Properties

Label 45.3.k.a.22.7
Level $45$
Weight $3$
Character 45.22
Analytic conductor $1.226$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(7,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.k (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 22.7
Character \(\chi\) \(=\) 45.22
Dual form 45.3.k.a.43.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.238965 - 0.891829i) q^{2} +(0.613889 + 2.93652i) q^{3} +(2.72585 + 1.57377i) q^{4} +(-3.51824 + 3.55274i) q^{5} +(2.76557 + 0.154241i) q^{6} +(2.96175 - 11.0534i) q^{7} +(4.66637 - 4.66637i) q^{8} +(-8.24628 + 3.60539i) q^{9} +O(q^{10})\) \(q+(0.238965 - 0.891829i) q^{2} +(0.613889 + 2.93652i) q^{3} +(2.72585 + 1.57377i) q^{4} +(-3.51824 + 3.55274i) q^{5} +(2.76557 + 0.154241i) q^{6} +(2.96175 - 11.0534i) q^{7} +(4.66637 - 4.66637i) q^{8} +(-8.24628 + 3.60539i) q^{9} +(2.32770 + 3.98665i) q^{10} +(-1.30484 - 2.26005i) q^{11} +(-2.94803 + 8.97062i) q^{12} +(-0.764853 - 2.85447i) q^{13} +(-9.15000 - 5.28276i) q^{14} +(-12.5925 - 8.15040i) q^{15} +(3.24857 + 5.62669i) q^{16} +(-13.6850 - 13.6850i) q^{17} +(1.24482 + 8.21583i) q^{18} +11.4465i q^{19} +(-15.1814 + 4.14733i) q^{20} +(34.2768 + 1.91167i) q^{21} +(-2.32738 + 0.623621i) q^{22} +(2.89082 + 10.7887i) q^{23} +(16.5675 + 10.8382i) q^{24} +(-0.243925 - 24.9988i) q^{25} -2.72847 q^{26} +(-15.6496 - 22.0020i) q^{27} +(25.4688 - 25.4688i) q^{28} +(23.0262 - 13.2942i) q^{29} +(-10.2779 + 9.28269i) q^{30} +(-21.8787 + 37.8950i) q^{31} +(31.2919 - 8.38463i) q^{32} +(5.83564 - 5.21910i) q^{33} +(-15.4750 + 8.93448i) q^{34} +(28.8498 + 49.4110i) q^{35} +(-28.1522 - 3.14999i) q^{36} +(14.4324 + 14.4324i) q^{37} +(10.2083 + 2.73530i) q^{38} +(7.91267 - 3.99833i) q^{39} +(0.160974 + 32.9958i) q^{40} +(-0.924605 + 1.60146i) q^{41} +(9.89582 - 30.1122i) q^{42} +(-49.0742 - 13.1494i) q^{43} -8.21405i q^{44} +(16.2034 - 41.9815i) q^{45} +10.3125 q^{46} +(-16.4309 + 61.3211i) q^{47} +(-14.5286 + 12.9936i) q^{48} +(-70.9709 - 40.9750i) q^{49} +(-22.3529 - 5.75630i) q^{50} +(31.7853 - 48.5875i) q^{51} +(2.40740 - 8.98455i) q^{52} +(6.43481 - 6.43481i) q^{53} +(-23.3618 + 8.69905i) q^{54} +(12.6201 + 3.31564i) q^{55} +(-37.7587 - 65.4000i) q^{56} +(-33.6128 + 7.02686i) q^{57} +(-6.35367 - 23.7122i) q^{58} +(49.5170 + 28.5886i) q^{59} +(-21.4984 - 42.0344i) q^{60} +(16.8393 + 29.1666i) q^{61} +(28.5676 + 28.5676i) q^{62} +(15.4285 + 101.828i) q^{63} -3.92205i q^{64} +(12.8321 + 7.32540i) q^{65} +(-3.26003 - 6.45157i) q^{66} +(31.4072 - 8.41554i) q^{67} +(-15.7663 - 58.8405i) q^{68} +(-29.9066 + 15.1120i) q^{69} +(50.9602 - 13.9216i) q^{70} -63.3498 q^{71} +(-21.6561 + 55.3043i) q^{72} +(-50.9063 + 50.9063i) q^{73} +(16.3201 - 9.42239i) q^{74} +(73.2597 - 16.0628i) q^{75} +(-18.0141 + 31.2013i) q^{76} +(-28.8458 + 7.72922i) q^{77} +(-1.67498 - 8.01221i) q^{78} +(59.5972 - 34.4084i) q^{79} +(-31.4194 - 8.25473i) q^{80} +(55.0023 - 59.4622i) q^{81} +(1.20728 + 1.20728i) q^{82} +(101.841 + 27.2882i) q^{83} +(90.4247 + 59.1546i) q^{84} +(96.7668 - 0.472089i) q^{85} +(-23.4540 + 40.6236i) q^{86} +(53.1740 + 59.4556i) q^{87} +(-16.6351 - 4.45735i) q^{88} -136.887i q^{89} +(-33.5683 - 24.4828i) q^{90} -33.8170 q^{91} +(-9.09897 + 33.9578i) q^{92} +(-124.710 - 40.9838i) q^{93} +(50.7615 + 29.3072i) q^{94} +(-40.6663 - 40.2715i) q^{95} +(43.8313 + 86.7419i) q^{96} +(-9.45952 + 35.3034i) q^{97} +(-53.5023 + 53.5023i) q^{98} +(18.9084 + 13.9325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.238965 0.891829i 0.119482 0.445914i −0.880101 0.474787i \(-0.842525\pi\)
0.999583 + 0.0288727i \(0.00919174\pi\)
\(3\) 0.613889 + 2.93652i 0.204630 + 0.978839i
\(4\) 2.72585 + 1.57377i 0.681462 + 0.393442i
\(5\) −3.51824 + 3.55274i −0.703649 + 0.710548i
\(6\) 2.76557 + 0.154241i 0.460928 + 0.0257068i
\(7\) 2.96175 11.0534i 0.423108 1.57906i −0.344913 0.938635i \(-0.612091\pi\)
0.768021 0.640425i \(-0.221242\pi\)
\(8\) 4.66637 4.66637i 0.583296 0.583296i
\(9\) −8.24628 + 3.60539i −0.916253 + 0.400599i
\(10\) 2.32770 + 3.98665i 0.232770 + 0.398665i
\(11\) −1.30484 2.26005i −0.118622 0.205459i 0.800600 0.599199i \(-0.204514\pi\)
−0.919222 + 0.393740i \(0.871181\pi\)
\(12\) −2.94803 + 8.97062i −0.245669 + 0.747552i
\(13\) −0.764853 2.85447i −0.0588349 0.219575i 0.930249 0.366929i \(-0.119591\pi\)
−0.989084 + 0.147354i \(0.952924\pi\)
\(14\) −9.15000 5.28276i −0.653572 0.377340i
\(15\) −12.5925 8.15040i −0.839500 0.543360i
\(16\) 3.24857 + 5.62669i 0.203036 + 0.351668i
\(17\) −13.6850 13.6850i −0.805003 0.805003i 0.178870 0.983873i \(-0.442756\pi\)
−0.983873 + 0.178870i \(0.942756\pi\)
\(18\) 1.24482 + 8.21583i 0.0691568 + 0.456435i
\(19\) 11.4465i 0.602446i 0.953554 + 0.301223i \(0.0973948\pi\)
−0.953554 + 0.301223i \(0.902605\pi\)
\(20\) −15.1814 + 4.14733i −0.759069 + 0.207366i
\(21\) 34.2768 + 1.91167i 1.63223 + 0.0910321i
\(22\) −2.32738 + 0.623621i −0.105790 + 0.0283464i
\(23\) 2.89082 + 10.7887i 0.125688 + 0.469074i 0.999863 0.0165366i \(-0.00526400\pi\)
−0.874175 + 0.485611i \(0.838597\pi\)
\(24\) 16.5675 + 10.8382i 0.690313 + 0.451594i
\(25\) −0.243925 24.9988i −0.00975701 0.999952i
\(26\) −2.72847 −0.104941
\(27\) −15.6496 22.0020i −0.579615 0.814890i
\(28\) 25.4688 25.4688i 0.909601 0.909601i
\(29\) 23.0262 13.2942i 0.794005 0.458419i −0.0473654 0.998878i \(-0.515083\pi\)
0.841371 + 0.540458i \(0.181749\pi\)
\(30\) −10.2779 + 9.28269i −0.342597 + 0.309423i
\(31\) −21.8787 + 37.8950i −0.705764 + 1.22242i 0.260652 + 0.965433i \(0.416063\pi\)
−0.966415 + 0.256985i \(0.917271\pi\)
\(32\) 31.2919 8.38463i 0.977870 0.262020i
\(33\) 5.83564 5.21910i 0.176838 0.158154i
\(34\) −15.4750 + 8.93448i −0.455146 + 0.262779i
\(35\) 28.8498 + 49.4110i 0.824279 + 1.41174i
\(36\) −28.1522 3.14999i −0.782004 0.0874996i
\(37\) 14.4324 + 14.4324i 0.390065 + 0.390065i 0.874711 0.484646i \(-0.161051\pi\)
−0.484646 + 0.874711i \(0.661051\pi\)
\(38\) 10.2083 + 2.73530i 0.268639 + 0.0719817i
\(39\) 7.91267 3.99833i 0.202889 0.102521i
\(40\) 0.160974 + 32.9958i 0.00402435 + 0.824896i
\(41\) −0.924605 + 1.60146i −0.0225513 + 0.0390601i −0.877081 0.480343i \(-0.840512\pi\)
0.854529 + 0.519403i \(0.173846\pi\)
\(42\) 9.89582 30.1122i 0.235615 0.716957i
\(43\) −49.0742 13.1494i −1.14126 0.305800i −0.361803 0.932255i \(-0.617839\pi\)
−0.779458 + 0.626455i \(0.784505\pi\)
\(44\) 8.21405i 0.186683i
\(45\) 16.2034 41.9815i 0.360075 0.932923i
\(46\) 10.3125 0.224184
\(47\) −16.4309 + 61.3211i −0.349594 + 1.30470i 0.537558 + 0.843227i \(0.319347\pi\)
−0.887152 + 0.461477i \(0.847320\pi\)
\(48\) −14.5286 + 12.9936i −0.302679 + 0.270701i
\(49\) −70.9709 40.9750i −1.44838 0.836225i
\(50\) −22.3529 5.75630i −0.447059 0.115126i
\(51\) 31.7853 48.5875i 0.623241 0.952696i
\(52\) 2.40740 8.98455i 0.0462962 0.172780i
\(53\) 6.43481 6.43481i 0.121412 0.121412i −0.643790 0.765202i \(-0.722639\pi\)
0.765202 + 0.643790i \(0.222639\pi\)
\(54\) −23.3618 + 8.69905i −0.432625 + 0.161094i
\(55\) 12.6201 + 3.31564i 0.229456 + 0.0602844i
\(56\) −37.7587 65.4000i −0.674262 1.16786i
\(57\) −33.6128 + 7.02686i −0.589698 + 0.123278i
\(58\) −6.35367 23.7122i −0.109546 0.408831i
\(59\) 49.5170 + 28.5886i 0.839271 + 0.484553i 0.857016 0.515289i \(-0.172316\pi\)
−0.0177457 + 0.999843i \(0.505649\pi\)
\(60\) −21.4984 42.0344i −0.358306 0.700574i
\(61\) 16.8393 + 29.1666i 0.276055 + 0.478141i 0.970401 0.241501i \(-0.0776396\pi\)
−0.694346 + 0.719641i \(0.744306\pi\)
\(62\) 28.5676 + 28.5676i 0.460768 + 0.460768i
\(63\) 15.4285 + 101.828i 0.244896 + 1.61632i
\(64\) 3.92205i 0.0612820i
\(65\) 12.8321 + 7.32540i 0.197417 + 0.112698i
\(66\) −3.26003 6.45157i −0.0493944 0.0977511i
\(67\) 31.4072 8.41554i 0.468765 0.125605i −0.0167016 0.999861i \(-0.505317\pi\)
0.485466 + 0.874255i \(0.338650\pi\)
\(68\) −15.7663 58.8405i −0.231857 0.865301i
\(69\) −29.9066 + 15.1120i −0.433429 + 0.219015i
\(70\) 50.9602 13.9216i 0.728003 0.198879i
\(71\) −63.3498 −0.892251 −0.446126 0.894970i \(-0.647197\pi\)
−0.446126 + 0.894970i \(0.647197\pi\)
\(72\) −21.6561 + 55.3043i −0.300779 + 0.768115i
\(73\) −50.9063 + 50.9063i −0.697347 + 0.697347i −0.963838 0.266491i \(-0.914136\pi\)
0.266491 + 0.963838i \(0.414136\pi\)
\(74\) 16.3201 9.42239i 0.220541 0.127330i
\(75\) 73.2597 16.0628i 0.976796 0.214171i
\(76\) −18.0141 + 31.2013i −0.237028 + 0.410544i
\(77\) −28.8458 + 7.72922i −0.374621 + 0.100379i
\(78\) −1.67498 8.01221i −0.0214741 0.102721i
\(79\) 59.5972 34.4084i 0.754395 0.435550i −0.0728850 0.997340i \(-0.523221\pi\)
0.827280 + 0.561790i \(0.189887\pi\)
\(80\) −31.4194 8.25473i −0.392743 0.103184i
\(81\) 55.0023 59.4622i 0.679040 0.734101i
\(82\) 1.20728 + 1.20728i 0.0147230 + 0.0147230i
\(83\) 101.841 + 27.2882i 1.22700 + 0.328773i 0.813410 0.581691i \(-0.197609\pi\)
0.413589 + 0.910464i \(0.364275\pi\)
\(84\) 90.4247 + 59.1546i 1.07648 + 0.704222i
\(85\) 96.7668 0.472089i 1.13843 0.00555398i
\(86\) −23.4540 + 40.6236i −0.272721 + 0.472367i
\(87\) 53.1740 + 59.4556i 0.611196 + 0.683398i
\(88\) −16.6351 4.45735i −0.189035 0.0506517i
\(89\) 136.887i 1.53806i −0.639213 0.769029i \(-0.720740\pi\)
0.639213 0.769029i \(-0.279260\pi\)
\(90\) −33.5683 24.4828i −0.372981 0.272031i
\(91\) −33.8170 −0.371615
\(92\) −9.09897 + 33.9578i −0.0989019 + 0.369107i
\(93\) −124.710 40.9838i −1.34097 0.440686i
\(94\) 50.7615 + 29.3072i 0.540016 + 0.311778i
\(95\) −40.6663 40.2715i −0.428067 0.423910i
\(96\) 43.8313 + 86.7419i 0.456576 + 0.903561i
\(97\) −9.45952 + 35.3034i −0.0975209 + 0.363953i −0.997390 0.0722080i \(-0.976995\pi\)
0.899869 + 0.436161i \(0.143662\pi\)
\(98\) −53.5023 + 53.5023i −0.545941 + 0.545941i
\(99\) 18.9084 + 13.9325i 0.190994 + 0.140732i
\(100\) 38.6774 68.5268i 0.386774 0.685268i
\(101\) −48.3142 83.6827i −0.478359 0.828541i 0.521334 0.853353i \(-0.325435\pi\)
−0.999692 + 0.0248116i \(0.992101\pi\)
\(102\) −35.7362 39.9577i −0.350355 0.391743i
\(103\) −6.87754 25.6673i −0.0667723 0.249198i 0.924470 0.381255i \(-0.124508\pi\)
−0.991242 + 0.132058i \(0.957842\pi\)
\(104\) −16.8891 9.75093i −0.162395 0.0937589i
\(105\) −127.386 + 115.051i −1.21320 + 1.09572i
\(106\) −4.20106 7.27645i −0.0396326 0.0686457i
\(107\) −43.8389 43.8389i −0.409709 0.409709i 0.471928 0.881637i \(-0.343558\pi\)
−0.881637 + 0.471928i \(0.843558\pi\)
\(108\) −8.03231 84.6031i −0.0743732 0.783362i
\(109\) 13.1212i 0.120378i 0.998187 + 0.0601892i \(0.0191704\pi\)
−0.998187 + 0.0601892i \(0.980830\pi\)
\(110\) 5.97274 10.4626i 0.0542977 0.0951149i
\(111\) −33.5211 + 51.2409i −0.301992 + 0.461630i
\(112\) 71.8156 19.2429i 0.641211 0.171812i
\(113\) −8.41629 31.4100i −0.0744805 0.277965i 0.918635 0.395108i \(-0.129293\pi\)
−0.993115 + 0.117143i \(0.962626\pi\)
\(114\) −1.76551 + 31.6560i −0.0154869 + 0.277684i
\(115\) −48.5001 27.6869i −0.421740 0.240756i
\(116\) 83.6877 0.721446
\(117\) 16.5987 + 20.7812i 0.141869 + 0.177617i
\(118\) 37.3290 37.3290i 0.316347 0.316347i
\(119\) −191.798 + 110.735i −1.61175 + 0.930545i
\(120\) −96.7940 + 20.7285i −0.806617 + 0.172737i
\(121\) 57.0948 98.8911i 0.471858 0.817282i
\(122\) 30.0356 8.04801i 0.246193 0.0659673i
\(123\) −5.27033 1.73200i −0.0428482 0.0140813i
\(124\) −119.276 + 68.8639i −0.961902 + 0.555354i
\(125\) 89.6725 + 87.0853i 0.717380 + 0.696682i
\(126\) 94.4999 + 10.5737i 0.749999 + 0.0839185i
\(127\) −108.223 108.223i −0.852153 0.852153i 0.138245 0.990398i \(-0.455854\pi\)
−0.990398 + 0.138245i \(0.955854\pi\)
\(128\) 121.670 + 32.6013i 0.950544 + 0.254697i
\(129\) 8.48732 152.180i 0.0657932 1.17969i
\(130\) 9.59943 9.69355i 0.0738418 0.0745658i
\(131\) −3.28859 + 5.69601i −0.0251038 + 0.0434810i −0.878304 0.478102i \(-0.841325\pi\)
0.853201 + 0.521583i \(0.174658\pi\)
\(132\) 24.1207 5.04252i 0.182733 0.0382009i
\(133\) 126.523 + 33.9016i 0.951298 + 0.254900i
\(134\) 30.0209i 0.224036i
\(135\) 133.227 + 21.8096i 0.986864 + 0.161552i
\(136\) −127.719 −0.939110
\(137\) 22.5393 84.1178i 0.164520 0.613998i −0.833581 0.552398i \(-0.813713\pi\)
0.998101 0.0616003i \(-0.0196204\pi\)
\(138\) 6.33072 + 30.2828i 0.0458748 + 0.219440i
\(139\) −75.7500 43.7343i −0.544964 0.314635i 0.202124 0.979360i \(-0.435215\pi\)
−0.747088 + 0.664725i \(0.768549\pi\)
\(140\) 0.878589 + 180.090i 0.00627564 + 1.28635i
\(141\) −190.157 10.6054i −1.34863 0.0752156i
\(142\) −15.1384 + 56.4972i −0.106608 + 0.397868i
\(143\) −5.45322 + 5.45322i −0.0381344 + 0.0381344i
\(144\) −47.0750 34.6869i −0.326910 0.240881i
\(145\) −33.7809 + 128.578i −0.232972 + 0.886745i
\(146\) 33.2349 + 57.5646i 0.227636 + 0.394278i
\(147\) 76.7557 233.561i 0.522148 1.58885i
\(148\) 16.6273 + 62.0538i 0.112346 + 0.419282i
\(149\) 144.963 + 83.6946i 0.972909 + 0.561709i 0.900122 0.435638i \(-0.143477\pi\)
0.0727869 + 0.997348i \(0.476811\pi\)
\(150\) 3.18124 69.1736i 0.0212082 0.461157i
\(151\) 124.775 + 216.117i 0.826325 + 1.43124i 0.900902 + 0.434022i \(0.142906\pi\)
−0.0745766 + 0.997215i \(0.523761\pi\)
\(152\) 53.4135 + 53.4135i 0.351404 + 0.351404i
\(153\) 162.191 + 63.5108i 1.06007 + 0.415103i
\(154\) 27.5726i 0.179043i
\(155\) −57.6565 211.053i −0.371977 1.36163i
\(156\) 27.8612 + 1.55387i 0.178597 + 0.00996068i
\(157\) −48.3954 + 12.9675i −0.308251 + 0.0825957i −0.409629 0.912252i \(-0.634342\pi\)
0.101377 + 0.994848i \(0.467675\pi\)
\(158\) −16.4448 61.3729i −0.104081 0.388436i
\(159\) 22.8462 + 14.9457i 0.143687 + 0.0939980i
\(160\) −80.3040 + 140.671i −0.501900 + 0.879194i
\(161\) 127.814 0.793875
\(162\) −39.8865 63.2620i −0.246213 0.390506i
\(163\) −23.5188 + 23.5188i −0.144287 + 0.144287i −0.775560 0.631273i \(-0.782533\pi\)
0.631273 + 0.775560i \(0.282533\pi\)
\(164\) −5.04066 + 2.91023i −0.0307358 + 0.0177453i
\(165\) −1.98910 + 39.0946i −0.0120552 + 0.236937i
\(166\) 48.6728 84.3037i 0.293210 0.507854i
\(167\) 106.889 28.6408i 0.640052 0.171502i 0.0758252 0.997121i \(-0.475841\pi\)
0.564227 + 0.825620i \(0.309174\pi\)
\(168\) 168.869 151.027i 1.00517 0.898973i
\(169\) 138.795 80.1335i 0.821274 0.474163i
\(170\) 22.7028 86.4122i 0.133546 0.508307i
\(171\) −41.2690 94.3908i −0.241339 0.551993i
\(172\) −113.075 113.075i −0.657411 0.657411i
\(173\) −65.8811 17.6528i −0.380816 0.102039i 0.0633327 0.997992i \(-0.479827\pi\)
−0.444149 + 0.895953i \(0.646494\pi\)
\(174\) 65.7309 33.2143i 0.377764 0.190887i
\(175\) −277.045 71.3441i −1.58311 0.407681i
\(176\) 8.47772 14.6838i 0.0481688 0.0834309i
\(177\) −53.5531 + 162.958i −0.302560 + 0.920665i
\(178\) −122.080 32.7112i −0.685843 0.183771i
\(179\) 303.920i 1.69788i 0.528490 + 0.848939i \(0.322758\pi\)
−0.528490 + 0.848939i \(0.677242\pi\)
\(180\) 110.237 88.9349i 0.612429 0.494083i
\(181\) 172.576 0.953460 0.476730 0.879050i \(-0.341822\pi\)
0.476730 + 0.879050i \(0.341822\pi\)
\(182\) −8.08107 + 30.1589i −0.0444015 + 0.165708i
\(183\) −75.3107 + 67.3540i −0.411534 + 0.368055i
\(184\) 63.8337 + 36.8544i 0.346922 + 0.200296i
\(185\) −102.051 + 0.497870i −0.551628 + 0.00269119i
\(186\) −66.3519 + 101.427i −0.356731 + 0.545304i
\(187\) −13.0721 + 48.7856i −0.0699041 + 0.260886i
\(188\) −141.293 + 141.293i −0.751561 + 0.751561i
\(189\) −289.548 + 107.817i −1.53200 + 0.570460i
\(190\) −45.6331 + 26.6439i −0.240174 + 0.140231i
\(191\) 143.618 + 248.754i 0.751927 + 1.30238i 0.946887 + 0.321565i \(0.104209\pi\)
−0.194960 + 0.980811i \(0.562458\pi\)
\(192\) 11.5172 2.40770i 0.0599852 0.0125401i
\(193\) 9.52264 + 35.5390i 0.0493401 + 0.184140i 0.986198 0.165571i \(-0.0529466\pi\)
−0.936858 + 0.349711i \(0.886280\pi\)
\(194\) 29.2241 + 16.8725i 0.150640 + 0.0869719i
\(195\) −13.6337 + 42.1788i −0.0699162 + 0.216301i
\(196\) −128.970 223.383i −0.658013 1.13971i
\(197\) −226.659 226.659i −1.15056 1.15056i −0.986441 0.164114i \(-0.947524\pi\)
−0.164114 0.986441i \(-0.552476\pi\)
\(198\) 16.9439 13.5337i 0.0855751 0.0683520i
\(199\) 107.508i 0.540240i −0.962827 0.270120i \(-0.912937\pi\)
0.962827 0.270120i \(-0.0870633\pi\)
\(200\) −117.792 115.515i −0.588960 0.577577i
\(201\) 43.9930 + 87.0617i 0.218870 + 0.433143i
\(202\) −86.1760 + 23.0908i −0.426614 + 0.114311i
\(203\) −78.7481 293.892i −0.387922 1.44774i
\(204\) 163.107 82.4194i 0.799546 0.404017i
\(205\) −2.43660 8.91922i −0.0118858 0.0435084i
\(206\) −24.5344 −0.119099
\(207\) −62.7360 78.5441i −0.303073 0.379440i
\(208\) 13.5765 13.5765i 0.0652718 0.0652718i
\(209\) 25.8695 14.9358i 0.123778 0.0714631i
\(210\) 72.1648 + 141.099i 0.343642 + 0.671901i
\(211\) 45.5871 78.9591i 0.216053 0.374214i −0.737545 0.675298i \(-0.764015\pi\)
0.953598 + 0.301084i \(0.0973484\pi\)
\(212\) 27.6672 7.41341i 0.130506 0.0349689i
\(213\) −38.8898 186.028i −0.182581 0.873371i
\(214\) −49.5727 + 28.6208i −0.231648 + 0.133742i
\(215\) 219.371 128.085i 1.02033 0.595745i
\(216\) −175.697 29.6428i −0.813410 0.137235i
\(217\) 354.070 + 354.070i 1.63166 + 1.63166i
\(218\) 11.7019 + 3.13551i 0.0536784 + 0.0143831i
\(219\) −180.738 118.237i −0.825289 0.539893i
\(220\) 29.1824 + 28.8990i 0.132647 + 0.131359i
\(221\) −28.5965 + 49.5306i −0.129396 + 0.224120i
\(222\) 37.6877 + 42.1399i 0.169765 + 0.189819i
\(223\) 229.262 + 61.4305i 1.02808 + 0.275473i 0.733165 0.680051i \(-0.238042\pi\)
0.294914 + 0.955524i \(0.404709\pi\)
\(224\) 370.715i 1.65498i
\(225\) 92.1420 + 205.268i 0.409520 + 0.912301i
\(226\) −30.0236 −0.132848
\(227\) −31.7905 + 118.644i −0.140046 + 0.522660i 0.859880 + 0.510497i \(0.170538\pi\)
−0.999926 + 0.0121631i \(0.996128\pi\)
\(228\) −102.682 33.7446i −0.450359 0.148003i
\(229\) 285.203 + 164.662i 1.24543 + 0.719048i 0.970194 0.242329i \(-0.0779114\pi\)
0.275234 + 0.961377i \(0.411245\pi\)
\(230\) −36.2818 + 36.6376i −0.157747 + 0.159294i
\(231\) −40.4051 79.9615i −0.174914 0.346154i
\(232\) 45.4131 169.484i 0.195746 0.730534i
\(233\) −227.098 + 227.098i −0.974670 + 0.974670i −0.999687 0.0250170i \(-0.992036\pi\)
0.0250170 + 0.999687i \(0.492036\pi\)
\(234\) 22.4997 9.83722i 0.0961528 0.0420394i
\(235\) −160.050 274.117i −0.681063 1.16646i
\(236\) 89.9838 + 155.856i 0.381287 + 0.660409i
\(237\) 137.627 + 153.885i 0.580705 + 0.649305i
\(238\) 52.9235 + 197.513i 0.222367 + 0.829887i
\(239\) −123.443 71.2696i −0.516496 0.298199i 0.219004 0.975724i \(-0.429719\pi\)
−0.735500 + 0.677525i \(0.763053\pi\)
\(240\) 4.95214 97.3312i 0.0206339 0.405547i
\(241\) −228.867 396.410i −0.949656 1.64485i −0.746148 0.665780i \(-0.768099\pi\)
−0.203509 0.979073i \(-0.565234\pi\)
\(242\) −74.5503 74.5503i −0.308059 0.308059i
\(243\) 208.377 + 125.012i 0.857519 + 0.514453i
\(244\) 106.005i 0.434446i
\(245\) 395.266 107.981i 1.61333 0.440738i
\(246\) −2.80407 + 4.28634i −0.0113987 + 0.0174242i
\(247\) 32.6736 8.75487i 0.132282 0.0354448i
\(248\) 74.7380 + 278.926i 0.301363 + 1.12470i
\(249\) −17.6132 + 315.810i −0.0707359 + 1.26831i
\(250\) 99.0937 59.1622i 0.396375 0.236649i
\(251\) 102.580 0.408684 0.204342 0.978900i \(-0.434494\pi\)
0.204342 + 0.978900i \(0.434494\pi\)
\(252\) −118.198 + 301.848i −0.469039 + 1.19781i
\(253\) 20.6109 20.6109i 0.0814660 0.0814660i
\(254\) −122.378 + 70.6552i −0.481805 + 0.278170i
\(255\) 60.7904 + 283.868i 0.238394 + 1.11321i
\(256\) 65.9936 114.304i 0.257788 0.446501i
\(257\) −108.426 + 29.0526i −0.421890 + 0.113045i −0.463517 0.886088i \(-0.653413\pi\)
0.0416268 + 0.999133i \(0.486746\pi\)
\(258\) −133.690 43.9348i −0.518178 0.170290i
\(259\) 202.273 116.782i 0.780975 0.450896i
\(260\) 23.4499 + 40.1627i 0.0901921 + 0.154472i
\(261\) −141.949 + 192.646i −0.543868 + 0.738106i
\(262\) 4.29401 + 4.29401i 0.0163893 + 0.0163893i
\(263\) −143.911 38.5609i −0.547191 0.146619i −0.0253757 0.999678i \(-0.508078\pi\)
−0.521815 + 0.853059i \(0.674745\pi\)
\(264\) 2.87701 51.5855i 0.0108978 0.195400i
\(265\) 0.221980 + 45.5005i 0.000837659 + 0.171700i
\(266\) 60.4689 104.735i 0.227327 0.393742i
\(267\) 401.972 84.0336i 1.50551 0.314733i
\(268\) 98.8554 + 26.4882i 0.368864 + 0.0988367i
\(269\) 31.0843i 0.115555i 0.998329 + 0.0577774i \(0.0184014\pi\)
−0.998329 + 0.0577774i \(0.981599\pi\)
\(270\) 51.2869 113.604i 0.189951 0.420754i
\(271\) 4.22458 0.0155889 0.00779444 0.999970i \(-0.497519\pi\)
0.00779444 + 0.999970i \(0.497519\pi\)
\(272\) 32.5447 121.458i 0.119650 0.446538i
\(273\) −20.7599 99.3042i −0.0760435 0.363751i
\(274\) −69.6325 40.2024i −0.254133 0.146724i
\(275\) −56.1802 + 33.1707i −0.204292 + 0.120621i
\(276\) −105.304 5.87296i −0.381535 0.0212788i
\(277\) −35.9912 + 134.321i −0.129932 + 0.484913i −0.999967 0.00807616i \(-0.997429\pi\)
0.870035 + 0.492990i \(0.164096\pi\)
\(278\) −57.1051 + 57.1051i −0.205414 + 0.205414i
\(279\) 43.7914 391.374i 0.156958 1.40277i
\(280\) 365.193 + 95.9462i 1.30426 + 0.342665i
\(281\) −251.702 435.961i −0.895737 1.55146i −0.832890 0.553439i \(-0.813315\pi\)
−0.0628471 0.998023i \(-0.520018\pi\)
\(282\) −54.8991 + 167.053i −0.194678 + 0.592388i
\(283\) −37.9311 141.561i −0.134032 0.500214i −1.00000 0.000114837i \(-0.999963\pi\)
0.865968 0.500099i \(-0.166703\pi\)
\(284\) −172.682 99.6980i −0.608035 0.351049i
\(285\) 93.2933 144.140i 0.327345 0.505753i
\(286\) 3.56021 + 6.16647i 0.0124483 + 0.0215611i
\(287\) 14.9632 + 14.9632i 0.0521365 + 0.0521365i
\(288\) −227.812 + 181.961i −0.791012 + 0.631811i
\(289\) 85.5611i 0.296059i
\(290\) 106.597 + 60.8524i 0.367576 + 0.209836i
\(291\) −109.476 6.10568i −0.376207 0.0209817i
\(292\) −218.878 + 58.6481i −0.749581 + 0.200850i
\(293\) −88.7756 331.315i −0.302988 1.13077i −0.934663 0.355535i \(-0.884299\pi\)
0.631675 0.775234i \(-0.282368\pi\)
\(294\) −189.955 124.266i −0.646105 0.422673i
\(295\) −275.781 + 75.3391i −0.934850 + 0.255387i
\(296\) 134.694 0.455047
\(297\) −29.3054 + 64.0779i −0.0986714 + 0.215751i
\(298\) 109.282 109.282i 0.366720 0.366720i
\(299\) 28.5850 16.5035i 0.0956019 0.0551958i
\(300\) 224.974 + 71.5091i 0.749913 + 0.238364i
\(301\) −290.692 + 503.493i −0.965753 + 1.67273i
\(302\) 222.556 59.6337i 0.736941 0.197463i
\(303\) 216.076 193.247i 0.713123 0.637780i
\(304\) −64.4057 + 37.1847i −0.211861 + 0.122318i
\(305\) −162.866 42.7894i −0.533987 0.140293i
\(306\) 95.3986 129.470i 0.311760 0.423103i
\(307\) −19.2282 19.2282i −0.0626327 0.0626327i 0.675097 0.737729i \(-0.264102\pi\)
−0.737729 + 0.675097i \(0.764102\pi\)
\(308\) −90.7934 24.3280i −0.294784 0.0789870i
\(309\) 71.1506 35.9529i 0.230261 0.116353i
\(310\) −202.001 + 0.985487i −0.651616 + 0.00317899i
\(311\) −275.689 + 477.507i −0.886459 + 1.53539i −0.0424271 + 0.999100i \(0.513509\pi\)
−0.844032 + 0.536293i \(0.819824\pi\)
\(312\) 18.2657 55.5811i 0.0585440 0.178145i
\(313\) −463.260 124.130i −1.48006 0.396582i −0.573694 0.819070i \(-0.694490\pi\)
−0.906368 + 0.422488i \(0.861157\pi\)
\(314\) 46.2592i 0.147322i
\(315\) −416.049 303.442i −1.32079 0.963308i
\(316\) 216.604 0.685455
\(317\) −72.3487 + 270.009i −0.228229 + 0.851763i 0.752856 + 0.658186i \(0.228676\pi\)
−0.981085 + 0.193578i \(0.937991\pi\)
\(318\) 18.7884 16.8034i 0.0590831 0.0528409i
\(319\) −60.0908 34.6934i −0.188372 0.108757i
\(320\) 13.9340 + 13.7987i 0.0435438 + 0.0431210i
\(321\) 101.821 155.646i 0.317201 0.484878i
\(322\) 30.5430 113.988i 0.0948541 0.354000i
\(323\) 156.646 156.646i 0.484971 0.484971i
\(324\) 243.508 75.5239i 0.751566 0.233099i
\(325\) −71.1718 + 19.8167i −0.218990 + 0.0609744i
\(326\) 15.3545 + 26.5949i 0.0470998 + 0.0815793i
\(327\) −38.5307 + 8.05498i −0.117831 + 0.0246330i
\(328\) 3.15847 + 11.7876i 0.00962948 + 0.0359377i
\(329\) 629.143 + 363.236i 1.91229 + 1.10406i
\(330\) 34.3903 + 11.1162i 0.104213 + 0.0336853i
\(331\) −61.1788 105.965i −0.184830 0.320136i 0.758689 0.651453i \(-0.225840\pi\)
−0.943519 + 0.331317i \(0.892507\pi\)
\(332\) 234.657 + 234.657i 0.706800 + 0.706800i
\(333\) −171.048 66.9791i −0.513658 0.201139i
\(334\) 102.171i 0.305900i
\(335\) −80.6001 + 141.190i −0.240597 + 0.421462i
\(336\) 100.594 + 199.075i 0.299387 + 0.592485i
\(337\) −319.193 + 85.5276i −0.947161 + 0.253791i −0.699157 0.714968i \(-0.746441\pi\)
−0.248004 + 0.968759i \(0.579775\pi\)
\(338\) −38.2982 142.931i −0.113308 0.422872i
\(339\) 87.0694 43.9969i 0.256842 0.129784i
\(340\) 264.514 + 151.002i 0.777983 + 0.444122i
\(341\) 114.192 0.334875
\(342\) −94.0423 + 14.2488i −0.274977 + 0.0416632i
\(343\) −266.621 + 266.621i −0.777321 + 0.777321i
\(344\) −290.358 + 167.638i −0.844065 + 0.487321i
\(345\) 51.5295 159.418i 0.149361 0.462081i
\(346\) −31.4865 + 54.5363i −0.0910016 + 0.157619i
\(347\) 343.816 92.1251i 0.990823 0.265490i 0.273227 0.961950i \(-0.411909\pi\)
0.717596 + 0.696459i \(0.245242\pi\)
\(348\) 51.3750 + 245.750i 0.147629 + 0.706180i
\(349\) −43.1516 + 24.9136i −0.123644 + 0.0713857i −0.560546 0.828123i \(-0.689409\pi\)
0.436903 + 0.899509i \(0.356075\pi\)
\(350\) −129.831 + 230.028i −0.370945 + 0.657222i
\(351\) −50.8345 + 61.4997i −0.144828 + 0.175213i
\(352\) −59.7804 59.7804i −0.169831 0.169831i
\(353\) 606.831 + 162.600i 1.71907 + 0.460623i 0.977619 0.210385i \(-0.0674718\pi\)
0.741450 + 0.671008i \(0.234138\pi\)
\(354\) 132.533 + 86.7014i 0.374387 + 0.244919i
\(355\) 222.880 225.065i 0.627831 0.633987i
\(356\) 215.429 373.134i 0.605137 1.04813i
\(357\) −442.918 495.240i −1.24067 1.38723i
\(358\) 271.045 + 72.6263i 0.757109 + 0.202867i
\(359\) 81.3046i 0.226475i 0.993568 + 0.113238i \(0.0361221\pi\)
−0.993568 + 0.113238i \(0.963878\pi\)
\(360\) −120.290 271.512i −0.334140 0.754201i
\(361\) 229.978 0.637059
\(362\) 41.2397 153.908i 0.113922 0.425162i
\(363\) 325.445 + 106.952i 0.896544 + 0.294633i
\(364\) −92.1799 53.2201i −0.253241 0.146209i
\(365\) −1.75610 359.958i −0.00481123 0.986186i
\(366\) 42.0717 + 83.2595i 0.114950 + 0.227485i
\(367\) 15.5484 58.0273i 0.0423661 0.158113i −0.941502 0.337007i \(-0.890585\pi\)
0.983868 + 0.178894i \(0.0572521\pi\)
\(368\) −51.3136 + 51.3136i −0.139439 + 0.139439i
\(369\) 1.85065 16.5397i 0.00501531 0.0448230i
\(370\) −23.9426 + 91.1312i −0.0647098 + 0.246301i
\(371\) −52.0684 90.1851i −0.140346 0.243086i
\(372\) −275.442 307.981i −0.740436 0.827906i
\(373\) −50.4882 188.424i −0.135357 0.505159i −0.999996 0.00276585i \(-0.999120\pi\)
0.864639 0.502393i \(-0.167547\pi\)
\(374\) 40.3846 + 23.3161i 0.107980 + 0.0623425i
\(375\) −200.679 + 316.786i −0.535143 + 0.844761i
\(376\) 209.474 + 362.820i 0.557112 + 0.964946i
\(377\) −55.5594 55.5594i −0.147372 0.147372i
\(378\) 26.9625 + 283.992i 0.0713294 + 0.751301i
\(379\) 145.837i 0.384795i −0.981317 0.192398i \(-0.938374\pi\)
0.981317 0.192398i \(-0.0616263\pi\)
\(380\) −47.4722 173.773i −0.124927 0.457298i
\(381\) 251.363 384.237i 0.659745 1.00850i
\(382\) 256.166 68.6394i 0.670591 0.179684i
\(383\) 195.458 + 729.460i 0.510335 + 1.90459i 0.416854 + 0.908973i \(0.363133\pi\)
0.0934803 + 0.995621i \(0.470201\pi\)
\(384\) −21.0426 + 377.299i −0.0547984 + 0.982549i
\(385\) 74.0268 129.675i 0.192277 0.336818i
\(386\) 33.9703 0.0880059
\(387\) 452.088 68.4982i 1.16819 0.176998i
\(388\) −81.3446 + 81.3446i −0.209651 + 0.209651i
\(389\) −37.3613 + 21.5705i −0.0960444 + 0.0554512i −0.547253 0.836967i \(-0.684326\pi\)
0.451209 + 0.892419i \(0.350993\pi\)
\(390\) 34.3583 + 22.2381i 0.0880982 + 0.0570209i
\(391\) 108.083 187.205i 0.276427 0.478785i
\(392\) −522.381 + 139.972i −1.33260 + 0.357070i
\(393\) −18.7453 6.16029i −0.0476979 0.0156750i
\(394\) −256.305 + 147.978i −0.650520 + 0.375578i
\(395\) −87.4331 + 332.791i −0.221350 + 0.842508i
\(396\) 29.6149 + 67.7354i 0.0747851 + 0.171049i
\(397\) −89.7953 89.7953i −0.226185 0.226185i 0.584912 0.811097i \(-0.301129\pi\)
−0.811097 + 0.584912i \(0.801129\pi\)
\(398\) −95.8785 25.6906i −0.240901 0.0645491i
\(399\) −21.8819 + 392.348i −0.0548419 + 0.983328i
\(400\) 139.868 82.5829i 0.349670 0.206457i
\(401\) −144.777 + 250.762i −0.361041 + 0.625341i −0.988132 0.153604i \(-0.950912\pi\)
0.627092 + 0.778946i \(0.284245\pi\)
\(402\) 88.1569 18.4295i 0.219296 0.0458445i
\(403\) 124.904 + 33.4679i 0.309936 + 0.0830470i
\(404\) 304.142i 0.752826i
\(405\) 17.7422 + 404.611i 0.0438080 + 0.999040i
\(406\) −280.919 −0.691919
\(407\) 13.7859 51.4498i 0.0338721 0.126412i
\(408\) −78.4053 375.049i −0.192170 0.919238i
\(409\) −178.588 103.108i −0.436646 0.252098i 0.265528 0.964103i \(-0.414454\pi\)
−0.702174 + 0.712006i \(0.747787\pi\)
\(410\) −8.53667 + 0.0416472i −0.0208212 + 0.000101579i
\(411\) 260.850 + 14.5480i 0.634671 + 0.0353967i
\(412\) 21.6473 80.7889i 0.0525421 0.196090i
\(413\) 462.659 462.659i 1.12024 1.12024i
\(414\) −85.0396 + 37.1805i −0.205410 + 0.0898081i
\(415\) −455.249 + 265.808i −1.09699 + 0.640501i
\(416\) −47.8673 82.9087i −0.115066 0.199300i
\(417\) 81.9244 249.289i 0.196461 0.597816i
\(418\) −7.13826 26.6403i −0.0170772 0.0637329i
\(419\) −621.108 358.597i −1.48236 0.855839i −0.482558 0.875864i \(-0.660292\pi\)
−0.999799 + 0.0200248i \(0.993625\pi\)
\(420\) −528.297 + 113.135i −1.25785 + 0.269369i
\(421\) 124.562 + 215.747i 0.295871 + 0.512463i 0.975187 0.221382i \(-0.0710569\pi\)
−0.679316 + 0.733846i \(0.737724\pi\)
\(422\) −59.5243 59.5243i −0.141053 0.141053i
\(423\) −85.5925 564.911i −0.202346 1.33549i
\(424\) 60.0544i 0.141638i
\(425\) −338.772 + 345.448i −0.797110 + 0.812819i
\(426\) −175.198 9.77111i −0.411264 0.0229369i
\(427\) 372.264 99.7479i 0.871814 0.233602i
\(428\) −50.5058 188.490i −0.118004 0.440398i
\(429\) −19.3612 12.6658i −0.0451309 0.0295241i
\(430\) −61.8080 226.250i −0.143739 0.526162i
\(431\) −234.096 −0.543146 −0.271573 0.962418i \(-0.587544\pi\)
−0.271573 + 0.962418i \(0.587544\pi\)
\(432\) 72.9598 159.531i 0.168888 0.369284i
\(433\) 372.915 372.915i 0.861236 0.861236i −0.130245 0.991482i \(-0.541577\pi\)
0.991482 + 0.130245i \(0.0415765\pi\)
\(434\) 400.380 231.159i 0.922534 0.532625i
\(435\) −398.309 20.2657i −0.915654 0.0465878i
\(436\) −20.6498 + 35.7665i −0.0473619 + 0.0820332i
\(437\) −123.493 + 33.0897i −0.282592 + 0.0757202i
\(438\) −148.637 + 132.933i −0.339353 + 0.303500i
\(439\) −558.854 + 322.654i −1.27302 + 0.734976i −0.975554 0.219758i \(-0.929473\pi\)
−0.297461 + 0.954734i \(0.596140\pi\)
\(440\) 74.3620 43.4180i 0.169005 0.0986773i
\(441\) 732.977 + 82.0138i 1.66208 + 0.185972i
\(442\) 37.3393 + 37.3393i 0.0844780 + 0.0844780i
\(443\) −265.585 71.1633i −0.599515 0.160640i −0.0537167 0.998556i \(-0.517107\pi\)
−0.545798 + 0.837917i \(0.683773\pi\)
\(444\) −172.015 + 86.9204i −0.387421 + 0.195767i
\(445\) 486.325 + 481.603i 1.09286 + 1.08225i
\(446\) 109.571 189.782i 0.245675 0.425521i
\(447\) −156.779 + 477.067i −0.350737 + 1.06726i
\(448\) −43.3520 11.6161i −0.0967679 0.0259289i
\(449\) 190.668i 0.424651i 0.977199 + 0.212325i \(0.0681036\pi\)
−0.977199 + 0.212325i \(0.931896\pi\)
\(450\) 205.082 33.1231i 0.455739 0.0736070i
\(451\) 4.82584 0.0107003
\(452\) 26.4906 98.8642i 0.0586075 0.218726i
\(453\) −558.033 + 499.076i −1.23186 + 1.10171i
\(454\) 98.2131 + 56.7034i 0.216328 + 0.124897i
\(455\) 118.976 120.143i 0.261486 0.264050i
\(456\) −124.060 + 189.640i −0.272061 + 0.415876i
\(457\) 80.9404 302.074i 0.177112 0.660993i −0.819070 0.573694i \(-0.805510\pi\)
0.996182 0.0872988i \(-0.0278235\pi\)
\(458\) 215.004 215.004i 0.469441 0.469441i
\(459\) −86.9334 + 515.265i −0.189397 + 1.12258i
\(460\) −88.6310 151.798i −0.192676 0.329996i
\(461\) −110.361 191.151i −0.239395 0.414645i 0.721146 0.692784i \(-0.243616\pi\)
−0.960541 + 0.278139i \(0.910283\pi\)
\(462\) −80.9673 + 16.9265i −0.175254 + 0.0366374i
\(463\) 74.7605 + 279.010i 0.161470 + 0.602613i 0.998464 + 0.0554018i \(0.0176440\pi\)
−0.836994 + 0.547211i \(0.815689\pi\)
\(464\) 149.604 + 86.3740i 0.322423 + 0.186151i
\(465\) 584.366 298.872i 1.25670 0.642736i
\(466\) 148.264 + 256.801i 0.318163 + 0.551075i
\(467\) −249.664 249.664i −0.534613 0.534613i 0.387329 0.921942i \(-0.373398\pi\)
−0.921942 + 0.387329i \(0.873398\pi\)
\(468\) 12.5407 + 82.7688i 0.0267964 + 0.176856i
\(469\) 372.082i 0.793352i
\(470\) −282.712 + 77.2327i −0.601515 + 0.164325i
\(471\) −67.7888 134.153i −0.143925 0.284827i
\(472\) 364.470 97.6593i 0.772181 0.206905i
\(473\) 34.3157 + 128.068i 0.0725490 + 0.270756i
\(474\) 170.127 85.9666i 0.358918 0.181364i
\(475\) 286.148 2.79208i 0.602417 0.00587807i
\(476\) −697.084 −1.46446
\(477\) −29.8632 + 76.2633i −0.0626064 + 0.159881i
\(478\) −93.0588 + 93.0588i −0.194684 + 0.194684i
\(479\) 757.971 437.615i 1.58240 0.913600i 0.587895 0.808938i \(-0.299957\pi\)
0.994508 0.104663i \(-0.0333763\pi\)
\(480\) −462.381 149.458i −0.963293 0.311370i
\(481\) 30.1582 52.2355i 0.0626989 0.108598i
\(482\) −408.221 + 109.382i −0.846931 + 0.226934i
\(483\) 78.4636 + 375.328i 0.162450 + 0.777077i
\(484\) 311.263 179.708i 0.643106 0.371298i
\(485\) −92.1430 157.813i −0.189986 0.325388i
\(486\) 161.284 155.963i 0.331860 0.320912i
\(487\) −241.500 241.500i −0.495894 0.495894i 0.414263 0.910157i \(-0.364039\pi\)
−0.910157 + 0.414263i \(0.864039\pi\)
\(488\) 214.681 + 57.5235i 0.439919 + 0.117876i
\(489\) −83.5012 54.6253i −0.170759 0.111708i
\(490\) −1.84565 378.314i −0.00376663 0.772069i
\(491\) −14.2377 + 24.6604i −0.0289973 + 0.0502248i −0.880160 0.474677i \(-0.842565\pi\)
0.851163 + 0.524902i \(0.175898\pi\)
\(492\) −11.6403 13.0154i −0.0236592 0.0264542i
\(493\) −497.045 133.183i −1.00821 0.270148i
\(494\) 31.2314i 0.0632214i
\(495\) −116.023 + 18.1587i −0.234390 + 0.0366842i
\(496\) −284.298 −0.573181
\(497\) −187.627 + 700.232i −0.377518 + 1.40892i
\(498\) 277.439 + 91.1754i 0.557107 + 0.183083i
\(499\) 409.907 + 236.660i 0.821457 + 0.474269i 0.850919 0.525297i \(-0.176046\pi\)
−0.0294615 + 0.999566i \(0.509379\pi\)
\(500\) 107.381 + 378.505i 0.214763 + 0.757010i
\(501\) 149.722 + 296.298i 0.298846 + 0.591414i
\(502\) 24.5130 91.4836i 0.0488306 0.182238i
\(503\) 58.9981 58.9981i 0.117292 0.117292i −0.646024 0.763317i \(-0.723570\pi\)
0.763317 + 0.646024i \(0.223570\pi\)
\(504\) 547.161 + 403.172i 1.08564 + 0.799944i
\(505\) 467.284 + 122.768i 0.925315 + 0.243105i
\(506\) −13.4561 23.3067i −0.0265931 0.0460606i
\(507\) 320.518 + 358.382i 0.632186 + 0.706868i
\(508\) −124.682 465.319i −0.245437 0.915983i
\(509\) −388.655 224.390i −0.763565 0.440844i 0.0670093 0.997752i \(-0.478654\pi\)
−0.830574 + 0.556908i \(0.811988\pi\)
\(510\) 267.688 + 13.6198i 0.524878 + 0.0267054i
\(511\) 411.917 + 713.461i 0.806100 + 1.39621i
\(512\) 270.104 + 270.104i 0.527546 + 0.527546i
\(513\) 251.846 179.133i 0.490927 0.349187i
\(514\) 103.640i 0.201634i
\(515\) 115.386 + 65.8698i 0.224051 + 0.127903i
\(516\) 262.631 401.461i 0.508974 0.778026i
\(517\) 160.028 42.8794i 0.309532 0.0829389i
\(518\) −55.8136 208.299i −0.107748 0.402122i
\(519\) 11.3941 204.298i 0.0219539 0.393638i
\(520\) 94.0625 25.6965i 0.180889 0.0494163i
\(521\) −548.131 −1.05208 −0.526038 0.850461i \(-0.676323\pi\)
−0.526038 + 0.850461i \(0.676323\pi\)
\(522\) 137.886 + 172.630i 0.264150 + 0.330709i
\(523\) −237.559 + 237.559i −0.454224 + 0.454224i −0.896754 0.442530i \(-0.854081\pi\)
0.442530 + 0.896754i \(0.354081\pi\)
\(524\) −17.9284 + 10.3510i −0.0342145 + 0.0197538i
\(525\) 39.4286 857.344i 0.0751021 1.63304i
\(526\) −68.7794 + 119.129i −0.130759 + 0.226482i
\(527\) 818.005 219.184i 1.55219 0.415909i
\(528\) 48.3237 + 15.8807i 0.0915222 + 0.0300771i
\(529\) 350.088 202.124i 0.661793 0.382086i
\(530\) 40.6317 + 10.6750i 0.0766635 + 0.0201416i
\(531\) −511.404 57.2217i −0.963096 0.107762i
\(532\) 291.528 + 291.528i 0.547985 + 0.547985i
\(533\) 5.27851 + 1.41437i 0.00990340 + 0.00265361i
\(534\) 21.1136 378.571i 0.0395385 0.708935i
\(535\) 309.984 1.51229i 0.579409 0.00282672i
\(536\) 107.288 185.828i 0.200164 0.346694i
\(537\) −892.468 + 186.573i −1.66195 + 0.347436i
\(538\) 27.7218 + 7.42804i 0.0515276 + 0.0138068i
\(539\) 213.863i 0.396778i
\(540\) 328.832 + 269.117i 0.608949 + 0.498366i
\(541\) −694.204 −1.28319 −0.641593 0.767045i \(-0.721726\pi\)
−0.641593 + 0.767045i \(0.721726\pi\)
\(542\) 1.00953 3.76761i 0.00186260 0.00695130i
\(543\) 105.943 + 506.773i 0.195106 + 0.933284i
\(544\) −542.975 313.487i −0.998115 0.576262i
\(545\) −46.6163 46.1637i −0.0855346 0.0847040i
\(546\) −93.5232 5.21595i −0.171288 0.00955302i
\(547\) −229.183 + 855.323i −0.418982 + 1.56366i 0.357742 + 0.933820i \(0.383547\pi\)
−0.776724 + 0.629841i \(0.783120\pi\)
\(548\) 193.821 193.821i 0.353687 0.353687i
\(549\) −244.019 179.803i −0.444479 0.327511i
\(550\) 16.1575 + 58.0297i 0.0293772 + 0.105509i
\(551\) 152.171 + 263.568i 0.276173 + 0.478345i
\(552\) −69.0368 + 210.073i −0.125067 + 0.380568i
\(553\) −203.819 760.662i −0.368569 1.37552i
\(554\) 111.191 + 64.1960i 0.200705 + 0.115877i
\(555\) −64.1101 299.370i −0.115514 0.539405i
\(556\) −137.655 238.426i −0.247581 0.428824i
\(557\) 598.653 + 598.653i 1.07478 + 1.07478i 0.996968 + 0.0778138i \(0.0247940\pi\)
0.0778138 + 0.996968i \(0.475206\pi\)
\(558\) −338.574 132.579i −0.606763 0.237597i
\(559\) 150.138i 0.268584i
\(560\) −184.300 + 322.844i −0.329107 + 0.576506i
\(561\) −151.285 8.43740i −0.269670 0.0150399i
\(562\) −448.950 + 120.296i −0.798844 + 0.214050i
\(563\) 80.5980 + 300.796i 0.143158 + 0.534273i 0.999830 + 0.0184123i \(0.00586116\pi\)
−0.856672 + 0.515861i \(0.827472\pi\)
\(564\) −501.649 328.172i −0.889449 0.581866i
\(565\) 141.202 + 80.6072i 0.249915 + 0.142668i
\(566\) −135.312 −0.239067
\(567\) −494.357 784.076i −0.871882 1.38285i
\(568\) −295.614 + 295.614i −0.520447 + 0.520447i
\(569\) 20.4998 11.8356i 0.0360278 0.0208006i −0.481878 0.876238i \(-0.660045\pi\)
0.517906 + 0.855438i \(0.326712\pi\)
\(570\) −106.254 117.646i −0.186411 0.206396i
\(571\) 22.7049 39.3260i 0.0397633 0.0688721i −0.845459 0.534041i \(-0.820673\pi\)
0.885222 + 0.465169i \(0.154006\pi\)
\(572\) −23.4468 + 6.28254i −0.0409909 + 0.0109835i
\(573\) −642.305 + 574.445i −1.12095 + 1.00252i
\(574\) 16.9203 9.76892i 0.0294778 0.0170190i
\(575\) 269.000 74.8988i 0.467825 0.130259i
\(576\) 14.1405 + 32.3423i 0.0245495 + 0.0561498i
\(577\) −333.577 333.577i −0.578124 0.578124i 0.356262 0.934386i \(-0.384051\pi\)
−0.934386 + 0.356262i \(0.884051\pi\)
\(578\) 76.3059 + 20.4461i 0.132017 + 0.0353739i
\(579\) −98.5150 + 49.7804i −0.170147 + 0.0859765i
\(580\) −294.434 + 297.321i −0.507644 + 0.512622i
\(581\) 603.256 1044.87i 1.03831 1.79840i
\(582\) −31.6062 + 96.1750i −0.0543062 + 0.165249i
\(583\) −22.9394 6.14658i −0.0393471 0.0105430i
\(584\) 475.096i 0.813520i
\(585\) −132.228 14.1424i −0.226031 0.0241751i
\(586\) −316.691 −0.540428
\(587\) 201.489 751.967i 0.343252 1.28103i −0.551388 0.834249i \(-0.685902\pi\)
0.894641 0.446786i \(-0.147432\pi\)
\(588\) 576.796 515.857i 0.980945 0.877307i
\(589\) −433.764 250.434i −0.736441 0.425184i
\(590\) 1.28773 + 263.953i 0.00218258 + 0.447377i
\(591\) 526.446 804.733i 0.890771 1.36165i
\(592\) −34.3219 + 128.091i −0.0579763 + 0.216370i
\(593\) −464.151 + 464.151i −0.782717 + 0.782717i −0.980289 0.197571i \(-0.936695\pi\)
0.197571 + 0.980289i \(0.436695\pi\)
\(594\) 50.1436 + 41.4478i 0.0844168 + 0.0697774i
\(595\) 281.381 1071.00i 0.472910 1.80000i
\(596\) 263.432 + 456.278i 0.442000 + 0.765567i
\(597\) 315.698 65.9978i 0.528808 0.110549i
\(598\) −7.88753 29.4367i −0.0131899 0.0492252i
\(599\) −402.592 232.437i −0.672108 0.388042i 0.124767 0.992186i \(-0.460182\pi\)
−0.796875 + 0.604145i \(0.793515\pi\)
\(600\) 266.902 416.812i 0.444837 0.694686i
\(601\) −305.138 528.514i −0.507717 0.879392i −0.999960 0.00893383i \(-0.997156\pi\)
0.492243 0.870458i \(-0.336177\pi\)
\(602\) 379.564 + 379.564i 0.630505 + 0.630505i
\(603\) −228.651 + 182.632i −0.379190 + 0.302873i
\(604\) 785.469i 1.30045i
\(605\) 150.461 + 550.766i 0.248696 + 0.910357i
\(606\) −120.709 238.882i −0.199190 0.394195i
\(607\) 81.5905 21.8621i 0.134416 0.0360167i −0.190984 0.981593i \(-0.561168\pi\)
0.325400 + 0.945577i \(0.394501\pi\)
\(608\) 95.9744 + 358.181i 0.157853 + 0.589114i
\(609\) 814.676 411.662i 1.33773 0.675964i
\(610\) −77.0800 + 135.024i −0.126361 + 0.221350i
\(611\) 187.606 0.307048
\(612\) 342.156 + 428.371i 0.559078 + 0.699953i
\(613\) 463.301 463.301i 0.755793 0.755793i −0.219760 0.975554i \(-0.570528\pi\)
0.975554 + 0.219760i \(0.0705276\pi\)
\(614\) −21.7432 + 12.5534i −0.0354123 + 0.0204453i
\(615\) 24.6956 12.6305i 0.0401555 0.0205374i
\(616\) −98.5380 + 170.673i −0.159964 + 0.277066i
\(617\) −650.709 + 174.357i −1.05463 + 0.282588i −0.744165 0.667995i \(-0.767153\pi\)
−0.310468 + 0.950584i \(0.600486\pi\)
\(618\) −15.0614 72.0456i −0.0243712 0.116579i
\(619\) −759.400 + 438.440i −1.22682 + 0.708303i −0.966363 0.257183i \(-0.917206\pi\)
−0.260455 + 0.965486i \(0.583872\pi\)
\(620\) 174.986 666.036i 0.282235 1.07425i
\(621\) 192.133 232.443i 0.309393 0.374304i
\(622\) 359.975 + 359.975i 0.578737 + 0.578737i
\(623\) −1513.07 405.426i −2.42869 0.650765i
\(624\) 48.2022 + 31.5333i 0.0772472 + 0.0505341i
\(625\) −624.881 + 12.1957i −0.999810 + 0.0195131i
\(626\) −221.405 + 383.485i −0.353683 + 0.612597i
\(627\) 59.7403 + 66.7975i 0.0952795 + 0.106535i
\(628\) −152.326 40.8157i −0.242558 0.0649932i
\(629\) 395.016i 0.628007i
\(630\) −370.039 + 298.533i −0.587364 + 0.473861i
\(631\) 1077.51 1.70762 0.853812 0.520581i \(-0.174285\pi\)
0.853812 + 0.520581i \(0.174285\pi\)
\(632\) 117.540 438.665i 0.185981 0.694090i
\(633\) 259.850 + 85.3951i 0.410506 + 0.134905i
\(634\) 223.513 + 129.045i 0.352544 + 0.203541i
\(635\) 765.246 3.73335i 1.20511 0.00587929i
\(636\) 38.7542 + 76.6943i 0.0609343 + 0.120589i
\(637\) −62.6798 + 233.924i −0.0983984 + 0.367228i
\(638\) −45.3002 + 45.3002i −0.0710034 + 0.0710034i
\(639\) 522.400 228.401i 0.817528 0.357435i
\(640\) −543.887 + 317.561i −0.849824 + 0.496190i
\(641\) −332.614 576.105i −0.518899 0.898759i −0.999759 0.0219617i \(-0.993009\pi\)
0.480860 0.876797i \(-0.340325\pi\)
\(642\) −114.478 128.001i −0.178314 0.199379i
\(643\) 287.192 + 1071.82i 0.446644 + 1.66690i 0.711559 + 0.702626i \(0.247989\pi\)
−0.264915 + 0.964272i \(0.585344\pi\)
\(644\) 348.401 + 201.150i 0.540996 + 0.312344i
\(645\) 510.794 + 565.558i 0.791929 + 0.876834i
\(646\) −102.268 177.134i −0.158310 0.274201i
\(647\) −231.177 231.177i −0.357306 0.357306i 0.505513 0.862819i \(-0.331303\pi\)
−0.862819 + 0.505513i \(0.831303\pi\)
\(648\) −20.8115 534.133i −0.0321165 0.824280i
\(649\) 149.214i 0.229914i
\(650\) 0.665544 + 68.2086i 0.00102391 + 0.104936i
\(651\) −822.373 + 1257.09i −1.26325 + 1.93102i
\(652\) −101.122 + 27.0955i −0.155094 + 0.0415574i
\(653\) 174.987 + 653.059i 0.267974 + 1.00009i 0.960405 + 0.278607i \(0.0898728\pi\)
−0.692432 + 0.721484i \(0.743461\pi\)
\(654\) −2.02383 + 36.2877i −0.00309454 + 0.0554858i
\(655\) −8.66637 31.7235i −0.0132311 0.0484328i
\(656\) −12.0146 −0.0183149
\(657\) 236.251 603.325i 0.359590 0.918303i
\(658\) 474.287 474.287i 0.720802 0.720802i
\(659\) 138.847 80.1633i 0.210693 0.121644i −0.390940 0.920416i \(-0.627850\pi\)
0.601634 + 0.798772i \(0.294517\pi\)
\(660\) −66.9478 + 103.435i −0.101436 + 0.156720i
\(661\) −471.803 + 817.186i −0.713771 + 1.23629i 0.249660 + 0.968333i \(0.419681\pi\)
−0.963432 + 0.267954i \(0.913652\pi\)
\(662\) −109.122 + 29.2392i −0.164837 + 0.0441679i
\(663\) −163.003 53.5679i −0.245856 0.0807962i
\(664\) 602.564 347.891i 0.907476 0.523931i
\(665\) −565.581 + 330.228i −0.850498 + 0.496583i
\(666\) −100.608 + 136.540i −0.151064 + 0.205015i
\(667\) 209.991 + 209.991i 0.314829 + 0.314829i
\(668\) 336.436 + 90.1478i 0.503647 + 0.134952i
\(669\) −39.6505 + 710.943i −0.0592683 + 1.06269i
\(670\) 106.656 + 105.621i 0.159189 + 0.157643i
\(671\) 43.9452 76.1153i 0.0654921 0.113436i
\(672\) 1088.61 227.578i 1.61996 0.338658i
\(673\) 549.114 + 147.135i 0.815919 + 0.218625i 0.642562 0.766234i \(-0.277872\pi\)
0.173358 + 0.984859i \(0.444538\pi\)
\(674\) 305.104i 0.452676i
\(675\) −546.208 + 396.588i −0.809196 + 0.587538i
\(676\) 504.446 0.746222
\(677\) 76.2369 284.520i 0.112610 0.420266i −0.886487 0.462753i \(-0.846862\pi\)
0.999097 + 0.0424873i \(0.0135282\pi\)
\(678\) −18.4311 88.1647i −0.0271846 0.130036i
\(679\) 362.207 + 209.120i 0.533441 + 0.307983i
\(680\) 449.347 453.752i 0.660804 0.667283i
\(681\) −367.915 20.5193i −0.540258 0.0301311i
\(682\) 27.2880 101.840i 0.0400117 0.149326i
\(683\) 449.659 449.659i 0.658359 0.658359i −0.296632 0.954992i \(-0.595864\pi\)
0.954992 + 0.296632i \(0.0958636\pi\)
\(684\) 36.0562 322.243i 0.0527138 0.471115i
\(685\) 219.550 + 376.023i 0.320511 + 0.548939i
\(686\) 174.067 + 301.493i 0.253742 + 0.439495i
\(687\) −308.450 + 938.588i −0.448981 + 1.36621i
\(688\) −85.4335 318.842i −0.124177 0.463433i
\(689\) −23.2897 13.4463i −0.0338021 0.0195157i
\(690\) −129.860 84.0508i −0.188203 0.121813i
\(691\) −465.762 806.723i −0.674040 1.16747i −0.976748 0.214388i \(-0.931224\pi\)
0.302708 0.953083i \(-0.402109\pi\)
\(692\) −151.800 151.800i −0.219365 0.219365i
\(693\) 210.004 167.738i 0.303036 0.242046i
\(694\) 328.639i 0.473544i
\(695\) 421.883 115.252i 0.607027 0.165831i
\(696\) 525.571 + 29.3120i 0.755131 + 0.0421150i
\(697\) 34.5694 9.26283i 0.0495974 0.0132896i
\(698\) 11.9069 + 44.4373i 0.0170587 + 0.0636638i
\(699\) −806.291 527.465i −1.15349 0.754599i
\(700\) −642.903 630.478i −0.918432 0.900682i
\(701\) 1256.95 1.79308 0.896539 0.442964i \(-0.146073\pi\)
0.896539 + 0.442964i \(0.146073\pi\)
\(702\) 42.6995 + 60.0320i 0.0608255 + 0.0855156i
\(703\) −165.200 + 165.200i −0.234993 + 0.234993i
\(704\) −8.86400 + 5.11763i −0.0125909 + 0.00726937i
\(705\) 706.698 638.267i 1.00241 0.905343i
\(706\) 290.023 502.334i 0.410797 0.711521i
\(707\) −1068.07 + 286.190i −1.51071 + 0.404795i
\(708\) −402.435 + 359.918i −0.568412 + 0.508358i
\(709\) 631.908 364.832i 0.891267 0.514573i 0.0169102 0.999857i \(-0.494617\pi\)
0.874357 + 0.485284i \(0.161284\pi\)
\(710\) −147.459 252.554i −0.207689 0.355709i
\(711\) −367.399 + 498.613i −0.516736 + 0.701284i
\(712\) −638.766 638.766i −0.897144 0.897144i
\(713\) −472.085 126.495i −0.662111 0.177412i
\(714\) −547.511 + 276.662i −0.766823 + 0.387481i
\(715\) −0.188118 38.5597i −0.000263102 0.0539296i
\(716\) −478.300 + 828.440i −0.668017 + 1.15704i
\(717\) 133.505 406.243i 0.186199 0.566588i
\(718\) 72.5097 + 19.4289i 0.100988 + 0.0270598i
\(719\) 806.713i 1.12199i −0.827818 0.560997i \(-0.810418\pi\)
0.827818 0.560997i \(-0.189582\pi\)
\(720\) 288.855 45.2085i 0.401187 0.0627896i
\(721\) −304.082 −0.421750
\(722\) 54.9567 205.101i 0.0761173 0.284074i
\(723\) 1023.57 915.424i 1.41572 1.26615i
\(724\) 470.417 + 271.595i 0.649747 + 0.375131i
\(725\) −337.955 572.384i −0.466144 0.789495i
\(726\) 173.153 264.684i 0.238502 0.364578i
\(727\) 306.191 1142.72i 0.421171 1.57183i −0.350974 0.936385i \(-0.614150\pi\)
0.772145 0.635446i \(-0.219184\pi\)
\(728\) −157.802 + 157.802i −0.216762 + 0.216762i
\(729\) −239.180 + 688.647i −0.328093 + 0.944645i
\(730\) −321.440 84.4511i −0.440329 0.115686i
\(731\) 491.633 + 851.533i 0.672548 + 1.16489i
\(732\) −311.285 + 65.0752i −0.425253 + 0.0889006i
\(733\) 264.670 + 987.760i 0.361077 + 1.34756i 0.872662 + 0.488325i \(0.162392\pi\)
−0.511585 + 0.859233i \(0.670941\pi\)
\(734\) −48.0349 27.7330i −0.0654426 0.0377833i
\(735\) 559.737 + 1094.42i 0.761548 + 1.48901i
\(736\) 180.918 + 313.360i 0.245813 + 0.425761i
\(737\) −60.0009 60.0009i −0.0814123 0.0814123i
\(738\) −14.3083 5.60286i −0.0193880 0.00759195i
\(739\) 808.791i 1.09444i 0.836989 + 0.547220i \(0.184314\pi\)
−0.836989 + 0.547220i \(0.815686\pi\)
\(740\) −278.960 159.248i −0.376972 0.215200i
\(741\) 45.7668 + 90.5722i 0.0617636 + 0.122230i
\(742\) −92.8721 + 24.8850i −0.125165 + 0.0335378i
\(743\) −164.727 614.769i −0.221705 0.827415i −0.983698 0.179829i \(-0.942445\pi\)
0.761993 0.647586i \(-0.224221\pi\)
\(744\) −773.190 + 390.699i −1.03923 + 0.525133i
\(745\) −807.362 + 220.559i −1.08371 + 0.296052i
\(746\) −180.107 −0.241431
\(747\) −938.193 + 142.150i −1.25595 + 0.190295i
\(748\) −112.410 + 112.410i −0.150280 + 0.150280i
\(749\) −614.409 + 354.729i −0.820306 + 0.473604i
\(750\) 234.563 + 254.672i 0.312751 + 0.339562i
\(751\) 709.826 1229.46i 0.945175 1.63709i 0.189774 0.981828i \(-0.439224\pi\)
0.755401 0.655263i \(-0.227442\pi\)
\(752\) −398.412 + 106.754i −0.529803 + 0.141960i
\(753\) 62.9726 + 301.227i 0.0836290 + 0.400036i
\(754\) −62.8262 + 36.2727i −0.0833239 + 0.0481071i
\(755\) −1206.80 317.058i −1.59841 0.419945i
\(756\) −958.943 161.789i −1.26844 0.214007i
\(757\) 582.278 + 582.278i 0.769192 + 0.769192i 0.977964 0.208772i \(-0.0669467\pi\)
−0.208772 + 0.977964i \(0.566947\pi\)
\(758\) −130.062 34.8500i −0.171586 0.0459762i
\(759\) 73.1771 + 47.8715i 0.0964125 + 0.0630718i
\(760\) −377.686 + 1.84259i −0.496955 + 0.00242446i
\(761\) −73.5291 + 127.356i −0.0966217 + 0.167354i −0.910284 0.413984i \(-0.864137\pi\)
0.813663 + 0.581337i \(0.197470\pi\)
\(762\) −282.607 315.992i −0.370875 0.414687i
\(763\) 145.035 + 38.8619i 0.190085 + 0.0509330i
\(764\) 904.087i 1.18336i
\(765\) −796.264 + 352.775i −1.04087 + 0.461144i
\(766\) 697.261 0.910262
\(767\) 43.7322 163.211i 0.0570172 0.212791i
\(768\) 376.169 + 123.621i 0.489804 + 0.160965i
\(769\) −798.259 460.875i −1.03805 0.599317i −0.118768 0.992922i \(-0.537894\pi\)
−0.919280 + 0.393605i \(0.871228\pi\)
\(770\) −97.9582 97.0070i −0.127218 0.125983i
\(771\) −151.875 300.559i −0.196984 0.389830i
\(772\) −29.9729 + 111.860i −0.0388250 + 0.144897i
\(773\) 646.946 646.946i 0.836928 0.836928i −0.151525 0.988453i \(-0.548418\pi\)
0.988453 + 0.151525i \(0.0484185\pi\)
\(774\) 46.9445 419.554i 0.0606518 0.542060i
\(775\) 952.666 + 537.697i 1.22925 + 0.693803i
\(776\) 120.597 + 208.880i 0.155409 + 0.269176i
\(777\) 467.106 + 522.286i 0.601166 + 0.672183i
\(778\) 10.3092 + 38.4744i 0.0132509 + 0.0494530i
\(779\) −18.3311 10.5835i −0.0235316 0.0135860i
\(780\) −103.543 + 93.5167i −0.132747 + 0.119893i
\(781\) 82.6613 + 143.174i 0.105840 + 0.183321i
\(782\) −141.127 141.127i −0.180469 0.180469i
\(783\) −652.849 298.574i −0.833779 0.381321i
\(784\) 532.441i 0.679134i
\(785\) 124.197 217.559i 0.158212 0.277146i
\(786\) −9.97338 + 15.2455i −0.0126888 + 0.0193963i
\(787\) −105.372 + 28.2343i −0.133890 + 0.0358758i −0.325142 0.945665i \(-0.605412\pi\)
0.191251 + 0.981541i \(0.438745\pi\)
\(788\) −261.129 974.548i −0.331382 1.23674i
\(789\) 24.8892 446.270i 0.0315453 0.565614i
\(790\) 275.899 + 157.501i 0.349239 + 0.199368i
\(791\) −372.115 −0.470436
\(792\) 153.248 23.2194i 0.193495 0.0293174i
\(793\) 70.3755 70.3755i 0.0887459 0.0887459i
\(794\) −101.540 + 58.6241i −0.127884 + 0.0738339i
\(795\) −133.477 + 28.5841i −0.167895 + 0.0359548i
\(796\) 169.192 293.050i 0.212553 0.368153i
\(797\) 863.511 231.377i 1.08345 0.290310i 0.327443 0.944871i \(-0.393813\pi\)
0.756009 + 0.654561i \(0.227146\pi\)
\(798\) 344.678 + 113.272i 0.431928 + 0.141945i
\(799\) 1064.04 614.324i 1.33171 0.768866i
\(800\) −217.239 780.214i −0.271548 0.975267i
\(801\) 493.532 + 1128.81i 0.616145 + 1.40925i
\(802\) 189.040 + 189.040i 0.235711 + 0.235711i
\(803\) 181.475 + 48.6261i 0.225996 + 0.0605556i
\(804\) −17.0969 + 306.552i −0.0212648 + 0.381283i
\(805\) −449.681 + 454.090i −0.558609 + 0.564087i
\(806\) 59.6953 103.395i 0.0740637 0.128282i
\(807\) −91.2795 + 19.0823i −0.113110 + 0.0236460i
\(808\) −615.946 165.042i −0.762310 0.204260i
\(809\) 920.002i 1.13721i 0.822611 + 0.568604i \(0.192516\pi\)
−0.822611 + 0.568604i \(0.807484\pi\)
\(810\) 365.084 + 80.8648i 0.450721 + 0.0998331i
\(811\) −174.196 −0.214792 −0.107396 0.994216i \(-0.534251\pi\)
−0.107396 + 0.994216i \(0.534251\pi\)
\(812\) 247.862 925.035i 0.305249 1.13921i
\(813\) 2.59343 + 12.4056i 0.00318995 + 0.0152590i
\(814\) −42.5901 24.5894i −0.0523220 0.0302081i
\(815\) −0.811319 166.301i −0.000995483 0.204050i
\(816\) 376.643 + 21.0061i 0.461573 + 0.0257427i
\(817\) 150.514 561.727i 0.184228 0.687548i
\(818\) −134.631 + 134.631i −0.164585 + 0.164585i
\(819\) 278.864 121.923i 0.340494 0.148869i
\(820\) 7.39500 28.1471i 0.00901829 0.0343257i
\(821\) 425.992 + 737.840i 0.518869 + 0.898708i 0.999760 + 0.0219274i \(0.00698027\pi\)
−0.480890 + 0.876781i \(0.659686\pi\)
\(822\) 75.3083 229.157i 0.0916160 0.278780i
\(823\) −53.4313 199.408i −0.0649226 0.242295i 0.925837 0.377923i \(-0.123361\pi\)
−0.990760 + 0.135628i \(0.956695\pi\)
\(824\) −151.866 87.6802i −0.184304 0.106408i
\(825\) −131.895 144.611i −0.159872 0.175286i
\(826\) −302.054 523.172i −0.365682 0.633380i
\(827\) −66.1579 66.1579i −0.0799974 0.0799974i 0.665976 0.745973i \(-0.268015\pi\)
−0.745973 + 0.665976i \(0.768015\pi\)
\(828\) −47.3987 312.831i −0.0572448 0.377815i
\(829\) 71.1280i 0.0857998i −0.999079 0.0428999i \(-0.986340\pi\)
0.999079 0.0428999i \(-0.0136596\pi\)
\(830\) 128.267 + 469.523i 0.154538 + 0.565690i
\(831\) −416.531 23.2306i −0.501240 0.0279550i
\(832\) −11.1954 + 2.99979i −0.0134560 + 0.00360552i
\(833\) 410.494 + 1531.98i 0.492790 + 1.83912i
\(834\) −202.746 132.634i −0.243101 0.159033i
\(835\) −274.307 + 480.513i −0.328512 + 0.575465i
\(836\) 94.0219 0.112466
\(837\) 1176.16 111.666i 1.40521 0.133412i
\(838\) −468.230 + 468.230i −0.558747 + 0.558747i
\(839\) −327.523 + 189.096i −0.390373 + 0.225382i −0.682322 0.731052i \(-0.739030\pi\)
0.291949 + 0.956434i \(0.405696\pi\)
\(840\) −57.5596 + 1131.30i −0.0685233 + 1.34678i
\(841\) −67.0308 + 116.101i −0.0797037 + 0.138051i
\(842\) 222.175 59.5317i 0.263866 0.0707027i
\(843\) 1125.69 1006.76i 1.33534 1.19426i
\(844\) 248.527 143.487i 0.294463 0.170008i
\(845\) −203.622 + 775.033i −0.240973 + 0.917199i
\(846\) −524.257 58.6599i −0.619690 0.0693380i
\(847\) −923.984 923.984i −1.09089 1.09089i
\(848\) 57.1106 + 15.3028i 0.0673475 + 0.0180457i
\(849\) 392.410 198.288i 0.462203 0.233555i
\(850\) 227.126 + 384.676i 0.267207 + 0.452560i
\(851\) −113.985 + 197.428i −0.133943 + 0.231996i
\(852\) 186.757 568.287i 0.219199 0.667004i
\(853\) 629.719 + 168.733i 0.738240 + 0.197811i 0.608296 0.793711i \(-0.291854\pi\)
0.129944 + 0.991521i \(0.458520\pi\)
\(854\) 355.832i 0.416665i
\(855\) 480.541 + 185.472i 0.562036 + 0.216926i
\(856\) −409.137 −0.477963
\(857\) −145.445 + 542.809i −0.169714 + 0.633382i 0.827677 + 0.561204i \(0.189662\pi\)
−0.997392 + 0.0721782i \(0.977005\pi\)
\(858\) −15.9224 + 14.2402i −0.0185576 + 0.0165969i
\(859\) 468.778 + 270.649i 0.545725 + 0.315075i 0.747396 0.664379i \(-0.231304\pi\)
−0.201671 + 0.979453i \(0.564637\pi\)
\(860\) 799.549 3.90070i 0.929709 0.00453570i
\(861\) −34.7539 + 53.1254i −0.0403646 + 0.0617020i
\(862\) −55.9407 + 208.774i −0.0648964 + 0.242197i
\(863\) 24.2188 24.2188i 0.0280635 0.0280635i −0.692936 0.720999i \(-0.743683\pi\)
0.720999 + 0.692936i \(0.243683\pi\)
\(864\) −674.184 557.269i −0.780306 0.644987i
\(865\) 294.502 171.952i 0.340464 0.198788i
\(866\) −243.463 421.690i −0.281135 0.486940i
\(867\) −251.252 + 52.5250i −0.289794 + 0.0605825i
\(868\) 407.916 + 1522.36i 0.469950 + 1.75388i
\(869\) −155.529 89.7949i −0.178975 0.103331i
\(870\) −113.255 + 350.381i −0.130179 + 0.402737i
\(871\) −48.0438 83.2144i −0.0551594 0.0955389i
\(872\) 61.2285 + 61.2285i 0.0702162 + 0.0702162i
\(873\) −49.2768 325.227i −0.0564454 0.372540i
\(874\) 118.041i 0.135059i
\(875\) 1228.18 733.262i 1.40363 0.838014i
\(876\) −306.588 606.735i −0.349986 0.692620i
\(877\) −1200.73 + 321.735i −1.36913 + 0.366858i −0.867162 0.498025i \(-0.834059\pi\)
−0.501972 + 0.864884i \(0.667392\pi\)
\(878\) 154.206 + 575.505i 0.175633 + 0.655472i
\(879\) 918.415 464.082i 1.04484 0.527966i
\(880\) 22.3412 + 81.7804i 0.0253877 + 0.0929323i
\(881\) 1074.75 1.21993 0.609963 0.792430i \(-0.291184\pi\)
0.609963 + 0.792430i \(0.291184\pi\)
\(882\) 248.298 634.091i 0.281517 0.718924i
\(883\) 285.903 285.903i 0.323786 0.323786i −0.526432 0.850217i \(-0.676470\pi\)
0.850217 + 0.526432i \(0.176470\pi\)
\(884\) −155.899 + 90.0086i −0.176357 + 0.101820i
\(885\) −390.534 763.585i −0.441281 0.862808i
\(886\) −126.931 + 219.851i −0.143263 + 0.248139i
\(887\) 1036.58 277.751i 1.16864 0.313135i 0.378226 0.925713i \(-0.376534\pi\)
0.790410 + 0.612578i \(0.209868\pi\)
\(888\) 82.6871 + 395.531i 0.0931161 + 0.445418i
\(889\) −1516.77 + 875.708i −1.70615 + 0.985048i
\(890\) 545.722 318.632i 0.613170 0.358014i
\(891\) −206.156 46.7192i −0.231376 0.0524345i
\(892\) 528.255 + 528.255i 0.592214 + 0.592214i
\(893\) −701.910 188.076i −0.786013 0.210612i
\(894\) 387.997 + 253.823i 0.434001 + 0.283918i
\(895\) −1079.75 1069.27i −1.20642 1.19471i
\(896\) 720.711 1248.31i 0.804365 1.39320i
\(897\) 66.0110 + 73.8090i 0.0735908 + 0.0822842i
\(898\) 170.043 + 45.5630i 0.189358 + 0.0507383i
\(899\) 1163.43i 1.29414i
\(900\) −71.8789 + 704.539i −0.0798654 + 0.782821i
\(901\) −176.122 −0.195473
\(902\) 1.15321 4.30382i 0.00127850 0.00477142i
\(903\) −1656.97 544.533i −1.83496 0.603026i
\(904\) −185.844 107.297i −0.205580 0.118692i
\(905\) −607.165 + 613.119i −0.670901 + 0.677479i
\(906\) 311.740 + 616.932i 0.344084 + 0.680940i
\(907\) −442.672 + 1652.08i −0.488062 + 1.82147i 0.0777954 + 0.996969i \(0.475212\pi\)
−0.565858 + 0.824503i \(0.691455\pi\)
\(908\) −273.374 + 273.374i −0.301073 + 0.301073i
\(909\) 700.122 + 515.879i 0.770211 + 0.567524i
\(910\) −78.7157 134.816i −0.0865008 0.148150i
\(911\) −203.177 351.913i −0.223026 0.386293i 0.732699 0.680553i \(-0.238260\pi\)
−0.955726 + 0.294260i \(0.904927\pi\)
\(912\) −148.731 166.301i −0.163083 0.182348i
\(913\) −71.2133 265.772i −0.0779993 0.291097i
\(914\) −250.056 144.370i −0.273584 0.157954i
\(915\) 25.6700 504.527i 0.0280546 0.551396i
\(916\) 518.280 + 897.687i 0.565808 + 0.980008i
\(917\) 53.2204 + 53.2204i 0.0580375 + 0.0580375i
\(918\) 438.754 + 200.660i 0.477945 + 0.218584i
\(919\) 975.596i 1.06158i 0.847502 + 0.530792i \(0.178105\pi\)
−0.847502 + 0.530792i \(0.821895\pi\)
\(920\) −355.517 + 97.1218i −0.386431 + 0.105567i
\(921\) 44.6600 68.2681i 0.0484908 0.0741238i
\(922\) −196.847 + 52.7449i −0.213500 + 0.0572071i
\(923\) 48.4533 + 180.830i 0.0524955 + 0.195916i
\(924\) 15.7026 281.551i 0.0169941 0.304709i
\(925\) 357.272 364.313i 0.386240 0.393852i
\(926\) 266.694 0.288007
\(927\) 149.255 + 186.864i 0.161009 + 0.201579i
\(928\) 609.065 609.065i 0.656320 0.656320i
\(929\) 1121.09 647.262i 1.20677 0.696730i 0.244719 0.969594i \(-0.421304\pi\)
0.962052 + 0.272864i \(0.0879711\pi\)
\(930\) −126.900 592.575i −0.136452 0.637177i
\(931\) 469.020 812.366i 0.503780 0.872573i
\(932\) −976.435 + 261.635i −1.04768 + 0.280724i
\(933\) −1571.45 516.429i −1.68430 0.553514i
\(934\) −282.319 + 162.997i −0.302269 + 0.174515i
\(935\) −127.332 218.081i −0.136184 0.233242i
\(936\) 174.428 + 19.5170i 0.186355 + 0.0208515i
\(937\) −416.458 416.458i −0.444459 0.444459i 0.449049 0.893507i \(-0.351763\pi\)
−0.893507 + 0.449049i \(0.851763\pi\)
\(938\) −331.834 88.9145i −0.353767 0.0947916i
\(939\) 80.1201 1436.57i 0.0853249 1.52990i
\(940\) −4.87415 999.083i −0.00518527 1.06285i
\(941\) 6.23741 10.8035i 0.00662849 0.0114809i −0.862692 0.505729i \(-0.831223\pi\)
0.869321 + 0.494249i \(0.164557\pi\)
\(942\) −135.841 + 28.3980i −0.144205 + 0.0301465i
\(943\) −19.9506 5.34574i −0.0211565 0.00566886i
\(944\) 371.489i 0.393526i
\(945\) 635.655 1408.02i 0.672651 1.48996i
\(946\) 122.415 0.129403
\(947\) −307.908 + 1149.13i −0.325140 + 1.21344i 0.589031 + 0.808111i \(0.299510\pi\)
−0.914171 + 0.405329i \(0.867157\pi\)
\(948\) 132.971 + 636.061i 0.140264 + 0.670950i
\(949\) 184.246 + 106.375i 0.194148 + 0.112091i
\(950\) 65.8893 255.862i 0.0693571 0.269329i
\(951\) −837.300 46.6977i −0.880442 0.0491038i
\(952\) −378.272 + 1411.73i −0.397345 + 1.48291i
\(953\) −943.370 + 943.370i −0.989895 + 0.989895i −0.999949 0.0100546i \(-0.996799\pi\)
0.0100546 + 0.999949i \(0.496799\pi\)
\(954\) 60.8776 + 44.8572i 0.0638130 + 0.0470201i
\(955\) −1389.04 364.939i −1.45449 0.382135i
\(956\) −224.324 388.540i −0.234648 0.406423i
\(957\) 64.9888 197.756i 0.0679089 0.206641i
\(958\) −209.149 780.555i −0.218318 0.814775i
\(959\) −863.033 498.272i −0.899930 0.519575i
\(960\) −31.9662 + 49.3883i −0.0332982 + 0.0514462i
\(961\) −476.853 825.933i −0.496204 0.859451i
\(962\) −39.3784 39.3784i −0.0409339 0.0409339i
\(963\) 519.564 + 203.451i 0.539526 + 0.211268i
\(964\) 1440.74i 1.49454i
\(965\) −159.764 91.2033i −0.165558 0.0945112i
\(966\) 353.478 + 19.7141i 0.365920 + 0.0204080i
\(967\) 266.681 71.4571i 0.275782 0.0738956i −0.118277 0.992981i \(-0.537737\pi\)
0.394059 + 0.919085i \(0.371070\pi\)
\(968\) −195.037 727.888i −0.201484 0.751950i
\(969\) 556.155 + 363.829i 0.573948 + 0.375469i
\(970\) −162.761 + 44.4639i −0.167795 + 0.0458391i
\(971\) −311.097 −0.320388 −0.160194 0.987086i \(-0.551212\pi\)
−0.160194 + 0.987086i \(0.551212\pi\)
\(972\) 371.264 + 668.701i 0.381959 + 0.687964i
\(973\) −707.766 + 707.766i −0.727406 + 0.727406i
\(974\) −273.087 + 157.667i −0.280377 + 0.161876i
\(975\) −101.884 196.832i −0.104496 0.201879i
\(976\) −109.407 + 189.499i −0.112098 + 0.194159i
\(977\) 608.490 163.044i 0.622815 0.166883i 0.0664079 0.997793i \(-0.478846\pi\)
0.556407 + 0.830910i \(0.312179\pi\)
\(978\) −68.6703 + 61.4152i −0.0702150 + 0.0627967i
\(979\) −309.371 + 178.616i −0.316008 + 0.182447i
\(980\) 1247.37 + 327.719i 1.27283 + 0.334407i
\(981\) −47.3072 108.201i −0.0482235 0.110297i
\(982\) 18.5905 + 18.5905i 0.0189313 + 0.0189313i
\(983\) 305.307 + 81.8068i 0.310587 + 0.0832216i 0.410746 0.911750i \(-0.365268\pi\)
−0.100159 + 0.994971i \(0.531935\pi\)
\(984\) −32.6754 + 16.5112i −0.0332068 + 0.0167796i
\(985\) 1602.70 7.81899i 1.62711 0.00793806i
\(986\) −237.553 + 411.453i −0.240926 + 0.417295i
\(987\) −680.425 + 2070.48i −0.689387 + 2.09775i
\(988\) 102.841 + 27.5563i 0.104091 + 0.0278910i
\(989\) 567.460i 0.573771i
\(990\) −11.5310 + 107.812i −0.0116474 + 0.108901i
\(991\) −1401.99 −1.41472 −0.707362 0.706852i \(-0.750115\pi\)
−0.707362 + 0.706852i \(0.750115\pi\)
\(992\) −366.889 + 1369.25i −0.369848 + 1.38029i
\(993\) 273.611 244.703i 0.275539 0.246428i
\(994\) 579.651 + 334.662i 0.583150 + 0.336682i
\(995\) 381.947 + 378.238i 0.383866 + 0.380139i
\(996\) −545.022 + 833.130i −0.547211 + 0.836475i
\(997\) 349.692 1305.07i 0.350745 1.30900i −0.535011 0.844845i \(-0.679693\pi\)
0.885756 0.464152i \(-0.153641\pi\)
\(998\) 309.014 309.014i 0.309633 0.309633i
\(999\) 91.6809 543.404i 0.0917727 0.543947i
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 45.3.k.a.22.7 yes 40
3.2 odd 2 135.3.l.a.37.4 40
5.2 odd 4 225.3.o.b.193.7 40
5.3 odd 4 inner 45.3.k.a.13.4 yes 40
5.4 even 2 225.3.o.b.157.4 40
9.2 odd 6 135.3.l.a.127.7 40
9.4 even 3 405.3.g.h.82.7 20
9.5 odd 6 405.3.g.g.82.4 20
9.7 even 3 inner 45.3.k.a.7.4 40
15.8 even 4 135.3.l.a.118.7 40
45.7 odd 12 225.3.o.b.43.4 40
45.13 odd 12 405.3.g.h.163.7 20
45.23 even 12 405.3.g.g.163.4 20
45.34 even 6 225.3.o.b.7.7 40
45.38 even 12 135.3.l.a.73.4 40
45.43 odd 12 inner 45.3.k.a.43.7 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.4 40 9.7 even 3 inner
45.3.k.a.13.4 yes 40 5.3 odd 4 inner
45.3.k.a.22.7 yes 40 1.1 even 1 trivial
45.3.k.a.43.7 yes 40 45.43 odd 12 inner
135.3.l.a.37.4 40 3.2 odd 2
135.3.l.a.73.4 40 45.38 even 12
135.3.l.a.118.7 40 15.8 even 4
135.3.l.a.127.7 40 9.2 odd 6
225.3.o.b.7.7 40 45.34 even 6
225.3.o.b.43.4 40 45.7 odd 12
225.3.o.b.157.4 40 5.4 even 2
225.3.o.b.193.7 40 5.2 odd 4
405.3.g.g.82.4 20 9.5 odd 6
405.3.g.g.163.4 20 45.23 even 12
405.3.g.h.82.7 20 9.4 even 3
405.3.g.h.163.7 20 45.13 odd 12