Properties

Label 45.3.k.a.13.9
Level $45$
Weight $3$
Character 45.13
Analytic conductor $1.226$
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] = [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 13.9
Character \(\chi\) \(=\) 45.13
Dual form 45.3.k.a.7.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.40598 + 0.644680i) q^{2} +(-0.325974 - 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(0.360208 + 4.98701i) q^{5} +(1.13830 - 7.38535i) q^{6} +(-0.0658171 - 0.0176356i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +O(q^{10})\) \(q+(2.40598 + 0.644680i) q^{2} +(-0.325974 - 2.98224i) q^{3} +(1.90902 + 1.10217i) q^{4} +(0.360208 + 4.98701i) q^{5} +(1.13830 - 7.38535i) q^{6} +(-0.0658171 - 0.0176356i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(-8.78748 + 1.94426i) q^{9} +(-2.34837 + 12.2309i) q^{10} +(4.62292 + 8.00713i) q^{11} +(2.66465 - 6.05242i) q^{12} +(-12.6403 + 3.38696i) q^{13} +(-0.146985 - 0.0848619i) q^{14} +(14.7550 - 2.69986i) q^{15} +(-9.97912 - 17.2843i) q^{16} +(13.6029 - 13.6029i) q^{17} +(-22.3959 - 0.987258i) q^{18} -5.80704i q^{19} +(-4.80889 + 9.91729i) q^{20} +(-0.0311390 + 0.202031i) q^{21} +(5.96060 + 22.2453i) q^{22} +(43.8013 - 11.7365i) q^{23} +(-8.40093 + 10.4628i) q^{24} +(-24.7405 + 3.59273i) q^{25} -32.5958 q^{26} +(8.66274 + 25.5726i) q^{27} +(-0.106208 - 0.106208i) q^{28} +(-6.37222 + 3.67900i) q^{29} +(37.2408 + 3.01646i) q^{30} +(-8.35363 + 14.4689i) q^{31} +(-8.23618 - 30.7378i) q^{32} +(22.3722 - 16.3967i) q^{33} +(41.4978 - 23.9587i) q^{34} +(0.0642412 - 0.334583i) q^{35} +(-18.9184 - 5.97368i) q^{36} +(36.0680 - 36.0680i) q^{37} +(3.74368 - 13.9716i) q^{38} +(14.2211 + 36.5923i) q^{39} +(14.6331 - 16.9116i) q^{40} +(-31.1567 + 53.9649i) q^{41} +(-0.205165 + 0.466007i) q^{42} +(-2.59980 + 9.70259i) q^{43} +20.3810i q^{44} +(-12.8614 - 43.1229i) q^{45} +112.951 q^{46} +(-44.6476 - 11.9633i) q^{47} +(-48.2931 + 35.3944i) q^{48} +(-42.4312 - 24.4977i) q^{49} +(-61.8413 - 7.30568i) q^{50} +(-45.0012 - 36.1329i) q^{51} +(-27.8636 - 7.46602i) q^{52} +(28.0258 + 28.0258i) q^{53} +(4.35625 + 67.1118i) q^{54} +(-38.2664 + 25.9388i) q^{55} +(0.152383 + 0.263935i) q^{56} +(-17.3180 + 1.89294i) q^{57} +(-17.7032 + 4.74356i) q^{58} +(-16.3509 - 9.44022i) q^{59} +(31.1433 + 11.1085i) q^{60} +(2.69547 + 4.66870i) q^{61} +(-29.4265 + 29.4265i) q^{62} +(0.612655 + 0.0270071i) q^{63} +0.568692i q^{64} +(-21.4439 - 61.8173i) q^{65} +(64.3977 - 25.0273i) q^{66} +(12.8379 + 47.9117i) q^{67} +(40.9609 - 10.9754i) q^{68} +(-49.2792 - 126.800i) q^{69} +(0.370262 - 0.763584i) q^{70} +56.4200 q^{71} +(33.9412 + 21.6430i) q^{72} +(-54.7135 - 54.7135i) q^{73} +(110.031 - 63.5264i) q^{74} +(18.7791 + 72.6109i) q^{75} +(6.40036 - 11.0857i) q^{76} +(-0.163056 - 0.608534i) q^{77} +(10.6254 + 97.2084i) q^{78} +(40.9692 - 23.6536i) q^{79} +(82.6026 - 55.9919i) q^{80} +(73.4397 - 34.1704i) q^{81} +(-109.752 + 109.752i) q^{82} +(-16.0841 + 60.0267i) q^{83} +(-0.282117 + 0.351360i) q^{84} +(72.7376 + 62.9379i) q^{85} +(-12.5101 + 21.6682i) q^{86} +(13.0488 + 17.8042i) q^{87} +(10.7032 - 39.9449i) q^{88} +59.1599i q^{89} +(-3.14373 - 112.044i) q^{90} +0.891679 q^{91} +(96.5530 + 25.8713i) q^{92} +(45.8728 + 20.1960i) q^{93} +(-99.7085 - 57.5668i) q^{94} +(28.9598 - 2.09175i) q^{95} +(-88.9828 + 34.5820i) q^{96} +(-150.251 - 40.2595i) q^{97} +(-86.2954 - 86.2954i) q^{98} +(-56.1918 - 61.3743i) 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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.40598 + 0.644680i 1.20299 + 0.322340i 0.804008 0.594619i \(-0.202697\pi\)
0.398981 + 0.916959i \(0.369364\pi\)
\(3\) −0.325974 2.98224i −0.108658 0.994079i
\(4\) 1.90902 + 1.10217i 0.477254 + 0.275543i
\(5\) 0.360208 + 4.98701i 0.0720417 + 0.997402i
\(6\) 1.13830 7.38535i 0.189717 1.23089i
\(7\) −0.0658171 0.0176356i −0.00940244 0.00251938i 0.254115 0.967174i \(-0.418216\pi\)
−0.263517 + 0.964655i \(0.584883\pi\)
\(8\) −3.16269 3.16269i −0.395336 0.395336i
\(9\) −8.78748 + 1.94426i −0.976387 + 0.216029i
\(10\) −2.34837 + 12.2309i −0.234837 + 1.22309i
\(11\) 4.62292 + 8.00713i 0.420265 + 0.727921i 0.995965 0.0897404i \(-0.0286037\pi\)
−0.575700 + 0.817661i \(0.695270\pi\)
\(12\) 2.66465 6.05242i 0.222054 0.504368i
\(13\) −12.6403 + 3.38696i −0.972331 + 0.260535i −0.709812 0.704391i \(-0.751220\pi\)
−0.262519 + 0.964927i \(0.584553\pi\)
\(14\) −0.146985 0.0848619i −0.0104989 0.00606156i
\(15\) 14.7550 2.69986i 0.983668 0.179991i
\(16\) −9.97912 17.2843i −0.623695 1.08027i
\(17\) 13.6029 13.6029i 0.800170 0.800170i −0.182952 0.983122i \(-0.558565\pi\)
0.983122 + 0.182952i \(0.0585652\pi\)
\(18\) −22.3959 0.987258i −1.24422 0.0548477i
\(19\) 5.80704i 0.305634i −0.988255 0.152817i \(-0.951166\pi\)
0.988255 0.152817i \(-0.0488345\pi\)
\(20\) −4.80889 + 9.91729i −0.240445 + 0.495865i
\(21\) −0.0311390 + 0.202031i −0.00148281 + 0.00962052i
\(22\) 5.96060 + 22.2453i 0.270936 + 1.01115i
\(23\) 43.8013 11.7365i 1.90440 0.510283i 0.908728 0.417390i \(-0.137055\pi\)
0.995676 0.0928936i \(-0.0296117\pi\)
\(24\) −8.40093 + 10.4628i −0.350039 + 0.435952i
\(25\) −24.7405 + 3.59273i −0.989620 + 0.143709i
\(26\) −32.5958 −1.25368
\(27\) 8.66274 + 25.5726i 0.320842 + 0.947133i
\(28\) −0.106208 0.106208i −0.00379316 0.00379316i
\(29\) −6.37222 + 3.67900i −0.219732 + 0.126862i −0.605826 0.795597i \(-0.707157\pi\)
0.386094 + 0.922459i \(0.373824\pi\)
\(30\) 37.2408 + 3.01646i 1.24136 + 0.100549i
\(31\) −8.35363 + 14.4689i −0.269472 + 0.466739i −0.968726 0.248135i \(-0.920183\pi\)
0.699254 + 0.714874i \(0.253516\pi\)
\(32\) −8.23618 30.7378i −0.257381 0.960558i
\(33\) 22.3722 16.3967i 0.677946 0.496871i
\(34\) 41.4978 23.9587i 1.22052 0.704669i
\(35\) 0.0642412 0.334583i 0.00183546 0.00955951i
\(36\) −18.9184 5.97368i −0.525510 0.165936i
\(37\) 36.0680 36.0680i 0.974810 0.974810i −0.0248806 0.999690i \(-0.507921\pi\)
0.999690 + 0.0248806i \(0.00792055\pi\)
\(38\) 3.74368 13.9716i 0.0985180 0.367674i
\(39\) 14.2211 + 36.5923i 0.364644 + 0.938265i
\(40\) 14.6331 16.9116i 0.365828 0.422789i
\(41\) −31.1567 + 53.9649i −0.759919 + 1.31622i 0.182973 + 0.983118i \(0.441428\pi\)
−0.942892 + 0.333100i \(0.891905\pi\)
\(42\) −0.205165 + 0.466007i −0.00488488 + 0.0110954i
\(43\) −2.59980 + 9.70259i −0.0604605 + 0.225642i −0.989545 0.144227i \(-0.953931\pi\)
0.929084 + 0.369868i \(0.120597\pi\)
\(44\) 20.3810i 0.463204i
\(45\) −12.8614 43.1229i −0.285808 0.958287i
\(46\) 112.951 2.45546
\(47\) −44.6476 11.9633i −0.949948 0.254538i −0.249608 0.968347i \(-0.580302\pi\)
−0.700340 + 0.713809i \(0.746968\pi\)
\(48\) −48.2931 + 35.3944i −1.00611 + 0.737382i
\(49\) −42.4312 24.4977i −0.865943 0.499953i
\(50\) −61.8413 7.30568i −1.23683 0.146114i
\(51\) −45.0012 36.1329i −0.882377 0.708488i
\(52\) −27.8636 7.46602i −0.535838 0.143577i
\(53\) 28.0258 + 28.0258i 0.528789 + 0.528789i 0.920211 0.391423i \(-0.128017\pi\)
−0.391423 + 0.920211i \(0.628017\pi\)
\(54\) 4.35625 + 67.1118i 0.0806712 + 1.24281i
\(55\) −38.2664 + 25.9388i −0.695753 + 0.471614i
\(56\) 0.152383 + 0.263935i 0.00272112 + 0.00471312i
\(57\) −17.3180 + 1.89294i −0.303824 + 0.0332096i
\(58\) −17.7032 + 4.74356i −0.305228 + 0.0817855i
\(59\) −16.3509 9.44022i −0.277135 0.160004i 0.354991 0.934870i \(-0.384484\pi\)
−0.632126 + 0.774866i \(0.717817\pi\)
\(60\) 31.1433 + 11.1085i 0.519055 + 0.185141i
\(61\) 2.69547 + 4.66870i 0.0441881 + 0.0765360i 0.887274 0.461244i \(-0.152597\pi\)
−0.843085 + 0.537780i \(0.819263\pi\)
\(62\) −29.4265 + 29.4265i −0.474621 + 0.474621i
\(63\) 0.612655 + 0.0270071i 0.00972468 + 0.000428684i
\(64\) 0.568692i 0.00888582i
\(65\) −21.4439 61.8173i −0.329907 0.951035i
\(66\) 64.3977 25.0273i 0.975722 0.379202i
\(67\) 12.8379 + 47.9117i 0.191610 + 0.715100i 0.993118 + 0.117116i \(0.0373648\pi\)
−0.801508 + 0.597984i \(0.795969\pi\)
\(68\) 40.9609 10.9754i 0.602366 0.161403i
\(69\) −49.2792 126.800i −0.714191 1.83768i
\(70\) 0.370262 0.763584i 0.00528945 0.0109083i
\(71\) 56.4200 0.794648 0.397324 0.917678i \(-0.369939\pi\)
0.397324 + 0.917678i \(0.369939\pi\)
\(72\) 33.9412 + 21.6430i 0.471405 + 0.300597i
\(73\) −54.7135 54.7135i −0.749500 0.749500i 0.224885 0.974385i \(-0.427799\pi\)
−0.974385 + 0.224885i \(0.927799\pi\)
\(74\) 110.031 63.5264i 1.48691 0.858465i
\(75\) 18.7791 + 72.6109i 0.250388 + 0.968146i
\(76\) 6.40036 11.0857i 0.0842152 0.145865i
\(77\) −0.163056 0.608534i −0.00211761 0.00790303i
\(78\) 10.6254 + 97.2084i 0.136223 + 1.24626i
\(79\) 40.9692 23.6536i 0.518597 0.299412i −0.217763 0.976002i \(-0.569876\pi\)
0.736361 + 0.676589i \(0.236543\pi\)
\(80\) 82.6026 55.9919i 1.03253 0.699899i
\(81\) 73.4397 34.1704i 0.906663 0.421856i
\(82\) −109.752 + 109.752i −1.33844 + 1.33844i
\(83\) −16.0841 + 60.0267i −0.193784 + 0.723213i 0.798794 + 0.601605i \(0.205472\pi\)
−0.992578 + 0.121608i \(0.961195\pi\)
\(84\) −0.282117 + 0.351360i −0.00335854 + 0.00418285i
\(85\) 72.7376 + 62.9379i 0.855737 + 0.740445i
\(86\) −12.5101 + 21.6682i −0.145467 + 0.251956i
\(87\) 13.0488 + 17.8042i 0.149987 + 0.204646i
\(88\) 10.7032 39.9449i 0.121627 0.453919i
\(89\) 59.1599i 0.664718i 0.943153 + 0.332359i \(0.107844\pi\)
−0.943153 + 0.332359i \(0.892156\pi\)
\(90\) −3.14373 112.044i −0.0349304 1.24494i
\(91\) 0.891679 0.00979867
\(92\) 96.5530 + 25.8713i 1.04949 + 0.281210i
\(93\) 45.8728 + 20.1960i 0.493256 + 0.217162i
\(94\) −99.7085 57.5668i −1.06073 0.612412i
\(95\) 28.9598 2.09175i 0.304840 0.0220184i
\(96\) −88.9828 + 34.5820i −0.926904 + 0.360229i
\(97\) −150.251 40.2595i −1.54898 0.415047i −0.619823 0.784742i \(-0.712796\pi\)
−0.929153 + 0.369695i \(0.879462\pi\)
\(98\) −86.2954 86.2954i −0.880566 0.880566i
\(99\) −56.1918 61.3743i −0.567594 0.619943i
\(100\) −51.1898 20.4097i −0.511898 0.204097i
\(101\) 27.6053 + 47.8137i 0.273319 + 0.473403i 0.969710 0.244260i \(-0.0785451\pi\)
−0.696390 + 0.717663i \(0.745212\pi\)
\(102\) −84.9779 115.946i −0.833116 1.13673i
\(103\) 88.3218 23.6658i 0.857493 0.229765i 0.196821 0.980439i \(-0.436938\pi\)
0.660672 + 0.750675i \(0.270271\pi\)
\(104\) 50.6892 + 29.2654i 0.487397 + 0.281399i
\(105\) −1.01875 0.0825172i −0.00970234 0.000785878i
\(106\) 49.3618 + 85.4971i 0.465677 + 0.806576i
\(107\) −14.6336 + 14.6336i −0.136762 + 0.136762i −0.772174 0.635411i \(-0.780831\pi\)
0.635411 + 0.772174i \(0.280831\pi\)
\(108\) −11.6480 + 58.3663i −0.107852 + 0.540429i
\(109\) 112.055i 1.02803i 0.857781 + 0.514015i \(0.171843\pi\)
−0.857781 + 0.514015i \(0.828157\pi\)
\(110\) −108.790 + 37.7385i −0.989003 + 0.343077i
\(111\) −119.320 95.8060i −1.07496 0.863117i
\(112\) 0.351976 + 1.31359i 0.00314264 + 0.0117285i
\(113\) −35.8191 + 9.59771i −0.316984 + 0.0849355i −0.413803 0.910366i \(-0.635800\pi\)
0.0968194 + 0.995302i \(0.469133\pi\)
\(114\) −42.8870 6.61017i −0.376202 0.0579840i
\(115\) 74.3077 + 214.210i 0.646154 + 1.86269i
\(116\) −16.2196 −0.139824
\(117\) 104.491 54.3389i 0.893088 0.464435i
\(118\) −33.2541 33.2541i −0.281814 0.281814i
\(119\) −1.13520 + 0.655407i −0.00953948 + 0.00550762i
\(120\) −55.2044 38.1267i −0.460036 0.317723i
\(121\) 17.7573 30.7565i 0.146754 0.254186i
\(122\) 3.47543 + 12.9705i 0.0284872 + 0.106316i
\(123\) 171.092 + 75.3254i 1.39100 + 0.612402i
\(124\) −31.8944 + 18.4143i −0.257213 + 0.148502i
\(125\) −26.8287 122.087i −0.214629 0.976696i
\(126\) 1.45662 + 0.459945i 0.0115605 + 0.00365035i
\(127\) 151.793 151.793i 1.19522 1.19522i 0.219643 0.975580i \(-0.429511\pi\)
0.975580 0.219643i \(-0.0704892\pi\)
\(128\) −33.3113 + 124.320i −0.260245 + 0.971247i
\(129\) 29.7829 + 4.59044i 0.230875 + 0.0355848i
\(130\) −11.7413 162.556i −0.0903176 1.25043i
\(131\) −0.751448 + 1.30155i −0.00573624 + 0.00993547i −0.868879 0.495024i \(-0.835159\pi\)
0.863143 + 0.504960i \(0.168493\pi\)
\(132\) 60.7809 6.64367i 0.460462 0.0503308i
\(133\) −0.102411 + 0.382203i −0.000770006 + 0.00287370i
\(134\) 123.551i 0.922021i
\(135\) −124.410 + 52.4126i −0.921558 + 0.388242i
\(136\) −86.0434 −0.632672
\(137\) 67.4699 + 18.0785i 0.492481 + 0.131960i 0.496508 0.868032i \(-0.334615\pi\)
−0.00402717 + 0.999992i \(0.501282\pi\)
\(138\) −36.8192 336.847i −0.266805 2.44092i
\(139\) 106.332 + 61.3909i 0.764980 + 0.441661i 0.831081 0.556152i \(-0.187723\pi\)
−0.0661012 + 0.997813i \(0.521056\pi\)
\(140\) 0.491405 0.567919i 0.00351004 0.00405657i
\(141\) −21.1234 + 137.049i −0.149811 + 0.971981i
\(142\) 135.745 + 36.3728i 0.955953 + 0.256147i
\(143\) −85.5549 85.5549i −0.598286 0.598286i
\(144\) 121.297 + 132.484i 0.842338 + 0.920027i
\(145\) −20.6426 30.4531i −0.142362 0.210021i
\(146\) −96.3668 166.912i −0.660047 1.14323i
\(147\) −59.2264 + 134.526i −0.402901 + 0.915140i
\(148\) 108.607 29.1013i 0.733834 0.196630i
\(149\) 23.0090 + 13.2842i 0.154423 + 0.0891560i 0.575220 0.817999i \(-0.304916\pi\)
−0.420797 + 0.907155i \(0.638250\pi\)
\(150\) −1.62865 + 186.807i −0.0108577 + 1.24538i
\(151\) −49.2414 85.2887i −0.326102 0.564826i 0.655633 0.755080i \(-0.272402\pi\)
−0.981735 + 0.190254i \(0.939069\pi\)
\(152\) −18.3659 + 18.3659i −0.120828 + 0.120828i
\(153\) −93.0876 + 145.983i −0.608415 + 0.954136i
\(154\) 1.56924i 0.0101899i
\(155\) −75.1656 36.4478i −0.484940 0.235147i
\(156\) −13.1826 + 85.5295i −0.0845042 + 0.548266i
\(157\) −44.6968 166.811i −0.284693 1.06249i −0.949063 0.315086i \(-0.897967\pi\)
0.664370 0.747404i \(-0.268700\pi\)
\(158\) 113.820 30.4980i 0.720379 0.193025i
\(159\) 74.4439 92.7152i 0.468201 0.583115i
\(160\) 150.323 52.1459i 0.939520 0.325912i
\(161\) −3.08985 −0.0191916
\(162\) 198.723 34.8680i 1.22669 0.215235i
\(163\) −65.0824 65.0824i −0.399278 0.399278i 0.478700 0.877978i \(-0.341108\pi\)
−0.877978 + 0.478700i \(0.841108\pi\)
\(164\) −118.957 + 68.6800i −0.725349 + 0.418780i
\(165\) 89.8294 + 105.664i 0.544420 + 0.640389i
\(166\) −77.3960 + 134.054i −0.466241 + 0.807553i
\(167\) −51.7034 192.960i −0.309601 1.15545i −0.928912 0.370301i \(-0.879255\pi\)
0.619311 0.785146i \(-0.287412\pi\)
\(168\) 0.737444 0.540478i 0.00438955 0.00321713i
\(169\) 1.94752 1.12440i 0.0115238 0.00665325i
\(170\) 134.430 + 198.320i 0.790767 + 1.16659i
\(171\) 11.2904 + 51.0293i 0.0660258 + 0.298417i
\(172\) −15.6570 + 15.6570i −0.0910290 + 0.0910290i
\(173\) 8.94958 33.4003i 0.0517317 0.193065i −0.935224 0.354056i \(-0.884802\pi\)
0.986956 + 0.160991i \(0.0514689\pi\)
\(174\) 19.9172 + 51.2489i 0.114467 + 0.294534i
\(175\) 1.69171 + 0.199852i 0.00966690 + 0.00114201i
\(176\) 92.2653 159.808i 0.524235 0.908001i
\(177\) −22.8230 + 51.8397i −0.128944 + 0.292879i
\(178\) −38.1392 + 142.337i −0.214265 + 0.799648i
\(179\) 185.962i 1.03890i −0.854502 0.519448i \(-0.826138\pi\)
0.854502 0.519448i \(-0.173862\pi\)
\(180\) 22.9762 96.4978i 0.127646 0.536099i
\(181\) −97.7851 −0.540249 −0.270125 0.962825i \(-0.587065\pi\)
−0.270125 + 0.962825i \(0.587065\pi\)
\(182\) 2.14536 + 0.574847i 0.0117877 + 0.00315850i
\(183\) 13.0445 9.56041i 0.0712814 0.0522427i
\(184\) −175.649 101.411i −0.954613 0.551146i
\(185\) 192.863 + 166.879i 1.04250 + 0.902050i
\(186\) 97.3490 + 78.1645i 0.523382 + 0.420239i
\(187\) 171.805 + 46.0350i 0.918744 + 0.246177i
\(188\) −72.0473 72.0473i −0.383231 0.383231i
\(189\) −0.119168 1.83589i −0.000630518 0.00971368i
\(190\) 71.0251 + 13.6371i 0.373816 + 0.0717741i
\(191\) −68.2090 118.141i −0.357115 0.618542i 0.630362 0.776301i \(-0.282906\pi\)
−0.987478 + 0.157759i \(0.949573\pi\)
\(192\) 1.69598 0.185379i 0.00883321 0.000965515i
\(193\) −89.2148 + 23.9050i −0.462253 + 0.123860i −0.482427 0.875936i \(-0.660245\pi\)
0.0201740 + 0.999796i \(0.493578\pi\)
\(194\) −335.545 193.727i −1.72961 0.998594i
\(195\) −177.364 + 84.1017i −0.909557 + 0.431291i
\(196\) −54.0013 93.5329i −0.275517 0.477209i
\(197\) −170.623 + 170.623i −0.866107 + 0.866107i −0.992039 0.125932i \(-0.959808\pi\)
0.125932 + 0.992039i \(0.459808\pi\)
\(198\) −95.6294 183.891i −0.482977 0.928742i
\(199\) 36.4196i 0.183013i 0.995804 + 0.0915066i \(0.0291683\pi\)
−0.995804 + 0.0915066i \(0.970832\pi\)
\(200\) 89.6092 + 66.8838i 0.448046 + 0.334419i
\(201\) 138.699 53.9036i 0.690046 0.268177i
\(202\) 35.5931 + 132.835i 0.176204 + 0.657601i
\(203\) 0.484283 0.129763i 0.00238563 0.000639227i
\(204\) −46.0835 118.577i −0.225900 0.581261i
\(205\) −280.346 135.940i −1.36754 0.663121i
\(206\) 227.757 1.10562
\(207\) −362.084 + 188.296i −1.74920 + 0.909641i
\(208\) 184.681 + 184.681i 0.887887 + 0.887887i
\(209\) 46.4977 26.8455i 0.222477 0.128447i
\(210\) −2.39788 0.855300i −0.0114185 0.00407286i
\(211\) 96.8033 167.668i 0.458784 0.794636i −0.540113 0.841592i \(-0.681619\pi\)
0.998897 + 0.0469559i \(0.0149520\pi\)
\(212\) 22.6125 + 84.3909i 0.106663 + 0.398070i
\(213\) −18.3914 168.258i −0.0863448 0.789943i
\(214\) −44.6420 + 25.7741i −0.208607 + 0.120440i
\(215\) −49.3234 9.47028i −0.229411 0.0440478i
\(216\) 53.4805 108.276i 0.247595 0.501276i
\(217\) 0.804980 0.804980i 0.00370959 0.00370959i
\(218\) −72.2398 + 269.603i −0.331375 + 1.23671i
\(219\) −145.334 + 181.004i −0.663623 + 0.826502i
\(220\) −101.640 + 7.34140i −0.462001 + 0.0333700i
\(221\) −125.872 + 218.017i −0.569558 + 0.986503i
\(222\) −225.318 307.431i −1.01495 1.38482i
\(223\) −24.7802 + 92.4808i −0.111122 + 0.414712i −0.998968 0.0454290i \(-0.985535\pi\)
0.887846 + 0.460141i \(0.152201\pi\)
\(224\) 2.16833i 0.00968002i
\(225\) 210.421 79.6731i 0.935207 0.354102i
\(226\) −92.3675 −0.408706
\(227\) 318.219 + 85.2664i 1.40184 + 0.375623i 0.879007 0.476810i \(-0.158207\pi\)
0.522837 + 0.852433i \(0.324874\pi\)
\(228\) −35.1467 15.4737i −0.154152 0.0678672i
\(229\) 360.256 + 207.994i 1.57317 + 0.908269i 0.995777 + 0.0918017i \(0.0292626\pi\)
0.577391 + 0.816468i \(0.304071\pi\)
\(230\) 40.6860 + 563.289i 0.176896 + 2.44908i
\(231\) −1.76164 + 0.684638i −0.00762615 + 0.00296380i
\(232\) 31.7889 + 8.51781i 0.137021 + 0.0367147i
\(233\) −22.0213 22.0213i −0.0945121 0.0945121i 0.658270 0.752782i \(-0.271289\pi\)
−0.752782 + 0.658270i \(0.771289\pi\)
\(234\) 286.435 63.3748i 1.22408 0.270833i
\(235\) 43.5785 226.967i 0.185441 0.965817i
\(236\) −20.8095 36.0431i −0.0881758 0.152725i
\(237\) −83.8955 114.469i −0.353989 0.482993i
\(238\) −3.15379 + 0.845055i −0.0132512 + 0.00355065i
\(239\) −267.552 154.471i −1.11946 0.646323i −0.178200 0.983994i \(-0.557027\pi\)
−0.941264 + 0.337672i \(0.890361\pi\)
\(240\) −193.908 228.089i −0.807948 0.950370i
\(241\) −12.8569 22.2688i −0.0533481 0.0924016i 0.838118 0.545489i \(-0.183656\pi\)
−0.891466 + 0.453087i \(0.850323\pi\)
\(242\) 62.5517 62.5517i 0.258478 0.258478i
\(243\) −125.844 207.876i −0.517875 0.855457i
\(244\) 11.8835i 0.0487028i
\(245\) 106.886 220.429i 0.436270 0.899711i
\(246\) 363.084 + 291.531i 1.47595 + 1.18509i
\(247\) 19.6682 + 73.4028i 0.0796284 + 0.297177i
\(248\) 72.1806 19.3407i 0.291051 0.0779868i
\(249\) 184.257 + 28.3995i 0.739987 + 0.114054i
\(250\) 14.1578 311.034i 0.0566311 1.24414i
\(251\) 275.877 1.09911 0.549556 0.835457i \(-0.314797\pi\)
0.549556 + 0.835457i \(0.314797\pi\)
\(252\) 1.13980 + 0.726807i 0.00452302 + 0.00288416i
\(253\) 296.465 + 296.465i 1.17180 + 1.17180i
\(254\) 463.070 267.353i 1.82311 1.05257i
\(255\) 163.985 237.437i 0.643079 0.931125i
\(256\) −159.155 + 275.665i −0.621701 + 1.07682i
\(257\) 1.65593 + 6.18001i 0.00644330 + 0.0240467i 0.969073 0.246776i \(-0.0793711\pi\)
−0.962629 + 0.270822i \(0.912704\pi\)
\(258\) 68.6977 + 30.2449i 0.266270 + 0.117228i
\(259\) −3.00997 + 1.73781i −0.0116215 + 0.00670968i
\(260\) 27.1964 141.645i 0.104602 0.544789i
\(261\) 48.8428 44.7185i 0.187137 0.171335i
\(262\) −2.64705 + 2.64705i −0.0101032 + 0.0101032i
\(263\) 54.9964 205.249i 0.209112 0.780416i −0.779045 0.626968i \(-0.784296\pi\)
0.988157 0.153448i \(-0.0490377\pi\)
\(264\) −122.614 18.8985i −0.464447 0.0715852i
\(265\) −129.670 + 149.860i −0.489320 + 0.565509i
\(266\) −0.492797 + 0.853549i −0.00185262 + 0.00320883i
\(267\) 176.429 19.2846i 0.660782 0.0722269i
\(268\) −28.2991 + 105.614i −0.105594 + 0.394081i
\(269\) 349.046i 1.29757i 0.760973 + 0.648784i \(0.224722\pi\)
−0.760973 + 0.648784i \(0.775278\pi\)
\(270\) −333.118 + 45.8989i −1.23377 + 0.169996i
\(271\) −202.277 −0.746409 −0.373205 0.927749i \(-0.621741\pi\)
−0.373205 + 0.927749i \(0.621741\pi\)
\(272\) −370.862 99.3722i −1.36346 0.365339i
\(273\) −0.290664 2.65920i −0.00106470 0.00974065i
\(274\) 150.676 + 86.9930i 0.549913 + 0.317493i
\(275\) −143.141 181.491i −0.520512 0.659969i
\(276\) 45.6806 296.377i 0.165509 1.07383i
\(277\) −234.373 62.8000i −0.846112 0.226715i −0.190381 0.981710i \(-0.560972\pi\)
−0.655730 + 0.754995i \(0.727639\pi\)
\(278\) 216.255 + 216.255i 0.777897 + 0.777897i
\(279\) 45.2760 143.387i 0.162280 0.513932i
\(280\) −1.26136 + 0.855006i −0.00450484 + 0.00305359i
\(281\) 140.160 + 242.764i 0.498789 + 0.863929i 0.999999 0.00139729i \(-0.000444772\pi\)
−0.501210 + 0.865326i \(0.667111\pi\)
\(282\) −139.175 + 316.120i −0.493530 + 1.12099i
\(283\) −372.686 + 99.8610i −1.31691 + 0.352866i −0.847820 0.530283i \(-0.822086\pi\)
−0.469092 + 0.883149i \(0.655419\pi\)
\(284\) 107.707 + 62.1845i 0.379249 + 0.218959i
\(285\) −15.6782 85.6831i −0.0550113 0.300642i
\(286\) −150.688 260.999i −0.526880 0.912583i
\(287\) 3.00235 3.00235i 0.0104611 0.0104611i
\(288\) 132.138 + 254.095i 0.458812 + 0.882274i
\(289\) 81.0774i 0.280545i
\(290\) −30.0330 86.5774i −0.103562 0.298543i
\(291\) −71.0857 + 461.207i −0.244281 + 1.58490i
\(292\) −44.1453 164.753i −0.151183 0.564222i
\(293\) 40.8052 10.9337i 0.139267 0.0373164i −0.188512 0.982071i \(-0.560367\pi\)
0.327779 + 0.944754i \(0.393700\pi\)
\(294\) −229.223 + 285.484i −0.779672 + 0.971032i
\(295\) 41.1887 84.9427i 0.139623 0.287941i
\(296\) −228.143 −0.770755
\(297\) −164.716 + 187.584i −0.554598 + 0.631595i
\(298\) 46.7950 + 46.7950i 0.157030 + 0.157030i
\(299\) −513.910 + 296.706i −1.71876 + 0.992329i
\(300\) −44.1800 + 159.313i −0.147267 + 0.531044i
\(301\) 0.342223 0.592747i 0.00113695 0.00196926i
\(302\) −63.4899 236.948i −0.210232 0.784595i
\(303\) 133.593 97.9115i 0.440902 0.323140i
\(304\) −100.371 + 57.9492i −0.330168 + 0.190622i
\(305\) −22.3119 + 15.1240i −0.0731537 + 0.0495870i
\(306\) −318.079 + 291.220i −1.03947 + 0.951698i
\(307\) −85.1111 + 85.1111i −0.277235 + 0.277235i −0.832004 0.554769i \(-0.812806\pi\)
0.554769 + 0.832004i \(0.312806\pi\)
\(308\) 0.359431 1.34142i 0.00116699 0.00435525i
\(309\) −99.3675 255.682i −0.321578 0.827450i
\(310\) −157.350 136.150i −0.507580 0.439195i
\(311\) 227.093 393.336i 0.730202 1.26475i −0.226595 0.973989i \(-0.572759\pi\)
0.956797 0.290758i \(-0.0939074\pi\)
\(312\) 70.7531 160.707i 0.226773 0.515087i
\(313\) 76.9018 287.001i 0.245693 0.916937i −0.727342 0.686276i \(-0.759244\pi\)
0.973034 0.230661i \(-0.0740890\pi\)
\(314\) 430.158i 1.36993i
\(315\) 0.0859989 + 3.06504i 0.000273012 + 0.00973029i
\(316\) 104.281 0.330004
\(317\) 85.3965 + 22.8819i 0.269389 + 0.0721827i 0.390985 0.920397i \(-0.372134\pi\)
−0.121596 + 0.992580i \(0.538801\pi\)
\(318\) 238.882 175.078i 0.751201 0.550561i
\(319\) −58.9165 34.0155i −0.184691 0.106632i
\(320\) −2.83607 + 0.204848i −0.00886273 + 0.000640149i
\(321\) 48.4109 + 38.8706i 0.150813 + 0.121092i
\(322\) −7.43412 1.99197i −0.0230873 0.00618623i
\(323\) −78.9926 78.9926i −0.244559 0.244559i
\(324\) 177.859 + 15.7113i 0.548948 + 0.0484917i
\(325\) 300.559 129.208i 0.924797 0.397564i
\(326\) −114.629 198.544i −0.351624 0.609031i
\(327\) 334.176 36.5271i 1.02194 0.111704i
\(328\) 269.213 72.1354i 0.820771 0.219925i
\(329\) 2.72759 + 1.57478i 0.00829055 + 0.00478655i
\(330\) 148.008 + 312.137i 0.448509 + 0.945869i
\(331\) 223.152 + 386.510i 0.674175 + 1.16770i 0.976709 + 0.214566i \(0.0688338\pi\)
−0.302535 + 0.953138i \(0.597833\pi\)
\(332\) −96.8645 + 96.8645i −0.291761 + 0.291761i
\(333\) −246.821 + 387.072i −0.741204 + 1.16238i
\(334\) 497.589i 1.48979i
\(335\) −234.312 + 81.2809i −0.699438 + 0.242630i
\(336\) 3.80271 1.47787i 0.0113176 0.00439843i
\(337\) 7.58184 + 28.2958i 0.0224980 + 0.0839638i 0.976262 0.216593i \(-0.0694943\pi\)
−0.953764 + 0.300556i \(0.902828\pi\)
\(338\) 5.41056 1.44975i 0.0160076 0.00428921i
\(339\) 40.2988 + 103.693i 0.118875 + 0.305878i
\(340\) 69.4890 + 200.319i 0.204379 + 0.589173i
\(341\) −154.473 −0.452999
\(342\) −5.73305 + 130.054i −0.0167633 + 0.380275i
\(343\) 4.72156 + 4.72156i 0.0137655 + 0.0137655i
\(344\) 38.9086 22.4639i 0.113107 0.0653021i
\(345\) 614.602 291.430i 1.78146 0.844725i
\(346\) 43.0650 74.5907i 0.124465 0.215580i
\(347\) 87.3943 + 326.160i 0.251857 + 0.939942i 0.969812 + 0.243853i \(0.0784114\pi\)
−0.717956 + 0.696089i \(0.754922\pi\)
\(348\) 5.28716 + 48.3706i 0.0151930 + 0.138996i
\(349\) 51.4915 29.7286i 0.147540 0.0851823i −0.424413 0.905469i \(-0.639519\pi\)
0.571953 + 0.820287i \(0.306186\pi\)
\(350\) 3.94137 + 1.57145i 0.0112611 + 0.00448985i
\(351\) −196.113 293.905i −0.558727 0.837336i
\(352\) 208.047 208.047i 0.591042 0.591042i
\(353\) −137.840 + 514.426i −0.390482 + 1.45730i 0.438860 + 0.898555i \(0.355382\pi\)
−0.829342 + 0.558742i \(0.811284\pi\)
\(354\) −88.3316 + 110.012i −0.249524 + 0.310767i
\(355\) 20.3230 + 281.367i 0.0572478 + 0.792583i
\(356\) −65.2043 + 112.937i −0.183158 + 0.317239i
\(357\) 2.32462 + 3.17178i 0.00651155 + 0.00888455i
\(358\) 119.886 447.421i 0.334878 1.24978i
\(359\) 342.196i 0.953192i 0.879122 + 0.476596i \(0.158130\pi\)
−0.879122 + 0.476596i \(0.841870\pi\)
\(360\) −95.7078 + 177.061i −0.265855 + 0.491836i
\(361\) 327.278 0.906588
\(362\) −235.269 63.0401i −0.649914 0.174144i
\(363\) −97.5117 42.9306i −0.268627 0.118266i
\(364\) 1.70223 + 0.982783i 0.00467646 + 0.00269995i
\(365\) 253.148 292.565i 0.693557 0.801548i
\(366\) 37.5482 14.5926i 0.102591 0.0398705i
\(367\) 355.509 + 95.2584i 0.968690 + 0.259560i 0.708275 0.705937i \(-0.249474\pi\)
0.260416 + 0.965497i \(0.416140\pi\)
\(368\) −639.956 639.956i −1.73901 1.73901i
\(369\) 168.867 534.793i 0.457633 1.44930i
\(370\) 356.441 + 525.843i 0.963354 + 1.42120i
\(371\) −1.35032 2.33883i −0.00363968 0.00630412i
\(372\) 65.3125 + 89.1142i 0.175571 + 0.239554i
\(373\) −321.501 + 86.1459i −0.861933 + 0.230954i −0.662596 0.748977i \(-0.730545\pi\)
−0.199337 + 0.979931i \(0.563879\pi\)
\(374\) 383.681 + 221.519i 1.02589 + 0.592296i
\(375\) −355.347 + 119.807i −0.947592 + 0.319484i
\(376\) 103.370 + 179.042i 0.274921 + 0.476177i
\(377\) 68.0862 68.0862i 0.180600 0.180600i
\(378\) 0.896843 4.49392i 0.00237260 0.0118887i
\(379\) 203.700i 0.537466i 0.963215 + 0.268733i \(0.0866049\pi\)
−0.963215 + 0.268733i \(0.913395\pi\)
\(380\) 57.5901 + 27.9254i 0.151553 + 0.0734880i
\(381\) −502.164 403.203i −1.31802 1.05828i
\(382\) −87.9460 328.219i −0.230225 0.859212i
\(383\) 19.9865 5.35538i 0.0521842 0.0139827i −0.232633 0.972565i \(-0.574734\pi\)
0.284817 + 0.958582i \(0.408067\pi\)
\(384\) 381.609 + 58.8174i 0.993774 + 0.153170i
\(385\) 2.97603 1.03236i 0.00772994 0.00268146i
\(386\) −230.060 −0.596010
\(387\) 3.98132 90.3161i 0.0102876 0.233375i
\(388\) −242.458 242.458i −0.624892 0.624892i
\(389\) 160.439 92.6297i 0.412440 0.238123i −0.279397 0.960176i \(-0.590135\pi\)
0.691838 + 0.722053i \(0.256801\pi\)
\(390\) −480.952 + 88.0042i −1.23321 + 0.225652i
\(391\) 436.174 755.475i 1.11553 1.93216i
\(392\) 56.7182 + 211.675i 0.144689 + 0.539988i
\(393\) 4.12647 + 1.81673i 0.0104999 + 0.00462271i
\(394\) −520.513 + 300.518i −1.32110 + 0.762737i
\(395\) 132.718 + 195.793i 0.335995 + 0.495680i
\(396\) −39.6260 179.098i −0.100066 0.452266i
\(397\) −236.474 + 236.474i −0.595652 + 0.595652i −0.939152 0.343501i \(-0.888387\pi\)
0.343501 + 0.939152i \(0.388387\pi\)
\(398\) −23.4790 + 87.6248i −0.0589925 + 0.220163i
\(399\) 1.17320 + 0.180825i 0.00294036 + 0.000453197i
\(400\) 308.986 + 391.771i 0.772466 + 0.979428i
\(401\) −34.0375 + 58.9547i −0.0848816 + 0.147019i −0.905341 0.424686i \(-0.860385\pi\)
0.820459 + 0.571705i \(0.193718\pi\)
\(402\) 368.458 40.2743i 0.916562 0.100185i
\(403\) 56.5868 211.185i 0.140414 0.524032i
\(404\) 121.703i 0.301245i
\(405\) 196.861 + 353.936i 0.486078 + 0.873916i
\(406\) 1.24883 0.00307593
\(407\) 455.540 + 122.062i 1.11926 + 0.299906i
\(408\) 28.0479 + 256.602i 0.0687449 + 0.628926i
\(409\) −326.511 188.511i −0.798315 0.460907i 0.0445668 0.999006i \(-0.485809\pi\)
−0.842882 + 0.538099i \(0.819143\pi\)
\(410\) −586.870 507.802i −1.43139 1.23854i
\(411\) 31.9210 207.104i 0.0776666 0.503904i
\(412\) 194.691 + 52.1674i 0.472552 + 0.126620i
\(413\) 0.909687 + 0.909687i 0.00220263 + 0.00220263i
\(414\) −992.557 + 219.607i −2.39748 + 0.530451i
\(415\) −305.147 58.5894i −0.735295 0.141179i
\(416\) 208.216 + 360.640i 0.500518 + 0.866923i
\(417\) 148.421 337.120i 0.355925 0.808440i
\(418\) 129.179 34.6135i 0.309041 0.0828074i
\(419\) 198.025 + 114.330i 0.472613 + 0.272863i 0.717333 0.696731i \(-0.245363\pi\)
−0.244720 + 0.969594i \(0.578696\pi\)
\(420\) −1.85386 1.28036i −0.00441394 0.00304847i
\(421\) 204.894 + 354.887i 0.486684 + 0.842961i 0.999883 0.0153086i \(-0.00487306\pi\)
−0.513199 + 0.858270i \(0.671540\pi\)
\(422\) 340.999 340.999i 0.808055 0.808055i
\(423\) 415.599 + 18.3205i 0.982504 + 0.0433108i
\(424\) 177.274i 0.418098i
\(425\) −287.671 + 385.414i −0.676873 + 0.906856i
\(426\) 64.2230 416.681i 0.150758 0.978125i
\(427\) −0.0950727 0.354816i −0.000222653 0.000830951i
\(428\) −44.0644 + 11.8070i −0.102954 + 0.0275865i
\(429\) −227.256 + 283.034i −0.529735 + 0.659752i
\(430\) −112.566 54.5831i −0.261781 0.126937i
\(431\) 46.4787 0.107839 0.0539196 0.998545i \(-0.482829\pi\)
0.0539196 + 0.998545i \(0.482829\pi\)
\(432\) 355.559 404.922i 0.823053 0.937319i
\(433\) −430.638 430.638i −0.994544 0.994544i 0.00544093 0.999985i \(-0.498268\pi\)
−0.999985 + 0.00544093i \(0.998268\pi\)
\(434\) 2.45572 1.41781i 0.00565834 0.00326684i
\(435\) −84.0895 + 71.4879i −0.193309 + 0.164340i
\(436\) −123.504 + 213.916i −0.283266 + 0.490632i
\(437\) −68.1545 254.356i −0.155960 0.582050i
\(438\) −466.359 + 341.798i −1.06475 + 0.780360i
\(439\) −335.332 + 193.604i −0.763855 + 0.441012i −0.830678 0.556753i \(-0.812047\pi\)
0.0668232 + 0.997765i \(0.478714\pi\)
\(440\) 203.061 + 38.9885i 0.461502 + 0.0886101i
\(441\) 420.494 + 132.775i 0.953500 + 0.301078i
\(442\) −443.397 + 443.397i −1.00316 + 1.00316i
\(443\) 189.882 708.648i 0.428627 1.59966i −0.327247 0.944939i \(-0.606121\pi\)
0.755874 0.654717i \(-0.227212\pi\)
\(444\) −122.190 314.407i −0.275203 0.708124i
\(445\) −295.031 + 21.3099i −0.662990 + 0.0478874i
\(446\) −119.241 + 206.531i −0.267357 + 0.463075i
\(447\) 32.1164 72.9486i 0.0718489 0.163196i
\(448\) 0.0100292 0.0374297i 2.23867e−5 8.35483e-5i
\(449\) 141.098i 0.314250i −0.987579 0.157125i \(-0.949777\pi\)
0.987579 0.157125i \(-0.0502226\pi\)
\(450\) 557.633 56.0371i 1.23918 0.124527i
\(451\) −576.139 −1.27747
\(452\) −78.9577 21.1566i −0.174685 0.0468067i
\(453\) −238.300 + 174.652i −0.526048 + 0.385544i
\(454\) 710.657 + 410.298i 1.56532 + 0.903740i
\(455\) 0.321190 + 4.44681i 0.000705913 + 0.00977321i
\(456\) 60.7582 + 48.7846i 0.133242 + 0.106984i
\(457\) −709.254 190.044i −1.55198 0.415851i −0.621865 0.783124i \(-0.713625\pi\)
−0.930113 + 0.367273i \(0.880291\pi\)
\(458\) 732.678 + 732.678i 1.59973 + 1.59973i
\(459\) 465.699 + 230.023i 1.01460 + 0.501139i
\(460\) −94.2412 + 490.830i −0.204872 + 1.06702i
\(461\) −321.041 556.060i −0.696402 1.20620i −0.969706 0.244275i \(-0.921450\pi\)
0.273304 0.961928i \(-0.411883\pi\)
\(462\) −4.67984 + 0.511530i −0.0101295 + 0.00110721i
\(463\) 268.091 71.8346i 0.579029 0.155150i 0.0425948 0.999092i \(-0.486438\pi\)
0.536434 + 0.843942i \(0.319771\pi\)
\(464\) 127.178 + 73.4265i 0.274091 + 0.158247i
\(465\) −84.1940 + 236.043i −0.181062 + 0.507619i
\(466\) −38.7861 67.1795i −0.0832320 0.144162i
\(467\) −57.4439 + 57.4439i −0.123006 + 0.123006i −0.765930 0.642924i \(-0.777721\pi\)
0.642924 + 0.765930i \(0.277721\pi\)
\(468\) 259.366 + 11.4334i 0.554202 + 0.0244304i
\(469\) 3.37981i 0.00720642i
\(470\) 251.170 517.983i 0.534404 1.10209i
\(471\) −482.900 + 187.673i −1.02526 + 0.398456i
\(472\) 21.8565 + 81.5694i 0.0463061 + 0.172817i
\(473\) −89.7086 + 24.0373i −0.189659 + 0.0508189i
\(474\) −128.055 329.497i −0.270157 0.695140i
\(475\) 20.8631 + 143.669i 0.0439223 + 0.302461i
\(476\) −2.88948 −0.00607034
\(477\) −300.766 191.787i −0.630536 0.402068i
\(478\) −544.139 544.139i −1.13837 1.13837i
\(479\) 419.328 242.099i 0.875423 0.505426i 0.00627671 0.999980i \(-0.498002\pi\)
0.869147 + 0.494554i \(0.164669\pi\)
\(480\) −204.513 431.301i −0.426069 0.898544i
\(481\) −333.749 + 578.071i −0.693866 + 1.20181i
\(482\) −16.5771 61.8668i −0.0343924 0.128354i
\(483\) 1.00721 + 9.21467i 0.00208532 + 0.0190780i
\(484\) 67.7979 39.1431i 0.140078 0.0808742i
\(485\) 146.653 763.803i 0.302378 1.57485i
\(486\) −168.763 581.274i −0.347250 1.19604i
\(487\) −162.179 + 162.179i −0.333017 + 0.333017i −0.853731 0.520714i \(-0.825666\pi\)
0.520714 + 0.853731i \(0.325666\pi\)
\(488\) 6.24069 23.2906i 0.0127883 0.0477266i
\(489\) −172.876 + 215.306i −0.353530 + 0.440299i
\(490\) 399.272 461.440i 0.814840 0.941715i
\(491\) −395.023 + 684.199i −0.804527 + 1.39348i 0.112083 + 0.993699i \(0.464248\pi\)
−0.916610 + 0.399783i \(0.869086\pi\)
\(492\) 243.597 + 332.371i 0.495116 + 0.675550i
\(493\) −36.6356 + 136.726i −0.0743115 + 0.277334i
\(494\) 189.285i 0.383168i
\(495\) 285.833 302.336i 0.577441 0.610780i
\(496\) 333.448 0.672274
\(497\) −3.71340 0.995002i −0.00747163 0.00200202i
\(498\) 425.009 + 187.115i 0.853433 + 0.375733i
\(499\) −422.362 243.851i −0.846418 0.488680i 0.0130228 0.999915i \(-0.495855\pi\)
−0.859441 + 0.511236i \(0.829188\pi\)
\(500\) 83.3443 262.636i 0.166689 0.525272i
\(501\) −558.597 + 217.091i −1.11496 + 0.433316i
\(502\) 663.754 + 177.852i 1.32222 + 0.354288i
\(503\) 346.274 + 346.274i 0.688418 + 0.688418i 0.961882 0.273465i \(-0.0881696\pi\)
−0.273465 + 0.961882i \(0.588170\pi\)
\(504\) −1.85222 2.02305i −0.00367504 0.00401399i
\(505\) −228.504 + 154.891i −0.452483 + 0.306714i
\(506\) 522.164 + 904.415i 1.03194 + 1.78738i
\(507\) −3.98806 5.44143i −0.00786600 0.0107326i
\(508\) 457.078 122.474i 0.899760 0.241090i
\(509\) 362.182 + 209.106i 0.711557 + 0.410818i 0.811637 0.584162i \(-0.198577\pi\)
−0.100080 + 0.994979i \(0.531910\pi\)
\(510\) 547.615 465.550i 1.07376 0.912843i
\(511\) 2.63618 + 4.56599i 0.00515886 + 0.00893540i
\(512\) −196.607 + 196.607i −0.383998 + 0.383998i
\(513\) 148.501 50.3049i 0.289476 0.0980603i
\(514\) 15.9365i 0.0310049i
\(515\) 149.836 + 431.937i 0.290943 + 0.838712i
\(516\) 51.7966 + 41.5891i 0.100381 + 0.0805990i
\(517\) −110.610 412.804i −0.213947 0.798460i
\(518\) −8.36225 + 2.24066i −0.0161433 + 0.00432559i
\(519\) −102.525 15.8022i −0.197543 0.0304473i
\(520\) −127.688 + 263.329i −0.245554 + 0.506403i
\(521\) −17.3149 −0.0332341 −0.0166170 0.999862i \(-0.505290\pi\)
−0.0166170 + 0.999862i \(0.505290\pi\)
\(522\) 146.344 76.1036i 0.280352 0.145792i
\(523\) 577.571 + 577.571i 1.10434 + 1.10434i 0.993880 + 0.110462i \(0.0352329\pi\)
0.110462 + 0.993880i \(0.464767\pi\)
\(524\) −2.86905 + 1.65645i −0.00547529 + 0.00316116i
\(525\) 0.0445528 5.11022i 8.48625e−5 0.00973375i
\(526\) 264.640 458.370i 0.503118 0.871427i
\(527\) 83.1855 + 310.453i 0.157847 + 0.589094i
\(528\) −506.662 223.064i −0.959587 0.422469i
\(529\) 1322.68 763.649i 2.50034 1.44357i
\(530\) −408.594 + 276.964i −0.770932 + 0.522574i
\(531\) 162.038 + 51.1652i 0.305156 + 0.0963564i
\(532\) −0.616757 + 0.616757i −0.00115932 + 0.00115932i
\(533\) 211.053 787.659i 0.395971 1.47778i
\(534\) 436.916 + 67.3418i 0.818195 + 0.126108i
\(535\) −78.2488 67.7066i −0.146260 0.126554i
\(536\) 110.927 192.132i 0.206954 0.358455i
\(537\) −554.584 + 60.6189i −1.03274 + 0.112884i
\(538\) −225.023 + 839.797i −0.418258 + 1.56096i
\(539\) 453.003i 0.840451i
\(540\) −295.269 37.0648i −0.546794 0.0686386i
\(541\) 846.162 1.56407 0.782035 0.623234i \(-0.214182\pi\)
0.782035 + 0.623234i \(0.214182\pi\)
\(542\) −486.674 130.404i −0.897922 0.240598i
\(543\) 31.8754 + 291.618i 0.0587024 + 0.537050i
\(544\) −530.160 306.088i −0.974558 0.562661i
\(545\) −558.821 + 40.3633i −1.02536 + 0.0740611i
\(546\) 1.01500 6.58536i 0.00185897 0.0120611i
\(547\) 66.0385 + 17.6950i 0.120728 + 0.0323491i 0.318677 0.947863i \(-0.396761\pi\)
−0.197949 + 0.980212i \(0.563428\pi\)
\(548\) 108.876 + 108.876i 0.198678 + 0.198678i
\(549\) −32.7636 35.7854i −0.0596787 0.0651828i
\(550\) −227.389 528.944i −0.413435 0.961717i
\(551\) 21.3641 + 37.0038i 0.0387734 + 0.0671575i
\(552\) −245.174 + 556.884i −0.444156 + 1.00885i
\(553\) −3.11362 + 0.834291i −0.00563041 + 0.00150866i
\(554\) −523.410 302.191i −0.944784 0.545471i
\(555\) 434.805 629.562i 0.783433 1.13435i
\(556\) 135.327 + 234.392i 0.243393 + 0.421569i
\(557\) 367.003 367.003i 0.658893 0.658893i −0.296225 0.955118i \(-0.595728\pi\)
0.955118 + 0.296225i \(0.0957279\pi\)
\(558\) 201.372 315.797i 0.360881 0.565945i
\(559\) 131.449i 0.235151i
\(560\) −6.42411 + 2.22848i −0.0114716 + 0.00397942i
\(561\) 81.2835 527.370i 0.144890 0.940053i
\(562\) 180.716 + 674.443i 0.321560 + 1.20008i
\(563\) −303.953 + 81.4441i −0.539882 + 0.144661i −0.518448 0.855109i \(-0.673490\pi\)
−0.0214341 + 0.999770i \(0.506823\pi\)
\(564\) −191.377 + 238.348i −0.339320 + 0.422603i
\(565\) −60.7662 175.173i −0.107551 0.310041i
\(566\) −961.053 −1.69797
\(567\) −5.43620 + 0.953838i −0.00958765 + 0.00168225i
\(568\) −178.439 178.439i −0.314153 0.314153i
\(569\) −882.789 + 509.679i −1.55148 + 0.895745i −0.553453 + 0.832880i \(0.686690\pi\)
−0.998022 + 0.0628645i \(0.979976\pi\)
\(570\) 17.5167 216.259i 0.0307311 0.379402i
\(571\) 443.096 767.465i 0.776000 1.34407i −0.158231 0.987402i \(-0.550579\pi\)
0.934231 0.356669i \(-0.116088\pi\)
\(572\) −69.0296 257.622i −0.120681 0.450388i
\(573\) −330.092 + 241.927i −0.576076 + 0.422210i
\(574\) 9.15913 5.28803i 0.0159567 0.00921259i
\(575\) −1041.50 + 447.733i −1.81130 + 0.778667i
\(576\) −1.10569 4.99737i −0.00191960 0.00867600i
\(577\) 194.509 194.509i 0.337105 0.337105i −0.518172 0.855277i \(-0.673387\pi\)
0.855277 + 0.518172i \(0.173387\pi\)
\(578\) 52.2689 195.070i 0.0904307 0.337492i
\(579\) 100.372 + 258.267i 0.173354 + 0.446058i
\(580\) −5.84243 80.8871i −0.0100732 0.139461i
\(581\) 2.11722 3.66713i 0.00364409 0.00631175i
\(582\) −468.361 + 1063.83i −0.804745 + 1.82788i
\(583\) −94.8452 + 353.967i −0.162685 + 0.607147i
\(584\) 346.084i 0.592609i
\(585\) 308.627 + 501.526i 0.527568 + 0.857309i
\(586\) 105.225 0.179565
\(587\) −775.720 207.853i −1.32150 0.354095i −0.471960 0.881620i \(-0.656453\pi\)
−0.849539 + 0.527526i \(0.823120\pi\)
\(588\) −261.334 + 191.534i −0.444446 + 0.325738i
\(589\) 84.0216 + 48.5099i 0.142651 + 0.0823598i
\(590\) 153.860 177.817i 0.260780 0.301384i
\(591\) 564.457 + 453.220i 0.955089 + 0.766870i
\(592\) −983.338 263.485i −1.66104 0.445075i
\(593\) 572.308 + 572.308i 0.965106 + 0.965106i 0.999411 0.0343049i \(-0.0109217\pi\)
−0.0343049 + 0.999411i \(0.510922\pi\)
\(594\) −517.234 + 345.133i −0.870764 + 0.581032i
\(595\) −3.67743 5.42516i −0.00618055 0.00911791i
\(596\) 29.2830 + 50.7197i 0.0491326 + 0.0851001i
\(597\) 108.612 11.8718i 0.181930 0.0198858i
\(598\) −1427.74 + 382.561i −2.38752 + 0.639734i
\(599\) 263.198 + 151.957i 0.439396 + 0.253685i 0.703341 0.710852i \(-0.251691\pi\)
−0.263945 + 0.964538i \(0.585024\pi\)
\(600\) 170.253 289.038i 0.283755 0.481730i
\(601\) −52.0948 90.2308i −0.0866801 0.150134i 0.819426 0.573185i \(-0.194292\pi\)
−0.906106 + 0.423051i \(0.860959\pi\)
\(602\) 1.20551 1.20551i 0.00200251 0.00200251i
\(603\) −205.966 396.063i −0.341568 0.656821i
\(604\) 217.090i 0.359420i
\(605\) 159.779 + 77.4770i 0.264098 + 0.128061i
\(606\) 384.544 149.448i 0.634561 0.246614i
\(607\) 75.9472 + 283.439i 0.125119 + 0.466950i 0.999844 0.0176696i \(-0.00562469\pi\)
−0.874725 + 0.484620i \(0.838958\pi\)
\(608\) −178.496 + 47.8279i −0.293579 + 0.0786642i
\(609\) −0.544848 1.40195i −0.000894660 0.00230205i
\(610\) −63.4321 + 22.0041i −0.103987 + 0.0360723i
\(611\) 604.878 0.989980
\(612\) −338.604 + 176.085i −0.553274 + 0.287721i
\(613\) 610.767 + 610.767i 0.996357 + 0.996357i 0.999993 0.00363596i \(-0.00115736\pi\)
−0.00363596 + 0.999993i \(0.501157\pi\)
\(614\) −259.645 + 149.906i −0.422874 + 0.244147i
\(615\) −314.019 + 880.372i −0.510601 + 1.43150i
\(616\) −1.40891 + 2.44030i −0.00228719 + 0.00396152i
\(617\) −260.666 972.818i −0.422473 1.57669i −0.769381 0.638791i \(-0.779435\pi\)
0.346908 0.937899i \(-0.387232\pi\)
\(618\) −74.2429 679.226i −0.120134 1.09907i
\(619\) 189.444 109.376i 0.306049 0.176697i −0.339108 0.940747i \(-0.610125\pi\)
0.645157 + 0.764050i \(0.276792\pi\)
\(620\) −103.321 152.425i −0.166646 0.245847i
\(621\) 679.572 + 1018.44i 1.09432 + 1.64000i
\(622\) 799.956 799.956i 1.28610 1.28610i
\(623\) 1.04332 3.89373i 0.00167467 0.00624997i
\(624\) 490.560 610.962i 0.786154 0.979106i
\(625\) 599.185 177.772i 0.958695 0.284435i
\(626\) 370.048 640.942i 0.591131 1.02387i
\(627\) −95.2166 129.916i −0.151861 0.207203i
\(628\) 98.5271 367.708i 0.156890 0.585523i
\(629\) 981.257i 1.56003i
\(630\) −1.76906 + 7.42986i −0.00280803 + 0.0117934i
\(631\) −427.714 −0.677835 −0.338917 0.940816i \(-0.610061\pi\)
−0.338917 + 0.940816i \(0.610061\pi\)
\(632\) −204.382 54.7639i −0.323389 0.0866517i
\(633\) −531.582 234.035i −0.839782 0.369724i
\(634\) 190.711 + 110.107i 0.300805 + 0.173670i
\(635\) 811.672 + 702.317i 1.27822 + 1.10601i
\(636\) 244.303 94.9450i 0.384124 0.149285i
\(637\) 619.316 + 165.945i 0.972239 + 0.260511i
\(638\) −119.823 119.823i −0.187810 0.187810i
\(639\) −495.790 + 109.695i −0.775884 + 0.171667i
\(640\) −631.982 121.343i −0.987472 0.189598i
\(641\) −256.912 444.984i −0.400798 0.694203i 0.593024 0.805185i \(-0.297934\pi\)
−0.993822 + 0.110982i \(0.964600\pi\)
\(642\) 91.4165 + 124.731i 0.142393 + 0.194286i
\(643\) 187.988 50.3713i 0.292361 0.0783379i −0.109657 0.993969i \(-0.534975\pi\)
0.402019 + 0.915632i \(0.368309\pi\)
\(644\) −5.89858 3.40555i −0.00915929 0.00528812i
\(645\) −12.1645 + 150.181i −0.0188597 + 0.232839i
\(646\) −139.129 240.979i −0.215371 0.373033i
\(647\) −139.726 + 139.726i −0.215960 + 0.215960i −0.806794 0.590833i \(-0.798799\pi\)
0.590833 + 0.806794i \(0.298799\pi\)
\(648\) −340.337 124.197i −0.525211 0.191661i
\(649\) 174.565i 0.268976i
\(650\) 806.436 117.108i 1.24067 0.180166i
\(651\) −2.66304 2.13824i −0.00409070 0.00328455i
\(652\) −52.5114 195.975i −0.0805390 0.300576i
\(653\) 622.466 166.789i 0.953240 0.255420i 0.251503 0.967856i \(-0.419075\pi\)
0.701737 + 0.712437i \(0.252408\pi\)
\(654\) 827.568 + 127.553i 1.26539 + 0.195035i
\(655\) −6.76150 3.27865i −0.0103229 0.00500557i
\(656\) 1243.66 1.89583
\(657\) 587.172 + 374.417i 0.893716 + 0.569888i
\(658\) 5.54730 + 5.54730i 0.00843054 + 0.00843054i
\(659\) −210.200 + 121.359i −0.318968 + 0.184156i −0.650932 0.759136i \(-0.725622\pi\)
0.331965 + 0.943292i \(0.392289\pi\)
\(660\) 55.0258 + 300.722i 0.0833725 + 0.455639i
\(661\) −331.364 + 573.939i −0.501307 + 0.868288i 0.498692 + 0.866779i \(0.333814\pi\)
−0.999999 + 0.00150927i \(0.999520\pi\)
\(662\) 287.723 + 1073.80i 0.434627 + 1.62205i
\(663\) 691.210 + 304.313i 1.04255 + 0.458994i
\(664\) 240.715 138.977i 0.362522 0.209302i
\(665\) −1.94294 0.373051i −0.00292171 0.000560979i
\(666\) −843.384 + 772.167i −1.26634 + 1.15941i
\(667\) −235.933 + 235.933i −0.353722 + 0.353722i
\(668\) 113.972 425.349i 0.170617 0.636750i
\(669\) 283.877 + 43.7540i 0.424331 + 0.0654021i
\(670\) −616.149 + 44.5041i −0.919625 + 0.0664240i
\(671\) −24.9219 + 43.1660i −0.0371414 + 0.0643308i
\(672\) 6.46646 0.706817i 0.00962271 0.00105181i
\(673\) 125.305 467.643i 0.186188 0.694864i −0.808185 0.588929i \(-0.799550\pi\)
0.994373 0.105935i \(-0.0337835\pi\)
\(674\) 72.9670i 0.108260i
\(675\) −306.196 601.556i −0.453624 0.891193i
\(676\) 4.95712 0.00733302
\(677\) 425.004 + 113.880i 0.627776 + 0.168212i 0.558660 0.829397i \(-0.311316\pi\)
0.0691156 + 0.997609i \(0.477982\pi\)
\(678\) 30.1094 + 275.462i 0.0444091 + 0.406286i
\(679\) 9.17906 + 5.29953i 0.0135185 + 0.00780490i
\(680\) −30.9936 429.099i −0.0455788 0.631028i
\(681\) 150.554 976.798i 0.221077 1.43436i
\(682\) −371.658 99.5854i −0.544953 0.146020i
\(683\) −336.034 336.034i −0.491998 0.491998i 0.416938 0.908935i \(-0.363103\pi\)
−0.908935 + 0.416938i \(0.863103\pi\)
\(684\) −34.6894 + 109.860i −0.0507155 + 0.160614i
\(685\) −65.8544 + 342.985i −0.0961379 + 0.500708i
\(686\) 8.31607 + 14.4039i 0.0121226 + 0.0209969i
\(687\) 502.853 1142.17i 0.731954 1.66254i
\(688\) 193.647 51.8875i 0.281463 0.0754179i
\(689\) −449.177 259.332i −0.651926 0.376389i
\(690\) 1666.60 304.953i 2.41536 0.441960i
\(691\) −465.054 805.496i −0.673015 1.16570i −0.977045 0.213034i \(-0.931665\pi\)
0.304029 0.952663i \(-0.401668\pi\)
\(692\) 53.8977 53.8977i 0.0778869 0.0778869i
\(693\) 2.61600 + 5.03045i 0.00377489 + 0.00725895i
\(694\) 841.075i 1.21192i
\(695\) −267.855 + 552.393i −0.385403 + 0.794810i
\(696\) 15.0398 97.5786i 0.0216089 0.140199i
\(697\) 310.258 + 1157.90i 0.445134 + 1.66126i
\(698\) 143.053 38.3309i 0.204947 0.0549153i
\(699\) −58.4944 + 72.8512i −0.0836830 + 0.104222i
\(700\) 3.00923 + 2.24607i 0.00429889 + 0.00320867i
\(701\) −1057.58 −1.50868 −0.754338 0.656486i \(-0.772042\pi\)
−0.754338 + 0.656486i \(0.772042\pi\)
\(702\) −282.369 833.559i −0.402235 1.18741i
\(703\) −209.448 209.448i −0.297935 0.297935i
\(704\) −4.55359 + 2.62902i −0.00646817 + 0.00373440i
\(705\) −691.075 55.9762i −0.980248 0.0793989i
\(706\) −663.280 + 1148.83i −0.939490 + 1.62724i
\(707\) −0.973672 3.63379i −0.00137719 0.00513974i
\(708\) −100.706 + 73.8079i −0.142240 + 0.104248i
\(709\) −450.749 + 260.240i −0.635754 + 0.367053i −0.782977 0.622051i \(-0.786300\pi\)
0.147223 + 0.989103i \(0.452966\pi\)
\(710\) −132.495 + 690.065i −0.186613 + 0.971922i
\(711\) −314.027 + 287.510i −0.441670 + 0.404374i
\(712\) 187.104 187.104i 0.262787 0.262787i
\(713\) −196.085 + 731.800i −0.275014 + 1.02637i
\(714\) 3.54821 + 9.12988i 0.00496948 + 0.0127870i
\(715\) 395.845 457.481i 0.553630 0.639833i
\(716\) 204.962 355.005i 0.286260 0.495817i
\(717\) −373.455 + 848.257i −0.520857 + 1.18306i
\(718\) −220.607 + 823.316i −0.307252 + 1.14668i
\(719\) 1211.89i 1.68553i −0.538285 0.842763i \(-0.680928\pi\)
0.538285 0.842763i \(-0.319072\pi\)
\(720\) −617.006 + 652.629i −0.856953 + 0.906430i
\(721\) −6.23044 −0.00864139
\(722\) 787.424 + 210.990i 1.09062 + 0.292230i
\(723\) −62.2198 + 45.6013i −0.0860578 + 0.0630724i
\(724\) −186.673 107.776i −0.257836 0.148862i
\(725\) 144.434 113.914i 0.199220 0.157123i
\(726\) −206.934 166.154i −0.285034 0.228862i
\(727\) −201.292 53.9360i −0.276880 0.0741899i 0.117707 0.993048i \(-0.462446\pi\)
−0.394587 + 0.918859i \(0.629112\pi\)
\(728\) −2.82010 2.82010i −0.00387377 0.00387377i
\(729\) −578.914 + 443.057i −0.794120 + 0.607761i
\(730\) 797.680 540.705i 1.09271 0.740692i
\(731\) 96.6185 + 167.348i 0.132173 + 0.228930i
\(732\) 35.4394 3.87371i 0.0484145 0.00529195i
\(733\) 707.621 189.606i 0.965376 0.258672i 0.258502 0.966011i \(-0.416771\pi\)
0.706874 + 0.707339i \(0.250105\pi\)
\(734\) 793.936 + 458.379i 1.08166 + 0.624495i
\(735\) −692.214 246.905i −0.941788 0.335926i
\(736\) −721.511 1249.69i −0.980313 1.69795i
\(737\) −324.286 + 324.286i −0.440009 + 0.440009i
\(738\) 751.059 1177.83i 1.01770 1.59598i
\(739\) 1243.93i 1.68326i 0.540056 + 0.841629i \(0.318403\pi\)
−0.540056 + 0.841629i \(0.681597\pi\)
\(740\) 184.250 + 531.144i 0.248986 + 0.717762i
\(741\) 212.493 82.5827i 0.286766 0.111448i
\(742\) −1.74105 6.49769i −0.00234643 0.00875700i
\(743\) −1239.64 + 332.161i −1.66843 + 0.447054i −0.964687 0.263400i \(-0.915156\pi\)
−0.703743 + 0.710455i \(0.748489\pi\)
\(744\) −81.2077 208.955i −0.109150 0.280854i
\(745\) −57.9606 + 119.531i −0.0777995 + 0.160444i
\(746\) −829.060 −1.11134
\(747\) 24.6311 558.755i 0.0329733 0.747999i
\(748\) 277.240 + 277.240i 0.370642 + 0.370642i
\(749\) 1.22121 0.705066i 0.00163045 0.000941343i
\(750\) −932.194 + 59.1673i −1.24292 + 0.0788897i
\(751\) −470.274 + 814.539i −0.626198 + 1.08461i 0.362110 + 0.932135i \(0.382056\pi\)
−0.988308 + 0.152471i \(0.951277\pi\)
\(752\) 238.766 + 891.087i 0.317508 + 1.18496i
\(753\) −89.9287 822.731i −0.119427 1.09260i
\(754\) 207.708 119.920i 0.275474 0.159045i
\(755\) 407.598 276.289i 0.539865 0.365946i
\(756\) 1.79597 3.63608i 0.00237562 0.00480963i
\(757\) 872.169 872.169i 1.15214 1.15214i 0.166015 0.986123i \(-0.446910\pi\)
0.986123 0.166015i \(-0.0530901\pi\)
\(758\) −131.321 + 490.097i −0.173247 + 0.646566i
\(759\) 787.490 980.770i 1.03754 1.29219i
\(760\) −98.2063 84.9752i −0.129219 0.111809i
\(761\) −229.806 + 398.036i −0.301979 + 0.523043i −0.976584 0.215136i \(-0.930981\pi\)
0.674605 + 0.738179i \(0.264314\pi\)
\(762\) −948.260 1293.83i −1.24444 1.69794i
\(763\) 1.97617 7.37515i 0.00259000 0.00966599i
\(764\) 300.712i 0.393602i
\(765\) −761.548 411.644i −0.995488 0.538097i
\(766\) 51.5397 0.0672842
\(767\) 238.655 + 63.9473i 0.311153 + 0.0833733i
\(768\) 873.980 + 384.779i 1.13799 + 0.501015i
\(769\) −775.372 447.661i −1.00829 0.582134i −0.0975969 0.995226i \(-0.531116\pi\)
−0.910689 + 0.413092i \(0.864449\pi\)
\(770\) 7.82580 0.565253i 0.0101634 0.000734094i
\(771\) 17.8905 6.95289i 0.0232042 0.00901802i
\(772\) −196.660 52.6949i −0.254741 0.0682576i
\(773\) 94.0446 + 94.0446i 0.121662 + 0.121662i 0.765316 0.643654i \(-0.222583\pi\)
−0.643654 + 0.765316i \(0.722583\pi\)
\(774\) 67.8039 214.732i 0.0876020 0.277431i
\(775\) 154.690 387.981i 0.199600 0.500620i
\(776\) 347.868 + 602.524i 0.448283 + 0.776449i
\(777\) 6.16372 + 8.40996i 0.00793272 + 0.0108236i
\(778\) 445.730 119.433i 0.572918 0.153513i
\(779\) 313.377 + 180.928i 0.402281 + 0.232257i
\(780\) −431.285 34.9335i −0.552929 0.0447866i
\(781\) 260.825 + 451.762i 0.333963 + 0.578441i
\(782\) 1536.46 1536.46i 1.96479 1.96479i
\(783\) −149.283 131.084i −0.190655 0.167412i
\(784\) 977.861i 1.24727i
\(785\) 815.787 282.990i 1.03922 0.360497i
\(786\) 8.75699 + 7.03126i 0.0111412 + 0.00894562i
\(787\) −241.144 899.963i −0.306410 1.14354i −0.931725 0.363164i \(-0.881696\pi\)
0.625315 0.780372i \(-0.284970\pi\)
\(788\) −513.778 + 137.666i −0.652003 + 0.174704i
\(789\) −630.030 97.1064i −0.798517 0.123075i
\(790\) 193.093 + 556.635i 0.244421 + 0.704602i
\(791\) 2.52677 0.00319440
\(792\) −16.3908 + 371.825i −0.0206955 + 0.469476i
\(793\) −49.8843 49.8843i −0.0629058 0.0629058i
\(794\) −721.400 + 416.501i −0.908565 + 0.524560i
\(795\) 489.187 + 337.855i 0.615330 + 0.424975i
\(796\) −40.1407 + 69.5257i −0.0504280 + 0.0873438i
\(797\) −43.8496 163.649i −0.0550183 0.205331i 0.932945 0.360019i \(-0.117230\pi\)
−0.987963 + 0.154687i \(0.950563\pi\)
\(798\) 2.70612 + 1.19140i 0.00339113 + 0.00149298i
\(799\) −770.071 + 444.601i −0.963793 + 0.556446i
\(800\) 314.200 + 730.879i 0.392750 + 0.913599i
\(801\) −115.022 519.866i −0.143598 0.649022i
\(802\) −119.900 + 119.900i −0.149502 + 0.149502i
\(803\) 185.162 691.034i 0.230588 0.860565i
\(804\) 324.190 + 49.9674i 0.403222 + 0.0621485i
\(805\) −1.11299 15.4091i −0.00138260 0.0191418i
\(806\) 272.293 471.626i 0.337833 0.585144i
\(807\) 1040.94 113.780i 1.28989 0.140991i
\(808\) 63.9130 238.527i 0.0791003 0.295206i
\(809\) 1540.82i 1.90459i 0.305175 + 0.952296i \(0.401285\pi\)
−0.305175 + 0.952296i \(0.598715\pi\)
\(810\) 245.469 + 978.474i 0.303048 + 1.20799i
\(811\) −895.419 −1.10409 −0.552046 0.833813i \(-0.686153\pi\)
−0.552046 + 0.833813i \(0.686153\pi\)
\(812\) 1.06752 + 0.286042i 0.00131469 + 0.000352269i
\(813\) 65.9370 + 603.238i 0.0811033 + 0.741990i
\(814\) 1017.33 + 587.355i 1.24979 + 0.721566i
\(815\) 301.123 348.010i 0.369476 0.427006i
\(816\) −175.460 + 1138.39i −0.215025 + 1.39509i
\(817\) 56.3434 + 15.0972i 0.0689637 + 0.0184788i
\(818\) −664.048 664.048i −0.811795 0.811795i
\(819\) −7.83561 + 1.73366i −0.00956729 + 0.00211680i
\(820\) −385.357 568.501i −0.469947 0.693294i
\(821\) −322.268 558.185i −0.392531 0.679884i 0.600251 0.799811i \(-0.295067\pi\)
−0.992783 + 0.119927i \(0.961734\pi\)
\(822\) 210.317 477.710i 0.255860 0.581156i
\(823\) 211.257 56.6061i 0.256691 0.0687802i −0.128179 0.991751i \(-0.540913\pi\)
0.384870 + 0.922971i \(0.374246\pi\)
\(824\) −354.182 204.487i −0.429832 0.248164i
\(825\) −494.590 + 486.041i −0.599504 + 0.589141i
\(826\) 1.60223 + 2.77514i 0.00193975 + 0.00335974i
\(827\) −982.768 + 982.768i −1.18835 + 1.18835i −0.210831 + 0.977522i \(0.567617\pi\)
−0.977522 + 0.210831i \(0.932383\pi\)
\(828\) −898.759 39.6191i −1.08546 0.0478492i
\(829\) 763.031i 0.920424i 0.887809 + 0.460212i \(0.152227\pi\)
−0.887809 + 0.460212i \(0.847773\pi\)
\(830\) −696.406 337.687i −0.839044 0.406852i
\(831\) −110.885 + 719.427i −0.133436 + 0.865736i
\(832\) −1.92614 7.18844i −0.00231507 0.00863996i
\(833\) −910.427 + 243.948i −1.09295 + 0.292855i
\(834\) 574.431 715.418i 0.688766 0.857816i
\(835\) 943.667 327.351i 1.13014 0.392037i
\(836\) 118.353 0.141571
\(837\) −442.373 88.2834i −0.528522 0.105476i
\(838\) 402.737 + 402.737i 0.480593 + 0.480593i
\(839\) 946.477 546.449i 1.12810 0.651309i 0.184644 0.982805i \(-0.440887\pi\)
0.943457 + 0.331496i \(0.107553\pi\)
\(840\) 2.96100 + 3.48295i 0.00352500 + 0.00414637i
\(841\) −393.430 + 681.440i −0.467812 + 0.810274i
\(842\) 264.182 + 985.940i 0.313755 + 1.17095i
\(843\) 678.291 497.125i 0.804616 0.589709i
\(844\) 369.598 213.388i 0.437913 0.252829i
\(845\) 6.30890 + 9.30726i 0.00746615 + 0.0110145i
\(846\) 988.112 + 312.007i 1.16798 + 0.368803i
\(847\) −1.71114 + 1.71114i −0.00202024 + 0.00202024i
\(848\) 204.735 764.080i 0.241432 0.901038i
\(849\) 419.295 + 1078.89i 0.493870 + 1.27077i
\(850\) −940.598 + 741.842i −1.10659 + 0.872755i
\(851\) 1156.51 2003.14i 1.35900 2.35386i
\(852\) 150.339 341.478i 0.176455 0.400795i
\(853\) 425.510 1588.02i 0.498839 1.86169i −0.00853057 0.999964i \(-0.502715\pi\)
0.507369 0.861729i \(-0.330618\pi\)
\(854\) 0.914971i 0.00107140i
\(855\) −250.417 + 74.6866i −0.292885 + 0.0873527i
\(856\) 92.5628 0.108134
\(857\) −318.230 85.2695i −0.371330 0.0994977i 0.0683276 0.997663i \(-0.478234\pi\)
−0.439658 + 0.898165i \(0.644900\pi\)
\(858\) −729.240 + 534.465i −0.849930 + 0.622920i
\(859\) −1361.73 786.197i −1.58525 0.915247i −0.994074 0.108707i \(-0.965329\pi\)
−0.591180 0.806540i \(-0.701338\pi\)
\(860\) −83.7213 72.4417i −0.0973503 0.0842346i
\(861\) −9.93239 7.97502i −0.0115359 0.00926251i
\(862\) 111.827 + 29.9639i 0.129729 + 0.0347609i
\(863\) 458.505 + 458.505i 0.531292 + 0.531292i 0.920957 0.389665i \(-0.127409\pi\)
−0.389665 + 0.920957i \(0.627409\pi\)
\(864\) 714.698 476.895i 0.827197 0.551961i
\(865\) 169.791 + 32.6006i 0.196290 + 0.0376885i
\(866\) −758.481 1313.73i −0.875844 1.51701i
\(867\) −241.792 + 26.4291i −0.278883 + 0.0304834i
\(868\) 2.42395 0.649494i 0.00279256 0.000748265i
\(869\) 378.794 + 218.697i 0.435897 + 0.251665i
\(870\) −248.404 + 117.788i −0.285522 + 0.135388i
\(871\) −324.550 562.137i −0.372618 0.645393i
\(872\) 354.396 354.396i 0.406418 0.406418i
\(873\) 1398.60 + 61.6532i 1.60206 + 0.0706222i
\(874\) 655.913i 0.750472i
\(875\) −0.387295 + 8.50854i −0.000442622 + 0.00972405i
\(876\) −476.941 + 185.357i −0.544454 + 0.211595i
\(877\) 279.129 + 1041.72i 0.318277 + 1.18783i 0.920900 + 0.389800i \(0.127456\pi\)
−0.602623 + 0.798026i \(0.705878\pi\)
\(878\) −931.615 + 249.625i −1.06106 + 0.284311i
\(879\) −45.9083 118.127i −0.0522279 0.134387i
\(880\) 830.199 + 402.564i 0.943408 + 0.457459i
\(881\) 1585.15 1.79927 0.899633 0.436647i \(-0.143834\pi\)
0.899633 + 0.436647i \(0.143834\pi\)
\(882\) 926.101 + 590.539i 1.05000 + 0.669545i
\(883\) −1004.45 1004.45i −1.13755 1.13755i −0.988889 0.148657i \(-0.952505\pi\)
−0.148657 0.988889i \(-0.547495\pi\)
\(884\) −480.584 + 277.466i −0.543648 + 0.313875i
\(885\) −266.746 95.1454i −0.301408 0.107509i
\(886\) 913.702 1582.58i 1.03127 1.78621i
\(887\) 81.0299 + 302.408i 0.0913528 + 0.340933i 0.996441 0.0842901i \(-0.0268622\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(888\) 74.3688 + 680.378i 0.0837487 + 0.766191i
\(889\) −12.6676 + 7.31362i −0.0142492 + 0.00822680i
\(890\) −723.576 138.929i −0.813006 0.156100i
\(891\) 613.112 + 430.074i 0.688117 + 0.482687i
\(892\) −149.235 + 149.235i −0.167304 + 0.167304i
\(893\) −69.4713 + 259.270i −0.0777954 + 0.290336i
\(894\) 124.300 154.808i 0.139038 0.173163i
\(895\) 927.395 66.9852i 1.03620 0.0748438i
\(896\) 4.38491 7.59489i 0.00489387 0.00847644i
\(897\) 1052.37 + 1435.88i 1.17321 + 1.60076i
\(898\) 90.9632 339.479i 0.101295 0.378039i
\(899\) 122.932i 0.136743i
\(900\) 489.511 + 79.8233i 0.543902 + 0.0886926i
\(901\) 762.464 0.846242
\(902\) −1386.18 371.425i −1.53678 0.411779i
\(903\) −1.87927 0.827369i −0.00208114 0.000916245i
\(904\) 143.639 + 82.9302i 0.158893 + 0.0917370i
\(905\) −35.2230 487.655i −0.0389205 0.538845i
\(906\) −685.938 + 266.581i −0.757106 + 0.294239i
\(907\) −357.992 95.9237i −0.394699 0.105759i 0.0560100 0.998430i \(-0.482162\pi\)
−0.450709 + 0.892671i \(0.648829\pi\)
\(908\) 513.506 + 513.506i 0.565536 + 0.565536i
\(909\) −335.543 366.490i −0.369134 0.403180i
\(910\) −2.09399 + 10.9060i −0.00230109 + 0.0119846i
\(911\) 490.084 + 848.851i 0.537963 + 0.931779i 0.999014 + 0.0444052i \(0.0141393\pi\)
−0.461051 + 0.887374i \(0.652527\pi\)
\(912\) 205.537 + 280.440i 0.225369 + 0.307500i
\(913\) −554.997 + 148.711i −0.607883 + 0.162882i
\(914\) −1583.93 914.484i −1.73297 1.00053i
\(915\) 52.3766 + 61.6093i 0.0572422 + 0.0673326i
\(916\) 458.489 + 794.127i 0.500534 + 0.866951i
\(917\) 0.0724117 0.0724117i 7.89659e−5 7.89659e-5i
\(918\) 972.172 + 853.657i 1.05901 + 0.929909i
\(919\) 1321.17i 1.43762i −0.695205 0.718811i \(-0.744687\pi\)
0.695205 0.718811i \(-0.255313\pi\)
\(920\) 442.467 912.491i 0.480942 0.991838i
\(921\) 281.565 + 226.077i 0.305717 + 0.245470i
\(922\) −413.938 1544.84i −0.448956 1.67553i
\(923\) −713.166 + 191.092i −0.772661 + 0.207034i
\(924\) −4.11759 0.634643i −0.00445626 0.000686843i
\(925\) −762.757 + 1021.92i −0.824602 + 1.10478i
\(926\) 691.330 0.746577
\(927\) −730.114 + 379.683i −0.787609 + 0.409583i
\(928\) 165.567 + 165.567i 0.178413 + 0.178413i
\(929\) 672.297 388.151i 0.723678 0.417816i −0.0924267 0.995719i \(-0.529462\pi\)
0.816105 + 0.577904i \(0.196129\pi\)
\(930\) −354.741 + 513.636i −0.381442 + 0.552297i
\(931\) −142.259 + 246.400i −0.152802 + 0.264662i
\(932\) −17.7678 66.3103i −0.0190642 0.0711484i
\(933\) −1247.05 549.027i −1.33660 0.588454i
\(934\) −175.242 + 101.176i −0.187625 + 0.108325i
\(935\) −167.691 + 873.376i −0.179349 + 0.934092i
\(936\) −502.331 158.616i −0.536678 0.169462i
\(937\) 295.586 295.586i 0.315459 0.315459i −0.531561 0.847020i \(-0.678394\pi\)
0.847020 + 0.531561i \(0.178394\pi\)
\(938\) 2.17890 8.13175i 0.00232292 0.00866925i
\(939\) −880.974 135.784i −0.938205 0.144605i
\(940\) 333.349 385.253i 0.354626 0.409843i
\(941\) −48.8020 + 84.5275i −0.0518618 + 0.0898273i −0.890791 0.454413i \(-0.849849\pi\)
0.838929 + 0.544241i \(0.183182\pi\)
\(942\) −1282.83 + 140.220i −1.36182 + 0.148854i
\(943\) −731.341 + 2729.40i −0.775548 + 2.89438i
\(944\) 376.820i 0.399174i
\(945\) 9.11265 1.25559i 0.00964301 0.00132867i
\(946\) −231.333 −0.244538
\(947\) −177.098 47.4532i −0.187009 0.0501090i 0.164099 0.986444i \(-0.447528\pi\)
−0.351108 + 0.936335i \(0.614195\pi\)
\(948\) −33.9929 310.991i −0.0358575 0.328050i
\(949\) 876.908 + 506.283i 0.924034 + 0.533491i
\(950\) −42.4244 + 359.115i −0.0446573 + 0.378016i
\(951\) 40.4023 262.131i 0.0424840 0.275638i
\(952\) 5.66313 + 1.51743i 0.00594866 + 0.00159394i
\(953\) −16.8810 16.8810i −0.0177135 0.0177135i 0.698195 0.715908i \(-0.253987\pi\)
−0.715908 + 0.698195i \(0.753987\pi\)
\(954\) −599.995 655.332i −0.628925 0.686931i
\(955\) 564.603 382.714i 0.591207 0.400748i
\(956\) −340.507 589.776i −0.356179 0.616920i
\(957\) −82.2369 + 186.791i −0.0859320 + 0.195184i
\(958\) 1164.97 312.153i 1.21604 0.325838i
\(959\) −4.12185 2.37975i −0.00429807 0.00248149i
\(960\) 1.53539 + 8.39107i 0.00159937 + 0.00874070i
\(961\) 340.934 + 590.514i 0.354770 + 0.614479i
\(962\) −1175.66 + 1175.66i −1.22210 + 1.22210i
\(963\) 100.141 157.044i 0.103988 0.163078i
\(964\) 56.6819i 0.0587987i
\(965\) −151.351 436.304i −0.156840 0.452129i
\(966\) −3.51719 + 22.8196i −0.00364098 + 0.0236228i
\(967\) −311.140 1161.19i −0.321758 1.20082i −0.917531 0.397665i \(-0.869821\pi\)
0.595772 0.803153i \(-0.296846\pi\)
\(968\) −153.434 + 41.1125i −0.158506 + 0.0424716i
\(969\) −209.825 + 261.324i −0.216538 + 0.269684i
\(970\) 845.253 1743.15i 0.871395 1.79706i
\(971\) −608.975 −0.627163 −0.313582 0.949561i \(-0.601529\pi\)
−0.313582 + 0.949561i \(0.601529\pi\)
\(972\) −11.1225 535.540i −0.0114429 0.550967i
\(973\) −5.91580 5.91580i −0.00607996 0.00607996i
\(974\) −494.753 + 285.646i −0.507960 + 0.293271i
\(975\) −483.304 854.220i −0.495696 0.876123i
\(976\) 53.7969 93.1790i 0.0551198 0.0954702i
\(977\) −22.8425 85.2493i −0.0233802 0.0872562i 0.953250 0.302183i \(-0.0977154\pi\)
−0.976630 + 0.214927i \(0.931049\pi\)
\(978\) −554.739 + 406.572i −0.567218 + 0.415718i
\(979\) −473.701 + 273.491i −0.483862 + 0.279358i
\(980\) 446.998 302.996i 0.456120 0.309180i
\(981\) −217.865 984.684i −0.222085 1.00376i
\(982\) −1391.51 + 1391.51i −1.41701 + 1.41701i
\(983\) −369.494 + 1378.97i −0.375884 + 1.40282i 0.476166 + 0.879356i \(0.342026\pi\)
−0.852049 + 0.523461i \(0.824640\pi\)
\(984\) −302.881 779.343i −0.307806 0.792015i
\(985\) −912.359 789.439i −0.926253 0.801461i
\(986\) −176.289 + 305.341i −0.178792 + 0.309676i
\(987\) 3.80723 8.64766i 0.00385738 0.00876156i
\(988\) −43.3555 + 161.805i −0.0438821 + 0.163770i
\(989\) 455.499i 0.460565i
\(990\) 882.619 543.143i 0.891534 0.548630i
\(991\) 14.7275 0.0148613 0.00743063 0.999972i \(-0.497635\pi\)
0.00743063 + 0.999972i \(0.497635\pi\)
\(992\) 513.545 + 137.604i 0.517687 + 0.138714i
\(993\) 1079.92 791.484i 1.08754 0.797063i
\(994\) −8.29290 4.78791i −0.00834296 0.00481681i
\(995\) −181.625 + 13.1187i −0.182538 + 0.0131846i
\(996\) 320.448 + 257.298i 0.321735 + 0.258331i
\(997\) 222.758 + 59.6878i 0.223428 + 0.0598674i 0.368796 0.929510i \(-0.379770\pi\)
−0.145368 + 0.989378i \(0.546437\pi\)
\(998\) −858.989 858.989i −0.860710 0.860710i
\(999\) 1234.80 + 609.903i 1.23603 + 0.610514i
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.13.9 yes 40
3.2 odd 2 135.3.l.a.118.2 40
5.2 odd 4 inner 45.3.k.a.22.2 yes 40
5.3 odd 4 225.3.o.b.157.9 40
5.4 even 2 225.3.o.b.193.2 40
9.2 odd 6 135.3.l.a.73.9 40
9.4 even 3 405.3.g.h.163.2 20
9.5 odd 6 405.3.g.g.163.9 20
9.7 even 3 inner 45.3.k.a.43.2 yes 40
15.2 even 4 135.3.l.a.37.9 40
45.2 even 12 135.3.l.a.127.2 40
45.7 odd 12 inner 45.3.k.a.7.9 40
45.22 odd 12 405.3.g.h.82.2 20
45.32 even 12 405.3.g.g.82.9 20
45.34 even 6 225.3.o.b.43.9 40
45.43 odd 12 225.3.o.b.7.2 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.9 40 45.7 odd 12 inner
45.3.k.a.13.9 yes 40 1.1 even 1 trivial
45.3.k.a.22.2 yes 40 5.2 odd 4 inner
45.3.k.a.43.2 yes 40 9.7 even 3 inner
135.3.l.a.37.9 40 15.2 even 4
135.3.l.a.73.9 40 9.2 odd 6
135.3.l.a.118.2 40 3.2 odd 2
135.3.l.a.127.2 40 45.2 even 12
225.3.o.b.7.2 40 45.43 odd 12
225.3.o.b.43.9 40 45.34 even 6
225.3.o.b.157.9 40 5.3 odd 4
225.3.o.b.193.2 40 5.4 even 2
405.3.g.g.82.9 20 45.32 even 12
405.3.g.g.163.9 20 9.5 odd 6
405.3.g.h.82.2 20 45.22 odd 12
405.3.g.h.163.2 20 9.4 even 3