Properties

Label 380.2.k.a.343.1
Level $380$
Weight $2$
Character 380.343
Analytic conductor $3.034$
Analytic rank $0$
Dimension $2$
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] = [380,2,Mod(267,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.267");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 380.343
Dual form 380.2.k.a.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 + 1.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +(-2.00000 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 + 1.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +(-2.00000 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +(3.00000 + 1.00000i) q^{10} +(-2.00000 - 2.00000i) q^{12} +4.00000i q^{14} +(1.00000 - 3.00000i) q^{15} -4.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +(1.00000 - 1.00000i) q^{18} -1.00000 q^{19} +(-2.00000 - 4.00000i) q^{20} +4.00000 q^{21} +(4.00000 - 4.00000i) q^{23} +4.00000i q^{24} +(3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(4.00000 - 4.00000i) q^{28} -6.00000i q^{29} +(-4.00000 + 2.00000i) q^{30} +(4.00000 + 4.00000i) q^{32} -10.0000 q^{34} +(6.00000 + 2.00000i) q^{35} -2.00000 q^{36} +(1.00000 + 1.00000i) q^{38} +(-2.00000 + 6.00000i) q^{40} +2.00000 q^{41} +(-4.00000 - 4.00000i) q^{42} +(-6.00000 + 6.00000i) q^{43} +(-1.00000 - 2.00000i) q^{45} -8.00000 q^{46} +(-2.00000 - 2.00000i) q^{47} +(4.00000 - 4.00000i) q^{48} +1.00000i q^{49} +(-7.00000 + 1.00000i) q^{50} +10.0000i q^{51} +(-10.0000 - 10.0000i) q^{53} +8.00000i q^{54} -8.00000 q^{56} +(1.00000 - 1.00000i) q^{57} +(-6.00000 + 6.00000i) q^{58} +10.0000 q^{59} +(6.00000 + 2.00000i) q^{60} +2.00000 q^{61} +(2.00000 - 2.00000i) q^{63} -8.00000i q^{64} +(3.00000 + 3.00000i) q^{67} +(10.0000 + 10.0000i) q^{68} +8.00000i q^{69} +(-4.00000 - 8.00000i) q^{70} +(2.00000 + 2.00000i) q^{72} +(5.00000 + 5.00000i) q^{73} +(1.00000 + 7.00000i) q^{75} -2.00000i q^{76} -10.0000 q^{79} +(8.00000 - 4.00000i) q^{80} +5.00000 q^{81} +(-2.00000 - 2.00000i) q^{82} +(4.00000 - 4.00000i) q^{83} +8.00000i q^{84} +(-5.00000 + 15.0000i) q^{85} +12.0000 q^{86} +(6.00000 + 6.00000i) q^{87} -6.00000i q^{89} +(-1.00000 + 3.00000i) q^{90} +(8.00000 + 8.00000i) q^{92} +4.00000i q^{94} +(2.00000 - 1.00000i) q^{95} -8.00000 q^{96} +(-10.0000 + 10.0000i) q^{97} +(1.00000 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 2 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 4 q^{12} + 2 q^{15} - 8 q^{16} + 10 q^{17} + 2 q^{18} - 2 q^{19} - 4 q^{20} + 8 q^{21} + 8 q^{23} + 6 q^{25} - 8 q^{27} + 8 q^{28} - 8 q^{30} + 8 q^{32} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 2 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 12 q^{43} - 2 q^{45} - 16 q^{46} - 4 q^{47} + 8 q^{48} - 14 q^{50} - 20 q^{53} - 16 q^{56} + 2 q^{57} - 12 q^{58} + 20 q^{59} + 12 q^{60} + 4 q^{61} + 4 q^{63} + 6 q^{67} + 20 q^{68} - 8 q^{70} + 4 q^{72} + 10 q^{73} + 2 q^{75} - 20 q^{79} + 16 q^{80} + 10 q^{81} - 4 q^{82} + 8 q^{83} - 10 q^{85} + 24 q^{86} + 12 q^{87} - 2 q^{90} + 16 q^{92} + 4 q^{95} - 16 q^{96} - 20 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.707107 0.707107i
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 2.00000 0.816497
\(7\) −2.00000 2.00000i −0.755929 0.755929i 0.219650 0.975579i \(-0.429509\pi\)
−0.975579 + 0.219650i \(0.929509\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 1.00000i 0.333333i
\(10\) 3.00000 + 1.00000i 0.948683 + 0.316228i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −2.00000 2.00000i −0.577350 0.577350i
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) 4.00000i 1.06904i
\(15\) 1.00000 3.00000i 0.258199 0.774597i
\(16\) −4.00000 −1.00000
\(17\) 5.00000 5.00000i 1.21268 1.21268i 0.242536 0.970143i \(-0.422021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 1.00000 1.00000i 0.235702 0.235702i
\(19\) −1.00000 −0.229416
\(20\) −2.00000 4.00000i −0.447214 0.894427i
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 4.00000 4.00000i 0.834058 0.834058i −0.154011 0.988069i \(-0.549219\pi\)
0.988069 + 0.154011i \(0.0492193\pi\)
\(24\) 4.00000i 0.816497i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 0 0
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) 4.00000 4.00000i 0.755929 0.755929i
\(29\) 6.00000i 1.11417i −0.830455 0.557086i \(-0.811919\pi\)
0.830455 0.557086i \(-0.188081\pi\)
\(30\) −4.00000 + 2.00000i −0.730297 + 0.365148i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 0 0
\(34\) −10.0000 −1.71499
\(35\) 6.00000 + 2.00000i 1.01419 + 0.338062i
\(36\) −2.00000 −0.333333
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 1.00000 + 1.00000i 0.162221 + 0.162221i
\(39\) 0 0
\(40\) −2.00000 + 6.00000i −0.316228 + 0.948683i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −4.00000 4.00000i −0.617213 0.617213i
\(43\) −6.00000 + 6.00000i −0.914991 + 0.914991i −0.996660 0.0816682i \(-0.973975\pi\)
0.0816682 + 0.996660i \(0.473975\pi\)
\(44\) 0 0
\(45\) −1.00000 2.00000i −0.149071 0.298142i
\(46\) −8.00000 −1.17954
\(47\) −2.00000 2.00000i −0.291730 0.291730i 0.546033 0.837763i \(-0.316137\pi\)
−0.837763 + 0.546033i \(0.816137\pi\)
\(48\) 4.00000 4.00000i 0.577350 0.577350i
\(49\) 1.00000i 0.142857i
\(50\) −7.00000 + 1.00000i −0.989949 + 0.141421i
\(51\) 10.0000i 1.40028i
\(52\) 0 0
\(53\) −10.0000 10.0000i −1.37361 1.37361i −0.855034 0.518571i \(-0.826464\pi\)
−0.518571 0.855034i \(-0.673536\pi\)
\(54\) 8.00000i 1.08866i
\(55\) 0 0
\(56\) −8.00000 −1.06904
\(57\) 1.00000 1.00000i 0.132453 0.132453i
\(58\) −6.00000 + 6.00000i −0.787839 + 0.787839i
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 6.00000 + 2.00000i 0.774597 + 0.258199i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 2.00000 2.00000i 0.251976 0.251976i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 + 3.00000i 0.366508 + 0.366508i 0.866202 0.499694i \(-0.166554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 10.0000 + 10.0000i 1.21268 + 1.21268i
\(69\) 8.00000i 0.963087i
\(70\) −4.00000 8.00000i −0.478091 0.956183i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 2.00000 + 2.00000i 0.235702 + 0.235702i
\(73\) 5.00000 + 5.00000i 0.585206 + 0.585206i 0.936329 0.351123i \(-0.114200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 1.00000 + 7.00000i 0.115470 + 0.808290i
\(76\) 2.00000i 0.229416i
\(77\) 0 0
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 8.00000 4.00000i 0.894427 0.447214i
\(81\) 5.00000 0.555556
\(82\) −2.00000 2.00000i −0.220863 0.220863i
\(83\) 4.00000 4.00000i 0.439057 0.439057i −0.452638 0.891695i \(-0.649517\pi\)
0.891695 + 0.452638i \(0.149517\pi\)
\(84\) 8.00000i 0.872872i
\(85\) −5.00000 + 15.0000i −0.542326 + 1.62698i
\(86\) 12.0000 1.29399
\(87\) 6.00000 + 6.00000i 0.643268 + 0.643268i
\(88\) 0 0
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) −1.00000 + 3.00000i −0.105409 + 0.316228i
\(91\) 0 0
\(92\) 8.00000 + 8.00000i 0.834058 + 0.834058i
\(93\) 0 0
\(94\) 4.00000i 0.412568i
\(95\) 2.00000 1.00000i 0.205196 0.102598i
\(96\) −8.00000 −0.816497
\(97\) −10.0000 + 10.0000i −1.01535 + 1.01535i −0.0154658 + 0.999880i \(0.504923\pi\)
−0.999880 + 0.0154658i \(0.995077\pi\)
\(98\) 1.00000 1.00000i 0.101015 0.101015i
\(99\) 0 0
\(100\) 8.00000 + 6.00000i 0.800000 + 0.600000i
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 10.0000 10.0000i 0.990148 0.990148i
\(103\) 9.00000 9.00000i 0.886796 0.886796i −0.107418 0.994214i \(-0.534258\pi\)
0.994214 + 0.107418i \(0.0342582\pi\)
\(104\) 0 0
\(105\) −8.00000 + 4.00000i −0.780720 + 0.390360i
\(106\) 20.0000i 1.94257i
\(107\) −7.00000 7.00000i −0.676716 0.676716i 0.282540 0.959256i \(-0.408823\pi\)
−0.959256 + 0.282540i \(0.908823\pi\)
\(108\) 8.00000 8.00000i 0.769800 0.769800i
\(109\) 6.00000i 0.574696i −0.957826 0.287348i \(-0.907226\pi\)
0.957826 0.287348i \(-0.0927736\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 8.00000 + 8.00000i 0.755929 + 0.755929i
\(113\) −10.0000 10.0000i −0.940721 0.940721i 0.0576178 0.998339i \(-0.481650\pi\)
−0.998339 + 0.0576178i \(0.981650\pi\)
\(114\) −2.00000 −0.187317
\(115\) −4.00000 + 12.0000i −0.373002 + 1.11901i
\(116\) 12.0000 1.11417
\(117\) 0 0
\(118\) −10.0000 10.0000i −0.920575 0.920575i
\(119\) −20.0000 −1.83340
\(120\) −4.00000 8.00000i −0.365148 0.730297i
\(121\) 11.0000 1.00000
\(122\) −2.00000 2.00000i −0.181071 0.181071i
\(123\) −2.00000 + 2.00000i −0.180334 + 0.180334i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −4.00000 −0.356348
\(127\) −7.00000 7.00000i −0.621150 0.621150i 0.324676 0.945825i \(-0.394745\pi\)
−0.945825 + 0.324676i \(0.894745\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 12.0000i 1.05654i
\(130\) 0 0
\(131\) 20.0000i 1.74741i 0.486458 + 0.873704i \(0.338289\pi\)
−0.486458 + 0.873704i \(0.661711\pi\)
\(132\) 0 0
\(133\) 2.00000 + 2.00000i 0.173422 + 0.173422i
\(134\) 6.00000i 0.518321i
\(135\) 12.0000 + 4.00000i 1.03280 + 0.344265i
\(136\) 20.0000i 1.71499i
\(137\) 5.00000 5.00000i 0.427179 0.427179i −0.460487 0.887666i \(-0.652325\pi\)
0.887666 + 0.460487i \(0.152325\pi\)
\(138\) 8.00000 8.00000i 0.681005 0.681005i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) −4.00000 + 12.0000i −0.338062 + 1.01419i
\(141\) 4.00000 0.336861
\(142\) 0 0
\(143\) 0 0
\(144\) 4.00000i 0.333333i
\(145\) 6.00000 + 12.0000i 0.498273 + 0.996546i
\(146\) 10.0000i 0.827606i
\(147\) −1.00000 1.00000i −0.0824786 0.0824786i
\(148\) 0 0
\(149\) 4.00000i 0.327693i 0.986486 + 0.163846i \(0.0523901\pi\)
−0.986486 + 0.163846i \(0.947610\pi\)
\(150\) 6.00000 8.00000i 0.489898 0.653197i
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) −2.00000 + 2.00000i −0.162221 + 0.162221i
\(153\) 5.00000 + 5.00000i 0.404226 + 0.404226i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.0000 + 15.0000i −1.19713 + 1.19713i −0.222108 + 0.975022i \(0.571294\pi\)
−0.975022 + 0.222108i \(0.928706\pi\)
\(158\) 10.0000 + 10.0000i 0.795557 + 0.795557i
\(159\) 20.0000 1.58610
\(160\) −12.0000 4.00000i −0.948683 0.316228i
\(161\) −16.0000 −1.26098
\(162\) −5.00000 5.00000i −0.392837 0.392837i
\(163\) 14.0000 14.0000i 1.09656 1.09656i 0.101755 0.994809i \(-0.467554\pi\)
0.994809 0.101755i \(-0.0324458\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −8.00000 −0.620920
\(167\) −7.00000 7.00000i −0.541676 0.541676i 0.382344 0.924020i \(-0.375117\pi\)
−0.924020 + 0.382344i \(0.875117\pi\)
\(168\) 8.00000 8.00000i 0.617213 0.617213i
\(169\) 13.0000i 1.00000i
\(170\) 20.0000 10.0000i 1.53393 0.766965i
\(171\) 1.00000i 0.0764719i
\(172\) −12.0000 12.0000i −0.914991 0.914991i
\(173\) −10.0000 10.0000i −0.760286 0.760286i 0.216088 0.976374i \(-0.430670\pi\)
−0.976374 + 0.216088i \(0.930670\pi\)
\(174\) 12.0000i 0.909718i
\(175\) −14.0000 + 2.00000i −1.05830 + 0.151186i
\(176\) 0 0
\(177\) −10.0000 + 10.0000i −0.751646 + 0.751646i
\(178\) −6.00000 + 6.00000i −0.449719 + 0.449719i
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 4.00000 2.00000i 0.298142 0.149071i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −2.00000 + 2.00000i −0.147844 + 0.147844i
\(184\) 16.0000i 1.17954i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 4.00000 4.00000i 0.291730 0.291730i
\(189\) 16.0000i 1.16383i
\(190\) −3.00000 1.00000i −0.217643 0.0725476i
\(191\) 20.0000i 1.44715i −0.690246 0.723575i \(-0.742498\pi\)
0.690246 0.723575i \(-0.257502\pi\)
\(192\) 8.00000 + 8.00000i 0.577350 + 0.577350i
\(193\) −10.0000 10.0000i −0.719816 0.719816i 0.248752 0.968567i \(-0.419980\pi\)
−0.968567 + 0.248752i \(0.919980\pi\)
\(194\) 20.0000 1.43592
\(195\) 0 0
\(196\) −2.00000 −0.142857
\(197\) −15.0000 + 15.0000i −1.06871 + 1.06871i −0.0712470 + 0.997459i \(0.522698\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −2.00000 14.0000i −0.141421 0.989949i
\(201\) −6.00000 −0.423207
\(202\) −12.0000 12.0000i −0.844317 0.844317i
\(203\) −12.0000 + 12.0000i −0.842235 + 0.842235i
\(204\) −20.0000 −1.40028
\(205\) −4.00000 + 2.00000i −0.279372 + 0.139686i
\(206\) −18.0000 −1.25412
\(207\) 4.00000 + 4.00000i 0.278019 + 0.278019i
\(208\) 0 0
\(209\) 0 0
\(210\) 12.0000 + 4.00000i 0.828079 + 0.276026i
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 20.0000 20.0000i 1.37361 1.37361i
\(213\) 0 0
\(214\) 14.0000i 0.957020i
\(215\) 6.00000 18.0000i 0.409197 1.22759i
\(216\) −16.0000 −1.08866
\(217\) 0 0
\(218\) −6.00000 + 6.00000i −0.406371 + 0.406371i
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 9.00000 9.00000i 0.602685 0.602685i −0.338340 0.941024i \(-0.609865\pi\)
0.941024 + 0.338340i \(0.109865\pi\)
\(224\) 16.0000i 1.06904i
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 20.0000i 1.33038i
\(227\) 13.0000 + 13.0000i 0.862840 + 0.862840i 0.991667 0.128827i \(-0.0411211\pi\)
−0.128827 + 0.991667i \(0.541121\pi\)
\(228\) 2.00000 + 2.00000i 0.132453 + 0.132453i
\(229\) 6.00000i 0.396491i −0.980152 0.198246i \(-0.936476\pi\)
0.980152 0.198246i \(-0.0635244\pi\)
\(230\) 16.0000 8.00000i 1.05501 0.527504i
\(231\) 0 0
\(232\) −12.0000 12.0000i −0.787839 0.787839i
\(233\) 5.00000 + 5.00000i 0.327561 + 0.327561i 0.851658 0.524097i \(-0.175597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) 6.00000 + 2.00000i 0.391397 + 0.130466i
\(236\) 20.0000i 1.30189i
\(237\) 10.0000 10.0000i 0.649570 0.649570i
\(238\) 20.0000 + 20.0000i 1.29641 + 1.29641i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) −4.00000 + 12.0000i −0.258199 + 0.774597i
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −11.0000 11.0000i −0.707107 0.707107i
\(243\) 7.00000 7.00000i 0.449050 0.449050i
\(244\) 4.00000i 0.256074i
\(245\) −1.00000 2.00000i −0.0638877 0.127775i
\(246\) 4.00000 0.255031
\(247\) 0 0
\(248\) 0 0
\(249\) 8.00000i 0.506979i
\(250\) 13.0000 9.00000i 0.822192 0.569210i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 4.00000 + 4.00000i 0.251976 + 0.251976i
\(253\) 0 0
\(254\) 14.0000i 0.878438i
\(255\) −10.0000 20.0000i −0.626224 1.25245i
\(256\) 16.0000 1.00000
\(257\) −20.0000 + 20.0000i −1.24757 + 1.24757i −0.290774 + 0.956792i \(0.593913\pi\)
−0.956792 + 0.290774i \(0.906087\pi\)
\(258\) −12.0000 + 12.0000i −0.747087 + 0.747087i
\(259\) 0 0
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 20.0000 20.0000i 1.23560 1.23560i
\(263\) −16.0000 + 16.0000i −0.986602 + 0.986602i −0.999911 0.0133092i \(-0.995763\pi\)
0.0133092 + 0.999911i \(0.495763\pi\)
\(264\) 0 0
\(265\) 30.0000 + 10.0000i 1.84289 + 0.614295i
\(266\) 4.00000i 0.245256i
\(267\) 6.00000 + 6.00000i 0.367194 + 0.367194i
\(268\) −6.00000 + 6.00000i −0.366508 + 0.366508i
\(269\) 26.0000i 1.58525i −0.609711 0.792624i \(-0.708714\pi\)
0.609711 0.792624i \(-0.291286\pi\)
\(270\) −8.00000 16.0000i −0.486864 0.973729i
\(271\) 20.0000i 1.21491i 0.794353 + 0.607457i \(0.207810\pi\)
−0.794353 + 0.607457i \(0.792190\pi\)
\(272\) −20.0000 + 20.0000i −1.21268 + 1.21268i
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) 0 0
\(276\) −16.0000 −0.963087
\(277\) 5.00000 5.00000i 0.300421 0.300421i −0.540758 0.841178i \(-0.681862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 20.0000 + 20.0000i 1.19952 + 1.19952i
\(279\) 0 0
\(280\) 16.0000 8.00000i 0.956183 0.478091i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −4.00000 4.00000i −0.238197 0.238197i
\(283\) 4.00000 4.00000i 0.237775 0.237775i −0.578153 0.815928i \(-0.696226\pi\)
0.815928 + 0.578153i \(0.196226\pi\)
\(284\) 0 0
\(285\) −1.00000 + 3.00000i −0.0592349 + 0.177705i
\(286\) 0 0
\(287\) −4.00000 4.00000i −0.236113 0.236113i
\(288\) −4.00000 + 4.00000i −0.235702 + 0.235702i
\(289\) 33.0000i 1.94118i
\(290\) 6.00000 18.0000i 0.352332 1.05700i
\(291\) 20.0000i 1.17242i
\(292\) −10.0000 + 10.0000i −0.585206 + 0.585206i
\(293\) 10.0000 + 10.0000i 0.584206 + 0.584206i 0.936056 0.351850i \(-0.114447\pi\)
−0.351850 + 0.936056i \(0.614447\pi\)
\(294\) 2.00000i 0.116642i
\(295\) −20.0000 + 10.0000i −1.16445 + 0.582223i
\(296\) 0 0
\(297\) 0 0
\(298\) 4.00000 4.00000i 0.231714 0.231714i
\(299\) 0 0
\(300\) −14.0000 + 2.00000i −0.808290 + 0.115470i
\(301\) 24.0000 1.38334
\(302\) −10.0000 + 10.0000i −0.575435 + 0.575435i
\(303\) −12.0000 + 12.0000i −0.689382 + 0.689382i
\(304\) 4.00000 0.229416
\(305\) −4.00000 + 2.00000i −0.229039 + 0.114520i
\(306\) 10.0000i 0.571662i
\(307\) 13.0000 + 13.0000i 0.741949 + 0.741949i 0.972953 0.231004i \(-0.0742009\pi\)
−0.231004 + 0.972953i \(0.574201\pi\)
\(308\) 0 0
\(309\) 18.0000i 1.02398i
\(310\) 0 0
\(311\) 20.0000i 1.13410i −0.823685 0.567048i \(-0.808085\pi\)
0.823685 0.567048i \(-0.191915\pi\)
\(312\) 0 0
\(313\) 5.00000 + 5.00000i 0.282617 + 0.282617i 0.834152 0.551535i \(-0.185958\pi\)
−0.551535 + 0.834152i \(0.685958\pi\)
\(314\) 30.0000 1.69300
\(315\) −2.00000 + 6.00000i −0.112687 + 0.338062i
\(316\) 20.0000i 1.12509i
\(317\) 20.0000 20.0000i 1.12331 1.12331i 0.132072 0.991240i \(-0.457837\pi\)
0.991240 0.132072i \(-0.0421629\pi\)
\(318\) −20.0000 20.0000i −1.12154 1.12154i
\(319\) 0 0
\(320\) 8.00000 + 16.0000i 0.447214 + 0.894427i
\(321\) 14.0000 0.781404
\(322\) 16.0000 + 16.0000i 0.891645 + 0.891645i
\(323\) −5.00000 + 5.00000i −0.278207 + 0.278207i
\(324\) 10.0000i 0.555556i
\(325\) 0 0
\(326\) −28.0000 −1.55078
\(327\) 6.00000 + 6.00000i 0.331801 + 0.331801i
\(328\) 4.00000 4.00000i 0.220863 0.220863i
\(329\) 8.00000i 0.441054i
\(330\) 0 0
\(331\) 10.0000i 0.549650i 0.961494 + 0.274825i \(0.0886199\pi\)
−0.961494 + 0.274825i \(0.911380\pi\)
\(332\) 8.00000 + 8.00000i 0.439057 + 0.439057i
\(333\) 0 0
\(334\) 14.0000i 0.766046i
\(335\) −9.00000 3.00000i −0.491723 0.163908i
\(336\) −16.0000 −0.872872
\(337\) 10.0000 10.0000i 0.544735 0.544735i −0.380178 0.924913i \(-0.624137\pi\)
0.924913 + 0.380178i \(0.124137\pi\)
\(338\) −13.0000 + 13.0000i −0.707107 + 0.707107i
\(339\) 20.0000 1.08625
\(340\) −30.0000 10.0000i −1.62698 0.542326i
\(341\) 0 0
\(342\) −1.00000 + 1.00000i −0.0540738 + 0.0540738i
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 24.0000i 1.29399i
\(345\) −8.00000 16.0000i −0.430706 0.861411i
\(346\) 20.0000i 1.07521i
\(347\) 8.00000 + 8.00000i 0.429463 + 0.429463i 0.888445 0.458983i \(-0.151786\pi\)
−0.458983 + 0.888445i \(0.651786\pi\)
\(348\) −12.0000 + 12.0000i −0.643268 + 0.643268i
\(349\) 16.0000i 0.856460i −0.903670 0.428230i \(-0.859137\pi\)
0.903670 0.428230i \(-0.140863\pi\)
\(350\) 16.0000 + 12.0000i 0.855236 + 0.641427i
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 + 15.0000i 0.798369 + 0.798369i 0.982838 0.184469i \(-0.0590565\pi\)
−0.184469 + 0.982838i \(0.559057\pi\)
\(354\) 20.0000 1.06299
\(355\) 0 0
\(356\) 12.0000 0.635999
\(357\) 20.0000 20.0000i 1.05851 1.05851i
\(358\) −10.0000 10.0000i −0.528516 0.528516i
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) −6.00000 2.00000i −0.316228 0.105409i
\(361\) 1.00000 0.0526316
\(362\) −2.00000 2.00000i −0.105118 0.105118i
\(363\) −11.0000 + 11.0000i −0.577350 + 0.577350i
\(364\) 0 0
\(365\) −15.0000 5.00000i −0.785136 0.261712i
\(366\) 4.00000 0.209083
\(367\) 18.0000 + 18.0000i 0.939592 + 0.939592i 0.998277 0.0586842i \(-0.0186905\pi\)
−0.0586842 + 0.998277i \(0.518691\pi\)
\(368\) −16.0000 + 16.0000i −0.834058 + 0.834058i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) 40.0000i 2.07670i
\(372\) 0 0
\(373\) −10.0000 10.0000i −0.517780 0.517780i 0.399119 0.916899i \(-0.369316\pi\)
−0.916899 + 0.399119i \(0.869316\pi\)
\(374\) 0 0
\(375\) −9.00000 13.0000i −0.464758 0.671317i
\(376\) −8.00000 −0.412568
\(377\) 0 0
\(378\) 16.0000 16.0000i 0.822951 0.822951i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 2.00000 + 4.00000i 0.102598 + 0.205196i
\(381\) 14.0000 0.717242
\(382\) −20.0000 + 20.0000i −1.02329 + 1.02329i
\(383\) −21.0000 + 21.0000i −1.07305 + 1.07305i −0.0759373 + 0.997113i \(0.524195\pi\)
−0.997113 + 0.0759373i \(0.975805\pi\)
\(384\) 16.0000i 0.816497i
\(385\) 0 0
\(386\) 20.0000i 1.01797i
\(387\) −6.00000 6.00000i −0.304997 0.304997i
\(388\) −20.0000 20.0000i −1.01535 1.01535i
\(389\) 6.00000i 0.304212i −0.988364 0.152106i \(-0.951394\pi\)
0.988364 0.152106i \(-0.0486055\pi\)
\(390\) 0 0
\(391\) 40.0000i 2.02289i
\(392\) 2.00000 + 2.00000i 0.101015 + 0.101015i
\(393\) −20.0000 20.0000i −1.00887 1.00887i
\(394\) 30.0000 1.51138
\(395\) 20.0000 10.0000i 1.00631 0.503155i
\(396\) 0 0
\(397\) −15.0000 + 15.0000i −0.752828 + 0.752828i −0.975006 0.222178i \(-0.928683\pi\)
0.222178 + 0.975006i \(0.428683\pi\)
\(398\) 0 0
\(399\) −4.00000 −0.200250
\(400\) −12.0000 + 16.0000i −0.600000 + 0.800000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 6.00000 + 6.00000i 0.299253 + 0.299253i
\(403\) 0 0
\(404\) 24.0000i 1.19404i
\(405\) −10.0000 + 5.00000i −0.496904 + 0.248452i
\(406\) 24.0000 1.19110
\(407\) 0 0
\(408\) 20.0000 + 20.0000i 0.990148 + 0.990148i
\(409\) 34.0000i 1.68119i 0.541663 + 0.840596i \(0.317795\pi\)
−0.541663 + 0.840596i \(0.682205\pi\)
\(410\) 6.00000 + 2.00000i 0.296319 + 0.0987730i
\(411\) 10.0000i 0.493264i
\(412\) 18.0000 + 18.0000i 0.886796 + 0.886796i
\(413\) −20.0000 20.0000i −0.984136 0.984136i
\(414\) 8.00000i 0.393179i
\(415\) −4.00000 + 12.0000i −0.196352 + 0.589057i
\(416\) 0 0
\(417\) 20.0000 20.0000i 0.979404 0.979404i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −8.00000 16.0000i −0.390360 0.780720i
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −10.0000 + 10.0000i −0.486792 + 0.486792i
\(423\) 2.00000 2.00000i 0.0972433 0.0972433i
\(424\) −40.0000 −1.94257
\(425\) −5.00000 35.0000i −0.242536 1.69775i
\(426\) 0 0
\(427\) −4.00000 4.00000i −0.193574 0.193574i
\(428\) 14.0000 14.0000i 0.676716 0.676716i
\(429\) 0 0
\(430\) −24.0000 + 12.0000i −1.15738 + 0.578691i
\(431\) 10.0000i 0.481683i 0.970564 + 0.240842i \(0.0774234\pi\)
−0.970564 + 0.240842i \(0.922577\pi\)
\(432\) 16.0000 + 16.0000i 0.769800 + 0.769800i
\(433\) 10.0000 + 10.0000i 0.480569 + 0.480569i 0.905313 0.424744i \(-0.139636\pi\)
−0.424744 + 0.905313i \(0.639636\pi\)
\(434\) 0 0
\(435\) −18.0000 6.00000i −0.863034 0.287678i
\(436\) 12.0000 0.574696
\(437\) −4.00000 + 4.00000i −0.191346 + 0.191346i
\(438\) 10.0000 + 10.0000i 0.477818 + 0.477818i
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) −1.00000 −0.0476190
\(442\) 0 0
\(443\) 24.0000 24.0000i 1.14027 1.14027i 0.151875 0.988400i \(-0.451469\pi\)
0.988400 0.151875i \(-0.0485310\pi\)
\(444\) 0 0
\(445\) 6.00000 + 12.0000i 0.284427 + 0.568855i
\(446\) −18.0000 −0.852325
\(447\) −4.00000 4.00000i −0.189194 0.189194i
\(448\) −16.0000 + 16.0000i −0.755929 + 0.755929i
\(449\) 14.0000i 0.660701i 0.943858 + 0.330350i \(0.107167\pi\)
−0.943858 + 0.330350i \(0.892833\pi\)
\(450\) −1.00000 7.00000i −0.0471405 0.329983i
\(451\) 0 0
\(452\) 20.0000 20.0000i 0.940721 0.940721i
\(453\) 10.0000 + 10.0000i 0.469841 + 0.469841i
\(454\) 26.0000i 1.22024i
\(455\) 0 0
\(456\) 4.00000i 0.187317i
\(457\) 15.0000 15.0000i 0.701670 0.701670i −0.263099 0.964769i \(-0.584744\pi\)
0.964769 + 0.263099i \(0.0847444\pi\)
\(458\) −6.00000 + 6.00000i −0.280362 + 0.280362i
\(459\) −40.0000 −1.86704
\(460\) −24.0000 8.00000i −1.11901 0.373002i
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 4.00000 4.00000i 0.185896 0.185896i −0.608023 0.793919i \(-0.708037\pi\)
0.793919 + 0.608023i \(0.208037\pi\)
\(464\) 24.0000i 1.11417i
\(465\) 0 0
\(466\) 10.0000i 0.463241i
\(467\) −12.0000 12.0000i −0.555294 0.555294i 0.372670 0.927964i \(-0.378442\pi\)
−0.927964 + 0.372670i \(0.878442\pi\)
\(468\) 0 0
\(469\) 12.0000i 0.554109i
\(470\) −4.00000 8.00000i −0.184506 0.369012i
\(471\) 30.0000i 1.38233i
\(472\) 20.0000 20.0000i 0.920575 0.920575i
\(473\) 0 0
\(474\) −20.0000 −0.918630
\(475\) −3.00000 + 4.00000i −0.137649 + 0.183533i
\(476\) 40.0000i 1.83340i
\(477\) 10.0000 10.0000i 0.457869 0.457869i
\(478\) −20.0000 20.0000i −0.914779 0.914779i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 16.0000 8.00000i 0.730297 0.365148i
\(481\) 0 0
\(482\) −2.00000 2.00000i −0.0910975 0.0910975i
\(483\) 16.0000 16.0000i 0.728025 0.728025i
\(484\) 22.0000i 1.00000i
\(485\) 10.0000 30.0000i 0.454077 1.36223i
\(486\) −14.0000 −0.635053
\(487\) 3.00000 + 3.00000i 0.135943 + 0.135943i 0.771804 0.635861i \(-0.219355\pi\)
−0.635861 + 0.771804i \(0.719355\pi\)
\(488\) 4.00000 4.00000i 0.181071 0.181071i
\(489\) 28.0000i 1.26620i
\(490\) −1.00000 + 3.00000i −0.0451754 + 0.135526i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −4.00000 4.00000i −0.180334 0.180334i
\(493\) −30.0000 30.0000i −1.35113 1.35113i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 8.00000 8.00000i 0.358489 0.358489i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −22.0000 4.00000i −0.983870 0.178885i
\(501\) 14.0000 0.625474
\(502\) 0 0
\(503\) 24.0000 24.0000i 1.07011 1.07011i 0.0727574 0.997350i \(-0.476820\pi\)
0.997350 0.0727574i \(-0.0231799\pi\)
\(504\) 8.00000i 0.356348i
\(505\) −24.0000 + 12.0000i −1.06799 + 0.533993i
\(506\) 0 0
\(507\) 13.0000 + 13.0000i 0.577350 + 0.577350i
\(508\) 14.0000 14.0000i 0.621150 0.621150i
\(509\) 6.00000i 0.265945i −0.991120 0.132973i \(-0.957548\pi\)
0.991120 0.132973i \(-0.0424523\pi\)
\(510\) −10.0000 + 30.0000i −0.442807 + 1.32842i
\(511\) 20.0000i 0.884748i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 4.00000 + 4.00000i 0.176604 + 0.176604i
\(514\) 40.0000 1.76432
\(515\) −9.00000 + 27.0000i −0.396587 + 1.18976i
\(516\) 24.0000 1.05654
\(517\) 0 0
\(518\) 0 0
\(519\) 20.0000 0.877903
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) −6.00000 6.00000i −0.262613 0.262613i
\(523\) −21.0000 + 21.0000i −0.918266 + 0.918266i −0.996903 0.0786374i \(-0.974943\pi\)
0.0786374 + 0.996903i \(0.474943\pi\)
\(524\) −40.0000 −1.74741
\(525\) 12.0000 16.0000i 0.523723 0.698297i
\(526\) 32.0000 1.39527
\(527\) 0 0
\(528\) 0 0
\(529\) 9.00000i 0.391304i
\(530\) −20.0000 40.0000i −0.868744 1.73749i
\(531\) 10.0000i 0.433963i
\(532\) −4.00000 + 4.00000i −0.173422 + 0.173422i
\(533\) 0 0
\(534\) 12.0000i 0.519291i
\(535\) 21.0000 + 7.00000i 0.907909 + 0.302636i
\(536\) 12.0000 0.518321
\(537\) −10.0000 + 10.0000i −0.431532 + 0.431532i
\(538\) −26.0000 + 26.0000i −1.12094 + 1.12094i
\(539\) 0 0
\(540\) −8.00000 + 24.0000i −0.344265 + 1.03280i
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 20.0000 20.0000i 0.859074 0.859074i
\(543\) −2.00000 + 2.00000i −0.0858282 + 0.0858282i
\(544\) 40.0000 1.71499
\(545\) 6.00000 + 12.0000i 0.257012 + 0.514024i
\(546\) 0 0
\(547\) 23.0000 + 23.0000i 0.983409 + 0.983409i 0.999865 0.0164556i \(-0.00523822\pi\)
−0.0164556 + 0.999865i \(0.505238\pi\)
\(548\) 10.0000 + 10.0000i 0.427179 + 0.427179i
\(549\) 2.00000i 0.0853579i
\(550\) 0 0
\(551\) 6.00000i 0.255609i
\(552\) 16.0000 + 16.0000i 0.681005 + 0.681005i
\(553\) 20.0000 + 20.0000i 0.850487 + 0.850487i
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) 40.0000i 1.69638i
\(557\) −5.00000 + 5.00000i −0.211857 + 0.211857i −0.805056 0.593199i \(-0.797865\pi\)
0.593199 + 0.805056i \(0.297865\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −24.0000 8.00000i −1.01419 0.338062i
\(561\) 0 0
\(562\) 18.0000 + 18.0000i 0.759284 + 0.759284i
\(563\) −1.00000 + 1.00000i −0.0421450 + 0.0421450i −0.727865 0.685720i \(-0.759487\pi\)
0.685720 + 0.727865i \(0.259487\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 30.0000 + 10.0000i 1.26211 + 0.420703i
\(566\) −8.00000 −0.336265
\(567\) −10.0000 10.0000i −0.419961 0.419961i
\(568\) 0 0
\(569\) 34.0000i 1.42535i 0.701492 + 0.712677i \(0.252517\pi\)
−0.701492 + 0.712677i \(0.747483\pi\)
\(570\) 4.00000 2.00000i 0.167542 0.0837708i
\(571\) 20.0000i 0.836974i 0.908223 + 0.418487i \(0.137439\pi\)
−0.908223 + 0.418487i \(0.862561\pi\)
\(572\) 0 0
\(573\) 20.0000 + 20.0000i 0.835512 + 0.835512i
\(574\) 8.00000i 0.333914i
\(575\) −4.00000 28.0000i −0.166812 1.16768i
\(576\) 8.00000 0.333333
\(577\) −15.0000 + 15.0000i −0.624458 + 0.624458i −0.946668 0.322210i \(-0.895574\pi\)
0.322210 + 0.946668i \(0.395574\pi\)
\(578\) −33.0000 + 33.0000i −1.37262 + 1.37262i
\(579\) 20.0000 0.831172
\(580\) −24.0000 + 12.0000i −0.996546 + 0.498273i
\(581\) −16.0000 −0.663792
\(582\) −20.0000 + 20.0000i −0.829027 + 0.829027i
\(583\) 0 0
\(584\) 20.0000 0.827606
\(585\) 0 0
\(586\) 20.0000i 0.826192i
\(587\) −32.0000 32.0000i −1.32078 1.32078i −0.913144 0.407638i \(-0.866353\pi\)
−0.407638 0.913144i \(-0.633647\pi\)
\(588\) 2.00000 2.00000i 0.0824786 0.0824786i
\(589\) 0 0
\(590\) 30.0000 + 10.0000i 1.23508 + 0.411693i
\(591\) 30.0000i 1.23404i
\(592\) 0 0
\(593\) 5.00000 + 5.00000i 0.205325 + 0.205325i 0.802277 0.596952i \(-0.203622\pi\)
−0.596952 + 0.802277i \(0.703622\pi\)
\(594\) 0 0
\(595\) 40.0000 20.0000i 1.63984 0.819920i
\(596\) −8.00000 −0.327693
\(597\) 0 0
\(598\) 0 0
\(599\) 10.0000 0.408589 0.204294 0.978909i \(-0.434510\pi\)
0.204294 + 0.978909i \(0.434510\pi\)
\(600\) 16.0000 + 12.0000i 0.653197 + 0.489898i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −24.0000 24.0000i −0.978167 0.978167i
\(603\) −3.00000 + 3.00000i −0.122169 + 0.122169i
\(604\) 20.0000 0.813788
\(605\) −22.0000 + 11.0000i −0.894427 + 0.447214i
\(606\) 24.0000 0.974933
\(607\) −17.0000 17.0000i −0.690009 0.690009i 0.272225 0.962234i \(-0.412241\pi\)
−0.962234 + 0.272225i \(0.912241\pi\)
\(608\) −4.00000 4.00000i −0.162221 0.162221i
\(609\) 24.0000i 0.972529i
\(610\) 6.00000 + 2.00000i 0.242933 + 0.0809776i
\(611\) 0 0
\(612\) −10.0000 + 10.0000i −0.404226 + 0.404226i
\(613\) 25.0000 + 25.0000i 1.00974 + 1.00974i 0.999952 + 0.00978840i \(0.00311579\pi\)
0.00978840 + 0.999952i \(0.496884\pi\)
\(614\) 26.0000i 1.04927i
\(615\) 2.00000 6.00000i 0.0806478 0.241943i
\(616\) 0 0
\(617\) 15.0000 15.0000i 0.603877 0.603877i −0.337462 0.941339i \(-0.609568\pi\)
0.941339 + 0.337462i \(0.109568\pi\)
\(618\) 18.0000 18.0000i 0.724066 0.724066i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −32.0000 −1.28412
\(622\) −20.0000 + 20.0000i −0.801927 + 0.801927i
\(623\) −12.0000 + 12.0000i −0.480770 + 0.480770i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 10.0000i 0.399680i
\(627\) 0 0
\(628\) −30.0000 30.0000i −1.19713 1.19713i
\(629\) 0 0
\(630\) 8.00000 4.00000i 0.318728 0.159364i
\(631\) 40.0000i 1.59237i 0.605050 + 0.796187i \(0.293153\pi\)
−0.605050 + 0.796187i \(0.706847\pi\)
\(632\) −20.0000 + 20.0000i −0.795557 + 0.795557i
\(633\) 10.0000 + 10.0000i 0.397464 + 0.397464i
\(634\) −40.0000 −1.58860
\(635\) 21.0000 + 7.00000i 0.833360 + 0.277787i
\(636\) 40.0000i 1.58610i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 8.00000 24.0000i 0.316228 0.948683i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −14.0000 14.0000i −0.552536 0.552536i
\(643\) 4.00000 4.00000i 0.157745 0.157745i −0.623822 0.781567i \(-0.714421\pi\)
0.781567 + 0.623822i \(0.214421\pi\)
\(644\) 32.0000i 1.26098i
\(645\) 12.0000 + 24.0000i 0.472500 + 0.944999i
\(646\) 10.0000 0.393445
\(647\) −12.0000 12.0000i −0.471769 0.471769i 0.430718 0.902487i \(-0.358260\pi\)
−0.902487 + 0.430718i \(0.858260\pi\)
\(648\) 10.0000 10.0000i 0.392837 0.392837i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 28.0000 + 28.0000i 1.09656 + 1.09656i
\(653\) −25.0000 25.0000i −0.978326 0.978326i 0.0214444 0.999770i \(-0.493173\pi\)
−0.999770 + 0.0214444i \(0.993173\pi\)
\(654\) 12.0000i 0.469237i
\(655\) −20.0000 40.0000i −0.781465 1.56293i
\(656\) −8.00000 −0.312348
\(657\) −5.00000 + 5.00000i −0.195069 + 0.195069i
\(658\) 8.00000 8.00000i 0.311872 0.311872i
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 2.00000 0.0777910 0.0388955 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 10.0000 10.0000i 0.388661 0.388661i
\(663\) 0 0
\(664\) 16.0000i 0.620920i
\(665\) −6.00000 2.00000i −0.232670 0.0775567i
\(666\) 0 0
\(667\) −24.0000 24.0000i −0.929284 0.929284i
\(668\) 14.0000 14.0000i 0.541676 0.541676i
\(669\) 18.0000i 0.695920i
\(670\) 6.00000 + 12.0000i 0.231800 + 0.463600i
\(671\) 0 0
\(672\) 16.0000 + 16.0000i 0.617213 + 0.617213i
\(673\) −20.0000 20.0000i −0.770943 0.770943i 0.207328 0.978271i \(-0.433523\pi\)
−0.978271 + 0.207328i \(0.933523\pi\)
\(674\) −20.0000 −0.770371
\(675\) −28.0000 + 4.00000i −1.07772 + 0.153960i
\(676\) 26.0000 1.00000
\(677\) −10.0000 + 10.0000i −0.384331 + 0.384331i −0.872660 0.488329i \(-0.837607\pi\)
0.488329 + 0.872660i \(0.337607\pi\)
\(678\) −20.0000 20.0000i −0.768095 0.768095i
\(679\) 40.0000 1.53506
\(680\) 20.0000 + 40.0000i 0.766965 + 1.53393i
\(681\) −26.0000 −0.996322
\(682\) 0 0
\(683\) −11.0000 + 11.0000i −0.420903 + 0.420903i −0.885515 0.464611i \(-0.846194\pi\)
0.464611 + 0.885515i \(0.346194\pi\)
\(684\) 2.00000 0.0764719
\(685\) −5.00000 + 15.0000i −0.191040 + 0.573121i
\(686\) 24.0000 0.916324
\(687\) 6.00000 + 6.00000i 0.228914 + 0.228914i
\(688\) 24.0000 24.0000i 0.914991 0.914991i
\(689\) 0 0
\(690\) −8.00000 + 24.0000i −0.304555 + 0.913664i
\(691\) 20.0000i 0.760836i −0.924815 0.380418i \(-0.875780\pi\)
0.924815 0.380418i \(-0.124220\pi\)
\(692\) 20.0000 20.0000i 0.760286 0.760286i
\(693\) 0 0
\(694\) 16.0000i 0.607352i
\(695\) 40.0000 20.0000i 1.51729 0.758643i
\(696\) 24.0000 0.909718
\(697\) 10.0000 10.0000i 0.378777 0.378777i
\(698\) −16.0000 + 16.0000i −0.605609 + 0.605609i
\(699\) −10.0000 −0.378235
\(700\) −4.00000 28.0000i −0.151186 1.05830i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −8.00000 + 4.00000i −0.301297 + 0.150649i
\(706\) 30.0000i 1.12906i
\(707\) −24.0000 24.0000i −0.902613 0.902613i
\(708\) −20.0000 20.0000i −0.751646 0.751646i
\(709\) 16.0000i 0.600893i −0.953799 0.300446i \(-0.902864\pi\)
0.953799 0.300446i \(-0.0971356\pi\)
\(710\) 0 0
\(711\) 10.0000i 0.375029i
\(712\) −12.0000 12.0000i −0.449719 0.449719i
\(713\) 0 0
\(714\) −40.0000 −1.49696
\(715\) 0 0
\(716\) 20.0000i 0.747435i
\(717\) −20.0000 + 20.0000i −0.746914 + 0.746914i
\(718\) −20.0000 20.0000i −0.746393 0.746393i
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 4.00000 + 8.00000i 0.149071 + 0.298142i
\(721\) −36.0000 −1.34071
\(722\) −1.00000 1.00000i −0.0372161 0.0372161i
\(723\) −2.00000 + 2.00000i −0.0743808 + 0.0743808i
\(724\) 4.00000i 0.148659i
\(725\) −24.0000 18.0000i −0.891338 0.668503i
\(726\) 22.0000 0.816497
\(727\) 18.0000 + 18.0000i 0.667583 + 0.667583i 0.957156 0.289573i \(-0.0935133\pi\)
−0.289573 + 0.957156i \(0.593513\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 10.0000 + 20.0000i 0.370117 + 0.740233i
\(731\) 60.0000i 2.21918i
\(732\) −4.00000 4.00000i −0.147844 0.147844i
\(733\) 35.0000 + 35.0000i 1.29275 + 1.29275i 0.933076 + 0.359678i \(0.117113\pi\)
0.359678 + 0.933076i \(0.382887\pi\)
\(734\) 36.0000i 1.32878i
\(735\) 3.00000 + 1.00000i 0.110657 + 0.0368856i
\(736\) 32.0000 1.17954
\(737\) 0 0
\(738\) 2.00000 2.00000i 0.0736210 0.0736210i
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 40.0000 40.0000i 1.46845 1.46845i
\(743\) −31.0000 + 31.0000i −1.13728 + 1.13728i −0.148344 + 0.988936i \(0.547394\pi\)
−0.988936 + 0.148344i \(0.952606\pi\)
\(744\) 0 0
\(745\) −4.00000 8.00000i −0.146549 0.293097i
\(746\) 20.0000i 0.732252i
\(747\) 4.00000 + 4.00000i 0.146352 + 0.146352i
\(748\) 0 0
\(749\) 28.0000i 1.02310i
\(750\) −4.00000 + 22.0000i −0.146059 + 0.803326i
\(751\) 30.0000i 1.09472i 0.836899 + 0.547358i \(0.184366\pi\)
−0.836899 + 0.547358i \(0.815634\pi\)
\(752\) 8.00000 + 8.00000i 0.291730 + 0.291730i
\(753\) 0 0
\(754\) 0 0
\(755\) 10.0000 + 20.0000i 0.363937 + 0.727875i
\(756\) −32.0000 −1.16383
\(757\) −25.0000 + 25.0000i −0.908640 + 0.908640i −0.996163 0.0875221i \(-0.972105\pi\)
0.0875221 + 0.996163i \(0.472105\pi\)
\(758\) 20.0000 + 20.0000i 0.726433 + 0.726433i
\(759\) 0 0
\(760\) 2.00000 6.00000i 0.0725476 0.217643i
\(761\) −48.0000 −1.74000 −0.869999 0.493053i \(-0.835881\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(762\) −14.0000 14.0000i −0.507166 0.507166i
\(763\) −12.0000 + 12.0000i −0.434429 + 0.434429i
\(764\) 40.0000 1.44715
\(765\) −15.0000 5.00000i −0.542326 0.180775i
\(766\) 42.0000 1.51752
\(767\) 0 0
\(768\) −16.0000 + 16.0000i −0.577350 + 0.577350i
\(769\) 34.0000i 1.22607i 0.790055 + 0.613036i \(0.210052\pi\)
−0.790055 + 0.613036i \(0.789948\pi\)
\(770\) 0 0
\(771\) 40.0000i 1.44056i
\(772\) 20.0000 20.0000i 0.719816 0.719816i
\(773\) 20.0000 + 20.0000i 0.719350 + 0.719350i 0.968472 0.249122i \(-0.0801420\pi\)
−0.249122 + 0.968472i \(0.580142\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 0 0
\(776\) 40.0000i 1.43592i
\(777\) 0 0
\(778\) −6.00000 + 6.00000i −0.215110 + 0.215110