Properties

Label 361.2.e.f.62.1
Level $361$
Weight $2$
Character 361.62
Analytic conductor $2.883$
Analytic rank $0$
Dimension $6$
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] = [361,2,Mod(28,361)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(361, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("361.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.88259951297\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 62.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 361.62
Dual form 361.2.e.f.99.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26604 - 0.460802i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.673648 + 0.565258i) q^{5} +(0.673648 + 3.82045i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +O(q^{10})\) \(q+(1.26604 - 0.460802i) q^{2} +(-0.500000 + 2.83564i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.673648 + 0.565258i) q^{5} +(0.673648 + 3.82045i) q^{6} +(-0.173648 - 0.300767i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-4.97178 - 1.80958i) q^{9} +(1.11334 + 0.405223i) q^{10} +(1.11334 - 1.92836i) q^{11} +(-0.266044 - 0.460802i) q^{12} +(0.446967 + 2.53487i) q^{13} +(-0.358441 - 0.300767i) q^{14} +(-1.93969 + 1.62760i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(-0.439693 + 0.160035i) q^{17} -7.12836 q^{18} -0.162504 q^{20} +(0.939693 - 0.342020i) q^{21} +(0.520945 - 2.95442i) q^{22} +(-2.06418 + 1.73205i) q^{23} +(-6.49273 - 5.44804i) q^{24} +(-0.733956 - 4.16247i) q^{25} +(1.73396 + 3.00330i) q^{26} +(3.29813 - 5.71253i) q^{27} +(0.0603074 + 0.0219501i) q^{28} +(6.46451 + 2.35289i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(3.55303 + 6.15403i) q^{31} +(-0.180922 - 1.02606i) q^{32} +(4.91147 + 4.12122i) q^{33} +(-0.482926 + 0.405223i) q^{34} +(0.0530334 - 0.300767i) q^{35} +(0.918748 - 0.334397i) q^{36} +4.94356 q^{37} -7.41147 q^{39} +(-2.43242 + 0.885328i) q^{40} +(0.429892 - 2.43804i) q^{41} +(1.03209 - 0.866025i) q^{42} +(2.98886 + 2.50795i) q^{43} +(0.0714517 + 0.405223i) q^{44} +(-2.32635 - 4.02936i) q^{45} +(-1.81521 + 3.14403i) q^{46} +(6.85117 + 2.49362i) q^{47} +(-9.73055 - 3.54163i) q^{48} +(3.43969 - 5.95772i) q^{49} +(-2.84730 - 4.93166i) q^{50} +(-0.233956 - 1.32683i) q^{51} +(-0.364370 - 0.305743i) q^{52} +(-2.17365 + 1.82391i) q^{53} +(1.54323 - 8.75211i) q^{54} +(1.84002 - 0.669713i) q^{55} +1.02229 q^{56} +9.26857 q^{58} +(5.92514 - 2.15658i) q^{59} +(0.0812519 - 0.460802i) q^{60} +(6.99273 - 5.86759i) q^{61} +(7.33409 + 6.15403i) q^{62} +(0.319078 + 1.80958i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(-1.13176 + 1.96026i) q^{65} +(8.11721 + 2.95442i) q^{66} +(-7.21213 - 2.62500i) q^{67} +(0.0432332 - 0.0748822i) q^{68} +(-3.87939 - 6.71929i) q^{69} +(-0.0714517 - 0.405223i) q^{70} +(-7.12836 - 5.98140i) q^{71} +(11.9304 - 10.0108i) q^{72} +(0.241230 - 1.36808i) q^{73} +(6.25877 - 2.27801i) q^{74} +12.1702 q^{75} -0.773318 q^{77} +(-9.38326 + 3.41523i) q^{78} +(-2.05690 + 11.6653i) q^{79} +(-2.42262 + 2.03282i) q^{80} +(2.39053 + 2.00589i) q^{81} +(-0.579193 - 3.28476i) q^{82} +(7.41534 + 12.8438i) q^{83} +(-0.0923963 + 0.160035i) q^{84} +(-0.386659 - 0.140732i) q^{85} +(4.93969 + 1.79790i) q^{86} +(-9.90420 + 17.1546i) q^{87} +(3.27719 + 5.67626i) q^{88} +(-1.78699 - 10.1345i) q^{89} +(-4.80200 - 4.02936i) q^{90} +(0.684793 - 0.574609i) q^{91} +(0.0864665 - 0.490376i) q^{92} +(-19.2271 + 6.99811i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-8.88326 + 3.23324i) q^{97} +(1.60947 - 9.12776i) q^{98} +(-9.02481 + 7.57272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} + 3 q^{12} + 15 q^{13} + 6 q^{14} - 6 q^{15} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 6 q^{20} + 6 q^{23} - 21 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} + 6 q^{28} + 6 q^{29} + 9 q^{31} - 18 q^{32} + 9 q^{33} + 18 q^{34} - 12 q^{35} + 3 q^{36} - 24 q^{39} + 9 q^{40} - 6 q^{41} - 3 q^{42} + 24 q^{43} - 15 q^{45} - 18 q^{46} + 15 q^{47} - 21 q^{48} + 15 q^{49} - 15 q^{50} - 6 q^{51} - 21 q^{52} - 12 q^{53} - 6 q^{54} - 9 q^{55} - 6 q^{56} + 36 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 3 q^{62} - 15 q^{63} - 12 q^{64} - 12 q^{65} + 18 q^{66} + 6 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} + 30 q^{75} - 18 q^{77} - 21 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 45 q^{82} + 3 q^{84} - 9 q^{85} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 3 q^{89} + 9 q^{90} - 3 q^{91} - 30 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26604 0.460802i 0.895229 0.325837i 0.146889 0.989153i \(-0.453074\pi\)
0.748339 + 0.663316i \(0.230852\pi\)
\(3\) −0.500000 + 2.83564i −0.288675 + 1.63716i 0.403179 + 0.915121i \(0.367905\pi\)
−0.691854 + 0.722037i \(0.743206\pi\)
\(4\) −0.141559 + 0.118782i −0.0707796 + 0.0593912i
\(5\) 0.673648 + 0.565258i 0.301265 + 0.252791i 0.780870 0.624693i \(-0.214776\pi\)
−0.479606 + 0.877484i \(0.659220\pi\)
\(6\) 0.673648 + 3.82045i 0.275016 + 1.55969i
\(7\) −0.173648 0.300767i −0.0656328 0.113679i 0.831342 0.555762i \(-0.187573\pi\)
−0.896975 + 0.442082i \(0.854240\pi\)
\(8\) −1.47178 + 2.54920i −0.520353 + 0.901278i
\(9\) −4.97178 1.80958i −1.65726 0.603193i
\(10\) 1.11334 + 0.405223i 0.352069 + 0.128143i
\(11\) 1.11334 1.92836i 0.335685 0.581423i −0.647931 0.761699i \(-0.724366\pi\)
0.983616 + 0.180276i \(0.0576989\pi\)
\(12\) −0.266044 0.460802i −0.0768004 0.133022i
\(13\) 0.446967 + 2.53487i 0.123966 + 0.703047i 0.981916 + 0.189315i \(0.0606266\pi\)
−0.857950 + 0.513733i \(0.828262\pi\)
\(14\) −0.358441 0.300767i −0.0957973 0.0803835i
\(15\) −1.93969 + 1.62760i −0.500826 + 0.420243i
\(16\) −0.624485 + 3.54163i −0.156121 + 0.885408i
\(17\) −0.439693 + 0.160035i −0.106641 + 0.0388142i −0.394790 0.918772i \(-0.629183\pi\)
0.288149 + 0.957586i \(0.406960\pi\)
\(18\) −7.12836 −1.68017
\(19\) 0 0
\(20\) −0.162504 −0.0363370
\(21\) 0.939693 0.342020i 0.205058 0.0746349i
\(22\) 0.520945 2.95442i 0.111066 0.629885i
\(23\) −2.06418 + 1.73205i −0.430411 + 0.361158i −0.832107 0.554616i \(-0.812865\pi\)
0.401696 + 0.915773i \(0.368421\pi\)
\(24\) −6.49273 5.44804i −1.32532 1.11208i
\(25\) −0.733956 4.16247i −0.146791 0.832494i
\(26\) 1.73396 + 3.00330i 0.340057 + 0.588995i
\(27\) 3.29813 5.71253i 0.634726 1.09938i
\(28\) 0.0603074 + 0.0219501i 0.0113970 + 0.00414818i
\(29\) 6.46451 + 2.35289i 1.20043 + 0.436920i 0.863374 0.504565i \(-0.168347\pi\)
0.337055 + 0.941485i \(0.390569\pi\)
\(30\) −1.70574 + 2.95442i −0.311424 + 0.539401i
\(31\) 3.55303 + 6.15403i 0.638144 + 1.10530i 0.985840 + 0.167690i \(0.0536307\pi\)
−0.347696 + 0.937607i \(0.613036\pi\)
\(32\) −0.180922 1.02606i −0.0319828 0.181384i
\(33\) 4.91147 + 4.12122i 0.854978 + 0.717412i
\(34\) −0.482926 + 0.405223i −0.0828211 + 0.0694952i
\(35\) 0.0530334 0.300767i 0.00896428 0.0508390i
\(36\) 0.918748 0.334397i 0.153125 0.0557328i
\(37\) 4.94356 0.812717 0.406358 0.913714i \(-0.366798\pi\)
0.406358 + 0.913714i \(0.366798\pi\)
\(38\) 0 0
\(39\) −7.41147 −1.18679
\(40\) −2.43242 + 0.885328i −0.384599 + 0.139983i
\(41\) 0.429892 2.43804i 0.0671379 0.380758i −0.932662 0.360752i \(-0.882520\pi\)
0.999800 0.0200065i \(-0.00636868\pi\)
\(42\) 1.03209 0.866025i 0.159255 0.133631i
\(43\) 2.98886 + 2.50795i 0.455796 + 0.382458i 0.841581 0.540130i \(-0.181625\pi\)
−0.385785 + 0.922589i \(0.626069\pi\)
\(44\) 0.0714517 + 0.405223i 0.0107718 + 0.0610897i
\(45\) −2.32635 4.02936i −0.346792 0.600661i
\(46\) −1.81521 + 3.14403i −0.267638 + 0.463562i
\(47\) 6.85117 + 2.49362i 0.999345 + 0.363732i 0.789332 0.613967i \(-0.210427\pi\)
0.210013 + 0.977699i \(0.432649\pi\)
\(48\) −9.73055 3.54163i −1.40448 0.511190i
\(49\) 3.43969 5.95772i 0.491385 0.851103i
\(50\) −2.84730 4.93166i −0.402669 0.697442i
\(51\) −0.233956 1.32683i −0.0327603 0.185793i
\(52\) −0.364370 0.305743i −0.0505291 0.0423989i
\(53\) −2.17365 + 1.82391i −0.298574 + 0.250533i −0.779750 0.626091i \(-0.784654\pi\)
0.481177 + 0.876624i \(0.340210\pi\)
\(54\) 1.54323 8.75211i 0.210007 1.19101i
\(55\) 1.84002 0.669713i 0.248109 0.0903041i
\(56\) 1.02229 0.136609
\(57\) 0 0
\(58\) 9.26857 1.21702
\(59\) 5.92514 2.15658i 0.771388 0.280762i 0.0738112 0.997272i \(-0.476484\pi\)
0.697577 + 0.716510i \(0.254262\pi\)
\(60\) 0.0812519 0.460802i 0.0104896 0.0594893i
\(61\) 6.99273 5.86759i 0.895327 0.751268i −0.0739445 0.997262i \(-0.523559\pi\)
0.969271 + 0.245994i \(0.0791143\pi\)
\(62\) 7.33409 + 6.15403i 0.931431 + 0.781563i
\(63\) 0.319078 + 1.80958i 0.0402000 + 0.227986i
\(64\) −4.29813 7.44459i −0.537267 0.930573i
\(65\) −1.13176 + 1.96026i −0.140377 + 0.243141i
\(66\) 8.11721 + 2.95442i 0.999160 + 0.363664i
\(67\) −7.21213 2.62500i −0.881102 0.320695i −0.138448 0.990370i \(-0.544211\pi\)
−0.742655 + 0.669675i \(0.766434\pi\)
\(68\) 0.0432332 0.0748822i 0.00524280 0.00908080i
\(69\) −3.87939 6.71929i −0.467023 0.808908i
\(70\) −0.0714517 0.405223i −0.00854012 0.0484334i
\(71\) −7.12836 5.98140i −0.845980 0.709862i 0.112920 0.993604i \(-0.463979\pi\)
−0.958901 + 0.283742i \(0.908424\pi\)
\(72\) 11.9304 10.0108i 1.40601 1.17978i
\(73\) 0.241230 1.36808i 0.0282338 0.160122i −0.967431 0.253134i \(-0.918539\pi\)
0.995665 + 0.0930125i \(0.0296497\pi\)
\(74\) 6.25877 2.27801i 0.727567 0.264813i
\(75\) 12.1702 1.40530
\(76\) 0 0
\(77\) −0.773318 −0.0881278
\(78\) −9.38326 + 3.41523i −1.06244 + 0.386698i
\(79\) −2.05690 + 11.6653i −0.231420 + 1.31245i 0.618604 + 0.785703i \(0.287698\pi\)
−0.850024 + 0.526744i \(0.823413\pi\)
\(80\) −2.42262 + 2.03282i −0.270857 + 0.227276i
\(81\) 2.39053 + 2.00589i 0.265614 + 0.222877i
\(82\) −0.579193 3.28476i −0.0639611 0.362742i
\(83\) 7.41534 + 12.8438i 0.813940 + 1.40979i 0.910087 + 0.414418i \(0.136015\pi\)
−0.0961469 + 0.995367i \(0.530652\pi\)
\(84\) −0.0923963 + 0.160035i −0.0100813 + 0.0174613i
\(85\) −0.386659 0.140732i −0.0419391 0.0152646i
\(86\) 4.93969 + 1.79790i 0.532661 + 0.193873i
\(87\) −9.90420 + 17.1546i −1.06184 + 1.83916i
\(88\) 3.27719 + 5.67626i 0.349349 + 0.605091i
\(89\) −1.78699 10.1345i −0.189420 1.07426i −0.920143 0.391582i \(-0.871928\pi\)
0.730723 0.682674i \(-0.239183\pi\)
\(90\) −4.80200 4.02936i −0.506176 0.424732i
\(91\) 0.684793 0.574609i 0.0717858 0.0602354i
\(92\) 0.0864665 0.490376i 0.00901475 0.0511252i
\(93\) −19.2271 + 6.99811i −1.99376 + 0.725670i
\(94\) 9.82295 1.01316
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) −8.88326 + 3.23324i −0.901958 + 0.328286i −0.751037 0.660260i \(-0.770446\pi\)
−0.150921 + 0.988546i \(0.548224\pi\)
\(98\) 1.60947 9.12776i 0.162581 0.922043i
\(99\) −9.02481 + 7.57272i −0.907028 + 0.761087i
\(100\) 0.598326 + 0.502055i 0.0598326 + 0.0502055i
\(101\) −1.60607 9.10846i −0.159810 0.906325i −0.954256 0.298991i \(-0.903350\pi\)
0.794446 0.607334i \(-0.207761\pi\)
\(102\) −0.907604 1.57202i −0.0898662 0.155653i
\(103\) 2.75490 4.77163i 0.271448 0.470162i −0.697785 0.716308i \(-0.745831\pi\)
0.969233 + 0.246145i \(0.0791640\pi\)
\(104\) −7.11974 2.59137i −0.698148 0.254105i
\(105\) 0.826352 + 0.300767i 0.0806437 + 0.0293519i
\(106\) −1.91147 + 3.31077i −0.185659 + 0.321570i
\(107\) −5.11721 8.86327i −0.494699 0.856845i 0.505282 0.862954i \(-0.331389\pi\)
−0.999981 + 0.00610974i \(0.998055\pi\)
\(108\) 0.211667 + 1.20042i 0.0203677 + 0.115511i
\(109\) −1.39646 1.17177i −0.133757 0.112235i 0.573455 0.819237i \(-0.305603\pi\)
−0.707212 + 0.707002i \(0.750047\pi\)
\(110\) 2.02094 1.69577i 0.192690 0.161686i
\(111\) −2.47178 + 14.0182i −0.234611 + 1.33055i
\(112\) 1.17365 0.427173i 0.110899 0.0403641i
\(113\) −17.6878 −1.66393 −0.831963 0.554830i \(-0.812783\pi\)
−0.831963 + 0.554830i \(0.812783\pi\)
\(114\) 0 0
\(115\) −2.36959 −0.220965
\(116\) −1.19459 + 0.434796i −0.110915 + 0.0403698i
\(117\) 2.36484 13.4117i 0.218629 1.23991i
\(118\) 6.50774 5.46064i 0.599086 0.502693i
\(119\) 0.124485 + 0.104455i 0.0114115 + 0.00957541i
\(120\) −1.29426 7.34013i −0.118150 0.670059i
\(121\) 3.02094 + 5.23243i 0.274631 + 0.475675i
\(122\) 6.14930 10.6509i 0.556731 0.964287i
\(123\) 6.69846 + 2.43804i 0.603980 + 0.219831i
\(124\) −1.23396 0.449123i −0.110812 0.0403324i
\(125\) 4.05690 7.02676i 0.362861 0.628493i
\(126\) 1.23783 + 2.14398i 0.110274 + 0.191001i
\(127\) 2.01501 + 11.4277i 0.178804 + 1.01405i 0.933661 + 0.358157i \(0.116595\pi\)
−0.754858 + 0.655889i \(0.772294\pi\)
\(128\) −7.27584 6.10516i −0.643100 0.539625i
\(129\) −8.60607 + 7.22135i −0.757722 + 0.635804i
\(130\) −0.529563 + 3.00330i −0.0464457 + 0.263407i
\(131\) −1.73396 + 0.631108i −0.151496 + 0.0551402i −0.416655 0.909065i \(-0.636798\pi\)
0.265159 + 0.964205i \(0.414576\pi\)
\(132\) −1.18479 −0.103123
\(133\) 0 0
\(134\) −10.3405 −0.893282
\(135\) 5.45084 1.98394i 0.469133 0.170751i
\(136\) 0.239170 1.35640i 0.0205087 0.116310i
\(137\) 0.195937 0.164411i 0.0167400 0.0140465i −0.634379 0.773022i \(-0.718744\pi\)
0.651119 + 0.758975i \(0.274300\pi\)
\(138\) −8.00774 6.71929i −0.681664 0.571984i
\(139\) 0.740352 + 4.19875i 0.0627959 + 0.356133i 0.999973 + 0.00728048i \(0.00231747\pi\)
−0.937178 + 0.348852i \(0.886571\pi\)
\(140\) 0.0282185 + 0.0488759i 0.00238490 + 0.00413076i
\(141\) −10.4966 + 18.1806i −0.883973 + 1.53109i
\(142\) −11.7811 4.28795i −0.988645 0.359837i
\(143\) 5.38578 + 1.96026i 0.450382 + 0.163926i
\(144\) 9.51367 16.4782i 0.792806 1.37318i
\(145\) 3.02481 + 5.23913i 0.251197 + 0.435086i
\(146\) −0.325008 1.84321i −0.0268978 0.152545i
\(147\) 15.1741 + 12.7326i 1.25154 + 1.05017i
\(148\) −0.699807 + 0.587208i −0.0575238 + 0.0482682i
\(149\) 2.87551 16.3079i 0.235571 1.33599i −0.605836 0.795590i \(-0.707161\pi\)
0.841407 0.540402i \(-0.181728\pi\)
\(150\) 15.4081 5.60808i 1.25806 0.457898i
\(151\) −4.36184 −0.354962 −0.177481 0.984124i \(-0.556795\pi\)
−0.177481 + 0.984124i \(0.556795\pi\)
\(152\) 0 0
\(153\) 2.47565 0.200145
\(154\) −0.979055 + 0.356347i −0.0788945 + 0.0287153i
\(155\) −1.08512 + 6.15403i −0.0871591 + 0.494304i
\(156\) 1.04916 0.880352i 0.0840003 0.0704846i
\(157\) −7.36824 6.18269i −0.588050 0.493432i 0.299530 0.954087i \(-0.403170\pi\)
−0.887579 + 0.460655i \(0.847615\pi\)
\(158\) 2.77126 + 15.7166i 0.220470 + 1.25034i
\(159\) −4.08512 7.07564i −0.323971 0.561135i
\(160\) 0.458111 0.793471i 0.0362168 0.0627294i
\(161\) 0.879385 + 0.320070i 0.0693053 + 0.0252251i
\(162\) 3.95084 + 1.43799i 0.310407 + 0.112979i
\(163\) −4.17752 + 7.23567i −0.327209 + 0.566742i −0.981957 0.189105i \(-0.939441\pi\)
0.654748 + 0.755847i \(0.272775\pi\)
\(164\) 0.228741 + 0.396191i 0.0178617 + 0.0309373i
\(165\) 0.979055 + 5.55250i 0.0762194 + 0.432261i
\(166\) 15.3066 + 12.8438i 1.18802 + 0.996869i
\(167\) 3.09105 2.59370i 0.239193 0.200707i −0.515309 0.857004i \(-0.672323\pi\)
0.754502 + 0.656298i \(0.227878\pi\)
\(168\) −0.511144 + 2.89884i −0.0394356 + 0.223651i
\(169\) 5.99020 2.18025i 0.460785 0.167712i
\(170\) −0.554378 −0.0425188
\(171\) 0 0
\(172\) −0.721000 −0.0549758
\(173\) 18.9290 6.88960i 1.43915 0.523806i 0.499608 0.866251i \(-0.333477\pi\)
0.939538 + 0.342445i \(0.111255\pi\)
\(174\) −4.63429 + 26.2823i −0.351324 + 1.99246i
\(175\) −1.12449 + 0.943555i −0.0850031 + 0.0713261i
\(176\) 6.13429 + 5.14728i 0.462389 + 0.387991i
\(177\) 3.15270 + 17.8799i 0.236972 + 1.34393i
\(178\) −6.93242 12.0073i −0.519607 0.899985i
\(179\) 5.75624 9.97011i 0.430242 0.745201i −0.566652 0.823957i \(-0.691762\pi\)
0.996894 + 0.0787564i \(0.0250949\pi\)
\(180\) 0.807934 + 0.294064i 0.0602198 + 0.0219182i
\(181\) −8.02229 2.91987i −0.596292 0.217033i 0.0262026 0.999657i \(-0.491659\pi\)
−0.622495 + 0.782624i \(0.713881\pi\)
\(182\) 0.602196 1.04303i 0.0446378 0.0773149i
\(183\) 13.1420 + 22.7627i 0.971487 + 1.68266i
\(184\) −1.37733 7.81120i −0.101538 0.575850i
\(185\) 3.33022 + 2.79439i 0.244843 + 0.205448i
\(186\) −21.1177 + 17.7198i −1.54842 + 1.29928i
\(187\) −0.180922 + 1.02606i −0.0132303 + 0.0750330i
\(188\) −1.26604 + 0.460802i −0.0923358 + 0.0336075i
\(189\) −2.29086 −0.166635
\(190\) 0 0
\(191\) 18.3354 1.32671 0.663353 0.748307i \(-0.269133\pi\)
0.663353 + 0.748307i \(0.269133\pi\)
\(192\) 23.2592 8.46567i 1.67859 0.610957i
\(193\) 0.0516892 0.293144i 0.00372067 0.0211010i −0.982891 0.184189i \(-0.941034\pi\)
0.986612 + 0.163088i \(0.0521454\pi\)
\(194\) −9.75671 + 8.18685i −0.700491 + 0.587782i
\(195\) −4.99273 4.18939i −0.357537 0.300009i
\(196\) 0.220752 + 1.25195i 0.0157680 + 0.0894247i
\(197\) −6.57057 11.3806i −0.468134 0.810832i 0.531203 0.847245i \(-0.321740\pi\)
−0.999337 + 0.0364128i \(0.988407\pi\)
\(198\) −7.93629 + 13.7461i −0.564008 + 0.976890i
\(199\) 0.241230 + 0.0878004i 0.0171003 + 0.00622400i 0.350556 0.936542i \(-0.385993\pi\)
−0.333456 + 0.942766i \(0.608215\pi\)
\(200\) 11.6912 + 4.25524i 0.826692 + 0.300891i
\(201\) 11.0496 19.1385i 0.779381 1.34993i
\(202\) −6.23055 10.7916i −0.438380 0.759297i
\(203\) −0.414878 2.35289i −0.0291187 0.165140i
\(204\) 0.190722 + 0.160035i 0.0133532 + 0.0112047i
\(205\) 1.66772 1.39938i 0.116479 0.0977371i
\(206\) 1.28905 7.31056i 0.0898123 0.509351i
\(207\) 13.3969 4.87608i 0.931151 0.338911i
\(208\) −9.25671 −0.641837
\(209\) 0 0
\(210\) 1.18479 0.0817585
\(211\) −2.30066 + 0.837372i −0.158384 + 0.0576470i −0.419995 0.907526i \(-0.637968\pi\)
0.261611 + 0.965173i \(0.415746\pi\)
\(212\) 0.0910521 0.516382i 0.00625348 0.0354653i
\(213\) 20.5253 17.2228i 1.40637 1.18008i
\(214\) −10.5628 8.86327i −0.722060 0.605881i
\(215\) 0.595800 + 3.37895i 0.0406332 + 0.230442i
\(216\) 9.70826 + 16.8152i 0.660564 + 1.14413i
\(217\) 1.23396 2.13727i 0.0837664 0.145088i
\(218\) −2.30793 0.840019i −0.156313 0.0568933i
\(219\) 3.75877 + 1.36808i 0.253994 + 0.0924463i
\(220\) −0.180922 + 0.313366i −0.0121978 + 0.0211272i
\(221\) −0.602196 1.04303i −0.0405081 0.0701621i
\(222\) 3.33022 + 18.8866i 0.223510 + 1.26759i
\(223\) −6.51889 5.46999i −0.436537 0.366298i 0.397875 0.917440i \(-0.369748\pi\)
−0.834412 + 0.551142i \(0.814192\pi\)
\(224\) −0.277189 + 0.232589i −0.0185205 + 0.0155405i
\(225\) −3.88326 + 22.0230i −0.258884 + 1.46820i
\(226\) −22.3935 + 8.15058i −1.48959 + 0.542168i
\(227\) −14.1506 −0.939211 −0.469606 0.882876i \(-0.655604\pi\)
−0.469606 + 0.882876i \(0.655604\pi\)
\(228\) 0 0
\(229\) −20.5330 −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(230\) −3.00000 + 1.09191i −0.197814 + 0.0719985i
\(231\) 0.386659 2.19285i 0.0254403 0.144279i
\(232\) −15.5123 + 13.0164i −1.01843 + 0.854568i
\(233\) 13.5214 + 11.3458i 0.885817 + 0.743289i 0.967367 0.253380i \(-0.0815425\pi\)
−0.0815496 + 0.996669i \(0.525987\pi\)
\(234\) −3.18614 18.0695i −0.208284 1.18124i
\(235\) 3.20574 + 5.55250i 0.209119 + 0.362205i
\(236\) −0.582596 + 1.00909i −0.0379238 + 0.0656859i
\(237\) −32.0501 11.6653i −2.08188 0.757741i
\(238\) 0.205737 + 0.0748822i 0.0133360 + 0.00485389i
\(239\) −1.17617 + 2.03719i −0.0760804 + 0.131775i −0.901556 0.432663i \(-0.857574\pi\)
0.825475 + 0.564438i \(0.190907\pi\)
\(240\) −4.55303 7.88609i −0.293897 0.509045i
\(241\) 2.39646 + 13.5910i 0.154370 + 0.875473i 0.959360 + 0.282185i \(0.0910593\pi\)
−0.804990 + 0.593288i \(0.797830\pi\)
\(242\) 6.23577 + 5.23243i 0.400850 + 0.336353i
\(243\) 8.27584 6.94426i 0.530896 0.445474i
\(244\) −0.292919 + 1.66122i −0.0187522 + 0.106349i
\(245\) 5.68479 2.06910i 0.363188 0.132190i
\(246\) 9.60401 0.612329
\(247\) 0 0
\(248\) −20.9172 −1.32824
\(249\) −40.1279 + 14.6054i −2.54301 + 0.925578i
\(250\) 1.89827 10.7656i 0.120057 0.680878i
\(251\) −3.19072 + 2.67733i −0.201397 + 0.168992i −0.737908 0.674901i \(-0.764186\pi\)
0.536512 + 0.843893i \(0.319742\pi\)
\(252\) −0.260115 0.218262i −0.0163857 0.0137492i
\(253\) 1.04189 + 5.90885i 0.0655030 + 0.371486i
\(254\) 7.81702 + 13.5395i 0.490483 + 0.849542i
\(255\) 0.592396 1.02606i 0.0370973 0.0642544i
\(256\) 4.13088 + 1.50352i 0.258180 + 0.0939699i
\(257\) −0.627011 0.228213i −0.0391119 0.0142356i 0.322390 0.946607i \(-0.395514\pi\)
−0.361502 + 0.932371i \(0.617736\pi\)
\(258\) −7.56805 + 13.1082i −0.471166 + 0.816084i
\(259\) −0.858441 1.48686i −0.0533409 0.0923892i
\(260\) −0.0726338 0.411927i −0.00450456 0.0255466i
\(261\) −27.8824 23.3961i −1.72588 1.44818i
\(262\) −1.90445 + 1.59802i −0.117657 + 0.0987261i
\(263\) 1.97952 11.2264i 0.122063 0.692251i −0.860947 0.508695i \(-0.830128\pi\)
0.983009 0.183556i \(-0.0587609\pi\)
\(264\) −17.7344 + 6.45480i −1.09148 + 0.397266i
\(265\) −2.49525 −0.153282
\(266\) 0 0
\(267\) 29.6313 1.81341
\(268\) 1.33275 0.485081i 0.0814106 0.0296310i
\(269\) 3.36706 19.0955i 0.205293 1.16428i −0.691684 0.722200i \(-0.743131\pi\)
0.896978 0.442076i \(-0.145758\pi\)
\(270\) 5.98680 5.02352i 0.364345 0.305722i
\(271\) −10.2606 8.60965i −0.623286 0.522999i 0.275549 0.961287i \(-0.411141\pi\)
−0.898835 + 0.438288i \(0.855585\pi\)
\(272\) −0.292204 1.65717i −0.0177174 0.100481i
\(273\) 1.28699 + 2.22913i 0.0778921 + 0.134913i
\(274\) 0.172304 0.298439i 0.0104093 0.0180294i
\(275\) −8.84389 3.21891i −0.533307 0.194108i
\(276\) 1.34730 + 0.490376i 0.0810977 + 0.0295172i
\(277\) −8.87346 + 15.3693i −0.533154 + 0.923450i 0.466096 + 0.884734i \(0.345660\pi\)
−0.999250 + 0.0387161i \(0.987673\pi\)
\(278\) 2.87211 + 4.97464i 0.172258 + 0.298359i
\(279\) −6.52869 37.0260i −0.390862 2.21669i
\(280\) 0.688663 + 0.577857i 0.0411555 + 0.0345335i
\(281\) 14.0025 11.7495i 0.835321 0.700917i −0.121185 0.992630i \(-0.538670\pi\)
0.956506 + 0.291713i \(0.0942251\pi\)
\(282\) −4.91147 + 27.8544i −0.292474 + 1.65870i
\(283\) −7.22416 + 2.62938i −0.429431 + 0.156300i −0.547688 0.836683i \(-0.684492\pi\)
0.118256 + 0.992983i \(0.462270\pi\)
\(284\) 1.71957 0.102038
\(285\) 0 0
\(286\) 7.72193 0.456608
\(287\) −0.807934 + 0.294064i −0.0476908 + 0.0173580i
\(288\) −0.957234 + 5.42874i −0.0564055 + 0.319892i
\(289\) −12.8550 + 10.7867i −0.756179 + 0.634509i
\(290\) 6.24376 + 5.23913i 0.366646 + 0.307652i
\(291\) −4.72668 26.8063i −0.277083 1.57142i
\(292\) 0.128356 + 0.222318i 0.00751144 + 0.0130102i
\(293\) 5.25150 9.09586i 0.306796 0.531386i −0.670864 0.741581i \(-0.734076\pi\)
0.977660 + 0.210195i \(0.0674098\pi\)
\(294\) 25.0783 + 9.12776i 1.46260 + 0.532342i
\(295\) 5.21048 + 1.89646i 0.303366 + 0.110416i
\(296\) −7.27584 + 12.6021i −0.422900 + 0.732484i
\(297\) −7.34389 12.7200i −0.426136 0.738089i
\(298\) −3.87417 21.9715i −0.224425 1.27278i
\(299\) −5.31315 4.45826i −0.307267 0.257828i
\(300\) −1.72281 + 1.44561i −0.0994666 + 0.0834623i
\(301\) 0.235300 1.33445i 0.0135625 0.0769165i
\(302\) −5.52229 + 2.00995i −0.317772 + 0.115660i
\(303\) 26.6313 1.52993
\(304\) 0 0
\(305\) 8.02734 0.459644
\(306\) 3.13429 1.14079i 0.179175 0.0652144i
\(307\) −2.03091 + 11.5178i −0.115910 + 0.657358i 0.870386 + 0.492371i \(0.163870\pi\)
−0.986296 + 0.164988i \(0.947242\pi\)
\(308\) 0.109470 0.0918566i 0.00623766 0.00523401i
\(309\) 12.1532 + 10.1977i 0.691370 + 0.580128i
\(310\) 1.46198 + 8.29131i 0.0830350 + 0.470915i
\(311\) −7.98293 13.8268i −0.452670 0.784048i 0.545881 0.837863i \(-0.316195\pi\)
−0.998551 + 0.0538151i \(0.982862\pi\)
\(312\) 10.9081 18.8933i 0.617548 1.06962i
\(313\) 25.0228 + 9.10754i 1.41437 + 0.514788i 0.932409 0.361404i \(-0.117703\pi\)
0.481961 + 0.876193i \(0.339925\pi\)
\(314\) −12.1775 4.43225i −0.687217 0.250127i
\(315\) −0.807934 + 1.39938i −0.0455219 + 0.0788462i
\(316\) −1.09446 1.89565i −0.0615679 0.106639i
\(317\) 5.12819 + 29.0834i 0.288028 + 1.63349i 0.694264 + 0.719720i \(0.255730\pi\)
−0.406236 + 0.913768i \(0.633159\pi\)
\(318\) −8.43242 7.07564i −0.472867 0.396782i
\(319\) 11.7344 9.84635i 0.657002 0.551290i
\(320\) 1.31268 7.44459i 0.0733811 0.416165i
\(321\) 27.6917 10.0789i 1.54560 0.562551i
\(322\) 1.26083 0.0702633
\(323\) 0 0
\(324\) −0.576666 −0.0320370
\(325\) 10.2233 3.72097i 0.567085 0.206402i
\(326\) −1.95471 + 11.0857i −0.108261 + 0.613980i
\(327\) 4.02094 3.37397i 0.222359 0.186581i
\(328\) 5.58235 + 4.68415i 0.308234 + 0.258639i
\(329\) −0.439693 2.49362i −0.0242410 0.137478i
\(330\) 3.79813 + 6.57856i 0.209080 + 0.362138i
\(331\) −13.8327 + 23.9590i −0.760317 + 1.31691i 0.182371 + 0.983230i \(0.441623\pi\)
−0.942687 + 0.333677i \(0.891710\pi\)
\(332\) −2.57532 0.937341i −0.141339 0.0514432i
\(333\) −24.5783 8.94578i −1.34688 0.490225i
\(334\) 2.71823 4.70810i 0.148735 0.257616i
\(335\) −3.37464 5.84504i −0.184376 0.319349i
\(336\) 0.624485 + 3.54163i 0.0340685 + 0.193212i
\(337\) 13.6814 + 11.4800i 0.745273 + 0.625358i 0.934248 0.356624i \(-0.116072\pi\)
−0.188975 + 0.981982i \(0.560517\pi\)
\(338\) 6.57919 5.52060i 0.357861 0.300281i
\(339\) 8.84389 50.1562i 0.480334 2.72411i
\(340\) 0.0714517 0.0260063i 0.00387501 0.00141039i
\(341\) 15.8229 0.856861
\(342\) 0 0
\(343\) −4.82026 −0.260270
\(344\) −10.7922 + 3.92804i −0.581877 + 0.211786i
\(345\) 1.18479 6.71929i 0.0637871 0.361755i
\(346\) 20.7902 17.4451i 1.11769 0.937853i
\(347\) −4.44356 3.72859i −0.238543 0.200161i 0.515677 0.856783i \(-0.327540\pi\)
−0.754220 + 0.656622i \(0.771985\pi\)
\(348\) −0.635630 3.60483i −0.0340733 0.193239i
\(349\) −2.68614 4.65253i −0.143786 0.249044i 0.785134 0.619326i \(-0.212594\pi\)
−0.928919 + 0.370282i \(0.879261\pi\)
\(350\) −0.988856 + 1.71275i −0.0528566 + 0.0915502i
\(351\) 15.9547 + 5.80704i 0.851599 + 0.309957i
\(352\) −2.18004 0.793471i −0.116197 0.0422922i
\(353\) 12.6172 21.8537i 0.671546 1.16315i −0.305919 0.952057i \(-0.598964\pi\)
0.977466 0.211095i \(-0.0677029\pi\)
\(354\) 12.2306 + 21.1839i 0.650047 + 1.12591i
\(355\) −1.42097 8.05872i −0.0754172 0.427712i
\(356\) 1.45677 + 1.22237i 0.0772085 + 0.0647856i
\(357\) −0.358441 + 0.300767i −0.0189707 + 0.0159183i
\(358\) 2.69341 15.2751i 0.142351 0.807314i
\(359\) −6.28359 + 2.28704i −0.331635 + 0.120705i −0.502471 0.864594i \(-0.667575\pi\)
0.170836 + 0.985300i \(0.445353\pi\)
\(360\) 13.6955 0.721818
\(361\) 0 0
\(362\) −11.5021 −0.604535
\(363\) −16.3478 + 5.95010i −0.858035 + 0.312299i
\(364\) −0.0286853 + 0.162683i −0.00150352 + 0.00852688i
\(365\) 0.935822 0.785248i 0.0489832 0.0411018i
\(366\) 27.1275 + 22.7627i 1.41798 + 1.18982i
\(367\) 1.40983 + 7.99552i 0.0735923 + 0.417363i 0.999240 + 0.0389764i \(0.0124097\pi\)
−0.925648 + 0.378386i \(0.876479\pi\)
\(368\) −4.84524 8.39220i −0.252575 0.437473i
\(369\) −6.54916 + 11.3435i −0.340936 + 0.590518i
\(370\) 5.50387 + 2.00324i 0.286133 + 0.104144i
\(371\) 0.926022 + 0.337044i 0.0480767 + 0.0174985i
\(372\) 1.89053 3.27449i 0.0980194 0.169775i
\(373\) −17.4488 30.2222i −0.903463 1.56484i −0.822967 0.568090i \(-0.807683\pi\)
−0.0804968 0.996755i \(-0.525651\pi\)
\(374\) 0.243756 + 1.38241i 0.0126043 + 0.0714826i
\(375\) 17.8969 + 15.0173i 0.924193 + 0.775490i
\(376\) −16.4402 + 13.7949i −0.847836 + 0.711419i
\(377\) −3.07486 + 17.4384i −0.158363 + 0.898122i
\(378\) −2.90033 + 1.05563i −0.149177 + 0.0542959i
\(379\) 1.70140 0.0873950 0.0436975 0.999045i \(-0.486086\pi\)
0.0436975 + 0.999045i \(0.486086\pi\)
\(380\) 0 0
\(381\) −33.4124 −1.71177
\(382\) 23.2135 8.44901i 1.18770 0.432289i
\(383\) 0.509962 2.89214i 0.0260579 0.147781i −0.969003 0.247049i \(-0.920539\pi\)
0.995061 + 0.0992680i \(0.0316501\pi\)
\(384\) 20.9500 17.5791i 1.06910 0.897080i
\(385\) −0.520945 0.437124i −0.0265498 0.0222779i
\(386\) −0.0696407 0.394952i −0.00354462 0.0201025i
\(387\) −10.3216 17.8775i −0.524677 0.908767i
\(388\) 0.873455 1.51287i 0.0443430 0.0768043i
\(389\) 23.0856 + 8.40247i 1.17049 + 0.426022i 0.852832 0.522185i \(-0.174883\pi\)
0.317654 + 0.948207i \(0.397105\pi\)
\(390\) −8.25150 3.00330i −0.417831 0.152078i
\(391\) 0.630415 1.09191i 0.0318815 0.0552203i
\(392\) 10.1250 + 17.5369i 0.511387 + 0.885749i
\(393\) −0.922618 5.23243i −0.0465399 0.263941i
\(394\) −13.5628 11.3806i −0.683286 0.573345i
\(395\) −7.97952 + 6.69561i −0.401493 + 0.336893i
\(396\) 0.378041 2.14398i 0.0189973 0.107739i
\(397\) 29.9158 10.8885i 1.50143 0.546476i 0.545001 0.838436i \(-0.316529\pi\)
0.956431 + 0.291959i \(0.0943071\pi\)
\(398\) 0.345866 0.0173367
\(399\) 0 0
\(400\) 15.2003 0.760014
\(401\) 0.0812519 0.0295733i 0.00405753 0.00147682i −0.339991 0.940429i \(-0.610424\pi\)
0.344048 + 0.938952i \(0.388202\pi\)
\(402\) 5.17024 29.3219i 0.257868 1.46244i
\(403\) −14.0116 + 11.7571i −0.697968 + 0.585665i
\(404\) 1.30928 + 1.09861i 0.0651390 + 0.0546581i
\(405\) 0.476529 + 2.70253i 0.0236789 + 0.134290i
\(406\) −1.60947 2.78768i −0.0798767 0.138350i
\(407\) 5.50387 9.53298i 0.272817 0.472532i
\(408\) 3.72668 + 1.35640i 0.184498 + 0.0671519i
\(409\) −18.7995 6.84245i −0.929574 0.338337i −0.167534 0.985866i \(-0.553580\pi\)
−0.762041 + 0.647529i \(0.775802\pi\)
\(410\) 1.46657 2.54017i 0.0724286 0.125450i
\(411\) 0.368241 + 0.637812i 0.0181640 + 0.0314609i
\(412\) 0.176803 + 1.00270i 0.00871048 + 0.0493996i
\(413\) −1.67752 1.40761i −0.0825453 0.0692637i
\(414\) 14.7142 12.3467i 0.723163 0.606806i
\(415\) −2.26470 + 12.8438i −0.111170 + 0.630475i
\(416\) 2.52007 0.917229i 0.123556 0.0449709i
\(417\) −12.2763 −0.601174
\(418\) 0 0
\(419\) 25.4097 1.24135 0.620673 0.784070i \(-0.286859\pi\)
0.620673 + 0.784070i \(0.286859\pi\)
\(420\) −0.152704 + 0.0555796i −0.00745117 + 0.00271201i
\(421\) 0.758770 4.30320i 0.0369802 0.209725i −0.960719 0.277524i \(-0.910486\pi\)
0.997699 + 0.0677984i \(0.0215975\pi\)
\(422\) −2.52687 + 2.12030i −0.123006 + 0.103215i
\(423\) −29.5501 24.7955i −1.43677 1.20560i
\(424\) −1.45037 8.22546i −0.0704362 0.399464i
\(425\) 0.988856 + 1.71275i 0.0479665 + 0.0830805i
\(426\) 18.0496 31.2629i 0.874507 1.51469i
\(427\) −2.97906 1.08429i −0.144167 0.0524724i
\(428\) 1.77719 + 0.646844i 0.0859037 + 0.0312664i
\(429\) −8.25150 + 14.2920i −0.398386 + 0.690025i
\(430\) 2.31134 + 4.00335i 0.111463 + 0.193059i
\(431\) −6.65183 37.7244i −0.320407 1.81712i −0.540158 0.841564i \(-0.681636\pi\)
0.219751 0.975556i \(-0.429476\pi\)
\(432\) 18.1721 + 15.2482i 0.874303 + 0.733628i
\(433\) −13.8892 + 11.6544i −0.667472 + 0.560075i −0.912316 0.409487i \(-0.865708\pi\)
0.244844 + 0.969562i \(0.421263\pi\)
\(434\) 0.577382 3.27449i 0.0277152 0.157181i
\(435\) −16.3687 + 5.95772i −0.784819 + 0.285651i
\(436\) 0.336867 0.0161330
\(437\) 0 0
\(438\) 5.38919 0.257505
\(439\) 5.72328 2.08310i 0.273157 0.0994211i −0.201810 0.979425i \(-0.564682\pi\)
0.474967 + 0.880004i \(0.342460\pi\)
\(440\) −1.00088 + 5.67626i −0.0477150 + 0.270605i
\(441\) −27.8824 + 23.3961i −1.32773 + 1.11410i
\(442\) −1.24304 1.04303i −0.0591254 0.0496121i
\(443\) −5.19088 29.4390i −0.246626 1.39869i −0.816685 0.577084i \(-0.804191\pi\)
0.570059 0.821604i \(-0.306920\pi\)
\(444\) −1.31521 2.27801i −0.0624170 0.108109i
\(445\) 4.52481 7.83721i 0.214497 0.371519i
\(446\) −10.7738 3.92134i −0.510154 0.185681i
\(447\) 44.8055 + 16.3079i 2.11923 + 0.771335i
\(448\) −1.49273 + 2.58548i −0.0705247 + 0.122152i
\(449\) 5.62495 + 9.74270i 0.265458 + 0.459787i 0.967683 0.252168i \(-0.0811435\pi\)
−0.702226 + 0.711955i \(0.747810\pi\)
\(450\) 5.23190 + 29.6716i 0.246634 + 1.39873i
\(451\) −4.22281 3.54336i −0.198844 0.166850i
\(452\) 2.50387 2.10100i 0.117772 0.0988226i
\(453\) 2.18092 12.3686i 0.102469 0.581129i
\(454\) −17.9153 + 6.52065i −0.840809 + 0.306029i
\(455\) 0.786112 0.0368535
\(456\) 0 0
\(457\) −23.3901 −1.09414 −0.547072 0.837086i \(-0.684258\pi\)
−0.547072 + 0.837086i \(0.684258\pi\)
\(458\) −25.9957 + 9.46167i −1.21470 + 0.442115i
\(459\) −0.535959 + 3.03958i −0.0250164 + 0.141875i
\(460\) 0.335437 0.281465i 0.0156398 0.0131234i
\(461\) −28.0553 23.5412i −1.30667 1.09642i −0.988952 0.148237i \(-0.952640\pi\)
−0.317714 0.948187i \(-0.602915\pi\)
\(462\) −0.520945 2.95442i −0.0242365 0.137452i
\(463\) 21.4932 + 37.2273i 0.998873 + 1.73010i 0.540534 + 0.841322i \(0.318222\pi\)
0.458340 + 0.888777i \(0.348444\pi\)
\(464\) −12.3701 + 21.4256i −0.574265 + 0.994657i
\(465\) −16.9081 6.15403i −0.784093 0.285387i
\(466\) 22.3469 + 8.13360i 1.03520 + 0.376782i
\(467\) −12.7981 + 22.1670i −0.592227 + 1.02577i 0.401705 + 0.915769i \(0.368418\pi\)
−0.993932 + 0.109998i \(0.964916\pi\)
\(468\) 1.25830 + 2.17945i 0.0581651 + 0.100745i
\(469\) 0.462859 + 2.62500i 0.0213728 + 0.121211i
\(470\) 6.61721 + 5.55250i 0.305229 + 0.256118i
\(471\) 21.2160 17.8023i 0.977582 0.820289i
\(472\) −3.22297 + 18.2784i −0.148349 + 0.841331i
\(473\) 8.16385 2.97140i 0.375374 0.136625i
\(474\) −45.9522 −2.11066
\(475\) 0 0
\(476\) −0.0300295 −0.00137640
\(477\) 14.1074 5.13468i 0.645934 0.235101i
\(478\) −0.550345 + 3.12116i −0.0251722 + 0.142759i
\(479\) 29.2447 24.5392i 1.33622 1.12123i 0.353645 0.935380i \(-0.384942\pi\)
0.982579 0.185845i \(-0.0595023\pi\)
\(480\) 2.02094 + 1.69577i 0.0922431 + 0.0774011i
\(481\) 2.20961 + 12.5313i 0.100749 + 0.571378i
\(482\) 9.29679 + 16.1025i 0.423457 + 0.733449i
\(483\) −1.34730 + 2.33359i −0.0613041 + 0.106182i
\(484\) −1.04916 0.381864i −0.0476892 0.0173575i
\(485\) −7.81180 2.84326i −0.354716 0.129106i
\(486\) 7.27766 12.6053i 0.330121 0.571787i
\(487\) −3.88191 6.72367i −0.175906 0.304678i 0.764568 0.644543i \(-0.222952\pi\)
−0.940475 + 0.339864i \(0.889619\pi\)
\(488\) 4.66591 + 26.4617i 0.211216 + 1.19786i
\(489\) −18.4290 15.4638i −0.833389 0.699296i
\(490\) 6.24376 5.23913i 0.282064 0.236680i
\(491\) −6.37686 + 36.1650i −0.287784 + 1.63210i 0.407386 + 0.913256i \(0.366440\pi\)
−0.695169 + 0.718846i \(0.744671\pi\)
\(492\) −1.23783 + 0.450532i −0.0558055 + 0.0203115i
\(493\) −3.21894 −0.144974
\(494\) 0 0
\(495\) −10.3601 −0.465651
\(496\) −24.0141 + 8.74043i −1.07827 + 0.392457i
\(497\) −0.561185 + 3.18264i −0.0251726 + 0.142761i
\(498\) −44.0736 + 36.9821i −1.97498 + 1.65721i
\(499\) 3.77379 + 3.16658i 0.168938 + 0.141756i 0.723337 0.690495i \(-0.242607\pi\)
−0.554399 + 0.832251i \(0.687052\pi\)
\(500\) 0.260363 + 1.47659i 0.0116438 + 0.0660352i
\(501\) 5.80928 + 10.0620i 0.259539 + 0.449535i
\(502\) −2.80587 + 4.85992i −0.125232 + 0.216909i
\(503\) −30.9624 11.2694i −1.38055 0.502478i −0.458203 0.888847i \(-0.651507\pi\)
−0.922344 + 0.386369i \(0.873729\pi\)
\(504\) −5.08260 1.84991i −0.226397 0.0824017i
\(505\) 4.06670 7.04374i 0.180966 0.313442i
\(506\) 4.04189 + 7.00076i 0.179684 + 0.311222i
\(507\) 3.18732 + 18.0762i 0.141554 + 0.802791i
\(508\) −1.64266 1.37835i −0.0728810 0.0611544i
\(509\) −28.2939 + 23.7414i −1.25410 + 1.05232i −0.257819 + 0.966193i \(0.583004\pi\)
−0.996284 + 0.0861240i \(0.972552\pi\)
\(510\) 0.277189 1.57202i 0.0122741 0.0696100i
\(511\) −0.453363 + 0.165011i −0.0200556 + 0.00729964i
\(512\) 24.9186 1.10126
\(513\) 0 0
\(514\) −0.898986 −0.0396526
\(515\) 4.55303 1.65717i 0.200631 0.0730236i
\(516\) 0.360500 2.04450i 0.0158701 0.0900040i
\(517\) 12.4363 10.4353i 0.546947 0.458943i
\(518\) −1.77197 1.48686i −0.0778561 0.0653290i
\(519\) 10.0719 + 57.1207i 0.442108 + 2.50732i
\(520\) −3.33140 5.77016i −0.146092 0.253038i
\(521\) −4.64590 + 8.04693i −0.203540 + 0.352542i −0.949667 0.313262i \(-0.898578\pi\)
0.746126 + 0.665804i \(0.231912\pi\)
\(522\) −46.0813 16.7722i −2.01692 0.734100i
\(523\) 26.7015 + 9.71854i 1.16757 + 0.424962i 0.851797 0.523872i \(-0.175513\pi\)
0.315776 + 0.948834i \(0.397735\pi\)
\(524\) 0.170493 0.295303i 0.00744802 0.0129004i
\(525\) −2.11334 3.66041i −0.0922338 0.159754i
\(526\) −2.66700 15.1253i −0.116287 0.659496i
\(527\) −2.54710 2.13727i −0.110954 0.0931011i
\(528\) −17.6630 + 14.8210i −0.768682 + 0.645001i
\(529\) −2.73308 + 15.5001i −0.118829 + 0.673916i
\(530\) −3.15910 + 1.14982i −0.137223 + 0.0499449i
\(531\) −33.3610 −1.44775
\(532\) 0 0
\(533\) 6.37227 0.276014
\(534\) 37.5146 13.6542i 1.62342 0.590875i
\(535\) 1.56283 8.86327i 0.0675672 0.383193i
\(536\) 17.3063 14.5217i 0.747520 0.627244i
\(537\) 25.3935 + 21.3077i 1.09581 + 0.919495i
\(538\) −4.53643 25.7274i −0.195579 1.10918i
\(539\) −7.65910 13.2660i −0.329901 0.571405i
\(540\) −0.535959 + 0.928309i −0.0230640 + 0.0399480i
\(541\) −14.0817 5.12533i −0.605420 0.220355i 0.0210779 0.999778i \(-0.493290\pi\)
−0.626498 + 0.779423i \(0.715512\pi\)
\(542\) −16.9577 6.17210i −0.728396 0.265114i
\(543\) 12.2909 21.2884i 0.527451 0.913572i
\(544\) 0.243756 + 0.422197i 0.0104509 + 0.0181016i
\(545\) −0.278371 1.57872i −0.0119241 0.0676249i
\(546\) 2.65657 + 2.22913i 0.113691 + 0.0953980i
\(547\) −2.97771 + 2.49860i −0.127318 + 0.106832i −0.704223 0.709979i \(-0.748705\pi\)
0.576905 + 0.816811i \(0.304260\pi\)
\(548\) −0.00820761 + 0.0465477i −0.000350612 + 0.00198842i
\(549\) −45.3842 + 16.5185i −1.93695 + 0.704992i
\(550\) −12.6800 −0.540679
\(551\) 0 0
\(552\) 22.8384 0.972068
\(553\) 3.86571 1.40701i 0.164387 0.0598319i
\(554\) −4.15199 + 23.5471i −0.176401 + 1.00042i
\(555\) −9.58899 + 8.04612i −0.407030 + 0.341539i
\(556\) −0.603541 0.506431i −0.0255958 0.0214774i
\(557\) 2.29292 + 13.0038i 0.0971541 + 0.550988i 0.994066 + 0.108779i \(0.0346940\pi\)
−0.896912 + 0.442209i \(0.854195\pi\)
\(558\) −25.3273 43.8681i −1.07219 1.85709i
\(559\) −5.02141 + 8.69734i −0.212383 + 0.367858i
\(560\) 1.03209 + 0.375650i 0.0436137 + 0.0158741i
\(561\) −2.81908 1.02606i −0.119022 0.0433203i
\(562\) 12.3136 21.3278i 0.519418 0.899659i
\(563\) −5.35638 9.27752i −0.225745 0.391001i 0.730798 0.682594i \(-0.239148\pi\)
−0.956543 + 0.291593i \(0.905815\pi\)
\(564\) −0.673648 3.82045i −0.0283657 0.160870i
\(565\) −11.9153 9.99816i −0.501282 0.420626i
\(566\) −7.93448 + 6.65782i −0.333511 + 0.279849i
\(567\) 0.188196 1.06731i 0.00790349 0.0448229i
\(568\) 25.7392 9.36829i 1.07999 0.393085i
\(569\) −13.4706 −0.564717 −0.282358 0.959309i \(-0.591117\pi\)
−0.282358 + 0.959309i \(0.591117\pi\)
\(570\) 0 0
\(571\) 12.6655 0.530035 0.265017 0.964244i \(-0.414622\pi\)
0.265017 + 0.964244i \(0.414622\pi\)
\(572\) −0.995252 + 0.362242i −0.0416136 + 0.0151461i
\(573\) −9.16772 + 51.9927i −0.382987 + 2.17203i
\(574\) −0.887374 + 0.744596i −0.0370383 + 0.0310788i
\(575\) 8.72462 + 7.32083i 0.363842 + 0.305300i
\(576\) 7.89780 + 44.7907i 0.329075 + 1.86628i
\(577\) 5.27719 + 9.14036i 0.219692 + 0.380518i 0.954714 0.297526i \(-0.0961613\pi\)
−0.735022 + 0.678044i \(0.762828\pi\)
\(578\) −11.3045 + 19.5800i −0.470206 + 0.814421i
\(579\) 0.805407 + 0.293144i 0.0334716 + 0.0121827i
\(580\) −1.05051 0.382353i −0.0436199 0.0158764i
\(581\) 2.57532 4.46059i 0.106842 0.185056i
\(582\) −18.3366 31.7600i −0.760077 1.31649i
\(583\) 1.09714 + 6.22221i 0.0454391 + 0.257698i
\(584\) 3.13247 + 2.62846i 0.129623 + 0.108766i
\(585\) 9.17412 7.69800i 0.379303 0.318273i
\(586\) 2.45723 13.9357i 0.101507 0.575677i
\(587\) 17.9996 6.55131i 0.742923 0.270402i 0.0572981 0.998357i \(-0.481751\pi\)
0.685624 + 0.727955i \(0.259529\pi\)
\(588\) −3.66044 −0.150954
\(589\) 0 0
\(590\) 7.47060 0.307560
\(591\) 35.5565 12.9415i 1.46260 0.532342i
\(592\) −3.08718 + 17.5083i −0.126882 + 0.719586i
\(593\) −6.66044 + 5.58878i −0.273512 + 0.229504i −0.769218 0.638987i \(-0.779354\pi\)
0.495706 + 0.868490i \(0.334909\pi\)
\(594\) −15.1591 12.7200i −0.621985 0.521908i
\(595\) 0.0248149 + 0.140732i 0.00101731 + 0.00576947i
\(596\) 1.53003 + 2.65009i 0.0626724 + 0.108552i
\(597\) −0.369585 + 0.640140i −0.0151261 + 0.0261992i
\(598\) −8.78106 3.19604i −0.359084 0.130696i
\(599\) −18.6356 6.78281i −0.761431 0.277138i −0.0680235 0.997684i \(-0.521669\pi\)
−0.693408 + 0.720545i \(0.743891\pi\)
\(600\) −17.9119 + 31.0244i −0.731252 + 1.26657i
\(601\) 16.8807 + 29.2383i 0.688579 + 1.19265i 0.972298 + 0.233747i \(0.0750986\pi\)
−0.283718 + 0.958908i \(0.591568\pi\)
\(602\) −0.317018 1.79790i −0.0129207 0.0732770i
\(603\) 31.1070 + 26.1019i 1.26677 + 1.06295i
\(604\) 0.617460 0.518110i 0.0251241 0.0210816i
\(605\) −0.922618 + 5.23243i −0.0375098 + 0.212729i
\(606\) 33.7165 12.2718i 1.36964 0.498507i
\(607\) 35.2850 1.43217 0.716087 0.698011i \(-0.245932\pi\)
0.716087 + 0.698011i \(0.245932\pi\)
\(608\) 0 0
\(609\) 6.87939 0.278767
\(610\) 10.1630 3.69902i 0.411487 0.149769i
\(611\) −3.25877 + 18.4814i −0.131836 + 0.747678i
\(612\) −0.350452 + 0.294064i −0.0141662 + 0.0118868i
\(613\) 14.1361 + 11.8616i 0.570952 + 0.479085i 0.881962 0.471321i \(-0.156223\pi\)
−0.311010 + 0.950407i \(0.600667\pi\)
\(614\) 2.73623 + 15.5180i 0.110425 + 0.626254i
\(615\) 3.13429 + 5.42874i 0.126387 + 0.218908i
\(616\) 1.13816 1.97134i 0.0458576 0.0794277i
\(617\) 33.5333 + 12.2051i 1.35000 + 0.491360i 0.912948 0.408076i \(-0.133800\pi\)
0.437053 + 0.899436i \(0.356022\pi\)
\(618\) 20.0856 + 7.31056i 0.807961 + 0.294074i
\(619\) −1.82976 + 3.16923i −0.0735441 + 0.127382i −0.900452 0.434955i \(-0.856764\pi\)
0.826908 + 0.562337i \(0.190098\pi\)
\(620\) −0.577382 1.00005i −0.0231882 0.0401631i
\(621\) 3.08647 + 17.5042i 0.123856 + 0.702420i
\(622\) −16.4782 13.8268i −0.660715 0.554406i
\(623\) −2.73783 + 2.29731i −0.109689 + 0.0920397i
\(624\) 4.62836 26.2487i 0.185283 1.05079i
\(625\) −13.1540 + 4.78768i −0.526162 + 0.191507i
\(626\) 35.8767 1.43392
\(627\) 0 0
\(628\) 1.77744 0.0709275
\(629\) −2.17365 + 0.791143i −0.0866690 + 0.0315449i
\(630\) −0.378041 + 2.14398i −0.0150615 + 0.0854181i
\(631\) −0.608126 + 0.510278i −0.0242091 + 0.0203139i −0.654812 0.755792i \(-0.727252\pi\)
0.630603 + 0.776106i \(0.282808\pi\)
\(632\) −26.7098 22.4122i −1.06246 0.891510i
\(633\) −1.22416 6.94253i −0.0486558 0.275941i
\(634\) 19.8942 + 34.4578i 0.790101 + 1.36850i
\(635\) −5.10220 + 8.83726i −0.202474 + 0.350696i
\(636\) 1.41875 + 0.516382i 0.0562570 + 0.0204759i
\(637\) 16.6395 + 6.05628i 0.659281 + 0.239959i
\(638\) 10.3191 17.8732i 0.408536 0.707605i
\(639\) 24.6168 + 42.6375i 0.973826 + 1.68672i
\(640\) −1.45037 8.22546i −0.0573309 0.325140i
\(641\) 22.5082 + 18.8866i 0.889021 + 0.745977i 0.968013 0.250898i \(-0.0807259\pi\)
−0.0789927 + 0.996875i \(0.525170\pi\)
\(642\) 30.4145 25.5208i 1.20036 1.00722i
\(643\) 3.85740 21.8764i 0.152121 0.862721i −0.809250 0.587465i \(-0.800126\pi\)
0.961371 0.275257i \(-0.0887628\pi\)
\(644\) −0.162504 + 0.0591466i −0.00640355 + 0.00233070i
\(645\) −9.87939 −0.389000
\(646\) 0 0
\(647\) 11.2591 0.442640 0.221320 0.975201i \(-0.428963\pi\)
0.221320 + 0.975201i \(0.428963\pi\)
\(648\) −8.63176 + 3.14170i −0.339088 + 0.123418i
\(649\) 2.43804 13.8268i 0.0957016 0.542751i
\(650\) 11.2285 9.42182i 0.440418 0.369554i
\(651\) 5.44356 + 4.56769i 0.213350 + 0.179022i
\(652\) −0.268104 1.52049i −0.0104998 0.0595471i
\(653\) −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) 3.53596 6.12446i 0.138267 0.239485i
\(655\) −1.52481 0.554987i −0.0595794 0.0216851i
\(656\) 8.36618 + 3.04504i 0.326645 + 0.118889i
\(657\) −3.67499 + 6.36527i −0.143375 + 0.248333i
\(658\) −1.70574 2.95442i −0.0664966 0.115175i
\(659\) 4.86665 + 27.6001i 0.189578 + 1.07515i 0.919931 + 0.392079i \(0.128244\pi\)
−0.730354 + 0.683069i \(0.760645\pi\)
\(660\) −0.798133 0.669713i −0.0310673 0.0260686i
\(661\) 8.70826 7.30710i 0.338712 0.284213i −0.457526 0.889196i \(-0.651264\pi\)
0.796239 + 0.604983i \(0.206820\pi\)
\(662\) −6.47250 + 36.7074i −0.251561 + 1.42667i
\(663\) 3.25877 1.18610i 0.126560 0.0460641i
\(664\) −43.6551 −1.69415
\(665\) 0 0
\(666\) −35.2395 −1.36550
\(667\) −17.4192 + 6.34008i −0.674475 + 0.245489i
\(668\) −0.129481 + 0.734325i −0.00500978 + 0.0284119i
\(669\) 18.7704 15.7502i 0.725705 0.608939i
\(670\) −6.96585 5.84504i −0.269114 0.225814i
\(671\) −3.52956 20.0171i −0.136257 0.772753i
\(672\) −0.520945 0.902302i −0.0200959 0.0348071i
\(673\) 8.28359 14.3476i 0.319309 0.553059i −0.661035 0.750355i \(-0.729883\pi\)
0.980344 + 0.197296i \(0.0632160\pi\)
\(674\) 22.6113 + 8.22983i 0.870954 + 0.317001i
\(675\) −26.1989 9.53563i −1.00840 0.367027i
\(676\) −0.588993 + 1.02017i −0.0226536 + 0.0392371i
\(677\) 4.52481 + 7.83721i 0.173903 + 0.301208i 0.939781 0.341777i \(-0.111029\pi\)
−0.765878 + 0.642986i \(0.777695\pi\)
\(678\) −11.9153 67.5753i −0.457606 2.59521i
\(679\) 2.51501 + 2.11035i 0.0965174 + 0.0809877i
\(680\) 0.927833 0.778544i 0.0355808 0.0298558i
\(681\) 7.07532 40.1261i 0.271127 1.53764i
\(682\) 20.0326 7.29125i 0.767086 0.279197i
\(683\) 8.73143 0.334099 0.167049 0.985949i \(-0.446576\pi\)
0.167049 + 0.985949i \(0.446576\pi\)
\(684\) 0 0
\(685\) 0.224927 0.00859402
\(686\) −6.10266 + 2.22119i −0.233001 + 0.0848053i
\(687\) 10.2665 58.2243i 0.391692 2.22139i
\(688\) −10.7487 + 9.01925i −0.409791 + 0.343856i
\(689\) −5.59492 4.69470i −0.213150 0.178854i
\(690\) −1.59627 9.05288i −0.0607688 0.344637i
\(691\) −17.3601 30.0686i −0.660409 1.14386i −0.980508 0.196478i \(-0.937050\pi\)
0.320099 0.947384i \(-0.396284\pi\)
\(692\) −1.86122 + 3.22372i −0.0707528 + 0.122547i
\(693\) 3.84477 + 1.39938i 0.146051 + 0.0531581i
\(694\) −7.34389 2.67296i −0.278770 0.101464i
\(695\) −1.87464 + 3.24697i −0.0711091 + 0.123164i
\(696\) −29.1536 50.4956i −1.10507 1.91403i
\(697\) 0.201151 + 1.14079i 0.00761915 + 0.0432104i
\(698\) −5.54466 4.65253i −0.209869 0.176101i
\(699\) −38.9334 + 32.6690i −1.47259 + 1.23565i
\(700\) 0.0471036 0.267138i 0.00178035 0.0100969i
\(701\) −37.0381 + 13.4808i −1.39891 + 0.509161i −0.927854 0.372943i \(-0.878349\pi\)
−0.471055 + 0.882104i \(0.656126\pi\)
\(702\) 22.8753 0.863371
\(703\) 0 0
\(704\) −19.1411 −0.721409
\(705\) −17.3478 + 6.31407i −0.653355 + 0.237802i
\(706\) 5.90373 33.4817i 0.222190 1.26010i
\(707\) −2.46064 + 2.06472i −0.0925418 + 0.0776518i
\(708\) −2.57011 2.15658i −0.0965906 0.0810491i
\(709\) −7.14068 40.4968i −0.268174 1.52089i −0.759842 0.650107i \(-0.774724\pi\)
0.491668 0.870783i \(-0.336387\pi\)
\(710\) −5.51249 9.54791i −0.206880 0.358327i
\(711\) 31.3357 54.2751i 1.17518 2.03548i
\(712\) 28.4650 + 10.3604i 1.06677 + 0.388273i
\(713\) −17.9932 6.54899i −0.673850 0.245261i
\(714\) −0.315207 + 0.545955i −0.0117963 + 0.0204319i
\(715\) 2.52007 + 4.36488i 0.0942452 + 0.163237i
\(716\) 0.369423 + 2.09510i 0.0138060 + 0.0782976i
\(717\) −5.18866 4.35381i −0.193774 0.162596i
\(718\) −6.90143 + 5.79098i −0.257559 + 0.216118i
\(719\) −7.36190 + 41.7514i −0.274553 + 1.55706i 0.465827 + 0.884876i \(0.345757\pi\)
−0.740379 + 0.672189i \(0.765354\pi\)
\(720\) 15.7233 5.72281i 0.585972 0.213276i
\(721\) −1.91353 −0.0712637
\(722\) 0 0
\(723\) −39.7374 −1.47785
\(724\) 1.48246 0.539571i 0.0550952 0.0200530i
\(725\) 5.04916 28.6352i 0.187521 1.06349i
\(726\) −17.9552 + 15.0662i −0.666379 + 0.559158i
\(727\) 39.5710 + 33.2040i 1.46761 + 1.23147i 0.918321 + 0.395837i \(0.129545\pi\)
0.549288 + 0.835633i \(0.314899\pi\)
\(728\) 0.456929 + 2.59137i 0.0169349 + 0.0960427i
\(729\) 20.2344 + 35.0470i 0.749423 + 1.29804i
\(730\) 0.822948 1.42539i 0.0304587 0.0527560i
\(731\) −1.71554 0.624404i −0.0634514 0.0230944i
\(732\) −4.56418 1.66122i −0.168697 0.0614006i
\(733\) 11.4581 19.8460i 0.423215 0.733030i −0.573037 0.819530i \(-0.694235\pi\)
0.996252 + 0.0864997i \(0.0275682\pi\)
\(734\) 5.46926 + 9.47303i 0.201874 + 0.349656i
\(735\) 3.02481 + 17.1546i 0.111572 + 0.632756i
\(736\) 2.15064 + 1.80460i 0.0792738 + 0.0665186i
\(737\) −13.0915 + 10.9851i −0.482232 + 0.404641i
\(738\) −3.06443 + 17.3792i −0.112803 + 0.639738i
\(739\) −26.4304 + 9.61986i −0.972256 + 0.353872i −0.778825 0.627241i \(-0.784184\pi\)
−0.193432 + 0.981114i \(0.561962\pi\)
\(740\) −0.803348 −0.0295317
\(741\) 0 0
\(742\) 1.32770 0.0487413
\(743\) −5.76264 + 2.09743i −0.211411 + 0.0769472i −0.445555 0.895255i \(-0.646994\pi\)
0.234144 + 0.972202i \(0.424771\pi\)
\(744\) 10.4586 59.3135i 0.383430 2.17454i
\(745\) 11.1552 9.36035i 0.408696 0.342937i
\(746\) −36.0174 30.2222i −1.31869 1.10651i
\(747\) −13.6257 77.2750i −0.498537 2.82734i
\(748\) −0.0962667 0.166739i −0.00351986 0.00609657i
\(749\) −1.77719 + 3.07818i −0.0649371 + 0.112474i
\(750\) 29.5783 + 10.7656i 1.08005 + 0.393105i
\(751\) −5.30066 1.92928i −0.193424 0.0704005i 0.243492 0.969903i \(-0.421707\pi\)
−0.436916 + 0.899502i \(0.643929\pi\)
\(752\) −13.1099 + 22.7071i −0.478070 + 0.828042i
\(753\) −5.99660 10.3864i −0.218528 0.378502i
\(754\) 4.14274 + 23.4947i 0.150870 + 0.855625i
\(755\) −2.93835 2.46557i −0.106937 0.0897312i
\(756\) 0.324292 0.272114i 0.0117944 0.00989668i
\(757\) 2.72487 15.4535i 0.0990371 0.561667i −0.894398 0.447272i \(-0.852396\pi\)
0.993435 0.114396i \(-0.0364932\pi\)
\(758\) 2.15405 0.784009i 0.0782385 0.0284765i
\(759\) −17.2763 −0.627090
\(760\) 0 0
\(761\) 4.86484 0.176350 0.0881751 0.996105i \(-0.471896\pi\)
0.0881751 + 0.996105i \(0.471896\pi\)
\(762\) −42.3016 + 15.3965i −1.53243 + 0.557757i
\(763\) −0.109937 + 0.623485i −0.00398000 + 0.0225717i
\(764\) −2.59555 + 2.17793i −0.0939038 + 0.0787946i
\(765\) 1.66772 + 1.39938i 0.0602965 + 0.0505948i
\(766\) −0.687070 3.89657i −0.0248249 0.140789i
\(767\) 8.11499 + 14.0556i 0.293015 + 0.507517i
\(768\) −6.32888 + 10.9619i −0.228374 + 0.395555i
\(769\) −21.1732 7.70643i −0.763526 0.277901i −0.0692404 0.997600i \(-0.522058\pi\)
−0.694286 + 0.719699i \(0.744280\pi\)
\(770\) −0.860967 0.313366i −0.0310271 0.0112929i
\(771\) 0.960637 1.66387i 0.0345965 0.0599229i
\(772\) 0.0275033 + 0.0476371i 0.000989864 + 0.00171450i
\(773\) −4.58987 26.0304i −0.165086 0.936250i −0.948976 0.315350i \(-0.897878\pi\)
0.783889 0.620900i \(-0.213233\pi\)
\(774\) −21.3056 17.8775i −0.765815 0.642595i
\(775\) 23.0082 19.3062i 0.826479 0.693498i
\(776\) 4.83203 27.4038i 0.173460 0.983740i
\(777\) 4.64543 1.69080i 0.166654 0.0606570i
\(778\) 33.0993 1.18667
\(779\) 0 0
\(780\) 1.20439 0.0431242
\(781\) −19.4706 + 7.08672i −0.696713 + 0.253583i
\(782\) 0.294978 1.67290i 0.0105484 0.0598229i
\(783\) 34.7618 29.1686i 1.24228 1.04240i
\(784\) 18.9520 + 15.9026i 0.676858 + 0.567951i
\(785\) −1.46879 8.32991i −0.0524233 0.297307i
\(786\) −3.57919 6.19934i −0.127666 0.221123i
\(787\) 7.77884 13.4733i 0.277286 0.480273i −0.693424 0.720530i \(-0.743899\pi\)
0.970709 + 0.240257i \(0.0772318\pi\)
\(788\) 2.28194 + 0.830557i 0.0812906 + 0.0295874i
\(789\) 30.8444 + 11.2264i 1.09809 + 0.399671i
\(790\) −7.01707 + 12.1539i −0.249656 + 0.432417i
\(791\) 3.07145 + 5.31991i 0.109208 + 0.189154i
\(792\) −6.02182 34.1514i −0.213976 1.21352i
\(793\) 17.9991 + 15.1031i 0.639168 + 0.536325i
\(794\) 32.8573 27.5706i 1.16606 0.978443i
\(795\) 1.24763 7.07564i 0.0442487 0.250947i
\(796\) −0.0445774 + 0.0162249i −0.00158000 + 0.000575075i
\(797\) 33.4935 1.18640 0.593200 0.805055i \(-0.297864\pi\)
0.593200 + 0.805055i \(0.297864\pi\)
\(798\) 0 0
\(799\) −3.41147 −0.120689
\(800\) −4.13816 + 1.50617i −0.146306 + 0.0532510i
\(801\) −9.45471 + 53.6203i −0.334066 + 1.89458i
\(802\) 0.0892411 0.0748822i 0.00315121 0.00264418i
\(803\) −2.36959 1.98832i −0.0836208 0.0701662i
\(804\) 0.709141 + 4.02174i 0.0250095 + 0.141836i
\(805\) 0.411474 + 0.712694i 0.0145026 + 0.0251192i
\(806\) −12.3216 + 21.3416i −0.434010 + 0.751727i
\(807\) 52.4646 + 19.0955i 1.84684 + 0.672195i
\(808\) 25.5831 + 9.31147i 0.900009 + 0.327576i
\(809\) −20.5581 + 35.6076i −0.722784 + 1.25190i 0.237096 + 0.971486i \(0.423804\pi\)
−0.959880 + 0.280412i \(0.909529\pi\)
\(810\) 1.84864 + 3.20194i 0.0649546 + 0.112505i
\(811\) 2.89780 + 16.4343i 0.101756 + 0.577085i 0.992467 + 0.122515i \(0.0390959\pi\)
−0.890711 + 0.454570i \(0.849793\pi\)
\(812\) 0.338211 + 0.283793i 0.0118689 + 0.00995918i
\(813\) 29.5442 24.7905i 1.03616 0.869441i
\(814\) 2.57532 14.6054i 0.0902650 0.511918i
\(815\) −6.90420 + 2.51292i −0.241844 + 0.0880239i
\(816\) 4.84524 0.169617
\(817\) 0 0
\(818\) −26.9540 −0.942424
\(819\) −4.44444 + 1.61764i −0.155301 + 0.0565251i
\(820\) −0.0698592 + 0.396191i −0.00243959 + 0.0138356i
\(821\) −24.0462 + 20.1772i −0.839219 + 0.704188i −0.957388 0.288805i \(-0.906742\pi\)
0.118169 + 0.992994i \(0.462298\pi\)
\(822\) 0.760115 + 0.637812i 0.0265120 + 0.0222462i
\(823\) 8.04442 + 45.6221i 0.280411 + 1.59029i 0.721232 + 0.692693i \(0.243576\pi\)
−0.440822 + 0.897595i \(0.645313\pi\)
\(824\) 8.10922 + 14.0456i 0.282498 + 0.489301i
\(825\) 13.5496 23.4686i 0.471738 0.817073i
\(826\) −2.77244 1.00909i −0.0964656 0.0351106i
\(827\) −38.3007 13.9403i −1.33185 0.484752i −0.424611 0.905376i \(-0.639589\pi\)
−0.907235 + 0.420623i \(0.861811\pi\)
\(828\) −1.31727 + 2.28157i −0.0457782 + 0.0792901i
\(829\) 17.7417 + 30.7295i 0.616195 + 1.06728i 0.990174 + 0.139843i \(0.0446598\pi\)
−0.373979 + 0.927437i \(0.622007\pi\)
\(830\) 3.05122 + 17.3043i 0.105909 + 0.600642i
\(831\) −39.1450 32.8466i −1.35793 1.13943i
\(832\) 16.9500 14.2227i 0.587634 0.493084i
\(833\) −0.558963 + 3.17004i −0.0193669 + 0.109835i
\(834\) −15.5424 + 5.65695i −0.538188 + 0.195884i
\(835\) 3.54839 0.122797
\(836\) 0 0
\(837\) 46.8735 1.62019
\(838\) 32.1698 11.7089i 1.11129 0.404476i
\(839\) −6.63382 + 37.6223i −0.229025 + 1.29886i 0.625815 + 0.779972i \(0.284767\pi\)
−0.854839 + 0.518893i \(0.826344\pi\)
\(840\) −1.98293 + 1.66387i −0.0684174 + 0.0574091i
\(841\) 14.0385 + 11.7797i 0.484086 + 0.406196i
\(842\) −1.02229 5.79769i −0.0352304 0.199802i
\(843\) 26.3161 + 45.5809i 0.906376 + 1.56989i
\(844\) 0.226215 0.391815i 0.00778663 0.0134868i
\(845\) 5.26769 + 1.91728i 0.181214 + 0.0659566i
\(846\) −48.8376 17.7754i −1.67907 0.611131i
\(847\) 1.04916 1.81720i 0.0360497 0.0624399i
\(848\) −5.10220 8.83726i −0.175210 0.303473i
\(849\) −3.84389 21.7998i −0.131922 0.748167i
\(850\) 2.04117 + 1.71275i 0.0700117 + 0.0587468i
\(851\) −10.2044 + 8.56250i −0.349802 + 0.293519i
\(852\) −0.859785 + 4.87608i −0.0294557 + 0.167052i
\(853\) 24.0577 8.75628i 0.823719 0.299809i 0.104441 0.994531i \(-0.466695\pi\)
0.719278 + 0.694722i \(0.244473\pi\)
\(854\) −4.27126 −0.146159
\(855\) 0 0
\(856\) 30.1257 1.02967
\(857\) 19.8148 7.21200i 0.676861 0.246357i 0.0193616 0.999813i \(-0.493837\pi\)
0.657499 + 0.753455i \(0.271614\pi\)
\(858\) −3.86097 + 21.8966i −0.131811 + 0.747539i
\(859\) −14.9893 + 12.5775i −0.511429 + 0.429140i −0.861632 0.507534i \(-0.830557\pi\)
0.350203 + 0.936674i \(0.386113\pi\)
\(860\) −0.485700 0.407551i −0.0165622 0.0138974i
\(861\) −0.429892 2.43804i −0.0146507 0.0830882i
\(862\) −25.8050 44.6956i −0.878922 1.52234i
\(863\) −2.47447 + 4.28591i −0.0842319 + 0.145894i −0.905064 0.425276i \(-0.860177\pi\)
0.820832 + 0.571170i \(0.193510\pi\)
\(864\) −6.45811 2.35056i −0.219709 0.0799677i
\(865\) 16.6459 + 6.05861i 0.565977 + 0.205999i
\(866\) −12.2139 + 21.1552i −0.415047 + 0.718882i
\(867\) −24.1596 41.8456i −0.820502 1.42115i
\(868\) 0.0791925 + 0.449123i 0.00268797 + 0.0152442i
\(869\) 20.2049 + 16.9539i 0.685403 + 0.575121i
\(870\) −17.9782 + 15.0855i −0.609517 + 0.511446i
\(871\) 3.43047 19.4551i 0.116237 0.659212i
\(872\) 5.04236 1.83527i 0.170756 0.0621500i
\(873\) 50.0164 1.69280
\(874\) 0 0
\(875\) −2.81790 −0.0952623
\(876\) −0.694593 + 0.252811i −0.0234681 + 0.00854169i
\(877\) 0.211829 1.20134i 0.00715296 0.0405664i −0.981022 0.193895i \(-0.937888\pi\)
0.988175 + 0.153328i \(0.0489991\pi\)
\(878\) 6.28603 5.27460i 0.212143 0.178009i
\(879\) 23.1668 + 19.4393i 0.781398 + 0.655671i
\(880\) 1.22281 + 6.93491i 0.0412210 + 0.233776i
\(881\) −23.2515 40.2728i −0.783363 1.35682i −0.929972 0.367630i \(-0.880169\pi\)
0.146609 0.989194i \(-0.453164\pi\)
\(882\) −24.5194 + 42.4688i −0.825610 + 1.43000i
\(883\) −12.1454 4.42057i −0.408726 0.148764i 0.129471 0.991583i \(-0.458672\pi\)
−0.538197 + 0.842819i \(0.680894\pi\)
\(884\) 0.209141 + 0.0761210i 0.00703416 + 0.00256023i
\(885\) −7.98293 + 13.8268i −0.268343 + 0.464784i
\(886\) −20.1374 34.8791i −0.676531 1.17179i
\(887\) −4.03286 22.8715i −0.135410 0.767949i −0.974573 0.224069i \(-0.928066\pi\)
0.839163 0.543880i \(-0.183045\pi\)
\(888\) −32.0972 26.9327i −1.07711 0.903804i
\(889\) 3.08718 2.59045i 0.103541 0.0868810i
\(890\) 2.11721 12.0073i 0.0709691 0.402486i
\(891\) 6.52956 2.37657i 0.218749 0.0796180i
\(892\) 1.57255 0.0526528
\(893\) 0 0
\(894\) 64.2404 2.14852
\(895\) 9.51337 3.46258i 0.317997 0.115741i
\(896\) −0.572796 + 3.24849i −0.0191358 + 0.108524i
\(897\) 15.2986 12.8370i 0.510805 0.428617i
\(898\) 11.6109 + 9.74270i 0.387461 + 0.325118i
\(899\) 8.48886 + 48.1427i 0.283119 + 1.60565i
\(900\) −2.06624 3.57883i −0.0688746 0.119294i
\(901\) 0.663848 1.14982i 0.0221160 0.0383060i
\(902\) −6.97906 2.54017i −0.232377 0.0845784i
\(903\) 3.66637 + 1.33445i 0.122009 + 0.0444078i
\(904\) 26.0326 45.0897i 0.865830 1.49966i
\(905\) −3.75372 6.50163i −0.124778 0.216122i
\(906\) −2.93835 16.6642i −0.0976201 0.553631i
\(907\) −30.6393 25.7095i −1.01736 0.853669i −0.0280687 0.999606i \(-0.508936\pi\)
−0.989294 + 0.145937i \(0.953380\pi\)
\(908\) 2.00316 1.68085i 0.0664770 0.0557809i
\(909\) −8.49747 + 48.1916i −0.281843 + 1.59841i
\(910\) 0.995252 0.362242i 0.0329923 0.0120082i
\(911\) −18.7997 −0.622863 −0.311431 0.950269i \(-0.600808\pi\)
−0.311431 + 0.950269i \(0.600808\pi\)
\(912\) 0 0
\(913\) 33.0232 1.09291
\(914\) −29.6129 + 10.7782i −0.979509 + 0.356512i
\(915\) −4.01367 + 22.7627i −0.132688 + 0.752510i
\(916\) 2.90664 2.43896i 0.0960381 0.0805855i
\(917\) 0.490915 + 0.411927i 0.0162114 + 0.0136030i
\(918\) 0.722096 + 4.09521i 0.0238327 + 0.135162i
\(919\) −19.9158 34.4952i −0.656962 1.13789i −0.981398 0.191984i \(-0.938508\pi\)
0.324436 0.945908i \(-0.394825\pi\)
\(920\) 3.48751 6.04055i 0.114980 0.199151i
\(921\) −31.6450 11.5178i −1.04274 0.379526i
\(922\) −46.3671 16.8762i −1.52702 0.555790i
\(923\) 11.9760 20.7430i 0.394193 0.682763i
\(924\) 0.205737 + 0.356347i 0.00676825 + 0.0117230i
\(925\) −3.62836 20.5774i −0.119300 0.676582i
\(926\) 44.3658 + 37.2273i 1.45795 + 1.22337i
\(927\) −22.3314 + 18.7383i −0.733460 + 0.615446i
\(928\) 1.24463 7.05866i 0.0408571 0.231712i
\(929\) −25.3285 + 9.21881i −0.831000 + 0.302459i −0.722269 0.691612i \(-0.756901\pi\)
−0.108731 + 0.994071i \(0.534679\pi\)
\(930\) −24.2422 −0.794932
\(931\) 0 0
\(932\) −3.26176 −0.106843
\(933\) 43.1994 15.7233i 1.41428 0.514758i
\(934\) −5.98839 + 33.9618i −0.195946 + 1.11127i
\(935\) −0.701867 + 0.588936i −0.0229535 + 0.0192603i
\(936\) 30.7085 + 25.7675i 1.00374 + 0.842236i
\(937\) 0.455585 + 2.58375i 0.0148833 + 0.0844074i 0.991345 0.131285i \(-0.0419103\pi\)
−0.976461 + 0.215692i \(0.930799\pi\)
\(938\) 1.79561 + 3.11008i 0.0586287 + 0.101548i
\(939\) −38.3371 + 66.4018i −1.25108 + 2.16694i
\(940\) −1.11334 0.405223i −0.0363132 0.0132169i
\(941\) 17.5437 + 6.38538i 0.571908 + 0.208158i 0.611754 0.791048i \(-0.290464\pi\)
−0.0398455 + 0.999206i \(0.512687\pi\)
\(942\) 18.6570 32.3149i 0.607879 1.05288i
\(943\) 3.33544 + 5.77715i 0.108617 + 0.188130i
\(944\) 3.93763 + 22.3314i 0.128159 + 0.726826i
\(945\) −1.54323 1.29493i −0.0502014 0.0421240i
\(946\) 8.96657 7.52384i 0.291528 0.244621i
\(947\) 1.45858 8.27201i 0.0473974 0.268804i −0.951895 0.306425i \(-0.900867\pi\)
0.999292 + 0.0376214i \(0.0119781\pi\)
\(948\) 5.92262 2.15566i 0.192358 0.0700125i
\(949\) 3.57573 0.116073
\(950\) 0 0
\(951\) −85.0343 −2.75742
\(952\) −0.449493 + 0.163602i −0.0145681 + 0.00530237i
\(953\) 5.85070 33.1810i 0.189523 1.07484i −0.730483 0.682931i \(-0.760705\pi\)
0.920005 0.391906i \(-0.128184\pi\)
\(954\) 15.4945 13.0015i 0.501654 0.420938i
\(955\) 12.3516 + 10.3643i 0.399689 + 0.335379i
\(956\) −0.0754843 0.428092i −0.00244134 0.0138455i
\(957\) 22.0535 + 38.1978i 0.712888 + 1.23476i
\(958\) 25.7173 44.5438i 0.830890 1.43914i
\(959\) −0.0834734 0.0303818i −0.00269550 0.000981081i
\(960\) 20.4538 + 7.44459i 0.660145 + 0.240273i
\(961\) −9.74809 + 16.8842i −0.314455 + 0.544651i
\(962\) 8.57192 + 14.8470i 0.276370 + 0.478686i
\(963\) 9.40286 + 53.3262i 0.303003 + 1.71841i
\(964\) −1.95361 1.63927i −0.0629216 0.0527975i
\(965\) 0.200522 0.168258i 0.00645505 0.00541643i
\(966\) −0.630415 + 3.57526i −0.0202833 + 0.115032i
\(967\) −11.0351 + 4.01644i −0.354864 + 0.129160i −0.513300 0.858209i \(-0.671577\pi\)
0.158436 + 0.987369i \(0.449355\pi\)
\(968\) −17.7847 −0.571621
\(969\) 0 0
\(970\) −11.2003 −0.359619
\(971\) −12.0368 + 4.38105i −0.386280 + 0.140595i −0.527858 0.849333i \(-0.677005\pi\)
0.141578 + 0.989927i \(0.454783\pi\)
\(972\) −0.346667 + 1.96605i −0.0111194 + 0.0630610i
\(973\) 1.13429 0.951778i 0.0363635 0.0305126i
\(974\) −8.01296 6.72367i −0.256752 0.215440i
\(975\) 5.43969 + 30.8500i 0.174210 + 0.987992i
\(976\) 16.4140 + 28.4299i 0.525399 + 0.910018i
\(977\) −7.26382 + 12.5813i −0.232390 + 0.402512i −0.958511 0.285055i \(-0.907988\pi\)
0.726121 + 0.687567i \(0.241321\pi\)
\(978\) −30.4577 11.0857i −0.973930 0.354481i
\(979\) −21.5326 7.83721i −0.688183 0.250478i
\(980\) −0.558963 + 0.968153i −0.0178554 + 0.0309265i
\(981\) 4.82248 + 8.35278i 0.153970 + 0.266684i
\(982\) 8.59152 + 48.7249i 0.274166 + 1.55487i
\(983\) −28.3821 23.8154i −0.905249 0.759594i 0.0659599 0.997822i \(-0.478989\pi\)
−0.971209 + 0.238228i \(0.923433\pi\)
\(984\) −16.0737 + 13.4875i −0.512412 + 0.429965i
\(985\) 2.00670 11.3806i 0.0639388 0.362615i
\(986\) −4.07532 + 1.48330i −0.129785 + 0.0472378i
\(987\) 7.29086 0.232071
\(988\) 0 0
\(989\) −10.5134 −0.334307
\(990\) −13.1163 + 4.77396i −0.416864 + 0.151726i
\(991\) 0.595856 3.37927i 0.0189280 0.107346i −0.973880 0.227063i \(-0.927088\pi\)
0.992808 + 0.119717i \(0.0381988\pi\)
\(992\) 5.67159 4.75903i 0.180073 0.151099i
\(993\) −61.0228 51.2042i −1.93650 1.62492i
\(994\) 0.756082 + 4.28795i 0.0239815 + 0.136006i
\(995\) 0.112874 + 0.195503i 0.00357835 + 0.00619788i
\(996\) 3.94562 6.83402i 0.125022 0.216544i
\(997\) −12.0055 4.36965i −0.380219 0.138388i 0.144838 0.989455i \(-0.453734\pi\)
−0.525057 + 0.851067i \(0.675956\pi\)
\(998\) 6.23695 + 2.27006i 0.197427 + 0.0718576i
\(999\) 16.3045 28.2403i 0.515852 0.893483i
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 361.2.e.f.62.1 6
19.2 odd 18 361.2.a.h.1.2 3
19.3 odd 18 361.2.c.h.292.2 6
19.4 even 9 inner 361.2.e.f.99.1 6
19.5 even 9 361.2.c.i.68.2 6
19.6 even 9 19.2.e.a.9.1 6
19.7 even 3 19.2.e.a.17.1 yes 6
19.8 odd 6 361.2.e.a.54.1 6
19.9 even 9 361.2.e.g.234.1 6
19.10 odd 18 361.2.e.a.234.1 6
19.11 even 3 361.2.e.g.54.1 6
19.12 odd 6 361.2.e.h.245.1 6
19.13 odd 18 361.2.e.h.28.1 6
19.14 odd 18 361.2.c.h.68.2 6
19.15 odd 18 361.2.e.b.99.1 6
19.16 even 9 361.2.c.i.292.2 6
19.17 even 9 361.2.a.g.1.2 3
19.18 odd 2 361.2.e.b.62.1 6
57.2 even 18 3249.2.a.s.1.2 3
57.17 odd 18 3249.2.a.z.1.2 3
57.26 odd 6 171.2.u.c.55.1 6
57.44 odd 18 171.2.u.c.28.1 6
76.7 odd 6 304.2.u.b.17.1 6
76.55 odd 18 5776.2.a.br.1.3 3
76.59 even 18 5776.2.a.bi.1.1 3
76.63 odd 18 304.2.u.b.161.1 6
95.7 odd 12 475.2.u.a.74.1 12
95.44 even 18 475.2.l.a.351.1 6
95.59 odd 18 9025.2.a.x.1.2 3
95.63 odd 36 475.2.u.a.199.1 12
95.64 even 6 475.2.l.a.226.1 6
95.74 even 18 9025.2.a.bd.1.2 3
95.82 odd 36 475.2.u.a.199.2 12
95.83 odd 12 475.2.u.a.74.2 12
133.6 odd 18 931.2.w.a.883.1 6
133.25 even 9 931.2.v.b.275.1 6
133.26 odd 6 931.2.v.a.606.1 6
133.44 even 9 931.2.x.a.655.1 6
133.45 odd 6 931.2.x.b.226.1 6
133.82 odd 18 931.2.x.b.655.1 6
133.83 odd 6 931.2.w.a.834.1 6
133.101 odd 18 931.2.v.a.275.1 6
133.102 even 3 931.2.x.a.226.1 6
133.121 even 3 931.2.v.b.606.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.e.a.9.1 6 19.6 even 9
19.2.e.a.17.1 yes 6 19.7 even 3
171.2.u.c.28.1 6 57.44 odd 18
171.2.u.c.55.1 6 57.26 odd 6
304.2.u.b.17.1 6 76.7 odd 6
304.2.u.b.161.1 6 76.63 odd 18
361.2.a.g.1.2 3 19.17 even 9
361.2.a.h.1.2 3 19.2 odd 18
361.2.c.h.68.2 6 19.14 odd 18
361.2.c.h.292.2 6 19.3 odd 18
361.2.c.i.68.2 6 19.5 even 9
361.2.c.i.292.2 6 19.16 even 9
361.2.e.a.54.1 6 19.8 odd 6
361.2.e.a.234.1 6 19.10 odd 18
361.2.e.b.62.1 6 19.18 odd 2
361.2.e.b.99.1 6 19.15 odd 18
361.2.e.f.62.1 6 1.1 even 1 trivial
361.2.e.f.99.1 6 19.4 even 9 inner
361.2.e.g.54.1 6 19.11 even 3
361.2.e.g.234.1 6 19.9 even 9
361.2.e.h.28.1 6 19.13 odd 18
361.2.e.h.245.1 6 19.12 odd 6
475.2.l.a.226.1 6 95.64 even 6
475.2.l.a.351.1 6 95.44 even 18
475.2.u.a.74.1 12 95.7 odd 12
475.2.u.a.74.2 12 95.83 odd 12
475.2.u.a.199.1 12 95.63 odd 36
475.2.u.a.199.2 12 95.82 odd 36
931.2.v.a.275.1 6 133.101 odd 18
931.2.v.a.606.1 6 133.26 odd 6
931.2.v.b.275.1 6 133.25 even 9
931.2.v.b.606.1 6 133.121 even 3
931.2.w.a.834.1 6 133.83 odd 6
931.2.w.a.883.1 6 133.6 odd 18
931.2.x.a.226.1 6 133.102 even 3
931.2.x.a.655.1 6 133.44 even 9
931.2.x.b.226.1 6 133.45 odd 6
931.2.x.b.655.1 6 133.82 odd 18
3249.2.a.s.1.2 3 57.2 even 18
3249.2.a.z.1.2 3 57.17 odd 18
5776.2.a.bi.1.1 3 76.59 even 18
5776.2.a.br.1.3 3 76.55 odd 18
9025.2.a.x.1.2 3 95.59 odd 18
9025.2.a.bd.1.2 3 95.74 even 18