Properties

Label 91.2.bb.a.5.3
Level $91$
Weight $2$
Character 91.5
Analytic conductor $0.727$
Analytic rank $0$
Dimension $32$
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] = [91,2,Mod(5,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.bb (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: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 91.5
Dual form 91.2.bb.a.73.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.211401 - 0.788958i) q^{2} +(-2.60482 + 1.50389i) q^{3} +(1.15429 - 0.666428i) q^{4} +(3.03793 - 0.814012i) q^{5} +(1.73717 + 1.73717i) q^{6} +(2.28951 + 1.32595i) q^{7} +(-1.92491 - 1.92491i) q^{8} +(3.02338 - 5.23665i) q^{9} +O(q^{10})\) \(q+(-0.211401 - 0.788958i) q^{2} +(-2.60482 + 1.50389i) q^{3} +(1.15429 - 0.666428i) q^{4} +(3.03793 - 0.814012i) q^{5} +(1.73717 + 1.73717i) q^{6} +(2.28951 + 1.32595i) q^{7} +(-1.92491 - 1.92491i) q^{8} +(3.02338 - 5.23665i) q^{9} +(-1.28444 - 2.22472i) q^{10} +(-0.131620 + 0.491212i) q^{11} +(-2.00447 + 3.47185i) q^{12} +(-1.73717 + 3.15947i) q^{13} +(0.562115 - 2.08663i) q^{14} +(-6.68907 + 6.68907i) q^{15} +(0.221107 - 0.382969i) q^{16} +(-0.606654 - 1.05076i) q^{17} +(-4.77064 - 1.27829i) q^{18} +(-1.72169 + 0.461325i) q^{19} +(2.96417 - 2.96417i) q^{20} +(-7.95784 - 0.0106837i) q^{21} +0.415370 q^{22} +(-4.51168 - 2.60482i) q^{23} +(7.90891 + 2.11919i) q^{24} +(4.23629 - 2.44583i) q^{25} +(2.85993 + 0.702638i) q^{26} +9.16401i q^{27} +(3.52640 + 0.00473432i) q^{28} +1.64443 q^{29} +(6.69147 + 3.86332i) q^{30} +(-0.976210 + 3.64327i) q^{31} +(-5.60785 - 1.50262i) q^{32} +(-0.395884 - 1.47746i) q^{33} +(-0.700755 + 0.700755i) q^{34} +(8.03472 + 2.16446i) q^{35} -8.05946i q^{36} +(-2.66889 + 0.715128i) q^{37} +(0.727931 + 1.26081i) q^{38} +(-0.226498 - 10.8424i) q^{39} +(-7.41466 - 4.28086i) q^{40} +(-5.55629 - 5.55629i) q^{41} +(1.67386 + 6.28066i) q^{42} +7.46499i q^{43} +(0.175430 + 0.654714i) q^{44} +(4.92214 - 18.3697i) q^{45} +(-1.10132 + 4.11018i) q^{46} +(-1.26875 - 4.73504i) q^{47} +1.33009i q^{48} +(3.48371 + 6.07155i) q^{49} +(-2.82521 - 2.82521i) q^{50} +(3.16045 + 1.82468i) q^{51} +(0.100369 + 4.80463i) q^{52} +(4.30982 + 7.46483i) q^{53} +(7.23002 - 1.93728i) q^{54} +1.59941i q^{55} +(-1.85477 - 6.95945i) q^{56} +(3.79090 - 3.79090i) q^{57} +(-0.347632 - 1.29738i) q^{58} +(-2.41901 - 0.648171i) q^{59} +(-3.26333 + 12.1789i) q^{60} +(-9.09759 - 5.25249i) q^{61} +3.08076 q^{62} +(13.8656 - 7.98051i) q^{63} +3.85758i q^{64} +(-2.70555 + 11.0123i) q^{65} +(-1.08196 + 0.624671i) q^{66} +(7.15134 + 1.91620i) q^{67} +(-1.40051 - 0.808582i) q^{68} +15.6695 q^{69} +(0.00912470 - 6.79662i) q^{70} +(0.840390 - 0.840390i) q^{71} +(-15.8999 + 4.26035i) q^{72} +(2.36118 + 0.632677i) q^{73} +(1.12841 + 1.95447i) q^{74} +(-7.35651 + 12.7419i) q^{75} +(-1.67988 + 1.67988i) q^{76} +(-0.952667 + 0.950113i) q^{77} +(-8.50628 + 2.47078i) q^{78} +(6.20571 - 10.7486i) q^{79} +(0.359968 - 1.34342i) q^{80} +(-4.71154 - 8.16062i) q^{81} +(-3.20908 + 5.55828i) q^{82} +(-7.31472 - 7.31472i) q^{83} +(-9.19275 + 5.29099i) q^{84} +(-2.69830 - 2.69830i) q^{85} +(5.88956 - 1.57810i) q^{86} +(-4.28343 + 2.47304i) q^{87} +(1.19890 - 0.692184i) q^{88} +(2.52599 + 9.42713i) q^{89} -15.5334 q^{90} +(-8.16656 + 4.93024i) q^{91} -6.94369 q^{92} +(-2.93623 - 10.9582i) q^{93} +(-3.46753 + 2.00198i) q^{94} +(-4.85484 + 2.80295i) q^{95} +(16.8672 - 4.51956i) q^{96} +(-2.93184 - 2.93184i) q^{97} +(4.05374 - 4.03203i) q^{98} +(2.17437 + 2.17437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29} + 24 q^{31} + 4 q^{32} + 48 q^{33} + 28 q^{35} - 8 q^{37} - 6 q^{39} - 132 q^{40} - 16 q^{42} - 42 q^{44} - 24 q^{45} + 12 q^{46} + 30 q^{47} + 88 q^{50} + 36 q^{52} - 12 q^{53} + 78 q^{54} + 40 q^{57} + 26 q^{58} - 54 q^{59} + 16 q^{60} - 48 q^{61} + 24 q^{63} - 8 q^{65} + 12 q^{66} + 16 q^{67} - 48 q^{68} + 50 q^{70} - 36 q^{71} + 22 q^{72} + 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} + 138 q^{80} + 16 q^{81} - 58 q^{84} - 84 q^{85} + 42 q^{86} - 24 q^{87} - 60 q^{89} + 48 q^{92} + 6 q^{93} - 72 q^{94} - 42 q^{96} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.211401 0.788958i −0.149483 0.557877i −0.999515 0.0311464i \(-0.990084\pi\)
0.850032 0.526731i \(-0.176582\pi\)
\(3\) −2.60482 + 1.50389i −1.50389 + 0.868272i −0.503902 + 0.863761i \(0.668103\pi\)
−0.999990 + 0.00451177i \(0.998564\pi\)
\(4\) 1.15429 0.666428i 0.577143 0.333214i
\(5\) 3.03793 0.814012i 1.35860 0.364037i 0.495301 0.868721i \(-0.335058\pi\)
0.863304 + 0.504684i \(0.168391\pi\)
\(6\) 1.73717 + 1.73717i 0.709196 + 0.709196i
\(7\) 2.28951 + 1.32595i 0.865353 + 0.501162i
\(8\) −1.92491 1.92491i −0.680560 0.680560i
\(9\) 3.02338 5.23665i 1.00779 1.74555i
\(10\) −1.28444 2.22472i −0.406176 0.703518i
\(11\) −0.131620 + 0.491212i −0.0396849 + 0.148106i −0.982925 0.184004i \(-0.941094\pi\)
0.943241 + 0.332110i \(0.107761\pi\)
\(12\) −2.00447 + 3.47185i −0.578641 + 1.00224i
\(13\) −1.73717 + 3.15947i −0.481804 + 0.876279i
\(14\) 0.562115 2.08663i 0.150232 0.557676i
\(15\) −6.68907 + 6.68907i −1.72711 + 1.72711i
\(16\) 0.221107 0.382969i 0.0552768 0.0957423i
\(17\) −0.606654 1.05076i −0.147135 0.254846i 0.783032 0.621981i \(-0.213672\pi\)
−0.930168 + 0.367135i \(0.880339\pi\)
\(18\) −4.77064 1.27829i −1.12445 0.301296i
\(19\) −1.72169 + 0.461325i −0.394982 + 0.105835i −0.450843 0.892603i \(-0.648876\pi\)
0.0558606 + 0.998439i \(0.482210\pi\)
\(20\) 2.96417 2.96417i 0.662808 0.662808i
\(21\) −7.95784 0.0106837i −1.73654 0.00233137i
\(22\) 0.415370 0.0885572
\(23\) −4.51168 2.60482i −0.940750 0.543142i −0.0505543 0.998721i \(-0.516099\pi\)
−0.890195 + 0.455579i \(0.849432\pi\)
\(24\) 7.90891 + 2.11919i 1.61440 + 0.432577i
\(25\) 4.23629 2.44583i 0.847259 0.489165i
\(26\) 2.85993 + 0.702638i 0.560878 + 0.137799i
\(27\) 9.16401i 1.76361i
\(28\) 3.52640 + 0.00473432i 0.666427 + 0.000894702i
\(29\) 1.64443 0.305362 0.152681 0.988276i \(-0.451209\pi\)
0.152681 + 0.988276i \(0.451209\pi\)
\(30\) 6.69147 + 3.86332i 1.22169 + 0.705343i
\(31\) −0.976210 + 3.64327i −0.175333 + 0.654350i 0.821162 + 0.570695i \(0.193326\pi\)
−0.996495 + 0.0836552i \(0.973341\pi\)
\(32\) −5.60785 1.50262i −0.991338 0.265628i
\(33\) −0.395884 1.47746i −0.0689146 0.257193i
\(34\) −0.700755 + 0.700755i −0.120178 + 0.120178i
\(35\) 8.03472 + 2.16446i 1.35811 + 0.365861i
\(36\) 8.05946i 1.34324i
\(37\) −2.66889 + 0.715128i −0.438764 + 0.117566i −0.471437 0.881900i \(-0.656265\pi\)
0.0326734 + 0.999466i \(0.489598\pi\)
\(38\) 0.727931 + 1.26081i 0.118086 + 0.204531i
\(39\) −0.226498 10.8424i −0.0362687 1.73617i
\(40\) −7.41466 4.28086i −1.17236 0.676863i
\(41\) −5.55629 5.55629i −0.867747 0.867747i 0.124476 0.992223i \(-0.460275\pi\)
−0.992223 + 0.124476i \(0.960275\pi\)
\(42\) 1.67386 + 6.28066i 0.258283 + 0.969127i
\(43\) 7.46499i 1.13840i 0.822199 + 0.569200i \(0.192747\pi\)
−0.822199 + 0.569200i \(0.807253\pi\)
\(44\) 0.175430 + 0.654714i 0.0264471 + 0.0987019i
\(45\) 4.92214 18.3697i 0.733749 2.73839i
\(46\) −1.10132 + 4.11018i −0.162381 + 0.606013i
\(47\) −1.26875 4.73504i −0.185066 0.690677i −0.994616 0.103626i \(-0.966956\pi\)
0.809550 0.587051i \(-0.199711\pi\)
\(48\) 1.33009i 0.191981i
\(49\) 3.48371 + 6.07155i 0.497673 + 0.867365i
\(50\) −2.82521 2.82521i −0.399545 0.399545i
\(51\) 3.16045 + 1.82468i 0.442551 + 0.255507i
\(52\) 0.100369 + 4.80463i 0.0139187 + 0.666282i
\(53\) 4.30982 + 7.46483i 0.591999 + 1.02537i 0.993963 + 0.109717i \(0.0349945\pi\)
−0.401964 + 0.915656i \(0.631672\pi\)
\(54\) 7.23002 1.93728i 0.983881 0.263630i
\(55\) 1.59941i 0.215664i
\(56\) −1.85477 6.95945i −0.247854 0.929996i
\(57\) 3.79090 3.79090i 0.502117 0.502117i
\(58\) −0.347632 1.29738i −0.0456464 0.170355i
\(59\) −2.41901 0.648171i −0.314928 0.0843847i 0.0978928 0.995197i \(-0.468790\pi\)
−0.412821 + 0.910812i \(0.635456\pi\)
\(60\) −3.26333 + 12.1789i −0.421293 + 1.57229i
\(61\) −9.09759 5.25249i −1.16483 0.672513i −0.212371 0.977189i \(-0.568118\pi\)
−0.952456 + 0.304676i \(0.901452\pi\)
\(62\) 3.08076 0.391256
\(63\) 13.8656 7.98051i 1.74690 1.00545i
\(64\) 3.85758i 0.482198i
\(65\) −2.70555 + 11.0123i −0.335582 + 1.36591i
\(66\) −1.08196 + 0.624671i −0.133180 + 0.0768917i
\(67\) 7.15134 + 1.91620i 0.873675 + 0.234101i 0.667676 0.744452i \(-0.267289\pi\)
0.205999 + 0.978552i \(0.433956\pi\)
\(68\) −1.40051 0.808582i −0.169836 0.0980550i
\(69\) 15.6695 1.88638
\(70\) 0.00912470 6.79662i 0.00109061 0.812351i
\(71\) 0.840390 0.840390i 0.0997360 0.0997360i −0.655478 0.755214i \(-0.727533\pi\)
0.755214 + 0.655478i \(0.227533\pi\)
\(72\) −15.8999 + 4.26035i −1.87382 + 0.502088i
\(73\) 2.36118 + 0.632677i 0.276355 + 0.0740492i 0.394335 0.918967i \(-0.370975\pi\)
−0.117979 + 0.993016i \(0.537642\pi\)
\(74\) 1.12841 + 1.95447i 0.131175 + 0.227202i
\(75\) −7.35651 + 12.7419i −0.849457 + 1.47130i
\(76\) −1.67988 + 1.67988i −0.192695 + 0.192695i
\(77\) −0.952667 + 0.950113i −0.108567 + 0.108275i
\(78\) −8.50628 + 2.47078i −0.963146 + 0.279760i
\(79\) 6.20571 10.7486i 0.698197 1.20931i −0.270894 0.962609i \(-0.587319\pi\)
0.969091 0.246704i \(-0.0793474\pi\)
\(80\) 0.359968 1.34342i 0.0402456 0.150199i
\(81\) −4.71154 8.16062i −0.523504 0.906736i
\(82\) −3.20908 + 5.55828i −0.354383 + 0.613809i
\(83\) −7.31472 7.31472i −0.802894 0.802894i 0.180653 0.983547i \(-0.442179\pi\)
−0.983547 + 0.180653i \(0.942179\pi\)
\(84\) −9.19275 + 5.29099i −1.00301 + 0.577295i
\(85\) −2.69830 2.69830i −0.292672 0.292672i
\(86\) 5.88956 1.57810i 0.635088 0.170171i
\(87\) −4.28343 + 2.47304i −0.459232 + 0.265137i
\(88\) 1.19890 0.692184i 0.127803 0.0737870i
\(89\) 2.52599 + 9.42713i 0.267755 + 0.999273i 0.960543 + 0.278132i \(0.0897154\pi\)
−0.692788 + 0.721141i \(0.743618\pi\)
\(90\) −15.5334 −1.63737
\(91\) −8.16656 + 4.93024i −0.856088 + 0.516830i
\(92\) −6.94369 −0.723930
\(93\) −2.93623 10.9582i −0.304473 1.13631i
\(94\) −3.46753 + 2.00198i −0.357649 + 0.206489i
\(95\) −4.85484 + 2.80295i −0.498097 + 0.287576i
\(96\) 16.8672 4.51956i 1.72150 0.461275i
\(97\) −2.93184 2.93184i −0.297683 0.297683i 0.542423 0.840106i \(-0.317507\pi\)
−0.840106 + 0.542423i \(0.817507\pi\)
\(98\) 4.05374 4.03203i 0.409490 0.407297i
\(99\) 2.17437 + 2.17437i 0.218532 + 0.218532i
\(100\) 3.25993 5.64637i 0.325993 0.564637i
\(101\) 7.72587 + 13.3816i 0.768753 + 1.33152i 0.938240 + 0.345986i \(0.112456\pi\)
−0.169487 + 0.985532i \(0.554211\pi\)
\(102\) 0.771479 2.87920i 0.0763878 0.285083i
\(103\) 8.75030 15.1560i 0.862192 1.49336i −0.00761617 0.999971i \(-0.502424\pi\)
0.869808 0.493390i \(-0.164242\pi\)
\(104\) 9.42561 2.73781i 0.924257 0.268464i
\(105\) −24.1841 + 6.44532i −2.36012 + 0.628999i
\(106\) 4.97833 4.97833i 0.483538 0.483538i
\(107\) −1.06208 + 1.83958i −0.102675 + 0.177839i −0.912786 0.408438i \(-0.866074\pi\)
0.810111 + 0.586277i \(0.199407\pi\)
\(108\) 6.10715 + 10.5779i 0.587661 + 1.01786i
\(109\) −10.3442 2.77172i −0.990796 0.265483i −0.273211 0.961954i \(-0.588086\pi\)
−0.717585 + 0.696471i \(0.754752\pi\)
\(110\) 1.26187 0.338116i 0.120314 0.0322381i
\(111\) 5.87651 5.87651i 0.557773 0.557773i
\(112\) 1.01403 0.583634i 0.0958164 0.0551482i
\(113\) 5.21100 0.490210 0.245105 0.969497i \(-0.421178\pi\)
0.245105 + 0.969497i \(0.421178\pi\)
\(114\) −3.79226 2.18946i −0.355177 0.205062i
\(115\) −15.8265 4.24070i −1.47583 0.395448i
\(116\) 1.89814 1.09589i 0.176238 0.101751i
\(117\) 11.2929 + 18.6492i 1.04403 + 1.72412i
\(118\) 2.04552i 0.188305i
\(119\) 0.00430968 3.21011i 0.000395068 0.294270i
\(120\) 25.7518 2.35081
\(121\) 9.30231 + 5.37069i 0.845665 + 0.488245i
\(122\) −2.22076 + 8.28799i −0.201058 + 0.750359i
\(123\) 22.8292 + 6.11706i 2.05844 + 0.551557i
\(124\) 1.30115 + 4.85595i 0.116846 + 0.436077i
\(125\) −0.240960 + 0.240960i −0.0215521 + 0.0215521i
\(126\) −9.22748 9.25229i −0.822050 0.824260i
\(127\) 11.4359i 1.01477i −0.861720 0.507384i \(-0.830613\pi\)
0.861720 0.507384i \(-0.169387\pi\)
\(128\) −8.17223 + 2.18974i −0.722330 + 0.193548i
\(129\) −11.2265 19.4449i −0.988441 1.71203i
\(130\) 9.26022 0.193447i 0.812175 0.0169664i
\(131\) 6.07972 + 3.51013i 0.531188 + 0.306681i 0.741500 0.670953i \(-0.234115\pi\)
−0.210312 + 0.977634i \(0.567448\pi\)
\(132\) −1.44158 1.44158i −0.125474 0.125474i
\(133\) −4.55351 1.22666i −0.394840 0.106365i
\(134\) 6.04719i 0.522398i
\(135\) 7.45961 + 27.8397i 0.642021 + 2.39606i
\(136\) −0.854858 + 3.19037i −0.0733034 + 0.273572i
\(137\) 1.60979 6.00784i 0.137534 0.513284i −0.862441 0.506158i \(-0.831065\pi\)
0.999975 0.00712570i \(-0.00226820\pi\)
\(138\) −3.31253 12.3625i −0.281981 1.05237i
\(139\) 1.91666i 0.162569i 0.996691 + 0.0812847i \(0.0259023\pi\)
−0.996691 + 0.0812847i \(0.974098\pi\)
\(140\) 10.7168 2.85615i 0.905737 0.241389i
\(141\) 10.4259 + 10.4259i 0.878015 + 0.878015i
\(142\) −0.840691 0.485373i −0.0705493 0.0407316i
\(143\) −1.32332 1.26917i −0.110662 0.106133i
\(144\) −1.33698 2.31572i −0.111415 0.192977i
\(145\) 4.99565 1.33858i 0.414866 0.111163i
\(146\) 1.99662i 0.165242i
\(147\) −18.2054 10.5762i −1.50156 0.872307i
\(148\) −2.60409 + 2.60409i −0.214055 + 0.214055i
\(149\) 0.289039 + 1.07871i 0.0236790 + 0.0883711i 0.976754 0.214363i \(-0.0687674\pi\)
−0.953075 + 0.302734i \(0.902101\pi\)
\(150\) 11.6080 + 3.11034i 0.947786 + 0.253958i
\(151\) −3.41102 + 12.7301i −0.277585 + 1.03596i 0.676505 + 0.736438i \(0.263494\pi\)
−0.954089 + 0.299522i \(0.903173\pi\)
\(152\) 4.20211 + 2.42609i 0.340836 + 0.196782i
\(153\) −7.33659 −0.593128
\(154\) 0.950993 + 0.550760i 0.0766332 + 0.0443815i
\(155\) 11.8626i 0.952831i
\(156\) −7.48709 12.3642i −0.599447 0.989932i
\(157\) 12.0413 6.95203i 0.960998 0.554833i 0.0645182 0.997917i \(-0.479449\pi\)
0.896480 + 0.443084i \(0.146116\pi\)
\(158\) −9.79209 2.62378i −0.779017 0.208737i
\(159\) −22.4526 12.9630i −1.78061 1.02803i
\(160\) −18.2594 −1.44353
\(161\) −6.87567 11.9460i −0.541879 0.941478i
\(162\) −5.44236 + 5.44236i −0.427592 + 0.427592i
\(163\) 7.90791 2.11892i 0.619396 0.165967i 0.0645426 0.997915i \(-0.479441\pi\)
0.554853 + 0.831948i \(0.312774\pi\)
\(164\) −10.1164 2.71069i −0.789959 0.211669i
\(165\) −2.40534 4.16617i −0.187255 0.324336i
\(166\) −4.22467 + 7.31734i −0.327898 + 0.567936i
\(167\) 1.97146 1.97146i 0.152556 0.152556i −0.626702 0.779259i \(-0.715596\pi\)
0.779259 + 0.626702i \(0.215596\pi\)
\(168\) 15.2976 + 15.3387i 1.18024 + 1.18341i
\(169\) −6.96450 10.9771i −0.535731 0.844389i
\(170\) −1.55842 + 2.69927i −0.119526 + 0.207024i
\(171\) −2.78952 + 10.4106i −0.213320 + 0.796121i
\(172\) 4.97487 + 8.61674i 0.379331 + 0.657020i
\(173\) 0.901884 1.56211i 0.0685690 0.118765i −0.829703 0.558206i \(-0.811490\pi\)
0.898272 + 0.439441i \(0.144823\pi\)
\(174\) 2.85664 + 2.85664i 0.216561 + 0.216561i
\(175\) 12.9421 + 0.0173752i 0.978329 + 0.00131344i
\(176\) 0.159017 + 0.159017i 0.0119863 + 0.0119863i
\(177\) 7.27586 1.94956i 0.546887 0.146538i
\(178\) 6.90361 3.98580i 0.517447 0.298748i
\(179\) 14.8199 8.55629i 1.10769 0.639527i 0.169462 0.985537i \(-0.445797\pi\)
0.938231 + 0.346010i \(0.112464\pi\)
\(180\) −6.56050 24.4841i −0.488991 1.82494i
\(181\) 23.4682 1.74438 0.872190 0.489168i \(-0.162699\pi\)
0.872190 + 0.489168i \(0.162699\pi\)
\(182\) 5.61617 + 5.40082i 0.416298 + 0.400335i
\(183\) 31.5967 2.33570
\(184\) 3.67054 + 13.6986i 0.270596 + 1.00988i
\(185\) −7.52580 + 4.34502i −0.553308 + 0.319452i
\(186\) −8.02480 + 4.63312i −0.588407 + 0.339717i
\(187\) 0.595991 0.159695i 0.0435832 0.0116781i
\(188\) −4.62006 4.62006i −0.336953 0.336953i
\(189\) −12.1510 + 20.9811i −0.883857 + 1.52615i
\(190\) 3.23772 + 3.23772i 0.234889 + 0.234889i
\(191\) −12.6234 + 21.8644i −0.913400 + 1.58206i −0.104173 + 0.994559i \(0.533220\pi\)
−0.809227 + 0.587496i \(0.800114\pi\)
\(192\) −5.80139 10.0483i −0.418679 0.725174i
\(193\) 1.38209 5.15802i 0.0994848 0.371282i −0.898176 0.439635i \(-0.855108\pi\)
0.997661 + 0.0683529i \(0.0217744\pi\)
\(194\) −1.69330 + 2.93289i −0.121572 + 0.210569i
\(195\) −9.51389 32.7540i −0.681304 2.34556i
\(196\) 8.06745 + 4.68667i 0.576247 + 0.334762i
\(197\) −10.7141 + 10.7141i −0.763345 + 0.763345i −0.976926 0.213580i \(-0.931487\pi\)
0.213580 + 0.976926i \(0.431487\pi\)
\(198\) 1.25582 2.17515i 0.0892474 0.154581i
\(199\) −3.59015 6.21832i −0.254499 0.440805i 0.710260 0.703939i \(-0.248577\pi\)
−0.964759 + 0.263134i \(0.915244\pi\)
\(200\) −12.8625 3.44650i −0.909517 0.243704i
\(201\) −21.5097 + 5.76350i −1.51718 + 0.406526i
\(202\) 8.92426 8.92426i 0.627909 0.627909i
\(203\) 3.76493 + 2.18043i 0.264246 + 0.153036i
\(204\) 4.86408 0.340554
\(205\) −21.4025 12.3568i −1.49482 0.863033i
\(206\) −13.8072 3.69964i −0.961995 0.257766i
\(207\) −27.2810 + 15.7507i −1.89616 + 1.09475i
\(208\) 0.825879 + 1.36386i 0.0572644 + 0.0945669i
\(209\) 0.906432i 0.0626992i
\(210\) 10.1976 + 17.7177i 0.703702 + 1.22264i
\(211\) −2.72556 −0.187636 −0.0938178 0.995589i \(-0.529907\pi\)
−0.0938178 + 0.995589i \(0.529907\pi\)
\(212\) 9.94953 + 5.74437i 0.683337 + 0.394525i
\(213\) −0.925207 + 3.45292i −0.0633941 + 0.236590i
\(214\) 1.67587 + 0.449049i 0.114560 + 0.0306964i
\(215\) 6.07659 + 22.6781i 0.414420 + 1.54664i
\(216\) 17.6399 17.6399i 1.20025 1.20025i
\(217\) −7.06584 + 7.04689i −0.479660 + 0.478374i
\(218\) 8.74709i 0.592428i
\(219\) −7.10192 + 1.90296i −0.479904 + 0.128590i
\(220\) 1.06589 + 1.84618i 0.0718623 + 0.124469i
\(221\) 4.37369 0.0913669i 0.294206 0.00614601i
\(222\) −5.87861 3.39402i −0.394547 0.227792i
\(223\) −15.3311 15.3311i −1.02665 1.02665i −0.999635 0.0270132i \(-0.991400\pi\)
−0.0270132 0.999635i \(-0.508600\pi\)
\(224\) −10.8468 10.8760i −0.724735 0.726683i
\(225\) 29.5787i 1.97191i
\(226\) −1.10161 4.11126i −0.0732779 0.273477i
\(227\) −4.68443 + 17.4825i −0.310916 + 1.16036i 0.616815 + 0.787108i \(0.288423\pi\)
−0.927732 + 0.373248i \(0.878244\pi\)
\(228\) 1.84942 6.90214i 0.122481 0.457105i
\(229\) 1.11881 + 4.17546i 0.0739331 + 0.275922i 0.992989 0.118205i \(-0.0377138\pi\)
−0.919056 + 0.394126i \(0.871047\pi\)
\(230\) 13.3829i 0.882445i
\(231\) 1.05266 3.90758i 0.0692598 0.257100i
\(232\) −3.16538 3.16538i −0.207817 0.207817i
\(233\) 8.56327 + 4.94400i 0.560998 + 0.323892i 0.753546 0.657395i \(-0.228342\pi\)
−0.192548 + 0.981288i \(0.561675\pi\)
\(234\) 12.3261 12.8521i 0.805784 0.840168i
\(235\) −7.70876 13.3520i −0.502864 0.870986i
\(236\) −3.22419 + 0.863919i −0.209877 + 0.0562363i
\(237\) 37.3309i 2.42490i
\(238\) −2.53355 + 0.675219i −0.164226 + 0.0437679i
\(239\) −8.13735 + 8.13735i −0.526361 + 0.526361i −0.919485 0.393124i \(-0.871394\pi\)
0.393124 + 0.919485i \(0.371394\pi\)
\(240\) 1.08271 + 4.04071i 0.0698883 + 0.260827i
\(241\) 14.0777 + 3.77210i 0.906822 + 0.242982i 0.681944 0.731405i \(-0.261135\pi\)
0.224878 + 0.974387i \(0.427802\pi\)
\(242\) 2.27074 8.47450i 0.145968 0.544762i
\(243\) 0.736584 + 0.425267i 0.0472519 + 0.0272809i
\(244\) −14.0016 −0.896362
\(245\) 15.5256 + 15.6092i 0.991894 + 0.997235i
\(246\) 19.3044i 1.23080i
\(247\) 1.53332 6.24101i 0.0975626 0.397106i
\(248\) 8.89210 5.13386i 0.564649 0.326000i
\(249\) 30.0540 + 8.05296i 1.90460 + 0.510335i
\(250\) 0.241046 + 0.139168i 0.0152451 + 0.00880177i
\(251\) 2.29786 0.145040 0.0725198 0.997367i \(-0.476896\pi\)
0.0725198 + 0.997367i \(0.476896\pi\)
\(252\) 10.6865 18.4522i 0.673183 1.16238i
\(253\) 1.87334 1.87334i 0.117776 0.117776i
\(254\) −9.02241 + 2.41755i −0.566116 + 0.151690i
\(255\) 11.0865 + 2.97063i 0.694266 + 0.186028i
\(256\) 7.31281 + 12.6662i 0.457051 + 0.791635i
\(257\) 9.02516 15.6320i 0.562974 0.975100i −0.434261 0.900787i \(-0.642990\pi\)
0.997235 0.0743128i \(-0.0236763\pi\)
\(258\) −12.9679 + 12.9679i −0.807348 + 0.807348i
\(259\) −7.05869 1.90153i −0.438605 0.118155i
\(260\) 4.21594 + 14.5144i 0.261462 + 0.900148i
\(261\) 4.97173 8.61128i 0.307742 0.533025i
\(262\) 1.48409 5.53869i 0.0916872 0.342181i
\(263\) −3.98168 6.89647i −0.245521 0.425255i 0.716757 0.697323i \(-0.245626\pi\)
−0.962278 + 0.272068i \(0.912292\pi\)
\(264\) −2.08194 + 3.60603i −0.128135 + 0.221936i
\(265\) 19.1694 + 19.1694i 1.17757 + 1.17757i
\(266\) −0.00517124 + 3.85185i −0.000317069 + 0.236172i
\(267\) −20.7571 20.7571i −1.27032 1.27032i
\(268\) 9.53170 2.55401i 0.582241 0.156011i
\(269\) 6.97055 4.02445i 0.425002 0.245375i −0.272213 0.962237i \(-0.587756\pi\)
0.697215 + 0.716862i \(0.254422\pi\)
\(270\) 20.3873 11.7706i 1.24073 0.716338i
\(271\) 5.74808 + 21.4521i 0.349171 + 1.30312i 0.887663 + 0.460494i \(0.152328\pi\)
−0.538492 + 0.842631i \(0.681006\pi\)
\(272\) −0.536543 −0.0325327
\(273\) 13.8579 25.1240i 0.838716 1.52057i
\(274\) −5.08024 −0.306909
\(275\) 0.643838 + 2.40284i 0.0388249 + 0.144897i
\(276\) 18.0870 10.4426i 1.08871 0.628568i
\(277\) −1.27323 + 0.735098i −0.0765008 + 0.0441678i −0.537762 0.843096i \(-0.680730\pi\)
0.461262 + 0.887264i \(0.347397\pi\)
\(278\) 1.51217 0.405184i 0.0906938 0.0243013i
\(279\) 16.1271 + 16.1271i 0.965502 + 0.965502i
\(280\) −11.2997 19.6325i −0.675289 1.17327i
\(281\) −13.2274 13.2274i −0.789081 0.789081i 0.192263 0.981343i \(-0.438417\pi\)
−0.981343 + 0.192263i \(0.938417\pi\)
\(282\) 6.02153 10.4296i 0.358577 0.621073i
\(283\) 2.39327 + 4.14527i 0.142265 + 0.246411i 0.928349 0.371709i \(-0.121228\pi\)
−0.786084 + 0.618120i \(0.787895\pi\)
\(284\) 0.409992 1.53011i 0.0243285 0.0907954i
\(285\) 8.43066 14.6023i 0.499389 0.864967i
\(286\) −0.721567 + 1.31235i −0.0426671 + 0.0776008i
\(287\) −5.35381 20.0885i −0.316026 1.18579i
\(288\) −24.8234 + 24.8234i −1.46273 + 1.46273i
\(289\) 7.76394 13.4475i 0.456702 0.791032i
\(290\) −2.11217 3.65838i −0.124031 0.214828i
\(291\) 12.0461 + 3.22773i 0.706153 + 0.189213i
\(292\) 3.14711 0.843267i 0.184171 0.0493484i
\(293\) −15.3136 + 15.3136i −0.894628 + 0.894628i −0.994955 0.100326i \(-0.968011\pi\)
0.100326 + 0.994955i \(0.468011\pi\)
\(294\) −4.49552 + 16.5991i −0.262184 + 0.968079i
\(295\) −7.87640 −0.458582
\(296\) 6.51395 + 3.76083i 0.378616 + 0.218594i
\(297\) −4.50147 1.20617i −0.261202 0.0699888i
\(298\) 0.789951 0.456079i 0.0457607 0.0264199i
\(299\) 16.0674 9.72950i 0.929200 0.562672i
\(300\) 19.6103i 1.13220i
\(301\) −9.89820 + 17.0912i −0.570523 + 0.985118i
\(302\) 10.7646 0.619433
\(303\) −40.2489 23.2377i −2.31224 1.33497i
\(304\) −0.204004 + 0.761355i −0.0117005 + 0.0436667i
\(305\) −31.9134 8.55118i −1.82736 0.489639i
\(306\) 1.55096 + 5.78826i 0.0886624 + 0.330893i
\(307\) 9.36619 9.36619i 0.534556 0.534556i −0.387369 0.921925i \(-0.626616\pi\)
0.921925 + 0.387369i \(0.126616\pi\)
\(308\) −0.466470 + 1.73159i −0.0265796 + 0.0986663i
\(309\) 52.6380i 2.99447i
\(310\) 9.35913 2.50777i 0.531563 0.142432i
\(311\) −2.71082 4.69528i −0.153716 0.266245i 0.778874 0.627180i \(-0.215791\pi\)
−0.932591 + 0.360935i \(0.882458\pi\)
\(312\) −20.4346 + 21.3066i −1.15688 + 1.20625i
\(313\) −18.2670 10.5464i −1.03251 0.596120i −0.114807 0.993388i \(-0.536625\pi\)
−0.917703 + 0.397268i \(0.869958\pi\)
\(314\) −8.03039 8.03039i −0.453181 0.453181i
\(315\) 35.6266 35.5310i 2.00733 2.00195i
\(316\) 16.5426i 0.930596i
\(317\) −3.98815 14.8840i −0.223997 0.835968i −0.982804 0.184652i \(-0.940884\pi\)
0.758807 0.651316i \(-0.225783\pi\)
\(318\) −5.48077 + 20.4545i −0.307347 + 1.14703i
\(319\) −0.216439 + 0.807761i −0.0121183 + 0.0452259i
\(320\) 3.14012 + 11.7191i 0.175538 + 0.655117i
\(321\) 6.38902i 0.356600i
\(322\) −7.97138 + 7.95001i −0.444228 + 0.443036i
\(323\) 1.52921 + 1.52921i 0.0850874 + 0.0850874i
\(324\) −10.8769 6.27980i −0.604274 0.348878i
\(325\) 0.368361 + 17.6333i 0.0204330 + 0.978117i
\(326\) −3.34348 5.79107i −0.185178 0.320738i
\(327\) 31.1131 8.33674i 1.72056 0.461023i
\(328\) 21.3908i 1.18111i
\(329\) 3.37361 12.5232i 0.185993 0.690428i
\(330\) −2.77844 + 2.77844i −0.152948 + 0.152948i
\(331\) −2.44797 9.13594i −0.134552 0.502156i −0.999999 0.00115583i \(-0.999632\pi\)
0.865447 0.501001i \(-0.167035\pi\)
\(332\) −13.3180 3.56855i −0.730921 0.195850i
\(333\) −4.32421 + 16.1382i −0.236965 + 0.884367i
\(334\) −1.97217 1.13863i −0.107912 0.0623031i
\(335\) 23.2851 1.27220
\(336\) −1.76363 + 3.04525i −0.0962138 + 0.166132i
\(337\) 30.8890i 1.68263i 0.540545 + 0.841315i \(0.318218\pi\)
−0.540545 + 0.841315i \(0.681782\pi\)
\(338\) −7.18813 + 7.81525i −0.390983 + 0.425094i
\(339\) −13.5737 + 7.83678i −0.737222 + 0.425636i
\(340\) −4.91284 1.31639i −0.266436 0.0713913i
\(341\) −1.66113 0.959052i −0.0899551 0.0519356i
\(342\) 8.80326 0.476026
\(343\) −0.0745920 + 18.5201i −0.00402759 + 0.999992i
\(344\) 14.3695 14.3695i 0.774750 0.774750i
\(345\) 47.6028 12.7551i 2.56285 0.686713i
\(346\) −1.42310 0.381318i −0.0765062 0.0204998i
\(347\) −5.48714 9.50400i −0.294565 0.510201i 0.680319 0.732916i \(-0.261841\pi\)
−0.974884 + 0.222715i \(0.928508\pi\)
\(348\) −3.29620 + 5.70919i −0.176695 + 0.306045i
\(349\) −14.1593 + 14.1593i −0.757930 + 0.757930i −0.975945 0.218015i \(-0.930042\pi\)
0.218015 + 0.975945i \(0.430042\pi\)
\(350\) −2.72226 10.2144i −0.145511 0.545984i
\(351\) −28.9534 15.9194i −1.54542 0.849716i
\(352\) 1.47621 2.55687i 0.0786822 0.136282i
\(353\) 4.93709 18.4255i 0.262775 0.980688i −0.700824 0.713334i \(-0.747184\pi\)
0.963598 0.267354i \(-0.0861493\pi\)
\(354\) −3.07624 5.32820i −0.163500 0.283191i
\(355\) 1.86896 3.23714i 0.0991942 0.171809i
\(356\) 9.19822 + 9.19822i 0.487504 + 0.487504i
\(357\) 4.81643 + 8.36823i 0.254913 + 0.442894i
\(358\) −9.88349 9.88349i −0.522359 0.522359i
\(359\) 27.0728 7.25413i 1.42885 0.382858i 0.540233 0.841515i \(-0.318336\pi\)
0.888613 + 0.458657i \(0.151669\pi\)
\(360\) −44.8347 + 25.8853i −2.36300 + 1.36428i
\(361\) −13.7031 + 7.91149i −0.721216 + 0.416394i
\(362\) −4.96120 18.5154i −0.260755 0.973150i
\(363\) −32.3078 −1.69572
\(364\) −6.14091 + 11.1333i −0.321871 + 0.583545i
\(365\) 7.68812 0.402414
\(366\) −6.67957 24.9285i −0.349147 1.30303i
\(367\) 14.4837 8.36218i 0.756044 0.436502i −0.0718297 0.997417i \(-0.522884\pi\)
0.827874 + 0.560915i \(0.189550\pi\)
\(368\) −1.99513 + 1.15189i −0.104003 + 0.0600463i
\(369\) −45.8951 + 12.2976i −2.38921 + 0.640186i
\(370\) 5.01900 + 5.01900i 0.260925 + 0.260925i
\(371\) −0.0306170 + 22.8054i −0.00158956 + 1.18400i
\(372\) −10.6921 10.6921i −0.554358 0.554358i
\(373\) −8.19490 + 14.1940i −0.424316 + 0.734937i −0.996356 0.0852887i \(-0.972819\pi\)
0.572040 + 0.820226i \(0.306152\pi\)
\(374\) −0.251986 0.436452i −0.0130299 0.0225684i
\(375\) 0.265279 0.990035i 0.0136990 0.0511252i
\(376\) −6.67231 + 11.5568i −0.344098 + 0.595996i
\(377\) −2.85664 + 5.19551i −0.147125 + 0.267582i
\(378\) 19.1219 + 5.15123i 0.983526 + 0.264951i
\(379\) 2.80924 2.80924i 0.144301 0.144301i −0.631266 0.775567i \(-0.717464\pi\)
0.775567 + 0.631266i \(0.217464\pi\)
\(380\) −3.73592 + 6.47081i −0.191649 + 0.331945i
\(381\) 17.1983 + 29.7883i 0.881095 + 1.52610i
\(382\) 19.9187 + 5.33721i 1.01913 + 0.273075i
\(383\) 37.4573 10.0367i 1.91398 0.512849i 0.921867 0.387508i \(-0.126664\pi\)
0.992114 0.125342i \(-0.0400028\pi\)
\(384\) 17.9940 17.9940i 0.918255 0.918255i
\(385\) −2.12074 + 3.66186i −0.108083 + 0.186626i
\(386\) −4.36163 −0.222001
\(387\) 39.0915 + 22.5695i 1.98713 + 1.14727i
\(388\) −5.33804 1.43032i −0.270998 0.0726137i
\(389\) 4.22632 2.44006i 0.214283 0.123716i −0.389017 0.921230i \(-0.627185\pi\)
0.603300 + 0.797514i \(0.293852\pi\)
\(390\) −23.8303 + 14.4303i −1.20669 + 0.730705i
\(391\) 6.32089i 0.319661i
\(392\) 4.98138 18.3931i 0.251598 0.928990i
\(393\) −21.1154 −1.06513
\(394\) 10.7179 + 6.18798i 0.539960 + 0.311746i
\(395\) 10.1030 37.7051i 0.508339 1.89715i
\(396\) 3.95890 + 1.06079i 0.198942 + 0.0533065i
\(397\) −8.19329 30.5778i −0.411210 1.53466i −0.792308 0.610121i \(-0.791121\pi\)
0.381099 0.924534i \(-0.375546\pi\)
\(398\) −4.14703 + 4.14703i −0.207872 + 0.207872i
\(399\) 13.7058 3.65275i 0.686150 0.182866i
\(400\) 2.16316i 0.108158i
\(401\) −9.34436 + 2.50381i −0.466635 + 0.125035i −0.484473 0.874806i \(-0.660989\pi\)
0.0178375 + 0.999841i \(0.494322\pi\)
\(402\) 9.09432 + 15.7518i 0.453583 + 0.785630i
\(403\) −9.81495 9.41327i −0.488918 0.468908i
\(404\) 17.8357 + 10.2975i 0.887361 + 0.512318i
\(405\) −20.9562 20.9562i −1.04132 1.04132i
\(406\) 0.924356 3.43131i 0.0458750 0.170293i
\(407\) 1.40512i 0.0696491i
\(408\) −2.57123 9.59595i −0.127295 0.475070i
\(409\) 3.09562 11.5530i 0.153068 0.571259i −0.846195 0.532874i \(-0.821112\pi\)
0.999263 0.0383851i \(-0.0122214\pi\)
\(410\) −5.22445 + 19.4979i −0.258017 + 0.962933i
\(411\) 4.84191 + 18.0703i 0.238834 + 0.891341i
\(412\) 23.3258i 1.14918i
\(413\) −4.67890 4.69148i −0.230234 0.230853i
\(414\) 18.1939 + 18.1939i 0.894180 + 0.894180i
\(415\) −28.1759 16.2674i −1.38310 0.798533i
\(416\) 14.4893 15.1075i 0.710394 0.740708i
\(417\) −2.88246 4.99256i −0.141155 0.244487i
\(418\) −0.715137 + 0.191620i −0.0349785 + 0.00937246i
\(419\) 18.5355i 0.905516i −0.891633 0.452758i \(-0.850440\pi\)
0.891633 0.452758i \(-0.149560\pi\)
\(420\) −23.6200 + 23.5567i −1.15254 + 1.14945i
\(421\) 19.2884 19.2884i 0.940060 0.940060i −0.0582422 0.998302i \(-0.518550\pi\)
0.998302 + 0.0582422i \(0.0185496\pi\)
\(422\) 0.576186 + 2.15036i 0.0280483 + 0.104678i
\(423\) −28.6317 7.67184i −1.39212 0.373017i
\(424\) 6.07312 22.6652i 0.294937 1.10072i
\(425\) −5.13993 2.96754i −0.249323 0.143947i
\(426\) 2.91980 0.141465
\(427\) −13.8645 24.0886i −0.670948 1.16573i
\(428\) 2.83120i 0.136851i
\(429\) 5.35570 + 1.31581i 0.258576 + 0.0635279i
\(430\) 16.6075 9.58834i 0.800884 0.462391i
\(431\) 8.84924 + 2.37115i 0.426253 + 0.114214i 0.465567 0.885013i \(-0.345851\pi\)
−0.0393138 + 0.999227i \(0.512517\pi\)
\(432\) 3.50953 + 2.02623i 0.168852 + 0.0974870i
\(433\) 23.6700 1.13751 0.568755 0.822507i \(-0.307425\pi\)
0.568755 + 0.822507i \(0.307425\pi\)
\(434\) 7.05342 + 4.08493i 0.338575 + 0.196083i
\(435\) −10.9997 + 10.9997i −0.527394 + 0.527394i
\(436\) −13.7873 + 3.69431i −0.660294 + 0.176925i
\(437\) 8.96936 + 2.40333i 0.429063 + 0.114967i
\(438\) 3.00270 + 5.20083i 0.143475 + 0.248505i
\(439\) −5.64906 + 9.78446i −0.269615 + 0.466987i −0.968762 0.247991i \(-0.920230\pi\)
0.699148 + 0.714977i \(0.253563\pi\)
\(440\) 3.07872 3.07872i 0.146772 0.146772i
\(441\) 42.3272 + 0.113652i 2.01558 + 0.00541198i
\(442\) −0.996685 3.43134i −0.0474075 0.163212i
\(443\) −19.5144 + 33.7999i −0.927157 + 1.60588i −0.139103 + 0.990278i \(0.544422\pi\)
−0.788054 + 0.615606i \(0.788911\pi\)
\(444\) 2.86691 10.6994i 0.136057 0.507773i
\(445\) 15.3476 + 26.5828i 0.727545 + 1.26015i
\(446\) −8.85460 + 15.3366i −0.419278 + 0.726210i
\(447\) −2.37515 2.37515i −0.112341 0.112341i
\(448\) −5.11497 + 8.83198i −0.241659 + 0.417272i
\(449\) −8.82288 8.82288i −0.416378 0.416378i 0.467576 0.883953i \(-0.345128\pi\)
−0.883953 + 0.467576i \(0.845128\pi\)
\(450\) −23.3363 + 6.25295i −1.10008 + 0.294767i
\(451\) 3.46063 1.99800i 0.162955 0.0940820i
\(452\) 6.01499 3.47276i 0.282921 0.163345i
\(453\) −10.2596 38.2894i −0.482038 1.79899i
\(454\) 14.7833 0.693813
\(455\) −20.7962 + 21.6254i −0.974941 + 1.01381i
\(456\) −14.5943 −0.683441
\(457\) 5.91700 + 22.0825i 0.276786 + 1.03298i 0.954635 + 0.297777i \(0.0962453\pi\)
−0.677850 + 0.735200i \(0.737088\pi\)
\(458\) 3.05774 1.76539i 0.142879 0.0824912i
\(459\) 9.62914 5.55938i 0.449450 0.259490i
\(460\) −21.0945 + 5.65224i −0.983534 + 0.263537i
\(461\) −7.67189 7.67189i −0.357316 0.357316i 0.505507 0.862823i \(-0.331306\pi\)
−0.862823 + 0.505507i \(0.831306\pi\)
\(462\) −3.30545 0.00443768i −0.153783 0.000206459i
\(463\) 14.0571 + 14.0571i 0.653289 + 0.653289i 0.953783 0.300495i \(-0.0971518\pi\)
−0.300495 + 0.953783i \(0.597152\pi\)
\(464\) 0.363594 0.629764i 0.0168794 0.0292361i
\(465\) −17.8401 30.9000i −0.827317 1.43295i
\(466\) 2.09033 7.80122i 0.0968327 0.361385i
\(467\) 4.96276 8.59575i 0.229649 0.397764i −0.728055 0.685519i \(-0.759576\pi\)
0.957704 + 0.287755i \(0.0929088\pi\)
\(468\) 25.4636 + 14.0006i 1.17706 + 0.647180i
\(469\) 13.8323 + 13.8695i 0.638715 + 0.640433i
\(470\) −8.90450 + 8.90450i −0.410734 + 0.410734i
\(471\) −20.9102 + 36.2176i −0.963492 + 1.66882i
\(472\) 3.40871 + 5.90406i 0.156899 + 0.271756i
\(473\) −3.66689 0.982540i −0.168604 0.0451772i
\(474\) 29.4525 7.89177i 1.35280 0.362481i
\(475\) −6.16525 + 6.16525i −0.282881 + 0.282881i
\(476\) −2.13433 3.70826i −0.0978269 0.169968i
\(477\) 52.1209 2.38645
\(478\) 8.14026 + 4.69978i 0.372327 + 0.214963i
\(479\) 20.3767 + 5.45991i 0.931034 + 0.249470i 0.692295 0.721614i \(-0.256600\pi\)
0.238738 + 0.971084i \(0.423266\pi\)
\(480\) 47.5625 27.4602i 2.17092 1.25338i
\(481\) 2.37689 9.67459i 0.108377 0.441123i
\(482\) 11.9041i 0.542217i
\(483\) 35.8754 + 20.7769i 1.63239 + 0.945383i
\(484\) 14.3167 0.650760
\(485\) −11.2933 6.52018i −0.512801 0.296066i
\(486\) 0.179803 0.671035i 0.00815605 0.0304388i
\(487\) −42.3475 11.3470i −1.91895 0.514181i −0.989338 0.145637i \(-0.953477\pi\)
−0.929610 0.368544i \(-0.879856\pi\)
\(488\) 7.40147 + 27.6227i 0.335049 + 1.25042i
\(489\) −17.4120 + 17.4120i −0.787400 + 0.787400i
\(490\) 9.03287 15.5488i 0.408064 0.702424i
\(491\) 37.1276i 1.67554i −0.546021 0.837772i \(-0.683858\pi\)
0.546021 0.837772i \(-0.316142\pi\)
\(492\) 30.4280 8.15316i 1.37180 0.367573i
\(493\) −0.997597 1.72789i −0.0449295 0.0778202i
\(494\) −5.24804 + 0.109632i −0.236121 + 0.00493259i
\(495\) 8.37555 + 4.83562i 0.376453 + 0.217345i
\(496\) 1.17941 + 1.17941i 0.0529571 + 0.0529571i
\(497\) 3.03840 0.809766i 0.136291 0.0363230i
\(498\) 25.4138i 1.13882i
\(499\) −1.38618 5.17328i −0.0620538 0.231588i 0.927933 0.372747i \(-0.121584\pi\)
−0.989987 + 0.141159i \(0.954917\pi\)
\(500\) −0.117555 + 0.438720i −0.00525720 + 0.0196201i
\(501\) −2.17043 + 8.10016i −0.0969677 + 0.361888i
\(502\) −0.485769 1.81292i −0.0216809 0.0809144i
\(503\) 27.7355i 1.23666i 0.785917 + 0.618332i \(0.212191\pi\)
−0.785917 + 0.618332i \(0.787809\pi\)
\(504\) −42.0519 11.3283i −1.87314 0.504603i
\(505\) 34.3634 + 34.3634i 1.52915 + 1.52915i
\(506\) −1.87401 1.08196i −0.0833101 0.0480991i
\(507\) 34.6496 + 18.1194i 1.53884 + 0.804709i
\(508\) −7.62117 13.2003i −0.338135 0.585667i
\(509\) −29.2382 + 7.83435i −1.29596 + 0.347252i −0.839921 0.542708i \(-0.817399\pi\)
−0.456039 + 0.889960i \(0.650732\pi\)
\(510\) 9.37480i 0.415123i
\(511\) 4.56705 + 4.57933i 0.202034 + 0.202578i
\(512\) −3.51784 + 3.51784i −0.155468 + 0.155468i
\(513\) −4.22758 15.7776i −0.186652 0.696596i
\(514\) −14.2409 3.81585i −0.628141 0.168310i
\(515\) 14.2457 53.1656i 0.627740 2.34276i
\(516\) −25.9173 14.9633i −1.14094 0.658725i
\(517\) 2.49290 0.109638
\(518\) −0.00801626 + 5.97099i −0.000352214 + 0.262350i
\(519\) 5.42535i 0.238146i
\(520\) 26.4058 15.9898i 1.15797 0.701201i
\(521\) −36.7196 + 21.2001i −1.60872 + 0.928792i −0.619057 + 0.785346i \(0.712485\pi\)
−0.989658 + 0.143446i \(0.954182\pi\)
\(522\) −7.84496 2.10205i −0.343365 0.0920043i
\(523\) −3.60227 2.07977i −0.157516 0.0909420i 0.419170 0.907908i \(-0.362321\pi\)
−0.576686 + 0.816966i \(0.695654\pi\)
\(524\) 9.35699 0.408762
\(525\) −33.7379 + 19.4182i −1.47244 + 0.847481i
\(526\) −4.59929 + 4.59929i −0.200539 + 0.200539i
\(527\) 4.42040 1.18444i 0.192556 0.0515952i
\(528\) −0.653354 0.175066i −0.0284336 0.00761876i
\(529\) 2.07015 + 3.58560i 0.0900064 + 0.155896i
\(530\) 11.0714 19.1763i 0.480912 0.832964i
\(531\) −10.7078 + 10.7078i −0.464681 + 0.464681i
\(532\) −6.07354 + 1.61866i −0.263321 + 0.0701780i
\(533\) 27.2071 7.90273i 1.17847 0.342305i
\(534\) −11.9884 + 20.7646i −0.518790 + 0.898571i
\(535\) −1.72909 + 6.45306i −0.0747552 + 0.278990i
\(536\) −10.0772 17.4542i −0.435269 0.753908i
\(537\) −25.7355 + 44.5751i −1.11057 + 1.92356i
\(538\) −4.64870 4.64870i −0.200420 0.200420i
\(539\) −3.44094 + 0.912103i −0.148212 + 0.0392870i
\(540\) 27.1636 + 27.1636i 1.16894 + 1.16894i
\(541\) −40.4410 + 10.8361i −1.73869 + 0.465882i −0.982156 0.188068i \(-0.939777\pi\)
−0.756538 + 0.653950i \(0.773111\pi\)
\(542\) 15.7097 9.06999i 0.674789 0.389589i
\(543\) −61.1304 + 35.2937i −2.62336 + 1.51460i
\(544\) 1.82314 + 6.80405i 0.0781665 + 0.291721i
\(545\) −33.6812 −1.44275
\(546\) −22.7513 5.62203i −0.973667 0.240601i
\(547\) −13.4403 −0.574667 −0.287334 0.957831i \(-0.592769\pi\)
−0.287334 + 0.957831i \(0.592769\pi\)
\(548\) −2.14562 8.00758i −0.0916565 0.342067i
\(549\) −55.0110 + 31.7606i −2.34781 + 1.35551i
\(550\) 1.75963 1.01592i 0.0750308 0.0433191i
\(551\) −2.83118 + 0.758614i −0.120613 + 0.0323180i
\(552\) −30.1624 30.1624i −1.28380 1.28380i
\(553\) 28.4602 16.3806i 1.21025 0.696573i
\(554\) 0.849123 + 0.849123i 0.0360758 + 0.0360758i
\(555\) 13.0689 22.6360i 0.554743 0.960844i
\(556\) 1.27732 + 2.21238i 0.0541704 + 0.0938258i
\(557\) 5.40317 20.1649i 0.228940 0.854415i −0.751848 0.659337i \(-0.770837\pi\)
0.980788 0.195078i \(-0.0624961\pi\)
\(558\) 9.31430 16.1328i 0.394306 0.682958i
\(559\) −23.5854 12.9679i −0.997556 0.548485i
\(560\) 2.60546 2.59847i 0.110101 0.109805i
\(561\) −1.31228 + 1.31228i −0.0554047 + 0.0554047i
\(562\) −7.63958 + 13.2321i −0.322256 + 0.558164i
\(563\) 13.5788 + 23.5192i 0.572278 + 0.991215i 0.996331 + 0.0855779i \(0.0272737\pi\)
−0.424053 + 0.905637i \(0.639393\pi\)
\(564\) 18.9825 + 5.08635i 0.799308 + 0.214174i
\(565\) 15.8307 4.24181i 0.666001 0.178454i
\(566\) 2.76450 2.76450i 0.116201 0.116201i
\(567\) 0.0334708 24.9311i 0.00140564 1.04701i
\(568\) −3.23536 −0.135753
\(569\) −10.6066 6.12370i −0.444650 0.256719i 0.260918 0.965361i \(-0.415975\pi\)
−0.705568 + 0.708642i \(0.749308\pi\)
\(570\) −13.3029 3.56449i −0.557196 0.149300i
\(571\) −4.06355 + 2.34609i −0.170054 + 0.0981809i −0.582611 0.812751i \(-0.697969\pi\)
0.412557 + 0.910932i \(0.364636\pi\)
\(572\) −2.37330 0.583082i −0.0992327 0.0243799i
\(573\) 75.9372i 3.17232i
\(574\) −14.7172 + 8.47066i −0.614285 + 0.353559i
\(575\) −25.4837 −1.06274
\(576\) 20.2008 + 11.6630i 0.841701 + 0.485956i
\(577\) −4.41741 + 16.4860i −0.183899 + 0.686321i 0.810964 + 0.585095i \(0.198943\pi\)
−0.994864 + 0.101225i \(0.967724\pi\)
\(578\) −12.2508 3.28260i −0.509568 0.136538i
\(579\) 4.15702 + 15.5142i 0.172760 + 0.644749i
\(580\) 4.87435 4.87435i 0.202396 0.202396i
\(581\) −7.04816 26.4461i −0.292407 1.09717i
\(582\) 10.1862i 0.422231i
\(583\) −4.23407 + 1.13452i −0.175357 + 0.0469868i
\(584\) −3.32722 5.76292i −0.137682 0.238471i
\(585\) 49.4878 + 47.4625i 2.04607 + 1.96233i
\(586\) 15.3191 + 8.84446i 0.632824 + 0.365361i
\(587\) −6.21734 6.21734i −0.256617 0.256617i 0.567060 0.823677i \(-0.308081\pi\)
−0.823677 + 0.567060i \(0.808081\pi\)
\(588\) −28.0625 0.0753499i −1.15728 0.00310738i
\(589\) 6.72291i 0.277013i
\(590\) 1.66508 + 6.21415i 0.0685501 + 0.255833i
\(591\) 11.7954 44.0210i 0.485197 1.81078i
\(592\) −0.316240 + 1.18022i −0.0129974 + 0.0485069i
\(593\) 10.0703 + 37.5829i 0.413538 + 1.54334i 0.787747 + 0.615999i \(0.211248\pi\)
−0.374209 + 0.927344i \(0.622086\pi\)
\(594\) 3.80645i 0.156181i
\(595\) −2.59997 9.75560i −0.106589 0.399941i
\(596\) 1.05251 + 1.05251i 0.0431127 + 0.0431127i
\(597\) 18.7034 + 10.7984i 0.765478 + 0.441949i
\(598\) −11.0728 10.6197i −0.452801 0.434270i
\(599\) 17.4902 + 30.2939i 0.714629 + 1.23777i 0.963103 + 0.269135i \(0.0867377\pi\)
−0.248474 + 0.968639i \(0.579929\pi\)
\(600\) 38.6876 10.3663i 1.57942 0.423203i
\(601\) 11.7882i 0.480852i 0.970667 + 0.240426i \(0.0772872\pi\)
−0.970667 + 0.240426i \(0.922713\pi\)
\(602\) 15.5767 + 4.19618i 0.634859 + 0.171024i
\(603\) 31.6557 31.6557i 1.28912 1.28912i
\(604\) 4.54639 + 16.9674i 0.184990 + 0.690393i
\(605\) 32.6316 + 8.74361i 1.32666 + 0.355478i
\(606\) −9.82494 + 36.6672i −0.399111 + 1.48950i
\(607\) 16.5407 + 9.54978i 0.671366 + 0.387614i 0.796594 0.604514i \(-0.206633\pi\)
−0.125228 + 0.992128i \(0.539966\pi\)
\(608\) 10.3482 0.419673
\(609\) −13.0861 0.0175685i −0.530274 0.000711912i
\(610\) 26.9861i 1.09263i
\(611\) 17.1643 + 4.21698i 0.694391 + 0.170601i
\(612\) −8.46853 + 4.88931i −0.342320 + 0.197638i
\(613\) 24.5517 + 6.57860i 0.991632 + 0.265707i 0.717936 0.696109i \(-0.245087\pi\)
0.273696 + 0.961816i \(0.411754\pi\)
\(614\) −9.36954 5.40951i −0.378124 0.218310i
\(615\) 74.3329 2.99739
\(616\) 3.66269 + 0.00491729i 0.147574 + 0.000198123i
\(617\) −10.4089 + 10.4089i −0.419046 + 0.419046i −0.884875 0.465829i \(-0.845756\pi\)
0.465829 + 0.884875i \(0.345756\pi\)
\(618\) 41.5292 11.1277i 1.67055 0.447622i
\(619\) −30.7106 8.22887i −1.23436 0.330746i −0.418085 0.908408i \(-0.637299\pi\)
−0.816276 + 0.577661i \(0.803965\pi\)
\(620\) 7.90560 + 13.6929i 0.317496 + 0.549920i
\(621\) 23.8706 41.3451i 0.957893 1.65912i
\(622\) −3.13131 + 3.13131i −0.125554 + 0.125554i
\(623\) −6.71662 + 24.9328i −0.269096 + 0.998913i
\(624\) −4.20237 2.31058i −0.168229 0.0924973i
\(625\) −12.7650 + 22.1096i −0.510600 + 0.884385i
\(626\) −4.45905 + 16.6414i −0.178219 + 0.665124i
\(627\) 1.36318 + 2.36109i 0.0544400 + 0.0942929i
\(628\) 9.26606 16.0493i 0.369756 0.640436i
\(629\) 2.37052 + 2.37052i 0.0945188 + 0.0945188i
\(630\) −35.5639 20.5966i −1.41690 0.820587i
\(631\) 26.3103 + 26.3103i 1.04739 + 1.04739i 0.998820 + 0.0485754i \(0.0154681\pi\)
0.0485754 + 0.998820i \(0.484532\pi\)
\(632\) −32.6356 + 8.74469i −1.29817 + 0.347845i
\(633\) 7.09960 4.09896i 0.282184 0.162919i
\(634\) −10.8997 + 6.29297i −0.432884 + 0.249926i
\(635\) −9.30892 34.7414i −0.369413 1.37867i
\(636\) −34.5556 −1.37022
\(637\) −25.2347 + 0.459373i −0.999834 + 0.0182010i
\(638\) 0.683045 0.0270420
\(639\) −1.86001 6.94165i −0.0735809 0.274608i
\(640\) −23.0442 + 13.3046i −0.910903 + 0.525910i
\(641\) −20.0412 + 11.5708i −0.791579 + 0.457018i −0.840518 0.541784i \(-0.817749\pi\)
0.0489393 + 0.998802i \(0.484416\pi\)
\(642\) −5.04067 + 1.35064i −0.198939 + 0.0533056i
\(643\) 11.9385 + 11.9385i 0.470808 + 0.470808i 0.902176 0.431368i \(-0.141969\pi\)
−0.431368 + 0.902176i \(0.641969\pi\)
\(644\) −15.8976 9.20699i −0.626455 0.362806i
\(645\) −49.9339 49.9339i −1.96614 1.96614i
\(646\) 0.883205 1.52976i 0.0347492 0.0601874i
\(647\) 10.2367 + 17.7305i 0.402446 + 0.697056i 0.994020 0.109194i \(-0.0348269\pi\)
−0.591575 + 0.806250i \(0.701494\pi\)
\(648\) −6.63919 + 24.7778i −0.260812 + 0.973364i
\(649\) 0.636779 1.10293i 0.0249958 0.0432939i
\(650\) 13.8340 4.01830i 0.542615 0.157611i
\(651\) 7.80745 28.9821i 0.305998 1.13590i
\(652\) 7.71589 7.71589i 0.302178 0.302178i
\(653\) 20.9319 36.2552i 0.819130 1.41878i −0.0871932 0.996191i \(-0.527790\pi\)
0.906324 0.422584i \(-0.138877\pi\)
\(654\) −13.1547 22.7846i −0.514389 0.890947i
\(655\) 21.3271 + 5.71457i 0.833318 + 0.223287i
\(656\) −3.35642 + 0.899351i −0.131046 + 0.0351138i
\(657\) 10.4519 10.4519i 0.407766 0.407766i
\(658\) −10.5935 0.0142221i −0.412977 0.000554436i
\(659\) −36.8332 −1.43482 −0.717410 0.696651i \(-0.754672\pi\)
−0.717410 + 0.696651i \(0.754672\pi\)
\(660\) −5.55290 3.20597i −0.216146 0.124792i
\(661\) 7.01384 + 1.87935i 0.272807 + 0.0730983i 0.392629 0.919697i \(-0.371566\pi\)
−0.119822 + 0.992795i \(0.538232\pi\)
\(662\) −6.69037 + 3.86268i −0.260028 + 0.150128i
\(663\) −11.2553 + 6.81555i −0.437118 + 0.264694i
\(664\) 28.1604i 1.09284i
\(665\) −14.8318 0.0199122i −0.575152 0.000772161i
\(666\) 13.6465 0.528790
\(667\) −7.41911 4.28343i −0.287269 0.165855i
\(668\) 0.961794 3.58947i 0.0372129 0.138881i
\(669\) 62.9912 + 16.8784i 2.43538 + 0.652558i
\(670\) −4.92248 18.3710i −0.190172 0.709732i
\(671\) 3.77751 3.77751i 0.145829 0.145829i
\(672\) 44.6104 + 12.0175i 1.72088 + 0.463586i
\(673\) 28.4985i 1.09854i −0.835646 0.549269i \(-0.814906\pi\)
0.835646 0.549269i \(-0.185094\pi\)
\(674\) 24.3701 6.52995i 0.938701 0.251524i
\(675\) 22.4136 + 38.8214i 0.862699 + 1.49424i
\(676\) −15.3544 8.02933i −0.590556 0.308820i
\(677\) 13.1864 + 7.61318i 0.506795 + 0.292598i 0.731515 0.681825i \(-0.238814\pi\)
−0.224720 + 0.974423i \(0.572147\pi\)
\(678\) 9.05238 + 9.05238i 0.347655 + 0.347655i
\(679\) −2.82500 10.5999i −0.108414 0.406788i
\(680\) 10.3880i 0.398362i
\(681\) −14.0897 52.5837i −0.539920 2.01501i
\(682\) −0.405488 + 1.51330i −0.0155270 + 0.0579474i
\(683\) −11.1843 + 41.7404i −0.427956 + 1.59715i 0.329426 + 0.944182i \(0.393145\pi\)
−0.757382 + 0.652972i \(0.773522\pi\)
\(684\) 3.71803 + 13.8759i 0.142162 + 0.530557i
\(685\) 19.5618i 0.747418i
\(686\) 14.6274 3.85631i 0.558475 0.147235i
\(687\) −9.19373 9.19373i −0.350763 0.350763i
\(688\) 2.85886 + 1.65056i 0.108993 + 0.0629271i
\(689\) −31.0718 + 0.649093i −1.18374 + 0.0247285i
\(690\) −20.1265 34.8601i −0.766203 1.32710i
\(691\) 9.69593 2.59802i 0.368851 0.0988332i −0.0696323 0.997573i \(-0.522183\pi\)
0.438483 + 0.898739i \(0.355516\pi\)
\(692\) 2.40416i 0.0913926i
\(693\) 2.09513 + 7.86134i 0.0795875 + 0.298628i
\(694\) −6.33827 + 6.33827i −0.240597 + 0.240597i
\(695\) 1.56019 + 5.82270i 0.0591813 + 0.220868i
\(696\) 13.0056 + 3.48484i 0.492977 + 0.132093i
\(697\) −2.46756 + 9.20905i −0.0934654 + 0.348818i
\(698\) 14.1644 + 8.17781i 0.536130 + 0.309535i
\(699\) −29.7410 −1.12491
\(700\) 14.9504 8.60490i 0.565074 0.325235i
\(701\) 24.4239i 0.922479i −0.887276 0.461239i \(-0.847405\pi\)
0.887276 0.461239i \(-0.152595\pi\)
\(702\) −6.43898 + 26.2084i −0.243024 + 0.989172i
\(703\) 4.26509 2.46245i 0.160861 0.0928732i
\(704\) −1.89489 0.507735i −0.0714164 0.0191360i
\(705\) 40.1598 + 23.1863i 1.51251 + 0.873246i
\(706\) −15.5806 −0.586384
\(707\) −0.0548847 + 40.8814i −0.00206415 + 1.53750i
\(708\) 7.09918 7.09918i 0.266804 0.266804i
\(709\) −26.8785 + 7.20208i −1.00944 + 0.270480i −0.725397 0.688330i \(-0.758344\pi\)
−0.284047 + 0.958810i \(0.591677\pi\)
\(710\) −2.94906 0.790199i −0.110676 0.0296556i
\(711\) −37.5245 64.9943i −1.40728 2.43748i
\(712\) 13.2841 23.0087i 0.497843 0.862289i
\(713\) 13.8944 13.8944i 0.520349 0.520349i
\(714\) 5.58398 5.56901i 0.208975 0.208415i
\(715\) −5.05328 2.77844i −0.188982 0.103908i
\(716\) 11.4043 19.7528i 0.426199 0.738197i
\(717\) 8.95861 33.4340i 0.334565 1.24862i
\(718\) −11.4464 19.8258i −0.427176 0.739890i
\(719\) −6.94803 + 12.0343i −0.259118 + 0.448805i −0.966006 0.258520i \(-0.916765\pi\)
0.706888 + 0.707325i \(0.250098\pi\)
\(720\) −5.94669 5.94669i −0.221620 0.221620i
\(721\) 40.1299 23.0972i 1.49452 0.860187i
\(722\) 9.13867 + 9.13867i 0.340106 + 0.340106i
\(723\) −42.3426 + 11.3457i −1.57474 + 0.421950i
\(724\) 27.0891 15.6399i 1.00676 0.581251i
\(725\) 6.96627 4.02198i 0.258721 0.149372i
\(726\) 6.82988 + 25.4895i 0.253481 + 0.946003i
\(727\) 14.0631 0.521572 0.260786 0.965397i \(-0.416018\pi\)
0.260786 + 0.965397i \(0.416018\pi\)
\(728\) 25.2102 + 6.22965i 0.934353 + 0.230886i
\(729\) 25.7110 0.952259
\(730\) −1.62527 6.06560i −0.0601540 0.224498i
\(731\) 7.84388 4.52866i 0.290116 0.167499i
\(732\) 36.4717 21.0569i 1.34803 0.778287i
\(733\) −21.8735 + 5.86099i −0.807917 + 0.216481i −0.639057 0.769159i \(-0.720675\pi\)
−0.168860 + 0.985640i \(0.554009\pi\)
\(734\) −9.65927 9.65927i −0.356530 0.356530i
\(735\) −63.9159 17.3103i −2.35757 0.638499i
\(736\) 21.3868 + 21.3868i 0.788327 + 0.788327i
\(737\) −1.88252 + 3.26061i −0.0693434 + 0.120106i
\(738\) 19.4045 + 33.6096i 0.714290 + 1.23719i
\(739\) 0.258550 0.964923i 0.00951093 0.0354953i −0.961007 0.276523i \(-0.910818\pi\)
0.970518 + 0.241028i \(0.0774845\pi\)
\(740\) −5.79129 + 10.0308i −0.212892 + 0.368740i
\(741\) 5.39180 + 18.5626i 0.198073 + 0.681916i
\(742\) 17.9990 4.79692i 0.660763 0.176100i
\(743\) −7.54553 + 7.54553i −0.276819 + 0.276819i −0.831838 0.555019i \(-0.812711\pi\)
0.555019 + 0.831838i \(0.312711\pi\)
\(744\) −15.4415 + 26.7455i −0.566114 + 0.980538i
\(745\) 1.75616 + 3.04176i 0.0643407 + 0.111441i
\(746\) 12.9309 + 3.46481i 0.473433 + 0.126856i
\(747\) −60.4198 + 16.1894i −2.21065 + 0.592341i
\(748\) 0.581519 0.581519i 0.0212625 0.0212625i
\(749\) −4.87084 + 2.80347i −0.177976 + 0.102436i
\(750\) −0.837176 −0.0305693
\(751\) 36.8341 + 21.2662i 1.34409 + 0.776013i 0.987405 0.158210i \(-0.0505723\pi\)
0.356689 + 0.934223i \(0.383906\pi\)
\(752\) −2.09390 0.561060i −0.0763568 0.0204598i
\(753\) −5.98551 + 3.45573i −0.218124 + 0.125934i
\(754\) 4.70293 + 1.15544i 0.171271 + 0.0420785i
\(755\) 41.4498i 1.50851i
\(756\) −0.0433853 + 32.3160i −0.00157791 + 1.17532i
\(757\) 44.6260 1.62196 0.810979 0.585075i \(-0.198935\pi\)
0.810979 + 0.585075i \(0.198935\pi\)
\(758\) −2.81025 1.62250i −0.102073 0.0589317i
\(759\) −2.06241 + 7.69702i −0.0748608 + 0.279384i
\(760\) 14.7406 + 3.94973i 0.534697 + 0.143272i
\(761\) −12.2522 45.7257i −0.444141 1.65756i −0.718195 0.695842i \(-0.755032\pi\)
0.274054 0.961714i \(-0.411635\pi\)
\(762\) 19.8660 19.8660i 0.719669 0.719669i
\(763\) −20.0080 20.0618i −0.724338 0.726286i
\(764\) 33.6504i 1.21743i
\(765\) −22.2881 + 5.97207i −0.805827 + 0.215921i
\(766\) −15.8370 27.4305i −0.572214 0.991104i
\(767\) 6.25010 6.51680i 0.225678 0.235308i
\(768\) −38.0971 21.9954i −1.37471 0.793689i
\(769\) −17.0724 17.0724i −0.615648 0.615648i 0.328764 0.944412i \(-0.393368\pi\)
−0.944412 + 0.328764i \(0.893368\pi\)
\(770\) 3.33738 + 0.899052i 0.120271 + 0.0323996i
\(771\) 54.2915i 1.95526i
\(772\) −1.84212 6.87490i −0.0662994 0.247433i
\(773\) −10.1986 + 38.0617i −0.366818 + 1.36898i 0.498121 + 0.867107i \(0.334023\pi\)
−0.864939 + 0.501876i \(0.832643\pi\)
\(774\) 9.54242 35.6128i 0.342995 1.28008i
\(775\) 4.77528 + 17.8216i 0.171533 + 0.640170i
\(776\) 11.2871i 0.405182i
\(777\) 21.2463 5.66236i 0.762206 0.203136i
\(778\) −2.81855 2.81855i −0.101050 0.101050i
\(779\) 12.1294 + 7.00294i 0.434582 + 0.250906i
\(780\) −32.8099 31.4672i −1.17478 1.12670i
\(781\) 0.302198 + 0.523422i 0.0108135 + 0.0187295i
\(782\) 4.98692 1.33624i 0.178332 0.0477839i
\(783\) 15.0695i 0.538541i
\(784\) 3.09549 + 0.00831162i 0.110553 + 0.000296844i
\(785\) 30.9215 30.9215i 1.10364 1.10364i
\(786\) 4.46381 + 16.6592i 0.159219 + 0.594213i
\(787\) 14.0502 + 3.76475i 0.500837 + 0.134199i 0.500388 0.865801i \(-0.333191\pi\)
0.000448541 1.00000i \(0.499857\pi\)
\(788\) −5.22695 + 19.5072i −0.186202 + 0.694917i
\(789\) 20.7431 + 11.9760i 0.738474 + 0.426358i
\(790\) −31.8835 −1.13436
\(791\) 11.9306 + 6.90953i 0.424205 + 0.245675i
\(792\) 8.37095i 0.297449i
\(793\) 32.3991 19.6191i 1.15053 0.696694i
\(794\) −22.3925 + 12.9283i −0.794681 + 0.458809i
\(795\) −78.7615 21.1041i −2.79338 0.748484i
\(796\) −8.28813 4.78515i −0.293765 0.169605i
\(797\) −2.90737 −0.102984 −0.0514922 0.998673i \(-0.516398\pi\)
−0.0514922 + 0.998673i \(0.516398\pi\)
\(798\) −5.77929 10.0411i −0.204585 0.355452i
\(799\) −4.20568 + 4.20568i −0.148786 + 0.148786i
\(800\) −27.4317 + 7.35029i −0.969856 + 0.259872i
\(801\) 57.0036 + 15.2741i 2.01412 + 0.539683i
\(802\) 3.95081 + 6.84300i 0.139508 + 0.241635i
\(803\) −0.621557 + 1.07657i −0.0219343 + 0.0379912i
\(804\) −20.9874 + 20.9874i −0.740168 + 0.740168i
\(805\) −30.6120 30.6943i −1.07893 1.08183i
\(806\) −5.35179 + 9.73355i −0.188509 + 0.342850i
\(807\) −12.1047 + 20.9659i −0.426104 + 0.738035i
\(808\) 10.8868 40.6301i 0.382996 1.42936i
\(809\) −0.931766 1.61387i −0.0327591 0.0567405i 0.849181 0.528102i \(-0.177096\pi\)
−0.881940 + 0.471361i \(0.843763\pi\)
\(810\) −12.1034 + 20.9637i −0.425270 + 0.736589i
\(811\) −12.4905 12.4905i −0.438602 0.438602i 0.452940 0.891541i \(-0.350375\pi\)
−0.891541 + 0.452940i \(0.850375\pi\)
\(812\) 5.79890 + 0.00778523i 0.203502 + 0.000273208i
\(813\) −47.2344 47.2344i −1.65658 1.65658i
\(814\) −1.10858 + 0.297043i −0.0388557 + 0.0104113i
\(815\) 22.2989 12.8743i 0.781096 0.450966i
\(816\) 1.39760 0.806902i 0.0489256 0.0282472i
\(817\) −3.44378 12.8524i −0.120483 0.449647i
\(818\) −9.76924 −0.341574
\(819\) 1.12731 + 57.6714i 0.0393913 + 2.01520i
\(820\) −32.9395 −1.15030
\(821\) −6.65758 24.8464i −0.232351 0.867147i −0.979325 0.202293i \(-0.935161\pi\)
0.746974 0.664853i \(-0.231506\pi\)
\(822\) 13.2331 7.64013i 0.461557 0.266480i
\(823\) 14.7104 8.49308i 0.512774 0.296050i −0.221199 0.975229i \(-0.570997\pi\)
0.733973 + 0.679178i \(0.237664\pi\)
\(824\) −46.0175 + 12.3303i −1.60310 + 0.429548i
\(825\) −5.29069 5.29069i −0.184198 0.184198i
\(826\) −2.71226 + 4.68324i −0.0943715 + 0.162951i
\(827\) −10.3024 10.3024i −0.358251 0.358251i 0.504917 0.863168i \(-0.331523\pi\)
−0.863168 + 0.504917i \(0.831523\pi\)
\(828\) −20.9934 + 36.3617i −0.729572 + 1.26366i
\(829\) 2.24299 + 3.88497i 0.0779023 + 0.134931i 0.902345 0.431015i \(-0.141844\pi\)
−0.824442 + 0.565946i \(0.808511\pi\)
\(830\) −6.87786 + 25.6685i −0.238734 + 0.890967i
\(831\) 2.21102 3.82959i 0.0766993 0.132847i
\(832\) −12.1879 6.70127i −0.422540 0.232325i
\(833\) 4.26631 7.34386i 0.147819 0.254450i
\(834\) −3.32957 + 3.32957i −0.115293 + 0.115293i
\(835\) 4.38437 7.59395i 0.151727 0.262800i
\(836\) −0.604072 1.04628i −0.0208923 0.0361864i
\(837\) −33.3869 8.94600i −1.15402 0.309219i
\(838\) −14.6237 + 3.91841i −0.505167 + 0.135359i
\(839\) 3.77561 3.77561i 0.130348 0.130348i −0.638923 0.769271i \(-0.720620\pi\)
0.769271 + 0.638923i \(0.220620\pi\)
\(840\) 58.9590 + 34.1456i 2.03428 + 1.17814i
\(841\) −26.2959 −0.906754
\(842\) −19.2953 11.1402i −0.664961 0.383916i
\(843\) 54.3476 + 14.5624i 1.87183 + 0.501555i
\(844\) −3.14608 + 1.81639i −0.108293 + 0.0625228i
\(845\) −30.0931 27.6784i −1.03524 0.952165i
\(846\) 24.2110i 0.832392i
\(847\) 14.1765 + 24.6307i 0.487109 + 0.846320i
\(848\) 3.81173 0.130895
\(849\) −12.4681 7.19844i −0.427903 0.247050i
\(850\) −1.25468 + 4.68253i −0.0430351 + 0.160609i
\(851\) 13.9040 + 3.72556i 0.476622 + 0.127710i
\(852\) 1.23317 + 4.60224i 0.0422476 + 0.157670i
\(853\) 18.5441 18.5441i 0.634938 0.634938i −0.314364 0.949302i \(-0.601791\pi\)
0.949302 + 0.314364i \(0.101791\pi\)
\(854\) −16.0739 + 16.0308i −0.550038 + 0.548563i
\(855\) 33.8975i 1.15927i
\(856\) 5.58545 1.49662i 0.190907 0.0511533i
\(857\) −23.3241 40.3984i −0.796734 1.37998i −0.921732 0.387828i \(-0.873226\pi\)
0.124997 0.992157i \(-0.460108\pi\)
\(858\) −0.0940805 4.50359i −0.00321186 0.153750i
\(859\) 2.09313 + 1.20847i 0.0714165 + 0.0412323i 0.535283 0.844673i \(-0.320205\pi\)
−0.463867 + 0.885905i \(0.653538\pi\)
\(860\) 22.1275 + 22.1275i 0.754540 + 0.754540i
\(861\) 44.1567 + 44.2754i 1.50486 + 1.50890i
\(862\) 7.48294i 0.254870i
\(863\) 14.2951 + 53.3502i 0.486612 + 1.81606i 0.572690 + 0.819772i \(0.305900\pi\)
−0.0860781 + 0.996288i \(0.527433\pi\)
\(864\) 13.7700 51.3904i 0.468466 1.74834i
\(865\) 1.46829 5.47973i 0.0499233 0.186316i
\(866\) −5.00386 18.6747i −0.170038 0.634591i
\(867\) 46.7045i 1.58617i
\(868\) −3.45976 + 12.8430i −0.117432 + 0.435920i
\(869\) 4.46305 + 4.46305i 0.151399 + 0.151399i
\(870\) 11.0036 + 6.35295i 0.373058 + 0.215385i
\(871\) −18.4772 + 19.2657i −0.626077 + 0.652793i
\(872\) 14.5764 + 25.2470i 0.493619 + 0.854973i
\(873\) −24.2171 + 6.48895i −0.819624 + 0.219618i
\(874\) 7.58451i 0.256550i
\(875\) −0.871182 + 0.232179i −0.0294513 + 0.00784909i
\(876\) −6.92948 + 6.92948i −0.234125 + 0.234125i
\(877\) −6.65127 24.8229i −0.224597 0.838208i −0.982565 0.185917i \(-0.940474\pi\)
0.757968 0.652292i \(-0.226192\pi\)
\(878\) 8.91374 + 2.38843i 0.300824 + 0.0806056i
\(879\) 16.8591 62.9190i 0.568643 2.12221i
\(880\) 0.612524 + 0.353641i 0.0206482 + 0.0119212i
\(881\) −14.0101 −0.472014 −0.236007 0.971751i \(-0.575839\pi\)
−0.236007 + 0.971751i \(0.575839\pi\)
\(882\) −8.85833 33.4184i −0.298275 1.12526i
\(883\) 26.0607i 0.877012i −0.898728 0.438506i \(-0.855508\pi\)
0.898728 0.438506i \(-0.144492\pi\)
\(884\) 4.98760 3.02021i 0.167751 0.101581i
\(885\) 20.5166 11.8453i 0.689658 0.398174i
\(886\) 30.7921 + 8.25071i 1.03448 + 0.277188i
\(887\) −19.8272 11.4472i −0.665731 0.384360i 0.128726 0.991680i \(-0.458911\pi\)
−0.794457 + 0.607320i \(0.792244\pi\)
\(888\) −22.6236 −0.759197
\(889\) 15.1634 26.1825i 0.508563 0.878133i
\(890\) 17.7282 17.7282i 0.594251 0.594251i
\(891\) 4.62872 1.24026i 0.155068 0.0415504i
\(892\) −27.9136 7.47943i −0.934617 0.250430i
\(893\) 4.36878 + 7.56695i 0.146196 + 0.253218i
\(894\) −1.37179 + 2.37600i −0.0458794 + 0.0794654i
\(895\) 38.0570 38.0570i 1.27211 1.27211i
\(896\) −21.6139 5.82254i −0.722070 0.194517i
\(897\) −27.2205 + 49.5072i −0.908865 + 1.65300i
\(898\) −5.09572 + 8.82605i −0.170046 + 0.294529i
\(899\) −1.60530 + 5.99108i −0.0535399 + 0.199814i
\(900\) −19.7120 34.1423i −0.657068 1.13808i
\(901\) 5.22914 9.05713i 0.174208 0.301737i
\(902\) −2.30792 2.30792i −0.0768452 0.0768452i
\(903\) 0.0797535 59.4052i 0.00265403 1.97688i
\(904\) −10.0307 10.0307i −0.333617 0.333617i
\(905\) 71.2949 19.1034i 2.36992 0.635019i
\(906\) −28.0398 + 16.1888i −0.931560 + 0.537837i
\(907\) −19.6282 + 11.3323i −0.651742 + 0.376284i −0.789123 0.614235i \(-0.789465\pi\)
0.137381 + 0.990518i \(0.456132\pi\)
\(908\) 6.24367 + 23.3017i 0.207203 + 0.773293i
\(909\) 93.4330 3.09898
\(910\) 21.4579 + 11.8357i 0.711321 + 0.392349i
\(911\) −5.46179 −0.180957 −0.0904786 0.995898i \(-0.528840\pi\)
−0.0904786 + 0.995898i \(0.528840\pi\)
\(912\) −0.613601 2.28999i −0.0203184 0.0758292i
\(913\) 4.55584 2.63031i 0.150776 0.0870507i
\(914\) 16.1713 9.33653i 0.534900 0.308825i
\(915\) 95.9888 25.7201i 3.17329 0.850281i
\(916\) 4.07407 + 4.07407i 0.134611 + 0.134611i
\(917\) 9.26532 + 16.0979i 0.305968 + 0.531599i
\(918\) −6.42172 6.42172i −0.211948 0.211948i
\(919\) 10.9646 18.9912i 0.361688 0.626461i −0.626551 0.779380i \(-0.715534\pi\)
0.988239 + 0.152919i \(0.0488674\pi\)
\(920\) 22.3017 + 38.6277i 0.735266 + 1.27352i
\(921\) −10.3115 + 38.4829i −0.339775 + 1.26806i
\(922\) −4.43096 + 7.67464i −0.145926 + 0.252751i
\(923\) 1.19529 + 4.11509i 0.0393434 + 0.135450i
\(924\) −1.38905 5.21199i −0.0456964 0.171462i
\(925\) −9.55714 + 9.55714i −0.314237 + 0.314237i
\(926\) 8.11878 14.0621i 0.266800 0.462110i
\(927\) −52.9110 91.6445i −1.73782 3.01000i
\(928\) −9.22169 2.47095i −0.302717 0.0811128i
\(929\) −8.97788 + 2.40562i −0.294555 + 0.0789257i −0.403070 0.915169i \(-0.632057\pi\)
0.108515 + 0.994095i \(0.465390\pi\)
\(930\) −20.6074 + 20.6074i −0.675743 + 0.675743i
\(931\) −8.79881 8.84619i −0.288369 0.289922i
\(932\) 13.1793 0.431702
\(933\) 14.1224 + 8.15356i 0.462346 + 0.266936i
\(934\) −7.83081 2.09826i −0.256232 0.0686572i
\(935\) 1.68059 0.970288i 0.0549611 0.0317318i
\(936\) 14.1603 57.6361i 0.462842 1.88389i
\(937\) 3.37326i 0.110200i −0.998481 0.0550998i \(-0.982452\pi\)
0.998481 0.0550998i \(-0.0175477\pi\)
\(938\) 8.01827 13.8451i 0.261806 0.452058i
\(939\) 63.4428 2.07038
\(940\) −17.7962 10.2747i −0.580449 0.335122i
\(941\) −0.289236 + 1.07944i −0.00942881 + 0.0351888i −0.970480 0.241182i \(-0.922465\pi\)
0.961051 + 0.276371i \(0.0891317\pi\)
\(942\) 32.9946 + 8.84086i 1.07502 + 0.288051i
\(943\) 10.5951 + 39.5413i 0.345023 + 1.28764i
\(944\) −0.783090 + 0.783090i −0.0254874 + 0.0254874i
\(945\) −19.8351 + 73.6302i −0.645237 + 2.39519i
\(946\) 3.10073i 0.100813i
\(947\) −11.4772 + 3.07530i −0.372958 + 0.0999338i −0.440429 0.897787i \(-0.645174\pi\)
0.0674710 + 0.997721i \(0.478507\pi\)
\(948\) 24.8783 + 43.0905i 0.808011 + 1.39952i
\(949\) −6.10069 + 6.36102i −0.198037 + 0.206487i
\(950\) 6.16746 + 3.56078i 0.200099 + 0.115527i
\(951\) 32.7723 + 32.7723i 1.06272 + 1.06272i
\(952\) −6.18748 + 6.17089i −0.200537 + 0.200000i
\(953\) 27.4279i 0.888478i −0.895908 0.444239i \(-0.853474\pi\)
0.895908 0.444239i \(-0.146526\pi\)
\(954\) −11.0184 41.1212i −0.356734 1.33135i
\(955\) −20.5513 + 76.6983i −0.665023 + 2.48190i
\(956\) −3.96988 + 14.8158i −0.128395 + 0.479177i
\(957\) −0.651002 2.42957i −0.0210439 0.0785369i
\(958\) 17.2306i 0.556694i
\(959\) 11.6517 11.6205i 0.376254 0.375245i
\(960\) −25.8037 25.8037i −0.832810 0.832810i
\(961\) 14.5264 + 8.38681i 0.468593 + 0.270542i
\(962\) −8.13532 + 0.169948i −0.262293 + 0.00547934i
\(963\) 6.42216 + 11.1235i 0.206951 + 0.358450i
\(964\) 18.7635 5.02766i 0.604331 0.161930i
\(965\) 16.7948i 0.540642i
\(966\) 8.80804 32.6964i 0.283394 1.05199i
\(967\) −1.22569 + 1.22569i −0.0394155 + 0.0394155i −0.726540 0.687124i \(-0.758873\pi\)
0.687124 + 0.726540i \(0.258873\pi\)
\(968\) −7.56803 28.2443i −0.243246 0.907806i
\(969\) −6.28307 1.68354i −0.201841 0.0540832i
\(970\) −2.75674 + 10.2883i −0.0885135 + 0.330337i
\(971\) −10.7056 6.18087i −0.343559 0.198354i 0.318286 0.947995i \(-0.396893\pi\)
−0.661845 + 0.749641i \(0.730226\pi\)
\(972\) 1.13364 0.0363615
\(973\) −2.54140 + 4.38822i −0.0814736 + 0.140680i
\(974\) 35.8091i 1.14740i
\(975\) −27.4780 45.3774i −0.880001 1.45324i
\(976\) −4.02309 + 2.32273i −0.128776 + 0.0743488i
\(977\) 0.161930 + 0.0433889i 0.00518058 + 0.00138813i 0.261408 0.965228i \(-0.415813\pi\)
−0.256228 + 0.966616i \(0.582480\pi\)
\(978\) 17.4183 + 10.0565i 0.556975 + 0.321570i
\(979\) −4.96319 −0.158624
\(980\) 28.3234 + 7.67080i 0.904757 + 0.245035i
\(981\) −45.7890 + 45.7890i −1.46193 + 1.46193i
\(982\) −29.2921 + 7.84879i −0.934748 + 0.250465i
\(983\) −11.2297 3.00899i −0.358172 0.0959718i 0.0752459 0.997165i \(-0.476026\pi\)
−0.433418 + 0.901193i \(0.642693\pi\)
\(984\) −32.1694 55.7190i −1.02552 1.77626i
\(985\) −23.8272 + 41.2700i −0.759199 + 1.31497i
\(986\) −1.15234 + 1.15234i −0.0366979 + 0.0366979i
\(987\) 10.0459 + 37.6943i 0.319765 + 1.19982i
\(988\) −2.38930 8.22576i −0.0760137 0.261696i
\(989\) 19.4449 33.6796i 0.618313 1.07095i
\(990\) 2.04451 7.63021i 0.0649787 0.242504i
\(991\) −4.59806 7.96408i −0.146062 0.252987i 0.783707 0.621131i \(-0.213327\pi\)
−0.929769 + 0.368144i \(0.879993\pi\)
\(992\) 10.9489 18.9640i 0.347628 0.602109i
\(993\) 20.1160 + 20.1160i 0.638361 + 0.638361i
\(994\) −1.28119 2.22598i −0.0406369 0.0706039i
\(995\) −15.9684 15.9684i −0.506233 0.506233i
\(996\) 40.0577 10.7334i 1.26928 0.340102i
\(997\) −25.9655 + 14.9912i −0.822337 + 0.474776i −0.851222 0.524806i \(-0.824138\pi\)
0.0288849 + 0.999583i \(0.490804\pi\)
\(998\) −3.78846 + 2.18727i −0.119922 + 0.0692368i
\(999\) −6.55344 24.4578i −0.207342 0.773810i
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 91.2.bb.a.5.3 32
3.2 odd 2 819.2.fn.e.460.6 32
7.2 even 3 637.2.i.a.538.5 32
7.3 odd 6 inner 91.2.bb.a.31.6 yes 32
7.4 even 3 637.2.bc.b.31.6 32
7.5 odd 6 637.2.i.a.538.6 32
7.6 odd 2 637.2.bc.b.460.3 32
13.8 odd 4 inner 91.2.bb.a.47.6 yes 32
21.17 even 6 819.2.fn.e.577.3 32
39.8 even 4 819.2.fn.e.775.3 32
91.34 even 4 637.2.bc.b.411.6 32
91.47 even 12 637.2.i.a.489.6 32
91.60 odd 12 637.2.bc.b.619.3 32
91.73 even 12 inner 91.2.bb.a.73.3 yes 32
91.86 odd 12 637.2.i.a.489.5 32
273.164 odd 12 819.2.fn.e.73.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bb.a.5.3 32 1.1 even 1 trivial
91.2.bb.a.31.6 yes 32 7.3 odd 6 inner
91.2.bb.a.47.6 yes 32 13.8 odd 4 inner
91.2.bb.a.73.3 yes 32 91.73 even 12 inner
637.2.i.a.489.5 32 91.86 odd 12
637.2.i.a.489.6 32 91.47 even 12
637.2.i.a.538.5 32 7.2 even 3
637.2.i.a.538.6 32 7.5 odd 6
637.2.bc.b.31.6 32 7.4 even 3
637.2.bc.b.411.6 32 91.34 even 4
637.2.bc.b.460.3 32 7.6 odd 2
637.2.bc.b.619.3 32 91.60 odd 12
819.2.fn.e.73.6 32 273.164 odd 12
819.2.fn.e.460.6 32 3.2 odd 2
819.2.fn.e.577.3 32 21.17 even 6
819.2.fn.e.775.3 32 39.8 even 4