Properties

Label 819.2.n.e.172.5
Level $819$
Weight $2$
Character 819.172
Analytic conductor $6.540$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(100,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.n (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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 172.5
Root \(-0.0340180 + 0.0589209i\) of defining polynomial
Character \(\chi\) \(=\) 819.172
Dual form 819.2.n.e.100.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0340180 - 0.0589209i) q^{2} +(0.997686 + 1.72804i) q^{4} +(-1.52954 - 2.64923i) q^{5} +(-2.60654 + 0.453835i) q^{7} +0.271829 q^{8} +O(q^{10})\) \(q+(0.0340180 - 0.0589209i) q^{2} +(0.997686 + 1.72804i) q^{4} +(-1.52954 - 2.64923i) q^{5} +(-2.60654 + 0.453835i) q^{7} +0.271829 q^{8} -0.208127 q^{10} +4.35793 q^{11} +(-1.79952 - 3.12437i) q^{13} +(-0.0619288 + 0.169018i) q^{14} +(-1.98612 + 3.44007i) q^{16} +(-1.76434 - 3.05592i) q^{17} +6.90224 q^{19} +(3.05199 - 5.28621i) q^{20} +(0.148248 - 0.256773i) q^{22} +(1.66762 - 2.88840i) q^{23} +(-2.17896 + 3.77408i) q^{25} +(-0.245307 - 0.000255364i) q^{26} +(-3.38475 - 4.05142i) q^{28} +(-4.95991 - 8.59082i) q^{29} +(4.62451 - 8.00989i) q^{31} +(0.406957 + 0.704870i) q^{32} -0.240077 q^{34} +(5.18911 + 6.21117i) q^{35} +(0.0545230 - 0.0944366i) q^{37} +(0.234800 - 0.406686i) q^{38} +(-0.415772 - 0.720139i) q^{40} +(-1.76899 - 3.06399i) q^{41} +(-0.844102 + 1.46203i) q^{43} +(4.34784 + 7.53068i) q^{44} +(-0.113458 - 0.196515i) q^{46} +(-1.28133 - 2.21933i) q^{47} +(6.58807 - 2.36587i) q^{49} +(0.148248 + 0.256773i) q^{50} +(3.60369 - 6.22680i) q^{52} +(-2.65681 + 4.60173i) q^{53} +(-6.66561 - 11.5452i) q^{55} +(-0.708532 + 0.123365i) q^{56} -0.674905 q^{58} +(3.77852 + 6.54459i) q^{59} +4.87317 q^{61} +(-0.314633 - 0.544960i) q^{62} -7.88912 q^{64} +(-5.52476 + 9.54621i) q^{65} +0.680435 q^{67} +(3.52051 - 6.09770i) q^{68} +(0.542491 - 0.0944552i) q^{70} +(2.61572 - 4.53055i) q^{71} +(1.75956 - 3.04764i) q^{73} +(-0.00370952 - 0.00642508i) q^{74} +(6.88626 + 11.9274i) q^{76} +(-11.3591 + 1.97778i) q^{77} +(4.85408 + 8.40751i) q^{79} +12.1514 q^{80} -0.240710 q^{82} -5.41662 q^{83} +(-5.39723 + 9.34828i) q^{85} +(0.0574293 + 0.0994705i) q^{86} +1.18461 q^{88} +(-3.85207 + 6.67198i) q^{89} +(6.10848 + 7.32711i) q^{91} +6.65503 q^{92} -0.174354 q^{94} +(-10.5572 - 18.2856i) q^{95} +(-3.86359 + 6.69194i) q^{97} +(0.0847135 - 0.468657i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0340180 0.0589209i 0.0240543 0.0416633i −0.853748 0.520687i \(-0.825676\pi\)
0.877802 + 0.479024i \(0.159009\pi\)
\(3\) 0 0
\(4\) 0.997686 + 1.72804i 0.498843 + 0.864021i
\(5\) −1.52954 2.64923i −0.684030 1.18477i −0.973741 0.227660i \(-0.926893\pi\)
0.289711 0.957114i \(-0.406441\pi\)
\(6\) 0 0
\(7\) −2.60654 + 0.453835i −0.985178 + 0.171533i
\(8\) 0.271829 0.0961060
\(9\) 0 0
\(10\) −0.208127 −0.0658155
\(11\) 4.35793 1.31396 0.656982 0.753906i \(-0.271833\pi\)
0.656982 + 0.753906i \(0.271833\pi\)
\(12\) 0 0
\(13\) −1.79952 3.12437i −0.499098 0.866545i
\(14\) −0.0619288 + 0.169018i −0.0165512 + 0.0451719i
\(15\) 0 0
\(16\) −1.98612 + 3.44007i −0.496531 + 0.860017i
\(17\) −1.76434 3.05592i −0.427914 0.741170i 0.568773 0.822494i \(-0.307418\pi\)
−0.996688 + 0.0813248i \(0.974085\pi\)
\(18\) 0 0
\(19\) 6.90224 1.58348 0.791741 0.610857i \(-0.209175\pi\)
0.791741 + 0.610857i \(0.209175\pi\)
\(20\) 3.05199 5.28621i 0.682446 1.18203i
\(21\) 0 0
\(22\) 0.148248 0.256773i 0.0316066 0.0547442i
\(23\) 1.66762 2.88840i 0.347722 0.602273i −0.638122 0.769935i \(-0.720289\pi\)
0.985844 + 0.167662i \(0.0536218\pi\)
\(24\) 0 0
\(25\) −2.17896 + 3.77408i −0.435793 + 0.754815i
\(26\) −0.245307 0.000255364i −0.0481087 5.00811e-5i
\(27\) 0 0
\(28\) −3.38475 4.05142i −0.639658 0.765647i
\(29\) −4.95991 8.59082i −0.921033 1.59528i −0.797820 0.602896i \(-0.794013\pi\)
−0.123213 0.992380i \(-0.539320\pi\)
\(30\) 0 0
\(31\) 4.62451 8.00989i 0.830587 1.43862i −0.0669867 0.997754i \(-0.521339\pi\)
0.897574 0.440865i \(-0.145328\pi\)
\(32\) 0.406957 + 0.704870i 0.0719405 + 0.124605i
\(33\) 0 0
\(34\) −0.240077 −0.0411728
\(35\) 5.18911 + 6.21117i 0.877119 + 1.04988i
\(36\) 0 0
\(37\) 0.0545230 0.0944366i 0.00896352 0.0155253i −0.861509 0.507743i \(-0.830480\pi\)
0.870472 + 0.492217i \(0.163813\pi\)
\(38\) 0.234800 0.406686i 0.0380896 0.0659731i
\(39\) 0 0
\(40\) −0.415772 0.720139i −0.0657394 0.113864i
\(41\) −1.76899 3.06399i −0.276270 0.478514i 0.694185 0.719797i \(-0.255765\pi\)
−0.970455 + 0.241283i \(0.922432\pi\)
\(42\) 0 0
\(43\) −0.844102 + 1.46203i −0.128724 + 0.222957i −0.923183 0.384362i \(-0.874422\pi\)
0.794458 + 0.607319i \(0.207755\pi\)
\(44\) 4.34784 + 7.53068i 0.655462 + 1.13529i
\(45\) 0 0
\(46\) −0.113458 0.196515i −0.0167285 0.0289746i
\(47\) −1.28133 2.21933i −0.186902 0.323723i 0.757314 0.653051i \(-0.226511\pi\)
−0.944216 + 0.329328i \(0.893178\pi\)
\(48\) 0 0
\(49\) 6.58807 2.36587i 0.941153 0.337982i
\(50\) 0.148248 + 0.256773i 0.0209654 + 0.0363132i
\(51\) 0 0
\(52\) 3.60369 6.22680i 0.499742 0.863501i
\(53\) −2.65681 + 4.60173i −0.364941 + 0.632097i −0.988767 0.149467i \(-0.952244\pi\)
0.623825 + 0.781564i \(0.285578\pi\)
\(54\) 0 0
\(55\) −6.66561 11.5452i −0.898791 1.55675i
\(56\) −0.708532 + 0.123365i −0.0946816 + 0.0164854i
\(57\) 0 0
\(58\) −0.674905 −0.0886194
\(59\) 3.77852 + 6.54459i 0.491921 + 0.852033i 0.999957 0.00930353i \(-0.00296145\pi\)
−0.508035 + 0.861336i \(0.669628\pi\)
\(60\) 0 0
\(61\) 4.87317 0.623945 0.311973 0.950091i \(-0.399010\pi\)
0.311973 + 0.950091i \(0.399010\pi\)
\(62\) −0.314633 0.544960i −0.0399584 0.0692101i
\(63\) 0 0
\(64\) −7.88912 −0.986140
\(65\) −5.52476 + 9.54621i −0.685263 + 1.18406i
\(66\) 0 0
\(67\) 0.680435 0.0831284 0.0415642 0.999136i \(-0.486766\pi\)
0.0415642 + 0.999136i \(0.486766\pi\)
\(68\) 3.52051 6.09770i 0.426924 0.739454i
\(69\) 0 0
\(70\) 0.542491 0.0944552i 0.0648400 0.0112896i
\(71\) 2.61572 4.53055i 0.310428 0.537678i −0.668027 0.744137i \(-0.732861\pi\)
0.978455 + 0.206460i \(0.0661942\pi\)
\(72\) 0 0
\(73\) 1.75956 3.04764i 0.205941 0.356699i −0.744491 0.667632i \(-0.767308\pi\)
0.950432 + 0.310933i \(0.100641\pi\)
\(74\) −0.00370952 0.00642508i −0.000431223 0.000746901i
\(75\) 0 0
\(76\) 6.88626 + 11.9274i 0.789908 + 1.36816i
\(77\) −11.3591 + 1.97778i −1.29449 + 0.225389i
\(78\) 0 0
\(79\) 4.85408 + 8.40751i 0.546126 + 0.945919i 0.998535 + 0.0541080i \(0.0172315\pi\)
−0.452409 + 0.891811i \(0.649435\pi\)
\(80\) 12.1514 1.35857
\(81\) 0 0
\(82\) −0.240710 −0.0265820
\(83\) −5.41662 −0.594551 −0.297275 0.954792i \(-0.596078\pi\)
−0.297275 + 0.954792i \(0.596078\pi\)
\(84\) 0 0
\(85\) −5.39723 + 9.34828i −0.585412 + 1.01396i
\(86\) 0.0574293 + 0.0994705i 0.00619276 + 0.0107262i
\(87\) 0 0
\(88\) 1.18461 0.126280
\(89\) −3.85207 + 6.67198i −0.408319 + 0.707229i −0.994702 0.102805i \(-0.967218\pi\)
0.586383 + 0.810034i \(0.300551\pi\)
\(90\) 0 0
\(91\) 6.10848 + 7.32711i 0.640342 + 0.768090i
\(92\) 6.65503 0.693835
\(93\) 0 0
\(94\) −0.174354 −0.0179832
\(95\) −10.5572 18.2856i −1.08315 1.87607i
\(96\) 0 0
\(97\) −3.86359 + 6.69194i −0.392288 + 0.679463i −0.992751 0.120189i \(-0.961650\pi\)
0.600463 + 0.799653i \(0.294983\pi\)
\(98\) 0.0847135 0.468657i 0.00855735 0.0473415i
\(99\) 0 0
\(100\) −8.69568 −0.869568
\(101\) 3.88031 0.386105 0.193053 0.981188i \(-0.438161\pi\)
0.193053 + 0.981188i \(0.438161\pi\)
\(102\) 0 0
\(103\) −4.29088 7.43202i −0.422793 0.732299i 0.573419 0.819263i \(-0.305617\pi\)
−0.996211 + 0.0869638i \(0.972284\pi\)
\(104\) −0.489163 0.849295i −0.0479663 0.0832802i
\(105\) 0 0
\(106\) 0.180759 + 0.313083i 0.0175568 + 0.0304093i
\(107\) −5.60158 + 9.70222i −0.541525 + 0.937949i 0.457291 + 0.889317i \(0.348820\pi\)
−0.998817 + 0.0486324i \(0.984514\pi\)
\(108\) 0 0
\(109\) 6.98282 12.0946i 0.668833 1.15845i −0.309398 0.950933i \(-0.600128\pi\)
0.978231 0.207520i \(-0.0665391\pi\)
\(110\) −0.907002 −0.0864793
\(111\) 0 0
\(112\) 3.61568 9.86804i 0.341650 0.932442i
\(113\) 3.38888 5.86972i 0.318799 0.552176i −0.661439 0.749999i \(-0.730054\pi\)
0.980238 + 0.197823i \(0.0633871\pi\)
\(114\) 0 0
\(115\) −10.2027 −0.951410
\(116\) 9.89687 17.1419i 0.918901 1.59158i
\(117\) 0 0
\(118\) 0.514150 0.0473314
\(119\) 5.98569 + 7.16465i 0.548707 + 0.656783i
\(120\) 0 0
\(121\) 7.99154 0.726503
\(122\) 0.165775 0.287131i 0.0150086 0.0259956i
\(123\) 0 0
\(124\) 18.4552 1.65733
\(125\) −1.96415 −0.175679
\(126\) 0 0
\(127\) −6.68899 11.5857i −0.593552 1.02806i −0.993750 0.111633i \(-0.964392\pi\)
0.400198 0.916429i \(-0.368941\pi\)
\(128\) −1.08229 + 1.87457i −0.0956614 + 0.165690i
\(129\) 0 0
\(130\) 0.374529 + 0.650266i 0.0328484 + 0.0570321i
\(131\) −9.06148 15.6949i −0.791705 1.37127i −0.924910 0.380185i \(-0.875860\pi\)
0.133205 0.991089i \(-0.457473\pi\)
\(132\) 0 0
\(133\) −17.9909 + 3.13247i −1.56001 + 0.271620i
\(134\) 0.0231470 0.0400918i 0.00199960 0.00346341i
\(135\) 0 0
\(136\) −0.479598 0.830688i −0.0411252 0.0712309i
\(137\) 10.6703 + 18.4814i 0.911622 + 1.57898i 0.811773 + 0.583973i \(0.198503\pi\)
0.0998490 + 0.995003i \(0.468164\pi\)
\(138\) 0 0
\(139\) −0.0705287 + 0.122159i −0.00598217 + 0.0103614i −0.869001 0.494810i \(-0.835238\pi\)
0.863019 + 0.505172i \(0.168571\pi\)
\(140\) −5.55607 + 15.1638i −0.469573 + 1.28157i
\(141\) 0 0
\(142\) −0.177963 0.308240i −0.0149343 0.0258670i
\(143\) −7.84220 13.6158i −0.655797 1.13861i
\(144\) 0 0
\(145\) −15.1727 + 26.2800i −1.26003 + 2.18243i
\(146\) −0.119713 0.207349i −0.00990753 0.0171603i
\(147\) 0 0
\(148\) 0.217587 0.0178856
\(149\) 14.3559 1.17609 0.588043 0.808830i \(-0.299899\pi\)
0.588043 + 0.808830i \(0.299899\pi\)
\(150\) 0 0
\(151\) −7.83172 + 13.5649i −0.637336 + 1.10390i 0.348679 + 0.937242i \(0.386631\pi\)
−0.986015 + 0.166657i \(0.946703\pi\)
\(152\) 1.87623 0.152182
\(153\) 0 0
\(154\) −0.269881 + 0.736568i −0.0217476 + 0.0593543i
\(155\) −28.2934 −2.27258
\(156\) 0 0
\(157\) −6.75022 + 11.6917i −0.538726 + 0.933101i 0.460247 + 0.887791i \(0.347761\pi\)
−0.998973 + 0.0453098i \(0.985572\pi\)
\(158\) 0.660504 0.0525469
\(159\) 0 0
\(160\) 1.24491 2.15625i 0.0984188 0.170466i
\(161\) −3.03585 + 8.28554i −0.239259 + 0.652992i
\(162\) 0 0
\(163\) −2.65724 −0.208131 −0.104066 0.994570i \(-0.533185\pi\)
−0.104066 + 0.994570i \(0.533185\pi\)
\(164\) 3.52980 6.11379i 0.275631 0.477407i
\(165\) 0 0
\(166\) −0.184262 + 0.319152i −0.0143015 + 0.0247710i
\(167\) 10.9142 + 18.9040i 0.844567 + 1.46283i 0.885997 + 0.463692i \(0.153475\pi\)
−0.0414294 + 0.999141i \(0.513191\pi\)
\(168\) 0 0
\(169\) −6.52343 + 11.2448i −0.501802 + 0.864983i
\(170\) 0.367206 + 0.636019i 0.0281634 + 0.0487805i
\(171\) 0 0
\(172\) −3.36860 −0.256853
\(173\) −17.6824 −1.34437 −0.672184 0.740384i \(-0.734644\pi\)
−0.672184 + 0.740384i \(0.734644\pi\)
\(174\) 0 0
\(175\) 3.96674 10.8262i 0.299858 0.818381i
\(176\) −8.65539 + 14.9916i −0.652424 + 1.13003i
\(177\) 0 0
\(178\) 0.262079 + 0.453935i 0.0196437 + 0.0340239i
\(179\) −9.72998 −0.727253 −0.363626 0.931545i \(-0.618462\pi\)
−0.363626 + 0.931545i \(0.618462\pi\)
\(180\) 0 0
\(181\) 4.01332 0.298308 0.149154 0.988814i \(-0.452345\pi\)
0.149154 + 0.988814i \(0.452345\pi\)
\(182\) 0.639518 0.110663i 0.0474042 0.00820290i
\(183\) 0 0
\(184\) 0.453307 0.785150i 0.0334182 0.0578820i
\(185\) −0.333580 −0.0245253
\(186\) 0 0
\(187\) −7.68885 13.3175i −0.562265 0.973871i
\(188\) 2.55674 4.42840i 0.186469 0.322974i
\(189\) 0 0
\(190\) −1.43654 −0.104218
\(191\) 14.7904 1.07019 0.535097 0.844790i \(-0.320275\pi\)
0.535097 + 0.844790i \(0.320275\pi\)
\(192\) 0 0
\(193\) 22.3431 1.60829 0.804146 0.594432i \(-0.202623\pi\)
0.804146 + 0.594432i \(0.202623\pi\)
\(194\) 0.262863 + 0.455292i 0.0188725 + 0.0326881i
\(195\) 0 0
\(196\) 10.6611 + 9.02406i 0.761511 + 0.644576i
\(197\) 3.16282 + 5.47816i 0.225342 + 0.390303i 0.956422 0.291988i \(-0.0943169\pi\)
−0.731080 + 0.682291i \(0.760984\pi\)
\(198\) 0 0
\(199\) 3.01808 + 5.22748i 0.213946 + 0.370566i 0.952946 0.303140i \(-0.0980349\pi\)
−0.739000 + 0.673706i \(0.764702\pi\)
\(200\) −0.592305 + 1.02590i −0.0418823 + 0.0725423i
\(201\) 0 0
\(202\) 0.132000 0.228631i 0.00928751 0.0160864i
\(203\) 16.8270 + 20.1413i 1.18102 + 1.41364i
\(204\) 0 0
\(205\) −5.41148 + 9.37295i −0.377954 + 0.654636i
\(206\) −0.583868 −0.0406800
\(207\) 0 0
\(208\) 14.3221 + 0.0149093i 0.993061 + 0.00103378i
\(209\) 30.0795 2.08064
\(210\) 0 0
\(211\) 0.646092 + 1.11906i 0.0444788 + 0.0770395i 0.887408 0.460985i \(-0.152504\pi\)
−0.842929 + 0.538025i \(0.819171\pi\)
\(212\) −10.6027 −0.728193
\(213\) 0 0
\(214\) 0.381109 + 0.660100i 0.0260521 + 0.0451235i
\(215\) 5.16434 0.352205
\(216\) 0 0
\(217\) −8.41880 + 22.9768i −0.571505 + 1.55977i
\(218\) −0.475083 0.822868i −0.0321767 0.0557316i
\(219\) 0 0
\(220\) 13.3004 23.0369i 0.896710 1.55315i
\(221\) −6.37287 + 11.0117i −0.428686 + 0.740724i
\(222\) 0 0
\(223\) 5.79892 + 10.0440i 0.388324 + 0.672597i 0.992224 0.124463i \(-0.0397207\pi\)
−0.603900 + 0.797060i \(0.706387\pi\)
\(224\) −1.38064 1.65258i −0.0922480 0.110418i
\(225\) 0 0
\(226\) −0.230566 0.399352i −0.0153370 0.0265645i
\(227\) −0.399249 0.691520i −0.0264991 0.0458978i 0.852472 0.522773i \(-0.175103\pi\)
−0.878971 + 0.476876i \(0.841769\pi\)
\(228\) 0 0
\(229\) −11.6073 20.1044i −0.767030 1.32854i −0.939166 0.343463i \(-0.888400\pi\)
0.172136 0.985073i \(-0.444933\pi\)
\(230\) −0.347076 + 0.601154i −0.0228855 + 0.0396389i
\(231\) 0 0
\(232\) −1.34825 2.33523i −0.0885168 0.153316i
\(233\) −6.09388 10.5549i −0.399223 0.691475i 0.594407 0.804164i \(-0.297387\pi\)
−0.993630 + 0.112689i \(0.964054\pi\)
\(234\) 0 0
\(235\) −3.91969 + 6.78911i −0.255693 + 0.442873i
\(236\) −7.53955 + 13.0589i −0.490783 + 0.850061i
\(237\) 0 0
\(238\) 0.625769 0.108955i 0.0405626 0.00706251i
\(239\) 0.484332 0.0313289 0.0156644 0.999877i \(-0.495014\pi\)
0.0156644 + 0.999877i \(0.495014\pi\)
\(240\) 0 0
\(241\) 1.16006 + 2.00929i 0.0747261 + 0.129429i 0.900967 0.433887i \(-0.142858\pi\)
−0.826241 + 0.563317i \(0.809525\pi\)
\(242\) 0.271856 0.470868i 0.0174756 0.0302686i
\(243\) 0 0
\(244\) 4.86189 + 8.42104i 0.311251 + 0.539102i
\(245\) −16.3444 13.8347i −1.04421 0.883863i
\(246\) 0 0
\(247\) −12.4207 21.5652i −0.790313 1.37216i
\(248\) 1.25708 2.17732i 0.0798244 0.138260i
\(249\) 0 0
\(250\) −0.0668163 + 0.115729i −0.00422583 + 0.00731935i
\(251\) −13.7950 + 23.8936i −0.870732 + 1.50815i −0.00949135 + 0.999955i \(0.503021\pi\)
−0.861241 + 0.508197i \(0.830312\pi\)
\(252\) 0 0
\(253\) 7.26736 12.5874i 0.456895 0.791365i
\(254\) −0.910183 −0.0571100
\(255\) 0 0
\(256\) −7.81549 13.5368i −0.488468 0.846051i
\(257\) 4.56503 7.90686i 0.284758 0.493216i −0.687792 0.725908i \(-0.741420\pi\)
0.972551 + 0.232692i \(0.0747533\pi\)
\(258\) 0 0
\(259\) −0.0992576 + 0.270897i −0.00616757 + 0.0168327i
\(260\) −22.0082 0.0229105i −1.36489 0.00142085i
\(261\) 0 0
\(262\) −1.23301 −0.0761758
\(263\) 5.58969 0.344675 0.172338 0.985038i \(-0.444868\pi\)
0.172338 + 0.985038i \(0.444868\pi\)
\(264\) 0 0
\(265\) 16.2548 0.998522
\(266\) −0.427447 + 1.16660i −0.0262085 + 0.0715290i
\(267\) 0 0
\(268\) 0.678860 + 1.17582i 0.0414680 + 0.0718247i
\(269\) 10.6461 + 18.4395i 0.649102 + 1.12428i 0.983338 + 0.181789i \(0.0581886\pi\)
−0.334235 + 0.942490i \(0.608478\pi\)
\(270\) 0 0
\(271\) −5.66348 + 9.80944i −0.344032 + 0.595881i −0.985177 0.171539i \(-0.945126\pi\)
0.641145 + 0.767419i \(0.278460\pi\)
\(272\) 14.0168 0.849891
\(273\) 0 0
\(274\) 1.45192 0.0877139
\(275\) −9.49577 + 16.4472i −0.572616 + 0.991801i
\(276\) 0 0
\(277\) 5.68116 + 9.84006i 0.341348 + 0.591232i 0.984683 0.174353i \(-0.0557832\pi\)
−0.643335 + 0.765584i \(0.722450\pi\)
\(278\) 0.00479849 + 0.00831123i 0.000287794 + 0.000498474i
\(279\) 0 0
\(280\) 1.41055 + 1.68838i 0.0842965 + 0.100900i
\(281\) −7.98667 −0.476445 −0.238222 0.971211i \(-0.576565\pi\)
−0.238222 + 0.971211i \(0.576565\pi\)
\(282\) 0 0
\(283\) 4.13874 0.246022 0.123011 0.992405i \(-0.460745\pi\)
0.123011 + 0.992405i \(0.460745\pi\)
\(284\) 10.4386 0.619420
\(285\) 0 0
\(286\) −1.06903 0.00111286i −0.0632131 6.58048e-5i
\(287\) 6.00149 + 7.18356i 0.354257 + 0.424032i
\(288\) 0 0
\(289\) 2.27423 3.93909i 0.133778 0.231711i
\(290\) 1.03229 + 1.78798i 0.0606183 + 0.104994i
\(291\) 0 0
\(292\) 7.02194 0.410928
\(293\) 14.1626 24.5303i 0.827385 1.43307i −0.0726976 0.997354i \(-0.523161\pi\)
0.900083 0.435719i \(-0.143506\pi\)
\(294\) 0 0
\(295\) 11.5588 20.0204i 0.672977 1.16563i
\(296\) 0.0148209 0.0256706i 0.000861449 0.00149207i
\(297\) 0 0
\(298\) 0.488360 0.845865i 0.0282900 0.0489996i
\(299\) −12.0254 0.0125184i −0.695444 0.000723957i
\(300\) 0 0
\(301\) 1.53666 4.19391i 0.0885719 0.241733i
\(302\) 0.532839 + 0.922904i 0.0306614 + 0.0531071i
\(303\) 0 0
\(304\) −13.7087 + 23.7442i −0.786248 + 1.36182i
\(305\) −7.45369 12.9102i −0.426797 0.739234i
\(306\) 0 0
\(307\) 18.0617 1.03083 0.515417 0.856939i \(-0.327637\pi\)
0.515417 + 0.856939i \(0.327637\pi\)
\(308\) −14.7505 17.6558i −0.840487 1.00603i
\(309\) 0 0
\(310\) −0.962486 + 1.66707i −0.0546655 + 0.0946834i
\(311\) 6.03959 10.4609i 0.342474 0.593182i −0.642418 0.766355i \(-0.722069\pi\)
0.984891 + 0.173173i \(0.0554019\pi\)
\(312\) 0 0
\(313\) −10.3790 17.9769i −0.586654 1.01611i −0.994667 0.103138i \(-0.967112\pi\)
0.408013 0.912976i \(-0.366222\pi\)
\(314\) 0.459257 + 0.795457i 0.0259174 + 0.0448902i
\(315\) 0 0
\(316\) −9.68569 + 16.7761i −0.544862 + 0.943729i
\(317\) 8.73476 + 15.1290i 0.490593 + 0.849732i 0.999941 0.0108284i \(-0.00344685\pi\)
−0.509348 + 0.860560i \(0.670114\pi\)
\(318\) 0 0
\(319\) −21.6150 37.4382i −1.21020 2.09614i
\(320\) 12.0667 + 20.9001i 0.674549 + 1.16835i
\(321\) 0 0
\(322\) 0.384918 + 0.460732i 0.0214506 + 0.0256756i
\(323\) −12.1779 21.0927i −0.677595 1.17363i
\(324\) 0 0
\(325\) 15.7127 + 0.0163569i 0.871585 + 0.000907319i
\(326\) −0.0903939 + 0.156567i −0.00500646 + 0.00867144i
\(327\) 0 0
\(328\) −0.480863 0.832880i −0.0265512 0.0459881i
\(329\) 4.34705 + 5.20326i 0.239661 + 0.286865i
\(330\) 0 0
\(331\) 7.12617 0.391690 0.195845 0.980635i \(-0.437255\pi\)
0.195845 + 0.980635i \(0.437255\pi\)
\(332\) −5.40408 9.36014i −0.296587 0.513705i
\(333\) 0 0
\(334\) 1.48512 0.0812620
\(335\) −1.04075 1.80263i −0.0568623 0.0984883i
\(336\) 0 0
\(337\) −22.8396 −1.24415 −0.622077 0.782956i \(-0.713711\pi\)
−0.622077 + 0.782956i \(0.713711\pi\)
\(338\) 0.440638 + 0.766890i 0.0239675 + 0.0417133i
\(339\) 0 0
\(340\) −21.5390 −1.16811
\(341\) 20.1533 34.9065i 1.09136 1.89029i
\(342\) 0 0
\(343\) −16.0983 + 9.15663i −0.869228 + 0.494412i
\(344\) −0.229451 + 0.397422i −0.0123712 + 0.0214275i
\(345\) 0 0
\(346\) −0.601520 + 1.04186i −0.0323379 + 0.0560109i
\(347\) −8.62904 14.9459i −0.463231 0.802340i 0.535889 0.844289i \(-0.319977\pi\)
−0.999120 + 0.0419489i \(0.986643\pi\)
\(348\) 0 0
\(349\) −15.3687 26.6193i −0.822665 1.42490i −0.903691 0.428186i \(-0.859153\pi\)
0.0810257 0.996712i \(-0.474180\pi\)
\(350\) −0.502946 0.602008i −0.0268836 0.0321787i
\(351\) 0 0
\(352\) 1.77349 + 3.07177i 0.0945272 + 0.163726i
\(353\) 0.960641 0.0511298 0.0255649 0.999673i \(-0.491862\pi\)
0.0255649 + 0.999673i \(0.491862\pi\)
\(354\) 0 0
\(355\) −16.0033 −0.849369
\(356\) −15.3726 −0.814748
\(357\) 0 0
\(358\) −0.330994 + 0.573299i −0.0174936 + 0.0302998i
\(359\) −16.4526 28.4967i −0.868334 1.50400i −0.863698 0.504009i \(-0.831858\pi\)
−0.00463555 0.999989i \(-0.501476\pi\)
\(360\) 0 0
\(361\) 28.6409 1.50741
\(362\) 0.136525 0.236468i 0.00717559 0.0124285i
\(363\) 0 0
\(364\) −6.56722 + 17.8659i −0.344216 + 0.936425i
\(365\) −10.7652 −0.563478
\(366\) 0 0
\(367\) 22.0554 1.15129 0.575643 0.817701i \(-0.304752\pi\)
0.575643 + 0.817701i \(0.304752\pi\)
\(368\) 6.62419 + 11.4734i 0.345310 + 0.598094i
\(369\) 0 0
\(370\) −0.0113477 + 0.0196548i −0.000589939 + 0.00102180i
\(371\) 4.83665 13.2003i 0.251107 0.685328i
\(372\) 0 0
\(373\) 25.9119 1.34167 0.670835 0.741607i \(-0.265936\pi\)
0.670835 + 0.741607i \(0.265936\pi\)
\(374\) −1.04624 −0.0540996
\(375\) 0 0
\(376\) −0.348303 0.603279i −0.0179624 0.0311118i
\(377\) −17.9155 + 30.9560i −0.922693 + 1.59432i
\(378\) 0 0
\(379\) −1.77121 3.06783i −0.0909811 0.157584i 0.816943 0.576718i \(-0.195667\pi\)
−0.907924 + 0.419134i \(0.862334\pi\)
\(380\) 21.0656 36.4867i 1.08064 1.87173i
\(381\) 0 0
\(382\) 0.503139 0.871462i 0.0257428 0.0445879i
\(383\) 29.3950 1.50202 0.751008 0.660293i \(-0.229568\pi\)
0.751008 + 0.660293i \(0.229568\pi\)
\(384\) 0 0
\(385\) 22.6138 + 27.0678i 1.15250 + 1.37950i
\(386\) 0.760067 1.31648i 0.0386864 0.0670068i
\(387\) 0 0
\(388\) −15.4186 −0.782761
\(389\) −1.32057 + 2.28730i −0.0669556 + 0.115971i −0.897560 0.440893i \(-0.854662\pi\)
0.830604 + 0.556863i \(0.187995\pi\)
\(390\) 0 0
\(391\) −11.7690 −0.595182
\(392\) 1.79083 0.643113i 0.0904504 0.0324821i
\(393\) 0 0
\(394\) 0.430371 0.0216818
\(395\) 14.8490 25.7192i 0.747133 1.29407i
\(396\) 0 0
\(397\) 0.575977 0.0289075 0.0144537 0.999896i \(-0.495399\pi\)
0.0144537 + 0.999896i \(0.495399\pi\)
\(398\) 0.410677 0.0205854
\(399\) 0 0
\(400\) −8.65539 14.9916i −0.432769 0.749578i
\(401\) −4.75598 + 8.23761i −0.237503 + 0.411366i −0.959997 0.280010i \(-0.909662\pi\)
0.722494 + 0.691377i \(0.242995\pi\)
\(402\) 0 0
\(403\) −33.3478 0.0347150i −1.66117 0.00172928i
\(404\) 3.87133 + 6.70534i 0.192606 + 0.333603i
\(405\) 0 0
\(406\) 1.75916 0.306295i 0.0873059 0.0152012i
\(407\) 0.237607 0.411548i 0.0117778 0.0203997i
\(408\) 0 0
\(409\) 0.0931606 + 0.161359i 0.00460649 + 0.00797868i 0.868319 0.496005i \(-0.165200\pi\)
−0.863713 + 0.503984i \(0.831867\pi\)
\(410\) 0.368175 + 0.637698i 0.0181829 + 0.0314937i
\(411\) 0 0
\(412\) 8.56190 14.8296i 0.421814 0.730604i
\(413\) −12.8190 15.3439i −0.630782 0.755023i
\(414\) 0 0
\(415\) 8.28491 + 14.3499i 0.406690 + 0.704408i
\(416\) 1.46995 2.53992i 0.0720701 0.124530i
\(417\) 0 0
\(418\) 1.02324 1.77231i 0.0500484 0.0866864i
\(419\) 0.448814 + 0.777369i 0.0219260 + 0.0379769i 0.876780 0.480891i \(-0.159687\pi\)
−0.854854 + 0.518868i \(0.826354\pi\)
\(420\) 0 0
\(421\) −4.34862 −0.211939 −0.105969 0.994369i \(-0.533795\pi\)
−0.105969 + 0.994369i \(0.533795\pi\)
\(422\) 0.0879150 0.00427963
\(423\) 0 0
\(424\) −0.722198 + 1.25088i −0.0350731 + 0.0607483i
\(425\) 15.3777 0.745928
\(426\) 0 0
\(427\) −12.7021 + 2.21161i −0.614697 + 0.107027i
\(428\) −22.3545 −1.08054
\(429\) 0 0
\(430\) 0.175680 0.304287i 0.00847206 0.0146740i
\(431\) 10.7267 0.516685 0.258342 0.966053i \(-0.416824\pi\)
0.258342 + 0.966053i \(0.416824\pi\)
\(432\) 0 0
\(433\) 3.46111 5.99482i 0.166330 0.288093i −0.770797 0.637081i \(-0.780142\pi\)
0.937127 + 0.348989i \(0.113475\pi\)
\(434\) 1.06742 + 1.27767i 0.0512380 + 0.0613300i
\(435\) 0 0
\(436\) 27.8666 1.33457
\(437\) 11.5103 19.9364i 0.550612 0.953688i
\(438\) 0 0
\(439\) −12.6090 + 21.8394i −0.601794 + 1.04234i 0.390756 + 0.920494i \(0.372214\pi\)
−0.992549 + 0.121843i \(0.961120\pi\)
\(440\) −1.81191 3.13831i −0.0863792 0.149613i
\(441\) 0 0
\(442\) 0.432024 + 0.750089i 0.0205493 + 0.0356781i
\(443\) 8.71266 + 15.0908i 0.413951 + 0.716984i 0.995318 0.0966574i \(-0.0308151\pi\)
−0.581367 + 0.813642i \(0.697482\pi\)
\(444\) 0 0
\(445\) 23.5675 1.11721
\(446\) 0.789070 0.0373635
\(447\) 0 0
\(448\) 20.5633 3.58036i 0.971524 0.169156i
\(449\) 5.91239 10.2406i 0.279023 0.483282i −0.692119 0.721783i \(-0.743323\pi\)
0.971142 + 0.238501i \(0.0766561\pi\)
\(450\) 0 0
\(451\) −7.70914 13.3526i −0.363009 0.628751i
\(452\) 13.5242 0.636123
\(453\) 0 0
\(454\) −0.0543266 −0.00254967
\(455\) 10.0681 27.3899i 0.472000 1.28406i
\(456\) 0 0
\(457\) 4.16626 7.21617i 0.194889 0.337558i −0.751975 0.659192i \(-0.770899\pi\)
0.946864 + 0.321634i \(0.104232\pi\)
\(458\) −1.57942 −0.0738017
\(459\) 0 0
\(460\) −10.1791 17.6307i −0.474604 0.822038i
\(461\) −2.20305 + 3.81579i −0.102606 + 0.177719i −0.912758 0.408502i \(-0.866051\pi\)
0.810152 + 0.586221i \(0.199385\pi\)
\(462\) 0 0
\(463\) 20.2243 0.939904 0.469952 0.882692i \(-0.344271\pi\)
0.469952 + 0.882692i \(0.344271\pi\)
\(464\) 39.4040 1.82929
\(465\) 0 0
\(466\) −0.829206 −0.0384122
\(467\) 3.27010 + 5.66398i 0.151322 + 0.262098i 0.931714 0.363193i \(-0.118314\pi\)
−0.780392 + 0.625291i \(0.784980\pi\)
\(468\) 0 0
\(469\) −1.77358 + 0.308805i −0.0818963 + 0.0142593i
\(470\) 0.266680 + 0.461903i 0.0123010 + 0.0213060i
\(471\) 0 0
\(472\) 1.02711 + 1.77901i 0.0472766 + 0.0818855i
\(473\) −3.67854 + 6.37141i −0.169139 + 0.292958i
\(474\) 0 0
\(475\) −15.0397 + 26.0496i −0.690070 + 1.19524i
\(476\) −6.40898 + 17.4916i −0.293755 + 0.801726i
\(477\) 0 0
\(478\) 0.0164760 0.0285373i 0.000753595 0.00130527i
\(479\) 7.81335 0.357001 0.178500 0.983940i \(-0.442875\pi\)
0.178500 + 0.983940i \(0.442875\pi\)
\(480\) 0 0
\(481\) −0.393171 0.000409290i −0.0179270 1.86620e-5i
\(482\) 0.157852 0.00718995
\(483\) 0 0
\(484\) 7.97304 + 13.8097i 0.362411 + 0.627714i
\(485\) 23.6380 1.07335
\(486\) 0 0
\(487\) 10.5370 + 18.2507i 0.477479 + 0.827018i 0.999667 0.0258123i \(-0.00821724\pi\)
−0.522188 + 0.852831i \(0.674884\pi\)
\(488\) 1.32467 0.0599649
\(489\) 0 0
\(490\) −1.37115 + 0.492402i −0.0619425 + 0.0222445i
\(491\) 4.36913 + 7.56755i 0.197176 + 0.341519i 0.947612 0.319425i \(-0.103490\pi\)
−0.750436 + 0.660943i \(0.770156\pi\)
\(492\) 0 0
\(493\) −17.5019 + 30.3142i −0.788247 + 1.36528i
\(494\) −1.69317 0.00176259i −0.0761792 7.93025e-5i
\(495\) 0 0
\(496\) 18.3697 + 31.8173i 0.824824 + 1.42864i
\(497\) −4.76184 + 12.9962i −0.213598 + 0.582957i
\(498\) 0 0
\(499\) −10.6426 18.4336i −0.476430 0.825200i 0.523206 0.852206i \(-0.324736\pi\)
−0.999635 + 0.0270062i \(0.991403\pi\)
\(500\) −1.95960 3.39413i −0.0876360 0.151790i
\(501\) 0 0
\(502\) 0.938555 + 1.62563i 0.0418898 + 0.0725552i
\(503\) 2.29846 3.98105i 0.102483 0.177506i −0.810224 0.586120i \(-0.800655\pi\)
0.912707 + 0.408614i \(0.133988\pi\)
\(504\) 0 0
\(505\) −5.93508 10.2799i −0.264107 0.457448i
\(506\) −0.494442 0.856398i −0.0219806 0.0380715i
\(507\) 0 0
\(508\) 13.3470 23.1177i 0.592178 1.02568i
\(509\) −6.85316 + 11.8700i −0.303761 + 0.526129i −0.976985 0.213309i \(-0.931576\pi\)
0.673224 + 0.739439i \(0.264909\pi\)
\(510\) 0 0
\(511\) −3.20322 + 8.74234i −0.141702 + 0.386738i
\(512\) −5.39261 −0.238322
\(513\) 0 0
\(514\) −0.310586 0.537950i −0.0136994 0.0237280i
\(515\) −13.1261 + 22.7351i −0.578406 + 1.00183i
\(516\) 0 0
\(517\) −5.58396 9.67170i −0.245582 0.425361i
\(518\) 0.0125849 + 0.0150637i 0.000552950 + 0.000661861i
\(519\) 0 0
\(520\) −1.50179 + 2.59493i −0.0658579 + 0.113795i
\(521\) 2.13457 3.69718i 0.0935172 0.161977i −0.815472 0.578797i \(-0.803522\pi\)
0.908989 + 0.416821i \(0.136856\pi\)
\(522\) 0 0
\(523\) 14.0853 24.3964i 0.615907 1.06678i −0.374318 0.927300i \(-0.622123\pi\)
0.990225 0.139481i \(-0.0445436\pi\)
\(524\) 18.0810 31.3172i 0.789873 1.36810i
\(525\) 0 0
\(526\) 0.190150 0.329350i 0.00829094 0.0143603i
\(527\) −32.6368 −1.42168
\(528\) 0 0
\(529\) 5.93810 + 10.2851i 0.258178 + 0.447178i
\(530\) 0.552954 0.957745i 0.0240188 0.0416018i
\(531\) 0 0
\(532\) −23.3623 27.9639i −1.01289 1.21239i
\(533\) −6.38969 + 11.0407i −0.276768 + 0.478226i
\(534\) 0 0
\(535\) 34.2713 1.48168
\(536\) 0.184962 0.00798914
\(537\) 0 0
\(538\) 1.44863 0.0624549
\(539\) 28.7103 10.3103i 1.23664 0.444096i
\(540\) 0 0
\(541\) 9.24717 + 16.0166i 0.397567 + 0.688606i 0.993425 0.114484i \(-0.0365214\pi\)
−0.595858 + 0.803089i \(0.703188\pi\)
\(542\) 0.385320 + 0.667394i 0.0165509 + 0.0286670i
\(543\) 0 0
\(544\) 1.43602 2.48726i 0.0615687 0.106640i
\(545\) −42.7219 −1.83001
\(546\) 0 0
\(547\) 24.6951 1.05589 0.527943 0.849280i \(-0.322963\pi\)
0.527943 + 0.849280i \(0.322963\pi\)
\(548\) −21.2911 + 36.8773i −0.909512 + 1.57532i
\(549\) 0 0
\(550\) 0.646054 + 1.11900i 0.0275478 + 0.0477142i
\(551\) −34.2345 59.2959i −1.45844 2.52609i
\(552\) 0 0
\(553\) −16.4680 19.7115i −0.700289 0.838220i
\(554\) 0.773046 0.0328436
\(555\) 0 0
\(556\) −0.281462 −0.0119366
\(557\) 2.97174 0.125917 0.0629584 0.998016i \(-0.479946\pi\)
0.0629584 + 0.998016i \(0.479946\pi\)
\(558\) 0 0
\(559\) 6.08691 + 0.00633646i 0.257449 + 0.000268004i
\(560\) −31.6731 + 5.51472i −1.33843 + 0.233040i
\(561\) 0 0
\(562\) −0.271690 + 0.470581i −0.0114606 + 0.0198503i
\(563\) −1.60029 2.77179i −0.0674443 0.116817i 0.830331 0.557270i \(-0.188151\pi\)
−0.897776 + 0.440453i \(0.854818\pi\)
\(564\) 0 0
\(565\) −20.7337 −0.872272
\(566\) 0.140791 0.243858i 0.00591791 0.0102501i
\(567\) 0 0
\(568\) 0.711027 1.23154i 0.0298340 0.0516741i
\(569\) −6.29189 + 10.8979i −0.263770 + 0.456862i −0.967241 0.253862i \(-0.918299\pi\)
0.703471 + 0.710724i \(0.251633\pi\)
\(570\) 0 0
\(571\) 11.8472 20.5200i 0.495792 0.858736i −0.504197 0.863589i \(-0.668211\pi\)
0.999988 + 0.00485262i \(0.00154464\pi\)
\(572\) 15.7046 27.1359i 0.656643 1.13461i
\(573\) 0 0
\(574\) 0.627420 0.109243i 0.0261880 0.00455970i
\(575\) 7.26736 + 12.5874i 0.303070 + 0.524932i
\(576\) 0 0
\(577\) −1.67873 + 2.90764i −0.0698863 + 0.121047i −0.898851 0.438254i \(-0.855597\pi\)
0.828965 + 0.559301i \(0.188930\pi\)
\(578\) −0.154730 0.267999i −0.00643590 0.0111473i
\(579\) 0 0
\(580\) −60.5505 −2.51422
\(581\) 14.1186 2.45825i 0.585739 0.101985i
\(582\) 0 0
\(583\) −11.5782 + 20.0540i −0.479520 + 0.830553i
\(584\) 0.478298 0.828437i 0.0197921 0.0342810i
\(585\) 0 0
\(586\) −0.963563 1.66894i −0.0398044 0.0689433i
\(587\) 4.99547 + 8.65242i 0.206185 + 0.357123i 0.950510 0.310695i \(-0.100562\pi\)
−0.744324 + 0.667818i \(0.767228\pi\)
\(588\) 0 0
\(589\) 31.9195 55.2862i 1.31522 2.27803i
\(590\) −0.786412 1.36210i −0.0323761 0.0560770i
\(591\) 0 0
\(592\) 0.216579 + 0.375126i 0.00890133 + 0.0154176i
\(593\) 16.4331 + 28.4629i 0.674825 + 1.16883i 0.976520 + 0.215426i \(0.0691141\pi\)
−0.301695 + 0.953404i \(0.597553\pi\)
\(594\) 0 0
\(595\) 9.82552 26.8161i 0.402807 1.09935i
\(596\) 14.3227 + 24.8077i 0.586682 + 1.01616i
\(597\) 0 0
\(598\) −0.409816 + 0.708119i −0.0167586 + 0.0289571i
\(599\) −10.6138 + 18.3836i −0.433667 + 0.751133i −0.997186 0.0749700i \(-0.976114\pi\)
0.563519 + 0.826103i \(0.309447\pi\)
\(600\) 0 0
\(601\) 0.776508 + 1.34495i 0.0316744 + 0.0548617i 0.881428 0.472318i \(-0.156583\pi\)
−0.849754 + 0.527180i \(0.823249\pi\)
\(602\) −0.194835 0.233210i −0.00794087 0.00950493i
\(603\) 0 0
\(604\) −31.2544 −1.27172
\(605\) −12.2233 21.1715i −0.496950 0.860742i
\(606\) 0 0
\(607\) 6.61104 0.268334 0.134167 0.990959i \(-0.457164\pi\)
0.134167 + 0.990959i \(0.457164\pi\)
\(608\) 2.80891 + 4.86518i 0.113916 + 0.197309i
\(609\) 0 0
\(610\) −1.01424 −0.0410653
\(611\) −4.62824 + 7.99711i −0.187239 + 0.323529i
\(612\) 0 0
\(613\) −12.0584 −0.487034 −0.243517 0.969897i \(-0.578301\pi\)
−0.243517 + 0.969897i \(0.578301\pi\)
\(614\) 0.614422 1.06421i 0.0247960 0.0429480i
\(615\) 0 0
\(616\) −3.08773 + 0.537617i −0.124408 + 0.0216612i
\(617\) 16.5723 28.7040i 0.667175 1.15558i −0.311515 0.950241i \(-0.600837\pi\)
0.978691 0.205340i \(-0.0658301\pi\)
\(618\) 0 0
\(619\) 23.8269 41.2695i 0.957686 1.65876i 0.229587 0.973288i \(-0.426263\pi\)
0.728099 0.685472i \(-0.240404\pi\)
\(620\) −28.2280 48.8923i −1.13366 1.96356i
\(621\) 0 0
\(622\) −0.410909 0.711716i −0.0164760 0.0285372i
\(623\) 7.01259 19.1390i 0.280953 0.766787i
\(624\) 0 0
\(625\) 13.8991 + 24.0739i 0.555962 + 0.962955i
\(626\) −1.41229 −0.0564463
\(627\) 0 0
\(628\) −26.9384 −1.07496
\(629\) −0.384788 −0.0153425
\(630\) 0 0
\(631\) 1.28825 2.23132i 0.0512846 0.0888276i −0.839243 0.543756i \(-0.817002\pi\)
0.890528 + 0.454928i \(0.150335\pi\)
\(632\) 1.31948 + 2.28540i 0.0524860 + 0.0909085i
\(633\) 0 0
\(634\) 1.18856 0.0472036
\(635\) −20.4621 + 35.4414i −0.812014 + 1.40645i
\(636\) 0 0
\(637\) −19.2473 16.3261i −0.762604 0.646865i
\(638\) −2.94119 −0.116443
\(639\) 0 0
\(640\) 6.62158 0.261741
\(641\) 20.3763 + 35.2928i 0.804815 + 1.39398i 0.916416 + 0.400227i \(0.131069\pi\)
−0.111601 + 0.993753i \(0.535598\pi\)
\(642\) 0 0
\(643\) −4.68006 + 8.10610i −0.184564 + 0.319674i −0.943429 0.331574i \(-0.892420\pi\)
0.758866 + 0.651247i \(0.225754\pi\)
\(644\) −17.3466 + 3.02028i −0.683551 + 0.119016i
\(645\) 0 0
\(646\) −1.65707 −0.0651964
\(647\) −25.0197 −0.983625 −0.491812 0.870701i \(-0.663665\pi\)
−0.491812 + 0.870701i \(0.663665\pi\)
\(648\) 0 0
\(649\) 16.4665 + 28.5208i 0.646367 + 1.11954i
\(650\) 0.535479 0.925251i 0.0210032 0.0362913i
\(651\) 0 0
\(652\) −2.65109 4.59182i −0.103825 0.179830i
\(653\) −9.28070 + 16.0746i −0.363182 + 0.629049i −0.988483 0.151334i \(-0.951643\pi\)
0.625301 + 0.780384i \(0.284976\pi\)
\(654\) 0 0
\(655\) −27.7197 + 48.0120i −1.08310 + 1.87598i
\(656\) 14.0538 0.548707
\(657\) 0 0
\(658\) 0.454459 0.0791277i 0.0177167 0.00308472i
\(659\) −18.4907 + 32.0268i −0.720295 + 1.24759i 0.240587 + 0.970628i \(0.422660\pi\)
−0.960882 + 0.276960i \(0.910673\pi\)
\(660\) 0 0
\(661\) 15.9233 0.619344 0.309672 0.950843i \(-0.399781\pi\)
0.309672 + 0.950843i \(0.399781\pi\)
\(662\) 0.242418 0.419880i 0.00942184 0.0163191i
\(663\) 0 0
\(664\) −1.47239 −0.0571399
\(665\) 35.8165 + 42.8710i 1.38890 + 1.66247i
\(666\) 0 0
\(667\) −33.0850 −1.28106
\(668\) −21.7779 + 37.7204i −0.842612 + 1.45945i
\(669\) 0 0
\(670\) −0.141617 −0.00547114
\(671\) 21.2369 0.819842
\(672\) 0 0
\(673\) 10.9624 + 18.9874i 0.422569 + 0.731910i 0.996190 0.0872103i \(-0.0277952\pi\)
−0.573621 + 0.819121i \(0.694462\pi\)
\(674\) −0.776958 + 1.34573i −0.0299273 + 0.0518356i
\(675\) 0 0
\(676\) −25.9398 0.0540066i −0.997683 0.00207718i
\(677\) 16.0122 + 27.7339i 0.615398 + 1.06590i 0.990315 + 0.138842i \(0.0443380\pi\)
−0.374917 + 0.927059i \(0.622329\pi\)
\(678\) 0 0
\(679\) 7.03356 19.1962i 0.269923 0.736683i
\(680\) −1.46712 + 2.54113i −0.0562617 + 0.0974480i
\(681\) 0 0
\(682\) −1.37115 2.37490i −0.0525040 0.0909396i
\(683\) −1.51134 2.61772i −0.0578300 0.100164i 0.835661 0.549245i \(-0.185085\pi\)
−0.893491 + 0.449081i \(0.851751\pi\)
\(684\) 0 0
\(685\) 32.6411 56.5361i 1.24715 2.16013i
\(686\) −0.00811601 + 1.26002i −0.000309871 + 0.0481077i
\(687\) 0 0
\(688\) −3.35298 5.80754i −0.127831 0.221410i
\(689\) 19.1585 + 0.0199440i 0.729882 + 0.000759807i
\(690\) 0 0
\(691\) 5.94954 10.3049i 0.226331 0.392017i −0.730387 0.683034i \(-0.760660\pi\)
0.956718 + 0.291017i \(0.0939936\pi\)
\(692\) −17.6415 30.5559i −0.670628 1.16156i
\(693\) 0 0
\(694\) −1.17417 −0.0445709
\(695\) 0.431505 0.0163679
\(696\) 0 0
\(697\) −6.24220 + 10.8118i −0.236440 + 0.409526i
\(698\) −2.09124 −0.0791547
\(699\) 0 0
\(700\) 22.6656 3.94640i 0.856680 0.149160i
\(701\) −2.07215 −0.0782642 −0.0391321 0.999234i \(-0.512459\pi\)
−0.0391321 + 0.999234i \(0.512459\pi\)
\(702\) 0 0
\(703\) 0.376331 0.651824i 0.0141936 0.0245840i
\(704\) −34.3802 −1.29575
\(705\) 0 0
\(706\) 0.0326791 0.0566018i 0.00122989 0.00213024i
\(707\) −10.1142 + 1.76102i −0.380383 + 0.0662300i
\(708\) 0 0
\(709\) 7.23998 0.271903 0.135952 0.990715i \(-0.456591\pi\)
0.135952 + 0.990715i \(0.456591\pi\)
\(710\) −0.544401 + 0.942930i −0.0204310 + 0.0353875i
\(711\) 0 0
\(712\) −1.04710 + 1.81364i −0.0392419 + 0.0679690i
\(713\) −15.4238 26.7149i −0.577627 1.00048i
\(714\) 0 0
\(715\) −24.0765 + 41.6017i −0.900411 + 1.55581i
\(716\) −9.70746 16.8138i −0.362785 0.628362i
\(717\) 0 0
\(718\) −2.23873 −0.0835488
\(719\) −50.9305 −1.89939 −0.949694 0.313179i \(-0.898606\pi\)
−0.949694 + 0.313179i \(0.898606\pi\)
\(720\) 0 0
\(721\) 14.5572 + 17.4245i 0.542140 + 0.648922i
\(722\) 0.974305 1.68755i 0.0362599 0.0628039i
\(723\) 0 0
\(724\) 4.00403 + 6.93518i 0.148809 + 0.257744i
\(725\) 43.2299 1.60552
\(726\) 0 0
\(727\) −21.6848 −0.804244 −0.402122 0.915586i \(-0.631727\pi\)
−0.402122 + 0.915586i \(0.631727\pi\)
\(728\) 1.66046 + 1.99172i 0.0615407 + 0.0738181i
\(729\) 0 0
\(730\) −0.366211 + 0.634296i −0.0135541 + 0.0234764i
\(731\) 5.95712 0.220332
\(732\) 0 0
\(733\) 10.8930 + 18.8673i 0.402343 + 0.696879i 0.994008 0.109305i \(-0.0348625\pi\)
−0.591665 + 0.806184i \(0.701529\pi\)
\(734\) 0.750282 1.29953i 0.0276934 0.0479664i
\(735\) 0 0
\(736\) 2.71459 0.100061
\(737\) 2.96529 0.109228
\(738\) 0 0
\(739\) 35.9065 1.32084 0.660421 0.750895i \(-0.270378\pi\)
0.660421 + 0.750895i \(0.270378\pi\)
\(740\) −0.332808 0.576440i −0.0122342 0.0211903i
\(741\) 0 0
\(742\) −0.613242 0.734029i −0.0225128 0.0269470i
\(743\) −25.6310 44.3942i −0.940310 1.62867i −0.764879 0.644174i \(-0.777201\pi\)
−0.175431 0.984492i \(-0.556132\pi\)
\(744\) 0 0
\(745\) −21.9579 38.0323i −0.804477 1.39339i
\(746\) 0.881472 1.52675i 0.0322730 0.0558984i
\(747\) 0 0
\(748\) 15.3421 26.5733i 0.560963 0.971617i
\(749\) 10.1975 27.8314i 0.372609 1.01694i
\(750\) 0 0
\(751\) −24.3770 + 42.2222i −0.889530 + 1.54071i −0.0490976 + 0.998794i \(0.515635\pi\)
−0.840432 + 0.541917i \(0.817699\pi\)
\(752\) 10.1795 0.371210
\(753\) 0 0
\(754\) 1.21451 + 2.10866i 0.0442298 + 0.0767927i
\(755\) 47.9156 1.74383
\(756\) 0 0
\(757\) 7.41023 + 12.8349i 0.269329 + 0.466492i 0.968689 0.248278i \(-0.0798647\pi\)
−0.699360 + 0.714770i \(0.746531\pi\)
\(758\) −0.241012 −0.00875396
\(759\) 0 0
\(760\) −2.86976 4.97057i −0.104097 0.180301i
\(761\) −11.3103 −0.409998 −0.204999 0.978762i \(-0.565719\pi\)
−0.204999 + 0.978762i \(0.565719\pi\)
\(762\) 0 0
\(763\) −12.7120 + 34.6941i −0.460206 + 1.25601i
\(764\) 14.7562 + 25.5584i 0.533859 + 0.924671i
\(765\) 0 0
\(766\) 0.999960 1.73198i 0.0361300 0.0625790i
\(767\) 13.6482 23.5826i 0.492808 0.851520i
\(768\) 0 0
\(769\) 8.92963 + 15.4666i 0.322011 + 0.557739i 0.980903 0.194498i \(-0.0623079\pi\)
−0.658892 + 0.752238i \(0.728975\pi\)
\(770\) 2.36413 0.411629i 0.0851975 0.0148341i
\(771\) 0 0
\(772\) 22.2914 + 38.6098i 0.802285 + 1.38960i
\(773\) 1.43276 + 2.48162i 0.0515329 + 0.0892575i 0.890641 0.454707i \(-0.150256\pi\)
−0.839108 + 0.543964i \(0.816923\pi\)
\(774\) 0 0
\(775\) 20.1533 + 34.9065i 0.723928 + 1.25388i
\(776\) −1.05024 + 1.81906i −0.0377013 + 0.0653005i
\(777\) 0 0
\(778\) 0.0898463 + 0.155618i 0.00322115 + 0.00557919i
\(779\) −12.2100 21.1484i −0.437469 0.757718i
\(780\) 0 0
\(781\) 11.3991 19.7438i 0.407892 0.706489i
\(782\) −0.400356 + 0.693437i −0.0143167 + 0.0247973i
\(783\) 0 0
\(784\) −4.94596 + 27.3623i −0.176641 + 0.977226i
\(785\) 41.2988 1.47402
\(786\) 0 0
\(787\) −1.58257 2.74109i −0.0564125 0.0977094i 0.836440 0.548058i \(-0.184633\pi\)
−0.892853 + 0.450349i \(0.851300\pi\)
\(788\) −6.31100 + 10.9310i −0.224820 + 0.389400i
\(789\) 0 0
\(790\) −1.01026 1.74983i −0.0359436 0.0622561i
\(791\) −6.16936 + 16.8376i −0.219357 + 0.598677i
\(792\) 0 0
\(793\) −8.76938 15.2256i −0.311410 0.540677i
\(794\) 0.0195936 0.0339371i 0.000695350 0.00120438i
\(795\) 0 0
\(796\) −6.02220 + 10.4308i −0.213451 + 0.369708i
\(797\) −12.0425 + 20.8583i −0.426568 + 0.738838i −0.996565 0.0828085i \(-0.973611\pi\)
0.569997 + 0.821647i \(0.306944\pi\)
\(798\) 0 0
\(799\) −4.52141 + 7.83131i −0.159956 + 0.277052i
\(800\) −3.54698 −0.125405
\(801\) 0 0
\(802\) 0.323578 + 0.560453i 0.0114259 + 0.0197903i
\(803\) 7.66802 13.2814i 0.270599 0.468690i
\(804\) 0 0
\(805\) 26.5938 4.63035i 0.937308 0.163198i
\(806\) −1.13647 + 1.96370i −0.0400305 + 0.0691684i
\(807\) 0 0
\(808\) 1.05478 0.0371071
\(809\) 38.3111 1.34695 0.673474 0.739211i \(-0.264801\pi\)
0.673474 + 0.739211i \(0.264801\pi\)
\(810\) 0 0
\(811\) 2.79091 0.0980022 0.0490011 0.998799i \(-0.484396\pi\)
0.0490011 + 0.998799i \(0.484396\pi\)
\(812\) −18.0170 + 49.1725i −0.632272 + 1.72562i
\(813\) 0 0
\(814\) −0.0161658 0.0280000i −0.000566612 0.000981401i
\(815\) 4.06434 + 7.03965i 0.142368 + 0.246588i
\(816\) 0 0
\(817\) −5.82620 + 10.0913i −0.203833 + 0.353049i
\(818\) 0.0126765 0.000443225
\(819\) 0 0
\(820\) −21.5958 −0.754158
\(821\) −22.1855 + 38.4264i −0.774279 + 1.34109i 0.160919 + 0.986968i \(0.448554\pi\)
−0.935199 + 0.354124i \(0.884779\pi\)
\(822\) 0 0
\(823\) 4.10746 + 7.11433i 0.143177 + 0.247990i 0.928691 0.370853i \(-0.120935\pi\)
−0.785514 + 0.618844i \(0.787601\pi\)
\(824\) −1.16639 2.02024i −0.0406329 0.0703783i
\(825\) 0 0
\(826\) −1.34015 + 0.233339i −0.0466298 + 0.00811891i
\(827\) 37.0687 1.28900 0.644502 0.764603i \(-0.277065\pi\)
0.644502 + 0.764603i \(0.277065\pi\)
\(828\) 0 0
\(829\) −42.4586 −1.47465 −0.737323 0.675540i \(-0.763911\pi\)
−0.737323 + 0.675540i \(0.763911\pi\)
\(830\) 1.12734 0.0391307
\(831\) 0 0
\(832\) 14.1967 + 24.6486i 0.492181 + 0.854535i
\(833\) −18.8535 15.9584i −0.653235 0.552926i
\(834\) 0 0
\(835\) 33.3874 57.8286i 1.15542 2.00124i
\(836\) 30.0098 + 51.9786i 1.03791 + 1.79772i
\(837\) 0 0
\(838\) 0.0610710 0.00210966
\(839\) −0.873903 + 1.51365i −0.0301705 + 0.0522568i −0.880716 0.473644i \(-0.842938\pi\)
0.850546 + 0.525901i \(0.176272\pi\)
\(840\) 0 0
\(841\) −34.7015 + 60.1048i −1.19660 + 2.07258i
\(842\) −0.147931 + 0.256225i −0.00509805 + 0.00883008i
\(843\) 0 0
\(844\) −1.28919 + 2.23295i −0.0443759 + 0.0768612i
\(845\) 39.7679 + 0.0827967i 1.36806 + 0.00284829i
\(846\) 0 0
\(847\) −20.8302 + 3.62684i −0.715735 + 0.124620i
\(848\) −10.5535 18.2792i −0.362409 0.627711i
\(849\) 0 0
\(850\) 0.523118 0.906068i 0.0179428 0.0310779i
\(851\) −0.181847 0.314968i −0.00623364 0.0107970i
\(852\) 0 0
\(853\) −55.5244 −1.90112 −0.950560 0.310540i \(-0.899490\pi\)
−0.950560 + 0.310540i \(0.899490\pi\)
\(854\) −0.301789 + 0.823653i −0.0103270 + 0.0281848i
\(855\) 0 0
\(856\) −1.52267 + 2.63734i −0.0520438 + 0.0901426i
\(857\) −14.8303 + 25.6869i −0.506595 + 0.877448i 0.493376 + 0.869816i \(0.335763\pi\)
−0.999971 + 0.00763209i \(0.997571\pi\)
\(858\) 0 0
\(859\) −10.6791 18.4967i −0.364365 0.631098i 0.624309 0.781177i \(-0.285381\pi\)
−0.988674 + 0.150079i \(0.952047\pi\)
\(860\) 5.15239 + 8.92420i 0.175695 + 0.304313i
\(861\) 0 0
\(862\) 0.364899 0.632024i 0.0124285 0.0215268i
\(863\) −17.5615 30.4174i −0.597800 1.03542i −0.993145 0.116887i \(-0.962708\pi\)
0.395345 0.918533i \(-0.370625\pi\)
\(864\) 0 0
\(865\) 27.0459 + 46.8448i 0.919587 + 1.59277i
\(866\) −0.235480 0.407863i −0.00800194 0.0138598i
\(867\) 0 0
\(868\) −48.1042 + 8.37562i −1.63276 + 0.284287i
\(869\) 21.1537 + 36.6393i 0.717591 + 1.24290i
\(870\) 0 0
\(871\) −1.22446 2.12593i −0.0414892 0.0720345i
\(872\) 1.89813 3.28766i 0.0642789 0.111334i
\(873\) 0 0
\(874\) −0.783114 1.35639i −0.0264892 0.0458807i
\(875\) 5.11962 0.891397i 0.173075 0.0301347i
\(876\) 0 0
\(877\) 18.8056 0.635019 0.317509 0.948255i \(-0.397153\pi\)
0.317509 + 0.948255i \(0.397153\pi\)
\(878\) 0.857864 + 1.48586i 0.0289515 + 0.0501455i
\(879\) 0 0
\(880\) 52.9549 1.78511
\(881\) 22.3970 + 38.7927i 0.754573 + 1.30696i 0.945586 + 0.325371i \(0.105489\pi\)
−0.191013 + 0.981587i \(0.561177\pi\)
\(882\) 0 0
\(883\) −2.57264 −0.0865764 −0.0432882 0.999063i \(-0.513783\pi\)
−0.0432882 + 0.999063i \(0.513783\pi\)
\(884\) −25.3867 0.0264275i −0.853848 0.000888855i
\(885\) 0 0
\(886\) 1.18555 0.0398293
\(887\) −18.4051 + 31.8786i −0.617983 + 1.07038i 0.371870 + 0.928285i \(0.378717\pi\)
−0.989853 + 0.142093i \(0.954617\pi\)
\(888\) 0 0
\(889\) 22.6931 + 27.1628i 0.761101 + 0.911010i
\(890\) 0.801720 1.38862i 0.0268737 0.0465466i
\(891\) 0 0
\(892\) −11.5710 + 20.0415i −0.387425 + 0.671041i
\(893\) −8.84407 15.3184i −0.295955 0.512610i
\(894\) 0 0
\(895\) 14.8824 + 25.7770i 0.497462 + 0.861630i
\(896\) 1.97027 5.37732i 0.0658221 0.179644i
\(897\) 0 0
\(898\) −0.402255 0.696726i −0.0134234 0.0232501i
\(899\) −91.7487 −3.05999
\(900\) 0 0
\(901\) 18.7500 0.624655
\(902\) −1.04900 −0.0349278
\(903\) 0 0
\(904\) 0.921196 1.59556i 0.0306385 0.0530675i
\(905\) −6.13852 10.6322i −0.204051 0.353427i
\(906\) 0 0
\(907\) 3.84939 0.127817 0.0639084 0.997956i \(-0.479643\pi\)
0.0639084 + 0.997956i \(0.479643\pi\)
\(908\) 0.796650 1.37984i 0.0264378 0.0457915i
\(909\) 0 0
\(910\) −1.27134 1.52497i −0.0421445 0.0505522i
\(911\) 47.0839 1.55996 0.779980 0.625804i \(-0.215229\pi\)
0.779980 + 0.625804i \(0.215229\pi\)
\(912\) 0 0
\(913\) −23.6052 −0.781219
\(914\) −0.283455 0.490959i −0.00937587 0.0162395i
\(915\) 0 0
\(916\) 23.1608 40.1157i 0.765255 1.32546i
\(917\) 30.7420 + 36.7970i 1.01519 + 1.21515i
\(918\) 0 0
\(919\) −55.7761 −1.83989 −0.919943 0.392053i \(-0.871765\pi\)
−0.919943 + 0.392053i \(0.871765\pi\)
\(920\) −2.77340 −0.0914362
\(921\) 0 0
\(922\) 0.149886 + 0.259611i 0.00493625 + 0.00854983i
\(923\) −18.8622 0.0196355i −0.620856 0.000646311i
\(924\) 0 0
\(925\) 0.237607 + 0.411548i 0.00781248 + 0.0135316i
\(926\) 0.687990 1.19163i 0.0226088 0.0391595i
\(927\) 0 0
\(928\) 4.03694 6.99219i 0.132519 0.229530i
\(929\) −38.9439 −1.27771 −0.638855 0.769327i \(-0.720591\pi\)
−0.638855 + 0.769327i \(0.720591\pi\)
\(930\) 0 0
\(931\) 45.4724 16.3298i 1.49030 0.535188i
\(932\) 12.1596 21.0610i 0.398299 0.689875i
\(933\) 0 0
\(934\) 0.444969 0.0145598
\(935\) −23.5208 + 40.7392i −0.769211 + 1.33231i
\(936\) 0 0
\(937\) 19.5763 0.639531 0.319765 0.947497i \(-0.396396\pi\)
0.319765 + 0.947497i \(0.396396\pi\)
\(938\) −0.0421385 + 0.115006i −0.00137587 + 0.00375507i
\(939\) 0 0
\(940\) −15.6425 −0.510202
\(941\) −3.84200 + 6.65455i −0.125246 + 0.216932i −0.921829 0.387597i \(-0.873305\pi\)
0.796583 + 0.604529i \(0.206639\pi\)
\(942\) 0 0
\(943\) −11.8000 −0.384261
\(944\) −30.0184 −0.977017
\(945\) 0 0
\(946\) 0.250273 + 0.433485i 0.00813707 + 0.0140938i
\(947\) 17.1984 29.7886i 0.558874 0.967998i −0.438717 0.898625i \(-0.644567\pi\)
0.997591 0.0693727i \(-0.0220998\pi\)
\(948\) 0 0
\(949\) −12.6883 0.0132085i −0.411881 0.000428767i
\(950\) 1.02324 + 1.77231i 0.0331984 + 0.0575012i
\(951\) 0 0
\(952\) 1.62708 + 1.94756i 0.0527341 + 0.0631208i
\(953\) 23.8888 41.3766i 0.773834 1.34032i −0.161613 0.986854i \(-0.551670\pi\)
0.935447 0.353466i \(-0.114997\pi\)
\(954\) 0 0
\(955\) −22.6224 39.1832i −0.732045 1.26794i
\(956\) 0.483211 + 0.836947i 0.0156282 + 0.0270688i
\(957\) 0 0
\(958\) 0.265794 0.460369i 0.00858742 0.0148739i
\(959\) −36.1999 43.3300i −1.16896 1.39920i
\(960\) 0 0
\(961\) −27.2722 47.2369i −0.879749 1.52377i
\(962\) −0.0133990 + 0.0231520i −0.000432001 + 0.000746451i
\(963\) 0 0
\(964\) −2.31475 + 4.00927i −0.0745532 + 0.129130i
\(965\) −34.1746 59.1921i −1.10012 1.90546i
\(966\) 0 0
\(967\) 52.1099 1.67574 0.837871 0.545869i \(-0.183800\pi\)
0.837871 + 0.545869i \(0.183800\pi\)
\(968\) 2.17233 0.0698213
\(969\) 0 0
\(970\) 0.804118 1.39277i 0.0258187 0.0447192i
\(971\) −20.6294 −0.662028 −0.331014 0.943626i \(-0.607391\pi\)
−0.331014 + 0.943626i \(0.607391\pi\)
\(972\) 0 0
\(973\) 0.128396 0.350421i 0.00411617 0.0112340i
\(974\) 1.43380 0.0459418
\(975\) 0 0
\(976\) −9.67871 + 16.7640i −0.309808 + 0.536603i
\(977\) 25.9590 0.830501 0.415251 0.909707i \(-0.363694\pi\)
0.415251 + 0.909707i \(0.363694\pi\)
\(978\) 0 0
\(979\) −16.7871 + 29.0760i −0.536516 + 0.929274i
\(980\) 7.60024 42.0465i 0.242781 1.34313i
\(981\) 0 0
\(982\) 0.594516 0.0189718
\(983\) 19.0424 32.9825i 0.607359 1.05198i −0.384315 0.923202i \(-0.625562\pi\)
0.991674 0.128775i \(-0.0411045\pi\)
\(984\) 0 0
\(985\) 9.67529 16.7581i 0.308281 0.533958i
\(986\) 1.19076 + 2.06246i 0.0379215 + 0.0656820i
\(987\) 0 0
\(988\) 24.8735 42.9788i 0.791332 1.36734i
\(989\) 2.81528 + 4.87621i 0.0895207 + 0.155054i
\(990\) 0 0
\(991\) −61.3614 −1.94921 −0.974605 0.223930i \(-0.928111\pi\)
−0.974605 + 0.223930i \(0.928111\pi\)
\(992\) 7.52791 0.239011
\(993\) 0 0
\(994\) 0.603757 + 0.722675i 0.0191500 + 0.0229218i
\(995\) 9.23254 15.9912i 0.292691 0.506956i
\(996\) 0 0
\(997\) 9.66583 + 16.7417i 0.306120 + 0.530215i 0.977510 0.210889i \(-0.0676358\pi\)
−0.671390 + 0.741104i \(0.734302\pi\)
\(998\) −1.44816 −0.0458408
\(999\) 0 0
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 819.2.n.e.172.5 16
3.2 odd 2 273.2.j.b.172.4 yes 16
7.2 even 3 819.2.s.e.289.4 16
13.9 even 3 819.2.s.e.802.4 16
21.2 odd 6 273.2.l.b.16.5 yes 16
39.35 odd 6 273.2.l.b.256.5 yes 16
91.9 even 3 inner 819.2.n.e.100.5 16
273.191 odd 6 273.2.j.b.100.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.j.b.100.4 16 273.191 odd 6
273.2.j.b.172.4 yes 16 3.2 odd 2
273.2.l.b.16.5 yes 16 21.2 odd 6
273.2.l.b.256.5 yes 16 39.35 odd 6
819.2.n.e.100.5 16 91.9 even 3 inner
819.2.n.e.172.5 16 1.1 even 1 trivial
819.2.s.e.289.4 16 7.2 even 3
819.2.s.e.802.4 16 13.9 even 3