Properties

Label 475.2.j.c.49.6
Level $475$
Weight $2$
Character 475.49
Analytic conductor $3.793$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(49,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.1387535264013605949997056.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.6
Root \(-1.77290 + 1.02359i\) of defining polynomial
Character \(\chi\) \(=\) 475.49
Dual form 475.2.j.c.349.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.03136 + 0.595455i) q^{2} +(2.63893 + 1.52359i) q^{3} +(-0.290867 - 0.503797i) q^{4} +(1.81445 + 3.14272i) q^{6} -0.609175i q^{7} -3.07461i q^{8} +(3.14263 + 5.44319i) q^{9} +O(q^{10})\) \(q+(1.03136 + 0.595455i) q^{2} +(2.63893 + 1.52359i) q^{3} +(-0.290867 - 0.503797i) q^{4} +(1.81445 + 3.14272i) q^{6} -0.609175i q^{7} -3.07461i q^{8} +(3.14263 + 5.44319i) q^{9} +4.48517 q^{11} -1.77264i q^{12} +(-3.84342 + 2.21900i) q^{13} +(0.362736 - 0.628278i) q^{14} +(1.24906 - 2.16343i) q^{16} +(-2.51445 - 1.45172i) q^{17} +7.48517i q^{18} +(-3.60532 + 2.44983i) q^{19} +(0.928131 - 1.60757i) q^{21} +(4.62581 + 2.67071i) q^{22} +(2.46580 - 1.42363i) q^{23} +(4.68443 - 8.11368i) q^{24} -5.28525 q^{26} +10.0107i q^{27} +(-0.306901 + 0.177189i) q^{28} +(0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(-2.74893 + 1.58710i) q^{32} +(11.8360 + 6.83354i) q^{33} +(-1.72886 - 2.99448i) q^{34} +(1.82817 - 3.16649i) q^{36} -3.77264i q^{37} +(-5.17714 + 0.379847i) q^{38} -13.5233 q^{39} +(4.15184 - 7.19120i) q^{41} +(1.91447 - 1.10532i) q^{42} +(-8.65053 - 4.99438i) q^{43} +(-1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(-5.09656 + 2.94250i) q^{47} +(6.59235 - 3.80609i) q^{48} +6.62891 q^{49} +(-4.42363 - 7.66195i) q^{51} +(2.23585 + 1.29087i) q^{52} +(-7.31681 + 4.22436i) q^{53} +(-5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(-13.2467 + 0.971912i) q^{57} +1.32941i q^{58} +(5.11793 - 8.86451i) q^{59} +(2.49099 + 4.31453i) q^{61} +(-6.42441 - 3.70913i) q^{62} +(3.31586 - 1.91441i) q^{63} -8.77641 q^{64} +(8.13812 + 14.0956i) q^{66} +(7.34057 - 4.23808i) q^{67} +1.68903i q^{68} +8.67608 q^{69} +(-5.80995 + 10.0631i) q^{71} +(16.7357 - 9.66236i) q^{72} +(3.22443 + 1.86162i) q^{73} +(2.24644 - 3.89095i) q^{74} +(2.28289 + 1.10377i) q^{76} -2.73225i q^{77} +(-13.9474 - 8.05253i) q^{78} +(4.51908 - 7.82728i) q^{79} +(-5.82432 + 10.0880i) q^{81} +(8.56407 - 4.94447i) q^{82} +2.12178i q^{83} -1.07985 q^{84} +(-5.94786 - 10.3020i) q^{86} +3.40155i q^{87} -13.7901i q^{88} +(3.96608 + 6.86946i) q^{89} +(1.35176 + 2.34131i) q^{91} +(-1.43444 - 0.828173i) q^{92} +(-16.4381 - 9.49053i) q^{93} -7.00850 q^{94} -9.67231 q^{96} +(8.37668 + 4.83628i) q^{97} +(6.83677 + 3.94721i) q^{98} +(14.0952 + 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49} - 44 q^{51} - 68 q^{54} - 164 q^{56} - 10 q^{59} - 224 q^{64} + 62 q^{66} + 36 q^{69} - 40 q^{71} + 50 q^{74} + 126 q^{76} + 34 q^{79} - 24 q^{81} + 80 q^{84} - 16 q^{86} + 22 q^{89} - 12 q^{91} + 124 q^{94} + 84 q^{96} + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03136 + 0.595455i 0.729280 + 0.421050i 0.818159 0.574992i \(-0.194995\pi\)
−0.0888786 + 0.996042i \(0.528328\pi\)
\(3\) 2.63893 + 1.52359i 1.52359 + 0.879643i 0.999610 + 0.0279089i \(0.00888485\pi\)
0.523975 + 0.851734i \(0.324448\pi\)
\(4\) −0.290867 0.503797i −0.145434 0.251898i
\(5\) 0 0
\(6\) 1.81445 + 3.14272i 0.740747 + 1.28301i
\(7\) 0.609175i 0.230247i −0.993351 0.115123i \(-0.963274\pi\)
0.993351 0.115123i \(-0.0367263\pi\)
\(8\) 3.07461i 1.08704i
\(9\) 3.14263 + 5.44319i 1.04754 + 1.81440i
\(10\) 0 0
\(11\) 4.48517 1.35233 0.676164 0.736751i \(-0.263641\pi\)
0.676164 + 0.736751i \(0.263641\pi\)
\(12\) 1.77264i 0.511718i
\(13\) −3.84342 + 2.21900i −1.06597 + 0.615439i −0.927078 0.374868i \(-0.877688\pi\)
−0.138894 + 0.990307i \(0.544355\pi\)
\(14\) 0.362736 0.628278i 0.0969454 0.167914i
\(15\) 0 0
\(16\) 1.24906 2.16343i 0.312265 0.540858i
\(17\) −2.51445 1.45172i −0.609843 0.352093i 0.163061 0.986616i \(-0.447863\pi\)
−0.772904 + 0.634523i \(0.781197\pi\)
\(18\) 7.48517i 1.76427i
\(19\) −3.60532 + 2.44983i −0.827117 + 0.562030i
\(20\) 0 0
\(21\) 0.928131 1.60757i 0.202535 0.350800i
\(22\) 4.62581 + 2.67071i 0.986227 + 0.569398i
\(23\) 2.46580 1.42363i 0.514154 0.296847i −0.220386 0.975413i \(-0.570732\pi\)
0.734540 + 0.678566i \(0.237398\pi\)
\(24\) 4.68443 8.11368i 0.956206 1.65620i
\(25\) 0 0
\(26\) −5.28525 −1.03652
\(27\) 10.0107i 1.92656i
\(28\) −0.306901 + 0.177189i −0.0579987 + 0.0334856i
\(29\) 0.558149 + 0.966742i 0.103646 + 0.179519i 0.913184 0.407547i \(-0.133616\pi\)
−0.809538 + 0.587067i \(0.800283\pi\)
\(30\) 0 0
\(31\) −6.22908 −1.11877 −0.559387 0.828906i \(-0.688964\pi\)
−0.559387 + 0.828906i \(0.688964\pi\)
\(32\) −2.74893 + 1.58710i −0.485947 + 0.280562i
\(33\) 11.8360 + 6.83354i 2.06039 + 1.18957i
\(34\) −1.72886 2.99448i −0.296498 0.513549i
\(35\) 0 0
\(36\) 1.82817 3.16649i 0.304696 0.527748i
\(37\) 3.77264i 0.620219i −0.950701 0.310109i \(-0.899634\pi\)
0.950701 0.310109i \(-0.100366\pi\)
\(38\) −5.17714 + 0.379847i −0.839843 + 0.0616193i
\(39\) −13.5233 −2.16547
\(40\) 0 0
\(41\) 4.15184 7.19120i 0.648409 1.12308i −0.335094 0.942185i \(-0.608768\pi\)
0.983503 0.180893i \(-0.0578987\pi\)
\(42\) 1.91447 1.10532i 0.295409 0.170555i
\(43\) −8.65053 4.99438i −1.31919 0.761637i −0.335594 0.942007i \(-0.608937\pi\)
−0.983599 + 0.180370i \(0.942270\pi\)
\(44\) −1.30459 2.25961i −0.196674 0.340649i
\(45\) 0 0
\(46\) 3.39082 0.499950
\(47\) −5.09656 + 2.94250i −0.743409 + 0.429208i −0.823308 0.567595i \(-0.807874\pi\)
0.0798983 + 0.996803i \(0.474540\pi\)
\(48\) 6.59235 3.80609i 0.951524 0.549362i
\(49\) 6.62891 0.946986
\(50\) 0 0
\(51\) −4.42363 7.66195i −0.619432 1.07289i
\(52\) 2.23585 + 1.29087i 0.310056 + 0.179011i
\(53\) −7.31681 + 4.22436i −1.00504 + 0.580261i −0.909736 0.415188i \(-0.863716\pi\)
−0.0953049 + 0.995448i \(0.530383\pi\)
\(54\) −5.96093 + 10.3246i −0.811180 + 1.40501i
\(55\) 0 0
\(56\) −1.87298 −0.250287
\(57\) −13.2467 + 0.971912i −1.75457 + 0.128733i
\(58\) 1.32941i 0.174560i
\(59\) 5.11793 8.86451i 0.666297 1.15406i −0.312634 0.949874i \(-0.601211\pi\)
0.978932 0.204187i \(-0.0654552\pi\)
\(60\) 0 0
\(61\) 2.49099 + 4.31453i 0.318939 + 0.552419i 0.980267 0.197678i \(-0.0633401\pi\)
−0.661328 + 0.750097i \(0.730007\pi\)
\(62\) −6.42441 3.70913i −0.815900 0.471060i
\(63\) 3.31586 1.91441i 0.417759 0.241193i
\(64\) −8.77641 −1.09705
\(65\) 0 0
\(66\) 8.13812 + 14.0956i 1.00173 + 1.73505i
\(67\) 7.34057 4.23808i 0.896794 0.517764i 0.0206350 0.999787i \(-0.493431\pi\)
0.876159 + 0.482023i \(0.160098\pi\)
\(68\) 1.68903i 0.204825i
\(69\) 8.67608 1.04448
\(70\) 0 0
\(71\) −5.80995 + 10.0631i −0.689514 + 1.19427i 0.282481 + 0.959273i \(0.408843\pi\)
−0.971995 + 0.235001i \(0.924491\pi\)
\(72\) 16.7357 9.66236i 1.97232 1.13872i
\(73\) 3.22443 + 1.86162i 0.377391 + 0.217887i 0.676682 0.736275i \(-0.263417\pi\)
−0.299292 + 0.954162i \(0.596750\pi\)
\(74\) 2.24644 3.89095i 0.261143 0.452313i
\(75\) 0 0
\(76\) 2.28289 + 1.10377i 0.261865 + 0.126611i
\(77\) 2.73225i 0.311369i
\(78\) −13.9474 8.05253i −1.57923 0.911770i
\(79\) 4.51908 7.82728i 0.508437 0.880638i −0.491516 0.870869i \(-0.663557\pi\)
0.999952 0.00976923i \(-0.00310969\pi\)
\(80\) 0 0
\(81\) −5.82432 + 10.0880i −0.647146 + 1.12089i
\(82\) 8.56407 4.94447i 0.945744 0.546025i
\(83\) 2.12178i 0.232896i 0.993197 + 0.116448i \(0.0371508\pi\)
−0.993197 + 0.116448i \(0.962849\pi\)
\(84\) −1.07985 −0.117821
\(85\) 0 0
\(86\) −5.94786 10.3020i −0.641374 1.11089i
\(87\) 3.40155i 0.364684i
\(88\) 13.7901i 1.47003i
\(89\) 3.96608 + 6.86946i 0.420404 + 0.728161i 0.995979 0.0895879i \(-0.0285550\pi\)
−0.575575 + 0.817749i \(0.695222\pi\)
\(90\) 0 0
\(91\) 1.35176 + 2.34131i 0.141703 + 0.245436i
\(92\) −1.43444 0.828173i −0.149551 0.0863430i
\(93\) −16.4381 9.49053i −1.70455 0.984122i
\(94\) −7.00850 −0.722872
\(95\) 0 0
\(96\) −9.67231 −0.987176
\(97\) 8.37668 + 4.83628i 0.850523 + 0.491050i 0.860827 0.508897i \(-0.169947\pi\)
−0.0103043 + 0.999947i \(0.503280\pi\)
\(98\) 6.83677 + 3.94721i 0.690619 + 0.398729i
\(99\) 14.0952 + 24.4136i 1.41662 + 2.45366i
\(100\) 0 0
\(101\) 0.485632 + 0.841140i 0.0483222 + 0.0836965i 0.889175 0.457568i \(-0.151279\pi\)
−0.840853 + 0.541264i \(0.817946\pi\)
\(102\) 10.5363i 1.04325i
\(103\) 3.34143i 0.329241i 0.986357 + 0.164620i \(0.0526399\pi\)
−0.986357 + 0.164620i \(0.947360\pi\)
\(104\) 6.82256 + 11.8170i 0.669007 + 1.15875i
\(105\) 0 0
\(106\) −10.0617 −0.977275
\(107\) 9.51655i 0.920000i 0.887919 + 0.460000i \(0.152151\pi\)
−0.887919 + 0.460000i \(0.847849\pi\)
\(108\) 5.04337 2.91179i 0.485298 0.280187i
\(109\) 2.77178 4.80087i 0.265489 0.459840i −0.702203 0.711977i \(-0.747800\pi\)
0.967692 + 0.252137i \(0.0811333\pi\)
\(110\) 0 0
\(111\) 5.74795 9.95573i 0.545571 0.944956i
\(112\) −1.31791 0.760896i −0.124531 0.0718979i
\(113\) 1.54134i 0.144997i −0.997369 0.0724987i \(-0.976903\pi\)
0.997369 0.0724987i \(-0.0230973\pi\)
\(114\) −14.2408 6.88542i −1.33378 0.644879i
\(115\) 0 0
\(116\) 0.324694 0.562387i 0.0301471 0.0522163i
\(117\) −24.1568 13.9470i −2.23330 1.28940i
\(118\) 10.5568 6.09499i 0.971835 0.561089i
\(119\) −0.884350 + 1.53174i −0.0810682 + 0.140414i
\(120\) 0 0
\(121\) 9.11672 0.828793
\(122\) 5.93310i 0.537158i
\(123\) 21.9128 12.6514i 1.97581 1.14074i
\(124\) 1.81183 + 3.13819i 0.162707 + 0.281818i
\(125\) 0 0
\(126\) 4.55978 0.406217
\(127\) 1.99661 1.15274i 0.177171 0.102289i −0.408792 0.912628i \(-0.634050\pi\)
0.585963 + 0.810338i \(0.300717\pi\)
\(128\) −3.55376 2.05176i −0.314111 0.181352i
\(129\) −15.2187 26.3596i −1.33994 2.32084i
\(130\) 0 0
\(131\) 6.45905 11.1874i 0.564330 0.977448i −0.432782 0.901499i \(-0.642468\pi\)
0.997112 0.0759493i \(-0.0241987\pi\)
\(132\) 7.95060i 0.692011i
\(133\) 1.49238 + 2.19627i 0.129405 + 0.190441i
\(134\) 10.0943 0.872018
\(135\) 0 0
\(136\) −4.46346 + 7.73095i −0.382739 + 0.662923i
\(137\) −11.0276 + 6.36677i −0.942149 + 0.543950i −0.890633 0.454722i \(-0.849739\pi\)
−0.0515159 + 0.998672i \(0.516405\pi\)
\(138\) 8.94814 + 5.16621i 0.761716 + 0.439777i
\(139\) 5.30433 + 9.18738i 0.449908 + 0.779263i 0.998380 0.0569059i \(-0.0181235\pi\)
−0.548472 + 0.836169i \(0.684790\pi\)
\(140\) 0 0
\(141\) −17.9326 −1.51020
\(142\) −11.9843 + 6.91913i −1.00570 + 0.580640i
\(143\) −17.2384 + 9.95258i −1.44154 + 0.832276i
\(144\) 15.7013 1.30844
\(145\) 0 0
\(146\) 2.21703 + 3.84000i 0.183482 + 0.317801i
\(147\) 17.4932 + 10.0997i 1.44281 + 0.833010i
\(148\) −1.90065 + 1.09734i −0.156232 + 0.0902006i
\(149\) 1.88653 3.26757i 0.154551 0.267690i −0.778344 0.627837i \(-0.783940\pi\)
0.932895 + 0.360147i \(0.117274\pi\)
\(150\) 0 0
\(151\) −9.51562 −0.774370 −0.387185 0.922002i \(-0.626553\pi\)
−0.387185 + 0.922002i \(0.626553\pi\)
\(152\) 7.53228 + 11.0850i 0.610948 + 0.899109i
\(153\) 18.2488i 1.47533i
\(154\) 1.62693 2.81793i 0.131102 0.227075i
\(155\) 0 0
\(156\) 3.93349 + 6.81301i 0.314931 + 0.545477i
\(157\) 2.99336 + 1.72822i 0.238896 + 0.137927i 0.614669 0.788785i \(-0.289290\pi\)
−0.375773 + 0.926712i \(0.622623\pi\)
\(158\) 9.32158 5.38182i 0.741585 0.428155i
\(159\) −25.7447 −2.04169
\(160\) 0 0
\(161\) −0.867239 1.50210i −0.0683480 0.118382i
\(162\) −12.0139 + 6.93624i −0.943902 + 0.544962i
\(163\) 6.65283i 0.521090i −0.965462 0.260545i \(-0.916098\pi\)
0.965462 0.260545i \(-0.0839022\pi\)
\(164\) −4.83054 −0.377202
\(165\) 0 0
\(166\) −1.26343 + 2.18832i −0.0980609 + 0.169846i
\(167\) −14.2509 + 8.22775i −1.10277 + 0.636682i −0.936946 0.349474i \(-0.886360\pi\)
−0.165820 + 0.986156i \(0.553027\pi\)
\(168\) −4.94265 2.85364i −0.381334 0.220163i
\(169\) 3.34790 5.79874i 0.257531 0.446057i
\(170\) 0 0
\(171\) −24.6651 11.9255i −1.88618 0.911968i
\(172\) 5.81081i 0.443070i
\(173\) −19.7302 11.3912i −1.50006 0.866058i −1.00000 6.58713e-5i \(-0.999979\pi\)
−0.500057 0.865992i \(-0.666688\pi\)
\(174\) −2.02547 + 3.50822i −0.153550 + 0.265957i
\(175\) 0 0
\(176\) 5.60224 9.70336i 0.422284 0.731418i
\(177\) 27.0117 15.5952i 2.03032 1.17221i
\(178\) 9.44650i 0.708045i
\(179\) 2.32916 0.174090 0.0870449 0.996204i \(-0.472258\pi\)
0.0870449 + 0.996204i \(0.472258\pi\)
\(180\) 0 0
\(181\) 11.1696 + 19.3463i 0.830230 + 1.43800i 0.897856 + 0.440290i \(0.145124\pi\)
−0.0676258 + 0.997711i \(0.521542\pi\)
\(182\) 3.21965i 0.238656i
\(183\) 15.1810i 1.12221i
\(184\) −4.37710 7.58137i −0.322684 0.558906i
\(185\) 0 0
\(186\) −11.3024 19.5763i −0.828729 1.43540i
\(187\) −11.2777 6.51119i −0.824708 0.476145i
\(188\) 2.96484 + 1.71175i 0.216233 + 0.124842i
\(189\) 6.09829 0.443585
\(190\) 0 0
\(191\) 2.23766 0.161911 0.0809556 0.996718i \(-0.474203\pi\)
0.0809556 + 0.996718i \(0.474203\pi\)
\(192\) −23.1603 13.3716i −1.67145 0.965013i
\(193\) −3.93441 2.27153i −0.283205 0.163508i 0.351669 0.936125i \(-0.385614\pi\)
−0.634873 + 0.772616i \(0.718948\pi\)
\(194\) 5.75957 + 9.97587i 0.413513 + 0.716226i
\(195\) 0 0
\(196\) −1.92813 3.33962i −0.137724 0.238544i
\(197\) 19.2236i 1.36962i −0.728720 0.684812i \(-0.759884\pi\)
0.728720 0.684812i \(-0.240116\pi\)
\(198\) 33.5722i 2.38587i
\(199\) −3.07547 5.32687i −0.218014 0.377612i 0.736186 0.676779i \(-0.236625\pi\)
−0.954201 + 0.299167i \(0.903291\pi\)
\(200\) 0 0
\(201\) 25.8283 1.82179
\(202\) 1.15669i 0.0813843i
\(203\) 0.588915 0.340010i 0.0413338 0.0238641i
\(204\) −2.57338 + 4.45722i −0.180172 + 0.312068i
\(205\) 0 0
\(206\) −1.98967 + 3.44621i −0.138627 + 0.240109i
\(207\) 15.4981 + 8.94786i 1.07720 + 0.621919i
\(208\) 11.0866i 0.768720i
\(209\) −16.1705 + 10.9879i −1.11853 + 0.760049i
\(210\) 0 0
\(211\) −6.34661 + 10.9926i −0.436919 + 0.756765i −0.997450 0.0713679i \(-0.977264\pi\)
0.560531 + 0.828133i \(0.310597\pi\)
\(212\) 4.25644 + 2.45746i 0.292333 + 0.168779i
\(213\) −30.6641 + 17.7039i −2.10107 + 1.21305i
\(214\) −5.66668 + 9.81497i −0.387366 + 0.670938i
\(215\) 0 0
\(216\) 30.7791 2.09425
\(217\) 3.79460i 0.257594i
\(218\) 5.71740 3.30094i 0.387231 0.223568i
\(219\) 5.67269 + 9.82538i 0.383325 + 0.663938i
\(220\) 0 0
\(221\) 12.8854 0.866767
\(222\) 11.8564 6.84528i 0.795748 0.459425i
\(223\) 19.5181 + 11.2688i 1.30703 + 0.754614i 0.981599 0.190952i \(-0.0611575\pi\)
0.325430 + 0.945566i \(0.394491\pi\)
\(224\) 0.966820 + 1.67458i 0.0645984 + 0.111888i
\(225\) 0 0
\(226\) 0.917800 1.58968i 0.0610512 0.105744i
\(227\) 18.1124i 1.20216i 0.799189 + 0.601080i \(0.205263\pi\)
−0.799189 + 0.601080i \(0.794737\pi\)
\(228\) 4.34268 + 6.39095i 0.287601 + 0.423251i
\(229\) 9.41604 0.622229 0.311115 0.950372i \(-0.399298\pi\)
0.311115 + 0.950372i \(0.399298\pi\)
\(230\) 0 0
\(231\) 4.16282 7.21022i 0.273894 0.474398i
\(232\) 2.97236 1.71609i 0.195145 0.112667i
\(233\) 13.5966 + 7.85000i 0.890743 + 0.514271i 0.874185 0.485592i \(-0.161396\pi\)
0.0165573 + 0.999863i \(0.494729\pi\)
\(234\) −16.6096 28.7686i −1.08580 1.88066i
\(235\) 0 0
\(236\) −5.95455 −0.387608
\(237\) 23.8511 13.7704i 1.54929 0.894485i
\(238\) −1.82416 + 1.05318i −0.118243 + 0.0682676i
\(239\) 23.4610 1.51757 0.758783 0.651344i \(-0.225795\pi\)
0.758783 + 0.651344i \(0.225795\pi\)
\(240\) 0 0
\(241\) −6.58469 11.4050i −0.424157 0.734662i 0.572184 0.820125i \(-0.306096\pi\)
−0.996341 + 0.0854634i \(0.972763\pi\)
\(242\) 9.40260 + 5.42860i 0.604422 + 0.348963i
\(243\) −4.73128 + 2.73161i −0.303512 + 0.175233i
\(244\) 1.44910 2.50991i 0.0927689 0.160680i
\(245\) 0 0
\(246\) 30.1333 1.92123
\(247\) 8.42058 17.4159i 0.535789 1.10815i
\(248\) 19.1520i 1.21615i
\(249\) −3.23272 + 5.59923i −0.204865 + 0.354837i
\(250\) 0 0
\(251\) 8.66257 + 15.0040i 0.546776 + 0.947045i 0.998493 + 0.0548830i \(0.0174786\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(252\) −1.92895 1.11368i −0.121512 0.0701551i
\(253\) 11.0595 6.38521i 0.695305 0.401435i
\(254\) 2.74563 0.172276
\(255\) 0 0
\(256\) 6.33295 + 10.9690i 0.395809 + 0.685562i
\(257\) −4.91867 + 2.83980i −0.306818 + 0.177142i −0.645502 0.763759i \(-0.723352\pi\)
0.338683 + 0.940900i \(0.390018\pi\)
\(258\) 36.2483i 2.25672i
\(259\) −2.29820 −0.142803
\(260\) 0 0
\(261\) −3.50811 + 6.07622i −0.217146 + 0.376108i
\(262\) 13.3232 7.69215i 0.823109 0.475222i
\(263\) 4.89966 + 2.82882i 0.302126 + 0.174433i 0.643398 0.765532i \(-0.277524\pi\)
−0.341272 + 0.939965i \(0.610858\pi\)
\(264\) 21.0105 36.3912i 1.29311 2.23972i
\(265\) 0 0
\(266\) 0.231393 + 3.15379i 0.0141876 + 0.193371i
\(267\) 24.1707i 1.47922i
\(268\) −4.27026 2.46544i −0.260848 0.150601i
\(269\) −11.9959 + 20.7775i −0.731402 + 1.26683i 0.224881 + 0.974386i \(0.427801\pi\)
−0.956284 + 0.292440i \(0.905533\pi\)
\(270\) 0 0
\(271\) 10.6497 18.4459i 0.646926 1.12051i −0.336927 0.941531i \(-0.609388\pi\)
0.983853 0.178978i \(-0.0572791\pi\)
\(272\) −6.28138 + 3.62656i −0.380865 + 0.219892i
\(273\) 8.23808i 0.498591i
\(274\) −15.1645 −0.916121
\(275\) 0 0
\(276\) −2.52359 4.37098i −0.151902 0.263102i
\(277\) 0.821109i 0.0493357i −0.999696 0.0246678i \(-0.992147\pi\)
0.999696 0.0246678i \(-0.00785281\pi\)
\(278\) 12.6340i 0.757735i
\(279\) −19.5757 33.9060i −1.17196 2.02990i
\(280\) 0 0
\(281\) 0.293739 + 0.508772i 0.0175230 + 0.0303508i 0.874654 0.484748i \(-0.161089\pi\)
−0.857131 + 0.515099i \(0.827755\pi\)
\(282\) −18.4949 10.6780i −1.10136 0.635869i
\(283\) 26.7969 + 15.4712i 1.59291 + 0.919667i 0.992805 + 0.119746i \(0.0382080\pi\)
0.600105 + 0.799921i \(0.295125\pi\)
\(284\) 6.75969 0.401114
\(285\) 0 0
\(286\) −23.7052 −1.40172
\(287\) −4.38070 2.52920i −0.258585 0.149294i
\(288\) −17.2777 9.97530i −1.01810 0.587800i
\(289\) −4.28504 7.42191i −0.252061 0.436583i
\(290\) 0 0
\(291\) 14.7370 + 25.5252i 0.863896 + 1.49631i
\(292\) 2.16594i 0.126752i
\(293\) 3.76271i 0.219820i −0.993942 0.109910i \(-0.964944\pi\)
0.993942 0.109910i \(-0.0350562\pi\)
\(294\) 12.0278 + 20.8328i 0.701478 + 1.21499i
\(295\) 0 0
\(296\) −11.5994 −0.674202
\(297\) 44.8998i 2.60535i
\(298\) 3.89138 2.24669i 0.225422 0.130147i
\(299\) −6.31806 + 10.9432i −0.365383 + 0.632861i
\(300\) 0 0
\(301\) −3.04246 + 5.26969i −0.175364 + 0.303740i
\(302\) −9.81401 5.66612i −0.564733 0.326049i
\(303\) 2.95961i 0.170025i
\(304\) 0.796788 + 10.8598i 0.0456989 + 0.622855i
\(305\) 0 0
\(306\) 10.8663 18.8211i 0.621187 1.07593i
\(307\) −17.6166 10.1709i −1.00543 0.580485i −0.0955798 0.995422i \(-0.530471\pi\)
−0.909850 + 0.414936i \(0.863804\pi\)
\(308\) −1.37650 + 0.794723i −0.0784334 + 0.0452835i
\(309\) −5.09095 + 8.81779i −0.289614 + 0.501626i
\(310\) 0 0
\(311\) −7.67830 −0.435397 −0.217698 0.976016i \(-0.569855\pi\)
−0.217698 + 0.976016i \(0.569855\pi\)
\(312\) 41.5790i 2.35395i
\(313\) −20.7783 + 11.9964i −1.17446 + 0.678074i −0.954726 0.297486i \(-0.903852\pi\)
−0.219733 + 0.975560i \(0.570519\pi\)
\(314\) 2.05815 + 3.56482i 0.116148 + 0.201174i
\(315\) 0 0
\(316\) −5.25781 −0.295775
\(317\) 0.899831 0.519518i 0.0505395 0.0291790i −0.474517 0.880246i \(-0.657377\pi\)
0.525057 + 0.851067i \(0.324044\pi\)
\(318\) −26.5520 15.3298i −1.48896 0.859653i
\(319\) 2.50339 + 4.33600i 0.140163 + 0.242769i
\(320\) 0 0
\(321\) −14.4993 + 25.1135i −0.809271 + 1.40170i
\(322\) 2.06561i 0.115112i
\(323\) 12.6218 0.926066i 0.702298 0.0515277i
\(324\) 6.77641 0.376467
\(325\) 0 0
\(326\) 3.96146 6.86145i 0.219405 0.380020i
\(327\) 14.6291 8.44610i 0.808990 0.467070i
\(328\) −22.1102 12.7653i −1.22083 0.704846i
\(329\) 1.79250 + 3.10470i 0.0988236 + 0.171167i
\(330\) 0 0
\(331\) 30.8316 1.69466 0.847328 0.531069i \(-0.178210\pi\)
0.847328 + 0.531069i \(0.178210\pi\)
\(332\) 1.06895 0.617157i 0.0586661 0.0338709i
\(333\) 20.5352 11.8560i 1.12532 0.649705i
\(334\) −19.5970 −1.07230
\(335\) 0 0
\(336\) −2.31858 4.01590i −0.126489 0.219085i
\(337\) −17.9400 10.3576i −0.977252 0.564217i −0.0758124 0.997122i \(-0.524155\pi\)
−0.901439 + 0.432906i \(0.857488\pi\)
\(338\) 6.90577 3.98705i 0.375625 0.216867i
\(339\) 2.34837 4.06749i 0.127546 0.220916i
\(340\) 0 0
\(341\) −27.9384 −1.51295
\(342\) −18.3374 26.9864i −0.991572 1.45926i
\(343\) 8.30239i 0.448287i
\(344\) −15.3558 + 26.5970i −0.827929 + 1.43402i
\(345\) 0 0
\(346\) −13.5659 23.4968i −0.729308 1.26320i
\(347\) −7.11991 4.11068i −0.382217 0.220673i 0.296566 0.955013i \(-0.404159\pi\)
−0.678782 + 0.734340i \(0.737492\pi\)
\(348\) 1.71369 0.989399i 0.0918634 0.0530373i
\(349\) −11.9216 −0.638150 −0.319075 0.947730i \(-0.603372\pi\)
−0.319075 + 0.947730i \(0.603372\pi\)
\(350\) 0 0
\(351\) −22.2138 38.4754i −1.18568 2.05366i
\(352\) −12.3294 + 7.11839i −0.657160 + 0.379412i
\(353\) 11.7983i 0.627959i 0.949430 + 0.313980i \(0.101662\pi\)
−0.949430 + 0.313980i \(0.898338\pi\)
\(354\) 37.1450 1.97423
\(355\) 0 0
\(356\) 2.30721 3.99620i 0.122282 0.211798i
\(357\) −4.66747 + 2.69477i −0.247029 + 0.142622i
\(358\) 2.40220 + 1.38691i 0.126960 + 0.0733005i
\(359\) 0.0554058 0.0959656i 0.00292420 0.00506487i −0.864560 0.502530i \(-0.832403\pi\)
0.867484 + 0.497465i \(0.165736\pi\)
\(360\) 0 0
\(361\) 6.99666 17.6648i 0.368245 0.929729i
\(362\) 26.6040i 1.39827i
\(363\) 24.0584 + 13.8901i 1.26274 + 0.729042i
\(364\) 0.786364 1.36202i 0.0412167 0.0713894i
\(365\) 0 0
\(366\) −9.03958 + 15.6570i −0.472507 + 0.818405i
\(367\) 10.1669 5.86986i 0.530708 0.306404i −0.210597 0.977573i \(-0.567541\pi\)
0.741305 + 0.671169i \(0.234207\pi\)
\(368\) 7.11278i 0.370779i
\(369\) 52.1908 2.71694
\(370\) 0 0
\(371\) 2.57338 + 4.45722i 0.133603 + 0.231407i
\(372\) 11.0419i 0.572498i
\(373\) 14.5190i 0.751763i −0.926668 0.375882i \(-0.877340\pi\)
0.926668 0.375882i \(-0.122660\pi\)
\(374\) −7.75424 13.4307i −0.400962 0.694487i
\(375\) 0 0
\(376\) 9.04704 + 15.6699i 0.466566 + 0.808115i
\(377\) −4.29040 2.47706i −0.220967 0.127575i
\(378\) 6.28952 + 3.63125i 0.323498 + 0.186772i
\(379\) 6.59023 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(380\) 0 0
\(381\) 7.02522 0.359913
\(382\) 2.30782 + 1.33242i 0.118079 + 0.0681727i
\(383\) −2.48481 1.43461i −0.126968 0.0733049i 0.435171 0.900348i \(-0.356688\pi\)
−0.562139 + 0.827043i \(0.690021\pi\)
\(384\) −6.25207 10.8289i −0.319050 0.552610i
\(385\) 0 0
\(386\) −2.70519 4.68552i −0.137690 0.238487i
\(387\) 62.7819i 3.19138i
\(388\) 5.62686i 0.285660i
\(389\) −3.16575 5.48323i −0.160510 0.278011i 0.774542 0.632523i \(-0.217980\pi\)
−0.935052 + 0.354512i \(0.884647\pi\)
\(390\) 0 0
\(391\) −8.26682 −0.418071
\(392\) 20.3813i 1.02941i
\(393\) 34.0899 19.6818i 1.71961 0.992817i
\(394\) 11.4468 19.8264i 0.576680 0.998840i
\(395\) 0 0
\(396\) 8.19966 14.2022i 0.412049 0.713689i
\(397\) 26.4569 + 15.2749i 1.32784 + 0.766626i 0.984965 0.172756i \(-0.0552672\pi\)
0.342871 + 0.939382i \(0.388601\pi\)
\(398\) 7.32522i 0.367180i
\(399\) 0.592065 + 8.06957i 0.0296403 + 0.403984i
\(400\) 0 0
\(401\) −15.1711 + 26.2771i −0.757609 + 1.31222i 0.186458 + 0.982463i \(0.440299\pi\)
−0.944067 + 0.329754i \(0.893034\pi\)
\(402\) 26.6382 + 15.3796i 1.32859 + 0.767064i
\(403\) 23.9409 13.8223i 1.19258 0.688538i
\(404\) 0.282509 0.489320i 0.0140553 0.0243446i
\(405\) 0 0
\(406\) 0.809843 0.0401919
\(407\) 16.9209i 0.838740i
\(408\) −23.5575 + 13.6009i −1.16627 + 0.673347i
\(409\) −7.48628 12.9666i −0.370173 0.641158i 0.619419 0.785060i \(-0.287368\pi\)
−0.989592 + 0.143903i \(0.954035\pi\)
\(410\) 0 0
\(411\) −38.8013 −1.91393
\(412\) 1.68340 0.971912i 0.0829352 0.0478827i
\(413\) −5.40004 3.11772i −0.265719 0.153413i
\(414\) 10.6561 + 18.4569i 0.523718 + 0.907107i
\(415\) 0 0
\(416\) 7.04353 12.1997i 0.345337 0.598142i
\(417\) 32.3264i 1.58303i
\(418\) −23.2203 + 1.70368i −1.13574 + 0.0833296i
\(419\) 6.17419 0.301629 0.150815 0.988562i \(-0.451810\pi\)
0.150815 + 0.988562i \(0.451810\pi\)
\(420\) 0 0
\(421\) 13.7714 23.8528i 0.671177 1.16251i −0.306394 0.951905i \(-0.599122\pi\)
0.977571 0.210608i \(-0.0675443\pi\)
\(422\) −13.0913 + 7.55824i −0.637272 + 0.367929i
\(423\) −32.0331 18.4943i −1.55750 0.899226i
\(424\) 12.9883 + 22.4963i 0.630766 + 1.09252i
\(425\) 0 0
\(426\) −42.1675 −2.04302
\(427\) 2.62830 1.51745i 0.127193 0.0734347i
\(428\) 4.79441 2.76805i 0.231746 0.133799i
\(429\) −60.6544 −2.92842
\(430\) 0 0
\(431\) 7.52941 + 13.0413i 0.362679 + 0.628179i 0.988401 0.151868i \(-0.0485288\pi\)
−0.625722 + 0.780046i \(0.715195\pi\)
\(432\) 21.6575 + 12.5040i 1.04200 + 0.601598i
\(433\) 0.840772 0.485420i 0.0404049 0.0233278i −0.479661 0.877454i \(-0.659241\pi\)
0.520066 + 0.854126i \(0.325907\pi\)
\(434\) −2.25951 + 3.91359i −0.108460 + 0.187858i
\(435\) 0 0
\(436\) −3.22488 −0.154444
\(437\) −5.40234 + 11.1734i −0.258429 + 0.534497i
\(438\) 13.5113i 0.645596i
\(439\) −13.7187 + 23.7616i −0.654760 + 1.13408i 0.327194 + 0.944957i \(0.393897\pi\)
−0.981954 + 0.189120i \(0.939436\pi\)
\(440\) 0 0
\(441\) 20.8322 + 36.0824i 0.992008 + 1.71821i
\(442\) 13.2895 + 7.67269i 0.632116 + 0.364952i
\(443\) 7.59109 4.38272i 0.360664 0.208229i −0.308708 0.951157i \(-0.599897\pi\)
0.669372 + 0.742928i \(0.266563\pi\)
\(444\) −6.68755 −0.317377
\(445\) 0 0
\(446\) 13.4201 + 23.2443i 0.635461 + 1.10065i
\(447\) 9.95686 5.74859i 0.470943 0.271899i
\(448\) 5.34637i 0.252592i
\(449\) 9.63397 0.454655 0.227327 0.973818i \(-0.427001\pi\)
0.227327 + 0.973818i \(0.427001\pi\)
\(450\) 0 0
\(451\) 18.6217 32.2538i 0.876862 1.51877i
\(452\) −0.776524 + 0.448326i −0.0365246 + 0.0210875i
\(453\) −25.1110 14.4979i −1.17982 0.681169i
\(454\) −10.7851 + 18.6803i −0.506169 + 0.876711i
\(455\) 0 0
\(456\) 2.98825 + 40.7285i 0.139938 + 1.90729i
\(457\) 10.6708i 0.499161i −0.968354 0.249580i \(-0.919707\pi\)
0.968354 0.249580i \(-0.0802927\pi\)
\(458\) 9.71131 + 5.60683i 0.453780 + 0.261990i
\(459\) 14.5327 25.1714i 0.678330 1.17490i
\(460\) 0 0
\(461\) −2.84340 + 4.92491i −0.132430 + 0.229376i −0.924613 0.380908i \(-0.875611\pi\)
0.792183 + 0.610284i \(0.208945\pi\)
\(462\) 8.58672 4.95754i 0.399490 0.230646i
\(463\) 35.3550i 1.64309i −0.570147 0.821543i \(-0.693114\pi\)
0.570147 0.821543i \(-0.306886\pi\)
\(464\) 2.78864 0.129459
\(465\) 0 0
\(466\) 9.34864 + 16.1923i 0.433067 + 0.750095i
\(467\) 32.9071i 1.52276i −0.648306 0.761380i \(-0.724522\pi\)
0.648306 0.761380i \(-0.275478\pi\)
\(468\) 16.2269i 0.750086i
\(469\) −2.58173 4.47169i −0.119213 0.206484i
\(470\) 0 0
\(471\) 5.26617 + 9.12127i 0.242652 + 0.420286i
\(472\) −27.2549 15.7356i −1.25451 0.724292i
\(473\) −38.7991 22.4006i −1.78398 1.02998i
\(474\) 32.7986 1.50649
\(475\) 0 0
\(476\) 1.02891 0.0471602
\(477\) −45.9880 26.5512i −2.10564 1.21569i
\(478\) 24.1967 + 13.9700i 1.10673 + 0.638971i
\(479\) −4.52861 7.84378i −0.206917 0.358391i 0.743825 0.668375i \(-0.233010\pi\)
−0.950742 + 0.309984i \(0.899676\pi\)
\(480\) 0 0
\(481\) 8.37149 + 14.4998i 0.381707 + 0.661136i
\(482\) 15.6835i 0.714366i
\(483\) 5.28525i 0.240487i
\(484\) −2.65175 4.59297i −0.120534 0.208772i
\(485\) 0 0
\(486\) −6.50619 −0.295127
\(487\) 16.5206i 0.748620i −0.927304 0.374310i \(-0.877880\pi\)
0.927304 0.374310i \(-0.122120\pi\)
\(488\) 13.2655 7.65884i 0.600501 0.346700i
\(489\) 10.1362 17.5563i 0.458373 0.793925i
\(490\) 0 0
\(491\) 0.695625 1.20486i 0.0313931 0.0543745i −0.849902 0.526941i \(-0.823339\pi\)
0.881295 + 0.472566i \(0.156672\pi\)
\(492\) −12.7474 7.35974i −0.574699 0.331803i
\(493\) 3.24109i 0.145972i
\(494\) 19.0550 12.9480i 0.857326 0.582557i
\(495\) 0 0
\(496\) −7.78048 + 13.4762i −0.349354 + 0.605099i
\(497\) 6.13021 + 3.53928i 0.274977 + 0.158758i
\(498\) −6.66818 + 3.84988i −0.298808 + 0.172517i
\(499\) −8.33255 + 14.4324i −0.373016 + 0.646083i −0.990028 0.140871i \(-0.955010\pi\)
0.617012 + 0.786954i \(0.288343\pi\)
\(500\) 0 0
\(501\) −50.1427 −2.24021
\(502\) 20.6327i 0.920881i
\(503\) −13.5439 + 7.81956i −0.603892 + 0.348657i −0.770571 0.637354i \(-0.780029\pi\)
0.166679 + 0.986011i \(0.446696\pi\)
\(504\) −5.88607 10.1950i −0.262186 0.454120i
\(505\) 0 0
\(506\) 15.2084 0.676096
\(507\) 17.6697 10.2016i 0.784741 0.453070i
\(508\) −1.16150 0.670591i −0.0515331 0.0297526i
\(509\) −9.57702 16.5879i −0.424494 0.735245i 0.571879 0.820338i \(-0.306215\pi\)
−0.996373 + 0.0850929i \(0.972881\pi\)
\(510\) 0 0
\(511\) 1.13406 1.96424i 0.0501677 0.0868929i
\(512\) 23.2910i 1.02933i
\(513\) −24.5246 36.0919i −1.08279 1.59349i
\(514\) −6.76389 −0.298342
\(515\) 0 0
\(516\) −8.85327 + 15.3343i −0.389743 + 0.675055i
\(517\) −22.8589 + 13.1976i −1.00533 + 0.580430i
\(518\) −2.37027 1.36848i −0.104144 0.0601273i
\(519\) −34.7110 60.1212i −1.52364 2.63903i
\(520\) 0 0
\(521\) −19.2394 −0.842892 −0.421446 0.906853i \(-0.638477\pi\)
−0.421446 + 0.906853i \(0.638477\pi\)
\(522\) −7.23622 + 4.17784i −0.316721 + 0.182859i
\(523\) −5.74993 + 3.31973i −0.251427 + 0.145161i −0.620418 0.784272i \(-0.713037\pi\)
0.368990 + 0.929433i \(0.379704\pi\)
\(524\) −7.51490 −0.328290
\(525\) 0 0
\(526\) 3.36887 + 5.83505i 0.146890 + 0.254420i
\(527\) 15.6627 + 9.04285i 0.682277 + 0.393913i
\(528\) 29.5678 17.0710i 1.28677 0.742919i
\(529\) −7.44657 + 12.8978i −0.323764 + 0.560775i
\(530\) 0 0
\(531\) 64.3349 2.79190
\(532\) 0.672391 1.39068i 0.0291519 0.0602935i
\(533\) 36.8517i 1.59623i
\(534\) −14.3925 + 24.9286i −0.622826 + 1.07877i
\(535\) 0 0
\(536\) −13.0305 22.5694i −0.562830 0.974850i
\(537\) 6.14649 + 3.54868i 0.265241 + 0.153137i
\(538\) −24.7441 + 14.2860i −1.06679 + 0.615914i
\(539\) 29.7317 1.28064
\(540\) 0 0
\(541\) −20.8756 36.1575i −0.897510 1.55453i −0.830667 0.556770i \(-0.812040\pi\)
−0.0668435 0.997763i \(-0.521293\pi\)
\(542\) 21.9674 12.6829i 0.943581 0.544777i
\(543\) 68.0714i 2.92122i
\(544\) 9.21606 0.395135
\(545\) 0 0
\(546\) −4.90540 + 8.49641i −0.209932 + 0.363613i
\(547\) 10.5700 6.10258i 0.451939 0.260927i −0.256710 0.966489i \(-0.582638\pi\)
0.708649 + 0.705561i \(0.249305\pi\)
\(548\) 6.41512 + 3.70377i 0.274040 + 0.158217i
\(549\) −15.6565 + 27.1179i −0.668204 + 1.15736i
\(550\) 0 0
\(551\) −4.38066 2.11804i −0.186622 0.0902317i
\(552\) 26.6756i 1.13539i
\(553\) −4.76819 2.75291i −0.202764 0.117066i
\(554\) 0.488934 0.846858i 0.0207728 0.0359795i
\(555\) 0 0
\(556\) 3.08571 5.34461i 0.130863 0.226662i
\(557\) 30.4450 17.5774i 1.28999 0.744779i 0.311342 0.950298i \(-0.399222\pi\)
0.978653 + 0.205519i \(0.0658883\pi\)
\(558\) 46.6257i 1.97382i
\(559\) 44.3301 1.87496
\(560\) 0 0
\(561\) −19.8407 34.3651i −0.837675 1.45090i
\(562\) 0.699634i 0.0295123i
\(563\) 17.8406i 0.751891i −0.926642 0.375945i \(-0.877318\pi\)
0.926642 0.375945i \(-0.122682\pi\)
\(564\) 5.21600 + 9.03438i 0.219633 + 0.380416i
\(565\) 0 0
\(566\) 18.4248 + 31.9127i 0.774452 + 1.34139i
\(567\) 6.14537 + 3.54803i 0.258081 + 0.149003i
\(568\) 30.9402 + 17.8633i 1.29822 + 0.749529i
\(569\) −31.6042 −1.32492 −0.662459 0.749098i \(-0.730487\pi\)
−0.662459 + 0.749098i \(0.730487\pi\)
\(570\) 0 0
\(571\) −4.73053 −0.197967 −0.0989833 0.995089i \(-0.531559\pi\)
−0.0989833 + 0.995089i \(0.531559\pi\)
\(572\) 10.0281 + 5.78975i 0.419298 + 0.242082i
\(573\) 5.90501 + 3.40926i 0.246685 + 0.142424i
\(574\) −3.01205 5.21702i −0.125721 0.217754i
\(575\) 0 0
\(576\) −27.5810 47.7717i −1.14921 1.99049i
\(577\) 24.4074i 1.01609i 0.861330 + 0.508047i \(0.169632\pi\)
−0.861330 + 0.508047i \(0.830368\pi\)
\(578\) 10.2062i 0.424522i
\(579\) −6.92174 11.9888i −0.287658 0.498238i
\(580\) 0 0
\(581\) 1.29254 0.0536235
\(582\) 35.1008i 1.45497i
\(583\) −32.8171 + 18.9470i −1.35915 + 0.784703i
\(584\) 5.72377 9.91386i 0.236851 0.410239i
\(585\) 0 0
\(586\) 2.24052 3.88070i 0.0925551 0.160310i
\(587\) 24.7817 + 14.3077i 1.02285 + 0.590543i 0.914928 0.403616i \(-0.132247\pi\)
0.107922 + 0.994159i \(0.465580\pi\)
\(588\) 11.7507i 0.484590i
\(589\) 22.4578 15.2602i 0.925358 0.628785i
\(590\) 0 0
\(591\) 29.2888 50.7297i 1.20478 2.08674i
\(592\) −8.16186 4.71225i −0.335450 0.193672i
\(593\) −3.21738 + 1.85756i −0.132122 + 0.0762807i −0.564604 0.825362i \(-0.690971\pi\)
0.432482 + 0.901642i \(0.357638\pi\)
\(594\) −26.7358 + 46.3077i −1.09698 + 1.90003i
\(595\) 0 0
\(596\) −2.19492 −0.0899076
\(597\) 18.7430i 0.767099i
\(598\) −13.0324 + 7.52423i −0.532933 + 0.307689i
\(599\) 3.54970 + 6.14826i 0.145037 + 0.251211i 0.929387 0.369108i \(-0.120337\pi\)
−0.784350 + 0.620319i \(0.787003\pi\)
\(600\) 0 0
\(601\) −11.0596 −0.451131 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(602\) −6.27572 + 3.62329i −0.255779 + 0.147674i
\(603\) 46.1373 + 26.6374i 1.87886 + 1.08476i
\(604\) 2.76778 + 4.79394i 0.112619 + 0.195063i
\(605\) 0 0
\(606\) −1.76231 + 3.05242i −0.0715891 + 0.123996i
\(607\) 27.1193i 1.10074i 0.834921 + 0.550369i \(0.185513\pi\)
−0.834921 + 0.550369i \(0.814487\pi\)
\(608\) 6.02266 12.4564i 0.244251 0.505174i
\(609\) 2.07214 0.0839673
\(610\) 0 0
\(611\) 13.0588 22.6185i 0.528302 0.915046i
\(612\) −9.19369 + 5.30798i −0.371633 + 0.214562i
\(613\) 36.2268 + 20.9156i 1.46319 + 0.844772i 0.999157 0.0410468i \(-0.0130693\pi\)
0.464031 + 0.885819i \(0.346403\pi\)
\(614\) −12.1127 20.9797i −0.488827 0.846673i
\(615\) 0 0
\(616\) −8.40062 −0.338471
\(617\) −15.3332 + 8.85262i −0.617291 + 0.356393i −0.775813 0.630962i \(-0.782660\pi\)
0.158523 + 0.987355i \(0.449327\pi\)
\(618\) −10.5012 + 6.06286i −0.422420 + 0.243884i
\(619\) 39.8064 1.59995 0.799976 0.600032i \(-0.204845\pi\)
0.799976 + 0.600032i \(0.204845\pi\)
\(620\) 0 0
\(621\) 14.2515 + 24.6844i 0.571895 + 0.990551i
\(622\) −7.91908 4.57208i −0.317526 0.183324i
\(623\) 4.18471 2.41604i 0.167657 0.0967966i
\(624\) −16.8914 + 29.2568i −0.676198 + 1.17121i
\(625\) 0 0
\(626\) −28.5732 −1.14201
\(627\) −59.4137 + 4.35919i −2.37275 + 0.174089i
\(628\) 2.01072i 0.0802366i
\(629\) −5.47681 + 9.48611i −0.218375 + 0.378236i
\(630\) 0 0
\(631\) −23.0990 40.0087i −0.919557 1.59272i −0.800088 0.599882i \(-0.795214\pi\)
−0.119469 0.992838i \(-0.538119\pi\)
\(632\) −24.0659 13.8944i −0.957288 0.552691i
\(633\) −33.4965 + 19.3392i −1.33137 + 0.768664i
\(634\) 1.23740 0.0491433
\(635\) 0 0
\(636\) 7.48829 + 12.9701i 0.296930 + 0.514298i
\(637\) −25.4776 + 14.7095i −1.00946 + 0.582813i
\(638\) 5.96262i 0.236062i
\(639\) −73.0340 −2.88918
\(640\) 0 0
\(641\) −3.30674 + 5.72744i −0.130608 + 0.226220i −0.923911 0.382607i \(-0.875026\pi\)
0.793303 + 0.608827i \(0.208360\pi\)
\(642\) −29.9079 + 17.2673i −1.18037 + 0.681487i
\(643\) −26.5135 15.3076i −1.04559 0.603673i −0.124180 0.992260i \(-0.539630\pi\)
−0.921412 + 0.388587i \(0.872963\pi\)
\(644\) −0.504503 + 0.873824i −0.0198802 + 0.0344335i
\(645\) 0 0
\(646\) 13.5691 + 6.56063i 0.533868 + 0.258125i
\(647\) 11.8979i 0.467753i −0.972266 0.233877i \(-0.924859\pi\)
0.972266 0.233877i \(-0.0751412\pi\)
\(648\) 31.0167 + 17.9075i 1.21845 + 0.703474i
\(649\) 22.9548 39.7588i 0.901053 1.56067i
\(650\) 0 0
\(651\) −5.78140 + 10.0137i −0.226591 + 0.392467i
\(652\) −3.35167 + 1.93509i −0.131262 + 0.0757839i
\(653\) 1.42899i 0.0559207i 0.999609 + 0.0279604i \(0.00890122\pi\)
−0.999609 + 0.0279604i \(0.991099\pi\)
\(654\) 20.1171 0.786640
\(655\) 0 0
\(656\) −10.3718 17.9645i −0.404950 0.701395i
\(657\) 23.4015i 0.912981i
\(658\) 4.26941i 0.166439i
\(659\) −12.2485 21.2150i −0.477134 0.826420i 0.522523 0.852625i \(-0.324991\pi\)
−0.999657 + 0.0262051i \(0.991658\pi\)
\(660\) 0 0
\(661\) 1.61303 + 2.79385i 0.0627396 + 0.108668i 0.895689 0.444681i \(-0.146683\pi\)
−0.832949 + 0.553349i \(0.813350\pi\)
\(662\) 31.7984 + 18.3588i 1.23588 + 0.713535i
\(663\) 34.0037 + 19.6320i 1.32059 + 0.762445i
\(664\) 6.52366 0.253167
\(665\) 0 0
\(666\) 28.2389 1.09423
\(667\) 2.75256 + 1.58919i 0.106580 + 0.0615338i
\(668\) 8.29023 + 4.78636i 0.320758 + 0.185190i
\(669\) 34.3379 + 59.4750i 1.32758 + 2.29944i
\(670\) 0 0
\(671\) 11.1725 + 19.3514i 0.431311 + 0.747052i
\(672\) 5.89213i 0.227294i
\(673\) 37.1424i 1.43173i −0.698237 0.715866i \(-0.746032\pi\)
0.698237 0.715866i \(-0.253968\pi\)
\(674\) −12.3350 21.3649i −0.475127 0.822944i
\(675\) 0 0
\(676\) −3.89518 −0.149815
\(677\) 24.7550i 0.951412i −0.879604 0.475706i \(-0.842193\pi\)
0.879604 0.475706i \(-0.157807\pi\)
\(678\) 4.84402 2.79669i 0.186033 0.107406i
\(679\) 2.94614 5.10287i 0.113063 0.195830i
\(680\) 0 0
\(681\) −27.5957 + 47.7972i −1.05747 + 1.83159i
\(682\) −28.8145 16.6361i −1.10337 0.637028i
\(683\) 40.1153i 1.53497i −0.641068 0.767484i \(-0.721508\pi\)
0.641068 0.767484i \(-0.278492\pi\)
\(684\) 1.16621 + 15.8949i 0.0445912 + 0.607757i
\(685\) 0 0
\(686\) 4.94370 8.56274i 0.188751 0.326927i
\(687\) 24.8482 + 14.3461i 0.948020 + 0.547340i
\(688\) −21.6100 + 12.4766i −0.823875 + 0.475664i
\(689\) 18.7477 32.4720i 0.714230 1.23708i
\(690\) 0 0
\(691\) 39.4963 1.50251 0.751254 0.660013i \(-0.229449\pi\)
0.751254 + 0.660013i \(0.229449\pi\)
\(692\) 13.2533i 0.503816i
\(693\) 14.8722 8.58645i 0.564947 0.326172i
\(694\) −4.89545 8.47917i −0.185829 0.321865i
\(695\) 0 0
\(696\) 10.4584 0.396426
\(697\) −20.8792 + 12.0546i −0.790855 + 0.456600i
\(698\) −12.2955 7.09879i −0.465390 0.268693i
\(699\) 23.9203 + 41.4312i 0.904748 + 1.56707i
\(700\) 0 0
\(701\) −0.0109776 + 0.0190137i −0.000414618 + 0.000718139i −0.866233 0.499641i \(-0.833465\pi\)
0.865818 + 0.500359i \(0.166799\pi\)
\(702\) 52.9092i 1.99693i
\(703\) 9.24234 + 13.6016i 0.348581 + 0.512994i
\(704\) −39.3637 −1.48357
\(705\) 0 0
\(706\) −7.02535 + 12.1683i −0.264402 + 0.457958i
\(707\) 0.512402 0.295835i 0.0192708 0.0111260i
\(708\) −15.7136 9.07226i −0.590554 0.340957i
\(709\) −8.90087 15.4168i −0.334279 0.578989i 0.649067 0.760731i \(-0.275160\pi\)
−0.983346 + 0.181743i \(0.941826\pi\)
\(710\) 0 0
\(711\) 56.8071 2.13043
\(712\) 21.1209 12.1942i 0.791540 0.456996i
\(713\) −15.3596 + 8.86789i −0.575223 + 0.332105i
\(714\) −6.41844 −0.240204
\(715\) 0 0
\(716\) −0.677477 1.17342i −0.0253185 0.0438529i
\(717\) 61.9118 + 35.7448i 2.31214 + 1.33491i
\(718\) 0.114286 0.0659833i 0.00426513 0.00246247i
\(719\) 9.40515 16.2902i 0.350753 0.607522i −0.635629 0.771995i \(-0.719259\pi\)
0.986382 + 0.164473i \(0.0525923\pi\)
\(720\) 0 0
\(721\) 2.03552 0.0758066
\(722\) 17.7347 14.0526i 0.660016 0.522983i
\(723\) 40.1294i 1.49243i
\(724\) 6.49774 11.2544i 0.241487 0.418267i
\(725\) 0 0
\(726\) 16.5419 + 28.6513i 0.613926 + 1.06335i
\(727\) −4.33274 2.50151i −0.160692 0.0927758i 0.417497 0.908678i \(-0.362907\pi\)
−0.578190 + 0.815902i \(0.696241\pi\)
\(728\) 7.19864 4.15613i 0.266799 0.154037i
\(729\) 18.2986 0.677725
\(730\) 0 0
\(731\) 14.5009 + 25.1162i 0.536334 + 0.928957i
\(732\) 7.64812 4.41565i 0.282683 0.163207i
\(733\) 23.5259i 0.868950i 0.900684 + 0.434475i \(0.143066\pi\)
−0.900684 + 0.434475i \(0.856934\pi\)
\(734\) 13.9809 0.516046
\(735\) 0 0
\(736\) −4.51887 + 7.82691i −0.166568 + 0.288504i
\(737\) 32.9237 19.0085i 1.21276 0.700187i
\(738\) 53.8274 + 31.0772i 1.98141 + 1.14397i
\(739\) −18.6918 + 32.3752i −0.687590 + 1.19094i 0.285026 + 0.958520i \(0.407998\pi\)
−0.972615 + 0.232421i \(0.925335\pi\)
\(740\) 0 0
\(741\) 48.7559 33.1299i 1.79109 1.21706i
\(742\) 6.12932i 0.225014i
\(743\) 8.99679 + 5.19430i 0.330060 + 0.190560i 0.655868 0.754876i \(-0.272303\pi\)
−0.325808 + 0.945436i \(0.605636\pi\)
\(744\) −29.1797 + 50.5407i −1.06978 + 1.85291i
\(745\) 0 0
\(746\) 8.64539 14.9742i 0.316530 0.548246i
\(747\) −11.5493 + 6.66797i −0.422566 + 0.243968i
\(748\) 7.57556i 0.276990i
\(749\) 5.79725 0.211827
\(750\) 0 0
\(751\) 15.6413 + 27.0915i 0.570758 + 0.988581i 0.996488 + 0.0837314i \(0.0266838\pi\)
−0.425731 + 0.904850i \(0.639983\pi\)
\(752\) 14.7014i 0.536105i
\(753\) 52.7927i 1.92387i
\(754\) −2.94996 5.10947i −0.107431 0.186076i
\(755\) 0 0
\(756\) −1.77379 3.07230i −0.0645122 0.111738i
\(757\) 10.9328 + 6.31205i 0.397359 + 0.229415i 0.685344 0.728220i \(-0.259652\pi\)
−0.287985 + 0.957635i \(0.592985\pi\)
\(758\) 6.79689 + 3.92419i 0.246874 + 0.142533i
\(759\) 38.9137 1.41248
\(760\) 0 0
\(761\) 11.5495 0.418668 0.209334 0.977844i \(-0.432870\pi\)
0.209334 + 0.977844i \(0.432870\pi\)
\(762\) 7.24551 + 4.18320i 0.262477 + 0.151541i
\(763\) −2.92457 1.68850i −0.105877 0.0611279i
\(764\) −0.650861 1.12732i −0.0235473 0.0407851i
\(765\) 0 0
\(766\) −1.70849 2.95918i −0.0617301 0.106920i
\(767\) 45.4267i 1.64026i
\(768\) 38.5951i 1.39268i
\(769\) −13.4603 23.3140i −0.485392 0.840724i 0.514467 0.857510i \(-0.327990\pi\)
−0.999859 + 0.0167864i \(0.994656\pi\)
\(770\) 0 0
\(771\) −17.3067 −0.623286
\(772\) 2.64286i 0.0951184i
\(773\) −18.4750 + 10.6666i −0.664500 + 0.383649i −0.793989 0.607932i \(-0.791999\pi\)
0.129489 + 0.991581i \(0.458666\pi\)
\(774\) 37.3838 64.7506i 1.34373 2.32741i
\(775\) 0 0
\(776\) 14.8697 25.7550i 0.533790 0.924552i
\(777\) −6.06479 3.50151i −0.217573 0.125616i
\(778\) 7.54024i 0.270331i