Properties

Label 363.2.f.i.233.1
Level $363$
Weight $2$
Character 363.233
Analytic conductor $2.899$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $16$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(161,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 233.1
Character \(\chi\) \(=\) 363.233
Dual form 363.2.f.i.215.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.739839 + 2.27699i) q^{2} +(-1.29120 - 1.15447i) q^{3} +(-3.01929 - 2.19364i) q^{4} +(-1.17866 + 0.382969i) q^{5} +(3.58400 - 2.08594i) q^{6} +(1.66251 - 2.28825i) q^{7} +(3.35485 - 2.43744i) q^{8} +(0.334407 + 2.98130i) q^{9} +O(q^{10})\) \(q+(-0.739839 + 2.27699i) q^{2} +(-1.29120 - 1.15447i) q^{3} +(-3.01929 - 2.19364i) q^{4} +(-1.17866 + 0.382969i) q^{5} +(3.58400 - 2.08594i) q^{6} +(1.66251 - 2.28825i) q^{7} +(3.35485 - 2.43744i) q^{8} +(0.334407 + 2.98130i) q^{9} -2.96713i q^{10} +(1.36603 + 6.31812i) q^{12} +(3.18230 + 1.03399i) q^{13} +(3.98033 + 5.47845i) q^{14} +(1.96401 + 0.866232i) q^{15} +(0.761449 + 2.34350i) q^{16} +(1.28144 + 3.94386i) q^{17} +(-7.03581 - 1.44424i) q^{18} +(1.43977 + 1.98168i) q^{19} +(4.39881 + 1.42926i) q^{20} +(-4.78834 + 1.03528i) q^{21} +(-7.14574 - 0.725837i) q^{24} +(-2.80252 + 2.03615i) q^{25} +(-4.70878 + 6.48108i) q^{26} +(3.01003 - 4.23553i) q^{27} +(-10.0392 + 3.26193i) q^{28} +(4.39285 + 3.19159i) q^{29} +(-3.42545 + 3.83116i) q^{30} +(0.0606144 - 0.186552i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(-1.08320 + 3.33375i) q^{35} +(5.53025 - 9.73500i) q^{36} +(8.46564 + 6.15064i) q^{37} +(-5.57747 + 1.81223i) q^{38} +(-2.91528 - 5.00895i) q^{39} +(-3.02076 + 4.15771i) q^{40} +(5.81077 - 4.22177i) q^{41} +(1.18529 - 11.6689i) q^{42} +4.24264i q^{43} +(-1.53590 - 3.38587i) q^{45} +(-1.99016 - 2.73922i) q^{47} +(1.72231 - 3.90500i) q^{48} +(-0.309017 - 0.951057i) q^{49} +(-2.56288 - 7.88773i) q^{50} +(2.89847 - 6.57171i) q^{51} +(-7.34008 - 10.1027i) q^{52} +(-6.75612 - 2.19520i) q^{53} +(7.41732 + 9.98743i) q^{54} -11.7290i q^{56} +(0.428745 - 4.22092i) q^{57} +(-10.5172 + 7.64121i) q^{58} +(7.42739 - 10.2229i) q^{59} +(-4.02972 - 6.92375i) q^{60} +(4.29882 - 1.39677i) q^{61} +(0.379932 + 0.276037i) q^{62} +(7.37791 + 4.19123i) q^{63} +(-3.29420 + 10.1385i) q^{64} -4.14682 q^{65} +2.00000 q^{67} +(4.78240 - 14.7187i) q^{68} +(-6.78952 - 4.93287i) q^{70} +(7.93478 - 2.57817i) q^{71} +(8.38864 + 9.18673i) q^{72} +(-4.76479 + 6.55817i) q^{73} +(-20.2682 + 14.7257i) q^{74} +(5.96928 + 0.606337i) q^{75} -9.14162i q^{76} +(13.5622 - 2.93225i) q^{78} +(6.98881 + 2.27080i) q^{79} +(-1.79498 - 2.47057i) q^{80} +(-8.77634 + 1.99394i) q^{81} +(5.31390 + 16.3545i) q^{82} +(4.58416 + 14.1086i) q^{83} +(16.7284 + 7.37811i) q^{84} +(-3.02076 - 4.15771i) q^{85} +(-9.66046 - 3.13887i) q^{86} +(-1.98747 - 9.19239i) q^{87} +9.58244i q^{89} +(8.84591 - 0.992229i) q^{90} +(7.65662 - 5.56286i) q^{91} +(-0.293634 + 0.170899i) q^{93} +(7.70959 - 2.50500i) q^{94} +(-2.45592 - 1.78433i) q^{95} +(-3.09136 - 2.76399i) q^{96} +(0.700835 - 2.15695i) q^{97} +2.39417 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.739839 + 2.27699i −0.523145 + 1.61008i 0.244809 + 0.969571i \(0.421275\pi\)
−0.767954 + 0.640505i \(0.778725\pi\)
\(3\) −1.29120 1.15447i −0.745476 0.666532i
\(4\) −3.01929 2.19364i −1.50965 1.09682i
\(5\) −1.17866 + 0.382969i −0.527112 + 0.171269i −0.560470 0.828175i \(-0.689380\pi\)
0.0333587 + 0.999443i \(0.489380\pi\)
\(6\) 3.58400 2.08594i 1.46316 0.851580i
\(7\) 1.66251 2.28825i 0.628369 0.864876i −0.369560 0.929207i \(-0.620491\pi\)
0.997929 + 0.0643314i \(0.0204915\pi\)
\(8\) 3.35485 2.43744i 1.18612 0.861766i
\(9\) 0.334407 + 2.98130i 0.111469 + 0.993768i
\(10\) 2.96713i 0.938288i
\(11\) 0 0
\(12\) 1.36603 + 6.31812i 0.394338 + 1.82388i
\(13\) 3.18230 + 1.03399i 0.882610 + 0.286778i 0.715041 0.699083i \(-0.246408\pi\)
0.167570 + 0.985860i \(0.446408\pi\)
\(14\) 3.98033 + 5.47845i 1.06379 + 1.46418i
\(15\) 1.96401 + 0.866232i 0.507105 + 0.223660i
\(16\) 0.761449 + 2.34350i 0.190362 + 0.585875i
\(17\) 1.28144 + 3.94386i 0.310795 + 0.956528i 0.977451 + 0.211162i \(0.0677249\pi\)
−0.666656 + 0.745365i \(0.732275\pi\)
\(18\) −7.03581 1.44424i −1.65836 0.340411i
\(19\) 1.43977 + 1.98168i 0.330307 + 0.454628i 0.941579 0.336792i \(-0.109342\pi\)
−0.611272 + 0.791420i \(0.709342\pi\)
\(20\) 4.39881 + 1.42926i 0.983604 + 0.319592i
\(21\) −4.78834 + 1.03528i −1.04490 + 0.225916i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −7.14574 0.725837i −1.45862 0.148161i
\(25\) −2.80252 + 2.03615i −0.560503 + 0.407230i
\(26\) −4.70878 + 6.48108i −0.923467 + 1.27104i
\(27\) 3.01003 4.23553i 0.579281 0.815128i
\(28\) −10.0392 + 3.26193i −1.89723 + 0.616447i
\(29\) 4.39285 + 3.19159i 0.815731 + 0.592663i 0.915486 0.402349i \(-0.131806\pi\)
−0.0997555 + 0.995012i \(0.531806\pi\)
\(30\) −3.42545 + 3.83116i −0.625400 + 0.699471i
\(31\) 0.0606144 0.186552i 0.0108867 0.0335057i −0.945466 0.325722i \(-0.894393\pi\)
0.956352 + 0.292216i \(0.0943927\pi\)
\(32\) 2.39417 0.423233
\(33\) 0 0
\(34\) −9.92820 −1.70267
\(35\) −1.08320 + 3.33375i −0.183094 + 0.563506i
\(36\) 5.53025 9.73500i 0.921708 1.62250i
\(37\) 8.46564 + 6.15064i 1.39174 + 1.01116i 0.995672 + 0.0929395i \(0.0296263\pi\)
0.396070 + 0.918220i \(0.370374\pi\)
\(38\) −5.57747 + 1.81223i −0.904785 + 0.293982i
\(39\) −2.91528 5.00895i −0.466818 0.802074i
\(40\) −3.02076 + 4.15771i −0.477623 + 0.657392i
\(41\) 5.81077 4.22177i 0.907490 0.659330i −0.0328886 0.999459i \(-0.510471\pi\)
0.940379 + 0.340129i \(0.110471\pi\)
\(42\) 1.18529 11.6689i 0.182894 1.80056i
\(43\) 4.24264i 0.646997i 0.946229 + 0.323498i \(0.104859\pi\)
−0.946229 + 0.323498i \(0.895141\pi\)
\(44\) 0 0
\(45\) −1.53590 3.38587i −0.228958 0.504735i
\(46\) 0 0
\(47\) −1.99016 2.73922i −0.290295 0.399557i 0.638815 0.769361i \(-0.279425\pi\)
−0.929110 + 0.369804i \(0.879425\pi\)
\(48\) 1.72231 3.90500i 0.248594 0.563638i
\(49\) −0.309017 0.951057i −0.0441453 0.135865i
\(50\) −2.56288 7.88773i −0.362446 1.11549i
\(51\) 2.89847 6.57171i 0.405867 0.920223i
\(52\) −7.34008 10.1027i −1.01789 1.40100i
\(53\) −6.75612 2.19520i −0.928025 0.301534i −0.194270 0.980948i \(-0.562234\pi\)
−0.733755 + 0.679414i \(0.762234\pi\)
\(54\) 7.41732 + 9.98743i 1.00937 + 1.35912i
\(55\) 0 0
\(56\) 11.7290i 1.56735i
\(57\) 0.428745 4.22092i 0.0567887 0.559075i
\(58\) −10.5172 + 7.64121i −1.38098 + 1.00334i
\(59\) 7.42739 10.2229i 0.966964 1.33091i 0.0233981 0.999726i \(-0.492551\pi\)
0.943566 0.331185i \(-0.107449\pi\)
\(60\) −4.02972 6.92375i −0.520234 0.893852i
\(61\) 4.29882 1.39677i 0.550407 0.178838i −0.0205933 0.999788i \(-0.506556\pi\)
0.571000 + 0.820950i \(0.306556\pi\)
\(62\) 0.379932 + 0.276037i 0.0482515 + 0.0350567i
\(63\) 7.37791 + 4.19123i 0.929529 + 0.528046i
\(64\) −3.29420 + 10.1385i −0.411775 + 1.26731i
\(65\) −4.14682 −0.514350
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 4.78240 14.7187i 0.579951 1.78490i
\(69\) 0 0
\(70\) −6.78952 4.93287i −0.811503 0.589591i
\(71\) 7.93478 2.57817i 0.941685 0.305972i 0.202353 0.979313i \(-0.435141\pi\)
0.739332 + 0.673341i \(0.235141\pi\)
\(72\) 8.38864 + 9.18673i 0.988611 + 1.08267i
\(73\) −4.76479 + 6.55817i −0.557676 + 0.767576i −0.991029 0.133649i \(-0.957331\pi\)
0.433352 + 0.901225i \(0.357331\pi\)
\(74\) −20.2682 + 14.7257i −2.35613 + 1.71183i
\(75\) 5.96928 + 0.606337i 0.689274 + 0.0700138i
\(76\) 9.14162i 1.04862i
\(77\) 0 0
\(78\) 13.5622 2.93225i 1.53561 0.332012i
\(79\) 6.98881 + 2.27080i 0.786303 + 0.255485i 0.674529 0.738249i \(-0.264347\pi\)
0.111774 + 0.993734i \(0.464347\pi\)
\(80\) −1.79498 2.47057i −0.200684 0.276218i
\(81\) −8.77634 + 1.99394i −0.975149 + 0.221549i
\(82\) 5.31390 + 16.3545i 0.586822 + 1.80605i
\(83\) 4.58416 + 14.1086i 0.503177 + 1.54862i 0.803815 + 0.594880i \(0.202800\pi\)
−0.300638 + 0.953738i \(0.597200\pi\)
\(84\) 16.7284 + 7.37811i 1.82522 + 0.805018i
\(85\) −3.02076 4.15771i −0.327647 0.450967i
\(86\) −9.66046 3.13887i −1.04171 0.338473i
\(87\) −1.98747 9.19239i −0.213079 0.985527i
\(88\) 0 0
\(89\) 9.58244i 1.01574i 0.861435 + 0.507868i \(0.169566\pi\)
−0.861435 + 0.507868i \(0.830434\pi\)
\(90\) 8.84591 0.992229i 0.932441 0.104590i
\(91\) 7.65662 5.56286i 0.802632 0.583146i
\(92\) 0 0
\(93\) −0.293634 + 0.170899i −0.0304484 + 0.0177214i
\(94\) 7.70959 2.50500i 0.795184 0.258371i
\(95\) −2.45592 1.78433i −0.251972 0.183069i
\(96\) −3.09136 2.76399i −0.315510 0.282099i
\(97\) 0.700835 2.15695i 0.0711590 0.219005i −0.909152 0.416464i \(-0.863269\pi\)
0.980311 + 0.197459i \(0.0632691\pi\)
\(98\) 2.39417 0.241848
\(99\) 0 0
\(100\) 12.9282 1.29282
\(101\) 0.145121 0.446637i 0.0144401 0.0444421i −0.943577 0.331154i \(-0.892562\pi\)
0.958017 + 0.286712i \(0.0925621\pi\)
\(102\) 12.8193 + 11.4618i 1.26930 + 1.13489i
\(103\) −10.3004 7.48371i −1.01493 0.737392i −0.0496950 0.998764i \(-0.515825\pi\)
−0.965238 + 0.261372i \(0.915825\pi\)
\(104\) 13.1964 4.28778i 1.29402 0.420451i
\(105\) 5.24733 3.05402i 0.512087 0.298042i
\(106\) 9.99689 13.7595i 0.970984 1.33644i
\(107\) −2.83585 + 2.06037i −0.274152 + 0.199183i −0.716363 0.697728i \(-0.754194\pi\)
0.442210 + 0.896911i \(0.354194\pi\)
\(108\) −18.3794 + 6.18536i −1.76856 + 0.595187i
\(109\) 10.6945i 1.02435i −0.858881 0.512175i \(-0.828840\pi\)
0.858881 0.512175i \(-0.171160\pi\)
\(110\) 0 0
\(111\) −3.83013 17.7150i −0.363540 1.68144i
\(112\) 6.62842 + 2.15370i 0.626327 + 0.203506i
\(113\) −7.62258 10.4916i −0.717072 0.986965i −0.999616 0.0277104i \(-0.991178\pi\)
0.282544 0.959254i \(-0.408822\pi\)
\(114\) 9.29380 + 4.09905i 0.870444 + 0.383911i
\(115\) 0 0
\(116\) −6.26207 19.2727i −0.581419 1.78942i
\(117\) −2.01846 + 9.83317i −0.186607 + 0.909077i
\(118\) 17.7824 + 24.4754i 1.63701 + 2.25315i
\(119\) 11.1549 + 3.62446i 1.02257 + 0.332253i
\(120\) 8.70035 1.88108i 0.794230 0.171719i
\(121\) 0 0
\(122\) 10.8217i 0.979755i
\(123\) −12.3768 1.25719i −1.11598 0.113357i
\(124\) −0.592242 + 0.430289i −0.0531849 + 0.0386411i
\(125\) 6.16568 8.48633i 0.551475 0.759040i
\(126\) −15.0019 + 13.6986i −1.33647 + 1.22037i
\(127\) −13.7138 + 4.45588i −1.21690 + 0.395396i −0.845953 0.533257i \(-0.820968\pi\)
−0.370949 + 0.928653i \(0.620968\pi\)
\(128\) −16.7743 12.1872i −1.48265 1.07721i
\(129\) 4.89799 5.47811i 0.431244 0.482320i
\(130\) 3.06798 9.44228i 0.269080 0.828143i
\(131\) 13.5516 1.18401 0.592005 0.805934i \(-0.298337\pi\)
0.592005 + 0.805934i \(0.298337\pi\)
\(132\) 0 0
\(133\) 6.92820 0.600751
\(134\) −1.47968 + 4.55398i −0.127825 + 0.393404i
\(135\) −1.92572 + 6.14499i −0.165740 + 0.528876i
\(136\) 13.9120 + 10.1076i 1.19294 + 0.866723i
\(137\) −16.9636 + 5.51181i −1.44930 + 0.470905i −0.924783 0.380496i \(-0.875753\pi\)
−0.524515 + 0.851401i \(0.675753\pi\)
\(138\) 0 0
\(139\) −3.04260 + 4.18778i −0.258070 + 0.355203i −0.918317 0.395846i \(-0.870452\pi\)
0.660247 + 0.751048i \(0.270452\pi\)
\(140\) 10.5836 7.68940i 0.894473 0.649873i
\(141\) −0.592644 + 5.83447i −0.0499096 + 0.491351i
\(142\) 19.9749i 1.67625i
\(143\) 0 0
\(144\) −6.73205 + 3.05379i −0.561004 + 0.254483i
\(145\) −6.39994 2.07947i −0.531486 0.172690i
\(146\) −11.4077 15.7014i −0.944109 1.29946i
\(147\) −0.698961 + 1.58476i −0.0576493 + 0.130709i
\(148\) −12.0679 37.1412i −0.991976 3.05299i
\(149\) −2.90624 8.94448i −0.238088 0.732761i −0.996697 0.0812137i \(-0.974120\pi\)
0.758608 0.651547i \(-0.225880\pi\)
\(150\) −5.79694 + 13.1434i −0.473318 + 1.07316i
\(151\) −9.69263 13.3408i −0.788775 1.08566i −0.994260 0.106995i \(-0.965877\pi\)
0.205484 0.978660i \(-0.434123\pi\)
\(152\) 9.66046 + 3.13887i 0.783566 + 0.254596i
\(153\) −11.3293 + 5.13922i −0.915922 + 0.415481i
\(154\) 0 0
\(155\) 0.243094i 0.0195258i
\(156\) −2.18578 + 21.5186i −0.175002 + 1.72287i
\(157\) 9.27465 6.73843i 0.740198 0.537785i −0.152575 0.988292i \(-0.548757\pi\)
0.892773 + 0.450507i \(0.148757\pi\)
\(158\) −10.3412 + 14.2334i −0.822701 + 1.13235i
\(159\) 6.18924 + 10.6342i 0.490838 + 0.843345i
\(160\) −2.82191 + 0.916893i −0.223091 + 0.0724868i
\(161\) 0 0
\(162\) 1.95290 21.4589i 0.153434 1.68597i
\(163\) 3.82943 11.7858i 0.299944 0.923134i −0.681571 0.731752i \(-0.738703\pi\)
0.981516 0.191382i \(-0.0612969\pi\)
\(164\) −26.8055 −2.09316
\(165\) 0 0
\(166\) −35.5167 −2.75663
\(167\) −1.62480 + 5.00062i −0.125731 + 0.386960i −0.994034 0.109075i \(-0.965211\pi\)
0.868303 + 0.496035i \(0.165211\pi\)
\(168\) −13.5407 + 15.1445i −1.04469 + 1.16842i
\(169\) −1.45934 1.06028i −0.112257 0.0815596i
\(170\) 11.7019 3.80219i 0.897499 0.291615i
\(171\) −5.42652 + 4.95509i −0.414976 + 0.378925i
\(172\) 9.30685 12.8098i 0.709640 0.976736i
\(173\) −9.16562 + 6.65922i −0.696850 + 0.506291i −0.878905 0.476998i \(-0.841725\pi\)
0.182055 + 0.983288i \(0.441725\pi\)
\(174\) 22.4014 + 2.27545i 1.69825 + 0.172501i
\(175\) 9.79796i 0.740656i
\(176\) 0 0
\(177\) −21.3923 + 4.62518i −1.60794 + 0.347650i
\(178\) −21.8191 7.08946i −1.63541 0.531378i
\(179\) 13.3979 + 18.4406i 1.00140 + 1.37832i 0.924460 + 0.381280i \(0.124517\pi\)
0.0769449 + 0.997035i \(0.475483\pi\)
\(180\) −2.79006 + 13.5921i −0.207959 + 1.01310i
\(181\) 3.97285 + 12.2272i 0.295299 + 0.908838i 0.983121 + 0.182958i \(0.0585673\pi\)
−0.687821 + 0.725880i \(0.741433\pi\)
\(182\) 7.00191 + 21.5497i 0.519016 + 1.59737i
\(183\) −7.16317 3.15933i −0.529517 0.233545i
\(184\) 0 0
\(185\) −12.3336 4.00743i −0.906784 0.294632i
\(186\) −0.171894 0.795040i −0.0126039 0.0582951i
\(187\) 0 0
\(188\) 12.6362i 0.921592i
\(189\) −4.68773 13.9293i −0.340982 1.01321i
\(190\) 5.87989 4.27199i 0.426572 0.309923i
\(191\) −1.45690 + 2.00525i −0.105418 + 0.145095i −0.858466 0.512870i \(-0.828582\pi\)
0.753049 + 0.657965i \(0.228582\pi\)
\(192\) 15.9581 9.28781i 1.15167 0.670290i
\(193\) −2.72534 + 0.885517i −0.196174 + 0.0637409i −0.405456 0.914114i \(-0.632887\pi\)
0.209282 + 0.977855i \(0.432887\pi\)
\(194\) 4.39285 + 3.19159i 0.315388 + 0.229143i
\(195\) 5.35439 + 4.78738i 0.383436 + 0.342831i
\(196\) −1.15327 + 3.54939i −0.0823762 + 0.253528i
\(197\) −10.6878 −0.761476 −0.380738 0.924683i \(-0.624330\pi\)
−0.380738 + 0.924683i \(0.624330\pi\)
\(198\) 0 0
\(199\) 7.66025 0.543021 0.271511 0.962435i \(-0.412477\pi\)
0.271511 + 0.962435i \(0.412477\pi\)
\(200\) −4.43904 + 13.6619i −0.313887 + 0.966046i
\(201\) −2.58240 2.30894i −0.182149 0.162860i
\(202\) 0.909623 + 0.660880i 0.0640008 + 0.0464993i
\(203\) 14.6063 4.74587i 1.02516 0.333095i
\(204\) −23.1673 + 13.4837i −1.62204 + 0.944048i
\(205\) −5.23210 + 7.20137i −0.365426 + 0.502966i
\(206\) 24.6610 17.9173i 1.71821 1.24836i
\(207\) 0 0
\(208\) 8.24504i 0.571691i
\(209\) 0 0
\(210\) 3.07180 + 14.2076i 0.211974 + 0.980419i
\(211\) −1.80195 0.585490i −0.124052 0.0403068i 0.246333 0.969185i \(-0.420774\pi\)
−0.370385 + 0.928878i \(0.620774\pi\)
\(212\) 15.5832 + 21.4485i 1.07026 + 1.47309i
\(213\) −13.2218 5.83152i −0.905944 0.399569i
\(214\) −2.59336 7.98156i −0.177279 0.545608i
\(215\) −1.62480 5.00062i −0.110810 0.341039i
\(216\) −0.225646 21.5464i −0.0153532 1.46604i
\(217\) −0.326105 0.448845i −0.0221374 0.0304696i
\(218\) 24.3514 + 7.91224i 1.64928 + 0.535884i
\(219\) 13.7235 2.96713i 0.927349 0.200500i
\(220\) 0 0
\(221\) 13.8755i 0.933370i
\(222\) 43.1707 + 4.38511i 2.89742 + 0.294309i
\(223\) −10.4591 + 7.59901i −0.700396 + 0.508867i −0.880061 0.474861i \(-0.842498\pi\)
0.179665 + 0.983728i \(0.442498\pi\)
\(224\) 3.98033 5.47845i 0.265947 0.366044i
\(225\) −7.00756 7.67425i −0.467170 0.511617i
\(226\) 29.5287 9.59446i 1.96422 0.638214i
\(227\) −4.25378 3.09055i −0.282333 0.205127i 0.437601 0.899169i \(-0.355828\pi\)
−0.719935 + 0.694042i \(0.755828\pi\)
\(228\) −10.5537 + 11.8037i −0.698936 + 0.781718i
\(229\) 1.71069 5.26495i 0.113045 0.347918i −0.878489 0.477763i \(-0.841448\pi\)
0.991534 + 0.129845i \(0.0414479\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 22.5167 1.47829
\(233\) 1.67792 5.16410i 0.109924 0.338311i −0.880931 0.473246i \(-0.843082\pi\)
0.990855 + 0.134934i \(0.0430823\pi\)
\(234\) −20.8967 11.8710i −1.36606 0.776030i
\(235\) 3.39476 + 2.46644i 0.221450 + 0.160893i
\(236\) −44.8509 + 14.5729i −2.91955 + 0.948618i
\(237\) −6.40240 11.0004i −0.415881 0.714554i
\(238\) −16.5057 + 22.7182i −1.06991 + 1.47260i
\(239\) 8.12763 5.90507i 0.525733 0.381967i −0.293026 0.956104i \(-0.594662\pi\)
0.818759 + 0.574137i \(0.194662\pi\)
\(240\) −0.534520 + 5.26225i −0.0345031 + 0.339677i
\(241\) 3.76217i 0.242343i −0.992632 0.121171i \(-0.961335\pi\)
0.992632 0.121171i \(-0.0386650\pi\)
\(242\) 0 0
\(243\) 13.6340 + 7.55743i 0.874620 + 0.484809i
\(244\) −16.0434 5.21282i −1.02707 0.333716i
\(245\) 0.728450 + 1.00263i 0.0465390 + 0.0640554i
\(246\) 12.0194 27.2517i 0.766331 1.73751i
\(247\) 2.53275 + 7.79500i 0.161155 + 0.495984i
\(248\) −0.251357 0.773599i −0.0159612 0.0491236i
\(249\) 10.3688 23.5093i 0.657098 1.48984i
\(250\) 14.7617 + 20.3177i 0.933611 + 1.28500i
\(251\) −8.16598 2.65329i −0.515432 0.167474i 0.0397393 0.999210i \(-0.487347\pi\)
−0.555171 + 0.831736i \(0.687347\pi\)
\(252\) −13.0820 28.8391i −0.824088 1.81669i
\(253\) 0 0
\(254\) 34.5228i 2.16615i
\(255\) −0.899540 + 8.85581i −0.0563314 + 0.554573i
\(256\) 22.9118 16.6464i 1.43199 1.04040i
\(257\) −13.5931 + 18.7093i −0.847912 + 1.16705i 0.136407 + 0.990653i \(0.456445\pi\)
−0.984319 + 0.176398i \(0.943555\pi\)
\(258\) 8.84988 + 15.2056i 0.550969 + 0.946660i
\(259\) 28.1484 9.14596i 1.74905 0.568302i
\(260\) 12.5205 + 9.09666i 0.776487 + 0.564151i
\(261\) −8.04610 + 14.1637i −0.498041 + 0.876711i
\(262\) −10.0260 + 30.8569i −0.619409 + 1.90635i
\(263\) 23.4721 1.44735 0.723675 0.690141i \(-0.242451\pi\)
0.723675 + 0.690141i \(0.242451\pi\)
\(264\) 0 0
\(265\) 8.80385 0.540816
\(266\) −5.12576 + 15.7755i −0.314280 + 0.967255i
\(267\) 11.0626 12.3729i 0.677021 0.757207i
\(268\) −6.03859 4.38729i −0.368865 0.267996i
\(269\) −15.5537 + 5.05372i −0.948328 + 0.308131i −0.742036 0.670360i \(-0.766140\pi\)
−0.206292 + 0.978490i \(0.566140\pi\)
\(270\) −12.5674 8.93115i −0.764825 0.543533i
\(271\) 5.37331 7.39573i 0.326405 0.449258i −0.614004 0.789303i \(-0.710442\pi\)
0.940409 + 0.340045i \(0.110442\pi\)
\(272\) −8.26669 + 6.00611i −0.501242 + 0.364174i
\(273\) −16.3084 1.65654i −0.987029 0.100259i
\(274\) 42.7038i 2.57983i
\(275\) 0 0
\(276\) 0 0
\(277\) 5.96886 + 1.93940i 0.358634 + 0.116527i 0.482792 0.875735i \(-0.339623\pi\)
−0.124158 + 0.992262i \(0.539623\pi\)
\(278\) −7.28450 10.0263i −0.436895 0.601335i
\(279\) 0.576438 + 0.118326i 0.0345105 + 0.00708397i
\(280\) 4.49184 + 13.8245i 0.268439 + 0.826170i
\(281\) −0.251357 0.773599i −0.0149947 0.0461490i 0.943279 0.332001i \(-0.107724\pi\)
−0.958274 + 0.285852i \(0.907724\pi\)
\(282\) −12.8466 5.66602i −0.765003 0.337406i
\(283\) −3.99322 5.49619i −0.237372 0.326715i 0.673667 0.739035i \(-0.264718\pi\)
−0.911039 + 0.412321i \(0.864718\pi\)
\(284\) −29.6130 9.62185i −1.75721 0.570952i
\(285\) 1.11114 + 5.13922i 0.0658181 + 0.304421i
\(286\) 0 0
\(287\) 20.3152i 1.19917i
\(288\) 0.800628 + 7.13775i 0.0471774 + 0.420596i
\(289\) −0.158691 + 0.115296i −0.00933474 + 0.00678209i
\(290\) 9.46985 13.0341i 0.556089 0.765391i
\(291\) −3.39505 + 1.97596i −0.199021 + 0.115833i
\(292\) 28.7726 9.34878i 1.68379 0.547096i
\(293\) 26.3198 + 19.1225i 1.53762 + 1.11715i 0.951806 + 0.306701i \(0.0992251\pi\)
0.585814 + 0.810446i \(0.300775\pi\)
\(294\) −3.09136 2.76399i −0.180292 0.161199i
\(295\) −4.83928 + 14.8938i −0.281754 + 0.867150i
\(296\) 43.3928 2.52215
\(297\) 0 0
\(298\) 22.5167 1.30436
\(299\) 0 0
\(300\) −16.6929 14.9252i −0.963767 0.861707i
\(301\) 9.70820 + 7.05342i 0.559572 + 0.406553i
\(302\) 37.5478 12.2000i 2.16063 0.702032i
\(303\) −0.703009 + 0.409161i −0.0403868 + 0.0235057i
\(304\) −3.54775 + 4.88306i −0.203477 + 0.280063i
\(305\) −4.53191 + 3.29263i −0.259496 + 0.188535i
\(306\) −3.32006 29.5990i −0.189795 1.69206i
\(307\) 31.1870i 1.77994i 0.456021 + 0.889969i \(0.349274\pi\)
−0.456021 + 0.889969i \(0.650726\pi\)
\(308\) 0 0
\(309\) 4.66025 + 21.5545i 0.265113 + 1.22619i
\(310\) −0.553524 0.179851i −0.0314380 0.0102148i
\(311\) 0.390375 + 0.537306i 0.0221362 + 0.0304678i 0.819942 0.572447i \(-0.194006\pi\)
−0.797805 + 0.602915i \(0.794006\pi\)
\(312\) −21.9894 9.69846i −1.24490 0.549067i
\(313\) −2.28435 7.03050i −0.129119 0.397387i 0.865510 0.500892i \(-0.166994\pi\)
−0.994629 + 0.103504i \(0.966994\pi\)
\(314\) 8.48159 + 26.1037i 0.478644 + 1.47311i
\(315\) −10.3011 2.11452i −0.580404 0.119140i
\(316\) −16.1199 22.1872i −0.906817 1.24813i
\(317\) 23.4039 + 7.60439i 1.31449 + 0.427105i 0.880601 0.473859i \(-0.157139\pi\)
0.433893 + 0.900964i \(0.357139\pi\)
\(318\) −28.7930 + 6.22526i −1.61463 + 0.349095i
\(319\) 0 0
\(320\) 13.2114i 0.738540i
\(321\) 6.04029 + 0.613550i 0.337136 + 0.0342450i
\(322\) 0 0
\(323\) −5.97049 + 8.21767i −0.332207 + 0.457244i
\(324\) 30.8723 + 13.2319i 1.71513 + 0.735105i
\(325\) −11.0238 + 3.58185i −0.611490 + 0.198685i
\(326\) 24.0030 + 17.4392i 1.32940 + 0.965866i
\(327\) −12.3465 + 13.8088i −0.682763 + 0.763629i
\(328\) 9.20395 28.3268i 0.508203 1.56409i
\(329\) −9.57668 −0.527979
\(330\) 0 0
\(331\) −0.392305 −0.0215630 −0.0107815 0.999942i \(-0.503432\pi\)
−0.0107815 + 0.999942i \(0.503432\pi\)
\(332\) 17.1083 52.6540i 0.938940 2.88976i
\(333\) −15.5060 + 27.2955i −0.849722 + 1.49578i
\(334\) −10.1843 7.39931i −0.557259 0.404872i
\(335\) −2.35731 + 0.765938i −0.128794 + 0.0418477i
\(336\) −6.07225 10.4332i −0.331268 0.569176i
\(337\) 5.00937 6.89480i 0.272878 0.375584i −0.650481 0.759523i \(-0.725433\pi\)
0.923359 + 0.383939i \(0.125433\pi\)
\(338\) 3.49392 2.53848i 0.190044 0.138075i
\(339\) −2.26990 + 22.3468i −0.123284 + 1.21371i
\(340\) 19.1798i 1.04017i
\(341\) 0 0
\(342\) −7.26795 16.0221i −0.393006 0.866376i
\(343\) 16.1400 + 5.24419i 0.871476 + 0.283160i
\(344\) 10.3412 + 14.2334i 0.557560 + 0.767415i
\(345\) 0 0
\(346\) −8.38189 25.7968i −0.450613 1.38684i
\(347\) 0.396479 + 1.22024i 0.0212841 + 0.0655057i 0.961134 0.276081i \(-0.0890358\pi\)
−0.939850 + 0.341587i \(0.889036\pi\)
\(348\) −14.1641 + 32.1143i −0.759275 + 1.72151i
\(349\) 11.9418 + 16.4365i 0.639231 + 0.879826i 0.998574 0.0533798i \(-0.0169994\pi\)
−0.359344 + 0.933205i \(0.616999\pi\)
\(350\) −22.3099 7.24891i −1.19251 0.387471i
\(351\) 13.9583 10.3664i 0.745040 0.553316i
\(352\) 0 0
\(353\) 9.58244i 0.510022i −0.966938 0.255011i \(-0.917921\pi\)
0.966938 0.255011i \(-0.0820790\pi\)
\(354\) 5.29537 52.1320i 0.281446 2.77078i
\(355\) −8.36503 + 6.07755i −0.443970 + 0.322563i
\(356\) 21.0205 28.9322i 1.11408 1.53340i
\(357\) −10.2190 17.5579i −0.540844 0.929264i
\(358\) −51.9014 + 16.8638i −2.74307 + 0.891278i
\(359\) −27.8768 20.2537i −1.47128 1.06895i −0.980240 0.197813i \(-0.936616\pi\)
−0.491042 0.871136i \(-0.663384\pi\)
\(360\) −13.4056 7.61542i −0.706535 0.401368i
\(361\) 4.01722 12.3637i 0.211433 0.650723i
\(362\) −30.7804 −1.61778
\(363\) 0 0
\(364\) −35.3205 −1.85130
\(365\) 3.10448 9.55460i 0.162496 0.500111i
\(366\) 12.4934 13.9731i 0.653039 0.730384i
\(367\) 19.3002 + 14.0224i 1.00746 + 0.731966i 0.963676 0.267075i \(-0.0860572\pi\)
0.0437885 + 0.999041i \(0.486057\pi\)
\(368\) 0 0
\(369\) 14.5296 + 15.9119i 0.756378 + 0.828340i
\(370\) 18.2497 25.1186i 0.948759 1.30586i
\(371\) −16.2553 + 11.8101i −0.843931 + 0.613152i
\(372\) 1.26146 + 0.128134i 0.0654036 + 0.00664345i
\(373\) 9.62209i 0.498213i −0.968476 0.249107i \(-0.919863\pi\)
0.968476 0.249107i \(-0.0801369\pi\)
\(374\) 0 0
\(375\) −17.7583 + 3.83949i −0.917036 + 0.198270i
\(376\) −13.3534 4.33878i −0.688649 0.223756i
\(377\) 10.6793 + 14.6987i 0.550010 + 0.757024i
\(378\) 35.1850 0.368478i 1.80972 0.0189525i
\(379\) −9.45235 29.0914i −0.485535 1.49432i −0.831205 0.555966i \(-0.812348\pi\)
0.345670 0.938356i \(-0.387652\pi\)
\(380\) 3.50096 + 10.7748i 0.179595 + 0.552738i
\(381\) 22.8515 + 10.0787i 1.17072 + 0.516347i
\(382\) −3.48807 4.80091i −0.178465 0.245636i
\(383\) 9.02881 + 2.93364i 0.461351 + 0.149902i 0.530465 0.847707i \(-0.322017\pi\)
−0.0691142 + 0.997609i \(0.522017\pi\)
\(384\) 7.58922 + 35.1015i 0.387286 + 1.79127i
\(385\) 0 0
\(386\) 6.86071i 0.349201i
\(387\) −12.6486 + 1.41877i −0.642964 + 0.0721201i
\(388\) −6.84760 + 4.97507i −0.347634 + 0.252571i
\(389\) −11.2125 + 15.4327i −0.568498 + 0.782470i −0.992376 0.123249i \(-0.960669\pi\)
0.423878 + 0.905719i \(0.360669\pi\)
\(390\) −14.8622 + 8.65001i −0.752577 + 0.438010i
\(391\) 0 0
\(392\) −3.35485 2.43744i −0.169446 0.123109i
\(393\) −17.4979 15.6449i −0.882651 0.789181i
\(394\) 7.90727 24.3361i 0.398362 1.22603i
\(395\) −9.10706 −0.458226
\(396\) 0 0
\(397\) −21.1962 −1.06380 −0.531902 0.846806i \(-0.678523\pi\)
−0.531902 + 0.846806i \(0.678523\pi\)
\(398\) −5.66736 + 17.4423i −0.284079 + 0.874305i
\(399\) −8.94571 7.99839i −0.447846 0.400420i
\(400\) −6.90569 5.01728i −0.345284 0.250864i
\(401\) −1.17866 + 0.382969i −0.0588593 + 0.0191246i −0.338299 0.941039i \(-0.609851\pi\)
0.279439 + 0.960163i \(0.409851\pi\)
\(402\) 7.16799 4.17187i 0.357507 0.208074i
\(403\) 0.385786 0.530989i 0.0192174 0.0264505i
\(404\) −1.41793 + 1.03018i −0.0705445 + 0.0512536i
\(405\) 9.58069 5.71124i 0.476068 0.283794i
\(406\) 36.7696i 1.82484i
\(407\) 0 0
\(408\) −6.29423 29.1120i −0.311611 1.44126i
\(409\) 31.5945 + 10.2657i 1.56225 + 0.507605i 0.957407 0.288742i \(-0.0932370\pi\)
0.604840 + 0.796347i \(0.293237\pi\)
\(410\) −12.5265 17.2413i −0.618642 0.851487i
\(411\) 28.2666 + 12.4671i 1.39429 + 0.614955i
\(412\) 14.6835 + 45.1910i 0.723402 + 2.22640i
\(413\) −11.0445 33.9914i −0.543463 1.67261i
\(414\) 0 0
\(415\) −10.8063 14.8736i −0.530460 0.730116i
\(416\) 7.61896 + 2.47555i 0.373550 + 0.121374i
\(417\) 8.76327 1.89469i 0.429139 0.0927832i
\(418\) 0 0
\(419\) 11.0648i 0.540553i −0.962783 0.270277i \(-0.912885\pi\)
0.962783 0.270277i \(-0.0871151\pi\)
\(420\) −22.5427 2.28980i −1.09997 0.111731i
\(421\) 15.5300 11.2832i 0.756887 0.549910i −0.141067 0.990000i \(-0.545053\pi\)
0.897954 + 0.440090i \(0.145053\pi\)
\(422\) 2.66631 3.66987i 0.129794 0.178646i
\(423\) 7.50094 6.84930i 0.364708 0.333024i
\(424\) −28.0165 + 9.10310i −1.36060 + 0.442086i
\(425\) −11.6215 8.44355i −0.563728 0.409572i
\(426\) 23.0603 25.7916i 1.11728 1.24961i
\(427\) 3.95066 12.1589i 0.191186 0.588410i
\(428\) 13.0820 0.632342
\(429\) 0 0
\(430\) 12.5885 0.607069
\(431\) −6.46031 + 19.8828i −0.311182 + 0.957721i 0.666115 + 0.745849i \(0.267956\pi\)
−0.977297 + 0.211872i \(0.932044\pi\)
\(432\) 12.2179 + 3.82887i 0.587836 + 0.184217i
\(433\) −10.5597 7.67210i −0.507469 0.368698i 0.304394 0.952546i \(-0.401546\pi\)
−0.811863 + 0.583849i \(0.801546\pi\)
\(434\) 1.26328 0.410465i 0.0606394 0.0197029i
\(435\) 5.86294 + 10.0735i 0.281106 + 0.482989i
\(436\) −23.4600 + 32.2899i −1.12353 + 1.54641i
\(437\) 0 0
\(438\) −3.39706 + 33.4435i −0.162318 + 1.59799i
\(439\) 8.38375i 0.400134i −0.979782 0.200067i \(-0.935884\pi\)
0.979782 0.200067i \(-0.0641160\pi\)
\(440\) 0 0
\(441\) 2.73205 1.23931i 0.130098 0.0590149i
\(442\) −31.5945 10.2657i −1.50280 0.488288i
\(443\) −14.9977 20.6425i −0.712561 0.980756i −0.999738 0.0228783i \(-0.992717\pi\)
0.287178 0.957877i \(-0.407283\pi\)
\(444\) −27.2962 + 61.8888i −1.29542 + 2.93711i
\(445\) −3.66978 11.2944i −0.173964 0.535406i
\(446\) −9.56479 29.4374i −0.452906 1.39390i
\(447\) −6.57358 + 14.9043i −0.310920 + 0.704949i
\(448\) 17.7228 + 24.3933i 0.837321 + 1.15247i
\(449\) −38.3260 12.4529i −1.80872 0.587687i −0.808716 0.588199i \(-0.799837\pi\)
−1.00000 0.000512011i \(0.999837\pi\)
\(450\) 22.6587 10.2784i 1.06814 0.484530i
\(451\) 0 0
\(452\) 48.3984i 2.27647i
\(453\) −2.88633 + 28.4155i −0.135612 + 1.33507i
\(454\) 10.1843 7.39931i 0.477972 0.347267i
\(455\) −6.89413 + 9.48895i −0.323202 + 0.444849i
\(456\) −8.84988 15.2056i −0.414433 0.712068i
\(457\) −17.5203 + 5.69269i −0.819565 + 0.266293i −0.688644 0.725100i \(-0.741794\pi\)
−0.130922 + 0.991393i \(0.541794\pi\)
\(458\) 10.7226 + 7.79044i 0.501035 + 0.364023i
\(459\) 20.5615 + 6.44359i 0.959730 + 0.300761i
\(460\) 0 0
\(461\) 2.86379 0.133380 0.0666901 0.997774i \(-0.478756\pi\)
0.0666901 + 0.997774i \(0.478756\pi\)
\(462\) 0 0
\(463\) −1.26795 −0.0589266 −0.0294633 0.999566i \(-0.509380\pi\)
−0.0294633 + 0.999566i \(0.509380\pi\)
\(464\) −4.13456 + 12.7249i −0.191942 + 0.590737i
\(465\) 0.280645 0.313884i 0.0130146 0.0145560i
\(466\) 10.5172 + 7.64121i 0.487201 + 0.353972i
\(467\) 18.4581 5.99739i 0.854138 0.277526i 0.150960 0.988540i \(-0.451764\pi\)
0.703178 + 0.711014i \(0.251764\pi\)
\(468\) 27.6648 25.2614i 1.27881 1.16771i
\(469\) 3.32502 4.57649i 0.153535 0.211323i
\(470\) −8.12763 + 5.90507i −0.374900 + 0.272381i
\(471\) −19.7548 2.00661i −0.910251 0.0924599i
\(472\) 52.4002i 2.41192i
\(473\) 0 0
\(474\) 29.7846 6.43966i 1.36805 0.295784i
\(475\) −8.06998 2.62210i −0.370276 0.120310i
\(476\) −25.7292 35.4133i −1.17930 1.62316i
\(477\) 4.28525 20.8761i 0.196208 0.955853i
\(478\) 7.43265 + 22.8753i 0.339961 + 1.04629i
\(479\) −2.02128 6.22086i −0.0923546 0.284238i 0.894201 0.447666i \(-0.147745\pi\)
−0.986555 + 0.163428i \(0.947745\pi\)
\(480\) 4.70218 + 2.07391i 0.214624 + 0.0946604i
\(481\) 20.5805 + 28.3266i 0.938388 + 1.29158i
\(482\) 8.56642 + 2.78340i 0.390190 + 0.126780i
\(483\) 0 0
\(484\) 0 0
\(485\) 2.81070i 0.127627i
\(486\) −27.2951 + 25.4532i −1.23813 + 1.15458i
\(487\) −26.8407 + 19.5009i −1.21627 + 0.883670i −0.995785 0.0917207i \(-0.970763\pi\)
−0.220483 + 0.975391i \(0.570763\pi\)
\(488\) 11.0173 15.1641i 0.498732 0.686445i
\(489\) −18.5509 + 10.7969i −0.838900 + 0.488251i
\(490\) −2.82191 + 0.916893i −0.127481 + 0.0414210i
\(491\) −16.9133 12.2882i −0.763288 0.554561i 0.136629 0.990622i \(-0.456373\pi\)
−0.899917 + 0.436061i \(0.856373\pi\)
\(492\) 34.6113 + 30.9461i 1.56040 + 1.39516i
\(493\) −6.95803 + 21.4146i −0.313374 + 0.964466i
\(494\) −19.6230 −0.882880
\(495\) 0 0
\(496\) 0.483340 0.0217026
\(497\) 7.29216 22.4430i 0.327098 1.00670i
\(498\) 45.8592 + 41.0028i 2.05500 + 1.83738i
\(499\) −20.8758 15.1671i −0.934527 0.678974i 0.0125700 0.999921i \(-0.495999\pi\)
−0.947097 + 0.320947i \(0.895999\pi\)
\(500\) −37.2320 + 12.0974i −1.66506 + 0.541012i
\(501\) 7.87100 4.58103i 0.351650 0.204665i
\(502\) 12.0830 16.6309i 0.539292 0.742271i
\(503\) −2.83585 + 2.06037i −0.126444 + 0.0918673i −0.649210 0.760609i \(-0.724900\pi\)
0.522765 + 0.852477i \(0.324900\pi\)
\(504\) 34.9677 3.92226i 1.55758 0.174711i
\(505\) 0.582009i 0.0258991i
\(506\) 0 0
\(507\) 0.660254 + 3.05379i 0.0293229 + 0.135624i
\(508\) 51.1806 + 16.6296i 2.27077 + 0.737818i
\(509\) 6.89413 + 9.48895i 0.305577 + 0.420590i 0.933995 0.357285i \(-0.116297\pi\)
−0.628419 + 0.777875i \(0.716297\pi\)
\(510\) −19.4991 8.60012i −0.863435 0.380820i
\(511\) 7.08520 + 21.8060i 0.313431 + 0.964641i
\(512\) 8.13823 + 25.0469i 0.359662 + 1.10693i
\(513\) 12.7272 0.133287i 0.561921 0.00588475i
\(514\) −32.5441 44.7931i −1.43546 1.97574i
\(515\) 15.0067 + 4.87598i 0.661275 + 0.214861i
\(516\) −26.8055 + 5.79555i −1.18005 + 0.255135i
\(517\) 0 0
\(518\) 70.8601i 3.11342i
\(519\) 19.5225 + 1.98302i 0.856944 + 0.0870451i
\(520\) −13.9120 + 10.1076i −0.610081 + 0.443250i
\(521\) −1.45690 + 2.00525i −0.0638280 + 0.0878517i −0.839738 0.542992i \(-0.817291\pi\)
0.775910 + 0.630844i \(0.217291\pi\)
\(522\) −26.2978 28.7998i −1.15102 1.26053i
\(523\) 34.3198 11.1512i 1.50070 0.487607i 0.560479 0.828169i \(-0.310617\pi\)
0.940222 + 0.340561i \(0.110617\pi\)
\(524\) −40.9163 29.7274i −1.78744 1.29865i
\(525\) 11.3114 12.6511i 0.493671 0.552141i
\(526\) −17.3656 + 53.4457i −0.757175 + 2.33034i
\(527\) 0.813410 0.0354327
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) −6.51343 + 20.0463i −0.282925 + 0.870755i
\(531\) 32.9614 + 18.7247i 1.43040 + 0.812582i
\(532\) −20.9183 15.1980i −0.906922 0.658917i
\(533\) 22.8569 7.42665i 0.990041 0.321684i
\(534\) 19.9883 + 34.3434i 0.864980 + 1.48618i
\(535\) 2.55344 3.51451i 0.110395 0.151946i
\(536\) 6.70970 4.87488i 0.289815 0.210563i
\(537\) 3.98971 39.2780i 0.172169 1.69497i
\(538\) 39.1547i 1.68808i
\(539\) 0 0
\(540\) 19.2942 14.3292i 0.830291 0.616629i
\(541\) −5.01960 1.63097i −0.215809 0.0701207i 0.199117 0.979976i \(-0.436193\pi\)
−0.414926 + 0.909855i \(0.636193\pi\)
\(542\) 12.8646 + 17.7066i 0.552583 + 0.760565i
\(543\) 8.98612 20.3743i 0.385632 0.874344i
\(544\) 3.06798 + 9.44228i 0.131539 + 0.404835i
\(545\) 4.09568 + 12.6052i 0.175439 + 0.539947i
\(546\) 15.8375 35.9085i 0.677783 1.53674i
\(547\) −12.4091 17.0797i −0.530576 0.730275i 0.456642 0.889650i \(-0.349052\pi\)
−0.987218 + 0.159375i \(0.949052\pi\)
\(548\) 63.3090 + 20.5703i 2.70443 + 0.878721i
\(549\) 5.60175 + 12.3490i 0.239077 + 0.527042i
\(550\) 0 0
\(551\) 13.3004i 0.566615i
\(552\) 0 0
\(553\) 16.8151 12.2169i 0.715051 0.519515i
\(554\) −8.83199 + 12.1562i −0.375235 + 0.516467i
\(555\) 11.2987 + 19.4131i 0.479604 + 0.824042i
\(556\) 18.3730 5.96975i 0.779189 0.253174i
\(557\) 8.40576 + 6.10714i 0.356163 + 0.258768i 0.751450 0.659790i \(-0.229355\pi\)
−0.395287 + 0.918558i \(0.629355\pi\)
\(558\) −0.695898 + 1.22500i −0.0294597 + 0.0518585i
\(559\) −4.38685 + 13.5013i −0.185544 + 0.571046i
\(560\) −8.63744 −0.364998
\(561\) 0 0
\(562\) 1.94744 0.0821478
\(563\) 10.9382 33.6644i 0.460992 1.41879i −0.402963 0.915216i \(-0.632020\pi\)
0.863954 0.503570i \(-0.167980\pi\)
\(564\) 14.5881 16.3159i 0.614271 0.687025i
\(565\) 13.0024 + 9.44677i 0.547013 + 0.397428i
\(566\) 15.4691 5.02622i 0.650216 0.211268i
\(567\) −10.0281 + 23.3974i −0.421141 + 0.982597i
\(568\) 20.3359 27.9899i 0.853275 1.17443i
\(569\) 25.4209 18.4694i 1.06570 0.774276i 0.0905647 0.995891i \(-0.471133\pi\)
0.975134 + 0.221615i \(0.0711328\pi\)
\(570\) −12.5240 1.27214i −0.524573 0.0532842i
\(571\) 27.3233i 1.14345i −0.820447 0.571723i \(-0.806275\pi\)
0.820447 0.571723i \(-0.193725\pi\)
\(572\) 0 0
\(573\) 4.19615 0.907241i 0.175297 0.0379005i
\(574\) 46.2575 + 15.0300i 1.93075 + 0.627340i
\(575\) 0 0
\(576\) −31.3276 6.43062i −1.30532 0.267943i
\(577\) 1.48447 + 4.56873i 0.0617993 + 0.190199i 0.977190 0.212369i \(-0.0681178\pi\)
−0.915390 + 0.402568i \(0.868118\pi\)
\(578\) −0.145121 0.446637i −0.00603625 0.0185777i
\(579\) 4.54127 + 2.00294i 0.188729 + 0.0832392i
\(580\) 14.7617 + 20.3177i 0.612945 + 0.843647i
\(581\) 39.9051 + 12.9660i 1.65554 + 0.537918i
\(582\) −1.98747 9.19239i −0.0823831 0.381037i
\(583\) 0 0
\(584\) 33.6156i 1.39102i
\(585\) −1.38673 12.3629i −0.0573341 0.511145i
\(586\) −63.0141 + 45.7824i −2.60309 + 1.89125i
\(587\) −3.83744 + 5.28178i −0.158388 + 0.218002i −0.880834 0.473425i \(-0.843018\pi\)
0.722446 + 0.691427i \(0.243018\pi\)
\(588\) 5.58676 3.25157i 0.230394 0.134093i
\(589\) 0.456957 0.148474i 0.0188286 0.00611778i
\(590\) −30.3327 22.0380i −1.24878 0.907291i
\(591\) 13.8001 + 12.3387i 0.567662 + 0.507548i
\(592\) −7.96788 + 24.5226i −0.327478 + 1.00787i
\(593\) −26.3359 −1.08148 −0.540742 0.841188i \(-0.681857\pi\)
−0.540742 + 0.841188i \(0.681857\pi\)
\(594\) 0 0
\(595\) −14.5359 −0.595914
\(596\) −10.8462 + 33.3813i −0.444279 + 1.36735i
\(597\) −9.89094 8.84352i −0.404809 0.361941i
\(598\) 0 0
\(599\) −2.58851 + 0.841058i −0.105764 + 0.0343647i −0.361421 0.932403i \(-0.617708\pi\)
0.255657 + 0.966768i \(0.417708\pi\)
\(600\) 21.5040 12.5156i 0.877896 0.510948i
\(601\) −24.4106 + 33.5983i −0.995730 + 1.37050i −0.0678213 + 0.997697i \(0.521605\pi\)
−0.927909 + 0.372807i \(0.878395\pi\)
\(602\) −23.2431 + 16.8871i −0.947318 + 0.688267i
\(603\) 0.668814 + 5.96261i 0.0272362 + 0.242816i
\(604\) 61.5419i 2.50410i
\(605\) 0 0
\(606\) −0.411543 1.90346i −0.0167178 0.0773228i
\(607\) −42.2226 13.7189i −1.71376 0.556835i −0.722808 0.691049i \(-0.757149\pi\)
−0.990952 + 0.134214i \(0.957149\pi\)
\(608\) 3.44706 + 4.74448i 0.139797 + 0.192414i
\(609\) −24.3386 10.7346i −0.986251 0.434988i
\(610\) −4.14439 12.7551i −0.167802 0.516440i
\(611\) −3.50096 10.7748i −0.141634 0.435903i
\(612\) 45.4802 + 9.33574i 1.83843 + 0.377375i
\(613\) −9.06227 12.4731i −0.366021 0.503785i 0.585793 0.810461i \(-0.300783\pi\)
−0.951814 + 0.306676i \(0.900783\pi\)
\(614\) −71.0126 23.0734i −2.86583 0.931166i
\(615\) 15.0695 3.25813i 0.607659 0.131381i
\(616\) 0 0
\(617\) 13.6325i 0.548822i −0.961613 0.274411i \(-0.911517\pi\)
0.961613 0.274411i \(-0.0884828\pi\)
\(618\) −52.5273 5.33552i −2.11296 0.214626i
\(619\) 0.116170 0.0844022i 0.00466925 0.00339241i −0.585448 0.810710i \(-0.699081\pi\)
0.590117 + 0.807317i \(0.299081\pi\)
\(620\) 0.533263 0.733973i 0.0214163 0.0294771i
\(621\) 0 0
\(622\) −1.51226 + 0.491361i −0.0606359 + 0.0197018i
\(623\) 21.9270 + 15.9309i 0.878485 + 0.638257i
\(624\) 9.51864 10.6460i 0.381051 0.426182i
\(625\) 1.33511 4.10905i 0.0534044 0.164362i
\(626\) 17.6984 0.707372
\(627\) 0 0
\(628\) −42.7846 −1.70729
\(629\) −13.4091 + 41.2690i −0.534656 + 1.64550i
\(630\) 12.4359 21.8912i 0.495459 0.872166i
\(631\) −22.1028 16.0586i −0.879897 0.639282i 0.0533274 0.998577i \(-0.483017\pi\)
−0.933224 + 0.359295i \(0.883017\pi\)
\(632\) 28.9814 9.41662i 1.15282 0.374573i
\(633\) 1.65076 + 2.83629i 0.0656117 + 0.112732i
\(634\) −34.6302 + 47.6644i −1.37534 + 1.89300i
\(635\) 14.4574 10.5039i 0.573724 0.416835i
\(636\) 4.64048 45.6847i 0.184007 1.81151i
\(637\) 3.34607i 0.132576i
\(638\) 0 0
\(639\) 10.3397 + 22.7938i 0.409034 + 0.901710i
\(640\) 24.4384 + 7.94053i 0.966014 + 0.313877i
\(641\) −27.7717 38.2245i −1.09692 1.50978i −0.839410 0.543499i \(-0.817099\pi\)
−0.257506 0.966277i \(-0.582901\pi\)
\(642\) −5.86589 + 13.2998i −0.231508 + 0.524900i
\(643\) −1.17545 3.61767i −0.0463554 0.142667i 0.925200 0.379480i \(-0.123897\pi\)
−0.971555 + 0.236813i \(0.923897\pi\)
\(644\) 0 0
\(645\) −3.67511 + 8.33259i −0.144707 + 0.328095i
\(646\) −14.2944 19.6745i −0.562404 0.774083i
\(647\) −15.8696 5.15633i −0.623897 0.202716i −0.0200272 0.999799i \(-0.506375\pi\)
−0.603870 + 0.797083i \(0.706375\pi\)
\(648\) −24.5832 + 28.0812i −0.965720 + 1.10313i
\(649\) 0 0
\(650\) 27.7511i 1.08849i
\(651\) −0.0971096 + 0.956027i −0.00380603 + 0.0374697i
\(652\) −37.4160 + 27.1843i −1.46532 + 1.06462i
\(653\) 22.8154 31.4028i 0.892837 1.22888i −0.0798602 0.996806i \(-0.525447\pi\)
0.972697 0.232079i \(-0.0745526\pi\)
\(654\) −22.3081 38.3292i −0.872316 1.49879i
\(655\) −15.9727 + 5.18985i −0.624105 + 0.202784i
\(656\) 14.3183 + 10.4029i 0.559037 + 0.406164i
\(657\) −21.1453 12.0122i −0.824956 0.468640i
\(658\) 7.08520 21.8060i 0.276210 0.850087i
\(659\) −13.5516 −0.527896 −0.263948 0.964537i \(-0.585025\pi\)
−0.263948 + 0.964537i \(0.585025\pi\)
\(660\) 0 0
\(661\) 3.19615 0.124316 0.0621580 0.998066i \(-0.480202\pi\)
0.0621580 + 0.998066i \(0.480202\pi\)
\(662\) 0.290243 0.893275i 0.0112806 0.0347181i
\(663\) 16.0189 17.9161i 0.622121 0.695805i
\(664\) 49.7680 + 36.1586i 1.93137 + 1.40323i
\(665\) −8.16598 + 2.65329i −0.316663 + 0.102890i
\(666\) −50.6796 55.5012i −1.96379 2.15063i
\(667\) 0 0
\(668\) 15.8753 11.5341i 0.614235 0.446268i
\(669\) 22.2777 + 2.26288i 0.861305 + 0.0874881i
\(670\) 5.93426i 0.229260i
\(671\) 0 0
\(672\) −11.4641 + 2.47863i −0.442237 + 0.0956151i
\(673\) −34.6095 11.2453i −1.33410 0.433475i −0.446785 0.894641i \(-0.647431\pi\)
−0.887314 + 0.461166i \(0.847431\pi\)
\(674\) 11.9933 + 16.5073i 0.461964 + 0.635839i
\(675\) 0.188496 + 17.9990i 0.00725521 + 0.692782i
\(676\) 2.08032 + 6.40256i 0.0800122 + 0.246252i
\(677\) −3.55408 10.9383i −0.136594 0.420394i 0.859240 0.511572i \(-0.170937\pi\)
−0.995835 + 0.0911783i \(0.970937\pi\)
\(678\) −49.2040 21.7016i −1.88967 0.833444i
\(679\) −3.77048 5.18962i −0.144698 0.199160i
\(680\) −20.2684 6.58559i −0.777257 0.252546i
\(681\) 1.92455 + 8.90138i 0.0737488 + 0.341102i
\(682\) 0 0
\(683\) 41.2946i 1.58009i −0.613047 0.790046i \(-0.710056\pi\)
0.613047 0.790046i \(-0.289944\pi\)
\(684\) 27.2539 3.05702i 1.04208 0.116888i
\(685\) 17.8834 12.9931i 0.683290 0.496439i
\(686\) −23.8820 + 32.8707i −0.911817 + 1.25501i
\(687\) −8.28706 + 4.82319i −0.316171 + 0.184016i
\(688\) −9.94263 + 3.23056i −0.379059 + 0.123164i
\(689\) −19.2302 13.9715i −0.732611 0.532273i
\(690\) 0 0
\(691\) 0.799877 2.46177i 0.0304288 0.0936501i −0.934689 0.355467i \(-0.884322\pi\)
0.965117 + 0.261817i \(0.0843217\pi\)
\(692\) 42.2817 1.60731
\(693\) 0 0
\(694\) −3.07180 −0.116604
\(695\) 1.98239 6.10118i 0.0751965 0.231431i
\(696\) −29.0736 25.9948i −1.10203 0.985329i
\(697\) 24.0963 + 17.5070i 0.912711 + 0.663123i
\(698\) −46.2608 + 15.0310i −1.75100 + 0.568933i
\(699\) −8.12832 + 4.73080i −0.307441 + 0.178935i
\(700\) 21.4932 29.5829i 0.812368 1.11813i
\(701\) −16.1162 + 11.7091i −0.608700 + 0.442247i −0.848956 0.528463i \(-0.822769\pi\)
0.240256 + 0.970710i \(0.422769\pi\)
\(702\) 13.2772 + 39.4524i 0.501116 + 1.48904i
\(703\) 25.6317i 0.966718i
\(704\) 0 0
\(705\) −1.53590 7.10381i −0.0578453 0.267545i
\(706\) 21.8191 + 7.08946i 0.821174 + 0.266815i
\(707\) −0.780751 1.07461i −0.0293632 0.0404149i
\(708\) 74.7356 + 32.9623i 2.80874 + 1.23880i
\(709\) 12.1507 + 37.3960i 0.456329 + 1.40444i 0.869567 + 0.493814i \(0.164398\pi\)
−0.413238 + 0.910623i \(0.635602\pi\)
\(710\) −7.64975 23.5435i −0.287090 0.883572i
\(711\) −4.43284 + 21.5951i −0.166245 + 0.809881i
\(712\) 23.3566 + 32.1476i 0.875327 + 1.20478i
\(713\) 0 0
\(714\) 47.5396 10.2784i 1.77913 0.384661i
\(715\) 0 0
\(716\) 85.0677i 3.17913i
\(717\) −17.3116 1.75845i −0.646515 0.0656705i
\(718\) 66.7418 48.4908i 2.49078 1.80966i
\(719\) 21.0728 29.0042i 0.785881 1.08167i −0.208727 0.977974i \(-0.566932\pi\)
0.994609 0.103699i \(-0.0330678\pi\)
\(720\) 6.76527 6.17754i 0.252127 0.230223i
\(721\) −34.2491 + 11.1282i −1.27550 + 0.414437i
\(722\) 25.1800 + 18.2944i 0.937103 + 0.680845i
\(723\) −4.34330 + 4.85772i −0.161529 + 0.180661i
\(724\) 14.8269 45.6324i 0.551036 1.69592i
\(725\) −18.8096 −0.698570
\(726\) 0 0
\(727\) −28.9282 −1.07289 −0.536444 0.843936i \(-0.680233\pi\)
−0.536444 + 0.843936i \(0.680233\pi\)
\(728\) 12.1277 37.3251i 0.449481 1.38336i
\(729\) −8.87941 25.4982i −0.328867 0.944376i
\(730\) 19.4589 + 14.1377i 0.720207 + 0.523261i
\(731\) −16.7324 + 5.43669i −0.618870 + 0.201083i
\(732\) 14.6972 + 25.2524i 0.543226 + 0.933355i
\(733\) 16.8697 23.2191i 0.623095 0.857617i −0.374479 0.927236i \(-0.622178\pi\)
0.997574 + 0.0696189i \(0.0221783\pi\)
\(734\) −46.2081 + 33.5721i −1.70557 + 1.23917i
\(735\) 0.216923 2.13557i 0.00800131 0.0787715i
\(736\) 0 0
\(737\) 0 0
\(738\) −46.9808 + 21.3114i −1.72939 + 0.784484i
\(739\) −21.4234 6.96088i −0.788072 0.256060i −0.112789 0.993619i \(-0.535978\pi\)
−0.675283 + 0.737559i \(0.735978\pi\)
\(740\) 28.4478 + 39.1551i 1.04576 + 1.43937i
\(741\) 5.72879 12.9889i 0.210452 0.477159i
\(742\) −14.8653 45.7507i −0.545722 1.67956i
\(743\) 8.77184 + 26.9969i 0.321807 + 0.990421i 0.972861 + 0.231390i \(0.0743273\pi\)
−0.651054 + 0.759032i \(0.725673\pi\)
\(744\) −0.568541 + 1.28906i −0.0208437 + 0.0472591i
\(745\) 6.85092 + 9.42948i 0.250998 + 0.345470i
\(746\) 21.9094 + 7.11880i 0.802161 + 0.260638i
\(747\) −40.5290 + 18.3848i −1.48288 + 0.672664i
\(748\) 0 0
\(749\) 9.91451i 0.362268i
\(750\) 4.39583 43.2762i 0.160513 1.58022i
\(751\) −3.94448 + 2.86583i −0.143936 + 0.104576i −0.657423 0.753522i \(-0.728353\pi\)
0.513487 + 0.858097i \(0.328353\pi\)
\(752\) 4.90396 6.74973i 0.178829 0.246137i
\(753\) 7.48079 + 12.8533i 0.272615 + 0.468400i
\(754\) −41.3699 + 13.4419i −1.50660 + 0.489525i
\(755\) 16.5334 + 12.0122i 0.601712 + 0.437169i
\(756\) −16.4023 + 52.3398i −0.596546 + 1.90358i
\(757\) −2.05813 + 6.33428i −0.0748041 + 0.230223i −0.981467 0.191634i \(-0.938621\pi\)
0.906662 + 0.421857i \(0.138621\pi\)
\(758\) 73.2340 2.65998
\(759\) 0 0
\(760\) −12.5885 −0.456631
\(761\) 8.93119 27.4874i 0.323755 0.996417i −0.648244 0.761433i \(-0.724496\pi\)
0.971999 0.234984i \(-0.0755037\pi\)
\(762\) −39.8555 + 44.5760i −1.44381 + 1.61482i
\(763\) −24.4717 17.7797i −0.885936 0.643670i
\(764\) 8.79762 2.85852i 0.318287 0.103418i
\(765\) 11.3852 10.3962i 0.411634 0.375874i
\(766\) −13.3597 + 18.3881i −0.482707 + 0.664389i
\(767\) 34.2066 24.8525i 1.23513 0.897373i
\(768\) −48.8014 4.95707i −1.76097 0.178873i
\(769\) 11.9329i 0.430311i −0.976580 0.215155i \(-0.930974\pi\)
0.976580 0.215155i \(-0.0690258\pi\)
\(770\) 0 0
\(771\) 39.1506 8.46467i 1.40998 0.304848i
\(772\) 10.1711 + 3.30479i 0.366066 + 0.118942i
\(773\) 18.1590 + 24.9937i 0.653132 + 0.898959i 0.999230 0.0392390i \(-0.0124934\pi\)
−0.346098 + 0.938199i \(0.612493\pi\)
\(774\) 6.12741 29.8504i 0.220245 1.07295i
\(775\) 0.209975 + 0.646235i 0.00754251 + 0.0232135i
\(776\) −2.90624 8.94448i −0.104328 0.321088i
\(777\) −46.9040 20.6871i −1.68267 0.742146i
\(778\) −26.8447 36.9486i −0.962429 1.32467i
\(779\) 16.7324 + 5.43669i 0.599500 + 0.194789i
\(780\) −5.66467 26.2001i −0.202828 0.938115i
\(781\) 0 0
\(782\) 0 0
\(783\) 26.7407 8.99924i 0.955634 0.321607i
\(784\) 1.99350 1.44836i 0.0711964 0.0517272i
\(785\) −8.35103 + 11.4942i −0.298061 + 0.410246i
\(786\) 48.5689 28.2678i 1.73240 1.00828i
\(787\) −43.3037 + 14.0702i −1.54361 + 0.501550i −0.952370 0.304945i \(-0.901362\pi\)
−0.591241 + 0.806495i \(0.701362\pi\)
\(788\) 32.2697 + 23.4453i 1.14956 + 0.835203i
\(789\) −30.3072 27.0978i −1.07897 0.964706i
\(790\) 6.73776 20.7367i 0.239719 0.737778i
\(791\) −36.6799 −1.30419
\(792\) 0 0
\(793\) 15.1244 0.537082
\(794\) 15.6817 48.2635i 0.556524 1.71281i
\(795\) −11.3675 10.1638i −0.403165 0.360471i
\(796\) −23.1285 16.8039i −0.819770 0.595598i
\(797\) 14.6063 4.74587i 0.517381 0.168107i −0.0386754 0.999252i \(-0.512314\pi\)
0.556056 + 0.831145i \(0.312314\pi\)
\(798\) 24.8307 14.4518i 0.878995 0.511588i
\(799\) 8.25286 11.3591i 0.291965 0.401855i
\(800\) −6.70970 + 4.87488i −0.237224 + 0.172353i
\(801\) −28.5682 + 3.20444i −1.00941 + 0.113223i
\(802\) 2.96713i 0.104773i
\(803\) 0 0
\(804\) 2.73205 + 12.6362i 0.0963520 + 0.445646i
\(805\) 0 0
\(806\) 0.923638 + 1.27128i 0.0325338 + 0.0447789i
\(807\) 25.9174 + 11.4309i 0.912335 + 0.402388i
\(808\) −0.601792 1.85213i −0.0211710 0.0651576i
\(809\) 16.0251 + 49.3202i 0.563413 + 1.73401i 0.672621 + 0.739987i \(0.265168\pi\)
−0.109208 + 0.994019i \(0.534832\pi\)
\(810\) 5.91627 + 26.0405i 0.207877 + 0.914971i
\(811\) 15.2887 + 21.0431i 0.536858 + 0.738922i 0.988156 0.153452i \(-0.0490389\pi\)
−0.451298 + 0.892373i \(0.649039\pi\)
\(812\) −54.5114 17.7118i −1.91297 0.621563i
\(813\) −15.4762 + 3.34607i −0.542773 + 0.117352i
\(814\) 0 0
\(815\) 15.3580i 0.537966i
\(816\) 17.6078 + 1.78854i 0.616397 + 0.0626113i
\(817\) −8.40755 + 6.10844i −0.294143 + 0.213707i
\(818\) −46.7497 + 64.3454i −1.63456 + 2.24979i
\(819\) 19.1450 + 20.9664i 0.668981 + 0.732627i
\(820\) 31.5945 10.2657i 1.10333 0.358493i
\(821\) 17.6732 + 12.8403i 0.616798 + 0.448130i 0.851802 0.523864i \(-0.175510\pi\)
−0.235003 + 0.971995i \(0.575510\pi\)
\(822\) −49.3002 + 55.1393i −1.71954 + 1.92320i
\(823\) 10.1591 31.2666i 0.354125 1.08989i −0.602390 0.798202i \(-0.705785\pi\)
0.956515 0.291683i \(-0.0942152\pi\)
\(824\) −52.7976 −1.83929
\(825\) 0 0
\(826\) 85.5692 2.97733
\(827\) −5.81248 + 17.8890i −0.202120 + 0.622060i 0.797700 + 0.603055i \(0.206050\pi\)
−0.999819 + 0.0190055i \(0.993950\pi\)
\(828\) 0 0
\(829\) −15.8474 11.5138i −0.550403 0.399891i 0.277531 0.960717i \(-0.410484\pi\)
−0.827934 + 0.560826i \(0.810484\pi\)
\(830\) 41.8620 13.6018i 1.45305 0.472125i
\(831\) −5.46803 9.39501i −0.189684 0.325909i
\(832\) −20.9662 + 28.8576i −0.726874 + 1.00046i
\(833\) 3.35485 2.43744i 0.116239 0.0844524i
\(834\) −2.16923 + 21.3557i −0.0751142 + 0.739486i
\(835\) 6.51626i 0.225505i
\(836\) 0 0
\(837\) −0.607695 0.818262i −0.0210050 0.0282833i
\(838\) 25.1946 + 8.18621i 0.870331 + 0.282788i
\(839\) 11.0173 + 15.1641i 0.380361 + 0.523522i 0.955680 0.294407i \(-0.0951222\pi\)
−0.575319 + 0.817929i \(0.695122\pi\)
\(840\) 10.1600 23.0359i 0.350554 0.794813i
\(841\) 0.149360 + 0.459683i 0.00515035 + 0.0158511i
\(842\) 14.2021 + 43.7095i 0.489436 + 1.50633i
\(843\) −0.568541 + 1.28906i −0.0195816 + 0.0443975i
\(844\) 4.15627 + 5.72061i 0.143065 + 0.196912i
\(845\) 2.12612 + 0.690818i 0.0731407 + 0.0237649i
\(846\) 10.0463 + 22.1469i 0.345399 + 0.761428i
\(847\) 0 0
\(848\) 17.5045i 0.601107i
\(849\) −1.18913 + 11.7067i −0.0408107 + 0.401774i
\(850\) 27.8240 20.2153i 0.954354 0.693379i
\(851\) 0 0
\(852\) 27.1283 + 46.6110i 0.929399 + 1.59687i
\(853\) 40.4818 13.1533i 1.38607 0.450362i 0.481411 0.876495i \(-0.340125\pi\)
0.904660 + 0.426133i \(0.140125\pi\)
\(854\) 24.7628 + 17.9912i 0.847366 + 0.615648i
\(855\) 4.49836 7.91854i 0.153841 0.270808i
\(856\) −4.49184 + 13.8245i −0.153528 + 0.472510i
\(857\) 56.3029 1.92327 0.961635 0.274332i \(-0.0884568\pi\)
0.961635 + 0.274332i \(0.0884568\pi\)
\(858\) 0 0
\(859\) 1.12436 0.0383625 0.0191813 0.999816i \(-0.493894\pi\)
0.0191813 + 0.999816i \(0.493894\pi\)
\(860\) −6.06384 + 18.6626i −0.206775 + 0.636388i
\(861\) −23.4533 + 26.2310i −0.799285 + 0.893952i
\(862\) −40.4934 29.4202i −1.37921 1.00205i
\(863\) −27.4869 + 8.93103i −0.935665 + 0.304016i −0.736877 0.676027i \(-0.763700\pi\)
−0.198787 + 0.980043i \(0.563700\pi\)
\(864\) 7.20653 10.1406i 0.245171 0.344989i
\(865\) 8.25286 11.3591i 0.280606 0.386220i
\(866\) 25.2818 18.3683i 0.859111 0.624181i
\(867\) 0.338007 + 0.0343334i 0.0114793 + 0.00116602i
\(868\) 2.07055i 0.0702791i
\(869\) 0 0
\(870\) −27.2750 + 5.89706i −0.924709 + 0.199929i
\(871\) 6.36459 + 2.06798i 0.215656 + 0.0700709i
\(872\) −26.0673 35.8786i −0.882750 1.21500i
\(873\) 6.66488 + 1.36810i 0.225572 + 0.0463033i
\(874\) 0 0
\(875\) −9.16831 28.2172i −0.309946 0.953914i
\(876\) −47.9441 21.1459i −1.61988 0.714453i
\(877\) 16.9133 + 23.2792i 0.571123 + 0.786084i 0.992687 0.120715i \(-0.0385187\pi\)
−0.421564 + 0.906799i \(0.638519\pi\)
\(878\) 19.0897 + 6.20262i 0.644247 + 0.209328i
\(879\) −11.9079 55.0764i −0.401645 1.85768i
\(880\) 0 0
\(881\) 13.6325i 0.459289i −0.973275 0.229644i \(-0.926244\pi\)
0.973275 0.229644i \(-0.0737563\pi\)
\(882\) 0.800628 + 7.13775i 0.0269585 + 0.240340i
\(883\) 9.27465 6.73843i 0.312117 0.226766i −0.420687 0.907206i \(-0.638211\pi\)
0.732804 + 0.680439i \(0.238211\pi\)
\(884\) 30.4380 41.8943i 1.02374 1.40906i
\(885\) 23.4429 13.6441i 0.788024 0.458641i
\(886\) 58.0987 18.8774i 1.95186 0.634199i
\(887\) 36.6625 + 26.6369i 1.23101 + 0.894378i 0.996965 0.0778484i \(-0.0248050\pi\)
0.234041 + 0.972227i \(0.424805\pi\)
\(888\) −56.0289 50.0956i −1.88021 1.68110i
\(889\) −12.6031 + 38.7885i −0.422696 + 1.30092i
\(890\) 28.4323 0.953053
\(891\) 0 0
\(892\) 48.2487 1.61549
\(893\) 2.56288 7.88773i 0.0857635 0.263953i
\(894\) −29.0736 25.9948i −0.972365 0.869395i
\(895\) −22.8537 16.6042i −0.763915 0.555016i
\(896\) −55.7747 + 18.1223i −1.86330 + 0.605423i
\(897\) 0 0
\(898\) 56.7102 78.0548i 1.89244 2.60472i
\(899\) 0.861667 0.626038i 0.0287382 0.0208795i
\(900\) 4.32328 + 38.5429i 0.144109 + 1.28476i
\(901\) 29.4582i 0.981397i
\(902\) 0 0
\(903\) −4.39230 20.3152i −0.146167 0.676048i
\(904\) −51.1452 16.6181i −1.70107 0.552710i
\(905\) −9.36525 12.8902i −0.311312 0.428484i
\(906\) −62.5663 27.5950i −2.07863 0.916783i
\(907\) −8.17191 25.1506i −0.271344 0.835111i −0.990164 0.139914i \(-0.955317\pi\)
0.718820 0.695196i \(-0.244683\pi\)
\(908\) 6.06384 + 18.6626i 0.201235 + 0.619339i
\(909\) 1.38009 + 0.283292i 0.0457747 + 0.00939620i
\(910\) −16.5057 22.7182i −0.547159 0.753100i
\(911\) −30.2446 9.82708i −1.00205 0.325586i −0.238365 0.971176i \(-0.576612\pi\)
−0.763684 + 0.645590i \(0.776612\pi\)
\(912\) 10.2182 2.20925i 0.338358 0.0731557i
\(913\) 0 0
\(914\) 44.1053i 1.45887i
\(915\) 9.65285 + 0.980500i 0.319113 + 0.0324143i
\(916\) −16.7145 + 12.1438i −0.552263 + 0.401242i
\(917\) 22.5297 31.0094i 0.743995 1.02402i
\(918\) −29.8842 + 42.0512i −0.986326 + 1.38790i
\(919\) 37.1064 12.0566i 1.22403 0.397710i 0.375480 0.926831i \(-0.377478\pi\)
0.848547 + 0.529120i \(0.177478\pi\)
\(920\) 0 0
\(921\) 36.0044 40.2688i 1.18639 1.32690i
\(922\) −2.11875 + 6.52083i −0.0697772 + 0.214752i
\(923\) 27.9166 0.918887
\(924\) 0 0
\(925\) −36.2487 −1.19185
\(926\) 0.938079 2.88711i 0.0308272 0.0948763i
\(927\) 18.8667 33.2114i 0.619663 1.09080i
\(928\) 10.5172 + 7.64121i 0.345245 + 0.250835i
\(929\) 30.3912 9.87471i 0.997104 0.323979i 0.235396 0.971900i \(-0.424361\pi\)
0.761708 + 0.647921i \(0.224361\pi\)
\(930\) 0.507079 + 0.871249i 0.0166278 + 0.0285694i
\(931\) 1.43977 1.98168i 0.0471867 0.0649469i
\(932\) −16.3943 + 11.9112i −0.537014 + 0.390163i
\(933\) 0.116249 1.14445i 0.00380581 0.0374675i
\(934\) 46.4660i 1.52041i
\(935\) 0 0
\(936\) 17.1962 + 37.9087i 0.562074 + 1.23908i
\(937\) 27.1991 + 8.83753i 0.888556 + 0.288709i 0.717506 0.696553i \(-0.245284\pi\)
0.171051 + 0.985262i \(0.445284\pi\)
\(938\) 7.96065 + 10.9569i 0.259925 + 0.357755i
\(939\) −5.16693 + 11.7150i −0.168616 + 0.382305i
\(940\) −4.83928 14.8938i −0.157840 0.485782i
\(941\) 0.633603 + 1.95003i 0.0206549 + 0.0635692i 0.960853 0.277060i \(-0.0893600\pi\)
−0.940198 + 0.340629i \(0.889360\pi\)
\(942\) 19.1844 43.4968i 0.625061 1.41720i
\(943\) 0 0
\(944\) 29.6130 + 9.62185i 0.963821 + 0.313165i
\(945\) 10.8597 + 14.6226i 0.353266 + 0.475674i
\(946\) 0 0
\(947\) 30.2297i 0.982334i 0.871065 + 0.491167i \(0.163429\pi\)
−0.871065 + 0.491167i \(0.836571\pi\)
\(948\) −4.80030 + 47.2581i −0.155906 + 1.53487i
\(949\) −21.9441 + 15.9433i −0.712334 + 0.517541i
\(950\) 11.9410 16.4353i 0.387417 0.533233i
\(951\) −21.4401 36.8379i −0.695244 1.19455i
\(952\) 46.2575 15.0300i 1.49922 0.487125i
\(953\) −44.5493 32.3669i −1.44309 1.04847i −0.987385 0.158338i \(-0.949386\pi\)
−0.455707 0.890130i \(-0.650614\pi\)
\(954\) 44.3644 + 25.2025i 1.43635 + 0.815960i
\(955\) 0.949237 2.92145i 0.0307166 0.0945360i
\(956\) −37.4933 −1.21262
\(957\) 0 0
\(958\) 15.6603 0.505960
\(959\) −15.5897 + 47.9803i −0.503419 + 1.54936i
\(960\) −15.2521 + 17.0586i −0.492261 + 0.550564i
\(961\) 25.0484 + 18.1987i 0.808013 + 0.587056i
\(962\) −79.7256 + 25.9044i −2.57046 + 0.835192i
\(963\) −7.09091 7.76554i −0.228502 0.250241i
\(964\) −8.25286 + 11.3591i −0.265807 + 0.365851i
\(965\) 2.87312 2.08744i 0.0924889 0.0671971i
\(966\) 0 0
\(967\) 45.0518i 1.44877i 0.689397 + 0.724383i \(0.257875\pi\)
−0.689397 + 0.724383i \(0.742125\pi\)
\(968\) 0 0
\(969\) 17.1962 3.71794i 0.552420 0.119437i
\(970\) −6.39994 2.07947i −0.205490 0.0667676i
\(971\) −4.37070 6.01575i −0.140262 0.193055i 0.733107 0.680114i \(-0.238070\pi\)
−0.873369 + 0.487059i \(0.838070\pi\)
\(972\) −24.5866 52.7262i −0.788617 1.69119i
\(973\) 4.52432 + 13.9244i 0.145043 + 0.446397i
\(974\) −24.5456 75.5435i −0.786491 2.42057i
\(975\) 18.3691 + 8.10173i 0.588282 + 0.259463i
\(976\) 6.54666 + 9.01070i 0.209553 + 0.288426i
\(977\) −10.6079 3.44672i −0.339377 0.110270i 0.134370 0.990931i \(-0.457099\pi\)
−0.473747 + 0.880661i \(0.657099\pi\)
\(978\) −10.8597 50.2281i −0.347255 1.60612i
\(979\) 0 0
\(980\) 4.62518i 0.147746i
\(981\) 31.8837 3.57633i 1.01797 0.114183i
\(982\) 40.4934 29.4202i 1.29220 0.938835i
\(983\) 0.285775 0.393335i 0.00911479 0.0125454i −0.804435 0.594040i \(-0.797532\pi\)
0.813550 + 0.581495i \(0.197532\pi\)
\(984\) −44.5866 + 25.9500i −1.42137 + 0.827257i
\(985\) 12.5973 4.09310i 0.401383 0.130417i
\(986\) −43.6131 31.6867i −1.38892 1.00911i
\(987\) 12.3654 + 11.0560i 0.393596 + 0.351915i
\(988\) 9.45235 29.0914i 0.300719 0.925519i
\(989\) 0 0
\(990\) 0 0
\(991\) 19.8564 0.630760 0.315380 0.948966i \(-0.397868\pi\)
0.315380 + 0.948966i \(0.397868\pi\)
\(992\) 0.145121 0.446637i 0.00460760 0.0141807i
\(993\) 0.506545 + 0.452903i 0.0160747 + 0.0143725i
\(994\) 45.7074 + 33.2084i 1.44975 + 1.05330i
\(995\) −9.02881 + 2.93364i −0.286233 + 0.0930026i
\(996\) −82.8776 + 48.2359i −2.62608 + 1.52841i
\(997\) −35.5430 + 48.9208i −1.12566 + 1.54934i −0.329597 + 0.944122i \(0.606913\pi\)
−0.796062 + 0.605215i \(0.793087\pi\)
\(998\) 49.9801 36.3127i 1.58209 1.14946i
\(999\) 51.5331 17.3428i 1.63043 0.548702i
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 363.2.f.i.233.1 32
3.2 odd 2 inner 363.2.f.i.233.8 32
11.2 odd 10 inner 363.2.f.i.239.1 32
11.3 even 5 inner 363.2.f.i.161.8 32
11.4 even 5 363.2.d.e.362.2 yes 8
11.5 even 5 inner 363.2.f.i.215.2 32
11.6 odd 10 inner 363.2.f.i.215.8 32
11.7 odd 10 363.2.d.e.362.8 yes 8
11.8 odd 10 inner 363.2.f.i.161.2 32
11.9 even 5 inner 363.2.f.i.239.7 32
11.10 odd 2 inner 363.2.f.i.233.7 32
33.2 even 10 inner 363.2.f.i.239.8 32
33.5 odd 10 inner 363.2.f.i.215.7 32
33.8 even 10 inner 363.2.f.i.161.7 32
33.14 odd 10 inner 363.2.f.i.161.1 32
33.17 even 10 inner 363.2.f.i.215.1 32
33.20 odd 10 inner 363.2.f.i.239.2 32
33.26 odd 10 363.2.d.e.362.7 yes 8
33.29 even 10 363.2.d.e.362.1 8
33.32 even 2 inner 363.2.f.i.233.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.d.e.362.1 8 33.29 even 10
363.2.d.e.362.2 yes 8 11.4 even 5
363.2.d.e.362.7 yes 8 33.26 odd 10
363.2.d.e.362.8 yes 8 11.7 odd 10
363.2.f.i.161.1 32 33.14 odd 10 inner
363.2.f.i.161.2 32 11.8 odd 10 inner
363.2.f.i.161.7 32 33.8 even 10 inner
363.2.f.i.161.8 32 11.3 even 5 inner
363.2.f.i.215.1 32 33.17 even 10 inner
363.2.f.i.215.2 32 11.5 even 5 inner
363.2.f.i.215.7 32 33.5 odd 10 inner
363.2.f.i.215.8 32 11.6 odd 10 inner
363.2.f.i.233.1 32 1.1 even 1 trivial
363.2.f.i.233.2 32 33.32 even 2 inner
363.2.f.i.233.7 32 11.10 odd 2 inner
363.2.f.i.233.8 32 3.2 odd 2 inner
363.2.f.i.239.1 32 11.2 odd 10 inner
363.2.f.i.239.2 32 33.20 odd 10 inner
363.2.f.i.239.7 32 11.9 even 5 inner
363.2.f.i.239.8 32 33.2 even 10 inner