Properties

Label 504.2.br.a.155.16
Level $504$
Weight $2$
Character 504.155
Analytic conductor $4.024$
Analytic rank $0$
Dimension $144$
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] = [504,2,Mod(155,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.br (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(72\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 155.16
Character \(\chi\) \(=\) 504.155
Dual form 504.2.br.a.491.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.06211 + 0.933765i) q^{2} +(1.61727 - 0.620022i) q^{3} +(0.256166 - 1.98353i) q^{4} +(1.88595 + 3.26656i) q^{5} +(-1.13877 + 2.16869i) q^{6} +(0.866025 + 0.500000i) q^{7} +(1.58007 + 2.34593i) q^{8} +(2.23114 - 2.00549i) q^{9} +O(q^{10})\) \(q+(-1.06211 + 0.933765i) q^{2} +(1.61727 - 0.620022i) q^{3} +(0.256166 - 1.98353i) q^{4} +(1.88595 + 3.26656i) q^{5} +(-1.13877 + 2.16869i) q^{6} +(0.866025 + 0.500000i) q^{7} +(1.58007 + 2.34593i) q^{8} +(2.23114 - 2.00549i) q^{9} +(-5.05329 - 1.70842i) q^{10} +(2.42860 + 1.40215i) q^{11} +(-0.815540 - 3.36673i) q^{12} +(-0.853096 + 0.492535i) q^{13} +(-1.38670 + 0.277608i) q^{14} +(5.07543 + 4.11359i) q^{15} +(-3.86876 - 1.01623i) q^{16} -1.53304i q^{17} +(-0.497071 + 4.21342i) q^{18} -6.57757 q^{19} +(6.96242 - 2.90405i) q^{20} +(1.71061 + 0.271682i) q^{21} +(-3.88872 + 0.778496i) q^{22} +(-2.63634 - 4.56627i) q^{23} +(4.00993 + 2.81433i) q^{24} +(-4.61360 + 7.99099i) q^{25} +(0.446172 - 1.31972i) q^{26} +(2.36492 - 4.62679i) q^{27} +(1.21361 - 1.58970i) q^{28} +(-2.72838 + 4.72570i) q^{29} +(-9.23180 + 0.370167i) q^{30} +(7.27190 - 4.19843i) q^{31} +(5.05797 - 2.53316i) q^{32} +(4.79707 + 0.761877i) q^{33} +(1.43150 + 1.62826i) q^{34} +3.77190i q^{35} +(-3.40640 - 4.93928i) q^{36} +6.35752i q^{37} +(6.98612 - 6.14190i) q^{38} +(-1.07431 + 1.32550i) q^{39} +(-4.68318 + 9.58569i) q^{40} +(4.11031 - 2.37309i) q^{41} +(-2.07055 + 1.30875i) q^{42} +(4.91459 - 8.51232i) q^{43} +(3.40333 - 4.45800i) q^{44} +(10.7589 + 3.50591i) q^{45} +(7.06391 + 2.38817i) q^{46} +(-4.07519 + 7.05844i) q^{47} +(-6.88692 + 0.755201i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.56154 - 12.7954i) q^{50} +(-0.950520 - 2.47935i) q^{51} +(0.758422 + 1.81831i) q^{52} -0.00523494 q^{53} +(1.80852 + 7.12245i) q^{54} +10.5775i q^{55} +(0.195417 + 2.82167i) q^{56} +(-10.6377 + 4.07824i) q^{57} +(-1.51484 - 7.56689i) q^{58} +(6.93375 - 4.00320i) q^{59} +(9.45956 - 9.01349i) q^{60} +(-7.06965 - 4.08166i) q^{61} +(-3.80323 + 11.2495i) q^{62} +(2.93497 - 0.621233i) q^{63} +(-3.00676 + 7.41346i) q^{64} +(-3.21779 - 1.85779i) q^{65} +(-5.80644 + 3.67013i) q^{66} +(3.33500 + 5.77638i) q^{67} +(-3.04083 - 0.392714i) q^{68} +(-7.09486 - 5.75032i) q^{69} +(-3.52206 - 4.00618i) q^{70} -0.840883 q^{71} +(8.23010 + 2.06529i) q^{72} -13.9167 q^{73} +(-5.93643 - 6.75240i) q^{74} +(-2.50686 + 15.7841i) q^{75} +(-1.68495 + 13.0468i) q^{76} +(1.40215 + 2.42860i) q^{77} +(-0.0966731 - 2.41098i) q^{78} +(-11.7620 - 6.79080i) q^{79} +(-3.97672 - 14.5541i) q^{80} +(0.956016 - 8.94908i) q^{81} +(-2.14970 + 6.35854i) q^{82} +(9.52050 + 5.49666i) q^{83} +(0.977089 - 3.32345i) q^{84} +(5.00777 - 2.89124i) q^{85} +(2.72866 + 13.6301i) q^{86} +(-1.48250 + 9.33440i) q^{87} +(0.548008 + 7.91281i) q^{88} +0.335563i q^{89} +(-14.7008 + 6.32258i) q^{90} -0.985070 q^{91} +(-9.73266 + 4.05952i) q^{92} +(9.15753 - 11.2988i) q^{93} +(-2.26261 - 11.3021i) q^{94} +(-12.4050 - 21.4860i) q^{95} +(6.60950 - 7.23287i) q^{96} +(5.06556 - 8.77381i) q^{97} +(-1.33972 - 0.452934i) q^{98} +(8.23055 - 1.74212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06211 + 0.933765i −0.751027 + 0.660271i
\(3\) 1.61727 0.620022i 0.933733 0.357970i
\(4\) 0.256166 1.98353i 0.128083 0.991763i
\(5\) 1.88595 + 3.26656i 0.843422 + 1.46085i 0.886985 + 0.461798i \(0.152796\pi\)
−0.0435632 + 0.999051i \(0.513871\pi\)
\(6\) −1.13877 + 2.16869i −0.464901 + 0.885362i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.58007 + 2.34593i 0.558639 + 0.829411i
\(9\) 2.23114 2.00549i 0.743715 0.668497i
\(10\) −5.05329 1.70842i −1.59799 0.540250i
\(11\) 2.42860 + 1.40215i 0.732249 + 0.422764i 0.819244 0.573444i \(-0.194393\pi\)
−0.0869953 + 0.996209i \(0.527727\pi\)
\(12\) −0.815540 3.36673i −0.235426 0.971892i
\(13\) −0.853096 + 0.492535i −0.236606 + 0.136605i −0.613616 0.789605i \(-0.710286\pi\)
0.377010 + 0.926209i \(0.376952\pi\)
\(14\) −1.38670 + 0.277608i −0.370611 + 0.0741938i
\(15\) 5.07543 + 4.11359i 1.31047 + 1.06212i
\(16\) −3.86876 1.01623i −0.967189 0.254056i
\(17\) 1.53304i 0.371817i −0.982567 0.185909i \(-0.940477\pi\)
0.982567 0.185909i \(-0.0595228\pi\)
\(18\) −0.497071 + 4.21342i −0.117161 + 0.993113i
\(19\) −6.57757 −1.50900 −0.754499 0.656301i \(-0.772120\pi\)
−0.754499 + 0.656301i \(0.772120\pi\)
\(20\) 6.96242 2.90405i 1.55684 0.649365i
\(21\) 1.71061 + 0.271682i 0.373286 + 0.0592858i
\(22\) −3.88872 + 0.778496i −0.829078 + 0.165976i
\(23\) −2.63634 4.56627i −0.549714 0.952133i −0.998294 0.0583899i \(-0.981403\pi\)
0.448580 0.893743i \(-0.351930\pi\)
\(24\) 4.00993 + 2.81433i 0.818524 + 0.574472i
\(25\) −4.61360 + 7.99099i −0.922720 + 1.59820i
\(26\) 0.446172 1.31972i 0.0875015 0.258818i
\(27\) 2.36492 4.62679i 0.455130 0.890425i
\(28\) 1.21361 1.58970i 0.229351 0.300425i
\(29\) −2.72838 + 4.72570i −0.506648 + 0.877540i 0.493322 + 0.869847i \(0.335782\pi\)
−0.999970 + 0.00769350i \(0.997551\pi\)
\(30\) −9.23180 + 0.370167i −1.68549 + 0.0675830i
\(31\) 7.27190 4.19843i 1.30607 0.754061i 0.324634 0.945840i \(-0.394759\pi\)
0.981438 + 0.191779i \(0.0614256\pi\)
\(32\) 5.05797 2.53316i 0.894132 0.447804i
\(33\) 4.79707 + 0.761877i 0.835062 + 0.132626i
\(34\) 1.43150 + 1.62826i 0.245500 + 0.279245i
\(35\) 3.77190i 0.637567i
\(36\) −3.40640 4.93928i −0.567733 0.823213i
\(37\) 6.35752i 1.04517i 0.852587 + 0.522585i \(0.175032\pi\)
−0.852587 + 0.522585i \(0.824968\pi\)
\(38\) 6.98612 6.14190i 1.13330 0.996348i
\(39\) −1.07431 + 1.32550i −0.172027 + 0.212250i
\(40\) −4.68318 + 9.58569i −0.740476 + 1.51563i
\(41\) 4.11031 2.37309i 0.641922 0.370614i −0.143433 0.989660i \(-0.545814\pi\)
0.785354 + 0.619046i \(0.212481\pi\)
\(42\) −2.07055 + 1.30875i −0.319492 + 0.201945i
\(43\) 4.91459 8.51232i 0.749468 1.29812i −0.198610 0.980079i \(-0.563643\pi\)
0.948078 0.318038i \(-0.103024\pi\)
\(44\) 3.40333 4.45800i 0.513071 0.672069i
\(45\) 10.7589 + 3.50591i 1.60384 + 0.522631i
\(46\) 7.06391 + 2.38817i 1.04152 + 0.352117i
\(47\) −4.07519 + 7.05844i −0.594428 + 1.02958i 0.399199 + 0.916864i \(0.369288\pi\)
−0.993627 + 0.112715i \(0.964045\pi\)
\(48\) −6.88692 + 0.755201i −0.994041 + 0.109004i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −2.56154 12.7954i −0.362257 1.80954i
\(51\) −0.950520 2.47935i −0.133099 0.347178i
\(52\) 0.758422 + 1.81831i 0.105174 + 0.252154i
\(53\) −0.00523494 −0.000719075 −0.000359537 1.00000i \(-0.500114\pi\)
−0.000359537 1.00000i \(0.500114\pi\)
\(54\) 1.80852 + 7.12245i 0.246108 + 0.969242i
\(55\) 10.5775i 1.42627i
\(56\) 0.195417 + 2.82167i 0.0261137 + 0.377061i
\(57\) −10.6377 + 4.07824i −1.40900 + 0.540176i
\(58\) −1.51484 7.56689i −0.198908 0.993581i
\(59\) 6.93375 4.00320i 0.902697 0.521173i 0.0246230 0.999697i \(-0.492161\pi\)
0.878074 + 0.478524i \(0.158828\pi\)
\(60\) 9.45956 9.01349i 1.22122 1.16364i
\(61\) −7.06965 4.08166i −0.905176 0.522604i −0.0263001 0.999654i \(-0.508373\pi\)
−0.878876 + 0.477051i \(0.841706\pi\)
\(62\) −3.80323 + 11.2495i −0.483010 + 1.42868i
\(63\) 2.93497 0.621233i 0.369772 0.0782680i
\(64\) −3.00676 + 7.41346i −0.375845 + 0.926683i
\(65\) −3.21779 1.85779i −0.399118 0.230431i
\(66\) −5.80644 + 3.67013i −0.714723 + 0.451762i
\(67\) 3.33500 + 5.77638i 0.407435 + 0.705697i 0.994601 0.103769i \(-0.0330901\pi\)
−0.587167 + 0.809466i \(0.699757\pi\)
\(68\) −3.04083 0.392714i −0.368755 0.0476235i
\(69\) −7.09486 5.75032i −0.854121 0.692257i
\(70\) −3.52206 4.00618i −0.420967 0.478830i
\(71\) −0.840883 −0.0997945 −0.0498972 0.998754i \(-0.515889\pi\)
−0.0498972 + 0.998754i \(0.515889\pi\)
\(72\) 8.23010 + 2.06529i 0.969927 + 0.243397i
\(73\) −13.9167 −1.62883 −0.814416 0.580282i \(-0.802943\pi\)
−0.814416 + 0.580282i \(0.802943\pi\)
\(74\) −5.93643 6.75240i −0.690096 0.784951i
\(75\) −2.50686 + 15.7841i −0.289467 + 1.82260i
\(76\) −1.68495 + 13.0468i −0.193277 + 1.49657i
\(77\) 1.40215 + 2.42860i 0.159790 + 0.276764i
\(78\) −0.0966731 2.41098i −0.0109461 0.272990i
\(79\) −11.7620 6.79080i −1.32333 0.764025i −0.339072 0.940760i \(-0.610113\pi\)
−0.984258 + 0.176735i \(0.943446\pi\)
\(80\) −3.97672 14.5541i −0.444610 1.62719i
\(81\) 0.956016 8.94908i 0.106224 0.994342i
\(82\) −2.14970 + 6.35854i −0.237395 + 0.702184i
\(83\) 9.52050 + 5.49666i 1.04501 + 0.603337i 0.921248 0.388975i \(-0.127171\pi\)
0.123762 + 0.992312i \(0.460504\pi\)
\(84\) 0.977089 3.32345i 0.106609 0.362618i
\(85\) 5.00777 2.89124i 0.543169 0.313599i
\(86\) 2.72866 + 13.6301i 0.294239 + 1.46977i
\(87\) −1.48250 + 9.33440i −0.158941 + 1.00075i
\(88\) 0.548008 + 7.91281i 0.0584178 + 0.843508i
\(89\) 0.335563i 0.0355696i 0.999842 + 0.0177848i \(0.00566137\pi\)
−0.999842 + 0.0177848i \(0.994339\pi\)
\(90\) −14.7008 + 6.32258i −1.54960 + 0.666459i
\(91\) −0.985070 −0.103263
\(92\) −9.73266 + 4.05952i −1.01470 + 0.423234i
\(93\) 9.15753 11.2988i 0.949591 1.17163i
\(94\) −2.26261 11.3021i −0.233370 1.16573i
\(95\) −12.4050 21.4860i −1.27272 2.20442i
\(96\) 6.60950 7.23287i 0.674580 0.738202i
\(97\) 5.06556 8.77381i 0.514330 0.890846i −0.485532 0.874219i \(-0.661374\pi\)
0.999862 0.0166266i \(-0.00529265\pi\)
\(98\) −1.33972 0.452934i −0.135332 0.0457532i
\(99\) 8.23055 1.74212i 0.827201 0.175090i
\(100\) 14.6685 + 11.1982i 1.46685 + 1.11982i
\(101\) 5.71100 9.89174i 0.568265 0.984264i −0.428472 0.903555i \(-0.640948\pi\)
0.996738 0.0807096i \(-0.0257186\pi\)
\(102\) 3.32469 + 1.74578i 0.329193 + 0.172858i
\(103\) 7.53252 4.34890i 0.742201 0.428510i −0.0806681 0.996741i \(-0.525705\pi\)
0.822869 + 0.568231i \(0.192372\pi\)
\(104\) −2.50340 1.22306i −0.245479 0.119931i
\(105\) 2.33866 + 6.10019i 0.228230 + 0.595317i
\(106\) 0.00556010 0.00488821i 0.000540044 0.000474784i
\(107\) 4.90915i 0.474585i 0.971438 + 0.237293i \(0.0762600\pi\)
−0.971438 + 0.237293i \(0.923740\pi\)
\(108\) −8.57154 5.87611i −0.824797 0.565429i
\(109\) 4.49181i 0.430237i 0.976588 + 0.215118i \(0.0690138\pi\)
−0.976588 + 0.215118i \(0.930986\pi\)
\(110\) −9.87693 11.2345i −0.941728 1.07117i
\(111\) 3.94180 + 10.2818i 0.374139 + 0.975910i
\(112\) −2.84233 2.81446i −0.268575 0.265941i
\(113\) −7.31585 + 4.22381i −0.688217 + 0.397343i −0.802944 0.596055i \(-0.796734\pi\)
0.114726 + 0.993397i \(0.463401\pi\)
\(114\) 7.49035 14.2647i 0.701535 1.33601i
\(115\) 9.94399 17.2235i 0.927281 1.60610i
\(116\) 8.67463 + 6.62239i 0.805419 + 0.614873i
\(117\) −0.915606 + 2.80979i −0.0846478 + 0.259765i
\(118\) −3.62637 + 10.7263i −0.333835 + 0.987440i
\(119\) 0.766521 1.32765i 0.0702668 0.121706i
\(120\) −1.63064 + 18.4064i −0.148856 + 1.68026i
\(121\) −1.56795 2.71577i −0.142541 0.246888i
\(122\) 11.3201 2.26620i 1.02487 0.205172i
\(123\) 5.17612 6.38641i 0.466715 0.575843i
\(124\) −6.46489 15.4995i −0.580564 1.39190i
\(125\) −15.9446 −1.42613
\(126\) −2.53719 + 3.40039i −0.226031 + 0.302931i
\(127\) 12.3907i 1.09950i −0.835331 0.549748i \(-0.814724\pi\)
0.835331 0.549748i \(-0.185276\pi\)
\(128\) −3.72892 10.6815i −0.329593 0.944123i
\(129\) 2.67041 16.8139i 0.235116 1.48038i
\(130\) 5.15240 1.03147i 0.451895 0.0904663i
\(131\) 5.52709 3.19107i 0.482904 0.278805i −0.238722 0.971088i \(-0.576728\pi\)
0.721626 + 0.692283i \(0.243395\pi\)
\(132\) 2.74005 9.31994i 0.238491 0.811197i
\(133\) −5.69634 3.28878i −0.493935 0.285174i
\(134\) −8.93592 3.02107i −0.771946 0.260980i
\(135\) 19.5738 1.00072i 1.68464 0.0861284i
\(136\) 3.59641 2.42231i 0.308389 0.207712i
\(137\) −4.63584 2.67650i −0.396067 0.228669i 0.288719 0.957414i \(-0.406771\pi\)
−0.684785 + 0.728745i \(0.740104\pi\)
\(138\) 12.9050 0.517451i 1.09855 0.0440483i
\(139\) −9.41646 16.3098i −0.798694 1.38338i −0.920467 0.390821i \(-0.872191\pi\)
0.121773 0.992558i \(-0.461142\pi\)
\(140\) 7.48166 + 0.966233i 0.632315 + 0.0816616i
\(141\) −2.21431 + 13.9421i −0.186479 + 1.17414i
\(142\) 0.893112 0.785187i 0.0749483 0.0658914i
\(143\) −2.76243 −0.231006
\(144\) −10.6698 + 5.49141i −0.889149 + 0.457617i
\(145\) −20.5824 −1.70927
\(146\) 14.7812 12.9950i 1.22330 1.07547i
\(147\) 1.34559 + 1.09059i 0.110983 + 0.0899502i
\(148\) 12.6103 + 1.62858i 1.03656 + 0.133869i
\(149\) −1.75436 3.03864i −0.143723 0.248935i 0.785173 0.619277i \(-0.212574\pi\)
−0.928896 + 0.370341i \(0.879241\pi\)
\(150\) −12.0761 19.1054i −0.986011 1.55995i
\(151\) −7.16647 4.13757i −0.583199 0.336710i 0.179204 0.983812i \(-0.442648\pi\)
−0.762404 + 0.647102i \(0.775981\pi\)
\(152\) −10.3930 15.4305i −0.842985 1.25158i
\(153\) −3.07450 3.42044i −0.248559 0.276526i
\(154\) −3.75698 1.27016i −0.302746 0.102353i
\(155\) 27.4289 + 15.8361i 2.20314 + 1.27198i
\(156\) 2.35397 + 2.47046i 0.188468 + 0.197795i
\(157\) −5.99184 + 3.45939i −0.478201 + 0.276089i −0.719666 0.694320i \(-0.755705\pi\)
0.241466 + 0.970409i \(0.422372\pi\)
\(158\) 18.8336 3.77036i 1.49832 0.299954i
\(159\) −0.00846633 + 0.00324578i −0.000671424 + 0.000257407i
\(160\) 17.8138 + 11.7447i 1.40830 + 0.928504i
\(161\) 5.27267i 0.415545i
\(162\) 7.34094 + 10.3976i 0.576759 + 0.816915i
\(163\) 15.1043 1.18306 0.591531 0.806282i \(-0.298524\pi\)
0.591531 + 0.806282i \(0.298524\pi\)
\(164\) −3.65416 8.76081i −0.285342 0.684104i
\(165\) 6.55830 + 17.1068i 0.510563 + 1.33176i
\(166\) −15.2444 + 3.05183i −1.18320 + 0.236868i
\(167\) 0.945482 + 1.63762i 0.0731636 + 0.126723i 0.900286 0.435298i \(-0.143357\pi\)
−0.827123 + 0.562021i \(0.810024\pi\)
\(168\) 2.06554 + 4.44225i 0.159360 + 0.342727i
\(169\) −6.01482 + 10.4180i −0.462678 + 0.801382i
\(170\) −2.61908 + 7.74690i −0.200874 + 0.594160i
\(171\) −14.6755 + 13.1913i −1.12226 + 1.00876i
\(172\) −15.6255 11.9288i −1.19143 0.909562i
\(173\) −7.57215 + 13.1153i −0.575700 + 0.997141i 0.420266 + 0.907401i \(0.361937\pi\)
−0.995965 + 0.0897400i \(0.971396\pi\)
\(174\) −7.14155 11.2985i −0.541400 0.856537i
\(175\) −7.99099 + 4.61360i −0.604062 + 0.348755i
\(176\) −7.97075 7.89258i −0.600818 0.594926i
\(177\) 8.73169 10.7734i 0.656314 0.809775i
\(178\) −0.313336 0.356405i −0.0234856 0.0267137i
\(179\) 13.1476i 0.982696i 0.870963 + 0.491348i \(0.163496\pi\)
−0.870963 + 0.491348i \(0.836504\pi\)
\(180\) 9.71014 20.4424i 0.723751 1.52369i
\(181\) 13.0831i 0.972463i −0.873830 0.486231i \(-0.838371\pi\)
0.873830 0.486231i \(-0.161629\pi\)
\(182\) 1.04626 0.919824i 0.0775536 0.0681819i
\(183\) −13.9643 2.21783i −1.03227 0.163946i
\(184\) 6.54654 13.3997i 0.482617 0.987837i
\(185\) −20.7672 + 11.9900i −1.52684 + 0.881519i
\(186\) 0.824054 + 20.5515i 0.0604226 + 1.50691i
\(187\) 2.14955 3.72314i 0.157191 0.272263i
\(188\) 12.9567 + 9.89139i 0.944963 + 0.721404i
\(189\) 4.36148 2.82445i 0.317251 0.205449i
\(190\) 33.2383 + 11.2373i 2.41136 + 0.815236i
\(191\) −2.09273 + 3.62471i −0.151425 + 0.262275i −0.931751 0.363097i \(-0.881719\pi\)
0.780327 + 0.625372i \(0.215053\pi\)
\(192\) −0.266236 + 13.8538i −0.0192139 + 0.999815i
\(193\) 4.22026 + 7.30970i 0.303781 + 0.526164i 0.976989 0.213289i \(-0.0684177\pi\)
−0.673208 + 0.739453i \(0.735084\pi\)
\(194\) 2.81248 + 14.0488i 0.201924 + 1.00865i
\(195\) −6.35592 1.00946i −0.455157 0.0722886i
\(196\) 1.84587 0.769917i 0.131848 0.0549941i
\(197\) −12.8051 −0.912329 −0.456164 0.889896i \(-0.650777\pi\)
−0.456164 + 0.889896i \(0.650777\pi\)
\(198\) −7.11503 + 9.53573i −0.505643 + 0.677675i
\(199\) 10.0904i 0.715291i −0.933857 0.357646i \(-0.883580\pi\)
0.933857 0.357646i \(-0.116420\pi\)
\(200\) −26.0361 + 1.80315i −1.84103 + 0.127502i
\(201\) 8.97508 + 7.27422i 0.633054 + 0.513084i
\(202\) 3.17083 + 15.8389i 0.223099 + 1.11442i
\(203\) −4.72570 + 2.72838i −0.331679 + 0.191495i
\(204\) −5.16134 + 1.25026i −0.361366 + 0.0875354i
\(205\) 15.5036 + 8.95103i 1.08282 + 0.625167i
\(206\) −3.93953 + 11.6526i −0.274480 + 0.811877i
\(207\) −15.0397 4.90086i −1.04533 0.340633i
\(208\) 3.80095 1.03856i 0.263548 0.0720113i
\(209\) −15.9743 9.22274i −1.10496 0.637950i
\(210\) −8.18006 4.29533i −0.564478 0.296406i
\(211\) 1.07014 + 1.85353i 0.0736712 + 0.127602i 0.900508 0.434840i \(-0.143195\pi\)
−0.826836 + 0.562442i \(0.809862\pi\)
\(212\) −0.00134102 + 0.0103836i −9.21014e−5 + 0.000713152i
\(213\) −1.35994 + 0.521366i −0.0931814 + 0.0357234i
\(214\) −4.58399 5.21407i −0.313355 0.356426i
\(215\) 37.0747 2.52847
\(216\) 14.5908 1.76271i 0.992781 0.119937i
\(217\) 8.39687 0.570017
\(218\) −4.19429 4.77080i −0.284073 0.323120i
\(219\) −22.5072 + 8.62869i −1.52089 + 0.583073i
\(220\) 20.9808 + 2.70961i 1.41453 + 0.182682i
\(221\) 0.755077 + 1.30783i 0.0507920 + 0.0879743i
\(222\) −13.7875 7.23976i −0.925354 0.485901i
\(223\) −19.7757 11.4175i −1.32428 0.764572i −0.339870 0.940473i \(-0.610383\pi\)
−0.984408 + 0.175900i \(0.943716\pi\)
\(224\) 5.64691 + 0.335202i 0.377300 + 0.0223966i
\(225\) 5.73224 + 27.0816i 0.382150 + 1.80544i
\(226\) 3.82621 11.3174i 0.254516 0.752825i
\(227\) −17.3371 10.0096i −1.15071 0.664361i −0.201648 0.979458i \(-0.564630\pi\)
−0.949059 + 0.315097i \(0.897963\pi\)
\(228\) 5.36427 + 22.1449i 0.355257 + 1.46658i
\(229\) 23.1551 13.3686i 1.53013 0.883423i 0.530779 0.847510i \(-0.321899\pi\)
0.999355 0.0359130i \(-0.0114339\pi\)
\(230\) 5.52106 + 27.5786i 0.364048 + 1.81848i
\(231\) 3.77344 + 3.05834i 0.248274 + 0.201224i
\(232\) −15.3972 + 1.06634i −1.01087 + 0.0700089i
\(233\) 22.1554i 1.45145i 0.687987 + 0.725723i \(0.258495\pi\)
−0.687987 + 0.725723i \(0.741505\pi\)
\(234\) −1.65121 3.83928i −0.107943 0.250981i
\(235\) −30.7424 −2.00541
\(236\) −6.16427 14.7788i −0.401260 0.962016i
\(237\) −23.2328 3.68987i −1.50914 0.239683i
\(238\) 0.425584 + 2.12587i 0.0275865 + 0.137799i
\(239\) 7.90282 + 13.6881i 0.511191 + 0.885408i 0.999916 + 0.0129706i \(0.00412877\pi\)
−0.488725 + 0.872438i \(0.662538\pi\)
\(240\) −15.4553 21.0723i −0.997634 1.36021i
\(241\) −4.90907 + 8.50276i −0.316221 + 0.547711i −0.979696 0.200487i \(-0.935747\pi\)
0.663475 + 0.748198i \(0.269081\pi\)
\(242\) 4.20123 + 1.42035i 0.270065 + 0.0913039i
\(243\) −4.00249 15.0659i −0.256760 0.966475i
\(244\) −9.90710 + 12.9773i −0.634237 + 0.830784i
\(245\) −1.88595 + 3.26656i −0.120489 + 0.208693i
\(246\) 0.465781 + 11.6164i 0.0296971 + 0.740632i
\(247\) 5.61130 3.23968i 0.357038 0.206136i
\(248\) 21.3393 + 10.4255i 1.35505 + 0.662022i
\(249\) 18.8053 + 2.98668i 1.19174 + 0.189273i
\(250\) 16.9349 14.8885i 1.07106 0.941630i
\(251\) 2.29373i 0.144779i −0.997376 0.0723894i \(-0.976938\pi\)
0.997376 0.0723894i \(-0.0230624\pi\)
\(252\) −0.480391 5.98074i −0.0302618 0.376751i
\(253\) 14.7862i 0.929598i
\(254\) 11.5700 + 13.1603i 0.725966 + 0.825751i
\(255\) 6.30630 7.78085i 0.394916 0.487256i
\(256\) 13.9346 + 7.86306i 0.870911 + 0.491441i
\(257\) 14.2418 8.22253i 0.888382 0.512907i 0.0149690 0.999888i \(-0.495235\pi\)
0.873413 + 0.486980i \(0.161902\pi\)
\(258\) 12.8640 + 20.3518i 0.800875 + 1.26705i
\(259\) −3.17876 + 5.50577i −0.197519 + 0.342112i
\(260\) −4.50927 + 5.90667i −0.279653 + 0.366316i
\(261\) 3.38992 + 16.0155i 0.209831 + 0.991332i
\(262\) −2.89068 + 8.55027i −0.178587 + 0.528238i
\(263\) −0.0689161 + 0.119366i −0.00424955 + 0.00736043i −0.868142 0.496315i \(-0.834686\pi\)
0.863893 + 0.503676i \(0.168019\pi\)
\(264\) 5.79239 + 12.4574i 0.356497 + 0.766700i
\(265\) −0.00987283 0.0171002i −0.000606483 0.00105046i
\(266\) 9.12111 1.82598i 0.559251 0.111958i
\(267\) 0.208056 + 0.542696i 0.0127328 + 0.0332125i
\(268\) 12.3119 5.13534i 0.752070 0.313691i
\(269\) −15.9079 −0.969922 −0.484961 0.874536i \(-0.661166\pi\)
−0.484961 + 0.874536i \(0.661166\pi\)
\(270\) −19.8551 + 19.3402i −1.20834 + 1.17701i
\(271\) 2.54719i 0.154731i 0.997003 + 0.0773654i \(0.0246508\pi\)
−0.997003 + 0.0773654i \(0.975349\pi\)
\(272\) −1.55792 + 5.93097i −0.0944625 + 0.359618i
\(273\) −1.59313 + 0.610766i −0.0964205 + 0.0369652i
\(274\) 7.42301 1.48604i 0.448440 0.0897748i
\(275\) −22.4091 + 12.9379i −1.35132 + 0.780186i
\(276\) −13.2234 + 12.5998i −0.795953 + 0.758420i
\(277\) 22.6437 + 13.0733i 1.36053 + 0.785500i 0.989694 0.143200i \(-0.0457392\pi\)
0.370832 + 0.928700i \(0.379073\pi\)
\(278\) 25.2309 + 8.53007i 1.51325 + 0.511600i
\(279\) 7.80475 23.9510i 0.467258 1.43391i
\(280\) −8.84860 + 5.95986i −0.528805 + 0.356170i
\(281\) −16.9266 9.77257i −1.00976 0.582982i −0.0986352 0.995124i \(-0.531448\pi\)
−0.911120 + 0.412141i \(0.864781\pi\)
\(282\) −10.6668 16.8758i −0.635200 1.00494i
\(283\) 8.56119 + 14.8284i 0.508910 + 0.881458i 0.999947 + 0.0103191i \(0.00328473\pi\)
−0.491037 + 0.871139i \(0.663382\pi\)
\(284\) −0.215406 + 1.66791i −0.0127820 + 0.0989725i
\(285\) −33.3840 27.0574i −1.97750 1.60274i
\(286\) 2.93402 2.57946i 0.173492 0.152527i
\(287\) 4.74617 0.280158
\(288\) 6.20483 15.7956i 0.365623 0.930763i
\(289\) 14.6498 0.861752
\(290\) 21.8608 19.2191i 1.28371 1.12858i
\(291\) 2.75244 17.3304i 0.161351 1.01593i
\(292\) −3.56500 + 27.6042i −0.208626 + 1.61542i
\(293\) 4.03356 + 6.98634i 0.235643 + 0.408146i 0.959459 0.281847i \(-0.0909470\pi\)
−0.723816 + 0.689993i \(0.757614\pi\)
\(294\) −2.44752 + 0.0981383i −0.142742 + 0.00572354i
\(295\) 26.1534 + 15.0997i 1.52271 + 0.879136i
\(296\) −14.9143 + 10.0453i −0.866875 + 0.583873i
\(297\) 12.2309 7.92061i 0.709708 0.459601i
\(298\) 4.70071 + 1.58922i 0.272305 + 0.0920611i
\(299\) 4.49810 + 2.59698i 0.260132 + 0.150187i
\(300\) 30.6661 + 9.01579i 1.77051 + 0.520527i
\(301\) 8.51232 4.91459i 0.490642 0.283272i
\(302\) 11.4751 2.29724i 0.660319 0.132191i
\(303\) 3.10315 19.5386i 0.178271 1.12246i
\(304\) 25.4470 + 6.68429i 1.45949 + 0.383371i
\(305\) 30.7912i 1.76310i
\(306\) 6.45935 + 0.762030i 0.369256 + 0.0435624i
\(307\) 7.15256 0.408218 0.204109 0.978948i \(-0.434570\pi\)
0.204109 + 0.978948i \(0.434570\pi\)
\(308\) 5.17637 2.15908i 0.294951 0.123025i
\(309\) 9.48572 11.7037i 0.539624 0.665800i
\(310\) −43.9197 + 8.79243i −2.49447 + 0.499376i
\(311\) −0.436065 0.755286i −0.0247270 0.0428284i 0.853397 0.521261i \(-0.174538\pi\)
−0.878124 + 0.478433i \(0.841205\pi\)
\(312\) −4.80701 0.425859i −0.272144 0.0241095i
\(313\) −12.2525 + 21.2220i −0.692553 + 1.19954i 0.278446 + 0.960452i \(0.410181\pi\)
−0.970999 + 0.239085i \(0.923153\pi\)
\(314\) 3.13375 9.26923i 0.176848 0.523093i
\(315\) 7.56450 + 8.41565i 0.426211 + 0.474168i
\(316\) −16.4828 + 21.5907i −0.927228 + 1.21457i
\(317\) 1.11462 1.93059i 0.0626036 0.108433i −0.833025 0.553236i \(-0.813393\pi\)
0.895628 + 0.444803i \(0.146726\pi\)
\(318\) 0.00596140 0.0113529i 0.000334299 0.000636642i
\(319\) −13.2523 + 7.65121i −0.741985 + 0.428385i
\(320\) −29.8871 + 4.15966i −1.67074 + 0.232532i
\(321\) 3.04378 + 7.93944i 0.169887 + 0.443136i
\(322\) 4.92344 + 5.60017i 0.274372 + 0.312085i
\(323\) 10.0837i 0.561071i
\(324\) −17.5058 4.18874i −0.972547 0.232708i
\(325\) 9.08944i 0.504192i
\(326\) −16.0425 + 14.1039i −0.888511 + 0.781142i
\(327\) 2.78502 + 7.26448i 0.154012 + 0.401726i
\(328\) 12.0617 + 5.89284i 0.665994 + 0.325378i
\(329\) −7.05844 + 4.07519i −0.389144 + 0.224673i
\(330\) −22.9393 12.0454i −1.26277 0.663077i
\(331\) 0.554537 0.960486i 0.0304801 0.0527931i −0.850383 0.526164i \(-0.823630\pi\)
0.880863 + 0.473371i \(0.156963\pi\)
\(332\) 13.3416 17.4761i 0.732216 0.959126i
\(333\) 12.7499 + 14.1845i 0.698693 + 0.777308i
\(334\) −2.53336 0.856482i −0.138619 0.0468646i
\(335\) −12.5793 + 21.7879i −0.687278 + 1.19040i
\(336\) −6.34185 2.78944i −0.345976 0.152176i
\(337\) 13.7826 + 23.8721i 0.750785 + 1.30040i 0.947443 + 0.319926i \(0.103658\pi\)
−0.196657 + 0.980472i \(0.563009\pi\)
\(338\) −3.33952 16.6815i −0.181646 0.907353i
\(339\) −9.21288 + 11.3670i −0.500375 + 0.617373i
\(340\) −4.45202 10.6737i −0.241445 0.578862i
\(341\) 23.5473 1.27516
\(342\) 3.26952 27.7141i 0.176795 1.49861i
\(343\) 1.00000i 0.0539949i
\(344\) 27.7347 1.92079i 1.49535 0.103562i
\(345\) 5.40320 34.0206i 0.290898 1.83161i
\(346\) −4.20417 21.0006i −0.226018 1.12900i
\(347\) 12.7104 7.33834i 0.682329 0.393943i −0.118403 0.992966i \(-0.537777\pi\)
0.800732 + 0.599023i \(0.204444\pi\)
\(348\) 18.1353 + 5.33174i 0.972152 + 0.285811i
\(349\) −15.4774 8.93588i −0.828486 0.478327i 0.0248481 0.999691i \(-0.492090\pi\)
−0.853334 + 0.521365i \(0.825423\pi\)
\(350\) 4.17931 12.3619i 0.223394 0.660770i
\(351\) 0.261349 + 5.11190i 0.0139498 + 0.272853i
\(352\) 15.8356 + 0.940007i 0.844043 + 0.0501025i
\(353\) 21.7765 + 12.5726i 1.15904 + 0.669175i 0.951075 0.308961i \(-0.0999812\pi\)
0.207969 + 0.978135i \(0.433315\pi\)
\(354\) 0.785735 + 19.5959i 0.0417613 + 1.04151i
\(355\) −1.58586 2.74679i −0.0841688 0.145785i
\(356\) 0.665597 + 0.0859598i 0.0352766 + 0.00455586i
\(357\) 0.416499 2.62244i 0.0220435 0.138794i
\(358\) −12.2767 13.9642i −0.648846 0.738031i
\(359\) −21.9911 −1.16065 −0.580323 0.814387i \(-0.697074\pi\)
−0.580323 + 0.814387i \(0.697074\pi\)
\(360\) 8.77516 + 30.7791i 0.462491 + 1.62220i
\(361\) 24.2644 1.27707
\(362\) 12.2166 + 13.8958i 0.642089 + 0.730346i
\(363\) −4.21964 3.41997i −0.221474 0.179502i
\(364\) −0.252342 + 1.95391i −0.0132263 + 0.102413i
\(365\) −26.2463 45.4599i −1.37379 2.37948i
\(366\) 16.9026 10.6838i 0.883511 0.558450i
\(367\) −18.5649 10.7184i −0.969080 0.559498i −0.0701240 0.997538i \(-0.522340\pi\)
−0.898956 + 0.438040i \(0.855673\pi\)
\(368\) 5.55899 + 20.3449i 0.289782 + 1.06055i
\(369\) 4.41149 13.5379i 0.229653 0.704754i
\(370\) 10.8613 32.1264i 0.564653 1.67017i
\(371\) −0.00453359 0.00261747i −0.000235372 0.000135892i
\(372\) −20.0655 21.0586i −1.04035 1.09184i
\(373\) 8.65167 4.99504i 0.447966 0.258633i −0.259005 0.965876i \(-0.583394\pi\)
0.706971 + 0.707243i \(0.250061\pi\)
\(374\) 1.19347 + 5.96157i 0.0617127 + 0.308265i
\(375\) −25.7867 + 9.88598i −1.33162 + 0.510510i
\(376\) −22.9977 + 1.59272i −1.18601 + 0.0821384i
\(377\) 5.37530i 0.276842i
\(378\) −1.99500 + 7.07248i −0.102612 + 0.363769i
\(379\) −34.8839 −1.79187 −0.895933 0.444190i \(-0.853492\pi\)
−0.895933 + 0.444190i \(0.853492\pi\)
\(380\) −45.7958 + 19.1016i −2.34928 + 0.979890i
\(381\) −7.68250 20.0391i −0.393586 1.02664i
\(382\) −1.16192 5.80397i −0.0594488 0.296957i
\(383\) 1.59336 + 2.75978i 0.0814170 + 0.141018i 0.903859 0.427831i \(-0.140722\pi\)
−0.822442 + 0.568849i \(0.807389\pi\)
\(384\) −12.6535 14.9629i −0.645719 0.763575i
\(385\) −5.28877 + 9.16041i −0.269540 + 0.466858i
\(386\) −11.3079 3.82300i −0.575558 0.194585i
\(387\) −6.10621 28.8484i −0.310396 1.46645i
\(388\) −16.1055 12.2952i −0.817631 0.624196i
\(389\) −3.61162 + 6.25551i −0.183116 + 0.317167i −0.942940 0.332962i \(-0.891952\pi\)
0.759824 + 0.650129i \(0.225285\pi\)
\(390\) 7.69329 4.86278i 0.389565 0.246236i
\(391\) −7.00028 + 4.04161i −0.354019 + 0.204393i
\(392\) −1.24160 + 2.54134i −0.0627102 + 0.128357i
\(393\) 6.96028 8.58774i 0.351100 0.433194i
\(394\) 13.6005 11.9570i 0.685184 0.602385i
\(395\) 51.2284i 2.57758i
\(396\) −1.34716 16.7718i −0.0676974 0.842814i
\(397\) 5.27745i 0.264868i −0.991192 0.132434i \(-0.957721\pi\)
0.991192 0.132434i \(-0.0422792\pi\)
\(398\) 9.42208 + 10.7172i 0.472286 + 0.537203i
\(399\) −11.2517 1.78700i −0.563287 0.0894621i
\(400\) 25.9696 26.2267i 1.29848 1.31134i
\(401\) −13.4017 + 7.73749i −0.669250 + 0.386392i −0.795792 0.605570i \(-0.792945\pi\)
0.126542 + 0.991961i \(0.459612\pi\)
\(402\) −16.3250 + 0.654581i −0.814215 + 0.0326475i
\(403\) −4.13575 + 7.16333i −0.206017 + 0.356831i
\(404\) −18.1576 13.8618i −0.903372 0.689653i
\(405\) 31.0357 13.7546i 1.54218 0.683473i
\(406\) 2.47156 7.31054i 0.122661 0.362816i
\(407\) −8.91420 + 15.4398i −0.441860 + 0.765325i
\(408\) 4.31448 6.14739i 0.213599 0.304341i
\(409\) −12.1348 21.0182i −0.600029 1.03928i −0.992816 0.119651i \(-0.961822\pi\)
0.392787 0.919629i \(-0.371511\pi\)
\(410\) −24.8248 + 4.96975i −1.22601 + 0.245439i
\(411\) −9.15691 1.45431i −0.451677 0.0717360i
\(412\) −6.69658 16.0550i −0.329917 0.790973i
\(413\) 8.00640 0.393969
\(414\) 20.5501 8.83824i 1.00998 0.434376i
\(415\) 41.4657i 2.03547i
\(416\) −3.06726 + 4.65226i −0.150385 + 0.228096i
\(417\) −25.3414 20.5390i −1.24098 1.00580i
\(418\) 25.5783 5.12061i 1.25108 0.250457i
\(419\) −28.7613 + 16.6054i −1.40508 + 0.811225i −0.994908 0.100783i \(-0.967865\pi\)
−0.410174 + 0.912007i \(0.634532\pi\)
\(420\) 12.6990 3.07613i 0.619646 0.150100i
\(421\) 9.27082 + 5.35251i 0.451832 + 0.260865i 0.708604 0.705607i \(-0.249325\pi\)
−0.256772 + 0.966472i \(0.582659\pi\)
\(422\) −2.86737 0.969402i −0.139581 0.0471898i
\(423\) 5.06329 + 23.9212i 0.246186 + 1.16309i
\(424\) −0.00827158 0.0122808i −0.000401703 0.000596408i
\(425\) 12.2505 + 7.07284i 0.594238 + 0.343083i
\(426\) 0.957573 1.82361i 0.0463946 0.0883543i
\(427\) −4.08166 7.06965i −0.197526 0.342124i
\(428\) 9.73743 + 1.25756i 0.470676 + 0.0607864i
\(429\) −4.46761 + 1.71277i −0.215698 + 0.0826933i
\(430\) −39.3775 + 34.6190i −1.89895 + 1.66948i
\(431\) 17.8880 0.861635 0.430818 0.902439i \(-0.358225\pi\)
0.430818 + 0.902439i \(0.358225\pi\)
\(432\) −13.8512 + 15.4966i −0.666415 + 0.745581i
\(433\) 22.8075 1.09606 0.548030 0.836459i \(-0.315378\pi\)
0.548030 + 0.836459i \(0.315378\pi\)
\(434\) −8.91842 + 7.84070i −0.428098 + 0.376366i
\(435\) −33.2873 + 12.7615i −1.59600 + 0.611868i
\(436\) 8.90962 + 1.15065i 0.426693 + 0.0551061i
\(437\) 17.3407 + 30.0349i 0.829517 + 1.43677i
\(438\) 15.8480 30.1811i 0.757246 1.44211i
\(439\) 12.5582 + 7.25048i 0.599370 + 0.346046i 0.768794 0.639497i \(-0.220857\pi\)
−0.169424 + 0.985543i \(0.554191\pi\)
\(440\) −24.8141 + 16.7132i −1.18297 + 0.796773i
\(441\) 2.85238 + 0.929483i 0.135828 + 0.0442611i
\(442\) −2.02318 0.684000i −0.0962330 0.0325346i
\(443\) 32.7852 + 18.9285i 1.55767 + 0.899322i 0.997479 + 0.0709598i \(0.0226062\pi\)
0.560193 + 0.828362i \(0.310727\pi\)
\(444\) 21.4041 5.18481i 1.01579 0.246060i
\(445\) −1.09613 + 0.632854i −0.0519618 + 0.0300001i
\(446\) 31.6653 6.33917i 1.49939 0.300168i
\(447\) −4.72131 3.82658i −0.223310 0.180991i
\(448\) −6.31066 + 4.91687i −0.298151 + 0.232300i
\(449\) 7.39596i 0.349037i −0.984654 0.174518i \(-0.944163\pi\)
0.984654 0.174518i \(-0.0558368\pi\)
\(450\) −31.3761 23.4111i −1.47908 1.10361i
\(451\) 13.3097 0.626729
\(452\) 6.50396 + 15.5932i 0.305921 + 0.733442i
\(453\) −14.1555 2.24820i −0.665085 0.105630i
\(454\) 27.7606 5.55749i 1.30287 0.260826i
\(455\) −1.85779 3.21779i −0.0870946 0.150852i
\(456\) −26.3756 18.5114i −1.23515 0.866877i
\(457\) −17.7591 + 30.7597i −0.830735 + 1.43888i 0.0667206 + 0.997772i \(0.478746\pi\)
−0.897456 + 0.441104i \(0.854587\pi\)
\(458\) −12.1102 + 35.8204i −0.565873 + 1.67378i
\(459\) −7.09305 3.62552i −0.331075 0.169225i
\(460\) −31.6159 24.1362i −1.47410 1.12536i
\(461\) −14.0793 + 24.3861i −0.655740 + 1.13577i 0.325968 + 0.945381i \(0.394310\pi\)
−0.981708 + 0.190394i \(0.939023\pi\)
\(462\) −6.86359 + 0.275209i −0.319323 + 0.0128039i
\(463\) 29.3394 16.9391i 1.36352 0.787228i 0.373429 0.927659i \(-0.378182\pi\)
0.990091 + 0.140431i \(0.0448487\pi\)
\(464\) 15.3578 15.5099i 0.712969 0.720030i
\(465\) 54.1787 + 8.60473i 2.51248 + 0.399035i
\(466\) −20.6879 23.5315i −0.958348 1.09008i
\(467\) 0.227729i 0.0105380i 0.999986 + 0.00526902i \(0.00167719\pi\)
−0.999986 + 0.00526902i \(0.998323\pi\)
\(468\) 5.33875 + 2.53590i 0.246784 + 0.117222i
\(469\) 6.66999i 0.307992i
\(470\) 32.6519 28.7062i 1.50612 1.32412i
\(471\) −7.54554 + 9.30985i −0.347680 + 0.428975i
\(472\) 20.3470 + 9.94074i 0.936548 + 0.457560i
\(473\) 23.8711 13.7820i 1.09759 0.633697i
\(474\) 28.1214 17.7750i 1.29166 0.816431i
\(475\) 30.3463 52.5613i 1.39238 2.41168i
\(476\) −2.43708 1.86051i −0.111703 0.0852765i
\(477\) −0.0116799 + 0.0104986i −0.000534787 + 0.000480699i
\(478\) −21.1751 7.15891i −0.968528 0.327441i
\(479\) −3.27213 + 5.66749i −0.149507 + 0.258954i −0.931045 0.364903i \(-0.881102\pi\)
0.781538 + 0.623857i \(0.214435\pi\)
\(480\) 36.0918 + 7.94951i 1.64736 + 0.362844i
\(481\) −3.13130 5.42357i −0.142775 0.247294i
\(482\) −2.72559 13.6148i −0.124147 0.620137i
\(483\) −3.26917 8.52735i −0.148753 0.388008i
\(484\) −5.78845 + 2.41438i −0.263111 + 0.109745i
\(485\) 38.2136 1.73519
\(486\) 18.3191 + 12.2643i 0.830970 + 0.556318i
\(487\) 13.4811i 0.610887i −0.952210 0.305444i \(-0.901195\pi\)
0.952210 0.305444i \(-0.0988048\pi\)
\(488\) −1.59525 23.0342i −0.0722137 1.04271i
\(489\) 24.4278 9.36501i 1.10466 0.423501i
\(490\) −1.04711 5.23048i −0.0473035 0.236289i
\(491\) −11.2758 + 6.51010i −0.508871 + 0.293797i −0.732369 0.680908i \(-0.761586\pi\)
0.223499 + 0.974704i \(0.428252\pi\)
\(492\) −11.3417 11.9030i −0.511322 0.536627i
\(493\) 7.24469 + 4.18272i 0.326284 + 0.188380i
\(494\) −2.93473 + 8.68054i −0.132040 + 0.390556i
\(495\) 21.2131 + 23.6000i 0.953460 + 1.06074i
\(496\) −32.3998 + 8.85283i −1.45479 + 0.397504i
\(497\) −0.728226 0.420442i −0.0326654 0.0188594i
\(498\) −22.7622 + 14.3875i −1.02000 + 0.644721i
\(499\) 10.0816 + 17.4619i 0.451316 + 0.781703i 0.998468 0.0553306i \(-0.0176213\pi\)
−0.547152 + 0.837033i \(0.684288\pi\)
\(500\) −4.08446 + 31.6265i −0.182663 + 1.41438i
\(501\) 2.54446 + 2.06226i 0.113678 + 0.0921351i
\(502\) 2.14180 + 2.43620i 0.0955933 + 0.108733i
\(503\) 10.8372 0.483205 0.241602 0.970375i \(-0.422327\pi\)
0.241602 + 0.970375i \(0.422327\pi\)
\(504\) 6.09483 + 5.90364i 0.271485 + 0.262969i
\(505\) 43.0826 1.91715
\(506\) 13.8068 + 15.7046i 0.613787 + 0.698153i
\(507\) −3.26823 + 20.5780i −0.145147 + 0.913902i
\(508\) −24.5773 3.17408i −1.09044 0.140827i
\(509\) −6.11814 10.5969i −0.271182 0.469700i 0.697983 0.716114i \(-0.254081\pi\)
−0.969165 + 0.246414i \(0.920748\pi\)
\(510\) 0.567482 + 14.1527i 0.0251285 + 0.626694i
\(511\) −12.0523 6.95837i −0.533160 0.307820i
\(512\) −22.1423 + 4.66016i −0.978562 + 0.205952i
\(513\) −15.5554 + 30.4330i −0.686789 + 1.34365i
\(514\) −7.44853 + 22.0318i −0.328541 + 0.971781i
\(515\) 28.4119 + 16.4036i 1.25198 + 0.722829i
\(516\) −32.6668 9.60398i −1.43807 0.422792i
\(517\) −19.7940 + 11.4281i −0.870539 + 0.502606i
\(518\) −1.76490 8.81596i −0.0775451 0.387351i
\(519\) −4.11443 + 25.9060i −0.180603 + 1.13715i
\(520\) −0.726088 10.4841i −0.0318411 0.459760i
\(521\) 42.1821i 1.84803i −0.382352 0.924017i \(-0.624886\pi\)
0.382352 0.924017i \(-0.375114\pi\)
\(522\) −18.5552 13.8448i −0.812137 0.605972i
\(523\) 2.13407 0.0933164 0.0466582 0.998911i \(-0.485143\pi\)
0.0466582 + 0.998911i \(0.485143\pi\)
\(524\) −4.91371 11.7806i −0.214656 0.514637i
\(525\) −10.0631 + 12.4160i −0.439189 + 0.541881i
\(526\) −0.0382633 0.191132i −0.00166836 0.00833374i
\(527\) −6.43637 11.1481i −0.280373 0.485620i
\(528\) −17.7844 7.82242i −0.773969 0.340427i
\(529\) −2.40054 + 4.15785i −0.104371 + 0.180776i
\(530\) 0.0264537 + 0.00894348i 0.00114907 + 0.000388480i
\(531\) 7.44182 22.8373i 0.322947 0.991054i
\(532\) −7.98260 + 10.4564i −0.346090 + 0.453341i
\(533\) −2.33766 + 4.04894i −0.101255 + 0.175379i
\(534\) −0.727730 0.382129i −0.0314919 0.0165363i
\(535\) −16.0360 + 9.25840i −0.693298 + 0.400276i
\(536\) −8.28145 + 16.9507i −0.357704 + 0.732161i
\(537\) 8.15179 + 21.2632i 0.351776 + 0.917575i
\(538\) 16.8960 14.8542i 0.728437 0.640412i
\(539\) 2.80430i 0.120790i
\(540\) 3.02919 39.0815i 0.130355 1.68180i
\(541\) 30.2209i 1.29930i 0.760235 + 0.649649i \(0.225084\pi\)
−0.760235 + 0.649649i \(0.774916\pi\)
\(542\) −2.37848 2.70540i −0.102164 0.116207i
\(543\) −8.11184 21.1590i −0.348112 0.908021i
\(544\) −3.88345 7.75408i −0.166501 0.332453i
\(545\) −14.6727 + 8.47131i −0.628511 + 0.362871i
\(546\) 1.12177 2.13631i 0.0480073 0.0914256i
\(547\) 6.85264 11.8691i 0.292998 0.507487i −0.681519 0.731800i \(-0.738680\pi\)
0.974517 + 0.224313i \(0.0720138\pi\)
\(548\) −6.49646 + 8.50968i −0.277515 + 0.363516i
\(549\) −23.9592 + 5.07133i −1.02255 + 0.216439i
\(550\) 11.7201 34.6664i 0.499745 1.47818i
\(551\) 17.9461 31.0836i 0.764531 1.32421i
\(552\) 2.27945 25.7299i 0.0970197 1.09514i
\(553\) −6.79080 11.7620i −0.288774 0.500172i
\(554\) −36.2575 + 7.25851i −1.54043 + 0.308385i
\(555\) −26.1522 + 32.2672i −1.11010 + 1.36966i
\(556\) −34.7631 + 14.4998i −1.47428 + 0.614928i
\(557\) 21.1048 0.894238 0.447119 0.894474i \(-0.352450\pi\)
0.447119 + 0.894474i \(0.352450\pi\)
\(558\) 14.0751 + 32.7265i 0.595847 + 1.38542i
\(559\) 9.68244i 0.409523i
\(560\) 3.83310 14.5926i 0.161978 0.616648i
\(561\) 1.16799 7.35410i 0.0493125 0.310490i
\(562\) 27.1032 5.42588i 1.14328 0.228877i
\(563\) −14.4082 + 8.31857i −0.607233 + 0.350586i −0.771882 0.635766i \(-0.780684\pi\)
0.164649 + 0.986352i \(0.447351\pi\)
\(564\) 27.0874 + 7.96365i 1.14058 + 0.335330i
\(565\) −27.5946 15.9318i −1.16091 0.670255i
\(566\) −22.9392 7.75531i −0.964207 0.325980i
\(567\) 5.30247 7.27212i 0.222683 0.305400i
\(568\) −1.32865 1.97265i −0.0557491 0.0827706i
\(569\) 31.2042 + 18.0157i 1.30815 + 0.755258i 0.981787 0.189987i \(-0.0608447\pi\)
0.326359 + 0.945246i \(0.394178\pi\)
\(570\) 60.7228 2.43480i 2.54340 0.101983i
\(571\) −14.8055 25.6438i −0.619590 1.07316i −0.989561 0.144118i \(-0.953965\pi\)
0.369970 0.929044i \(-0.379368\pi\)
\(572\) −0.707643 + 5.47936i −0.0295880 + 0.229104i
\(573\) −1.13711 + 7.15969i −0.0475035 + 0.299100i
\(574\) −5.04097 + 4.43181i −0.210406 + 0.184980i
\(575\) 48.6520 2.02893
\(576\) 8.15912 + 22.5705i 0.339963 + 0.940439i
\(577\) −11.1412 −0.463815 −0.231908 0.972738i \(-0.574497\pi\)
−0.231908 + 0.972738i \(0.574497\pi\)
\(578\) −15.5597 + 13.6795i −0.647199 + 0.568990i
\(579\) 11.3575 + 9.20513i 0.472001 + 0.382552i
\(580\) −5.27251 + 40.8257i −0.218929 + 1.69519i
\(581\) 5.49666 + 9.52050i 0.228040 + 0.394977i
\(582\) 13.2591 + 20.9770i 0.549609 + 0.869524i
\(583\) −0.0127136 0.00734018i −0.000526542 0.000303999i
\(584\) −21.9894 32.6477i −0.909929 1.35097i
\(585\) −10.9051 + 2.30824i −0.450872 + 0.0954341i
\(586\) −10.8077 3.65388i −0.446462 0.150940i
\(587\) −6.87113 3.96705i −0.283602 0.163738i 0.351451 0.936206i \(-0.385688\pi\)
−0.635053 + 0.772469i \(0.719022\pi\)
\(588\) 2.50791 2.38964i 0.103424 0.0985473i
\(589\) −47.8314 + 27.6155i −1.97086 + 1.13788i
\(590\) −41.8774 + 8.38357i −1.72406 + 0.345146i
\(591\) −20.7094 + 7.93947i −0.851872 + 0.326586i
\(592\) 6.46067 24.5957i 0.265532 1.01088i
\(593\) 4.02471i 0.165275i 0.996580 + 0.0826375i \(0.0263344\pi\)
−0.996580 + 0.0826375i \(0.973666\pi\)
\(594\) −5.59459 + 19.8334i −0.229549 + 0.813773i
\(595\) 5.78247 0.237058
\(596\) −6.47664 + 2.70143i −0.265294 + 0.110655i
\(597\) −6.25629 16.3190i −0.256053 0.667891i
\(598\) −7.20245 + 1.44188i −0.294530 + 0.0589629i
\(599\) −9.09149 15.7469i −0.371468 0.643402i 0.618323 0.785924i \(-0.287812\pi\)
−0.989792 + 0.142522i \(0.954479\pi\)
\(600\) −40.9895 + 19.0591i −1.67339 + 0.778086i
\(601\) 8.31549 14.4028i 0.339196 0.587504i −0.645086 0.764110i \(-0.723178\pi\)
0.984282 + 0.176606i \(0.0565118\pi\)
\(602\) −4.45197 + 13.1684i −0.181449 + 0.536702i
\(603\) 19.0253 + 6.19964i 0.774772 + 0.252469i
\(604\) −10.0428 + 13.1550i −0.408635 + 0.535269i
\(605\) 5.91414 10.2436i 0.240444 0.416461i
\(606\) 14.9486 + 23.6498i 0.607243 + 0.960707i
\(607\) −4.12950 + 2.38417i −0.167611 + 0.0967704i −0.581459 0.813576i \(-0.697518\pi\)
0.413848 + 0.910346i \(0.364185\pi\)
\(608\) −33.2692 + 16.6621i −1.34924 + 0.675736i
\(609\) −5.95109 + 7.34258i −0.241150 + 0.297536i
\(610\) 28.7518 + 32.7038i 1.16413 + 1.32414i
\(611\) 8.02870i 0.324807i
\(612\) −7.57211 + 5.22215i −0.306085 + 0.211093i
\(613\) 12.7687i 0.515722i 0.966182 + 0.257861i \(0.0830176\pi\)
−0.966182 + 0.257861i \(0.916982\pi\)
\(614\) −7.59683 + 6.67881i −0.306583 + 0.269535i
\(615\) 30.6235 + 4.86366i 1.23486 + 0.196122i
\(616\) −3.48181 + 7.12670i −0.140286 + 0.287143i
\(617\) 12.6927 7.32813i 0.510989 0.295019i −0.222251 0.974989i \(-0.571341\pi\)
0.733240 + 0.679970i \(0.238007\pi\)
\(618\) 0.853587 + 21.2881i 0.0343363 + 0.856332i
\(619\) −0.0928058 + 0.160744i −0.00373018 + 0.00646086i −0.867884 0.496766i \(-0.834521\pi\)
0.864154 + 0.503227i \(0.167854\pi\)
\(620\) 38.4376 50.3492i 1.54369 2.02207i
\(621\) −27.3619 + 1.39889i −1.09799 + 0.0561356i
\(622\) 1.16841 + 0.395017i 0.0468490 + 0.0158387i
\(623\) −0.167781 + 0.290606i −0.00672201 + 0.0116429i
\(624\) 5.50324 4.03631i 0.220306 0.161582i
\(625\) −7.00262 12.1289i −0.280105 0.485156i
\(626\) −6.80278 33.9811i −0.271894 1.35816i
\(627\) −31.5530 5.01130i −1.26011 0.200132i
\(628\) 5.32688 + 12.7712i 0.212566 + 0.509624i
\(629\) 9.74634 0.388612
\(630\) −15.8926 1.87490i −0.633176 0.0746978i
\(631\) 3.98492i 0.158637i 0.996849 + 0.0793185i \(0.0252744\pi\)
−0.996849 + 0.0793185i \(0.974726\pi\)
\(632\) −2.65408 38.3228i −0.105573 1.52440i
\(633\) 2.87993 + 2.33416i 0.114467 + 0.0927744i
\(634\) 0.618857 + 3.09130i 0.0245780 + 0.122771i
\(635\) 40.4749 23.3682i 1.60620 0.927338i
\(636\) 0.00426930 + 0.0176247i 0.000169289 + 0.000698863i
\(637\) −0.853096 0.492535i −0.0338009 0.0195150i
\(638\) 6.93098 20.5010i 0.274400 0.811640i
\(639\) −1.87613 + 1.68638i −0.0742186 + 0.0667123i
\(640\) 27.8593 32.3255i 1.10124 1.27778i
\(641\) 17.6085 + 10.1663i 0.695496 + 0.401545i 0.805668 0.592368i \(-0.201807\pi\)
−0.110172 + 0.993913i \(0.535140\pi\)
\(642\) −10.6464 5.59040i −0.420180 0.220635i
\(643\) 17.8106 + 30.8489i 0.702383 + 1.21656i 0.967628 + 0.252382i \(0.0812141\pi\)
−0.265244 + 0.964181i \(0.585453\pi\)
\(644\) −10.4585 1.35068i −0.412122 0.0532243i
\(645\) 59.9598 22.9871i 2.36092 0.905117i
\(646\) −9.41579 10.7100i −0.370459 0.421380i
\(647\) −31.2351 −1.22798 −0.613989 0.789314i \(-0.710436\pi\)
−0.613989 + 0.789314i \(0.710436\pi\)
\(648\) 22.5045 11.8974i 0.884059 0.467375i
\(649\) 22.4524 0.881332
\(650\) 8.48740 + 9.65401i 0.332903 + 0.378662i
\(651\) 13.5800 5.20624i 0.532243 0.204049i
\(652\) 3.86922 29.9598i 0.151530 1.17332i
\(653\) 12.7104 + 22.0151i 0.497398 + 0.861519i 0.999995 0.00300167i \(-0.000955464\pi\)
−0.502597 + 0.864521i \(0.667622\pi\)
\(654\) −9.74132 5.11514i −0.380916 0.200018i
\(655\) 20.8476 + 12.0364i 0.814583 + 0.470300i
\(656\) −18.3134 + 5.00390i −0.715017 + 0.195369i
\(657\) −31.0503 + 27.9099i −1.21139 + 1.08887i
\(658\) 3.69159 10.9192i 0.143913 0.425676i
\(659\) −41.6059 24.0211i −1.62073 0.935731i −0.986724 0.162406i \(-0.948075\pi\)
−0.634010 0.773325i \(-0.718592\pi\)
\(660\) 35.6117 8.62640i 1.38618 0.335782i
\(661\) −16.3590 + 9.44488i −0.636292 + 0.367363i −0.783185 0.621789i \(-0.786406\pi\)
0.146893 + 0.989152i \(0.453073\pi\)
\(662\) 0.307887 + 1.53795i 0.0119664 + 0.0597742i
\(663\) 2.03205 + 1.64696i 0.0789183 + 0.0639625i
\(664\) 2.14828 + 31.0195i 0.0833695 + 1.20379i
\(665\) 24.8099i 0.962087i
\(666\) −26.7869 3.16014i −1.03797 0.122453i
\(667\) 28.7717 1.11405
\(668\) 3.49047 1.45588i 0.135050 0.0563299i
\(669\) −39.0618 6.20385i −1.51022 0.239855i
\(670\) −6.98420 34.8873i −0.269823 1.34781i
\(671\) −11.4462 19.8254i −0.441876 0.765352i
\(672\) 9.34044 2.95910i 0.360315 0.114150i
\(673\) 18.1140 31.3744i 0.698244 1.20939i −0.270830 0.962627i \(-0.587298\pi\)
0.969075 0.246768i \(-0.0793684\pi\)
\(674\) −36.9296 12.4852i −1.42248 0.480912i
\(675\) 26.0618 + 40.2442i 1.00312 + 1.54900i
\(676\) 19.1235 + 14.5993i 0.735520 + 0.561511i
\(677\) 7.60017 13.1639i 0.292098 0.505929i −0.682208 0.731159i \(-0.738980\pi\)
0.974306 + 0.225230i \(0.0723133\pi\)
\(678\) −0.829035 20.6757i −0.0318389 0.794047i
\(679\) 8.77381 5.06556i 0.336708 0.194398i
\(680\) 14.6953 + 7.17951i 0.563538 + 0.275322i
\(681\) −34.2451 5.43885i −1.31227 0.208417i
\(682\) −25.0099 + 21.9877i −0.957680 + 0.841952i
\(683\) 13.4656i 0.515247i 0.966245 + 0.257623i \(0.0829394\pi\)
−0.966245 + 0.257623i \(0.917061\pi\)
\(684\) 22.4058 + 32.4884i 0.856708 + 1.24223i
\(685\) 20.1910i 0.771458i
\(686\) −0.933765 1.06211i −0.0356513 0.0405516i
\(687\) 29.1593 35.9774i 1.11250 1.37262i
\(688\) −27.6638 + 27.9378i −1.05467 + 1.06512i
\(689\) 0.00446591 0.00257839i 0.000170138 9.82290e-5i
\(690\) 26.0284 + 41.1790i 0.990885 + 1.56766i
\(691\) 2.62563 4.54773i 0.0998838 0.173004i −0.811753 0.584001i \(-0.801486\pi\)
0.911636 + 0.410998i \(0.134820\pi\)
\(692\) 24.0749 + 18.3793i 0.915191 + 0.698675i
\(693\) 7.99893 + 2.60655i 0.303854 + 0.0990146i
\(694\) −6.64757 + 19.6626i −0.252338 + 0.746384i
\(695\) 35.5179 61.5189i 1.34727 2.33354i
\(696\) −24.2403 + 11.2712i −0.918826 + 0.427232i
\(697\) −3.63804 6.30127i −0.137801 0.238678i
\(698\) 24.7827 4.96134i 0.938041 0.187789i
\(699\) 13.7368 + 35.8313i 0.519574 + 1.35526i
\(700\) 7.10418 + 17.0322i 0.268513 + 0.643756i
\(701\) 36.4901 1.37821 0.689105 0.724661i \(-0.258004\pi\)
0.689105 + 0.724661i \(0.258004\pi\)
\(702\) −5.05089 5.18537i −0.190634 0.195709i
\(703\) 41.8170i 1.57716i
\(704\) −17.6970 + 13.7884i −0.666980 + 0.519669i
\(705\) −49.7189 + 19.0610i −1.87252 + 0.717878i
\(706\) −34.8690 + 6.98053i −1.31231 + 0.262716i
\(707\) 9.89174 5.71100i 0.372017 0.214784i
\(708\) −19.1325 20.0793i −0.719042 0.754627i
\(709\) 28.3816 + 16.3861i 1.06589 + 0.615393i 0.927056 0.374922i \(-0.122330\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(710\) 4.24922 + 1.43658i 0.159470 + 0.0539140i
\(711\) −39.8617 + 8.43735i −1.49493 + 0.316425i
\(712\) −0.787206 + 0.530212i −0.0295018 + 0.0198705i
\(713\) −38.3423 22.1370i −1.43593 0.829036i
\(714\) 2.00637 + 3.17424i 0.0750865 + 0.118793i
\(715\) −5.20981 9.02365i −0.194836 0.337465i
\(716\) 26.0786 + 3.36797i 0.974602 + 0.125867i
\(717\) 21.2679 + 17.2374i 0.794265 + 0.643744i
\(718\) 23.3570 20.5345i 0.871676 0.766341i
\(719\) −32.5845 −1.21520 −0.607599 0.794244i \(-0.707867\pi\)
−0.607599 + 0.794244i \(0.707867\pi\)
\(720\) −38.0607 24.4970i −1.41844 0.912948i
\(721\) 8.69780 0.323923
\(722\) −25.7715 + 22.6572i −0.959117 + 0.843215i
\(723\) −2.66741 + 16.7950i −0.0992020 + 0.624613i
\(724\) −25.9508 3.35146i −0.964453 0.124556i
\(725\) −25.1753 43.6050i −0.934989 1.61945i
\(726\) 7.67518 0.307752i 0.284853 0.0114217i
\(727\) 25.2051 + 14.5522i 0.934807 + 0.539711i 0.888329 0.459208i \(-0.151867\pi\)
0.0464785 + 0.998919i \(0.485200\pi\)
\(728\) −1.55648 2.31090i −0.0576870 0.0856478i
\(729\) −15.8143 21.8840i −0.585714 0.810518i
\(730\) 70.3253 + 23.7757i 2.60286 + 0.879976i
\(731\) −13.0497 7.53427i −0.482662 0.278665i
\(732\) −7.97630 + 27.1304i −0.294812 + 1.00277i
\(733\) −29.1201 + 16.8125i −1.07557 + 0.620983i −0.929699 0.368320i \(-0.879933\pi\)
−0.145875 + 0.989303i \(0.546600\pi\)
\(734\) 29.7265 5.95105i 1.09723 0.219657i
\(735\) −1.02475 + 6.45225i −0.0377987 + 0.237995i
\(736\) −24.9016 16.4178i −0.917886 0.605168i
\(737\) 18.7047i 0.688995i
\(738\) 7.95570 + 18.4980i 0.292853 + 0.680922i
\(739\) −30.6587 −1.12780 −0.563899 0.825844i \(-0.690699\pi\)
−0.563899 + 0.825844i \(0.690699\pi\)
\(740\) 18.4625 + 44.2637i 0.678696 + 1.62717i
\(741\) 7.06632 8.71858i 0.259588 0.320285i
\(742\) 0.00725929 0.00145326i 0.000266497 5.33509e-5i
\(743\) 12.9076 + 22.3566i 0.473534 + 0.820185i 0.999541 0.0302953i \(-0.00964477\pi\)
−0.526007 + 0.850480i \(0.676311\pi\)
\(744\) 40.9756 + 3.63008i 1.50224 + 0.133085i
\(745\) 6.61727 11.4615i 0.242438 0.419915i
\(746\) −4.52485 + 13.3839i −0.165666 + 0.490020i
\(747\) 32.2651 6.82942i 1.18052 0.249875i
\(748\) −6.83430 5.21744i −0.249887 0.190769i
\(749\) −2.45457 + 4.25145i −0.0896882 + 0.155345i
\(750\) 18.1572 34.5788i 0.663008 1.26264i
\(751\) 1.76786 1.02067i 0.0645101 0.0372449i −0.467398 0.884047i \(-0.654808\pi\)
0.531908 + 0.846802i \(0.321475\pi\)
\(752\) 22.9389 23.1661i 0.836496 0.844780i
\(753\) −1.42216 3.70958i −0.0518264 0.135185i
\(754\) 5.01926 + 5.70917i 0.182791 + 0.207916i
\(755\) 31.2129i 1.13595i
\(756\) −4.48511 9.37463i −0.163122 0.340952i
\(757\) 35.5941i 1.29369i 0.762622 + 0.646845i \(0.223912\pi\)
−0.762622 + 0.646845i \(0.776088\pi\)
\(758\) 37.0506 32.5734i 1.34574 1.18312i
\(759\) −9.16775 23.9133i −0.332768 0.867996i
\(760\) 30.8039 63.0505i 1.11738 2.28708i
\(761\) −42.4648 + 24.5171i −1.53935 + 0.888743i −0.540472 + 0.841362i \(0.681754\pi\)
−0.998877 + 0.0473814i \(0.984912\pi\)
\(762\) 26.8715 + 14.1102i 0.973452 + 0.511157i
\(763\) −2.24590 + 3.89002i −0.0813071 + 0.140828i
\(764\) 6.65363 + 5.07951i 0.240720 + 0.183770i
\(765\) 5.37471 16.4938i 0.194323 0.596335i
\(766\) −4.26932 1.44338i −0.154257 0.0521513i
\(767\) −3.94344 + 6.83023i −0.142389 + 0.246625i
\(768\) 27.4113 + 4.07698i 0.989119 + 0.147115i
\(769\) −0.499248 0.864723i −0.0180034 0.0311827i 0.856883 0.515510i \(-0.172398\pi\)
−0.874887 + 0.484328i \(0.839064\pi\)
\(770\) −2.93641 14.6679i −0.105821 0.528593i
\(771\) 17.9348 22.1283i 0.645906 0.796933i
\(772\) 15.5801 6.49849i 0.560739 0.233886i
\(773\) 34.0335 1.22410 0.612051 0.790818i \(-0.290345\pi\)
0.612051 + 0.790818i \(0.290345\pi\)
\(774\) 33.4231 + 24.9385i 1.20137 + 0.896395i
\(775\) 77.4796i 2.78315i
\(776\) 28.5867 1.97979i 1.02620 0.0710704i
\(777\) −1.72722 + 10.8752i −0.0619637 + 0.390147i
\(778\) −2.00523 10.0165i −0.0718909 0.359107i
\(779\) −27.0358 + 15.6091i −0.968659 + 0.559255i
\(780\) −3.63045 + 12.3485i −0.129991 + 0.442149i
\(781\) −2.04216 1.17904i −0.0730744 0.0421895i
\(782\) 3.66117 10.8293i 0.130923 0.387254i
\(783\) 15.4124 + 23.7995i 0.550793 + 0.850527i
\(784\) −1.05430 3.85856i −0.0376536 0.137806i
\(785\) −22.6006 13.0485i −0.806650 0.465719i
\(786\) 0.626331 + 15.6204i 0.0223405 + 0.557162i
\(787\) 0.323547 + 0.560399i 0.0115332 + 0.0199761i 0.871734 0.489979i \(-0.162995\pi\)
−0.860201 + 0.509955i \(0.829662\pi\)
\(788\) −3.28025 + 25.3993i −0.116854 + 0.904814i
\(789\) −0.0374465 + 0.235777i −0.00133313 + 0.00839389i
\(790\) 47.8353 + 54.4103i 1.70190 + 1.93583i
\(791\) −8.44762 −0.300363
\(792\) 17.0917 + 16.5556i 0.607329 + 0.588277i
\(793\) 8.04145 0.285560
\(794\) 4.92790 + 5.60525i 0.174885 + 0.198923i
\(795\) −0.0265696 0.0215344i −0.000942326 0.000763746i
\(796\) −20.0146 2.58483i −0.709400 0.0916168i
\(797\) 2.67150 + 4.62717i 0.0946293 + 0.163903i 0.909454 0.415805i \(-0.136500\pi\)
−0.814825 + 0.579708i \(0.803167\pi\)
\(798\) 13.6192 8.60840i 0.482113 0.304734i
\(799\) 10.8209 + 6.24744i 0.382815 + 0.221019i
\(800\) −3.09298 + 52.1052i −0.109353 + 1.84220i
\(801\) 0.672967 + 0.748689i 0.0237781 + 0.0264536i
\(802\) 7.00914 20.7321i 0.247501 0.732077i
\(803\) −33.7981 19.5134i −1.19271 0.688612i
\(804\) 16.7277 15.9389i 0.589941 0.562122i
\(805\) 17.2235 9.94399i 0.607048 0.350479i
\(806\) −2.29623 11.4701i −0.0808814 0.404017i
\(807\) −25.7274 + 9.86325i −0.905648 + 0.347203i
\(808\) 32.2291 2.23205i 1.13381 0.0785233i
\(809\) 14.2977i 0.502682i −0.967899 0.251341i \(-0.919129\pi\)
0.967899 0.251341i \(-0.0808715\pi\)
\(810\) −20.1198 + 43.5890i −0.706938 + 1.53156i
\(811\) −22.3167 −0.783645 −0.391822 0.920041i \(-0.628155\pi\)
−0.391822 + 0.920041i \(0.628155\pi\)
\(812\) 4.20126 + 10.0725i 0.147435 + 0.353474i
\(813\) 1.57931 + 4.11950i 0.0553890 + 0.144477i
\(814\) −4.94930 24.7226i −0.173473 0.866527i
\(815\) 28.4860 + 49.3391i 0.997820 + 1.72827i
\(816\) 1.15775 + 10.5579i 0.0405295 + 0.369602i
\(817\) −32.3261 + 55.9904i −1.13095 + 1.95886i
\(818\) 32.5146 + 10.9926i 1.13685 + 0.384346i
\(819\) −2.19783 + 1.97555i −0.0767986 + 0.0690313i
\(820\) 21.7261 28.4589i 0.758709 0.993830i
\(821\) −19.5730 + 33.9015i −0.683103 + 1.18317i 0.290925 + 0.956746i \(0.406037\pi\)
−0.974029 + 0.226424i \(0.927296\pi\)
\(822\) 11.0837 7.00576i 0.386587 0.244354i
\(823\) 11.4224 6.59472i 0.398160 0.229877i −0.287530 0.957772i \(-0.592834\pi\)
0.685690 + 0.727894i \(0.259501\pi\)
\(824\) 22.1041 + 10.7992i 0.770033 + 0.376207i
\(825\) −28.2199 + 34.8183i −0.982491 + 1.21222i
\(826\) −8.50370 + 7.47610i −0.295882 + 0.260127i
\(827\) 18.9006i 0.657237i 0.944463 + 0.328619i \(0.106583\pi\)
−0.944463 + 0.328619i \(0.893417\pi\)
\(828\) −13.5736 + 28.5761i −0.471717 + 0.993089i
\(829\) 22.6130i 0.785381i 0.919671 + 0.392691i \(0.128456\pi\)
−0.919671 + 0.392691i \(0.871544\pi\)
\(830\) −38.7192 44.0412i −1.34396 1.52869i
\(831\) 44.7267 + 7.10356i 1.55155 + 0.246420i
\(832\) −1.08634 7.80533i −0.0376620 0.270601i
\(833\) 1.32765 0.766521i 0.0460004 0.0265584i
\(834\) 46.0940 1.84823i 1.59611 0.0639990i
\(835\) −3.56626 + 6.17694i −0.123415 + 0.213762i
\(836\) −22.3856 + 29.3228i −0.774223 + 1.01415i
\(837\) −2.22777 43.5745i −0.0770031 1.50615i
\(838\) 15.0423 44.4931i 0.519626 1.53699i
\(839\) 17.0984 29.6154i 0.590304 1.02244i −0.403888 0.914809i \(-0.632341\pi\)
0.994191 0.107627i \(-0.0343253\pi\)
\(840\) −10.6154 + 15.1250i −0.366264 + 0.521864i
\(841\) −0.388146 0.672288i −0.0133843 0.0231823i
\(842\) −14.8446 + 2.97180i −0.511580 + 0.102415i
\(843\) −33.4341 5.31005i −1.15153 0.182888i
\(844\) 3.95066 1.64783i 0.135987 0.0567207i
\(845\) −45.3745 −1.56093
\(846\) −27.7145 20.6790i −0.952845 0.710960i
\(847\) 3.13590i 0.107751i
\(848\) 0.0202527 + 0.00531988i 0.000695481 + 0.000182686i
\(849\) 23.0397 + 18.6735i 0.790722 + 0.640872i
\(850\) −19.6158 + 3.92695i −0.672817 + 0.134693i
\(851\) 29.0301 16.7606i 0.995140 0.574544i
\(852\) 0.685774 + 2.83103i 0.0234942 + 0.0969895i
\(853\) 25.7709 + 14.8788i 0.882379 + 0.509442i 0.871442 0.490498i \(-0.163185\pi\)
0.0109369 + 0.999940i \(0.496519\pi\)
\(854\) 10.9366 + 3.69745i 0.374242 + 0.126524i
\(855\) −70.7672 23.0604i −2.42019 0.788648i
\(856\) −11.5165 + 7.75680i −0.393626 + 0.265122i
\(857\) 5.16613 + 2.98266i 0.176471 + 0.101886i 0.585634 0.810576i \(-0.300846\pi\)
−0.409162 + 0.912462i \(0.634179\pi\)
\(858\) 3.14578 5.99085i 0.107395 0.204524i
\(859\) 27.4126 + 47.4800i 0.935305 + 1.62000i 0.774089 + 0.633077i \(0.218208\pi\)
0.161217 + 0.986919i \(0.448458\pi\)
\(860\) 9.49728 73.5386i 0.323855 2.50764i
\(861\) 7.67586 2.94273i 0.261593 0.100288i
\(862\) −18.9991 + 16.7032i −0.647112 + 0.568913i
\(863\) −49.3401 −1.67956 −0.839778 0.542929i \(-0.817315\pi\)
−0.839778 + 0.542929i \(0.817315\pi\)
\(864\) 0.241306 29.3929i 0.00820939 0.999966i
\(865\) −57.1227 −1.94223
\(866\) −24.2241 + 21.2969i −0.823170 + 0.723697i
\(867\) 23.6927 9.08319i 0.804646 0.308481i
\(868\) 2.15100 16.6554i 0.0730095 0.565322i
\(869\) −19.0435 32.9842i −0.646005 1.11891i
\(870\) 23.4386 44.6367i 0.794643 1.51332i
\(871\) −5.69014 3.28521i −0.192803 0.111315i
\(872\) −10.5375 + 7.09737i −0.356843 + 0.240347i
\(873\) −6.29379 29.7346i −0.213013 1.00636i
\(874\) −46.4633 15.7084i −1.57165 0.531344i
\(875\) −13.8084 7.97228i −0.466809 0.269512i
\(876\) 11.3497 + 46.8540i 0.383469 + 1.58305i
\(877\) 16.0741 9.28039i 0.542784 0.313376i −0.203423 0.979091i \(-0.565207\pi\)
0.746206 + 0.665715i \(0.231873\pi\)
\(878\) −20.1085 + 4.02558i −0.678628 + 0.135857i
\(879\) 10.8551 + 8.79792i 0.366132 + 0.296746i
\(880\) 10.7492 40.9219i 0.362354 1.37948i
\(881\) 6.96036i 0.234501i −0.993102 0.117250i \(-0.962592\pi\)
0.993102 0.117250i \(-0.0374080\pi\)
\(882\) −3.89747 + 1.67623i −0.131234 + 0.0564418i
\(883\) −4.48837 −0.151046 −0.0755228 0.997144i \(-0.524063\pi\)
−0.0755228 + 0.997144i \(0.524063\pi\)
\(884\) 2.78754 1.16269i 0.0937553 0.0391056i
\(885\) 51.6593 + 8.20460i 1.73651 + 0.275795i
\(886\) −52.4964 + 10.5094i −1.76365 + 0.353071i
\(887\) −17.7337 30.7156i −0.595439 1.03133i −0.993485 0.113965i \(-0.963645\pi\)
0.398046 0.917366i \(-0.369688\pi\)
\(888\) −17.8921 + 25.4932i −0.600421 + 0.855496i
\(889\) 6.19534 10.7306i 0.207785 0.359894i
\(890\) 0.573282 1.69569i 0.0192165 0.0568398i
\(891\) 14.8697 20.3932i 0.498155 0.683199i
\(892\) −27.7128 + 36.3008i −0.927892 + 1.21544i
\(893\) 26.8049 46.4274i 0.896990 1.55363i
\(894\) 8.58768 0.344340i 0.287215 0.0115165i
\(895\) −42.9473 + 24.7956i −1.43557 + 0.828827i
\(896\) 2.11143 11.1149i 0.0705380 0.371324i
\(897\) 8.88483 + 1.41110i 0.296656 + 0.0471153i
\(898\) 6.90608 + 7.85534i 0.230459 + 0.262136i
\(899\) 45.8197i 1.52817i
\(900\) 55.1855 4.43267i 1.83952 0.147756i
\(901\) 0.00802538i 0.000267364i
\(902\) −14.1364 + 12.4281i −0.470690 + 0.413811i
\(903\) 10.7196 13.2261i 0.356726 0.440136i
\(904\) −21.4683 10.4885i −0.714025 0.348844i
\(905\) 42.7369 24.6741i 1.42062 0.820196i
\(906\) 17.1341 10.8301i 0.569241 0.359806i
\(907\) −9.48856 + 16.4347i −0.315062 + 0.545704i −0.979451 0.201683i \(-0.935359\pi\)
0.664388 + 0.747388i \(0.268692\pi\)
\(908\) −24.2955 + 31.8246i −0.806275 + 1.05614i
\(909\) −7.09572 33.5232i −0.235350 1.11190i
\(910\) 4.97784 + 1.68291i 0.165014 + 0.0557881i
\(911\) −8.19874 + 14.2006i −0.271636 + 0.470488i −0.969281 0.245956i \(-0.920898\pi\)
0.697645 + 0.716444i \(0.254231\pi\)
\(912\) 45.2992 4.96739i 1.50001 0.164487i
\(913\) 15.4143 + 26.6983i 0.510139 + 0.883586i
\(914\) −9.86013 49.2530i −0.326144 1.62915i
\(915\) −19.0912 49.7978i −0.631137 1.64627i
\(916\) −20.5855 49.3534i −0.680162 1.63068i
\(917\) 6.38213 0.210757
\(918\) 10.9190 2.77253i 0.360381 0.0915071i
\(919\) 3.11937i 0.102899i −0.998676 0.0514493i \(-0.983616\pi\)
0.998676 0.0514493i \(-0.0163841\pi\)
\(920\) 56.1173 3.88645i 1.85013 0.128132i
\(921\) 11.5677 4.43475i 0.381167 0.146130i
\(922\) −7.81707 39.0476i −0.257441 1.28596i
\(923\) 0.717354 0.414165i 0.0236120 0.0136324i
\(924\) 7.03293 6.70128i 0.231366 0.220456i
\(925\) −50.8029 29.3311i −1.67039 0.964399i
\(926\) −15.3446 + 45.3874i −0.504255 + 1.49152i
\(927\) 8.08446 24.8094i 0.265528 0.814848i
\(928\) −1.82912 + 30.8139i −0.0600437 + 1.01152i
\(929\) 9.56436 + 5.52199i 0.313797 + 0.181171i 0.648624 0.761109i \(-0.275345\pi\)
−0.334828 + 0.942279i \(0.608678\pi\)
\(930\) −65.5786 + 41.4509i −2.15041 + 1.35923i
\(931\) −3.28878 5.69634i −0.107786 0.186690i
\(932\) 43.9458 + 5.67546i 1.43949 + 0.185906i
\(933\) −1.17353 0.951135i −0.0384197 0.0311387i
\(934\) −0.212645 0.241874i −0.00695797 0.00791435i
\(935\) 16.2158 0.530313
\(936\) −8.03829 + 2.29172i −0.262740 + 0.0749074i
\(937\) −12.0261 −0.392875 −0.196438 0.980516i \(-0.562937\pi\)
−0.196438 + 0.980516i \(0.562937\pi\)
\(938\) −6.22820 7.08428i −0.203358 0.231310i
\(939\) −6.65756 + 41.9185i −0.217261 + 1.36796i
\(940\) −7.87517 + 60.9784i −0.256860 + 1.98890i
\(941\) −11.9730 20.7378i −0.390308 0.676034i 0.602182 0.798359i \(-0.294298\pi\)
−0.992490 + 0.122325i \(0.960965\pi\)
\(942\) −0.678997 16.9339i −0.0221229 0.551735i
\(943\) −21.6723 12.5125i −0.705747 0.407463i
\(944\) −30.8932 + 8.44116i −1.00549 + 0.274737i
\(945\) 17.4518 + 8.92024i 0.567706 + 0.290175i
\(946\) −12.4847 + 36.9280i −0.405912 + 1.20063i
\(947\) 13.6235 + 7.86551i 0.442703 + 0.255595i 0.704744 0.709462i \(-0.251062\pi\)
−0.262040 + 0.965057i \(0.584395\pi\)
\(948\) −13.2704 + 45.1377i −0.431004 + 1.46601i
\(949\) 11.8723 6.85449i 0.385392 0.222506i
\(950\) 16.8487 + 84.1623i 0.546645 + 2.73059i
\(951\) 0.605646 3.81338i 0.0196394 0.123657i
\(952\) 4.32573 0.299582i 0.140198 0.00970952i
\(953\) 24.0024i 0.777515i 0.921340 + 0.388757i \(0.127096\pi\)
−0.921340 + 0.388757i \(0.872904\pi\)
\(954\) 0.00260214 0.0220570i 8.42473e−5 0.000714122i
\(955\) −15.7871 −0.510859
\(956\) 29.1751 12.1690i 0.943591 0.393574i
\(957\) −16.6886 + 20.5908i −0.539467 + 0.665606i
\(958\) −1.81674 9.07491i −0.0586961 0.293197i
\(959\) −2.67650 4.63584i −0.0864288 0.149699i
\(960\) −45.7565 + 25.2580i −1.47678 + 0.815197i
\(961\) 19.7537 34.2144i 0.637216 1.10369i
\(962\) 8.39014 + 2.83655i 0.270509 + 0.0914539i
\(963\) 9.84525 + 10.9530i 0.317259 + 0.352956i
\(964\) 15.6079 + 11.9154i 0.502697 + 0.383769i
\(965\) −15.9184 + 27.5714i −0.512430 + 0.887555i
\(966\) 11.4348 + 6.00437i 0.367908 + 0.193187i
\(967\) −42.2386 + 24.3865i −1.35830 + 0.784216i −0.989395 0.145251i \(-0.953601\pi\)
−0.368907 + 0.929466i \(0.620268\pi\)
\(968\) 3.89352 7.96940i 0.125143 0.256146i
\(969\) 6.25211 + 16.3081i 0.200847 + 0.523891i
\(970\) −40.5871 + 35.6825i −1.30317 + 1.14570i
\(971\) 16.9946i 0.545382i 0.962102 + 0.272691i \(0.0879137\pi\)
−0.962102 + 0.272691i \(0.912086\pi\)
\(972\) −30.9088 + 4.07968i −0.991401 + 0.130856i
\(973\) 18.8329i 0.603756i
\(974\) 12.5882 + 14.3185i 0.403351 + 0.458793i
\(975\) −5.63566 14.7001i −0.180485 0.470780i
\(976\) 23.2029 + 22.9753i 0.742706 + 0.735422i
\(977\) −17.8888 + 10.3281i −0.572315 + 0.330426i −0.758073 0.652169i \(-0.773859\pi\)
0.185759 + 0.982595i \(0.440526\pi\)
\(978\) −17.2004 + 32.7565i −0.550007 + 1.04744i
\(979\) −0.470509 + 0.814946i −0.0150375 + 0.0260458i
\(980\) 5.99619 + 4.57761i 0.191541 + 0.146226i
\(981\) 9.00827 + 10.0219i 0.287612 + 0.319974i
\(982\) 5.89729 17.4434i 0.188190 0.556642i
\(983\) −16.6473 + 28.8341i −0.530968 + 0.919663i 0.468379 + 0.883528i \(0.344838\pi\)
−0.999347 + 0.0361358i \(0.988495\pi\)
\(984\) 23.1607 + 2.05183i 0.738336 + 0.0654100i
\(985\) −24.1498 41.8287i −0.769478 1.33277i
\(986\) −11.6004 + 2.32231i −0.369431 + 0.0739575i
\(987\) −8.88872 + 10.9671i −0.282931 + 0.349086i
\(988\) −4.98857 11.9601i −0.158708 0.380500i
\(989\) −51.8261 −1.64797
\(990\) −44.5676 5.25778i −1.41645 0.167103i
\(991\) 15.8848i 0.504597i −0.967649 0.252298i \(-0.918814\pi\)
0.967649 0.252298i \(-0.0811865\pi\)
\(992\) 26.1458 39.6565i 0.830128 1.25909i
\(993\) 0.301315 1.89719i 0.00956194 0.0602056i
\(994\) 1.16605 0.233436i 0.0369849 0.00740413i
\(995\) 32.9610 19.0300i 1.04493 0.603292i
\(996\) 10.7415 36.5357i 0.340356 1.15768i
\(997\) 4.19703 + 2.42316i 0.132921 + 0.0767422i 0.564986 0.825100i \(-0.308881\pi\)
−0.432065 + 0.901843i \(0.642215\pi\)
\(998\) −27.0132 9.13264i −0.855087 0.289089i
\(999\) 29.4149 + 15.0350i 0.930645 + 0.475688i
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 504.2.br.a.155.16 144
8.3 odd 2 inner 504.2.br.a.155.41 yes 144
9.5 odd 6 inner 504.2.br.a.491.41 yes 144
72.59 even 6 inner 504.2.br.a.491.16 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.br.a.155.16 144 1.1 even 1 trivial
504.2.br.a.155.41 yes 144 8.3 odd 2 inner
504.2.br.a.491.16 yes 144 72.59 even 6 inner
504.2.br.a.491.41 yes 144 9.5 odd 6 inner