Properties

Label 36.5.f.a.31.2
Level $36$
Weight $5$
Character 36.31
Analytic conductor $3.721$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [36,5,Mod(7,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 36.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.72131867102\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Character \(\chi\) \(=\) 36.31
Dual form 36.5.f.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.93519 + 0.717143i) q^{2} +(2.22096 + 8.72166i) q^{3} +(14.9714 - 5.64418i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-14.9946 - 32.7286i) q^{6} +(-10.3188 + 5.95759i) q^{7} +(-54.8676 + 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +O(q^{10})\) \(q+(-3.93519 + 0.717143i) q^{2} +(2.22096 + 8.72166i) q^{3} +(14.9714 - 5.64418i) q^{4} +(-5.51579 + 9.55363i) q^{5} +(-14.9946 - 32.7286i) q^{6} +(-10.3188 + 5.95759i) q^{7} +(-54.8676 + 32.9476i) q^{8} +(-71.1347 + 38.7409i) q^{9} +(14.8544 - 41.5509i) q^{10} +(-189.995 + 109.694i) q^{11} +(82.4775 + 118.040i) q^{12} +(18.5350 - 32.1036i) q^{13} +(36.3341 - 30.8443i) q^{14} +(-95.5738 - 26.8886i) q^{15} +(192.286 - 169.003i) q^{16} +284.021 q^{17} +(252.146 - 203.466i) q^{18} +45.4901i q^{19} +(-28.6568 + 174.163i) q^{20} +(-74.8777 - 76.7659i) q^{21} +(669.000 - 567.918i) q^{22} +(-174.319 - 100.643i) q^{23} +(-409.216 - 405.362i) q^{24} +(251.652 + 435.874i) q^{25} +(-49.9160 + 139.626i) q^{26} +(-495.872 - 534.371i) q^{27} +(-120.862 + 147.435i) q^{28} +(614.153 + 1063.74i) q^{29} +(395.384 + 37.2718i) q^{30} +(1311.83 + 757.384i) q^{31} +(-635.484 + 802.954i) q^{32} +(-1378.68 - 1413.45i) q^{33} +(-1117.68 + 203.683i) q^{34} -131.443i q^{35} +(-846.326 + 981.503i) q^{36} -1521.29 q^{37} +(-32.6229 - 179.012i) q^{38} +(321.162 + 90.3555i) q^{39} +(-12.1303 - 705.917i) q^{40} +(1316.97 - 2281.07i) q^{41} +(349.710 + 248.390i) q^{42} +(34.6057 - 19.9796i) q^{43} +(-2225.36 + 2714.63i) q^{44} +(22.2482 - 893.281i) q^{45} +(758.153 + 271.038i) q^{46} +(2498.36 - 1442.43i) q^{47} +(1901.04 + 1301.71i) q^{48} +(-1129.51 + 1956.38i) q^{49} +(-1302.88 - 1534.78i) q^{50} +(630.798 + 2477.13i) q^{51} +(96.2969 - 585.252i) q^{52} +1415.13 q^{53} +(2334.57 + 1747.24i) q^{54} -2420.19i q^{55} +(369.883 - 666.859i) q^{56} +(-396.749 + 101.032i) q^{57} +(-3179.66 - 3745.60i) q^{58} +(-2453.33 - 1416.43i) q^{59} +(-1582.64 + 136.875i) q^{60} +(2628.64 + 4552.93i) q^{61} +(-5705.44 - 2039.68i) q^{62} +(503.226 - 823.552i) q^{63} +(1924.92 - 3615.51i) q^{64} +(204.471 + 354.154i) q^{65} +(6439.01 + 4573.46i) q^{66} +(-805.917 - 465.296i) q^{67} +(4252.19 - 1603.07i) q^{68} +(490.620 - 1743.87i) q^{69} +(94.2635 + 517.254i) q^{70} +1162.75i q^{71} +(2626.58 - 4469.33i) q^{72} -2162.87 q^{73} +(5986.57 - 1090.98i) q^{74} +(-3242.64 + 3162.88i) q^{75} +(256.754 + 681.051i) q^{76} +(1307.02 - 2263.82i) q^{77} +(-1328.63 - 125.247i) q^{78} +(-6482.54 + 3742.70i) q^{79} +(553.978 + 2769.22i) q^{80} +(3559.29 - 5511.64i) q^{81} +(-3546.69 + 9920.88i) q^{82} +(966.756 - 558.157i) q^{83} +(-1554.31 - 726.670i) q^{84} +(-1566.60 + 2713.43i) q^{85} +(-121.852 + 103.441i) q^{86} +(-7913.60 + 7718.96i) q^{87} +(6810.44 - 12278.5i) q^{88} -6739.71 q^{89} +(553.059 + 3531.18i) q^{90} +441.696i q^{91} +(-3177.85 - 522.881i) q^{92} +(-3692.13 + 13123.4i) q^{93} +(-8797.09 + 7467.91i) q^{94} +(-434.596 - 250.914i) q^{95} +(-8414.48 - 3759.15i) q^{96} +(-6023.28 - 10432.6i) q^{97} +(3041.85 - 8508.73i) q^{98} +(9265.60 - 15163.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.93519 + 0.717143i −0.983797 + 0.179286i
\(3\) 2.22096 + 8.72166i 0.246773 + 0.969073i
\(4\) 14.9714 5.64418i 0.935713 0.352761i
\(5\) −5.51579 + 9.55363i −0.220632 + 0.382145i −0.955000 0.296606i \(-0.904145\pi\)
0.734368 + 0.678751i \(0.237479\pi\)
\(6\) −14.9946 32.7286i −0.416516 0.909129i
\(7\) −10.3188 + 5.95759i −0.210589 + 0.121583i −0.601585 0.798809i \(-0.705464\pi\)
0.390996 + 0.920392i \(0.372131\pi\)
\(8\) −54.8676 + 32.9476i −0.857307 + 0.514806i
\(9\) −71.1347 + 38.7409i −0.878206 + 0.478282i
\(10\) 14.8544 41.5509i 0.148544 0.415509i
\(11\) −189.995 + 109.694i −1.57021 + 0.906559i −0.574063 + 0.818811i \(0.694633\pi\)
−0.996143 + 0.0877473i \(0.972033\pi\)
\(12\) 82.4775 + 118.040i 0.572760 + 0.819723i
\(13\) 18.5350 32.1036i 0.109675 0.189962i −0.805964 0.591965i \(-0.798352\pi\)
0.915639 + 0.402003i \(0.131686\pi\)
\(14\) 36.3341 30.8443i 0.185378 0.157369i
\(15\) −95.5738 26.8886i −0.424773 0.119505i
\(16\) 192.286 169.003i 0.751119 0.660167i
\(17\) 284.021 0.982771 0.491386 0.870942i \(-0.336491\pi\)
0.491386 + 0.870942i \(0.336491\pi\)
\(18\) 252.146 203.466i 0.778227 0.627982i
\(19\) 45.4901i 0.126011i 0.998013 + 0.0630057i \(0.0200686\pi\)
−0.998013 + 0.0630057i \(0.979931\pi\)
\(20\) −28.6568 + 174.163i −0.0716419 + 0.435409i
\(21\) −74.8777 76.7659i −0.169791 0.174072i
\(22\) 669.000 567.918i 1.38223 1.17338i
\(23\) −174.319 100.643i −0.329525 0.190252i 0.326105 0.945334i \(-0.394264\pi\)
−0.655630 + 0.755082i \(0.727597\pi\)
\(24\) −409.216 405.362i −0.710445 0.703753i
\(25\) 251.652 + 435.874i 0.402643 + 0.697399i
\(26\) −49.9160 + 139.626i −0.0738402 + 0.206547i
\(27\) −495.872 534.371i −0.680208 0.733019i
\(28\) −120.862 + 147.435i −0.154161 + 0.188055i
\(29\) 614.153 + 1063.74i 0.730265 + 1.26486i 0.956770 + 0.290846i \(0.0939366\pi\)
−0.226505 + 0.974010i \(0.572730\pi\)
\(30\) 395.384 + 37.2718i 0.439316 + 0.0414131i
\(31\) 1311.83 + 757.384i 1.36507 + 0.788121i 0.990293 0.138996i \(-0.0443875\pi\)
0.374773 + 0.927117i \(0.377721\pi\)
\(32\) −635.484 + 802.954i −0.620590 + 0.784135i
\(33\) −1378.68 1413.45i −1.26601 1.29793i
\(34\) −1117.68 + 203.683i −0.966847 + 0.176197i
\(35\) 131.443i 0.107301i
\(36\) −846.326 + 981.503i −0.653030 + 0.757332i
\(37\) −1521.29 −1.11124 −0.555622 0.831435i \(-0.687520\pi\)
−0.555622 + 0.831435i \(0.687520\pi\)
\(38\) −32.6229 179.012i −0.0225920 0.123970i
\(39\) 321.162 + 90.3555i 0.211152 + 0.0594053i
\(40\) −12.1303 705.917i −0.00758145 0.441198i
\(41\) 1316.97 2281.07i 0.783447 1.35697i −0.146476 0.989214i \(-0.546793\pi\)
0.929923 0.367755i \(-0.119874\pi\)
\(42\) 349.710 + 248.390i 0.198248 + 0.140811i
\(43\) 34.6057 19.9796i 0.0187159 0.0108056i −0.490613 0.871378i \(-0.663227\pi\)
0.509329 + 0.860572i \(0.329894\pi\)
\(44\) −2225.36 + 2714.63i −1.14946 + 1.40219i
\(45\) 22.2482 893.281i 0.0109868 0.441126i
\(46\) 758.153 + 271.038i 0.358295 + 0.128090i
\(47\) 2498.36 1442.43i 1.13099 0.652978i 0.186807 0.982397i \(-0.440186\pi\)
0.944184 + 0.329419i \(0.106853\pi\)
\(48\) 1901.04 + 1301.71i 0.825106 + 0.564978i
\(49\) −1129.51 + 1956.38i −0.470435 + 0.814817i
\(50\) −1302.88 1534.78i −0.521153 0.613911i
\(51\) 630.798 + 2477.13i 0.242521 + 0.952377i
\(52\) 96.2969 585.252i 0.0356128 0.216439i
\(53\) 1415.13 0.503783 0.251892 0.967755i \(-0.418947\pi\)
0.251892 + 0.967755i \(0.418947\pi\)
\(54\) 2334.57 + 1747.24i 0.800607 + 0.599190i
\(55\) 2420.19i 0.800062i
\(56\) 369.883 666.859i 0.117947 0.212646i
\(57\) −396.749 + 101.032i −0.122114 + 0.0310962i
\(58\) −3179.66 3745.60i −0.945203 1.11344i
\(59\) −2453.33 1416.43i −0.704778 0.406904i 0.104346 0.994541i \(-0.466725\pi\)
−0.809125 + 0.587637i \(0.800058\pi\)
\(60\) −1582.64 + 136.875i −0.439622 + 0.0380209i
\(61\) 2628.64 + 4552.93i 0.706433 + 1.22358i 0.966172 + 0.257899i \(0.0830300\pi\)
−0.259739 + 0.965679i \(0.583637\pi\)
\(62\) −5705.44 2039.68i −1.48425 0.530614i
\(63\) 503.226 823.552i 0.126789 0.207496i
\(64\) 1924.92 3615.51i 0.469950 0.882693i
\(65\) 204.471 + 354.154i 0.0483954 + 0.0838233i
\(66\) 6439.01 + 4573.46i 1.47819 + 1.04992i
\(67\) −805.917 465.296i −0.179531 0.103653i 0.407541 0.913187i \(-0.366386\pi\)
−0.587073 + 0.809534i \(0.699720\pi\)
\(68\) 4252.19 1603.07i 0.919592 0.346684i
\(69\) 490.620 1743.87i 0.103050 0.366283i
\(70\) 94.2635 + 517.254i 0.0192375 + 0.105562i
\(71\) 1162.75i 0.230659i 0.993327 + 0.115329i \(0.0367923\pi\)
−0.993327 + 0.115329i \(0.963208\pi\)
\(72\) 2626.58 4469.33i 0.506670 0.862140i
\(73\) −2162.87 −0.405867 −0.202934 0.979192i \(-0.565048\pi\)
−0.202934 + 0.979192i \(0.565048\pi\)
\(74\) 5986.57 1090.98i 1.09324 0.199230i
\(75\) −3242.64 + 3162.88i −0.576469 + 0.562290i
\(76\) 256.754 + 681.051i 0.0444519 + 0.117911i
\(77\) 1307.02 2263.82i 0.220445 0.381822i
\(78\) −1328.63 125.247i −0.218381 0.0205862i
\(79\) −6482.54 + 3742.70i −1.03870 + 0.599695i −0.919466 0.393171i \(-0.871378\pi\)
−0.119237 + 0.992866i \(0.538045\pi\)
\(80\) 553.978 + 2769.22i 0.0865591 + 0.432690i
\(81\) 3559.29 5511.64i 0.542492 0.840061i
\(82\) −3546.69 + 9920.88i −0.527467 + 1.47544i
\(83\) 966.756 558.157i 0.140333 0.0810215i −0.428190 0.903689i \(-0.640848\pi\)
0.568523 + 0.822667i \(0.307515\pi\)
\(84\) −1554.31 726.670i −0.220282 0.102986i
\(85\) −1566.60 + 2713.43i −0.216830 + 0.375561i
\(86\) −121.852 + 103.441i −0.0164754 + 0.0139861i
\(87\) −7913.60 + 7718.96i −1.04553 + 1.01981i
\(88\) 6810.44 12278.5i 0.879447 1.58555i
\(89\) −6739.71 −0.850866 −0.425433 0.904990i \(-0.639878\pi\)
−0.425433 + 0.904990i \(0.639878\pi\)
\(90\) 553.059 + 3531.18i 0.0682789 + 0.435949i
\(91\) 441.696i 0.0533385i
\(92\) −3177.85 522.881i −0.375455 0.0617771i
\(93\) −3692.13 + 13123.4i −0.426886 + 1.51734i
\(94\) −8797.09 + 7467.91i −0.995596 + 0.845168i
\(95\) −434.596 250.914i −0.0481546 0.0278021i
\(96\) −8414.48 3759.15i −0.913029 0.407894i
\(97\) −6023.28 10432.6i −0.640161 1.10879i −0.985396 0.170276i \(-0.945534\pi\)
0.345235 0.938516i \(-0.387799\pi\)
\(98\) 3041.85 8508.73i 0.316727 0.885957i
\(99\) 9265.60 15163.6i 0.945373 1.54715i
\(100\) 6227.74 + 5105.28i 0.622774 + 0.510528i
\(101\) 4777.60 + 8275.04i 0.468346 + 0.811199i 0.999346 0.0361728i \(-0.0115167\pi\)
−0.530999 + 0.847372i \(0.678183\pi\)
\(102\) −4258.77 9295.61i −0.409339 0.893465i
\(103\) 9962.26 + 5751.71i 0.939039 + 0.542154i 0.889659 0.456626i \(-0.150942\pi\)
0.0493798 + 0.998780i \(0.484276\pi\)
\(104\) 40.7622 + 2372.13i 0.00376870 + 0.219317i
\(105\) 1146.40 291.930i 0.103982 0.0264789i
\(106\) −5568.79 + 1014.85i −0.495620 + 0.0903211i
\(107\) 6602.72i 0.576707i 0.957524 + 0.288353i \(0.0931078\pi\)
−0.957524 + 0.288353i \(0.906892\pi\)
\(108\) −10440.0 5201.50i −0.895061 0.445944i
\(109\) 12045.3 1.01383 0.506913 0.861997i \(-0.330786\pi\)
0.506913 + 0.861997i \(0.330786\pi\)
\(110\) 1735.62 + 9523.89i 0.143440 + 0.787099i
\(111\) −3378.73 13268.2i −0.274225 1.07688i
\(112\) −977.325 + 2889.48i −0.0779117 + 0.230347i
\(113\) −1865.35 + 3230.88i −0.146084 + 0.253025i −0.929777 0.368124i \(-0.880000\pi\)
0.783693 + 0.621149i \(0.213334\pi\)
\(114\) 1488.83 682.104i 0.114561 0.0524857i
\(115\) 1923.01 1110.25i 0.145407 0.0839510i
\(116\) 15198.7 + 12459.4i 1.12951 + 0.925933i
\(117\) −74.7620 + 3001.74i −0.00546146 + 0.219281i
\(118\) 10670.1 + 3814.54i 0.766311 + 0.273954i
\(119\) −2930.77 + 1692.08i −0.206960 + 0.119489i
\(120\) 6129.83 1673.61i 0.425682 0.116223i
\(121\) 16744.9 29003.0i 1.14370 1.98094i
\(122\) −13609.3 16031.5i −0.914356 1.07710i
\(123\) 22819.6 + 6420.05i 1.50834 + 0.424354i
\(124\) 23914.7 + 3934.92i 1.55533 + 0.255913i
\(125\) −12447.0 −0.796607
\(126\) −1389.68 + 3601.72i −0.0875336 + 0.226865i
\(127\) 26549.7i 1.64608i −0.567980 0.823042i \(-0.692275\pi\)
0.567980 0.823042i \(-0.307725\pi\)
\(128\) −4982.07 + 15608.2i −0.304082 + 0.952646i
\(129\) 251.113 + 257.445i 0.0150900 + 0.0154706i
\(130\) −1058.61 1247.03i −0.0626396 0.0737886i
\(131\) 1142.84 + 659.821i 0.0665954 + 0.0384489i 0.532928 0.846161i \(-0.321092\pi\)
−0.466333 + 0.884609i \(0.654425\pi\)
\(132\) −28618.5 13379.8i −1.64248 0.767892i
\(133\) −271.011 469.405i −0.0153209 0.0265366i
\(134\) 3505.12 + 1253.07i 0.195206 + 0.0697856i
\(135\) 7840.31 1789.90i 0.430195 0.0982111i
\(136\) −15583.6 + 9357.79i −0.842537 + 0.505936i
\(137\) −12906.5 22354.7i −0.687648 1.19104i −0.972597 0.232499i \(-0.925310\pi\)
0.284949 0.958543i \(-0.408023\pi\)
\(138\) −680.075 + 7214.32i −0.0357107 + 0.378824i
\(139\) 11377.8 + 6569.00i 0.588885 + 0.339993i 0.764656 0.644438i \(-0.222909\pi\)
−0.175772 + 0.984431i \(0.556242\pi\)
\(140\) −741.889 1967.89i −0.0378515 0.100403i
\(141\) 18129.1 + 18586.3i 0.911881 + 0.934876i
\(142\) −833.858 4575.64i −0.0413538 0.226921i
\(143\) 8132.70i 0.397706i
\(144\) −7130.92 + 19471.3i −0.343891 + 0.939010i
\(145\) −13550.2 −0.644478
\(146\) 8511.29 1551.08i 0.399291 0.0727662i
\(147\) −19571.5 5506.21i −0.905708 0.254811i
\(148\) −22775.9 + 8586.46i −1.03981 + 0.392004i
\(149\) −12968.2 + 22461.6i −0.584128 + 1.01174i 0.410856 + 0.911700i \(0.365230\pi\)
−0.994984 + 0.100038i \(0.968103\pi\)
\(150\) 10492.2 14772.0i 0.466318 0.656532i
\(151\) −24591.2 + 14197.8i −1.07852 + 0.622681i −0.930496 0.366303i \(-0.880623\pi\)
−0.148020 + 0.988984i \(0.547290\pi\)
\(152\) −1498.79 2495.93i −0.0648714 0.108030i
\(153\) −20203.7 + 11003.2i −0.863076 + 0.470042i
\(154\) −3519.88 + 9845.88i −0.148418 + 0.415158i
\(155\) −14471.5 + 8355.15i −0.602353 + 0.347769i
\(156\) 5318.24 459.950i 0.218534 0.0189000i
\(157\) 2760.19 4780.78i 0.111980 0.193954i −0.804589 0.593832i \(-0.797614\pi\)
0.916568 + 0.399878i \(0.130948\pi\)
\(158\) 22826.0 19377.1i 0.914356 0.776203i
\(159\) 3142.94 + 12342.3i 0.124320 + 0.488203i
\(160\) −4165.93 10500.1i −0.162732 0.410161i
\(161\) 2398.36 0.0925257
\(162\) −10053.8 + 24241.9i −0.383091 + 0.923711i
\(163\) 407.281i 0.0153292i 0.999971 + 0.00766459i \(0.00243974\pi\)
−0.999971 + 0.00766459i \(0.997560\pi\)
\(164\) 6842.21 41584.0i 0.254395 1.54610i
\(165\) 21108.1 5375.13i 0.775319 0.197434i
\(166\) −3404.09 + 2889.76i −0.123534 + 0.104868i
\(167\) 20561.9 + 11871.4i 0.737277 + 0.425667i 0.821078 0.570816i \(-0.193373\pi\)
−0.0838016 + 0.996482i \(0.526706\pi\)
\(168\) 6637.61 + 1744.92i 0.235176 + 0.0618241i
\(169\) 13593.4 + 23544.5i 0.475943 + 0.824357i
\(170\) 4218.95 11801.3i 0.145984 0.408351i
\(171\) −1762.33 3235.92i −0.0602690 0.110664i
\(172\) 405.328 494.444i 0.0137009 0.0167132i
\(173\) 1413.25 + 2447.82i 0.0472200 + 0.0817874i 0.888669 0.458549i \(-0.151630\pi\)
−0.841449 + 0.540336i \(0.818297\pi\)
\(174\) 25605.9 36050.7i 0.845750 1.19074i
\(175\) −5193.52 2998.48i −0.169584 0.0979095i
\(176\) −17994.9 + 53202.2i −0.580931 + 1.71753i
\(177\) 6904.89 24543.0i 0.220399 0.783395i
\(178\) 26522.0 4833.34i 0.837080 0.152548i
\(179\) 45743.4i 1.42765i −0.700323 0.713826i \(-0.746961\pi\)
0.700323 0.713826i \(-0.253039\pi\)
\(180\) −4708.75 13499.3i −0.145332 0.416644i
\(181\) −24226.2 −0.739483 −0.369742 0.929135i \(-0.620554\pi\)
−0.369742 + 0.929135i \(0.620554\pi\)
\(182\) −316.759 1738.16i −0.00956283 0.0524743i
\(183\) −33871.0 + 33037.9i −1.01141 + 0.986531i
\(184\) 12880.4 221.334i 0.380447 0.00653752i
\(185\) 8391.13 14533.9i 0.245176 0.424657i
\(186\) 5117.87 54291.0i 0.147932 1.56928i
\(187\) −53962.5 + 31155.3i −1.54315 + 0.890940i
\(188\) 29262.6 35696.4i 0.827938 1.00997i
\(189\) 8300.38 + 2559.89i 0.232367 + 0.0716634i
\(190\) 1890.16 + 675.726i 0.0523589 + 0.0187182i
\(191\) 19504.6 11261.0i 0.534651 0.308681i −0.208257 0.978074i \(-0.566779\pi\)
0.742908 + 0.669393i \(0.233446\pi\)
\(192\) 35808.4 + 8758.58i 0.971365 + 0.237592i
\(193\) −9144.35 + 15838.5i −0.245493 + 0.425205i −0.962270 0.272097i \(-0.912283\pi\)
0.716777 + 0.697302i \(0.245616\pi\)
\(194\) 31184.4 + 36734.8i 0.828579 + 0.976055i
\(195\) −2634.69 + 2569.88i −0.0692883 + 0.0675841i
\(196\) −5868.28 + 35664.9i −0.152756 + 0.928387i
\(197\) 36300.2 0.935356 0.467678 0.883899i \(-0.345091\pi\)
0.467678 + 0.883899i \(0.345091\pi\)
\(198\) −25587.4 + 66316.3i −0.652674 + 1.69157i
\(199\) 47336.5i 1.19533i −0.801744 0.597667i \(-0.796094\pi\)
0.801744 0.597667i \(-0.203906\pi\)
\(200\) −28168.6 15624.1i −0.704214 0.390602i
\(201\) 2268.25 8062.33i 0.0561434 0.199558i
\(202\) −24735.1 29137.6i −0.606194 0.714088i
\(203\) −12674.7 7317.73i −0.307571 0.177576i
\(204\) 23425.3 + 33525.8i 0.562892 + 0.805600i
\(205\) 14528.3 + 25163.8i 0.345706 + 0.598781i
\(206\) −43328.2 15489.7i −1.02102 0.365014i
\(207\) 16299.1 + 405.949i 0.380385 + 0.00947394i
\(208\) −1861.57 9305.56i −0.0430280 0.215088i
\(209\) −4989.97 8642.89i −0.114237 0.197864i
\(210\) −4301.96 + 1970.93i −0.0975500 + 0.0446923i
\(211\) 40261.7 + 23245.1i 0.904330 + 0.522115i 0.878602 0.477554i \(-0.158476\pi\)
0.0257275 + 0.999669i \(0.491810\pi\)
\(212\) 21186.5 7987.24i 0.471397 0.177715i
\(213\) −10141.1 + 2582.42i −0.223525 + 0.0569203i
\(214\) −4735.09 25982.9i −0.103395 0.567363i
\(215\) 440.814i 0.00953626i
\(216\) 44813.5 + 12981.9i 0.960509 + 0.278247i
\(217\) −18048.7 −0.383290
\(218\) −47400.4 + 8638.18i −0.997400 + 0.181765i
\(219\) −4803.64 18863.8i −0.100157 0.393315i
\(220\) −13660.0 36233.6i −0.282231 0.748629i
\(221\) 5264.34 9118.10i 0.107785 0.186689i
\(222\) 22811.1 + 49789.8i 0.462850 + 1.01026i
\(223\) 71531.9 41298.9i 1.43843 0.830480i 0.440693 0.897658i \(-0.354733\pi\)
0.997741 + 0.0671780i \(0.0213996\pi\)
\(224\) 1773.79 12071.5i 0.0353514 0.240583i
\(225\) −34787.3 21256.6i −0.687157 0.419883i
\(226\) 5023.49 14051.8i 0.0983533 0.275116i
\(227\) −25722.3 + 14850.8i −0.499182 + 0.288203i −0.728376 0.685178i \(-0.759724\pi\)
0.229194 + 0.973381i \(0.426391\pi\)
\(228\) −5369.66 + 3751.91i −0.103294 + 0.0721743i
\(229\) −22667.9 + 39262.0i −0.432256 + 0.748690i −0.997067 0.0765307i \(-0.975616\pi\)
0.564811 + 0.825220i \(0.308949\pi\)
\(230\) −6771.21 + 5748.13i −0.128000 + 0.108660i
\(231\) 22647.1 + 6371.52i 0.424413 + 0.119404i
\(232\) −68744.9 38130.3i −1.27722 0.708425i
\(233\) 50931.3 0.938151 0.469075 0.883158i \(-0.344587\pi\)
0.469075 + 0.883158i \(0.344587\pi\)
\(234\) −1858.48 11866.0i −0.0339411 0.216708i
\(235\) 31824.5i 0.576270i
\(236\) −44724.5 7358.94i −0.803010 0.132127i
\(237\) −47040.0 48226.2i −0.837472 0.858590i
\(238\) 10319.7 8760.43i 0.182184 0.154658i
\(239\) 31946.2 + 18444.1i 0.559272 + 0.322896i 0.752853 0.658188i \(-0.228677\pi\)
−0.193581 + 0.981084i \(0.562010\pi\)
\(240\) −22921.8 + 10981.9i −0.397948 + 0.190658i
\(241\) −4193.64 7263.59i −0.0722033 0.125060i 0.827663 0.561225i \(-0.189670\pi\)
−0.899867 + 0.436165i \(0.856336\pi\)
\(242\) −45094.9 + 126141.i −0.770011 + 2.15389i
\(243\) 55975.7 + 18801.8i 0.947953 + 0.318410i
\(244\) 65052.0 + 53327.3i 1.09265 + 0.895715i
\(245\) −12460.3 21581.9i −0.207586 0.359549i
\(246\) −94403.6 8899.18i −1.55998 0.147055i
\(247\) 1460.40 + 843.160i 0.0239374 + 0.0138203i
\(248\) −96930.9 + 1665.64i −1.57601 + 0.0270818i
\(249\) 7015.18 + 7192.08i 0.113146 + 0.115999i
\(250\) 48981.2 8926.26i 0.783699 0.142820i
\(251\) 1475.47i 0.0234198i −0.999931 0.0117099i \(-0.996273\pi\)
0.999931 0.0117099i \(-0.00372746\pi\)
\(252\) 2885.72 15170.0i 0.0454416 0.238883i
\(253\) 44159.6 0.689897
\(254\) 19039.9 + 104478.i 0.295119 + 1.61941i
\(255\) −27145.0 7636.94i −0.417454 0.117446i
\(256\) 8412.13 64993.9i 0.128359 0.991728i
\(257\) −17336.5 + 30027.8i −0.262480 + 0.454629i −0.966900 0.255154i \(-0.917874\pi\)
0.704420 + 0.709783i \(0.251207\pi\)
\(258\) −1172.80 833.012i −0.0176192 0.0125145i
\(259\) 15698.0 9063.23i 0.234015 0.135109i
\(260\) 5060.12 + 4148.11i 0.0748539 + 0.0613626i
\(261\) −84897.9 51876.3i −1.24628 0.761531i
\(262\) −4970.49 1776.94i −0.0724097 0.0258863i
\(263\) 16482.5 9516.19i 0.238294 0.137579i −0.376099 0.926580i \(-0.622735\pi\)
0.614392 + 0.789001i \(0.289401\pi\)
\(264\) 122215. + 32128.3i 1.75354 + 0.460977i
\(265\) −7805.54 + 13519.6i −0.111151 + 0.192518i
\(266\) 1403.11 + 1652.84i 0.0198303 + 0.0233598i
\(267\) −14968.6 58781.5i −0.209971 0.824552i
\(268\) −14691.9 2417.40i −0.204555 0.0336573i
\(269\) 58724.1 0.811544 0.405772 0.913974i \(-0.367003\pi\)
0.405772 + 0.913974i \(0.367003\pi\)
\(270\) −29569.5 + 12666.2i −0.405617 + 0.173748i
\(271\) 31474.1i 0.428563i 0.976772 + 0.214281i \(0.0687409\pi\)
−0.976772 + 0.214281i \(0.931259\pi\)
\(272\) 54613.4 48000.3i 0.738178 0.648793i
\(273\) −3852.32 + 980.988i −0.0516889 + 0.0131625i
\(274\) 66820.8 + 78714.0i 0.890043 + 1.04846i
\(275\) −95625.2 55209.2i −1.26447 0.730040i
\(276\) −2497.47 28877.4i −0.0327856 0.379088i
\(277\) −33265.8 57618.0i −0.433549 0.750929i 0.563627 0.826029i \(-0.309405\pi\)
−0.997176 + 0.0751008i \(0.976072\pi\)
\(278\) −49484.8 17690.7i −0.640299 0.228905i
\(279\) −122658. 3054.95i −1.57575 0.0392460i
\(280\) 4330.73 + 7211.98i 0.0552389 + 0.0919895i
\(281\) 61859.9 + 107145.i 0.783424 + 1.35693i 0.929936 + 0.367721i \(0.119862\pi\)
−0.146512 + 0.989209i \(0.546805\pi\)
\(282\) −84670.5 60139.3i −1.06472 0.756241i
\(283\) 47401.9 + 27367.5i 0.591865 + 0.341713i 0.765835 0.643038i \(-0.222326\pi\)
−0.173970 + 0.984751i \(0.555659\pi\)
\(284\) 6562.78 + 17408.0i 0.0813675 + 0.215830i
\(285\) 1223.17 4347.66i 0.0150590 0.0535262i
\(286\) −5832.30 32003.7i −0.0713030 0.391262i
\(287\) 31383.9i 0.381016i
\(288\) 14097.8 81737.1i 0.169968 0.985450i
\(289\) −2853.15 −0.0341609
\(290\) 53322.4 9717.39i 0.634036 0.115546i
\(291\) 77612.4 75703.4i 0.916526 0.893983i
\(292\) −32381.2 + 12207.6i −0.379776 + 0.143174i
\(293\) 44309.0 76745.4i 0.516127 0.893958i −0.483698 0.875235i \(-0.660707\pi\)
0.999825 0.0187226i \(-0.00595995\pi\)
\(294\) 80966.1 + 7632.46i 0.936717 + 0.0883019i
\(295\) 27064.1 15625.5i 0.310993 0.179552i
\(296\) 83469.8 50122.9i 0.952677 0.572075i
\(297\) 152830. + 47133.8i 1.73259 + 0.534342i
\(298\) 34924.2 97690.7i 0.393273 1.10007i
\(299\) −6462.01 + 3730.84i −0.0722812 + 0.0417316i
\(300\) −30695.0 + 65654.9i −0.341055 + 0.729498i
\(301\) −238.061 + 412.333i −0.00262757 + 0.00455109i
\(302\) 86589.3 73506.3i 0.949403 0.805955i
\(303\) −61561.3 + 60047.1i −0.670536 + 0.654044i
\(304\) 7687.95 + 8747.13i 0.0831886 + 0.0946495i
\(305\) −57996.0 −0.623446
\(306\) 71614.6 57788.7i 0.764820 0.617163i
\(307\) 123447.i 1.30980i 0.755716 + 0.654900i \(0.227289\pi\)
−0.755716 + 0.654900i \(0.772711\pi\)
\(308\) 6790.48 41269.7i 0.0715813 0.435040i
\(309\) −28038.7 + 99661.8i −0.293658 + 1.04379i
\(310\) 50956.4 43257.2i 0.530243 0.450127i
\(311\) 52431.9 + 30271.6i 0.542094 + 0.312978i 0.745927 0.666027i \(-0.232007\pi\)
−0.203833 + 0.979006i \(0.565340\pi\)
\(312\) −20598.4 + 5623.92i −0.211604 + 0.0577737i
\(313\) 26193.1 + 45367.8i 0.267361 + 0.463083i 0.968180 0.250257i \(-0.0805150\pi\)
−0.700818 + 0.713340i \(0.747182\pi\)
\(314\) −7433.35 + 20792.7i −0.0753920 + 0.210888i
\(315\) 5092.22 + 9350.17i 0.0513200 + 0.0942320i
\(316\) −75928.4 + 92622.1i −0.760378 + 0.927557i
\(317\) 12998.7 + 22514.4i 0.129354 + 0.224048i 0.923427 0.383775i \(-0.125376\pi\)
−0.794072 + 0.607823i \(0.792043\pi\)
\(318\) −21219.2 46315.2i −0.209834 0.458004i
\(319\) −233372. 134737.i −2.29333 1.32406i
\(320\) 23923.8 + 38332.3i 0.233631 + 0.374339i
\(321\) −57586.7 + 14664.4i −0.558871 + 0.142316i
\(322\) −9437.99 + 1719.97i −0.0910265 + 0.0165885i
\(323\) 12920.1i 0.123840i
\(324\) 22178.9 102606.i 0.211276 0.977426i
\(325\) 18657.5 0.176639
\(326\) −292.079 1602.73i −0.00274830 0.0150808i
\(327\) 26752.0 + 105055.i 0.250185 + 0.982472i
\(328\) 2896.29 + 168548.i 0.0269212 + 1.56666i
\(329\) −17186.8 + 29768.4i −0.158783 + 0.275019i
\(330\) −79209.4 + 36289.6i −0.727359 + 0.333238i
\(331\) −37439.2 + 21615.5i −0.341720 + 0.197292i −0.661032 0.750357i \(-0.729881\pi\)
0.319312 + 0.947650i \(0.396548\pi\)
\(332\) 11323.4 13812.9i 0.102731 0.125317i
\(333\) 108217. 58936.2i 0.975901 0.531488i
\(334\) −89428.5 31970.5i −0.801647 0.286587i
\(335\) 8890.54 5132.95i 0.0792206 0.0457381i
\(336\) −27371.6 2106.49i −0.242450 0.0186587i
\(337\) −5926.38 + 10264.8i −0.0521831 + 0.0903837i −0.890937 0.454127i \(-0.849951\pi\)
0.838754 + 0.544511i \(0.183285\pi\)
\(338\) −70377.3 82903.5i −0.616027 0.725671i
\(339\) −32321.5 9093.29i −0.281249 0.0791264i
\(340\) −8139.12 + 49466.1i −0.0704076 + 0.427907i
\(341\) −332321. −2.85791
\(342\) 9255.70 + 11470.1i 0.0791329 + 0.0980655i
\(343\) 55525.0i 0.471955i
\(344\) −1240.45 + 2236.41i −0.0104825 + 0.0188988i
\(345\) 13954.2 + 14306.0i 0.117237 + 0.120194i
\(346\) −7316.83 8619.12i −0.0611182 0.0719964i
\(347\) −25222.5 14562.2i −0.209473 0.120940i 0.391593 0.920138i \(-0.371924\pi\)
−0.601067 + 0.799199i \(0.705257\pi\)
\(348\) −74910.6 + 160230.i −0.618564 + 1.32307i
\(349\) −59988.4 103903.i −0.492512 0.853055i 0.507451 0.861681i \(-0.330588\pi\)
−0.999963 + 0.00862528i \(0.997254\pi\)
\(350\) 22587.8 + 8075.08i 0.184390 + 0.0659191i
\(351\) −26346.2 + 6014.70i −0.213848 + 0.0488202i
\(352\) 32659.8 222266.i 0.263589 1.79385i
\(353\) −77379.0 134024.i −0.620975 1.07556i −0.989305 0.145865i \(-0.953404\pi\)
0.368330 0.929695i \(-0.379930\pi\)
\(354\) −9571.25 + 101533.i −0.0763769 + 0.810216i
\(355\) −11108.5 6413.49i −0.0881451 0.0508906i
\(356\) −100903. + 38040.2i −0.796167 + 0.300153i
\(357\) −21266.8 21803.1i −0.166866 0.171073i
\(358\) 32804.5 + 180009.i 0.255957 + 1.40452i
\(359\) 66839.6i 0.518615i 0.965795 + 0.259307i \(0.0834942\pi\)
−0.965795 + 0.259307i \(0.916506\pi\)
\(360\) 28210.7 + 49745.3i 0.217675 + 0.383837i
\(361\) 128252. 0.984121
\(362\) 95334.7 17373.6i 0.727501 0.132579i
\(363\) 290144. + 81628.7i 2.20191 + 0.619483i
\(364\) 2493.01 + 6612.82i 0.0188158 + 0.0499096i
\(365\) 11929.9 20663.2i 0.0895472 0.155100i
\(366\) 109596. 154301.i 0.818149 1.15188i
\(367\) 81901.3 47285.7i 0.608077 0.351073i −0.164136 0.986438i \(-0.552483\pi\)
0.772212 + 0.635364i \(0.219150\pi\)
\(368\) −50528.1 + 10108.1i −0.373110 + 0.0746403i
\(369\) −5312.08 + 213284.i −0.0390132 + 1.56641i
\(370\) −22597.8 + 63211.2i −0.165068 + 0.461732i
\(371\) −14602.5 + 8430.74i −0.106091 + 0.0612517i
\(372\) 18794.6 + 217315.i 0.135815 + 1.57038i
\(373\) 90530.4 156803.i 0.650694 1.12704i −0.332260 0.943188i \(-0.607811\pi\)
0.982955 0.183848i \(-0.0588554\pi\)
\(374\) 190010. 161301.i 1.35842 1.15317i
\(375\) −27644.2 108558.i −0.196581 0.771970i
\(376\) −89554.6 + 161457.i −0.633450 + 1.14204i
\(377\) 45533.4 0.320366
\(378\) −34499.4 4121.09i −0.241450 0.0288422i
\(379\) 51191.3i 0.356384i −0.983996 0.178192i \(-0.942975\pi\)
0.983996 0.178192i \(-0.0570248\pi\)
\(380\) −7922.71 1303.60i −0.0548664 0.00902769i
\(381\) 231557. 58965.7i 1.59518 0.406209i
\(382\) −68678.6 + 58301.7i −0.470646 + 0.399535i
\(383\) 132128. + 76284.0i 0.900734 + 0.520039i 0.877438 0.479690i \(-0.159251\pi\)
0.0232957 + 0.999729i \(0.492584\pi\)
\(384\) −147194. 8786.92i −0.998223 0.0595901i
\(385\) 14418.5 + 24973.5i 0.0972742 + 0.168484i
\(386\) 24626.3 68885.2i 0.165282 0.462329i
\(387\) −1687.64 + 2761.90i −0.0112683 + 0.0184411i
\(388\) −149061. 122195.i −0.990147 0.811687i
\(389\) −33948.4 58800.3i −0.224347 0.388580i 0.731776 0.681545i \(-0.238692\pi\)
−0.956123 + 0.292965i \(0.905358\pi\)
\(390\) 8525.02 12002.4i 0.0560488 0.0789114i
\(391\) −49510.2 28584.7i −0.323848 0.186974i
\(392\) −2484.03 144556.i −0.0161653 0.940731i
\(393\) −3216.53 + 11432.9i −0.0208258 + 0.0740240i
\(394\) −142848. + 26032.5i −0.920201 + 0.167696i
\(395\) 82575.7i 0.529247i
\(396\) 53133.1 279317.i 0.338825 1.78118i
\(397\) −126087. −0.799998 −0.399999 0.916516i \(-0.630990\pi\)
−0.399999 + 0.916516i \(0.630990\pi\)
\(398\) 33947.0 + 186278.i 0.214306 + 1.17597i
\(399\) 3492.09 3406.20i 0.0219351 0.0213956i
\(400\) 122053. + 41282.8i 0.762833 + 0.258017i
\(401\) −35445.4 + 61393.2i −0.220430 + 0.381796i −0.954939 0.296803i \(-0.904079\pi\)
0.734509 + 0.678599i \(0.237413\pi\)
\(402\) −3144.14 + 33353.5i −0.0194558 + 0.206390i
\(403\) 48629.5 28076.3i 0.299426 0.172874i
\(404\) 118233. + 96923.5i 0.724398 + 0.593836i
\(405\) 33023.9 + 64405.2i 0.201334 + 0.392655i
\(406\) 55125.1 + 19707.1i 0.334424 + 0.119556i
\(407\) 289038. 166876.i 1.74488 1.00741i
\(408\) −116226. 115131.i −0.698204 0.691628i
\(409\) −21772.1 + 37710.4i −0.130153 + 0.225432i −0.923735 0.383031i \(-0.874880\pi\)
0.793582 + 0.608463i \(0.208214\pi\)
\(410\) −75217.6 88605.3i −0.447458 0.527099i
\(411\) 166305. 162215.i 0.984513 0.960298i
\(412\) 181613. + 29882.5i 1.06992 + 0.176044i
\(413\) 33754.1 0.197891
\(414\) −64431.2 + 10091.3i −0.375920 + 0.0588772i
\(415\) 12314.7i 0.0715036i
\(416\) 13999.0 + 35284.1i 0.0808930 + 0.203888i
\(417\) −32022.9 + 113823.i −0.184157 + 0.654573i
\(418\) 25834.7 + 30432.9i 0.147860 + 0.174177i
\(419\) −182385. 105300.i −1.03887 0.599792i −0.119357 0.992851i \(-0.538083\pi\)
−0.919513 + 0.393060i \(0.871417\pi\)
\(420\) 15515.6 10841.1i 0.0879567 0.0614575i
\(421\) −42063.0 72855.3i −0.237321 0.411052i 0.722624 0.691242i \(-0.242936\pi\)
−0.959945 + 0.280190i \(0.909603\pi\)
\(422\) −175107. 62600.4i −0.983285 0.351522i
\(423\) −121839. + 199395.i −0.680935 + 1.11438i
\(424\) −77644.7 + 46625.0i −0.431897 + 0.259350i
\(425\) 71474.4 + 123797.i 0.395706 + 0.685383i
\(426\) 38055.2 17434.9i 0.209698 0.0960729i
\(427\) −54249.0 31320.7i −0.297533 0.171781i
\(428\) 37266.9 + 98852.0i 0.203440 + 0.539632i
\(429\) −70930.6 + 18062.4i −0.385407 + 0.0981432i
\(430\) −316.126 1734.69i −0.00170972 0.00938175i
\(431\) 150083.i 0.807933i 0.914774 + 0.403967i \(0.132369\pi\)
−0.914774 + 0.403967i \(0.867631\pi\)
\(432\) −185660. 18948.5i −0.994832 0.101533i
\(433\) 71221.5 0.379871 0.189935 0.981797i \(-0.439172\pi\)
0.189935 + 0.981797i \(0.439172\pi\)
\(434\) 71025.1 12943.5i 0.377079 0.0687183i
\(435\) −30094.3 118180.i −0.159040 0.624546i
\(436\) 180335. 67985.7i 0.948651 0.357639i
\(437\) 4578.26 7929.78i 0.0239739 0.0415239i
\(438\) 32431.2 + 70787.7i 0.169050 + 0.368986i
\(439\) 94609.3 54622.7i 0.490913 0.283429i −0.234040 0.972227i \(-0.575195\pi\)
0.724953 + 0.688798i \(0.241861\pi\)
\(440\) 79739.3 + 132790.i 0.411876 + 0.685899i
\(441\) 4555.95 182925.i 0.0234262 0.940578i
\(442\) −14177.2 + 39656.7i −0.0725680 + 0.202989i
\(443\) −199756. + 115329.i −1.01787 + 0.587666i −0.913486 0.406871i \(-0.866620\pi\)
−0.104382 + 0.994537i \(0.533287\pi\)
\(444\) −125472. 179574.i −0.636477 0.910912i
\(445\) 37174.8 64388.7i 0.187728 0.325154i
\(446\) −251874. + 213818.i −1.26623 + 1.07491i
\(447\) −224704. 63218.1i −1.12460 0.316393i
\(448\) 1676.80 + 48775.7i 0.00835458 + 0.243023i
\(449\) −9751.64 −0.0483710 −0.0241855 0.999707i \(-0.507699\pi\)
−0.0241855 + 0.999707i \(0.507699\pi\)
\(450\) 152139. + 58701.1i 0.751302 + 0.289882i
\(451\) 577854.i 2.84096i
\(452\) −9691.23 + 58899.1i −0.0474353 + 0.288292i
\(453\) −178444. 182944.i −0.869573 0.891500i
\(454\) 90572.1 76887.2i 0.439423 0.373029i
\(455\) −4219.80 2436.30i −0.0203831 0.0117682i
\(456\) 18440.0 18615.3i 0.0886809 0.0895241i
\(457\) −33069.5 57278.1i −0.158342 0.274256i 0.775929 0.630820i \(-0.217281\pi\)
−0.934271 + 0.356564i \(0.883948\pi\)
\(458\) 61046.1 170760.i 0.291023 0.814056i
\(459\) −140838. 151772.i −0.668489 0.720390i
\(460\) 22523.8 27475.9i 0.106445 0.129848i
\(461\) 86994.6 + 150679.i 0.409346 + 0.709008i 0.994817 0.101686i \(-0.0324236\pi\)
−0.585471 + 0.810694i \(0.699090\pi\)
\(462\) −93689.9 8831.90i −0.438944 0.0413781i
\(463\) 150682. + 86996.3i 0.702909 + 0.405825i 0.808430 0.588592i \(-0.200318\pi\)
−0.105521 + 0.994417i \(0.533651\pi\)
\(464\) 297869. + 100750.i 1.38353 + 0.467960i
\(465\) −105011. 107659.i −0.485658 0.497905i
\(466\) −200424. + 36525.0i −0.922950 + 0.168197i
\(467\) 172090.i 0.789080i 0.918879 + 0.394540i \(0.129096\pi\)
−0.918879 + 0.394540i \(0.870904\pi\)
\(468\) 15823.1 + 45362.3i 0.0722437 + 0.207111i
\(469\) 11088.2 0.0504097
\(470\) −22822.7 125236.i −0.103317 0.566933i
\(471\) 47826.6 + 13455.5i 0.215590 + 0.0606538i
\(472\) 181277. 3115.02i 0.813688 0.0139822i
\(473\) −4383.27 + 7592.05i −0.0195919 + 0.0339341i
\(474\) 219696. + 156045.i 0.977836 + 0.694532i
\(475\) −19828.0 + 11447.7i −0.0878802 + 0.0507376i
\(476\) −34327.3 + 41874.6i −0.151505 + 0.184815i
\(477\) −100665. + 54823.3i −0.442426 + 0.240951i
\(478\) −138941. 49671.2i −0.608101 0.217395i
\(479\) −189138. + 109199.i −0.824343 + 0.475935i −0.851912 0.523685i \(-0.824557\pi\)
0.0275690 + 0.999620i \(0.491223\pi\)
\(480\) 82326.0 59654.1i 0.357318 0.258916i
\(481\) −28197.2 + 48839.0i −0.121875 + 0.211094i
\(482\) 21711.8 + 25576.2i 0.0934548 + 0.110088i
\(483\) 5326.65 + 20917.7i 0.0228328 + 0.0896642i
\(484\) 86996.3 528726.i 0.371373 2.25705i
\(485\) 132893. 0.564959
\(486\) −233758. 33846.1i −0.989680 0.143297i
\(487\) 392112.i 1.65330i −0.562716 0.826650i \(-0.690243\pi\)
0.562716 0.826650i \(-0.309757\pi\)
\(488\) −294235. 163201.i −1.23553 0.685306i
\(489\) −3552.17 + 904.554i −0.0148551 + 0.00378283i
\(490\) 64511.1 + 75993.1i 0.268684 + 0.316506i
\(491\) −181620. 104859.i −0.753358 0.434951i 0.0735480 0.997292i \(-0.476568\pi\)
−0.826906 + 0.562340i \(0.809901\pi\)
\(492\) 377878. 32680.9i 1.56107 0.135009i
\(493\) 174432. + 302125.i 0.717683 + 1.24306i
\(494\) −6351.60 2270.68i −0.0260273 0.00930470i
\(495\) 93760.2 + 172159.i 0.382655 + 0.702619i
\(496\) 380247. 76067.9i 1.54562 0.309199i
\(497\) −6927.19 11998.2i −0.0280443 0.0485741i
\(498\) −32763.8 23271.3i −0.132110 0.0938344i
\(499\) −117681. 67943.0i −0.472611 0.272862i 0.244721 0.969594i \(-0.421304\pi\)
−0.717332 + 0.696731i \(0.754637\pi\)
\(500\) −186349. + 70253.0i −0.745395 + 0.281012i
\(501\) −57871.4 + 205700.i −0.230562 + 0.819518i
\(502\) 1058.12 + 5806.24i 0.00419883 + 0.0230403i
\(503\) 232332.i 0.918275i −0.888365 0.459137i \(-0.848159\pi\)
0.888365 0.459137i \(-0.151841\pi\)
\(504\) −476.781 + 61766.4i −0.00187697 + 0.243160i
\(505\) −105409. −0.413328
\(506\) −173776. + 31668.7i −0.678718 + 0.123689i
\(507\) −175156. + 170848.i −0.681413 + 0.664653i
\(508\) −149851. 397486.i −0.580675 1.54026i
\(509\) 72659.4 125850.i 0.280451 0.485755i −0.691045 0.722812i \(-0.742849\pi\)
0.971496 + 0.237057i \(0.0761827\pi\)
\(510\) 112297. + 10586.0i 0.431747 + 0.0406996i
\(511\) 22318.3 12885.5i 0.0854711 0.0493467i
\(512\) 13506.6 + 261796.i 0.0515234 + 0.998672i
\(513\) 24308.6 22557.3i 0.0923687 0.0857140i
\(514\) 46688.3 130598.i 0.176719 0.494321i
\(515\) −109899. + 63450.5i −0.414363 + 0.239233i
\(516\) 5212.59 + 2436.99i 0.0195774 + 0.00915282i
\(517\) −316450. + 548108.i −1.18393 + 2.05062i
\(518\) −55274.9 + 46923.2i −0.206001 + 0.174875i
\(519\) −18210.3 + 17762.4i −0.0676054 + 0.0659426i
\(520\) −22887.3 12694.8i −0.0846425 0.0469481i
\(521\) 443088. 1.63235 0.816177 0.577803i \(-0.196090\pi\)
0.816177 + 0.577803i \(0.196090\pi\)
\(522\) 371292. + 143259.i 1.36262 + 0.525752i
\(523\) 73202.4i 0.267622i 0.991007 + 0.133811i \(0.0427215\pi\)
−0.991007 + 0.133811i \(0.957278\pi\)
\(524\) 20834.1 + 3428.04i 0.0758775 + 0.0124848i
\(525\) 14617.1 51955.6i 0.0530327 0.188501i
\(526\) −58037.4 + 49268.3i −0.209767 + 0.178072i
\(527\) 372587. + 215113.i 1.34155 + 0.774543i
\(528\) −503978. 38785.6i −1.80777 0.139124i
\(529\) −119662. 207261.i −0.427609 0.740640i
\(530\) 21020.8 58799.9i 0.0748338 0.209327i
\(531\) 229391. + 5713.25i 0.813555 + 0.0202626i
\(532\) −6706.83 5498.02i −0.0236970 0.0194260i
\(533\) −48820.3 84559.2i −0.171849 0.297651i
\(534\) 101059. + 220582.i 0.354399 + 0.773547i
\(535\) −63079.9 36419.2i −0.220386 0.127240i
\(536\) 59549.1 1023.28i 0.207274 0.00356176i
\(537\) 398958. 101594.i 1.38350 0.352306i
\(538\) −231090. + 42113.6i −0.798394 + 0.145498i
\(539\) 495602.i 1.70591i
\(540\) 107278. 71049.4i 0.367894 0.243654i
\(541\) 438165. 1.49707 0.748536 0.663094i \(-0.230757\pi\)
0.748536 + 0.663094i \(0.230757\pi\)
\(542\) −22571.4 123856.i −0.0768351 0.421619i
\(543\) −53805.4 211293.i −0.182485 0.716613i
\(544\) −180491. + 228056.i −0.609898 + 0.770625i
\(545\) −66439.2 + 115076.i −0.223682 + 0.387429i
\(546\) 14456.1 6623.04i 0.0484916 0.0222163i
\(547\) 270221. 156012.i 0.903118 0.521416i 0.0249077 0.999690i \(-0.492071\pi\)
0.878211 + 0.478274i \(0.158737\pi\)
\(548\) −319402. 261834.i −1.06359 0.871898i
\(549\) −363372. 222036.i −1.20561 0.736679i
\(550\) 415896. + 148682.i 1.37486 + 0.491510i
\(551\) −48389.8 + 27937.9i −0.159386 + 0.0920217i
\(552\) 30537.2 + 111847.i 0.100219 + 0.367068i
\(553\) 44594.9 77240.6i 0.145826 0.252578i
\(554\) 172227. + 202881.i 0.561155 + 0.661032i
\(555\) 145396. + 40905.5i 0.472026 + 0.132799i
\(556\) 207419. + 34128.6i 0.670963 + 0.110400i
\(557\) 312549. 1.00741 0.503707 0.863874i \(-0.331969\pi\)
0.503707 + 0.863874i \(0.331969\pi\)
\(558\) 484874. 75941.6i 1.55726 0.243900i
\(559\) 1481.29i 0.00474042i
\(560\) −22214.3 25274.7i −0.0708363 0.0805955i
\(561\) −391574. 401448.i −1.24419 1.27557i
\(562\) −320268. 377272.i −1.01401 1.19449i
\(563\) 74780.6 + 43174.6i 0.235924 + 0.136211i 0.613302 0.789849i \(-0.289841\pi\)
−0.377378 + 0.926059i \(0.623174\pi\)
\(564\) 376323. + 175939.i 1.18305 + 0.553099i
\(565\) −20577.7 35641.7i −0.0644615 0.111651i
\(566\) −206162. 73702.3i −0.643539 0.230064i
\(567\) −3891.69 + 78078.5i −0.0121052 + 0.242865i
\(568\) −38309.8 63797.4i −0.118744 0.197745i
\(569\) −277479. 480608.i −0.857049 1.48445i −0.874731 0.484609i \(-0.838962\pi\)
0.0176822 0.999844i \(-0.494371\pi\)
\(570\) −1695.50 + 17986.1i −0.00521852 + 0.0553588i
\(571\) 262848. + 151755.i 0.806181 + 0.465449i 0.845628 0.533773i \(-0.179226\pi\)
−0.0394467 + 0.999222i \(0.512560\pi\)
\(572\) 45902.4 + 121758.i 0.140295 + 0.372139i
\(573\) 141533. + 145102.i 0.431072 + 0.441942i
\(574\) −22506.8 123502.i −0.0683108 0.374843i
\(575\) 101308.i 0.306414i
\(576\) 3139.60 + 331761.i 0.00946301 + 0.999955i
\(577\) −500884. −1.50448 −0.752238 0.658892i \(-0.771026\pi\)
−0.752238 + 0.658892i \(0.771026\pi\)
\(578\) 11227.7 2046.12i 0.0336074 0.00612456i
\(579\) −158447. 44577.3i −0.472636 0.132971i
\(580\) −202865. + 76479.5i −0.603047 + 0.227347i
\(581\) −6650.54 + 11519.1i −0.0197017 + 0.0341244i
\(582\) −251129. + 353566.i −0.741398 + 1.04382i
\(583\) −268867. + 155230.i −0.791043 + 0.456709i
\(584\) 118671. 71261.2i 0.347953 0.208943i
\(585\) −28265.2 17271.2i −0.0825924 0.0504675i
\(586\) −119327. + 333783.i −0.347490 + 0.972007i
\(587\) 498580. 287855.i 1.44697 0.835406i 0.448666 0.893699i \(-0.351899\pi\)
0.998300 + 0.0582932i \(0.0185658\pi\)
\(588\) −324090. + 28029.1i −0.937371 + 0.0810688i
\(589\) −34453.5 + 59675.2i −0.0993122 + 0.172014i
\(590\) −95296.8 + 80898.1i −0.273763 + 0.232399i
\(591\) 80621.3 + 316598.i 0.230821 + 0.906429i
\(592\) −292524. + 257103.i −0.834676 + 0.733607i
\(593\) −138143. −0.392843 −0.196421 0.980520i \(-0.562932\pi\)
−0.196421 + 0.980520i \(0.562932\pi\)
\(594\) −635217. 75879.2i −1.80032 0.215055i
\(595\) 37332.6i 0.105452i
\(596\) −67375.1 + 409477.i −0.189674 + 1.15275i
\(597\) 412852. 105132.i 1.15837 0.294976i
\(598\) 22753.7 19315.8i 0.0636282 0.0540144i
\(599\) 165665. + 95646.9i 0.461719 + 0.266574i 0.712767 0.701401i \(-0.247442\pi\)
−0.251048 + 0.967975i \(0.580775\pi\)
\(600\) 73706.7 280377.i 0.204741 0.778825i
\(601\) 203120. + 351814.i 0.562346 + 0.974012i 0.997291 + 0.0735551i \(0.0234345\pi\)
−0.434945 + 0.900457i \(0.643232\pi\)
\(602\) 641.112 1793.33i 0.00176905 0.00494843i
\(603\) 75354.6 + 1876.80i 0.207241 + 0.00516158i
\(604\) −288031. + 351358.i −0.789524 + 0.963110i
\(605\) 184722. + 319948.i 0.504671 + 0.874117i
\(606\) 199193. 280445.i 0.542411 0.763664i
\(607\) −59466.9 34333.2i −0.161398 0.0931831i 0.417126 0.908849i \(-0.363038\pi\)
−0.578523 + 0.815666i \(0.696371\pi\)
\(608\) −36526.5 28908.2i −0.0988100 0.0782014i
\(609\) 35672.9 126797.i 0.0961841 0.341880i
\(610\) 228225. 41591.4i 0.613344 0.111775i
\(611\) 106942.i 0.286461i
\(612\) −240374. + 278767.i −0.641779 + 0.744284i
\(613\) −572114. −1.52252 −0.761258 0.648450i \(-0.775418\pi\)
−0.761258 + 0.648450i \(0.775418\pi\)
\(614\) −88529.3 485788.i −0.234828 1.28858i
\(615\) −187203. + 182599.i −0.494951 + 0.482778i
\(616\) 2874.39 + 167274.i 0.00757504 + 0.440825i
\(617\) −10190.4 + 17650.3i −0.0267684 + 0.0463642i −0.879099 0.476639i \(-0.841855\pi\)
0.852331 + 0.523003i \(0.175188\pi\)
\(618\) 38866.0 412296.i 0.101764 1.07952i
\(619\) −388604. + 224361.i −1.01421 + 0.585552i −0.912420 0.409254i \(-0.865789\pi\)
−0.101786 + 0.994806i \(0.532456\pi\)
\(620\) −169501. + 206768.i −0.440951 + 0.537899i
\(621\) 32659.1 + 143057.i 0.0846878 + 0.370959i
\(622\) −228038. 81523.2i −0.589423 0.210717i
\(623\) 69546.0 40152.4i 0.179183 0.103451i
\(624\) 77025.5 36903.2i 0.197818 0.0947752i
\(625\) −88627.6 + 153508.i −0.226887 + 0.392979i
\(626\) −135610. 159747.i −0.346053 0.407646i
\(627\) 64297.8 62716.3i 0.163554 0.159531i
\(628\) 14340.3 87154.1i 0.0363612 0.220988i
\(629\) −432079. −1.09210
\(630\) −26744.3 33142.8i −0.0673829 0.0835042i
\(631\) 402529.i 1.01097i −0.862835 0.505486i \(-0.831313\pi\)
0.862835 0.505486i \(-0.168687\pi\)
\(632\) 232369. 418937.i 0.581760 1.04885i
\(633\) −113316. + 402775.i −0.282804 + 1.00521i
\(634\) −67298.3 79276.4i −0.167427 0.197227i
\(635\) 253646. + 146443.i 0.629043 + 0.363178i
\(636\) 116716. + 167042.i 0.288547 + 0.412963i
\(637\) 41871.2 + 72523.0i 0.103190 + 0.178730i
\(638\) 1.01499e6 + 362856.i 2.49356 + 0.891441i
\(639\) −45046.0 82711.9i −0.110320 0.202566i
\(640\) −121634. 133688.i −0.296959 0.326387i
\(641\) −176906. 306411.i −0.430554 0.745741i 0.566367 0.824153i \(-0.308348\pi\)
−0.996921 + 0.0784117i \(0.975015\pi\)
\(642\) 216098. 99004.8i 0.524301 0.240207i
\(643\) 227886. + 131570.i 0.551184 + 0.318226i 0.749599 0.661892i \(-0.230246\pi\)
−0.198415 + 0.980118i \(0.563580\pi\)
\(644\) 35906.8 13536.8i 0.0865775 0.0326395i
\(645\) −3844.63 + 979.028i −0.00924134 + 0.00235329i
\(646\) −9265.58 50843.2i −0.0222028 0.121834i
\(647\) 265174.i 0.633464i 0.948515 + 0.316732i \(0.102586\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(648\) −13694.8 + 419681.i −0.0326142 + 0.999468i
\(649\) 621494. 1.47553
\(650\) −73420.8 + 13380.1i −0.173777 + 0.0316689i
\(651\) −40085.5 157415.i −0.0945856 0.371436i
\(652\) 2298.77 + 6097.57i 0.00540754 + 0.0143437i
\(653\) 2938.96 5090.43i 0.00689235 0.0119379i −0.862559 0.505957i \(-0.831139\pi\)
0.869451 + 0.494019i \(0.164473\pi\)
\(654\) −180614. 394225.i −0.422274 0.921699i
\(655\) −12607.4 + 7278.87i −0.0293861 + 0.0169661i
\(656\) −132270. 661190.i −0.307365 1.53645i
\(657\) 153855. 83791.4i 0.356435 0.194119i
\(658\) 46285.0 129470.i 0.106903 0.299031i
\(659\) −480334. + 277321.i −1.10604 + 0.638575i −0.937802 0.347171i \(-0.887142\pi\)
−0.168242 + 0.985746i \(0.553809\pi\)
\(660\) 285679. 199611.i 0.655829 0.458244i
\(661\) 410614. 711204.i 0.939789 1.62776i 0.173926 0.984759i \(-0.444355\pi\)
0.765863 0.643004i \(-0.222312\pi\)
\(662\) 131829. 111910.i 0.300812 0.255361i
\(663\) 91216.8 + 25662.8i 0.207514 + 0.0583818i
\(664\) −34653.7 + 62477.0i −0.0785984 + 0.141705i
\(665\) 5979.36 0.0135211
\(666\) −383588. + 309532.i −0.864801 + 0.697842i
\(667\) 247241.i 0.555736i
\(668\) 374845. + 61676.8i 0.840039 + 0.138219i
\(669\) 519065. + 532153.i 1.15976 + 1.18901i
\(670\) −31304.9 + 26574.9i −0.0697368 + 0.0592001i
\(671\) −998855. 576689.i −2.21849 1.28085i
\(672\) 109223. 11339.9i 0.241867 0.0251114i
\(673\) −258432. 447618.i −0.570580 0.988274i −0.996506 0.0835158i \(-0.973385\pi\)
0.425926 0.904758i \(-0.359948\pi\)
\(674\) 15960.1 44643.9i 0.0351330 0.0982749i
\(675\) 108131. 350613.i 0.237325 0.769522i
\(676\) 336402. + 275770.i 0.736148 + 0.603468i
\(677\) 345343. + 598152.i 0.753483 + 1.30507i 0.946125 + 0.323801i \(0.104961\pi\)
−0.192642 + 0.981269i \(0.561706\pi\)
\(678\) 133712. + 12604.7i 0.290879 + 0.0274204i
\(679\) 124307. + 71768.4i 0.269621 + 0.155666i
\(680\) −3445.26 200495.i −0.00745083 0.433597i
\(681\) −186652. 191358.i −0.402474 0.412623i
\(682\) 1.30774e6 238321.i 2.81160 0.512382i
\(683\) 764551.i 1.63895i 0.573117 + 0.819474i \(0.305734\pi\)
−0.573117 + 0.819474i \(0.694266\pi\)
\(684\) −44648.7 38499.5i −0.0954325 0.0822892i
\(685\) 284757. 0.606868
\(686\) 39819.4 + 218502.i 0.0846148 + 0.464308i
\(687\) −392775. 110503.i −0.832204 0.234131i
\(688\) 3277.60 9690.27i 0.00692435 0.0204719i
\(689\) 26229.4 45430.7i 0.0552523 0.0956998i
\(690\) −65171.8 46289.8i −0.136887 0.0972271i
\(691\) −278107. + 160565.i −0.582445 + 0.336275i −0.762105 0.647454i \(-0.775834\pi\)
0.179659 + 0.983729i \(0.442500\pi\)
\(692\) 34974.2 + 28670.6i 0.0730358 + 0.0598722i
\(693\) −5271.92 + 211671.i −0.0109775 + 0.440753i
\(694\) 109698. + 39216.9i 0.227762 + 0.0814244i
\(695\) −125516. + 72466.4i −0.259853 + 0.150026i
\(696\) 179880. 684255.i 0.371334 1.41254i
\(697\) 374048. 647870.i 0.769949 1.33359i
\(698\) 310579. + 365858.i 0.637472 + 0.750933i
\(699\) 113116. + 444205.i 0.231510 + 0.909137i
\(700\) −94678.2 15578.3i −0.193221 0.0317925i
\(701\) −621799. −1.26536 −0.632680 0.774413i \(-0.718045\pi\)
−0.632680 + 0.774413i \(0.718045\pi\)
\(702\) 99364.0 42563.0i 0.201630 0.0863690i
\(703\) 69203.8i 0.140029i
\(704\) 30873.9 + 898079.i 0.0622940 + 1.81205i
\(705\) −277563. + 70680.9i −0.558448 + 0.142208i
\(706\) 400616. + 471920.i 0.803745 + 0.946801i
\(707\) −98598.6 56925.9i −0.197257 0.113886i
\(708\) −35149.0 406415.i −0.0701207 0.810781i
\(709\) 262435. + 454550.i 0.522070 + 0.904252i 0.999670 + 0.0256748i \(0.00817343\pi\)
−0.477600 + 0.878577i \(0.658493\pi\)
\(710\) 48313.4 + 17271.9i 0.0958409 + 0.0342629i
\(711\) 316138. 517375.i 0.625371 1.02345i
\(712\) 369792. 222057.i 0.729454 0.438031i
\(713\) −152451. 264053.i −0.299882 0.519412i
\(714\) 99325.0 + 70548.0i 0.194833 + 0.138385i
\(715\) −77696.8 44858.2i −0.151982 0.0877466i
\(716\) −258184. 684843.i −0.503620 1.33587i
\(717\) −89912.4 + 319588.i −0.174897 + 0.621658i
\(718\) −47933.5 263026.i −0.0929801 0.510211i
\(719\) 348658.i 0.674438i 0.941426 + 0.337219i \(0.109486\pi\)
−0.941426 + 0.337219i \(0.890514\pi\)
\(720\) −146689. 175526.i −0.282965 0.338591i
\(721\) −137065. −0.263668
\(722\) −504694. + 91974.7i −0.968175 + 0.176439i
\(723\) 54036.7 52707.6i 0.103374 0.100832i
\(724\) −362701. + 136737.i −0.691944 + 0.260861i
\(725\) −309106. + 535387.i −0.588073 + 1.01857i
\(726\) −1.20031e6 113150.i −2.27730 0.214675i
\(727\) −523789. + 302410.i −0.991032 + 0.572173i −0.905583 0.424170i \(-0.860566\pi\)
−0.0854497 + 0.996342i \(0.527233\pi\)
\(728\) −14552.8 24234.8i −0.0274590 0.0457275i
\(729\) −39663.4 + 529959.i −0.0746336 + 0.997211i
\(730\) −32128.0 + 89869.2i −0.0602890 + 0.168642i
\(731\) 9828.75 5674.63i 0.0183935 0.0106195i
\(732\) −320625. + 685799.i −0.598378 + 1.27990i
\(733\) 237805. 411891.i 0.442602 0.766609i −0.555280 0.831664i \(-0.687389\pi\)
0.997882 + 0.0650546i \(0.0207222\pi\)
\(734\) −288386. + 244813.i −0.535282 + 0.454404i
\(735\) 160556. 156607.i 0.297203 0.289893i
\(736\) 191589. 76013.1i 0.353683 0.140324i
\(737\) 204160. 0.375868
\(738\) −132051. 843121.i −0.242453 1.54802i
\(739\) 844449.i 1.54627i −0.634244 0.773133i \(-0.718688\pi\)
0.634244 0.773133i \(-0.281312\pi\)
\(740\) 43595.3 264954.i 0.0796116 0.483845i
\(741\) −4110.28 + 14609.7i −0.00748574 + 0.0266076i
\(742\) 51417.4 43648.6i 0.0933905 0.0792798i
\(743\) 537216. + 310162.i 0.973131 + 0.561837i 0.900189 0.435499i \(-0.143428\pi\)
0.0729415 + 0.997336i \(0.476761\pi\)
\(744\) −229806. 841699.i −0.415161 1.52059i
\(745\) −143060. 247787.i −0.257754 0.446443i
\(746\) −243804. + 681974.i −0.438090 + 1.22543i
\(747\) −47146.4 + 77157.3i −0.0844905 + 0.138273i
\(748\) −632049. + 771013.i −1.12966 + 1.37803i
\(749\) −39336.3 68132.4i −0.0701180 0.121448i
\(750\) 186637. + 407373.i 0.331799 + 0.724218i
\(751\) 632847. + 365374.i 1.12207 + 0.647825i 0.941928 0.335816i \(-0.109012\pi\)
0.180139 + 0.983641i \(0.442345\pi\)
\(752\) 236626. 699589.i 0.418434 1.23711i
\(753\) 12868.5 3276.95i 0.0226955 0.00577936i
\(754\) −179182. + 32653.9i −0.315176 + 0.0574371i
\(755\) 313247.i 0.549533i
\(756\) 138717. 8523.71i 0.242709 0.0149137i
\(757\) −769023. −1.34198 −0.670992 0.741465i \(-0.734132\pi\)
−0.670992 + 0.741465i \(0.734132\pi\)
\(758\) 36711.5 + 201447.i 0.0638945 + 0.350609i
\(759\) 98076.6 + 385145.i 0.170248 + 0.668560i
\(760\) 32112.2 551.810i 0.0555960 0.000955349i
\(761\) −137697. + 238498.i −0.237769 + 0.411828i −0.960074 0.279747i \(-0.909749\pi\)
0.722305 + 0.691575i \(0.243083\pi\)
\(762\) −868935. + 398101.i −1.49650 + 0.685620i
\(763\) −124293. + 71760.8i −0.213500 + 0.123264i
\(764\) 228452. 278680.i 0.391389 0.477441i
\(765\) 6318.96 253710.i 0.0107975 0.433526i
\(766\) −574654. 205437.i −0.979375 0.350124i
\(767\) −90945.2 + 52507.2i −0.154593 + 0.0892541i
\(768\) 585537. 70980.9i 0.992732 0.120342i
\(769\) 26421.1 45762.6i 0.0446784 0.0773853i −0.842821 0.538193i \(-0.819107\pi\)
0.887500 + 0.460808i \(0.152440\pi\)
\(770\) −74649.0 87935.4i −0.125905 0.148314i
\(771\) −300396. 84513.0i −0.505341 0.142172i
\(772\) −47508.6 + 288737.i −0.0797145 + 0.484471i
\(773\) −195309. −0.326861 −0.163430 0.986555i \(-0.552256\pi\)
−0.163430 + 0.986555i \(0.552256\pi\)
\(774\) 4660.50 12078.9i 0.00777949 0.0201625i
\(775\) 762389.i 1.26933i
\(776\) 674213. + 373961.i 1.11963 + 0.621017i
\(777\) 113911. + 116783.i 0.188679 + 0.193437i
\(778\) 175761. + 207045.i 0.290379 + 0.342062i
\(779\) 103766. + 59909.3i 0.170994 + 0.0987232i
\(780\) −24940.1 + 53345.4i −0.0409929 + 0.0876815i
\(781\) −127546. 220917.i −0.209106 0.362182i
\(782\) 215331. + 76980.4i 0.352122 + 0.125883i
\(783\) 263893. 855666.i 0.430431 1.39566i
\(784\) 113443. + 567076.i 0.184563 + 0.922590i
\(785\) 30449.2 + 52739.6i 0.0494125 + 0.0855849i
\(786\) 4458.60 47297.4i 0.00721695 0.0765583i
\(787\) 677438. + 391119.i 1.09375 + 0.631480i 0.934574 0.355770i \(-0.115781\pi\)
0.159181 + 0.987249i \(0.449115\pi\)
\(788\) 543466. 204885.i 0.875225 0.329958i
\(789\) 119604. + 122620.i 0.192128 + 0.196973i
\(790\) 59218.6 + 324951.i 0.0948864 + 0.520672i
\(791\) 44451.9i 0.0710456i
\(792\) −8778.69 + 1.13727e6i −0.0139952 + 1.81306i
\(793\) 194887. 0.309911
\(794\) 496176. 90422.3i 0.787036 0.143428i
\(795\) −135249. 38050.9i −0.213993 0.0602047i
\(796\) −267176. 708694.i −0.421668 1.11849i
\(797\) 586714. 1.01622e6i 0.923655 1.59982i 0.129944 0.991521i \(-0.458520\pi\)
0.793711 0.608296i \(-0.208146\pi\)
\(798\) −11299.3 + 15908.3i −0.0177438 + 0.0249815i
\(799\) 709586. 409680.i 1.11151 0.641728i
\(800\) −509908. 74926.0i −0.796731 0.117072i
\(801\) 479427. 261102.i 0.747236 0.406954i
\(802\) 95456.6 267013.i 0.148408 0.415130i
\(803\) 410934. 237253.i 0.637295 0.367943i
\(804\) −11546.4 133507.i −0.0178622 0.206534i
\(805\) −13228.8 + 22913.0i −0.0204141 + 0.0353583i
\(806\) −171232. + 145360.i −0.263581 + 0.223756i
\(807\) 130424. + 512172.i 0.200267 + 0.786445i
\(808\) −534778. 296622.i −0.819126 0.454340i
\(809\) −421614. −0.644196 −0.322098 0.946706i \(-0.604388\pi\)
−0.322098 + 0.946706i \(0.604388\pi\)
\(810\) −176143. 229764.i −0.268469 0.350196i
\(811\) 504037.i 0.766339i −0.923678 0.383169i \(-0.874833\pi\)
0.923678 0.383169i \(-0.125167\pi\)
\(812\) −231061. 38018.6i −0.350440 0.0576612i
\(813\) −274506. + 69902.6i −0.415309 + 0.105758i
\(814\) −1.01774e6 + 863970.i −1.53600 + 1.30392i
\(815\) −3891.01 2246.48i −0.00585797 0.00338210i
\(816\) 539936. + 369712.i 0.810890 + 0.555244i
\(817\) 908.875 + 1574.22i 0.00136163 + 0.00235842i
\(818\) 58633.6 164011.i 0.0876275 0.245113i
\(819\) −17111.7 31419.9i −0.0255109 0.0468422i
\(820\) 359538. + 294737.i 0.534709 + 0.438335i
\(821\) 35777.1 + 61967.7i 0.0530785 + 0.0919346i 0.891344 0.453328i \(-0.149763\pi\)
−0.838265 + 0.545262i \(0.816430\pi\)
\(822\) −538110. + 757609.i −0.796394 + 1.12125i
\(823\) −703826. 406354.i −1.03912 0.599936i −0.119536 0.992830i \(-0.538141\pi\)
−0.919584 + 0.392893i \(0.871474\pi\)
\(824\) −736111. + 12649.2i −1.08415 + 0.0186298i
\(825\) 269137. 956628.i 0.395426 1.40551i
\(826\) −132829. + 24206.5i −0.194685 + 0.0354790i
\(827\) 375951.i 0.549693i −0.961488 0.274847i \(-0.911373\pi\)
0.961488 0.274847i \(-0.0886271\pi\)
\(828\) 246312. 85917.6i 0.359273 0.125320i
\(829\) 423699. 0.616522 0.308261 0.951302i \(-0.400253\pi\)
0.308261 + 0.951302i \(0.400253\pi\)
\(830\) −8831.40 48460.7i −0.0128196 0.0703450i
\(831\) 428643. 418100.i 0.620717 0.605449i
\(832\) −80392.5 128810.i −0.116137 0.186082i
\(833\) −320806. + 555652.i −0.462330 + 0.800779i
\(834\) 44388.6 470880.i 0.0638175 0.676984i
\(835\) −226830. + 130961.i −0.325333 + 0.187831i
\(836\) −123489. 101232.i −0.176691 0.144845i
\(837\) −245774. 1.07657e6i −0.350821 1.53671i
\(838\) 793234. + 283579.i 1.12957 + 0.403819i
\(839\) 959899. 554198.i 1.36365 0.787302i 0.373539 0.927614i \(-0.378144\pi\)
0.990107 + 0.140313i \(0.0448108\pi\)
\(840\) −53282.0 + 53788.7i −0.0755131 + 0.0762311i
\(841\) −400727. + 694079.i −0.566573 + 0.981334i
\(842\) 217773. + 256534.i 0.307171 + 0.361843i
\(843\) −797090. + 777485.i −1.12164 + 1.09405i
\(844\) 733974. + 120768.i 1.03038 + 0.169537i
\(845\) −299914. −0.420032
\(846\) 336465. 872034.i 0.470109 1.21841i
\(847\) 399036.i 0.556218i
\(848\) 272110. 239160.i 0.378401 0.332581i
\(849\) −133412. + 474205.i −0.185089 + 0.657886i
\(850\) −370046. 435909.i −0.512174 0.603334i
\(851\) 265190. + 153108.i 0.366183 + 0.211416i
\(852\) −137251. + 95900.8i −0.189076 + 0.132112i
\(853\) 254659. + 441083.i 0.349995 + 0.606209i 0.986248 0.165272i \(-0.0528501\pi\)
−0.636253 + 0.771480i \(0.719517\pi\)
\(854\) 235941. + 84348.4i 0.323510 + 0.115654i
\(855\) 40635.4 + 1012.07i 0.0555869 + 0.00138446i
\(856\) −217543. 362276.i −0.296892 0.494415i
\(857\) 328394. + 568795.i 0.447130 + 0.774452i 0.998198 0.0600088i \(-0.0191129\pi\)
−0.551068 + 0.834460i \(0.685780\pi\)
\(858\) 266172. 121946.i 0.361566 0.165651i
\(859\) −916830. 529332.i −1.24252 0.717368i −0.272912 0.962039i \(-0.587987\pi\)
−0.969606 + 0.244671i \(0.921320\pi\)
\(860\) 2488.03 + 6599.60i 0.00336403 + 0.00892321i
\(861\) −273720. + 69702.4i −0.369233 + 0.0940246i
\(862\) −107631. 590603.i −0.144851 0.794842i
\(863\) 676878.i 0.908844i −0.890787 0.454422i \(-0.849846\pi\)
0.890787 0.454422i \(-0.150154\pi\)
\(864\) 744194. 58578.3i 0.996916 0.0784710i
\(865\) −31180.7 −0.0416729
\(866\) −280270. + 51076.0i −0.373716 + 0.0681053i
\(867\) −6336.73 24884.2i −0.00842999 0.0331044i
\(868\) −270215. + 101870.i −0.358649 + 0.135210i
\(869\) 821100. 1.42219e6i 1.08732 1.88329i
\(870\) 203179. + 443478.i 0.268435 + 0.585913i
\(871\) −29875.4 + 17248.6i −0.0393801 + 0.0227361i
\(872\) −660896. + 396862.i −0.869161 + 0.521924i
\(873\) 832633. + 508775.i 1.09251 + 0.667570i
\(874\) −12329.5 + 34488.5i −0.0161408 + 0.0451493i
\(875\) 128438. 74154.0i 0.167756 0.0968541i
\(876\) −178388. 255305.i −0.232465 0.332699i
\(877\) −737914. + 1.27810e6i −0.959415 + 1.66176i −0.235490 + 0.971877i \(0.575669\pi\)
−0.723925 + 0.689879i \(0.757664\pi\)
\(878\) −333133. + 282799.i −0.432144 + 0.366850i
\(879\) 767755. + 215999.i 0.993677 + 0.279560i
\(880\) −409018. 465369.i −0.528175 0.600942i
\(881\) 599513. 0.772408 0.386204 0.922413i \(-0.373786\pi\)
0.386204 + 0.922413i \(0.373786\pi\)
\(882\) 113254. + 723110.i 0.145586 + 0.929538i
\(883\) 729187.i 0.935229i −0.883933 0.467614i \(-0.845114\pi\)
0.883933 0.467614i \(-0.154886\pi\)
\(884\) 27350.3 166224.i 0.0349992 0.212710i
\(885\) 196388. + 201341.i 0.250743 + 0.257066i
\(886\) 703369. 597094.i 0.896015 0.760634i
\(887\) −1.26218e6 728722.i −1.60426 0.926221i −0.990621 0.136636i \(-0.956371\pi\)
−0.613641 0.789585i \(-0.710296\pi\)
\(888\) 622538. + 616674.i 0.789477 + 0.782041i
\(889\) 158172. + 273962.i 0.200137 + 0.346647i
\(890\) −100114. + 280041.i −0.126391 + 0.353543i
\(891\) −71655.4 + 1.43761e6i −0.0902596 + 1.81087i
\(892\) 837834. 1.02204e6i 1.05300 1.28452i
\(893\) 65616.2 + 113651.i 0.0822826 + 0.142518i
\(894\) 929590. + 87630.0i 1.16310 + 0.109642i
\(895\) 437015. + 252311.i 0.545570 + 0.314985i
\(896\) −41577.7 190739.i −0.0517898 0.237588i
\(897\) −46891.0 48073.4i −0.0582780 0.0597476i
\(898\) 38374.5 6993.32i 0.0475872 0.00867223i
\(899\) 1.86060e6i 2.30215i
\(900\) −640792. 121895.i −0.791101 0.150487i
\(901\) 401926. 0.495104
\(902\) −414404. 2.27397e6i −0.509344 2.79493i
\(903\) −4124.95 1160.51i −0.00505875 0.00142322i
\(904\) −4102.27 238729.i −0.00501981 0.292125i
\(905\) 133627. 231448.i 0.163153 0.282590i
\(906\) 833408. + 591948.i 1.01532 + 0.721153i
\(907\) −3010.76 + 1738.27i −0.00365984 + 0.00211301i −0.501829 0.864967i \(-0.667339\pi\)
0.498169 + 0.867080i \(0.334006\pi\)
\(908\) −301279. + 367519.i −0.365424 + 0.445767i
\(909\) −660435. 403554.i −0.799287 0.488399i
\(910\) 18352.9 + 6561.11i 0.0221627 + 0.00792309i
\(911\) −712683. + 411468.i −0.858736 + 0.495791i −0.863589 0.504197i \(-0.831789\pi\)
0.00485282 + 0.999988i \(0.498455\pi\)
\(912\) −59214.9 + 86478.7i −0.0711936 + 0.103973i
\(913\) −122453. + 212094.i −0.146901 + 0.254441i
\(914\) 171211. + 201685.i 0.204946 + 0.241424i
\(915\) −128807. 505822.i −0.153850 0.604164i
\(916\) −117769. + 715750.i −0.140359 + 0.853042i
\(917\) −15723.8 −0.0186990
\(918\) 663066. + 496252.i 0.786813 + 0.588867i
\(919\) 873279.i 1.03400i 0.855984 + 0.517002i \(0.172952\pi\)
−0.855984 + 0.517002i \(0.827048\pi\)
\(920\) −68931.1 + 124276.i −0.0814403 + 0.146828i
\(921\) −1.07667e6 + 274171.i −1.26929 + 0.323223i
\(922\) −450398. 530563.i −0.529828 0.624130i
\(923\) 37328.5 + 21551.6i 0.0438164 + 0.0252974i
\(924\) 375021. 32433.8i 0.439250 0.0379887i
\(925\) −382837. 663092.i −0.447435 0.774980i
\(926\) −655351. 234286.i −0.764279 0.273228i
\(927\) −931489. 23199.8i −1.08397 0.0269976i
\(928\) −1.24442e6 182856.i −1.44501 0.212330i
\(929\) −172980. 299611.i −0.200431 0.347157i 0.748236 0.663433i \(-0.230901\pi\)
−0.948667 + 0.316275i \(0.897568\pi\)
\(930\) 490447. + 348352.i 0.567056 + 0.402765i
\(931\) −88995.8 51381.7i −0.102676 0.0592802i
\(932\) 762513. 287465.i 0.877840 0.330943i
\(933\) −147569. + 524525.i −0.169525 + 0.602564i
\(934\) −123413. 677205.i −0.141471 0.776295i
\(935\) 687384.i 0.786278i
\(936\) −94798.1 167162.i −0.108205 0.190803i
\(937\) −1.10958e6 −1.26380 −0.631901 0.775049i \(-0.717725\pi\)
−0.631901 + 0.775049i \(0.717725\pi\)
\(938\) −43634.0 + 7951.80i −0.0495929 + 0.00903774i
\(939\) −337509. + 329207.i −0.382784 + 0.373369i
\(940\) 179623. + 476458.i 0.203286 + 0.539224i
\(941\) −161271. + 279330.i −0.182129 + 0.315456i −0.942605 0.333909i \(-0.891632\pi\)
0.760477 + 0.649365i \(0.224965\pi\)
\(942\) −197856. 18651.4i −0.222971 0.0210189i
\(943\) −459147. + 265089.i −0.516331 + 0.298104i
\(944\) −711124. + 142259.i −0.797997 + 0.159638i
\(945\) −70239.4 + 65179.0i −0.0786533 + 0.0729867i
\(946\) 11804.4 33019.6i 0.0131905 0.0368969i
\(947\) −120742. + 69710.2i −0.134635 + 0.0777314i −0.565805 0.824539i \(-0.691434\pi\)
0.431170 + 0.902271i \(0.358101\pi\)
\(948\) −976452. 456511.i −1.08651 0.507966i
\(949\) −40088.8 + 69435.9i −0.0445134 + 0.0770995i
\(950\) 69817.2 59268.3i 0.0773597 0.0656712i
\(951\) −167493. + 163374.i −0.185198 + 0.180643i
\(952\) 105054. 189402.i 0.115915 0.208983i
\(953\) 1.68438e6 1.85462 0.927308 0.374300i \(-0.122117\pi\)
0.927308 + 0.374300i \(0.122117\pi\)
\(954\) 356818. 287931.i 0.392058 0.316367i
\(955\) 248453.i 0.272419i
\(956\) 582382. + 95824.8i 0.637224 + 0.104848i
\(957\) 656824. 2.33463e6i 0.717175 2.54915i
\(958\) 665983. 565357.i 0.725658 0.616016i
\(959\) 266360. + 153783.i 0.289622 + 0.167213i
\(960\) −281188. + 293790.i −0.305108 + 0.318782i
\(961\) 685501. + 1.18732e6i 0.742269 + 1.28565i
\(962\) 75936.8 212412.i 0.0820545 0.229525i
\(963\) −255795. 469682.i −0.275829 0.506468i
\(964\) −103782. 85076.6i −0.111678 0.0915495i
\(965\) −100877. 174723.i −0.108327 0.187628i
\(966\) −35962.3 78495.0i −0.0385384 0.0841178i
\(967\) −39280.8 22678.8i −0.0420075 0.0242530i 0.478849 0.877897i \(-0.341054\pi\)
−0.520857 + 0.853644i \(0.674387\pi\)
\(968\) 36825.3 + 2.14303e6i 0.0393003 + 2.28706i
\(969\) −112685. + 28695.1i −0.120010 + 0.0305605i
\(970\) −522957. + 95302.9i −0.555805 + 0.101289i
\(971\) 1.18319e6i 1.25492i −0.778648 0.627461i \(-0.784094\pi\)
0.778648 0.627461i \(-0.215906\pi\)
\(972\) 944156. 34447.3i 0.999335 0.0364605i
\(973\) −156541. −0.165350
\(974\) 281200. + 1.54303e6i 0.296413 + 1.62651i
\(975\) 41437.6 + 162725.i 0.0435898 + 0.171176i
\(976\) 1.27491e6 + 431220.i 1.33838 + 0.452688i
\(977\) −562965. + 975083.i −0.589783 + 1.02153i 0.404478 + 0.914548i \(0.367453\pi\)
−0.994261 + 0.106986i \(0.965880\pi\)
\(978\) 13329.7 6107.00i 0.0139362 0.00638484i
\(979\) 1.28051e6 739303.i 1.33604 0.771360i
\(980\) −308361. 252784.i −0.321076 0.263206i
\(981\) −856837. + 466644.i −0.890349 + 0.484895i
\(982\) 789909. + 282390.i 0.819132 + 0.292838i
\(983\) −1.17197e6 + 676638.i −1.21286 + 0.700243i −0.963381 0.268137i \(-0.913592\pi\)
−0.249476 + 0.968381i \(0.580259\pi\)
\(984\) −1.46358e6 + 399598.i −1.51157 + 0.412699i
\(985\) −200225. + 346799.i −0.206369 + 0.357442i
\(986\) −903090. 1.06383e6i −0.928918 1.09425i
\(987\) −297801. 83783.0i −0.305697 0.0860045i
\(988\) 26623.2 + 4380.56i 0.0272738 + 0.00448761i
\(989\) −8043.24 −0.00822316
\(990\) −492427. 610240.i −0.502425 0.622630i
\(991\) 1.02847e6i 1.04724i 0.851953 + 0.523619i \(0.175418\pi\)
−0.851953 + 0.523619i \(0.824582\pi\)
\(992\) −1.44179e6 + 572032.i −1.46514 + 0.581296i
\(993\) −271674. 278525.i −0.275518 0.282466i
\(994\) 35864.2 + 42247.5i 0.0362985 + 0.0427591i
\(995\) 452235. + 261098.i 0.456791 + 0.263729i
\(996\) 145621. + 68080.6i 0.146793 + 0.0686285i
\(997\) −564030. 976929.i −0.567430 0.982817i −0.996819 0.0796977i \(-0.974605\pi\)
0.429389 0.903119i \(-0.358729\pi\)
\(998\) 511821. + 182975.i 0.513874 + 0.183709i
\(999\) 754366. + 812935.i 0.755877 + 0.814563i
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 36.5.f.a.31.2 yes 44
3.2 odd 2 108.5.f.a.91.21 44
4.3 odd 2 inner 36.5.f.a.31.16 yes 44
9.2 odd 6 108.5.f.a.19.7 44
9.4 even 3 324.5.d.f.163.13 22
9.5 odd 6 324.5.d.e.163.10 22
9.7 even 3 inner 36.5.f.a.7.16 yes 44
12.11 even 2 108.5.f.a.91.7 44
36.7 odd 6 inner 36.5.f.a.7.2 44
36.11 even 6 108.5.f.a.19.21 44
36.23 even 6 324.5.d.e.163.9 22
36.31 odd 6 324.5.d.f.163.14 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.5.f.a.7.2 44 36.7 odd 6 inner
36.5.f.a.7.16 yes 44 9.7 even 3 inner
36.5.f.a.31.2 yes 44 1.1 even 1 trivial
36.5.f.a.31.16 yes 44 4.3 odd 2 inner
108.5.f.a.19.7 44 9.2 odd 6
108.5.f.a.19.21 44 36.11 even 6
108.5.f.a.91.7 44 12.11 even 2
108.5.f.a.91.21 44 3.2 odd 2
324.5.d.e.163.9 22 36.23 even 6
324.5.d.e.163.10 22 9.5 odd 6
324.5.d.f.163.13 22 9.4 even 3
324.5.d.f.163.14 22 36.31 odd 6