Properties

Label 28.4.f.a.19.7
Level $28$
Weight $4$
Character 28.19
Analytic conductor $1.652$
Analytic rank $0$
Dimension $20$
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] = [28,4,Mod(3,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("28.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 28.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.65205348016\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + 5376 x^{11} - 41472 x^{10} + 43008 x^{9} - 28672 x^{8} + 180224 x^{7} + \cdots + 1073741824 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.7
Root \(-2.82600 - 0.117237i\) of defining polynomial
Character \(\chi\) \(=\) 28.19
Dual form 28.4.f.a.3.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31147 + 2.50600i) q^{2} +(-0.0469307 - 0.0812864i) q^{3} +(-4.56010 + 6.57309i) q^{4} +(12.4861 + 7.20883i) q^{5} +(0.142156 - 0.224213i) q^{6} +(-15.0686 - 10.7674i) q^{7} +(-22.4526 - 2.80725i) q^{8} +(13.4956 - 23.3751i) q^{9} +O(q^{10})\) \(q+(1.31147 + 2.50600i) q^{2} +(-0.0469307 - 0.0812864i) q^{3} +(-4.56010 + 6.57309i) q^{4} +(12.4861 + 7.20883i) q^{5} +(0.142156 - 0.224213i) q^{6} +(-15.0686 - 10.7674i) q^{7} +(-22.4526 - 2.80725i) q^{8} +(13.4956 - 23.3751i) q^{9} +(-1.69029 + 40.7443i) q^{10} +(31.6215 - 18.2567i) q^{11} +(0.748311 + 0.0621947i) q^{12} -15.3232i q^{13} +(7.22125 - 51.8831i) q^{14} -1.35326i q^{15} +(-22.4109 - 59.9479i) q^{16} +(-54.1508 + 31.2640i) q^{17} +(76.2770 + 3.16437i) q^{18} +(-34.6779 + 60.0639i) q^{19} +(-104.322 + 49.1989i) q^{20} +(-0.168066 + 1.73019i) q^{21} +(87.2219 + 55.3005i) q^{22} +(-12.3839 - 7.14987i) q^{23} +(0.825526 + 1.95684i) q^{24} +(41.4345 + 71.7667i) q^{25} +(38.3999 - 20.0959i) q^{26} -5.06769 q^{27} +(139.490 - 49.9465i) q^{28} -157.182 q^{29} +(3.39128 - 1.77476i) q^{30} +(165.570 + 286.776i) q^{31} +(120.838 - 134.782i) q^{32} +(-2.96804 - 1.71360i) q^{33} +(-149.365 - 94.7003i) q^{34} +(-110.527 - 243.070i) q^{35} +(92.1049 + 195.300i) q^{36} +(-38.0629 + 65.9269i) q^{37} +(-195.999 - 8.13108i) q^{38} +(-1.24557 + 0.719127i) q^{39} +(-260.108 - 196.909i) q^{40} -335.509i q^{41} +(-4.55628 + 1.84792i) q^{42} -484.545i q^{43} +(-24.1946 + 291.103i) q^{44} +(337.014 - 194.575i) q^{45} +(1.67646 - 40.4110i) q^{46} +(-187.406 + 324.597i) q^{47} +(-3.82119 + 4.63510i) q^{48} +(111.125 + 324.500i) q^{49} +(-125.508 + 197.955i) q^{50} +(5.08266 + 2.93448i) q^{51} +(100.721 + 69.8753i) q^{52} +(70.8847 + 122.776i) q^{53} +(-6.64611 - 12.6996i) q^{54} +526.438 q^{55} +(308.102 + 284.058i) q^{56} +6.50983 q^{57} +(-206.139 - 393.899i) q^{58} +(-159.945 - 277.033i) q^{59} +(8.89511 + 6.17102i) q^{60} +(213.882 + 123.485i) q^{61} +(-501.521 + 791.016i) q^{62} +(-455.049 + 206.916i) q^{63} +(496.239 + 126.060i) q^{64} +(110.462 - 191.326i) q^{65} +(0.401795 - 9.68524i) q^{66} +(-178.009 + 102.774i) q^{67} +(41.4324 - 498.504i) q^{68} +1.34219i q^{69} +(464.181 - 595.759i) q^{70} +82.4401i q^{71} +(-368.631 + 486.945i) q^{72} +(-575.023 + 331.990i) q^{73} +(-215.131 - 8.92477i) q^{74} +(3.88910 - 6.73613i) q^{75} +(-236.670 - 501.838i) q^{76} +(-673.069 - 65.3800i) q^{77} +(-3.43565 - 2.17828i) q^{78} +(564.130 + 325.700i) q^{79} +(152.330 - 910.070i) q^{80} +(-364.143 - 630.715i) q^{81} +(840.787 - 440.010i) q^{82} +790.194 q^{83} +(-10.6063 - 8.99458i) q^{84} -901.506 q^{85} +(1214.27 - 635.465i) q^{86} +(7.37667 + 12.7768i) q^{87} +(-761.236 + 321.141i) q^{88} +(631.309 + 364.487i) q^{89} +(929.588 + 589.379i) q^{90} +(-164.991 + 230.899i) q^{91} +(103.469 - 48.7965i) q^{92} +(15.5406 - 26.9172i) q^{93} +(-1059.22 - 43.9419i) q^{94} +(-865.981 + 499.974i) q^{95} +(-16.6269 - 3.49713i) q^{96} +386.693i q^{97} +(-667.462 + 704.050i) q^{98} -985.539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31147 + 2.50600i 0.463674 + 0.886006i
\(3\) −0.0469307 0.0812864i −0.00903182 0.0156436i 0.861474 0.507801i \(-0.169542\pi\)
−0.870506 + 0.492158i \(0.836208\pi\)
\(4\) −4.56010 + 6.57309i −0.570013 + 0.821636i
\(5\) 12.4861 + 7.20883i 1.11679 + 0.644778i 0.940579 0.339575i \(-0.110283\pi\)
0.176209 + 0.984353i \(0.443617\pi\)
\(6\) 0.142156 0.224213i 0.00967247 0.0152558i
\(7\) −15.0686 10.7674i −0.813627 0.581387i
\(8\) −22.4526 2.80725i −0.992274 0.124064i
\(9\) 13.4956 23.3751i 0.499837 0.865743i
\(10\) −1.69029 + 40.7443i −0.0534515 + 1.28845i
\(11\) 31.6215 18.2567i 0.866749 0.500418i 0.000482758 1.00000i \(-0.499846\pi\)
0.866267 + 0.499582i \(0.166513\pi\)
\(12\) 0.748311 + 0.0621947i 0.0180016 + 0.00149617i
\(13\) 15.3232i 0.326914i −0.986550 0.163457i \(-0.947735\pi\)
0.986550 0.163457i \(-0.0522645\pi\)
\(14\) 7.22125 51.8831i 0.137854 0.990453i
\(15\) 1.35326i 0.0232941i
\(16\) −22.4109 59.9479i −0.350170 0.936686i
\(17\) −54.1508 + 31.2640i −0.772558 + 0.446037i −0.833786 0.552087i \(-0.813832\pi\)
0.0612284 + 0.998124i \(0.480498\pi\)
\(18\) 76.2770 + 3.16437i 0.998815 + 0.0414361i
\(19\) −34.6779 + 60.0639i −0.418719 + 0.725242i −0.995811 0.0914368i \(-0.970854\pi\)
0.577092 + 0.816679i \(0.304187\pi\)
\(20\) −104.322 + 49.1989i −1.16636 + 0.550061i
\(21\) −0.168066 + 1.73019i −0.00174643 + 0.0179790i
\(22\) 87.2219 + 55.3005i 0.845262 + 0.535914i
\(23\) −12.3839 7.14987i −0.112271 0.0648196i 0.442813 0.896614i \(-0.353981\pi\)
−0.555084 + 0.831794i \(0.687314\pi\)
\(24\) 0.825526 + 1.95684i 0.00702124 + 0.0166432i
\(25\) 41.4345 + 71.7667i 0.331476 + 0.574134i
\(26\) 38.3999 20.0959i 0.289648 0.151582i
\(27\) −5.06769 −0.0361214
\(28\) 139.490 49.9465i 0.941466 0.337107i
\(29\) −157.182 −1.00648 −0.503241 0.864146i \(-0.667859\pi\)
−0.503241 + 0.864146i \(0.667859\pi\)
\(30\) 3.39128 1.77476i 0.0206387 0.0108008i
\(31\) 165.570 + 286.776i 0.959266 + 1.66150i 0.724289 + 0.689496i \(0.242168\pi\)
0.234977 + 0.972001i \(0.424499\pi\)
\(32\) 120.838 134.782i 0.667545 0.744570i
\(33\) −2.96804 1.71360i −0.0156566 0.00903937i
\(34\) −149.365 94.7003i −0.753406 0.477675i
\(35\) −110.527 243.070i −0.533784 1.17389i
\(36\) 92.1049 + 195.300i 0.426412 + 0.904168i
\(37\) −38.0629 + 65.9269i −0.169122 + 0.292927i −0.938111 0.346334i \(-0.887426\pi\)
0.768990 + 0.639261i \(0.220760\pi\)
\(38\) −195.999 8.13108i −0.836718 0.0347114i
\(39\) −1.24557 + 0.719127i −0.00511410 + 0.00295263i
\(40\) −260.108 196.909i −1.02817 0.778349i
\(41\) 335.509i 1.27799i −0.769209 0.638997i \(-0.779350\pi\)
0.769209 0.638997i \(-0.220650\pi\)
\(42\) −4.55628 + 1.84792i −0.0167393 + 0.00678905i
\(43\) 484.545i 1.71843i −0.511617 0.859213i \(-0.670953\pi\)
0.511617 0.859213i \(-0.329047\pi\)
\(44\) −24.1946 + 291.103i −0.0828972 + 0.997397i
\(45\) 337.014 194.575i 1.11642 0.644567i
\(46\) 1.67646 40.4110i 0.00537349 0.129528i
\(47\) −187.406 + 324.597i −0.581617 + 1.00739i 0.413671 + 0.910427i \(0.364247\pi\)
−0.995288 + 0.0969640i \(0.969087\pi\)
\(48\) −3.82119 + 4.63510i −0.0114904 + 0.0139379i
\(49\) 111.125 + 324.500i 0.323979 + 0.946064i
\(50\) −125.508 + 197.955i −0.354989 + 0.559901i
\(51\) 5.08266 + 2.93448i 0.0139552 + 0.00805704i
\(52\) 100.721 + 69.8753i 0.268604 + 0.186345i
\(53\) 70.8847 + 122.776i 0.183712 + 0.318199i 0.943142 0.332390i \(-0.107855\pi\)
−0.759429 + 0.650590i \(0.774522\pi\)
\(54\) −6.64611 12.6996i −0.0167485 0.0320038i
\(55\) 526.438 1.29063
\(56\) 308.102 + 284.058i 0.735212 + 0.677837i
\(57\) 6.50983 0.0151272
\(58\) −206.139 393.899i −0.466680 0.891749i
\(59\) −159.945 277.033i −0.352933 0.611298i 0.633829 0.773473i \(-0.281482\pi\)
−0.986762 + 0.162175i \(0.948149\pi\)
\(60\) 8.89511 + 6.17102i 0.0191392 + 0.0132779i
\(61\) 213.882 + 123.485i 0.448932 + 0.259191i 0.707379 0.706835i \(-0.249877\pi\)
−0.258447 + 0.966025i \(0.583211\pi\)
\(62\) −501.521 + 791.016i −1.02731 + 1.62031i
\(63\) −455.049 + 206.916i −0.910012 + 0.413793i
\(64\) 496.239 + 126.060i 0.969216 + 0.246211i
\(65\) 110.462 191.326i 0.210787 0.365094i
\(66\) 0.401795 9.68524i 0.000749356 0.0180632i
\(67\) −178.009 + 102.774i −0.324586 + 0.187400i −0.653435 0.756983i \(-0.726673\pi\)
0.328849 + 0.944383i \(0.393339\pi\)
\(68\) 41.4324 498.504i 0.0738886 0.889008i
\(69\) 1.34219i 0.00234176i
\(70\) 464.181 595.759i 0.792576 1.01724i
\(71\) 82.4401i 0.137801i 0.997624 + 0.0689003i \(0.0219490\pi\)
−0.997624 + 0.0689003i \(0.978051\pi\)
\(72\) −368.631 + 486.945i −0.603383 + 0.797043i
\(73\) −575.023 + 331.990i −0.921937 + 0.532280i −0.884252 0.467009i \(-0.845331\pi\)
−0.0376842 + 0.999290i \(0.511998\pi\)
\(74\) −215.131 8.92477i −0.337953 0.0140200i
\(75\) 3.88910 6.73613i 0.00598767 0.0103709i
\(76\) −236.670 501.838i −0.357210 0.757432i
\(77\) −673.069 65.3800i −0.996147 0.0967629i
\(78\) −3.43565 2.17828i −0.00498732 0.00316207i
\(79\) 564.130 + 325.700i 0.803412 + 0.463850i 0.844663 0.535299i \(-0.179801\pi\)
−0.0412508 + 0.999149i \(0.513134\pi\)
\(80\) 152.330 910.070i 0.212888 1.27186i
\(81\) −364.143 630.715i −0.499511 0.865178i
\(82\) 840.787 440.010i 1.13231 0.592572i
\(83\) 790.194 1.04500 0.522500 0.852639i \(-0.324999\pi\)
0.522500 + 0.852639i \(0.324999\pi\)
\(84\) −10.6063 8.99458i −0.0137767 0.0116832i
\(85\) −901.506 −1.15038
\(86\) 1214.27 635.465i 1.52254 0.796790i
\(87\) 7.37667 + 12.7768i 0.00909037 + 0.0157450i
\(88\) −761.236 + 321.141i −0.922137 + 0.389020i
\(89\) 631.309 + 364.487i 0.751895 + 0.434107i 0.826378 0.563115i \(-0.190397\pi\)
−0.0744832 + 0.997222i \(0.523731\pi\)
\(90\) 929.588 + 589.379i 1.08875 + 0.690289i
\(91\) −164.991 + 230.899i −0.190064 + 0.265986i
\(92\) 103.469 48.7965i 0.117254 0.0552977i
\(93\) 15.5406 26.9172i 0.0173278 0.0300127i
\(94\) −1059.22 43.9419i −1.16223 0.0482156i
\(95\) −865.981 + 499.974i −0.935240 + 0.539961i
\(96\) −16.6269 3.49713i −0.0176769 0.00371796i
\(97\) 386.693i 0.404771i 0.979306 + 0.202385i \(0.0648694\pi\)
−0.979306 + 0.202385i \(0.935131\pi\)
\(98\) −667.462 + 704.050i −0.687998 + 0.725713i
\(99\) 985.539i 1.00051i
\(100\) −660.675 54.9110i −0.660675 0.0549110i
\(101\) 1133.54 654.448i 1.11674 0.644753i 0.176176 0.984359i \(-0.443627\pi\)
0.940568 + 0.339606i \(0.110294\pi\)
\(102\) −0.688059 + 16.5856i −0.000667922 + 0.0161002i
\(103\) −59.8337 + 103.635i −0.0572388 + 0.0991405i −0.893225 0.449610i \(-0.851563\pi\)
0.835986 + 0.548750i \(0.184896\pi\)
\(104\) −43.0159 + 344.045i −0.0405582 + 0.324389i
\(105\) −14.5712 + 20.3918i −0.0135429 + 0.0189527i
\(106\) −214.714 + 338.654i −0.196744 + 0.310311i
\(107\) −672.944 388.524i −0.607999 0.351028i 0.164183 0.986430i \(-0.447501\pi\)
−0.772182 + 0.635401i \(0.780835\pi\)
\(108\) 23.1092 33.3103i 0.0205897 0.0296786i
\(109\) 626.620 + 1085.34i 0.550636 + 0.953729i 0.998229 + 0.0594916i \(0.0189480\pi\)
−0.447593 + 0.894237i \(0.647719\pi\)
\(110\) 690.406 + 1319.25i 0.598433 + 1.14351i
\(111\) 7.14527 0.00610990
\(112\) −307.784 + 1144.64i −0.259669 + 0.965698i
\(113\) 1151.72 0.958799 0.479400 0.877597i \(-0.340854\pi\)
0.479400 + 0.877597i \(0.340854\pi\)
\(114\) 8.53744 + 16.3137i 0.00701407 + 0.0134028i
\(115\) −103.084 178.547i −0.0835885 0.144779i
\(116\) 716.767 1033.17i 0.573708 0.826962i
\(117\) −358.180 206.795i −0.283024 0.163404i
\(118\) 484.482 764.142i 0.377968 0.596143i
\(119\) 1152.61 + 111.961i 0.887894 + 0.0862475i
\(120\) −3.79894 + 30.3843i −0.00288995 + 0.0231141i
\(121\) 1.11324 1.92819i 0.000836394 0.00144868i
\(122\) −28.9541 + 697.937i −0.0214867 + 0.517936i
\(123\) −27.2723 + 15.7457i −0.0199924 + 0.0115426i
\(124\) −2640.02 219.421i −1.91194 0.158908i
\(125\) 607.429i 0.434641i
\(126\) −1115.31 868.990i −0.788572 0.614411i
\(127\) 146.370i 0.102270i 0.998692 + 0.0511348i \(0.0162838\pi\)
−0.998692 + 0.0511348i \(0.983716\pi\)
\(128\) 334.895 + 1408.90i 0.231256 + 0.972893i
\(129\) −39.3869 + 22.7400i −0.0268823 + 0.0155205i
\(130\) 624.332 + 25.9005i 0.421212 + 0.0174741i
\(131\) 712.329 1233.79i 0.475088 0.822876i −0.524505 0.851407i \(-0.675750\pi\)
0.999593 + 0.0285313i \(0.00908303\pi\)
\(132\) 24.7982 11.6950i 0.0163516 0.00771150i
\(133\) 1169.28 531.686i 0.762327 0.346639i
\(134\) −491.004 311.307i −0.316539 0.200693i
\(135\) −63.2755 36.5321i −0.0403399 0.0232903i
\(136\) 1303.59 549.943i 0.821926 0.346744i
\(137\) −684.509 1185.60i −0.426872 0.739365i 0.569721 0.821838i \(-0.307051\pi\)
−0.996593 + 0.0824737i \(0.973718\pi\)
\(138\) −3.36354 + 1.76024i −0.00207481 + 0.00108581i
\(139\) −1844.54 −1.12556 −0.562778 0.826608i \(-0.690267\pi\)
−0.562778 + 0.826608i \(0.690267\pi\)
\(140\) 2101.73 + 381.922i 1.26878 + 0.230559i
\(141\) 35.1804 0.0210122
\(142\) −206.595 + 108.117i −0.122092 + 0.0638945i
\(143\) −279.750 484.542i −0.163594 0.283353i
\(144\) −1703.73 285.177i −0.985957 0.165033i
\(145\) −1962.59 1133.10i −1.12403 0.648957i
\(146\) −1586.09 1005.62i −0.899081 0.570037i
\(147\) 21.1623 24.2619i 0.0118737 0.0136129i
\(148\) −259.772 550.824i −0.144278 0.305929i
\(149\) −731.393 + 1266.81i −0.402135 + 0.696518i −0.993983 0.109531i \(-0.965065\pi\)
0.591849 + 0.806049i \(0.298398\pi\)
\(150\) 21.9812 + 0.911895i 0.0119650 + 0.000496373i
\(151\) 2067.95 1193.93i 1.11448 0.643447i 0.174497 0.984658i \(-0.444170\pi\)
0.939987 + 0.341210i \(0.110837\pi\)
\(152\) 947.223 1251.24i 0.505460 0.667691i
\(153\) 1687.70i 0.891782i
\(154\) −718.866 1772.46i −0.376155 0.927459i
\(155\) 4774.27i 2.47405i
\(156\) 0.953021 11.4665i 0.000489120 0.00588497i
\(157\) −1916.04 + 1106.23i −0.973993 + 0.562335i −0.900451 0.434957i \(-0.856764\pi\)
−0.0735417 + 0.997292i \(0.523430\pi\)
\(158\) −76.3684 + 1840.86i −0.0384528 + 0.926903i
\(159\) 6.65333 11.5239i 0.00331851 0.00574783i
\(160\) 2480.41 811.787i 1.22559 0.401109i
\(161\) 109.623 + 241.082i 0.0536614 + 0.118012i
\(162\) 1103.01 1739.71i 0.534943 0.843730i
\(163\) 886.780 + 511.982i 0.426122 + 0.246022i 0.697693 0.716397i \(-0.254210\pi\)
−0.271571 + 0.962418i \(0.587543\pi\)
\(164\) 2205.33 + 1529.96i 1.05005 + 0.728473i
\(165\) −24.7061 42.7922i −0.0116568 0.0201901i
\(166\) 1036.31 + 1980.23i 0.484539 + 0.925876i
\(167\) −3232.62 −1.49789 −0.748945 0.662632i \(-0.769439\pi\)
−0.748945 + 0.662632i \(0.769439\pi\)
\(168\) 8.63060 38.3756i 0.00396348 0.0176234i
\(169\) 1962.20 0.893127
\(170\) −1182.30 2259.18i −0.533400 1.01924i
\(171\) 935.998 + 1621.20i 0.418582 + 0.725006i
\(172\) 3184.95 + 2209.57i 1.41192 + 0.979526i
\(173\) −43.1092 24.8891i −0.0189453 0.0109381i 0.490497 0.871443i \(-0.336815\pi\)
−0.509443 + 0.860505i \(0.670148\pi\)
\(174\) −22.3443 + 35.2423i −0.00973518 + 0.0153547i
\(175\) 148.383 1527.57i 0.0640956 0.659847i
\(176\) −1803.12 1486.49i −0.772245 0.636641i
\(177\) −15.0126 + 26.0027i −0.00637525 + 0.0110423i
\(178\) −85.4627 + 2060.08i −0.0359871 + 0.867468i
\(179\) 2521.36 1455.71i 1.05282 0.607847i 0.129384 0.991595i \(-0.458700\pi\)
0.923438 + 0.383748i \(0.125367\pi\)
\(180\) −257.860 + 3102.50i −0.106776 + 1.28470i
\(181\) 1071.48i 0.440015i −0.975498 0.220008i \(-0.929392\pi\)
0.975498 0.220008i \(-0.0706082\pi\)
\(182\) −795.014 110.653i −0.323793 0.0450666i
\(183\) 23.1810i 0.00936386i
\(184\) 257.980 + 195.298i 0.103362 + 0.0782476i
\(185\) −950.512 + 548.778i −0.377746 + 0.218092i
\(186\) 87.8355 + 3.64388i 0.0346259 + 0.00143646i
\(187\) −1141.55 + 1977.23i −0.446409 + 0.773204i
\(188\) −1279.01 2712.03i −0.496179 1.05210i
\(189\) 76.3629 + 54.5660i 0.0293893 + 0.0210005i
\(190\) −2388.64 1514.45i −0.912055 0.578262i
\(191\) −2656.30 1533.62i −1.00630 0.580987i −0.0961935 0.995363i \(-0.530667\pi\)
−0.910106 + 0.414375i \(0.864000\pi\)
\(192\) −13.0419 46.2535i −0.00490217 0.0173857i
\(193\) 540.113 + 935.502i 0.201441 + 0.348906i 0.948993 0.315297i \(-0.102104\pi\)
−0.747552 + 0.664204i \(0.768771\pi\)
\(194\) −969.055 + 507.136i −0.358629 + 0.187682i
\(195\) −20.7363 −0.00761516
\(196\) −2639.71 749.322i −0.961992 0.273076i
\(197\) −1207.76 −0.436798 −0.218399 0.975860i \(-0.570083\pi\)
−0.218399 + 0.975860i \(0.570083\pi\)
\(198\) 2469.76 1292.50i 0.886457 0.463910i
\(199\) −1028.47 1781.36i −0.366364 0.634561i 0.622630 0.782516i \(-0.286064\pi\)
−0.988994 + 0.147955i \(0.952731\pi\)
\(200\) −728.847 1727.67i −0.257686 0.610822i
\(201\) 16.7082 + 9.64647i 0.00586320 + 0.00338512i
\(202\) 3126.65 + 1982.36i 1.08906 + 0.690487i
\(203\) 2368.51 + 1692.45i 0.818902 + 0.585156i
\(204\) −42.4661 + 20.0273i −0.0145746 + 0.00687348i
\(205\) 2418.63 4189.19i 0.824022 1.42725i
\(206\) −338.180 14.0295i −0.114379 0.00474505i
\(207\) −334.257 + 192.983i −0.112234 + 0.0647985i
\(208\) −918.592 + 343.406i −0.306216 + 0.114476i
\(209\) 2532.41i 0.838138i
\(210\) −70.2114 9.77225i −0.0230717 0.00321119i
\(211\) 762.431i 0.248758i −0.992235 0.124379i \(-0.960306\pi\)
0.992235 0.124379i \(-0.0396938\pi\)
\(212\) −1130.26 93.9397i −0.366162 0.0304330i
\(213\) 6.70125 3.86897i 0.00215569 0.00124459i
\(214\) 91.0989 2195.94i 0.0291000 0.701454i
\(215\) 3493.00 6050.06i 1.10800 1.91912i
\(216\) 113.783 + 14.2262i 0.0358423 + 0.00448136i
\(217\) 592.932 6104.07i 0.185488 1.90954i
\(218\) −1898.07 + 2993.70i −0.589694 + 0.930086i
\(219\) 53.9725 + 31.1610i 0.0166535 + 0.00961492i
\(220\) −2400.61 + 3460.32i −0.735678 + 1.06043i
\(221\) 479.063 + 829.762i 0.145816 + 0.252560i
\(222\) 9.37080 + 17.9061i 0.00283300 + 0.00541341i
\(223\) −1016.07 −0.305118 −0.152559 0.988294i \(-0.548751\pi\)
−0.152559 + 0.988294i \(0.548751\pi\)
\(224\) −3272.12 + 729.847i −0.976016 + 0.217701i
\(225\) 2236.74 0.662736
\(226\) 1510.44 + 2886.20i 0.444570 + 0.849502i
\(227\) 569.879 + 987.060i 0.166627 + 0.288606i 0.937232 0.348707i \(-0.113379\pi\)
−0.770605 + 0.637313i \(0.780046\pi\)
\(228\) −29.6855 + 42.7897i −0.00862268 + 0.0124290i
\(229\) 2960.58 + 1709.29i 0.854326 + 0.493245i 0.862108 0.506724i \(-0.169144\pi\)
−0.00778216 + 0.999970i \(0.502477\pi\)
\(230\) 312.249 492.489i 0.0895177 0.141190i
\(231\) 26.2731 + 57.7797i 0.00748330 + 0.0164572i
\(232\) 3529.15 + 441.249i 0.998707 + 0.124868i
\(233\) −1338.11 + 2317.67i −0.376234 + 0.651656i −0.990511 0.137435i \(-0.956114\pi\)
0.614277 + 0.789090i \(0.289448\pi\)
\(234\) 48.4882 1168.81i 0.0135460 0.326527i
\(235\) −4679.93 + 2701.96i −1.29909 + 0.750028i
\(236\) 2550.32 + 211.966i 0.703440 + 0.0584654i
\(237\) 61.1414i 0.0167576i
\(238\) 1231.03 + 3035.27i 0.335278 + 0.826670i
\(239\) 747.415i 0.202285i 0.994872 + 0.101143i \(0.0322499\pi\)
−0.994872 + 0.101143i \(0.967750\pi\)
\(240\) −81.1252 + 30.3278i −0.0218192 + 0.00815689i
\(241\) 1485.20 857.481i 0.396972 0.229192i −0.288205 0.957569i \(-0.593058\pi\)
0.685176 + 0.728377i \(0.259725\pi\)
\(242\) 6.29203 + 0.261026i 0.00167135 + 6.93364e-5i
\(243\) −102.593 + 177.696i −0.0270837 + 0.0469103i
\(244\) −1787.00 + 842.763i −0.468857 + 0.221116i
\(245\) −951.756 + 4852.81i −0.248186 + 1.26545i
\(246\) −75.2255 47.6946i −0.0194968 0.0123614i
\(247\) 920.370 + 531.376i 0.237092 + 0.136885i
\(248\) −2912.43 6903.65i −0.745723 1.76767i
\(249\) −37.0843 64.2320i −0.00943825 0.0163475i
\(250\) 1522.22 796.624i 0.385095 0.201532i
\(251\) −1604.07 −0.403379 −0.201690 0.979449i \(-0.564643\pi\)
−0.201690 + 0.979449i \(0.564643\pi\)
\(252\) 714.993 3934.63i 0.178731 0.983566i
\(253\) −522.132 −0.129748
\(254\) −366.804 + 191.960i −0.0906115 + 0.0474198i
\(255\) 42.3083 + 73.2802i 0.0103900 + 0.0179960i
\(256\) −3091.50 + 2686.97i −0.754761 + 0.655999i
\(257\) −4485.57 2589.74i −1.08872 0.628575i −0.155487 0.987838i \(-0.549695\pi\)
−0.933236 + 0.359263i \(0.883028\pi\)
\(258\) −108.641 68.8808i −0.0262159 0.0166214i
\(259\) 1283.42 583.585i 0.307906 0.140009i
\(260\) 753.884 + 1598.54i 0.179823 + 0.381298i
\(261\) −2121.27 + 3674.14i −0.503077 + 0.871355i
\(262\) 4026.08 + 167.023i 0.949359 + 0.0393844i
\(263\) 830.165 479.296i 0.194639 0.112375i −0.399513 0.916727i \(-0.630821\pi\)
0.594153 + 0.804352i \(0.297487\pi\)
\(264\) 61.8297 + 46.8067i 0.0144142 + 0.0109120i
\(265\) 2043.98i 0.473815i
\(266\) 2865.88 + 2232.93i 0.660596 + 0.514699i
\(267\) 68.4224i 0.0156831i
\(268\) 136.200 1638.73i 0.0310439 0.373512i
\(269\) 1986.56 1146.94i 0.450270 0.259963i −0.257674 0.966232i \(-0.582956\pi\)
0.707944 + 0.706268i \(0.249623\pi\)
\(270\) 8.56584 206.479i 0.00193074 0.0465405i
\(271\) −3136.93 + 5433.33i −0.703156 + 1.21790i 0.264197 + 0.964469i \(0.414893\pi\)
−0.967353 + 0.253433i \(0.918440\pi\)
\(272\) 3087.78 + 2545.57i 0.688323 + 0.567456i
\(273\) 26.5121 + 2.57531i 0.00587759 + 0.000570933i
\(274\) 2073.42 3270.26i 0.457152 0.721035i
\(275\) 2620.45 + 1512.91i 0.574614 + 0.331753i
\(276\) −8.82235 6.12054i −0.00192407 0.00133483i
\(277\) −3630.91 6288.92i −0.787582 1.36413i −0.927445 0.373961i \(-0.878000\pi\)
0.139863 0.990171i \(-0.455334\pi\)
\(278\) −2419.06 4622.43i −0.521891 0.997249i
\(279\) 8937.86 1.91791
\(280\) 1799.26 + 5767.83i 0.384022 + 1.23105i
\(281\) −3850.59 −0.817463 −0.408732 0.912655i \(-0.634029\pi\)
−0.408732 + 0.912655i \(0.634029\pi\)
\(282\) 46.1380 + 88.1623i 0.00974283 + 0.0186170i
\(283\) −2470.76 4279.48i −0.518980 0.898899i −0.999757 0.0220565i \(-0.992979\pi\)
0.480777 0.876843i \(-0.340355\pi\)
\(284\) −541.886 375.935i −0.113222 0.0785481i
\(285\) 81.2822 + 46.9283i 0.0168938 + 0.00975366i
\(286\) 847.380 1336.52i 0.175198 0.276328i
\(287\) −3612.57 + 5055.65i −0.743009 + 1.03981i
\(288\) −1519.74 4643.56i −0.310943 0.950085i
\(289\) −501.631 + 868.850i −0.102103 + 0.176847i
\(290\) 265.683 6404.27i 0.0537980 1.29680i
\(291\) 31.4329 18.1478i 0.00633206 0.00365582i
\(292\) 439.968 5293.58i 0.0881753 1.06090i
\(293\) 6898.69i 1.37551i −0.725941 0.687757i \(-0.758595\pi\)
0.725941 0.687757i \(-0.241405\pi\)
\(294\) 88.5541 + 21.2140i 0.0175666 + 0.00420824i
\(295\) 4612.06i 0.910253i
\(296\) 1039.68 1373.38i 0.204157 0.269682i
\(297\) −160.248 + 92.5192i −0.0313082 + 0.0180758i
\(298\) −4133.83 171.493i −0.803578 0.0333366i
\(299\) −109.559 + 189.761i −0.0211904 + 0.0367029i
\(300\) 26.5424 + 56.2808i 0.00510809 + 0.0108313i
\(301\) −5217.30 + 7301.40i −0.999071 + 1.39816i
\(302\) 5704.03 + 3616.48i 1.08686 + 0.689089i
\(303\) −106.395 61.4274i −0.0201725 0.0116466i
\(304\) 4377.87 + 732.782i 0.825947 + 0.138250i
\(305\) 1780.37 + 3083.69i 0.334241 + 0.578922i
\(306\) −4229.39 + 2213.37i −0.790124 + 0.413496i
\(307\) 7512.51 1.39662 0.698308 0.715797i \(-0.253936\pi\)
0.698308 + 0.715797i \(0.253936\pi\)
\(308\) 3499.01 4126.00i 0.647321 0.763314i
\(309\) 11.2322 0.00206788
\(310\) −11964.3 + 6261.30i −2.19203 + 1.14715i
\(311\) −383.616 664.443i −0.0699450 0.121148i 0.828932 0.559350i \(-0.188949\pi\)
−0.898877 + 0.438201i \(0.855616\pi\)
\(312\) 29.9849 12.6497i 0.00544091 0.00229534i
\(313\) 2460.41 + 1420.52i 0.444315 + 0.256525i 0.705426 0.708783i \(-0.250756\pi\)
−0.261111 + 0.965309i \(0.584089\pi\)
\(314\) −5285.04 3350.83i −0.949847 0.602223i
\(315\) −7173.39 696.803i −1.28310 0.124636i
\(316\) −4713.35 + 2222.84i −0.839071 + 0.395711i
\(317\) 2859.85 4953.41i 0.506704 0.877638i −0.493266 0.869879i \(-0.664197\pi\)
0.999970 0.00775892i \(-0.00246977\pi\)
\(318\) 37.6046 + 1.56004i 0.00663132 + 0.000275102i
\(319\) −4970.34 + 2869.63i −0.872368 + 0.503662i
\(320\) 5287.32 + 5151.29i 0.923658 + 0.899894i
\(321\) 72.9348i 0.0126817i
\(322\) −460.385 + 590.886i −0.0796778 + 0.102263i
\(323\) 4336.67i 0.747056i
\(324\) 5806.27 + 482.580i 0.995588 + 0.0827468i
\(325\) 1099.69 634.909i 0.187693 0.108364i
\(326\) −120.047 + 2893.72i −0.0203950 + 0.491621i
\(327\) 58.8154 101.871i 0.00994648 0.0172278i
\(328\) −941.857 + 7533.06i −0.158553 + 1.26812i
\(329\) 6319.03 2873.34i 1.05890 0.481496i
\(330\) 74.8361 118.034i 0.0124836 0.0196896i
\(331\) 1667.18 + 962.546i 0.276847 + 0.159838i 0.631995 0.774972i \(-0.282236\pi\)
−0.355148 + 0.934810i \(0.615570\pi\)
\(332\) −3603.37 + 5194.01i −0.595664 + 0.858610i
\(333\) 1027.36 + 1779.44i 0.169066 + 0.292832i
\(334\) −4239.48 8100.96i −0.694533 1.32714i
\(335\) −2963.51 −0.483325
\(336\) 107.488 28.7000i 0.0174522 0.00465986i
\(337\) 4006.13 0.647561 0.323780 0.946132i \(-0.395046\pi\)
0.323780 + 0.946132i \(0.395046\pi\)
\(338\) 2573.36 + 4917.28i 0.414120 + 0.791316i
\(339\) −54.0508 93.6188i −0.00865970 0.0149990i
\(340\) 4110.96 5925.68i 0.655730 0.945191i
\(341\) 10471.1 + 6045.52i 1.66289 + 0.960068i
\(342\) −2835.19 + 4471.76i −0.448274 + 0.707032i
\(343\) 1819.54 6086.29i 0.286431 0.958101i
\(344\) −1360.24 + 10879.3i −0.213195 + 1.70515i
\(345\) −9.67565 + 16.7587i −0.00150991 + 0.00261524i
\(346\) 5.83585 140.673i 0.000906756 0.0218573i
\(347\) 1679.92 969.900i 0.259892 0.150049i −0.364393 0.931245i \(-0.618724\pi\)
0.624285 + 0.781196i \(0.285390\pi\)
\(348\) −117.621 9.77590i −0.0181183 0.00150587i
\(349\) 1677.48i 0.257288i −0.991691 0.128644i \(-0.958938\pi\)
0.991691 0.128644i \(-0.0410624\pi\)
\(350\) 4022.69 1631.51i 0.614348 0.249165i
\(351\) 77.6531i 0.0118086i
\(352\) 1360.43 6468.11i 0.205998 0.979407i
\(353\) 2078.17 1199.83i 0.313342 0.180908i −0.335079 0.942190i \(-0.608763\pi\)
0.648421 + 0.761282i \(0.275430\pi\)
\(354\) −84.8514 3.52008i −0.0127395 0.000528503i
\(355\) −594.297 + 1029.35i −0.0888507 + 0.153894i
\(356\) −5274.64 + 2487.55i −0.785268 + 0.370337i
\(357\) −44.9918 98.9457i −0.00667008 0.0146688i
\(358\) 6954.68 + 4409.42i 1.02672 + 0.650964i
\(359\) 1299.08 + 750.025i 0.190983 + 0.110264i 0.592443 0.805613i \(-0.298164\pi\)
−0.401460 + 0.915877i \(0.631497\pi\)
\(360\) −8113.06 + 3422.63i −1.18777 + 0.501080i
\(361\) 1024.39 + 1774.29i 0.149349 + 0.258680i
\(362\) 2685.14 1405.22i 0.389856 0.204024i
\(363\) −0.208981 −3.02166e−5
\(364\) −765.339 2137.42i −0.110205 0.307779i
\(365\) −9573.04 −1.37281
\(366\) 58.0916 30.4011i 0.00829643 0.00434178i
\(367\) 4603.51 + 7973.52i 0.654772 + 1.13410i 0.981951 + 0.189136i \(0.0605687\pi\)
−0.327179 + 0.944962i \(0.606098\pi\)
\(368\) −151.085 + 902.626i −0.0214017 + 0.127860i
\(369\) −7842.55 4527.90i −1.10641 0.638788i
\(370\) −2621.81 1662.28i −0.368382 0.233562i
\(371\) 253.849 2613.30i 0.0355234 0.365704i
\(372\) 106.062 + 224.895i 0.0147824 + 0.0313448i
\(373\) 218.738 378.866i 0.0303642 0.0525923i −0.850444 0.526066i \(-0.823667\pi\)
0.880808 + 0.473473i \(0.157000\pi\)
\(374\) −6452.05 267.665i −0.892052 0.0370070i
\(375\) −49.3757 + 28.5071i −0.00679934 + 0.00392560i
\(376\) 5118.98 6761.96i 0.702105 0.927450i
\(377\) 2408.53i 0.329033i
\(378\) −36.5951 + 262.927i −0.00497949 + 0.0357765i
\(379\) 8880.19i 1.20355i −0.798667 0.601774i \(-0.794461\pi\)
0.798667 0.601774i \(-0.205539\pi\)
\(380\) 662.589 7972.10i 0.0894477 1.07621i
\(381\) 11.8979 6.86925i 0.00159986 0.000923680i
\(382\) 359.593 8667.99i 0.0481634 1.16098i
\(383\) −3177.82 + 5504.15i −0.423967 + 0.734332i −0.996323 0.0856729i \(-0.972696\pi\)
0.572357 + 0.820005i \(0.306029\pi\)
\(384\) 98.8075 93.3430i 0.0131309 0.0124047i
\(385\) −7932.67 5668.38i −1.05009 0.750357i
\(386\) −1636.03 + 2580.41i −0.215730 + 0.340257i
\(387\) −11326.3 6539.22i −1.48772 0.858933i
\(388\) −2541.77 1763.36i −0.332574 0.230725i
\(389\) 1433.01 + 2482.05i 0.186778 + 0.323509i 0.944174 0.329446i \(-0.106862\pi\)
−0.757396 + 0.652956i \(0.773529\pi\)
\(390\) −27.1950 51.9652i −0.00353095 0.00674707i
\(391\) 894.133 0.115648
\(392\) −1584.09 7597.83i −0.204103 0.978949i
\(393\) −133.720 −0.0171636
\(394\) −1583.94 3026.64i −0.202532 0.387005i
\(395\) 4695.84 + 8133.43i 0.598160 + 1.03604i
\(396\) 6478.03 + 4494.16i 0.822054 + 0.570303i
\(397\) 4872.27 + 2813.01i 0.615951 + 0.355619i 0.775291 0.631604i \(-0.217603\pi\)
−0.159340 + 0.987224i \(0.550937\pi\)
\(398\) 3115.30 4913.55i 0.392351 0.618830i
\(399\) −98.0940 70.0942i −0.0123079 0.00879473i
\(400\) 3373.68 4092.27i 0.421710 0.511534i
\(401\) 1959.77 3394.43i 0.244056 0.422718i −0.717810 0.696239i \(-0.754855\pi\)
0.961866 + 0.273522i \(0.0881886\pi\)
\(402\) −2.26185 + 54.5218i −0.000280624 + 0.00676442i
\(403\) 4394.31 2537.06i 0.543167 0.313598i
\(404\) −867.305 + 10435.2i −0.106807 + 1.28507i
\(405\) 10500.2i 1.28829i
\(406\) −1135.05 + 8155.09i −0.138748 + 0.996873i
\(407\) 2779.61i 0.338526i
\(408\) −105.881 80.1550i −0.0128478 0.00972613i
\(409\) −9123.48 + 5267.45i −1.10300 + 0.636818i −0.937008 0.349309i \(-0.886416\pi\)
−0.165993 + 0.986127i \(0.553083\pi\)
\(410\) 13670.1 + 567.107i 1.64663 + 0.0683107i
\(411\) −64.2489 + 111.282i −0.00771087 + 0.0133556i
\(412\) −408.354 865.879i −0.0488305 0.103541i
\(413\) −572.787 + 5896.69i −0.0682446 + 0.702559i
\(414\) −921.985 584.558i −0.109452 0.0693948i
\(415\) 9866.41 + 5696.37i 1.16704 + 0.673793i
\(416\) −2065.28 1851.63i −0.243410 0.218230i
\(417\) 86.5657 + 149.936i 0.0101658 + 0.0176077i
\(418\) −6346.24 + 3321.18i −0.742595 + 0.388623i
\(419\) −2243.25 −0.261551 −0.130776 0.991412i \(-0.541747\pi\)
−0.130776 + 0.991412i \(0.541747\pi\)
\(420\) −67.5907 188.766i −0.00785259 0.0219306i
\(421\) −14402.2 −1.66727 −0.833635 0.552316i \(-0.813744\pi\)
−0.833635 + 0.552316i \(0.813744\pi\)
\(422\) 1910.65 999.903i 0.220401 0.115342i
\(423\) 5058.32 + 8761.26i 0.581427 + 1.00706i
\(424\) −1246.88 2955.63i −0.142816 0.338533i
\(425\) −4487.42 2590.82i −0.512169 0.295701i
\(426\) 18.4841 + 11.7193i 0.00210225 + 0.00133287i
\(427\) −1893.29 4163.71i −0.214573 0.471888i
\(428\) 5622.50 2651.60i 0.634985 0.299463i
\(429\) −26.2578 + 45.4798i −0.00295510 + 0.00511838i
\(430\) 19742.4 + 819.019i 2.21410 + 0.0918525i
\(431\) 1912.19 1104.01i 0.213706 0.123383i −0.389327 0.921100i \(-0.627292\pi\)
0.603032 + 0.797717i \(0.293959\pi\)
\(432\) 113.571 + 303.797i 0.0126486 + 0.0338344i
\(433\) 12802.5i 1.42089i 0.703751 + 0.710446i \(0.251507\pi\)
−0.703751 + 0.710446i \(0.748493\pi\)
\(434\) 16074.4 6519.40i 1.77787 0.721063i
\(435\) 212.709i 0.0234451i
\(436\) −9991.47 830.426i −1.09749 0.0912160i
\(437\) 858.898 495.885i 0.0940198 0.0542824i
\(438\) −7.30646 + 176.122i −0.000797068 + 0.0192133i
\(439\) −6900.24 + 11951.6i −0.750183 + 1.29936i 0.197551 + 0.980293i \(0.436701\pi\)
−0.947734 + 0.319062i \(0.896632\pi\)
\(440\) −11819.9 1477.84i −1.28066 0.160121i
\(441\) 9084.90 + 1781.77i 0.980985 + 0.192395i
\(442\) −1451.11 + 2288.74i −0.156159 + 0.246299i
\(443\) −4670.84 2696.71i −0.500945 0.289221i 0.228159 0.973624i \(-0.426729\pi\)
−0.729104 + 0.684403i \(0.760063\pi\)
\(444\) −32.5832 + 46.9665i −0.00348272 + 0.00502011i
\(445\) 5255.05 + 9102.01i 0.559805 + 0.969610i
\(446\) −1332.55 2546.28i −0.141475 0.270336i
\(447\) 137.299 0.0145280
\(448\) −6120.28 7242.76i −0.645437 0.763813i
\(449\) 15602.5 1.63992 0.819962 0.572417i \(-0.193994\pi\)
0.819962 + 0.572417i \(0.193994\pi\)
\(450\) 2933.41 + 5605.27i 0.307294 + 0.587188i
\(451\) −6125.29 10609.3i −0.639531 1.10770i
\(452\) −5251.94 + 7570.33i −0.546528 + 0.787784i
\(453\) −194.100 112.064i −0.0201316 0.0116230i
\(454\) −1726.20 + 2722.62i −0.178446 + 0.281451i
\(455\) −3724.60 + 1693.62i −0.383763 + 0.174501i
\(456\) −146.163 18.2747i −0.0150103 0.00187673i
\(457\) −2733.79 + 4735.06i −0.279828 + 0.484676i −0.971342 0.237687i \(-0.923611\pi\)
0.691514 + 0.722363i \(0.256944\pi\)
\(458\) −400.785 + 9660.90i −0.0408896 + 0.985643i
\(459\) 274.419 158.436i 0.0279059 0.0161115i
\(460\) 1643.68 + 136.612i 0.166602 + 0.0138469i
\(461\) 14746.1i 1.48979i −0.667182 0.744895i \(-0.732500\pi\)
0.667182 0.744895i \(-0.267500\pi\)
\(462\) −110.340 + 141.617i −0.0111114 + 0.0142610i
\(463\) 8510.80i 0.854278i 0.904186 + 0.427139i \(0.140478\pi\)
−0.904186 + 0.427139i \(0.859522\pi\)
\(464\) 3522.59 + 9422.74i 0.352440 + 0.942758i
\(465\) 388.083 224.060i 0.0387030 0.0223452i
\(466\) −7562.98 313.752i −0.751821 0.0311894i
\(467\) 7878.11 13645.3i 0.780632 1.35209i −0.150942 0.988543i \(-0.548231\pi\)
0.931574 0.363552i \(-0.118436\pi\)
\(468\) 2992.62 1411.34i 0.295586 0.139400i
\(469\) 3788.95 + 368.048i 0.373044 + 0.0362364i
\(470\) −12908.7 8184.39i −1.26688 0.803230i
\(471\) 179.842 + 103.832i 0.0175939 + 0.0101578i
\(472\) 2813.48 + 6669.11i 0.274366 + 0.650361i
\(473\) −8846.18 15322.0i −0.859932 1.48945i
\(474\) 153.221 80.1850i 0.0148474 0.00777008i
\(475\) −5747.45 −0.555182
\(476\) −5991.94 + 7065.64i −0.576975 + 0.680363i
\(477\) 3826.52 0.367305
\(478\) −1873.02 + 980.210i −0.179226 + 0.0937945i
\(479\) −7222.76 12510.2i −0.688969 1.19333i −0.972172 0.234270i \(-0.924730\pi\)
0.283202 0.959060i \(-0.408603\pi\)
\(480\) −182.395 163.526i −0.0173441 0.0155498i
\(481\) 1010.21 + 583.244i 0.0957621 + 0.0552883i
\(482\) 4096.64 + 2597.36i 0.387130 + 0.245449i
\(483\) 14.4520 20.2250i 0.00136147 0.00190532i
\(484\) 7.59766 + 16.1102i 0.000713529 + 0.00151298i
\(485\) −2787.61 + 4828.28i −0.260987 + 0.452043i
\(486\) −579.854 24.0554i −0.0541208 0.00224521i
\(487\) 6588.32 3803.77i 0.613029 0.353933i −0.161121 0.986935i \(-0.551511\pi\)
0.774150 + 0.633002i \(0.218178\pi\)
\(488\) −4455.56 3372.98i −0.413307 0.312885i
\(489\) 96.1108i 0.00888810i
\(490\) −13409.4 + 3979.20i −1.23627 + 0.366861i
\(491\) 7521.86i 0.691358i 0.938353 + 0.345679i \(0.112351\pi\)
−0.938353 + 0.345679i \(0.887649\pi\)
\(492\) 20.8669 251.065i 0.00191210 0.0230059i
\(493\) 8511.53 4914.13i 0.777566 0.448928i
\(494\) −124.594 + 3003.33i −0.0113477 + 0.273535i
\(495\) 7104.59 12305.5i 0.645106 1.11736i
\(496\) 13481.0 16352.5i 1.22039 1.48034i
\(497\) 887.668 1242.26i 0.0801154 0.112118i
\(498\) 112.331 177.172i 0.0101077 0.0159423i
\(499\) 12351.3 + 7131.05i 1.10806 + 0.639739i 0.938326 0.345751i \(-0.112376\pi\)
0.169734 + 0.985490i \(0.445709\pi\)
\(500\) 3992.69 + 2769.94i 0.357117 + 0.247751i
\(501\) 151.709 + 262.768i 0.0135287 + 0.0234323i
\(502\) −2103.69 4019.81i −0.187036 0.357396i
\(503\) −3887.75 −0.344625 −0.172312 0.985042i \(-0.555124\pi\)
−0.172312 + 0.985042i \(0.555124\pi\)
\(504\) 10797.9 3368.37i 0.954319 0.297697i
\(505\) 18871.2 1.66289
\(506\) −684.759 1308.46i −0.0601606 0.114957i
\(507\) −92.0874 159.500i −0.00806656 0.0139717i
\(508\) −962.103 667.463i −0.0840284 0.0582950i
\(509\) −14200.0 8198.40i −1.23655 0.713924i −0.268165 0.963373i \(-0.586417\pi\)
−0.968388 + 0.249448i \(0.919751\pi\)
\(510\) −128.154 + 202.129i −0.0111270 + 0.0175499i
\(511\) 12239.5 + 1188.91i 1.05957 + 0.102924i
\(512\) −10788.0 4223.44i −0.931183 0.364553i
\(513\) 175.737 304.385i 0.0151247 0.0261967i
\(514\) 607.228 14637.2i 0.0521083 1.25607i
\(515\) −1494.18 + 862.663i −0.127847 + 0.0738126i
\(516\) 30.1361 362.590i 0.00257106 0.0309344i
\(517\) 13685.7i 1.16421i
\(518\) 3145.63 + 2450.89i 0.266816 + 0.207888i
\(519\) 4.67225i 0.000395162i
\(520\) −3017.26 + 3985.68i −0.254453 + 0.336122i
\(521\) −3203.82 + 1849.73i −0.269409 + 0.155543i −0.628619 0.777713i \(-0.716379\pi\)
0.359210 + 0.933257i \(0.383046\pi\)
\(522\) −11989.4 497.382i −1.00529 0.0417047i
\(523\) −4152.31 + 7192.01i −0.347166 + 0.601309i −0.985745 0.168247i \(-0.946189\pi\)
0.638579 + 0.769556i \(0.279523\pi\)
\(524\) 4861.51 + 10308.4i 0.405298 + 0.859399i
\(525\) −131.134 + 59.6282i −0.0109013 + 0.00495693i
\(526\) 2289.85 + 1451.82i 0.189814 + 0.120346i
\(527\) −17931.5 10352.7i −1.48218 0.855735i
\(528\) −36.2102 + 216.331i −0.00298456 + 0.0178307i
\(529\) −5981.26 10359.8i −0.491597 0.851471i
\(530\) −5122.23 + 2680.62i −0.419803 + 0.219695i
\(531\) −8634.20 −0.705636
\(532\) −1837.23 + 10110.3i −0.149725 + 0.823944i
\(533\) −5141.07 −0.417794
\(534\) 171.467 89.7338i 0.0138953 0.00727184i
\(535\) −5601.61 9702.28i −0.452671 0.784049i
\(536\) 4285.28 1807.82i 0.345328 0.145683i
\(537\) −236.658 136.635i −0.0190178 0.0109799i
\(538\) 5479.54 + 3474.15i 0.439107 + 0.278403i
\(539\) 9438.23 + 8232.41i 0.754236 + 0.657876i
\(540\) 528.672 249.325i 0.0421304 0.0198690i
\(541\) 4989.02 8641.23i 0.396478 0.686720i −0.596811 0.802382i \(-0.703566\pi\)
0.993289 + 0.115662i \(0.0368990\pi\)
\(542\) −17729.9 735.530i −1.40510 0.0582910i
\(543\) −87.0970 + 50.2855i −0.00688341 + 0.00397414i
\(544\) −2329.69 + 11076.4i −0.183611 + 0.872973i
\(545\) 18068.8i 1.42015i
\(546\) 28.3160 + 69.8167i 0.00221944 + 0.00547231i
\(547\) 8278.49i 0.647098i 0.946211 + 0.323549i \(0.104876\pi\)
−0.946211 + 0.323549i \(0.895124\pi\)
\(548\) 10914.5 + 907.143i 0.850811 + 0.0707139i
\(549\) 5772.94 3333.01i 0.448785 0.259106i
\(550\) −354.740 + 8550.98i −0.0275021 + 0.662937i
\(551\) 5450.75 9440.97i 0.421433 0.729944i
\(552\) 3.76787 30.1357i 0.000290527 0.00232366i
\(553\) −4993.68 10982.1i −0.384002 0.844494i
\(554\) 10998.2 17346.8i 0.843448 1.33031i
\(555\) 89.2163 + 51.5091i 0.00682346 + 0.00393953i
\(556\) 8411.31 12124.3i 0.641581 0.924796i
\(557\) 9289.00 + 16089.0i 0.706620 + 1.22390i 0.966104 + 0.258155i \(0.0831144\pi\)
−0.259483 + 0.965748i \(0.583552\pi\)
\(558\) 11721.7 + 22398.3i 0.889283 + 1.69928i
\(559\) −7424.76 −0.561778
\(560\) −12094.5 + 12073.3i −0.912655 + 0.911051i
\(561\) 214.295 0.0161276
\(562\) −5049.93 9649.60i −0.379036 0.724277i
\(563\) 5985.39 + 10367.0i 0.448054 + 0.776052i 0.998259 0.0589776i \(-0.0187841\pi\)
−0.550206 + 0.835029i \(0.685451\pi\)
\(564\) −160.426 + 231.244i −0.0119773 + 0.0172644i
\(565\) 14380.4 + 8302.53i 1.07078 + 0.618212i
\(566\) 7484.07 11804.1i 0.555793 0.876615i
\(567\) −1304.05 + 13424.9i −0.0965874 + 0.994341i
\(568\) 231.429 1850.99i 0.0170961 0.136736i
\(569\) −6586.01 + 11407.3i −0.485237 + 0.840455i −0.999856 0.0169638i \(-0.994600\pi\)
0.514619 + 0.857419i \(0.327933\pi\)
\(570\) −11.0035 + 265.238i −0.000808570 + 0.0194906i
\(571\) −11143.6 + 6433.76i −0.816717 + 0.471532i −0.849283 0.527938i \(-0.822965\pi\)
0.0325660 + 0.999470i \(0.489632\pi\)
\(572\) 4460.63 + 370.738i 0.326063 + 0.0271003i
\(573\) 287.895i 0.0209895i
\(574\) −17407.3 2422.80i −1.26579 0.176177i
\(575\) 1185.01i 0.0859447i
\(576\) 9643.69 9898.36i 0.697605 0.716027i
\(577\) −15701.9 + 9065.48i −1.13289 + 0.654075i −0.944660 0.328050i \(-0.893608\pi\)
−0.188230 + 0.982125i \(0.560275\pi\)
\(578\) −2835.21 117.619i −0.204030 0.00846423i
\(579\) 50.6957 87.8076i 0.00363876 0.00630252i
\(580\) 16397.6 7733.20i 1.17392 0.553627i
\(581\) −11907.1 8508.36i −0.850241 0.607549i
\(582\) 86.7017 + 54.9707i 0.00617509 + 0.00391514i
\(583\) 4482.96 + 2588.24i 0.318465 + 0.183866i
\(584\) 13842.7 5839.80i 0.980851 0.413789i
\(585\) −2981.51 5164.12i −0.210718 0.364975i
\(586\) 17288.1 9047.41i 1.21871 0.637790i
\(587\) 24252.4 1.70529 0.852644 0.522492i \(-0.174998\pi\)
0.852644 + 0.522492i \(0.174998\pi\)
\(588\) 62.9737 + 249.738i 0.00441665 + 0.0175154i
\(589\) −22966.5 −1.60665
\(590\) 11557.8 6048.57i 0.806490 0.422061i
\(591\) 56.6809 + 98.1742i 0.00394508 + 0.00683307i
\(592\) 4805.20 + 804.310i 0.333602 + 0.0558394i
\(593\) −6524.07 3766.67i −0.451790 0.260841i 0.256796 0.966466i \(-0.417333\pi\)
−0.708586 + 0.705625i \(0.750666\pi\)
\(594\) −442.013 280.246i −0.0305320 0.0193580i
\(595\) 13584.4 + 9706.91i 0.935979 + 0.668814i
\(596\) −4991.62 10584.3i −0.343062 0.727432i
\(597\) −96.5337 + 167.201i −0.00661786 + 0.0114625i
\(598\) −619.225 25.6887i −0.0423445 0.00175667i
\(599\) −20430.0 + 11795.3i −1.39357 + 0.804578i −0.993709 0.111997i \(-0.964275\pi\)
−0.399862 + 0.916575i \(0.630942\pi\)
\(600\) −106.230 + 140.326i −0.00722807 + 0.00954797i
\(601\) 585.188i 0.0397177i 0.999803 + 0.0198588i \(0.00632168\pi\)
−0.999803 + 0.0198588i \(0.993678\pi\)
\(602\) −25139.7 3499.02i −1.70202 0.236893i
\(603\) 5547.96i 0.374677i
\(604\) −1582.25 + 19037.2i −0.106591 + 1.28247i
\(605\) 27.8000 16.0503i 0.00186815 0.00107858i
\(606\) 14.4031 347.187i 0.000965491 0.0232731i
\(607\) 11750.3 20352.1i 0.785715 1.36090i −0.142856 0.989744i \(-0.545629\pi\)
0.928571 0.371155i \(-0.121038\pi\)
\(608\) 3905.08 + 11932.0i 0.260480 + 0.795897i
\(609\) 26.4170 271.956i 0.00175775 0.0180956i
\(610\) −5392.83 + 8505.76i −0.357950 + 0.564571i
\(611\) 4973.86 + 2871.66i 0.329330 + 0.190139i
\(612\) −11093.4 7696.10i −0.732720 0.508327i
\(613\) −2807.61 4862.93i −0.184989 0.320411i 0.758584 0.651576i \(-0.225892\pi\)
−0.943573 + 0.331165i \(0.892558\pi\)
\(614\) 9852.41 + 18826.4i 0.647575 + 1.23741i
\(615\) −454.032 −0.0297697
\(616\) 14928.6 + 3357.42i 0.976447 + 0.219601i
\(617\) 18767.7 1.22457 0.612286 0.790636i \(-0.290250\pi\)
0.612286 + 0.790636i \(0.290250\pi\)
\(618\) 14.7306 + 28.1478i 0.000958822 + 0.00183215i
\(619\) −10954.8 18974.3i −0.711325 1.23205i −0.964360 0.264594i \(-0.914762\pi\)
0.253034 0.967457i \(-0.418571\pi\)
\(620\) −31381.7 21771.1i −2.03277 1.41024i
\(621\) 62.7579 + 36.2333i 0.00405538 + 0.00234137i
\(622\) 1162.00 1832.74i 0.0749064 0.118145i
\(623\) −5588.36 12289.9i −0.359378 0.790343i
\(624\) 71.0244 + 58.5527i 0.00455649 + 0.00375639i
\(625\) 9558.18 16555.2i 0.611723 1.05954i
\(626\) −333.075 + 8028.76i −0.0212657 + 0.512610i
\(627\) 205.851 118.848i 0.0131115 0.00756991i
\(628\) 1466.02 17638.8i 0.0931541 1.12081i
\(629\) 4759.99i 0.301738i
\(630\) −7661.49 18890.4i −0.484509 1.19462i
\(631\) 6303.66i 0.397694i −0.980031 0.198847i \(-0.936280\pi\)
0.980031 0.198847i \(-0.0637197\pi\)
\(632\) −11751.9 8896.47i −0.739658 0.559941i
\(633\) −61.9752 + 35.7814i −0.00389146 + 0.00224673i
\(634\) 16163.9 + 670.562i 1.01254 + 0.0420054i
\(635\) −1055.16 + 1827.59i −0.0659412 + 0.114213i
\(636\) 45.4078 + 96.2832i 0.00283103 + 0.00600295i
\(637\) 4972.37 1702.78i 0.309282 0.105913i
\(638\) −13709.7 8692.26i −0.850742 0.539388i
\(639\) 1927.04 + 1112.58i 0.119300 + 0.0688778i
\(640\) −5975.00 + 20005.8i −0.369036 + 1.23562i
\(641\) −3879.08 6718.77i −0.239024 0.414002i 0.721410 0.692508i \(-0.243494\pi\)
−0.960435 + 0.278506i \(0.910161\pi\)
\(642\) −182.775 + 95.6517i −0.0112361 + 0.00588017i
\(643\) −31588.3 −1.93735 −0.968677 0.248323i \(-0.920121\pi\)
−0.968677 + 0.248323i \(0.920121\pi\)
\(644\) −2084.54 378.798i −0.127550 0.0231782i
\(645\) −655.716 −0.0400291
\(646\) 10867.7 5687.41i 0.661896 0.346390i
\(647\) 1356.83 + 2350.10i 0.0824461 + 0.142801i 0.904300 0.426897i \(-0.140393\pi\)
−0.821854 + 0.569698i \(0.807060\pi\)
\(648\) 6405.39 + 15183.4i 0.388314 + 0.920465i
\(649\) −10115.4 5840.13i −0.611809 0.353228i
\(650\) 3033.30 + 1923.18i 0.183040 + 0.116051i
\(651\) −524.004 + 238.271i −0.0315474 + 0.0143450i
\(652\) −7409.11 + 3494.19i −0.445036 + 0.209882i
\(653\) −7502.94 + 12995.5i −0.449637 + 0.778794i −0.998362 0.0572087i \(-0.981780\pi\)
0.548725 + 0.836003i \(0.315113\pi\)
\(654\) 332.424 + 13.7907i 0.0198759 + 0.000824555i
\(655\) 17788.4 10270.1i 1.06114 0.612652i
\(656\) −20113.1 + 7519.07i −1.19708 + 0.447516i
\(657\) 17921.6i 1.06421i
\(658\) 15487.8 + 12067.2i 0.917594 + 0.714937i
\(659\) 16279.4i 0.962301i 0.876638 + 0.481150i \(0.159781\pi\)
−0.876638 + 0.481150i \(0.840219\pi\)
\(660\) 393.939 + 32.7417i 0.0232334 + 0.00193101i
\(661\) 9763.98 5637.24i 0.574546 0.331714i −0.184417 0.982848i \(-0.559040\pi\)
0.758963 + 0.651134i \(0.225706\pi\)
\(662\) −225.692 + 5440.30i −0.0132504 + 0.319401i
\(663\) 44.9655 77.8826i 0.00263396 0.00456215i
\(664\) −17741.9 2218.27i −1.03693 0.129647i
\(665\) 18432.6 + 1790.49i 1.07486 + 0.104409i
\(666\) −3111.94 + 4908.26i −0.181059 + 0.285572i
\(667\) 1946.53 + 1123.83i 0.112999 + 0.0652398i
\(668\) 14741.1 21248.3i 0.853817 1.23072i
\(669\) 47.6850 + 82.5928i 0.00275577 + 0.00477313i
\(670\) −3886.55 7426.56i −0.224105 0.428229i
\(671\) 9017.71 0.518815
\(672\) 212.889 + 231.726i 0.0122208 + 0.0133021i
\(673\) 17159.1 0.982813 0.491406 0.870930i \(-0.336483\pi\)
0.491406 + 0.870930i \(0.336483\pi\)
\(674\) 5253.91 + 10039.4i 0.300257 + 0.573743i
\(675\) −209.977 363.691i −0.0119734 0.0207385i
\(676\) −8947.84 + 12897.7i −0.509094 + 0.733825i
\(677\) 13993.3 + 8079.03i 0.794395 + 0.458644i 0.841508 0.540245i \(-0.181668\pi\)
−0.0471122 + 0.998890i \(0.515002\pi\)
\(678\) 163.723 258.230i 0.00927396 0.0146272i
\(679\) 4163.70 5826.93i 0.235328 0.329333i
\(680\) 20241.2 + 2530.75i 1.14149 + 0.142720i
\(681\) 53.4897 92.6468i 0.00300988 0.00521327i
\(682\) −1417.52 + 34169.2i −0.0795888 + 1.91849i
\(683\) 26743.3 15440.3i 1.49825 0.865015i 0.498252 0.867032i \(-0.333975\pi\)
0.999998 + 0.00201701i \(0.000642035\pi\)
\(684\) −14924.5 1240.43i −0.834288 0.0693406i
\(685\) 19738.0i 1.10095i
\(686\) 17638.5 3422.20i 0.981694 0.190467i
\(687\) 320.873i 0.0178196i
\(688\) −29047.4 + 10859.1i −1.60963 + 0.601742i
\(689\) 1881.32 1086.18i 0.104024 0.0600582i
\(690\) −54.6867 2.26869i −0.00301723 0.000125170i
\(691\) −12232.5 + 21187.3i −0.673438 + 1.16643i 0.303485 + 0.952836i \(0.401850\pi\)
−0.976923 + 0.213593i \(0.931483\pi\)
\(692\) 360.181 169.864i 0.0197861 0.00933127i
\(693\) −10611.7 + 14850.7i −0.581683 + 0.814042i
\(694\) 4633.73 + 2937.88i 0.253449 + 0.160692i
\(695\) −23031.1 13297.0i −1.25701 0.725733i
\(696\) −129.758 307.580i −0.00706675 0.0167511i
\(697\) 10489.3 + 18168.1i 0.570032 + 0.987324i
\(698\) 4203.77 2199.96i 0.227959 0.119298i
\(699\) 251.194 0.0135923
\(700\) 9364.18 + 7941.20i 0.505618 + 0.428785i
\(701\) 19017.1 1.02463 0.512316 0.858797i \(-0.328788\pi\)
0.512316 + 0.858797i \(0.328788\pi\)
\(702\) −194.599 + 101.840i −0.0104625 + 0.00547533i
\(703\) −2639.88 4572.41i −0.141629 0.245308i
\(704\) 17993.3 5073.47i 0.963276 0.271610i
\(705\) 439.265 + 253.610i 0.0234662 + 0.0135482i
\(706\) 5732.24 + 3634.36i 0.305575 + 0.193741i
\(707\) −24127.5 2343.68i −1.28346 0.124672i
\(708\) −102.459 217.254i −0.00543874 0.0115324i
\(709\) 7409.95 12834.4i 0.392506 0.679840i −0.600274 0.799795i \(-0.704942\pi\)
0.992779 + 0.119955i \(0.0382750\pi\)
\(710\) −3358.96 139.347i −0.177549 0.00736565i
\(711\) 15226.5 8791.04i 0.803150 0.463699i
\(712\) −13151.3 9955.91i −0.692229 0.524036i
\(713\) 4735.21i 0.248717i
\(714\) 188.953 242.514i 0.00990390 0.0127113i
\(715\) 8066.70i 0.421926i
\(716\) −1929.17 + 23211.3i −0.100693 + 1.21152i
\(717\) 60.7546 35.0767i 0.00316447 0.00182701i
\(718\) −175.862 + 4239.14i −0.00914080 + 0.220339i
\(719\) −7996.54 + 13850.4i −0.414771 + 0.718405i −0.995404 0.0957604i \(-0.969472\pi\)
0.580633 + 0.814165i \(0.302805\pi\)
\(720\) −19217.1 15842.7i −0.994695 0.820030i
\(721\) 2017.49 917.379i 0.104210 0.0473855i
\(722\) −3102.92 + 4894.03i −0.159943 + 0.252267i
\(723\) −139.403 80.4843i −0.00717075 0.00414003i
\(724\) 7042.96 + 4886.08i 0.361532 + 0.250814i
\(725\) −6512.77 11280.4i −0.333625 0.577856i
\(726\) −0.274071 0.523706i −1.40107e−5 2.67721e-5i
\(727\) −11418.3 −0.582503 −0.291252 0.956646i \(-0.594072\pi\)
−0.291252 + 0.956646i \(0.594072\pi\)
\(728\) 4352.67 4721.10i 0.221595 0.240351i
\(729\) −19644.5 −0.998043
\(730\) −12554.7 23990.1i −0.636536 1.21632i
\(731\) 15148.8 + 26238.5i 0.766481 + 1.32758i
\(732\) 152.370 + 105.708i 0.00769368 + 0.00533752i
\(733\) −3692.15 2131.66i −0.186047 0.107414i 0.404084 0.914722i \(-0.367590\pi\)
−0.590131 + 0.807308i \(0.700924\pi\)
\(734\) −13944.3 + 21993.4i −0.701217 + 1.10598i
\(735\) 439.134 150.381i 0.0220377 0.00754678i
\(736\) −2460.13 + 805.147i −0.123209 + 0.0403235i
\(737\) −3752.61 + 6499.71i −0.187556 + 0.324857i
\(738\) 1061.68 25591.6i 0.0529550 1.27648i
\(739\) −25655.7 + 14812.3i −1.27708 + 0.737321i −0.976310 0.216376i \(-0.930576\pi\)
−0.300768 + 0.953697i \(0.597243\pi\)
\(740\) 727.266 8750.28i 0.0361282 0.434685i
\(741\) 99.7513i 0.00494529i
\(742\) 6881.86 2791.12i 0.340487 0.138093i
\(743\) 9471.33i 0.467657i −0.972278 0.233829i \(-0.924875\pi\)
0.972278 0.233829i \(-0.0751255\pi\)
\(744\) −424.491 + 560.734i −0.0209174 + 0.0276311i
\(745\) −18264.4 + 10545.0i −0.898198 + 0.518575i
\(746\) 1236.31 + 51.2885i 0.0606762 + 0.00251716i
\(747\) 10664.1 18470.8i 0.522330 0.904702i
\(748\) −7790.88 16519.9i −0.380833 0.807522i
\(749\) 5956.90 + 13100.4i 0.290601 + 0.639089i
\(750\) −136.194 86.3496i −0.00663078 0.00420405i
\(751\) 16235.4 + 9373.53i 0.788868 + 0.455453i 0.839564 0.543261i \(-0.182811\pi\)
−0.0506961 + 0.998714i \(0.516144\pi\)
\(752\) 23658.9 + 3960.10i 1.14727 + 0.192034i
\(753\) 75.2802 + 130.389i 0.00364325 + 0.00631029i
\(754\) −6035.78 + 3158.71i −0.291526 + 0.152564i
\(755\) 34427.3 1.65952
\(756\) −706.890 + 253.113i −0.0340071 + 0.0121768i
\(757\) −28442.9 −1.36562 −0.682809 0.730597i \(-0.739242\pi\)
−0.682809 + 0.730597i \(0.739242\pi\)
\(758\) 22253.8 11646.1i 1.06635 0.558054i
\(759\) 24.5040 + 42.4422i 0.00117186 + 0.00202971i
\(760\) 20847.1 8794.71i 0.995004 0.419760i
\(761\) −23807.4 13745.2i −1.13406 0.654749i −0.189106 0.981957i \(-0.560559\pi\)
−0.944953 + 0.327207i \(0.893892\pi\)
\(762\) 32.8181 + 20.8073i 0.00156020 + 0.000989200i
\(763\) 2244.02 23101.6i 0.106473 1.09611i
\(764\) 22193.6 10466.6i 1.05096 0.495641i
\(765\) −12166.4 + 21072.8i −0.575001 + 0.995931i
\(766\) −17961.0 745.118i −0.847205 0.0351465i
\(767\) −4245.02 + 2450.86i −0.199842 + 0.115379i
\(768\) 363.501 + 125.195i 0.0170790 + 0.00588229i
\(769\) 36762.3i 1.72390i −0.506991 0.861952i \(-0.669242\pi\)
0.506991 0.861952i \(-0.330758\pi\)
\(770\) 3801.54 27313.2i 0.177919 1.27831i
\(771\) 486.154i 0.0227087i
\(772\) −8612.11 715.782i −0.401498 0.0333699i
\(773\) 7076.12 4085.40i 0.329250 0.190093i −0.326258 0.945281i \(-0.605788\pi\)
0.655508 + 0.755188i \(0.272454\pi\)
\(774\) 1533.28 36959.6i 0.0712048 1.71639i
\(775\) −13720.6 + 23764.8i −0.635948 + 1.10149i
\(776\) 1085.54 8682.28i 0.0502174 0.401644i
\(777\) −107.669 76.9363i −0.00497118 0.00355222i
\(778\) −4340.68 + 6846.27i −0.200027 + 0.315489i
\(779\) 20152.0 + 11634.8i 0.926855 + 0.535120i
\(780\) 94.5596 136.301i 0.00434074 0.00625688i
\(781\) 1505.08 + 2606.88i 0.0689579 + 0.119439i
\(782\) 1172.63 + 2240.70i 0.0536228 + 0.102465i
\(783\) 796.550 0.0363555
\(784\) 16962.7 13934.0i 0.772717 0.634750i
\(785\) −31898.5 −1.45032
\(786\) −175.370 335.104i −0.00795832 0.0152071i
\(787\) 16883.2 + 29242.6i 0.764703 + 1.32450i 0.940403 + 0.340061i \(0.110448\pi\)
−0.175700 + 0.984444i \(0.556219\pi\)
\(788\) 5507.50 7938.69i 0.248980 0.358889i
\(789\) −77.9205 44.9874i −0.00351590 0.00202990i
\(790\) −14224.0 + 22434.5i −0.640590 + 1.01036i
\(791\) −17354.7 12401.0i −0.780105 0.557433i
\(792\) −2766.65 + 22127.9i −0.124127 + 0.992780i
\(793\) 1892.18 3277.36i 0.0847332 0.146762i
\(794\) −659.578 + 15899.1i −0.0294805 + 0.710627i
\(795\) 166.148 95.9255i 0.00741215 0.00427941i
\(796\) 16399.0 + 1362.98i 0.730210 + 0.0606903i
\(797\) 3635.92i 0.161595i −0.996731 0.0807973i \(-0.974253\pi\)
0.996731 0.0807973i \(-0.0257466\pi\)
\(798\) 47.0092 337.750i 0.00208535 0.0149827i
\(799\) 23436.2i 1.03769i
\(800\) 14679.7 + 3087.57i 0.648758 + 0.136453i
\(801\) 17039.8 9837.93i 0.751650 0.433965i
\(802\) 11076.6 + 459.517i 0.487693 + 0.0202320i
\(803\) −12122.1 + 20996.0i −0.532725 + 0.922707i
\(804\) −139.598 + 65.8353i −0.00612344 + 0.00288785i
\(805\) −369.161 + 3800.41i −0.0161630 + 0.166394i
\(806\) 12120.9 + 7684.89i 0.529702 + 0.335842i
\(807\) −186.461 107.653i −0.00813351 0.00469588i
\(808\) −27288.1 + 11511.9i −1.18811 + 0.501224i
\(809\) 18106.2 + 31360.8i 0.786871 + 1.36290i 0.927875 + 0.372891i \(0.121634\pi\)
−0.141004 + 0.990009i \(0.545033\pi\)
\(810\) 26313.5 13770.7i 1.14144 0.597348i
\(811\) −3940.47 −0.170615 −0.0853074 0.996355i \(-0.527187\pi\)
−0.0853074 + 0.996355i \(0.527187\pi\)
\(812\) −21925.3 + 7850.70i −0.947569 + 0.339292i
\(813\) 588.874 0.0254031
\(814\) −6965.71 + 3645.37i −0.299936 + 0.156966i
\(815\) 7381.59 + 12785.3i 0.317259 + 0.549508i
\(816\) 62.0087 370.459i 0.00266022 0.0158930i
\(817\) 29103.6 + 16803.0i 1.24628 + 0.719538i
\(818\) −25165.4 15955.4i −1.07566 0.681989i
\(819\) 3170.61 + 6972.80i 0.135275 + 0.297496i
\(820\) 16506.7 + 35001.0i 0.702974 + 1.49060i
\(821\) 6397.96 11081.6i 0.271973 0.471072i −0.697394 0.716688i \(-0.745657\pi\)
0.969367 + 0.245616i \(0.0789904\pi\)
\(822\) −363.134 15.0647i −0.0154085 0.000639224i
\(823\) −12548.2 + 7244.68i −0.531472 + 0.306845i −0.741616 0.670825i \(-0.765940\pi\)
0.210144 + 0.977671i \(0.432607\pi\)
\(824\) 1634.35 2158.91i 0.0690963 0.0912733i
\(825\) 284.009i 0.0119853i
\(826\) −15528.3 + 6297.91i −0.654115 + 0.265293i
\(827\) 42110.7i 1.77066i −0.464965 0.885329i \(-0.653933\pi\)
0.464965 0.885329i \(-0.346067\pi\)
\(828\) 255.751 3077.13i 0.0107342 0.129152i
\(829\) −19713.8 + 11381.8i −0.825922 + 0.476846i −0.852454 0.522802i \(-0.824887\pi\)
0.0265323 + 0.999648i \(0.491554\pi\)
\(830\) −1335.65 + 32195.9i −0.0558569 + 1.34643i
\(831\) −340.802 + 590.287i −0.0142266 + 0.0246412i
\(832\) 1931.64 7603.95i 0.0804898 0.316851i
\(833\) −16162.6 14097.7i −0.672272 0.586383i
\(834\) −262.213 + 413.571i −0.0108869 + 0.0171712i
\(835\) −40362.7 23303.4i −1.67283 0.965806i
\(836\) −16645.8 11548.1i −0.688644 0.477749i
\(837\) −839.057 1453.29i −0.0346500 0.0600156i
\(838\) −2941.95 5621.59i −0.121274 0.231736i
\(839\) 5492.90 0.226026 0.113013 0.993594i \(-0.463950\pi\)
0.113013 + 0.993594i \(0.463950\pi\)
\(840\) 384.405 416.943i 0.0157896 0.0171261i
\(841\) 317.228 0.0130070
\(842\) −18888.0 36092.0i −0.773069 1.47721i
\(843\) 180.711 + 313.001i 0.00738318 + 0.0127880i
\(844\) 5011.52 + 3476.76i 0.204388 + 0.141795i
\(845\) 24500.2 + 14145.2i 0.997433 + 0.575868i
\(846\) −15321.9 + 24166.3i −0.622670 + 0.982097i
\(847\) −37.5366 + 17.0683i −0.00152275 + 0.000692415i
\(848\) 5771.57 7000.90i 0.233722 0.283505i
\(849\) −231.909 + 401.678i −0.00937466 + 0.0162374i
\(850\) 607.479 14643.3i 0.0245134 0.590894i
\(851\) 942.737 544.290i 0.0379749 0.0219248i
\(852\) −5.12734 + 61.6908i −0.000206173 + 0.00248062i
\(853\) 14715.4i 0.590675i 0.955393 + 0.295338i \(0.0954321\pi\)
−0.955393 + 0.295338i \(0.904568\pi\)
\(854\) 7951.29 10205.2i 0.318603 0.408915i
\(855\) 26989.8i 1.07957i
\(856\) 14018.7 + 10612.5i 0.559752 + 0.423747i
\(857\) 14391.2 8308.75i 0.573621 0.331180i −0.184973 0.982744i \(-0.559220\pi\)
0.758594 + 0.651563i \(0.225887\pi\)
\(858\) −148.409 6.15677i −0.00590512 0.000244975i
\(859\) 11713.7 20288.7i 0.465268 0.805868i −0.533945 0.845519i \(-0.679291\pi\)
0.999214 + 0.0396508i \(0.0126245\pi\)
\(860\) 23839.1 + 50548.7i 0.945239 + 2.00430i
\(861\) 580.496 + 56.3877i 0.0229771 + 0.00223193i
\(862\) 5274.43 + 3344.10i 0.208408 + 0.132135i
\(863\) 16181.8 + 9342.55i 0.638278 + 0.368510i 0.783951 0.620823i \(-0.213201\pi\)
−0.145673 + 0.989333i \(0.546535\pi\)
\(864\) −612.372 + 683.031i −0.0241126 + 0.0268949i
\(865\) −358.843 621.534i −0.0141052 0.0244310i
\(866\) −32083.0 + 16790.0i −1.25892 + 0.658831i
\(867\) 94.1675 0.00368869
\(868\) 37418.7 + 31732.6i 1.46322 + 1.24087i
\(869\) 23784.8 0.928476
\(870\) −533.049 + 278.961i −0.0207725 + 0.0108709i
\(871\) 1574.82 + 2727.66i 0.0612636 + 0.106112i
\(872\) −11022.4 26127.7i −0.428058 1.01467i
\(873\) 9038.98 + 5218.66i 0.350427 + 0.202319i
\(874\) 2369.11 + 1502.06i 0.0916891 + 0.0581328i
\(875\) −6540.46 + 9153.10i −0.252695 + 0.353636i
\(876\) −450.944 + 212.668i −0.0173927 + 0.00820250i
\(877\) 21490.9 37223.4i 0.827477 1.43323i −0.0725340 0.997366i \(-0.523109\pi\)
0.900011 0.435867i \(-0.143558\pi\)
\(878\) −39000.1 1617.93i −1.49908 0.0621895i
\(879\) −560.769 + 323.760i −0.0215180 + 0.0124234i
\(880\) −11797.9 31558.8i −0.451942 1.20892i
\(881\) 36788.9i 1.40687i 0.710761 + 0.703434i \(0.248351\pi\)
−0.710761 + 0.703434i \(0.751649\pi\)
\(882\) 7449.42 + 25103.5i 0.284394 + 0.958367i
\(883\) 6006.92i 0.228934i −0.993427 0.114467i \(-0.963484\pi\)
0.993427 0.114467i \(-0.0365161\pi\)
\(884\) −7638.67 634.877i −0.290629 0.0241552i
\(885\) −374.898 + 216.447i −0.0142396 + 0.00822124i
\(886\) 632.310 15241.8i 0.0239761 0.577944i
\(887\) −5667.43 + 9816.29i −0.214536 + 0.371588i −0.953129 0.302564i \(-0.902157\pi\)
0.738593 + 0.674152i \(0.235491\pi\)
\(888\) −160.430 20.0585i −0.00606270 0.000758018i
\(889\) 1576.03 2205.59i 0.0594582 0.0832094i
\(890\) −15917.8 + 25106.2i −0.599514 + 0.945573i
\(891\) −23029.5 13296.1i −0.865901 0.499928i
\(892\) 4633.40 6678.73i 0.173921 0.250696i
\(893\) −12997.7 22512.7i −0.487068 0.843627i
\(894\) 180.063 + 344.072i 0.00673627 + 0.0128719i
\(895\) 41975.8 1.56770
\(896\) 10123.8 24836.1i 0.377471 0.926021i
\(897\) 20.5667 0.000765553
\(898\) 20462.1 + 39099.9i 0.760390 + 1.45298i
\(899\) −26024.6 45076.0i −0.965484 1.67227i
\(900\) −10199.7 + 14702.3i −0.377768 + 0.544528i
\(901\) −7676.92 4432.27i −0.283857 0.163885i
\(902\) 18553.8 29263.8i 0.684895 1.08024i
\(903\) 838.356 + 81.4355i 0.0308956 + 0.00300111i
\(904\) −25859.0 3233.15i −0.951392 0.118952i
\(905\) 7724.15 13378.6i 0.283712 0.491404i
\(906\) 26.2761 633.384i 0.000963537 0.0232260i
\(907\) 23176.8 13381.1i 0.848482 0.489871i −0.0116566 0.999932i \(-0.503711\pi\)
0.860138 + 0.510061i \(0.170377\pi\)
\(908\) −9086.74 755.231i −0.332108 0.0276027i
\(909\) 35328.7i 1.28908i
\(910\) −9128.91 7112.73i −0.332550 0.259104i
\(911\) 26600.8i 0.967425i −0.875227 0.483712i \(-0.839288\pi\)
0.875227 0.483712i \(-0.160712\pi\)
\(912\) −145.891 390.251i −0.00529708 0.0141694i
\(913\) 24987.1 14426.3i 0.905753 0.522937i
\(914\) −15451.4 641.003i −0.559174 0.0231975i
\(915\) 167.108 289.439i 0.00603761 0.0104574i
\(916\) −24735.9 + 11665.6i −0.892245 + 0.420788i
\(917\) −24018.5 + 10921.5i −0.864953 + 0.393305i
\(918\) 756.933 + 479.912i 0.0272141 + 0.0172543i
\(919\) 32169.8 + 18573.2i 1.15472 + 0.666675i 0.950032 0.312153i \(-0.101050\pi\)
0.204684 + 0.978828i \(0.434383\pi\)
\(920\) 1813.29 + 4298.24i 0.0649808 + 0.154031i
\(921\) −352.567 610.664i −0.0126140 0.0218481i
\(922\) 36953.7 19339.0i 1.31996 0.690777i
\(923\) 1263.24 0.0450489
\(924\) −499.599 90.7859i −0.0177874 0.00323229i
\(925\) −6308.47 −0.224239
\(926\) −21328.1 + 11161.6i −0.756895 + 0.396106i
\(927\) 1614.98 + 2797.23i 0.0572201 + 0.0991081i
\(928\) −18993.6 + 21185.3i −0.671872 + 0.749397i
\(929\) 8412.37 + 4856.89i 0.297095 + 0.171528i 0.641137 0.767426i \(-0.278463\pi\)
−0.344042 + 0.938954i \(0.611796\pi\)
\(930\) 1070.45 + 678.689i 0.0377435 + 0.0239302i
\(931\) −23344.3 4578.40i −0.821782 0.161172i
\(932\) −9132.34 19364.3i −0.320966 0.680579i
\(933\) −36.0068 + 62.3656i −0.00126346 + 0.00218838i
\(934\) 44527.0 + 1847.21i 1.55992 + 0.0647138i
\(935\) −28507.0 + 16458.5i −0.997089 + 0.575670i
\(936\) 7461.55 + 5648.59i 0.260565 + 0.197254i
\(937\) 26889.4i 0.937501i −0.883331 0.468750i \(-0.844704\pi\)
0.883331 0.468750i \(-0.155296\pi\)
\(938\) 4046.76 + 9977.81i 0.140865 + 0.347321i
\(939\) 266.664i 0.00926756i
\(940\) 3580.76 43082.8i 0.124246 1.49490i
\(941\) −30074.6 + 17363.6i −1.04188 + 0.601527i −0.920364 0.391063i \(-0.872107\pi\)
−0.121511 + 0.992590i \(0.538774\pi\)
\(942\) −24.3460 + 586.858i −0.000842074 + 0.0202982i
\(943\) −2398.85 + 4154.93i −0.0828391 + 0.143481i
\(944\) −13023.0 + 15796.9i −0.449007 + 0.544646i
\(945\) 560.115 + 1231.80i 0.0192810 + 0.0424027i
\(946\) 26795.6 42262.9i 0.920930 1.45252i
\(947\) 21993.8 + 12698.1i 0.754702 + 0.435727i 0.827390 0.561628i \(-0.189825\pi\)
−0.0726886 + 0.997355i \(0.523158\pi\)
\(948\) 401.888 + 278.811i 0.0137687 + 0.00955207i
\(949\) 5087.14 + 8811.18i 0.174010 + 0.301394i
\(950\) −7537.60 14403.1i −0.257423 0.491894i
\(951\) −536.859 −0.0183058
\(952\) −25564.7 5749.47i −0.870334 0.195737i
\(953\) −23212.4 −0.789005 −0.394503 0.918895i \(-0.629083\pi\)
−0.394503 + 0.918895i \(0.629083\pi\)
\(954\) 5018.36 + 9589.28i 0.170310 + 0.325434i
\(955\) −22111.2 38297.7i −0.749215 1.29768i
\(956\) −4912.82 3408.29i −0.166205 0.115305i
\(957\) 466.523 + 269.347i 0.0157581 + 0.00909797i
\(958\) 21878.1 34507.0i 0.737840 1.16375i
\(959\) −2451.33 + 25235.8i −0.0825418 + 0.849745i
\(960\) 170.592 671.541i 0.00573525 0.0225770i
\(961\) −39931.3 + 69163.1i −1.34038 + 2.32161i
\(962\) −136.756 + 3296.49i −0.00458335 + 0.110482i
\(963\) −18163.5 + 10486.7i −0.607801 + 0.350914i
\(964\) −1136.37 + 13672.5i −0.0379669 + 0.456808i
\(965\) 15574.3i 0.519539i
\(966\) 69.6371 + 9.69232i 0.00231940 + 0.000322821i
\(967\) 57399.1i 1.90882i 0.298494 + 0.954412i \(0.403516\pi\)
−0.298494 + 0.954412i \(0.596484\pi\)
\(968\) −30.4080 + 40.1677i −0.00100966 + 0.00133372i
\(969\) −352.512 + 203.523i −0.0116866 + 0.00674727i
\(970\) −15755.5 653.622i −0.521526 0.0216356i
\(971\) 5194.04 8996.34i 0.171663 0.297329i −0.767338 0.641242i \(-0.778419\pi\)
0.939001 + 0.343913i \(0.111753\pi\)
\(972\) −700.177 1484.66i −0.0231051 0.0489924i
\(973\) 27794.7 + 19861.0i 0.915783 + 0.654383i
\(974\) 18172.6 + 11521.8i 0.597832 + 0.379038i
\(975\) −103.219 59.5934i −0.00339041 0.00195745i
\(976\) 2609.37 15589.2i 0.0855779 0.511269i
\(977\) −23494.7 40694.1i −0.769358 1.33257i −0.937911 0.346875i \(-0.887243\pi\)
0.168553 0.985693i \(-0.446091\pi\)
\(978\) 240.854 126.046i 0.00787491 0.00412118i
\(979\) 26617.3 0.868940
\(980\) −27557.8 28385.3i −0.898268 0.925239i
\(981\) 33826.4 1.10091
\(982\) −18849.8 + 9864.68i −0.612547 + 0.320565i
\(983\) 8426.43 + 14595.0i 0.273409 + 0.473559i 0.969733 0.244170i \(-0.0785154\pi\)
−0.696323 + 0.717728i \(0.745182\pi\)
\(984\) 656.537 276.972i 0.0212699 0.00897310i
\(985\) −15080.1 8706.52i −0.487810 0.281637i
\(986\) 23477.4 + 14885.2i 0.758290 + 0.480772i
\(987\) −530.119 378.803i −0.0170961 0.0122162i
\(988\) −7689.76 + 3626.54i −0.247615 + 0.116777i
\(989\) −3464.43 + 6000.57i −0.111388 + 0.192929i
\(990\) 40155.1 + 1665.84i 1.28910 + 0.0534788i
\(991\) 1218.57 703.544i 0.0390608 0.0225518i −0.480342 0.877081i \(-0.659488\pi\)
0.519403 + 0.854529i \(0.326154\pi\)
\(992\) 58659.3 + 12337.7i 1.87745 + 0.394883i
\(993\) 180.692i 0.00577450i
\(994\) 4277.24 + 595.321i 0.136485 + 0.0189964i
\(995\) 29656.3i 0.944893i
\(996\) 591.311 + 49.1459i 0.0188116 + 0.00156350i
\(997\) 6527.66 3768.75i 0.207355 0.119717i −0.392726 0.919655i \(-0.628468\pi\)
0.600082 + 0.799939i \(0.295135\pi\)
\(998\) −1672.05 + 40304.7i −0.0530338 + 1.27838i
\(999\) 192.891 334.097i 0.00610891 0.0105809i
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 28.4.f.a.19.7 yes 20
4.3 odd 2 inner 28.4.f.a.19.1 yes 20
7.2 even 3 196.4.d.b.195.14 20
7.3 odd 6 inner 28.4.f.a.3.1 20
7.4 even 3 196.4.f.d.31.1 20
7.5 odd 6 196.4.d.b.195.13 20
7.6 odd 2 196.4.f.d.19.7 20
8.3 odd 2 448.4.p.h.383.5 20
8.5 even 2 448.4.p.h.383.6 20
28.3 even 6 inner 28.4.f.a.3.7 yes 20
28.11 odd 6 196.4.f.d.31.7 20
28.19 even 6 196.4.d.b.195.16 20
28.23 odd 6 196.4.d.b.195.15 20
28.27 even 2 196.4.f.d.19.1 20
56.3 even 6 448.4.p.h.255.6 20
56.45 odd 6 448.4.p.h.255.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.f.a.3.1 20 7.3 odd 6 inner
28.4.f.a.3.7 yes 20 28.3 even 6 inner
28.4.f.a.19.1 yes 20 4.3 odd 2 inner
28.4.f.a.19.7 yes 20 1.1 even 1 trivial
196.4.d.b.195.13 20 7.5 odd 6
196.4.d.b.195.14 20 7.2 even 3
196.4.d.b.195.15 20 28.23 odd 6
196.4.d.b.195.16 20 28.19 even 6
196.4.f.d.19.1 20 28.27 even 2
196.4.f.d.19.7 20 7.6 odd 2
196.4.f.d.31.1 20 7.4 even 3
196.4.f.d.31.7 20 28.11 odd 6
448.4.p.h.255.5 20 56.45 odd 6
448.4.p.h.255.6 20 56.3 even 6
448.4.p.h.383.5 20 8.3 odd 2
448.4.p.h.383.6 20 8.5 even 2