Properties

Label 240.2.s.c.61.6
Level $240$
Weight $2$
Character 240.61
Analytic conductor $1.916$
Analytic rank $0$
Dimension $20$
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] = [240,2,Mod(61,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.s (of order \(4\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 61.6
Root \(-0.0861743 + 1.41159i\) of defining polynomial
Character \(\chi\) \(=\) 240.61
Dual form 240.2.s.c.181.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0861743 + 1.41159i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.98515 - 0.243285i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.05908 - 0.937207i) q^{6} +2.76462i q^{7} +(0.514486 - 2.78124i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.0861743 + 1.41159i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.98515 - 0.243285i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.05908 - 0.937207i) q^{6} +2.76462i q^{7} +(0.514486 - 2.78124i) q^{8} +1.00000i q^{9} +(-0.937207 - 1.05908i) q^{10} +(-3.51009 + 3.51009i) q^{11} +(1.23168 + 1.57574i) q^{12} +(-4.55960 - 4.55960i) q^{13} +(-3.90250 - 0.238239i) q^{14} +1.00000 q^{15} +(3.88162 + 0.965913i) q^{16} -5.00550 q^{17} +(-1.41159 - 0.0861743i) q^{18} +(-0.812949 - 0.812949i) q^{19} +(1.57574 - 1.23168i) q^{20} +(1.95488 - 1.95488i) q^{21} +(-4.65232 - 5.25728i) q^{22} +7.48205i q^{23} +(-2.33043 + 1.60284i) q^{24} -1.00000i q^{25} +(6.82919 - 6.04335i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.672590 - 5.48818i) q^{28} +(6.03354 + 6.03354i) q^{29} +(-0.0861743 + 1.41159i) q^{30} +7.58233 q^{31} +(-1.69796 + 5.39601i) q^{32} +4.96402 q^{33} +(0.431345 - 7.06569i) q^{34} +(-1.95488 - 1.95488i) q^{35} +(0.243285 - 1.98515i) q^{36} +(1.08674 - 1.08674i) q^{37} +(1.21760 - 1.07749i) q^{38} +6.44825i q^{39} +(1.60284 + 2.33043i) q^{40} -3.15671i q^{41} +(2.59102 + 2.92794i) q^{42} +(-3.10932 + 3.10932i) q^{43} +(7.82201 - 6.11410i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(-10.5616 - 0.644760i) q^{46} -2.76008 q^{47} +(-2.06172 - 3.42773i) q^{48} -0.643123 q^{49} +(1.41159 + 0.0861743i) q^{50} +(3.53942 + 3.53942i) q^{51} +(7.94221 + 10.1608i) q^{52} +(6.41096 - 6.41096i) q^{53} +(0.937207 + 1.05908i) q^{54} -4.96402i q^{55} +(7.68908 + 1.42236i) q^{56} +1.14968i q^{57} +(-9.03679 + 7.99692i) q^{58} +(-5.13756 + 5.13756i) q^{59} +(-1.98515 - 0.243285i) q^{60} +(-2.49234 - 2.49234i) q^{61} +(-0.653402 + 10.7031i) q^{62} -2.76462 q^{63} +(-7.47061 - 2.86182i) q^{64} +6.44825 q^{65} +(-0.427771 + 7.00714i) q^{66} +(-3.14625 - 3.14625i) q^{67} +(9.93666 + 1.21776i) q^{68} +(5.29061 - 5.29061i) q^{69} +(2.92794 - 2.59102i) q^{70} +3.50237i q^{71} +(2.78124 + 0.514486i) q^{72} +14.6145i q^{73} +(1.44038 + 1.62767i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(1.41605 + 1.81160i) q^{76} +(-9.70408 - 9.70408i) q^{77} +(-9.10226 - 0.555674i) q^{78} +8.95325 q^{79} +(-3.42773 + 2.06172i) q^{80} -1.00000 q^{81} +(4.45596 + 0.272027i) q^{82} +(-2.86293 - 2.86293i) q^{83} +(-4.35632 + 3.40514i) q^{84} +(3.53942 - 3.53942i) q^{85} +(-4.12112 - 4.65701i) q^{86} -8.53271i q^{87} +(7.95653 + 11.5683i) q^{88} +7.23560i q^{89} +(1.05908 - 0.937207i) q^{90} +(12.6056 - 12.6056i) q^{91} +(1.82027 - 14.8530i) q^{92} +(-5.36151 - 5.36151i) q^{93} +(0.237848 - 3.89609i) q^{94} +1.14968 q^{95} +(5.01620 - 2.61491i) q^{96} -8.24056 q^{97} +(0.0554207 - 0.907823i) q^{98} +(-3.51009 - 3.51009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0861743 + 1.41159i −0.0609344 + 0.998142i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.98515 0.243285i −0.992574 0.121642i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 1.05908 0.937207i 0.432366 0.382613i
\(7\) 2.76462i 1.04493i 0.852661 + 0.522464i \(0.174987\pi\)
−0.852661 + 0.522464i \(0.825013\pi\)
\(8\) 0.514486 2.78124i 0.181898 0.983317i
\(9\) 1.00000i 0.333333i
\(10\) −0.937207 1.05908i −0.296371 0.334909i
\(11\) −3.51009 + 3.51009i −1.05833 + 1.05833i −0.0601437 + 0.998190i \(0.519156\pi\)
−0.998190 + 0.0601437i \(0.980844\pi\)
\(12\) 1.23168 + 1.57574i 0.355556 + 0.454877i
\(13\) −4.55960 4.55960i −1.26461 1.26461i −0.948835 0.315771i \(-0.897737\pi\)
−0.315771 0.948835i \(-0.602263\pi\)
\(14\) −3.90250 0.238239i −1.04299 0.0636721i
\(15\) 1.00000 0.258199
\(16\) 3.88162 + 0.965913i 0.970406 + 0.241478i
\(17\) −5.00550 −1.21401 −0.607006 0.794697i \(-0.707630\pi\)
−0.607006 + 0.794697i \(0.707630\pi\)
\(18\) −1.41159 0.0861743i −0.332714 0.0203115i
\(19\) −0.812949 0.812949i −0.186503 0.186503i 0.607679 0.794183i \(-0.292101\pi\)
−0.794183 + 0.607679i \(0.792101\pi\)
\(20\) 1.57574 1.23168i 0.352346 0.275413i
\(21\) 1.95488 1.95488i 0.426590 0.426590i
\(22\) −4.65232 5.25728i −0.991878 1.12086i
\(23\) 7.48205i 1.56011i 0.625708 + 0.780057i \(0.284810\pi\)
−0.625708 + 0.780057i \(0.715190\pi\)
\(24\) −2.33043 + 1.60284i −0.475697 + 0.327178i
\(25\) 1.00000i 0.200000i
\(26\) 6.82919 6.04335i 1.33931 1.18520i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.672590 5.48818i 0.127108 1.03717i
\(29\) 6.03354 + 6.03354i 1.12040 + 1.12040i 0.991681 + 0.128719i \(0.0410866\pi\)
0.128719 + 0.991681i \(0.458913\pi\)
\(30\) −0.0861743 + 1.41159i −0.0157332 + 0.257719i
\(31\) 7.58233 1.36183 0.680913 0.732364i \(-0.261583\pi\)
0.680913 + 0.732364i \(0.261583\pi\)
\(32\) −1.69796 + 5.39601i −0.300161 + 0.953889i
\(33\) 4.96402 0.864126
\(34\) 0.431345 7.06569i 0.0739751 1.21176i
\(35\) −1.95488 1.95488i −0.330435 0.330435i
\(36\) 0.243285 1.98515i 0.0405475 0.330858i
\(37\) 1.08674 1.08674i 0.178659 0.178659i −0.612112 0.790771i \(-0.709680\pi\)
0.790771 + 0.612112i \(0.209680\pi\)
\(38\) 1.21760 1.07749i 0.197521 0.174792i
\(39\) 6.44825i 1.03255i
\(40\) 1.60284 + 2.33043i 0.253431 + 0.368474i
\(41\) 3.15671i 0.492995i −0.969143 0.246497i \(-0.920720\pi\)
0.969143 0.246497i \(-0.0792797\pi\)
\(42\) 2.59102 + 2.92794i 0.399803 + 0.451791i
\(43\) −3.10932 + 3.10932i −0.474166 + 0.474166i −0.903260 0.429094i \(-0.858833\pi\)
0.429094 + 0.903260i \(0.358833\pi\)
\(44\) 7.82201 6.11410i 1.17921 0.921736i
\(45\) −0.707107 0.707107i −0.105409 0.105409i
\(46\) −10.5616 0.644760i −1.55722 0.0950647i
\(47\) −2.76008 −0.402599 −0.201299 0.979530i \(-0.564516\pi\)
−0.201299 + 0.979530i \(0.564516\pi\)
\(48\) −2.06172 3.42773i −0.297584 0.494750i
\(49\) −0.643123 −0.0918747
\(50\) 1.41159 + 0.0861743i 0.199628 + 0.0121869i
\(51\) 3.53942 + 3.53942i 0.495618 + 0.495618i
\(52\) 7.94221 + 10.1608i 1.10139 + 1.40905i
\(53\) 6.41096 6.41096i 0.880613 0.880613i −0.112983 0.993597i \(-0.536041\pi\)
0.993597 + 0.112983i \(0.0360407\pi\)
\(54\) 0.937207 + 1.05908i 0.127538 + 0.144122i
\(55\) 4.96402i 0.669349i
\(56\) 7.68908 + 1.42236i 1.02750 + 0.190071i
\(57\) 1.14968i 0.152279i
\(58\) −9.03679 + 7.99692i −1.18659 + 1.05005i
\(59\) −5.13756 + 5.13756i −0.668854 + 0.668854i −0.957451 0.288597i \(-0.906811\pi\)
0.288597 + 0.957451i \(0.406811\pi\)
\(60\) −1.98515 0.243285i −0.256282 0.0314079i
\(61\) −2.49234 2.49234i −0.319111 0.319111i 0.529314 0.848426i \(-0.322449\pi\)
−0.848426 + 0.529314i \(0.822449\pi\)
\(62\) −0.653402 + 10.7031i −0.0829821 + 1.35930i
\(63\) −2.76462 −0.348309
\(64\) −7.47061 2.86182i −0.933826 0.357728i
\(65\) 6.44825 0.799807
\(66\) −0.427771 + 7.00714i −0.0526550 + 0.862520i
\(67\) −3.14625 3.14625i −0.384376 0.384376i 0.488300 0.872676i \(-0.337617\pi\)
−0.872676 + 0.488300i \(0.837617\pi\)
\(68\) 9.93666 + 1.21776i 1.20500 + 0.147675i
\(69\) 5.29061 5.29061i 0.636914 0.636914i
\(70\) 2.92794 2.59102i 0.349956 0.309686i
\(71\) 3.50237i 0.415655i 0.978166 + 0.207827i \(0.0666392\pi\)
−0.978166 + 0.207827i \(0.933361\pi\)
\(72\) 2.78124 + 0.514486i 0.327772 + 0.0606328i
\(73\) 14.6145i 1.71050i 0.518217 + 0.855249i \(0.326596\pi\)
−0.518217 + 0.855249i \(0.673404\pi\)
\(74\) 1.44038 + 1.62767i 0.167440 + 0.189213i
\(75\) −0.707107 + 0.707107i −0.0816497 + 0.0816497i
\(76\) 1.41605 + 1.81160i 0.162432 + 0.207805i
\(77\) −9.70408 9.70408i −1.10588 1.10588i
\(78\) −9.10226 0.555674i −1.03063 0.0629177i
\(79\) 8.95325 1.00732 0.503660 0.863902i \(-0.331987\pi\)
0.503660 + 0.863902i \(0.331987\pi\)
\(80\) −3.42773 + 2.06172i −0.383232 + 0.230507i
\(81\) −1.00000 −0.111111
\(82\) 4.45596 + 0.272027i 0.492079 + 0.0300404i
\(83\) −2.86293 2.86293i −0.314247 0.314247i 0.532305 0.846553i \(-0.321326\pi\)
−0.846553 + 0.532305i \(0.821326\pi\)
\(84\) −4.35632 + 3.40514i −0.475314 + 0.371531i
\(85\) 3.53942 3.53942i 0.383904 0.383904i
\(86\) −4.12112 4.65701i −0.444392 0.502178i
\(87\) 8.53271i 0.914803i
\(88\) 7.95653 + 11.5683i 0.848169 + 1.23319i
\(89\) 7.23560i 0.766972i 0.923547 + 0.383486i \(0.125277\pi\)
−0.923547 + 0.383486i \(0.874723\pi\)
\(90\) 1.05908 0.937207i 0.111636 0.0987903i
\(91\) 12.6056 12.6056i 1.32142 1.32142i
\(92\) 1.82027 14.8530i 0.189776 1.54853i
\(93\) −5.36151 5.36151i −0.555963 0.555963i
\(94\) 0.237848 3.89609i 0.0245321 0.401851i
\(95\) 1.14968 0.117955
\(96\) 5.01620 2.61491i 0.511963 0.266883i
\(97\) −8.24056 −0.836702 −0.418351 0.908285i \(-0.637392\pi\)
−0.418351 + 0.908285i \(0.637392\pi\)
\(98\) 0.0554207 0.907823i 0.00559833 0.0917040i
\(99\) −3.51009 3.51009i −0.352778 0.352778i
\(100\) −0.243285 + 1.98515i −0.0243285 + 0.198515i
\(101\) 1.07326 1.07326i 0.106794 0.106794i −0.651691 0.758485i \(-0.725940\pi\)
0.758485 + 0.651691i \(0.225940\pi\)
\(102\) −5.30121 + 4.69119i −0.524898 + 0.464497i
\(103\) 1.66763i 0.164316i −0.996619 0.0821582i \(-0.973819\pi\)
0.996619 0.0821582i \(-0.0261813\pi\)
\(104\) −15.0272 + 10.3355i −1.47354 + 1.01348i
\(105\) 2.76462i 0.269799i
\(106\) 8.49716 + 9.60208i 0.825317 + 0.932637i
\(107\) −6.08860 + 6.08860i −0.588607 + 0.588607i −0.937254 0.348647i \(-0.886641\pi\)
0.348647 + 0.937254i \(0.386641\pi\)
\(108\) −1.57574 + 1.23168i −0.151626 + 0.118519i
\(109\) 2.92136 + 2.92136i 0.279816 + 0.279816i 0.833035 0.553220i \(-0.186601\pi\)
−0.553220 + 0.833035i \(0.686601\pi\)
\(110\) 7.00714 + 0.427771i 0.668105 + 0.0407864i
\(111\) −1.53688 −0.145874
\(112\) −2.67038 + 10.7312i −0.252327 + 1.01400i
\(113\) −2.84395 −0.267536 −0.133768 0.991013i \(-0.542708\pi\)
−0.133768 + 0.991013i \(0.542708\pi\)
\(114\) −1.62288 0.0990732i −0.151996 0.00927905i
\(115\) −5.29061 5.29061i −0.493352 0.493352i
\(116\) −10.5096 13.4453i −0.975792 1.24837i
\(117\) 4.55960 4.55960i 0.421535 0.421535i
\(118\) −6.80938 7.69483i −0.626855 0.708367i
\(119\) 13.8383i 1.26856i
\(120\) 0.514486 2.78124i 0.0469659 0.253891i
\(121\) 13.6415i 1.24014i
\(122\) 3.73293 3.30337i 0.337963 0.299073i
\(123\) −2.23213 + 2.23213i −0.201264 + 0.201264i
\(124\) −15.0520 1.84466i −1.35171 0.165656i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 0.238239 3.90250i 0.0212240 0.347662i
\(127\) −6.61073 −0.586607 −0.293304 0.956019i \(-0.594755\pi\)
−0.293304 + 0.956019i \(0.594755\pi\)
\(128\) 4.68348 10.2988i 0.413965 0.910293i
\(129\) 4.39724 0.387155
\(130\) −0.555674 + 9.10226i −0.0487358 + 0.798321i
\(131\) −6.70125 6.70125i −0.585491 0.585491i 0.350916 0.936407i \(-0.385870\pi\)
−0.936407 + 0.350916i \(0.885870\pi\)
\(132\) −9.85432 1.20767i −0.857709 0.105114i
\(133\) 2.24749 2.24749i 0.194883 0.194883i
\(134\) 4.71233 4.17008i 0.407083 0.360240i
\(135\) 1.00000i 0.0860663i
\(136\) −2.57526 + 13.9215i −0.220827 + 1.19376i
\(137\) 14.3908i 1.22949i −0.788725 0.614746i \(-0.789258\pi\)
0.788725 0.614746i \(-0.210742\pi\)
\(138\) 7.01223 + 7.92406i 0.596921 + 0.674541i
\(139\) 0.292743 0.292743i 0.0248302 0.0248302i −0.694583 0.719413i \(-0.744411\pi\)
0.719413 + 0.694583i \(0.244411\pi\)
\(140\) 3.40514 + 4.35632i 0.287787 + 0.368176i
\(141\) 1.95167 + 1.95167i 0.164360 + 0.164360i
\(142\) −4.94389 0.301814i −0.414882 0.0253277i
\(143\) 32.0093 2.67675
\(144\) −0.965913 + 3.88162i −0.0804927 + 0.323469i
\(145\) −8.53271 −0.708603
\(146\) −20.6296 1.25940i −1.70732 0.104228i
\(147\) 0.454757 + 0.454757i 0.0375077 + 0.0375077i
\(148\) −2.42172 + 1.89295i −0.199065 + 0.155600i
\(149\) −10.9363 + 10.9363i −0.895934 + 0.895934i −0.995074 0.0991393i \(-0.968391\pi\)
0.0991393 + 0.995074i \(0.468391\pi\)
\(150\) −0.937207 1.05908i −0.0765227 0.0864732i
\(151\) 13.5225i 1.10045i 0.835017 + 0.550223i \(0.185457\pi\)
−0.835017 + 0.550223i \(0.814543\pi\)
\(152\) −2.67926 + 1.84276i −0.217317 + 0.149467i
\(153\) 5.00550i 0.404671i
\(154\) 14.5344 12.8619i 1.17121 1.03644i
\(155\) −5.36151 + 5.36151i −0.430647 + 0.430647i
\(156\) 1.56876 12.8007i 0.125601 1.02488i
\(157\) 2.76487 + 2.76487i 0.220661 + 0.220661i 0.808777 0.588116i \(-0.200130\pi\)
−0.588116 + 0.808777i \(0.700130\pi\)
\(158\) −0.771540 + 12.6383i −0.0613804 + 1.00545i
\(159\) −9.06647 −0.719018
\(160\) −2.61491 5.01620i −0.206727 0.396565i
\(161\) −20.6850 −1.63021
\(162\) 0.0861743 1.41159i 0.00677049 0.110905i
\(163\) 15.4942 + 15.4942i 1.21360 + 1.21360i 0.969834 + 0.243767i \(0.0783834\pi\)
0.243767 + 0.969834i \(0.421617\pi\)
\(164\) −0.767979 + 6.26653i −0.0599691 + 0.489334i
\(165\) −3.51009 + 3.51009i −0.273261 + 0.273261i
\(166\) 4.28798 3.79456i 0.332812 0.294515i
\(167\) 1.76898i 0.136888i −0.997655 0.0684439i \(-0.978197\pi\)
0.997655 0.0684439i \(-0.0218034\pi\)
\(168\) −4.43124 6.44276i −0.341877 0.497069i
\(169\) 28.5800i 2.19846i
\(170\) 4.69119 + 5.30121i 0.359798 + 0.406584i
\(171\) 0.812949 0.812949i 0.0621678 0.0621678i
\(172\) 6.92890 5.41600i 0.528324 0.412966i
\(173\) 4.01351 + 4.01351i 0.305142 + 0.305142i 0.843022 0.537880i \(-0.180775\pi\)
−0.537880 + 0.843022i \(0.680775\pi\)
\(174\) 12.0447 + 0.735301i 0.913103 + 0.0557430i
\(175\) 2.76462 0.208986
\(176\) −17.0153 + 10.2344i −1.28258 + 0.771449i
\(177\) 7.26561 0.546117
\(178\) −10.2137 0.623523i −0.765547 0.0467350i
\(179\) −5.31340 5.31340i −0.397142 0.397142i 0.480082 0.877224i \(-0.340607\pi\)
−0.877224 + 0.480082i \(0.840607\pi\)
\(180\) 1.23168 + 1.57574i 0.0918042 + 0.117449i
\(181\) −8.74918 + 8.74918i −0.650321 + 0.650321i −0.953070 0.302749i \(-0.902096\pi\)
0.302749 + 0.953070i \(0.402096\pi\)
\(182\) 16.7076 + 18.8801i 1.23845 + 1.39949i
\(183\) 3.52470i 0.260553i
\(184\) 20.8094 + 3.84941i 1.53409 + 0.283782i
\(185\) 1.53688i 0.112994i
\(186\) 8.03026 7.10621i 0.588807 0.521053i
\(187\) 17.5698 17.5698i 1.28483 1.28483i
\(188\) 5.47917 + 0.671485i 0.399609 + 0.0489731i
\(189\) 1.95488 + 1.95488i 0.142197 + 0.142197i
\(190\) −0.0990732 + 1.62288i −0.00718752 + 0.117736i
\(191\) −4.03787 −0.292170 −0.146085 0.989272i \(-0.546667\pi\)
−0.146085 + 0.989272i \(0.546667\pi\)
\(192\) 3.25891 + 7.30613i 0.235191 + 0.527275i
\(193\) 0.437111 0.0314639 0.0157320 0.999876i \(-0.494992\pi\)
0.0157320 + 0.999876i \(0.494992\pi\)
\(194\) 0.710124 11.6323i 0.0509840 0.835147i
\(195\) −4.55960 4.55960i −0.326520 0.326520i
\(196\) 1.27669 + 0.156462i 0.0911924 + 0.0111759i
\(197\) 11.6836 11.6836i 0.832424 0.832424i −0.155424 0.987848i \(-0.549674\pi\)
0.987848 + 0.155424i \(0.0496743\pi\)
\(198\) 5.25728 4.65232i 0.373619 0.330626i
\(199\) 15.7412i 1.11587i −0.829886 0.557933i \(-0.811595\pi\)
0.829886 0.557933i \(-0.188405\pi\)
\(200\) −2.78124 0.514486i −0.196663 0.0363797i
\(201\) 4.44947i 0.313842i
\(202\) 1.42251 + 1.60749i 0.100088 + 0.113103i
\(203\) −16.6804 + 16.6804i −1.17074 + 1.17074i
\(204\) −6.16519 7.88737i −0.431650 0.552226i
\(205\) 2.23213 + 2.23213i 0.155899 + 0.155899i
\(206\) 2.35400 + 0.143707i 0.164011 + 0.0100125i
\(207\) −7.48205 −0.520038
\(208\) −13.2945 22.1029i −0.921807 1.53256i
\(209\) 5.70706 0.394765
\(210\) −3.90250 0.238239i −0.269298 0.0164401i
\(211\) −2.13765 2.13765i −0.147162 0.147162i 0.629687 0.776849i \(-0.283183\pi\)
−0.776849 + 0.629687i \(0.783183\pi\)
\(212\) −14.2864 + 11.1670i −0.981194 + 0.766954i
\(213\) 2.47655 2.47655i 0.169690 0.169690i
\(214\) −8.06989 9.11926i −0.551647 0.623379i
\(215\) 4.39724i 0.299889i
\(216\) −1.60284 2.33043i −0.109059 0.158566i
\(217\) 20.9622i 1.42301i
\(218\) −4.37550 + 3.87201i −0.296346 + 0.262245i
\(219\) 10.3340 10.3340i 0.698308 0.698308i
\(220\) −1.20767 + 9.85432i −0.0814212 + 0.664378i
\(221\) 22.8231 + 22.8231i 1.53525 + 1.53525i
\(222\) 0.132440 2.16944i 0.00888877 0.145603i
\(223\) 13.4768 0.902476 0.451238 0.892404i \(-0.350983\pi\)
0.451238 + 0.892404i \(0.350983\pi\)
\(224\) −14.9179 4.69423i −0.996745 0.313646i
\(225\) 1.00000 0.0666667
\(226\) 0.245075 4.01447i 0.0163021 0.267039i
\(227\) −2.70567 2.70567i −0.179582 0.179582i 0.611592 0.791174i \(-0.290530\pi\)
−0.791174 + 0.611592i \(0.790530\pi\)
\(228\) 0.279701 2.28229i 0.0185236 0.151148i
\(229\) 0.507051 0.507051i 0.0335069 0.0335069i −0.690155 0.723662i \(-0.742458\pi\)
0.723662 + 0.690155i \(0.242458\pi\)
\(230\) 7.92406 7.01223i 0.522497 0.462373i
\(231\) 13.7236i 0.902949i
\(232\) 19.8849 13.6766i 1.30551 0.897910i
\(233\) 8.16109i 0.534651i 0.963606 + 0.267325i \(0.0861399\pi\)
−0.963606 + 0.267325i \(0.913860\pi\)
\(234\) 6.04335 + 6.82919i 0.395066 + 0.446438i
\(235\) 1.95167 1.95167i 0.127313 0.127313i
\(236\) 11.4487 8.94893i 0.745248 0.582526i
\(237\) −6.33090 6.33090i −0.411236 0.411236i
\(238\) 19.5340 + 1.19251i 1.26620 + 0.0772987i
\(239\) −2.46397 −0.159381 −0.0796905 0.996820i \(-0.525393\pi\)
−0.0796905 + 0.996820i \(0.525393\pi\)
\(240\) 3.88162 + 0.965913i 0.250558 + 0.0623494i
\(241\) 7.38073 0.475434 0.237717 0.971334i \(-0.423601\pi\)
0.237717 + 0.971334i \(0.423601\pi\)
\(242\) 19.2562 + 1.17555i 1.23783 + 0.0755672i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 4.34131 + 5.55401i 0.277924 + 0.355559i
\(245\) 0.454757 0.454757i 0.0290533 0.0290533i
\(246\) −2.95849 3.34319i −0.188626 0.213154i
\(247\) 7.41345i 0.471707i
\(248\) 3.90100 21.0883i 0.247714 1.33911i
\(249\) 4.04880i 0.256582i
\(250\) −1.05908 + 0.937207i −0.0669819 + 0.0592742i
\(251\) −5.15322 + 5.15322i −0.325268 + 0.325268i −0.850784 0.525516i \(-0.823872\pi\)
0.525516 + 0.850784i \(0.323872\pi\)
\(252\) 5.48818 + 0.672590i 0.345723 + 0.0423692i
\(253\) −26.2627 26.2627i −1.65112 1.65112i
\(254\) 0.569675 9.33161i 0.0357446 0.585517i
\(255\) −5.00550 −0.313457
\(256\) 14.1340 + 7.49862i 0.883377 + 0.468664i
\(257\) 9.84129 0.613883 0.306942 0.951728i \(-0.400694\pi\)
0.306942 + 0.951728i \(0.400694\pi\)
\(258\) −0.378929 + 6.20708i −0.0235911 + 0.386436i
\(259\) 3.00442 + 3.00442i 0.186686 + 0.186686i
\(260\) −12.8007 1.56876i −0.793868 0.0972905i
\(261\) −6.03354 + 6.03354i −0.373467 + 0.373467i
\(262\) 10.0369 8.88192i 0.620080 0.548727i
\(263\) 27.5027i 1.69589i −0.530086 0.847944i \(-0.677840\pi\)
0.530086 0.847944i \(-0.322160\pi\)
\(264\) 2.55392 13.8061i 0.157183 0.849710i
\(265\) 9.06647i 0.556949i
\(266\) 2.97886 + 3.36621i 0.182645 + 0.206395i
\(267\) 5.11634 5.11634i 0.313115 0.313115i
\(268\) 5.48034 + 7.01121i 0.334765 + 0.428278i
\(269\) 7.35280 + 7.35280i 0.448308 + 0.448308i 0.894792 0.446484i \(-0.147324\pi\)
−0.446484 + 0.894792i \(0.647324\pi\)
\(270\) −1.41159 0.0861743i −0.0859064 0.00524440i
\(271\) −16.1826 −0.983023 −0.491511 0.870871i \(-0.663555\pi\)
−0.491511 + 0.870871i \(0.663555\pi\)
\(272\) −19.4295 4.83488i −1.17808 0.293157i
\(273\) −17.8270 −1.07894
\(274\) 20.3139 + 1.24012i 1.22721 + 0.0749185i
\(275\) 3.51009 + 3.51009i 0.211667 + 0.211667i
\(276\) −11.7898 + 9.21551i −0.709660 + 0.554709i
\(277\) −19.3725 + 19.3725i −1.16398 + 1.16398i −0.180381 + 0.983597i \(0.557733\pi\)
−0.983597 + 0.180381i \(0.942267\pi\)
\(278\) 0.388005 + 0.438459i 0.0232710 + 0.0262970i
\(279\) 7.58233i 0.453942i
\(280\) −6.44276 + 4.43124i −0.385028 + 0.264817i
\(281\) 18.1786i 1.08445i −0.840235 0.542223i \(-0.817583\pi\)
0.840235 0.542223i \(-0.182417\pi\)
\(282\) −2.92313 + 2.58677i −0.174070 + 0.154040i
\(283\) −7.74925 + 7.74925i −0.460645 + 0.460645i −0.898867 0.438222i \(-0.855609\pi\)
0.438222 + 0.898867i \(0.355609\pi\)
\(284\) 0.852073 6.95272i 0.0505612 0.412568i
\(285\) −0.812949 0.812949i −0.0481549 0.0481549i
\(286\) −2.75838 + 45.1838i −0.163106 + 2.67178i
\(287\) 8.72709 0.515144
\(288\) −5.39601 1.69796i −0.317963 0.100054i
\(289\) 8.05503 0.473825
\(290\) 0.735301 12.0447i 0.0431783 0.707287i
\(291\) 5.82695 + 5.82695i 0.341582 + 0.341582i
\(292\) 3.55549 29.0120i 0.208069 1.69780i
\(293\) −1.24572 + 1.24572i −0.0727760 + 0.0727760i −0.742558 0.669782i \(-0.766388\pi\)
0.669782 + 0.742558i \(0.266388\pi\)
\(294\) −0.681116 + 0.602739i −0.0397235 + 0.0351525i
\(295\) 7.26561i 0.423020i
\(296\) −2.46337 3.58160i −0.143181 0.208176i
\(297\) 4.96402i 0.288042i
\(298\) −14.4951 16.3799i −0.839676 0.948863i
\(299\) 34.1152 34.1152i 1.97293 1.97293i
\(300\) 1.57574 1.23168i 0.0909754 0.0711113i
\(301\) −8.59608 8.59608i −0.495470 0.495470i
\(302\) −19.0882 1.16529i −1.09840 0.0670551i
\(303\) −1.51782 −0.0871966
\(304\) −2.37033 3.94080i −0.135947 0.226020i
\(305\) 3.52470 0.201824
\(306\) 7.06569 + 0.431345i 0.403919 + 0.0246584i
\(307\) 13.5042 + 13.5042i 0.770727 + 0.770727i 0.978234 0.207506i \(-0.0665348\pi\)
−0.207506 + 0.978234i \(0.566535\pi\)
\(308\) 16.9032 + 21.6249i 0.963148 + 1.23219i
\(309\) −1.17919 + 1.17919i −0.0670819 + 0.0670819i
\(310\) −7.10621 8.03026i −0.403606 0.456088i
\(311\) 11.9549i 0.677901i 0.940804 + 0.338951i \(0.110072\pi\)
−0.940804 + 0.338951i \(0.889928\pi\)
\(312\) 17.9341 + 3.31754i 1.01532 + 0.187819i
\(313\) 15.2385i 0.861333i −0.902511 0.430667i \(-0.858279\pi\)
0.902511 0.430667i \(-0.141721\pi\)
\(314\) −4.14111 + 3.66459i −0.233697 + 0.206805i
\(315\) 1.95488 1.95488i 0.110145 0.110145i
\(316\) −17.7735 2.17819i −0.999839 0.122533i
\(317\) 22.4062 + 22.4062i 1.25846 + 1.25846i 0.951830 + 0.306625i \(0.0991998\pi\)
0.306625 + 0.951830i \(0.400800\pi\)
\(318\) 0.781297 12.7981i 0.0438129 0.717682i
\(319\) −42.3566 −2.37151
\(320\) 7.30613 3.25891i 0.408425 0.182178i
\(321\) 8.61058 0.480595
\(322\) 1.78252 29.1987i 0.0993358 1.62718i
\(323\) 4.06922 + 4.06922i 0.226417 + 0.226417i
\(324\) 1.98515 + 0.243285i 0.110286 + 0.0135158i
\(325\) −4.55960 + 4.55960i −0.252921 + 0.252921i
\(326\) −23.2066 + 20.5362i −1.28530 + 1.13740i
\(327\) 4.13143i 0.228469i
\(328\) −8.77956 1.62408i −0.484770 0.0896749i
\(329\) 7.63057i 0.420687i
\(330\) −4.65232 5.25728i −0.256102 0.289404i
\(331\) 8.11650 8.11650i 0.446123 0.446123i −0.447940 0.894063i \(-0.647842\pi\)
0.894063 + 0.447940i \(0.147842\pi\)
\(332\) 4.98683 + 6.37985i 0.273688 + 0.350140i
\(333\) 1.08674 + 1.08674i 0.0595529 + 0.0595529i
\(334\) 2.49707 + 0.152441i 0.136633 + 0.00834118i
\(335\) 4.44947 0.243101
\(336\) 9.47636 5.69987i 0.516978 0.310953i
\(337\) −19.1995 −1.04587 −0.522933 0.852374i \(-0.675162\pi\)
−0.522933 + 0.852374i \(0.675162\pi\)
\(338\) −40.3431 2.46286i −2.19437 0.133962i
\(339\) 2.01097 + 2.01097i 0.109221 + 0.109221i
\(340\) −7.88737 + 6.16519i −0.427752 + 0.334354i
\(341\) −26.6147 + 26.6147i −1.44127 + 1.44127i
\(342\) 1.07749 + 1.21760i 0.0582641 + 0.0658404i
\(343\) 17.5743i 0.948926i
\(344\) 7.04806 + 10.2475i 0.380006 + 0.552506i
\(345\) 7.48205i 0.402820i
\(346\) −6.01128 + 5.31956i −0.323169 + 0.285981i
\(347\) −3.64968 + 3.64968i −0.195925 + 0.195925i −0.798251 0.602325i \(-0.794241\pi\)
0.602325 + 0.798251i \(0.294241\pi\)
\(348\) −2.07588 + 16.9387i −0.111279 + 0.908010i
\(349\) 16.7180 + 16.7180i 0.894896 + 0.894896i 0.994979 0.100083i \(-0.0319107\pi\)
−0.100083 + 0.994979i \(0.531911\pi\)
\(350\) −0.238239 + 3.90250i −0.0127344 + 0.208597i
\(351\) −6.44825 −0.344182
\(352\) −12.9805 24.9005i −0.691862 1.32720i
\(353\) 9.42887 0.501848 0.250924 0.968007i \(-0.419266\pi\)
0.250924 + 0.968007i \(0.419266\pi\)
\(354\) −0.626109 + 10.2560i −0.0332773 + 0.545102i
\(355\) −2.47655 2.47655i −0.131442 0.131442i
\(356\) 1.76031 14.3637i 0.0932963 0.761276i
\(357\) −9.78516 + 9.78516i −0.517886 + 0.517886i
\(358\) 7.95820 7.04244i 0.420604 0.372204i
\(359\) 1.12135i 0.0591826i −0.999562 0.0295913i \(-0.990579\pi\)
0.999562 0.0295913i \(-0.00942059\pi\)
\(360\) −2.33043 + 1.60284i −0.122825 + 0.0844770i
\(361\) 17.6782i 0.930433i
\(362\) −11.5963 13.1042i −0.609486 0.688740i
\(363\) −9.64602 + 9.64602i −0.506285 + 0.506285i
\(364\) −28.0907 + 21.9572i −1.47235 + 1.15087i
\(365\) −10.3340 10.3340i −0.540907 0.540907i
\(366\) −4.97541 0.303739i −0.260069 0.0158767i
\(367\) −7.22666 −0.377228 −0.188614 0.982051i \(-0.560400\pi\)
−0.188614 + 0.982051i \(0.560400\pi\)
\(368\) −7.22701 + 29.0425i −0.376734 + 1.51395i
\(369\) 3.15671 0.164332
\(370\) −2.16944 0.132440i −0.112784 0.00688521i
\(371\) 17.7239 + 17.7239i 0.920178 + 0.920178i
\(372\) 9.33902 + 11.9478i 0.484206 + 0.619463i
\(373\) −8.83590 + 8.83590i −0.457506 + 0.457506i −0.897836 0.440330i \(-0.854861\pi\)
0.440330 + 0.897836i \(0.354861\pi\)
\(374\) 23.2872 + 26.3153i 1.20415 + 1.36073i
\(375\) 1.00000i 0.0516398i
\(376\) −1.42002 + 7.67645i −0.0732321 + 0.395883i
\(377\) 55.0211i 2.83373i
\(378\) −2.92794 + 2.59102i −0.150597 + 0.133268i
\(379\) −26.2339 + 26.2339i −1.34754 + 1.34754i −0.459223 + 0.888321i \(0.651872\pi\)
−0.888321 + 0.459223i \(0.848128\pi\)
\(380\) −2.28229 0.279701i −0.117079 0.0143483i
\(381\) 4.67449 + 4.67449i 0.239481 + 0.239481i
\(382\) 0.347961 5.69980i 0.0178032 0.291627i
\(383\) 14.3557 0.733544 0.366772 0.930311i \(-0.380463\pi\)
0.366772 + 0.930311i \(0.380463\pi\)
\(384\) −10.5941 + 3.97062i −0.540626 + 0.202625i
\(385\) 13.7236 0.699421
\(386\) −0.0376677 + 0.617019i −0.00191724 + 0.0314054i
\(387\) −3.10932 3.10932i −0.158055 0.158055i
\(388\) 16.3587 + 2.00480i 0.830489 + 0.101778i
\(389\) −1.07721 + 1.07721i −0.0546168 + 0.0546168i −0.733888 0.679271i \(-0.762296\pi\)
0.679271 + 0.733888i \(0.262296\pi\)
\(390\) 6.82919 6.04335i 0.345810 0.306017i
\(391\) 37.4514i 1.89400i
\(392\) −0.330878 + 1.78868i −0.0167119 + 0.0903420i
\(393\) 9.47700i 0.478052i
\(394\) 15.4856 + 17.4993i 0.780154 + 0.881601i
\(395\) −6.33090 + 6.33090i −0.318542 + 0.318542i
\(396\) 6.11410 + 7.82201i 0.307245 + 0.393071i
\(397\) 16.8838 + 16.8838i 0.847376 + 0.847376i 0.989805 0.142429i \(-0.0454913\pi\)
−0.142429 + 0.989805i \(0.545491\pi\)
\(398\) 22.2201 + 1.35649i 1.11379 + 0.0679947i
\(399\) −3.17844 −0.159121
\(400\) 0.965913 3.88162i 0.0482956 0.194081i
\(401\) −0.406306 −0.0202900 −0.0101450 0.999949i \(-0.503229\pi\)
−0.0101450 + 0.999949i \(0.503229\pi\)
\(402\) −6.28081 0.383430i −0.313258 0.0191238i
\(403\) −34.5724 34.5724i −1.72217 1.72217i
\(404\) −2.39169 + 1.86948i −0.118991 + 0.0930099i
\(405\) 0.707107 0.707107i 0.0351364 0.0351364i
\(406\) −22.1085 24.9833i −1.09722 1.23990i
\(407\) 7.62911i 0.378161i
\(408\) 11.6650 8.02301i 0.577502 0.397198i
\(409\) 38.0171i 1.87983i −0.341413 0.939913i \(-0.610906\pi\)
0.341413 0.939913i \(-0.389094\pi\)
\(410\) −3.34319 + 2.95849i −0.165109 + 0.146109i
\(411\) −10.1759 + 10.1759i −0.501938 + 0.501938i
\(412\) −0.405709 + 3.31049i −0.0199878 + 0.163096i
\(413\) −14.2034 14.2034i −0.698904 0.698904i
\(414\) 0.644760 10.5616i 0.0316882 0.519072i
\(415\) 4.04880 0.198748
\(416\) 32.3457 16.8616i 1.58588 0.826709i
\(417\) −0.414002 −0.0202737
\(418\) −0.491802 + 8.05600i −0.0240548 + 0.394032i
\(419\) −23.2302 23.2302i −1.13487 1.13487i −0.989357 0.145512i \(-0.953517\pi\)
−0.145512 0.989357i \(-0.546483\pi\)
\(420\) 0.672590 5.48818i 0.0328190 0.267796i
\(421\) 26.7883 26.7883i 1.30558 1.30558i 0.381009 0.924572i \(-0.375577\pi\)
0.924572 0.381009i \(-0.124423\pi\)
\(422\) 3.20168 2.83326i 0.155855 0.137921i
\(423\) 2.76008i 0.134200i
\(424\) −14.5321 21.1288i −0.705740 1.02610i
\(425\) 5.00550i 0.242802i
\(426\) 3.28245 + 3.70927i 0.159035 + 0.179715i
\(427\) 6.89037 6.89037i 0.333448 0.333448i
\(428\) 13.5680 10.6055i 0.655835 0.512636i
\(429\) −22.6340 22.6340i −1.09278 1.09278i
\(430\) 6.20708 + 0.378929i 0.299332 + 0.0182736i
\(431\) −9.17509 −0.441949 −0.220974 0.975280i \(-0.570924\pi\)
−0.220974 + 0.975280i \(0.570924\pi\)
\(432\) 3.42773 2.06172i 0.164917 0.0991945i
\(433\) 36.5762 1.75774 0.878869 0.477063i \(-0.158299\pi\)
0.878869 + 0.477063i \(0.158299\pi\)
\(434\) −29.5900 1.80641i −1.42037 0.0867103i
\(435\) 6.03354 + 6.03354i 0.289286 + 0.289286i
\(436\) −5.08861 6.51006i −0.243700 0.311775i
\(437\) 6.08252 6.08252i 0.290967 0.290967i
\(438\) 13.6968 + 15.4779i 0.654460 + 0.739562i
\(439\) 6.96346i 0.332348i 0.986096 + 0.166174i \(0.0531413\pi\)
−0.986096 + 0.166174i \(0.946859\pi\)
\(440\) −13.8061 2.55392i −0.658182 0.121753i
\(441\) 0.643123i 0.0306249i
\(442\) −34.1835 + 30.2500i −1.62594 + 1.43885i
\(443\) 2.15777 2.15777i 0.102519 0.102519i −0.653987 0.756506i \(-0.726905\pi\)
0.756506 + 0.653987i \(0.226905\pi\)
\(444\) 3.05094 + 0.373900i 0.144791 + 0.0177445i
\(445\) −5.11634 5.11634i −0.242538 0.242538i
\(446\) −1.16136 + 19.0237i −0.0549919 + 0.900799i
\(447\) 15.4662 0.731527
\(448\) 7.91185 20.6534i 0.373800 0.975781i
\(449\) 13.1720 0.621627 0.310814 0.950471i \(-0.399398\pi\)
0.310814 + 0.950471i \(0.399398\pi\)
\(450\) −0.0861743 + 1.41159i −0.00406230 + 0.0665428i
\(451\) 11.0803 + 11.0803i 0.521753 + 0.521753i
\(452\) 5.64565 + 0.691889i 0.265549 + 0.0325437i
\(453\) 9.56186 9.56186i 0.449256 0.449256i
\(454\) 4.05245 3.58613i 0.190191 0.168305i
\(455\) 17.8270i 0.835741i
\(456\) 3.19755 + 0.591496i 0.149739 + 0.0276993i
\(457\) 10.0012i 0.467834i −0.972257 0.233917i \(-0.924846\pi\)
0.972257 0.233917i \(-0.0751545\pi\)
\(458\) 0.672051 + 0.759441i 0.0314029 + 0.0354863i
\(459\) −3.53942 + 3.53942i −0.165206 + 0.165206i
\(460\) 9.21551 + 11.7898i 0.429676 + 0.549700i
\(461\) −1.79443 1.79443i −0.0835750 0.0835750i 0.664083 0.747658i \(-0.268822\pi\)
−0.747658 + 0.664083i \(0.768822\pi\)
\(462\) −19.3721 1.18263i −0.901271 0.0550207i
\(463\) −2.58325 −0.120054 −0.0600269 0.998197i \(-0.519119\pi\)
−0.0600269 + 0.998197i \(0.519119\pi\)
\(464\) 17.5921 + 29.2478i 0.816691 + 1.35780i
\(465\) 7.58233 0.351622
\(466\) −11.5201 0.703277i −0.533657 0.0325787i
\(467\) 24.6809 + 24.6809i 1.14210 + 1.14210i 0.988066 + 0.154029i \(0.0492250\pi\)
0.154029 + 0.988066i \(0.450775\pi\)
\(468\) −10.1608 + 7.94221i −0.469682 + 0.367129i
\(469\) 8.69819 8.69819i 0.401645 0.401645i
\(470\) 2.58677 + 2.92313i 0.119319 + 0.134834i
\(471\) 3.91012i 0.180169i
\(472\) 11.6456 + 16.9320i 0.536032 + 0.779359i
\(473\) 21.8280i 1.00365i
\(474\) 9.48217 8.39105i 0.435531 0.385414i
\(475\) −0.812949 + 0.812949i −0.0373007 + 0.0373007i
\(476\) −3.36665 + 27.4711i −0.154310 + 1.25913i
\(477\) 6.41096 + 6.41096i 0.293538 + 0.293538i
\(478\) 0.212331 3.47810i 0.00971179 0.159085i
\(479\) 1.39344 0.0636679 0.0318339 0.999493i \(-0.489865\pi\)
0.0318339 + 0.999493i \(0.489865\pi\)
\(480\) −1.69796 + 5.39601i −0.0775011 + 0.246293i
\(481\) −9.91020 −0.451866
\(482\) −0.636029 + 10.4185i −0.0289703 + 0.474551i
\(483\) 14.6265 + 14.6265i 0.665530 + 0.665530i
\(484\) −3.31878 + 27.0805i −0.150854 + 1.23093i
\(485\) 5.82695 5.82695i 0.264588 0.264588i
\(486\) −1.05908 + 0.937207i −0.0480407 + 0.0425126i
\(487\) 26.7044i 1.21009i 0.796191 + 0.605045i \(0.206845\pi\)
−0.796191 + 0.605045i \(0.793155\pi\)
\(488\) −8.21407 + 5.64952i −0.371833 + 0.255742i
\(489\) 21.9121i 0.990901i
\(490\) 0.602739 + 0.681116i 0.0272290 + 0.0307697i
\(491\) 16.3259 16.3259i 0.736775 0.736775i −0.235177 0.971953i \(-0.575567\pi\)
0.971953 + 0.235177i \(0.0755670\pi\)
\(492\) 4.97415 3.88806i 0.224252 0.175287i
\(493\) −30.2009 30.2009i −1.36018 1.36018i
\(494\) −10.4647 0.638849i −0.470830 0.0287432i
\(495\) 4.96402 0.223116
\(496\) 29.4317 + 7.32387i 1.32152 + 0.328851i
\(497\) −9.68272 −0.434329
\(498\) −5.71522 0.348902i −0.256105 0.0156347i
\(499\) 26.4923 + 26.4923i 1.18596 + 1.18596i 0.978175 + 0.207783i \(0.0666247\pi\)
0.207783 + 0.978175i \(0.433375\pi\)
\(500\) −1.23168 1.57574i −0.0550825 0.0704692i
\(501\) −1.25086 + 1.25086i −0.0558842 + 0.0558842i
\(502\) −6.83013 7.71828i −0.304844 0.344484i
\(503\) 14.2132i 0.633737i −0.948470 0.316868i \(-0.897369\pi\)
0.948470 0.316868i \(-0.102631\pi\)
\(504\) −1.42236 + 7.68908i −0.0633569 + 0.342499i
\(505\) 1.51782i 0.0675422i
\(506\) 39.3352 34.8089i 1.74866 1.54744i
\(507\) 20.2091 20.2091i 0.897517 0.897517i
\(508\) 13.1233 + 1.60829i 0.582251 + 0.0713563i
\(509\) 4.26128 + 4.26128i 0.188878 + 0.188878i 0.795211 0.606333i \(-0.207360\pi\)
−0.606333 + 0.795211i \(0.707360\pi\)
\(510\) 0.431345 7.06569i 0.0191003 0.312874i
\(511\) −40.4036 −1.78735
\(512\) −11.8029 + 19.3052i −0.521621 + 0.853177i
\(513\) −1.14968 −0.0507598
\(514\) −0.848067 + 13.8918i −0.0374066 + 0.612742i
\(515\) 1.17919 + 1.17919i 0.0519614 + 0.0519614i
\(516\) −8.72917 1.06978i −0.384280 0.0470945i
\(517\) 9.68814 9.68814i 0.426084 0.426084i
\(518\) −4.49990 + 3.98209i −0.197714 + 0.174963i
\(519\) 5.67597i 0.249147i
\(520\) 3.31754 17.9341i 0.145484 0.786464i
\(521\) 31.9522i 1.39985i −0.714215 0.699926i \(-0.753216\pi\)
0.714215 0.699926i \(-0.246784\pi\)
\(522\) −7.99692 9.03679i −0.350016 0.395530i
\(523\) 12.3608 12.3608i 0.540498 0.540498i −0.383177 0.923675i \(-0.625170\pi\)
0.923675 + 0.383177i \(0.125170\pi\)
\(524\) 11.6727 + 14.9333i 0.509923 + 0.652364i
\(525\) −1.95488 1.95488i −0.0853180 0.0853180i
\(526\) 38.8224 + 2.37002i 1.69274 + 0.103338i
\(527\) −37.9533 −1.65327
\(528\) 19.2685 + 4.79481i 0.838553 + 0.208667i
\(529\) −32.9810 −1.43396
\(530\) −12.7981 0.781297i −0.555914 0.0339374i
\(531\) −5.13756 5.13756i −0.222951 0.222951i
\(532\) −5.00839 + 3.91483i −0.217141 + 0.169729i
\(533\) −14.3933 + 14.3933i −0.623444 + 0.623444i
\(534\) 6.78126 + 7.66305i 0.293454 + 0.331613i
\(535\) 8.61058i 0.372268i
\(536\) −10.3692 + 7.13179i −0.447881 + 0.308046i
\(537\) 7.51428i 0.324265i
\(538\) −11.0127 + 9.74549i −0.474793 + 0.420158i
\(539\) 2.25742 2.25742i 0.0972341 0.0972341i
\(540\) 0.243285 1.98515i 0.0104693 0.0854272i
\(541\) 25.6126 + 25.6126i 1.10117 + 1.10117i 0.994270 + 0.106902i \(0.0340932\pi\)
0.106902 + 0.994270i \(0.465907\pi\)
\(542\) 1.39452 22.8431i 0.0598999 0.981196i
\(543\) 12.3732 0.530985
\(544\) 8.49916 27.0097i 0.364399 1.15803i
\(545\) −4.13143 −0.176971
\(546\) 1.53623 25.1643i 0.0657444 1.07693i
\(547\) 1.56643 + 1.56643i 0.0669759 + 0.0669759i 0.739801 0.672825i \(-0.234919\pi\)
−0.672825 + 0.739801i \(0.734919\pi\)
\(548\) −3.50107 + 28.5680i −0.149558 + 1.22036i
\(549\) 2.49234 2.49234i 0.106370 0.106370i
\(550\) −5.25728 + 4.65232i −0.224171 + 0.198376i
\(551\) 9.80992i 0.417917i
\(552\) −11.9925 17.4364i −0.510435 0.742142i
\(553\) 24.7523i 1.05258i
\(554\) −25.6765 29.0153i −1.09089 1.23274i
\(555\) 1.08674 1.08674i 0.0461295 0.0461295i
\(556\) −0.652359 + 0.509919i −0.0276662 + 0.0216254i
\(557\) 3.96707 + 3.96707i 0.168090 + 0.168090i 0.786139 0.618049i \(-0.212077\pi\)
−0.618049 + 0.786139i \(0.712077\pi\)
\(558\) −10.7031 0.653402i −0.453098 0.0276607i
\(559\) 28.3545 1.19927
\(560\) −5.69987 9.47636i −0.240864 0.400449i
\(561\) −24.8474 −1.04906
\(562\) 25.6607 + 1.56653i 1.08243 + 0.0660801i
\(563\) 23.0565 + 23.0565i 0.971715 + 0.971715i 0.999611 0.0278956i \(-0.00888059\pi\)
−0.0278956 + 0.999611i \(0.508881\pi\)
\(564\) −3.39954 4.34917i −0.143147 0.183133i
\(565\) 2.01097 2.01097i 0.0846023 0.0846023i
\(566\) −10.2709 11.6065i −0.431720 0.487859i
\(567\) 2.76462i 0.116103i
\(568\) 9.74093 + 1.80192i 0.408720 + 0.0756069i
\(569\) 32.6228i 1.36762i 0.729660 + 0.683810i \(0.239678\pi\)
−0.729660 + 0.683810i \(0.760322\pi\)
\(570\) 1.21760 1.07749i 0.0509998 0.0451312i
\(571\) 13.3559 13.3559i 0.558926 0.558926i −0.370076 0.929002i \(-0.620668\pi\)
0.929002 + 0.370076i \(0.120668\pi\)
\(572\) −63.5432 7.78737i −2.65687 0.325606i
\(573\) 2.85521 + 2.85521i 0.119278 + 0.119278i
\(574\) −0.752051 + 12.3190i −0.0313900 + 0.514187i
\(575\) 7.48205 0.312023
\(576\) 2.86182 7.47061i 0.119243 0.311275i
\(577\) 46.5999 1.93998 0.969989 0.243147i \(-0.0781798\pi\)
0.969989 + 0.243147i \(0.0781798\pi\)
\(578\) −0.694137 + 11.3704i −0.0288723 + 0.472945i
\(579\) −0.309084 0.309084i −0.0128451 0.0128451i
\(580\) 16.9387 + 2.07588i 0.703341 + 0.0861962i
\(581\) 7.91492 7.91492i 0.328366 0.328366i
\(582\) −8.72738 + 7.72311i −0.361762 + 0.320133i
\(583\) 45.0062i 1.86397i
\(584\) 40.6465 + 7.51896i 1.68196 + 0.311137i
\(585\) 6.44825i 0.266602i
\(586\) −1.65110 1.86580i −0.0682062 0.0770753i
\(587\) −29.5590 + 29.5590i −1.22003 + 1.22003i −0.252408 + 0.967621i \(0.581222\pi\)
−0.967621 + 0.252408i \(0.918778\pi\)
\(588\) −0.792124 1.01339i −0.0326666 0.0417917i
\(589\) −6.16404 6.16404i −0.253985 0.253985i
\(590\) 10.2560 + 0.626109i 0.422234 + 0.0257765i
\(591\) −16.5231 −0.679671
\(592\) 5.26801 3.16862i 0.216514 0.130229i
\(593\) −35.4555 −1.45598 −0.727991 0.685587i \(-0.759546\pi\)
−0.727991 + 0.685587i \(0.759546\pi\)
\(594\) −7.00714 0.427771i −0.287507 0.0175517i
\(595\) 9.78516 + 9.78516i 0.401152 + 0.401152i
\(596\) 24.3707 19.0495i 0.998265 0.780297i
\(597\) −11.1307 + 11.1307i −0.455551 + 0.455551i
\(598\) 45.2166 + 51.0963i 1.84905 + 2.08948i
\(599\) 22.8571i 0.933915i −0.884280 0.466958i \(-0.845350\pi\)
0.884280 0.466958i \(-0.154650\pi\)
\(600\) 1.60284 + 2.33043i 0.0654356 + 0.0951395i
\(601\) 19.4253i 0.792374i −0.918170 0.396187i \(-0.870333\pi\)
0.918170 0.396187i \(-0.129667\pi\)
\(602\) 12.8749 11.3933i 0.524740 0.464358i
\(603\) 3.14625 3.14625i 0.128125 0.128125i
\(604\) 3.28982 26.8442i 0.133861 1.09227i
\(605\) 9.64602 + 9.64602i 0.392166 + 0.392166i
\(606\) 0.130797 2.14254i 0.00531327 0.0870345i
\(607\) −19.2455 −0.781149 −0.390574 0.920571i \(-0.627724\pi\)
−0.390574 + 0.920571i \(0.627724\pi\)
\(608\) 5.76704 3.00632i 0.233884 0.121922i
\(609\) 23.5897 0.955903
\(610\) −0.303739 + 4.97541i −0.0122980 + 0.201449i
\(611\) 12.5849 + 12.5849i 0.509129 + 0.509129i
\(612\) −1.21776 + 9.93666i −0.0492251 + 0.401666i
\(613\) 17.3922 17.3922i 0.702465 0.702465i −0.262474 0.964939i \(-0.584538\pi\)
0.964939 + 0.262474i \(0.0845383\pi\)
\(614\) −20.2261 + 17.8987i −0.816259 + 0.722331i
\(615\) 3.15671i 0.127291i
\(616\) −31.9820 + 21.9968i −1.28859 + 0.886275i
\(617\) 29.7863i 1.19915i 0.800318 + 0.599576i \(0.204664\pi\)
−0.800318 + 0.599576i \(0.795336\pi\)
\(618\) −1.56291 1.76615i −0.0628696 0.0710448i
\(619\) −10.6404 + 10.6404i −0.427673 + 0.427673i −0.887835 0.460162i \(-0.847791\pi\)
0.460162 + 0.887835i \(0.347791\pi\)
\(620\) 11.9478 9.33902i 0.479834 0.375064i
\(621\) 5.29061 + 5.29061i 0.212305 + 0.212305i
\(622\) −16.8754 1.03021i −0.676642 0.0413075i
\(623\) −20.0037 −0.801430
\(624\) −6.22845 + 25.0297i −0.249338 + 1.00199i
\(625\) −1.00000 −0.0400000
\(626\) 21.5105 + 1.31317i 0.859732 + 0.0524848i
\(627\) −4.03550 4.03550i −0.161162 0.161162i
\(628\) −4.81603 6.16133i −0.192180 0.245864i
\(629\) −5.43967 + 5.43967i −0.216894 + 0.216894i
\(630\) 2.59102 + 2.92794i 0.103229 + 0.116652i
\(631\) 38.7660i 1.54325i 0.636078 + 0.771625i \(0.280556\pi\)
−0.636078 + 0.771625i \(0.719444\pi\)
\(632\) 4.60632 24.9011i 0.183230 0.990515i
\(633\) 3.02309i 0.120157i
\(634\) −33.5591 + 29.6974i −1.33280 + 1.17943i
\(635\) 4.67449 4.67449i 0.185502 0.185502i
\(636\) 17.9983 + 2.20573i 0.713678 + 0.0874631i
\(637\) 2.93239 + 2.93239i 0.116185 + 0.116185i
\(638\) 3.65005 59.7900i 0.144507 2.36711i
\(639\) −3.50237 −0.138552
\(640\) 3.97062 + 10.5941i 0.156953 + 0.418767i
\(641\) 3.84117 0.151717 0.0758585 0.997119i \(-0.475830\pi\)
0.0758585 + 0.997119i \(0.475830\pi\)
\(642\) −0.742010 + 12.1546i −0.0292848 + 0.479702i
\(643\) −4.00729 4.00729i −0.158032 0.158032i 0.623662 0.781694i \(-0.285644\pi\)
−0.781694 + 0.623662i \(0.785644\pi\)
\(644\) 41.0628 + 5.03235i 1.61810 + 0.198302i
\(645\) −3.10932 + 3.10932i −0.122429 + 0.122429i
\(646\) −6.09471 + 5.39338i −0.239793 + 0.212200i
\(647\) 25.3385i 0.996158i 0.867132 + 0.498079i \(0.165961\pi\)
−0.867132 + 0.498079i \(0.834039\pi\)
\(648\) −0.514486 + 2.78124i −0.0202109 + 0.109257i
\(649\) 36.0667i 1.41574i
\(650\) −6.04335 6.82919i −0.237040 0.267863i
\(651\) 14.8225 14.8225i 0.580941 0.580941i
\(652\) −26.9888 34.5278i −1.05696 1.35221i
\(653\) 0.690132 + 0.690132i 0.0270069 + 0.0270069i 0.720481 0.693474i \(-0.243921\pi\)
−0.693474 + 0.720481i \(0.743921\pi\)
\(654\) 5.83187 + 0.356023i 0.228044 + 0.0139216i
\(655\) 9.47700 0.370297
\(656\) 3.04910 12.2532i 0.119048 0.478405i
\(657\) −14.6145 −0.570166
\(658\) 10.7712 + 0.657559i 0.419905 + 0.0256343i
\(659\) −27.4031 27.4031i −1.06747 1.06747i −0.997552 0.0699222i \(-0.977725\pi\)
−0.0699222 0.997552i \(-0.522275\pi\)
\(660\) 7.82201 6.11410i 0.304471 0.237991i
\(661\) 14.4586 14.4586i 0.562373 0.562373i −0.367608 0.929981i \(-0.619823\pi\)
0.929981 + 0.367608i \(0.119823\pi\)
\(662\) 10.7577 + 12.1566i 0.418110 + 0.472479i
\(663\) 32.2767i 1.25352i
\(664\) −9.43544 + 6.48956i −0.366166 + 0.251844i
\(665\) 3.17844i 0.123255i
\(666\) −1.62767 + 1.44038i −0.0630711 + 0.0558134i
\(667\) −45.1432 + 45.1432i −1.74795 + 1.74795i
\(668\) −0.430366 + 3.51169i −0.0166514 + 0.135871i
\(669\) −9.52957 9.52957i −0.368434 0.368434i
\(670\) −0.383430 + 6.28081i −0.0148132 + 0.242649i
\(671\) 17.4967 0.675452
\(672\) 7.22924 + 13.8679i 0.278874 + 0.534965i
\(673\) 38.4496 1.48212 0.741061 0.671438i \(-0.234323\pi\)
0.741061 + 0.671438i \(0.234323\pi\)
\(674\) 1.65451 27.1018i 0.0637292 1.04392i
\(675\) −0.707107 0.707107i −0.0272166 0.0272166i
\(676\) 6.95307 56.7355i 0.267426 2.18213i
\(677\) −15.2625 + 15.2625i −0.586586 + 0.586586i −0.936705 0.350119i \(-0.886141\pi\)
0.350119 + 0.936705i \(0.386141\pi\)
\(678\) −3.01195 + 2.66537i −0.115673 + 0.102363i
\(679\) 22.7820i 0.874293i
\(680\) −8.02301 11.6650i −0.307668 0.447331i
\(681\) 3.82640i 0.146628i
\(682\) −35.2754 39.8624i −1.35076 1.52641i
\(683\) −31.6516 + 31.6516i −1.21111 + 1.21111i −0.240453 + 0.970661i \(0.577296\pi\)
−0.970661 + 0.240453i \(0.922704\pi\)
\(684\) −1.81160 + 1.41605i −0.0692683 + 0.0541439i
\(685\) 10.1759 + 10.1759i 0.388800 + 0.388800i
\(686\) −24.8077 1.51446i −0.947162 0.0578223i
\(687\) −0.717078 −0.0273582
\(688\) −15.0725 + 9.06587i −0.574635 + 0.345633i
\(689\) −58.4629 −2.22726
\(690\) −10.5616 0.644760i −0.402071 0.0245456i
\(691\) −12.0010 12.0010i −0.456539 0.456539i 0.440979 0.897518i \(-0.354631\pi\)
−0.897518 + 0.440979i \(0.854631\pi\)
\(692\) −6.99099 8.94385i −0.265758 0.339994i
\(693\) 9.70408 9.70408i 0.368627 0.368627i
\(694\) −4.83733 5.46635i −0.183623 0.207500i
\(695\) 0.414002i 0.0157040i
\(696\) −23.7315 4.38996i −0.899542 0.166401i
\(697\) 15.8009i 0.598502i
\(698\) −25.0396 + 22.1583i −0.947763 + 0.838703i
\(699\) 5.77076 5.77076i 0.218270 0.218270i
\(700\) −5.48818 0.672590i −0.207434 0.0254215i
\(701\) −0.298277 0.298277i −0.0112658 0.0112658i 0.701451 0.712717i \(-0.252536\pi\)
−0.712717 + 0.701451i \(0.752536\pi\)
\(702\) 0.555674 9.10226i 0.0209726 0.343543i
\(703\) −1.76693 −0.0666409
\(704\) 36.2678 16.1773i 1.36689 0.609704i
\(705\) −2.76008 −0.103951
\(706\) −0.812526 + 13.3097i −0.0305798 + 0.500915i
\(707\) 2.96716 + 2.96716i 0.111592 + 0.111592i
\(708\) −14.4233 1.76761i −0.542061 0.0664310i
\(709\) −11.6489 + 11.6489i −0.437485 + 0.437485i −0.891165 0.453680i \(-0.850111\pi\)
0.453680 + 0.891165i \(0.350111\pi\)
\(710\) 3.70927 3.28245i 0.139207 0.123188i
\(711\) 8.95325i 0.335773i
\(712\) 20.1239 + 3.72262i 0.754177 + 0.139511i
\(713\) 56.7313i 2.12460i
\(714\) −12.9694 14.6558i −0.485366 0.548480i
\(715\) −22.6340 + 22.6340i −0.846463 + 0.846463i
\(716\) 9.25521 + 11.8406i 0.345884 + 0.442502i
\(717\) 1.74229 + 1.74229i 0.0650670 + 0.0650670i
\(718\) 1.58288 + 0.0966317i 0.0590727 + 0.00360626i
\(719\) 1.69024 0.0630353 0.0315177 0.999503i \(-0.489966\pi\)
0.0315177 + 0.999503i \(0.489966\pi\)
\(720\) −2.06172 3.42773i −0.0768358 0.127744i
\(721\) 4.61036 0.171699
\(722\) 24.9543 + 1.52341i 0.928704 + 0.0566954i
\(723\) −5.21896 5.21896i −0.194095 0.194095i
\(724\) 19.4970 15.2399i 0.724599 0.566385i
\(725\) 6.03354 6.03354i 0.224080 0.224080i
\(726\) −12.7849 14.4474i −0.474494 0.536194i
\(727\) 27.2221i 1.00961i −0.863233 0.504805i \(-0.831564\pi\)
0.863233 0.504805i \(-0.168436\pi\)
\(728\) −28.5737 41.5445i −1.05901 1.53974i
\(729\) 1.00000i 0.0370370i
\(730\) 15.4779 13.6968i 0.572862 0.506942i
\(731\) 15.5637 15.5637i 0.575644 0.575644i
\(732\) 0.857506 6.99705i 0.0316943 0.258618i
\(733\) 20.9172 + 20.9172i 0.772596 + 0.772596i 0.978560 0.205963i \(-0.0660328\pi\)
−0.205963 + 0.978560i \(0.566033\pi\)
\(734\) 0.622752 10.2010i 0.0229862 0.376528i
\(735\) −0.643123 −0.0237219
\(736\) −40.3732 12.7043i −1.48818 0.468285i
\(737\) 22.0873 0.813596
\(738\) −0.272027 + 4.45596i −0.0100135 + 0.164026i
\(739\) −3.53634 3.53634i −0.130086 0.130086i 0.639066 0.769152i \(-0.279321\pi\)
−0.769152 + 0.639066i \(0.779321\pi\)
\(740\) 0.373900 3.05094i 0.0137448 0.112155i
\(741\) 5.24210 5.24210i 0.192573 0.192573i
\(742\) −26.5461 + 23.4914i −0.974538 + 0.862397i
\(743\) 38.5438i 1.41403i −0.707196 0.707017i \(-0.750040\pi\)
0.707196 0.707017i \(-0.249960\pi\)
\(744\) −17.6701 + 12.1532i −0.647817 + 0.445559i
\(745\) 15.4662i 0.566639i
\(746\) −11.7112 13.2341i −0.428778 0.484533i
\(747\) 2.86293 2.86293i 0.104749 0.104749i
\(748\) −39.1531 + 30.6042i −1.43158 + 1.11900i
\(749\) −16.8327 16.8327i −0.615052 0.615052i
\(750\) 1.41159 + 0.0861743i 0.0515438 + 0.00314664i
\(751\) −7.07646 −0.258224 −0.129112 0.991630i \(-0.541213\pi\)
−0.129112 + 0.991630i \(0.541213\pi\)
\(752\) −10.7136 2.66600i −0.390685 0.0972189i
\(753\) 7.28775 0.265580
\(754\) 77.6670 + 4.74141i 2.82847 + 0.172672i
\(755\) −9.56186 9.56186i −0.347992 0.347992i
\(756\) −3.40514 4.35632i −0.123844 0.158438i
\(757\) −32.5233 + 32.5233i −1.18208 + 1.18208i −0.202873 + 0.979205i \(0.565028\pi\)
−0.979205 + 0.202873i \(0.934972\pi\)
\(758\) −34.7707 39.2921i −1.26293 1.42715i
\(759\) 37.1411i 1.34814i
\(760\) 0.591496 3.19755i 0.0214558 0.115987i
\(761\) 43.1903i 1.56565i 0.622243 + 0.782824i \(0.286222\pi\)
−0.622243 + 0.782824i \(0.713778\pi\)
\(762\) −7.00127 + 6.19562i −0.253629 + 0.224444i
\(763\) −8.07645 + 8.07645i −0.292387 + 0.292387i
\(764\) 8.01577 + 0.982353i 0.290000 + 0.0355403i
\(765\) 3.53942 + 3.53942i 0.127968 + 0.127968i
\(766\) −1.23710 + 20.2644i −0.0446981 + 0.732181i
\(767\) 46.8505 1.69167
\(768\) −4.69194 15.2966i −0.169306 0.551968i
\(769\) −31.1675 −1.12393 −0.561965 0.827161i \(-0.689955\pi\)
−0.561965 + 0.827161i \(0.689955\pi\)
\(770\) −1.18263 + 19.3721i −0.0426188 + 0.698122i
\(771\) −6.95885 6.95885i −0.250617 0.250617i
\(772\) −0.867729 0.106342i −0.0312303 0.00382735i
\(773\) 11.7904 11.7904i 0.424072 0.424072i −0.462531 0.886603i \(-0.653059\pi\)
0.886603 + 0.462531i \(0.153059\pi\)
\(774\) 4.65701 4.12112i 0.167393 0.148131i
\(775\) 7.58233i 0.272365i
\(776\) −4.23965 + 22.9190i −0.152195 + 0.822743i
\(777\) 4.24889i 0.152428i
\(778\) −1.42775 1.61340i −0.0511873 0.0578434i
\(779\) −2.56624 + 2.56624i −0.0919452 + 0.0919452i
\(780\) 7.94221 + 10.1608i 0.284377 + 0.363814i
\(781\) −12.2936 12.2936i −0.439901 0.439901i
\(782\) 52.8658 + 3.22735i 1.89048 + 0.115410i
\(783\) 8.53271 0.304934
\(784\) −2.49636 0.621201i −0.0891558 0.0221857i
\(785\) −3.91012 −0.139558
\(786\) −13.3776 0.816674i −0.477163 0.0291298i
\(787\) −3.50469 3.50469i −0.124929 0.124929i 0.641878 0.766807i \(-0.278156\pi\)
−0.766807 + 0.641878i \(0.778156\pi\)
\(788\) −26.0362 + 20.3513i −0.927501 + 0.724984i
\(789\) −19.4473 + 19.4473i −0.692343 + 0.692343i
\(790\) −8.39105 9.48217i −0.298540 0.337361i
\(791\) 7.86243i 0.279556i
\(792\) −11.5683 + 7.95653i −0.411062 + 0.282723i
\(793\) 22.7282i 0.807100i
\(794\) −25.2880 + 22.3780i −0.897436 + 0.794167i
\(795\) 6.41096 6.41096i 0.227373 0.227373i
\(796\) −3.82960 + 31.2487i −0.135737 + 1.10758i
\(797\) −34.1882 34.1882i −1.21101 1.21101i −0.970696 0.240312i \(-0.922750\pi\)
−0.240312 0.970696i \(-0.577250\pi\)
\(798\) 0.273900 4.48664i 0.00969594 0.158825i
\(799\) 13.8156 0.488760
\(800\) 5.39601 + 1.69796i 0.190778 + 0.0600321i
\(801\) −7.23560 −0.255657
\(802\) 0.0350132 0.573536i 0.00123636 0.0202523i
\(803\) −51.2983 51.2983i −1.81028 1.81028i
\(804\) 1.08249 8.83286i 0.0381765 0.311511i
\(805\) 14.6265 14.6265i 0.515517 0.515517i
\(806\) 51.7812 45.8227i 1.82391 1.61403i
\(807\) 10.3984i 0.366042i
\(808\) −2.43282 3.53718i −0.0855864 0.124438i
\(809\) 0.637755i 0.0224223i −0.999937 0.0112111i \(-0.996431\pi\)
0.999937 0.0112111i \(-0.00356869\pi\)
\(810\) 0.937207 + 1.05908i 0.0329301 + 0.0372121i
\(811\) 30.6724 30.6724i 1.07705 1.07705i 0.0802798 0.996772i \(-0.474419\pi\)
0.996772 0.0802798i \(-0.0255814\pi\)
\(812\) 37.1713 29.0551i 1.30446 1.01963i
\(813\) 11.4428 + 11.4428i 0.401317 + 0.401317i
\(814\) −10.7691 0.657434i −0.377458 0.0230430i
\(815\) −21.9121 −0.767549
\(816\) 10.3199 + 17.1575i 0.361270 + 0.600632i
\(817\) 5.05543 0.176867
\(818\) 53.6645 + 3.27610i 1.87633 + 0.114546i
\(819\) 12.6056 + 12.6056i 0.440474 + 0.440474i
\(820\) −3.88806 4.97415i −0.135777 0.173705i
\(821\) 2.40778 2.40778i 0.0840320 0.0840320i −0.663841 0.747873i \(-0.731075\pi\)
0.747873 + 0.663841i \(0.231075\pi\)
\(822\) −13.4872 15.2410i −0.470420 0.531591i
\(823\) 32.4455i 1.13098i −0.824755 0.565490i \(-0.808687\pi\)
0.824755 0.565490i \(-0.191313\pi\)
\(824\) −4.63808 0.857972i −0.161575 0.0298889i
\(825\) 4.96402i 0.172825i
\(826\) 21.2733 18.8254i 0.740193 0.655018i
\(827\) 32.2278 32.2278i 1.12067 1.12067i 0.129028 0.991641i \(-0.458814\pi\)
0.991641 0.129028i \(-0.0411857\pi\)
\(828\) 14.8530 + 1.82027i 0.516176 + 0.0632587i
\(829\) 29.6767 + 29.6767i 1.03072 + 1.03072i 0.999513 + 0.0312027i \(0.00993375\pi\)
0.0312027 + 0.999513i \(0.490066\pi\)
\(830\) −0.348902 + 5.71522i −0.0121106 + 0.198378i
\(831\) 27.3968 0.950384
\(832\) 21.0142 + 47.1118i 0.728538 + 1.63331i
\(833\) 3.21915 0.111537
\(834\) 0.0356763 0.584399i 0.00123537 0.0202361i
\(835\) 1.25086 + 1.25086i 0.0432877 + 0.0432877i
\(836\) −11.3294 1.38844i −0.391834 0.0480202i
\(837\) 5.36151 5.36151i 0.185321 0.185321i
\(838\) 34.7932 30.7895i 1.20191 1.06361i
\(839\) 42.4417i 1.46525i 0.680632 + 0.732625i \(0.261705\pi\)
−0.680632 + 0.732625i \(0.738295\pi\)
\(840\) 7.68908 + 1.42236i 0.265298 + 0.0490760i
\(841\) 43.8072i 1.51059i
\(842\) 35.5055 + 40.1224i 1.22360 + 1.38271i
\(843\) −12.8542 + 12.8542i −0.442723 + 0.442723i
\(844\) 3.72349 + 4.76360i 0.128168 + 0.163970i
\(845\) −20.2091 20.2091i −0.695214 0.695214i
\(846\) 3.89609 + 0.237848i 0.133950 + 0.00817738i
\(847\) 37.7136 1.29586
\(848\) 31.0774 18.6925i 1.06720 0.641904i
\(849\) 10.9591 0.376115
\(850\) −7.06569 0.431345i −0.242351 0.0147950i
\(851\) 8.13103 + 8.13103i 0.278728 + 0.278728i
\(852\) −5.51882 + 4.31381i −0.189072 + 0.147789i
\(853\) −16.7844 + 16.7844i −0.574686 + 0.574686i −0.933434 0.358748i \(-0.883204\pi\)
0.358748 + 0.933434i \(0.383204\pi\)
\(854\) 9.13257 + 10.3201i 0.312510 + 0.353147i
\(855\) 1.14968i 0.0393183i
\(856\) 13.8014 + 20.0664i 0.471721 + 0.685854i
\(857\) 31.0924i 1.06210i −0.847341 0.531049i \(-0.821798\pi\)
0.847341 0.531049i \(-0.178202\pi\)
\(858\) 33.9003 29.9993i 1.15734 1.02416i
\(859\) −16.2508 + 16.2508i −0.554469 + 0.554469i −0.927727 0.373258i \(-0.878241\pi\)
0.373258 + 0.927727i \(0.378241\pi\)
\(860\) −1.06978 + 8.72917i −0.0364792 + 0.297662i
\(861\) −6.17099 6.17099i −0.210307 0.210307i
\(862\) 0.790657 12.9514i 0.0269299 0.441127i
\(863\) −22.4656 −0.764739 −0.382369 0.924010i \(-0.624892\pi\)
−0.382369 + 0.924010i \(0.624892\pi\)
\(864\) 2.61491 + 5.01620i 0.0889611 + 0.170654i
\(865\) −5.67597 −0.192989
\(866\) −3.15193 + 51.6304i −0.107107 + 1.75447i
\(867\) −5.69577 5.69577i −0.193438 0.193438i
\(868\) 5.09980 41.6132i 0.173098 1.41244i
\(869\) −31.4268 + 31.4268i −1.06608 + 1.06608i
\(870\) −9.03679 + 7.99692i −0.306376 + 0.271121i
\(871\) 28.6913i 0.972169i
\(872\) 9.62801 6.62201i 0.326046 0.224250i
\(873\) 8.24056i 0.278901i
\(874\) 8.06185 + 9.11016i 0.272696 + 0.308156i
\(875\) −1.95488 + 1.95488i −0.0660871 + 0.0660871i
\(876\) −23.0287 + 18.0004i −0.778066 + 0.608179i
\(877\) 1.46527 + 1.46527i 0.0494785 + 0.0494785i 0.731413 0.681935i \(-0.238861\pi\)
−0.681935 + 0.731413i \(0.738861\pi\)
\(878\) −9.82952 0.600071i −0.331730 0.0202514i
\(879\) 1.76172 0.0594213
\(880\) 4.79481 19.2685i 0.161633 0.649540i
\(881\) 0.578022 0.0194740 0.00973702 0.999953i \(-0.496901\pi\)
0.00973702 + 0.999953i \(0.496901\pi\)
\(882\) 0.907823 + 0.0554207i 0.0305680 + 0.00186611i
\(883\) −10.1372 10.1372i −0.341144 0.341144i 0.515653 0.856797i \(-0.327549\pi\)
−0.856797 + 0.515653i \(0.827549\pi\)
\(884\) −39.7547 50.8597i −1.33710 1.71060i
\(885\) −5.13756 + 5.13756i −0.172697 + 0.172697i
\(886\) 2.85993 + 3.23182i 0.0960813 + 0.108575i
\(887\) 56.0202i 1.88097i 0.339831 + 0.940487i \(0.389630\pi\)
−0.339831 + 0.940487i \(0.610370\pi\)
\(888\) −0.790704 + 4.27444i −0.0265343 + 0.143441i
\(889\) 18.2762i 0.612962i
\(890\) 7.66305 6.78126i 0.256866 0.227308i
\(891\) 3.51009 3.51009i 0.117593 0.117593i
\(892\) −26.7535 3.27871i −0.895774 0.109779i
\(893\) 2.24380 + 2.24380i 0.0750860 + 0.0750860i
\(894\) −1.33279 + 21.8319i −0.0445752 + 0.730168i
\(895\) 7.51428 0.251175
\(896\) 28.4722 + 12.9480i 0.951191 + 0.432564i
\(897\) −48.2461 −1.61089
\(898\) −1.13509 + 18.5935i −0.0378785 + 0.620472i
\(899\) 45.7483 + 45.7483i 1.52579 + 1.52579i
\(900\) −1.98515 0.243285i −0.0661716 0.00810949i
\(901\) −32.0901 + 32.0901i −1.06908 + 1.06908i
\(902\) −16.5957 + 14.6860i −0.552576 + 0.488991i
\(903\) 12.1567i 0.404549i
\(904\) −1.46317 + 7.90970i −0.0486643 + 0.263073i
\(905\) 12.3732i 0.411299i
\(906\) 12.6734 + 14.3214i 0.421046 + 0.475796i
\(907\) 31.3292 31.3292i 1.04027 1.04027i 0.0411133 0.999154i \(-0.486910\pi\)
0.999154 0.0411133i \(-0.0130905\pi\)
\(908\) 4.71291 + 6.02941i 0.156404 + 0.200093i
\(909\) 1.07326 + 1.07326i 0.0355979 + 0.0355979i
\(910\) −25.1643 1.53623i −0.834188 0.0509254i
\(911\) −24.7701 −0.820670 −0.410335 0.911935i \(-0.634588\pi\)
−0.410335 + 0.911935i \(0.634588\pi\)
\(912\) −1.11049 + 4.46264i −0.0367721 + 0.147773i
\(913\) 20.0983 0.665157
\(914\) 14.1175 + 0.861843i 0.466965 + 0.0285072i
\(915\) −2.49234 2.49234i −0.0823942 0.0823942i
\(916\) −1.12993 + 0.883214i −0.0373339 + 0.0291822i
\(917\) 18.5264 18.5264i 0.611796 0.611796i
\(918\) −4.69119 5.30121i −0.154832 0.174966i
\(919\) 7.82495i 0.258121i 0.991637 + 0.129061i \(0.0411962\pi\)
−0.991637 + 0.129061i \(0.958804\pi\)
\(920\) −17.4364 + 11.9925i −0.574861 + 0.395381i
\(921\) 19.0979i 0.629296i
\(922\) 2.68763 2.37836i 0.0885122 0.0783271i
\(923\) 15.9694 15.9694i 0.525640 0.525640i
\(924\) 3.33875 27.2435i 0.109837 0.896244i
\(925\) −1.08674 1.08674i −0.0357318 0.0357318i
\(926\) 0.222610 3.64648i 0.00731542 0.119831i
\(927\) 1.66763 0.0547721
\(928\) −42.8018 + 22.3123i −1.40504 + 0.732437i
\(929\) 54.8650 1.80006 0.900031 0.435826i \(-0.143544\pi\)
0.900031 + 0.435826i \(0.143544\pi\)
\(930\) −0.653402 + 10.7031i −0.0214259 + 0.350969i
\(931\) 0.522826 + 0.522826i 0.0171349 + 0.0171349i
\(932\) 1.98547 16.2010i 0.0650362 0.530681i
\(933\) 8.45340 8.45340i 0.276752 0.276752i
\(934\) −36.9661 + 32.7123i −1.20957 + 1.07038i
\(935\) 24.8474i 0.812598i
\(936\) −10.3355 15.0272i −0.337827 0.491180i
\(937\) 19.3306i 0.631504i 0.948842 + 0.315752i \(0.102257\pi\)
−0.948842 + 0.315752i \(0.897743\pi\)
\(938\) 11.5287 + 13.0278i 0.376425 + 0.425373i
\(939\) −10.7753 + 10.7753i −0.351638 + 0.351638i
\(940\) −4.34917 + 3.39954i −0.141854 + 0.110881i
\(941\) 11.4226 + 11.4226i 0.372365 + 0.372365i 0.868338 0.495973i \(-0.165188\pi\)
−0.495973 + 0.868338i \(0.665188\pi\)
\(942\) 5.51947 + 0.336952i 0.179834 + 0.0109785i
\(943\) 23.6186 0.769129
\(944\) −24.9045 + 14.9797i −0.810573 + 0.487546i
\(945\) −2.76462 −0.0899331
\(946\) 30.8121 + 1.88101i 1.00179 + 0.0611570i
\(947\) −26.8761 26.8761i −0.873357 0.873357i 0.119480 0.992837i \(-0.461877\pi\)
−0.992837 + 0.119480i \(0.961877\pi\)
\(948\) 11.0276 + 14.1080i 0.358159 + 0.458206i
\(949\) 66.6364 66.6364i 2.16311 2.16311i
\(950\) −1.07749 1.21760i −0.0349584 0.0395042i
\(951\) 31.6871i 1.02752i
\(952\) −38.4877 7.11962i −1.24739 0.230748i
\(953\) 36.6661i 1.18773i 0.804564 + 0.593866i \(0.202399\pi\)
−0.804564 + 0.593866i \(0.797601\pi\)
\(954\) −9.60208 + 8.49716i −0.310879 + 0.275106i
\(955\) 2.85521 2.85521i 0.0923923 0.0923923i
\(956\) 4.89134 + 0.599446i 0.158197 + 0.0193875i
\(957\) 29.9506 + 29.9506i 0.968167 + 0.968167i
\(958\) −0.120079 + 1.96696i −0.00387957 + 0.0635496i
\(959\) 39.7852 1.28473
\(960\) −7.47061 2.86182i −0.241113 0.0923649i
\(961\) 26.4917 0.854570
\(962\) 0.854004 13.9891i 0.0275342 0.451026i
\(963\) −6.08860 6.08860i −0.196202 0.196202i
\(964\) −14.6518 1.79562i −0.471904 0.0578330i
\(965\) −0.309084 + 0.309084i −0.00994976 + 0.00994976i
\(966\) −21.9070 + 19.3862i −0.704847 + 0.623739i
\(967\) 43.0462i 1.38427i −0.721767 0.692136i \(-0.756670\pi\)
0.721767 0.692136i \(-0.243330\pi\)
\(968\) −37.9404 7.01838i −1.21945 0.225579i
\(969\) 5.75474i 0.184869i
\(970\) 7.72311 + 8.72738i 0.247974 + 0.280219i
\(971\) −3.26831 + 3.26831i −0.104885 + 0.104885i −0.757602 0.652717i \(-0.773629\pi\)
0.652717 + 0.757602i \(0.273629\pi\)
\(972\) −1.23168 1.57574i −0.0395063 0.0505419i
\(973\) 0.809324 + 0.809324i 0.0259457 + 0.0259457i
\(974\) −37.6955 2.30123i −1.20784 0.0737362i
\(975\) 6.44825 0.206509
\(976\) −7.26694 12.0817i −0.232609 0.386726i
\(977\) 1.62437 0.0519681 0.0259840 0.999662i \(-0.491728\pi\)
0.0259840 + 0.999662i \(0.491728\pi\)
\(978\) 30.9309 + 1.88826i 0.989060 + 0.0603800i
\(979\) −25.3976 25.3976i −0.811712 0.811712i
\(980\) −1.01339 + 0.792124i −0.0323717 + 0.0253035i
\(981\) −2.92136 + 2.92136i −0.0932719 + 0.0932719i
\(982\) 21.6385 + 24.4522i 0.690511 + 0.780301i
\(983\) 45.7756i 1.46001i −0.683439 0.730007i \(-0.739517\pi\)
0.683439 0.730007i \(-0.260483\pi\)
\(984\) 5.05969 + 7.35649i 0.161297 + 0.234516i
\(985\) 16.5231i 0.526471i
\(986\) 45.2337 40.0286i 1.44053 1.27477i
\(987\) −5.39563 + 5.39563i −0.171745 + 0.171745i
\(988\) 1.80358 14.7168i 0.0573795 0.468204i
\(989\) −23.2641 23.2641i −0.739754 0.739754i
\(990\) −0.427771 + 7.00714i −0.0135955 + 0.222702i
\(991\) 11.0608 0.351357 0.175679 0.984448i \(-0.443788\pi\)
0.175679 + 0.984448i \(0.443788\pi\)
\(992\) −12.8745 + 40.9143i −0.408767 + 1.29903i
\(993\) −11.4785 −0.364258
\(994\) 0.834401 13.6680i 0.0264656 0.433522i
\(995\) 11.1307 + 11.1307i 0.352868 + 0.352868i
\(996\) 0.985011 8.03746i 0.0312113 0.254677i
\(997\) 21.9716 21.9716i 0.695848 0.695848i −0.267664 0.963512i \(-0.586252\pi\)
0.963512 + 0.267664i \(0.0862518\pi\)
\(998\) −39.6791 + 35.1132i −1.25602 + 1.11149i
\(999\) 1.53688i 0.0486248i
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 240.2.s.c.61.6 20
3.2 odd 2 720.2.t.d.541.5 20
4.3 odd 2 960.2.s.c.721.7 20
8.3 odd 2 1920.2.s.f.1441.2 20
8.5 even 2 1920.2.s.e.1441.9 20
12.11 even 2 2880.2.t.d.721.7 20
16.3 odd 4 1920.2.s.f.481.4 20
16.5 even 4 inner 240.2.s.c.181.6 yes 20
16.11 odd 4 960.2.s.c.241.9 20
16.13 even 4 1920.2.s.e.481.7 20
48.5 odd 4 720.2.t.d.181.5 20
48.11 even 4 2880.2.t.d.2161.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.s.c.61.6 20 1.1 even 1 trivial
240.2.s.c.181.6 yes 20 16.5 even 4 inner
720.2.t.d.181.5 20 48.5 odd 4
720.2.t.d.541.5 20 3.2 odd 2
960.2.s.c.241.9 20 16.11 odd 4
960.2.s.c.721.7 20 4.3 odd 2
1920.2.s.e.481.7 20 16.13 even 4
1920.2.s.e.1441.9 20 8.5 even 2
1920.2.s.f.481.4 20 16.3 odd 4
1920.2.s.f.1441.2 20 8.3 odd 2
2880.2.t.d.721.7 20 12.11 even 2
2880.2.t.d.2161.9 20 48.11 even 4