Properties

Label 1110.2.o.b.253.3
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(253,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.253");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.3
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.b.487.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.26431 - 1.84432i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64144 - 1.64144i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.26431 - 1.84432i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64144 - 1.64144i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(1.26431 - 1.84432i) q^{10} -4.17593i q^{11} +(-0.707107 + 0.707107i) q^{12} -1.20051 q^{13} +(1.64144 - 1.64144i) q^{14} +(0.410132 + 2.19813i) q^{15} +1.00000 q^{16} +0.221929i q^{17} -1.00000i q^{18} +(-3.73909 - 3.73909i) q^{19} +(1.26431 - 1.84432i) q^{20} +2.32134i q^{21} -4.17593i q^{22} -4.24635 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-1.80305 - 4.66358i) q^{25} -1.20051 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.64144 - 1.64144i) q^{28} +(-5.45356 + 5.45356i) q^{29} +(0.410132 + 2.19813i) q^{30} +(1.77644 + 1.77644i) q^{31} +1.00000 q^{32} +(2.95283 + 2.95283i) q^{33} +0.221929i q^{34} +(-0.952057 - 5.10263i) q^{35} -1.00000i q^{36} +(6.07033 + 0.388773i) q^{37} +(-3.73909 - 3.73909i) q^{38} +(0.848892 - 0.848892i) q^{39} +(1.26431 - 1.84432i) q^{40} -2.58213i q^{41} +2.32134i q^{42} +7.69386 q^{43} -4.17593i q^{44} +(-1.84432 - 1.26431i) q^{45} -4.24635 q^{46} +(5.62938 - 5.62938i) q^{47} +(-0.707107 + 0.707107i) q^{48} +1.61136i q^{49} +(-1.80305 - 4.66358i) q^{50} +(-0.156927 - 0.156927i) q^{51} -1.20051 q^{52} +(-4.45920 - 4.45920i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-7.70175 - 5.27966i) q^{55} +(1.64144 - 1.64144i) q^{56} +5.28787 q^{57} +(-5.45356 + 5.45356i) q^{58} +(3.90868 + 3.90868i) q^{59} +(0.410132 + 2.19813i) q^{60} +(0.901511 + 0.901511i) q^{61} +(1.77644 + 1.77644i) q^{62} +(-1.64144 - 1.64144i) q^{63} +1.00000 q^{64} +(-1.51782 + 2.21414i) q^{65} +(2.95283 + 2.95283i) q^{66} +(10.3479 + 10.3479i) q^{67} +0.221929i q^{68} +(3.00262 - 3.00262i) q^{69} +(-0.952057 - 5.10263i) q^{70} +9.11658 q^{71} -1.00000i q^{72} +(-3.76725 + 3.76725i) q^{73} +(6.07033 + 0.388773i) q^{74} +(4.57260 + 2.02270i) q^{75} +(-3.73909 - 3.73909i) q^{76} +(-6.85453 - 6.85453i) q^{77} +(0.848892 - 0.848892i) q^{78} +(0.571724 + 0.571724i) q^{79} +(1.26431 - 1.84432i) q^{80} -1.00000 q^{81} -2.58213i q^{82} +(7.69554 + 7.69554i) q^{83} +2.32134i q^{84} +(0.409308 + 0.280587i) q^{85} +7.69386 q^{86} -7.71250i q^{87} -4.17593i q^{88} +(4.28275 - 4.28275i) q^{89} +(-1.84432 - 1.26431i) q^{90} +(-1.97057 + 1.97057i) q^{91} -4.24635 q^{92} -2.51226 q^{93} +(5.62938 - 5.62938i) q^{94} +(-11.6234 + 2.16872i) q^{95} +(-0.707107 + 0.707107i) q^{96} +8.59029i q^{97} +1.61136i q^{98} -4.17593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) 1.26431 1.84432i 0.565416 0.824806i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 1.64144 1.64144i 0.620405 0.620405i −0.325230 0.945635i \(-0.605442\pi\)
0.945635 + 0.325230i \(0.105442\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000i 0.333333i
\(10\) 1.26431 1.84432i 0.399809 0.583226i
\(11\) 4.17593i 1.25909i −0.776964 0.629545i \(-0.783241\pi\)
0.776964 0.629545i \(-0.216759\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −1.20051 −0.332963 −0.166481 0.986045i \(-0.553241\pi\)
−0.166481 + 0.986045i \(0.553241\pi\)
\(14\) 1.64144 1.64144i 0.438693 0.438693i
\(15\) 0.410132 + 2.19813i 0.105896 + 0.567556i
\(16\) 1.00000 0.250000
\(17\) 0.221929i 0.0538257i 0.999638 + 0.0269128i \(0.00856766\pi\)
−0.999638 + 0.0269128i \(0.991432\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.73909 3.73909i −0.857805 0.857805i 0.133274 0.991079i \(-0.457451\pi\)
−0.991079 + 0.133274i \(0.957451\pi\)
\(20\) 1.26431 1.84432i 0.282708 0.412403i
\(21\) 2.32134i 0.506559i
\(22\) 4.17593i 0.890311i
\(23\) −4.24635 −0.885425 −0.442713 0.896664i \(-0.645984\pi\)
−0.442713 + 0.896664i \(0.645984\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −1.80305 4.66358i −0.360610 0.932717i
\(26\) −1.20051 −0.235440
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 1.64144 1.64144i 0.310203 0.310203i
\(29\) −5.45356 + 5.45356i −1.01270 + 1.01270i −0.0127828 + 0.999918i \(0.504069\pi\)
−0.999918 + 0.0127828i \(0.995931\pi\)
\(30\) 0.410132 + 2.19813i 0.0748795 + 0.401322i
\(31\) 1.77644 + 1.77644i 0.319058 + 0.319058i 0.848405 0.529347i \(-0.177563\pi\)
−0.529347 + 0.848405i \(0.677563\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.95283 + 2.95283i 0.514021 + 0.514021i
\(34\) 0.221929i 0.0380605i
\(35\) −0.952057 5.10263i −0.160927 0.862501i
\(36\) 1.00000i 0.166667i
\(37\) 6.07033 + 0.388773i 0.997955 + 0.0639139i
\(38\) −3.73909 3.73909i −0.606560 0.606560i
\(39\) 0.848892 0.848892i 0.135932 0.135932i
\(40\) 1.26431 1.84432i 0.199905 0.291613i
\(41\) 2.58213i 0.403261i −0.979462 0.201631i \(-0.935376\pi\)
0.979462 0.201631i \(-0.0646240\pi\)
\(42\) 2.32134i 0.358191i
\(43\) 7.69386 1.17330 0.586651 0.809840i \(-0.300446\pi\)
0.586651 + 0.809840i \(0.300446\pi\)
\(44\) 4.17593i 0.629545i
\(45\) −1.84432 1.26431i −0.274935 0.188472i
\(46\) −4.24635 −0.626090
\(47\) 5.62938 5.62938i 0.821129 0.821129i −0.165141 0.986270i \(-0.552808\pi\)
0.986270 + 0.165141i \(0.0528079\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 1.61136i 0.230194i
\(50\) −1.80305 4.66358i −0.254990 0.659530i
\(51\) −0.156927 0.156927i −0.0219742 0.0219742i
\(52\) −1.20051 −0.166481
\(53\) −4.45920 4.45920i −0.612518 0.612518i 0.331084 0.943601i \(-0.392586\pi\)
−0.943601 + 0.331084i \(0.892586\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −7.70175 5.27966i −1.03850 0.711909i
\(56\) 1.64144 1.64144i 0.219346 0.219346i
\(57\) 5.28787 0.700395
\(58\) −5.45356 + 5.45356i −0.716088 + 0.716088i
\(59\) 3.90868 + 3.90868i 0.508866 + 0.508866i 0.914178 0.405312i \(-0.132837\pi\)
−0.405312 + 0.914178i \(0.632837\pi\)
\(60\) 0.410132 + 2.19813i 0.0529478 + 0.283778i
\(61\) 0.901511 + 0.901511i 0.115427 + 0.115427i 0.762461 0.647034i \(-0.223991\pi\)
−0.647034 + 0.762461i \(0.723991\pi\)
\(62\) 1.77644 + 1.77644i 0.225608 + 0.225608i
\(63\) −1.64144 1.64144i −0.206802 0.206802i
\(64\) 1.00000 0.125000
\(65\) −1.51782 + 2.21414i −0.188262 + 0.274630i
\(66\) 2.95283 + 2.95283i 0.363468 + 0.363468i
\(67\) 10.3479 + 10.3479i 1.26420 + 1.26420i 0.949038 + 0.315162i \(0.102059\pi\)
0.315162 + 0.949038i \(0.397941\pi\)
\(68\) 0.221929i 0.0269128i
\(69\) 3.00262 3.00262i 0.361473 0.361473i
\(70\) −0.952057 5.10263i −0.113793 0.609880i
\(71\) 9.11658 1.08194 0.540969 0.841042i \(-0.318058\pi\)
0.540969 + 0.841042i \(0.318058\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −3.76725 + 3.76725i −0.440923 + 0.440923i −0.892322 0.451399i \(-0.850925\pi\)
0.451399 + 0.892322i \(0.350925\pi\)
\(74\) 6.07033 + 0.388773i 0.705661 + 0.0451939i
\(75\) 4.57260 + 2.02270i 0.527998 + 0.233562i
\(76\) −3.73909 3.73909i −0.428903 0.428903i
\(77\) −6.85453 6.85453i −0.781146 0.781146i
\(78\) 0.848892 0.848892i 0.0961181 0.0961181i
\(79\) 0.571724 + 0.571724i 0.0643239 + 0.0643239i 0.738537 0.674213i \(-0.235517\pi\)
−0.674213 + 0.738537i \(0.735517\pi\)
\(80\) 1.26431 1.84432i 0.141354 0.206201i
\(81\) −1.00000 −0.111111
\(82\) 2.58213i 0.285149i
\(83\) 7.69554 + 7.69554i 0.844695 + 0.844695i 0.989465 0.144770i \(-0.0462443\pi\)
−0.144770 + 0.989465i \(0.546244\pi\)
\(84\) 2.32134i 0.253279i
\(85\) 0.409308 + 0.280587i 0.0443957 + 0.0304339i
\(86\) 7.69386 0.829650
\(87\) 7.71250i 0.826867i
\(88\) 4.17593i 0.445155i
\(89\) 4.28275 4.28275i 0.453971 0.453971i −0.442699 0.896670i \(-0.645979\pi\)
0.896670 + 0.442699i \(0.145979\pi\)
\(90\) −1.84432 1.26431i −0.194409 0.133270i
\(91\) −1.97057 + 1.97057i −0.206572 + 0.206572i
\(92\) −4.24635 −0.442713
\(93\) −2.51226 −0.260509
\(94\) 5.62938 5.62938i 0.580626 0.580626i
\(95\) −11.6234 + 2.16872i −1.19254 + 0.222506i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 8.59029i 0.872212i 0.899895 + 0.436106i \(0.143643\pi\)
−0.899895 + 0.436106i \(0.856357\pi\)
\(98\) 1.61136i 0.162772i
\(99\) −4.17593 −0.419696
\(100\) −1.80305 4.66358i −0.180305 0.466358i
\(101\) 9.72766i 0.967938i 0.875085 + 0.483969i \(0.160805\pi\)
−0.875085 + 0.483969i \(0.839195\pi\)
\(102\) −0.156927 0.156927i −0.0155381 0.0155381i
\(103\) 15.6866i 1.54565i −0.634621 0.772824i \(-0.718844\pi\)
0.634621 0.772824i \(-0.281156\pi\)
\(104\) −1.20051 −0.117720
\(105\) 4.28131 + 2.93490i 0.417813 + 0.286416i
\(106\) −4.45920 4.45920i −0.433115 0.433115i
\(107\) 1.59584 1.59584i 0.154275 0.154275i −0.625749 0.780024i \(-0.715207\pi\)
0.780024 + 0.625749i \(0.215207\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 6.35309 + 6.35309i 0.608516 + 0.608516i 0.942558 0.334042i \(-0.108413\pi\)
−0.334042 + 0.942558i \(0.608413\pi\)
\(110\) −7.70175 5.27966i −0.734333 0.503396i
\(111\) −4.56727 + 4.01746i −0.433506 + 0.381321i
\(112\) 1.64144 1.64144i 0.155101 0.155101i
\(113\) 11.7528i 1.10561i −0.833311 0.552805i \(-0.813558\pi\)
0.833311 0.552805i \(-0.186442\pi\)
\(114\) 5.28787 0.495254
\(115\) −5.36870 + 7.83164i −0.500633 + 0.730304i
\(116\) −5.45356 + 5.45356i −0.506351 + 0.506351i
\(117\) 1.20051i 0.110988i
\(118\) 3.90868 + 3.90868i 0.359823 + 0.359823i
\(119\) 0.364283 + 0.364283i 0.0333937 + 0.0333937i
\(120\) 0.410132 + 2.19813i 0.0374397 + 0.200661i
\(121\) −6.43836 −0.585306
\(122\) 0.901511 + 0.901511i 0.0816189 + 0.0816189i
\(123\) 1.82584 + 1.82584i 0.164631 + 0.164631i
\(124\) 1.77644 + 1.77644i 0.159529 + 0.159529i
\(125\) −10.8808 2.57081i −0.973205 0.229940i
\(126\) −1.64144 1.64144i −0.146231 0.146231i
\(127\) 9.18790 9.18790i 0.815295 0.815295i −0.170127 0.985422i \(-0.554418\pi\)
0.985422 + 0.170127i \(0.0544179\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.44038 + 5.44038i −0.478999 + 0.478999i
\(130\) −1.51782 + 2.21414i −0.133122 + 0.194193i
\(131\) −10.7012 10.7012i −0.934966 0.934966i 0.0630449 0.998011i \(-0.479919\pi\)
−0.998011 + 0.0630449i \(0.979919\pi\)
\(132\) 2.95283 + 2.95283i 0.257011 + 0.257011i
\(133\) −12.2750 −1.06437
\(134\) 10.3479 + 10.3479i 0.893924 + 0.893924i
\(135\) 2.19813 0.410132i 0.189185 0.0352985i
\(136\) 0.221929i 0.0190303i
\(137\) −4.35277 + 4.35277i −0.371882 + 0.371882i −0.868162 0.496280i \(-0.834699\pi\)
0.496280 + 0.868162i \(0.334699\pi\)
\(138\) 3.00262 3.00262i 0.255600 0.255600i
\(139\) 18.3422 1.55577 0.777883 0.628409i \(-0.216293\pi\)
0.777883 + 0.628409i \(0.216293\pi\)
\(140\) −0.952057 5.10263i −0.0804635 0.431251i
\(141\) 7.96114i 0.670449i
\(142\) 9.11658 0.765046
\(143\) 5.01326i 0.419230i
\(144\) 1.00000i 0.0833333i
\(145\) 3.16314 + 16.9531i 0.262685 + 1.40788i
\(146\) −3.76725 + 3.76725i −0.311780 + 0.311780i
\(147\) −1.13940 1.13940i −0.0939764 0.0939764i
\(148\) 6.07033 + 0.388773i 0.498978 + 0.0319569i
\(149\) 9.29218i 0.761245i 0.924731 + 0.380622i \(0.124290\pi\)
−0.924731 + 0.380622i \(0.875710\pi\)
\(150\) 4.57260 + 2.02270i 0.373351 + 0.165153i
\(151\) 10.0875i 0.820910i 0.911881 + 0.410455i \(0.134630\pi\)
−0.911881 + 0.410455i \(0.865370\pi\)
\(152\) −3.73909 3.73909i −0.303280 0.303280i
\(153\) 0.221929 0.0179419
\(154\) −6.85453 6.85453i −0.552353 0.552353i
\(155\) 5.52229 1.03036i 0.443561 0.0827604i
\(156\) 0.848892 0.848892i 0.0679658 0.0679658i
\(157\) −15.8215 + 15.8215i −1.26269 + 1.26269i −0.312906 + 0.949784i \(0.601302\pi\)
−0.949784 + 0.312906i \(0.898698\pi\)
\(158\) 0.571724 + 0.571724i 0.0454839 + 0.0454839i
\(159\) 6.30625 0.500119
\(160\) 1.26431 1.84432i 0.0999524 0.145806i
\(161\) −6.97012 + 6.97012i −0.549323 + 0.549323i
\(162\) −1.00000 −0.0785674
\(163\) 18.7947i 1.47212i 0.676918 + 0.736058i \(0.263315\pi\)
−0.676918 + 0.736058i \(0.736685\pi\)
\(164\) 2.58213i 0.201631i
\(165\) 9.17925 1.71268i 0.714603 0.133332i
\(166\) 7.69554 + 7.69554i 0.597290 + 0.597290i
\(167\) 14.4189i 1.11577i −0.829920 0.557883i \(-0.811614\pi\)
0.829920 0.557883i \(-0.188386\pi\)
\(168\) 2.32134i 0.179096i
\(169\) −11.5588 −0.889136
\(170\) 0.409308 + 0.280587i 0.0313925 + 0.0215200i
\(171\) −3.73909 + 3.73909i −0.285935 + 0.285935i
\(172\) 7.69386 0.586651
\(173\) 13.9023 13.9023i 1.05697 1.05697i 0.0586938 0.998276i \(-0.481306\pi\)
0.998276 0.0586938i \(-0.0186935\pi\)
\(174\) 7.71250i 0.584683i
\(175\) −10.6146 4.69539i −0.802387 0.354938i
\(176\) 4.17593i 0.314772i
\(177\) −5.52770 −0.415487
\(178\) 4.28275 4.28275i 0.321006 0.321006i
\(179\) −11.4245 + 11.4245i −0.853906 + 0.853906i −0.990612 0.136705i \(-0.956349\pi\)
0.136705 + 0.990612i \(0.456349\pi\)
\(180\) −1.84432 1.26431i −0.137468 0.0942360i
\(181\) −18.4010 −1.36774 −0.683869 0.729605i \(-0.739704\pi\)
−0.683869 + 0.729605i \(0.739704\pi\)
\(182\) −1.97057 + 1.97057i −0.146068 + 0.146068i
\(183\) −1.27493 −0.0942454
\(184\) −4.24635 −0.313045
\(185\) 8.39179 10.7041i 0.616976 0.786982i
\(186\) −2.51226 −0.184208
\(187\) 0.926759 0.0677713
\(188\) 5.62938 5.62938i 0.410565 0.410565i
\(189\) 2.32134 0.168853
\(190\) −11.6234 + 2.16872i −0.843253 + 0.157336i
\(191\) −3.52951 + 3.52951i −0.255386 + 0.255386i −0.823175 0.567788i \(-0.807799\pi\)
0.567788 + 0.823175i \(0.307799\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 9.24953 0.665796 0.332898 0.942963i \(-0.391974\pi\)
0.332898 + 0.942963i \(0.391974\pi\)
\(194\) 8.59029i 0.616747i
\(195\) −0.492369 2.63889i −0.0352593 0.188975i
\(196\) 1.61136i 0.115097i
\(197\) −1.75235 + 1.75235i −0.124850 + 0.124850i −0.766771 0.641921i \(-0.778138\pi\)
0.641921 + 0.766771i \(0.278138\pi\)
\(198\) −4.17593 −0.296770
\(199\) −1.94022 + 1.94022i −0.137538 + 0.137538i −0.772524 0.634986i \(-0.781006\pi\)
0.634986 + 0.772524i \(0.281006\pi\)
\(200\) −1.80305 4.66358i −0.127495 0.329765i
\(201\) −14.6342 −1.03222
\(202\) 9.72766i 0.684436i
\(203\) 17.9034i 1.25657i
\(204\) −0.156927 0.156927i −0.0109871 0.0109871i
\(205\) −4.76228 3.26461i −0.332612 0.228010i
\(206\) 15.6866i 1.09294i
\(207\) 4.24635i 0.295142i
\(208\) −1.20051 −0.0832407
\(209\) −15.6141 + 15.6141i −1.08005 + 1.08005i
\(210\) 4.28131 + 2.93490i 0.295438 + 0.202527i
\(211\) −4.88849 −0.336538 −0.168269 0.985741i \(-0.553818\pi\)
−0.168269 + 0.985741i \(0.553818\pi\)
\(212\) −4.45920 4.45920i −0.306259 0.306259i
\(213\) −6.44639 + 6.44639i −0.441700 + 0.441700i
\(214\) 1.59584 1.59584i 0.109089 0.109089i
\(215\) 9.72741 14.1899i 0.663404 0.967746i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 5.83183 0.395890
\(218\) 6.35309 + 6.35309i 0.430285 + 0.430285i
\(219\) 5.32769i 0.360012i
\(220\) −7.70175 5.27966i −0.519252 0.355955i
\(221\) 0.266429i 0.0179219i
\(222\) −4.56727 + 4.01746i −0.306535 + 0.269635i
\(223\) 16.9445 + 16.9445i 1.13469 + 1.13469i 0.989388 + 0.145300i \(0.0464147\pi\)
0.145300 + 0.989388i \(0.453585\pi\)
\(224\) 1.64144 1.64144i 0.109673 0.109673i
\(225\) −4.66358 + 1.80305i −0.310906 + 0.120203i
\(226\) 11.7528i 0.781784i
\(227\) 22.8426i 1.51612i −0.652187 0.758058i \(-0.726148\pi\)
0.652187 0.758058i \(-0.273852\pi\)
\(228\) 5.28787 0.350197
\(229\) 16.1156i 1.06495i 0.846446 + 0.532474i \(0.178738\pi\)
−0.846446 + 0.532474i \(0.821262\pi\)
\(230\) −5.36870 + 7.83164i −0.354001 + 0.516403i
\(231\) 9.69376 0.637803
\(232\) −5.45356 + 5.45356i −0.358044 + 0.358044i
\(233\) −3.66171 + 3.66171i −0.239886 + 0.239886i −0.816803 0.576917i \(-0.804256\pi\)
0.576917 + 0.816803i \(0.304256\pi\)
\(234\) 1.20051i 0.0784801i
\(235\) −3.26512 17.4997i −0.212993 1.14155i
\(236\) 3.90868 + 3.90868i 0.254433 + 0.254433i
\(237\) −0.808539 −0.0525203
\(238\) 0.364283 + 0.364283i 0.0236129 + 0.0236129i
\(239\) −2.75228 2.75228i −0.178030 0.178030i 0.612467 0.790497i \(-0.290177\pi\)
−0.790497 + 0.612467i \(0.790177\pi\)
\(240\) 0.410132 + 2.19813i 0.0264739 + 0.141889i
\(241\) −19.9398 + 19.9398i −1.28444 + 1.28444i −0.346319 + 0.938117i \(0.612569\pi\)
−0.938117 + 0.346319i \(0.887431\pi\)
\(242\) −6.43836 −0.413874
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 0.901511 + 0.901511i 0.0577133 + 0.0577133i
\(245\) 2.97187 + 2.03726i 0.189866 + 0.130156i
\(246\) 1.82584 + 1.82584i 0.116411 + 0.116411i
\(247\) 4.48883 + 4.48883i 0.285617 + 0.285617i
\(248\) 1.77644 + 1.77644i 0.112804 + 0.112804i
\(249\) −10.8831 −0.689691
\(250\) −10.8808 2.57081i −0.688160 0.162592i
\(251\) −12.4982 12.4982i −0.788880 0.788880i 0.192430 0.981311i \(-0.438363\pi\)
−0.981311 + 0.192430i \(0.938363\pi\)
\(252\) −1.64144 1.64144i −0.103401 0.103401i
\(253\) 17.7324i 1.11483i
\(254\) 9.18790 9.18790i 0.576500 0.576500i
\(255\) −0.487830 + 0.0910201i −0.0305491 + 0.00569990i
\(256\) 1.00000 0.0625000
\(257\) 23.1067i 1.44136i −0.693269 0.720679i \(-0.743830\pi\)
0.693269 0.720679i \(-0.256170\pi\)
\(258\) −5.44038 + 5.44038i −0.338703 + 0.338703i
\(259\) 10.6022 9.32592i 0.658789 0.579484i
\(260\) −1.51782 + 2.21414i −0.0941312 + 0.137315i
\(261\) 5.45356 + 5.45356i 0.337567 + 0.337567i
\(262\) −10.7012 10.7012i −0.661121 0.661121i
\(263\) 8.68658 8.68658i 0.535638 0.535638i −0.386607 0.922245i \(-0.626353\pi\)
0.922245 + 0.386607i \(0.126353\pi\)
\(264\) 2.95283 + 2.95283i 0.181734 + 0.181734i
\(265\) −13.8620 + 2.58639i −0.851535 + 0.158881i
\(266\) −12.2750 −0.752626
\(267\) 6.05673i 0.370666i
\(268\) 10.3479 + 10.3479i 0.632100 + 0.632100i
\(269\) 30.1717i 1.83960i 0.392388 + 0.919800i \(0.371649\pi\)
−0.392388 + 0.919800i \(0.628351\pi\)
\(270\) 2.19813 0.410132i 0.133774 0.0249598i
\(271\) −7.28060 −0.442265 −0.221133 0.975244i \(-0.570975\pi\)
−0.221133 + 0.975244i \(0.570975\pi\)
\(272\) 0.221929i 0.0134564i
\(273\) 2.78681i 0.168665i
\(274\) −4.35277 + 4.35277i −0.262960 + 0.262960i
\(275\) −19.4748 + 7.52940i −1.17437 + 0.454040i
\(276\) 3.00262 3.00262i 0.180737 0.180737i
\(277\) 20.3131 1.22050 0.610249 0.792210i \(-0.291069\pi\)
0.610249 + 0.792210i \(0.291069\pi\)
\(278\) 18.3422 1.10009
\(279\) 1.77644 1.77644i 0.106353 0.106353i
\(280\) −0.952057 5.10263i −0.0568963 0.304940i
\(281\) −5.88467 + 5.88467i −0.351050 + 0.351050i −0.860500 0.509450i \(-0.829849\pi\)
0.509450 + 0.860500i \(0.329849\pi\)
\(282\) 7.96114i 0.474079i
\(283\) 3.93264i 0.233771i 0.993145 + 0.116886i \(0.0372911\pi\)
−0.993145 + 0.116886i \(0.962709\pi\)
\(284\) 9.11658 0.540969
\(285\) 6.68549 9.75253i 0.396014 0.577690i
\(286\) 5.01326i 0.296440i
\(287\) −4.23841 4.23841i −0.250185 0.250185i
\(288\) 1.00000i 0.0589256i
\(289\) 16.9507 0.997103
\(290\) 3.16314 + 16.9531i 0.185746 + 0.995521i
\(291\) −6.07425 6.07425i −0.356079 0.356079i
\(292\) −3.76725 + 3.76725i −0.220461 + 0.220461i
\(293\) −3.68251 3.68251i −0.215135 0.215135i 0.591310 0.806444i \(-0.298611\pi\)
−0.806444 + 0.591310i \(0.798611\pi\)
\(294\) −1.13940 1.13940i −0.0664514 0.0664514i
\(295\) 12.1506 2.26709i 0.707437 0.131995i
\(296\) 6.07033 + 0.388773i 0.352831 + 0.0225970i
\(297\) 2.95283 2.95283i 0.171340 0.171340i
\(298\) 9.29218i 0.538281i
\(299\) 5.09780 0.294814
\(300\) 4.57260 + 2.02270i 0.263999 + 0.116781i
\(301\) 12.6290 12.6290i 0.727923 0.727923i
\(302\) 10.0875i 0.580471i
\(303\) −6.87849 6.87849i −0.395159 0.395159i
\(304\) −3.73909 3.73909i −0.214451 0.214451i
\(305\) 2.80246 0.522889i 0.160469 0.0299405i
\(306\) 0.221929 0.0126868
\(307\) −16.3345 16.3345i −0.932257 0.932257i 0.0655896 0.997847i \(-0.479107\pi\)
−0.997847 + 0.0655896i \(0.979107\pi\)
\(308\) −6.85453 6.85453i −0.390573 0.390573i
\(309\) 11.0921 + 11.0921i 0.631008 + 0.631008i
\(310\) 5.52229 1.03036i 0.313645 0.0585204i
\(311\) −0.811220 0.811220i −0.0460001 0.0460001i 0.683733 0.729733i \(-0.260355\pi\)
−0.729733 + 0.683733i \(0.760355\pi\)
\(312\) 0.848892 0.848892i 0.0480590 0.0480590i
\(313\) −3.61149 −0.204133 −0.102067 0.994778i \(-0.532546\pi\)
−0.102067 + 0.994778i \(0.532546\pi\)
\(314\) −15.8215 + 15.8215i −0.892857 + 0.892857i
\(315\) −5.10263 + 0.952057i −0.287500 + 0.0536423i
\(316\) 0.571724 + 0.571724i 0.0321620 + 0.0321620i
\(317\) 9.01704 + 9.01704i 0.506447 + 0.506447i 0.913434 0.406987i \(-0.133420\pi\)
−0.406987 + 0.913434i \(0.633420\pi\)
\(318\) 6.30625 0.353637
\(319\) 22.7737 + 22.7737i 1.27508 + 1.27508i
\(320\) 1.26431 1.84432i 0.0706770 0.103101i
\(321\) 2.25685i 0.125965i
\(322\) −6.97012 + 6.97012i −0.388430 + 0.388430i
\(323\) 0.829811 0.829811i 0.0461719 0.0461719i
\(324\) −1.00000 −0.0555556
\(325\) 2.16459 + 5.59870i 0.120070 + 0.310560i
\(326\) 18.7947i 1.04094i
\(327\) −8.98462 −0.496851
\(328\) 2.58213i 0.142574i
\(329\) 18.4806i 1.01887i
\(330\) 9.17925 1.71268i 0.505301 0.0942799i
\(331\) 2.86838 2.86838i 0.157660 0.157660i −0.623869 0.781529i \(-0.714440\pi\)
0.781529 + 0.623869i \(0.214440\pi\)
\(332\) 7.69554 + 7.69554i 0.422347 + 0.422347i
\(333\) 0.388773 6.07033i 0.0213046 0.332652i
\(334\) 14.4189i 0.788966i
\(335\) 32.1679 6.00194i 1.75752 0.327921i
\(336\) 2.32134i 0.126640i
\(337\) 2.56826 + 2.56826i 0.139902 + 0.139902i 0.773589 0.633687i \(-0.218459\pi\)
−0.633687 + 0.773589i \(0.718459\pi\)
\(338\) −11.5588 −0.628714
\(339\) 8.31048 + 8.31048i 0.451363 + 0.451363i
\(340\) 0.409308 + 0.280587i 0.0221979 + 0.0152169i
\(341\) 7.41827 7.41827i 0.401722 0.401722i
\(342\) −3.73909 + 3.73909i −0.202187 + 0.202187i
\(343\) 14.1350 + 14.1350i 0.763219 + 0.763219i
\(344\) 7.69386 0.414825
\(345\) −1.74156 9.33405i −0.0937626 0.502528i
\(346\) 13.9023 13.9023i 0.747391 0.747391i
\(347\) −6.67064 −0.358099 −0.179049 0.983840i \(-0.557302\pi\)
−0.179049 + 0.983840i \(0.557302\pi\)
\(348\) 7.71250i 0.413433i
\(349\) 15.3388i 0.821066i −0.911846 0.410533i \(-0.865343\pi\)
0.911846 0.410533i \(-0.134657\pi\)
\(350\) −10.6146 4.69539i −0.567373 0.250979i
\(351\) −0.848892 0.848892i −0.0453105 0.0453105i
\(352\) 4.17593i 0.222578i
\(353\) 29.7766i 1.58485i −0.609971 0.792423i \(-0.708819\pi\)
0.609971 0.792423i \(-0.291181\pi\)
\(354\) −5.52770 −0.293794
\(355\) 11.5262 16.8139i 0.611745 0.892389i
\(356\) 4.28275 4.28275i 0.226985 0.226985i
\(357\) −0.515174 −0.0272659
\(358\) −11.4245 + 11.4245i −0.603803 + 0.603803i
\(359\) 13.0032i 0.686284i −0.939284 0.343142i \(-0.888509\pi\)
0.939284 0.343142i \(-0.111491\pi\)
\(360\) −1.84432 1.26431i −0.0972043 0.0666349i
\(361\) 8.96152i 0.471659i
\(362\) −18.4010 −0.967136
\(363\) 4.55261 4.55261i 0.238950 0.238950i
\(364\) −1.97057 + 1.97057i −0.103286 + 0.103286i
\(365\) 2.18506 + 11.7110i 0.114371 + 0.612981i
\(366\) −1.27493 −0.0666416
\(367\) −11.3147 + 11.3147i −0.590624 + 0.590624i −0.937800 0.347176i \(-0.887141\pi\)
0.347176 + 0.937800i \(0.387141\pi\)
\(368\) −4.24635 −0.221356
\(369\) −2.58213 −0.134420
\(370\) 8.39179 10.7041i 0.436268 0.556480i
\(371\) −14.6390 −0.760018
\(372\) −2.51226 −0.130255
\(373\) 15.2041 15.2041i 0.787238 0.787238i −0.193803 0.981041i \(-0.562082\pi\)
0.981041 + 0.193803i \(0.0620821\pi\)
\(374\) 0.926759 0.0479216
\(375\) 9.51169 5.87603i 0.491182 0.303437i
\(376\) 5.62938 5.62938i 0.290313 0.290313i
\(377\) 6.54708 6.54708i 0.337192 0.337192i
\(378\) 2.32134 0.119397
\(379\) 1.94256i 0.0997828i 0.998755 + 0.0498914i \(0.0158875\pi\)
−0.998755 + 0.0498914i \(0.984112\pi\)
\(380\) −11.6234 + 2.16872i −0.596270 + 0.111253i
\(381\) 12.9937i 0.665685i
\(382\) −3.52951 + 3.52951i −0.180585 + 0.180585i
\(383\) −14.7331 −0.752827 −0.376413 0.926452i \(-0.622843\pi\)
−0.376413 + 0.926452i \(0.622843\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −21.3082 + 3.97572i −1.08597 + 0.202621i
\(386\) 9.24953 0.470789
\(387\) 7.69386i 0.391101i
\(388\) 8.59029i 0.436106i
\(389\) −11.3037 11.3037i −0.573121 0.573121i 0.359879 0.932999i \(-0.382818\pi\)
−0.932999 + 0.359879i \(0.882818\pi\)
\(390\) −0.492369 2.63889i −0.0249321 0.133625i
\(391\) 0.942388i 0.0476586i
\(392\) 1.61136i 0.0813860i
\(393\) 15.1337 0.763396
\(394\) −1.75235 + 1.75235i −0.0882823 + 0.0882823i
\(395\) 1.77728 0.331608i 0.0894245 0.0166850i
\(396\) −4.17593 −0.209848
\(397\) 5.54983 + 5.54983i 0.278538 + 0.278538i 0.832525 0.553987i \(-0.186894\pi\)
−0.553987 + 0.832525i \(0.686894\pi\)
\(398\) −1.94022 + 1.94022i −0.0972542 + 0.0972542i
\(399\) 8.67970 8.67970i 0.434529 0.434529i
\(400\) −1.80305 4.66358i −0.0901524 0.233179i
\(401\) 10.5726 + 10.5726i 0.527970 + 0.527970i 0.919967 0.391996i \(-0.128215\pi\)
−0.391996 + 0.919967i \(0.628215\pi\)
\(402\) −14.6342 −0.729886
\(403\) −2.13264 2.13264i −0.106234 0.106234i
\(404\) 9.72766i 0.483969i
\(405\) −1.26431 + 1.84432i −0.0628240 + 0.0916451i
\(406\) 17.9034i 0.888529i
\(407\) 1.62349 25.3492i 0.0804732 1.25651i
\(408\) −0.156927 0.156927i −0.00776907 0.00776907i
\(409\) 25.5820 25.5820i 1.26495 1.26495i 0.316284 0.948665i \(-0.397565\pi\)
0.948665 0.316284i \(-0.102435\pi\)
\(410\) −4.76228 3.26461i −0.235192 0.161228i
\(411\) 6.15574i 0.303640i
\(412\) 15.6866i 0.772824i
\(413\) 12.8317 0.631407
\(414\) 4.24635i 0.208697i
\(415\) 23.9226 4.46352i 1.17431 0.219105i
\(416\) −1.20051 −0.0588601
\(417\) −12.9699 + 12.9699i −0.635139 + 0.635139i
\(418\) −15.6141 + 15.6141i −0.763713 + 0.763713i
\(419\) 3.51437i 0.171688i 0.996309 + 0.0858441i \(0.0273587\pi\)
−0.996309 + 0.0858441i \(0.972641\pi\)
\(420\) 4.28131 + 2.93490i 0.208906 + 0.143208i
\(421\) −0.351376 0.351376i −0.0171250 0.0171250i 0.698492 0.715617i \(-0.253855\pi\)
−0.715617 + 0.698492i \(0.753855\pi\)
\(422\) −4.88849 −0.237968
\(423\) −5.62938 5.62938i −0.273710 0.273710i
\(424\) −4.45920 4.45920i −0.216558 0.216558i
\(425\) 1.03498 0.400149i 0.0502041 0.0194101i
\(426\) −6.44639 + 6.44639i −0.312329 + 0.312329i
\(427\) 2.95955 0.143223
\(428\) 1.59584 1.59584i 0.0771377 0.0771377i
\(429\) −3.54491 3.54491i −0.171150 0.171150i
\(430\) 9.72741 14.1899i 0.469097 0.684300i
\(431\) −11.7580 11.7580i −0.566362 0.566362i 0.364745 0.931107i \(-0.381156\pi\)
−0.931107 + 0.364745i \(0.881156\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 12.6439 + 12.6439i 0.607628 + 0.607628i 0.942326 0.334697i \(-0.108634\pi\)
−0.334697 + 0.942326i \(0.608634\pi\)
\(434\) 5.83183 0.279937
\(435\) −14.2243 9.75098i −0.682005 0.467524i
\(436\) 6.35309 + 6.35309i 0.304258 + 0.304258i
\(437\) 15.8775 + 15.8775i 0.759522 + 0.759522i
\(438\) 5.32769i 0.254567i
\(439\) −2.75100 + 2.75100i −0.131298 + 0.131298i −0.769702 0.638404i \(-0.779595\pi\)
0.638404 + 0.769702i \(0.279595\pi\)
\(440\) −7.70175 5.27966i −0.367167 0.251698i
\(441\) 1.61136 0.0767314
\(442\) 0.266429i 0.0126727i
\(443\) 8.68051 8.68051i 0.412423 0.412423i −0.470158 0.882582i \(-0.655803\pi\)
0.882582 + 0.470158i \(0.155803\pi\)
\(444\) −4.56727 + 4.01746i −0.216753 + 0.190660i
\(445\) −2.48406 13.3135i −0.117756 0.631120i
\(446\) 16.9445 + 16.9445i 0.802345 + 0.802345i
\(447\) −6.57056 6.57056i −0.310777 0.310777i
\(448\) 1.64144 1.64144i 0.0775507 0.0775507i
\(449\) 11.3699 + 11.3699i 0.536577 + 0.536577i 0.922522 0.385945i \(-0.126124\pi\)
−0.385945 + 0.922522i \(0.626124\pi\)
\(450\) −4.66358 + 1.80305i −0.219843 + 0.0849965i
\(451\) −10.7828 −0.507742
\(452\) 11.7528i 0.552805i
\(453\) −7.13295 7.13295i −0.335135 0.335135i
\(454\) 22.8426i 1.07206i
\(455\) 1.14296 + 6.12578i 0.0535827 + 0.287181i
\(456\) 5.28787 0.247627
\(457\) 19.6985i 0.921456i 0.887541 + 0.460728i \(0.152412\pi\)
−0.887541 + 0.460728i \(0.847588\pi\)
\(458\) 16.1156i 0.753032i
\(459\) −0.156927 + 0.156927i −0.00732475 + 0.00732475i
\(460\) −5.36870 + 7.83164i −0.250317 + 0.365152i
\(461\) −19.2408 + 19.2408i −0.896135 + 0.896135i −0.995092 0.0989566i \(-0.968449\pi\)
0.0989566 + 0.995092i \(0.468449\pi\)
\(462\) 9.69376 0.450995
\(463\) 1.97887 0.0919658 0.0459829 0.998942i \(-0.485358\pi\)
0.0459829 + 0.998942i \(0.485358\pi\)
\(464\) −5.45356 + 5.45356i −0.253175 + 0.253175i
\(465\) −3.17627 + 4.63342i −0.147296 + 0.214870i
\(466\) −3.66171 + 3.66171i −0.169625 + 0.169625i
\(467\) 24.0229i 1.11165i 0.831300 + 0.555824i \(0.187597\pi\)
−0.831300 + 0.555824i \(0.812403\pi\)
\(468\) 1.20051i 0.0554938i
\(469\) 33.9710 1.56863
\(470\) −3.26512 17.4997i −0.150609 0.807199i
\(471\) 22.3749i 1.03098i
\(472\) 3.90868 + 3.90868i 0.179911 + 0.179911i
\(473\) 32.1290i 1.47729i
\(474\) −0.808539 −0.0371374
\(475\) −10.6958 + 24.1793i −0.490756 + 1.10942i
\(476\) 0.364283 + 0.364283i 0.0166969 + 0.0166969i
\(477\) −4.45920 + 4.45920i −0.204173 + 0.204173i
\(478\) −2.75228 2.75228i −0.125886 0.125886i
\(479\) 2.92694 + 2.92694i 0.133735 + 0.133735i 0.770806 0.637070i \(-0.219854\pi\)
−0.637070 + 0.770806i \(0.719854\pi\)
\(480\) 0.410132 + 2.19813i 0.0187199 + 0.100331i
\(481\) −7.28751 0.466727i −0.332282 0.0212809i
\(482\) −19.9398 + 19.9398i −0.908233 + 0.908233i
\(483\) 9.85724i 0.448520i
\(484\) −6.43836 −0.292653
\(485\) 15.8433 + 10.8608i 0.719406 + 0.493163i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 20.3915i 0.924029i −0.886872 0.462014i \(-0.847127\pi\)
0.886872 0.462014i \(-0.152873\pi\)
\(488\) 0.901511 + 0.901511i 0.0408095 + 0.0408095i
\(489\) −13.2899 13.2899i −0.600989 0.600989i
\(490\) 2.97187 + 2.03726i 0.134255 + 0.0920338i
\(491\) 19.2062 0.866762 0.433381 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(492\) 1.82584 + 1.82584i 0.0823153 + 0.0823153i
\(493\) −1.21030 1.21030i −0.0545093 0.0545093i
\(494\) 4.48883 + 4.48883i 0.201962 + 0.201962i
\(495\) −5.27966 + 7.70175i −0.237303 + 0.346168i
\(496\) 1.77644 + 1.77644i 0.0797644 + 0.0797644i
\(497\) 14.9643 14.9643i 0.671240 0.671240i
\(498\) −10.8831 −0.487685
\(499\) 3.71349 3.71349i 0.166238 0.166238i −0.619085 0.785324i \(-0.712496\pi\)
0.785324 + 0.619085i \(0.212496\pi\)
\(500\) −10.8808 2.57081i −0.486602 0.114970i
\(501\) 10.1957 + 10.1957i 0.455510 + 0.455510i
\(502\) −12.4982 12.4982i −0.557823 0.557823i
\(503\) −16.4264 −0.732415 −0.366207 0.930533i \(-0.619344\pi\)
−0.366207 + 0.930533i \(0.619344\pi\)
\(504\) −1.64144 1.64144i −0.0731155 0.0731155i
\(505\) 17.9409 + 12.2988i 0.798361 + 0.547288i
\(506\) 17.7324i 0.788303i
\(507\) 8.17328 8.17328i 0.362988 0.362988i
\(508\) 9.18790 9.18790i 0.407647 0.407647i
\(509\) −37.6361 −1.66819 −0.834096 0.551619i \(-0.814010\pi\)
−0.834096 + 0.551619i \(0.814010\pi\)
\(510\) −0.487830 + 0.0910201i −0.0216015 + 0.00403044i
\(511\) 12.3674i 0.547102i
\(512\) 1.00000 0.0441942
\(513\) 5.28787i 0.233465i
\(514\) 23.1067i 1.01919i
\(515\) −28.9312 19.8327i −1.27486 0.873934i
\(516\) −5.44038 + 5.44038i −0.239499 + 0.239499i
\(517\) −23.5079 23.5079i −1.03387 1.03387i
\(518\) 10.6022 9.32592i 0.465834 0.409757i
\(519\) 19.6608i 0.863012i
\(520\) −1.51782 + 2.21414i −0.0665608 + 0.0970963i
\(521\) 4.55515i 0.199565i 0.995009 + 0.0997823i \(0.0318146\pi\)
−0.995009 + 0.0997823i \(0.968185\pi\)
\(522\) 5.45356 + 5.45356i 0.238696 + 0.238696i
\(523\) −25.6939 −1.12352 −0.561759 0.827301i \(-0.689875\pi\)
−0.561759 + 0.827301i \(0.689875\pi\)
\(524\) −10.7012 10.7012i −0.467483 0.467483i
\(525\) 10.8258 4.18550i 0.472476 0.182670i
\(526\) 8.68658 8.68658i 0.378753 0.378753i
\(527\) −0.394243 + 0.394243i −0.0171735 + 0.0171735i
\(528\) 2.95283 + 2.95283i 0.128505 + 0.128505i
\(529\) −4.96851 −0.216022
\(530\) −13.8620 + 2.58639i −0.602126 + 0.112346i
\(531\) 3.90868 3.90868i 0.169622 0.169622i
\(532\) −12.2750 −0.532187
\(533\) 3.09989i 0.134271i
\(534\) 6.05673i 0.262100i
\(535\) −0.925607 4.96087i −0.0400175 0.214477i
\(536\) 10.3479 + 10.3479i 0.446962 + 0.446962i
\(537\) 16.1567i 0.697212i
\(538\) 30.1717i 1.30079i
\(539\) 6.72892 0.289835
\(540\) 2.19813 0.410132i 0.0945926 0.0176493i
\(541\) −5.59059 + 5.59059i −0.240358 + 0.240358i −0.816998 0.576640i \(-0.804363\pi\)
0.576640 + 0.816998i \(0.304363\pi\)
\(542\) −7.28060 −0.312729
\(543\) 13.0115 13.0115i 0.558376 0.558376i
\(544\) 0.221929i 0.00951513i
\(545\) 19.7494 3.68488i 0.845972 0.157843i
\(546\) 2.78681i 0.119264i
\(547\) 24.5372 1.04913 0.524567 0.851369i \(-0.324227\pi\)
0.524567 + 0.851369i \(0.324227\pi\)
\(548\) −4.35277 + 4.35277i −0.185941 + 0.185941i
\(549\) 0.901511 0.901511i 0.0384755 0.0384755i
\(550\) −19.4748 + 7.52940i −0.830408 + 0.321055i
\(551\) 40.7827 1.73740
\(552\) 3.00262 3.00262i 0.127800 0.127800i
\(553\) 1.87690 0.0798138
\(554\) 20.3131 0.863022
\(555\) 1.63506 + 13.5028i 0.0694044 + 0.573163i
\(556\) 18.3422 0.777883
\(557\) −11.2422 −0.476345 −0.238173 0.971223i \(-0.576548\pi\)
−0.238173 + 0.971223i \(0.576548\pi\)
\(558\) 1.77644 1.77644i 0.0752026 0.0752026i
\(559\) −9.23659 −0.390666
\(560\) −0.952057 5.10263i −0.0402317 0.215625i
\(561\) −0.655318 + 0.655318i −0.0276675 + 0.0276675i
\(562\) −5.88467 + 5.88467i −0.248230 + 0.248230i
\(563\) −27.5300 −1.16025 −0.580125 0.814528i \(-0.696996\pi\)
−0.580125 + 0.814528i \(0.696996\pi\)
\(564\) 7.96114i 0.335225i
\(565\) −21.6759 14.8592i −0.911913 0.625129i
\(566\) 3.93264i 0.165301i
\(567\) −1.64144 + 1.64144i −0.0689339 + 0.0689339i
\(568\) 9.11658 0.382523
\(569\) 2.67462 2.67462i 0.112126 0.112126i −0.648818 0.760944i \(-0.724736\pi\)
0.760944 + 0.648818i \(0.224736\pi\)
\(570\) 6.68549 9.75253i 0.280024 0.408488i
\(571\) −39.5492 −1.65508 −0.827541 0.561405i \(-0.810261\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(572\) 5.01326i 0.209615i
\(573\) 4.99148i 0.208522i
\(574\) −4.23841 4.23841i −0.176908 0.176908i
\(575\) 7.65637 + 19.8032i 0.319293 + 0.825851i
\(576\) 1.00000i 0.0416667i
\(577\) 22.0030i 0.915996i −0.888953 0.457998i \(-0.848567\pi\)
0.888953 0.457998i \(-0.151433\pi\)
\(578\) 16.9507 0.705058
\(579\) −6.54040 + 6.54040i −0.271810 + 0.271810i
\(580\) 3.16314 + 16.9531i 0.131342 + 0.703940i
\(581\) 25.2635 1.04811
\(582\) −6.07425 6.07425i −0.251786 0.251786i
\(583\) −18.6213 + 18.6213i −0.771214 + 0.771214i
\(584\) −3.76725 + 3.76725i −0.155890 + 0.155890i
\(585\) 2.21414 + 1.51782i 0.0915432 + 0.0627542i
\(586\) −3.68251 3.68251i −0.152123 0.152123i
\(587\) 20.8362 0.860000 0.430000 0.902829i \(-0.358514\pi\)
0.430000 + 0.902829i \(0.358514\pi\)
\(588\) −1.13940 1.13940i −0.0469882 0.0469882i
\(589\) 13.2845i 0.547379i
\(590\) 12.1506 2.26709i 0.500233 0.0933344i
\(591\) 2.47820i 0.101940i
\(592\) 6.07033 + 0.388773i 0.249489 + 0.0159785i
\(593\) −4.26861 4.26861i −0.175291 0.175291i 0.614009 0.789299i \(-0.289556\pi\)
−0.789299 + 0.614009i \(0.789556\pi\)
\(594\) 2.95283 2.95283i 0.121156 0.121156i
\(595\) 1.13242 0.211289i 0.0464247 0.00866200i
\(596\) 9.29218i 0.380622i
\(597\) 2.74388i 0.112300i
\(598\) 5.09780 0.208465
\(599\) 12.4209i 0.507503i −0.967269 0.253752i \(-0.918335\pi\)
0.967269 0.253752i \(-0.0816646\pi\)
\(600\) 4.57260 + 2.02270i 0.186676 + 0.0825765i
\(601\) −26.7404 −1.09076 −0.545382 0.838187i \(-0.683615\pi\)
−0.545382 + 0.838187i \(0.683615\pi\)
\(602\) 12.6290 12.6290i 0.514719 0.514719i
\(603\) 10.3479 10.3479i 0.421400 0.421400i
\(604\) 10.0875i 0.410455i
\(605\) −8.14008 + 11.8744i −0.330941 + 0.482764i
\(606\) −6.87849 6.87849i −0.279420 0.279420i
\(607\) 21.5222 0.873559 0.436780 0.899569i \(-0.356119\pi\)
0.436780 + 0.899569i \(0.356119\pi\)
\(608\) −3.73909 3.73909i −0.151640 0.151640i
\(609\) −12.6596 12.6596i −0.512993 0.512993i
\(610\) 2.80246 0.522889i 0.113468 0.0211711i
\(611\) −6.75815 + 6.75815i −0.273405 + 0.273405i
\(612\) 0.221929 0.00897095
\(613\) 12.0786 12.0786i 0.487851 0.487851i −0.419777 0.907627i \(-0.637892\pi\)
0.907627 + 0.419777i \(0.137892\pi\)
\(614\) −16.3345 16.3345i −0.659205 0.659205i
\(615\) 5.67587 1.05901i 0.228873 0.0427035i
\(616\) −6.85453 6.85453i −0.276177 0.276177i
\(617\) 19.9970 + 19.9970i 0.805049 + 0.805049i 0.983880 0.178831i \(-0.0572315\pi\)
−0.178831 + 0.983880i \(0.557231\pi\)
\(618\) 11.0921 + 11.0921i 0.446190 + 0.446190i
\(619\) −43.2741 −1.73933 −0.869666 0.493640i \(-0.835666\pi\)
−0.869666 + 0.493640i \(0.835666\pi\)
\(620\) 5.52229 1.03036i 0.221780 0.0413802i
\(621\) −3.00262 3.00262i −0.120491 0.120491i
\(622\) −0.811220 0.811220i −0.0325270 0.0325270i
\(623\) 14.0598i 0.563292i
\(624\) 0.848892 0.848892i 0.0339829 0.0339829i
\(625\) −18.4980 + 16.8173i −0.739921 + 0.672693i
\(626\) −3.61149 −0.144344
\(627\) 22.0817i 0.881860i
\(628\) −15.8215 + 15.8215i −0.631345 + 0.631345i
\(629\) −0.0862799 + 1.34718i −0.00344021 + 0.0537156i
\(630\) −5.10263 + 0.952057i −0.203293 + 0.0379309i
\(631\) 23.4422 + 23.4422i 0.933219 + 0.933219i 0.997906 0.0646863i \(-0.0206047\pi\)
−0.0646863 + 0.997906i \(0.520605\pi\)
\(632\) 0.571724 + 0.571724i 0.0227419 + 0.0227419i
\(633\) 3.45668 3.45668i 0.137391 0.137391i
\(634\) 9.01704 + 9.01704i 0.358112 + 0.358112i
\(635\) −5.32911 28.5618i −0.211479 1.13344i
\(636\) 6.30625 0.250059
\(637\) 1.93446i 0.0766461i
\(638\) 22.7737 + 22.7737i 0.901618 + 0.901618i
\(639\) 9.11658i 0.360646i
\(640\) 1.26431 1.84432i 0.0499762 0.0729032i
\(641\) 12.8649 0.508132 0.254066 0.967187i \(-0.418232\pi\)
0.254066 + 0.967187i \(0.418232\pi\)
\(642\) 2.25685i 0.0890709i
\(643\) 6.91522i 0.272709i −0.990660 0.136355i \(-0.956461\pi\)
0.990660 0.136355i \(-0.0435387\pi\)
\(644\) −6.97012 + 6.97012i −0.274661 + 0.274661i
\(645\) 3.15549 + 16.9121i 0.124247 + 0.665914i
\(646\) 0.829811 0.829811i 0.0326485 0.0326485i
\(647\) −28.0603 −1.10317 −0.551583 0.834120i \(-0.685976\pi\)
−0.551583 + 0.834120i \(0.685976\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 16.3223 16.3223i 0.640708 0.640708i
\(650\) 2.16459 + 5.59870i 0.0849020 + 0.219599i
\(651\) −4.12372 + 4.12372i −0.161621 + 0.161621i
\(652\) 18.7947i 0.736058i
\(653\) 18.1283i 0.709417i 0.934977 + 0.354708i \(0.115420\pi\)
−0.934977 + 0.354708i \(0.884580\pi\)
\(654\) −8.98462 −0.351327
\(655\) −33.2660 + 6.20683i −1.29981 + 0.242521i
\(656\) 2.58213i 0.100815i
\(657\) 3.76725 + 3.76725i 0.146974 + 0.146974i
\(658\) 18.4806i 0.720447i
\(659\) −3.13030 −0.121939 −0.0609695 0.998140i \(-0.519419\pi\)
−0.0609695 + 0.998140i \(0.519419\pi\)
\(660\) 9.17925 1.71268i 0.357302 0.0666660i
\(661\) −0.420561 0.420561i −0.0163579 0.0163579i 0.698881 0.715238i \(-0.253682\pi\)
−0.715238 + 0.698881i \(0.753682\pi\)
\(662\) 2.86838 2.86838i 0.111483 0.111483i
\(663\) 0.188394 + 0.188394i 0.00731661 + 0.00731661i
\(664\) 7.69554 + 7.69554i 0.298645 + 0.298645i
\(665\) −15.5193 + 22.6390i −0.601814 + 0.877902i
\(666\) 0.388773 6.07033i 0.0150646 0.235220i
\(667\) 23.1577 23.1577i 0.896671 0.896671i
\(668\) 14.4189i 0.557883i
\(669\) −23.9631 −0.926469
\(670\) 32.1679 6.00194i 1.24275 0.231875i
\(671\) 3.76464 3.76464i 0.145332 0.145332i
\(672\) 2.32134i 0.0895478i
\(673\) −11.5151 11.5151i −0.443875 0.443875i 0.449437 0.893312i \(-0.351625\pi\)
−0.893312 + 0.449437i \(0.851625\pi\)
\(674\) 2.56826 + 2.56826i 0.0989258 + 0.0989258i
\(675\) 2.02270 4.57260i 0.0778539 0.175999i
\(676\) −11.5588 −0.444568
\(677\) 10.6365 + 10.6365i 0.408794 + 0.408794i 0.881318 0.472524i \(-0.156657\pi\)
−0.472524 + 0.881318i \(0.656657\pi\)
\(678\) 8.31048 + 8.31048i 0.319162 + 0.319162i
\(679\) 14.1004 + 14.1004i 0.541125 + 0.541125i
\(680\) 0.409308 + 0.280587i 0.0156963 + 0.0107600i
\(681\) 16.1521 + 16.1521i 0.618952 + 0.618952i
\(682\) 7.41827 7.41827i 0.284060 0.284060i
\(683\) −21.3995 −0.818828 −0.409414 0.912349i \(-0.634267\pi\)
−0.409414 + 0.912349i \(0.634267\pi\)
\(684\) −3.73909 + 3.73909i −0.142968 + 0.142968i
\(685\) 2.52467 + 13.5311i 0.0964625 + 0.516999i
\(686\) 14.1350 + 14.1350i 0.539677 + 0.539677i
\(687\) −11.3954 11.3954i −0.434763 0.434763i
\(688\) 7.69386 0.293325
\(689\) 5.35333 + 5.35333i 0.203946 + 0.203946i
\(690\) −1.74156 9.33405i −0.0663002 0.355341i
\(691\) 15.8189i 0.601778i −0.953659 0.300889i \(-0.902717\pi\)
0.953659 0.300889i \(-0.0972834\pi\)
\(692\) 13.9023 13.9023i 0.528485 0.528485i
\(693\) −6.85453 + 6.85453i −0.260382 + 0.260382i
\(694\) −6.67064 −0.253214
\(695\) 23.1902 33.8290i 0.879655 1.28321i
\(696\) 7.71250i 0.292342i
\(697\) 0.573050 0.0217058
\(698\) 15.3388i 0.580582i
\(699\) 5.17843i 0.195866i
\(700\) −10.6146 4.69539i −0.401193 0.177469i
\(701\) −23.5884 + 23.5884i −0.890921 + 0.890921i −0.994610 0.103688i \(-0.966935\pi\)
0.103688 + 0.994610i \(0.466935\pi\)
\(702\) −0.848892 0.848892i −0.0320394 0.0320394i
\(703\) −21.2438 24.1511i −0.801226 0.910877i
\(704\) 4.17593i 0.157386i
\(705\) 14.6829 + 10.0653i 0.552990 + 0.379083i
\(706\) 29.7766i 1.12066i
\(707\) 15.9674 + 15.9674i 0.600514 + 0.600514i
\(708\) −5.52770 −0.207744
\(709\) −20.0563 20.0563i −0.753229 0.753229i 0.221851 0.975080i \(-0.428790\pi\)
−0.975080 + 0.221851i \(0.928790\pi\)
\(710\) 11.5262 16.8139i 0.432569 0.631015i
\(711\) 0.571724 0.571724i 0.0214413 0.0214413i
\(712\) 4.28275 4.28275i 0.160503 0.160503i
\(713\) −7.54338 7.54338i −0.282502 0.282502i
\(714\) −0.515174 −0.0192799
\(715\) 9.24607 + 6.33831i 0.345783 + 0.237039i
\(716\) −11.4245 + 11.4245i −0.426953 + 0.426953i
\(717\) 3.89231 0.145361
\(718\) 13.0032i 0.485276i
\(719\) 26.6689i 0.994583i 0.867584 + 0.497291i \(0.165672\pi\)
−0.867584 + 0.497291i \(0.834328\pi\)
\(720\) −1.84432 1.26431i −0.0687338 0.0471180i
\(721\) −25.7486 25.7486i −0.958928 0.958928i
\(722\) 8.96152i 0.333513i
\(723\) 28.1991i 1.04874i
\(724\) −18.4010 −0.683869
\(725\) 35.2662 + 15.6001i 1.30975 + 0.579373i
\(726\) 4.55261 4.55261i 0.168963 0.168963i
\(727\) 36.3257 1.34725 0.673623 0.739075i \(-0.264737\pi\)
0.673623 + 0.739075i \(0.264737\pi\)
\(728\) −1.97057 + 1.97057i −0.0730342 + 0.0730342i
\(729\) 1.00000i 0.0370370i
\(730\) 2.18506 + 11.7110i 0.0808725 + 0.433443i
\(731\) 1.70749i 0.0631538i
\(732\) −1.27493 −0.0471227
\(733\) 3.69185 3.69185i 0.136362 0.136362i −0.635631 0.771993i \(-0.719260\pi\)
0.771993 + 0.635631i \(0.219260\pi\)
\(734\) −11.3147 + 11.3147i −0.417634 + 0.417634i
\(735\) −3.54198 + 0.660870i −0.130648 + 0.0243765i
\(736\) −4.24635 −0.156523
\(737\) 43.2122 43.2122i 1.59174 1.59174i
\(738\) −2.58213 −0.0950495
\(739\) 32.1208 1.18158 0.590792 0.806824i \(-0.298815\pi\)
0.590792 + 0.806824i \(0.298815\pi\)
\(740\) 8.39179 10.7041i 0.308488 0.393491i
\(741\) −6.34816 −0.233205
\(742\) −14.6390 −0.537414
\(743\) 14.6516 14.6516i 0.537516 0.537516i −0.385283 0.922799i \(-0.625896\pi\)
0.922799 + 0.385283i \(0.125896\pi\)
\(744\) −2.51226 −0.0921040
\(745\) 17.1378 + 11.7482i 0.627879 + 0.430420i
\(746\) 15.2041 15.2041i 0.556661 0.556661i
\(747\) 7.69554 7.69554i 0.281565 0.281565i
\(748\) 0.926759 0.0338857
\(749\) 5.23894i 0.191427i
\(750\) 9.51169 5.87603i 0.347318 0.214562i
\(751\) 23.7777i 0.867660i −0.900995 0.433830i \(-0.857162\pi\)
0.900995 0.433830i \(-0.142838\pi\)
\(752\) 5.62938 5.62938i 0.205282 0.205282i
\(753\) 17.6751 0.644118
\(754\) 6.54708 6.54708i 0.238431 0.238431i
\(755\) 18.6046 + 12.7537i 0.677092 + 0.464156i
\(756\) 2.32134 0.0844265
\(757\) 11.8515i 0.430750i −0.976531 0.215375i \(-0.930903\pi\)
0.976531 0.215375i \(-0.0690974\pi\)
\(758\) 1.94256i 0.0705571i
\(759\) −12.5387 12.5387i −0.455127 0.455127i
\(760\) −11.6234 + 2.16872i −0.421626 + 0.0786678i
\(761\) 0.483135i 0.0175136i 0.999962 + 0.00875681i \(0.00278741\pi\)
−0.999962 + 0.00875681i \(0.997213\pi\)
\(762\) 12.9937i 0.470711i
\(763\) 20.8564 0.755053
\(764\) −3.52951 + 3.52951i −0.127693 + 0.127693i
\(765\) 0.280587 0.409308i 0.0101446 0.0147986i
\(766\) −14.7331 −0.532329
\(767\) −4.69242 4.69242i −0.169434 0.169434i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 13.0162 13.0162i 0.469377 0.469377i −0.432336 0.901713i \(-0.642310\pi\)
0.901713 + 0.432336i \(0.142310\pi\)
\(770\) −21.3082 + 3.97572i −0.767894 + 0.143275i
\(771\) 16.3389 + 16.3389i 0.588432 + 0.588432i
\(772\) 9.24953 0.332898
\(773\) 5.46633 + 5.46633i 0.196610 + 0.196610i 0.798545 0.601935i \(-0.205603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(774\) 7.69386i 0.276550i
\(775\) 5.08156 11.4876i 0.182535 0.412646i
\(776\) 8.59029i 0.308374i
\(777\) −0.902476 + 14.0913i −0.0323761 + 0.505523i
\(778\) −11.3037 11.3037i −0.405257 0.405257i
\(779\) −9.65481 + 9.65481i −0.345919 + 0.345919i
\(780\) −0.492369 2.63889i −0.0176296 0.0944875i
\(781\) 38.0701i 1.36226i
\(782\) 0.942388i 0.0336997i
\(783\) −7.71250 −0.275622
\(784\) 1.61136i 0.0575486i
\(785\) 9.17666 + 49.1831i 0.327529 + 1.75542i
\(786\) 15.1337 0.539803
\(787\) 29.3423 29.3423i 1.04594 1.04594i 0.0470485 0.998893i \(-0.485018\pi\)
0.998893 0.0470485i \(-0.0149815\pi\)
\(788\) −1.75235 + 1.75235i −0.0624250 + 0.0624250i
\(789\) 12.2847i 0.437346i
\(790\) 1.77728 0.331608i 0.0632327 0.0117981i
\(791\) −19.2915 19.2915i −0.685926 0.685926i
\(792\) −4.17593 −0.148385
\(793\) −1.08228 1.08228i −0.0384328 0.0384328i
\(794\) 5.54983 + 5.54983i 0.196956 + 0.196956i
\(795\) 7.97305 11.6308i 0.282775 0.412501i
\(796\) −1.94022 + 1.94022i −0.0687691 + 0.0687691i
\(797\) −16.4749 −0.583569 −0.291785 0.956484i \(-0.594249\pi\)
−0.291785 + 0.956484i \(0.594249\pi\)
\(798\) 8.67970 8.67970i 0.307258 0.307258i
\(799\) 1.24932 + 1.24932i 0.0441978 + 0.0441978i
\(800\) −1.80305 4.66358i −0.0637474 0.164883i
\(801\) −4.28275 4.28275i −0.151324 0.151324i
\(802\) 10.5726 + 10.5726i 0.373331 + 0.373331i
\(803\) 15.7317 + 15.7317i 0.555161 + 0.555161i
\(804\) −14.6342 −0.516108
\(805\) 4.04277 + 21.6675i 0.142489 + 0.763680i
\(806\) −2.13264 2.13264i −0.0751190 0.0751190i
\(807\) −21.3346 21.3346i −0.751013 0.751013i
\(808\) 9.72766i 0.342218i
\(809\) −36.4616 + 36.4616i −1.28192 + 1.28192i −0.342347 + 0.939574i \(0.611222\pi\)
−0.939574 + 0.342347i \(0.888778\pi\)
\(810\) −1.26431 + 1.84432i −0.0444233 + 0.0648029i
\(811\) 17.4891 0.614126 0.307063 0.951689i \(-0.400654\pi\)
0.307063 + 0.951689i \(0.400654\pi\)
\(812\) 17.9034i 0.628285i
\(813\) 5.14816 5.14816i 0.180554 0.180554i
\(814\) 1.62349 25.3492i 0.0569032 0.888490i
\(815\) 34.6635 + 23.7623i 1.21421 + 0.832358i
\(816\) −0.156927 0.156927i −0.00549356 0.00549356i
\(817\) −28.7680 28.7680i −1.00646 1.00646i
\(818\) 25.5820 25.5820i 0.894454 0.894454i
\(819\) 1.97057 + 1.97057i 0.0688573 + 0.0688573i
\(820\) −4.76228 3.26461i −0.166306 0.114005i
\(821\) 55.0645 1.92176 0.960882 0.276959i \(-0.0893267\pi\)
0.960882 + 0.276959i \(0.0893267\pi\)
\(822\) 6.15574i 0.214706i
\(823\) 39.8287 + 39.8287i 1.38834 + 1.38834i 0.828808 + 0.559533i \(0.189019\pi\)
0.559533 + 0.828808i \(0.310981\pi\)
\(824\) 15.6866i 0.546469i
\(825\) 8.44666 19.0948i 0.294075 0.664797i
\(826\) 12.8317 0.446472
\(827\) 47.2289i 1.64231i 0.570705 + 0.821155i \(0.306670\pi\)
−0.570705 + 0.821155i \(0.693330\pi\)
\(828\) 4.24635i 0.147571i
\(829\) −13.9841 + 13.9841i −0.485688 + 0.485688i −0.906943 0.421254i \(-0.861590\pi\)
0.421254 + 0.906943i \(0.361590\pi\)
\(830\) 23.9226 4.46352i 0.830365 0.154931i
\(831\) −14.3636 + 14.3636i −0.498266 + 0.498266i
\(832\) −1.20051 −0.0416204
\(833\) −0.357607 −0.0123904
\(834\) −12.9699 + 12.9699i −0.449111 + 0.449111i
\(835\) −26.5930 18.2299i −0.920290 0.630872i
\(836\) −15.6141 + 15.6141i −0.540027 + 0.540027i
\(837\) 2.51226i 0.0868365i
\(838\) 3.51437i 0.121402i
\(839\) 33.7851 1.16639 0.583196 0.812332i \(-0.301802\pi\)
0.583196 + 0.812332i \(0.301802\pi\)
\(840\) 4.28131 + 2.93490i 0.147719 + 0.101264i
\(841\) 30.4827i 1.05113i
\(842\) −0.351376 0.351376i −0.0121092 0.0121092i
\(843\) 8.32219i 0.286631i
\(844\) −4.88849 −0.168269
\(845\) −14.6138 + 21.3181i −0.502732 + 0.733364i
\(846\) −5.62938 5.62938i −0.193542 0.193542i
\(847\) −10.5682 + 10.5682i −0.363127 + 0.363127i
\(848\) −4.45920 4.45920i −0.153129 0.153129i
\(849\) −2.78079 2.78079i −0.0954366 0.0954366i
\(850\) 1.03498 0.400149i 0.0354997 0.0137250i
\(851\) −25.7767 1.65087i −0.883615 0.0565909i
\(852\) −6.44639 + 6.44639i −0.220850 + 0.220850i
\(853\) 30.3087i 1.03775i 0.854850 + 0.518875i \(0.173649\pi\)
−0.854850 + 0.518875i \(0.826351\pi\)
\(854\) 2.95955 0.101274
\(855\) 2.16872 + 11.6234i 0.0741687 + 0.397513i
\(856\) 1.59584 1.59584i 0.0545446 0.0545446i
\(857\) 4.58564i 0.156642i 0.996928 + 0.0783212i \(0.0249560\pi\)
−0.996928 + 0.0783212i \(0.975044\pi\)
\(858\) −3.54491 3.54491i −0.121021 0.121021i
\(859\) −39.7203 39.7203i −1.35524 1.35524i −0.879689 0.475549i \(-0.842249\pi\)
−0.475549 0.879689i \(-0.657751\pi\)
\(860\) 9.72741 14.1899i 0.331702 0.483873i
\(861\) 5.99401 0.204275
\(862\) −11.7580 11.7580i −0.400478 0.400478i
\(863\) −12.7595 12.7595i −0.434339 0.434339i 0.455762 0.890101i \(-0.349367\pi\)
−0.890101 + 0.455762i \(0.849367\pi\)
\(864\) 0.707107 + 0.707107i 0.0240563 + 0.0240563i
\(865\) −8.06351 43.2170i −0.274167 1.46942i
\(866\) 12.6439 + 12.6439i 0.429658 + 0.429658i
\(867\) −11.9860 + 11.9860i −0.407066 + 0.407066i
\(868\) 5.83183 0.197945
\(869\) 2.38748 2.38748i 0.0809896 0.0809896i
\(870\) −14.2243 9.75098i −0.482250 0.330589i
\(871\) −12.4228 12.4228i −0.420932 0.420932i
\(872\) 6.35309 + 6.35309i 0.215143 + 0.215143i
\(873\) 8.59029 0.290737
\(874\) 15.8775 + 15.8775i 0.537063 + 0.537063i
\(875\) −22.0799 + 13.6403i −0.746437 + 0.461126i
\(876\) 5.32769i 0.180006i
\(877\) −25.2001 + 25.2001i −0.850947 + 0.850947i −0.990250 0.139303i \(-0.955514\pi\)
0.139303 + 0.990250i \(0.455514\pi\)
\(878\) −2.75100 + 2.75100i −0.0928416 + 0.0928416i
\(879\) 5.20786 0.175657
\(880\) −7.70175 5.27966i −0.259626 0.177977i
\(881\) 24.1141i 0.812426i −0.913778 0.406213i \(-0.866849\pi\)
0.913778 0.406213i \(-0.133151\pi\)
\(882\) 1.61136 0.0542573
\(883\) 39.4787i 1.32856i 0.747482 + 0.664282i \(0.231263\pi\)
−0.747482 + 0.664282i \(0.768737\pi\)
\(884\) 0.266429i 0.00896097i
\(885\) −6.98872 + 10.1949i −0.234923 + 0.342697i
\(886\) 8.68051 8.68051i 0.291627 0.291627i
\(887\) −15.0650 15.0650i −0.505834 0.505834i 0.407411 0.913245i \(-0.366432\pi\)
−0.913245 + 0.407411i \(0.866432\pi\)
\(888\) −4.56727 + 4.01746i −0.153268 + 0.134817i
\(889\) 30.1628i 1.01163i
\(890\) −2.48406 13.3135i −0.0832657 0.446269i
\(891\) 4.17593i 0.139899i
\(892\) 16.9445 + 16.9445i 0.567344 + 0.567344i
\(893\) −42.0974 −1.40874
\(894\) −6.57056 6.57056i −0.219752 0.219752i
\(895\) 6.62636 + 35.5145i 0.221495 + 1.18712i
\(896\) 1.64144 1.64144i 0.0548366 0.0548366i
\(897\) −3.60469 + 3.60469i −0.120357 + 0.120357i
\(898\) 11.3699 + 11.3699i 0.379418 + 0.379418i
\(899\) −19.3758 −0.646220
\(900\) −4.66358 + 1.80305i −0.155453 + 0.0601016i
\(901\) 0.989625 0.989625i 0.0329692 0.0329692i
\(902\) −10.7828 −0.359028
\(903\) 17.8601i 0.594347i
\(904\) 11.7528i 0.390892i
\(905\) −23.2646 + 33.9374i −0.773340 + 1.12812i
\(906\) −7.13295 7.13295i −0.236976 0.236976i
\(907\) 14.7767i 0.490653i −0.969441 0.245326i \(-0.921105\pi\)
0.969441 0.245326i \(-0.0788951\pi\)
\(908\) 22.8426i 0.758058i
\(909\) 9.72766 0.322646
\(910\) 1.14296 + 6.12578i 0.0378887 + 0.203067i
\(911\) 24.5510 24.5510i 0.813410 0.813410i −0.171734 0.985143i \(-0.554937\pi\)
0.985143 + 0.171734i \(0.0549369\pi\)
\(912\) 5.28787 0.175099
\(913\) 32.1360 32.1360i 1.06355 1.06355i
\(914\) 19.6985i 0.651568i
\(915\) −1.61190 + 2.35138i −0.0532879 + 0.0777342i
\(916\) 16.1156i 0.532474i
\(917\) −35.1306 −1.16012
\(918\) −0.156927 + 0.156927i −0.00517938 + 0.00517938i
\(919\) −34.9734 + 34.9734i −1.15367 + 1.15367i −0.167855 + 0.985812i \(0.553684\pi\)
−0.985812 + 0.167855i \(0.946316\pi\)
\(920\) −5.36870 + 7.83164i −0.177001 + 0.258201i
\(921\) 23.1004 0.761185
\(922\) −19.2408 + 19.2408i −0.633663 + 0.633663i
\(923\) −10.9446 −0.360245
\(924\) 9.69376 0.318901
\(925\) −9.13202 29.0105i −0.300259 0.953858i
\(926\) 1.97887 0.0650296
\(927\) −15.6866 −0.515216
\(928\) −5.45356 + 5.45356i −0.179022 + 0.179022i
\(929\) 51.4784 1.68895 0.844476 0.535593i \(-0.179912\pi\)
0.844476 + 0.535593i \(0.179912\pi\)
\(930\) −3.17627 + 4.63342i −0.104154 + 0.151936i
\(931\) 6.02501 6.02501i 0.197462 0.197462i
\(932\) −3.66171 + 3.66171i −0.119943 + 0.119943i
\(933\) 1.14724 0.0375589
\(934\) 24.0229i 0.786054i
\(935\) 1.17171 1.70924i 0.0383190 0.0558982i
\(936\) 1.20051i 0.0392400i
\(937\) −12.8685 + 12.8685i −0.420395 + 0.420395i −0.885340 0.464945i \(-0.846074\pi\)
0.464945 + 0.885340i \(0.346074\pi\)
\(938\) 33.9710 1.10919
\(939\) 2.55371 2.55371i 0.0833371 0.0833371i
\(940\) −3.26512 17.4997i −0.106496 0.570776i
\(941\) −18.7889 −0.612499 −0.306250 0.951951i \(-0.599074\pi\)
−0.306250 + 0.951951i \(0.599074\pi\)
\(942\) 22.3749i 0.729014i
\(943\) 10.9646i 0.357057i
\(944\) 3.90868 + 3.90868i 0.127217 + 0.127217i
\(945\) 2.93490 4.28131i 0.0954722 0.139271i
\(946\) 32.1290i 1.04460i
\(947\) 44.6439i 1.45073i 0.688363 + 0.725366i \(0.258329\pi\)
−0.688363 + 0.725366i \(0.741671\pi\)
\(948\) −0.808539 −0.0262601
\(949\) 4.52263 4.52263i 0.146811 0.146811i
\(950\) −10.6958 + 24.1793i −0.347017 + 0.784480i
\(951\) −12.7520 −0.413513
\(952\) 0.364283 + 0.364283i 0.0118065 + 0.0118065i
\(953\) −30.4910 + 30.4910i −0.987700 + 0.987700i −0.999925 0.0122255i \(-0.996108\pi\)
0.0122255 + 0.999925i \(0.496108\pi\)
\(954\) −4.45920 + 4.45920i −0.144372 + 0.144372i
\(955\) 2.04716 + 10.9719i 0.0662446 + 0.355043i
\(956\) −2.75228 2.75228i −0.0890150 0.0890150i
\(957\) −32.2068 −1.04110
\(958\) 2.92694 + 2.92694i 0.0945651 + 0.0945651i
\(959\) 14.2896i 0.461435i
\(960\) 0.410132 + 2.19813i 0.0132369 + 0.0709445i
\(961\) 24.6885i 0.796404i
\(962\) −7.28751 0.466727i −0.234959 0.0150479i
\(963\) −1.59584 1.59584i −0.0514251 0.0514251i
\(964\) −19.9398 + 19.9398i −0.642218 + 0.642218i
\(965\) 11.6943 17.0591i 0.376451 0.549152i
\(966\) 9.85724i 0.317152i
\(967\) 25.9848i 0.835614i 0.908536 + 0.417807i \(0.137201\pi\)
−0.908536 + 0.417807i \(0.862799\pi\)
\(968\) −6.43836 −0.206937
\(969\) 1.17353i 0.0376992i
\(970\) 15.8433 + 10.8608i 0.508697 + 0.348719i
\(971\) −29.3865 −0.943058 −0.471529 0.881851i \(-0.656298\pi\)
−0.471529 + 0.881851i \(0.656298\pi\)
\(972\) 0.707107 0.707107i 0.0226805 0.0226805i
\(973\) 30.1076 30.1076i 0.965206 0.965206i
\(974\) 20.3915i 0.653387i
\(975\) −5.48947 2.42829i −0.175804 0.0777674i
\(976\) 0.901511 + 0.901511i 0.0288567 + 0.0288567i
\(977\) −20.9434 −0.670037 −0.335019 0.942211i \(-0.608743\pi\)
−0.335019 + 0.942211i \(0.608743\pi\)
\(978\) −13.2899 13.2899i −0.424963 0.424963i
\(979\) −17.8845 17.8845i −0.571590 0.571590i
\(980\) 2.97187 + 2.03726i 0.0949328 + 0.0650778i
\(981\) 6.35309 6.35309i 0.202839 0.202839i
\(982\) 19.2062 0.612893
\(983\) −29.6368 + 29.6368i −0.945266 + 0.945266i −0.998578 0.0533119i \(-0.983022\pi\)
0.0533119 + 0.998578i \(0.483022\pi\)
\(984\) 1.82584 + 1.82584i 0.0582057 + 0.0582057i
\(985\) 1.01639 + 5.44742i 0.0323849 + 0.173569i
\(986\) −1.21030 1.21030i −0.0385439 0.0385439i
\(987\) 13.0677 + 13.0677i 0.415950 + 0.415950i
\(988\) 4.48883 + 4.48883i 0.142809 + 0.142809i
\(989\) −32.6708 −1.03887
\(990\) −5.27966 + 7.70175i −0.167799 + 0.244778i
\(991\) 1.54828 + 1.54828i 0.0491828 + 0.0491828i 0.731270 0.682088i \(-0.238928\pi\)
−0.682088 + 0.731270i \(0.738928\pi\)
\(992\) 1.77644 + 1.77644i 0.0564020 + 0.0564020i
\(993\) 4.05650i 0.128729i
\(994\) 14.9643 14.9643i 0.474639 0.474639i
\(995\) 1.12535 + 6.03141i 0.0356761 + 0.191209i
\(996\) −10.8831 −0.344845
\(997\) 39.3599i 1.24654i −0.782007 0.623270i \(-0.785804\pi\)
0.782007 0.623270i \(-0.214196\pi\)
\(998\) 3.71349 3.71349i 0.117548 0.117548i
\(999\) 4.01746 + 4.56727i 0.127107 + 0.144502i
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 1110.2.o.b.253.3 yes 40
5.2 odd 4 1110.2.l.b.697.18 yes 40
37.6 odd 4 1110.2.l.b.43.18 40
185.117 even 4 inner 1110.2.o.b.487.3 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.l.b.43.18 40 37.6 odd 4
1110.2.l.b.697.18 yes 40 5.2 odd 4
1110.2.o.b.253.3 yes 40 1.1 even 1 trivial
1110.2.o.b.487.3 yes 40 185.117 even 4 inner