Properties

Label 475.2.e.e.26.2
Level $475$
Weight $2$
Character 475.26
Analytic conductor $3.793$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
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([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 26.2
Root \(-1.02359 - 1.77290i\) of defining polynomial
Character \(\chi\) \(=\) 475.26
Dual form 475.2.e.e.201.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.595455 - 1.03136i) q^{2} +(1.52359 + 2.63893i) q^{3} +(0.290867 - 0.503797i) q^{4} +(1.81445 - 3.14272i) q^{6} +0.609175 q^{7} -3.07461 q^{8} +(-3.14263 + 5.44319i) q^{9} +O(q^{10})\) \(q+(-0.595455 - 1.03136i) q^{2} +(1.52359 + 2.63893i) q^{3} +(0.290867 - 0.503797i) q^{4} +(1.81445 - 3.14272i) q^{6} +0.609175 q^{7} -3.07461 q^{8} +(-3.14263 + 5.44319i) q^{9} +4.48517 q^{11} +1.77264 q^{12} +(2.21900 - 3.84342i) q^{13} +(-0.362736 - 0.628278i) q^{14} +(1.24906 + 2.16343i) q^{16} +(1.45172 + 2.51445i) q^{17} +7.48517 q^{18} +(3.60532 + 2.44983i) q^{19} +(0.928131 + 1.60757i) q^{21} +(-2.67071 - 4.62581i) q^{22} +(-1.42363 + 2.46580i) q^{23} +(-4.68443 - 8.11368i) q^{24} -5.28525 q^{26} -10.0107 q^{27} +(0.177189 - 0.306901i) q^{28} +(-0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(-1.58710 + 2.74893i) q^{32} +(6.83354 + 11.8360i) q^{33} +(1.72886 - 2.99448i) q^{34} +(1.82817 + 3.16649i) q^{36} +3.77264 q^{37} +(0.379847 - 5.17714i) q^{38} +13.5233 q^{39} +(4.15184 + 7.19120i) q^{41} +(1.10532 - 1.91447i) q^{42} +(-4.99438 - 8.65053i) q^{43} +(1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(-2.94250 + 5.09656i) q^{47} +(-3.80609 + 6.59235i) q^{48} -6.62891 q^{49} +(-4.42363 + 7.66195i) q^{51} +(-1.29087 - 2.23585i) q^{52} +(4.22436 - 7.31681i) q^{53} +(5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(-0.971912 + 13.2467i) q^{57} +1.32941 q^{58} +(-5.11793 - 8.86451i) q^{59} +(2.49099 - 4.31453i) q^{61} +(3.70913 + 6.42441i) q^{62} +(-1.91441 + 3.31586i) q^{63} +8.77641 q^{64} +(8.13812 - 14.0956i) q^{66} +(4.23808 - 7.34057i) q^{67} +1.68903 q^{68} -8.67608 q^{69} +(-5.80995 - 10.0631i) q^{71} +(9.66236 - 16.7357i) q^{72} +(1.86162 + 3.22443i) q^{73} +(-2.24644 - 3.89095i) q^{74} +(2.28289 - 1.10377i) q^{76} +2.73225 q^{77} +(-8.05253 - 13.9474i) q^{78} +(-4.51908 - 7.82728i) q^{79} +(-5.82432 - 10.0880i) q^{81} +(4.94447 - 8.56407i) q^{82} +2.12178 q^{83} +1.07985 q^{84} +(-5.94786 + 10.3020i) q^{86} -3.40155 q^{87} -13.7901 q^{88} +(-3.96608 + 6.86946i) q^{89} +(1.35176 - 2.34131i) q^{91} +(0.828173 + 1.43444i) q^{92} +(-9.49053 - 16.4381i) q^{93} +7.00850 q^{94} -9.67231 q^{96} +(-4.83628 - 8.37668i) q^{97} +(3.94721 + 6.83677i) q^{98} +(-14.0952 + 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24} + 6 q^{26} - 24 q^{27} - 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} + 7 q^{36} + 4 q^{37} - 13 q^{38} + 30 q^{39} + 8 q^{41} - 15 q^{42} + q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} + 23 q^{48} - 20 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} + 34 q^{54} - 82 q^{56} - 7 q^{57} + 54 q^{58} + 5 q^{59} + 37 q^{62} - 3 q^{63} + 112 q^{64} + 31 q^{66} + 4 q^{67} - 32 q^{68} - 18 q^{69} - 20 q^{71} + 17 q^{72} - 20 q^{73} - 25 q^{74} + 63 q^{76} - 28 q^{77} - 18 q^{78} - 17 q^{79} - 12 q^{81} + 21 q^{82} - 2 q^{83} - 40 q^{84} - 8 q^{86} + 32 q^{87} + 14 q^{88} - 11 q^{89} - 6 q^{91} - q^{92} - 8 q^{93} - 62 q^{94} + 42 q^{96} + q^{97} + 9 q^{98} - 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.595455 1.03136i −0.421050 0.729280i 0.574992 0.818159i \(-0.305005\pi\)
−0.996042 + 0.0888786i \(0.971672\pi\)
\(3\) 1.52359 + 2.63893i 0.879643 + 1.52359i 0.851734 + 0.523975i \(0.175552\pi\)
0.0279089 + 0.999610i \(0.491115\pi\)
\(4\) 0.290867 0.503797i 0.145434 0.251898i
\(5\) 0 0
\(6\) 1.81445 3.14272i 0.740747 1.28301i
\(7\) 0.609175 0.230247 0.115123 0.993351i \(-0.463274\pi\)
0.115123 + 0.993351i \(0.463274\pi\)
\(8\) −3.07461 −1.08704
\(9\) −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 \(0.263641\pi\)
\(12\) 1.77264 0.511718
\(13\) 2.21900 3.84342i 0.615439 1.06597i −0.374868 0.927078i \(-0.622312\pi\)
0.990307 0.138894i \(-0.0443547\pi\)
\(14\) −0.362736 0.628278i −0.0969454 0.167914i
\(15\) 0 0
\(16\) 1.24906 + 2.16343i 0.312265 + 0.540858i
\(17\) 1.45172 + 2.51445i 0.352093 + 0.609843i 0.986616 0.163061i \(-0.0521368\pi\)
−0.634523 + 0.772904i \(0.718803\pi\)
\(18\) 7.48517 1.76427
\(19\) 3.60532 + 2.44983i 0.827117 + 0.562030i
\(20\) 0 0
\(21\) 0.928131 + 1.60757i 0.202535 + 0.350800i
\(22\) −2.67071 4.62581i −0.569398 0.986227i
\(23\) −1.42363 + 2.46580i −0.296847 + 0.514154i −0.975413 0.220386i \(-0.929268\pi\)
0.678566 + 0.734540i \(0.262602\pi\)
\(24\) −4.68443 8.11368i −0.956206 1.65620i
\(25\) 0 0
\(26\) −5.28525 −1.03652
\(27\) −10.0107 −1.92656
\(28\) 0.177189 0.306901i 0.0334856 0.0579987i
\(29\) −0.558149 + 0.966742i −0.103646 + 0.179519i −0.913184 0.407547i \(-0.866384\pi\)
0.809538 + 0.587067i \(0.199717\pi\)
\(30\) 0 0
\(31\) −6.22908 −1.11877 −0.559387 0.828906i \(-0.688964\pi\)
−0.559387 + 0.828906i \(0.688964\pi\)
\(32\) −1.58710 + 2.74893i −0.280562 + 0.485947i
\(33\) 6.83354 + 11.8360i 1.18957 + 2.06039i
\(34\) 1.72886 2.99448i 0.296498 0.513549i
\(35\) 0 0
\(36\) 1.82817 + 3.16649i 0.304696 + 0.527748i
\(37\) 3.77264 0.620219 0.310109 0.950701i \(-0.399634\pi\)
0.310109 + 0.950701i \(0.399634\pi\)
\(38\) 0.379847 5.17714i 0.0616193 0.839843i
\(39\) 13.5233 2.16547
\(40\) 0 0
\(41\) 4.15184 + 7.19120i 0.648409 + 1.12308i 0.983503 + 0.180893i \(0.0578987\pi\)
−0.335094 + 0.942185i \(0.608768\pi\)
\(42\) 1.10532 1.91447i 0.170555 0.295409i
\(43\) −4.99438 8.65053i −0.761637 1.31919i −0.942007 0.335594i \(-0.891063\pi\)
0.180370 0.983599i \(-0.442270\pi\)
\(44\) 1.30459 2.25961i 0.196674 0.340649i
\(45\) 0 0
\(46\) 3.39082 0.499950
\(47\) −2.94250 + 5.09656i −0.429208 + 0.743409i −0.996803 0.0798983i \(-0.974540\pi\)
0.567595 + 0.823308i \(0.307874\pi\)
\(48\) −3.80609 + 6.59235i −0.549362 + 0.951524i
\(49\) −6.62891 −0.946986
\(50\) 0 0
\(51\) −4.42363 + 7.66195i −0.619432 + 1.07289i
\(52\) −1.29087 2.23585i −0.179011 0.310056i
\(53\) 4.22436 7.31681i 0.580261 1.00504i −0.415188 0.909736i \(-0.636284\pi\)
0.995448 0.0953049i \(-0.0303826\pi\)
\(54\) 5.96093 + 10.3246i 0.811180 + 1.40501i
\(55\) 0 0
\(56\) −1.87298 −0.250287
\(57\) −0.971912 + 13.2467i −0.128733 + 1.75457i
\(58\) 1.32941 0.174560
\(59\) −5.11793 8.86451i −0.666297 1.15406i −0.978932 0.204187i \(-0.934545\pi\)
0.312634 0.949874i \(-0.398789\pi\)
\(60\) 0 0
\(61\) 2.49099 4.31453i 0.318939 0.552419i −0.661328 0.750097i \(-0.730007\pi\)
0.980267 + 0.197678i \(0.0633401\pi\)
\(62\) 3.70913 + 6.42441i 0.471060 + 0.815900i
\(63\) −1.91441 + 3.31586i −0.241193 + 0.417759i
\(64\) 8.77641 1.09705
\(65\) 0 0
\(66\) 8.13812 14.0956i 1.00173 1.73505i
\(67\) 4.23808 7.34057i 0.517764 0.896794i −0.482023 0.876159i \(-0.660098\pi\)
0.999787 0.0206350i \(-0.00656879\pi\)
\(68\) 1.68903 0.204825
\(69\) −8.67608 −1.04448
\(70\) 0 0
\(71\) −5.80995 10.0631i −0.689514 1.19427i −0.971995 0.235001i \(-0.924491\pi\)
0.282481 0.959273i \(-0.408843\pi\)
\(72\) 9.66236 16.7357i 1.13872 1.97232i
\(73\) 1.86162 + 3.22443i 0.217887 + 0.377391i 0.954162 0.299292i \(-0.0967504\pi\)
−0.736275 + 0.676682i \(0.763417\pi\)
\(74\) −2.24644 3.89095i −0.261143 0.452313i
\(75\) 0 0
\(76\) 2.28289 1.10377i 0.261865 0.126611i
\(77\) 2.73225 0.311369
\(78\) −8.05253 13.9474i −0.911770 1.57923i
\(79\) −4.51908 7.82728i −0.508437 0.880638i −0.999952 0.00976923i \(-0.996890\pi\)
0.491516 0.870869i \(-0.336443\pi\)
\(80\) 0 0
\(81\) −5.82432 10.0880i −0.647146 1.12089i
\(82\) 4.94447 8.56407i 0.546025 0.945744i
\(83\) 2.12178 0.232896 0.116448 0.993197i \(-0.462849\pi\)
0.116448 + 0.993197i \(0.462849\pi\)
\(84\) 1.07985 0.117821
\(85\) 0 0
\(86\) −5.94786 + 10.3020i −0.641374 + 1.11089i
\(87\) −3.40155 −0.364684
\(88\) −13.7901 −1.47003
\(89\) −3.96608 + 6.86946i −0.420404 + 0.728161i −0.995979 0.0895879i \(-0.971445\pi\)
0.575575 + 0.817749i \(0.304778\pi\)
\(90\) 0 0
\(91\) 1.35176 2.34131i 0.141703 0.245436i
\(92\) 0.828173 + 1.43444i 0.0863430 + 0.149551i
\(93\) −9.49053 16.4381i −0.984122 1.70455i
\(94\) 7.00850 0.722872
\(95\) 0 0
\(96\) −9.67231 −0.987176
\(97\) −4.83628 8.37668i −0.491050 0.850523i 0.508897 0.860827i \(-0.330053\pi\)
−0.999947 + 0.0103043i \(0.996720\pi\)
\(98\) 3.94721 + 6.83677i 0.398729 + 0.690619i
\(99\) −14.0952 + 24.4136i −1.41662 + 2.45366i
\(100\) 0 0
\(101\) 0.485632 0.841140i 0.0483222 0.0836965i −0.840853 0.541264i \(-0.817946\pi\)
0.889175 + 0.457568i \(0.151279\pi\)
\(102\) 10.5363 1.04325
\(103\) 3.34143 0.329241 0.164620 0.986357i \(-0.447360\pi\)
0.164620 + 0.986357i \(0.447360\pi\)
\(104\) −6.82256 + 11.8170i −0.669007 + 1.15875i
\(105\) 0 0
\(106\) −10.0617 −0.977275
\(107\) −9.51655 −0.920000 −0.460000 0.887919i \(-0.652151\pi\)
−0.460000 + 0.887919i \(0.652151\pi\)
\(108\) −2.91179 + 5.04337i −0.280187 + 0.485298i
\(109\) −2.77178 4.80087i −0.265489 0.459840i 0.702203 0.711977i \(-0.252200\pi\)
−0.967692 + 0.252137i \(0.918867\pi\)
\(110\) 0 0
\(111\) 5.74795 + 9.95573i 0.545571 + 0.944956i
\(112\) 0.760896 + 1.31791i 0.0718979 + 0.124531i
\(113\) −1.54134 −0.144997 −0.0724987 0.997369i \(-0.523097\pi\)
−0.0724987 + 0.997369i \(0.523097\pi\)
\(114\) 14.2408 6.88542i 1.33378 0.644879i
\(115\) 0 0
\(116\) 0.324694 + 0.562387i 0.0301471 + 0.0522163i
\(117\) 13.9470 + 24.1568i 1.28940 + 2.23330i
\(118\) −6.09499 + 10.5568i −0.561089 + 0.971835i
\(119\) 0.884350 + 1.53174i 0.0810682 + 0.140414i
\(120\) 0 0
\(121\) 9.11672 0.828793
\(122\) −5.93310 −0.537158
\(123\) −12.6514 + 21.9128i −1.14074 + 1.97581i
\(124\) −1.81183 + 3.13819i −0.162707 + 0.281818i
\(125\) 0 0
\(126\) 4.55978 0.406217
\(127\) 1.15274 1.99661i 0.102289 0.177171i −0.810338 0.585963i \(-0.800717\pi\)
0.912628 + 0.408792i \(0.134050\pi\)
\(128\) −2.05176 3.55376i −0.181352 0.314111i
\(129\) 15.2187 26.3596i 1.33994 2.32084i
\(130\) 0 0
\(131\) 6.45905 + 11.1874i 0.564330 + 0.977448i 0.997112 + 0.0759493i \(0.0241987\pi\)
−0.432782 + 0.901499i \(0.642468\pi\)
\(132\) 7.95060 0.692011
\(133\) 2.19627 + 1.49238i 0.190441 + 0.129405i
\(134\) −10.0943 −0.872018
\(135\) 0 0
\(136\) −4.46346 7.73095i −0.382739 0.662923i
\(137\) −6.36677 + 11.0276i −0.543950 + 0.942149i 0.454722 + 0.890633i \(0.349739\pi\)
−0.998672 + 0.0515159i \(0.983595\pi\)
\(138\) 5.16621 + 8.94814i 0.439777 + 0.761716i
\(139\) −5.30433 + 9.18738i −0.449908 + 0.779263i −0.998380 0.0569059i \(-0.981876\pi\)
0.548472 + 0.836169i \(0.315210\pi\)
\(140\) 0 0
\(141\) −17.9326 −1.51020
\(142\) −6.91913 + 11.9843i −0.580640 + 1.00570i
\(143\) 9.95258 17.2384i 0.832276 1.44154i
\(144\) −15.7013 −1.30844
\(145\) 0 0
\(146\) 2.21703 3.84000i 0.183482 0.317801i
\(147\) −10.0997 17.4932i −0.833010 1.44281i
\(148\) 1.09734 1.90065i 0.0902006 0.156232i
\(149\) −1.88653 3.26757i −0.154551 0.267690i 0.778344 0.627837i \(-0.216060\pi\)
−0.932895 + 0.360147i \(0.882726\pi\)
\(150\) 0 0
\(151\) −9.51562 −0.774370 −0.387185 0.922002i \(-0.626553\pi\)
−0.387185 + 0.922002i \(0.626553\pi\)
\(152\) −11.0850 7.53228i −0.899109 0.610948i
\(153\) −18.2488 −1.47533
\(154\) −1.62693 2.81793i −0.131102 0.227075i
\(155\) 0 0
\(156\) 3.93349 6.81301i 0.314931 0.545477i
\(157\) −1.72822 2.99336i −0.137927 0.238896i 0.788785 0.614669i \(-0.210710\pi\)
−0.926712 + 0.375773i \(0.877377\pi\)
\(158\) −5.38182 + 9.32158i −0.428155 + 0.741585i
\(159\) 25.7447 2.04169
\(160\) 0 0
\(161\) −0.867239 + 1.50210i −0.0683480 + 0.118382i
\(162\) −6.93624 + 12.0139i −0.544962 + 0.943902i
\(163\) −6.65283 −0.521090 −0.260545 0.965462i \(-0.583902\pi\)
−0.260545 + 0.965462i \(0.583902\pi\)
\(164\) 4.83054 0.377202
\(165\) 0 0
\(166\) −1.26343 2.18832i −0.0980609 0.169846i
\(167\) −8.22775 + 14.2509i −0.636682 + 1.10277i 0.349474 + 0.936946i \(0.386360\pi\)
−0.986156 + 0.165820i \(0.946973\pi\)
\(168\) −2.85364 4.94265i −0.220163 0.381334i
\(169\) −3.34790 5.79874i −0.257531 0.446057i
\(170\) 0 0
\(171\) −24.6651 + 11.9255i −1.88618 + 0.911968i
\(172\) −5.81081 −0.443070
\(173\) −11.3912 19.7302i −0.866058 1.50006i −0.865992 0.500057i \(-0.833312\pi\)
−6.58713e−5 1.00000i \(-0.500021\pi\)
\(174\) 2.02547 + 3.50822i 0.153550 + 0.265957i
\(175\) 0 0
\(176\) 5.60224 + 9.70336i 0.422284 + 0.731418i
\(177\) 15.5952 27.0117i 1.17221 2.03032i
\(178\) 9.44650 0.708045
\(179\) −2.32916 −0.174090 −0.0870449 0.996204i \(-0.527742\pi\)
−0.0870449 + 0.996204i \(0.527742\pi\)
\(180\) 0 0
\(181\) 11.1696 19.3463i 0.830230 1.43800i −0.0676258 0.997711i \(-0.521542\pi\)
0.897856 0.440290i \(-0.145124\pi\)
\(182\) −3.21965 −0.238656
\(183\) 15.1810 1.12221
\(184\) 4.37710 7.58137i 0.322684 0.558906i
\(185\) 0 0
\(186\) −11.3024 + 19.5763i −0.828729 + 1.43540i
\(187\) 6.51119 + 11.2777i 0.476145 + 0.824708i
\(188\) 1.71175 + 2.96484i 0.124842 + 0.216233i
\(189\) −6.09829 −0.443585
\(190\) 0 0
\(191\) 2.23766 0.161911 0.0809556 0.996718i \(-0.474203\pi\)
0.0809556 + 0.996718i \(0.474203\pi\)
\(192\) 13.3716 + 23.1603i 0.965013 + 1.67145i
\(193\) −2.27153 3.93441i −0.163508 0.283205i 0.772616 0.634873i \(-0.218948\pi\)
−0.936125 + 0.351669i \(0.885614\pi\)
\(194\) −5.75957 + 9.97587i −0.413513 + 0.716226i
\(195\) 0 0
\(196\) −1.92813 + 3.33962i −0.137724 + 0.238544i
\(197\) 19.2236 1.36962 0.684812 0.728720i \(-0.259884\pi\)
0.684812 + 0.728720i \(0.259884\pi\)
\(198\) 33.5722 2.38587
\(199\) 3.07547 5.32687i 0.218014 0.377612i −0.736186 0.676779i \(-0.763375\pi\)
0.954201 + 0.299167i \(0.0967087\pi\)
\(200\) 0 0
\(201\) 25.8283 1.82179
\(202\) −1.15669 −0.0813843
\(203\) −0.340010 + 0.588915i −0.0238641 + 0.0413338i
\(204\) 2.57338 + 4.45722i 0.180172 + 0.312068i
\(205\) 0 0
\(206\) −1.98967 3.44621i −0.138627 0.240109i
\(207\) −8.94786 15.4981i −0.621919 1.07720i
\(208\) 11.0866 0.768720
\(209\) 16.1705 + 10.9879i 1.11853 + 0.760049i
\(210\) 0 0
\(211\) −6.34661 10.9926i −0.436919 0.756765i 0.560531 0.828133i \(-0.310597\pi\)
−0.997450 + 0.0713679i \(0.977264\pi\)
\(212\) −2.45746 4.25644i −0.168779 0.292333i
\(213\) 17.7039 30.6641i 1.21305 2.10107i
\(214\) 5.66668 + 9.81497i 0.387366 + 0.670938i
\(215\) 0 0
\(216\) 30.7791 2.09425
\(217\) −3.79460 −0.257594
\(218\) −3.30094 + 5.71740i −0.223568 + 0.387231i
\(219\) −5.67269 + 9.82538i −0.383325 + 0.663938i
\(220\) 0 0
\(221\) 12.8854 0.866767
\(222\) 6.84528 11.8564i 0.459425 0.795748i
\(223\) 11.2688 + 19.5181i 0.754614 + 1.30703i 0.945566 + 0.325430i \(0.105509\pi\)
−0.190952 + 0.981599i \(0.561158\pi\)
\(224\) −0.966820 + 1.67458i −0.0645984 + 0.111888i
\(225\) 0 0
\(226\) 0.917800 + 1.58968i 0.0610512 + 0.105744i
\(227\) −18.1124 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(228\) 6.39095 + 4.34268i 0.423251 + 0.287601i
\(229\) −9.41604 −0.622229 −0.311115 0.950372i \(-0.600702\pi\)
−0.311115 + 0.950372i \(0.600702\pi\)
\(230\) 0 0
\(231\) 4.16282 + 7.21022i 0.273894 + 0.474398i
\(232\) 1.71609 2.97236i 0.112667 0.195145i
\(233\) 7.85000 + 13.5966i 0.514271 + 0.890743i 0.999863 + 0.0165573i \(0.00527061\pi\)
−0.485592 + 0.874185i \(0.661396\pi\)
\(234\) 16.6096 28.7686i 1.08580 1.88066i
\(235\) 0 0
\(236\) −5.95455 −0.387608
\(237\) 13.7704 23.8511i 0.894485 1.54929i
\(238\) 1.05318 1.82416i 0.0682676 0.118243i
\(239\) −23.4610 −1.51757 −0.758783 0.651344i \(-0.774205\pi\)
−0.758783 + 0.651344i \(0.774205\pi\)
\(240\) 0 0
\(241\) −6.58469 + 11.4050i −0.424157 + 0.734662i −0.996341 0.0854634i \(-0.972763\pi\)
0.572184 + 0.820125i \(0.306096\pi\)
\(242\) −5.42860 9.40260i −0.348963 0.604422i
\(243\) 2.73161 4.73128i 0.175233 0.303512i
\(244\) −1.44910 2.50991i −0.0927689 0.160680i
\(245\) 0 0
\(246\) 30.1333 1.92123
\(247\) 17.4159 8.42058i 1.10815 0.535789i
\(248\) 19.1520 1.21615
\(249\) 3.23272 + 5.59923i 0.204865 + 0.354837i
\(250\) 0 0
\(251\) 8.66257 15.0040i 0.546776 0.947045i −0.451716 0.892162i \(-0.649188\pi\)
0.998493 0.0548830i \(-0.0174786\pi\)
\(252\) 1.11368 + 1.92895i 0.0701551 + 0.121512i
\(253\) −6.38521 + 11.0595i −0.401435 + 0.695305i
\(254\) −2.74563 −0.172276
\(255\) 0 0
\(256\) 6.33295 10.9690i 0.395809 0.685562i
\(257\) −2.83980 + 4.91867i −0.177142 + 0.306818i −0.940900 0.338683i \(-0.890018\pi\)
0.763759 + 0.645502i \(0.223352\pi\)
\(258\) −36.2483 −2.25672
\(259\) 2.29820 0.142803
\(260\) 0 0
\(261\) −3.50811 6.07622i −0.217146 0.376108i
\(262\) 7.69215 13.3232i 0.475222 0.823109i
\(263\) 2.82882 + 4.89966i 0.174433 + 0.302126i 0.939965 0.341272i \(-0.110858\pi\)
−0.765532 + 0.643398i \(0.777524\pi\)
\(264\) −21.0105 36.3912i −1.29311 2.23972i
\(265\) 0 0
\(266\) 0.231393 3.15379i 0.0141876 0.193371i
\(267\) −24.1707 −1.47922
\(268\) −2.46544 4.27026i −0.150601 0.260848i
\(269\) 11.9959 + 20.7775i 0.731402 + 1.26683i 0.956284 + 0.292440i \(0.0944672\pi\)
−0.224881 + 0.974386i \(0.572199\pi\)
\(270\) 0 0
\(271\) 10.6497 + 18.4459i 0.646926 + 1.12051i 0.983853 + 0.178978i \(0.0572791\pi\)
−0.336927 + 0.941531i \(0.609388\pi\)
\(272\) −3.62656 + 6.28138i −0.219892 + 0.380865i
\(273\) 8.23808 0.498591
\(274\) 15.1645 0.916121
\(275\) 0 0
\(276\) −2.52359 + 4.37098i −0.151902 + 0.263102i
\(277\) 0.821109 0.0493357 0.0246678 0.999696i \(-0.492147\pi\)
0.0246678 + 0.999696i \(0.492147\pi\)
\(278\) 12.6340 0.757735
\(279\) 19.5757 33.9060i 1.17196 2.02990i
\(280\) 0 0
\(281\) 0.293739 0.508772i 0.0175230 0.0303508i −0.857131 0.515099i \(-0.827755\pi\)
0.874654 + 0.484748i \(0.161089\pi\)
\(282\) 10.6780 + 18.4949i 0.635869 + 1.10136i
\(283\) 15.4712 + 26.7969i 0.919667 + 1.59291i 0.799921 + 0.600105i \(0.204875\pi\)
0.119746 + 0.992805i \(0.461792\pi\)
\(284\) −6.75969 −0.401114
\(285\) 0 0
\(286\) −23.7052 −1.40172
\(287\) 2.52920 + 4.38070i 0.149294 + 0.258585i
\(288\) −9.97530 17.2777i −0.587800 1.01810i
\(289\) 4.28504 7.42191i 0.252061 0.436583i
\(290\) 0 0
\(291\) 14.7370 25.5252i 0.863896 1.49631i
\(292\) 2.16594 0.126752
\(293\) −3.76271 −0.219820 −0.109910 0.993942i \(-0.535056\pi\)
−0.109910 + 0.993942i \(0.535056\pi\)
\(294\) −12.0278 + 20.8328i −0.701478 + 1.21499i
\(295\) 0 0
\(296\) −11.5994 −0.674202
\(297\) −44.8998 −2.60535
\(298\) −2.24669 + 3.89138i −0.130147 + 0.225422i
\(299\) 6.31806 + 10.9432i 0.365383 + 0.632861i
\(300\) 0 0
\(301\) −3.04246 5.26969i −0.175364 0.303740i
\(302\) 5.66612 + 9.81401i 0.326049 + 0.564733i
\(303\) 2.95961 0.170025
\(304\) −0.796788 + 10.8598i −0.0456989 + 0.622855i
\(305\) 0 0
\(306\) 10.8663 + 18.8211i 0.621187 + 1.07593i
\(307\) 10.1709 + 17.6166i 0.580485 + 1.00543i 0.995422 + 0.0955798i \(0.0304705\pi\)
−0.414936 + 0.909850i \(0.636196\pi\)
\(308\) 0.794723 1.37650i 0.0452835 0.0784334i
\(309\) 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 \(0.569855\pi\)
\(312\) −41.5790 −2.35395
\(313\) 11.9964 20.7783i 0.678074 1.17446i −0.297486 0.954726i \(-0.596148\pi\)
0.975560 0.219733i \(-0.0705185\pi\)
\(314\) −2.05815 + 3.56482i −0.116148 + 0.201174i
\(315\) 0 0
\(316\) −5.25781 −0.295775
\(317\) 0.519518 0.899831i 0.0291790 0.0505395i −0.851067 0.525057i \(-0.824044\pi\)
0.880246 + 0.474517i \(0.157377\pi\)
\(318\) −15.3298 26.5520i −0.859653 1.48896i
\(319\) −2.50339 + 4.33600i −0.140163 + 0.242769i
\(320\) 0 0
\(321\) −14.4993 25.1135i −0.809271 1.40170i
\(322\) 2.06561 0.115112
\(323\) −0.926066 + 12.6218i −0.0515277 + 0.702298i
\(324\) −6.77641 −0.376467
\(325\) 0 0
\(326\) 3.96146 + 6.86145i 0.219405 + 0.380020i
\(327\) 8.44610 14.6291i 0.467070 0.808990i
\(328\) −12.7653 22.1102i −0.704846 1.22083i
\(329\) −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 \(0.178210\pi\)
\(332\) 0.617157 1.06895i 0.0338709 0.0586661i
\(333\) −11.8560 + 20.5352i −0.649705 + 1.12532i
\(334\) 19.5970 1.07230
\(335\) 0 0
\(336\) −2.31858 + 4.01590i −0.126489 + 0.219085i
\(337\) 10.3576 + 17.9400i 0.564217 + 0.977252i 0.997122 + 0.0758124i \(0.0241550\pi\)
−0.432906 + 0.901439i \(0.642512\pi\)
\(338\) −3.98705 + 6.90577i −0.216867 + 0.375625i
\(339\) −2.34837 4.06749i −0.127546 0.220916i
\(340\) 0 0
\(341\) −27.9384 −1.51295
\(342\) 26.9864 + 18.3374i 1.45926 + 0.991572i
\(343\) −8.30239 −0.448287
\(344\) 15.3558 + 26.5970i 0.827929 + 1.43402i
\(345\) 0 0
\(346\) −13.5659 + 23.4968i −0.729308 + 1.26320i
\(347\) 4.11068 + 7.11991i 0.220673 + 0.382217i 0.955013 0.296566i \(-0.0958413\pi\)
−0.734340 + 0.678782i \(0.762508\pi\)
\(348\) −0.989399 + 1.71369i −0.0530373 + 0.0918634i
\(349\) 11.9216 0.638150 0.319075 0.947730i \(-0.396628\pi\)
0.319075 + 0.947730i \(0.396628\pi\)
\(350\) 0 0
\(351\) −22.2138 + 38.4754i −1.18568 + 2.05366i
\(352\) −7.11839 + 12.3294i −0.379412 + 0.657160i
\(353\) 11.7983 0.627959 0.313980 0.949430i \(-0.398338\pi\)
0.313980 + 0.949430i \(0.398338\pi\)
\(354\) −37.1450 −1.97423
\(355\) 0 0
\(356\) 2.30721 + 3.99620i 0.122282 + 0.211798i
\(357\) −2.69477 + 4.66747i −0.142622 + 0.247029i
\(358\) 1.38691 + 2.40220i 0.0733005 + 0.126960i
\(359\) −0.0554058 0.0959656i −0.00292420 0.00506487i 0.864560 0.502530i \(-0.167597\pi\)
−0.867484 + 0.497465i \(0.834264\pi\)
\(360\) 0 0
\(361\) 6.99666 + 17.6648i 0.368245 + 0.929729i
\(362\) −26.6040 −1.39827
\(363\) 13.8901 + 24.0584i 0.729042 + 1.26274i
\(364\) −0.786364 1.36202i −0.0412167 0.0713894i
\(365\) 0 0
\(366\) −9.03958 15.6570i −0.472507 0.818405i
\(367\) 5.86986 10.1669i 0.306404 0.530708i −0.671169 0.741305i \(-0.734207\pi\)
0.977573 + 0.210597i \(0.0675408\pi\)
\(368\) −7.11278 −0.370779
\(369\) −52.1908 −2.71694
\(370\) 0 0
\(371\) 2.57338 4.45722i 0.133603 0.231407i
\(372\) −11.0419 −0.572498
\(373\) −14.5190 −0.751763 −0.375882 0.926668i \(-0.622660\pi\)
−0.375882 + 0.926668i \(0.622660\pi\)
\(374\) 7.75424 13.4307i 0.400962 0.694487i
\(375\) 0 0
\(376\) 9.04704 15.6699i 0.466566 0.808115i
\(377\) 2.47706 + 4.29040i 0.127575 + 0.220967i
\(378\) 3.63125 + 6.28952i 0.186772 + 0.323498i
\(379\) −6.59023 −0.338518 −0.169259 0.985572i \(-0.554137\pi\)
−0.169259 + 0.985572i \(0.554137\pi\)
\(380\) 0 0
\(381\) 7.02522 0.359913
\(382\) −1.33242 2.30782i −0.0681727 0.118079i
\(383\) −1.43461 2.48481i −0.0733049 0.126968i 0.827043 0.562139i \(-0.190021\pi\)
−0.900348 + 0.435171i \(0.856688\pi\)
\(384\) 6.25207 10.8289i 0.319050 0.552610i
\(385\) 0 0
\(386\) −2.70519 + 4.68552i −0.137690 + 0.238487i
\(387\) 62.7819 3.19138
\(388\) −5.62686 −0.285660
\(389\) 3.16575 5.48323i 0.160510 0.278011i −0.774542 0.632523i \(-0.782020\pi\)
0.935052 + 0.354512i \(0.115353\pi\)
\(390\) 0 0
\(391\) −8.26682 −0.418071
\(392\) 20.3813 1.02941
\(393\) −19.6818 + 34.0899i −0.992817 + 1.71961i
\(394\) −11.4468 19.8264i −0.576680 0.998840i
\(395\) 0 0
\(396\) 8.19966 + 14.2022i 0.412049 + 0.713689i
\(397\) −15.2749 26.4569i −0.766626 1.32784i −0.939382 0.342871i \(-0.888601\pi\)
0.172756 0.984965i \(-0.444733\pi\)
\(398\) −7.32522 −0.367180
\(399\) −0.592065 + 8.06957i −0.0296403 + 0.403984i
\(400\) 0 0
\(401\) −15.1711 26.2771i −0.757609 1.31222i −0.944067 0.329754i \(-0.893034\pi\)
0.186458 0.982463i \(-0.440299\pi\)
\(402\) −15.3796 26.6382i −0.767064 1.32859i
\(403\) −13.8223 + 23.9409i −0.688538 + 1.19258i
\(404\) −0.282509 0.489320i −0.0140553 0.0243446i
\(405\) 0 0
\(406\) 0.809843 0.0401919
\(407\) 16.9209 0.838740
\(408\) 13.6009 23.5575i 0.673347 1.16627i
\(409\) 7.48628 12.9666i 0.370173 0.641158i −0.619419 0.785060i \(-0.712632\pi\)
0.989592 + 0.143903i \(0.0459652\pi\)
\(410\) 0 0
\(411\) −38.8013 −1.91393
\(412\) 0.971912 1.68340i 0.0478827 0.0829352i
\(413\) −3.11772 5.40004i −0.153413 0.265719i
\(414\) −10.6561 + 18.4569i −0.523718 + 0.907107i
\(415\) 0 0
\(416\) 7.04353 + 12.1997i 0.345337 + 0.598142i
\(417\) −32.3264 −1.58303
\(418\) 1.70368 23.2203i 0.0833296 1.13574i
\(419\) −6.17419 −0.301629 −0.150815 0.988562i \(-0.548190\pi\)
−0.150815 + 0.988562i \(0.548190\pi\)
\(420\) 0 0
\(421\) 13.7714 + 23.8528i 0.671177 + 1.16251i 0.977571 + 0.210608i \(0.0675443\pi\)
−0.306394 + 0.951905i \(0.599122\pi\)
\(422\) −7.55824 + 13.0913i −0.367929 + 0.637272i
\(423\) −18.4943 32.0331i −0.899226 1.55750i
\(424\) −12.9883 + 22.4963i −0.630766 + 1.09252i
\(425\) 0 0
\(426\) −42.1675 −2.04302
\(427\) 1.51745 2.62830i 0.0734347 0.127193i
\(428\) −2.76805 + 4.79441i −0.133799 + 0.231746i
\(429\) 60.6544 2.92842
\(430\) 0 0
\(431\) 7.52941 13.0413i 0.362679 0.628179i −0.625722 0.780046i \(-0.715195\pi\)
0.988401 + 0.151868i \(0.0485288\pi\)
\(432\) −12.5040 21.6575i −0.601598 1.04200i
\(433\) −0.485420 + 0.840772i −0.0233278 + 0.0404049i −0.877454 0.479661i \(-0.840759\pi\)
0.854126 + 0.520066i \(0.174093\pi\)
\(434\) 2.25951 + 3.91359i 0.108460 + 0.187858i
\(435\) 0 0
\(436\) −3.22488 −0.154444
\(437\) −11.1734 + 5.40234i −0.534497 + 0.258429i
\(438\) 13.5113 0.645596
\(439\) 13.7187 + 23.7616i 0.654760 + 1.13408i 0.981954 + 0.189120i \(0.0605636\pi\)
−0.327194 + 0.944957i \(0.606103\pi\)
\(440\) 0 0
\(441\) 20.8322 36.0824i 0.992008 1.71821i
\(442\) −7.67269 13.2895i −0.364952 0.632116i
\(443\) −4.38272 + 7.59109i −0.208229 + 0.360664i −0.951157 0.308708i \(-0.900103\pi\)
0.742928 + 0.669372i \(0.233437\pi\)
\(444\) 6.68755 0.317377
\(445\) 0 0
\(446\) 13.4201 23.2443i 0.635461 1.10065i
\(447\) 5.74859 9.95686i 0.271899 0.470943i
\(448\) 5.34637 0.252592
\(449\) −9.63397 −0.454655 −0.227327 0.973818i \(-0.572999\pi\)
−0.227327 + 0.973818i \(0.572999\pi\)
\(450\) 0 0
\(451\) 18.6217 + 32.2538i 0.876862 + 1.51877i
\(452\) −0.448326 + 0.776524i −0.0210875 + 0.0365246i
\(453\) −14.4979 25.1110i −0.681169 1.17982i
\(454\) 10.7851 + 18.6803i 0.506169 + 0.876711i
\(455\) 0 0
\(456\) 2.98825 40.7285i 0.139938 1.90729i
\(457\) 10.6708 0.499161 0.249580 0.968354i \(-0.419707\pi\)
0.249580 + 0.968354i \(0.419707\pi\)
\(458\) 5.60683 + 9.71131i 0.261990 + 0.453780i
\(459\) −14.5327 25.1714i −0.678330 1.17490i
\(460\) 0 0
\(461\) −2.84340 4.92491i −0.132430 0.229376i 0.792183 0.610284i \(-0.208945\pi\)
−0.924613 + 0.380908i \(0.875611\pi\)
\(462\) 4.95754 8.58672i 0.230646 0.399490i
\(463\) −35.3550 −1.64309 −0.821543 0.570147i \(-0.806886\pi\)
−0.821543 + 0.570147i \(0.806886\pi\)
\(464\) −2.78864 −0.129459
\(465\) 0 0
\(466\) 9.34864 16.1923i 0.433067 0.750095i
\(467\) 32.9071 1.52276 0.761380 0.648306i \(-0.224522\pi\)
0.761380 + 0.648306i \(0.224522\pi\)
\(468\) 16.2269 0.750086
\(469\) 2.58173 4.47169i 0.119213 0.206484i
\(470\) 0 0
\(471\) 5.26617 9.12127i 0.242652 0.420286i
\(472\) 15.7356 + 27.2549i 0.724292 + 1.25451i
\(473\) −22.4006 38.7991i −1.02998 1.78398i
\(474\) −32.7986 −1.50649
\(475\) 0 0
\(476\) 1.02891 0.0471602
\(477\) 26.5512 + 45.9880i 1.21569 + 2.10564i
\(478\) 13.9700 + 24.1967i 0.638971 + 1.10673i
\(479\) 4.52861 7.84378i 0.206917 0.358391i −0.743825 0.668375i \(-0.766990\pi\)
0.950742 + 0.309984i \(0.100324\pi\)
\(480\) 0 0
\(481\) 8.37149 14.4998i 0.381707 0.661136i
\(482\) 15.6835 0.714366
\(483\) −5.28525 −0.240487
\(484\) 2.65175 4.59297i 0.120534 0.208772i
\(485\) 0 0
\(486\) −6.50619 −0.295127
\(487\) 16.5206 0.748620 0.374310 0.927304i \(-0.377880\pi\)
0.374310 + 0.927304i \(0.377880\pi\)
\(488\) −7.65884 + 13.2655i −0.346700 + 0.600501i
\(489\) −10.1362 17.5563i −0.458373 0.793925i
\(490\) 0 0
\(491\) 0.695625 + 1.20486i 0.0313931 + 0.0543745i 0.881295 0.472566i \(-0.156672\pi\)
−0.849902 + 0.526941i \(0.823339\pi\)
\(492\) 7.35974 + 12.7474i 0.331803 + 0.574699i
\(493\) −3.24109 −0.145972
\(494\) −19.0550 12.9480i −0.857326 0.582557i
\(495\) 0 0
\(496\) −7.78048 13.4762i −0.349354 0.605099i
\(497\) −3.53928 6.13021i −0.158758 0.274977i
\(498\) 3.84988 6.66818i 0.172517 0.298808i
\(499\) 8.33255 + 14.4324i 0.373016 + 0.646083i 0.990028 0.140871i \(-0.0449902\pi\)
−0.617012 + 0.786954i \(0.711657\pi\)
\(500\) 0 0
\(501\) −50.1427 −2.24021
\(502\) −20.6327 −0.920881
\(503\) 7.81956 13.5439i 0.348657 0.603892i −0.637354 0.770571i \(-0.719971\pi\)
0.986011 + 0.166679i \(0.0533045\pi\)
\(504\) 5.88607 10.1950i 0.262186 0.454120i
\(505\) 0 0
\(506\) 15.2084 0.676096
\(507\) 10.2016 17.6697i 0.453070 0.784741i
\(508\) −0.670591 1.16150i −0.0297526 0.0515331i
\(509\) 9.57702 16.5879i 0.424494 0.735245i −0.571879 0.820338i \(-0.693785\pi\)
0.996373 + 0.0850929i \(0.0271187\pi\)
\(510\) 0 0
\(511\) 1.13406 + 1.96424i 0.0501677 + 0.0868929i
\(512\) −23.2910 −1.02933
\(513\) −36.0919 24.5246i −1.59349 1.08279i
\(514\) 6.76389 0.298342
\(515\) 0 0
\(516\) −8.85327 15.3343i −0.389743 0.675055i
\(517\) −13.1976 + 22.8589i −0.580430 + 1.00533i
\(518\) −1.36848 2.37027i −0.0601273 0.104144i
\(519\) 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 \(0.638477\pi\)
\(522\) −4.17784 + 7.23622i −0.182859 + 0.316721i
\(523\) 3.31973 5.74993i 0.145161 0.251427i −0.784272 0.620418i \(-0.786963\pi\)
0.929433 + 0.368990i \(0.120296\pi\)
\(524\) 7.51490 0.328290
\(525\) 0 0
\(526\) 3.36887 5.83505i 0.146890 0.254420i
\(527\) −9.04285 15.6627i −0.393913 0.682277i
\(528\) −17.0710 + 29.5678i −0.742919 + 1.28677i
\(529\) 7.44657 + 12.8978i 0.323764 + 0.560775i
\(530\) 0 0
\(531\) 64.3349 2.79190
\(532\) 1.39068 0.672391i 0.0602935 0.0291519i
\(533\) 36.8517 1.59623
\(534\) 14.3925 + 24.9286i 0.622826 + 1.07877i
\(535\) 0 0
\(536\) −13.0305 + 22.5694i −0.562830 + 0.974850i
\(537\) −3.54868 6.14649i −0.153137 0.265241i
\(538\) 14.2860 24.7441i 0.615914 1.06679i
\(539\) −29.7317 −1.28064
\(540\) 0 0
\(541\) −20.8756 + 36.1575i −0.897510 + 1.55453i −0.0668435 + 0.997763i \(0.521293\pi\)
−0.830667 + 0.556770i \(0.812040\pi\)
\(542\) 12.6829 21.9674i 0.544777 0.943581i
\(543\) 68.0714 2.92122
\(544\) −9.21606 −0.395135
\(545\) 0 0
\(546\) −4.90540 8.49641i −0.209932 0.363613i
\(547\) 6.10258 10.5700i 0.260927 0.451939i −0.705561 0.708649i \(-0.749305\pi\)
0.966489 + 0.256710i \(0.0826384\pi\)
\(548\) 3.70377 + 6.41512i 0.158217 + 0.274040i
\(549\) 15.6565 + 27.1179i 0.668204 + 1.15736i
\(550\) 0 0
\(551\) −4.38066 + 2.11804i −0.186622 + 0.0902317i
\(552\) 26.6756 1.13539
\(553\) −2.75291 4.76819i −0.117066 0.202764i
\(554\) −0.488934 0.846858i −0.0207728 0.0359795i
\(555\) 0 0
\(556\) 3.08571 + 5.34461i 0.130863 + 0.226662i
\(557\) 17.5774 30.4450i 0.744779 1.28999i −0.205519 0.978653i \(-0.565888\pi\)
0.950298 0.311342i \(-0.100778\pi\)
\(558\) −46.6257 −1.97382
\(559\) −44.3301 −1.87496
\(560\) 0 0
\(561\) −19.8407 + 34.3651i −0.837675 + 1.45090i
\(562\) −0.699634 −0.0295123
\(563\) −17.8406 −0.751891 −0.375945 0.926642i \(-0.622682\pi\)
−0.375945 + 0.926642i \(0.622682\pi\)
\(564\) −5.21600 + 9.03438i −0.219633 + 0.380416i
\(565\) 0 0
\(566\) 18.4248 31.9127i 0.774452 1.34139i
\(567\) −3.54803 6.14537i −0.149003 0.258081i
\(568\) 17.8633 + 30.9402i 0.749529 + 1.29822i
\(569\) 31.6042 1.32492 0.662459 0.749098i \(-0.269513\pi\)
0.662459 + 0.749098i \(0.269513\pi\)
\(570\) 0 0
\(571\) −4.73053 −0.197967 −0.0989833 0.995089i \(-0.531559\pi\)
−0.0989833 + 0.995089i \(0.531559\pi\)
\(572\) −5.78975 10.0281i −0.242082 0.419298i
\(573\) 3.40926 + 5.90501i 0.142424 + 0.246685i
\(574\) 3.01205 5.21702i 0.125721 0.217754i
\(575\) 0 0
\(576\) −27.5810 + 47.7717i −1.14921 + 1.99049i
\(577\) −24.4074 −1.01609 −0.508047 0.861330i \(-0.669632\pi\)
−0.508047 + 0.861330i \(0.669632\pi\)
\(578\) −10.2062 −0.424522
\(579\) 6.92174 11.9888i 0.287658 0.498238i
\(580\) 0 0
\(581\) 1.29254 0.0536235
\(582\) −35.1008 −1.45497
\(583\) 18.9470 32.8171i 0.784703 1.35915i
\(584\) −5.72377 9.91386i −0.236851 0.410239i
\(585\) 0 0
\(586\) 2.24052 + 3.88070i 0.0925551 + 0.160310i
\(587\) −14.3077 24.7817i −0.590543 1.02285i −0.994159 0.107922i \(-0.965580\pi\)
0.403616 0.914928i \(-0.367753\pi\)
\(588\) −11.7507 −0.484590
\(589\) −22.4578 15.2602i −0.925358 0.628785i
\(590\) 0 0
\(591\) 29.2888 + 50.7297i 1.20478 + 2.08674i
\(592\) 4.71225 + 8.16186i 0.193672 + 0.335450i
\(593\) 1.85756 3.21738i 0.0762807 0.132122i −0.825362 0.564604i \(-0.809029\pi\)
0.901642 + 0.432482i \(0.142362\pi\)
\(594\) 26.7358 + 46.3077i 1.09698 + 1.90003i
\(595\) 0 0
\(596\) −2.19492 −0.0899076
\(597\) 18.7430 0.767099
\(598\) 7.52423 13.0324i 0.307689 0.532933i
\(599\) −3.54970 + 6.14826i −0.145037 + 0.251211i −0.929387 0.369108i \(-0.879663\pi\)
0.784350 + 0.620319i \(0.212997\pi\)
\(600\) 0 0
\(601\) −11.0596 −0.451131 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(602\) −3.62329 + 6.27572i −0.147674 + 0.255779i
\(603\) 26.6374 + 46.1373i 1.08476 + 1.87886i
\(604\) −2.76778 + 4.79394i −0.112619 + 0.195063i
\(605\) 0 0
\(606\) −1.76231 3.05242i −0.0715891 0.123996i
\(607\) −27.1193 −1.10074 −0.550369 0.834921i \(-0.685513\pi\)
−0.550369 + 0.834921i \(0.685513\pi\)
\(608\) −12.4564 + 6.02266i −0.505174 + 0.244251i
\(609\) −2.07214 −0.0839673
\(610\) 0 0
\(611\) 13.0588 + 22.6185i 0.528302 + 0.915046i
\(612\) −5.30798 + 9.19369i −0.214562 + 0.371633i
\(613\) 20.9156 + 36.2268i 0.844772 + 1.46319i 0.885819 + 0.464031i \(0.153597\pi\)
−0.0410468 + 0.999157i \(0.513069\pi\)
\(614\) 12.1127 20.9797i 0.488827 0.846673i
\(615\) 0 0
\(616\) −8.40062 −0.338471
\(617\) −8.85262 + 15.3332i −0.356393 + 0.617291i −0.987355 0.158523i \(-0.949327\pi\)
0.630962 + 0.775813i \(0.282660\pi\)
\(618\) 6.06286 10.5012i 0.243884 0.422420i
\(619\) −39.8064 −1.59995 −0.799976 0.600032i \(-0.795155\pi\)
−0.799976 + 0.600032i \(0.795155\pi\)
\(620\) 0 0
\(621\) 14.2515 24.6844i 0.571895 0.990551i
\(622\) 4.57208 + 7.91908i 0.183324 + 0.317526i
\(623\) −2.41604 + 4.18471i −0.0967966 + 0.167657i
\(624\) 16.8914 + 29.2568i 0.676198 + 1.17121i
\(625\) 0 0
\(626\) −28.5732 −1.14201
\(627\) −4.35919 + 59.4137i −0.174089 + 2.37275i
\(628\) −2.01072 −0.0802366
\(629\) 5.47681 + 9.48611i 0.218375 + 0.378236i
\(630\) 0 0
\(631\) −23.0990 + 40.0087i −0.919557 + 1.59272i −0.119469 + 0.992838i \(0.538119\pi\)
−0.800088 + 0.599882i \(0.795214\pi\)
\(632\) 13.8944 + 24.0659i 0.552691 + 0.957288i
\(633\) 19.3392 33.4965i 0.768664 1.33137i
\(634\) −1.23740 −0.0491433
\(635\) 0 0
\(636\) 7.48829 12.9701i 0.296930 0.514298i
\(637\) −14.7095 + 25.4776i −0.582813 + 1.00946i
\(638\) 5.96262 0.236062
\(639\) 73.0340 2.88918
\(640\) 0 0
\(641\) −3.30674 5.72744i −0.130608 0.226220i 0.793303 0.608827i \(-0.208360\pi\)
−0.923911 + 0.382607i \(0.875026\pi\)
\(642\) −17.2673 + 29.9079i −0.681487 + 1.18037i
\(643\) −15.3076 26.5135i −0.603673 1.04559i −0.992260 0.124180i \(-0.960370\pi\)
0.388587 0.921412i \(-0.372963\pi\)
\(644\) 0.504503 + 0.873824i 0.0198802 + 0.0344335i
\(645\) 0 0
\(646\) 13.5691 6.56063i 0.533868 0.258125i
\(647\) 11.8979 0.467753 0.233877 0.972266i \(-0.424859\pi\)
0.233877 + 0.972266i \(0.424859\pi\)
\(648\) 17.9075 + 31.0167i 0.703474 + 1.21845i
\(649\) −22.9548 39.7588i −0.901053 1.56067i
\(650\) 0 0
\(651\) −5.78140 10.0137i −0.226591 0.392467i
\(652\) −1.93509 + 3.35167i −0.0757839 + 0.131262i
\(653\) 1.42899 0.0559207 0.0279604 0.999609i \(-0.491099\pi\)
0.0279604 + 0.999609i \(0.491099\pi\)
\(654\) −20.1171 −0.786640
\(655\) 0 0
\(656\) −10.3718 + 17.9645i −0.404950 + 0.701395i
\(657\) −23.4015 −0.912981
\(658\) 4.26941 0.166439
\(659\) 12.2485 21.2150i 0.477134 0.826420i −0.522523 0.852625i \(-0.675009\pi\)
0.999657 + 0.0262051i \(0.00834231\pi\)
\(660\) 0 0
\(661\) 1.61303 2.79385i 0.0627396 0.108668i −0.832949 0.553349i \(-0.813350\pi\)
0.895689 + 0.444681i \(0.146683\pi\)
\(662\) −18.3588 31.7984i −0.713535 1.23588i
\(663\) 19.6320 + 34.0037i 0.762445 + 1.32059i
\(664\) −6.52366 −0.253167
\(665\) 0 0
\(666\) 28.2389 1.09423
\(667\) −1.58919 2.75256i −0.0615338 0.106580i
\(668\) 4.78636 + 8.29023i 0.185190 + 0.320758i
\(669\) −34.3379 + 59.4750i −1.32758 + 2.29944i
\(670\) 0 0
\(671\) 11.1725 19.3514i 0.431311 0.747052i
\(672\) −5.89213 −0.227294
\(673\) −37.1424 −1.43173 −0.715866 0.698237i \(-0.753968\pi\)
−0.715866 + 0.698237i \(0.753968\pi\)
\(674\) 12.3350 21.3649i 0.475127 0.822944i
\(675\) 0 0
\(676\) −3.89518 −0.149815
\(677\) 24.7550 0.951412 0.475706 0.879604i \(-0.342193\pi\)
0.475706 + 0.879604i \(0.342193\pi\)
\(678\) −2.79669 + 4.84402i −0.107406 + 0.186033i
\(679\) −2.94614 5.10287i −0.113063 0.195830i
\(680\) 0 0
\(681\) −27.5957 47.7972i −1.05747 1.83159i
\(682\) 16.6361 + 28.8145i 0.637028 + 1.10337i
\(683\) −40.1153 −1.53497 −0.767484 0.641068i \(-0.778492\pi\)
−0.767484 + 0.641068i \(0.778492\pi\)
\(684\) −1.16621 + 15.8949i −0.0445912 + 0.607757i
\(685\) 0 0
\(686\) 4.94370 + 8.56274i 0.188751 + 0.326927i
\(687\) −14.3461 24.8482i −0.547340 0.948020i
\(688\) 12.4766 21.6100i 0.475664 0.823875i
\(689\) −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 \(0.229449\pi\)
\(692\) −13.2533 −0.503816
\(693\) −8.58645 + 14.8722i −0.326172 + 0.564947i
\(694\) 4.89545 8.47917i 0.185829 0.321865i
\(695\) 0 0
\(696\) 10.4584 0.396426
\(697\) −12.0546 + 20.8792i −0.456600 + 0.790855i
\(698\) −7.09879 12.2955i −0.268693 0.465390i
\(699\) −23.9203 + 41.4312i −0.904748 + 1.56707i
\(700\) 0 0
\(701\) −0.0109776 0.0190137i −0.000414618 0.000718139i 0.865818 0.500359i \(-0.166799\pi\)
−0.866233 + 0.499641i \(0.833465\pi\)
\(702\) 52.9092 1.99693
\(703\) 13.6016 + 9.24234i 0.512994 + 0.348581i
\(704\) 39.3637 1.48357
\(705\) 0 0
\(706\) −7.02535 12.1683i −0.264402 0.457958i
\(707\) 0.295835 0.512402i 0.0111260 0.0192708i
\(708\) −9.07226 15.7136i −0.340957 0.590554i
\(709\) 8.90087 15.4168i 0.334279 0.578989i −0.649067 0.760731i \(-0.724840\pi\)
0.983346 + 0.181743i \(0.0581738\pi\)
\(710\) 0 0
\(711\) 56.8071 2.13043
\(712\) 12.1942 21.1209i 0.456996 0.791540i
\(713\) 8.86789 15.3596i 0.332105 0.575223i
\(714\) 6.41844 0.240204
\(715\) 0 0
\(716\) −0.677477 + 1.17342i −0.0253185 + 0.0438529i
\(717\) −35.7448 61.9118i −1.33491 2.31214i
\(718\) −0.0659833 + 0.114286i −0.00246247 + 0.00426513i
\(719\) −9.40515 16.2902i −0.350753 0.607522i 0.635629 0.771995i \(-0.280741\pi\)
−0.986382 + 0.164473i \(0.947408\pi\)
\(720\) 0 0
\(721\) 2.03552 0.0758066
\(722\) 14.0526 17.7347i 0.522983 0.660016i
\(723\) −40.1294 −1.49243
\(724\) −6.49774 11.2544i −0.241487 0.418267i
\(725\) 0 0
\(726\) 16.5419 28.6513i 0.613926 1.06335i
\(727\) 2.50151 + 4.33274i 0.0927758 + 0.160692i 0.908678 0.417497i \(-0.137093\pi\)
−0.815902 + 0.578190i \(0.803759\pi\)
\(728\) −4.15613 + 7.19864i −0.154037 + 0.266799i
\(729\) −18.2986 −0.677725
\(730\) 0 0
\(731\) 14.5009 25.1162i 0.536334 0.928957i
\(732\) 4.41565 7.64812i 0.163207 0.282683i
\(733\) 23.5259 0.868950 0.434475 0.900684i \(-0.356934\pi\)
0.434475 + 0.900684i \(0.356934\pi\)
\(734\) −13.9809 −0.516046
\(735\) 0 0
\(736\) −4.51887 7.82691i −0.166568 0.288504i
\(737\) 19.0085 32.9237i 0.700187 1.21276i
\(738\) 31.0772 + 53.8274i 1.14397 + 1.98141i
\(739\) 18.6918 + 32.3752i 0.687590 + 1.19094i 0.972615 + 0.232421i \(0.0746646\pi\)
−0.285026 + 0.958520i \(0.592002\pi\)
\(740\) 0 0
\(741\) 48.7559 + 33.1299i 1.79109 + 1.21706i
\(742\) −6.12932 −0.225014
\(743\) 5.19430 + 8.99679i 0.190560 + 0.330060i 0.945436 0.325808i \(-0.105636\pi\)
−0.754876 + 0.655868i \(0.772303\pi\)
\(744\) 29.1797 + 50.5407i 1.06978 + 1.85291i
\(745\) 0 0
\(746\) 8.64539 + 14.9742i 0.316530 + 0.548246i
\(747\) −6.66797 + 11.5493i −0.243968 + 0.422566i
\(748\) 7.57556 0.276990
\(749\) −5.79725 −0.211827
\(750\) 0 0
\(751\) 15.6413 27.0915i 0.570758 0.988581i −0.425731 0.904850i \(-0.639983\pi\)
0.996488 0.0837314i \(-0.0266838\pi\)
\(752\) −14.7014 −0.536105
\(753\) 52.7927 1.92387
\(754\) 2.94996 5.10947i 0.107431 0.186076i
\(755\) 0 0
\(756\) −1.77379 + 3.07230i −0.0645122 + 0.111738i
\(757\) −6.31205 10.9328i −0.229415 0.397359i 0.728220 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287985i \(0.907015\pi\)
\(758\) 3.92419 + 6.79689i 0.142533 + 0.246874i
\(759\) −38.9137 −1.41248
\(760\) 0 0
\(761\) 11.5495 0.418668 0.209334 0.977844i \(-0.432870\pi\)
0.209334 + 0.977844i \(0.432870\pi\)
\(762\) −4.18320 7.24551i −0.151541 0.262477i
\(763\) −1.68850 2.92457i −0.0611279 0.105877i
\(764\) 0.650861 1.12732i 0.0235473 0.0407851i
\(765\) 0 0
\(766\) −1.70849 + 2.95918i −0.0617301 + 0.106920i
\(767\) −45.4267 −1.64026
\(768\) 38.5951 1.39268
\(769\) 13.4603 23.3140i 0.485392 0.840724i −0.514467 0.857510i \(-0.672010\pi\)
0.999859 + 0.0167864i \(0.00534353\pi\)
\(770\) 0 0
\(771\) −17.3067 −0.623286
\(772\) −2.64286 −0.0951184
\(773\) 10.6666 18.4750i 0.383649 0.664500i −0.607932 0.793989i \(-0.708001\pi\)
0.991581 + 0.129489i \(0.0413338\pi\)
\(774\) −37.3838 64.7506i −1.34373 2.32741i
\(775\) 0 0
\(776\) 14.8697 + 25.7550i 0.533790 + 0.924552i
\(777\) 3.50151 + 6.06479i 0.125616 + 0.217573i
\(778\) −7.54024