Properties

Label 380.2.k.b.267.1
Level $380$
Weight $2$
Character 380.267
Analytic conductor $3.034$
Analytic rank $0$
Dimension $2$
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 267.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 380.267
Dual form 380.2.k.b.343.1

$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

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

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 \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 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 \(-0.570491\pi\)
0.975579 + 0.219650i \(0.0704915\pi\)
\(8\) −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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 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 0.970143 + 0.242536i \(0.0779791\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −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 \(-0.450781\pi\)
−0.988069 + 0.154011i \(0.950781\pi\)
\(24\) 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 \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) −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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 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 \(-0.0260248\pi\)
−0.0816682 + 0.996660i \(0.526025\pi\)
\(44\) 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 \(-0.683863\pi\)
0.837763 + 0.546033i \(0.183863\pi\)
\(48\) −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 −0.518571 + 0.855034i \(0.673536\pi\)
−0.855034 + 0.518571i \(0.826464\pi\)
\(54\) 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 \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −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 \(-0.833446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(68\) 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 −0.351123 0.936329i \(-0.614200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) 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 \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 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 \(-0.350483\pi\)
−0.891695 + 0.452638i \(0.850483\pi\)
\(84\) 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 \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 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 −0.999880 0.0154658i \(-0.995077\pi\)
−0.0154658 0.999880i \(-0.504923\pi\)
\(98\) −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 \(-0.465742\pi\)
−0.994214 + 0.107418i \(0.965742\pi\)
\(104\) 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 \(-0.591177\pi\)
0.959256 + 0.282540i \(0.0911770\pi\)
\(108\) −8.00000 8.00000i −0.769800 0.769800i
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −8.00000 + 8.00000i −0.755929 + 0.755929i
\(113\) −10.0000 + 10.0000i −0.940721 + 0.940721i −0.998339 0.0576178i \(-0.981650\pi\)
0.0576178 + 0.998339i \(0.481650\pi\)
\(114\) 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 \(-0.605255\pi\)
0.945825 + 0.324676i \(0.105255\pi\)
\(128\) 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 0.887666 0.460487i \(-0.152325\pi\)
−0.460487 + 0.887666i \(0.652325\pi\)
\(138\) −8.00000 8.00000i −0.681005 0.681005i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 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 \(-0.947610\pi\)
0.986486 0.163846i \(-0.0523901\pi\)
\(150\) 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 −0.975022 0.222108i \(-0.928706\pi\)
−0.222108 0.975022i \(-0.571294\pi\)
\(158\) 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 −0.994809 0.101755i \(-0.967554\pi\)
−0.101755 0.994809i \(-0.532446\pi\)
\(164\) 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 \(-0.624883\pi\)
0.924020 + 0.382344i \(0.124883\pi\)
\(168\) −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 −0.976374 0.216088i \(-0.930670\pi\)
0.216088 + 0.976374i \(0.430670\pi\)
\(174\) 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 \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 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 −0.968567 0.248752i \(-0.919980\pi\)
0.248752 + 0.968567i \(0.419980\pi\)
\(194\) −20.0000 −1.43592
\(195\) 0 0
\(196\) −2.00000 −0.142857
\(197\) −15.0000 15.0000i −1.06871 1.06871i −0.997459 0.0712470i \(-0.977302\pi\)
−0.0712470 0.997459i \(-0.522698\pi\)
\(198\) 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 \(-0.390135\pi\)
−0.941024 + 0.338340i \(0.890135\pi\)
\(224\) 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 \(-0.958879\pi\)
0.128827 + 0.991667i \(0.458879\pi\)
\(228\) 2.00000 2.00000i 0.132453 0.132453i
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) 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 −0.524097 0.851658i \(-0.675597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 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 \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 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 −0.956792 0.290774i \(-0.906087\pi\)
−0.290774 0.956792i \(-0.593913\pi\)
\(258\) 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 \(-0.00423656\pi\)
−0.0133092 + 0.999911i \(0.504237\pi\)
\(264\) 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 \(0.291286\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) −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 0.841178 0.540758i \(-0.181862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 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 \(-0.303774\pi\)
−0.815928 + 0.578153i \(0.803774\pi\)
\(284\) 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 −0.351850 0.936056i \(-0.614447\pi\)
0.936056 + 0.351850i \(0.114447\pi\)
\(294\) 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 \(-0.925799\pi\)
0.231004 + 0.972953i \(0.425799\pi\)
\(308\) 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 −0.551535 0.834152i \(-0.685958\pi\)
0.834152 + 0.551535i \(0.185958\pi\)
\(314\) −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 0.991240 + 0.132072i \(0.0421629\pi\)
0.132072 + 0.991240i \(0.457837\pi\)
\(318\) −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 0.924913 0.380178i \(-0.124137\pi\)
−0.380178 + 0.924913i \(0.624137\pi\)
\(338\) 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 \(-0.848214\pi\)
0.458983 + 0.888445i \(0.348214\pi\)
\(348\) 12.0000 + 12.0000i 0.643268 + 0.643268i
\(349\) 16.0000i 0.856460i 0.903670 + 0.428230i \(0.140863\pi\)
−0.903670 + 0.428230i \(0.859137\pi\)
\(350\) 16.0000 12.0000i 0.855236 0.641427i
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 15.0000i 0.798369 0.798369i −0.184469 0.982838i \(-0.559057\pi\)
0.982838 + 0.184469i \(0.0590565\pi\)
\(354\) −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 \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 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 \(-0.981309\pi\)
0.0586842 + 0.998277i \(0.481309\pi\)
\(368\) 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 −0.916899 0.399119i \(-0.869316\pi\)
0.399119 + 0.916899i \(0.369316\pi\)
\(374\) 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 \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −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 0.997113 + 0.0759373i \(0.0241949\pi\)
0.0759373 + 0.997113i \(0.475805\pi\)
\(384\) 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 \(0.0486055\pi\)
−0.988364 + 0.152106i \(0.951394\pi\)
\(390\) 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 0.222178 0.975006i \(-0.428683\pi\)
−0.975006 + 0.222178i \(0.928683\pi\)
\(398\) 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 \(-0.682205\pi\)
0.541663 0.840596i \(-0.317795\pi\)
\(410\) −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 −0.424744 0.905313i \(-0.639636\pi\)
0.905313 + 0.424744i \(0.139636\pi\)
\(434\) 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 \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −1.00000 −0.0476190
\(442\) 0 0
\(443\) −24.0000 24.0000i −1.14027 1.14027i −0.988400 0.151875i \(-0.951469\pi\)
−0.151875 0.988400i \(-0.548531\pi\)
\(444\) 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 \(-0.892833\pi\)
0.943858 0.330350i \(-0.107167\pi\)
\(450\) 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 0.964769 0.263099i \(-0.0847444\pi\)
−0.263099 + 0.964769i \(0.584744\pi\)
\(458\) 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 \(-0.291963\pi\)
−0.793919 + 0.608023i \(0.791963\pi\)
\(464\) 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 \(-0.621558\pi\)
0.927964 + 0.372670i \(0.121558\pi\)
\(468\) 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 \(-0.780645\pi\)
0.635861 + 0.771804i \(0.280645\pi\)
\(488\) −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 −0.997350 0.0727574i \(-0.976820\pi\)
−0.0727574 0.997350i \(-0.523180\pi\)
\(504\) 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 \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) −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 \(-0.0250569\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(524\) 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 \(-0.994762\pi\)
0.0164556 + 0.999865i \(0.494762\pi\)
\(548\) 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 0.593199 0.805056i \(-0.297865\pi\)
−0.805056 + 0.593199i \(0.797865\pi\)
\(558\) 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 \(-0.240513\pi\)
−0.685720 + 0.727865i \(0.740513\pi\)
\(564\) 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 \(-0.747483\pi\)
0.701492 0.712677i \(-0.252517\pi\)
\(570\) −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 0.322210 0.946668i \(-0.395574\pi\)
−0.946668 + 0.322210i \(0.895574\pi\)
\(578\) 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 0.407638 0.913144i \(-0.366353\pi\)
0.913144 0.407638i \(-0.133647\pi\)
\(588\) −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 −0.596952 0.802277i \(-0.703622\pi\)
0.802277 + 0.596952i \(0.203622\pi\)
\(594\) 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 \(-0.565490\pi\)
−0.204294 + 0.978909i \(0.565490\pi\)
\(600\) 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 \(-0.587759\pi\)
0.962234 + 0.272225i \(0.0877595\pi\)
\(608\) −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 0.00978840 0.999952i \(-0.496884\pi\)
0.999952 0.00978840i \(-0.00311579\pi\)
\(614\) 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 0.941339 0.337462i \(-0.109568\pi\)
−0.337462 + 0.941339i \(0.609568\pi\)
\(618\) −18.0000 18.0000i −0.724066 0.724066i
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 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 \(-0.285579\pi\)
−0.781567 + 0.623822i \(0.785579\pi\)
\(644\) 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 \(-0.641740\pi\)
0.902487 + 0.430718i \(0.141740\pi\)
\(648\) −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 −0.999770 0.0214444i \(-0.993173\pi\)
0.0214444 + 0.999770i \(0.493173\pi\)
\(654\) 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 \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 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 −0.978271 0.207328i \(-0.933523\pi\)
0.207328 + 0.978271i \(0.433523\pi\)
\(674\) 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 0.488329 0.872660i \(-0.337607\pi\)
−0.872660 + 0.488329i \(0.837607\pi\)
\(678\) −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 \(-0.153806\pi\)
−0.464611 + 0.885515i \(0.653806\pi\)
\(684\) −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 \(0.0971356\pi\)
−0.953799 + 0.300446i \(0.902864\pi\)
\(710\) 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 \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 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 \(-0.906487\pi\)
0.289573 + 0.957156i \(0.406487\pi\)
\(728\) 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 0.359678 0.933076i \(-0.382887\pi\)
0.933076 0.359678i \(-0.117113\pi\)
\(734\) 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 \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 40.0000 + 40.0000i 1.46845 + 1.46845i
\(743\) 31.0000 + 31.0000i 1.13728 + 1.13728i 0.988936 + 0.148344i \(0.0473942\pi\)
0.148344 + 0.988936i \(0.452606\pi\)
\(744\) 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 0.0875221 0.996163i \(-0.472105\pi\)
−0.996163 + 0.0875221i \(0.972105\pi\)
\(758\) 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 \(-0.789948\pi\)
0.790055 0.613036i \(-0.210052\pi\)
\(770\) 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 −0.249122 0.968472i \(-0.580142\pi\)
0.968472 + 0.249122i \(0.0801420\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 0 0
\(776\) 40.0000i 1.43592i
\(777\) 0 0
\(778\) 6.00000 + 6.00000i 0.215110 + 0.215110i
\(779\)