Properties

Label 625.2.d.p.501.2
Level $625$
Weight $2$
Character 625.501
Analytic conductor $4.991$
Analytic rank $0$
Dimension $16$
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] = [625,2,Mod(126,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.d (of order \(5\), degree \(4\), not 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: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 501.2
Root \(1.20005i\) of defining polynomial
Character \(\chi\) \(=\) 625.501
Dual form 625.2.d.p.126.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.718805 + 2.21225i) q^{2} +(-1.86261 - 1.35327i) q^{3} +(-2.75935 - 2.00479i) q^{4} +(4.33262 - 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 - 1.92884i) q^{8} +(0.710939 + 2.18805i) q^{9} +O(q^{10})\) \(q+(-0.718805 + 2.21225i) q^{2} +(-1.86261 - 1.35327i) q^{3} +(-2.75935 - 2.00479i) q^{4} +(4.33262 - 3.14783i) q^{6} -3.59425 q^{7} +(2.65482 - 1.92884i) q^{8} +(0.710939 + 2.18805i) q^{9} +(-0.153825 + 0.473424i) q^{11} +(2.42659 + 7.46828i) q^{12} +(-0.818243 - 2.51829i) q^{13} +(2.58356 - 7.95139i) q^{14} +(0.250832 + 0.771980i) q^{16} +(4.13180 - 3.00193i) q^{17} -5.35154 q^{18} +(0.798724 - 0.580307i) q^{19} +(6.69468 + 4.86397i) q^{21} +(-0.936765 - 0.680599i) q^{22} +(-1.98198 + 6.09991i) q^{23} -7.55514 q^{24} +6.15926 q^{26} +(-0.497557 + 1.53132i) q^{27} +(9.91780 + 7.20570i) q^{28} +(4.50623 + 3.27397i) q^{29} +(-4.89866 + 3.55908i) q^{31} +4.67497 q^{32} +(0.927185 - 0.673639i) q^{33} +(3.67107 + 11.2984i) q^{34} +(2.42484 - 7.46288i) q^{36} +(1.42028 + 4.37117i) q^{37} +(0.709660 + 2.18411i) q^{38} +(-1.88385 + 5.79790i) q^{39} +(-0.888346 - 2.73405i) q^{41} +(-15.5725 + 11.3141i) q^{42} +9.48858 q^{43} +(1.37357 - 0.997959i) q^{44} +(-12.0699 - 8.76929i) q^{46} +(4.34308 + 3.15543i) q^{47} +(0.577493 - 1.77734i) q^{48} +5.91861 q^{49} -11.7583 q^{51} +(-2.79082 + 8.58926i) q^{52} +(-0.248854 - 0.180803i) q^{53} +(-3.03003 - 2.20144i) q^{54} +(-9.54209 + 6.93274i) q^{56} -2.27302 q^{57} +(-10.4820 + 7.61558i) q^{58} +(-0.391355 - 1.20447i) q^{59} +(-1.92402 + 5.92152i) q^{61} +(-4.35242 - 13.3954i) q^{62} +(-2.55529 - 7.86438i) q^{63} +(-3.86206 + 11.8862i) q^{64} +(0.823796 + 2.53538i) q^{66} +(-4.27667 + 3.10718i) q^{67} -17.4193 q^{68} +(11.9465 - 8.67961i) q^{69} +(0.122941 + 0.0893215i) q^{71} +(6.10782 + 4.43759i) q^{72} +(4.59634 - 14.1461i) q^{73} -10.6910 q^{74} -3.36735 q^{76} +(0.552884 - 1.70160i) q^{77} +(-11.4723 - 8.33512i) q^{78} +(13.4205 + 9.75053i) q^{79} +(8.58283 - 6.23579i) q^{81} +6.68696 q^{82} +(11.8084 - 8.57929i) q^{83} +(-8.72176 - 26.8428i) q^{84} +(-6.82044 + 20.9912i) q^{86} +(-3.96281 - 12.1963i) q^{87} +(0.504783 + 1.55356i) q^{88} +(3.51731 - 10.8252i) q^{89} +(2.94097 + 9.05136i) q^{91} +(17.6980 - 12.8584i) q^{92} +13.9407 q^{93} +(-10.1024 + 7.33985i) q^{94} +(-8.70766 - 6.32648i) q^{96} +(0.687010 + 0.499142i) q^{97} +(-4.25432 + 13.0935i) q^{98} -1.14523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.718805 + 2.21225i −0.508272 + 1.56430i 0.286928 + 0.957952i \(0.407366\pi\)
−0.795200 + 0.606348i \(0.792634\pi\)
\(3\) −1.86261 1.35327i −1.07538 0.781309i −0.0985075 0.995136i \(-0.531407\pi\)
−0.976871 + 0.213828i \(0.931407\pi\)
\(4\) −2.75935 2.00479i −1.37968 1.00239i
\(5\) 0 0
\(6\) 4.33262 3.14783i 1.76879 1.28510i
\(7\) −3.59425 −1.35850 −0.679249 0.733908i \(-0.737694\pi\)
−0.679249 + 0.733908i \(0.737694\pi\)
\(8\) 2.65482 1.92884i 0.938622 0.681949i
\(9\) 0.710939 + 2.18805i 0.236980 + 0.729349i
\(10\) 0 0
\(11\) −0.153825 + 0.473424i −0.0463799 + 0.142743i −0.971565 0.236774i \(-0.923910\pi\)
0.925185 + 0.379517i \(0.123910\pi\)
\(12\) 2.42659 + 7.46828i 0.700496 + 2.15591i
\(13\) −0.818243 2.51829i −0.226940 0.698449i −0.998089 0.0617942i \(-0.980318\pi\)
0.771149 0.636655i \(-0.219682\pi\)
\(14\) 2.58356 7.95139i 0.690486 2.12510i
\(15\) 0 0
\(16\) 0.250832 + 0.771980i 0.0627079 + 0.192995i
\(17\) 4.13180 3.00193i 1.00211 0.728075i 0.0395697 0.999217i \(-0.487401\pi\)
0.962539 + 0.271142i \(0.0874013\pi\)
\(18\) −5.35154 −1.26137
\(19\) 0.798724 0.580307i 0.183240 0.133132i −0.492384 0.870378i \(-0.663874\pi\)
0.675624 + 0.737247i \(0.263874\pi\)
\(20\) 0 0
\(21\) 6.69468 + 4.86397i 1.46090 + 1.06141i
\(22\) −0.936765 0.680599i −0.199719 0.145104i
\(23\) −1.98198 + 6.09991i −0.413271 + 1.27192i 0.500517 + 0.865727i \(0.333143\pi\)
−0.913788 + 0.406192i \(0.866857\pi\)
\(24\) −7.55514 −1.54219
\(25\) 0 0
\(26\) 6.15926 1.20793
\(27\) −0.497557 + 1.53132i −0.0957548 + 0.294703i
\(28\) 9.91780 + 7.20570i 1.87429 + 1.36175i
\(29\) 4.50623 + 3.27397i 0.836786 + 0.607961i 0.921471 0.388447i \(-0.126988\pi\)
−0.0846848 + 0.996408i \(0.526988\pi\)
\(30\) 0 0
\(31\) −4.89866 + 3.55908i −0.879825 + 0.639230i −0.933205 0.359344i \(-0.883000\pi\)
0.0533803 + 0.998574i \(0.483000\pi\)
\(32\) 4.67497 0.826426
\(33\) 0.927185 0.673639i 0.161402 0.117266i
\(34\) 3.67107 + 11.2984i 0.629584 + 1.93766i
\(35\) 0 0
\(36\) 2.42484 7.46288i 0.404139 1.24381i
\(37\) 1.42028 + 4.37117i 0.233493 + 0.718616i 0.997318 + 0.0731932i \(0.0233190\pi\)
−0.763825 + 0.645423i \(0.776681\pi\)
\(38\) 0.709660 + 2.18411i 0.115122 + 0.354309i
\(39\) −1.88385 + 5.79790i −0.301658 + 0.928407i
\(40\) 0 0
\(41\) −0.888346 2.73405i −0.138736 0.426987i 0.857416 0.514624i \(-0.172068\pi\)
−0.996152 + 0.0876372i \(0.972068\pi\)
\(42\) −15.5725 + 11.3141i −2.40289 + 1.74580i
\(43\) 9.48858 1.44700 0.723498 0.690327i \(-0.242533\pi\)
0.723498 + 0.690327i \(0.242533\pi\)
\(44\) 1.37357 0.997959i 0.207074 0.150448i
\(45\) 0 0
\(46\) −12.0699 8.76929i −1.77961 1.29296i
\(47\) 4.34308 + 3.15543i 0.633503 + 0.460267i 0.857612 0.514297i \(-0.171947\pi\)
−0.224109 + 0.974564i \(0.571947\pi\)
\(48\) 0.577493 1.77734i 0.0833539 0.256537i
\(49\) 5.91861 0.845515
\(50\) 0 0
\(51\) −11.7583 −1.64650
\(52\) −2.79082 + 8.58926i −0.387017 + 1.19112i
\(53\) −0.248854 0.180803i −0.0341827 0.0248352i 0.570563 0.821254i \(-0.306725\pi\)
−0.604745 + 0.796419i \(0.706725\pi\)
\(54\) −3.03003 2.20144i −0.412334 0.299578i
\(55\) 0 0
\(56\) −9.54209 + 6.93274i −1.27512 + 0.926426i
\(57\) −2.27302 −0.301069
\(58\) −10.4820 + 7.61558i −1.37635 + 0.999975i
\(59\) −0.391355 1.20447i −0.0509500 0.156808i 0.922344 0.386369i \(-0.126271\pi\)
−0.973294 + 0.229561i \(0.926271\pi\)
\(60\) 0 0
\(61\) −1.92402 + 5.92152i −0.246345 + 0.758173i 0.749067 + 0.662494i \(0.230502\pi\)
−0.995412 + 0.0956787i \(0.969498\pi\)
\(62\) −4.35242 13.3954i −0.552757 1.70121i
\(63\) −2.55529 7.86438i −0.321936 0.990818i
\(64\) −3.86206 + 11.8862i −0.482757 + 1.48577i
\(65\) 0 0
\(66\) 0.823796 + 2.53538i 0.101402 + 0.312084i
\(67\) −4.27667 + 3.10718i −0.522479 + 0.379603i −0.817537 0.575876i \(-0.804661\pi\)
0.295058 + 0.955479i \(0.404661\pi\)
\(68\) −17.4193 −2.11240
\(69\) 11.9465 8.67961i 1.43818 1.04490i
\(70\) 0 0
\(71\) 0.122941 + 0.0893215i 0.0145904 + 0.0106005i 0.595057 0.803684i \(-0.297130\pi\)
−0.580466 + 0.814284i \(0.697130\pi\)
\(72\) 6.10782 + 4.43759i 0.719813 + 0.522975i
\(73\) 4.59634 14.1461i 0.537961 1.65567i −0.199202 0.979959i \(-0.563835\pi\)
0.737163 0.675715i \(-0.236165\pi\)
\(74\) −10.6910 −1.24281
\(75\) 0 0
\(76\) −3.36735 −0.386262
\(77\) 0.552884 1.70160i 0.0630070 0.193916i
\(78\) −11.4723 8.33512i −1.29898 0.943766i
\(79\) 13.4205 + 9.75053i 1.50992 + 1.09702i 0.966213 + 0.257745i \(0.0829795\pi\)
0.543706 + 0.839275i \(0.317021\pi\)
\(80\) 0 0
\(81\) 8.58283 6.23579i 0.953648 0.692866i
\(82\) 6.68696 0.738451
\(83\) 11.8084 8.57929i 1.29614 0.941700i 0.296228 0.955117i \(-0.404271\pi\)
0.999910 + 0.0134174i \(0.00427102\pi\)
\(84\) −8.72176 26.8428i −0.951623 2.92879i
\(85\) 0 0
\(86\) −6.82044 + 20.9912i −0.735467 + 2.26354i
\(87\) −3.96281 12.1963i −0.424857 1.30758i
\(88\) 0.504783 + 1.55356i 0.0538101 + 0.165610i
\(89\) 3.51731 10.8252i 0.372834 1.14746i −0.572095 0.820188i \(-0.693869\pi\)
0.944928 0.327277i \(-0.106131\pi\)
\(90\) 0 0
\(91\) 2.94097 + 9.05136i 0.308297 + 0.948841i
\(92\) 17.6980 12.8584i 1.84514 1.34058i
\(93\) 13.9407 1.44558
\(94\) −10.1024 + 7.33985i −1.04199 + 0.757048i
\(95\) 0 0
\(96\) −8.70766 6.32648i −0.888721 0.645694i
\(97\) 0.687010 + 0.499142i 0.0697553 + 0.0506802i 0.622116 0.782925i \(-0.286273\pi\)
−0.552361 + 0.833605i \(0.686273\pi\)
\(98\) −4.25432 + 13.0935i −0.429751 + 1.32264i
\(99\) −1.14523 −0.115100
\(100\) 0 0
\(101\) −13.2498 −1.31841 −0.659203 0.751965i \(-0.729106\pi\)
−0.659203 + 0.751965i \(0.729106\pi\)
\(102\) 8.45196 26.0125i 0.836869 2.57562i
\(103\) 0.672220 + 0.488396i 0.0662358 + 0.0481231i 0.620410 0.784277i \(-0.286966\pi\)
−0.554175 + 0.832400i \(0.686966\pi\)
\(104\) −7.02968 5.10736i −0.689317 0.500818i
\(105\) 0 0
\(106\) 0.578859 0.420566i 0.0562237 0.0408489i
\(107\) 0.0722844 0.00698800 0.00349400 0.999994i \(-0.498888\pi\)
0.00349400 + 0.999994i \(0.498888\pi\)
\(108\) 4.44291 3.22796i 0.427519 0.310611i
\(109\) 1.72933 + 5.32232i 0.165639 + 0.509785i 0.999083 0.0428192i \(-0.0136340\pi\)
−0.833444 + 0.552605i \(0.813634\pi\)
\(110\) 0 0
\(111\) 3.26993 10.0638i 0.310368 0.955215i
\(112\) −0.901550 2.77469i −0.0851885 0.262183i
\(113\) 0.804183 + 2.47502i 0.0756512 + 0.232830i 0.981730 0.190278i \(-0.0609389\pi\)
−0.906079 + 0.423108i \(0.860939\pi\)
\(114\) 1.63386 5.02850i 0.153025 0.470962i
\(115\) 0 0
\(116\) −5.87067 18.0681i −0.545078 1.67758i
\(117\) 4.92842 3.58071i 0.455633 0.331036i
\(118\) 2.94589 0.271191
\(119\) −14.8507 + 10.7897i −1.36136 + 0.989088i
\(120\) 0 0
\(121\) 8.69872 + 6.31999i 0.790793 + 0.574544i
\(122\) −11.7169 8.51284i −1.06080 0.770716i
\(123\) −2.04525 + 6.29464i −0.184414 + 0.567568i
\(124\) 20.6523 1.85463
\(125\) 0 0
\(126\) 19.2348 1.71357
\(127\) −1.52804 + 4.70281i −0.135591 + 0.417307i −0.995682 0.0928348i \(-0.970407\pi\)
0.860090 + 0.510142i \(0.170407\pi\)
\(128\) −15.9549 11.5919i −1.41023 1.02459i
\(129\) −17.6735 12.8406i −1.55607 1.13055i
\(130\) 0 0
\(131\) −2.18711 + 1.58903i −0.191089 + 0.138834i −0.679216 0.733938i \(-0.737680\pi\)
0.488127 + 0.872772i \(0.337680\pi\)
\(132\) −3.90893 −0.340229
\(133\) −2.87081 + 2.08577i −0.248931 + 0.180859i
\(134\) −3.79979 11.6945i −0.328252 1.01025i
\(135\) 0 0
\(136\) 5.17896 15.9392i 0.444092 1.36677i
\(137\) 0.694787 + 2.13833i 0.0593596 + 0.182690i 0.976340 0.216243i \(-0.0693804\pi\)
−0.916980 + 0.398933i \(0.869380\pi\)
\(138\) 10.6143 + 32.6675i 0.903551 + 2.78085i
\(139\) −3.33838 + 10.2745i −0.283158 + 0.871469i 0.703787 + 0.710411i \(0.251491\pi\)
−0.986945 + 0.161059i \(0.948509\pi\)
\(140\) 0 0
\(141\) −3.81933 11.7547i −0.321645 0.989923i
\(142\) −0.285972 + 0.207771i −0.0239983 + 0.0174358i
\(143\) 1.31809 0.110224
\(144\) −1.51080 + 1.09766i −0.125900 + 0.0914719i
\(145\) 0 0
\(146\) 27.9909 + 20.3365i 2.31654 + 1.68306i
\(147\) −11.0241 8.00945i −0.909249 0.660608i
\(148\) 4.84422 14.9090i 0.398192 1.22551i
\(149\) 12.1878 0.998460 0.499230 0.866469i \(-0.333616\pi\)
0.499230 + 0.866469i \(0.333616\pi\)
\(150\) 0 0
\(151\) 17.0860 1.39044 0.695220 0.718797i \(-0.255307\pi\)
0.695220 + 0.718797i \(0.255307\pi\)
\(152\) 1.00115 3.08123i 0.0812041 0.249920i
\(153\) 9.50582 + 6.90638i 0.768500 + 0.558348i
\(154\) 3.36696 + 2.44624i 0.271318 + 0.197124i
\(155\) 0 0
\(156\) 16.8218 12.2217i 1.34682 0.978522i
\(157\) 7.49835 0.598433 0.299217 0.954185i \(-0.403275\pi\)
0.299217 + 0.954185i \(0.403275\pi\)
\(158\) −31.2173 + 22.6807i −2.48352 + 1.80438i
\(159\) 0.218843 + 0.673530i 0.0173554 + 0.0534144i
\(160\) 0 0
\(161\) 7.12372 21.9246i 0.561428 1.72790i
\(162\) 7.62577 + 23.4697i 0.599137 + 1.84396i
\(163\) −0.603383 1.85702i −0.0472606 0.145453i 0.924641 0.380839i \(-0.124365\pi\)
−0.971902 + 0.235386i \(0.924365\pi\)
\(164\) −3.02993 + 9.32515i −0.236597 + 0.728172i
\(165\) 0 0
\(166\) 10.4917 + 32.2900i 0.814310 + 2.50619i
\(167\) −0.288478 + 0.209591i −0.0223231 + 0.0162187i −0.598891 0.800831i \(-0.704392\pi\)
0.576568 + 0.817049i \(0.304392\pi\)
\(168\) 27.1550 2.09506
\(169\) 4.84494 3.52006i 0.372688 0.270774i
\(170\) 0 0
\(171\) 1.83758 + 1.33508i 0.140523 + 0.102096i
\(172\) −26.1824 19.0226i −1.99639 1.45046i
\(173\) 3.07482 9.46332i 0.233774 0.719483i −0.763508 0.645799i \(-0.776524\pi\)
0.997282 0.0736838i \(-0.0234756\pi\)
\(174\) 29.8297 2.26138
\(175\) 0 0
\(176\) −0.404058 −0.0304570
\(177\) −0.901021 + 2.77306i −0.0677249 + 0.208436i
\(178\) 21.4197 + 15.5624i 1.60548 + 1.16645i
\(179\) −12.4446 9.04154i −0.930154 0.675797i 0.0158762 0.999874i \(-0.494946\pi\)
−0.946031 + 0.324077i \(0.894946\pi\)
\(180\) 0 0
\(181\) −7.21576 + 5.24256i −0.536343 + 0.389676i −0.822725 0.568439i \(-0.807547\pi\)
0.286382 + 0.958116i \(0.407547\pi\)
\(182\) −22.1379 −1.64097
\(183\) 11.5971 8.42578i 0.857282 0.622852i
\(184\) 6.50395 + 20.0171i 0.479478 + 1.47568i
\(185\) 0 0
\(186\) −10.0206 + 30.8403i −0.734748 + 2.26132i
\(187\) 0.785612 + 2.41787i 0.0574497 + 0.176812i
\(188\) −5.65812 17.4139i −0.412661 1.27004i
\(189\) 1.78834 5.50395i 0.130083 0.400353i
\(190\) 0 0
\(191\) −3.51929 10.8313i −0.254647 0.783724i −0.993899 0.110294i \(-0.964821\pi\)
0.739252 0.673429i \(-0.235179\pi\)
\(192\) 23.2787 16.9130i 1.67999 1.22059i
\(193\) −17.3321 −1.24759 −0.623795 0.781588i \(-0.714410\pi\)
−0.623795 + 0.781588i \(0.714410\pi\)
\(194\) −1.59806 + 1.16106i −0.114734 + 0.0833589i
\(195\) 0 0
\(196\) −16.3315 11.8655i −1.16654 0.847539i
\(197\) 21.0028 + 15.2595i 1.49639 + 1.08719i 0.971792 + 0.235842i \(0.0757847\pi\)
0.524599 + 0.851350i \(0.324215\pi\)
\(198\) 0.823200 2.53355i 0.0585023 0.180052i
\(199\) −8.38571 −0.594447 −0.297223 0.954808i \(-0.596061\pi\)
−0.297223 + 0.954808i \(0.596061\pi\)
\(200\) 0 0
\(201\) 12.1706 0.858450
\(202\) 9.52403 29.3120i 0.670109 2.06238i
\(203\) −16.1965 11.7675i −1.13677 0.825913i
\(204\) 32.4454 + 23.5730i 2.27164 + 1.65044i
\(205\) 0 0
\(206\) −1.56365 + 1.13606i −0.108945 + 0.0791530i
\(207\) −14.7559 −1.02561
\(208\) 1.73883 1.26333i 0.120566 0.0875965i
\(209\) 0.151868 + 0.467401i 0.0105049 + 0.0323308i
\(210\) 0 0
\(211\) 4.91754 15.1346i 0.338537 1.04191i −0.626416 0.779489i \(-0.715479\pi\)
0.964953 0.262422i \(-0.0845212\pi\)
\(212\) 0.324204 + 0.997797i 0.0222664 + 0.0685290i
\(213\) −0.108115 0.332743i −0.00740789 0.0227991i
\(214\) −0.0519584 + 0.159911i −0.00355180 + 0.0109313i
\(215\) 0 0
\(216\) 1.63275 + 5.02510i 0.111095 + 0.341915i
\(217\) 17.6070 12.7922i 1.19524 0.868392i
\(218\) −13.0174 −0.881647
\(219\) −27.7046 + 20.1286i −1.87210 + 1.36016i
\(220\) 0 0
\(221\) −10.9406 7.94878i −0.735941 0.534693i
\(222\) 19.9133 + 14.4678i 1.33649 + 0.971017i
\(223\) 0.117335 0.361121i 0.00785736 0.0241825i −0.947051 0.321083i \(-0.895953\pi\)
0.954908 + 0.296901i \(0.0959531\pi\)
\(224\) −16.8030 −1.12270
\(225\) 0 0
\(226\) −6.05343 −0.402668
\(227\) −6.27333 + 19.3073i −0.416376 + 1.28147i 0.494639 + 0.869099i \(0.335300\pi\)
−0.911015 + 0.412374i \(0.864700\pi\)
\(228\) 6.27207 + 4.55693i 0.415378 + 0.301790i
\(229\) 9.63592 + 7.00091i 0.636759 + 0.462633i 0.858735 0.512419i \(-0.171251\pi\)
−0.221976 + 0.975052i \(0.571251\pi\)
\(230\) 0 0
\(231\) −3.33253 + 2.42123i −0.219264 + 0.159305i
\(232\) 18.2782 1.20002
\(233\) −15.4207 + 11.2038i −1.01024 + 0.733984i −0.964260 0.264958i \(-0.914642\pi\)
−0.0459827 + 0.998942i \(0.514642\pi\)
\(234\) 4.37886 + 13.4767i 0.286255 + 0.881003i
\(235\) 0 0
\(236\) −1.33481 + 4.10813i −0.0868889 + 0.267417i
\(237\) −11.8020 36.3229i −0.766624 2.35943i
\(238\) −13.1947 40.6092i −0.855288 2.63230i
\(239\) 1.27467 3.92304i 0.0824517 0.253760i −0.901329 0.433135i \(-0.857407\pi\)
0.983781 + 0.179375i \(0.0574074\pi\)
\(240\) 0 0
\(241\) 5.00169 + 15.3936i 0.322187 + 0.991590i 0.972694 + 0.232090i \(0.0745564\pi\)
−0.650507 + 0.759500i \(0.725444\pi\)
\(242\) −20.2341 + 14.7009i −1.30070 + 0.945012i
\(243\) −19.5948 −1.25701
\(244\) 17.1804 12.4823i 1.09986 0.799099i
\(245\) 0 0
\(246\) −12.4552 9.04923i −0.794115 0.576958i
\(247\) −2.11493 1.53659i −0.134570 0.0977708i
\(248\) −6.14016 + 18.8975i −0.389901 + 1.19999i
\(249\) −33.6045 −2.12960
\(250\) 0 0
\(251\) 11.8718 0.749344 0.374672 0.927157i \(-0.377755\pi\)
0.374672 + 0.927157i \(0.377755\pi\)
\(252\) −8.71546 + 26.8234i −0.549022 + 1.68972i
\(253\) −2.58297 1.87663i −0.162390 0.117983i
\(254\) −9.30546 6.76081i −0.583876 0.424211i
\(255\) 0 0
\(256\) 16.8908 12.2719i 1.05568 0.766993i
\(257\) 18.9164 1.17997 0.589986 0.807414i \(-0.299133\pi\)
0.589986 + 0.807414i \(0.299133\pi\)
\(258\) 41.1105 29.8685i 2.55943 1.85953i
\(259\) −5.10484 15.7111i −0.317199 0.976239i
\(260\) 0 0
\(261\) −3.95994 + 12.1874i −0.245114 + 0.754383i
\(262\) −1.94323 5.98065i −0.120053 0.369486i
\(263\) 2.08495 + 6.41680i 0.128563 + 0.395677i 0.994533 0.104419i \(-0.0332982\pi\)
−0.865970 + 0.500096i \(0.833298\pi\)
\(264\) 1.16217 3.57679i 0.0715266 0.220136i
\(265\) 0 0
\(266\) −2.55069 7.85022i −0.156393 0.481328i
\(267\) −21.2007 + 15.4032i −1.29746 + 0.942661i
\(268\) 18.0301 1.10136
\(269\) 20.4947 14.8903i 1.24959 0.907877i 0.251387 0.967887i \(-0.419113\pi\)
0.998198 + 0.0600099i \(0.0191132\pi\)
\(270\) 0 0
\(271\) −7.61070 5.52950i −0.462317 0.335893i 0.332122 0.943236i \(-0.392235\pi\)
−0.794440 + 0.607343i \(0.792235\pi\)
\(272\) 3.35382 + 2.43669i 0.203355 + 0.147746i
\(273\) 6.77103 20.8391i 0.409801 1.26124i
\(274\) −5.22995 −0.315953
\(275\) 0 0
\(276\) −50.3653 −3.03163
\(277\) 1.84402 5.67530i 0.110796 0.340996i −0.880251 0.474509i \(-0.842626\pi\)
0.991047 + 0.133513i \(0.0426258\pi\)
\(278\) −20.3301 14.7707i −1.21932 0.885887i
\(279\) −11.2701 8.18820i −0.674722 0.490215i
\(280\) 0 0
\(281\) −8.95766 + 6.50812i −0.534369 + 0.388242i −0.821990 0.569503i \(-0.807136\pi\)
0.287620 + 0.957744i \(0.407136\pi\)
\(282\) 28.7497 1.71202
\(283\) −2.44652 + 1.77750i −0.145431 + 0.105661i −0.658121 0.752912i \(-0.728649\pi\)
0.512691 + 0.858573i \(0.328649\pi\)
\(284\) −0.160166 0.492939i −0.00950409 0.0292506i
\(285\) 0 0
\(286\) −0.947447 + 2.91594i −0.0560237 + 0.172423i
\(287\) 3.19293 + 9.82684i 0.188473 + 0.580060i
\(288\) 3.32362 + 10.2291i 0.195846 + 0.602753i
\(289\) 2.80691 8.63880i 0.165113 0.508164i
\(290\) 0 0
\(291\) −0.604161 1.85942i −0.0354165 0.109001i
\(292\) −41.0428 + 29.8194i −2.40185 + 1.74505i
\(293\) −6.26426 −0.365962 −0.182981 0.983116i \(-0.558575\pi\)
−0.182981 + 0.983116i \(0.558575\pi\)
\(294\) 25.6431 18.6308i 1.49553 1.08657i
\(295\) 0 0
\(296\) 12.2019 + 8.86520i 0.709221 + 0.515279i
\(297\) −0.648428 0.471111i −0.0376256 0.0273366i
\(298\) −8.76062 + 26.9624i −0.507489 + 1.56189i
\(299\) 16.9831 0.982158
\(300\) 0 0
\(301\) −34.1043 −1.96574
\(302\) −12.2815 + 37.7986i −0.706721 + 2.17506i
\(303\) 24.6793 + 17.9305i 1.41779 + 1.03008i
\(304\) 0.648331 + 0.471040i 0.0371843 + 0.0270160i
\(305\) 0 0
\(306\) −22.1115 + 16.0650i −1.26403 + 0.918372i
\(307\) −25.8734 −1.47667 −0.738337 0.674432i \(-0.764388\pi\)
−0.738337 + 0.674432i \(0.764388\pi\)
\(308\) −4.93696 + 3.58691i −0.281309 + 0.204383i
\(309\) −0.591154 1.81938i −0.0336296 0.103501i
\(310\) 0 0
\(311\) −2.78201 + 8.56214i −0.157753 + 0.485514i −0.998429 0.0560237i \(-0.982158\pi\)
0.840676 + 0.541538i \(0.182158\pi\)
\(312\) 6.18194 + 19.0261i 0.349984 + 1.07714i
\(313\) 10.2678 + 31.6011i 0.580372 + 1.78620i 0.617110 + 0.786877i \(0.288304\pi\)
−0.0367373 + 0.999325i \(0.511696\pi\)
\(314\) −5.38985 + 16.5882i −0.304167 + 0.936129i
\(315\) 0 0
\(316\) −17.4840 53.8103i −0.983554 3.02707i
\(317\) −21.0096 + 15.2644i −1.18002 + 0.857332i −0.992174 0.124867i \(-0.960150\pi\)
−0.187843 + 0.982199i \(0.560150\pi\)
\(318\) −1.64733 −0.0923774
\(319\) −2.24315 + 1.62974i −0.125592 + 0.0912480i
\(320\) 0 0
\(321\) −0.134638 0.0978200i −0.00751475 0.00545978i
\(322\) 43.3821 + 31.5190i 2.41759 + 1.75648i
\(323\) 1.55813 4.79543i 0.0866966 0.266825i
\(324\) −36.1845 −2.01025
\(325\) 0 0
\(326\) 4.54192 0.251554
\(327\) 3.98145 12.2536i 0.220175 0.677628i
\(328\) −7.63195 5.54494i −0.421404 0.306168i
\(329\) −15.6101 11.3414i −0.860612 0.625272i
\(330\) 0 0
\(331\) −9.81206 + 7.12888i −0.539320 + 0.391839i −0.823832 0.566834i \(-0.808168\pi\)
0.284513 + 0.958672i \(0.408168\pi\)
\(332\) −49.7832 −2.73221
\(333\) −8.55460 + 6.21528i −0.468789 + 0.340595i
\(334\) −0.256310 0.788841i −0.0140247 0.0431635i
\(335\) 0 0
\(336\) −2.07565 + 6.38820i −0.113236 + 0.348505i
\(337\) 9.34835 + 28.7713i 0.509237 + 1.56727i 0.793529 + 0.608533i \(0.208241\pi\)
−0.284292 + 0.958738i \(0.591759\pi\)
\(338\) 4.30469 + 13.2485i 0.234144 + 0.720622i
\(339\) 1.85148 5.69828i 0.100559 0.309488i
\(340\) 0 0
\(341\) −0.931421 2.86662i −0.0504393 0.155236i
\(342\) −4.27440 + 3.10554i −0.231133 + 0.167928i
\(343\) 3.88680 0.209867
\(344\) 25.1905 18.3020i 1.35818 0.986777i
\(345\) 0 0
\(346\) 18.7251 + 13.6046i 1.00667 + 0.731386i
\(347\) −10.7828 7.83419i −0.578853 0.420561i 0.259457 0.965755i \(-0.416456\pi\)
−0.838310 + 0.545193i \(0.816456\pi\)
\(348\) −13.5161 + 41.5984i −0.724541 + 2.22991i
\(349\) −27.4444 −1.46906 −0.734532 0.678574i \(-0.762598\pi\)
−0.734532 + 0.678574i \(0.762598\pi\)
\(350\) 0 0
\(351\) 4.26344 0.227566
\(352\) −0.719127 + 2.21325i −0.0383296 + 0.117966i
\(353\) 12.5854 + 9.14382i 0.669853 + 0.486676i 0.869976 0.493094i \(-0.164134\pi\)
−0.200123 + 0.979771i \(0.564134\pi\)
\(354\) −5.48705 3.98658i −0.291634 0.211884i
\(355\) 0 0
\(356\) −31.4076 + 22.8190i −1.66460 + 1.20940i
\(357\) 42.2624 2.23676
\(358\) 28.9474 21.0315i 1.52992 1.11155i
\(359\) −6.79310 20.9070i −0.358526 1.10343i −0.953937 0.300008i \(-0.903011\pi\)
0.595410 0.803422i \(-0.296989\pi\)
\(360\) 0 0
\(361\) −5.57012 + 17.1431i −0.293164 + 0.902267i
\(362\) −6.41114 19.7315i −0.336962 1.03706i
\(363\) −7.64970 23.5434i −0.401505 1.23571i
\(364\) 10.0309 30.8719i 0.525762 1.61813i
\(365\) 0 0
\(366\) 10.3039 + 31.7122i 0.538594 + 1.65762i
\(367\) 9.79748 7.11829i 0.511424 0.371571i −0.301939 0.953327i \(-0.597634\pi\)
0.813364 + 0.581756i \(0.197634\pi\)
\(368\) −5.20615 −0.271389
\(369\) 5.35066 3.88749i 0.278544 0.202374i
\(370\) 0 0
\(371\) 0.894441 + 0.649850i 0.0464371 + 0.0337385i
\(372\) −38.4673 27.9481i −1.99443 1.44904i
\(373\) −2.18971 + 6.73922i −0.113379 + 0.348944i −0.991605 0.129301i \(-0.958727\pi\)
0.878227 + 0.478245i \(0.158727\pi\)
\(374\) −5.91364 −0.305787
\(375\) 0 0
\(376\) 17.6164 0.908499
\(377\) 4.55762 14.0269i 0.234729 0.722423i
\(378\) 10.8907 + 7.91253i 0.560155 + 0.406977i
\(379\) 17.3963 + 12.6391i 0.893586 + 0.649228i 0.936810 0.349837i \(-0.113763\pi\)
−0.0432246 + 0.999065i \(0.513763\pi\)
\(380\) 0 0
\(381\) 9.21029 6.69167i 0.471858 0.342825i
\(382\) 26.4912 1.35541
\(383\) 20.1297 14.6251i 1.02858 0.747305i 0.0605541 0.998165i \(-0.480713\pi\)
0.968023 + 0.250860i \(0.0807132\pi\)
\(384\) 14.0309 + 43.1825i 0.716009 + 2.20365i
\(385\) 0 0
\(386\) 12.4584 38.3429i 0.634115 1.95160i
\(387\) 6.74581 + 20.7615i 0.342909 + 1.05536i
\(388\) −0.895030 2.75462i −0.0454383 0.139845i
\(389\) −10.9436 + 33.6809i −0.554862 + 1.70769i 0.141446 + 0.989946i \(0.454825\pi\)
−0.696308 + 0.717743i \(0.745175\pi\)
\(390\) 0 0
\(391\) 10.1223 + 31.1534i 0.511909 + 1.57549i
\(392\) 15.7129 11.4161i 0.793619 0.576598i
\(393\) 6.22412 0.313965
\(394\) −48.8547 + 35.4950i −2.46127 + 1.78821i
\(395\) 0 0
\(396\) 3.16011 + 2.29595i 0.158801 + 0.115376i
\(397\) 4.44720 + 3.23108i 0.223199 + 0.162163i 0.693765 0.720201i \(-0.255950\pi\)
−0.470567 + 0.882364i \(0.655950\pi\)
\(398\) 6.02769 18.5513i 0.302141 0.929893i
\(399\) 8.16980 0.409001
\(400\) 0 0
\(401\) 24.8463 1.24077 0.620383 0.784299i \(-0.286977\pi\)
0.620383 + 0.784299i \(0.286977\pi\)
\(402\) −8.74830 + 26.9245i −0.436326 + 1.34287i
\(403\) 12.9711 + 9.42406i 0.646137 + 0.469446i
\(404\) 36.5609 + 26.5631i 1.81897 + 1.32156i
\(405\) 0 0
\(406\) 37.6747 27.3723i 1.86976 1.35846i
\(407\) −2.28789 −0.113407
\(408\) −31.2164 + 22.6800i −1.54544 + 1.12283i
\(409\) 1.21492 + 3.73915i 0.0600741 + 0.184889i 0.976590 0.215109i \(-0.0690107\pi\)
−0.916516 + 0.399998i \(0.869011\pi\)
\(410\) 0 0
\(411\) 1.59962 4.92312i 0.0789033 0.242839i
\(412\) −0.875761 2.69531i −0.0431456 0.132789i
\(413\) 1.40663 + 4.32915i 0.0692155 + 0.213023i
\(414\) 10.6066 32.6439i 0.521288 1.60436i
\(415\) 0 0
\(416\) −3.82526 11.7730i −0.187549 0.577216i
\(417\) 20.1222 14.6196i 0.985388 0.715926i
\(418\) −1.14317 −0.0559144
\(419\) 3.85581 2.80141i 0.188369 0.136858i −0.489604 0.871945i \(-0.662859\pi\)
0.677973 + 0.735087i \(0.262859\pi\)
\(420\) 0 0
\(421\) −12.9913 9.43872i −0.633157 0.460015i 0.224336 0.974512i \(-0.427979\pi\)
−0.857492 + 0.514497i \(0.827979\pi\)
\(422\) 29.9469 + 21.7577i 1.45779 + 1.05915i
\(423\) −3.81657 + 11.7462i −0.185568 + 0.571119i
\(424\) −1.00940 −0.0490209
\(425\) 0 0
\(426\) 0.813824 0.0394299
\(427\) 6.91540 21.2834i 0.334659 1.02998i
\(428\) −0.199458 0.144915i −0.00964118 0.00700473i
\(429\) −2.45508 1.78372i −0.118533 0.0861189i
\(430\) 0 0
\(431\) 33.4684 24.3162i 1.61212 1.17127i 0.755841 0.654755i \(-0.227228\pi\)
0.856277 0.516517i \(-0.172772\pi\)
\(432\) −1.30695 −0.0628808
\(433\) 12.2852 8.92574i 0.590391 0.428944i −0.252065 0.967710i \(-0.581110\pi\)
0.842455 + 0.538767i \(0.181110\pi\)
\(434\) 15.6437 + 48.1462i 0.750920 + 2.31109i
\(435\) 0 0
\(436\) 5.89829 18.1531i 0.282477 0.869375i
\(437\) 1.95676 + 6.02230i 0.0936047 + 0.288086i
\(438\) −24.6153 75.7582i −1.17617 3.61986i
\(439\) 5.29018 16.2815i 0.252486 0.777074i −0.741828 0.670590i \(-0.766041\pi\)
0.994314 0.106483i \(-0.0339591\pi\)
\(440\) 0 0
\(441\) 4.20777 + 12.9502i 0.200370 + 0.616675i
\(442\) 25.4488 18.4897i 1.21048 0.879464i
\(443\) −35.3909 −1.68147 −0.840736 0.541445i \(-0.817877\pi\)
−0.840736 + 0.541445i \(0.817877\pi\)
\(444\) −29.1987 + 21.2141i −1.38571 + 1.00678i
\(445\) 0 0
\(446\) 0.714551 + 0.519152i 0.0338350 + 0.0245825i
\(447\) −22.7011 16.4933i −1.07372 0.780106i
\(448\) 13.8812 42.7219i 0.655824 2.01842i
\(449\) 20.6830 0.976090 0.488045 0.872818i \(-0.337710\pi\)
0.488045 + 0.872818i \(0.337710\pi\)
\(450\) 0 0
\(451\) 1.43101 0.0673838
\(452\) 2.74287 8.44168i 0.129014 0.397063i
\(453\) −31.8246 23.1219i −1.49525 1.08636i
\(454\) −38.2034 27.7564i −1.79298 1.30267i
\(455\) 0 0
\(456\) −6.03447 + 4.38430i −0.282590 + 0.205314i
\(457\) −41.7664 −1.95375 −0.976876 0.213807i \(-0.931414\pi\)
−0.976876 + 0.213807i \(0.931414\pi\)
\(458\) −22.4141 + 16.2848i −1.04734 + 0.760940i
\(459\) 2.54112 + 7.82075i 0.118609 + 0.365041i
\(460\) 0 0
\(461\) −3.29979 + 10.1557i −0.153686 + 0.472998i −0.998025 0.0628112i \(-0.979993\pi\)
0.844339 + 0.535809i \(0.179993\pi\)
\(462\) −2.96093 9.11279i −0.137755 0.423965i
\(463\) 2.41971 + 7.44709i 0.112453 + 0.346096i 0.991407 0.130811i \(-0.0417581\pi\)
−0.878954 + 0.476906i \(0.841758\pi\)
\(464\) −1.39713 + 4.29994i −0.0648603 + 0.199620i
\(465\) 0 0
\(466\) −13.7012 42.1678i −0.634694 1.95339i
\(467\) 4.02971 2.92776i 0.186473 0.135480i −0.490632 0.871367i \(-0.663234\pi\)
0.677105 + 0.735886i \(0.263234\pi\)
\(468\) −20.7778 −0.960455
\(469\) 15.3714 11.1680i 0.709786 0.515690i
\(470\) 0 0
\(471\) −13.9665 10.1473i −0.643542 0.467561i
\(472\) −3.36220 2.44278i −0.154758 0.112438i
\(473\) −1.45958 + 4.49213i −0.0671116 + 0.206548i
\(474\) 88.8388 4.08050
\(475\) 0 0
\(476\) 62.6094 2.86970
\(477\) 0.218685 0.673043i 0.0100129 0.0308165i
\(478\) 7.76252 + 5.63980i 0.355049 + 0.257958i
\(479\) 13.2663 + 9.63854i 0.606153 + 0.440396i 0.848058 0.529904i \(-0.177772\pi\)
−0.241904 + 0.970300i \(0.577772\pi\)
\(480\) 0 0
\(481\) 9.84576 7.15336i 0.448928 0.326165i
\(482\) −37.6498 −1.71490
\(483\) −42.9385 + 31.1966i −1.95377 + 1.41950i
\(484\) −11.3326 34.8782i −0.515118 1.58537i
\(485\) 0 0
\(486\) 14.0848 43.3486i 0.638901 1.96633i
\(487\) −0.270856 0.833609i −0.0122737 0.0377744i 0.944732 0.327843i \(-0.106322\pi\)
−0.957006 + 0.290069i \(0.906322\pi\)
\(488\) 6.31375 + 19.4317i 0.285810 + 0.879633i
\(489\) −1.38918 + 4.27545i −0.0628208 + 0.193343i
\(490\) 0 0
\(491\) 3.77366 + 11.6141i 0.170303 + 0.524138i 0.999388 0.0349842i \(-0.0111381\pi\)
−0.829085 + 0.559123i \(0.811138\pi\)
\(492\) 18.2630 13.2688i 0.823359 0.598205i
\(493\) 28.4471 1.28119
\(494\) 4.91955 3.57426i 0.221341 0.160814i
\(495\) 0 0
\(496\) −3.97628 2.88894i −0.178540 0.129717i
\(497\) −0.441879 0.321044i −0.0198210 0.0144008i
\(498\) 24.1551 74.3417i 1.08241 3.33133i
\(499\) −3.34603 −0.149789 −0.0748945 0.997191i \(-0.523862\pi\)
−0.0748945 + 0.997191i \(0.523862\pi\)
\(500\) 0 0
\(501\) 0.820954 0.0366775
\(502\) −8.53353 + 26.2635i −0.380870 + 1.17220i
\(503\) 9.61274 + 6.98407i 0.428611 + 0.311404i 0.781093 0.624414i \(-0.214662\pi\)
−0.352482 + 0.935819i \(0.614662\pi\)
\(504\) −21.9530 15.9498i −0.977864 0.710460i
\(505\) 0 0
\(506\) 6.00824 4.36524i 0.267099 0.194059i
\(507\) −13.7878 −0.612339
\(508\) 13.6445 9.91333i 0.605378 0.439833i
\(509\) 11.2230 + 34.5407i 0.497449 + 1.53099i 0.813105 + 0.582118i \(0.197776\pi\)
−0.315655 + 0.948874i \(0.602224\pi\)
\(510\) 0 0
\(511\) −16.5204 + 50.8445i −0.730819 + 2.24923i
\(512\) 2.81886 + 8.67556i 0.124577 + 0.383409i
\(513\) 0.491226 + 1.51184i 0.0216882 + 0.0667493i
\(514\) −13.5972 + 41.8478i −0.599746 + 1.84583i
\(515\) 0 0
\(516\) 23.0249 + 70.8634i 1.01362 + 3.11959i
\(517\) −2.16193 + 1.57074i −0.0950816 + 0.0690809i
\(518\) 38.4263 1.68835
\(519\) −18.5336 + 13.4654i −0.813534 + 0.591067i
\(520\) 0 0
\(521\) −0.165221 0.120040i −0.00723845 0.00525904i 0.584160 0.811638i \(-0.301424\pi\)
−0.591399 + 0.806379i \(0.701424\pi\)
\(522\) −24.1153 17.5208i −1.05550 0.766864i
\(523\) −8.66211 + 26.6592i −0.378768 + 1.16573i 0.562134 + 0.827046i \(0.309981\pi\)
−0.940901 + 0.338681i \(0.890019\pi\)
\(524\) 9.22069 0.402808
\(525\) 0 0
\(526\) −15.6943 −0.684303
\(527\) −9.55616 + 29.4108i −0.416273 + 1.28116i
\(528\) 0.752603 + 0.546798i 0.0327529 + 0.0237963i
\(529\) −14.6732 10.6607i −0.637967 0.463510i
\(530\) 0 0
\(531\) 2.35720 1.71260i 0.102294 0.0743207i
\(532\) 12.1031 0.524736
\(533\) −6.15825 + 4.47423i −0.266743 + 0.193800i
\(534\) −18.8366 57.9732i −0.815141 2.50875i
\(535\) 0 0
\(536\) −5.36054 + 16.4981i −0.231540 + 0.712608i
\(537\) 10.9439 + 33.6818i 0.472263 + 1.45348i
\(538\) 18.2094 + 56.0427i 0.785062 + 2.41617i
\(539\) −0.910429 + 2.80201i −0.0392149 + 0.120691i
\(540\) 0 0
\(541\) −2.88071 8.86590i −0.123851 0.381175i 0.869839 0.493336i \(-0.164223\pi\)
−0.993690 + 0.112161i \(0.964223\pi\)
\(542\) 17.7033 12.8622i 0.760421 0.552478i
\(543\) 20.5347 0.881230
\(544\) 19.3161 14.0339i 0.828169 0.601700i
\(545\) 0 0
\(546\) 41.2343 + 29.9585i 1.76466 + 1.28210i
\(547\) −16.2109 11.7779i −0.693129 0.503588i 0.184558 0.982822i \(-0.440915\pi\)
−0.877687 + 0.479234i \(0.840915\pi\)
\(548\) 2.36974 7.29332i 0.101230 0.311555i
\(549\) −14.3244 −0.611351
\(550\) 0 0
\(551\) 5.49914 0.234271
\(552\) 14.9741 46.0857i 0.637342 1.96154i
\(553\) −48.2364 35.0458i −2.05122 1.49030i
\(554\) 11.2297 + 8.15886i 0.477105 + 0.346637i
\(555\) 0 0
\(556\) 29.8099 21.6582i 1.26422 0.918511i
\(557\) 28.9839 1.22809 0.614043 0.789272i \(-0.289542\pi\)
0.614043 + 0.789272i \(0.289542\pi\)
\(558\) 26.2154 19.0466i 1.10979 0.806306i
\(559\) −7.76397 23.8950i −0.328381 1.01065i
\(560\) 0 0
\(561\) 1.80873 5.56669i 0.0763645 0.235026i
\(562\) −7.95880 24.4947i −0.335722 1.03325i
\(563\) −4.23431 13.0319i −0.178455 0.549228i 0.821320 0.570468i \(-0.193238\pi\)
−0.999774 + 0.0212408i \(0.993238\pi\)
\(564\) −13.0268 + 40.0923i −0.548526 + 1.68819i
\(565\) 0 0
\(566\) −2.17371 6.69000i −0.0913680 0.281202i
\(567\) −30.8488 + 22.4130i −1.29553 + 0.941256i
\(568\) 0.498673 0.0209239
\(569\) −28.0043 + 20.3463i −1.17400 + 0.852962i −0.991482 0.130241i \(-0.958425\pi\)
−0.182519 + 0.983202i \(0.558425\pi\)
\(570\) 0 0
\(571\) 34.3182 + 24.9337i 1.43617 + 1.04344i 0.988825 + 0.149082i \(0.0476317\pi\)
0.447349 + 0.894360i \(0.352368\pi\)
\(572\) −3.63707 2.64248i −0.152073 0.110488i
\(573\) −8.10252 + 24.9370i −0.338488 + 1.04176i
\(574\) −24.0346 −1.00318
\(575\) 0 0
\(576\) −28.7532 −1.19805
\(577\) 10.6008 32.6259i 0.441317 1.35824i −0.445155 0.895454i \(-0.646851\pi\)
0.886472 0.462782i \(-0.153149\pi\)
\(578\) 17.0936 + 12.4192i 0.710999 + 0.516571i
\(579\) 32.2829 + 23.4549i 1.34163 + 0.974752i
\(580\) 0 0
\(581\) −42.4422 + 30.8361i −1.76080 + 1.27930i
\(582\) 4.54777 0.188511
\(583\) 0.123876 0.0900014i 0.00513043 0.00372748i
\(584\) −15.0831 46.4210i −0.624143 1.92091i
\(585\) 0 0
\(586\) 4.50278 13.8581i 0.186008 0.572474i
\(587\) −9.19392 28.2960i −0.379474 1.16790i −0.940411 0.340041i \(-0.889559\pi\)
0.560937 0.827859i \(-0.310441\pi\)
\(588\) 14.3620 + 44.2018i 0.592280 + 1.82285i
\(589\) −1.84731 + 5.68545i −0.0761173 + 0.234265i
\(590\) 0 0
\(591\) −18.4700 56.8449i −0.759755 2.33828i
\(592\) −3.01821 + 2.19286i −0.124048 + 0.0901259i
\(593\) 14.8105 0.608195 0.304098 0.952641i \(-0.401645\pi\)
0.304098 + 0.952641i \(0.401645\pi\)
\(594\) 1.50831 1.09585i 0.0618867 0.0449633i
\(595\) 0 0
\(596\) −33.6303 24.4339i −1.37755 1.00085i
\(597\) 15.6193 + 11.3481i 0.639256 + 0.464446i
\(598\) −12.2075 + 37.5709i −0.499203 + 1.53639i
\(599\) 27.2394 1.11297 0.556486 0.830857i \(-0.312149\pi\)
0.556486 + 0.830857i \(0.312149\pi\)
\(600\) 0 0
\(601\) 33.1682 1.35296 0.676480 0.736461i \(-0.263505\pi\)
0.676480 + 0.736461i \(0.263505\pi\)
\(602\) 24.5143 75.4474i 0.999130 3.07501i
\(603\) −9.83912 7.14854i −0.400680 0.291111i
\(604\) −47.1463 34.2538i −1.91836 1.39377i
\(605\) 0 0
\(606\) −57.4065 + 41.7082i −2.33198 + 1.69428i
\(607\) −5.79849 −0.235353 −0.117677 0.993052i \(-0.537545\pi\)
−0.117677 + 0.993052i \(0.537545\pi\)
\(608\) 3.73401 2.71292i 0.151434 0.110023i
\(609\) 14.2433 + 43.8364i 0.577168 + 1.77634i
\(610\) 0 0
\(611\) 4.39261 13.5191i 0.177706 0.546922i
\(612\) −12.3841 38.1143i −0.500597 1.54068i
\(613\) −1.25045 3.84848i −0.0505051 0.155439i 0.922623 0.385703i \(-0.126041\pi\)
−0.973128 + 0.230264i \(0.926041\pi\)
\(614\) 18.5979 57.2385i 0.750551 2.30996i
\(615\) 0 0
\(616\) −1.81431 5.58389i −0.0731008 0.224981i
\(617\) 30.0752 21.8509i 1.21078 0.879683i 0.215479 0.976509i \(-0.430869\pi\)
0.995301 + 0.0968252i \(0.0308688\pi\)
\(618\) 4.44986 0.179000
\(619\) 30.5095 22.1664i 1.22628 0.890944i 0.229674 0.973268i \(-0.426234\pi\)
0.996606 + 0.0823236i \(0.0262341\pi\)
\(620\) 0 0
\(621\) −8.35477 6.07010i −0.335266 0.243585i
\(622\) −16.9419 12.3090i −0.679309 0.493547i
\(623\) −12.6421 + 38.9083i −0.506494 + 1.55883i
\(624\) −4.94839 −0.198094
\(625\) 0 0
\(626\) −77.2903 −3.08914
\(627\) 0.349647 1.07610i 0.0139636 0.0429754i
\(628\) −20.6906 15.0326i −0.825644 0.599866i
\(629\) 18.9903 + 13.7972i 0.757192 + 0.550132i
\(630\) 0 0
\(631\) −14.9850 + 10.8872i −0.596543 + 0.433414i −0.844650 0.535319i \(-0.820192\pi\)
0.248107 + 0.968733i \(0.420192\pi\)
\(632\) 54.4362 2.16536
\(633\) −29.6406 + 21.5352i −1.17811 + 0.855947i
\(634\) −18.6669 57.4507i −0.741356 2.28166i
\(635\) 0 0
\(636\) 0.746419 2.29724i 0.0295975 0.0910916i
\(637\) −4.84286 14.9048i −0.191881 0.590549i
\(638\) −1.99302 6.13388i −0.0789043 0.242843i
\(639\) −0.108036 + 0.332502i −0.00427385 + 0.0131536i
\(640\) 0 0
\(641\) −6.09121 18.7468i −0.240588 0.740454i −0.996331 0.0855856i \(-0.972724\pi\)
0.755743 0.654869i \(-0.227276\pi\)
\(642\) 0.313181 0.227539i 0.0123603 0.00898026i
\(643\) −42.5897 −1.67957 −0.839787 0.542916i \(-0.817320\pi\)
−0.839787 + 0.542916i \(0.817320\pi\)
\(644\) −63.6110 + 46.2161i −2.50662 + 1.82117i
\(645\) 0 0
\(646\) 9.48871 + 6.89395i 0.373328 + 0.271239i
\(647\) 22.1685 + 16.1064i 0.871535 + 0.633207i 0.930998 0.365023i \(-0.118939\pi\)
−0.0594633 + 0.998230i \(0.518939\pi\)
\(648\) 10.7580 33.1099i 0.422616 1.30068i
\(649\) 0.630424 0.0247463
\(650\) 0 0
\(651\) −50.1062 −1.96382
\(652\) −2.05799 + 6.33384i −0.0805971 + 0.248052i
\(653\) 17.3465 + 12.6030i 0.678820 + 0.493192i 0.872966 0.487781i \(-0.162193\pi\)
−0.194146 + 0.980973i \(0.562193\pi\)
\(654\) 24.2463 + 17.6160i 0.948105 + 0.688838i
\(655\) 0 0
\(656\) 1.88781 1.37157i 0.0737064 0.0535509i
\(657\) 34.2200 1.33505
\(658\) 36.3107 26.3812i 1.41554 1.02845i
\(659\) −11.3515 34.9363i −0.442191 1.36092i −0.885535 0.464572i \(-0.846208\pi\)
0.443344 0.896351i \(-0.353792\pi\)
\(660\) 0 0
\(661\) −4.86750 + 14.9806i −0.189324 + 0.582678i −0.999996 0.00282182i \(-0.999102\pi\)
0.810672 + 0.585500i \(0.199102\pi\)
\(662\) −8.71794 26.8310i −0.338832 1.04282i
\(663\) 9.62119 + 29.6110i 0.373656 + 1.14999i
\(664\) 14.8011 45.5530i 0.574393 1.76780i
\(665\) 0 0
\(666\) −7.60069 23.3925i −0.294521 0.906442i
\(667\) −28.9022 + 20.9987i −1.11910 + 0.813071i
\(668\) 1.21620 0.0470561
\(669\) −0.707244 + 0.513843i −0.0273436 + 0.0198663i
\(670\) 0 0
\(671\) −2.50743 1.82175i −0.0967982 0.0703280i
\(672\) 31.2975 + 22.7389i 1.20733 + 0.877173i
\(673\) −9.58283 + 29.4929i −0.369391 + 1.13687i 0.577795 + 0.816182i \(0.303913\pi\)
−0.947186 + 0.320686i \(0.896087\pi\)
\(674\) −70.3690 −2.71051
\(675\) 0 0
\(676\) −20.4259 −0.785611
\(677\) 2.96620 9.12902i 0.114000 0.350857i −0.877737 0.479143i \(-0.840948\pi\)
0.991737 + 0.128286i \(0.0409476\pi\)
\(678\) 11.2752 + 8.19190i 0.433021 + 0.314608i
\(679\) −2.46928 1.79404i −0.0947624 0.0688489i
\(680\) 0 0
\(681\) 37.8127 27.4726i 1.44899 1.05275i
\(682\) 7.01120 0.268473
\(683\) −0.702510 + 0.510403i −0.0268808 + 0.0195300i −0.601145 0.799140i \(-0.705288\pi\)
0.574264 + 0.818670i \(0.305288\pi\)
\(684\) −2.39398 7.36793i −0.0915363 0.281720i
\(685\) 0 0
\(686\) −2.79385 + 8.59859i −0.106670 + 0.328296i
\(687\) −8.47388 26.0799i −0.323299 0.995011i
\(688\) 2.38004 + 7.32500i 0.0907381 + 0.279263i
\(689\) −0.251692 + 0.774627i −0.00958868 + 0.0295109i
\(690\) 0 0
\(691\) −4.05970 12.4945i −0.154438 0.475312i 0.843665 0.536869i \(-0.180393\pi\)
−0.998104 + 0.0615577i \(0.980393\pi\)
\(692\) −27.4565 + 19.9483i −1.04374 + 0.758320i
\(693\) 4.11625 0.156364
\(694\) 25.0820 18.2231i 0.952099 0.691740i
\(695\) 0 0
\(696\) −34.0452 24.7353i −1.29048 0.937589i
\(697\) −11.8779 8.62979i −0.449907 0.326877i
\(698\) 19.7272 60.7139i 0.746684 2.29806i
\(699\) 43.8844 1.65986
\(700\) 0 0
\(701\) 7.13602 0.269524 0.134762 0.990878i \(-0.456973\pi\)
0.134762 + 0.990878i \(0.456973\pi\)
\(702\) −3.06458 + 9.43181i −0.115665 + 0.355981i
\(703\) 3.67103 + 2.66716i 0.138456 + 0.100594i
\(704\) −5.03313 3.65678i −0.189693 0.137820i
\(705\) 0 0
\(706\) −29.2749 + 21.2695i −1.10178 + 0.800486i
\(707\) 47.6231 1.79105
\(708\) 8.04563 5.84549i 0.302373 0.219687i
\(709\) −2.47372 7.61333i −0.0929025 0.285925i 0.893799 0.448468i \(-0.148030\pi\)
−0.986701 + 0.162543i \(0.948030\pi\)
\(710\) 0 0
\(711\) −11.7935 + 36.2966i −0.442290 + 1.36123i
\(712\) −11.5422 35.5232i −0.432562 1.33129i
\(713\) −12.0010 36.9354i −0.449442 1.38324i
\(714\) −30.3784 + 93.4952i −1.13688 + 3.49897i
\(715\) 0 0
\(716\) 16.2127 + 49.8976i 0.605898 + 1.86476i
\(717\) −7.68313 + 5.58212i −0.286932 + 0.208468i
\(718\) 51.1345 1.90832
\(719\) 33.3774 24.2501i 1.24477 0.904375i 0.246859 0.969051i \(-0.420602\pi\)
0.997906 + 0.0646763i \(0.0206015\pi\)
\(720\) 0 0
\(721\) −2.41612 1.75542i −0.0899811 0.0653751i
\(722\) −33.9210 24.6450i −1.26241 0.917193i
\(723\) 11.5155 35.4409i 0.428265 1.31806i
\(724\) 30.4210 1.13059
\(725\) 0 0
\(726\) 57.5825 2.13709
\(727\) −12.1321 + 37.3387i −0.449954 + 1.38482i 0.427005 + 0.904249i \(0.359569\pi\)
−0.876959 + 0.480566i \(0.840431\pi\)
\(728\) 25.2664 + 18.3571i 0.936436 + 0.680360i
\(729\) 10.7490 + 7.80957i 0.398109 + 0.289243i
\(730\) 0 0
\(731\) 39.2050 28.4841i 1.45005 1.05352i
\(732\) −48.8924 −1.80711
\(733\) 0.737868 0.536092i 0.0272538 0.0198010i −0.574075 0.818803i \(-0.694638\pi\)
0.601329 + 0.799002i \(0.294638\pi\)
\(734\) 8.70498 + 26.7912i 0.321307 + 0.988880i
\(735\) 0 0
\(736\) −9.26570 + 28.5169i −0.341538 + 1.05115i
\(737\) −0.813158 2.50264i −0.0299531 0.0921860i
\(738\) 4.75402 + 14.6314i 0.174998 + 0.538588i
\(739\) −3.61367 + 11.1217i −0.132931 + 0.409119i −0.995262 0.0972247i \(-0.969003\pi\)
0.862331 + 0.506344i \(0.169003\pi\)
\(740\) 0 0
\(741\) 1.85988 + 5.72413i 0.0683245 + 0.210281i
\(742\) −2.08056 + 1.51162i −0.0763798 + 0.0554932i
\(743\) −11.5631 −0.424211 −0.212105 0.977247i \(-0.568032\pi\)
−0.212105 + 0.977247i \(0.568032\pi\)
\(744\) 37.0101 26.8894i 1.35685 0.985813i
\(745\) 0 0
\(746\) −13.3349 9.68837i −0.488225 0.354717i
\(747\) 27.1669 + 19.7379i 0.993986 + 0.722173i
\(748\) 2.67953 8.24673i 0.0979732 0.301530i
\(749\) −0.259808 −0.00949318
\(750\) 0 0
\(751\) −27.2430 −0.994112 −0.497056 0.867718i \(-0.665586\pi\)
−0.497056 + 0.867718i \(0.665586\pi\)
\(752\) −1.34655 + 4.14425i −0.0491036 + 0.151125i
\(753\) −22.1126 16.0658i −0.805828 0.585469i
\(754\) 27.7551 + 20.1652i 1.01078 + 0.734374i
\(755\) 0 0
\(756\) −15.9689 + 11.6021i −0.580784 + 0.421964i
\(757\) −17.1080 −0.621800 −0.310900 0.950443i \(-0.600630\pi\)
−0.310900 + 0.950443i \(0.600630\pi\)
\(758\) −40.4655 + 29.3999i −1.46977 + 1.06785i
\(759\) 2.27147 + 6.99088i 0.0824493 + 0.253753i
\(760\) 0 0
\(761\) 11.6553 35.8713i 0.422504 1.30033i −0.482861 0.875697i \(-0.660402\pi\)
0.905364 0.424635i \(-0.139598\pi\)
\(762\) 8.18327 + 25.1855i 0.296449 + 0.912375i
\(763\) −6.21562 19.1297i −0.225021 0.692542i
\(764\) −12.0034 + 36.9428i −0.434269 + 1.33654i
\(765\) 0 0
\(766\) 17.8850 + 55.0445i 0.646213 + 1.98884i
\(767\) −2.71297 + 1.97109i −0.0979598 + 0.0711720i
\(768\) −48.0682 −1.73451
\(769\) 4.80028 3.48761i 0.173102 0.125766i −0.497861 0.867257i \(-0.665881\pi\)
0.670963 + 0.741491i \(0.265881\pi\)
\(770\) 0 0
\(771\) −35.2338 25.5989i −1.26892 0.921921i
\(772\) 47.8253 + 34.7471i 1.72127 + 1.25058i
\(773\) −7.28997 + 22.4362i −0.262202 + 0.806975i 0.730123 + 0.683316i \(0.239463\pi\)
−0.992325 + 0.123659i \(0.960537\pi\)
\(774\) −50.7786 −1.82520
\(775\) 0 0
\(776\) 2.78666 0.100035
\(777\) −11.7529 + 36.1718i −0.421634 + 1.29766i
\(778\) −66.6444 48.4200i −2.38932 1.73594i
\(779\) −2.29613 1.66824i −0.0822674 0.0597708i
\(780\) 0 0
\(781\) −0.0611983 + 0.0444632i −0.00218985 + 0.00159102i
\(782\) −76.1952 −2.72473
\(783\) −7.25561 + 5.27151i −0.259294 + 0.188388i
\(784\) 1.48457 + 4.56905i 0.0530205 + 0.163180i
\(785\) 0 0
\(786\) −4.47393 + 13.7693i −0.159580 + 0.491136i
\(787\) 5.63359 + 17.3384i 0.200816 + 0.618048i 0.999859 + 0.0167744i \(0.00533970\pi\)
−0.799043 + 0.601273i \(0.794660\pi\)
\(788\) −27.3623 84.2125i −0.974741 2.99994i
\(789\) 4.80020 14.7735i 0.170892 0.525950i
\(790\) 0 0
\(791\) −2.89043 8.89584i −0.102772 0.316300i
\(792\) −3.04040 + 2.20898i −0.108036 + 0.0784926i
\(793\) 16.4864 0.585451
\(794\) −10.3446 + 7.51583i −0.367118 + 0.266727i
\(795\) 0 0
\(796\) 23.1391 + 16.8116i 0.820145 + 0.595870i
\(797\) −8.76130 6.36546i −0.310341 0.225476i 0.421702 0.906735i \(-0.361433\pi\)
−0.732043 + 0.681259i \(0.761433\pi\)
\(798\) −5.87249 + 18.0737i −0.207884 + 0.639801i
\(799\) 27.4171 0.969948
\(800\) 0 0
\(801\) 26.1865 0.925256
\(802\) −17.8596 + 54.9663i −0.630646 + 1.94093i
\(803\) 5.99007 + 4.35204i 0.211385 + 0.153580i
\(804\) −33.5830 24.3995i −1.18438 0.860505i
\(805\) 0 0
\(806\) −30.1721 + 21.9213i −1.06277 + 0.772145i
\(807\) −58.3242 −2.05311
\(808\) −35.1759 + 25.5568i −1.23749 + 0.899086i
\(809\) 13.8494 + 42.6242i 0.486920 + 1.49859i 0.829180 + 0.558981i \(0.188808\pi\)
−0.342260 + 0.939605i \(0.611192\pi\)
\(810\) 0 0
\(811\) −0.946507 + 2.91305i −0.0332363 + 0.102291i −0.966298 0.257424i \(-0.917126\pi\)
0.933062 + 0.359715i \(0.117126\pi\)
\(812\) 21.1006 + 64.9411i 0.740487 + 2.27899i
\(813\) 6.69289 + 20.5986i 0.234730 + 0.722425i
\(814\) 1.64455 5.06140i 0.0576414 0.177402i
\(815\) 0 0
\(816\) −2.94937 9.07721i −0.103248 0.317766i
\(817\) 7.57876 5.50629i 0.265147 0.192641i
\(818\) −9.14524 −0.319756
\(819\) −17.7140 + 12.8699i −0.618976 + 0.449712i
\(820\) 0 0
\(821\) −16.4400 11.9444i −0.573761 0.416862i 0.262708 0.964875i \(-0.415384\pi\)
−0.836470 + 0.548013i \(0.815384\pi\)
\(822\) 9.74137 + 7.07752i 0.339769 + 0.246857i
\(823\) 15.4623 47.5879i 0.538980 1.65881i −0.195907 0.980622i \(-0.562765\pi\)
0.734888 0.678189i \(-0.237235\pi\)
\(824\) 2.72666 0.0949879
\(825\) 0 0
\(826\) −10.5883 −0.368413
\(827\) 9.77399 30.0812i 0.339875 1.04603i −0.624396 0.781108i \(-0.714655\pi\)
0.964271 0.264919i \(-0.0853453\pi\)
\(828\) 40.7169 + 29.5825i 1.41501 + 1.02806i
\(829\) −26.8083 19.4774i −0.931090 0.676477i 0.0151691 0.999885i \(-0.495171\pi\)
−0.946260 + 0.323408i \(0.895171\pi\)
\(830\) 0 0
\(831\) −11.1149 + 8.07543i −0.385571 + 0.280133i
\(832\) 33.0930 1.14729
\(833\) 24.4545 17.7672i 0.847298 0.615598i
\(834\) 17.8784 + 55.0241i 0.619078 + 1.90533i
\(835\) 0 0
\(836\) 0.517983 1.59419i 0.0179148 0.0551361i
\(837\) −3.01274 9.27227i −0.104136 0.320496i
\(838\) 3.42586 + 10.5437i 0.118344 + 0.364226i
\(839\) 3.20925 9.87707i 0.110796 0.340994i −0.880251 0.474508i \(-0.842626\pi\)
0.991047 + 0.133514i \(0.0426260\pi\)
\(840\) 0 0
\(841\) 0.625759 + 1.92589i 0.0215779 + 0.0664099i
\(842\) 30.2191 21.9554i 1.04142 0.756634i
\(843\) 25.4918 0.877986
\(844\) −43.9110 + 31.9032i −1.51148 + 1.09815i
\(845\) 0 0
\(846\) −23.2422 16.8864i −0.799082 0.580567i
\(847\) −31.2653 22.7156i −1.07429 0.780517i
\(848\) 0.0771558 0.237461i 0.00264954 0.00815445i
\(849\) 6.96235 0.238947
\(850\) 0 0
\(851\) −29.4787 −1.01052
\(852\) −0.368752 + 1.13490i −0.0126332 + 0.0388811i
\(853\) −7.53563 5.47496i −0.258015 0.187459i 0.451256 0.892394i \(-0.350976\pi\)
−0.709272 + 0.704935i \(0.750976\pi\)
\(854\) 42.1135 + 30.5972i 1.44109 + 1.04702i
\(855\) 0 0
\(856\) 0.191902 0.139425i 0.00655909 0.00476546i
\(857\) 34.0314 1.16249 0.581245 0.813729i \(-0.302566\pi\)
0.581245 + 0.813729i \(0.302566\pi\)
\(858\) 5.71077 4.14912i 0.194963 0.141649i
\(859\) 10.3287 + 31.7884i 0.352410 + 1.08461i 0.957496 + 0.288446i \(0.0931386\pi\)
−0.605086 + 0.796160i \(0.706861\pi\)
\(860\) 0 0
\(861\) 7.35114 22.6245i 0.250526 0.771040i
\(862\) 29.7364 + 91.5193i 1.01283 + 3.11716i
\(863\) −5.12659 15.7780i −0.174511 0.537091i 0.825099 0.564987i \(-0.191119\pi\)
−0.999611 + 0.0278969i \(0.991119\pi\)
\(864\) −2.32606 + 7.15889i −0.0791343 + 0.243550i
\(865\) 0 0
\(866\) 10.9153 + 33.5939i 0.370918 + 1.14157i
\(867\) −16.9188 + 12.2922i −0.574592 + 0.417465i
\(868\) −74.2296 −2.51952
\(869\) −6.68054 + 4.85370i −0.226622 + 0.164650i
\(870\) 0 0
\(871\) 11.3242 + 8.22748i 0.383704 + 0.278778i
\(872\) 14.8570 + 10.7942i 0.503120 + 0.365538i
\(873\) −0.603724 + 1.85807i −0.0204330 + 0.0628862i
\(874\) −14.7294 −0.498229
\(875\) 0 0
\(876\) 116.800 3.94632
\(877\) 10.1833 31.3409i 0.343865 1.05831i −0.618324 0.785923i \(-0.712188\pi\)
0.962189 0.272383i \(-0.0878118\pi\)
\(878\) 32.2162 + 23.4064i 1.08724 + 0.789929i
\(879\) 11.6679 + 8.47721i 0.393548 + 0.285929i
\(880\) 0 0
\(881\) 40.5119 29.4337i 1.36488 0.991645i 0.366765 0.930314i \(-0.380465\pi\)
0.998117 0.0613312i \(-0.0195346\pi\)
\(882\) −31.6737 −1.06651
\(883\) 10.1398 7.36700i 0.341232 0.247919i −0.403950 0.914781i \(-0.632363\pi\)
0.745181 + 0.666862i \(0.232363\pi\)
\(884\) 14.2532 + 43.8670i 0.479389 + 1.47541i
\(885\) 0 0
\(886\) 25.4391 78.2936i 0.854645 2.63033i
\(887\) −8.32361 25.6174i −0.279480 0.860150i −0.987999 0.154459i \(-0.950637\pi\)
0.708520 0.705691i \(-0.249363\pi\)
\(888\) −10.7304 33.0248i −0.360089 1.10824i
\(889\) 5.49214 16.9031i 0.184200 0.566911i
\(890\) 0 0
\(891\) 1.63192 + 5.02254i 0.0546715 + 0.168261i
\(892\) −1.04774 + 0.761229i −0.0350810 + 0.0254878i
\(893\) 5.30004 0.177359
\(894\) 52.8050 38.3651i 1.76606 1.28312i
\(895\) 0 0
\(896\) 57.3460 + 41.6643i 1.91579 + 1.39191i
\(897\) −31.6329 22.9826i −1.05619 0.767368i
\(898\) −14.8670 + 45.7560i −0.496119 + 1.52690i
\(899\) −33.7268 −1.12485
\(900\) 0 0
\(901\) −1.57097 −0.0523366
\(902\) −1.02862 + 3.16577i −0.0342493 + 0.105409i
\(903\) 63.5231 + 46.1522i 2.11392 + 1.53585i
\(904\) 6.90889 + 5.01961i 0.229786 + 0.166950i
\(905\) 0 0
\(906\) 74.0272 53.7839i 2.45939 1.78685i
\(907\) 28.6510 0.951342 0.475671 0.879623i \(-0.342205\pi\)
0.475671 + 0.879623i \(0.342205\pi\)
\(908\) 56.0174 40.6991i 1.85900 1.35065i
\(909\) −9.41982 28.9912i −0.312436 0.961578i
\(910\) 0 0
\(911\) −2.75047 + 8.46508i −0.0911271 + 0.280461i −0.986225 0.165409i \(-0.947106\pi\)
0.895098 + 0.445870i \(0.147106\pi\)
\(912\) −0.570146 1.75473i −0.0188794 0.0581048i
\(913\) 2.24522 + 6.91008i 0.0743060 + 0.228690i
\(914\) 30.0219 92.3980i 0.993037 3.05625i
\(915\) 0 0
\(916\) −12.5536 38.6359i −0.414782 1.27657i
\(917\) 7.86102 5.71137i 0.259594 0.188606i
\(918\) −19.1280 −0.631320
\(919\) −13.9071 + 10.1041i −0.458753 + 0.333303i −0.793042 0.609167i \(-0.791504\pi\)
0.334289 + 0.942471i \(0.391504\pi\)
\(920\) 0 0
\(921\) 48.1921 + 35.0136i 1.58798 + 1.15374i
\(922\) −20.0951 14.5999i −0.661796 0.480823i
\(923\) 0.124343 0.382687i 0.00409279 0.0125963i
\(924\) 14.0497 0.462200
\(925\) 0 0
\(926\) −18.2141 −0.598554
\(927\) −0.590726 + 1.81807i −0.0194020 + 0.0597132i
\(928\) 21.0665 + 15.3057i 0.691542 + 0.502435i
\(929\) −28.1367 20.4425i −0.923137 0.670698i 0.0211662 0.999776i \(-0.493262\pi\)
−0.944303 + 0.329078i \(0.893262\pi\)
\(930\) 0 0
\(931\) 4.72733 3.43461i 0.154932 0.112565i
\(932\) 65.0123 2.12955
\(933\) 16.7686 12.1831i 0.548981 0.398858i
\(934\) 3.58036 + 11.0192i 0.117153 + 0.360560i
\(935\) 0 0
\(936\) 6.17747 19.0123i 0.201917 0.621437i
\(937\) 5.11071 + 15.7291i 0.166960 + 0.513849i 0.999175 0.0406033i \(-0.0129280\pi\)
−0.832216 + 0.554452i \(0.812928\pi\)
\(938\) 13.6574 + 42.0331i 0.445929 + 1.37243i
\(939\) 23.6398 72.7557i 0.771455 2.37429i
\(940\) 0 0
\(941\) 12.7310 + 39.1818i 0.415017 + 1.27729i 0.912235 + 0.409666i \(0.134355\pi\)
−0.497218 + 0.867626i \(0.665645\pi\)
\(942\) 32.4875 23.6036i 1.05850 0.769045i
\(943\) 18.4381 0.600428
\(944\) 0.831660 0.604236i 0.0270682 0.0196662i
\(945\) 0 0
\(946\) −8.88857 6.45792i −0.288992 0.209965i
\(947\) −30.0234 21.8133i −0.975629 0.708836i −0.0189019 0.999821i \(-0.506017\pi\)
−0.956728 + 0.290985i \(0.906017\pi\)
\(948\) −40.2537 + 123.888i −1.30738 + 4.02370i
\(949\) −39.3849 −1.27849
\(950\) 0 0
\(951\) 59.7895 1.93881
\(952\) −18.6145 + 57.2894i −0.603298 + 1.85676i
\(953\) 16.9054 + 12.2825i 0.547619 + 0.397869i 0.826907 0.562339i \(-0.190098\pi\)
−0.279288 + 0.960207i \(0.590098\pi\)
\(954\) 1.33175 + 0.967573i 0.0431170 + 0.0313263i
\(955\) 0 0
\(956\) −11.3821 + 8.26960i −0.368124 + 0.267458i
\(957\) 6.38358 0.206352
\(958\) −30.8588 + 22.4202i −0.997002 + 0.724364i
\(959\) −2.49723 7.68570i −0.0806399 0.248184i
\(960\) 0 0
\(961\) 1.75025 5.38670i 0.0564595 0.173765i
\(962\) 8.74788 + 26.9232i 0.282043 + 0.868039i
\(963\) 0.0513898 + 0.158162i 0.00165601 + 0.00509669i
\(964\) 17.0595 52.5038i 0.549450 1.69103i
\(965\) 0 0
\(966\) −38.1505 117.415i −1.22747 3.77777i
\(967\) 6.69912 4.86720i 0.215429 0.156518i −0.474838 0.880073i \(-0.657493\pi\)
0.690267 + 0.723555i \(0.257493\pi\)
\(968\) 35.2838 1.13407
\(969\) −9.39167 + 6.82345i −0.301704 + 0.219201i
\(970\) 0 0
\(971\) 21.3643 + 15.5220i 0.685612 + 0.498126i 0.875215 0.483735i \(-0.160720\pi\)
−0.189603 + 0.981861i \(0.560720\pi\)
\(972\) 54.0689 + 39.2834i 1.73426 + 1.26001i
\(973\) 11.9990 36.9290i 0.384669 1.18389i
\(974\) 2.03885 0.0653289
\(975\) 0 0
\(976\) −5.05390 −0.161771
\(977\) −7.82677 + 24.0883i −0.250401 + 0.770654i 0.744300 + 0.667845i \(0.232783\pi\)
−0.994701 + 0.102809i \(0.967217\pi\)
\(978\) −8.45983 6.14643i −0.270516 0.196541i
\(979\) 4.58384 + 3.33036i 0.146500 + 0.106439i
\(980\) 0 0
\(981\) −10.4160 + 7.56769i −0.332558 + 0.241618i
\(982\) −28.4059 −0.906470
\(983\) −4.14873 + 3.01423i −0.132324 + 0.0961390i −0.651978 0.758238i \(-0.726061\pi\)
0.519654 + 0.854377i \(0.326061\pi\)
\(984\) 6.71158 + 20.6561i 0.213957 + 0.658493i
\(985\) 0 0
\(986\) −20.4479 + 62.9322i −0.651194 + 2.00417i
\(987\) 13.7276 + 42.2492i 0.436954 + 1.34481i
\(988\) 2.75531 + 8.47998i 0.0876582 + 0.269784i
\(989\) −18.8062 + 57.8795i −0.598002 + 1.84046i
\(990\) 0 0
\(991\) −8.20120 25.2407i −0.260520 0.801797i −0.992692 0.120677i \(-0.961493\pi\)
0.732172 0.681120i \(-0.238507\pi\)
\(992\) −22.9011 + 16.6386i −0.727110 + 0.528277i
\(993\) 27.9233 0.886120
\(994\) 1.02785 0.746780i 0.0326016 0.0236864i
\(995\) 0 0
\(996\) 92.7267 + 67.3699i 2.93816 + 2.13470i
\(997\) 35.9991 + 26.1549i 1.14010 + 0.828332i 0.987133 0.159899i \(-0.0511168\pi\)
0.152968 + 0.988231i \(0.451117\pi\)
\(998\) 2.40514 7.40227i 0.0761335 0.234315i
\(999\) −7.40034 −0.234136
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 625.2.d.p.501.2 16
5.2 odd 4 625.2.e.k.124.2 32
5.3 odd 4 625.2.e.k.124.7 32
5.4 even 2 625.2.d.n.501.3 16
25.2 odd 20 625.2.e.j.249.2 32
25.3 odd 20 625.2.e.j.374.2 32
25.4 even 10 625.2.d.m.251.2 16
25.6 even 5 inner 625.2.d.p.126.2 16
25.8 odd 20 625.2.e.k.499.2 32
25.9 even 10 625.2.a.g.1.6 yes 8
25.11 even 5 625.2.d.q.376.3 16
25.12 odd 20 625.2.b.d.624.3 16
25.13 odd 20 625.2.b.d.624.14 16
25.14 even 10 625.2.d.m.376.2 16
25.16 even 5 625.2.a.e.1.3 8
25.17 odd 20 625.2.e.k.499.7 32
25.19 even 10 625.2.d.n.126.3 16
25.21 even 5 625.2.d.q.251.3 16
25.22 odd 20 625.2.e.j.374.7 32
25.23 odd 20 625.2.e.j.249.7 32
75.41 odd 10 5625.2.a.be.1.6 8
75.59 odd 10 5625.2.a.s.1.3 8
100.59 odd 10 10000.2.a.be.1.8 8
100.91 odd 10 10000.2.a.bn.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
625.2.a.e.1.3 8 25.16 even 5
625.2.a.g.1.6 yes 8 25.9 even 10
625.2.b.d.624.3 16 25.12 odd 20
625.2.b.d.624.14 16 25.13 odd 20
625.2.d.m.251.2 16 25.4 even 10
625.2.d.m.376.2 16 25.14 even 10
625.2.d.n.126.3 16 25.19 even 10
625.2.d.n.501.3 16 5.4 even 2
625.2.d.p.126.2 16 25.6 even 5 inner
625.2.d.p.501.2 16 1.1 even 1 trivial
625.2.d.q.251.3 16 25.21 even 5
625.2.d.q.376.3 16 25.11 even 5
625.2.e.j.249.2 32 25.2 odd 20
625.2.e.j.249.7 32 25.23 odd 20
625.2.e.j.374.2 32 25.3 odd 20
625.2.e.j.374.7 32 25.22 odd 20
625.2.e.k.124.2 32 5.2 odd 4
625.2.e.k.124.7 32 5.3 odd 4
625.2.e.k.499.2 32 25.8 odd 20
625.2.e.k.499.7 32 25.17 odd 20
5625.2.a.s.1.3 8 75.59 odd 10
5625.2.a.be.1.6 8 75.41 odd 10
10000.2.a.be.1.8 8 100.59 odd 10
10000.2.a.bn.1.1 8 100.91 odd 10