Properties

Label 72.3.p.b.43.15
Level $72$
Weight $3$
Character 72.43
Analytic conductor $1.962$
Analytic rank $0$
Dimension $40$
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] = [72,3,Mod(43,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.15
Character \(\chi\) \(=\) 72.43
Dual form 72.3.p.b.67.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35259 + 1.47326i) q^{2} +(2.76566 - 1.16239i) q^{3} +(-0.340985 + 3.98544i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(5.45330 + 2.50229i) q^{6} +(-4.07208 - 2.35102i) q^{7} +(-6.33280 + 4.88832i) q^{8} +(6.29772 - 6.42952i) q^{9} +O(q^{10})\) \(q+(1.35259 + 1.47326i) q^{2} +(2.76566 - 1.16239i) q^{3} +(-0.340985 + 3.98544i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(5.45330 + 2.50229i) q^{6} +(-4.07208 - 2.35102i) q^{7} +(-6.33280 + 4.88832i) q^{8} +(6.29772 - 6.42952i) q^{9} +(0.0365734 + 0.0114930i) q^{10} +(2.84945 - 4.93540i) q^{11} +(3.68957 + 11.4187i) q^{12} +(-10.0617 + 5.80910i) q^{13} +(-2.04421 - 9.17921i) q^{14} +(0.0347702 - 0.0458025i) q^{15} +(-15.7675 - 2.71795i) q^{16} -0.376814 q^{17} +(17.9906 + 0.581644i) q^{18} -15.0519 q^{19} +(0.0325368 + 0.0694276i) q^{20} +(-13.9948 - 1.76878i) q^{21} +(11.1253 - 2.47760i) q^{22} +(39.1821 - 22.6218i) q^{23} +(-11.8322 + 20.8806i) q^{24} +(-12.4998 + 21.6503i) q^{25} +(-22.1676 - 6.96608i) q^{26} +(9.94374 - 25.1022i) q^{27} +(10.7584 - 15.4274i) q^{28} +(-32.0010 - 18.4758i) q^{29} +(0.114509 - 0.0107266i) q^{30} +(26.3839 - 15.2328i) q^{31} +(-17.3227 - 26.9058i) q^{32} +(2.14377 - 16.9618i) q^{33} +(-0.509675 - 0.555144i) q^{34} -0.0901304 q^{35} +(23.4770 + 27.2915i) q^{36} +53.4253i q^{37} +(-20.3591 - 22.1754i) q^{38} +(-21.0747 + 27.7615i) q^{39} +(-0.0582758 + 0.141842i) q^{40} +(29.0192 + 50.2628i) q^{41} +(-16.3234 - 23.0104i) q^{42} +(-23.0516 + 39.9265i) q^{43} +(18.6981 + 13.0392i) q^{44} +(0.0429223 - 0.167090i) q^{45} +(86.3252 + 27.1273i) q^{46} +(34.2487 + 19.7735i) q^{47} +(-46.7667 + 10.8110i) q^{48} +(-13.4454 - 23.2882i) q^{49} +(-48.8037 + 10.8686i) q^{50} +(-1.04214 + 0.438003i) q^{51} +(-19.7209 - 42.0809i) q^{52} +0.989874i q^{53} +(50.4319 - 19.3034i) q^{54} -0.109239i q^{55} +(37.2802 - 5.01711i) q^{56} +(-41.6285 + 17.4962i) q^{57} +(-16.0647 - 72.1360i) q^{58} +(29.4331 + 50.9797i) q^{59} +(0.170687 + 0.154193i) q^{60} +(75.1051 + 43.3619i) q^{61} +(58.1285 + 18.2666i) q^{62} +(-40.7608 + 11.3755i) q^{63} +(16.2087 - 61.9135i) q^{64} +(-0.111351 + 0.192866i) q^{65} +(27.8888 - 19.7841i) q^{66} +(-34.1445 - 59.1400i) q^{67} +(0.128488 - 1.50177i) q^{68} +(82.0690 - 108.109i) q^{69} +(-0.121910 - 0.132785i) q^{70} +42.3565i q^{71} +(-8.45263 + 71.5021i) q^{72} +26.6644 q^{73} +(-78.7093 + 72.2627i) q^{74} +(-9.40418 + 74.4070i) q^{75} +(5.13248 - 59.9886i) q^{76} +(-23.2064 + 13.3982i) q^{77} +(-69.4053 + 6.50156i) q^{78} +(-121.208 - 69.9797i) q^{79} +(-0.287794 + 0.106000i) q^{80} +(-1.67750 - 80.9826i) q^{81} +(-34.7989 + 110.738i) q^{82} +(40.9931 - 71.0021i) q^{83} +(11.8214 - 55.1722i) q^{84} +(-0.00625522 + 0.00361145i) q^{85} +(-90.0015 + 20.0434i) q^{86} +(-109.980 - 13.9002i) q^{87} +(6.08078 + 45.1839i) q^{88} -42.6370 q^{89} +(0.304224 - 0.162770i) q^{90} +54.6292 q^{91} +(76.7973 + 163.872i) q^{92} +(55.2625 - 72.7969i) q^{93} +(17.1930 + 77.2026i) q^{94} +(-0.249867 + 0.144261i) q^{95} +(-79.1836 - 54.2766i) q^{96} +(55.9278 - 96.8698i) q^{97} +(16.1233 - 51.3080i) q^{98} +(-13.7872 - 49.4024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 5 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} + 46 q^{8} - 18 q^{9} - 12 q^{10} - 16 q^{11} - 12 q^{12} + 6 q^{14} + 31 q^{16} - 4 q^{17} - 114 q^{18} - 76 q^{19} - 12 q^{20} + 35 q^{22} + 39 q^{24} + 118 q^{25} - 72 q^{26} - 144 q^{27} - 36 q^{28} - 90 q^{30} - 5 q^{32} + 156 q^{33} + 5 q^{34} - 108 q^{35} + 51 q^{36} - 169 q^{38} - 6 q^{40} + 20 q^{41} - 42 q^{42} - 16 q^{43} + 362 q^{44} - 96 q^{46} + 183 q^{48} + 166 q^{49} + 73 q^{50} + 330 q^{51} - 24 q^{52} + 57 q^{54} + 186 q^{56} - 258 q^{57} + 36 q^{58} - 64 q^{59} + 150 q^{60} + 384 q^{62} - 518 q^{64} - 102 q^{65} + 486 q^{66} - 64 q^{67} - 295 q^{68} - 6 q^{70} - 225 q^{72} - 292 q^{73} + 318 q^{74} + 138 q^{75} + 197 q^{76} + 174 q^{78} - 720 q^{80} - 42 q^{81} + 386 q^{82} + 554 q^{83} - 720 q^{84} - 295 q^{86} + 59 q^{88} - 688 q^{89} - 696 q^{90} - 204 q^{91} - 378 q^{92} - 66 q^{94} - 222 q^{96} + 92 q^{97} - 614 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35259 + 1.47326i 0.676296 + 0.736630i
\(3\) 2.76566 1.16239i 0.921886 0.387462i
\(4\) −0.340985 + 3.98544i −0.0852462 + 0.996360i
\(5\) 0.0166003 0.00958419i 0.00332006 0.00191684i −0.498339 0.866982i \(-0.666057\pi\)
0.501659 + 0.865065i \(0.332723\pi\)
\(6\) 5.45330 + 2.50229i 0.908884 + 0.417049i
\(7\) −4.07208 2.35102i −0.581726 0.335860i 0.180093 0.983650i \(-0.442360\pi\)
−0.761819 + 0.647790i \(0.775694\pi\)
\(8\) −6.33280 + 4.88832i −0.791600 + 0.611040i
\(9\) 6.29772 6.42952i 0.699746 0.714391i
\(10\) 0.0365734 + 0.0114930i 0.00365734 + 0.00114930i
\(11\) 2.84945 4.93540i 0.259041 0.448673i −0.706944 0.707269i \(-0.749927\pi\)
0.965985 + 0.258597i \(0.0832601\pi\)
\(12\) 3.68957 + 11.4187i 0.307464 + 0.951560i
\(13\) −10.0617 + 5.80910i −0.773974 + 0.446854i −0.834290 0.551325i \(-0.814122\pi\)
0.0603167 + 0.998179i \(0.480789\pi\)
\(14\) −2.04421 9.17921i −0.146015 0.655658i
\(15\) 0.0347702 0.0458025i 0.00231801 0.00305350i
\(16\) −15.7675 2.71795i −0.985466 0.169872i
\(17\) −0.376814 −0.0221655 −0.0110828 0.999939i \(-0.503528\pi\)
−0.0110828 + 0.999939i \(0.503528\pi\)
\(18\) 17.9906 + 0.581644i 0.999478 + 0.0323136i
\(19\) −15.0519 −0.792207 −0.396103 0.918206i \(-0.629638\pi\)
−0.396103 + 0.918206i \(0.629638\pi\)
\(20\) 0.0325368 + 0.0694276i 0.00162684 + 0.00347138i
\(21\) −13.9948 1.76878i −0.666418 0.0842275i
\(22\) 11.1253 2.47760i 0.505694 0.112618i
\(23\) 39.1821 22.6218i 1.70357 0.983556i 0.761484 0.648184i \(-0.224471\pi\)
0.942086 0.335372i \(-0.108862\pi\)
\(24\) −11.8322 + 20.8806i −0.493010 + 0.870024i
\(25\) −12.4998 + 21.6503i −0.499993 + 0.866013i
\(26\) −22.1676 6.96608i −0.852601 0.267926i
\(27\) 9.94374 25.1022i 0.368287 0.929712i
\(28\) 10.7584 15.4274i 0.384227 0.550978i
\(29\) −32.0010 18.4758i −1.10348 0.637096i −0.166349 0.986067i \(-0.553198\pi\)
−0.937134 + 0.348971i \(0.886531\pi\)
\(30\) 0.114509 0.0107266i 0.00381696 0.000357555i
\(31\) 26.3839 15.2328i 0.851094 0.491379i −0.00992571 0.999951i \(-0.503160\pi\)
0.861020 + 0.508571i \(0.169826\pi\)
\(32\) −17.3227 26.9058i −0.541335 0.840807i
\(33\) 2.14377 16.9618i 0.0649628 0.513994i
\(34\) −0.509675 0.555144i −0.0149905 0.0163278i
\(35\) −0.0901304 −0.00257515
\(36\) 23.4770 + 27.2915i 0.652140 + 0.758098i
\(37\) 53.4253i 1.44393i 0.691931 + 0.721964i \(0.256760\pi\)
−0.691931 + 0.721964i \(0.743240\pi\)
\(38\) −20.3591 22.1754i −0.535767 0.583563i
\(39\) −21.0747 + 27.7615i −0.540376 + 0.711834i
\(40\) −0.0582758 + 0.141842i −0.00145689 + 0.00354606i
\(41\) 29.0192 + 50.2628i 0.707786 + 1.22592i 0.965677 + 0.259747i \(0.0836392\pi\)
−0.257891 + 0.966174i \(0.583027\pi\)
\(42\) −16.3234 23.0104i −0.388652 0.547866i
\(43\) −23.0516 + 39.9265i −0.536083 + 0.928524i 0.463027 + 0.886344i \(0.346763\pi\)
−0.999110 + 0.0421794i \(0.986570\pi\)
\(44\) 18.6981 + 13.0392i 0.424957 + 0.296346i
\(45\) 0.0429223 0.167090i 0.000953828 0.00371312i
\(46\) 86.3252 + 27.1273i 1.87663 + 0.589724i
\(47\) 34.2487 + 19.7735i 0.728695 + 0.420712i 0.817944 0.575297i \(-0.195114\pi\)
−0.0892497 + 0.996009i \(0.528447\pi\)
\(48\) −46.7667 + 10.8110i −0.974306 + 0.225228i
\(49\) −13.4454 23.2882i −0.274396 0.475268i
\(50\) −48.8037 + 10.8686i −0.976074 + 0.217372i
\(51\) −1.04214 + 0.438003i −0.0204341 + 0.00858829i
\(52\) −19.7209 42.0809i −0.379249 0.809249i
\(53\) 0.989874i 0.0186769i 0.999956 + 0.00933844i \(0.00297256\pi\)
−0.999956 + 0.00933844i \(0.997027\pi\)
\(54\) 50.4319 19.3034i 0.933925 0.357470i
\(55\) 0.109239i 0.00198616i
\(56\) 37.2802 5.01711i 0.665718 0.0895913i
\(57\) −41.6285 + 17.4962i −0.730324 + 0.306950i
\(58\) −16.0647 72.1360i −0.276978 1.24372i
\(59\) 29.4331 + 50.9797i 0.498866 + 0.864062i 0.999999 0.00130851i \(-0.000416510\pi\)
−0.501133 + 0.865370i \(0.667083\pi\)
\(60\) 0.170687 + 0.154193i 0.00284479 + 0.00256988i
\(61\) 75.1051 + 43.3619i 1.23123 + 0.710851i 0.967286 0.253687i \(-0.0816432\pi\)
0.263944 + 0.964538i \(0.414977\pi\)
\(62\) 58.1285 + 18.2666i 0.937557 + 0.294623i
\(63\) −40.7608 + 11.3755i −0.646996 + 0.180564i
\(64\) 16.2087 61.9135i 0.253261 0.967398i
\(65\) −0.111351 + 0.192866i −0.00171309 + 0.00296716i
\(66\) 27.8888 19.7841i 0.422557 0.299758i
\(67\) −34.1445 59.1400i −0.509620 0.882687i −0.999938 0.0111436i \(-0.996453\pi\)
0.490318 0.871543i \(-0.336881\pi\)
\(68\) 0.128488 1.50177i 0.00188953 0.0220848i
\(69\) 82.0690 108.109i 1.18941 1.56679i
\(70\) −0.121910 0.132785i −0.00174157 0.00189694i
\(71\) 42.3565i 0.596571i 0.954477 + 0.298285i \(0.0964147\pi\)
−0.954477 + 0.298285i \(0.903585\pi\)
\(72\) −8.45263 + 71.5021i −0.117398 + 0.993085i
\(73\) 26.6644 0.365266 0.182633 0.983181i \(-0.441538\pi\)
0.182633 + 0.983181i \(0.441538\pi\)
\(74\) −78.7093 + 72.2627i −1.06364 + 0.976523i
\(75\) −9.40418 + 74.4070i −0.125389 + 0.992093i
\(76\) 5.13248 59.9886i 0.0675326 0.789323i
\(77\) −23.2064 + 13.3982i −0.301382 + 0.174003i
\(78\) −69.4053 + 6.50156i −0.889812 + 0.0833533i
\(79\) −121.208 69.9797i −1.53428 0.885819i −0.999157 0.0410462i \(-0.986931\pi\)
−0.535126 0.844772i \(-0.679736\pi\)
\(80\) −0.287794 + 0.106000i −0.00359742 + 0.00132499i
\(81\) −1.67750 80.9826i −0.0207099 0.999786i
\(82\) −34.7989 + 110.738i −0.424377 + 1.35046i
\(83\) 40.9931 71.0021i 0.493892 0.855447i −0.506083 0.862485i \(-0.668907\pi\)
0.999975 + 0.00703820i \(0.00224035\pi\)
\(84\) 11.8214 55.1722i 0.140731 0.656812i
\(85\) −0.00625522 + 0.00361145i −7.35908e−5 + 4.24877e-5i
\(86\) −90.0015 + 20.0434i −1.04653 + 0.233062i
\(87\) −109.980 13.9002i −1.26414 0.159772i
\(88\) 6.08078 + 45.1839i 0.0690998 + 0.513454i
\(89\) −42.6370 −0.479068 −0.239534 0.970888i \(-0.576995\pi\)
−0.239534 + 0.970888i \(0.576995\pi\)
\(90\) 0.304224 0.162770i 0.00338027 0.00180855i
\(91\) 54.6292 0.600321
\(92\) 76.7973 + 163.872i 0.834753 + 1.78121i
\(93\) 55.2625 72.7969i 0.594221 0.782762i
\(94\) 17.1930 + 77.2026i 0.182905 + 0.821304i
\(95\) −0.249867 + 0.144261i −0.00263017 + 0.00151853i
\(96\) −79.1836 54.2766i −0.824830 0.565381i
\(97\) 55.9278 96.8698i 0.576576 0.998658i −0.419293 0.907851i \(-0.637722\pi\)
0.995868 0.0908072i \(-0.0289447\pi\)
\(98\) 16.1233 51.3080i 0.164523 0.523551i
\(99\) −13.7872 49.4024i −0.139265 0.499014i
\(100\) −82.0238 57.1997i −0.820238 0.571997i
\(101\) −92.9636 53.6726i −0.920432 0.531412i −0.0366592 0.999328i \(-0.511672\pi\)
−0.883773 + 0.467916i \(0.845005\pi\)
\(102\) −2.05488 0.942899i −0.0201459 0.00924410i
\(103\) 44.0704 25.4441i 0.427868 0.247030i −0.270570 0.962700i \(-0.587212\pi\)
0.698438 + 0.715671i \(0.253879\pi\)
\(104\) 35.3217 85.9724i 0.339632 0.826658i
\(105\) −0.249270 + 0.104766i −0.00237400 + 0.000997775i
\(106\) −1.45834 + 1.33890i −0.0137579 + 0.0126311i
\(107\) −49.7181 −0.464656 −0.232328 0.972638i \(-0.574634\pi\)
−0.232328 + 0.972638i \(0.574634\pi\)
\(108\) 96.6528 + 48.1897i 0.894933 + 0.446201i
\(109\) 40.3370i 0.370064i −0.982732 0.185032i \(-0.940761\pi\)
0.982732 0.185032i \(-0.0592389\pi\)
\(110\) 0.160937 0.147756i 0.00146306 0.00134323i
\(111\) 62.1008 + 147.756i 0.559467 + 1.33114i
\(112\) 57.8165 + 48.1373i 0.516218 + 0.429797i
\(113\) −12.9411 22.4146i −0.114523 0.198360i 0.803066 0.595890i \(-0.203201\pi\)
−0.917589 + 0.397530i \(0.869867\pi\)
\(114\) −82.0828 37.6644i −0.720024 0.330389i
\(115\) 0.433623 0.751057i 0.00377063 0.00653093i
\(116\) 84.5460 121.238i 0.728845 1.04516i
\(117\) −26.0157 + 101.276i −0.222357 + 0.865604i
\(118\) −35.2952 + 112.317i −0.299112 + 0.951842i
\(119\) 1.53442 + 0.885896i 0.0128943 + 0.00744450i
\(120\) 0.00370461 + 0.460026i 3.08717e−5 + 0.00383355i
\(121\) 44.2612 + 76.6627i 0.365795 + 0.633576i
\(122\) 37.7032 + 169.300i 0.309043 + 1.38771i
\(123\) 138.682 + 105.278i 1.12750 + 0.855919i
\(124\) 51.7127 + 110.346i 0.417038 + 0.889884i
\(125\) 0.958412i 0.00766729i
\(126\) −71.8918 44.6647i −0.570570 0.354482i
\(127\) 38.2335i 0.301051i −0.988606 0.150526i \(-0.951903\pi\)
0.988606 0.150526i \(-0.0480966\pi\)
\(128\) 113.138 59.8641i 0.883893 0.467689i
\(129\) −17.3428 + 137.218i −0.134440 + 1.06370i
\(130\) −0.434754 + 0.0968198i −0.00334426 + 0.000744767i
\(131\) −61.9020 107.217i −0.472534 0.818453i 0.526972 0.849883i \(-0.323327\pi\)
−0.999506 + 0.0314294i \(0.989994\pi\)
\(132\) 66.8692 + 14.3276i 0.506585 + 0.108542i
\(133\) 61.2927 + 35.3874i 0.460848 + 0.266070i
\(134\) 40.9450 130.296i 0.305559 0.972359i
\(135\) −0.0755154 0.512007i −0.000559373 0.00379265i
\(136\) 2.38628 1.84198i 0.0175462 0.0135440i
\(137\) 56.1949 97.3324i 0.410182 0.710456i −0.584728 0.811230i \(-0.698799\pi\)
0.994909 + 0.100774i \(0.0321319\pi\)
\(138\) 270.278 25.3184i 1.95854 0.183466i
\(139\) 56.1874 + 97.3194i 0.404226 + 0.700140i 0.994231 0.107260i \(-0.0342077\pi\)
−0.590005 + 0.807399i \(0.700874\pi\)
\(140\) 0.0307331 0.359209i 0.000219522 0.00256578i
\(141\) 117.704 + 14.8765i 0.834783 + 0.105507i
\(142\) −62.4021 + 57.2911i −0.439452 + 0.403459i
\(143\) 66.2111i 0.463014i
\(144\) −116.774 + 84.2603i −0.810931 + 0.585141i
\(145\) −0.708302 −0.00488484
\(146\) 36.0661 + 39.2836i 0.247028 + 0.269066i
\(147\) −64.2552 48.7783i −0.437110 0.331825i
\(148\) −212.923 18.2172i −1.43867 0.123089i
\(149\) 0.193825 0.111905i 0.00130084 0.000751040i −0.499349 0.866401i \(-0.666428\pi\)
0.500650 + 0.865650i \(0.333094\pi\)
\(150\) −122.341 + 86.7875i −0.815605 + 0.578584i
\(151\) −106.870 61.7013i −0.707747 0.408618i 0.102479 0.994735i \(-0.467323\pi\)
−0.810226 + 0.586117i \(0.800656\pi\)
\(152\) 95.3209 73.5786i 0.627111 0.484070i
\(153\) −2.37307 + 2.42273i −0.0155102 + 0.0158348i
\(154\) −51.1279 16.0667i −0.332000 0.104329i
\(155\) 0.291987 0.505737i 0.00188379 0.00326282i
\(156\) −103.456 93.4581i −0.663177 0.599090i
\(157\) −169.459 + 97.8372i −1.07936 + 0.623167i −0.930723 0.365726i \(-0.880821\pi\)
−0.148634 + 0.988892i \(0.547488\pi\)
\(158\) −60.8474 273.225i −0.385110 1.72927i
\(159\) 1.15062 + 2.73765i 0.00723658 + 0.0172179i
\(160\) −0.545433 0.280621i −0.00340895 0.00175388i
\(161\) −212.737 −1.32135
\(162\) 117.039 112.008i 0.722466 0.691407i
\(163\) 36.1007 0.221477 0.110738 0.993850i \(-0.464678\pi\)
0.110738 + 0.993850i \(0.464678\pi\)
\(164\) −210.214 + 98.5155i −1.28179 + 0.600704i
\(165\) −0.126978 0.302117i −0.000769562 0.00183101i
\(166\) 160.051 35.6435i 0.964165 0.214720i
\(167\) 89.8711 51.8871i 0.538150 0.310701i −0.206179 0.978514i \(-0.566103\pi\)
0.744329 + 0.667813i \(0.232770\pi\)
\(168\) 97.2725 57.2096i 0.579003 0.340533i
\(169\) −17.0087 + 29.4600i −0.100643 + 0.174319i
\(170\) −0.0137814 0.00433073i −8.10669e−5 2.54749e-5i
\(171\) −94.7928 + 96.7767i −0.554344 + 0.565946i
\(172\) −151.265 105.485i −0.879445 0.613285i
\(173\) 53.5978 + 30.9447i 0.309814 + 0.178871i 0.646843 0.762623i \(-0.276089\pi\)
−0.337029 + 0.941494i \(0.609422\pi\)
\(174\) −128.279 180.830i −0.737238 1.03925i
\(175\) 101.801 58.7746i 0.581718 0.335855i
\(176\) −58.3428 + 70.0740i −0.331493 + 0.398148i
\(177\) 140.660 + 106.780i 0.794689 + 0.603275i
\(178\) −57.6705 62.8154i −0.323992 0.352895i
\(179\) −235.967 −1.31825 −0.659125 0.752033i \(-0.729073\pi\)
−0.659125 + 0.752033i \(0.729073\pi\)
\(180\) 0.651293 + 0.228039i 0.00361830 + 0.00126689i
\(181\) 274.398i 1.51601i −0.652250 0.758004i \(-0.726175\pi\)
0.652250 0.758004i \(-0.273825\pi\)
\(182\) 73.8911 + 80.4830i 0.405995 + 0.442214i
\(183\) 258.118 + 32.6232i 1.41048 + 0.178269i
\(184\) −137.550 + 334.794i −0.747553 + 1.81953i
\(185\) 0.512038 + 0.886876i 0.00276777 + 0.00479392i
\(186\) 181.996 17.0486i 0.978475 0.0916589i
\(187\) −1.07371 + 1.85973i −0.00574178 + 0.00994506i
\(188\) −90.4842 + 129.753i −0.481299 + 0.690178i
\(189\) −99.5076 + 78.8405i −0.526495 + 0.417145i
\(190\) −0.550501 0.172992i −0.00289737 0.000910486i
\(191\) −75.3616 43.5100i −0.394563 0.227801i 0.289572 0.957156i \(-0.406487\pi\)
−0.684135 + 0.729355i \(0.739820\pi\)
\(192\) −27.1397 190.072i −0.141353 0.989959i
\(193\) 51.8130 + 89.7428i 0.268461 + 0.464989i 0.968465 0.249151i \(-0.0801515\pi\)
−0.700003 + 0.714140i \(0.746818\pi\)
\(194\) 218.362 48.6293i 1.12558 0.250666i
\(195\) −0.0837744 + 0.662833i −0.000429612 + 0.00339914i
\(196\) 97.3982 45.6450i 0.496930 0.232883i
\(197\) 200.158i 1.01603i 0.861349 + 0.508014i \(0.169620\pi\)
−0.861349 + 0.508014i \(0.830380\pi\)
\(198\) 54.1340 87.1334i 0.273404 0.440068i
\(199\) 178.871i 0.898847i 0.893319 + 0.449424i \(0.148371\pi\)
−0.893319 + 0.449424i \(0.851629\pi\)
\(200\) −26.6748 198.210i −0.133374 0.991051i
\(201\) −163.176 123.872i −0.811819 0.616278i
\(202\) −46.6683 209.557i −0.231031 1.03741i
\(203\) 86.8738 + 150.470i 0.427950 + 0.741231i
\(204\) −1.39028 4.30273i −0.00681510 0.0210918i
\(205\) 0.963456 + 0.556251i 0.00469978 + 0.00271342i
\(206\) 97.0951 + 30.5117i 0.471335 + 0.148115i
\(207\) 101.310 394.388i 0.489423 1.90526i
\(208\) 174.436 64.2477i 0.838633 0.308883i
\(209\) −42.8898 + 74.2873i −0.205214 + 0.355442i
\(210\) −0.491509 0.225533i −0.00234052 0.00107397i
\(211\) −95.3087 165.079i −0.451700 0.782367i 0.546792 0.837269i \(-0.315849\pi\)
−0.998492 + 0.0549013i \(0.982516\pi\)
\(212\) −3.94508 0.337532i −0.0186089 0.00159213i
\(213\) 49.2346 + 117.144i 0.231148 + 0.549970i
\(214\) −67.2484 73.2477i −0.314245 0.342279i
\(215\) 0.883723i 0.00411034i
\(216\) 59.7360 + 207.576i 0.276555 + 0.960998i
\(217\) −143.250 −0.660139
\(218\) 59.4269 54.5596i 0.272600 0.250273i
\(219\) 73.7446 30.9943i 0.336733 0.141527i
\(220\) 0.435365 + 0.0372488i 0.00197893 + 0.000169313i
\(221\) 3.79137 2.18895i 0.0171555 0.00990474i
\(222\) −133.686 + 291.344i −0.602188 + 1.31236i
\(223\) 188.439 + 108.795i 0.845018 + 0.487871i 0.858967 0.512031i \(-0.171107\pi\)
−0.0139487 + 0.999903i \(0.504440\pi\)
\(224\) 7.28342 + 150.289i 0.0325153 + 0.670932i
\(225\) 60.4809 + 216.715i 0.268804 + 0.963180i
\(226\) 15.5185 49.3835i 0.0686661 0.218511i
\(227\) 68.5871 118.796i 0.302146 0.523332i −0.674476 0.738297i \(-0.735630\pi\)
0.976622 + 0.214965i \(0.0689637\pi\)
\(228\) −55.5352 171.874i −0.243575 0.753832i
\(229\) −222.151 + 128.259i −0.970090 + 0.560082i −0.899264 0.437407i \(-0.855897\pi\)
−0.0708262 + 0.997489i \(0.522564\pi\)
\(230\) 1.69302 0.377035i 0.00736094 0.00163928i
\(231\) −48.6071 + 64.0298i −0.210420 + 0.277185i
\(232\) 292.971 39.4276i 1.26281 0.169947i
\(233\) 305.481 1.31108 0.655538 0.755162i \(-0.272442\pi\)
0.655538 + 0.755162i \(0.272442\pi\)
\(234\) −184.394 + 98.6569i −0.788009 + 0.421611i
\(235\) 0.758051 0.00322575
\(236\) −213.213 + 99.9206i −0.903443 + 0.423392i
\(237\) −416.564 52.6489i −1.75765 0.222147i
\(238\) 0.770287 + 3.45885i 0.00323650 + 0.0145330i
\(239\) −68.4669 + 39.5294i −0.286472 + 0.165395i −0.636350 0.771401i \(-0.719557\pi\)
0.349878 + 0.936795i \(0.386223\pi\)
\(240\) −0.672727 + 0.627686i −0.00280303 + 0.00261536i
\(241\) 111.403 192.956i 0.462254 0.800647i −0.536819 0.843697i \(-0.680374\pi\)
0.999073 + 0.0430503i \(0.0137076\pi\)
\(242\) −53.0766 + 168.902i −0.219325 + 0.697941i
\(243\) −98.7725 222.020i −0.406471 0.913664i
\(244\) −198.426 + 284.541i −0.813221 + 1.16615i
\(245\) −0.446396 0.257727i −0.00182202 0.00105195i
\(246\) 32.4784 + 346.713i 0.132026 + 1.40940i
\(247\) 151.447 87.4382i 0.613147 0.354001i
\(248\) −92.6215 + 225.439i −0.373474 + 0.909028i
\(249\) 30.8409 244.017i 0.123859 0.979989i
\(250\) −1.41199 + 1.29634i −0.00564795 + 0.00518536i
\(251\) 393.373 1.56722 0.783611 0.621252i \(-0.213376\pi\)
0.783611 + 0.621252i \(0.213376\pi\)
\(252\) −31.4376 166.328i −0.124752 0.660034i
\(253\) 257.839i 1.01913i
\(254\) 56.3279 51.7144i 0.221763 0.203600i
\(255\) −0.0131019 + 0.0172590i −5.13800e−5 + 6.76824e-5i
\(256\) 241.226 + 85.7103i 0.942287 + 0.334806i
\(257\) 89.6613 + 155.298i 0.348877 + 0.604272i 0.986050 0.166448i \(-0.0532299\pi\)
−0.637173 + 0.770720i \(0.719897\pi\)
\(258\) −225.615 + 160.050i −0.874478 + 0.620347i
\(259\) 125.604 217.552i 0.484957 0.839970i
\(260\) −0.730685 0.509547i −0.00281033 0.00195980i
\(261\) −320.324 + 89.3958i −1.22729 + 0.342513i
\(262\) 74.2308 236.219i 0.283324 0.901600i
\(263\) −241.721 139.558i −0.919092 0.530638i −0.0357465 0.999361i \(-0.511381\pi\)
−0.883345 + 0.468723i \(0.844714\pi\)
\(264\) 69.3385 + 117.895i 0.262646 + 0.446572i
\(265\) 0.00948714 + 0.0164322i 3.58005e−5 + 6.20083e-5i
\(266\) 30.7693 + 138.165i 0.115674 + 0.519416i
\(267\) −117.919 + 49.5607i −0.441646 + 0.185621i
\(268\) 247.342 115.915i 0.922917 0.432519i
\(269\) 112.462i 0.418076i −0.977908 0.209038i \(-0.932967\pi\)
0.977908 0.209038i \(-0.0670332\pi\)
\(270\) 0.652178 0.803791i 0.00241547 0.00297700i
\(271\) 500.279i 1.84605i 0.384740 + 0.923025i \(0.374291\pi\)
−0.384740 + 0.923025i \(0.625709\pi\)
\(272\) 5.94139 + 1.02416i 0.0218434 + 0.00376529i
\(273\) 151.086 63.5002i 0.553427 0.232602i
\(274\) 219.405 48.8615i 0.800747 0.178327i
\(275\) 71.2353 + 123.383i 0.259037 + 0.448666i
\(276\) 402.877 + 363.944i 1.45970 + 1.31864i
\(277\) 222.630 + 128.535i 0.803718 + 0.464027i 0.844770 0.535130i \(-0.179737\pi\)
−0.0410514 + 0.999157i \(0.513071\pi\)
\(278\) −67.3780 + 214.412i −0.242367 + 0.771267i
\(279\) 68.2191 265.568i 0.244513 0.951855i
\(280\) 0.570778 0.440586i 0.00203849 0.00157352i
\(281\) 139.228 241.150i 0.495474 0.858187i −0.504512 0.863405i \(-0.668328\pi\)
0.999986 + 0.00521797i \(0.00166094\pi\)
\(282\) 137.289 + 193.531i 0.486841 + 0.686280i
\(283\) 93.9509 + 162.728i 0.331982 + 0.575009i 0.982900 0.184138i \(-0.0589494\pi\)
−0.650919 + 0.759148i \(0.725616\pi\)
\(284\) −168.809 14.4429i −0.594399 0.0508554i
\(285\) −0.523359 + 0.689417i −0.00183635 + 0.00241901i
\(286\) −97.5460 + 89.5566i −0.341070 + 0.313135i
\(287\) 272.899i 0.950868i
\(288\) −282.085 58.0686i −0.979462 0.201627i
\(289\) −288.858 −0.999509
\(290\) −0.958044 1.04351i −0.00330360 0.00359832i
\(291\) 42.0771 332.918i 0.144595 1.14405i
\(292\) −9.09216 + 106.269i −0.0311375 + 0.363936i
\(293\) 442.987 255.759i 1.51190 0.872897i 0.511999 0.858986i \(-0.328905\pi\)
0.999903 0.0139109i \(-0.00442813\pi\)
\(294\) −15.0482 160.642i −0.0511842 0.546401i
\(295\) 0.977197 + 0.564185i 0.00331253 + 0.00191249i
\(296\) −261.160 338.332i −0.882297 1.14301i
\(297\) −95.5553 120.604i −0.321735 0.406074i
\(298\) 0.427031 + 0.134193i 0.00143299 + 0.000450311i
\(299\) −262.825 + 455.225i −0.879012 + 1.52249i
\(300\) −293.338 62.8514i −0.977793 0.209505i
\(301\) 187.736 108.389i 0.623708 0.360098i
\(302\) −53.6494 240.904i −0.177647 0.797695i
\(303\) −319.494 40.3803i −1.05444 0.133268i
\(304\) 237.331 + 40.9104i 0.780693 + 0.134574i
\(305\) 1.66236 0.00545035
\(306\) −6.77910 0.219171i −0.0221539 0.000716247i
\(307\) −195.885 −0.638061 −0.319031 0.947744i \(-0.603357\pi\)
−0.319031 + 0.947744i \(0.603357\pi\)
\(308\) −45.4848 97.0564i −0.147678 0.315118i
\(309\) 92.3079 121.596i 0.298731 0.393516i
\(310\) 1.14002 0.253883i 0.00367749 0.000818978i
\(311\) −395.492 + 228.338i −1.27168 + 0.734205i −0.975304 0.220867i \(-0.929111\pi\)
−0.296376 + 0.955071i \(0.595778\pi\)
\(312\) −2.24541 278.828i −0.00719683 0.893679i
\(313\) −185.314 + 320.973i −0.592058 + 1.02547i 0.401897 + 0.915685i \(0.368351\pi\)
−0.993955 + 0.109789i \(0.964982\pi\)
\(314\) −373.348 117.323i −1.18901 0.373640i
\(315\) −0.567616 + 0.579496i −0.00180196 + 0.00183967i
\(316\) 320.230 459.207i 1.01339 1.45319i
\(317\) 435.393 + 251.374i 1.37348 + 0.792979i 0.991364 0.131136i \(-0.0418624\pi\)
0.382115 + 0.924115i \(0.375196\pi\)
\(318\) −2.47696 + 5.39809i −0.00778917 + 0.0169751i
\(319\) −182.371 + 105.292i −0.571695 + 0.330068i
\(320\) −0.324321 1.18313i −0.00101350 0.00369728i
\(321\) −137.503 + 57.7917i −0.428359 + 0.180036i
\(322\) −287.747 313.417i −0.893623 0.973344i
\(323\) 5.67177 0.0175597
\(324\) 323.323 + 20.9283i 0.997912 + 0.0645934i
\(325\) 290.451i 0.893695i
\(326\) 48.8296 + 53.1858i 0.149784 + 0.163146i
\(327\) −46.8872 111.558i −0.143386 0.341157i
\(328\) −429.473 176.449i −1.30937 0.537954i
\(329\) −92.9756 161.038i −0.282601 0.489479i
\(330\) 0.273348 0.595712i 0.000828326 0.00180519i
\(331\) −187.810 + 325.297i −0.567402 + 0.982769i 0.429420 + 0.903105i \(0.358718\pi\)
−0.996822 + 0.0796642i \(0.974615\pi\)
\(332\) 268.996 + 187.586i 0.810230 + 0.565018i
\(333\) 343.499 + 336.457i 1.03153 + 1.01038i
\(334\) 198.002 + 62.2213i 0.592821 + 0.186291i
\(335\) −1.13362 0.654495i −0.00338394 0.00195372i
\(336\) 215.855 + 65.9262i 0.642425 + 0.196209i
\(337\) −161.252 279.296i −0.478492 0.828772i 0.521204 0.853432i \(-0.325483\pi\)
−0.999696 + 0.0246599i \(0.992150\pi\)
\(338\) −66.4080 + 14.7891i −0.196473 + 0.0437547i
\(339\) −61.8451 46.9487i −0.182434 0.138492i
\(340\) −0.0122603 0.0261612i −3.60597e−5 7.69448e-5i
\(341\) 173.620i 0.509150i
\(342\) −270.793 8.75487i −0.791793 0.0255990i
\(343\) 356.842i 1.04035i
\(344\) −49.1925 365.530i −0.143001 1.06259i
\(345\) 0.326234 2.58120i 0.000945607 0.00748175i
\(346\) 26.9064 + 120.819i 0.0777642 + 0.349188i
\(347\) −42.4458 73.5183i −0.122322 0.211868i 0.798361 0.602179i \(-0.205701\pi\)
−0.920683 + 0.390311i \(0.872367\pi\)
\(348\) 92.8997 433.578i 0.266953 1.24591i
\(349\) −35.4597 20.4727i −0.101604 0.0586610i 0.448337 0.893865i \(-0.352016\pi\)
−0.549941 + 0.835204i \(0.685350\pi\)
\(350\) 224.285 + 70.4806i 0.640814 + 0.201373i
\(351\) 45.7709 + 310.334i 0.130401 + 0.884143i
\(352\) −182.151 + 8.82757i −0.517475 + 0.0250783i
\(353\) −272.714 + 472.355i −0.772561 + 1.33812i 0.163593 + 0.986528i \(0.447691\pi\)
−0.936155 + 0.351588i \(0.885642\pi\)
\(354\) 32.9416 + 351.658i 0.0930554 + 0.993384i
\(355\) 0.405953 + 0.703131i 0.00114353 + 0.00198065i
\(356\) 14.5386 169.927i 0.0408387 0.477324i
\(357\) 5.27342 + 0.666500i 0.0147715 + 0.00186695i
\(358\) −319.167 347.640i −0.891528 0.971062i
\(359\) 24.1503i 0.0672710i 0.999434 + 0.0336355i \(0.0107085\pi\)
−0.999434 + 0.0336355i \(0.989291\pi\)
\(360\) 0.544974 + 1.26797i 0.00151382 + 0.00352213i
\(361\) −134.439 −0.372408
\(362\) 404.259 371.148i 1.11674 1.02527i
\(363\) 211.523 + 160.574i 0.582708 + 0.442353i
\(364\) −18.6277 + 217.721i −0.0511751 + 0.598136i
\(365\) 0.442637 0.255557i 0.00121270 0.000700155i
\(366\) 301.066 + 424.401i 0.822586 + 1.15956i
\(367\) −227.281 131.221i −0.619295 0.357550i 0.157299 0.987551i \(-0.449721\pi\)
−0.776595 + 0.630001i \(0.783055\pi\)
\(368\) −679.287 + 250.193i −1.84589 + 0.679873i
\(369\) 505.920 + 129.961i 1.37106 + 0.352198i
\(370\) −0.614019 + 1.95395i −0.00165951 + 0.00528094i
\(371\) 2.32721 4.03085i 0.00627281 0.0108648i
\(372\) 271.284 + 245.068i 0.729258 + 0.658785i
\(373\) −97.0579 + 56.0364i −0.260209 + 0.150232i −0.624430 0.781081i \(-0.714669\pi\)
0.364221 + 0.931313i \(0.381335\pi\)
\(374\) −4.19215 + 0.933594i −0.0112090 + 0.00249624i
\(375\) 1.11404 + 2.65064i 0.00297078 + 0.00706837i
\(376\) −313.549 + 42.1969i −0.833907 + 0.112226i
\(377\) 429.311 1.13876
\(378\) −250.746 39.9614i −0.663348 0.105718i
\(379\) 305.554 0.806210 0.403105 0.915154i \(-0.367931\pi\)
0.403105 + 0.915154i \(0.367931\pi\)
\(380\) −0.489741 1.04502i −0.00128879 0.00275005i
\(381\) −44.4421 105.741i −0.116646 0.277535i
\(382\) −37.8320 169.878i −0.0990366 0.444708i
\(383\) 50.9660 29.4252i 0.133070 0.0768283i −0.431987 0.901880i \(-0.642187\pi\)
0.565057 + 0.825052i \(0.308854\pi\)
\(384\) 243.317 297.074i 0.633637 0.773630i
\(385\) −0.256823 + 0.444830i −0.000667071 + 0.00115540i
\(386\) −62.1325 + 197.719i −0.160965 + 0.512227i
\(387\) 111.536 + 399.657i 0.288207 + 1.03270i
\(388\) 366.998 + 255.928i 0.945872 + 0.659609i
\(389\) 417.667 + 241.140i 1.07369 + 0.619897i 0.929188 0.369607i \(-0.120508\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(390\) −1.08984 + 0.773122i −0.00279445 + 0.00198236i
\(391\) −14.7643 + 8.52420i −0.0377605 + 0.0218010i
\(392\) 198.987 + 81.7537i 0.507620 + 0.208555i
\(393\) −295.828 224.573i −0.752742 0.571431i
\(394\) −294.884 + 270.732i −0.748436 + 0.687136i
\(395\) −2.68279 −0.00679188
\(396\) 201.591 38.1026i 0.509069 0.0962187i
\(397\) 74.8863i 0.188631i 0.995542 + 0.0943153i \(0.0300662\pi\)
−0.995542 + 0.0943153i \(0.969934\pi\)
\(398\) −263.523 + 241.939i −0.662117 + 0.607887i
\(399\) 210.648 + 26.6235i 0.527941 + 0.0667256i
\(400\) 255.935 307.397i 0.639837 0.768492i
\(401\) −299.864 519.380i −0.747791 1.29521i −0.948879 0.315639i \(-0.897781\pi\)
0.201088 0.979573i \(-0.435552\pi\)
\(402\) −38.2146 407.948i −0.0950613 1.01480i
\(403\) −176.977 + 306.534i −0.439150 + 0.760629i
\(404\) 245.608 352.199i 0.607941 0.871781i
\(405\) −0.804000 1.32826i −0.00198518 0.00327965i
\(406\) −104.176 + 331.512i −0.256592 + 0.816533i
\(407\) 263.675 + 152.233i 0.647851 + 0.374037i
\(408\) 4.45855 7.86808i 0.0109278 0.0192845i
\(409\) 274.176 + 474.886i 0.670356 + 1.16109i 0.977803 + 0.209526i \(0.0671921\pi\)
−0.307447 + 0.951565i \(0.599475\pi\)
\(410\) 0.483661 + 2.17180i 0.00117966 + 0.00529708i
\(411\) 42.2780 334.508i 0.102866 0.813889i
\(412\) 86.3785 + 184.316i 0.209656 + 0.447369i
\(413\) 276.791i 0.670197i
\(414\) 718.067 384.190i 1.73446 0.927994i
\(415\) 1.57154i 0.00378685i
\(416\) 330.594 + 170.088i 0.794697 + 0.408865i
\(417\) 268.518 + 203.841i 0.643927 + 0.488827i
\(418\) −167.457 + 37.2927i −0.400614 + 0.0892170i
\(419\) −134.464 232.899i −0.320917 0.555845i 0.659761 0.751476i \(-0.270658\pi\)
−0.980677 + 0.195631i \(0.937324\pi\)
\(420\) −0.332543 1.02917i −0.000791768 0.00245041i
\(421\) −235.498 135.965i −0.559378 0.322957i 0.193518 0.981097i \(-0.438010\pi\)
−0.752896 + 0.658140i \(0.771344\pi\)
\(422\) 114.291 363.700i 0.270832 0.861848i
\(423\) 342.822 95.6747i 0.810455 0.226181i
\(424\) −4.83882 6.26867i −0.0114123 0.0147846i
\(425\) 4.71010 8.15813i 0.0110826 0.0191956i
\(426\) −105.988 + 230.983i −0.248799 + 0.542214i
\(427\) −203.889 353.147i −0.477493 0.827042i
\(428\) 16.9531 198.149i 0.0396101 0.462964i
\(429\) 76.9628 + 183.117i 0.179400 + 0.426846i
\(430\) −1.30195 + 1.19532i −0.00302780 + 0.00277981i
\(431\) 140.920i 0.326960i −0.986547 0.163480i \(-0.947728\pi\)
0.986547 0.163480i \(-0.0522719\pi\)
\(432\) −225.014 + 368.772i −0.520866 + 0.853638i
\(433\) 649.144 1.49918 0.749589 0.661903i \(-0.230251\pi\)
0.749589 + 0.661903i \(0.230251\pi\)
\(434\) −193.759 211.044i −0.446449 0.486278i
\(435\) −1.95892 + 0.823320i −0.00450326 + 0.00189269i
\(436\) 160.761 + 13.7543i 0.368717 + 0.0315466i
\(437\) −589.766 + 340.502i −1.34958 + 0.779180i
\(438\) 145.409 + 66.7222i 0.331984 + 0.152334i
\(439\) −135.712 78.3535i −0.309140 0.178482i 0.337402 0.941361i \(-0.390452\pi\)
−0.646541 + 0.762879i \(0.723785\pi\)
\(440\) 0.533994 + 0.691787i 0.00121362 + 0.00157224i
\(441\) −234.407 60.2146i −0.531535 0.136541i
\(442\) 8.35307 + 2.62491i 0.0188983 + 0.00593872i
\(443\) 6.92104 11.9876i 0.0156231 0.0270600i −0.858108 0.513469i \(-0.828360\pi\)
0.873731 + 0.486409i \(0.161693\pi\)
\(444\) −610.048 + 197.117i −1.37398 + 0.443956i
\(445\) −0.707787 + 0.408641i −0.00159053 + 0.000918295i
\(446\) 94.5976 + 424.775i 0.212102 + 0.952411i
\(447\) 0.405977 0.534790i 0.000908225 0.00119640i
\(448\) −211.563 + 214.010i −0.472239 + 0.477701i
\(449\) −682.313 −1.51963 −0.759814 0.650140i \(-0.774710\pi\)
−0.759814 + 0.650140i \(0.774710\pi\)
\(450\) −237.472 + 382.232i −0.527716 + 0.849404i
\(451\) 330.756 0.733383
\(452\) 93.7449 43.9329i 0.207400 0.0971967i
\(453\) −367.286 46.4207i −0.810786 0.102474i
\(454\) 267.788 59.6365i 0.589842 0.131358i
\(455\) 0.906861 0.523577i 0.00199310 0.00115072i
\(456\) 178.098 314.293i 0.390566 0.689239i
\(457\) −140.879 + 244.010i −0.308270 + 0.533938i −0.977984 0.208680i \(-0.933083\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(458\) −489.438 153.804i −1.06864 0.335816i
\(459\) −3.74694 + 9.45886i −0.00816326 + 0.0206075i
\(460\) 2.84543 + 1.98428i 0.00618573 + 0.00431365i
\(461\) −556.528 321.312i −1.20722 0.696989i −0.245069 0.969506i \(-0.578811\pi\)
−0.962151 + 0.272517i \(0.912144\pi\)
\(462\) −160.078 + 14.9953i −0.346489 + 0.0324575i
\(463\) 528.367 305.053i 1.14118 0.658861i 0.194458 0.980911i \(-0.437705\pi\)
0.946723 + 0.322050i \(0.104372\pi\)
\(464\) 454.358 + 378.293i 0.979220 + 0.815287i
\(465\) 0.219675 1.73810i 0.000472420 0.00373784i
\(466\) 413.191 + 450.052i 0.886676 + 0.965777i
\(467\) 289.260 0.619400 0.309700 0.950834i \(-0.399771\pi\)
0.309700 + 0.950834i \(0.399771\pi\)
\(468\) −394.757 138.218i −0.843498 0.295337i
\(469\) 321.098i 0.684643i
\(470\) 1.02533 + 1.11680i 0.00218156 + 0.00237618i
\(471\) −354.941 + 467.561i −0.753590 + 0.992698i
\(472\) −435.599 178.965i −0.922879 0.379164i
\(473\) 131.369 + 227.538i 0.277736 + 0.481052i
\(474\) −485.876 684.919i −1.02506 1.44498i
\(475\) 188.146 325.879i 0.396098 0.686061i
\(476\) −4.05390 + 5.81325i −0.00851659 + 0.0122127i
\(477\) 6.36442 + 6.23395i 0.0133426 + 0.0130691i
\(478\) −150.845 47.4023i −0.315575 0.0991680i
\(479\) 115.068 + 66.4346i 0.240226 + 0.138694i 0.615281 0.788308i \(-0.289043\pi\)
−0.375055 + 0.927003i \(0.622376\pi\)
\(480\) −1.83467 0.142097i −0.00382223 0.000296036i
\(481\) −310.353 537.547i −0.645224 1.11756i
\(482\) 434.957 96.8651i 0.902401 0.200965i
\(483\) −588.358 + 247.283i −1.21813 + 0.511972i
\(484\) −320.627 + 150.260i −0.662452 + 0.310454i
\(485\) 2.14409i 0.00442081i
\(486\) 193.494 445.820i 0.398137 0.917326i
\(487\) 800.882i 1.64452i −0.569111 0.822261i \(-0.692713\pi\)
0.569111 0.822261i \(-0.307287\pi\)
\(488\) −687.592 + 92.5351i −1.40900 + 0.189621i
\(489\) 99.8423 41.9630i 0.204176 0.0858139i
\(490\) −0.224094 1.00626i −0.000457334 0.00205358i
\(491\) −416.975 722.222i −0.849236 1.47092i −0.881891 0.471454i \(-0.843730\pi\)
0.0326547 0.999467i \(-0.489604\pi\)
\(492\) −466.868 + 516.810i −0.948918 + 1.05043i
\(493\) 12.0584 + 6.96193i 0.0244593 + 0.0141216i
\(494\) 333.666 + 104.853i 0.675437 + 0.212253i
\(495\) −0.702353 0.687955i −0.00141890 0.00138981i
\(496\) −457.409 + 168.472i −0.922196 + 0.339661i
\(497\) 99.5810 172.479i 0.200364 0.347041i
\(498\) 401.216 284.619i 0.805654 0.571524i
\(499\) −62.9732 109.073i −0.126199 0.218583i 0.796002 0.605294i \(-0.206944\pi\)
−0.922201 + 0.386711i \(0.873611\pi\)
\(500\) −3.81969 0.326804i −0.00763938 0.000653608i
\(501\) 188.240 247.967i 0.375728 0.494944i
\(502\) 532.073 + 579.540i 1.05991 + 1.15446i
\(503\) 321.537i 0.639239i −0.947546 0.319619i \(-0.896445\pi\)
0.947546 0.319619i \(-0.103555\pi\)
\(504\) 202.523 271.290i 0.401831 0.538275i
\(505\) −2.05763 −0.00407452
\(506\) 379.864 348.751i 0.750719 0.689232i
\(507\) −12.7964 + 101.247i −0.0252395 + 0.199698i
\(508\) 152.377 + 13.0370i 0.299955 + 0.0256635i
\(509\) −473.601 + 273.434i −0.930455 + 0.537198i −0.886955 0.461855i \(-0.847184\pi\)
−0.0434992 + 0.999053i \(0.513851\pi\)
\(510\) −0.0431485 + 0.00404195i −8.46049e−5 + 7.92539e-6i
\(511\) −108.580 62.6885i −0.212485 0.122678i
\(512\) 200.006 + 471.319i 0.390638 + 0.920545i
\(513\) −149.673 + 377.837i −0.291759 + 0.736524i
\(514\) −107.519 + 342.149i −0.209181 + 0.665660i
\(515\) 0.487722 0.844758i 0.000947032 0.00164031i
\(516\) −540.960 115.908i −1.04837 0.224627i
\(517\) 195.180 112.687i 0.377524 0.217964i
\(518\) 490.402 109.213i 0.946722 0.210835i
\(519\) 184.203 + 23.2811i 0.354919 + 0.0448576i
\(520\) −0.237625 1.76570i −0.000456971 0.00339557i
\(521\) 774.144 1.48588 0.742940 0.669358i \(-0.233431\pi\)
0.742940 + 0.669358i \(0.233431\pi\)
\(522\) −564.971 351.004i −1.08232 0.672421i
\(523\) 126.448 0.241774 0.120887 0.992666i \(-0.461426\pi\)
0.120887 + 0.992666i \(0.461426\pi\)
\(524\) 448.416 210.147i 0.855756 0.401044i
\(525\) 213.227 280.882i 0.406146 0.535013i
\(526\) −121.346 544.883i −0.230695 1.03590i
\(527\) −9.94182 + 5.73991i −0.0188649 + 0.0108917i
\(528\) −79.9031 + 261.618i −0.151332 + 0.495488i
\(529\) 758.991 1314.61i 1.43477 2.48509i
\(530\) −0.0113767 + 0.0362031i −2.14654e−5 + 6.83077e-5i
\(531\) 513.136 + 131.815i 0.966358 + 0.248238i
\(532\) −161.934 + 232.212i −0.304387 + 0.436489i
\(533\) −583.963 337.151i −1.09562 0.632554i
\(534\) −232.513 106.690i −0.435417 0.199795i
\(535\) −0.825336 + 0.476508i −0.00154268 + 0.000890669i
\(536\) 505.326 + 207.613i 0.942772 + 0.387337i
\(537\) −652.603 + 274.284i −1.21528 + 0.510772i
\(538\) 165.686 152.116i 0.307967 0.282743i
\(539\) −153.248 −0.284320
\(540\) 2.06632 0.126375i 0.00382653 0.000234028i
\(541\) 323.091i 0.597210i 0.954377 + 0.298605i \(0.0965213\pi\)
−0.954377 + 0.298605i \(0.903479\pi\)
\(542\) −737.041 + 676.674i −1.35985 + 1.24848i
\(543\) −318.956 758.889i −0.587396 1.39759i
\(544\) 6.52743 + 10.1385i 0.0119990 + 0.0186369i
\(545\) −0.386598 0.669607i −0.000709353 0.00122864i
\(546\) 297.910 + 136.698i 0.545622 + 0.250363i
\(547\) 42.9079 74.3187i 0.0784423 0.135866i −0.824136 0.566392i \(-0.808339\pi\)
0.902578 + 0.430526i \(0.141672\pi\)
\(548\) 368.751 + 257.150i 0.672903 + 0.469252i
\(549\) 751.787 209.808i 1.36938 0.382165i
\(550\) −85.4230 + 271.835i −0.155315 + 0.494246i
\(551\) 481.677 + 278.096i 0.874187 + 0.504712i
\(552\) 8.74408 + 1085.81i 0.0158407 + 1.96705i
\(553\) 329.047 + 569.926i 0.595022 + 1.03061i
\(554\) 111.762 + 501.848i 0.201736 + 0.905863i
\(555\) 2.44701 + 1.85761i 0.00440903 + 0.00334704i
\(556\) −407.020 + 190.747i −0.732050 + 0.343070i
\(557\) 666.623i 1.19681i 0.801194 + 0.598405i \(0.204199\pi\)
−0.801194 + 0.598405i \(0.795801\pi\)
\(558\) 483.523 258.700i 0.866528 0.463621i
\(559\) 535.636i 0.958204i
\(560\) 1.42113 + 0.244970i 0.00253773 + 0.000437446i
\(561\) −0.807803 + 6.39143i −0.00143993 + 0.0113929i
\(562\) 543.596 121.059i 0.967253 0.215408i
\(563\) 234.690 + 406.495i 0.416856 + 0.722016i 0.995621 0.0934780i \(-0.0297985\pi\)
−0.578765 + 0.815494i \(0.696465\pi\)
\(564\) −99.4247 + 464.031i −0.176285 + 0.822750i
\(565\) −0.429652 0.248060i −0.000760446 0.000439044i
\(566\) −112.663 + 358.518i −0.199051 + 0.633424i
\(567\) −183.561 + 333.712i −0.323740 + 0.588557i
\(568\) −207.052 268.235i −0.364528 0.472245i
\(569\) −129.732 + 224.702i −0.228000 + 0.394907i −0.957215 0.289377i \(-0.906552\pi\)
0.729215 + 0.684284i \(0.239885\pi\)
\(570\) −1.72358 + 0.161457i −0.00302383 + 0.000283258i
\(571\) 38.3743 + 66.4663i 0.0672055 + 0.116403i 0.897670 0.440668i \(-0.145258\pi\)
−0.830465 + 0.557071i \(0.811925\pi\)
\(572\) −263.880 22.5770i −0.461329 0.0394702i
\(573\) −259.000 32.7346i −0.452006 0.0571284i
\(574\) 402.051 369.121i 0.700437 0.643068i
\(575\) 1131.07i 1.96708i
\(576\) −295.996 494.128i −0.513883 0.857861i
\(577\) 289.811 0.502272 0.251136 0.967952i \(-0.419196\pi\)
0.251136 + 0.967952i \(0.419196\pi\)
\(578\) −390.707 425.563i −0.675964 0.736268i
\(579\) 247.613 + 187.971i 0.427656 + 0.324648i
\(580\) 0.241520 2.82289i 0.000416414 0.00486706i
\(581\) −333.854 + 192.751i −0.574620 + 0.331757i
\(582\) 547.388 388.313i 0.940530 0.667204i
\(583\) 4.88542 + 2.82060i 0.00837980 + 0.00483808i
\(584\) −168.860 + 130.344i −0.289144 + 0.223192i
\(585\) 0.538776 + 1.93055i 0.000920985 + 0.00330008i
\(586\) 975.981 + 306.697i 1.66550 + 0.523375i
\(587\) 136.875 237.074i 0.233177 0.403874i −0.725565 0.688154i \(-0.758421\pi\)
0.958741 + 0.284280i \(0.0917547\pi\)
\(588\) 216.313 239.453i 0.367879 0.407233i
\(589\) −397.129 + 229.282i −0.674243 + 0.389274i
\(590\) 0.490559 + 2.20278i 0.000831456 + 0.00373352i
\(591\) 232.660 + 553.567i 0.393672 + 0.936662i
\(592\) 145.207 842.381i 0.245282 1.42294i
\(593\) −461.865 −0.778861 −0.389431 0.921056i \(-0.627328\pi\)
−0.389431 + 0.921056i \(0.627328\pi\)
\(594\) 48.4335 303.906i 0.0815379 0.511626i
\(595\) 0.0339624 5.70796e−5
\(596\) 0.379899 + 0.810636i 0.000637414 + 0.00136013i
\(597\) 207.917 + 494.695i 0.348269 + 0.828634i
\(598\) −1026.16 + 228.526i −1.71599 + 0.382151i
\(599\) 551.557 318.442i 0.920797 0.531622i 0.0369077 0.999319i \(-0.488249\pi\)
0.883889 + 0.467696i \(0.154916\pi\)
\(600\) −304.170 517.175i −0.506950 0.861958i
\(601\) −456.737 + 791.092i −0.759962 + 1.31629i 0.182908 + 0.983130i \(0.441449\pi\)
−0.942869 + 0.333162i \(0.891884\pi\)
\(602\) 413.616 + 129.977i 0.687070 + 0.215909i
\(603\) −595.275 152.914i −0.987189 0.253589i
\(604\) 282.348 404.884i 0.467464 0.670338i
\(605\) 1.46950 + 0.848416i 0.00242892 + 0.00140234i
\(606\) −372.654 525.315i −0.614941 0.866857i
\(607\) −108.688 + 62.7511i −0.179058 + 0.103379i −0.586850 0.809696i \(-0.699632\pi\)
0.407792 + 0.913075i \(0.366299\pi\)
\(608\) 260.740 + 404.985i 0.428849 + 0.666093i
\(609\) 415.167 + 315.167i 0.681720 + 0.517516i
\(610\) 2.24849 + 2.44908i 0.00368605 + 0.00401489i
\(611\) −459.464 −0.751987
\(612\) −8.84647 10.2838i −0.0144550 0.0168036i
\(613\) 929.305i 1.51600i 0.652257 + 0.757998i \(0.273822\pi\)
−0.652257 + 0.757998i \(0.726178\pi\)
\(614\) −264.952 288.589i −0.431519 0.470015i
\(615\) 3.31117 + 0.418493i 0.00538401 + 0.000680477i
\(616\) 81.4668 198.289i 0.132251 0.321897i
\(617\) 9.42520 + 16.3249i 0.0152759 + 0.0264585i 0.873562 0.486712i \(-0.161804\pi\)
−0.858286 + 0.513171i \(0.828471\pi\)
\(618\) 303.998 28.4771i 0.491906 0.0460794i
\(619\) 158.239 274.079i 0.255637 0.442777i −0.709431 0.704775i \(-0.751048\pi\)
0.965068 + 0.261998i \(0.0843814\pi\)
\(620\) 1.91602 + 1.33615i 0.00309036 + 0.00215507i
\(621\) −178.241 1208.50i −0.287022 1.94606i
\(622\) −871.341 273.815i −1.40087 0.440217i
\(623\) 173.622 + 100.240i 0.278686 + 0.160900i
\(624\) 407.748 380.449i 0.653443 0.609693i
\(625\) −312.486 541.242i −0.499978 0.865987i
\(626\) −723.532 + 161.131i −1.15580 + 0.257397i
\(627\) −32.2679 + 255.308i −0.0514640 + 0.407189i
\(628\) −332.141 708.729i −0.528887 1.12855i
\(629\) 20.1314i 0.0320054i
\(630\) −1.62150 0.0524238i −0.00257381 8.32125e-5i
\(631\) 254.226i 0.402893i −0.979499 0.201447i \(-0.935436\pi\)
0.979499 0.201447i \(-0.0645643\pi\)
\(632\) 1109.67 149.338i 1.75581 0.236294i
\(633\) −455.477 345.768i −0.719553 0.546237i
\(634\) 218.570 + 981.454i 0.344748 + 1.54803i
\(635\) −0.366437 0.634688i −0.000577066 0.000999508i
\(636\) −11.3031 + 3.65221i −0.0177722 + 0.00574247i
\(637\) 270.566 + 156.212i 0.424751 + 0.245230i
\(638\) −401.796 126.262i −0.629774 0.197904i
\(639\) 272.332 + 266.749i 0.426185 + 0.417448i
\(640\) 1.30438 2.07810i 0.00203810 0.00324703i
\(641\) −509.350 + 882.221i −0.794618 + 1.37632i 0.128463 + 0.991714i \(0.458996\pi\)
−0.923081 + 0.384605i \(0.874338\pi\)
\(642\) −271.128 124.409i −0.422318 0.193784i
\(643\) 302.348 + 523.683i 0.470215 + 0.814436i 0.999420 0.0340578i \(-0.0108430\pi\)
−0.529205 + 0.848494i \(0.677510\pi\)
\(644\) 72.5401 847.851i 0.112640 1.31654i
\(645\) 1.02723 + 2.44407i 0.00159260 + 0.00378926i
\(646\) 7.67160 + 8.35599i 0.0118755 + 0.0129350i
\(647\) 86.7767i 0.134122i −0.997749 0.0670608i \(-0.978638\pi\)
0.997749 0.0670608i \(-0.0213622\pi\)
\(648\) 406.492 + 504.647i 0.627303 + 0.778776i
\(649\) 335.473 0.516908
\(650\) 427.909 392.862i 0.658322 0.604402i
\(651\) −396.181 + 166.512i −0.608572 + 0.255779i
\(652\) −12.3098 + 143.877i −0.0188801 + 0.220671i
\(653\) 346.903 200.285i 0.531245 0.306714i −0.210278 0.977642i \(-0.567437\pi\)
0.741523 + 0.670927i \(0.234104\pi\)
\(654\) 100.935 219.970i 0.154335 0.336346i
\(655\) −2.05518 1.18656i −0.00313768 0.00181154i
\(656\) −320.948 871.389i −0.489250 1.32834i
\(657\) 167.925 171.439i 0.255593 0.260943i
\(658\) 111.493 354.797i 0.169443 0.539205i
\(659\) 28.0360 48.5597i 0.0425432 0.0736870i −0.843970 0.536391i \(-0.819787\pi\)
0.886513 + 0.462704i \(0.153121\pi\)
\(660\) 1.24737 0.403044i 0.00188995 0.000610673i
\(661\) 675.562 390.036i 1.02203 0.590069i 0.107339 0.994222i \(-0.465767\pi\)
0.914691 + 0.404153i \(0.132434\pi\)
\(662\) −733.277 + 163.301i −1.10767 + 0.246678i
\(663\) 7.94122 10.4609i 0.0119777 0.0157781i
\(664\) 87.4799 + 650.029i 0.131747 + 0.978959i
\(665\) 1.35664 0.00204006
\(666\) −31.0745 + 961.153i −0.0466584 + 1.44317i
\(667\) −1671.82 −2.50648
\(668\) 176.148 + 375.868i 0.263695 + 0.562677i
\(669\) 647.620 + 81.8517i 0.968042 + 0.122349i
\(670\) −0.569084 2.55538i −0.000849379 0.00381400i
\(671\) 428.017 247.116i 0.637879 0.368280i
\(672\) 194.837 + 407.181i 0.289936 + 0.605924i
\(673\) −353.998 + 613.143i −0.526001 + 0.911060i 0.473541 + 0.880772i \(0.342976\pi\)
−0.999541 + 0.0302878i \(0.990358\pi\)
\(674\) 193.368 615.340i 0.286896 0.912967i
\(675\) 419.176 + 529.058i 0.621002 + 0.783790i
\(676\) −111.611 77.8326i −0.165105 0.115137i
\(677\) −503.417 290.648i −0.743600 0.429318i 0.0797769 0.996813i \(-0.474579\pi\)
−0.823377 + 0.567495i \(0.807913\pi\)
\(678\) −14.4837 154.616i −0.0213624 0.228048i
\(679\) −455.486 + 262.975i −0.670818 + 0.387297i
\(680\) 0.0219591 0.0534481i 3.22928e−5 7.86001e-5i
\(681\) 51.6012 408.275i 0.0757727 0.599522i
\(682\) 255.788 234.838i 0.375055 0.344337i
\(683\) 558.887 0.818282 0.409141 0.912471i \(-0.365828\pi\)
0.409141 + 0.912471i \(0.365828\pi\)
\(684\) −353.375 410.790i −0.516630 0.600571i
\(685\) 2.15433i 0.00314501i
\(686\) −525.720 + 482.661i −0.766356 + 0.703588i
\(687\) −465.306 + 612.944i −0.677302 + 0.892204i
\(688\) 471.983 566.887i 0.686022 0.823963i
\(689\) −5.75028 9.95977i −0.00834583 0.0144554i
\(690\) 4.24404 3.01069i 0.00615079 0.00436332i
\(691\) −158.856 + 275.147i −0.229893 + 0.398187i −0.957776 0.287515i \(-0.907171\pi\)
0.727883 + 0.685701i \(0.240504\pi\)
\(692\) −141.604 + 203.059i −0.204630 + 0.293438i
\(693\) −60.0033 + 233.585i −0.0865848 + 0.337063i
\(694\) 50.8996 161.974i 0.0733423 0.233392i
\(695\) 1.86545 + 1.07702i 0.00268411 + 0.00154967i
\(696\) 764.428 449.589i 1.09832 0.645962i
\(697\) −10.9348 18.9397i −0.0156884 0.0271732i
\(698\) −17.8010 79.9326i −0.0255029 0.114517i
\(699\) 844.854 355.086i 1.20866 0.507992i
\(700\) 199.530 + 425.761i 0.285043 + 0.608231i
\(701\) 731.568i 1.04361i −0.853066 0.521803i \(-0.825259\pi\)
0.853066 0.521803i \(-0.174741\pi\)
\(702\) −395.293 + 487.188i −0.563096 + 0.694000i
\(703\) 804.154i 1.14389i
\(704\) −259.382 256.416i −0.368440 0.364227i
\(705\) 2.09651 0.881147i 0.00297377 0.00124985i
\(706\) −1064.77 + 237.125i −1.50818 + 0.335871i
\(707\) 252.371 + 437.119i 0.356960 + 0.618272i
\(708\) −473.527 + 524.181i −0.668823 + 0.740369i
\(709\) 112.277 + 64.8230i 0.158359 + 0.0914288i 0.577085 0.816684i \(-0.304190\pi\)
−0.418726 + 0.908113i \(0.637523\pi\)
\(710\) −0.486805 + 1.54912i −0.000685641 + 0.00218186i
\(711\) −1213.27 + 338.600i −1.70643 + 0.476230i
\(712\) 270.012 208.423i 0.379230 0.292729i
\(713\) 689.185 1193.70i 0.966599 1.67420i
\(714\) 6.15087 + 8.67062i 0.00861466 + 0.0121437i
\(715\) 0.634579 + 1.09912i 0.000887523 + 0.00153724i
\(716\) 80.4611 940.431i 0.112376 1.31345i
\(717\) −143.407 + 188.910i −0.200010 + 0.263472i
\(718\) −35.5796 + 32.6655i −0.0495538 + 0.0454951i
\(719\) 726.317i 1.01018i −0.863068 0.505088i \(-0.831460\pi\)
0.863068 0.505088i \(-0.168540\pi\)
\(720\) −1.13092 + 2.51793i −0.00157072 + 0.00349713i
\(721\) −239.278 −0.331870
\(722\) −181.842 198.064i −0.251858 0.274327i
\(723\) 83.8137 663.143i 0.115925 0.917211i
\(724\) 1093.59 + 93.5654i 1.51049 + 0.129234i
\(725\) 800.013 461.888i 1.10347 0.637087i
\(726\) 49.5373 + 528.820i 0.0682332 + 0.728402i
\(727\) 498.049 + 287.549i 0.685075 + 0.395528i 0.801764 0.597640i \(-0.203895\pi\)
−0.116690 + 0.993168i \(0.537228\pi\)
\(728\) −345.956 + 267.045i −0.475214 + 0.366820i
\(729\) −531.244 499.220i −0.728730 0.684801i
\(730\) 0.975209 + 0.306455i 0.00133590 + 0.000419801i
\(731\) 8.68615 15.0449i 0.0118826 0.0205812i
\(732\) −218.032 + 1017.59i −0.297858 + 1.39015i
\(733\) 113.103 65.3000i 0.154301 0.0890859i −0.420861 0.907125i \(-0.638272\pi\)
0.575163 + 0.818039i \(0.304939\pi\)
\(734\) −114.097 512.333i −0.155445 0.698001i
\(735\) −1.53416 0.193900i −0.00208729 0.000263809i
\(736\) −1287.40 662.356i −1.74918 0.899940i
\(737\) −389.173 −0.528050
\(738\) 492.838 + 921.136i 0.667802 + 1.24815i
\(739\) −61.7030 −0.0834953 −0.0417477 0.999128i \(-0.513293\pi\)
−0.0417477 + 0.999128i \(0.513293\pi\)
\(740\) −3.70919 + 1.73829i −0.00501242 + 0.00234903i
\(741\) 317.215 417.864i 0.428090 0.563919i
\(742\) 9.08626 2.02351i 0.0122456 0.00272711i
\(743\) −368.246 + 212.607i −0.495620 + 0.286147i −0.726903 0.686740i \(-0.759041\pi\)
0.231283 + 0.972887i \(0.425708\pi\)
\(744\) 5.88797 + 731.149i 0.00791394 + 0.982727i
\(745\) 0.00214503 0.00371531i 2.87924e−6 4.98699e-6i
\(746\) −213.836 67.1970i −0.286644 0.0900764i
\(747\) −198.347 710.717i −0.265524 0.951428i
\(748\) −7.04570 4.91336i −0.00941939 0.00656866i
\(749\) 202.456 + 116.888i 0.270302 + 0.156059i
\(750\) −2.39823 + 5.22651i −0.00319764 + 0.00696868i
\(751\) −1180.47 + 681.543i −1.57186 + 0.907514i −0.575920 + 0.817506i \(0.695356\pi\)
−0.995941 + 0.0900084i \(0.971311\pi\)
\(752\) −486.271 404.863i −0.646637 0.538382i
\(753\) 1087.93 457.251i 1.44480 0.607239i
\(754\) 580.683 + 632.486i 0.770136 + 0.838841i
\(755\) −2.36543 −0.00313302
\(756\) −280.283 423.465i −0.370745 0.560139i
\(757\) 105.684i 0.139610i −0.997561 0.0698048i \(-0.977762\pi\)
0.997561 0.0698048i \(-0.0222376\pi\)
\(758\) 413.290 + 450.159i 0.545237 + 0.593878i
\(759\) −299.709 713.094i −0.394873 0.939518i
\(760\) 0.877163 2.13500i 0.00115416 0.00280921i
\(761\) 452.651 + 784.015i 0.594811 + 1.03024i 0.993574 + 0.113189i \(0.0361064\pi\)
−0.398763 + 0.917054i \(0.630560\pi\)
\(762\) 95.6715 208.499i 0.125553 0.273621i
\(763\) −94.8331 + 164.256i −0.124290 + 0.215276i
\(764\) 199.104 285.513i 0.260607 0.373708i
\(765\) −0.0161737 + 0.0629620i −2.11421e−5 + 8.23032e-5i
\(766\) 112.287 + 35.2858i 0.146589 + 0.0460650i
\(767\) −592.292 341.960i −0.772219 0.445841i
\(768\) 766.775 43.3519i 0.998406 0.0564478i
\(769\) −16.2383 28.1255i −0.0211161 0.0365741i 0.855274 0.518176i \(-0.173389\pi\)
−0.876390 + 0.481601i \(0.840055\pi\)
\(770\) −1.00273 + 0.223307i −0.00130224 + 0.000290010i
\(771\) 428.489 + 325.280i 0.555757 + 0.421893i
\(772\) −375.332 + 175.897i −0.486181 + 0.227846i
\(773\) 367.930i 0.475976i −0.971268 0.237988i \(-0.923512\pi\)
0.971268 0.237988i \(-0.0764880\pi\)
\(774\) −437.935 + 704.894i −0.565807 + 0.910716i
\(775\) 761.627i 0.982744i
\(776\) 119.351 + 886.850i 0.153803 + 1.14285i
\(777\) 94.4975 747.675i 0.121618 0.962259i
\(778\) 209.671 + 941.496i 0.269501 + 1.21015i
\(779\) −436.795 756.552i −0.560713 0.971183i
\(780\) −2.61311 0.559894i −0.00335015 0.000717813i
\(781\) 209.046 + 120.693i 0.267665 + 0.154536i
\(782\) −32.5285 10.2219i −0.0415966 0.0130715i
\(783\) −781.993 + 619.578i −0.998714 + 0.791287i
\(784\) 148.704 + 403.739i 0.189674 + 0.514973i
\(785\) −1.87538 + 3.24825i −0.00238902 + 0.00413790i
\(786\) −69.2809 739.586i −0.0881436 0.940949i
\(787\) 563.311 + 975.684i 0.715770 + 1.23975i 0.962662 + 0.270707i \(0.0872576\pi\)
−0.246891 + 0.969043i \(0.579409\pi\)
\(788\) −797.716 68.2507i −1.01233 0.0866125i
\(789\) −830.738 104.996i −1.05290 0.133074i
\(790\) −3.62873 3.95245i −0.00459333 0.00500310i
\(791\) 121.699i 0.153855i
\(792\) 328.806 + 245.459i 0.415159 + 0.309923i
\(793\) −1007.58 −1.27059
\(794\) −110.327 + 101.291i −0.138951 + 0.127570i
\(795\) 0.0453387 + 0.0344181i 5.70299e−5 + 4.32933e-5i
\(796\) −712.878 60.9921i −0.895575 0.0766233i
\(797\) 297.816 171.944i 0.373672 0.215739i −0.301390 0.953501i \(-0.597450\pi\)
0.675061 + 0.737762i \(0.264117\pi\)
\(798\) 245.698 + 346.351i 0.307893 + 0.434023i
\(799\) −12.9054 7.45091i −0.0161519 0.00932530i
\(800\) 799.050 38.7242i 0.998813 0.0484053i
\(801\) −268.516 + 274.136i −0.335226 + 0.342242i
\(802\) 359.587 1144.29i 0.448363 1.42679i
\(803\) 75.9790 131.600i 0.0946189 0.163885i
\(804\) 549.325 608.088i 0.683240 0.756328i
\(805\) −3.53150 + 2.03891i −0.00438696 + 0.00253281i
\(806\) −690.982 + 153.882i −0.857297 + 0.190920i
\(807\) −130.725 311.032i −0.161988 0.385418i
\(808\) 851.089 114.538i 1.05333 0.141755i
\(809\) 273.136 0.337622 0.168811 0.985648i \(-0.446007\pi\)
0.168811 + 0.985648i \(0.446007\pi\)
\(810\) 0.869384 2.98109i 0.00107331 0.00368036i
\(811\) 615.310 0.758705 0.379352 0.925252i \(-0.376147\pi\)
0.379352 + 0.925252i \(0.376147\pi\)
\(812\) −629.311 + 294.923i −0.775014 + 0.363205i
\(813\) 581.518 + 1383.60i 0.715274 + 1.70185i
\(814\) 132.367 + 594.371i 0.162613 + 0.730186i
\(815\) 0.599283 0.345996i 0.000735317 0.000424535i
\(816\) 17.6223 4.07372i 0.0215960 0.00499230i
\(817\) 346.971 600.971i 0.424689 0.735583i
\(818\) −328.782 + 1046.26i −0.401935 + 1.27905i
\(819\) 344.039 351.240i 0.420073 0.428864i
\(820\) −2.54543 + 3.65012i −0.00310418 + 0.00445137i
\(821\) 1110.25 + 641.002i 1.35231 + 0.780757i 0.988573 0.150744i \(-0.0481668\pi\)
0.363739 + 0.931501i \(0.381500\pi\)
\(822\) 550.002 390.167i 0.669102 0.474656i
\(823\) −241.117 + 139.209i −0.292973 + 0.169148i −0.639282 0.768972i \(-0.720768\pi\)
0.346309 + 0.938121i \(0.387435\pi\)
\(824\) −154.710 + 376.562i −0.187755 + 0.456993i
\(825\) 340.431 + 258.433i 0.412644 + 0.313252i
\(826\) 407.785 374.386i 0.493687 0.453252i
\(827\) 88.6450 0.107189 0.0535943 0.998563i \(-0.482932\pi\)
0.0535943 + 0.998563i \(0.482932\pi\)
\(828\) 1537.26 + 538.247i 1.85660 + 0.650057i
\(829\) 673.447i 0.812361i 0.913793 + 0.406180i \(0.133140\pi\)
−0.913793 + 0.406180i \(0.866860\pi\)
\(830\) 2.31529 2.12566i 0.00278950 0.00256103i
\(831\) 765.126 + 96.7031i 0.920729 + 0.116370i
\(832\) 196.575 + 717.110i 0.236268 + 0.861911i
\(833\) 5.06642 + 8.77529i 0.00608213 + 0.0105346i
\(834\) 62.8851 + 671.310i 0.0754018 + 0.804928i
\(835\) 0.994591 1.72268i 0.00119113 0.00206309i
\(836\) −281.443 196.265i −0.336654 0.234767i
\(837\) −120.021 813.766i −0.143395 0.972241i
\(838\) 161.245 513.118i 0.192416 0.612313i
\(839\) 29.6126 + 17.0968i 0.0352951 + 0.0203776i 0.517544 0.855657i \(-0.326846\pi\)
−0.482249 + 0.876034i \(0.660180\pi\)
\(840\) 1.06644 1.88197i 0.00126958 0.00224045i
\(841\) 262.209 + 454.160i 0.311783 + 0.540024i
\(842\) −118.222 530.855i −0.140406 0.630469i
\(843\) 104.748 828.776i 0.124256 0.983127i
\(844\) 690.413 323.557i 0.818025 0.383362i
\(845\) 0.652059i 0.000771667i
\(846\) 604.653 + 375.657i 0.714720 + 0.444039i
\(847\) 416.236i 0.491424i
\(848\) 2.69043 15.6078i 0.00317267 0.0184054i
\(849\) 448.988 + 340.842i 0.528844 + 0.401463i
\(850\) 18.3899 4.09544i 0.0216352 0.00481816i
\(851\) 1208.58 + 2093.32i 1.42018 + 2.45983i
\(852\) −483.657 + 156.277i −0.567673 + 0.183424i
\(853\) −1052.33 607.564i −1.23368 0.712267i −0.265887 0.964004i \(-0.585665\pi\)
−0.967796 + 0.251737i \(0.918998\pi\)
\(854\) 244.497 778.046i 0.286297 0.911061i
\(855\) −0.646063 + 2.51503i −0.000755629 + 0.00294156i
\(856\) 314.855 243.038i 0.367821 0.283923i
\(857\) 462.160 800.484i 0.539276 0.934054i −0.459667 0.888091i \(-0.652031\pi\)
0.998943 0.0459627i \(-0.0146355\pi\)
\(858\) −165.680 + 361.069i −0.193100 + 0.420826i
\(859\) −625.687 1083.72i −0.728390 1.26161i −0.957563 0.288223i \(-0.906936\pi\)
0.229174 0.973386i \(-0.426398\pi\)
\(860\) −3.52202 0.301336i −0.00409538 0.000350391i
\(861\) −317.214 754.745i −0.368425 0.876591i
\(862\) 207.611 190.607i 0.240848 0.221122i
\(863\) 291.210i 0.337439i 0.985664 + 0.168719i \(0.0539632\pi\)
−0.985664 + 0.168719i \(0.946037\pi\)
\(864\) −847.649 + 167.294i −0.981075 + 0.193627i
\(865\) 1.18632 0.00137147
\(866\) 878.028 + 956.358i 1.01389 + 1.10434i
\(867\) −798.882 + 335.764i −0.921433 + 0.387272i
\(868\) 48.8461 570.914i 0.0562743 0.657736i
\(869\) −690.755 + 398.808i −0.794885 + 0.458927i
\(870\) −3.86258 1.77238i −0.00443975 0.00203722i
\(871\) 687.101 + 396.698i 0.788864 + 0.455451i
\(872\) 197.180 + 255.446i 0.226124 + 0.292943i
\(873\) −270.609 969.648i −0.309976 1.11071i
\(874\) −1299.36 408.318i −1.48668 0.467183i
\(875\) 2.25324 3.90273i 0.00257514 0.00446027i
\(876\) 98.3803 + 304.473i 0.112306 + 0.347572i
\(877\) 623.417 359.930i 0.710851 0.410410i −0.100525 0.994935i \(-0.532052\pi\)
0.811376 + 0.584524i \(0.198719\pi\)
\(878\) −68.1284 305.920i −0.0775950 0.348428i
\(879\) 927.860 1222.26i 1.05559 1.39052i
\(880\) −0.296905 + 1.72242i −0.000337393 + 0.00195729i
\(881\) 136.645 0.155102 0.0775512 0.996988i \(-0.475290\pi\)
0.0775512 + 0.996988i \(0.475290\pi\)
\(882\) −228.346 426.788i −0.258895 0.483887i
\(883\) −795.629 −0.901052 −0.450526 0.892763i \(-0.648764\pi\)
−0.450526 + 0.892763i \(0.648764\pi\)
\(884\) 7.43112 + 15.8567i 0.00840625 + 0.0179374i
\(885\) 3.35839 + 0.424462i 0.00379479 + 0.000479618i
\(886\) 27.0222 6.01785i 0.0304991 0.00679215i
\(887\) 92.9513 53.6654i 0.104793 0.0605022i −0.446688 0.894690i \(-0.647396\pi\)
0.551480 + 0.834188i \(0.314063\pi\)
\(888\) −1115.55 632.141i −1.25625 0.711870i
\(889\) −89.8877 + 155.690i −0.101111 + 0.175129i
\(890\) −1.55938 0.490029i −0.00175212 0.000550594i
\(891\) −404.462 222.477i −0.453941 0.249694i
\(892\) −497.852 + 713.915i −0.558130 + 0.800353i
\(893\) −515.508 297.629i −0.577277 0.333291i
\(894\) 1.33701 0.125244i 0.00149553 0.000140094i
\(895\) −3.91712 + 2.26155i −0.00437667 + 0.00252687i
\(896\) −601.451 22.2186i −0.671262 0.0247975i
\(897\) −197.735 + 1564.50i −0.220440 + 1.74415i
\(898\) −922.892 1005.22i −1.02772 1.11940i
\(899\) −1125.75 −1.25222
\(900\) −884.329 + 167.146i −0.982588 + 0.185718i
\(901\) 0.372998i 0.000413982i
\(902\) 447.378 + 487.289i 0.495984 + 0.540232i
\(903\) 393.223 517.990i 0.435463 0.573632i
\(904\) 191.523 + 78.6872i 0.211862 + 0.0870434i
\(905\) −2.62988 4.55508i −0.00290594 0.00503324i
\(906\) −428.399 603.896i −0.472847 0.666552i
\(907\) 686.970 1189.87i 0.757409 1.31187i −0.186759 0.982406i \(-0.559798\pi\)
0.944168 0.329465i \(-0.106868\pi\)
\(908\) 450.068 + 313.857i 0.495670 + 0.345658i
\(909\) −930.548 + 259.697i −1.02371 + 0.285695i
\(910\) 1.99798 + 0.627856i 0.00219558 + 0.000689951i
\(911\) 166.832 + 96.3207i 0.183131 + 0.105731i 0.588763 0.808306i \(-0.299615\pi\)
−0.405632 + 0.914037i \(0.632949\pi\)
\(912\) 703.929 162.726i 0.771852 0.178427i
\(913\) −233.616 404.634i −0.255877 0.443192i
\(914\) −550.042 + 122.495i −0.601796 + 0.134020i
\(915\) 4.59750 1.93230i 0.00502460 0.00211180i
\(916\) −435.417 929.102i −0.475346 1.01430i
\(917\) 582.131i 0.634821i
\(918\) −19.0034 + 7.27378i −0.0207009 + 0.00792351i
\(919\) 818.741i 0.890905i −0.895306 0.445452i \(-0.853043\pi\)
0.895306 0.445452i \(-0.146957\pi\)
\(920\) 0.925359 + 6.87598i 0.00100582 + 0.00747389i
\(921\) −541.750 + 227.694i −0.588220 + 0.247225i
\(922\) −279.381 1254.51i −0.303016 1.36064i
\(923\) −246.053 426.177i −0.266580 0.461730i
\(924\) −238.613 215.554i −0.258239 0.233283i
\(925\) −1156.67 667.807i −1.25046 0.721953i
\(926\) 1164.09 + 365.809i 1.25711 + 0.395042i
\(927\) 113.950 443.591i 0.122923 0.478524i
\(928\) 57.2377 + 1181.06i 0.0616786 + 1.27270i
\(929\) −657.748 + 1139.25i −0.708017 + 1.22632i 0.257575 + 0.966258i \(0.417077\pi\)
−0.965592 + 0.260063i \(0.916257\pi\)
\(930\) 2.85780 2.02730i 0.00307290 0.00217989i
\(931\) 202.380 + 350.532i 0.217379 + 0.376511i
\(932\) −104.164 + 1217.47i −0.111764 + 1.30630i
\(933\) −828.380 + 1091.22i −0.887867 + 1.16958i
\(934\) 391.251 + 426.155i 0.418898 + 0.456268i
\(935\) 0.0411627i 4.40242e-5i
\(936\) −330.316 768.532i −0.352901 0.821081i
\(937\) −521.572 −0.556640 −0.278320 0.960488i \(-0.589778\pi\)
−0.278320 + 0.960488i \(0.589778\pi\)
\(938\) −473.060 + 434.314i −0.504328 + 0.463022i
\(939\) −139.420 + 1103.11i −0.148477 + 1.17477i
\(940\) −0.258484 + 3.02116i −0.000274983 + 0.00321401i
\(941\) 340.545 196.614i 0.361896 0.208941i −0.308016 0.951381i \(-0.599665\pi\)
0.669912 + 0.742440i \(0.266332\pi\)
\(942\) −1168.93 + 109.500i −1.24090 + 0.116242i
\(943\) 2274.07 + 1312.93i 2.41153 + 1.39229i
\(944\) −325.525 883.817i −0.344836 0.936247i
\(945\) −0.896234 + 2.26247i −0.000948395 + 0.00239415i
\(946\) −157.533 + 501.306i −0.166526 + 0.529922i
\(947\) 437.860 758.396i 0.462366 0.800841i −0.536713 0.843765i \(-0.680334\pi\)
0.999078 + 0.0429244i \(0.0136675\pi\)
\(948\) 351.871 1642.24i 0.371172 1.73232i
\(949\) −268.288 + 154.896i −0.282706 + 0.163220i
\(950\) 734.590 163.593i 0.773252 0.172204i
\(951\) 1496.34 + 189.120i 1.57344 + 0.198865i
\(952\) −14.0477 + 1.89052i −0.0147560 + 0.00198584i
\(953\) 71.0166 0.0745190 0.0372595 0.999306i \(-0.488137\pi\)
0.0372595 + 0.999306i \(0.488137\pi\)
\(954\) −0.575755 + 17.8084i −0.000603516 + 0.0186671i
\(955\) −1.66803 −0.00174663
\(956\) −134.196 286.349i −0.140372 0.299529i
\(957\) −381.985 + 503.186i −0.399149 + 0.525795i
\(958\) 57.7650 + 259.384i 0.0602974 + 0.270756i
\(959\) −457.661 + 264.231i −0.477227 + 0.275527i
\(960\) −2.27221 2.89514i −0.00236689 0.00301577i
\(961\) −16.4259 + 28.4504i −0.0170925 + 0.0296050i
\(962\) 372.165 1184.31i 0.386866 1.23109i
\(963\) −313.111 + 319.664i −0.325141 + 0.331946i
\(964\) 731.028 + 509.786i 0.758327 + 0.528823i
\(965\) 1.72022 + 0.993171i 0.00178261 + 0.00102919i
\(966\) −1160.12 532.331i −1.20095 0.551067i
\(967\) 194.113 112.071i 0.200737 0.115896i −0.396262 0.918137i \(-0.629693\pi\)
0.596999 + 0.802242i \(0.296359\pi\)
\(968\) −655.049 269.126i −0.676704 0.278023i
\(969\) 15.6862 6.59279i 0.0161880 0.00680370i
\(970\) 3.15880 2.90008i 0.00325650 0.00298978i
\(971\) 91.8845 0.0946287 0.0473144 0.998880i \(-0.484934\pi\)
0.0473144 + 0.998880i \(0.484934\pi\)
\(972\) 918.528 317.946i 0.944988 0.327105i
\(973\) 528.390i 0.543053i
\(974\) 1179.91 1083.27i 1.21140 1.11218i
\(975\) −337.616 803.287i −0.346273 0.823884i
\(976\) −1066.36 887.839i −1.09258 0.909671i
\(977\) 368.517 + 638.289i 0.377192 + 0.653316i 0.990653 0.136410i \(-0.0435564\pi\)
−0.613461 + 0.789725i \(0.710223\pi\)
\(978\) 196.868 + 90.3347i 0.201297 + 0.0923668i
\(979\) −121.492 + 210.431i −0.124098 + 0.214945i
\(980\) 1.17937 1.69120i 0.00120344 0.00172572i
\(981\) −259.348 254.031i −0.264371 0.258951i
\(982\) 500.022 1591.18i 0.509188 1.62035i
\(983\) −1534.66 886.034i −1.56120 0.901357i −0.997136 0.0756241i \(-0.975905\pi\)
−0.564061 0.825733i \(-0.690762\pi\)
\(984\) −1392.88 + 11.2169i −1.41553 + 0.0113993i
\(985\) 1.91835 + 3.32267i 0.00194756 + 0.00337327i
\(986\) 6.05340 + 27.1818i 0.00613935 + 0.0275678i
\(987\) −444.327 337.304i −0.450180 0.341746i
\(988\) 296.838 + 633.399i 0.300444 + 0.641093i
\(989\) 2085.87i 2.10907i
\(990\) 0.0635381 1.96527i 6.41799e−5 0.00198512i
\(991\) 1115.19i 1.12532i 0.826689 + 0.562659i \(0.190221\pi\)
−0.826689 + 0.562659i \(0.809779\pi\)
\(992\) −866.891 446.009i −0.873882 0.449605i
\(993\) −141.298 + 1117.97i −0.142294 + 1.12585i
\(994\) 388.799 86.5857i 0.391146 0.0871084i
\(995\) 1.71433 + 2.96930i 0.00172294 + 0.00298423i
\(996\) 961.999 + 206.121i 0.965863 + 0.206949i
\(997\) 193.012 + 111.435i 0.193593 + 0.111771i 0.593663 0.804714i \(-0.297681\pi\)
−0.400071 + 0.916484i \(0.631014\pi\)
\(998\) 75.5153 240.307i 0.0756666 0.240788i
\(999\) 1341.09 + 531.247i 1.34244 + 0.531779i
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 72.3.p.b.43.15 yes 40
3.2 odd 2 216.3.p.b.19.6 40
4.3 odd 2 288.3.t.b.79.2 40
8.3 odd 2 inner 72.3.p.b.43.2 40
8.5 even 2 288.3.t.b.79.1 40
9.2 odd 6 648.3.b.e.163.10 20
9.4 even 3 inner 72.3.p.b.67.2 yes 40
9.5 odd 6 216.3.p.b.91.19 40
9.7 even 3 648.3.b.f.163.11 20
12.11 even 2 864.3.t.b.559.10 40
24.5 odd 2 864.3.t.b.559.11 40
24.11 even 2 216.3.p.b.19.19 40
36.7 odd 6 2592.3.b.e.1135.11 20
36.11 even 6 2592.3.b.f.1135.10 20
36.23 even 6 864.3.t.b.847.11 40
36.31 odd 6 288.3.t.b.175.1 40
72.5 odd 6 864.3.t.b.847.10 40
72.11 even 6 648.3.b.e.163.9 20
72.13 even 6 288.3.t.b.175.2 40
72.29 odd 6 2592.3.b.f.1135.11 20
72.43 odd 6 648.3.b.f.163.12 20
72.59 even 6 216.3.p.b.91.6 40
72.61 even 6 2592.3.b.e.1135.10 20
72.67 odd 6 inner 72.3.p.b.67.15 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.p.b.43.2 40 8.3 odd 2 inner
72.3.p.b.43.15 yes 40 1.1 even 1 trivial
72.3.p.b.67.2 yes 40 9.4 even 3 inner
72.3.p.b.67.15 yes 40 72.67 odd 6 inner
216.3.p.b.19.6 40 3.2 odd 2
216.3.p.b.19.19 40 24.11 even 2
216.3.p.b.91.6 40 72.59 even 6
216.3.p.b.91.19 40 9.5 odd 6
288.3.t.b.79.1 40 8.5 even 2
288.3.t.b.79.2 40 4.3 odd 2
288.3.t.b.175.1 40 36.31 odd 6
288.3.t.b.175.2 40 72.13 even 6
648.3.b.e.163.9 20 72.11 even 6
648.3.b.e.163.10 20 9.2 odd 6
648.3.b.f.163.11 20 9.7 even 3
648.3.b.f.163.12 20 72.43 odd 6
864.3.t.b.559.10 40 12.11 even 2
864.3.t.b.559.11 40 24.5 odd 2
864.3.t.b.847.10 40 72.5 odd 6
864.3.t.b.847.11 40 36.23 even 6
2592.3.b.e.1135.10 20 72.61 even 6
2592.3.b.e.1135.11 20 36.7 odd 6
2592.3.b.f.1135.10 20 36.11 even 6
2592.3.b.f.1135.11 20 72.29 odd 6