Properties

Label 60.2.j.a.43.4
Level $60$
Weight $2$
Character 60.43
Analytic conductor $0.479$
Analytic rank $0$
Dimension $12$
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] = [60,2,Mod(7,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.j (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: \(0.479102412128\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.426337261060096.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.4
Root \(-0.394157 - 1.35818i\) of defining polynomial
Character \(\chi\) \(=\) 60.43
Dual form 60.2.j.a.7.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.394157 - 1.35818i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-1.75233 + 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(2.47817 + 2.47817i) q^{7} +(-2.12000 + 1.87233i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.394157 - 1.35818i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.68928 - 1.07067i) q^{4} +(-1.75233 + 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(2.47817 + 2.47817i) q^{7} +(-2.12000 + 1.87233i) q^{8} -1.00000i q^{9} +(1.19582 + 2.92746i) q^{10} -3.02831i q^{11} +(-1.95158 + 0.437425i) q^{12} +(0.363328 + 0.363328i) q^{13} +(4.34258 - 2.38900i) q^{14} +(-0.256912 + 2.22126i) q^{15} +(1.70734 + 3.61732i) q^{16} +(-2.36333 + 2.36333i) q^{17} +(-1.35818 - 0.394157i) q^{18} -4.95634 q^{19} +(4.44734 - 0.470252i) q^{20} +3.50466 q^{21} +(-4.11297 - 1.19363i) q^{22} +(-0.900390 + 0.900390i) q^{23} +(-0.175128 + 2.82300i) q^{24} +(1.14134 - 4.86799i) q^{25} +(0.636672 - 0.350255i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.53303 - 6.83963i) q^{28} -3.50466i q^{29} +(2.91560 + 1.22446i) q^{30} -3.85607i q^{31} +(5.58591 - 0.893077i) q^{32} +(-2.14134 - 2.14134i) q^{33} +(2.27829 + 4.14134i) q^{34} +(-7.78477 - 0.900390i) q^{35} +(-1.07067 + 1.68928i) q^{36} +(-0.363328 + 0.363328i) q^{37} +(-1.95358 + 6.73158i) q^{38} +0.513824 q^{39} +(1.11427 - 6.22563i) q^{40} +2.72666 q^{41} +(1.38139 - 4.75995i) q^{42} +(3.92870 - 3.92870i) q^{43} +(-3.24231 + 5.11566i) q^{44} +(1.38900 + 1.75233i) q^{45} +(0.867993 + 1.57778i) q^{46} +(5.85673 + 5.85673i) q^{47} +(3.76510 + 1.35056i) q^{48} +5.28267i q^{49} +(-6.16172 - 3.46889i) q^{50} +3.34225i q^{51} +(-0.224760 - 1.00277i) q^{52} +(3.14134 + 3.14134i) q^{53} +(-1.23909 + 0.681664i) q^{54} +(4.20633 + 5.30660i) q^{55} +(-9.89367 - 0.613763i) q^{56} +(-3.50466 + 3.50466i) q^{57} +(-4.75995 - 1.38139i) q^{58} +8.68516 q^{59} +(2.81223 - 3.47726i) q^{60} -15.2920 q^{61} +(-5.23723 - 1.51990i) q^{62} +(2.47817 - 2.47817i) q^{63} +(0.988770 - 7.93866i) q^{64} +(-1.14134 - 0.132007i) q^{65} +(-3.75233 + 2.06429i) q^{66} +(-3.92870 - 3.92870i) q^{67} +(6.52267 - 1.46199i) q^{68} +1.27334i q^{69} +(-4.29131 + 10.2182i) q^{70} +4.25583i q^{71} +(1.87233 + 2.12000i) q^{72} +(9.28267 + 9.28267i) q^{73} +(0.350255 + 0.636672i) q^{74} +(-2.63514 - 4.24924i) q^{75} +(8.37266 + 5.30660i) q^{76} +(7.50466 - 7.50466i) q^{77} +(0.202527 - 0.697863i) q^{78} +0.399759 q^{79} +(-8.01630 - 3.96724i) q^{80} -1.00000 q^{81} +(1.07473 - 3.70328i) q^{82} +(-0.199879 + 0.199879i) q^{83} +(-5.92036 - 3.75233i) q^{84} +(0.858664 - 7.42401i) q^{85} +(-3.78734 - 6.88438i) q^{86} +(-2.47817 - 2.47817i) q^{87} +(5.66999 + 6.42000i) q^{88} -4.28267i q^{89} +(2.92746 - 1.19582i) q^{90} +1.80078i q^{91} +(2.48503 - 0.556993i) q^{92} +(-2.72666 - 2.72666i) q^{93} +(10.2629 - 5.64600i) q^{94} +(8.68516 - 6.88438i) q^{95} +(3.31834 - 4.58134i) q^{96} +(6.73599 - 6.73599i) q^{97} +(7.17480 + 2.08220i) q^{98} -3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.394157 1.35818i 0.278711 0.960375i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) −1.68928 1.07067i −0.844640 0.535334i
\(5\) −1.75233 + 1.38900i −0.783667 + 0.621181i
\(6\) −0.681664 1.23909i −0.278288 0.505855i
\(7\) 2.47817 + 2.47817i 0.936661 + 0.936661i 0.998110 0.0614493i \(-0.0195722\pi\)
−0.0614493 + 0.998110i \(0.519572\pi\)
\(8\) −2.12000 + 1.87233i −0.749532 + 0.661968i
\(9\) 1.00000i 0.333333i
\(10\) 1.19582 + 2.92746i 0.378151 + 0.925744i
\(11\) 3.02831i 0.913069i −0.889706 0.456534i \(-0.849091\pi\)
0.889706 0.456534i \(-0.150909\pi\)
\(12\) −1.95158 + 0.437425i −0.563372 + 0.126274i
\(13\) 0.363328 + 0.363328i 0.100769 + 0.100769i 0.755694 0.654925i \(-0.227300\pi\)
−0.654925 + 0.755694i \(0.727300\pi\)
\(14\) 4.34258 2.38900i 1.16060 0.638488i
\(15\) −0.256912 + 2.22126i −0.0663344 + 0.573527i
\(16\) 1.70734 + 3.61732i 0.426835 + 0.904330i
\(17\) −2.36333 + 2.36333i −0.573191 + 0.573191i −0.933019 0.359828i \(-0.882836\pi\)
0.359828 + 0.933019i \(0.382836\pi\)
\(18\) −1.35818 0.394157i −0.320125 0.0929036i
\(19\) −4.95634 −1.13706 −0.568532 0.822661i \(-0.692488\pi\)
−0.568532 + 0.822661i \(0.692488\pi\)
\(20\) 4.44734 0.470252i 0.994456 0.105151i
\(21\) 3.50466 0.764780
\(22\) −4.11297 1.19363i −0.876888 0.254482i
\(23\) −0.900390 + 0.900390i −0.187744 + 0.187744i −0.794720 0.606976i \(-0.792382\pi\)
0.606976 + 0.794720i \(0.292382\pi\)
\(24\) −0.175128 + 2.82300i −0.0357478 + 0.576243i
\(25\) 1.14134 4.86799i 0.228267 0.973599i
\(26\) 0.636672 0.350255i 0.124862 0.0686907i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −1.53303 6.83963i −0.289715 1.29257i
\(29\) 3.50466i 0.650800i −0.945576 0.325400i \(-0.894501\pi\)
0.945576 0.325400i \(-0.105499\pi\)
\(30\) 2.91560 + 1.22446i 0.532313 + 0.223554i
\(31\) 3.85607i 0.692571i −0.938129 0.346286i \(-0.887443\pi\)
0.938129 0.346286i \(-0.112557\pi\)
\(32\) 5.58591 0.893077i 0.987459 0.157875i
\(33\) −2.14134 2.14134i −0.372759 0.372759i
\(34\) 2.27829 + 4.14134i 0.390724 + 0.710233i
\(35\) −7.78477 0.900390i −1.31587 0.152194i
\(36\) −1.07067 + 1.68928i −0.178445 + 0.281547i
\(37\) −0.363328 + 0.363328i −0.0597308 + 0.0597308i −0.736341 0.676610i \(-0.763448\pi\)
0.676610 + 0.736341i \(0.263448\pi\)
\(38\) −1.95358 + 6.73158i −0.316912 + 1.09201i
\(39\) 0.513824 0.0822776
\(40\) 1.11427 6.22563i 0.176181 0.984358i
\(41\) 2.72666 0.425832 0.212916 0.977070i \(-0.431704\pi\)
0.212916 + 0.977070i \(0.431704\pi\)
\(42\) 1.38139 4.75995i 0.213153 0.734476i
\(43\) 3.92870 3.92870i 0.599121 0.599121i −0.340958 0.940079i \(-0.610751\pi\)
0.940079 + 0.340958i \(0.110751\pi\)
\(44\) −3.24231 + 5.11566i −0.488797 + 0.771215i
\(45\) 1.38900 + 1.75233i 0.207060 + 0.261222i
\(46\) 0.867993 + 1.57778i 0.127979 + 0.232631i
\(47\) 5.85673 + 5.85673i 0.854292 + 0.854292i 0.990659 0.136366i \(-0.0435423\pi\)
−0.136366 + 0.990659i \(0.543542\pi\)
\(48\) 3.76510 + 1.35056i 0.543446 + 0.194936i
\(49\) 5.28267i 0.754667i
\(50\) −6.16172 3.46889i −0.871399 0.490575i
\(51\) 3.34225i 0.468009i
\(52\) −0.224760 1.00277i −0.0311685 0.139059i
\(53\) 3.14134 + 3.14134i 0.431496 + 0.431496i 0.889137 0.457641i \(-0.151306\pi\)
−0.457641 + 0.889137i \(0.651306\pi\)
\(54\) −1.23909 + 0.681664i −0.168618 + 0.0927627i
\(55\) 4.20633 + 5.30660i 0.567181 + 0.715542i
\(56\) −9.89367 0.613763i −1.32210 0.0820176i
\(57\) −3.50466 + 3.50466i −0.464204 + 0.464204i
\(58\) −4.75995 1.38139i −0.625012 0.181385i
\(59\) 8.68516 1.13071 0.565356 0.824847i \(-0.308739\pi\)
0.565356 + 0.824847i \(0.308739\pi\)
\(60\) 2.81223 3.47726i 0.363057 0.448913i
\(61\) −15.2920 −1.95794 −0.978970 0.204004i \(-0.934604\pi\)
−0.978970 + 0.204004i \(0.934604\pi\)
\(62\) −5.23723 1.51990i −0.665128 0.193027i
\(63\) 2.47817 2.47817i 0.312220 0.312220i
\(64\) 0.988770 7.93866i 0.123596 0.992333i
\(65\) −1.14134 0.132007i −0.141565 0.0163735i
\(66\) −3.75233 + 2.06429i −0.461880 + 0.254096i
\(67\) −3.92870 3.92870i −0.479967 0.479967i 0.425154 0.905121i \(-0.360220\pi\)
−0.905121 + 0.425154i \(0.860220\pi\)
\(68\) 6.52267 1.46199i 0.790989 0.177292i
\(69\) 1.27334i 0.153293i
\(70\) −4.29131 + 10.2182i −0.512909 + 1.22131i
\(71\) 4.25583i 0.505075i 0.967587 + 0.252537i \(0.0812650\pi\)
−0.967587 + 0.252537i \(0.918735\pi\)
\(72\) 1.87233 + 2.12000i 0.220656 + 0.249844i
\(73\) 9.28267 + 9.28267i 1.08645 + 1.08645i 0.995891 + 0.0905640i \(0.0288670\pi\)
0.0905640 + 0.995891i \(0.471133\pi\)
\(74\) 0.350255 + 0.636672i 0.0407163 + 0.0740116i
\(75\) −2.63514 4.24924i −0.304280 0.490660i
\(76\) 8.37266 + 5.30660i 0.960410 + 0.608709i
\(77\) 7.50466 7.50466i 0.855236 0.855236i
\(78\) 0.202527 0.697863i 0.0229317 0.0790174i
\(79\) 0.399759 0.0449764 0.0224882 0.999747i \(-0.492841\pi\)
0.0224882 + 0.999747i \(0.492841\pi\)
\(80\) −8.01630 3.96724i −0.896249 0.443551i
\(81\) −1.00000 −0.111111
\(82\) 1.07473 3.70328i 0.118684 0.408959i
\(83\) −0.199879 + 0.199879i −0.0219396 + 0.0219396i −0.717991 0.696052i \(-0.754938\pi\)
0.696052 + 0.717991i \(0.254938\pi\)
\(84\) −5.92036 3.75233i −0.645965 0.409413i
\(85\) 0.858664 7.42401i 0.0931352 0.805247i
\(86\) −3.78734 6.88438i −0.408399 0.742362i
\(87\) −2.47817 2.47817i −0.265688 0.265688i
\(88\) 5.66999 + 6.42000i 0.604422 + 0.684374i
\(89\) 4.28267i 0.453962i −0.973899 0.226981i \(-0.927114\pi\)
0.973899 0.226981i \(-0.0728856\pi\)
\(90\) 2.92746 1.19582i 0.308581 0.126050i
\(91\) 1.80078i 0.188773i
\(92\) 2.48503 0.556993i 0.259082 0.0580705i
\(93\) −2.72666 2.72666i −0.282741 0.282741i
\(94\) 10.2629 5.64600i 1.05854 0.582340i
\(95\) 8.68516 6.88438i 0.891079 0.706323i
\(96\) 3.31834 4.58134i 0.338676 0.467581i
\(97\) 6.73599 6.73599i 0.683936 0.683936i −0.276949 0.960885i \(-0.589323\pi\)
0.960885 + 0.276949i \(0.0893233\pi\)
\(98\) 7.17480 + 2.08220i 0.724764 + 0.210334i
\(99\) −3.02831 −0.304356
\(100\) −7.14004 + 7.00141i −0.714004 + 0.700141i
\(101\) 5.78734 0.575862 0.287931 0.957651i \(-0.407033\pi\)
0.287931 + 0.957651i \(0.407033\pi\)
\(102\) 4.53936 + 1.31737i 0.449464 + 0.130439i
\(103\) −13.0914 + 13.0914i −1.28993 + 1.28993i −0.355104 + 0.934827i \(0.615555\pi\)
−0.934827 + 0.355104i \(0.884445\pi\)
\(104\) −1.45052 0.0899847i −0.142236 0.00882373i
\(105\) −6.14134 + 4.86799i −0.599333 + 0.475067i
\(106\) 5.50466 3.02831i 0.534660 0.294135i
\(107\) −9.71281 9.71281i −0.938973 0.938973i 0.0592694 0.998242i \(-0.481123\pi\)
−0.998242 + 0.0592694i \(0.981123\pi\)
\(108\) 0.437425 + 1.95158i 0.0420913 + 0.187791i
\(109\) 10.4626i 1.00214i 0.865407 + 0.501070i \(0.167060\pi\)
−0.865407 + 0.501070i \(0.832940\pi\)
\(110\) 8.86525 3.62130i 0.845268 0.345278i
\(111\) 0.513824i 0.0487700i
\(112\) −4.73325 + 13.1954i −0.447251 + 1.24685i
\(113\) −10.6460 10.6460i −1.00149 1.00149i −0.999999 0.00149259i \(-0.999525\pi\)
−0.00149259 0.999999i \(-0.500475\pi\)
\(114\) 3.37856 + 6.14134i 0.316431 + 0.575189i
\(115\) 0.327137 2.82843i 0.0305057 0.263752i
\(116\) −3.75233 + 5.92036i −0.348395 + 0.549692i
\(117\) 0.363328 0.363328i 0.0335897 0.0335897i
\(118\) 3.42331 11.7960i 0.315142 1.08591i
\(119\) −11.7135 −1.07377
\(120\) −3.61428 5.19009i −0.329937 0.473788i
\(121\) 1.82936 0.166305
\(122\) −6.02745 + 20.7692i −0.545699 + 1.88036i
\(123\) 1.92804 1.92804i 0.173845 0.173845i
\(124\) −4.12858 + 6.51399i −0.370757 + 0.584974i
\(125\) 4.76166 + 10.1157i 0.425896 + 0.904772i
\(126\) −2.38900 4.34258i −0.212829 0.386868i
\(127\) −1.77766 1.77766i −0.157742 0.157742i 0.623823 0.781565i \(-0.285578\pi\)
−0.781565 + 0.623823i \(0.785578\pi\)
\(128\) −10.3924 4.47200i −0.918564 0.395273i
\(129\) 5.55602i 0.489180i
\(130\) −0.629155 + 1.49810i −0.0551805 + 0.131392i
\(131\) 18.1981i 1.58997i 0.606626 + 0.794987i \(0.292523\pi\)
−0.606626 + 0.794987i \(0.707477\pi\)
\(132\) 1.32466 + 5.90998i 0.115297 + 0.514398i
\(133\) −12.2827 12.2827i −1.06504 1.06504i
\(134\) −6.88438 + 3.78734i −0.594720 + 0.327176i
\(135\) 2.22126 + 0.256912i 0.191176 + 0.0221115i
\(136\) 0.585320 9.43517i 0.0501908 0.809060i
\(137\) −5.91934 + 5.91934i −0.505724 + 0.505724i −0.913211 0.407487i \(-0.866405\pi\)
0.407487 + 0.913211i \(0.366405\pi\)
\(138\) 1.72942 + 0.501897i 0.147218 + 0.0427243i
\(139\) 12.4140 1.05294 0.526470 0.850194i \(-0.323515\pi\)
0.526470 + 0.850194i \(0.323515\pi\)
\(140\) 12.1866 + 9.85592i 1.02996 + 0.832977i
\(141\) 8.28267 0.697527
\(142\) 5.78017 + 1.67747i 0.485061 + 0.140770i
\(143\) 1.10027 1.10027i 0.0920091 0.0920091i
\(144\) 3.61732 1.70734i 0.301443 0.142278i
\(145\) 4.86799 + 6.14134i 0.404265 + 0.510010i
\(146\) 16.2663 8.94867i 1.34621 0.740597i
\(147\) 3.73541 + 3.73541i 0.308092 + 0.308092i
\(148\) 1.00277 0.224760i 0.0824270 0.0184751i
\(149\) 5.78734i 0.474117i 0.971495 + 0.237059i \(0.0761833\pi\)
−0.971495 + 0.237059i \(0.923817\pi\)
\(150\) −6.80987 + 1.90412i −0.556023 + 0.155471i
\(151\) 18.0708i 1.47058i −0.677751 0.735292i \(-0.737045\pi\)
0.677751 0.735292i \(-0.262955\pi\)
\(152\) 10.5074 9.27990i 0.852265 0.752700i
\(153\) 2.36333 + 2.36333i 0.191064 + 0.191064i
\(154\) −7.23464 13.1507i −0.582984 1.05971i
\(155\) 5.35610 + 6.75712i 0.430213 + 0.542745i
\(156\) −0.867993 0.550135i −0.0694950 0.0440460i
\(157\) −3.91934 + 3.91934i −0.312798 + 0.312798i −0.845992 0.533195i \(-0.820991\pi\)
0.533195 + 0.845992i \(0.320991\pi\)
\(158\) 0.157568 0.542943i 0.0125354 0.0431942i
\(159\) 4.44252 0.352315
\(160\) −8.54789 + 9.32382i −0.675770 + 0.737113i
\(161\) −4.46264 −0.351705
\(162\) −0.394157 + 1.35818i −0.0309679 + 0.106708i
\(163\) −3.22819 + 3.22819i −0.252851 + 0.252851i −0.822139 0.569287i \(-0.807219\pi\)
0.569287 + 0.822139i \(0.307219\pi\)
\(164\) −4.60609 2.91934i −0.359675 0.227962i
\(165\) 6.72666 + 0.778008i 0.523669 + 0.0605678i
\(166\) 0.192688 + 0.350255i 0.0149555 + 0.0271851i
\(167\) −6.95700 6.95700i −0.538349 0.538349i 0.384695 0.923044i \(-0.374307\pi\)
−0.923044 + 0.384695i \(0.874307\pi\)
\(168\) −7.42988 + 6.56188i −0.573227 + 0.506260i
\(169\) 12.7360i 0.979691i
\(170\) −9.74466 4.09244i −0.747381 0.313876i
\(171\) 4.95634i 0.379021i
\(172\) −10.8430 + 2.43034i −0.826771 + 0.185312i
\(173\) 0.627343 + 0.627343i 0.0476960 + 0.0476960i 0.730553 0.682857i \(-0.239263\pi\)
−0.682857 + 0.730553i \(0.739263\pi\)
\(174\) −4.34258 + 2.38900i −0.329210 + 0.181110i
\(175\) 14.8921 9.23530i 1.12574 0.698123i
\(176\) 10.9543 5.17035i 0.825715 0.389730i
\(177\) 6.14134 6.14134i 0.461611 0.461611i
\(178\) −5.81662 1.68804i −0.435974 0.126524i
\(179\) 8.93968 0.668183 0.334091 0.942541i \(-0.391571\pi\)
0.334091 + 0.942541i \(0.391571\pi\)
\(180\) −0.470252 4.44734i −0.0350505 0.331485i
\(181\) −1.00933 −0.0750228 −0.0375114 0.999296i \(-0.511943\pi\)
−0.0375114 + 0.999296i \(0.511943\pi\)
\(182\) 2.44577 + 0.709789i 0.181293 + 0.0526131i
\(183\) −10.8131 + 10.8131i −0.799326 + 0.799326i
\(184\) 0.222998 3.59465i 0.0164396 0.265001i
\(185\) 0.132007 1.14134i 0.00970538 0.0839127i
\(186\) −4.77801 + 2.62855i −0.350341 + 0.192734i
\(187\) 7.15688 + 7.15688i 0.523363 + 0.523363i
\(188\) −3.62305 16.1643i −0.264238 1.17890i
\(189\) 3.50466i 0.254927i
\(190\) −5.92688 14.5095i −0.429981 1.05263i
\(191\) 21.6262i 1.56481i −0.622768 0.782407i \(-0.713992\pi\)
0.622768 0.782407i \(-0.286008\pi\)
\(192\) −4.91431 6.31265i −0.354660 0.455576i
\(193\) 11.5653 + 11.5653i 0.832492 + 0.832492i 0.987857 0.155365i \(-0.0496555\pi\)
−0.155365 + 0.987857i \(0.549655\pi\)
\(194\) −6.49362 11.8037i −0.466214 0.847455i
\(195\) −0.900390 + 0.713703i −0.0644783 + 0.0511093i
\(196\) 5.65599 8.92392i 0.403999 0.637423i
\(197\) −9.42401 + 9.42401i −0.671433 + 0.671433i −0.958046 0.286614i \(-0.907470\pi\)
0.286614 + 0.958046i \(0.407470\pi\)
\(198\) −1.19363 + 4.11297i −0.0848274 + 0.292296i
\(199\) −11.0130 −0.780688 −0.390344 0.920669i \(-0.627644\pi\)
−0.390344 + 0.920669i \(0.627644\pi\)
\(200\) 6.69485 + 12.4571i 0.473398 + 0.880849i
\(201\) −5.55602 −0.391891
\(202\) 2.28112 7.86022i 0.160499 0.553043i
\(203\) 8.68516 8.68516i 0.609579 0.609579i
\(204\) 3.57844 5.64600i 0.250541 0.395299i
\(205\) −4.77801 + 3.78734i −0.333711 + 0.264519i
\(206\) 12.6203 + 22.9404i 0.879300 + 1.59834i
\(207\) 0.900390 + 0.900390i 0.0625814 + 0.0625814i
\(208\) −0.693949 + 1.93460i −0.0481167 + 0.134140i
\(209\) 15.0093i 1.03822i
\(210\) 4.19094 + 10.2598i 0.289202 + 0.707991i
\(211\) 27.9835i 1.92646i 0.268669 + 0.963232i \(0.413416\pi\)
−0.268669 + 0.963232i \(0.586584\pi\)
\(212\) −1.94327 8.66993i −0.133464 0.595453i
\(213\) 3.00933 + 3.00933i 0.206196 + 0.206196i
\(214\) −17.0201 + 9.36333i −1.16347 + 0.640064i
\(215\) −1.42741 + 12.3414i −0.0973483 + 0.841673i
\(216\) 2.82300 + 0.175128i 0.192081 + 0.0119159i
\(217\) 9.55602 9.55602i 0.648705 0.648705i
\(218\) 14.2101 + 4.12392i 0.962430 + 0.279307i
\(219\) 13.1277 0.887086
\(220\) −1.42407 13.4679i −0.0960105 0.908007i
\(221\) −1.71733 −0.115520
\(222\) 0.697863 + 0.202527i 0.0468375 + 0.0135927i
\(223\) 8.53479 8.53479i 0.571531 0.571531i −0.361025 0.932556i \(-0.617573\pi\)
0.932556 + 0.361025i \(0.117573\pi\)
\(224\) 16.0560 + 11.6297i 1.07279 + 0.777039i
\(225\) −4.86799 1.14134i −0.324533 0.0760891i
\(226\) −18.6553 + 10.2629i −1.24093 + 0.682681i
\(227\) 1.02765 + 1.02765i 0.0682074 + 0.0682074i 0.740388 0.672180i \(-0.234642\pi\)
−0.672180 + 0.740388i \(0.734642\pi\)
\(228\) 9.67269 2.16803i 0.640590 0.143581i
\(229\) 8.84802i 0.584693i −0.956312 0.292347i \(-0.905564\pi\)
0.956312 0.292347i \(-0.0944361\pi\)
\(230\) −3.71256 1.55915i −0.244799 0.102808i
\(231\) 10.6132i 0.698297i
\(232\) 6.56188 + 7.42988i 0.430809 + 0.487795i
\(233\) −4.91002 4.91002i −0.321666 0.321666i 0.527740 0.849406i \(-0.323040\pi\)
−0.849406 + 0.527740i \(0.823040\pi\)
\(234\) −0.350255 0.636672i −0.0228969 0.0416205i
\(235\) −18.3980 2.12792i −1.20015 0.138810i
\(236\) −14.6717 9.29892i −0.955045 0.605308i
\(237\) 0.282672 0.282672i 0.0183615 0.0183615i
\(238\) −4.61694 + 15.9089i −0.299272 + 1.03122i
\(239\) −19.0259 −1.23068 −0.615340 0.788262i \(-0.710981\pi\)
−0.615340 + 0.788262i \(0.710981\pi\)
\(240\) −8.47364 + 2.86311i −0.546971 + 0.184813i
\(241\) 2.90663 0.187232 0.0936161 0.995608i \(-0.470157\pi\)
0.0936161 + 0.995608i \(0.470157\pi\)
\(242\) 0.721054 2.48459i 0.0463511 0.159716i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 25.8325 + 16.3727i 1.65376 + 1.04815i
\(245\) −7.33765 9.25700i −0.468785 0.591408i
\(246\) −1.85866 3.37856i −0.118504 0.215409i
\(247\) −1.80078 1.80078i −0.114581 0.114581i
\(248\) 7.21984 + 8.17486i 0.458460 + 0.519104i
\(249\) 0.282672i 0.0179136i
\(250\) 15.6157 2.48001i 0.987622 0.156850i
\(251\) 2.77379i 0.175080i 0.996161 + 0.0875401i \(0.0279006\pi\)
−0.996161 + 0.0875401i \(0.972099\pi\)
\(252\) −6.83963 + 1.53303i −0.430856 + 0.0965717i
\(253\) 2.72666 + 2.72666i 0.171423 + 0.171423i
\(254\) −3.11505 + 1.71370i −0.195456 + 0.107527i
\(255\) −4.64240 5.85673i −0.290718 0.366763i
\(256\) −10.1700 + 12.3520i −0.635624 + 0.771999i
\(257\) −2.08066 + 2.08066i −0.129788 + 0.129788i −0.769017 0.639229i \(-0.779254\pi\)
0.639229 + 0.769017i \(0.279254\pi\)
\(258\) −7.54604 2.18994i −0.469796 0.136340i
\(259\) −1.80078 −0.111895
\(260\) 1.78670 + 1.44499i 0.110807 + 0.0896145i
\(261\) −3.50466 −0.216933
\(262\) 24.7162 + 7.17290i 1.52697 + 0.443143i
\(263\) −4.75646 + 4.75646i −0.293296 + 0.293296i −0.838381 0.545085i \(-0.816497\pi\)
0.545085 + 0.838381i \(0.316497\pi\)
\(264\) 8.54891 + 0.530340i 0.526149 + 0.0326402i
\(265\) −9.86799 1.14134i −0.606186 0.0701117i
\(266\) −21.5233 + 11.8407i −1.31968 + 0.726001i
\(267\) −3.02831 3.02831i −0.185329 0.185329i
\(268\) 2.43034 + 10.8430i 0.148457 + 0.662342i
\(269\) 21.6846i 1.32214i −0.750326 0.661068i \(-0.770104\pi\)
0.750326 0.661068i \(-0.229896\pi\)
\(270\) 1.22446 2.91560i 0.0745180 0.177438i
\(271\) 3.15556i 0.191687i 0.995396 + 0.0958434i \(0.0305548\pi\)
−0.995396 + 0.0958434i \(0.969445\pi\)
\(272\) −12.5839 4.51391i −0.763012 0.273696i
\(273\) 1.27334 + 1.27334i 0.0770663 + 0.0770663i
\(274\) 5.70636 + 10.3727i 0.344734 + 0.626635i
\(275\) −14.7418 3.45632i −0.888962 0.208424i
\(276\) 1.36333 2.15103i 0.0820627 0.129477i
\(277\) −3.53397 + 3.53397i −0.212336 + 0.212336i −0.805259 0.592923i \(-0.797974\pi\)
0.592923 + 0.805259i \(0.297974\pi\)
\(278\) 4.89305 16.8604i 0.293466 1.01122i
\(279\) −3.85607 −0.230857
\(280\) 18.1895 12.6668i 1.08703 0.756988i
\(281\) 0.179969 0.0107361 0.00536804 0.999986i \(-0.498291\pi\)
0.00536804 + 0.999986i \(0.498291\pi\)
\(282\) 3.26467 11.2493i 0.194408 0.669887i
\(283\) 9.84007 9.84007i 0.584931 0.584931i −0.351323 0.936254i \(-0.614268\pi\)
0.936254 + 0.351323i \(0.114268\pi\)
\(284\) 4.55658 7.18930i 0.270384 0.426606i
\(285\) 1.27334 11.0093i 0.0754264 0.652136i
\(286\) −1.06068 1.92804i −0.0627193 0.114007i
\(287\) 6.75712 + 6.75712i 0.398860 + 0.398860i
\(288\) −0.893077 5.58591i −0.0526250 0.329153i
\(289\) 5.82936i 0.342903i
\(290\) 10.2598 4.19094i 0.602474 0.246100i
\(291\) 9.52612i 0.558431i
\(292\) −5.74238 25.6197i −0.336047 1.49928i
\(293\) 15.8680 + 15.8680i 0.927018 + 0.927018i 0.997512 0.0704942i \(-0.0224576\pi\)
−0.0704942 + 0.997512i \(0.522458\pi\)
\(294\) 6.54569 3.60101i 0.381752 0.210015i
\(295\) −15.2193 + 12.0637i −0.886101 + 0.702377i
\(296\) 0.0899847 1.45052i 0.00523026 0.0843100i
\(297\) −2.14134 + 2.14134i −0.124253 + 0.124253i
\(298\) 7.86022 + 2.28112i 0.455330 + 0.132142i
\(299\) −0.654274 −0.0378376
\(300\) −0.0980239 + 9.99952i −0.00565941 + 0.577323i
\(301\) 19.4720 1.12235
\(302\) −24.5434 7.12274i −1.41231 0.409868i
\(303\) 4.09226 4.09226i 0.235094 0.235094i
\(304\) −8.46216 17.9287i −0.485338 1.02828i
\(305\) 26.7967 21.2406i 1.53437 1.21624i
\(306\) 4.14134 2.27829i 0.236744 0.130241i
\(307\) 7.78477 + 7.78477i 0.444300 + 0.444300i 0.893454 0.449154i \(-0.148275\pi\)
−0.449154 + 0.893454i \(0.648275\pi\)
\(308\) −20.7125 + 4.64248i −1.18020 + 0.264530i
\(309\) 18.5140i 1.05322i
\(310\) 11.2885 4.61116i 0.641144 0.261896i
\(311\) 7.05788i 0.400215i −0.979774 0.200108i \(-0.935871\pi\)
0.979774 0.200108i \(-0.0641292\pi\)
\(312\) −1.08930 + 0.962047i −0.0616697 + 0.0544652i
\(313\) −11.3013 11.3013i −0.638789 0.638789i 0.311468 0.950257i \(-0.399179\pi\)
−0.950257 + 0.311468i \(0.899179\pi\)
\(314\) 3.77832 + 6.86799i 0.213223 + 0.387583i
\(315\) −0.900390 + 7.78477i −0.0507312 + 0.438622i
\(316\) −0.675305 0.428009i −0.0379889 0.0240774i
\(317\) 19.4754 19.4754i 1.09385 1.09385i 0.0987310 0.995114i \(-0.468522\pi\)
0.995114 0.0987310i \(-0.0314783\pi\)
\(318\) 1.75105 6.03372i 0.0981940 0.338354i
\(319\) −10.6132 −0.594225
\(320\) 9.29418 + 15.2846i 0.519560 + 0.854434i
\(321\) −13.7360 −0.766668
\(322\) −1.75898 + 6.06105i −0.0980241 + 0.337769i
\(323\) 11.7135 11.7135i 0.651755 0.651755i
\(324\) 1.68928 + 1.07067i 0.0938489 + 0.0594816i
\(325\) 2.18336 1.35400i 0.121111 0.0751064i
\(326\) 3.11203 + 5.65685i 0.172359 + 0.313304i
\(327\) 7.39820 + 7.39820i 0.409122 + 0.409122i
\(328\) −5.78050 + 5.10520i −0.319175 + 0.281887i
\(329\) 29.0280i 1.60036i
\(330\) 3.70803 8.82932i 0.204120 0.486038i
\(331\) 15.0143i 0.825259i −0.910899 0.412630i \(-0.864610\pi\)
0.910899 0.412630i \(-0.135390\pi\)
\(332\) 0.551657 0.123648i 0.0302761 0.00678607i
\(333\) 0.363328 + 0.363328i 0.0199103 + 0.0199103i
\(334\) −12.1910 + 6.70668i −0.667061 + 0.366973i
\(335\) 12.3414 + 1.42741i 0.674280 + 0.0779875i
\(336\) 5.98365 + 12.6775i 0.326435 + 0.691614i
\(337\) −21.5840 + 21.5840i −1.17576 + 1.17576i −0.194940 + 0.980815i \(0.562451\pi\)
−0.980815 + 0.194940i \(0.937549\pi\)
\(338\) −17.2977 5.01997i −0.940871 0.273051i
\(339\) −15.0557 −0.817714
\(340\) −9.39917 + 11.6219i −0.509742 + 0.630286i
\(341\) −11.6774 −0.632365
\(342\) 6.73158 + 1.95358i 0.364002 + 0.105637i
\(343\) 4.25583 4.25583i 0.229793 0.229793i
\(344\) −0.973012 + 15.6846i −0.0524613 + 0.845659i
\(345\) −1.76868 2.23132i −0.0952225 0.120130i
\(346\) 1.09931 0.604770i 0.0590995 0.0325127i
\(347\) 16.9969 + 16.9969i 0.912444 + 0.912444i 0.996464 0.0840201i \(-0.0267760\pi\)
−0.0840201 + 0.996464i \(0.526776\pi\)
\(348\) 1.53303 + 6.83963i 0.0821790 + 0.366643i
\(349\) 4.38538i 0.234744i 0.993088 + 0.117372i \(0.0374469\pi\)
−0.993088 + 0.117372i \(0.962553\pi\)
\(350\) −6.67331 23.8663i −0.356703 1.27571i
\(351\) 0.513824i 0.0274259i
\(352\) −2.70451 16.9159i −0.144151 0.901618i
\(353\) −2.62734 2.62734i −0.139839 0.139839i 0.633722 0.773561i \(-0.281526\pi\)
−0.773561 + 0.633722i \(0.781526\pi\)
\(354\) −5.92036 10.7617i −0.314664 0.571976i
\(355\) −5.91137 7.45763i −0.313743 0.395810i
\(356\) −4.58532 + 7.23464i −0.243021 + 0.383435i
\(357\) −8.28267 + 8.28267i −0.438366 + 0.438366i
\(358\) 3.52363 12.1416i 0.186230 0.641706i
\(359\) 34.9952 1.84697 0.923487 0.383630i \(-0.125326\pi\)
0.923487 + 0.383630i \(0.125326\pi\)
\(360\) −6.22563 1.11427i −0.328119 0.0587270i
\(361\) 5.56534 0.292913
\(362\) −0.397834 + 1.37085i −0.0209097 + 0.0720500i
\(363\) 1.29355 1.29355i 0.0678939 0.0678939i
\(364\) 1.92804 3.04202i 0.101057 0.159445i
\(365\) −29.1600 3.37266i −1.52630 0.176533i
\(366\) 10.4240 + 18.9481i 0.544872 + 0.990433i
\(367\) 9.93581 + 9.93581i 0.518645 + 0.518645i 0.917161 0.398516i \(-0.130475\pi\)
−0.398516 + 0.917161i \(0.630475\pi\)
\(368\) −4.79427 1.71973i −0.249918 0.0896469i
\(369\) 2.72666i 0.141944i
\(370\) −1.49810 0.629155i −0.0778827 0.0327082i
\(371\) 15.5695i 0.808330i
\(372\) 1.68674 + 7.52543i 0.0874536 + 0.390176i
\(373\) −7.08998 7.08998i −0.367105 0.367105i 0.499315 0.866421i \(-0.333585\pi\)
−0.866421 + 0.499315i \(0.833585\pi\)
\(374\) 12.5412 6.89937i 0.648492 0.356758i
\(375\) 10.5199 + 3.78585i 0.543243 + 0.195500i
\(376\) −23.3820 1.45052i −1.20583 0.0748051i
\(377\) 1.27334 1.27334i 0.0655805 0.0655805i
\(378\) −4.75995 1.38139i −0.244825 0.0710509i
\(379\) 30.0388 1.54299 0.771495 0.636235i \(-0.219509\pi\)
0.771495 + 0.636235i \(0.219509\pi\)
\(380\) −22.0426 + 2.33073i −1.13076 + 0.119564i
\(381\) −2.51399 −0.128796
\(382\) −29.3721 8.52410i −1.50281 0.436131i
\(383\) −11.9133 + 11.9133i −0.608744 + 0.608744i −0.942618 0.333874i \(-0.891644\pi\)
0.333874 + 0.942618i \(0.391644\pi\)
\(384\) −10.5107 + 4.18633i −0.536372 + 0.213633i
\(385\) −2.72666 + 23.5747i −0.138963 + 1.20148i
\(386\) 20.2663 11.1492i 1.03153 0.567480i
\(387\) −3.92870 3.92870i −0.199707 0.199707i
\(388\) −18.5910 + 4.16697i −0.943814 + 0.211546i
\(389\) 16.3340i 0.828168i −0.910239 0.414084i \(-0.864102\pi\)
0.910239 0.414084i \(-0.135898\pi\)
\(390\) 0.614439 + 1.50420i 0.0311133 + 0.0761680i
\(391\) 4.25583i 0.215227i
\(392\) −9.89090 11.1992i −0.499566 0.565647i
\(393\) 12.8680 + 12.8680i 0.649104 + 0.649104i
\(394\) 9.08492 + 16.5140i 0.457692 + 0.831963i
\(395\) −0.700510 + 0.555267i −0.0352465 + 0.0279385i
\(396\) 5.11566 + 3.24231i 0.257072 + 0.162932i
\(397\) −19.1927 + 19.1927i −0.963253 + 0.963253i −0.999348 0.0360950i \(-0.988508\pi\)
0.0360950 + 0.999348i \(0.488508\pi\)
\(398\) −4.34083 + 14.9575i −0.217586 + 0.749753i
\(399\) −17.3703 −0.869604
\(400\) 19.5577 4.18274i 0.977886 0.209137i
\(401\) 26.5653 1.32661 0.663305 0.748349i \(-0.269153\pi\)
0.663305 + 0.748349i \(0.269153\pi\)
\(402\) −2.18994 + 7.54604i −0.109224 + 0.376362i
\(403\) 1.40102 1.40102i 0.0697898 0.0697898i
\(404\) −9.77644 6.19632i −0.486396 0.308278i
\(405\) 1.75233 1.38900i 0.0870741 0.0690202i
\(406\) −8.37266 15.2193i −0.415528 0.755321i
\(407\) 1.10027 + 1.10027i 0.0545383 + 0.0545383i
\(408\) −6.25779 7.08556i −0.309807 0.350787i
\(409\) 25.3947i 1.25569i −0.778339 0.627844i \(-0.783938\pi\)
0.778339 0.627844i \(-0.216062\pi\)
\(410\) 3.26058 + 7.98218i 0.161029 + 0.394212i
\(411\) 8.37122i 0.412922i
\(412\) 36.1315 8.09849i 1.78007 0.398984i
\(413\) 21.5233 + 21.5233i 1.05909 + 1.05909i
\(414\) 1.57778 0.867993i 0.0775438 0.0426595i
\(415\) 0.0726218 0.627889i 0.00356487 0.0308218i
\(416\) 2.35400 + 1.70504i 0.115414 + 0.0835964i
\(417\) 8.77801 8.77801i 0.429861 0.429861i
\(418\) 20.3853 + 5.91603i 0.997078 + 0.289362i
\(419\) −40.0788 −1.95798 −0.978988 0.203919i \(-0.934632\pi\)
−0.978988 + 0.203919i \(0.934632\pi\)
\(420\) 15.5864 1.64807i 0.760541 0.0804178i
\(421\) 19.3947 0.945240 0.472620 0.881266i \(-0.343308\pi\)
0.472620 + 0.881266i \(0.343308\pi\)
\(422\) 38.0065 + 11.0299i 1.85013 + 0.536927i
\(423\) 5.85673 5.85673i 0.284764 0.284764i
\(424\) −12.5412 0.778008i −0.609056 0.0377834i
\(425\) 8.80731 + 14.2020i 0.427217 + 0.688899i
\(426\) 5.27334 2.90105i 0.255494 0.140556i
\(427\) −37.8962 37.8962i −1.83393 1.83393i
\(428\) 6.00847 + 26.8069i 0.290430 + 1.29576i
\(429\) 1.55602i 0.0751251i
\(430\) 16.1991 + 6.80310i 0.781190 + 0.328074i
\(431\) 15.8241i 0.762218i −0.924530 0.381109i \(-0.875542\pi\)
0.924530 0.381109i \(-0.124458\pi\)
\(432\) 1.35056 3.76510i 0.0649788 0.181149i
\(433\) −21.1214 21.1214i −1.01503 1.01503i −0.999885 0.0151424i \(-0.995180\pi\)
−0.0151424 0.999885i \(-0.504820\pi\)
\(434\) −9.21218 16.7453i −0.442199 0.803801i
\(435\) 7.78477 + 0.900390i 0.373251 + 0.0431704i
\(436\) 11.2020 17.6743i 0.536479 0.846447i
\(437\) 4.46264 4.46264i 0.213477 0.213477i
\(438\) 5.17436 17.8297i 0.247241 0.851936i
\(439\) 6.61188 0.315568 0.157784 0.987474i \(-0.449565\pi\)
0.157784 + 0.987474i \(0.449565\pi\)
\(440\) −18.8531 3.37434i −0.898786 0.160865i
\(441\) 5.28267 0.251556
\(442\) −0.676896 + 2.33243i −0.0321967 + 0.110942i
\(443\) −14.5419 + 14.5419i −0.690906 + 0.690906i −0.962431 0.271525i \(-0.912472\pi\)
0.271525 + 0.962431i \(0.412472\pi\)
\(444\) 0.550135 0.867993i 0.0261082 0.0411931i
\(445\) 5.94865 + 7.50466i 0.281993 + 0.355755i
\(446\) −8.22769 14.9558i −0.389593 0.708177i
\(447\) 4.09226 + 4.09226i 0.193557 + 0.193557i
\(448\) 22.1237 17.2230i 1.04525 0.813711i
\(449\) 33.6120i 1.58625i −0.609060 0.793124i \(-0.708453\pi\)
0.609060 0.793124i \(-0.291547\pi\)
\(450\) −3.46889 + 6.16172i −0.163525 + 0.290466i
\(451\) 8.25715i 0.388814i
\(452\) 6.58575 + 29.3824i 0.309768 + 1.38203i
\(453\) −12.7780 12.7780i −0.600363 0.600363i
\(454\) 1.80078 0.990671i 0.0845148 0.0464945i
\(455\) −2.50129 3.15556i −0.117262 0.147935i
\(456\) 0.867993 13.9918i 0.0406475 0.655224i
\(457\) 15.5653 15.5653i 0.728116 0.728116i −0.242128 0.970244i \(-0.577845\pi\)
0.970244 + 0.242128i \(0.0778454\pi\)
\(458\) −12.0172 3.48751i −0.561525 0.162960i
\(459\) 3.34225 0.156003
\(460\) −3.58093 + 4.42775i −0.166962 + 0.206445i
\(461\) −26.1473 −1.21780 −0.608900 0.793247i \(-0.708389\pi\)
−0.608900 + 0.793247i \(0.708389\pi\)
\(462\) −14.4146 4.18326i −0.670627 0.194623i
\(463\) −5.77898 + 5.77898i −0.268572 + 0.268572i −0.828525 0.559953i \(-0.810819\pi\)
0.559953 + 0.828525i \(0.310819\pi\)
\(464\) 12.6775 5.98365i 0.588538 0.277784i
\(465\) 8.56534 + 0.990671i 0.397208 + 0.0459413i
\(466\) −8.60398 + 4.73335i −0.398572 + 0.219268i
\(467\) −2.25517 2.25517i −0.104357 0.104357i 0.653000 0.757357i \(-0.273510\pi\)
−0.757357 + 0.653000i \(0.773510\pi\)
\(468\) −1.00277 + 0.224760i −0.0463529 + 0.0103895i
\(469\) 19.4720i 0.899132i
\(470\) −10.1418 + 24.1489i −0.467805 + 1.11391i
\(471\) 5.54279i 0.255398i
\(472\) −18.4125 + 16.2615i −0.847505 + 0.748495i
\(473\) −11.8973 11.8973i −0.547038 0.547038i
\(474\) −0.272501 0.495336i −0.0125164 0.0227515i
\(475\) −5.65685 + 24.1274i −0.259554 + 1.10704i
\(476\) 19.7873 + 12.5412i 0.906951 + 0.574827i
\(477\) 3.14134 3.14134i 0.143832 0.143832i
\(478\) −7.49917 + 25.8405i −0.343004 + 1.18191i
\(479\) −1.40102 −0.0640143 −0.0320071 0.999488i \(-0.510190\pi\)
−0.0320071 + 0.999488i \(0.510190\pi\)
\(480\) 0.548668 + 12.6372i 0.0250432 + 0.576807i
\(481\) −0.264015 −0.0120380
\(482\) 1.14567 3.94771i 0.0521837 0.179813i
\(483\) −3.15556 + 3.15556i −0.143583 + 0.143583i
\(484\) −3.09030 1.95864i −0.140468 0.0890289i
\(485\) −2.44737 + 21.1600i −0.111130 + 0.960826i
\(486\) 0.681664 + 1.23909i 0.0309209 + 0.0562061i
\(487\) −0.978144 0.978144i −0.0443239 0.0443239i 0.684597 0.728921i \(-0.259978\pi\)
−0.728921 + 0.684597i \(0.759978\pi\)
\(488\) 32.4190 28.6317i 1.46754 1.29609i
\(489\) 4.56534i 0.206452i
\(490\) −15.4648 + 6.31711i −0.698629 + 0.285378i
\(491\) 36.1134i 1.62978i −0.579619 0.814888i \(-0.696799\pi\)
0.579619 0.814888i \(-0.303201\pi\)
\(492\) −5.32128 + 1.19271i −0.239902 + 0.0537715i
\(493\) 8.28267 + 8.28267i 0.373033 + 0.373033i
\(494\) −3.15556 + 1.73599i −0.141976 + 0.0781057i
\(495\) 5.30660 4.20633i 0.238514 0.189060i
\(496\) 13.9486 6.58363i 0.626313 0.295614i
\(497\) −10.5467 + 10.5467i −0.473084 + 0.473084i
\(498\) 0.383918 + 0.111417i 0.0172038 + 0.00499272i
\(499\) −6.35736 −0.284595 −0.142297 0.989824i \(-0.545449\pi\)
−0.142297 + 0.989824i \(0.545449\pi\)
\(500\) 2.78673 22.1863i 0.124626 0.992204i
\(501\) −9.83869 −0.439560
\(502\) 3.76730 + 1.09331i 0.168143 + 0.0487968i
\(503\) −17.1704 + 17.1704i −0.765592 + 0.765592i −0.977327 0.211735i \(-0.932089\pi\)
0.211735 + 0.977327i \(0.432089\pi\)
\(504\) −0.613763 + 9.89367i −0.0273392 + 0.440699i
\(505\) −10.1413 + 8.03863i −0.451284 + 0.357714i
\(506\) 4.77801 2.62855i 0.212408 0.116853i
\(507\) −9.00570 9.00570i −0.399957 0.399957i
\(508\) 1.09968 + 4.90626i 0.0487906 + 0.217680i
\(509\) 18.8739i 0.836572i 0.908315 + 0.418286i \(0.137369\pi\)
−0.908315 + 0.418286i \(0.862631\pi\)
\(510\) −9.78430 + 3.99672i −0.433256 + 0.176978i
\(511\) 46.0081i 2.03528i
\(512\) 12.7676 + 18.6812i 0.564253 + 0.825602i
\(513\) 3.50466 + 3.50466i 0.154735 + 0.154735i
\(514\) 2.00579 + 3.64600i 0.0884717 + 0.160818i
\(515\) 4.75646 41.1244i 0.209595 1.81216i
\(516\) −5.94865 + 9.38567i −0.261875 + 0.413181i
\(517\) 17.7360 17.7360i 0.780028 0.780028i
\(518\) −0.709789 + 2.44577i −0.0311864 + 0.107461i
\(519\) 0.887197 0.0389436
\(520\) 2.66679 1.85710i 0.116946 0.0814393i
\(521\) −33.9346 −1.48670 −0.743351 0.668901i \(-0.766765\pi\)
−0.743351 + 0.668901i \(0.766765\pi\)
\(522\) −1.38139 + 4.75995i −0.0604617 + 0.208337i
\(523\) −3.78345 + 3.78345i −0.165439 + 0.165439i −0.784971 0.619532i \(-0.787322\pi\)
0.619532 + 0.784971i \(0.287322\pi\)
\(524\) 19.4841 30.7417i 0.851167 1.34296i
\(525\) 4.00000 17.0607i 0.174574 0.744589i
\(526\) 4.58532 + 8.33491i 0.199929 + 0.363419i
\(527\) 9.11317 + 9.11317i 0.396976 + 0.396976i
\(528\) 4.08991 11.4019i 0.177990 0.496203i
\(529\) 21.3786i 0.929504i
\(530\) −5.43967 + 12.9526i −0.236284 + 0.562625i
\(531\) 8.68516i 0.376904i
\(532\) 7.59822 + 33.8995i 0.329425 + 1.46973i
\(533\) 0.990671 + 0.990671i 0.0429107 + 0.0429107i
\(534\) −5.30660 + 2.91934i −0.229639 + 0.126332i
\(535\) 30.5112 + 3.52894i 1.31911 + 0.152569i
\(536\) 15.6846 + 0.973012i 0.677473 + 0.0420277i
\(537\) 6.32131 6.32131i 0.272784 0.272784i
\(538\) −29.4515 8.54715i −1.26975 0.368494i
\(539\) 15.9976 0.689063
\(540\) −3.47726 2.81223i −0.149638 0.121019i
\(541\) 28.4813 1.22451 0.612253 0.790662i \(-0.290263\pi\)
0.612253 + 0.790662i \(0.290263\pi\)
\(542\) 4.28581 + 1.24379i 0.184091 + 0.0534252i
\(543\) −0.713703 + 0.713703i −0.0306279 + 0.0306279i
\(544\) −11.0907 + 15.3120i −0.475510 + 0.656496i
\(545\) −14.5327 18.3340i −0.622510 0.785343i
\(546\) 2.23132 1.22753i 0.0954917 0.0525333i
\(547\) −0.726896 0.726896i −0.0310798 0.0310798i 0.691396 0.722476i \(-0.256996\pi\)
−0.722476 + 0.691396i \(0.756996\pi\)
\(548\) 16.3371 3.66178i 0.697886 0.156424i
\(549\) 15.2920i 0.652647i
\(550\) −10.5049 + 18.6596i −0.447928 + 0.795647i
\(551\) 17.3703i 0.740001i
\(552\) −2.38412 2.69948i −0.101475 0.114898i
\(553\) 0.990671 + 0.990671i 0.0421276 + 0.0421276i
\(554\) 3.40681 + 6.19269i 0.144742 + 0.263102i
\(555\) −0.713703 0.900390i −0.0302950 0.0382194i
\(556\) −20.9707 13.2912i −0.889356 0.563675i
\(557\) −11.4427 + 11.4427i −0.484841 + 0.484841i −0.906674 0.421832i \(-0.861387\pi\)
0.421832 + 0.906674i \(0.361387\pi\)
\(558\) −1.51990 + 5.23723i −0.0643424 + 0.221709i
\(559\) 2.85481 0.120746
\(560\) −10.0343 29.6973i −0.424025 1.25494i
\(561\) 10.1214 0.427324
\(562\) 0.0709362 0.244430i 0.00299226 0.0103107i
\(563\) 7.08426 7.08426i 0.298566 0.298566i −0.541886 0.840452i \(-0.682290\pi\)
0.840452 + 0.541886i \(0.182290\pi\)
\(564\) −13.9918 8.86799i −0.589159 0.373410i
\(565\) 33.4427 + 3.86799i 1.40694 + 0.162728i
\(566\) −9.48601 17.2431i −0.398727 0.724780i
\(567\) −2.47817 2.47817i −0.104073 0.104073i
\(568\) −7.96832 9.02235i −0.334343 0.378569i
\(569\) 46.2427i 1.93860i 0.245890 + 0.969298i \(0.420920\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(570\) −14.4507 6.06883i −0.605273 0.254195i
\(571\) 31.2381i 1.30727i 0.756808 + 0.653637i \(0.226758\pi\)
−0.756808 + 0.653637i \(0.773242\pi\)
\(572\) −3.03669 + 0.680641i −0.126970 + 0.0284590i
\(573\) −15.2920 15.2920i −0.638833 0.638833i
\(574\) 11.8407 6.51399i 0.494222 0.271889i
\(575\) 3.35544 + 5.41074i 0.139932 + 0.225643i
\(576\) −7.93866 0.988770i −0.330778 0.0411988i
\(577\) 1.16131 1.16131i 0.0483461 0.0483461i −0.682520 0.730866i \(-0.739116\pi\)
0.730866 + 0.682520i \(0.239116\pi\)
\(578\) 7.91729 + 2.29768i 0.329316 + 0.0955709i
\(579\) 16.3559 0.679727
\(580\) −1.64807 15.5864i −0.0684326 0.647192i
\(581\) −0.990671 −0.0411000
\(582\) −12.9381 3.75479i −0.536303 0.155641i
\(583\) 9.51293 9.51293i 0.393985 0.393985i
\(584\) −37.0594 2.29902i −1.53353 0.0951341i
\(585\) −0.132007 + 1.14134i −0.00545783 + 0.0471884i
\(586\) 27.8060 15.2970i 1.14866 0.631915i
\(587\) −23.6268 23.6268i −0.975183 0.975183i 0.0245164 0.999699i \(-0.492195\pi\)
−0.999699 + 0.0245164i \(0.992195\pi\)
\(588\) −2.31077 10.3096i −0.0952947 0.425159i
\(589\) 19.1120i 0.787498i
\(590\) 10.3859 + 25.4255i 0.427579 + 1.04675i
\(591\) 13.3276i 0.548223i
\(592\) −1.93460 0.693949i −0.0795115 0.0285211i
\(593\) −0.260625 0.260625i −0.0107026 0.0107026i 0.701735 0.712438i \(-0.252409\pi\)
−0.712438 + 0.701735i \(0.752409\pi\)
\(594\) 2.06429 + 3.75233i 0.0846988 + 0.153960i
\(595\) 20.5259 16.2701i 0.841479 0.667007i
\(596\) 6.19632 9.77644i 0.253811 0.400458i
\(597\) −7.78734 + 7.78734i −0.318714 + 0.318714i
\(598\) −0.257887 + 0.888619i −0.0105458 + 0.0363383i
\(599\) 33.0851 1.35182 0.675910 0.736984i \(-0.263751\pi\)
0.675910 + 0.736984i \(0.263751\pi\)
\(600\) 13.5425 + 4.07451i 0.552869 + 0.166341i
\(601\) −24.3200 −0.992033 −0.496016 0.868313i \(-0.665204\pi\)
−0.496016 + 0.868313i \(0.665204\pi\)
\(602\) 7.67501 26.4464i 0.312810 1.07787i
\(603\) −3.92870 + 3.92870i −0.159989 + 0.159989i
\(604\) −19.3479 + 30.5267i −0.787253 + 1.24211i
\(605\) −3.20565 + 2.54099i −0.130328 + 0.103306i
\(606\) −3.94502 7.17101i −0.160255 0.291302i
\(607\) 4.53347 + 4.53347i 0.184008 + 0.184008i 0.793100 0.609092i \(-0.208466\pi\)
−0.609092 + 0.793100i \(0.708466\pi\)
\(608\) −27.6857 + 4.42639i −1.12280 + 0.179514i
\(609\) 12.2827i 0.497719i
\(610\) −18.2864 44.7667i −0.740396 1.81255i
\(611\) 4.25583i 0.172173i
\(612\) −1.46199 6.52267i −0.0590972 0.263663i
\(613\) −20.2793 20.2793i −0.819073 0.819073i 0.166901 0.985974i \(-0.446624\pi\)
−0.985974 + 0.166901i \(0.946624\pi\)
\(614\) 13.6415 7.50466i 0.550526 0.302864i
\(615\) −0.700510 + 6.05661i −0.0282473 + 0.244226i
\(616\) −1.85866 + 29.9611i −0.0748877 + 1.20717i
\(617\) 17.1086 17.1086i 0.688768 0.688768i −0.273192 0.961960i \(-0.588079\pi\)
0.961960 + 0.273192i \(0.0880793\pi\)
\(618\) 25.1453 + 7.29742i 1.01149 + 0.293545i
\(619\) −29.4373 −1.18319 −0.591593 0.806237i \(-0.701501\pi\)
−0.591593 + 0.806237i \(0.701501\pi\)
\(620\) −1.81333 17.1493i −0.0728249 0.688732i
\(621\) 1.27334 0.0510975
\(622\) −9.58583 2.78191i −0.384357 0.111544i
\(623\) 10.6132 10.6132i 0.425209 0.425209i
\(624\) 0.877272 + 1.85866i 0.0351190 + 0.0744061i
\(625\) −22.3947 11.1120i −0.895788 0.444481i
\(626\) −19.8037 + 10.8947i −0.791514 + 0.435439i
\(627\) 10.6132 + 10.6132i 0.423850 + 0.423850i
\(628\) 10.8172 2.42456i 0.431653 0.0967503i
\(629\) 1.71733i 0.0684743i
\(630\) 10.2182 + 4.29131i 0.407102 + 0.170970i
\(631\) 5.25710i 0.209282i −0.994510 0.104641i \(-0.966631\pi\)
0.994510 0.104641i \(-0.0333693\pi\)
\(632\) −0.847487 + 0.748480i −0.0337112 + 0.0297729i
\(633\) 19.7873 + 19.7873i 0.786476 + 0.786476i
\(634\) −18.7746 34.1273i −0.745635 1.35537i
\(635\) 5.58423 + 0.645875i 0.221604 + 0.0256308i
\(636\) −7.50466 4.75646i −0.297579 0.188606i
\(637\) −1.91934 + 1.91934i −0.0760472 + 0.0760472i
\(638\) −4.18326 + 14.4146i −0.165617 + 0.570679i
\(639\) 4.25583 0.168358
\(640\) 24.4225 6.59860i 0.965384 0.260833i
\(641\) 20.0773 0.793004 0.396502 0.918034i \(-0.370224\pi\)
0.396502 + 0.918034i \(0.370224\pi\)
\(642\) −5.41413 + 18.6559i −0.213679 + 0.736289i
\(643\) 9.28480 9.28480i 0.366157 0.366157i −0.499917 0.866073i \(-0.666636\pi\)
0.866073 + 0.499917i \(0.166636\pi\)
\(644\) 7.53866 + 4.77801i 0.297065 + 0.188280i
\(645\) 7.71733 + 9.73599i 0.303869 + 0.383354i
\(646\) −11.2920 20.5259i −0.444278 0.807580i
\(647\) −28.7387 28.7387i −1.12983 1.12983i −0.990204 0.139630i \(-0.955409\pi\)
−0.139630 0.990204i \(-0.544591\pi\)
\(648\) 2.12000 1.87233i 0.0832813 0.0735520i
\(649\) 26.3013i 1.03242i
\(650\) −0.978383 3.49907i −0.0383753 0.137245i
\(651\) 13.5142i 0.529665i
\(652\) 8.90963 1.99700i 0.348928 0.0782084i
\(653\) −11.9380 11.9380i −0.467170 0.467170i 0.433826 0.900996i \(-0.357163\pi\)
−0.900996 + 0.433826i \(0.857163\pi\)
\(654\) 12.9641 7.13201i 0.506937 0.278884i
\(655\) −25.2772 31.8891i −0.987663 1.24601i
\(656\) 4.65533 + 9.86318i 0.181760 + 0.385093i
\(657\) 9.28267 9.28267i 0.362152 0.362152i
\(658\) 39.4251 + 11.4416i 1.53695 + 0.446039i
\(659\) 17.9963 0.701038 0.350519 0.936556i \(-0.386005\pi\)
0.350519 + 0.936556i \(0.386005\pi\)
\(660\) −10.5302 8.51629i −0.409888 0.331496i
\(661\) −9.06794 −0.352702 −0.176351 0.984327i \(-0.556429\pi\)
−0.176351 + 0.984327i \(0.556429\pi\)
\(662\) −20.3920 5.91798i −0.792558 0.230009i
\(663\) −1.21433 + 1.21433i −0.0471608 + 0.0471608i
\(664\) 0.0495037 0.797984i 0.00192112 0.0309678i
\(665\) 38.5840 + 4.46264i 1.49622 + 0.173054i
\(666\) 0.636672 0.350255i 0.0246705 0.0135721i
\(667\) 3.15556 + 3.15556i 0.122184 + 0.122184i
\(668\) 4.30369 + 19.2010i 0.166515 + 0.742908i
\(669\) 12.0700i 0.466654i
\(670\) 6.80310 16.1991i 0.262827 0.625826i
\(671\) 46.3089i 1.78773i
\(672\) 19.5767 3.12993i 0.755189 0.120740i
\(673\) 35.7640 + 35.7640i 1.37860 + 1.37860i 0.846988 + 0.531611i \(0.178413\pi\)
0.531611 + 0.846988i \(0.321587\pi\)
\(674\) 20.8074 + 37.8223i 0.801470 + 1.45686i
\(675\) −4.24924 + 2.63514i −0.163553 + 0.101427i
\(676\) −13.6360 + 21.5147i −0.524462 + 0.827487i
\(677\) 16.2020 16.2020i 0.622694 0.622694i −0.323525 0.946219i \(-0.604868\pi\)
0.946219 + 0.323525i \(0.104868\pi\)
\(678\) −5.93431 + 20.4483i −0.227906 + 0.785312i
\(679\) 33.3859 1.28123
\(680\) 12.0798 + 17.3466i 0.463240 + 0.665211i
\(681\) 1.45331 0.0556911
\(682\) −4.60272 + 15.8599i −0.176247 + 0.607308i
\(683\) −33.3943 + 33.3943i −1.27780 + 1.27780i −0.335897 + 0.941899i \(0.609039\pi\)
−0.941899 + 0.335897i \(0.890961\pi\)
\(684\) 5.30660 8.37266i 0.202903 0.320137i
\(685\) 2.15066 18.5946i 0.0821727 0.710465i
\(686\) −4.10270 7.45763i −0.156642 0.284734i
\(687\) −6.25649 6.25649i −0.238700 0.238700i
\(688\) 20.9190 + 7.50373i 0.797528 + 0.286077i
\(689\) 2.28267i 0.0869629i
\(690\) −3.72766 + 1.52269i −0.141910 + 0.0579677i
\(691\) 24.6365i 0.937216i −0.883406 0.468608i \(-0.844756\pi\)
0.883406 0.468608i \(-0.155244\pi\)
\(692\) −0.388082 1.73143i −0.0147527 0.0658193i
\(693\) −7.50466 7.50466i −0.285079 0.285079i
\(694\) 29.7843 16.3854i 1.13060 0.621980i
\(695\) −21.7534 + 17.2431i −0.825154 + 0.654067i
\(696\) 9.89367 + 0.613763i 0.375019 + 0.0232646i
\(697\) −6.44398 + 6.44398i −0.244083 + 0.244083i
\(698\) 5.95611 + 1.72853i 0.225442 + 0.0654256i
\(699\) −6.94381 −0.262639
\(700\) −35.0450 0.343541i −1.32457 0.0129846i
\(701\) −23.0420 −0.870285 −0.435143 0.900362i \(-0.643302\pi\)
−0.435143 + 0.900362i \(0.643302\pi\)
\(702\) −0.697863 0.202527i −0.0263391 0.00764389i
\(703\) 1.80078 1.80078i 0.0679177 0.0679177i
\(704\) −24.0407 2.99430i −0.906068 0.112852i
\(705\) −14.5140 + 11.5047i −0.546629 + 0.433291i
\(706\) −4.60398 + 2.53281i −0.173273 + 0.0953235i
\(707\) 14.3420 + 14.3420i 0.539387 + 0.539387i
\(708\) −16.9498 + 3.79911i −0.637012 + 0.142779i
\(709\) 37.7360i 1.41720i 0.705608 + 0.708602i \(0.250674\pi\)
−0.705608 + 0.708602i \(0.749326\pi\)
\(710\) −12.4588 + 5.08920i −0.467570 + 0.190994i
\(711\) 0.399759i 0.0149921i
\(712\) 8.01857 + 9.07925i 0.300509 + 0.340259i
\(713\) 3.47197 + 3.47197i 0.130026 + 0.130026i
\(714\) 7.98465 + 14.5140i 0.298818 + 0.543173i
\(715\) −0.399759 + 3.45632i −0.0149501 + 0.129259i
\(716\) −15.1016 9.57143i −0.564374 0.357701i
\(717\) −13.4533 + 13.4533i −0.502423 + 0.502423i
\(718\) 13.7936 47.5296i 0.514772 1.77379i
\(719\) −41.3423 −1.54181 −0.770903 0.636953i \(-0.780195\pi\)
−0.770903 + 0.636953i \(0.780195\pi\)
\(720\) −3.96724 + 8.01630i −0.147850 + 0.298750i
\(721\) −64.8853 −2.41646
\(722\) 2.19362 7.55871i 0.0816380 0.281306i
\(723\) 2.05529 2.05529i 0.0764372 0.0764372i
\(724\) 1.70504 + 1.08066i 0.0633673 + 0.0401623i
\(725\) −17.0607 4.00000i −0.633618 0.148556i
\(726\) −1.24701 2.26673i −0.0462808 0.0841264i
\(727\) −9.48981 9.48981i −0.351958 0.351958i 0.508880 0.860838i \(-0.330060\pi\)
−0.860838 + 0.508880i \(0.830060\pi\)
\(728\) −3.37165 3.81765i −0.124962 0.141491i
\(729\) 1.00000i 0.0370370i
\(730\) −16.0743 + 38.2750i −0.594935 + 1.41662i
\(731\) 18.5696i 0.686821i
\(732\) 29.8435 6.68911i 1.10305 0.247237i
\(733\) 3.21134 + 3.21134i 0.118614 + 0.118614i 0.763922 0.645308i \(-0.223271\pi\)
−0.645308 + 0.763922i \(0.723271\pi\)
\(734\) 17.4108 9.57830i 0.642646 0.353542i
\(735\) −11.7342 1.35718i −0.432822 0.0500604i
\(736\) −4.22538 + 5.83362i −0.155750 + 0.215030i
\(737\) −11.8973 + 11.8973i −0.438243 + 0.438243i
\(738\) −3.70328 1.07473i −0.136320 0.0395614i
\(739\) −25.3832 −0.933737 −0.466868 0.884327i \(-0.654618\pi\)
−0.466868 + 0.884327i \(0.654618\pi\)
\(740\) −1.44499 + 1.78670i −0.0531189 + 0.0656804i
\(741\) −2.54669 −0.0935549
\(742\) 21.1462 + 6.13684i 0.776300 + 0.225290i
\(743\) 32.7400 32.7400i 1.20111 1.20111i 0.227285 0.973828i \(-0.427015\pi\)
0.973828 0.227285i \(-0.0729850\pi\)
\(744\) 10.8857 + 0.675305i 0.399089 + 0.0247579i
\(745\) −8.03863 10.1413i −0.294513 0.371550i
\(746\) −12.4240 + 6.83488i −0.454875 + 0.250243i
\(747\) 0.199879 + 0.199879i 0.00731321 + 0.00731321i
\(748\) −4.42734 19.7526i −0.161880 0.722228i
\(749\) 48.1400i 1.75900i
\(750\) 9.28832 12.7956i 0.339161 0.467229i
\(751\) 24.4810i 0.893323i −0.894703 0.446662i \(-0.852613\pi\)
0.894703 0.446662i \(-0.147387\pi\)
\(752\) −11.1862 + 31.1851i −0.407920 + 1.13720i
\(753\) 1.96137 + 1.96137i 0.0714762 + 0.0714762i
\(754\) −1.22753 2.23132i −0.0447039 0.0812599i
\(755\) 25.1005 + 31.6661i 0.913499 + 1.15245i
\(756\) −3.75233 + 5.92036i −0.136471 + 0.215322i
\(757\) 22.9473 22.9473i 0.834035 0.834035i −0.154031 0.988066i \(-0.549226\pi\)
0.988066 + 0.154031i \(0.0492256\pi\)
\(758\) 11.8400 40.7980i 0.430048 1.48185i
\(759\) 3.85607 0.139967
\(760\) −5.52269 + 30.8563i −0.200329 + 1.11928i
\(761\) 37.0466 1.34294 0.671470 0.741032i \(-0.265663\pi\)
0.671470 + 0.741032i \(0.265663\pi\)
\(762\) −0.990907 + 3.41444i −0.0358968 + 0.123692i
\(763\) −25.9282 + 25.9282i −0.938665 + 0.938665i
\(764\) −23.1544 + 36.5327i −0.837698 + 1.32170i
\(765\) −7.42401 0.858664i −0.268416 0.0310451i
\(766\) 11.4847 + 20.8761i 0.414959 + 0.754286i
\(767\) 3.15556 + 3.15556i 0.113941 + 0.113941i
\(768\) 1.54291 + 15.9254i 0.0556749 + 0.574660i
\(769\) 6.62395i 0.238866i −0.992842 0.119433i \(-0.961892\pi\)
0.992842 0.119433i \(-0.0381077\pi\)
\(770\) 30.9438 + 12.9954i 1.11514 + 0.468322i
\(771\) 2.94249i 0.105971i
\(772\) −7.15447 31.9198i −0.257495 1.14882i
\(773\) 16.2606 + 16.2606i 0.584854 + 0.584854i 0.936233 0.351379i \(-0.114287\pi\)
−0.351379 + 0.936233i \(0.614287\pi\)
\(774\) −6.88438 + 3.78734i −0.247454 + 0.136133i
\(775\) −18.7713 4.40108i −0.674287 0.158091i
\(776\) −1.66829 + 26.8922i −0.0598880 + 0.965375i
\(777\) −1.27334 + 1.27334i −0.0456809 + 0.0456809i
\(778\) −22.1845 6.43817i −0.795352 0.230819i
\(779\) −13.5142 −0.484198
\(780\) 2.28515 0.241626i 0.0818215 0.00865162i
\(781\) 12.8880 0.461168
\(782\) −5.78017 1.67747i −0.206698 0.0599860i
\(783\) −2.47817 + 2.47817i −0.0885626 + 0.0885626i
\(784\) −19.1091 + 9.01932i −0.682468 + 0.322118i
\(785\) 1.42401 12.3120i 0.0508250 0.439433i
\(786\) 22.5490 12.4050i 0.804296 0.442471i
\(787\) 31.2117 + 31.2117i 1.11258 + 1.11258i 0.992801 + 0.119776i \(0.0382177\pi\)
0.119776 + 0.992801i \(0.461782\pi\)
\(788\) 26.0098 5.82981i 0.926560 0.207678i
\(789\) 6.72666i 0.239475i
\(790\) 0.478039 + 1.17028i 0.0170079 + 0.0416366i
\(791\) 52.7652i 1.87612i
\(792\) 6.42000 5.66999i 0.228125 0.201474i
\(793\) −5.55602 5.55602i −0.197300 0.197300i
\(794\) 18.5021 + 33.6320i 0.656615 + 1.19355i
\(795\) −7.78477 + 6.17068i −0.276097 + 0.218851i
\(796\) 18.6040 + 11.7912i 0.659401 + 0.417929i
\(797\) 17.3540 17.3540i 0.614710 0.614710i −0.329460 0.944170i \(-0.606867\pi\)
0.944170 + 0.329460i \(0.106867\pi\)
\(798\) −6.84663 + 23.5919i −0.242368 + 0.835146i
\(799\) −27.6828 −0.979346
\(800\) 2.02791 28.2115i 0.0716976 0.997426i
\(801\) −4.28267 −0.151321
\(802\) 10.4709 36.0804i 0.369741 1.27404i
\(803\) 28.1108 28.1108i 0.992008 0.992008i
\(804\) 9.38567 + 5.94865i 0.331007 + 0.209793i
\(805\) 7.82003 6.19863i 0.275620 0.218473i
\(806\) −1.35061 2.45505i −0.0475732 0.0864756i
\(807\) −15.3334 15.3334i −0.539760 0.539760i
\(808\) −12.2691 + 10.8358i −0.431627 + 0.381202i
\(809\) 27.4320i 0.964458i −0.876045 0.482229i \(-0.839827\pi\)
0.876045 0.482229i \(-0.160173\pi\)
\(810\) −1.19582 2.92746i −0.0420167 0.102860i
\(811\) 27.1840i 0.954559i −0.878751 0.477280i \(-0.841623\pi\)
0.878751 0.477280i \(-0.158377\pi\)
\(812\) −23.9706 + 5.37275i −0.841203 + 0.188547i
\(813\) 2.23132 + 2.23132i 0.0782558 + 0.0782558i
\(814\) 1.92804 1.06068i 0.0675777 0.0371768i
\(815\) 1.17289 10.1408i 0.0410846 0.355217i
\(816\) −12.0900 + 5.70636i −0.423234 + 0.199762i
\(817\) −19.4720 + 19.4720i −0.681238 + 0.681238i
\(818\) −34.4905 10.0095i −1.20593 0.349974i
\(819\) 1.80078 0.0629243
\(820\) 12.1264 1.28221i 0.423471 0.0447769i
\(821\) 23.6074 0.823903 0.411951 0.911206i \(-0.364847\pi\)
0.411951 + 0.911206i \(0.364847\pi\)
\(822\) 11.3696 + 3.29957i 0.396560 + 0.115086i
\(823\) −24.6596 + 24.6596i −0.859579 + 0.859579i −0.991288 0.131709i \(-0.957954\pi\)
0.131709 + 0.991288i \(0.457954\pi\)
\(824\) 3.24231 52.2650i 0.112951 1.82074i
\(825\) −12.8680 + 7.98002i −0.448006 + 0.277829i
\(826\) 37.7160 20.7489i 1.31231 0.721946i
\(827\) 13.5406 + 13.5406i 0.470854 + 0.470854i 0.902191 0.431337i \(-0.141958\pi\)
−0.431337 + 0.902191i \(0.641958\pi\)
\(828\) −0.556993 2.48503i −0.0193568 0.0863608i
\(829\) 9.00933i 0.312907i 0.987685 + 0.156453i \(0.0500061\pi\)
−0.987685 + 0.156453i \(0.949994\pi\)
\(830\) −0.824158 0.346120i −0.0286070 0.0120140i
\(831\) 4.99779i 0.173371i
\(832\) 3.24359 2.52509i 0.112451 0.0875418i
\(833\) −12.4847 12.4847i −0.432569 0.432569i
\(834\) −8.46216 15.3820i −0.293021 0.532635i
\(835\) 21.8543 + 2.52768i 0.756299 + 0.0874738i
\(836\) 16.0700 25.3550i 0.555793 0.876920i
\(837\) −2.72666 + 2.72666i −0.0942470 + 0.0942470i
\(838\) −15.7973 + 54.4340i −0.545709 + 1.88039i
\(839\) 10.2597 0.354203 0.177102 0.984193i \(-0.443328\pi\)
0.177102 + 0.984193i \(0.443328\pi\)
\(840\) 3.90513 21.8187i 0.134740 0.752818i
\(841\) 16.7173 0.576460
\(842\) 7.64455 26.3414i 0.263449 0.907785i
\(843\) 0.127258 0.127258i 0.00438298 0.00438298i
\(844\) 29.9611 47.2720i 1.03130 1.62717i
\(845\) 17.6903 + 22.3177i 0.608566 + 0.767751i
\(846\) −5.64600 10.2629i −0.194113 0.352847i
\(847\) 4.53347 + 4.53347i 0.155772 + 0.155772i
\(848\) −5.99988 + 16.7265i −0.206037 + 0.574392i
\(849\) 13.9160i 0.477594i
\(850\) 22.7603 6.36405i 0.780672 0.218285i
\(851\) 0.654274i 0.0224282i
\(852\) −1.86161 8.30559i −0.0637777 0.284545i
\(853\) 17.1086 + 17.1086i 0.585789 + 0.585789i 0.936488 0.350699i \(-0.114056\pi\)
−0.350699 + 0.936488i \(0.614056\pi\)
\(854\) −66.4067 + 36.5327i −2.27239 + 1.25012i
\(855\) −6.88438 8.68516i −0.235441 0.297026i
\(856\) 38.7767 + 2.40555i 1.32536 + 0.0822200i
\(857\) −26.7674 + 26.7674i −0.914356 + 0.914356i −0.996611 0.0822556i \(-0.973788\pi\)
0.0822556 + 0.996611i \(0.473788\pi\)
\(858\) −2.11334 0.613314i −0.0721483 0.0209382i
\(859\) 28.6378 0.977109 0.488554 0.872533i \(-0.337524\pi\)
0.488554 + 0.872533i \(0.337524\pi\)
\(860\) 15.6248 19.3197i 0.532801 0.658798i
\(861\) 9.55602 0.325668
\(862\) −21.4918 6.23716i −0.732015 0.212438i
\(863\) 15.8157 15.8157i 0.538371 0.538371i −0.384679 0.923050i \(-0.625688\pi\)
0.923050 + 0.384679i \(0.125688\pi\)
\(864\) −4.58134 3.31834i −0.155860 0.112892i
\(865\) −1.97070 0.227931i −0.0670057 0.00774990i
\(866\) −37.0116 + 20.3614i −1.25771 + 0.691908i
\(867\) 4.12198 + 4.12198i 0.139990 + 0.139990i
\(868\) −26.3741 + 5.91147i −0.895196 + 0.200648i
\(869\) 1.21059i 0.0410665i
\(870\) 4.29131 10.2182i 0.145489 0.346429i
\(871\) 2.85481i 0.0967316i
\(872\) −19.5895 22.1808i −0.663384 0.751135i
\(873\) −6.73599 6.73599i −0.227979 0.227979i
\(874\) −4.30207 7.82003i −0.145520 0.264516i
\(875\) −13.2681 + 36.8686i −0.448545 + 1.24638i
\(876\) −22.1763 14.0554i −0.749269 0.474888i
\(877\) −17.3727 + 17.3727i −0.586633 + 0.586633i −0.936718 0.350085i \(-0.886153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(878\) 2.60612 8.98009i 0.0879522 0.303063i
\(879\) 22.4407 0.756907
\(880\) −12.0140 + 24.2758i −0.404993 + 0.818337i
\(881\) 56.5254 1.90439 0.952194 0.305493i \(-0.0988211\pi\)
0.952194 + 0.305493i \(0.0988211\pi\)
\(882\) 2.08220 7.17480i 0.0701114 0.241588i
\(883\) 15.1962 15.1962i 0.511392 0.511392i −0.403561 0.914953i \(-0.632228\pi\)
0.914953 + 0.403561i \(0.132228\pi\)
\(884\) 2.90105 + 1.83869i 0.0975728 + 0.0618418i
\(885\) −2.23132 + 19.2920i −0.0750050 + 0.648494i
\(886\) 14.0187 + 25.4822i 0.470966 + 0.856092i
\(887\) 11.0676 + 11.0676i 0.371613 + 0.371613i 0.868065 0.496451i \(-0.165364\pi\)
−0.496451 + 0.868065i \(0.665364\pi\)
\(888\) −0.962047 1.08930i −0.0322842 0.0365547i
\(889\) 8.81070i 0.295501i
\(890\) 12.5374 5.12129i 0.420253 0.171666i
\(891\) 3.02831i 0.101452i
\(892\) −23.5556 + 5.27973i −0.788699 + 0.176778i
\(893\) −29.0280 29.0280i −0.971385 0.971385i
\(894\) 7.17101 3.94502i 0.239834 0.131941i
\(895\) −15.6653 + 12.4172i −0.523633 + 0.415063i
\(896\) −14.6717 36.8364i −0.490146 1.23062i
\(897\) −0.462642 + 0.462642i −0.0154472 + 0.0154472i
\(898\) −45.6510 13.2484i −1.52339 0.442105i
\(899\) −13.5142 −0.450725
\(900\) 7.00141 + 7.14004i 0.233380 + 0.238001i
\(901\) −14.8480 −0.494659
\(902\) −11.2147 3.25461i −0.373407 0.108367i
\(903\) 13.7688 13.7688i 0.458196 0.458196i
\(904\) 42.5023 + 2.63667i 1.41361 + 0.0876944i
\(905\) 1.76868 1.40196i 0.0587929 0.0466028i
\(906\) −22.3913 + 12.3182i −0.743902 + 0.409246i
\(907\) 28.1654 + 28.1654i 0.935217 + 0.935217i 0.998026 0.0628084i \(-0.0200057\pi\)
−0.0628084 + 0.998026i \(0.520006\pi\)
\(908\) −0.635716 2.83625i −0.0210970 0.0941244i
\(909\) 5.78734i 0.191954i
\(910\) −5.27171 + 2.15340i −0.174755 + 0.0713846i
\(911\) 34.8499i 1.15463i 0.816522 + 0.577315i \(0.195899\pi\)
−0.816522 + 0.577315i \(0.804101\pi\)
\(912\) −18.6611 6.69383i −0.617932 0.221655i
\(913\) 0.605296 + 0.605296i 0.0200324 + 0.0200324i
\(914\) −15.0053 27.2757i −0.496331 0.902198i
\(915\) 3.92870 33.9675i 0.129879 1.12293i
\(916\) −9.47329 + 14.9468i −0.313006 + 0.493856i
\(917\) −45.0980 + 45.0980i −1.48927 + 1.48927i
\(918\) 1.31737 4.53936i 0.0434797 0.149821i
\(919\) 21.1171 0.696590 0.348295 0.937385i \(-0.386761\pi\)
0.348295 + 0.937385i \(0.386761\pi\)
\(920\) 4.60222 + 6.60876i 0.151731 + 0.217884i
\(921\) 11.0093 0.362770
\(922\) −10.3061 + 35.5126i −0.339414 + 1.16954i
\(923\) −1.54626 + 1.54626i −0.0508959 + 0.0508959i
\(924\) −11.3632 + 17.9287i −0.373822 + 0.589810i
\(925\) 1.35400 + 2.18336i 0.0445192 + 0.0717884i
\(926\) 5.57104 + 10.1267i 0.183076 + 0.332784i
\(927\) 13.0914 + 13.0914i 0.429977 + 0.429977i
\(928\) −3.12993 19.5767i −0.102745 0.642638i
\(929\) 39.0653i 1.28169i 0.767670 + 0.640845i \(0.221416\pi\)
−0.767670 + 0.640845i \(0.778584\pi\)
\(930\) 4.72159 11.2428i 0.154827 0.368665i
\(931\) 26.1827i 0.858105i
\(932\) 3.03740 + 13.5514i 0.0994933 + 0.443891i
\(933\) −4.99067 4.99067i −0.163387 0.163387i
\(934\) −3.95181 + 2.17403i −0.129307 + 0.0711364i
\(935\) −22.4822 2.60030i −0.735246 0.0850388i
\(936\) −0.0899847 + 1.45052i −0.00294124 + 0.0474119i
\(937\) 1.82936 1.82936i 0.0597626 0.0597626i −0.676594 0.736356i \(-0.736545\pi\)
0.736356 + 0.676594i \(0.236545\pi\)
\(938\) −26.4464 7.67501i −0.863504 0.250598i
\(939\) −15.9825 −0.521569
\(940\) 28.8010 + 23.2928i 0.939387 + 0.759726i
\(941\) 1.58193 0.0515695 0.0257847 0.999668i \(-0.491792\pi\)
0.0257847 + 0.999668i \(0.491792\pi\)
\(942\) 7.52808 + 2.18473i 0.245278 + 0.0711823i
\(943\) −2.45505 + 2.45505i −0.0799476 + 0.0799476i
\(944\) 14.8285 + 31.4170i 0.482627 + 1.02254i
\(945\) 4.86799 + 6.14134i 0.158356 + 0.199778i
\(946\) −20.8480 + 11.4692i −0.677827 + 0.372896i
\(947\) 15.9429 + 15.9429i 0.518075 + 0.518075i 0.916989 0.398913i \(-0.130613\pi\)
−0.398913 + 0.916989i \(0.630613\pi\)
\(948\) −0.780161 + 0.174865i −0.0253384 + 0.00567934i
\(949\) 6.74531i 0.218962i
\(950\) 30.5396 + 17.1930i 0.990836 + 0.557814i
\(951\) 27.5423i 0.893121i
\(952\) 24.8325 21.9315i 0.804826 0.710803i
\(953\) −27.2113 27.2113i −0.881462 0.881462i 0.112221 0.993683i \(-0.464203\pi\)
−0.993683 + 0.112221i \(0.964203\pi\)
\(954\) −3.02831 5.50466i −0.0980450 0.178220i
\(955\) 30.0388 + 37.8962i 0.972033 + 1.22629i
\(956\) 32.1400 + 20.3704i 1.03948 + 0.658825i
\(957\) −7.50466 + 7.50466i −0.242591 + 0.242591i
\(958\) −0.552222 + 1.90283i −0.0178415 + 0.0614777i
\(959\) −29.3383 −0.947383
\(960\) 17.3798 + 4.23585i 0.560931 + 0.136712i
\(961\) 16.1307 0.520345
\(962\) −0.104063 + 0.358578i −0.00335513 + 0.0115610i
\(963\) −9.71281 + 9.71281i −0.312991 + 0.312991i
\(964\) −4.91011 3.11203i −0.158144 0.100232i
\(965\) −36.3306 4.20202i −1.16952 0.135268i
\(966\) 3.04202 + 5.52960i 0.0978755 + 0.177912i
\(967\) −14.8921 14.8921i −0.478899 0.478899i 0.425880 0.904780i \(-0.359964\pi\)
−0.904780 + 0.425880i \(0.859964\pi\)
\(968\) −3.87824 + 3.42516i −0.124651 + 0.110089i
\(969\) 16.5653i 0.532156i
\(970\) 27.7743 + 11.6643i 0.891780 + 0.374519i
\(971\) 41.6250i 1.33581i −0.744246 0.667905i \(-0.767191\pi\)
0.744246 0.667905i \(-0.232809\pi\)
\(972\) 1.95158 0.437425i 0.0625969 0.0140304i
\(973\) 30.7640 + 30.7640i 0.986248 + 0.986248i
\(974\) −1.71403 + 0.942949i −0.0549212 + 0.0302140i
\(975\) 0.586446 2.50129i 0.0187813 0.0801054i
\(976\) −26.1086 55.3160i −0.835717 1.77062i
\(977\) −12.0807 + 12.0807i −0.386494 + 0.386494i −0.873435 0.486941i \(-0.838113\pi\)
0.486941 + 0.873435i \(0.338113\pi\)
\(978\) 6.20054 + 1.79946i 0.198271 + 0.0575404i
\(979\) −12.9692 −0.414499
\(980\) 2.48419 + 23.4939i 0.0793544 + 0.750484i
\(981\) 10.4626 0.334046
\(982\) −49.0484 14.2343i −1.56520 0.454236i
\(983\) 22.2258 22.2258i 0.708893 0.708893i −0.257410 0.966302i \(-0.582869\pi\)
0.966302 + 0.257410i \(0.0828690\pi\)
\(984\) −0.477513 + 7.69735i −0.0152226 + 0.245383i
\(985\) 3.42401 29.6040i 0.109098 0.943261i
\(986\) 14.5140 7.98465i 0.462220 0.254283i
\(987\) 20.5259 + 20.5259i 0.653346 + 0.653346i
\(988\) 1.11399 + 4.97006i 0.0354406 + 0.158119i
\(989\) 7.07472i 0.224963i
\(990\) −3.62130 8.86525i −0.115093 0.281756i
\(991\) 0.353523i 0.0112300i −0.999984 0.00561501i \(-0.998213\pi\)
0.999984 0.00561501i \(-0.00178732\pi\)
\(992\) −3.44377 21.5397i −0.109340 0.683886i
\(993\) −10.6167 10.6167i −0.336911 0.336911i
\(994\) 10.1672 + 18.4813i 0.322484 + 0.586191i
\(995\) 19.2984 15.2970i 0.611799 0.484949i
\(996\) 0.302648 0.477513i 0.00958977 0.0151306i
\(997\) 27.9380 27.9380i 0.884805 0.884805i −0.109213 0.994018i \(-0.534833\pi\)
0.994018 + 0.109213i \(0.0348331\pi\)
\(998\) −2.50580 + 8.63442i −0.0793197 + 0.273318i
\(999\) 0.513824 0.0162567
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 60.2.j.a.43.4 yes 12
3.2 odd 2 180.2.k.e.163.3 12
4.3 odd 2 inner 60.2.j.a.43.6 yes 12
5.2 odd 4 inner 60.2.j.a.7.6 yes 12
5.3 odd 4 300.2.j.d.7.1 12
5.4 even 2 300.2.j.d.43.3 12
8.3 odd 2 960.2.w.g.703.6 12
8.5 even 2 960.2.w.g.703.3 12
12.11 even 2 180.2.k.e.163.1 12
15.2 even 4 180.2.k.e.127.1 12
15.8 even 4 900.2.k.n.307.6 12
15.14 odd 2 900.2.k.n.343.4 12
20.3 even 4 300.2.j.d.7.3 12
20.7 even 4 inner 60.2.j.a.7.4 12
20.19 odd 2 300.2.j.d.43.1 12
40.27 even 4 960.2.w.g.127.3 12
40.37 odd 4 960.2.w.g.127.6 12
60.23 odd 4 900.2.k.n.307.4 12
60.47 odd 4 180.2.k.e.127.3 12
60.59 even 2 900.2.k.n.343.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.2.j.a.7.4 12 20.7 even 4 inner
60.2.j.a.7.6 yes 12 5.2 odd 4 inner
60.2.j.a.43.4 yes 12 1.1 even 1 trivial
60.2.j.a.43.6 yes 12 4.3 odd 2 inner
180.2.k.e.127.1 12 15.2 even 4
180.2.k.e.127.3 12 60.47 odd 4
180.2.k.e.163.1 12 12.11 even 2
180.2.k.e.163.3 12 3.2 odd 2
300.2.j.d.7.1 12 5.3 odd 4
300.2.j.d.7.3 12 20.3 even 4
300.2.j.d.43.1 12 20.19 odd 2
300.2.j.d.43.3 12 5.4 even 2
900.2.k.n.307.4 12 60.23 odd 4
900.2.k.n.307.6 12 15.8 even 4
900.2.k.n.343.4 12 15.14 odd 2
900.2.k.n.343.6 12 60.59 even 2
960.2.w.g.127.3 12 40.27 even 4
960.2.w.g.127.6 12 40.37 odd 4
960.2.w.g.703.3 12 8.5 even 2
960.2.w.g.703.6 12 8.3 odd 2