Properties

Label 55.2.j.a.49.3
Level $55$
Weight $2$
Character 55.49
Analytic conductor $0.439$
Analytic rank $0$
Dimension $16$
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] = [55,2,Mod(4,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 49.3
Root \(0.471815 - 0.649397i\) of defining polynomial
Character \(\chi\) \(=\) 55.49
Dual form 55.2.j.a.9.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.763412 - 0.248048i) q^{2} +(1.03494 - 1.42447i) q^{3} +(-1.09676 + 0.796845i) q^{4} +(-2.16717 + 0.550792i) q^{5} +(0.436748 - 1.34417i) q^{6} +(0.348029 + 0.479022i) q^{7} +(-1.58326 + 2.17917i) q^{8} +(-0.0309674 - 0.0953077i) q^{9} +O(q^{10})\) \(q+(0.763412 - 0.248048i) q^{2} +(1.03494 - 1.42447i) q^{3} +(-1.09676 + 0.796845i) q^{4} +(-2.16717 + 0.550792i) q^{5} +(0.436748 - 1.34417i) q^{6} +(0.348029 + 0.479022i) q^{7} +(-1.58326 + 2.17917i) q^{8} +(-0.0309674 - 0.0953077i) q^{9} +(-1.51782 + 0.958043i) q^{10} +(1.96213 - 2.67395i) q^{11} +2.38699i q^{12} +(1.70704 - 0.554651i) q^{13} +(0.384510 + 0.279363i) q^{14} +(-1.45830 + 3.65711i) q^{15} +(0.169713 - 0.522322i) q^{16} +(-6.73074 - 2.18695i) q^{17} +(-0.0472817 - 0.0650777i) q^{18} +(-1.85009 - 1.34417i) q^{19} +(1.93798 - 2.33099i) q^{20} +1.04254 q^{21} +(0.834650 - 2.52803i) q^{22} +1.49081i q^{23} +(1.46558 + 4.51060i) q^{24} +(4.39326 - 2.38732i) q^{25} +(1.16560 - 0.846855i) q^{26} +(4.85588 + 1.57777i) q^{27} +(-0.763412 - 0.248048i) q^{28} +(2.89263 - 2.10162i) q^{29} +(-0.206148 + 3.15361i) q^{30} +(1.90578 + 5.86539i) q^{31} -5.82804i q^{32} +(-1.77828 - 5.56238i) q^{33} -5.68079 q^{34} +(-1.01808 - 0.846429i) q^{35} +(0.109909 + 0.0798539i) q^{36} +(4.31283 + 5.93610i) q^{37} +(-1.74580 - 0.567246i) q^{38} +(0.976598 - 3.00566i) q^{39} +(2.23092 - 5.59467i) q^{40} +(-6.80400 - 4.94339i) q^{41} +(0.795888 - 0.258600i) q^{42} +9.51936i q^{43} +(-0.0212704 + 4.49621i) q^{44} +(0.119606 + 0.189492i) q^{45} +(0.369792 + 1.13810i) q^{46} +(-1.13540 + 1.56274i) q^{47} +(-0.568389 - 0.782321i) q^{48} +(2.05478 - 6.32397i) q^{49} +(2.76170 - 2.91225i) q^{50} +(-10.0811 + 7.32438i) q^{51} +(-1.43025 + 1.96857i) q^{52} +(-2.26628 + 0.736359i) q^{53} +4.09840 q^{54} +(-2.77949 + 6.87564i) q^{55} -1.59489 q^{56} +(-3.82947 + 1.24427i) q^{57} +(1.68697 - 2.32192i) q^{58} +(-0.0309674 + 0.0224991i) q^{59} +(-1.31474 - 5.17302i) q^{60} +(-1.06351 + 3.27314i) q^{61} +(2.90979 + 4.00499i) q^{62} +(0.0348769 - 0.0480039i) q^{63} +(-1.10621 - 3.40455i) q^{64} +(-3.39395 + 2.14225i) q^{65} +(-2.73729 - 3.80529i) q^{66} -6.79162i q^{67} +(9.12469 - 2.96479i) q^{68} +(2.12361 + 1.54290i) q^{69} +(-0.987170 - 0.393642i) q^{70} +(-3.64439 + 11.2163i) q^{71} +(0.256721 + 0.0834136i) q^{72} +(-4.01031 - 5.51972i) q^{73} +(4.76490 + 3.46191i) q^{74} +(1.14608 - 8.72879i) q^{75} +3.10021 q^{76} +(1.96376 + 0.00929006i) q^{77} -2.53680i q^{78} +(-1.39863 - 4.30453i) q^{79} +(-0.0801054 + 1.22544i) q^{80} +(7.51625 - 5.46087i) q^{81} +(-6.42045 - 2.08613i) q^{82} +(5.65177 + 1.83637i) q^{83} +(-1.14342 + 0.830744i) q^{84} +(15.7912 + 1.03225i) q^{85} +(2.36125 + 7.26720i) q^{86} -6.29552i q^{87} +(2.72042 + 8.50937i) q^{88} +6.21375 q^{89} +(0.138312 + 0.114992i) q^{90} +(0.859791 + 0.624675i) q^{91} +(-1.18795 - 1.63507i) q^{92} +(10.3274 + 3.35559i) q^{93} +(-0.479142 + 1.47465i) q^{94} +(4.74983 + 1.89403i) q^{95} +(-8.30186 - 6.03166i) q^{96} +(-5.11260 + 1.66119i) q^{97} -5.33748i q^{98} +(-0.315611 - 0.104201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.763412 0.248048i 0.539814 0.175396i −0.0264046 0.999651i \(-0.508406\pi\)
0.566219 + 0.824255i \(0.308406\pi\)
\(3\) 1.03494 1.42447i 0.597522 0.822418i −0.397957 0.917404i \(-0.630281\pi\)
0.995479 + 0.0949859i \(0.0302806\pi\)
\(4\) −1.09676 + 0.796845i −0.548382 + 0.398423i
\(5\) −2.16717 + 0.550792i −0.969188 + 0.246322i
\(6\) 0.436748 1.34417i 0.178302 0.548756i
\(7\) 0.348029 + 0.479022i 0.131543 + 0.181053i 0.869708 0.493567i \(-0.164307\pi\)
−0.738165 + 0.674620i \(0.764307\pi\)
\(8\) −1.58326 + 2.17917i −0.559766 + 0.770451i
\(9\) −0.0309674 0.0953077i −0.0103225 0.0317692i
\(10\) −1.51782 + 0.958043i −0.479977 + 0.302960i
\(11\) 1.96213 2.67395i 0.591606 0.806227i
\(12\) 2.38699i 0.689065i
\(13\) 1.70704 0.554651i 0.473448 0.153833i −0.0625674 0.998041i \(-0.519929\pi\)
0.536016 + 0.844208i \(0.319929\pi\)
\(14\) 0.384510 + 0.279363i 0.102765 + 0.0746629i
\(15\) −1.45830 + 3.65711i −0.376532 + 0.944261i
\(16\) 0.169713 0.522322i 0.0424281 0.130580i
\(17\) −6.73074 2.18695i −1.63244 0.530413i −0.657612 0.753357i \(-0.728433\pi\)
−0.974831 + 0.222944i \(0.928433\pi\)
\(18\) −0.0472817 0.0650777i −0.0111444 0.0153390i
\(19\) −1.85009 1.34417i −0.424441 0.308374i 0.354981 0.934873i \(-0.384487\pi\)
−0.779422 + 0.626499i \(0.784487\pi\)
\(20\) 1.93798 2.33099i 0.433345 0.521225i
\(21\) 1.04254 0.227501
\(22\) 0.834650 2.52803i 0.177948 0.538978i
\(23\) 1.49081i 0.310855i 0.987847 + 0.155428i \(0.0496756\pi\)
−0.987847 + 0.155428i \(0.950324\pi\)
\(24\) 1.46558 + 4.51060i 0.299161 + 0.920723i
\(25\) 4.39326 2.38732i 0.878651 0.477464i
\(26\) 1.16560 0.846855i 0.228592 0.166082i
\(27\) 4.85588 + 1.57777i 0.934515 + 0.303642i
\(28\) −0.763412 0.248048i −0.144271 0.0468766i
\(29\) 2.89263 2.10162i 0.537149 0.390261i −0.285876 0.958267i \(-0.592285\pi\)
0.823025 + 0.568005i \(0.192285\pi\)
\(30\) −0.206148 + 3.15361i −0.0376372 + 0.575767i
\(31\) 1.90578 + 5.86539i 0.342288 + 1.05346i 0.963020 + 0.269432i \(0.0868358\pi\)
−0.620731 + 0.784023i \(0.713164\pi\)
\(32\) 5.82804i 1.03026i
\(33\) −1.77828 5.56238i −0.309559 0.968286i
\(34\) −5.68079 −0.974248
\(35\) −1.01808 0.846429i −0.172087 0.143073i
\(36\) 0.109909 + 0.0798539i 0.0183182 + 0.0133090i
\(37\) 4.31283 + 5.93610i 0.709025 + 0.975889i 0.999818 + 0.0191031i \(0.00608108\pi\)
−0.290792 + 0.956786i \(0.593919\pi\)
\(38\) −1.74580 0.567246i −0.283207 0.0920194i
\(39\) 0.976598 3.00566i 0.156381 0.481291i
\(40\) 2.23092 5.59467i 0.352739 0.884595i
\(41\) −6.80400 4.94339i −1.06261 0.772028i −0.0880369 0.996117i \(-0.528059\pi\)
−0.974569 + 0.224089i \(0.928059\pi\)
\(42\) 0.795888 0.258600i 0.122808 0.0399028i
\(43\) 9.51936i 1.45169i 0.687859 + 0.725844i \(0.258551\pi\)
−0.687859 + 0.725844i \(0.741449\pi\)
\(44\) −0.0212704 + 4.49621i −0.00320664 + 0.677830i
\(45\) 0.119606 + 0.189492i 0.0178299 + 0.0282477i
\(46\) 0.369792 + 1.13810i 0.0545228 + 0.167804i
\(47\) −1.13540 + 1.56274i −0.165615 + 0.227949i −0.883756 0.467948i \(-0.844993\pi\)
0.718141 + 0.695898i \(0.244993\pi\)
\(48\) −0.568389 0.782321i −0.0820400 0.112918i
\(49\) 2.05478 6.32397i 0.293540 0.903424i
\(50\) 2.76170 2.91225i 0.390563 0.411854i
\(51\) −10.0811 + 7.32438i −1.41164 + 1.02562i
\(52\) −1.43025 + 1.96857i −0.198340 + 0.272991i
\(53\) −2.26628 + 0.736359i −0.311298 + 0.101147i −0.460499 0.887660i \(-0.652330\pi\)
0.149202 + 0.988807i \(0.452330\pi\)
\(54\) 4.09840 0.557722
\(55\) −2.77949 + 6.87564i −0.374786 + 0.927111i
\(56\) −1.59489 −0.213126
\(57\) −3.82947 + 1.24427i −0.507225 + 0.164807i
\(58\) 1.68697 2.32192i 0.221510 0.304882i
\(59\) −0.0309674 + 0.0224991i −0.00403161 + 0.00292913i −0.589799 0.807550i \(-0.700793\pi\)
0.585768 + 0.810479i \(0.300793\pi\)
\(60\) −1.31474 5.17302i −0.169732 0.667834i
\(61\) −1.06351 + 3.27314i −0.136168 + 0.419082i −0.995770 0.0918822i \(-0.970712\pi\)
0.859602 + 0.510965i \(0.170712\pi\)
\(62\) 2.90979 + 4.00499i 0.369544 + 0.508634i
\(63\) 0.0348769 0.0480039i 0.00439408 0.00604793i
\(64\) −1.10621 3.40455i −0.138276 0.425569i
\(65\) −3.39395 + 2.14225i −0.420968 + 0.265713i
\(66\) −2.73729 3.80529i −0.336938 0.468399i
\(67\) 6.79162i 0.829728i −0.909883 0.414864i \(-0.863829\pi\)
0.909883 0.414864i \(-0.136171\pi\)
\(68\) 9.12469 2.96479i 1.10653 0.359534i
\(69\) 2.12361 + 1.54290i 0.255653 + 0.185743i
\(70\) −0.987170 0.393642i −0.117989 0.0470492i
\(71\) −3.64439 + 11.2163i −0.432510 + 1.33113i 0.463107 + 0.886302i \(0.346735\pi\)
−0.895617 + 0.444826i \(0.853265\pi\)
\(72\) 0.256721 + 0.0834136i 0.0302548 + 0.00983038i
\(73\) −4.01031 5.51972i −0.469372 0.646035i 0.507048 0.861918i \(-0.330737\pi\)
−0.976419 + 0.215884i \(0.930737\pi\)
\(74\) 4.76490 + 3.46191i 0.553909 + 0.402438i
\(75\) 1.14608 8.72879i 0.132338 1.00791i
\(76\) 3.10021 0.355619
\(77\) 1.96376 + 0.00929006i 0.223791 + 0.00105870i
\(78\) 2.53680i 0.287236i
\(79\) −1.39863 4.30453i −0.157358 0.484298i 0.841034 0.540982i \(-0.181947\pi\)
−0.998392 + 0.0566840i \(0.981947\pi\)
\(80\) −0.0801054 + 1.22544i −0.00895605 + 0.137008i
\(81\) 7.51625 5.46087i 0.835139 0.606764i
\(82\) −6.42045 2.08613i −0.709020 0.230375i
\(83\) 5.65177 + 1.83637i 0.620363 + 0.201568i 0.602301 0.798269i \(-0.294251\pi\)
0.0180613 + 0.999837i \(0.494251\pi\)
\(84\) −1.14342 + 0.830744i −0.124757 + 0.0906416i
\(85\) 15.7912 + 1.03225i 1.71280 + 0.111964i
\(86\) 2.36125 + 7.26720i 0.254621 + 0.783642i
\(87\) 6.29552i 0.674951i
\(88\) 2.72042 + 8.50937i 0.289998 + 0.907102i
\(89\) 6.21375 0.658656 0.329328 0.944216i \(-0.393178\pi\)
0.329328 + 0.944216i \(0.393178\pi\)
\(90\) 0.138312 + 0.114992i 0.0145793 + 0.0121212i
\(91\) 0.859791 + 0.624675i 0.0901306 + 0.0654837i
\(92\) −1.18795 1.63507i −0.123852 0.170467i
\(93\) 10.3274 + 3.35559i 1.07091 + 0.347958i
\(94\) −0.479142 + 1.47465i −0.0494197 + 0.152098i
\(95\) 4.74983 + 1.89403i 0.487322 + 0.194324i
\(96\) −8.30186 6.03166i −0.847305 0.615603i
\(97\) −5.11260 + 1.66119i −0.519106 + 0.168668i −0.556840 0.830620i \(-0.687986\pi\)
0.0377334 + 0.999288i \(0.487986\pi\)
\(98\) 5.33748i 0.539167i
\(99\) −0.315611 0.104201i −0.0317201 0.0104726i
\(100\) −2.91604 + 6.11907i −0.291604 + 0.611907i
\(101\) −3.06894 9.44523i −0.305371 0.939835i −0.979538 0.201257i \(-0.935497\pi\)
0.674167 0.738579i \(-0.264503\pi\)
\(102\) −5.87927 + 8.09212i −0.582135 + 0.801239i
\(103\) −7.94766 10.9390i −0.783107 1.07785i −0.994932 0.100546i \(-0.967941\pi\)
0.211826 0.977307i \(-0.432059\pi\)
\(104\) −1.49401 + 4.59808i −0.146499 + 0.450879i
\(105\) −2.25936 + 0.574223i −0.220491 + 0.0560385i
\(106\) −1.54745 + 1.12429i −0.150302 + 0.109201i
\(107\) 3.29418 4.53405i 0.318461 0.438323i −0.619536 0.784968i \(-0.712679\pi\)
0.937996 + 0.346645i \(0.112679\pi\)
\(108\) −6.58300 + 2.13895i −0.633449 + 0.205820i
\(109\) −18.6001 −1.78157 −0.890784 0.454428i \(-0.849844\pi\)
−0.890784 + 0.454428i \(0.849844\pi\)
\(110\) −0.416408 + 5.93839i −0.0397029 + 0.566204i
\(111\) 12.9193 1.22625
\(112\) 0.309268 0.100487i 0.0292231 0.00949516i
\(113\) −6.93668 + 9.54752i −0.652548 + 0.898155i −0.999206 0.0398362i \(-0.987316\pi\)
0.346658 + 0.937992i \(0.387316\pi\)
\(114\) −2.61482 + 1.89978i −0.244901 + 0.177931i
\(115\) −0.821127 3.23084i −0.0765705 0.301277i
\(116\) −1.49787 + 4.60997i −0.139074 + 0.428025i
\(117\) −0.105725 0.145518i −0.00977429 0.0134532i
\(118\) −0.0180600 + 0.0248575i −0.00166256 + 0.00228832i
\(119\) −1.29490 3.98529i −0.118703 0.365331i
\(120\) −5.66057 8.96801i −0.516737 0.818664i
\(121\) −3.30005 10.4933i −0.300005 0.953938i
\(122\) 2.76255i 0.250110i
\(123\) −14.0834 + 4.57598i −1.26986 + 0.412603i
\(124\) −6.76400 4.91433i −0.607425 0.441320i
\(125\) −8.20602 + 7.59350i −0.733968 + 0.679184i
\(126\) 0.0147182 0.0452979i 0.00131120 0.00403546i
\(127\) 15.2707 + 4.96177i 1.35506 + 0.440286i 0.894391 0.447287i \(-0.147610\pi\)
0.460669 + 0.887572i \(0.347610\pi\)
\(128\) 5.16229 + 7.10528i 0.456286 + 0.628024i
\(129\) 13.5600 + 9.85195i 1.19390 + 0.867416i
\(130\) −2.05960 + 2.47728i −0.180639 + 0.217272i
\(131\) 18.0296 1.57525 0.787625 0.616154i \(-0.211310\pi\)
0.787625 + 0.616154i \(0.211310\pi\)
\(132\) 6.38271 + 4.68360i 0.555543 + 0.407655i
\(133\) 1.35405i 0.117411i
\(134\) −1.68464 5.18480i −0.145531 0.447899i
\(135\) −11.3926 0.744718i −0.980515 0.0640951i
\(136\) 15.4222 11.2049i 1.32244 0.960811i
\(137\) 3.83473 + 1.24598i 0.327623 + 0.106451i 0.468210 0.883617i \(-0.344899\pi\)
−0.140587 + 0.990068i \(0.544899\pi\)
\(138\) 2.00390 + 0.651108i 0.170584 + 0.0554260i
\(139\) 6.41949 4.66403i 0.544494 0.395598i −0.281258 0.959632i \(-0.590752\pi\)
0.825751 + 0.564035i \(0.190752\pi\)
\(140\) 1.79107 + 0.117080i 0.151373 + 0.00989507i
\(141\) 1.05101 + 3.23468i 0.0885111 + 0.272409i
\(142\) 9.46663i 0.794422i
\(143\) 1.86633 5.65285i 0.156071 0.472715i
\(144\) −0.0550368 −0.00458640
\(145\) −5.11128 + 6.14781i −0.424468 + 0.510548i
\(146\) −4.43068 3.21907i −0.366685 0.266412i
\(147\) −6.88173 9.47189i −0.567596 0.781228i
\(148\) −9.46031 3.07384i −0.777633 0.252668i
\(149\) −3.86298 + 11.8890i −0.316468 + 0.973988i 0.658678 + 0.752425i \(0.271116\pi\)
−0.975146 + 0.221563i \(0.928884\pi\)
\(150\) −1.29023 6.94795i −0.105346 0.567298i
\(151\) −6.79775 4.93885i −0.553193 0.401918i 0.275768 0.961224i \(-0.411068\pi\)
−0.828961 + 0.559306i \(0.811068\pi\)
\(152\) 5.85835 1.90349i 0.475175 0.154394i
\(153\) 0.709215i 0.0573367i
\(154\) 1.50146 0.480014i 0.120991 0.0386807i
\(155\) −7.36076 11.6616i −0.591231 0.936683i
\(156\) 1.32395 + 4.07470i 0.106001 + 0.326237i
\(157\) 8.22657 11.3229i 0.656552 0.903666i −0.342809 0.939405i \(-0.611379\pi\)
0.999361 + 0.0357391i \(0.0113785\pi\)
\(158\) −2.13546 2.93921i −0.169888 0.233831i
\(159\) −1.29654 + 3.99034i −0.102822 + 0.316454i
\(160\) 3.21004 + 12.6303i 0.253776 + 0.998517i
\(161\) −0.714130 + 0.518846i −0.0562813 + 0.0408908i
\(162\) 4.38344 6.03329i 0.344395 0.474020i
\(163\) 11.2619 3.65922i 0.882101 0.286612i 0.167272 0.985911i \(-0.446504\pi\)
0.714830 + 0.699299i \(0.246504\pi\)
\(164\) 11.4015 0.890307
\(165\) 6.91755 + 11.0752i 0.538530 + 0.862200i
\(166\) 4.77014 0.370235
\(167\) −8.29919 + 2.69657i −0.642210 + 0.208667i −0.611976 0.790876i \(-0.709625\pi\)
−0.0302340 + 0.999543i \(0.509625\pi\)
\(168\) −1.65061 + 2.27187i −0.127347 + 0.175278i
\(169\) −7.91087 + 5.74758i −0.608528 + 0.442122i
\(170\) 12.3112 3.12894i 0.944230 0.239979i
\(171\) −0.0708175 + 0.217954i −0.00541555 + 0.0166673i
\(172\) −7.58546 10.4405i −0.578386 0.796080i
\(173\) 5.39505 7.42565i 0.410178 0.564562i −0.553084 0.833126i \(-0.686549\pi\)
0.963262 + 0.268564i \(0.0865490\pi\)
\(174\) −1.56159 4.80608i −0.118384 0.364348i
\(175\) 2.67256 + 1.27361i 0.202027 + 0.0962755i
\(176\) −1.06366 1.47867i −0.0801767 0.111459i
\(177\) 0.0673973i 0.00506589i
\(178\) 4.74365 1.54130i 0.355552 0.115526i
\(179\) 1.17159 + 0.851209i 0.0875687 + 0.0636224i 0.630708 0.776020i \(-0.282765\pi\)
−0.543139 + 0.839642i \(0.682765\pi\)
\(180\) −0.282175 0.112520i −0.0210321 0.00838672i
\(181\) 0.245206 0.754665i 0.0182260 0.0560938i −0.941530 0.336930i \(-0.890612\pi\)
0.959756 + 0.280836i \(0.0906116\pi\)
\(182\) 0.811324 + 0.263615i 0.0601393 + 0.0195404i
\(183\) 3.56182 + 4.90243i 0.263298 + 0.362398i
\(184\) −3.24872 2.36033i −0.239499 0.174006i
\(185\) −12.6162 10.4891i −0.927561 0.771172i
\(186\) 8.71644 0.639120
\(187\) −19.0544 + 13.7066i −1.39340 + 1.00233i
\(188\) 2.61869i 0.190988i
\(189\) 0.934204 + 2.87518i 0.0679533 + 0.209139i
\(190\) 4.09589 + 0.267743i 0.297147 + 0.0194242i
\(191\) 6.59373 4.79062i 0.477105 0.346637i −0.323099 0.946365i \(-0.604725\pi\)
0.800204 + 0.599728i \(0.204725\pi\)
\(192\) −5.99454 1.94774i −0.432618 0.140566i
\(193\) 4.15456 + 1.34990i 0.299052 + 0.0971678i 0.454700 0.890645i \(-0.349747\pi\)
−0.155648 + 0.987813i \(0.549747\pi\)
\(194\) −3.49097 + 2.53634i −0.250637 + 0.182098i
\(195\) −0.460960 + 7.05168i −0.0330101 + 0.504981i
\(196\) 2.78561 + 8.57324i 0.198972 + 0.612374i
\(197\) 15.6525i 1.11520i 0.830111 + 0.557599i \(0.188277\pi\)
−0.830111 + 0.557599i \(0.811723\pi\)
\(198\) −0.266788 0.00126211i −0.0189598 8.96940e-5i
\(199\) −1.43830 −0.101959 −0.0509793 0.998700i \(-0.516234\pi\)
−0.0509793 + 0.998700i \(0.516234\pi\)
\(200\) −1.75328 + 13.3534i −0.123976 + 0.944226i
\(201\) −9.67446 7.02890i −0.682383 0.495781i
\(202\) −4.68573 6.44936i −0.329687 0.453775i
\(203\) 2.01344 + 0.654208i 0.141316 + 0.0459164i
\(204\) 5.22023 16.0662i 0.365489 1.12486i
\(205\) 17.4682 + 6.96559i 1.22003 + 0.486498i
\(206\) −8.78074 6.37958i −0.611783 0.444486i
\(207\) 0.142086 0.0461665i 0.00987564 0.00320879i
\(208\) 0.985756i 0.0683499i
\(209\) −7.22439 + 2.30962i −0.499721 + 0.159760i
\(210\) −1.58239 + 0.998799i −0.109195 + 0.0689237i
\(211\) 2.68267 + 8.25641i 0.184683 + 0.568395i 0.999943 0.0107002i \(-0.00340605\pi\)
−0.815260 + 0.579095i \(0.803406\pi\)
\(212\) 1.89881 2.61349i 0.130411 0.179495i
\(213\) 12.2055 + 16.7995i 0.836310 + 1.15108i
\(214\) 1.39016 4.27846i 0.0950292 0.292470i
\(215\) −5.24319 20.6301i −0.357583 1.40696i
\(216\) −11.1263 + 8.08375i −0.757051 + 0.550030i
\(217\) −2.14638 + 2.95424i −0.145706 + 0.200547i
\(218\) −14.1995 + 4.61371i −0.961715 + 0.312480i
\(219\) −12.0131 −0.811770
\(220\) −2.43038 9.75577i −0.163856 0.657734i
\(221\) −12.7026 −0.854472
\(222\) 9.86276 3.20461i 0.661945 0.215079i
\(223\) 3.70660 5.10169i 0.248212 0.341635i −0.666672 0.745351i \(-0.732282\pi\)
0.914884 + 0.403717i \(0.132282\pi\)
\(224\) 2.79175 2.02833i 0.186532 0.135523i
\(225\) −0.363578 0.344782i −0.0242385 0.0229855i
\(226\) −2.92731 + 9.00932i −0.194721 + 0.599291i
\(227\) 0.656444 + 0.903517i 0.0435697 + 0.0599686i 0.830246 0.557397i \(-0.188200\pi\)
−0.786676 + 0.617366i \(0.788200\pi\)
\(228\) 3.20853 4.41616i 0.212490 0.292467i
\(229\) 1.29669 + 3.99079i 0.0856874 + 0.263719i 0.984715 0.174173i \(-0.0557253\pi\)
−0.899028 + 0.437892i \(0.855725\pi\)
\(230\) −1.42826 2.26278i −0.0941767 0.149204i
\(231\) 2.04561 2.78771i 0.134591 0.183418i
\(232\) 9.63094i 0.632302i
\(233\) −6.44766 + 2.09497i −0.422400 + 0.137246i −0.512501 0.858686i \(-0.671281\pi\)
0.0901010 + 0.995933i \(0.471281\pi\)
\(234\) −0.116807 0.0848655i −0.00763593 0.00554783i
\(235\) 1.59985 4.01209i 0.104363 0.261720i
\(236\) 0.0160356 0.0493524i 0.00104383 0.00321257i
\(237\) −7.57917 2.46262i −0.492320 0.159965i
\(238\) −1.97708 2.72122i −0.128155 0.176391i
\(239\) 3.55812 + 2.58513i 0.230156 + 0.167218i 0.696886 0.717182i \(-0.254568\pi\)
−0.466731 + 0.884400i \(0.654568\pi\)
\(240\) 1.66269 + 1.38236i 0.107326 + 0.0892309i
\(241\) −9.61218 −0.619175 −0.309587 0.950871i \(-0.600191\pi\)
−0.309587 + 0.950871i \(0.600191\pi\)
\(242\) −5.12214 7.19215i −0.329264 0.462329i
\(243\) 1.04101i 0.0667807i
\(244\) −1.44177 4.43731i −0.0922998 0.284070i
\(245\) −0.969870 + 14.8369i −0.0619627 + 0.947893i
\(246\) −9.61640 + 6.98672i −0.613119 + 0.445457i
\(247\) −3.90373 1.26840i −0.248389 0.0807064i
\(248\) −15.7990 5.13340i −1.00324 0.325971i
\(249\) 8.46509 6.15025i 0.536453 0.389756i
\(250\) −4.38102 + 7.83246i −0.277080 + 0.495368i
\(251\) 4.14719 + 12.7637i 0.261768 + 0.805640i 0.992420 + 0.122890i \(0.0392163\pi\)
−0.730652 + 0.682750i \(0.760784\pi\)
\(252\) 0.0804405i 0.00506727i
\(253\) 3.98636 + 2.92517i 0.250620 + 0.183904i
\(254\) 12.8886 0.808704
\(255\) 17.8133 21.4258i 1.11551 1.34173i
\(256\) 11.4956 + 8.35202i 0.718473 + 0.522001i
\(257\) 6.35829 + 8.75143i 0.396619 + 0.545899i 0.959891 0.280372i \(-0.0904578\pi\)
−0.563272 + 0.826271i \(0.690458\pi\)
\(258\) 12.7957 + 4.15756i 0.796623 + 0.258838i
\(259\) −1.34253 + 4.13188i −0.0834207 + 0.256742i
\(260\) 2.01532 5.05400i 0.124985 0.313436i
\(261\) −0.289878 0.210609i −0.0179430 0.0130364i
\(262\) 13.7640 4.47219i 0.850342 0.276293i
\(263\) 24.6351i 1.51906i −0.650471 0.759531i \(-0.725428\pi\)
0.650471 0.759531i \(-0.274572\pi\)
\(264\) 14.9368 + 4.93151i 0.919297 + 0.303513i
\(265\) 4.50584 2.84407i 0.276791 0.174710i
\(266\) −0.335868 1.03370i −0.0205934 0.0633799i
\(267\) 6.43084 8.85130i 0.393561 0.541691i
\(268\) 5.41187 + 7.44880i 0.330582 + 0.455008i
\(269\) 1.48359 4.56603i 0.0904563 0.278396i −0.895587 0.444887i \(-0.853244\pi\)
0.986043 + 0.166491i \(0.0532438\pi\)
\(270\) −8.88194 + 2.25737i −0.540538 + 0.137379i
\(271\) −18.8746 + 13.7132i −1.14655 + 0.833019i −0.988019 0.154334i \(-0.950677\pi\)
−0.158534 + 0.987353i \(0.550677\pi\)
\(272\) −2.28458 + 3.14446i −0.138523 + 0.190661i
\(273\) 1.77966 0.578247i 0.107710 0.0349971i
\(274\) 3.23654 0.195527
\(275\) 2.23657 16.4316i 0.134870 0.990863i
\(276\) −3.55855 −0.214200
\(277\) 20.8256 6.76663i 1.25129 0.406568i 0.392905 0.919579i \(-0.371470\pi\)
0.858382 + 0.513012i \(0.171470\pi\)
\(278\) 3.74381 5.15291i 0.224539 0.309051i
\(279\) 0.500000 0.363271i 0.0299342 0.0217485i
\(280\) 3.45639 0.878451i 0.206559 0.0524975i
\(281\) 4.87488 15.0033i 0.290811 0.895024i −0.693785 0.720182i \(-0.744058\pi\)
0.984596 0.174842i \(-0.0559416\pi\)
\(282\) 1.60471 + 2.20869i 0.0955590 + 0.131526i
\(283\) −13.2893 + 18.2912i −0.789968 + 1.08730i 0.204144 + 0.978941i \(0.434559\pi\)
−0.994112 + 0.108356i \(0.965441\pi\)
\(284\) −4.94061 15.2056i −0.293171 0.902288i
\(285\) 7.61377 4.80578i 0.451001 0.284670i
\(286\) 0.0226054 4.77839i 0.00133668 0.282552i
\(287\) 4.97971i 0.293943i
\(288\) −0.555457 + 0.180479i −0.0327306 + 0.0106348i
\(289\) 26.7668 + 19.4472i 1.57452 + 1.14395i
\(290\) −2.37706 + 5.96116i −0.139586 + 0.350051i
\(291\) −2.92492 + 9.00198i −0.171462 + 0.527705i
\(292\) 8.79673 + 2.85823i 0.514790 + 0.167265i
\(293\) −7.79380 10.7272i −0.455319 0.626693i 0.518211 0.855253i \(-0.326598\pi\)
−0.973530 + 0.228560i \(0.926598\pi\)
\(294\) −7.60308 5.52396i −0.443421 0.322164i
\(295\) 0.0547192 0.0658160i 0.00318588 0.00383195i
\(296\) −19.7641 −1.14876
\(297\) 13.7468 9.88860i 0.797669 0.573795i
\(298\) 10.0344i 0.581280i
\(299\) 0.826880 + 2.54487i 0.0478197 + 0.147174i
\(300\) 5.69852 + 10.4867i 0.329004 + 0.605448i
\(301\) −4.55998 + 3.31302i −0.262833 + 0.190959i
\(302\) −6.41455 2.08421i −0.369116 0.119933i
\(303\) −16.6306 5.40361i −0.955404 0.310429i
\(304\) −1.01607 + 0.738221i −0.0582758 + 0.0423399i
\(305\) 0.501982 7.67922i 0.0287434 0.439711i
\(306\) 0.175919 + 0.541424i 0.0100566 + 0.0309511i
\(307\) 10.0161i 0.571650i 0.958282 + 0.285825i \(0.0922676\pi\)
−0.958282 + 0.285825i \(0.907732\pi\)
\(308\) −2.16119 + 1.55463i −0.123145 + 0.0885830i
\(309\) −23.8076 −1.35437
\(310\) −8.51193 7.07679i −0.483445 0.401935i
\(311\) 2.75734 + 2.00332i 0.156354 + 0.113598i 0.663212 0.748432i \(-0.269193\pi\)
−0.506857 + 0.862030i \(0.669193\pi\)
\(312\) 5.00362 + 6.88690i 0.283274 + 0.389894i
\(313\) −23.3017 7.57117i −1.31709 0.427948i −0.435594 0.900143i \(-0.643462\pi\)
−0.881494 + 0.472196i \(0.843462\pi\)
\(314\) 3.47164 10.6846i 0.195916 0.602968i
\(315\) −0.0491440 + 0.123243i −0.00276895 + 0.00694394i
\(316\) 4.96401 + 3.60657i 0.279247 + 0.202885i
\(317\) −6.64646 + 2.15957i −0.373303 + 0.121293i −0.489659 0.871914i \(-0.662879\pi\)
0.116356 + 0.993208i \(0.462879\pi\)
\(318\) 3.36787i 0.188861i
\(319\) 0.0560993 11.8584i 0.00314096 0.663945i
\(320\) 4.27254 + 6.76895i 0.238842 + 0.378396i
\(321\) −3.04935 9.38493i −0.170198 0.523816i
\(322\) −0.416477 + 0.573232i −0.0232094 + 0.0319449i
\(323\) 9.51286 + 13.0933i 0.529310 + 0.728532i
\(324\) −3.89208 + 11.9786i −0.216226 + 0.665476i
\(325\) 6.17534 6.51198i 0.342546 0.361220i
\(326\) 7.68982 5.58698i 0.425900 0.309434i
\(327\) −19.2500 + 26.4953i −1.06453 + 1.46519i
\(328\) 21.5449 7.00037i 1.18962 0.386531i
\(329\) −1.14374 −0.0630563
\(330\) 8.02811 + 6.73903i 0.441933 + 0.370971i
\(331\) 5.64321 0.310179 0.155089 0.987900i \(-0.450433\pi\)
0.155089 + 0.987900i \(0.450433\pi\)
\(332\) −7.66196 + 2.48952i −0.420505 + 0.136630i
\(333\) 0.432200 0.594872i 0.0236844 0.0325988i
\(334\) −5.66682 + 4.11719i −0.310075 + 0.225282i
\(335\) 3.74077 + 14.7186i 0.204380 + 0.804162i
\(336\) 0.176932 0.544542i 0.00965245 0.0297072i
\(337\) −13.2936 18.2970i −0.724146 0.996702i −0.999376 0.0353234i \(-0.988754\pi\)
0.275230 0.961379i \(-0.411246\pi\)
\(338\) −4.61358 + 6.35005i −0.250946 + 0.345397i
\(339\) 6.42112 + 19.7622i 0.348748 + 1.07333i
\(340\) −18.1418 + 11.4510i −0.983876 + 0.621018i
\(341\) 19.4232 + 6.41272i 1.05182 + 0.347268i
\(342\) 0.183955i 0.00994713i
\(343\) 7.68631 2.49743i 0.415022 0.134849i
\(344\) −20.7443 15.0716i −1.11846 0.812605i
\(345\) −5.45205 2.17405i −0.293529 0.117047i
\(346\) 2.27673 7.00706i 0.122398 0.376702i
\(347\) −0.173468 0.0563630i −0.00931223 0.00302573i 0.304357 0.952558i \(-0.401558\pi\)
−0.313669 + 0.949532i \(0.601558\pi\)
\(348\) 5.01656 + 6.90470i 0.268916 + 0.370131i
\(349\) −12.4809 9.06792i −0.668089 0.485395i 0.201296 0.979530i \(-0.435485\pi\)
−0.869385 + 0.494136i \(0.835485\pi\)
\(350\) 2.35618 + 0.309364i 0.125943 + 0.0165362i
\(351\) 9.16431 0.489155
\(352\) −15.5839 11.4354i −0.830625 0.609508i
\(353\) 23.9103i 1.27262i 0.771435 + 0.636308i \(0.219539\pi\)
−0.771435 + 0.636308i \(0.780461\pi\)
\(354\) 0.0167177 + 0.0514519i 0.000888537 + 0.00273464i
\(355\) 1.72018 26.3149i 0.0912975 1.39665i
\(356\) −6.81501 + 4.95139i −0.361195 + 0.262423i
\(357\) −7.01707 2.27998i −0.371383 0.120670i
\(358\) 1.10555 + 0.359214i 0.0584299 + 0.0189850i
\(359\) −7.09293 + 5.15332i −0.374351 + 0.271982i −0.759013 0.651076i \(-0.774318\pi\)
0.384662 + 0.923057i \(0.374318\pi\)
\(360\) −0.602301 0.0393717i −0.0317440 0.00207507i
\(361\) −4.25527 13.0964i −0.223962 0.689283i
\(362\) 0.636943i 0.0334770i
\(363\) −18.3628 6.15910i −0.963795 0.323269i
\(364\) −1.44076 −0.0755161
\(365\) 11.7313 + 9.75333i 0.614042 + 0.510513i
\(366\) 3.93518 + 2.85907i 0.205695 + 0.149446i
\(367\) −3.16365 4.35439i −0.165141 0.227297i 0.718424 0.695605i \(-0.244864\pi\)
−0.883565 + 0.468308i \(0.844864\pi\)
\(368\) 0.778682 + 0.253009i 0.0405916 + 0.0131890i
\(369\) −0.260442 + 0.801557i −0.0135581 + 0.0417274i
\(370\) −12.2331 4.87807i −0.635971 0.253599i
\(371\) −1.14146 0.829322i −0.0592619 0.0430563i
\(372\) −14.0006 + 4.54908i −0.725899 + 0.235859i
\(373\) 3.22450i 0.166958i 0.996510 + 0.0834792i \(0.0266032\pi\)
−0.996510 + 0.0834792i \(0.973397\pi\)
\(374\) −11.1465 + 15.1902i −0.576371 + 0.785465i
\(375\) 2.32400 + 19.5480i 0.120011 + 1.00946i
\(376\) −1.60784 4.94844i −0.0829183 0.255196i
\(377\) 3.77218 5.19196i 0.194277 0.267400i
\(378\) 1.42637 + 1.96322i 0.0733643 + 0.100977i
\(379\) 6.07632 18.7010i 0.312119 0.960605i −0.664804 0.747017i \(-0.731485\pi\)
0.976924 0.213588i \(-0.0685149\pi\)
\(380\) −6.71869 + 1.70757i −0.344661 + 0.0875967i
\(381\) 22.8722 16.6176i 1.17178 0.851345i
\(382\) 3.84543 5.29278i 0.196749 0.270802i
\(383\) 26.6059 8.64478i 1.35950 0.441728i 0.463623 0.886033i \(-0.346549\pi\)
0.895876 + 0.444305i \(0.146549\pi\)
\(384\) 15.4639 0.789139
\(385\) −4.26092 + 1.06149i −0.217157 + 0.0540986i
\(386\) 3.50648 0.178475
\(387\) 0.907269 0.294789i 0.0461191 0.0149850i
\(388\) 4.28361 5.89588i 0.217467 0.299318i
\(389\) 10.5496 7.66472i 0.534885 0.388617i −0.287297 0.957842i \(-0.592757\pi\)
0.822182 + 0.569225i \(0.192757\pi\)
\(390\) 1.39725 + 5.49768i 0.0707525 + 0.278386i
\(391\) 3.26033 10.0343i 0.164882 0.507454i
\(392\) 10.5277 + 14.4902i 0.531730 + 0.731864i
\(393\) 18.6595 25.6826i 0.941247 1.29552i
\(394\) 3.88258 + 11.9493i 0.195601 + 0.601999i
\(395\) 5.40197 + 8.55830i 0.271803 + 0.430615i
\(396\) 0.429183 0.137209i 0.0215672 0.00689499i
\(397\) 1.82243i 0.0914651i −0.998954 0.0457325i \(-0.985438\pi\)
0.998954 0.0457325i \(-0.0145622\pi\)
\(398\) −1.09802 + 0.356768i −0.0550387 + 0.0178831i
\(399\) −1.92880 1.40135i −0.0965607 0.0701555i
\(400\) −0.501359 2.69985i −0.0250679 0.134993i
\(401\) 1.66277 5.11749i 0.0830349 0.255555i −0.900916 0.433993i \(-0.857104\pi\)
0.983951 + 0.178438i \(0.0571043\pi\)
\(402\) −9.12910 2.96622i −0.455318 0.147942i
\(403\) 6.50649 + 8.95542i 0.324111 + 0.446101i
\(404\) 10.8923 + 7.91371i 0.541912 + 0.393722i
\(405\) −13.2812 + 15.9745i −0.659947 + 0.793781i
\(406\) 1.69936 0.0843379
\(407\) 24.3352 + 0.115124i 1.20625 + 0.00570647i
\(408\) 33.5648i 1.66171i
\(409\) 11.3354 + 34.8867i 0.560499 + 1.72504i 0.680961 + 0.732320i \(0.261562\pi\)
−0.120462 + 0.992718i \(0.538438\pi\)
\(410\) 15.0632 + 0.984666i 0.743920 + 0.0486292i
\(411\) 5.74357 4.17295i 0.283309 0.205836i
\(412\) 17.4334 + 5.66446i 0.858883 + 0.279068i
\(413\) −0.0215551 0.00700368i −0.00106066 0.000344629i
\(414\) 0.0970185 0.0704881i 0.00476820 0.00346430i
\(415\) −13.2598 0.866779i −0.650899 0.0425485i
\(416\) −3.23253 9.94870i −0.158488 0.487775i
\(417\) 13.9713i 0.684180i
\(418\) −4.94229 + 3.55518i −0.241735 + 0.173890i
\(419\) −2.86630 −0.140028 −0.0700141 0.997546i \(-0.522304\pi\)
−0.0700141 + 0.997546i \(0.522304\pi\)
\(420\) 2.02042 2.43015i 0.0985864 0.118579i
\(421\) −3.76982 2.73893i −0.183730 0.133487i 0.492119 0.870528i \(-0.336223\pi\)
−0.675848 + 0.737041i \(0.736223\pi\)
\(422\) 4.09597 + 5.63761i 0.199389 + 0.274435i
\(423\) 0.184102 + 0.0598182i 0.00895132 + 0.00290846i
\(424\) 1.98345 6.10445i 0.0963251 0.296458i
\(425\) −34.7908 + 6.46061i −1.68760 + 0.313385i
\(426\) 13.4849 + 9.79738i 0.653347 + 0.474685i
\(427\) −1.93804 + 0.629706i −0.0937881 + 0.0304736i
\(428\) 7.59774i 0.367250i
\(429\) −6.12078 8.50889i −0.295514 0.410813i
\(430\) −9.11996 14.4487i −0.439803 0.696778i
\(431\) 6.41801 + 19.7526i 0.309145 + 0.951450i 0.978098 + 0.208145i \(0.0667426\pi\)
−0.668953 + 0.743304i \(0.733257\pi\)
\(432\) 1.64821 2.26856i 0.0792995 0.109146i
\(433\) −7.52199 10.3531i −0.361484 0.497540i 0.589078 0.808076i \(-0.299491\pi\)
−0.950561 + 0.310537i \(0.899491\pi\)
\(434\) −0.905781 + 2.78771i −0.0434789 + 0.133814i
\(435\) 3.46752 + 13.6435i 0.166255 + 0.654154i
\(436\) 20.3999 14.8214i 0.976979 0.709817i
\(437\) 2.00390 2.75814i 0.0958598 0.131940i
\(438\) −9.17095 + 2.97982i −0.438205 + 0.142381i
\(439\) 10.6208 0.506905 0.253452 0.967348i \(-0.418434\pi\)
0.253452 + 0.967348i \(0.418434\pi\)
\(440\) −10.5825 16.9429i −0.504502 0.807719i
\(441\) −0.666354 −0.0317312
\(442\) −9.69735 + 3.15086i −0.461256 + 0.149871i
\(443\) −3.87876 + 5.33865i −0.184285 + 0.253647i −0.891157 0.453695i \(-0.850106\pi\)
0.706872 + 0.707342i \(0.250106\pi\)
\(444\) −14.1694 + 10.2947i −0.672452 + 0.488565i
\(445\) −13.4662 + 3.42248i −0.638361 + 0.162241i
\(446\) 1.56420 4.81411i 0.0740669 0.227955i
\(447\) 12.9376 + 17.8071i 0.611929 + 0.842248i
\(448\) 1.24586 1.71478i 0.0588614 0.0810158i
\(449\) −4.21130 12.9610i −0.198743 0.611670i −0.999912 0.0132314i \(-0.995788\pi\)
0.801169 0.598438i \(-0.204212\pi\)
\(450\) −0.363082 0.173026i −0.0171159 0.00815654i
\(451\) −26.5688 + 8.49397i −1.25107 + 0.399965i
\(452\) 15.9988i 0.752522i
\(453\) −14.0705 + 4.57178i −0.661090 + 0.214801i
\(454\) 0.725253 + 0.526927i 0.0340378 + 0.0247299i
\(455\) −2.20738 0.880210i −0.103484 0.0412649i
\(456\) 3.35156 10.3150i 0.156951 0.483046i
\(457\) −12.8392 4.17169i −0.600590 0.195144i −0.00708664 0.999975i \(-0.502256\pi\)
−0.593504 + 0.804831i \(0.702256\pi\)
\(458\) 1.97981 + 2.72498i 0.0925105 + 0.127330i
\(459\) −29.2332 21.2391i −1.36449 0.991358i
\(460\) 3.47506 + 2.88916i 0.162026 + 0.134708i
\(461\) 11.3217 0.527303 0.263652 0.964618i \(-0.415073\pi\)
0.263652 + 0.964618i \(0.415073\pi\)
\(462\) 0.870156 2.63558i 0.0404833 0.122618i
\(463\) 4.82990i 0.224464i 0.993682 + 0.112232i \(0.0358001\pi\)
−0.993682 + 0.112232i \(0.964200\pi\)
\(464\) −0.606806 1.86756i −0.0281703 0.0866992i
\(465\) −24.2295 1.58386i −1.12362 0.0734497i
\(466\) −4.40257 + 3.19865i −0.203945 + 0.148175i
\(467\) 22.8418 + 7.42175i 1.05699 + 0.343437i 0.785409 0.618978i \(-0.212453\pi\)
0.271583 + 0.962415i \(0.412453\pi\)
\(468\) 0.231911 + 0.0753524i 0.0107201 + 0.00348317i
\(469\) 3.25333 2.36368i 0.150225 0.109145i
\(470\) 0.226158 3.45972i 0.0104319 0.159585i
\(471\) −7.61514 23.4370i −0.350887 1.07992i
\(472\) 0.103105i 0.00474579i
\(473\) 25.4543 + 18.6783i 1.17039 + 0.858828i
\(474\) −6.39688 −0.293818
\(475\) −11.3369 1.48852i −0.520173 0.0682981i
\(476\) 4.59586 + 3.33909i 0.210651 + 0.153047i
\(477\) 0.140361 + 0.193191i 0.00642671 + 0.00884561i
\(478\) 3.35755 + 1.09093i 0.153571 + 0.0498981i
\(479\) −13.3573 + 41.1095i −0.610309 + 1.87834i −0.155258 + 0.987874i \(0.549621\pi\)
−0.455052 + 0.890465i \(0.650379\pi\)
\(480\) 21.3137 + 8.49903i 0.972835 + 0.387926i
\(481\) 10.6546 + 7.74106i 0.485810 + 0.352962i
\(482\) −7.33805 + 2.38428i −0.334239 + 0.108601i
\(483\) 1.55423i 0.0707199i
\(484\) 11.9809 + 8.87905i 0.544588 + 0.403593i
\(485\) 10.1649 6.41606i 0.461565 0.291338i
\(486\) −0.258219 0.794718i −0.0117131 0.0360491i
\(487\) −24.6640 + 33.9471i −1.11763 + 1.53829i −0.307966 + 0.951397i \(0.599648\pi\)
−0.809666 + 0.586891i \(0.800352\pi\)
\(488\) −5.44890 7.49977i −0.246660 0.339499i
\(489\) 6.44294 19.8293i 0.291360 0.896713i
\(490\) 2.93984 + 11.5672i 0.132809 + 0.522554i
\(491\) 7.32956 5.32524i 0.330778 0.240325i −0.409982 0.912093i \(-0.634465\pi\)
0.740761 + 0.671769i \(0.234465\pi\)
\(492\) 11.7998 16.2411i 0.531978 0.732205i
\(493\) −24.0657 + 7.81942i −1.08386 + 0.352169i
\(494\) −3.29478 −0.148239
\(495\) 0.741375 + 0.0519862i 0.0333223 + 0.00233661i
\(496\) 3.38705 0.152083
\(497\) −6.64120 + 2.15786i −0.297898 + 0.0967931i
\(498\) 4.93680 6.79492i 0.221223 0.304488i
\(499\) 24.4965 17.7977i 1.09661 0.796736i 0.116109 0.993236i \(-0.462958\pi\)
0.980504 + 0.196501i \(0.0629578\pi\)
\(500\) 2.94921 14.8672i 0.131893 0.664882i
\(501\) −4.74796 + 14.6127i −0.212123 + 0.652849i
\(502\) 6.33203 + 8.71530i 0.282612 + 0.388983i
\(503\) −10.6177 + 14.6139i −0.473418 + 0.651604i −0.977223 0.212213i \(-0.931933\pi\)
0.503806 + 0.863817i \(0.331933\pi\)
\(504\) 0.0493894 + 0.152005i 0.00219998 + 0.00677084i
\(505\) 11.8533 + 18.7791i 0.527464 + 0.835658i
\(506\) 3.76881 + 1.24430i 0.167544 + 0.0553161i
\(507\) 17.2172i 0.764642i
\(508\) −20.7022 + 6.72654i −0.918510 + 0.298442i
\(509\) −20.1572 14.6451i −0.893453 0.649132i 0.0433229 0.999061i \(-0.486206\pi\)
−0.936776 + 0.349929i \(0.886206\pi\)
\(510\) 8.28430 20.7753i 0.366835 0.919944i
\(511\) 1.24836 3.84205i 0.0552241 0.169962i
\(512\) −5.85796 1.90337i −0.258888 0.0841177i
\(513\) −6.86304 9.44617i −0.303011 0.417058i
\(514\) 7.02477 + 5.10379i 0.309849 + 0.225119i
\(515\) 23.2491 + 19.3292i 1.02448 + 0.851747i
\(516\) −22.7226 −1.00031
\(517\) 1.95089 + 6.10231i 0.0858002 + 0.268379i
\(518\) 3.48734i 0.153225i
\(519\) −4.99407 15.3702i −0.219216 0.674676i
\(520\) 0.705181 10.7877i 0.0309242 0.473072i
\(521\) −29.3537 + 21.3267i −1.28601 + 0.934339i −0.999717 0.0238032i \(-0.992422\pi\)
−0.286291 + 0.958143i \(0.592422\pi\)
\(522\) −0.273537 0.0888777i −0.0119724 0.00389007i
\(523\) 23.4978 + 7.63489i 1.02749 + 0.333850i 0.773796 0.633435i \(-0.218356\pi\)
0.253690 + 0.967286i \(0.418356\pi\)
\(524\) −19.7742 + 14.3668i −0.863839 + 0.627616i
\(525\) 4.58015 2.48888i 0.199894 0.108624i
\(526\) −6.11067 18.8067i −0.266438 0.820011i
\(527\) 43.6462i 1.90126i
\(528\) −3.20715 0.0151722i −0.139573 0.000660285i
\(529\) 20.7775 0.903369
\(530\) 2.73435 3.28886i 0.118772 0.142859i
\(531\) 0.00310332 + 0.00225469i 0.000134672 + 9.78453e-5i
\(532\) 1.07897 + 1.48507i 0.0467791 + 0.0643859i
\(533\) −14.3566 4.66473i −0.621852 0.202052i
\(534\) 2.71384 8.35234i 0.117439 0.361441i
\(535\) −4.64173 + 11.6405i −0.200680 + 0.503262i
\(536\) 14.8001 + 10.7529i 0.639265 + 0.464453i
\(537\) 2.42504 0.787945i 0.104648 0.0340023i
\(538\) 3.85376i 0.166148i
\(539\) −12.8782 17.9029i −0.554705 0.771131i
\(540\) 13.0884 8.26132i 0.563233 0.355511i
\(541\) −3.87568 11.9281i −0.166628 0.512829i 0.832524 0.553989i \(-0.186895\pi\)
−0.999153 + 0.0411593i \(0.986895\pi\)
\(542\) −11.0076 + 15.1507i −0.472817 + 0.650776i
\(543\) −0.821226 1.13032i −0.0352422 0.0485067i
\(544\) −12.7456 + 39.2270i −0.546464 + 1.68184i
\(545\) 40.3096 10.2448i 1.72667 0.438839i
\(546\) 1.21518 0.882881i 0.0520050 0.0377838i
\(547\) 18.0689 24.8698i 0.772572 1.06335i −0.223491 0.974706i \(-0.571745\pi\)
0.996063 0.0886479i \(-0.0282546\pi\)
\(548\) −5.19865 + 1.68914i −0.222075 + 0.0721566i
\(549\) 0.344889 0.0147195
\(550\) −2.36839 13.0989i −0.100989 0.558538i
\(551\) −8.17659 −0.348334
\(552\) −6.72445 + 2.18491i −0.286212 + 0.0929958i
\(553\) 1.57520 2.16808i 0.0669843 0.0921960i
\(554\) 14.2200 10.3315i 0.604151 0.438942i
\(555\) −27.9984 + 7.11586i −1.18846 + 0.302051i
\(556\) −3.32415 + 10.2307i −0.140975 + 0.433877i
\(557\) −7.89359 10.8646i −0.334462 0.460347i 0.608352 0.793668i \(-0.291831\pi\)
−0.942814 + 0.333320i \(0.891831\pi\)
\(558\) 0.291597 0.401350i 0.0123443 0.0169905i
\(559\) 5.27993 + 16.2499i 0.223317 + 0.687299i
\(560\) −0.614889 + 0.388116i −0.0259838 + 0.0164009i
\(561\) −0.195512 + 41.3279i −0.00825452 + 1.74487i
\(562\) 12.6629i 0.534154i
\(563\) 29.0454 9.43741i 1.22412 0.397740i 0.375537 0.926807i \(-0.377458\pi\)
0.848580 + 0.529068i \(0.177458\pi\)
\(564\) −3.73025 2.71019i −0.157072 0.114119i
\(565\) 9.77427 24.5118i 0.411207 1.03122i
\(566\) −5.60814 + 17.2601i −0.235728 + 0.725495i
\(567\) 5.23175 + 1.69990i 0.219713 + 0.0713891i
\(568\) −18.6721 25.7000i −0.783465 1.07835i
\(569\) 20.8082 + 15.1181i 0.872327 + 0.633783i 0.931210 0.364482i \(-0.118754\pi\)
−0.0588833 + 0.998265i \(0.518754\pi\)
\(570\) 4.62038 5.55737i 0.193527 0.232773i
\(571\) −27.1115 −1.13458 −0.567291 0.823518i \(-0.692008\pi\)
−0.567291 + 0.823518i \(0.692008\pi\)
\(572\) 2.45752 + 7.68702i 0.102754 + 0.321410i
\(573\) 14.3506i 0.599504i
\(574\) −1.23520 3.80157i −0.0515564 0.158674i
\(575\) 3.55904 + 6.54951i 0.148422 + 0.273133i
\(576\) −0.290224 + 0.210860i −0.0120927 + 0.00878583i
\(577\) 2.72968 + 0.886926i 0.113638 + 0.0369232i 0.365284 0.930896i \(-0.380972\pi\)
−0.251646 + 0.967819i \(0.580972\pi\)
\(578\) 25.2579 + 8.20680i 1.05059 + 0.341358i
\(579\) 6.22260 4.52098i 0.258602 0.187886i
\(580\) 0.707003 10.8156i 0.0293567 0.449093i
\(581\) 1.08732 + 3.34643i 0.0451097 + 0.138833i
\(582\) 7.59774i 0.314936i
\(583\) −2.47776 + 7.50476i −0.102618 + 0.310816i
\(584\) 18.3777 0.760476
\(585\) 0.309275 + 0.257130i 0.0127869 + 0.0106310i
\(586\) −8.61075 6.25608i −0.355707 0.258436i
\(587\) −26.3539 36.2731i −1.08774 1.49715i −0.850701 0.525651i \(-0.823822\pi\)
−0.237042 0.971499i \(-0.576178\pi\)
\(588\) 15.0953 + 4.90475i 0.622518 + 0.202268i
\(589\) 4.35822 13.4132i 0.179577 0.552682i
\(590\) 0.0254478 0.0638177i 0.00104767 0.00262733i
\(591\) 22.2966 + 16.1994i 0.917159 + 0.666355i
\(592\) 3.83250 1.24525i 0.157515 0.0511796i
\(593\) 6.09322i 0.250219i 0.992143 + 0.125109i \(0.0399282\pi\)
−0.992143 + 0.125109i \(0.960072\pi\)
\(594\) 8.04162 10.9589i 0.329952 0.449651i
\(595\) 5.00133 + 7.92358i 0.205035 + 0.324835i
\(596\) −5.23695 16.1177i −0.214514 0.660206i
\(597\) −1.48855 + 2.04882i −0.0609225 + 0.0838526i
\(598\) 1.26250 + 1.73768i 0.0516275 + 0.0710591i
\(599\) 3.99674 12.3007i 0.163302 0.502593i −0.835605 0.549331i \(-0.814883\pi\)
0.998907 + 0.0467381i \(0.0148826\pi\)
\(600\) 17.2069 + 16.3174i 0.702471 + 0.666156i
\(601\) 8.93729 6.49332i 0.364560 0.264868i −0.390392 0.920649i \(-0.627660\pi\)
0.754951 + 0.655781i \(0.227660\pi\)
\(602\) −2.65936 + 3.66029i −0.108387 + 0.149182i
\(603\) −0.647294 + 0.210318i −0.0263598 + 0.00856483i
\(604\) 11.3910 0.463494
\(605\) 12.9314 + 20.9232i 0.525737 + 0.850647i
\(606\) −14.0364 −0.570188
\(607\) −0.110239 + 0.0358189i −0.00447448 + 0.00145385i −0.311253 0.950327i \(-0.600749\pi\)
0.306779 + 0.951781i \(0.400749\pi\)
\(608\) −7.83388 + 10.7824i −0.317706 + 0.437285i
\(609\) 3.01569 2.19103i 0.122202 0.0887849i
\(610\) −1.52159 5.98692i −0.0616075 0.242404i
\(611\) −1.07139 + 3.29741i −0.0433440 + 0.133399i
\(612\) −0.565135 0.777842i −0.0228442 0.0314424i
\(613\) 11.1941 15.4074i 0.452125 0.622297i −0.520727 0.853723i \(-0.674339\pi\)
0.972853 + 0.231426i \(0.0743391\pi\)
\(614\) 2.48447 + 7.64643i 0.100265 + 0.308585i
\(615\) 28.0008 17.6740i 1.12910 0.712684i
\(616\) −3.12938 + 4.26465i −0.126086 + 0.171828i
\(617\) 30.8894i 1.24356i 0.783192 + 0.621780i \(0.213590\pi\)
−0.783192 + 0.621780i \(0.786410\pi\)
\(618\) −18.1750 + 5.90543i −0.731108 + 0.237551i
\(619\) 27.1584 + 19.7317i 1.09159 + 0.793086i 0.979667 0.200631i \(-0.0642993\pi\)
0.111922 + 0.993717i \(0.464299\pi\)
\(620\) 17.3655 + 6.92464i 0.697416 + 0.278100i
\(621\) −2.35216 + 7.23920i −0.0943889 + 0.290499i
\(622\) 2.60191 + 0.845410i 0.104327 + 0.0338979i
\(623\) 2.16257 + 2.97652i 0.0866414 + 0.119252i
\(624\) −1.40418 1.02020i −0.0562122 0.0408405i
\(625\) 13.6014 20.9762i 0.544056 0.839049i
\(626\) −19.6668 −0.786043
\(627\) −4.18681 + 12.6812i −0.167205 + 0.506440i
\(628\) 18.9738i 0.757139i
\(629\) −16.0466 49.3863i −0.639819 1.96916i
\(630\) −0.00694707 + 0.106275i −0.000276778 + 0.00423410i
\(631\) −19.9482 + 14.4932i −0.794123 + 0.576964i −0.909184 0.416394i \(-0.863294\pi\)
0.115061 + 0.993358i \(0.463294\pi\)
\(632\) 11.5947 + 3.76734i 0.461211 + 0.149857i
\(633\) 14.5374 + 4.72349i 0.577810 + 0.187742i
\(634\) −4.53832 + 3.29728i −0.180240 + 0.130952i
\(635\) −35.8272 2.34198i −1.42176 0.0929388i
\(636\) −1.75768 5.40960i −0.0696967 0.214504i
\(637\) 11.9350i 0.472880i
\(638\) −2.89863 9.06679i −0.114758 0.358958i
\(639\) 1.18186 0.0467535
\(640\) −15.1011 12.5550i −0.596923 0.496280i
\(641\) −5.67644 4.12418i −0.224206 0.162895i 0.470012 0.882660i \(-0.344250\pi\)
−0.694218 + 0.719765i \(0.744250\pi\)
\(642\) −4.65582 6.40818i −0.183751 0.252911i
\(643\) −11.6528 3.78623i −0.459543 0.149315i 0.0700915 0.997541i \(-0.477671\pi\)
−0.529634 + 0.848226i \(0.677671\pi\)
\(644\) 0.369792 1.13810i 0.0145718 0.0448475i
\(645\) −34.8133 13.8821i −1.37077 0.546607i
\(646\) 10.5100 + 7.63596i 0.413510 + 0.300433i
\(647\) −5.82060 + 1.89123i −0.228832 + 0.0743519i −0.421188 0.906973i \(-0.638387\pi\)
0.192357 + 0.981325i \(0.438387\pi\)
\(648\) 25.0251i 0.983079i
\(649\) −0.000600576 0.126952i −2.35747e−5 0.00498328i
\(650\) 3.09905 6.50310i 0.121555 0.255073i
\(651\) 1.98685 + 6.11491i 0.0778710 + 0.239662i
\(652\) −9.43583 + 12.9873i −0.369536 + 0.508622i
\(653\) −22.3544 30.7682i −0.874795 1.20405i −0.977835 0.209375i \(-0.932857\pi\)
0.103041 0.994677i \(-0.467143\pi\)
\(654\) −8.12356 + 25.0017i −0.317656 + 0.977645i
\(655\) −39.0732 + 9.93055i −1.52671 + 0.388019i
\(656\) −3.73676 + 2.71492i −0.145896 + 0.106000i
\(657\) −0.401883 + 0.553145i −0.0156790 + 0.0215802i
\(658\) −0.873144 + 0.283702i −0.0340387 + 0.0110598i
\(659\) −15.7879 −0.615011 −0.307505 0.951546i \(-0.599494\pi\)
−0.307505 + 0.951546i \(0.599494\pi\)
\(660\) −16.4121 6.63462i −0.638840 0.258252i
\(661\) −24.5794 −0.956027 −0.478014 0.878352i \(-0.658643\pi\)
−0.478014 + 0.878352i \(0.658643\pi\)
\(662\) 4.30809 1.39978i 0.167439 0.0544042i
\(663\) −13.1464 + 18.0945i −0.510566 + 0.702733i
\(664\) −12.9500 + 9.40870i −0.502556 + 0.365128i
\(665\) 0.745798 + 2.93445i 0.0289208 + 0.113793i
\(666\) 0.182390 0.561338i 0.00706746 0.0217514i
\(667\) 3.13312 + 4.31237i 0.121315 + 0.166976i
\(668\) 6.95350 9.57067i 0.269039 0.370300i
\(669\) −3.43111 10.5599i −0.132654 0.408268i
\(670\) 6.50666 + 10.3085i 0.251374 + 0.398251i
\(671\) 6.66547 + 9.26611i 0.257318 + 0.357714i
\(672\) 6.07597i 0.234385i
\(673\) 28.5063 9.26226i 1.09884 0.357034i 0.297182 0.954821i \(-0.403953\pi\)
0.801655 + 0.597787i \(0.203953\pi\)
\(674\) −14.6870 10.6707i −0.565722 0.411021i
\(675\) 25.0998 4.66100i 0.966091 0.179402i
\(676\) 4.09642 12.6075i 0.157555 0.484903i
\(677\) 3.57321 + 1.16101i 0.137330 + 0.0446211i 0.376875 0.926264i \(-0.376999\pi\)
−0.239546 + 0.970885i \(0.576999\pi\)
\(678\) 9.80393 + 13.4940i 0.376518 + 0.518232i
\(679\) −2.57508 1.87091i −0.0988225 0.0717988i
\(680\) −27.2510 + 32.7773i −1.04503 + 1.25695i
\(681\) 1.96641 0.0753531
\(682\) 16.4185 + 0.0776720i 0.628699 + 0.00297421i
\(683\) 21.0157i 0.804144i −0.915608 0.402072i \(-0.868290\pi\)
0.915608 0.402072i \(-0.131710\pi\)
\(684\) −0.0960054 0.295474i −0.00367086 0.0112977i
\(685\) −8.99679 0.588110i −0.343750 0.0224705i
\(686\) 5.24834 3.81314i 0.200382 0.145586i
\(687\) 7.02675 + 2.28313i 0.268087 + 0.0871068i
\(688\) 4.97217 + 1.61555i 0.189562 + 0.0615925i
\(689\) −3.46021 + 2.51399i −0.131824 + 0.0957754i
\(690\) −4.70143 0.307327i −0.178980 0.0116997i
\(691\) −11.8299 36.4088i −0.450032 1.38506i −0.876870 0.480728i \(-0.840372\pi\)
0.426837 0.904328i \(-0.359628\pi\)
\(692\) 12.4432i 0.473020i
\(693\) −0.0599271 0.187449i −0.00227644 0.00712061i
\(694\) −0.146408 −0.00555757
\(695\) −11.3432 + 13.6435i −0.430272 + 0.517529i
\(696\) 13.7190 + 9.96742i 0.520017 + 0.377814i
\(697\) 34.9850 + 48.1527i 1.32515 + 1.82391i
\(698\) −11.7774 3.82670i −0.445780 0.144843i
\(699\) −3.68870 + 11.3527i −0.139520 + 0.429397i
\(700\) −3.94603 + 0.732773i −0.149146 + 0.0276962i
\(701\) 27.6963 + 20.1225i 1.04607 + 0.760016i 0.971462 0.237196i \(-0.0762284\pi\)
0.0746112 + 0.997213i \(0.476228\pi\)
\(702\) 6.99614 2.27318i 0.264052 0.0857958i
\(703\) 16.7795i 0.632852i
\(704\) −11.2741 3.72224i −0.424910 0.140287i
\(705\) −4.05936 6.43121i −0.152884 0.242214i
\(706\) 5.93089 + 18.2534i 0.223212 + 0.686976i
\(707\) 3.45639 4.75731i 0.129991 0.178917i
\(708\) −0.0537052 0.0739189i −0.00201836 0.00277804i
\(709\) 1.27462 3.92289i 0.0478695 0.147327i −0.924265 0.381752i \(-0.875321\pi\)
0.972134 + 0.234425i \(0.0753207\pi\)
\(710\) −5.21415 20.5158i −0.195683 0.769945i
\(711\) −0.366944 + 0.266600i −0.0137615 + 0.00999828i
\(712\) −9.83795 + 13.5408i −0.368693 + 0.507462i
\(713\) −8.74418 + 2.84116i −0.327472 + 0.106402i
\(714\) −5.92246 −0.221642
\(715\) −0.931116 + 13.2787i −0.0348218 + 0.496593i
\(716\) −1.96324 −0.0733697
\(717\) 7.36487 2.39299i 0.275046 0.0893679i
\(718\) −4.13656 + 5.69349i −0.154375 + 0.212479i
\(719\) 23.7524 17.2571i 0.885814 0.643582i −0.0489689 0.998800i \(-0.515594\pi\)
0.934783 + 0.355218i \(0.115594\pi\)
\(720\) 0.119274 0.0303139i 0.00444509 0.00112973i
\(721\) 2.47400 7.61420i 0.0921367 0.283568i
\(722\) −6.49706 8.94243i −0.241795 0.332803i
\(723\) −9.94801 + 13.6923i −0.369970 + 0.509221i
\(724\) 0.332419 + 1.02308i 0.0123543 + 0.0380225i
\(725\) 7.69084 16.1386i 0.285630 0.599373i
\(726\) −15.5461 0.147093i −0.576970 0.00545912i
\(727\) 44.0893i 1.63518i −0.575799 0.817591i \(-0.695309\pi\)
0.575799 0.817591i \(-0.304691\pi\)
\(728\) −2.72254 + 0.884606i −0.100904 + 0.0327857i
\(729\) 21.0659 + 15.3052i 0.780217 + 0.566861i
\(730\) 11.3751 + 4.53590i 0.421010 + 0.167881i
\(731\) 20.8184 64.0723i 0.769995 2.36980i
\(732\) −7.81296 2.53858i −0.288775 0.0938287i
\(733\) 28.7715 + 39.6006i 1.06270 + 1.46268i 0.877254 + 0.480026i \(0.159373\pi\)
0.185446 + 0.982654i \(0.440627\pi\)
\(734\) −3.49526 2.53946i −0.129012 0.0937331i
\(735\) 20.1309 + 16.7368i 0.742541 + 0.617346i
\(736\) 8.68849 0.320262
\(737\) −18.1605 13.3261i −0.668949 0.490872i
\(738\) 0.676520i 0.0249031i
\(739\) 6.38498 + 19.6509i 0.234875 + 0.722872i 0.997138 + 0.0756039i \(0.0240884\pi\)
−0.762263 + 0.647268i \(0.775912\pi\)
\(740\) 22.1952 + 1.45087i 0.815910 + 0.0533351i
\(741\) −5.84692 + 4.24804i −0.214792 + 0.156056i
\(742\) −1.07712 0.349977i −0.0395423 0.0128481i
\(743\) −28.6868 9.32091i −1.05242 0.341951i −0.268801 0.963196i \(-0.586627\pi\)
−0.783617 + 0.621245i \(0.786627\pi\)
\(744\) −23.6634 + 17.1924i −0.867541 + 0.630305i
\(745\) 1.82335 27.8933i 0.0668025 1.02193i
\(746\) 0.799830 + 2.46162i 0.0292839 + 0.0901264i
\(747\) 0.595525i 0.0217891i
\(748\) 9.97615 30.2163i 0.364764 1.10482i
\(749\) 3.31838 0.121251
\(750\) 6.62301 + 14.3467i 0.241838 + 0.523869i
\(751\) −9.78637 7.11021i −0.357110 0.259455i 0.394736 0.918795i \(-0.370836\pi\)
−0.751846 + 0.659339i \(0.770836\pi\)
\(752\) 0.623562 + 0.858259i 0.0227390 + 0.0312975i
\(753\) 22.4737 + 7.30213i 0.818986 + 0.266105i
\(754\) 1.59187 4.89929i 0.0579726 0.178421i
\(755\) 17.4522 + 6.95919i 0.635149 + 0.253271i
\(756\) −3.31568 2.40898i −0.120590 0.0876138i
\(757\) −19.6013 + 6.36886i −0.712423 + 0.231480i −0.642735 0.766089i \(-0.722200\pi\)
−0.0696881 + 0.997569i \(0.522200\pi\)
\(758\) 15.7838i 0.573293i
\(759\) 8.29245 2.65108i 0.300997 0.0962280i
\(760\) −11.6476 + 7.35192i −0.422503 + 0.266682i
\(761\) 6.44146 + 19.8248i 0.233503 + 0.718648i 0.997316 + 0.0732111i \(0.0233247\pi\)
−0.763814 + 0.645437i \(0.776675\pi\)
\(762\) 13.3389 18.3595i 0.483219 0.665093i
\(763\) −6.47339 8.90985i −0.234352 0.322558i
\(764\) −3.41437 + 10.5084i −0.123528 + 0.380179i
\(765\) −0.390630 1.53699i −0.0141233 0.0555700i
\(766\) 18.1670 13.1991i 0.656399 0.476902i
\(767\) −0.0403834 + 0.0555830i −0.00145816 + 0.00200699i
\(768\) 23.7944 7.73127i 0.858607 0.278978i
\(769\) −10.7167 −0.386455 −0.193228 0.981154i \(-0.561896\pi\)
−0.193228 + 0.981154i \(0.561896\pi\)
\(770\) −2.98954 + 1.86727i −0.107736 + 0.0672917i
\(771\) 19.0466 0.685946
\(772\) −5.63223 + 1.83002i −0.202708 + 0.0658639i
\(773\) 11.9651 16.4686i 0.430355 0.592333i −0.537679 0.843149i \(-0.680699\pi\)
0.968035 + 0.250816i \(0.0806990\pi\)
\(774\) 0.619498 0.450092i 0.0222674 0.0161782i
\(775\) 22.3752 + 21.2184i 0.803739 + 0.762189i
\(776\) 4.47456 13.7713i 0.160627 0.494361i
\(777\) 4.49630 + 6.18863i 0.161304 + 0.222016i
\(778\) 6.15247 8.46814i 0.220577 0.303598i
\(779\) 5.94326 + 18.2915i 0.212939 + 0.655360i
\(780\) −5.11353 8.10134i −0.183094 0.290074i
\(781\) 22.8410 + 31.7528i 0.817317 + 1.13620i
\(782\) 8.46898i 0.302850i
\(783\) 17.3622 5.64131i 0.620474 0.201604i
\(784\) −2.95442 2.14651i −0.105515 0.0766612i
\(785\) −11.5918 + 29.0698i −0.413729 + 1.03755i
\(786\) 7.87438 24.2348i 0.280870 0.864428i
\(787\) 13.5261 + 4.39491i 0.482154 + 0.156661i 0.540002 0.841664i \(-0.318424\pi\)
−0.0578472 + 0.998325i \(0.518424\pi\)
\(788\) −12.4727 17.1671i −0.444320 0.611554i
\(789\) −35.0919 25.4958i −1.24930 0.907673i
\(790\) 6.24680 + 5.19357i 0.222251 + 0.184779i
\(791\) −6.98764 −0.248452
\(792\) 0.726764 0.522790i 0.0258244 0.0185765i
\(793\) 6.17726i 0.219361i
\(794\) −0.452049 1.39126i −0.0160426 0.0493741i
\(795\) 0.611974 9.36186i 0.0217045 0.332031i
\(796\) 1.57748 1.14610i 0.0559122 0.0406226i
\(797\) −42.8341 13.9176i −1.51726 0.492988i −0.572264 0.820069i \(-0.693935\pi\)
−0.944996 + 0.327081i \(0.893935\pi\)
\(798\) −1.82007 0.591377i −0.0644298 0.0209345i
\(799\) 11.0597 8.03534i 0.391264 0.284270i
\(800\) −13.9134 25.6041i −0.491913 0.905240i
\(801\) −0.192423 0.592218i −0.00679894 0.0209250i
\(802\) 4.31920i 0.152516i
\(803\) −22.6283 0.107049i −0.798534 0.00377766i
\(804\) 16.2115 0.571737
\(805\) 1.26187 1.51776i 0.0444749 0.0534942i
\(806\) 7.18851 + 5.22276i 0.253204 + 0.183964i
\(807\) −4.96875 6.83889i −0.174908 0.240740i
\(808\) 25.4416 + 8.26649i 0.895034 + 0.290814i
\(809\) −7.34698 + 22.6117i −0.258306 + 0.794984i 0.734854 + 0.678225i \(0.237251\pi\)
−0.993160 + 0.116759i \(0.962749\pi\)
\(810\) −6.17657 + 15.4895i −0.217023 + 0.544246i
\(811\) 6.63288 + 4.81907i 0.232912 + 0.169220i 0.698120 0.715981i \(-0.254020\pi\)
−0.465208 + 0.885202i \(0.654020\pi\)
\(812\) −2.72957 + 0.886893i −0.0957893 + 0.0311238i
\(813\) 41.0787i 1.44069i
\(814\) 18.6064 5.94841i 0.652152 0.208492i
\(815\) −22.3910 + 14.1331i −0.784323 + 0.495062i
\(816\) 2.11478 + 6.50864i 0.0740322 + 0.227848i
\(817\) 12.7957 17.6117i 0.447663 0.616156i
\(818\) 17.3071 + 23.8212i 0.605130 + 0.832890i
\(819\) 0.0329109 0.101289i 0.00115000 0.00353933i
\(820\) −24.7090 + 6.27985i −0.862875 + 0.219302i
\(821\) 35.1415 25.5318i 1.22645 0.891066i 0.229828 0.973231i \(-0.426184\pi\)
0.996619 + 0.0821658i \(0.0261837\pi\)
\(822\) 3.34962 4.61036i 0.116831 0.160805i
\(823\) −49.1507 + 15.9700i −1.71328 + 0.556680i −0.990875 0.134785i \(-0.956966\pi\)
−0.722410 + 0.691465i \(0.756966\pi\)
\(824\) 36.4211 1.26879
\(825\) −21.0916 20.1916i −0.734316 0.702982i
\(826\) −0.0181927 −0.000633004
\(827\) −24.0692 + 7.82057i −0.836970 + 0.271948i −0.695978 0.718063i \(-0.745029\pi\)
−0.140991 + 0.990011i \(0.545029\pi\)
\(828\) −0.119047 + 0.163854i −0.00413717 + 0.00569432i
\(829\) −33.8784 + 24.6141i −1.17665 + 0.854883i −0.991789 0.127883i \(-0.959182\pi\)
−0.184856 + 0.982766i \(0.559182\pi\)
\(830\) −10.3377 + 2.62736i −0.358827 + 0.0911968i
\(831\) 11.9143 36.6684i 0.413302 1.27201i
\(832\) −3.77668 5.19815i −0.130933 0.180213i
\(833\) −27.6604 + 38.0713i −0.958376 + 1.31909i
\(834\) −3.46556 10.6659i −0.120003 0.369330i
\(835\) 16.5005 10.4151i 0.571024 0.360428i
\(836\) 6.08303 8.28982i 0.210386 0.286710i
\(837\) 31.4885i 1.08840i
\(838\) −2.18817 + 0.710980i −0.0755891 + 0.0245604i
\(839\) −11.6376 8.45518i −0.401773 0.291905i 0.368490 0.929632i \(-0.379875\pi\)
−0.770263 + 0.637727i \(0.779875\pi\)
\(840\) 2.32582 5.83267i 0.0802486 0.201246i
\(841\) −5.01097 + 15.4222i −0.172792 + 0.531800i
\(842\) −3.55731 1.15584i −0.122593 0.0398329i
\(843\) −16.3266 22.4716i −0.562318 0.773965i
\(844\) −9.52134 6.91766i −0.327738 0.238116i
\(845\) 13.9785 16.8132i 0.480874 0.578393i
\(846\) 0.155383 0.00534218
\(847\) 3.87801 5.23278i 0.133250 0.179800i
\(848\) 1.30870i 0.0449408i
\(849\) 12.3016 + 37.8605i 0.422190 + 1.29937i
\(850\) −24.9572 + 13.5619i −0.856024 + 0.465169i
\(851\) −8.84960 + 6.42961i −0.303360 + 0.220404i
\(852\) −26.7732 8.69914i −0.917235 0.298028i
\(853\) −40.8968 13.2882i −1.40028 0.454978i −0.490998 0.871161i \(-0.663368\pi\)
−0.909281 + 0.416183i \(0.863368\pi\)
\(854\) −1.32332 + 0.961450i −0.0452832 + 0.0329001i
\(855\) 0.0334263 0.511349i 0.00114315 0.0174878i
\(856\) 4.66492 + 14.3571i 0.159444 + 0.490717i
\(857\) 54.3052i 1.85503i 0.373784 + 0.927516i \(0.378060\pi\)
−0.373784 + 0.927516i \(0.621940\pi\)
\(858\) −6.78328 4.97754i −0.231578 0.169931i
\(859\) −24.3361 −0.830336 −0.415168 0.909745i \(-0.636277\pi\)
−0.415168 + 0.909745i \(0.636277\pi\)
\(860\) 22.1895 + 18.4483i 0.756656 + 0.629082i
\(861\) −7.09344 5.15369i −0.241744 0.175637i
\(862\) 9.79917 + 13.4874i 0.333761 + 0.459383i
\(863\) 37.2339 + 12.0980i 1.26746 + 0.411822i 0.864146 0.503241i \(-0.167859\pi\)
0.403312 + 0.915063i \(0.367859\pi\)
\(864\) 9.19531 28.3003i 0.312831 0.962795i
\(865\) −7.60200 + 19.0642i −0.258476 + 0.648202i
\(866\) −8.31045 6.03789i −0.282400 0.205176i
\(867\) 55.4039 18.0018i 1.88162 0.611374i
\(868\) 4.95043i 0.168029i
\(869\) −14.2544 4.70621i −0.483548 0.159647i
\(870\) 6.03138 + 9.55548i 0.204483 + 0.323961i
\(871\) −3.76698 11.5936i −0.127639 0.392833i
\(872\) 29.4487 40.5327i 0.997260 1.37261i
\(873\) 0.316648 + 0.435828i 0.0107169 + 0.0147505i
\(874\) 0.845656 2.60266i 0.0286047 0.0880363i
\(875\) −6.49339 1.28809i −0.219517 0.0435456i
\(876\) 13.1755 9.57259i 0.445160 0.323428i
\(877\) −25.3266 + 34.8591i −0.855219 + 1.17711i 0.127470 + 0.991842i \(0.459314\pi\)
−0.982689 + 0.185265i \(0.940686\pi\)
\(878\) 8.10808 2.63447i 0.273634 0.0889092i
\(879\) −23.3468 −0.787466
\(880\) 3.11958 + 2.61867i 0.105161 + 0.0882753i
\(881\) −38.1083 −1.28390 −0.641950 0.766746i \(-0.721874\pi\)
−0.641950 + 0.766746i \(0.721874\pi\)
\(882\) −0.508703 + 0.165288i −0.0171289 + 0.00556552i
\(883\) 17.0611 23.4826i 0.574152 0.790252i −0.418887 0.908038i \(-0.637580\pi\)
0.993039 + 0.117786i \(0.0375797\pi\)
\(884\) 13.9318 10.1220i 0.468577 0.340441i
\(885\) −0.0371219 0.146061i −0.00124784 0.00490980i
\(886\) −1.63685 + 5.03771i −0.0549911 + 0.169245i
\(887\) 1.30003 + 1.78934i 0.0436508 + 0.0600801i 0.830284 0.557340i \(-0.188178\pi\)
−0.786634 + 0.617420i \(0.788178\pi\)
\(888\) −20.4546 + 28.1533i −0.686411 + 0.944764i
\(889\) 2.93788 + 9.04186i 0.0985332 + 0.303254i
\(890\) −9.43136 + 5.95304i −0.316140 + 0.199546i
\(891\) 0.145769 30.8131i 0.00488344 1.03228i
\(892\) 8.54894i 0.286240i
\(893\) 4.20118 1.36505i 0.140587 0.0456796i
\(894\) 14.2938 + 10.3850i 0.478055 + 0.347327i
\(895\) −3.00787 1.19941i −0.100542 0.0400920i
\(896\) −1.60695 + 4.94569i −0.0536845 + 0.165224i
\(897\) 4.48087 + 1.45592i 0.149612 + 0.0486118i
\(898\) −6.42991 8.85002i −0.214569 0.295329i
\(899\) 17.8396 + 12.9612i 0.594983 + 0.432280i
\(900\) 0.673497 + 0.0884293i 0.0224499 + 0.00294764i
\(901\) 16.8641 0.561825
\(902\) −18.1760 + 13.0747i −0.605195 + 0.435340i
\(903\) 9.92432i 0.330261i
\(904\) −9.82309 30.2323i −0.326711 1.00551i
\(905\) −0.115739 + 1.77055i −0.00384728 + 0.0588549i
\(906\) −9.60757 + 6.98031i −0.319190 + 0.231905i
\(907\) −25.3802 8.24653i −0.842736 0.273822i −0.144336 0.989529i \(-0.546105\pi\)
−0.698401 + 0.715707i \(0.746105\pi\)
\(908\) −1.43993 0.467861i −0.0477857 0.0155265i
\(909\) −0.805166 + 0.584988i −0.0267057 + 0.0194028i
\(910\) −1.90347 0.124428i −0.0630995 0.00412475i
\(911\) −11.2092 34.4983i −0.371376 1.14298i −0.945891 0.324484i \(-0.894809\pi\)
0.574515 0.818494i \(-0.305191\pi\)
\(912\) 2.21138i 0.0732261i
\(913\) 15.9999 11.5094i 0.529520 0.380904i
\(914\) −10.8363 −0.358434
\(915\) −10.4193 8.66258i −0.344451 0.286376i
\(916\) −4.60220 3.34369i −0.152061 0.110479i
\(917\) 6.27482 + 8.63655i 0.207213 + 0.285204i
\(918\) −27.5853 8.96300i −0.910450 0.295823i
\(919\) 9.16908 28.2195i 0.302460 0.930876i −0.678153 0.734921i \(-0.737219\pi\)
0.980613 0.195955i \(-0.0627808\pi\)
\(920\) 8.34059 + 3.32588i 0.274981 + 0.109651i
\(921\) 14.2677 + 10.3661i 0.470135 + 0.341573i
\(922\) 8.64311 2.80832i 0.284646 0.0924870i
\(923\) 21.1680i 0.696754i
\(924\) −0.0221753 + 4.68749i −0.000729514 + 0.154207i
\(925\) 33.1188 + 15.7827i 1.08894 + 0.518932i
\(926\) 1.19805 + 3.68720i 0.0393702 + 0.121169i
\(927\) −0.796455 + 1.09623i −0.0261590 + 0.0360048i
\(928\) −12.2483 16.8584i −0.402071 0.553403i
\(929\) −8.58220 + 26.4133i −0.281573 + 0.866592i 0.705832 + 0.708379i \(0.250573\pi\)
−0.987405 + 0.158213i \(0.949427\pi\)
\(930\) −18.8900 + 4.80095i −0.619428 + 0.157429i
\(931\) −12.3020 + 8.93795i −0.403183 + 0.292930i
\(932\) 5.40219 7.43548i 0.176955 0.243557i
\(933\) 5.70735 1.85443i 0.186850 0.0607113i
\(934\) 19.2786 0.630817
\(935\) 33.7447 40.1995i 1.10357 1.31467i
\(936\) 0.484498 0.0158363
\(937\) 28.7620 9.34532i 0.939612 0.305298i 0.201125 0.979566i \(-0.435540\pi\)
0.738487 + 0.674267i \(0.235540\pi\)
\(938\) 1.89733 2.61144i 0.0619499 0.0852667i
\(939\) −34.9007 + 25.3568i −1.13894 + 0.827489i
\(940\) 1.44236 + 5.67515i 0.0470445 + 0.185103i
\(941\) −1.85618 + 5.71273i −0.0605097 + 0.186230i −0.976742 0.214418i \(-0.931215\pi\)
0.916232 + 0.400647i \(0.131215\pi\)
\(942\) −11.6270 16.0032i −0.378828 0.521412i
\(943\) 7.36966 10.1435i 0.239989 0.330317i
\(944\) 0.00649622 + 0.0199933i 0.000211434 + 0.000650727i
\(945\) −3.60821 5.71646i −0.117375 0.185956i
\(946\) 24.0652 + 7.94533i 0.782428 + 0.258325i
\(947\) 10.0218i 0.325665i 0.986654 + 0.162833i \(0.0520630\pi\)
−0.986654 + 0.162833i \(0.947937\pi\)
\(948\) 10.2749 3.33851i 0.333713 0.108430i
\(949\) −9.90729 7.19807i −0.321604 0.233659i
\(950\) −9.02396 + 1.67574i −0.292776 + 0.0543681i
\(951\) −3.80244 + 11.7027i −0.123303 + 0.379486i
\(952\) 10.7348 + 3.48794i 0.347916 + 0.113045i
\(953\) −5.74934 7.91329i −0.186239 0.256336i 0.705680 0.708530i \(-0.250641\pi\)
−0.891920 + 0.452194i \(0.850641\pi\)
\(954\) 0.155074 + 0.112668i 0.00502071 + 0.00364776i
\(955\) −11.6511 + 14.0139i −0.377021 + 0.453478i
\(956\) −5.96237 −0.192837
\(957\) −16.8339 12.3527i −0.544164 0.399305i
\(958\) 34.6967i 1.12100i
\(959\) 0.737749 + 2.27056i 0.0238231 + 0.0733201i
\(960\) 14.0640 + 0.919346i 0.453913 + 0.0296718i
\(961\) −5.69127 + 4.13495i −0.183589 + 0.133385i
\(962\) 10.0540 + 3.26676i 0.324155 + 0.105324i
\(963\) −0.534142 0.173553i −0.0172125 0.00559268i
\(964\) 10.5423 7.65942i 0.339544 0.246693i
\(965\) −9.74715 0.637160i −0.313772 0.0205109i
\(966\) 0.385523 + 1.18652i 0.0124040 + 0.0381756i
\(967\) 1.22635i 0.0394367i −0.999806 0.0197184i \(-0.993723\pi\)
0.999806 0.0197184i \(-0.00627695\pi\)
\(968\) 28.0915 + 9.42224i 0.902895 + 0.302842i
\(969\) 28.4963 0.915432
\(970\) 6.16853 7.41948i 0.198060 0.238225i
\(971\) 36.1199 + 26.2426i 1.15914 + 0.842167i 0.989669 0.143368i \(-0.0457933\pi\)
0.169473 + 0.985535i \(0.445793\pi\)
\(972\) 0.829522 + 1.14174i 0.0266069 + 0.0366213i
\(973\) 4.46834 + 1.45185i 0.143248 + 0.0465442i
\(974\) −10.4083 + 32.0335i −0.333503 + 1.02642i
\(975\) −2.88503 15.5361i −0.0923949 0.497553i
\(976\) 1.52914 + 1.11099i 0.0489466 + 0.0355618i
\(977\) 44.9328 14.5996i 1.43753 0.467081i 0.516402 0.856346i \(-0.327271\pi\)
0.921126 + 0.389265i \(0.127271\pi\)
\(978\) 16.7361i 0.535162i
\(979\) 12.1922 16.6153i 0.389665 0.531026i
\(980\) −10.7590 17.0454i −0.343683 0.544495i
\(981\) 0.575996 + 1.77273i 0.0183901 + 0.0565991i
\(982\) 4.27456 5.88343i 0.136407 0.187748i
\(983\) 8.19082 + 11.2737i 0.261247 + 0.359575i 0.919410 0.393300i \(-0.128667\pi\)
−0.658164 + 0.752875i \(0.728667\pi\)
\(984\) 12.3259 37.9351i 0.392934 1.20933i
\(985\) −8.62130 33.9217i −0.274698 1.08084i
\(986\) −16.4325 + 11.9389i −0.523316 + 0.380211i
\(987\) −1.18370 + 1.62922i −0.0376775 + 0.0518587i
\(988\) 5.29219 1.71954i 0.168367 0.0547058i
\(989\) −14.1916 −0.451265
\(990\) 0.578870 0.144209i 0.0183977 0.00458328i
\(991\) 36.5755 1.16186 0.580930 0.813953i \(-0.302689\pi\)
0.580930 + 0.813953i \(0.302689\pi\)
\(992\) 34.1837 11.1070i 1.08533 0.352646i
\(993\) 5.84037 8.03858i 0.185339 0.255097i
\(994\) −4.53472 + 3.29467i −0.143833 + 0.104501i
\(995\) 3.11705 0.792206i 0.0988170 0.0251146i
\(996\) −4.38341 + 13.4907i −0.138894 + 0.427470i
\(997\) −11.3687 15.6476i −0.360049 0.495565i 0.590113 0.807320i \(-0.299083\pi\)
−0.950162 + 0.311755i \(0.899083\pi\)
\(998\) 14.2862 19.6633i 0.452222 0.622431i
\(999\) 11.5768 + 35.6297i 0.366273 + 1.12727i
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 55.2.j.a.49.3 yes 16
3.2 odd 2 495.2.ba.a.379.2 16
4.3 odd 2 880.2.cd.c.49.2 16
5.2 odd 4 275.2.h.d.126.3 16
5.3 odd 4 275.2.h.d.126.2 16
5.4 even 2 inner 55.2.j.a.49.2 yes 16
11.2 odd 10 605.2.j.d.9.3 16
11.3 even 5 605.2.b.g.364.4 8
11.4 even 5 605.2.j.h.124.3 16
11.5 even 5 605.2.j.h.444.2 16
11.6 odd 10 605.2.j.g.444.3 16
11.7 odd 10 605.2.j.g.124.2 16
11.8 odd 10 605.2.b.f.364.5 8
11.9 even 5 inner 55.2.j.a.9.2 16
11.10 odd 2 605.2.j.d.269.2 16
15.14 odd 2 495.2.ba.a.379.3 16
20.19 odd 2 880.2.cd.c.49.3 16
33.20 odd 10 495.2.ba.a.64.3 16
44.31 odd 10 880.2.cd.c.449.3 16
55.3 odd 20 3025.2.a.bl.1.4 8
55.4 even 10 605.2.j.h.124.2 16
55.8 even 20 3025.2.a.bk.1.5 8
55.9 even 10 inner 55.2.j.a.9.3 yes 16
55.14 even 10 605.2.b.g.364.5 8
55.19 odd 10 605.2.b.f.364.4 8
55.24 odd 10 605.2.j.d.9.2 16
55.29 odd 10 605.2.j.g.124.3 16
55.39 odd 10 605.2.j.g.444.2 16
55.42 odd 20 275.2.h.d.251.3 16
55.47 odd 20 3025.2.a.bl.1.5 8
55.49 even 10 605.2.j.h.444.3 16
55.52 even 20 3025.2.a.bk.1.4 8
55.53 odd 20 275.2.h.d.251.2 16
55.54 odd 2 605.2.j.d.269.3 16
165.119 odd 10 495.2.ba.a.64.2 16
220.119 odd 10 880.2.cd.c.449.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.9.2 16 11.9 even 5 inner
55.2.j.a.9.3 yes 16 55.9 even 10 inner
55.2.j.a.49.2 yes 16 5.4 even 2 inner
55.2.j.a.49.3 yes 16 1.1 even 1 trivial
275.2.h.d.126.2 16 5.3 odd 4
275.2.h.d.126.3 16 5.2 odd 4
275.2.h.d.251.2 16 55.53 odd 20
275.2.h.d.251.3 16 55.42 odd 20
495.2.ba.a.64.2 16 165.119 odd 10
495.2.ba.a.64.3 16 33.20 odd 10
495.2.ba.a.379.2 16 3.2 odd 2
495.2.ba.a.379.3 16 15.14 odd 2
605.2.b.f.364.4 8 55.19 odd 10
605.2.b.f.364.5 8 11.8 odd 10
605.2.b.g.364.4 8 11.3 even 5
605.2.b.g.364.5 8 55.14 even 10
605.2.j.d.9.2 16 55.24 odd 10
605.2.j.d.9.3 16 11.2 odd 10
605.2.j.d.269.2 16 11.10 odd 2
605.2.j.d.269.3 16 55.54 odd 2
605.2.j.g.124.2 16 11.7 odd 10
605.2.j.g.124.3 16 55.29 odd 10
605.2.j.g.444.2 16 55.39 odd 10
605.2.j.g.444.3 16 11.6 odd 10
605.2.j.h.124.2 16 55.4 even 10
605.2.j.h.124.3 16 11.4 even 5
605.2.j.h.444.2 16 11.5 even 5
605.2.j.h.444.3 16 55.49 even 10
880.2.cd.c.49.2 16 4.3 odd 2
880.2.cd.c.49.3 16 20.19 odd 2
880.2.cd.c.449.2 16 220.119 odd 10
880.2.cd.c.449.3 16 44.31 odd 10
3025.2.a.bk.1.4 8 55.52 even 20
3025.2.a.bk.1.5 8 55.8 even 20
3025.2.a.bl.1.4 8 55.3 odd 20
3025.2.a.bl.1.5 8 55.47 odd 20