Properties

Label 325.2.e.c.276.3
Level $325$
Weight $2$
Character 325.276
Analytic conductor $2.595$
Analytic rank $0$
Dimension $10$
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] = [325,2,Mod(126,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\), 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: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 276.3
Root \(-0.134432 - 0.232843i\) of defining polynomial
Character \(\chi\) \(=\) 325.276
Dual form 325.2.e.c.126.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.134432 - 0.232843i) q^{2} +(0.301414 + 0.522064i) q^{3} +(0.963856 - 1.66945i) q^{4} +(0.0810394 - 0.140364i) q^{6} +(0.715471 - 1.23923i) q^{7} -1.05602 q^{8} +(1.31830 - 2.28336i) q^{9} +O(q^{10})\) \(q+(-0.134432 - 0.232843i) q^{2} +(0.301414 + 0.522064i) q^{3} +(0.963856 - 1.66945i) q^{4} +(0.0810394 - 0.140364i) q^{6} +(0.715471 - 1.23923i) q^{7} -1.05602 q^{8} +(1.31830 - 2.28336i) q^{9} +(0.0810394 + 0.140364i) q^{11} +1.16208 q^{12} +(-2.41659 + 2.67584i) q^{13} -0.384729 q^{14} +(-1.78575 - 3.09301i) q^{16} +(1.41046 - 2.44299i) q^{17} -0.708886 q^{18} +(1.96386 - 3.40150i) q^{19} +0.862612 q^{21} +(0.0217886 - 0.0377389i) q^{22} +(2.36356 + 4.09380i) q^{23} +(-0.318299 - 0.551310i) q^{24} +(0.947917 + 0.202967i) q^{26} +3.39790 q^{27} +(-1.37922 - 2.38888i) q^{28} +(1.99641 + 3.45788i) q^{29} -0.453192 q^{31} +(-1.53614 + 2.66068i) q^{32} +(-0.0488528 + 0.0846155i) q^{33} -0.758446 q^{34} +(-2.54130 - 4.40166i) q^{36} +(-2.52179 - 4.36787i) q^{37} -1.05602 q^{38} +(-2.12535 - 0.455079i) q^{39} +(4.29450 + 7.43829i) q^{41} +(-0.115963 - 0.200853i) q^{42} +(2.33101 - 4.03742i) q^{43} +0.312441 q^{44} +(0.635476 - 1.10068i) q^{46} -11.4269 q^{47} +(1.07650 - 1.86455i) q^{48} +(2.47620 + 4.28891i) q^{49} +1.70053 q^{51} +(2.13793 + 6.61349i) q^{52} +7.30525 q^{53} +(-0.456786 - 0.791177i) q^{54} +(-0.755552 + 1.30865i) q^{56} +2.36773 q^{57} +(0.536762 - 0.929698i) q^{58} +(-4.98327 + 8.63128i) q^{59} +(-0.726596 + 1.25850i) q^{61} +(0.0609235 + 0.105523i) q^{62} +(-1.88641 - 3.26736i) q^{63} -6.31697 q^{64} +0.0262695 q^{66} +(3.17765 + 5.50384i) q^{67} +(-2.71897 - 4.70939i) q^{68} +(-1.42482 + 2.46786i) q^{69} +(-7.02110 + 12.1609i) q^{71} +(-1.39215 + 2.41128i) q^{72} -7.75845 q^{73} +(-0.678018 + 1.17436i) q^{74} +(-3.78575 - 6.55711i) q^{76} +0.231925 q^{77} +(0.179753 + 0.556051i) q^{78} -11.2447 q^{79} +(-2.93072 - 5.07616i) q^{81} +(1.15464 - 1.99989i) q^{82} +9.45997 q^{83} +(0.831434 - 1.44009i) q^{84} -1.25345 q^{86} +(-1.20349 + 2.08450i) q^{87} +(-0.0855792 - 0.148228i) q^{88} +(4.33064 + 7.50090i) q^{89} +(1.58699 + 4.90920i) q^{91} +9.11252 q^{92} +(-0.136599 - 0.236596i) q^{93} +(1.53614 + 2.66068i) q^{94} -1.85206 q^{96} +(-7.40687 + 12.8291i) q^{97} +(0.665761 - 1.15313i) q^{98} +0.427336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.134432 0.232843i −0.0950578 0.164645i 0.814575 0.580058i \(-0.196970\pi\)
−0.909633 + 0.415413i \(0.863637\pi\)
\(3\) 0.301414 + 0.522064i 0.174021 + 0.301414i 0.939822 0.341664i \(-0.110990\pi\)
−0.765801 + 0.643078i \(0.777657\pi\)
\(4\) 0.963856 1.66945i 0.481928 0.834724i
\(5\) 0 0
\(6\) 0.0810394 0.140364i 0.0330842 0.0573035i
\(7\) 0.715471 1.23923i 0.270423 0.468386i −0.698547 0.715564i \(-0.746170\pi\)
0.968970 + 0.247178i \(0.0795032\pi\)
\(8\) −1.05602 −0.373360
\(9\) 1.31830 2.28336i 0.439433 0.761120i
\(10\) 0 0
\(11\) 0.0810394 + 0.140364i 0.0244343 + 0.0423214i 0.877984 0.478690i \(-0.158888\pi\)
−0.853550 + 0.521011i \(0.825555\pi\)
\(12\) 1.16208 0.335463
\(13\) −2.41659 + 2.67584i −0.670241 + 0.742144i
\(14\) −0.384729 −0.102823
\(15\) 0 0
\(16\) −1.78575 3.09301i −0.446437 0.773252i
\(17\) 1.41046 2.44299i 0.342088 0.592513i −0.642733 0.766091i \(-0.722199\pi\)
0.984820 + 0.173577i \(0.0555327\pi\)
\(18\) −0.708886 −0.167086
\(19\) 1.96386 3.40150i 0.450539 0.780357i −0.547880 0.836557i \(-0.684565\pi\)
0.998420 + 0.0561996i \(0.0178983\pi\)
\(20\) 0 0
\(21\) 0.862612 0.188237
\(22\) 0.0217886 0.0377389i 0.00464534 0.00804596i
\(23\) 2.36356 + 4.09380i 0.492836 + 0.853617i 0.999966 0.00825269i \(-0.00262694\pi\)
−0.507130 + 0.861870i \(0.669294\pi\)
\(24\) −0.318299 0.551310i −0.0649726 0.112536i
\(25\) 0 0
\(26\) 0.947917 + 0.202967i 0.185902 + 0.0398052i
\(27\) 3.39790 0.653926
\(28\) −1.37922 2.38888i −0.260649 0.451457i
\(29\) 1.99641 + 3.45788i 0.370723 + 0.642112i 0.989677 0.143316i \(-0.0457765\pi\)
−0.618954 + 0.785427i \(0.712443\pi\)
\(30\) 0 0
\(31\) −0.453192 −0.0813958 −0.0406979 0.999171i \(-0.512958\pi\)
−0.0406979 + 0.999171i \(0.512958\pi\)
\(32\) −1.53614 + 2.66068i −0.271554 + 0.470346i
\(33\) −0.0488528 + 0.0846155i −0.00850418 + 0.0147297i
\(34\) −0.758446 −0.130072
\(35\) 0 0
\(36\) −2.54130 4.40166i −0.423550 0.733611i
\(37\) −2.52179 4.36787i −0.414579 0.718073i 0.580805 0.814043i \(-0.302738\pi\)
−0.995384 + 0.0959702i \(0.969405\pi\)
\(38\) −1.05602 −0.171309
\(39\) −2.12535 0.455079i −0.340329 0.0728710i
\(40\) 0 0
\(41\) 4.29450 + 7.43829i 0.670688 + 1.16167i 0.977709 + 0.209964i \(0.0673345\pi\)
−0.307021 + 0.951703i \(0.599332\pi\)
\(42\) −0.115963 0.200853i −0.0178934 0.0309923i
\(43\) 2.33101 4.03742i 0.355475 0.615701i −0.631724 0.775194i \(-0.717652\pi\)
0.987199 + 0.159492i \(0.0509856\pi\)
\(44\) 0.312441 0.0471023
\(45\) 0 0
\(46\) 0.635476 1.10068i 0.0936958 0.162286i
\(47\) −11.4269 −1.66679 −0.833394 0.552679i \(-0.813605\pi\)
−0.833394 + 0.552679i \(0.813605\pi\)
\(48\) 1.07650 1.86455i 0.155379 0.269125i
\(49\) 2.47620 + 4.28891i 0.353743 + 0.612701i
\(50\) 0 0
\(51\) 1.70053 0.238122
\(52\) 2.13793 + 6.61349i 0.296477 + 0.917126i
\(53\) 7.30525 1.00345 0.501727 0.865026i \(-0.332698\pi\)
0.501727 + 0.865026i \(0.332698\pi\)
\(54\) −0.456786 0.791177i −0.0621607 0.107666i
\(55\) 0 0
\(56\) −0.755552 + 1.30865i −0.100965 + 0.174876i
\(57\) 2.36773 0.313614
\(58\) 0.536762 0.929698i 0.0704803 0.122075i
\(59\) −4.98327 + 8.63128i −0.648767 + 1.12370i 0.334651 + 0.942342i \(0.391382\pi\)
−0.983418 + 0.181355i \(0.941952\pi\)
\(60\) 0 0
\(61\) −0.726596 + 1.25850i −0.0930311 + 0.161135i −0.908785 0.417264i \(-0.862989\pi\)
0.815754 + 0.578399i \(0.196322\pi\)
\(62\) 0.0609235 + 0.105523i 0.00773730 + 0.0134014i
\(63\) −1.88641 3.26736i −0.237665 0.411649i
\(64\) −6.31697 −0.789621
\(65\) 0 0
\(66\) 0.0262695 0.00323355
\(67\) 3.17765 + 5.50384i 0.388211 + 0.672402i 0.992209 0.124584i \(-0.0397598\pi\)
−0.603998 + 0.796986i \(0.706426\pi\)
\(68\) −2.71897 4.70939i −0.329723 0.571097i
\(69\) −1.42482 + 2.46786i −0.171528 + 0.297095i
\(70\) 0 0
\(71\) −7.02110 + 12.1609i −0.833251 + 1.44323i 0.0621957 + 0.998064i \(0.480190\pi\)
−0.895447 + 0.445169i \(0.853144\pi\)
\(72\) −1.39215 + 2.41128i −0.164067 + 0.284172i
\(73\) −7.75845 −0.908057 −0.454029 0.890987i \(-0.650014\pi\)
−0.454029 + 0.890987i \(0.650014\pi\)
\(74\) −0.678018 + 1.17436i −0.0788180 + 0.136517i
\(75\) 0 0
\(76\) −3.78575 6.55711i −0.434255 0.752152i
\(77\) 0.231925 0.0264303
\(78\) 0.179753 + 0.556051i 0.0203531 + 0.0629603i
\(79\) −11.2447 −1.26513 −0.632563 0.774509i \(-0.717997\pi\)
−0.632563 + 0.774509i \(0.717997\pi\)
\(80\) 0 0
\(81\) −2.93072 5.07616i −0.325636 0.564018i
\(82\) 1.15464 1.99989i 0.127508 0.220851i
\(83\) 9.45997 1.03837 0.519183 0.854663i \(-0.326236\pi\)
0.519183 + 0.854663i \(0.326236\pi\)
\(84\) 0.831434 1.44009i 0.0907169 0.157126i
\(85\) 0 0
\(86\) −1.25345 −0.135163
\(87\) −1.20349 + 2.08450i −0.129028 + 0.223482i
\(88\) −0.0855792 0.148228i −0.00912277 0.0158011i
\(89\) 4.33064 + 7.50090i 0.459047 + 0.795093i 0.998911 0.0466592i \(-0.0148575\pi\)
−0.539863 + 0.841753i \(0.681524\pi\)
\(90\) 0 0
\(91\) 1.58699 + 4.90920i 0.166361 + 0.514624i
\(92\) 9.11252 0.950046
\(93\) −0.136599 0.236596i −0.0141646 0.0245338i
\(94\) 1.53614 + 2.66068i 0.158441 + 0.274428i
\(95\) 0 0
\(96\) −1.85206 −0.189025
\(97\) −7.40687 + 12.8291i −0.752054 + 1.30260i 0.194772 + 0.980849i \(0.437603\pi\)
−0.946826 + 0.321747i \(0.895730\pi\)
\(98\) 0.665761 1.15313i 0.0672521 0.116484i
\(99\) 0.427336 0.0429489
\(100\) 0 0
\(101\) 3.06790 + 5.31377i 0.305268 + 0.528740i 0.977321 0.211763i \(-0.0679206\pi\)
−0.672053 + 0.740503i \(0.734587\pi\)
\(102\) −0.228606 0.395957i −0.0226354 0.0392056i
\(103\) 5.63543 0.555276 0.277638 0.960686i \(-0.410448\pi\)
0.277638 + 0.960686i \(0.410448\pi\)
\(104\) 2.55197 2.82574i 0.250241 0.277086i
\(105\) 0 0
\(106\) −0.982060 1.70098i −0.0953861 0.165214i
\(107\) −8.25677 14.3012i −0.798212 1.38254i −0.920779 0.390084i \(-0.872446\pi\)
0.122567 0.992460i \(-0.460887\pi\)
\(108\) 3.27509 5.67261i 0.315145 0.545848i
\(109\) 6.24468 0.598132 0.299066 0.954232i \(-0.403325\pi\)
0.299066 + 0.954232i \(0.403325\pi\)
\(110\) 0 0
\(111\) 1.52020 2.63307i 0.144291 0.249920i
\(112\) −5.11061 −0.482907
\(113\) −6.95036 + 12.0384i −0.653835 + 1.13247i 0.328350 + 0.944556i \(0.393507\pi\)
−0.982185 + 0.187919i \(0.939826\pi\)
\(114\) −0.318299 0.551310i −0.0298115 0.0516350i
\(115\) 0 0
\(116\) 7.69699 0.714648
\(117\) 2.92412 + 9.04550i 0.270335 + 0.836256i
\(118\) 2.67964 0.246681
\(119\) −2.01829 3.49578i −0.185017 0.320458i
\(120\) 0 0
\(121\) 5.48687 9.50353i 0.498806 0.863957i
\(122\) 0.390711 0.0353733
\(123\) −2.58884 + 4.48401i −0.233428 + 0.404310i
\(124\) −0.436812 + 0.756581i −0.0392269 + 0.0679430i
\(125\) 0 0
\(126\) −0.507188 + 0.878475i −0.0451839 + 0.0782608i
\(127\) −2.85158 4.93907i −0.253036 0.438272i 0.711324 0.702864i \(-0.248096\pi\)
−0.964360 + 0.264592i \(0.914763\pi\)
\(128\) 3.92149 + 6.79222i 0.346614 + 0.600353i
\(129\) 2.81039 0.247441
\(130\) 0 0
\(131\) 10.7915 0.942857 0.471428 0.881904i \(-0.343739\pi\)
0.471428 + 0.881904i \(0.343739\pi\)
\(132\) 0.0941741 + 0.163114i 0.00819680 + 0.0141973i
\(133\) −2.81017 4.86735i −0.243672 0.422053i
\(134\) 0.854354 1.47979i 0.0738050 0.127834i
\(135\) 0 0
\(136\) −1.48948 + 2.57985i −0.127722 + 0.221220i
\(137\) 11.0943 19.2158i 0.947847 1.64172i 0.197900 0.980222i \(-0.436588\pi\)
0.749947 0.661497i \(-0.230079\pi\)
\(138\) 0.766165 0.0652203
\(139\) 4.29809 7.44452i 0.364560 0.631436i −0.624146 0.781308i \(-0.714553\pi\)
0.988705 + 0.149872i \(0.0478862\pi\)
\(140\) 0 0
\(141\) −3.44423 5.96559i −0.290057 0.502393i
\(142\) 3.77544 0.316828
\(143\) −0.571431 0.122354i −0.0477854 0.0102318i
\(144\) −9.41661 −0.784717
\(145\) 0 0
\(146\) 1.04298 + 1.80650i 0.0863179 + 0.149507i
\(147\) −1.49272 + 2.58547i −0.123118 + 0.213246i
\(148\) −9.72256 −0.799190
\(149\) 9.14309 15.8363i 0.749031 1.29736i −0.199257 0.979947i \(-0.563853\pi\)
0.948288 0.317412i \(-0.102814\pi\)
\(150\) 0 0
\(151\) −13.0967 −1.06580 −0.532899 0.846179i \(-0.678897\pi\)
−0.532899 + 0.846179i \(0.678897\pi\)
\(152\) −2.07387 + 3.59205i −0.168213 + 0.291354i
\(153\) −3.71883 6.44120i −0.300649 0.520740i
\(154\) −0.0311782 0.0540022i −0.00251241 0.00435162i
\(155\) 0 0
\(156\) −2.80826 + 3.10953i −0.224841 + 0.248962i
\(157\) 23.1007 1.84363 0.921817 0.387627i \(-0.126705\pi\)
0.921817 + 0.387627i \(0.126705\pi\)
\(158\) 1.51164 + 2.61825i 0.120260 + 0.208296i
\(159\) 2.20191 + 3.81381i 0.174622 + 0.302455i
\(160\) 0 0
\(161\) 6.76423 0.533096
\(162\) −0.787966 + 1.36480i −0.0619085 + 0.107229i
\(163\) −0.655857 + 1.13598i −0.0513707 + 0.0889767i −0.890567 0.454852i \(-0.849692\pi\)
0.839197 + 0.543828i \(0.183026\pi\)
\(164\) 16.5571 1.29289
\(165\) 0 0
\(166\) −1.27172 2.20269i −0.0987048 0.170962i
\(167\) −8.87911 15.3791i −0.687086 1.19007i −0.972776 0.231746i \(-0.925556\pi\)
0.285690 0.958322i \(-0.407777\pi\)
\(168\) −0.910936 −0.0702802
\(169\) −1.32021 12.9328i −0.101555 0.994830i
\(170\) 0 0
\(171\) −5.17790 8.96839i −0.395964 0.685830i
\(172\) −4.49351 7.78299i −0.342627 0.593448i
\(173\) −6.83327 + 11.8356i −0.519524 + 0.899842i 0.480218 + 0.877149i \(0.340557\pi\)
−0.999742 + 0.0226931i \(0.992776\pi\)
\(174\) 0.647150 0.0490603
\(175\) 0 0
\(176\) 0.289432 0.501311i 0.0218168 0.0377877i
\(177\) −6.00811 −0.451597
\(178\) 1.16435 2.01672i 0.0872720 0.151160i
\(179\) −4.06599 7.04251i −0.303907 0.526382i 0.673111 0.739542i \(-0.264958\pi\)
−0.977017 + 0.213160i \(0.931624\pi\)
\(180\) 0 0
\(181\) 4.39262 0.326501 0.163250 0.986585i \(-0.447802\pi\)
0.163250 + 0.986585i \(0.447802\pi\)
\(182\) 0.929731 1.02947i 0.0689163 0.0763095i
\(183\) −0.876025 −0.0647576
\(184\) −2.49597 4.32314i −0.184005 0.318706i
\(185\) 0 0
\(186\) −0.0367264 + 0.0636120i −0.00269291 + 0.00466426i
\(187\) 0.457212 0.0334347
\(188\) −11.0139 + 19.0767i −0.803272 + 1.39131i
\(189\) 2.43110 4.21079i 0.176836 0.306290i
\(190\) 0 0
\(191\) −1.00707 + 1.74430i −0.0728690 + 0.126213i −0.900158 0.435564i \(-0.856549\pi\)
0.827289 + 0.561777i \(0.189882\pi\)
\(192\) −1.90402 3.29786i −0.137411 0.238003i
\(193\) −9.55328 16.5468i −0.687660 1.19106i −0.972593 0.232515i \(-0.925304\pi\)
0.284932 0.958548i \(-0.408029\pi\)
\(194\) 3.98288 0.285954
\(195\) 0 0
\(196\) 9.54681 0.681915
\(197\) 7.96965 + 13.8038i 0.567814 + 0.983483i 0.996782 + 0.0801631i \(0.0255441\pi\)
−0.428968 + 0.903320i \(0.641123\pi\)
\(198\) −0.0574477 0.0995023i −0.00408263 0.00707132i
\(199\) −5.84073 + 10.1164i −0.414038 + 0.717135i −0.995327 0.0965623i \(-0.969215\pi\)
0.581289 + 0.813697i \(0.302549\pi\)
\(200\) 0 0
\(201\) −1.91557 + 3.31787i −0.135114 + 0.234025i
\(202\) 0.824849 1.42868i 0.0580362 0.100522i
\(203\) 5.71349 0.401008
\(204\) 1.63907 2.83895i 0.114758 0.198766i
\(205\) 0 0
\(206\) −0.757583 1.31217i −0.0527833 0.0914233i
\(207\) 12.4635 0.866274
\(208\) 12.5918 + 2.69615i 0.873085 + 0.186944i
\(209\) 0.636599 0.0440344
\(210\) 0 0
\(211\) −10.6092 18.3757i −0.730368 1.26503i −0.956726 0.290990i \(-0.906015\pi\)
0.226358 0.974044i \(-0.427318\pi\)
\(212\) 7.04121 12.1957i 0.483592 0.837607i
\(213\) −8.46503 −0.580014
\(214\) −2.21995 + 3.84506i −0.151753 + 0.262843i
\(215\) 0 0
\(216\) −3.58825 −0.244150
\(217\) −0.324246 + 0.561611i −0.0220113 + 0.0381246i
\(218\) −0.839485 1.45403i −0.0568571 0.0984794i
\(219\) −2.33850 4.05041i −0.158021 0.273701i
\(220\) 0 0
\(221\) 3.12855 + 9.67788i 0.210449 + 0.651005i
\(222\) −0.817456 −0.0548641
\(223\) 9.67826 + 16.7632i 0.648104 + 1.12255i 0.983575 + 0.180499i \(0.0577713\pi\)
−0.335471 + 0.942051i \(0.608895\pi\)
\(224\) 2.19813 + 3.80728i 0.146869 + 0.254385i
\(225\) 0 0
\(226\) 3.73740 0.248608
\(227\) −12.2306 + 21.1840i −0.811773 + 1.40603i 0.0998492 + 0.995003i \(0.468164\pi\)
−0.911622 + 0.411029i \(0.865169\pi\)
\(228\) 2.28216 3.95281i 0.151139 0.261781i
\(229\) 18.1921 1.20217 0.601085 0.799185i \(-0.294735\pi\)
0.601085 + 0.799185i \(0.294735\pi\)
\(230\) 0 0
\(231\) 0.0699055 + 0.121080i 0.00459945 + 0.00796647i
\(232\) −2.10825 3.65159i −0.138413 0.239738i
\(233\) 11.1406 0.729842 0.364921 0.931038i \(-0.381096\pi\)
0.364921 + 0.931038i \(0.381096\pi\)
\(234\) 1.71309 1.89686i 0.111988 0.124002i
\(235\) 0 0
\(236\) 9.60631 + 16.6386i 0.625318 + 1.08308i
\(237\) −3.38930 5.87045i −0.220159 0.381326i
\(238\) −0.542646 + 0.939891i −0.0351745 + 0.0609241i
\(239\) −20.5517 −1.32938 −0.664690 0.747119i \(-0.731436\pi\)
−0.664690 + 0.747119i \(0.731436\pi\)
\(240\) 0 0
\(241\) 1.07397 1.86017i 0.0691805 0.119824i −0.829360 0.558714i \(-0.811295\pi\)
0.898541 + 0.438890i \(0.144628\pi\)
\(242\) −2.95044 −0.189662
\(243\) 6.86357 11.8881i 0.440298 0.762619i
\(244\) 1.40067 + 2.42603i 0.0896686 + 0.155311i
\(245\) 0 0
\(246\) 1.39209 0.0887567
\(247\) 4.35603 + 13.4750i 0.277167 + 0.857392i
\(248\) 0.478580 0.0303899
\(249\) 2.85137 + 4.93871i 0.180698 + 0.312978i
\(250\) 0 0
\(251\) 8.42052 14.5848i 0.531499 0.920583i −0.467825 0.883821i \(-0.654962\pi\)
0.999324 0.0367619i \(-0.0117043\pi\)
\(252\) −7.27291 −0.458150
\(253\) −0.383082 + 0.663518i −0.0240842 + 0.0417150i
\(254\) −0.766686 + 1.32794i −0.0481062 + 0.0833223i
\(255\) 0 0
\(256\) −5.26262 + 9.11513i −0.328914 + 0.569696i
\(257\) 0.195356 + 0.338366i 0.0121859 + 0.0211067i 0.872054 0.489410i \(-0.162788\pi\)
−0.859868 + 0.510516i \(0.829454\pi\)
\(258\) −0.377807 0.654381i −0.0235212 0.0407400i
\(259\) −7.21707 −0.448447
\(260\) 0 0
\(261\) 10.5274 0.651632
\(262\) −1.45072 2.51272i −0.0896259 0.155237i
\(263\) −1.96886 3.41016i −0.121405 0.210280i 0.798917 0.601441i \(-0.205407\pi\)
−0.920322 + 0.391162i \(0.872073\pi\)
\(264\) 0.0515895 0.0893557i 0.00317512 0.00549946i
\(265\) 0 0
\(266\) −0.755552 + 1.30865i −0.0463259 + 0.0802388i
\(267\) −2.61063 + 4.52175i −0.159768 + 0.276727i
\(268\) 12.2512 0.748359
\(269\) −7.66555 + 13.2771i −0.467377 + 0.809521i −0.999305 0.0372686i \(-0.988134\pi\)
0.531928 + 0.846789i \(0.321468\pi\)
\(270\) 0 0
\(271\) 3.06333 + 5.30584i 0.186084 + 0.322307i 0.943941 0.330113i \(-0.107087\pi\)
−0.757857 + 0.652420i \(0.773754\pi\)
\(272\) −10.0749 −0.610883
\(273\) −2.08458 + 2.30821i −0.126164 + 0.139699i
\(274\) −5.96570 −0.360401
\(275\) 0 0
\(276\) 2.74664 + 4.75732i 0.165328 + 0.286357i
\(277\) −2.27139 + 3.93417i −0.136475 + 0.236381i −0.926160 0.377131i \(-0.876911\pi\)
0.789685 + 0.613512i \(0.210244\pi\)
\(278\) −2.31121 −0.138617
\(279\) −0.597443 + 1.03480i −0.0357680 + 0.0619520i
\(280\) 0 0
\(281\) −18.6453 −1.11229 −0.556144 0.831086i \(-0.687720\pi\)
−0.556144 + 0.831086i \(0.687720\pi\)
\(282\) −0.926030 + 1.60393i −0.0551443 + 0.0955127i
\(283\) −9.65211 16.7179i −0.573759 0.993779i −0.996175 0.0873772i \(-0.972151\pi\)
0.422417 0.906402i \(-0.361182\pi\)
\(284\) 13.5347 + 23.4427i 0.803134 + 1.39107i
\(285\) 0 0
\(286\) 0.0483292 + 0.149502i 0.00285776 + 0.00884024i
\(287\) 12.2904 0.725478
\(288\) 4.05019 + 7.01514i 0.238660 + 0.413371i
\(289\) 4.52119 + 7.83092i 0.265952 + 0.460643i
\(290\) 0 0
\(291\) −8.93014 −0.523494
\(292\) −7.47802 + 12.9523i −0.437618 + 0.757977i
\(293\) 11.9331 20.6688i 0.697142 1.20748i −0.272312 0.962209i \(-0.587788\pi\)
0.969453 0.245276i \(-0.0788785\pi\)
\(294\) 0.802679 0.0468132
\(295\) 0 0
\(296\) 2.66306 + 4.61255i 0.154787 + 0.268099i
\(297\) 0.275364 + 0.476944i 0.0159782 + 0.0276751i
\(298\) −4.91649 −0.284805
\(299\) −16.6661 3.56853i −0.963825 0.206374i
\(300\) 0 0
\(301\) −3.33554 5.77732i −0.192257 0.332999i
\(302\) 1.76062 + 3.04949i 0.101312 + 0.175478i
\(303\) −1.84942 + 3.20329i −0.106246 + 0.184024i
\(304\) −14.0278 −0.804551
\(305\) 0 0
\(306\) −0.999858 + 1.73181i −0.0571581 + 0.0990007i
\(307\) −10.7241 −0.612059 −0.306030 0.952022i \(-0.599001\pi\)
−0.306030 + 0.952022i \(0.599001\pi\)
\(308\) 0.223543 0.387187i 0.0127375 0.0220620i
\(309\) 1.69860 + 2.94206i 0.0966299 + 0.167368i
\(310\) 0 0
\(311\) −26.9755 −1.52964 −0.764821 0.644243i \(-0.777172\pi\)
−0.764821 + 0.644243i \(0.777172\pi\)
\(312\) 2.24442 + 0.480573i 0.127065 + 0.0272071i
\(313\) −1.08863 −0.0615328 −0.0307664 0.999527i \(-0.509795\pi\)
−0.0307664 + 0.999527i \(0.509795\pi\)
\(314\) −3.10547 5.37883i −0.175252 0.303545i
\(315\) 0 0
\(316\) −10.8383 + 18.7724i −0.609699 + 1.05603i
\(317\) −3.45818 −0.194231 −0.0971154 0.995273i \(-0.530962\pi\)
−0.0971154 + 0.995273i \(0.530962\pi\)
\(318\) 0.592013 1.02540i 0.0331984 0.0575014i
\(319\) −0.323575 + 0.560448i −0.0181167 + 0.0313791i
\(320\) 0 0
\(321\) 4.97741 8.62113i 0.277812 0.481185i
\(322\) −0.909329 1.57500i −0.0506749 0.0877716i
\(323\) −5.53989 9.59538i −0.308248 0.533901i
\(324\) −11.2992 −0.627732
\(325\) 0 0
\(326\) 0.352673 0.0195327
\(327\) 1.88223 + 3.26013i 0.104088 + 0.180285i
\(328\) −4.53508 7.85499i −0.250408 0.433719i
\(329\) −8.17564 + 14.1606i −0.450737 + 0.780700i
\(330\) 0 0
\(331\) −0.303060 + 0.524916i −0.0166577 + 0.0288520i −0.874234 0.485505i \(-0.838636\pi\)
0.857576 + 0.514357i \(0.171969\pi\)
\(332\) 9.11805 15.7929i 0.500418 0.866749i
\(333\) −13.2979 −0.728720
\(334\) −2.38727 + 4.13488i −0.130626 + 0.226251i
\(335\) 0 0
\(336\) −1.54041 2.66807i −0.0840362 0.145555i
\(337\) 23.0099 1.25343 0.626715 0.779249i \(-0.284399\pi\)
0.626715 + 0.779249i \(0.284399\pi\)
\(338\) −2.83383 + 2.04598i −0.154140 + 0.111287i
\(339\) −8.37974 −0.455125
\(340\) 0 0
\(341\) −0.0367264 0.0636120i −0.00198885 0.00344478i
\(342\) −1.39215 + 2.41128i −0.0752789 + 0.130387i
\(343\) 17.1032 0.923486
\(344\) −2.46159 + 4.26360i −0.132720 + 0.229878i
\(345\) 0 0
\(346\) 3.67444 0.197539
\(347\) −15.1085 + 26.1687i −0.811068 + 1.40481i 0.101050 + 0.994881i \(0.467780\pi\)
−0.912117 + 0.409929i \(0.865554\pi\)
\(348\) 2.31998 + 4.01832i 0.124364 + 0.215405i
\(349\) −1.71944 2.97815i −0.0920394 0.159417i 0.816330 0.577586i \(-0.196005\pi\)
−0.908369 + 0.418169i \(0.862672\pi\)
\(350\) 0 0
\(351\) −8.21132 + 9.09222i −0.438288 + 0.485307i
\(352\) −0.497952 −0.0265410
\(353\) −5.85761 10.1457i −0.311769 0.540000i 0.666976 0.745079i \(-0.267588\pi\)
−0.978745 + 0.205079i \(0.934255\pi\)
\(354\) 0.807682 + 1.39895i 0.0429278 + 0.0743532i
\(355\) 0 0
\(356\) 16.6965 0.884911
\(357\) 1.21668 2.10736i 0.0643937 0.111533i
\(358\) −1.09320 + 1.89348i −0.0577774 + 0.100073i
\(359\) −7.27898 −0.384170 −0.192085 0.981378i \(-0.561525\pi\)
−0.192085 + 0.981378i \(0.561525\pi\)
\(360\) 0 0
\(361\) 1.78654 + 3.09438i 0.0940283 + 0.162862i
\(362\) −0.590509 1.02279i −0.0310365 0.0537567i
\(363\) 6.61527 0.347212
\(364\) 9.72528 + 2.08237i 0.509743 + 0.109146i
\(365\) 0 0
\(366\) 0.117766 + 0.203976i 0.00615572 + 0.0106620i
\(367\) −6.29346 10.9006i −0.328516 0.569006i 0.653702 0.756752i \(-0.273215\pi\)
−0.982218 + 0.187746i \(0.939882\pi\)
\(368\) 8.44144 14.6210i 0.440041 0.762173i
\(369\) 22.6457 1.17889
\(370\) 0 0
\(371\) 5.22670 9.05291i 0.271357 0.470004i
\(372\) −0.526645 −0.0273053
\(373\) −2.18009 + 3.77602i −0.112881 + 0.195515i −0.916931 0.399047i \(-0.869341\pi\)
0.804050 + 0.594562i \(0.202674\pi\)
\(374\) −0.0614639 0.106459i −0.00317822 0.00550485i
\(375\) 0 0
\(376\) 12.0671 0.622311
\(377\) −14.0772 3.01420i −0.725013 0.155239i
\(378\) −1.30727 −0.0672387
\(379\) 2.90067 + 5.02410i 0.148997 + 0.258071i 0.930857 0.365383i \(-0.119062\pi\)
−0.781860 + 0.623454i \(0.785729\pi\)
\(380\) 0 0
\(381\) 1.71901 2.97741i 0.0880675 0.152537i
\(382\) 0.541530 0.0277071
\(383\) 7.61084 13.1824i 0.388896 0.673588i −0.603405 0.797435i \(-0.706190\pi\)
0.992301 + 0.123847i \(0.0395232\pi\)
\(384\) −2.36398 + 4.09454i −0.120637 + 0.208949i
\(385\) 0 0
\(386\) −2.56853 + 4.44883i −0.130735 + 0.226440i
\(387\) −6.14593 10.6451i −0.312415 0.541119i
\(388\) 14.2783 + 24.7308i 0.724871 + 1.25551i
\(389\) 6.51012 0.330076 0.165038 0.986287i \(-0.447225\pi\)
0.165038 + 0.986287i \(0.447225\pi\)
\(390\) 0 0
\(391\) 13.3348 0.674372
\(392\) −2.61492 4.52917i −0.132073 0.228758i
\(393\) 3.25271 + 5.63385i 0.164077 + 0.284190i
\(394\) 2.14275 3.71136i 0.107950 0.186975i
\(395\) 0 0
\(396\) 0.411891 0.713416i 0.0206983 0.0358505i
\(397\) −6.25576 + 10.8353i −0.313968 + 0.543808i −0.979218 0.202813i \(-0.934992\pi\)
0.665250 + 0.746621i \(0.268325\pi\)
\(398\) 3.14072 0.157430
\(399\) 1.69405 2.93417i 0.0848084 0.146892i
\(400\) 0 0
\(401\) −3.02478 5.23907i −0.151050 0.261627i 0.780564 0.625076i \(-0.214932\pi\)
−0.931614 + 0.363450i \(0.881599\pi\)
\(402\) 1.03006 0.0513746
\(403\) 1.09518 1.21267i 0.0545547 0.0604073i
\(404\) 11.8281 0.588469
\(405\) 0 0
\(406\) −0.768075 1.33035i −0.0381189 0.0660239i
\(407\) 0.408728 0.707938i 0.0202599 0.0350912i
\(408\) −1.79580 −0.0889052
\(409\) 13.6067 23.5676i 0.672810 1.16534i −0.304294 0.952578i \(-0.598421\pi\)
0.977104 0.212763i \(-0.0682461\pi\)
\(410\) 0 0
\(411\) 13.3759 0.659783
\(412\) 5.43175 9.40806i 0.267603 0.463502i
\(413\) 7.13078 + 12.3509i 0.350883 + 0.607746i
\(414\) −1.67549 2.90204i −0.0823460 0.142628i
\(415\) 0 0
\(416\) −3.40732 10.5402i −0.167058 0.516778i
\(417\) 5.18202 0.253765
\(418\) −0.0855792 0.148228i −0.00418582 0.00725005i
\(419\) −1.18807 2.05780i −0.0580410 0.100530i 0.835545 0.549422i \(-0.185152\pi\)
−0.893586 + 0.448892i \(0.851819\pi\)
\(420\) 0 0
\(421\) −26.9425 −1.31310 −0.656548 0.754284i \(-0.727984\pi\)
−0.656548 + 0.754284i \(0.727984\pi\)
\(422\) −2.85243 + 4.94056i −0.138854 + 0.240503i
\(423\) −15.0641 + 26.0918i −0.732442 + 1.26863i
\(424\) −7.71450 −0.374649
\(425\) 0 0
\(426\) 1.13797 + 1.97102i 0.0551348 + 0.0954963i
\(427\) 1.03972 + 1.80084i 0.0503155 + 0.0871489i
\(428\) −31.8334 −1.53872
\(429\) −0.108360 0.335203i −0.00523169 0.0161837i
\(430\) 0 0
\(431\) −1.19512 2.07001i −0.0575670 0.0997090i 0.835806 0.549025i \(-0.185001\pi\)
−0.893373 + 0.449316i \(0.851668\pi\)
\(432\) −6.06780 10.5097i −0.291937 0.505650i
\(433\) −2.74609 + 4.75636i −0.131968 + 0.228576i −0.924435 0.381339i \(-0.875463\pi\)
0.792467 + 0.609915i \(0.208796\pi\)
\(434\) 0.174356 0.00836937
\(435\) 0 0
\(436\) 6.01897 10.4252i 0.288257 0.499275i
\(437\) 18.5668 0.888168
\(438\) −0.628739 + 1.08901i −0.0300423 + 0.0520348i
\(439\) 1.38322 + 2.39580i 0.0660173 + 0.114345i 0.897145 0.441737i \(-0.145637\pi\)
−0.831128 + 0.556082i \(0.812304\pi\)
\(440\) 0 0
\(441\) 13.0575 0.621786
\(442\) 1.83285 2.02948i 0.0871798 0.0965324i
\(443\) 21.7259 1.03223 0.516115 0.856519i \(-0.327378\pi\)
0.516115 + 0.856519i \(0.327378\pi\)
\(444\) −2.93052 5.07580i −0.139076 0.240887i
\(445\) 0 0
\(446\) 2.60214 4.50703i 0.123215 0.213414i
\(447\) 11.0234 0.521390
\(448\) −4.51961 + 7.82820i −0.213532 + 0.369847i
\(449\) 2.16868 3.75627i 0.102347 0.177269i −0.810304 0.586009i \(-0.800698\pi\)
0.912651 + 0.408740i \(0.134032\pi\)
\(450\) 0 0
\(451\) −0.696047 + 1.20559i −0.0327756 + 0.0567690i
\(452\) 13.3983 + 23.2065i 0.630203 + 1.09154i
\(453\) −3.94754 6.83734i −0.185472 0.321246i
\(454\) 6.57673 0.308661
\(455\) 0 0
\(456\) −2.50038 −0.117091
\(457\) −6.46078 11.1904i −0.302223 0.523465i 0.674416 0.738351i \(-0.264395\pi\)
−0.976639 + 0.214886i \(0.931062\pi\)
\(458\) −2.44561 4.23591i −0.114276 0.197931i
\(459\) 4.79261 8.30105i 0.223700 0.387460i
\(460\) 0 0
\(461\) −1.73028 + 2.99693i −0.0805871 + 0.139581i −0.903502 0.428583i \(-0.859013\pi\)
0.822915 + 0.568164i \(0.192346\pi\)
\(462\) 0.0187951 0.0325540i 0.000874426 0.00151455i
\(463\) −40.1003 −1.86362 −0.931810 0.362947i \(-0.881771\pi\)
−0.931810 + 0.362947i \(0.881771\pi\)
\(464\) 7.13016 12.3498i 0.331009 0.573325i
\(465\) 0 0
\(466\) −1.49765 2.59400i −0.0693772 0.120165i
\(467\) −14.6666 −0.678690 −0.339345 0.940662i \(-0.610205\pi\)
−0.339345 + 0.940662i \(0.610205\pi\)
\(468\) 17.9194 + 3.83689i 0.828325 + 0.177360i
\(469\) 9.09406 0.419925
\(470\) 0 0
\(471\) 6.96286 + 12.0600i 0.320832 + 0.555697i
\(472\) 5.26244 9.11481i 0.242223 0.419543i
\(473\) 0.755614 0.0347431
\(474\) −0.911262 + 1.57835i −0.0418556 + 0.0724961i
\(475\) 0 0
\(476\) −7.78137 −0.356659
\(477\) 9.63051 16.6805i 0.440951 0.763749i
\(478\) 2.76281 + 4.78532i 0.126368 + 0.218876i
\(479\) −8.20396 14.2097i −0.374849 0.649257i 0.615456 0.788171i \(-0.288972\pi\)
−0.990304 + 0.138915i \(0.955639\pi\)
\(480\) 0 0
\(481\) 17.7818 + 3.80743i 0.810781 + 0.173604i
\(482\) −0.577503 −0.0263046
\(483\) 2.03883 + 3.53136i 0.0927702 + 0.160683i
\(484\) −10.5771 18.3201i −0.480777 0.832730i
\(485\) 0 0
\(486\) −3.69073 −0.167415
\(487\) 19.2692 33.3752i 0.873170 1.51238i 0.0144709 0.999895i \(-0.495394\pi\)
0.858699 0.512480i \(-0.171273\pi\)
\(488\) 0.767300 1.32900i 0.0347341 0.0601611i
\(489\) −0.790738 −0.0357584
\(490\) 0 0
\(491\) −14.4700 25.0629i −0.653024 1.13107i −0.982385 0.186867i \(-0.940167\pi\)
0.329361 0.944204i \(-0.393167\pi\)
\(492\) 4.99055 + 8.64388i 0.224991 + 0.389696i
\(493\) 11.2634 0.507279
\(494\) 2.55197 2.82574i 0.114818 0.127136i
\(495\) 0 0
\(496\) 0.809288 + 1.40173i 0.0363381 + 0.0629394i
\(497\) 10.0468 + 17.4015i 0.450660 + 0.780566i
\(498\) 0.766630 1.32784i 0.0343535 0.0595020i
\(499\) 29.7078 1.32990 0.664951 0.746887i \(-0.268452\pi\)
0.664951 + 0.746887i \(0.268452\pi\)
\(500\) 0 0
\(501\) 5.35258 9.27094i 0.239136 0.414195i
\(502\) −4.52795 −0.202092
\(503\) −10.8914 + 18.8644i −0.485623 + 0.841124i −0.999863 0.0165222i \(-0.994741\pi\)
0.514240 + 0.857646i \(0.328074\pi\)
\(504\) 1.99209 + 3.45040i 0.0887346 + 0.153693i
\(505\) 0 0
\(506\) 0.205994 0.00915756
\(507\) 6.35382 4.58736i 0.282183 0.203732i
\(508\) −10.9940 −0.487781
\(509\) −15.9771 27.6731i −0.708171 1.22659i −0.965535 0.260274i \(-0.916187\pi\)
0.257364 0.966315i \(-0.417146\pi\)
\(510\) 0 0
\(511\) −5.55095 + 9.61452i −0.245559 + 0.425321i
\(512\) 18.5158 0.818291
\(513\) 6.67298 11.5579i 0.294619 0.510296i
\(514\) 0.0525241 0.0909743i 0.00231674 0.00401271i
\(515\) 0 0
\(516\) 2.70881 4.69181i 0.119249 0.206545i
\(517\) −0.926030 1.60393i −0.0407268 0.0705408i
\(518\) 0.970205 + 1.68044i 0.0426284 + 0.0738345i
\(519\) −8.23857 −0.361633
\(520\) 0 0
\(521\) −36.0985 −1.58151 −0.790753 0.612136i \(-0.790311\pi\)
−0.790753 + 0.612136i \(0.790311\pi\)
\(522\) −1.41522 2.45124i −0.0619427 0.107288i
\(523\) 11.8702 + 20.5598i 0.519048 + 0.899018i 0.999755 + 0.0221363i \(0.00704678\pi\)
−0.480707 + 0.876881i \(0.659620\pi\)
\(524\) 10.4014 18.0158i 0.454389 0.787025i
\(525\) 0 0
\(526\) −0.529355 + 0.916869i −0.0230810 + 0.0399774i
\(527\) −0.639211 + 1.10715i −0.0278445 + 0.0482281i
\(528\) 0.348955 0.0151863
\(529\) 0.327186 0.566703i 0.0142255 0.0246393i
\(530\) 0 0
\(531\) 13.1389 + 22.7572i 0.570179 + 0.987579i
\(532\) −10.8344 −0.469730
\(533\) −30.2817 6.48390i −1.31165 0.280849i
\(534\) 1.40381 0.0607488
\(535\) 0 0
\(536\) −3.35566 5.81217i −0.144942 0.251048i
\(537\) 2.45109 4.24542i 0.105773 0.183203i
\(538\) 4.12198 0.177711
\(539\) −0.401340 + 0.695140i −0.0172869 + 0.0299418i
\(540\) 0 0
\(541\) 30.4301 1.30829 0.654145 0.756369i \(-0.273029\pi\)
0.654145 + 0.756369i \(0.273029\pi\)
\(542\) 0.823619 1.42655i 0.0353775 0.0612756i
\(543\) 1.32400 + 2.29323i 0.0568182 + 0.0984119i
\(544\) 4.33335 + 7.50558i 0.185791 + 0.321799i
\(545\) 0 0
\(546\) 0.817685 + 0.175082i 0.0349937 + 0.00749282i
\(547\) −16.6979 −0.713950 −0.356975 0.934114i \(-0.616192\pi\)
−0.356975 + 0.934114i \(0.616192\pi\)
\(548\) −21.3866 37.0426i −0.913588 1.58238i
\(549\) 1.91574 + 3.31816i 0.0817619 + 0.141616i
\(550\) 0 0
\(551\) 15.6826 0.668102
\(552\) 1.50464 2.60611i 0.0640416 0.110923i
\(553\) −8.04525 + 13.9348i −0.342119 + 0.592567i
\(554\) 1.22139 0.0518920
\(555\) 0 0
\(556\) −8.28549 14.3509i −0.351383 0.608613i
\(557\) −4.21691 7.30390i −0.178676 0.309476i 0.762751 0.646692i \(-0.223848\pi\)
−0.941427 + 0.337216i \(0.890515\pi\)
\(558\) 0.321262 0.0136001
\(559\) 5.17041 + 15.9942i 0.218685 + 0.676482i
\(560\) 0 0
\(561\) 0.137810 + 0.238694i 0.00581835 + 0.0100777i
\(562\) 2.50653 + 4.34144i 0.105732 + 0.183132i
\(563\) −8.30116 + 14.3780i −0.349852 + 0.605962i −0.986223 0.165422i \(-0.947102\pi\)
0.636371 + 0.771383i \(0.280435\pi\)
\(564\) −13.2790 −0.559146
\(565\) 0 0
\(566\) −2.59511 + 4.49485i −0.109080 + 0.188933i
\(567\) −8.38739 −0.352237
\(568\) 7.41442 12.8422i 0.311102 0.538845i
\(569\) 0.296709 + 0.513914i 0.0124387 + 0.0215444i 0.872178 0.489189i \(-0.162707\pi\)
−0.859739 + 0.510734i \(0.829374\pi\)
\(570\) 0 0
\(571\) 2.03617 0.0852111 0.0426056 0.999092i \(-0.486434\pi\)
0.0426056 + 0.999092i \(0.486434\pi\)
\(572\) −0.755041 + 0.836042i −0.0315699 + 0.0349567i
\(573\) −1.21418 −0.0507231
\(574\) −1.65222 2.86173i −0.0689623 0.119446i
\(575\) 0 0
\(576\) −8.32766 + 14.4239i −0.346986 + 0.600997i
\(577\) −13.6818 −0.569583 −0.284791 0.958590i \(-0.591924\pi\)
−0.284791 + 0.958590i \(0.591924\pi\)
\(578\) 1.21558 2.10545i 0.0505616 0.0875753i
\(579\) 5.75899 9.97486i 0.239335 0.414541i
\(580\) 0 0
\(581\) 6.76833 11.7231i 0.280798 0.486356i
\(582\) 1.20050 + 2.07932i 0.0497622 + 0.0861906i
\(583\) 0.592013 + 1.02540i 0.0245187 + 0.0424676i
\(584\) 8.19308 0.339032
\(585\) 0 0
\(586\) −6.41679 −0.265075
\(587\) 4.49375 + 7.78340i 0.185477 + 0.321255i 0.943737 0.330697i \(-0.107284\pi\)
−0.758260 + 0.651952i \(0.773950\pi\)
\(588\) 2.87754 + 4.98405i 0.118668 + 0.205539i
\(589\) −0.890005 + 1.54153i −0.0366720 + 0.0635178i
\(590\) 0 0
\(591\) −4.80433 + 8.32134i −0.197624 + 0.342294i
\(592\) −9.00656 + 15.5998i −0.370168 + 0.641149i
\(593\) 8.67720 0.356330 0.178165 0.984001i \(-0.442984\pi\)
0.178165 + 0.984001i \(0.442984\pi\)
\(594\) 0.0740353 0.128233i 0.00303771 0.00526146i
\(595\) 0 0
\(596\) −17.6252 30.5278i −0.721958 1.25047i
\(597\) −7.04191 −0.288206
\(598\) 1.40955 + 4.36031i 0.0576407 + 0.178306i
\(599\) 18.8190 0.768924 0.384462 0.923141i \(-0.374387\pi\)
0.384462 + 0.923141i \(0.374387\pi\)
\(600\) 0 0
\(601\) 12.6673 + 21.9404i 0.516709 + 0.894967i 0.999812 + 0.0194029i \(0.00617651\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(602\) −0.896806 + 1.55331i −0.0365511 + 0.0633084i
\(603\) 16.7564 0.682371
\(604\) −12.6234 + 21.8643i −0.513638 + 0.889647i
\(605\) 0 0
\(606\) 0.994484 0.0403982
\(607\) 10.5111 18.2058i 0.426633 0.738950i −0.569939 0.821687i \(-0.693033\pi\)
0.996571 + 0.0827376i \(0.0263663\pi\)
\(608\) 6.03353 + 10.4504i 0.244692 + 0.423819i
\(609\) 1.72212 + 2.98281i 0.0697840 + 0.120869i
\(610\) 0 0
\(611\) 27.6142 30.5766i 1.11715 1.23700i
\(612\) −14.3377 −0.579565
\(613\) 3.53721 + 6.12662i 0.142866 + 0.247452i 0.928575 0.371145i \(-0.121035\pi\)
−0.785708 + 0.618597i \(0.787701\pi\)
\(614\) 1.44167 + 2.49704i 0.0581810 + 0.100772i
\(615\) 0 0
\(616\) −0.244918 −0.00986802
\(617\) 8.86509 15.3548i 0.356895 0.618160i −0.630545 0.776152i \(-0.717169\pi\)
0.987440 + 0.157992i \(0.0505021\pi\)
\(618\) 0.456692 0.791014i 0.0183708 0.0318192i
\(619\) −28.9519 −1.16368 −0.581838 0.813305i \(-0.697666\pi\)
−0.581838 + 0.813305i \(0.697666\pi\)
\(620\) 0 0
\(621\) 8.03113 + 13.9103i 0.322278 + 0.558202i
\(622\) 3.62637 + 6.28106i 0.145404 + 0.251848i
\(623\) 12.3938 0.496547
\(624\) 2.38778 + 7.38639i 0.0955878 + 0.295692i
\(625\) 0 0
\(626\) 0.146346 + 0.253479i 0.00584917 + 0.0101311i
\(627\) 0.191880 + 0.332345i 0.00766294 + 0.0132726i
\(628\) 22.2657 38.5653i 0.888498 1.53892i
\(629\) −14.2276 −0.567290
\(630\) 0 0
\(631\) −19.0058 + 32.9191i −0.756611 + 1.31049i 0.187959 + 0.982177i \(0.439813\pi\)
−0.944570 + 0.328311i \(0.893521\pi\)
\(632\) 11.8746 0.472347
\(633\) 6.39553 11.0774i 0.254199 0.440286i
\(634\) 0.464890 + 0.805214i 0.0184631 + 0.0319791i
\(635\) 0 0
\(636\) 8.48928 0.336622
\(637\) −17.4604 3.73861i −0.691805 0.148129i
\(638\) 0.173995 0.00688854
\(639\) 18.5118 + 32.0634i 0.732316 + 1.26841i
\(640\) 0 0
\(641\) −1.51046 + 2.61619i −0.0596595 + 0.103333i −0.894313 0.447443i \(-0.852335\pi\)
0.834653 + 0.550776i \(0.185668\pi\)
\(642\) −2.67649 −0.105633
\(643\) 13.4774 23.3436i 0.531499 0.920583i −0.467825 0.883821i \(-0.654962\pi\)
0.999324 0.0367618i \(-0.0117043\pi\)
\(644\) 6.51975 11.2925i 0.256914 0.444988i
\(645\) 0 0
\(646\) −1.48948 + 2.57985i −0.0586027 + 0.101503i
\(647\) 7.86878 + 13.6291i 0.309354 + 0.535817i 0.978221 0.207565i \(-0.0665539\pi\)
−0.668867 + 0.743382i \(0.733221\pi\)
\(648\) 3.09490 + 5.36053i 0.121579 + 0.210582i
\(649\) −1.61536 −0.0634086
\(650\) 0 0
\(651\) −0.390929 −0.0153217
\(652\) 1.26430 + 2.18984i 0.0495140 + 0.0857607i
\(653\) 7.15913 + 12.4000i 0.280158 + 0.485249i 0.971424 0.237353i \(-0.0762796\pi\)
−0.691265 + 0.722601i \(0.742946\pi\)
\(654\) 0.506065 0.876530i 0.0197887 0.0342750i
\(655\) 0 0
\(656\) 15.3378 26.5659i 0.598841 1.03722i
\(657\) −10.2280 + 17.7153i −0.399030 + 0.691141i
\(658\) 4.39627 0.171384
\(659\) −9.66057 + 16.7326i −0.376322 + 0.651809i −0.990524 0.137340i \(-0.956145\pi\)
0.614202 + 0.789149i \(0.289478\pi\)
\(660\) 0 0
\(661\) 16.6729 + 28.8783i 0.648501 + 1.12324i 0.983481 + 0.181011i \(0.0579370\pi\)
−0.334980 + 0.942225i \(0.608730\pi\)
\(662\) 0.162964 0.00633378
\(663\) −4.10949 + 4.55035i −0.159599 + 0.176721i
\(664\) −9.98992 −0.387684
\(665\) 0 0
\(666\) 1.78766 + 3.09632i 0.0692705 + 0.119980i
\(667\) −9.43724 + 16.3458i −0.365412 + 0.632911i
\(668\) −34.2328 −1.32450
\(669\) −5.83433 + 10.1054i −0.225568 + 0.390695i
\(670\) 0 0
\(671\) −0.235532 −0.00909259
\(672\) −1.32510 + 2.29513i −0.0511167 + 0.0885367i
\(673\) 6.48159 + 11.2264i 0.249847 + 0.432747i 0.963483 0.267769i \(-0.0862864\pi\)
−0.713636 + 0.700516i \(0.752953\pi\)
\(674\) −3.09327 5.35770i −0.119148 0.206371i
\(675\) 0 0
\(676\) −22.8631 10.2613i −0.879350 0.394666i
\(677\) −42.5281 −1.63449 −0.817243 0.576293i \(-0.804499\pi\)
−0.817243 + 0.576293i \(0.804499\pi\)
\(678\) 1.12651 + 1.95116i 0.0432632 + 0.0749340i
\(679\) 10.5988 + 18.3577i 0.406745 + 0.704503i
\(680\) 0 0
\(681\) −14.7459 −0.565064
\(682\) −0.00987441 + 0.0171030i −0.000378111 + 0.000654907i
\(683\) 17.8080 30.8444i 0.681406 1.18023i −0.293146 0.956068i \(-0.594702\pi\)
0.974552 0.224162i \(-0.0719645\pi\)
\(684\) −19.9630 −0.763304
\(685\) 0 0
\(686\) −2.29922 3.98236i −0.0877845 0.152047i
\(687\) 5.48337 + 9.49747i 0.209203 + 0.362351i
\(688\) −16.6504 −0.634790
\(689\) −17.6538 + 19.5477i −0.672556 + 0.744707i
\(690\) 0 0
\(691\) −4.61739 7.99755i −0.175654 0.304241i 0.764734 0.644347i \(-0.222871\pi\)
−0.940387 + 0.340105i \(0.889537\pi\)
\(692\) 13.1726 + 22.8156i 0.500746 + 0.867318i
\(693\) 0.305747 0.529569i 0.0116144 0.0201167i
\(694\) 8.12427 0.308393
\(695\) 0 0
\(696\) 1.27091 2.20128i 0.0481737 0.0834393i
\(697\) 24.2289 0.917737
\(698\) −0.462295 + 0.800718i −0.0174981 + 0.0303076i
\(699\) 3.35792 + 5.81609i 0.127008 + 0.219985i
\(700\) 0 0
\(701\) −37.7408 −1.42545 −0.712726 0.701443i \(-0.752539\pi\)
−0.712726 + 0.701443i \(0.752539\pi\)
\(702\) 3.22093 + 0.689663i 0.121566 + 0.0260296i
\(703\) −19.8097 −0.747138
\(704\) −0.511923 0.886677i −0.0192938 0.0334179i
\(705\) 0 0
\(706\) −1.57490 + 2.72781i −0.0592722 + 0.102662i
\(707\) 8.77999 0.330206
\(708\) −5.79095 + 10.0302i −0.217637 + 0.376959i
\(709\) −21.8160 + 37.7865i −0.819318 + 1.41910i 0.0868677 + 0.996220i \(0.472314\pi\)
−0.906186 + 0.422880i \(0.861019\pi\)
\(710\) 0 0
\(711\) −14.8239 + 25.6757i −0.555938 + 0.962913i
\(712\) −4.57325 7.92110i −0.171390 0.296856i
\(713\) −1.07115 1.85528i −0.0401148 0.0694808i
\(714\) −0.654244 −0.0244845
\(715\) 0 0
\(716\) −15.6761 −0.585844
\(717\) −6.19458 10.7293i −0.231341 0.400694i
\(718\) 0.978528 + 1.69486i 0.0365183 + 0.0632516i
\(719\) −4.33064 + 7.50090i −0.161506 + 0.279736i −0.935409 0.353568i \(-0.884968\pi\)
0.773903 + 0.633304i \(0.218302\pi\)
\(720\) 0 0
\(721\) 4.03199 6.98361i 0.150159 0.260083i
\(722\) 0.480336 0.831966i 0.0178762 0.0309626i
\(723\) 1.29484 0.0481555
\(724\) 4.23385 7.33325i 0.157350 0.272538i
\(725\) 0 0
\(726\) −0.889304 1.54032i −0.0330052 0.0571666i
\(727\) −11.1560 −0.413752 −0.206876 0.978367i \(-0.566330\pi\)
−0.206876 + 0.978367i \(0.566330\pi\)
\(728\) −1.67589 5.18421i −0.0621126 0.192140i
\(729\) −9.30924 −0.344787
\(730\) 0 0
\(731\) −6.57560 11.3893i −0.243207 0.421248i
\(732\) −0.844362 + 1.46248i −0.0312085 + 0.0540547i
\(733\) 14.3003 0.528192 0.264096 0.964496i \(-0.414926\pi\)
0.264096 + 0.964496i \(0.414926\pi\)
\(734\) −1.69208 + 2.93078i −0.0624560 + 0.108177i
\(735\) 0 0
\(736\) −14.5231 −0.535327
\(737\) −0.515029 + 0.892056i −0.0189713 + 0.0328593i
\(738\) −3.04431 5.27290i −0.112063 0.194098i
\(739\) −23.8783 41.3584i −0.878376 1.52139i −0.853122 0.521712i \(-0.825294\pi\)
−0.0252546 0.999681i \(-0.508040\pi\)
\(740\) 0 0
\(741\) −5.72184 + 6.33567i −0.210197 + 0.232747i
\(742\) −2.81054 −0.103178
\(743\) −14.3652 24.8813i −0.527009 0.912807i −0.999505 0.0314736i \(-0.989980\pi\)
0.472495 0.881333i \(-0.343353\pi\)
\(744\) 0.144251 + 0.249850i 0.00528849 + 0.00915993i
\(745\) 0 0
\(746\) 1.17229 0.0429207
\(747\) 12.4711 21.6005i 0.456292 0.790322i
\(748\) 0.440687 0.763292i 0.0161131 0.0279087i
\(749\) −23.6299 −0.863419
\(750\) 0 0
\(751\) 15.6734 + 27.1472i 0.571932 + 0.990614i 0.996368 + 0.0851565i \(0.0271390\pi\)
−0.424436 + 0.905458i \(0.639528\pi\)
\(752\) 20.4056 + 35.3436i 0.744116 + 1.28885i
\(753\) 10.1523 0.369969
\(754\) 1.19059 + 3.68298i 0.0433587 + 0.134126i
\(755\) 0 0
\(756\) −4.68646 8.11719i −0.170445 0.295219i
\(757\) 24.7737 + 42.9093i 0.900416 + 1.55957i 0.826955 + 0.562268i \(0.190071\pi\)
0.0734612 + 0.997298i \(0.476595\pi\)
\(758\) 0.779885 1.35080i 0.0283267 0.0490633i
\(759\) −0.461866 −0.0167647
\(760\) 0 0
\(761\) −3.96245 + 6.86317i −0.143639 + 0.248790i −0.928864 0.370420i \(-0.879214\pi\)
0.785225 + 0.619210i \(0.212547\pi\)
\(762\) −0.924360 −0.0334860
\(763\) 4.46789 7.73861i 0.161749 0.280157i
\(764\) 1.94134 + 3.36250i 0.0702352 + 0.121651i
\(765\) 0 0
\(766\) −4.09256 −0.147870
\(767\) −11.0534 34.1927i −0.399115 1.23463i
\(768\) −6.34491 −0.228952
\(769\) 25.2077 + 43.6611i 0.909015 + 1.57446i 0.815436 + 0.578848i \(0.196497\pi\)
0.0935790 + 0.995612i \(0.470169\pi\)
\(770\) 0 0
\(771\) −0.117766 + 0.203976i −0.00424123 + 0.00734603i
\(772\) −36.8320 −1.32561
\(773\) 5.41692 9.38239i 0.194833 0.337461i −0.752013 0.659149i \(-0.770917\pi\)
0.946846 + 0.321688i \(0.104250\pi\)
\(774\) −1.65242 + 2.86208i −0.0593950 + 0.102875i
\(775\) 0 0
\(776\) 7.82180 13.5478i 0.280786 0.486336i
\(777\) −2.17533 3.76777i −0.0780394 0.135168i
\(778\) −0.875168 1.51584i −0.0313763 0.0543453i
\(779\) 33.7351 1.20869
\(780\) 0 0
\(781\) −2.27594 −0.0814396
\(782\) −1.79263 3.10493i −0.0641043 0.111032i
\(783\) 6.78359 + 11.7495i 0.242426 + 0.419893i
\(784\) 8.84375 15.3178i 0.315848 0.547065i
\(785\) 0 0
\(786\) 0.874535 1.51474i 0.0311936 0.0540290i
\(787\) −8.13008 + 14.0817i −0.289806 + 0.501959i −0.973763 0.227563i \(-0.926924\pi\)
0.683957 + 0.729522i \(0.260257\pi\)
\(788\) 30.7264 1.09458
\(789\) 1.18688 2.05574i 0.0422541 0.0731863i
\(790\) 0 0
\(791\) 9.94556 + 17.2262i 0.353624 + 0.612494i
\(792\) −0.451276 −0.0160354
\(793\) −1.61166 4.98553i −0.0572318 0.177041i
\(794\) 3.36390 0.119380
\(795\) 0 0
\(796\) 11.2592 + 19.5016i 0.399073 + 0.691215i
\(797\) −13.0790 + 22.6535i −0.463283 + 0.802430i −0.999122 0.0418904i \(-0.986662\pi\)
0.535839 + 0.844320i \(0.319995\pi\)
\(798\) −0.910936 −0.0322468
\(799\) −16.1173 + 27.9159i −0.570188 + 0.987594i
\(800\) 0 0
\(801\) 22.8363 0.806882
\(802\) −0.813254 + 1.40860i −0.0287170 + 0.0497393i
\(803\) −0.628739 1.08901i −0.0221877 0.0384303i
\(804\) 3.69267 + 6.39590i 0.130231 + 0.225566i
\(805\) 0 0
\(806\) −0.429589 0.0919833i −0.0151316 0.00323997i
\(807\) −9.24202 −0.325335
\(808\) −3.23977 5.61145i −0.113975 0.197410i
\(809\) −23.6424 40.9499i −0.831223 1.43972i −0.897069 0.441891i \(-0.854308\pi\)
0.0658456 0.997830i \(-0.479026\pi\)
\(810\) 0 0
\(811\) 37.8864 1.33037 0.665185 0.746678i \(-0.268353\pi\)
0.665185 + 0.746678i \(0.268353\pi\)
\(812\) 5.50698 9.53836i 0.193257 0.334731i
\(813\) −1.84666 + 3.19851i −0.0647652 + 0.112177i
\(814\) −0.219785 −0.00770345
\(815\) 0 0
\(816\) −3.03673 5.25976i −0.106307 0.184129i
\(817\) −9.15553 15.8578i −0.320311 0.554796i
\(818\) −7.31672 −0.255823
\(819\) 13.3016 + 2.84813i 0.464795 + 0.0995217i
\(820\) 0 0
\(821\) 6.38473 + 11.0587i 0.222829 + 0.385950i 0.955666 0.294454i \(-0.0951376\pi\)
−0.732837 + 0.680404i \(0.761804\pi\)
\(822\) −1.79814 3.11448i −0.0627175 0.108630i
\(823\) −24.9511 + 43.2166i −0.869741 + 1.50644i −0.00747918 + 0.999972i \(0.502381\pi\)
−0.862262 + 0.506463i \(0.830953\pi\)
\(824\) −5.95113 −0.207318
\(825\) 0 0
\(826\) 1.91721 3.32070i 0.0667082 0.115542i
\(827\) 23.5258 0.818072 0.409036 0.912518i \(-0.365865\pi\)
0.409036 + 0.912518i \(0.365865\pi\)
\(828\) 12.0130 20.8072i 0.417482 0.723099i
\(829\) −14.2560 24.6921i −0.495132 0.857594i 0.504852 0.863206i \(-0.331547\pi\)
−0.999984 + 0.00561208i \(0.998214\pi\)
\(830\) 0 0
\(831\) −2.73852 −0.0949982
\(832\) 15.2655 16.9032i 0.529236 0.586012i
\(833\) 13.9704 0.484045
\(834\) −0.696630 1.20660i −0.0241223 0.0417811i
\(835\) 0 0
\(836\) 0.613589 1.06277i 0.0212214 0.0367566i
\(837\) −1.53990 −0.0532268
\(838\) −0.319429 + 0.553268i −0.0110345 + 0.0191123i
\(839\) 18.8853 32.7103i 0.651992 1.12928i −0.330647 0.943755i \(-0.607267\pi\)
0.982639 0.185529i \(-0.0593998\pi\)
\(840\) 0 0
\(841\) 6.52873 11.3081i 0.225128 0.389934i
\(842\) 3.62193 + 6.27337i 0.124820 + 0.216194i
\(843\) −5.61996 9.73406i −0.193562 0.335259i
\(844\) −40.9030 −1.40794
\(845\) 0 0
\(846\) 8.10039 0.278497
\(847\) −7.85139 13.5990i −0.269777 0.467267i
\(848\) −13.0454 22.5952i −0.447979 0.775923i
\(849\) 5.81856 10.0780i 0.199693 0.345878i
\(850\) 0 0
\(851\) 11.9208 20.6474i 0.408639 0.707784i
\(852\) −8.15907 + 14.1319i −0.279525 + 0.484152i
\(853\) 31.3114 1.07208 0.536041 0.844192i \(-0.319919\pi\)
0.536041 + 0.844192i \(0.319919\pi\)
\(854\) 0.279543 0.484182i 0.00956575 0.0165684i
\(855\) 0 0
\(856\) 8.71932 + 15.1023i 0.298020 + 0.516186i
\(857\) −4.22466 −0.144312 −0.0721558 0.997393i \(-0.522988\pi\)
−0.0721558 + 0.997393i \(0.522988\pi\)
\(858\) −0.0634826 + 0.0702929i −0.00216726 + 0.00239976i
\(859\) 49.6240 1.69315 0.846574 0.532271i \(-0.178661\pi\)
0.846574 + 0.532271i \(0.178661\pi\)
\(860\) 0 0
\(861\) 3.70449 + 6.41636i 0.126249 + 0.218669i
\(862\) −0.321325 + 0.556552i −0.0109444 + 0.0189562i
\(863\) −9.56249 −0.325511 −0.162755 0.986666i \(-0.552038\pi\)
−0.162755 + 0.986666i \(0.552038\pi\)
\(864\) −5.21966 + 9.04072i −0.177576 + 0.307572i
\(865\) 0 0
\(866\) 1.47665 0.0501785
\(867\) −2.72550 + 4.72070i −0.0925627 + 0.160323i
\(868\) 0.625053 + 1.08262i 0.0212157 + 0.0367467i
\(869\) −0.911262 1.57835i −0.0309124 0.0535419i
\(870\) 0 0
\(871\) −22.4064 4.79766i −0.759214 0.162562i
\(872\) −6.59451 −0.223318
\(873\) 19.5289 + 33.8251i 0.660955 + 1.14481i
\(874\) −2.49597 4.32314i −0.0844273 0.146232i
\(875\) 0 0
\(876\) −9.01592 −0.304620
\(877\) 14.2949 24.7595i 0.482706 0.836071i −0.517097 0.855927i \(-0.672987\pi\)
0.999803 + 0.0198561i \(0.00632079\pi\)
\(878\) 0.371897 0.644144i 0.0125509 0.0217388i
\(879\) 14.3873 0.485270
\(880\) 0 0
\(881\) −0.267005 0.462467i −0.00899564 0.0155809i 0.861493 0.507770i \(-0.169530\pi\)
−0.870488 + 0.492189i \(0.836197\pi\)
\(882\) −1.75535 3.04035i −0.0591056 0.102374i
\(883\) −6.51376 −0.219206 −0.109603 0.993975i \(-0.534958\pi\)
−0.109603 + 0.993975i \(0.534958\pi\)
\(884\) 19.1722 + 4.10514i 0.644830 + 0.138071i
\(885\) 0 0
\(886\) −2.92066 5.05873i −0.0981215 0.169951i
\(887\) 3.80456 + 6.58969i 0.127745 + 0.221260i 0.922802 0.385273i \(-0.125893\pi\)
−0.795058 + 0.606534i \(0.792560\pi\)
\(888\) −1.60537 + 2.78058i −0.0538726 + 0.0933101i
\(889\) −8.16088 −0.273707
\(890\) 0 0
\(891\) 0.475008 0.822738i 0.0159134 0.0275628i
\(892\) 37.3138 1.24936
\(893\) −22.4408 + 38.8687i −0.750954 + 1.30069i
\(894\) −1.48190 2.56673i −0.0495621 0.0858441i
\(895\) 0 0
\(896\) 11.2229 0.374929
\(897\) −3.16039 9.77638i −0.105522 0.326424i
\(898\) −1.16616 −0.0389153
\(899\) −0.904756 1.56708i −0.0301753 0.0522652i
\(900\) 0 0
\(901\) 10.3038 17.8467i 0.343269 0.594560i
\(902\) 0.374284 0.0124623
\(903\) 2.01076 3.48273i 0.0669138 0.115898i
\(904\) 7.33972 12.7128i 0.244115 0.422820i
\(905\) 0 0
\(906\) −1.06135 + 1.83831i −0.0352610 + 0.0610739i
\(907\) 1.81063 + 3.13610i 0.0601209 + 0.104132i 0.894519 0.447029i \(-0.147518\pi\)
−0.834398 + 0.551162i \(0.814185\pi\)
\(908\) 23.5771 + 40.8367i 0.782432 + 1.35521i
\(909\) 16.1777 0.536579
\(910\) 0 0
\(911\) −45.7945 −1.51724 −0.758620 0.651533i \(-0.774126\pi\)
−0.758620 + 0.651533i \(0.774126\pi\)
\(912\) −4.22818 7.32342i −0.140009 0.242503i
\(913\) 0.766630 + 1.32784i 0.0253717 + 0.0439451i
\(914\) −1.73707 + 3.00870i −0.0574572 + 0.0995188i
\(915\) 0 0
\(916\) 17.5346 30.3708i 0.579360 1.00348i
\(917\) 7.72100 13.3732i 0.254970 0.441621i
\(918\) −2.57712 −0.0850577
\(919\) 6.09866 10.5632i 0.201176 0.348447i −0.747731 0.664001i \(-0.768857\pi\)
0.948908 + 0.315554i \(0.102190\pi\)
\(920\) 0 0
\(921\) −3.23241 5.59869i −0.106511 0.184483i
\(922\) 0.930419 0.0306417
\(923\) −15.5735 48.1752i −0.512608 1.58571i
\(924\) 0.269515 0.00886641
\(925\) 0 0
\(926\) 5.39076 + 9.33708i 0.177152 + 0.306835i
\(927\) 7.42919 12.8677i 0.244007 0.422632i
\(928\) −12.2671 −0.402686
\(929\) −0.251057 + 0.434843i −0.00823690 + 0.0142667i −0.870114 0.492850i \(-0.835955\pi\)
0.861878 + 0.507116i \(0.169289\pi\)
\(930\) 0 0
\(931\) 19.4516 0.637501
\(932\) 10.7379 18.5986i 0.351731 0.609217i
\(933\) −8.13080 14.0830i −0.266190 0.461055i
\(934\) 1.97166 + 3.41502i 0.0645148 + 0.111743i
\(935\) 0 0
\(936\) −3.08793 9.55223i −0.100932 0.312224i
\(937\) −54.6246 −1.78451 −0.892254 0.451535i \(-0.850877\pi\)
−0.892254 + 0.451535i \(0.850877\pi\)
\(938\) −1.22253 2.11749i −0.0399171 0.0691384i
\(939\) −0.328127 0.568333i −0.0107080 0.0185468i
\(940\) 0 0
\(941\) −32.3464 −1.05446 −0.527231 0.849722i \(-0.676770\pi\)
−0.527231 + 0.849722i \(0.676770\pi\)
\(942\) 1.87206 3.24251i 0.0609951 0.105647i
\(943\) −20.3006 + 35.1617i −0.661079 + 1.14502i
\(944\) 35.5955 1.15853
\(945\) 0 0
\(946\) −0.101579 0.175939i −0.00330261 0.00572028i
\(947\) 22.0840 + 38.2506i 0.717633 + 1.24298i 0.961935 + 0.273278i \(0.0881078\pi\)
−0.244302 + 0.969699i \(0.578559\pi\)
\(948\) −13.0672 −0.424403
\(949\) 18.7490 20.7603i 0.608617 0.673909i
\(950\) 0 0
\(951\) −1.04234 1.80539i −0.0338003 0.0585439i
\(952\) 2.13136 + 3.69162i 0.0690777 + 0.119646i
\(953\) −18.4347 + 31.9299i −0.597159 + 1.03431i 0.396079 + 0.918217i \(0.370371\pi\)
−0.993238 + 0.116094i \(0.962963\pi\)
\(954\) −5.17859 −0.167663
\(955\) 0 0
\(956\) −19.8089 + 34.3100i −0.640666 + 1.10967i
\(957\) −0.390120 −0.0126108
\(958\) −2.20575 + 3.82047i −0.0712645 + 0.123434i
\(959\) −15.8753 27.4968i −0.512639 0.887917i
\(960\) 0 0
\(961\) −30.7946 −0.993375
\(962\) −1.50391 4.65221i −0.0484880 0.149993i
\(963\) −43.5396 −1.40304
\(964\) −2.07030 3.58587i −0.0666800 0.115493i
\(965\) 0 0
\(966\) 0.548169 0.949457i 0.0176370 0.0305483i
\(967\) 48.7127 1.56649 0.783247 0.621711i \(-0.213562\pi\)
0.783247 + 0.621711i \(0.213562\pi\)
\(968\) −5.79424 + 10.0359i −0.186234 + 0.322567i
\(969\) 3.33960 5.78436i 0.107284 0.185820i
\(970\) 0 0
\(971\) 29.2890 50.7301i 0.939930 1.62801i 0.174331 0.984687i \(-0.444224\pi\)
0.765598 0.643319i \(-0.222443\pi\)
\(972\) −13.2310 22.9167i −0.424384 0.735055i
\(973\) −6.15033 10.6527i −0.197170 0.341509i
\(974\) −10.3616 −0.332006
\(975\) 0 0
\(976\) 5.19007 0.166130
\(977\) −11.5653 20.0317i −0.370006 0.640870i 0.619560 0.784949i \(-0.287311\pi\)
−0.989566 + 0.144080i \(0.953978\pi\)
\(978\) 0.106300 + 0.184118i 0.00339911 + 0.00588744i
\(979\) −0.701905 + 1.21574i −0.0224330 + 0.0388551i
\(980\) 0 0
\(981\) 8.23236 14.2589i 0.262839 0.455251i
\(982\) −3.89047 + 6.73850i −0.124150 + 0.215034i
\(983\) 32.4869 1.03617 0.518085 0.855329i \(-0.326645\pi\)
0.518085 + 0.855329i \(0.326645\pi\)
\(984\) 2.73387 4.73521i 0.0871527 0.150953i
\(985\) 0 0
\(986\) −1.51417 2.62261i −0.0482209 0.0835210i
\(987\) −9.85700 −0.313752
\(988\) 26.6944 + 5.71578i 0.849261 + 0.181843i
\(989\) 22.0379 0.700764
\(990\) 0 0
\(991\) −2.66758 4.62039i −0.0847386 0.146772i 0.820541 0.571587i \(-0.193672\pi\)
−0.905280 + 0.424816i \(0.860339\pi\)
\(992\) 0.696169 1.20580i 0.0221034 0.0382842i
\(993\) −0.365387 −0.0115952
\(994\) 2.70122 4.67865i 0.0856775 0.148398i
\(995\) 0 0
\(996\) 10.9932 0.348334
\(997\) 13.2926 23.0234i 0.420980 0.729158i −0.575056 0.818114i \(-0.695020\pi\)
0.996036 + 0.0889559i \(0.0283530\pi\)
\(998\) −3.99368 6.91725i −0.126418 0.218962i
\(999\) −8.56878 14.8416i −0.271104 0.469566i
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 325.2.e.c.276.3 yes 10
5.2 odd 4 325.2.o.c.224.6 20
5.3 odd 4 325.2.o.c.224.5 20
5.4 even 2 325.2.e.d.276.3 yes 10
13.3 even 3 4225.2.a.bp.1.3 5
13.9 even 3 inner 325.2.e.c.126.3 10
13.10 even 6 4225.2.a.bo.1.3 5
65.9 even 6 325.2.e.d.126.3 yes 10
65.22 odd 12 325.2.o.c.74.5 20
65.29 even 6 4225.2.a.bn.1.3 5
65.48 odd 12 325.2.o.c.74.6 20
65.49 even 6 4225.2.a.bm.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.2.e.c.126.3 10 13.9 even 3 inner
325.2.e.c.276.3 yes 10 1.1 even 1 trivial
325.2.e.d.126.3 yes 10 65.9 even 6
325.2.e.d.276.3 yes 10 5.4 even 2
325.2.o.c.74.5 20 65.22 odd 12
325.2.o.c.74.6 20 65.48 odd 12
325.2.o.c.224.5 20 5.3 odd 4
325.2.o.c.224.6 20 5.2 odd 4
4225.2.a.bm.1.3 5 65.49 even 6
4225.2.a.bn.1.3 5 65.29 even 6
4225.2.a.bo.1.3 5 13.10 even 6
4225.2.a.bp.1.3 5 13.3 even 3