Properties

Label 33.3.h.b.14.4
Level $33$
Weight $3$
Character 33.14
Analytic conductor $0.899$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,3,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), degree \(4\), 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: \(0.899184872389\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 14.4
Root \(2.10855 + 2.90217i\) of defining polynomial
Character \(\chi\) \(=\) 33.14
Dual form 33.3.h.b.26.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.10855 + 2.90217i) q^{2} +(-2.00253 - 2.23380i) q^{3} +(-2.74053 + 8.43448i) q^{4} +(1.22635 - 1.68793i) q^{5} +(2.26043 - 10.5218i) q^{6} +(2.73883 - 8.42924i) q^{7} +(-16.6100 + 5.39692i) q^{8} +(-0.979734 + 8.94651i) q^{9} +O(q^{10})\) \(q+(2.10855 + 2.90217i) q^{2} +(-2.00253 - 2.23380i) q^{3} +(-2.74053 + 8.43448i) q^{4} +(1.22635 - 1.68793i) q^{5} +(2.26043 - 10.5218i) q^{6} +(2.73883 - 8.42924i) q^{7} +(-16.6100 + 5.39692i) q^{8} +(-0.979734 + 8.94651i) q^{9} +7.48447 q^{10} +(-10.8108 + 2.03154i) q^{11} +(24.3290 - 10.7685i) q^{12} +(1.33068 - 0.966792i) q^{13} +(30.2380 - 9.82492i) q^{14} +(-6.22630 + 0.640704i) q^{15} +(-21.9865 - 15.9742i) q^{16} +(-7.30235 + 10.0508i) q^{17} +(-28.0301 + 16.0208i) q^{18} +(3.26497 + 10.0485i) q^{19} +(10.8759 + 14.9695i) q^{20} +(-24.3138 + 10.7618i) q^{21} +(-28.6909 - 27.0911i) q^{22} -20.3378i q^{23} +(45.3177 + 26.2959i) q^{24} +(6.38026 + 19.6364i) q^{25} +(5.61158 + 1.82331i) q^{26} +(21.9467 - 15.7271i) q^{27} +(63.5904 + 46.2012i) q^{28} +(-11.0405 - 3.58727i) q^{29} +(-14.9879 - 16.7188i) q^{30} +(18.9215 - 13.7473i) q^{31} -27.6317i q^{32} +(26.1870 + 20.0809i) q^{33} -44.5665 q^{34} +(-10.8692 - 14.9601i) q^{35} +(-72.7742 - 32.7817i) q^{36} +(2.23911 - 6.89128i) q^{37} +(-22.2782 + 30.6633i) q^{38} +(-4.82434 - 1.03643i) q^{39} +(-11.2601 + 34.6550i) q^{40} +(36.9741 - 12.0136i) q^{41} +(-82.4995 - 47.8710i) q^{42} -15.8444 q^{43} +(12.4923 - 96.7508i) q^{44} +(13.8996 + 12.6253i) q^{45} +(59.0236 - 42.8832i) q^{46} +(43.0910 - 14.0011i) q^{47} +(8.34565 + 81.1023i) q^{48} +(-23.9091 - 17.3709i) q^{49} +(-43.5351 + 59.9209i) q^{50} +(37.0747 - 3.81509i) q^{51} +(4.50764 + 13.8731i) q^{52} +(23.6972 + 32.6164i) q^{53} +(91.9184 + 30.5315i) q^{54} +(-9.82872 + 20.7392i) q^{55} +154.791i q^{56} +(15.9082 - 27.4158i) q^{57} +(-12.8685 - 39.6053i) q^{58} +(-107.642 - 34.9750i) q^{59} +(11.6594 - 54.2715i) q^{60} +(-62.7118 - 45.5628i) q^{61} +(79.7937 + 25.9266i) q^{62} +(72.7290 + 32.7614i) q^{63} +(-7.75446 + 5.63395i) q^{64} -3.43171i q^{65} +(-3.06166 + 118.340i) q^{66} +62.9082 q^{67} +(-64.7612 - 89.1361i) q^{68} +(-45.4306 + 40.7270i) q^{69} +(20.4987 - 63.0884i) q^{70} +(6.00278 - 8.26212i) q^{71} +(-32.0102 - 153.889i) q^{72} +(-23.0595 + 70.9699i) q^{73} +(24.7209 - 8.03232i) q^{74} +(31.0872 - 53.5748i) q^{75} -93.7020 q^{76} +(-12.4845 + 96.6906i) q^{77} +(-7.16445 - 16.1864i) q^{78} +(-69.8281 + 50.7331i) q^{79} +(-53.9264 + 17.5218i) q^{80} +(-79.0802 - 17.5304i) q^{81} +(112.827 + 81.9736i) q^{82} +(-6.94074 + 9.55311i) q^{83} +(-24.1377 - 234.568i) q^{84} +(8.00981 + 24.6517i) q^{85} +(-33.4086 - 45.9830i) q^{86} +(14.0957 + 31.8459i) q^{87} +(168.603 - 92.0887i) q^{88} -74.5782i q^{89} +(-7.33279 + 66.9599i) q^{90} +(-4.50483 - 13.8645i) q^{91} +(171.539 + 55.7363i) q^{92} +(-68.5996 - 14.7375i) q^{93} +(131.493 + 95.5353i) q^{94} +(20.9652 + 6.81201i) q^{95} +(-61.7236 + 55.3333i) q^{96} +(62.4301 - 45.3581i) q^{97} -106.016i q^{98} +(-7.58349 - 98.7091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 10 q^{3} + 8 q^{4} - 33 q^{6} + 6 q^{7} - 28 q^{9} - 12 q^{10} + 106 q^{12} - 42 q^{13} + 82 q^{15} - 88 q^{16} - 43 q^{18} - 134 q^{19} - 12 q^{21} + 78 q^{22} + 41 q^{24} + 134 q^{25} + 80 q^{27} + 264 q^{28} - 120 q^{30} + 124 q^{31} - 79 q^{33} - 132 q^{34} - 219 q^{36} + 90 q^{37} - 174 q^{39} - 284 q^{40} - 102 q^{42} - 156 q^{43} - 72 q^{45} - 22 q^{46} + 30 q^{48} - 30 q^{49} + 111 q^{51} + 326 q^{52} + 1046 q^{54} - 172 q^{55} + 281 q^{57} - 116 q^{58} + 54 q^{60} - 126 q^{61} - 138 q^{63} + 236 q^{64} - 236 q^{66} + 368 q^{67} + 198 q^{69} - 322 q^{70} - 562 q^{72} + 24 q^{73} - 21 q^{75} - 900 q^{76} - 492 q^{78} - 314 q^{79} - 388 q^{81} + 270 q^{84} + 318 q^{85} + 132 q^{87} + 1064 q^{88} + 176 q^{90} + 374 q^{91} - 10 q^{93} + 990 q^{94} - 332 q^{96} + 72 q^{97} - 530 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.10855 + 2.90217i 1.05427 + 1.45108i 0.885045 + 0.465506i \(0.154128\pi\)
0.169229 + 0.985577i \(0.445872\pi\)
\(3\) −2.00253 2.23380i −0.667511 0.744600i
\(4\) −2.74053 + 8.43448i −0.685132 + 2.10862i
\(5\) 1.22635 1.68793i 0.245270 0.337586i −0.668578 0.743642i \(-0.733097\pi\)
0.913848 + 0.406057i \(0.133097\pi\)
\(6\) 2.26043 10.5218i 0.376738 1.75363i
\(7\) 2.73883 8.42924i 0.391261 1.20418i −0.540575 0.841296i \(-0.681793\pi\)
0.931836 0.362881i \(-0.118207\pi\)
\(8\) −16.6100 + 5.39692i −2.07625 + 0.674615i
\(9\) −0.979734 + 8.94651i −0.108859 + 0.994057i
\(10\) 7.48447 0.748447
\(11\) −10.8108 + 2.03154i −0.982798 + 0.184685i
\(12\) 24.3290 10.7685i 2.02741 0.897377i
\(13\) 1.33068 0.966792i 0.102360 0.0743686i −0.535428 0.844581i \(-0.679850\pi\)
0.637788 + 0.770212i \(0.279850\pi\)
\(14\) 30.2380 9.82492i 2.15986 0.701780i
\(15\) −6.22630 + 0.640704i −0.415087 + 0.0427136i
\(16\) −21.9865 15.9742i −1.37416 0.998385i
\(17\) −7.30235 + 10.0508i −0.429550 + 0.591225i −0.967850 0.251529i \(-0.919067\pi\)
0.538300 + 0.842753i \(0.319067\pi\)
\(18\) −28.0301 + 16.0208i −1.55723 + 0.890044i
\(19\) 3.26497 + 10.0485i 0.171841 + 0.528871i 0.999475 0.0323966i \(-0.0103140\pi\)
−0.827635 + 0.561267i \(0.810314\pi\)
\(20\) 10.8759 + 14.9695i 0.543797 + 0.748473i
\(21\) −24.3138 + 10.7618i −1.15780 + 0.512468i
\(22\) −28.6909 27.0911i −1.30413 1.23141i
\(23\) 20.3378i 0.884251i −0.896953 0.442126i \(-0.854225\pi\)
0.896953 0.442126i \(-0.145775\pi\)
\(24\) 45.3177 + 26.2959i 1.88824 + 1.09566i
\(25\) 6.38026 + 19.6364i 0.255210 + 0.785457i
\(26\) 5.61158 + 1.82331i 0.215830 + 0.0701275i
\(27\) 21.9467 15.7271i 0.812840 0.582487i
\(28\) 63.5904 + 46.2012i 2.27109 + 1.65004i
\(29\) −11.0405 3.58727i −0.380707 0.123699i 0.112411 0.993662i \(-0.464143\pi\)
−0.493118 + 0.869963i \(0.664143\pi\)
\(30\) −14.9879 16.7188i −0.499596 0.557294i
\(31\) 18.9215 13.7473i 0.610371 0.443460i −0.239174 0.970977i \(-0.576877\pi\)
0.849545 + 0.527516i \(0.176877\pi\)
\(32\) 27.6317i 0.863489i
\(33\) 26.1870 + 20.0809i 0.793544 + 0.608512i
\(34\) −44.5665 −1.31078
\(35\) −10.8692 14.9601i −0.310548 0.427433i
\(36\) −72.7742 32.7817i −2.02151 0.910604i
\(37\) 2.23911 6.89128i 0.0605166 0.186251i −0.916228 0.400657i \(-0.868782\pi\)
0.976745 + 0.214407i \(0.0687817\pi\)
\(38\) −22.2782 + 30.6633i −0.586269 + 0.806929i
\(39\) −4.82434 1.03643i −0.123701 0.0265752i
\(40\) −11.2601 + 34.6550i −0.281502 + 0.866375i
\(41\) 36.9741 12.0136i 0.901806 0.293015i 0.178824 0.983881i \(-0.442771\pi\)
0.722982 + 0.690866i \(0.242771\pi\)
\(42\) −82.4995 47.8710i −1.96427 1.13978i
\(43\) −15.8444 −0.368474 −0.184237 0.982882i \(-0.558981\pi\)
−0.184237 + 0.982882i \(0.558981\pi\)
\(44\) 12.4923 96.7508i 0.283916 2.19888i
\(45\) 13.8996 + 12.6253i 0.308879 + 0.280562i
\(46\) 59.0236 42.8832i 1.28312 0.932243i
\(47\) 43.0910 14.0011i 0.916831 0.297896i 0.187665 0.982233i \(-0.439908\pi\)
0.729166 + 0.684337i \(0.239908\pi\)
\(48\) 8.34565 + 81.1023i 0.173868 + 1.68963i
\(49\) −23.9091 17.3709i −0.487940 0.354509i
\(50\) −43.5351 + 59.9209i −0.870702 + 1.19842i
\(51\) 37.0747 3.81509i 0.726955 0.0748057i
\(52\) 4.50764 + 13.8731i 0.0866853 + 0.266790i
\(53\) 23.6972 + 32.6164i 0.447116 + 0.615403i 0.971775 0.235910i \(-0.0758070\pi\)
−0.524658 + 0.851313i \(0.675807\pi\)
\(54\) 91.9184 + 30.5315i 1.70219 + 0.565398i
\(55\) −9.82872 + 20.7392i −0.178704 + 0.377076i
\(56\) 154.791i 2.76412i
\(57\) 15.9082 27.4158i 0.279092 0.480979i
\(58\) −12.8685 39.6053i −0.221871 0.682850i
\(59\) −107.642 34.9750i −1.82444 0.592797i −0.999625 0.0273946i \(-0.991279\pi\)
−0.824816 0.565402i \(-0.808721\pi\)
\(60\) 11.6594 54.2715i 0.194323 0.904525i
\(61\) −62.7118 45.5628i −1.02806 0.746931i −0.0601426 0.998190i \(-0.519156\pi\)
−0.967920 + 0.251259i \(0.919156\pi\)
\(62\) 79.7937 + 25.9266i 1.28700 + 0.418170i
\(63\) 72.7290 + 32.7614i 1.15443 + 0.520022i
\(64\) −7.75446 + 5.63395i −0.121163 + 0.0880304i
\(65\) 3.43171i 0.0527956i
\(66\) −3.06166 + 118.340i −0.0463888 + 1.79304i
\(67\) 62.9082 0.938929 0.469464 0.882951i \(-0.344447\pi\)
0.469464 + 0.882951i \(0.344447\pi\)
\(68\) −64.7612 89.1361i −0.952370 1.31082i
\(69\) −45.4306 + 40.7270i −0.658414 + 0.590247i
\(70\) 20.4987 63.0884i 0.292838 0.901262i
\(71\) 6.00278 8.26212i 0.0845462 0.116368i −0.764649 0.644447i \(-0.777088\pi\)
0.849195 + 0.528079i \(0.177088\pi\)
\(72\) −32.0102 153.889i −0.444586 2.13735i
\(73\) −23.0595 + 70.9699i −0.315884 + 0.972191i 0.659505 + 0.751700i \(0.270766\pi\)
−0.975389 + 0.220491i \(0.929234\pi\)
\(74\) 24.7209 8.03232i 0.334067 0.108545i
\(75\) 31.0872 53.5748i 0.414496 0.714331i
\(76\) −93.7020 −1.23292
\(77\) −12.4845 + 96.6906i −0.162137 + 1.25572i
\(78\) −7.16445 16.1864i −0.0918519 0.207518i
\(79\) −69.8281 + 50.7331i −0.883900 + 0.642191i −0.934280 0.356539i \(-0.883957\pi\)
0.0503802 + 0.998730i \(0.483957\pi\)
\(80\) −53.9264 + 17.5218i −0.674081 + 0.219022i
\(81\) −79.0802 17.5304i −0.976299 0.216425i
\(82\) 112.827 + 81.9736i 1.37594 + 0.999678i
\(83\) −6.94074 + 9.55311i −0.0836234 + 0.115098i −0.848779 0.528747i \(-0.822662\pi\)
0.765156 + 0.643845i \(0.222662\pi\)
\(84\) −24.1377 234.568i −0.287353 2.79247i
\(85\) 8.00981 + 24.6517i 0.0942331 + 0.290020i
\(86\) −33.4086 45.9830i −0.388472 0.534686i
\(87\) 14.0957 + 31.8459i 0.162019 + 0.366045i
\(88\) 168.603 92.0887i 1.91594 1.04646i
\(89\) 74.5782i 0.837957i −0.907996 0.418979i \(-0.862388\pi\)
0.907996 0.418979i \(-0.137612\pi\)
\(90\) −7.33279 + 66.9599i −0.0814755 + 0.743999i
\(91\) −4.50483 13.8645i −0.0495037 0.152357i
\(92\) 171.539 + 55.7363i 1.86455 + 0.605829i
\(93\) −68.5996 14.7375i −0.737630 0.158468i
\(94\) 131.493 + 95.5353i 1.39886 + 1.01633i
\(95\) 20.9652 + 6.81201i 0.220687 + 0.0717054i
\(96\) −61.7236 + 55.3333i −0.642955 + 0.576388i
\(97\) 62.4301 45.3581i 0.643609 0.467609i −0.217479 0.976065i \(-0.569783\pi\)
0.861088 + 0.508456i \(0.169783\pi\)
\(98\) 106.016i 1.08179i
\(99\) −7.58349 98.7091i −0.0766009 0.997062i
\(100\) −183.108 −1.83108
\(101\) 7.52095 + 10.3517i 0.0744649 + 0.102492i 0.844625 0.535359i \(-0.179824\pi\)
−0.770160 + 0.637851i \(0.779824\pi\)
\(102\) 89.2458 + 99.5527i 0.874959 + 0.976007i
\(103\) 21.8055 67.1104i 0.211704 0.651558i −0.787667 0.616101i \(-0.788711\pi\)
0.999371 0.0354567i \(-0.0112886\pi\)
\(104\) −16.8848 + 23.2400i −0.162354 + 0.223461i
\(105\) −11.6521 + 54.2378i −0.110972 + 0.516550i
\(106\) −44.6915 + 137.546i −0.421618 + 1.29761i
\(107\) −175.204 + 56.9272i −1.63742 + 0.532029i −0.975959 0.217952i \(-0.930062\pi\)
−0.661459 + 0.749981i \(0.730062\pi\)
\(108\) 72.5048 + 228.210i 0.671341 + 2.11305i
\(109\) −58.5394 −0.537058 −0.268529 0.963272i \(-0.586538\pi\)
−0.268529 + 0.963272i \(0.586538\pi\)
\(110\) −80.9129 + 15.2050i −0.735572 + 0.138227i
\(111\) −19.8777 + 8.79828i −0.179078 + 0.0792638i
\(112\) −194.867 + 141.579i −1.73989 + 1.26410i
\(113\) 144.558 46.9698i 1.27927 0.415662i 0.410950 0.911658i \(-0.365197\pi\)
0.868325 + 0.495996i \(0.165197\pi\)
\(114\) 113.109 11.6392i 0.992180 0.102098i
\(115\) −34.3287 24.9413i −0.298510 0.216881i
\(116\) 60.5136 83.2899i 0.521669 0.718016i
\(117\) 7.34571 + 12.8521i 0.0627839 + 0.109847i
\(118\) −125.465 386.141i −1.06326 3.27238i
\(119\) 64.7209 + 89.0807i 0.543873 + 0.748577i
\(120\) 99.9611 44.2449i 0.833009 0.368708i
\(121\) 112.746 43.9250i 0.931783 0.363016i
\(122\) 278.071i 2.27927i
\(123\) −100.878 58.5351i −0.820144 0.475895i
\(124\) 64.0962 + 197.268i 0.516905 + 1.59087i
\(125\) 90.5763 + 29.4300i 0.724610 + 0.235440i
\(126\) 58.2736 + 280.150i 0.462489 + 2.22342i
\(127\) 11.5481 + 8.39020i 0.0909301 + 0.0660646i 0.632321 0.774706i \(-0.282102\pi\)
−0.541391 + 0.840771i \(0.682102\pi\)
\(128\) −137.818 44.7799i −1.07671 0.349843i
\(129\) 31.7289 + 35.3932i 0.245960 + 0.274366i
\(130\) 9.95940 7.23592i 0.0766107 0.0556610i
\(131\) 153.686i 1.17318i 0.809885 + 0.586589i \(0.199529\pi\)
−0.809885 + 0.586589i \(0.800471\pi\)
\(132\) −241.138 + 165.841i −1.82680 + 1.25637i
\(133\) 93.6438 0.704088
\(134\) 132.645 + 182.570i 0.989888 + 1.36246i
\(135\) 0.368057 56.3314i 0.00272635 0.417270i
\(136\) 67.0486 206.354i 0.493004 1.51731i
\(137\) 47.3996 65.2400i 0.345983 0.476205i −0.600194 0.799854i \(-0.704910\pi\)
0.946177 + 0.323650i \(0.104910\pi\)
\(138\) −213.989 45.9721i −1.55065 0.333131i
\(139\) 65.4935 201.568i 0.471176 1.45013i −0.379870 0.925040i \(-0.624031\pi\)
0.851046 0.525091i \(-0.175969\pi\)
\(140\) 155.968 50.6772i 1.11406 0.361980i
\(141\) −117.567 68.2191i −0.833808 0.483824i
\(142\) 36.6352 0.257994
\(143\) −12.4216 + 13.1551i −0.0868640 + 0.0919936i
\(144\) 164.454 181.052i 1.14204 1.25731i
\(145\) −19.5946 + 14.2363i −0.135135 + 0.0981814i
\(146\) −254.589 + 82.7209i −1.74376 + 0.566581i
\(147\) 9.07540 + 88.1940i 0.0617374 + 0.599959i
\(148\) 51.9881 + 37.7715i 0.351271 + 0.255213i
\(149\) 133.033 183.104i 0.892840 1.22889i −0.0798559 0.996806i \(-0.525446\pi\)
0.972696 0.232083i \(-0.0745540\pi\)
\(150\) 221.032 22.7448i 1.47355 0.151632i
\(151\) 84.2779 + 259.381i 0.558132 + 1.71775i 0.687527 + 0.726159i \(0.258696\pi\)
−0.129395 + 0.991593i \(0.541304\pi\)
\(152\) −108.462 149.286i −0.713568 0.982142i
\(153\) −82.7654 75.1777i −0.540951 0.491357i
\(154\) −306.936 + 167.645i −1.99309 + 1.08860i
\(155\) 48.7971i 0.314820i
\(156\) 21.9630 37.8504i 0.140789 0.242631i
\(157\) 1.87243 + 5.76274i 0.0119263 + 0.0367054i 0.956843 0.290607i \(-0.0938571\pi\)
−0.944916 + 0.327312i \(0.893857\pi\)
\(158\) −294.472 95.6797i −1.86375 0.605568i
\(159\) 25.4041 118.250i 0.159774 0.743711i
\(160\) −46.6403 33.8861i −0.291502 0.211788i
\(161\) −171.432 55.7016i −1.06479 0.345973i
\(162\) −115.868 266.468i −0.715236 1.64486i
\(163\) −131.002 + 95.1782i −0.803691 + 0.583915i −0.911994 0.410202i \(-0.865458\pi\)
0.108304 + 0.994118i \(0.465458\pi\)
\(164\) 344.781i 2.10232i
\(165\) 66.0095 19.5755i 0.400058 0.118639i
\(166\) −42.3596 −0.255178
\(167\) 93.5806 + 128.803i 0.560363 + 0.771274i 0.991373 0.131074i \(-0.0418425\pi\)
−0.431010 + 0.902347i \(0.641842\pi\)
\(168\) 345.772 309.974i 2.05817 1.84508i
\(169\) −51.3879 + 158.156i −0.304070 + 0.935832i
\(170\) −54.6542 + 75.2250i −0.321495 + 0.442500i
\(171\) −93.0983 + 19.3652i −0.544434 + 0.113247i
\(172\) 43.4220 133.639i 0.252453 0.776972i
\(173\) −36.5394 + 11.8724i −0.211210 + 0.0686264i −0.412711 0.910862i \(-0.635418\pi\)
0.201501 + 0.979488i \(0.435418\pi\)
\(174\) −62.7007 + 108.057i −0.360349 + 0.621015i
\(175\) 182.995 1.04568
\(176\) 270.144 + 128.027i 1.53491 + 0.727423i
\(177\) 137.429 + 310.489i 0.776437 + 1.75418i
\(178\) 216.438 157.252i 1.21595 0.883436i
\(179\) −129.490 + 42.0738i −0.723407 + 0.235049i −0.647500 0.762066i \(-0.724185\pi\)
−0.0759072 + 0.997115i \(0.524185\pi\)
\(180\) −144.580 + 82.6357i −0.803222 + 0.459087i
\(181\) 105.447 + 76.6119i 0.582581 + 0.423270i 0.839654 0.543122i \(-0.182758\pi\)
−0.257072 + 0.966392i \(0.582758\pi\)
\(182\) 30.7383 42.3076i 0.168892 0.232460i
\(183\) 23.8042 + 231.327i 0.130077 + 1.26408i
\(184\) 109.761 + 337.811i 0.596529 + 1.83593i
\(185\) −8.88605 12.2306i −0.0480327 0.0661114i
\(186\) −101.875 230.162i −0.547713 1.23743i
\(187\) 58.5254 123.492i 0.312970 0.660386i
\(188\) 401.821i 2.13735i
\(189\) −72.4597 228.068i −0.383385 1.20671i
\(190\) 24.4366 + 75.2080i 0.128613 + 0.395832i
\(191\) 300.134 + 97.5195i 1.57138 + 0.510574i 0.959819 0.280621i \(-0.0905403\pi\)
0.611565 + 0.791194i \(0.290540\pi\)
\(192\) 28.1137 + 6.03977i 0.146425 + 0.0314571i
\(193\) −118.448 86.0576i −0.613721 0.445894i 0.237002 0.971509i \(-0.423835\pi\)
−0.850723 + 0.525615i \(0.823835\pi\)
\(194\) 263.273 + 85.5427i 1.35708 + 0.440942i
\(195\) −7.66576 + 6.87211i −0.0393116 + 0.0352416i
\(196\) 212.038 154.055i 1.08183 0.785995i
\(197\) 229.459i 1.16476i −0.812915 0.582382i \(-0.802121\pi\)
0.812915 0.582382i \(-0.197879\pi\)
\(198\) 270.480 230.141i 1.36606 1.16233i
\(199\) −389.358 −1.95657 −0.978287 0.207253i \(-0.933548\pi\)
−0.978287 + 0.207253i \(0.933548\pi\)
\(200\) −211.952 291.727i −1.05976 1.45864i
\(201\) −125.976 140.524i −0.626745 0.699127i
\(202\) −14.1841 + 43.6541i −0.0702182 + 0.216109i
\(203\) −60.4760 + 83.2381i −0.297911 + 0.410040i
\(204\) −69.4260 + 323.161i −0.340324 + 1.58412i
\(205\) 25.0651 77.1425i 0.122269 0.376305i
\(206\) 240.744 78.2223i 1.16866 0.379720i
\(207\) 181.952 + 19.9256i 0.878996 + 0.0962590i
\(208\) −44.7006 −0.214907
\(209\) −55.7108 102.000i −0.266559 0.488037i
\(210\) −181.976 + 80.5465i −0.866553 + 0.383555i
\(211\) −165.031 + 119.902i −0.782137 + 0.568256i −0.905620 0.424091i \(-0.860594\pi\)
0.123483 + 0.992347i \(0.460594\pi\)
\(212\) −340.045 + 110.487i −1.60399 + 0.521167i
\(213\) −30.4767 + 3.13614i −0.143083 + 0.0147236i
\(214\) −534.637 388.437i −2.49831 1.81513i
\(215\) −19.4308 + 26.7442i −0.0903757 + 0.124391i
\(216\) −279.656 + 379.672i −1.29471 + 1.75774i
\(217\) −64.0564 197.145i −0.295191 0.908503i
\(218\) −123.433 169.891i −0.566207 0.779316i
\(219\) 204.710 90.6091i 0.934750 0.413740i
\(220\) −147.988 139.737i −0.672675 0.635166i
\(221\) 20.4342i 0.0924626i
\(222\) −67.4470 39.1367i −0.303816 0.176291i
\(223\) −5.10490 15.7113i −0.0228919 0.0704542i 0.938958 0.344032i \(-0.111793\pi\)
−0.961850 + 0.273578i \(0.911793\pi\)
\(224\) −232.914 75.6783i −1.03979 0.337850i
\(225\) −181.929 + 37.8426i −0.808571 + 0.168189i
\(226\) 441.122 + 320.494i 1.95187 + 1.41811i
\(227\) −107.335 34.8751i −0.472840 0.153635i 0.0628969 0.998020i \(-0.479966\pi\)
−0.535737 + 0.844385i \(0.679966\pi\)
\(228\) 187.641 + 209.312i 0.822988 + 0.918034i
\(229\) 298.218 216.668i 1.30226 0.946150i 0.302289 0.953216i \(-0.402249\pi\)
0.999975 + 0.00706607i \(0.00224922\pi\)
\(230\) 152.217i 0.661815i
\(231\) 240.988 165.738i 1.04324 0.717481i
\(232\) 202.743 0.873892
\(233\) 102.592 + 141.206i 0.440310 + 0.606034i 0.970281 0.241981i \(-0.0777972\pi\)
−0.529971 + 0.848016i \(0.677797\pi\)
\(234\) −21.8102 + 48.4177i −0.0932058 + 0.206913i
\(235\) 29.2119 89.9049i 0.124306 0.382574i
\(236\) 589.992 812.054i 2.49997 3.44091i
\(237\) 253.161 + 54.3875i 1.06819 + 0.229483i
\(238\) −122.060 + 375.662i −0.512856 + 1.57841i
\(239\) −328.450 + 106.720i −1.37427 + 0.446527i −0.900781 0.434273i \(-0.857005\pi\)
−0.473488 + 0.880800i \(0.657005\pi\)
\(240\) 147.130 + 85.3731i 0.613040 + 0.355721i
\(241\) −261.447 −1.08484 −0.542421 0.840107i \(-0.682492\pi\)
−0.542421 + 0.840107i \(0.682492\pi\)
\(242\) 365.207 + 234.589i 1.50912 + 0.969376i
\(243\) 119.201 + 211.755i 0.490540 + 0.871419i
\(244\) 556.162 404.076i 2.27935 1.65605i
\(245\) −58.6418 + 19.0539i −0.239354 + 0.0777710i
\(246\) −42.8269 416.188i −0.174093 1.69182i
\(247\) 14.0595 + 10.2148i 0.0569209 + 0.0413555i
\(248\) −240.093 + 330.460i −0.968118 + 1.33250i
\(249\) 35.2388 3.62617i 0.141521 0.0145629i
\(250\) 105.574 + 324.922i 0.422294 + 1.29969i
\(251\) −116.584 160.465i −0.464480 0.639302i 0.510950 0.859610i \(-0.329294\pi\)
−0.975430 + 0.220309i \(0.929294\pi\)
\(252\) −475.641 + 523.648i −1.88746 + 2.07797i
\(253\) 41.3169 + 219.867i 0.163308 + 0.869040i
\(254\) 51.2057i 0.201597i
\(255\) 39.0270 67.2581i 0.153047 0.263757i
\(256\) −148.790 457.929i −0.581211 1.78878i
\(257\) 1.77390 + 0.576376i 0.00690234 + 0.00224271i 0.312466 0.949929i \(-0.398845\pi\)
−0.305564 + 0.952172i \(0.598845\pi\)
\(258\) −35.8151 + 166.711i −0.138818 + 0.646165i
\(259\) −51.9557 37.7481i −0.200601 0.145745i
\(260\) 28.9447 + 9.40471i 0.111326 + 0.0361719i
\(261\) 42.9104 95.2594i 0.164408 0.364978i
\(262\) −446.023 + 324.055i −1.70238 + 1.23685i
\(263\) 27.0901i 0.103004i 0.998673 + 0.0515020i \(0.0164009\pi\)
−0.998673 + 0.0515020i \(0.983599\pi\)
\(264\) −543.341 192.215i −2.05811 0.728087i
\(265\) 84.1151 0.317416
\(266\) 197.452 + 271.770i 0.742302 + 1.02169i
\(267\) −166.593 + 149.345i −0.623943 + 0.559345i
\(268\) −172.402 + 530.599i −0.643291 + 1.97985i
\(269\) −83.9639 + 115.566i −0.312133 + 0.429615i −0.936045 0.351880i \(-0.885542\pi\)
0.623912 + 0.781495i \(0.285542\pi\)
\(270\) 164.259 117.709i 0.608368 0.435960i
\(271\) −32.5479 + 100.172i −0.120103 + 0.369639i −0.992977 0.118306i \(-0.962254\pi\)
0.872874 + 0.487945i \(0.162254\pi\)
\(272\) 321.107 104.334i 1.18054 0.383580i
\(273\) −21.9494 + 37.8269i −0.0804006 + 0.138560i
\(274\) 289.282 1.05577
\(275\) −108.868 199.323i −0.395883 0.724812i
\(276\) −219.008 494.797i −0.793507 1.79274i
\(277\) −198.144 + 143.960i −0.715322 + 0.519712i −0.884886 0.465807i \(-0.845764\pi\)
0.169564 + 0.985519i \(0.445764\pi\)
\(278\) 723.081 234.943i 2.60101 0.845119i
\(279\) 104.452 + 182.750i 0.374380 + 0.655018i
\(280\) 261.276 + 189.828i 0.933128 + 0.677957i
\(281\) 38.2716 52.6763i 0.136198 0.187460i −0.735470 0.677557i \(-0.763039\pi\)
0.871668 + 0.490097i \(0.163039\pi\)
\(282\) −49.9122 485.042i −0.176994 1.72001i
\(283\) −48.6936 149.864i −0.172062 0.529553i 0.827425 0.561576i \(-0.189805\pi\)
−0.999487 + 0.0320232i \(0.989805\pi\)
\(284\) 53.2359 + 73.2729i 0.187450 + 0.258003i
\(285\) −26.7668 60.4734i −0.0939187 0.212187i
\(286\) −64.3697 8.31130i −0.225069 0.0290605i
\(287\) 344.566i 1.20058i
\(288\) 247.207 + 27.0717i 0.858358 + 0.0939989i
\(289\) 41.6112 + 128.066i 0.143984 + 0.443136i
\(290\) −82.6322 26.8488i −0.284939 0.0925822i
\(291\) −226.339 48.6253i −0.777798 0.167097i
\(292\) −535.399 388.991i −1.83356 1.33216i
\(293\) 175.003 + 56.8620i 0.597280 + 0.194068i 0.592027 0.805918i \(-0.298328\pi\)
0.00525314 + 0.999986i \(0.498328\pi\)
\(294\) −236.818 + 212.299i −0.805502 + 0.722107i
\(295\) −191.042 + 138.800i −0.647601 + 0.470509i
\(296\) 126.549i 0.427529i
\(297\) −205.310 + 214.608i −0.691281 + 0.722586i
\(298\) 811.906 2.72452
\(299\) −19.6624 27.0630i −0.0657605 0.0905116i
\(300\) 366.680 + 409.028i 1.22227 + 1.36343i
\(301\) −43.3950 + 133.556i −0.144169 + 0.443708i
\(302\) −575.062 + 791.505i −1.90418 + 2.62088i
\(303\) 8.06270 37.5299i 0.0266096 0.123861i
\(304\) 88.7316 273.088i 0.291880 0.898315i
\(305\) −153.813 + 49.9770i −0.504306 + 0.163859i
\(306\) 43.6633 398.715i 0.142691 1.30299i
\(307\) 386.672 1.25952 0.629759 0.776790i \(-0.283154\pi\)
0.629759 + 0.776790i \(0.283154\pi\)
\(308\) −781.321 370.284i −2.53676 1.20222i
\(309\) −193.578 + 85.6816i −0.626465 + 0.277287i
\(310\) 141.617 102.891i 0.456830 0.331907i
\(311\) 87.7273 28.5043i 0.282081 0.0916538i −0.164559 0.986367i \(-0.552620\pi\)
0.446641 + 0.894713i \(0.352620\pi\)
\(312\) 85.7259 8.82143i 0.274762 0.0282738i
\(313\) 60.1890 + 43.7299i 0.192297 + 0.139712i 0.679768 0.733427i \(-0.262080\pi\)
−0.487471 + 0.873139i \(0.662080\pi\)
\(314\) −12.7763 + 17.5851i −0.0406889 + 0.0560035i
\(315\) 144.490 82.5843i 0.458699 0.262173i
\(316\) −236.541 728.000i −0.748549 2.30380i
\(317\) 307.870 + 423.746i 0.971198 + 1.33674i 0.941440 + 0.337182i \(0.109474\pi\)
0.0297582 + 0.999557i \(0.490526\pi\)
\(318\) 396.747 175.609i 1.24763 0.552229i
\(319\) 126.644 + 16.3520i 0.397003 + 0.0512603i
\(320\) 19.9982i 0.0624943i
\(321\) 478.015 + 277.372i 1.48914 + 0.864087i
\(322\) −199.817 614.974i −0.620550 1.90986i
\(323\) −124.838 40.5623i −0.386495 0.125580i
\(324\) 364.582 618.958i 1.12525 1.91037i
\(325\) 27.4744 + 19.9613i 0.0845366 + 0.0614194i
\(326\) −552.446 179.501i −1.69462 0.550615i
\(327\) 117.227 + 130.765i 0.358492 + 0.399894i
\(328\) −549.303 + 399.092i −1.67470 + 1.21674i
\(329\) 401.571i 1.22058i
\(330\) 195.996 + 150.295i 0.593926 + 0.455439i
\(331\) 251.706 0.760441 0.380221 0.924896i \(-0.375848\pi\)
0.380221 + 0.924896i \(0.375848\pi\)
\(332\) −61.5542 84.7221i −0.185404 0.255187i
\(333\) 59.4592 + 26.7839i 0.178556 + 0.0804321i
\(334\) −176.488 + 543.173i −0.528406 + 1.62627i
\(335\) 77.1476 106.185i 0.230291 0.316969i
\(336\) 706.488 + 151.778i 2.10264 + 0.451719i
\(337\) −15.3428 + 47.2202i −0.0455275 + 0.140119i −0.971236 0.238118i \(-0.923470\pi\)
0.925709 + 0.378237i \(0.123470\pi\)
\(338\) −567.348 + 184.342i −1.67854 + 0.545392i
\(339\) −394.403 228.855i −1.16343 0.675090i
\(340\) −229.875 −0.676104
\(341\) −176.628 + 187.058i −0.517971 + 0.548558i
\(342\) −252.503 229.354i −0.738313 0.670626i
\(343\) 139.440 101.309i 0.406531 0.295362i
\(344\) 263.175 85.5108i 0.765044 0.248578i
\(345\) 13.0305 + 126.629i 0.0377695 + 0.367041i
\(346\) −111.501 81.0099i −0.322256 0.234133i
\(347\) 270.251 371.969i 0.778822 1.07196i −0.216589 0.976263i \(-0.569493\pi\)
0.995411 0.0956933i \(-0.0305068\pi\)
\(348\) −307.233 + 31.6152i −0.882855 + 0.0908482i
\(349\) −121.675 374.478i −0.348640 1.07300i −0.959606 0.281346i \(-0.909219\pi\)
0.610967 0.791656i \(-0.290781\pi\)
\(350\) 385.853 + 531.081i 1.10244 + 1.51737i
\(351\) 13.9990 42.1456i 0.0398833 0.120073i
\(352\) 56.1347 + 298.720i 0.159474 + 0.848635i
\(353\) 16.9433i 0.0479980i 0.999712 + 0.0239990i \(0.00763985\pi\)
−0.999712 + 0.0239990i \(0.992360\pi\)
\(354\) −611.315 + 1053.52i −1.72688 + 2.97606i
\(355\) −6.58434 20.2645i −0.0185474 0.0570832i
\(356\) 629.029 + 204.384i 1.76693 + 0.574112i
\(357\) 69.3828 322.960i 0.194350 0.904651i
\(358\) −395.141 287.086i −1.10374 0.801917i
\(359\) 72.1739 + 23.4507i 0.201041 + 0.0653223i 0.407807 0.913068i \(-0.366294\pi\)
−0.206765 + 0.978391i \(0.566294\pi\)
\(360\) −299.010 134.691i −0.830582 0.374143i
\(361\) 201.742 146.574i 0.558842 0.406022i
\(362\) 467.565i 1.29162i
\(363\) −323.897 163.890i −0.892277 0.451489i
\(364\) 129.285 0.355179
\(365\) 91.5131 + 125.957i 0.250721 + 0.345087i
\(366\) −621.156 + 556.847i −1.69715 + 1.52144i
\(367\) 191.376 588.996i 0.521462 1.60489i −0.249747 0.968311i \(-0.580347\pi\)
0.771209 0.636583i \(-0.219653\pi\)
\(368\) −324.879 + 447.157i −0.882823 + 1.21510i
\(369\) 71.2551 + 342.559i 0.193103 + 0.928345i
\(370\) 16.7586 51.5776i 0.0452935 0.139399i
\(371\) 339.833 110.419i 0.915993 0.297624i
\(372\) 312.302 538.213i 0.839523 1.44681i
\(373\) −365.674 −0.980359 −0.490179 0.871622i \(-0.663069\pi\)
−0.490179 + 0.871622i \(0.663069\pi\)
\(374\) 481.798 90.5385i 1.28823 0.242081i
\(375\) −115.641 261.264i −0.308376 0.696704i
\(376\) −640.180 + 465.118i −1.70261 + 1.23702i
\(377\) −18.1595 + 5.90037i −0.0481683 + 0.0156508i
\(378\) 509.106 691.182i 1.34684 1.82852i
\(379\) 331.603 + 240.924i 0.874943 + 0.635683i 0.931909 0.362693i \(-0.118143\pi\)
−0.0569658 + 0.998376i \(0.518143\pi\)
\(380\) −114.912 + 158.162i −0.302399 + 0.416217i
\(381\) −4.38344 42.5979i −0.0115051 0.111805i
\(382\) 349.829 + 1076.66i 0.915784 + 2.81849i
\(383\) 31.1300 + 42.8468i 0.0812795 + 0.111872i 0.847721 0.530443i \(-0.177974\pi\)
−0.766441 + 0.642314i \(0.777974\pi\)
\(384\) 175.956 + 397.532i 0.458219 + 1.03524i
\(385\) 147.896 + 139.650i 0.384147 + 0.362726i
\(386\) 525.213i 1.36065i
\(387\) 15.5233 141.752i 0.0401118 0.366284i
\(388\) 211.481 + 650.871i 0.545053 + 1.67750i
\(389\) −86.2286 28.0174i −0.221667 0.0720241i 0.196078 0.980588i \(-0.437179\pi\)
−0.417745 + 0.908564i \(0.637179\pi\)
\(390\) −36.1076 7.75714i −0.0925836 0.0198901i
\(391\) 204.411 + 148.514i 0.522791 + 0.379830i
\(392\) 490.879 + 159.496i 1.25224 + 0.406878i
\(393\) 343.304 307.762i 0.873548 0.783108i
\(394\) 665.927 483.824i 1.69017 1.22798i
\(395\) 180.081i 0.455902i
\(396\) 853.343 + 206.553i 2.15491 + 0.521597i
\(397\) −335.768 −0.845763 −0.422882 0.906185i \(-0.638981\pi\)
−0.422882 + 0.906185i \(0.638981\pi\)
\(398\) −820.981 1129.98i −2.06277 2.83915i
\(399\) −187.525 209.182i −0.469986 0.524264i
\(400\) 173.395 533.656i 0.433489 1.33414i
\(401\) 11.1216 15.3075i 0.0277346 0.0381734i −0.794925 0.606708i \(-0.792490\pi\)
0.822659 + 0.568535i \(0.192490\pi\)
\(402\) 142.200 661.905i 0.353730 1.64653i
\(403\) 11.8876 36.5863i 0.0294978 0.0907849i
\(404\) −107.923 + 35.0662i −0.267135 + 0.0867975i
\(405\) −126.570 + 111.983i −0.312519 + 0.276502i
\(406\) −369.087 −0.909082
\(407\) −10.2067 + 79.0490i −0.0250778 + 0.194224i
\(408\) −595.221 + 263.458i −1.45888 + 0.645730i
\(409\) 96.4856 70.1009i 0.235906 0.171396i −0.463551 0.886070i \(-0.653425\pi\)
0.699457 + 0.714674i \(0.253425\pi\)
\(410\) 276.731 89.9154i 0.674954 0.219306i
\(411\) −240.653 + 24.7638i −0.585529 + 0.0602526i
\(412\) 506.283 + 367.836i 1.22884 + 0.892806i
\(413\) −589.625 + 811.549i −1.42766 + 1.96501i
\(414\) 325.827 + 570.070i 0.787023 + 1.37698i
\(415\) 7.61317 + 23.4309i 0.0183450 + 0.0564601i
\(416\) −26.7141 36.7688i −0.0642165 0.0883865i
\(417\) −581.416 + 257.347i −1.39428 + 0.617140i
\(418\) 178.551 376.753i 0.427155 0.901324i
\(419\) 412.874i 0.985381i 0.870205 + 0.492690i \(0.163986\pi\)
−0.870205 + 0.492690i \(0.836014\pi\)
\(420\) −425.535 246.920i −1.01318 0.587904i
\(421\) 186.937 + 575.334i 0.444032 + 1.36659i 0.883542 + 0.468351i \(0.155152\pi\)
−0.439511 + 0.898237i \(0.644848\pi\)
\(422\) −695.951 226.128i −1.64917 0.535849i
\(423\) 83.0435 + 399.232i 0.196320 + 0.943811i
\(424\) −569.638 413.866i −1.34349 0.976100i
\(425\) −243.953 79.2651i −0.574007 0.186506i
\(426\) −73.3631 81.8357i −0.172214 0.192103i
\(427\) −555.816 + 403.824i −1.30168 + 0.945724i
\(428\) 1633.76i 3.81721i
\(429\) 54.2604 + 1.40381i 0.126481 + 0.00327228i
\(430\) −118.587 −0.275783
\(431\) −260.636 358.735i −0.604724 0.832331i 0.391407 0.920218i \(-0.371989\pi\)
−0.996130 + 0.0878868i \(0.971989\pi\)
\(432\) −733.759 4.79422i −1.69852 0.0110977i
\(433\) 67.6685 208.262i 0.156278 0.480975i −0.842010 0.539462i \(-0.818628\pi\)
0.998288 + 0.0584870i \(0.0186276\pi\)
\(434\) 437.082 601.592i 1.00710 1.38616i
\(435\) 71.0399 + 15.2618i 0.163310 + 0.0350845i
\(436\) 160.429 493.749i 0.367956 1.13245i
\(437\) 204.365 66.4022i 0.467655 0.151950i
\(438\) 694.604 + 403.049i 1.58585 + 0.920204i
\(439\) 171.641 0.390982 0.195491 0.980705i \(-0.437370\pi\)
0.195491 + 0.980705i \(0.437370\pi\)
\(440\) 51.3274 397.523i 0.116653 0.903461i
\(441\) 178.834 196.884i 0.405519 0.446449i
\(442\) −59.3035 + 43.0865i −0.134171 + 0.0974808i
\(443\) 563.538 183.105i 1.27209 0.413328i 0.406305 0.913737i \(-0.366817\pi\)
0.865789 + 0.500409i \(0.166817\pi\)
\(444\) −19.7336 191.770i −0.0444451 0.431914i
\(445\) −125.883 91.4591i −0.282882 0.205526i
\(446\) 34.8328 47.9432i 0.0781005 0.107496i
\(447\) −675.422 + 69.5028i −1.51101 + 0.155487i
\(448\) 26.2518 + 80.7946i 0.0585977 + 0.180345i
\(449\) −256.349 352.835i −0.570934 0.785823i 0.421731 0.906721i \(-0.361423\pi\)
−0.992665 + 0.120898i \(0.961423\pi\)
\(450\) −493.430 448.194i −1.09651 0.995986i
\(451\) −375.312 + 204.991i −0.832178 + 0.454524i
\(452\) 1347.99i 2.98229i
\(453\) 410.636 707.678i 0.906480 1.56220i
\(454\) −125.107 385.039i −0.275566 0.848103i
\(455\) −28.9267 9.39886i −0.0635752 0.0206568i
\(456\) −116.275 + 541.232i −0.254989 + 1.18691i
\(457\) −192.984 140.211i −0.422285 0.306808i 0.356272 0.934382i \(-0.384048\pi\)
−0.778556 + 0.627575i \(0.784048\pi\)
\(458\) 1257.62 + 408.624i 2.74589 + 0.892192i
\(459\) −2.19161 + 335.427i −0.00477474 + 0.730778i
\(460\) 304.446 221.193i 0.661838 0.480854i
\(461\) 711.175i 1.54268i 0.636424 + 0.771339i \(0.280413\pi\)
−0.636424 + 0.771339i \(0.719587\pi\)
\(462\) 989.135 + 349.921i 2.14098 + 0.757406i
\(463\) −461.487 −0.996732 −0.498366 0.866967i \(-0.666066\pi\)
−0.498366 + 0.866967i \(0.666066\pi\)
\(464\) 185.439 + 255.234i 0.399652 + 0.550074i
\(465\) −109.003 + 97.7178i −0.234415 + 0.210146i
\(466\) −193.483 + 595.479i −0.415199 + 1.27785i
\(467\) 28.4397 39.1438i 0.0608986 0.0838198i −0.777481 0.628906i \(-0.783503\pi\)
0.838380 + 0.545086i \(0.183503\pi\)
\(468\) −128.532 + 26.7357i −0.274641 + 0.0571276i
\(469\) 172.295 530.269i 0.367366 1.13064i
\(470\) 322.514 104.791i 0.686199 0.222960i
\(471\) 9.12322 15.7227i 0.0193699 0.0333815i
\(472\) 1976.69 4.18790
\(473\) 171.290 32.1884i 0.362135 0.0680517i
\(474\) 375.960 + 849.393i 0.793164 + 1.79197i
\(475\) −176.486 + 128.225i −0.371550 + 0.269947i
\(476\) −928.719 + 301.759i −1.95109 + 0.633948i
\(477\) −315.020 + 180.052i −0.660419 + 0.377467i
\(478\) −1002.27 728.193i −2.09680 1.52342i
\(479\) −100.761 + 138.685i −0.210357 + 0.289531i −0.901138 0.433533i \(-0.857267\pi\)
0.690781 + 0.723064i \(0.257267\pi\)
\(480\) 17.7037 + 172.043i 0.0368827 + 0.358423i
\(481\) −3.68291 11.3348i −0.00765677 0.0235651i
\(482\) −551.274 758.763i −1.14372 1.57420i
\(483\) 218.872 + 494.489i 0.453150 + 1.02379i
\(484\) 61.5015 + 1071.33i 0.127069 + 2.21349i
\(485\) 161.002i 0.331964i
\(486\) −363.206 + 792.437i −0.747338 + 1.63053i
\(487\) −153.117 471.247i −0.314409 0.967653i −0.975997 0.217785i \(-0.930117\pi\)
0.661587 0.749868i \(-0.269883\pi\)
\(488\) 1287.54 + 418.348i 2.63841 + 0.857270i
\(489\) 474.944 + 102.034i 0.971256 + 0.208659i
\(490\) −178.947 130.012i −0.365197 0.265331i
\(491\) 314.085 + 102.052i 0.639684 + 0.207846i 0.610860 0.791738i \(-0.290824\pi\)
0.0288242 + 0.999584i \(0.490824\pi\)
\(492\) 770.172 690.434i 1.56539 1.40332i
\(493\) 116.677 84.7705i 0.236666 0.171948i
\(494\) 62.3413i 0.126197i
\(495\) −175.914 108.252i −0.355382 0.218690i
\(496\) −635.619 −1.28149
\(497\) −53.2028 73.2274i −0.107048 0.147339i
\(498\) 84.8264 + 94.6229i 0.170334 + 0.190006i
\(499\) 33.9303 104.427i 0.0679966 0.209272i −0.911285 0.411777i \(-0.864908\pi\)
0.979281 + 0.202505i \(0.0649083\pi\)
\(500\) −496.454 + 683.310i −0.992908 + 1.36662i
\(501\) 100.321 466.972i 0.200242 0.932080i
\(502\) 219.872 676.695i 0.437991 1.34800i
\(503\) 543.721 176.666i 1.08096 0.351224i 0.286210 0.958167i \(-0.407604\pi\)
0.794745 + 0.606943i \(0.207604\pi\)
\(504\) −1384.84 151.654i −2.74770 0.300901i
\(505\) 26.6963 0.0528639
\(506\) −550.972 + 583.509i −1.08888 + 1.15318i
\(507\) 456.194 201.921i 0.899791 0.398267i
\(508\) −102.415 + 74.4089i −0.201604 + 0.146474i
\(509\) −514.449 + 167.155i −1.01071 + 0.328398i −0.767136 0.641485i \(-0.778319\pi\)
−0.243570 + 0.969883i \(0.578319\pi\)
\(510\) 277.484 28.5539i 0.544087 0.0559881i
\(511\) 535.067 + 388.749i 1.04710 + 0.760760i
\(512\) 674.549 928.437i 1.31748 1.81335i
\(513\) 229.690 + 169.184i 0.447739 + 0.329793i
\(514\) 2.06762 + 6.36348i 0.00402260 + 0.0123803i
\(515\) −86.5364 119.107i −0.168032 0.231276i
\(516\) −385.477 + 170.620i −0.747049 + 0.330660i
\(517\) −437.404 + 238.904i −0.846042 + 0.462097i
\(518\) 230.378i 0.444745i
\(519\) 99.6917 + 57.8469i 0.192084 + 0.111458i
\(520\) 18.5207 + 57.0007i 0.0356167 + 0.109617i
\(521\) −321.351 104.413i −0.616796 0.200409i −0.0160786 0.999871i \(-0.505118\pi\)
−0.600717 + 0.799462i \(0.705118\pi\)
\(522\) 366.937 76.3259i 0.702945 0.146218i
\(523\) −248.719 180.705i −0.475562 0.345516i 0.324043 0.946042i \(-0.394958\pi\)
−0.799605 + 0.600526i \(0.794958\pi\)
\(524\) −1296.26 421.182i −2.47379 0.803782i
\(525\) −366.452 408.773i −0.698004 0.778616i
\(526\) −78.6199 + 57.1207i −0.149467 + 0.108594i
\(527\) 290.564i 0.551355i
\(528\) −254.985 859.824i −0.482927 1.62845i
\(529\) 115.375 0.218100
\(530\) 177.361 + 244.116i 0.334643 + 0.460596i
\(531\) 418.365 928.754i 0.787881 1.74907i
\(532\) −256.634 + 789.837i −0.482394 + 1.48466i
\(533\) 37.5858 51.7324i 0.0705175 0.0970590i
\(534\) −784.693 168.579i −1.46946 0.315691i
\(535\) −118.772 + 365.544i −0.222005 + 0.683260i
\(536\) −1044.91 + 339.511i −1.94945 + 0.633415i
\(537\) 353.292 + 205.000i 0.657899 + 0.381751i
\(538\) −512.434 −0.952480
\(539\) 293.765 + 139.221i 0.545019 + 0.258296i
\(540\) 474.118 + 157.482i 0.877996 + 0.291634i
\(541\) 66.9072 48.6109i 0.123673 0.0898538i −0.524229 0.851577i \(-0.675646\pi\)
0.647902 + 0.761723i \(0.275646\pi\)
\(542\) −359.345 + 116.758i −0.662998 + 0.215421i
\(543\) −40.0257 388.966i −0.0737121 0.716327i
\(544\) 277.721 + 201.776i 0.510516 + 0.370912i
\(545\) −71.7898 + 98.8103i −0.131724 + 0.181303i
\(546\) −156.061 + 16.0591i −0.285826 + 0.0294123i
\(547\) −122.586 377.280i −0.224105 0.689725i −0.998381 0.0568769i \(-0.981886\pi\)
0.774276 0.632848i \(-0.218114\pi\)
\(548\) 420.366 + 578.584i 0.767091 + 1.05581i
\(549\) 469.069 516.413i 0.854407 0.940642i
\(550\) 348.917 736.235i 0.634394 1.33861i
\(551\) 122.653i 0.222601i
\(552\) 534.801 921.661i 0.968843 1.66968i
\(553\) 236.394 + 727.547i 0.427476 + 1.31564i
\(554\) −835.593 271.500i −1.50829 0.490073i
\(555\) −9.52613 + 44.3418i −0.0171642 + 0.0798952i
\(556\) 1520.64 + 1104.81i 2.73496 + 1.98706i
\(557\) 364.339 + 118.381i 0.654109 + 0.212533i 0.617225 0.786787i \(-0.288257\pi\)
0.0368842 + 0.999320i \(0.488257\pi\)
\(558\) −310.129 + 688.475i −0.555787 + 1.23383i
\(559\) −21.0837 + 15.3182i −0.0377168 + 0.0274029i
\(560\) 502.548i 0.897407i
\(561\) −393.056 + 116.563i −0.700634 + 0.207777i
\(562\) 233.573 0.415610
\(563\) 85.1328 + 117.175i 0.151213 + 0.208127i 0.877903 0.478839i \(-0.158942\pi\)
−0.726690 + 0.686966i \(0.758942\pi\)
\(564\) 897.589 804.660i 1.59147 1.42670i
\(565\) 97.9974 301.605i 0.173447 0.533814i
\(566\) 332.256 457.311i 0.587025 0.807971i
\(567\) −364.355 + 618.573i −0.642601 + 1.09096i
\(568\) −55.1163 + 169.630i −0.0970357 + 0.298645i
\(569\) 877.968 285.269i 1.54300 0.501352i 0.590800 0.806818i \(-0.298812\pi\)
0.952203 + 0.305466i \(0.0988124\pi\)
\(570\) 119.065 205.193i 0.208886 0.359987i
\(571\) 421.725 0.738573 0.369287 0.929316i \(-0.379602\pi\)
0.369287 + 0.929316i \(0.379602\pi\)
\(572\) −76.9147 140.821i −0.134466 0.246191i
\(573\) −383.189 865.726i −0.668742 1.51087i
\(574\) 999.989 726.534i 1.74214 1.26574i
\(575\) 399.361 129.760i 0.694541 0.225670i
\(576\) −42.8069 74.8952i −0.0743175 0.130026i
\(577\) −372.478 270.621i −0.645542 0.469014i 0.216208 0.976347i \(-0.430631\pi\)
−0.861750 + 0.507334i \(0.830631\pi\)
\(578\) −283.930 + 390.796i −0.491229 + 0.676118i
\(579\) 44.9605 + 436.923i 0.0776521 + 0.754616i
\(580\) −66.3763 204.285i −0.114442 0.352216i
\(581\) 61.5160 + 84.6694i 0.105879 + 0.145731i
\(582\) −336.128 759.403i −0.577539 1.30482i
\(583\) −322.446 304.466i −0.553081 0.522241i
\(584\) 1303.26i 2.23161i
\(585\) 30.7019 + 3.36217i 0.0524818 + 0.00574729i
\(586\) 203.979 + 627.784i 0.348088 + 1.07130i
\(587\) −40.3860 13.1222i −0.0688007 0.0223547i 0.274414 0.961612i \(-0.411516\pi\)
−0.343215 + 0.939257i \(0.611516\pi\)
\(588\) −768.742 165.152i −1.30738 0.280870i
\(589\) 199.918 + 145.249i 0.339420 + 0.246603i
\(590\) −805.643 261.769i −1.36550 0.443677i
\(591\) −512.565 + 459.498i −0.867284 + 0.777492i
\(592\) −159.313 + 115.748i −0.269109 + 0.195519i
\(593\) 106.267i 0.179203i −0.995978 0.0896015i \(-0.971441\pi\)
0.995978 0.0896015i \(-0.0285593\pi\)
\(594\) −1055.74 143.333i −1.77733 0.241302i
\(595\) 229.732 0.386105
\(596\) 1179.81 + 1623.87i 1.97955 + 2.72461i
\(597\) 779.702 + 869.749i 1.30603 + 1.45687i
\(598\) 37.0822 114.127i 0.0620103 0.190848i
\(599\) −427.915 + 588.974i −0.714382 + 0.983263i 0.285309 + 0.958435i \(0.407904\pi\)
−0.999692 + 0.0248274i \(0.992096\pi\)
\(600\) −227.220 + 1057.65i −0.378699 + 1.76275i
\(601\) −36.6474 + 112.789i −0.0609774 + 0.187669i −0.976905 0.213675i \(-0.931457\pi\)
0.915927 + 0.401344i \(0.131457\pi\)
\(602\) −479.102 + 155.670i −0.795851 + 0.258588i
\(603\) −61.6334 + 562.809i −0.102211 + 0.933349i
\(604\) −2418.71 −4.00448
\(605\) 64.1237 244.174i 0.105990 0.403594i
\(606\) 125.919 55.7343i 0.207787 0.0919708i
\(607\) −576.993 + 419.210i −0.950565 + 0.690626i −0.950941 0.309374i \(-0.899881\pi\)
0.000375194 1.00000i \(0.499881\pi\)
\(608\) 277.658 90.2165i 0.456674 0.148382i
\(609\) 307.042 31.5955i 0.504175 0.0518810i
\(610\) −469.365 341.013i −0.769450 0.559038i
\(611\) 43.8040 60.2910i 0.0716923 0.0986760i
\(612\) 860.906 492.057i 1.40671 0.804015i
\(613\) 212.439 + 653.818i 0.346555 + 1.06659i 0.960746 + 0.277430i \(0.0894827\pi\)
−0.614190 + 0.789158i \(0.710517\pi\)
\(614\) 815.316 + 1122.19i 1.32788 + 1.82767i
\(615\) −222.515 + 98.4898i −0.361812 + 0.160146i
\(616\) −314.463 1673.41i −0.510493 2.71657i
\(617\) 762.156i 1.23526i −0.786468 0.617631i \(-0.788093\pi\)
0.786468 0.617631i \(-0.211907\pi\)
\(618\) −656.830 381.131i −1.06283 0.616716i
\(619\) −163.995 504.724i −0.264935 0.815386i −0.991708 0.128509i \(-0.958981\pi\)
0.726773 0.686877i \(-0.241019\pi\)
\(620\) 411.578 + 133.730i 0.663836 + 0.215693i
\(621\) −319.855 446.347i −0.515065 0.718755i
\(622\) 267.702 + 194.497i 0.430388 + 0.312695i
\(623\) −628.637 204.257i −1.00905 0.327860i
\(624\) 89.5144 + 99.8523i 0.143453 + 0.160020i
\(625\) −256.839 + 186.605i −0.410943 + 0.298568i
\(626\) 266.885i 0.426334i
\(627\) −116.284 + 328.704i −0.185461 + 0.524250i
\(628\) −53.7372 −0.0855688
\(629\) 52.9123 + 72.8275i 0.0841212 + 0.115783i
\(630\) 544.338 + 245.201i 0.864028 + 0.389208i
\(631\) 209.034 643.341i 0.331274 1.01956i −0.637254 0.770654i \(-0.719930\pi\)
0.968528 0.248904i \(-0.0800703\pi\)
\(632\) 886.043 1219.53i 1.40197 1.92964i
\(633\) 598.317 + 128.539i 0.945208 + 0.203063i
\(634\) −580.624 + 1786.98i −0.915811 + 2.81858i
\(635\) 28.3241 9.20306i 0.0446049 0.0144930i
\(636\) 927.757 + 538.338i 1.45874 + 0.846444i
\(637\) −48.6093 −0.0763097
\(638\) 219.579 + 402.021i 0.344167 + 0.630127i
\(639\) 68.0360 + 61.7987i 0.106473 + 0.0967115i
\(640\) −244.599 + 177.712i −0.382186 + 0.277674i
\(641\) −747.420 + 242.852i −1.16602 + 0.378864i −0.827157 0.561971i \(-0.810043\pi\)
−0.338865 + 0.940835i \(0.610043\pi\)
\(642\) 202.938 + 1972.13i 0.316102 + 3.07185i
\(643\) 687.427 + 499.445i 1.06909 + 0.776741i 0.975749 0.218893i \(-0.0702444\pi\)
0.0933438 + 0.995634i \(0.470244\pi\)
\(644\) 939.629 1293.29i 1.45905 2.00821i
\(645\) 98.6519 10.1516i 0.152949 0.0157388i
\(646\) −145.508 447.828i −0.225245 0.693233i
\(647\) −687.343 946.046i −1.06235 1.46220i −0.877584 0.479422i \(-0.840846\pi\)
−0.184769 0.982782i \(-0.559154\pi\)
\(648\) 1408.13 135.609i 2.17305 0.209274i
\(649\) 1234.75 + 159.428i 1.90254 + 0.245652i
\(650\) 121.825i 0.187423i
\(651\) −312.108 + 537.879i −0.479429 + 0.826234i
\(652\) −443.765 1365.77i −0.680622 2.09474i
\(653\) −509.322 165.489i −0.779972 0.253428i −0.108144 0.994135i \(-0.534491\pi\)
−0.671828 + 0.740707i \(0.734491\pi\)
\(654\) −132.324 + 615.937i −0.202330 + 0.941800i
\(655\) 259.411 + 188.473i 0.396048 + 0.287746i
\(656\) −1004.84 326.492i −1.53177 0.497701i
\(657\) −612.341 275.834i −0.932027 0.419839i
\(658\) 1165.43 846.732i 1.77117 1.28683i
\(659\) 138.756i 0.210555i 0.994443 + 0.105278i \(0.0335731\pi\)
−0.994443 + 0.105278i \(0.966427\pi\)
\(660\) −15.7921 + 610.404i −0.0239275 + 0.924854i
\(661\) 27.1690 0.0411029 0.0205515 0.999789i \(-0.493458\pi\)
0.0205515 + 0.999789i \(0.493458\pi\)
\(662\) 530.734 + 730.493i 0.801713 + 1.10346i
\(663\) 45.6460 40.9202i 0.0688477 0.0617197i
\(664\) 63.7284 196.136i 0.0959765 0.295385i
\(665\) 114.840 158.064i 0.172692 0.237690i
\(666\) 47.6413 + 229.036i 0.0715335 + 0.343897i
\(667\) −72.9572 + 224.539i −0.109381 + 0.336640i
\(668\) −1342.84 + 436.317i −2.01025 + 0.653169i
\(669\) −24.8731 + 42.8657i −0.0371796 + 0.0640742i
\(670\) 470.835 0.702738
\(671\) 770.526 + 365.168i 1.14832 + 0.544214i
\(672\) 297.367 + 671.831i 0.442511 + 0.999749i
\(673\) 531.916 386.460i 0.790366 0.574234i −0.117706 0.993048i \(-0.537554\pi\)
0.908072 + 0.418814i \(0.137554\pi\)
\(674\) −169.392 + 55.0388i −0.251323 + 0.0816599i
\(675\) 448.851 + 330.611i 0.664964 + 0.489794i
\(676\) −1193.13 866.860i −1.76499 1.28234i
\(677\) 359.292 494.523i 0.530712 0.730463i −0.456526 0.889710i \(-0.650907\pi\)
0.987239 + 0.159247i \(0.0509066\pi\)
\(678\) −167.441 1627.18i −0.246963 2.39996i
\(679\) −211.349 650.466i −0.311265 0.957976i
\(680\) −266.086 366.236i −0.391303 0.538583i
\(681\) 137.037 + 309.603i 0.201229 + 0.454630i
\(682\) −915.303 118.182i −1.34209 0.173288i
\(683\) 990.520i 1.45025i 0.688618 + 0.725124i \(0.258218\pi\)
−0.688618 + 0.725124i \(0.741782\pi\)
\(684\) 91.8031 838.307i 0.134215 1.22559i
\(685\) −51.9918 160.014i −0.0759005 0.233598i
\(686\) 588.032 + 191.063i 0.857189 + 0.278518i
\(687\) −1081.19 232.275i −1.57378 0.338101i
\(688\) 348.363 + 253.100i 0.506341 + 0.367879i
\(689\) 63.0665 + 20.4915i 0.0915333 + 0.0297410i
\(690\) −340.024 + 304.820i −0.492788 + 0.441768i
\(691\) −463.629 + 336.846i −0.670954 + 0.487477i −0.870344 0.492443i \(-0.836104\pi\)
0.199390 + 0.979920i \(0.436104\pi\)
\(692\) 340.727i 0.492380i
\(693\) −852.813 206.424i −1.23061 0.297870i
\(694\) 1649.35 2.37659
\(695\) −259.915 357.742i −0.373978 0.514737i
\(696\) −405.999 452.887i −0.583332 0.650700i
\(697\) −149.251 + 459.347i −0.214133 + 0.659035i
\(698\) 830.239 1142.73i 1.18945 1.63714i
\(699\) 109.982 511.940i 0.157342 0.732389i
\(700\) −501.502 + 1543.46i −0.716431 + 2.20495i
\(701\) −778.940 + 253.093i −1.11118 + 0.361046i −0.806397 0.591375i \(-0.798585\pi\)
−0.304787 + 0.952420i \(0.598585\pi\)
\(702\) 151.831 48.2385i 0.216284 0.0687158i
\(703\) 76.5580 0.108902
\(704\) 72.3862 76.6608i 0.102821 0.108893i
\(705\) −259.327 + 114.784i −0.367840 + 0.162814i
\(706\) −49.1722 + 35.7257i −0.0696490 + 0.0506030i
\(707\) 107.856 35.0444i 0.152554 0.0495677i
\(708\) −2995.45 + 308.240i −4.23086 + 0.435367i
\(709\) −145.495 105.708i −0.205212 0.149095i 0.480433 0.877032i \(-0.340480\pi\)
−0.685645 + 0.727936i \(0.740480\pi\)
\(710\) 44.9276 61.8376i 0.0632783 0.0870952i
\(711\) −385.471 674.423i −0.542154 0.948556i
\(712\) 402.492 + 1238.74i 0.565298 + 1.73981i
\(713\) −279.589 384.821i −0.392130 0.539721i
\(714\) 1083.58 479.617i 1.51762 0.671732i
\(715\) 6.97165 + 37.0995i 0.00975056 + 0.0518873i
\(716\) 1207.48i 1.68643i
\(717\) 896.123 + 519.983i 1.24982 + 0.725220i
\(718\) 84.1241 + 258.907i 0.117165 + 0.360595i
\(719\) 633.724 + 205.910i 0.881397 + 0.286383i 0.714537 0.699597i \(-0.246637\pi\)
0.166860 + 0.985981i \(0.446637\pi\)
\(720\) −103.925 499.620i −0.144340 0.693917i
\(721\) −505.968 367.607i −0.701759 0.509858i
\(722\) 850.765 + 276.430i 1.17834 + 0.382867i
\(723\) 523.556 + 584.021i 0.724144 + 0.807774i
\(724\) −935.163 + 679.436i −1.29166 + 0.938447i
\(725\) 239.684i 0.330598i
\(726\) −207.314 1285.57i −0.285557 1.77076i
\(727\) 162.429 0.223424 0.111712 0.993741i \(-0.464367\pi\)
0.111712 + 0.993741i \(0.464367\pi\)
\(728\) 149.651 + 205.976i 0.205564 + 0.282935i
\(729\) 234.314 690.317i 0.321418 0.946937i
\(730\) −172.588 + 531.172i −0.236422 + 0.727633i
\(731\) 115.701 159.249i 0.158278 0.217851i
\(732\) −2016.36 433.182i −2.75459 0.591778i
\(733\) 361.513 1112.62i 0.493196 1.51790i −0.326552 0.945179i \(-0.605887\pi\)
0.819749 0.572723i \(-0.194113\pi\)
\(734\) 2112.89 686.520i 2.87860 0.935313i
\(735\) 159.995 + 92.8382i 0.217680 + 0.126310i
\(736\) −561.967 −0.763542
\(737\) −680.087 + 127.800i −0.922777 + 0.173406i
\(738\) −843.919 + 929.096i −1.14352 + 1.25894i
\(739\) 196.087 142.465i 0.265341 0.192781i −0.447157 0.894455i \(-0.647564\pi\)
0.712498 + 0.701674i \(0.247564\pi\)
\(740\) 127.511 41.4309i 0.172313 0.0559877i
\(741\) −5.33669 51.8615i −0.00720202 0.0699886i
\(742\) 1037.01 + 753.430i 1.39759 + 1.01540i
\(743\) −484.132 + 666.351i −0.651591 + 0.896838i −0.999167 0.0408136i \(-0.987005\pi\)
0.347576 + 0.937652i \(0.387005\pi\)
\(744\) 1218.98 125.436i 1.63841 0.168597i
\(745\) −145.922 449.101i −0.195868 0.602820i
\(746\) −771.041 1061.25i −1.03357 1.42258i
\(747\) −78.6669 71.4549i −0.105310 0.0956559i
\(748\) 881.202 + 832.066i 1.17808 + 1.11239i
\(749\) 1632.75i 2.17990i
\(750\) 514.397 886.497i 0.685862 1.18200i
\(751\) −1.89680 5.83775i −0.00252570 0.00777330i 0.949786 0.312901i \(-0.101301\pi\)
−0.952311 + 0.305128i \(0.901301\pi\)
\(752\) −1171.08 380.507i −1.55729 0.505993i
\(753\) −124.982 + 581.762i −0.165979 + 0.772592i
\(754\) −55.4139 40.2606i −0.0734933 0.0533960i
\(755\) 541.170 + 175.837i 0.716782 + 0.232896i
\(756\) 2122.21 + 13.8660i 2.80716 + 0.0183413i
\(757\) 891.755 647.898i 1.17801 0.855876i 0.186066 0.982537i \(-0.440426\pi\)
0.991946 + 0.126661i \(0.0404261\pi\)
\(758\) 1470.37i 1.93980i
\(759\) 408.401 532.585i 0.538078 0.701693i
\(760\) −384.996 −0.506574
\(761\) −705.506 971.046i −0.927078 1.27601i −0.960989 0.276588i \(-0.910796\pi\)
0.0339108 0.999425i \(-0.489204\pi\)
\(762\) 114.383 102.541i 0.150109 0.134568i
\(763\) −160.329 + 493.442i −0.210130 + 0.646713i
\(764\) −1645.05 + 2264.22i −2.15321 + 2.96364i
\(765\) −228.394 + 47.5078i −0.298554 + 0.0621017i
\(766\) −58.7094 + 180.689i −0.0766442 + 0.235887i
\(767\) −177.050 + 57.5270i −0.230834 + 0.0750027i
\(768\) −724.965 + 1249.38i −0.943965 + 1.62680i
\(769\) −1038.16 −1.35001 −0.675007 0.737811i \(-0.735859\pi\)
−0.675007 + 0.737811i \(0.735859\pi\)
\(770\) −93.4400 + 723.678i −0.121351 + 0.939841i
\(771\) −2.26479 5.11676i −0.00293747 0.00663652i
\(772\) 1050.46 763.205i 1.36070 0.988608i
\(773\) −557.520 + 181.149i −0.721242 + 0.234346i −0.646562 0.762862i \(-0.723794\pi\)
−0.0746805 + 0.997208i \(0.523794\pi\)
\(774\) 444.119 253.839i 0.573797 0.327958i
\(775\) 390.671 + 283.839i 0.504092 + 0.366244i
\(776\) −792.170 + 1090.33i −1.02084 + 1.40506i
\(777\) 19.7214 + 191.650i 0.0253814 + 0.246654i
\(778\) −100.506 309.326i −0.129185 0.397591i
\(779\) 241.438 + 332.311i 0.309934 + 0.426587i
\(780\) −36.9545 83.4899i −0.0473775 0.107038i
\(781\) −48.1099 + 101.515i −0.0616004 + 0.129981i
\(782\) 906.383i 1.15906i
\(783\) −298.720 + 94.9067i −0.381507 + 0.121209i
\(784\) 248.191 + 763.854i 0.316570 + 0.974303i
\(785\) 12.0233 + 3.90662i 0.0153164 + 0.00497659i
\(786\) 1617.05 + 347.397i 2.05731 + 0.441981i
\(787\) −302.139 219.517i −0.383912 0.278928i 0.379044 0.925379i \(-0.376253\pi\)
−0.762956 + 0.646450i \(0.776253\pi\)
\(788\) 1935.36 + 628.838i 2.45605 + 0.798018i
\(789\) 60.5138 54.2487i 0.0766969 0.0687563i
\(790\) −522.626 + 379.710i −0.661552 + 0.480646i
\(791\) 1347.16i 1.70311i
\(792\) 658.687 + 1598.63i 0.831675 + 2.01847i
\(793\) −127.499 −0.160780
\(794\) −707.983 974.454i −0.891666 1.22727i
\(795\) −168.443 187.896i −0.211878 0.236348i
\(796\) 1067.05 3284.04i 1.34051 4.12567i
\(797\) 491.864 676.992i 0.617144 0.849426i −0.379997 0.924988i \(-0.624075\pi\)
0.997141 + 0.0755619i \(0.0240751\pi\)
\(798\) 211.675 985.297i 0.265257 1.23471i
\(799\) −173.943 + 535.341i −0.217701 + 0.670014i
\(800\) 542.587 176.297i 0.678234 0.220372i
\(801\) 667.215 + 73.0668i 0.832977 + 0.0912195i
\(802\) 67.8754 0.0846326
\(803\) 105.113 814.086i 0.130901 1.01381i
\(804\) 1530.49 677.429i 1.90360 0.842573i
\(805\) −304.256 + 221.055i −0.377958 + 0.274603i
\(806\) 131.245 42.6441i 0.162835 0.0529083i
\(807\) 426.292 43.8667i 0.528243 0.0543577i
\(808\) −180.790 131.352i −0.223750 0.162564i
\(809\) 304.962 419.745i 0.376962 0.518844i −0.577814 0.816168i \(-0.696094\pi\)
0.954777 + 0.297324i \(0.0960942\pi\)
\(810\) −591.874 131.206i −0.730708 0.161983i
\(811\) 241.858 + 744.364i 0.298222 + 0.917834i 0.982120 + 0.188256i \(0.0602836\pi\)
−0.683897 + 0.729578i \(0.739716\pi\)
\(812\) −536.334 738.200i −0.660510 0.909113i
\(813\) 288.943 127.892i 0.355403 0.157309i
\(814\) −250.934 + 137.057i −0.308273 + 0.168375i
\(815\) 337.843i 0.414531i
\(816\) −876.087 508.356i −1.07364 0.622986i
\(817\) −51.7314 159.213i −0.0633187 0.194875i
\(818\) 406.889 + 132.206i 0.497419 + 0.161621i
\(819\) 128.452 26.7191i 0.156840 0.0326240i
\(820\) 581.965 + 422.822i 0.709714 + 0.515637i
\(821\) 524.622 + 170.460i 0.639004 + 0.207625i 0.610560 0.791970i \(-0.290945\pi\)
0.0284445 + 0.999595i \(0.490945\pi\)
\(822\) −579.296 646.198i −0.704740 0.786129i
\(823\) 37.3544 27.1396i 0.0453881 0.0329764i −0.564860 0.825187i \(-0.691070\pi\)
0.610248 + 0.792210i \(0.291070\pi\)
\(824\) 1232.39i 1.49562i
\(825\) −227.237 + 642.340i −0.275439 + 0.778594i
\(826\) −3598.50 −4.35654
\(827\) 350.444 + 482.345i 0.423753 + 0.583247i 0.966505 0.256646i \(-0.0826176\pi\)
−0.542752 + 0.839893i \(0.682618\pi\)
\(828\) −666.708 + 1480.07i −0.805203 + 1.78752i
\(829\) −428.629 + 1319.18i −0.517043 + 1.59129i 0.262491 + 0.964935i \(0.415456\pi\)
−0.779534 + 0.626360i \(0.784544\pi\)
\(830\) −51.9477 + 71.4999i −0.0625876 + 0.0861445i
\(831\) 718.368 + 154.330i 0.864462 + 0.185716i
\(832\) −4.87182 + 14.9939i −0.00585555 + 0.0180215i
\(833\) 349.184 113.457i 0.419189 0.136203i
\(834\) −1972.81 1144.74i −2.36548 1.37259i
\(835\) 332.172 0.397811
\(836\) 1012.99 190.359i 1.21171 0.227702i
\(837\) 199.059 599.288i 0.237824 0.715995i
\(838\) −1198.23 + 870.565i −1.42987 + 1.03886i
\(839\) −1583.51 + 514.515i −1.88738 + 0.613247i −0.905305 + 0.424761i \(0.860358\pi\)
−0.982076 + 0.188486i \(0.939642\pi\)
\(840\) −99.1751 963.775i −0.118066 1.14735i
\(841\) −571.359 415.117i −0.679381 0.493599i
\(842\) −1275.55 + 1755.64i −1.51490 + 2.08509i
\(843\) −194.308 + 19.9949i −0.230496 + 0.0237187i
\(844\) −559.039 1720.55i −0.662369 2.03856i
\(845\) 203.936 + 280.693i 0.241344 + 0.332181i
\(846\) −983.537 + 1082.81i −1.16257 + 1.27991i
\(847\) −61.4633 1070.66i −0.0725658 1.26407i
\(848\) 1095.66i 1.29206i
\(849\) −237.255 + 408.878i −0.279452 + 0.481600i
\(850\) −284.346 875.127i −0.334525 1.02956i
\(851\) −140.153 45.5386i −0.164693 0.0535119i
\(852\) 57.0706 265.650i 0.0669843 0.311796i
\(853\) 657.366 + 477.604i 0.770652 + 0.559911i 0.902159 0.431404i \(-0.141982\pi\)
−0.131507 + 0.991315i \(0.541982\pi\)
\(854\) −2343.93 761.589i −2.74465 0.891791i
\(855\) −81.4841 + 180.892i −0.0953031 + 0.211569i
\(856\) 2602.90 1891.12i 3.04078 2.20925i
\(857\) 551.421i 0.643431i −0.946836 0.321716i \(-0.895740\pi\)
0.946836 0.321716i \(-0.104260\pi\)
\(858\) 110.337 + 160.433i 0.128597 + 0.186985i
\(859\) −1196.04 −1.39236 −0.696180 0.717868i \(-0.745118\pi\)
−0.696180 + 0.717868i \(0.745118\pi\)
\(860\) −172.323 237.182i −0.200375 0.275793i
\(861\) −769.693 + 690.005i −0.893952 + 0.801400i
\(862\) 491.544 1512.82i 0.570237 1.75501i
\(863\) 421.079 579.565i 0.487924 0.671570i −0.492079 0.870550i \(-0.663763\pi\)
0.980003 + 0.198980i \(0.0637630\pi\)
\(864\) −434.567 606.423i −0.502971 0.701879i
\(865\) −24.7704 + 76.2355i −0.0286363 + 0.0881335i
\(866\) 747.094 242.745i 0.862695 0.280307i
\(867\) 202.747 349.408i 0.233848 0.403008i
\(868\) 1838.37 2.11793
\(869\) 651.830 690.323i 0.750092 0.794387i
\(870\) 105.499 + 238.350i 0.121263 + 0.273965i
\(871\) 83.7104 60.8192i 0.0961084 0.0698269i
\(872\) 972.339 315.932i 1.11507 0.362308i
\(873\) 344.632 + 602.970i 0.394767 + 0.690688i
\(874\) 623.624 + 453.089i 0.713528 + 0.518409i
\(875\) 496.145 682.885i 0.567023 0.780440i
\(876\) 203.227 + 1974.94i 0.231994 + 2.25450i
\(877\) 306.432 + 943.101i 0.349410 + 1.07537i 0.959181 + 0.282794i \(0.0912614\pi\)
−0.609771 + 0.792578i \(0.708739\pi\)
\(878\) 361.913 + 498.131i 0.412202 + 0.567348i
\(879\) −223.431 504.790i −0.254188 0.574278i
\(880\) 547.391 298.977i 0.622035 0.339747i
\(881\) 1256.55i 1.42628i 0.701021 + 0.713140i \(0.252728\pi\)
−0.701021 + 0.713140i \(0.747272\pi\)
\(882\) 948.469 + 103.867i 1.07536 + 0.117763i
\(883\) 86.0075 + 264.704i 0.0974037 + 0.299778i 0.987873 0.155266i \(-0.0496235\pi\)
−0.890469 + 0.455044i \(0.849624\pi\)
\(884\) −172.352 56.0006i −0.194968 0.0633491i
\(885\) 692.620 + 148.798i 0.782622 + 0.168134i
\(886\) 1719.65 + 1249.40i 1.94091 + 1.41015i
\(887\) −1116.54 362.787i −1.25879 0.409005i −0.397725 0.917505i \(-0.630200\pi\)
−0.861062 + 0.508500i \(0.830200\pi\)
\(888\) 282.684 253.418i 0.318338 0.285380i
\(889\) 102.351 74.3626i 0.115131 0.0836475i
\(890\) 558.178i 0.627166i
\(891\) 890.532 + 28.8630i 0.999475 + 0.0323939i
\(892\) 146.507 0.164245
\(893\) 281.382 + 387.289i 0.315097 + 0.433694i
\(894\) −1625.87 1813.64i −1.81864 2.02868i
\(895\) −87.7825 + 270.167i −0.0980810 + 0.301862i
\(896\) −754.921 + 1039.06i −0.842546 + 1.15966i
\(897\) −21.0787 + 98.1164i −0.0234991 + 0.109383i
\(898\) 483.460 1487.94i 0.538374 1.65695i
\(899\) −258.218 + 83.9001i −0.287228 + 0.0933260i
\(900\) 179.398 1638.18i 0.199331 1.82020i
\(901\) −500.866 −0.555900
\(902\) −1386.28 656.986i −1.53690 0.728366i
\(903\) 385.237 170.514i 0.426619 0.188831i
\(904\) −2147.62 + 1560.34i −2.37568 + 1.72604i
\(905\) 258.631 84.0342i 0.285780 0.0928555i
\(906\) 2919.64 300.439i 3.22256 0.331611i
\(907\) −117.806 85.5912i −0.129885 0.0943673i 0.520946 0.853590i \(-0.325579\pi\)
−0.650831 + 0.759223i \(0.725579\pi\)
\(908\) 588.308 809.736i 0.647916 0.891780i
\(909\) −99.9802 + 57.1444i −0.109989 + 0.0628651i
\(910\) −33.7163 103.768i −0.0370509 0.114031i
\(911\) 632.867 + 871.067i 0.694695 + 0.956166i 0.999992 + 0.00390866i \(0.00124417\pi\)
−0.305297 + 0.952257i \(0.598756\pi\)
\(912\) −787.712 + 348.658i −0.863719 + 0.382301i
\(913\) 55.6273 117.377i 0.0609280 0.128562i
\(914\) 855.714i 0.936230i
\(915\) 419.655 + 243.508i 0.458639 + 0.266129i
\(916\) 1010.21 + 3109.11i 1.10285 + 3.39422i
\(917\) 1295.46 + 420.920i 1.41271 + 0.459018i
\(918\) −978.087 + 700.904i −1.06545 + 0.763512i
\(919\) −255.740 185.806i −0.278280 0.202183i 0.439887 0.898053i \(-0.355019\pi\)
−0.718167 + 0.695871i \(0.755019\pi\)
\(920\) 704.806 + 229.005i 0.766093 + 0.248919i
\(921\) −774.323 863.749i −0.840742 0.937838i
\(922\) −2063.95 + 1499.55i −2.23855 + 1.62640i
\(923\) 16.7976i 0.0181990i
\(924\) 737.480 + 2486.82i 0.798138 + 2.69137i
\(925\) 149.606 0.161737
\(926\) −973.067 1339.31i −1.05083 1.44634i
\(927\) 579.041 + 260.834i 0.624639 + 0.281374i
\(928\) −99.1224 + 305.067i −0.106813 + 0.328736i
\(929\) −657.526 + 905.007i −0.707778 + 0.974173i 0.292064 + 0.956399i \(0.405658\pi\)
−0.999842 + 0.0177741i \(0.994342\pi\)
\(930\) −513.431 110.302i −0.552077 0.118605i
\(931\) 96.4904 296.967i 0.103642 0.318976i
\(932\) −1472.16 + 478.333i −1.57957 + 0.513233i
\(933\) −239.350 138.885i −0.256538 0.148858i
\(934\) 173.568 0.185833
\(935\) −136.673 250.231i −0.146174 0.267627i
\(936\) −191.374 173.829i −0.204459 0.185715i
\(937\) −850.451 + 617.889i −0.907632 + 0.659433i −0.940415 0.340029i \(-0.889563\pi\)
0.0327830 + 0.999462i \(0.489563\pi\)
\(938\) 1902.22 618.068i 2.02795 0.658922i
\(939\) −22.8466 222.021i −0.0243307 0.236444i
\(940\) 678.245 + 492.774i 0.721538 + 0.524228i
\(941\) −188.418 + 259.335i −0.200231 + 0.275595i −0.897311 0.441399i \(-0.854482\pi\)
0.697080 + 0.716994i \(0.254482\pi\)
\(942\) 64.8666 6.67496i 0.0688605 0.00708594i
\(943\) −244.330 751.970i −0.259099 0.797423i
\(944\) 1807.98 + 2488.47i 1.91523 + 2.63609i
\(945\) −473.823 157.384i −0.501400 0.166544i
\(946\) 454.589 + 429.241i 0.480538 + 0.453743i
\(947\) 689.980i 0.728596i −0.931283 0.364298i \(-0.881309\pi\)
0.931283 0.364298i \(-0.118691\pi\)
\(948\) −1152.52 + 1986.23i −1.21574 + 2.09518i
\(949\) 37.9284 + 116.732i 0.0399667 + 0.123005i
\(950\) −744.259 241.824i −0.783430 0.254552i
\(951\) 330.046 1536.28i 0.347052 1.61544i
\(952\) −1555.78 1130.34i −1.63422 1.18733i
\(953\) 1276.39 + 414.726i 1.33934 + 0.435179i 0.889094 0.457724i \(-0.151335\pi\)
0.450249 + 0.892903i \(0.351335\pi\)
\(954\) −1186.77 534.592i −1.24400 0.560369i
\(955\) 532.676 387.012i 0.557776 0.405248i
\(956\) 3062.78i 3.20374i
\(957\) −217.081 315.643i −0.226835 0.329826i
\(958\) −614.947 −0.641907
\(959\) −420.104 578.224i −0.438065 0.602945i
\(960\) 44.6719 40.0470i 0.0465333 0.0417156i
\(961\) −127.930 + 393.727i −0.133122 + 0.409706i
\(962\) 25.1299 34.5884i 0.0261226 0.0359547i
\(963\) −337.646 1623.24i −0.350619 1.68560i
\(964\) 716.504 2205.17i 0.743261 2.28752i
\(965\) −290.518 + 94.3950i −0.301055 + 0.0978187i
\(966\) −973.589 + 1677.86i −1.00786 + 1.73691i
\(967\) 1283.30 1.32709 0.663546 0.748135i \(-0.269051\pi\)
0.663546 + 0.748135i \(0.269051\pi\)
\(968\) −1635.65 + 1338.07i −1.68972 + 1.38231i
\(969\) 159.384 + 360.091i 0.164483 + 0.371611i
\(970\) 467.256 339.481i 0.481707 0.349981i
\(971\) 809.179 262.918i 0.833346 0.270770i 0.138892 0.990308i \(-0.455646\pi\)
0.694454 + 0.719537i \(0.255646\pi\)
\(972\) −2112.72 + 425.081i −2.17358 + 0.437326i
\(973\) −1519.69 1104.12i −1.56186 1.13476i
\(974\) 1044.78 1438.02i 1.07267 1.47640i
\(975\) −10.4287 101.346i −0.0106961 0.103944i
\(976\) 650.988 + 2003.54i 0.666996 + 2.05280i
\(977\) 712.767 + 981.039i 0.729546 + 1.00413i 0.999152 + 0.0411637i \(0.0131065\pi\)
−0.269606 + 0.962971i \(0.586893\pi\)
\(978\) 705.322 + 1593.51i 0.721188 + 1.62936i
\(979\) 151.508 + 806.248i 0.154758 + 0.823542i
\(980\) 546.831i 0.557991i
\(981\) 57.3530 523.723i 0.0584639 0.533867i
\(982\) 366.090 + 1126.71i 0.372801 + 1.14736i
\(983\) −432.404 140.496i −0.439882 0.142926i 0.0806993 0.996738i \(-0.474285\pi\)
−0.520581 + 0.853812i \(0.674285\pi\)
\(984\) 1991.49 + 427.839i 2.02387 + 0.434796i
\(985\) −387.310 281.397i −0.393208 0.285682i
\(986\) 492.036 + 159.872i 0.499022 + 0.162142i
\(987\) −897.030 + 804.159i −0.908845 + 0.814751i
\(988\) −124.687 + 90.5904i −0.126201 + 0.0916907i
\(989\) 322.239i 0.325823i
\(990\) −56.7584 738.785i −0.0573317 0.746248i
\(991\) 697.554 0.703889 0.351945 0.936021i \(-0.385521\pi\)
0.351945 + 0.936021i \(0.385521\pi\)
\(992\) −379.860 522.832i −0.382923 0.527049i
\(993\) −504.049 562.261i −0.507602 0.566225i
\(994\) 100.337 308.807i 0.100943 0.310671i
\(995\) −477.490 + 657.209i −0.479890 + 0.660512i
\(996\) −65.9881 + 307.159i −0.0662531 + 0.308392i
\(997\) 202.089 621.967i 0.202697 0.623839i −0.797103 0.603844i \(-0.793635\pi\)
0.999800 0.0199948i \(-0.00636496\pi\)
\(998\) 374.607 121.717i 0.375358 0.121961i
\(999\) −59.2391 186.456i −0.0592984 0.186642i
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 33.3.h.b.14.4 yes 16
3.2 odd 2 inner 33.3.h.b.14.1 16
11.2 odd 10 363.3.b.l.122.8 8
11.3 even 5 363.3.h.o.269.4 16
11.4 even 5 inner 33.3.h.b.26.1 yes 16
11.5 even 5 363.3.h.o.251.1 16
11.6 odd 10 363.3.h.n.251.4 16
11.7 odd 10 363.3.h.j.323.4 16
11.8 odd 10 363.3.h.n.269.1 16
11.9 even 5 363.3.b.m.122.1 8
11.10 odd 2 363.3.h.j.245.1 16
33.2 even 10 363.3.b.l.122.1 8
33.5 odd 10 363.3.h.o.251.4 16
33.8 even 10 363.3.h.n.269.4 16
33.14 odd 10 363.3.h.o.269.1 16
33.17 even 10 363.3.h.n.251.1 16
33.20 odd 10 363.3.b.m.122.8 8
33.26 odd 10 inner 33.3.h.b.26.4 yes 16
33.29 even 10 363.3.h.j.323.1 16
33.32 even 2 363.3.h.j.245.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.h.b.14.1 16 3.2 odd 2 inner
33.3.h.b.14.4 yes 16 1.1 even 1 trivial
33.3.h.b.26.1 yes 16 11.4 even 5 inner
33.3.h.b.26.4 yes 16 33.26 odd 10 inner
363.3.b.l.122.1 8 33.2 even 10
363.3.b.l.122.8 8 11.2 odd 10
363.3.b.m.122.1 8 11.9 even 5
363.3.b.m.122.8 8 33.20 odd 10
363.3.h.j.245.1 16 11.10 odd 2
363.3.h.j.245.4 16 33.32 even 2
363.3.h.j.323.1 16 33.29 even 10
363.3.h.j.323.4 16 11.7 odd 10
363.3.h.n.251.1 16 33.17 even 10
363.3.h.n.251.4 16 11.6 odd 10
363.3.h.n.269.1 16 11.8 odd 10
363.3.h.n.269.4 16 33.8 even 10
363.3.h.o.251.1 16 11.5 even 5
363.3.h.o.251.4 16 33.5 odd 10
363.3.h.o.269.1 16 33.14 odd 10
363.3.h.o.269.4 16 11.3 even 5