Properties

Label 273.2.p.f.265.6
Level $273$
Weight $2$
Character 273.265
Analytic conductor $2.180$
Analytic rank $0$
Dimension $12$
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] = [273,2,Mod(34,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.p (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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.6
Root \(1.27310 + 1.27310i\) of defining polynomial
Character \(\chi\) \(=\) 273.265
Dual form 273.2.p.f.34.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.75588 - 1.75588i) q^{2} -1.00000i q^{3} -4.16620i q^{4} +(2.27310 + 2.27310i) q^{5} +(-1.75588 - 1.75588i) q^{6} +(-2.08970 - 1.62270i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.75588 - 1.75588i) q^{2} -1.00000i q^{3} -4.16620i q^{4} +(2.27310 + 2.27310i) q^{5} +(-1.75588 - 1.75588i) q^{6} +(-2.08970 - 1.62270i) q^{7} +(-3.80357 - 3.80357i) q^{8} -1.00000 q^{9} +7.98257 q^{10} +(3.22478 + 3.22478i) q^{11} -4.16620 q^{12} +(-3.60399 - 0.106106i) q^{13} +(-6.51851 + 0.819979i) q^{14} +(2.27310 - 2.27310i) q^{15} -5.02479 q^{16} -4.17939 q^{17} +(-1.75588 + 1.75588i) q^{18} +(0.774590 + 0.774590i) q^{19} +(9.47019 - 9.47019i) q^{20} +(-1.62270 + 2.08970i) q^{21} +11.3246 q^{22} +3.94079i q^{23} +(-3.80357 + 3.80357i) q^{24} +5.33399i q^{25} +(-6.51447 + 6.14185i) q^{26} +1.00000i q^{27} +(-6.76050 + 8.70608i) q^{28} +3.61222 q^{29} -7.98257i q^{30} +(4.54621 + 4.54621i) q^{31} +(-1.21577 + 1.21577i) q^{32} +(3.22478 - 3.22478i) q^{33} +(-7.33849 + 7.33849i) q^{34} +(-1.06152 - 8.43867i) q^{35} +4.16620i q^{36} +(-7.34938 - 7.34938i) q^{37} +2.72017 q^{38} +(-0.106106 + 3.60399i) q^{39} -17.2918i q^{40} +(-6.60549 - 6.60549i) q^{41} +(0.819979 + 6.51851i) q^{42} +5.39841i q^{43} +(13.4351 - 13.4351i) q^{44} +(-2.27310 - 2.27310i) q^{45} +(6.91953 + 6.91953i) q^{46} +(7.77396 - 7.77396i) q^{47} +5.02479i q^{48} +(1.73366 + 6.78192i) q^{49} +(9.36583 + 9.36583i) q^{50} +4.17939i q^{51} +(-0.442060 + 15.0149i) q^{52} -0.429035 q^{53} +(1.75588 + 1.75588i) q^{54} +14.6605i q^{55} +(1.77623 + 14.1204i) q^{56} +(0.774590 - 0.774590i) q^{57} +(6.34261 - 6.34261i) q^{58} +(1.29667 - 1.29667i) q^{59} +(-9.47019 - 9.47019i) q^{60} -3.25050i q^{61} +15.9651 q^{62} +(2.08970 + 1.62270i) q^{63} -5.78010i q^{64} +(-7.95105 - 8.43343i) q^{65} -11.3246i q^{66} +(1.90336 - 1.90336i) q^{67} +17.4122i q^{68} +3.94079 q^{69} +(-16.6811 - 12.9534i) q^{70} +(-3.74459 + 3.74459i) q^{71} +(3.80357 + 3.80357i) q^{72} +(-2.36752 + 2.36752i) q^{73} -25.8092 q^{74} +5.33399 q^{75} +(3.22709 - 3.22709i) q^{76} +(-1.50594 - 11.9717i) q^{77} +(6.14185 + 6.51447i) q^{78} +3.64288 q^{79} +(-11.4219 - 11.4219i) q^{80} +1.00000 q^{81} -23.1968 q^{82} +(0.336521 + 0.336521i) q^{83} +(8.70608 + 6.76050i) q^{84} +(-9.50019 - 9.50019i) q^{85} +(9.47893 + 9.47893i) q^{86} -3.61222i q^{87} -24.5313i q^{88} +(-11.2471 + 11.2471i) q^{89} -7.98257 q^{90} +(7.35906 + 6.06994i) q^{91} +16.4181 q^{92} +(4.54621 - 4.54621i) q^{93} -27.3002i q^{94} +3.52145i q^{95} +(1.21577 + 1.21577i) q^{96} +(-0.459600 - 0.459600i) q^{97} +(14.9523 + 8.86411i) q^{98} +(-3.22478 - 3.22478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.75588 1.75588i 1.24159 1.24159i 0.282250 0.959341i \(-0.408919\pi\)
0.959341 0.282250i \(-0.0910809\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 4.16620i 2.08310i
\(5\) 2.27310 + 2.27310i 1.01656 + 1.01656i 0.999861 + 0.0167020i \(0.00531665\pi\)
0.0167020 + 0.999861i \(0.494683\pi\)
\(6\) −1.75588 1.75588i −0.716833 0.716833i
\(7\) −2.08970 1.62270i −0.789831 0.613325i
\(8\) −3.80357 3.80357i −1.34476 1.34476i
\(9\) −1.00000 −0.333333
\(10\) 7.98257 2.52431
\(11\) 3.22478 + 3.22478i 0.972308 + 0.972308i 0.999627 0.0273189i \(-0.00869695\pi\)
−0.0273189 + 0.999627i \(0.508697\pi\)
\(12\) −4.16620 −1.20268
\(13\) −3.60399 0.106106i −0.999567 0.0294286i
\(14\) −6.51851 + 0.819979i −1.74215 + 0.219148i
\(15\) 2.27310 2.27310i 0.586913 0.586913i
\(16\) −5.02479 −1.25620
\(17\) −4.17939 −1.01365 −0.506826 0.862049i \(-0.669181\pi\)
−0.506826 + 0.862049i \(0.669181\pi\)
\(18\) −1.75588 + 1.75588i −0.413864 + 0.413864i
\(19\) 0.774590 + 0.774590i 0.177703 + 0.177703i 0.790354 0.612651i \(-0.209897\pi\)
−0.612651 + 0.790354i \(0.709897\pi\)
\(20\) 9.47019 9.47019i 2.11760 2.11760i
\(21\) −1.62270 + 2.08970i −0.354103 + 0.456009i
\(22\) 11.3246 2.41442
\(23\) 3.94079i 0.821711i 0.911701 + 0.410855i \(0.134770\pi\)
−0.911701 + 0.410855i \(0.865230\pi\)
\(24\) −3.80357 + 3.80357i −0.776400 + 0.776400i
\(25\) 5.33399i 1.06680i
\(26\) −6.51447 + 6.14185i −1.27759 + 1.20452i
\(27\) 1.00000i 0.192450i
\(28\) −6.76050 + 8.70608i −1.27762 + 1.64529i
\(29\) 3.61222 0.670773 0.335386 0.942081i \(-0.391133\pi\)
0.335386 + 0.942081i \(0.391133\pi\)
\(30\) 7.98257i 1.45741i
\(31\) 4.54621 + 4.54621i 0.816523 + 0.816523i 0.985602 0.169080i \(-0.0540795\pi\)
−0.169080 + 0.985602i \(0.554080\pi\)
\(32\) −1.21577 + 1.21577i −0.214920 + 0.214920i
\(33\) 3.22478 3.22478i 0.561362 0.561362i
\(34\) −7.33849 + 7.33849i −1.25854 + 1.25854i
\(35\) −1.06152 8.43867i −0.179430 1.42640i
\(36\) 4.16620i 0.694366i
\(37\) −7.34938 7.34938i −1.20823 1.20823i −0.971599 0.236632i \(-0.923957\pi\)
−0.236632 0.971599i \(-0.576043\pi\)
\(38\) 2.72017 0.441269
\(39\) −0.106106 + 3.60399i −0.0169906 + 0.577100i
\(40\) 17.2918i 2.73407i
\(41\) −6.60549 6.60549i −1.03160 1.03160i −0.999484 0.0321207i \(-0.989774\pi\)
−0.0321207 0.999484i \(-0.510226\pi\)
\(42\) 0.819979 + 6.51851i 0.126525 + 1.00583i
\(43\) 5.39841i 0.823249i 0.911353 + 0.411625i \(0.135039\pi\)
−0.911353 + 0.411625i \(0.864961\pi\)
\(44\) 13.4351 13.4351i 2.02541 2.02541i
\(45\) −2.27310 2.27310i −0.338854 0.338854i
\(46\) 6.91953 + 6.91953i 1.02023 + 1.02023i
\(47\) 7.77396 7.77396i 1.13395 1.13395i 0.144434 0.989514i \(-0.453864\pi\)
0.989514 0.144434i \(-0.0461362\pi\)
\(48\) 5.02479i 0.725266i
\(49\) 1.73366 + 6.78192i 0.247666 + 0.968846i
\(50\) 9.36583 + 9.36583i 1.32453 + 1.32453i
\(51\) 4.17939i 0.585232i
\(52\) −0.442060 + 15.0149i −0.0613027 + 2.08220i
\(53\) −0.429035 −0.0589325 −0.0294662 0.999566i \(-0.509381\pi\)
−0.0294662 + 0.999566i \(0.509381\pi\)
\(54\) 1.75588 + 1.75588i 0.238944 + 0.238944i
\(55\) 14.6605i 1.97682i
\(56\) 1.77623 + 14.1204i 0.237359 + 1.88691i
\(57\) 0.774590 0.774590i 0.102597 0.102597i
\(58\) 6.34261 6.34261i 0.832826 0.832826i
\(59\) 1.29667 1.29667i 0.168812 0.168812i −0.617645 0.786457i \(-0.711913\pi\)
0.786457 + 0.617645i \(0.211913\pi\)
\(60\) −9.47019 9.47019i −1.22260 1.22260i
\(61\) 3.25050i 0.416183i −0.978109 0.208092i \(-0.933275\pi\)
0.978109 0.208092i \(-0.0667252\pi\)
\(62\) 15.9651 2.02757
\(63\) 2.08970 + 1.62270i 0.263277 + 0.204442i
\(64\) 5.78010i 0.722513i
\(65\) −7.95105 8.43343i −0.986206 1.04604i
\(66\) 11.3246i 1.39396i
\(67\) 1.90336 1.90336i 0.232532 0.232532i −0.581217 0.813749i \(-0.697423\pi\)
0.813749 + 0.581217i \(0.197423\pi\)
\(68\) 17.4122i 2.11153i
\(69\) 3.94079 0.474415
\(70\) −16.6811 12.9534i −1.99378 1.54822i
\(71\) −3.74459 + 3.74459i −0.444401 + 0.444401i −0.893488 0.449087i \(-0.851749\pi\)
0.449087 + 0.893488i \(0.351749\pi\)
\(72\) 3.80357 + 3.80357i 0.448255 + 0.448255i
\(73\) −2.36752 + 2.36752i −0.277097 + 0.277097i −0.831949 0.554852i \(-0.812775\pi\)
0.554852 + 0.831949i \(0.312775\pi\)
\(74\) −25.8092 −3.00026
\(75\) 5.33399 0.615916
\(76\) 3.22709 3.22709i 0.370173 0.370173i
\(77\) −1.50594 11.9717i −0.171618 1.36430i
\(78\) 6.14185 + 6.51447i 0.695427 + 0.737618i
\(79\) 3.64288 0.409856 0.204928 0.978777i \(-0.434304\pi\)
0.204928 + 0.978777i \(0.434304\pi\)
\(80\) −11.4219 11.4219i −1.27700 1.27700i
\(81\) 1.00000 0.111111
\(82\) −23.1968 −2.56166
\(83\) 0.336521 + 0.336521i 0.0369379 + 0.0369379i 0.725335 0.688397i \(-0.241685\pi\)
−0.688397 + 0.725335i \(0.741685\pi\)
\(84\) 8.70608 + 6.76050i 0.949911 + 0.737631i
\(85\) −9.50019 9.50019i −1.03044 1.03044i
\(86\) 9.47893 + 9.47893i 1.02214 + 1.02214i
\(87\) 3.61222i 0.387271i
\(88\) 24.5313i 2.61505i
\(89\) −11.2471 + 11.2471i −1.19219 + 1.19219i −0.215737 + 0.976451i \(0.569215\pi\)
−0.976451 + 0.215737i \(0.930785\pi\)
\(90\) −7.98257 −0.841437
\(91\) 7.35906 + 6.06994i 0.771439 + 0.636303i
\(92\) 16.4181 1.71170
\(93\) 4.54621 4.54621i 0.471420 0.471420i
\(94\) 27.3002i 2.81580i
\(95\) 3.52145i 0.361293i
\(96\) 1.21577 + 1.21577i 0.124084 + 0.124084i
\(97\) −0.459600 0.459600i −0.0466653 0.0466653i 0.683389 0.730054i \(-0.260505\pi\)
−0.730054 + 0.683389i \(0.760505\pi\)
\(98\) 14.9523 + 8.86411i 1.51041 + 0.895411i
\(99\) −3.22478 3.22478i −0.324103 0.324103i
\(100\) 22.2225 2.22225
\(101\) 5.58367 0.555596 0.277798 0.960640i \(-0.410395\pi\)
0.277798 + 0.960640i \(0.410395\pi\)
\(102\) 7.33849 + 7.33849i 0.726619 + 0.726619i
\(103\) −14.4248 −1.42131 −0.710657 0.703538i \(-0.751602\pi\)
−0.710657 + 0.703538i \(0.751602\pi\)
\(104\) 13.3044 + 14.1116i 1.30461 + 1.38376i
\(105\) −8.43867 + 1.06152i −0.823530 + 0.103594i
\(106\) −0.753332 + 0.753332i −0.0731701 + 0.0731701i
\(107\) 0.723995 0.0699912 0.0349956 0.999387i \(-0.488858\pi\)
0.0349956 + 0.999387i \(0.488858\pi\)
\(108\) 4.16620 0.400892
\(109\) −3.82447 + 3.82447i −0.366318 + 0.366318i −0.866132 0.499815i \(-0.833401\pi\)
0.499815 + 0.866132i \(0.333401\pi\)
\(110\) 25.7420 + 25.7420i 2.45441 + 2.45441i
\(111\) −7.34938 + 7.34938i −0.697573 + 0.697573i
\(112\) 10.5003 + 8.15375i 0.992184 + 0.770457i
\(113\) −18.2068 −1.71275 −0.856374 0.516357i \(-0.827288\pi\)
−0.856374 + 0.516357i \(0.827288\pi\)
\(114\) 2.72017i 0.254767i
\(115\) −8.95781 + 8.95781i −0.835320 + 0.835320i
\(116\) 15.0492i 1.39729i
\(117\) 3.60399 + 0.106106i 0.333189 + 0.00980954i
\(118\) 4.55357i 0.419190i
\(119\) 8.73366 + 6.78192i 0.800613 + 0.621698i
\(120\) −17.2918 −1.57852
\(121\) 9.79842i 0.890765i
\(122\) −5.70747 5.70747i −0.516730 0.516730i
\(123\) −6.60549 + 6.60549i −0.595597 + 0.595597i
\(124\) 18.9404 18.9404i 1.70090 1.70090i
\(125\) −0.759200 + 0.759200i −0.0679049 + 0.0679049i
\(126\) 6.51851 0.819979i 0.580715 0.0730495i
\(127\) 4.35712i 0.386632i 0.981137 + 0.193316i \(0.0619242\pi\)
−0.981137 + 0.193316i \(0.938076\pi\)
\(128\) −12.5807 12.5807i −1.11199 1.11199i
\(129\) 5.39841 0.475303
\(130\) −28.7691 0.847002i −2.52322 0.0742870i
\(131\) 19.9916i 1.74668i −0.487115 0.873338i \(-0.661951\pi\)
0.487115 0.873338i \(-0.338049\pi\)
\(132\) −13.4351 13.4351i −1.16937 1.16937i
\(133\) −0.361727 2.87559i −0.0313657 0.249345i
\(134\) 6.68411i 0.577419i
\(135\) −2.27310 + 2.27310i −0.195638 + 0.195638i
\(136\) 15.8966 + 15.8966i 1.36312 + 1.36312i
\(137\) 5.53907 + 5.53907i 0.473235 + 0.473235i 0.902960 0.429725i \(-0.141390\pi\)
−0.429725 + 0.902960i \(0.641390\pi\)
\(138\) 6.91953 6.91953i 0.589029 0.589029i
\(139\) 18.8236i 1.59659i −0.602265 0.798296i \(-0.705735\pi\)
0.602265 0.798296i \(-0.294265\pi\)
\(140\) −35.1571 + 4.42250i −2.97132 + 0.373769i
\(141\) −7.77396 7.77396i −0.654686 0.654686i
\(142\) 13.1501i 1.10353i
\(143\) −11.2799 11.9642i −0.943273 1.00050i
\(144\) 5.02479 0.418733
\(145\) 8.21095 + 8.21095i 0.681883 + 0.681883i
\(146\) 8.31412i 0.688082i
\(147\) 6.78192 1.73366i 0.559363 0.142990i
\(148\) −30.6190 + 30.6190i −2.51686 + 2.51686i
\(149\) 0.387442 0.387442i 0.0317405 0.0317405i −0.691058 0.722799i \(-0.742855\pi\)
0.722799 + 0.691058i \(0.242855\pi\)
\(150\) 9.36583 9.36583i 0.764716 0.764716i
\(151\) 2.85380 + 2.85380i 0.232239 + 0.232239i 0.813627 0.581387i \(-0.197490\pi\)
−0.581387 + 0.813627i \(0.697490\pi\)
\(152\) 5.89241i 0.477938i
\(153\) 4.17939 0.337884
\(154\) −23.6650 18.3765i −1.90698 1.48082i
\(155\) 20.6680i 1.66009i
\(156\) 15.0149 + 0.442060i 1.20216 + 0.0353931i
\(157\) 21.8189i 1.74134i 0.491869 + 0.870669i \(0.336314\pi\)
−0.491869 + 0.870669i \(0.663686\pi\)
\(158\) 6.39645 6.39645i 0.508874 0.508874i
\(159\) 0.429035i 0.0340247i
\(160\) −5.52714 −0.436959
\(161\) 6.39473 8.23504i 0.503975 0.649012i
\(162\) 1.75588 1.75588i 0.137955 0.137955i
\(163\) −15.2280 15.2280i −1.19275 1.19275i −0.976293 0.216455i \(-0.930551\pi\)
−0.216455 0.976293i \(-0.569449\pi\)
\(164\) −27.5198 + 27.5198i −2.14893 + 2.14893i
\(165\) 14.6605 1.14132
\(166\) 1.18178 0.0917236
\(167\) 0.578070 0.578070i 0.0447324 0.0447324i −0.684387 0.729119i \(-0.739930\pi\)
0.729119 + 0.684387i \(0.239930\pi\)
\(168\) 14.1204 1.77623i 1.08941 0.137039i
\(169\) 12.9775 + 0.764813i 0.998268 + 0.0588318i
\(170\) −33.3623 −2.55877
\(171\) −0.774590 0.774590i −0.0592344 0.0592344i
\(172\) 22.4908 1.71491
\(173\) −0.696157 −0.0529279 −0.0264639 0.999650i \(-0.508425\pi\)
−0.0264639 + 0.999650i \(0.508425\pi\)
\(174\) −6.34261 6.34261i −0.480832 0.480832i
\(175\) 8.65550 11.1464i 0.654294 0.842590i
\(176\) −16.2038 16.2038i −1.22141 1.22141i
\(177\) −1.29667 1.29667i −0.0974634 0.0974634i
\(178\) 39.4970i 2.96042i
\(179\) 0.801167i 0.0598820i −0.999552 0.0299410i \(-0.990468\pi\)
0.999552 0.0299410i \(-0.00953194\pi\)
\(180\) −9.47019 + 9.47019i −0.705866 + 0.705866i
\(181\) 22.4677 1.67001 0.835005 0.550242i \(-0.185465\pi\)
0.835005 + 0.550242i \(0.185465\pi\)
\(182\) 23.5797 2.26354i 1.74784 0.167785i
\(183\) −3.25050 −0.240284
\(184\) 14.9890 14.9890i 1.10501 1.10501i
\(185\) 33.4118i 2.45648i
\(186\) 15.9651i 1.17062i
\(187\) −13.4776 13.4776i −0.985581 0.985581i
\(188\) −32.3878 32.3878i −2.36213 2.36213i
\(189\) 1.62270 2.08970i 0.118034 0.152003i
\(190\) 6.18322 + 6.18322i 0.448578 + 0.448578i
\(191\) 15.7270 1.13796 0.568982 0.822350i \(-0.307337\pi\)
0.568982 + 0.822350i \(0.307337\pi\)
\(192\) −5.78010 −0.417143
\(193\) 6.55862 + 6.55862i 0.472100 + 0.472100i 0.902594 0.430494i \(-0.141661\pi\)
−0.430494 + 0.902594i \(0.641661\pi\)
\(194\) −1.61400 −0.115879
\(195\) −8.43343 + 7.95105i −0.603930 + 0.569386i
\(196\) 28.2548 7.22276i 2.01820 0.515912i
\(197\) −0.440789 + 0.440789i −0.0314049 + 0.0314049i −0.722635 0.691230i \(-0.757069\pi\)
0.691230 + 0.722635i \(0.257069\pi\)
\(198\) −11.3246 −0.804806
\(199\) 12.3117 0.872750 0.436375 0.899765i \(-0.356262\pi\)
0.436375 + 0.899765i \(0.356262\pi\)
\(200\) 20.2882 20.2882i 1.43459 1.43459i
\(201\) −1.90336 1.90336i −0.134252 0.134252i
\(202\) 9.80422 9.80422i 0.689823 0.689823i
\(203\) −7.54845 5.86157i −0.529797 0.411402i
\(204\) 17.4122 1.21910
\(205\) 30.0299i 2.09738i
\(206\) −25.3281 + 25.3281i −1.76469 + 1.76469i
\(207\) 3.94079i 0.273904i
\(208\) 18.1093 + 0.533163i 1.25565 + 0.0369682i
\(209\) 4.99577i 0.345564i
\(210\) −12.9534 + 16.6811i −0.893866 + 1.15111i
\(211\) −1.27815 −0.0879914 −0.0439957 0.999032i \(-0.514009\pi\)
−0.0439957 + 0.999032i \(0.514009\pi\)
\(212\) 1.78744i 0.122762i
\(213\) 3.74459 + 3.74459i 0.256575 + 0.256575i
\(214\) 1.27125 1.27125i 0.0869005 0.0869005i
\(215\) −12.2711 + 12.2711i −0.836884 + 0.836884i
\(216\) 3.80357 3.80357i 0.258800 0.258800i
\(217\) −2.12304 16.8773i −0.144121 1.14571i
\(218\) 13.4306i 0.909633i
\(219\) 2.36752 + 2.36752i 0.159982 + 0.159982i
\(220\) 61.0786 4.11792
\(221\) 15.0625 + 0.443460i 1.01321 + 0.0298304i
\(222\) 25.8092i 1.73220i
\(223\) 8.41160 + 8.41160i 0.563283 + 0.563283i 0.930238 0.366956i \(-0.119600\pi\)
−0.366956 + 0.930238i \(0.619600\pi\)
\(224\) 4.51343 0.567754i 0.301566 0.0379347i
\(225\) 5.33399i 0.355600i
\(226\) −31.9688 + 31.9688i −2.12653 + 2.12653i
\(227\) −2.87572 2.87572i −0.190869 0.190869i 0.605203 0.796071i \(-0.293092\pi\)
−0.796071 + 0.605203i \(0.793092\pi\)
\(228\) −3.22709 3.22709i −0.213720 0.213720i
\(229\) 3.18307 3.18307i 0.210343 0.210343i −0.594070 0.804413i \(-0.702480\pi\)
0.804413 + 0.594070i \(0.202480\pi\)
\(230\) 31.4576i 2.07425i
\(231\) −11.9717 + 1.50594i −0.787679 + 0.0990839i
\(232\) −13.7393 13.7393i −0.902032 0.902032i
\(233\) 17.7925i 1.16563i −0.812607 0.582813i \(-0.801952\pi\)
0.812607 0.582813i \(-0.198048\pi\)
\(234\) 6.51447 6.14185i 0.425864 0.401505i
\(235\) 35.3420 2.30546
\(236\) −5.40216 5.40216i −0.351651 0.351651i
\(237\) 3.64288i 0.236631i
\(238\) 27.2434 3.42701i 1.76593 0.222140i
\(239\) 11.1681 11.1681i 0.722407 0.722407i −0.246688 0.969095i \(-0.579342\pi\)
0.969095 + 0.246688i \(0.0793424\pi\)
\(240\) −11.4219 + 11.4219i −0.737278 + 0.737278i
\(241\) −5.05729 + 5.05729i −0.325768 + 0.325768i −0.850975 0.525206i \(-0.823988\pi\)
0.525206 + 0.850975i \(0.323988\pi\)
\(242\) 17.2048 + 17.2048i 1.10597 + 1.10597i
\(243\) 1.00000i 0.0641500i
\(244\) −13.5422 −0.866951
\(245\) −11.4752 + 19.3568i −0.733125 + 1.23666i
\(246\) 23.1968i 1.47898i
\(247\) −2.70943 2.87380i −0.172397 0.182856i
\(248\) 34.5836i 2.19606i
\(249\) 0.336521 0.336521i 0.0213261 0.0213261i
\(250\) 2.66612i 0.168620i
\(251\) −1.12847 −0.0712284 −0.0356142 0.999366i \(-0.511339\pi\)
−0.0356142 + 0.999366i \(0.511339\pi\)
\(252\) 6.76050 8.70608i 0.425872 0.548432i
\(253\) −12.7082 + 12.7082i −0.798956 + 0.798956i
\(254\) 7.65055 + 7.65055i 0.480038 + 0.480038i
\(255\) −9.50019 + 9.50019i −0.594925 + 0.594925i
\(256\) −32.6200 −2.03875
\(257\) 28.2971 1.76512 0.882562 0.470196i \(-0.155817\pi\)
0.882562 + 0.470196i \(0.155817\pi\)
\(258\) 9.47893 9.47893i 0.590132 0.590132i
\(259\) 3.43210 + 27.2839i 0.213260 + 1.69534i
\(260\) −35.1353 + 33.1256i −2.17900 + 2.05436i
\(261\) −3.61222 −0.223591
\(262\) −35.1028 35.1028i −2.16866 2.16866i
\(263\) 17.0950 1.05412 0.527061 0.849828i \(-0.323294\pi\)
0.527061 + 0.849828i \(0.323294\pi\)
\(264\) −24.5313 −1.50980
\(265\) −0.975241 0.975241i −0.0599086 0.0599086i
\(266\) −5.68432 4.41403i −0.348528 0.270641i
\(267\) 11.2471 + 11.2471i 0.688310 + 0.688310i
\(268\) −7.92975 7.92975i −0.484387 0.484387i
\(269\) 4.65103i 0.283578i 0.989897 + 0.141789i \(0.0452855\pi\)
−0.989897 + 0.141789i \(0.954715\pi\)
\(270\) 7.98257i 0.485804i
\(271\) −9.51718 + 9.51718i −0.578128 + 0.578128i −0.934387 0.356259i \(-0.884052\pi\)
0.356259 + 0.934387i \(0.384052\pi\)
\(272\) 21.0006 1.27335
\(273\) 6.06994 7.35906i 0.367370 0.445391i
\(274\) 19.4518 1.17513
\(275\) −17.2010 + 17.2010i −1.03726 + 1.03726i
\(276\) 16.4181i 0.988252i
\(277\) 18.5055i 1.11189i 0.831220 + 0.555943i \(0.187643\pi\)
−0.831220 + 0.555943i \(0.812357\pi\)
\(278\) −33.0518 33.0518i −1.98232 1.98232i
\(279\) −4.54621 4.54621i −0.272174 0.272174i
\(280\) −28.0595 + 36.1346i −1.67688 + 2.15946i
\(281\) −14.2256 14.2256i −0.848630 0.848630i 0.141332 0.989962i \(-0.454861\pi\)
−0.989962 + 0.141332i \(0.954861\pi\)
\(282\) −27.3002 −1.62570
\(283\) 6.56107 0.390015 0.195008 0.980802i \(-0.437527\pi\)
0.195008 + 0.980802i \(0.437527\pi\)
\(284\) 15.6007 + 15.6007i 0.925731 + 0.925731i
\(285\) 3.52145 0.208592
\(286\) −40.8138 1.20162i −2.41337 0.0710530i
\(287\) 3.08471 + 24.5222i 0.182085 + 1.44750i
\(288\) 1.21577 1.21577i 0.0716399 0.0716399i
\(289\) 0.467318 0.0274893
\(290\) 28.8348 1.69324
\(291\) −0.459600 + 0.459600i −0.0269422 + 0.0269422i
\(292\) 9.86353 + 9.86353i 0.577220 + 0.577220i
\(293\) 0.883923 0.883923i 0.0516393 0.0516393i −0.680816 0.732455i \(-0.738374\pi\)
0.732455 + 0.680816i \(0.238374\pi\)
\(294\) 8.86411 14.9523i 0.516966 0.872035i
\(295\) 5.89491 0.343215
\(296\) 55.9078i 3.24957i
\(297\) −3.22478 + 3.22478i −0.187121 + 0.187121i
\(298\) 1.36060i 0.0788175i
\(299\) 0.418143 14.2025i 0.0241818 0.821355i
\(300\) 22.2225i 1.28301i
\(301\) 8.76002 11.2810i 0.504919 0.650228i
\(302\) 10.0218 0.576693
\(303\) 5.58367i 0.320773i
\(304\) −3.89215 3.89215i −0.223230 0.223230i
\(305\) 7.38871 7.38871i 0.423076 0.423076i
\(306\) 7.33849 7.33849i 0.419514 0.419514i
\(307\) 3.01480 3.01480i 0.172064 0.172064i −0.615822 0.787885i \(-0.711176\pi\)
0.787885 + 0.615822i \(0.211176\pi\)
\(308\) −49.8763 + 6.27406i −2.84197 + 0.357498i
\(309\) 14.4248i 0.820596i
\(310\) 36.2904 + 36.2904i 2.06116 + 2.06116i
\(311\) 19.0648 1.08107 0.540533 0.841323i \(-0.318222\pi\)
0.540533 + 0.841323i \(0.318222\pi\)
\(312\) 14.1116 13.3044i 0.798912 0.753215i
\(313\) 5.98295i 0.338176i 0.985601 + 0.169088i \(0.0540822\pi\)
−0.985601 + 0.169088i \(0.945918\pi\)
\(314\) 38.3113 + 38.3113i 2.16203 + 2.16203i
\(315\) 1.06152 + 8.43867i 0.0598098 + 0.475465i
\(316\) 15.1770i 0.853771i
\(317\) −4.18438 + 4.18438i −0.235018 + 0.235018i −0.814783 0.579765i \(-0.803144\pi\)
0.579765 + 0.814783i \(0.303144\pi\)
\(318\) 0.753332 + 0.753332i 0.0422448 + 0.0422448i
\(319\) 11.6486 + 11.6486i 0.652198 + 0.652198i
\(320\) 13.1388 13.1388i 0.734479 0.734479i
\(321\) 0.723995i 0.0404095i
\(322\) −3.23136 25.6881i −0.180077 1.43154i
\(323\) −3.23732 3.23732i −0.180129 0.180129i
\(324\) 4.16620i 0.231455i
\(325\) 0.565971 19.2237i 0.0313944 1.06634i
\(326\) −53.4769 −2.96181
\(327\) 3.82447 + 3.82447i 0.211494 + 0.211494i
\(328\) 50.2489i 2.77453i
\(329\) −28.8601 + 3.63037i −1.59111 + 0.200149i
\(330\) 25.7420 25.7420i 1.41705 1.41705i
\(331\) −12.8296 + 12.8296i −0.705179 + 0.705179i −0.965517 0.260339i \(-0.916166\pi\)
0.260339 + 0.965517i \(0.416166\pi\)
\(332\) 1.40201 1.40201i 0.0769453 0.0769453i
\(333\) 7.34938 + 7.34938i 0.402744 + 0.402744i
\(334\) 2.03004i 0.111079i
\(335\) 8.65304 0.472766
\(336\) 8.15375 10.5003i 0.444824 0.572838i
\(337\) 24.2890i 1.32310i −0.749899 0.661552i \(-0.769898\pi\)
0.749899 0.661552i \(-0.230102\pi\)
\(338\) 24.1298 21.4439i 1.31249 1.16640i
\(339\) 18.2068i 0.988855i
\(340\) −39.5796 + 39.5796i −2.14651 + 2.14651i
\(341\) 29.3210i 1.58782i
\(342\) −2.72017 −0.147090
\(343\) 7.38223 16.9854i 0.398603 0.917124i
\(344\) 20.5332 20.5332i 1.10708 1.10708i
\(345\) 8.95781 + 8.95781i 0.482272 + 0.482272i
\(346\) −1.22237 + 1.22237i −0.0657148 + 0.0657148i
\(347\) 23.6977 1.27216 0.636080 0.771623i \(-0.280555\pi\)
0.636080 + 0.771623i \(0.280555\pi\)
\(348\) −15.0492 −0.806723
\(349\) 16.5957 16.5957i 0.888347 0.888347i −0.106017 0.994364i \(-0.533810\pi\)
0.994364 + 0.106017i \(0.0338098\pi\)
\(350\) −4.37376 34.7697i −0.233787 1.85852i
\(351\) 0.106106 3.60399i 0.00566354 0.192367i
\(352\) −7.84118 −0.417936
\(353\) 6.69947 + 6.69947i 0.356577 + 0.356577i 0.862550 0.505973i \(-0.168866\pi\)
−0.505973 + 0.862550i \(0.668866\pi\)
\(354\) −4.55357 −0.242019
\(355\) −17.0237 −0.903523
\(356\) 46.8575 + 46.8575i 2.48345 + 2.48345i
\(357\) 6.78192 8.73366i 0.358937 0.462234i
\(358\) −1.40675 1.40675i −0.0743490 0.0743490i
\(359\) 20.8627 + 20.8627i 1.10109 + 1.10109i 0.994279 + 0.106812i \(0.0340642\pi\)
0.106812 + 0.994279i \(0.465936\pi\)
\(360\) 17.2918i 0.911358i
\(361\) 17.8000i 0.936843i
\(362\) 39.4505 39.4505i 2.07347 2.07347i
\(363\) 9.79842 0.514284
\(364\) 25.2886 30.6593i 1.32548 1.60698i
\(365\) −10.7632 −0.563372
\(366\) −5.70747 + 5.70747i −0.298334 + 0.298334i
\(367\) 0.958792i 0.0500485i −0.999687 0.0250243i \(-0.992034\pi\)
0.999687 0.0250243i \(-0.00796630\pi\)
\(368\) 19.8016i 1.03223i
\(369\) 6.60549 + 6.60549i 0.343868 + 0.343868i
\(370\) −58.6670 58.6670i −3.04995 3.04995i
\(371\) 0.896553 + 0.696197i 0.0465467 + 0.0361447i
\(372\) −18.9404 18.9404i −0.982013 0.982013i
\(373\) 0.340995 0.0176560 0.00882802 0.999961i \(-0.497190\pi\)
0.00882802 + 0.999961i \(0.497190\pi\)
\(374\) −47.3300 −2.44738
\(375\) 0.759200 + 0.759200i 0.0392049 + 0.0392049i
\(376\) −59.1376 −3.04979
\(377\) −13.0184 0.383280i −0.670482 0.0197399i
\(378\) −0.819979 6.51851i −0.0421751 0.335276i
\(379\) −17.4497 + 17.4497i −0.896330 + 0.896330i −0.995109 0.0987798i \(-0.968506\pi\)
0.0987798 + 0.995109i \(0.468506\pi\)
\(380\) 14.6710 0.752608
\(381\) 4.35712 0.223222
\(382\) 27.6146 27.6146i 1.41289 1.41289i
\(383\) −0.285743 0.285743i −0.0146008 0.0146008i 0.699769 0.714369i \(-0.253286\pi\)
−0.714369 + 0.699769i \(0.753286\pi\)
\(384\) −12.5807 + 12.5807i −0.642005 + 0.642005i
\(385\) 23.7897 30.6360i 1.21243 1.56136i
\(386\) 23.0322 1.17231
\(387\) 5.39841i 0.274416i
\(388\) −1.91478 + 1.91478i −0.0972084 + 0.0972084i
\(389\) 24.5975i 1.24714i 0.781766 + 0.623572i \(0.214319\pi\)
−0.781766 + 0.623572i \(0.785681\pi\)
\(390\) −0.847002 + 28.7691i −0.0428896 + 1.45678i
\(391\) 16.4701i 0.832928i
\(392\) 19.2014 32.3896i 0.969817 1.63592i
\(393\) −19.9916 −1.00844
\(394\) 1.54794i 0.0779842i
\(395\) 8.28065 + 8.28065i 0.416645 + 0.416645i
\(396\) −13.4351 + 13.4351i −0.675137 + 0.675137i
\(397\) −13.7002 + 13.7002i −0.687593 + 0.687593i −0.961699 0.274106i \(-0.911618\pi\)
0.274106 + 0.961699i \(0.411618\pi\)
\(398\) 21.6177 21.6177i 1.08360 1.08360i
\(399\) −2.87559 + 0.361727i −0.143960 + 0.0181090i
\(400\) 26.8022i 1.34011i
\(401\) −20.6555 20.6555i −1.03149 1.03149i −0.999488 0.0320001i \(-0.989812\pi\)
−0.0320001 0.999488i \(-0.510188\pi\)
\(402\) −6.68411 −0.333373
\(403\) −15.9021 16.8669i −0.792140 0.840198i
\(404\) 23.2626i 1.15736i
\(405\) 2.27310 + 2.27310i 0.112951 + 0.112951i
\(406\) −23.5463 + 2.96195i −1.16858 + 0.146999i
\(407\) 47.4003i 2.34955i
\(408\) 15.8966 15.8966i 0.786999 0.786999i
\(409\) −13.1018 13.1018i −0.647845 0.647845i 0.304627 0.952472i \(-0.401468\pi\)
−0.952472 + 0.304627i \(0.901468\pi\)
\(410\) −52.7288 52.7288i −2.60409 2.60409i
\(411\) 5.53907 5.53907i 0.273222 0.273222i
\(412\) 60.0964i 2.96074i
\(413\) −4.81374 + 0.605532i −0.236869 + 0.0297963i
\(414\) −6.91953 6.91953i −0.340076 0.340076i
\(415\) 1.52989i 0.0750995i
\(416\) 4.51062 4.25262i 0.221152 0.208502i
\(417\) −18.8236 −0.921793
\(418\) 8.77194 + 8.77194i 0.429050 + 0.429050i
\(419\) 27.3048i 1.33392i 0.745091 + 0.666962i \(0.232406\pi\)
−0.745091 + 0.666962i \(0.767594\pi\)
\(420\) 4.42250 + 35.1571i 0.215796 + 1.71549i
\(421\) 0.649398 0.649398i 0.0316497 0.0316497i −0.691105 0.722755i \(-0.742876\pi\)
0.722755 + 0.691105i \(0.242876\pi\)
\(422\) −2.24427 + 2.24427i −0.109249 + 0.109249i
\(423\) −7.77396 + 7.77396i −0.377983 + 0.377983i
\(424\) 1.63186 + 1.63186i 0.0792503 + 0.0792503i
\(425\) 22.2928i 1.08136i
\(426\) 13.1501 0.637123
\(427\) −5.27460 + 6.79255i −0.255256 + 0.328714i
\(428\) 3.01630i 0.145799i
\(429\) −11.9642 + 11.2799i −0.577639 + 0.544599i
\(430\) 43.0932i 2.07814i
\(431\) −17.5655 + 17.5655i −0.846102 + 0.846102i −0.989644 0.143542i \(-0.954151\pi\)
0.143542 + 0.989644i \(0.454151\pi\)
\(432\) 5.02479i 0.241755i
\(433\) −27.3091 −1.31239 −0.656196 0.754590i \(-0.727836\pi\)
−0.656196 + 0.754590i \(0.727836\pi\)
\(434\) −33.3623 25.9067i −1.60144 1.24356i
\(435\) 8.21095 8.21095i 0.393685 0.393685i
\(436\) 15.9335 + 15.9335i 0.763075 + 0.763075i
\(437\) −3.05249 + 3.05249i −0.146021 + 0.146021i
\(438\) 8.31412 0.397264
\(439\) −1.15280 −0.0550201 −0.0275100 0.999622i \(-0.508758\pi\)
−0.0275100 + 0.999622i \(0.508758\pi\)
\(440\) 55.7623 55.7623i 2.65836 2.65836i
\(441\) −1.73366 6.78192i −0.0825552 0.322949i
\(442\) 27.2265 25.6692i 1.29503 1.22096i
\(443\) 8.04614 0.382284 0.191142 0.981562i \(-0.438781\pi\)
0.191142 + 0.981562i \(0.438781\pi\)
\(444\) 30.6190 + 30.6190i 1.45311 + 1.45311i
\(445\) −51.1316 −2.42387
\(446\) 29.5395 1.39873
\(447\) −0.387442 0.387442i −0.0183254 0.0183254i
\(448\) −9.37940 + 12.0787i −0.443135 + 0.570663i
\(449\) 9.18043 + 9.18043i 0.433251 + 0.433251i 0.889733 0.456482i \(-0.150891\pi\)
−0.456482 + 0.889733i \(0.650891\pi\)
\(450\) −9.36583 9.36583i −0.441509 0.441509i
\(451\) 42.6025i 2.00607i
\(452\) 75.8529i 3.56782i
\(453\) 2.85380 2.85380i 0.134083 0.134083i
\(454\) −10.0988 −0.473961
\(455\) 2.93031 + 30.5255i 0.137375 + 1.43106i
\(456\) −5.89241 −0.275938
\(457\) 25.8083 25.8083i 1.20726 1.20726i 0.235354 0.971910i \(-0.424375\pi\)
0.971910 0.235354i \(-0.0756248\pi\)
\(458\) 11.1781i 0.522320i
\(459\) 4.17939i 0.195077i
\(460\) 37.3200 + 37.3200i 1.74005 + 1.74005i
\(461\) −22.8970 22.8970i −1.06642 1.06642i −0.997631 0.0687888i \(-0.978087\pi\)
−0.0687888 0.997631i \(-0.521913\pi\)
\(462\) −18.3765 + 23.6650i −0.854953 + 1.10100i
\(463\) 6.51855 + 6.51855i 0.302943 + 0.302943i 0.842164 0.539221i \(-0.181281\pi\)
−0.539221 + 0.842164i \(0.681281\pi\)
\(464\) −18.1507 −0.842624
\(465\) 20.6680 0.958455
\(466\) −31.2414 31.2414i −1.44723 1.44723i
\(467\) 22.5573 1.04383 0.521914 0.852998i \(-0.325218\pi\)
0.521914 + 0.852998i \(0.325218\pi\)
\(468\) 0.442060 15.0149i 0.0204342 0.694065i
\(469\) −7.06602 + 0.888850i −0.326278 + 0.0410433i
\(470\) 62.0562 62.0562i 2.86244 2.86244i
\(471\) 21.8189 1.00536
\(472\) −9.86391 −0.454023
\(473\) −17.4087 + 17.4087i −0.800452 + 0.800452i
\(474\) −6.39645 6.39645i −0.293799 0.293799i
\(475\) −4.13166 + 4.13166i −0.189573 + 0.189573i
\(476\) 28.2548 36.3861i 1.29506 1.66776i
\(477\) 0.429035 0.0196442
\(478\) 39.2197i 1.79387i
\(479\) 9.06086 9.06086i 0.414001 0.414001i −0.469129 0.883130i \(-0.655432\pi\)
0.883130 + 0.469129i \(0.155432\pi\)
\(480\) 5.52714i 0.252278i
\(481\) 25.7073 + 27.2669i 1.17215 + 1.24326i
\(482\) 17.7599i 0.808942i
\(483\) −8.23504 6.39473i −0.374707 0.290970i
\(484\) 40.8221 1.85555
\(485\) 2.08944i 0.0948764i
\(486\) −1.75588 1.75588i −0.0796481 0.0796481i
\(487\) 1.61762 1.61762i 0.0733015 0.0733015i −0.669506 0.742807i \(-0.733494\pi\)
0.742807 + 0.669506i \(0.233494\pi\)
\(488\) −12.3635 + 12.3635i −0.559669 + 0.559669i
\(489\) −15.2280 + 15.2280i −0.688633 + 0.688633i
\(490\) 13.8391 + 54.1371i 0.625185 + 2.44567i
\(491\) 9.87760i 0.445770i −0.974845 0.222885i \(-0.928453\pi\)
0.974845 0.222885i \(-0.0715474\pi\)
\(492\) 27.5198 + 27.5198i 1.24069 + 1.24069i
\(493\) −15.0969 −0.679930
\(494\) −9.80345 0.288627i −0.441078 0.0129860i
\(495\) 14.6605i 0.658941i
\(496\) −22.8437 22.8437i −1.02571 1.02571i
\(497\) 13.9014 1.74869i 0.623564 0.0784396i
\(498\) 1.18178i 0.0529567i
\(499\) −23.4077 + 23.4077i −1.04787 + 1.04787i −0.0490768 + 0.998795i \(0.515628\pi\)
−0.998795 + 0.0490768i \(0.984372\pi\)
\(500\) 3.16297 + 3.16297i 0.141453 + 0.141453i
\(501\) −0.578070 0.578070i −0.0258263 0.0258263i
\(502\) −1.98145 + 1.98145i −0.0884366 + 0.0884366i
\(503\) 5.15552i 0.229873i −0.993373 0.114937i \(-0.963334\pi\)
0.993373 0.114937i \(-0.0366665\pi\)
\(504\) −1.77623 14.1204i −0.0791197 0.628971i
\(505\) 12.6923 + 12.6923i 0.564798 + 0.564798i
\(506\) 44.6279i 1.98395i
\(507\) 0.764813 12.9775i 0.0339665 0.576350i
\(508\) 18.1526 0.805391
\(509\) −4.51339 4.51339i −0.200053 0.200053i 0.599970 0.800023i \(-0.295179\pi\)
−0.800023 + 0.599970i \(0.795179\pi\)
\(510\) 33.3623i 1.47731i
\(511\) 8.78917 1.10561i 0.388810 0.0489093i
\(512\) −32.1153 + 32.1153i −1.41931 + 1.41931i
\(513\) −0.774590 + 0.774590i −0.0341990 + 0.0341990i
\(514\) 49.6862 49.6862i 2.19156 2.19156i
\(515\) −32.7890 32.7890i −1.44486 1.44486i
\(516\) 22.4908i 0.990103i
\(517\) 50.1386 2.20509
\(518\) 53.9334 + 41.8807i 2.36970 + 1.84013i
\(519\) 0.696157i 0.0305579i
\(520\) −1.83477 + 62.3195i −0.0804600 + 2.73289i
\(521\) 4.80886i 0.210680i 0.994436 + 0.105340i \(0.0335931\pi\)
−0.994436 + 0.105340i \(0.966407\pi\)
\(522\) −6.34261 + 6.34261i −0.277609 + 0.277609i
\(523\) 34.0474i 1.48879i 0.667740 + 0.744395i \(0.267262\pi\)
−0.667740 + 0.744395i \(0.732738\pi\)
\(524\) −83.2890 −3.63850
\(525\) −11.1464 8.65550i −0.486470 0.377757i
\(526\) 30.0167 30.0167i 1.30879 1.30879i
\(527\) −19.0004 19.0004i −0.827669 0.827669i
\(528\) −16.2038 + 16.2038i −0.705182 + 0.705182i
\(529\) 7.47021 0.324792
\(530\) −3.42480 −0.148764
\(531\) −1.29667 + 1.29667i −0.0562705 + 0.0562705i
\(532\) −11.9803 + 1.50702i −0.519410 + 0.0653378i
\(533\) 23.1052 + 24.5070i 1.00080 + 1.06152i
\(534\) 39.4970 1.70920
\(535\) 1.64572 + 1.64572i 0.0711505 + 0.0711505i
\(536\) −14.4791 −0.625401
\(537\) −0.801167 −0.0345729
\(538\) 8.16662 + 8.16662i 0.352088 + 0.352088i
\(539\) −16.2795 + 27.4609i −0.701209 + 1.18282i
\(540\) 9.47019 + 9.47019i 0.407532 + 0.407532i
\(541\) 13.3027 + 13.3027i 0.571929 + 0.571929i 0.932667 0.360738i \(-0.117475\pi\)
−0.360738 + 0.932667i \(0.617475\pi\)
\(542\) 33.4220i 1.43560i
\(543\) 22.4677i 0.964181i
\(544\) 5.08118 5.08118i 0.217854 0.217854i
\(545\) −17.3868 −0.744769
\(546\) −2.26354 23.5797i −0.0968705 1.00912i
\(547\) −42.9461 −1.83624 −0.918122 0.396298i \(-0.870295\pi\)
−0.918122 + 0.396298i \(0.870295\pi\)
\(548\) 23.0768 23.0768i 0.985794 0.985794i
\(549\) 3.25050i 0.138728i
\(550\) 60.4055i 2.57570i
\(551\) 2.79799 + 2.79799i 0.119198 + 0.119198i
\(552\) −14.9890 14.9890i −0.637976 0.637976i
\(553\) −7.61252 5.91132i −0.323717 0.251375i
\(554\) 32.4933 + 32.4933i 1.38051 + 1.38051i
\(555\) −33.4118 −1.41825
\(556\) −78.4226 −3.32586
\(557\) −21.0174 21.0174i −0.890534 0.890534i 0.104039 0.994573i \(-0.466823\pi\)
−0.994573 + 0.104039i \(0.966823\pi\)
\(558\) −15.9651 −0.675858
\(559\) 0.572806 19.4558i 0.0242271 0.822893i
\(560\) 5.33391 + 42.4025i 0.225399 + 1.79183i
\(561\) −13.4776 + 13.4776i −0.569026 + 0.569026i
\(562\) −49.9569 −2.10730
\(563\) 18.6622 0.786518 0.393259 0.919428i \(-0.371348\pi\)
0.393259 + 0.919428i \(0.371348\pi\)
\(564\) −32.3878 + 32.3878i −1.36377 + 1.36377i
\(565\) −41.3858 41.3858i −1.74111 1.74111i
\(566\) 11.5204 11.5204i 0.484239 0.484239i
\(567\) −2.08970 1.62270i −0.0877590 0.0681472i
\(568\) 28.4856 1.19523
\(569\) 21.7954i 0.913711i 0.889541 + 0.456855i \(0.151024\pi\)
−0.889541 + 0.456855i \(0.848976\pi\)
\(570\) 6.18322 6.18322i 0.258987 0.258987i
\(571\) 0.292431i 0.0122378i −0.999981 0.00611892i \(-0.998052\pi\)
0.999981 0.00611892i \(-0.00194773\pi\)
\(572\) −49.8454 + 46.9943i −2.08414 + 1.96493i
\(573\) 15.7270i 0.657004i
\(574\) 48.4743 + 37.6416i 2.02328 + 1.57113i
\(575\) −21.0201 −0.876600
\(576\) 5.78010i 0.240838i
\(577\) 11.7221 + 11.7221i 0.487999 + 0.487999i 0.907674 0.419675i \(-0.137856\pi\)
−0.419675 + 0.907674i \(0.637856\pi\)
\(578\) 0.820552 0.820552i 0.0341305 0.0341305i
\(579\) 6.55862 6.55862i 0.272567 0.272567i
\(580\) 34.2084 34.2084i 1.42043 1.42043i
\(581\) −0.157152 1.24930i −0.00651977 0.0518297i
\(582\) 1.61400i 0.0669025i
\(583\) −1.38354 1.38354i −0.0573005 0.0573005i
\(584\) 18.0100 0.745260
\(585\) 7.95105 + 8.43343i 0.328735 + 0.348679i
\(586\) 3.10412i 0.128230i
\(587\) −18.3164 18.3164i −0.756000 0.756000i 0.219591 0.975592i \(-0.429528\pi\)
−0.975592 + 0.219591i \(0.929528\pi\)
\(588\) −7.22276 28.2548i −0.297862 1.16521i
\(589\) 7.04289i 0.290197i
\(590\) 10.3507 10.3507i 0.426133 0.426133i
\(591\) 0.440789 + 0.440789i 0.0181316 + 0.0181316i
\(592\) 36.9291 + 36.9291i 1.51778 + 1.51778i
\(593\) −21.2377 + 21.2377i −0.872129 + 0.872129i −0.992704 0.120575i \(-0.961526\pi\)
0.120575 + 0.992704i \(0.461526\pi\)
\(594\) 11.3246i 0.464655i
\(595\) 4.43651 + 35.2685i 0.181879 + 1.44587i
\(596\) −1.61416 1.61416i −0.0661186 0.0661186i
\(597\) 12.3117i 0.503883i
\(598\) −24.2037 25.6721i −0.989763 1.04981i
\(599\) −3.95433 −0.161569 −0.0807847 0.996732i \(-0.525743\pi\)
−0.0807847 + 0.996732i \(0.525743\pi\)
\(600\) −20.2882 20.2882i −0.828262 0.828262i
\(601\) 8.53122i 0.347996i −0.984746 0.173998i \(-0.944331\pi\)
0.984746 0.173998i \(-0.0556686\pi\)
\(602\) −4.42658 35.1896i −0.180414 1.43422i
\(603\) −1.90336 + 1.90336i −0.0775106 + 0.0775106i
\(604\) 11.8895 11.8895i 0.483777 0.483777i
\(605\) −22.2728 + 22.2728i −0.905519 + 0.905519i
\(606\) −9.80422 9.80422i −0.398269 0.398269i
\(607\) 4.46430i 0.181200i −0.995887 0.0906002i \(-0.971121\pi\)
0.995887 0.0906002i \(-0.0288786\pi\)
\(608\) −1.88345 −0.0763839
\(609\) −5.86157 + 7.54845i −0.237523 + 0.305879i
\(610\) 25.9473i 1.05058i
\(611\) −28.8421 + 27.1924i −1.16683 + 1.10009i
\(612\) 17.4122i 0.703845i
\(613\) −5.06578 + 5.06578i −0.204605 + 0.204605i −0.801970 0.597365i \(-0.796214\pi\)
0.597365 + 0.801970i \(0.296214\pi\)
\(614\) 10.5872i 0.427266i
\(615\) −30.0299 −1.21092
\(616\) −39.8071 + 51.2631i −1.60387 + 2.06545i
\(617\) 11.0059 11.0059i 0.443081 0.443081i −0.449965 0.893046i \(-0.648564\pi\)
0.893046 + 0.449965i \(0.148564\pi\)
\(618\) 25.3281 + 25.3281i 1.01885 + 1.01885i
\(619\) −21.1306 + 21.1306i −0.849311 + 0.849311i −0.990047 0.140737i \(-0.955053\pi\)
0.140737 + 0.990047i \(0.455053\pi\)
\(620\) 86.1069 3.45813
\(621\) −3.94079 −0.158138
\(622\) 33.4754 33.4754i 1.34224 1.34224i
\(623\) 41.7537 5.25229i 1.67283 0.210429i
\(624\) 0.533163 18.1093i 0.0213436 0.724952i
\(625\) 23.2185 0.928739
\(626\) 10.5053 + 10.5053i 0.419876 + 0.419876i
\(627\) 4.99577 0.199512
\(628\) 90.9018 3.62738
\(629\) 30.7160 + 30.7160i 1.22473 + 1.22473i
\(630\) 16.6811 + 12.9534i 0.664593 + 0.516074i
\(631\) −18.3511 18.3511i −0.730547 0.730547i 0.240181 0.970728i \(-0.422793\pi\)
−0.970728 + 0.240181i \(0.922793\pi\)
\(632\) −13.8560 13.8560i −0.551160 0.551160i
\(633\) 1.27815i 0.0508019i
\(634\) 14.6945i 0.583592i
\(635\) −9.90418 + 9.90418i −0.393035 + 0.393035i
\(636\) 1.78744 0.0708767
\(637\) −5.52848 24.6259i −0.219047 0.975714i
\(638\) 40.9071 1.61953
\(639\) 3.74459 3.74459i 0.148134 0.148134i
\(640\) 57.1943i 2.26081i
\(641\) 0.380630i 0.0150340i −0.999972 0.00751698i \(-0.997607\pi\)
0.999972 0.00751698i \(-0.00239275\pi\)
\(642\) −1.27125 1.27125i −0.0501720 0.0501720i
\(643\) 23.7225 + 23.7225i 0.935524 + 0.935524i 0.998044 0.0625195i \(-0.0199136\pi\)
−0.0625195 + 0.998044i \(0.519914\pi\)
\(644\) −34.3088 26.6417i −1.35196 1.04983i
\(645\) 12.2711 + 12.2711i 0.483175 + 0.483175i
\(646\) −11.3686 −0.447293
\(647\) 15.5748 0.612310 0.306155 0.951982i \(-0.400958\pi\)
0.306155 + 0.951982i \(0.400958\pi\)
\(648\) −3.80357 3.80357i −0.149418 0.149418i
\(649\) 8.36292 0.328274
\(650\) −32.7606 34.7481i −1.28498 1.36293i
\(651\) −16.8773 + 2.12304i −0.661475 + 0.0832084i
\(652\) −63.4427 + 63.4427i −2.48461 + 2.48461i
\(653\) 1.83334 0.0717443 0.0358722 0.999356i \(-0.488579\pi\)
0.0358722 + 0.999356i \(0.488579\pi\)
\(654\) 13.4306 0.525177
\(655\) 45.4430 45.4430i 1.77560 1.77560i
\(656\) 33.1912 + 33.1912i 1.29590 + 1.29590i
\(657\) 2.36752 2.36752i 0.0923656 0.0923656i
\(658\) −44.3002 + 57.0491i −1.72700 + 2.22401i
\(659\) −24.7339 −0.963495 −0.481748 0.876310i \(-0.659998\pi\)
−0.481748 + 0.876310i \(0.659998\pi\)
\(660\) 61.0786i 2.37748i
\(661\) −14.8957 + 14.8957i −0.579377 + 0.579377i −0.934732 0.355354i \(-0.884360\pi\)
0.355354 + 0.934732i \(0.384360\pi\)
\(662\) 45.0544i 1.75109i
\(663\) 0.443460 15.0625i 0.0172226 0.584978i
\(664\) 2.55996i 0.0993457i
\(665\) 5.71427 7.35875i 0.221590 0.285360i
\(666\) 25.8092 1.00009
\(667\) 14.2350i 0.551181i
\(668\) −2.40835 2.40835i −0.0931820 0.0931820i
\(669\) 8.41160 8.41160i 0.325211 0.325211i
\(670\) 15.1937 15.1937i 0.586983 0.586983i
\(671\) 10.4821 10.4821i 0.404658 0.404658i
\(672\) −0.567754 4.51343i −0.0219016 0.174109i
\(673\) 15.2799i 0.588997i 0.955652 + 0.294499i \(0.0951527\pi\)
−0.955652 + 0.294499i \(0.904847\pi\)
\(674\) −42.6484 42.6484i −1.64275 1.64275i
\(675\) −5.33399 −0.205305
\(676\) 3.18636 54.0667i 0.122552 2.07949i
\(677\) 23.9366i 0.919960i 0.887929 + 0.459980i \(0.152143\pi\)
−0.887929 + 0.459980i \(0.847857\pi\)
\(678\) 31.9688 + 31.9688i 1.22775 + 1.22775i
\(679\) 0.214629 + 1.70622i 0.00823672 + 0.0654787i
\(680\) 72.2692i 2.77140i
\(681\) −2.87572 + 2.87572i −0.110198 + 0.110198i
\(682\) 51.4841 + 51.4841i 1.97143 + 1.97143i
\(683\) 6.15176 + 6.15176i 0.235391 + 0.235391i 0.814938 0.579548i \(-0.196771\pi\)
−0.579548 + 0.814938i \(0.696771\pi\)
\(684\) −3.22709 + 3.22709i −0.123391 + 0.123391i
\(685\) 25.1817i 0.962145i
\(686\) −16.8619 42.7865i −0.643791 1.63359i
\(687\) −3.18307 3.18307i −0.121442 0.121442i
\(688\) 27.1259i 1.03416i
\(689\) 1.54624 + 0.0455234i 0.0589070 + 0.00173430i
\(690\) 31.4576 1.19757
\(691\) −5.18585 5.18585i −0.197279 0.197279i 0.601553 0.798833i \(-0.294549\pi\)
−0.798833 + 0.601553i \(0.794549\pi\)
\(692\) 2.90033i 0.110254i
\(693\) 1.50594 + 11.9717i 0.0572061 + 0.454766i
\(694\) 41.6102 41.6102i 1.57950 1.57950i
\(695\) 42.7879 42.7879i 1.62304 1.62304i
\(696\) −13.7393 + 13.7393i −0.520788 + 0.520788i
\(697\) 27.6069 + 27.6069i 1.04569 + 1.04569i
\(698\) 58.2799i 2.20593i
\(699\) −17.7925 −0.672974
\(700\) −46.4382 36.0605i −1.75520 1.36296i
\(701\) 34.5225i 1.30390i −0.758264 0.651948i \(-0.773952\pi\)
0.758264 0.651948i \(-0.226048\pi\)
\(702\) −6.14185 6.51447i −0.231809 0.245873i
\(703\) 11.3855i 0.429413i
\(704\) 18.6396 18.6396i 0.702505 0.702505i
\(705\) 35.3420i 1.33106i
\(706\) 23.5269 0.885446
\(707\) −11.6682 9.06064i −0.438827 0.340761i
\(708\) −5.40216 + 5.40216i −0.203026 + 0.203026i
\(709\) −4.95440 4.95440i −0.186066 0.186066i 0.607927 0.793993i \(-0.292001\pi\)
−0.793993 + 0.607927i \(0.792001\pi\)
\(710\) −29.8915 + 29.8915i −1.12181 + 1.12181i
\(711\) −3.64288 −0.136619
\(712\) 85.5581 3.20643
\(713\) −17.9156 + 17.9156i −0.670945 + 0.670945i
\(714\) −3.42701 27.2434i −0.128253 1.01956i
\(715\) 1.55557 52.8363i 0.0581752 1.97597i
\(716\) −3.33782 −0.124740
\(717\) −11.1681 11.1681i −0.417082 0.417082i
\(718\) 73.2646 2.73421
\(719\) 10.1245 0.377581 0.188791 0.982017i \(-0.439543\pi\)
0.188791 + 0.982017i \(0.439543\pi\)
\(720\) 11.4219 + 11.4219i 0.425668 + 0.425668i
\(721\) 30.1434 + 23.4071i 1.12260 + 0.871727i
\(722\) −31.2546 31.2546i −1.16318 1.16318i
\(723\) 5.05729 + 5.05729i 0.188082 + 0.188082i
\(724\) 93.6048i 3.47879i
\(725\) 19.2676i 0.715580i
\(726\) 17.2048 17.2048i 0.638530 0.638530i
\(727\) −35.4617 −1.31520 −0.657601 0.753367i \(-0.728429\pi\)
−0.657601 + 0.753367i \(0.728429\pi\)
\(728\) −4.90327 51.0781i −0.181727 1.89308i
\(729\) −1.00000 −0.0370370
\(730\) −18.8989 + 18.8989i −0.699478 + 0.699478i
\(731\) 22.5621i 0.834488i
\(732\) 13.5422i 0.500534i
\(733\) −9.46985 9.46985i −0.349777 0.349777i 0.510249 0.860026i \(-0.329553\pi\)
−0.860026 + 0.510249i \(0.829553\pi\)
\(734\) −1.68352 1.68352i −0.0621398 0.0621398i
\(735\) 19.3568 + 11.4752i 0.713986 + 0.423270i
\(736\) −4.79109 4.79109i −0.176602 0.176602i
\(737\) 12.2758 0.452185
\(738\) 23.1968 0.853888
\(739\) −3.06141 3.06141i −0.112616 0.112616i 0.648553 0.761169i \(-0.275374\pi\)
−0.761169 + 0.648553i \(0.775374\pi\)
\(740\) −139.200 −5.11710
\(741\) −2.87380 + 2.70943i −0.105572 + 0.0995333i
\(742\) 2.79667 0.351799i 0.102669 0.0129150i
\(743\) 6.17880 6.17880i 0.226678 0.226678i −0.584625 0.811303i \(-0.698758\pi\)
0.811303 + 0.584625i \(0.198758\pi\)
\(744\) −34.5836 −1.26790
\(745\) 1.76139 0.0645325
\(746\) 0.598745 0.598745i 0.0219216 0.0219216i
\(747\) −0.336521 0.336521i −0.0123126 0.0123126i
\(748\) −56.1504 + 56.1504i −2.05306 + 2.05306i
\(749\) −1.51293 1.17483i −0.0552812 0.0429274i
\(750\) 2.66612 0.0973530
\(751\) 42.5093i 1.55119i 0.631232 + 0.775594i \(0.282549\pi\)
−0.631232 + 0.775594i \(0.717451\pi\)
\(752\) −39.0625 + 39.0625i −1.42446 + 1.42446i
\(753\) 1.12847i 0.0411237i
\(754\) −23.5317 + 22.1857i −0.856974 + 0.807956i
\(755\) 12.9740i 0.472172i
\(756\) −8.70608 6.76050i −0.316637 0.245877i
\(757\) 35.1636 1.27804 0.639022 0.769189i \(-0.279339\pi\)
0.639022 + 0.769189i \(0.279339\pi\)
\(758\) 61.2789i 2.22575i
\(759\) 12.7082 + 12.7082i 0.461277 + 0.461277i
\(760\) 13.3941 13.3941i 0.485854 0.485854i
\(761\) 10.5424 10.5424i 0.382161 0.382161i −0.489719 0.871880i \(-0.662901\pi\)
0.871880 + 0.489719i \(0.162901\pi\)
\(762\) 7.65055 7.65055i 0.277150 0.277150i
\(763\) 14.1980 1.78599i 0.514001 0.0646573i
\(764\) 65.5216i 2.37049i
\(765\) 9.50019 + 9.50019i 0.343480 + 0.343480i
\(766\) −1.00346 −0.0362564
\(767\) −4.81075 + 4.53559i −0.173706 + 0.163771i
\(768\) 32.6200i 1.17707i
\(769\) −19.7441 19.7441i −0.711991 0.711991i 0.254961 0.966951i \(-0.417937\pi\)
−0.966951 + 0.254961i \(0.917937\pi\)
\(770\) −12.0213 95.5647i −0.433218 3.44391i
\(771\) 28.2971i 1.01909i
\(772\) 27.3245 27.3245i 0.983430 0.983430i
\(773\) 30.5394 + 30.5394i 1.09843 + 1.09843i 0.994595 + 0.103831i \(0.0331103\pi\)
0.103831 + 0.994595i \(0.466890\pi\)
\(774\) −9.47893 9.47893i −0.340713 0.340713i
\(775\) −24.2494 + 24.2494i −0.871065 + 0.871065i
\(776\) 3.49624i 0.125508i
\(777\) 27.2839 3.43210i 0.978803 0.123126i
\(778\) 43.1902 + 43.1902i 1.54844 + 1.54844i
\(779\) 10.2331i 0.366639i
\(780\) 33.1256 + 35.1353i 1.18609 + 1.25805i
\(781\) −24.1510 −0.864190
\(782\) −28.9194 28.9194i −1.03416 1.03416i
\(783\) 3.61222i 0.129090i
\(784\) −8.71128 34.0777i −0.311117 1.21706i
\(785\) −49.5966 + 49.5966i −1.77018 + 1.77018i
\(786\) −35.1028 + 35.1028i −1.25207 + 1.25207i
\(787\) −29.9108 + 29.9108i −1.06620 + 1.06620i −0.0685564 + 0.997647i \(0.521839\pi\)
−0.997647 + 0.0685564i \(0.978161\pi\)
\(788\) 1.83641 + 1.83641i 0.0654195 + 0.0654195i
\(789\) 17.0950i 0.608597i
\(790\) 29.0796 1.03460
\(791\) 38.0466 + 29.5442i 1.35278 + 1.05047i
\(792\) 24.5313i 0.871683i
\(793\) −0.344898 + 11.7148i −0.0122477 + 0.416003i
\(794\) 48.1117i 1.70742i
\(795\) −0.975241 + 0.975241i −0.0345882 + 0.0345882i
\(796\) 51.2928i 1.81802i
\(797\) 45.4348 1.60938 0.804691 0.593694i \(-0.202331\pi\)
0.804691 + 0.593694i \(0.202331\pi\)
\(798\) −4.41403 + 5.68432i −0.156255 + 0.201223i
\(799\) −32.4904 + 32.4904i −1.14943 + 1.14943i
\(800\) −6.48491 6.48491i −0.229276 0.229276i
\(801\) 11.2471 11.2471i 0.397396 0.397396i
\(802\) −72.5371 −2.56137
\(803\) −15.2694 −0.538847
\(804\) −7.92975 + 7.92975i −0.279661 + 0.279661i
\(805\) 33.2550 4.18322i 1.17208 0.147439i
\(806\) −57.5382 1.69400i −2.02670 0.0596687i
\(807\) 4.65103 0.163724
\(808\) −21.2379 21.2379i −0.747145 0.747145i
\(809\) 22.6070 0.794820 0.397410 0.917641i \(-0.369909\pi\)
0.397410 + 0.917641i \(0.369909\pi\)
\(810\) 7.98257 0.280479
\(811\) 21.4603 + 21.4603i 0.753572 + 0.753572i 0.975144 0.221572i \(-0.0711188\pi\)
−0.221572 + 0.975144i \(0.571119\pi\)
\(812\) −24.4204 + 31.4483i −0.856990 + 1.10362i
\(813\) 9.51718 + 9.51718i 0.333782 + 0.333782i
\(814\) −83.2290 83.2290i −2.91717 2.91717i
\(815\) 69.2295i 2.42500i
\(816\) 21.0006i 0.735167i
\(817\) −4.18155 + 4.18155i −0.146294 + 0.146294i
\(818\) −46.0104 −1.60872
\(819\) −7.35906 6.06994i −0.257146 0.212101i
\(820\) −125.111 −4.36905
\(821\) −14.9292 + 14.9292i −0.521032 + 0.521032i −0.917883 0.396851i \(-0.870103\pi\)
0.396851 + 0.917883i \(0.370103\pi\)
\(822\) 19.4518i 0.678460i
\(823\) 17.8395i 0.621847i −0.950435 0.310924i \(-0.899362\pi\)
0.950435 0.310924i \(-0.100638\pi\)
\(824\) 54.8656 + 54.8656i 1.91133 + 1.91133i
\(825\) 17.2010 + 17.2010i 0.598860 + 0.598860i
\(826\) −7.38909 + 9.51557i −0.257099 + 0.331089i
\(827\) −7.65905 7.65905i −0.266331 0.266331i 0.561289 0.827620i \(-0.310306\pi\)
−0.827620 + 0.561289i \(0.810306\pi\)
\(828\) −16.4181 −0.570568
\(829\) −41.4811 −1.44070 −0.720350 0.693611i \(-0.756019\pi\)
−0.720350 + 0.693611i \(0.756019\pi\)
\(830\) 2.68630 + 2.68630i 0.0932428 + 0.0932428i
\(831\) 18.5055 0.641948
\(832\) −0.613306 + 20.8314i −0.0212626 + 0.722200i
\(833\) −7.24564 28.3443i −0.251047 0.982072i
\(834\) −33.0518 + 33.0518i −1.14449 + 1.14449i
\(835\) 2.62803 0.0909466
\(836\) 20.8133 0.719844
\(837\) −4.54621 + 4.54621i −0.157140 + 0.157140i
\(838\) 47.9438 + 47.9438i 1.65619 + 1.65619i
\(839\) 36.9935 36.9935i 1.27716 1.27716i 0.334905 0.942252i \(-0.391296\pi\)
0.942252 0.334905i \(-0.108704\pi\)
\(840\) 36.1346 + 28.0595i 1.24676 + 0.968144i
\(841\) −15.9518 −0.550064
\(842\) 2.28052i 0.0785920i
\(843\) −14.2256 + 14.2256i −0.489957 + 0.489957i
\(844\) 5.32502i 0.183295i
\(845\) 27.7607 + 31.2377i 0.954996 + 1.07461i
\(846\) 27.3002i 0.938601i
\(847\) 15.8999 20.4757i 0.546328 0.703554i
\(848\) 2.15581 0.0740309
\(849\) 6.56107i 0.225175i
\(850\) −39.1435 39.1435i −1.34261 1.34261i
\(851\) 28.9623 28.9623i 0.992816 0.992816i
\(852\) 15.6007 15.6007i 0.534471 0.534471i
\(853\) 28.9726 28.9726i 0.992002 0.992002i −0.00796604 0.999968i \(-0.502536\pi\)
0.999968 + 0.00796604i \(0.00253570\pi\)
\(854\) 2.66534 + 21.1884i 0.0912060 + 0.725052i
\(855\) 3.52145i 0.120431i
\(856\) −2.75376 2.75376i −0.0941217 0.0941217i
\(857\) −33.3898 −1.14057 −0.570287 0.821446i \(-0.693168\pi\)
−0.570287 + 0.821446i \(0.693168\pi\)
\(858\) −1.20162 + 40.8138i −0.0410225 + 1.39336i
\(859\) 2.81316i 0.0959838i 0.998848 + 0.0479919i \(0.0152822\pi\)
−0.998848 + 0.0479919i \(0.984718\pi\)
\(860\) 51.1239 + 51.1239i 1.74331 + 1.74331i
\(861\) 24.5222 3.08471i 0.835716 0.105127i
\(862\) 61.6858i 2.10103i
\(863\) 16.9046 16.9046i 0.575440 0.575440i −0.358203 0.933644i \(-0.616611\pi\)
0.933644 + 0.358203i \(0.116611\pi\)
\(864\) −1.21577 1.21577i −0.0413613 0.0413613i
\(865\) −1.58244 1.58244i −0.0538045 0.0538045i
\(866\) −47.9514 + 47.9514i −1.62945 + 1.62945i
\(867\) 0.467318i 0.0158710i
\(868\) −70.3143 + 8.84499i −2.38662 + 0.300219i
\(869\) 11.7475 + 11.7475i 0.398506 + 0.398506i
\(870\) 28.8348i 0.977592i
\(871\) −7.06163 + 6.65771i −0.239274 + 0.225588i
\(872\) 29.0932 0.985222
\(873\) 0.459600 + 0.459600i 0.0155551 + 0.0155551i
\(874\) 10.7196i 0.362596i
\(875\) 2.81845 0.354540i 0.0952811 0.0119856i
\(876\) 9.86353 9.86353i 0.333258 0.333258i
\(877\) −15.4720 + 15.4720i −0.522452 + 0.522452i −0.918311 0.395860i \(-0.870447\pi\)
0.395860 + 0.918311i \(0.370447\pi\)
\(878\) −2.02417 + 2.02417i −0.0683124 + 0.0683124i
\(879\) −0.883923 0.883923i −0.0298140 0.0298140i
\(880\) 73.6660i 2.48328i
\(881\) −32.1869 −1.08440 −0.542202 0.840248i \(-0.682409\pi\)
−0.542202 + 0.840248i \(0.682409\pi\)
\(882\) −14.9523 8.86411i −0.503470 0.298470i
\(883\) 40.9812i 1.37913i 0.724226 + 0.689563i \(0.242197\pi\)
−0.724226 + 0.689563i \(0.757803\pi\)
\(884\) 1.84754 62.7533i 0.0621396 2.11062i
\(885\) 5.89491i 0.198155i
\(886\) 14.1280 14.1280i 0.474640 0.474640i
\(887\) 14.9900i 0.503314i 0.967816 + 0.251657i \(0.0809755\pi\)
−0.967816 + 0.251657i \(0.919024\pi\)
\(888\) 55.9078 1.87614
\(889\) 7.07032 9.10505i 0.237131 0.305374i
\(890\) −89.7806 + 89.7806i −3.00945 + 3.00945i
\(891\) 3.22478 + 3.22478i 0.108034 + 0.108034i
\(892\) 35.0444 35.0444i 1.17337 1.17337i
\(893\) 12.0433 0.403013
\(894\) −1.36060 −0.0455053
\(895\) 1.82113 1.82113i 0.0608738 0.0608738i
\(896\) 5.87507 + 46.7045i 0.196272 + 1.56029i
\(897\) −14.2025 0.418143i −0.474209 0.0139614i
\(898\) 32.2394 1.07584
\(899\) 16.4219 + 16.4219i 0.547701 + 0.547701i
\(900\) −22.2225 −0.740748
\(901\) 1.79311 0.0597370
\(902\) −74.8047 74.8047i −2.49072 2.49072i
\(903\) −11.2810 8.76002i −0.375409 0.291515i
\(904\) 69.2506 + 69.2506i 2.30324 + 2.30324i
\(905\) 51.0714 + 51.0714i 1.69767 + 1.69767i
\(906\) 10.0218i 0.332954i
\(907\) 51.1729i 1.69917i −0.527453 0.849584i \(-0.676853\pi\)
0.527453 0.849584i \(-0.323147\pi\)
\(908\) −11.9808 + 11.9808i −0.397598 + 0.397598i
\(909\) −5.58367 −0.185199
\(910\) 58.7442 + 48.4537i 1.94735 + 1.60623i
\(911\) 45.1111 1.49460 0.747299 0.664488i \(-0.231350\pi\)
0.747299 + 0.664488i \(0.231350\pi\)
\(912\) −3.89215 + 3.89215i −0.128882 + 0.128882i
\(913\) 2.17041i 0.0718301i
\(914\) 90.6325i 2.99786i
\(915\) −7.38871 7.38871i −0.244263 0.244263i
\(916\) −13.2613 13.2613i −0.438165 0.438165i
\(917\) −32.4405 + 41.7764i −1.07128 + 1.37958i
\(918\) −7.33849 7.33849i −0.242206 0.242206i
\(919\) 32.8195 1.08262 0.541308 0.840825i \(-0.317929\pi\)
0.541308 + 0.840825i \(0.317929\pi\)
\(920\) 68.1433 2.24662
\(921\) −3.01480 3.01480i −0.0993410 0.0993410i
\(922\) −80.4086 −2.64812
\(923\) 13.8928 13.0981i 0.457287 0.431131i
\(924\) 6.27406 + 49.8763i 0.206401 + 1.64081i
\(925\) 39.2016 39.2016i 1.28894 1.28894i
\(926\) 22.8915 0.752262
\(927\) 14.4248 0.473772
\(928\) −4.39163 + 4.39163i −0.144162 + 0.144162i
\(929\) −2.98532 2.98532i −0.0979452 0.0979452i 0.656436 0.754381i \(-0.272063\pi\)
−0.754381 + 0.656436i \(0.772063\pi\)
\(930\) 36.2904 36.2904i 1.19001 1.19001i
\(931\) −3.91033 + 6.59608i −0.128156 + 0.216178i
\(932\) −74.1270 −2.42811
\(933\) 19.0648i 0.624154i
\(934\) 39.6078 39.6078i 1.29601 1.29601i
\(935\) 61.2720i 2.00381i
\(936\) −13.3044 14.1116i −0.434869 0.461252i
\(937\) 27.2131i 0.889014i 0.895775 + 0.444507i \(0.146621\pi\)
−0.895775 + 0.444507i \(0.853379\pi\)
\(938\) −10.8463 + 13.9678i −0.354145 + 0.456063i
\(939\) 5.98295 0.195246
\(940\) 147.242i 4.80250i
\(941\) −36.8328 36.8328i −1.20072 1.20072i −0.973949 0.226767i \(-0.927184\pi\)
−0.226767 0.973949i \(-0.572816\pi\)
\(942\) 38.3113 38.3113i 1.24825 1.24825i
\(943\) 26.0308 26.0308i 0.847680 0.847680i
\(944\) −6.51548 + 6.51548i −0.212061 + 0.212061i
\(945\) 8.43867 1.06152i 0.274510 0.0345312i
\(946\) 61.1349i 1.98767i
\(947\) −5.92747 5.92747i −0.192617 0.192617i 0.604209 0.796826i \(-0.293489\pi\)
−0.796826 + 0.604209i \(0.793489\pi\)
\(948\) −15.1770 −0.492925
\(949\) 8.78371 8.28129i 0.285131 0.268822i
\(950\) 14.5094i 0.470746i
\(951\) 4.18438 + 4.18438i 0.135688 + 0.135688i
\(952\) −7.42358 59.0146i −0.240599 1.91267i
\(953\) 9.13478i 0.295905i 0.988994 + 0.147952i \(0.0472682\pi\)
−0.988994 + 0.147952i \(0.952732\pi\)
\(954\) 0.753332 0.753332i 0.0243900 0.0243900i
\(955\) 35.7490 + 35.7490i 1.15681 + 1.15681i
\(956\) −46.5286 46.5286i −1.50484 1.50484i
\(957\) 11.6486 11.6486i 0.376547 0.376547i
\(958\) 31.8195i 1.02804i
\(959\) −2.58670 20.5632i −0.0835288 0.664022i
\(960\) −13.1388 13.1388i −0.424052 0.424052i
\(961\) 10.3360i 0.333418i
\(962\) 93.0161 + 2.73852i 2.99896 + 0.0882935i
\(963\) −0.723995 −0.0233304
\(964\) 21.0696 + 21.0696i 0.678607 + 0.678607i
\(965\) 29.8168i 0.959838i
\(966\) −25.6881 + 3.23136i −0.826500 + 0.103967i
\(967\) 23.6616 23.6616i 0.760907 0.760907i −0.215580 0.976486i \(-0.569164\pi\)
0.976486 + 0.215580i \(0.0691641\pi\)
\(968\) 37.2689 37.2689i 1.19787 1.19787i
\(969\) −3.23732 + 3.23732i −0.103998 + 0.103998i
\(970\) −3.66879 3.66879i −0.117798 0.117798i
\(971\) 36.6944i 1.17758i 0.808286 + 0.588789i \(0.200395\pi\)
−0.808286 + 0.588789i \(0.799605\pi\)
\(972\) −4.16620 −0.133631
\(973\) −30.5451 + 39.3355i −0.979230 + 1.26104i
\(974\) 5.68069i 0.182021i
\(975\) −19.2237 0.565971i −0.615650 0.0181256i
\(976\) 16.3331i 0.522809i
\(977\) −4.94849 + 4.94849i −0.158316 + 0.158316i −0.781820 0.623504i \(-0.785709\pi\)
0.623504 + 0.781820i \(0.285709\pi\)
\(978\) 53.4769i 1.71000i
\(979\) −72.5388 −2.31835
\(980\) 80.6441 + 47.8080i 2.57608 + 1.52717i
\(981\) 3.82447 3.82447i 0.122106 0.122106i
\(982\) −17.3438 17.3438i −0.553464 0.553464i
\(983\) −9.25132 + 9.25132i −0.295071 + 0.295071i −0.839080 0.544008i \(-0.816906\pi\)
0.544008 + 0.839080i \(0.316906\pi\)
\(984\) 50.2489 1.60188
\(985\) −2.00392 −0.0638501
\(986\) −26.5083 + 26.5083i −0.844195 + 0.844195i
\(987\) 3.63037 + 28.8601i 0.115556 + 0.918626i
\(988\) −11.9728 + 11.2880i −0.380906 + 0.359119i
\(989\) −21.2740 −0.676473
\(990\) −25.7420 25.7420i −0.818136 0.818136i
\(991\) −34.2453 −1.08784 −0.543918 0.839138i \(-0.683060\pi\)
−0.543918 + 0.839138i \(0.683060\pi\)
\(992\) −11.0543 −0.350974
\(993\) 12.8296 + 12.8296i 0.407135 + 0.407135i
\(994\) 21.3387 27.4797i 0.676822 0.871602i
\(995\) 27.9857 + 27.9857i 0.887205 + 0.887205i
\(996\) −1.40201 1.40201i −0.0444244 0.0444244i
\(997\) 2.69156i 0.0852425i −0.999091 0.0426212i \(-0.986429\pi\)
0.999091 0.0426212i \(-0.0135709\pi\)
\(998\) 82.2019i 2.60206i
\(999\) 7.34938 7.34938i 0.232524 0.232524i
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 273.2.p.f.265.6 yes 12
3.2 odd 2 819.2.y.f.811.1 12
7.6 odd 2 273.2.p.e.265.6 yes 12
13.8 odd 4 273.2.p.e.34.6 12
21.20 even 2 819.2.y.g.811.1 12
39.8 even 4 819.2.y.g.307.1 12
91.34 even 4 inner 273.2.p.f.34.6 yes 12
273.125 odd 4 819.2.y.f.307.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.p.e.34.6 12 13.8 odd 4
273.2.p.e.265.6 yes 12 7.6 odd 2
273.2.p.f.34.6 yes 12 91.34 even 4 inner
273.2.p.f.265.6 yes 12 1.1 even 1 trivial
819.2.y.f.307.1 12 273.125 odd 4
819.2.y.f.811.1 12 3.2 odd 2
819.2.y.g.307.1 12 39.8 even 4
819.2.y.g.811.1 12 21.20 even 2