Properties

Label 605.2.e.a.362.1
Level $605$
Weight $2$
Character 605.362
Analytic conductor $4.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(362,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.e (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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 362.1
Root \(-1.76854 + 1.76854i\) of defining polynomial
Character \(\chi\) \(=\) 605.362
Dual form 605.2.e.a.483.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.76854 + 1.76854i) q^{2} +(1.85563 - 1.85563i) q^{3} -4.25546i q^{4} +(-2.19774 + 0.412263i) q^{5} +6.56351i q^{6} +(0.260724 - 0.260724i) q^{7} +(3.98886 + 3.98886i) q^{8} -3.88674i q^{9} +O(q^{10})\) \(q+(-1.76854 + 1.76854i) q^{2} +(1.85563 - 1.85563i) q^{3} -4.25546i q^{4} +(-2.19774 + 0.412263i) q^{5} +6.56351i q^{6} +(0.260724 - 0.260724i) q^{7} +(3.98886 + 3.98886i) q^{8} -3.88674i q^{9} +(3.15768 - 4.61588i) q^{10} +(-7.89656 - 7.89656i) q^{12} +(-3.13314 - 3.13314i) q^{13} +0.922200i q^{14} +(-3.31318 + 4.84319i) q^{15} -5.59800 q^{16} +(0.608103 - 0.608103i) q^{17} +(6.87385 + 6.87385i) q^{18} -4.44065 q^{19} +(1.75437 + 9.35237i) q^{20} -0.967614i q^{21} +(-2.17112 + 2.17112i) q^{23} +14.8037 q^{24} +(4.66008 - 1.81209i) q^{25} +11.0822 q^{26} +(-1.64546 - 1.64546i) q^{27} +(-1.10950 - 1.10950i) q^{28} -0.769606 q^{29} +(-2.70589 - 14.4249i) q^{30} -4.53579 q^{31} +(1.92256 - 1.92256i) q^{32} +2.15091i q^{34} +(-0.465515 + 0.680488i) q^{35} -16.5398 q^{36} +(-7.75001 - 7.75001i) q^{37} +(7.85346 - 7.85346i) q^{38} -11.6279 q^{39} +(-10.4109 - 7.12201i) q^{40} +5.01533i q^{41} +(1.71126 + 1.71126i) q^{42} +(-4.69057 - 4.69057i) q^{43} +(1.60236 + 8.54202i) q^{45} -7.67942i q^{46} +(-7.64329 - 7.64329i) q^{47} +(-10.3878 + 10.3878i) q^{48} +6.86405i q^{49} +(-5.03678 + 11.4463i) q^{50} -2.25683i q^{51} +(-13.3330 + 13.3330i) q^{52} +(0.711263 - 0.711263i) q^{53} +5.82012 q^{54} +2.07998 q^{56} +(-8.24021 + 8.24021i) q^{57} +(1.36108 - 1.36108i) q^{58} -1.09798i q^{59} +(20.6100 + 14.0991i) q^{60} -11.3546i q^{61} +(8.02172 - 8.02172i) q^{62} +(-1.01336 - 1.01336i) q^{63} -4.39578i q^{64} +(8.17749 + 5.59414i) q^{65} +(4.17112 + 4.17112i) q^{67} +(-2.58775 - 2.58775i) q^{68} +8.05760i q^{69} +(-0.380189 - 2.02675i) q^{70} +1.94677 q^{71} +(15.5037 - 15.5037i) q^{72} +(-9.10112 - 9.10112i) q^{73} +27.4124 q^{74} +(5.28482 - 12.0100i) q^{75} +18.8970i q^{76} +(20.5644 - 20.5644i) q^{78} +12.3728 q^{79} +(12.3029 - 2.30785i) q^{80} +5.55348 q^{81} +(-8.86981 - 8.86981i) q^{82} +(-5.04875 - 5.04875i) q^{83} -4.11764 q^{84} +(-1.08575 + 1.58715i) q^{85} +16.5909 q^{86} +(-1.42811 + 1.42811i) q^{87} +8.87803i q^{89} +(-17.9407 - 12.2731i) q^{90} -1.63377 q^{91} +(9.23911 + 9.23911i) q^{92} +(-8.41675 + 8.41675i) q^{93} +27.0349 q^{94} +(9.75937 - 1.83071i) q^{95} -7.13511i q^{96} +(5.07639 + 5.07639i) q^{97} +(-12.1393 - 12.1393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76854 + 1.76854i −1.25055 + 1.25055i −0.295070 + 0.955476i \(0.595343\pi\)
−0.955476 + 0.295070i \(0.904657\pi\)
\(3\) 1.85563 1.85563i 1.07135 1.07135i 0.0740986 0.997251i \(-0.476392\pi\)
0.997251 0.0740986i \(-0.0236079\pi\)
\(4\) 4.25546i 2.12773i
\(5\) −2.19774 + 0.412263i −0.982857 + 0.184369i
\(6\) 6.56351i 2.67954i
\(7\) 0.260724 0.260724i 0.0985443 0.0985443i −0.656116 0.754660i \(-0.727802\pi\)
0.754660 + 0.656116i \(0.227802\pi\)
\(8\) 3.98886 + 3.98886i 1.41028 + 1.41028i
\(9\) 3.88674i 1.29558i
\(10\) 3.15768 4.61588i 0.998545 1.45967i
\(11\) 0 0
\(12\) −7.89656 7.89656i −2.27954 2.27954i
\(13\) −3.13314 3.13314i −0.868977 0.868977i 0.123382 0.992359i \(-0.460626\pi\)
−0.992359 + 0.123382i \(0.960626\pi\)
\(14\) 0.922200i 0.246468i
\(15\) −3.31318 + 4.84319i −0.855459 + 1.25051i
\(16\) −5.59800 −1.39950
\(17\) 0.608103 0.608103i 0.147487 0.147487i −0.629508 0.776994i \(-0.716743\pi\)
0.776994 + 0.629508i \(0.216743\pi\)
\(18\) 6.87385 + 6.87385i 1.62018 + 1.62018i
\(19\) −4.44065 −1.01875 −0.509377 0.860543i \(-0.670124\pi\)
−0.509377 + 0.860543i \(0.670124\pi\)
\(20\) 1.75437 + 9.35237i 0.392288 + 2.09125i
\(21\) 0.967614i 0.211151i
\(22\) 0 0
\(23\) −2.17112 + 2.17112i −0.452710 + 0.452710i −0.896253 0.443543i \(-0.853721\pi\)
0.443543 + 0.896253i \(0.353721\pi\)
\(24\) 14.8037 3.02180
\(25\) 4.66008 1.81209i 0.932016 0.362418i
\(26\) 11.0822 2.17339
\(27\) −1.64546 1.64546i −0.316669 0.316669i
\(28\) −1.10950 1.10950i −0.209676 0.209676i
\(29\) −0.769606 −0.142912 −0.0714561 0.997444i \(-0.522765\pi\)
−0.0714561 + 0.997444i \(0.522765\pi\)
\(30\) −2.70589 14.4249i −0.494026 2.63361i
\(31\) −4.53579 −0.814652 −0.407326 0.913283i \(-0.633539\pi\)
−0.407326 + 0.913283i \(0.633539\pi\)
\(32\) 1.92256 1.92256i 0.339863 0.339863i
\(33\) 0 0
\(34\) 2.15091i 0.368877i
\(35\) −0.465515 + 0.680488i −0.0786864 + 0.115024i
\(36\) −16.5398 −2.75664
\(37\) −7.75001 7.75001i −1.27409 1.27409i −0.943920 0.330174i \(-0.892893\pi\)
−0.330174 0.943920i \(-0.607107\pi\)
\(38\) 7.85346 7.85346i 1.27400 1.27400i
\(39\) −11.6279 −1.86196
\(40\) −10.4109 7.12201i −1.64611 1.12609i
\(41\) 5.01533i 0.783263i 0.920122 + 0.391632i \(0.128089\pi\)
−0.920122 + 0.391632i \(0.871911\pi\)
\(42\) 1.71126 + 1.71126i 0.264054 + 0.264054i
\(43\) −4.69057 4.69057i −0.715305 0.715305i 0.252335 0.967640i \(-0.418801\pi\)
−0.967640 + 0.252335i \(0.918801\pi\)
\(44\) 0 0
\(45\) 1.60236 + 8.54202i 0.238865 + 1.27337i
\(46\) 7.67942i 1.13227i
\(47\) −7.64329 7.64329i −1.11489 1.11489i −0.992480 0.122408i \(-0.960938\pi\)
−0.122408 0.992480i \(-0.539062\pi\)
\(48\) −10.3878 + 10.3878i −1.49935 + 1.49935i
\(49\) 6.86405i 0.980578i
\(50\) −5.03678 + 11.4463i −0.712309 + 1.61875i
\(51\) 2.25683i 0.316019i
\(52\) −13.3330 + 13.3330i −1.84895 + 1.84895i
\(53\) 0.711263 0.711263i 0.0976995 0.0976995i −0.656568 0.754267i \(-0.727992\pi\)
0.754267 + 0.656568i \(0.227992\pi\)
\(54\) 5.82012 0.792018
\(55\) 0 0
\(56\) 2.07998 0.277949
\(57\) −8.24021 + 8.24021i −1.09144 + 1.09144i
\(58\) 1.36108 1.36108i 0.178718 0.178718i
\(59\) 1.09798i 0.142945i −0.997443 0.0714724i \(-0.977230\pi\)
0.997443 0.0714724i \(-0.0227698\pi\)
\(60\) 20.6100 + 14.0991i 2.66074 + 1.82019i
\(61\) 11.3546i 1.45381i −0.686738 0.726905i \(-0.740958\pi\)
0.686738 0.726905i \(-0.259042\pi\)
\(62\) 8.02172 8.02172i 1.01876 1.01876i
\(63\) −1.01336 1.01336i −0.127672 0.127672i
\(64\) 4.39578i 0.549472i
\(65\) 8.17749 + 5.59414i 1.01429 + 0.693868i
\(66\) 0 0
\(67\) 4.17112 + 4.17112i 0.509583 + 0.509583i 0.914399 0.404815i \(-0.132664\pi\)
−0.404815 + 0.914399i \(0.632664\pi\)
\(68\) −2.58775 2.58775i −0.313811 0.313811i
\(69\) 8.05760i 0.970021i
\(70\) −0.380189 2.02675i −0.0454412 0.242243i
\(71\) 1.94677 0.231039 0.115519 0.993305i \(-0.463147\pi\)
0.115519 + 0.993305i \(0.463147\pi\)
\(72\) 15.5037 15.5037i 1.82712 1.82712i
\(73\) −9.10112 9.10112i −1.06521 1.06521i −0.997720 0.0674849i \(-0.978503\pi\)
−0.0674849 0.997720i \(-0.521497\pi\)
\(74\) 27.4124 3.18663
\(75\) 5.28482 12.0100i 0.610239 1.38679i
\(76\) 18.8970i 2.16763i
\(77\) 0 0
\(78\) 20.5644 20.5644i 2.32846 2.32846i
\(79\) 12.3728 1.39205 0.696026 0.718017i \(-0.254950\pi\)
0.696026 + 0.718017i \(0.254950\pi\)
\(80\) 12.3029 2.30785i 1.37551 0.258025i
\(81\) 5.55348 0.617053
\(82\) −8.86981 8.86981i −0.979507 0.979507i
\(83\) −5.04875 5.04875i −0.554172 0.554172i 0.373470 0.927642i \(-0.378168\pi\)
−0.927642 + 0.373470i \(0.878168\pi\)
\(84\) −4.11764 −0.449272
\(85\) −1.08575 + 1.58715i −0.117766 + 0.172150i
\(86\) 16.5909 1.78904
\(87\) −1.42811 + 1.42811i −0.153109 + 0.153109i
\(88\) 0 0
\(89\) 8.87803i 0.941069i 0.882382 + 0.470535i \(0.155939\pi\)
−0.882382 + 0.470535i \(0.844061\pi\)
\(90\) −17.9407 12.2731i −1.89112 1.29369i
\(91\) −1.63377 −0.171266
\(92\) 9.23911 + 9.23911i 0.963243 + 0.963243i
\(93\) −8.41675 + 8.41675i −0.872777 + 0.872777i
\(94\) 27.0349 2.78844
\(95\) 9.75937 1.83071i 1.00129 0.187827i
\(96\) 7.13511i 0.728224i
\(97\) 5.07639 + 5.07639i 0.515429 + 0.515429i 0.916185 0.400756i \(-0.131252\pi\)
−0.400756 + 0.916185i \(0.631252\pi\)
\(98\) −12.1393 12.1393i −1.22626 1.22626i
\(99\) 0 0
\(100\) −7.71126 19.8308i −0.771126 1.98308i
\(101\) 2.04877i 0.203861i 0.994792 + 0.101930i \(0.0325019\pi\)
−0.994792 + 0.101930i \(0.967498\pi\)
\(102\) 3.99129 + 3.99129i 0.395197 + 0.395197i
\(103\) 3.07204 3.07204i 0.302697 0.302697i −0.539371 0.842068i \(-0.681338\pi\)
0.842068 + 0.539371i \(0.181338\pi\)
\(104\) 24.9953i 2.45100i
\(105\) 0.398911 + 2.12656i 0.0389298 + 0.207531i
\(106\) 2.51579i 0.244355i
\(107\) 8.89695 8.89695i 0.860101 0.860101i −0.131249 0.991349i \(-0.541899\pi\)
0.991349 + 0.131249i \(0.0418987\pi\)
\(108\) −7.00218 + 7.00218i −0.673785 + 0.673785i
\(109\) 4.04420 0.387364 0.193682 0.981064i \(-0.437957\pi\)
0.193682 + 0.981064i \(0.437957\pi\)
\(110\) 0 0
\(111\) −28.7623 −2.73000
\(112\) −1.45953 + 1.45953i −0.137913 + 0.137913i
\(113\) −2.21453 + 2.21453i −0.208325 + 0.208325i −0.803555 0.595230i \(-0.797061\pi\)
0.595230 + 0.803555i \(0.297061\pi\)
\(114\) 29.1463i 2.72980i
\(115\) 3.87647 5.66662i 0.361483 0.528415i
\(116\) 3.27503i 0.304079i
\(117\) −12.1777 + 12.1777i −1.12583 + 1.12583i
\(118\) 1.94182 + 1.94182i 0.178759 + 0.178759i
\(119\) 0.317094i 0.0290679i
\(120\) −32.5347 + 6.10302i −2.96999 + 0.557127i
\(121\) 0 0
\(122\) 20.0811 + 20.0811i 1.81806 + 1.81806i
\(123\) 9.30661 + 9.30661i 0.839149 + 0.839149i
\(124\) 19.3019i 1.73336i
\(125\) −9.49456 + 5.90367i −0.849220 + 0.528040i
\(126\) 3.58435 0.319319
\(127\) −10.4053 + 10.4053i −0.923321 + 0.923321i −0.997263 0.0739411i \(-0.976442\pi\)
0.0739411 + 0.997263i \(0.476442\pi\)
\(128\) 11.6192 + 11.6192i 1.02700 + 1.02700i
\(129\) −17.4079 −1.53268
\(130\) −24.3557 + 4.56876i −2.13613 + 0.400707i
\(131\) 9.05953i 0.791535i 0.918351 + 0.395768i \(0.129521\pi\)
−0.918351 + 0.395768i \(0.870479\pi\)
\(132\) 0 0
\(133\) −1.15778 + 1.15778i −0.100392 + 0.100392i
\(134\) −14.7536 −1.27451
\(135\) 4.29465 + 2.93792i 0.369624 + 0.252856i
\(136\) 4.85128 0.415994
\(137\) 0.127440 + 0.127440i 0.0108880 + 0.0108880i 0.712530 0.701642i \(-0.247549\pi\)
−0.701642 + 0.712530i \(0.747549\pi\)
\(138\) −14.2502 14.2502i −1.21305 1.21305i
\(139\) 19.1456 1.62391 0.811954 0.583722i \(-0.198404\pi\)
0.811954 + 0.583722i \(0.198404\pi\)
\(140\) 2.89579 + 1.98098i 0.244739 + 0.167423i
\(141\) −28.3663 −2.38887
\(142\) −3.44294 + 3.44294i −0.288925 + 0.288925i
\(143\) 0 0
\(144\) 21.7580i 1.81316i
\(145\) 1.69139 0.317280i 0.140462 0.0263487i
\(146\) 32.1914 2.66418
\(147\) 12.7371 + 12.7371i 1.05054 + 1.05054i
\(148\) −32.9798 + 32.9798i −2.71093 + 2.71093i
\(149\) 8.70842 0.713422 0.356711 0.934215i \(-0.383898\pi\)
0.356711 + 0.934215i \(0.383898\pi\)
\(150\) 11.8937 + 30.5865i 0.971114 + 2.49738i
\(151\) 5.32028i 0.432958i −0.976287 0.216479i \(-0.930543\pi\)
0.976287 0.216479i \(-0.0694573\pi\)
\(152\) −17.7131 17.7131i −1.43673 1.43673i
\(153\) −2.36354 2.36354i −0.191081 0.191081i
\(154\) 0 0
\(155\) 9.96846 1.86994i 0.800686 0.150197i
\(156\) 49.4821i 3.96174i
\(157\) −3.92579 3.92579i −0.313312 0.313312i 0.532879 0.846191i \(-0.321110\pi\)
−0.846191 + 0.532879i \(0.821110\pi\)
\(158\) −21.8818 + 21.8818i −1.74082 + 1.74082i
\(159\) 2.63969i 0.209341i
\(160\) −3.43267 + 5.01787i −0.271376 + 0.396697i
\(161\) 1.13212i 0.0892239i
\(162\) −9.82155 + 9.82155i −0.771653 + 0.771653i
\(163\) 2.79201 2.79201i 0.218687 0.218687i −0.589258 0.807945i \(-0.700580\pi\)
0.807945 + 0.589258i \(0.200580\pi\)
\(164\) 21.3425 1.66657
\(165\) 0 0
\(166\) 17.8578 1.38604
\(167\) 1.88219 1.88219i 0.145648 0.145648i −0.630523 0.776171i \(-0.717159\pi\)
0.776171 + 0.630523i \(0.217159\pi\)
\(168\) 3.85968 3.85968i 0.297781 0.297781i
\(169\) 6.63316i 0.510243i
\(170\) −0.886738 4.72712i −0.0680097 0.362554i
\(171\) 17.2596i 1.31988i
\(172\) −19.9605 + 19.9605i −1.52197 + 1.52197i
\(173\) −14.9413 14.9413i −1.13596 1.13596i −0.989166 0.146798i \(-0.953103\pi\)
−0.146798 0.989166i \(-0.546897\pi\)
\(174\) 5.05132i 0.382940i
\(175\) 0.742539 1.68745i 0.0561307 0.127559i
\(176\) 0 0
\(177\) −2.03745 2.03745i −0.153144 0.153144i
\(178\) −15.7011 15.7011i −1.17685 1.17685i
\(179\) 3.00130i 0.224328i −0.993690 0.112164i \(-0.964222\pi\)
0.993690 0.112164i \(-0.0357782\pi\)
\(180\) 36.3502 6.81876i 2.70938 0.508240i
\(181\) 10.2448 0.761493 0.380747 0.924679i \(-0.375667\pi\)
0.380747 + 0.924679i \(0.375667\pi\)
\(182\) 2.88938 2.88938i 0.214175 0.214175i
\(183\) −21.0700 21.0700i −1.55754 1.55754i
\(184\) −17.3206 −1.27689
\(185\) 20.2275 + 13.8374i 1.48716 + 1.01735i
\(186\) 29.7707i 2.18289i
\(187\) 0 0
\(188\) −32.5257 + 32.5257i −2.37218 + 2.37218i
\(189\) −0.858021 −0.0624118
\(190\) −14.0221 + 20.4975i −1.01727 + 1.48705i
\(191\) −13.8027 −0.998729 −0.499365 0.866392i \(-0.666433\pi\)
−0.499365 + 0.866392i \(0.666433\pi\)
\(192\) −8.15694 8.15694i −0.588677 0.588677i
\(193\) 9.55080 + 9.55080i 0.687482 + 0.687482i 0.961675 0.274193i \(-0.0884107\pi\)
−0.274193 + 0.961675i \(0.588411\pi\)
\(194\) −17.9556 −1.28914
\(195\) 25.5551 4.79376i 1.83004 0.343288i
\(196\) 29.2097 2.08640
\(197\) 10.9820 10.9820i 0.782434 0.782434i −0.197807 0.980241i \(-0.563382\pi\)
0.980241 + 0.197807i \(0.0633820\pi\)
\(198\) 0 0
\(199\) 16.1982i 1.14826i −0.818765 0.574129i \(-0.805341\pi\)
0.818765 0.574129i \(-0.194659\pi\)
\(200\) 25.8166 + 11.3602i 1.82551 + 0.803291i
\(201\) 15.4801 1.09188
\(202\) −3.62333 3.62333i −0.254937 0.254937i
\(203\) −0.200655 + 0.200655i −0.0140832 + 0.0140832i
\(204\) −9.60384 −0.672403
\(205\) −2.06763 11.0224i −0.144410 0.769836i
\(206\) 10.8660i 0.757072i
\(207\) 8.43857 + 8.43857i 0.586521 + 0.586521i
\(208\) 17.5393 + 17.5393i 1.21613 + 1.21613i
\(209\) 0 0
\(210\) −4.46639 3.05541i −0.308210 0.210844i
\(211\) 3.67640i 0.253094i −0.991961 0.126547i \(-0.959611\pi\)
0.991961 0.126547i \(-0.0403894\pi\)
\(212\) −3.02675 3.02675i −0.207878 0.207878i
\(213\) 3.61249 3.61249i 0.247523 0.247523i
\(214\) 31.4692i 2.15119i
\(215\) 12.2424 + 8.37488i 0.834923 + 0.571162i
\(216\) 13.1270i 0.893181i
\(217\) −1.18259 + 1.18259i −0.0802793 + 0.0802793i
\(218\) −7.15232 + 7.15232i −0.484417 + 0.484417i
\(219\) −33.7766 −2.28241
\(220\) 0 0
\(221\) −3.81054 −0.256325
\(222\) 50.8673 50.8673i 3.41399 3.41399i
\(223\) 16.8846 16.8846i 1.13067 1.13067i 0.140609 0.990065i \(-0.455094\pi\)
0.990065 0.140609i \(-0.0449060\pi\)
\(224\) 1.00251i 0.0669831i
\(225\) −7.04311 18.1125i −0.469541 1.20750i
\(226\) 7.83295i 0.521040i
\(227\) −13.1257 + 13.1257i −0.871183 + 0.871183i −0.992601 0.121418i \(-0.961256\pi\)
0.121418 + 0.992601i \(0.461256\pi\)
\(228\) 35.0659 + 35.0659i 2.32229 + 2.32229i
\(229\) 16.0685i 1.06184i 0.847422 + 0.530919i \(0.178153\pi\)
−0.847422 + 0.530919i \(0.821847\pi\)
\(230\) 3.16594 + 16.8773i 0.208756 + 1.11286i
\(231\) 0 0
\(232\) −3.06985 3.06985i −0.201546 0.201546i
\(233\) −2.36045 2.36045i −0.154638 0.154638i 0.625548 0.780186i \(-0.284876\pi\)
−0.780186 + 0.625548i \(0.784876\pi\)
\(234\) 43.0735i 2.81580i
\(235\) 19.9490 + 13.6469i 1.30133 + 0.890224i
\(236\) −4.67241 −0.304148
\(237\) 22.9594 22.9594i 1.49137 1.49137i
\(238\) 0.560792 + 0.560792i 0.0363508 + 0.0363508i
\(239\) 0.467778 0.0302581 0.0151290 0.999886i \(-0.495184\pi\)
0.0151290 + 0.999886i \(0.495184\pi\)
\(240\) 18.5472 27.1122i 1.19722 1.75009i
\(241\) 16.5275i 1.06463i 0.846547 + 0.532314i \(0.178678\pi\)
−0.846547 + 0.532314i \(0.821322\pi\)
\(242\) 0 0
\(243\) 15.2416 15.2416i 0.977749 0.977749i
\(244\) −48.3191 −3.09332
\(245\) −2.82979 15.0854i −0.180789 0.963768i
\(246\) −32.9182 −2.09879
\(247\) 13.9132 + 13.9132i 0.885275 + 0.885275i
\(248\) −18.0926 18.0926i −1.14888 1.14888i
\(249\) −18.7372 −1.18742
\(250\) 6.35064 27.2324i 0.401650 1.72233i
\(251\) 6.54236 0.412950 0.206475 0.978452i \(-0.433801\pi\)
0.206475 + 0.978452i \(0.433801\pi\)
\(252\) −4.31233 + 4.31233i −0.271651 + 0.271651i
\(253\) 0 0
\(254\) 36.8044i 2.30931i
\(255\) 0.930406 + 4.95991i 0.0582643 + 0.310602i
\(256\) −32.3065 −2.01916
\(257\) −16.0840 16.0840i −1.00329 1.00329i −0.999995 0.00330040i \(-0.998949\pi\)
−0.00330040 0.999995i \(-0.501051\pi\)
\(258\) 30.7866 30.7866i 1.91669 1.91669i
\(259\) −4.04122 −0.251109
\(260\) 23.8056 34.7990i 1.47636 2.15814i
\(261\) 2.99126i 0.185154i
\(262\) −16.0221 16.0221i −0.989851 0.989851i
\(263\) 17.4444 + 17.4444i 1.07567 + 1.07567i 0.996892 + 0.0787777i \(0.0251017\pi\)
0.0787777 + 0.996892i \(0.474898\pi\)
\(264\) 0 0
\(265\) −1.26994 + 1.85640i −0.0780119 + 0.114037i
\(266\) 4.09517i 0.251091i
\(267\) 16.4743 + 16.4743i 1.00821 + 1.00821i
\(268\) 17.7500 17.7500i 1.08426 1.08426i
\(269\) 6.15996i 0.375580i −0.982209 0.187790i \(-0.939868\pi\)
0.982209 0.187790i \(-0.0601324\pi\)
\(270\) −12.7911 + 2.39942i −0.778440 + 0.146024i
\(271\) 6.98883i 0.424541i −0.977211 0.212270i \(-0.931914\pi\)
0.977211 0.212270i \(-0.0680858\pi\)
\(272\) −3.40416 + 3.40416i −0.206407 + 0.206407i
\(273\) −3.03167 + 3.03167i −0.183485 + 0.183485i
\(274\) −0.450766 −0.0272318
\(275\) 0 0
\(276\) 34.2888 2.06394
\(277\) −0.619989 + 0.619989i −0.0372515 + 0.0372515i −0.725487 0.688236i \(-0.758386\pi\)
0.688236 + 0.725487i \(0.258386\pi\)
\(278\) −33.8597 + 33.8597i −2.03077 + 2.03077i
\(279\) 17.6294i 1.05545i
\(280\) −4.57125 + 0.857499i −0.273184 + 0.0512454i
\(281\) 8.17465i 0.487659i −0.969818 0.243829i \(-0.921596\pi\)
0.969818 0.243829i \(-0.0784037\pi\)
\(282\) 50.1668 50.1668i 2.98739 2.98739i
\(283\) 5.06880 + 5.06880i 0.301309 + 0.301309i 0.841526 0.540217i \(-0.181658\pi\)
−0.540217 + 0.841526i \(0.681658\pi\)
\(284\) 8.28439i 0.491588i
\(285\) 14.7127 21.5069i 0.871503 1.27396i
\(286\) 0 0
\(287\) 1.30762 + 1.30762i 0.0771862 + 0.0771862i
\(288\) −7.47247 7.47247i −0.440320 0.440320i
\(289\) 16.2604i 0.956495i
\(290\) −2.43017 + 3.55241i −0.142704 + 0.208605i
\(291\) 18.8398 1.10441
\(292\) −38.7294 + 38.7294i −2.26647 + 2.26647i
\(293\) 16.4952 + 16.4952i 0.963659 + 0.963659i 0.999362 0.0357031i \(-0.0113671\pi\)
−0.0357031 + 0.999362i \(0.511367\pi\)
\(294\) −45.0523 −2.62750
\(295\) 0.452656 + 2.41307i 0.0263547 + 0.140494i
\(296\) 61.8275i 3.59365i
\(297\) 0 0
\(298\) −15.4012 + 15.4012i −0.892166 + 0.892166i
\(299\) 13.6049 0.786789
\(300\) −51.1079 22.4893i −2.95071 1.29842i
\(301\) −2.44588 −0.140978
\(302\) 9.40912 + 9.40912i 0.541434 + 0.541434i
\(303\) 3.80177 + 3.80177i 0.218406 + 0.218406i
\(304\) 24.8588 1.42575
\(305\) 4.68109 + 24.9545i 0.268038 + 1.42889i
\(306\) 8.36001 0.477910
\(307\) 4.25013 4.25013i 0.242568 0.242568i −0.575344 0.817912i \(-0.695132\pi\)
0.817912 + 0.575344i \(0.195132\pi\)
\(308\) 0 0
\(309\) 11.4011i 0.648588i
\(310\) −14.3226 + 20.9367i −0.813466 + 1.18912i
\(311\) −29.2801 −1.66032 −0.830160 0.557525i \(-0.811751\pi\)
−0.830160 + 0.557525i \(0.811751\pi\)
\(312\) −46.3822 46.3822i −2.62587 2.62587i
\(313\) −9.85366 + 9.85366i −0.556962 + 0.556962i −0.928441 0.371480i \(-0.878851\pi\)
0.371480 + 0.928441i \(0.378851\pi\)
\(314\) 13.8858 0.783622
\(315\) 2.64488 + 1.80934i 0.149022 + 0.101944i
\(316\) 52.6520i 2.96191i
\(317\) −5.09167 5.09167i −0.285977 0.285977i 0.549510 0.835487i \(-0.314814\pi\)
−0.835487 + 0.549510i \(0.814814\pi\)
\(318\) 4.66839 + 4.66839i 0.261790 + 0.261790i
\(319\) 0 0
\(320\) 1.81221 + 9.66075i 0.101306 + 0.540052i
\(321\) 33.0189i 1.84294i
\(322\) −2.00221 2.00221i −0.111579 0.111579i
\(323\) −2.70037 + 2.70037i −0.150253 + 0.150253i
\(324\) 23.6326i 1.31292i
\(325\) −20.2782 8.92316i −1.12483 0.494968i
\(326\) 9.87556i 0.546956i
\(327\) 7.50455 7.50455i 0.415002 0.415002i
\(328\) −20.0055 + 20.0055i −1.10462 + 1.10462i
\(329\) −3.98557 −0.219732
\(330\) 0 0
\(331\) −13.2203 −0.726652 −0.363326 0.931662i \(-0.618359\pi\)
−0.363326 + 0.931662i \(0.618359\pi\)
\(332\) −21.4847 + 21.4847i −1.17913 + 1.17913i
\(333\) −30.1223 + 30.1223i −1.65069 + 1.65069i
\(334\) 6.65746i 0.364280i
\(335\) −10.8866 7.44742i −0.594799 0.406896i
\(336\) 5.41671i 0.295506i
\(337\) 23.3891 23.3891i 1.27409 1.27409i 0.330162 0.943924i \(-0.392897\pi\)
0.943924 0.330162i \(-0.107103\pi\)
\(338\) −11.7310 11.7310i −0.638082 0.638082i
\(339\) 8.21870i 0.446378i
\(340\) 6.75403 + 4.62036i 0.366289 + 0.250574i
\(341\) 0 0
\(342\) −30.5243 30.5243i −1.65057 1.65057i
\(343\) 3.61469 + 3.61469i 0.195175 + 0.195175i
\(344\) 37.4201i 2.01755i
\(345\) −3.32185 17.7085i −0.178842 0.953392i
\(346\) 52.8485 2.84115
\(347\) 9.74724 9.74724i 0.523259 0.523259i −0.395295 0.918554i \(-0.629358\pi\)
0.918554 + 0.395295i \(0.129358\pi\)
\(348\) 6.07724 + 6.07724i 0.325774 + 0.325774i
\(349\) −8.23325 −0.440716 −0.220358 0.975419i \(-0.570723\pi\)
−0.220358 + 0.975419i \(0.570723\pi\)
\(350\) 1.67111 + 4.29752i 0.0893245 + 0.229712i
\(351\) 10.3109i 0.550356i
\(352\) 0 0
\(353\) 18.2121 18.2121i 0.969330 0.969330i −0.0302134 0.999543i \(-0.509619\pi\)
0.999543 + 0.0302134i \(0.00961869\pi\)
\(354\) 7.20661 0.383027
\(355\) −4.27848 + 0.802580i −0.227078 + 0.0425965i
\(356\) 37.7801 2.00234
\(357\) −0.588409 0.588409i −0.0311419 0.0311419i
\(358\) 5.30792 + 5.30792i 0.280532 + 0.280532i
\(359\) −8.87466 −0.468387 −0.234193 0.972190i \(-0.575245\pi\)
−0.234193 + 0.972190i \(0.575245\pi\)
\(360\) −27.6814 + 40.4645i −1.45894 + 2.13267i
\(361\) 0.719363 0.0378612
\(362\) −18.1184 + 18.1184i −0.952282 + 0.952282i
\(363\) 0 0
\(364\) 6.95243i 0.364407i
\(365\) 23.7539 + 16.2498i 1.24334 + 0.850553i
\(366\) 74.5262 3.89555
\(367\) 16.6120 + 16.6120i 0.867139 + 0.867139i 0.992155 0.125016i \(-0.0398982\pi\)
−0.125016 + 0.992155i \(0.539898\pi\)
\(368\) 12.1539 12.1539i 0.633567 0.633567i
\(369\) 19.4933 1.01478
\(370\) −60.2452 + 11.3011i −3.13200 + 0.587516i
\(371\) 0.370887i 0.0192555i
\(372\) 35.8171 + 35.8171i 1.85703 + 1.85703i
\(373\) −9.04941 9.04941i −0.468560 0.468560i 0.432887 0.901448i \(-0.357495\pi\)
−0.901448 + 0.432887i \(0.857495\pi\)
\(374\) 0 0
\(375\) −6.66338 + 28.5734i −0.344096 + 1.47553i
\(376\) 60.9760i 3.14460i
\(377\) 2.41129 + 2.41129i 0.124188 + 0.124188i
\(378\) 1.51744 1.51744i 0.0780488 0.0780488i
\(379\) 9.83221i 0.505047i −0.967591 0.252523i \(-0.918740\pi\)
0.967591 0.252523i \(-0.0812604\pi\)
\(380\) −7.79052 41.5306i −0.399645 2.13047i
\(381\) 38.6168i 1.97840i
\(382\) 24.4106 24.4106i 1.24896 1.24896i
\(383\) −1.11269 + 1.11269i −0.0568560 + 0.0568560i −0.734963 0.678107i \(-0.762801\pi\)
0.678107 + 0.734963i \(0.262801\pi\)
\(384\) 43.1219 2.20056
\(385\) 0 0
\(386\) −33.7819 −1.71945
\(387\) −18.2310 + 18.2310i −0.926734 + 0.926734i
\(388\) 21.6024 21.6024i 1.09669 1.09669i
\(389\) 20.4119i 1.03492i −0.855706 0.517462i \(-0.826877\pi\)
0.855706 0.517462i \(-0.173123\pi\)
\(390\) −36.7172 + 53.6731i −1.85925 + 2.71784i
\(391\) 2.64053i 0.133537i
\(392\) −27.3797 + 27.3797i −1.38289 + 1.38289i
\(393\) 16.8112 + 16.8112i 0.848011 + 0.848011i
\(394\) 38.8441i 1.95694i
\(395\) −27.1922 + 5.10085i −1.36819 + 0.256652i
\(396\) 0 0
\(397\) −0.702204 0.702204i −0.0352426 0.0352426i 0.689266 0.724508i \(-0.257933\pi\)
−0.724508 + 0.689266i \(0.757933\pi\)
\(398\) 28.6471 + 28.6471i 1.43595 + 1.43595i
\(399\) 4.29684i 0.215111i
\(400\) −26.0871 + 10.1441i −1.30436 + 0.507204i
\(401\) −28.0917 −1.40283 −0.701417 0.712751i \(-0.747449\pi\)
−0.701417 + 0.712751i \(0.747449\pi\)
\(402\) −27.3772 + 27.3772i −1.36545 + 1.36545i
\(403\) 14.2113 + 14.2113i 0.707914 + 0.707914i
\(404\) 8.71847 0.433760
\(405\) −12.2051 + 2.28949i −0.606475 + 0.113766i
\(406\) 0.709731i 0.0352233i
\(407\) 0 0
\(408\) 9.00218 9.00218i 0.445674 0.445674i
\(409\) 19.2579 0.952241 0.476120 0.879380i \(-0.342043\pi\)
0.476120 + 0.879380i \(0.342043\pi\)
\(410\) 23.1502 + 15.8368i 1.14331 + 0.782124i
\(411\) 0.472965 0.0233296
\(412\) −13.0729 13.0729i −0.644056 0.644056i
\(413\) −0.286269 0.286269i −0.0140864 0.0140864i
\(414\) −29.8479 −1.46694
\(415\) 13.1772 + 9.01441i 0.646845 + 0.442500i
\(416\) −12.0473 −0.590666
\(417\) 35.5271 35.5271i 1.73977 1.73977i
\(418\) 0 0
\(419\) 12.3724i 0.604429i −0.953240 0.302215i \(-0.902274\pi\)
0.953240 0.302215i \(-0.0977259\pi\)
\(420\) 9.04949 1.69755i 0.441570 0.0828320i
\(421\) −9.16536 −0.446692 −0.223346 0.974739i \(-0.571698\pi\)
−0.223346 + 0.974739i \(0.571698\pi\)
\(422\) 6.50186 + 6.50186i 0.316505 + 0.316505i
\(423\) −29.7075 + 29.7075i −1.44443 + 1.44443i
\(424\) 5.67426 0.275567
\(425\) 1.73187 3.93574i 0.0840081 0.190912i
\(426\) 12.7776i 0.619079i
\(427\) −2.96042 2.96042i −0.143265 0.143265i
\(428\) −37.8606 37.8606i −1.83006 1.83006i
\(429\) 0 0
\(430\) −36.4624 + 6.83981i −1.75837 + 0.329845i
\(431\) 21.5882i 1.03986i −0.854207 0.519932i \(-0.825957\pi\)
0.854207 0.519932i \(-0.174043\pi\)
\(432\) 9.21128 + 9.21128i 0.443178 + 0.443178i
\(433\) 5.16978 5.16978i 0.248444 0.248444i −0.571888 0.820332i \(-0.693789\pi\)
0.820332 + 0.571888i \(0.193789\pi\)
\(434\) 4.18290i 0.200786i
\(435\) 2.54984 3.72735i 0.122256 0.178713i
\(436\) 17.2099i 0.824206i
\(437\) 9.64118 9.64118i 0.461200 0.461200i
\(438\) 59.7353 59.7353i 2.85426 2.85426i
\(439\) −2.54287 −0.121365 −0.0606823 0.998157i \(-0.519328\pi\)
−0.0606823 + 0.998157i \(0.519328\pi\)
\(440\) 0 0
\(441\) 26.6788 1.27042
\(442\) 6.73909 6.73909i 0.320546 0.320546i
\(443\) −4.84165 + 4.84165i −0.230034 + 0.230034i −0.812707 0.582673i \(-0.802007\pi\)
0.582673 + 0.812707i \(0.302007\pi\)
\(444\) 122.397i 5.80870i
\(445\) −3.66008 19.5116i −0.173504 0.924936i
\(446\) 59.7220i 2.82792i
\(447\) 16.1596 16.1596i 0.764324 0.764324i
\(448\) −1.14608 1.14608i −0.0541473 0.0541473i
\(449\) 40.4649i 1.90966i −0.297159 0.954828i \(-0.596039\pi\)
0.297159 0.954828i \(-0.403961\pi\)
\(450\) 44.4887 + 19.5767i 2.09722 + 0.922852i
\(451\) 0 0
\(452\) 9.42383 + 9.42383i 0.443260 + 0.443260i
\(453\) −9.87248 9.87248i −0.463850 0.463850i
\(454\) 46.4266i 2.17891i
\(455\) 3.59059 0.673542i 0.168330 0.0315761i
\(456\) −65.7381 −3.07847
\(457\) −3.38525 + 3.38525i −0.158355 + 0.158355i −0.781838 0.623482i \(-0.785717\pi\)
0.623482 + 0.781838i \(0.285717\pi\)
\(458\) −28.4178 28.4178i −1.32788 1.32788i
\(459\) −2.00122 −0.0934088
\(460\) −24.1140 16.4962i −1.12432 0.769138i
\(461\) 23.9704i 1.11641i 0.829703 + 0.558206i \(0.188510\pi\)
−0.829703 + 0.558206i \(0.811490\pi\)
\(462\) 0 0
\(463\) 12.0906 12.0906i 0.561898 0.561898i −0.367948 0.929846i \(-0.619940\pi\)
0.929846 + 0.367948i \(0.119940\pi\)
\(464\) 4.30826 0.200006
\(465\) 15.0279 21.9677i 0.696901 1.01873i
\(466\) 8.34909 0.386764
\(467\) 11.2586 + 11.2586i 0.520985 + 0.520985i 0.917869 0.396884i \(-0.129908\pi\)
−0.396884 + 0.917869i \(0.629908\pi\)
\(468\) 51.8217 + 51.8217i 2.39546 + 2.39546i
\(469\) 2.17502 0.100433
\(470\) −59.4155 + 11.1455i −2.74063 + 0.514103i
\(471\) −14.5696 −0.671334
\(472\) 4.37969 4.37969i 0.201592 0.201592i
\(473\) 0 0
\(474\) 81.2092i 3.73006i
\(475\) −20.6938 + 8.04685i −0.949496 + 0.369215i
\(476\) −1.34938 −0.0618486
\(477\) −2.76449 2.76449i −0.126578 0.126578i
\(478\) −0.827284 + 0.827284i −0.0378391 + 0.0378391i
\(479\) −37.9796 −1.73533 −0.867666 0.497147i \(-0.834381\pi\)
−0.867666 + 0.497147i \(0.834381\pi\)
\(480\) 2.94154 + 15.6811i 0.134262 + 0.715740i
\(481\) 48.5638i 2.21432i
\(482\) −29.2295 29.2295i −1.33137 1.33137i
\(483\) 2.10081 + 2.10081i 0.0955900 + 0.0955900i
\(484\) 0 0
\(485\) −13.2494 9.06376i −0.601623 0.411564i
\(486\) 53.9107i 2.44544i
\(487\) 24.8084 + 24.8084i 1.12418 + 1.12418i 0.991107 + 0.133070i \(0.0424835\pi\)
0.133070 + 0.991107i \(0.457517\pi\)
\(488\) 45.2921 45.2921i 2.05027 2.05027i
\(489\) 10.3619i 0.468581i
\(490\) 31.6836 + 21.6744i 1.43132 + 0.979151i
\(491\) 29.4368i 1.32846i 0.747527 + 0.664232i \(0.231241\pi\)
−0.747527 + 0.664232i \(0.768759\pi\)
\(492\) 39.6039 39.6039i 1.78548 1.78548i
\(493\) −0.468000 + 0.468000i −0.0210776 + 0.0210776i
\(494\) −49.2120 −2.21415
\(495\) 0 0
\(496\) 25.3914 1.14011
\(497\) 0.507569 0.507569i 0.0227676 0.0227676i
\(498\) 33.1375 33.1375i 1.48493 1.48493i
\(499\) 28.2019i 1.26249i −0.775583 0.631246i \(-0.782544\pi\)
0.775583 0.631246i \(-0.217456\pi\)
\(500\) 25.1228 + 40.4037i 1.12353 + 1.80691i
\(501\) 6.98531i 0.312081i
\(502\) −11.5704 + 11.5704i −0.516413 + 0.516413i
\(503\) −25.4869 25.4869i −1.13640 1.13640i −0.989090 0.147313i \(-0.952938\pi\)
−0.147313 0.989090i \(-0.547062\pi\)
\(504\) 8.08435i 0.360105i
\(505\) −0.844633 4.50266i −0.0375857 0.200366i
\(506\) 0 0
\(507\) 12.3087 + 12.3087i 0.546648 + 0.546648i
\(508\) 44.2793 + 44.2793i 1.96458 + 1.96458i
\(509\) 31.3435i 1.38928i −0.719359 0.694639i \(-0.755564\pi\)
0.719359 0.694639i \(-0.244436\pi\)
\(510\) −10.4173 7.12634i −0.461284 0.315560i
\(511\) −4.74575 −0.209940
\(512\) 33.8969 33.8969i 1.49804 1.49804i
\(513\) 7.30691 + 7.30691i 0.322608 + 0.322608i
\(514\) 56.8905 2.50933
\(515\) −5.48504 + 8.01801i −0.241700 + 0.353316i
\(516\) 74.0787i 3.26113i
\(517\) 0 0
\(518\) 7.14706 7.14706i 0.314024 0.314024i
\(519\) −55.4510 −2.43403
\(520\) 10.3046 + 54.9332i 0.451889 + 2.40898i
\(521\) −35.6967 −1.56390 −0.781951 0.623340i \(-0.785775\pi\)
−0.781951 + 0.623340i \(0.785775\pi\)
\(522\) −5.29015 5.29015i −0.231544 0.231544i
\(523\) −7.14276 7.14276i −0.312331 0.312331i 0.533481 0.845812i \(-0.320884\pi\)
−0.845812 + 0.533481i \(0.820884\pi\)
\(524\) 38.5525 1.68417
\(525\) −1.75340 4.50916i −0.0765248 0.196796i
\(526\) −61.7023 −2.69035
\(527\) −2.75823 + 2.75823i −0.120150 + 0.120150i
\(528\) 0 0
\(529\) 13.5725i 0.590108i
\(530\) −1.03717 5.52905i −0.0450517 0.240166i
\(531\) −4.26756 −0.185196
\(532\) 4.92689 + 4.92689i 0.213608 + 0.213608i
\(533\) 15.7138 15.7138i 0.680638 0.680638i
\(534\) −58.2710 −2.52163
\(535\) −15.8853 + 23.2210i −0.686780 + 1.00393i
\(536\) 33.2760i 1.43731i
\(537\) −5.56931 5.56931i −0.240333 0.240333i
\(538\) 10.8941 + 10.8941i 0.469680 + 0.469680i
\(539\) 0 0
\(540\) 12.5022 18.2757i 0.538009 0.786460i
\(541\) 2.41825i 0.103969i −0.998648 0.0519844i \(-0.983445\pi\)
0.998648 0.0519844i \(-0.0165546\pi\)
\(542\) 12.3600 + 12.3600i 0.530908 + 0.530908i
\(543\) 19.0107 19.0107i 0.815826 0.815826i
\(544\) 2.33822i 0.100250i
\(545\) −8.88808 + 1.66727i −0.380724 + 0.0714181i
\(546\) 10.7233i 0.458913i
\(547\) −22.6752 + 22.6752i −0.969520 + 0.969520i −0.999549 0.0300287i \(-0.990440\pi\)
0.0300287 + 0.999549i \(0.490440\pi\)
\(548\) 0.542317 0.542317i 0.0231666 0.0231666i
\(549\) −44.1325 −1.88353
\(550\) 0 0
\(551\) 3.41755 0.145593
\(552\) −32.1406 + 32.1406i −1.36800 + 1.36800i
\(553\) 3.22589 3.22589i 0.137179 0.137179i
\(554\) 2.19295i 0.0931695i
\(555\) 63.2120 11.8576i 2.68320 0.503329i
\(556\) 81.4732i 3.45523i
\(557\) −15.0583 + 15.0583i −0.638039 + 0.638039i −0.950072 0.312032i \(-0.898990\pi\)
0.312032 + 0.950072i \(0.398990\pi\)
\(558\) −31.1783 31.1783i −1.31988 1.31988i
\(559\) 29.3924i 1.24317i
\(560\) 2.60595 3.80937i 0.110122 0.160975i
\(561\) 0 0
\(562\) 14.4572 + 14.4572i 0.609840 + 0.609840i
\(563\) −27.3299 27.3299i −1.15182 1.15182i −0.986188 0.165629i \(-0.947035\pi\)
−0.165629 0.986188i \(-0.552965\pi\)
\(564\) 120.711i 5.08287i
\(565\) 3.95398 5.77991i 0.166345 0.243163i
\(566\) −17.9287 −0.753601
\(567\) 1.44792 1.44792i 0.0608071 0.0608071i
\(568\) 7.76539 + 7.76539i 0.325829 + 0.325829i
\(569\) 9.21053 0.386125 0.193063 0.981186i \(-0.438158\pi\)
0.193063 + 0.981186i \(0.438158\pi\)
\(570\) 12.0159 + 64.0557i 0.503291 + 2.68300i
\(571\) 24.7774i 1.03690i −0.855107 0.518451i \(-0.826509\pi\)
0.855107 0.518451i \(-0.173491\pi\)
\(572\) 0 0
\(573\) −25.6128 + 25.6128i −1.06999 + 1.06999i
\(574\) −4.62514 −0.193050
\(575\) −6.18333 + 14.0518i −0.257863 + 0.586003i
\(576\) −17.0852 −0.711885
\(577\) −20.6537 20.6537i −0.859823 0.859823i 0.131494 0.991317i \(-0.458023\pi\)
−0.991317 + 0.131494i \(0.958023\pi\)
\(578\) −28.7572 28.7572i −1.19614 1.19614i
\(579\) 35.4455 1.47307
\(580\) −1.35017 7.19764i −0.0560628 0.298866i
\(581\) −2.63266 −0.109221
\(582\) −33.3190 + 33.3190i −1.38112 + 1.38112i
\(583\) 0 0
\(584\) 72.6062i 3.00447i
\(585\) 21.7430 31.7838i 0.898960 1.31410i
\(586\) −58.3448 −2.41020
\(587\) 2.60288 + 2.60288i 0.107432 + 0.107432i 0.758780 0.651347i \(-0.225796\pi\)
−0.651347 + 0.758780i \(0.725796\pi\)
\(588\) 54.2024 54.2024i 2.23527 2.23527i
\(589\) 20.1418 0.829930
\(590\) −5.06815 3.46707i −0.208652 0.142737i
\(591\) 40.7570i 1.67652i
\(592\) 43.3846 + 43.3846i 1.78309 + 1.78309i
\(593\) −12.2260 12.2260i −0.502062 0.502062i 0.410016 0.912078i \(-0.365523\pi\)
−0.912078 + 0.410016i \(0.865523\pi\)
\(594\) 0 0
\(595\) 0.130726 + 0.696888i 0.00535924 + 0.0285696i
\(596\) 37.0583i 1.51797i
\(597\) −30.0579 30.0579i −1.23019 1.23019i
\(598\) −24.0607 + 24.0607i −0.983915 + 0.983915i
\(599\) 42.4110i 1.73287i 0.499291 + 0.866434i \(0.333594\pi\)
−0.499291 + 0.866434i \(0.666406\pi\)
\(600\) 68.9865 26.8256i 2.81636 1.09515i
\(601\) 38.0290i 1.55123i −0.631204 0.775617i \(-0.717439\pi\)
0.631204 0.775617i \(-0.282561\pi\)
\(602\) 4.32564 4.32564i 0.176300 0.176300i
\(603\) 16.2120 16.2120i 0.660206 0.660206i
\(604\) −22.6402 −0.921218
\(605\) 0 0
\(606\) −13.4471 −0.546253
\(607\) −20.2562 + 20.2562i −0.822173 + 0.822173i −0.986419 0.164247i \(-0.947481\pi\)
0.164247 + 0.986419i \(0.447481\pi\)
\(608\) −8.53739 + 8.53739i −0.346237 + 0.346237i
\(609\) 0.744682i 0.0301760i
\(610\) −52.4116 35.8542i −2.12208 1.45170i
\(611\) 47.8950i 1.93762i
\(612\) −10.0579 + 10.0579i −0.406568 + 0.406568i
\(613\) −25.0196 25.0196i −1.01053 1.01053i −0.999944 0.0105882i \(-0.996630\pi\)
−0.0105882 0.999944i \(-0.503370\pi\)
\(614\) 15.0330i 0.606684i
\(615\) −24.2902 16.6167i −0.979477 0.670050i
\(616\) 0 0
\(617\) −6.86653 6.86653i −0.276436 0.276436i 0.555248 0.831685i \(-0.312623\pi\)
−0.831685 + 0.555248i \(0.812623\pi\)
\(618\) 20.1633 + 20.1633i 0.811089 + 0.811089i
\(619\) 13.1057i 0.526763i −0.964692 0.263381i \(-0.915162\pi\)
0.964692 0.263381i \(-0.0848378\pi\)
\(620\) −7.95743 42.4204i −0.319578 1.70364i
\(621\) 7.14498 0.286718
\(622\) 51.7829 51.7829i 2.07631 2.07631i
\(623\) 2.31471 + 2.31471i 0.0927370 + 0.0927370i
\(624\) 65.0931 2.60581
\(625\) 18.4327 16.8889i 0.737307 0.675558i
\(626\) 34.8531i 1.39301i
\(627\) 0 0
\(628\) −16.7060 + 16.7060i −0.666643 + 0.666643i
\(629\) −9.42560 −0.375823
\(630\) −7.87745 + 1.47769i −0.313845 + 0.0588727i
\(631\) 23.3545 0.929727 0.464863 0.885382i \(-0.346103\pi\)
0.464863 + 0.885382i \(0.346103\pi\)
\(632\) 49.3535 + 49.3535i 1.96318 + 1.96318i
\(633\) −6.82204 6.82204i −0.271152 0.271152i
\(634\) 18.0096 0.715254
\(635\) 18.5784 27.1578i 0.737261 1.07773i
\(636\) −11.2331 −0.445420
\(637\) 21.5060 21.5060i 0.852100 0.852100i
\(638\) 0 0
\(639\) 7.56658i 0.299329i
\(640\) −30.3261 20.7458i −1.19874 0.820049i
\(641\) 37.2830 1.47259 0.736296 0.676660i \(-0.236573\pi\)
0.736296 + 0.676660i \(0.236573\pi\)
\(642\) 58.3952 + 58.3952i 2.30468 + 2.30468i
\(643\) 4.39799 4.39799i 0.173440 0.173440i −0.615049 0.788489i \(-0.710864\pi\)
0.788489 + 0.615049i \(0.210864\pi\)
\(644\) 4.81771 0.189844
\(645\) 38.2580 7.17664i 1.50641 0.282580i
\(646\) 9.55142i 0.375796i
\(647\) 25.0575 + 25.0575i 0.985113 + 0.985113i 0.999891 0.0147777i \(-0.00470406\pi\)
−0.0147777 + 0.999891i \(0.504704\pi\)
\(648\) 22.1521 + 22.1521i 0.870216 + 0.870216i
\(649\) 0 0
\(650\) 51.6438 20.0819i 2.02564 0.787675i
\(651\) 4.38889i 0.172014i
\(652\) −11.8813 11.8813i −0.465307 0.465307i
\(653\) −23.8281 + 23.8281i −0.932467 + 0.932467i −0.997860 0.0653926i \(-0.979170\pi\)
0.0653926 + 0.997860i \(0.479170\pi\)
\(654\) 26.5442i 1.03796i
\(655\) −3.73491 19.9105i −0.145935 0.777966i
\(656\) 28.0758i 1.09618i
\(657\) −35.3737 + 35.3737i −1.38006 + 1.38006i
\(658\) 7.04864 7.04864i 0.274785 0.274785i
\(659\) 50.1826 1.95484 0.977419 0.211310i \(-0.0677729\pi\)
0.977419 + 0.211310i \(0.0677729\pi\)
\(660\) 0 0
\(661\) 28.3220 1.10160 0.550798 0.834638i \(-0.314323\pi\)
0.550798 + 0.834638i \(0.314323\pi\)
\(662\) 23.3806 23.3806i 0.908711 0.908711i
\(663\) −7.07097 + 7.07097i −0.274614 + 0.274614i
\(664\) 40.2776i 1.56307i
\(665\) 2.06719 3.02181i 0.0801621 0.117181i
\(666\) 106.545i 4.12853i
\(667\) 1.67091 1.67091i 0.0646978 0.0646978i
\(668\) −8.00958 8.00958i −0.309900 0.309900i
\(669\) 62.6631i 2.42269i
\(670\) 32.4244 6.08235i 1.25267 0.234982i
\(671\) 0 0
\(672\) −1.86029 1.86029i −0.0717623 0.0717623i
\(673\) −20.7252 20.7252i −0.798898 0.798898i 0.184024 0.982922i \(-0.441088\pi\)
−0.982922 + 0.184024i \(0.941088\pi\)
\(674\) 82.7291i 3.18661i
\(675\) −10.6497 4.68625i −0.409907 0.180374i
\(676\) 28.2271 1.08566
\(677\) −20.1880 + 20.1880i −0.775887 + 0.775887i −0.979129 0.203242i \(-0.934852\pi\)
0.203242 + 0.979129i \(0.434852\pi\)
\(678\) −14.5351 14.5351i −0.558216 0.558216i
\(679\) 2.64707 0.101585
\(680\) −10.6618 + 2.00000i −0.408862 + 0.0766965i
\(681\) 48.7129i 1.86668i
\(682\) 0 0
\(683\) 11.2345 11.2345i 0.429876 0.429876i −0.458710 0.888586i \(-0.651688\pi\)
0.888586 + 0.458710i \(0.151688\pi\)
\(684\) 73.4477 2.80834
\(685\) −0.332619 0.227541i −0.0127087 0.00869390i
\(686\) −12.7854 −0.488150
\(687\) 29.8173 + 29.8173i 1.13760 + 1.13760i
\(688\) 26.2578 + 26.2578i 1.00107 + 1.00107i
\(689\) −4.45698 −0.169797
\(690\) 37.1929 + 25.4433i 1.41591 + 0.968609i
\(691\) 9.97362 0.379414 0.189707 0.981841i \(-0.439246\pi\)
0.189707 + 0.981841i \(0.439246\pi\)
\(692\) −63.5820 + 63.5820i −2.41702 + 2.41702i
\(693\) 0 0
\(694\) 34.4767i 1.30872i
\(695\) −42.0769 + 7.89301i −1.59607 + 0.299399i
\(696\) −11.3930 −0.431852
\(697\) 3.04984 + 3.04984i 0.115521 + 0.115521i
\(698\) 14.5608 14.5608i 0.551135 0.551135i
\(699\) −8.76025 −0.331343
\(700\) −7.18086 3.15984i −0.271411 0.119431i
\(701\) 23.9400i 0.904201i −0.891967 0.452101i \(-0.850675\pi\)
0.891967 0.452101i \(-0.149325\pi\)
\(702\) −18.2353 18.2353i −0.688245 0.688245i
\(703\) 34.4151 + 34.4151i 1.29799 + 1.29799i
\(704\) 0 0
\(705\) 62.3415 11.6943i 2.34792 0.440435i
\(706\) 64.4175i 2.42438i
\(707\) 0.534164 + 0.534164i 0.0200893 + 0.0200893i
\(708\) −8.67027 + 8.67027i −0.325849 + 0.325849i
\(709\) 21.1788i 0.795385i −0.917519 0.397693i \(-0.869811\pi\)
0.917519 0.397693i \(-0.130189\pi\)
\(710\) 6.14727 8.98605i 0.230703 0.337241i
\(711\) 48.0899i 1.80351i
\(712\) −35.4132 + 35.4132i −1.32717 + 1.32717i
\(713\) 9.84774 9.84774i 0.368801 0.368801i
\(714\) 2.08125 0.0778887
\(715\) 0 0
\(716\) −12.7719 −0.477309
\(717\) 0.868025 0.868025i 0.0324170 0.0324170i
\(718\) 15.6952 15.6952i 0.585739 0.585739i
\(719\) 11.6286i 0.433672i −0.976208 0.216836i \(-0.930426\pi\)
0.976208 0.216836i \(-0.0695737\pi\)
\(720\) −8.97000 47.8182i −0.334292 1.78208i
\(721\) 1.60191i 0.0596581i
\(722\) −1.27222 + 1.27222i −0.0473472 + 0.0473472i
\(723\) 30.6689 + 30.6689i 1.14059 + 1.14059i
\(724\) 43.5965i 1.62025i
\(725\) −3.58643 + 1.39459i −0.133197 + 0.0517939i
\(726\) 0 0
\(727\) 9.80845 + 9.80845i 0.363775 + 0.363775i 0.865201 0.501426i \(-0.167191\pi\)
−0.501426 + 0.865201i \(0.667191\pi\)
\(728\) −6.51688 6.51688i −0.241532 0.241532i
\(729\) 39.9051i 1.47797i
\(730\) −70.7481 + 13.2713i −2.61850 + 0.491193i
\(731\) −5.70469 −0.210996
\(732\) −89.6625 + 89.6625i −3.31402 + 3.31402i
\(733\) −9.10112 9.10112i −0.336157 0.336157i 0.518762 0.854919i \(-0.326393\pi\)
−0.854919 + 0.518762i \(0.826393\pi\)
\(734\) −58.7579 −2.16879
\(735\) −33.2439 22.7418i −1.22622 0.838845i
\(736\) 8.34820i 0.307719i
\(737\) 0 0
\(738\) −34.4746 + 34.4746i −1.26903 + 1.26903i
\(739\) 36.2156 1.33221 0.666106 0.745857i \(-0.267960\pi\)
0.666106 + 0.745857i \(0.267960\pi\)
\(740\) 58.8846 86.0773i 2.16464 3.16426i
\(741\) 51.6355 1.89688
\(742\) 0.655927 + 0.655927i 0.0240798 + 0.0240798i
\(743\) 28.8534 + 28.8534i 1.05853 + 1.05853i 0.998177 + 0.0603500i \(0.0192217\pi\)
0.0603500 + 0.998177i \(0.480778\pi\)
\(744\) −67.1466 −2.46171
\(745\) −19.1388 + 3.59016i −0.701191 + 0.131533i
\(746\) 32.0084 1.17191
\(747\) −19.6232 + 19.6232i −0.717974 + 0.717974i
\(748\) 0 0
\(749\) 4.63929i 0.169516i
\(750\) −38.7488 62.3177i −1.41491 2.27552i
\(751\) −9.16953 −0.334601 −0.167301 0.985906i \(-0.553505\pi\)
−0.167301 + 0.985906i \(0.553505\pi\)
\(752\) 42.7871 + 42.7871i 1.56029 + 1.56029i
\(753\) 12.1402 12.1402i 0.442414 0.442414i
\(754\) −8.52890 −0.310604
\(755\) 2.19335 + 11.6926i 0.0798243 + 0.425536i
\(756\) 3.65127i 0.132795i
\(757\) −14.7393 14.7393i −0.535709 0.535709i 0.386557 0.922266i \(-0.373664\pi\)
−0.922266 + 0.386557i \(0.873664\pi\)
\(758\) 17.3886 + 17.3886i 0.631584 + 0.631584i
\(759\) 0 0
\(760\) 46.2313 + 31.6263i 1.67698 + 1.14721i
\(761\) 43.2073i 1.56626i 0.621855 + 0.783132i \(0.286379\pi\)
−0.621855 + 0.783132i \(0.713621\pi\)
\(762\) −68.2953 68.2953i −2.47408 2.47408i
\(763\) 1.05442 1.05442i 0.0381725 0.0381725i
\(764\) 58.7369i 2.12503i
\(765\) 6.16882 + 4.22003i 0.223034 + 0.152575i
\(766\) 3.93569i 0.142202i
\(767\) −3.44013 + 3.44013i −0.124216 + 0.124216i
\(768\) −59.9489 + 59.9489i −2.16322 + 2.16322i
\(769\) −17.6513 −0.636523 −0.318261 0.948003i \(-0.603099\pi\)
−0.318261 + 0.948003i \(0.603099\pi\)
\(770\) 0 0
\(771\) −59.6921 −2.14976
\(772\) 40.6430 40.6430i 1.46277 1.46277i
\(773\) −13.3581 + 13.3581i −0.480459 + 0.480459i −0.905278 0.424819i \(-0.860338\pi\)
0.424819 + 0.905278i \(0.360338\pi\)
\(774\) 64.4845i 2.31785i
\(775\) −21.1371 + 8.21925i −0.759268 + 0.295244i
\(776\) 40.4981i 1.45380i
\(777\) −7.49902 + 7.49902i −0.269026 + 0.269026i
\(778\) 36.0992 + 36.0992i 1.29422 + 1.29422i
\(779\) 22.2713i 0.797953i
\(780\) −20.3996 108.749i −0.730424 3.89382i
\(781\) 0 0
\(782\) −4.66987 4.66987i −0.166994 0.166994i
\(783\) 1.26636 + 1.26636i 0.0452559 + 0.0452559i
\(784\) 38.4249i 1.37232i
\(785\) 10.2463 + 7.00939i 0.365706 + 0.250176i
\(786\) −59.4624 −2.12095
\(787\) −32.6528 + 32.6528i −1.16395 + 1.16395i −0.180344 + 0.983604i \(0.557721\pi\)
−0.983604 + 0.180344i \(0.942279\pi\)
\(788\) −46.7333 46.7333i −1.66481 1.66481i
\(789\) 64.7409 2.30484
\(790\) 39.0694 57.1115i 1.39003 2.03194i
\(791\) 1.15476i 0.0410585i
\(792\) 0 0
\(793\) −35.5757 + 35.5757i −1.26333 + 1.26333i
\(794\) 2.48375 0.0881450
\(795\) 1.08824 + 5.80133i 0.0385960 + 0.205752i
\(796\) −68.9307 −2.44318
\(797\) 6.66696 + 6.66696i 0.236156 + 0.236156i 0.815256 0.579100i \(-0.196596\pi\)
−0.579100 + 0.815256i \(0.696596\pi\)
\(798\) −7.59912 7.59912i −0.269006 0.269006i
\(799\) −9.29581 −0.328862
\(800\) 5.47542 12.4431i 0.193585 0.439930i
\(801\) 34.5066 1.21923
\(802\) 49.6813 49.6813i 1.75431 1.75431i
\(803\) 0 0
\(804\) 65.8750i 2.32323i
\(805\) −0.466733 2.48811i −0.0164502 0.0876944i
\(806\) −50.2664 −1.77056
\(807\) −11.4306 11.4306i −0.402377 0.402377i
\(808\) −8.17228 + 8.17228i −0.287500 + 0.287500i
\(809\) −1.81466 −0.0638001 −0.0319001 0.999491i \(-0.510156\pi\)
−0.0319001 + 0.999491i \(0.510156\pi\)
\(810\) 17.5361 25.6342i 0.616156 0.900694i
\(811\) 30.4408i 1.06892i 0.845193 + 0.534461i \(0.179485\pi\)
−0.845193 + 0.534461i \(0.820515\pi\)
\(812\) 0.853877 + 0.853877i 0.0299652 + 0.0299652i
\(813\) −12.9687 12.9687i −0.454832 0.454832i
\(814\) 0 0
\(815\) −4.98506 + 7.28714i −0.174619 + 0.255257i
\(816\) 12.6337i 0.442269i
\(817\) 20.8292 + 20.8292i 0.728720 + 0.728720i
\(818\) −34.0583 + 34.0583i −1.19082 + 1.19082i
\(819\) 6.35003i 0.221888i
\(820\) −46.9052 + 8.79873i −1.63800 + 0.307265i
\(821\) 28.6807i 1.00096i 0.865747 + 0.500482i \(0.166844\pi\)
−0.865747 + 0.500482i \(0.833156\pi\)
\(822\) −0.836456 + 0.836456i −0.0291748 + 0.0291748i
\(823\) −23.4705 + 23.4705i −0.818128 + 0.818128i −0.985837 0.167708i \(-0.946363\pi\)
0.167708 + 0.985837i \(0.446363\pi\)
\(824\) 24.5079 0.853772
\(825\) 0 0
\(826\) 1.01256 0.0352314
\(827\) 0.278504 0.278504i 0.00968454 0.00968454i −0.702248 0.711932i \(-0.747820\pi\)
0.711932 + 0.702248i \(0.247820\pi\)
\(828\) 35.9100 35.9100i 1.24796 1.24796i
\(829\) 25.7237i 0.893421i −0.894679 0.446710i \(-0.852595\pi\)
0.894679 0.446710i \(-0.147405\pi\)
\(830\) −39.2468 + 7.36211i −1.36228 + 0.255543i
\(831\) 2.30094i 0.0798188i
\(832\) −13.7726 + 13.7726i −0.477479 + 0.477479i
\(833\) 4.17404 + 4.17404i 0.144622 + 0.144622i
\(834\) 125.662i 4.35133i
\(835\) −3.36060 + 4.91251i −0.116298 + 0.170005i
\(836\) 0 0
\(837\) 7.46346 + 7.46346i 0.257975 + 0.257975i
\(838\) 21.8810 + 21.8810i 0.755866 + 0.755866i
\(839\) 41.2331i 1.42353i 0.702420 + 0.711763i \(0.252103\pi\)
−0.702420 + 0.711763i \(0.747897\pi\)
\(840\) −6.89135 + 10.0738i −0.237774 + 0.347578i
\(841\) −28.4077 −0.979576
\(842\) 16.2093 16.2093i 0.558609 0.558609i
\(843\) −15.1691 15.1691i −0.522453 0.522453i
\(844\) −15.6448 −0.538515
\(845\) −2.73460 14.5779i −0.0940732 0.501496i
\(846\) 105.078i 3.61264i
\(847\) 0 0
\(848\) −3.98165 + 3.98165i −0.136731 + 0.136731i
\(849\) 18.8117 0.645615
\(850\) 3.89763 + 10.0234i 0.133688 + 0.343800i
\(851\) 33.6524 1.15359
\(852\) −15.3728 15.3728i −0.526663 0.526663i
\(853\) 4.69322 + 4.69322i 0.160693 + 0.160693i 0.782874 0.622181i \(-0.213753\pi\)
−0.622181 + 0.782874i \(0.713753\pi\)
\(854\) 10.4712 0.358318
\(855\) −7.11550 37.9321i −0.243345 1.29725i
\(856\) 70.9774 2.42596
\(857\) −28.1873 + 28.1873i −0.962858 + 0.962858i −0.999335 0.0364762i \(-0.988387\pi\)
0.0364762 + 0.999335i \(0.488387\pi\)
\(858\) 0 0
\(859\) 3.38503i 0.115496i 0.998331 + 0.0577479i \(0.0183920\pi\)
−0.998331 + 0.0577479i \(0.981608\pi\)
\(860\) 35.6389 52.0969i 1.21528 1.77649i
\(861\) 4.85291 0.165387
\(862\) 38.1795 + 38.1795i 1.30040 + 1.30040i
\(863\) −4.82257 + 4.82257i −0.164162 + 0.164162i −0.784408 0.620245i \(-0.787033\pi\)
0.620245 + 0.784408i \(0.287033\pi\)
\(864\) −6.32697 −0.215248
\(865\) 38.9967 + 26.6773i 1.32593 + 0.907054i
\(866\) 18.2859i 0.621380i
\(867\) 30.1734 + 30.1734i 1.02474 + 1.02474i
\(868\) 5.03245 + 5.03245i 0.170813 + 0.170813i
\(869\) 0 0
\(870\) 2.08247 + 11.1015i 0.0706024 + 0.376375i
\(871\) 26.1374i 0.885633i
\(872\) 16.1318 + 16.1318i 0.546290 + 0.546290i
\(873\) 19.7306 19.7306i 0.667780 0.667780i
\(874\) 34.1016i 1.15350i
\(875\) −0.936232 + 4.01468i −0.0316504 + 0.135721i
\(876\) 143.735i 4.85636i
\(877\) −2.93904 + 2.93904i −0.0992442 + 0.0992442i −0.754986 0.655741i \(-0.772356\pi\)
0.655741 + 0.754986i \(0.272356\pi\)
\(878\) 4.49716 4.49716i 0.151772 0.151772i
\(879\) 61.2180 2.06483
\(880\) 0 0
\(881\) −7.19015 −0.242242 −0.121121 0.992638i \(-0.538649\pi\)
−0.121121 + 0.992638i \(0.538649\pi\)
\(882\) −47.1824 + 47.1824i −1.58871 + 1.58871i
\(883\) 31.6567 31.6567i 1.06533 1.06533i 0.0676221 0.997711i \(-0.478459\pi\)
0.997711 0.0676221i \(-0.0215412\pi\)
\(884\) 16.2156i 0.545390i
\(885\) 5.31773 + 3.63781i 0.178754 + 0.122283i
\(886\) 17.1253i 0.575335i
\(887\) −10.5828 + 10.5828i −0.355337 + 0.355337i −0.862091 0.506754i \(-0.830845\pi\)
0.506754 + 0.862091i \(0.330845\pi\)
\(888\) −114.729 114.729i −3.85005 3.85005i
\(889\) 5.42582i 0.181976i
\(890\) 40.9799 + 28.0339i 1.37365 + 0.939700i
\(891\) 0 0
\(892\) −71.8515 71.8515i −2.40577 2.40577i
\(893\) 33.9412 + 33.9412i 1.13580 + 1.13580i
\(894\) 57.1578i 1.91164i
\(895\) 1.23732 + 6.59606i 0.0413592 + 0.220482i
\(896\) 6.05881 0.202411
\(897\) 25.2456 25.2456i 0.842926 0.842926i
\(898\) 71.5637 + 71.5637i 2.38811 + 2.38811i
\(899\) 3.49077 0.116424
\(900\) −77.0770 + 29.9717i −2.56923 + 0.999055i
\(901\) 0.865042i 0.0288187i
\(902\) 0 0
\(903\) −4.53866 + 4.53866i −0.151037 + 0.151037i
\(904\) −17.6669 −0.587592
\(905\) −22.5155 + 4.22357i −0.748439 + 0.140396i
\(906\) 34.9197 1.16013
\(907\) −7.39651 7.39651i −0.245597 0.245597i 0.573564 0.819161i \(-0.305560\pi\)
−0.819161 + 0.573564i \(0.805560\pi\)
\(908\) 55.8558 + 55.8558i 1.85364 + 1.85364i
\(909\) 7.96305 0.264118
\(910\) −5.15891 + 7.54128i −0.171016 + 0.249991i
\(911\) −1.97645 −0.0654827 −0.0327414 0.999464i \(-0.510424\pi\)
−0.0327414 + 0.999464i \(0.510424\pi\)
\(912\) 46.1287 46.1287i 1.52747 1.52747i
\(913\) 0 0
\(914\) 11.9739i 0.396061i
\(915\) 54.9927 + 37.6199i 1.81800 + 1.24368i
\(916\) 68.3790 2.25930
\(917\) 2.36204 + 2.36204i 0.0780013 + 0.0780013i
\(918\) 3.53923 3.53923i 0.116812 0.116812i
\(919\) 9.38958 0.309734 0.154867 0.987935i \(-0.450505\pi\)
0.154867 + 0.987935i \(0.450505\pi\)
\(920\) 38.0661 7.14063i 1.25500 0.235420i
\(921\) 15.7733i 0.519749i
\(922\) −42.3925 42.3925i −1.39612 1.39612i
\(923\) −6.09950 6.09950i −0.200768 0.200768i
\(924\) 0 0
\(925\) −50.1594 22.0720i −1.64923 0.725722i
\(926\) 42.7654i 1.40536i
\(927\) −11.9402 11.9402i −0.392168 0.392168i
\(928\) −1.47961 + 1.47961i −0.0485706 + 0.0485706i
\(929\) 16.3765i 0.537295i −0.963239 0.268648i \(-0.913423\pi\)
0.963239 0.268648i \(-0.0865767\pi\)
\(930\) 12.2733 + 65.4281i 0.402459 + 2.14547i
\(931\) 30.4808i 0.998969i
\(932\) −10.0448 + 10.0448i −0.329028 + 0.329028i
\(933\) −54.3330 + 54.3330i −1.77878 + 1.77878i
\(934\) −39.8225 −1.30303
\(935\) 0 0
\(936\) −97.1504 −3.17546
\(937\) 5.42428 5.42428i 0.177204 0.177204i −0.612932 0.790136i \(-0.710010\pi\)
0.790136 + 0.612932i \(0.210010\pi\)
\(938\) −3.84661 + 3.84661i −0.125596 + 0.125596i
\(939\) 36.5695i 1.19340i
\(940\) 58.0737 84.8919i 1.89416 2.76887i
\(941\) 52.3639i 1.70701i −0.521082 0.853507i \(-0.674471\pi\)
0.521082 0.853507i \(-0.325529\pi\)
\(942\) 25.7670 25.7670i 0.839534 0.839534i
\(943\) −10.8889 10.8889i −0.354591 0.354591i
\(944\) 6.14650i 0.200051i
\(945\) 1.88570 0.353730i 0.0613419 0.0115068i
\(946\) 0 0
\(947\) −18.6613 18.6613i −0.606410 0.606410i 0.335596 0.942006i \(-0.391062\pi\)
−0.942006 + 0.335596i \(0.891062\pi\)
\(948\) −97.7028 97.7028i −3.17324 3.17324i
\(949\) 57.0302i 1.85128i
\(950\) 22.3666 50.8289i 0.725668 1.64911i
\(951\) −18.8965 −0.612762
\(952\) 1.26484 1.26484i 0.0409938 0.0409938i
\(953\) −0.972028 0.972028i −0.0314871 0.0314871i 0.691188 0.722675i \(-0.257088\pi\)
−0.722675 + 0.691188i \(0.757088\pi\)
\(954\) 9.77823 0.316582
\(955\) 30.3347 5.69034i 0.981608 0.184135i
\(956\) 1.99061i 0.0643810i
\(957\) 0 0
\(958\) 67.1684 67.1684i 2.17011 2.17011i
\(959\) 0.0664534 0.00214589
\(960\) 21.2896 + 14.5640i 0.687119 + 0.470051i
\(961\) −10.4266 −0.336343
\(962\) −85.8869 85.8869i −2.76910 2.76910i
\(963\) −34.5801 34.5801i −1.11433 1.11433i
\(964\) 70.3320 2.26524
\(965\) −24.9276 17.0527i −0.802447 0.548946i
\(966\) −7.43071 −0.239079
\(967\) −13.4951 + 13.4951i −0.433974 + 0.433974i −0.889978 0.456004i \(-0.849280\pi\)
0.456004 + 0.889978i \(0.349280\pi\)
\(968\) 0 0
\(969\) 10.0218i 0.321946i
\(970\) 39.4616 7.40242i 1.26704 0.237677i
\(971\) −36.7311 −1.17876 −0.589379 0.807857i \(-0.700628\pi\)
−0.589379 + 0.807857i \(0.700628\pi\)
\(972\) −64.8599 64.8599i −2.08038 2.08038i
\(973\) 4.99171 4.99171i 0.160027 0.160027i
\(974\) −87.7493 −2.81167
\(975\) −54.1870 + 21.0708i −1.73537 + 0.674806i
\(976\) 63.5632i 2.03461i
\(977\) 25.5024 + 25.5024i 0.815895 + 0.815895i 0.985510 0.169615i \(-0.0542524\pi\)
−0.169615 + 0.985510i \(0.554252\pi\)
\(978\) 18.3254 + 18.3254i 0.585981 + 0.585981i
\(979\) 0 0
\(980\) −64.1951 + 12.0420i −2.05064 + 0.384669i
\(981\) 15.7187i 0.501861i
\(982\) −52.0601 52.0601i −1.66130 1.66130i
\(983\) 20.0309 20.0309i 0.638886 0.638886i −0.311395 0.950281i \(-0.600796\pi\)
0.950281 + 0.311395i \(0.100796\pi\)
\(984\) 74.2456i 2.36686i
\(985\) −19.6080 + 28.6629i −0.624764 + 0.913277i
\(986\) 1.65535i 0.0527171i
\(987\) −7.39575 + 7.39575i −0.235409 + 0.235409i
\(988\) 59.2070 59.2070i 1.88362 1.88362i
\(989\) 20.3676 0.647651
\(990\) 0 0
\(991\) 57.3361 1.82134 0.910671 0.413132i \(-0.135565\pi\)
0.910671 + 0.413132i \(0.135565\pi\)
\(992\) −8.72031 + 8.72031i −0.276870 + 0.276870i
\(993\) −24.5319 + 24.5319i −0.778498 + 0.778498i
\(994\) 1.79531i 0.0569438i
\(995\) 6.67791 + 35.5993i 0.211704 + 1.12857i
\(996\) 79.7356i 2.52652i
\(997\) −10.8951 + 10.8951i −0.345052 + 0.345052i −0.858263 0.513210i \(-0.828456\pi\)
0.513210 + 0.858263i \(0.328456\pi\)
\(998\) 49.8762 + 49.8762i 1.57880 + 1.57880i
\(999\) 25.5047i 0.806932i
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 605.2.e.a.362.1 20
5.3 odd 4 inner 605.2.e.a.483.10 yes 20
11.2 odd 10 605.2.m.f.282.1 80
11.3 even 5 605.2.m.f.112.10 80
11.4 even 5 605.2.m.f.457.1 80
11.5 even 5 605.2.m.f.602.10 80
11.6 odd 10 605.2.m.f.602.1 80
11.7 odd 10 605.2.m.f.457.10 80
11.8 odd 10 605.2.m.f.112.1 80
11.9 even 5 605.2.m.f.282.10 80
11.10 odd 2 inner 605.2.e.a.362.10 yes 20
55.3 odd 20 605.2.m.f.233.10 80
55.8 even 20 605.2.m.f.233.1 80
55.13 even 20 605.2.m.f.403.10 80
55.18 even 20 605.2.m.f.578.10 80
55.28 even 20 605.2.m.f.118.10 80
55.38 odd 20 605.2.m.f.118.1 80
55.43 even 4 inner 605.2.e.a.483.1 yes 20
55.48 odd 20 605.2.m.f.578.1 80
55.53 odd 20 605.2.m.f.403.1 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.e.a.362.1 20 1.1 even 1 trivial
605.2.e.a.362.10 yes 20 11.10 odd 2 inner
605.2.e.a.483.1 yes 20 55.43 even 4 inner
605.2.e.a.483.10 yes 20 5.3 odd 4 inner
605.2.m.f.112.1 80 11.8 odd 10
605.2.m.f.112.10 80 11.3 even 5
605.2.m.f.118.1 80 55.38 odd 20
605.2.m.f.118.10 80 55.28 even 20
605.2.m.f.233.1 80 55.8 even 20
605.2.m.f.233.10 80 55.3 odd 20
605.2.m.f.282.1 80 11.2 odd 10
605.2.m.f.282.10 80 11.9 even 5
605.2.m.f.403.1 80 55.53 odd 20
605.2.m.f.403.10 80 55.13 even 20
605.2.m.f.457.1 80 11.4 even 5
605.2.m.f.457.10 80 11.7 odd 10
605.2.m.f.578.1 80 55.48 odd 20
605.2.m.f.578.10 80 55.18 even 20
605.2.m.f.602.1 80 11.6 odd 10
605.2.m.f.602.10 80 11.5 even 5