Properties

Label 525.2.bc.e.418.3
Level $525$
Weight $2$
Character 525.418
Analytic conductor $4.192$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(82,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bc (of order \(12\), degree \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 418.3
Character \(\chi\) \(=\) 525.418
Dual form 525.2.bc.e.157.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.259789 - 0.969545i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.859523 - 0.496246i) q^{4} +1.00375i q^{6} +(1.06195 + 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.259789 - 0.969545i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.859523 - 0.496246i) q^{4} +1.00375i q^{6} +(1.06195 + 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.78283 - 3.08796i) q^{11} +(-0.958673 + 0.256876i) q^{12} +(2.78368 - 2.78368i) q^{13} +(2.07359 - 1.65915i) q^{14} +(-0.514988 + 0.891986i) q^{16} +(0.135713 - 0.506489i) q^{17} +(0.259789 - 0.969545i) q^{18} +(2.06188 - 3.57128i) q^{19} +(-0.398574 - 2.61556i) q^{21} +(-2.53075 + 2.53075i) q^{22} +(2.49427 - 0.668338i) q^{23} +(1.50185 + 2.60128i) q^{24} +(-3.42207 - 1.97574i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.11531 + 1.55587i) q^{28} -6.14396i q^{29} +(-1.71173 + 0.988266i) q^{31} +(-4.80410 - 1.28726i) q^{32} +(0.922863 + 3.44417i) q^{33} -0.526321 q^{34} +0.992492 q^{36} +(0.0409435 + 0.152803i) q^{37} +(-3.99817 - 1.07131i) q^{38} +(-3.40930 + 1.96836i) q^{39} +8.28475i q^{41} +(-2.43236 + 1.06593i) q^{42} +(-9.01253 - 9.01253i) q^{43} +(-3.06477 - 1.76945i) q^{44} +(-1.29597 - 2.24468i) q^{46} +(5.19095 - 1.39091i) q^{47} +(0.728304 - 0.728304i) q^{48} +(-4.74453 + 5.14679i) q^{49} +(-0.262178 + 0.454106i) q^{51} +(1.01125 - 3.77403i) q^{52} +(1.48765 - 5.55200i) q^{53} +(-0.501874 + 0.869271i) q^{54} +(2.89138 - 7.40241i) q^{56} +(-2.91594 + 2.91594i) q^{57} +(-5.95685 + 1.59613i) q^{58} +(-1.30044 - 2.25243i) q^{59} +(8.67653 + 5.00940i) q^{61} +(1.40286 + 1.40286i) q^{62} +(-0.291963 + 2.62959i) q^{63} +7.05216i q^{64} +(3.09953 - 1.78951i) q^{66} +(-5.32418 - 1.42661i) q^{67} +(-0.134694 - 0.502686i) q^{68} -2.58226 q^{69} -7.23274 q^{71} +(-0.777416 - 2.90136i) q^{72} +(14.8625 + 3.98240i) q^{73} +(0.137513 - 0.0793931i) q^{74} -4.09280i q^{76} +(5.58969 - 7.59955i) q^{77} +(2.79411 + 2.79411i) q^{78} +(13.1146 + 7.57171i) q^{79} +(0.500000 + 0.866025i) q^{81} +(8.03244 - 2.15229i) q^{82} +(-9.42372 + 9.42372i) q^{83} +(-1.64054 - 2.05034i) q^{84} +(-6.39670 + 11.0794i) q^{86} +(-1.59017 + 5.93461i) q^{87} +(-2.77201 + 10.3453i) q^{88} +(5.52672 - 9.57257i) q^{89} +(9.70175 + 3.78950i) q^{91} +(1.81222 - 1.81222i) q^{92} +(1.90918 - 0.511564i) q^{93} +(-2.69710 - 4.67152i) q^{94} +(4.30724 + 2.48679i) q^{96} +(2.48828 + 2.48828i) q^{97} +(6.22262 + 3.26295i) q^{98} -3.56567i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.259789 0.969545i −0.183698 0.685572i −0.994905 0.100813i \(-0.967856\pi\)
0.811207 0.584759i \(-0.198811\pi\)
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) 0.859523 0.496246i 0.429762 0.248123i
\(5\) 0 0
\(6\) 1.00375i 0.409778i
\(7\) 1.06195 + 2.42328i 0.401379 + 0.915912i
\(8\) −2.12394 2.12394i −0.750926 0.750926i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) −1.78283 3.08796i −0.537545 0.931054i −0.999036 0.0439095i \(-0.986019\pi\)
0.461491 0.887145i \(-0.347315\pi\)
\(12\) −0.958673 + 0.256876i −0.276745 + 0.0741536i
\(13\) 2.78368 2.78368i 0.772054 0.772054i −0.206411 0.978465i \(-0.566178\pi\)
0.978465 + 0.206411i \(0.0661785\pi\)
\(14\) 2.07359 1.65915i 0.554191 0.443426i
\(15\) 0 0
\(16\) −0.514988 + 0.891986i −0.128747 + 0.222997i
\(17\) 0.135713 0.506489i 0.0329153 0.122842i −0.947513 0.319716i \(-0.896412\pi\)
0.980429 + 0.196874i \(0.0630791\pi\)
\(18\) 0.259789 0.969545i 0.0612328 0.228524i
\(19\) 2.06188 3.57128i 0.473028 0.819308i −0.526496 0.850178i \(-0.676494\pi\)
0.999523 + 0.0308699i \(0.00982775\pi\)
\(20\) 0 0
\(21\) −0.398574 2.61556i −0.0869761 0.570761i
\(22\) −2.53075 + 2.53075i −0.539559 + 0.539559i
\(23\) 2.49427 0.668338i 0.520092 0.139358i 0.0107826 0.999942i \(-0.496568\pi\)
0.509309 + 0.860584i \(0.329901\pi\)
\(24\) 1.50185 + 2.60128i 0.306564 + 0.530985i
\(25\) 0 0
\(26\) −3.42207 1.97574i −0.671124 0.387474i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.11531 + 1.55587i 0.399756 + 0.294032i
\(29\) 6.14396i 1.14091i −0.821331 0.570453i \(-0.806768\pi\)
0.821331 0.570453i \(-0.193232\pi\)
\(30\) 0 0
\(31\) −1.71173 + 0.988266i −0.307435 + 0.177498i −0.645778 0.763525i \(-0.723467\pi\)
0.338343 + 0.941023i \(0.390134\pi\)
\(32\) −4.80410 1.28726i −0.849253 0.227557i
\(33\) 0.922863 + 3.44417i 0.160650 + 0.599553i
\(34\) −0.526321 −0.0902633
\(35\) 0 0
\(36\) 0.992492 0.165415
\(37\) 0.0409435 + 0.152803i 0.00673106 + 0.0251207i 0.969210 0.246237i \(-0.0791941\pi\)
−0.962479 + 0.271357i \(0.912527\pi\)
\(38\) −3.99817 1.07131i −0.648589 0.173789i
\(39\) −3.40930 + 1.96836i −0.545925 + 0.315190i
\(40\) 0 0
\(41\) 8.28475i 1.29386i 0.762549 + 0.646930i \(0.223948\pi\)
−0.762549 + 0.646930i \(0.776052\pi\)
\(42\) −2.43236 + 1.06593i −0.375321 + 0.164476i
\(43\) −9.01253 9.01253i −1.37440 1.37440i −0.853805 0.520594i \(-0.825711\pi\)
−0.520594 0.853805i \(-0.674289\pi\)
\(44\) −3.06477 1.76945i −0.462032 0.266754i
\(45\) 0 0
\(46\) −1.29597 2.24468i −0.191080 0.330960i
\(47\) 5.19095 1.39091i 0.757178 0.202885i 0.140478 0.990084i \(-0.455136\pi\)
0.616700 + 0.787198i \(0.288469\pi\)
\(48\) 0.728304 0.728304i 0.105122 0.105122i
\(49\) −4.74453 + 5.14679i −0.677790 + 0.735256i
\(50\) 0 0
\(51\) −0.262178 + 0.454106i −0.0367123 + 0.0635875i
\(52\) 1.01125 3.77403i 0.140235 0.523363i
\(53\) 1.48765 5.55200i 0.204345 0.762626i −0.785303 0.619111i \(-0.787493\pi\)
0.989648 0.143514i \(-0.0458404\pi\)
\(54\) −0.501874 + 0.869271i −0.0682963 + 0.118293i
\(55\) 0 0
\(56\) 2.89138 7.40241i 0.386376 0.989188i
\(57\) −2.91594 + 2.91594i −0.386225 + 0.386225i
\(58\) −5.95685 + 1.59613i −0.782173 + 0.209583i
\(59\) −1.30044 2.25243i −0.169303 0.293242i 0.768872 0.639403i \(-0.220818\pi\)
−0.938175 + 0.346161i \(0.887485\pi\)
\(60\) 0 0
\(61\) 8.67653 + 5.00940i 1.11092 + 0.641387i 0.939066 0.343736i \(-0.111692\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(62\) 1.40286 + 1.40286i 0.178163 + 0.178163i
\(63\) −0.291963 + 2.62959i −0.0367838 + 0.331298i
\(64\) 7.05216i 0.881521i
\(65\) 0 0
\(66\) 3.09953 1.78951i 0.381526 0.220274i
\(67\) −5.32418 1.42661i −0.650452 0.174288i −0.0815189 0.996672i \(-0.525977\pi\)
−0.568933 + 0.822384i \(0.692644\pi\)
\(68\) −0.134694 0.502686i −0.0163341 0.0609596i
\(69\) −2.58226 −0.310868
\(70\) 0 0
\(71\) −7.23274 −0.858369 −0.429184 0.903217i \(-0.641199\pi\)
−0.429184 + 0.903217i \(0.641199\pi\)
\(72\) −0.777416 2.90136i −0.0916194 0.341928i
\(73\) 14.8625 + 3.98240i 1.73953 + 0.466105i 0.982342 0.187096i \(-0.0599077\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(74\) 0.137513 0.0793931i 0.0159855 0.00922926i
\(75\) 0 0
\(76\) 4.09280i 0.469476i
\(77\) 5.58969 7.59955i 0.637005 0.866049i
\(78\) 2.79411 + 2.79411i 0.316371 + 0.316371i
\(79\) 13.1146 + 7.57171i 1.47551 + 0.851884i 0.999618 0.0276214i \(-0.00879330\pi\)
0.475888 + 0.879506i \(0.342127\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 8.03244 2.15229i 0.887035 0.237680i
\(83\) −9.42372 + 9.42372i −1.03439 + 1.03439i −0.0350007 + 0.999387i \(0.511143\pi\)
−0.999387 + 0.0350007i \(0.988857\pi\)
\(84\) −1.64054 2.05034i −0.178998 0.223710i
\(85\) 0 0
\(86\) −6.39670 + 11.0794i −0.689774 + 1.19472i
\(87\) −1.59017 + 5.93461i −0.170485 + 0.636257i
\(88\) −2.77201 + 10.3453i −0.295497 + 1.10281i
\(89\) 5.52672 9.57257i 0.585831 1.01469i −0.408940 0.912561i \(-0.634101\pi\)
0.994771 0.102128i \(-0.0325653\pi\)
\(90\) 0 0
\(91\) 9.70175 + 3.78950i 1.01702 + 0.397247i
\(92\) 1.81222 1.81222i 0.188937 0.188937i
\(93\) 1.90918 0.511564i 0.197973 0.0530467i
\(94\) −2.69710 4.67152i −0.278185 0.481830i
\(95\) 0 0
\(96\) 4.30724 + 2.48679i 0.439606 + 0.253807i
\(97\) 2.48828 + 2.48828i 0.252647 + 0.252647i 0.822055 0.569408i \(-0.192828\pi\)
−0.569408 + 0.822055i \(0.692828\pi\)
\(98\) 6.22262 + 3.26295i 0.628580 + 0.329608i
\(99\) 3.56567i 0.358363i
\(100\) 0 0
\(101\) 0.739502 0.426952i 0.0735832 0.0424833i −0.462757 0.886485i \(-0.653140\pi\)
0.536340 + 0.844002i \(0.319806\pi\)
\(102\) 0.508387 + 0.136222i 0.0503378 + 0.0134880i
\(103\) 1.57114 + 5.86357i 0.154809 + 0.577755i 0.999122 + 0.0419040i \(0.0133424\pi\)
−0.844313 + 0.535851i \(0.819991\pi\)
\(104\) −11.8247 −1.15951
\(105\) 0 0
\(106\) −5.76939 −0.560373
\(107\) 3.02740 + 11.2984i 0.292670 + 1.09226i 0.943051 + 0.332650i \(0.107943\pi\)
−0.650381 + 0.759608i \(0.725391\pi\)
\(108\) −0.958673 0.256876i −0.0922484 0.0247179i
\(109\) −10.8565 + 6.26802i −1.03987 + 0.600367i −0.919796 0.392398i \(-0.871646\pi\)
−0.120071 + 0.992765i \(0.538312\pi\)
\(110\) 0 0
\(111\) 0.158193i 0.0150151i
\(112\) −2.70842 0.300715i −0.255922 0.0284149i
\(113\) 7.25767 + 7.25767i 0.682744 + 0.682744i 0.960618 0.277874i \(-0.0896296\pi\)
−0.277874 + 0.960618i \(0.589630\pi\)
\(114\) 3.58466 + 2.06961i 0.335734 + 0.193836i
\(115\) 0 0
\(116\) −3.04892 5.28088i −0.283085 0.490317i
\(117\) 3.80258 1.01890i 0.351549 0.0941971i
\(118\) −1.84600 + 1.84600i −0.169938 + 0.169938i
\(119\) 1.37148 0.208995i 0.125724 0.0191585i
\(120\) 0 0
\(121\) −0.856990 + 1.48435i −0.0779082 + 0.134941i
\(122\) 2.60277 9.71367i 0.235644 0.879435i
\(123\) 2.14425 8.00245i 0.193341 0.721557i
\(124\) −0.980846 + 1.69887i −0.0880825 + 0.152563i
\(125\) 0 0
\(126\) 2.62536 0.400068i 0.233885 0.0356409i
\(127\) 1.06249 1.06249i 0.0942804 0.0942804i −0.658393 0.752674i \(-0.728764\pi\)
0.752674 + 0.658393i \(0.228764\pi\)
\(128\) −2.77081 + 0.742437i −0.244908 + 0.0656228i
\(129\) 6.37282 + 11.0381i 0.561096 + 0.971846i
\(130\) 0 0
\(131\) 10.3808 + 5.99337i 0.906976 + 0.523643i 0.879457 0.475979i \(-0.157906\pi\)
0.0275190 + 0.999621i \(0.491239\pi\)
\(132\) 2.50238 + 2.50238i 0.217804 + 0.217804i
\(133\) 10.8438 + 1.20398i 0.940277 + 0.104399i
\(134\) 5.53265i 0.477948i
\(135\) 0 0
\(136\) −1.36400 + 0.787505i −0.116962 + 0.0675280i
\(137\) 6.10553 + 1.63597i 0.521630 + 0.139770i 0.510021 0.860162i \(-0.329638\pi\)
0.0116098 + 0.999933i \(0.496304\pi\)
\(138\) 0.670842 + 2.50362i 0.0571059 + 0.213122i
\(139\) 5.07872 0.430772 0.215386 0.976529i \(-0.430899\pi\)
0.215386 + 0.976529i \(0.430899\pi\)
\(140\) 0 0
\(141\) −5.37407 −0.452578
\(142\) 1.87899 + 7.01247i 0.157681 + 0.588474i
\(143\) −13.5587 3.63305i −1.13384 0.303811i
\(144\) −0.891986 + 0.514988i −0.0743322 + 0.0429157i
\(145\) 0 0
\(146\) 15.4445i 1.27819i
\(147\) 5.91495 3.74344i 0.487857 0.308754i
\(148\) 0.111020 + 0.111020i 0.00912577 + 0.00912577i
\(149\) 13.1991 + 7.62048i 1.08131 + 0.624294i 0.931249 0.364383i \(-0.118720\pi\)
0.150060 + 0.988677i \(0.452053\pi\)
\(150\) 0 0
\(151\) −7.46500 12.9298i −0.607493 1.05221i −0.991652 0.128942i \(-0.958842\pi\)
0.384159 0.923267i \(-0.374491\pi\)
\(152\) −11.9645 + 3.20588i −0.970449 + 0.260031i
\(153\) 0.370776 0.370776i 0.0299754 0.0299754i
\(154\) −8.82025 3.44518i −0.710756 0.277621i
\(155\) 0 0
\(156\) −1.95358 + 3.38370i −0.156412 + 0.270913i
\(157\) −1.70656 + 6.36897i −0.136198 + 0.508299i 0.863792 + 0.503849i \(0.168083\pi\)
−0.999990 + 0.00445019i \(0.998583\pi\)
\(158\) 3.93409 14.6822i 0.312980 1.16806i
\(159\) −2.87393 + 4.97779i −0.227917 + 0.394764i
\(160\) 0 0
\(161\) 4.26836 + 5.33457i 0.336394 + 0.420423i
\(162\) 0.709756 0.709756i 0.0557637 0.0557637i
\(163\) 1.35039 0.361835i 0.105770 0.0283411i −0.205546 0.978648i \(-0.565897\pi\)
0.311316 + 0.950306i \(0.399230\pi\)
\(164\) 4.11127 + 7.12093i 0.321036 + 0.556051i
\(165\) 0 0
\(166\) 11.5849 + 6.68855i 0.899163 + 0.519132i
\(167\) 4.18179 + 4.18179i 0.323597 + 0.323597i 0.850145 0.526548i \(-0.176514\pi\)
−0.526548 + 0.850145i \(0.676514\pi\)
\(168\) −4.70874 + 6.40183i −0.363287 + 0.493912i
\(169\) 2.49776i 0.192135i
\(170\) 0 0
\(171\) 3.57128 2.06188i 0.273103 0.157676i
\(172\) −12.2189 3.27405i −0.931683 0.249644i
\(173\) 0.619668 + 2.31263i 0.0471125 + 0.175826i 0.985473 0.169832i \(-0.0543224\pi\)
−0.938361 + 0.345658i \(0.887656\pi\)
\(174\) 6.16698 0.467518
\(175\) 0 0
\(176\) 3.67255 0.276829
\(177\) 0.673159 + 2.51226i 0.0505977 + 0.188833i
\(178\) −10.7168 2.87156i −0.803259 0.215233i
\(179\) 1.63071 0.941493i 0.121885 0.0703705i −0.437818 0.899064i \(-0.644249\pi\)
0.559703 + 0.828693i \(0.310915\pi\)
\(180\) 0 0
\(181\) 17.7439i 1.31889i −0.751751 0.659447i \(-0.770791\pi\)
0.751751 0.659447i \(-0.229209\pi\)
\(182\) 1.15368 10.3908i 0.0855166 0.770214i
\(183\) −7.08436 7.08436i −0.523691 0.523691i
\(184\) −6.71719 3.87817i −0.495198 0.285903i
\(185\) 0 0
\(186\) −0.991969 1.71814i −0.0727347 0.125980i
\(187\) −1.80597 + 0.483908i −0.132066 + 0.0353869i
\(188\) 3.77151 3.77151i 0.275066 0.275066i
\(189\) 0.962603 2.46443i 0.0700191 0.179261i
\(190\) 0 0
\(191\) −5.37301 + 9.30633i −0.388778 + 0.673382i −0.992285 0.123975i \(-0.960436\pi\)
0.603508 + 0.797357i \(0.293769\pi\)
\(192\) 1.82523 6.81187i 0.131725 0.491604i
\(193\) 0.833614 3.11109i 0.0600049 0.223941i −0.929412 0.369045i \(-0.879685\pi\)
0.989416 + 0.145104i \(0.0463515\pi\)
\(194\) 1.76607 3.05893i 0.126797 0.219618i
\(195\) 0 0
\(196\) −1.52396 + 6.77824i −0.108854 + 0.484160i
\(197\) 10.9317 10.9317i 0.778852 0.778852i −0.200784 0.979636i \(-0.564349\pi\)
0.979636 + 0.200784i \(0.0643489\pi\)
\(198\) −3.45708 + 0.926321i −0.245684 + 0.0658307i
\(199\) −6.19974 10.7383i −0.439488 0.761215i 0.558162 0.829732i \(-0.311507\pi\)
−0.997650 + 0.0685166i \(0.978173\pi\)
\(200\) 0 0
\(201\) 4.77353 + 2.75600i 0.336699 + 0.194393i
\(202\) −0.606063 0.606063i −0.0426425 0.0426425i
\(203\) 14.8885 6.52458i 1.04497 0.457935i
\(204\) 0.520419i 0.0364366i
\(205\) 0 0
\(206\) 5.27683 3.04658i 0.367654 0.212265i
\(207\) 2.49427 + 0.668338i 0.173364 + 0.0464527i
\(208\) 1.04944 + 3.91657i 0.0727657 + 0.271565i
\(209\) −14.7040 −1.01709
\(210\) 0 0
\(211\) −13.4216 −0.923982 −0.461991 0.886885i \(-0.652865\pi\)
−0.461991 + 0.886885i \(0.652865\pi\)
\(212\) −1.47648 5.51031i −0.101405 0.378450i
\(213\) 6.98629 + 1.87197i 0.478693 + 0.128265i
\(214\) 10.1678 5.87040i 0.695058 0.401292i
\(215\) 0 0
\(216\) 3.00370i 0.204376i
\(217\) −4.21261 3.09850i −0.285970 0.210340i
\(218\) 8.89753 + 8.89753i 0.602617 + 0.602617i
\(219\) −13.3254 7.69341i −0.900445 0.519872i
\(220\) 0 0
\(221\) −1.03212 1.78769i −0.0694280 0.120253i
\(222\) −0.153376 + 0.0410969i −0.0102939 + 0.00275824i
\(223\) −1.60905 + 1.60905i −0.107750 + 0.107750i −0.758927 0.651176i \(-0.774276\pi\)
0.651176 + 0.758927i \(0.274276\pi\)
\(224\) −1.98234 13.0087i −0.132451 0.869178i
\(225\) 0 0
\(226\) 5.15118 8.92210i 0.342651 0.593489i
\(227\) −6.67262 + 24.9026i −0.442878 + 1.65284i 0.278603 + 0.960407i \(0.410129\pi\)
−0.721480 + 0.692435i \(0.756538\pi\)
\(228\) −1.05929 + 3.95334i −0.0701534 + 0.261816i
\(229\) −0.669566 + 1.15972i −0.0442462 + 0.0766366i −0.887300 0.461192i \(-0.847422\pi\)
0.843054 + 0.537829i \(0.180755\pi\)
\(230\) 0 0
\(231\) −7.36614 + 5.89388i −0.484656 + 0.387789i
\(232\) −13.0494 + 13.0494i −0.856736 + 0.856736i
\(233\) −20.7283 + 5.55413i −1.35796 + 0.363863i −0.863065 0.505093i \(-0.831458\pi\)
−0.494890 + 0.868956i \(0.664792\pi\)
\(234\) −1.97574 3.42207i −0.129158 0.223708i
\(235\) 0 0
\(236\) −2.23552 1.29068i −0.145520 0.0840161i
\(237\) −10.7080 10.7080i −0.695561 0.695561i
\(238\) −0.558926 1.27542i −0.0362298 0.0826732i
\(239\) 12.8433i 0.830767i 0.909646 + 0.415384i \(0.136353\pi\)
−0.909646 + 0.415384i \(0.863647\pi\)
\(240\) 0 0
\(241\) −22.0766 + 12.7459i −1.42208 + 0.821036i −0.996476 0.0838747i \(-0.973270\pi\)
−0.425601 + 0.904911i \(0.639937\pi\)
\(242\) 1.66178 + 0.445273i 0.106823 + 0.0286232i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 9.94357 0.636572
\(245\) 0 0
\(246\) −8.31579 −0.530196
\(247\) −4.20169 15.6809i −0.267347 0.997753i
\(248\) 5.73462 + 1.53659i 0.364149 + 0.0975734i
\(249\) 11.5417 6.66358i 0.731423 0.422287i
\(250\) 0 0
\(251\) 12.0858i 0.762849i 0.924400 + 0.381425i \(0.124566\pi\)
−0.924400 + 0.381425i \(0.875434\pi\)
\(252\) 1.05398 + 2.40508i 0.0663942 + 0.151506i
\(253\) −6.51067 6.51067i −0.409322 0.409322i
\(254\) −1.30615 0.754106i −0.0819552 0.0473168i
\(255\) 0 0
\(256\) 8.49182 + 14.7083i 0.530739 + 0.919266i
\(257\) −10.0104 + 2.68228i −0.624431 + 0.167316i −0.557141 0.830418i \(-0.688102\pi\)
−0.0672896 + 0.997733i \(0.521435\pi\)
\(258\) 9.04630 9.04630i 0.563198 0.563198i
\(259\) −0.326804 + 0.261486i −0.0203066 + 0.0162480i
\(260\) 0 0
\(261\) 3.07198 5.32083i 0.190151 0.329351i
\(262\) 3.11402 11.6217i 0.192385 0.717990i
\(263\) 2.05827 7.68155i 0.126918 0.473665i −0.872983 0.487751i \(-0.837817\pi\)
0.999901 + 0.0140863i \(0.00448397\pi\)
\(264\) 5.35511 9.27532i 0.329584 0.570856i
\(265\) 0 0
\(266\) −1.64978 10.8263i −0.101155 0.663806i
\(267\) −7.81597 + 7.81597i −0.478329 + 0.478329i
\(268\) −5.28421 + 1.41590i −0.322784 + 0.0864898i
\(269\) −0.857638 1.48547i −0.0522911 0.0905709i 0.838695 0.544601i \(-0.183319\pi\)
−0.890986 + 0.454030i \(0.849986\pi\)
\(270\) 0 0
\(271\) −10.0645 5.81076i −0.611377 0.352979i 0.162127 0.986770i \(-0.448164\pi\)
−0.773504 + 0.633791i \(0.781498\pi\)
\(272\) 0.381890 + 0.381890i 0.0231555 + 0.0231555i
\(273\) −8.39038 6.17137i −0.507809 0.373508i
\(274\) 6.34459i 0.383291i
\(275\) 0 0
\(276\) −2.21951 + 1.28144i −0.133599 + 0.0771334i
\(277\) 8.83410 + 2.36709i 0.530790 + 0.142225i 0.514253 0.857639i \(-0.328069\pi\)
0.0165369 + 0.999863i \(0.494736\pi\)
\(278\) −1.31940 4.92405i −0.0791321 0.295325i
\(279\) −1.97653 −0.118332
\(280\) 0 0
\(281\) 15.0644 0.898669 0.449334 0.893364i \(-0.351661\pi\)
0.449334 + 0.893364i \(0.351661\pi\)
\(282\) 1.39612 + 5.21040i 0.0831379 + 0.310275i
\(283\) −15.4679 4.14461i −0.919470 0.246371i −0.232111 0.972689i \(-0.574563\pi\)
−0.687359 + 0.726318i \(0.741230\pi\)
\(284\) −6.21671 + 3.58922i −0.368894 + 0.212981i
\(285\) 0 0
\(286\) 14.0896i 0.833137i
\(287\) −20.0762 + 8.79798i −1.18506 + 0.519329i
\(288\) −3.51685 3.51685i −0.207232 0.207232i
\(289\) 14.4843 + 8.36253i 0.852019 + 0.491913i
\(290\) 0 0
\(291\) −1.75948 3.04751i −0.103143 0.178648i
\(292\) 14.7509 3.95250i 0.863233 0.231302i
\(293\) −6.20477 + 6.20477i −0.362487 + 0.362487i −0.864728 0.502241i \(-0.832509\pi\)
0.502241 + 0.864728i \(0.332509\pi\)
\(294\) −5.16608 4.76231i −0.301292 0.277743i
\(295\) 0 0
\(296\) 0.237583 0.411506i 0.0138092 0.0239183i
\(297\) −0.922863 + 3.44417i −0.0535499 + 0.199851i
\(298\) 3.95943 14.7768i 0.229364 0.855997i
\(299\) 5.08282 8.80370i 0.293947 0.509131i
\(300\) 0 0
\(301\) 12.2690 31.4107i 0.707173 1.81048i
\(302\) −10.5967 + 10.5967i −0.609769 + 0.609769i
\(303\) −0.824807 + 0.221006i −0.0473839 + 0.0126965i
\(304\) 2.12369 + 3.67834i 0.121802 + 0.210967i
\(305\) 0 0
\(306\) −0.455807 0.263160i −0.0260568 0.0150439i
\(307\) −6.26397 6.26397i −0.357504 0.357504i 0.505388 0.862892i \(-0.331349\pi\)
−0.862892 + 0.505388i \(0.831349\pi\)
\(308\) 1.03322 9.30585i 0.0588735 0.530250i
\(309\) 6.07042i 0.345334i
\(310\) 0 0
\(311\) −5.78463 + 3.33976i −0.328016 + 0.189380i −0.654960 0.755664i \(-0.727315\pi\)
0.326944 + 0.945044i \(0.393981\pi\)
\(312\) 11.4218 + 3.06047i 0.646633 + 0.173265i
\(313\) 0.480011 + 1.79143i 0.0271318 + 0.101257i 0.978164 0.207835i \(-0.0666416\pi\)
−0.951032 + 0.309092i \(0.899975\pi\)
\(314\) 6.61835 0.373495
\(315\) 0 0
\(316\) 15.0297 0.845488
\(317\) 0.446453 + 1.66619i 0.0250753 + 0.0935824i 0.977329 0.211724i \(-0.0679078\pi\)
−0.952254 + 0.305306i \(0.901241\pi\)
\(318\) 5.57280 + 1.49323i 0.312507 + 0.0837361i
\(319\) −18.9723 + 10.9537i −1.06224 + 0.613287i
\(320\) 0 0
\(321\) 11.6970i 0.652861i
\(322\) 4.06323 5.52423i 0.226435 0.307853i
\(323\) −1.52899 1.52899i −0.0850752 0.0850752i
\(324\) 0.859523 + 0.496246i 0.0477513 + 0.0275692i
\(325\) 0 0
\(326\) −0.701630 1.21526i −0.0388597 0.0673070i
\(327\) 12.1089 3.24457i 0.669623 0.179425i
\(328\) 17.5963 17.5963i 0.971594 0.971594i
\(329\) 8.88309 + 11.1020i 0.489741 + 0.612075i
\(330\) 0 0
\(331\) −13.0089 + 22.5320i −0.715032 + 1.23847i 0.247915 + 0.968782i \(0.420255\pi\)
−0.962947 + 0.269690i \(0.913079\pi\)
\(332\) −3.42342 + 12.7764i −0.187885 + 0.701196i
\(333\) −0.0409435 + 0.152803i −0.00224369 + 0.00837356i
\(334\) 2.96806 5.14082i 0.162405 0.281293i
\(335\) 0 0
\(336\) 2.53830 + 0.991459i 0.138476 + 0.0540885i
\(337\) 14.7150 14.7150i 0.801579 0.801579i −0.181763 0.983342i \(-0.558180\pi\)
0.983342 + 0.181763i \(0.0581805\pi\)
\(338\) −2.42169 + 0.648890i −0.131723 + 0.0352950i
\(339\) −5.13195 8.88879i −0.278729 0.482773i
\(340\) 0 0
\(341\) 6.10345 + 3.52383i 0.330520 + 0.190826i
\(342\) −2.92686 2.92686i −0.158267 0.158267i
\(343\) −17.5105 6.03166i −0.945480 0.325679i
\(344\) 38.2842i 2.06414i
\(345\) 0 0
\(346\) 2.08122 1.20159i 0.111887 0.0645980i
\(347\) −12.3723 3.31515i −0.664181 0.177967i −0.0890489 0.996027i \(-0.528383\pi\)
−0.575132 + 0.818060i \(0.695049\pi\)
\(348\) 1.57823 + 5.89005i 0.0846023 + 0.315740i
\(349\) 12.7510 0.682546 0.341273 0.939964i \(-0.389142\pi\)
0.341273 + 0.939964i \(0.389142\pi\)
\(350\) 0 0
\(351\) −3.93672 −0.210127
\(352\) 4.58992 + 17.1298i 0.244644 + 0.913023i
\(353\) 16.6743 + 4.46786i 0.887483 + 0.237800i 0.673633 0.739066i \(-0.264733\pi\)
0.213850 + 0.976866i \(0.431400\pi\)
\(354\) 2.26087 1.30532i 0.120164 0.0693768i
\(355\) 0 0
\(356\) 10.9705i 0.581433i
\(357\) −1.37884 0.153092i −0.0729761 0.00810250i
\(358\) −1.33646 1.33646i −0.0706342 0.0706342i
\(359\) −6.50719 3.75693i −0.343437 0.198283i 0.318354 0.947972i \(-0.396870\pi\)
−0.661791 + 0.749689i \(0.730203\pi\)
\(360\) 0 0
\(361\) 0.997305 + 1.72738i 0.0524897 + 0.0909149i
\(362\) −17.2035 + 4.60967i −0.904197 + 0.242279i
\(363\) 1.21197 1.21197i 0.0636118 0.0636118i
\(364\) 10.2194 1.55729i 0.535642 0.0816244i
\(365\) 0 0
\(366\) −5.02817 + 8.70904i −0.262826 + 0.455229i
\(367\) 1.78295 6.65407i 0.0930693 0.347340i −0.903650 0.428271i \(-0.859123\pi\)
0.996720 + 0.0809315i \(0.0257895\pi\)
\(368\) −0.688373 + 2.56904i −0.0358839 + 0.133921i
\(369\) −4.14237 + 7.17480i −0.215643 + 0.373505i
\(370\) 0 0
\(371\) 15.0338 2.29095i 0.780518 0.118940i
\(372\) 1.38713 1.38713i 0.0719191 0.0719191i
\(373\) 6.50499 1.74301i 0.336816 0.0902494i −0.0864472 0.996256i \(-0.527551\pi\)
0.423263 + 0.906007i \(0.360885\pi\)
\(374\) 0.938342 + 1.62526i 0.0485205 + 0.0840400i
\(375\) 0 0
\(376\) −13.9795 8.07106i −0.720937 0.416233i
\(377\) −17.1028 17.1028i −0.880840 0.880840i
\(378\) −2.63945 0.293057i −0.135758 0.0150732i
\(379\) 37.6021i 1.93149i −0.259496 0.965744i \(-0.583556\pi\)
0.259496 0.965744i \(-0.416444\pi\)
\(380\) 0 0
\(381\) −1.30127 + 0.751291i −0.0666663 + 0.0384898i
\(382\) 10.4188 + 2.79170i 0.533070 + 0.142836i
\(383\) 4.00163 + 14.9343i 0.204474 + 0.763106i 0.989609 + 0.143782i \(0.0459265\pi\)
−0.785136 + 0.619324i \(0.787407\pi\)
\(384\) 2.86856 0.146385
\(385\) 0 0
\(386\) −3.23291 −0.164551
\(387\) −3.29882 12.3113i −0.167688 0.625821i
\(388\) 3.37353 + 0.903935i 0.171265 + 0.0458904i
\(389\) 16.0657 9.27555i 0.814565 0.470289i −0.0339739 0.999423i \(-0.510816\pi\)
0.848539 + 0.529134i \(0.177483\pi\)
\(390\) 0 0
\(391\) 1.35402i 0.0684759i
\(392\) 21.0086 0.854385i 1.06109 0.0431530i
\(393\) −8.47590 8.47590i −0.427553 0.427553i
\(394\) −13.4387 7.75885i −0.677033 0.390885i
\(395\) 0 0
\(396\) −1.76945 3.06477i −0.0889181 0.154011i
\(397\) 4.39567 1.17781i 0.220612 0.0591128i −0.146820 0.989163i \(-0.546904\pi\)
0.367432 + 0.930050i \(0.380237\pi\)
\(398\) −8.80061 + 8.80061i −0.441135 + 0.441135i
\(399\) −10.1627 3.96954i −0.508771 0.198726i
\(400\) 0 0
\(401\) 11.1701 19.3471i 0.557806 0.966148i −0.439873 0.898060i \(-0.644977\pi\)
0.997679 0.0680885i \(-0.0216900\pi\)
\(402\) 1.43196 5.34413i 0.0714195 0.266541i
\(403\) −2.01388 + 7.51592i −0.100319 + 0.374395i
\(404\) 0.423746 0.733949i 0.0210821 0.0365153i
\(405\) 0 0
\(406\) −10.1937 12.7401i −0.505907 0.632279i
\(407\) 0.398854 0.398854i 0.0197705 0.0197705i
\(408\) 1.52134 0.407643i 0.0753177 0.0201813i
\(409\) 3.04693 + 5.27744i 0.150661 + 0.260953i 0.931471 0.363816i \(-0.118526\pi\)
−0.780810 + 0.624769i \(0.785193\pi\)
\(410\) 0 0
\(411\) −5.47407 3.16045i −0.270016 0.155894i
\(412\) 4.26020 + 4.26020i 0.209885 + 0.209885i
\(413\) 4.07726 5.54331i 0.200629 0.272768i
\(414\) 2.59194i 0.127387i
\(415\) 0 0
\(416\) −16.9564 + 9.78978i −0.831356 + 0.479984i
\(417\) −4.90567 1.31447i −0.240232 0.0643699i
\(418\) 3.81992 + 14.2561i 0.186839 + 0.697291i
\(419\) −23.3177 −1.13914 −0.569572 0.821942i \(-0.692891\pi\)
−0.569572 + 0.821942i \(0.692891\pi\)
\(420\) 0 0
\(421\) −0.0119079 −0.000580356 −0.000290178 1.00000i \(-0.500092\pi\)
−0.000290178 1.00000i \(0.500092\pi\)
\(422\) 3.48679 + 13.0129i 0.169734 + 0.633456i
\(423\) 5.19095 + 1.39091i 0.252393 + 0.0676284i
\(424\) −14.9518 + 8.63243i −0.726124 + 0.419228i
\(425\) 0 0
\(426\) 7.25985i 0.351741i
\(427\) −2.92511 + 26.3453i −0.141556 + 1.27494i
\(428\) 8.20890 + 8.20890i 0.396792 + 0.396792i
\(429\) 12.1564 + 7.01851i 0.586918 + 0.338857i
\(430\) 0 0
\(431\) −9.44866 16.3656i −0.455126 0.788301i 0.543569 0.839364i \(-0.317072\pi\)
−0.998695 + 0.0510628i \(0.983739\pi\)
\(432\) 0.994881 0.266578i 0.0478662 0.0128257i
\(433\) 18.7716 18.7716i 0.902105 0.902105i −0.0935133 0.995618i \(-0.529810\pi\)
0.995618 + 0.0935133i \(0.0298098\pi\)
\(434\) −1.90974 + 4.88927i −0.0916707 + 0.234692i
\(435\) 0 0
\(436\) −6.22096 + 10.7750i −0.297930 + 0.516029i
\(437\) 2.75607 10.2858i 0.131840 0.492035i
\(438\) −3.99732 + 14.9182i −0.190999 + 0.712820i
\(439\) 3.40990 5.90612i 0.162746 0.281884i −0.773107 0.634276i \(-0.781298\pi\)
0.935852 + 0.352392i \(0.114632\pi\)
\(440\) 0 0
\(441\) −6.68228 + 2.08499i −0.318204 + 0.0992852i
\(442\) −1.46511 + 1.46511i −0.0696881 + 0.0696881i
\(443\) 6.66435 1.78571i 0.316633 0.0848415i −0.0970026 0.995284i \(-0.530926\pi\)
0.413635 + 0.910443i \(0.364259\pi\)
\(444\) −0.0785028 0.135971i −0.00372558 0.00645289i
\(445\) 0 0
\(446\) 1.97807 + 1.14204i 0.0936641 + 0.0540770i
\(447\) −10.7770 10.7770i −0.509734 0.509734i
\(448\) −17.0893 + 7.48904i −0.807395 + 0.353824i
\(449\) 27.2653i 1.28673i 0.765560 + 0.643365i \(0.222462\pi\)
−0.765560 + 0.643365i \(0.777538\pi\)
\(450\) 0 0
\(451\) 25.5830 14.7703i 1.20465 0.695508i
\(452\) 9.83972 + 2.63655i 0.462822 + 0.124013i
\(453\) 3.86417 + 14.4213i 0.181554 + 0.677570i
\(454\) 25.8776 1.21450
\(455\) 0 0
\(456\) 12.3866 0.580054
\(457\) 4.49326 + 16.7691i 0.210186 + 0.784425i 0.987806 + 0.155690i \(0.0497602\pi\)
−0.777620 + 0.628735i \(0.783573\pi\)
\(458\) 1.29835 + 0.347892i 0.0606679 + 0.0162559i
\(459\) −0.454106 + 0.262178i −0.0211958 + 0.0122374i
\(460\) 0 0
\(461\) 41.8808i 1.95058i 0.220920 + 0.975292i \(0.429094\pi\)
−0.220920 + 0.975292i \(0.570906\pi\)
\(462\) 7.62803 + 5.61064i 0.354888 + 0.261031i
\(463\) 15.4654 + 15.4654i 0.718740 + 0.718740i 0.968347 0.249607i \(-0.0803016\pi\)
−0.249607 + 0.968347i \(0.580302\pi\)
\(464\) 5.48033 + 3.16407i 0.254418 + 0.146888i
\(465\) 0 0
\(466\) 10.7700 + 18.6541i 0.498909 + 0.864135i
\(467\) 32.4120 8.68477i 1.49985 0.401883i 0.586800 0.809732i \(-0.300388\pi\)
0.913049 + 0.407849i \(0.133721\pi\)
\(468\) 2.76278 2.76278i 0.127710 0.127710i
\(469\) −2.19694 14.4169i −0.101445 0.665713i
\(470\) 0 0
\(471\) 3.29682 5.71026i 0.151910 0.263115i
\(472\) −2.02197 + 7.54610i −0.0930688 + 0.347337i
\(473\) −11.7625 + 43.8982i −0.540839 + 2.01844i
\(474\) −7.60009 + 13.1637i −0.349083 + 0.604630i
\(475\) 0 0
\(476\) 1.07511 0.860229i 0.0492775 0.0394285i
\(477\) 4.06435 4.06435i 0.186094 0.186094i
\(478\) 12.4522 3.33656i 0.569551 0.152611i
\(479\) 8.19191 + 14.1888i 0.374298 + 0.648303i 0.990222 0.139503i \(-0.0445505\pi\)
−0.615924 + 0.787806i \(0.711217\pi\)
\(480\) 0 0
\(481\) 0.539329 + 0.311381i 0.0245913 + 0.0141978i
\(482\) 18.0930 + 18.0930i 0.824113 + 0.824113i
\(483\) −2.74223 6.25753i −0.124776 0.284727i
\(484\) 1.70111i 0.0773232i
\(485\) 0 0
\(486\) −0.869271 + 0.501874i −0.0394309 + 0.0227654i
\(487\) −4.22392 1.13179i −0.191404 0.0512865i 0.161844 0.986816i \(-0.448256\pi\)
−0.353248 + 0.935530i \(0.614923\pi\)
\(488\) −7.78877 29.0681i −0.352581 1.31585i
\(489\) −1.39802 −0.0632208
\(490\) 0 0
\(491\) 33.8633 1.52823 0.764116 0.645079i \(-0.223176\pi\)
0.764116 + 0.645079i \(0.223176\pi\)
\(492\) −2.12815 7.94237i −0.0959445 0.358070i
\(493\) −3.11185 0.833817i −0.140151 0.0375532i
\(494\) −14.1118 + 8.14746i −0.634920 + 0.366571i
\(495\) 0 0
\(496\) 2.03578i 0.0914093i
\(497\) −7.68081 17.5269i −0.344531 0.786190i
\(498\) −9.45904 9.45904i −0.423870 0.423870i
\(499\) −15.2390 8.79824i −0.682192 0.393864i 0.118489 0.992955i \(-0.462195\pi\)
−0.800680 + 0.599092i \(0.795528\pi\)
\(500\) 0 0
\(501\) −2.95698 5.12163i −0.132108 0.228818i
\(502\) 11.7177 3.13976i 0.522988 0.140134i
\(503\) −9.37063 + 9.37063i −0.417816 + 0.417816i −0.884450 0.466635i \(-0.845466\pi\)
0.466635 + 0.884450i \(0.345466\pi\)
\(504\) 6.20521 4.96499i 0.276402 0.221158i
\(505\) 0 0
\(506\) −4.62099 + 8.00379i −0.205428 + 0.355812i
\(507\) −0.646467 + 2.41265i −0.0287106 + 0.107150i
\(508\) 0.385977 1.44049i 0.0171250 0.0639112i
\(509\) −13.8907 + 24.0594i −0.615695 + 1.06641i 0.374567 + 0.927200i \(0.377791\pi\)
−0.990262 + 0.139215i \(0.955542\pi\)
\(510\) 0 0
\(511\) 6.13279 + 40.2451i 0.271299 + 1.78034i
\(512\) 7.99749 7.99749i 0.353442 0.353442i
\(513\) −3.98325 + 1.06731i −0.175865 + 0.0471228i
\(514\) 5.20118 + 9.00870i 0.229414 + 0.397357i
\(515\) 0 0
\(516\) 10.9552 + 6.32497i 0.482275 + 0.278441i
\(517\) −13.5497 13.5497i −0.595914 0.595914i
\(518\) 0.338423 + 0.248920i 0.0148695 + 0.0109369i
\(519\) 2.39421i 0.105094i
\(520\) 0 0
\(521\) 15.2942 8.83010i 0.670050 0.386854i −0.126045 0.992024i \(-0.540228\pi\)
0.796096 + 0.605171i \(0.206895\pi\)
\(522\) −5.95685 1.59613i −0.260724 0.0698608i
\(523\) −1.08429 4.04661i −0.0474125 0.176946i 0.938159 0.346204i \(-0.112530\pi\)
−0.985572 + 0.169258i \(0.945863\pi\)
\(524\) 11.8967 0.519711
\(525\) 0 0
\(526\) −7.98233 −0.348046
\(527\) 0.268242 + 1.00109i 0.0116848 + 0.0436082i
\(528\) −3.54742 0.950527i −0.154381 0.0413664i
\(529\) −14.1439 + 8.16597i −0.614951 + 0.355042i
\(530\) 0 0
\(531\) 2.60089i 0.112869i
\(532\) 9.91797 4.34634i 0.429999 0.188438i
\(533\) 23.0621 + 23.0621i 0.998930 + 0.998930i
\(534\) 9.60844 + 5.54743i 0.415798 + 0.240061i
\(535\) 0 0
\(536\) 8.27821 + 14.3383i 0.357564 + 0.619319i
\(537\) −1.81883 + 0.487353i −0.0784881 + 0.0210308i
\(538\) −1.21743 + 1.21743i −0.0524871 + 0.0524871i
\(539\) 24.3518 + 5.47503i 1.04891 + 0.235826i
\(540\) 0 0
\(541\) 9.49606 16.4477i 0.408267 0.707140i −0.586428 0.810001i \(-0.699466\pi\)
0.994696 + 0.102861i \(0.0327998\pi\)
\(542\) −3.01914 + 11.2676i −0.129683 + 0.483984i
\(543\) −4.59246 + 17.1393i −0.197081 + 0.735517i
\(544\) −1.30396 + 2.25853i −0.0559069 + 0.0968336i
\(545\) 0 0
\(546\) −3.80370 + 9.73811i −0.162783 + 0.416753i
\(547\) 4.10986 4.10986i 0.175725 0.175725i −0.613764 0.789489i \(-0.710345\pi\)
0.789489 + 0.613764i \(0.210345\pi\)
\(548\) 6.05969 1.62369i 0.258857 0.0693605i
\(549\) 5.00940 + 8.67653i 0.213796 + 0.370305i
\(550\) 0 0
\(551\) −21.9418 12.6681i −0.934752 0.539680i
\(552\) 5.48457 + 5.48457i 0.233439 + 0.233439i
\(553\) −4.42131 + 39.8210i −0.188013 + 1.69336i
\(554\) 9.18001i 0.390021i
\(555\) 0 0
\(556\) 4.36528 2.52029i 0.185129 0.106884i
\(557\) −27.2967 7.31412i −1.15660 0.309909i −0.370991 0.928637i \(-0.620982\pi\)
−0.785606 + 0.618727i \(0.787649\pi\)
\(558\) 0.513481 + 1.91634i 0.0217374 + 0.0811250i
\(559\) −50.1760 −2.12222
\(560\) 0 0
\(561\) 1.86968 0.0789379
\(562\) −3.91357 14.6057i −0.165084 0.616102i
\(563\) −23.8998 6.40394i −1.00726 0.269894i −0.282775 0.959186i \(-0.591255\pi\)
−0.724483 + 0.689292i \(0.757922\pi\)
\(564\) −4.61914 + 2.66686i −0.194501 + 0.112295i
\(565\) 0 0
\(566\) 16.0735i 0.675621i
\(567\) −1.56764 + 2.13131i −0.0658348 + 0.0895067i
\(568\) 15.3619 + 15.3619i 0.644572 + 0.644572i
\(569\) −31.0893 17.9494i −1.30333 0.752479i −0.322357 0.946618i \(-0.604475\pi\)
−0.980974 + 0.194140i \(0.937809\pi\)
\(570\) 0 0
\(571\) 3.51101 + 6.08125i 0.146931 + 0.254492i 0.930092 0.367327i \(-0.119727\pi\)
−0.783161 + 0.621820i \(0.786394\pi\)
\(572\) −13.4569 + 3.60577i −0.562662 + 0.150765i
\(573\) 7.59859 7.59859i 0.317436 0.317436i
\(574\) 13.7456 + 17.1792i 0.573731 + 0.717046i
\(575\) 0 0
\(576\) −3.52608 + 6.10735i −0.146920 + 0.254473i
\(577\) 6.47806 24.1765i 0.269685 1.00648i −0.689635 0.724157i \(-0.742229\pi\)
0.959320 0.282321i \(-0.0911045\pi\)
\(578\) 4.34498 16.2157i 0.180727 0.674484i
\(579\) −1.61042 + 2.78933i −0.0669267 + 0.115921i
\(580\) 0 0
\(581\) −32.8438 12.8288i −1.36259 0.532227i
\(582\) −2.49760 + 2.49760i −0.103529 + 0.103529i
\(583\) −19.7966 + 5.30448i −0.819891 + 0.219689i
\(584\) −23.1087 40.0255i −0.956246 1.65627i
\(585\) 0 0
\(586\) 7.62774 + 4.40388i 0.315099 + 0.181923i
\(587\) 22.0509 + 22.0509i 0.910139 + 0.910139i 0.996283 0.0861436i \(-0.0274544\pi\)
−0.0861436 + 0.996283i \(0.527454\pi\)
\(588\) 3.22637 6.15285i 0.133053 0.253739i
\(589\) 8.15074i 0.335845i
\(590\) 0 0
\(591\) −13.3885 + 7.72988i −0.550731 + 0.317965i
\(592\) −0.157384 0.0421708i −0.00646843 0.00173321i
\(593\) −11.1621 41.6575i −0.458372 1.71067i −0.677981 0.735079i \(-0.737145\pi\)
0.219609 0.975588i \(-0.429522\pi\)
\(594\) 3.57903 0.146849
\(595\) 0 0
\(596\) 15.1265 0.619607
\(597\) 3.20922 + 11.9770i 0.131345 + 0.490185i
\(598\) −9.85604 2.64092i −0.403043 0.107995i
\(599\) 23.6940 13.6797i 0.968111 0.558939i 0.0694514 0.997585i \(-0.477875\pi\)
0.898660 + 0.438646i \(0.144542\pi\)
\(600\) 0 0
\(601\) 7.61565i 0.310649i −0.987864 0.155324i \(-0.950358\pi\)
0.987864 0.155324i \(-0.0496423\pi\)
\(602\) −33.6414 3.73520i −1.37112 0.152235i
\(603\) −3.89757 3.89757i −0.158721 0.158721i
\(604\) −12.8327 7.40895i −0.522154 0.301466i
\(605\) 0 0
\(606\) 0.428551 + 0.742273i 0.0174087 + 0.0301528i
\(607\) −15.0249 + 4.02590i −0.609840 + 0.163406i −0.550505 0.834832i \(-0.685565\pi\)
−0.0593354 + 0.998238i \(0.518898\pi\)
\(608\) −14.5026 + 14.5026i −0.588159 + 0.588159i
\(609\) −16.0699 + 2.44883i −0.651184 + 0.0992314i
\(610\) 0 0
\(611\) 10.5781 18.3218i 0.427944 0.741221i
\(612\) 0.134694 0.502686i 0.00544469 0.0203199i
\(613\) −0.880848 + 3.28737i −0.0355771 + 0.132776i −0.981430 0.191819i \(-0.938561\pi\)
0.945853 + 0.324595i \(0.105228\pi\)
\(614\) −4.44590 + 7.70052i −0.179422 + 0.310768i
\(615\) 0 0
\(616\) −28.0132 + 4.26882i −1.12868 + 0.171996i
\(617\) 19.3906 19.3906i 0.780637 0.780637i −0.199301 0.979938i \(-0.563867\pi\)
0.979938 + 0.199301i \(0.0638671\pi\)
\(618\) −5.88554 + 1.57703i −0.236751 + 0.0634373i
\(619\) 15.4314 + 26.7280i 0.620240 + 1.07429i 0.989441 + 0.144938i \(0.0462982\pi\)
−0.369200 + 0.929350i \(0.620368\pi\)
\(620\) 0 0
\(621\) −2.23630 1.29113i −0.0897397 0.0518113i
\(622\) 4.74083 + 4.74083i 0.190090 + 0.190090i
\(623\) 29.0661 + 3.22719i 1.16451 + 0.129295i
\(624\) 4.05473i 0.162319i
\(625\) 0 0
\(626\) 1.61217 0.930785i 0.0644351 0.0372016i
\(627\) 14.2029 + 3.80566i 0.567210 + 0.151984i
\(628\) 1.69375 + 6.32115i 0.0675879 + 0.252241i
\(629\) 0.0829496 0.00330742
\(630\) 0 0
\(631\) −19.0017 −0.756446 −0.378223 0.925714i \(-0.623465\pi\)
−0.378223 + 0.925714i \(0.623465\pi\)
\(632\) −11.7727 43.9365i −0.468295 1.74770i
\(633\) 12.9643 + 3.47377i 0.515284 + 0.138070i
\(634\) 1.49946 0.865713i 0.0595512 0.0343819i
\(635\) 0 0
\(636\) 5.70470i 0.226206i
\(637\) 1.11978 + 27.5343i 0.0443671 + 1.09095i
\(638\) 15.5489 + 15.5489i 0.615585 + 0.615585i
\(639\) −6.26374 3.61637i −0.247790 0.143061i
\(640\) 0 0
\(641\) 8.84861 + 15.3262i 0.349499 + 0.605350i 0.986161 0.165793i \(-0.0530185\pi\)
−0.636661 + 0.771143i \(0.719685\pi\)
\(642\) −11.3407 + 3.03874i −0.447583 + 0.119930i
\(643\) 1.20751 1.20751i 0.0476194 0.0476194i −0.682896 0.730516i \(-0.739280\pi\)
0.730516 + 0.682896i \(0.239280\pi\)
\(644\) 6.31601 + 2.46703i 0.248886 + 0.0972145i
\(645\) 0 0
\(646\) −1.08521 + 1.87964i −0.0426970 + 0.0739534i
\(647\) −0.977939 + 3.64972i −0.0384468 + 0.143485i −0.982481 0.186362i \(-0.940330\pi\)
0.944034 + 0.329847i \(0.106997\pi\)
\(648\) 0.777416 2.90136i 0.0305398 0.113976i
\(649\) −4.63695 + 8.03143i −0.182016 + 0.315261i
\(650\) 0 0
\(651\) 3.26712 + 4.08322i 0.128048 + 0.160034i
\(652\) 0.981129 0.981129i 0.0384240 0.0384240i
\(653\) 8.72296 2.33731i 0.341356 0.0914660i −0.0840686 0.996460i \(-0.526791\pi\)
0.425424 + 0.904994i \(0.360125\pi\)
\(654\) −6.29151 10.8972i −0.246017 0.426115i
\(655\) 0 0
\(656\) −7.38988 4.26655i −0.288526 0.166581i
\(657\) 10.8801 + 10.8801i 0.424474 + 0.424474i
\(658\) 8.45619 11.4967i 0.329657 0.448190i
\(659\) 40.3378i 1.57134i −0.618648 0.785668i \(-0.712319\pi\)
0.618648 0.785668i \(-0.287681\pi\)
\(660\) 0 0
\(661\) 23.8392 13.7636i 0.927238 0.535341i 0.0413010 0.999147i \(-0.486850\pi\)
0.885937 + 0.463806i \(0.153516\pi\)
\(662\) 25.2254 + 6.75912i 0.980412 + 0.262701i
\(663\) 0.534265 + 1.99390i 0.0207491 + 0.0774368i
\(664\) 40.0308 1.55350
\(665\) 0 0
\(666\) 0.158786 0.00615284
\(667\) −4.10624 15.3247i −0.158994 0.593375i
\(668\) 5.66955 + 1.51915i 0.219361 + 0.0587777i
\(669\) 1.97068 1.13777i 0.0761909 0.0439889i
\(670\) 0 0
\(671\) 35.7237i 1.37910i
\(672\) −1.45210 + 13.0785i −0.0560159 + 0.504513i
\(673\) −22.5966 22.5966i −0.871035 0.871035i 0.121550 0.992585i \(-0.461213\pi\)
−0.992585 + 0.121550i \(0.961213\pi\)
\(674\) −18.0897 10.4441i −0.696789 0.402291i
\(675\) 0 0
\(676\) −1.23950 2.14688i −0.0476732 0.0825723i
\(677\) −8.93720 + 2.39472i −0.343484 + 0.0920364i −0.426437 0.904517i \(-0.640232\pi\)
0.0829529 + 0.996553i \(0.473565\pi\)
\(678\) −7.28486 + 7.28486i −0.279774 + 0.279774i
\(679\) −3.38736 + 8.67221i −0.129995 + 0.332809i
\(680\) 0 0
\(681\) 12.8905 22.3270i 0.493966 0.855574i
\(682\) 1.83090 6.83302i 0.0701089 0.261650i
\(683\) −1.20450 + 4.49527i −0.0460891 + 0.172007i −0.985134 0.171788i \(-0.945046\pi\)
0.939045 + 0.343794i \(0.111712\pi\)
\(684\) 2.04640 3.54447i 0.0782460 0.135526i
\(685\) 0 0
\(686\) −1.29893 + 18.5442i −0.0495933 + 0.708022i
\(687\) 0.946910 0.946910i 0.0361269 0.0361269i
\(688\) 12.6804 3.39770i 0.483436 0.129536i
\(689\) −11.3138 19.5961i −0.431023 0.746554i
\(690\) 0 0
\(691\) −6.52332 3.76624i −0.248159 0.143275i 0.370762 0.928728i \(-0.379097\pi\)
−0.618921 + 0.785453i \(0.712430\pi\)
\(692\) 1.68025 + 1.68025i 0.0638736 + 0.0638736i
\(693\) 8.64059 3.78656i 0.328229 0.143839i
\(694\) 12.8568i 0.488036i
\(695\) 0 0
\(696\) 15.9822 9.22732i 0.605804 0.349761i
\(697\) 4.19613 + 1.12435i 0.158940 + 0.0425878i
\(698\) −3.31257 12.3627i −0.125383 0.467934i
\(699\) 21.4595 0.811673
\(700\) 0 0
\(701\) −45.2736 −1.70996 −0.854981 0.518660i \(-0.826431\pi\)
−0.854981 + 0.518660i \(0.826431\pi\)
\(702\) 1.02272 + 3.81683i 0.0385999 + 0.144057i
\(703\) 0.630123 + 0.168841i 0.0237655 + 0.00636796i
\(704\) 21.7768 12.5728i 0.820744 0.473857i
\(705\) 0 0
\(706\) 17.3272i 0.652117i
\(707\) 1.81993 + 1.33862i 0.0684457 + 0.0503438i
\(708\) 1.82530 + 1.82530i 0.0685988 + 0.0685988i
\(709\) 27.8909 + 16.1028i 1.04747 + 0.604754i 0.921939 0.387336i \(-0.126605\pi\)
0.125527 + 0.992090i \(0.459938\pi\)
\(710\) 0 0
\(711\) 7.57171 + 13.1146i 0.283961 + 0.491836i
\(712\) −32.0700 + 8.59313i −1.20187 + 0.322041i
\(713\) −3.60902 + 3.60902i −0.135159 + 0.135159i
\(714\) 0.209778 + 1.37662i 0.00785074 + 0.0515188i
\(715\) 0 0
\(716\) 0.934424 1.61847i 0.0349211 0.0604851i
\(717\) 3.32410 12.4057i 0.124141 0.463300i
\(718\) −1.95202 + 7.28503i −0.0728486 + 0.271875i
\(719\) 14.8623 25.7422i 0.554270 0.960023i −0.443690 0.896180i \(-0.646331\pi\)
0.997960 0.0638430i \(-0.0203357\pi\)
\(720\) 0 0
\(721\) −12.5406 + 10.0341i −0.467036 + 0.373690i
\(722\) 1.41569 1.41569i 0.0526864 0.0526864i
\(723\) 24.6232 6.59777i 0.915747 0.245374i
\(724\) −8.80534 15.2513i −0.327248 0.566810i
\(725\) 0 0
\(726\) −1.48991 0.860202i −0.0552958 0.0319251i
\(727\) −8.03461 8.03461i −0.297987 0.297987i 0.542238 0.840225i \(-0.317577\pi\)
−0.840225 + 0.542238i \(0.817577\pi\)
\(728\) −12.5573 28.6546i −0.465404 1.06201i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −5.78787 + 3.34163i −0.214072 + 0.123595i
\(732\) −9.60475 2.57358i −0.355002 0.0951224i
\(733\) −7.77556 29.0188i −0.287197 1.07183i −0.947219 0.320587i \(-0.896120\pi\)
0.660022 0.751246i \(-0.270547\pi\)
\(734\) −6.91461 −0.255223
\(735\) 0 0
\(736\) −12.8431 −0.473401
\(737\) 5.08682 + 18.9843i 0.187375 + 0.699294i
\(738\) 8.03244 + 2.15229i 0.295678 + 0.0792267i
\(739\) 35.8813 20.7161i 1.31992 0.762054i 0.336202 0.941790i \(-0.390858\pi\)
0.983715 + 0.179736i \(0.0575243\pi\)
\(740\) 0 0
\(741\) 16.2341i 0.596374i
\(742\) −6.12680 13.9808i −0.224922 0.513252i
\(743\) −10.5103 10.5103i −0.385585 0.385585i 0.487525 0.873109i \(-0.337900\pi\)
−0.873109 + 0.487525i \(0.837900\pi\)
\(744\) −5.14152 2.96846i −0.188497 0.108829i
\(745\) 0 0
\(746\) −3.37985 5.85407i −0.123745 0.214333i
\(747\) −12.8730 + 3.44932i −0.471000 + 0.126204i
\(748\) −1.31214 + 1.31214i −0.0479764 + 0.0479764i
\(749\) −24.1642 + 19.3346i −0.882941 + 0.706469i
\(750\) 0 0
\(751\) 21.0235 36.4138i 0.767159 1.32876i −0.171938 0.985108i \(-0.555003\pi\)
0.939097 0.343651i \(-0.111664\pi\)
\(752\) −1.43261 + 5.34656i −0.0522418 + 0.194969i
\(753\) 3.12804 11.6740i 0.113992 0.425424i
\(754\) −12.1388 + 21.0251i −0.442071 + 0.765689i
\(755\) 0 0
\(756\) −0.395582 2.59592i −0.0143872 0.0944126i
\(757\) −12.0838 + 12.0838i −0.439193 + 0.439193i −0.891740 0.452547i \(-0.850515\pi\)
0.452547 + 0.891740i \(0.350515\pi\)
\(758\) −36.4569 + 9.76860i −1.32417 + 0.354811i
\(759\) 4.60374 + 7.97391i 0.167105 + 0.289435i
\(760\) 0 0
\(761\) −12.6620 7.31041i −0.458997 0.265002i 0.252625 0.967564i \(-0.418706\pi\)
−0.711623 + 0.702562i \(0.752039\pi\)
\(762\) 1.06647 + 1.06647i 0.0386340 + 0.0386340i
\(763\) −26.7182 19.6520i −0.967264 0.711451i
\(764\) 10.6653i 0.385858i
\(765\) 0 0
\(766\) 13.4399 7.75952i 0.485603 0.280363i
\(767\) −9.89008 2.65004i −0.357110 0.0956874i
\(768\) −4.39569 16.4049i −0.158616 0.591962i
\(769\) −5.95109 −0.214602 −0.107301 0.994227i \(-0.534221\pi\)
−0.107301 + 0.994227i \(0.534221\pi\)
\(770\) 0 0
\(771\) 10.3635 0.373233
\(772\) −0.827355 3.08773i −0.0297772 0.111130i
\(773\) −4.58677 1.22902i −0.164975 0.0442049i 0.175386 0.984500i \(-0.443883\pi\)
−0.340361 + 0.940295i \(0.610549\pi\)
\(774\) −11.0794 + 6.39670i −0.398241 + 0.229925i
\(775\) 0 0
\(776\) 10.5699i 0.379438i
\(777\) 0.383346 0.167993i 0.0137525 0.00602673i
\(778\) −13.1668 13.1668i −0.472051 0.472051i
\(779\) 29.5872 + 17.0822i 1.06007 + 0.612032i
\(780\) 0 0
\(781\) 12.8948 + 22.3344i 0.461411 + 0.799188i
\(782\) −1.31279 + 0.351760i −0.0469452 + 0.0125789i
\(783\) −4.34444 + 4.34444i −0.155258 + 0.155258i
\(784\) −2.14749 6.88259i −0.0766961 0.245807i
\(785\) 0 0
\(786\) −6.01582 + 10.4197i −0.214577 + 0.371659i
\(787\) −4.26300 + 15.9097i −0.151959 + 0.567120i 0.847387 + 0.530976i \(0.178174\pi\)
−0.999347 + 0.0361447i \(0.988492\pi\)
\(788\) 3.97124 14.8209i 0.141470 0.527971i
\(789\) −3.97626 + 6.88709i −0.141559 + 0.245187i
\(790\) 0 0
\(791\) −9.88005 + 25.2946i −0.351294 + 0.899373i
\(792\) −7.57326 + 7.57326i −0.269104 + 0.269104i
\(793\) 38.0972 10.2081i 1.35287 0.362501i
\(794\) −2.28389 3.95581i −0.0810522 0.140387i
\(795\) 0 0
\(796\) −10.6576 6.15319i −0.377750 0.218094i
\(797\) 33.5483 + 33.5483i 1.18834 + 1.18834i 0.977525 + 0.210818i \(0.0676127\pi\)
0.210818 + 0.977525i \(0.432387\pi\)
\(798\) −1.20849 + 10.8844i −0.0427803 + 0.385305i
\(799\) 2.81792i 0.0996910i
\(800\) 0 0
\(801\) 9.57257 5.52672i 0.338230 0.195277i
\(802\) −21.6598 5.80371i −0.764832 0.204936i
\(803\) −14.1999 52.9948i −0.501104 1.87015i
\(804\) 5.47061 0.192934
\(805\) 0 0
\(806\) 7.81021 0.275103
\(807\) 0.443946 + 1.65683i 0.0156276 + 0.0583232i
\(808\) −2.47748 0.663838i −0.0871573 0.0233537i
\(809\) 5.58195 3.22274i 0.196251 0.113306i −0.398655 0.917101i \(-0.630523\pi\)
0.594906 + 0.803796i \(0.297189\pi\)
\(810\) 0 0
\(811\) 0.116404i 0.00408751i 0.999998 + 0.00204375i \(0.000650547\pi\)
−0.999998 + 0.00204375i \(0.999349\pi\)
\(812\) 9.55922 12.9964i 0.335463 0.456084i
\(813\) 8.21766 + 8.21766i 0.288206 + 0.288206i
\(814\) −0.490325 0.283089i −0.0171859 0.00992227i
\(815\) 0 0
\(816\) −0.270037 0.467718i −0.00945319 0.0163734i
\(817\) −50.7690 + 13.6035i −1.77618 + 0.475927i
\(818\) 4.32516 4.32516i 0.151226 0.151226i
\(819\) 6.50722 + 8.13268i 0.227381 + 0.284179i
\(820\) 0 0
\(821\) 0.698986 1.21068i 0.0243948 0.0422530i −0.853570 0.520978i \(-0.825567\pi\)
0.877965 + 0.478725i \(0.158901\pi\)
\(822\) −1.64210 + 6.12841i −0.0572749 + 0.213753i
\(823\) 4.22216 15.7573i 0.147175 0.549265i −0.852474 0.522770i \(-0.824899\pi\)
0.999649 0.0264952i \(-0.00843466\pi\)
\(824\) 9.11687 15.7909i 0.317601 0.550101i
\(825\) 0 0
\(826\) −6.43371 2.51300i −0.223858 0.0874386i
\(827\) 29.7712 29.7712i 1.03524 1.03524i 0.0358886 0.999356i \(-0.488574\pi\)
0.999356 0.0358886i \(-0.0114262\pi\)
\(828\) 2.47554 0.663320i 0.0860311 0.0230520i
\(829\) −3.31772 5.74647i −0.115229 0.199583i 0.802642 0.596461i \(-0.203427\pi\)
−0.917871 + 0.396878i \(0.870094\pi\)
\(830\) 0 0
\(831\) −7.92044 4.57287i −0.274757 0.158631i
\(832\) 19.6310 + 19.6310i 0.680582 + 0.680582i
\(833\) 1.96290 + 3.10154i 0.0680104 + 0.107462i
\(834\) 5.09775i 0.176521i
\(835\) 0 0
\(836\) −12.6384 + 7.29677i −0.437108 + 0.252364i
\(837\) 1.90918 + 0.511564i 0.0659910 + 0.0176822i
\(838\) 6.05768 + 22.6076i 0.209259 + 0.780965i
\(839\) 18.1682 0.627234 0.313617 0.949550i \(-0.398459\pi\)
0.313617 + 0.949550i \(0.398459\pi\)
\(840\) 0 0
\(841\) −8.74827 −0.301664
\(842\) 0.00309354 + 0.0115453i 0.000106610 + 0.000397876i
\(843\) −14.5511 3.89896i −0.501167 0.134287i
\(844\) −11.5362 + 6.66042i −0.397092 + 0.229261i
\(845\) 0 0
\(846\) 5.39421i 0.185457i
\(847\) −4.50707 0.500418i −0.154865 0.0171946i
\(848\) 4.18618 + 4.18618i 0.143754 + 0.143754i
\(849\) 13.8681 + 8.00677i 0.475953 + 0.274791i
\(850\) 0 0
\(851\) 0.204248 + 0.353768i 0.00700154 + 0.0121270i
\(852\) 6.93384 1.85792i 0.237549 0.0636512i
\(853\) −34.0703 + 34.0703i −1.16654 + 1.16654i −0.183530 + 0.983014i \(0.558752\pi\)
−0.983014 + 0.183530i \(0.941248\pi\)
\(854\) 26.3029 4.00820i 0.900067 0.137158i
\(855\) 0 0
\(856\) 17.5671 30.4271i 0.600432 1.03998i
\(857\) 9.53874 35.5991i 0.325837 1.21604i −0.587631 0.809129i \(-0.699939\pi\)
0.913468 0.406911i \(-0.133394\pi\)
\(858\) 3.64666 13.6095i 0.124495 0.464622i
\(859\) −6.11471 + 10.5910i −0.208631 + 0.361360i −0.951284 0.308317i \(-0.900234\pi\)
0.742652 + 0.669677i \(0.233567\pi\)
\(860\) 0 0
\(861\) 21.6692 3.30209i 0.738486 0.112535i
\(862\) −13.4125 + 13.4125i −0.456831 + 0.456831i
\(863\) 40.1292 10.7526i 1.36601 0.366022i 0.499993 0.866030i \(-0.333336\pi\)
0.866021 + 0.500007i \(0.166669\pi\)
\(864\) 2.48679 + 4.30724i 0.0846022 + 0.146535i
\(865\) 0 0
\(866\) −23.0765 13.3233i −0.784173 0.452743i
\(867\) −11.8264 11.8264i −0.401645 0.401645i
\(868\) −5.15845 0.572740i −0.175089 0.0194401i
\(869\) 53.9964i 1.83170i
\(870\) 0 0
\(871\) −18.7920 + 10.8496i −0.636744 + 0.367624i
\(872\) 36.3715 + 9.74572i 1.23169 + 0.330032i
\(873\) 0.910774 + 3.39905i 0.0308250 + 0.115041i
\(874\) −10.6885 −0.361545
\(875\) 0 0
\(876\) −15.2713 −0.515969
\(877\) −0.648098 2.41873i −0.0218847 0.0816748i 0.954120 0.299425i \(-0.0967949\pi\)
−0.976005 + 0.217750i \(0.930128\pi\)
\(878\) −6.61211 1.77171i −0.223148 0.0597923i
\(879\) 7.59927 4.38744i 0.256317 0.147985i
\(880\) 0 0
\(881\) 48.7030i 1.64084i 0.571758 + 0.820422i \(0.306262\pi\)
−0.571758 + 0.820422i \(0.693738\pi\)
\(882\) 3.75747 + 5.93711i 0.126521 + 0.199913i
\(883\) 5.87749 + 5.87749i 0.197793 + 0.197793i 0.799053 0.601260i \(-0.205334\pi\)
−0.601260 + 0.799053i \(0.705334\pi\)
\(884\) −1.77426 1.02437i −0.0596749 0.0344533i
\(885\) 0 0
\(886\) −3.46265 5.99748i −0.116330 0.201489i
\(887\) −9.36397 + 2.50907i −0.314411 + 0.0842463i −0.412574 0.910924i \(-0.635370\pi\)
0.0981626 + 0.995170i \(0.468703\pi\)
\(888\) −0.335993 + 0.335993i −0.0112752 + 0.0112752i
\(889\) 3.70300 + 1.44639i 0.124195 + 0.0485104i
\(890\) 0 0
\(891\) 1.78283 3.08796i 0.0597272 0.103450i
\(892\) −0.584533 + 2.18151i −0.0195716 + 0.0730422i
\(893\) 5.73578 21.4062i 0.191941 0.716332i
\(894\) −7.64903 + 13.2485i −0.255822 + 0.443097i
\(895\) 0 0
\(896\) −4.74159 5.92601i −0.158406 0.197974i
\(897\) −7.18819 + 7.18819i −0.240007 + 0.240007i
\(898\) 26.4350 7.08322i 0.882146 0.236370i
\(899\) 6.07187 + 10.5168i 0.202508 + 0.350754i
\(900\) 0 0
\(901\) −2.61013 1.50696i −0.0869561 0.0502041i
\(902\) −20.9667 20.9667i −0.698114 0.698114i
\(903\) −19.9806 + 27.1650i −0.664914 + 0.903993i
\(904\) 30.8297i 1.02538i
\(905\) 0 0
\(906\) 12.9782 7.49297i 0.431172 0.248937i
\(907\) 31.8869 + 8.54407i 1.05879 + 0.283701i 0.745878 0.666082i \(-0.232030\pi\)
0.312909 + 0.949783i \(0.398697\pi\)
\(908\) 6.62252 + 24.7156i 0.219776 + 0.820216i
\(909\) 0.853903 0.0283222
\(910\) 0 0
\(911\) 33.1445 1.09813 0.549064 0.835781i \(-0.314984\pi\)
0.549064 + 0.835781i \(0.314984\pi\)
\(912\) −1.09930 4.10265i −0.0364015 0.135852i
\(913\) 45.9010 + 12.2991i 1.51910 + 0.407042i
\(914\) 15.0911 8.71284i 0.499169 0.288195i
\(915\) 0 0
\(916\) 1.32908i 0.0439140i
\(917\) −3.49968 + 31.5202i −0.115570 + 1.04089i
\(918\) 0.372165 + 0.372165i 0.0122833 + 0.0122833i
\(919\) −27.8600 16.0850i −0.919015 0.530594i −0.0356945 0.999363i \(-0.511364\pi\)
−0.883321 + 0.468769i \(0.844698\pi\)
\(920\) 0 0
\(921\) 4.42930 + 7.67177i 0.145950 + 0.252793i
\(922\) 40.6053 10.8802i 1.33727 0.358319i
\(923\) −20.1336 + 20.1336i −0.662707 + 0.662707i
\(924\) −3.40655 + 8.72134i −0.112067 + 0.286911i
\(925\) 0 0
\(926\) 10.9767 19.0122i 0.360716 0.624779i
\(927\) −1.57114 + 5.86357i −0.0516030 + 0.192585i
\(928\) −7.90885 + 29.5162i −0.259621 + 0.968918i
\(929\) 20.2533 35.0798i 0.664490 1.15093i −0.314934 0.949114i \(-0.601982\pi\)
0.979423 0.201816i \(-0.0646843\pi\)
\(930\) 0 0
\(931\) 8.59799 + 27.5561i 0.281788 + 0.903115i
\(932\) −15.0602 + 15.0602i −0.493314 + 0.493314i
\(933\) 6.45191 1.72878i 0.211226 0.0565979i
\(934\) −16.8406 29.1687i −0.551040 0.954429i
\(935\) 0 0
\(936\) −10.2405 5.91237i −0.334722 0.193252i
\(937\) −10.0291 10.0291i −0.327637 0.327637i 0.524050 0.851687i \(-0.324420\pi\)
−0.851687 + 0.524050i \(0.824420\pi\)
\(938\) −13.4071 + 5.87540i −0.437759 + 0.191838i
\(939\) 1.85462i 0.0605232i
\(940\) 0 0
\(941\) −32.3581 + 18.6820i −1.05485 + 0.609015i −0.924002 0.382388i \(-0.875102\pi\)
−0.130843 + 0.991403i \(0.541768\pi\)
\(942\) −6.39284 1.71296i −0.208290 0.0558111i
\(943\) 5.53701 + 20.6644i 0.180310 + 0.672926i
\(944\) 2.67885 0.0871893
\(945\) 0 0
\(946\) 45.6170 1.48314
\(947\) −0.500489 1.86785i −0.0162637 0.0606970i 0.957317 0.289040i \(-0.0933360\pi\)
−0.973581 + 0.228343i \(0.926669\pi\)
\(948\) −14.5176 3.88998i −0.471510 0.126341i
\(949\) 52.4582 30.2868i 1.70287 0.983150i
\(950\) 0 0
\(951\) 1.72496i 0.0559358i
\(952\) −3.35684 2.46905i −0.108796 0.0800225i
\(953\) −14.5970 14.5970i −0.472845 0.472845i 0.429989 0.902834i \(-0.358517\pi\)
−0.902834 + 0.429989i \(0.858517\pi\)
\(954\) −4.99644 2.88470i −0.161766 0.0933955i
\(955\) 0 0
\(956\) 6.37346 + 11.0392i 0.206132 + 0.357032i
\(957\) 21.1608 5.67003i 0.684033 0.183286i
\(958\) 11.6285 11.6285i 0.375700 0.375700i
\(959\) 2.51935 + 16.5327i 0.0813541 + 0.533869i
\(960\) 0 0
\(961\) −13.5467 + 23.4635i −0.436989 + 0.756887i
\(962\) 0.161787 0.603797i 0.00521622 0.0194672i
\(963\) −3.02740 + 11.2984i −0.0975565 + 0.364086i
\(964\) −12.6502 + 21.9108i −0.407436 + 0.705700i
\(965\) 0 0
\(966\) −5.35456 + 4.28435i −0.172280 + 0.137847i
\(967\) −34.5723 + 34.5723i −1.11177 + 1.11177i −0.118858 + 0.992911i \(0.537923\pi\)
−0.992911 + 0.118858i \(0.962077\pi\)
\(968\) 4.97287 1.33248i 0.159834 0.0428274i
\(969\) 1.08116 + 1.87262i 0.0347318 + 0.0601573i
\(970\) 0 0
\(971\) −2.45937 1.41992i −0.0789251 0.0455674i 0.460018 0.887910i \(-0.347843\pi\)
−0.538943 + 0.842342i \(0.681176\pi\)
\(972\) −0.701798 0.701798i −0.0225102 0.0225102i
\(973\) 5.39334 + 12.3071i 0.172903 + 0.394549i
\(974\) 4.38930i 0.140642i
\(975\) 0 0
\(976\) −8.93662 + 5.15956i −0.286054 + 0.165154i
\(977\) −36.0763 9.66661i −1.15418 0.309262i −0.369543 0.929214i \(-0.620486\pi\)
−0.784640 + 0.619951i \(0.787152\pi\)
\(978\) 0.363191 + 1.35545i 0.0116136 + 0.0433424i
\(979\) −39.4129 −1.25964
\(980\) 0 0
\(981\) −12.5360 −0.400245
\(982\) −8.79732 32.8320i −0.280734 1.04771i
\(983\) −30.9698 8.29834i −0.987784 0.264676i −0.271465 0.962448i \(-0.587508\pi\)
−0.716320 + 0.697772i \(0.754175\pi\)
\(984\) −21.5510 + 12.4425i −0.687021 + 0.396651i
\(985\) 0 0
\(986\) 3.23369i 0.102982i
\(987\) −5.70699 13.0228i −0.181655 0.414522i
\(988\) −11.3930 11.3930i −0.362461 0.362461i
\(989\) −28.5031 16.4563i −0.906346 0.523279i
\(990\) 0 0
\(991\) −20.9999 36.3729i −0.667084 1.15542i −0.978716 0.205221i \(-0.934209\pi\)
0.311632 0.950203i \(-0.399125\pi\)
\(992\) 9.49546 2.54430i 0.301481 0.0807817i
\(993\) 18.3973 18.3973i 0.583821 0.583821i
\(994\) −14.9978 + 12.0002i −0.475700 + 0.380623i
\(995\) 0 0
\(996\) 6.61355 11.4550i 0.209558 0.362966i
\(997\) −5.68114 + 21.2023i −0.179924 + 0.671484i 0.815737 + 0.578423i \(0.196332\pi\)
−0.995660 + 0.0930609i \(0.970335\pi\)
\(998\) −4.57137 + 17.0606i −0.144704 + 0.540044i
\(999\) 0.0790967 0.136999i 0.00250251 0.00433447i
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 525.2.bc.e.418.3 32
5.2 odd 4 inner 525.2.bc.e.82.6 32
5.3 odd 4 105.2.u.a.82.3 yes 32
5.4 even 2 105.2.u.a.103.6 yes 32
7.3 odd 6 inner 525.2.bc.e.493.6 32
15.8 even 4 315.2.bz.d.82.6 32
15.14 odd 2 315.2.bz.d.208.3 32
35.3 even 12 105.2.u.a.52.6 32
35.4 even 6 735.2.v.b.178.3 32
35.9 even 6 735.2.m.c.538.11 32
35.13 even 4 735.2.v.b.607.3 32
35.17 even 12 inner 525.2.bc.e.157.3 32
35.18 odd 12 735.2.v.b.472.6 32
35.19 odd 6 735.2.m.c.538.12 32
35.23 odd 12 735.2.m.c.97.12 32
35.24 odd 6 105.2.u.a.73.3 yes 32
35.33 even 12 735.2.m.c.97.11 32
35.34 odd 2 735.2.v.b.313.6 32
105.38 odd 12 315.2.bz.d.262.3 32
105.59 even 6 315.2.bz.d.73.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.u.a.52.6 32 35.3 even 12
105.2.u.a.73.3 yes 32 35.24 odd 6
105.2.u.a.82.3 yes 32 5.3 odd 4
105.2.u.a.103.6 yes 32 5.4 even 2
315.2.bz.d.73.6 32 105.59 even 6
315.2.bz.d.82.6 32 15.8 even 4
315.2.bz.d.208.3 32 15.14 odd 2
315.2.bz.d.262.3 32 105.38 odd 12
525.2.bc.e.82.6 32 5.2 odd 4 inner
525.2.bc.e.157.3 32 35.17 even 12 inner
525.2.bc.e.418.3 32 1.1 even 1 trivial
525.2.bc.e.493.6 32 7.3 odd 6 inner
735.2.m.c.97.11 32 35.33 even 12
735.2.m.c.97.12 32 35.23 odd 12
735.2.m.c.538.11 32 35.9 even 6
735.2.m.c.538.12 32 35.19 odd 6
735.2.v.b.178.3 32 35.4 even 6
735.2.v.b.313.6 32 35.34 odd 2
735.2.v.b.472.6 32 35.18 odd 12
735.2.v.b.607.3 32 35.13 even 4