Properties

Label 845.2.n.c.484.3
Level $845$
Weight $2$
Character 845.484
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
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] = [845,2,Mod(484,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.484");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 484.3
Root \(0.228425 - 1.39564i\) of defining polynomial
Character \(\chi\) \(=\) 845.484
Dual form 845.2.n.c.529.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.395644 - 0.228425i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.456850 + 2.18890i) q^{5} +(-0.228425 + 0.395644i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.395644 - 0.228425i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.456850 + 2.18890i) q^{5} +(-0.228425 + 0.395644i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(-1.00000 + 1.73205i) q^{9} +(0.319250 + 0.970381i) q^{10} +(1.32288 + 2.29129i) q^{11} -1.79129i q^{12} -0.791288 q^{14} +(-0.698807 - 2.12407i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-3.96863 - 2.29129i) q^{17} +0.913701i q^{18} +(0.866025 - 1.50000i) q^{19} +(-2.98647 - 2.66919i) q^{20} +1.73205 q^{21} +(1.04678 + 0.604356i) q^{22} +(3.96863 - 2.29129i) q^{23} +(-0.866025 - 1.50000i) q^{24} +(-4.58258 - 2.00000i) q^{25} -5.00000i q^{27} +(2.68693 - 1.55130i) q^{28} +(2.29129 + 3.96863i) q^{29} +(-0.761669 - 0.680750i) q^{30} +6.20520 q^{31} +(-4.10436 - 2.36965i) q^{32} +(-2.29129 - 1.32288i) q^{33} -2.09355 q^{34} +(2.58092 - 2.88771i) q^{35} +(-1.79129 - 3.10260i) q^{36} +(-6.87386 + 3.96863i) q^{37} -0.791288i q^{38} +(-3.79129 - 0.791288i) q^{40} +(1.32288 + 2.29129i) q^{41} +(0.685275 - 0.395644i) q^{42} +(-9.16478 - 5.29129i) q^{43} -4.73930 q^{44} +(-3.33444 - 2.98019i) q^{45} +(1.04678 - 1.81307i) q^{46} +1.82740i q^{47} +(2.41733 + 1.39564i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-2.26992 + 0.255488i) q^{50} +4.58258 q^{51} -7.58258i q^{53} +(-1.14213 - 1.97822i) q^{54} +(-5.61976 + 1.84887i) q^{55} +(1.50000 - 2.59808i) q^{56} +1.73205i q^{57} +(1.81307 + 1.04678i) q^{58} +(-6.97588 + 12.0826i) q^{59} +(3.92095 + 0.818350i) q^{60} +(0.708712 - 1.22753i) q^{61} +(2.45505 - 1.41742i) q^{62} +(3.00000 - 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 + 0.504525i) q^{67} +(7.10895 - 4.10436i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(0.361500 - 1.73205i) q^{70} +(-3.51178 + 6.08258i) q^{71} +(-3.00000 - 1.73205i) q^{72} +(-1.81307 + 3.14033i) q^{74} +(4.96863 - 0.559237i) q^{75} +(1.55130 + 2.68693i) q^{76} -4.58258i q^{77} +6.00000 q^{79} +(5.92889 - 1.95057i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.04678 + 0.604356i) q^{82} +6.01450i q^{83} +(-1.55130 + 2.68693i) q^{84} +(6.82847 - 7.64016i) q^{85} -4.83465 q^{86} +(-3.96863 - 2.29129i) q^{87} +(-3.96863 + 2.29129i) q^{88} +(-4.78698 - 8.29129i) q^{89} +(-2.00000 - 0.417424i) q^{90} +8.20871i q^{92} +(-5.37386 + 3.10260i) q^{93} +(0.417424 + 0.723000i) q^{94} +(2.88771 + 2.58092i) q^{95} +4.73930 q^{96} +(9.87386 + 5.70068i) q^{97} +(-1.58258 - 0.913701i) q^{98} -5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{2} + 2 q^{4} - 12 q^{7} - 8 q^{9} + 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 18 q^{20} - 6 q^{28} + 10 q^{30} - 42 q^{32} + 6 q^{35} + 4 q^{36} - 12 q^{40} - 12 q^{45} - 16 q^{49} - 42 q^{50} - 14 q^{55} + 12 q^{56} + 42 q^{58} + 24 q^{61} + 24 q^{63} + 64 q^{64} - 28 q^{66} + 48 q^{67} - 24 q^{72} - 42 q^{74} + 8 q^{75} + 48 q^{79} + 24 q^{80} - 4 q^{81} + 42 q^{85} - 16 q^{90} + 12 q^{93} + 40 q^{94} + 6 q^{95} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.395644 0.228425i 0.279763 0.161521i −0.353553 0.935414i \(-0.615027\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i \(-0.759881\pi\)
0.228714 + 0.973494i \(0.426548\pi\)
\(4\) −0.895644 + 1.55130i −0.447822 + 0.775650i
\(5\) −0.456850 + 2.18890i −0.204310 + 0.978906i
\(6\) −0.228425 + 0.395644i −0.0932542 + 0.161521i
\(7\) −1.50000 0.866025i −0.566947 0.327327i 0.188982 0.981981i \(-0.439481\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.73205i 0.612372i
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0.319250 + 0.970381i 0.100956 + 0.306862i
\(11\) 1.32288 + 2.29129i 0.398862 + 0.690849i 0.993586 0.113081i \(-0.0360719\pi\)
−0.594724 + 0.803930i \(0.702739\pi\)
\(12\) 1.79129i 0.517100i
\(13\) 0 0
\(14\) −0.791288 −0.211481
\(15\) −0.698807 2.12407i −0.180431 0.548432i
\(16\) −1.39564 2.41733i −0.348911 0.604332i
\(17\) −3.96863 2.29129i −0.962533 0.555719i −0.0655816 0.997847i \(-0.520890\pi\)
−0.896952 + 0.442128i \(0.854224\pi\)
\(18\) 0.913701i 0.215361i
\(19\) 0.866025 1.50000i 0.198680 0.344124i −0.749421 0.662094i \(-0.769668\pi\)
0.948101 + 0.317970i \(0.103001\pi\)
\(20\) −2.98647 2.66919i −0.667795 0.596849i
\(21\) 1.73205 0.377964
\(22\) 1.04678 + 0.604356i 0.223173 + 0.128849i
\(23\) 3.96863 2.29129i 0.827516 0.477767i −0.0254855 0.999675i \(-0.508113\pi\)
0.853001 + 0.521909i \(0.174780\pi\)
\(24\) −0.866025 1.50000i −0.176777 0.306186i
\(25\) −4.58258 2.00000i −0.916515 0.400000i
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 2.68693 1.55130i 0.507782 0.293168i
\(29\) 2.29129 + 3.96863i 0.425481 + 0.736956i 0.996465 0.0840058i \(-0.0267714\pi\)
−0.570984 + 0.820961i \(0.693438\pi\)
\(30\) −0.761669 0.680750i −0.139061 0.124287i
\(31\) 6.20520 1.11449 0.557244 0.830349i \(-0.311859\pi\)
0.557244 + 0.830349i \(0.311859\pi\)
\(32\) −4.10436 2.36965i −0.725555 0.418899i
\(33\) −2.29129 1.32288i −0.398862 0.230283i
\(34\) −2.09355 −0.359041
\(35\) 2.58092 2.88771i 0.436255 0.488112i
\(36\) −1.79129 3.10260i −0.298548 0.517100i
\(37\) −6.87386 + 3.96863i −1.13006 + 0.652438i −0.943949 0.330091i \(-0.892920\pi\)
−0.186107 + 0.982529i \(0.559587\pi\)
\(38\) 0.791288i 0.128364i
\(39\) 0 0
\(40\) −3.79129 0.791288i −0.599455 0.125114i
\(41\) 1.32288 + 2.29129i 0.206598 + 0.357839i 0.950641 0.310293i \(-0.100427\pi\)
−0.744042 + 0.668132i \(0.767094\pi\)
\(42\) 0.685275 0.395644i 0.105740 0.0610492i
\(43\) −9.16478 5.29129i −1.39762 0.806914i −0.403473 0.914991i \(-0.632197\pi\)
−0.994142 + 0.108078i \(0.965531\pi\)
\(44\) −4.73930 −0.714477
\(45\) −3.33444 2.98019i −0.497069 0.444260i
\(46\) 1.04678 1.81307i 0.154339 0.267322i
\(47\) 1.82740i 0.266554i 0.991079 + 0.133277i \(0.0425500\pi\)
−0.991079 + 0.133277i \(0.957450\pi\)
\(48\) 2.41733 + 1.39564i 0.348911 + 0.201444i
\(49\) −2.00000 3.46410i −0.285714 0.494872i
\(50\) −2.26992 + 0.255488i −0.321015 + 0.0361314i
\(51\) 4.58258 0.641689
\(52\) 0 0
\(53\) 7.58258i 1.04155i −0.853695 0.520773i \(-0.825644\pi\)
0.853695 0.520773i \(-0.174356\pi\)
\(54\) −1.14213 1.97822i −0.155424 0.269202i
\(55\) −5.61976 + 1.84887i −0.757768 + 0.249301i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 1.73205i 0.229416i
\(58\) 1.81307 + 1.04678i 0.238068 + 0.137448i
\(59\) −6.97588 + 12.0826i −0.908182 + 1.57302i −0.0915940 + 0.995796i \(0.529196\pi\)
−0.816588 + 0.577221i \(0.804137\pi\)
\(60\) 3.92095 + 0.818350i 0.506193 + 0.105649i
\(61\) 0.708712 1.22753i 0.0907413 0.157169i −0.817082 0.576522i \(-0.804410\pi\)
0.907823 + 0.419353i \(0.137743\pi\)
\(62\) 2.45505 1.41742i 0.311792 0.180013i
\(63\) 3.00000 1.73205i 0.377964 0.218218i
\(64\) 3.41742 0.427178
\(65\) 0 0
\(66\) −1.20871 −0.148782
\(67\) −0.873864 + 0.504525i −0.106759 + 0.0616376i −0.552429 0.833560i \(-0.686299\pi\)
0.445670 + 0.895198i \(0.352966\pi\)
\(68\) 7.10895 4.10436i 0.862087 0.497726i
\(69\) −2.29129 + 3.96863i −0.275839 + 0.477767i
\(70\) 0.361500 1.73205i 0.0432075 0.207020i
\(71\) −3.51178 + 6.08258i −0.416771 + 0.721869i −0.995613 0.0935712i \(-0.970172\pi\)
0.578841 + 0.815440i \(0.303505\pi\)
\(72\) −3.00000 1.73205i −0.353553 0.204124i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1.81307 + 3.14033i −0.210765 + 0.365056i
\(75\) 4.96863 0.559237i 0.573728 0.0645751i
\(76\) 1.55130 + 2.68693i 0.177946 + 0.308212i
\(77\) 4.58258i 0.522233i
\(78\) 0 0
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 5.92889 1.95057i 0.662870 0.218080i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.04678 + 0.604356i 0.115597 + 0.0667400i
\(83\) 6.01450i 0.660177i 0.943950 + 0.330089i \(0.107079\pi\)
−0.943950 + 0.330089i \(0.892921\pi\)
\(84\) −1.55130 + 2.68693i −0.169261 + 0.293168i
\(85\) 6.82847 7.64016i 0.740652 0.828691i
\(86\) −4.83465 −0.521334
\(87\) −3.96863 2.29129i −0.425481 0.245652i
\(88\) −3.96863 + 2.29129i −0.423057 + 0.244252i
\(89\) −4.78698 8.29129i −0.507419 0.878875i −0.999963 0.00858752i \(-0.997266\pi\)
0.492545 0.870287i \(-0.336067\pi\)
\(90\) −2.00000 0.417424i −0.210819 0.0440004i
\(91\) 0 0
\(92\) 8.20871i 0.855817i
\(93\) −5.37386 + 3.10260i −0.557244 + 0.321725i
\(94\) 0.417424 + 0.723000i 0.0430540 + 0.0745718i
\(95\) 2.88771 + 2.58092i 0.296273 + 0.264797i
\(96\) 4.73930 0.483703
\(97\) 9.87386 + 5.70068i 1.00254 + 0.578816i 0.908999 0.416799i \(-0.136848\pi\)
0.0935404 + 0.995615i \(0.470182\pi\)
\(98\) −1.58258 0.913701i −0.159864 0.0922977i
\(99\) −5.29150 −0.531816
\(100\) 7.20696 5.31767i 0.720696 0.531767i
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 1.81307 1.04678i 0.179521 0.103646i
\(103\) 3.16515i 0.311872i 0.987767 + 0.155936i \(0.0498393\pi\)
−0.987767 + 0.155936i \(0.950161\pi\)
\(104\) 0 0
\(105\) −0.791288 + 3.79129i −0.0772218 + 0.369992i
\(106\) −1.73205 3.00000i −0.168232 0.291386i
\(107\) −9.16478 + 5.29129i −0.885993 + 0.511528i −0.872630 0.488383i \(-0.837587\pi\)
−0.0133631 + 0.999911i \(0.504254\pi\)
\(108\) 7.75650 + 4.47822i 0.746370 + 0.430917i
\(109\) −13.1334 −1.25795 −0.628976 0.777425i \(-0.716526\pi\)
−0.628976 + 0.777425i \(0.716526\pi\)
\(110\) −1.80110 + 2.01519i −0.171728 + 0.192141i
\(111\) 3.96863 6.87386i 0.376685 0.652438i
\(112\) 4.83465i 0.456832i
\(113\) −6.42368 3.70871i −0.604289 0.348886i 0.166438 0.986052i \(-0.446773\pi\)
−0.770727 + 0.637166i \(0.780107\pi\)
\(114\) 0.395644 + 0.685275i 0.0370554 + 0.0641819i
\(115\) 3.20233 + 9.73371i 0.298619 + 0.907673i
\(116\) −8.20871 −0.762160
\(117\) 0 0
\(118\) 6.37386i 0.586762i
\(119\) 3.96863 + 6.87386i 0.363803 + 0.630126i
\(120\) 3.67900 1.21037i 0.335845 0.110491i
\(121\) 2.00000 3.46410i 0.181818 0.314918i
\(122\) 0.647551i 0.0586265i
\(123\) −2.29129 1.32288i −0.206598 0.119280i
\(124\) −5.55765 + 9.62614i −0.499092 + 0.864453i
\(125\) 6.47135 9.11710i 0.578815 0.815459i
\(126\) 0.791288 1.37055i 0.0704935 0.122098i
\(127\) −15.3700 + 8.87386i −1.36387 + 0.787428i −0.990136 0.140110i \(-0.955254\pi\)
−0.373729 + 0.927538i \(0.621921\pi\)
\(128\) 9.56080 5.51993i 0.845063 0.487897i
\(129\) 10.5826 0.931744
\(130\) 0 0
\(131\) −7.58258 −0.662493 −0.331246 0.943544i \(-0.607469\pi\)
−0.331246 + 0.943544i \(0.607469\pi\)
\(132\) 4.10436 2.36965i 0.357238 0.206252i
\(133\) −2.59808 + 1.50000i −0.225282 + 0.130066i
\(134\) −0.230493 + 0.399225i −0.0199115 + 0.0344878i
\(135\) 10.9445 + 2.28425i 0.941953 + 0.196597i
\(136\) 3.96863 6.87386i 0.340307 0.589429i
\(137\) 9.08258 + 5.24383i 0.775977 + 0.448010i 0.835003 0.550246i \(-0.185466\pi\)
−0.0590258 + 0.998256i \(0.518799\pi\)
\(138\) 2.09355i 0.178215i
\(139\) −10.8739 + 18.8341i −0.922309 + 1.59749i −0.126476 + 0.991970i \(0.540367\pi\)
−0.795833 + 0.605517i \(0.792967\pi\)
\(140\) 2.16812 + 6.59014i 0.183239 + 0.556968i
\(141\) −0.913701 1.58258i −0.0769475 0.133277i
\(142\) 3.20871i 0.269269i
\(143\) 0 0
\(144\) 5.58258 0.465215
\(145\) −9.73371 + 3.20233i −0.808340 + 0.265939i
\(146\) 0 0
\(147\) 3.46410 + 2.00000i 0.285714 + 0.164957i
\(148\) 14.2179i 1.16870i
\(149\) 8.34643 14.4564i 0.683766 1.18432i −0.290057 0.957009i \(-0.593674\pi\)
0.973823 0.227308i \(-0.0729925\pi\)
\(150\) 1.83806 1.35622i 0.150077 0.110735i
\(151\) 9.66930 0.786877 0.393438 0.919351i \(-0.371285\pi\)
0.393438 + 0.919351i \(0.371285\pi\)
\(152\) 2.59808 + 1.50000i 0.210732 + 0.121666i
\(153\) 7.93725 4.58258i 0.641689 0.370479i
\(154\) −1.04678 1.81307i −0.0843516 0.146101i
\(155\) −2.83485 + 13.5826i −0.227701 + 1.09098i
\(156\) 0 0
\(157\) 9.16515i 0.731459i 0.930721 + 0.365729i \(0.119180\pi\)
−0.930721 + 0.365729i \(0.880820\pi\)
\(158\) 2.37386 1.37055i 0.188854 0.109035i
\(159\) 3.79129 + 6.56670i 0.300669 + 0.520773i
\(160\) 7.06201 7.90145i 0.558301 0.624665i
\(161\) −7.93725 −0.625543
\(162\) −0.395644 0.228425i −0.0310847 0.0179468i
\(163\) 18.2477 + 10.5353i 1.42927 + 0.825191i 0.997063 0.0765827i \(-0.0244009\pi\)
0.432209 + 0.901773i \(0.357734\pi\)
\(164\) −4.73930 −0.370077
\(165\) 3.94242 4.41105i 0.306917 0.343399i
\(166\) 1.37386 + 2.37960i 0.106632 + 0.184693i
\(167\) 8.29129 4.78698i 0.641599 0.370427i −0.143631 0.989631i \(-0.545878\pi\)
0.785230 + 0.619204i \(0.212545\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 0 0
\(170\) 0.956439 4.58258i 0.0733555 0.351468i
\(171\) 1.73205 + 3.00000i 0.132453 + 0.229416i
\(172\) 16.4168 9.47822i 1.25177 0.722707i
\(173\) 14.3609 + 8.29129i 1.09184 + 0.630375i 0.934066 0.357100i \(-0.116234\pi\)
0.157775 + 0.987475i \(0.449568\pi\)
\(174\) −2.09355 −0.158712
\(175\) 5.14181 + 6.96863i 0.388685 + 0.526779i
\(176\) 3.69253 6.39564i 0.278335 0.482090i
\(177\) 13.9518i 1.04868i
\(178\) −3.78788 2.18693i −0.283913 0.163917i
\(179\) −9.08258 15.7315i −0.678864 1.17583i −0.975323 0.220781i \(-0.929139\pi\)
0.296460 0.955045i \(-0.404194\pi\)
\(180\) 7.60964 2.50353i 0.567189 0.186602i
\(181\) −8.74773 −0.650213 −0.325107 0.945677i \(-0.605400\pi\)
−0.325107 + 0.945677i \(0.605400\pi\)
\(182\) 0 0
\(183\) 1.41742i 0.104779i
\(184\) 3.96863 + 6.87386i 0.292571 + 0.506748i
\(185\) −5.54661 16.8593i −0.407795 1.23952i
\(186\) −1.41742 + 2.45505i −0.103931 + 0.180013i
\(187\) 12.1244i 0.886621i
\(188\) −2.83485 1.63670i −0.206753 0.119369i
\(189\) −4.33013 + 7.50000i −0.314970 + 0.545545i
\(190\) 1.73205 + 0.361500i 0.125656 + 0.0262260i
\(191\) 8.29129 14.3609i 0.599937 1.03912i −0.392893 0.919584i \(-0.628526\pi\)
0.992830 0.119536i \(-0.0381408\pi\)
\(192\) −2.95958 + 1.70871i −0.213589 + 0.123316i
\(193\) −12.8739 + 7.43273i −0.926681 + 0.535020i −0.885760 0.464143i \(-0.846362\pi\)
−0.0409206 + 0.999162i \(0.513029\pi\)
\(194\) 5.20871 0.373964
\(195\) 0 0
\(196\) 7.16515 0.511797
\(197\) −12.7087 + 7.33738i −0.905458 + 0.522767i −0.878967 0.476882i \(-0.841767\pi\)
−0.0264912 + 0.999649i \(0.508433\pi\)
\(198\) −2.09355 + 1.20871i −0.148782 + 0.0858994i
\(199\) −5.29129 + 9.16478i −0.375089 + 0.649674i −0.990340 0.138657i \(-0.955721\pi\)
0.615251 + 0.788331i \(0.289055\pi\)
\(200\) 3.46410 7.93725i 0.244949 0.561249i
\(201\) 0.504525 0.873864i 0.0355865 0.0616376i
\(202\) 3.56080 + 2.05583i 0.250537 + 0.144647i
\(203\) 7.93725i 0.557086i
\(204\) −4.10436 + 7.10895i −0.287362 + 0.497726i
\(205\) −5.61976 + 1.84887i −0.392501 + 0.129131i
\(206\) 0.723000 + 1.25227i 0.0503738 + 0.0872500i
\(207\) 9.16515i 0.637022i
\(208\) 0 0
\(209\) 4.58258 0.316983
\(210\) 0.552957 + 1.68075i 0.0381577 + 0.115983i
\(211\) 0.0825757 + 0.143025i 0.00568475 + 0.00984627i 0.868854 0.495069i \(-0.164857\pi\)
−0.863169 + 0.504915i \(0.831524\pi\)
\(212\) 11.7629 + 6.79129i 0.807876 + 0.466428i
\(213\) 7.02355i 0.481246i
\(214\) −2.41733 + 4.18693i −0.165245 + 0.286213i
\(215\) 15.7690 17.6435i 1.07544 1.20327i
\(216\) 8.66025 0.589256
\(217\) −9.30780 5.37386i −0.631855 0.364802i
\(218\) −5.19615 + 3.00000i −0.351928 + 0.203186i
\(219\) 0 0
\(220\) 2.16515 10.3739i 0.145974 0.699406i
\(221\) 0 0
\(222\) 3.62614i 0.243370i
\(223\) −7.50000 + 4.33013i −0.502237 + 0.289967i −0.729637 0.683835i \(-0.760311\pi\)
0.227400 + 0.973801i \(0.426978\pi\)
\(224\) 4.10436 + 7.10895i 0.274234 + 0.474987i
\(225\) 8.04668 5.93725i 0.536445 0.395817i
\(226\) −3.38865 −0.225410
\(227\) −0.708712 0.409175i −0.0470389 0.0271579i 0.476296 0.879285i \(-0.341979\pi\)
−0.523335 + 0.852127i \(0.675312\pi\)
\(228\) −2.68693 1.55130i −0.177946 0.102737i
\(229\) −26.2668 −1.73576 −0.867880 0.496774i \(-0.834518\pi\)
−0.867880 + 0.496774i \(0.834518\pi\)
\(230\) 3.49041 + 3.11959i 0.230151 + 0.205700i
\(231\) 2.29129 + 3.96863i 0.150756 + 0.261116i
\(232\) −6.87386 + 3.96863i −0.451291 + 0.260553i
\(233\) 2.83485i 0.185717i 0.995679 + 0.0928586i \(0.0296004\pi\)
−0.995679 + 0.0928586i \(0.970400\pi\)
\(234\) 0 0
\(235\) −4.00000 0.834849i −0.260931 0.0544595i
\(236\) −12.4958 21.6434i −0.813408 1.40886i
\(237\) −5.19615 + 3.00000i −0.337526 + 0.194871i
\(238\) 3.14033 + 1.81307i 0.203557 + 0.117524i
\(239\) 0.190700 0.0123354 0.00616769 0.999981i \(-0.498037\pi\)
0.00616769 + 0.999981i \(0.498037\pi\)
\(240\) −4.15928 + 4.65369i −0.268481 + 0.300394i
\(241\) −0.866025 + 1.50000i −0.0557856 + 0.0966235i −0.892570 0.450910i \(-0.851100\pi\)
0.836784 + 0.547533i \(0.184433\pi\)
\(242\) 1.82740i 0.117470i
\(243\) 13.8564 + 8.00000i 0.888889 + 0.513200i
\(244\) 1.26951 + 2.19885i 0.0812719 + 0.140767i
\(245\) 8.49628 2.79523i 0.542807 0.178580i
\(246\) −1.20871 −0.0770647
\(247\) 0 0
\(248\) 10.7477i 0.682481i
\(249\) −3.00725 5.20871i −0.190577 0.330089i
\(250\) 0.477776 5.08535i 0.0302172 0.321626i
\(251\) −0.0825757 + 0.143025i −0.00521213 + 0.00902768i −0.868620 0.495479i \(-0.834992\pi\)
0.863408 + 0.504507i \(0.168326\pi\)
\(252\) 6.20520i 0.390891i
\(253\) 10.5000 + 6.06218i 0.660129 + 0.381126i
\(254\) −4.05403 + 7.02178i −0.254372 + 0.440586i
\(255\) −2.09355 + 10.0308i −0.131103 + 0.628153i
\(256\) −0.895644 + 1.55130i −0.0559777 + 0.0969563i
\(257\) 15.7315 9.08258i 0.981303 0.566556i 0.0786397 0.996903i \(-0.474942\pi\)
0.902663 + 0.430348i \(0.141609\pi\)
\(258\) 4.18693 2.41733i 0.260667 0.150496i
\(259\) 13.7477 0.854242
\(260\) 0 0
\(261\) −9.16515 −0.567309
\(262\) −3.00000 + 1.73205i −0.185341 + 0.107006i
\(263\) −7.79423 + 4.50000i −0.480613 + 0.277482i −0.720672 0.693276i \(-0.756167\pi\)
0.240059 + 0.970758i \(0.422833\pi\)
\(264\) 2.29129 3.96863i 0.141019 0.244252i
\(265\) 16.5975 + 3.46410i 1.01958 + 0.212798i
\(266\) −0.685275 + 1.18693i −0.0420169 + 0.0727755i
\(267\) 8.29129 + 4.78698i 0.507419 + 0.292958i
\(268\) 1.80750i 0.110411i
\(269\) −7.50000 + 12.9904i −0.457283 + 0.792038i −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) 4.85191 1.59625i 0.295278 0.0971447i
\(271\) −4.33013 7.50000i −0.263036 0.455593i 0.704011 0.710189i \(-0.251391\pi\)
−0.967047 + 0.254597i \(0.918057\pi\)
\(272\) 12.7913i 0.775586i
\(273\) 0 0
\(274\) 4.79129 0.289452
\(275\) −1.47960 13.1458i −0.0892234 0.792719i
\(276\) −4.10436 7.10895i −0.247053 0.427909i
\(277\) −6.42368 3.70871i −0.385961 0.222835i 0.294447 0.955668i \(-0.404864\pi\)
−0.680409 + 0.732833i \(0.738198\pi\)
\(278\) 9.93545i 0.595889i
\(279\) −6.20520 + 10.7477i −0.371496 + 0.643450i
\(280\) 5.00166 + 4.47028i 0.298906 + 0.267151i
\(281\) −3.65480 −0.218027 −0.109014 0.994040i \(-0.534769\pi\)
−0.109014 + 0.994040i \(0.534769\pi\)
\(282\) −0.723000 0.417424i −0.0430540 0.0248573i
\(283\) −24.0302 + 13.8739i −1.42845 + 0.824716i −0.996998 0.0774209i \(-0.975331\pi\)
−0.431451 + 0.902136i \(0.641998\pi\)
\(284\) −6.29060 10.8956i −0.373279 0.646538i
\(285\) −3.79129 0.791288i −0.224577 0.0468718i
\(286\) 0 0
\(287\) 4.58258i 0.270501i
\(288\) 8.20871 4.73930i 0.483703 0.279266i
\(289\) 2.00000 + 3.46410i 0.117647 + 0.203771i
\(290\) −3.11959 + 3.49041i −0.183189 + 0.204964i
\(291\) −11.4014 −0.668359
\(292\) 0 0
\(293\) −15.7087 9.06943i −0.917713 0.529842i −0.0348081 0.999394i \(-0.511082\pi\)
−0.882905 + 0.469552i \(0.844415\pi\)
\(294\) 1.82740 0.106576
\(295\) −23.2606 20.7894i −1.35429 1.21041i
\(296\) −6.87386 11.9059i −0.399535 0.692015i
\(297\) 11.4564 6.61438i 0.664770 0.383805i
\(298\) 7.62614i 0.441770i
\(299\) 0 0
\(300\) −3.58258 + 8.20871i −0.206840 + 0.473930i
\(301\) 9.16478 + 15.8739i 0.528249 + 0.914954i
\(302\) 3.82560 2.20871i 0.220139 0.127097i
\(303\) −7.79423 4.50000i −0.447767 0.258518i
\(304\) −4.83465 −0.277286
\(305\) 2.36316 + 2.11210i 0.135314 + 0.120938i
\(306\) 2.09355 3.62614i 0.119680 0.207292i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) 7.10895 + 4.10436i 0.405070 + 0.233867i
\(309\) −1.58258 2.74110i −0.0900296 0.155936i
\(310\) 1.98101 + 6.02141i 0.112514 + 0.341993i
\(311\) −7.58258 −0.429968 −0.214984 0.976618i \(-0.568970\pi\)
−0.214984 + 0.976618i \(0.568970\pi\)
\(312\) 0 0
\(313\) 3.25227i 0.183829i 0.995767 + 0.0919147i \(0.0292987\pi\)
−0.995767 + 0.0919147i \(0.970701\pi\)
\(314\) 2.09355 + 3.62614i 0.118146 + 0.204635i
\(315\) 2.42074 + 7.35799i 0.136393 + 0.414576i
\(316\) −5.37386 + 9.30780i −0.302303 + 0.523605i
\(317\) 0.190700i 0.0107108i 0.999986 + 0.00535540i \(0.00170469\pi\)
−0.999986 + 0.00535540i \(0.998295\pi\)
\(318\) 3.00000 + 1.73205i 0.168232 + 0.0971286i
\(319\) −6.06218 + 10.5000i −0.339417 + 0.587887i
\(320\) −1.56125 + 7.48040i −0.0872766 + 0.418167i
\(321\) 5.29129 9.16478i 0.295331 0.511528i
\(322\) −3.14033 + 1.81307i −0.175004 + 0.101038i
\(323\) −6.87386 + 3.96863i −0.382472 + 0.220820i
\(324\) 1.79129 0.0995160
\(325\) 0 0
\(326\) 9.62614 0.533142
\(327\) 11.3739 6.56670i 0.628976 0.363140i
\(328\) −3.96863 + 2.29129i −0.219131 + 0.126515i
\(329\) 1.58258 2.74110i 0.0872502 0.151122i
\(330\) 0.552200 2.64575i 0.0303976 0.145644i
\(331\) 2.23658 3.87386i 0.122933 0.212927i −0.797990 0.602671i \(-0.794103\pi\)
0.920923 + 0.389744i \(0.127437\pi\)
\(332\) −9.33030 5.38685i −0.512067 0.295642i
\(333\) 15.8745i 0.869918i
\(334\) 2.18693 3.78788i 0.119664 0.207263i
\(335\) −0.705131 2.14329i −0.0385254 0.117101i
\(336\) −2.41733 4.18693i −0.131876 0.228416i
\(337\) 30.7477i 1.67494i −0.546487 0.837468i \(-0.684035\pi\)
0.546487 0.837468i \(-0.315965\pi\)
\(338\) 0 0
\(339\) 7.41742 0.402859
\(340\) 5.73630 + 17.4359i 0.311095 + 0.945593i
\(341\) 8.20871 + 14.2179i 0.444527 + 0.769943i
\(342\) 1.37055 + 0.791288i 0.0741109 + 0.0427879i
\(343\) 19.0526i 1.02874i
\(344\) 9.16478 15.8739i 0.494132 0.855861i
\(345\) −7.64016 6.82847i −0.411332 0.367633i
\(346\) 7.57575 0.407275
\(347\) 18.4726 + 10.6652i 0.991660 + 0.572535i 0.905770 0.423769i \(-0.139293\pi\)
0.0858901 + 0.996305i \(0.472627\pi\)
\(348\) 7.10895 4.10436i 0.381080 0.220017i
\(349\) −1.22753 2.12614i −0.0657079 0.113809i 0.831300 0.555824i \(-0.187597\pi\)
−0.897008 + 0.442015i \(0.854264\pi\)
\(350\) 3.62614 + 1.58258i 0.193825 + 0.0845922i
\(351\) 0 0
\(352\) 12.5390i 0.668332i
\(353\) 5.91742 3.41643i 0.314953 0.181838i −0.334188 0.942506i \(-0.608462\pi\)
0.649141 + 0.760668i \(0.275129\pi\)
\(354\) −3.18693 5.51993i −0.169384 0.293381i
\(355\) −11.7098 10.4658i −0.621492 0.555465i
\(356\) 17.1497 0.908933
\(357\) −6.87386 3.96863i −0.363803 0.210042i
\(358\) −7.18693 4.14938i −0.379841 0.219301i
\(359\) 19.5293 1.03072 0.515359 0.856975i \(-0.327659\pi\)
0.515359 + 0.856975i \(0.327659\pi\)
\(360\) 5.16184 5.77542i 0.272053 0.304391i
\(361\) 8.00000 + 13.8564i 0.421053 + 0.729285i
\(362\) −3.46099 + 1.99820i −0.181905 + 0.105023i
\(363\) 4.00000i 0.209946i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.323775 + 0.560795i 0.0169240 + 0.0293132i
\(367\) −1.51358 + 0.873864i −0.0790080 + 0.0456153i −0.538984 0.842316i \(-0.681192\pi\)
0.459976 + 0.887932i \(0.347858\pi\)
\(368\) −11.0776 6.39564i −0.577459 0.333396i
\(369\) −5.29150 −0.275465
\(370\) −6.04556 5.40329i −0.314294 0.280903i
\(371\) −6.56670 + 11.3739i −0.340926 + 0.590502i
\(372\) 11.1153i 0.576302i
\(373\) −11.2583 6.50000i −0.582934 0.336557i 0.179364 0.983783i \(-0.442596\pi\)
−0.762299 + 0.647225i \(0.775929\pi\)
\(374\) −2.76951 4.79693i −0.143208 0.248043i
\(375\) −1.04580 + 11.1313i −0.0540051 + 0.574819i
\(376\) −3.16515 −0.163230
\(377\) 0 0
\(378\) 3.95644i 0.203497i
\(379\) −5.33918 9.24773i −0.274255 0.475024i 0.695692 0.718340i \(-0.255098\pi\)
−0.969947 + 0.243317i \(0.921765\pi\)
\(380\) −6.59014 + 2.16812i −0.338067 + 0.111222i
\(381\) 8.87386 15.3700i 0.454622 0.787428i
\(382\) 7.57575i 0.387609i
\(383\) −20.4564 11.8105i −1.04528 0.603490i −0.123952 0.992288i \(-0.539557\pi\)
−0.921323 + 0.388798i \(0.872890\pi\)
\(384\) −5.51993 + 9.56080i −0.281688 + 0.487897i
\(385\) 10.0308 + 2.09355i 0.511217 + 0.106697i
\(386\) −3.39564 + 5.88143i −0.172834 + 0.299357i
\(387\) 18.3296 10.5826i 0.931744 0.537943i
\(388\) −17.6869 + 10.2116i −0.897918 + 0.518413i
\(389\) −3.16515 −0.160480 −0.0802398 0.996776i \(-0.525569\pi\)
−0.0802398 + 0.996776i \(0.525569\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 6.00000 3.46410i 0.303046 0.174964i
\(393\) 6.56670 3.79129i 0.331246 0.191245i
\(394\) −3.35208 + 5.80598i −0.168876 + 0.292501i
\(395\) −2.74110 + 13.1334i −0.137920 + 0.660813i
\(396\) 4.73930 8.20871i 0.238159 0.412503i
\(397\) −17.6216 10.1738i −0.884402 0.510610i −0.0122949 0.999924i \(-0.503914\pi\)
−0.872107 + 0.489315i \(0.837247\pi\)
\(398\) 4.83465i 0.242339i
\(399\) 1.50000 2.59808i 0.0750939 0.130066i
\(400\) 1.56099 + 13.8689i 0.0780496 + 0.693443i
\(401\) 14.9131 + 25.8303i 0.744726 + 1.28990i 0.950323 + 0.311267i \(0.100753\pi\)
−0.205596 + 0.978637i \(0.565913\pi\)
\(402\) 0.460985i 0.0229918i
\(403\) 0 0
\(404\) −16.1216 −0.802079
\(405\) 2.12407 0.698807i 0.105546 0.0347240i
\(406\) −1.81307 3.14033i −0.0899811 0.155852i
\(407\) −18.1865 10.5000i −0.901473 0.520466i
\(408\) 7.93725i 0.392953i
\(409\) −4.33013 + 7.50000i −0.214111 + 0.370851i −0.952997 0.302979i \(-0.902019\pi\)
0.738886 + 0.673830i \(0.235352\pi\)
\(410\) −1.80110 + 2.01519i −0.0889498 + 0.0995230i
\(411\) −10.4877 −0.517318
\(412\) −4.91010 2.83485i −0.241903 0.139663i
\(413\) 20.9276 12.0826i 1.02978 0.594545i
\(414\) 2.09355 + 3.62614i 0.102892 + 0.178215i
\(415\) −13.1652 2.74773i −0.646252 0.134881i
\(416\) 0 0
\(417\) 21.7477i 1.06499i
\(418\) 1.81307 1.04678i 0.0886801 0.0511995i
\(419\) −2.91742 5.05313i −0.142526 0.246861i 0.785922 0.618326i \(-0.212189\pi\)
−0.928447 + 0.371465i \(0.878856\pi\)
\(420\) −5.17272 4.62317i −0.252403 0.225588i
\(421\) 5.48220 0.267186 0.133593 0.991036i \(-0.457348\pi\)
0.133593 + 0.991036i \(0.457348\pi\)
\(422\) 0.0653411 + 0.0377247i 0.00318076 + 0.00183641i
\(423\) −3.16515 1.82740i −0.153895 0.0888513i
\(424\) 13.1334 0.637815
\(425\) 13.6040 + 18.4373i 0.659889 + 0.894338i
\(426\) −1.60436 2.77883i −0.0777313 0.134635i
\(427\) −2.12614 + 1.22753i −0.102891 + 0.0594041i
\(428\) 18.9564i 0.916294i
\(429\) 0 0
\(430\) 2.20871 10.5826i 0.106514 0.510337i
\(431\) 4.23478 + 7.33485i 0.203982 + 0.353307i 0.949808 0.312834i \(-0.101278\pi\)
−0.745826 + 0.666141i \(0.767945\pi\)
\(432\) −12.0866 + 6.97822i −0.581518 + 0.335740i
\(433\) −8.44178 4.87386i −0.405686 0.234223i 0.283248 0.959047i \(-0.408588\pi\)
−0.688934 + 0.724824i \(0.741921\pi\)
\(434\) −4.91010 −0.235692
\(435\) 6.82847 7.64016i 0.327400 0.366317i
\(436\) 11.7629 20.3739i 0.563339 0.975731i
\(437\) 7.93725i 0.379690i
\(438\) 0 0
\(439\) 7.24773 + 12.5534i 0.345915 + 0.599143i 0.985520 0.169562i \(-0.0542352\pi\)
−0.639604 + 0.768704i \(0.720902\pi\)
\(440\) −3.20233 9.73371i −0.152665 0.464036i
\(441\) 8.00000 0.380952
\(442\) 0 0
\(443\) 19.9129i 0.946089i −0.881038 0.473045i \(-0.843155\pi\)
0.881038 0.473045i \(-0.156845\pi\)
\(444\) 7.10895 + 12.3131i 0.337376 + 0.584352i
\(445\) 20.3357 6.69034i 0.964007 0.317153i
\(446\) −1.97822 + 3.42638i −0.0936714 + 0.162244i
\(447\) 16.6929i 0.789545i
\(448\) −5.12614 2.95958i −0.242187 0.139827i
\(449\) 5.50998 9.54356i 0.260032 0.450388i −0.706218 0.707994i \(-0.749600\pi\)
0.966250 + 0.257606i \(0.0829336\pi\)
\(450\) 1.82740 4.18710i 0.0861445 0.197382i
\(451\) −3.50000 + 6.06218i −0.164809 + 0.285457i
\(452\) 11.5067 6.64337i 0.541228 0.312478i
\(453\) −8.37386 + 4.83465i −0.393438 + 0.227152i
\(454\) −0.373864 −0.0175463
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 1.50000 0.866025i 0.0701670 0.0405110i −0.464506 0.885570i \(-0.653768\pi\)
0.534673 + 0.845059i \(0.320435\pi\)
\(458\) −10.3923 + 6.00000i −0.485601 + 0.280362i
\(459\) −11.4564 + 19.8431i −0.534741 + 0.926198i
\(460\) −17.9681 3.75015i −0.837765 0.174852i
\(461\) −17.9204 + 31.0390i −0.834635 + 1.44563i 0.0596914 + 0.998217i \(0.480988\pi\)
−0.894327 + 0.447414i \(0.852345\pi\)
\(462\) 1.81307 + 1.04678i 0.0843516 + 0.0487004i
\(463\) 39.4002i 1.83108i 0.402223 + 0.915542i \(0.368238\pi\)
−0.402223 + 0.915542i \(0.631762\pi\)
\(464\) 6.39564 11.0776i 0.296910 0.514264i
\(465\) −4.33624 13.1803i −0.201088 0.611221i
\(466\) 0.647551 + 1.12159i 0.0299972 + 0.0519567i
\(467\) 24.3303i 1.12587i 0.826500 + 0.562936i \(0.190328\pi\)
−0.826500 + 0.562936i \(0.809672\pi\)
\(468\) 0 0
\(469\) 1.74773 0.0807025
\(470\) −1.77328 + 0.583398i −0.0817951 + 0.0269101i
\(471\) −4.58258 7.93725i −0.211154 0.365729i
\(472\) −20.9276 12.0826i −0.963272 0.556146i
\(473\) 27.9989i 1.28739i
\(474\) −1.37055 + 2.37386i −0.0629515 + 0.109035i
\(475\) −6.96863 + 5.14181i −0.319743 + 0.235923i
\(476\) −14.2179 −0.651677
\(477\) 13.1334 + 7.58258i 0.601337 + 0.347182i
\(478\) 0.0754495 0.0435608i 0.00345098 0.00199242i
\(479\) −2.33193 4.03901i −0.106548 0.184547i 0.807821 0.589427i \(-0.200647\pi\)
−0.914370 + 0.404880i \(0.867313\pi\)
\(480\) −2.16515 + 10.3739i −0.0988252 + 0.473500i
\(481\) 0 0
\(482\) 0.791288i 0.0360422i
\(483\) 6.87386 3.96863i 0.312772 0.180579i
\(484\) 3.58258 + 6.20520i 0.162844 + 0.282055i
\(485\) −16.9891 + 19.0086i −0.771435 + 0.863134i
\(486\) 7.30960 0.331570
\(487\) −9.24773 5.33918i −0.419055 0.241941i 0.275618 0.961267i \(-0.411117\pi\)
−0.694673 + 0.719326i \(0.744451\pi\)
\(488\) 2.12614 + 1.22753i 0.0962457 + 0.0555675i
\(489\) −21.0707 −0.952848
\(490\) 2.72300 3.04668i 0.123013 0.137635i
\(491\) 9.70871 + 16.8160i 0.438148 + 0.758895i 0.997547 0.0700041i \(-0.0223012\pi\)
−0.559399 + 0.828899i \(0.688968\pi\)
\(492\) 4.10436 2.36965i 0.185039 0.106832i
\(493\) 21.0000i 0.945792i
\(494\) 0 0
\(495\) 2.41742 11.5826i 0.108655 0.520598i
\(496\) −8.66025 15.0000i −0.388857 0.673520i
\(497\) 10.5353 6.08258i 0.472574 0.272841i
\(498\) −2.37960 1.37386i −0.106632 0.0615643i
\(499\) 0.723000 0.0323659 0.0161830 0.999869i \(-0.494849\pi\)
0.0161830 + 0.999869i \(0.494849\pi\)
\(500\) 8.34734 + 18.2047i 0.373305 + 0.814139i
\(501\) −4.78698 + 8.29129i −0.213866 + 0.370427i
\(502\) 0.0754495i 0.00336747i
\(503\) 0.143025 + 0.0825757i 0.00637718 + 0.00368187i 0.503185 0.864179i \(-0.332161\pi\)
−0.496808 + 0.867860i \(0.665495\pi\)
\(504\) 3.00000 + 5.19615i 0.133631 + 0.231455i
\(505\) −19.1166 + 6.28926i −0.850678 + 0.279868i
\(506\) 5.53901 0.246239
\(507\) 0 0
\(508\) 31.7913i 1.41051i
\(509\) −4.23478 7.33485i −0.187703 0.325111i 0.756781 0.653669i \(-0.226771\pi\)
−0.944484 + 0.328557i \(0.893438\pi\)
\(510\) 1.46299 + 4.44685i 0.0647822 + 0.196910i
\(511\) 0 0
\(512\) 22.8981i 1.01196i
\(513\) −7.50000 4.33013i −0.331133 0.191180i
\(514\) 4.14938 7.18693i 0.183021 0.317002i
\(515\) −6.92820 1.44600i −0.305293 0.0637184i
\(516\) −9.47822 + 16.4168i −0.417255 + 0.722707i
\(517\) −4.18710 + 2.41742i −0.184149 + 0.106318i
\(518\) 5.43920 3.14033i 0.238985 0.137978i
\(519\) −16.5826 −0.727894
\(520\) 0 0
\(521\) 27.4955 1.20460 0.602299 0.798271i \(-0.294252\pi\)
0.602299 + 0.798271i \(0.294252\pi\)
\(522\) −3.62614 + 2.09355i −0.158712 + 0.0916322i
\(523\) −0.143025 + 0.0825757i −0.00625406 + 0.00361078i −0.503124 0.864214i \(-0.667816\pi\)
0.496870 + 0.867825i \(0.334483\pi\)
\(524\) 6.79129 11.7629i 0.296679 0.513863i
\(525\) −7.93725 3.46410i −0.346410 0.151186i
\(526\) −2.05583 + 3.56080i −0.0896383 + 0.155258i
\(527\) −24.6261 14.2179i −1.07273 0.619342i
\(528\) 7.38505i 0.321393i
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) 7.35799 2.42074i 0.319611 0.105150i
\(531\) −13.9518 24.1652i −0.605455 1.04868i
\(532\) 5.37386i 0.232987i
\(533\) 0 0
\(534\) 4.37386 0.189276
\(535\) −7.39517 22.4781i −0.319721 0.971814i
\(536\) −0.873864 1.51358i −0.0377452 0.0653765i
\(537\) 15.7315 + 9.08258i 0.678864 + 0.391942i
\(538\) 6.85275i 0.295443i
\(539\) 5.29150 9.16515i 0.227921 0.394771i
\(540\) −13.3459 + 14.9323i −0.574318 + 0.642586i
\(541\) 10.3923 0.446800 0.223400 0.974727i \(-0.428284\pi\)
0.223400 + 0.974727i \(0.428284\pi\)
\(542\) −3.42638 1.97822i −0.147175 0.0849718i
\(543\) 7.57575 4.37386i 0.325107 0.187700i
\(544\) 10.8591 + 18.8085i 0.465580 + 0.806409i
\(545\) 6.00000 28.7477i 0.257012 1.23142i
\(546\) 0 0
\(547\) 28.7477i 1.22916i 0.788853 + 0.614582i \(0.210675\pi\)
−0.788853 + 0.614582i \(0.789325\pi\)
\(548\) −16.2695 + 9.39320i −0.694999 + 0.401258i
\(549\) 1.41742 + 2.45505i 0.0604942 + 0.104779i
\(550\) −3.58822 4.86306i −0.153002 0.207362i
\(551\) 7.93725 0.338138
\(552\) −6.87386 3.96863i −0.292571 0.168916i
\(553\) −9.00000 5.19615i −0.382719 0.220963i
\(554\) −3.38865 −0.143970
\(555\) 13.2331 + 11.8273i 0.561715 + 0.502039i
\(556\) −19.4782 33.7373i −0.826061 1.43078i
\(557\) −6.70871 + 3.87328i −0.284257 + 0.164116i −0.635349 0.772225i \(-0.719144\pi\)
0.351092 + 0.936341i \(0.385810\pi\)
\(558\) 5.66970i 0.240017i
\(559\) 0 0
\(560\) −10.5826 2.20871i −0.447195 0.0933351i
\(561\) 6.06218 + 10.5000i 0.255945 + 0.443310i
\(562\) −1.44600 + 0.834849i −0.0609958 + 0.0352160i
\(563\) 7.79423 + 4.50000i 0.328488 + 0.189652i 0.655169 0.755482i \(-0.272597\pi\)
−0.326682 + 0.945134i \(0.605931\pi\)
\(564\) 3.27340 0.137835
\(565\) 11.0527 12.3665i 0.464989 0.520261i
\(566\) −6.33828 + 10.9782i −0.266418 + 0.461449i
\(567\) 1.73205i 0.0727393i
\(568\) −10.5353 6.08258i −0.442053 0.255219i
\(569\) −3.87386 6.70973i −0.162401 0.281286i 0.773328 0.634006i \(-0.218590\pi\)
−0.935729 + 0.352719i \(0.885257\pi\)
\(570\) −1.68075 + 0.552957i −0.0703989 + 0.0231608i
\(571\) 35.0780 1.46797 0.733985 0.679166i \(-0.237658\pi\)
0.733985 + 0.679166i \(0.237658\pi\)
\(572\) 0 0
\(573\) 16.5826i 0.692747i
\(574\) −1.04678 1.81307i −0.0436916 0.0756760i
\(575\) −22.7691 + 2.56275i −0.949537 + 0.106874i
\(576\) −3.41742 + 5.91915i −0.142393 + 0.246631i
\(577\) 6.92820i 0.288425i 0.989547 + 0.144212i \(0.0460649\pi\)
−0.989547 + 0.144212i \(0.953935\pi\)
\(578\) 1.58258 + 0.913701i 0.0658265 + 0.0380049i
\(579\) 7.43273 12.8739i 0.308894 0.535020i
\(580\) 3.75015 17.9681i 0.155717 0.746083i
\(581\) 5.20871 9.02175i 0.216094 0.374285i
\(582\) −4.51088 + 2.60436i −0.186982 + 0.107954i
\(583\) 17.3739 10.0308i 0.719552 0.415433i
\(584\) 0 0
\(585\) 0 0
\(586\) −8.28674 −0.342322
\(587\) 34.2042 19.7478i 1.41176 0.815078i 0.416203 0.909272i \(-0.363361\pi\)
0.995554 + 0.0941934i \(0.0300272\pi\)
\(588\) −6.20520 + 3.58258i −0.255898 + 0.147743i
\(589\) 5.37386 9.30780i 0.221426 0.383521i
\(590\) −13.9518 2.91190i −0.574385 0.119881i
\(591\) 7.33738 12.7087i 0.301819 0.522767i
\(592\) 19.1869 + 11.0776i 0.788578 + 0.455286i
\(593\) 21.1660i 0.869184i −0.900627 0.434592i \(-0.856893\pi\)
0.900627 0.434592i \(-0.143107\pi\)
\(594\) 3.02178 5.23388i 0.123985 0.214749i
\(595\) −16.8593 + 5.54661i −0.691163 + 0.227389i
\(596\) 14.9509 + 25.8956i 0.612411 + 1.06073i
\(597\) 10.5826i 0.433116i
\(598\) 0 0
\(599\) −15.4955 −0.633127 −0.316564 0.948571i \(-0.602529\pi\)
−0.316564 + 0.948571i \(0.602529\pi\)
\(600\) 0.968627 + 8.60591i 0.0395440 + 0.351335i
\(601\) −8.45644 14.6470i −0.344945 0.597463i 0.640398 0.768043i \(-0.278769\pi\)
−0.985344 + 0.170580i \(0.945436\pi\)
\(602\) 7.25198 + 4.18693i 0.295569 + 0.170647i
\(603\) 2.01810i 0.0821834i
\(604\) −8.66025 + 15.0000i −0.352381 + 0.610341i
\(605\) 6.66888 + 5.96038i 0.271128 + 0.242324i
\(606\) −4.11165 −0.167024
\(607\) −6.70973 3.87386i −0.272339 0.157235i 0.357611 0.933871i \(-0.383591\pi\)
−0.629950 + 0.776635i \(0.716925\pi\)
\(608\) −7.10895 + 4.10436i −0.288306 + 0.166454i
\(609\) 3.96863 + 6.87386i 0.160817 + 0.278543i
\(610\) 1.41742 + 0.295834i 0.0573898 + 0.0119780i
\(611\) 0 0
\(612\) 16.4174i 0.663635i
\(613\) −5.12614 + 2.95958i −0.207043 + 0.119536i −0.599936 0.800048i \(-0.704807\pi\)
0.392894 + 0.919584i \(0.371474\pi\)
\(614\) 5.53901 + 9.59386i 0.223536 + 0.387176i
\(615\) 3.94242 4.41105i 0.158974 0.177871i
\(616\) 7.93725 0.319801
\(617\) 12.0826 + 6.97588i 0.486426 + 0.280838i 0.723091 0.690753i \(-0.242721\pi\)
−0.236664 + 0.971591i \(0.576054\pi\)
\(618\) −1.25227 0.723000i −0.0503738 0.0290833i
\(619\) 29.7309 1.19499 0.597493 0.801874i \(-0.296164\pi\)
0.597493 + 0.801874i \(0.296164\pi\)
\(620\) −18.5316 16.5629i −0.744249 0.665180i
\(621\) −11.4564 19.8431i −0.459731 0.796278i
\(622\) −3.00000 + 1.73205i −0.120289 + 0.0694489i
\(623\) 16.5826i 0.664367i
\(624\) 0 0
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) 0.742901 + 1.28674i 0.0296923 + 0.0514286i
\(627\) −3.96863 + 2.29129i −0.158492 + 0.0915052i
\(628\) −14.2179 8.20871i −0.567356 0.327563i
\(629\) 36.3731 1.45029
\(630\) 2.63850 + 2.35819i 0.105120 + 0.0939524i
\(631\) −2.95958 + 5.12614i −0.117819 + 0.204068i −0.918903 0.394483i \(-0.870924\pi\)
0.801084 + 0.598552i \(0.204257\pi\)
\(632\) 10.3923i 0.413384i
\(633\) −0.143025 0.0825757i −0.00568475 0.00328209i
\(634\) 0.0435608 + 0.0754495i 0.00173002 + 0.00299648i
\(635\) −12.4022 37.6974i −0.492167 1.49598i
\(636\) −13.5826 −0.538584
\(637\) 0 0
\(638\) 5.53901i 0.219292i
\(639\) −7.02355 12.1652i −0.277847 0.481246i
\(640\) 7.71472 + 23.4494i 0.304951 + 0.926920i
\(641\) 9.08258 15.7315i 0.358740 0.621356i −0.629010 0.777397i \(-0.716540\pi\)
0.987751 + 0.156041i \(0.0498731\pi\)
\(642\) 4.83465i 0.190809i
\(643\) 18.8739 + 10.8968i 0.744313 + 0.429729i 0.823635 0.567120i \(-0.191942\pi\)
−0.0793227 + 0.996849i \(0.525276\pi\)
\(644\) 7.10895 12.3131i 0.280132 0.485203i
\(645\) −4.83465 + 23.1642i −0.190364 + 0.912090i
\(646\) −1.81307 + 3.14033i −0.0713342 + 0.123554i
\(647\) −23.3827 + 13.5000i −0.919268 + 0.530740i −0.883402 0.468617i \(-0.844753\pi\)
−0.0358667 + 0.999357i \(0.511419\pi\)
\(648\) 1.50000 0.866025i 0.0589256 0.0340207i
\(649\) −36.9129 −1.44896
\(650\) 0 0
\(651\) 10.7477 0.421237
\(652\) −32.6869 + 18.8718i −1.28012 + 0.739077i
\(653\) 37.0882 21.4129i 1.45137 0.837951i 0.452814 0.891605i \(-0.350420\pi\)
0.998560 + 0.0536545i \(0.0170870\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) 3.46410 16.5975i 0.135354 0.648518i
\(656\) 3.69253 6.39564i 0.144169 0.249708i
\(657\) 0 0
\(658\) 1.44600i 0.0563710i
\(659\) 15.2477 26.4098i 0.593967 1.02878i −0.399725 0.916635i \(-0.630894\pi\)
0.993692 0.112146i \(-0.0357724\pi\)
\(660\) 3.31186 + 10.0666i 0.128914 + 0.391842i
\(661\) −9.16478 15.8739i −0.356469 0.617422i 0.630900 0.775865i \(-0.282686\pi\)
−0.987368 + 0.158443i \(0.949353\pi\)
\(662\) 2.04356i 0.0794252i
\(663\) 0 0
\(664\) −10.4174 −0.404274
\(665\) −2.09642 6.37221i −0.0812957 0.247104i
\(666\) −3.62614 6.28065i −0.140510 0.243370i
\(667\) 18.1865 + 10.5000i 0.704185 + 0.406562i
\(668\) 17.1497i 0.663542i
\(669\) 4.33013 7.50000i 0.167412 0.289967i
\(670\) −0.768563 0.686911i −0.0296922 0.0265377i
\(671\) 3.75015 0.144773
\(672\) −7.10895 4.10436i −0.274234 0.158329i
\(673\) −20.9276 + 12.0826i −0.806701 + 0.465749i −0.845809 0.533486i \(-0.820882\pi\)
0.0391079 + 0.999235i \(0.487548\pi\)
\(674\) −7.02355 12.1652i −0.270537 0.468584i
\(675\) −10.0000 + 22.9129i −0.384900 + 0.881917i
\(676\) 0 0
\(677\) 2.83485i 0.108952i −0.998515 0.0544760i \(-0.982651\pi\)
0.998515 0.0544760i \(-0.0173489\pi\)
\(678\) 2.93466 1.69433i 0.112705 0.0650702i
\(679\) −9.87386 17.1020i −0.378924 0.656316i
\(680\) 13.2331 + 11.8273i 0.507468 + 0.453555i
\(681\) 0.818350 0.0313593
\(682\) 6.49545 + 3.75015i 0.248724 + 0.143601i
\(683\) 28.6652 + 16.5498i 1.09684 + 0.633262i 0.935390 0.353619i \(-0.115049\pi\)
0.161452 + 0.986881i \(0.448382\pi\)
\(684\) −6.20520 −0.237262
\(685\) −15.6276 + 17.4852i −0.597100 + 0.668076i
\(686\) 4.35208 + 7.53803i 0.166163 + 0.287803i
\(687\) 22.7477 13.1334i 0.867880 0.501071i
\(688\) 29.5390i 1.12616i
\(689\) 0 0
\(690\) −4.58258 0.956439i −0.174456 0.0364110i
\(691\) 9.88778 + 17.1261i 0.376149 + 0.651509i 0.990498 0.137525i \(-0.0439148\pi\)
−0.614349 + 0.789034i \(0.710581\pi\)
\(692\) −25.7246 + 14.8521i −0.977901 + 0.564591i
\(693\) 7.93725 + 4.58258i 0.301511 + 0.174078i
\(694\) 9.74475 0.369906
\(695\) −36.2582 32.4062i −1.37535 1.22924i
\(696\) 3.96863 6.87386i 0.150430 0.260553i
\(697\) 12.1244i 0.459243i
\(698\) −0.971326 0.560795i −0.0367652 0.0212264i
\(699\) −1.41742 2.45505i −0.0536119 0.0928586i
\(700\) −15.4157 + 1.73509i −0.582658 + 0.0655802i
\(701\) 21.1652 0.799397 0.399698 0.916647i \(-0.369115\pi\)
0.399698 + 0.916647i \(0.369115\pi\)
\(702\) 0 0
\(703\) 13.7477i 0.518505i
\(704\) 4.52083 + 7.83030i 0.170385 + 0.295116i
\(705\) 3.88153 1.27700i 0.146187 0.0480946i
\(706\) 1.56080 2.70338i 0.0587413 0.101743i
\(707\) 15.5885i 0.586264i
\(708\) 21.6434 + 12.4958i 0.813408 + 0.469621i
\(709\) 18.1865 31.5000i 0.683010 1.18301i −0.291048 0.956708i \(-0.594004\pi\)
0.974058 0.226299i \(-0.0726626\pi\)
\(710\) −7.02355 1.46590i −0.263589 0.0550143i
\(711\) −6.00000 + 10.3923i −0.225018 + 0.389742i
\(712\) 14.3609 8.29129i 0.538199 0.310729i
\(713\) 24.6261 14.2179i 0.922256 0.532465i
\(714\) −3.62614 −0.135705
\(715\) 0 0
\(716\) 32.5390 1.21604
\(717\) −0.165151 + 0.0953502i −0.00616769 + 0.00356092i
\(718\) 7.72665 4.46099i 0.288356 0.166482i
\(719\) 12.2477 21.2137i 0.456763 0.791137i −0.542025 0.840363i \(-0.682342\pi\)
0.998788 + 0.0492257i \(0.0156754\pi\)
\(720\) −2.55040 + 12.2197i −0.0950478 + 0.455402i
\(721\) 2.74110 4.74773i 0.102084 0.176815i
\(722\) 6.33030 + 3.65480i 0.235589 + 0.136018i
\(723\) 1.73205i 0.0644157i
\(724\) 7.83485 13.5704i 0.291180 0.504338i
\(725\) −2.56275 22.7691i −0.0951780 0.845623i
\(726\) 0.913701 + 1.58258i 0.0339106 + 0.0587349i
\(727\) 15.2523i 0.565675i 0.959168 + 0.282838i \(0.0912758\pi\)
−0.959168 + 0.282838i \(0.908724\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 24.2477 + 41.9983i 0.896835 + 1.55336i
\(732\) −2.19885 1.26951i −0.0812719 0.0469223i
\(733\) 22.8027i 0.842237i −0.907006 0.421119i \(-0.861638\pi\)
0.907006 0.421119i \(-0.138362\pi\)
\(734\) −0.399225 + 0.691478i −0.0147357 + 0.0255229i
\(735\) −5.96038 + 6.66888i −0.219852 + 0.245985i
\(736\) −21.7182 −0.800544
\(737\) −2.31203 1.33485i −0.0851646 0.0491698i
\(738\) −2.09355 + 1.20871i −0.0770647 + 0.0444933i
\(739\) 8.51723 + 14.7523i 0.313311 + 0.542671i 0.979077 0.203490i \(-0.0652283\pi\)
−0.665766 + 0.746161i \(0.731895\pi\)
\(740\) 31.1216 + 6.49545i 1.14405 + 0.238778i
\(741\) 0 0
\(742\) 6.00000i 0.220267i
\(743\) 4.96099 2.86423i 0.182001 0.105078i −0.406232 0.913770i \(-0.633157\pi\)
0.588232 + 0.808692i \(0.299824\pi\)
\(744\) −5.37386 9.30780i −0.197015 0.341241i
\(745\) 27.8306 + 24.8739i 1.01964 + 0.911310i
\(746\) −5.93905 −0.217444
\(747\) −10.4174 6.01450i −0.381154 0.220059i
\(748\) 18.8085 + 10.8591i 0.687708 + 0.397048i
\(749\) 18.3296 0.669748
\(750\) 2.12891 + 4.64293i 0.0777367 + 0.169536i
\(751\) 5.87386 + 10.1738i 0.214340 + 0.371248i 0.953068 0.302755i \(-0.0979065\pi\)
−0.738728 + 0.674004i \(0.764573\pi\)
\(752\) 4.41742 2.55040i 0.161087 0.0930036i
\(753\) 0.165151i 0.00601845i
\(754\) 0 0
\(755\) −4.41742 + 21.1652i −0.160767 + 0.770279i
\(756\) −7.75650 13.4347i −0.282101 0.488614i
\(757\) 8.44178 4.87386i 0.306822 0.177144i −0.338682 0.940901i \(-0.609981\pi\)
0.645503 + 0.763757i \(0.276648\pi\)
\(758\) −4.22483 2.43920i −0.153453 0.0885959i
\(759\) −12.1244 −0.440086
\(760\) −4.47028 + 5.00166i −0.162154 + 0.181429i
\(761\) −17.7297 + 30.7087i −0.642701 + 1.11319i 0.342127 + 0.939654i \(0.388853\pi\)
−0.984827 + 0.173536i \(0.944481\pi\)
\(762\) 8.10805i 0.293724i
\(763\) 19.7001 + 11.3739i 0.713192 + 0.411762i
\(764\) 14.8521 + 25.7246i 0.537330 + 0.930682i
\(765\) 6.40467 + 19.4674i 0.231561 + 0.703846i
\(766\) −10.7913 −0.389905
\(767\) 0 0
\(768\) 1.79129i 0.0646375i
\(769\) −7.79423 13.5000i −0.281067 0.486822i 0.690581 0.723255i \(-0.257355\pi\)
−0.971648 + 0.236433i \(0.924022\pi\)
\(770\) 4.44685 1.46299i 0.160253 0.0527224i
\(771\) −9.08258 + 15.7315i −0.327101 + 0.566556i
\(772\) 26.6283i 0.958374i
\(773\) 20.9174 + 12.0767i 0.752347 + 0.434368i 0.826541 0.562876i \(-0.190305\pi\)
−0.0741940 + 0.997244i \(0.523638\pi\)
\(774\) 4.83465 8.37386i 0.173778 0.300992i
\(775\) −28.4358 12.4104i −1.02144 0.445795i
\(776\) −9.87386 + 17.1020i −0.354451 + 0.613927i
\(777\) −11.9059 + 6.87386i −0.427121 + 0.246598i
\(778\) −1.25227 + 0.723000i −0.0448962 + 0.0259208i
\(779\) 4.58258 0.164188
\(780\) 0 0
\(781\) −18.5826 −0.664937
\(782\) −8.30852 + 4.79693i −0.297112 + 0.171538i
\(783\) 19.8431 11.4564i 0.709136 0.409420i
\(784\) −5.58258 + 9.66930i −0.199378 + 0.345332i
\(785\) −20.0616 4.18710i −0.716030 0.149444i
\(786\) 1.73205 3.00000i 0.0617802 0.107006i
\(787\) 14.1261 + 8.15573i 0.503542 + 0.290720i 0.730175 0.683260i \(-0.239438\pi\)
−0.226633 + 0.973980i \(0.572772\pi\)
\(788\) 26.2867i 0.936425i
\(789\) 4.50000 7.79423i 0.160204 0.277482i
\(790\) 1.91550 + 5.82229i 0.0681504 + 0.207148i
\(791\) 6.42368 + 11.1261i 0.228400 + 0.395600i
\(792\) 9.16515i 0.325669i
\(793\) 0 0
\(794\) −9.29583 −0.329897
\(795\) −16.1059 + 5.29875i −0.571218 + 0.187927i
\(796\) −9.47822 16.4168i −0.335947 0.581877i
\(797\) 38.1727 + 22.0390i 1.35215 + 0.780662i 0.988550 0.150895i \(-0.0482154\pi\)
0.363596 + 0.931557i \(0.381549\pi\)
\(798\) 1.37055i 0.0485170i
\(799\) 4.18710 7.25227i 0.148129 0.256567i
\(800\) 14.0692 + 19.0678i 0.497422 + 0.674149i
\(801\) 19.1479 0.676558
\(802\) 11.8006 + 6.81307i 0.416693 + 0.240578i
\(803\) 0 0
\(804\) 0.903750 + 1.56534i 0.0318728 + 0.0552053i
\(805\) 3.62614 17.3739i 0.127805 0.612348i
\(806\) 0 0
\(807\) 15.0000i 0.528025i
\(808\) −13.5000 + 7.79423i −0.474928 + 0.274200i
\(809\) −27.4129 47.4805i −0.963785 1.66933i −0.712843 0.701323i \(-0.752593\pi\)
−0.250942 0.968002i \(-0.580740\pi\)
\(810\) 0.680750 0.761669i 0.0239191 0.0267623i
\(811\) −50.5155 −1.77384 −0.886920 0.461923i \(-0.847160\pi\)
−0.886920 + 0.461923i \(0.847160\pi\)
\(812\) 12.3131 + 7.10895i 0.432104 + 0.249475i
\(813\) 7.50000 + 4.33013i 0.263036 + 0.151864i
\(814\) −9.59386 −0.336264
\(815\) −31.3973 + 35.1294i −1.09980 + 1.23053i
\(816\) −6.39564 11.0776i −0.223892 0.387793i
\(817\) −15.8739 + 9.16478i −0.555356 + 0.320635i
\(818\) 3.95644i 0.138334i
\(819\) 0 0
\(820\) 2.16515 10.3739i 0.0756104 0.362271i
\(821\) 9.06943 + 15.7087i 0.316525 + 0.548238i 0.979761 0.200173i \(-0.0641505\pi\)
−0.663235 + 0.748411i \(0.730817\pi\)
\(822\) −4.14938 + 2.39564i −0.144726 + 0.0835577i
\(823\) 27.2083 + 15.7087i 0.948421 + 0.547571i 0.892590 0.450869i \(-0.148886\pi\)
0.0558311 + 0.998440i \(0.482219\pi\)
\(824\) −5.48220 −0.190982
\(825\) 7.85425 + 10.6448i 0.273450 + 0.370603i
\(826\) 5.51993 9.56080i 0.192063 0.332663i
\(827\) 10.7737i 0.374638i 0.982299 + 0.187319i \(0.0599799\pi\)
−0.982299 + 0.187319i \(0.940020\pi\)
\(828\) −14.2179 8.20871i −0.494106 0.285272i
\(829\) 16.6652 + 28.8649i 0.578805 + 1.00252i 0.995617 + 0.0935264i \(0.0298139\pi\)
−0.416812 + 0.908993i \(0.636853\pi\)
\(830\) −5.83636 + 1.92013i −0.202583 + 0.0666487i
\(831\) 7.41742 0.257308
\(832\) 0 0
\(833\) 18.3303i 0.635107i
\(834\) −4.96773 8.60436i −0.172018 0.297944i
\(835\) 6.69034 + 20.3357i 0.231529 + 0.703747i
\(836\) −4.10436 + 7.10895i −0.141952 + 0.245868i
\(837\) 31.0260i 1.07242i
\(838\) −2.30852 1.33283i −0.0797466 0.0460417i
\(839\) 21.8413 37.8303i 0.754047 1.30605i −0.191800 0.981434i \(-0.561433\pi\)
0.945847 0.324613i \(-0.105234\pi\)
\(840\) −6.56670 1.37055i −0.226573 0.0472885i
\(841\) 4.00000 6.92820i 0.137931 0.238904i
\(842\) 2.16900 1.25227i 0.0747487 0.0431562i
\(843\) 3.16515 1.82740i 0.109014 0.0629390i
\(844\) −0.295834 −0.0101830
\(845\) 0 0
\(846\) −1.66970 −0.0574054
\(847\) −6.00000 + 3.46410i −0.206162 + 0.119028i
\(848\) −18.3296 + 10.5826i −0.629440 + 0.363407i
\(849\) 13.8739 24.0302i 0.476150 0.824716i
\(850\) 9.59386 + 4.18710i 0.329067 + 0.143616i
\(851\) −18.1865 + 31.5000i −0.623426 + 1.07981i
\(852\) 10.8956 + 6.29060i 0.373279 + 0.215513i
\(853\) 5.63310i 0.192874i −0.995339 0.0964369i \(-0.969255\pi\)
0.995339 0.0964369i \(-0.0307446\pi\)
\(854\) −0.560795 + 0.971326i −0.0191900 + 0.0332381i
\(855\) −7.35799 + 2.42074i −0.251638 + 0.0827875i
\(856\) −9.16478 15.8739i −0.313246 0.542557i
\(857\) 4.74773i 0.162179i 0.996707 + 0.0810896i \(0.0258400\pi\)
−0.996707 + 0.0810896i \(0.974160\pi\)
\(858\) 0 0
\(859\) 44.2432 1.50956 0.754779 0.655979i \(-0.227744\pi\)
0.754779 + 0.655979i \(0.227744\pi\)
\(860\) 13.2469 + 40.2648i 0.451715 + 1.37302i
\(861\) 2.29129 + 3.96863i 0.0780869 + 0.135250i
\(862\) 3.35093 + 1.93466i 0.114133 + 0.0658947i
\(863\) 13.6657i 0.465186i −0.972574 0.232593i \(-0.925279\pi\)
0.972574 0.232593i \(-0.0747210\pi\)
\(864\) −11.8483 + 20.5218i −0.403086 + 0.698165i
\(865\) −24.7096 + 27.6468i −0.840152 + 0.940019i
\(866\) −4.45325 −0.151328
\(867\) −3.46410 2.00000i −0.117647 0.0679236i
\(868\) 16.6730 9.62614i 0.565917 0.326732i
\(869\) 7.93725 + 13.7477i 0.269253 + 0.466360i
\(870\) 0.956439 4.58258i 0.0324263 0.155364i
\(871\) 0 0
\(872\) 22.7477i 0.770335i
\(873\) −19.7477 + 11.4014i −0.668359 + 0.385877i
\(874\) −1.81307 3.14033i −0.0613279 0.106223i
\(875\) −17.6027 + 8.07130i −0.595079 + 0.272860i
\(876\) 0 0
\(877\) 6.87386 + 3.96863i 0.232114 + 0.134011i 0.611547 0.791208i \(-0.290548\pi\)
−0.379433 + 0.925219i \(0.623881\pi\)
\(878\) 5.73504 + 3.31113i 0.193548 + 0.111745i
\(879\) 18.1389 0.611809
\(880\) 12.3125 + 11.0044i 0.415054 + 0.370959i
\(881\) 18.2477 + 31.6060i 0.614782 + 1.06483i 0.990423 + 0.138068i \(0.0440892\pi\)
−0.375641 + 0.926765i \(0.622578\pi\)
\(882\) 3.16515 1.82740i 0.106576 0.0615318i
\(883\) 36.2432i 1.21968i 0.792524 + 0.609840i \(0.208766\pi\)
−0.792524 + 0.609840i \(0.791234\pi\)
\(884\) 0 0
\(885\) 30.5390 + 6.37386i 1.02656 + 0.214255i
\(886\) −4.54860 7.87841i −0.152813 0.264680i
\(887\) 47.1944 27.2477i 1.58463 0.914889i 0.590465 0.807064i \(-0.298945\pi\)
0.994170 0.107826i \(-0.0343888\pi\)
\(888\) 11.9059 + 6.87386i 0.399535 + 0.230672i
\(889\) 30.7400 1.03099
\(890\) 6.51747 7.29219i 0.218466 0.244435i
\(891\) 1.32288 2.29129i 0.0443180 0.0767610i
\(892\) 15.5130i 0.519414i
\(893\) 2.74110 + 1.58258i 0.0917275 + 0.0529589i
\(894\) 3.81307 + 6.60443i 0.127528 + 0.220885i
\(895\) 38.5840 12.6939i 1.28972 0.424311i
\(896\) −19.1216 −0.638808
\(897\) 0 0
\(898\) 5.03447i 0.168002i
\(899\) 14.2179 + 24.6261i 0.474194 + 0.821328i
\(900\) 2.00351 + 17.8005i 0.0667836 + 0.593349i
\(901\) −17.3739 + 30.0924i −0.578807 + 1.00252i
\(902\) 3.19795i 0.106480i
\(903\) −15.8739 9.16478i −0.528249 0.304985i
\(904\) 6.42368 11.1261i 0.213648 0.370050i
\(905\) 3.99640 19.1479i 0.132845 0.636498i
\(906\) −2.20871 + 3.82560i −0.0733795 + 0.127097i
\(907\) 5.41463 3.12614i 0.179790 0.103802i −0.407404 0.913248i \(-0.633566\pi\)
0.587194 + 0.809446i \(0.300233\pi\)
\(908\) 1.26951 0.732950i 0.0421301 0.0243238i
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) −7.91288 −0.262165 −0.131083 0.991371i \(-0.541845\pi\)
−0.131083 + 0.991371i \(0.541845\pi\)
\(912\) 4.18693 2.41733i 0.138643 0.0800457i
\(913\) −13.7810 + 7.95644i −0.456083 + 0.263320i
\(914\) 0.395644 0.685275i 0.0130867 0.0226669i
\(915\) −3.10260 0.647551i −0.102569 0.0214074i
\(916\) 23.5257 40.7477i 0.777311 1.34634i
\(917\) 11.3739 + 6.56670i 0.375598 + 0.216852i
\(918\) 10.4678i 0.345487i
\(919\) 27.0826 46.9084i 0.893372 1.54737i 0.0575648 0.998342i \(-0.481666\pi\)
0.835807 0.549023i \(-0.185000\pi\)
\(920\) −16.8593 + 5.54661i −0.555834 + 0.182866i
\(921\) −12.1244 21.0000i −0.399511 0.691974i
\(922\) 16.3739i 0.539244i
\(923\) 0 0
\(924\) −8.20871 −0.270047
\(925\) 39.4373 4.43881i 1.29669 0.145947i
\(926\) 9.00000 + 15.5885i 0.295758 + 0.512268i
\(927\) −5.48220 3.16515i −0.180059 0.103957i
\(928\) 21.7182i 0.712935i
\(929\) −13.1811 + 22.8303i −0.432457 + 0.749038i −0.997084 0.0763082i \(-0.975687\pi\)
0.564627 + 0.825346i \(0.309020\pi\)
\(930\) −4.72631 4.22419i −0.154982 0.138517i
\(931\) −6.92820 −0.227063
\(932\) −4.39770 2.53901i −0.144052 0.0831682i
\(933\) 6.56670 3.79129i 0.214984 0.124121i
\(934\) 5.55765 + 9.62614i 0.181852 + 0.314977i
\(935\) 26.5390 + 5.53901i 0.867919 + 0.181145i
\(936\) 0 0
\(937\) 31.4955i 1.02891i 0.857517 + 0.514456i \(0.172006\pi\)
−0.857517 + 0.514456i \(0.827994\pi\)
\(938\) 0.691478 0.399225i 0.0225775 0.0130352i
\(939\) −1.62614 2.81655i −0.0530670 0.0919147i
\(940\) 4.87768 5.45748i 0.159092 0.178003i
\(941\) −26.4575 −0.862490 −0.431245 0.902235i \(-0.641926\pi\)
−0.431245 + 0.902235i \(0.641926\pi\)
\(942\) −3.62614 2.09355i −0.118146 0.0682116i
\(943\) 10.5000 + 6.06218i 0.341927 + 0.197412i
\(944\) 38.9434 1.26750
\(945\) −14.4385 12.9046i −0.469686 0.419787i
\(946\) −6.39564 11.0776i −0.207940 0.360163i
\(947\) −12.4129 + 7.16658i −0.403364 + 0.232883i −0.687935 0.725773i \(-0.741482\pi\)
0.284570 + 0.958655i \(0.408149\pi\)
\(948\) 10.7477i 0.349070i
\(949\) 0 0
\(950\) −1.58258 + 3.62614i −0.0513455 + 0.117647i
\(951\) −0.0953502 0.165151i −0.00309194 0.00535540i
\(952\) −11.9059 + 6.87386i −0.385872 + 0.222783i
\(953\) 6.99578 + 4.03901i 0.226616 + 0.130837i 0.609010 0.793163i \(-0.291567\pi\)
−0.382394 + 0.923999i \(0.624900\pi\)
\(954\) 6.92820 0.224309
\(955\) 27.6468 + 24.7096i 0.894629 + 0.799584i
\(956\) −0.170800 + 0.295834i −0.00552406 + 0.00956794i
\(957\) 12.1244i 0.391925i
\(958\) −1.84522 1.06534i −0.0596165 0.0344196i
\(959\) −9.08258 15.7315i −0.293292 0.507996i
\(960\) −2.38812 7.25885i −0.0770762 0.234278i
\(961\) 7.50455 0.242082
\(962\) 0 0
\(963\) 21.1652i 0.682037i
\(964\) −1.55130 2.68693i −0.0499640 0.0865402i
\(965\) −10.3881 31.5753i −0.334404 1.01644i
\(966\) 1.81307 3.14033i 0.0583345 0.101038i
\(967\) 37.3821i 1.20213i 0.799201 + 0.601064i \(0.205256\pi\)
−0.799201 + 0.601064i \(0.794744\pi\)
\(968\) 6.00000 + 3.46410i 0.192847 + 0.111340i
\(969\) 3.96863 6.87386i 0.127491 0.220820i
\(970\) −2.37960 + 11.4014i −0.0764044 + 0.366075i
\(971\) 9.24773 16.0175i 0.296774 0.514027i −0.678622 0.734487i \(-0.737423\pi\)
0.975396 + 0.220460i \(0.0707560\pi\)
\(972\) −24.8208 + 14.3303i −0.796128 + 0.459645i
\(973\) 32.6216 18.8341i 1.04580 0.603793i
\(974\) −4.87841 −0.156314
\(975\) 0 0
\(976\) −3.95644 −0.126643
\(977\) −30.5780 + 17.6542i −0.978278 + 0.564809i −0.901750 0.432258i \(-0.857717\pi\)
−0.0765281 + 0.997067i \(0.524383\pi\)
\(978\) −8.33648 + 4.81307i −0.266571 + 0.153905i
\(979\) 12.6652 21.9367i 0.404780 0.701100i
\(980\) −3.27340 + 15.6838i −0.104565 + 0.501001i
\(981\) 13.1334 22.7477i 0.419317 0.726279i
\(982\) 7.68239 + 4.43543i 0.245155 + 0.141540i
\(983\) 55.0840i 1.75691i 0.477827 + 0.878454i \(0.341424\pi\)
−0.477827 + 0.878454i \(0.658576\pi\)
\(984\) 2.29129 3.96863i 0.0730436 0.126515i
\(985\) −10.2548 31.1702i −0.326746 0.993165i
\(986\) −4.79693 8.30852i −0.152765 0.264597i
\(987\) 3.16515i 0.100748i
\(988\) 0 0
\(989\) −48.4955 −1.54207
\(990\) −1.68931 5.13478i −0.0536899 0.163194i
\(991\) 6.50000 + 11.2583i 0.206479 + 0.357633i 0.950603 0.310409i \(-0.100466\pi\)
−0.744124 + 0.668042i \(0.767133\pi\)
\(992\) −25.4684 14.7042i −0.808621 0.466858i
\(993\) 4.47315i 0.141951i
\(994\) 2.77883 4.81307i 0.0881390 0.152661i
\(995\) −17.6435 15.7690i −0.559336 0.499912i
\(996\) 10.7737 0.341378
\(997\) −0.143025 0.0825757i −0.00452966 0.00261520i 0.497733 0.867330i \(-0.334166\pi\)
−0.502263 + 0.864715i \(0.667499\pi\)
\(998\) 0.286051 0.165151i 0.00905477 0.00522778i
\(999\) 19.8431 + 34.3693i 0.627809 + 1.08740i
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 845.2.n.c.484.3 8
5.4 even 2 845.2.n.d.484.2 8
13.2 odd 12 845.2.d.c.844.5 8
13.3 even 3 845.2.b.f.339.5 8
13.4 even 6 inner 845.2.n.c.529.4 8
13.5 odd 4 65.2.l.a.49.2 yes 8
13.6 odd 12 845.2.l.c.654.2 8
13.7 odd 12 65.2.l.a.4.3 yes 8
13.8 odd 4 845.2.l.c.699.3 8
13.9 even 3 845.2.n.d.529.2 8
13.10 even 6 845.2.b.f.339.3 8
13.11 odd 12 845.2.d.c.844.3 8
13.12 even 2 845.2.n.d.484.1 8
39.5 even 4 585.2.bf.a.244.3 8
39.20 even 12 585.2.bf.a.199.2 8
52.7 even 12 1040.2.df.b.849.1 8
52.31 even 4 1040.2.df.b.49.4 8
65.3 odd 12 4225.2.a.bk.1.3 4
65.4 even 6 845.2.n.d.529.1 8
65.7 even 12 325.2.n.b.251.2 4
65.9 even 6 inner 845.2.n.c.529.3 8
65.18 even 4 325.2.n.c.101.1 4
65.19 odd 12 845.2.l.c.654.3 8
65.23 odd 12 4225.2.a.bk.1.2 4
65.24 odd 12 845.2.d.c.844.6 8
65.29 even 6 845.2.b.f.339.4 8
65.33 even 12 325.2.n.c.251.1 4
65.34 odd 4 845.2.l.c.699.2 8
65.42 odd 12 4225.2.a.bj.1.2 4
65.44 odd 4 65.2.l.a.49.3 yes 8
65.49 even 6 845.2.b.f.339.6 8
65.54 odd 12 845.2.d.c.844.4 8
65.57 even 4 325.2.n.b.101.2 4
65.59 odd 12 65.2.l.a.4.2 8
65.62 odd 12 4225.2.a.bj.1.3 4
65.64 even 2 inner 845.2.n.c.484.4 8
195.44 even 4 585.2.bf.a.244.2 8
195.59 even 12 585.2.bf.a.199.3 8
260.59 even 12 1040.2.df.b.849.4 8
260.239 even 4 1040.2.df.b.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.l.a.4.2 8 65.59 odd 12
65.2.l.a.4.3 yes 8 13.7 odd 12
65.2.l.a.49.2 yes 8 13.5 odd 4
65.2.l.a.49.3 yes 8 65.44 odd 4
325.2.n.b.101.2 4 65.57 even 4
325.2.n.b.251.2 4 65.7 even 12
325.2.n.c.101.1 4 65.18 even 4
325.2.n.c.251.1 4 65.33 even 12
585.2.bf.a.199.2 8 39.20 even 12
585.2.bf.a.199.3 8 195.59 even 12
585.2.bf.a.244.2 8 195.44 even 4
585.2.bf.a.244.3 8 39.5 even 4
845.2.b.f.339.3 8 13.10 even 6
845.2.b.f.339.4 8 65.29 even 6
845.2.b.f.339.5 8 13.3 even 3
845.2.b.f.339.6 8 65.49 even 6
845.2.d.c.844.3 8 13.11 odd 12
845.2.d.c.844.4 8 65.54 odd 12
845.2.d.c.844.5 8 13.2 odd 12
845.2.d.c.844.6 8 65.24 odd 12
845.2.l.c.654.2 8 13.6 odd 12
845.2.l.c.654.3 8 65.19 odd 12
845.2.l.c.699.2 8 65.34 odd 4
845.2.l.c.699.3 8 13.8 odd 4
845.2.n.c.484.3 8 1.1 even 1 trivial
845.2.n.c.484.4 8 65.64 even 2 inner
845.2.n.c.529.3 8 65.9 even 6 inner
845.2.n.c.529.4 8 13.4 even 6 inner
845.2.n.d.484.1 8 13.12 even 2
845.2.n.d.484.2 8 5.4 even 2
845.2.n.d.529.1 8 65.4 even 6
845.2.n.d.529.2 8 13.9 even 3
1040.2.df.b.49.1 8 260.239 even 4
1040.2.df.b.49.4 8 52.31 even 4
1040.2.df.b.849.1 8 52.7 even 12
1040.2.df.b.849.4 8 260.59 even 12
4225.2.a.bj.1.2 4 65.42 odd 12
4225.2.a.bj.1.3 4 65.62 odd 12
4225.2.a.bk.1.2 4 65.23 odd 12
4225.2.a.bk.1.3 4 65.3 odd 12