Properties

Label 78.3.f.a.31.2
Level $78$
Weight $3$
Character 78.31
Analytic conductor $2.125$
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] = [78,3,Mod(31,78)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(78, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("78.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.f (of order \(4\), 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: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.31
Dual form 78.3.f.a.73.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(1.26795 - 1.26795i) q^{5} +(1.73205 - 1.73205i) q^{6} +(0.732051 + 0.732051i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(1.26795 - 1.26795i) q^{5} +(1.73205 - 1.73205i) q^{6} +(0.732051 + 0.732051i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -2.53590i q^{10} +(-1.73205 - 1.73205i) q^{11} -3.46410i q^{12} +(-3.92820 + 12.3923i) q^{13} +1.46410 q^{14} +(2.19615 - 2.19615i) q^{15} -4.00000 q^{16} -5.32051i q^{17} +(3.00000 - 3.00000i) q^{18} +(-14.7321 + 14.7321i) q^{19} +(-2.53590 - 2.53590i) q^{20} +(1.26795 + 1.26795i) q^{21} -3.46410 q^{22} -5.32051i q^{23} +(-3.46410 - 3.46410i) q^{24} +21.7846i q^{25} +(8.46410 + 16.3205i) q^{26} +5.19615 q^{27} +(1.46410 - 1.46410i) q^{28} +4.14359 q^{29} -4.39230i q^{30} +(-24.9808 + 24.9808i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-3.00000 - 3.00000i) q^{33} +(-5.32051 - 5.32051i) q^{34} +1.85641 q^{35} -6.00000i q^{36} +(-3.14359 - 3.14359i) q^{37} +29.4641i q^{38} +(-6.80385 + 21.4641i) q^{39} -5.07180 q^{40} +(44.4449 - 44.4449i) q^{41} +2.53590 q^{42} -37.1769i q^{43} +(-3.46410 + 3.46410i) q^{44} +(3.80385 - 3.80385i) q^{45} +(-5.32051 - 5.32051i) q^{46} +(-30.8038 - 30.8038i) q^{47} -6.92820 q^{48} -47.9282i q^{49} +(21.7846 + 21.7846i) q^{50} -9.21539i q^{51} +(24.7846 + 7.85641i) q^{52} +57.7128 q^{53} +(5.19615 - 5.19615i) q^{54} -4.39230 q^{55} -2.92820i q^{56} +(-25.5167 + 25.5167i) q^{57} +(4.14359 - 4.14359i) q^{58} +(-66.6218 - 66.6218i) q^{59} +(-4.39230 - 4.39230i) q^{60} +103.426 q^{61} +49.9615i q^{62} +(2.19615 + 2.19615i) q^{63} +8.00000i q^{64} +(10.7321 + 20.6936i) q^{65} -6.00000 q^{66} +(46.6936 - 46.6936i) q^{67} -10.6410 q^{68} -9.21539i q^{69} +(1.85641 - 1.85641i) q^{70} +(-26.9090 + 26.9090i) q^{71} +(-6.00000 - 6.00000i) q^{72} +(5.67949 + 5.67949i) q^{73} -6.28719 q^{74} +37.7321i q^{75} +(29.4641 + 29.4641i) q^{76} -2.53590i q^{77} +(14.6603 + 28.2679i) q^{78} +4.21024 q^{79} +(-5.07180 + 5.07180i) q^{80} +9.00000 q^{81} -88.8897i q^{82} +(-109.799 + 109.799i) q^{83} +(2.53590 - 2.53590i) q^{84} +(-6.74613 - 6.74613i) q^{85} +(-37.1769 - 37.1769i) q^{86} +7.17691 q^{87} +6.92820i q^{88} +(-19.5167 - 19.5167i) q^{89} -7.60770i q^{90} +(-11.9474 + 6.19615i) q^{91} -10.6410 q^{92} +(-43.2679 + 43.2679i) q^{93} -61.6077 q^{94} +37.3590i q^{95} +(-6.92820 + 6.92820i) q^{96} +(4.03332 - 4.03332i) q^{97} +(-47.9282 - 47.9282i) q^{98} +(-5.19615 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{13} - 8 q^{14} - 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} - 24 q^{20} + 12 q^{21} + 20 q^{26} - 8 q^{28} + 72 q^{29} + 4 q^{31} - 16 q^{32} - 12 q^{33} + 48 q^{34} - 48 q^{35} - 68 q^{37} - 48 q^{39} - 48 q^{40} + 60 q^{41} + 24 q^{42} + 36 q^{45} + 48 q^{46} - 144 q^{47} + 4 q^{50} + 16 q^{52} + 120 q^{53} + 24 q^{55} - 12 q^{57} + 72 q^{58} - 24 q^{59} + 24 q^{60} + 192 q^{61} - 12 q^{63} + 36 q^{65} - 24 q^{66} - 28 q^{67} + 96 q^{68} - 48 q^{70} + 24 q^{71} - 24 q^{72} + 92 q^{73} - 136 q^{74} + 104 q^{76} + 24 q^{78} - 288 q^{79} - 48 q^{80} + 36 q^{81} - 72 q^{83} + 24 q^{84} + 264 q^{85} - 24 q^{86} - 96 q^{87} + 12 q^{89} - 124 q^{91} + 96 q^{92} - 180 q^{93} - 288 q^{94} - 164 q^{97} - 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) 1.73205 0.577350
\(4\) 2.00000i 0.500000i
\(5\) 1.26795 1.26795i 0.253590 0.253590i −0.568851 0.822441i \(-0.692612\pi\)
0.822441 + 0.568851i \(0.192612\pi\)
\(6\) 1.73205 1.73205i 0.288675 0.288675i
\(7\) 0.732051 + 0.732051i 0.104579 + 0.104579i 0.757460 0.652881i \(-0.226440\pi\)
−0.652881 + 0.757460i \(0.726440\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 2.53590i 0.253590i
\(11\) −1.73205 1.73205i −0.157459 0.157459i 0.623981 0.781440i \(-0.285514\pi\)
−0.781440 + 0.623981i \(0.785514\pi\)
\(12\) 3.46410i 0.288675i
\(13\) −3.92820 + 12.3923i −0.302169 + 0.953254i
\(14\) 1.46410 0.104579
\(15\) 2.19615 2.19615i 0.146410 0.146410i
\(16\) −4.00000 −0.250000
\(17\) 5.32051i 0.312971i −0.987680 0.156486i \(-0.949984\pi\)
0.987680 0.156486i \(-0.0500165\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) −14.7321 + 14.7321i −0.775371 + 0.775371i −0.979040 0.203669i \(-0.934713\pi\)
0.203669 + 0.979040i \(0.434713\pi\)
\(20\) −2.53590 2.53590i −0.126795 0.126795i
\(21\) 1.26795 + 1.26795i 0.0603785 + 0.0603785i
\(22\) −3.46410 −0.157459
\(23\) 5.32051i 0.231326i −0.993288 0.115663i \(-0.963101\pi\)
0.993288 0.115663i \(-0.0368993\pi\)
\(24\) −3.46410 3.46410i −0.144338 0.144338i
\(25\) 21.7846i 0.871384i
\(26\) 8.46410 + 16.3205i 0.325542 + 0.627712i
\(27\) 5.19615 0.192450
\(28\) 1.46410 1.46410i 0.0522893 0.0522893i
\(29\) 4.14359 0.142883 0.0714413 0.997445i \(-0.477240\pi\)
0.0714413 + 0.997445i \(0.477240\pi\)
\(30\) 4.39230i 0.146410i
\(31\) −24.9808 + 24.9808i −0.805831 + 0.805831i −0.984000 0.178169i \(-0.942983\pi\)
0.178169 + 0.984000i \(0.442983\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) −3.00000 3.00000i −0.0909091 0.0909091i
\(34\) −5.32051 5.32051i −0.156486 0.156486i
\(35\) 1.85641 0.0530402
\(36\) 6.00000i 0.166667i
\(37\) −3.14359 3.14359i −0.0849620 0.0849620i 0.663349 0.748311i \(-0.269135\pi\)
−0.748311 + 0.663349i \(0.769135\pi\)
\(38\) 29.4641i 0.775371i
\(39\) −6.80385 + 21.4641i −0.174458 + 0.550362i
\(40\) −5.07180 −0.126795
\(41\) 44.4449 44.4449i 1.08402 1.08402i 0.0878910 0.996130i \(-0.471987\pi\)
0.996130 0.0878910i \(-0.0280127\pi\)
\(42\) 2.53590 0.0603785
\(43\) 37.1769i 0.864579i −0.901735 0.432290i \(-0.857706\pi\)
0.901735 0.432290i \(-0.142294\pi\)
\(44\) −3.46410 + 3.46410i −0.0787296 + 0.0787296i
\(45\) 3.80385 3.80385i 0.0845299 0.0845299i
\(46\) −5.32051 5.32051i −0.115663 0.115663i
\(47\) −30.8038 30.8038i −0.655401 0.655401i 0.298887 0.954288i \(-0.403385\pi\)
−0.954288 + 0.298887i \(0.903385\pi\)
\(48\) −6.92820 −0.144338
\(49\) 47.9282i 0.978127i
\(50\) 21.7846 + 21.7846i 0.435692 + 0.435692i
\(51\) 9.21539i 0.180694i
\(52\) 24.7846 + 7.85641i 0.476627 + 0.151085i
\(53\) 57.7128 1.08892 0.544460 0.838786i \(-0.316734\pi\)
0.544460 + 0.838786i \(0.316734\pi\)
\(54\) 5.19615 5.19615i 0.0962250 0.0962250i
\(55\) −4.39230 −0.0798601
\(56\) 2.92820i 0.0522893i
\(57\) −25.5167 + 25.5167i −0.447661 + 0.447661i
\(58\) 4.14359 4.14359i 0.0714413 0.0714413i
\(59\) −66.6218 66.6218i −1.12918 1.12918i −0.990310 0.138872i \(-0.955652\pi\)
−0.138872 0.990310i \(-0.544348\pi\)
\(60\) −4.39230 4.39230i −0.0732051 0.0732051i
\(61\) 103.426 1.69550 0.847751 0.530394i \(-0.177956\pi\)
0.847751 + 0.530394i \(0.177956\pi\)
\(62\) 49.9615i 0.805831i
\(63\) 2.19615 + 2.19615i 0.0348596 + 0.0348596i
\(64\) 8.00000i 0.125000i
\(65\) 10.7321 + 20.6936i 0.165108 + 0.318363i
\(66\) −6.00000 −0.0909091
\(67\) 46.6936 46.6936i 0.696919 0.696919i −0.266826 0.963745i \(-0.585975\pi\)
0.963745 + 0.266826i \(0.0859748\pi\)
\(68\) −10.6410 −0.156486
\(69\) 9.21539i 0.133556i
\(70\) 1.85641 1.85641i 0.0265201 0.0265201i
\(71\) −26.9090 + 26.9090i −0.379000 + 0.379000i −0.870741 0.491742i \(-0.836360\pi\)
0.491742 + 0.870741i \(0.336360\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 5.67949 + 5.67949i 0.0778013 + 0.0778013i 0.744937 0.667135i \(-0.232480\pi\)
−0.667135 + 0.744937i \(0.732480\pi\)
\(74\) −6.28719 −0.0849620
\(75\) 37.7321i 0.503094i
\(76\) 29.4641 + 29.4641i 0.387686 + 0.387686i
\(77\) 2.53590i 0.0329337i
\(78\) 14.6603 + 28.2679i 0.187952 + 0.362410i
\(79\) 4.21024 0.0532941 0.0266471 0.999645i \(-0.491517\pi\)
0.0266471 + 0.999645i \(0.491517\pi\)
\(80\) −5.07180 + 5.07180i −0.0633975 + 0.0633975i
\(81\) 9.00000 0.111111
\(82\) 88.8897i 1.08402i
\(83\) −109.799 + 109.799i −1.32288 + 1.32288i −0.411438 + 0.911438i \(0.634973\pi\)
−0.911438 + 0.411438i \(0.865027\pi\)
\(84\) 2.53590 2.53590i 0.0301893 0.0301893i
\(85\) −6.74613 6.74613i −0.0793663 0.0793663i
\(86\) −37.1769 37.1769i −0.432290 0.432290i
\(87\) 7.17691 0.0824933
\(88\) 6.92820i 0.0787296i
\(89\) −19.5167 19.5167i −0.219288 0.219288i 0.588910 0.808198i \(-0.299557\pi\)
−0.808198 + 0.588910i \(0.799557\pi\)
\(90\) 7.60770i 0.0845299i
\(91\) −11.9474 + 6.19615i −0.131291 + 0.0680896i
\(92\) −10.6410 −0.115663
\(93\) −43.2679 + 43.2679i −0.465247 + 0.465247i
\(94\) −61.6077 −0.655401
\(95\) 37.3590i 0.393252i
\(96\) −6.92820 + 6.92820i −0.0721688 + 0.0721688i
\(97\) 4.03332 4.03332i 0.0415806 0.0415806i −0.686011 0.727591i \(-0.740640\pi\)
0.727591 + 0.686011i \(0.240640\pi\)
\(98\) −47.9282 47.9282i −0.489063 0.489063i
\(99\) −5.19615 5.19615i −0.0524864 0.0524864i
\(100\) 43.5692 0.435692
\(101\) 111.464i 1.10360i 0.833975 + 0.551802i \(0.186060\pi\)
−0.833975 + 0.551802i \(0.813940\pi\)
\(102\) −9.21539 9.21539i −0.0903470 0.0903470i
\(103\) 71.3205i 0.692432i 0.938155 + 0.346216i \(0.112534\pi\)
−0.938155 + 0.346216i \(0.887466\pi\)
\(104\) 32.6410 16.9282i 0.313856 0.162771i
\(105\) 3.21539 0.0306228
\(106\) 57.7128 57.7128i 0.544460 0.544460i
\(107\) −116.536 −1.08912 −0.544560 0.838722i \(-0.683303\pi\)
−0.544560 + 0.838722i \(0.683303\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −109.315 + 109.315i −1.00289 + 1.00289i −0.00289735 + 0.999996i \(0.500922\pi\)
−0.999996 + 0.00289735i \(0.999078\pi\)
\(110\) −4.39230 + 4.39230i −0.0399300 + 0.0399300i
\(111\) −5.44486 5.44486i −0.0490528 0.0490528i
\(112\) −2.92820 2.92820i −0.0261447 0.0261447i
\(113\) 148.277 1.31218 0.656092 0.754681i \(-0.272208\pi\)
0.656092 + 0.754681i \(0.272208\pi\)
\(114\) 51.0333i 0.447661i
\(115\) −6.74613 6.74613i −0.0586620 0.0586620i
\(116\) 8.28719i 0.0714413i
\(117\) −11.7846 + 37.1769i −0.100723 + 0.317751i
\(118\) −133.244 −1.12918
\(119\) 3.89488 3.89488i 0.0327301 0.0327301i
\(120\) −8.78461 −0.0732051
\(121\) 115.000i 0.950413i
\(122\) 103.426 103.426i 0.847751 0.847751i
\(123\) 76.9808 76.9808i 0.625860 0.625860i
\(124\) 49.9615 + 49.9615i 0.402916 + 0.402916i
\(125\) 59.3205 + 59.3205i 0.474564 + 0.474564i
\(126\) 4.39230 0.0348596
\(127\) 70.0385i 0.551484i −0.961232 0.275742i \(-0.911076\pi\)
0.961232 0.275742i \(-0.0889236\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 64.3923i 0.499165i
\(130\) 31.4256 + 9.96152i 0.241736 + 0.0766271i
\(131\) 238.890 1.82359 0.911793 0.410650i \(-0.134698\pi\)
0.911793 + 0.410650i \(0.134698\pi\)
\(132\) −6.00000 + 6.00000i −0.0454545 + 0.0454545i
\(133\) −21.5692 −0.162175
\(134\) 93.3872i 0.696919i
\(135\) 6.58846 6.58846i 0.0488034 0.0488034i
\(136\) −10.6410 + 10.6410i −0.0782428 + 0.0782428i
\(137\) −91.9474 91.9474i −0.671149 0.671149i 0.286832 0.957981i \(-0.407398\pi\)
−0.957981 + 0.286832i \(0.907398\pi\)
\(138\) −9.21539 9.21539i −0.0667782 0.0667782i
\(139\) 139.138 1.00100 0.500498 0.865738i \(-0.333150\pi\)
0.500498 + 0.865738i \(0.333150\pi\)
\(140\) 3.71281i 0.0265201i
\(141\) −53.3538 53.3538i −0.378396 0.378396i
\(142\) 53.8179i 0.379000i
\(143\) 28.2679 14.6603i 0.197678 0.102519i
\(144\) −12.0000 −0.0833333
\(145\) 5.25387 5.25387i 0.0362336 0.0362336i
\(146\) 11.3590 0.0778013
\(147\) 83.0141i 0.564722i
\(148\) −6.28719 + 6.28719i −0.0424810 + 0.0424810i
\(149\) 126.224 126.224i 0.847143 0.847143i −0.142633 0.989776i \(-0.545557\pi\)
0.989776 + 0.142633i \(0.0455567\pi\)
\(150\) 37.7321 + 37.7321i 0.251547 + 0.251547i
\(151\) 124.406 + 124.406i 0.823883 + 0.823883i 0.986663 0.162779i \(-0.0520458\pi\)
−0.162779 + 0.986663i \(0.552046\pi\)
\(152\) 58.9282 0.387686
\(153\) 15.9615i 0.104324i
\(154\) −2.53590 2.53590i −0.0164669 0.0164669i
\(155\) 63.3487i 0.408701i
\(156\) 42.9282 + 13.6077i 0.275181 + 0.0872288i
\(157\) −268.785 −1.71200 −0.856002 0.516973i \(-0.827059\pi\)
−0.856002 + 0.516973i \(0.827059\pi\)
\(158\) 4.21024 4.21024i 0.0266471 0.0266471i
\(159\) 99.9615 0.628689
\(160\) 10.1436i 0.0633975i
\(161\) 3.89488 3.89488i 0.0241918 0.0241918i
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) −46.4449 46.4449i −0.284938 0.284938i 0.550137 0.835075i \(-0.314576\pi\)
−0.835075 + 0.550137i \(0.814576\pi\)
\(164\) −88.8897 88.8897i −0.542011 0.542011i
\(165\) −7.60770 −0.0461072
\(166\) 219.597i 1.32288i
\(167\) −119.512 119.512i −0.715638 0.715638i 0.252071 0.967709i \(-0.418888\pi\)
−0.967709 + 0.252071i \(0.918888\pi\)
\(168\) 5.07180i 0.0301893i
\(169\) −138.138 97.3590i −0.817387 0.576089i
\(170\) −13.4923 −0.0793663
\(171\) −44.1962 + 44.1962i −0.258457 + 0.258457i
\(172\) −74.3538 −0.432290
\(173\) 242.603i 1.40233i 0.713001 + 0.701163i \(0.247336\pi\)
−0.713001 + 0.701163i \(0.752664\pi\)
\(174\) 7.17691 7.17691i 0.0412466 0.0412466i
\(175\) −15.9474 + 15.9474i −0.0911282 + 0.0911282i
\(176\) 6.92820 + 6.92820i 0.0393648 + 0.0393648i
\(177\) −115.392 115.392i −0.651934 0.651934i
\(178\) −39.0333 −0.219288
\(179\) 26.7180i 0.149262i −0.997211 0.0746312i \(-0.976222\pi\)
0.997211 0.0746312i \(-0.0237780\pi\)
\(180\) −7.60770 7.60770i −0.0422650 0.0422650i
\(181\) 256.144i 1.41516i 0.706634 + 0.707579i \(0.250213\pi\)
−0.706634 + 0.707579i \(0.749787\pi\)
\(182\) −5.75129 + 18.1436i −0.0316005 + 0.0996901i
\(183\) 179.138 0.978899
\(184\) −10.6410 + 10.6410i −0.0578316 + 0.0578316i
\(185\) −7.97183 −0.0430910
\(186\) 86.5359i 0.465247i
\(187\) −9.21539 + 9.21539i −0.0492802 + 0.0492802i
\(188\) −61.6077 + 61.6077i −0.327701 + 0.327701i
\(189\) 3.80385 + 3.80385i 0.0201262 + 0.0201262i
\(190\) 37.3590 + 37.3590i 0.196626 + 0.196626i
\(191\) −129.282 −0.676869 −0.338435 0.940990i \(-0.609897\pi\)
−0.338435 + 0.940990i \(0.609897\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −160.282 160.282i −0.830477 0.830477i 0.157105 0.987582i \(-0.449784\pi\)
−0.987582 + 0.157105i \(0.949784\pi\)
\(194\) 8.06664i 0.0415806i
\(195\) 18.5885 + 35.8423i 0.0953254 + 0.183807i
\(196\) −95.8564 −0.489063
\(197\) −109.268 + 109.268i −0.554660 + 0.554660i −0.927782 0.373122i \(-0.878287\pi\)
0.373122 + 0.927782i \(0.378287\pi\)
\(198\) −10.3923 −0.0524864
\(199\) 25.1000i 0.126130i 0.998009 + 0.0630652i \(0.0200876\pi\)
−0.998009 + 0.0630652i \(0.979912\pi\)
\(200\) 43.5692 43.5692i 0.217846 0.217846i
\(201\) 80.8756 80.8756i 0.402366 0.402366i
\(202\) 111.464 + 111.464i 0.551802 + 0.551802i
\(203\) 3.03332 + 3.03332i 0.0149425 + 0.0149425i
\(204\) −18.4308 −0.0903470
\(205\) 112.708i 0.549793i
\(206\) 71.3205 + 71.3205i 0.346216 + 0.346216i
\(207\) 15.9615i 0.0771088i
\(208\) 15.7128 49.5692i 0.0755424 0.238314i
\(209\) 51.0333 0.244179
\(210\) 3.21539 3.21539i 0.0153114 0.0153114i
\(211\) 206.718 0.979706 0.489853 0.871805i \(-0.337050\pi\)
0.489853 + 0.871805i \(0.337050\pi\)
\(212\) 115.426i 0.544460i
\(213\) −46.6077 + 46.6077i −0.218815 + 0.218815i
\(214\) −116.536 + 116.536i −0.544560 + 0.544560i
\(215\) −47.1384 47.1384i −0.219249 0.219249i
\(216\) −10.3923 10.3923i −0.0481125 0.0481125i
\(217\) −36.5744 −0.168546
\(218\) 218.631i 1.00289i
\(219\) 9.83717 + 9.83717i 0.0449186 + 0.0449186i
\(220\) 8.78461i 0.0399300i
\(221\) 65.9334 + 20.9000i 0.298341 + 0.0945703i
\(222\) −10.8897 −0.0490528
\(223\) 139.412 139.412i 0.625164 0.625164i −0.321683 0.946847i \(-0.604249\pi\)
0.946847 + 0.321683i \(0.104249\pi\)
\(224\) −5.85641 −0.0261447
\(225\) 65.3538i 0.290461i
\(226\) 148.277 148.277i 0.656092 0.656092i
\(227\) −97.3679 + 97.3679i −0.428934 + 0.428934i −0.888265 0.459331i \(-0.848089\pi\)
0.459331 + 0.888265i \(0.348089\pi\)
\(228\) 51.0333 + 51.0333i 0.223830 + 0.223830i
\(229\) 204.177 + 204.177i 0.891602 + 0.891602i 0.994674 0.103072i \(-0.0328671\pi\)
−0.103072 + 0.994674i \(0.532867\pi\)
\(230\) −13.4923 −0.0586620
\(231\) 4.39230i 0.0190143i
\(232\) −8.28719 8.28719i −0.0357206 0.0357206i
\(233\) 231.962i 0.995543i −0.867308 0.497772i \(-0.834152\pi\)
0.867308 0.497772i \(-0.165848\pi\)
\(234\) 25.3923 + 48.9615i 0.108514 + 0.209237i
\(235\) −78.1154 −0.332406
\(236\) −133.244 + 133.244i −0.564591 + 0.564591i
\(237\) 7.29234 0.0307694
\(238\) 7.78976i 0.0327301i
\(239\) 139.981 139.981i 0.585694 0.585694i −0.350769 0.936462i \(-0.614080\pi\)
0.936462 + 0.350769i \(0.114080\pi\)
\(240\) −8.78461 + 8.78461i −0.0366025 + 0.0366025i
\(241\) 53.4589 + 53.4589i 0.221821 + 0.221821i 0.809265 0.587444i \(-0.199866\pi\)
−0.587444 + 0.809265i \(0.699866\pi\)
\(242\) −115.000 115.000i −0.475207 0.475207i
\(243\) 15.5885 0.0641500
\(244\) 206.851i 0.847751i
\(245\) −60.7705 60.7705i −0.248043 0.248043i
\(246\) 153.962i 0.625860i
\(247\) −124.694 240.435i −0.504832 0.973419i
\(248\) 99.9230 0.402916
\(249\) −190.177 + 190.177i −0.763763 + 0.763763i
\(250\) 118.641 0.474564
\(251\) 421.377i 1.67879i 0.543520 + 0.839396i \(0.317091\pi\)
−0.543520 + 0.839396i \(0.682909\pi\)
\(252\) 4.39230 4.39230i 0.0174298 0.0174298i
\(253\) −9.21539 + 9.21539i −0.0364245 + 0.0364245i
\(254\) −70.0385 70.0385i −0.275742 0.275742i
\(255\) −11.6846 11.6846i −0.0458221 0.0458221i
\(256\) 16.0000 0.0625000
\(257\) 249.664i 0.971455i −0.874110 0.485728i \(-0.838555\pi\)
0.874110 0.485728i \(-0.161445\pi\)
\(258\) −64.3923 64.3923i −0.249583 0.249583i
\(259\) 4.60254i 0.0177704i
\(260\) 41.3872 21.4641i 0.159181 0.0825542i
\(261\) 12.4308 0.0476275
\(262\) 238.890 238.890i 0.911793 0.911793i
\(263\) −94.8897 −0.360797 −0.180399 0.983594i \(-0.557739\pi\)
−0.180399 + 0.983594i \(0.557739\pi\)
\(264\) 12.0000i 0.0454545i
\(265\) 73.1769 73.1769i 0.276139 0.276139i
\(266\) −21.5692 + 21.5692i −0.0810873 + 0.0810873i
\(267\) −33.8038 33.8038i −0.126606 0.126606i
\(268\) −93.3872 93.3872i −0.348460 0.348460i
\(269\) −208.774 −0.776113 −0.388056 0.921636i \(-0.626853\pi\)
−0.388056 + 0.921636i \(0.626853\pi\)
\(270\) 13.1769i 0.0488034i
\(271\) 381.047 + 381.047i 1.40608 + 1.40608i 0.778772 + 0.627307i \(0.215843\pi\)
0.627307 + 0.778772i \(0.284157\pi\)
\(272\) 21.2820i 0.0782428i
\(273\) −20.6936 + 10.7321i −0.0758006 + 0.0393115i
\(274\) −183.895 −0.671149
\(275\) 37.7321 37.7321i 0.137207 0.137207i
\(276\) −18.4308 −0.0667782
\(277\) 68.7846i 0.248320i −0.992262 0.124160i \(-0.960376\pi\)
0.992262 0.124160i \(-0.0396236\pi\)
\(278\) 139.138 139.138i 0.500498 0.500498i
\(279\) −74.9423 + 74.9423i −0.268610 + 0.268610i
\(280\) −3.71281 3.71281i −0.0132600 0.0132600i
\(281\) 69.6218 + 69.6218i 0.247764 + 0.247764i 0.820053 0.572288i \(-0.193944\pi\)
−0.572288 + 0.820053i \(0.693944\pi\)
\(282\) −106.708 −0.378396
\(283\) 425.808i 1.50462i −0.658809 0.752310i \(-0.728939\pi\)
0.658809 0.752310i \(-0.271061\pi\)
\(284\) 53.8179 + 53.8179i 0.189500 + 0.189500i
\(285\) 64.7077i 0.227044i
\(286\) 13.6077 42.9282i 0.0475794 0.150099i
\(287\) 65.0718 0.226731
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 260.692 0.902049
\(290\) 10.5077i 0.0362336i
\(291\) 6.98592 6.98592i 0.0240066 0.0240066i
\(292\) 11.3590 11.3590i 0.0389006 0.0389006i
\(293\) 306.042 + 306.042i 1.04451 + 1.04451i 0.998962 + 0.0455508i \(0.0145043\pi\)
0.0455508 + 0.998962i \(0.485496\pi\)
\(294\) −83.0141 83.0141i −0.282361 0.282361i
\(295\) −168.946 −0.572699
\(296\) 12.5744i 0.0424810i
\(297\) −9.00000 9.00000i −0.0303030 0.0303030i
\(298\) 252.449i 0.847143i
\(299\) 65.9334 + 20.9000i 0.220513 + 0.0698998i
\(300\) 75.4641 0.251547
\(301\) 27.2154 27.2154i 0.0904166 0.0904166i
\(302\) 248.813 0.823883
\(303\) 193.061i 0.637167i
\(304\) 58.9282 58.9282i 0.193843 0.193843i
\(305\) 131.138 131.138i 0.429962 0.429962i
\(306\) −15.9615 15.9615i −0.0521618 0.0521618i
\(307\) 246.512 + 246.512i 0.802969 + 0.802969i 0.983559 0.180589i \(-0.0578005\pi\)
−0.180589 + 0.983559i \(0.557801\pi\)
\(308\) −5.07180 −0.0164669
\(309\) 123.531i 0.399776i
\(310\) 63.3487 + 63.3487i 0.204351 + 0.204351i
\(311\) 313.377i 1.00764i −0.863808 0.503821i \(-0.831927\pi\)
0.863808 0.503821i \(-0.168073\pi\)
\(312\) 56.5359 29.3205i 0.181205 0.0939760i
\(313\) −262.841 −0.839747 −0.419874 0.907583i \(-0.637926\pi\)
−0.419874 + 0.907583i \(0.637926\pi\)
\(314\) −268.785 + 268.785i −0.856002 + 0.856002i
\(315\) 5.56922 0.0176801
\(316\) 8.42047i 0.0266471i
\(317\) −148.981 + 148.981i −0.469971 + 0.469971i −0.901905 0.431934i \(-0.857831\pi\)
0.431934 + 0.901905i \(0.357831\pi\)
\(318\) 99.9615 99.9615i 0.314344 0.314344i
\(319\) −7.17691 7.17691i −0.0224982 0.0224982i
\(320\) 10.1436 + 10.1436i 0.0316987 + 0.0316987i
\(321\) −201.846 −0.628804
\(322\) 7.78976i 0.0241918i
\(323\) 78.3820 + 78.3820i 0.242669 + 0.242669i
\(324\) 18.0000i 0.0555556i
\(325\) −269.962 85.5744i −0.830651 0.263306i
\(326\) −92.8897 −0.284938
\(327\) −189.340 + 189.340i −0.579021 + 0.579021i
\(328\) −177.779 −0.542011
\(329\) 45.1000i 0.137082i
\(330\) −7.60770 + 7.60770i −0.0230536 + 0.0230536i
\(331\) −295.870 + 295.870i −0.893869 + 0.893869i −0.994885 0.101016i \(-0.967791\pi\)
0.101016 + 0.994885i \(0.467791\pi\)
\(332\) 219.597 + 219.597i 0.661438 + 0.661438i
\(333\) −9.43078 9.43078i −0.0283207 0.0283207i
\(334\) −239.023 −0.715638
\(335\) 118.410i 0.353463i
\(336\) −5.07180 5.07180i −0.0150946 0.0150946i
\(337\) 48.9385i 0.145218i 0.997360 + 0.0726091i \(0.0231325\pi\)
−0.997360 + 0.0726091i \(0.976867\pi\)
\(338\) −235.497 + 40.7795i −0.696738 + 0.120649i
\(339\) 256.823 0.757590
\(340\) −13.4923 + 13.4923i −0.0396831 + 0.0396831i
\(341\) 86.5359 0.253771
\(342\) 88.3923i 0.258457i
\(343\) 70.9564 70.9564i 0.206870 0.206870i
\(344\) −74.3538 + 74.3538i −0.216145 + 0.216145i
\(345\) −11.6846 11.6846i −0.0338685 0.0338685i
\(346\) 242.603 + 242.603i 0.701163 + 0.701163i
\(347\) −552.133 −1.59116 −0.795581 0.605847i \(-0.792834\pi\)
−0.795581 + 0.605847i \(0.792834\pi\)
\(348\) 14.3538i 0.0412466i
\(349\) 189.210 + 189.210i 0.542150 + 0.542150i 0.924159 0.382009i \(-0.124768\pi\)
−0.382009 + 0.924159i \(0.624768\pi\)
\(350\) 31.8949i 0.0911282i
\(351\) −20.4115 + 64.3923i −0.0581525 + 0.183454i
\(352\) 13.8564 0.0393648
\(353\) −51.8705 + 51.8705i −0.146942 + 0.146942i −0.776750 0.629809i \(-0.783133\pi\)
0.629809 + 0.776750i \(0.283133\pi\)
\(354\) −230.785 −0.651934
\(355\) 68.2384i 0.192221i
\(356\) −39.0333 + 39.0333i −0.109644 + 0.109644i
\(357\) 6.74613 6.74613i 0.0188967 0.0188967i
\(358\) −26.7180 26.7180i −0.0746312 0.0746312i
\(359\) −205.119 205.119i −0.571363 0.571363i 0.361146 0.932509i \(-0.382385\pi\)
−0.932509 + 0.361146i \(0.882385\pi\)
\(360\) −15.2154 −0.0422650
\(361\) 73.0666i 0.202401i
\(362\) 256.144 + 256.144i 0.707579 + 0.707579i
\(363\) 199.186i 0.548721i
\(364\) 12.3923 + 23.8949i 0.0340448 + 0.0656453i
\(365\) 14.4026 0.0394592
\(366\) 179.138 179.138i 0.489449 0.489449i
\(367\) −351.292 −0.957200 −0.478600 0.878033i \(-0.658856\pi\)
−0.478600 + 0.878033i \(0.658856\pi\)
\(368\) 21.2820i 0.0578316i
\(369\) 133.335 133.335i 0.361340 0.361340i
\(370\) −7.97183 + 7.97183i −0.0215455 + 0.0215455i
\(371\) 42.2487 + 42.2487i 0.113878 + 0.113878i
\(372\) 86.5359 + 86.5359i 0.232623 + 0.232623i
\(373\) −131.836 −0.353447 −0.176724 0.984261i \(-0.556550\pi\)
−0.176724 + 0.984261i \(0.556550\pi\)
\(374\) 18.4308i 0.0492802i
\(375\) 102.746 + 102.746i 0.273990 + 0.273990i
\(376\) 123.215i 0.327701i
\(377\) −16.2769 + 51.3487i −0.0431747 + 0.136203i
\(378\) 7.60770 0.0201262
\(379\) −24.7987 + 24.7987i −0.0654319 + 0.0654319i −0.739065 0.673634i \(-0.764733\pi\)
0.673634 + 0.739065i \(0.264733\pi\)
\(380\) 74.7180 0.196626
\(381\) 121.310i 0.318399i
\(382\) −129.282 + 129.282i −0.338435 + 0.338435i
\(383\) 174.555 174.555i 0.455758 0.455758i −0.441502 0.897260i \(-0.645554\pi\)
0.897260 + 0.441502i \(0.145554\pi\)
\(384\) 13.8564 + 13.8564i 0.0360844 + 0.0360844i
\(385\) −3.21539 3.21539i −0.00835166 0.00835166i
\(386\) −320.564 −0.830477
\(387\) 111.531i 0.288193i
\(388\) −8.06664 8.06664i −0.0207903 0.0207903i
\(389\) 644.305i 1.65631i −0.560498 0.828156i \(-0.689390\pi\)
0.560498 0.828156i \(-0.310610\pi\)
\(390\) 54.4308 + 17.2539i 0.139566 + 0.0442407i
\(391\) −28.3078 −0.0723985
\(392\) −95.8564 + 95.8564i −0.244532 + 0.244532i
\(393\) 413.769 1.05285
\(394\) 218.536i 0.554660i
\(395\) 5.33836 5.33836i 0.0135148 0.0135148i
\(396\) −10.3923 + 10.3923i −0.0262432 + 0.0262432i
\(397\) 432.692 + 432.692i 1.08990 + 1.08990i 0.995537 + 0.0943673i \(0.0300828\pi\)
0.0943673 + 0.995537i \(0.469917\pi\)
\(398\) 25.1000 + 25.1000i 0.0630652 + 0.0630652i
\(399\) −37.3590 −0.0936315
\(400\) 87.1384i 0.217846i
\(401\) −274.550 274.550i −0.684663 0.684663i 0.276384 0.961047i \(-0.410864\pi\)
−0.961047 + 0.276384i \(0.910864\pi\)
\(402\) 161.751i 0.402366i
\(403\) −211.440 407.699i −0.524664 1.01166i
\(404\) 222.928 0.551802
\(405\) 11.4115 11.4115i 0.0281766 0.0281766i
\(406\) 6.06664 0.0149425
\(407\) 10.8897i 0.0267561i
\(408\) −18.4308 + 18.4308i −0.0451735 + 0.0451735i
\(409\) 76.1872 76.1872i 0.186277 0.186277i −0.607808 0.794084i \(-0.707951\pi\)
0.794084 + 0.607808i \(0.207951\pi\)
\(410\) −112.708 112.708i −0.274897 0.274897i
\(411\) −159.258 159.258i −0.387488 0.387488i
\(412\) 142.641 0.346216
\(413\) 97.5411i 0.236177i
\(414\) −15.9615 15.9615i −0.0385544 0.0385544i
\(415\) 278.438i 0.670936i
\(416\) −33.8564 65.2820i −0.0813856 0.156928i
\(417\) 240.995 0.577925
\(418\) 51.0333 51.0333i 0.122089 0.122089i
\(419\) 76.8231 0.183349 0.0916743 0.995789i \(-0.470778\pi\)
0.0916743 + 0.995789i \(0.470778\pi\)
\(420\) 6.43078i 0.0153114i
\(421\) 117.756 117.756i 0.279707 0.279707i −0.553285 0.832992i \(-0.686626\pi\)
0.832992 + 0.553285i \(0.186626\pi\)
\(422\) 206.718 206.718i 0.489853 0.489853i
\(423\) −92.4115 92.4115i −0.218467 0.218467i
\(424\) −115.426 115.426i −0.272230 0.272230i
\(425\) 115.905 0.272718
\(426\) 93.2154i 0.218815i
\(427\) 75.7128 + 75.7128i 0.177313 + 0.177313i
\(428\) 233.072i 0.544560i
\(429\) 48.9615 25.3923i 0.114129 0.0591895i
\(430\) −94.2769 −0.219249
\(431\) 362.478 362.478i 0.841017 0.841017i −0.147975 0.988991i \(-0.547275\pi\)
0.988991 + 0.147975i \(0.0472754\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 197.292i 0.455641i −0.973703 0.227820i \(-0.926840\pi\)
0.973703 0.227820i \(-0.0731599\pi\)
\(434\) −36.5744 + 36.5744i −0.0842728 + 0.0842728i
\(435\) 9.09996 9.09996i 0.0209195 0.0209195i
\(436\) 218.631 + 218.631i 0.501447 + 0.501447i
\(437\) 78.3820 + 78.3820i 0.179364 + 0.179364i
\(438\) 19.6743 0.0449186
\(439\) 272.238i 0.620133i 0.950715 + 0.310067i \(0.100351\pi\)
−0.950715 + 0.310067i \(0.899649\pi\)
\(440\) 8.78461 + 8.78461i 0.0199650 + 0.0199650i
\(441\) 143.785i 0.326042i
\(442\) 86.8334 45.0333i 0.196456 0.101885i
\(443\) 74.7358 0.168704 0.0843519 0.996436i \(-0.473118\pi\)
0.0843519 + 0.996436i \(0.473118\pi\)
\(444\) −10.8897 + 10.8897i −0.0245264 + 0.0245264i
\(445\) −49.4923 −0.111219
\(446\) 278.823i 0.625164i
\(447\) 218.627 218.627i 0.489098 0.489098i
\(448\) −5.85641 + 5.85641i −0.0130723 + 0.0130723i
\(449\) 516.224 + 516.224i 1.14972 + 1.14972i 0.986607 + 0.163113i \(0.0521534\pi\)
0.163113 + 0.986607i \(0.447847\pi\)
\(450\) 65.3538 + 65.3538i 0.145231 + 0.145231i
\(451\) −153.962 −0.341378
\(452\) 296.554i 0.656092i
\(453\) 215.478 + 215.478i 0.475669 + 0.475669i
\(454\) 194.736i 0.428934i
\(455\) −7.29234 + 23.0052i −0.0160271 + 0.0505608i
\(456\) 102.067 0.223830
\(457\) −50.9615 + 50.9615i −0.111513 + 0.111513i −0.760662 0.649149i \(-0.775125\pi\)
0.649149 + 0.760662i \(0.275125\pi\)
\(458\) 408.354 0.891602
\(459\) 27.6462i 0.0602313i
\(460\) −13.4923 + 13.4923i −0.0293310 + 0.0293310i
\(461\) 202.550 202.550i 0.439371 0.439371i −0.452429 0.891800i \(-0.649443\pi\)
0.891800 + 0.452429i \(0.149443\pi\)
\(462\) −4.39230 4.39230i −0.00950715 0.00950715i
\(463\) −223.247 223.247i −0.482176 0.482176i 0.423650 0.905826i \(-0.360749\pi\)
−0.905826 + 0.423650i \(0.860749\pi\)
\(464\) −16.5744 −0.0357206
\(465\) 109.723i 0.235964i
\(466\) −231.962 231.962i −0.497772 0.497772i
\(467\) 161.818i 0.346505i 0.984877 + 0.173253i \(0.0554277\pi\)
−0.984877 + 0.173253i \(0.944572\pi\)
\(468\) 74.3538 + 23.5692i 0.158876 + 0.0503616i
\(469\) 68.3641 0.145766
\(470\) −78.1154 + 78.1154i −0.166203 + 0.166203i
\(471\) −465.549 −0.988426
\(472\) 266.487i 0.564591i
\(473\) −64.3923 + 64.3923i −0.136136 + 0.136136i
\(474\) 7.29234 7.29234i 0.0153847 0.0153847i
\(475\) −320.932 320.932i −0.675646 0.675646i
\(476\) −7.78976 7.78976i −0.0163651 0.0163651i
\(477\) 173.138 0.362974
\(478\) 279.962i 0.585694i
\(479\) −89.1295 89.1295i −0.186074 0.186074i 0.607922 0.793996i \(-0.292003\pi\)
−0.793996 + 0.607922i \(0.792003\pi\)
\(480\) 17.5692i 0.0366025i
\(481\) 51.3050 26.6077i 0.106663 0.0553175i
\(482\) 106.918 0.221821
\(483\) 6.74613 6.74613i 0.0139672 0.0139672i
\(484\) −230.000 −0.475207
\(485\) 10.2281i 0.0210888i
\(486\) 15.5885 15.5885i 0.0320750 0.0320750i
\(487\) −527.440 + 527.440i −1.08304 + 1.08304i −0.0868139 + 0.996225i \(0.527669\pi\)
−0.996225 + 0.0868139i \(0.972331\pi\)
\(488\) −206.851 206.851i −0.423876 0.423876i
\(489\) −80.4449 80.4449i −0.164509 0.164509i
\(490\) −121.541 −0.248043
\(491\) 700.726i 1.42714i 0.700584 + 0.713570i \(0.252923\pi\)
−0.700584 + 0.713570i \(0.747077\pi\)
\(492\) −153.962 153.962i −0.312930 0.312930i
\(493\) 22.0460i 0.0447181i
\(494\) −365.128 115.741i −0.739126 0.234293i
\(495\) −13.1769 −0.0266200
\(496\) 99.9230 99.9230i 0.201458 0.201458i
\(497\) −39.3975 −0.0792705
\(498\) 380.354i 0.763763i
\(499\) 279.065 279.065i 0.559249 0.559249i −0.369845 0.929094i \(-0.620589\pi\)
0.929094 + 0.369845i \(0.120589\pi\)
\(500\) 118.641 118.641i 0.237282 0.237282i
\(501\) −207.000 207.000i −0.413174 0.413174i
\(502\) 421.377 + 421.377i 0.839396 + 0.839396i
\(503\) −23.9821 −0.0476782 −0.0238391 0.999716i \(-0.507589\pi\)
−0.0238391 + 0.999716i \(0.507589\pi\)
\(504\) 8.78461i 0.0174298i
\(505\) 141.331 + 141.331i 0.279863 + 0.279863i
\(506\) 18.4308i 0.0364245i
\(507\) −239.263 168.631i −0.471919 0.332605i
\(508\) −140.077 −0.275742
\(509\) −287.678 + 287.678i −0.565183 + 0.565183i −0.930775 0.365592i \(-0.880866\pi\)
0.365592 + 0.930775i \(0.380866\pi\)
\(510\) −23.3693 −0.0458221
\(511\) 8.31535i 0.0162727i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) −76.5500 + 76.5500i −0.149220 + 0.149220i
\(514\) −249.664 249.664i −0.485728 0.485728i
\(515\) 90.4308 + 90.4308i 0.175594 + 0.175594i
\(516\) −128.785 −0.249583
\(517\) 106.708i 0.206398i
\(518\) −4.60254 4.60254i −0.00888521 0.00888521i
\(519\) 420.200i 0.809634i
\(520\) 19.9230 62.8513i 0.0383136 0.120868i
\(521\) −921.349 −1.76842 −0.884212 0.467086i \(-0.845304\pi\)
−0.884212 + 0.467086i \(0.845304\pi\)
\(522\) 12.4308 12.4308i 0.0238138 0.0238138i
\(523\) −558.677 −1.06822 −0.534108 0.845416i \(-0.679352\pi\)
−0.534108 + 0.845416i \(0.679352\pi\)
\(524\) 477.779i 0.911793i
\(525\) −27.6218 + 27.6218i −0.0526129 + 0.0526129i
\(526\) −94.8897 + 94.8897i −0.180399 + 0.180399i
\(527\) 132.910 + 132.910i 0.252202 + 0.252202i
\(528\) 12.0000 + 12.0000i 0.0227273 + 0.0227273i
\(529\) 500.692 0.946488
\(530\) 146.354i 0.276139i
\(531\) −199.865 199.865i −0.376394 0.376394i
\(532\) 43.1384i 0.0810873i
\(533\) 376.186 + 725.363i 0.705790 + 1.36091i
\(534\) −67.6077 −0.126606
\(535\) −147.762 + 147.762i −0.276190 + 0.276190i
\(536\) −186.774 −0.348460
\(537\) 46.2769i 0.0861767i
\(538\) −208.774 + 208.774i −0.388056 + 0.388056i
\(539\) −83.0141 + 83.0141i −0.154015 + 0.154015i
\(540\) −13.1769 13.1769i −0.0244017 0.0244017i
\(541\) −101.756 101.756i −0.188090 0.188090i 0.606780 0.794870i \(-0.292461\pi\)
−0.794870 + 0.606780i \(0.792461\pi\)
\(542\) 762.095 1.40608
\(543\) 443.654i 0.817042i
\(544\) 21.2820 + 21.2820i 0.0391214 + 0.0391214i
\(545\) 277.213i 0.508647i
\(546\) −9.96152 + 31.4256i −0.0182445 + 0.0575561i
\(547\) 301.800 0.551737 0.275868 0.961195i \(-0.411035\pi\)
0.275868 + 0.961195i \(0.411035\pi\)
\(548\) −183.895 + 183.895i −0.335575 + 0.335575i
\(549\) 310.277 0.565167
\(550\) 75.4641i 0.137207i
\(551\) −61.0436 + 61.0436i −0.110787 + 0.110787i
\(552\) −18.4308 + 18.4308i −0.0333891 + 0.0333891i
\(553\) 3.08211 + 3.08211i 0.00557343 + 0.00557343i
\(554\) −68.7846 68.7846i −0.124160 0.124160i
\(555\) −13.8076 −0.0248786
\(556\) 278.277i 0.500498i
\(557\) −285.258 285.258i −0.512132 0.512132i 0.403047 0.915179i \(-0.367951\pi\)
−0.915179 + 0.403047i \(0.867951\pi\)
\(558\) 149.885i 0.268610i
\(559\) 460.708 + 146.038i 0.824164 + 0.261250i
\(560\) −7.42563 −0.0132600
\(561\) −15.9615 + 15.9615i −0.0284519 + 0.0284519i
\(562\) 139.244 0.247764
\(563\) 863.174i 1.53317i 0.642143 + 0.766585i \(0.278045\pi\)
−0.642143 + 0.766585i \(0.721955\pi\)
\(564\) −106.708 + 106.708i −0.189198 + 0.189198i
\(565\) 188.008 188.008i 0.332757 0.332757i
\(566\) −425.808 425.808i −0.752310 0.752310i
\(567\) 6.58846 + 6.58846i 0.0116199 + 0.0116199i
\(568\) 107.636 0.189500
\(569\) 317.223i 0.557510i 0.960362 + 0.278755i \(0.0899217\pi\)
−0.960362 + 0.278755i \(0.910078\pi\)
\(570\) 64.7077 + 64.7077i 0.113522 + 0.113522i
\(571\) 73.2539i 0.128290i −0.997941 0.0641452i \(-0.979568\pi\)
0.997941 0.0641452i \(-0.0204321\pi\)
\(572\) −29.3205 56.5359i −0.0512596 0.0988390i
\(573\) −223.923 −0.390791
\(574\) 65.0718 65.0718i 0.113365 0.113365i
\(575\) 115.905 0.201574
\(576\) 24.0000i 0.0416667i
\(577\) −81.6410 + 81.6410i −0.141492 + 0.141492i −0.774305 0.632813i \(-0.781900\pi\)
0.632813 + 0.774305i \(0.281900\pi\)
\(578\) 260.692 260.692i 0.451025 0.451025i
\(579\) −277.617 277.617i −0.479476 0.479476i
\(580\) −10.5077 10.5077i −0.0181168 0.0181168i
\(581\) −160.756 −0.276689
\(582\) 13.9718i 0.0240066i
\(583\) −99.9615 99.9615i −0.171461 0.171461i
\(584\) 22.7180i 0.0389006i
\(585\) 32.1962 + 62.0807i 0.0550362 + 0.106121i
\(586\) 612.084 1.04451
\(587\) 382.219 382.219i 0.651140 0.651140i −0.302128 0.953268i \(-0.597697\pi\)
0.953268 + 0.302128i \(0.0976968\pi\)
\(588\) −166.028 −0.282361
\(589\) 736.036i 1.24964i
\(590\) −168.946 + 168.946i −0.286349 + 0.286349i
\(591\) −189.258 + 189.258i −0.320233 + 0.320233i
\(592\) 12.5744 + 12.5744i 0.0212405 + 0.0212405i
\(593\) 171.355 + 171.355i 0.288963 + 0.288963i 0.836670 0.547707i \(-0.184499\pi\)
−0.547707 + 0.836670i \(0.684499\pi\)
\(594\) −18.0000 −0.0303030
\(595\) 9.87703i 0.0166000i
\(596\) −252.449 252.449i −0.423572 0.423572i
\(597\) 43.4744i 0.0728215i
\(598\) 86.8334 45.0333i 0.145206 0.0753066i
\(599\) −109.608 −0.182984 −0.0914922 0.995806i \(-0.529164\pi\)
−0.0914922 + 0.995806i \(0.529164\pi\)
\(600\) 75.4641 75.4641i 0.125774 0.125774i
\(601\) 779.108 1.29635 0.648176 0.761491i \(-0.275532\pi\)
0.648176 + 0.761491i \(0.275532\pi\)
\(602\) 54.4308i 0.0904166i
\(603\) 140.081 140.081i 0.232306 0.232306i
\(604\) 248.813 248.813i 0.411942 0.411942i
\(605\) −145.814 145.814i −0.241015 0.241015i
\(606\) 193.061 + 193.061i 0.318583 + 0.318583i
\(607\) 1144.40 1.88534 0.942669 0.333730i \(-0.108307\pi\)
0.942669 + 0.333730i \(0.108307\pi\)
\(608\) 117.856i 0.193843i
\(609\) 5.25387 + 5.25387i 0.00862704 + 0.00862704i
\(610\) 262.277i 0.429962i
\(611\) 502.734 260.727i 0.822806 0.426722i
\(612\) −31.9230 −0.0521618
\(613\) 292.349 292.349i 0.476915 0.476915i −0.427229 0.904144i \(-0.640510\pi\)
0.904144 + 0.427229i \(0.140510\pi\)
\(614\) 493.023 0.802969
\(615\) 195.215i 0.317423i
\(616\) −5.07180 + 5.07180i −0.00823344 + 0.00823344i
\(617\) −369.391 + 369.391i −0.598689 + 0.598689i −0.939964 0.341275i \(-0.889141\pi\)
0.341275 + 0.939964i \(0.389141\pi\)
\(618\) 123.531 + 123.531i 0.199888 + 0.199888i
\(619\) −446.070 446.070i −0.720631 0.720631i 0.248103 0.968734i \(-0.420193\pi\)
−0.968734 + 0.248103i \(0.920193\pi\)
\(620\) 126.697 0.204351
\(621\) 27.6462i 0.0445188i
\(622\) −313.377 313.377i −0.503821 0.503821i
\(623\) 28.5744i 0.0458658i
\(624\) 27.2154 85.8564i 0.0436144 0.137590i
\(625\) −394.184 −0.630695
\(626\) −262.841 + 262.841i −0.419874 + 0.419874i
\(627\) 88.3923 0.140977
\(628\) 537.569i 0.856002i
\(629\) −16.7255 + 16.7255i −0.0265906 + 0.0265906i
\(630\) 5.56922 5.56922i 0.00884003 0.00884003i
\(631\) −604.406 604.406i −0.957855 0.957855i 0.0412923 0.999147i \(-0.486853\pi\)
−0.999147 + 0.0412923i \(0.986853\pi\)
\(632\) −8.42047 8.42047i −0.0133235 0.0133235i
\(633\) 358.046 0.565634
\(634\) 297.962i 0.469971i
\(635\) −88.8052 88.8052i −0.139851 0.139851i
\(636\) 199.923i 0.314344i
\(637\) 593.941 + 188.272i 0.932403 + 0.295560i
\(638\) −14.3538 −0.0224982
\(639\) −80.7269 + 80.7269i −0.126333 + 0.126333i
\(640\) 20.2872 0.0316987
\(641\) 1213.91i 1.89378i −0.321565 0.946888i \(-0.604209\pi\)
0.321565 0.946888i \(-0.395791\pi\)
\(642\) −201.846 + 201.846i −0.314402 + 0.314402i
\(643\) 413.804 413.804i 0.643552 0.643552i −0.307875 0.951427i \(-0.599618\pi\)
0.951427 + 0.307875i \(0.0996178\pi\)
\(644\) −7.78976 7.78976i −0.0120959 0.0120959i
\(645\) −81.6462 81.6462i −0.126583 0.126583i
\(646\) 156.764 0.242669
\(647\) 117.913i 0.182245i 0.995840 + 0.0911227i \(0.0290455\pi\)
−0.995840 + 0.0911227i \(0.970954\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 230.785i 0.355600i
\(650\) −355.536 + 184.387i −0.546978 + 0.283673i
\(651\) −63.3487 −0.0973098
\(652\) −92.8897 + 92.8897i −0.142469 + 0.142469i
\(653\) −1088.62 −1.66711 −0.833553 0.552439i \(-0.813697\pi\)
−0.833553 + 0.552439i \(0.813697\pi\)
\(654\) 378.679i 0.579021i
\(655\) 302.900 302.900i 0.462443 0.462443i
\(656\) −177.779 + 177.779i −0.271005 + 0.271005i
\(657\) 17.0385 + 17.0385i 0.0259338 + 0.0259338i
\(658\) −45.1000 45.1000i −0.0685410 0.0685410i
\(659\) 1222.68 1.85535 0.927676 0.373387i \(-0.121804\pi\)
0.927676 + 0.373387i \(0.121804\pi\)
\(660\) 15.2154i 0.0230536i
\(661\) −667.851 667.851i −1.01036 1.01036i −0.999946 0.0104193i \(-0.996683\pi\)
−0.0104193 0.999946i \(-0.503317\pi\)
\(662\) 591.741i 0.893869i
\(663\) 114.200 + 36.1999i 0.172247 + 0.0546002i
\(664\) 439.195 0.661438
\(665\) −27.3487 + 27.3487i −0.0411258 + 0.0411258i
\(666\) −18.8616 −0.0283207
\(667\) 22.0460i 0.0330525i
\(668\) −239.023 + 239.023i −0.357819 + 0.357819i
\(669\) 241.468 241.468i 0.360939 0.360939i
\(670\) −118.410 118.410i −0.176732 0.176732i
\(671\) −179.138 179.138i −0.266972 0.266972i
\(672\) −10.1436 −0.0150946
\(673\) 411.779i 0.611857i 0.952055 + 0.305928i \(0.0989668\pi\)
−0.952055 + 0.305928i \(0.901033\pi\)
\(674\) 48.9385 + 48.9385i 0.0726091 + 0.0726091i
\(675\) 113.196i 0.167698i
\(676\) −194.718 + 276.277i −0.288044 + 0.408694i
\(677\) −948.600 −1.40118 −0.700591 0.713563i \(-0.747080\pi\)
−0.700591 + 0.713563i \(0.747080\pi\)
\(678\) 256.823 256.823i 0.378795 0.378795i
\(679\) 5.90519 0.00869690
\(680\) 26.9845i 0.0396831i
\(681\) −168.646 + 168.646i −0.247645 + 0.247645i
\(682\) 86.5359 86.5359i 0.126885 0.126885i
\(683\) 101.809 + 101.809i 0.149061 + 0.149061i 0.777699 0.628637i \(-0.216387\pi\)
−0.628637 + 0.777699i \(0.716387\pi\)
\(684\) 88.3923 + 88.3923i 0.129229 + 0.129229i
\(685\) −233.169 −0.340393
\(686\) 141.913i 0.206870i
\(687\) 353.645 + 353.645i 0.514767 + 0.514767i
\(688\) 148.708i 0.216145i
\(689\) −226.708 + 715.195i −0.329039 + 1.03802i
\(690\) −23.3693 −0.0338685
\(691\) −111.135 + 111.135i −0.160832 + 0.160832i −0.782935 0.622103i \(-0.786278\pi\)
0.622103 + 0.782935i \(0.286278\pi\)
\(692\) 485.205 0.701163
\(693\) 7.60770i 0.0109779i
\(694\) −552.133 + 552.133i −0.795581 + 0.795581i
\(695\) 176.420 176.420i 0.253842 0.253842i
\(696\) −14.3538 14.3538i −0.0206233 0.0206233i
\(697\) −236.469 236.469i −0.339267 0.339267i
\(698\) 378.420 0.542150
\(699\) 401.769i 0.574777i
\(700\) 31.8949 + 31.8949i 0.0455641 + 0.0455641i
\(701\) 779.520i 1.11201i −0.831178 0.556006i \(-0.812333\pi\)
0.831178 0.556006i \(-0.187667\pi\)
\(702\) 43.9808 + 84.8038i 0.0626507 + 0.120803i
\(703\) 92.6232 0.131754
\(704\) 13.8564 13.8564i 0.0196824 0.0196824i
\(705\) −135.300 −0.191915
\(706\) 103.741i 0.146942i
\(707\) −81.5974 + 81.5974i −0.115414 + 0.115414i
\(708\) −230.785 + 230.785i −0.325967 + 0.325967i
\(709\) 43.0179 + 43.0179i 0.0606740 + 0.0606740i 0.736793 0.676119i \(-0.236339\pi\)
−0.676119 + 0.736793i \(0.736339\pi\)
\(710\) 68.2384 + 68.2384i 0.0961104 + 0.0961104i
\(711\) 12.6307 0.0177647
\(712\) 78.0666i 0.109644i
\(713\) 132.910 + 132.910i 0.186410 + 0.186410i
\(714\) 13.4923i 0.0188967i
\(715\) 17.2539 54.4308i 0.0241313 0.0761270i
\(716\) −53.4359 −0.0746312
\(717\) 242.454 242.454i 0.338150 0.338150i
\(718\) −410.238 −0.571363
\(719\) 335.290i 0.466328i −0.972437 0.233164i \(-0.925092\pi\)
0.972437 0.233164i \(-0.0749078\pi\)
\(720\) −15.2154 + 15.2154i −0.0211325 + 0.0211325i
\(721\) −52.2102 + 52.2102i −0.0724136 + 0.0724136i
\(722\) −73.0666 73.0666i −0.101200 0.101200i
\(723\) 92.5936 + 92.5936i 0.128069 + 0.128069i
\(724\) 512.287 0.707579
\(725\) 90.2666i 0.124506i
\(726\) −199.186 199.186i −0.274361 0.274361i
\(727\) 537.577i 0.739445i 0.929142 + 0.369723i \(0.120547\pi\)
−0.929142 + 0.369723i \(0.879453\pi\)
\(728\) 36.2872 + 11.5026i 0.0498450 + 0.0158002i
\(729\) 27.0000 0.0370370
\(730\) 14.4026 14.4026i 0.0197296 0.0197296i
\(731\) −197.800 −0.270588
\(732\) 358.277i 0.489449i
\(733\) −479.946 + 479.946i −0.654770 + 0.654770i −0.954138 0.299368i \(-0.903224\pi\)
0.299368 + 0.954138i \(0.403224\pi\)
\(734\) −351.292 + 351.292i −0.478600 + 0.478600i
\(735\) −105.258 105.258i −0.143208 0.143208i
\(736\) 21.2820 + 21.2820i 0.0289158 + 0.0289158i
\(737\) −161.751 −0.219473
\(738\) 266.669i 0.361340i
\(739\) 512.788 + 512.788i 0.693895 + 0.693895i 0.963087 0.269192i \(-0.0867565\pi\)
−0.269192 + 0.963087i \(0.586757\pi\)
\(740\) 15.9437i 0.0215455i
\(741\) −215.976 416.445i −0.291465 0.562004i
\(742\) 84.4974 0.113878
\(743\) 801.509 801.509i 1.07875 1.07875i 0.0821246 0.996622i \(-0.473829\pi\)
0.996622 0.0821246i \(-0.0261705\pi\)
\(744\) 173.072 0.232623
\(745\) 320.092i 0.429654i
\(746\) −131.836 + 131.836i −0.176724 + 0.176724i
\(747\) −329.396 + 329.396i −0.440959 + 0.440959i
\(748\) 18.4308 + 18.4308i 0.0246401 + 0.0246401i
\(749\) −85.3102 85.3102i −0.113899 0.113899i
\(750\) 205.492 0.273990
\(751\) 1384.43i 1.84345i 0.387849 + 0.921723i \(0.373218\pi\)
−0.387849 + 0.921723i \(0.626782\pi\)
\(752\) 123.215 + 123.215i 0.163850 + 0.163850i
\(753\) 729.846i 0.969251i
\(754\) 35.0718 + 67.6256i 0.0465143 + 0.0896891i
\(755\) 315.482 0.417857
\(756\) 7.60770 7.60770i 0.0100631 0.0100631i
\(757\) −125.836 −0.166230 −0.0831148 0.996540i \(-0.526487\pi\)
−0.0831148 + 0.996540i \(0.526487\pi\)
\(758\) 49.5974i 0.0654319i
\(759\) −15.9615 + 15.9615i −0.0210297 + 0.0210297i
\(760\) 74.7180 74.7180i 0.0983131 0.0983131i
\(761\) −3.55514 3.55514i −0.00467166 0.00467166i 0.704767 0.709439i \(-0.251051\pi\)
−0.709439 + 0.704767i \(0.751051\pi\)
\(762\) −121.310 121.310i −0.159200 0.159200i
\(763\) −160.049 −0.209762
\(764\) 258.564i 0.338435i
\(765\) −20.2384 20.2384i −0.0264554 0.0264554i
\(766\) 349.110i 0.455758i
\(767\) 1087.30 563.894i 1.41760 0.735194i
\(768\) 27.7128 0.0360844
\(769\) −958.405 + 958.405i −1.24630 + 1.24630i −0.288959 + 0.957342i \(0.593309\pi\)
−0.957342 + 0.288959i \(0.906691\pi\)
\(770\) −6.43078 −0.00835166
\(771\) 432.431i 0.560870i
\(772\) −320.564 + 320.564i −0.415238 + 0.415238i
\(773\) 76.8165 76.8165i 0.0993746 0.0993746i −0.655672 0.755046i \(-0.727614\pi\)
0.755046 + 0.655672i \(0.227614\pi\)
\(774\) −111.531 111.531i −0.144097 0.144097i
\(775\) −544.196 544.196i −0.702189 0.702189i
\(776\) −16.1333 −0.0207903
\(777\) 7.97183i 0.0102598i
\(778\) −644.305 644.305i −0.828156 0.828156i
\(779\) 1309.53i 1.68104i
\(780\) 71.6846 37.1769i 0.0919034 0.0476627i
\(781\) 93.2154 0.119354
\(782\) −28.3078 + 28.3078i −0.0361992 + 0.0361992i
\(783\) 21.5307 0.0274978
\(784\) 191.713i 0.244532i
\(785\) −340.805 + 340.805i −0.434147 + 0.434147i
\(786\) 413.769 413.769i 0.526424 0.526424i
\(787\) −486.883 486.883i −0.618657 0.618657i 0.326530 0.945187i \(-0.394121\pi\)
−0.945187 + 0.326530i \(0.894121\pi\)
\(788\) 218.536 + 218.536i 0.277330 + 0.277330i
\(789\) −164.354 −0.208307
\(790\) 10.6767i 0.0135148i
\(791\) 108.546 + 108.546i 0.137227 + 0.137227i
\(792\) 20.7846i 0.0262432i
\(793\) −406.277 + 1281.68i −0.512329 + 1.61624i
\(794\) 865.384 1.08990
\(795\) 126.746 126.746i 0.159429 0.159429i
\(796\) 50.1999 0.0630652
\(797\) 713.587i 0.895341i −0.894198 0.447671i \(-0.852254\pi\)
0.894198 0.447671i \(-0.147746\pi\)
\(798\) −37.3590 + 37.3590i −0.0468158 + 0.0468158i
\(799\) −163.892 + 163.892i −0.205122 + 0.205122i
\(800\) −87.1384 87.1384i −0.108923 0.108923i
\(801\) −58.5500 58.5500i −0.0730961 0.0730961i
\(802\) −549.100 −0.684663
\(803\) 19.6743i 0.0245010i
\(804\) −161.751 161.751i −0.201183 0.201183i
\(805\) 9.87703i 0.0122696i
\(806\) −619.138 196.259i −0.768162 0.243498i
\(807\) −361.608 −0.448089
\(808\) 222.928 222.928i 0.275901 0.275901i
\(809\) −257.600 −0.318418 −0.159209 0.987245i \(-0.550894\pi\)
−0.159209 + 0.987245i \(0.550894\pi\)
\(810\) 22.8231i 0.0281766i
\(811\) −127.258 + 127.258i −0.156914 + 0.156914i −0.781198 0.624283i \(-0.785391\pi\)
0.624283 + 0.781198i \(0.285391\pi\)
\(812\) 6.06664 6.06664i 0.00747123 0.00747123i
\(813\) 659.993 + 659.993i 0.811800 + 0.811800i
\(814\) 10.8897 + 10.8897i 0.0133780 + 0.0133780i
\(815\) −117.779 −0.144515
\(816\) 36.8616i 0.0451735i
\(817\) 547.692 + 547.692i 0.670370 + 0.670370i
\(818\) 152.374i 0.186277i
\(819\) −35.8423 + 18.5885i −0.0437635 + 0.0226965i
\(820\) −225.415 −0.274897
\(821\) 1116.87 1116.87i 1.36038 1.36038i 0.486953 0.873428i \(-0.338108\pi\)
0.873428 0.486953i \(-0.161892\pi\)
\(822\) −318.515 −0.387488
\(823\) 617.920i 0.750814i 0.926860 + 0.375407i \(0.122497\pi\)
−0.926860 + 0.375407i \(0.877503\pi\)
\(824\) 142.641 142.641i 0.173108 0.173108i
\(825\) 65.3538 65.3538i 0.0792168 0.0792168i
\(826\) −97.5411 97.5411i −0.118088 0.118088i
\(827\) 349.847 + 349.847i 0.423032 + 0.423032i 0.886246 0.463214i \(-0.153304\pi\)
−0.463214 + 0.886246i \(0.653304\pi\)
\(828\) −31.9230 −0.0385544
\(829\) 247.646i 0.298729i −0.988782 0.149364i \(-0.952277\pi\)
0.988782 0.149364i \(-0.0477227\pi\)
\(830\) 278.438 + 278.438i 0.335468 + 0.335468i
\(831\) 119.138i 0.143368i
\(832\) −99.1384 31.4256i −0.119157 0.0377712i
\(833\) −255.002 −0.306125
\(834\) 240.995 240.995i 0.288963 0.288963i
\(835\) −303.069 −0.362957
\(836\) 102.067i 0.122089i
\(837\) −129.804 + 129.804i −0.155082 + 0.155082i
\(838\) 76.8231 76.8231i 0.0916743 0.0916743i
\(839\) −598.868 598.868i −0.713788 0.713788i 0.253538 0.967325i \(-0.418406\pi\)
−0.967325 + 0.253538i \(0.918406\pi\)
\(840\) −6.43078 6.43078i −0.00765569 0.00765569i
\(841\) −823.831 −0.979585
\(842\) 235.513i 0.279707i
\(843\) 120.588 + 120.588i 0.143047 + 0.143047i
\(844\) 413.436i 0.489853i
\(845\) −298.599 + 51.7063i −0.353371 + 0.0611909i
\(846\) −184.823 −0.218467
\(847\) 84.1858 84.1858i 0.0993930 0.0993930i
\(848\) −230.851 −0.272230
\(849\) 737.520i 0.868693i
\(850\) 115.905 115.905i 0.136359 0.136359i
\(851\) −16.7255 + 16.7255i −0.0196540 + 0.0196540i
\(852\) 93.2154 + 93.2154i 0.109408 + 0.109408i
\(853\) −519.210 519.210i −0.608687 0.608687i 0.333916 0.942603i \(-0.391630\pi\)
−0.942603 + 0.333916i \(0.891630\pi\)
\(854\) 151.426 0.177313
\(855\) 112.077i 0.131084i
\(856\) 233.072 + 233.072i 0.272280 + 0.272280i
\(857\) 226.756i 0.264593i 0.991210 + 0.132297i \(0.0422351\pi\)
−0.991210 + 0.132297i \(0.957765\pi\)
\(858\) 23.5692 74.3538i 0.0274700 0.0866595i
\(859\) 950.656 1.10670 0.553350 0.832949i \(-0.313349\pi\)
0.553350 + 0.832949i \(0.313349\pi\)
\(860\) −94.2769 + 94.2769i −0.109624 + 0.109624i
\(861\) 112.708 0.130903
\(862\) 724.956i 0.841017i
\(863\) 773.711 773.711i 0.896537 0.896537i −0.0985910 0.995128i \(-0.531434\pi\)
0.995128 + 0.0985910i \(0.0314336\pi\)
\(864\) −20.7846 + 20.7846i −0.0240563 + 0.0240563i
\(865\) 307.608 + 307.608i 0.355616 + 0.355616i
\(866\) −197.292 197.292i −0.227820 0.227820i
\(867\) 451.532 0.520798
\(868\) 73.1487i 0.0842728i
\(869\) −7.29234 7.29234i −0.00839165 0.00839165i
\(870\) 18.1999i 0.0209195i
\(871\) 395.219 + 762.063i 0.453753 + 0.874929i
\(872\) 437.261 0.501447
\(873\) 12.1000 12.1000i 0.0138602 0.0138602i
\(874\) 156.764 0.179364
\(875\) 86.8513i 0.0992586i
\(876\) 19.6743 19.6743i 0.0224593 0.0224593i
\(877\) 646.713 646.713i 0.737415 0.737415i −0.234662 0.972077i \(-0.575398\pi\)
0.972077 + 0.234662i \(0.0753984\pi\)
\(878\) 272.238 + 272.238i 0.310067 + 0.310067i
\(879\) 530.081 + 530.081i 0.603050 + 0.603050i
\(880\) 17.5692 0.0199650
\(881\) 783.997i 0.889895i −0.895557 0.444947i \(-0.853222\pi\)
0.895557 0.444947i \(-0.146778\pi\)
\(882\) −143.785 143.785i −0.163021 0.163021i
\(883\) 1089.81i 1.23421i −0.786881 0.617105i \(-0.788305\pi\)
0.786881 0.617105i \(-0.211695\pi\)
\(884\) 41.8001 131.867i 0.0472852 0.149170i
\(885\) −292.623 −0.330648
\(886\) 74.7358 74.7358i 0.0843519 0.0843519i
\(887\) −1057.03 −1.19169 −0.595846 0.803099i \(-0.703183\pi\)
−0.595846 + 0.803099i \(0.703183\pi\)
\(888\) 21.7795i 0.0245264i
\(889\) 51.2717 51.2717i 0.0576735 0.0576735i
\(890\) −49.4923 + 49.4923i −0.0556093 + 0.0556093i
\(891\) −15.5885 15.5885i −0.0174955 0.0174955i
\(892\) −278.823 278.823i −0.312582 0.312582i
\(893\) 907.608 1.01636
\(894\) 437.254i 0.489098i
\(895\) −33.8770 33.8770i −0.0378514 0.0378514i
\(896\) 11.7128i 0.0130723i
\(897\) 114.200 + 36.1999i 0.127313 + 0.0403567i
\(898\) 1032.45 1.14972
\(899\) −103.510 + 103.510i −0.115139 + 0.115139i
\(900\) 130.708 0.145231
\(901\) 307.061i 0.340801i
\(902\) −153.962 + 153.962i −0.170689 + 0.170689i
\(903\) 47.1384 47.1384i 0.0522020 0.0522020i
\(904\) −296.554 296.554i −0.328046 0.328046i
\(905\) 324.777 + 324.777i 0.358870 + 0.358870i
\(906\) 430.956 0.475669
\(907\) 546.669i 0.602722i 0.953510 + 0.301361i \(0.0974410\pi\)
−0.953510 + 0.301361i \(0.902559\pi\)
\(908\) 194.736 + 194.736i 0.214467 + 0.214467i
\(909\) 334.392i 0.367868i
\(910\) 15.7128 + 30.2975i 0.0172668 + 0.0332940i
\(911\) 724.743 0.795547 0.397774 0.917484i \(-0.369783\pi\)
0.397774 + 0.917484i \(0.369783\pi\)
\(912\) 102.067 102.067i 0.111915 0.111915i
\(913\) 380.354 0.416598
\(914\) 101.923i 0.111513i
\(915\) 227.138 227.138i 0.248239 0.248239i
\(916\) 408.354 408.354i 0.445801 0.445801i
\(917\) 174.879 + 174.879i 0.190708 + 0.190708i
\(918\) −27.6462 27.6462i −0.0301157 0.0301157i
\(919\) −941.108 −1.02406 −0.512028 0.858969i \(-0.671106\pi\)
−0.512028 + 0.858969i \(0.671106\pi\)
\(920\) 26.9845i 0.0293310i
\(921\) 426.970 + 426.970i 0.463594 + 0.463594i
\(922\) 405.100i 0.439371i
\(923\) −227.760 439.168i −0.246761 0.475805i
\(924\) −8.78461 −0.00950715
\(925\) 68.4820 68.4820i 0.0740345 0.0740345i
\(926\) −446.495 −0.482176
\(927\) 213.962i 0.230811i
\(928\) −16.5744 + 16.5744i −0.0178603 + 0.0178603i
\(929\) −260.130 + 260.130i −0.280010 + 0.280010i −0.833113 0.553103i \(-0.813444\pi\)
0.553103 + 0.833113i \(0.313444\pi\)
\(930\) 109.723 + 109.723i 0.117982 + 0.117982i
\(931\) 706.081 + 706.081i 0.758411 + 0.758411i
\(932\) −463.923 −0.497772
\(933\) 542.785i 0.581763i
\(934\) 161.818 + 161.818i 0.173253 + 0.173253i
\(935\) 23.3693i 0.0249939i
\(936\) 97.9230 50.7846i 0.104619 0.0542571i
\(937\) 1387.56 1.48085 0.740426 0.672138i \(-0.234624\pi\)
0.740426 + 0.672138i \(0.234624\pi\)
\(938\) 68.3641 68.3641i 0.0728829 0.0728829i
\(939\) −455.254 −0.484828
\(940\) 156.231i 0.166203i
\(941\) −61.6012 + 61.6012i −0.0654635 + 0.0654635i −0.739081 0.673617i \(-0.764740\pi\)
0.673617 + 0.739081i \(0.264740\pi\)
\(942\) −465.549 + 465.549i −0.494213 + 0.494213i
\(943\) −236.469 236.469i −0.250763 0.250763i
\(944\) 266.487 + 266.487i 0.282296 + 0.282296i
\(945\) 9.64617 0.0102076
\(946\) 128.785i 0.136136i
\(947\) 54.5064 + 54.5064i 0.0575569 + 0.0575569i 0.735299 0.677742i \(-0.237042\pi\)
−0.677742 + 0.735299i \(0.737042\pi\)
\(948\) 14.5847i 0.0153847i
\(949\) −92.6922 + 48.0718i −0.0976735 + 0.0506552i
\(950\) −641.864 −0.675646
\(951\) −258.042 + 258.042i −0.271338 + 0.271338i
\(952\) −15.5795 −0.0163651
\(953\) 1079.56i 1.13280i 0.824131 + 0.566399i \(0.191664\pi\)
−0.824131 + 0.566399i \(0.808336\pi\)
\(954\) 173.138 173.138i 0.181487 0.181487i
\(955\) −163.923 + 163.923i −0.171647 + 0.171647i
\(956\) −279.962 279.962i −0.292847 0.292847i
\(957\) −12.4308 12.4308i −0.0129893 0.0129893i
\(958\) −178.259 −0.186074
\(959\) 134.620i 0.140376i
\(960\) 17.5692 + 17.5692i 0.0183013 + 0.0183013i
\(961\) 287.077i 0.298727i
\(962\) 24.6973 77.9127i 0.0256729 0.0809904i
\(963\) −349.608 −0.363040
\(964\) 106.918 106.918i 0.110911 0.110911i
\(965\) −406.459 −0.421201
\(966\) 13.4923i 0.0139672i
\(967\) 493.745 493.745i 0.510594 0.510594i −0.404114 0.914709i \(-0.632420\pi\)
0.914709 + 0.404114i \(0.132420\pi\)
\(968\) −230.000 + 230.000i −0.237603 + 0.237603i
\(969\) 135.762 + 135.762i 0.140105 + 0.140105i
\(970\) −10.2281 10.2281i −0.0105444 0.0105444i
\(971\) −1694.52 −1.74513 −0.872566 0.488497i \(-0.837545\pi\)
−0.872566 + 0.488497i \(0.837545\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 101.856 + 101.856i 0.104683 + 0.104683i
\(974\) 1054.88i 1.08304i
\(975\) −467.587 148.219i −0.479576 0.152020i
\(976\) −413.703 −0.423876
\(977\) −390.060 + 390.060i −0.399243 + 0.399243i −0.877966 0.478723i \(-0.841100\pi\)
0.478723 + 0.877966i \(0.341100\pi\)
\(978\) −160.890 −0.164509
\(979\) 67.6077i 0.0690579i
\(980\) −121.541 + 121.541i −0.124021 + 0.124021i
\(981\) −327.946 + 327.946i −0.334298 + 0.334298i
\(982\) 700.726 + 700.726i 0.713570 + 0.713570i
\(983\) −1123.12 1123.12i −1.14254 1.14254i −0.987984 0.154559i \(-0.950604\pi\)
−0.154559 0.987984i \(-0.549396\pi\)
\(984\) −307.923 −0.312930
\(985\) 277.092i 0.281312i
\(986\) −22.0460 22.0460i −0.0223590 0.0223590i
\(987\) 78.1154i 0.0791443i
\(988\) −480.869 + 249.387i −0.486710 + 0.252416i
\(989\) −197.800 −0.200000
\(990\) −13.1769 + 13.1769i −0.0133100 + 0.0133100i
\(991\) 610.985 0.616533 0.308267 0.951300i \(-0.400251\pi\)
0.308267 + 0.951300i \(0.400251\pi\)
\(992\) 199.846i 0.201458i
\(993\) −512.463 + 512.463i −0.516075 + 0.516075i
\(994\) −39.3975 + 39.3975i −0.0396353 + 0.0396353i
\(995\) 31.8255 + 31.8255i 0.0319854 + 0.0319854i
\(996\) 380.354 + 380.354i 0.381881 + 0.381881i
\(997\) −412.123 −0.413363 −0.206682 0.978408i \(-0.566266\pi\)
−0.206682 + 0.978408i \(0.566266\pi\)
\(998\) 558.131i 0.559249i
\(999\) −16.3346 16.3346i −0.0163509 0.0163509i
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 78.3.f.a.31.2 4
3.2 odd 2 234.3.i.b.109.2 4
4.3 odd 2 624.3.ba.a.577.1 4
13.5 odd 4 1014.3.f.a.775.2 4
13.8 odd 4 inner 78.3.f.a.73.2 yes 4
13.12 even 2 1014.3.f.a.577.2 4
39.8 even 4 234.3.i.b.73.2 4
52.47 even 4 624.3.ba.a.385.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.f.a.31.2 4 1.1 even 1 trivial
78.3.f.a.73.2 yes 4 13.8 odd 4 inner
234.3.i.b.73.2 4 39.8 even 4
234.3.i.b.109.2 4 3.2 odd 2
624.3.ba.a.385.1 4 52.47 even 4
624.3.ba.a.577.1 4 4.3 odd 2
1014.3.f.a.577.2 4 13.12 even 2
1014.3.f.a.775.2 4 13.5 odd 4