Properties

Label 756.2.be.d.431.5
Level $756$
Weight $2$
Character 756.431
Analytic conductor $6.037$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(107,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.be (of order \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 431.5
Character \(\chi\) \(=\) 756.431
Dual form 756.2.be.d.107.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.498187 + 1.32356i) q^{2} +(-1.50362 - 1.31876i) q^{4} +(-0.936239 + 0.540538i) q^{5} +(0.749282 - 2.53743i) q^{7} +(2.49454 - 1.33314i) q^{8} +O(q^{10})\) \(q+(-0.498187 + 1.32356i) q^{2} +(-1.50362 - 1.31876i) q^{4} +(-0.936239 + 0.540538i) q^{5} +(0.749282 - 2.53743i) q^{7} +(2.49454 - 1.33314i) q^{8} +(-0.249012 - 1.50846i) q^{10} +(-2.43972 + 4.22571i) q^{11} +0.815997 q^{13} +(2.98516 + 2.25584i) q^{14} +(0.521749 + 3.96583i) q^{16} +(-1.47016 - 0.848796i) q^{17} +(-3.58740 + 2.07119i) q^{19} +(2.12059 + 0.421910i) q^{20} +(-4.37755 - 5.33430i) q^{22} +(-1.75645 - 3.04226i) q^{23} +(-1.91564 + 3.31798i) q^{25} +(-0.406519 + 1.08002i) q^{26} +(-4.47290 + 2.82722i) q^{28} +9.61003i q^{29} +(-7.73929 - 4.46828i) q^{31} +(-5.50894 - 1.28516i) q^{32} +(1.85585 - 1.52298i) q^{34} +(0.670072 + 2.78066i) q^{35} +(-3.37978 - 5.85395i) q^{37} +(-0.954144 - 5.77997i) q^{38} +(-1.61487 + 2.59653i) q^{40} +6.96667i q^{41} -0.510241i q^{43} +(9.24111 - 3.13647i) q^{44} +(4.90165 - 0.809152i) q^{46} +(-3.40777 - 5.90243i) q^{47} +(-5.87715 - 3.80251i) q^{49} +(-3.43720 - 4.18843i) q^{50} +(-1.22695 - 1.07610i) q^{52} +(-2.99884 - 1.73138i) q^{53} -5.27504i q^{55} +(-1.51365 - 7.32863i) q^{56} +(-12.7195 - 4.78759i) q^{58} +(2.50722 - 4.34263i) q^{59} +(6.85713 + 11.8769i) q^{61} +(9.76964 - 8.01737i) q^{62} +(4.44546 - 6.65116i) q^{64} +(-0.763968 + 0.441077i) q^{65} +(3.66826 + 2.11787i) q^{67} +(1.09120 + 3.21505i) q^{68} +(-4.01419 - 0.498407i) q^{70} -11.8557 q^{71} +(-1.49777 + 2.59421i) q^{73} +(9.43181 - 1.55698i) q^{74} +(8.12548 + 1.61664i) q^{76} +(8.89444 + 9.35688i) q^{77} +(-3.41517 + 1.97175i) q^{79} +(-2.63216 - 3.43094i) q^{80} +(-9.22080 - 3.47070i) q^{82} -11.3326 q^{83} +1.83523 q^{85} +(0.675334 + 0.254195i) q^{86} +(-0.452489 + 13.7937i) q^{88} +(0.313438 - 0.180963i) q^{89} +(0.611412 - 2.07054i) q^{91} +(-1.37097 + 6.89073i) q^{92} +(9.50992 - 1.56987i) q^{94} +(2.23911 - 3.87825i) q^{95} +8.12677 q^{97} +(7.96077 - 5.88440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.498187 + 1.32356i −0.352271 + 0.935898i
\(3\) 0 0
\(4\) −1.50362 1.31876i −0.751810 0.659380i
\(5\) −0.936239 + 0.540538i −0.418699 + 0.241736i −0.694520 0.719473i \(-0.744383\pi\)
0.275822 + 0.961209i \(0.411050\pi\)
\(6\) 0 0
\(7\) 0.749282 2.53743i 0.283202 0.959060i
\(8\) 2.49454 1.33314i 0.881953 0.471337i
\(9\) 0 0
\(10\) −0.249012 1.50846i −0.0787446 0.477016i
\(11\) −2.43972 + 4.22571i −0.735602 + 1.27410i 0.218856 + 0.975757i \(0.429767\pi\)
−0.954459 + 0.298343i \(0.903566\pi\)
\(12\) 0 0
\(13\) 0.815997 0.226317 0.113158 0.993577i \(-0.463903\pi\)
0.113158 + 0.993577i \(0.463903\pi\)
\(14\) 2.98516 + 2.25584i 0.797819 + 0.602897i
\(15\) 0 0
\(16\) 0.521749 + 3.96583i 0.130437 + 0.991457i
\(17\) −1.47016 0.848796i −0.356566 0.205863i 0.311007 0.950407i \(-0.399334\pi\)
−0.667573 + 0.744544i \(0.732667\pi\)
\(18\) 0 0
\(19\) −3.58740 + 2.07119i −0.823006 + 0.475163i −0.851452 0.524433i \(-0.824277\pi\)
0.0284462 + 0.999595i \(0.490944\pi\)
\(20\) 2.12059 + 0.421910i 0.474178 + 0.0943419i
\(21\) 0 0
\(22\) −4.37755 5.33430i −0.933297 1.13728i
\(23\) −1.75645 3.04226i −0.366245 0.634354i 0.622730 0.782436i \(-0.286023\pi\)
−0.988975 + 0.148082i \(0.952690\pi\)
\(24\) 0 0
\(25\) −1.91564 + 3.31798i −0.383128 + 0.663596i
\(26\) −0.406519 + 1.08002i −0.0797249 + 0.211810i
\(27\) 0 0
\(28\) −4.47290 + 2.82722i −0.845299 + 0.534294i
\(29\) 9.61003i 1.78454i 0.451504 + 0.892269i \(0.350888\pi\)
−0.451504 + 0.892269i \(0.649112\pi\)
\(30\) 0 0
\(31\) −7.73929 4.46828i −1.39002 0.802527i −0.396700 0.917948i \(-0.629845\pi\)
−0.993317 + 0.115422i \(0.963178\pi\)
\(32\) −5.50894 1.28516i −0.973851 0.227186i
\(33\) 0 0
\(34\) 1.85585 1.52298i 0.318275 0.261190i
\(35\) 0.670072 + 2.78066i 0.113263 + 0.470017i
\(36\) 0 0
\(37\) −3.37978 5.85395i −0.555632 0.962383i −0.997854 0.0654777i \(-0.979143\pi\)
0.442222 0.896906i \(-0.354190\pi\)
\(38\) −0.954144 5.77997i −0.154783 0.937635i
\(39\) 0 0
\(40\) −1.61487 + 2.59653i −0.255334 + 0.410548i
\(41\) 6.96667i 1.08801i 0.839082 + 0.544005i \(0.183093\pi\)
−0.839082 + 0.544005i \(0.816907\pi\)
\(42\) 0 0
\(43\) 0.510241i 0.0778110i −0.999243 0.0389055i \(-0.987613\pi\)
0.999243 0.0389055i \(-0.0123871\pi\)
\(44\) 9.24111 3.13647i 1.39315 0.472841i
\(45\) 0 0
\(46\) 4.90165 0.809152i 0.722708 0.119303i
\(47\) −3.40777 5.90243i −0.497074 0.860958i 0.502920 0.864333i \(-0.332259\pi\)
−0.999994 + 0.00337527i \(0.998926\pi\)
\(48\) 0 0
\(49\) −5.87715 3.80251i −0.839593 0.543216i
\(50\) −3.43720 4.18843i −0.486094 0.592334i
\(51\) 0 0
\(52\) −1.22695 1.07610i −0.170147 0.149229i
\(53\) −2.99884 1.73138i −0.411922 0.237824i 0.279693 0.960090i \(-0.409767\pi\)
−0.691615 + 0.722266i \(0.743101\pi\)
\(54\) 0 0
\(55\) 5.27504i 0.711286i
\(56\) −1.51365 7.32863i −0.202270 0.979330i
\(57\) 0 0
\(58\) −12.7195 4.78759i −1.67015 0.628641i
\(59\) 2.50722 4.34263i 0.326412 0.565362i −0.655385 0.755295i \(-0.727494\pi\)
0.981797 + 0.189933i \(0.0608270\pi\)
\(60\) 0 0
\(61\) 6.85713 + 11.8769i 0.877966 + 1.52068i 0.853569 + 0.520979i \(0.174433\pi\)
0.0243965 + 0.999702i \(0.492234\pi\)
\(62\) 9.76964 8.01737i 1.24075 1.01821i
\(63\) 0 0
\(64\) 4.44546 6.65116i 0.555682 0.831395i
\(65\) −0.763968 + 0.441077i −0.0947586 + 0.0547089i
\(66\) 0 0
\(67\) 3.66826 + 2.11787i 0.448150 + 0.258739i 0.707048 0.707165i \(-0.250026\pi\)
−0.258899 + 0.965904i \(0.583360\pi\)
\(68\) 1.09120 + 3.21505i 0.132328 + 0.389882i
\(69\) 0 0
\(70\) −4.01419 0.498407i −0.479788 0.0595711i
\(71\) −11.8557 −1.40701 −0.703503 0.710692i \(-0.748382\pi\)
−0.703503 + 0.710692i \(0.748382\pi\)
\(72\) 0 0
\(73\) −1.49777 + 2.59421i −0.175301 + 0.303630i −0.940265 0.340443i \(-0.889423\pi\)
0.764965 + 0.644072i \(0.222756\pi\)
\(74\) 9.43181 1.55698i 1.09643 0.180995i
\(75\) 0 0
\(76\) 8.12548 + 1.61664i 0.932056 + 0.185441i
\(77\) 8.89444 + 9.35688i 1.01362 + 1.06631i
\(78\) 0 0
\(79\) −3.41517 + 1.97175i −0.384237 + 0.221839i −0.679660 0.733527i \(-0.737873\pi\)
0.295423 + 0.955366i \(0.404539\pi\)
\(80\) −2.63216 3.43094i −0.294284 0.383590i
\(81\) 0 0
\(82\) −9.22080 3.47070i −1.01827 0.383275i
\(83\) −11.3326 −1.24392 −0.621960 0.783049i \(-0.713663\pi\)
−0.621960 + 0.783049i \(0.713663\pi\)
\(84\) 0 0
\(85\) 1.83523 0.199058
\(86\) 0.675334 + 0.254195i 0.0728232 + 0.0274106i
\(87\) 0 0
\(88\) −0.452489 + 13.7937i −0.0482355 + 1.47041i
\(89\) 0.313438 0.180963i 0.0332243 0.0191821i −0.483296 0.875457i \(-0.660560\pi\)
0.516520 + 0.856275i \(0.327227\pi\)
\(90\) 0 0
\(91\) 0.611412 2.07054i 0.0640934 0.217052i
\(92\) −1.37097 + 6.89073i −0.142934 + 0.718408i
\(93\) 0 0
\(94\) 9.50992 1.56987i 0.980873 0.161920i
\(95\) 2.23911 3.87825i 0.229728 0.397900i
\(96\) 0 0
\(97\) 8.12677 0.825148 0.412574 0.910924i \(-0.364630\pi\)
0.412574 + 0.910924i \(0.364630\pi\)
\(98\) 7.96077 5.88440i 0.804159 0.594414i
\(99\) 0 0
\(100\) 7.25601 2.46272i 0.725601 0.246272i
\(101\) −1.32037 0.762317i −0.131382 0.0758534i 0.432869 0.901457i \(-0.357501\pi\)
−0.564250 + 0.825604i \(0.690835\pi\)
\(102\) 0 0
\(103\) 6.69999 3.86824i 0.660170 0.381149i −0.132172 0.991227i \(-0.542195\pi\)
0.792342 + 0.610078i \(0.208862\pi\)
\(104\) 2.03554 1.08784i 0.199601 0.106672i
\(105\) 0 0
\(106\) 3.78557 3.10659i 0.367687 0.301739i
\(107\) 0.602928 + 1.04430i 0.0582873 + 0.100957i 0.893697 0.448672i \(-0.148103\pi\)
−0.835409 + 0.549628i \(0.814769\pi\)
\(108\) 0 0
\(109\) 0.314166 0.544151i 0.0300916 0.0521202i −0.850587 0.525834i \(-0.823753\pi\)
0.880679 + 0.473713i \(0.157087\pi\)
\(110\) 6.98183 + 2.62795i 0.665691 + 0.250565i
\(111\) 0 0
\(112\) 10.4540 + 1.64762i 0.987807 + 0.155686i
\(113\) 11.7870i 1.10882i 0.832242 + 0.554412i \(0.187057\pi\)
−0.832242 + 0.554412i \(0.812943\pi\)
\(114\) 0 0
\(115\) 3.28891 + 1.89885i 0.306692 + 0.177069i
\(116\) 12.6733 14.4498i 1.17669 1.34163i
\(117\) 0 0
\(118\) 4.49867 + 5.48189i 0.414136 + 0.504649i
\(119\) −3.25533 + 3.09444i −0.298416 + 0.283667i
\(120\) 0 0
\(121\) −6.40444 11.0928i −0.582222 1.00844i
\(122\) −19.1359 + 3.15891i −1.73248 + 0.285994i
\(123\) 0 0
\(124\) 5.74436 + 16.9248i 0.515859 + 1.51990i
\(125\) 9.54728i 0.853934i
\(126\) 0 0
\(127\) 5.46528i 0.484966i 0.970156 + 0.242483i \(0.0779618\pi\)
−0.970156 + 0.242483i \(0.922038\pi\)
\(128\) 6.58854 + 9.19735i 0.582350 + 0.812938i
\(129\) 0 0
\(130\) −0.203193 1.23090i −0.0178212 0.107957i
\(131\) −7.94069 13.7537i −0.693782 1.20167i −0.970590 0.240740i \(-0.922610\pi\)
0.276808 0.960925i \(-0.410723\pi\)
\(132\) 0 0
\(133\) 2.56752 + 10.6547i 0.222633 + 0.923879i
\(134\) −4.63061 + 3.80007i −0.400024 + 0.328276i
\(135\) 0 0
\(136\) −4.79894 0.157424i −0.411505 0.0134990i
\(137\) −10.7072 6.18180i −0.914777 0.528147i −0.0328121 0.999462i \(-0.510446\pi\)
−0.881965 + 0.471315i \(0.843780\pi\)
\(138\) 0 0
\(139\) 17.2243i 1.46095i 0.682941 + 0.730473i \(0.260701\pi\)
−0.682941 + 0.730473i \(0.739299\pi\)
\(140\) 2.65949 5.06472i 0.224768 0.428047i
\(141\) 0 0
\(142\) 5.90633 15.6917i 0.495648 1.31682i
\(143\) −1.99080 + 3.44817i −0.166479 + 0.288350i
\(144\) 0 0
\(145\) −5.19459 8.99729i −0.431387 0.747184i
\(146\) −2.68743 3.27479i −0.222413 0.271024i
\(147\) 0 0
\(148\) −2.63804 + 13.2592i −0.216846 + 1.08990i
\(149\) 9.97002 5.75619i 0.816776 0.471566i −0.0325274 0.999471i \(-0.510356\pi\)
0.849303 + 0.527905i \(0.177022\pi\)
\(150\) 0 0
\(151\) 9.30760 + 5.37375i 0.757442 + 0.437309i 0.828377 0.560172i \(-0.189265\pi\)
−0.0709346 + 0.997481i \(0.522598\pi\)
\(152\) −6.18772 + 9.94917i −0.501890 + 0.806984i
\(153\) 0 0
\(154\) −16.8155 + 7.11085i −1.35503 + 0.573008i
\(155\) 9.66109 0.775998
\(156\) 0 0
\(157\) 11.7042 20.2723i 0.934099 1.61791i 0.157865 0.987461i \(-0.449539\pi\)
0.776233 0.630446i \(-0.217128\pi\)
\(158\) −0.908337 5.50248i −0.0722634 0.437754i
\(159\) 0 0
\(160\) 5.85236 1.77458i 0.462669 0.140292i
\(161\) −9.03560 + 2.17736i −0.712105 + 0.171600i
\(162\) 0 0
\(163\) −2.35163 + 1.35771i −0.184193 + 0.106344i −0.589261 0.807942i \(-0.700581\pi\)
0.405068 + 0.914287i \(0.367248\pi\)
\(164\) 9.18736 10.4752i 0.717412 0.817978i
\(165\) 0 0
\(166\) 5.64577 14.9994i 0.438197 1.16418i
\(167\) 6.84595 0.529756 0.264878 0.964282i \(-0.414668\pi\)
0.264878 + 0.964282i \(0.414668\pi\)
\(168\) 0 0
\(169\) −12.3341 −0.948781
\(170\) −0.914285 + 2.42903i −0.0701224 + 0.186298i
\(171\) 0 0
\(172\) −0.672885 + 0.767209i −0.0513070 + 0.0584991i
\(173\) −7.19348 + 4.15316i −0.546910 + 0.315759i −0.747875 0.663840i \(-0.768926\pi\)
0.200965 + 0.979599i \(0.435592\pi\)
\(174\) 0 0
\(175\) 6.98381 + 7.34691i 0.527926 + 0.555374i
\(176\) −18.0314 7.47073i −1.35917 0.563128i
\(177\) 0 0
\(178\) 0.0833654 + 0.505007i 0.00624850 + 0.0378519i
\(179\) −10.4832 + 18.1575i −0.783554 + 1.35716i 0.146304 + 0.989240i \(0.453262\pi\)
−0.929859 + 0.367917i \(0.880071\pi\)
\(180\) 0 0
\(181\) 17.8558 1.32721 0.663605 0.748083i \(-0.269026\pi\)
0.663605 + 0.748083i \(0.269026\pi\)
\(182\) 2.43589 + 1.84076i 0.180560 + 0.136446i
\(183\) 0 0
\(184\) −8.43729 5.24743i −0.622005 0.386846i
\(185\) 6.32856 + 3.65380i 0.465285 + 0.268633i
\(186\) 0 0
\(187\) 7.17354 4.14165i 0.524581 0.302867i
\(188\) −2.65989 + 13.3690i −0.193992 + 0.975037i
\(189\) 0 0
\(190\) 4.01760 + 4.89568i 0.291467 + 0.355170i
\(191\) 9.10942 + 15.7780i 0.659135 + 1.14165i 0.980840 + 0.194815i \(0.0624106\pi\)
−0.321705 + 0.946840i \(0.604256\pi\)
\(192\) 0 0
\(193\) −9.35386 + 16.2014i −0.673306 + 1.16620i 0.303655 + 0.952782i \(0.401793\pi\)
−0.976961 + 0.213418i \(0.931540\pi\)
\(194\) −4.04865 + 10.7563i −0.290676 + 0.772255i
\(195\) 0 0
\(196\) 3.82241 + 13.4681i 0.273029 + 0.962006i
\(197\) 22.2223i 1.58327i 0.610994 + 0.791635i \(0.290770\pi\)
−0.610994 + 0.791635i \(0.709230\pi\)
\(198\) 0 0
\(199\) 13.8519 + 7.99738i 0.981934 + 0.566920i 0.902853 0.429949i \(-0.141468\pi\)
0.0790802 + 0.996868i \(0.474802\pi\)
\(200\) −0.355289 + 10.8307i −0.0251227 + 0.765843i
\(201\) 0 0
\(202\) 1.66676 1.36781i 0.117273 0.0962391i
\(203\) 24.3848 + 7.20063i 1.71148 + 0.505385i
\(204\) 0 0
\(205\) −3.76575 6.52247i −0.263011 0.455549i
\(206\) 1.78200 + 10.7949i 0.124158 + 0.752120i
\(207\) 0 0
\(208\) 0.425745 + 3.23610i 0.0295201 + 0.224383i
\(209\) 20.2124i 1.39812i
\(210\) 0 0
\(211\) 8.32079i 0.572827i −0.958106 0.286414i \(-0.907537\pi\)
0.958106 0.286414i \(-0.0924631\pi\)
\(212\) 2.22584 + 6.55809i 0.152872 + 0.450411i
\(213\) 0 0
\(214\) −1.68257 + 0.277754i −0.115018 + 0.0189869i
\(215\) 0.275804 + 0.477707i 0.0188097 + 0.0325794i
\(216\) 0 0
\(217\) −17.1369 + 16.2899i −1.16333 + 1.10583i
\(218\) 0.563704 + 0.686906i 0.0381788 + 0.0465232i
\(219\) 0 0
\(220\) −6.95650 + 7.93165i −0.469007 + 0.534752i
\(221\) −1.19965 0.692615i −0.0806969 0.0465904i
\(222\) 0 0
\(223\) 8.91285i 0.596848i −0.954433 0.298424i \(-0.903539\pi\)
0.954433 0.298424i \(-0.0964610\pi\)
\(224\) −7.38875 + 13.0156i −0.493681 + 0.869643i
\(225\) 0 0
\(226\) −15.6007 5.87210i −1.03775 0.390607i
\(227\) 10.2145 17.6920i 0.677957 1.17426i −0.297638 0.954679i \(-0.596199\pi\)
0.975595 0.219578i \(-0.0704679\pi\)
\(228\) 0 0
\(229\) 6.21367 + 10.7624i 0.410611 + 0.711199i 0.994957 0.100306i \(-0.0319821\pi\)
−0.584346 + 0.811505i \(0.698649\pi\)
\(230\) −4.15173 + 3.40708i −0.273757 + 0.224657i
\(231\) 0 0
\(232\) 12.8116 + 23.9726i 0.841120 + 1.57388i
\(233\) 2.18246 1.26005i 0.142978 0.0825484i −0.426805 0.904344i \(-0.640361\pi\)
0.569783 + 0.821796i \(0.307027\pi\)
\(234\) 0 0
\(235\) 6.38097 + 3.68405i 0.416249 + 0.240321i
\(236\) −9.49679 + 3.22325i −0.618188 + 0.209816i
\(237\) 0 0
\(238\) −2.47392 5.85023i −0.160360 0.379214i
\(239\) 25.2624 1.63409 0.817045 0.576574i \(-0.195611\pi\)
0.817045 + 0.576574i \(0.195611\pi\)
\(240\) 0 0
\(241\) 7.31705 12.6735i 0.471333 0.816372i −0.528130 0.849164i \(-0.677106\pi\)
0.999462 + 0.0327917i \(0.0104398\pi\)
\(242\) 17.8726 2.95037i 1.14889 0.189657i
\(243\) 0 0
\(244\) 5.35225 26.9013i 0.342643 1.72218i
\(245\) 7.55782 + 0.383236i 0.482851 + 0.0244841i
\(246\) 0 0
\(247\) −2.92731 + 1.69008i −0.186260 + 0.107537i
\(248\) −25.2628 0.828722i −1.60419 0.0526239i
\(249\) 0 0
\(250\) 12.6364 + 4.75632i 0.799195 + 0.300816i
\(251\) −11.3947 −0.719227 −0.359613 0.933101i \(-0.617091\pi\)
−0.359613 + 0.933101i \(0.617091\pi\)
\(252\) 0 0
\(253\) 17.1409 1.07764
\(254\) −7.23363 2.72273i −0.453878 0.170839i
\(255\) 0 0
\(256\) −15.4556 + 4.13833i −0.965972 + 0.258646i
\(257\) 19.8884 11.4826i 1.24060 0.716263i 0.271386 0.962471i \(-0.412518\pi\)
0.969217 + 0.246208i \(0.0791846\pi\)
\(258\) 0 0
\(259\) −17.3864 + 4.18971i −1.08034 + 0.260336i
\(260\) 1.73039 + 0.344277i 0.107314 + 0.0213512i
\(261\) 0 0
\(262\) 22.1598 3.65808i 1.36904 0.225997i
\(263\) −11.6566 + 20.1898i −0.718775 + 1.24495i 0.242711 + 0.970099i \(0.421963\pi\)
−0.961485 + 0.274856i \(0.911370\pi\)
\(264\) 0 0
\(265\) 3.74351 0.229962
\(266\) −15.3812 1.90975i −0.943084 0.117094i
\(267\) 0 0
\(268\) −2.72271 8.02203i −0.166316 0.490024i
\(269\) −25.3140 14.6150i −1.54342 0.891094i −0.998619 0.0525290i \(-0.983272\pi\)
−0.544801 0.838565i \(-0.683395\pi\)
\(270\) 0 0
\(271\) −0.829286 + 0.478788i −0.0503755 + 0.0290843i −0.524976 0.851117i \(-0.675926\pi\)
0.474601 + 0.880201i \(0.342592\pi\)
\(272\) 2.59913 6.27325i 0.157595 0.380372i
\(273\) 0 0
\(274\) 13.5162 11.0919i 0.816541 0.670087i
\(275\) −9.34723 16.1899i −0.563659 0.976286i
\(276\) 0 0
\(277\) −6.06856 + 10.5111i −0.364624 + 0.631548i −0.988716 0.149803i \(-0.952136\pi\)
0.624091 + 0.781351i \(0.285469\pi\)
\(278\) −22.7974 8.58092i −1.36730 0.514649i
\(279\) 0 0
\(280\) 5.37854 + 6.04317i 0.321429 + 0.361148i
\(281\) 23.7714i 1.41808i −0.705168 0.709041i \(-0.749128\pi\)
0.705168 0.709041i \(-0.250872\pi\)
\(282\) 0 0
\(283\) −2.93570 1.69493i −0.174509 0.100753i 0.410201 0.911995i \(-0.365458\pi\)
−0.584710 + 0.811242i \(0.698792\pi\)
\(284\) 17.8264 + 15.6347i 1.05780 + 0.927752i
\(285\) 0 0
\(286\) −3.57207 4.35278i −0.211221 0.257385i
\(287\) 17.6775 + 5.22000i 1.04347 + 0.308127i
\(288\) 0 0
\(289\) −7.05909 12.2267i −0.415241 0.719218i
\(290\) 14.4963 2.39302i 0.851253 0.140523i
\(291\) 0 0
\(292\) 5.67322 1.92552i 0.332000 0.112682i
\(293\) 14.2017i 0.829673i −0.909896 0.414837i \(-0.863839\pi\)
0.909896 0.414837i \(-0.136161\pi\)
\(294\) 0 0
\(295\) 5.42099i 0.315622i
\(296\) −16.2351 10.0972i −0.943649 0.586887i
\(297\) 0 0
\(298\) 2.65174 + 16.0636i 0.153611 + 0.930538i
\(299\) −1.43326 2.48247i −0.0828873 0.143565i
\(300\) 0 0
\(301\) −1.29470 0.382315i −0.0746254 0.0220362i
\(302\) −11.7494 + 9.64204i −0.676102 + 0.554837i
\(303\) 0 0
\(304\) −10.0857 13.1464i −0.578454 0.753995i
\(305\) −12.8398 7.41308i −0.735206 0.424472i
\(306\) 0 0
\(307\) 25.7078i 1.46722i −0.679571 0.733610i \(-0.737834\pi\)
0.679571 0.733610i \(-0.262166\pi\)
\(308\) −1.03439 25.7988i −0.0589399 1.47002i
\(309\) 0 0
\(310\) −4.81303 + 12.7870i −0.273362 + 0.726255i
\(311\) 4.39864 7.61867i 0.249424 0.432015i −0.713942 0.700205i \(-0.753092\pi\)
0.963366 + 0.268190i \(0.0864254\pi\)
\(312\) 0 0
\(313\) −6.87877 11.9144i −0.388811 0.673440i 0.603479 0.797379i \(-0.293781\pi\)
−0.992290 + 0.123939i \(0.960447\pi\)
\(314\) 21.0007 + 25.5906i 1.18514 + 1.44416i
\(315\) 0 0
\(316\) 7.73539 + 1.53902i 0.435149 + 0.0865769i
\(317\) 9.53960 5.50769i 0.535797 0.309343i −0.207577 0.978219i \(-0.566558\pi\)
0.743374 + 0.668876i \(0.233224\pi\)
\(318\) 0 0
\(319\) −40.6092 23.4458i −2.27368 1.31271i
\(320\) −0.566808 + 8.63001i −0.0316855 + 0.482432i
\(321\) 0 0
\(322\) 1.61955 13.0439i 0.0902538 0.726908i
\(323\) 7.03206 0.391274
\(324\) 0 0
\(325\) −1.56316 + 2.70746i −0.0867082 + 0.150183i
\(326\) −0.625464 3.78891i −0.0346413 0.209848i
\(327\) 0 0
\(328\) 9.28757 + 17.3786i 0.512820 + 0.959574i
\(329\) −17.5304 + 4.22440i −0.966483 + 0.232899i
\(330\) 0 0
\(331\) −2.42290 + 1.39886i −0.133175 + 0.0768884i −0.565107 0.825017i \(-0.691165\pi\)
0.431933 + 0.901906i \(0.357832\pi\)
\(332\) 17.0400 + 14.9450i 0.935191 + 0.820215i
\(333\) 0 0
\(334\) −3.41056 + 9.06103i −0.186618 + 0.495797i
\(335\) −4.57916 −0.250186
\(336\) 0 0
\(337\) −3.38341 −0.184306 −0.0921530 0.995745i \(-0.529375\pi\)
−0.0921530 + 0.995745i \(0.529375\pi\)
\(338\) 6.14471 16.3250i 0.334228 0.887962i
\(339\) 0 0
\(340\) −2.75948 2.42022i −0.149654 0.131255i
\(341\) 37.7633 21.8027i 2.04500 1.18068i
\(342\) 0 0
\(343\) −14.0523 + 12.0637i −0.758751 + 0.651380i
\(344\) −0.680224 1.27282i −0.0366752 0.0686257i
\(345\) 0 0
\(346\) −1.91326 11.5901i −0.102857 0.623085i
\(347\) 1.96566 3.40462i 0.105522 0.182770i −0.808429 0.588593i \(-0.799682\pi\)
0.913951 + 0.405824i \(0.133015\pi\)
\(348\) 0 0
\(349\) 16.1233 0.863058 0.431529 0.902099i \(-0.357974\pi\)
0.431529 + 0.902099i \(0.357974\pi\)
\(350\) −13.2033 + 5.58336i −0.705747 + 0.298443i
\(351\) 0 0
\(352\) 18.8709 20.1438i 1.00582 1.07367i
\(353\) 32.2263 + 18.6059i 1.71523 + 0.990290i 0.927126 + 0.374750i \(0.122272\pi\)
0.788106 + 0.615539i \(0.211062\pi\)
\(354\) 0 0
\(355\) 11.0997 6.40843i 0.589112 0.340124i
\(356\) −0.709939 0.141249i −0.0376267 0.00748617i
\(357\) 0 0
\(358\) −18.8099 22.9210i −0.994136 1.21141i
\(359\) −10.7770 18.6664i −0.568790 0.985173i −0.996686 0.0813452i \(-0.974078\pi\)
0.427896 0.903828i \(-0.359255\pi\)
\(360\) 0 0
\(361\) −0.920383 + 1.59415i −0.0484412 + 0.0839026i
\(362\) −8.89551 + 23.6332i −0.467538 + 1.24213i
\(363\) 0 0
\(364\) −3.64988 + 2.30700i −0.191305 + 0.120920i
\(365\) 3.23841i 0.169506i
\(366\) 0 0
\(367\) 1.45961 + 0.842704i 0.0761908 + 0.0439888i 0.537611 0.843193i \(-0.319327\pi\)
−0.461421 + 0.887182i \(0.652660\pi\)
\(368\) 11.1486 8.55306i 0.581163 0.445859i
\(369\) 0 0
\(370\) −7.98882 + 6.55596i −0.415319 + 0.340828i
\(371\) −6.64025 + 6.31207i −0.344744 + 0.327706i
\(372\) 0 0
\(373\) 2.14560 + 3.71630i 0.111095 + 0.192422i 0.916212 0.400694i \(-0.131231\pi\)
−0.805117 + 0.593116i \(0.797897\pi\)
\(374\) 1.90795 + 11.5579i 0.0986579 + 0.597646i
\(375\) 0 0
\(376\) −16.3696 10.1808i −0.844197 0.525035i
\(377\) 7.84176i 0.403871i
\(378\) 0 0
\(379\) 3.00059i 0.154130i −0.997026 0.0770650i \(-0.975445\pi\)
0.997026 0.0770650i \(-0.0245549\pi\)
\(380\) −8.48124 + 2.87857i −0.435079 + 0.147668i
\(381\) 0 0
\(382\) −25.4213 + 4.19649i −1.30067 + 0.214711i
\(383\) −10.5636 18.2967i −0.539774 0.934916i −0.998916 0.0465530i \(-0.985176\pi\)
0.459142 0.888363i \(-0.348157\pi\)
\(384\) 0 0
\(385\) −13.3851 3.95249i −0.682166 0.201438i
\(386\) −16.7835 20.4517i −0.854258 1.04096i
\(387\) 0 0
\(388\) −12.2196 10.7172i −0.620355 0.544086i
\(389\) −29.5830 17.0798i −1.49992 0.865979i −0.499920 0.866072i \(-0.666637\pi\)
−1.00000 9.28896e-5i \(0.999970\pi\)
\(390\) 0 0
\(391\) 5.96347i 0.301585i
\(392\) −19.7301 1.65043i −0.996520 0.0833593i
\(393\) 0 0
\(394\) −29.4125 11.0708i −1.48178 0.557740i
\(395\) 2.13161 3.69206i 0.107253 0.185768i
\(396\) 0 0
\(397\) 8.42503 + 14.5926i 0.422840 + 0.732380i 0.996216 0.0869120i \(-0.0276999\pi\)
−0.573376 + 0.819292i \(0.694367\pi\)
\(398\) −17.4858 + 14.3496i −0.876486 + 0.719280i
\(399\) 0 0
\(400\) −14.1580 5.86593i −0.707901 0.293297i
\(401\) 8.58950 4.95915i 0.428939 0.247648i −0.269956 0.962873i \(-0.587009\pi\)
0.698894 + 0.715225i \(0.253676\pi\)
\(402\) 0 0
\(403\) −6.31524 3.64610i −0.314584 0.181625i
\(404\) 0.980025 + 2.88749i 0.0487581 + 0.143658i
\(405\) 0 0
\(406\) −21.6787 + 28.6875i −1.07589 + 1.42374i
\(407\) 32.9828 1.63490
\(408\) 0 0
\(409\) −18.0859 + 31.3257i −0.894291 + 1.54896i −0.0596111 + 0.998222i \(0.518986\pi\)
−0.834680 + 0.550736i \(0.814347\pi\)
\(410\) 10.5089 1.73479i 0.518998 0.0856750i
\(411\) 0 0
\(412\) −15.1755 3.01931i −0.747645 0.148751i
\(413\) −9.14053 9.61576i −0.449776 0.473161i
\(414\) 0 0
\(415\) 10.6101 6.12572i 0.520828 0.300700i
\(416\) −4.49528 1.04868i −0.220399 0.0514159i
\(417\) 0 0
\(418\) 26.7523 + 10.0696i 1.30850 + 0.492518i
\(419\) 30.7098 1.50027 0.750137 0.661283i \(-0.229988\pi\)
0.750137 + 0.661283i \(0.229988\pi\)
\(420\) 0 0
\(421\) 10.9036 0.531411 0.265706 0.964054i \(-0.414395\pi\)
0.265706 + 0.964054i \(0.414395\pi\)
\(422\) 11.0131 + 4.14531i 0.536108 + 0.201790i
\(423\) 0 0
\(424\) −9.78891 0.321116i −0.475391 0.0155947i
\(425\) 5.63258 3.25197i 0.273220 0.157744i
\(426\) 0 0
\(427\) 35.2748 8.50037i 1.70707 0.411362i
\(428\) 0.470608 2.36535i 0.0227477 0.114334i
\(429\) 0 0
\(430\) −0.769676 + 0.127056i −0.0371171 + 0.00612720i
\(431\) −7.83169 + 13.5649i −0.377239 + 0.653398i −0.990659 0.136359i \(-0.956460\pi\)
0.613420 + 0.789757i \(0.289793\pi\)
\(432\) 0 0
\(433\) −22.8956 −1.10029 −0.550145 0.835069i \(-0.685428\pi\)
−0.550145 + 0.835069i \(0.685428\pi\)
\(434\) −13.0233 30.7971i −0.625140 1.47831i
\(435\) 0 0
\(436\) −1.18999 + 0.403888i −0.0569902 + 0.0193427i
\(437\) 12.6022 + 7.27586i 0.602843 + 0.348051i
\(438\) 0 0
\(439\) −14.9901 + 8.65454i −0.715438 + 0.413059i −0.813071 0.582164i \(-0.802206\pi\)
0.0976331 + 0.995222i \(0.468873\pi\)
\(440\) −7.03238 13.1588i −0.335256 0.627321i
\(441\) 0 0
\(442\) 1.51436 1.24275i 0.0720310 0.0591116i
\(443\) 5.69268 + 9.86000i 0.270467 + 0.468463i 0.968982 0.247133i \(-0.0794885\pi\)
−0.698514 + 0.715596i \(0.746155\pi\)
\(444\) 0 0
\(445\) −0.195635 + 0.338850i −0.00927400 + 0.0160630i
\(446\) 11.7967 + 4.44026i 0.558589 + 0.210252i
\(447\) 0 0
\(448\) −13.5460 16.2637i −0.639987 0.768386i
\(449\) 11.1088i 0.524258i −0.965033 0.262129i \(-0.915575\pi\)
0.965033 0.262129i \(-0.0844245\pi\)
\(450\) 0 0
\(451\) −29.4391 16.9967i −1.38624 0.800343i
\(452\) 15.5442 17.7231i 0.731136 0.833625i
\(453\) 0 0
\(454\) 18.3277 + 22.3333i 0.860160 + 1.04816i
\(455\) 0.546777 + 2.26901i 0.0256333 + 0.106373i
\(456\) 0 0
\(457\) −13.5658 23.4967i −0.634582 1.09913i −0.986604 0.163136i \(-0.947839\pi\)
0.352022 0.935992i \(-0.385494\pi\)
\(458\) −17.3402 + 2.86248i −0.810256 + 0.133755i
\(459\) 0 0
\(460\) −2.44114 7.19243i −0.113819 0.335349i
\(461\) 13.2528i 0.617246i −0.951184 0.308623i \(-0.900132\pi\)
0.951184 0.308623i \(-0.0998682\pi\)
\(462\) 0 0
\(463\) 4.07186i 0.189235i 0.995514 + 0.0946176i \(0.0301629\pi\)
−0.995514 + 0.0946176i \(0.969837\pi\)
\(464\) −38.1117 + 5.01402i −1.76929 + 0.232770i
\(465\) 0 0
\(466\) 0.580472 + 3.51636i 0.0268899 + 0.162892i
\(467\) 11.7529 + 20.3565i 0.543857 + 0.941988i 0.998678 + 0.0514053i \(0.0163700\pi\)
−0.454821 + 0.890583i \(0.650297\pi\)
\(468\) 0 0
\(469\) 8.12253 7.72109i 0.375064 0.356527i
\(470\) −8.05498 + 6.61025i −0.371549 + 0.304908i
\(471\) 0 0
\(472\) 0.465008 14.1753i 0.0214037 0.652473i
\(473\) 2.15613 + 1.24484i 0.0991390 + 0.0572380i
\(474\) 0 0
\(475\) 15.8706i 0.728191i
\(476\) 8.97560 0.359872i 0.411396 0.0164947i
\(477\) 0 0
\(478\) −12.5854 + 33.4363i −0.575643 + 1.52934i
\(479\) 1.86090 3.22317i 0.0850266 0.147270i −0.820376 0.571825i \(-0.806236\pi\)
0.905403 + 0.424554i \(0.139569\pi\)
\(480\) 0 0
\(481\) −2.75789 4.77681i −0.125749 0.217804i
\(482\) 13.1289 + 15.9983i 0.598004 + 0.728704i
\(483\) 0 0
\(484\) −4.99890 + 25.1253i −0.227223 + 1.14206i
\(485\) −7.60860 + 4.39283i −0.345489 + 0.199468i
\(486\) 0 0
\(487\) 14.5697 + 8.41182i 0.660216 + 0.381176i 0.792359 0.610055i \(-0.208853\pi\)
−0.132143 + 0.991231i \(0.542186\pi\)
\(488\) 32.9390 + 20.4859i 1.49108 + 0.927352i
\(489\) 0 0
\(490\) −4.27244 + 9.81230i −0.193009 + 0.443275i
\(491\) −6.75735 −0.304955 −0.152477 0.988307i \(-0.548725\pi\)
−0.152477 + 0.988307i \(0.548725\pi\)
\(492\) 0 0
\(493\) 8.15696 14.1283i 0.367371 0.636305i
\(494\) −0.778579 4.71644i −0.0350299 0.212203i
\(495\) 0 0
\(496\) 13.6825 33.0240i 0.614360 1.48282i
\(497\) −8.88323 + 30.0829i −0.398467 + 1.34940i
\(498\) 0 0
\(499\) −14.9780 + 8.64752i −0.670505 + 0.387116i −0.796268 0.604944i \(-0.793195\pi\)
0.125763 + 0.992060i \(0.459862\pi\)
\(500\) −12.5906 + 14.3555i −0.563067 + 0.641997i
\(501\) 0 0
\(502\) 5.67668 15.0816i 0.253363 0.673123i
\(503\) −6.05186 −0.269839 −0.134920 0.990857i \(-0.543078\pi\)
−0.134920 + 0.990857i \(0.543078\pi\)
\(504\) 0 0
\(505\) 1.64824 0.0733459
\(506\) −8.53938 + 22.6871i −0.379622 + 1.00856i
\(507\) 0 0
\(508\) 7.20739 8.21771i 0.319776 0.364602i
\(509\) −15.4989 + 8.94831i −0.686978 + 0.396627i −0.802479 0.596681i \(-0.796486\pi\)
0.115501 + 0.993307i \(0.463153\pi\)
\(510\) 0 0
\(511\) 5.46040 + 5.74429i 0.241554 + 0.254113i
\(512\) 2.22242 22.5180i 0.0982182 0.995165i
\(513\) 0 0
\(514\) 5.28973 + 32.0439i 0.233320 + 1.41340i
\(515\) −4.18186 + 7.24320i −0.184275 + 0.319173i
\(516\) 0 0
\(517\) 33.2560 1.46260
\(518\) 3.11635 25.0992i 0.136925 1.10280i
\(519\) 0 0
\(520\) −1.31773 + 2.11876i −0.0577863 + 0.0929140i
\(521\) 6.17964 + 3.56782i 0.270735 + 0.156309i 0.629222 0.777226i \(-0.283374\pi\)
−0.358487 + 0.933535i \(0.616707\pi\)
\(522\) 0 0
\(523\) −37.1480 + 21.4474i −1.62437 + 0.937830i −0.638638 + 0.769507i \(0.720502\pi\)
−0.985732 + 0.168323i \(0.946165\pi\)
\(524\) −6.19801 + 31.1522i −0.270761 + 1.36089i
\(525\) 0 0
\(526\) −20.9152 25.4864i −0.911947 1.11126i
\(527\) 7.58532 + 13.1382i 0.330422 + 0.572307i
\(528\) 0 0
\(529\) 5.32978 9.23146i 0.231730 0.401368i
\(530\) −1.86497 + 4.95476i −0.0810089 + 0.215221i
\(531\) 0 0
\(532\) 10.1904 19.4066i 0.441810 0.841381i
\(533\) 5.68478i 0.246235i
\(534\) 0 0
\(535\) −1.12897 0.651811i −0.0488096 0.0281803i
\(536\) 11.9741 + 0.392797i 0.517200 + 0.0169663i
\(537\) 0 0
\(538\) 31.9550 26.2235i 1.37768 1.13058i
\(539\) 30.4069 15.5581i 1.30972 0.670135i
\(540\) 0 0
\(541\) 6.68983 + 11.5871i 0.287618 + 0.498170i 0.973241 0.229788i \(-0.0738032\pi\)
−0.685622 + 0.727957i \(0.740470\pi\)
\(542\) −0.220566 1.33614i −0.00947412 0.0573919i
\(543\) 0 0
\(544\) 7.00817 + 6.56535i 0.300473 + 0.281487i
\(545\) 0.679274i 0.0290969i
\(546\) 0 0
\(547\) 16.1576i 0.690849i −0.938447 0.345424i \(-0.887735\pi\)
0.938447 0.345424i \(-0.112265\pi\)
\(548\) 7.94725 + 23.4153i 0.339490 + 1.00025i
\(549\) 0 0
\(550\) 26.0849 4.30604i 1.11226 0.183610i
\(551\) −19.9042 34.4750i −0.847946 1.46869i
\(552\) 0 0
\(553\) 2.44426 + 10.1432i 0.103940 + 0.431332i
\(554\) −10.8887 13.2686i −0.462618 0.563727i
\(555\) 0 0
\(556\) 22.7147 25.8988i 0.963318 1.09835i
\(557\) −4.80203 2.77245i −0.203469 0.117473i 0.394804 0.918765i \(-0.370813\pi\)
−0.598272 + 0.801293i \(0.704146\pi\)
\(558\) 0 0
\(559\) 0.416355i 0.0176099i
\(560\) −10.6780 + 4.10820i −0.451228 + 0.173603i
\(561\) 0 0
\(562\) 31.4628 + 11.8426i 1.32718 + 0.499549i
\(563\) −21.7530 + 37.6772i −0.916778 + 1.58791i −0.112501 + 0.993652i \(0.535886\pi\)
−0.804277 + 0.594255i \(0.797447\pi\)
\(564\) 0 0
\(565\) −6.37130 11.0354i −0.268042 0.464263i
\(566\) 3.70586 3.04118i 0.155769 0.127830i
\(567\) 0 0
\(568\) −29.5744 + 15.8053i −1.24091 + 0.663175i
\(569\) −31.6927 + 18.2978i −1.32863 + 0.767083i −0.985087 0.172056i \(-0.944959\pi\)
−0.343539 + 0.939138i \(0.611626\pi\)
\(570\) 0 0
\(571\) 17.5668 + 10.1422i 0.735148 + 0.424438i 0.820303 0.571930i \(-0.193805\pi\)
−0.0851545 + 0.996368i \(0.527138\pi\)
\(572\) 7.54072 2.55935i 0.315293 0.107012i
\(573\) 0 0
\(574\) −15.7157 + 20.7966i −0.655959 + 0.868035i
\(575\) 13.4589 0.561274
\(576\) 0 0
\(577\) 4.86675 8.42945i 0.202605 0.350923i −0.746762 0.665092i \(-0.768392\pi\)
0.949367 + 0.314169i \(0.101726\pi\)
\(578\) 19.6995 3.25195i 0.819392 0.135263i
\(579\) 0 0
\(580\) −4.05457 + 20.3789i −0.168357 + 0.846188i
\(581\) −8.49135 + 28.7559i −0.352281 + 1.19299i
\(582\) 0 0
\(583\) 14.6326 8.44816i 0.606022 0.349887i
\(584\) −0.277788 + 8.46811i −0.0114950 + 0.350413i
\(585\) 0 0
\(586\) 18.7968 + 7.07510i 0.776489 + 0.292270i
\(587\) −32.9781 −1.36115 −0.680576 0.732678i \(-0.738270\pi\)
−0.680576 + 0.732678i \(0.738270\pi\)
\(588\) 0 0
\(589\) 37.0185 1.52532
\(590\) −7.17500 2.70066i −0.295390 0.111184i
\(591\) 0 0
\(592\) 21.4524 16.4579i 0.881686 0.676416i
\(593\) 30.7424 17.7491i 1.26244 0.728869i 0.288892 0.957362i \(-0.406713\pi\)
0.973546 + 0.228493i \(0.0733798\pi\)
\(594\) 0 0
\(595\) 1.37510 4.65677i 0.0563737 0.190909i
\(596\) −22.5822 4.49293i −0.925001 0.184037i
\(597\) 0 0
\(598\) 3.99973 0.660266i 0.163561 0.0270003i
\(599\) −14.8924 + 25.7944i −0.608488 + 1.05393i 0.383002 + 0.923748i \(0.374890\pi\)
−0.991490 + 0.130185i \(0.958443\pi\)
\(600\) 0 0
\(601\) −46.8743 −1.91204 −0.956021 0.293298i \(-0.905247\pi\)
−0.956021 + 0.293298i \(0.905247\pi\)
\(602\) 1.15102 1.52315i 0.0469121 0.0620791i
\(603\) 0 0
\(604\) −6.90842 20.3546i −0.281100 0.828215i
\(605\) 11.9922 + 6.92368i 0.487551 + 0.281488i
\(606\) 0 0
\(607\) 19.2150 11.0938i 0.779912 0.450283i −0.0564869 0.998403i \(-0.517990\pi\)
0.836399 + 0.548121i \(0.184657\pi\)
\(608\) 22.4245 6.79966i 0.909435 0.275763i
\(609\) 0 0
\(610\) 16.2083 13.3012i 0.656254 0.538549i
\(611\) −2.78073 4.81636i −0.112496 0.194849i
\(612\) 0 0
\(613\) −6.05599 + 10.4893i −0.244599 + 0.423658i −0.962019 0.272983i \(-0.911990\pi\)
0.717420 + 0.696641i \(0.245323\pi\)
\(614\) 34.0258 + 12.8073i 1.37317 + 0.516859i
\(615\) 0 0
\(616\) 34.6616 + 11.4835i 1.39655 + 0.462685i
\(617\) 19.5363i 0.786501i −0.919431 0.393250i \(-0.871351\pi\)
0.919431 0.393250i \(-0.128649\pi\)
\(618\) 0 0
\(619\) 0.819203 + 0.472967i 0.0329265 + 0.0190102i 0.516373 0.856364i \(-0.327282\pi\)
−0.483446 + 0.875374i \(0.660615\pi\)
\(620\) −14.5266 12.7407i −0.583403 0.511677i
\(621\) 0 0
\(622\) 7.89242 + 9.61738i 0.316457 + 0.385622i
\(623\) −0.224329 0.930921i −0.00898757 0.0372966i
\(624\) 0 0
\(625\) −4.41753 7.65138i −0.176701 0.306055i
\(626\) 19.1963 3.16888i 0.767238 0.126654i
\(627\) 0 0
\(628\) −44.3330 + 15.0468i −1.76908 + 0.600433i
\(629\) 11.4750i 0.457537i
\(630\) 0 0
\(631\) 6.23847i 0.248350i 0.992260 + 0.124175i \(0.0396284\pi\)
−0.992260 + 0.124175i \(0.960372\pi\)
\(632\) −5.89066 + 9.47152i −0.234318 + 0.376757i
\(633\) 0 0
\(634\) 2.53726 + 15.3701i 0.100767 + 0.610424i
\(635\) −2.95419 5.11681i −0.117234 0.203054i
\(636\) 0 0
\(637\) −4.79574 3.10284i −0.190014 0.122939i
\(638\) 51.2628 42.0684i 2.02952 1.66550i
\(639\) 0 0
\(640\) −11.1400 5.04956i −0.440346 0.199601i
\(641\) −6.36278 3.67355i −0.251315 0.145097i 0.369051 0.929409i \(-0.379683\pi\)
−0.620366 + 0.784312i \(0.713016\pi\)
\(642\) 0 0
\(643\) 44.8033i 1.76687i 0.468553 + 0.883436i \(0.344776\pi\)
−0.468553 + 0.883436i \(0.655224\pi\)
\(644\) 16.4575 + 8.64186i 0.648518 + 0.340537i
\(645\) 0 0
\(646\) −3.50328 + 9.30735i −0.137835 + 0.366193i
\(647\) 4.89449 8.47750i 0.192422 0.333285i −0.753630 0.657299i \(-0.771699\pi\)
0.946052 + 0.324014i \(0.105032\pi\)
\(648\) 0 0
\(649\) 12.2338 + 21.1896i 0.480219 + 0.831764i
\(650\) −2.80475 3.41775i −0.110011 0.134055i
\(651\) 0 0
\(652\) 5.32645 + 1.05974i 0.208600 + 0.0415028i
\(653\) −0.378115 + 0.218305i −0.0147968 + 0.00854292i −0.507380 0.861722i \(-0.669386\pi\)
0.492583 + 0.870265i \(0.336053\pi\)
\(654\) 0 0
\(655\) 14.8688 + 8.58449i 0.580971 + 0.335424i
\(656\) −27.6286 + 3.63485i −1.07872 + 0.141917i
\(657\) 0 0
\(658\) 3.14216 25.3071i 0.122494 0.986573i
\(659\) 26.0531 1.01489 0.507443 0.861685i \(-0.330591\pi\)
0.507443 + 0.861685i \(0.330591\pi\)
\(660\) 0 0
\(661\) −19.9044 + 34.4754i −0.774191 + 1.34094i 0.161057 + 0.986945i \(0.448510\pi\)
−0.935248 + 0.353993i \(0.884824\pi\)
\(662\) −0.644421 3.90375i −0.0250461 0.151723i
\(663\) 0 0
\(664\) −28.2697 + 15.1080i −1.09708 + 0.586306i
\(665\) −8.16308 8.58749i −0.316551 0.333009i
\(666\) 0 0
\(667\) 29.2362 16.8795i 1.13203 0.653578i
\(668\) −10.2937 9.02816i −0.398276 0.349310i
\(669\) 0 0
\(670\) 2.28128 6.06079i 0.0881334 0.234149i
\(671\) −66.9179 −2.58333
\(672\) 0 0
\(673\) −8.26652 −0.318651 −0.159326 0.987226i \(-0.550932\pi\)
−0.159326 + 0.987226i \(0.550932\pi\)
\(674\) 1.68557 4.47814i 0.0649257 0.172492i
\(675\) 0 0
\(676\) 18.5459 + 16.2658i 0.713303 + 0.625607i
\(677\) 3.77905 2.18184i 0.145241 0.0838548i −0.425619 0.904903i \(-0.639943\pi\)
0.570859 + 0.821048i \(0.306610\pi\)
\(678\) 0 0
\(679\) 6.08924 20.6211i 0.233684 0.791367i
\(680\) 4.57804 2.44662i 0.175560 0.0938236i
\(681\) 0 0
\(682\) 10.0440 + 60.8438i 0.384603 + 2.32983i
\(683\) −11.8552 + 20.5339i −0.453628 + 0.785706i −0.998608 0.0527426i \(-0.983204\pi\)
0.544981 + 0.838449i \(0.316537\pi\)
\(684\) 0 0
\(685\) 13.3660 0.510688
\(686\) −8.96642 24.6090i −0.342340 0.939576i
\(687\) 0 0
\(688\) 2.02353 0.266218i 0.0771462 0.0101494i
\(689\) −2.44705 1.41280i −0.0932250 0.0538235i
\(690\) 0 0
\(691\) −19.8985 + 11.4884i −0.756974 + 0.437039i −0.828208 0.560421i \(-0.810639\pi\)
0.0712345 + 0.997460i \(0.477306\pi\)
\(692\) 16.2933 + 3.24170i 0.619378 + 0.123231i
\(693\) 0 0
\(694\) 3.52695 + 4.29780i 0.133881 + 0.163142i
\(695\) −9.31039 16.1261i −0.353163 0.611697i
\(696\) 0 0
\(697\) 5.91328 10.2421i 0.223982 0.387947i
\(698\) −8.03239 + 21.3401i −0.304030 + 0.807735i
\(699\) 0 0
\(700\) −0.812191 20.2569i −0.0306979 0.765640i
\(701\) 37.9118i 1.43191i 0.698146 + 0.715955i \(0.254009\pi\)
−0.698146 + 0.715955i \(0.745991\pi\)
\(702\) 0 0
\(703\) 24.2492 + 14.0003i 0.914577 + 0.528031i
\(704\) 17.2602 + 35.0122i 0.650519 + 1.31957i
\(705\) 0 0
\(706\) −40.6807 + 33.3842i −1.53104 + 1.25643i
\(707\) −2.92366 + 2.77917i −0.109956 + 0.104521i
\(708\) 0 0
\(709\) 14.4546 + 25.0361i 0.542855 + 0.940252i 0.998739 + 0.0502127i \(0.0159899\pi\)
−0.455884 + 0.890039i \(0.650677\pi\)
\(710\) 2.95220 + 17.8837i 0.110794 + 0.671165i
\(711\) 0 0
\(712\) 0.540633 0.869278i 0.0202611 0.0325776i
\(713\) 31.3932i 1.17568i
\(714\) 0 0
\(715\) 4.30441i 0.160976i
\(716\) 39.7082 13.4771i 1.48397 0.503664i
\(717\) 0 0
\(718\) 30.0750 4.96471i 1.12239 0.185281i
\(719\) −15.2533 26.4195i −0.568852 0.985280i −0.996680 0.0814198i \(-0.974055\pi\)
0.427828 0.903860i \(-0.359279\pi\)
\(720\) 0 0
\(721\) −4.79523 19.8992i −0.178584 0.741085i
\(722\) −1.65143 2.01237i −0.0614599 0.0748925i
\(723\) 0 0
\(724\) −26.8483 23.5475i −0.997810 0.875135i
\(725\) −31.8859 18.4093i −1.18421 0.683706i
\(726\) 0 0
\(727\) 19.4515i 0.721415i 0.932679 + 0.360708i \(0.117465\pi\)
−0.932679 + 0.360708i \(0.882535\pi\)
\(728\) −1.23513 5.98014i −0.0457771 0.221639i
\(729\) 0 0
\(730\) 4.28622 + 1.61333i 0.158640 + 0.0597120i
\(731\) −0.433091 + 0.750135i −0.0160184 + 0.0277447i
\(732\) 0 0
\(733\) −9.52314 16.4946i −0.351745 0.609241i 0.634810 0.772668i \(-0.281078\pi\)
−0.986555 + 0.163428i \(0.947745\pi\)
\(734\) −1.84253 + 1.51205i −0.0680089 + 0.0558109i
\(735\) 0 0
\(736\) 5.76638 + 19.0169i 0.212552 + 0.700972i
\(737\) −17.8990 + 10.3340i −0.659320 + 0.380658i
\(738\) 0 0
\(739\) 26.3030 + 15.1860i 0.967571 + 0.558628i 0.898495 0.438984i \(-0.144661\pi\)
0.0690765 + 0.997611i \(0.477995\pi\)
\(740\) −4.69728 13.8398i −0.172675 0.508760i
\(741\) 0 0
\(742\) −5.04632 11.9334i −0.185256 0.438087i
\(743\) 13.1841 0.483676 0.241838 0.970317i \(-0.422250\pi\)
0.241838 + 0.970317i \(0.422250\pi\)
\(744\) 0 0
\(745\) −6.22288 + 10.7783i −0.227989 + 0.394888i
\(746\) −5.98765 + 0.988427i −0.219223 + 0.0361889i
\(747\) 0 0
\(748\) −16.2481 3.23271i −0.594090 0.118200i
\(749\) 3.10161 0.747414i 0.113331 0.0273099i
\(750\) 0 0
\(751\) −28.5934 + 16.5084i −1.04339 + 0.602400i −0.920791 0.390057i \(-0.872455\pi\)
−0.122596 + 0.992457i \(0.539122\pi\)
\(752\) 21.6300 16.5942i 0.788765 0.605128i
\(753\) 0 0
\(754\) −10.3790 3.90666i −0.377982 0.142272i
\(755\) −11.6189 −0.422853
\(756\) 0 0
\(757\) −31.2886 −1.13720 −0.568601 0.822613i \(-0.692515\pi\)
−0.568601 + 0.822613i \(0.692515\pi\)
\(758\) 3.97146 + 1.49485i 0.144250 + 0.0542956i
\(759\) 0 0
\(760\) 0.415282 12.6595i 0.0150639 0.459208i
\(761\) −4.37627 + 2.52664i −0.158640 + 0.0915906i −0.577218 0.816590i \(-0.695862\pi\)
0.418579 + 0.908181i \(0.362528\pi\)
\(762\) 0 0
\(763\) −1.14535 1.20490i −0.0414644 0.0436203i
\(764\) 7.11024 35.7372i 0.257240 1.29293i
\(765\) 0 0
\(766\) 29.4794 4.86638i 1.06513 0.175830i
\(767\) 2.04588 3.54357i 0.0738726 0.127951i
\(768\) 0 0
\(769\) −5.29930 −0.191098 −0.0955489 0.995425i \(-0.530461\pi\)
−0.0955489 + 0.995425i \(0.530461\pi\)
\(770\) 11.8996 15.7468i 0.428832 0.567477i
\(771\) 0 0
\(772\) 35.4304 12.0252i 1.27517 0.432797i
\(773\) 20.1963 + 11.6604i 0.726411 + 0.419394i 0.817108 0.576485i \(-0.195576\pi\)
−0.0906965 + 0.995879i \(0.528909\pi\)
\(774\) 0 0
\(775\) 29.6513 17.1192i 1.06511 0.614940i
\(776\) 20.2725 10.8341i 0.727742 0.388923i
\(777\) 0 0
\(778\) 37.3440 30.6460i 1.33885 1.09871i
\(779\) −14.4293 24.9922i −0.516982 0.895439i
\(780\) 0 0
\(781\) 28.9244 50.0986i 1.03500 1.79267i
\(782\) −7.89300 2.97092i −0.282253 0.106240i
\(783\) 0 0
\(784\) 12.0137 25.2917i 0.429061 0.903276i
\(785\) 25.3063i 0.903220i
\(786\) 0 0
\(787\) 36.4126 + 21.0228i 1.29797 + 0.749383i 0.980053 0.198735i \(-0.0636834\pi\)
0.317917 + 0.948119i \(0.397017\pi\)
\(788\) 29.3058 33.4138i 1.04398 1.19032i
\(789\) 0 0
\(790\) 3.82472 + 4.66065i 0.136077 + 0.165818i
\(791\) 29.9086 + 8.83176i 1.06343 + 0.314021i
\(792\) 0 0
\(793\) 5.59540 + 9.69152i 0.198699 + 0.344156i
\(794\) −23.5114 + 3.88120i −0.834388 + 0.137739i
\(795\) 0 0
\(796\) −10.2813 30.2923i −0.364412 1.07368i
\(797\) 21.9503i 0.777519i 0.921339 + 0.388760i \(0.127096\pi\)
−0.921339 + 0.388760i \(0.872904\pi\)
\(798\) 0 0
\(799\) 11.5700i 0.409317i
\(800\) 14.8172 15.8167i 0.523869 0.559203i
\(801\) 0 0
\(802\) 2.28456 + 13.8393i 0.0806705 + 0.488682i
\(803\) −7.30827 12.6583i −0.257903 0.446702i
\(804\) 0 0
\(805\) 7.28254 6.92262i 0.256676 0.243990i
\(806\) 7.97200 6.54215i 0.280802 0.230437i
\(807\) 0 0
\(808\) −4.31000 0.141385i −0.151625 0.00497392i
\(809\) 42.1387 + 24.3288i 1.48152 + 0.855355i 0.999780 0.0209595i \(-0.00667210\pi\)
0.481739 + 0.876315i \(0.340005\pi\)
\(810\) 0 0
\(811\) 2.14916i 0.0754672i 0.999288 + 0.0377336i \(0.0120138\pi\)
−0.999288 + 0.0377336i \(0.987986\pi\)
\(812\) −27.1696 42.9847i −0.953467 1.50847i
\(813\) 0 0
\(814\) −16.4316 + 43.6547i −0.575927 + 1.53010i
\(815\) 1.46779 2.54228i 0.0514144 0.0890523i
\(816\) 0 0
\(817\) 1.05680 + 1.83044i 0.0369729 + 0.0640389i
\(818\) −32.4513 39.5438i −1.13463 1.38262i
\(819\) 0 0
\(820\) −2.93931 + 14.7734i −0.102645 + 0.515910i
\(821\) 11.4656 6.61966i 0.400152 0.231028i −0.286398 0.958111i \(-0.592458\pi\)
0.686549 + 0.727083i \(0.259125\pi\)
\(822\) 0 0
\(823\) −48.8020 28.1759i −1.70113 0.982149i −0.944618 0.328172i \(-0.893568\pi\)
−0.756514 0.653977i \(-0.773099\pi\)
\(824\) 11.5565 18.5815i 0.402589 0.647319i
\(825\) 0 0
\(826\) 17.2807 7.30759i 0.601273 0.254264i
\(827\) −44.4024 −1.54402 −0.772011 0.635609i \(-0.780749\pi\)
−0.772011 + 0.635609i \(0.780749\pi\)
\(828\) 0 0
\(829\) 16.2282 28.1080i 0.563627 0.976231i −0.433549 0.901130i \(-0.642739\pi\)
0.997176 0.0751011i \(-0.0239279\pi\)
\(830\) 2.82197 + 17.0948i 0.0979520 + 0.593369i
\(831\) 0 0
\(832\) 3.62748 5.42733i 0.125760 0.188159i
\(833\) 5.41279 + 10.5788i 0.187542 + 0.366534i
\(834\) 0 0
\(835\) −6.40945 + 3.70050i −0.221808 + 0.128061i
\(836\) −26.6553 + 30.3918i −0.921893 + 1.05112i
\(837\) 0 0
\(838\) −15.2992 + 40.6463i −0.528503 + 1.40410i
\(839\) 25.8761 0.893342 0.446671 0.894698i \(-0.352609\pi\)
0.446671 + 0.894698i \(0.352609\pi\)
\(840\) 0 0
\(841\) −63.3527 −2.18458
\(842\) −5.43205 + 14.4316i −0.187201 + 0.497347i
\(843\) 0 0
\(844\) −10.9731 + 12.5113i −0.377710 + 0.430657i
\(845\) 11.5477 6.66707i 0.397253 0.229354i
\(846\) 0 0
\(847\) −32.9460 + 7.93919i −1.13204 + 0.272794i
\(848\) 5.30172 12.7962i 0.182062 0.439424i
\(849\) 0 0
\(850\) 1.49810 + 9.07515i 0.0513845 + 0.311275i
\(851\) −11.8728 + 20.5643i −0.406995 + 0.704936i
\(852\) 0 0
\(853\) 14.9017 0.510225 0.255113 0.966911i \(-0.417887\pi\)
0.255113 + 0.966911i \(0.417887\pi\)
\(854\) −6.32268 + 50.9231i −0.216358 + 1.74255i
\(855\) 0 0
\(856\) 2.89623 + 1.80126i 0.0989912 + 0.0615660i
\(857\) 17.4299 + 10.0632i 0.595395 + 0.343751i 0.767228 0.641375i \(-0.221636\pi\)
−0.171833 + 0.985126i \(0.554969\pi\)
\(858\) 0 0
\(859\) −9.71584 + 5.60944i −0.331500 + 0.191392i −0.656507 0.754320i \(-0.727967\pi\)
0.325007 + 0.945712i \(0.394633\pi\)
\(860\) 0.215276 1.08201i 0.00734084 0.0368962i
\(861\) 0 0
\(862\) −14.0523 17.1236i −0.478623 0.583231i
\(863\) −16.4955 28.5711i −0.561514 0.972571i −0.997365 0.0725520i \(-0.976886\pi\)
0.435850 0.900019i \(-0.356448\pi\)
\(864\) 0 0
\(865\) 4.48988 7.77670i 0.152660 0.264416i
\(866\) 11.4063 30.3036i 0.387600 1.02976i
\(867\) 0 0
\(868\) 47.2499 1.89446i 1.60376 0.0643021i
\(869\) 19.2420i 0.652742i
\(870\) 0 0
\(871\) 2.99329 + 1.72818i 0.101424 + 0.0585571i
\(872\) 0.0582677 1.77624i 0.00197319 0.0601509i
\(873\) 0 0
\(874\) −15.9083 + 13.0550i −0.538105 + 0.441591i
\(875\) −24.2256 7.15361i −0.818974 0.241836i
\(876\) 0 0
\(877\) 17.8909 + 30.9880i 0.604134 + 1.04639i 0.992188 + 0.124754i \(0.0398142\pi\)
−0.388054 + 0.921637i \(0.626852\pi\)
\(878\) −3.98693 24.1519i −0.134552 0.815086i
\(879\) 0 0
\(880\) 20.9199 2.75224i 0.705209 0.0927781i
\(881\) 3.68853i 0.124270i −0.998068 0.0621348i \(-0.980209\pi\)
0.998068 0.0621348i \(-0.0197909\pi\)
\(882\) 0 0
\(883\) 12.4938i 0.420449i 0.977653 + 0.210224i \(0.0674195\pi\)
−0.977653 + 0.210224i \(0.932581\pi\)
\(884\) 0.890418 + 2.62347i 0.0299480 + 0.0882370i
\(885\) 0 0
\(886\) −15.8863 + 2.62248i −0.533711 + 0.0881038i
\(887\) 0.427511 + 0.740471i 0.0143544 + 0.0248626i 0.873113 0.487517i \(-0.162097\pi\)
−0.858759 + 0.512380i \(0.828764\pi\)
\(888\) 0 0
\(889\) 13.8678 + 4.09504i 0.465111 + 0.137343i
\(890\) −0.351025 0.427745i −0.0117664 0.0143381i
\(891\) 0 0
\(892\) −11.7539 + 13.4015i −0.393550 + 0.448717i
\(893\) 24.4500 + 14.1162i 0.818190 + 0.472382i
\(894\) 0 0
\(895\) 22.6664i 0.757653i
\(896\) 28.2743 9.82658i 0.944579 0.328283i
\(897\) 0 0
\(898\) 14.7032 + 5.53426i 0.490652 + 0.184681i
\(899\) 42.9403 74.3748i 1.43214 2.48054i
\(900\) 0 0
\(901\) 2.93918 + 5.09081i 0.0979183 + 0.169599i
\(902\) 37.1623 30.4969i 1.23737 1.01544i
\(903\) 0 0
\(904\) 15.7137 + 29.4030i 0.522630 + 0.977930i
\(905\) −16.7173 + 9.65172i −0.555701 + 0.320834i
\(906\) 0 0
\(907\) 25.5068 + 14.7264i 0.846939 + 0.488981i 0.859617 0.510939i \(-0.170702\pi\)
−0.0126776 + 0.999920i \(0.504036\pi\)
\(908\) −38.6901 + 13.1316i −1.28398 + 0.435787i
\(909\) 0 0
\(910\) −3.27557 0.406699i −0.108584 0.0134819i
\(911\) −9.62988 −0.319052 −0.159526 0.987194i \(-0.550997\pi\)
−0.159526 + 0.987194i \(0.550997\pi\)
\(912\) 0 0
\(913\) 27.6484 47.8885i 0.915030 1.58488i
\(914\) 37.8575 6.24943i 1.25222 0.206713i
\(915\) 0 0
\(916\) 4.85000 24.3769i 0.160249 0.805435i
\(917\) −40.8489 + 9.84360i −1.34895 + 0.325064i
\(918\) 0 0
\(919\) −5.68583 + 3.28272i −0.187558 + 0.108287i −0.590839 0.806790i \(-0.701203\pi\)
0.403281 + 0.915076i \(0.367870\pi\)
\(920\) 10.7358 + 0.352176i 0.353947 + 0.0116109i
\(921\) 0 0
\(922\) 17.5409 + 6.60239i 0.577680 + 0.217438i
\(923\) −9.67418 −0.318429
\(924\) 0 0
\(925\) 25.8977 0.851512
\(926\) −5.38935 2.02854i −0.177105 0.0666621i
\(927\) 0 0
\(928\) 12.3504 52.9411i 0.405421 1.73788i
\(929\) −18.6881 + 10.7896i −0.613137 + 0.353995i −0.774192 0.632951i \(-0.781844\pi\)
0.161055 + 0.986945i \(0.448510\pi\)
\(930\) 0 0
\(931\) 28.9594 + 1.46845i 0.949106 + 0.0481265i
\(932\) −4.94330 0.983513i −0.161923 0.0322161i
\(933\) 0 0
\(934\) −32.7982 + 5.41425i −1.07319 + 0.177160i
\(935\) −4.47743 + 7.75514i −0.146428 + 0.253620i
\(936\) 0 0
\(937\) −38.5055 −1.25792 −0.628960 0.777437i \(-0.716519\pi\)
−0.628960 + 0.777437i \(0.716519\pi\)
\(938\) 6.17279 + 14.5972i 0.201549 + 0.476615i
\(939\) 0 0
\(940\) −4.73618 13.9544i −0.154477 0.455142i
\(941\) 1.30779 + 0.755052i 0.0426327 + 0.0246140i 0.521165 0.853456i \(-0.325498\pi\)
−0.478532 + 0.878070i \(0.658831\pi\)
\(942\) 0 0
\(943\) 21.1944 12.2366i 0.690184 0.398478i
\(944\) 18.5303 + 7.67743i 0.603108 + 0.249879i
\(945\) 0 0
\(946\) −2.72178 + 2.23361i −0.0884927 + 0.0726208i
\(947\) 2.64972 + 4.58945i 0.0861044 + 0.149137i 0.905861 0.423574i \(-0.139225\pi\)
−0.819757 + 0.572712i \(0.805891\pi\)
\(948\) 0 0
\(949\) −1.22218 + 2.11687i −0.0396735 + 0.0687166i
\(950\) 21.0056 + 7.90650i 0.681513 + 0.256521i
\(951\) 0 0
\(952\) −3.99521 + 12.0590i −0.129486 + 0.390835i
\(953\) 60.6268i 1.96390i 0.189151 + 0.981948i \(0.439426\pi\)
−0.189151 + 0.981948i \(0.560574\pi\)
\(954\) 0 0
\(955\) −17.0572 9.84797i −0.551958 0.318673i
\(956\) −37.9851 33.3150i −1.22853 1.07749i
\(957\) 0 0
\(958\) 3.33899 + 4.06875i 0.107878 + 0.131455i
\(959\) −23.7086 + 22.5369i −0.765592 + 0.727754i
\(960\) 0 0
\(961\) 24.4310 + 42.3158i 0.788098 + 1.36503i
\(962\) 7.69633 1.27049i 0.248140 0.0409623i
\(963\) 0 0
\(964\) −27.7154 + 9.40671i −0.892652 + 0.302970i
\(965\) 20.2245i 0.651049i
\(966\) 0 0
\(967\) 43.5917i 1.40181i −0.713253 0.700907i \(-0.752779\pi\)
0.713253 0.700907i \(-0.247221\pi\)
\(968\) −30.7644 19.1334i −0.988806 0.614972i
\(969\) 0 0
\(970\) −2.02367 12.2589i −0.0649760 0.393609i
\(971\) 9.75149 + 16.8901i 0.312940 + 0.542028i 0.978997 0.203872i \(-0.0653527\pi\)
−0.666057 + 0.745901i \(0.732019\pi\)
\(972\) 0 0
\(973\) 43.7056 + 12.9059i 1.40114 + 0.413743i
\(974\) −18.3920 + 15.0932i −0.589317 + 0.483618i
\(975\) 0 0
\(976\) −43.5240 + 33.3910i −1.39317 + 1.06882i
\(977\) −51.2227 29.5734i −1.63876 0.946137i −0.981262 0.192679i \(-0.938282\pi\)
−0.657496 0.753458i \(-0.728384\pi\)
\(978\) 0 0
\(979\) 1.76600i 0.0564416i
\(980\) −10.8587 10.5432i −0.346868 0.336790i
\(981\) 0 0
\(982\) 3.36642 8.94376i 0.107427 0.285407i
\(983\) −21.1885 + 36.6996i −0.675809 + 1.17054i 0.300423 + 0.953806i \(0.402872\pi\)
−0.976232 + 0.216729i \(0.930461\pi\)
\(984\) 0 0
\(985\) −12.0120 20.8053i −0.382733 0.662913i
\(986\) 14.6359 + 17.8347i 0.466103 + 0.567974i
\(987\) 0 0
\(988\) 6.63037 + 1.31917i 0.210940 + 0.0419684i
\(989\) −1.55228 + 0.896211i −0.0493597 + 0.0284979i
\(990\) 0 0
\(991\) 17.1417 + 9.89678i 0.544525 + 0.314381i 0.746911 0.664924i \(-0.231536\pi\)
−0.202386 + 0.979306i \(0.564870\pi\)
\(992\) 36.8928 + 34.5616i 1.17135 + 1.09733i
\(993\) 0 0
\(994\) −35.3911 26.7444i −1.12254 0.848281i
\(995\) −17.2916 −0.548179
\(996\) 0 0
\(997\) −20.1621 + 34.9217i −0.638539 + 1.10598i 0.347214 + 0.937786i \(0.387128\pi\)
−0.985753 + 0.168197i \(0.946206\pi\)
\(998\) −3.98370 24.1323i −0.126102 0.763894i
\(999\) 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 756.2.be.d.431.5 yes 28
3.2 odd 2 inner 756.2.be.d.431.10 yes 28
4.3 odd 2 756.2.be.c.431.1 yes 28
7.2 even 3 756.2.be.c.107.14 yes 28
12.11 even 2 756.2.be.c.431.14 yes 28
21.2 odd 6 756.2.be.c.107.1 28
28.23 odd 6 inner 756.2.be.d.107.10 yes 28
84.23 even 6 inner 756.2.be.d.107.5 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.be.c.107.1 28 21.2 odd 6
756.2.be.c.107.14 yes 28 7.2 even 3
756.2.be.c.431.1 yes 28 4.3 odd 2
756.2.be.c.431.14 yes 28 12.11 even 2
756.2.be.d.107.5 yes 28 84.23 even 6 inner
756.2.be.d.107.10 yes 28 28.23 odd 6 inner
756.2.be.d.431.5 yes 28 1.1 even 1 trivial
756.2.be.d.431.10 yes 28 3.2 odd 2 inner