Properties

Label 507.2.j.g.361.4
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
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] = [507,2,Mod(316,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.4
Root \(2.21837 - 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.g.316.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.21837 - 1.28078i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.28078 - 3.95042i) q^{4} +0.561553i q^{5} +(-2.21837 - 1.28078i) q^{6} +(-3.08440 - 1.78078i) q^{7} -6.56155i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(2.21837 - 1.28078i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.28078 - 3.95042i) q^{4} +0.561553i q^{5} +(-2.21837 - 1.28078i) q^{6} +(-3.08440 - 1.78078i) q^{7} -6.56155i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.719224 + 1.24573i) q^{10} +(1.73205 - 1.00000i) q^{11} -4.56155 q^{12} -9.12311 q^{14} +(0.486319 - 0.280776i) q^{15} +(-3.84233 - 6.65511i) q^{16} +(1.28078 - 2.21837i) q^{17} +2.56155i q^{18} +(0.972638 + 0.561553i) q^{19} +(2.21837 + 1.28078i) q^{20} +3.56155i q^{21} +(2.56155 - 4.43674i) q^{22} +(1.00000 + 1.73205i) q^{23} +(-5.68247 + 3.28078i) q^{24} +4.68466 q^{25} +1.00000 q^{27} +(-14.0696 + 8.12311i) q^{28} +(2.84233 + 4.92306i) q^{29} +(0.719224 - 1.24573i) q^{30} -1.56155i q^{31} +(-5.68247 - 3.28078i) q^{32} +(-1.73205 - 1.00000i) q^{33} -6.56155i q^{34} +(1.00000 - 1.73205i) q^{35} +(2.28078 + 3.95042i) q^{36} +(-2.97778 + 1.71922i) q^{37} +2.87689 q^{38} +3.68466 q^{40} +(2.21837 - 1.28078i) q^{41} +(4.56155 + 7.90084i) q^{42} +(0.219224 - 0.379706i) q^{43} -9.12311i q^{44} +(-0.486319 - 0.280776i) q^{45} +(4.43674 + 2.56155i) q^{46} +8.24621i q^{47} +(-3.84233 + 6.65511i) q^{48} +(2.84233 + 4.92306i) q^{49} +(10.3923 - 6.00000i) q^{50} -2.56155 q^{51} +11.6847 q^{53} +(2.21837 - 1.28078i) q^{54} +(0.561553 + 0.972638i) q^{55} +(-11.6847 + 20.2384i) q^{56} -1.12311i q^{57} +(12.6107 + 7.28078i) q^{58} +(-9.63289 - 5.56155i) q^{59} -2.56155i q^{60} +(-6.06155 + 10.4989i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(3.08440 - 1.78078i) q^{63} -1.43845 q^{64} -5.12311 q^{66} +(0.379706 - 0.219224i) q^{67} +(-5.84233 - 10.1192i) q^{68} +(1.00000 - 1.73205i) q^{69} -5.12311i q^{70} +(-12.1244 - 7.00000i) q^{71} +(5.68247 + 3.28078i) q^{72} +1.87689i q^{73} +(-4.40388 + 7.62775i) q^{74} +(-2.34233 - 4.05703i) q^{75} +(4.43674 - 2.56155i) q^{76} -7.12311 q^{77} +9.56155 q^{79} +(3.73720 - 2.15767i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.28078 - 5.68247i) q^{82} -9.12311i q^{83} +(14.0696 + 8.12311i) q^{84} +(1.24573 + 0.719224i) q^{85} -1.12311i q^{86} +(2.84233 - 4.92306i) q^{87} +(-6.56155 - 11.3649i) q^{88} +(-11.3649 + 6.56155i) q^{89} -1.43845 q^{90} +9.12311 q^{92} +(-1.35234 + 0.780776i) q^{93} +(10.5616 + 18.2931i) q^{94} +(-0.315342 + 0.546188i) q^{95} +6.56155i q^{96} +(3.84381 + 2.21922i) q^{97} +(12.6107 + 7.28078i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.21837 1.28078i 1.56862 0.905646i 0.572295 0.820048i \(-0.306053\pi\)
0.996330 0.0855975i \(-0.0272799\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 2.28078 3.95042i 1.14039 1.97521i
\(5\) 0.561553i 0.251134i 0.992085 + 0.125567i \(0.0400750\pi\)
−0.992085 + 0.125567i \(0.959925\pi\)
\(6\) −2.21837 1.28078i −0.905646 0.522875i
\(7\) −3.08440 1.78078i −1.16579 0.673070i −0.213107 0.977029i \(-0.568358\pi\)
−0.952685 + 0.303959i \(0.901692\pi\)
\(8\) 6.56155i 2.31986i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.719224 + 1.24573i 0.227438 + 0.393935i
\(11\) 1.73205 1.00000i 0.522233 0.301511i −0.215615 0.976478i \(-0.569176\pi\)
0.737848 + 0.674967i \(0.235842\pi\)
\(12\) −4.56155 −1.31681
\(13\) 0 0
\(14\) −9.12311 −2.43825
\(15\) 0.486319 0.280776i 0.125567 0.0724962i
\(16\) −3.84233 6.65511i −0.960582 1.66378i
\(17\) 1.28078 2.21837i 0.310634 0.538034i −0.667866 0.744282i \(-0.732792\pi\)
0.978500 + 0.206248i \(0.0661254\pi\)
\(18\) 2.56155i 0.603764i
\(19\) 0.972638 + 0.561553i 0.223138 + 0.128829i 0.607403 0.794394i \(-0.292211\pi\)
−0.384264 + 0.923223i \(0.625545\pi\)
\(20\) 2.21837 + 1.28078i 0.496043 + 0.286390i
\(21\) 3.56155i 0.777195i
\(22\) 2.56155 4.43674i 0.546125 0.945916i
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) −5.68247 + 3.28078i −1.15993 + 0.669686i
\(25\) 4.68466 0.936932
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −14.0696 + 8.12311i −2.65891 + 1.53512i
\(29\) 2.84233 + 4.92306i 0.527807 + 0.914189i 0.999475 + 0.0324124i \(0.0103190\pi\)
−0.471667 + 0.881777i \(0.656348\pi\)
\(30\) 0.719224 1.24573i 0.131312 0.227438i
\(31\) 1.56155i 0.280463i −0.990119 0.140232i \(-0.955215\pi\)
0.990119 0.140232i \(-0.0447847\pi\)
\(32\) −5.68247 3.28078i −1.00453 0.579965i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 6.56155i 1.12530i
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) 2.28078 + 3.95042i 0.380129 + 0.658403i
\(37\) −2.97778 + 1.71922i −0.489544 + 0.282639i −0.724385 0.689395i \(-0.757876\pi\)
0.234841 + 0.972034i \(0.424543\pi\)
\(38\) 2.87689 0.466694
\(39\) 0 0
\(40\) 3.68466 0.582596
\(41\) 2.21837 1.28078i 0.346451 0.200024i −0.316670 0.948536i \(-0.602565\pi\)
0.663121 + 0.748512i \(0.269231\pi\)
\(42\) 4.56155 + 7.90084i 0.703863 + 1.21913i
\(43\) 0.219224 0.379706i 0.0334313 0.0579047i −0.848826 0.528673i \(-0.822690\pi\)
0.882257 + 0.470768i \(0.156023\pi\)
\(44\) 9.12311i 1.37536i
\(45\) −0.486319 0.280776i −0.0724962 0.0418557i
\(46\) 4.43674 + 2.56155i 0.654162 + 0.377680i
\(47\) 8.24621i 1.20283i 0.798935 + 0.601417i \(0.205397\pi\)
−0.798935 + 0.601417i \(0.794603\pi\)
\(48\) −3.84233 + 6.65511i −0.554592 + 0.960582i
\(49\) 2.84233 + 4.92306i 0.406047 + 0.703294i
\(50\) 10.3923 6.00000i 1.46969 0.848528i
\(51\) −2.56155 −0.358689
\(52\) 0 0
\(53\) 11.6847 1.60501 0.802506 0.596645i \(-0.203500\pi\)
0.802506 + 0.596645i \(0.203500\pi\)
\(54\) 2.21837 1.28078i 0.301882 0.174292i
\(55\) 0.561553 + 0.972638i 0.0757198 + 0.131150i
\(56\) −11.6847 + 20.2384i −1.56143 + 2.70447i
\(57\) 1.12311i 0.148759i
\(58\) 12.6107 + 7.28078i 1.65586 + 0.956013i
\(59\) −9.63289 5.56155i −1.25410 0.724053i −0.282175 0.959363i \(-0.591056\pi\)
−0.971920 + 0.235310i \(0.924389\pi\)
\(60\) 2.56155i 0.330695i
\(61\) −6.06155 + 10.4989i −0.776102 + 1.34425i 0.158071 + 0.987428i \(0.449473\pi\)
−0.934173 + 0.356821i \(0.883861\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 3.08440 1.78078i 0.388597 0.224357i
\(64\) −1.43845 −0.179806
\(65\) 0 0
\(66\) −5.12311 −0.630611
\(67\) 0.379706 0.219224i 0.0463885 0.0267824i −0.476626 0.879106i \(-0.658141\pi\)
0.523015 + 0.852324i \(0.324807\pi\)
\(68\) −5.84233 10.1192i −0.708486 1.22713i
\(69\) 1.00000 1.73205i 0.120386 0.208514i
\(70\) 5.12311i 0.612328i
\(71\) −12.1244 7.00000i −1.43890 0.830747i −0.441123 0.897447i \(-0.645420\pi\)
−0.997773 + 0.0666994i \(0.978753\pi\)
\(72\) 5.68247 + 3.28078i 0.669686 + 0.386643i
\(73\) 1.87689i 0.219674i 0.993950 + 0.109837i \(0.0350329\pi\)
−0.993950 + 0.109837i \(0.964967\pi\)
\(74\) −4.40388 + 7.62775i −0.511941 + 0.886708i
\(75\) −2.34233 4.05703i −0.270469 0.468466i
\(76\) 4.43674 2.56155i 0.508929 0.293830i
\(77\) −7.12311 −0.811753
\(78\) 0 0
\(79\) 9.56155 1.07576 0.537879 0.843022i \(-0.319226\pi\)
0.537879 + 0.843022i \(0.319226\pi\)
\(80\) 3.73720 2.15767i 0.417831 0.241235i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.28078 5.68247i 0.362301 0.627524i
\(83\) 9.12311i 1.00139i −0.865624 0.500695i \(-0.833078\pi\)
0.865624 0.500695i \(-0.166922\pi\)
\(84\) 14.0696 + 8.12311i 1.53512 + 0.886303i
\(85\) 1.24573 + 0.719224i 0.135119 + 0.0780108i
\(86\) 1.12311i 0.121108i
\(87\) 2.84233 4.92306i 0.304730 0.527807i
\(88\) −6.56155 11.3649i −0.699464 1.21151i
\(89\) −11.3649 + 6.56155i −1.20468 + 0.695523i −0.961593 0.274481i \(-0.911494\pi\)
−0.243089 + 0.970004i \(0.578161\pi\)
\(90\) −1.43845 −0.151626
\(91\) 0 0
\(92\) 9.12311 0.951150
\(93\) −1.35234 + 0.780776i −0.140232 + 0.0809627i
\(94\) 10.5616 + 18.2931i 1.08934 + 1.88679i
\(95\) −0.315342 + 0.546188i −0.0323534 + 0.0560377i
\(96\) 6.56155i 0.669686i
\(97\) 3.84381 + 2.21922i 0.390280 + 0.225328i 0.682281 0.731090i \(-0.260988\pi\)
−0.292002 + 0.956418i \(0.594321\pi\)
\(98\) 12.6107 + 7.28078i 1.27387 + 0.735469i
\(99\) 2.00000i 0.201008i
\(100\) 10.6847 18.5064i 1.06847 1.85064i
\(101\) −1.71922 2.97778i −0.171069 0.296300i 0.767725 0.640780i \(-0.221389\pi\)
−0.938794 + 0.344479i \(0.888055\pi\)
\(102\) −5.68247 + 3.28078i −0.562649 + 0.324845i
\(103\) 7.56155 0.745062 0.372531 0.928020i \(-0.378490\pi\)
0.372531 + 0.928020i \(0.378490\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 25.9209 14.9654i 2.51766 1.45357i
\(107\) −4.12311 7.14143i −0.398596 0.690388i 0.594957 0.803757i \(-0.297169\pi\)
−0.993553 + 0.113369i \(0.963836\pi\)
\(108\) 2.28078 3.95042i 0.219468 0.380129i
\(109\) 17.8078i 1.70567i 0.522177 + 0.852837i \(0.325120\pi\)
−0.522177 + 0.852837i \(0.674880\pi\)
\(110\) 2.49146 + 1.43845i 0.237552 + 0.137151i
\(111\) 2.97778 + 1.71922i 0.282639 + 0.163181i
\(112\) 27.3693i 2.58616i
\(113\) 7.40388 12.8239i 0.696499 1.20637i −0.273174 0.961965i \(-0.588074\pi\)
0.969673 0.244406i \(-0.0785931\pi\)
\(114\) −1.43845 2.49146i −0.134723 0.233347i
\(115\) −0.972638 + 0.561553i −0.0906990 + 0.0523651i
\(116\) 25.9309 2.40762
\(117\) 0 0
\(118\) −28.4924 −2.62294
\(119\) −7.90084 + 4.56155i −0.724269 + 0.418157i
\(120\) −1.84233 3.19101i −0.168181 0.291298i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 31.0540i 2.81149i
\(123\) −2.21837 1.28078i −0.200024 0.115484i
\(124\) −6.16879 3.56155i −0.553974 0.319837i
\(125\) 5.43845i 0.486430i
\(126\) 4.56155 7.90084i 0.406375 0.703863i
\(127\) 4.78078 + 8.28055i 0.424225 + 0.734780i 0.996348 0.0853884i \(-0.0272131\pi\)
−0.572122 + 0.820168i \(0.693880\pi\)
\(128\) 8.17394 4.71922i 0.722481 0.417124i
\(129\) −0.438447 −0.0386031
\(130\) 0 0
\(131\) −17.3693 −1.51756 −0.758782 0.651345i \(-0.774205\pi\)
−0.758782 + 0.651345i \(0.774205\pi\)
\(132\) −7.90084 + 4.56155i −0.687680 + 0.397032i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 0.561553 0.972638i 0.0485108 0.0840231i
\(135\) 0.561553i 0.0483308i
\(136\) −14.5560 8.40388i −1.24816 0.720627i
\(137\) −1.24573 0.719224i −0.106430 0.0614474i 0.445840 0.895113i \(-0.352905\pi\)
−0.552270 + 0.833665i \(0.686238\pi\)
\(138\) 5.12311i 0.436108i
\(139\) −5.46543 + 9.46641i −0.463572 + 0.802930i −0.999136 0.0415643i \(-0.986766\pi\)
0.535564 + 0.844495i \(0.320099\pi\)
\(140\) −4.56155 7.90084i −0.385522 0.667743i
\(141\) 7.14143 4.12311i 0.601417 0.347228i
\(142\) −35.8617 −3.00945
\(143\) 0 0
\(144\) 7.68466 0.640388
\(145\) −2.76456 + 1.59612i −0.229584 + 0.132550i
\(146\) 2.40388 + 4.16365i 0.198947 + 0.344586i
\(147\) 2.84233 4.92306i 0.234431 0.406047i
\(148\) 15.6847i 1.28927i
\(149\) 5.68247 + 3.28078i 0.465526 + 0.268772i 0.714365 0.699773i \(-0.246716\pi\)
−0.248839 + 0.968545i \(0.580049\pi\)
\(150\) −10.3923 6.00000i −0.848528 0.489898i
\(151\) 15.3693i 1.25074i −0.780329 0.625369i \(-0.784949\pi\)
0.780329 0.625369i \(-0.215051\pi\)
\(152\) 3.68466 6.38202i 0.298865 0.517650i
\(153\) 1.28078 + 2.21837i 0.103545 + 0.179345i
\(154\) −15.8017 + 9.12311i −1.27334 + 0.735161i
\(155\) 0.876894 0.0704339
\(156\) 0 0
\(157\) −4.36932 −0.348709 −0.174355 0.984683i \(-0.555784\pi\)
−0.174355 + 0.984683i \(0.555784\pi\)
\(158\) 21.2111 12.2462i 1.68746 0.974256i
\(159\) −5.84233 10.1192i −0.463327 0.802506i
\(160\) 1.84233 3.19101i 0.145649 0.252271i
\(161\) 7.12311i 0.561379i
\(162\) −2.21837 1.28078i −0.174292 0.100627i
\(163\) 13.6899 + 7.90388i 1.07228 + 0.619080i 0.928803 0.370574i \(-0.120839\pi\)
0.143475 + 0.989654i \(0.454172\pi\)
\(164\) 11.6847i 0.912419i
\(165\) 0.561553 0.972638i 0.0437168 0.0757198i
\(166\) −11.6847 20.2384i −0.906905 1.57081i
\(167\) 5.40938 3.12311i 0.418590 0.241673i −0.275884 0.961191i \(-0.588970\pi\)
0.694474 + 0.719518i \(0.255637\pi\)
\(168\) 23.3693 1.80298
\(169\) 0 0
\(170\) 3.68466 0.282600
\(171\) −0.972638 + 0.561553i −0.0743795 + 0.0429430i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 1.87689 3.25088i 0.142698 0.247160i −0.785814 0.618463i \(-0.787756\pi\)
0.928512 + 0.371303i \(0.121089\pi\)
\(174\) 14.5616i 1.10391i
\(175\) −14.4493 8.34233i −1.09227 0.630621i
\(176\) −13.3102 7.68466i −1.00330 0.579253i
\(177\) 11.1231i 0.836064i
\(178\) −16.8078 + 29.1119i −1.25980 + 2.18203i
\(179\) −6.56155 11.3649i −0.490433 0.849456i 0.509506 0.860467i \(-0.329828\pi\)
−0.999939 + 0.0110115i \(0.996495\pi\)
\(180\) −2.21837 + 1.28078i −0.165348 + 0.0954634i
\(181\) −9.68466 −0.719855 −0.359927 0.932980i \(-0.617199\pi\)
−0.359927 + 0.932980i \(0.617199\pi\)
\(182\) 0 0
\(183\) 12.1231 0.896166
\(184\) 11.3649 6.56155i 0.837835 0.483724i
\(185\) −0.965435 1.67218i −0.0709802 0.122941i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 5.12311i 0.374639i
\(188\) 32.5760 + 18.8078i 2.37585 + 1.37170i
\(189\) −3.08440 1.78078i −0.224357 0.129532i
\(190\) 1.61553i 0.117203i
\(191\) 0.438447 0.759413i 0.0317249 0.0549492i −0.849727 0.527223i \(-0.823233\pi\)
0.881452 + 0.472274i \(0.156567\pi\)
\(192\) 0.719224 + 1.24573i 0.0519055 + 0.0899029i
\(193\) −16.8809 + 9.74621i −1.21512 + 0.701548i −0.963869 0.266375i \(-0.914174\pi\)
−0.251247 + 0.967923i \(0.580841\pi\)
\(194\) 11.3693 0.816269
\(195\) 0 0
\(196\) 25.9309 1.85220
\(197\) −9.84612 + 5.68466i −0.701507 + 0.405015i −0.807908 0.589308i \(-0.799400\pi\)
0.106402 + 0.994323i \(0.466067\pi\)
\(198\) 2.56155 + 4.43674i 0.182042 + 0.315305i
\(199\) −11.5885 + 20.0719i −0.821490 + 1.42286i 0.0830828 + 0.996543i \(0.473523\pi\)
−0.904573 + 0.426320i \(0.859810\pi\)
\(200\) 30.7386i 2.17355i
\(201\) −0.379706 0.219224i −0.0267824 0.0154628i
\(202\) −7.62775 4.40388i −0.536686 0.309856i
\(203\) 20.2462i 1.42101i
\(204\) −5.84233 + 10.1192i −0.409045 + 0.708486i
\(205\) 0.719224 + 1.24573i 0.0502328 + 0.0870057i
\(206\) 16.7743 9.68466i 1.16872 0.674762i
\(207\) −2.00000 −0.139010
\(208\) 0 0
\(209\) 2.24621 0.155374
\(210\) −4.43674 + 2.56155i −0.306164 + 0.176764i
\(211\) −3.65767 6.33527i −0.251804 0.436138i 0.712218 0.701958i \(-0.247691\pi\)
−0.964023 + 0.265820i \(0.914357\pi\)
\(212\) 26.6501 46.1593i 1.83034 3.17023i
\(213\) 14.0000i 0.959264i
\(214\) −18.2931 10.5616i −1.25049 0.721973i
\(215\) 0.213225 + 0.123106i 0.0145418 + 0.00839573i
\(216\) 6.56155i 0.446457i
\(217\) −2.78078 + 4.81645i −0.188771 + 0.326962i
\(218\) 22.8078 + 39.5042i 1.54474 + 2.67556i
\(219\) 1.62544 0.938447i 0.109837 0.0634144i
\(220\) 5.12311 0.345400
\(221\) 0 0
\(222\) 8.80776 0.591138
\(223\) 6.92820 4.00000i 0.463947 0.267860i −0.249756 0.968309i \(-0.580350\pi\)
0.713702 + 0.700449i \(0.247017\pi\)
\(224\) 11.6847 + 20.2384i 0.780714 + 1.35224i
\(225\) −2.34233 + 4.05703i −0.156155 + 0.270469i
\(226\) 37.9309i 2.52312i
\(227\) 0.972638 + 0.561553i 0.0645563 + 0.0372716i 0.531931 0.846788i \(-0.321467\pi\)
−0.467374 + 0.884059i \(0.654800\pi\)
\(228\) −4.43674 2.56155i −0.293830 0.169643i
\(229\) 0.246211i 0.0162701i −0.999967 0.00813505i \(-0.997411\pi\)
0.999967 0.00813505i \(-0.00258949\pi\)
\(230\) −1.43845 + 2.49146i −0.0948484 + 0.164282i
\(231\) 3.56155 + 6.16879i 0.234333 + 0.405877i
\(232\) 32.3029 18.6501i 2.12079 1.22444i
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) −4.63068 −0.302072
\(236\) −43.9409 + 25.3693i −2.86031 + 1.65140i
\(237\) −4.78078 8.28055i −0.310545 0.537879i
\(238\) −11.6847 + 20.2384i −0.757404 + 1.31186i
\(239\) 0.630683i 0.0407955i −0.999792 0.0203977i \(-0.993507\pi\)
0.999792 0.0203977i \(-0.00649326\pi\)
\(240\) −3.73720 2.15767i −0.241235 0.139277i
\(241\) 2.43160 + 1.40388i 0.156633 + 0.0904320i 0.576268 0.817261i \(-0.304509\pi\)
−0.419635 + 0.907693i \(0.637842\pi\)
\(242\) 17.9309i 1.15264i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 27.6501 + 47.8914i 1.77012 + 3.06593i
\(245\) −2.76456 + 1.59612i −0.176621 + 0.101972i
\(246\) −6.56155 −0.418349
\(247\) 0 0
\(248\) −10.2462 −0.650635
\(249\) −7.90084 + 4.56155i −0.500695 + 0.289077i
\(250\) 6.96543 + 12.0645i 0.440533 + 0.763025i
\(251\) −15.3693 + 26.6204i −0.970103 + 1.68027i −0.274871 + 0.961481i \(0.588635\pi\)
−0.695231 + 0.718786i \(0.744698\pi\)
\(252\) 16.2462i 1.02342i
\(253\) 3.46410 + 2.00000i 0.217786 + 0.125739i
\(254\) 21.2111 + 12.2462i 1.33090 + 0.768396i
\(255\) 1.43845i 0.0900791i
\(256\) 13.5270 23.4294i 0.845437 1.46434i
\(257\) −8.08854 14.0098i −0.504549 0.873905i −0.999986 0.00526106i \(-0.998325\pi\)
0.495437 0.868644i \(-0.335008\pi\)
\(258\) −0.972638 + 0.561553i −0.0605538 + 0.0349608i
\(259\) 12.2462 0.760943
\(260\) 0 0
\(261\) −5.68466 −0.351872
\(262\) −38.5316 + 22.2462i −2.38049 + 1.37438i
\(263\) 7.68466 + 13.3102i 0.473856 + 0.820743i 0.999552 0.0299295i \(-0.00952826\pi\)
−0.525696 + 0.850673i \(0.676195\pi\)
\(264\) −6.56155 + 11.3649i −0.403836 + 0.699464i
\(265\) 6.56155i 0.403073i
\(266\) −8.87348 5.12311i −0.544068 0.314118i
\(267\) 11.3649 + 6.56155i 0.695523 + 0.401561i
\(268\) 2.00000i 0.122169i
\(269\) −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) 0.719224 + 1.24573i 0.0437706 + 0.0758128i
\(271\) 0.925894 0.534565i 0.0562441 0.0324725i −0.471614 0.881805i \(-0.656329\pi\)
0.527858 + 0.849332i \(0.322995\pi\)
\(272\) −19.6847 −1.19356
\(273\) 0 0
\(274\) −3.68466 −0.222598
\(275\) 8.11407 4.68466i 0.489297 0.282496i
\(276\) −4.56155 7.90084i −0.274573 0.475575i
\(277\) 8.84233 15.3154i 0.531284 0.920211i −0.468049 0.883702i \(-0.655043\pi\)
0.999333 0.0365086i \(-0.0116236\pi\)
\(278\) 28.0000i 1.67933i
\(279\) 1.35234 + 0.780776i 0.0809627 + 0.0467439i
\(280\) −11.3649 6.56155i −0.679185 0.392128i
\(281\) 2.80776i 0.167497i 0.996487 + 0.0837486i \(0.0266893\pi\)
−0.996487 + 0.0837486i \(0.973311\pi\)
\(282\) 10.5616 18.2931i 0.628931 1.08934i
\(283\) −0.657671 1.13912i −0.0390945 0.0677136i 0.845816 0.533475i \(-0.179114\pi\)
−0.884911 + 0.465761i \(0.845781\pi\)
\(284\) −55.3059 + 31.9309i −3.28180 + 1.89475i
\(285\) 0.630683 0.0373584
\(286\) 0 0
\(287\) −9.12311 −0.538520
\(288\) 5.68247 3.28078i 0.334843 0.193322i
\(289\) 5.21922 + 9.03996i 0.307013 + 0.531762i
\(290\) −4.08854 + 7.08156i −0.240087 + 0.415844i
\(291\) 4.43845i 0.260186i
\(292\) 7.41452 + 4.28078i 0.433902 + 0.250513i
\(293\) 21.2709 + 12.2808i 1.24266 + 0.717451i 0.969635 0.244556i \(-0.0786422\pi\)
0.273026 + 0.962007i \(0.411976\pi\)
\(294\) 14.5616i 0.849247i
\(295\) 3.12311 5.40938i 0.181834 0.314946i
\(296\) 11.2808 + 19.5389i 0.655682 + 1.13567i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 16.8078 0.973648
\(299\) 0 0
\(300\) −21.3693 −1.23376
\(301\) −1.35234 + 0.780776i −0.0779478 + 0.0450032i
\(302\) −19.6847 34.0948i −1.13272 1.96194i
\(303\) −1.71922 + 2.97778i −0.0987668 + 0.171069i
\(304\) 8.63068i 0.495004i
\(305\) −5.89570 3.40388i −0.337587 0.194906i
\(306\) 5.68247 + 3.28078i 0.324845 + 0.187550i
\(307\) 10.1922i 0.581702i −0.956768 0.290851i \(-0.906062\pi\)
0.956768 0.290851i \(-0.0939383\pi\)
\(308\) −16.2462 + 28.1393i −0.925714 + 1.60338i
\(309\) −3.78078 6.54850i −0.215081 0.372531i
\(310\) 1.94528 1.12311i 0.110484 0.0637881i
\(311\) 10.8769 0.616772 0.308386 0.951261i \(-0.400211\pi\)
0.308386 + 0.951261i \(0.400211\pi\)
\(312\) 0 0
\(313\) −1.31534 −0.0743475 −0.0371738 0.999309i \(-0.511835\pi\)
−0.0371738 + 0.999309i \(0.511835\pi\)
\(314\) −9.69276 + 5.59612i −0.546994 + 0.315807i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) 21.8078 37.7722i 1.22678 2.12485i
\(317\) 23.0540i 1.29484i −0.762133 0.647420i \(-0.775848\pi\)
0.762133 0.647420i \(-0.224152\pi\)
\(318\) −25.9209 14.9654i −1.45357 0.839220i
\(319\) 9.84612 + 5.68466i 0.551277 + 0.318280i
\(320\) 0.807764i 0.0451554i
\(321\) −4.12311 + 7.14143i −0.230129 + 0.398596i
\(322\) −9.12311 15.8017i −0.508411 0.880593i
\(323\) 2.49146 1.43845i 0.138629 0.0800373i
\(324\) −4.56155 −0.253420
\(325\) 0 0
\(326\) 40.4924 2.24267
\(327\) 15.4220 8.90388i 0.852837 0.492386i
\(328\) −8.40388 14.5560i −0.464027 0.803718i
\(329\) 14.6847 25.4346i 0.809591 1.40225i
\(330\) 2.87689i 0.158368i
\(331\) 20.6181 + 11.9039i 1.13327 + 0.654297i 0.944756 0.327773i \(-0.106298\pi\)
0.188518 + 0.982070i \(0.439631\pi\)
\(332\) −36.0401 20.8078i −1.97796 1.14197i
\(333\) 3.43845i 0.188426i
\(334\) 8.00000 13.8564i 0.437741 0.758189i
\(335\) 0.123106 + 0.213225i 0.00672598 + 0.0116497i
\(336\) 23.7025 13.6847i 1.29308 0.746559i
\(337\) −2.12311 −0.115653 −0.0578265 0.998327i \(-0.518417\pi\)
−0.0578265 + 0.998327i \(0.518417\pi\)
\(338\) 0 0
\(339\) −14.8078 −0.804247
\(340\) 5.68247 3.28078i 0.308175 0.177925i
\(341\) −1.56155 2.70469i −0.0845628 0.146467i
\(342\) −1.43845 + 2.49146i −0.0777823 + 0.134723i
\(343\) 4.68466i 0.252948i
\(344\) −2.49146 1.43845i −0.134331 0.0775559i
\(345\) 0.972638 + 0.561553i 0.0523651 + 0.0302330i
\(346\) 9.61553i 0.516934i
\(347\) 6.80776 11.7914i 0.365460 0.632995i −0.623390 0.781911i \(-0.714245\pi\)
0.988850 + 0.148916i \(0.0475784\pi\)
\(348\) −12.9654 22.4568i −0.695020 1.20381i
\(349\) 11.9579 6.90388i 0.640090 0.369556i −0.144559 0.989496i \(-0.546176\pi\)
0.784649 + 0.619940i \(0.212843\pi\)
\(350\) −42.7386 −2.28448
\(351\) 0 0
\(352\) −13.1231 −0.699464
\(353\) 15.3154 8.84233i 0.815155 0.470630i −0.0335881 0.999436i \(-0.510693\pi\)
0.848743 + 0.528806i \(0.177360\pi\)
\(354\) 14.2462 + 24.6752i 0.757178 + 1.31147i
\(355\) 3.93087 6.80847i 0.208629 0.361356i
\(356\) 59.8617i 3.17267i
\(357\) 7.90084 + 4.56155i 0.418157 + 0.241423i
\(358\) −29.1119 16.8078i −1.53861 0.888318i
\(359\) 15.3693i 0.811162i −0.914059 0.405581i \(-0.867069\pi\)
0.914059 0.405581i \(-0.132931\pi\)
\(360\) −1.84233 + 3.19101i −0.0970993 + 0.168181i
\(361\) −8.86932 15.3621i −0.466806 0.808532i
\(362\) −21.4842 + 12.4039i −1.12918 + 0.651934i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −1.05398 −0.0551676
\(366\) 26.8935 15.5270i 1.40575 0.811609i
\(367\) −10.0270 17.3673i −0.523404 0.906563i −0.999629 0.0272394i \(-0.991328\pi\)
0.476224 0.879324i \(-0.342005\pi\)
\(368\) 7.68466 13.3102i 0.400591 0.693843i
\(369\) 2.56155i 0.133349i
\(370\) −4.28338 2.47301i −0.222682 0.128566i
\(371\) −36.0401 20.8078i −1.87111 1.08029i
\(372\) 7.12311i 0.369316i
\(373\) −1.81534 + 3.14426i −0.0939948 + 0.162804i −0.909189 0.416384i \(-0.863297\pi\)
0.815194 + 0.579188i \(0.196630\pi\)
\(374\) −6.56155 11.3649i −0.339290 0.587667i
\(375\) 4.70983 2.71922i 0.243215 0.140420i
\(376\) 54.1080 2.79040
\(377\) 0 0
\(378\) −9.12311 −0.469242
\(379\) 9.79937 5.65767i 0.503360 0.290615i −0.226740 0.973955i \(-0.572807\pi\)
0.730100 + 0.683340i \(0.239473\pi\)
\(380\) 1.43845 + 2.49146i 0.0737908 + 0.127809i
\(381\) 4.78078 8.28055i 0.244927 0.424225i
\(382\) 2.24621i 0.114926i
\(383\) −23.1563 13.3693i −1.18323 0.683140i −0.226473 0.974017i \(-0.572720\pi\)
−0.956760 + 0.290877i \(0.906053\pi\)
\(384\) −8.17394 4.71922i −0.417124 0.240827i
\(385\) 4.00000i 0.203859i
\(386\) −24.9654 + 43.2414i −1.27071 + 2.20093i
\(387\) 0.219224 + 0.379706i 0.0111438 + 0.0193016i
\(388\) 17.5337 10.1231i 0.890140 0.513923i
\(389\) 3.05398 0.154843 0.0774213 0.996998i \(-0.475331\pi\)
0.0774213 + 0.996998i \(0.475331\pi\)
\(390\) 0 0
\(391\) 5.12311 0.259087
\(392\) 32.3029 18.6501i 1.63154 0.941972i
\(393\) 8.68466 + 15.0423i 0.438083 + 0.758782i
\(394\) −14.5616 + 25.2213i −0.733600 + 1.27063i
\(395\) 5.36932i 0.270160i
\(396\) 7.90084 + 4.56155i 0.397032 + 0.229227i
\(397\) −10.4390 6.02699i −0.523921 0.302486i 0.214617 0.976698i \(-0.431150\pi\)
−0.738537 + 0.674213i \(0.764483\pi\)
\(398\) 59.3693i 2.97591i
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) −18.0000 31.1769i −0.900000 1.55885i
\(401\) −16.0748 + 9.28078i −0.802736 + 0.463460i −0.844427 0.535671i \(-0.820059\pi\)
0.0416909 + 0.999131i \(0.486726\pi\)
\(402\) −1.12311 −0.0560154
\(403\) 0 0
\(404\) −15.6847 −0.780341
\(405\) 0.486319 0.280776i 0.0241654 0.0139519i
\(406\) −25.9309 44.9136i −1.28693 2.22902i
\(407\) −3.43845 + 5.95557i −0.170437 + 0.295206i
\(408\) 16.8078i 0.832108i
\(409\) 15.9083 + 9.18466i 0.786615 + 0.454152i 0.838769 0.544487i \(-0.183276\pi\)
−0.0521548 + 0.998639i \(0.516609\pi\)
\(410\) 3.19101 + 1.84233i 0.157593 + 0.0909862i
\(411\) 1.43845i 0.0709534i
\(412\) 17.2462 29.8713i 0.849660 1.47165i
\(413\) 19.8078 + 34.3081i 0.974676 + 1.68819i
\(414\) −4.43674 + 2.56155i −0.218054 + 0.125893i
\(415\) 5.12311 0.251483
\(416\) 0 0
\(417\) 10.9309 0.535287
\(418\) 4.98293 2.87689i 0.243723 0.140714i
\(419\) 8.87689 + 15.3752i 0.433665 + 0.751129i 0.997186 0.0749725i \(-0.0238869\pi\)
−0.563521 + 0.826102i \(0.690554\pi\)
\(420\) −4.56155 + 7.90084i −0.222581 + 0.385522i
\(421\) 14.7538i 0.719056i 0.933134 + 0.359528i \(0.117062\pi\)
−0.933134 + 0.359528i \(0.882938\pi\)
\(422\) −16.2281 9.36932i −0.789973 0.456091i
\(423\) −7.14143 4.12311i −0.347228 0.200472i
\(424\) 76.6695i 3.72340i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 17.9309 + 31.0572i 0.868753 + 1.50473i
\(427\) 37.3924 21.5885i 1.80955 1.04474i
\(428\) −37.6155 −1.81822
\(429\) 0 0
\(430\) 0.630683 0.0304142
\(431\) −2.49146 + 1.43845i −0.120010 + 0.0692876i −0.558803 0.829300i \(-0.688739\pi\)
0.438794 + 0.898588i \(0.355406\pi\)
\(432\) −3.84233 6.65511i −0.184864 0.320194i
\(433\) 12.6231 21.8639i 0.606628 1.05071i −0.385164 0.922848i \(-0.625855\pi\)
0.991792 0.127862i \(-0.0408115\pi\)
\(434\) 14.2462i 0.683840i
\(435\) 2.76456 + 1.59612i 0.132550 + 0.0765280i
\(436\) 70.3482 + 40.6155i 3.36907 + 1.94513i
\(437\) 2.24621i 0.107451i
\(438\) 2.40388 4.16365i 0.114862 0.198947i
\(439\) −0.657671 1.13912i −0.0313889 0.0543672i 0.849904 0.526937i \(-0.176660\pi\)
−0.881293 + 0.472570i \(0.843326\pi\)
\(440\) 6.38202 3.68466i 0.304251 0.175659i
\(441\) −5.68466 −0.270698
\(442\) 0 0
\(443\) 14.7386 0.700254 0.350127 0.936702i \(-0.386138\pi\)
0.350127 + 0.936702i \(0.386138\pi\)
\(444\) 13.5833 7.84233i 0.644635 0.372180i
\(445\) −3.68466 6.38202i −0.174670 0.302537i
\(446\) 10.2462 17.7470i 0.485172 0.840343i
\(447\) 6.56155i 0.310351i
\(448\) 4.43674 + 2.56155i 0.209616 + 0.121022i
\(449\) 7.14143 + 4.12311i 0.337025 + 0.194581i 0.658956 0.752182i \(-0.270998\pi\)
−0.321931 + 0.946763i \(0.604332\pi\)
\(450\) 12.0000i 0.565685i
\(451\) 2.56155 4.43674i 0.120619 0.208918i
\(452\) −33.7732 58.4969i −1.58856 2.75146i
\(453\) −13.3102 + 7.68466i −0.625369 + 0.361057i
\(454\) 2.87689 0.135019
\(455\) 0 0
\(456\) −7.36932 −0.345100
\(457\) −24.7818 + 14.3078i −1.15924 + 0.669289i −0.951122 0.308814i \(-0.900068\pi\)
−0.208120 + 0.978103i \(0.566735\pi\)
\(458\) −0.315342 0.546188i −0.0147349 0.0255217i
\(459\) 1.28078 2.21837i 0.0597815 0.103545i
\(460\) 5.12311i 0.238866i
\(461\) 31.8765 + 18.4039i 1.48463 + 0.857154i 0.999847 0.0174778i \(-0.00556363\pi\)
0.484787 + 0.874632i \(0.338897\pi\)
\(462\) 15.8017 + 9.12311i 0.735161 + 0.424445i
\(463\) 26.6847i 1.24014i 0.784546 + 0.620071i \(0.212896\pi\)
−0.784546 + 0.620071i \(0.787104\pi\)
\(464\) 21.8423 37.8320i 1.01400 1.75631i
\(465\) −0.438447 0.759413i −0.0203325 0.0352169i
\(466\) −57.6776 + 33.3002i −2.67186 + 1.54260i
\(467\) 26.0000 1.20314 0.601568 0.798821i \(-0.294543\pi\)
0.601568 + 0.798821i \(0.294543\pi\)
\(468\) 0 0
\(469\) −1.56155 −0.0721058
\(470\) −10.2726 + 5.93087i −0.473838 + 0.273571i
\(471\) 2.18466 + 3.78394i 0.100664 + 0.174355i
\(472\) −36.4924 + 63.2067i −1.67970 + 2.90933i
\(473\) 0.876894i 0.0403196i
\(474\) −21.2111 12.2462i −0.974256 0.562487i
\(475\) 4.55648 + 2.63068i 0.209065 + 0.120704i
\(476\) 41.6155i 1.90744i
\(477\) −5.84233 + 10.1192i −0.267502 + 0.463327i
\(478\) −0.807764 1.39909i −0.0369463 0.0639928i
\(479\) 5.40938 3.12311i 0.247161 0.142698i −0.371303 0.928512i \(-0.621089\pi\)
0.618463 + 0.785814i \(0.287755\pi\)
\(480\) −3.68466 −0.168181
\(481\) 0 0
\(482\) 7.19224 0.327597
\(483\) −6.16879 + 3.56155i −0.280690 + 0.162056i
\(484\) 15.9654 + 27.6529i 0.725702 + 1.25695i
\(485\) −1.24621 + 2.15850i −0.0565875 + 0.0980125i
\(486\) 2.56155i 0.116194i
\(487\) 0.972638 + 0.561553i 0.0440744 + 0.0254464i 0.521875 0.853022i \(-0.325233\pi\)
−0.477801 + 0.878468i \(0.658566\pi\)
\(488\) 68.8892 + 39.7732i 3.11847 + 1.80045i
\(489\) 15.8078i 0.714852i
\(490\) −4.08854 + 7.08156i −0.184701 + 0.319912i
\(491\) −9.87689 17.1073i −0.445738 0.772041i 0.552365 0.833602i \(-0.313725\pi\)
−0.998103 + 0.0615613i \(0.980392\pi\)
\(492\) −10.1192 + 5.84233i −0.456209 + 0.263393i
\(493\) 14.5616 0.655819
\(494\) 0 0
\(495\) −1.12311 −0.0504798
\(496\) −10.3923 + 6.00000i −0.466628 + 0.269408i
\(497\) 24.9309 + 43.1815i 1.11830 + 1.93696i
\(498\) −11.6847 + 20.2384i −0.523602 + 0.906905i
\(499\) 28.4924i 1.27550i −0.770245 0.637748i \(-0.779866\pi\)
0.770245 0.637748i \(-0.220134\pi\)
\(500\) 21.4842 + 12.4039i 0.960801 + 0.554718i
\(501\) −5.40938 3.12311i −0.241673 0.139530i
\(502\) 78.7386i 3.51428i
\(503\) 5.87689 10.1791i 0.262038 0.453863i −0.704746 0.709460i \(-0.748939\pi\)
0.966783 + 0.255597i \(0.0822722\pi\)
\(504\) −11.6847 20.2384i −0.520476 0.901491i
\(505\) 1.67218 0.965435i 0.0744111 0.0429613i
\(506\) 10.2462 0.455500
\(507\) 0 0
\(508\) 43.6155 1.93513
\(509\) 5.89570 3.40388i 0.261322 0.150874i −0.363615 0.931549i \(-0.618458\pi\)
0.624938 + 0.780675i \(0.285124\pi\)
\(510\) −1.84233 3.19101i −0.0815797 0.141300i
\(511\) 3.34233 5.78908i 0.147856 0.256094i
\(512\) 50.4233i 2.22842i
\(513\) 0.972638 + 0.561553i 0.0429430 + 0.0247932i
\(514\) −35.8867 20.7192i −1.58290 0.913886i
\(515\) 4.24621i 0.187110i
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 8.24621 + 14.2829i 0.362668 + 0.628159i
\(518\) 27.1666 15.6847i 1.19363 0.689144i
\(519\) −3.75379 −0.164773
\(520\) 0 0
\(521\) −37.9309 −1.66178 −0.830891 0.556436i \(-0.812169\pi\)
−0.830891 + 0.556436i \(0.812169\pi\)
\(522\) −12.6107 + 7.28078i −0.551954 + 0.318671i
\(523\) 11.9309 + 20.6649i 0.521701 + 0.903612i 0.999681 + 0.0252415i \(0.00803549\pi\)
−0.477981 + 0.878370i \(0.658631\pi\)
\(524\) −39.6155 + 68.6161i −1.73061 + 2.99751i
\(525\) 16.6847i 0.728178i
\(526\) 34.0948 + 19.6847i 1.48661 + 0.858292i
\(527\) −3.46410 2.00000i −0.150899 0.0871214i
\(528\) 15.3693i 0.668864i
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 8.40388 + 14.5560i 0.365041 + 0.632270i
\(531\) 9.63289 5.56155i 0.418032 0.241351i
\(532\) −18.2462 −0.791074
\(533\) 0 0
\(534\) 33.6155 1.45469
\(535\) 4.01029 2.31534i 0.173380 0.100101i
\(536\) −1.43845 2.49146i −0.0621315 0.107615i
\(537\) −6.56155 + 11.3649i −0.283152 + 0.490433i
\(538\) 8.63068i 0.372095i
\(539\) 9.84612 + 5.68466i 0.424102 + 0.244856i
\(540\) 2.21837 + 1.28078i 0.0954634 + 0.0551158i
\(541\) 29.7386i 1.27856i 0.768972 + 0.639282i \(0.220768\pi\)
−0.768972 + 0.639282i \(0.779232\pi\)
\(542\) 1.36932 2.37173i 0.0588172 0.101874i
\(543\) 4.84233 + 8.38716i 0.207804 + 0.359927i
\(544\) −14.5560 + 8.40388i −0.624081 + 0.360313i
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) −24.9309 −1.06597 −0.532984 0.846126i \(-0.678929\pi\)
−0.532984 + 0.846126i \(0.678929\pi\)
\(548\) −5.68247 + 3.28078i −0.242743 + 0.140148i
\(549\) −6.06155 10.4989i −0.258701 0.448083i
\(550\) 12.0000 20.7846i 0.511682 0.886259i
\(551\) 6.38447i 0.271988i
\(552\) −11.3649 6.56155i −0.483724 0.279278i
\(553\) −29.4916 17.0270i −1.25411 0.724061i
\(554\) 45.3002i 1.92462i
\(555\) −0.965435 + 1.67218i −0.0409804 + 0.0709802i
\(556\) 24.9309 + 43.1815i 1.05730 + 1.83130i
\(557\) 12.1842 7.03457i 0.516262 0.298064i −0.219142 0.975693i \(-0.570326\pi\)
0.735404 + 0.677629i \(0.236992\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) −15.3693 −0.649472
\(561\) −4.43674 + 2.56155i −0.187319 + 0.108149i
\(562\) 3.59612 + 6.22866i 0.151693 + 0.262740i
\(563\) 0.684658 1.18586i 0.0288549 0.0499782i −0.851237 0.524781i \(-0.824147\pi\)
0.880092 + 0.474803i \(0.157481\pi\)
\(564\) 37.6155i 1.58390i
\(565\) 7.20130 + 4.15767i 0.302961 + 0.174915i
\(566\) −2.91791 1.68466i −0.122649 0.0708115i
\(567\) 3.56155i 0.149571i
\(568\) −45.9309 + 79.5546i −1.92722 + 3.33804i
\(569\) 20.3693 + 35.2807i 0.853926 + 1.47904i 0.877638 + 0.479325i \(0.159118\pi\)
−0.0237115 + 0.999719i \(0.507548\pi\)
\(570\) 1.39909 0.807764i 0.0586014 0.0338335i
\(571\) −19.3693 −0.810581 −0.405290 0.914188i \(-0.632830\pi\)
−0.405290 + 0.914188i \(0.632830\pi\)
\(572\) 0 0
\(573\) −0.876894 −0.0366328
\(574\) −20.2384 + 11.6847i −0.844735 + 0.487708i
\(575\) 4.68466 + 8.11407i 0.195364 + 0.338380i
\(576\) 0.719224 1.24573i 0.0299676 0.0519055i
\(577\) 29.6847i 1.23579i −0.786261 0.617894i \(-0.787986\pi\)
0.786261 0.617894i \(-0.212014\pi\)
\(578\) 23.1563 + 13.3693i 0.963177 + 0.556090i
\(579\) 16.8809 + 9.74621i 0.701548 + 0.405039i
\(580\) 14.5616i 0.604636i
\(581\) −16.2462 + 28.1393i −0.674006 + 1.16741i
\(582\) −5.68466 9.84612i −0.235637 0.408135i
\(583\) 20.2384 11.6847i 0.838190 0.483929i
\(584\) 12.3153 0.509612
\(585\) 0 0
\(586\) 62.9157 2.59902
\(587\) 12.6705 7.31534i 0.522969 0.301936i −0.215179 0.976575i \(-0.569034\pi\)
0.738149 + 0.674638i \(0.235700\pi\)
\(588\) −12.9654 22.4568i −0.534686 0.926102i
\(589\) 0.876894 1.51883i 0.0361318 0.0625821i
\(590\) 16.0000i 0.658710i
\(591\) 9.84612 + 5.68466i 0.405015 + 0.233836i
\(592\) 22.8832 + 13.2116i 0.940495 + 0.542995i
\(593\) 44.4233i 1.82425i −0.409917 0.912123i \(-0.634442\pi\)
0.409917 0.912123i \(-0.365558\pi\)
\(594\) 2.56155 4.43674i 0.105102 0.182042i
\(595\) −2.56155 4.43674i −0.105013 0.181889i
\(596\) 25.9209 14.9654i 1.06176 0.613008i
\(597\) 23.1771 0.948575
\(598\) 0 0
\(599\) −0.384472 −0.0157091 −0.00785455 0.999969i \(-0.502500\pi\)
−0.00785455 + 0.999969i \(0.502500\pi\)
\(600\) −26.6204 + 15.3693i −1.08677 + 0.627450i
\(601\) 17.9654 + 31.1170i 0.732825 + 1.26929i 0.955671 + 0.294437i \(0.0951321\pi\)
−0.222846 + 0.974854i \(0.571535\pi\)
\(602\) −2.00000 + 3.46410i −0.0815139 + 0.141186i
\(603\) 0.438447i 0.0178549i
\(604\) −60.7153 35.0540i −2.47047 1.42633i
\(605\) −3.40423 1.96543i −0.138402 0.0799063i
\(606\) 8.80776i 0.357791i
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −3.68466 6.38202i −0.149433 0.258825i
\(609\) −17.5337 + 10.1231i −0.710503 + 0.410209i
\(610\) −17.4384 −0.706062
\(611\) 0 0
\(612\) 11.6847 0.472324
\(613\) 19.7988 11.4309i 0.799668 0.461688i −0.0436871 0.999045i \(-0.513910\pi\)
0.843355 + 0.537357i \(0.180577\pi\)
\(614\) −13.0540 22.6101i −0.526816 0.912471i
\(615\) 0.719224 1.24573i 0.0290019 0.0502328i
\(616\) 46.7386i 1.88315i
\(617\) 9.35980 + 5.40388i 0.376811 + 0.217552i 0.676430 0.736507i \(-0.263526\pi\)
−0.299619 + 0.954059i \(0.596859\pi\)
\(618\) −16.7743 9.68466i −0.674762 0.389574i
\(619\) 24.3002i 0.976707i 0.872646 + 0.488353i \(0.162402\pi\)
−0.872646 + 0.488353i \(0.837598\pi\)
\(620\) 2.00000 3.46410i 0.0803219 0.139122i
\(621\) 1.00000 + 1.73205i 0.0401286 + 0.0695048i
\(622\) 24.1290 13.9309i 0.967484 0.558577i
\(623\) 46.7386 1.87254
\(624\) 0 0
\(625\) 20.3693 0.814773
\(626\) −2.91791 + 1.68466i −0.116623 + 0.0673325i
\(627\) −1.12311 1.94528i −0.0448525 0.0776868i
\(628\) −9.96543 + 17.2606i −0.397664 + 0.688774i
\(629\) 8.80776i 0.351189i
\(630\) 4.43674 + 2.56155i 0.176764 + 0.102055i
\(631\) −12.5041 7.21922i −0.497779 0.287393i 0.230017 0.973187i \(-0.426122\pi\)
−0.727796 + 0.685794i \(0.759455\pi\)
\(632\) 62.7386i 2.49561i
\(633\) −3.65767 + 6.33527i −0.145379 + 0.251804i
\(634\) −29.5270 51.1422i −1.17267 2.03112i
\(635\) −4.64996 + 2.68466i −0.184528 + 0.106537i
\(636\) −53.3002 −2.11349
\(637\) 0 0
\(638\) 29.1231 1.15299
\(639\) 12.1244 7.00000i 0.479632 0.276916i
\(640\) 2.65009 + 4.59010i 0.104754 + 0.181439i
\(641\) 13.0885 22.6700i 0.516966 0.895412i −0.482840 0.875709i \(-0.660395\pi\)
0.999806 0.0197030i \(-0.00627208\pi\)
\(642\) 21.1231i 0.833662i
\(643\) −33.3822 19.2732i −1.31646 0.760061i −0.333306 0.942819i \(-0.608164\pi\)
−0.983158 + 0.182758i \(0.941498\pi\)
\(644\) −28.1393 16.2462i −1.10884 0.640190i
\(645\) 0.246211i 0.00969456i
\(646\) 3.68466 6.38202i 0.144971 0.251097i
\(647\) −23.8078 41.2363i −0.935980 1.62116i −0.772877 0.634555i \(-0.781183\pi\)
−0.163102 0.986609i \(-0.552150\pi\)
\(648\) −5.68247 + 3.28078i −0.223229 + 0.128881i
\(649\) −22.2462 −0.873240
\(650\) 0 0
\(651\) 5.56155 0.217974
\(652\) 62.4473 36.0540i 2.44563 1.41198i
\(653\) −7.43845 12.8838i −0.291089 0.504181i 0.682979 0.730438i \(-0.260684\pi\)
−0.974068 + 0.226258i \(0.927351\pi\)
\(654\) 22.8078 39.5042i 0.891854 1.54474i
\(655\) 9.75379i 0.381112i
\(656\) −17.0474 9.84233i −0.665590 0.384278i
\(657\) −1.62544 0.938447i −0.0634144 0.0366123i
\(658\) 75.2311i 2.93281i
\(659\) −7.12311 + 12.3376i −0.277477 + 0.480604i −0.970757 0.240064i \(-0.922831\pi\)
0.693280 + 0.720668i \(0.256165\pi\)
\(660\) −2.56155 4.43674i −0.0997083 0.172700i
\(661\) −26.3006 + 15.1847i −1.02297 + 0.590615i −0.914964 0.403535i \(-0.867781\pi\)
−0.108011 + 0.994150i \(0.534448\pi\)
\(662\) 60.9848 2.37024
\(663\) 0 0
\(664\) −59.8617 −2.32309
\(665\) 1.94528 1.12311i 0.0754346 0.0435522i
\(666\) −4.40388 7.62775i −0.170647 0.295569i
\(667\) −5.68466 + 9.84612i −0.220111 + 0.381243i
\(668\) 28.4924i 1.10240i
\(669\) −6.92820 4.00000i −0.267860 0.154649i
\(670\) 0.546188 + 0.315342i 0.0211011 + 0.0121827i
\(671\) 24.2462i 0.936015i
\(672\) 11.6847 20.2384i 0.450745 0.780714i
\(673\) −3.37689 5.84895i −0.130170 0.225461i 0.793572 0.608476i \(-0.208219\pi\)
−0.923742 + 0.383016i \(0.874886\pi\)
\(674\) −4.70983 + 2.71922i −0.181416 + 0.104741i
\(675\) 4.68466 0.180313
\(676\) 0 0
\(677\) 25.6155 0.984485 0.492242 0.870458i \(-0.336177\pi\)
0.492242 + 0.870458i \(0.336177\pi\)
\(678\) −32.8491 + 18.9654i −1.26156 + 0.728363i
\(679\) −7.90388 13.6899i −0.303323 0.525371i
\(680\) 4.71922 8.17394i 0.180974 0.313456i
\(681\) 1.12311i 0.0430375i
\(682\) −6.92820 4.00000i −0.265295 0.153168i
\(683\) 31.2704 + 18.0540i 1.19653 + 0.690816i 0.959780 0.280755i \(-0.0905847\pi\)
0.236749 + 0.971571i \(0.423918\pi\)
\(684\) 5.12311i 0.195887i
\(685\) 0.403882 0.699544i 0.0154315 0.0267282i
\(686\) 6.00000 + 10.3923i 0.229081 + 0.396780i
\(687\) −0.213225 + 0.123106i −0.00813505 + 0.00469677i
\(688\) −3.36932 −0.128454
\(689\) 0 0
\(690\) 2.87689 0.109521
\(691\) 1.99202 1.15009i 0.0757800 0.0437516i −0.461631 0.887072i \(-0.652736\pi\)
0.537411 + 0.843320i \(0.319402\pi\)
\(692\) −8.56155 14.8290i −0.325461 0.563716i
\(693\) 3.56155 6.16879i 0.135292 0.234333i
\(694\) 34.8769i 1.32391i
\(695\) −5.31589 3.06913i −0.201643 0.116419i
\(696\) −32.3029 18.6501i −1.22444 0.706930i
\(697\) 6.56155i 0.248537i
\(698\) 17.6847 30.6307i 0.669374 1.15939i
\(699\) 13.0000 + 22.5167i 0.491705 + 0.851658i
\(700\) −65.9114 + 38.0540i −2.49122 + 1.43831i
\(701\) −19.3693 −0.731569 −0.365785 0.930700i \(-0.619199\pi\)
−0.365785 + 0.930700i \(0.619199\pi\)
\(702\) 0 0
\(703\) −3.86174 −0.145648
\(704\) −2.49146 + 1.43845i −0.0939006 + 0.0542135i
\(705\) 2.31534 + 4.01029i 0.0872008 + 0.151036i
\(706\) 22.6501 39.2311i 0.852448 1.47648i
\(707\) 12.2462i 0.460566i
\(708\) 43.9409 + 25.3693i 1.65140 + 0.953437i
\(709\) 22.0771 + 12.7462i 0.829122 + 0.478694i 0.853552 0.521008i \(-0.174444\pi\)
−0.0244297 + 0.999702i \(0.507777\pi\)
\(710\) 20.1383i 0.755775i
\(711\) −4.78078 + 8.28055i −0.179293 + 0.310545i
\(712\) 43.0540 + 74.5717i 1.61352 + 2.79469i
\(713\) 2.70469 1.56155i 0.101291 0.0584806i
\(714\) 23.3693 0.874575
\(715\) 0 0
\(716\) −59.8617 −2.23714
\(717\) −0.546188 + 0.315342i −0.0203977 + 0.0117766i
\(718\) −19.6847 34.0948i −0.734625 1.27241i
\(719\) 0.684658 1.18586i 0.0255335 0.0442252i −0.852976 0.521950i \(-0.825205\pi\)
0.878510 + 0.477724i \(0.158538\pi\)
\(720\) 4.31534i 0.160823i
\(721\) −23.3228 13.4654i −0.868587 0.501479i
\(722\) −39.3508 22.7192i −1.46449 0.845522i
\(723\) 2.80776i 0.104422i
\(724\) −22.0885 + 38.2585i −0.820914 + 1.42187i
\(725\) 13.3153 + 23.0628i 0.494519 + 0.856533i
\(726\) 15.5286 8.96543i 0.576320 0.332738i
\(727\) −39.6695 −1.47126 −0.735630 0.677383i \(-0.763114\pi\)
−0.735630 + 0.677383i \(0.763114\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.33811 + 1.34991i −0.0865372 + 0.0499623i
\(731\) −0.561553 0.972638i −0.0207698 0.0359743i
\(732\) 27.6501 47.8914i 1.02198 1.77012i
\(733\) 53.4924i 1.97579i 0.155131 + 0.987894i \(0.450420\pi\)
−0.155131 + 0.987894i \(0.549580\pi\)
\(734\) −44.4871 25.6847i −1.64205 0.948038i
\(735\) 2.76456 + 1.59612i 0.101972 + 0.0588737i
\(736\) 13.1231i 0.483724i
\(737\) 0.438447 0.759413i 0.0161504 0.0279733i
\(738\) 3.28078 + 5.68247i 0.120767 + 0.209175i
\(739\) 5.40938 3.12311i 0.198987 0.114885i −0.397196 0.917734i \(-0.630017\pi\)
0.596183 + 0.802849i \(0.296683\pi\)
\(740\) −8.80776 −0.323780
\(741\) 0 0
\(742\) −106.600 −3.91342
\(743\) −32.3628 + 18.6847i −1.18728 + 0.685474i −0.957686 0.287814i \(-0.907071\pi\)
−0.229589 + 0.973288i \(0.573738\pi\)
\(744\) 5.12311 + 8.87348i 0.187822 + 0.325318i
\(745\) −1.84233 + 3.19101i −0.0674977 + 0.116909i
\(746\) 9.30019i 0.340504i
\(747\) 7.90084 + 4.56155i 0.289077 + 0.166898i
\(748\) −20.2384 11.6847i −0.739990 0.427233i
\(749\) 29.3693i 1.07313i
\(750\) 6.96543 12.0645i 0.254342 0.440533i
\(751\) −15.0540 26.0743i −0.549327 0.951463i −0.998321 0.0579278i \(-0.981551\pi\)
0.448993 0.893535i \(-0.351783\pi\)
\(752\) 54.8794 31.6847i 2.00125 1.15542i
\(753\) 30.7386 1.12018
\(754\) 0 0
\(755\) 8.63068 0.314103
\(756\) −14.0696 + 8.12311i −0.511708 + 0.295434i
\(757\) −15.0000 25.9808i −0.545184 0.944287i −0.998595 0.0529853i \(-0.983126\pi\)
0.453411 0.891302i \(-0.350207\pi\)
\(758\) 14.4924 25.1016i 0.526388 0.911732i
\(759\) 4.00000i 0.145191i
\(760\) 3.58384 + 2.06913i 0.129999 + 0.0750552i
\(761\) −13.3102 7.68466i −0.482495 0.278569i 0.238961 0.971029i \(-0.423193\pi\)
−0.721456 + 0.692461i \(0.756527\pi\)
\(762\) 24.4924i 0.887267i
\(763\) 31.7116 54.9262i 1.14804 1.98846i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) −1.24573 + 0.719224i −0.0450395 + 0.0260036i
\(766\) −68.4924 −2.47473
\(767\) 0 0
\(768\) −27.0540 −0.976226
\(769\) −15.5885 + 9.00000i −0.562134 + 0.324548i −0.754002 0.656873i \(-0.771879\pi\)
0.191867 + 0.981421i \(0.438546\pi\)
\(770\) −5.12311 8.87348i −0.184624 0.319778i
\(771\) −8.08854 + 14.0098i −0.291302 + 0.504549i
\(772\) 88.9157i 3.20015i
\(773\) 6.71498 + 3.87689i 0.241521 + 0.139442i 0.615876 0.787843i \(-0.288802\pi\)
−0.374355 + 0.927286i \(0.622136\pi\)
\(774\) 0.972638 + 0.561553i 0.0349608 + 0.0201846i
\(775\) 7.31534i 0.262775i
\(776\) 14.5616 25.2213i 0.522729 0.905394i
\(777\) −6.12311 10.6055i −0.219665 0.380471i
\(778\) 6.77485 3.91146i 0.242890 0.140233i
\(779\) 2.87689 0.103075
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) 11.3649 6.56155i 0.406410 0.234641i
\(783\) 2.84233 + 4.92306i 0.101577 + 0.175936i
\(784\) 21.8423 37.8320i 0.780083 1.35114i
\(785\) 2.45360i 0.0875728i
\(786\) 38.5316 + 22.2462i 1.37438 + 0.793496i
\(787\) −1.01938 0.588540i −0.0363370 0.0209792i 0.481721 0.876324i \(-0.340012\pi\)
−0.518058 + 0.855345i \(0.673345\pi\)
\(788\) 51.8617i 1.84750i
\(789\) 7.68466 13.3102i 0.273581 0.473856i
\(790\) 6.87689 + 11.9111i 0.244669 + 0.423779i
\(791\) −45.6730 + 26.3693i −1.62394 + 0.937585i
\(792\) 13.1231 0.466309
\(793\) 0 0
\(794\) −30.8769 −1.09578
\(795\) 5.68247 3.28078i 0.201536 0.116357i
\(796\) 52.8617 + 91.5592i 1.87363 + 3.24523i
\(797\) −20.8078 + 36.0401i −0.737049 + 1.27661i 0.216770 + 0.976223i \(0.430448\pi\)
−0.953819 + 0.300383i \(0.902885\pi\)
\(798\) 10.2462i 0.362712i
\(799\) 18.2931 + 10.5616i 0.647165 + 0.373641i
\(800\) −26.6204 15.3693i −0.941175 0.543387i
\(801\) 13.1231i 0.463682i
\(802\) −23.7732 + 41.1764i −0.839461 + 1.45399i
\(803\) 1.87689 + 3.25088i 0.0662342 + 0.114721i
\(804\) −1.73205 + 1.00000i −0.0610847 + 0.0352673i
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 3.36932 0.118606
\(808\) −19.5389 + 11.2808i −0.687375 + 0.396856i
\(809\) −18.6501 32.3029i −0.655702 1.13571i −0.981717 0.190345i \(-0.939039\pi\)
0.326015 0.945365i \(-0.394294\pi\)
\(810\) 0.719224 1.24573i 0.0252709 0.0437706i
\(811\) 1.56155i 0.0548335i −0.999624 0.0274168i \(-0.991272\pi\)
0.999624 0.0274168i \(-0.00872812\pi\)
\(812\) −79.9811 46.1771i −2.80678 1.62050i
\(813\) −0.925894 0.534565i −0.0324725 0.0187480i
\(814\) 17.6155i 0.617424i
\(815\) −4.43845 + 7.68762i −0.155472 + 0.269285i
\(816\) 9.84233 + 17.0474i 0.344550 + 0.596779i
\(817\) 0.426450 0.246211i 0.0149196 0.00861384i
\(818\) 47.0540 1.64520
\(819\) 0 0
\(820\) 6.56155 0.229139
\(821\) −22.9431 + 13.2462i −0.800720 + 0.462296i −0.843723 0.536779i \(-0.819641\pi\)
0.0430028 + 0.999075i \(0.486308\pi\)
\(822\) 1.84233 + 3.19101i 0.0642586 + 0.111299i
\(823\) 4.00000 6.92820i 0.139431 0.241502i −0.787850 0.615867i \(-0.788806\pi\)
0.927281 + 0.374365i \(0.122139\pi\)
\(824\) 49.6155i 1.72844i
\(825\) −8.11407 4.68466i −0.282496 0.163099i
\(826\) 87.8819 + 50.7386i 3.05780 + 1.76542i
\(827\) 34.7386i 1.20798i −0.796992 0.603990i \(-0.793577\pi\)
0.796992 0.603990i \(-0.206423\pi\)
\(828\) −4.56155 + 7.90084i −0.158525 + 0.274573i
\(829\) −9.74621 16.8809i −0.338500 0.586299i 0.645651 0.763633i \(-0.276586\pi\)
−0.984151 + 0.177334i \(0.943253\pi\)
\(830\) 11.3649 6.56155i 0.394483 0.227755i
\(831\) −17.6847 −0.613474
\(832\) 0 0
\(833\) 14.5616 0.504528
\(834\) 24.2487 14.0000i 0.839664 0.484780i
\(835\) 1.75379 + 3.03765i 0.0606924 + 0.105122i
\(836\) 5.12311 8.87348i 0.177186 0.306896i
\(837\) 1.56155i 0.0539752i
\(838\) 39.3845 + 22.7386i 1.36051 + 0.785493i
\(839\) −16.9875 9.80776i −0.586475 0.338602i 0.177227 0.984170i \(-0.443287\pi\)
−0.763703 + 0.645568i \(0.776621\pi\)
\(840\) 13.1231i 0.452790i
\(841\) −1.65767 + 2.87117i −0.0571611 + 0.0990059i
\(842\) 18.8963 + 32.7294i 0.651210 + 1.12793i
\(843\) 2.43160 1.40388i 0.0837486 0.0483523i
\(844\) −33.3693 −1.14862
\(845\) 0 0
\(846\) −21.1231 −0.726227
\(847\) 21.5908 12.4654i 0.741868 0.428317i
\(848\) −44.8963 77.7627i −1.54175 2.67038i
\(849\) −0.657671 + 1.13912i −0.0225712 + 0.0390945i
\(850\) 30.7386i 1.05433i
\(851\) −5.95557 3.43845i −0.204154 0.117868i
\(852\) 55.3059 + 31.9309i 1.89475 + 1.09393i
\(853\) 6.12311i 0.209651i 0.994491 + 0.104826i \(0.0334284\pi\)
−0.994491 + 0.104826i \(0.966572\pi\)
\(854\) 55.3002 95.7827i 1.89233 3.27762i
\(855\) −0.315342 0.546188i −0.0107845 0.0186792i
\(856\) −46.8589 + 27.0540i −1.60160 + 0.924686i
\(857\) −31.4384 −1.07392 −0.536958 0.843609i \(-0.680427\pi\)
−0.536958 + 0.843609i \(0.680427\pi\)
\(858\) 0 0
\(859\) 20.4384 0.697351 0.348675 0.937244i \(-0.386632\pi\)
0.348675 + 0.937244i \(0.386632\pi\)
\(860\) 0.972638 0.561553i 0.0331667 0.0191488i
\(861\) 4.56155 + 7.90084i 0.155457 + 0.269260i
\(862\) −3.68466 + 6.38202i −0.125500 + 0.217372i
\(863\) 2.49242i 0.0848430i −0.999100 0.0424215i \(-0.986493\pi\)
0.999100 0.0424215i \(-0.0135072\pi\)
\(864\) −5.68247 3.28078i −0.193322 0.111614i
\(865\) 1.82554 + 1.05398i 0.0620702 + 0.0358362i
\(866\) 64.6695i 2.19756i
\(867\) 5.21922 9.03996i 0.177254 0.307013i
\(868\) 12.6847 + 21.9705i 0.430545 + 0.745726i
\(869\) 16.5611 9.56155i 0.561797 0.324353i
\(870\) 8.17708 0.277229
\(871\) 0 0
\(872\) 116.847 3.95692
\(873\) −3.84381 + 2.21922i −0.130093 + 0.0751093i
\(874\) 2.87689 + 4.98293i 0.0973124 + 0.168550i
\(875\) 9.68466 16.7743i 0.327401 0.567076i
\(876\) 8.56155i 0.289268i
\(877\) −16.8342 9.71922i −0.568450 0.328195i 0.188080 0.982154i \(-0.439774\pi\)
−0.756530 + 0.653959i \(0.773107\pi\)
\(878\) −2.91791 1.68466i −0.0984748 0.0568545i
\(879\) 24.5616i 0.828441i
\(880\) 4.31534 7.47439i 0.145470 0.251962i
\(881\) −18.9654 32.8491i −0.638962 1.10671i −0.985661 0.168738i \(-0.946031\pi\)
0.346699 0.937976i \(-0.387302\pi\)
\(882\) −12.6107 + 7.28078i −0.424624 + 0.245156i
\(883\) 11.8078 0.397363 0.198681 0.980064i \(-0.436334\pi\)
0.198681 + 0.980064i \(0.436334\pi\)
\(884\) 0 0
\(885\) −6.24621 −0.209964
\(886\) 32.6957 18.8769i 1.09843 0.634182i
\(887\) −24.6847 42.7551i −0.828830 1.43558i −0.898957 0.438037i \(-0.855674\pi\)
0.0701272 0.997538i \(-0.477659\pi\)
\(888\) 11.2808 19.5389i 0.378558 0.655682i
\(889\) 34.0540i 1.14213i
\(890\) −16.3479 9.43845i −0.547982 0.316377i
\(891\) −1.73205 1.00000i −0.0580259 0.0335013i
\(892\) 36.4924i 1.22186i
\(893\) −4.63068 + 8.02058i −0.154960 + 0.268398i
\(894\) −8.40388 14.5560i −0.281068 0.486824i
\(895\) 6.38202 3.68466i 0.213327 0.123165i
\(896\) −33.6155 −1.12302
\(897\) 0 0
\(898\) 21.1231 0.704887
\(899\) 7.68762 4.43845i 0.256396 0.148031i
\(900\) 10.6847 + 18.5064i 0.356155 + 0.616879i
\(901\) 14.9654 25.9209i 0.498571 0.863550i
\(902\) 13.1231i 0.436952i
\(903\) 1.35234 + 0.780776i 0.0450032 + 0.0259826i
\(904\) −84.1447 48.5810i −2.79861 1.61578i
\(905\) 5.43845i 0.180780i
\(906\) −19.6847 + 34.0948i −0.653979 + 1.13272i
\(907\) 14.0000 + 24.2487i 0.464862 + 0.805165i 0.999195 0.0401089i \(-0.0127705\pi\)
−0.534333 + 0.845274i \(0.679437\pi\)
\(908\) 4.43674 2.56155i 0.147238 0.0850081i
\(909\) 3.43845 0.114046
\(910\) 0 0
\(911\) −10.7386 −0.355787 −0.177893 0.984050i \(-0.556928\pi\)
−0.177893 + 0.984050i \(0.556928\pi\)
\(912\) −7.47439 + 4.31534i −0.247502 + 0.142895i
\(913\) −9.12311 15.8017i −0.301931 0.522959i
\(914\) −36.6501 + 63.4798i −1.21228 + 2.09973i
\(915\) 6.80776i 0.225058i
\(916\) −0.972638 0.561553i −0.0321369 0.0185542i
\(917\) 53.5738 + 30.9309i 1.76916 + 1.02143i
\(918\) 6.56155i 0.216564i
\(919\) −22.2462 + 38.5316i −0.733835 + 1.27104i 0.221398 + 0.975184i \(0.428938\pi\)
−0.955233 + 0.295856i \(0.904395\pi\)
\(920\) 3.68466 + 6.38202i 0.121480 + 0.210409i
\(921\) −8.82674 + 5.09612i −0.290851 + 0.167923i
\(922\) 94.2850 3.10511
\(923\) 0 0
\(924\) 32.4924 1.06892
\(925\) −13.9499 + 8.05398i −0.458670 + 0.264813i
\(926\) 34.1771 + 59.1964i 1.12313 + 1.94532i
\(927\) −3.78078 + 6.54850i −0.124177 + 0.215081i
\(928\) 37.3002i 1.22444i
\(929\) −11.0918 6.40388i −0.363912 0.210105i 0.306884 0.951747i \(-0.400714\pi\)
−0.670795 + 0.741643i \(0.734047\pi\)
\(930\) −1.94528 1.12311i −0.0637881 0.0368281i
\(931\) 6.38447i 0.209243i
\(932\) −59.3002 + 102.711i −1.94244 + 3.36441i
\(933\) −5.43845 9.41967i −0.178047 0.308386i
\(934\) 57.6776 33.3002i 1.88727 1.08962i
\(935\) 2.87689 0.0940845
\(936\) 0 0
\(937\) −3.43845 −0.112329 −0.0561646 0.998422i \(-0.517887\pi\)
−0.0561646 + 0.998422i \(0.517887\pi\)
\(938\) −3.46410 + 2.00000i −0.113107 + 0.0653023i
\(939\) 0.657671 + 1.13912i 0.0214623 + 0.0371738i
\(940\) −10.5616 + 18.2931i −0.344480 + 0.596657i
\(941\) 2.49242i 0.0812507i −0.999174 0.0406253i \(-0.987065\pi\)
0.999174 0.0406253i \(-0.0129350\pi\)
\(942\) 9.69276 + 5.59612i 0.315807 + 0.182331i
\(943\) 4.43674 + 2.56155i 0.144480 + 0.0834156i
\(944\) 85.4773i 2.78205i
\(945\) 1.00000 1.73205i 0.0325300 0.0563436i
\(946\) −1.12311 1.94528i −0.0365153 0.0632464i
\(947\) −9.29993 + 5.36932i −0.302207 + 0.174479i −0.643434 0.765502i \(-0.722491\pi\)
0.341227 + 0.939981i \(0.389158\pi\)
\(948\) −43.6155 −1.41657
\(949\) 0 0
\(950\) 13.4773 0.437260
\(951\) −19.9653 + 11.5270i −0.647420 + 0.373788i
\(952\) 29.9309 + 51.8418i 0.970065 + 1.68020i
\(953\) −17.4924 + 30.2978i −0.566635 + 0.981441i 0.430260 + 0.902705i \(0.358422\pi\)
−0.996896 + 0.0787360i \(0.974912\pi\)
\(954\) 29.9309i 0.969048i
\(955\) 0.426450 + 0.246211i 0.0137996 + 0.00796721i
\(956\) −2.49146 1.43845i −0.0805797 0.0465227i
\(957\) 11.3693i 0.367518i
\(958\) 8.00000 13.8564i 0.258468 0.447680i
\(959\) 2.56155 + 4.43674i 0.0827169 + 0.143270i
\(960\) −0.699544 + 0.403882i −0.0225777 + 0.0130352i
\(961\) 28.5616 0.921340
\(962\) 0 0
\(963\) 8.24621 0.265730
\(964\) 11.0918 6.40388i 0.357244 0.206255i
\(965\) −5.47301 9.47954i −0.176183 0.305157i
\(966\) −9.12311 + 15.8017i −0.293531 + 0.508411i
\(967\) 9.12311i 0.293379i −0.989183 0.146690i \(-0.953138\pi\)
0.989183 0.146690i \(-0.0468619\pi\)
\(968\) 39.7773 + 22.9654i 1.27849 + 0.738137i
\(969\) −2.49146 1.43845i −0.0800373 0.0462096i
\(970\) 6.38447i 0.204993i
\(971\) −26.4924 + 45.8862i −0.850182 + 1.47256i 0.0308612 + 0.999524i \(0.490175\pi\)
−0.881043 + 0.473035i \(0.843158\pi\)
\(972\) 2.28078 + 3.95042i 0.0731559 + 0.126710i
\(973\) 33.7151 19.4654i 1.08086 0.624033i
\(974\) 2.87689 0.0921816
\(975\) 0 0
\(976\) 93.1619 2.98204
\(977\) 13.7030 7.91146i 0.438399 0.253110i −0.264519 0.964380i \(-0.585213\pi\)
0.702918 + 0.711270i \(0.251880\pi\)
\(978\) −20.2462 35.0675i −0.647402 1.12133i
\(979\) −13.1231 + 22.7299i −0.419416 + 0.726450i
\(980\) 14.5616i 0.465152i
\(981\) −15.4220 8.90388i −0.492386 0.284279i
\(982\) −43.8212 25.3002i −1.39839 0.807361i
\(983\) 27.6155i 0.880799i 0.897802 + 0.440399i \(0.145163\pi\)
−0.897802 + 0.440399i \(0.854837\pi\)
\(984\) −8.40388 + 14.5560i −0.267906 + 0.464027i
\(985\) −3.19224 5.52911i −0.101713 0.176172i
\(986\) 32.3029 18.6501i 1.02873 0.593940i
\(987\) −29.3693 −0.934836
\(988\) 0 0
\(989\) 0.876894 0.0278836
\(990\) −2.49146 + 1.43845i −0.0791839 + 0.0457169i
\(991\) −20.1771 34.9477i −0.640946 1.11015i −0.985222 0.171283i \(-0.945209\pi\)
0.344276 0.938869i \(-0.388124\pi\)
\(992\) −5.12311 + 8.87348i −0.162659 + 0.281733i
\(993\) 23.8078i 0.755517i
\(994\) 110.612 + 63.8617i 3.50839 + 2.02557i
\(995\) −11.2715 6.50758i −0.357329 0.206304i
\(996\) 41.6155i 1.31864i
\(997\) −10.3078 + 17.8536i −0.326450 + 0.565428i −0.981805 0.189893i \(-0.939186\pi\)
0.655355 + 0.755321i \(0.272519\pi\)
\(998\) −36.4924 63.2067i −1.15515 2.00077i
\(999\) −2.97778 + 1.71922i −0.0942129 + 0.0543938i
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 507.2.j.g.361.4 8
13.2 odd 12 507.2.a.g.1.2 2
13.3 even 3 507.2.b.d.337.4 4
13.4 even 6 inner 507.2.j.g.316.4 8
13.5 odd 4 39.2.e.b.16.1 4
13.6 odd 12 39.2.e.b.22.1 yes 4
13.7 odd 12 507.2.e.g.22.2 4
13.8 odd 4 507.2.e.g.484.2 4
13.9 even 3 inner 507.2.j.g.316.1 8
13.10 even 6 507.2.b.d.337.1 4
13.11 odd 12 507.2.a.d.1.1 2
13.12 even 2 inner 507.2.j.g.361.1 8
39.2 even 12 1521.2.a.g.1.1 2
39.5 even 4 117.2.g.c.55.2 4
39.11 even 12 1521.2.a.m.1.2 2
39.23 odd 6 1521.2.b.h.1351.4 4
39.29 odd 6 1521.2.b.h.1351.1 4
39.32 even 12 117.2.g.c.100.2 4
52.11 even 12 8112.2.a.bo.1.1 2
52.15 even 12 8112.2.a.bk.1.2 2
52.19 even 12 624.2.q.h.529.2 4
52.31 even 4 624.2.q.h.289.2 4
65.18 even 4 975.2.bb.i.874.1 8
65.19 odd 12 975.2.i.k.451.2 4
65.32 even 12 975.2.bb.i.724.1 8
65.44 odd 4 975.2.i.k.601.2 4
65.57 even 4 975.2.bb.i.874.4 8
65.58 even 12 975.2.bb.i.724.4 8
156.71 odd 12 1872.2.t.r.1153.1 4
156.83 odd 4 1872.2.t.r.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.e.b.16.1 4 13.5 odd 4
39.2.e.b.22.1 yes 4 13.6 odd 12
117.2.g.c.55.2 4 39.5 even 4
117.2.g.c.100.2 4 39.32 even 12
507.2.a.d.1.1 2 13.11 odd 12
507.2.a.g.1.2 2 13.2 odd 12
507.2.b.d.337.1 4 13.10 even 6
507.2.b.d.337.4 4 13.3 even 3
507.2.e.g.22.2 4 13.7 odd 12
507.2.e.g.484.2 4 13.8 odd 4
507.2.j.g.316.1 8 13.9 even 3 inner
507.2.j.g.316.4 8 13.4 even 6 inner
507.2.j.g.361.1 8 13.12 even 2 inner
507.2.j.g.361.4 8 1.1 even 1 trivial
624.2.q.h.289.2 4 52.31 even 4
624.2.q.h.529.2 4 52.19 even 12
975.2.i.k.451.2 4 65.19 odd 12
975.2.i.k.601.2 4 65.44 odd 4
975.2.bb.i.724.1 8 65.32 even 12
975.2.bb.i.724.4 8 65.58 even 12
975.2.bb.i.874.1 8 65.18 even 4
975.2.bb.i.874.4 8 65.57 even 4
1521.2.a.g.1.1 2 39.2 even 12
1521.2.a.m.1.2 2 39.11 even 12
1521.2.b.h.1351.1 4 39.29 odd 6
1521.2.b.h.1351.4 4 39.23 odd 6
1872.2.t.r.289.1 4 156.83 odd 4
1872.2.t.r.1153.1 4 156.71 odd 12
8112.2.a.bk.1.2 2 52.15 even 12
8112.2.a.bo.1.1 2 52.11 even 12