Properties

Label 17.3.e.a.6.1
Level $17$
Weight $3$
Character 17.6
Analytic conductor $0.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [17,3,Mod(3,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 17.e (of order \(16\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.463216449413\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{16})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 6.1
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 17.6
Dual form 17.3.e.a.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23044 + 0.509666i) q^{2} +(-2.63099 + 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(0.902812 - 1.35115i) q^{5} +(-3.50400 - 0.696990i) q^{6} +(4.92562 + 7.37170i) q^{7} +(-3.17331 - 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +O(q^{10})\) \(q+(1.23044 + 0.509666i) q^{2} +(-2.63099 + 0.523336i) q^{3} +(-1.57420 - 1.57420i) q^{4} +(0.902812 - 1.35115i) q^{5} +(-3.50400 - 0.696990i) q^{6} +(4.92562 + 7.37170i) q^{7} +(-3.17331 - 7.66104i) q^{8} +(-1.66671 + 0.690373i) q^{9} +(1.79949 - 1.20238i) q^{10} +(-1.61572 + 8.12279i) q^{11} +(4.96553 + 3.31786i) q^{12} +(16.1480 - 16.1480i) q^{13} +(2.30358 + 11.5809i) q^{14} +(-1.66818 + 4.02734i) q^{15} -2.13880i q^{16} +(-15.7060 - 6.50562i) q^{17} -2.40265 q^{18} +(-1.20778 - 0.500280i) q^{19} +(-3.54819 + 0.705778i) q^{20} +(-16.8171 - 16.8171i) q^{21} +(-6.12797 + 9.17115i) q^{22} +(-26.2400 - 5.21946i) q^{23} +(12.3582 + 18.4954i) q^{24} +(8.55654 + 20.6573i) q^{25} +(28.0993 - 11.6391i) q^{26} +(24.0978 - 16.1016i) q^{27} +(3.85063 - 19.3584i) q^{28} +(13.7583 + 9.19303i) q^{29} +(-4.10520 + 4.10520i) q^{30} +(2.68003 + 13.4734i) q^{31} +(-11.6032 + 28.0125i) q^{32} -22.2165i q^{33} +(-16.0096 - 16.0096i) q^{34} +14.4072 q^{35} +(3.71051 + 1.53694i) q^{36} +(18.9648 - 3.77234i) q^{37} +(-1.23113 - 1.23113i) q^{38} +(-34.0344 + 50.9361i) q^{39} +(-13.2161 - 2.62885i) q^{40} +(-14.6853 - 21.9781i) q^{41} +(-12.1214 - 29.2636i) q^{42} +(-21.8944 + 9.06895i) q^{43} +(15.3303 - 10.2434i) q^{44} +(-0.571923 + 2.87525i) q^{45} +(-29.6266 - 19.7959i) q^{46} +(26.8680 - 26.8680i) q^{47} +(1.11931 + 5.62714i) q^{48} +(-11.3288 + 27.3503i) q^{49} +29.7786i q^{50} +(44.7268 + 8.89671i) q^{51} -50.8404 q^{52} +(26.1557 + 10.8340i) q^{53} +(37.8574 - 7.53030i) q^{54} +(9.51644 + 9.51644i) q^{55} +(40.8445 - 61.1281i) q^{56} +(3.43947 + 0.684154i) q^{57} +(12.2435 + 18.3236i) q^{58} +(9.12070 + 22.0193i) q^{59} +(8.96587 - 3.71379i) q^{60} +(-42.9373 + 28.6898i) q^{61} +(-3.56932 + 17.9442i) q^{62} +(-13.2988 - 8.88596i) q^{63} +(-34.6035 + 34.6035i) q^{64} +(-7.23983 - 36.3971i) q^{65} +(11.3230 - 27.3362i) q^{66} -70.4415i q^{67} +(14.4831 + 34.9654i) q^{68} +71.7687 q^{69} +(17.7272 + 7.34286i) q^{70} +(-102.865 + 20.4612i) q^{71} +(10.5780 + 10.5780i) q^{72} +(19.7693 - 29.5868i) q^{73} +(25.2578 + 5.02408i) q^{74} +(-33.3228 - 49.8712i) q^{75} +(1.11375 + 2.68883i) q^{76} +(-67.8373 + 28.0991i) q^{77} +(-67.8377 + 45.3277i) q^{78} +(-1.41599 + 7.11865i) q^{79} +(-2.88984 - 1.93093i) q^{80} +(-43.4936 + 43.4936i) q^{81} +(-6.86792 - 34.5274i) q^{82} +(51.5218 - 124.385i) q^{83} +52.9469i q^{84} +(-22.9696 + 15.3478i) q^{85} -31.5619 q^{86} +(-41.0090 - 16.9865i) q^{87} +(67.3563 - 13.3980i) q^{88} +(38.6522 + 38.6522i) q^{89} +(-2.16914 + 3.24634i) q^{90} +(198.577 + 39.4995i) q^{91} +(33.0905 + 49.5234i) q^{92} +(-14.1023 - 34.0458i) q^{93} +(46.7533 - 19.3658i) q^{94} +(-1.76635 + 1.18024i) q^{95} +(15.8678 - 79.7729i) q^{96} +(65.9209 + 44.0470i) q^{97} +(-27.8790 + 27.8790i) q^{98} +(-2.91482 - 14.6538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{11} + 48 q^{12} + 16 q^{13} + 8 q^{14} - 16 q^{15} + 56 q^{18} - 80 q^{20} - 64 q^{21} - 104 q^{22} - 56 q^{23} - 80 q^{24} + 64 q^{25} + 176 q^{26} + 40 q^{27} + 152 q^{28} + 48 q^{29} + 16 q^{30} + 24 q^{31} + 88 q^{32} - 136 q^{34} - 160 q^{35} - 128 q^{36} + 32 q^{37} - 120 q^{38} + 48 q^{39} + 64 q^{40} + 48 q^{41} + 16 q^{42} - 232 q^{43} + 120 q^{44} - 88 q^{46} + 192 q^{47} + 136 q^{48} + 16 q^{49} + 136 q^{51} - 384 q^{52} - 32 q^{53} + 8 q^{54} + 224 q^{55} - 120 q^{56} + 24 q^{57} + 240 q^{58} - 48 q^{59} + 64 q^{60} - 160 q^{61} - 168 q^{62} + 56 q^{63} - 64 q^{64} - 96 q^{65} - 8 q^{66} + 272 q^{68} + 240 q^{69} + 224 q^{70} + 40 q^{71} + 40 q^{72} + 48 q^{73} - 160 q^{74} - 296 q^{75} + 80 q^{76} - 48 q^{77} - 400 q^{78} - 136 q^{79} - 240 q^{80} - 424 q^{81} - 64 q^{82} - 264 q^{83} - 272 q^{85} + 832 q^{86} + 208 q^{87} + 264 q^{88} + 160 q^{89} + 448 q^{90} + 320 q^{91} + 24 q^{92} - 64 q^{93} + 32 q^{94} + 272 q^{95} - 56 q^{96} + 48 q^{97} - 120 q^{98} - 224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{15}{16}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23044 + 0.509666i 0.615221 + 0.254833i 0.668459 0.743749i \(-0.266954\pi\)
−0.0532379 + 0.998582i \(0.516954\pi\)
\(3\) −2.63099 + 0.523336i −0.876995 + 0.174445i −0.613004 0.790080i \(-0.710039\pi\)
−0.263991 + 0.964525i \(0.585039\pi\)
\(4\) −1.57420 1.57420i −0.393549 0.393549i
\(5\) 0.902812 1.35115i 0.180562 0.270231i −0.730137 0.683301i \(-0.760544\pi\)
0.910699 + 0.413070i \(0.135544\pi\)
\(6\) −3.50400 0.696990i −0.584001 0.116165i
\(7\) 4.92562 + 7.37170i 0.703659 + 1.05310i 0.995325 + 0.0965803i \(0.0307905\pi\)
−0.291666 + 0.956520i \(0.594210\pi\)
\(8\) −3.17331 7.66104i −0.396664 0.957631i
\(9\) −1.66671 + 0.690373i −0.185190 + 0.0767081i
\(10\) 1.79949 1.20238i 0.179949 0.120238i
\(11\) −1.61572 + 8.12279i −0.146884 + 0.738436i 0.835193 + 0.549957i \(0.185356\pi\)
−0.982077 + 0.188479i \(0.939644\pi\)
\(12\) 4.96553 + 3.31786i 0.413794 + 0.276488i
\(13\) 16.1480 16.1480i 1.24216 1.24216i 0.283051 0.959105i \(-0.408654\pi\)
0.959105 0.283051i \(-0.0913464\pi\)
\(14\) 2.30358 + 11.5809i 0.164541 + 0.827205i
\(15\) −1.66818 + 4.02734i −0.111212 + 0.268489i
\(16\) 2.13880i 0.133675i
\(17\) −15.7060 6.50562i −0.923880 0.382683i
\(18\) −2.40265 −0.133480
\(19\) −1.20778 0.500280i −0.0635675 0.0263305i 0.350673 0.936498i \(-0.385953\pi\)
−0.414241 + 0.910167i \(0.635953\pi\)
\(20\) −3.54819 + 0.705778i −0.177409 + 0.0352889i
\(21\) −16.8171 16.8171i −0.800814 0.800814i
\(22\) −6.12797 + 9.17115i −0.278544 + 0.416870i
\(23\) −26.2400 5.21946i −1.14087 0.226933i −0.411735 0.911303i \(-0.635077\pi\)
−0.729135 + 0.684370i \(0.760077\pi\)
\(24\) 12.3582 + 18.4954i 0.514926 + 0.770642i
\(25\) 8.55654 + 20.6573i 0.342262 + 0.826293i
\(26\) 28.0993 11.6391i 1.08074 0.447658i
\(27\) 24.0978 16.1016i 0.892510 0.596356i
\(28\) 3.85063 19.3584i 0.137522 0.691372i
\(29\) 13.7583 + 9.19303i 0.474425 + 0.317001i 0.769694 0.638414i \(-0.220409\pi\)
−0.295268 + 0.955414i \(0.595409\pi\)
\(30\) −4.10520 + 4.10520i −0.136840 + 0.136840i
\(31\) 2.68003 + 13.4734i 0.0864526 + 0.434627i 0.999633 + 0.0270721i \(0.00861839\pi\)
−0.913181 + 0.407555i \(0.866382\pi\)
\(32\) −11.6032 + 28.0125i −0.362599 + 0.875391i
\(33\) 22.2165i 0.673228i
\(34\) −16.0096 16.0096i −0.470870 0.470870i
\(35\) 14.4072 0.411634
\(36\) 3.71051 + 1.53694i 0.103070 + 0.0426929i
\(37\) 18.9648 3.77234i 0.512563 0.101955i 0.0679693 0.997687i \(-0.478348\pi\)
0.444594 + 0.895732i \(0.353348\pi\)
\(38\) −1.23113 1.23113i −0.0323982 0.0323982i
\(39\) −34.0344 + 50.9361i −0.872677 + 1.30605i
\(40\) −13.2161 2.62885i −0.330404 0.0657214i
\(41\) −14.6853 21.9781i −0.358178 0.536051i 0.607997 0.793939i \(-0.291973\pi\)
−0.966175 + 0.257888i \(0.916973\pi\)
\(42\) −12.1214 29.2636i −0.288604 0.696752i
\(43\) −21.8944 + 9.06895i −0.509172 + 0.210906i −0.622453 0.782657i \(-0.713864\pi\)
0.113281 + 0.993563i \(0.463864\pi\)
\(44\) 15.3303 10.2434i 0.348417 0.232805i
\(45\) −0.571923 + 2.87525i −0.0127094 + 0.0638945i
\(46\) −29.6266 19.7959i −0.644058 0.430345i
\(47\) 26.8680 26.8680i 0.571660 0.571660i −0.360932 0.932592i \(-0.617541\pi\)
0.932592 + 0.360932i \(0.117541\pi\)
\(48\) 1.11931 + 5.62714i 0.0233189 + 0.117232i
\(49\) −11.3288 + 27.3503i −0.231201 + 0.558169i
\(50\) 29.7786i 0.595572i
\(51\) 44.7268 + 8.89671i 0.876995 + 0.174445i
\(52\) −50.8404 −0.977699
\(53\) 26.1557 + 10.8340i 0.493503 + 0.204416i 0.615533 0.788111i \(-0.288941\pi\)
−0.122031 + 0.992526i \(0.538941\pi\)
\(54\) 37.8574 7.53030i 0.701062 0.139450i
\(55\) 9.51644 + 9.51644i 0.173026 + 0.173026i
\(56\) 40.8445 61.1281i 0.729365 1.09157i
\(57\) 3.43947 + 0.684154i 0.0603416 + 0.0120027i
\(58\) 12.2435 + 18.3236i 0.211094 + 0.315925i
\(59\) 9.12070 + 22.0193i 0.154588 + 0.373209i 0.982132 0.188192i \(-0.0602627\pi\)
−0.827544 + 0.561401i \(0.810263\pi\)
\(60\) 8.96587 3.71379i 0.149431 0.0618964i
\(61\) −42.9373 + 28.6898i −0.703890 + 0.470324i −0.855291 0.518148i \(-0.826622\pi\)
0.151401 + 0.988472i \(0.451622\pi\)
\(62\) −3.56932 + 17.9442i −0.0575697 + 0.289423i
\(63\) −13.2988 8.88596i −0.211092 0.141047i
\(64\) −34.6035 + 34.6035i −0.540679 + 0.540679i
\(65\) −7.23983 36.3971i −0.111382 0.559955i
\(66\) 11.3230 27.3362i 0.171561 0.414184i
\(67\) 70.4415i 1.05137i −0.850681 0.525683i \(-0.823810\pi\)
0.850681 0.525683i \(-0.176190\pi\)
\(68\) 14.4831 + 34.9654i 0.212987 + 0.514197i
\(69\) 71.7687 1.04013
\(70\) 17.7272 + 7.34286i 0.253246 + 0.104898i
\(71\) −102.865 + 20.4612i −1.44881 + 0.288185i −0.855923 0.517104i \(-0.827010\pi\)
−0.592883 + 0.805289i \(0.702010\pi\)
\(72\) 10.5780 + 10.5780i 0.146916 + 0.146916i
\(73\) 19.7693 29.5868i 0.270812 0.405299i −0.670990 0.741466i \(-0.734131\pi\)
0.941802 + 0.336167i \(0.109131\pi\)
\(74\) 25.2578 + 5.02408i 0.341321 + 0.0678930i
\(75\) −33.3228 49.8712i −0.444305 0.664949i
\(76\) 1.11375 + 2.68883i 0.0146546 + 0.0353793i
\(77\) −67.8373 + 28.0991i −0.881003 + 0.364924i
\(78\) −67.8377 + 45.3277i −0.869715 + 0.581125i
\(79\) −1.41599 + 7.11865i −0.0179239 + 0.0901095i −0.988712 0.149830i \(-0.952127\pi\)
0.970788 + 0.239939i \(0.0771275\pi\)
\(80\) −2.88984 1.93093i −0.0361230 0.0241366i
\(81\) −43.4936 + 43.4936i −0.536958 + 0.536958i
\(82\) −6.86792 34.5274i −0.0837551 0.421066i
\(83\) 51.5218 124.385i 0.620745 1.49861i −0.230085 0.973170i \(-0.573901\pi\)
0.850830 0.525441i \(-0.176099\pi\)
\(84\) 52.9469i 0.630320i
\(85\) −22.9696 + 15.3478i −0.270231 + 0.180562i
\(86\) −31.5619 −0.366999
\(87\) −41.0090 16.9865i −0.471368 0.195247i
\(88\) 67.3563 13.3980i 0.765412 0.152250i
\(89\) 38.6522 + 38.6522i 0.434294 + 0.434294i 0.890086 0.455792i \(-0.150644\pi\)
−0.455792 + 0.890086i \(0.650644\pi\)
\(90\) −2.16914 + 3.24634i −0.0241015 + 0.0360705i
\(91\) 198.577 + 39.4995i 2.18217 + 0.434060i
\(92\) 33.0905 + 49.5234i 0.359679 + 0.538298i
\(93\) −14.1023 34.0458i −0.151637 0.366084i
\(94\) 46.7533 19.3658i 0.497375 0.206020i
\(95\) −1.76635 + 1.18024i −0.0185932 + 0.0124236i
\(96\) 15.8678 79.7729i 0.165290 0.830968i
\(97\) 65.9209 + 44.0470i 0.679597 + 0.454092i 0.846857 0.531820i \(-0.178492\pi\)
−0.167260 + 0.985913i \(0.553492\pi\)
\(98\) −27.8790 + 27.8790i −0.284480 + 0.284480i
\(99\) −2.91482 14.6538i −0.0294426 0.148018i
\(100\) 19.0490 45.9884i 0.190490 0.459884i
\(101\) 140.647i 1.39254i 0.717779 + 0.696271i \(0.245159\pi\)
−0.717779 + 0.696271i \(0.754841\pi\)
\(102\) 50.4994 + 33.7426i 0.495092 + 0.330810i
\(103\) −42.3283 −0.410954 −0.205477 0.978662i \(-0.565875\pi\)
−0.205477 + 0.978662i \(0.565875\pi\)
\(104\) −174.953 72.4681i −1.68224 0.696808i
\(105\) −37.9052 + 7.53981i −0.361002 + 0.0718077i
\(106\) 26.6613 + 26.6613i 0.251522 + 0.251522i
\(107\) 40.9741 61.3221i 0.382936 0.573104i −0.589064 0.808086i \(-0.700503\pi\)
0.972000 + 0.234983i \(0.0755034\pi\)
\(108\) −63.2818 12.5875i −0.585942 0.116551i
\(109\) −116.798 174.800i −1.07154 1.60367i −0.755770 0.654837i \(-0.772737\pi\)
−0.315770 0.948836i \(-0.602263\pi\)
\(110\) 6.85923 + 16.5596i 0.0623566 + 0.150542i
\(111\) −47.9220 + 19.8500i −0.431730 + 0.178828i
\(112\) 15.7666 10.5349i 0.140773 0.0940615i
\(113\) −28.0222 + 140.877i −0.247984 + 1.24670i 0.633224 + 0.773969i \(0.281731\pi\)
−0.881208 + 0.472729i \(0.843269\pi\)
\(114\) 3.88338 + 2.59479i 0.0340648 + 0.0227613i
\(115\) −30.7421 + 30.7421i −0.267323 + 0.267323i
\(116\) −7.18670 36.1300i −0.0619543 0.311465i
\(117\) −15.7659 + 38.0622i −0.134751 + 0.325318i
\(118\) 31.7420i 0.269000i
\(119\) −29.4040 147.824i −0.247092 1.24222i
\(120\) 36.1473 0.301227
\(121\) 48.4202 + 20.0563i 0.400167 + 0.165755i
\(122\) −67.4541 + 13.4175i −0.552902 + 0.109979i
\(123\) 50.1387 + 50.1387i 0.407632 + 0.407632i
\(124\) 16.9909 25.4287i 0.137024 0.205070i
\(125\) 75.4810 + 15.0141i 0.603848 + 0.120113i
\(126\) −11.8345 17.7116i −0.0939247 0.140568i
\(127\) 41.4251 + 100.009i 0.326182 + 0.787472i 0.998869 + 0.0475454i \(0.0151399\pi\)
−0.672687 + 0.739927i \(0.734860\pi\)
\(128\) 51.8363 21.4713i 0.404971 0.167744i
\(129\) 52.8577 35.3184i 0.409750 0.273786i
\(130\) 9.64216 48.4744i 0.0741705 0.372880i
\(131\) −77.0656 51.4936i −0.588287 0.393081i 0.225501 0.974243i \(-0.427598\pi\)
−0.813788 + 0.581162i \(0.802598\pi\)
\(132\) −34.9732 + 34.9732i −0.264948 + 0.264948i
\(133\) −2.26116 11.3676i −0.0170012 0.0854707i
\(134\) 35.9016 86.6742i 0.267923 0.646822i
\(135\) 47.0965i 0.348863i
\(136\) 140.968i 1.03653i
\(137\) 102.046 0.744863 0.372431 0.928060i \(-0.378524\pi\)
0.372431 + 0.928060i \(0.378524\pi\)
\(138\) 88.3072 + 36.5780i 0.639907 + 0.265058i
\(139\) 30.2420 6.01550i 0.217568 0.0432770i −0.0851025 0.996372i \(-0.527122\pi\)
0.302671 + 0.953095i \(0.402122\pi\)
\(140\) −22.6798 22.6798i −0.161999 0.161999i
\(141\) −56.6284 + 84.7504i −0.401620 + 0.601067i
\(142\) −136.998 27.2506i −0.964775 0.191906i
\(143\) 105.076 + 157.258i 0.734799 + 1.09970i
\(144\) 1.47657 + 3.56475i 0.0102539 + 0.0247552i
\(145\) 24.8424 10.2900i 0.171327 0.0709659i
\(146\) 39.4044 26.3292i 0.269893 0.180337i
\(147\) 15.4927 77.8870i 0.105392 0.529843i
\(148\) −35.7928 23.9160i −0.241843 0.161595i
\(149\) 23.3099 23.3099i 0.156443 0.156443i −0.624546 0.780988i \(-0.714716\pi\)
0.780988 + 0.624546i \(0.214716\pi\)
\(150\) −15.5842 78.3471i −0.103895 0.522314i
\(151\) −53.9466 + 130.239i −0.357262 + 0.862507i 0.638421 + 0.769688i \(0.279588\pi\)
−0.995683 + 0.0928198i \(0.970412\pi\)
\(152\) 10.8404i 0.0713185i
\(153\) 30.6685 0.200448
\(154\) −97.7910 −0.635006
\(155\) 20.6242 + 8.54284i 0.133060 + 0.0551151i
\(156\) 133.760 26.6066i 0.857438 0.170555i
\(157\) −78.3942 78.3942i −0.499326 0.499326i 0.411902 0.911228i \(-0.364865\pi\)
−0.911228 + 0.411902i \(0.864865\pi\)
\(158\) −5.37042 + 8.03741i −0.0339900 + 0.0508697i
\(159\) −74.4850 14.8160i −0.468459 0.0931823i
\(160\) 27.3737 + 40.9677i 0.171086 + 0.256048i
\(161\) −90.7719 219.143i −0.563800 1.36113i
\(162\) −75.6835 + 31.3491i −0.467182 + 0.193513i
\(163\) −135.804 + 90.7416i −0.833156 + 0.556697i −0.897390 0.441238i \(-0.854539\pi\)
0.0642345 + 0.997935i \(0.479539\pi\)
\(164\) −11.4803 + 57.7154i −0.0700019 + 0.351923i
\(165\) −30.0179 20.0573i −0.181927 0.121560i
\(166\) 126.789 126.789i 0.763791 0.763791i
\(167\) 32.5256 + 163.517i 0.194764 + 0.979145i 0.947240 + 0.320525i \(0.103859\pi\)
−0.752476 + 0.658620i \(0.771141\pi\)
\(168\) −75.4707 + 182.202i −0.449230 + 1.08454i
\(169\) 352.517i 2.08590i
\(170\) −36.0850 + 7.17776i −0.212265 + 0.0422221i
\(171\) 2.35840 0.0137918
\(172\) 48.7424 + 20.1898i 0.283386 + 0.117382i
\(173\) 16.3948 3.26113i 0.0947676 0.0188504i −0.147479 0.989065i \(-0.547116\pi\)
0.242246 + 0.970215i \(0.422116\pi\)
\(174\) −41.8018 41.8018i −0.240240 0.240240i
\(175\) −110.133 + 164.826i −0.629334 + 0.941864i
\(176\) 17.3730 + 3.45570i 0.0987102 + 0.0196347i
\(177\) −35.5199 53.1594i −0.200678 0.300335i
\(178\) 27.8596 + 67.2590i 0.156514 + 0.377859i
\(179\) −35.7824 + 14.8215i −0.199901 + 0.0828019i −0.480388 0.877056i \(-0.659504\pi\)
0.280487 + 0.959858i \(0.409504\pi\)
\(180\) 5.42654 3.62590i 0.0301474 0.0201439i
\(181\) 8.42674 42.3641i 0.0465566 0.234056i −0.950500 0.310724i \(-0.899428\pi\)
0.997057 + 0.0766687i \(0.0244284\pi\)
\(182\) 224.207 + 149.810i 1.23190 + 0.823132i
\(183\) 97.9531 97.9531i 0.535263 0.535263i
\(184\) 43.2811 + 217.589i 0.235223 + 1.18255i
\(185\) 12.0247 29.0301i 0.0649982 0.156920i
\(186\) 49.0789i 0.263865i
\(187\) 78.2203 117.065i 0.418290 0.626015i
\(188\) −84.5912 −0.449953
\(189\) 237.393 + 98.3313i 1.25605 + 0.520271i
\(190\) −2.77493 + 0.551967i −0.0146049 + 0.00290509i
\(191\) −107.196 107.196i −0.561234 0.561234i 0.368424 0.929658i \(-0.379898\pi\)
−0.929658 + 0.368424i \(0.879898\pi\)
\(192\) 72.9320 109.151i 0.379854 0.568492i
\(193\) −201.713 40.1233i −1.04515 0.207893i −0.357482 0.933920i \(-0.616364\pi\)
−0.687666 + 0.726028i \(0.741364\pi\)
\(194\) 58.6627 + 87.7949i 0.302385 + 0.452551i
\(195\) 38.0958 + 91.9714i 0.195363 + 0.471648i
\(196\) 60.8886 25.2209i 0.310656 0.128678i
\(197\) 116.416 77.7868i 0.590945 0.394857i −0.223835 0.974627i \(-0.571858\pi\)
0.814780 + 0.579770i \(0.196858\pi\)
\(198\) 3.88201 19.5162i 0.0196061 0.0985667i
\(199\) −123.283 82.3749i −0.619511 0.413944i 0.205823 0.978589i \(-0.434013\pi\)
−0.825334 + 0.564645i \(0.809013\pi\)
\(200\) 131.104 131.104i 0.655520 0.655520i
\(201\) 36.8645 + 185.331i 0.183406 + 0.922043i
\(202\) −71.6828 + 173.058i −0.354865 + 0.856721i
\(203\) 146.704i 0.722678i
\(204\) −56.4036 84.4140i −0.276488 0.413794i
\(205\) −42.9538 −0.209531
\(206\) −52.0825 21.5733i −0.252828 0.104725i
\(207\) 47.3378 9.41607i 0.228685 0.0454883i
\(208\) −34.5373 34.5373i −0.166045 0.166045i
\(209\) 6.01511 9.00225i 0.0287804 0.0430730i
\(210\) −50.4829 10.0417i −0.240395 0.0478175i
\(211\) 113.713 + 170.184i 0.538925 + 0.806559i 0.996585 0.0825683i \(-0.0263123\pi\)
−0.457660 + 0.889127i \(0.651312\pi\)
\(212\) −24.1193 58.2291i −0.113770 0.274665i
\(213\) 259.929 107.666i 1.22032 0.505474i
\(214\) 81.6701 54.5702i 0.381636 0.255001i
\(215\) −7.51296 + 37.7702i −0.0349440 + 0.175675i
\(216\) −199.825 133.519i −0.925115 0.618142i
\(217\) −86.1213 + 86.1213i −0.396872 + 0.396872i
\(218\) −54.6233 274.610i −0.250565 1.25968i
\(219\) −36.5289 + 88.1885i −0.166799 + 0.402687i
\(220\) 29.9615i 0.136189i
\(221\) −358.673 + 148.567i −1.62295 + 0.672250i
\(222\) −69.0821 −0.311181
\(223\) −107.408 44.4897i −0.481649 0.199506i 0.128629 0.991693i \(-0.458942\pi\)
−0.610278 + 0.792187i \(0.708942\pi\)
\(224\) −263.653 + 52.4438i −1.17702 + 0.234124i
\(225\) −28.5225 28.5225i −0.126767 0.126767i
\(226\) −106.280 + 159.059i −0.470265 + 0.703801i
\(227\) −150.469 29.9302i −0.662859 0.131851i −0.147816 0.989015i \(-0.547224\pi\)
−0.515044 + 0.857164i \(0.672224\pi\)
\(228\) −4.33742 6.49140i −0.0190238 0.0284711i
\(229\) 3.69064 + 8.91000i 0.0161164 + 0.0389083i 0.931733 0.363144i \(-0.118297\pi\)
−0.915617 + 0.402053i \(0.868297\pi\)
\(230\) −53.4946 + 22.1582i −0.232585 + 0.0963399i
\(231\) 163.774 109.430i 0.708977 0.473723i
\(232\) 26.7687 134.576i 0.115382 0.580067i
\(233\) 324.315 + 216.700i 1.39191 + 0.930044i 0.999949 + 0.0100614i \(0.00320271\pi\)
0.391960 + 0.919982i \(0.371797\pi\)
\(234\) −38.7980 + 38.7980i −0.165803 + 0.165803i
\(235\) −12.0461 60.5596i −0.0512598 0.257700i
\(236\) 20.3050 49.0206i 0.0860381 0.207714i
\(237\) 19.4701i 0.0821523i
\(238\) 39.1609 196.875i 0.164541 0.827205i
\(239\) 372.281 1.55766 0.778831 0.627233i \(-0.215813\pi\)
0.778831 + 0.627233i \(0.215813\pi\)
\(240\) 8.61365 + 3.56789i 0.0358902 + 0.0148662i
\(241\) 136.315 27.1147i 0.565621 0.112509i 0.0960065 0.995381i \(-0.469393\pi\)
0.469614 + 0.882872i \(0.344393\pi\)
\(242\) 49.3563 + 49.3563i 0.203952 + 0.203952i
\(243\) −53.2453 + 79.6872i −0.219116 + 0.327931i
\(244\) 112.755 + 22.4284i 0.462111 + 0.0919197i
\(245\) 26.7266 + 39.9992i 0.109088 + 0.163262i
\(246\) 36.1388 + 87.2468i 0.146906 + 0.354662i
\(247\) −27.5818 + 11.4248i −0.111667 + 0.0462541i
\(248\) 94.7160 63.2872i 0.381919 0.255190i
\(249\) −70.4583 + 354.218i −0.282965 + 1.42256i
\(250\) 85.2228 + 56.9441i 0.340891 + 0.227776i
\(251\) 154.052 154.052i 0.613754 0.613754i −0.330168 0.943922i \(-0.607106\pi\)
0.943922 + 0.330168i \(0.107106\pi\)
\(252\) 6.94665 + 34.9232i 0.0275661 + 0.138584i
\(253\) 84.7932 204.709i 0.335151 0.809126i
\(254\) 144.168i 0.567591i
\(255\) 52.4007 52.4007i 0.205493 0.205493i
\(256\) 270.472 1.05653
\(257\) −391.977 162.362i −1.52520 0.631760i −0.546578 0.837408i \(-0.684070\pi\)
−0.978626 + 0.205648i \(0.934070\pi\)
\(258\) 83.0389 16.5175i 0.321856 0.0640212i
\(259\) 121.222 + 121.222i 0.468039 + 0.468039i
\(260\) −45.8993 + 68.6931i −0.176536 + 0.264204i
\(261\) −29.2777 5.82370i −0.112175 0.0223130i
\(262\) −68.5803 102.638i −0.261757 0.391747i
\(263\) −54.7003 132.058i −0.207986 0.502122i 0.785120 0.619344i \(-0.212601\pi\)
−0.993106 + 0.117221i \(0.962601\pi\)
\(264\) −170.202 + 70.4999i −0.644704 + 0.267045i
\(265\) 38.2521 25.5592i 0.144347 0.0964499i
\(266\) 3.01146 15.1396i 0.0113213 0.0569158i
\(267\) −121.921 81.4652i −0.456634 0.305113i
\(268\) −110.889 + 110.889i −0.413764 + 0.413764i
\(269\) 8.93614 + 44.9250i 0.0332199 + 0.167008i 0.993834 0.110878i \(-0.0353663\pi\)
−0.960614 + 0.277886i \(0.910366\pi\)
\(270\) 24.0035 57.9495i 0.0889018 0.214628i
\(271\) 329.809i 1.21701i 0.793550 + 0.608504i \(0.208230\pi\)
−0.793550 + 0.608504i \(0.791770\pi\)
\(272\) −13.9142 + 33.5918i −0.0511551 + 0.123499i
\(273\) −543.126 −1.98947
\(274\) 125.562 + 52.0095i 0.458255 + 0.189816i
\(275\) −181.620 + 36.1265i −0.660437 + 0.131369i
\(276\) −112.978 112.978i −0.409341 0.409341i
\(277\) 156.783 234.642i 0.566002 0.847082i −0.432509 0.901629i \(-0.642372\pi\)
0.998511 + 0.0545479i \(0.0173717\pi\)
\(278\) 40.2769 + 8.01157i 0.144881 + 0.0288186i
\(279\) −13.7685 20.6060i −0.0493495 0.0738568i
\(280\) −45.7185 110.374i −0.163280 0.394194i
\(281\) 141.231 58.4999i 0.502603 0.208185i −0.116953 0.993137i \(-0.537313\pi\)
0.619556 + 0.784953i \(0.287313\pi\)
\(282\) −112.872 + 75.4189i −0.400257 + 0.267443i
\(283\) 62.0182 311.786i 0.219145 1.10172i −0.701904 0.712272i \(-0.747666\pi\)
0.921049 0.389447i \(-0.127334\pi\)
\(284\) 194.140 + 129.720i 0.683592 + 0.456761i
\(285\) 4.02959 4.02959i 0.0141389 0.0141389i
\(286\) 49.1414 + 247.050i 0.171823 + 0.863813i
\(287\) 89.6819 216.511i 0.312480 0.754395i
\(288\) 54.6992i 0.189928i
\(289\) 204.354 + 204.354i 0.707107 + 0.707107i
\(290\) 35.8116 0.123488
\(291\) −196.488 81.3882i −0.675218 0.279684i
\(292\) −77.6963 + 15.4548i −0.266083 + 0.0529272i
\(293\) −27.2633 27.2633i −0.0930488 0.0930488i 0.659050 0.752099i \(-0.270958\pi\)
−0.752099 + 0.659050i \(0.770958\pi\)
\(294\) 58.7592 87.9393i 0.199861 0.299113i
\(295\) 37.9858 + 7.55584i 0.128765 + 0.0256130i
\(296\) −89.0814 133.320i −0.300951 0.450404i
\(297\) 91.8547 + 221.757i 0.309275 + 0.746656i
\(298\) 40.5618 16.8013i 0.136114 0.0563801i
\(299\) −508.008 + 339.440i −1.69902 + 1.13525i
\(300\) −26.0503 + 130.964i −0.0868344 + 0.436546i
\(301\) −174.697 116.729i −0.580388 0.387803i
\(302\) −132.756 + 132.756i −0.439591 + 0.439591i
\(303\) −73.6054 370.039i −0.242922 1.22125i
\(304\) −1.07000 + 2.58320i −0.00351972 + 0.00849736i
\(305\) 83.9164i 0.275136i
\(306\) 37.7359 + 15.6307i 0.123320 + 0.0510807i
\(307\) −4.80965 −0.0156666 −0.00783330 0.999969i \(-0.502493\pi\)
−0.00783330 + 0.999969i \(0.502493\pi\)
\(308\) 151.023 + 62.5557i 0.490334 + 0.203103i
\(309\) 111.365 22.1519i 0.360405 0.0716890i
\(310\) 21.0229 + 21.0229i 0.0678159 + 0.0678159i
\(311\) 267.024 399.630i 0.858598 1.28498i −0.0984763 0.995139i \(-0.531397\pi\)
0.957074 0.289843i \(-0.0936031\pi\)
\(312\) 498.225 + 99.1031i 1.59688 + 0.317638i
\(313\) −49.2742 73.7441i −0.157426 0.235604i 0.744369 0.667768i \(-0.232750\pi\)
−0.901795 + 0.432164i \(0.857750\pi\)
\(314\) −56.5047 136.414i −0.179951 0.434441i
\(315\) −24.0126 + 9.94634i −0.0762305 + 0.0315757i
\(316\) 13.4352 8.97712i 0.0425165 0.0284086i
\(317\) −23.4692 + 117.988i −0.0740353 + 0.372201i −0.999985 0.00544574i \(-0.998267\pi\)
0.925950 + 0.377647i \(0.123267\pi\)
\(318\) −84.0983 56.1927i −0.264460 0.176707i
\(319\) −96.9027 + 96.9027i −0.303770 + 0.303770i
\(320\) 15.5142 + 77.9950i 0.0484818 + 0.243734i
\(321\) −75.7103 + 182.781i −0.235858 + 0.569411i
\(322\) 315.906i 0.981074i
\(323\) 15.7147 + 15.7147i 0.0486524 + 0.0486524i
\(324\) 136.935 0.422639
\(325\) 471.746 + 195.404i 1.45153 + 0.601242i
\(326\) −213.347 + 42.4374i −0.654440 + 0.130176i
\(327\) 398.773 + 398.773i 1.21949 + 1.21949i
\(328\) −121.774 + 182.248i −0.371263 + 0.555634i
\(329\) 330.405 + 65.7216i 1.00427 + 0.199762i
\(330\) −26.7128 39.9785i −0.0809478 0.121147i
\(331\) 38.9023 + 93.9184i 0.117530 + 0.283741i 0.971687 0.236274i \(-0.0759262\pi\)
−0.854157 + 0.520015i \(0.825926\pi\)
\(332\) −276.912 + 114.701i −0.834071 + 0.345484i
\(333\) −29.0045 + 19.3802i −0.0871006 + 0.0581988i
\(334\) −43.3183 + 217.776i −0.129695 + 0.652023i
\(335\) −95.1772 63.5954i −0.284111 0.189837i
\(336\) −35.9683 + 35.9683i −0.107049 + 0.107049i
\(337\) −107.223 539.044i −0.318168 1.59954i −0.726807 0.686842i \(-0.758996\pi\)
0.408639 0.912696i \(-0.366004\pi\)
\(338\) 179.666 433.752i 0.531556 1.28329i
\(339\) 385.310i 1.13661i
\(340\) 60.3192 + 11.9982i 0.177409 + 0.0352889i
\(341\) −113.772 −0.333642
\(342\) 2.90187 + 1.20200i 0.00848501 + 0.00351461i
\(343\) 168.661 33.5487i 0.491722 0.0978097i
\(344\) 138.955 + 138.955i 0.403940 + 0.403940i
\(345\) 64.7936 96.9704i 0.187807 0.281074i
\(346\) 21.8349 + 4.34324i 0.0631067 + 0.0125527i
\(347\) 141.826 + 212.258i 0.408722 + 0.611695i 0.977535 0.210771i \(-0.0675975\pi\)
−0.568814 + 0.822466i \(0.692597\pi\)
\(348\) 37.8162 + 91.2964i 0.108667 + 0.262346i
\(349\) −513.215 + 212.580i −1.47053 + 0.609113i −0.966980 0.254854i \(-0.917973\pi\)
−0.503549 + 0.863967i \(0.667973\pi\)
\(350\) −219.519 + 146.678i −0.627198 + 0.419080i
\(351\) 129.122 649.141i 0.367869 1.84940i
\(352\) −208.792 139.511i −0.593160 0.396337i
\(353\) −408.644 + 408.644i −1.15763 + 1.15763i −0.172648 + 0.984984i \(0.555232\pi\)
−0.984984 + 0.172648i \(0.944768\pi\)
\(354\) −16.6117 83.5128i −0.0469258 0.235912i
\(355\) −65.2217 + 157.459i −0.183723 + 0.443547i
\(356\) 121.692i 0.341832i
\(357\) 154.723 + 373.534i 0.433398 + 1.04631i
\(358\) −51.5822 −0.144084
\(359\) −159.526 66.0778i −0.444362 0.184061i 0.149272 0.988796i \(-0.452307\pi\)
−0.593634 + 0.804735i \(0.702307\pi\)
\(360\) 23.8423 4.74254i 0.0662287 0.0131737i
\(361\) −254.057 254.057i −0.703759 0.703759i
\(362\) 31.9602 47.8317i 0.0882877 0.132132i
\(363\) −137.889 27.4279i −0.379860 0.0755588i
\(364\) −250.420 374.780i −0.687967 1.02962i
\(365\) −22.1284 53.4227i −0.0606257 0.146363i
\(366\) 170.449 70.6023i 0.465708 0.192902i
\(367\) −16.9759 + 11.3429i −0.0462558 + 0.0309071i −0.578483 0.815694i \(-0.696355\pi\)
0.532227 + 0.846601i \(0.321355\pi\)
\(368\) −11.1634 + 56.1220i −0.0303352 + 0.152505i
\(369\) 39.6492 + 26.4927i 0.107450 + 0.0717960i
\(370\) 29.5913 29.5913i 0.0799766 0.0799766i
\(371\) 48.9675 + 246.176i 0.131988 + 0.663547i
\(372\) −31.3952 + 75.7946i −0.0843956 + 0.203749i
\(373\) 690.960i 1.85244i 0.376983 + 0.926220i \(0.376961\pi\)
−0.376983 + 0.926220i \(0.623039\pi\)
\(374\) 155.910 104.175i 0.416870 0.278544i
\(375\) −206.447 −0.550525
\(376\) −291.098 120.577i −0.774196 0.320682i
\(377\) 370.619 73.7207i 0.983075 0.195546i
\(378\) 241.982 + 241.982i 0.640164 + 0.640164i
\(379\) −97.1405 + 145.381i −0.256308 + 0.383591i −0.937200 0.348792i \(-0.886592\pi\)
0.680893 + 0.732383i \(0.261592\pi\)
\(380\) 4.63852 + 0.922659i 0.0122066 + 0.00242805i
\(381\) −161.327 241.443i −0.423431 0.633709i
\(382\) −77.2642 186.532i −0.202262 0.488304i
\(383\) 440.512 182.466i 1.15016 0.476412i 0.275574 0.961280i \(-0.411132\pi\)
0.874588 + 0.484868i \(0.161132\pi\)
\(384\) −125.144 + 83.6184i −0.325895 + 0.217756i
\(385\) −23.2781 + 117.027i −0.0604625 + 0.303966i
\(386\) −227.747 152.176i −0.590019 0.394238i
\(387\) 30.2306 30.2306i 0.0781151 0.0781151i
\(388\) −34.4340 173.111i −0.0887473 0.446163i
\(389\) 84.5808 204.196i 0.217431 0.524926i −0.777098 0.629379i \(-0.783309\pi\)
0.994530 + 0.104453i \(0.0333092\pi\)
\(390\) 132.582i 0.339953i
\(391\) 378.169 + 252.684i 0.967183 + 0.646251i
\(392\) 245.482 0.626228
\(393\) 229.707 + 95.1478i 0.584496 + 0.242106i
\(394\) 182.889 36.3788i 0.464184 0.0923320i
\(395\) 8.34002 + 8.34002i 0.0211140 + 0.0211140i
\(396\) −18.4794 + 27.6564i −0.0466652 + 0.0698395i
\(397\) −118.666 23.6042i −0.298908 0.0594565i 0.0433581 0.999060i \(-0.486194\pi\)
−0.342266 + 0.939603i \(0.611194\pi\)
\(398\) −109.709 164.191i −0.275650 0.412539i
\(399\) 11.8981 + 28.7246i 0.0298199 + 0.0719916i
\(400\) 44.1818 18.3007i 0.110454 0.0457517i
\(401\) 434.146 290.087i 1.08266 0.723409i 0.119633 0.992818i \(-0.461828\pi\)
0.963026 + 0.269409i \(0.0868282\pi\)
\(402\) −49.0970 + 246.827i −0.122132 + 0.613998i
\(403\) 260.846 + 174.292i 0.647262 + 0.432486i
\(404\) 221.406 221.406i 0.548034 0.548034i
\(405\) 19.5000 + 98.0330i 0.0481481 + 0.242057i
\(406\) −74.7699 + 180.510i −0.184162 + 0.444607i
\(407\) 160.142i 0.393471i
\(408\) −73.7738 370.886i −0.180818 0.909034i
\(409\) 136.013 0.332550 0.166275 0.986079i \(-0.446826\pi\)
0.166275 + 0.986079i \(0.446826\pi\)
\(410\) −52.8522 21.8921i −0.128908 0.0533954i
\(411\) −268.482 + 53.4044i −0.653241 + 0.129938i
\(412\) 66.6331 + 66.6331i 0.161731 + 0.161731i
\(413\) −117.395 + 175.694i −0.284249 + 0.425409i
\(414\) 63.0455 + 12.5405i 0.152284 + 0.0302911i
\(415\) −121.548 181.910i −0.292887 0.438337i
\(416\) 264.979 + 639.715i 0.636968 + 1.53778i
\(417\) −76.4181 + 31.6534i −0.183257 + 0.0759074i
\(418\) 11.9894 8.01105i 0.0286827 0.0191652i
\(419\) 73.0669 367.332i 0.174384 0.876687i −0.790187 0.612865i \(-0.790017\pi\)
0.964571 0.263822i \(-0.0849832\pi\)
\(420\) 71.5394 + 47.8011i 0.170332 + 0.113812i
\(421\) −273.997 + 273.997i −0.650824 + 0.650824i −0.953192 0.302367i \(-0.902223\pi\)
0.302367 + 0.953192i \(0.402223\pi\)
\(422\) 53.1807 + 267.357i 0.126021 + 0.633548i
\(423\) −26.2322 + 63.3301i −0.0620146 + 0.149716i
\(424\) 234.759i 0.553678i
\(425\) 380.108i 0.894373i
\(426\) 374.701 0.879580
\(427\) −422.985 175.206i −0.990598 0.410319i
\(428\) −161.034 + 32.0318i −0.376249 + 0.0748405i
\(429\) −358.753 358.753i −0.836254 0.836254i
\(430\) −28.4945 + 42.6450i −0.0662662 + 0.0991744i
\(431\) 67.5084 + 13.4283i 0.156632 + 0.0311561i 0.272783 0.962075i \(-0.412056\pi\)
−0.116151 + 0.993232i \(0.537056\pi\)
\(432\) −34.4381 51.5402i −0.0797177 0.119306i
\(433\) −104.262 251.710i −0.240790 0.581317i 0.756572 0.653910i \(-0.226873\pi\)
−0.997362 + 0.0725929i \(0.976873\pi\)
\(434\) −149.860 + 62.0742i −0.345301 + 0.143028i
\(435\) −59.9748 + 40.0739i −0.137873 + 0.0921239i
\(436\) −91.3074 + 459.033i −0.209421 + 1.05283i
\(437\) 29.0810 + 19.4313i 0.0665470 + 0.0444653i
\(438\) −89.8934 + 89.8934i −0.205236 + 0.205236i
\(439\) −28.7213 144.392i −0.0654244 0.328910i 0.934187 0.356783i \(-0.116127\pi\)
−0.999611 + 0.0278730i \(0.991127\pi\)
\(440\) 42.7073 103.105i 0.0970620 0.234328i
\(441\) 53.4060i 0.121102i
\(442\) −517.046 −1.16979
\(443\) −619.331 −1.39804 −0.699019 0.715103i \(-0.746380\pi\)
−0.699019 + 0.715103i \(0.746380\pi\)
\(444\) 106.687 + 44.1910i 0.240285 + 0.0995293i
\(445\) 87.1206 17.3294i 0.195777 0.0389424i
\(446\) −109.484 109.484i −0.245480 0.245480i
\(447\) −49.1292 + 73.5271i −0.109909 + 0.164490i
\(448\) −425.530 84.6432i −0.949844 0.188936i
\(449\) 348.576 + 521.681i 0.776339 + 1.16187i 0.983026 + 0.183466i \(0.0587318\pi\)
−0.206687 + 0.978407i \(0.566268\pi\)
\(450\) −20.5583 49.6322i −0.0456852 0.110294i
\(451\) 202.251 83.7750i 0.448450 0.185754i
\(452\) 265.880 177.656i 0.588231 0.393043i
\(453\) 73.7743 370.888i 0.162857 0.818738i
\(454\) −169.889 113.516i −0.374205 0.250036i
\(455\) 232.648 232.648i 0.511314 0.511314i
\(456\) −5.67318 28.5210i −0.0124412 0.0625460i
\(457\) −52.9634 + 127.865i −0.115894 + 0.279792i −0.971173 0.238375i \(-0.923385\pi\)
0.855280 + 0.518167i \(0.173385\pi\)
\(458\) 12.8442i 0.0280442i
\(459\) −483.229 + 96.1203i −1.05279 + 0.209412i
\(460\) 96.7883 0.210409
\(461\) −135.609 56.1709i −0.294162 0.121846i 0.230722 0.973020i \(-0.425891\pi\)
−0.524884 + 0.851174i \(0.675891\pi\)
\(462\) 257.287 51.1775i 0.556898 0.110774i
\(463\) 522.332 + 522.332i 1.12815 + 1.12815i 0.990478 + 0.137669i \(0.0439609\pi\)
0.137669 + 0.990478i \(0.456039\pi\)
\(464\) 19.6620 29.4263i 0.0423750 0.0634187i
\(465\) −58.7328 11.6827i −0.126307 0.0251241i
\(466\) 288.606 + 431.929i 0.619326 + 0.926887i
\(467\) −2.92741 7.06740i −0.00626855 0.0151336i 0.920714 0.390237i \(-0.127607\pi\)
−0.926983 + 0.375104i \(0.877607\pi\)
\(468\) 84.7360 35.0988i 0.181060 0.0749974i
\(469\) 519.274 346.968i 1.10719 0.739803i
\(470\) 16.0432 80.6546i 0.0341344 0.171605i
\(471\) 247.281 + 165.228i 0.525012 + 0.350802i
\(472\) 139.748 139.748i 0.296077 0.296077i
\(473\) −38.2899 192.496i −0.0809512 0.406969i
\(474\) 9.92325 23.9568i 0.0209351 0.0505419i
\(475\) 29.2302i 0.0615372i
\(476\) −186.416 + 278.992i −0.391631 + 0.586117i
\(477\) −51.0733 −0.107072
\(478\) 458.071 + 189.739i 0.958307 + 0.396944i
\(479\) −742.358 + 147.664i −1.54981 + 0.308276i −0.894493 0.447081i \(-0.852464\pi\)
−0.655314 + 0.755357i \(0.727464\pi\)
\(480\) −93.4598 93.4598i −0.194708 0.194708i
\(481\) 245.329 367.160i 0.510039 0.763327i
\(482\) 181.547 + 36.1119i 0.376653 + 0.0749209i
\(483\) 353.505 + 529.057i 0.731894 + 1.09536i
\(484\) −44.6504 107.796i −0.0922529 0.222718i
\(485\) 119.028 49.3032i 0.245419 0.101656i
\(486\) −106.129 + 70.9132i −0.218373 + 0.145912i
\(487\) 1.72321 8.66318i 0.00353843 0.0177889i −0.978976 0.203977i \(-0.934613\pi\)
0.982514 + 0.186188i \(0.0596133\pi\)
\(488\) 356.047 + 237.903i 0.729605 + 0.487506i
\(489\) 309.811 309.811i 0.633561 0.633561i
\(490\) 12.4993 + 62.8383i 0.0255088 + 0.128241i
\(491\) −224.608 + 542.252i −0.457450 + 1.10438i 0.511976 + 0.859000i \(0.328914\pi\)
−0.969426 + 0.245383i \(0.921086\pi\)
\(492\) 157.857i 0.320847i
\(493\) −156.281 233.892i −0.317001 0.474425i
\(494\) −39.7607 −0.0804871
\(495\) −22.4310 9.29123i −0.0453152 0.0187702i
\(496\) 28.8169 5.73204i 0.0580986 0.0115565i
\(497\) −657.508 657.508i −1.32295 1.32295i
\(498\) −267.228 + 399.934i −0.536602 + 0.803081i
\(499\) −109.936 21.8676i −0.220312 0.0438229i 0.0836997 0.996491i \(-0.473326\pi\)
−0.304012 + 0.952668i \(0.598326\pi\)
\(500\) −95.1868 142.457i −0.190374 0.284914i
\(501\) −171.149 413.190i −0.341614 0.824730i
\(502\) 268.067 111.037i 0.533999 0.221190i
\(503\) −397.401 + 265.535i −0.790061 + 0.527902i −0.883895 0.467686i \(-0.845088\pi\)
0.0938335 + 0.995588i \(0.470088\pi\)
\(504\) −25.8746 + 130.080i −0.0513385 + 0.258096i
\(505\) 190.035 + 126.977i 0.376307 + 0.251441i
\(506\) 208.666 208.666i 0.412384 0.412384i
\(507\) 184.485 + 927.468i 0.363875 + 1.82933i
\(508\) 92.2226 222.645i 0.181541 0.438278i
\(509\) 235.103i 0.461891i −0.972967 0.230946i \(-0.925818\pi\)
0.972967 0.230946i \(-0.0741820\pi\)
\(510\) 91.1828 37.7692i 0.178790 0.0740572i
\(511\) 315.481 0.617380
\(512\) 125.455 + 51.9650i 0.245029 + 0.101494i
\(513\) −37.1602 + 7.39162i −0.0724370 + 0.0144086i
\(514\) −399.555 399.555i −0.777345 0.777345i
\(515\) −38.2145 + 57.1920i −0.0742029 + 0.111052i
\(516\) −138.807 27.6104i −0.269005 0.0535084i
\(517\) 174.832 + 261.655i 0.338166 + 0.506102i
\(518\) 87.3740 + 210.940i 0.168676 + 0.407219i
\(519\) −41.4278 + 17.1600i −0.0798223 + 0.0330635i
\(520\) −255.865 + 170.964i −0.492049 + 0.328777i
\(521\) −118.016 + 593.308i −0.226519 + 1.13879i 0.685321 + 0.728241i \(0.259662\pi\)
−0.911840 + 0.410546i \(0.865338\pi\)
\(522\) −33.0564 22.0876i −0.0633265 0.0423134i
\(523\) 721.650 721.650i 1.37983 1.37983i 0.534934 0.844894i \(-0.320336\pi\)
0.844894 0.534934i \(-0.179664\pi\)
\(524\) 40.2554 + 202.378i 0.0768233 + 0.386217i
\(525\) 203.500 491.292i 0.387619 0.935795i
\(526\) 190.369i 0.361918i
\(527\) 45.5605 229.048i 0.0864526 0.434627i
\(528\) −47.5166 −0.0899935
\(529\) 172.563 + 71.4781i 0.326207 + 0.135119i
\(530\) 60.0936 11.9534i 0.113384 0.0225535i
\(531\) −30.4031 30.4031i −0.0572563 0.0572563i
\(532\) −14.3353 + 21.4544i −0.0269461 + 0.0403277i
\(533\) −592.041 117.764i −1.11077 0.220946i
\(534\) −108.497 162.377i −0.203178 0.304078i
\(535\) −45.8636 110.725i −0.0857264 0.206962i
\(536\) −539.655 + 223.533i −1.00682 + 0.417038i
\(537\) 86.3863 57.7215i 0.160868 0.107489i
\(538\) −11.9013 + 59.8321i −0.0221215 + 0.111212i
\(539\) −203.856 136.212i −0.378212 0.252713i
\(540\) −74.1392 + 74.1392i −0.137295 + 0.137295i
\(541\) 110.903 + 557.546i 0.204996 + 1.03058i 0.937012 + 0.349297i \(0.113580\pi\)
−0.732016 + 0.681288i \(0.761420\pi\)
\(542\) −168.093 + 405.812i −0.310134 + 0.748730i
\(543\) 115.869i 0.213387i
\(544\) 364.477 364.477i 0.669995 0.669995i
\(545\) −341.629 −0.626841
\(546\) −668.285 276.813i −1.22397 0.506983i
\(547\) −359.860 + 71.5805i −0.657879 + 0.130860i −0.512730 0.858550i \(-0.671366\pi\)
−0.145148 + 0.989410i \(0.546366\pi\)
\(548\) −160.641 160.641i −0.293140 0.293140i
\(549\) 51.7573 77.4602i 0.0942755 0.141093i
\(550\) −241.885 48.1140i −0.439792 0.0874800i
\(551\) −12.0180 17.9862i −0.0218112 0.0326428i
\(552\) −227.744 549.823i −0.412580 0.996056i
\(553\) −59.4512 + 24.6255i −0.107507 + 0.0445307i
\(554\) 312.501 208.806i 0.564081 0.376907i
\(555\) −16.4442 + 82.6708i −0.0296293 + 0.148956i
\(556\) −57.0764 38.1372i −0.102655 0.0685922i
\(557\) −146.512 + 146.512i −0.263038 + 0.263038i −0.826287 0.563249i \(-0.809551\pi\)
0.563249 + 0.826287i \(0.309551\pi\)
\(558\) −6.43917 32.3719i −0.0115397 0.0580141i
\(559\) −207.105 + 499.996i −0.370493 + 0.894448i
\(560\) 30.8141i 0.0550251i
\(561\) −144.532 + 348.932i −0.257633 + 0.621981i
\(562\) 203.593 0.362264
\(563\) 793.273 + 328.584i 1.40901 + 0.583631i 0.952074 0.305868i \(-0.0989467\pi\)
0.456936 + 0.889499i \(0.348947\pi\)
\(564\) 222.558 44.2696i 0.394607 0.0784922i
\(565\) 165.048 + 165.048i 0.292120 + 0.292120i
\(566\) 235.217 352.027i 0.415577 0.621955i
\(567\) −534.854 106.389i −0.943306 0.187635i
\(568\) 483.177 + 723.125i 0.850663 + 1.27311i
\(569\) 120.952 + 292.003i 0.212569 + 0.513187i 0.993817 0.111034i \(-0.0354164\pi\)
−0.781248 + 0.624221i \(0.785416\pi\)
\(570\) 7.01193 2.90444i 0.0123016 0.00509550i
\(571\) 224.810 150.213i 0.393713 0.263071i −0.342918 0.939365i \(-0.611415\pi\)
0.736631 + 0.676294i \(0.236415\pi\)
\(572\) 82.1440 412.966i 0.143608 0.721968i
\(573\) 338.130 + 225.931i 0.590105 + 0.394295i
\(574\) 220.697 220.697i 0.384489 0.384489i
\(575\) −116.704 586.709i −0.202963 1.02036i
\(576\) 33.7846 81.5632i 0.0586538 0.141603i
\(577\) 63.2031i 0.109537i 0.998499 + 0.0547687i \(0.0174421\pi\)
−0.998499 + 0.0547687i \(0.982558\pi\)
\(578\) 147.293 + 355.598i 0.254833 + 0.615221i
\(579\) 551.703 0.952855
\(580\) −55.3054 22.9082i −0.0953541 0.0394970i
\(581\) 1170.70 232.868i 2.01498 0.400805i
\(582\) −200.287 200.287i −0.344136 0.344136i
\(583\) −130.263 + 194.952i −0.223435 + 0.334395i
\(584\) −289.400 57.5653i −0.495548 0.0985706i
\(585\) 37.1942 + 55.6651i 0.0635799 + 0.0951540i
\(586\) −19.6507 47.4411i −0.0335337 0.0809575i
\(587\) 685.040 283.753i 1.16702 0.483395i 0.286812 0.957987i \(-0.407404\pi\)
0.880206 + 0.474592i \(0.157404\pi\)
\(588\) −146.998 + 98.2209i −0.249997 + 0.167042i
\(589\) 3.50359 17.6137i 0.00594837 0.0299045i
\(590\) 42.8883 + 28.6571i 0.0726921 + 0.0485713i
\(591\) −265.581 + 265.581i −0.449375 + 0.449375i
\(592\) −8.06826 40.5619i −0.0136288 0.0685167i
\(593\) −76.8977 + 185.647i −0.129676 + 0.313065i −0.975360 0.220618i \(-0.929192\pi\)
0.845685 + 0.533683i \(0.179192\pi\)
\(594\) 319.674i 0.538172i
\(595\) −226.279 93.7278i −0.380301 0.157526i
\(596\) −73.3889 −0.123136
\(597\) 367.465 + 152.209i 0.615519 + 0.254956i
\(598\) −798.076 + 158.747i −1.33458 + 0.265464i
\(599\) 457.825 + 457.825i 0.764316 + 0.764316i 0.977099 0.212784i \(-0.0682529\pi\)
−0.212784 + 0.977099i \(0.568253\pi\)
\(600\) −276.322 + 413.544i −0.460536 + 0.689241i
\(601\) 703.378 + 139.911i 1.17035 + 0.232796i 0.741735 0.670693i \(-0.234003\pi\)
0.428611 + 0.903489i \(0.359003\pi\)
\(602\) −155.462 232.665i −0.258242 0.386487i
\(603\) 48.6309 + 117.405i 0.0806482 + 0.194702i
\(604\) 289.944 120.099i 0.480040 0.198839i
\(605\) 70.8135 47.3161i 0.117047 0.0782084i
\(606\) 98.0293 492.826i 0.161764 0.813245i
\(607\) −863.573 577.021i −1.42269 0.950612i −0.998996 0.0448067i \(-0.985733\pi\)
−0.423695 0.905805i \(-0.639267\pi\)
\(608\) 28.0282 28.0282i 0.0460990 0.0460990i
\(609\) −76.7753 385.975i −0.126068 0.633786i
\(610\) −42.7693 + 103.254i −0.0701136 + 0.169269i
\(611\) 867.731i 1.42018i
\(612\) −48.2783 48.2783i −0.0788861 0.0788861i
\(613\) −626.391 −1.02185 −0.510923 0.859627i \(-0.670696\pi\)
−0.510923 + 0.859627i \(0.670696\pi\)
\(614\) −5.91799 2.45131i −0.00963842 0.00399237i
\(615\) 113.011 22.4793i 0.183758 0.0365517i
\(616\) 430.537 + 430.537i 0.698924 + 0.698924i
\(617\) −372.249 + 557.109i −0.603320 + 0.902933i −0.999886 0.0150736i \(-0.995202\pi\)
0.396566 + 0.918006i \(0.370202\pi\)
\(618\) 148.319 + 29.5024i 0.239998 + 0.0477385i
\(619\) −437.249 654.389i −0.706379 1.05717i −0.995014 0.0997323i \(-0.968201\pi\)
0.288635 0.957439i \(-0.406799\pi\)
\(620\) −19.0185 45.9147i −0.0306750 0.0740560i
\(621\) −716.368 + 296.729i −1.15357 + 0.477825i
\(622\) 532.235 355.628i 0.855684 0.571749i
\(623\) −94.5466 + 475.318i −0.151760 + 0.762950i
\(624\) 108.942 + 72.7926i 0.174586 + 0.116655i
\(625\) −306.829 + 306.829i −0.490927 + 0.490927i
\(626\) −23.0442 115.851i −0.0368119 0.185066i
\(627\) −11.1145 + 26.8327i −0.0177264 + 0.0427954i
\(628\) 246.816i 0.393019i
\(629\) −322.402 64.1298i −0.512563 0.101955i
\(630\) −34.6154 −0.0549451
\(631\) −767.465 317.894i −1.21627 0.503794i −0.320046 0.947402i \(-0.603698\pi\)
−0.896221 + 0.443608i \(0.853698\pi\)
\(632\) 59.0297 11.7417i 0.0934013 0.0185787i
\(633\) −388.241 388.241i −0.613336 0.613336i
\(634\) −89.0118 + 133.216i −0.140397 + 0.210119i
\(635\) 172.526 + 34.3176i 0.271695 + 0.0540435i
\(636\) 93.9308 + 140.577i 0.147690 + 0.221034i
\(637\) 258.714 + 624.591i 0.406145 + 0.980520i
\(638\) −168.621 + 69.8452i −0.264297 + 0.109475i
\(639\) 157.320 105.118i 0.246198 0.164504i
\(640\) 17.7874 89.4233i 0.0277928 0.139724i
\(641\) −703.209 469.870i −1.09705 0.733026i −0.131001 0.991382i \(-0.541819\pi\)
−0.966050 + 0.258357i \(0.916819\pi\)
\(642\) −186.314 + 186.314i −0.290209 + 0.290209i
\(643\) −144.203 724.957i −0.224266 1.12746i −0.914721 0.404085i \(-0.867590\pi\)
0.690456 0.723375i \(-0.257410\pi\)
\(644\) −202.081 + 487.867i −0.313790 + 0.757557i
\(645\) 103.305i 0.160162i
\(646\) 11.3268 + 27.3453i 0.0175338 + 0.0423303i
\(647\) 874.070 1.35096 0.675479 0.737379i \(-0.263937\pi\)
0.675479 + 0.737379i \(0.263937\pi\)
\(648\) 471.225 + 195.188i 0.727199 + 0.301216i
\(649\) −193.595 + 38.5084i −0.298297 + 0.0593350i
\(650\) 480.866 + 480.866i 0.739793 + 0.739793i
\(651\) 181.514 271.654i 0.278823 0.417288i
\(652\) 356.628 + 70.9377i 0.546976 + 0.108800i
\(653\) −642.117 960.997i −0.983335 1.47166i −0.878827 0.477140i \(-0.841673\pi\)
−0.104507 0.994524i \(-0.533327\pi\)
\(654\) 287.426 + 693.908i 0.439489 + 1.06102i
\(655\) −139.151 + 57.6384i −0.212445 + 0.0879976i
\(656\) −47.0066 + 31.4088i −0.0716565 + 0.0478793i
\(657\) −12.5237 + 62.9607i −0.0190619 + 0.0958307i
\(658\) 373.048 + 249.263i 0.566942 + 0.378819i
\(659\) −318.726 + 318.726i −0.483651 + 0.483651i −0.906295 0.422645i \(-0.861102\pi\)
0.422645 + 0.906295i \(0.361102\pi\)
\(660\) 15.6799 + 78.8284i 0.0237575 + 0.119437i
\(661\) 191.121 461.408i 0.289140 0.698045i −0.710846 0.703347i \(-0.751688\pi\)
0.999986 + 0.00530241i \(0.00168782\pi\)
\(662\) 135.388i 0.204514i
\(663\) 865.913 578.585i 1.30605 0.872677i
\(664\) −1116.41 −1.68134
\(665\) −17.4008 7.20763i −0.0261666 0.0108385i
\(666\) −45.5658 + 9.06360i −0.0684171 + 0.0136090i
\(667\) −313.036 313.036i −0.469320 0.469320i
\(668\) 206.207 308.610i 0.308693 0.461991i
\(669\) 305.871 + 60.8416i 0.457207 + 0.0909441i
\(670\) −84.6977 126.759i −0.126414 0.189193i
\(671\) −163.666 395.126i −0.243914 0.588861i
\(672\) 666.221 275.958i 0.991400 0.410651i
\(673\) −781.320 + 522.061i −1.16095 + 0.775722i −0.978247 0.207446i \(-0.933485\pi\)
−0.182704 + 0.983168i \(0.558485\pi\)
\(674\) 142.801 717.911i 0.211871 1.06515i
\(675\) 538.810 + 360.021i 0.798236 + 0.533365i
\(676\) −554.932 + 554.932i −0.820905 + 0.820905i
\(677\) 217.100 + 1091.43i 0.320679 + 1.61216i 0.719065 + 0.694943i \(0.244570\pi\)
−0.398386 + 0.917218i \(0.630430\pi\)
\(678\) 196.379 474.102i 0.289645 0.699265i
\(679\) 702.908i 1.03521i
\(680\) 190.470 + 127.268i 0.280103 + 0.187159i
\(681\) 411.546 0.604325
\(682\) −139.990 57.9857i −0.205264 0.0850231i
\(683\) 1289.29 256.456i 1.88769 0.375484i 0.890804 0.454387i \(-0.150142\pi\)
0.996882 + 0.0789027i \(0.0251417\pi\)
\(684\) −3.71259 3.71259i −0.00542776 0.00542776i
\(685\) 92.1285 137.880i 0.134494 0.201285i
\(686\) 224.626 + 44.6809i 0.327443 + 0.0651325i
\(687\) −14.3730 21.5107i −0.0209213 0.0313110i
\(688\) 19.3966 + 46.8276i 0.0281928 + 0.0680634i
\(689\) 597.310 247.414i 0.866923 0.359091i
\(690\) 129.147 86.2935i 0.187170 0.125063i
\(691\) 93.4894 470.003i 0.135296 0.680178i −0.852286 0.523075i \(-0.824785\pi\)
0.987582 0.157103i \(-0.0502154\pi\)
\(692\) −30.9423 20.6750i −0.0447143 0.0298771i
\(693\) 93.6660 93.6660i 0.135160 0.135160i
\(694\) 66.3285 + 333.456i 0.0955742 + 0.480484i
\(695\) 19.1749 46.2924i 0.0275898 0.0666078i
\(696\) 368.075i 0.528844i
\(697\) 87.6654 + 440.724i 0.125775 + 0.632315i
\(698\) −739.826 −1.05992
\(699\) −966.675 400.410i −1.38294 0.572832i
\(700\) 432.841 86.0974i 0.618344 0.122996i
\(701\) 777.458 + 777.458i 1.10907 + 1.10907i 0.993273 + 0.115796i \(0.0369420\pi\)
0.115796 + 0.993273i \(0.463058\pi\)
\(702\) 489.722 732.921i 0.697610 1.04405i
\(703\) −24.7926 4.93156i −0.0352669 0.00701502i
\(704\) −225.167 336.987i −0.319840 0.478674i
\(705\) 63.3860 + 153.027i 0.0899092 + 0.217060i
\(706\) −711.085 + 294.541i −1.00720 + 0.417197i
\(707\) −1036.81 + 692.771i −1.46649 + 0.979875i
\(708\) −27.7679 + 139.599i −0.0392202 + 0.197173i
\(709\) 433.937 + 289.947i 0.612041 + 0.408953i 0.822593 0.568630i \(-0.192526\pi\)
−0.210553 + 0.977583i \(0.567526\pi\)
\(710\) −160.503 + 160.503i −0.226061 + 0.226061i
\(711\) −2.55448 12.8423i −0.00359281 0.0180623i
\(712\) 173.461 418.771i 0.243625 0.588162i
\(713\) 367.531i 0.515472i
\(714\) 538.469i 0.754159i
\(715\) 307.343 0.429851
\(716\) 79.6605 + 32.9965i 0.111258 + 0.0460845i
\(717\) −979.467 + 194.828i −1.36606 + 0.271727i
\(718\) −162.610 162.610i −0.226476 0.226476i
\(719\) −345.349 + 516.851i −0.480318 + 0.718847i −0.989930 0.141557i \(-0.954789\pi\)
0.509612 + 0.860404i \(0.329789\pi\)
\(720\) 6.14958 + 1.22323i 0.00854108 + 0.00169893i
\(721\) −208.493 312.032i −0.289172 0.432776i
\(722\) −183.118 442.087i −0.253627 0.612309i
\(723\) −344.452 + 142.677i −0.476420 + 0.197340i
\(724\) −79.9548 + 53.4241i −0.110435 + 0.0737902i
\(725\) −72.1795 + 362.871i −0.0995579 + 0.500511i
\(726\) −155.686 104.026i −0.214443 0.143286i
\(727\) 181.405 181.405i 0.249526 0.249526i −0.571250 0.820776i \(-0.693541\pi\)
0.820776 + 0.571250i \(0.193541\pi\)
\(728\) −327.540 1646.65i −0.449917 2.26189i
\(729\) 310.231 748.965i 0.425557 1.02739i
\(730\) 77.0116i 0.105495i
\(731\) 402.871 0.551123
\(732\) −308.395 −0.421305
\(733\) 204.776 + 84.8211i 0.279367 + 0.115718i 0.517968 0.855400i \(-0.326689\pi\)
−0.238600 + 0.971118i \(0.576689\pi\)
\(734\) −26.6690 + 5.30478i −0.0363337 + 0.00722723i
\(735\) −91.2502 91.2502i −0.124150 0.124150i
\(736\) 450.677 674.487i 0.612334 0.916422i
\(737\) 572.182 + 113.814i 0.776366 + 0.154429i
\(738\) 35.2836 + 52.8056i 0.0478097 + 0.0715523i
\(739\) 113.071 + 272.978i 0.153006 + 0.369388i 0.981733 0.190265i \(-0.0609346\pi\)
−0.828727 + 0.559653i \(0.810935\pi\)
\(740\) −64.6284 + 26.7699i −0.0873356 + 0.0361756i
\(741\) 66.5884 44.4929i 0.0898629 0.0600445i
\(742\) −65.2159 + 327.862i −0.0878920 + 0.441863i
\(743\) −622.570 415.988i −0.837914 0.559876i 0.0609312 0.998142i \(-0.480593\pi\)
−0.898846 + 0.438265i \(0.855593\pi\)
\(744\) −216.076 + 216.076i −0.290425 + 0.290425i
\(745\) −10.4508 52.5398i −0.0140279 0.0705232i
\(746\) −352.159 + 850.187i −0.472063 + 1.13966i
\(747\) 242.882i 0.325143i
\(748\) −307.417 + 61.1491i −0.410986 + 0.0817502i
\(749\) 653.871 0.872992
\(750\) −254.021 105.219i −0.338695 0.140292i
\(751\) −683.178 + 135.892i −0.909691 + 0.180949i −0.627688 0.778465i \(-0.715999\pi\)
−0.282003 + 0.959414i \(0.590999\pi\)
\(752\) −57.4652 57.4652i −0.0764165 0.0764165i
\(753\) −324.688 + 485.930i −0.431193 + 0.645326i
\(754\) 493.598 + 98.1828i 0.654640 + 0.130216i
\(755\) 127.269 + 190.471i 0.168568 + 0.252280i
\(756\) −218.910 528.496i −0.289564 0.699069i
\(757\) −633.525 + 262.415i −0.836889 + 0.346651i −0.759626 0.650360i \(-0.774618\pi\)
−0.0772631 + 0.997011i \(0.524618\pi\)
\(758\) −193.622 + 129.374i −0.255438 + 0.170678i
\(759\) −115.958 + 582.962i −0.152778 + 0.768066i
\(760\) 14.6471 + 9.78685i 0.0192724 + 0.0128774i
\(761\) −305.005 + 305.005i −0.400795 + 0.400795i −0.878513 0.477718i \(-0.841464\pi\)
0.477718 + 0.878513i \(0.341464\pi\)
\(762\) −75.4484 379.305i −0.0990136 0.497775i
\(763\) 713.275 1722.00i 0.934830 2.25688i
\(764\) 337.495i 0.441747i
\(765\) 27.6879 41.4379i 0.0361933 0.0541672i
\(766\) 635.021 0.829009
\(767\) 502.850 + 208.287i 0.655606 + 0.271561i
\(768\) −711.607 + 141.547i −0.926572 + 0.184307i
\(769\) 303.275 + 303.275i 0.394376 + 0.394376i 0.876244 0.481868i \(-0.160041\pi\)
−0.481868 + 0.876244i \(0.660041\pi\)
\(770\) −88.2869 + 132.131i −0.114658 + 0.171598i
\(771\) 1116.26 + 222.037i 1.44780 + 0.287986i
\(772\) 254.375 + 380.699i 0.329501 + 0.493133i
\(773\) −79.8088 192.675i −0.103246 0.249257i 0.863812 0.503814i \(-0.168070\pi\)
−0.967058 + 0.254557i \(0.918070\pi\)
\(774\) 52.6045 21.7895i 0.0679644 0.0281518i
\(775\) −255.393 + 170.648i −0.329539 + 0.220191i
\(776\) 128.258 644.798i 0.165281 0.830925i
\(777\) −382.373 255.494i −0.492115 0.328821i
\(778\) 208.144 208.144i 0.267537 0.267537i
\(779\) 6.74144 + 33.8915i 0.00865396 + 0.0435064i
\(780\) 84.8108 204.751i 0.108732 0.262502i
\(781\) 868.612i 1.11218i
\(782\) 336.530 + 503.653i 0.430345 + 0.644058i
\(783\) 479.568 0.612475
\(784\) 58.4966 + 24.2301i 0.0746130 + 0.0309057i
\(785\) −176.698 + 35.1474i −0.225093 + 0.0447737i
\(786\) 234.148 + 234.148i 0.297898 + 0.297898i
\(787\) 614.498 919.662i 0.780811 1.16857i −0.201164 0.979558i \(-0.564473\pi\)
0.981975 0.189009i \(-0.0605275\pi\)
\(788\) −305.714 60.8102i −0.387962 0.0771703i
\(789\) 213.027 + 318.817i 0.269996 + 0.404077i
\(790\) 6.01129 + 14.5125i 0.00760922 + 0.0183703i
\(791\) −1176.53 + 487.334i −1.48739 + 0.616099i
\(792\) −103.014 + 68.8315i −0.130068 + 0.0869084i
\(793\) −230.069 + 1156.64i −0.290125 + 1.45856i
\(794\) −133.982 89.5239i −0.168743 0.112750i
\(795\) −87.2646 + 87.2646i −0.109767 + 0.109767i
\(796\) 64.3970 + 323.746i 0.0809008 + 0.406716i
\(797\) −23.4701 + 56.6619i −0.0294481 + 0.0710940i −0.937919 0.346853i \(-0.887250\pi\)
0.908471 + 0.417947i \(0.137250\pi\)
\(798\) 41.4081i 0.0518899i
\(799\) −596.781 + 247.195i −0.746910 + 0.309380i
\(800\) −677.946 −0.847433
\(801\) −91.1062 37.7374i −0.113741 0.0471129i
\(802\) 682.039 135.666i 0.850423 0.169160i
\(803\) 208.386 + 208.386i 0.259509 + 0.259509i
\(804\) 233.715 349.779i 0.290690 0.435049i
\(805\) −378.045 75.1979i −0.469621 0.0934135i
\(806\) 232.126 + 347.401i 0.287997 + 0.431018i
\(807\) −47.0217 113.521i −0.0582673 0.140670i
\(808\) 1077.50 446.315i 1.33354 0.552370i
\(809\) 676.209 451.829i 0.835858 0.558503i −0.0623592 0.998054i \(-0.519862\pi\)
0.898218 + 0.439551i \(0.144862\pi\)
\(810\) −25.9705 + 130.562i −0.0320623 + 0.161188i
\(811\) 961.868 + 642.700i 1.18603 + 0.792478i 0.982440 0.186579i \(-0.0597399\pi\)
0.203587 + 0.979057i \(0.434740\pi\)
\(812\) 230.941 230.941i 0.284410 0.284410i
\(813\) −172.601 867.724i −0.212301 1.06731i
\(814\) −81.6192 + 197.046i −0.100269 + 0.242071i
\(815\) 265.415i 0.325663i
\(816\) 19.0282 95.6614i 0.0233189 0.117232i
\(817\) 30.9806 0.0379200
\(818\) 167.356 + 69.3211i 0.204592 + 0.0847446i
\(819\) −358.240 + 71.2583i −0.437411 + 0.0870065i
\(820\) 67.6178 + 67.6178i 0.0824608 + 0.0824608i
\(821\) 555.958 832.050i 0.677172 1.01346i −0.320631 0.947204i \(-0.603895\pi\)
0.997803 0.0662547i \(-0.0211050\pi\)
\(822\) −357.570 71.1252i −0.435000 0.0865270i
\(823\) 30.1009 + 45.0492i 0.0365746 + 0.0547378i 0.849306 0.527900i \(-0.177021\pi\)
−0.812732 + 0.582638i \(0.802021\pi\)
\(824\) 134.321 + 324.279i 0.163011 + 0.393542i
\(825\) 458.934 190.097i 0.556283 0.230420i
\(826\) −233.993 + 156.349i −0.283284 + 0.189285i
\(827\) 80.0267 402.321i 0.0967675 0.486483i −0.901760 0.432237i \(-0.857724\pi\)
0.998528 0.0542461i \(-0.0172756\pi\)
\(828\) −89.3418 59.6963i −0.107901 0.0720970i
\(829\) −153.097 + 153.097i −0.184677 + 0.184677i −0.793390 0.608713i \(-0.791686\pi\)
0.608713 + 0.793390i \(0.291686\pi\)
\(830\) −56.8449 285.779i −0.0684878 0.344312i
\(831\) −289.696 + 699.389i −0.348612 + 0.841623i
\(832\) 1117.56i 1.34322i
\(833\) 355.861 355.861i 0.427204 0.427204i
\(834\) −110.161 −0.132087
\(835\) 250.301 + 103.678i 0.299762 + 0.124165i
\(836\) −23.6403 + 4.70235i −0.0282779 + 0.00562482i
\(837\) 281.527 + 281.527i 0.336352 + 0.336352i
\(838\) 277.121 414.741i 0.330694 0.494918i
\(839\) −278.253 55.3480i −0.331648 0.0659690i 0.0264576 0.999650i \(-0.491577\pi\)
−0.358106 + 0.933681i \(0.616577\pi\)
\(840\) 178.048 + 266.467i 0.211961 + 0.317223i
\(841\) −217.057 524.021i −0.258094 0.623093i
\(842\) −476.785 + 197.491i −0.566252 + 0.234549i
\(843\) −340.963 + 227.824i −0.404463 + 0.270254i
\(844\) 88.8960 446.910i 0.105327 0.529515i
\(845\) −476.305 318.257i −0.563674 0.376635i
\(846\) −64.5544 + 64.5544i −0.0763054 + 0.0763054i
\(847\) 90.6502 + 455.729i 0.107025 + 0.538051i
\(848\) 23.1718 55.9416i 0.0273252 0.0659689i
\(849\) 852.762i 1.00443i
\(850\) 193.728 467.701i 0.227916 0.550237i
\(851\) −517.327 −0.607905
\(852\) −578.667 239.692i −0.679187 0.281328i
\(853\) −559.124 + 111.217i −0.655479 + 0.130383i −0.511615 0.859215i \(-0.670953\pi\)
−0.143864 + 0.989598i \(0.545953\pi\)
\(854\) −431.162 431.162i −0.504874 0.504874i
\(855\) 2.12919 3.18656i 0.00249028 0.00372697i
\(856\) −599.815 119.311i −0.700718 0.139382i
\(857\) −738.200 1104.79i −0.861377 1.28914i −0.955922 0.293622i \(-0.905139\pi\)
0.0945445 0.995521i \(-0.469861\pi\)
\(858\) −258.581 624.269i −0.301376 0.727586i
\(859\) 260.316 107.826i 0.303046 0.125526i −0.225979 0.974132i \(-0.572558\pi\)
0.529024 + 0.848607i \(0.322558\pi\)
\(860\) 71.2847 47.6309i 0.0828892 0.0553848i
\(861\) −122.644 + 616.572i −0.142443 + 0.716111i
\(862\) 76.2213 + 50.9295i 0.0884238 + 0.0590829i
\(863\) 44.4457 44.4457i 0.0515014 0.0515014i −0.680887 0.732388i \(-0.738406\pi\)
0.732388 + 0.680887i \(0.238406\pi\)
\(864\) 171.436 + 861.869i 0.198422 + 0.997533i
\(865\) 10.3951 25.0961i 0.0120175 0.0290128i
\(866\) 362.854i 0.419000i
\(867\) −644.598 430.707i −0.743481 0.496778i
\(868\) 271.144 0.312378
\(869\) −55.5355 23.0035i −0.0639073 0.0264713i
\(870\) −94.2198 + 18.7415i −0.108299 + 0.0215419i
\(871\) −1137.49 1137.49i −1.30596 1.30596i
\(872\) −968.518 + 1449.49i −1.11069 + 1.66226i
\(873\) −140.280 27.9034i −0.160687 0.0319626i
\(874\) 25.8790 + 38.7307i 0.0296099 + 0.0443143i
\(875\) 261.111 + 630.377i 0.298412 + 0.720431i
\(876\) 196.330 81.3225i 0.224121 0.0928339i
\(877\) 374.931 250.521i 0.427515 0.285657i −0.323139 0.946351i \(-0.604738\pi\)
0.750655 + 0.660695i \(0.229738\pi\)
\(878\) 38.2516 192.304i 0.0435668 0.219025i
\(879\) 85.9972 + 57.4615i 0.0978353 + 0.0653714i
\(880\) 20.3537 20.3537i 0.0231292 0.0231292i
\(881\) 192.046 + 965.483i 0.217987 + 1.09589i 0.922439 + 0.386143i \(0.126193\pi\)
−0.704452 + 0.709752i \(0.748807\pi\)
\(882\) 27.2192 65.7130i 0.0308608 0.0745046i
\(883\) 908.452i 1.02882i −0.857543 0.514412i \(-0.828010\pi\)
0.857543 0.514412i \(-0.171990\pi\)
\(884\) 798.496 + 330.748i 0.903276 + 0.374149i
\(885\) −103.894 −0.117395
\(886\) −762.051 315.652i −0.860103 0.356266i
\(887\) 245.627 48.8583i 0.276919 0.0550827i −0.0546769 0.998504i \(-0.517413\pi\)
0.331596 + 0.943421i \(0.392413\pi\)
\(888\) 304.143 + 304.143i 0.342503 + 0.342503i
\(889\) −533.193 + 797.979i −0.599767 + 0.897614i
\(890\) 116.029 + 23.0796i 0.130370 + 0.0259322i
\(891\) −283.016 423.563i −0.317638 0.475379i
\(892\) 99.0454 + 239.117i 0.111037 + 0.268068i
\(893\) −45.8922 + 19.0092i −0.0513911 + 0.0212869i
\(894\) −97.9249 + 65.4313i −0.109536 + 0.0731894i
\(895\) −12.2786 + 61.7285i −0.0137191 + 0.0689704i
\(896\) 413.605 + 276.362i 0.461613 + 0.308440i
\(897\) 1158.92 1158.92i 1.29200 1.29200i
\(898\) 163.020 + 819.556i 0.181537 + 0.912646i
\(899\) −86.9888 + 210.010i −0.0967617 + 0.233604i
\(900\) 89.8001i 0.0997779i
\(901\) −340.317 340.317i −0.377711 0.377711i
\(902\) 291.555 0.323232
\(903\) 520.713 + 215.687i 0.576648 + 0.238856i
\(904\) 1168.19 232.367i 1.29224 0.257043i
\(905\) −49.6326 49.6326i −0.0548427 0.0548427i
\(906\) 279.804 418.756i 0.308835 0.462204i
\(907\) 1703.05 + 338.757i 1.87767 + 0.373492i 0.995281 0.0970321i \(-0.0309350\pi\)
0.882387 + 0.470524i \(0.155935\pi\)
\(908\) 189.752 + 283.984i 0.208978 + 0.312758i
\(909\) −97.0986 234.417i −0.106819 0.257884i
\(910\) 404.833 167.687i 0.444871 0.184272i
\(911\) 1492.51 997.265i 1.63832 1.09469i 0.723922 0.689882i \(-0.242337\pi\)
0.914401 0.404811i \(-0.132663\pi\)
\(912\) 1.46326 7.35633i 0.00160446 0.00806615i
\(913\) 927.106 + 619.472i 1.01545 + 0.678502i
\(914\) −130.337 + 130.337i −0.142600 + 0.142600i
\(915\) −43.9164 220.783i −0.0479961 0.241293i
\(916\) 8.21630 19.8359i 0.00896976 0.0216549i
\(917\) 821.743i 0.896121i
\(918\) −643.575 128.015i −0.701062 0.139450i
\(919\) −506.869 −0.551544 −0.275772 0.961223i \(-0.588933\pi\)
−0.275772 + 0.961223i \(0.588933\pi\)
\(920\) 333.071 + 137.962i 0.362033 + 0.149959i
\(921\) 12.6541 2.51706i 0.0137395 0.00273296i
\(922\) −138.230 138.230i −0.149924 0.149924i
\(923\) −1330.66 + 1991.48i −1.44167 + 2.15761i
\(924\) −430.077 85.5476i −0.465451 0.0925839i
\(925\) 240.200 + 359.484i 0.259675 + 0.388632i
\(926\) 376.485 + 908.914i 0.406571 + 0.981549i
\(927\) 70.5489 29.2223i 0.0761045 0.0315235i
\(928\) −417.160 + 278.737i −0.449526 + 0.300364i
\(929\) 272.070 1367.79i 0.292863 1.47232i −0.501646 0.865073i \(-0.667272\pi\)
0.794510 0.607251i \(-0.207728\pi\)
\(930\) −66.3131 44.3090i −0.0713044 0.0476441i
\(931\) 27.3656 27.3656i 0.0293937 0.0293937i
\(932\) −169.407 851.665i −0.181767 0.913803i
\(933\) −493.396 + 1191.16i −0.528827 + 1.27670i
\(934\) 10.1880i 0.0109080i
\(935\) −87.5544 211.375i −0.0936411 0.226070i
\(936\) 341.626 0.364985
\(937\) −185.233 76.7261i −0.197687 0.0818848i 0.281643 0.959519i \(-0.409121\pi\)
−0.479331 + 0.877634i \(0.659121\pi\)
\(938\) 815.774 162.268i 0.869695 0.172993i
\(939\) 168.233 + 168.233i 0.179162 + 0.179162i
\(940\) −76.3699 + 114.296i −0.0812446 + 0.121591i
\(941\) −1497.87 297.945i −1.59179 0.316626i −0.681889 0.731456i \(-0.738841\pi\)
−0.909899 + 0.414830i \(0.863841\pi\)
\(942\) 220.054 + 329.334i 0.233603 + 0.349611i
\(943\) 270.628 + 653.355i 0.286987 + 0.692847i
\(944\) 47.0948 19.5073i 0.0498886 0.0206645i
\(945\) 347.182 231.979i 0.367388 0.245481i
\(946\) 50.9953 256.371i 0.0539063 0.271005i
\(947\) −845.726 565.096i −0.893058 0.596723i 0.0221273 0.999755i \(-0.492956\pi\)
−0.915186 + 0.403033i \(0.867956\pi\)
\(948\) −30.6498 + 30.6498i −0.0323310 + 0.0323310i
\(949\) −158.534 797.004i −0.167054 0.839835i
\(950\) 14.8976 35.9661i 0.0156817 0.0378590i
\(951\) 322.706i 0.339334i
\(952\) −1039.18 + 694.356i −1.09157 + 0.729365i
\(953\) 297.230 0.311889 0.155945 0.987766i \(-0.450158\pi\)
0.155945 + 0.987766i \(0.450158\pi\)
\(954\) −62.8428 26.0303i −0.0658730 0.0272855i
\(955\) −241.616 + 48.0603i −0.253001 + 0.0503249i
\(956\) −586.045 586.045i −0.613017 0.613017i
\(957\) 204.237 305.662i 0.213414 0.319396i
\(958\) −988.688 196.662i −1.03203 0.205284i
\(959\) 502.640 + 752.255i 0.524130 + 0.784416i
\(960\) −81.6352 197.085i −0.0850366 0.205297i
\(961\) 713.498 295.540i 0.742453 0.307534i
\(962\) 488.992 326.734i 0.508308 0.339640i
\(963\) −25.9567 + 130.493i −0.0269540 + 0.135507i
\(964\) −257.270 171.902i −0.266878 0.178322i
\(965\) −236.322 + 236.322i −0.244893 + 0.244893i
\(966\) 165.325 + 831.144i 0.171144 + 0.860397i
\(967\) −452.787 + 1093.12i −0.468239 + 1.13043i 0.496692 + 0.867927i \(0.334548\pi\)
−0.964931 + 0.262502i \(0.915452\pi\)
\(968\) 434.595i 0.448961i
\(969\) −49.5693 33.1212i −0.0511551 0.0341808i
\(970\) 171.586 0.176893
\(971\) 510.211 + 211.336i 0.525449 + 0.217648i 0.629608 0.776913i \(-0.283215\pi\)
−0.104160 + 0.994561i \(0.533215\pi\)
\(972\) 209.262 41.6248i 0.215290 0.0428239i
\(973\) 193.305 + 193.305i 0.198669 + 0.198669i
\(974\) 6.53565 9.78129i 0.00671011 0.0100424i
\(975\) −1343.42 267.223i −1.37787 0.274074i
\(976\) 61.3616 + 91.8341i 0.0628705 + 0.0940923i
\(977\) −125.177 302.204i −0.128124 0.309318i 0.846781 0.531942i \(-0.178538\pi\)
−0.974904 + 0.222624i \(0.928538\pi\)
\(978\) 539.105 223.305i 0.551232 0.228328i
\(979\) −376.415 + 251.512i −0.384489 + 0.256907i
\(980\) 20.8937 105.039i 0.0213201 0.107183i
\(981\) 315.345 + 210.707i 0.321453 + 0.214788i
\(982\) −552.735 + 552.735i −0.562866 + 0.562866i
\(983\) 199.903 + 1004.98i 0.203360 + 1.02236i 0.938719 + 0.344683i \(0.112014\pi\)
−0.735359 + 0.677678i \(0.762986\pi\)
\(984\) 225.009 543.221i 0.228668 0.552053i
\(985\) 227.523i 0.230988i
\(986\) −73.0887 367.442i −0.0741265 0.372659i
\(987\) −903.685 −0.915587
\(988\) 61.4041 + 25.4344i 0.0621499 + 0.0257433i
\(989\) 621.844 123.692i 0.628760 0.125068i
\(990\) −22.8646 22.8646i −0.0230956 0.0230956i
\(991\) −229.264 + 343.118i −0.231346 + 0.346234i −0.928921 0.370278i \(-0.879262\pi\)
0.697575 + 0.716512i \(0.254262\pi\)
\(992\) −408.521 81.2600i −0.411816 0.0819153i
\(993\) −151.502 226.739i −0.152570 0.228338i
\(994\) −473.916 1144.14i −0.476777 1.15104i
\(995\) −222.602 + 92.2048i −0.223721 + 0.0926682i
\(996\) 668.524 446.693i 0.671209 0.448487i
\(997\) 245.429 1233.85i 0.246167 1.23757i −0.637867 0.770146i \(-0.720183\pi\)
0.884035 0.467421i \(-0.154817\pi\)
\(998\) −124.125 82.9374i −0.124373 0.0831037i
\(999\) 396.270 396.270i 0.396666 0.396666i
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 17.3.e.a.6.1 yes 8
3.2 odd 2 153.3.p.b.91.1 8
4.3 odd 2 272.3.bh.c.193.1 8
5.2 odd 4 425.3.t.a.74.1 8
5.3 odd 4 425.3.t.c.74.1 8
5.4 even 2 425.3.u.b.176.1 8
17.2 even 8 289.3.e.b.75.1 8
17.3 odd 16 inner 17.3.e.a.3.1 8
17.4 even 4 289.3.e.i.249.1 8
17.5 odd 16 289.3.e.i.65.1 8
17.6 odd 16 289.3.e.l.131.1 8
17.7 odd 16 289.3.e.d.158.1 8
17.8 even 8 289.3.e.k.214.1 8
17.9 even 8 289.3.e.l.214.1 8
17.10 odd 16 289.3.e.b.158.1 8
17.11 odd 16 289.3.e.k.131.1 8
17.12 odd 16 289.3.e.m.65.1 8
17.13 even 4 289.3.e.m.249.1 8
17.14 odd 16 289.3.e.c.224.1 8
17.15 even 8 289.3.e.d.75.1 8
17.16 even 2 289.3.e.c.40.1 8
51.20 even 16 153.3.p.b.37.1 8
68.3 even 16 272.3.bh.c.241.1 8
85.3 even 16 425.3.t.a.224.1 8
85.37 even 16 425.3.t.c.224.1 8
85.54 odd 16 425.3.u.b.326.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.3.e.a.3.1 8 17.3 odd 16 inner
17.3.e.a.6.1 yes 8 1.1 even 1 trivial
153.3.p.b.37.1 8 51.20 even 16
153.3.p.b.91.1 8 3.2 odd 2
272.3.bh.c.193.1 8 4.3 odd 2
272.3.bh.c.241.1 8 68.3 even 16
289.3.e.b.75.1 8 17.2 even 8
289.3.e.b.158.1 8 17.10 odd 16
289.3.e.c.40.1 8 17.16 even 2
289.3.e.c.224.1 8 17.14 odd 16
289.3.e.d.75.1 8 17.15 even 8
289.3.e.d.158.1 8 17.7 odd 16
289.3.e.i.65.1 8 17.5 odd 16
289.3.e.i.249.1 8 17.4 even 4
289.3.e.k.131.1 8 17.11 odd 16
289.3.e.k.214.1 8 17.8 even 8
289.3.e.l.131.1 8 17.6 odd 16
289.3.e.l.214.1 8 17.9 even 8
289.3.e.m.65.1 8 17.12 odd 16
289.3.e.m.249.1 8 17.13 even 4
425.3.t.a.74.1 8 5.2 odd 4
425.3.t.a.224.1 8 85.3 even 16
425.3.t.c.74.1 8 5.3 odd 4
425.3.t.c.224.1 8 85.37 even 16
425.3.u.b.176.1 8 5.4 even 2
425.3.u.b.326.1 8 85.54 odd 16