Properties

Label 432.2.u.c.97.1
Level $432$
Weight $2$
Character 432.97
Analytic conductor $3.450$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(49,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.u (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 97.1
Root \(0.500000 + 0.258654i\) of defining polynomial
Character \(\chi\) \(=\) 432.97
Dual form 432.2.u.c.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.159815 - 1.72466i) q^{3} +(-2.08159 - 0.757639i) q^{5} +(0.229151 - 1.29958i) q^{7} +(-2.94892 + 0.551252i) q^{9} +O(q^{10})\) \(q+(-0.159815 - 1.72466i) q^{3} +(-2.08159 - 0.757639i) q^{5} +(0.229151 - 1.29958i) q^{7} +(-2.94892 + 0.551252i) q^{9} +(-4.90067 + 1.78370i) q^{11} +(-0.0138336 + 0.0116078i) q^{13} +(-0.974001 + 3.71113i) q^{15} +(1.56640 + 2.71308i) q^{17} +(0.208676 - 0.361438i) q^{19} +(-2.27796 - 0.187516i) q^{21} +(0.179619 + 1.01867i) q^{23} +(-0.0712019 - 0.0597455i) q^{25} +(1.42200 + 4.99779i) q^{27} +(-5.98068 - 5.01839i) q^{29} +(-0.647649 - 3.67300i) q^{31} +(3.85948 + 8.16694i) q^{33} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(0.0222303 + 0.0220032i) q^{39} +(-2.81517 + 2.36221i) q^{41} +(-7.80685 + 2.84146i) q^{43} +(6.55610 + 1.08673i) q^{45} +(1.23254 - 6.99008i) q^{47} +(4.94145 + 1.79854i) q^{49} +(4.42881 - 3.13510i) q^{51} -1.30057 q^{53} +11.5526 q^{55} +(-0.656707 - 0.302133i) q^{57} +(-3.47856 - 1.26609i) q^{59} +(1.20064 - 6.80919i) q^{61} +(0.0406486 + 3.95868i) q^{63} +(0.0375905 - 0.0136818i) q^{65} +(8.44702 - 7.08789i) q^{67} +(1.72816 - 0.472581i) q^{69} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(-0.0916617 + 0.132347i) q^{75} +(1.19507 + 6.77756i) q^{77} +(-0.374706 - 0.314416i) q^{79} +(8.39224 - 3.25120i) q^{81} +(-3.53428 - 2.96561i) q^{83} +(-1.20507 - 6.83430i) q^{85} +(-7.69922 + 11.1167i) q^{87} +(1.68653 - 2.92116i) q^{89} +(0.0119153 + 0.0206379i) q^{91} +(-6.23118 + 1.70398i) q^{93} +(-0.708218 + 0.594266i) q^{95} +(-9.34182 + 3.40014i) q^{97} +(13.4684 - 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\)

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 0
\(3\) −0.159815 1.72466i −0.0922690 0.995734i
\(4\) 0 0
\(5\) −2.08159 0.757639i −0.930917 0.338826i −0.168344 0.985728i \(-0.553842\pi\)
−0.762573 + 0.646902i \(0.776064\pi\)
\(6\) 0 0
\(7\) 0.229151 1.29958i 0.0866110 0.491195i −0.910386 0.413759i \(-0.864216\pi\)
0.996997 0.0774361i \(-0.0246734\pi\)
\(8\) 0 0
\(9\) −2.94892 + 0.551252i −0.982973 + 0.183751i
\(10\) 0 0
\(11\) −4.90067 + 1.78370i −1.47761 + 0.537805i −0.950155 0.311778i \(-0.899075\pi\)
−0.527454 + 0.849584i \(0.676853\pi\)
\(12\) 0 0
\(13\) −0.0138336 + 0.0116078i −0.00383676 + 0.00321942i −0.644704 0.764432i \(-0.723019\pi\)
0.640867 + 0.767652i \(0.278575\pi\)
\(14\) 0 0
\(15\) −0.974001 + 3.71113i −0.251486 + 0.958209i
\(16\) 0 0
\(17\) 1.56640 + 2.71308i 0.379907 + 0.658019i 0.991048 0.133503i \(-0.0426226\pi\)
−0.611141 + 0.791522i \(0.709289\pi\)
\(18\) 0 0
\(19\) 0.208676 0.361438i 0.0478736 0.0829195i −0.841096 0.540886i \(-0.818089\pi\)
0.888969 + 0.457967i \(0.151422\pi\)
\(20\) 0 0
\(21\) −2.27796 0.187516i −0.497092 0.0409194i
\(22\) 0 0
\(23\) 0.179619 + 1.01867i 0.0374532 + 0.212408i 0.997791 0.0664316i \(-0.0211614\pi\)
−0.960338 + 0.278839i \(0.910050\pi\)
\(24\) 0 0
\(25\) −0.0712019 0.0597455i −0.0142404 0.0119491i
\(26\) 0 0
\(27\) 1.42200 + 4.99779i 0.273665 + 0.961825i
\(28\) 0 0
\(29\) −5.98068 5.01839i −1.11058 0.931891i −0.112493 0.993652i \(-0.535884\pi\)
−0.998091 + 0.0617615i \(0.980328\pi\)
\(30\) 0 0
\(31\) −0.647649 3.67300i −0.116321 0.659691i −0.986088 0.166227i \(-0.946842\pi\)
0.869766 0.493464i \(-0.164270\pi\)
\(32\) 0 0
\(33\) 3.85948 + 8.16694i 0.671849 + 1.42168i
\(34\) 0 0
\(35\) −1.46161 + 2.53159i −0.247058 + 0.427916i
\(36\) 0 0
\(37\) −2.21238 3.83195i −0.363713 0.629969i 0.624856 0.780740i \(-0.285158\pi\)
−0.988569 + 0.150771i \(0.951824\pi\)
\(38\) 0 0
\(39\) 0.0222303 + 0.0220032i 0.00355970 + 0.00352334i
\(40\) 0 0
\(41\) −2.81517 + 2.36221i −0.439655 + 0.368915i −0.835580 0.549368i \(-0.814868\pi\)
0.395925 + 0.918283i \(0.370424\pi\)
\(42\) 0 0
\(43\) −7.80685 + 2.84146i −1.19053 + 0.433319i −0.859911 0.510445i \(-0.829481\pi\)
−0.330622 + 0.943763i \(0.607259\pi\)
\(44\) 0 0
\(45\) 6.55610 + 1.08673i 0.977326 + 0.162000i
\(46\) 0 0
\(47\) 1.23254 6.99008i 0.179784 1.01961i −0.752691 0.658374i \(-0.771245\pi\)
0.932475 0.361234i \(-0.117644\pi\)
\(48\) 0 0
\(49\) 4.94145 + 1.79854i 0.705921 + 0.256934i
\(50\) 0 0
\(51\) 4.42881 3.13510i 0.620158 0.439001i
\(52\) 0 0
\(53\) −1.30057 −0.178648 −0.0893238 0.996003i \(-0.528471\pi\)
−0.0893238 + 0.996003i \(0.528471\pi\)
\(54\) 0 0
\(55\) 11.5526 1.55775
\(56\) 0 0
\(57\) −0.656707 0.302133i −0.0869830 0.0400185i
\(58\) 0 0
\(59\) −3.47856 1.26609i −0.452871 0.164831i 0.105507 0.994419i \(-0.466354\pi\)
−0.558377 + 0.829587i \(0.688576\pi\)
\(60\) 0 0
\(61\) 1.20064 6.80919i 0.153727 0.871828i −0.806214 0.591624i \(-0.798487\pi\)
0.959941 0.280204i \(-0.0904020\pi\)
\(62\) 0 0
\(63\) 0.0406486 + 3.95868i 0.00512125 + 0.498747i
\(64\) 0 0
\(65\) 0.0375905 0.0136818i 0.00466253 0.00169702i
\(66\) 0 0
\(67\) 8.44702 7.08789i 1.03197 0.865923i 0.0408835 0.999164i \(-0.486983\pi\)
0.991084 + 0.133241i \(0.0425383\pi\)
\(68\) 0 0
\(69\) 1.72816 0.472581i 0.208046 0.0568921i
\(70\) 0 0
\(71\) −3.04214 5.26914i −0.361035 0.625332i 0.627096 0.778942i \(-0.284243\pi\)
−0.988132 + 0.153610i \(0.950910\pi\)
\(72\) 0 0
\(73\) 0.273486 0.473692i 0.0320092 0.0554415i −0.849577 0.527465i \(-0.823143\pi\)
0.881586 + 0.472023i \(0.156476\pi\)
\(74\) 0 0
\(75\) −0.0916617 + 0.132347i −0.0105842 + 0.0152822i
\(76\) 0 0
\(77\) 1.19507 + 6.77756i 0.136190 + 0.772374i
\(78\) 0 0
\(79\) −0.374706 0.314416i −0.0421577 0.0353745i 0.621465 0.783442i \(-0.286538\pi\)
−0.663623 + 0.748067i \(0.730982\pi\)
\(80\) 0 0
\(81\) 8.39224 3.25120i 0.932471 0.361244i
\(82\) 0 0
\(83\) −3.53428 2.96561i −0.387937 0.325518i 0.427872 0.903839i \(-0.359263\pi\)
−0.815809 + 0.578321i \(0.803708\pi\)
\(84\) 0 0
\(85\) −1.20507 6.83430i −0.130708 0.741284i
\(86\) 0 0
\(87\) −7.69922 + 11.1167i −0.825443 + 1.19183i
\(88\) 0 0
\(89\) 1.68653 2.92116i 0.178772 0.309642i −0.762688 0.646766i \(-0.776121\pi\)
0.941460 + 0.337124i \(0.109454\pi\)
\(90\) 0 0
\(91\) 0.0119153 + 0.0206379i 0.00124906 + 0.00216344i
\(92\) 0 0
\(93\) −6.23118 + 1.70398i −0.646144 + 0.176694i
\(94\) 0 0
\(95\) −0.708218 + 0.594266i −0.0726617 + 0.0609704i
\(96\) 0 0
\(97\) −9.34182 + 3.40014i −0.948518 + 0.345232i −0.769524 0.638618i \(-0.779507\pi\)
−0.178994 + 0.983850i \(0.557284\pi\)
\(98\) 0 0
\(99\) 13.4684 7.96149i 1.35363 0.800160i
\(100\) 0 0
\(101\) 2.39626 13.5898i 0.238436 1.35224i −0.596818 0.802377i \(-0.703569\pi\)
0.835255 0.549863i \(-0.185320\pi\)
\(102\) 0 0
\(103\) 4.28981 + 1.56136i 0.422687 + 0.153846i 0.544601 0.838695i \(-0.316681\pi\)
−0.121914 + 0.992541i \(0.538903\pi\)
\(104\) 0 0
\(105\) 4.59972 + 2.11620i 0.448887 + 0.206520i
\(106\) 0 0
\(107\) 11.2965 1.09207 0.546035 0.837762i \(-0.316136\pi\)
0.546035 + 0.837762i \(0.316136\pi\)
\(108\) 0 0
\(109\) 14.5032 1.38915 0.694577 0.719419i \(-0.255592\pi\)
0.694577 + 0.719419i \(0.255592\pi\)
\(110\) 0 0
\(111\) −6.25525 + 4.42801i −0.593722 + 0.420288i
\(112\) 0 0
\(113\) −11.8011 4.29523i −1.11015 0.404062i −0.279102 0.960262i \(-0.590037\pi\)
−0.831049 + 0.556200i \(0.812259\pi\)
\(114\) 0 0
\(115\) 0.397890 2.25655i 0.0371035 0.210424i
\(116\) 0 0
\(117\) 0.0343954 0.0418563i 0.00317986 0.00386961i
\(118\) 0 0
\(119\) 3.88481 1.41395i 0.356120 0.129617i
\(120\) 0 0
\(121\) 12.4085 10.4120i 1.12805 0.946544i
\(122\) 0 0
\(123\) 4.52391 + 4.47770i 0.407907 + 0.403740i
\(124\) 0 0
\(125\) 5.64092 + 9.77035i 0.504539 + 0.873887i
\(126\) 0 0
\(127\) −4.19749 + 7.27027i −0.372467 + 0.645132i −0.989944 0.141456i \(-0.954821\pi\)
0.617477 + 0.786589i \(0.288155\pi\)
\(128\) 0 0
\(129\) 6.14821 + 13.0101i 0.541319 + 1.14547i
\(130\) 0 0
\(131\) 2.69761 + 15.2989i 0.235691 + 1.33667i 0.841154 + 0.540796i \(0.181877\pi\)
−0.605463 + 0.795874i \(0.707012\pi\)
\(132\) 0 0
\(133\) −0.421899 0.354015i −0.0365833 0.0306970i
\(134\) 0 0
\(135\) 0.826482 11.4807i 0.0711323 0.988105i
\(136\) 0 0
\(137\) 9.19820 + 7.71820i 0.785855 + 0.659411i 0.944716 0.327890i \(-0.106338\pi\)
−0.158861 + 0.987301i \(0.550782\pi\)
\(138\) 0 0
\(139\) −1.06709 6.05176i −0.0905093 0.513304i −0.996031 0.0890042i \(-0.971632\pi\)
0.905522 0.424299i \(-0.139480\pi\)
\(140\) 0 0
\(141\) −12.2525 1.00860i −1.03185 0.0849392i
\(142\) 0 0
\(143\) 0.0470893 0.0815610i 0.00393780 0.00682047i
\(144\) 0 0
\(145\) 8.64723 + 14.9774i 0.718113 + 1.24381i
\(146\) 0 0
\(147\) 2.31216 8.80976i 0.190704 0.726617i
\(148\) 0 0
\(149\) 0.676280 0.567466i 0.0554030 0.0464886i −0.614666 0.788788i \(-0.710709\pi\)
0.670069 + 0.742299i \(0.266265\pi\)
\(150\) 0 0
\(151\) 7.72942 2.81328i 0.629011 0.228941i −0.00778980 0.999970i \(-0.502480\pi\)
0.636801 + 0.771028i \(0.280257\pi\)
\(152\) 0 0
\(153\) −6.11477 7.13717i −0.494350 0.577006i
\(154\) 0 0
\(155\) −1.43466 + 8.13639i −0.115235 + 0.653530i
\(156\) 0 0
\(157\) −11.8024 4.29571i −0.941932 0.342835i −0.175003 0.984568i \(-0.555994\pi\)
−0.766928 + 0.641733i \(0.778216\pi\)
\(158\) 0 0
\(159\) 0.207851 + 2.24305i 0.0164836 + 0.177886i
\(160\) 0 0
\(161\) 1.36501 0.107578
\(162\) 0 0
\(163\) −3.31466 −0.259624 −0.129812 0.991539i \(-0.541437\pi\)
−0.129812 + 0.991539i \(0.541437\pi\)
\(164\) 0 0
\(165\) −1.84628 19.9244i −0.143732 1.55111i
\(166\) 0 0
\(167\) −19.3229 7.03295i −1.49525 0.544226i −0.540424 0.841393i \(-0.681736\pi\)
−0.954826 + 0.297167i \(0.903958\pi\)
\(168\) 0 0
\(169\) −2.25737 + 12.8022i −0.173644 + 0.984783i
\(170\) 0 0
\(171\) −0.416126 + 1.18088i −0.0318219 + 0.0903044i
\(172\) 0 0
\(173\) −13.1870 + 4.79966i −1.00259 + 0.364911i −0.790581 0.612357i \(-0.790221\pi\)
−0.212005 + 0.977269i \(0.567999\pi\)
\(174\) 0 0
\(175\) −0.0939601 + 0.0788419i −0.00710272 + 0.00595989i
\(176\) 0 0
\(177\) −1.62766 + 6.20169i −0.122342 + 0.466148i
\(178\) 0 0
\(179\) 5.09500 + 8.82479i 0.380818 + 0.659596i 0.991179 0.132527i \(-0.0423091\pi\)
−0.610361 + 0.792123i \(0.708976\pi\)
\(180\) 0 0
\(181\) −12.0274 + 20.8320i −0.893987 + 1.54843i −0.0589331 + 0.998262i \(0.518770\pi\)
−0.835054 + 0.550169i \(0.814563\pi\)
\(182\) 0 0
\(183\) −11.9354 0.982498i −0.882293 0.0726283i
\(184\) 0 0
\(185\) 1.70204 + 9.65275i 0.125137 + 0.709685i
\(186\) 0 0
\(187\) −12.5157 10.5019i −0.915240 0.767978i
\(188\) 0 0
\(189\) 6.82089 0.702760i 0.496146 0.0511182i
\(190\) 0 0
\(191\) −8.38541 7.03619i −0.606747 0.509121i 0.286860 0.957973i \(-0.407389\pi\)
−0.893606 + 0.448852i \(0.851833\pi\)
\(192\) 0 0
\(193\) −1.87644 10.6418i −0.135069 0.766013i −0.974812 0.223029i \(-0.928405\pi\)
0.839743 0.542984i \(-0.182706\pi\)
\(194\) 0 0
\(195\) −0.0296040 0.0626444i −0.00211999 0.00448606i
\(196\) 0 0
\(197\) 11.0367 19.1161i 0.786331 1.36196i −0.141870 0.989885i \(-0.545311\pi\)
0.928201 0.372080i \(-0.121355\pi\)
\(198\) 0 0
\(199\) 6.44338 + 11.1603i 0.456759 + 0.791130i 0.998787 0.0492301i \(-0.0156768\pi\)
−0.542028 + 0.840360i \(0.682343\pi\)
\(200\) 0 0
\(201\) −13.5742 13.4355i −0.957448 0.947667i
\(202\) 0 0
\(203\) −7.89228 + 6.62241i −0.553929 + 0.464802i
\(204\) 0 0
\(205\) 7.64974 2.78428i 0.534281 0.194462i
\(206\) 0 0
\(207\) −1.09123 2.90496i −0.0758456 0.201909i
\(208\) 0 0
\(209\) −0.377957 + 2.14350i −0.0261439 + 0.148269i
\(210\) 0 0
\(211\) −22.5485 8.20699i −1.55230 0.564992i −0.583347 0.812223i \(-0.698257\pi\)
−0.968957 + 0.247230i \(0.920480\pi\)
\(212\) 0 0
\(213\) −8.60131 + 6.08875i −0.589352 + 0.417194i
\(214\) 0 0
\(215\) 18.4035 1.25511
\(216\) 0 0
\(217\) −4.92177 −0.334112
\(218\) 0 0
\(219\) −0.860667 0.395969i −0.0581585 0.0267571i
\(220\) 0 0
\(221\) −0.0531618 0.0193493i −0.00357605 0.00130158i
\(222\) 0 0
\(223\) −3.76160 + 21.3331i −0.251895 + 1.42857i 0.552023 + 0.833829i \(0.313856\pi\)
−0.803918 + 0.594740i \(0.797255\pi\)
\(224\) 0 0
\(225\) 0.242903 + 0.136934i 0.0161936 + 0.00912896i
\(226\) 0 0
\(227\) 20.3367 7.40196i 1.34979 0.491285i 0.436911 0.899505i \(-0.356072\pi\)
0.912884 + 0.408220i \(0.133850\pi\)
\(228\) 0 0
\(229\) −8.27739 + 6.94555i −0.546985 + 0.458975i −0.873919 0.486072i \(-0.838429\pi\)
0.326934 + 0.945047i \(0.393985\pi\)
\(230\) 0 0
\(231\) 11.4980 3.14424i 0.756513 0.206876i
\(232\) 0 0
\(233\) −3.81950 6.61557i −0.250224 0.433400i 0.713364 0.700794i \(-0.247171\pi\)
−0.963587 + 0.267394i \(0.913838\pi\)
\(234\) 0 0
\(235\) −7.86160 + 13.6167i −0.512834 + 0.888255i
\(236\) 0 0
\(237\) −0.482377 + 0.696490i −0.0313338 + 0.0452419i
\(238\) 0 0
\(239\) 0.561143 + 3.18240i 0.0362973 + 0.205852i 0.997563 0.0697711i \(-0.0222269\pi\)
−0.961266 + 0.275623i \(0.911116\pi\)
\(240\) 0 0
\(241\) −20.3346 17.0628i −1.30987 1.09911i −0.988349 0.152206i \(-0.951362\pi\)
−0.321518 0.946903i \(-0.604193\pi\)
\(242\) 0 0
\(243\) −6.94842 13.9542i −0.445741 0.895162i
\(244\) 0 0
\(245\) −8.92345 7.48766i −0.570098 0.478369i
\(246\) 0 0
\(247\) 0.00130875 + 0.00742226i 8.32735e−5 + 0.000472267i
\(248\) 0 0
\(249\) −4.54985 + 6.56938i −0.288335 + 0.416318i
\(250\) 0 0
\(251\) −2.24965 + 3.89651i −0.141997 + 0.245945i −0.928248 0.371961i \(-0.878686\pi\)
0.786252 + 0.617906i \(0.212019\pi\)
\(252\) 0 0
\(253\) −2.69726 4.67179i −0.169575 0.293713i
\(254\) 0 0
\(255\) −11.5943 + 3.17056i −0.726061 + 0.198548i
\(256\) 0 0
\(257\) 10.5219 8.82895i 0.656340 0.550735i −0.252647 0.967559i \(-0.581301\pi\)
0.908987 + 0.416824i \(0.136857\pi\)
\(258\) 0 0
\(259\) −5.48690 + 1.99707i −0.340939 + 0.124092i
\(260\) 0 0
\(261\) 20.4029 + 11.5020i 1.26291 + 0.711953i
\(262\) 0 0
\(263\) 4.20273 23.8349i 0.259151 1.46972i −0.526036 0.850462i \(-0.676322\pi\)
0.785187 0.619258i \(-0.212567\pi\)
\(264\) 0 0
\(265\) 2.70727 + 0.985365i 0.166306 + 0.0605305i
\(266\) 0 0
\(267\) −5.30755 2.44185i −0.324817 0.149439i
\(268\) 0 0
\(269\) 12.0062 0.732032 0.366016 0.930609i \(-0.380722\pi\)
0.366016 + 0.930609i \(0.380722\pi\)
\(270\) 0 0
\(271\) −3.71777 −0.225839 −0.112919 0.993604i \(-0.536020\pi\)
−0.112919 + 0.993604i \(0.536020\pi\)
\(272\) 0 0
\(273\) 0.0336891 0.0238481i 0.00203896 0.00144335i
\(274\) 0 0
\(275\) 0.455505 + 0.165790i 0.0274680 + 0.00999753i
\(276\) 0 0
\(277\) −4.07780 + 23.1264i −0.245011 + 1.38953i 0.575455 + 0.817833i \(0.304825\pi\)
−0.820466 + 0.571695i \(0.806286\pi\)
\(278\) 0 0
\(279\) 3.93462 + 10.4744i 0.235559 + 0.627084i
\(280\) 0 0
\(281\) 19.1432 6.96754i 1.14199 0.415649i 0.299356 0.954142i \(-0.403228\pi\)
0.842630 + 0.538493i \(0.181006\pi\)
\(282\) 0 0
\(283\) −8.88607 + 7.45630i −0.528222 + 0.443231i −0.867487 0.497460i \(-0.834266\pi\)
0.339265 + 0.940691i \(0.389822\pi\)
\(284\) 0 0
\(285\) 1.13809 + 1.12646i 0.0674147 + 0.0667260i
\(286\) 0 0
\(287\) 2.42478 + 4.19984i 0.143130 + 0.247909i
\(288\) 0 0
\(289\) 3.59280 6.22291i 0.211341 0.366053i
\(290\) 0 0
\(291\) 7.35706 + 15.5681i 0.431279 + 0.912618i
\(292\) 0 0
\(293\) 5.48280 + 31.0945i 0.320308 + 1.81656i 0.540779 + 0.841165i \(0.318130\pi\)
−0.220470 + 0.975394i \(0.570759\pi\)
\(294\) 0 0
\(295\) 6.28172 + 5.27099i 0.365736 + 0.306889i
\(296\) 0 0
\(297\) −15.8833 21.9561i −0.921644 1.27402i
\(298\) 0 0
\(299\) −0.0143093 0.0120069i −0.000827529 0.000694379i
\(300\) 0 0
\(301\) 1.90376 + 10.7968i 0.109731 + 0.622315i
\(302\) 0 0
\(303\) −23.8208 1.96088i −1.36847 0.112649i
\(304\) 0 0
\(305\) −7.65816 + 13.2643i −0.438505 + 0.759513i
\(306\) 0 0
\(307\) −4.06027 7.03259i −0.231732 0.401371i 0.726586 0.687075i \(-0.241106\pi\)
−0.958318 + 0.285704i \(0.907773\pi\)
\(308\) 0 0
\(309\) 2.00725 7.64800i 0.114188 0.435079i
\(310\) 0 0
\(311\) 18.2691 15.3296i 1.03594 0.869259i 0.0443970 0.999014i \(-0.485863\pi\)
0.991546 + 0.129754i \(0.0414189\pi\)
\(312\) 0 0
\(313\) −25.2876 + 9.20392i −1.42934 + 0.520236i −0.936742 0.350022i \(-0.886174\pi\)
−0.492596 + 0.870258i \(0.663952\pi\)
\(314\) 0 0
\(315\) 2.91463 8.27116i 0.164221 0.466027i
\(316\) 0 0
\(317\) −1.44689 + 8.20574i −0.0812657 + 0.460881i 0.916834 + 0.399268i \(0.130736\pi\)
−0.998100 + 0.0616130i \(0.980376\pi\)
\(318\) 0 0
\(319\) 38.2606 + 13.9257i 2.14218 + 0.779692i
\(320\) 0 0
\(321\) −1.80534 19.4826i −0.100764 1.08741i
\(322\) 0 0
\(323\) 1.30748 0.0727501
\(324\) 0 0
\(325\) 0.00167849 9.31061e−5
\(326\) 0 0
\(327\) −2.31782 25.0131i −0.128176 1.38323i
\(328\) 0 0
\(329\) −8.80173 3.20357i −0.485255 0.176618i
\(330\) 0 0
\(331\) 1.11487 6.32272i 0.0612786 0.347528i −0.938717 0.344688i \(-0.887985\pi\)
0.999996 0.00284030i \(-0.000904096\pi\)
\(332\) 0 0
\(333\) 8.63650 + 10.0805i 0.473277 + 0.552410i
\(334\) 0 0
\(335\) −22.9533 + 8.35432i −1.25407 + 0.456446i
\(336\) 0 0
\(337\) 5.72610 4.80477i 0.311921 0.261732i −0.473365 0.880867i \(-0.656961\pi\)
0.785285 + 0.619134i \(0.212516\pi\)
\(338\) 0 0
\(339\) −5.52185 + 21.0393i −0.299906 + 1.14270i
\(340\) 0 0
\(341\) 9.72545 + 16.8450i 0.526663 + 0.912206i
\(342\) 0 0
\(343\) 8.08839 14.0095i 0.436732 0.756442i
\(344\) 0 0
\(345\) −3.95537 0.325597i −0.212950 0.0175296i
\(346\) 0 0
\(347\) 5.46202 + 30.9766i 0.293216 + 1.66291i 0.674364 + 0.738399i \(0.264418\pi\)
−0.381148 + 0.924514i \(0.624471\pi\)
\(348\) 0 0
\(349\) 9.07988 + 7.61893i 0.486035 + 0.407832i 0.852603 0.522560i \(-0.175023\pi\)
−0.366568 + 0.930391i \(0.619467\pi\)
\(350\) 0 0
\(351\) −0.0776848 0.0526312i −0.00414651 0.00280925i
\(352\) 0 0
\(353\) −6.28699 5.27541i −0.334623 0.280782i 0.459958 0.887941i \(-0.347865\pi\)
−0.794580 + 0.607159i \(0.792309\pi\)
\(354\) 0 0
\(355\) 2.34040 + 13.2731i 0.124215 + 0.704461i
\(356\) 0 0
\(357\) −3.05944 6.47401i −0.161923 0.342641i
\(358\) 0 0
\(359\) 8.86365 15.3523i 0.467806 0.810263i −0.531517 0.847047i \(-0.678378\pi\)
0.999323 + 0.0367840i \(0.0117114\pi\)
\(360\) 0 0
\(361\) 9.41291 + 16.3036i 0.495416 + 0.858086i
\(362\) 0 0
\(363\) −19.9402 19.7365i −1.04659 1.03590i
\(364\) 0 0
\(365\) −0.928176 + 0.778832i −0.0485829 + 0.0407659i
\(366\) 0 0
\(367\) −19.0941 + 6.94969i −0.996704 + 0.362771i −0.788313 0.615275i \(-0.789045\pi\)
−0.208392 + 0.978045i \(0.566823\pi\)
\(368\) 0 0
\(369\) 6.99953 8.51782i 0.364381 0.443420i
\(370\) 0 0
\(371\) −0.298028 + 1.69020i −0.0154728 + 0.0877509i
\(372\) 0 0
\(373\) 9.09758 + 3.31125i 0.471055 + 0.171450i 0.566630 0.823972i \(-0.308247\pi\)
−0.0955754 + 0.995422i \(0.530469\pi\)
\(374\) 0 0
\(375\) 15.9491 11.2901i 0.823606 0.583019i
\(376\) 0 0
\(377\) 0.140987 0.00726119
\(378\) 0 0
\(379\) 4.12905 0.212095 0.106048 0.994361i \(-0.466180\pi\)
0.106048 + 0.994361i \(0.466180\pi\)
\(380\) 0 0
\(381\) 13.2096 + 6.07736i 0.676748 + 0.311353i
\(382\) 0 0
\(383\) 4.46371 + 1.62466i 0.228085 + 0.0830162i 0.453535 0.891239i \(-0.350163\pi\)
−0.225450 + 0.974255i \(0.572385\pi\)
\(384\) 0 0
\(385\) 2.64729 15.0136i 0.134919 0.765162i
\(386\) 0 0
\(387\) 21.4554 12.6828i 1.09064 0.644702i
\(388\) 0 0
\(389\) 20.4978 7.46059i 1.03928 0.378267i 0.234673 0.972074i \(-0.424598\pi\)
0.804607 + 0.593807i \(0.202376\pi\)
\(390\) 0 0
\(391\) −2.48238 + 2.08297i −0.125539 + 0.105340i
\(392\) 0 0
\(393\) 25.9543 7.09745i 1.30922 0.358019i
\(394\) 0 0
\(395\) 0.541773 + 0.938378i 0.0272595 + 0.0472149i
\(396\) 0 0
\(397\) 17.4245 30.1802i 0.874512 1.51470i 0.0172294 0.999852i \(-0.494515\pi\)
0.857282 0.514847i \(-0.172151\pi\)
\(398\) 0 0
\(399\) −0.543131 + 0.784210i −0.0271906 + 0.0392596i
\(400\) 0 0
\(401\) −3.26911 18.5401i −0.163252 0.925847i −0.950849 0.309656i \(-0.899786\pi\)
0.787597 0.616191i \(-0.211325\pi\)
\(402\) 0 0
\(403\) 0.0515948 + 0.0432932i 0.00257012 + 0.00215659i
\(404\) 0 0
\(405\) −19.9325 + 0.409386i −0.990453 + 0.0203426i
\(406\) 0 0
\(407\) 17.6772 + 14.8329i 0.876226 + 0.735241i
\(408\) 0 0
\(409\) −1.10439 6.26334i −0.0546088 0.309702i 0.945253 0.326339i \(-0.105815\pi\)
−0.999862 + 0.0166371i \(0.994704\pi\)
\(410\) 0 0
\(411\) 11.8413 17.0973i 0.584088 0.843346i
\(412\) 0 0
\(413\) −2.44251 + 4.23055i −0.120188 + 0.208172i
\(414\) 0 0
\(415\) 5.11007 + 8.85090i 0.250843 + 0.434474i
\(416\) 0 0
\(417\) −10.2667 + 2.80753i −0.502763 + 0.137485i
\(418\) 0 0
\(419\) 18.6286 15.6313i 0.910069 0.763638i −0.0620632 0.998072i \(-0.519768\pi\)
0.972132 + 0.234434i \(0.0753236\pi\)
\(420\) 0 0
\(421\) 7.50818 2.73275i 0.365926 0.133186i −0.152511 0.988302i \(-0.548736\pi\)
0.518438 + 0.855115i \(0.326514\pi\)
\(422\) 0 0
\(423\) 0.218637 + 21.2926i 0.0106305 + 1.03528i
\(424\) 0 0
\(425\) 0.0505638 0.286762i 0.00245271 0.0139100i
\(426\) 0 0
\(427\) −8.57397 3.12067i −0.414924 0.151020i
\(428\) 0 0
\(429\) −0.148191 0.0681784i −0.00715472 0.00329169i
\(430\) 0 0
\(431\) −9.87124 −0.475481 −0.237740 0.971329i \(-0.576407\pi\)
−0.237740 + 0.971329i \(0.576407\pi\)
\(432\) 0 0
\(433\) −6.10369 −0.293325 −0.146662 0.989187i \(-0.546853\pi\)
−0.146662 + 0.989187i \(0.546853\pi\)
\(434\) 0 0
\(435\) 24.4491 17.3072i 1.17224 0.829815i
\(436\) 0 0
\(437\) 0.405669 + 0.147651i 0.0194058 + 0.00706312i
\(438\) 0 0
\(439\) 2.62800 14.9041i 0.125427 0.711334i −0.855626 0.517595i \(-0.826827\pi\)
0.981053 0.193739i \(-0.0620615\pi\)
\(440\) 0 0
\(441\) −15.5634 2.57976i −0.741113 0.122846i
\(442\) 0 0
\(443\) −0.679204 + 0.247210i −0.0322699 + 0.0117453i −0.358105 0.933681i \(-0.616577\pi\)
0.325835 + 0.945427i \(0.394355\pi\)
\(444\) 0 0
\(445\) −5.72386 + 4.80289i −0.271337 + 0.227679i
\(446\) 0 0
\(447\) −1.08677 1.07566i −0.0514023 0.0508772i
\(448\) 0 0
\(449\) −0.834224 1.44492i −0.0393695 0.0681899i 0.845669 0.533707i \(-0.179202\pi\)
−0.885039 + 0.465517i \(0.845868\pi\)
\(450\) 0 0
\(451\) 9.58275 16.5978i 0.451234 0.781560i
\(452\) 0 0
\(453\) −6.08723 12.8810i −0.286003 0.605204i
\(454\) 0 0
\(455\) −0.00916673 0.0519871i −0.000429743 0.00243719i
\(456\) 0 0
\(457\) 8.49041 + 7.12430i 0.397165 + 0.333261i 0.819397 0.573227i \(-0.194309\pi\)
−0.422232 + 0.906488i \(0.638753\pi\)
\(458\) 0 0
\(459\) −11.3320 + 11.6865i −0.528932 + 0.545481i
\(460\) 0 0
\(461\) −16.7644 14.0670i −0.780797 0.655166i 0.162653 0.986683i \(-0.447995\pi\)
−0.943449 + 0.331517i \(0.892439\pi\)
\(462\) 0 0
\(463\) −4.31546 24.4742i −0.200556 1.13741i −0.904281 0.426938i \(-0.859592\pi\)
0.703724 0.710473i \(-0.251519\pi\)
\(464\) 0 0
\(465\) 14.2618 + 1.17400i 0.661375 + 0.0544429i
\(466\) 0 0
\(467\) −5.91777 + 10.2499i −0.273842 + 0.474308i −0.969842 0.243734i \(-0.921628\pi\)
0.696001 + 0.718041i \(0.254961\pi\)
\(468\) 0 0
\(469\) −7.27564 12.6018i −0.335958 0.581896i
\(470\) 0 0
\(471\) −5.52246 + 21.0416i −0.254462 + 0.969547i
\(472\) 0 0
\(473\) 33.1905 27.8501i 1.52610 1.28055i
\(474\) 0 0
\(475\) −0.0364524 + 0.0132676i −0.00167255 + 0.000608759i
\(476\) 0 0
\(477\) 3.83529 0.716944i 0.175606 0.0328266i
\(478\) 0 0
\(479\) −0.501383 + 2.84349i −0.0229088 + 0.129922i −0.994117 0.108309i \(-0.965456\pi\)
0.971209 + 0.238231i \(0.0765676\pi\)
\(480\) 0 0
\(481\) 0.0750857 + 0.0273290i 0.00342361 + 0.00124609i
\(482\) 0 0
\(483\) −0.218148 2.35417i −0.00992607 0.107119i
\(484\) 0 0
\(485\) 22.0220 0.999966
\(486\) 0 0
\(487\) −8.75903 −0.396910 −0.198455 0.980110i \(-0.563592\pi\)
−0.198455 + 0.980110i \(0.563592\pi\)
\(488\) 0 0
\(489\) 0.529731 + 5.71667i 0.0239553 + 0.258517i
\(490\) 0 0
\(491\) −21.2117 7.72044i −0.957272 0.348418i −0.184308 0.982869i \(-0.559004\pi\)
−0.772964 + 0.634450i \(0.781227\pi\)
\(492\) 0 0
\(493\) 4.24716 24.0869i 0.191283 1.08482i
\(494\) 0 0
\(495\) −34.0677 + 6.36840i −1.53123 + 0.286238i
\(496\) 0 0
\(497\) −7.54478 + 2.74608i −0.338430 + 0.123178i
\(498\) 0 0
\(499\) 19.4061 16.2836i 0.868734 0.728955i −0.0950968 0.995468i \(-0.530316\pi\)
0.963831 + 0.266513i \(0.0858716\pi\)
\(500\) 0 0
\(501\) −9.04139 + 34.4494i −0.403940 + 1.53909i
\(502\) 0 0
\(503\) 1.87207 + 3.24252i 0.0834714 + 0.144577i 0.904739 0.425967i \(-0.140066\pi\)
−0.821267 + 0.570543i \(0.806733\pi\)
\(504\) 0 0
\(505\) −15.2842 + 26.4731i −0.680139 + 1.17804i
\(506\) 0 0
\(507\) 22.4402 + 1.84723i 0.996604 + 0.0820382i
\(508\) 0 0
\(509\) 4.22831 + 23.9800i 0.187417 + 1.06289i 0.922811 + 0.385253i \(0.125886\pi\)
−0.735394 + 0.677640i \(0.763003\pi\)
\(510\) 0 0
\(511\) −0.552932 0.463965i −0.0244603 0.0205246i
\(512\) 0 0
\(513\) 2.10313 + 0.528954i 0.0928554 + 0.0233539i
\(514\) 0 0
\(515\) −7.74669 6.50025i −0.341360 0.286435i
\(516\) 0 0
\(517\) 6.42792 + 36.4546i 0.282700 + 1.60327i
\(518\) 0 0
\(519\) 10.3853 + 21.9760i 0.455862 + 0.964639i
\(520\) 0 0
\(521\) −9.81046 + 16.9922i −0.429804 + 0.744443i −0.996856 0.0792397i \(-0.974751\pi\)
0.567051 + 0.823682i \(0.308084\pi\)
\(522\) 0 0
\(523\) 10.4077 + 18.0267i 0.455097 + 0.788251i 0.998694 0.0510956i \(-0.0162713\pi\)
−0.543597 + 0.839346i \(0.682938\pi\)
\(524\) 0 0
\(525\) 0.150992 + 0.149449i 0.00658982 + 0.00652251i
\(526\) 0 0
\(527\) 8.95067 7.51051i 0.389897 0.327163i
\(528\) 0 0
\(529\) 20.6075 7.50052i 0.895978 0.326109i
\(530\) 0 0
\(531\) 10.9559 + 1.81604i 0.475447 + 0.0788095i
\(532\) 0 0
\(533\) 0.0115240 0.0653558i 0.000499159 0.00283087i
\(534\) 0 0
\(535\) −23.5147 8.55864i −1.01663 0.370022i
\(536\) 0 0
\(537\) 14.4055 10.1975i 0.621645 0.440054i
\(538\) 0 0
\(539\) −27.4245 −1.18126
\(540\) 0 0
\(541\) −30.6272 −1.31676 −0.658382 0.752684i \(-0.728759\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(542\) 0 0
\(543\) 37.8503 + 17.4139i 1.62431 + 0.747301i
\(544\) 0 0
\(545\) −30.1898 10.9882i −1.29319 0.470682i
\(546\) 0 0
\(547\) −3.93273 + 22.3036i −0.168151 + 0.953633i 0.777604 + 0.628754i \(0.216435\pi\)
−0.945756 + 0.324879i \(0.894676\pi\)
\(548\) 0 0
\(549\) 0.212980 + 20.7416i 0.00908976 + 0.885231i
\(550\) 0 0
\(551\) −3.06186 + 1.11443i −0.130440 + 0.0474761i
\(552\) 0 0
\(553\) −0.494473 + 0.414912i −0.0210271 + 0.0176439i
\(554\) 0 0
\(555\) 16.3757 4.47810i 0.695111 0.190085i
\(556\) 0 0
\(557\) −18.2259 31.5682i −0.772256 1.33759i −0.936324 0.351138i \(-0.885795\pi\)
0.164067 0.986449i \(-0.447539\pi\)
\(558\) 0 0
\(559\) 0.0750139 0.129928i 0.00317275 0.00549537i
\(560\) 0 0
\(561\) −16.1121 + 23.2637i −0.680253 + 0.982196i
\(562\) 0 0
\(563\) −4.60450 26.1134i −0.194056 1.10055i −0.913756 0.406263i \(-0.866832\pi\)
0.719700 0.694285i \(-0.244279\pi\)
\(564\) 0 0
\(565\) 21.3108 + 17.8819i 0.896552 + 0.752296i
\(566\) 0 0
\(567\) −2.30210 11.6514i −0.0966791 0.489313i
\(568\) 0 0
\(569\) 17.5941 + 14.7632i 0.737581 + 0.618904i 0.932187 0.361978i \(-0.117898\pi\)
−0.194606 + 0.980882i \(0.562343\pi\)
\(570\) 0 0
\(571\) 0.833165 + 4.72511i 0.0348669 + 0.197740i 0.997266 0.0739009i \(-0.0235449\pi\)
−0.962399 + 0.271641i \(0.912434\pi\)
\(572\) 0 0
\(573\) −10.7949 + 15.5865i −0.450965 + 0.651134i
\(574\) 0 0
\(575\) 0.0480718 0.0832628i 0.00200473 0.00347230i
\(576\) 0 0
\(577\) 2.15666 + 3.73545i 0.0897831 + 0.155509i 0.907419 0.420226i \(-0.138049\pi\)
−0.817636 + 0.575735i \(0.804716\pi\)
\(578\) 0 0
\(579\) −18.0536 + 4.93693i −0.750283 + 0.205172i
\(580\) 0 0
\(581\) −4.66393 + 3.91351i −0.193493 + 0.162360i
\(582\) 0 0
\(583\) 6.37369 2.31983i 0.263971 0.0960777i
\(584\) 0 0
\(585\) −0.103309 + 0.0610685i −0.00427131 + 0.00252487i
\(586\) 0 0
\(587\) −7.26235 + 41.1868i −0.299749 + 1.69996i 0.347497 + 0.937681i \(0.387032\pi\)
−0.647246 + 0.762281i \(0.724079\pi\)
\(588\) 0 0
\(589\) −1.46271 0.532383i −0.0602699 0.0219365i
\(590\) 0 0
\(591\) −34.7326 15.9795i −1.42871 0.657309i
\(592\) 0 0
\(593\) −31.5370 −1.29507 −0.647536 0.762035i \(-0.724200\pi\)
−0.647536 + 0.762035i \(0.724200\pi\)
\(594\) 0 0
\(595\) −9.15786 −0.375436
\(596\) 0 0
\(597\) 18.2179 12.8962i 0.745611 0.527807i
\(598\) 0 0
\(599\) −11.8686 4.31982i −0.484938 0.176503i 0.0879695 0.996123i \(-0.471962\pi\)
−0.572907 + 0.819620i \(0.694184\pi\)
\(600\) 0 0
\(601\) 3.56725 20.2309i 0.145511 0.825235i −0.821444 0.570289i \(-0.806831\pi\)
0.966955 0.254946i \(-0.0820577\pi\)
\(602\) 0 0
\(603\) −21.0023 + 25.5580i −0.855282 + 1.04080i
\(604\) 0 0
\(605\) −33.7180 + 12.2724i −1.37083 + 0.498942i
\(606\) 0 0
\(607\) −9.89160 + 8.30003i −0.401487 + 0.336888i −0.821068 0.570830i \(-0.806622\pi\)
0.419581 + 0.907718i \(0.362177\pi\)
\(608\) 0 0
\(609\) 12.6827 + 12.5532i 0.513930 + 0.508680i
\(610\) 0 0
\(611\) 0.0640889 + 0.111005i 0.00259276 + 0.00449079i
\(612\) 0 0
\(613\) 15.5799 26.9851i 0.629265 1.08992i −0.358434 0.933555i \(-0.616689\pi\)
0.987699 0.156364i \(-0.0499774\pi\)
\(614\) 0 0
\(615\) −6.02447 12.7482i −0.242930 0.514059i
\(616\) 0 0
\(617\) −1.23998 7.03230i −0.0499199 0.283110i 0.949621 0.313400i \(-0.101468\pi\)
−0.999541 + 0.0302901i \(0.990357\pi\)
\(618\) 0 0
\(619\) 7.68412 + 6.44774i 0.308851 + 0.259157i 0.784017 0.620740i \(-0.213168\pi\)
−0.475166 + 0.879896i \(0.657612\pi\)
\(620\) 0 0
\(621\) −4.83569 + 2.34625i −0.194049 + 0.0941520i
\(622\) 0 0
\(623\) −3.40981 2.86117i −0.136611 0.114630i
\(624\) 0 0
\(625\) −4.25900 24.1540i −0.170360 0.966160i
\(626\) 0 0
\(627\) 3.75722 + 0.309286i 0.150049 + 0.0123517i
\(628\) 0 0
\(629\) 6.93093 12.0047i 0.276354 0.478660i
\(630\) 0 0
\(631\) −3.53780 6.12765i −0.140838 0.243938i 0.786975 0.616985i \(-0.211646\pi\)
−0.927812 + 0.373047i \(0.878313\pi\)
\(632\) 0 0
\(633\) −10.5507 + 40.2002i −0.419353 + 1.59781i
\(634\) 0 0
\(635\) 14.2457 11.9536i 0.565324 0.474363i
\(636\) 0 0
\(637\) −0.0892352 + 0.0324790i −0.00353563 + 0.00128686i
\(638\) 0 0
\(639\) 11.8756 + 13.8613i 0.469793 + 0.548344i
\(640\) 0 0
\(641\) −0.870188 + 4.93508i −0.0343704 + 0.194924i −0.997158 0.0753337i \(-0.975998\pi\)
0.962788 + 0.270258i \(0.0871089\pi\)
\(642\) 0 0
\(643\) 1.53960 + 0.560367i 0.0607157 + 0.0220987i 0.372199 0.928153i \(-0.378604\pi\)
−0.311484 + 0.950251i \(0.600826\pi\)
\(644\) 0 0
\(645\) −2.94115 31.7398i −0.115807 1.24975i
\(646\) 0 0
\(647\) −34.4927 −1.35605 −0.678024 0.735040i \(-0.737164\pi\)
−0.678024 + 0.735040i \(0.737164\pi\)
\(648\) 0 0
\(649\) 19.3056 0.757813
\(650\) 0 0
\(651\) 0.786571 + 8.48840i 0.0308282 + 0.332687i
\(652\) 0 0
\(653\) −36.4230 13.2569i −1.42534 0.518783i −0.489751 0.871862i \(-0.662912\pi\)
−0.935593 + 0.353080i \(0.885134\pi\)
\(654\) 0 0
\(655\) 5.97570 33.8899i 0.233490 1.32419i
\(656\) 0 0
\(657\) −0.545365 + 1.54764i −0.0212767 + 0.0603792i
\(658\) 0 0
\(659\) 8.82552 3.21223i 0.343794 0.125131i −0.164352 0.986402i \(-0.552553\pi\)
0.508146 + 0.861271i \(0.330331\pi\)
\(660\) 0 0
\(661\) −18.4980 + 15.5217i −0.719489 + 0.603723i −0.927244 0.374458i \(-0.877829\pi\)
0.207755 + 0.978181i \(0.433384\pi\)
\(662\) 0 0
\(663\) −0.0248750 + 0.0947785i −0.000966065 + 0.00368089i
\(664\) 0 0
\(665\) 0.610007 + 1.05656i 0.0236551 + 0.0409718i
\(666\) 0 0
\(667\) 4.03784 6.99375i 0.156346 0.270799i
\(668\) 0 0
\(669\) 37.3935 + 3.07815i 1.44572 + 0.119008i
\(670\) 0 0
\(671\) 6.26159 + 35.5112i 0.241726 + 1.37090i
\(672\) 0 0
\(673\) −20.2742 17.0121i −0.781514 0.655768i 0.162115 0.986772i \(-0.448168\pi\)
−0.943630 + 0.331003i \(0.892613\pi\)
\(674\) 0 0
\(675\) 0.197346 0.440811i 0.00759585 0.0169668i
\(676\) 0 0
\(677\) 23.7986 + 19.9694i 0.914654 + 0.767486i 0.972999 0.230811i \(-0.0741378\pi\)
−0.0583448 + 0.998296i \(0.518582\pi\)
\(678\) 0 0
\(679\) 2.27807 + 12.9196i 0.0874245 + 0.495809i
\(680\) 0 0
\(681\) −16.0160 33.8910i −0.613734 1.29871i
\(682\) 0 0
\(683\) 19.0681 33.0268i 0.729619 1.26374i −0.227425 0.973796i \(-0.573031\pi\)
0.957044 0.289942i \(-0.0936359\pi\)
\(684\) 0 0
\(685\) −13.2993 23.0351i −0.508140 0.880125i
\(686\) 0 0
\(687\) 13.3016 + 13.1657i 0.507487 + 0.502303i
\(688\) 0 0
\(689\) 0.0179917 0.0150968i 0.000685428 0.000575142i
\(690\) 0 0
\(691\) 30.9436 11.2626i 1.17715 0.428448i 0.321957 0.946754i \(-0.395659\pi\)
0.855195 + 0.518306i \(0.173437\pi\)
\(692\) 0 0
\(693\) −7.26030 19.3277i −0.275796 0.734198i
\(694\) 0 0
\(695\) −2.36380 + 13.4058i −0.0896641 + 0.508510i
\(696\) 0 0
\(697\) −10.8185 3.93762i −0.409781 0.149148i
\(698\) 0 0
\(699\) −10.7992 + 7.64461i −0.408463 + 0.289146i
\(700\) 0 0
\(701\) −2.30710 −0.0871381 −0.0435690 0.999050i \(-0.513873\pi\)
−0.0435690 + 0.999050i \(0.513873\pi\)
\(702\) 0 0
\(703\) −1.84668 −0.0696490
\(704\) 0 0
\(705\) 24.7406 + 11.3825i 0.931784 + 0.428688i
\(706\) 0 0
\(707\) −17.1120 6.22826i −0.643563 0.234238i
\(708\) 0 0
\(709\) −1.93654 + 10.9826i −0.0727281 + 0.412462i 0.926608 + 0.376029i \(0.122711\pi\)
−0.999336 + 0.0364329i \(0.988400\pi\)
\(710\) 0 0
\(711\) 1.27830 + 0.720629i 0.0479400 + 0.0270257i
\(712\) 0 0
\(713\) 3.62525 1.31948i 0.135767 0.0494151i
\(714\) 0 0
\(715\) −0.159815 + 0.134100i −0.00597673 + 0.00501507i
\(716\) 0 0
\(717\) 5.39888 1.47637i 0.201625 0.0551362i
\(718\) 0 0
\(719\) −16.0850 27.8600i −0.599869 1.03900i −0.992840 0.119453i \(-0.961886\pi\)
0.392971 0.919551i \(-0.371447\pi\)
\(720\) 0 0
\(721\) 3.01213 5.21717i 0.112178 0.194297i
\(722\) 0 0
\(723\) −26.1777 + 37.7972i −0.973560 + 1.40569i
\(724\) 0 0
\(725\) 0.126010 + 0.714637i 0.00467989 + 0.0265410i
\(726\) 0 0
\(727\) 4.11022 + 3.44888i 0.152440 + 0.127912i 0.715818 0.698287i \(-0.246054\pi\)
−0.563378 + 0.826199i \(0.690499\pi\)
\(728\) 0 0
\(729\) −22.9558 + 14.2138i −0.850215 + 0.526435i
\(730\) 0 0
\(731\) −19.9377 16.7297i −0.737424 0.618772i
\(732\) 0 0
\(733\) −2.53463 14.3746i −0.0936187 0.530938i −0.995162 0.0982489i \(-0.968676\pi\)
0.901543 0.432689i \(-0.142435\pi\)
\(734\) 0 0
\(735\) −11.4876 + 16.5866i −0.423726 + 0.611805i
\(736\) 0 0
\(737\) −28.7534 + 49.8023i −1.05915 + 1.83449i
\(738\) 0 0
\(739\) −21.6083 37.4266i −0.794873 1.37676i −0.922920 0.384992i \(-0.874204\pi\)
0.128047 0.991768i \(-0.459129\pi\)
\(740\) 0 0
\(741\) 0.0125917 0.00344333i 0.000462569 0.000126494i
\(742\) 0 0
\(743\) −6.21431 + 5.21443i −0.227981 + 0.191299i −0.749622 0.661866i \(-0.769765\pi\)
0.521641 + 0.853165i \(0.325320\pi\)
\(744\) 0 0
\(745\) −1.83767 + 0.668859i −0.0673272 + 0.0245051i
\(746\) 0 0
\(747\) 12.0571 + 6.79706i 0.441146 + 0.248692i
\(748\) 0 0
\(749\) 2.58860 14.6807i 0.0945854 0.536420i
\(750\) 0 0
\(751\) 8.22744 + 2.99454i 0.300223 + 0.109272i 0.487740 0.872989i \(-0.337822\pi\)
−0.187516 + 0.982261i \(0.560044\pi\)
\(752\) 0 0
\(753\) 7.07968 + 3.25717i 0.257998 + 0.118698i
\(754\) 0 0
\(755\) −18.2210 −0.663129
\(756\) 0 0
\(757\) −32.1511 −1.16855 −0.584276 0.811555i \(-0.698622\pi\)
−0.584276 + 0.811555i \(0.698622\pi\)
\(758\) 0 0
\(759\) −7.62620 + 5.39848i −0.276813 + 0.195952i
\(760\) 0 0
\(761\) 23.0656 + 8.39520i 0.836128 + 0.304326i 0.724371 0.689410i \(-0.242130\pi\)
0.111756 + 0.993736i \(0.464352\pi\)
\(762\) 0 0
\(763\) 3.32342 18.8481i 0.120316 0.682346i
\(764\) 0 0
\(765\) 7.32108 + 19.4895i 0.264694 + 0.704644i
\(766\) 0 0
\(767\) 0.0628177 0.0228638i 0.00226822 0.000825563i
\(768\) 0 0
\(769\) 24.0648 20.1928i 0.867800 0.728170i −0.0958338 0.995397i \(-0.530552\pi\)
0.963634 + 0.267227i \(0.0861073\pi\)
\(770\) 0 0
\(771\) −16.9085 16.7358i −0.608945 0.602725i
\(772\) 0 0
\(773\) −14.3573 24.8675i −0.516395 0.894422i −0.999819 0.0190355i \(-0.993940\pi\)
0.483424 0.875386i \(-0.339393\pi\)
\(774\) 0 0
\(775\) −0.173332 + 0.300219i −0.00622625 + 0.0107842i
\(776\) 0 0
\(777\) 4.32116 + 9.14389i 0.155021 + 0.328035i
\(778\) 0 0
\(779\) 0.266332 + 1.51044i 0.00954233 + 0.0541173i
\(780\) 0 0
\(781\) 24.3071 + 20.3961i 0.869776 + 0.729829i
\(782\) 0 0
\(783\) 16.5763 37.0263i 0.592388 1.32321i
\(784\) 0 0
\(785\) 21.3132 + 17.8839i 0.760699 + 0.638303i
\(786\) 0 0
\(787\) 6.74033 + 38.2263i 0.240267 + 1.36262i 0.831233 +