Properties

Label 76.3.g.a.11.1
Level $76$
Weight $3$
Character 76.11
Analytic conductor $2.071$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,3,Mod(7,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 10x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-2.73861 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 76.11
Dual form 76.3.g.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.23861 - 0.715113i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.73861 + 6.47547i) q^{5} +2.86045i q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 - 6.02273i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.23861 - 0.715113i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.73861 + 6.47547i) q^{5} +2.86045i q^{6} +3.76593i q^{7} +8.00000 q^{8} +(-3.47723 - 6.02273i) q^{9} +14.9545 q^{10} +14.0793i q^{11} +(4.95445 - 2.86045i) q^{12} +(-3.00000 - 5.19615i) q^{13} +(6.52277 - 3.76593i) q^{14} +(9.26139 - 5.34706i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.4772 + 23.3432i) q^{17} +(-6.95445 + 12.0455i) q^{18} +(-18.7158 + 3.27374i) q^{19} +(-14.9545 - 25.9019i) q^{20} +(2.69306 - 4.66452i) q^{21} +(24.3861 - 14.0793i) q^{22} +(21.6475 - 12.4982i) q^{23} +(-9.90890 - 5.72091i) q^{24} +(-15.4545 - 26.7679i) q^{25} +(-6.00000 + 10.3923i) q^{26} +22.8185i q^{27} +(-13.0455 - 7.53185i) q^{28} +(1.73861 + 3.01137i) q^{29} +(-18.5228 - 10.6941i) q^{30} -39.4565i q^{31} +(-16.0000 + 27.7128i) q^{32} +(10.0683 - 17.4388i) q^{33} +53.9089 q^{34} +(-24.3861 - 14.0793i) q^{35} +27.8178 q^{36} +3.38613 q^{37} +(24.3861 + 29.1430i) q^{38} +8.58136i q^{39} +(-29.9089 + 51.8037i) q^{40} +(-4.45445 + 7.71534i) q^{41} -10.7723 q^{42} +(45.3861 + 26.2037i) q^{43} +(-48.7723 - 28.1587i) q^{44} +52.0000 q^{45} +(-43.2950 - 24.9964i) q^{46} +(-19.1703 + 11.0680i) q^{47} +22.8836i q^{48} +34.8178 q^{49} +(-30.9089 + 53.5358i) q^{50} +(33.3861 - 19.2755i) q^{51} +24.0000 q^{52} +(41.9545 + 72.6672i) q^{53} +(39.5228 - 22.8185i) q^{54} +(-91.1703 - 52.6372i) q^{55} +30.1274i q^{56} +(25.5228 + 9.32905i) q^{57} +(3.47723 - 6.02273i) q^{58} +(22.2386 + 12.8395i) q^{59} +42.7765i q^{60} +(-13.7386 - 23.7960i) q^{61} +(-68.3406 + 39.4565i) q^{62} +(22.6812 - 13.0950i) q^{63} +64.0000 q^{64} +44.8634 q^{65} -40.2733 q^{66} +(-32.0109 + 18.4815i) q^{67} +(-53.9089 - 93.3730i) q^{68} -35.7505 q^{69} +56.3173i q^{70} +(-89.3406 - 51.5808i) q^{71} +(-27.8178 - 48.1819i) q^{72} +(4.45445 - 7.71534i) q^{73} +(-3.38613 - 5.86495i) q^{74} +44.2067i q^{75} +(26.0911 - 71.3811i) q^{76} -53.0217 q^{77} +(14.8634 - 8.58136i) q^{78} +(111.909 + 64.6106i) q^{79} +119.636 q^{80} +(-14.9772 + 25.9413i) q^{81} +17.8178 q^{82} +27.1743i q^{83} +(10.7723 + 18.6581i) q^{84} +(-100.772 - 174.543i) q^{85} -104.815i q^{86} -4.97322i q^{87} +112.635i q^{88} +(-64.2495 - 111.283i) q^{89} +(-52.0000 - 90.0666i) q^{90} +(19.5683 - 11.2978i) q^{91} +99.9856i q^{92} +(-28.2158 + 48.8713i) q^{93} +(38.3406 + 22.1359i) q^{94} +(48.7723 - 133.433i) q^{95} +(39.6356 - 22.8836i) q^{96} +(-53.0228 + 91.8381i) q^{97} +(-34.8178 - 60.3062i) q^{98} +(84.7961 - 48.9570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9} + 16 q^{10} - 24 q^{12} - 12 q^{13} + 48 q^{14} + 48 q^{15} - 32 q^{16} - 32 q^{17} + 16 q^{18} - 42 q^{19} - 16 q^{20} - 44 q^{21} - 12 q^{22} - 12 q^{23} + 48 q^{24} - 18 q^{25} - 24 q^{26} - 96 q^{28} - 4 q^{29} - 96 q^{30} - 64 q^{32} + 106 q^{33} + 128 q^{34} + 12 q^{35} - 64 q^{36} - 96 q^{37} - 12 q^{38} - 32 q^{40} + 26 q^{41} + 176 q^{42} + 72 q^{43} + 24 q^{44} + 208 q^{45} + 24 q^{46} - 36 q^{49} - 36 q^{50} + 24 q^{51} + 96 q^{52} + 124 q^{53} + 180 q^{54} - 288 q^{55} + 124 q^{57} - 8 q^{58} + 78 q^{59} - 44 q^{61} - 120 q^{62} - 216 q^{63} + 256 q^{64} + 48 q^{65} - 424 q^{66} + 102 q^{67} - 128 q^{68} - 384 q^{69} - 204 q^{71} + 64 q^{72} - 26 q^{73} + 96 q^{74} + 192 q^{76} + 248 q^{77} - 72 q^{78} + 360 q^{79} + 128 q^{80} - 38 q^{81} - 104 q^{82} - 176 q^{84} - 184 q^{85} - 16 q^{89} - 208 q^{90} + 144 q^{91} - 80 q^{93} - 24 q^{95} - 192 q^{96} - 234 q^{97} + 36 q^{98} + 624 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.500000 0.866025i
\(3\) −1.23861 0.715113i −0.412871 0.238371i 0.279152 0.960247i \(-0.409947\pi\)
−0.692023 + 0.721876i \(0.743280\pi\)
\(4\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(5\) −3.73861 + 6.47547i −0.747723 + 1.29509i 0.201189 + 0.979552i \(0.435519\pi\)
−0.948912 + 0.315541i \(0.897814\pi\)
\(6\) 2.86045i 0.476742i
\(7\) 3.76593i 0.537989i 0.963142 + 0.268995i \(0.0866914\pi\)
−0.963142 + 0.268995i \(0.913309\pi\)
\(8\) 8.00000 1.00000
\(9\) −3.47723 6.02273i −0.386358 0.669192i
\(10\) 14.9545 1.49545
\(11\) 14.0793i 1.27994i 0.768400 + 0.639970i \(0.221053\pi\)
−0.768400 + 0.639970i \(0.778947\pi\)
\(12\) 4.95445 2.86045i 0.412871 0.238371i
\(13\) −3.00000 5.19615i −0.230769 0.399704i 0.727265 0.686356i \(-0.240791\pi\)
−0.958035 + 0.286652i \(0.907458\pi\)
\(14\) 6.52277 3.76593i 0.465912 0.268995i
\(15\) 9.26139 5.34706i 0.617426 0.356471i
\(16\) −8.00000 13.8564i −0.500000 0.866025i
\(17\) −13.4772 + 23.3432i −0.792778 + 1.37313i 0.131463 + 0.991321i \(0.458033\pi\)
−0.924241 + 0.381811i \(0.875301\pi\)
\(18\) −6.95445 + 12.0455i −0.386358 + 0.669192i
\(19\) −18.7158 + 3.27374i −0.985044 + 0.172302i
\(20\) −14.9545 25.9019i −0.747723 1.29509i
\(21\) 2.69306 4.66452i 0.128241 0.222120i
\(22\) 24.3861 14.0793i 1.10846 0.639970i
\(23\) 21.6475 12.4982i 0.941196 0.543400i 0.0508612 0.998706i \(-0.483803\pi\)
0.890335 + 0.455306i \(0.150470\pi\)
\(24\) −9.90890 5.72091i −0.412871 0.238371i
\(25\) −15.4545 26.7679i −0.618178 1.07072i
\(26\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(27\) 22.8185i 0.845129i
\(28\) −13.0455 7.53185i −0.465912 0.268995i
\(29\) 1.73861 + 3.01137i 0.0599522 + 0.103840i 0.894444 0.447181i \(-0.147572\pi\)
−0.834492 + 0.551021i \(0.814239\pi\)
\(30\) −18.5228 10.6941i −0.617426 0.356471i
\(31\) 39.4565i 1.27279i −0.771364 0.636394i \(-0.780425\pi\)
0.771364 0.636394i \(-0.219575\pi\)
\(32\) −16.0000 + 27.7128i −0.500000 + 0.866025i
\(33\) 10.0683 17.4388i 0.305101 0.528450i
\(34\) 53.9089 1.58556
\(35\) −24.3861 14.0793i −0.696747 0.402267i
\(36\) 27.8178 0.772717
\(37\) 3.38613 0.0915170 0.0457585 0.998953i \(-0.485430\pi\)
0.0457585 + 0.998953i \(0.485430\pi\)
\(38\) 24.3861 + 29.1430i 0.641740 + 0.766922i
\(39\) 8.58136i 0.220035i
\(40\) −29.9089 + 51.8037i −0.747723 + 1.29509i
\(41\) −4.45445 + 7.71534i −0.108645 + 0.188179i −0.915222 0.402951i \(-0.867985\pi\)
0.806576 + 0.591130i \(0.201318\pi\)
\(42\) −10.7723 −0.256482
\(43\) 45.3861 + 26.2037i 1.05549 + 0.609388i 0.924182 0.381953i \(-0.124748\pi\)
0.131310 + 0.991341i \(0.458082\pi\)
\(44\) −48.7723 28.1587i −1.10846 0.639970i
\(45\) 52.0000 1.15556
\(46\) −43.2950 24.9964i −0.941196 0.543400i
\(47\) −19.1703 + 11.0680i −0.407879 + 0.235489i −0.689878 0.723926i \(-0.742336\pi\)
0.281999 + 0.959415i \(0.409002\pi\)
\(48\) 22.8836i 0.476742i
\(49\) 34.8178 0.710567
\(50\) −30.9089 + 53.5358i −0.618178 + 1.07072i
\(51\) 33.3861 19.2755i 0.654630 0.377951i
\(52\) 24.0000 0.461538
\(53\) 41.9545 + 72.6672i 0.791593 + 1.37108i 0.924980 + 0.380016i \(0.124081\pi\)
−0.133387 + 0.991064i \(0.542585\pi\)
\(54\) 39.5228 22.8185i 0.731903 0.422565i
\(55\) −91.1703 52.6372i −1.65764 0.957040i
\(56\) 30.1274i 0.537989i
\(57\) 25.5228 + 9.32905i 0.447768 + 0.163667i
\(58\) 3.47723 6.02273i 0.0599522 0.103840i
\(59\) 22.2386 + 12.8395i 0.376926 + 0.217618i 0.676480 0.736461i \(-0.263505\pi\)
−0.299554 + 0.954079i \(0.596838\pi\)
\(60\) 42.7765i 0.712942i
\(61\) −13.7386 23.7960i −0.225223 0.390098i 0.731163 0.682203i \(-0.238978\pi\)
−0.956386 + 0.292105i \(0.905644\pi\)
\(62\) −68.3406 + 39.4565i −1.10227 + 0.636394i
\(63\) 22.6812 13.0950i 0.360018 0.207857i
\(64\) 64.0000 1.00000
\(65\) 44.8634 0.690205
\(66\) −40.2733 −0.610201
\(67\) −32.0109 + 18.4815i −0.477774 + 0.275843i −0.719488 0.694504i \(-0.755624\pi\)
0.241714 + 0.970347i \(0.422290\pi\)
\(68\) −53.9089 93.3730i −0.792778 1.37313i
\(69\) −35.7505 −0.518123
\(70\) 56.3173i 0.804534i
\(71\) −89.3406 51.5808i −1.25832 0.726490i −0.285571 0.958358i \(-0.592183\pi\)
−0.972747 + 0.231867i \(0.925516\pi\)
\(72\) −27.8178 48.1819i −0.386358 0.669192i
\(73\) 4.45445 7.71534i 0.0610199 0.105690i −0.833902 0.551913i \(-0.813898\pi\)
0.894922 + 0.446224i \(0.147231\pi\)
\(74\) −3.38613 5.86495i −0.0457585 0.0792560i
\(75\) 44.2067i 0.589423i
\(76\) 26.0911 71.3811i 0.343304 0.939224i
\(77\) −53.0217 −0.688594
\(78\) 14.8634 8.58136i 0.190556 0.110017i
\(79\) 111.909 + 64.6106i 1.41657 + 0.817856i 0.995996 0.0894026i \(-0.0284958\pi\)
0.420573 + 0.907259i \(0.361829\pi\)
\(80\) 119.636 1.49545
\(81\) −14.9772 + 25.9413i −0.184904 + 0.320263i
\(82\) 17.8178 0.217290
\(83\) 27.1743i 0.327401i 0.986510 + 0.163701i \(0.0523431\pi\)
−0.986510 + 0.163701i \(0.947657\pi\)
\(84\) 10.7723 + 18.6581i 0.128241 + 0.222120i
\(85\) −100.772 174.543i −1.18556 2.05344i
\(86\) 104.815i 1.21878i
\(87\) 4.97322i 0.0571635i
\(88\) 112.635i 1.27994i
\(89\) −64.2495 111.283i −0.721904 1.25037i −0.960236 0.279191i \(-0.909934\pi\)
0.238331 0.971184i \(-0.423400\pi\)
\(90\) −52.0000 90.0666i −0.577778 1.00074i
\(91\) 19.5683 11.2978i 0.215037 0.124151i
\(92\) 99.9856i 1.08680i
\(93\) −28.2158 + 48.8713i −0.303396 + 0.525497i
\(94\) 38.3406 + 22.1359i 0.407879 + 0.235489i
\(95\) 48.7723 133.433i 0.513392 1.40456i
\(96\) 39.6356 22.8836i 0.412871 0.238371i
\(97\) −53.0228 + 91.8381i −0.546627 + 0.946785i 0.451876 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547042i \(0.982578\pi\)
\(98\) −34.8178 60.3062i −0.355284 0.615369i
\(99\) 84.7961 48.9570i 0.856526 0.494515i
\(100\) 123.636 1.23636
\(101\) 66.9425 + 115.948i 0.662797 + 1.14800i 0.979877 + 0.199600i \(0.0639643\pi\)
−0.317080 + 0.948399i \(0.602702\pi\)
\(102\) −66.7723 38.5510i −0.654630 0.377951i
\(103\) 103.477i 1.00463i 0.864684 + 0.502316i \(0.167519\pi\)
−0.864684 + 0.502316i \(0.832481\pi\)
\(104\) −24.0000 41.5692i −0.230769 0.399704i
\(105\) 20.1366 + 34.8777i 0.191778 + 0.332169i
\(106\) 83.9089 145.334i 0.791593 1.37108i
\(107\) 67.7867i 0.633520i 0.948506 + 0.316760i \(0.102595\pi\)
−0.948506 + 0.316760i \(0.897405\pi\)
\(108\) −79.0455 45.6370i −0.731903 0.422565i
\(109\) 24.8634 43.0646i 0.228104 0.395088i −0.729142 0.684362i \(-0.760081\pi\)
0.957246 + 0.289274i \(0.0934140\pi\)
\(110\) 210.549i 1.91408i
\(111\) −4.19410 2.42147i −0.0377847 0.0218150i
\(112\) 52.1822 30.1274i 0.465912 0.268995i
\(113\) −70.9089 −0.627512 −0.313756 0.949504i \(-0.601587\pi\)
−0.313756 + 0.949504i \(0.601587\pi\)
\(114\) −9.36439 53.5358i −0.0821438 0.469612i
\(115\) 186.904i 1.62525i
\(116\) −13.9089 −0.119904
\(117\) −20.8634 + 36.1364i −0.178319 + 0.308858i
\(118\) 51.3579i 0.435236i
\(119\) −87.9089 50.7542i −0.738730 0.426506i
\(120\) 74.0911 42.7765i 0.617426 0.356471i
\(121\) −77.2277 −0.638246
\(122\) −27.4772 + 47.5920i −0.225223 + 0.390098i
\(123\) 11.0347 6.37088i 0.0897128 0.0517957i
\(124\) 136.681 + 78.9129i 1.10227 + 0.636394i
\(125\) 44.1822 0.353458
\(126\) −45.3623 26.1899i −0.360018 0.207857i
\(127\) −20.2039 + 11.6647i −0.159086 + 0.0918484i −0.577430 0.816441i \(-0.695944\pi\)
0.418343 + 0.908289i \(0.362611\pi\)
\(128\) −64.0000 110.851i −0.500000 0.866025i
\(129\) −37.4772 64.9125i −0.290521 0.503197i
\(130\) −44.8634 77.7056i −0.345103 0.597735i
\(131\) −23.9436 13.8238i −0.182775 0.105525i 0.405821 0.913953i \(-0.366986\pi\)
−0.588596 + 0.808427i \(0.700319\pi\)
\(132\) 40.2733 + 69.7554i 0.305101 + 0.528450i
\(133\) −12.3287 70.4825i −0.0926968 0.529943i
\(134\) 64.0217 + 36.9630i 0.477774 + 0.275843i
\(135\) −147.760 85.3095i −1.09452 0.631922i
\(136\) −107.818 + 186.746i −0.792778 + 1.37313i
\(137\) 99.4089 + 172.181i 0.725612 + 1.25680i 0.958721 + 0.284347i \(0.0917768\pi\)
−0.233109 + 0.972451i \(0.574890\pi\)
\(138\) 35.7505 + 61.9217i 0.259062 + 0.448708i
\(139\) −232.738 + 134.371i −1.67437 + 0.966699i −0.709227 + 0.704981i \(0.750956\pi\)
−0.965144 + 0.261718i \(0.915711\pi\)
\(140\) 97.5445 56.3173i 0.696747 0.402267i
\(141\) 31.6594 0.224535
\(142\) 206.323i 1.45298i
\(143\) 73.1584 42.2380i 0.511597 0.295371i
\(144\) −55.6356 + 96.3637i −0.386358 + 0.669192i
\(145\) −26.0000 −0.179310
\(146\) −17.8178 −0.122040
\(147\) −43.1258 24.8987i −0.293373 0.169379i
\(148\) −6.77226 + 11.7299i −0.0457585 + 0.0792560i
\(149\) 36.2158 62.7277i 0.243059 0.420991i −0.718525 0.695501i \(-0.755182\pi\)
0.961584 + 0.274510i \(0.0885157\pi\)
\(150\) 76.5683 44.2067i 0.510455 0.294712i
\(151\) 39.4565i 0.261301i −0.991428 0.130651i \(-0.958293\pi\)
0.991428 0.130651i \(-0.0417066\pi\)
\(152\) −149.727 + 26.1899i −0.985044 + 0.172302i
\(153\) 187.453 1.22519
\(154\) 53.0217 + 91.8363i 0.344297 + 0.596340i
\(155\) 255.499 + 147.512i 1.64838 + 0.951693i
\(156\) −29.7267 17.1627i −0.190556 0.110017i
\(157\) −50.9545 + 88.2557i −0.324551 + 0.562138i −0.981421 0.191865i \(-0.938546\pi\)
0.656871 + 0.754003i \(0.271880\pi\)
\(158\) 258.443i 1.63571i
\(159\) 120.009i 0.754772i
\(160\) −119.636 207.215i −0.747723 1.29509i
\(161\) 47.0673 + 81.5229i 0.292343 + 0.506354i
\(162\) 59.9089 0.369808
\(163\) 190.563i 1.16910i −0.811358 0.584550i \(-0.801271\pi\)
0.811358 0.584550i \(-0.198729\pi\)
\(164\) −17.8178 30.8613i −0.108645 0.188179i
\(165\) 75.2831 + 130.394i 0.456261 + 0.790268i
\(166\) 47.0673 27.1743i 0.283538 0.163701i
\(167\) 256.681 148.195i 1.53701 0.887395i 0.538001 0.842944i \(-0.319180\pi\)
0.999012 0.0444508i \(-0.0141538\pi\)
\(168\) 21.5445 37.3162i 0.128241 0.222120i
\(169\) 66.5000 115.181i 0.393491 0.681547i
\(170\) −201.545 + 349.085i −1.18556 + 2.05344i
\(171\) 84.7961 + 101.337i 0.495883 + 0.592614i
\(172\) −181.545 + 104.815i −1.05549 + 0.609388i
\(173\) 113.863 197.217i 0.658170 1.13998i −0.322919 0.946426i \(-0.604664\pi\)
0.981089 0.193557i \(-0.0620024\pi\)
\(174\) −8.61387 + 4.97322i −0.0495050 + 0.0285817i
\(175\) 100.806 58.2003i 0.576034 0.332573i
\(176\) 195.089 112.635i 1.10846 0.639970i
\(177\) −18.3634 31.8063i −0.103748 0.179696i
\(178\) −128.499 + 222.567i −0.721904 + 1.25037i
\(179\) 262.287i 1.46529i 0.680610 + 0.732646i \(0.261715\pi\)
−0.680610 + 0.732646i \(0.738285\pi\)
\(180\) −104.000 + 180.133i −0.577778 + 1.00074i
\(181\) −39.9425 69.1825i −0.220677 0.382224i 0.734337 0.678785i \(-0.237493\pi\)
−0.955014 + 0.296562i \(0.904160\pi\)
\(182\) −39.1366 22.5956i −0.215037 0.124151i
\(183\) 39.2987i 0.214747i
\(184\) 173.180 99.9856i 0.941196 0.543400i
\(185\) −12.6594 + 21.9268i −0.0684293 + 0.118523i
\(186\) 112.863 0.606792
\(187\) −328.657 189.750i −1.75753 1.01471i
\(188\) 88.5438i 0.470978i
\(189\) −85.9327 −0.454670
\(190\) −279.885 + 48.9570i −1.47308 + 0.257669i
\(191\) 233.144i 1.22065i −0.792151 0.610325i \(-0.791039\pi\)
0.792151 0.610325i \(-0.208961\pi\)
\(192\) −79.2712 45.7673i −0.412871 0.238371i
\(193\) 61.4772 106.482i 0.318535 0.551719i −0.661648 0.749815i \(-0.730143\pi\)
0.980183 + 0.198096i \(0.0634759\pi\)
\(194\) 212.091 1.09325
\(195\) −55.5683 32.0824i −0.284966 0.164525i
\(196\) −69.6356 + 120.612i −0.355284 + 0.615369i
\(197\) −154.158 −0.782530 −0.391265 0.920278i \(-0.627962\pi\)
−0.391265 + 0.920278i \(0.627962\pi\)
\(198\) −169.592 97.9141i −0.856526 0.494515i
\(199\) 92.9762 53.6798i 0.467217 0.269748i −0.247857 0.968797i \(-0.579726\pi\)
0.715074 + 0.699049i \(0.246393\pi\)
\(200\) −123.636 214.143i −0.618178 1.07072i
\(201\) 52.8654 0.263012
\(202\) 133.885 231.896i 0.662797 1.14800i
\(203\) −11.3406 + 6.54749i −0.0558649 + 0.0322536i
\(204\) 154.204i 0.755902i
\(205\) −33.3069 57.6893i −0.162473 0.281411i
\(206\) 179.228 103.477i 0.870038 0.502316i
\(207\) −150.547 86.9181i −0.727278 0.419894i
\(208\) −48.0000 + 83.1384i −0.230769 + 0.399704i
\(209\) −46.0921 263.507i −0.220537 1.26080i
\(210\) 40.2733 69.7554i 0.191778 0.332169i
\(211\) 117.226 + 67.6803i 0.555572 + 0.320760i 0.751366 0.659885i \(-0.229395\pi\)
−0.195794 + 0.980645i \(0.562729\pi\)
\(212\) −335.636 −1.58319
\(213\) 73.7723 + 127.777i 0.346349 + 0.599893i
\(214\) 117.410 67.7867i 0.548645 0.316760i
\(215\) −339.362 + 195.931i −1.57843 + 0.911307i
\(216\) 182.548i 0.845129i
\(217\) 148.590 0.684747
\(218\) −99.4534 −0.456208
\(219\) −11.0347 + 6.37088i −0.0503867 + 0.0290908i
\(220\) 364.681 210.549i 1.65764 0.957040i
\(221\) 161.727 0.731795
\(222\) 9.68586i 0.0436300i
\(223\) 118.943 + 68.6715i 0.533375 + 0.307944i 0.742390 0.669968i \(-0.233692\pi\)
−0.209015 + 0.977912i \(0.567026\pi\)
\(224\) −104.364 60.2548i −0.465912 0.268995i
\(225\) −107.477 + 186.156i −0.477677 + 0.827360i
\(226\) 70.9089 + 122.818i 0.313756 + 0.543442i
\(227\) 92.9922i 0.409657i −0.978798 0.204829i \(-0.934336\pi\)
0.978798 0.204829i \(-0.0656637\pi\)
\(228\) −83.3623 + 69.7554i −0.365624 + 0.305945i
\(229\) −164.182 −0.716953 −0.358476 0.933539i \(-0.616704\pi\)
−0.358476 + 0.933539i \(0.616704\pi\)
\(230\) 323.727 186.904i 1.40751 0.812625i
\(231\) 65.6734 + 37.9166i 0.284300 + 0.164141i
\(232\) 13.9089 + 24.0909i 0.0599522 + 0.103840i
\(233\) −27.2723 + 47.2369i −0.117048 + 0.202734i −0.918597 0.395196i \(-0.870677\pi\)
0.801548 + 0.597930i \(0.204010\pi\)
\(234\) 83.4534 0.356639
\(235\) 165.515i 0.704321i
\(236\) −88.9545 + 51.3579i −0.376926 + 0.217618i
\(237\) −92.4079 160.055i −0.389907 0.675338i
\(238\) 203.017i 0.853012i
\(239\) 285.524i 1.19466i 0.801995 + 0.597331i \(0.203772\pi\)
−0.801995 + 0.597331i \(0.796228\pi\)
\(240\) −148.182 85.5530i −0.617426 0.356471i
\(241\) 87.8861 + 152.223i 0.364673 + 0.631632i 0.988724 0.149752i \(-0.0478475\pi\)
−0.624051 + 0.781384i \(0.714514\pi\)
\(242\) 77.2277 + 133.762i 0.319123 + 0.552737i
\(243\) 214.954 124.104i 0.884586 0.510716i
\(244\) 109.909 0.450446
\(245\) −130.170 + 225.462i −0.531307 + 0.920251i
\(246\) −22.0694 12.7418i −0.0897128 0.0517957i
\(247\) 73.1584 + 87.4291i 0.296188 + 0.353964i
\(248\) 315.652i 1.27279i
\(249\) 19.4327 33.6584i 0.0780430 0.135174i
\(250\) −44.1822 76.5258i −0.176729 0.306103i
\(251\) −140.124 + 80.9005i −0.558262 + 0.322313i −0.752448 0.658652i \(-0.771127\pi\)
0.194186 + 0.980965i \(0.437794\pi\)
\(252\) 104.760i 0.415713i
\(253\) 175.966 + 304.783i 0.695519 + 1.20467i
\(254\) 40.4079 + 23.3295i 0.159086 + 0.0918484i
\(255\) 288.254i 1.13041i
\(256\) −128.000 + 221.703i −0.500000 + 0.866025i
\(257\) 154.862 + 268.229i 0.602577 + 1.04369i 0.992429 + 0.122817i \(0.0391927\pi\)
−0.389852 + 0.920877i \(0.627474\pi\)
\(258\) −74.9545 + 129.825i −0.290521 + 0.503197i
\(259\) 12.7519i 0.0492352i
\(260\) −89.7267 + 155.411i −0.345103 + 0.597735i
\(261\) 12.0911 20.9424i 0.0463260 0.0802391i
\(262\) 55.2953i 0.211051i
\(263\) 171.238 + 98.8641i 0.651093 + 0.375909i 0.788875 0.614554i \(-0.210664\pi\)
−0.137782 + 0.990463i \(0.543997\pi\)
\(264\) 80.5466 139.511i 0.305101 0.528450i
\(265\) −627.406 −2.36757
\(266\) −109.751 + 91.8363i −0.412596 + 0.345249i
\(267\) 183.783i 0.688325i
\(268\) 147.852i 0.551686i
\(269\) 77.6356 134.469i 0.288608 0.499884i −0.684870 0.728666i \(-0.740141\pi\)
0.973478 + 0.228782i \(0.0734742\pi\)
\(270\) 341.238i 1.26384i
\(271\) −52.0098 30.0279i −0.191918 0.110804i 0.400962 0.916095i \(-0.368676\pi\)
−0.592880 + 0.805291i \(0.702009\pi\)
\(272\) 431.271 1.58556
\(273\) −32.3168 −0.118376
\(274\) 198.818 344.363i 0.725612 1.25680i
\(275\) 376.874 217.588i 1.37045 0.791231i
\(276\) 71.5010 123.843i 0.259062 0.448708i
\(277\) 399.430 1.44198 0.720992 0.692943i \(-0.243686\pi\)
0.720992 + 0.692943i \(0.243686\pi\)
\(278\) 465.475 + 268.742i 1.67437 + 0.966699i
\(279\) −237.636 + 137.199i −0.851741 + 0.491753i
\(280\) −195.089 112.635i −0.696747 0.402267i
\(281\) −228.999 396.638i −0.814943 1.41152i −0.909369 0.415991i \(-0.863435\pi\)
0.0944260 0.995532i \(-0.469898\pi\)
\(282\) −31.6594 54.8357i −0.112267 0.194453i
\(283\) −362.237 209.137i −1.27999 0.739001i −0.303142 0.952945i \(-0.598036\pi\)
−0.976846 + 0.213944i \(0.931369\pi\)
\(284\) 357.362 206.323i 1.25832 0.726490i
\(285\) −155.830 + 130.394i −0.546771 + 0.457523i
\(286\) −146.317 84.4760i −0.511597 0.295371i
\(287\) −29.0554 16.7751i −0.101238 0.0584499i
\(288\) 222.542 0.772717
\(289\) −218.771 378.923i −0.756994 1.31115i
\(290\) 26.0000 + 45.0333i 0.0896552 + 0.155287i
\(291\) 131.349 75.8346i 0.451372 0.260600i
\(292\) 17.8178 + 30.8613i 0.0610199 + 0.105690i
\(293\) −123.794 −0.422505 −0.211253 0.977432i \(-0.567754\pi\)
−0.211253 + 0.977432i \(0.567754\pi\)
\(294\) 99.5947i 0.338758i
\(295\) −166.283 + 96.0036i −0.563672 + 0.325436i
\(296\) 27.0890 0.0915170
\(297\) −321.269 −1.08171
\(298\) −144.863 −0.486119
\(299\) −129.885 74.9892i −0.434398 0.250800i
\(300\) −153.137 88.4135i −0.510455 0.294712i
\(301\) −98.6812 + 170.921i −0.327844 + 0.567843i
\(302\) −68.3406 + 39.4565i −0.226293 + 0.130651i
\(303\) 191.486i 0.631967i
\(304\) 195.089 + 233.144i 0.641740 + 0.766922i
\(305\) 205.453 0.673618
\(306\) −187.453 324.679i −0.612593 1.06104i
\(307\) 146.783 + 84.7453i 0.478121 + 0.276043i 0.719633 0.694355i \(-0.244310\pi\)
−0.241512 + 0.970398i \(0.577643\pi\)
\(308\) 106.043 183.673i 0.344297 0.596340i
\(309\) 73.9979 128.168i 0.239475 0.414784i
\(310\) 590.050i 1.90339i
\(311\) 407.488i 1.31025i 0.755520 + 0.655125i \(0.227384\pi\)
−0.755520 + 0.655125i \(0.772616\pi\)
\(312\) 68.6509i 0.220035i
\(313\) 286.361 + 495.992i 0.914892 + 1.58464i 0.807059 + 0.590471i \(0.201058\pi\)
0.107833 + 0.994169i \(0.465609\pi\)
\(314\) 203.818 0.649101
\(315\) 195.828i 0.621677i
\(316\) −447.636 + 258.443i −1.41657 + 0.817856i
\(317\) −264.453 458.047i −0.834238 1.44494i −0.894649 0.446769i \(-0.852575\pi\)
0.0604115 0.998174i \(-0.480759\pi\)
\(318\) −207.861 + 120.009i −0.653652 + 0.377386i
\(319\) −42.3980 + 24.4785i −0.132909 + 0.0767352i
\(320\) −239.271 + 414.430i −0.747723 + 1.29509i
\(321\) 48.4752 83.9614i 0.151013 0.261562i
\(322\) 94.1346 163.046i 0.292343 0.506354i
\(323\) 175.818 481.009i 0.544328 1.48919i
\(324\) −59.9089 103.765i −0.184904 0.320263i
\(325\) −92.7267 + 160.607i −0.285313 + 0.494177i
\(326\) −330.065 + 190.563i −1.01247 + 0.584550i
\(327\) −61.5921 + 35.5602i −0.188355 + 0.108747i
\(328\) −35.6356 + 61.7227i −0.108645 + 0.188179i
\(329\) −41.6812 72.1939i −0.126690 0.219434i
\(330\) 150.566 260.788i 0.456261 0.790268i
\(331\) 59.2704i 0.179065i 0.995984 + 0.0895324i \(0.0285373\pi\)
−0.995984 + 0.0895324i \(0.971463\pi\)
\(332\) −94.1346 54.3486i −0.283538 0.163701i
\(333\) −11.7743 20.3937i −0.0353583 0.0612425i
\(334\) −513.362 296.390i −1.53701 0.887395i
\(335\) 276.380i 0.825016i
\(336\) −86.1780 −0.256482
\(337\) −135.203 + 234.178i −0.401196 + 0.694891i −0.993870 0.110551i \(-0.964739\pi\)
0.592675 + 0.805442i \(0.298072\pi\)
\(338\) −266.000 −0.786982
\(339\) 87.8287 + 50.7079i 0.259082 + 0.149581i
\(340\) 806.178 2.37111
\(341\) 555.521 1.62909
\(342\) 90.7246 248.208i 0.265277 0.725754i
\(343\) 315.652i 0.920267i
\(344\) 363.089 + 209.630i 1.05549 + 0.609388i
\(345\) 133.657 231.501i 0.387413 0.671018i
\(346\) −455.453 −1.31634
\(347\) −292.649 168.961i −0.843368 0.486919i 0.0150399 0.999887i \(-0.495212\pi\)
−0.858407 + 0.512968i \(0.828546\pi\)
\(348\) 17.2277 + 9.94644i 0.0495050 + 0.0285817i
\(349\) −156.729 −0.449080 −0.224540 0.974465i \(-0.572088\pi\)
−0.224540 + 0.974465i \(0.572088\pi\)
\(350\) −201.612 116.401i −0.576034 0.332573i
\(351\) 118.568 68.4555i 0.337801 0.195030i
\(352\) −390.178 225.269i −1.10846 0.639970i
\(353\) 13.7723 0.0390149 0.0195074 0.999810i \(-0.493790\pi\)
0.0195074 + 0.999810i \(0.493790\pi\)
\(354\) −36.7267 + 63.6125i −0.103748 + 0.179696i
\(355\) 668.020 385.681i 1.88175 1.08643i
\(356\) 513.996 1.44381
\(357\) 72.5901 + 125.730i 0.203334 + 0.352184i
\(358\) 454.295 262.287i 1.26898 0.732646i
\(359\) −71.7148 41.4046i −0.199763 0.115333i 0.396782 0.917913i \(-0.370127\pi\)
−0.596545 + 0.802580i \(0.703460\pi\)
\(360\) 416.000 1.15556
\(361\) 339.565 122.542i 0.940624 0.339451i
\(362\) −79.8851 + 138.365i −0.220677 + 0.382224i
\(363\) 95.6553 + 55.2266i 0.263513 + 0.152139i
\(364\) 90.3822i 0.248303i
\(365\) 33.3069 + 57.6893i 0.0912519 + 0.158053i
\(366\) 68.0673 39.2987i 0.185976 0.107373i
\(367\) 261.398 150.918i 0.712256 0.411221i −0.0996397 0.995024i \(-0.531769\pi\)
0.811896 + 0.583802i \(0.198436\pi\)
\(368\) −346.360 199.971i −0.941196 0.543400i
\(369\) 61.9565 0.167904
\(370\) 50.6377 0.136859
\(371\) −273.659 + 157.997i −0.737626 + 0.425869i
\(372\) −112.863 195.485i −0.303396 0.525497i
\(373\) 301.909 0.809407 0.404704 0.914448i \(-0.367375\pi\)
0.404704 + 0.914448i \(0.367375\pi\)
\(374\) 759.002i 2.02942i
\(375\) −54.7246 31.5953i −0.145932 0.0842541i
\(376\) −153.362 + 88.5438i −0.407879 + 0.235489i
\(377\) 10.4317 18.0682i 0.0276702 0.0479262i
\(378\) 85.9327 + 148.840i 0.227335 + 0.393756i
\(379\) 498.042i 1.31409i −0.753850 0.657047i \(-0.771805\pi\)
0.753850 0.657047i \(-0.228195\pi\)
\(380\) 364.681 + 435.818i 0.959687 + 1.14689i
\(381\) 33.3665 0.0875760
\(382\) −403.818 + 233.144i −1.05711 + 0.610325i
\(383\) 30.0771 + 17.3650i 0.0785303 + 0.0453395i 0.538751 0.842465i \(-0.318896\pi\)
−0.460221 + 0.887805i \(0.652230\pi\)
\(384\) 183.069i 0.476742i
\(385\) 198.228 343.341i 0.514877 0.891794i
\(386\) −245.909 −0.637070
\(387\) 364.465i 0.941769i
\(388\) −212.091 367.353i −0.546627 0.946785i
\(389\) −189.046 327.436i −0.485978 0.841739i 0.513892 0.857855i \(-0.328203\pi\)
−0.999870 + 0.0161159i \(0.994870\pi\)
\(390\) 128.330i 0.329050i
\(391\) 673.764i 1.72318i
\(392\) 278.542 0.710567
\(393\) 19.7712 + 34.2448i 0.0503084 + 0.0871368i
\(394\) 154.158 + 267.010i 0.391265 + 0.677691i
\(395\) −836.768 + 483.108i −2.11840 + 1.22306i
\(396\) 391.656i 0.989031i
\(397\) −80.5326 + 139.487i −0.202853 + 0.351352i −0.949447 0.313929i \(-0.898355\pi\)
0.746594 + 0.665280i \(0.231688\pi\)
\(398\) −185.952 107.360i −0.467217 0.269748i
\(399\) −35.1325 + 96.1169i −0.0880514 + 0.240894i
\(400\) −247.271 + 428.286i −0.618178 + 1.07072i
\(401\) −220.045 + 381.128i −0.548739 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572256i \(0.981775\pi\)
\(402\) −52.8654 91.5656i −0.131506 0.227775i
\(403\) −205.022 + 118.369i −0.508739 + 0.293720i
\(404\) −535.540 −1.32559
\(405\) −111.988 193.969i −0.276514 0.478936i
\(406\) 22.6812 + 13.0950i 0.0558649 + 0.0322536i
\(407\) 47.6744i 0.117136i
\(408\) 267.089 154.204i 0.654630 0.377951i
\(409\) 110.068 + 190.644i 0.269116 + 0.466122i 0.968634 0.248493i \(-0.0799353\pi\)
−0.699518 + 0.714615i \(0.746602\pi\)
\(410\) −66.6139 + 115.379i −0.162473 + 0.281411i
\(411\) 284.355i 0.691860i
\(412\) −358.455 206.954i −0.870038 0.502316i
\(413\) −48.3525 + 83.7490i −0.117076 + 0.202782i
\(414\) 347.672i 0.839789i
\(415\) −175.966 101.594i −0.424015 0.244805i
\(416\) 192.000 0.461538
\(417\) 384.362 0.921732
\(418\) −410.315 + 343.341i −0.981614 + 0.821389i
\(419\) 431.538i 1.02992i −0.857213 0.514961i \(-0.827806\pi\)
0.857213 0.514961i \(-0.172194\pi\)
\(420\) −161.093 −0.383555
\(421\) 27.0357 46.8272i 0.0642179 0.111229i −0.832129 0.554582i \(-0.812878\pi\)
0.896347 + 0.443354i \(0.146211\pi\)
\(422\) 270.721i 0.641519i
\(423\) 133.319 + 76.9717i 0.315175 + 0.181966i
\(424\) 335.636 + 581.338i 0.791593 + 1.37108i
\(425\) 833.132 1.96031
\(426\) 147.545 255.555i 0.346349 0.599893i
\(427\) 89.6139 51.7386i 0.209869 0.121168i
\(428\) −234.820 135.573i −0.548645 0.316760i
\(429\) −120.820 −0.281631
\(430\) 678.725 + 391.862i 1.57843 + 0.911307i
\(431\) 708.564 409.090i 1.64400 0.949164i 0.664609 0.747191i \(-0.268598\pi\)
0.979391 0.201973i \(-0.0647353\pi\)
\(432\) 316.182 182.548i 0.731903 0.422565i
\(433\) 186.863 + 323.657i 0.431555 + 0.747475i 0.997007 0.0773056i \(-0.0246317\pi\)
−0.565452 + 0.824781i \(0.691298\pi\)
\(434\) −148.590 257.366i −0.342373 0.593008i
\(435\) 32.2039 + 18.5929i 0.0740320 + 0.0427424i
\(436\) 99.4534 + 172.258i 0.228104 + 0.395088i
\(437\) −364.236 + 304.783i −0.833491 + 0.697443i
\(438\) 22.0694 + 12.7418i 0.0503867 + 0.0290908i
\(439\) 234.784 + 135.553i 0.534816 + 0.308776i 0.742975 0.669319i \(-0.233414\pi\)
−0.208159 + 0.978095i \(0.566747\pi\)
\(440\) −729.362 421.098i −1.65764 0.957040i
\(441\) −121.069 209.698i −0.274534 0.475506i
\(442\) −161.727 280.119i −0.365898 0.633753i
\(443\) −379.351 + 219.019i −0.856324 + 0.494399i −0.862780 0.505580i \(-0.831278\pi\)
0.00645570 + 0.999979i \(0.497945\pi\)
\(444\) 16.7764 9.68586i 0.0377847 0.0218150i
\(445\) 960.816 2.15914
\(446\) 274.686i 0.615888i
\(447\) −89.7148 + 51.7969i −0.200704 + 0.115877i
\(448\) 241.019i 0.537989i
\(449\) −710.180 −1.58169 −0.790846 0.612015i \(-0.790359\pi\)
−0.790846 + 0.612015i \(0.790359\pi\)
\(450\) 429.909 0.955353
\(451\) −108.627 62.7157i −0.240858 0.139059i
\(452\) 141.818 245.636i 0.313756 0.543442i
\(453\) −28.2158 + 48.8713i −0.0622866 + 0.107884i
\(454\) −161.067 + 92.9922i −0.354774 + 0.204829i
\(455\) 168.952i 0.371323i
\(456\) 204.182 + 74.6324i 0.447768 + 0.163667i
\(457\) 320.996 0.702398 0.351199 0.936301i \(-0.385774\pi\)
0.351199 + 0.936301i \(0.385774\pi\)
\(458\) 164.182 + 284.372i 0.358476 + 0.620899i
\(459\) −532.657 307.530i −1.16047 0.670000i
\(460\) −647.453 373.807i −1.40751 0.812625i
\(461\) −415.907 + 720.372i −0.902184 + 1.56263i −0.0775307 + 0.996990i \(0.524704\pi\)
−0.824653 + 0.565639i \(0.808630\pi\)
\(462\) 151.666i 0.328282i
\(463\) 231.176i 0.499299i −0.968336 0.249650i \(-0.919685\pi\)
0.968336 0.249650i \(-0.0803155\pi\)
\(464\) 27.8178 48.1819i 0.0599522 0.103840i
\(465\) −210.976 365.421i −0.453712 0.785853i
\(466\) 109.089 0.234097
\(467\) 327.762i 0.701846i 0.936404 + 0.350923i \(0.114132\pi\)
−0.936404 + 0.350923i \(0.885868\pi\)
\(468\) −83.4534 144.546i −0.178319 0.308858i
\(469\) −69.5999 120.551i −0.148401 0.257037i
\(470\) −286.681 + 165.515i −0.609960 + 0.352161i
\(471\) 126.226 72.8764i 0.267995 0.154727i
\(472\) 177.909 + 102.716i 0.376926 + 0.217618i
\(473\) −368.931 + 639.007i −0.779980 + 1.35097i
\(474\) −184.816 + 320.110i −0.389907 + 0.675338i
\(475\) 376.874 + 450.390i 0.793419 + 0.948189i
\(476\) 351.636 203.017i 0.738730 0.426506i
\(477\) 291.770 505.361i 0.611678 1.05946i
\(478\) 494.542 285.524i 1.03461 0.597331i
\(479\) −67.8178 + 39.1546i −0.141582 + 0.0817424i −0.569118 0.822256i \(-0.692715\pi\)
0.427536 + 0.903998i \(0.359382\pi\)
\(480\) 342.212i 0.712942i
\(481\) −10.1584 17.5948i −0.0211193 0.0365797i
\(482\) 175.772 304.446i 0.364673 0.631632i
\(483\) 134.634i 0.278745i
\(484\) 154.455 267.525i 0.319123 0.552737i
\(485\) −396.463 686.694i −0.817450 1.41586i
\(486\) −429.909 248.208i −0.884586 0.510716i
\(487\) 13.2665i 0.0272413i 0.999907 + 0.0136206i \(0.00433572\pi\)
−0.999907 + 0.0136206i \(0.995664\pi\)
\(488\) −109.909 190.368i −0.225223 0.390098i
\(489\) −136.274 + 236.034i −0.278680 + 0.482687i
\(490\) 520.681 1.06261
\(491\) 139.069 + 80.2917i 0.283237 + 0.163527i 0.634888 0.772604i \(-0.281046\pi\)
−0.351651 + 0.936131i \(0.614380\pi\)
\(492\) 50.9670i 0.103591i
\(493\) −93.7267 −0.190115
\(494\) 78.2733 214.143i 0.158448 0.433488i
\(495\) 732.126i 1.47904i
\(496\) −546.725 + 315.652i −1.10227 + 0.636394i
\(497\) 194.249 336.450i 0.390844 0.676962i
\(498\) −77.7309 −0.156086
\(499\) 522.621 + 301.735i 1.04734 + 0.604680i 0.921902 0.387422i \(-0.126634\pi\)
0.125434 + 0.992102i \(0.459968\pi\)
\(500\) −88.3644 + 153.052i −0.176729 + 0.306103i
\(501\) −423.905 −0.846117
\(502\) 280.247 + 161.801i 0.558262 + 0.322313i
\(503\) 220.170 127.115i 0.437714 0.252714i −0.264913 0.964272i \(-0.585343\pi\)
0.702628 + 0.711558i \(0.252010\pi\)
\(504\) 181.449 104.760i 0.360018 0.207857i
\(505\) −1001.09 −1.98235
\(506\) 351.933 609.565i 0.695519 1.20467i
\(507\) −164.736 + 95.1101i −0.324922 + 0.187594i
\(508\) 93.3180i 0.183697i
\(509\) 49.0455 + 84.9494i 0.0963567 + 0.166895i 0.910174 0.414226i \(-0.135948\pi\)
−0.813817 + 0.581121i \(0.802614\pi\)
\(510\) 499.271 288.254i 0.978963 0.565205i
\(511\) 29.0554 + 16.7751i 0.0568598 + 0.0328280i
\(512\) 512.000 1.00000
\(513\) −74.7019 427.067i −0.145618 0.832489i
\(514\) 309.725 536.459i 0.602577 1.04369i
\(515\) −670.063 386.861i −1.30109 0.751187i
\(516\) 299.818 0.581042
\(517\) −155.830 269.905i −0.301411 0.522060i
\(518\) 22.0869 12.7519i 0.0426389 0.0246176i
\(519\) −282.065 + 162.850i −0.543478 + 0.313777i
\(520\) 358.907 0.690205
\(521\) −491.317 −0.943026 −0.471513 0.881859i \(-0.656292\pi\)
−0.471513 + 0.881859i \(0.656292\pi\)
\(522\) −48.3644 −0.0926521
\(523\) 399.564 230.688i 0.763985 0.441087i −0.0667397 0.997770i \(-0.521260\pi\)
0.830725 + 0.556683i \(0.187926\pi\)
\(524\) 95.7743 55.2953i 0.182775 0.105525i
\(525\) −166.479 −0.317103
\(526\) 395.456i 0.751818i
\(527\) 921.041 + 531.763i 1.74771 + 1.00904i
\(528\) −322.186 −0.610201
\(529\) 47.9099 82.9824i 0.0905670 0.156867i
\(530\) 627.406 + 1086.70i 1.18378 + 2.05037i
\(531\) 178.583i 0.336314i
\(532\) 268.816 + 98.2571i 0.505293 + 0.184694i
\(533\) 53.4534 0.100288
\(534\) 318.321 183.783i 0.596107 0.344162i
\(535\) −438.950 253.428i −0.820468 0.473697i
\(536\) −256.087 + 147.852i −0.477774 + 0.275843i
\(537\) 187.565 324.872i 0.349283 0.604977i
\(538\) −310.542 −0.577216
\(539\) 490.212i 0.909484i
\(540\) 591.041 341.238i 1.09452 0.631922i
\(541\) −38.1822 66.1335i −0.0705771 0.122243i 0.828577 0.559875i \(-0.189151\pi\)
−0.899154 + 0.437632i \(0.855817\pi\)
\(542\) 120.112i 0.221608i
\(543\) 114.254i 0.210412i
\(544\) −431.271 746.984i −0.792778 1.37313i
\(545\) 185.909 + 322.004i 0.341117 + 0.590832i
\(546\) 32.3168 + 55.9743i 0.0591882 + 0.102517i
\(547\) 181.521 104.801i 0.331848 0.191592i −0.324813 0.945778i \(-0.605302\pi\)
0.656661 + 0.754186i \(0.271968\pi\)
\(548\) −795.271 −1.45122
\(549\) −95.5445 + 165.488i −0.174034 + 0.301435i
\(550\) −753.748 435.177i −1.37045 0.791231i
\(551\) −42.3980 50.6685i −0.0769474 0.0919573i
\(552\) −286.004 −0.518123
\(553\) −243.319 + 421.441i −0.439998 + 0.762099i
\(554\) −399.430 691.832i −0.720992 1.24879i
\(555\) 31.3602 18.1058i 0.0565049 0.0326231i
\(556\) 1074.97i 1.93340i
\(557\) 91.1801 + 157.929i 0.163699 + 0.283534i 0.936192 0.351488i \(-0.114324\pi\)
−0.772494 + 0.635022i \(0.780991\pi\)
\(558\) 475.271 + 274.398i 0.851741 + 0.491753i
\(559\) 314.444i 0.562512i
\(560\) 450.539i 0.804534i
\(561\) 271.386 + 470.055i 0.483754 + 0.837887i
\(562\) −457.998 + 793.276i −0.814943 + 1.41152i
\(563\) 483.962i 0.859613i −0.902921 0.429807i \(-0.858582\pi\)
0.902921 0.429807i \(-0.141418\pi\)
\(564\) −63.3188 + 109.671i −0.112267 + 0.194453i
\(565\) 265.101 459.168i 0.469205 0.812687i
\(566\) 836.549i 1.47800i
\(567\) −97.6931 56.4031i −0.172298 0.0994764i
\(568\) −714.725 412.646i −1.25832 0.726490i
\(569\) 64.9586 0.114163 0.0570814 0.998370i \(-0.481821\pi\)
0.0570814 + 0.998370i \(0.481821\pi\)
\(570\) 381.679 + 139.511i 0.669612 + 0.244756i
\(571\) 553.718i 0.969733i −0.874588 0.484867i \(-0.838868\pi\)
0.874588 0.484867i \(-0.161132\pi\)
\(572\) 337.904i 0.590741i
\(573\) −166.725 + 288.776i −0.290968 + 0.503971i
\(574\) 67.1005i 0.116900i
\(575\) −669.101 386.306i −1.16365 0.671836i
\(576\) −222.542 385.455i −0.386358 0.669192i
\(577\) −21.9979 −0.0381247 −0.0190623 0.999818i \(-0.506068\pi\)
−0.0190623 + 0.999818i \(0.506068\pi\)
\(578\) −437.542 + 757.846i −0.756994 + 1.31115i
\(579\) −152.293 + 87.9264i −0.263028 + 0.151859i
\(580\) 52.0000 90.0666i 0.0896552 0.155287i
\(581\) −102.336 −0.176138
\(582\) −262.699 151.669i −0.451372 0.260600i
\(583\) −1023.11 + 590.691i −1.75490 + 1.01319i
\(584\) 35.6356 61.7227i 0.0610199 0.105690i
\(585\) −156.000 270.200i −0.266667 0.461880i
\(586\) 123.794 + 214.417i 0.211253 + 0.365900i
\(587\) 838.432 + 484.069i 1.42833 + 0.824649i 0.996989 0.0775389i \(-0.0247062\pi\)
0.431344 + 0.902188i \(0.358040\pi\)
\(588\) 172.503 99.5947i 0.293373 0.169379i
\(589\) 129.170 + 738.461i 0.219304 + 1.25375i
\(590\) 332.566 + 192.007i 0.563672 + 0.325436i
\(591\) 190.943 + 110.241i 0.323084 + 0.186533i
\(592\) −27.0890 46.9196i −0.0457585 0.0792560i
\(593\) 64.8188 + 112.270i 0.109307 + 0.189325i 0.915490 0.402342i \(-0.131804\pi\)
−0.806183 + 0.591666i \(0.798470\pi\)
\(594\) 321.269 + 556.454i 0.540857 + 0.936792i
\(595\) 657.315 379.501i 1.10473 0.637816i
\(596\) 144.863 + 250.911i 0.243059 + 0.420991i
\(597\) −153.549 −0.257200
\(598\) 299.957i 0.501600i
\(599\) −636.142 + 367.277i −1.06201 + 0.613150i −0.925987 0.377556i \(-0.876765\pi\)
−0.136020 + 0.990706i \(0.543431\pi\)
\(600\) 353.654i 0.589423i
\(601\) 964.041 1.60406 0.802031 0.597282i \(-0.203753\pi\)
0.802031 + 0.597282i \(0.203753\pi\)
\(602\) 394.725 0.655689
\(603\) 222.618 + 128.529i 0.369184 + 0.213149i
\(604\) 136.681 + 78.9129i 0.226293 + 0.130651i
\(605\) 288.725 500.086i 0.477231 0.826588i
\(606\) −331.664 + 191.486i −0.547300 + 0.315984i
\(607\) 526.372i 0.867170i −0.901113 0.433585i \(-0.857248\pi\)
0.901113 0.433585i \(-0.142752\pi\)
\(608\) 208.729 571.048i 0.343304 0.939224i
\(609\) 18.7288 0.0307533
\(610\) −205.453 355.856i −0.336809 0.583370i
\(611\) 115.022 + 66.4078i 0.188252 + 0.108687i
\(612\) −374.907 + 649.358i −0.612593 + 1.06104i
\(613\) 38.9565 67.4747i 0.0635506 0.110073i −0.832500 0.554026i \(-0.813091\pi\)
0.896050 + 0.443953i \(0.146424\pi\)
\(614\) 338.981i 0.552086i
\(615\) 95.2729i 0.154915i
\(616\) −424.174 −0.688594
\(617\) 98.9317 + 171.355i 0.160343 + 0.277722i 0.934992 0.354669i \(-0.115407\pi\)
−0.774649 + 0.632392i \(0.782073\pi\)
\(618\) −295.992 −0.478951
\(619\) 86.1017i 0.139098i −0.997579 0.0695490i \(-0.977844\pi\)
0.997579 0.0695490i \(-0.0221560\pi\)
\(620\) −1022.00 + 590.050i −1.64838 + 0.951693i
\(621\) 285.190 + 493.963i 0.459243 + 0.795432i
\(622\) 705.790 407.488i 1.13471 0.655125i
\(623\) 419.085 241.959i 0.672688 0.388377i
\(624\) 118.907 68.6509i 0.190556 0.110017i
\(625\) 221.181 383.097i 0.353890 0.612955i
\(626\) 572.723 991.985i 0.914892 1.58464i
\(627\) −131.347 + 359.344i −0.209485 + 0.573116i
\(628\) −203.818 353.023i −0.324551 0.562138i
\(629\) −45.6356 + 79.0432i −0.0725526 + 0.125665i
\(630\) 339.184 195.828i 0.538388 0.310838i
\(631\) −367.717 + 212.301i −0.582753 + 0.336452i −0.762227 0.647310i \(-0.775894\pi\)
0.179474 + 0.983763i \(0.442560\pi\)
\(632\) 895.271 + 516.885i 1.41657 + 0.817856i
\(633\) −96.7981 167.659i −0.152920 0.264865i
\(634\) −528.907 + 916.093i −0.834238 + 1.44494i
\(635\) 174.440i 0.274708i
\(636\) 415.723 + 240.018i 0.653652 + 0.377386i
\(637\) −104.453 180.919i −0.163977 0.284017i
\(638\) 84.7961 + 48.9570i 0.132909 + 0.0767352i
\(639\) 717.432i 1.12274i
\(640\) 957.085 1.49545
\(641\) 131.637 228.001i 0.205361 0.355696i −0.744886 0.667191i \(-0.767496\pi\)
0.950248 + 0.311495i \(0.100830\pi\)
\(642\) −193.901 −0.302026
\(643\) −71.3256 41.1798i −0.110926 0.0640433i 0.443510 0.896269i \(-0.353733\pi\)
−0.554437 + 0.832226i \(0.687066\pi\)
\(644\) −376.538 −0.584687
\(645\) 560.451 0.868917
\(646\) −1008.95 + 176.484i −1.56184 + 0.273195i
\(647\) 149.354i 0.230841i −0.993317 0.115421i \(-0.963178\pi\)
0.993317 0.115421i \(-0.0368216\pi\)
\(648\) −119.818 + 207.531i −0.184904 + 0.320263i
\(649\) −180.771 + 313.105i −0.278538 + 0.482442i
\(650\) 370.907 0.570626
\(651\) −184.046 106.259i −0.282712 0.163224i
\(652\) 660.130 + 381.126i 1.01247 + 0.584550i
\(653\) 335.540 0.513844 0.256922 0.966432i \(-0.417292\pi\)
0.256922 + 0.966432i \(0.417292\pi\)
\(654\) 123.184 + 71.1205i 0.188355 + 0.108747i
\(655\) 179.032 103.364i 0.273331 0.157808i
\(656\) 142.542 0.217290
\(657\) −61.9565 −0.0943022
\(658\) −83.3623 + 144.388i −0.126690 + 0.219434i
\(659\) −741.636 + 428.184i −1.12540 + 0.649747i −0.942773 0.333436i \(-0.891792\pi\)
−0.182623 + 0.983183i \(0.558459\pi\)
\(660\) −602.265 −0.912523
\(661\) 115.830 + 200.623i 0.175234 + 0.303514i 0.940242 0.340506i \(-0.110598\pi\)
−0.765008 + 0.644021i \(0.777265\pi\)
\(662\) 102.659 59.2704i 0.155075 0.0895324i
\(663\) −200.317 115.653i −0.302137 0.174439i
\(664\) 217.394i 0.327401i
\(665\) 502.499 + 183.673i 0.755638 + 0.276200i
\(666\) −23.5487 + 40.7875i −0.0353583 + 0.0612425i
\(667\) 75.2733 + 43.4591i 0.112854 + 0.0651560i
\(668\) 1185.56i 1.77479i
\(669\) −98.2158 170.115i −0.146810 0.254282i
\(670\) −478.705 + 276.380i −0.714485 + 0.412508i
\(671\) 335.032 193.431i 0.499302 0.288272i
\(672\) 86.1780 + 149.265i 0.128241 + 0.222120i
\(673\) 241.727 0.359178 0.179589 0.983742i \(-0.442523\pi\)
0.179589 + 0.983742i \(0.442523\pi\)
\(674\) 540.812 0.802391
\(675\) 610.803 352.647i 0.904893 0.522440i
\(676\) 266.000 + 460.726i 0.393491 + 0.681547i
\(677\) 842.356 1.24425 0.622124 0.782919i \(-0.286270\pi\)
0.622124 + 0.782919i \(0.286270\pi\)
\(678\) 202.832i 0.299162i
\(679\) −345.856 199.680i −0.509360 0.294079i
\(680\) −806.178 1396.34i −1.18556 2.05344i
\(681\) −66.5000 + 115.181i −0.0976505 + 0.169136i
\(682\) −555.521 962.190i −0.814546 1.41084i
\(683\) 469.540i 0.687467i 0.939067 + 0.343734i \(0.111692\pi\)
−0.939067 + 0.343734i \(0.888308\pi\)
\(684\) −520.634 + 91.0683i −0.761160 + 0.133141i
\(685\) −1486.61 −2.17023
\(686\) 546.725 315.652i 0.796975 0.460134i
\(687\) 203.358 + 117.409i 0.296009 + 0.170901i
\(688\) 838.518i 1.21878i
\(689\) 251.727 436.003i 0.365351 0.632806i
\(690\) −534.629 −0.774825
\(691\) 627.366i 0.907910i −0.891025 0.453955i \(-0.850013\pi\)
0.891025 0.453955i \(-0.149987\pi\)
\(692\) 455.453 + 788.868i 0.658170 + 1.13998i
\(693\) 184.369 + 319.336i 0.266044 + 0.460802i
\(694\) 675.843i 0.973837i
\(695\) 2009.45i 2.89129i
\(696\) 39.7858i 0.0571635i
\(697\) −120.067 207.963i −0.172263 0.298368i
\(698\) 156.729 + 271.462i 0.224540 + 0.388914i
\(699\) 67.5595 39.0055i 0.0966517 0.0558019i
\(700\) 465.603i 0.665146i
\(701\) 440.075 762.232i 0.627782 1.08735i −0.360214 0.932870i \(-0.617296\pi\)
0.987996 0.154480i \(-0.0493703\pi\)
\(702\) −237.137 136.911i −0.337801 0.195030i
\(703\) −63.3742 + 11.0853i −0.0901483 + 0.0157686i
\(704\) 901.078i 1.27994i
\(705\) −118.362 + 205.010i −0.167890 + 0.290794i
\(706\) −13.7723 23.8542i −0.0195074 0.0337879i
\(707\) −436.651 + 252.101i −0.617611 + 0.356578i
\(708\) 146.907 0.207496
\(709\) 533.689 + 924.376i 0.752735 + 1.30377i 0.946493 + 0.322725i \(0.104599\pi\)
−0.193758 + 0.981049i \(0.562068\pi\)
\(710\) −1336.04 771.363i −1.88175 1.08643i
\(711\) 898.663i 1.26394i
\(712\) −513.996 890.267i −0.721904 1.25037i
\(713\) −493.135 854.134i −0.691633 1.19794i
\(714\) 145.180 251.459i 0.203334 0.352184i
\(715\) 631.646i 0.883421i
\(716\) −908.590 524.575i −1.26898 0.732646i
\(717\) 204.182 353.654i 0.284773 0.493241i
\(718\) 165.618i 0.230666i
\(719\) 517.610 + 298.842i 0.719902 + 0.415636i 0.814717 0.579859i \(-0.196892\pi\)
−0.0948144 + 0.995495i \(0.530226\pi\)
\(720\) −416.000 720.533i −0.577778 1.00074i
\(721\) −389.687 −0.540482
\(722\) −551.814 465.603i −0.764285 0.644879i
\(723\) 251.394i 0.347710i
\(724\) 319.540 0.441354
\(725\) 53.7386 93.0780i 0.0741222 0.128383i
\(726\) 220.906i 0.304279i
\(727\) 209.050 + 120.695i 0.287551 + 0.166018i 0.636837 0.770998i \(-0.280242\pi\)
−0.349286 + 0.937016i \(0.613576\pi\)
\(728\) 156.547 90.3822i 0.215037 0.124151i
\(729\) −85.4037 −0.117152
\(730\) 66.6139 115.379i 0.0912519 0.158053i
\(731\) −1223.36 + 706.306i −1.67354 + 0.966219i
\(732\) −136.135 78.5973i −0.185976 0.107373i
\(733\) 201.525 0.274932 0.137466 0.990507i \(-0.456104\pi\)
0.137466 + 0.990507i \(0.456104\pi\)
\(734\) −522.796 301.836i −0.712256 0.411221i
\(735\) 322.461 186.173i 0.438723 0.253297i
\(736\) 799.885i 1.08680i
\(737\) −260.207 450.692i −0.353062 0.611522i
\(738\) −61.9565 107.312i −0.0839519 0.145409i
\(739\) 258.757 + 149.394i 0.350145 + 0.202156i 0.664749 0.747067i \(-0.268538\pi\)
−0.314604 + 0.949223i \(0.601872\pi\)
\(740\) −50.6377 87.7070i −0.0684293 0.118523i
\(741\) −28.0932 160.607i −0.0379125 0.216744i
\(742\) 547.319 + 315.995i 0.737626 + 0.425869i
\(743\) 510.962 + 295.004i 0.687701 + 0.397045i 0.802750 0.596315i \(-0.203369\pi\)
−0.115049 + 0.993360i \(0.536702\pi\)
\(744\) −225.727 + 390.970i −0.303396 + 0.525497i
\(745\) 270.794 + 469.029i 0.363482 + 0.629569i
\(746\) −301.909 522.922i −0.404704 0.700967i
\(747\) 163.664 94.4912i 0.219094 0.126494i
\(748\) 1314.63 759.002i 1.75753 1.01471i
\(749\) −255.280 −0.340827
\(750\) 126.381i 0.168508i
\(751\) 360.208 207.966i 0.479638 0.276919i −0.240628 0.970617i \(-0.577353\pi\)
0.720266 + 0.693698i \(0.244020\pi\)
\(752\) 306.725 + 177.088i 0.407879 + 0.235489i
\(753\) 231.412 0.307320
\(754\) −41.7267 −0.0553405
\(755\) 255.499 + 147.512i 0.338409 + 0.195381i
\(756\) 171.865 297.680i 0.227335 0.393756i
\(757\) −94.9565 + 164.470i −0.125438 + 0.217265i −0.921904 0.387418i \(-0.873367\pi\)
0.796466 + 0.604683i \(0.206700\pi\)
\(758\) −862.634 + 498.042i −1.13804 + 0.657047i
\(759\) 503.344i 0.663167i
\(760\) 390.178 1067.46i 0.513392 1.40456i
\(761\) −418.493 −0.549925 −0.274962 0.961455i \(-0.588665\pi\)
−0.274962 + 0.961455i \(0.588665\pi\)
\(762\) −33.3665 57.7924i −0.0437880 0.0758431i
\(763\) 162.178 + 93.6335i 0.212553 + 0.122718i
\(764\) 807.636 + 466.289i 1.05711 + 0.610325i
\(765\) −700.816 + 1213.85i −0.916099 + 1.58673i
\(766\) 69.4601i 0.0906790i
\(767\) 154.074i 0.200878i
\(768\) 317.085 183.069i 0.412871 0.238371i
\(769\) −26.8157 46.4462i −0.0348709 0.0603982i 0.848063 0.529895i \(-0.177769\pi\)
−0.882934 + 0.469497i \(0.844435\pi\)
\(770\) −792.911 −1.02975
\(771\) 442.976i 0.574548i
\(772\) 245.909 + 425.927i 0.318535 + 0.551719i
\(773\) −271.667 470.541i −0.351445 0.608721i 0.635058 0.772465i \(-0.280976\pi\)
−0.986503 + 0.163744i \(0.947643\pi\)
\(774\) −631.271 + 364.465i −0.815596 + 0.470885i
\(775\) −1056.17 + 609.778i −1.36280 + 0.786810i
\(776\) −424.182 + 734.705i −0.546627 + 0.946785i
\(777\) 9.11906 15.7947i 0.0117362 0.0203278i
\(778\) −378.091 + 654.873i −0.485978 + 0.841739i
\(779\) 58.1108 158.982i 0.0745966 0.204084i
\(780\) 222.273 128.330i 0.284966 0.164525i
\(781\) 726.224 1257.86i 0.929864 1.61057i
\(782\) 1166.99 673.764i 1.49232 0.861591i
\(783\) −68.7148 + 39.6725i −0.0877584 + 0.0506673i
\(784\) −278.542 482.450i −0.355284 0.615369i
\(785\) −380.998 659.908i −0.485348 0.840647i
\(786\) 39.5424 68.4895i 0.0503084 0.0871368i
\(787\) 976.098i 1.24028i 0.784492 + 0.620138i \(0.212924\pi\)
−0.784492 + 0.620138i \(0.787076\pi\)
\(788\) 308.317 534.020i 0.391265 0.677691i
\(789\) −141.398 244.909i −0.179212 0.310404i
\(790\) 1673.54 + 966.217i 2.11840 + 1.22306i
\(791\) 267.038i 0.337595i
\(792\) 678.369 391.656i 0.856526 0.494515i
\(793\) −82.4317 + 142.776i −0.103949 + 0.180045i
\(794\) 322.130 0.405706
\(795\) 777.113 + 448.666i 0.977500 + 0.564360i
\(796\) 429.439i 0.539496i
\(797\) −596.606 −0.748564 −0.374282 0.927315i \(-0.622111\pi\)
−0.374282 + 0.927315i \(0.622111\pi\)
\(798\) 201.612 35.2656i 0.252646 0.0441925i
\(799\) 596.662i 0.746761i
\(800\) 989.085 1.23636
\(801\) −446.820 + 773.915i −0.557828 + 0.966186i
\(802\) 880.178 1.09748
\(803\) 108.627 + 62.7157i 0.135276 + 0.0781018i
\(804\) −105.731 + 183.131i −0.131506 + 0.227775i
\(805\) −703.865 −0.874367
\(806\) 410.043 + 236.739i 0.508739 + 0.293720i
\(807\) −192.321 + 111.037i −0.238316 + 0.137592i
\(808\) 535.540 + 927.583i 0.662797 + 1.14800i
\(809\) 718.128 0.887674 0.443837 0.896108i \(-0.353617\pi\)
0.443837 + 0.896108i \(0.353617\pi\)
\(810\) −223.976 + 387.938i −0.276514 + 0.478936i
\(811\) −548.471 + 316.660i −0.676290 + 0.390456i −0.798456 0.602054i \(-0.794349\pi\)
0.122166 + 0.992510i \(0.461016\pi\)
\(812\) 52.3799i 0.0645073i
\(813\) 42.9467 + 74.3859i 0.0528250 + 0.0914955i
\(814\) 82.5745 47.6744i 0.101443 0.0585681i
\(815\) 1233.99 + 712.442i 1.51409 + 0.874162i
\(816\) −534.178 308.408i −0.654630 0.377951i
\(817\) −935.224 341.842i −1.14470 0.418411i
\(818\) 220.137 381.288i 0.269116 0.466122i
\(819\) −136.087 78.5698i −0.166162 0.0959339i
\(820\) 266.455 0.324946
\(821\) 390.770 + 676.834i 0.475969 + 0.824402i 0.999621 0.0275303i \(-0.00876427\pi\)
−0.523652 + 0.851932i \(0.675431\pi\)
\(822\) −492.517 + 284.355i −0.599169 + 0.345930i
\(823\) 117.748 67.9821i 0.143072 0.0826028i −0.426755 0.904367i \(-0.640343\pi\)
0.569827 + 0.821764i \(0.307010\pi\)
\(824\) 827.817i 1.00463i
\(825\) −622.402 −0.754426
\(826\) 193.410 0.234152
\(827\) −447.466 + 258.345i −0.541072 + 0.312388i −0.745513 0.666491i \(-0.767796\pi\)
0.204441 + 0.978879i \(0.434462\pi\)
\(828\) 602.186 347.672i 0.727278 0.419894i
\(829\) −1147.72 −1.38447 −0.692233 0.721674i \(-0.743373\pi\)
−0.692233 + 0.721674i \(0.743373\pi\)
\(830\) 406.377i 0.489611i
\(831\) −494.739 285.637i −0.595353 0.343727i
\(832\) −192.000 332.554i −0.230769 0.399704i
\(833\) −469.247 + 812.760i −0.563322 + 0.975703i
\(834\) −384.362 665.735i −0.460866 0.798243i
\(835\) 2216.17i 2.65410i
\(836\) 1005.00 + 367.345i 1.20215 + 0.439408i
\(837\) 900.336 1.07567
\(838\) −747.445 + 431.538i −0.891939 + 0.514961i
\(839\) 166.461 + 96.1064i 0.198404 + 0.114549i 0.595911 0.803051i \(-0.296791\pi\)
−0.397507 + 0.917599i \(0.630124\pi\)
\(840\) 161.093 + 279.022i 0.191778 + 0.332169i
\(841\) 414.454 717.856i 0.492811 0.853575i
\(842\) −108.143 −0.128436
\(843\) 655.041i 0.777036i
\(844\) −468.903 + 270.721i −0.555572 + 0.320760i
\(845\) 497.236 + 861.237i 0.588444 + 1.01922i
\(846\) 307.887i 0.363932i
\(847\) 290.834i 0.343369i
\(848\) 671.271 1162.68i 0.791593 1.37108i
\(849\) 299.114 + 518.080i 0.352313 + 0.610224i
\(850\) −833.132 1443.03i −0.980156 1.69768i
\(851\) 73.3013 42.3205i 0.0861354 0.0497303i
\(852\) −590.178 −0.692697
\(853\) 449.317 778.239i 0.526749 0.912356i −0.472765 0.881188i \(-0.656744\pi\)
0.999514 0.0311674i \(-0.00992250\pi\)
\(854\) −179.228 103.477i −0.209869 0.121168i
\(855\) −973.224 + 170.235i −1.13827 + 0.199105i
\(856\) 542.293i 0.633520i
\(857\) −62.9555 + 109.042i −0.0734603 + 0.127237i −0.900416 0.435031i \(-0.856738\pi\)
0.826955 + 0.562268i \(0.190071\pi\)
\(858\) 120.820 + 209.266i 0.140816 + 0.243900i
\(859\) 503.551 290.725i 0.586206 0.338446i −0.177390 0.984141i \(-0.556765\pi\)
0.763596 + 0.645694i \(0.223432\pi\)
\(860\) 1567.45i 1.82261i
\(861\) 23.9922 + 41.5558i 0.0278656 + 0.0482646i
\(862\) −1417.13 818.179i −1.64400 0.949164i
\(863\) 1700.91i 1.97092i −0.169894 0.985462i \(-0.554343\pi\)
0.169894 0.985462i \(-0.445657\pi\)
\(864\) −632.364 365.096i −0.731903 0.422565i
\(865\) 851.382 + 1474.64i 0.984257 + 1.70478i
\(866\) 373.727 647.314i 0.431555 0.747475i
\(867\) 625.785i 0.721782i
\(868\) −297.180 + 514.731i −0.342373 + 0.593008i
\(869\) −909.675 + 1575.60i −1.04681 + 1.81312i
\(870\) 74.3718i 0.0854848i
\(871\) 192.065 + 110.889i 0.220511 + 0.127312i
\(872\) 198.907 344.517i 0.228104 0.395088i
\(873\) 737.489 0.844775
\(874\) 892.135 + 326.092i 1.02075 + 0.373103i
\(875\) 166.387i 0.190156i
\(876\) 50.9670i 0.0581815i
\(877\) −36.2417 + 62.7725i −0.0413247 + 0.0715764i −0.885948 0.463785i \(-0.846491\pi\)
0.844623 + 0.535361i \(0.179824\pi\)
\(878\) 542.211i 0.617552i
\(879\) 153.333 + 88.5267i 0.174440 + 0.100713i
\(880\) 1684.39i 1.91408i
\(881\) 201.998 0.229283 0.114641 0.993407i \(-0.463428\pi\)
0.114641 + 0.993407i \(0.463428\pi\)
\(882\) −242.139 + 419.397i −0.274534 + 0.475506i
\(883\) −752.052 + 434.198i −0.851701 + 0.491730i −0.861225 0.508225i \(-0.830302\pi\)
0.00952321 + 0.999955i \(0.496969\pi\)
\(884\) −323.453 + 560.238i −0.365898 + 0.633753i
\(885\) 274.614 0.310298
\(886\) 758.703 + 438.037i 0.856324 + 0.494399i
\(887\) 511.770 295.471i 0.576968 0.333112i −0.182960 0.983120i \(-0.558568\pi\)
0.759927 + 0.650008i \(0.225234\pi\)
\(888\) −33.5528 19.3717i −0.0377847 0.0218150i
\(889\) −43.9286 76.0865i −0.0494135 0.0855866i
\(890\) −960.816 1664.18i −1.07957 1.86987i
\(891\) −365.237 210.869i −0.409918 0.236666i
\(892\) −475.770 + 274.686i −0.533375 + 0.307944i
\(893\) 322.554 269.905i 0.361203 0.302245i
\(894\) 179.430 + 103.594i 0.200704 + 0.115877i
\(895\) −1698.43 980.591i −1.89769 1.09563i
\(896\) 417.458 241.019i 0.465912 0.268995i
\(897\) 107.252 + 185.765i 0.119567 + 0.207096i
\(898\) 710.180 + 1230.07i 0.790846 + 1.36979i
\(899\) 118.818 68.5995i 0.132167 0.0763064i
\(900\) −429.909 744.624i −0.477677 0.827360i
\(901\) −2261.72 −2.51023
\(902\) 250.863i 0.278118i
\(903\) 244.455 141.136i 0.270715 0.156297i
\(904\) −567.271 −0.627512
\(905\) 597.319 0.660021
\(906\) 112.863 0.124573
\(907\) −774.413 447.107i −0.853818 0.492952i 0.00811954 0.999967i \(-0.497415\pi\)
−0.861937 + 0.507015i \(0.830749\pi\)
\(908\) 322.135 + 185.984i 0.354774 + 0.204829i
\(909\) 465.549 806.354i 0.512155 0.887078i
\(910\) 292.634 168.952i 0.321575 0.185662i
\(911\) 1132.77i 1.24343i 0.783242 + 0.621717i \(0.213564\pi\)
−0.783242 + 0.621717i \(0.786436\pi\)
\(912\) −74.9151 428.286i −0.0821438 0.469612i
\(913\) −382.596 −0.419054
\(914\) −320.996 555.981i −0.351199 0.608294i
\(915\) −254.477 146.922i −0.278117 0.160571i
\(916\) 328.364 568.744i 0.358476 0.620899i
\(917\) 52.0595 90.1697i 0.0567716 0.0983312i
\(918\) 1230.12i 1.34000i
\(919\) 103.477i 0.112598i 0.998414 + 0.0562988i \(0.0179299\pi\)
−0.998414 + 0.0562988i \(0.982070\pi\)
\(920\) 1495.23i 1.62525i
\(921\) −121.205 209.933i −0.131601 0.227940i
\(922\) 1663.63 1.80437
\(923\) 618.970i 0.670606i
\(924\) −262.694 + 151.666i −0.284300 + 0.164141i
\(925\) −52.3307 90.6395i −0.0565738 0.0979887i
\(926\) −400.408 + 231.176i −0.432406 + 0.249650i
\(927\) 623.215 359.814i 0.672293 0.388148i
\(928\) −111.271 −0.119904
\(929\) 622.997 1079.06i 0.670610 1.16153i −0.307121 0.951670i \(-0.599366\pi\)
0.977731 0.209861i \(-0.0673010\pi\)
\(930\) −421.952 + 730.843i −0.453712 + 0.785853i
\(931\) −651.644 + 113.985i −0.699940 + 0.122432i
\(932\) −109.089 188.948i −0.117048 0.202734i
\(933\) 291.400 504.720i 0.312326 0.540964i
\(934\) 567.701 327.762i 0.607817 0.350923i
\(935\) 2457.45 1418.81i 2.62828 1.51744i
\(936\) −166.907 + 289.091i −0.178319 + 0.308858i
\(937\) −831.676 1440.51i −0.887594 1.53736i −0.842711 0.538366i \(-0.819042\pi\)
−0.0448835 0.998992i \(-0.514292\pi\)
\(938\) −139.200 + 241.101i −0.148401 + 0.257037i
\(939\) 819.123i 0.872336i
\(940\) 573.362 + 331.031i 0.609960 + 0.352161i
\(941\) −156.636 271.301i −0.166457 0.288311i 0.770715 0.637180i \(-0.219899\pi\)
−0.937172 + 0.348869i \(0.886566\pi\)
\(942\) −252.451 145.753i −0.267995 0.154727i
\(943\) 222.690i 0.236151i
\(944\) 410.863i 0.435236i
\(945\) 321.269 556.454i 0.339967 0.588841i
\(946\) 1475.72 1.55996
\(947\) −918.950 530.556i −0.970380 0.560249i −0.0710283 0.997474i \(-0.522628\pi\)
−0.899352 + 0.437225i \(0.855961\pi\)
\(948\) 739.263 0.779813
\(949\) −53.4534 −0.0563260
\(950\) 403.224 1103.15i 0.424446 1.16122i
\(951\) 756.457i 0.795433i
\(952\) −703.271 406.034i −0.738730 0.426506i
\(953\) −649.318 + 1124.65i −0.681341 + 1.18012i 0.293231 + 0.956042i \(0.405269\pi\)
−0.974572 + 0.224075i \(0.928064\pi\)
\(954\) −1167.08 −1.22336
\(955\) 1509.72 + 871.636i 1.58086 + 0.912708i
\(956\) −989.085 571.048i −1.03461 0.597331i
\(957\) 70.0197 0.0731658
\(958\) 135.636 + 78.3093i 0.141582 + 0.0817424i
\(959\) −648.422 + 374.367i −0.676144 + 0.390372i
\(960\) 592.729 342.212i 0.617426 0.356471i
\(961\) −595.812 −0.619991
\(962\) −20.3168 + 35.1897i −0.0211193 + 0.0365797i
\(963\) 408.261 235.710i 0.423947 0.244766i
\(964\) −703.089 −0.729345
\(965\) 459.679 + 796.188i 0.476351 + 0.825065i
\(966\) −233.193 + 134.634i −0.241400 + 0.139372i
\(967\) 312.980 + 180.699i 0.323661 + 0.186866i 0.653023 0.757338i \(-0.273500\pi\)
−0.329362 + 0.944204i \(0.606834\pi\)
\(968\) −617.822 −0.638246
\(969\) −561.746 + 470.055i −0.579718 + 0.485092i
\(970\) −792.926 + 1373.39i −0.817450 + 1.41586i
\(971\) 1318.71 + 761.356i 1.35809 + 0.784095i 0.989367 0.145443i \(-0.0464609\pi\)
0.368726 + 0.929538i \(0.379794\pi\)
\(972\) 992.832i 1.02143i
\(973\) −506.032 876.472i −0.520074 0.900794i
\(974\) 22.9783 13.2665i 0.0235916 0.0136206i
\(975\) 229.705 132.620i 0.235595 0.136021i
\(976\) −219.818 + 380.736i −0.225223 + 0.390098i
\(977\) −12.6874 −0.0129861 −0.00649303 0.999979i \(-0.502067\pi\)
−0.00649303 + 0.999979i \(0.502067\pi\)
\(978\) 545.097 0.557359
\(979\) 1566.80 904.590i 1.60040 0.923994i
\(980\) −520.681 901.846i −0.531307 0.920251i
\(981\) −345.822 −0.352520
\(982\) 321.167i 0.327054i
\(983\) −726.273 419.314i −0.738833 0.426566i 0.0828116 0.996565i \(-0.473610\pi\)
−0.821645 + 0.570000i \(0.806943\pi\)
\(984\) 88.2774 50.9670i 0.0897128 0.0517957i
\(985\) 576.339 998.248i 0.585115 1.01345i
\(986\) 93.7267 + 162.339i 0.0950575 + 0.164644i
\(987\) 119.227i 0.120797i
\(988\) −449.180 + 78.5698i −0.454636 + 0.0795241i
\(989\) 1310.00 1.32457
\(990\) 1268.08 732.126i 1.28089 0.739521i
\(991\) −1478.90 853.842i −1.49233 0.861597i −0.492368 0.870387i \(-0.663869\pi\)
−0.999961 + 0.00879022i \(0.997202\pi\)
\(992\) 1093.45 + 631.303i 1.10227 + 0.636394i
\(993\) 42.3851 73.4131i 0.0426839 0.0739306i
\(994\) −776.998 −0.781688
\(995\) 802.752i 0.806786i
\(996\) 77.7309 + 134.634i 0.0780430 + 0.135174i
\(997\) 329.734 + 571.117i 0.330727 + 0.572835i 0.982655 0.185446i \(-0.0593729\pi\)
−0.651928 + 0.758281i \(0.726040\pi\)
\(998\) 1206.94i 1.20936i
\(999\) 77.2663i 0.0773436i
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 76.3.g.a.11.1 yes 4
4.3 odd 2 76.3.g.b.11.2 yes 4
19.7 even 3 76.3.g.b.7.2 yes 4
76.7 odd 6 inner 76.3.g.a.7.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.3.g.a.7.1 4 76.7 odd 6 inner
76.3.g.a.11.1 yes 4 1.1 even 1 trivial
76.3.g.b.7.2 yes 4 19.7 even 3
76.3.g.b.11.2 yes 4 4.3 odd 2