Properties

Label 975.2.bb.i.874.1
Level $975$
Weight $2$
Character 975.874
Analytic conductor $7.785$
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] = [975,2,Mod(724,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.724");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.bb (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: \(7.78541419707\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 874.1
Root \(-2.21837 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 975.874
Dual form 975.2.bb.i.724.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.21837 + 1.28078i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.28078 - 3.95042i) q^{4} +(-1.28078 + 2.21837i) q^{6} +(-3.08440 - 1.78078i) q^{7} +6.56155i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.21837 + 1.28078i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.28078 - 3.95042i) q^{4} +(-1.28078 + 2.21837i) q^{6} +(-3.08440 - 1.78078i) q^{7} +6.56155i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -4.56155i q^{12} +(-3.57071 + 0.500000i) q^{13} +9.12311 q^{14} +(-3.84233 - 6.65511i) q^{16} +(2.21837 + 1.28078i) q^{17} +2.56155i q^{18} +(-0.561553 + 0.972638i) q^{19} -3.56155 q^{21} +(-4.43674 - 2.56155i) q^{22} +(1.73205 - 1.00000i) q^{23} +(3.28078 + 5.68247i) q^{24} +(7.28078 - 5.68247i) q^{26} -1.00000i q^{27} +(-14.0696 + 8.12311i) q^{28} +(-2.84233 - 4.92306i) q^{29} -1.56155 q^{31} +(5.68247 + 3.28078i) q^{32} +(1.73205 + 1.00000i) q^{33} -6.56155 q^{34} +(-2.28078 - 3.95042i) q^{36} +(-2.97778 + 1.71922i) q^{37} -2.87689i q^{38} +(-2.84233 + 2.21837i) q^{39} +(-1.28078 - 2.21837i) q^{41} +(7.90084 - 4.56155i) q^{42} +(-0.379706 - 0.219224i) q^{43} +9.12311 q^{44} +(-2.56155 + 4.43674i) q^{46} +8.24621i q^{47} +(-6.65511 - 3.84233i) q^{48} +(2.84233 + 4.92306i) q^{49} +2.56155 q^{51} +(-6.16879 + 15.2462i) q^{52} +11.6847i q^{53} +(1.28078 + 2.21837i) q^{54} +(11.6847 - 20.2384i) q^{56} +1.12311i q^{57} +(12.6107 + 7.28078i) q^{58} +(-5.56155 + 9.63289i) q^{59} +(-6.06155 + 10.4989i) q^{61} +(3.46410 - 2.00000i) q^{62} +(-3.08440 + 1.78078i) q^{63} -1.43845 q^{64} -5.12311 q^{66} +(-0.379706 + 0.219224i) q^{67} +(10.1192 - 5.84233i) q^{68} +(1.00000 - 1.73205i) q^{69} +(-7.00000 + 12.1244i) q^{71} +(5.68247 + 3.28078i) q^{72} -1.87689i q^{73} +(4.40388 - 7.62775i) q^{74} +(2.56155 + 4.43674i) q^{76} -7.12311i q^{77} +(3.46410 - 8.56155i) q^{78} -9.56155 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.68247 + 3.28078i) q^{82} -9.12311i q^{83} +(-8.12311 + 14.0696i) q^{84} +1.12311 q^{86} +(-4.92306 - 2.84233i) q^{87} +(-11.3649 + 6.56155i) q^{88} +(6.56155 + 11.3649i) q^{89} +(11.9039 + 4.81645i) q^{91} -9.12311i q^{92} +(-1.35234 + 0.780776i) q^{93} +(-10.5616 - 18.2931i) q^{94} +6.56155 q^{96} +(-3.84381 - 2.21922i) q^{97} +(-12.6107 - 7.28078i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9} + 8 q^{11} + 40 q^{14} - 6 q^{16} + 12 q^{19} - 12 q^{21} + 18 q^{24} + 50 q^{26} + 2 q^{29} + 4 q^{31} - 36 q^{34} - 10 q^{36} + 2 q^{39} - 2 q^{41} + 40 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{51} + 2 q^{54} + 44 q^{56} - 28 q^{59} - 32 q^{61} - 28 q^{64} - 8 q^{66} + 8 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} - 60 q^{79} - 4 q^{81} - 32 q^{84} - 24 q^{86} + 36 q^{89} + 54 q^{91} - 68 q^{94} + 36 q^{96} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21837 + 1.28078i −1.56862 + 0.905646i −0.572295 + 0.820048i \(0.693947\pi\)
−0.996330 + 0.0855975i \(0.972720\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 2.28078 3.95042i 1.14039 1.97521i
\(5\) 0 0
\(6\) −1.28078 + 2.21837i −0.522875 + 0.905646i
\(7\) −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 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 4.56155i 1.31681i
\(13\) −3.57071 + 0.500000i −0.990338 + 0.138675i
\(14\) 9.12311 2.43825
\(15\) 0 0
\(16\) −3.84233 6.65511i −0.960582 1.66378i
\(17\) 2.21837 + 1.28078i 0.538034 + 0.310634i 0.744282 0.667866i \(-0.232792\pi\)
−0.206248 + 0.978500i \(0.566125\pi\)
\(18\) 2.56155i 0.603764i
\(19\) −0.561553 + 0.972638i −0.128829 + 0.223138i −0.923223 0.384264i \(-0.874455\pi\)
0.794394 + 0.607403i \(0.207789\pi\)
\(20\) 0 0
\(21\) −3.56155 −0.777195
\(22\) −4.43674 2.56155i −0.945916 0.546125i
\(23\) 1.73205 1.00000i 0.361158 0.208514i −0.308431 0.951247i \(-0.599804\pi\)
0.669588 + 0.742732i \(0.266471\pi\)
\(24\) 3.28078 + 5.68247i 0.669686 + 1.15993i
\(25\) 0 0
\(26\) 7.28078 5.68247i 1.42788 1.11442i
\(27\) 1.00000i 0.192450i
\(28\) −14.0696 + 8.12311i −2.65891 + 1.53512i
\(29\) −2.84233 4.92306i −0.527807 0.914189i −0.999475 0.0324124i \(-0.989681\pi\)
0.471667 0.881777i \(-0.343652\pi\)
\(30\) 0 0
\(31\) −1.56155 −0.280463 −0.140232 0.990119i \(-0.544785\pi\)
−0.140232 + 0.990119i \(0.544785\pi\)
\(32\) 5.68247 + 3.28078i 1.00453 + 0.579965i
\(33\) 1.73205 + 1.00000i 0.301511 + 0.174078i
\(34\) −6.56155 −1.12530
\(35\) 0 0
\(36\) −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 \(0.424543\pi\)
\(38\) 2.87689i 0.466694i
\(39\) −2.84233 + 2.21837i −0.455137 + 0.355223i
\(40\) 0 0
\(41\) −1.28078 2.21837i −0.200024 0.346451i 0.748512 0.663121i \(-0.230769\pi\)
−0.948536 + 0.316670i \(0.897435\pi\)
\(42\) 7.90084 4.56155i 1.21913 0.703863i
\(43\) −0.379706 0.219224i −0.0579047 0.0334313i 0.470768 0.882257i \(-0.343977\pi\)
−0.528673 + 0.848826i \(0.677310\pi\)
\(44\) 9.12311 1.37536
\(45\) 0 0
\(46\) −2.56155 + 4.43674i −0.377680 + 0.654162i
\(47\) 8.24621i 1.20283i 0.798935 + 0.601417i \(0.205397\pi\)
−0.798935 + 0.601417i \(0.794603\pi\)
\(48\) −6.65511 3.84233i −0.960582 0.554592i
\(49\) 2.84233 + 4.92306i 0.406047 + 0.703294i
\(50\) 0 0
\(51\) 2.56155 0.358689
\(52\) −6.16879 + 15.2462i −0.855457 + 2.11427i
\(53\) 11.6847i 1.60501i 0.596645 + 0.802506i \(0.296500\pi\)
−0.596645 + 0.802506i \(0.703500\pi\)
\(54\) 1.28078 + 2.21837i 0.174292 + 0.301882i
\(55\) 0 0
\(56\) 11.6847 20.2384i 1.56143 2.70447i
\(57\) 1.12311i 0.148759i
\(58\) 12.6107 + 7.28078i 1.65586 + 0.956013i
\(59\) −5.56155 + 9.63289i −0.724053 + 1.25410i 0.235310 + 0.971920i \(0.424389\pi\)
−0.959363 + 0.282175i \(0.908944\pi\)
\(60\) 0 0
\(61\) −6.06155 + 10.4989i −0.776102 + 1.34425i 0.158071 + 0.987428i \(0.449473\pi\)
−0.934173 + 0.356821i \(0.883861\pi\)
\(62\) 3.46410 2.00000i 0.439941 0.254000i
\(63\) −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 −0.523015 0.852324i \(-0.675193\pi\)
0.476626 + 0.879106i \(0.341859\pi\)
\(68\) 10.1192 5.84233i 1.22713 0.708486i
\(69\) 1.00000 1.73205i 0.120386 0.208514i
\(70\) 0 0
\(71\) −7.00000 + 12.1244i −0.830747 + 1.43890i 0.0666994 + 0.997773i \(0.478753\pi\)
−0.897447 + 0.441123i \(0.854580\pi\)
\(72\) 5.68247 + 3.28078i 0.669686 + 0.386643i
\(73\) 1.87689i 0.219674i −0.993950 0.109837i \(-0.964967\pi\)
0.993950 0.109837i \(-0.0350329\pi\)
\(74\) 4.40388 7.62775i 0.511941 0.886708i
\(75\) 0 0
\(76\) 2.56155 + 4.43674i 0.293830 + 0.508929i
\(77\) 7.12311i 0.811753i
\(78\) 3.46410 8.56155i 0.392232 0.969405i
\(79\) −9.56155 −1.07576 −0.537879 0.843022i \(-0.680774\pi\)
−0.537879 + 0.843022i \(0.680774\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.68247 + 3.28078i 0.627524 + 0.362301i
\(83\) 9.12311i 1.00139i −0.865624 0.500695i \(-0.833078\pi\)
0.865624 0.500695i \(-0.166922\pi\)
\(84\) −8.12311 + 14.0696i −0.886303 + 1.53512i
\(85\) 0 0
\(86\) 1.12311 0.121108
\(87\) −4.92306 2.84233i −0.527807 0.304730i
\(88\) −11.3649 + 6.56155i −1.21151 + 0.699464i
\(89\) 6.56155 + 11.3649i 0.695523 + 1.20468i 0.970004 + 0.243089i \(0.0781607\pi\)
−0.274481 + 0.961593i \(0.588506\pi\)
\(90\) 0 0
\(91\) 11.9039 + 4.81645i 1.24787 + 0.504901i
\(92\) 9.12311i 0.951150i
\(93\) −1.35234 + 0.780776i −0.140232 + 0.0809627i
\(94\) −10.5616 18.2931i −1.08934 1.88679i
\(95\) 0 0
\(96\) 6.56155 0.669686
\(97\) −3.84381 2.21922i −0.390280 0.225328i 0.292002 0.956418i \(-0.405679\pi\)
−0.682281 + 0.731090i \(0.739012\pi\)
\(98\) −12.6107 7.28078i −1.27387 0.735469i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 1.71922 + 2.97778i 0.171069 + 0.296300i 0.938794 0.344479i \(-0.111945\pi\)
−0.767725 + 0.640780i \(0.778611\pi\)
\(102\) −5.68247 + 3.28078i −0.562649 + 0.324845i
\(103\) 7.56155i 0.745062i −0.928020 0.372531i \(-0.878490\pi\)
0.928020 0.372531i \(-0.121510\pi\)
\(104\) −3.28078 23.4294i −0.321707 2.29744i
\(105\) 0 0
\(106\) −14.9654 25.9209i −1.45357 2.51766i
\(107\) −7.14143 + 4.12311i −0.690388 + 0.398596i −0.803757 0.594957i \(-0.797169\pi\)
0.113369 + 0.993553i \(0.463836\pi\)
\(108\) −3.95042 2.28078i −0.380129 0.219468i
\(109\) −17.8078 −1.70567 −0.852837 0.522177i \(-0.825120\pi\)
−0.852837 + 0.522177i \(0.825120\pi\)
\(110\) 0 0
\(111\) −1.71922 + 2.97778i −0.163181 + 0.282639i
\(112\) 27.3693i 2.58616i
\(113\) 12.8239 + 7.40388i 1.20637 + 0.696499i 0.961965 0.273174i \(-0.0880736\pi\)
0.244406 + 0.969673i \(0.421407\pi\)
\(114\) −1.43845 2.49146i −0.134723 0.233347i
\(115\) 0 0
\(116\) −25.9309 −2.40762
\(117\) −1.35234 + 3.34233i −0.125024 + 0.308998i
\(118\) 28.4924i 2.62294i
\(119\) −4.56155 7.90084i −0.418157 0.724269i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 31.0540i 2.81149i
\(123\) −2.21837 1.28078i −0.200024 0.115484i
\(124\) −3.56155 + 6.16879i −0.319837 + 0.553974i
\(125\) 0 0
\(126\) 4.56155 7.90084i 0.406375 0.703863i
\(127\) −8.28055 + 4.78078i −0.734780 + 0.424225i −0.820168 0.572122i \(-0.806120\pi\)
0.0853884 + 0.996348i \(0.472787\pi\)
\(128\) −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
\(133\) 3.46410 2.00000i 0.300376 0.173422i
\(134\) 0.561553 0.972638i 0.0485108 0.0840231i
\(135\) 0 0
\(136\) −8.40388 + 14.5560i −0.720627 + 1.24816i
\(137\) −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 −0.535564 0.844495i \(-0.679901\pi\)
0.999136 + 0.0415643i \(0.0132342\pi\)
\(140\) 0 0
\(141\) 4.12311 + 7.14143i 0.347228 + 0.601417i
\(142\) 35.8617i 3.00945i
\(143\) −4.43674 5.68466i −0.371019 0.475375i
\(144\) −7.68466 −0.640388
\(145\) 0 0
\(146\) 2.40388 + 4.16365i 0.198947 + 0.344586i
\(147\) 4.92306 + 2.84233i 0.406047 + 0.234431i
\(148\) 15.6847i 1.28927i
\(149\) −3.28078 + 5.68247i −0.268772 + 0.465526i −0.968545 0.248839i \(-0.919951\pi\)
0.699773 + 0.714365i \(0.253284\pi\)
\(150\) 0 0
\(151\) 15.3693 1.25074 0.625369 0.780329i \(-0.284949\pi\)
0.625369 + 0.780329i \(0.284949\pi\)
\(152\) −6.38202 3.68466i −0.517650 0.298865i
\(153\) 2.21837 1.28078i 0.179345 0.103545i
\(154\) 9.12311 + 15.8017i 0.735161 + 1.27334i
\(155\) 0 0
\(156\) 2.28078 + 16.2880i 0.182608 + 1.30408i
\(157\) 4.36932i 0.348709i 0.984683 + 0.174355i \(0.0557839\pi\)
−0.984683 + 0.174355i \(0.944216\pi\)
\(158\) 21.2111 12.2462i 1.68746 0.974256i
\(159\) 5.84233 + 10.1192i 0.463327 + 0.802506i
\(160\) 0 0
\(161\) −7.12311 −0.561379
\(162\) 2.21837 + 1.28078i 0.174292 + 0.100627i
\(163\) −13.6899 7.90388i −1.07228 0.619080i −0.143475 0.989654i \(-0.545828\pi\)
−0.928803 + 0.370574i \(0.879161\pi\)
\(164\) −11.6847 −0.912419
\(165\) 0 0
\(166\) 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 \(0.255637\pi\)
\(168\) 23.3693i 1.80298i
\(169\) 12.5000 3.57071i 0.961538 0.274670i
\(170\) 0 0
\(171\) 0.561553 + 0.972638i 0.0429430 + 0.0743795i
\(172\) −1.73205 + 1.00000i −0.132068 + 0.0762493i
\(173\) −3.25088 1.87689i −0.247160 0.142698i 0.371303 0.928512i \(-0.378911\pi\)
−0.618463 + 0.785814i \(0.712244\pi\)
\(174\) 14.5616 1.10391
\(175\) 0 0
\(176\) 7.68466 13.3102i 0.579253 1.00330i
\(177\) 11.1231i 0.836064i
\(178\) −29.1119 16.8078i −2.18203 1.25980i
\(179\) −6.56155 11.3649i −0.490433 0.849456i 0.509506 0.860467i \(-0.329828\pi\)
−0.999939 + 0.0110115i \(0.996495\pi\)
\(180\) 0 0
\(181\) 9.68466 0.719855 0.359927 0.932980i \(-0.382801\pi\)
0.359927 + 0.932980i \(0.382801\pi\)
\(182\) −32.5760 + 4.56155i −2.41469 + 0.338125i
\(183\) 12.1231i 0.896166i
\(184\) 6.56155 + 11.3649i 0.483724 + 0.837835i
\(185\) 0 0
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) 5.12311i 0.374639i
\(188\) 32.5760 + 18.8078i 2.37585 + 1.37170i
\(189\) −1.78078 + 3.08440i −0.129532 + 0.224357i
\(190\) 0 0
\(191\) 0.438447 0.759413i 0.0317249 0.0549492i −0.849727 0.527223i \(-0.823233\pi\)
0.881452 + 0.472274i \(0.156567\pi\)
\(192\) −1.24573 + 0.719224i −0.0899029 + 0.0519055i
\(193\) 16.8809 9.74621i 1.21512 0.701548i 0.251247 0.967923i \(-0.419159\pi\)
0.963869 + 0.266375i \(0.0858261\pi\)
\(194\) 11.3693 0.816269
\(195\) 0 0
\(196\) 25.9309 1.85220
\(197\) 9.84612 5.68466i 0.701507 0.405015i −0.106402 0.994323i \(-0.533933\pi\)
0.807908 + 0.589308i \(0.200600\pi\)
\(198\) −4.43674 + 2.56155i −0.315305 + 0.182042i
\(199\) −11.5885 + 20.0719i −0.821490 + 1.42286i 0.0830828 + 0.996543i \(0.473523\pi\)
−0.904573 + 0.426320i \(0.859810\pi\)
\(200\) 0 0
\(201\) −0.219224 + 0.379706i −0.0154628 + 0.0267824i
\(202\) −7.62775 4.40388i −0.536686 0.309856i
\(203\) 20.2462i 1.42101i
\(204\) 5.84233 10.1192i 0.409045 0.708486i
\(205\) 0 0
\(206\) 9.68466 + 16.7743i 0.674762 + 1.16872i
\(207\) 2.00000i 0.139010i
\(208\) 17.0474 + 21.8423i 1.18203 + 1.51449i
\(209\) −2.24621 −0.155374
\(210\) 0 0
\(211\) −3.65767 6.33527i −0.251804 0.436138i 0.712218 0.701958i \(-0.247691\pi\)
−0.964023 + 0.265820i \(0.914357\pi\)
\(212\) 46.1593 + 26.6501i 3.17023 + 1.83034i
\(213\) 14.0000i 0.959264i
\(214\) 10.5616 18.2931i 0.721973 1.25049i
\(215\) 0 0
\(216\) 6.56155 0.446457
\(217\) 4.81645 + 2.78078i 0.326962 + 0.188771i
\(218\) 39.5042 22.8078i 2.67556 1.54474i
\(219\) −0.938447 1.62544i −0.0634144 0.109837i
\(220\) 0 0
\(221\) −8.56155 3.46410i −0.575912 0.233021i
\(222\) 8.80776i 0.591138i
\(223\) 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
\(225\) 0 0
\(226\) −37.9309 −2.52312
\(227\) −0.972638 0.561553i −0.0645563 0.0372716i 0.467374 0.884059i \(-0.345200\pi\)
−0.531931 + 0.846788i \(0.678533\pi\)
\(228\) 4.43674 + 2.56155i 0.293830 + 0.169643i
\(229\) −0.246211 −0.0162701 −0.00813505 0.999967i \(-0.502589\pi\)
−0.00813505 + 0.999967i \(0.502589\pi\)
\(230\) 0 0
\(231\) −3.56155 6.16879i −0.234333 0.405877i
\(232\) 32.3029 18.6501i 2.12079 1.22444i
\(233\) 26.0000i 1.70332i 0.524097 + 0.851658i \(0.324403\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) −1.28078 9.14657i −0.0837270 0.597930i
\(235\) 0 0
\(236\) 25.3693 + 43.9409i 1.65140 + 2.86031i
\(237\) −8.28055 + 4.78078i −0.537879 + 0.310545i
\(238\) 20.2384 + 11.6847i 1.31186 + 0.757404i
\(239\) 0.630683 0.0407955 0.0203977 0.999792i \(-0.493507\pi\)
0.0203977 + 0.999792i \(0.493507\pi\)
\(240\) 0 0
\(241\) −1.40388 + 2.43160i −0.0904320 + 0.156633i −0.907693 0.419635i \(-0.862158\pi\)
0.817261 + 0.576268i \(0.195491\pi\)
\(242\) 17.9309i 1.15264i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 27.6501 + 47.8914i 1.77012 + 3.06593i
\(245\) 0 0
\(246\) 6.56155 0.418349
\(247\) 1.51883 3.75379i 0.0966406 0.238848i
\(248\) 10.2462i 0.650635i
\(249\) −4.56155 7.90084i −0.289077 0.500695i
\(250\) 0 0
\(251\) 15.3693 26.6204i 0.970103 1.68027i 0.274871 0.961481i \(-0.411365\pi\)
0.695231 0.718786i \(-0.255302\pi\)
\(252\) 16.2462i 1.02342i
\(253\) 3.46410 + 2.00000i 0.217786 + 0.125739i
\(254\) 12.2462 21.2111i 0.768396 1.33090i
\(255\) 0 0
\(256\) 13.5270 23.4294i 0.845437 1.46434i
\(257\) 14.0098 8.08854i 0.873905 0.504549i 0.00526106 0.999986i \(-0.498325\pi\)
0.868644 + 0.495437i \(0.164992\pi\)
\(258\) 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
\(263\) −13.3102 + 7.68466i −0.820743 + 0.473856i −0.850673 0.525696i \(-0.823805\pi\)
0.0299295 + 0.999552i \(0.490472\pi\)
\(264\) −6.56155 + 11.3649i −0.403836 + 0.699464i
\(265\) 0 0
\(266\) −5.12311 + 8.87348i −0.314118 + 0.544068i
\(267\) 11.3649 + 6.56155i 0.695523 + 0.401561i
\(268\) 2.00000i 0.122169i
\(269\) 1.68466 2.91791i 0.102715 0.177908i −0.810087 0.586310i \(-0.800580\pi\)
0.912803 + 0.408401i \(0.133914\pi\)
\(270\) 0 0
\(271\) 0.534565 + 0.925894i 0.0324725 + 0.0562441i 0.881805 0.471614i \(-0.156329\pi\)
−0.849332 + 0.527858i \(0.822995\pi\)
\(272\) 19.6847i 1.19356i
\(273\) 12.7173 1.78078i 0.769685 0.107777i
\(274\) 3.68466 0.222598
\(275\) 0 0
\(276\) −4.56155 7.90084i −0.274573 0.475575i
\(277\) 15.3154 + 8.84233i 0.920211 + 0.531284i 0.883702 0.468049i \(-0.155043\pi\)
0.0365086 + 0.999333i \(0.488376\pi\)
\(278\) 28.0000i 1.67933i
\(279\) −0.780776 + 1.35234i −0.0467439 + 0.0809627i
\(280\) 0 0
\(281\) −2.80776 −0.167497 −0.0837486 0.996487i \(-0.526689\pi\)
−0.0837486 + 0.996487i \(0.526689\pi\)
\(282\) −18.2931 10.5616i −1.08934 0.628931i
\(283\) −1.13912 + 0.657671i −0.0677136 + 0.0390945i −0.533475 0.845816i \(-0.679114\pi\)
0.465761 + 0.884911i \(0.345781\pi\)
\(284\) 31.9309 + 55.3059i 1.89475 + 3.28180i
\(285\) 0 0
\(286\) 17.1231 + 6.92820i 1.01251 + 0.409673i
\(287\) 9.12311i 0.538520i
\(288\) 5.68247 3.28078i 0.334843 0.193322i
\(289\) −5.21922 9.03996i −0.307013 0.531762i
\(290\) 0 0
\(291\) −4.43845 −0.260186
\(292\) −7.41452 4.28078i −0.433902 0.250513i
\(293\) −21.2709 12.2808i −1.24266 0.717451i −0.273026 0.962007i \(-0.588024\pi\)
−0.969635 + 0.244556i \(0.921358\pi\)
\(294\) −14.5616 −0.849247
\(295\) 0 0
\(296\) −11.2808 19.5389i −0.655682 1.13567i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) 16.8078i 0.973648i
\(299\) −5.68466 + 4.43674i −0.328752 + 0.256583i
\(300\) 0 0
\(301\) 0.780776 + 1.35234i 0.0450032 + 0.0779478i
\(302\) −34.0948 + 19.6847i −1.96194 + 1.13272i
\(303\) 2.97778 + 1.71922i 0.171069 + 0.0987668i
\(304\) 8.63068 0.495004
\(305\) 0 0
\(306\) −3.28078 + 5.68247i −0.187550 + 0.324845i
\(307\) 10.1922i 0.581702i −0.956768 0.290851i \(-0.906062\pi\)
0.956768 0.290851i \(-0.0939383\pi\)
\(308\) −28.1393 16.2462i −1.60338 0.925714i
\(309\) −3.78078 6.54850i −0.215081 0.372531i
\(310\) 0 0
\(311\) −10.8769 −0.616772 −0.308386 0.951261i \(-0.599789\pi\)
−0.308386 + 0.951261i \(0.599789\pi\)
\(312\) −14.5560 18.6501i −0.824068 1.05585i
\(313\) 1.31534i 0.0743475i −0.999309 0.0371738i \(-0.988165\pi\)
0.999309 0.0371738i \(-0.0118355\pi\)
\(314\) −5.59612 9.69276i −0.315807 0.546994i
\(315\) 0 0
\(316\) −21.8078 + 37.7722i −1.22678 + 2.12485i
\(317\) 23.0540i 1.29484i 0.762133 + 0.647420i \(0.224152\pi\)
−0.762133 + 0.647420i \(0.775848\pi\)
\(318\) −25.9209 14.9654i −1.45357 0.839220i
\(319\) 5.68466 9.84612i 0.318280 0.551277i
\(320\) 0 0
\(321\) −4.12311 + 7.14143i −0.230129 + 0.398596i
\(322\) 15.8017 9.12311i 0.880593 0.508411i
\(323\) −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
\(328\) 14.5560 8.40388i 0.803718 0.464027i
\(329\) 14.6847 25.4346i 0.809591 1.40225i
\(330\) 0 0
\(331\) 11.9039 20.6181i 0.654297 1.13327i −0.327773 0.944756i \(-0.606298\pi\)
0.982070 0.188518i \(-0.0603685\pi\)
\(332\) −36.0401 20.8078i −1.97796 1.14197i
\(333\) 3.43845i 0.188426i
\(334\) −8.00000 + 13.8564i −0.437741 + 0.758189i
\(335\) 0 0
\(336\) 13.6847 + 23.7025i 0.746559 + 1.29308i
\(337\) 2.12311i 0.115653i −0.998327 0.0578265i \(-0.981583\pi\)
0.998327 0.0578265i \(-0.0184170\pi\)
\(338\) −23.1563 + 23.9309i −1.25954 + 1.30167i
\(339\) 14.8078 0.804247
\(340\) 0 0
\(341\) −1.56155 2.70469i −0.0845628 0.146467i
\(342\) −2.49146 1.43845i −0.134723 0.0777823i
\(343\) 4.68466i 0.252948i
\(344\) 1.43845 2.49146i 0.0775559 0.134331i
\(345\) 0 0
\(346\) 9.61553 0.516934
\(347\) −11.7914 6.80776i −0.632995 0.365460i 0.148916 0.988850i \(-0.452422\pi\)
−0.781911 + 0.623390i \(0.785755\pi\)
\(348\) −22.4568 + 12.9654i −1.20381 + 0.695020i
\(349\) −6.90388 11.9579i −0.369556 0.640090i 0.619940 0.784649i \(-0.287157\pi\)
−0.989496 + 0.144559i \(0.953824\pi\)
\(350\) 0 0
\(351\) 0.500000 + 3.57071i 0.0266880 + 0.190591i
\(352\) 13.1231i 0.699464i
\(353\) 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
\(355\) 0 0
\(356\) 59.8617 3.17267
\(357\) −7.90084 4.56155i −0.418157 0.241423i
\(358\) 29.1119 + 16.8078i 1.53861 + 0.888318i
\(359\) −15.3693 −0.811162 −0.405581 0.914059i \(-0.632931\pi\)
−0.405581 + 0.914059i \(0.632931\pi\)
\(360\) 0 0
\(361\) 8.86932 + 15.3621i 0.466806 + 0.808532i
\(362\) −21.4842 + 12.4039i −1.12918 + 0.651934i
\(363\) 7.00000i 0.367405i
\(364\) 46.1771 36.0401i 2.42034 1.88901i
\(365\) 0 0
\(366\) −15.5270 26.8935i −0.811609 1.40575i
\(367\) −17.3673 + 10.0270i −0.906563 + 0.523404i −0.879324 0.476224i \(-0.842005\pi\)
−0.0272394 + 0.999629i \(0.508672\pi\)
\(368\) −13.3102 7.68466i −0.693843 0.400591i
\(369\) −2.56155 −0.133349
\(370\) 0 0
\(371\) 20.8078 36.0401i 1.08029 1.87111i
\(372\) 7.12311i 0.369316i
\(373\) −3.14426 1.81534i −0.162804 0.0939948i 0.416384 0.909189i \(-0.363297\pi\)
−0.579188 + 0.815194i \(0.696630\pi\)
\(374\) −6.56155 11.3649i −0.339290 0.587667i
\(375\) 0 0
\(376\) −54.1080 −2.79040
\(377\) 12.6107 + 16.1577i 0.649483 + 0.832162i
\(378\) 9.12311i 0.469242i
\(379\) 5.65767 + 9.79937i 0.290615 + 0.503360i 0.973955 0.226740i \(-0.0728068\pi\)
−0.683340 + 0.730100i \(0.739473\pi\)
\(380\) 0 0
\(381\) −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 \(0.906053\pi\)
\(384\) −4.71922 + 8.17394i −0.240827 + 0.417124i
\(385\) 0 0
\(386\) −24.9654 + 43.2414i −1.27071 + 2.20093i
\(387\) −0.379706 + 0.219224i −0.0193016 + 0.0111438i
\(388\) −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
\(393\) −15.0423 + 8.68466i −0.758782 + 0.438083i
\(394\) −14.5616 + 25.2213i −0.733600 + 1.27063i
\(395\) 0 0
\(396\) 4.56155 7.90084i 0.229227 0.397032i
\(397\) −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
\(400\) 0 0
\(401\) −9.28078 16.0748i −0.463460 0.802736i 0.535671 0.844427i \(-0.320059\pi\)
−0.999131 + 0.0416909i \(0.986726\pi\)
\(402\) 1.12311i 0.0560154i
\(403\) 5.57586 0.780776i 0.277753 0.0388932i
\(404\) 15.6847 0.780341
\(405\) 0 0
\(406\) −25.9309 44.9136i −1.28693 2.22902i
\(407\) −5.95557 3.43845i −0.295206 0.170437i
\(408\) 16.8078i 0.832108i
\(409\) −9.18466 + 15.9083i −0.454152 + 0.786615i −0.998639 0.0521548i \(-0.983391\pi\)
0.544487 + 0.838769i \(0.316724\pi\)
\(410\) 0 0
\(411\) −1.43845 −0.0709534
\(412\) −29.8713 17.2462i −1.47165 0.849660i
\(413\) 34.3081 19.8078i 1.68819 0.974676i
\(414\) 2.56155 + 4.43674i 0.125893 + 0.218054i
\(415\) 0 0
\(416\) −21.9309 8.87348i −1.07525 0.435058i
\(417\) 10.9309i 0.535287i
\(418\) 4.98293 2.87689i 0.243723 0.140714i
\(419\) −8.87689 15.3752i −0.433665 0.751129i 0.563521 0.826102i \(-0.309446\pi\)
−0.997186 + 0.0749725i \(0.976113\pi\)
\(420\) 0 0
\(421\) 14.7538 0.719056 0.359528 0.933134i \(-0.382938\pi\)
0.359528 + 0.933134i \(0.382938\pi\)
\(422\) 16.2281 + 9.36932i 0.789973 + 0.456091i
\(423\) 7.14143 + 4.12311i 0.347228 + 0.200472i
\(424\) −76.6695 −3.72340
\(425\) 0 0
\(426\) −17.9309 31.0572i −0.868753 1.50473i
\(427\) 37.3924 21.5885i 1.80955 1.04474i
\(428\) 37.6155i 1.81822i
\(429\) −6.68466 2.70469i −0.322738 0.130584i
\(430\) 0 0
\(431\) 1.43845 + 2.49146i 0.0692876 + 0.120010i 0.898588 0.438794i \(-0.144594\pi\)
−0.829300 + 0.558803i \(0.811261\pi\)
\(432\) −6.65511 + 3.84233i −0.320194 + 0.184864i
\(433\) −21.8639 12.6231i −1.05071 0.606628i −0.127862 0.991792i \(-0.540811\pi\)
−0.922848 + 0.385164i \(0.874145\pi\)
\(434\) −14.2462 −0.683840
\(435\) 0 0
\(436\) −40.6155 + 70.3482i −1.94513 + 3.36907i
\(437\) 2.24621i 0.107451i
\(438\) 4.16365 + 2.40388i 0.198947 + 0.114862i
\(439\) −0.657671 1.13912i −0.0313889 0.0543672i 0.849904 0.526937i \(-0.176660\pi\)
−0.881293 + 0.472570i \(0.843326\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) 23.4294 3.28078i 1.11442 0.156051i
\(443\) 14.7386i 0.700254i 0.936702 + 0.350127i \(0.113862\pi\)
−0.936702 + 0.350127i \(0.886138\pi\)
\(444\) 7.84233 + 13.5833i 0.372180 + 0.644635i
\(445\) 0 0
\(446\) −10.2462 + 17.7470i −0.485172 + 0.840343i
\(447\) 6.56155i 0.310351i
\(448\) 4.43674 + 2.56155i 0.209616 + 0.121022i
\(449\) 4.12311 7.14143i 0.194581 0.337025i −0.752182 0.658956i \(-0.770998\pi\)
0.946763 + 0.321931i \(0.104332\pi\)
\(450\) 0 0
\(451\) 2.56155 4.43674i 0.120619 0.208918i
\(452\) 58.4969 33.7732i 2.75146 1.58856i
\(453\) 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 0.208120 0.978103i \(-0.433265\pi\)
0.951122 + 0.308814i \(0.0999322\pi\)
\(458\) 0.546188 0.315342i 0.0255217 0.0147349i
\(459\) 1.28078 2.21837i 0.0597815 0.103545i
\(460\) 0 0
\(461\) 18.4039 31.8765i 0.857154 1.48463i −0.0174778 0.999847i \(-0.505564\pi\)
0.874632 0.484787i \(-0.161103\pi\)
\(462\) 15.8017 + 9.12311i 0.735161 + 0.424445i
\(463\) 26.6847i 1.24014i −0.784546 0.620071i \(-0.787104\pi\)
0.784546 0.620071i \(-0.212896\pi\)
\(464\) −21.8423 + 37.8320i −1.01400 + 1.75631i
\(465\) 0 0
\(466\) −33.3002 57.6776i −1.54260 2.67186i
\(467\) 26.0000i 1.20314i 0.798821 + 0.601568i \(0.205457\pi\)
−0.798821 + 0.601568i \(0.794543\pi\)
\(468\) 10.1192 + 12.9654i 0.467761 + 0.599327i
\(469\) 1.56155 0.0721058
\(470\) 0 0
\(471\) 2.18466 + 3.78394i 0.100664 + 0.174355i
\(472\) −63.2067 36.4924i −2.90933 1.67970i
\(473\) 0.876894i 0.0403196i
\(474\) 12.2462 21.2111i 0.562487 0.974256i
\(475\) 0 0
\(476\) −41.6155 −1.90744
\(477\) 10.1192 + 5.84233i 0.463327 + 0.267502i
\(478\) −1.39909 + 0.807764i −0.0639928 + 0.0369463i
\(479\) −3.12311 5.40938i −0.142698 0.247161i 0.785814 0.618463i \(-0.212245\pi\)
−0.928512 + 0.371303i \(0.878911\pi\)
\(480\) 0 0
\(481\) 9.77320 7.62775i 0.445620 0.347795i
\(482\) 7.19224i 0.327597i
\(483\) −6.16879 + 3.56155i −0.280690 + 0.162056i
\(484\) −15.9654 27.6529i −0.725702 1.25695i
\(485\) 0 0
\(486\) 2.56155 0.116194
\(487\) −0.972638 0.561553i −0.0440744 0.0254464i 0.477801 0.878468i \(-0.341434\pi\)
−0.521875 + 0.853022i \(0.674767\pi\)
\(488\) −68.8892 39.7732i −3.11847 1.80045i
\(489\) −15.8078 −0.714852
\(490\) 0 0
\(491\) 9.87689 + 17.1073i 0.445738 + 0.772041i 0.998103 0.0615613i \(-0.0196080\pi\)
−0.552365 + 0.833602i \(0.686275\pi\)
\(492\) −10.1192 + 5.84233i −0.456209 + 0.263393i
\(493\) 14.5616i 0.655819i
\(494\) 1.43845 + 10.2726i 0.0647188 + 0.462185i
\(495\) 0 0
\(496\) 6.00000 + 10.3923i 0.269408 + 0.466628i
\(497\) 43.1815 24.9309i 1.93696 1.11830i
\(498\) 20.2384 + 11.6847i 0.906905 + 0.523602i
\(499\) 28.4924 1.27550 0.637748 0.770245i \(-0.279866\pi\)
0.637748 + 0.770245i \(0.279866\pi\)
\(500\) 0 0
\(501\) 3.12311 5.40938i 0.139530 0.241673i
\(502\) 78.7386i 3.51428i
\(503\) 10.1791 + 5.87689i 0.453863 + 0.262038i 0.709460 0.704746i \(-0.248939\pi\)
−0.255597 + 0.966783i \(0.582272\pi\)
\(504\) −11.6847 20.2384i −0.520476 0.901491i
\(505\) 0 0
\(506\) −10.2462 −0.455500
\(507\) 9.03996 9.34233i 0.401479 0.414907i
\(508\) 43.6155i 1.93513i
\(509\) 3.40388 + 5.89570i 0.150874 + 0.261322i 0.931549 0.363615i \(-0.118458\pi\)
−0.780675 + 0.624938i \(0.785124\pi\)
\(510\) 0 0
\(511\) −3.34233 + 5.78908i −0.147856 + 0.256094i
\(512\) 50.4233i 2.22842i
\(513\) 0.972638 + 0.561553i 0.0429430 + 0.0247932i
\(514\) −20.7192 + 35.8867i −0.913886 + 1.58290i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) −14.2829 + 8.24621i −0.628159 + 0.362668i
\(518\) −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
\(523\) −20.6649 + 11.9309i −0.903612 + 0.521701i −0.878370 0.477981i \(-0.841369\pi\)
−0.0252415 + 0.999681i \(0.508035\pi\)
\(524\) −39.6155 + 68.6161i −1.73061 + 2.99751i
\(525\) 0 0
\(526\) 19.6847 34.0948i 0.858292 1.48661i
\(527\) −3.46410 2.00000i −0.150899 0.0871214i
\(528\) 15.3693i 0.668864i
\(529\) −9.50000 + 16.4545i −0.413043 + 0.715412i
\(530\) 0 0
\(531\) 5.56155 + 9.63289i 0.241351 + 0.418032i
\(532\) 18.2462i 0.791074i
\(533\) 5.68247 + 7.28078i 0.246135 + 0.315365i
\(534\) −33.6155 −1.45469
\(535\) 0 0
\(536\) −1.43845 2.49146i −0.0621315 0.107615i
\(537\) −11.3649 6.56155i −0.490433 0.283152i
\(538\) 8.63068i 0.372095i
\(539\) −5.68466 + 9.84612i −0.244856 + 0.424102i
\(540\) 0 0
\(541\) −29.7386 −1.27856 −0.639282 0.768972i \(-0.720768\pi\)
−0.639282 + 0.768972i \(0.720768\pi\)
\(542\) −2.37173 1.36932i −0.101874 0.0588172i
\(543\) 8.38716 4.84233i 0.359927 0.207804i
\(544\) 8.40388 + 14.5560i 0.360313 + 0.624081i
\(545\) 0 0
\(546\) −25.9309 + 20.2384i −1.10974 + 0.866125i
\(547\) 24.9309i 1.06597i 0.846126 + 0.532984i \(0.178929\pi\)
−0.846126 + 0.532984i \(0.821071\pi\)
\(548\) −5.68247 + 3.28078i −0.242743 + 0.140148i
\(549\) 6.06155 + 10.4989i 0.258701 + 0.448083i
\(550\) 0 0
\(551\) 6.38447 0.271988
\(552\) 11.3649 + 6.56155i 0.483724 + 0.279278i
\(553\) 29.4916 + 17.0270i 1.25411 + 0.724061i
\(554\) −45.3002 −1.92462
\(555\) 0 0
\(556\) −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 \(0.236992\pi\)
\(558\) 4.00000i 0.169334i
\(559\) 1.46543 + 0.592932i 0.0619813 + 0.0250783i
\(560\) 0 0
\(561\) 2.56155 + 4.43674i 0.108149 + 0.187319i
\(562\) 6.22866 3.59612i 0.262740 0.151693i
\(563\) −1.18586 0.684658i −0.0499782 0.0288549i 0.474803 0.880092i \(-0.342519\pi\)
−0.524781 + 0.851237i \(0.675853\pi\)
\(564\) 37.6155 1.58390
\(565\) 0 0
\(566\) 1.68466 2.91791i 0.0708115 0.122649i
\(567\) 3.56155i 0.149571i
\(568\) −79.5546 45.9309i −3.33804 1.92722i
\(569\) 20.3693 + 35.2807i 0.853926 + 1.47904i 0.877638 + 0.479325i \(0.159118\pi\)
−0.0237115 + 0.999719i \(0.507548\pi\)
\(570\) 0 0
\(571\) 19.3693 0.810581 0.405290 0.914188i \(-0.367170\pi\)
0.405290 + 0.914188i \(0.367170\pi\)
\(572\) −32.5760 + 4.56155i −1.36207 + 0.190728i
\(573\) 0.876894i 0.0366328i
\(574\) −11.6847 20.2384i −0.487708 0.844735i
\(575\) 0 0
\(576\) −0.719224 + 1.24573i −0.0299676 + 0.0519055i
\(577\) 29.6847i 1.23579i 0.786261 + 0.617894i \(0.212014\pi\)
−0.786261 + 0.617894i \(0.787986\pi\)
\(578\) 23.1563 + 13.3693i 0.963177 + 0.556090i
\(579\) 9.74621 16.8809i 0.405039 0.701548i
\(580\) 0 0
\(581\) −16.2462 + 28.1393i −0.674006 + 1.16741i
\(582\) 9.84612 5.68466i 0.408135 0.235637i
\(583\) −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 −0.738149 0.674638i \(-0.764300\pi\)
0.215179 + 0.976575i \(0.430966\pi\)
\(588\) 22.4568 12.9654i 0.926102 0.534686i
\(589\) 0.876894 1.51883i 0.0361318 0.0625821i
\(590\) 0 0
\(591\) 5.68466 9.84612i 0.233836 0.405015i
\(592\) 22.8832 + 13.2116i 0.940495 + 0.542995i
\(593\) 44.4233i 1.82425i 0.409917 + 0.912123i \(0.365558\pi\)
−0.409917 + 0.912123i \(0.634442\pi\)
\(594\) −2.56155 + 4.43674i −0.105102 + 0.182042i
\(595\) 0 0
\(596\) 14.9654 + 25.9209i 0.613008 + 1.06176i
\(597\) 23.1771i 0.948575i
\(598\) 6.92820 17.1231i 0.283315 0.700216i
\(599\) 0.384472 0.0157091 0.00785455 0.999969i \(-0.497500\pi\)
0.00785455 + 0.999969i \(0.497500\pi\)
\(600\) 0 0
\(601\) 17.9654 + 31.1170i 0.732825 + 1.26929i 0.955671 + 0.294437i \(0.0951321\pi\)
−0.222846 + 0.974854i \(0.571535\pi\)
\(602\) −3.46410 2.00000i −0.141186 0.0815139i
\(603\) 0.438447i 0.0178549i
\(604\) 35.0540 60.7153i 1.42633 2.47047i
\(605\) 0 0
\(606\) −8.80776 −0.357791
\(607\) −13.8564 8.00000i −0.562414 0.324710i 0.191700 0.981454i \(-0.438600\pi\)
−0.754114 + 0.656744i \(0.771933\pi\)
\(608\) −6.38202 + 3.68466i −0.258825 + 0.149433i
\(609\) 10.1231 + 17.5337i 0.410209 + 0.710503i
\(610\) 0 0
\(611\) −4.12311 29.4449i −0.166803 1.19121i
\(612\) 11.6847i 0.472324i
\(613\) 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 0
\(616\) 46.7386 1.88315
\(617\) −9.35980 5.40388i −0.376811 0.217552i 0.299619 0.954059i \(-0.403141\pi\)
−0.676430 + 0.736507i \(0.736474\pi\)
\(618\) 16.7743 + 9.68466i 0.674762 + 0.389574i
\(619\) 24.3002 0.976707 0.488353 0.872646i \(-0.337598\pi\)
0.488353 + 0.872646i \(0.337598\pi\)
\(620\) 0 0
\(621\) −1.00000 1.73205i −0.0401286 0.0695048i
\(622\) 24.1290 13.9309i 0.967484 0.558577i
\(623\) 46.7386i 1.87254i
\(624\) 25.6847 + 10.3923i 1.02821 + 0.416025i
\(625\) 0 0
\(626\) 1.68466 + 2.91791i 0.0673325 + 0.116623i
\(627\) −1.94528 + 1.12311i −0.0776868 + 0.0448525i
\(628\) 17.2606 + 9.96543i 0.688774 + 0.397664i
\(629\) −8.80776 −0.351189
\(630\) 0 0
\(631\) 7.21922 12.5041i 0.287393 0.497779i −0.685794 0.727796i \(-0.740545\pi\)
0.973187 + 0.230017i \(0.0738782\pi\)
\(632\) 62.7386i 2.49561i
\(633\) −6.33527 3.65767i −0.251804 0.145379i
\(634\) −29.5270 51.1422i −1.17267 2.03112i
\(635\) 0 0
\(636\) 53.3002 2.11349
\(637\) −12.6107 16.1577i −0.499653 0.640190i
\(638\) 29.1231i 1.15299i
\(639\) 7.00000 + 12.1244i 0.276916 + 0.479632i
\(640\) 0 0
\(641\) −13.0885 + 22.6700i −0.516966 + 0.895412i 0.482840 + 0.875709i \(0.339605\pi\)
−0.999806 + 0.0197030i \(0.993728\pi\)
\(642\) 21.1231i 0.833662i
\(643\) −33.3822 19.2732i −1.31646 0.760061i −0.333306 0.942819i \(-0.608164\pi\)
−0.983158 + 0.182758i \(0.941498\pi\)
\(644\) −16.2462 + 28.1393i −0.640190 + 1.10884i
\(645\) 0 0
\(646\) 3.68466 6.38202i 0.144971 0.251097i
\(647\) 41.2363 23.8078i 1.62116 0.935980i 0.634555 0.772877i \(-0.281183\pi\)
0.986609 0.163102i \(-0.0521501\pi\)
\(648\) 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
\(653\) 12.8838 7.43845i 0.504181 0.291089i −0.226258 0.974068i \(-0.572649\pi\)
0.730438 + 0.682979i \(0.239316\pi\)
\(654\) 22.8078 39.5042i 0.891854 1.54474i
\(655\) 0 0
\(656\) −9.84233 + 17.0474i −0.384278 + 0.665590i
\(657\) −1.62544 0.938447i −0.0634144 0.0366123i
\(658\) 75.2311i 2.93281i
\(659\) 7.12311 12.3376i 0.277477 0.480604i −0.693280 0.720668i \(-0.743835\pi\)
0.970757 + 0.240064i \(0.0771685\pi\)
\(660\) 0 0
\(661\) −15.1847 26.3006i −0.590615 1.02297i −0.994150 0.108011i \(-0.965552\pi\)
0.403535 0.914964i \(-0.367781\pi\)
\(662\) 60.9848i 2.37024i
\(663\) −9.14657 + 1.28078i −0.355223 + 0.0497412i
\(664\) 59.8617 2.32309
\(665\) 0 0
\(666\) −4.40388 7.62775i −0.170647 0.295569i
\(667\) −9.84612 5.68466i −0.381243 0.220111i
\(668\) 28.4924i 1.10240i
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) 0 0
\(671\) −24.2462 −0.936015
\(672\) −20.2384 11.6847i −0.780714 0.450745i
\(673\) −5.84895 + 3.37689i −0.225461 + 0.130170i −0.608476 0.793572i \(-0.708219\pi\)
0.383016 + 0.923742i \(0.374886\pi\)
\(674\) 2.71922 + 4.70983i 0.104741 + 0.181416i
\(675\) 0 0
\(676\) 14.4039 57.5243i 0.553995 2.21247i
\(677\) 25.6155i 0.984485i −0.870458 0.492242i \(-0.836177\pi\)
0.870458 0.492242i \(-0.163823\pi\)
\(678\) −32.8491 + 18.9654i −1.26156 + 0.728363i
\(679\) 7.90388 + 13.6899i 0.303323 + 0.525371i
\(680\) 0 0
\(681\) −1.12311 −0.0430375
\(682\) 6.92820 + 4.00000i 0.265295 + 0.153168i
\(683\) −31.2704 18.0540i −1.19653 0.690816i −0.236749 0.971571i \(-0.576082\pi\)
−0.959780 + 0.280755i \(0.909415\pi\)
\(684\) 5.12311 0.195887
\(685\) 0 0
\(686\) −6.00000 10.3923i −0.229081 0.396780i
\(687\) −0.213225 + 0.123106i −0.00813505 + 0.00469677i
\(688\) 3.36932i 0.128454i
\(689\) −5.84233 41.7226i −0.222575 1.58950i
\(690\) 0 0
\(691\) −1.15009 1.99202i −0.0437516 0.0757800i 0.843320 0.537411i \(-0.180598\pi\)
−0.887072 + 0.461631i \(0.847264\pi\)
\(692\) −14.8290 + 8.56155i −0.563716 + 0.325461i
\(693\) −6.16879 3.56155i −0.234333 0.135292i
\(694\) 34.8769 1.32391
\(695\) 0 0
\(696\) 18.6501 32.3029i 0.706930 1.22444i
\(697\) 6.56155i 0.248537i
\(698\) 30.6307 + 17.6847i 1.15939 + 0.669374i
\(699\) 13.0000 + 22.5167i 0.491705 + 0.851658i
\(700\) 0 0
\(701\) 19.3693 0.731569 0.365785 0.930700i \(-0.380801\pi\)
0.365785 + 0.930700i \(0.380801\pi\)
\(702\) −5.68247 7.28078i −0.214471 0.274795i
\(703\) 3.86174i 0.145648i
\(704\) −1.43845 2.49146i −0.0542135 0.0939006i
\(705\) 0 0
\(706\) −22.6501 + 39.2311i −0.852448 + 1.47648i
\(707\) 12.2462i 0.460566i
\(708\) 43.9409 + 25.3693i 1.65140 + 0.953437i
\(709\) 12.7462 22.0771i 0.478694 0.829122i −0.521008 0.853552i \(-0.674444\pi\)
0.999702 + 0.0244297i \(0.00777700\pi\)
\(710\) 0 0
\(711\) −4.78078 + 8.28055i −0.179293 + 0.310545i
\(712\) −74.5717 + 43.0540i −2.79469 + 1.61352i
\(713\) −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
\(718\) 34.0948 19.6847i 1.27241 0.734625i
\(719\) 0.684658 1.18586i 0.0255335 0.0442252i −0.852976 0.521950i \(-0.825205\pi\)
0.878510 + 0.477724i \(0.158538\pi\)
\(720\) 0 0
\(721\) −13.4654 + 23.3228i −0.501479 + 0.868587i
\(722\) −39.3508 22.7192i −1.46449 0.845522i
\(723\) 2.80776i 0.104422i
\(724\) 22.0885 38.2585i 0.820914 1.42187i
\(725\) 0 0
\(726\) 8.96543 + 15.5286i 0.332738 + 0.576320i
\(727\) 39.6695i 1.47126i −0.677383 0.735630i \(-0.736886\pi\)
0.677383 0.735630i \(-0.263114\pi\)
\(728\) −31.6034 + 78.1080i −1.17130 + 2.89487i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −0.561553 0.972638i −0.0207698 0.0359743i
\(732\) 47.8914 + 27.6501i 1.77012 + 1.02198i
\(733\) 53.4924i 1.97579i 0.155131 + 0.987894i \(0.450420\pi\)
−0.155131 + 0.987894i \(0.549580\pi\)
\(734\) 25.6847 44.4871i 0.948038 1.64205i
\(735\) 0 0
\(736\) 13.1231 0.483724
\(737\) −0.759413 0.438447i −0.0279733 0.0161504i
\(738\) 5.68247 3.28078i 0.209175 0.120767i
\(739\) −3.12311 5.40938i −0.114885 0.198987i 0.802849 0.596183i \(-0.203317\pi\)
−0.917734 + 0.397196i \(0.869983\pi\)
\(740\) 0 0
\(741\) −0.561553 4.01029i −0.0206292 0.147322i
\(742\) 106.600i 3.91342i
\(743\) −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
\(745\) 0 0
\(746\) 9.30019 0.340504
\(747\) −7.90084 4.56155i −0.289077 0.166898i
\(748\) 20.2384 + 11.6847i 0.739990 + 0.427233i
\(749\) 29.3693 1.07313
\(750\) 0 0
\(751\) 15.0540 + 26.0743i 0.549327 + 0.951463i 0.998321 + 0.0579278i \(0.0184493\pi\)
−0.448993 + 0.893535i \(0.648217\pi\)
\(752\) 54.8794 31.6847i 2.00125 1.15542i
\(753\) 30.7386i 1.12018i
\(754\) −48.6695 19.6922i −1.77244 0.717149i
\(755\) 0 0
\(756\) 8.12311 + 14.0696i 0.295434 + 0.511708i
\(757\) −25.9808 + 15.0000i −0.944287 + 0.545184i −0.891302 0.453411i \(-0.850207\pi\)
−0.0529853 + 0.998595i \(0.516874\pi\)
\(758\) −25.1016 14.4924i −0.911732 0.526388i
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 7.68466 13.3102i 0.278569 0.482495i −0.692461 0.721456i \(-0.743473\pi\)
0.971029 + 0.238961i \(0.0768067\pi\)
\(762\) 24.4924i 0.887267i
\(763\) 54.9262 + 31.7116i 1.98846 + 1.14804i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 0 0
\(766\) 68.4924 2.47473
\(767\) 15.0423 37.1771i 0.543145 1.34239i
\(768\) 27.0540i 0.976226i
\(769\) −9.00000 15.5885i −0.324548 0.562134i 0.656873 0.754002i \(-0.271879\pi\)
−0.981421 + 0.191867i \(0.938546\pi\)
\(770\) 0 0
\(771\) 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 \(0.622136\pi\)
\(774\) 0.561553 0.972638i 0.0201846 0.0349608i
\(775\) 0 0
\(776\) 14.5616 25.2213i 0.522729 0.905394i
\(777\) 10.6055 6.12311i 0.380471 0.219665i
\(778\) −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
\(783\) −4.92306 + 2.84233i −0.175936 + 0.101577i
\(784\) 21.8423 37.8320i 0.780083 1.35114i
\(785\) 0 0
\(786\) 22.2462 38.5316i 0.793496 1.37438i
\(787\) −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
\(790\) 0 0
\(791\) −26.3693 45.6730i −0.937585 1.62394i
\(792\) 13.1231i 0.466309i
\(793\) 16.3946 40.5194i 0.582190 1.43889i
\(794\) 30.8769 1.09578
\(795\) 0 0
\(796\) 52.8617 + 91.5592i 1.87363 + 3.24523i
\(797\) −36.0401 20.8078i −1.27661 0.737049i −0.300383 0.953819i \(-0.597115\pi\)
−0.976223 + 0.216770i \(0.930448\pi\)
\(798\) 10.2462i 0.362712i
\(799\) −10.5616 + 18.2931i −0.373641 + 0.647165i
\(800\) 0 0
\(801\) 13.1231 0.463682
\(802\) 41.1764 + 23.7732i 1.45399 + 0.839461i
\(803\) 3.25088 1.87689i 0.114721 0.0662342i
\(804\) 1.00000 + 1.73205i 0.0352673 + 0.0610847i
\(805\) 0 0
\(806\) −11.3693 + 8.87348i −0.400467 + 0.312555i
\(807\) 3.36932i 0.118606i
\(808\) −19.5389 + 11.2808i −0.687375 + 0.396856i
\(809\) 18.6501 + 32.3029i 0.655702 + 1.13571i 0.981717 + 0.190345i \(0.0609607\pi\)
−0.326015 + 0.945365i \(0.605706\pi\)
\(810\) 0 0
\(811\) −1.56155 −0.0548335 −0.0274168 0.999624i \(-0.508728\pi\)
−0.0274168 + 0.999624i \(0.508728\pi\)
\(812\) 79.9811 + 46.1771i 2.80678 + 1.62050i
\(813\) 0.925894 + 0.534565i 0.0324725 + 0.0187480i
\(814\) 17.6155 0.617424
\(815\) 0 0
\(816\) −9.84233 17.0474i −0.344550 0.596779i
\(817\) 0.426450 0.246211i 0.0149196 0.00861384i
\(818\) 47.0540i 1.64520i
\(819\) 10.1231 7.90084i 0.353730 0.276078i
\(820\) 0 0
\(821\) 13.2462 + 22.9431i 0.462296 + 0.800720i 0.999075 0.0430028i \(-0.0136924\pi\)
−0.536779 + 0.843723i \(0.680359\pi\)
\(822\) 3.19101 1.84233i 0.111299 0.0642586i
\(823\) −6.92820 4.00000i −0.241502 0.139431i 0.374365 0.927281i \(-0.377861\pi\)
−0.615867 + 0.787850i \(0.711194\pi\)
\(824\) 49.6155 1.72844
\(825\) 0 0
\(826\) −50.7386 + 87.8819i −1.76542 + 3.05780i
\(827\) 34.7386i 1.20798i −0.796992 0.603990i \(-0.793577\pi\)
0.796992 0.603990i \(-0.206423\pi\)
\(828\) −7.90084 4.56155i −0.274573 0.158525i
\(829\) −9.74621 16.8809i −0.338500 0.586299i 0.645651 0.763633i \(-0.276586\pi\)
−0.984151 + 0.177334i \(0.943253\pi\)
\(830\) 0 0
\(831\) 17.6847 0.613474
\(832\) 5.13628 0.719224i 0.178069 0.0249346i
\(833\) 14.5616i 0.504528i
\(834\) 14.0000 + 24.2487i 0.484780 + 0.839664i
\(835\) 0 0
\(836\) −5.12311 + 8.87348i −0.177186 + 0.306896i
\(837\) 1.56155i 0.0539752i
\(838\) 39.3845 + 22.7386i 1.36051 + 0.785493i
\(839\) −9.80776 + 16.9875i −0.338602 + 0.586475i −0.984170 0.177227i \(-0.943287\pi\)
0.645568 + 0.763703i \(0.276621\pi\)
\(840\) 0 0
\(841\) −1.65767 + 2.87117i −0.0571611 + 0.0990059i
\(842\) −32.7294 + 18.8963i −1.12793 + 0.651210i
\(843\) −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
\(848\) 77.7627 44.8963i 2.67038 1.54175i
\(849\) −0.657671 + 1.13912i −0.0225712 + 0.0390945i
\(850\) 0 0
\(851\) −3.43845 + 5.95557i −0.117868 + 0.204154i
\(852\) 55.3059 + 31.9309i 1.89475 + 1.09393i
\(853\) 6.12311i 0.209651i −0.994491 0.104826i \(-0.966572\pi\)
0.994491 0.104826i \(-0.0334284\pi\)
\(854\) −55.3002 + 95.7827i −1.89233 + 3.27762i
\(855\) 0 0
\(856\) −27.0540 46.8589i −0.924686 1.60160i
\(857\) 31.4384i 1.07392i −0.843609 0.536958i \(-0.819573\pi\)
0.843609 0.536958i \(-0.180427\pi\)
\(858\) 18.2931 2.56155i 0.624518 0.0874500i
\(859\) −20.4384 −0.697351 −0.348675 0.937244i \(-0.613368\pi\)
−0.348675 + 0.937244i \(0.613368\pi\)
\(860\) 0 0
\(861\) 4.56155 + 7.90084i 0.155457 + 0.269260i
\(862\) −6.38202 3.68466i −0.217372 0.125500i
\(863\) 2.49242i 0.0848430i −0.999100 0.0424215i \(-0.986493\pi\)
0.999100 0.0424215i \(-0.0135072\pi\)
\(864\) 3.28078 5.68247i 0.111614 0.193322i
\(865\) 0 0
\(866\) 64.6695 2.19756
\(867\) −9.03996 5.21922i −0.307013 0.177254i
\(868\) 21.9705 12.6847i 0.745726 0.430545i
\(869\) −9.56155 16.5611i −0.324353 0.561797i
\(870\) 0 0
\(871\) 1.24621 0.972638i 0.0422263 0.0329566i
\(872\) 116.847i 3.95692i
\(873\) −3.84381 + 2.21922i −0.130093 + 0.0751093i
\(874\) −2.87689 4.98293i −0.0973124 0.168550i
\(875\) 0 0
\(876\) −8.56155 −0.289268
\(877\) 16.8342 + 9.71922i 0.568450 + 0.328195i 0.756530 0.653959i \(-0.226893\pi\)
−0.188080 + 0.982154i \(0.560226\pi\)
\(878\) 2.91791 + 1.68466i 0.0984748 + 0.0568545i
\(879\) −24.5616 −0.828441
\(880\) 0 0
\(881\) 18.9654 + 32.8491i 0.638962 + 1.10671i 0.985661 + 0.168738i \(0.0539691\pi\)
−0.346699 + 0.937976i \(0.612698\pi\)
\(882\) −12.6107 + 7.28078i −0.424624 + 0.245156i
\(883\) 11.8078i 0.397363i −0.980064 0.198681i \(-0.936334\pi\)
0.980064 0.198681i \(-0.0636659\pi\)
\(884\) −33.2116 + 25.9209i −1.11703 + 0.871814i
\(885\) 0 0
\(886\) −18.8769 32.6957i −0.634182 1.09843i
\(887\) −42.7551 + 24.6847i −1.43558 + 0.828830i −0.997538 0.0701272i \(-0.977659\pi\)
−0.438037 + 0.898957i \(0.644326\pi\)
\(888\) −19.5389 11.2808i −0.655682 0.378558i
\(889\) 34.0540 1.14213
\(890\) 0 0
\(891\) 1.00000 1.73205i 0.0335013 0.0580259i
\(892\) 36.4924i 1.22186i
\(893\) −8.02058 4.63068i −0.268398 0.154960i
\(894\) −8.40388 14.5560i −0.281068 0.486824i
\(895\) 0 0
\(896\) 33.6155 1.12302
\(897\) −2.70469 + 6.68466i −0.0903069 + 0.223194i
\(898\) 21.1231i 0.704887i
\(899\) 4.43845 + 7.68762i 0.148031 + 0.256396i
\(900\) 0 0
\(901\) −14.9654 + 25.9209i −0.498571 + 0.863550i
\(902\) 13.1231i 0.436952i
\(903\) 1.35234 + 0.780776i 0.0450032 + 0.0259826i
\(904\) −48.5810 + 84.1447i −1.61578 + 2.79861i
\(905\) 0 0
\(906\) −19.6847 + 34.0948i −0.653979 + 1.13272i
\(907\) −24.2487 + 14.0000i −0.805165 + 0.464862i −0.845274 0.534333i \(-0.820563\pi\)
0.0401089 + 0.999195i \(0.487230\pi\)
\(908\) −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
\(913\) 15.8017 9.12311i 0.522959 0.301931i
\(914\) −36.6501 + 63.4798i −1.21228 + 2.09973i
\(915\) 0 0
\(916\) −0.561553 + 0.972638i −0.0185542 + 0.0321369i
\(917\) 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 \(-0.571062\pi\)
0.955233 0.295856i \(-0.0956047\pi\)
\(920\) 0 0
\(921\) −5.09612 8.82674i −0.167923 0.290851i
\(922\) 94.2850i 3.10511i
\(923\) 18.9328 46.7926i 0.623181 1.54020i
\(924\) −32.4924 −1.06892
\(925\) 0 0
\(926\) 34.1771 + 59.1964i 1.12313 + 1.94532i
\(927\) −6.54850 3.78078i −0.215081 0.124177i
\(928\) 37.3002i 1.22444i
\(929\) 6.40388 11.0918i 0.210105 0.363912i −0.741643 0.670795i \(-0.765953\pi\)
0.951747 + 0.306884i \(0.0992862\pi\)
\(930\) 0 0
\(931\) −6.38447 −0.209243
\(932\) 102.711 + 59.3002i 3.36441 + 1.94244i
\(933\) −9.41967 + 5.43845i −0.308386 + 0.178047i
\(934\) −33.3002 57.6776i −1.08962 1.88727i
\(935\) 0 0
\(936\) −21.9309 8.87348i −0.716833 0.290039i
\(937\) 3.43845i 0.112329i 0.998422 + 0.0561646i \(0.0178872\pi\)
−0.998422 + 0.0561646i \(0.982113\pi\)
\(938\) −3.46410 + 2.00000i −0.113107 + 0.0653023i
\(939\) −0.657671 1.13912i −0.0214623 0.0371738i
\(940\) 0 0
\(941\) −2.49242 −0.0812507 −0.0406253 0.999174i \(-0.512935\pi\)
−0.0406253 + 0.999174i \(0.512935\pi\)
\(942\) −9.69276 5.59612i −0.315807 0.182331i
\(943\) −4.43674 2.56155i −0.144480 0.0834156i
\(944\) 85.4773 2.78205
\(945\) 0 0
\(946\) 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 \(0.389158\pi\)
\(948\) 43.6155i 1.41657i
\(949\) 0.938447 + 6.70185i 0.0304633 + 0.217551i
\(950\) 0 0
\(951\) 11.5270 + 19.9653i 0.373788 + 0.647420i
\(952\) 51.8418 29.9309i 1.68020 0.970065i
\(953\) 30.2978 + 17.4924i 0.981441 + 0.566635i 0.902705 0.430260i \(-0.141578\pi\)
0.0787360 + 0.996896i \(0.474912\pi\)
\(954\) −29.9309 −0.969048
\(955\) 0 0
\(956\) 1.43845 2.49146i 0.0465227 0.0805797i
\(957\) 11.3693i 0.367518i
\(958\) 13.8564 + 8.00000i 0.447680 + 0.258468i
\(959\) 2.56155 + 4.43674i 0.0827169 + 0.143270i
\(960\) 0 0
\(961\) −28.5616 −0.921340
\(962\) −11.9111 + 29.4384i −0.384030 + 0.949134i
\(963\) 8.24621i 0.265730i
\(964\) 6.40388 + 11.0918i 0.206255 + 0.357244i
\(965\) 0 0
\(966\) 9.12311 15.8017i 0.293531 0.508411i
\(967\) 9.12311i 0.293379i 0.989183 + 0.146690i \(0.0468619\pi\)
−0.989183 + 0.146690i \(0.953138\pi\)
\(968\) 39.7773 + 22.9654i 1.27849 + 0.738137i
\(969\) −1.43845 + 2.49146i −0.0462096 + 0.0800373i
\(970\) 0 0
\(971\) −26.4924 + 45.8862i −0.850182 + 1.47256i 0.0308612 + 0.999524i \(0.490175\pi\)
−0.881043 + 0.473035i \(0.843158\pi\)
\(972\) −3.95042 + 2.28078i −0.126710 + 0.0731559i
\(973\) −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 −0.702918 0.711270i \(-0.748120\pi\)
0.264519 + 0.964380i \(0.414787\pi\)
\(978\) 35.0675 20.2462i 1.12133 0.647402i
\(979\) −13.1231 + 22.7299i −0.419416 + 0.726450i
\(980\) 0 0
\(981\) −8.90388 + 15.4220i −0.284279 + 0.492386i
\(982\) −43.8212 25.3002i −1.39839 0.807361i
\(983\) 27.6155i 0.880799i −0.897802 0.440399i \(-0.854837\pi\)
0.897802 0.440399i \(-0.145163\pi\)
\(984\) 8.40388 14.5560i 0.267906 0.464027i
\(985\) 0 0
\(986\) 18.6501 + 32.3029i 0.593940 + 1.02873i
\(987\) 29.3693i 0.934836i
\(988\) −11.3649 14.5616i −0.361567 0.463265i
\(989\) −0.876894 −0.0278836
\(990\) 0 0
\(991\) −20.1771 34.9477i −0.640946 1.11015i −0.985222 0.171283i \(-0.945209\pi\)
0.344276 0.938869i \(-0.388124\pi\)
\(992\) −8.87348 5.12311i −0.281733 0.162659i
\(993\) 23.8078i 0.755517i
\(994\) −63.8617 + 110.612i −2.02557 + 3.50839i
\(995\) 0 0
\(996\) −41.6155 −1.31864
\(997\) 17.8536 + 10.3078i 0.565428 + 0.326450i 0.755321 0.655355i \(-0.227481\pi\)
−0.189893 + 0.981805i \(0.560814\pi\)
\(998\) −63.2067 + 36.4924i −2.00077 + 1.15515i
\(999\) 1.71922 + 2.97778i 0.0543938 + 0.0942129i
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 975.2.bb.i.874.1 8
5.2 odd 4 39.2.e.b.16.1 4
5.3 odd 4 975.2.i.k.601.2 4
5.4 even 2 inner 975.2.bb.i.874.4 8
13.9 even 3 inner 975.2.bb.i.724.4 8
15.2 even 4 117.2.g.c.55.2 4
20.7 even 4 624.2.q.h.289.2 4
60.47 odd 4 1872.2.t.r.289.1 4
65.2 even 12 507.2.b.d.337.1 4
65.7 even 12 507.2.j.g.316.1 8
65.9 even 6 inner 975.2.bb.i.724.1 8
65.12 odd 4 507.2.e.g.484.2 4
65.17 odd 12 507.2.e.g.22.2 4
65.22 odd 12 39.2.e.b.22.1 yes 4
65.32 even 12 507.2.j.g.316.4 8
65.37 even 12 507.2.b.d.337.4 4
65.42 odd 12 507.2.a.g.1.2 2
65.47 even 4 507.2.j.g.361.4 8
65.48 odd 12 975.2.i.k.451.2 4
65.57 even 4 507.2.j.g.361.1 8
65.62 odd 12 507.2.a.d.1.1 2
195.2 odd 12 1521.2.b.h.1351.4 4
195.62 even 12 1521.2.a.m.1.2 2
195.107 even 12 1521.2.a.g.1.1 2
195.152 even 12 117.2.g.c.100.2 4
195.167 odd 12 1521.2.b.h.1351.1 4
260.87 even 12 624.2.q.h.529.2 4
260.107 even 12 8112.2.a.bk.1.2 2
260.127 even 12 8112.2.a.bo.1.1 2
780.347 odd 12 1872.2.t.r.1153.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.e.b.16.1 4 5.2 odd 4
39.2.e.b.22.1 yes 4 65.22 odd 12
117.2.g.c.55.2 4 15.2 even 4
117.2.g.c.100.2 4 195.152 even 12
507.2.a.d.1.1 2 65.62 odd 12
507.2.a.g.1.2 2 65.42 odd 12
507.2.b.d.337.1 4 65.2 even 12
507.2.b.d.337.4 4 65.37 even 12
507.2.e.g.22.2 4 65.17 odd 12
507.2.e.g.484.2 4 65.12 odd 4
507.2.j.g.316.1 8 65.7 even 12
507.2.j.g.316.4 8 65.32 even 12
507.2.j.g.361.1 8 65.57 even 4
507.2.j.g.361.4 8 65.47 even 4
624.2.q.h.289.2 4 20.7 even 4
624.2.q.h.529.2 4 260.87 even 12
975.2.i.k.451.2 4 65.48 odd 12
975.2.i.k.601.2 4 5.3 odd 4
975.2.bb.i.724.1 8 65.9 even 6 inner
975.2.bb.i.724.4 8 13.9 even 3 inner
975.2.bb.i.874.1 8 1.1 even 1 trivial
975.2.bb.i.874.4 8 5.4 even 2 inner
1521.2.a.g.1.1 2 195.107 even 12
1521.2.a.m.1.2 2 195.62 even 12
1521.2.b.h.1351.1 4 195.167 odd 12
1521.2.b.h.1351.4 4 195.2 odd 12
1872.2.t.r.289.1 4 60.47 odd 4
1872.2.t.r.1153.1 4 780.347 odd 12
8112.2.a.bk.1.2 2 260.107 even 12
8112.2.a.bo.1.1 2 260.127 even 12