Properties

Label 392.3.k.n.275.7
Level $392$
Weight $3$
Character 392.275
Analytic conductor $10.681$
Analytic rank $0$
Dimension $16$
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] = [392,3,Mod(67,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.67");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} - 448 x^{7} - 320 x^{6} + 2816 x^{5} - 5632 x^{4} + 6144 x^{3} + 12288 x^{2} + \cdots + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.7
Root \(0.109554 + 1.99700i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.n.67.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.78423 - 0.903622i) q^{2} +(2.28374 + 3.95555i) q^{3} +(2.36693 - 3.22453i) q^{4} +(4.96451 + 2.86626i) q^{5} +(7.64902 + 4.99396i) q^{6} +(1.30939 - 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +O(q^{10})\) \(q+(1.78423 - 0.903622i) q^{2} +(2.28374 + 3.95555i) q^{3} +(2.36693 - 3.22453i) q^{4} +(4.96451 + 2.86626i) q^{5} +(7.64902 + 4.99396i) q^{6} +(1.30939 - 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +(11.4478 + 0.628019i) q^{10} +(0.700323 + 1.21300i) q^{11} +(18.1602 + 1.99853i) q^{12} +19.0821i q^{13} +26.1831i q^{15} +(-4.79525 - 15.2645i) q^{16} +(-16.1349 - 27.9465i) q^{17} +(-1.29950 + 23.6880i) q^{18} +(6.28374 - 10.8837i) q^{19} +(20.9930 - 9.22398i) q^{20} +(2.34563 + 1.53143i) q^{22} +(-13.7605 - 7.94464i) q^{23} +(34.2079 - 12.8442i) q^{24} +(3.93090 + 6.80852i) q^{25} +(17.2430 + 34.0468i) q^{26} -13.0712 q^{27} -3.29194i q^{29} +(23.6597 + 46.7166i) q^{30} +(-19.6332 + 11.3352i) q^{31} +(-22.3492 - 22.9023i) q^{32} +(-3.19871 + 5.54032i) q^{33} +(-54.0415 - 35.2831i) q^{34} +(19.0864 + 43.4390i) q^{36} +(46.8985 + 27.0769i) q^{37} +(1.37681 - 25.0972i) q^{38} +(-75.4801 + 43.5785i) q^{39} +(29.1213 - 35.4274i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(5.56897 + 0.612863i) q^{44} +(-58.8880 + 33.9990i) q^{45} +(-31.7309 - 1.74073i) q^{46} +(18.7394 + 10.8192i) q^{47} +(49.4284 - 53.8280i) q^{48} +(13.1659 + 8.59589i) q^{50} +(73.6959 - 127.645i) q^{51} +(61.5309 + 45.1661i) q^{52} +(0.308883 - 0.178334i) q^{53} +(-23.3220 + 11.8114i) q^{54} +8.02924i q^{55} +57.4016 q^{57} +(-2.97467 - 5.87357i) q^{58} +(13.4292 + 23.2600i) q^{59} +(84.4284 + 61.9737i) q^{60} +(74.6763 + 43.1144i) q^{61} +(-24.7873 + 37.9656i) q^{62} +(-60.5710 - 20.6676i) q^{64} +(-54.6943 + 94.7333i) q^{65} +(-0.700861 + 12.7756i) q^{66} +(-57.2613 - 99.1794i) q^{67} +(-128.305 - 14.1199i) q^{68} -72.5739i q^{69} -104.792i q^{71} +(73.3069 + 60.2582i) q^{72} +(-12.1987 - 21.1288i) q^{73} +(108.145 + 5.93274i) q^{74} +(-17.9543 + 31.0977i) q^{75} +(-20.2218 - 46.0232i) q^{76} +(-95.2952 + 145.959i) q^{78} +(-101.436 - 58.5639i) q^{79} +(19.9460 - 89.5253i) q^{80} +(23.5270 + 40.7499i) q^{81} +(13.5531 - 6.86398i) q^{82} -79.2706 q^{83} -184.988i q^{85} +(-37.1973 + 18.8386i) q^{86} +(13.0214 - 7.51793i) q^{87} +(10.4901 - 3.93875i) q^{88} +(1.33039 - 2.30431i) q^{89} +(-74.3473 + 113.874i) q^{90} +(-58.1880 + 25.5669i) q^{92} +(-89.6741 - 51.7734i) q^{93} +(43.2119 + 2.37057i) q^{94} +(62.3913 - 36.0216i) q^{95} +(39.5514 - 140.706i) q^{96} +52.0930 q^{97} -16.6142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78423 0.903622i 0.892114 0.451811i
\(3\) 2.28374 + 3.95555i 0.761245 + 1.31852i 0.942209 + 0.335026i \(0.108745\pi\)
−0.180964 + 0.983490i \(0.557922\pi\)
\(4\) 2.36693 3.22453i 0.591733 0.806134i
\(5\) 4.96451 + 2.86626i 0.992902 + 0.573252i 0.906140 0.422977i \(-0.139015\pi\)
0.0867614 + 0.996229i \(0.472348\pi\)
\(6\) 7.64902 + 4.99396i 1.27484 + 0.832327i
\(7\) 0 0
\(8\) 1.30939 7.89212i 0.163673 0.986515i
\(9\) −5.93090 + 10.2726i −0.658989 + 1.14140i
\(10\) 11.4478 + 0.628019i 1.14478 + 0.0628019i
\(11\) 0.700323 + 1.21300i 0.0636658 + 0.110272i 0.896101 0.443849i \(-0.146388\pi\)
−0.832436 + 0.554122i \(0.813054\pi\)
\(12\) 18.1602 + 1.99853i 1.51335 + 0.166544i
\(13\) 19.0821i 1.46785i 0.679228 + 0.733927i \(0.262315\pi\)
−0.679228 + 0.733927i \(0.737685\pi\)
\(14\) 0 0
\(15\) 26.1831i 1.74554i
\(16\) −4.79525 15.2645i −0.299703 0.954032i
\(17\) −16.1349 27.9465i −0.949114 1.64391i −0.747296 0.664491i \(-0.768648\pi\)
−0.201818 0.979423i \(-0.564685\pi\)
\(18\) −1.29950 + 23.6880i −0.0721947 + 1.31600i
\(19\) 6.28374 10.8837i 0.330723 0.572829i −0.651931 0.758278i \(-0.726041\pi\)
0.982654 + 0.185449i \(0.0593741\pi\)
\(20\) 20.9930 9.22398i 1.04965 0.461199i
\(21\) 0 0
\(22\) 2.34563 + 1.53143i 0.106619 + 0.0696105i
\(23\) −13.7605 7.94464i −0.598284 0.345419i 0.170082 0.985430i \(-0.445597\pi\)
−0.768366 + 0.640011i \(0.778930\pi\)
\(24\) 34.2079 12.8442i 1.42533 0.535174i
\(25\) 3.93090 + 6.80852i 0.157236 + 0.272341i
\(26\) 17.2430 + 34.0468i 0.663193 + 1.30949i
\(27\) −13.0712 −0.484118
\(28\) 0 0
\(29\) 3.29194i 0.113515i −0.998388 0.0567576i \(-0.981924\pi\)
0.998388 0.0567576i \(-0.0180762\pi\)
\(30\) 23.6597 + 46.7166i 0.788655 + 1.55722i
\(31\) −19.6332 + 11.3352i −0.633329 + 0.365653i −0.782040 0.623228i \(-0.785821\pi\)
0.148711 + 0.988881i \(0.452488\pi\)
\(32\) −22.3492 22.9023i −0.698412 0.715696i
\(33\) −3.19871 + 5.54032i −0.0969305 + 0.167889i
\(34\) −54.0415 35.2831i −1.58946 1.03774i
\(35\) 0 0
\(36\) 19.0864 + 43.4390i 0.530177 + 1.20664i
\(37\) 46.8985 + 27.0769i 1.26753 + 0.731807i 0.974519 0.224303i \(-0.0720105\pi\)
0.293008 + 0.956110i \(0.405344\pi\)
\(38\) 1.37681 25.0972i 0.0362319 0.660453i
\(39\) −75.4801 + 43.5785i −1.93539 + 1.11740i
\(40\) 29.1213 35.4274i 0.728033 0.885686i
\(41\) 7.59607 0.185270 0.0926350 0.995700i \(-0.470471\pi\)
0.0926350 + 0.995700i \(0.470471\pi\)
\(42\) 0 0
\(43\) −20.8478 −0.484833 −0.242417 0.970172i \(-0.577940\pi\)
−0.242417 + 0.970172i \(0.577940\pi\)
\(44\) 5.56897 + 0.612863i 0.126567 + 0.0139287i
\(45\) −58.8880 + 33.9990i −1.30862 + 0.755533i
\(46\) −31.7309 1.74073i −0.689801 0.0378420i
\(47\) 18.7394 + 10.8192i 0.398711 + 0.230196i 0.685928 0.727670i \(-0.259397\pi\)
−0.287217 + 0.957866i \(0.592730\pi\)
\(48\) 49.4284 53.8280i 1.02976 1.12142i
\(49\) 0 0
\(50\) 13.1659 + 8.59589i 0.263319 + 0.171918i
\(51\) 73.6959 127.645i 1.44502 2.50284i
\(52\) 61.5309 + 45.1661i 1.18329 + 0.868578i
\(53\) 0.308883 0.178334i 0.00582798 0.00336479i −0.497083 0.867703i \(-0.665596\pi\)
0.502911 + 0.864338i \(0.332262\pi\)
\(54\) −23.3220 + 11.8114i −0.431888 + 0.218730i
\(55\) 8.02924i 0.145986i
\(56\) 0 0
\(57\) 57.4016 1.00705
\(58\) −2.97467 5.87357i −0.0512875 0.101269i
\(59\) 13.4292 + 23.2600i 0.227613 + 0.394237i 0.957100 0.289757i \(-0.0935746\pi\)
−0.729487 + 0.683994i \(0.760241\pi\)
\(60\) 84.4284 + 61.9737i 1.40714 + 1.03290i
\(61\) 74.6763 + 43.1144i 1.22420 + 0.706793i 0.965811 0.259248i \(-0.0834746\pi\)
0.258390 + 0.966041i \(0.416808\pi\)
\(62\) −24.7873 + 37.9656i −0.399796 + 0.612349i
\(63\) 0 0
\(64\) −60.5710 20.6676i −0.946422 0.322932i
\(65\) −54.6943 + 94.7333i −0.841450 + 1.45743i
\(66\) −0.700861 + 12.7756i −0.0106191 + 0.193570i
\(67\) −57.2613 99.1794i −0.854646 1.48029i −0.876973 0.480539i \(-0.840441\pi\)
0.0223272 0.999751i \(-0.492892\pi\)
\(68\) −128.305 14.1199i −1.88684 0.207646i
\(69\) 72.5739i 1.05180i
\(70\) 0 0
\(71\) 104.792i 1.47594i −0.674834 0.737969i \(-0.735785\pi\)
0.674834 0.737969i \(-0.264215\pi\)
\(72\) 73.3069 + 60.2582i 1.01815 + 0.836919i
\(73\) −12.1987 21.1288i −0.167106 0.289435i 0.770295 0.637687i \(-0.220109\pi\)
−0.937401 + 0.348252i \(0.886775\pi\)
\(74\) 108.145 + 5.93274i 1.46142 + 0.0801722i
\(75\) −17.9543 + 31.0977i −0.239390 + 0.414636i
\(76\) −20.2218 46.0232i −0.266077 0.605569i
\(77\) 0 0
\(78\) −95.2952 + 145.959i −1.22173 + 1.87127i
\(79\) −101.436 58.5639i −1.28400 0.741315i −0.306420 0.951897i \(-0.599131\pi\)
−0.977576 + 0.210581i \(0.932464\pi\)
\(80\) 19.9460 89.5253i 0.249325 1.11907i
\(81\) 23.5270 + 40.7499i 0.290456 + 0.503085i
\(82\) 13.5531 6.86398i 0.165282 0.0837070i
\(83\) −79.2706 −0.955067 −0.477534 0.878614i \(-0.658469\pi\)
−0.477534 + 0.878614i \(0.658469\pi\)
\(84\) 0 0
\(85\) 184.988i 2.17633i
\(86\) −37.1973 + 18.8386i −0.432526 + 0.219053i
\(87\) 13.0214 7.51793i 0.149672 0.0864130i
\(88\) 10.4901 3.93875i 0.119206 0.0447586i
\(89\) 1.33039 2.30431i 0.0149482 0.0258911i −0.858455 0.512890i \(-0.828575\pi\)
0.873403 + 0.486999i \(0.161908\pi\)
\(90\) −74.3473 + 113.874i −0.826081 + 1.26527i
\(91\) 0 0
\(92\) −58.1880 + 25.5669i −0.632479 + 0.277901i
\(93\) −89.6741 51.7734i −0.964238 0.556703i
\(94\) 43.2119 + 2.37057i 0.459701 + 0.0252188i
\(95\) 62.3913 36.0216i 0.656751 0.379175i
\(96\) 39.5514 140.706i 0.411994 1.46569i
\(97\) 52.0930 0.537042 0.268521 0.963274i \(-0.413465\pi\)
0.268521 + 0.963274i \(0.413465\pi\)
\(98\) 0 0
\(99\) −16.6142 −0.167820
\(100\) 31.2585 + 3.43999i 0.312585 + 0.0343999i
\(101\) −79.2189 + 45.7371i −0.784346 + 0.452842i −0.837968 0.545719i \(-0.816257\pi\)
0.0536223 + 0.998561i \(0.482923\pi\)
\(102\) 16.1473 294.341i 0.158307 2.88570i
\(103\) 34.4584 + 19.8946i 0.334548 + 0.193151i 0.657858 0.753142i \(-0.271463\pi\)
−0.323311 + 0.946293i \(0.604796\pi\)
\(104\) 150.598 + 24.9858i 1.44806 + 0.240248i
\(105\) 0 0
\(106\) 0.389971 0.597301i 0.00367897 0.00563492i
\(107\) −41.3316 + 71.5884i −0.386276 + 0.669050i −0.991945 0.126667i \(-0.959572\pi\)
0.605669 + 0.795717i \(0.292906\pi\)
\(108\) −30.9386 + 42.1485i −0.286469 + 0.390264i
\(109\) −25.5234 + 14.7359i −0.234160 + 0.135192i −0.612490 0.790479i \(-0.709832\pi\)
0.378330 + 0.925671i \(0.376499\pi\)
\(110\) 7.25540 + 14.3260i 0.0659582 + 0.130236i
\(111\) 247.346i 2.22834i
\(112\) 0 0
\(113\) 159.133 1.40826 0.704130 0.710071i \(-0.251337\pi\)
0.704130 + 0.710071i \(0.251337\pi\)
\(114\) 102.417 51.8693i 0.898399 0.454994i
\(115\) −45.5428 78.8825i −0.396025 0.685935i
\(116\) −10.6150 7.79181i −0.0915085 0.0671708i
\(117\) −196.023 113.174i −1.67541 0.967299i
\(118\) 44.9789 + 29.3662i 0.381177 + 0.248866i
\(119\) 0 0
\(120\) 206.640 + 34.2838i 1.72200 + 0.285698i
\(121\) 59.5191 103.090i 0.491893 0.851984i
\(122\) 172.199 + 9.44668i 1.41146 + 0.0774318i
\(123\) 17.3474 + 30.0466i 0.141036 + 0.244281i
\(124\) −9.91963 + 90.1377i −0.0799970 + 0.726917i
\(125\) 98.2451i 0.785961i
\(126\) 0 0
\(127\) 16.0834i 0.126641i 0.997993 + 0.0633205i \(0.0201690\pi\)
−0.997993 + 0.0633205i \(0.979831\pi\)
\(128\) −126.748 + 17.8575i −0.990220 + 0.139512i
\(129\) −47.6110 82.4646i −0.369077 0.639260i
\(130\) −11.9839 + 218.449i −0.0921840 + 1.68037i
\(131\) −59.0678 + 102.308i −0.450899 + 0.780981i −0.998442 0.0557972i \(-0.982230\pi\)
0.547543 + 0.836778i \(0.315563\pi\)
\(132\) 10.2938 + 23.4279i 0.0779836 + 0.177484i
\(133\) 0 0
\(134\) −191.788 125.216i −1.43125 0.934448i
\(135\) −64.8920 37.4654i −0.480681 0.277522i
\(136\) −241.684 + 90.7461i −1.77709 + 0.667250i
\(137\) 9.58539 + 16.6024i 0.0699664 + 0.121185i 0.898886 0.438182i \(-0.144377\pi\)
−0.828920 + 0.559367i \(0.811044\pi\)
\(138\) −65.5794 129.488i −0.475213 0.938321i
\(139\) −104.954 −0.755062 −0.377531 0.925997i \(-0.623227\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(140\) 0 0
\(141\) 98.8329i 0.700942i
\(142\) −94.6920 186.972i −0.666845 1.31670i
\(143\) −23.1465 + 13.3636i −0.161864 + 0.0934520i
\(144\) 185.247 + 41.2725i 1.28644 + 0.286615i
\(145\) 9.43556 16.3429i 0.0650729 0.112709i
\(146\) −40.8577 26.6755i −0.279847 0.182709i
\(147\) 0 0
\(148\) 198.316 87.1367i 1.33997 0.588762i
\(149\) 71.3523 + 41.1953i 0.478875 + 0.276478i 0.719947 0.694029i \(-0.244166\pi\)
−0.241073 + 0.970507i \(0.577499\pi\)
\(150\) −3.93392 + 71.7093i −0.0262261 + 0.478062i
\(151\) −50.0038 + 28.8697i −0.331151 + 0.191190i −0.656352 0.754455i \(-0.727901\pi\)
0.325201 + 0.945645i \(0.394568\pi\)
\(152\) −77.6680 63.8430i −0.510974 0.420020i
\(153\) 382.779 2.50182
\(154\) 0 0
\(155\) −129.959 −0.838445
\(156\) −38.1361 + 346.536i −0.244462 + 2.22138i
\(157\) −3.23006 + 1.86488i −0.0205736 + 0.0118782i −0.510252 0.860025i \(-0.670448\pi\)
0.489678 + 0.871903i \(0.337114\pi\)
\(158\) −233.904 12.8318i −1.48040 0.0812139i
\(159\) 1.41081 + 0.814534i 0.00887305 + 0.00512286i
\(160\) −45.3088 177.757i −0.283180 1.11098i
\(161\) 0 0
\(162\) 78.8000 + 51.4476i 0.486420 + 0.317578i
\(163\) −38.8534 + 67.2961i −0.238365 + 0.412860i −0.960245 0.279158i \(-0.909945\pi\)
0.721881 + 0.692018i \(0.243278\pi\)
\(164\) 17.9794 24.4938i 0.109630 0.149352i
\(165\) −31.7600 + 18.3367i −0.192485 + 0.111131i
\(166\) −141.437 + 71.6306i −0.852028 + 0.431510i
\(167\) 62.0837i 0.371759i −0.982573 0.185879i \(-0.940487\pi\)
0.982573 0.185879i \(-0.0595133\pi\)
\(168\) 0 0
\(169\) −195.127 −1.15459
\(170\) −167.159 330.060i −0.983289 1.94153i
\(171\) 74.5364 + 129.101i 0.435885 + 0.754976i
\(172\) −49.3454 + 67.2246i −0.286892 + 0.390841i
\(173\) −169.407 97.8069i −0.979228 0.565358i −0.0771913 0.997016i \(-0.524595\pi\)
−0.902037 + 0.431659i \(0.857929\pi\)
\(174\) 16.4398 25.1801i 0.0944818 0.144713i
\(175\) 0 0
\(176\) 15.1576 16.5067i 0.0861225 0.0937882i
\(177\) −61.3373 + 106.239i −0.346538 + 0.600222i
\(178\) 0.291499 5.31358i 0.00163763 0.0298515i
\(179\) −36.1049 62.5356i −0.201704 0.349361i 0.747374 0.664404i \(-0.231314\pi\)
−0.949077 + 0.315043i \(0.897981\pi\)
\(180\) −29.7530 + 270.360i −0.165295 + 1.50200i
\(181\) 140.980i 0.778895i 0.921049 + 0.389448i \(0.127334\pi\)
−0.921049 + 0.389448i \(0.872666\pi\)
\(182\) 0 0
\(183\) 393.847i 2.15217i
\(184\) −80.7179 + 98.1971i −0.438684 + 0.533680i
\(185\) 155.219 + 268.847i 0.839020 + 1.45323i
\(186\) −206.783 11.3439i −1.11173 0.0609889i
\(187\) 22.5994 39.1432i 0.120852 0.209322i
\(188\) 79.2419 34.8176i 0.421499 0.185200i
\(189\) 0 0
\(190\) 78.7703 120.649i 0.414581 0.634995i
\(191\) 246.361 + 142.236i 1.28985 + 0.744693i 0.978627 0.205645i \(-0.0659293\pi\)
0.311219 + 0.950338i \(0.399263\pi\)
\(192\) −56.5764 286.791i −0.294669 1.49370i
\(193\) 61.9251 + 107.257i 0.320855 + 0.555738i 0.980665 0.195695i \(-0.0626964\pi\)
−0.659810 + 0.751433i \(0.729363\pi\)
\(194\) 92.9458 47.0724i 0.479102 0.242641i
\(195\) −499.629 −2.56220
\(196\) 0 0
\(197\) 108.098i 0.548721i 0.961627 + 0.274361i \(0.0884662\pi\)
−0.961627 + 0.274361i \(0.911534\pi\)
\(198\) −29.6435 + 15.0129i −0.149715 + 0.0758230i
\(199\) −287.394 + 165.927i −1.44419 + 0.833804i −0.998126 0.0611961i \(-0.980508\pi\)
−0.446065 + 0.895000i \(0.647175\pi\)
\(200\) 58.8807 22.1081i 0.294403 0.110541i
\(201\) 261.539 452.999i 1.30119 2.25373i
\(202\) −100.016 + 153.189i −0.495127 + 0.758363i
\(203\) 0 0
\(204\) −237.163 539.762i −1.16256 2.64589i
\(205\) 37.7107 + 21.7723i 0.183955 + 0.106206i
\(206\) 79.4588 + 4.35905i 0.385722 + 0.0211604i
\(207\) 163.225 94.2378i 0.788525 0.455255i
\(208\) 291.279 91.5035i 1.40038 0.439920i
\(209\) 17.6026 0.0842229
\(210\) 0 0
\(211\) 26.3950 0.125095 0.0625475 0.998042i \(-0.480078\pi\)
0.0625475 + 0.998042i \(0.480078\pi\)
\(212\) 0.156062 1.41811i 0.000736143 0.00668919i
\(213\) 414.508 239.316i 1.94605 1.12355i
\(214\) −9.05606 + 165.078i −0.0423180 + 0.771393i
\(215\) −103.499 59.7553i −0.481392 0.277932i
\(216\) −17.1152 + 103.159i −0.0792371 + 0.477589i
\(217\) 0 0
\(218\) −32.2238 + 49.3558i −0.147816 + 0.226403i
\(219\) 55.7172 96.5051i 0.254417 0.440663i
\(220\) 25.8906 + 19.0047i 0.117684 + 0.0863849i
\(221\) 533.279 307.889i 2.41303 1.39316i
\(222\) 223.507 + 441.321i 1.00679 + 1.98793i
\(223\) 161.183i 0.722796i 0.932412 + 0.361398i \(0.117700\pi\)
−0.932412 + 0.361398i \(0.882300\pi\)
\(224\) 0 0
\(225\) −93.2551 −0.414467
\(226\) 283.930 143.797i 1.25633 0.636268i
\(227\) −85.6395 148.332i −0.377266 0.653445i 0.613397 0.789775i \(-0.289803\pi\)
−0.990663 + 0.136330i \(0.956469\pi\)
\(228\) 135.866 185.093i 0.595902 0.811813i
\(229\) 198.537 + 114.626i 0.866975 + 0.500548i 0.866342 0.499452i \(-0.166465\pi\)
0.000632973 1.00000i \(0.499799\pi\)
\(230\) −152.539 99.5908i −0.663212 0.433003i
\(231\) 0 0
\(232\) −25.9804 4.31042i −0.111984 0.0185794i
\(233\) 135.077 233.961i 0.579730 1.00412i −0.415780 0.909465i \(-0.636491\pi\)
0.995510 0.0946571i \(-0.0301755\pi\)
\(234\) −452.016 24.7973i −1.93169 0.105971i
\(235\) 62.0214 + 107.424i 0.263921 + 0.457124i
\(236\) 106.789 + 11.7520i 0.452494 + 0.0497968i
\(237\) 534.978i 2.25729i
\(238\) 0 0
\(239\) 157.155i 0.657551i −0.944408 0.328776i \(-0.893364\pi\)
0.944408 0.328776i \(-0.106636\pi\)
\(240\) 399.673 125.555i 1.66530 0.523144i
\(241\) −48.8562 84.6214i −0.202723 0.351126i 0.746682 0.665181i \(-0.231646\pi\)
−0.949405 + 0.314055i \(0.898312\pi\)
\(242\) 13.0411 237.719i 0.0538888 0.982310i
\(243\) −166.279 + 288.004i −0.684276 + 1.18520i
\(244\) 315.778 138.747i 1.29417 0.568637i
\(245\) 0 0
\(246\) 58.1025 + 37.9345i 0.236189 + 0.154205i
\(247\) 207.685 + 119.907i 0.840829 + 0.485453i
\(248\) 63.7516 + 169.790i 0.257063 + 0.684636i
\(249\) −181.033 313.558i −0.727040 1.25927i
\(250\) −88.7765 175.292i −0.355106 0.701166i
\(251\) 313.145 1.24759 0.623796 0.781587i \(-0.285590\pi\)
0.623796 + 0.781587i \(0.285590\pi\)
\(252\) 0 0
\(253\) 22.2553i 0.0879655i
\(254\) 14.5333 + 28.6965i 0.0572178 + 0.112978i
\(255\) 731.728 422.463i 2.86952 1.65672i
\(256\) −210.011 + 146.394i −0.820356 + 0.571853i
\(257\) −174.428 + 302.118i −0.678707 + 1.17555i 0.296664 + 0.954982i \(0.404126\pi\)
−0.975371 + 0.220573i \(0.929207\pi\)
\(258\) −159.466 104.113i −0.618084 0.403540i
\(259\) 0 0
\(260\) 176.013 + 400.591i 0.676973 + 1.54073i
\(261\) 33.8169 + 19.5242i 0.129567 + 0.0748053i
\(262\) −12.9422 + 235.917i −0.0493977 + 0.900445i
\(263\) −332.869 + 192.182i −1.26566 + 0.730729i −0.974164 0.225843i \(-0.927486\pi\)
−0.291496 + 0.956572i \(0.594153\pi\)
\(264\) 39.5365 + 32.4990i 0.149760 + 0.123102i
\(265\) 2.04460 0.00771548
\(266\) 0 0
\(267\) 12.1530 0.0455170
\(268\) −455.341 50.1102i −1.69903 0.186978i
\(269\) 32.7022 18.8806i 0.121570 0.0701882i −0.437982 0.898984i \(-0.644307\pi\)
0.559552 + 0.828795i \(0.310973\pi\)
\(270\) −149.637 8.20895i −0.554210 0.0304035i
\(271\) 267.368 + 154.365i 0.986597 + 0.569612i 0.904255 0.426992i \(-0.140427\pi\)
0.0823420 + 0.996604i \(0.473760\pi\)
\(272\) −349.219 + 380.303i −1.28389 + 1.39817i
\(273\) 0 0
\(274\) 32.1048 + 20.9609i 0.117171 + 0.0764995i
\(275\) −5.50580 + 9.53633i −0.0200211 + 0.0346775i
\(276\) −234.017 171.778i −0.847888 0.622382i
\(277\) −211.492 + 122.105i −0.763508 + 0.440812i −0.830554 0.556938i \(-0.811976\pi\)
0.0670458 + 0.997750i \(0.478643\pi\)
\(278\) −187.261 + 94.8385i −0.673601 + 0.341146i
\(279\) 268.913i 0.963845i
\(280\) 0 0
\(281\) 266.569 0.948646 0.474323 0.880351i \(-0.342693\pi\)
0.474323 + 0.880351i \(0.342693\pi\)
\(282\) 89.3076 + 176.340i 0.316694 + 0.625320i
\(283\) 82.8026 + 143.418i 0.292589 + 0.506778i 0.974421 0.224730i \(-0.0721501\pi\)
−0.681833 + 0.731508i \(0.738817\pi\)
\(284\) −337.904 248.035i −1.18980 0.873362i
\(285\) 284.971 + 164.528i 0.999897 + 0.577291i
\(286\) −29.2229 + 44.7595i −0.102178 + 0.156502i
\(287\) 0 0
\(288\) 367.817 93.7535i 1.27714 0.325533i
\(289\) −376.173 + 651.550i −1.30164 + 2.25450i
\(290\) 2.06740 37.6856i 0.00712898 0.129950i
\(291\) 118.967 + 206.056i 0.408820 + 0.708098i
\(292\) −97.0040 10.6753i −0.332206 0.0365591i
\(293\) 34.3652i 0.117288i 0.998279 + 0.0586438i \(0.0186776\pi\)
−0.998279 + 0.0586438i \(0.981322\pi\)
\(294\) 0 0
\(295\) 153.966i 0.521918i
\(296\) 275.102 334.674i 0.929399 1.13066i
\(297\) −9.15405 15.8553i −0.0308217 0.0533848i
\(298\) 164.534 + 9.02620i 0.552127 + 0.0302893i
\(299\) 151.600 262.580i 0.507025 0.878193i
\(300\) 57.7791 + 131.500i 0.192597 + 0.438335i
\(301\) 0 0
\(302\) −63.1309 + 96.6947i −0.209043 + 0.320181i
\(303\) −361.830 208.903i −1.19416 0.689448i
\(304\) −196.267 43.7279i −0.645616 0.143842i
\(305\) 247.154 + 428.083i 0.810341 + 1.40355i
\(306\) 682.964 345.888i 2.23191 1.13035i
\(307\) 222.934 0.726170 0.363085 0.931756i \(-0.381724\pi\)
0.363085 + 0.931756i \(0.381724\pi\)
\(308\) 0 0
\(309\) 181.736i 0.588141i
\(310\) −231.876 + 117.434i −0.747988 + 0.378819i
\(311\) 363.673 209.967i 1.16937 0.675135i 0.215837 0.976429i \(-0.430752\pi\)
0.953531 + 0.301294i \(0.0974187\pi\)
\(312\) 245.094 + 652.759i 0.785557 + 2.09218i
\(313\) −146.934 + 254.498i −0.469439 + 0.813092i −0.999390 0.0349363i \(-0.988877\pi\)
0.529950 + 0.848029i \(0.322211\pi\)
\(314\) −4.07802 + 6.24612i −0.0129873 + 0.0198921i
\(315\) 0 0
\(316\) −428.933 + 188.466i −1.35738 + 0.596411i
\(317\) 366.728 + 211.730i 1.15687 + 0.667919i 0.950552 0.310566i \(-0.100519\pi\)
0.206318 + 0.978485i \(0.433852\pi\)
\(318\) 3.25324 + 0.178471i 0.0102303 + 0.000561228i
\(319\) 3.99311 2.30542i 0.0125176 0.00722703i
\(320\) −241.466 276.217i −0.754583 0.863178i
\(321\) −377.561 −1.17620
\(322\) 0 0
\(323\) −405.551 −1.25558
\(324\) 187.086 + 20.5888i 0.577427 + 0.0635456i
\(325\) −129.921 + 75.0098i −0.399756 + 0.230799i
\(326\) −8.51308 + 155.180i −0.0261137 + 0.476014i
\(327\) −116.577 67.3060i −0.356506 0.205829i
\(328\) 9.94618 59.9491i 0.0303237 0.182772i
\(329\) 0 0
\(330\) −40.0977 + 61.4158i −0.121508 + 0.186109i
\(331\) 63.3332 109.696i 0.191339 0.331409i −0.754355 0.656467i \(-0.772050\pi\)
0.945694 + 0.325057i \(0.105384\pi\)
\(332\) −187.628 + 255.611i −0.565145 + 0.769912i
\(333\) −556.301 + 321.180i −1.67057 + 0.964505i
\(334\) −56.1002 110.771i −0.167965 0.331651i
\(335\) 656.503i 1.95971i
\(336\) 0 0
\(337\) 302.404 0.897341 0.448671 0.893697i \(-0.351898\pi\)
0.448671 + 0.893697i \(0.351898\pi\)
\(338\) −348.150 + 176.321i −1.03003 + 0.521659i
\(339\) 363.419 + 629.460i 1.07203 + 1.85681i
\(340\) −596.500 437.854i −1.75441 1.28781i
\(341\) −27.4992 15.8767i −0.0806428 0.0465591i
\(342\) 249.648 + 162.992i 0.729966 + 0.476586i
\(343\) 0 0
\(344\) −27.2979 + 164.534i −0.0793542 + 0.478295i
\(345\) 208.016 360.294i 0.602944 1.04433i
\(346\) −390.640 21.4302i −1.12902 0.0619371i
\(347\) −160.266 277.589i −0.461862 0.799969i 0.537192 0.843460i \(-0.319485\pi\)
−0.999054 + 0.0434916i \(0.986152\pi\)
\(348\) 6.57904 59.7825i 0.0189053 0.171789i
\(349\) 380.678i 1.09077i 0.838186 + 0.545385i \(0.183616\pi\)
−0.838186 + 0.545385i \(0.816384\pi\)
\(350\) 0 0
\(351\) 249.426i 0.710614i
\(352\) 12.1287 43.1485i 0.0344566 0.122581i
\(353\) −182.185 315.553i −0.516104 0.893918i −0.999825 0.0186962i \(-0.994048\pi\)
0.483721 0.875222i \(-0.339285\pi\)
\(354\) −13.4395 + 244.981i −0.0379646 + 0.692036i
\(355\) 300.360 520.239i 0.846085 1.46546i
\(356\) −4.28137 9.74403i −0.0120263 0.0273709i
\(357\) 0 0
\(358\) −120.928 78.9525i −0.337788 0.220538i
\(359\) 96.9908 + 55.9977i 0.270169 + 0.155982i 0.628965 0.777434i \(-0.283479\pi\)
−0.358795 + 0.933416i \(0.616812\pi\)
\(360\) 191.217 + 509.269i 0.531158 + 1.41464i
\(361\) 101.529 + 175.854i 0.281245 + 0.487130i
\(362\) 127.393 + 251.540i 0.351914 + 0.694863i
\(363\) 543.704 1.49781
\(364\) 0 0
\(365\) 139.859i 0.383174i
\(366\) 355.889 + 702.713i 0.972375 + 1.91998i
\(367\) −380.222 + 219.521i −1.03603 + 0.598150i −0.918705 0.394944i \(-0.870764\pi\)
−0.117321 + 0.993094i \(0.537431\pi\)
\(368\) −55.2860 + 248.144i −0.150234 + 0.674305i
\(369\) −45.0515 + 78.0315i −0.122091 + 0.211468i
\(370\) 519.881 + 339.424i 1.40508 + 0.917363i
\(371\) 0 0
\(372\) −379.198 + 166.613i −1.01935 + 0.447885i
\(373\) −220.833 127.498i −0.592047 0.341818i 0.173860 0.984770i \(-0.444376\pi\)
−0.765906 + 0.642952i \(0.777709\pi\)
\(374\) 4.95169 90.2617i 0.0132398 0.241341i
\(375\) 388.613 224.366i 1.03630 0.598309i
\(376\) 109.924 133.727i 0.292350 0.355657i
\(377\) 62.8172 0.166624
\(378\) 0 0
\(379\) 603.048 1.59116 0.795578 0.605852i \(-0.207167\pi\)
0.795578 + 0.605852i \(0.207167\pi\)
\(380\) 31.5231 286.444i 0.0829554 0.753800i
\(381\) −63.6187 + 36.7303i −0.166978 + 0.0964049i
\(382\) 568.091 + 31.1651i 1.48715 + 0.0815839i
\(383\) 63.5537 + 36.6927i 0.165937 + 0.0958035i 0.580668 0.814140i \(-0.302791\pi\)
−0.414732 + 0.909944i \(0.636125\pi\)
\(384\) −360.096 460.577i −0.937749 1.19942i
\(385\) 0 0
\(386\) 207.408 + 135.415i 0.537328 + 0.350815i
\(387\) 123.646 214.162i 0.319500 0.553390i
\(388\) 123.301 167.976i 0.317785 0.432927i
\(389\) 295.141 170.400i 0.758718 0.438046i −0.0701174 0.997539i \(-0.522337\pi\)
0.828835 + 0.559493i \(0.189004\pi\)
\(390\) −891.452 + 451.476i −2.28577 + 1.15763i
\(391\) 512.745i 1.31137i
\(392\) 0 0
\(393\) −539.581 −1.37298
\(394\) 97.6799 + 192.872i 0.247918 + 0.489522i
\(395\) −335.719 581.482i −0.849921 1.47211i
\(396\) −39.3247 + 53.5730i −0.0993047 + 0.135285i
\(397\) −96.5963 55.7699i −0.243316 0.140478i 0.373384 0.927677i \(-0.378197\pi\)
−0.616700 + 0.787199i \(0.711531\pi\)
\(398\) −362.841 + 555.747i −0.911661 + 1.39635i
\(399\) 0 0
\(400\) 85.0791 92.6518i 0.212698 0.231630i
\(401\) −170.268 + 294.912i −0.424607 + 0.735441i −0.996384 0.0849681i \(-0.972921\pi\)
0.571776 + 0.820410i \(0.306254\pi\)
\(402\) 57.3052 1044.59i 0.142550 2.59847i
\(403\) −216.300 374.643i −0.536725 0.929635i
\(404\) −40.0252 + 363.701i −0.0990722 + 0.900250i
\(405\) 269.738i 0.666019i
\(406\) 0 0
\(407\) 75.8502i 0.186364i
\(408\) −910.893 748.753i −2.23258 1.83518i
\(409\) 333.480 + 577.604i 0.815354 + 1.41223i 0.909074 + 0.416635i \(0.136791\pi\)
−0.0937202 + 0.995599i \(0.529876\pi\)
\(410\) 86.9585 + 4.77048i 0.212094 + 0.0116353i
\(411\) −43.7810 + 75.8309i −0.106523 + 0.184503i
\(412\) 145.711 64.0232i 0.353669 0.155396i
\(413\) 0 0
\(414\) 206.074 315.635i 0.497764 0.762403i
\(415\) −393.539 227.210i −0.948288 0.547494i
\(416\) 437.024 426.469i 1.05054 1.02517i
\(417\) −239.686 415.149i −0.574788 0.995561i
\(418\) 31.4070 15.9061i 0.0751364 0.0380528i
\(419\) 200.191 0.477783 0.238891 0.971046i \(-0.423216\pi\)
0.238891 + 0.971046i \(0.423216\pi\)
\(420\) 0 0
\(421\) 15.9136i 0.0377996i −0.999821 0.0188998i \(-0.993984\pi\)
0.999821 0.0188998i \(-0.00601636\pi\)
\(422\) 47.0947 23.8511i 0.111599 0.0565193i
\(423\) −222.283 + 128.335i −0.525492 + 0.303393i
\(424\) −1.00298 2.67125i −0.00236553 0.00630011i
\(425\) 126.850 219.710i 0.298470 0.516965i
\(426\) 523.325 801.554i 1.22846 1.88158i
\(427\) 0 0
\(428\) 133.010 + 302.720i 0.310771 + 0.707290i
\(429\) −105.721 61.0380i −0.246436 0.142280i
\(430\) −238.662 13.0928i −0.555029 0.0304485i
\(431\) 543.875 314.006i 1.26189 0.728553i 0.288451 0.957495i \(-0.406860\pi\)
0.973440 + 0.228941i \(0.0735264\pi\)
\(432\) 62.6796 + 199.525i 0.145092 + 0.461864i
\(433\) −789.232 −1.82271 −0.911353 0.411625i \(-0.864961\pi\)
−0.911353 + 0.411625i \(0.864961\pi\)
\(434\) 0 0
\(435\) 86.1933 0.198146
\(436\) −12.8956 + 117.180i −0.0295771 + 0.268762i
\(437\) −172.935 + 99.8441i −0.395732 + 0.228476i
\(438\) 12.2081 222.534i 0.0278723 0.508069i
\(439\) −576.400 332.785i −1.31298 0.758052i −0.330395 0.943843i \(-0.607182\pi\)
−0.982589 + 0.185791i \(0.940515\pi\)
\(440\) 63.3677 + 10.5134i 0.144017 + 0.0238940i
\(441\) 0 0
\(442\) 673.275 1031.23i 1.52325 2.33309i
\(443\) −253.576 + 439.206i −0.572406 + 0.991436i 0.423912 + 0.905703i \(0.360656\pi\)
−0.996318 + 0.0857327i \(0.972677\pi\)
\(444\) 797.575 + 585.451i 1.79634 + 1.31858i
\(445\) 13.2095 7.62650i 0.0296842 0.0171382i
\(446\) 145.649 + 287.588i 0.326567 + 0.644816i
\(447\) 376.317i 0.841872i
\(448\) 0 0
\(449\) −279.029 −0.621446 −0.310723 0.950501i \(-0.600571\pi\)
−0.310723 + 0.950501i \(0.600571\pi\)
\(450\) −166.388 + 84.2673i −0.369752 + 0.187261i
\(451\) 5.31970 + 9.21400i 0.0117954 + 0.0204301i
\(452\) 376.658 513.131i 0.833315 1.13525i
\(453\) −228.391 131.862i −0.504175 0.291085i
\(454\) −286.836 187.272i −0.631798 0.412494i
\(455\) 0 0
\(456\) 75.1608 453.020i 0.164826 0.993465i
\(457\) 360.441 624.302i 0.788710 1.36609i −0.138047 0.990426i \(-0.544082\pi\)
0.926757 0.375661i \(-0.122584\pi\)
\(458\) 457.814 + 25.1153i 0.999593 + 0.0548369i
\(459\) 210.903 + 365.294i 0.459483 + 0.795848i
\(460\) −362.156 39.8552i −0.787296 0.0866417i
\(461\) 483.262i 1.04829i 0.851629 + 0.524145i \(0.175615\pi\)
−0.851629 + 0.524145i \(0.824385\pi\)
\(462\) 0 0
\(463\) 39.6326i 0.0855995i 0.999084 + 0.0427997i \(0.0136277\pi\)
−0.999084 + 0.0427997i \(0.986372\pi\)
\(464\) −50.2499 + 15.7857i −0.108297 + 0.0340209i
\(465\) −296.792 514.059i −0.638262 1.10550i
\(466\) 29.5964 539.498i 0.0635116 1.15772i
\(467\) 8.89340 15.4038i 0.0190437 0.0329846i −0.856347 0.516402i \(-0.827271\pi\)
0.875390 + 0.483417i \(0.160605\pi\)
\(468\) −828.907 + 364.208i −1.77117 + 0.778222i
\(469\) 0 0
\(470\) 207.731 + 135.625i 0.441981 + 0.288564i
\(471\) −14.7532 8.51777i −0.0313232 0.0180844i
\(472\) 201.154 75.5282i 0.426175 0.160017i
\(473\) −14.6002 25.2883i −0.0308673 0.0534637i
\(474\) −483.418 954.522i −1.01987 2.01376i
\(475\) 98.8029 0.208006
\(476\) 0 0
\(477\) 4.23072i 0.00886943i
\(478\) −142.008 280.400i −0.297089 0.586610i
\(479\) −579.039 + 334.308i −1.20885 + 0.697930i −0.962508 0.271254i \(-0.912562\pi\)
−0.246341 + 0.969183i \(0.579228\pi\)
\(480\) 599.653 585.171i 1.24928 1.21911i
\(481\) −516.683 + 894.922i −1.07419 + 1.86054i
\(482\) −163.636 106.836i −0.339494 0.221652i
\(483\) 0 0
\(484\) −191.540 435.929i −0.395744 0.900679i
\(485\) 258.616 + 149.312i 0.533230 + 0.307860i
\(486\) −36.4330 + 664.118i −0.0749650 + 1.36650i
\(487\) −362.418 + 209.242i −0.744185 + 0.429656i −0.823589 0.567187i \(-0.808032\pi\)
0.0794038 + 0.996843i \(0.474698\pi\)
\(488\) 438.044 532.901i 0.897631 1.09201i
\(489\) −354.924 −0.725816
\(490\) 0 0
\(491\) 381.031 0.776030 0.388015 0.921653i \(-0.373161\pi\)
0.388015 + 0.921653i \(0.373161\pi\)
\(492\) 137.946 + 15.1810i 0.280379 + 0.0308556i
\(493\) −91.9984 + 53.1153i −0.186609 + 0.107739i
\(494\) 478.907 + 26.2725i 0.969448 + 0.0531832i
\(495\) −82.4813 47.6206i −0.166629 0.0962032i
\(496\) 267.173 + 245.336i 0.538656 + 0.494629i
\(497\) 0 0
\(498\) −606.342 395.874i −1.21756 0.794928i
\(499\) 219.196 379.659i 0.439271 0.760839i −0.558363 0.829597i \(-0.688570\pi\)
0.997633 + 0.0687578i \(0.0219036\pi\)
\(500\) −316.795 232.540i −0.633590 0.465079i
\(501\) 245.575 141.783i 0.490169 0.282999i
\(502\) 558.723 282.965i 1.11299 0.563676i
\(503\) 754.754i 1.50050i −0.661151 0.750252i \(-0.729932\pi\)
0.661151 0.750252i \(-0.270068\pi\)
\(504\) 0 0
\(505\) −524.378 −1.03837
\(506\) −20.1104 39.7085i −0.0397438 0.0784752i
\(507\) −445.617 771.832i −0.878930 1.52235i
\(508\) 51.8615 + 38.0684i 0.102090 + 0.0749377i
\(509\) −427.842 247.015i −0.840554 0.485294i 0.0168985 0.999857i \(-0.494621\pi\)
−0.857452 + 0.514563i \(0.827954\pi\)
\(510\) 923.822 1414.98i 1.81141 2.77446i
\(511\) 0 0
\(512\) −242.422 + 450.972i −0.473481 + 0.880804i
\(513\) −82.1358 + 142.263i −0.160109 + 0.277317i
\(514\) −38.2184 + 696.663i −0.0743549 + 1.35538i
\(515\) 114.046 + 197.533i 0.221449 + 0.383560i
\(516\) −378.602 41.6650i −0.733725 0.0807462i
\(517\) 30.3078i 0.0586224i
\(518\) 0 0
\(519\) 893.460i 1.72150i
\(520\) 676.030 + 555.696i 1.30006 + 1.06865i
\(521\) −16.4374 28.4704i −0.0315496 0.0546456i 0.849819 0.527074i \(-0.176711\pi\)
−0.881369 + 0.472428i \(0.843378\pi\)
\(522\) 77.9795 + 4.27789i 0.149386 + 0.00819520i
\(523\) −14.1377 + 24.4873i −0.0270320 + 0.0468208i −0.879225 0.476407i \(-0.841939\pi\)
0.852193 + 0.523228i \(0.175272\pi\)
\(524\) 190.088 + 432.624i 0.362763 + 0.825617i
\(525\) 0 0
\(526\) −420.254 + 643.684i −0.798961 + 1.22373i
\(527\) 633.561 + 365.787i 1.20220 + 0.694093i
\(528\) 99.9090 + 22.2595i 0.189222 + 0.0421581i
\(529\) −138.265 239.482i −0.261371 0.452708i
\(530\) 3.64804 1.84755i 0.00688309 0.00348594i
\(531\) −318.588 −0.599977
\(532\) 0 0
\(533\) 144.949i 0.271949i
\(534\) 21.6838 10.9818i 0.0406064 0.0205651i
\(535\) −410.382 + 236.934i −0.767069 + 0.442867i
\(536\) −857.713 + 322.049i −1.60021 + 0.600837i
\(537\) 164.908 285.629i 0.307092 0.531898i
\(538\) 41.2872 63.2378i 0.0767420 0.117542i
\(539\) 0 0
\(540\) −274.404 + 120.568i −0.508155 + 0.223275i
\(541\) −928.028 535.797i −1.71539 0.990383i −0.926873 0.375375i \(-0.877514\pi\)
−0.788521 0.615008i \(-0.789153\pi\)
\(542\) 616.533 + 33.8225i 1.13751 + 0.0624032i
\(543\) −557.653 + 321.961i −1.02699 + 0.592930i
\(544\) −279.437 + 994.109i −0.513670 + 1.82741i
\(545\) −168.948 −0.309997
\(546\) 0 0
\(547\) −986.888 −1.80418 −0.902091 0.431545i \(-0.857968\pi\)
−0.902091 + 0.431545i \(0.857968\pi\)
\(548\) 76.2230 + 8.38831i 0.139093 + 0.0153071i
\(549\) −885.795 + 511.414i −1.61347 + 0.931537i
\(550\) −1.20636 + 21.9901i −0.00219339 + 0.0399821i
\(551\) −35.8287 20.6857i −0.0650248 0.0375421i
\(552\) −572.761 95.0272i −1.03761 0.172151i
\(553\) 0 0
\(554\) −267.013 + 408.971i −0.481972 + 0.738215i
\(555\) −708.957 + 1227.95i −1.27740 + 2.21252i
\(556\) −248.418 + 338.427i −0.446796 + 0.608681i
\(557\) −418.767 + 241.775i −0.751826 + 0.434067i −0.826353 0.563152i \(-0.809588\pi\)
0.0745276 + 0.997219i \(0.476255\pi\)
\(558\) −242.995 479.801i −0.435476 0.859859i
\(559\) 397.821i 0.711665i
\(560\) 0 0
\(561\) 206.444 0.367993
\(562\) 475.620 240.878i 0.846300 0.428609i
\(563\) 260.447 + 451.107i 0.462605 + 0.801256i 0.999090 0.0426543i \(-0.0135814\pi\)
−0.536485 + 0.843910i \(0.680248\pi\)
\(564\) 318.690 + 233.931i 0.565053 + 0.414771i
\(565\) 790.020 + 456.118i 1.39826 + 0.807289i
\(566\) 277.334 + 181.068i 0.489990 + 0.319909i
\(567\) 0 0
\(568\) −827.028 137.213i −1.45603 0.241572i
\(569\) 366.480 634.761i 0.644077 1.11557i −0.340437 0.940267i \(-0.610575\pi\)
0.984514 0.175306i \(-0.0560916\pi\)
\(570\) 657.123 + 36.0493i 1.15285 + 0.0632444i
\(571\) 499.792 + 865.665i 0.875292 + 1.51605i 0.856451 + 0.516228i \(0.172664\pi\)
0.0188408 + 0.999822i \(0.494002\pi\)
\(572\) −11.6947 + 106.268i −0.0204453 + 0.185782i
\(573\) 1299.32i 2.26758i
\(574\) 0 0
\(575\) 124.918i 0.217249i
\(576\) 571.551 499.645i 0.992277 0.867440i
\(577\) 232.929 + 403.445i 0.403690 + 0.699212i 0.994168 0.107842i \(-0.0343940\pi\)
−0.590478 + 0.807054i \(0.701061\pi\)
\(578\) −82.4223 + 1502.43i −0.142599 + 2.59936i
\(579\) −282.841 + 489.895i −0.488499 + 0.846105i
\(580\) −30.3648 69.1078i −0.0523531 0.119151i
\(581\) 0 0
\(582\) 398.461 + 260.150i 0.684641 + 0.446994i
\(583\) 0.432636 + 0.249782i 0.000742086 + 0.000428443i
\(584\) −182.724 + 68.6079i −0.312883 + 0.117479i
\(585\) −648.772 1123.71i −1.10901 1.92087i
\(586\) 31.0532 + 61.3154i 0.0529918 + 0.104634i
\(587\) 574.851 0.979303 0.489651 0.871918i \(-0.337124\pi\)
0.489651 + 0.871918i \(0.337124\pi\)
\(588\) 0 0
\(589\) 284.911i 0.483719i
\(590\) 139.127 + 274.710i 0.235808 + 0.465610i
\(591\) −427.587 + 246.868i −0.723498 + 0.417712i
\(592\) 188.425 845.724i 0.318286 1.42859i
\(593\) 471.528 816.710i 0.795156 1.37725i −0.127584 0.991828i \(-0.540722\pi\)
0.922740 0.385423i \(-0.125945\pi\)
\(594\) −30.6601 20.0176i −0.0516163 0.0336997i
\(595\) 0 0
\(596\) 301.722 132.572i 0.506245 0.222436i
\(597\) −1312.66 757.867i −2.19877 1.26946i
\(598\) 33.2168 605.491i 0.0555465 1.01253i
\(599\) 8.02545 4.63349i 0.0133981 0.00773538i −0.493286 0.869867i \(-0.664204\pi\)
0.506684 + 0.862132i \(0.330871\pi\)
\(600\) 221.918 + 182.416i 0.369863 + 0.304027i
\(601\) −57.7003 −0.0960072 −0.0480036 0.998847i \(-0.515286\pi\)
−0.0480036 + 0.998847i \(0.515286\pi\)
\(602\) 0 0
\(603\) 1358.44 2.25281
\(604\) −25.2643 + 229.572i −0.0418283 + 0.380086i
\(605\) 590.966 341.194i 0.976804 0.563958i
\(606\) −834.357 45.7722i −1.37683 0.0755316i
\(607\) −887.396 512.339i −1.46194 0.844050i −0.462837 0.886443i \(-0.653169\pi\)
−0.999101 + 0.0423930i \(0.986502\pi\)
\(608\) −389.699 + 99.3310i −0.640952 + 0.163373i
\(609\) 0 0
\(610\) 827.805 + 540.464i 1.35706 + 0.886007i
\(611\) −206.453 + 357.588i −0.337894 + 0.585250i
\(612\) 906.012 1234.28i 1.48041 2.01680i
\(613\) −350.583 + 202.409i −0.571914 + 0.330195i −0.757913 0.652355i \(-0.773781\pi\)
0.186000 + 0.982550i \(0.440448\pi\)
\(614\) 397.765 201.448i 0.647826 0.328091i
\(615\) 198.889i 0.323396i
\(616\) 0 0
\(617\) 894.209 1.44928 0.724642 0.689125i \(-0.242005\pi\)
0.724642 + 0.689125i \(0.242005\pi\)
\(618\) 164.220 + 324.258i 0.265729 + 0.524689i
\(619\) −389.694 674.970i −0.629554 1.09042i −0.987641 0.156731i \(-0.949904\pi\)
0.358087 0.933688i \(-0.383429\pi\)
\(620\) −307.604 + 419.057i −0.496136 + 0.675899i
\(621\) 179.866 + 103.846i 0.289640 + 0.167224i
\(622\) 459.145 703.252i 0.738176 1.13063i
\(623\) 0 0
\(624\) 1027.15 + 943.198i 1.64607 + 1.51154i
\(625\) 379.869 657.952i 0.607790 1.05272i
\(626\) −32.1944 + 586.855i −0.0514288 + 0.937469i
\(627\) 40.1997 + 69.6278i 0.0641143 + 0.111049i
\(628\) −1.63198 + 14.8295i −0.00259869 + 0.0236138i
\(629\) 1747.53i 2.77827i
\(630\) 0 0
\(631\) 780.191i 1.23644i −0.786007 0.618218i \(-0.787855\pi\)
0.786007 0.618218i \(-0.212145\pi\)
\(632\) −595.012 + 723.859i −0.941474 + 1.14535i
\(633\) 60.2793 + 104.407i 0.0952279 + 0.164940i
\(634\) 845.650 + 46.3917i 1.33383 + 0.0731730i
\(635\) −46.0992 + 79.8462i −0.0725972 + 0.125742i
\(636\) 5.96580 2.62127i 0.00938018 0.00412150i
\(637\) 0 0
\(638\) 5.04139 7.72166i 0.00790186 0.0121029i
\(639\) 1076.48 + 621.509i 1.68464 + 0.972627i
\(640\) −680.427 274.639i −1.06317 0.429124i
\(641\) 11.6570 + 20.1905i 0.0181856 + 0.0314984i 0.874975 0.484168i \(-0.160878\pi\)
−0.856789 + 0.515667i \(0.827544\pi\)
\(642\) −673.655 + 341.173i −1.04931 + 0.531422i
\(643\) −530.706 −0.825360 −0.412680 0.910876i \(-0.635407\pi\)
−0.412680 + 0.910876i \(0.635407\pi\)
\(644\) 0 0
\(645\) 545.862i 0.846297i
\(646\) −723.595 + 366.465i −1.12012 + 0.567283i
\(647\) 184.840 106.717i 0.285687 0.164942i −0.350308 0.936635i \(-0.613923\pi\)
0.635995 + 0.771693i \(0.280590\pi\)
\(648\) 352.409 132.320i 0.543841 0.204198i
\(649\) −18.8095 + 32.5790i −0.0289823 + 0.0501988i
\(650\) −164.028 + 251.234i −0.252350 + 0.386514i
\(651\) 0 0
\(652\) 125.035 + 284.570i 0.191772 + 0.436457i
\(653\) −238.048 137.437i −0.364545 0.210470i 0.306528 0.951862i \(-0.400833\pi\)
−0.671073 + 0.741392i \(0.734166\pi\)
\(654\) −268.820 14.7473i −0.411039 0.0225493i
\(655\) −586.485 + 338.607i −0.895397 + 0.516958i
\(656\) −36.4251 115.950i −0.0555260 0.176754i
\(657\) 289.397 0.440483
\(658\) 0 0
\(659\) 1234.48 1.87327 0.936633 0.350313i \(-0.113925\pi\)
0.936633 + 0.350313i \(0.113925\pi\)
\(660\) −16.0467 + 145.813i −0.0243131 + 0.220929i
\(661\) 504.662 291.367i 0.763482 0.440797i −0.0670625 0.997749i \(-0.521363\pi\)
0.830545 + 0.556952i \(0.188029\pi\)
\(662\) 13.8768 252.953i 0.0209619 0.382104i
\(663\) 2435.74 + 1406.27i 3.67381 + 2.12107i
\(664\) −103.796 + 625.613i −0.156319 + 0.942188i
\(665\) 0 0
\(666\) −702.341 + 1075.74i −1.05457 + 1.61523i
\(667\) −26.1533 + 45.2989i −0.0392104 + 0.0679143i
\(668\) −200.191 146.948i −0.299687 0.219982i
\(669\) −637.569 + 368.101i −0.953018 + 0.550225i
\(670\) −593.231 1171.35i −0.885419 1.74828i
\(671\) 120.776i 0.179994i
\(672\) 0 0
\(673\) −399.145 −0.593083 −0.296542 0.955020i \(-0.595833\pi\)
−0.296542 + 0.955020i \(0.595833\pi\)
\(674\) 539.558 273.259i 0.800530 0.405429i
\(675\) −51.3815 88.9953i −0.0761207 0.131845i
\(676\) −461.851 + 629.192i −0.683212 + 0.930758i
\(677\) 653.388 + 377.234i 0.965123 + 0.557214i 0.897746 0.440514i \(-0.145204\pi\)
0.0673768 + 0.997728i \(0.478537\pi\)
\(678\) 1217.22 + 794.706i 1.79530 + 1.17213i
\(679\) 0 0
\(680\) −1459.95 242.220i −2.14698 0.356206i
\(681\) 391.156 677.502i 0.574384 0.994863i
\(682\) −63.4113 3.47870i −0.0929785 0.00510073i
\(683\) −144.132 249.644i −0.211028 0.365511i 0.741009 0.671495i \(-0.234348\pi\)
−0.952036 + 0.305985i \(0.901014\pi\)
\(684\) 592.713 + 65.2279i 0.866539 + 0.0953624i
\(685\) 109.897i 0.160433i
\(686\) 0 0
\(687\) 1047.10i 1.52416i
\(688\) 99.9706 + 318.232i 0.145306 + 0.462547i
\(689\) 3.40298 + 5.89414i 0.00493901 + 0.00855462i
\(690\) 45.5778 830.813i 0.0660548 1.20408i
\(691\) −78.3458 + 135.699i −0.113380 + 0.196380i −0.917131 0.398586i \(-0.869501\pi\)
0.803751 + 0.594966i \(0.202835\pi\)
\(692\) −716.356 + 314.755i −1.03520 + 0.454848i
\(693\) 0 0
\(694\) −536.787 350.462i −0.773468 0.504988i
\(695\) −521.043 300.824i −0.749703 0.432841i
\(696\) −42.2823 112.611i −0.0607504 0.161797i
\(697\) −122.562 212.284i −0.175842 0.304568i
\(698\) 343.990 + 679.217i 0.492822 + 0.973090i
\(699\) 1233.92 1.76527
\(700\) 0 0
\(701\) 1126.50i 1.60700i −0.595307 0.803498i \(-0.702970\pi\)
0.595307 0.803498i \(-0.297030\pi\)
\(702\) −225.386 445.032i −0.321063 0.633949i
\(703\) 589.396 340.288i 0.838401 0.484051i
\(704\) −17.3495 87.9464i −0.0246442 0.124924i
\(705\) −283.281 + 490.657i −0.401817 + 0.695967i
\(706\) −610.200 398.392i −0.864306 0.564295i
\(707\) 0 0
\(708\) 197.391 + 449.246i 0.278801 + 0.634528i
\(709\) 949.313 + 548.086i 1.33895 + 0.773041i 0.986651 0.162847i \(-0.0520678\pi\)
0.352296 + 0.935889i \(0.385401\pi\)
\(710\) 65.8112 1199.64i 0.0926918 1.68963i
\(711\) 1203.21 694.673i 1.69228 0.977037i
\(712\) −16.4439 13.5168i −0.0230953 0.0189843i
\(713\) 360.218 0.505214
\(714\) 0 0
\(715\) −153.215 −0.214286
\(716\) −287.106 31.5959i −0.400986 0.0441284i
\(717\) 621.633 358.900i 0.866991 0.500558i
\(718\) 223.654 + 12.2695i 0.311496 + 0.0170885i
\(719\) 524.259 + 302.681i 0.729150 + 0.420975i 0.818111 0.575060i \(-0.195021\pi\)
−0.0889614 + 0.996035i \(0.528355\pi\)
\(720\) 801.361 + 735.863i 1.11300 + 1.02203i
\(721\) 0 0
\(722\) 340.057 + 222.019i 0.470993 + 0.307506i
\(723\) 223.149 386.506i 0.308643 0.534586i
\(724\) 454.595 + 333.690i 0.627894 + 0.460898i
\(725\) 22.4132 12.9403i 0.0309148 0.0178487i
\(726\) 970.091 491.303i 1.33621 0.676725i
\(727\) 443.659i 0.610260i 0.952311 + 0.305130i \(0.0986999\pi\)
−0.952311 + 0.305130i \(0.901300\pi\)
\(728\) 0 0
\(729\) −1095.46 −1.50269
\(730\) −126.379 249.540i −0.173123 0.341835i
\(731\) 336.379 + 582.625i 0.460162 + 0.797025i
\(732\) 1269.97 + 932.210i 1.73494 + 1.27351i
\(733\) 649.541 + 375.013i 0.886141 + 0.511614i 0.872678 0.488296i \(-0.162381\pi\)
0.0134626 + 0.999909i \(0.495715\pi\)
\(734\) −480.038 + 735.252i −0.654002 + 1.00171i
\(735\) 0 0
\(736\) 125.586 + 492.704i 0.170633 + 0.669434i
\(737\) 80.2028 138.915i 0.108823 0.188488i
\(738\) −9.87113 + 179.935i −0.0133755 + 0.243815i
\(739\) −309.646 536.323i −0.419007 0.725742i 0.576833 0.816862i \(-0.304288\pi\)
−0.995840 + 0.0911205i \(0.970955\pi\)
\(740\) 1234.30 + 135.834i 1.66797 + 0.183560i
\(741\) 1095.34i 1.47819i
\(742\) 0 0
\(743\) 30.5255i 0.0410842i −0.999789 0.0205421i \(-0.993461\pi\)
0.999789 0.0205421i \(-0.00653921\pi\)
\(744\) −526.020 + 639.927i −0.707016 + 0.860117i
\(745\) 236.153 + 409.029i 0.316984 + 0.549032i
\(746\) −509.227 27.9358i −0.682610 0.0374475i
\(747\) 470.146 814.316i 0.629378 1.09012i
\(748\) −72.7275 165.522i −0.0972293 0.221286i
\(749\) 0 0
\(750\) 490.632 751.479i 0.654176 1.00197i
\(751\) −838.498 484.107i −1.11651 0.644616i −0.176001 0.984390i \(-0.556316\pi\)
−0.940507 + 0.339773i \(0.889650\pi\)
\(752\) 75.2898 337.929i 0.100119 0.449374i
\(753\) 715.142 + 1238.66i 0.949723 + 1.64497i
\(754\) 112.080 56.7630i 0.148647 0.0752825i
\(755\) −330.993 −0.438401
\(756\) 0 0
\(757\) 1171.15i 1.54710i 0.633736 + 0.773550i \(0.281521\pi\)
−0.633736 + 0.773550i \(0.718479\pi\)
\(758\) 1075.97 544.927i 1.41949 0.718902i
\(759\) 88.0318 50.8252i 0.115984 0.0669633i
\(760\) −202.593 539.566i −0.266569 0.709955i
\(761\) 117.998 204.379i 0.155057 0.268566i −0.778023 0.628236i \(-0.783777\pi\)
0.933080 + 0.359670i \(0.117111\pi\)
\(762\) −80.3199 + 123.022i −0.105407 + 0.161447i
\(763\) 0 0
\(764\) 1041.77 457.734i 1.36357 0.599129i
\(765\) 1900.31 + 1097.14i 2.48406 + 1.43418i
\(766\) 146.551 + 8.03966i 0.191319 + 0.0104956i
\(767\) −443.849 + 256.257i −0.578682 + 0.334102i
\(768\) −1058.68 496.383i −1.37849 0.646332i
\(769\) 124.257 0.161582 0.0807912 0.996731i \(-0.474255\pi\)
0.0807912 + 0.996731i \(0.474255\pi\)
\(770\) 0 0
\(771\) −1593.39 −2.06665
\(772\) 492.428 + 54.1915i 0.637859 + 0.0701962i
\(773\) 154.345 89.1114i 0.199671 0.115280i −0.396831 0.917892i \(-0.629890\pi\)
0.596502 + 0.802612i \(0.296557\pi\)
\(774\) 27.0919 493.843i 0.0350024 0.638040i
\(775\) −154.352 89.1154i −0.199164 0.114988i
\(776\) 68.2099 411.124i 0.0878993 0.529799i
\(777\) 0 0
\(778\) 372.622 570.728i 0.478948 0.733584i
\(779\) 47.7317 82.6737i 0.0612730 0.106128i
\(780\) −1182.59 + 1611.07i −1.51614 + 2.06548i
\(781\) 127.112 73.3880i 0.162755 0.0939667i
\(782\) 463.328 + 914.854i 0.592491 + 1.16989i
\(783\) 43.0296i 0.0549548i
\(784\) 0 0
\(785\) −21.3809 −0.0272368
\(786\) −962.735 + 487.578i −1.22485 + 0.620328i
\(787\) −553.948 959.466i −0.703873 1.21914i −0.967097 0.254409i \(-0.918119\pi\)
0.263224 0.964735i \(-0.415214\pi\)
\(788\) 348.566 + 255.861i 0.442343 + 0.324697i
\(789\) −1520.37 877.785i −1.92696 1.11253i
\(790\) −1124.44 734.133i −1.42334 0.929283i
\(791\) 0 0
\(792\) −21.7544 + 131.121i −0.0274676 + 0.165557i
\(793\) −822.713 + 1424.98i −1.03747 + 1.79695i
\(794\) −222.745 12.2196i −0.280535 0.0153899i
\(795\) 4.66933 + 8.08752i 0.00587338 + 0.0101730i
\(796\) −145.205 + 1319.45i −0.182418 + 1.65760i
\(797\) 1094.69i 1.37351i −0.726889 0.686755i \(-0.759034\pi\)
0.726889 0.686755i \(-0.240966\pi\)
\(798\) 0 0
\(799\) 698.269i 0.873929i
\(800\) 68.0782 242.191i 0.0850977 0.302739i
\(801\) 15.7808 + 27.3332i 0.0197014 + 0.0341238i
\(802\) −37.3069 + 680.048i −0.0465173 + 0.847940i
\(803\) 17.0861 29.5940i 0.0212778 0.0368542i
\(804\) −841.666 1915.56i −1.04685 2.38254i
\(805\) 0 0
\(806\) −724.464 472.994i −0.898839 0.586842i
\(807\) 149.366 + 86.2367i 0.185089 + 0.106861i
\(808\) 257.234 + 685.093i 0.318359 + 0.847887i
\(809\) 693.377 + 1200.96i 0.857079 + 1.48450i 0.874703 + 0.484659i \(0.161056\pi\)
−0.0176240 + 0.999845i \(0.505610\pi\)
\(810\) 243.741 + 481.273i 0.300915 + 0.594165i
\(811\) 312.204 0.384962 0.192481 0.981301i \(-0.438347\pi\)
0.192481 + 0.981301i \(0.438347\pi\)
\(812\) 0 0
\(813\) 1410.11i 1.73446i
\(814\) 68.5400 + 135.334i 0.0842014 + 0.166258i
\(815\) −385.776 + 222.728i −0.473345 + 0.273286i
\(816\) −2301.83 512.842i −2.82087 0.628483i
\(817\) −131.002 + 226.903i −0.160346 + 0.277727i
\(818\) 1116.94 + 729.237i 1.36545 + 0.891487i
\(819\) 0 0
\(820\) 159.464 70.0660i 0.194469 0.0854464i
\(821\) −946.469 546.444i −1.15282 0.665583i −0.203250 0.979127i \(-0.565150\pi\)
−0.949574 + 0.313544i \(0.898484\pi\)
\(822\) −9.59275 + 174.861i −0.0116700 + 0.212726i
\(823\) 785.625 453.581i 0.954587 0.551131i 0.0600842 0.998193i \(-0.480863\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(824\) 202.130 245.900i 0.245303 0.298422i
\(825\) −50.2952 −0.0609638
\(826\) 0 0
\(827\) −607.144 −0.734152 −0.367076 0.930191i \(-0.619641\pi\)
−0.367076 + 0.930191i \(0.619641\pi\)
\(828\) 82.4688 749.378i 0.0996000 0.905046i
\(829\) −370.632 + 213.984i −0.447083 + 0.258124i −0.706598 0.707616i \(-0.749771\pi\)
0.259514 + 0.965739i \(0.416438\pi\)
\(830\) −907.476 49.7834i −1.09334 0.0599800i
\(831\) −965.982 557.710i −1.16243 0.671131i
\(832\) 394.382 1155.82i 0.474017 1.38921i
\(833\) 0 0
\(834\) −802.793 524.134i −0.962581 0.628458i
\(835\) 177.948 308.215i 0.213111 0.369120i
\(836\) 41.6642 56.7602i 0.0498375 0.0678949i
\(837\) 256.629 148.165i 0.306606 0.177019i
\(838\) 357.186 180.897i 0.426237 0.215868i
\(839\) 1133.09i 1.35053i −0.737575 0.675265i \(-0.764029\pi\)
0.737575 0.675265i \(-0.235971\pi\)
\(840\) 0 0
\(841\) 830.163 0.987114
\(842\) −14.3799 28.3936i −0.0170783 0.0337216i
\(843\) 608.774 + 1054.43i 0.722152 + 1.25080i
\(844\) 62.4753 85.1117i 0.0740228 0.100843i
\(845\) −968.707 559.283i −1.14640 0.661874i
\(846\) −280.637 + 429.839i −0.331722 + 0.508084i
\(847\) 0 0
\(848\) −4.20335 3.85980i −0.00495678 0.00455165i
\(849\) −378.198 + 655.059i −0.445463 + 0.771565i
\(850\) 27.7937 506.637i 0.0326985 0.596043i
\(851\) −430.232 745.184i −0.505561 0.875657i
\(852\) 209.429 1903.04i 0.245809 2.23362i
\(853\) 169.502i 0.198712i −0.995052 0.0993562i \(-0.968322\pi\)
0.995052 0.0993562i \(-0.0316783\pi\)
\(854\) 0 0
\(855\) 854.563i 0.999489i
\(856\) 510.865 + 419.930i 0.596805 + 0.490573i
\(857\) −117.039 202.718i −0.136569 0.236544i 0.789627 0.613587i \(-0.210274\pi\)
−0.926196 + 0.377043i \(0.876941\pi\)
\(858\) −243.786 13.3739i −0.284132 0.0155873i
\(859\) 447.171 774.523i 0.520571 0.901656i −0.479143 0.877737i \(-0.659052\pi\)
0.999714 0.0239189i \(-0.00761436\pi\)
\(860\) −437.659 + 192.300i −0.508906 + 0.223605i
\(861\) 0 0
\(862\) 686.654 1051.72i 0.796582 1.22009i
\(863\) 674.270 + 389.290i 0.781309 + 0.451089i 0.836894 0.547365i \(-0.184369\pi\)
−0.0555850 + 0.998454i \(0.517702\pi\)
\(864\) 292.130 + 299.360i 0.338114 + 0.346481i
\(865\) −560.680 971.126i −0.648185 1.12269i
\(866\) −1408.17 + 713.168i −1.62606 + 0.823519i
\(867\) −3436.32 −3.96346
\(868\) 0 0
\(869\) 164.055i 0.188786i
\(870\) 153.789 77.8862i 0.176768 0.0895244i
\(871\) 1892.55 1092.67i 2.17285 1.25450i
\(872\) 82.8778 + 220.729i 0.0950434 + 0.253129i
\(873\) −308.959 + 535.132i −0.353904 + 0.612980i
\(874\) −218.334 + 334.412i −0.249810 + 0.382623i
\(875\) 0 0
\(876\) −179.305 408.083i −0.204686 0.465849i
\(877\) 14.9632 + 8.63901i 0.0170618 + 0.00985064i 0.508507 0.861058i \(-0.330198\pi\)
−0.491445 + 0.870909i \(0.663531\pi\)
\(878\) −1329.14 72.9157i −1.51383 0.0830475i
\(879\) −135.933 + 78.4811i −0.154645 + 0.0892846i
\(880\) 122.562 38.5022i 0.139275 0.0437525i
\(881\) −770.918 −0.875049 −0.437524 0.899207i \(-0.644145\pi\)
−0.437524 + 0.899207i \(0.644145\pi\)
\(882\) 0 0
\(883\) 776.362 0.879232 0.439616 0.898186i \(-0.355114\pi\)
0.439616 + 0.898186i \(0.355114\pi\)
\(884\) 269.438 2448.33i 0.304794 2.76960i
\(885\) −609.019 + 351.617i −0.688157 + 0.397308i
\(886\) −55.5604 + 1012.78i −0.0627092 + 1.14309i
\(887\) −1412.32 815.402i −1.59224 0.919280i −0.992922 0.118770i \(-0.962105\pi\)
−0.599319 0.800511i \(-0.704562\pi\)
\(888\) 1952.08 + 323.871i 2.19829 + 0.364719i
\(889\) 0 0
\(890\) 16.6772 25.5438i 0.0187385 0.0287009i
\(891\) −32.9530 + 57.0762i −0.0369842 + 0.0640586i
\(892\) 519.742 + 381.511i 0.582670 + 0.427702i
\(893\) 235.507 135.970i 0.263726 0.152262i
\(894\) 340.048 + 671.434i 0.380367 + 0.751045i
\(895\) 413.945i 0.462508i
\(896\) 0 0
\(897\) 1384.86 1.54388
\(898\) −497.852 + 252.137i −0.554400 + 0.280776i
\(899\) 37.3150 + 64.6314i 0.0415072 + 0.0718925i
\(900\) −220.729 + 300.704i −0.245254 + 0.334116i
\(901\) −9.96762 5.75481i −0.0110628 0.00638713i
\(902\) 17.8175 + 11.6329i 0.0197534 + 0.0128967i
\(903\) 0 0
\(904\) 208.367 1255.90i 0.230495 1.38927i
\(905\) −404.086 + 699.897i −0.446503 + 0.773367i
\(906\) −526.655 28.8919i −0.581297 0.0318895i
\(907\) 476.931 + 826.069i 0.525834 + 0.910771i 0.999547 + 0.0300919i \(0.00958001\pi\)
−0.473713 + 0.880679i \(0.657087\pi\)
\(908\) −681.004 74.9443i −0.750005 0.0825378i
\(909\) 1085.05i 1.19367i
\(910\) 0 0
\(911\) 1681.15i 1.84539i 0.385534 + 0.922694i \(0.374017\pi\)
−0.385534 + 0.922694i \(0.625983\pi\)
\(912\) −275.255 876.207i −0.301815 0.960754i
\(913\) −55.5150 96.1548i −0.0608051 0.105317i
\(914\) 78.9753 1439.60i 0.0864062 1.57505i
\(915\) −1128.87 + 1955.26i −1.23374 + 2.13689i
\(916\) 839.538 368.879i 0.916527 0.402707i
\(917\) 0 0
\(918\) 706.386 + 461.192i 0.769484 + 0.502387i
\(919\) −437.335 252.495i −0.475881 0.274750i 0.242817 0.970072i \(-0.421929\pi\)
−0.718698 + 0.695322i \(0.755262\pi\)
\(920\) −682.183 + 256.142i −0.741503 + 0.278415i
\(921\) 509.122 + 881.826i 0.552793 + 0.957466i
\(922\) 436.686 + 862.249i 0.473630 + 0.935195i
\(923\) 1999.64 2.16646
\(924\) 0 0
\(925\) 425.746i 0.460266i
\(926\) 35.8129 + 70.7135i 0.0386748 + 0.0763645i
\(927\) −408.739 + 235.985i −0.440926 + 0.254569i
\(928\) −75.3930 + 73.5722i −0.0812424 + 0.0792804i
\(929\) 491.925 852.040i 0.529521 0.917158i −0.469886 0.882727i \(-0.655705\pi\)
0.999407 0.0344306i \(-0.0109618\pi\)
\(930\) −994.059 649.010i −1.06888 0.697860i
\(931\) 0 0
\(932\) −434.695 989.330i −0.466411 1.06151i
\(933\) 1661.07 + 959.018i 1.78035 + 1.02789i
\(934\) 1.94861 35.5202i 0.00208631 0.0380302i
\(935\) 224.389 129.551i 0.239989 0.138558i
\(936\) −1149.85 + 1398.85i −1.22847 + 1.49450i
\(937\) 389.648 0.415846 0.207923 0.978145i \(-0.433330\pi\)
0.207923 + 0.978145i \(0.433330\pi\)
\(938\) 0 0
\(939\) −1342.24 −1.42943
\(940\) 493.193 + 54.2758i 0.524674 + 0.0577402i
\(941\) −758.175 + 437.732i −0.805712 + 0.465178i −0.845464 0.534032i \(-0.820676\pi\)
0.0397529 + 0.999210i \(0.487343\pi\)
\(942\) −34.0199 1.86631i −0.0361146 0.00198122i
\(943\) −104.526 60.3481i −0.110844 0.0639958i
\(944\) 290.656 316.527i 0.307899 0.335304i
\(945\) 0 0
\(946\) −48.9012 31.9270i −0.0516926 0.0337495i
\(947\) 625.646 1083.65i 0.660661 1.14430i −0.319781 0.947491i \(-0.603609\pi\)
0.980442 0.196807i \(-0.0630572\pi\)
\(948\) −1725.06 1266.26i −1.81968 1.33571i
\(949\) 403.181 232.777i 0.424849 0.245287i
\(950\) 176.287 89.2805i 0.185565 0.0939795i
\(951\) 1934.14i 2.03380i
\(952\) 0 0
\(953\) −882.129 −0.925633 −0.462817 0.886454i \(-0.653161\pi\)
−0.462817 + 0.886454i \(0.653161\pi\)
\(954\) 3.82297 + 7.54856i 0.00400731 + 0.00791254i
\(955\) 815.373 + 1412.27i 0.853793 + 1.47881i
\(956\) −506.751 371.975i −0.530074 0.389095i
\(957\) 18.2384 + 10.5300i 0.0190579 + 0.0110031i
\(958\) −731.049 + 1119.71i −0.763099 + 1.16880i
\(959\) 0 0
\(960\) 541.144 1585.94i 0.563691 1.65202i
\(961\) −223.525 + 387.156i −0.232596 + 0.402868i
\(962\) −113.209 + 2063.63i −0.117681 + 2.14515i
\(963\) −490.267 849.167i −0.509103 0.881793i
\(964\) −388.504 42.7547i −0.403012 0.0443514i
\(965\) 709.973i 0.735724i
\(966\) 0 0
\(967\) 1410.24i 1.45836i 0.684320 + 0.729182i \(0.260099\pi\)
−0.684320 + 0.729182i \(0.739901\pi\)
\(968\) −735.666 604.716i −0.759985 0.624707i
\(969\) −926.171 1604.18i −0.955801 1.65550i
\(970\) 596.352 + 32.7154i 0.614796 + 0.0337272i
\(971\) 339.275 587.641i 0.349408 0.605192i −0.636737 0.771081i \(-0.719716\pi\)
0.986144 + 0.165889i \(0.0530495\pi\)
\(972\) 535.107 + 1217.86i 0.550521 + 1.25294i
\(973\) 0 0
\(974\) −457.560 + 700.825i −0.469775 + 0.719533i
\(975\) −593.410 342.605i −0.608625 0.351390i
\(976\) 300.029 1346.64i 0.307406 1.37976i
\(977\) −55.9074 96.8344i −0.0572235 0.0991141i 0.835995 0.548738i \(-0.184891\pi\)
−0.893218 + 0.449624i \(0.851558\pi\)
\(978\) −633.265 + 320.717i −0.647510 + 0.327932i
\(979\) 3.72682 0.00380676
\(980\) 0 0
\(981\) 349.590i 0.356360i
\(982\) 679.845 344.308i 0.692307 0.350619i
\(983\) 175.133 101.113i 0.178162 0.102862i −0.408267 0.912863i \(-0.633867\pi\)
0.586429 + 0.810001i \(0.300533\pi\)
\(984\) 259.846 97.5652i 0.264071 0.0991517i
\(985\) −309.837 + 536.654i −0.314556 + 0.544826i
\(986\) −116.150 + 177.902i −0.117799 + 0.180428i
\(987\) 0 0
\(988\) 878.220 385.875i 0.888887 0.390562i
\(989\) 286.877 + 165.629i 0.290068 + 0.167471i
\(990\) −190.196 10.4340i −0.192118 0.0105394i
\(991\) 163.735 94.5322i 0.165222 0.0953907i −0.415109 0.909772i \(-0.636257\pi\)
0.580331 + 0.814381i \(0.302923\pi\)
\(992\) 698.389 + 196.312i 0.704021 + 0.197895i
\(993\) 578.546 0.582624
\(994\) 0 0
\(995\) −1902.36 −1.91192
\(996\) −1439.57 158.425i −1.44535 0.159061i
\(997\) 1414.14 816.457i 1.41840 0.818914i 0.422241 0.906483i \(-0.361243\pi\)
0.996158 + 0.0875699i \(0.0279101\pi\)
\(998\) 48.0275 875.468i 0.0481238 0.877222i
\(999\) −613.019 353.927i −0.613632 0.354281i
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 392.3.k.n.275.7 16
7.2 even 3 392.3.g.m.99.1 8
7.3 odd 6 392.3.k.o.67.5 16
7.4 even 3 inner 392.3.k.n.67.5 16
7.5 odd 6 56.3.g.b.43.1 8
7.6 odd 2 392.3.k.o.275.7 16
8.3 odd 2 inner 392.3.k.n.275.5 16
21.5 even 6 504.3.g.b.379.8 8
28.19 even 6 224.3.g.b.15.2 8
28.23 odd 6 1568.3.g.m.687.7 8
56.3 even 6 392.3.k.o.67.7 16
56.5 odd 6 224.3.g.b.15.1 8
56.11 odd 6 inner 392.3.k.n.67.7 16
56.19 even 6 56.3.g.b.43.2 yes 8
56.27 even 2 392.3.k.o.275.5 16
56.37 even 6 1568.3.g.m.687.8 8
56.51 odd 6 392.3.g.m.99.2 8
84.47 odd 6 2016.3.g.b.1135.2 8
112.5 odd 12 1792.3.d.j.1023.3 16
112.19 even 12 1792.3.d.j.1023.4 16
112.61 odd 12 1792.3.d.j.1023.14 16
112.75 even 12 1792.3.d.j.1023.13 16
168.5 even 6 2016.3.g.b.1135.7 8
168.131 odd 6 504.3.g.b.379.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.g.b.43.1 8 7.5 odd 6
56.3.g.b.43.2 yes 8 56.19 even 6
224.3.g.b.15.1 8 56.5 odd 6
224.3.g.b.15.2 8 28.19 even 6
392.3.g.m.99.1 8 7.2 even 3
392.3.g.m.99.2 8 56.51 odd 6
392.3.k.n.67.5 16 7.4 even 3 inner
392.3.k.n.67.7 16 56.11 odd 6 inner
392.3.k.n.275.5 16 8.3 odd 2 inner
392.3.k.n.275.7 16 1.1 even 1 trivial
392.3.k.o.67.5 16 7.3 odd 6
392.3.k.o.67.7 16 56.3 even 6
392.3.k.o.275.5 16 56.27 even 2
392.3.k.o.275.7 16 7.6 odd 2
504.3.g.b.379.7 8 168.131 odd 6
504.3.g.b.379.8 8 21.5 even 6
1568.3.g.m.687.7 8 28.23 odd 6
1568.3.g.m.687.8 8 56.37 even 6
1792.3.d.j.1023.3 16 112.5 odd 12
1792.3.d.j.1023.4 16 112.19 even 12
1792.3.d.j.1023.13 16 112.75 even 12
1792.3.d.j.1023.14 16 112.61 odd 12
2016.3.g.b.1135.2 8 84.47 odd 6
2016.3.g.b.1135.7 8 168.5 even 6