Properties

Label 273.2.cg.a.262.4
Level $273$
Weight $2$
Character 273.262
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(19,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cg (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 262.4
Character \(\chi\) \(=\) 273.262
Dual form 273.2.cg.a.124.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.273028 - 1.01896i) q^{2} -1.00000i q^{3} +(0.768324 - 0.443592i) q^{4} +(1.01943 - 3.80456i) q^{5} +(-1.01896 + 0.273028i) q^{6} +(1.44977 + 2.21318i) q^{7} +(-2.15363 - 2.15363i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.273028 - 1.01896i) q^{2} -1.00000i q^{3} +(0.768324 - 0.443592i) q^{4} +(1.01943 - 3.80456i) q^{5} +(-1.01896 + 0.273028i) q^{6} +(1.44977 + 2.21318i) q^{7} +(-2.15363 - 2.15363i) q^{8} -1.00000 q^{9} -4.15502 q^{10} +(0.669085 + 0.669085i) q^{11} +(-0.443592 - 0.768324i) q^{12} +(0.783899 + 3.51930i) q^{13} +(1.85931 - 2.08151i) q^{14} +(-3.80456 - 1.01943i) q^{15} +(-0.719268 + 1.24581i) q^{16} +(3.98087 + 6.89506i) q^{17} +(0.273028 + 1.01896i) q^{18} +(-1.23405 - 1.23405i) q^{19} +(-0.904422 - 3.37535i) q^{20} +(2.21318 - 1.44977i) q^{21} +(0.499089 - 0.864448i) q^{22} +(-6.00569 - 3.46739i) q^{23} +(-2.15363 + 2.15363i) q^{24} +(-9.10535 - 5.25697i) q^{25} +(3.37199 - 1.75963i) q^{26} +1.00000i q^{27} +(2.09564 + 1.05734i) q^{28} +(1.71573 + 2.97173i) q^{29} +4.15502i q^{30} +(-4.37613 + 1.17258i) q^{31} +(-4.41802 - 1.18381i) q^{32} +(0.669085 - 0.669085i) q^{33} +(5.93888 - 5.93888i) q^{34} +(9.89813 - 3.25954i) q^{35} +(-0.768324 + 0.443592i) q^{36} +(9.40483 - 2.52002i) q^{37} +(-0.920514 + 1.59438i) q^{38} +(3.51930 - 0.783899i) q^{39} +(-10.3891 + 5.99815i) q^{40} +(0.117207 - 0.437421i) q^{41} +(-2.08151 - 1.85931i) q^{42} +(0.0936549 + 0.0540717i) q^{43} +(0.810875 + 0.217273i) q^{44} +(-1.01943 + 3.80456i) q^{45} +(-1.89339 + 7.06623i) q^{46} +(4.45738 + 1.19435i) q^{47} +(1.24581 + 0.719268i) q^{48} +(-2.79636 + 6.41720i) q^{49} +(-2.87061 + 10.7132i) q^{50} +(6.89506 - 3.98087i) q^{51} +(2.16342 + 2.35623i) q^{52} +(0.747827 - 1.29527i) q^{53} +(1.01896 - 0.273028i) q^{54} +(3.22766 - 1.86349i) q^{55} +(1.64412 - 7.88864i) q^{56} +(-1.23405 + 1.23405i) q^{57} +(2.55962 - 2.55962i) q^{58} +(-4.68445 - 1.25519i) q^{59} +(-3.37535 + 0.904422i) q^{60} +6.61892i q^{61} +(2.38961 + 4.13893i) q^{62} +(-1.44977 - 2.21318i) q^{63} +7.70205i q^{64} +(14.1885 + 0.605291i) q^{65} +(-0.864448 - 0.499089i) q^{66} +(3.19896 - 3.19896i) q^{67} +(6.11719 + 3.53176i) q^{68} +(-3.46739 + 6.00569i) q^{69} +(-6.02380 - 9.19581i) q^{70} +(-2.68009 - 10.0022i) q^{71} +(2.15363 + 2.15363i) q^{72} +(1.05974 + 3.95501i) q^{73} +(-5.13557 - 8.89507i) q^{74} +(-5.25697 + 9.10535i) q^{75} +(-1.49557 - 0.400736i) q^{76} +(-0.510791 + 2.45082i) q^{77} +(-1.75963 - 3.37199i) q^{78} +(0.473848 + 0.820728i) q^{79} +(4.00652 + 4.00652i) q^{80} +1.00000 q^{81} -0.477714 q^{82} +(8.26062 + 8.26062i) q^{83} +(1.05734 - 2.09564i) q^{84} +(30.2909 - 8.11643i) q^{85} +(0.0295262 - 0.110193i) q^{86} +(2.97173 - 1.71573i) q^{87} -2.88192i q^{88} +(-1.38773 - 5.17908i) q^{89} +4.15502 q^{90} +(-6.65239 + 6.83708i) q^{91} -6.15242 q^{92} +(1.17258 + 4.37613i) q^{93} -4.86796i q^{94} +(-5.95306 + 3.43700i) q^{95} +(-1.18381 + 4.41802i) q^{96} +(11.5503 - 3.09490i) q^{97} +(7.30232 + 1.09729i) q^{98} +(-0.669085 - 0.669085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.273028 1.01896i −0.193060 0.720511i −0.992760 0.120111i \(-0.961675\pi\)
0.799700 0.600400i \(-0.204992\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 0.768324 0.443592i 0.384162 0.221796i
\(5\) 1.01943 3.80456i 0.455903 1.70145i −0.229517 0.973305i \(-0.573715\pi\)
0.685420 0.728148i \(-0.259619\pi\)
\(6\) −1.01896 + 0.273028i −0.415987 + 0.111463i
\(7\) 1.44977 + 2.21318i 0.547960 + 0.836504i
\(8\) −2.15363 2.15363i −0.761423 0.761423i
\(9\) −1.00000 −0.333333
\(10\) −4.15502 −1.31393
\(11\) 0.669085 + 0.669085i 0.201737 + 0.201737i 0.800744 0.599007i \(-0.204438\pi\)
−0.599007 + 0.800744i \(0.704438\pi\)
\(12\) −0.443592 0.768324i −0.128054 0.221796i
\(13\) 0.783899 + 3.51930i 0.217414 + 0.976079i
\(14\) 1.85931 2.08151i 0.496921 0.556307i
\(15\) −3.80456 1.01943i −0.982334 0.263216i
\(16\) −0.719268 + 1.24581i −0.179817 + 0.311452i
\(17\) 3.98087 + 6.89506i 0.965502 + 1.67230i 0.708260 + 0.705952i \(0.249481\pi\)
0.257242 + 0.966347i \(0.417186\pi\)
\(18\) 0.273028 + 1.01896i 0.0643534 + 0.240170i
\(19\) −1.23405 1.23405i −0.283111 0.283111i 0.551237 0.834348i \(-0.314156\pi\)
−0.834348 + 0.551237i \(0.814156\pi\)
\(20\) −0.904422 3.37535i −0.202235 0.754751i
\(21\) 2.21318 1.44977i 0.482956 0.316365i
\(22\) 0.499089 0.864448i 0.106406 0.184301i
\(23\) −6.00569 3.46739i −1.25227 0.723000i −0.280712 0.959792i \(-0.590571\pi\)
−0.971560 + 0.236792i \(0.923904\pi\)
\(24\) −2.15363 + 2.15363i −0.439608 + 0.439608i
\(25\) −9.10535 5.25697i −1.82107 1.05139i
\(26\) 3.37199 1.75963i 0.661302 0.345092i
\(27\) 1.00000i 0.192450i
\(28\) 2.09564 + 1.05734i 0.396039 + 0.199818i
\(29\) 1.71573 + 2.97173i 0.318603 + 0.551836i 0.980197 0.198026i \(-0.0634531\pi\)
−0.661594 + 0.749862i \(0.730120\pi\)
\(30\) 4.15502i 0.758599i
\(31\) −4.37613 + 1.17258i −0.785976 + 0.210602i −0.629418 0.777067i \(-0.716707\pi\)
−0.156558 + 0.987669i \(0.550040\pi\)
\(32\) −4.41802 1.18381i −0.781003 0.209269i
\(33\) 0.669085 0.669085i 0.116473 0.116473i
\(34\) 5.93888 5.93888i 1.01851 1.01851i
\(35\) 9.89813 3.25954i 1.67309 0.550964i
\(36\) −0.768324 + 0.443592i −0.128054 + 0.0739320i
\(37\) 9.40483 2.52002i 1.54614 0.414288i 0.617899 0.786257i \(-0.287984\pi\)
0.928245 + 0.371969i \(0.121317\pi\)
\(38\) −0.920514 + 1.59438i −0.149327 + 0.258642i
\(39\) 3.51930 0.783899i 0.563540 0.125524i
\(40\) −10.3891 + 5.99815i −1.64266 + 0.948391i
\(41\) 0.117207 0.437421i 0.0183046 0.0683137i −0.956169 0.292814i \(-0.905408\pi\)
0.974474 + 0.224500i \(0.0720750\pi\)
\(42\) −2.08151 1.85931i −0.321184 0.286898i
\(43\) 0.0936549 + 0.0540717i 0.0142822 + 0.00824585i 0.507124 0.861873i \(-0.330709\pi\)
−0.492842 + 0.870119i \(0.664042\pi\)
\(44\) 0.810875 + 0.217273i 0.122244 + 0.0327552i
\(45\) −1.01943 + 3.80456i −0.151968 + 0.567151i
\(46\) −1.89339 + 7.06623i −0.279165 + 1.04186i
\(47\) 4.45738 + 1.19435i 0.650175 + 0.174214i 0.568808 0.822470i \(-0.307405\pi\)
0.0813671 + 0.996684i \(0.474071\pi\)
\(48\) 1.24581 + 0.719268i 0.179817 + 0.103817i
\(49\) −2.79636 + 6.41720i −0.399479 + 0.916742i
\(50\) −2.87061 + 10.7132i −0.405965 + 1.51508i
\(51\) 6.89506 3.98087i 0.965502 0.557433i
\(52\) 2.16342 + 2.35623i 0.300013 + 0.326751i
\(53\) 0.747827 1.29527i 0.102722 0.177920i −0.810083 0.586315i \(-0.800578\pi\)
0.912805 + 0.408395i \(0.133911\pi\)
\(54\) 1.01896 0.273028i 0.138662 0.0371545i
\(55\) 3.22766 1.86349i 0.435218 0.251273i
\(56\) 1.64412 7.88864i 0.219704 1.05416i
\(57\) −1.23405 + 1.23405i −0.163454 + 0.163454i
\(58\) 2.55962 2.55962i 0.336094 0.336094i
\(59\) −4.68445 1.25519i −0.609863 0.163412i −0.0593479 0.998237i \(-0.518902\pi\)
−0.550515 + 0.834825i \(0.685569\pi\)
\(60\) −3.37535 + 0.904422i −0.435756 + 0.116760i
\(61\) 6.61892i 0.847465i 0.905787 + 0.423733i \(0.139280\pi\)
−0.905787 + 0.423733i \(0.860720\pi\)
\(62\) 2.38961 + 4.13893i 0.303481 + 0.525645i
\(63\) −1.44977 2.21318i −0.182653 0.278835i
\(64\) 7.70205i 0.962757i
\(65\) 14.1885 + 0.605291i 1.75987 + 0.0750771i
\(66\) −0.864448 0.499089i −0.106406 0.0614336i
\(67\) 3.19896 3.19896i 0.390815 0.390815i −0.484163 0.874978i \(-0.660876\pi\)
0.874978 + 0.484163i \(0.160876\pi\)
\(68\) 6.11719 + 3.53176i 0.741819 + 0.428289i
\(69\) −3.46739 + 6.00569i −0.417424 + 0.723000i
\(70\) −6.02380 9.19581i −0.719982 1.09911i
\(71\) −2.68009 10.0022i −0.318068 1.18705i −0.921099 0.389329i \(-0.872707\pi\)
0.603030 0.797718i \(-0.293960\pi\)
\(72\) 2.15363 + 2.15363i 0.253808 + 0.253808i
\(73\) 1.05974 + 3.95501i 0.124033 + 0.462899i 0.999803 0.0198296i \(-0.00631239\pi\)
−0.875770 + 0.482729i \(0.839646\pi\)
\(74\) −5.13557 8.89507i −0.596998 1.03403i
\(75\) −5.25697 + 9.10535i −0.607023 + 1.05139i
\(76\) −1.49557 0.400736i −0.171553 0.0459676i
\(77\) −0.510791 + 2.45082i −0.0582100 + 0.279297i
\(78\) −1.75963 3.37199i −0.199239 0.381803i
\(79\) 0.473848 + 0.820728i 0.0533120 + 0.0923391i 0.891450 0.453119i \(-0.149689\pi\)
−0.838138 + 0.545459i \(0.816356\pi\)
\(80\) 4.00652 + 4.00652i 0.447942 + 0.447942i
\(81\) 1.00000 0.111111
\(82\) −0.477714 −0.0527546
\(83\) 8.26062 + 8.26062i 0.906721 + 0.906721i 0.996006 0.0892850i \(-0.0284582\pi\)
−0.0892850 + 0.996006i \(0.528458\pi\)
\(84\) 1.05734 2.09564i 0.115365 0.228653i
\(85\) 30.2909 8.11643i 3.28551 0.880351i
\(86\) 0.0295262 0.110193i 0.00318389 0.0118824i
\(87\) 2.97173 1.71573i 0.318603 0.183945i
\(88\) 2.88192i 0.307214i
\(89\) −1.38773 5.17908i −0.147099 0.548982i −0.999653 0.0263421i \(-0.991614\pi\)
0.852554 0.522639i \(-0.175053\pi\)
\(90\) 4.15502 0.437977
\(91\) −6.65239 + 6.83708i −0.697360 + 0.716721i
\(92\) −6.15242 −0.641434
\(93\) 1.17258 + 4.37613i 0.121591 + 0.453783i
\(94\) 4.86796i 0.502092i
\(95\) −5.95306 + 3.43700i −0.610771 + 0.352629i
\(96\) −1.18381 + 4.41802i −0.120822 + 0.450913i
\(97\) 11.5503 3.09490i 1.17276 0.314240i 0.380708 0.924695i \(-0.375680\pi\)
0.792050 + 0.610456i \(0.209014\pi\)
\(98\) 7.30232 + 1.09729i 0.737646 + 0.110843i
\(99\) −0.669085 0.669085i −0.0672456 0.0672456i
\(100\) −9.32781 −0.932781
\(101\) −18.7168 −1.86239 −0.931194 0.364525i \(-0.881232\pi\)
−0.931194 + 0.364525i \(0.881232\pi\)
\(102\) −5.93888 5.93888i −0.588036 0.588036i
\(103\) −3.28825 5.69542i −0.324001 0.561186i 0.657309 0.753621i \(-0.271695\pi\)
−0.981310 + 0.192435i \(0.938361\pi\)
\(104\) 5.89105 9.26751i 0.577665 0.908754i
\(105\) −3.25954 9.89813i −0.318099 0.965959i
\(106\) −1.52400 0.408356i −0.148024 0.0396630i
\(107\) −2.59676 + 4.49772i −0.251038 + 0.434811i −0.963812 0.266583i \(-0.914105\pi\)
0.712774 + 0.701394i \(0.247439\pi\)
\(108\) 0.443592 + 0.768324i 0.0426847 + 0.0739320i
\(109\) −2.95407 11.0247i −0.282949 1.05598i −0.950325 0.311259i \(-0.899249\pi\)
0.667377 0.744720i \(-0.267417\pi\)
\(110\) −2.78006 2.78006i −0.265068 0.265068i
\(111\) −2.52002 9.40483i −0.239189 0.892667i
\(112\) −3.79997 + 0.214260i −0.359064 + 0.0202456i
\(113\) −1.34429 + 2.32838i −0.126460 + 0.219036i −0.922303 0.386468i \(-0.873695\pi\)
0.795842 + 0.605504i \(0.207028\pi\)
\(114\) 1.59438 + 0.920514i 0.149327 + 0.0862140i
\(115\) −19.3143 + 19.3143i −1.80107 + 1.80107i
\(116\) 2.63647 + 1.52217i 0.244790 + 0.141330i
\(117\) −0.783899 3.51930i −0.0724715 0.325360i
\(118\) 5.11595i 0.470961i
\(119\) −9.48871 + 18.8066i −0.869829 + 1.72400i
\(120\) 5.99815 + 10.3891i 0.547554 + 0.948391i
\(121\) 10.1046i 0.918605i
\(122\) 6.74438 1.80715i 0.610608 0.163612i
\(123\) −0.437421 0.117207i −0.0394409 0.0105682i
\(124\) −2.84214 + 2.84214i −0.255231 + 0.255231i
\(125\) −15.3571 + 15.3571i −1.37358 + 1.37358i
\(126\) −1.85931 + 2.08151i −0.165640 + 0.185436i
\(127\) −7.89995 + 4.56104i −0.701007 + 0.404727i −0.807722 0.589563i \(-0.799300\pi\)
0.106715 + 0.994290i \(0.465967\pi\)
\(128\) −0.987991 + 0.264731i −0.0873269 + 0.0233992i
\(129\) 0.0540717 0.0936549i 0.00476074 0.00824585i
\(130\) −3.25711 14.6228i −0.285668 1.28250i
\(131\) −6.79059 + 3.92055i −0.593297 + 0.342540i −0.766400 0.642364i \(-0.777954\pi\)
0.173103 + 0.984904i \(0.444621\pi\)
\(132\) 0.217273 0.810875i 0.0189112 0.0705776i
\(133\) 0.942096 4.52027i 0.0816901 0.391957i
\(134\) −4.13300 2.38619i −0.357037 0.206135i
\(135\) 3.80456 + 1.01943i 0.327445 + 0.0877386i
\(136\) 6.27610 23.4227i 0.538171 2.00848i
\(137\) 1.96981 7.35143i 0.168292 0.628075i −0.829305 0.558796i \(-0.811263\pi\)
0.997597 0.0692792i \(-0.0220699\pi\)
\(138\) 7.06623 + 1.89339i 0.601517 + 0.161176i
\(139\) −3.86004 2.22859i −0.327404 0.189027i 0.327284 0.944926i \(-0.393867\pi\)
−0.654688 + 0.755899i \(0.727200\pi\)
\(140\) 6.15906 6.89512i 0.520536 0.582744i
\(141\) 1.19435 4.45738i 0.100582 0.375379i
\(142\) −9.46010 + 5.46179i −0.793874 + 0.458343i
\(143\) −1.83022 + 2.87921i −0.153051 + 0.240772i
\(144\) 0.719268 1.24581i 0.0599390 0.103817i
\(145\) 13.0552 3.49813i 1.08417 0.290504i
\(146\) 3.74064 2.15966i 0.309578 0.178735i
\(147\) 6.41720 + 2.79636i 0.529281 + 0.230640i
\(148\) 6.10810 6.10810i 0.502082 0.502082i
\(149\) 0.532092 0.532092i 0.0435907 0.0435907i −0.684975 0.728566i \(-0.740187\pi\)
0.728566 + 0.684975i \(0.240187\pi\)
\(150\) 10.7132 + 2.87061i 0.874733 + 0.234384i
\(151\) 0.0631804 0.0169291i 0.00514154 0.00137767i −0.256247 0.966611i \(-0.582486\pi\)
0.261389 + 0.965234i \(0.415819\pi\)
\(152\) 5.31538i 0.431135i
\(153\) −3.98087 6.89506i −0.321834 0.557433i
\(154\) 2.63674 0.148672i 0.212475 0.0119803i
\(155\) 17.8446i 1.43331i
\(156\) 2.35623 2.16342i 0.188650 0.173213i
\(157\) 6.41355 + 3.70286i 0.511857 + 0.295521i 0.733597 0.679585i \(-0.237840\pi\)
−0.221740 + 0.975106i \(0.571174\pi\)
\(158\) 0.706912 0.706912i 0.0562389 0.0562389i
\(159\) −1.29527 0.747827i −0.102722 0.0593065i
\(160\) −9.00773 + 15.6018i −0.712124 + 1.23343i
\(161\) −1.03289 18.3186i −0.0814028 1.44371i
\(162\) −0.273028 1.01896i −0.0214511 0.0800567i
\(163\) −3.27600 3.27600i −0.256596 0.256596i 0.567072 0.823668i \(-0.308076\pi\)
−0.823668 + 0.567072i \(0.808076\pi\)
\(164\) −0.103984 0.388073i −0.00811978 0.0303034i
\(165\) −1.86349 3.22766i −0.145073 0.251273i
\(166\) 6.16183 10.6726i 0.478250 0.828354i
\(167\) −12.2105 3.27179i −0.944874 0.253178i −0.246688 0.969095i \(-0.579342\pi\)
−0.698186 + 0.715916i \(0.746009\pi\)
\(168\) −7.88864 1.64412i −0.608622 0.126846i
\(169\) −11.7710 + 5.51756i −0.905462 + 0.424427i
\(170\) −16.5406 28.6491i −1.26860 2.19729i
\(171\) 1.23405 + 1.23405i 0.0943703 + 0.0943703i
\(172\) 0.0959431 0.00731559
\(173\) 18.3187 1.39275 0.696374 0.717679i \(-0.254795\pi\)
0.696374 + 0.717679i \(0.254795\pi\)
\(174\) −2.55962 2.55962i −0.194044 0.194044i
\(175\) −1.56598 27.7732i −0.118377 2.09945i
\(176\) −1.31480 + 0.352301i −0.0991070 + 0.0265557i
\(177\) −1.25519 + 4.68445i −0.0943462 + 0.352105i
\(178\) −4.89837 + 2.82807i −0.367148 + 0.211973i
\(179\) 17.9406i 1.34095i 0.741934 + 0.670473i \(0.233909\pi\)
−0.741934 + 0.670473i \(0.766091\pi\)
\(180\) 0.904422 + 3.37535i 0.0674116 + 0.251584i
\(181\) 11.3348 0.842512 0.421256 0.906942i \(-0.361589\pi\)
0.421256 + 0.906942i \(0.361589\pi\)
\(182\) 8.78298 + 4.91178i 0.651037 + 0.364085i
\(183\) 6.61892 0.489284
\(184\) 5.46657 + 20.4015i 0.403001 + 1.50402i
\(185\) 38.3503i 2.81957i
\(186\) 4.13893 2.38961i 0.303481 0.175215i
\(187\) −1.94985 + 7.27693i −0.142587 + 0.532141i
\(188\) 3.95451 1.05961i 0.288413 0.0772799i
\(189\) −2.21318 + 1.44977i −0.160985 + 0.105455i
\(190\) 5.12751 + 5.12751i 0.371989 + 0.371989i
\(191\) −14.6688 −1.06139 −0.530697 0.847562i \(-0.678070\pi\)
−0.530697 + 0.847562i \(0.678070\pi\)
\(192\) 7.70205 0.555848
\(193\) 8.28684 + 8.28684i 0.596500 + 0.596500i 0.939379 0.342880i \(-0.111402\pi\)
−0.342880 + 0.939379i \(0.611402\pi\)
\(194\) −6.30714 10.9243i −0.452826 0.784318i
\(195\) 0.605291 14.1885i 0.0433458 1.01606i
\(196\) 0.698110 + 6.17093i 0.0498650 + 0.440781i
\(197\) −10.2849 2.75584i −0.732772 0.196346i −0.126909 0.991914i \(-0.540505\pi\)
−0.605863 + 0.795569i \(0.707172\pi\)
\(198\) −0.499089 + 0.864448i −0.0354687 + 0.0614336i
\(199\) 10.6276 + 18.4076i 0.753372 + 1.30488i 0.946179 + 0.323643i \(0.104908\pi\)
−0.192807 + 0.981237i \(0.561759\pi\)
\(200\) 8.28797 + 30.9311i 0.586048 + 2.18716i
\(201\) −3.19896 3.19896i −0.225637 0.225637i
\(202\) 5.11021 + 19.0716i 0.359553 + 1.34187i
\(203\) −4.08957 + 8.10553i −0.287032 + 0.568897i
\(204\) 3.53176 6.11719i 0.247273 0.428289i
\(205\) −1.54471 0.891841i −0.107887 0.0622888i
\(206\) −4.90559 + 4.90559i −0.341789 + 0.341789i
\(207\) 6.00569 + 3.46739i 0.417424 + 0.241000i
\(208\) −4.94821 1.55473i −0.343097 0.107801i
\(209\) 1.65137i 0.114228i
\(210\) −9.19581 + 6.02380i −0.634571 + 0.415682i
\(211\) −11.7558 20.3617i −0.809305 1.40176i −0.913346 0.407184i \(-0.866511\pi\)
0.104041 0.994573i \(-0.466823\pi\)
\(212\) 1.32692i 0.0911332i
\(213\) −10.0022 + 2.68009i −0.685342 + 0.183637i
\(214\) 5.29197 + 1.41798i 0.361752 + 0.0969310i
\(215\) 0.301194 0.301194i 0.0205412 0.0205412i
\(216\) 2.15363 2.15363i 0.146536 0.146536i
\(217\) −8.93950 7.98521i −0.606853 0.542071i
\(218\) −10.4272 + 6.02014i −0.706218 + 0.407735i
\(219\) 3.95501 1.05974i 0.267255 0.0716107i
\(220\) 1.65326 2.86353i 0.111463 0.193059i
\(221\) −21.1452 + 19.4149i −1.42238 + 1.30599i
\(222\) −8.89507 + 5.13557i −0.596998 + 0.344677i
\(223\) 1.56806 5.85209i 0.105005 0.391885i −0.893341 0.449380i \(-0.851645\pi\)
0.998346 + 0.0574955i \(0.0183115\pi\)
\(224\) −3.78512 11.4941i −0.252904 0.767984i
\(225\) 9.10535 + 5.25697i 0.607023 + 0.350465i
\(226\) 2.73955 + 0.734061i 0.182232 + 0.0488290i
\(227\) −5.40197 + 20.1604i −0.358541 + 1.33809i 0.517427 + 0.855727i \(0.326890\pi\)
−0.875969 + 0.482368i \(0.839777\pi\)
\(228\) −0.400736 + 1.49557i −0.0265394 + 0.0990464i
\(229\) 21.1882 + 5.67737i 1.40016 + 0.375171i 0.878402 0.477923i \(-0.158610\pi\)
0.521756 + 0.853094i \(0.325277\pi\)
\(230\) 24.9537 + 14.4070i 1.64540 + 0.949973i
\(231\) 2.45082 + 0.510791i 0.161252 + 0.0336076i
\(232\) 2.70496 10.0950i 0.177589 0.662772i
\(233\) −9.92317 + 5.72914i −0.650088 + 0.375329i −0.788490 0.615048i \(-0.789137\pi\)
0.138402 + 0.990376i \(0.455803\pi\)
\(234\) −3.37199 + 1.75963i −0.220434 + 0.115031i
\(235\) 9.08797 15.7408i 0.592833 1.02682i
\(236\) −4.15597 + 1.11359i −0.270531 + 0.0724884i
\(237\) 0.820728 0.473848i 0.0533120 0.0307797i
\(238\) 21.7538 + 4.53384i 1.41009 + 0.293885i
\(239\) 4.89413 4.89413i 0.316575 0.316575i −0.530875 0.847450i \(-0.678137\pi\)
0.847450 + 0.530875i \(0.178137\pi\)
\(240\) 4.00652 4.00652i 0.258619 0.258619i
\(241\) −8.01914 2.14872i −0.516559 0.138411i −0.00888426 0.999961i \(-0.502828\pi\)
−0.507674 + 0.861549i \(0.669495\pi\)
\(242\) −10.2962 + 2.75886i −0.661864 + 0.177346i
\(243\) 1.00000i 0.0641500i
\(244\) 2.93610 + 5.08547i 0.187964 + 0.325564i
\(245\) 21.5639 + 17.1808i 1.37767 + 1.09764i
\(246\) 0.477714i 0.0304579i
\(247\) 3.37563 5.31038i 0.214786 0.337891i
\(248\) 11.9499 + 6.89926i 0.758817 + 0.438103i
\(249\) 8.26062 8.26062i 0.523496 0.523496i
\(250\) 19.8411 + 11.4553i 1.25486 + 0.724495i
\(251\) 7.81291 13.5324i 0.493146 0.854155i −0.506822 0.862050i \(-0.669180\pi\)
0.999969 + 0.00789592i \(0.00251338\pi\)
\(252\) −2.09564 1.05734i −0.132013 0.0666060i
\(253\) −1.69834 6.33829i −0.106774 0.398485i
\(254\) 6.80441 + 6.80441i 0.426946 + 0.426946i
\(255\) −8.11643 30.2909i −0.508271 1.89689i
\(256\) 8.24155 + 14.2748i 0.515097 + 0.892174i
\(257\) 0.281936 0.488328i 0.0175867 0.0304611i −0.857098 0.515153i \(-0.827735\pi\)
0.874685 + 0.484692i \(0.161068\pi\)
\(258\) −0.110193 0.0295262i −0.00686033 0.00183822i
\(259\) 19.2121 + 17.1612i 1.19378 + 1.06634i
\(260\) 11.1699 5.82887i 0.692728 0.361491i
\(261\) −1.71573 2.97173i −0.106201 0.183945i
\(262\) 5.84889 + 5.84889i 0.361346 + 0.361346i
\(263\) 1.80864 0.111526 0.0557628 0.998444i \(-0.482241\pi\)
0.0557628 + 0.998444i \(0.482241\pi\)
\(264\) −2.88192 −0.177370
\(265\) −4.16560 4.16560i −0.255891 0.255891i
\(266\) −4.86318 + 0.274208i −0.298180 + 0.0168128i
\(267\) −5.17908 + 1.38773i −0.316955 + 0.0849277i
\(268\) 1.03880 3.87687i 0.0634550 0.236817i
\(269\) 3.98883 2.30295i 0.243203 0.140413i −0.373445 0.927652i \(-0.621824\pi\)
0.616648 + 0.787239i \(0.288490\pi\)
\(270\) 4.15502i 0.252866i
\(271\) −1.05005 3.91882i −0.0637857 0.238052i 0.926671 0.375872i \(-0.122657\pi\)
−0.990457 + 0.137821i \(0.955990\pi\)
\(272\) −11.4532 −0.694455
\(273\) 6.83708 + 6.65239i 0.413799 + 0.402621i
\(274\) −8.02860 −0.485026
\(275\) −2.57489 9.60962i −0.155272 0.579482i
\(276\) 6.15242i 0.370332i
\(277\) −10.5733 + 6.10452i −0.635291 + 0.366785i −0.782798 0.622276i \(-0.786208\pi\)
0.147507 + 0.989061i \(0.452875\pi\)
\(278\) −1.21694 + 4.54168i −0.0729871 + 0.272392i
\(279\) 4.37613 1.17258i 0.261992 0.0702005i
\(280\) −28.3368 14.2971i −1.69345 0.854413i
\(281\) 0.757979 + 0.757979i 0.0452172 + 0.0452172i 0.729354 0.684137i \(-0.239821\pi\)
−0.684137 + 0.729354i \(0.739821\pi\)
\(282\) −4.86796 −0.289883
\(283\) 20.6773 1.22914 0.614568 0.788864i \(-0.289331\pi\)
0.614568 + 0.788864i \(0.289331\pi\)
\(284\) −6.49609 6.49609i −0.385472 0.385472i
\(285\) 3.43700 + 5.95306i 0.203590 + 0.352629i
\(286\) 3.43349 + 1.07881i 0.203026 + 0.0637912i
\(287\) 1.13802 0.374759i 0.0671749 0.0221213i
\(288\) 4.41802 + 1.18381i 0.260334 + 0.0697564i
\(289\) −23.1946 + 40.1742i −1.36439 + 2.36319i
\(290\) −7.12888 12.3476i −0.418622 0.725075i
\(291\) −3.09490 11.5503i −0.181426 0.677092i
\(292\) 2.56864 + 2.56864i 0.150318 + 0.150318i
\(293\) 0.652210 + 2.43408i 0.0381025 + 0.142201i 0.982357 0.187017i \(-0.0598818\pi\)
−0.944254 + 0.329217i \(0.893215\pi\)
\(294\) 1.09729 7.30232i 0.0639951 0.425880i
\(295\) −9.55094 + 16.5427i −0.556077 + 0.963154i
\(296\) −25.6817 14.8273i −1.49272 0.861822i
\(297\) −0.669085 + 0.669085i −0.0388243 + 0.0388243i
\(298\) −0.687454 0.396902i −0.0398232 0.0229919i
\(299\) 7.49493 23.8539i 0.433443 1.37951i
\(300\) 9.32781i 0.538541i
\(301\) 0.0161072 + 0.285667i 0.000928403 + 0.0164655i
\(302\) −0.0345001 0.0597559i −0.00198526 0.00343856i
\(303\) 18.7168i 1.07525i
\(304\) 2.42501 0.649779i 0.139084 0.0372674i
\(305\) 25.1821 + 6.74752i 1.44192 + 0.386362i
\(306\) −5.93888 + 5.93888i −0.339503 + 0.339503i
\(307\) −14.0560 + 14.0560i −0.802217 + 0.802217i −0.983442 0.181225i \(-0.941994\pi\)
0.181225 + 0.983442i \(0.441994\pi\)
\(308\) 0.694714 + 2.10961i 0.0395850 + 0.120206i
\(309\) −5.69542 + 3.28825i −0.324001 + 0.187062i
\(310\) 18.1829 4.87209i 1.03272 0.276716i
\(311\) −5.07374 + 8.78798i −0.287706 + 0.498321i −0.973262 0.229699i \(-0.926226\pi\)
0.685556 + 0.728020i \(0.259559\pi\)
\(312\) −9.26751 5.89105i −0.524669 0.333515i
\(313\) −23.2110 + 13.4009i −1.31196 + 0.757461i −0.982421 0.186680i \(-0.940227\pi\)
−0.329540 + 0.944141i \(0.606894\pi\)
\(314\) 2.02197 7.54611i 0.114107 0.425852i
\(315\) −9.89813 + 3.25954i −0.557697 + 0.183655i
\(316\) 0.728137 + 0.420390i 0.0409609 + 0.0236488i
\(317\) 12.3700 + 3.31452i 0.694767 + 0.186162i 0.588885 0.808217i \(-0.299567\pi\)
0.105881 + 0.994379i \(0.466234\pi\)
\(318\) −0.408356 + 1.52400i −0.0228995 + 0.0854620i
\(319\) −0.840371 + 3.13631i −0.0470517 + 0.175599i
\(320\) 29.3030 + 7.85171i 1.63809 + 0.438924i
\(321\) 4.49772 + 2.59676i 0.251038 + 0.144937i
\(322\) −18.3838 + 6.05396i −1.02449 + 0.337374i
\(323\) 3.59627 13.4215i 0.200102 0.746791i
\(324\) 0.768324 0.443592i 0.0426847 0.0246440i
\(325\) 11.3632 36.1654i 0.630318 2.00610i
\(326\) −2.44366 + 4.23254i −0.135342 + 0.234419i
\(327\) −11.0247 + 2.95407i −0.609670 + 0.163361i
\(328\) −1.19446 + 0.689624i −0.0659532 + 0.0380781i
\(329\) 3.81884 + 11.5965i 0.210539 + 0.639337i
\(330\) −2.78006 + 2.78006i −0.153037 + 0.153037i
\(331\) −0.534490 + 0.534490i −0.0293782 + 0.0293782i −0.721643 0.692265i \(-0.756613\pi\)
0.692265 + 0.721643i \(0.256613\pi\)
\(332\) 10.0112 + 2.68249i 0.549435 + 0.147221i
\(333\) −9.40483 + 2.52002i −0.515381 + 0.138096i
\(334\) 13.3352i 0.729671i
\(335\) −8.90953 15.4318i −0.486779 0.843127i
\(336\) 0.214260 + 3.79997i 0.0116888 + 0.207305i
\(337\) 12.9685i 0.706440i −0.935540 0.353220i \(-0.885087\pi\)
0.935540 0.353220i \(-0.114913\pi\)
\(338\) 8.83597 + 10.4877i 0.480613 + 0.570455i
\(339\) 2.32838 + 1.34429i 0.126460 + 0.0730120i
\(340\) 19.6729 19.6729i 1.06691 1.06691i
\(341\) −3.71256 2.14345i −0.201046 0.116074i
\(342\) 0.920514 1.59438i 0.0497757 0.0862140i
\(343\) −18.2565 + 3.11459i −0.985758 + 0.168172i
\(344\) −0.0852476 0.318148i −0.00459624 0.0171534i
\(345\) 19.3143 + 19.3143i 1.03985 + 1.03985i
\(346\) −5.00154 18.6660i −0.268884 1.00349i
\(347\) 7.19316 + 12.4589i 0.386149 + 0.668830i 0.991928 0.126803i \(-0.0404718\pi\)
−0.605779 + 0.795633i \(0.707138\pi\)
\(348\) 1.52217 2.63647i 0.0815967 0.141330i
\(349\) −32.9693 8.83410i −1.76481 0.472879i −0.777125 0.629347i \(-0.783323\pi\)
−0.987683 + 0.156468i \(0.949989\pi\)
\(350\) −27.8721 + 9.17853i −1.48983 + 0.490613i
\(351\) −3.51930 + 0.783899i −0.187847 + 0.0418414i
\(352\) −2.16397 3.74810i −0.115340 0.199774i
\(353\) −3.92198 3.92198i −0.208746 0.208746i 0.594988 0.803734i \(-0.297157\pi\)
−0.803734 + 0.594988i \(0.797157\pi\)
\(354\) 5.11595 0.271910
\(355\) −40.7863 −2.16471
\(356\) −3.36363 3.36363i −0.178272 0.178272i
\(357\) 18.8066 + 9.48871i 0.995352 + 0.502196i
\(358\) 18.2807 4.89831i 0.966166 0.258883i
\(359\) 1.72057 6.42126i 0.0908083 0.338901i −0.905542 0.424256i \(-0.860536\pi\)
0.996351 + 0.0853548i \(0.0272024\pi\)
\(360\) 10.3891 5.99815i 0.547554 0.316130i
\(361\) 15.9542i 0.839696i
\(362\) −3.09473 11.5497i −0.162656 0.607039i
\(363\) −10.1046 −0.530357
\(364\) −2.07832 + 8.20404i −0.108934 + 0.430009i
\(365\) 16.1274 0.844148
\(366\) −1.80715 6.74438i −0.0944614 0.352535i
\(367\) 7.15046i 0.373251i −0.982431 0.186626i \(-0.940245\pi\)
0.982431 0.186626i \(-0.0597551\pi\)
\(368\) 8.63940 4.98796i 0.450360 0.260015i
\(369\) −0.117207 + 0.437421i −0.00610153 + 0.0227712i
\(370\) −39.0772 + 10.4707i −2.03153 + 0.544346i
\(371\) 3.95085 0.222767i 0.205118 0.0115655i
\(372\) 2.84214 + 2.84214i 0.147358 + 0.147358i
\(373\) 15.3396 0.794254 0.397127 0.917764i \(-0.370007\pi\)
0.397127 + 0.917764i \(0.370007\pi\)
\(374\) 7.94723 0.410941
\(375\) 15.3571 + 15.3571i 0.793037 + 0.793037i
\(376\) −7.02735 12.1717i −0.362408 0.627709i
\(377\) −9.11346 + 8.36770i −0.469367 + 0.430958i
\(378\) 2.08151 + 1.85931i 0.107061 + 0.0956325i
\(379\) −22.8646 6.12656i −1.17448 0.314700i −0.381743 0.924268i \(-0.624676\pi\)
−0.792734 + 0.609568i \(0.791343\pi\)
\(380\) −3.04925 + 5.28146i −0.156423 + 0.270933i
\(381\) 4.56104 + 7.89995i 0.233669 + 0.404727i
\(382\) 4.00499 + 14.9468i 0.204913 + 0.764746i
\(383\) −0.437956 0.437956i −0.0223785 0.0223785i 0.695829 0.718207i \(-0.255037\pi\)
−0.718207 + 0.695829i \(0.755037\pi\)
\(384\) 0.264731 + 0.987991i 0.0135095 + 0.0504182i
\(385\) 8.80361 + 4.44178i 0.448673 + 0.226374i
\(386\) 6.18138 10.7065i 0.314624 0.544945i
\(387\) −0.0936549 0.0540717i −0.00476074 0.00274862i
\(388\) 7.50152 7.50152i 0.380832 0.380832i
\(389\) 8.18610 + 4.72624i 0.415052 + 0.239630i 0.692958 0.720978i \(-0.256307\pi\)
−0.277906 + 0.960608i \(0.589640\pi\)
\(390\) −14.6228 + 3.25711i −0.740453 + 0.164930i
\(391\) 55.2128i 2.79223i
\(392\) 19.8426 7.79795i 1.00220 0.393856i
\(393\) 3.92055 + 6.79059i 0.197766 + 0.342540i
\(394\) 11.2323i 0.565876i
\(395\) 3.60557 0.966109i 0.181416 0.0486102i
\(396\) −0.810875 0.217273i −0.0407480 0.0109184i
\(397\) 6.32238 6.32238i 0.317311 0.317311i −0.530422 0.847734i \(-0.677967\pi\)
0.847734 + 0.530422i \(0.177967\pi\)
\(398\) 15.8549 15.8549i 0.794733 0.794733i
\(399\) −4.52027 0.942096i −0.226297 0.0471638i
\(400\) 13.0984 7.56234i 0.654918 0.378117i
\(401\) 6.40587 1.71645i 0.319894 0.0857153i −0.0952991 0.995449i \(-0.530381\pi\)
0.415193 + 0.909733i \(0.363714\pi\)
\(402\) −2.38619 + 4.13300i −0.119012 + 0.206135i
\(403\) −7.55711 14.4817i −0.376446 0.721387i
\(404\) −14.3805 + 8.30261i −0.715459 + 0.413070i
\(405\) 1.01943 3.80456i 0.0506559 0.189050i
\(406\) 9.37575 + 1.95405i 0.465310 + 0.0969781i
\(407\) 7.97874 + 4.60653i 0.395491 + 0.228337i
\(408\) −23.4227 6.27610i −1.15960 0.310713i
\(409\) −4.23667 + 15.8115i −0.209490 + 0.781826i 0.778544 + 0.627590i \(0.215958\pi\)
−0.988034 + 0.154236i \(0.950708\pi\)
\(410\) −0.486996 + 1.81749i −0.0240510 + 0.0897596i
\(411\) −7.35143 1.96981i −0.362619 0.0971636i
\(412\) −5.05288 2.91728i −0.248938 0.143724i
\(413\) −4.01338 12.1873i −0.197486 0.599697i
\(414\) 1.89339 7.06623i 0.0930550 0.347286i
\(415\) 39.8492 23.0069i 1.95612 1.12937i
\(416\) 0.702890 16.4763i 0.0344620 0.807820i
\(417\) −2.22859 + 3.86004i −0.109135 + 0.189027i
\(418\) −1.68268 + 0.450872i −0.0823024 + 0.0220529i
\(419\) −19.8994 + 11.4889i −0.972150 + 0.561271i −0.899891 0.436115i \(-0.856354\pi\)
−0.0722588 + 0.997386i \(0.523021\pi\)
\(420\) −6.89512 6.15906i −0.336447 0.300532i
\(421\) −3.33707 + 3.33707i −0.162639 + 0.162639i −0.783735 0.621096i \(-0.786688\pi\)
0.621096 + 0.783735i \(0.286688\pi\)
\(422\) −17.5380 + 17.5380i −0.853736 + 0.853736i
\(423\) −4.45738 1.19435i −0.216725 0.0580713i
\(424\) −4.40008 + 1.17900i −0.213687 + 0.0572572i
\(425\) 83.7093i 4.06050i
\(426\) 5.46179 + 9.46010i 0.264625 + 0.458343i
\(427\) −14.6489 + 9.59588i −0.708909 + 0.464377i
\(428\) 4.60761i 0.222717i
\(429\) 2.87921 + 1.83022i 0.139010 + 0.0883638i
\(430\) −0.389138 0.224669i −0.0187659 0.0108345i
\(431\) 19.9189 19.9189i 0.959459 0.959459i −0.0397503 0.999210i \(-0.512656\pi\)
0.999210 + 0.0397503i \(0.0126562\pi\)
\(432\) −1.24581 0.719268i −0.0599390 0.0346058i
\(433\) 9.88975 17.1295i 0.475271 0.823193i −0.524328 0.851516i \(-0.675683\pi\)
0.999599 + 0.0283231i \(0.00901674\pi\)
\(434\) −5.69584 + 11.2891i −0.273409 + 0.541896i
\(435\) −3.49813 13.0552i −0.167722 0.625948i
\(436\) −7.16017 7.16017i −0.342910 0.342910i
\(437\) 3.13240 + 11.6903i 0.149843 + 0.559221i
\(438\) −2.15966 3.74064i −0.103193 0.178735i
\(439\) 10.9538 18.9726i 0.522797 0.905511i −0.476851 0.878984i \(-0.658222\pi\)
0.999648 0.0265271i \(-0.00844483\pi\)
\(440\) −10.9645 2.93792i −0.522710 0.140060i
\(441\) 2.79636 6.41720i 0.133160 0.305581i
\(442\) 25.5562 + 16.2452i 1.21558 + 0.772707i
\(443\) 9.87688 + 17.1073i 0.469265 + 0.812791i 0.999383 0.0351334i \(-0.0111856\pi\)
−0.530118 + 0.847924i \(0.677852\pi\)
\(444\) −6.10810 6.10810i −0.289877 0.289877i
\(445\) −21.1188 −1.00113
\(446\) −6.39114 −0.302629
\(447\) −0.532092 0.532092i −0.0251671 0.0251671i
\(448\) −17.0461 + 11.1662i −0.805350 + 0.527552i
\(449\) −31.7673 + 8.51202i −1.49919 + 0.401707i −0.912829 0.408342i \(-0.866107\pi\)
−0.586362 + 0.810049i \(0.699440\pi\)
\(450\) 2.87061 10.7132i 0.135322 0.505027i
\(451\) 0.371093 0.214251i 0.0174741 0.0100887i
\(452\) 2.38527i 0.112194i
\(453\) −0.0169291 0.0631804i −0.000795400 0.00296847i
\(454\) 22.0175 1.03333
\(455\) 19.2305 + 32.2794i 0.901538 + 1.51328i
\(456\) 5.31538 0.248916
\(457\) 4.06045 + 15.1538i 0.189940 + 0.708866i 0.993519 + 0.113668i \(0.0362599\pi\)
−0.803579 + 0.595198i \(0.797073\pi\)
\(458\) 23.1400i 1.08126i
\(459\) −6.89506 + 3.98087i −0.321834 + 0.185811i
\(460\) −6.27196 + 23.4073i −0.292432 + 1.09137i
\(461\) 1.60974 0.431329i 0.0749731 0.0200890i −0.221138 0.975243i \(-0.570977\pi\)
0.296111 + 0.955154i \(0.404310\pi\)
\(462\) −0.148672 2.63674i −0.00691683 0.122672i
\(463\) −18.8646 18.8646i −0.876713 0.876713i 0.116480 0.993193i \(-0.462839\pi\)
−0.993193 + 0.116480i \(0.962839\pi\)
\(464\) −4.93627 −0.229161
\(465\) 17.8446 0.827525
\(466\) 8.54705 + 8.54705i 0.395934 + 0.395934i
\(467\) 11.4518 + 19.8351i 0.529926 + 0.917859i 0.999391 + 0.0349075i \(0.0111136\pi\)
−0.469465 + 0.882951i \(0.655553\pi\)
\(468\) −2.16342 2.35623i −0.100004 0.108917i
\(469\) 11.7176 + 2.44214i 0.541069 + 0.112767i
\(470\) −18.5205 4.96255i −0.854286 0.228905i
\(471\) 3.70286 6.41355i 0.170619 0.295521i
\(472\) 7.38535 + 12.7918i 0.339938 + 0.588790i
\(473\) 0.0264845 + 0.0988416i 0.00121776 + 0.00454474i
\(474\) −0.706912 0.706912i −0.0324695 0.0324695i
\(475\) 4.74909 + 17.7239i 0.217903 + 0.813226i
\(476\) 1.05206 + 18.6587i 0.0482212 + 0.855220i
\(477\) −0.747827 + 1.29527i −0.0342406 + 0.0593065i
\(478\) −6.32315 3.65067i −0.289214 0.166978i
\(479\) −0.542389 + 0.542389i −0.0247824 + 0.0247824i −0.719389 0.694607i \(-0.755578\pi\)
0.694607 + 0.719389i \(0.255578\pi\)
\(480\) 15.6018 + 9.00773i 0.712124 + 0.411145i
\(481\) 16.2411 + 31.1230i 0.740532 + 1.41909i
\(482\) 8.75782i 0.398908i
\(483\) −18.3186 + 1.03289i −0.833524 + 0.0469979i
\(484\) −4.48234 7.76365i −0.203743 0.352893i
\(485\) 47.0990i 2.13866i
\(486\) −1.01896 + 0.273028i −0.0462208 + 0.0123848i
\(487\) 7.13339 + 1.91138i 0.323245 + 0.0866131i 0.416792 0.909002i \(-0.363154\pi\)
−0.0935479 + 0.995615i \(0.529821\pi\)
\(488\) 14.2547 14.2547i 0.645280 0.645280i
\(489\) −3.27600 + 3.27600i −0.148146 + 0.148146i
\(490\) 11.6189 26.6636i 0.524889 1.20454i
\(491\) 6.17910 3.56750i 0.278859 0.160999i −0.354048 0.935227i \(-0.615195\pi\)
0.632907 + 0.774228i \(0.281862\pi\)
\(492\) −0.388073 + 0.103984i −0.0174957 + 0.00468796i
\(493\) −13.6602 + 23.6601i −0.615223 + 1.06560i
\(494\) −6.33269 1.98974i −0.284921 0.0895226i
\(495\) −3.22766 + 1.86349i −0.145073 + 0.0837577i
\(496\) 1.68680 6.29522i 0.0757395 0.282664i
\(497\) 18.2513 20.4324i 0.818682 0.916520i
\(498\) −10.6726 6.16183i −0.478250 0.276118i
\(499\) 20.6974 + 5.54585i 0.926542 + 0.248266i 0.690380 0.723447i \(-0.257444\pi\)
0.236163 + 0.971714i \(0.424110\pi\)
\(500\) −4.98694 + 18.6115i −0.223023 + 0.832332i
\(501\) −3.27179 + 12.2105i −0.146173 + 0.545523i
\(502\) −15.9220 4.26629i −0.710634 0.190414i
\(503\) 20.5890 + 11.8871i 0.918020 + 0.530019i 0.883003 0.469367i \(-0.155518\pi\)
0.0350174 + 0.999387i \(0.488851\pi\)
\(504\) −1.64412 + 7.88864i −0.0732348 + 0.351388i
\(505\) −19.0804 + 71.2091i −0.849068 + 3.16876i
\(506\) −5.99475 + 3.46107i −0.266499 + 0.153863i
\(507\) 5.51756 + 11.7710i 0.245043 + 0.522769i
\(508\) −4.04648 + 7.00871i −0.179534 + 0.310961i
\(509\) 29.9347 8.02098i 1.32683 0.355524i 0.475299 0.879824i \(-0.342340\pi\)
0.851533 + 0.524301i \(0.175673\pi\)
\(510\) −28.6491 + 16.5406i −1.26860 + 0.732429i
\(511\) −7.21678 + 8.07924i −0.319252 + 0.357405i
\(512\) 10.8487 10.8487i 0.479449 0.479449i
\(513\) 1.23405 1.23405i 0.0544847 0.0544847i
\(514\) −0.574561 0.153953i −0.0253428 0.00679059i
\(515\) −25.0207 + 6.70428i −1.10254 + 0.295426i
\(516\) 0.0959431i 0.00422366i
\(517\) 2.18324 + 3.78149i 0.0960189 + 0.166310i
\(518\) 12.2410 24.2617i 0.537840 1.06600i
\(519\) 18.3187i 0.804104i
\(520\) −29.2533 31.8605i −1.28284 1.39717i
\(521\) 23.5185 + 13.5784i 1.03036 + 0.594881i 0.917089 0.398683i \(-0.130533\pi\)
0.113275 + 0.993564i \(0.463866\pi\)
\(522\) −2.55962 + 2.55962i −0.112031 + 0.112031i
\(523\) −36.5550 21.1050i −1.59844 0.922859i −0.991788 0.127891i \(-0.959179\pi\)
−0.606651 0.794968i \(-0.707487\pi\)
\(524\) −3.47825 + 6.02451i −0.151948 + 0.263182i
\(525\) −27.7732 + 1.56598i −1.21212 + 0.0683449i
\(526\) −0.493811 1.84293i −0.0215312 0.0803554i
\(527\) −25.5058 25.5058i −1.11105 1.11105i
\(528\) 0.352301 + 1.31480i 0.0153319 + 0.0572195i
\(529\) 12.5455 + 21.7295i 0.545458 + 0.944761i
\(530\) −3.10723 + 5.38188i −0.134970 + 0.233774i
\(531\) 4.68445 + 1.25519i 0.203288 + 0.0544708i
\(532\) −1.28132 3.89094i −0.0555523 0.168694i
\(533\) 1.63130 + 0.0695920i 0.0706593 + 0.00301436i
\(534\) 2.82807 + 4.89837i 0.122383 + 0.211973i
\(535\) 14.4647 + 14.4647i 0.625361 + 0.625361i
\(536\) −13.7787 −0.595151
\(537\) 17.9406 0.774196
\(538\) −3.43567 3.43567i −0.148122 0.148122i
\(539\) −6.16465 + 2.42265i −0.265530 + 0.104351i
\(540\) 3.37535 0.904422i 0.145252 0.0389201i
\(541\) −1.79457 + 6.69743i −0.0771547 + 0.287945i −0.993713 0.111955i \(-0.964289\pi\)
0.916559 + 0.399900i \(0.130955\pi\)
\(542\) −3.70642 + 2.13990i −0.159204 + 0.0919166i
\(543\) 11.3348i 0.486425i
\(544\) −9.42515 35.1751i −0.404100 1.50812i
\(545\) −44.9558 −1.92570
\(546\) 4.91178 8.78298i 0.210205 0.375877i
\(547\) 32.4507 1.38749 0.693747 0.720219i \(-0.255959\pi\)
0.693747 + 0.720219i \(0.255959\pi\)
\(548\) −1.74759 6.52208i −0.0746531 0.278609i
\(549\) 6.61892i 0.282488i
\(550\) −9.08876 + 5.24740i −0.387546 + 0.223750i
\(551\) 1.54997 5.78456i 0.0660309 0.246431i
\(552\) 20.4015 5.46657i 0.868345 0.232672i
\(553\) −1.12945 + 2.23858i −0.0480292 + 0.0951939i
\(554\) 9.10707 + 9.10707i 0.386922 + 0.386922i
\(555\) −38.3503 −1.62788
\(556\) −3.95434 −0.167702
\(557\) −4.06289 4.06289i −0.172150 0.172150i 0.615773 0.787923i \(-0.288844\pi\)
−0.787923 + 0.615773i \(0.788844\pi\)
\(558\) −2.38961 4.13893i −0.101160 0.175215i
\(559\) −0.116879 + 0.371987i −0.00494344 + 0.0157334i
\(560\) −3.05864 + 14.6757i −0.129251 + 0.620160i
\(561\) 7.27693 + 1.94985i 0.307232 + 0.0823226i
\(562\) 0.565397 0.979297i 0.0238498 0.0413091i
\(563\) −21.8237 37.7998i −0.919760 1.59307i −0.799779 0.600294i \(-0.795050\pi\)
−0.119981 0.992776i \(-0.538283\pi\)
\(564\) −1.05961 3.95451i −0.0446176 0.166515i
\(565\) 7.48808 + 7.48808i 0.315026 + 0.315026i
\(566\) −5.64548 21.0692i −0.237297 0.885605i
\(567\) 1.44977 + 2.21318i 0.0608845 + 0.0929449i
\(568\) −15.7692 + 27.3130i −0.661661 + 1.14603i
\(569\) −2.73813 1.58086i −0.114788 0.0662730i 0.441507 0.897258i \(-0.354444\pi\)
−0.556295 + 0.830985i \(0.687778\pi\)
\(570\) 5.12751 5.12751i 0.214768 0.214768i
\(571\) 31.3887 + 18.1222i 1.31357 + 0.758393i 0.982686 0.185277i \(-0.0593184\pi\)
0.330888 + 0.943670i \(0.392652\pi\)
\(572\) −0.129007 + 3.02404i −0.00539406 + 0.126441i
\(573\) 14.6688i 0.612796i
\(574\) −0.692573 1.05727i −0.0289074 0.0441295i
\(575\) 36.4559 + 63.1435i 1.52032 + 2.63327i
\(576\) 7.70205i 0.320919i
\(577\) 5.03959 1.35035i 0.209801 0.0562160i −0.152388 0.988321i \(-0.548696\pi\)
0.362189 + 0.932105i \(0.382030\pi\)
\(578\) 47.2686 + 12.6656i 1.96611 + 0.526819i
\(579\) 8.28684 8.28684i 0.344389 0.344389i
\(580\) 8.47888 8.47888i 0.352066 0.352066i
\(581\) −6.30630 + 30.2582i −0.261629 + 1.25532i
\(582\) −10.9243 + 6.30714i −0.452826 + 0.261439i
\(583\) 1.36701 0.366289i 0.0566157 0.0151701i
\(584\) 6.23534 10.7999i 0.258020 0.446904i
\(585\) −14.1885 0.605291i −0.586624 0.0250257i
\(586\) 2.30215 1.32915i 0.0951010 0.0549066i
\(587\) −9.40982 + 35.1179i −0.388385 + 1.44947i 0.444377 + 0.895840i \(0.353425\pi\)
−0.832762 + 0.553632i \(0.813242\pi\)
\(588\) 6.17093 0.698110i 0.254485 0.0287896i
\(589\) 6.84740 + 3.95335i 0.282142 + 0.162895i
\(590\) 19.4640 + 5.21535i 0.801319 + 0.214713i
\(591\) −2.75584 + 10.2849i −0.113360 + 0.423066i
\(592\) −3.62513 + 13.5292i −0.148992 + 0.556046i
\(593\) −40.8740 10.9522i −1.67849 0.449751i −0.711113 0.703078i \(-0.751809\pi\)
−0.967381 + 0.253327i \(0.918475\pi\)
\(594\) 0.864448 + 0.499089i 0.0354687 + 0.0204779i
\(595\) 61.8779 + 55.2724i 2.53675 + 2.26595i
\(596\) 0.172787 0.644851i 0.00707764 0.0264141i
\(597\) 18.4076 10.6276i 0.753372 0.434960i
\(598\) −26.3524 1.12421i −1.07763 0.0459723i
\(599\) 16.9264 29.3174i 0.691594 1.19788i −0.279721 0.960081i \(-0.590242\pi\)
0.971315 0.237795i \(-0.0764246\pi\)
\(600\) 30.9311 8.28797i 1.26276 0.338355i
\(601\) 21.1918 12.2351i 0.864431 0.499080i −0.00106241 0.999999i \(-0.500338\pi\)
0.865494 + 0.500920i \(0.167005\pi\)
\(602\) 0.286684 0.0944076i 0.0116844 0.00384777i
\(603\) −3.19896 + 3.19896i −0.130272 + 0.130272i
\(604\) 0.0410334 0.0410334i 0.00166962 0.00166962i
\(605\) −38.4438 10.3010i −1.56296 0.418795i
\(606\) 19.0716 5.11021i 0.774729 0.207588i
\(607\) 22.9026i 0.929589i −0.885419 0.464795i \(-0.846128\pi\)
0.885419 0.464795i \(-0.153872\pi\)
\(608\) 3.99119 + 6.91295i 0.161864 + 0.280357i
\(609\) 8.10553 + 4.08957i 0.328453 + 0.165718i
\(610\) 27.5017i 1.11351i
\(611\) −0.709151 + 16.6231i −0.0286892 + 0.672499i
\(612\) −6.11719 3.53176i −0.247273 0.142763i
\(613\) −24.6071 + 24.6071i −0.993870 + 0.993870i −0.999981 0.00611091i \(-0.998055\pi\)
0.00611091 + 0.999981i \(0.498055\pi\)
\(614\) 18.1601 + 10.4847i 0.732882 + 0.423130i
\(615\) −0.891841 + 1.54471i −0.0359625 + 0.0622888i
\(616\) 6.37822 4.17812i 0.256986 0.168341i
\(617\) −8.38788 31.3040i −0.337684 1.26025i −0.900930 0.433963i \(-0.857115\pi\)
0.563247 0.826289i \(-0.309552\pi\)
\(618\) 4.90559 + 4.90559i 0.197332 + 0.197332i
\(619\) −10.1821 38.0001i −0.409253 1.52735i −0.796074 0.605200i \(-0.793093\pi\)
0.386820 0.922155i \(-0.373573\pi\)
\(620\) 7.91574 + 13.7105i 0.317904 + 0.550625i
\(621\) 3.46739 6.00569i 0.139141 0.241000i
\(622\) 10.3398 + 2.77055i 0.414590 + 0.111089i
\(623\) 9.45037 10.5798i 0.378621 0.423869i
\(624\) −1.55473 + 4.94821i −0.0622392 + 0.198087i
\(625\) 16.4867 + 28.5558i 0.659467 + 1.14223i
\(626\) 19.9921 + 19.9921i 0.799046 + 0.799046i
\(627\) −1.65137 −0.0659495
\(628\) 6.57024 0.262181
\(629\) 54.8150 + 54.8150i 2.18562 + 2.18562i
\(630\) 6.02380 + 9.19581i 0.239994 + 0.366370i
\(631\) 15.0028 4.01998i 0.597251 0.160033i 0.0524858 0.998622i \(-0.483286\pi\)
0.544765 + 0.838589i \(0.316619\pi\)
\(632\) 0.747052 2.78804i 0.0297161 0.110902i
\(633\) −20.3617 + 11.7558i −0.809305 + 0.467252i
\(634\) 13.5094i 0.536527i
\(635\) 9.29932 + 34.7055i 0.369032 + 1.37725i
\(636\) −1.32692 −0.0526158
\(637\) −24.7761 4.81080i −0.981666 0.190611i
\(638\) 3.42520 0.135605
\(639\) 2.68009 + 10.0022i 0.106023 + 0.395682i
\(640\) 4.02875i 0.159250i
\(641\) 11.6981 6.75390i 0.462047 0.266763i −0.250857 0.968024i \(-0.580713\pi\)
0.712905 + 0.701261i \(0.247379\pi\)
\(642\) 1.41798 5.29197i 0.0559632 0.208857i
\(643\) −25.1020 + 6.72606i −0.989926 + 0.265250i −0.717219 0.696848i \(-0.754585\pi\)
−0.272706 + 0.962097i \(0.587919\pi\)
\(644\) −8.91957 13.6164i −0.351480 0.536563i
\(645\) −0.301194 0.301194i −0.0118595 0.0118595i
\(646\) −14.6578 −0.576702
\(647\) 23.1112 0.908596 0.454298 0.890850i \(-0.349890\pi\)
0.454298 + 0.890850i \(0.349890\pi\)
\(648\) −2.15363 2.15363i −0.0846026 0.0846026i
\(649\) −2.29446 3.97413i −0.0900656 0.155998i
\(650\) −39.9535 1.70444i −1.56710 0.0668535i
\(651\) −7.98521 + 8.93950i −0.312965 + 0.350367i
\(652\) −3.97023 1.06382i −0.155486 0.0416624i
\(653\) 16.7511 29.0138i 0.655522 1.13540i −0.326241 0.945287i \(-0.605782\pi\)
0.981763 0.190110i \(-0.0608846\pi\)
\(654\) 6.02014 + 10.4272i 0.235406 + 0.407735i
\(655\) 7.99345 + 29.8320i 0.312330 + 1.16563i
\(656\) 0.460640 + 0.460640i 0.0179850 + 0.0179850i
\(657\) −1.05974 3.95501i −0.0413445 0.154300i
\(658\) 10.7737 7.05741i 0.420002 0.275126i
\(659\) 0.940246 1.62855i 0.0366268 0.0634395i −0.847131 0.531384i \(-0.821672\pi\)
0.883758 + 0.467945i \(0.155005\pi\)
\(660\) −2.86353 1.65326i −0.111463 0.0643531i
\(661\) 34.5943 34.5943i 1.34556 1.34556i 0.455148 0.890416i \(-0.349586\pi\)
0.890416 0.455148i \(-0.150414\pi\)
\(662\) 0.690553 + 0.398691i 0.0268391 + 0.0154956i
\(663\) 19.4149 + 21.1452i 0.754013 + 0.821213i
\(664\) 35.5807i 1.38080i
\(665\) −16.2373 8.19236i −0.629654 0.317686i
\(666\) 5.13557 + 8.89507i 0.198999 + 0.344677i
\(667\) 23.7964i 0.921399i
\(668\) −10.8329 + 2.90268i −0.419139 + 0.112308i
\(669\) −5.85209 1.56806i −0.226255 0.0606248i
\(670\) −13.2917 + 13.2917i −0.513504 + 0.513504i
\(671\) −4.42862 + 4.42862i −0.170965 + 0.170965i
\(672\) −11.4941 + 3.78512i −0.443396 + 0.146014i
\(673\) −16.4185 + 9.47923i −0.632887 + 0.365397i −0.781869 0.623442i \(-0.785734\pi\)
0.148982 + 0.988840i \(0.452400\pi\)
\(674\) −13.2143 + 3.54077i −0.508998 + 0.136386i
\(675\) 5.25697 9.10535i 0.202341 0.350465i
\(676\) −6.59640 + 9.46080i −0.253708 + 0.363877i
\(677\) −7.78358 + 4.49385i −0.299147 + 0.172713i −0.642060 0.766655i \(-0.721920\pi\)
0.342913 + 0.939367i \(0.388587\pi\)
\(678\) 0.734061 2.73955i 0.0281914 0.105212i
\(679\) 23.5949 + 21.0761i 0.905488 + 0.808827i
\(680\) −82.7153 47.7557i −3.17199 1.83135i
\(681\) 20.1604 + 5.40197i 0.772549 + 0.207004i
\(682\) −1.17044 + 4.36816i −0.0448186 + 0.167265i
\(683\) −7.52839 + 28.0963i −0.288066 + 1.07508i 0.658504 + 0.752577i \(0.271190\pi\)
−0.946570 + 0.322499i \(0.895477\pi\)
\(684\) 1.49557 + 0.400736i 0.0571845 + 0.0153225i
\(685\) −25.9609 14.9885i −0.991916 0.572683i
\(686\) 8.15817 + 17.7522i 0.311480 + 0.677782i
\(687\) 5.67737 21.1882i 0.216605 0.808382i
\(688\) −0.134726 + 0.0777840i −0.00513638 + 0.00296549i
\(689\) 5.14468 + 1.61647i 0.195997 + 0.0615825i
\(690\) 14.4070 24.9537i 0.548467 0.949973i
\(691\) −19.4172 + 5.20283i −0.738666 + 0.197925i −0.608485 0.793565i \(-0.708222\pi\)
−0.130181 + 0.991490i \(0.541556\pi\)
\(692\) 14.0747 8.12605i 0.535041 0.308906i
\(693\) 0.510791 2.45082i 0.0194033 0.0930991i
\(694\) 10.7311 10.7311i 0.407349 0.407349i
\(695\) −12.4139 + 12.4139i −0.470885 + 0.470885i
\(696\) −10.0950 2.70496i −0.382652 0.102531i
\(697\) 3.48263 0.933168i 0.131914 0.0353463i
\(698\) 36.0063i 1.36286i
\(699\) 5.72914 + 9.92317i 0.216696 + 0.375329i
\(700\) −13.5231 20.6441i −0.511127 0.780275i
\(701\) 26.4403i 0.998636i −0.866419 0.499318i \(-0.833584\pi\)
0.866419 0.499318i \(-0.166416\pi\)
\(702\) 1.75963 + 3.37199i 0.0664129 + 0.127268i
\(703\) −14.7159 8.49622i −0.555020 0.320441i
\(704\) −5.15333 + 5.15333i −0.194223 + 0.194223i
\(705\) −15.7408 9.08797i −0.592833 0.342273i
\(706\) −2.92551 + 5.06714i −0.110103 + 0.190704i
\(707\) −27.1349 41.4236i −1.02051 1.55790i
\(708\) 1.11359 + 4.15597i 0.0418512 + 0.156191i
\(709\) 0.719284 + 0.719284i 0.0270133 + 0.0270133i 0.720484 0.693471i \(-0.243920\pi\)
−0.693471 + 0.720484i \(0.743920\pi\)
\(710\) 11.1358 + 41.5595i 0.417920 + 1.55970i
\(711\) −0.473848 0.820728i −0.0177707 0.0307797i
\(712\) −8.16517 + 14.1425i −0.306003 + 0.530012i
\(713\) 30.3475 + 8.13158i 1.13652 + 0.304530i
\(714\) 4.53384 21.7538i 0.169675 0.814116i
\(715\) 9.08836 + 9.89834i 0.339885 + 0.370177i
\(716\) 7.95833 + 13.7842i 0.297417 + 0.515141i
\(717\) −4.89413 4.89413i −0.182775 0.182775i
\(718\) −7.01275 −0.261713
\(719\) 32.2667 1.20334 0.601672 0.798743i \(-0.294502\pi\)
0.601672 + 0.798743i \(0.294502\pi\)
\(720\) −4.00652 4.00652i −0.149314 0.149314i
\(721\) 7.83781 15.5345i 0.291895 0.578536i
\(722\) −16.2567 + 4.35596i −0.605010 + 0.162112i
\(723\) −2.14872 + 8.01914i −0.0799119 + 0.298235i
\(724\) 8.70883 5.02805i 0.323661 0.186866i
\(725\) 36.0781i 1.33991i
\(726\) 2.75886 + 10.2962i 0.102391 + 0.382128i
\(727\) 14.6393 0.542941 0.271471 0.962447i \(-0.412490\pi\)
0.271471 + 0.962447i \(0.412490\pi\)
\(728\) 29.0513 0.397744i 1.07671 0.0147414i
\(729\) −1.00000 −0.0370370
\(730\) −4.40325 16.4331i −0.162971 0.608218i
\(731\) 0.861008i 0.0318455i
\(732\) 5.08547 2.93610i 0.187964 0.108521i
\(733\) 13.0234 48.6040i 0.481031 1.79523i −0.116275 0.993217i \(-0.537095\pi\)
0.597305 0.802014i \(-0.296238\pi\)
\(734\) −7.28601 + 1.95228i −0.268931 + 0.0720599i
\(735\) 17.1808 21.5639i 0.633723 0.795398i
\(736\) 22.4286 + 22.4286i 0.826728 + 0.826728i
\(737\) 4.28075 0.157683
\(738\) 0.477714 0.0175849
\(739\) −14.7764 14.7764i −0.543558 0.543558i 0.381012 0.924570i \(-0.375576\pi\)
−0.924570 + 0.381012i \(0.875576\pi\)
\(740\) −17.0119 29.4654i −0.625369 1.08317i
\(741\) −5.31038 3.37563i −0.195082 0.124007i
\(742\) −1.30568 3.96492i −0.0479332 0.145557i
\(743\) 25.4705 + 6.82479i 0.934421 + 0.250377i 0.693739 0.720227i \(-0.255962\pi\)
0.240682 + 0.970604i \(0.422629\pi\)
\(744\) 6.89926 11.9499i 0.252939 0.438103i
\(745\) −1.48195 2.56681i −0.0542943 0.0940406i
\(746\) −4.18815 15.6304i −0.153339 0.572269i
\(747\) −8.26062 8.26062i −0.302240 0.302240i
\(748\) 1.72987 + 6.45597i 0.0632504 + 0.236054i
\(749\) −13.7190 + 0.773538i −0.501280 + 0.0282645i
\(750\) 11.4553 19.8411i 0.418287 0.724495i
\(751\) 13.2528 + 7.65152i 0.483602 + 0.279208i 0.721916 0.691980i \(-0.243261\pi\)
−0.238314 + 0.971188i \(0.576595\pi\)
\(752\) −4.69398 + 4.69398i −0.171172 + 0.171172i
\(753\) −13.5324 7.81291i −0.493146 0.284718i
\(754\) 11.0145 + 7.00159i 0.401126 + 0.254983i
\(755\) 0.257632i 0.00937618i
\(756\) −1.05734 + 2.09564i −0.0384550 + 0.0762177i
\(757\) 9.00227 + 15.5924i 0.327193 + 0.566715i 0.981954 0.189121i \(-0.0605640\pi\)
−0.654761 + 0.755836i \(0.727231\pi\)
\(758\) 24.9708i 0.906979i
\(759\) −6.33829 + 1.69834i −0.230065 + 0.0616459i
\(760\) 20.2227 + 5.41866i 0.733555 + 0.196556i
\(761\) −29.9052 + 29.9052i −1.08406 + 1.08406i −0.0879379 + 0.996126i \(0.528028\pi\)
−0.996126 + 0.0879379i \(0.971972\pi\)
\(762\) 6.80441 6.80441i 0.246498 0.246498i
\(763\) 20.1171 22.5212i 0.728287 0.815322i
\(764\) −11.2704 + 6.50694i −0.407747 + 0.235413i
\(765\) −30.2909 + 8.11643i −1.09517 + 0.293450i
\(766\) −0.326683 + 0.565832i −0.0118035 + 0.0204443i
\(767\) 0.745278 17.4699i 0.0269104 0.630803i
\(768\) 14.2748 8.24155i 0.515097 0.297391i
\(769\) −2.44052 + 9.10816i −0.0880075 + 0.328449i −0.995867 0.0908266i \(-0.971049\pi\)
0.907859 + 0.419275i \(0.137716\pi\)
\(770\) 2.12234 10.1832i 0.0764840 0.366978i
\(771\) −0.488328 0.281936i −0.0175867 0.0101537i
\(772\) 10.0430 + 2.69100i 0.361454 + 0.0968513i
\(773\) 6.30495 23.5304i 0.226773 0.846329i −0.754913 0.655825i \(-0.772321\pi\)
0.981686 0.190504i \(-0.0610124\pi\)
\(774\) −0.0295262 + 0.110193i −0.00106130 + 0.00396082i
\(775\) 46.0104 + 12.3284i 1.65274 + 0.442851i
\(776\) −31.5404 18.2099i −1.13223 0.653696i
\(777\) 17.1612 19.2121i 0.615653 0.689229i
\(778\) 2.58080 9.63167i 0.0925261 0.345312i
\(779\) −0.684440 + 0.395162i −0.0245226 + 0.0141581i
\(780\) −5.82887 11.1699i −0.208707 0.399947i
\(781\) 4.89914 8.48556i 0.175305 0.303637i
\(782\) −56.2594 + 15.0747i −2.01183 + 0.539069i
\(783\) −2.97173 + 1.71573i −0.106201 + 0.0613151i
\(784\) −5.98327 8.09941i −0.213688 0.289264i
\(785\) 20.6259 20.6259i 0.736171 0.736171i
\(786\) 5.84889 5.84889i 0.208623 0.208623i
\(787\) −16.1021 4.31455i −0.573979 0.153797i −0.0398580 0.999205i \(-0.512691\pi\)
−0.534121 + 0.845408i \(0.679357\pi\)
\(788\) −9.12464 + 2.44494i −0.325052 + 0.0870974i
\(789\) 1.80864i 0.0643894i
\(790\) −1.96884 3.41014i −0.0700484 0.121327i
\(791\) −7.10205 + 0.400446i −0.252520 + 0.0142382i
\(792\) 2.88192i 0.102405i
\(793\) −23.2940 + 5.18856i −0.827193 + 0.184251i
\(794\) −8.16842 4.71604i −0.289886 0.167366i
\(795\) −4.16560 + 4.16560i −0.147738 + 0.147738i
\(796\) 16.3309 + 9.42866i 0.578834 + 0.334190i
\(797\) 7.91214 13.7042i 0.280263 0.485429i −0.691187 0.722676i \(-0.742912\pi\)
0.971449 + 0.237247i \(0.0762451\pi\)
\(798\) 0.274208 + 4.86318i 0.00970686 + 0.172155i
\(799\) 9.50910 + 35.4884i 0.336408 + 1.25549i
\(800\) 34.0044 + 34.0044i 1.20224 + 1.20224i
\(801\) 1.38773 + 5.17908i 0.0490331 + 0.182994i
\(802\) −3.49797 6.05866i −0.123518 0.213939i
\(803\) −1.93718 + 3.35530i −0.0683617 + 0.118406i
\(804\) −3.87687 1.03880i −0.136727 0.0366358i
\(805\) −70.7472 14.7448i −2.49351 0.519687i
\(806\) −12.6930 + 11.6543i −0.447090 + 0.410505i
\(807\) −2.30295 3.98883i −0.0810677 0.140413i
\(808\) 40.3090 + 40.3090i 1.41807 + 1.41807i
\(809\) −36.4976 −1.28319 −0.641594 0.767044i \(-0.721727\pi\)
−0.641594 + 0.767044i \(0.721727\pi\)
\(810\) −4.15502 −0.145992
\(811\) −33.0051 33.0051i −1.15897 1.15897i −0.984698 0.174269i \(-0.944244\pi\)
−0.174269 0.984698i \(-0.555756\pi\)
\(812\) 0.453432 + 8.04177i 0.0159123 + 0.282211i
\(813\) −3.91882 + 1.05005i −0.137439 + 0.0368267i
\(814\) 2.51542 9.38769i 0.0881656 0.329038i
\(815\) −15.8034 + 9.12409i −0.553569 + 0.319603i
\(816\) 11.4532i 0.400944i
\(817\) −0.0488477 0.182302i −0.00170897 0.00637795i
\(818\) 17.2679 0.603758
\(819\) 6.65239 6.83708i 0.232453 0.238907i
\(820\) −1.58245 −0.0552617
\(821\) −9.07253 33.8592i −0.316634 1.18169i −0.922459 0.386095i \(-0.873824\pi\)
0.605825 0.795598i \(-0.292843\pi\)
\(822\) 8.02860i 0.280030i
\(823\) 11.1912 6.46124i 0.390100 0.225225i −0.292103 0.956387i \(-0.594355\pi\)
0.682204 + 0.731162i \(0.261022\pi\)
\(824\) −5.18415 + 19.3475i −0.180598 + 0.674002i
\(825\) −9.60962 + 2.57489i −0.334564 + 0.0896461i
\(826\) −11.3225 + 7.41693i −0.393961 + 0.258068i
\(827\) 16.1945 + 16.1945i 0.563138 + 0.563138i 0.930198 0.367059i \(-0.119635\pi\)
−0.367059 + 0.930198i \(0.619635\pi\)
\(828\) 6.15242 0.213811
\(829\) 18.0216 0.625918 0.312959 0.949767i \(-0.398680\pi\)
0.312959 + 0.949767i \(0.398680\pi\)
\(830\) −34.3230 34.3230i −1.19137 1.19137i
\(831\) 6.10452 + 10.5733i 0.211764 + 0.366785i
\(832\) −27.1059 + 6.03763i −0.939727 + 0.209317i
\(833\) −55.3789 + 6.26495i −1.91877 + 0.217068i
\(834\) 4.54168 + 1.21694i 0.157265 + 0.0421391i
\(835\) −24.8954 + 43.1202i −0.861542 + 1.49223i
\(836\) −0.732536 1.26879i −0.0253353 0.0438820i
\(837\) −1.17258 4.37613i −0.0405303 0.151261i
\(838\) 17.1398 + 17.1398i 0.592085 + 0.592085i
\(839\) −9.35633 34.9183i −0.323016 1.20551i −0.916291 0.400513i \(-0.868832\pi\)
0.593275 0.805000i \(-0.297835\pi\)
\(840\) −14.2971 + 28.3368i −0.493296 + 0.977711i
\(841\) 8.61256 14.9174i 0.296985 0.514393i
\(842\) 4.31145 + 2.48921i 0.148582 + 0.0857840i
\(843\) 0.757979 0.757979i 0.0261062 0.0261062i
\(844\) −18.0646 10.4296i −0.621808 0.359001i
\(845\) 8.99218 + 50.4083i 0.309340 + 1.73410i
\(846\) 4.86796i 0.167364i
\(847\) 22.3634 14.6494i 0.768417 0.503359i
\(848\) 1.07578 + 1.86330i 0.0369423 + 0.0639859i
\(849\) 20.6773i 0.709641i
\(850\) −85.2961 + 22.8550i −2.92563 + 0.783920i
\(851\) −65.2203 17.4757i −2.23572 0.599060i
\(852\) −6.49609 + 6.49609i −0.222552 + 0.222552i
\(853\) −9.67121 + 9.67121i −0.331136 + 0.331136i −0.853018 0.521882i \(-0.825230\pi\)
0.521882 + 0.853018i \(0.325230\pi\)
\(854\) 13.7773 + 12.3066i 0.471451 + 0.421123i
\(855\) 5.95306 3.43700i 0.203590 0.117543i
\(856\) 15.2789 4.09397i 0.522222 0.139929i
\(857\) −15.8586 + 27.4680i −0.541720 + 0.938287i 0.457085 + 0.889423i \(0.348894\pi\)
−0.998805 + 0.0488643i \(0.984440\pi\)
\(858\) 1.07881 3.43349i 0.0368299 0.117217i
\(859\) 3.30317 1.90709i 0.112703 0.0650690i −0.442589 0.896725i \(-0.645940\pi\)
0.555292 + 0.831656i \(0.312607\pi\)
\(860\) 0.0978072 0.365022i 0.00333520 0.0124471i
\(861\) −0.374759 1.13802i −0.0127717 0.0387835i
\(862\) −25.7349 14.8581i −0.876534 0.506067i
\(863\) 25.7366 + 6.89611i 0.876086 + 0.234746i 0.668718 0.743517i \(-0.266844\pi\)
0.207368 + 0.978263i \(0.433510\pi\)
\(864\) 1.18381 4.41802i 0.0402739 0.150304i
\(865\) 18.6747 69.6948i 0.634958 2.36970i
\(866\) −20.1544 5.40036i −0.684875 0.183512i
\(867\) 40.1742 + 23.1946i 1.36439 + 0.787730i
\(868\) −10.4106 2.16974i −0.353359 0.0736456i
\(869\) −0.232093 + 0.866181i −0.00787320 + 0.0293832i
\(870\) −12.3476 + 7.12888i −0.418622 + 0.241692i
\(871\) 13.7658 + 8.75045i 0.466435 + 0.296498i
\(872\) −17.3812 + 30.1052i −0.588603 + 1.01949i
\(873\) −11.5503 + 3.09490i −0.390919 + 0.104747i
\(874\) 11.0566 6.38355i 0.373996 0.215927i
\(875\) −56.2522 11.7239i −1.90167 0.396339i
\(876\) 2.56864 2.56864i 0.0867862 0.0867862i
\(877\) −0.217046 + 0.217046i −0.00732914 + 0.00732914i −0.710762 0.703433i \(-0.751650\pi\)
0.703433 + 0.710762i \(0.251650\pi\)
\(878\) −22.3229 5.98141i −0.753362 0.201863i
\(879\) 2.43408 0.652210i 0.0820996 0.0219985i
\(880\) 5.36140i 0.180733i
\(881\) 4.00050 + 6.92907i 0.134780 + 0.233446i 0.925513 0.378715i \(-0.123634\pi\)
−0.790733 + 0.612161i \(0.790300\pi\)
\(882\) −7.30232 1.09729i −0.245882 0.0369476i
\(883\) 49.8829i 1.67869i −0.543597 0.839346i \(-0.682938\pi\)
0.543597 0.839346i \(-0.317062\pi\)
\(884\) −7.63409 + 24.2968i −0.256762 + 0.817190i
\(885\) 16.5427 + 9.55094i 0.556077 + 0.321051i
\(886\) 14.7349 14.7349i 0.495028 0.495028i
\(887\) 8.54675 + 4.93447i 0.286972 + 0.165683i 0.636575 0.771215i \(-0.280350\pi\)
−0.349604 + 0.936898i \(0.613684\pi\)
\(888\) −14.8273 + 25.6817i −0.497573 + 0.861822i
\(889\) −21.5475 10.8716i −0.722680 0.364621i
\(890\) 5.76604 + 21.5192i 0.193278 + 0.721324i
\(891\) 0.669085 + 0.669085i 0.0224152 + 0.0224152i
\(892\) −1.39116 5.19188i −0.0465795 0.173837i
\(893\) −4.02674 6.97453i −0.134750 0.233394i
\(894\) −0.396902 + 0.687454i −0.0132744 + 0.0229919i
\(895\) 68.2563 + 18.2892i 2.28156 + 0.611341i
\(896\) −2.01825 1.80281i −0.0674252 0.0602275i
\(897\) −23.8539 7.49493i −0.796459 0.250249i
\(898\) 17.3467 + 30.0454i 0.578868 + 1.00263i
\(899\) −10.9928 10.9928i −0.366631 0.366631i
\(900\) 9.32781 0.310927
\(901\) 11.9080 0.396713
\(902\) −0.319631 0.319631i −0.0106426 0.0106426i
\(903\) 0.285667 0.0161072i 0.00950639 0.000536014i
\(904\) 7.90959 2.11937i 0.263069 0.0704891i
\(905\) 11.5551 43.1241i 0.384104 1.43349i
\(906\) −0.0597559 + 0.0345001i −0.00198526 + 0.00114619i
\(907\) 20.7745i 0.689806i −0.938638 0.344903i \(-0.887912\pi\)
0.938638 0.344903i \(-0.112088\pi\)
\(908\) 4.79254 + 17.8860i 0.159046 + 0.593568i
\(909\) 18.7168 0.620796
\(910\) 27.6408 28.4082i 0.916284 0.941722i
\(911\) 15.1029 0.500380 0.250190 0.968197i \(-0.419507\pi\)
0.250190 + 0.968197i \(0.419507\pi\)
\(912\) −0.649779 2.42501i −0.0215163 0.0803000i
\(913\) 11.0541i 0.365838i
\(914\) 14.3325 8.27485i 0.474076 0.273708i
\(915\) 6.74752 25.1821i 0.223066 0.832494i
\(916\) 18.7979 5.03687i 0.621099 0.166423i
\(917\) −18.5217 9.34494i −0.611639 0.308597i
\(918\) 5.93888 + 5.93888i 0.196012 + 0.196012i
\(919\) −8.72439 −0.287791 −0.143896 0.989593i \(-0.545963\pi\)
−0.143896 + 0.989593i \(0.545963\pi\)
\(920\) 83.1916 2.74275
\(921\) 14.0560 + 14.0560i 0.463160 + 0.463160i
\(922\) −0.879010 1.52249i −0.0289486 0.0501405i
\(923\) 33.1000 17.2728i 1.08950 0.568541i
\(924\) 2.10961 0.694714i 0.0694011 0.0228544i
\(925\) −98.8819 26.4953i −3.25122 0.871161i
\(926\) −14.0716 + 24.3728i −0.462422 + 0.800939i
\(927\) 3.28825 + 5.69542i 0.108000 + 0.187062i
\(928\) −4.06218 15.1602i −0.133347 0.497659i
\(929\) 13.2612 + 13.2612i 0.435087 + 0.435087i 0.890355 0.455268i \(-0.150457\pi\)
−0.455268 + 0.890355i \(0.650457\pi\)
\(930\) −4.87209 18.1829i −0.159762 0.596240i
\(931\) 11.3700 4.46831i 0.372637 0.146443i
\(932\) −5.08280 + 8.80368i −0.166493 + 0.288374i
\(933\) 8.78798 + 5.07374i 0.287706 + 0.166107i
\(934\) 17.0844 17.0844i 0.559019 0.559019i
\(935\) 25.6978 + 14.8366i 0.840408 + 0.485210i
\(936\) −5.89105 + 9.26751i −0.192555 + 0.302918i
\(937\) 21.0904i 0.688992i 0.938788 + 0.344496i \(0.111950\pi\)
−0.938788 + 0.344496i \(0.888050\pi\)
\(938\) −0.710813 12.6065i −0.0232089 0.411617i
\(939\) 13.4009 + 23.2110i 0.437320 + 0.757461i
\(940\) 16.1254i 0.525953i
\(941\) −4.47139 + 1.19811i −0.145763 + 0.0390572i −0.330963 0.943644i \(-0.607374\pi\)
0.185200 + 0.982701i \(0.440707\pi\)
\(942\) −7.54611 2.02197i −0.245866 0.0658795i
\(943\) −2.22061 + 2.22061i −0.0723132 + 0.0723132i
\(944\) 4.93311 4.93311i 0.160559 0.160559i
\(945\) 3.25954 + 9.89813i 0.106033 + 0.321986i
\(946\) 0.0934842 0.0539732i 0.00303943 0.00175482i
\(947\) −31.7665 + 8.51180i −1.03227 + 0.276596i −0.734907 0.678168i \(-0.762774\pi\)
−0.297364 + 0.954764i \(0.596108\pi\)
\(948\) 0.420390 0.728137i 0.0136536 0.0236488i
\(949\) −13.0882 + 6.82988i −0.424860 + 0.221707i
\(950\) 16.7632 9.67823i 0.543870 0.314003i
\(951\) 3.31452 12.3700i 0.107481 0.401124i
\(952\) 60.9377 20.0673i 1.97500 0.650386i
\(953\) −2.61428 1.50935i −0.0846848 0.0488928i 0.457060 0.889436i \(-0.348903\pi\)
−0.541744 + 0.840543i \(0.682236\pi\)
\(954\) 1.52400 + 0.408356i 0.0493415 + 0.0132210i
\(955\) −14.9538 + 55.8082i −0.483893 + 1.80591i
\(956\) 1.58928 5.93128i 0.0514011 0.191831i
\(957\) 3.13631 + 0.840371i 0.101382 + 0.0271653i
\(958\) 0.700759 + 0.404583i 0.0226405 + 0.0130715i
\(959\) 19.1258 6.29831i 0.617605 0.203383i
\(960\) 7.85171 29.3030i 0.253413 0.945749i
\(961\) −9.07123 + 5.23728i −0.292620 + 0.168944i
\(962\) 27.2787 25.0465i 0.879500 0.807531i
\(963\) 2.59676 4.49772i 0.0836794 0.144937i
\(964\) −7.11446 + 1.90631i −0.229141 + 0.0613982i
\(965\) 39.9757 23.0800i 1.28686 0.742970i
\(966\) 6.05396 + 18.3838i 0.194783 + 0.591490i
\(967\) −13.5833 + 13.5833i −0.436809 + 0.436809i −0.890936 0.454128i \(-0.849951\pi\)
0.454128 + 0.890936i \(0.349951\pi\)
\(968\) −21.7617 + 21.7617i −0.699447 + 0.699447i
\(969\) −13.4215 3.59627i −0.431160 0.115529i
\(970\) −47.9918 + 12.8594i −1.54092 + 0.412889i
\(971\) 30.1296i 0.966904i −0.875371 0.483452i \(-0.839383\pi\)
0.875371 0.483452i \(-0.160617\pi\)
\(972\) −0.443592 0.768324i −0.0142282 0.0246440i
\(973\) −0.663866 11.7739i −0.0212826 0.377454i
\(974\) 7.79047i 0.249623i
\(975\) −36.1654 11.3632i −1.15822 0.363914i
\(976\) −8.24590 4.76077i −0.263945 0.152389i
\(977\) 14.7964 14.7964i 0.473379 0.473379i −0.429628 0.903006i \(-0.641355\pi\)
0.903006 + 0.429628i \(0.141355\pi\)
\(978\) 4.23254 + 2.44366i 0.135342 + 0.0781395i
\(979\) 2.53674 4.39376i 0.0810745 0.140425i
\(980\) 24.1894 + 3.63483i 0.772701 + 0.116110i
\(981\) 2.95407 + 11.0247i 0.0943162 + 0.351993i
\(982\) −5.32220 5.32220i −0.169838 0.169838i
\(983\) 1.47016 + 5.48673i 0.0468910 + 0.174999i 0.985400 0.170255i \(-0.0544592\pi\)
−0.938509 + 0.345255i \(0.887793\pi\)
\(984\) 0.689624 + 1.19446i 0.0219844 + 0.0380781i
\(985\) −20.9696 + 36.3203i −0.668146 + 1.15726i
\(986\) 27.8382 + 7.45923i 0.886549 + 0.237550i
\(987\) 11.5965 3.81884i 0.369121 0.121555i
\(988\) 0.237939 5.57750i 0.00756985 0.177444i
\(989\) −0.374975 0.649475i −0.0119235 0.0206521i
\(990\) 2.78006 + 2.78006i 0.0883561 + 0.0883561i
\(991\) −52.6658 −1.67298 −0.836492 0.547979i \(-0.815397\pi\)
−0.836492 + 0.547979i \(0.815397\pi\)
\(992\) 20.7219 0.657922
\(993\) 0.534490 + 0.534490i 0.0169615 + 0.0169615i
\(994\) −25.8029 13.0186i −0.818417 0.412925i
\(995\) 80.8670 21.6682i 2.56366 0.686929i
\(996\) 2.68249 10.0112i 0.0849979 0.317216i
\(997\) 22.9450 13.2473i 0.726675 0.419546i −0.0905295 0.995894i \(-0.528856\pi\)
0.817205 + 0.576348i \(0.195523\pi\)
\(998\) 22.6039i 0.715514i
\(999\) 2.52002 + 9.40483i 0.0797298 + 0.297556i
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 273.2.cg.a.262.4 yes 36
3.2 odd 2 819.2.gh.c.262.6 36
7.5 odd 6 273.2.bt.a.145.4 36
13.7 odd 12 273.2.bt.a.241.4 yes 36
21.5 even 6 819.2.et.c.145.6 36
39.20 even 12 819.2.et.c.514.6 36
91.33 even 12 inner 273.2.cg.a.124.4 yes 36
273.215 odd 12 819.2.gh.c.397.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.145.4 36 7.5 odd 6
273.2.bt.a.241.4 yes 36 13.7 odd 12
273.2.cg.a.124.4 yes 36 91.33 even 12 inner
273.2.cg.a.262.4 yes 36 1.1 even 1 trivial
819.2.et.c.145.6 36 21.5 even 6
819.2.et.c.514.6 36 39.20 even 12
819.2.gh.c.262.6 36 3.2 odd 2
819.2.gh.c.397.6 36 273.215 odd 12