0502404i
\(165\) 0 0
\(166\) 17.6207 54.2310i 0.106149 0.326693i
\(167\) 58.2426 9.22473i 0.348758 0.0552379i 0.0204021 0.999792i \(-0.493505\pi\)
0.328356 + 0.944554i \(0.393505\pi\)
\(168\) 0 0
\(169\) −64.4505 + 88.7086i −0.381364 + 0.524903i
\(170\) −202.218 + 376.121i −1.18951 + 2.21248i
\(171\) 0 0
\(172\) 49.6919 313.742i 0.288907 1.82408i
\(173\) −35.3231 + 69.3255i −0.204180 + 0.400726i −0.970276 0.242000i \(-0.922197\pi\)
0.766096 + 0.642726i \(0.222197\pi\)
\(174\) 0 0
\(175\) −139.784 + 63.6194i −0.798765 + 0.363539i
\(176\) −48.2993 −0.274428
\(177\) 0 0
\(178\) −291.446 46.1605i −1.63734 0.259329i
\(179\) 89.6932 + 123.452i 0.501080 + 0.689677i 0.982383 0.186877i \(-0.0598366\pi\)
−0.481304 + 0.876554i \(0.659837\pi\)
\(180\) 0 0
\(181\) −26.4190 19.1945i −0.145961 0.106047i 0.512408 0.858742i \(-0.328753\pi\)
−0.658369 + 0.752695i \(0.728753\pi\)
\(182\) −110.119 + 110.119i −0.605047 + 0.605047i
\(183\) 0 0
\(184\) −41.9945 13.6449i −0.228231 0.0741568i
\(185\) −197.611 + 59.4207i −1.06817 + 0.321193i
\(186\) 0 0
\(187\) 172.116 + 337.797i 0.920408 + 1.80640i
\(188\) 500.792 255.166i 2.66379 1.35727i
\(189\) 0 0
\(190\) −10.0127 33.2984i −0.0526982 0.175255i
\(191\) −15.5033 + 47.7143i −0.0811692 + 0.249813i −0.983403 0.181434i \(-0.941926\pi\)
0.902234 + 0.431247i \(0.141926\pi\)
\(192\) 0 0
\(193\) 49.2763 + 49.2763i 0.255318 + 0.255318i 0.823147 0.567829i \(-0.192216\pi\)
−0.567829 + 0.823147i \(0.692216\pi\)
\(194\) −17.0507 + 23.4683i −0.0878902 + 0.120971i
\(195\) 0 0
\(196\) −62.2017 + 45.1922i −0.317356 + 0.230572i
\(197\) 54.5847 344.634i 0.277080 1.74941i −0.320174 0.947359i \(-0.603741\pi\)
0.597253 0.802053i \(-0.296259\pi\)
\(198\) 0 0
\(199\) 39.9002i 0.200504i −0.994962 0.100252i \(-0.968035\pi\)
0.994962 0.100252i \(-0.0319648\pi\)
\(200\) −46.4895 + 227.924i −0.232448 + 1.13962i
\(201\) 0 0
\(202\) 13.3296 + 6.79175i 0.0659879 + 0.0336225i
\(203\) −336.786 53.3416i −1.65904 0.262766i
\(204\) 0 0
\(205\) −17.1979 9.24625i −0.0838920 0.0451037i
\(206\) −264.464 192.145i −1.28381 0.932741i
\(207\) 0 0
\(208\) 3.98506 + 25.1607i 0.0191589 + 0.120965i
\(209\) −29.3587 9.53923i −0.140472 0.0456422i
\(210\) 0 0
\(211\) 59.1092 + 181.919i 0.280138 + 0.862177i 0.987814 + 0.155640i \(0.0497439\pi\)
−0.707676 + 0.706538i \(0.750256\pi\)
\(212\) 254.797 + 500.068i 1.20187 + 2.35881i
\(213\) 0 0
\(214\) 256.785 83.4346i 1.19993 0.389882i
\(215\) −191.165 + 132.546i −0.889141 + 0.616492i
\(216\) 0 0
\(217\) 203.667 32.2577i 0.938557 0.148653i
\(218\) −190.416 190.416i −0.873467 0.873467i
\(219\) 0 0
\(220\) 344.732 + 360.291i 1.56696 + 1.63769i
\(221\) 161.769 117.532i 0.731985 0.531818i
\(222\) 0 0
\(223\) 82.3253 161.572i 0.369172 0.724540i −0.629449 0.777042i \(-0.716719\pi\)
0.998621 + 0.0525014i \(0.0167194\pi\)
\(224\) 161.800i 0.722320i
\(225\) 0 0
\(226\) 622.875 2.75608
\(227\) 266.514 + 135.796i 1.17407 + 0.598220i 0.928563 0.371174i \(-0.121045\pi\)
0.245509 + 0.969394i \(0.421045\pi\)
\(228\) 0 0
\(229\) −128.483 176.841i −0.561060 0.772232i 0.430401 0.902638i \(-0.358372\pi\)
−0.991461 + 0.130405i \(0.958372\pi\)
\(230\) 33.9027 + 70.3323i 0.147403 + 0.305792i
\(231\) 0 0
\(232\) −365.194 + 365.194i −1.57411 + 1.57411i
\(233\) 28.5917 + 180.521i 0.122711 + 0.774767i 0.969905 + 0.243484i \(0.0782902\pi\)
−0.847194 + 0.531284i \(0.821710\pi\)
\(234\) 0 0
\(235\) −388.551 135.796i −1.65341 0.577856i
\(236\) 23.7598 + 73.1250i 0.100677 + 0.309852i
\(237\) 0 0
\(238\) −467.488 + 238.197i −1.96424 + 1.00083i
\(239\) 434.275 141.105i 1.81705 0.590396i 0.817149 0.576427i \(-0.195553\pi\)
0.999902 0.0139688i \(-0.00444655\pi\)
\(240\) 0 0
\(241\) −123.592 + 380.378i −0.512831 + 1.57833i 0.274363 + 0.961626i \(0.411533\pi\)
−0.787194 + 0.616706i \(0.788467\pi\)
\(242\) 300.151 47.5393i 1.24029 0.196443i
\(243\) 0 0
\(244\) 127.905 176.046i 0.524200 0.721499i
\(245\) 55.4031 + 10.0327i 0.226135 + 0.0409499i
\(246\) 0 0
\(247\) −2.54698 + 16.0810i −0.0103116 + 0.0651051i
\(248\) 141.792 278.283i 0.571743 1.12211i
\(249\) 0 0
\(250\) 348.027 219.226i 1.39211 0.876905i
\(251\) −153.360 −0.610995 −0.305497 0.952193i \(-0.598823\pi\)
−0.305497 + 0.952193i \(0.598823\pi\)
\(252\) 0 0
\(253\) 68.4628 + 10.8434i 0.270604 + 0.0428595i
\(254\) 216.319 + 297.738i 0.851652 + 1.17220i
\(255\) 0 0
\(256\) 271.323 + 197.128i 1.05986 + 0.770030i
\(257\) −208.413 + 208.413i −0.810947 + 0.810947i −0.984776 0.173829i \(-0.944386\pi\)
0.173829 + 0.984776i \(0.444386\pi\)
\(258\) 0 0
\(259\) −241.124 78.3459i −0.930981 0.302494i
\(260\) 159.244 209.309i 0.612478 0.805034i
\(261\) 0 0
\(262\) −155.773 305.722i −0.594554 1.16688i
\(263\) 9.36797 4.77322i 0.0356197 0.0181491i −0.436090 0.899903i \(-0.643637\pi\)
0.471710 + 0.881754i \(0.343637\pi\)
\(264\) 0 0
\(265\) 135.600 387.989i 0.511698 1.46411i
\(266\) 13.2016 40.6305i 0.0496302 0.152746i
\(267\) 0 0
\(268\) −1.71833 1.71833i −0.00641167 0.00641167i
\(269\) −270.816 + 372.747i −1.00675 + 1.38568i −0.0856627 + 0.996324i \(0.527301\pi\)
−0.921089 + 0.389351i \(0.872699\pi\)
\(270\) 0 0
\(271\) 120.422 87.4918i 0.444362 0.322848i −0.343004 0.939334i \(-0.611444\pi\)
0.787366 + 0.616486i \(0.211444\pi\)
\(272\) −13.4261 + 84.7689i −0.0493606 + 0.311651i
\(273\) 0 0
\(274\) 502.986i 1.83572i
\(275\) 16.1095 364.810i 0.0585798 1.32658i
\(276\) 0 0
\(277\) −229.696 117.036i −0.829229 0.422513i −0.0127710 0.999918i \(-0.504065\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(278\) −511.692 81.0441i −1.84062 0.291526i
\(279\) 0 0
\(280\) −206.503 + 197.586i −0.737511 + 0.705663i
\(281\) 64.5890 + 46.9267i 0.229854 + 0.166999i 0.696751 0.717313i \(-0.254628\pi\)
−0.466897 + 0.884312i \(0.654628\pi\)
\(282\) 0 0
\(283\) 5.52224 + 34.8661i 0.0195132 + 0.123202i 0.995522 0.0945291i \(-0.0301345\pi\)
−0.976009 + 0.217731i \(0.930135\pi\)
\(284\) −710.761 230.940i −2.50268 0.813170i
\(285\) 0 0
\(286\) −114.422 352.156i −0.400078 1.23131i
\(287\) −10.8914 21.3756i −0.0379491 0.0744793i
\(288\) 0 0
\(289\) 365.849 118.871i 1.26591 0.411320i
\(290\) 912.998 + 20.1485i 3.14827 + 0.0694775i
\(291\) 0 0
\(292\) −298.810 + 47.3269i −1.02332 + 0.162078i
\(293\) 16.7371 + 16.7371i 0.0571231 + 0.0571231i 0.735091 0.677968i \(-0.237139\pi\)
−0.677968 + 0.735091i \(0.737139\pi\)
\(294\) 0 0
\(295\) 26.6631 49.5929i 0.0903834 0.168112i
\(296\) −310.668 + 225.714i −1.04955 + 0.762546i
\(297\) 0 0
\(298\) −120.210 + 235.925i −0.403389 + 0.791696i
\(299\) 36.5592i 0.122271i
\(300\) 0 0
\(301\) −285.809 −0.949530
\(302\) −549.541 280.005i −1.81967 0.927170i
\(303\) 0 0
\(304\) −4.10763 5.65367i −0.0135119 0.0185976i
\(305\) −157.904 + 21.4499i −0.517718 + 0.0703275i
\(306\) 0 0
\(307\) 14.0410 14.0410i 0.0457363 0.0457363i −0.683869 0.729605i \(-0.739704\pi\)
0.729605 + 0.683869i \(0.239704\pi\)
\(308\) 95.8413 + 605.118i 0.311173 + 1.96467i
\(309\) 0 0
\(310\) −528.867 + 159.028i −1.70602 + 0.512992i
\(311\) 59.5063 + 183.142i 0.191339 + 0.588880i 1.00000 0.000605266i \(0.000192662\pi\)
−0.808661 + 0.588275i \(0.799807\pi\)
\(312\) 0 0
\(313\) 141.673 72.1860i 0.452629 0.230626i −0.212787 0.977099i \(-0.568254\pi\)
0.665416 + 0.746473i \(0.268254\pi\)
\(314\) 398.702 129.546i 1.26975 0.412567i
\(315\) 0 0
\(316\) −118.974 + 366.164i −0.376500 + 1.15875i
\(317\) −378.338 + 59.9228i −1.19349 + 0.189031i −0.721401 0.692518i \(-0.756501\pi\)
−0.472093 + 0.881549i \(0.656501\pi\)
\(318\) 0 0
\(319\) 476.547 655.911i 1.49388 2.05615i
\(320\) −67.2304 494.919i −0.210095 1.54662i
\(321\) 0 0
\(322\) −15.0066 + 94.7479i −0.0466043 + 0.294248i
\(323\) −24.9031 + 48.8751i −0.0770994 + 0.151316i
\(324\) 0 0
\(325\) −191.370 + 21.7076i −0.588832 + 0.0667928i
\(326\) 112.698 0.345699
\(327\) 0 0
\(328\) −35.8890 5.68426i −0.109418 0.0173301i
\(329\) −297.247 409.125i −0.903486 1.24354i
\(330\) 0 0
\(331\) −450.680 327.439i −1.36157 0.989240i −0.998343 0.0575405i \(-0.981674\pi\)
−0.363229 0.931700i \(-0.618326\pi\)
\(332\) −83.6628 + 83.6628i −0.251996 + 0.251996i
\(333\) 0 0
\(334\) −184.542 59.9614i −0.552521 0.179525i
\(335\) −0.0392630 + 1.77914i −0.000117203 + 0.00531088i
\(336\) 0 0
\(337\) 86.1758 + 169.130i 0.255715 + 0.501868i 0.982799 0.184680i \(-0.0591250\pi\)
−0.727084 + 0.686548i \(0.759125\pi\)
\(338\) 321.482 163.803i 0.951131 0.484625i
\(339\) 0 0
\(340\) 728.165 504.878i 2.14166 1.48494i
\(341\) −151.508 + 466.295i −0.444306 + 1.36743i
\(342\) 0 0
\(343\) 261.768 + 261.768i 0.763172 + 0.763172i
\(344\) −254.448 + 350.217i −0.739674 + 1.01807i
\(345\) 0 0
\(346\) 207.128 150.487i 0.598635 0.434934i
\(347\) −23.6780 + 149.497i −0.0682362 + 0.430827i 0.929793 + 0.368082i \(0.119985\pi\)
−0.998030 + 0.0627447i \(0.980015\pi\)
\(348\) 0 0
\(349\) 124.533i 0.356829i 0.983955 + 0.178415i \(0.0570968\pi\)
−0.983955 + 0.178415i \(0.942903\pi\)
\(350\) 504.872 + 22.2944i 1.44249 + 0.0636982i
\(351\) 0 0
\(352\) −342.777 174.654i −0.973800 0.496176i
\(353\) 367.421 + 58.1938i 1.04085 + 0.164855i 0.653383 0.757027i \(-0.273349\pi\)
0.387470 + 0.921882i \(0.373349\pi\)
\(354\) 0 0
\(355\) 237.643 + 492.997i 0.669416 + 1.38872i
\(356\) 495.338 + 359.884i 1.39140 + 1.01091i
\(357\) 0 0
\(358\) −78.5492 495.940i −0.219411 1.38531i
\(359\) 232.340 + 75.4918i 0.647186 + 0.210283i 0.614173 0.789171i \(-0.289490\pi\)
0.0330130 + 0.999455i \(0.489490\pi\)
\(360\) 0 0
\(361\) 110.175 + 339.084i 0.305194 + 0.939290i
\(362\) 48.7835 + 95.7430i 0.134761 + 0.264483i
\(363\) 0 0
\(364\) 307.318 99.8537i 0.844280 0.274323i
\(365\) 176.321 + 134.147i 0.483071 + 0.367525i
\(366\) 0 0
\(367\) −170.553 + 27.0130i −0.464723 + 0.0736049i −0.384405 0.923164i \(-0.625593\pi\)
−0.0803176 + 0.996769i \(0.525593\pi\)
\(368\) 11.0959 + 11.0959i 0.0301518 + 0.0301518i
\(369\) 0 0
\(370\) 668.143 + 120.991i 1.80579 + 0.327004i
\(371\) 408.534 296.817i 1.10117 0.800046i
\(372\) 0 0
\(373\) −17.9357 + 35.2007i −0.0480849 + 0.0943718i −0.913799 0.406168i \(-0.866865\pi\)
0.865714 + 0.500539i \(0.166865\pi\)
\(374\) 1247.51i 3.33558i
\(375\) 0 0
\(376\) −765.956 −2.03712
\(377\) −381.004 194.131i −1.01062 0.514937i
\(378\) 0 0
\(379\) −52.2973 71.9811i −0.137988 0.189924i 0.734431 0.678684i \(-0.237449\pi\)
−0.872418 + 0.488760i \(0.837449\pi\)
\(380\) −12.8559 + 70.9936i −0.0338314 + 0.186825i
\(381\) 0 0
\(382\) 116.734 116.734i 0.305585 0.305585i
\(383\) 50.0372 + 315.922i 0.130645 + 0.824863i 0.962779 + 0.270288i \(0.0871190\pi\)
−0.832134 + 0.554575i \(0.812881\pi\)
\(384\) 0 0
\(385\) 271.659 357.066i 0.705608 0.927443i
\(386\) −70.8604 218.086i −0.183576 0.564989i
\(387\) 0 0
\(388\) 53.6304 27.3260i 0.138223 0.0704279i
\(389\) 77.7419 25.2599i 0.199851 0.0649354i −0.207381 0.978260i \(-0.566494\pi\)
0.407232 + 0.913325i \(0.366494\pi\)
\(390\) 0 0
\(391\) 38.0621 117.143i 0.0973456 0.299599i
\(392\) 103.488 16.3909i 0.264001 0.0418136i
\(393\) 0 0
\(394\) −674.878 + 928.889i −1.71289 + 2.35759i
\(395\) 253.978 122.427i 0.642983 0.309941i
\(396\) 0 0
\(397\) 8.70402 54.9550i 0.0219245 0.138426i −0.974298 0.225263i \(-0.927676\pi\)
0.996223 + 0.0868371i \(0.0276760\pi\)
\(398\) −59.6060 + 116.983i −0.149764 + 0.293928i
\(399\) 0 0
\(400\) 51.4934 64.6702i 0.128734 0.161675i
\(401\) −706.598 −1.76209 −0.881045 0.473032i \(-0.843160\pi\)
−0.881045 + 0.473032i \(0.843160\pi\)
\(402\) 0 0
\(403\) 255.409 + 40.4527i 0.633768 + 0.100379i
\(404\) −18.2457 25.1130i −0.0451626 0.0621609i
\(405\) 0 0
\(406\) 907.735 + 659.508i 2.23580 + 1.62440i
\(407\) 426.258 426.258i 1.04732 1.04732i
\(408\) 0 0
\(409\) 225.857 + 73.3853i 0.552217 + 0.179426i 0.571816 0.820382i \(-0.306239\pi\)
−0.0195993 + 0.999808i \(0.506239\pi\)
\(410\) 36.6096 + 52.8006i 0.0892918 + 0.128782i
\(411\) 0 0
\(412\) 307.938 + 604.362i 0.747421 + 1.46690i
\(413\) 61.6400 31.4071i 0.149249 0.0760463i
\(414\) 0 0
\(415\) 86.6238 + 1.91166i 0.208732 + 0.00460640i
\(416\) −62.7011 + 192.974i −0.150724 + 0.463880i
\(417\) 0 0
\(418\) 71.8264 + 71.8264i 0.171833 + 0.171833i
\(419\) −140.550 + 193.451i −0.335443 + 0.461697i −0.943103 0.332500i \(-0.892108\pi\)
0.607661 + 0.794197i \(0.292108\pi\)
\(420\) 0 0
\(421\) −392.951 + 285.496i −0.933375 + 0.678137i −0.946817 0.321773i \(-0.895721\pi\)
0.0134415 + 0.999910i \(0.495721\pi\)
\(422\) 98.4630 621.671i 0.233325 1.47315i
\(423\) 0 0
\(424\) 764.848i 1.80389i
\(425\) −635.791 129.682i −1.49598 0.305134i
\(426\) 0 0
\(427\) −174.450 88.8867i −0.408548 0.208166i
\(428\) −553.338 87.6401i −1.29285 0.204767i
\(429\) 0 0
\(430\) 758.484 103.033i 1.76392 0.239613i
\(431\) 224.130 + 162.840i 0.520023 + 0.377819i 0.816613 0.577186i \(-0.195849\pi\)
−0.296589 + 0.955005i \(0.595849\pi\)
\(432\) 0 0
\(433\) 78.8616 + 497.912i 0.182128 + 1.14991i 0.894154 + 0.447760i \(0.147778\pi\)
−0.712026 + 0.702154i \(0.752222\pi\)
\(434\) −645.320 209.677i −1.48691 0.483127i
\(435\) 0 0
\(436\) 172.666 + 531.411i 0.396023 + 1.21883i
\(437\) 4.55316 + 8.93609i 0.0104191 + 0.0204487i
\(438\) 0 0
\(439\) −644.964 + 209.562i −1.46917 + 0.477361i −0.930856 0.365385i \(-0.880937\pi\)
−0.538310 + 0.842747i \(0.680937\pi\)
\(440\) −195.682 650.765i −0.444732 1.47901i
\(441\) 0 0
\(442\) −649.867 + 102.929i −1.47029 + 0.232871i
\(443\) −229.580 229.580i −0.518238 0.518238i 0.398800 0.917038i \(-0.369427\pi\)
−0.917038 + 0.398800i \(0.869427\pi\)
\(444\) 0 0
\(445\) −60.3533 444.293i −0.135625 0.998412i
\(446\) −482.739 + 350.730i −1.08237 + 0.786391i
\(447\) 0 0
\(448\) 278.598 546.779i 0.621870 1.22049i
\(449\) 72.7747i 0.162082i 0.996711 + 0.0810409i \(0.0258244\pi\)
−0.996711 + 0.0810409i \(0.974176\pi\)
\(450\) 0 0
\(451\) 57.0414 0.126478
\(452\) −1151.56 586.751i −2.54771 1.29812i
\(453\) 0 0
\(454\) −578.531 796.280i −1.27430 1.75392i
\(455\) −208.421 112.055i −0.458068 0.246275i
\(456\) 0 0
\(457\) 209.874 209.874i 0.459243 0.459243i −0.439164 0.898407i \(-0.644725\pi\)
0.898407 + 0.439164i \(0.144725\pi\)
\(458\) 112.519 + 710.418i 0.245675 + 1.55113i
\(459\) 0 0
\(460\) 3.57435 161.966i 0.00777032 0.352100i
\(461\) −41.7392 128.460i −0.0905406 0.278655i 0.895525 0.445011i \(-0.146800\pi\)
−0.986066 + 0.166355i \(0.946800\pi\)
\(462\) 0 0
\(463\) −657.694 + 335.112i −1.42051 + 0.723784i −0.984373 0.176099i \(-0.943652\pi\)
−0.436133 + 0.899882i \(0.643652\pi\)
\(464\) 174.556 56.7167i 0.376198 0.122234i
\(465\) 0 0
\(466\) 185.848 571.981i 0.398815 1.22743i
\(467\) 193.470 30.6426i 0.414282 0.0656158i 0.0541855 0.998531i \(-0.482744\pi\)
0.360096 + 0.932915i \(0.382744\pi\)
\(468\) 0 0
\(469\) −1.28517 + 1.76889i −0.00274024 + 0.00377162i
\(470\) 936.328 + 978.588i 1.99219 + 2.08210i
\(471\) 0 0
\(472\) 16.3915 103.492i 0.0347278 0.219263i
\(473\) 308.514 605.494i 0.652250 1.28011i
\(474\) 0 0
\(475\) 44.0728 29.1397i 0.0927848 0.0613467i
\(476\) 1088.67 2.28712
\(477\) 0 0
\(478\) −1484.04 235.049i −3.10469 0.491735i
\(479\) 84.2910 + 116.017i 0.175973 + 0.242206i 0.887888 0.460060i \(-0.152172\pi\)
−0.711915 + 0.702265i \(0.752172\pi\)
\(480\) 0 0
\(481\) −257.221 186.882i −0.534763 0.388528i
\(482\) 930.598 930.598i 1.93070 1.93070i
\(483\) 0 0
\(484\) −599.698 194.854i −1.23905 0.402590i
\(485\) −41.6103 14.5426i −0.0857944 0.0299847i
\(486\) 0 0
\(487\) 152.898 + 300.080i 0.313959 + 0.616180i 0.993026 0.117897i \(-0.0376152\pi\)
−0.679067 + 0.734077i \(0.737615\pi\)
\(488\) −264.226 + 134.630i −0.541447 + 0.275881i
\(489\) 0 0
\(490\) −147.449 112.180i −0.300916 0.228939i
\(491\) −196.552 + 604.925i −0.400310 + 1.23203i 0.524439 + 0.851448i \(0.324275\pi\)
−0.924748 + 0.380579i \(0.875725\pi\)
\(492\) 0 0
\(493\) −1018.70 1018.70i −2.06634 2.06634i
\(494\) 31.4905 43.3429i 0.0637459 0.0877387i
\(495\) 0 0
\(496\) −89.7953 + 65.2401i −0.181039 + 0.131532i
\(497\) −105.189 + 664.139i −0.211649 + 1.33630i
\(498\) 0 0
\(499\) 220.616i 0.442116i −0.975261 0.221058i \(-0.929049\pi\)
0.975261 0.221058i \(-0.0709511\pi\)
\(500\) −849.940 + 77.4601i −1.69988 + 0.154920i
\(501\) 0 0
\(502\) 449.635 + 229.100i 0.895687 + 0.456375i
\(503\) 377.227 + 59.7469i 0.749954 + 0.118781i 0.519699 0.854349i \(-0.326044\pi\)
0.230255 + 0.973130i \(0.426044\pi\)
\(504\) 0 0
\(505\) −4.05056 + 22.3682i −0.00802091 + 0.0442934i
\(506\) −184.527 134.067i −0.364678 0.264954i
\(507\) 0 0
\(508\) −119.458 754.229i −0.235154 1.48470i
\(509\) 54.3299 + 17.6528i 0.106738 + 0.0346814i 0.361899 0.932217i \(-0.382128\pi\)
−0.255161 + 0.966899i \(0.582128\pi\)
\(510\) 0 0
\(511\) 84.1163 + 258.883i 0.164611 + 0.506621i
\(512\) −95.4111 187.255i −0.186350 0.365732i
\(513\) 0 0
\(514\) 922.391 299.703i 1.79454 0.583080i
\(515\) 163.880 468.907i 0.318214 0.910499i
\(516\) 0 0
\(517\) 1187.60 188.098i 2.29711 0.363826i
\(518\) 589.912 + 589.912i 1.13883 + 1.13883i
\(519\) 0 0
\(520\) −322.860 + 155.630i −0.620884 + 0.299289i
\(521\) −37.2208 + 27.0425i −0.0714410 + 0.0519050i −0.622933 0.782276i \(-0.714059\pi\)
0.551492 + 0.834181i \(0.314059\pi\)
\(522\) 0 0
\(523\) 138.623 272.063i 0.265053 0.520197i −0.719671 0.694315i \(-0.755707\pi\)
0.984725 + 0.174118i \(0.0557075\pi\)
\(524\) 711.954i 1.35869i
\(525\) 0 0
\(526\) −34.5965 −0.0657729
\(527\) 776.267 + 395.528i 1.47299 + 0.750527i
\(528\) 0 0
\(529\) 297.701 + 409.751i 0.562763 + 0.774576i
\(530\) −977.173 + 934.974i −1.84372 + 1.76410i
\(531\) 0 0
\(532\) −62.6811 + 62.6811i −0.117822 + 0.117822i
\(533\) −4.70635 29.7147i −0.00882992 0.0557499i
\(534\) 0 0
\(535\) 233.767 + 337.152i 0.436947 + 0.630191i
\(536\) 1.02336 + 3.14959i 0.00190926 + 0.00587610i
\(537\) 0 0
\(538\) 1350.84 688.289i 2.51086 1.27935i
\(539\) −156.432 + 50.8279i −0.290227 + 0.0943004i
\(540\) 0 0
\(541\) −72.3805 + 222.764i −0.133790 + 0.411764i −0.995400 0.0958075i \(-0.969457\pi\)
0.861610 + 0.507571i \(0.169457\pi\)
\(542\) −483.768 + 76.6213i −0.892560 + 0.141368i
\(543\) 0 0
\(544\) −401.815 + 553.051i −0.738630 + 1.01664i
\(545\) 193.765 360.399i 0.355532 0.661283i
\(546\) 0 0
\(547\) −126.813 + 800.663i −0.231833 + 1.46374i 0.547332 + 0.836916i \(0.315644\pi\)
−0.779164 + 0.626819i \(0.784356\pi\)
\(548\) 473.815 929.914i 0.864626 1.69692i
\(549\) 0 0
\(550\) −592.212 + 1045.52i −1.07675 + 1.90095i
\(551\) 117.306 0.212896
\(552\) 0 0
\(553\) 342.146 + 54.1906i 0.618708 + 0.0979938i
\(554\) 498.609 + 686.276i 0.900016 + 1.23877i
\(555\) 0 0
\(556\) 869.667 + 631.850i 1.56415 + 1.13642i
\(557\) −581.702 + 581.702i −1.04435 + 1.04435i −0.0453787 + 0.998970i \(0.514449\pi\)
−0.998970 + 0.0453787i \(0.985551\pi\)
\(558\) 0 0
\(559\) −340.876 110.757i −0.609796 0.198135i
\(560\) 97.2660 29.2474i 0.173689 0.0522275i
\(561\) 0 0
\(562\) −119.266 234.072i −0.212217 0.416499i
\(563\) 376.119 191.642i 0.668062 0.340395i −0.0868492 0.996221i \(-0.527680\pi\)
0.754911 + 0.655827i \(0.227680\pi\)
\(564\) 0 0
\(565\) 272.542 + 906.372i 0.482375 + 1.60420i
\(566\) 35.8950 110.473i 0.0634187 0.195183i
\(567\) 0 0
\(568\) 720.161 + 720.161i 1.26789 + 1.26789i
\(569\) 470.636 647.774i 0.827128 1.13844i −0.161323 0.986902i \(-0.551576\pi\)
0.988451 0.151542i \(-0.0484239\pi\)
\(570\) 0 0
\(571\) 545.948 396.655i 0.956127 0.694667i 0.00387883 0.999992i \(-0.498765\pi\)
0.952248 + 0.305326i \(0.0987653\pi\)
\(572\) −120.190 + 758.848i −0.210122 + 1.32666i
\(573\) 0 0
\(574\) 78.9414i 0.137529i
\(575\) −87.5092 + 80.1075i −0.152190 + 0.139317i
\(576\) 0 0
\(577\) −809.001 412.206i −1.40208 0.714396i −0.420831 0.907139i \(-0.638262\pi\)
−0.981249 + 0.192743i \(0.938262\pi\)
\(578\) −1250.21 198.014i −2.16299 0.342585i
\(579\) 0 0
\(580\) −1668.96 897.298i −2.87752 1.54707i
\(581\) 86.1245 + 62.5731i 0.148235 + 0.107699i
\(582\) 0 0
\(583\) 187.826 + 1185.89i 0.322172 + 2.03411i
\(584\) 392.111 + 127.405i 0.671423 + 0.218159i
\(585\) 0 0
\(586\) −24.0682 74.0745i −0.0410721 0.126407i
\(587\) −54.6357 107.229i −0.0930761 0.182672i 0.839775 0.542935i \(-0.182687\pi\)
−0.932851 + 0.360263i \(0.882687\pi\)
\(588\) 0 0
\(589\) −67.4671 + 21.9214i −0.114545 + 0.0372180i
\(590\) −152.259 + 105.570i −0.258066 + 0.178932i
\(591\) 0 0
\(592\) 134.787 21.3482i 0.227681 0.0360612i
\(593\) −255.390 255.390i −0.430674 0.430674i 0.458183 0.888858i \(-0.348500\pi\)
−0.888858 + 0.458183i \(0.848500\pi\)
\(594\) 0 0
\(595\) −551.162 576.038i −0.926323 0.968131i
\(596\) 444.486 322.938i 0.745781 0.541842i
\(597\) 0 0
\(598\) −54.6149 + 107.188i −0.0913293 + 0.179244i
\(599\) 546.766i 0.912799i 0.889775 + 0.456399i \(0.150861\pi\)
−0.889775 + 0.456399i \(0.849139\pi\)
\(600\) 0 0
\(601\) −768.536 −1.27876 −0.639381 0.768890i \(-0.720809\pi\)
−0.639381 + 0.768890i \(0.720809\pi\)
\(602\) 837.962 + 426.963i 1.39196 + 0.709241i
\(603\) 0 0
\(604\) 752.219 + 1035.34i 1.24540 + 1.71414i
\(605\) 200.509 + 415.962i 0.331420 + 0.687540i
\(606\) 0 0
\(607\) −163.485 + 163.485i −0.269333 + 0.269333i −0.828832 0.559498i \(-0.810994\pi\)
0.559498 + 0.828832i \(0.310994\pi\)
\(608\) −8.70754 54.9772i −0.0143216 0.0904231i
\(609\) 0 0
\(610\) 495.002 + 173.000i 0.811479 + 0.283607i
\(611\) −195.973 603.142i −0.320741 0.987140i
\(612\) 0 0
\(613\) 530.506 270.306i 0.865426 0.440957i 0.0358546 0.999357i \(-0.488585\pi\)
0.829572 + 0.558400i \(0.188585\pi\)
\(614\) −62.1425 + 20.1913i −0.101209 + 0.0328849i
\(615\) 0 0
\(616\) 258.006 794.060i 0.418840 1.28906i
\(617\) −319.636 + 50.6254i −0.518049 + 0.0820509i −0.409984 0.912093i \(-0.634466\pi\)
−0.108065 + 0.994144i \(0.534466\pi\)
\(618\) 0 0
\(619\) 6.19820 8.53110i 0.0100133 0.0137821i −0.803981 0.594655i \(-0.797289\pi\)
0.813994 + 0.580873i \(0.197289\pi\)
\(620\) 1127.57 + 204.186i 1.81866 + 0.329333i
\(621\) 0 0
\(622\) 99.1246 625.848i 0.159364 1.00619i
\(623\) 250.100 490.848i 0.401444 0.787878i
\(624\) 0 0
\(625\) 471.286 + 410.505i 0.754058 + 0.656808i
\(626\) −523.208 −0.835795
\(627\) 0 0
\(628\) −859.149 136.076i −1.36807 0.216681i
\(629\) −629.625 866.605i −1.00099 1.37775i
\(630\) 0 0
\(631\) −25.4826 18.5142i −0.0403844 0.0293410i 0.567410 0.823435i \(-0.307946\pi\)
−0.607794 + 0.794094i \(0.707946\pi\)
\(632\) 371.006 371.006i 0.587035 0.587035i
\(633\) 0 0
\(634\) 1198.77 + 389.502i 1.89080 + 0.614357i
\(635\) −338.600 + 445.052i −0.533228 + 0.700870i
\(636\) 0 0
\(637\) 39.3848 + 77.2970i 0.0618285 + 0.121345i
\(638\) −2377.04 + 1211.16i −3.72576 + 1.89837i
\(639\) 0 0
\(640\) −368.445 + 1054.22i −0.575695 + 1.64722i
\(641\) 347.695 1070.09i 0.542425 1.66941i −0.184609 0.982812i \(-0.559102\pi\)
0.727034 0.686601i \(-0.240898\pi\)
\(642\) 0 0
\(643\) 737.920 + 737.920i 1.14762 + 1.14762i 0.987019 + 0.160602i \(0.0513436\pi\)
0.160602 + 0.987019i \(0.448656\pi\)
\(644\) 116.997 161.032i 0.181672 0.250050i
\(645\) 0 0
\(646\) 146.027 106.095i 0.226048 0.164233i
\(647\) −167.580 + 1058.06i −0.259011 + 1.63533i 0.424525 + 0.905416i \(0.360441\pi\)
−0.683536 + 0.729916i \(0.739559\pi\)
\(648\) 0 0
\(649\) 164.488i 0.253449i
\(650\) 593.507 + 222.239i 0.913088 + 0.341907i
\(651\) 0 0
\(652\) −208.354 106.162i −0.319562 0.162825i
\(653\) 375.029 + 59.3987i 0.574317 + 0.0909628i 0.436835 0.899542i \(-0.356099\pi\)
0.137481 + 0.990504i \(0.456099\pi\)
\(654\) 0 0
\(655\) 376.710 360.442i 0.575130 0.550293i
\(656\) 10.4469 + 7.59015i 0.0159252 + 0.0115704i
\(657\) 0 0
\(658\) 260.315 + 1643.56i 0.395615 + 2.49782i
\(659\) −329.556 107.079i −0.500085 0.162487i 0.0481033 0.998842i \(-0.484682\pi\)
−0.548188 + 0.836355i \(0.684682\pi\)
\(660\) 0 0
\(661\) −246.800 759.573i −0.373374 1.14913i −0.944569 0.328312i \(-0.893520\pi\)
0.571195 0.820814i \(-0.306480\pi\)
\(662\) 832.197 + 1633.28i 1.25709 + 2.46719i
\(663\) 0 0
\(664\) 153.349 49.8260i 0.230947 0.0750392i
\(665\) 64.8995 + 1.43224i 0.0975933 + 0.00215374i
\(666\) 0 0
\(667\) −260.161 + 41.2055i −0.390047 + 0.0617773i
\(668\) 284.695 + 284.695i 0.426191 + 0.426191i
\(669\) 0 0
\(670\) 2.77294 5.15761i 0.00413871 0.00769793i
\(671\) 376.618 273.629i 0.561279 0.407793i
\(672\) 0 0
\(673\) 32.9059 64.5815i 0.0488944 0.0959606i −0.865267 0.501312i \(-0.832851\pi\)
0.914161 + 0.405352i \(0.132851\pi\)
\(674\) 624.607i 0.926716i
\(675\) 0 0
\(676\) −748.656 −1.10748
\(677\) 529.170 + 269.626i 0.781640 + 0.398265i 0.798807 0.601587i \(-0.205465\pi\)
−0.0171675 + 0.999853i \(0.505465\pi\)
\(678\) 0 0
\(679\) −31.8325 43.8136i −0.0468814 0.0645267i
\(680\) −1196.54 + 162.539i −1.75961 + 0.239028i
\(681\) 0 0
\(682\) 1140.79 1140.79i 1.67272 1.67272i
\(683\) −114.459 722.664i −0.167582 1.05807i −0.917847 0.396935i \(-0.870074\pi\)
0.750264 0.661138i \(-0.229926\pi\)
\(684\) 0 0
\(685\) −731.916 + 220.084i −1.06849 + 0.321290i
\(686\) −376.428 1158.53i −0.548729 1.68881i
\(687\) 0 0
\(688\) 137.073 69.8421i 0.199234 0.101515i
\(689\) 602.270 195.689i 0.874122 0.284019i
\(690\) 0 0
\(691\) 161.872 498.191i 0.234257 0.720970i −0.762962 0.646444i \(-0.776255\pi\)
0.997219 0.0745265i \(-0.0237445\pi\)
\(692\) −524.694 + 83.1034i −0.758229 + 0.120092i
\(693\) 0 0
\(694\) 292.751 402.938i 0.421832 0.580602i
\(695\) −105.962 780.046i −0.152464 1.12237i
\(696\) 0 0
\(697\) 15.8562 100.112i 0.0227492 0.143633i
\(698\) 186.038 365.119i 0.266530 0.523094i
\(699\) 0 0
\(700\) −912.400 516.809i −1.30343 0.738299i
\(701\) 699.523 0.997893 0.498947 0.866633i \(-0.333720\pi\)
0.498947 + 0.866633i \(0.333720\pi\)
\(702\) 0 0
\(703\) 86.1468 + 13.6443i 0.122542 + 0.0194087i
\(704\) 857.636 + 1180.43i 1.21823 + 1.67675i
\(705\) 0 0
\(706\) −990.308 719.501i −1.40270 1.01912i
\(707\) −19.7491 + 19.7491i −0.0279337 + 0.0279337i
\(708\) 0 0
\(709\) 145.144 + 47.1600i 0.204716 + 0.0665162i 0.409580 0.912274i \(-0.365675\pi\)
−0.204864 + 0.978790i \(0.565675\pi\)
\(710\) 39.7327 1800.43i 0.0559616 2.53581i
\(711\) 0 0
\(712\) −378.807 743.451i −0.532032 1.04417i
\(713\) 141.929 72.3163i 0.199059 0.101425i
\(714\) 0 0
\(715\) 462.371 320.588i 0.646673 0.448375i
\(716\) −321.957 + 990.882i −0.449661 + 1.38391i
\(717\) 0 0
\(718\) −568.421 568.421i −0.791673 0.791673i
\(719\) −431.478 + 593.879i −0.600109 + 0.825979i −0.995718 0.0924401i \(-0.970533\pi\)
0.395610 + 0.918419i \(0.370533\pi\)
\(720\) 0 0
\(721\) 493.737 358.721i 0.684794 0.497532i
\(722\) 183.527 1158.75i 0.254193 1.60491i
\(723\) 0 0
\(724\) 222.963i 0.307960i
\(725\) 370.167 + 1337.36i 0.510575 + 1.84463i
\(726\) 0 0
\(727\) 1179.77 + 601.120i 1.62279 + 0.826851i 0.998975 + 0.0452756i \(0.0144166\pi\)
0.623811 + 0.781575i \(0.285583\pi\)
\(728\) −434.939 68.8876i −0.597444 0.0946258i
\(729\) 0 0
\(730\) −316.556 656.706i −0.433639 0.899597i
\(731\) −976.927 709.779i −1.33643 0.970970i
\(732\) 0 0
\(733\) −133.600 843.514i −0.182264 1.15077i −0.893915 0.448237i \(-0.852052\pi\)
0.711651 0.702533i \(-0.247948\pi\)
\(734\) 540.399 + 175.586i 0.736238 + 0.239218i
\(735\) 0 0
\(736\) 38.6233 + 118.870i 0.0524773 + 0.161509i
\(737\) −2.36017 4.63209i −0.00320240 0.00628506i
\(738\) 0 0
\(739\) 32.3337 10.5059i 0.0437534 0.0142163i −0.287059 0.957913i \(-0.592677\pi\)
0.330812 + 0.943697i \(0.392677\pi\)
\(740\) −1121.28 853.081i −1.51524 1.15281i
\(741\) 0 0
\(742\) −1641.19 + 259.938i −2.21184 + 0.350321i
\(743\) 327.809 + 327.809i 0.441197 + 0.441197i 0.892414 0.451217i \(-0.149010\pi\)
−0.451217 + 0.892414i \(0.649010\pi\)
\(744\) 0 0
\(745\) −395.904 71.6925i −0.531414 0.0962316i
\(746\) 105.171 76.4112i 0.140980 0.102428i
\(747\) 0 0
\(748\) −1175.16 + 2306.38i −1.57107 + 3.08339i
\(749\) 504.071i 0.672993i
\(750\) 0 0
\(751\) 436.259 0.580905 0.290452 0.956889i \(-0.406194\pi\)
0.290452 + 0.956889i \(0.406194\pi\)
\(752\) 242.535 + 123.578i 0.322520 + 0.164332i
\(753\) 0 0
\(754\) 827.057 + 1138.35i 1.09689 + 1.50974i
\(755\) 166.993 922.178i 0.221183 1.22143i
\(756\) 0 0
\(757\) −667.784 + 667.784i −0.882145 + 0.882145i −0.993752 0.111607i \(-0.964400\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(758\) 45.7996 + 289.167i 0.0604216 + 0.381487i
\(759\) 0 0
\(760\) 59.5334 78.2500i 0.0783334 0.102961i
\(761\) −265.924 818.431i −0.349440 1.07547i −0.959163 0.282853i \(-0.908719\pi\)
0.609723 0.792615i \(-0.291281\pi\)
\(762\) 0 0
\(763\) 447.947 228.241i 0.587087 0.299136i
\(764\) −325.779 + 105.852i −0.426412 + 0.138550i
\(765\) 0 0
\(766\) 325.245 1001.00i 0.424602 1.30679i
\(767\) 85.6873 13.5715i 0.111717 0.0176943i
\(768\) 0 0
\(769\) 534.634 735.861i 0.695233 0.956907i −0.304757 0.952430i \(-0.598575\pi\)
0.999990 0.00447640i \(-0.00142489\pi\)
\(770\) −1329.89 + 641.055i −1.72713 + 0.832539i
\(771\) 0 0
\(772\) −74.4320 + 469.945i −0.0964146 + 0.608738i
\(773\) 330.014 647.689i 0.426926 0.837889i −0.572907 0.819620i \(-0.694184\pi\)
0.999833 0.0182691i \(-0.00581557\pi\)
\(774\) 0 0
\(775\) −462.816 699.993i −0.597181 0.903217i
\(776\) −82.0270 −0.105705
\(777\) 0 0
\(778\) −265.666 42.0774i −0.341474 0.0540841i
\(779\) 4.85110 + 6.67697i 0.00622734 + 0.00857120i
\(780\) 0 0
\(781\) −1293.45 939.748i −1.65615 1.20326i
\(782\) −286.592 + 286.592i −0.366486 + 0.366486i
\(783\) 0 0
\(784\) −35.4134 11.5065i −0.0451702 0.0146767i
\(785\) 362.962 + 523.485i 0.462372 + 0.666860i
\(786\) 0 0
\(787\) −665.324 1305.77i −0.845393 1.65918i −0.747774 0.663953i \(-0.768877\pi\)
−0.0976189 0.995224i \(-0.531123\pi\)
\(788\) 2122.72 1081.58i 2.69381 1.37257i
\(789\) 0 0
\(790\) −927.529 20.4692i −1.17409 0.0259103i
\(791\) −359.345 + 1105.95i −0.454292 + 1.39817i
\(792\) 0 0
\(793\) −173.616 173.616i −0.218936 0.218936i
\(794\) −107.615 + 148.120i −0.135536 + 0.186549i
\(795\) 0 0
\(796\) 220.398 160.128i 0.276882 0.201166i
\(797\) 118.617 748.917i 0.148829 0.939669i −0.794368 0.607436i \(-0.792198\pi\)
0.943197 0.332233i \(-0.107802\pi\)
\(798\) 0 0
\(799\) 2136.62i 2.67412i
\(800\) 599.298 272.757i 0.749123 0.340946i
\(801\) 0 0
\(802\) 2071.68 + 1055.57i 2.58314 + 1.31617i
\(803\) −639.250 101.247i −0.796078 0.126086i
\(804\) 0 0
\(805\) −144.438 + 19.6206i −0.179426 + 0.0243734i
\(806\) −688.401 500.152i −0.854095 0.620536i
\(807\) 0 0
\(808\) 6.61760 + 41.7819i 0.00819010 + 0.0517102i
\(809\) 684.508 + 222.410i 0.846116 + 0.274920i 0.699818 0.714321i \(-0.253264\pi\)
0.146298 + 0.989241i \(0.453264\pi\)
\(810\) 0 0
\(811\) −27.5305 84.7302i −0.0339464 0.104476i 0.932648 0.360789i \(-0.117492\pi\)
−0.966594 + 0.256312i \(0.917492\pi\)
\(812\) −1056.95 2074.38i −1.30166 2.55466i
\(813\) 0 0
\(814\) −1886.52 + 612.968i −2.31760 + 0.753032i
\(815\) 49.3114 + 163.991i 0.0605048 + 0.201216i
\(816\) 0 0
\(817\) 97.1136 15.3813i 0.118866 0.0188265i
\(818\) −552.560 552.560i −0.675502 0.675502i
\(819\) 0 0
\(820\) −17.9451 132.104i −0.0218843 0.161102i
\(821\) −543.123 + 394.602i −0.661538 + 0.480635i −0.867182 0.497991i \(-0.834071\pi\)
0.205644 + 0.978627i \(0.434071\pi\)
\(822\) 0 0
\(823\) 558.523 1096.16i 0.678643 1.33191i −0.252620 0.967566i \(-0.581292\pi\)
0.931263 0.364347i \(-0.118708\pi\)
\(824\) 924.364i 1.12180i
\(825\) 0 0
\(826\) −227.641 −0.275594
\(827\) −150.479 76.6727i −0.181957 0.0927119i 0.360639 0.932705i \(-0.382559\pi\)
−0.542596 + 0.839994i \(0.682559\pi\)
\(828\) 0 0
\(829\) 637.618 + 877.605i 0.769141 + 1.05863i 0.996398 + 0.0847965i \(0.0270240\pi\)
−0.227258 + 0.973835i \(0.572976\pi\)
\(830\) −251.116 135.010i −0.302550 0.162663i
\(831\) 0 0
\(832\) 544.165 544.165i 0.654045 0.654045i
\(833\) 45.7223 + 288.679i 0.0548888 + 0.346554i
\(834\) 0 0
\(835\) 6.50516 294.771i 0.00779061 0.353020i
\(836\) −65.1310 200.453i −0.0779079 0.239776i
\(837\) 0 0
\(838\) 701.072 357.214i 0.836601 0.426270i
\(839\) −1156.94 + 375.911i −1.37895 + 0.448047i −0.902323 0.431061i \(-0.858139\pi\)
−0.476623 + 0.879108i \(0.658139\pi\)
\(840\) 0 0
\(841\) −692.161 + 2130.25i −0.823021 + 2.53300i
\(842\) 1578.59 250.024i 1.87481 0.296940i
\(843\) 0 0
\(844\) −767.654 + 1056.59i −0.909543 + 1.25188i
\(845\) 379.023 + 396.129i 0.448548 + 0.468792i
\(846\) 0 0
\(847\) −88.7525 + 560.361i −0.104785 + 0.661584i
\(848\) −123.399 + 242.184i −0.145518 + 0.285595i
\(849\) 0 0
\(850\) 1670.35 + 1330.01i 1.96511 + 1.56472i
\(851\) −195.850 −0.230141
\(852\) 0 0
\(853\) −182.560 28.9147i −0.214021 0.0338977i 0.0485029 0.998823i \(-0.484555\pi\)
−0.262524 + 0.964925i \(0.584555\pi\)
\(854\) 378.684 + 521.214i 0.443424 + 0.610320i
\(855\) 0 0
\(856\) 617.668 + 448.762i 0.721574 + 0.524254i
\(857\) −203.015 + 203.015i −0.236890 + 0.236890i −0.815561 0.578671i \(-0.803572\pi\)
0.578671 + 0.815561i \(0.303572\pi\)
\(858\) 0 0
\(859\) −1263.62 410.575i −1.47103 0.477968i −0.539614 0.841913i \(-0.681430\pi\)
−0.931421 + 0.363944i \(0.881430\pi\)
\(860\) −1499.33 524.009i −1.74341 0.609313i
\(861\) 0 0
\(862\) −413.864 812.253i −0.480120 0.942289i
\(863\) −1200.75 + 611.814i −1.39137 + 0.708938i −0.979338 0.202231i \(-0.935181\pi\)
−0.412032 + 0.911169i \(0.635181\pi\)
\(864\) 0 0
\(865\) 309.610 + 235.554i 0.357930 + 0.272317i
\(866\) 512.606 1577.64i 0.591924 1.82175i
\(867\) 0 0
\(868\) 995.543 + 995.543i 1.14694 + 1.14694i
\(869\) −484.132 + 666.350i −0.557113 + 0.766801i
\(870\) 0 0
\(871\) −2.21828 + 1.61167i −0.00254681 + 0.00185037i
\(872\) 119.120 752.092i 0.136605 0.862491i
\(873\) 0 0
\(874\) 33.0016i 0.0377592i
\(875\) 188.467 + 744.416i 0.215391 + 0.850761i
\(876\) 0 0
\(877\) 892.419 + 454.710i 1.01758 + 0.518484i 0.881485 0.472212i \(-0.156544\pi\)
0.136096 + 0.990696i \(0.456544\pi\)
\(878\) 2204.03 + 349.084i 2.51028 + 0.397590i
\(879\) 0 0
\(880\) −43.0318 + 237.632i −0.0488997 + 0.270036i
\(881\) −610.778 443.756i −0.693278 0.503696i 0.184458 0.982840i \(-0.440947\pi\)
−0.877736 + 0.479145i \(0.840947\pi\)
\(882\) 0 0
\(883\) −143.134 903.715i −0.162100 1.02346i −0.925835 0.377929i \(-0.876636\pi\)
0.763735 0.645530i \(-0.223364\pi\)
\(884\) 1298.43 + 421.884i 1.46881 + 0.477245i
\(885\) 0 0
\(886\) 330.140 + 1016.07i 0.372619 + 1.14680i
\(887\) −668.313 1311.64i −0.753453 1.47874i −0.873947 0.486021i \(-0.838448\pi\)
0.120494 0.992714i \(-0.461552\pi\)
\(888\) 0 0
\(889\) −653.449 + 212.318i −0.735038 + 0.238828i
\(890\) −486.770 + 1392.78i −0.546932 + 1.56492i
\(891\) 0 0
\(892\) 1222.87 193.684i 1.37093 0.217134i
\(893\) 123.018 + 123.018i 0.137758 + 0.137758i
\(894\) 0 0
\(895\) 687.294 331.301i 0.767926 0.370169i
\(896\) −1110.05 + 806.495i −1.23889 + 0.900106i
\(897\) 0 0
\(898\) 108.716 213.368i 0.121065 0.237604i
\(899\) 1863.12i 2.07244i
\(900\) 0 0
\(901\) 2133.53 2.36796
\(902\) −167.240 85.2128i −0.185410 0.0944710i
\(903\) 0 0
\(904\) 1035.27 + 1424.92i 1.14521 + 1.57624i
\(905\) −117.974 + 112.880i −0.130358 + 0.124729i
\(906\) 0 0
\(907\) −511.441 + 511.441i −0.563882 + 0.563882i −0.930408 0.366526i \(-0.880547\pi\)
0.366526 + 0.930408i \(0.380547\pi\)
\(908\) 319.482 + 2017.13i 0.351853 + 2.22151i
\(909\) 0 0
\(910\) 443.672 + 639.890i 0.487552 + 0.703176i
\(911\) 196.843 + 605.821i 0.216074 + 0.665007i 0.999076 + 0.0429874i \(0.0136875\pi\)
−0.783002 + 0.622019i \(0.786312\pi\)
\(912\) 0 0
\(913\) −225.530 + 114.913i −0.247020 + 0.125863i
\(914\) −928.856 + 301.803i −1.01625 + 0.330201i
\(915\) 0 0
\(916\) 461.193 1419.41i 0.503486 1.54957i
\(917\) 632.694 100.209i 0.689961 0.109279i
\(918\) 0 0
\(919\) −576.765 + 793.848i −0.627600 + 0.863818i −0.997879 0.0651032i \(-0.979262\pi\)
0.370278 + 0.928921i \(0.379262\pi\)
\(920\) −104.547 + 194.456i −0.113638 + 0.211365i
\(921\) 0 0
\(922\) −69.5284 + 438.985i −0.0754105 + 0.476123i
\(923\) −382.826 + 751.338i −0.414762 + 0.814017i
\(924\) 0 0
\(925\) 116.289 + 1025.18i 0.125718 + 1.10831i
\(926\) 2428.91 2.62301
\(927\) 0 0
\(928\) 1443.91 + 228.692i 1.55593 + 0.246436i
\(929\) 503.341 + 692.790i 0.541810 + 0.745737i 0.988873 0.148765i \(-0.0475299\pi\)
−0.447063 + 0.894503i \(0.647530\pi\)
\(930\) 0 0
\(931\) −19.2535 13.9885i −0.0206804 0.0150252i
\(932\) −882.402 + 882.402i −0.946784 + 0.946784i
\(933\) 0 0
\(934\) −613.010 199.179i −0.656327 0.213254i
\(935\) 1815.30 545.852i 1.94150 0.583799i
\(936\) 0 0
\(937\) −80.6308 158.247i −0.0860521 0.168887i 0.843970 0.536390i \(-0.180213\pi\)
−0.930022 + 0.367504i \(0.880213\pi\)
\(938\) 6.41050 3.26631i 0.00683422 0.00348221i
\(939\) 0 0
\(940\) −809.239 2691.23i −0.860892 2.86301i
\(941\) 254.617 783.630i 0.270581 0.832763i −0.719774 0.694209i \(-0.755755\pi\)
0.990355 0.138554i \(-0.0442455\pi\)
\(942\) 0 0
\(943\) −13.1042 13.1042i −0.0138963 0.0138963i
\(944\) −21.8875 + 30.1255i −0.0231859 + 0.0319126i
\(945\) 0 0
\(946\) −1809.07 + 1314.36i −1.91233 + 1.38939i
\(947\) −34.8644 + 220.125i −0.0368156 + 0.232444i −0.999234 0.0391254i \(-0.987543\pi\)
0.962419 + 0.271570i \(0.0875428\pi\)
\(948\) 0 0
\(949\) 341.360i 0.359705i
\(950\) −172.748 + 19.5953i −0.181840 + 0.0206266i
\(951\) 0 0
\(952\) −1321.92 673.550i −1.38857 0.707510i
\(953\) 794.568 + 125.847i 0.833754 + 0.132054i 0.558694 0.829374i \(-0.311302\pi\)
0.275060 + 0.961427i \(0.411302\pi\)
\(954\) 0 0
\(955\) 220.941 + 118.787i 0.231352 + 0.124384i
\(956\) 2522.26 + 1832.53i 2.63835 + 1.91688i
\(957\) 0 0
\(958\) −73.8181 466.069i −0.0770544 0.486502i
\(959\) −893.080 290.179i −0.931261 0.302585i
\(960\) 0 0
\(961\) 51.2046 + 157.592i 0.0532826 + 0.163987i
\(962\) 474.968 + 932.176i 0.493729 + 0.968998i
\(963\) 0 0
\(964\) −2597.11 + 843.851i −2.69409 + 0.875364i
\(965\) 286.341 198.536i 0.296726 0.205737i
\(966\) 0 0
\(967\) 193.991 30.7251i 0.200611 0.0317736i −0.0553203 0.998469i \(-0.517618\pi\)
0.255931 + 0.966695i \(0.417618\pi\)
\(968\) 607.629 + 607.629i 0.627716 + 0.627716i
\(969\) 0 0
\(970\) 100.272 + 104.798i 0.103374 + 0.108039i
\(971\) 465.952 338.534i 0.479868 0.348645i −0.321406 0.946941i \(-0.604156\pi\)
0.801275 + 0.598297i \(0.204156\pi\)
\(972\) 0 0
\(973\) 439.100 861.783i 0.451285 0.885697i
\(974\) 1108.21i 1.13780i
\(975\) 0 0
\(976\) 105.387 0.107978
\(977\) 478.563 + 243.840i 0.489829 + 0.249581i 0.681418 0.731895i \(-0.261364\pi\)
−0.191588 + 0.981475i \(0.561364\pi\)
\(978\) 0 0
\(979\) 769.907 + 1059.69i 0.786422 + 1.08242i
\(980\) 166.927 + 346.295i 0.170334 + 0.353362i
\(981\) 0 0
\(982\) 1479.96 1479.96i 1.50708 1.50708i
\(983\) 81.0532 + 511.749i 0.0824549 + 0.520600i 0.993998 + 0.109396i \(0.0348916\pi\)
−0.911543 + 0.411204i \(0.865108\pi\)
\(984\) 0 0
\(985\) −1646.96 575.604i −1.67204 0.584369i
\(986\) 1464.92 + 4508.55i 1.48572 + 4.57257i
\(987\) 0 0
\(988\) −99.0484 + 50.4677i −0.100251 + 0.0510807i
\(989\) −209.976 + 68.2255i −0.212312 + 0.0689843i
\(990\) 0 0
\(991\) −372.803 + 1147.37i −0.376189 + 1.15779i 0.566485 + 0.824072i \(0.308303\pi\)
−0.942673 + 0.333717i \(0.891697\pi\)
\(992\) −873.185 + 138.299i −0.880226 + 0.139414i
\(993\) 0 0
\(994\) 1300.55 1790.05i 1.30840 1.80085i
\(995\) −196.308 35.5487i −0.197295 0.0357273i
\(996\) 0 0
\(997\) 24.0632 151.929i 0.0241356 0.152386i −0.972677 0.232161i \(-0.925420\pi\)
0.996813 + 0.0797753i \(0.0254203\pi\)
\(998\) −329.573 + 646.824i −0.330234 + 0.648120i
\(999\) 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 225.3.r.b.208.1 80
3.2 odd 2 75.3.k.a.58.10 yes 80
15.2 even 4 375.3.k.c.232.1 80
15.8 even 4 375.3.k.b.232.10 80
15.14 odd 2 375.3.k.a.268.1 80
25.22 odd 20 inner 225.3.r.b.172.1 80
75.29 odd 10 375.3.k.b.118.10 80
75.47 even 20 75.3.k.a.22.10 80
75.53 even 20 375.3.k.a.7.1 80
75.71 odd 10 375.3.k.c.118.1 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.k.a.22.10 80 75.47 even 20
75.3.k.a.58.10 yes 80 3.2 odd 2
225.3.r.b.172.1 80 25.22 odd 20 inner
225.3.r.b.208.1 80 1.1 even 1 trivial
375.3.k.a.7.1 80 75.53 even 20
375.3.k.a.268.1 80 15.14 odd 2
375.3.k.b.118.10 80 75.29 odd 10
375.3.k.b.232.10 80 15.8 even 4
375.3.k.c.118.1 80 75.71 odd 10
375.3.k.c.232.1 80 15.2 even 4