Properties

Label 380.2.u.a.321.2
Level $380$
Weight $2$
Character 380.321
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
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(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), 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: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 321.2
Root \(-0.168248 - 0.0612373i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.a.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +O(q^{10})\) \(q+(0.137157 + 0.115088i) q^{3} +(0.939693 - 0.342020i) q^{5} +(-1.55670 - 2.69628i) q^{7} +(-0.515378 - 2.92285i) q^{9} +(0.132577 - 0.229630i) q^{11} +(1.46159 - 1.22642i) q^{13} +(0.168248 + 0.0612373i) q^{15} +(0.886403 - 5.02704i) q^{17} +(0.524618 + 4.32721i) q^{19} +(0.0967984 - 0.548971i) q^{21} +(2.59422 + 0.944218i) q^{23} +(0.766044 - 0.642788i) q^{25} +(0.534268 - 0.925379i) q^{27} +(0.236980 + 1.34398i) q^{29} +(-0.337771 - 0.585037i) q^{31} +(0.0446117 - 0.0162373i) q^{33} +(-2.38500 - 2.00125i) q^{35} +6.05525 q^{37} +0.341614 q^{39} +(1.29142 + 1.08363i) q^{41} +(-6.23816 + 2.27050i) q^{43} +(-1.48397 - 2.57031i) q^{45} +(-1.49075 - 8.45444i) q^{47} +(-1.34660 + 2.33239i) q^{49} +(0.700131 - 0.587480i) q^{51} +(-2.22464 - 0.809704i) q^{53} +(0.0460435 - 0.261126i) q^{55} +(-0.426057 + 0.653886i) q^{57} +(-2.24310 + 12.7213i) q^{59} +(3.92356 + 1.42806i) q^{61} +(-7.07853 + 5.93959i) q^{63} +(0.953985 - 1.65235i) q^{65} +(0.447524 + 2.53804i) q^{67} +(0.247147 + 0.428071i) q^{69} +(-6.34605 + 2.30977i) q^{71} +(8.15753 + 6.84498i) q^{73} +0.179046 q^{75} -0.825529 q^{77} +(8.28927 + 6.95552i) q^{79} +(-8.18708 + 2.97985i) q^{81} +(1.66076 + 2.87651i) q^{83} +(-0.886403 - 5.02704i) q^{85} +(-0.122173 + 0.211610i) q^{87} +(-12.5017 + 10.4902i) q^{89} +(-5.58202 - 2.03169i) q^{91} +(0.0210033 - 0.119115i) q^{93} +(1.97297 + 3.88682i) q^{95} +(2.07945 - 11.7931i) q^{97} +(-0.739503 - 0.269157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.137157 + 0.115088i 0.0791877 + 0.0664464i 0.681522 0.731797i \(-0.261318\pi\)
−0.602335 + 0.798244i \(0.705763\pi\)
\(4\) 0 0
\(5\) 0.939693 0.342020i 0.420243 0.152956i
\(6\) 0 0
\(7\) −1.55670 2.69628i −0.588376 1.01910i −0.994445 0.105254i \(-0.966434\pi\)
0.406070 0.913842i \(-0.366899\pi\)
\(8\) 0 0
\(9\) −0.515378 2.92285i −0.171793 0.974284i
\(10\) 0 0
\(11\) 0.132577 0.229630i 0.0399735 0.0692361i −0.845346 0.534218i \(-0.820606\pi\)
0.885320 + 0.464982i \(0.153939\pi\)
\(12\) 0 0
\(13\) 1.46159 1.22642i 0.405372 0.340148i −0.417194 0.908818i \(-0.636986\pi\)
0.822566 + 0.568670i \(0.192542\pi\)
\(14\) 0 0
\(15\) 0.168248 + 0.0612373i 0.0434415 + 0.0158114i
\(16\) 0 0
\(17\) 0.886403 5.02704i 0.214984 1.21924i −0.665949 0.745997i \(-0.731973\pi\)
0.880934 0.473240i \(-0.156916\pi\)
\(18\) 0 0
\(19\) 0.524618 + 4.32721i 0.120356 + 0.992731i
\(20\) 0 0
\(21\) 0.0967984 0.548971i 0.0211232 0.119795i
\(22\) 0 0
\(23\) 2.59422 + 0.944218i 0.540932 + 0.196883i 0.598013 0.801486i \(-0.295957\pi\)
−0.0570811 + 0.998370i \(0.518179\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) 0.534268 0.925379i 0.102820 0.178089i
\(28\) 0 0
\(29\) 0.236980 + 1.34398i 0.0440060 + 0.249570i 0.998873 0.0474633i \(-0.0151137\pi\)
−0.954867 + 0.297034i \(0.904003\pi\)
\(30\) 0 0
\(31\) −0.337771 0.585037i −0.0606655 0.105076i 0.834098 0.551617i \(-0.185989\pi\)
−0.894763 + 0.446541i \(0.852656\pi\)
\(32\) 0 0
\(33\) 0.0446117 0.0162373i 0.00776590 0.00282656i
\(34\) 0 0
\(35\) −2.38500 2.00125i −0.403138 0.338273i
\(36\) 0 0
\(37\) 6.05525 0.995477 0.497738 0.867327i \(-0.334164\pi\)
0.497738 + 0.867327i \(0.334164\pi\)
\(38\) 0 0
\(39\) 0.341614 0.0547021
\(40\) 0 0
\(41\) 1.29142 + 1.08363i 0.201686 + 0.169235i 0.738037 0.674761i \(-0.235753\pi\)
−0.536351 + 0.843995i \(0.680198\pi\)
\(42\) 0 0
\(43\) −6.23816 + 2.27050i −0.951310 + 0.346249i −0.770622 0.637292i \(-0.780055\pi\)
−0.180688 + 0.983541i \(0.557832\pi\)
\(44\) 0 0
\(45\) −1.48397 2.57031i −0.221217 0.383160i
\(46\) 0 0
\(47\) −1.49075 8.45444i −0.217448 1.23321i −0.876608 0.481204i \(-0.840199\pi\)
0.659161 0.752002i \(-0.270912\pi\)
\(48\) 0 0
\(49\) −1.34660 + 2.33239i −0.192372 + 0.333198i
\(50\) 0 0
\(51\) 0.700131 0.587480i 0.0980380 0.0822636i
\(52\) 0 0
\(53\) −2.22464 0.809704i −0.305578 0.111221i 0.184680 0.982799i \(-0.440875\pi\)
−0.490258 + 0.871577i \(0.663097\pi\)
\(54\) 0 0
\(55\) 0.0460435 0.261126i 0.00620851 0.0352102i
\(56\) 0 0
\(57\) −0.426057 + 0.653886i −0.0564327 + 0.0866093i
\(58\) 0 0
\(59\) −2.24310 + 12.7213i −0.292027 + 1.65617i 0.387020 + 0.922071i \(0.373504\pi\)
−0.679047 + 0.734095i \(0.737607\pi\)
\(60\) 0 0
\(61\) 3.92356 + 1.42806i 0.502360 + 0.182844i 0.580755 0.814078i \(-0.302757\pi\)
−0.0783949 + 0.996922i \(0.524980\pi\)
\(62\) 0 0
\(63\) −7.07853 + 5.93959i −0.891811 + 0.748318i
\(64\) 0 0
\(65\) 0.953985 1.65235i 0.118327 0.204949i
\(66\) 0 0
\(67\) 0.447524 + 2.53804i 0.0546738 + 0.310070i 0.999865 0.0164477i \(-0.00523570\pi\)
−0.945191 + 0.326518i \(0.894125\pi\)
\(68\) 0 0
\(69\) 0.247147 + 0.428071i 0.0297530 + 0.0515337i
\(70\) 0 0
\(71\) −6.34605 + 2.30977i −0.753138 + 0.274120i −0.689926 0.723880i \(-0.742357\pi\)
−0.0632124 + 0.998000i \(0.520135\pi\)
\(72\) 0 0
\(73\) 8.15753 + 6.84498i 0.954767 + 0.801144i 0.980094 0.198535i \(-0.0636183\pi\)
−0.0253270 + 0.999679i \(0.508063\pi\)
\(74\) 0 0
\(75\) 0.179046 0.0206744
\(76\) 0 0
\(77\) −0.825529 −0.0940777
\(78\) 0 0
\(79\) 8.28927 + 6.95552i 0.932616 + 0.782557i 0.976285 0.216489i \(-0.0694604\pi\)
−0.0436696 + 0.999046i \(0.513905\pi\)
\(80\) 0 0
\(81\) −8.18708 + 2.97985i −0.909676 + 0.331095i
\(82\) 0 0
\(83\) 1.66076 + 2.87651i 0.182292 + 0.315738i 0.942661 0.333753i \(-0.108315\pi\)
−0.760369 + 0.649491i \(0.774982\pi\)
\(84\) 0 0
\(85\) −0.886403 5.02704i −0.0961439 0.545259i
\(86\) 0 0
\(87\) −0.122173 + 0.211610i −0.0130983 + 0.0226870i
\(88\) 0 0
\(89\) −12.5017 + 10.4902i −1.32518 + 1.11196i −0.340005 + 0.940424i \(0.610429\pi\)
−0.985178 + 0.171536i \(0.945127\pi\)
\(90\) 0 0
\(91\) −5.58202 2.03169i −0.585154 0.212979i
\(92\) 0 0
\(93\) 0.0210033 0.119115i 0.00217794 0.0123517i
\(94\) 0 0
\(95\) 1.97297 + 3.88682i 0.202423 + 0.398779i
\(96\) 0 0
\(97\) 2.07945 11.7931i 0.211136 1.19741i −0.676352 0.736579i \(-0.736440\pi\)
0.887487 0.460832i \(-0.152449\pi\)
\(98\) 0 0
\(99\) −0.739503 0.269157i −0.0743228 0.0270513i
\(100\) 0 0
\(101\) −3.01399 + 2.52904i −0.299903 + 0.251649i −0.780304 0.625400i \(-0.784936\pi\)
0.480401 + 0.877049i \(0.340491\pi\)
\(102\) 0 0
\(103\) −4.89662 + 8.48119i −0.482478 + 0.835677i −0.999798 0.0201156i \(-0.993597\pi\)
0.517319 + 0.855792i \(0.326930\pi\)
\(104\) 0 0
\(105\) −0.0967984 0.548971i −0.00944656 0.0535741i
\(106\) 0 0
\(107\) −2.26321 3.91999i −0.218792 0.378959i 0.735647 0.677365i \(-0.236878\pi\)
−0.954439 + 0.298406i \(0.903545\pi\)
\(108\) 0 0
\(109\) 13.9978 5.09478i 1.34075 0.487991i 0.430698 0.902496i \(-0.358267\pi\)
0.910047 + 0.414505i \(0.136045\pi\)
\(110\) 0 0
\(111\) 0.830521 + 0.696890i 0.0788295 + 0.0661458i
\(112\) 0 0
\(113\) 7.08578 0.666574 0.333287 0.942825i \(-0.391842\pi\)
0.333287 + 0.942825i \(0.391842\pi\)
\(114\) 0 0
\(115\) 2.76071 0.257437
\(116\) 0 0
\(117\) −4.33792 3.63994i −0.401040 0.336513i
\(118\) 0 0
\(119\) −14.9342 + 5.43559i −1.36901 + 0.498279i
\(120\) 0 0
\(121\) 5.46485 + 9.46539i 0.496804 + 0.860490i
\(122\) 0 0
\(123\) 0.0524141 + 0.297255i 0.00472602 + 0.0268026i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) 6.06757 5.09129i 0.538409 0.451779i −0.332584 0.943074i \(-0.607921\pi\)
0.870994 + 0.491294i \(0.163476\pi\)
\(128\) 0 0
\(129\) −1.11692 0.406524i −0.0983390 0.0357925i
\(130\) 0 0
\(131\) 0.344789 1.95540i 0.0301244 0.170844i −0.966034 0.258416i \(-0.916800\pi\)
0.996158 + 0.0875718i \(0.0279107\pi\)
\(132\) 0 0
\(133\) 10.8507 8.15067i 0.940874 0.706753i
\(134\) 0 0
\(135\) 0.185549 1.05230i 0.0159695 0.0905678i
\(136\) 0 0
\(137\) −14.6490 5.33180i −1.25155 0.455527i −0.370625 0.928783i \(-0.620856\pi\)
−0.880925 + 0.473256i \(0.843079\pi\)
\(138\) 0 0
\(139\) −4.09214 + 3.43371i −0.347091 + 0.291244i −0.799621 0.600506i \(-0.794966\pi\)
0.452530 + 0.891749i \(0.350522\pi\)
\(140\) 0 0
\(141\) 0.768542 1.33115i 0.0647229 0.112103i
\(142\) 0 0
\(143\) −0.0878497 0.498220i −0.00734636 0.0416633i
\(144\) 0 0
\(145\) 0.682356 + 1.18187i 0.0566665 + 0.0981493i
\(146\) 0 0
\(147\) −0.453127 + 0.164925i −0.0373733 + 0.0136028i
\(148\) 0 0
\(149\) 4.46146 + 3.74361i 0.365497 + 0.306689i 0.806977 0.590582i \(-0.201102\pi\)
−0.441480 + 0.897271i \(0.645546\pi\)
\(150\) 0 0
\(151\) 18.8838 1.53674 0.768371 0.640005i \(-0.221068\pi\)
0.768371 + 0.640005i \(0.221068\pi\)
\(152\) 0 0
\(153\) −15.1501 −1.22482
\(154\) 0 0
\(155\) −0.517495 0.434230i −0.0415662 0.0348782i
\(156\) 0 0
\(157\) 14.2666 5.19261i 1.13860 0.414415i 0.297190 0.954818i \(-0.403951\pi\)
0.841406 + 0.540403i \(0.181728\pi\)
\(158\) 0 0
\(159\) −0.211938 0.367088i −0.0168078 0.0291119i
\(160\) 0 0
\(161\) −1.49254 8.46459i −0.117628 0.667103i
\(162\) 0 0
\(163\) −8.16395 + 14.1404i −0.639450 + 1.10756i 0.346104 + 0.938196i \(0.387504\pi\)
−0.985554 + 0.169363i \(0.945829\pi\)
\(164\) 0 0
\(165\) 0.0363678 0.0305162i 0.00283123 0.00237568i
\(166\) 0 0
\(167\) −6.23503 2.26937i −0.482481 0.175609i 0.0893166 0.996003i \(-0.471532\pi\)
−0.571798 + 0.820394i \(0.693754\pi\)
\(168\) 0 0
\(169\) −1.62529 + 9.21746i −0.125022 + 0.709035i
\(170\) 0 0
\(171\) 12.3774 3.76353i 0.946526 0.287804i
\(172\) 0 0
\(173\) 4.35064 24.6737i 0.330773 1.87591i −0.134761 0.990878i \(-0.543027\pi\)
0.465534 0.885030i \(-0.345862\pi\)
\(174\) 0 0
\(175\) −2.92563 1.06484i −0.221157 0.0804945i
\(176\) 0 0
\(177\) −1.77173 + 1.48666i −0.133171 + 0.111744i
\(178\) 0 0
\(179\) 11.1911 19.3836i 0.836463 1.44880i −0.0563712 0.998410i \(-0.517953\pi\)
0.892834 0.450386i \(-0.148714\pi\)
\(180\) 0 0
\(181\) 2.58924 + 14.6843i 0.192457 + 1.09148i 0.915994 + 0.401192i \(0.131404\pi\)
−0.723537 + 0.690286i \(0.757485\pi\)
\(182\) 0 0
\(183\) 0.373791 + 0.647425i 0.0276314 + 0.0478590i
\(184\) 0 0
\(185\) 5.69007 2.07102i 0.418343 0.152264i
\(186\) 0 0
\(187\) −1.03684 0.870016i −0.0758216 0.0636218i
\(188\) 0 0
\(189\) −3.32677 −0.241987
\(190\) 0 0
\(191\) −6.51501 −0.471409 −0.235705 0.971825i \(-0.575740\pi\)
−0.235705 + 0.971825i \(0.575740\pi\)
\(192\) 0 0
\(193\) −3.58822 3.01087i −0.258286 0.216728i 0.504445 0.863444i \(-0.331697\pi\)
−0.762730 + 0.646717i \(0.776142\pi\)
\(194\) 0 0
\(195\) 0.321012 0.116839i 0.0229882 0.00836701i
\(196\) 0 0
\(197\) −0.757915 1.31275i −0.0539992 0.0935293i 0.837762 0.546035i \(-0.183864\pi\)
−0.891761 + 0.452506i \(0.850530\pi\)
\(198\) 0 0
\(199\) −2.33312 13.2318i −0.165390 0.937974i −0.948661 0.316294i \(-0.897561\pi\)
0.783271 0.621680i \(-0.213550\pi\)
\(200\) 0 0
\(201\) −0.230718 + 0.399615i −0.0162736 + 0.0281866i
\(202\) 0 0
\(203\) 3.25483 2.73113i 0.228444 0.191688i
\(204\) 0 0
\(205\) 1.58416 + 0.576588i 0.110643 + 0.0402706i
\(206\) 0 0
\(207\) 1.42281 8.06915i 0.0988920 0.560844i
\(208\) 0 0
\(209\) 1.06321 + 0.453221i 0.0735439 + 0.0313500i
\(210\) 0 0
\(211\) 4.56298 25.8780i 0.314129 1.78151i −0.262935 0.964814i \(-0.584690\pi\)
0.577064 0.816699i \(-0.304198\pi\)
\(212\) 0 0
\(213\) −1.13623 0.413556i −0.0778535 0.0283364i
\(214\) 0 0
\(215\) −5.08539 + 4.26715i −0.346821 + 0.291017i
\(216\) 0 0
\(217\) −1.05161 + 1.82145i −0.0713882 + 0.123648i
\(218\) 0 0
\(219\) 0.331085 + 1.87768i 0.0223726 + 0.126882i
\(220\) 0 0
\(221\) −4.86970 8.43458i −0.327572 0.567371i
\(222\) 0 0
\(223\) 10.5393 3.83599i 0.705764 0.256877i 0.0358940 0.999356i \(-0.488572\pi\)
0.669870 + 0.742479i \(0.266350\pi\)
\(224\) 0 0
\(225\) −2.27358 1.90776i −0.151572 0.127184i
\(226\) 0 0
\(227\) 25.4125 1.68669 0.843345 0.537373i \(-0.180583\pi\)
0.843345 + 0.537373i \(0.180583\pi\)
\(228\) 0 0
\(229\) 19.4056 1.28236 0.641180 0.767391i \(-0.278445\pi\)
0.641180 + 0.767391i \(0.278445\pi\)
\(230\) 0 0
\(231\) −0.113227 0.0950089i −0.00744980 0.00625112i
\(232\) 0 0
\(233\) 0.417709 0.152034i 0.0273650 0.00996005i −0.328301 0.944573i \(-0.606476\pi\)
0.355666 + 0.934613i \(0.384254\pi\)
\(234\) 0 0
\(235\) −4.29243 7.43471i −0.280007 0.484987i
\(236\) 0 0
\(237\) 0.336432 + 1.90800i 0.0218536 + 0.123938i
\(238\) 0 0
\(239\) 3.60952 6.25187i 0.233480 0.404400i −0.725350 0.688381i \(-0.758322\pi\)
0.958830 + 0.283981i \(0.0916552\pi\)
\(240\) 0 0
\(241\) −16.9786 + 14.2468i −1.09369 + 0.917715i −0.996985 0.0775979i \(-0.975275\pi\)
−0.0967055 + 0.995313i \(0.530831\pi\)
\(242\) 0 0
\(243\) −4.47815 1.62991i −0.287273 0.104559i
\(244\) 0 0
\(245\) −0.467670 + 2.65229i −0.0298784 + 0.169449i
\(246\) 0 0
\(247\) 6.07376 + 5.68121i 0.386464 + 0.361487i
\(248\) 0 0
\(249\) −0.103269 + 0.585668i −0.00654441 + 0.0371152i
\(250\) 0 0
\(251\) −16.3734 5.95944i −1.03348 0.376156i −0.231076 0.972936i \(-0.574224\pi\)
−0.802405 + 0.596780i \(0.796447\pi\)
\(252\) 0 0
\(253\) 0.560755 0.470529i 0.0352544 0.0295819i
\(254\) 0 0
\(255\) 0.456978 0.791509i 0.0286171 0.0495662i
\(256\) 0 0
\(257\) 4.85152 + 27.5143i 0.302630 + 1.71630i 0.634458 + 0.772958i \(0.281224\pi\)
−0.331828 + 0.943340i \(0.607665\pi\)
\(258\) 0 0
\(259\) −9.42618 16.3266i −0.585714 1.01449i
\(260\) 0 0
\(261\) 3.80612 1.38531i 0.235593 0.0857487i
\(262\) 0 0
\(263\) 6.02485 + 5.05545i 0.371508 + 0.311733i 0.809358 0.587316i \(-0.199815\pi\)
−0.437850 + 0.899048i \(0.644260\pi\)
\(264\) 0 0
\(265\) −2.36742 −0.145429
\(266\) 0 0
\(267\) −2.92201 −0.178824
\(268\) 0 0
\(269\) 5.86938 + 4.92499i 0.357862 + 0.300282i 0.803938 0.594713i \(-0.202734\pi\)
−0.446076 + 0.894995i \(0.647179\pi\)
\(270\) 0 0
\(271\) 7.47803 2.72178i 0.454258 0.165336i −0.104750 0.994499i \(-0.533404\pi\)
0.559008 + 0.829162i \(0.311182\pi\)
\(272\) 0 0
\(273\) −0.531789 0.921086i −0.0321854 0.0557467i
\(274\) 0 0
\(275\) −0.0460435 0.261126i −0.00277653 0.0157465i
\(276\) 0 0
\(277\) −10.1397 + 17.5624i −0.609233 + 1.05522i 0.382134 + 0.924107i \(0.375189\pi\)
−0.991367 + 0.131116i \(0.958144\pi\)
\(278\) 0 0
\(279\) −1.53590 + 1.28877i −0.0919517 + 0.0771566i
\(280\) 0 0
\(281\) −25.1981 9.17135i −1.50319 0.547117i −0.546306 0.837585i \(-0.683967\pi\)
−0.956884 + 0.290469i \(0.906189\pi\)
\(282\) 0 0
\(283\) −2.60987 + 14.8013i −0.155141 + 0.879846i 0.803517 + 0.595282i \(0.202960\pi\)
−0.958657 + 0.284563i \(0.908151\pi\)
\(284\) 0 0
\(285\) −0.176721 + 0.760172i −0.0104680 + 0.0450287i
\(286\) 0 0
\(287\) 0.911418 5.16891i 0.0537993 0.305111i
\(288\) 0 0
\(289\) −8.51066 3.09763i −0.500627 0.182213i
\(290\) 0 0
\(291\) 1.64246 1.37819i 0.0962830 0.0807910i
\(292\) 0 0
\(293\) 0.701131 1.21439i 0.0409605 0.0709457i −0.844818 0.535053i \(-0.820292\pi\)
0.885779 + 0.464108i \(0.153625\pi\)
\(294\) 0 0
\(295\) 2.24310 + 12.7213i 0.130598 + 0.740660i
\(296\) 0 0
\(297\) −0.141663 0.245368i −0.00822014 0.0142377i
\(298\) 0 0
\(299\) 4.94969 1.80154i 0.286248 0.104186i
\(300\) 0 0
\(301\) 15.8328 + 13.2853i 0.912588 + 0.765753i
\(302\) 0 0
\(303\) −0.704454 −0.0404698
\(304\) 0 0
\(305\) 4.17537 0.239081
\(306\) 0 0
\(307\) 11.5407 + 9.68381i 0.658664 + 0.552684i 0.909686 0.415297i \(-0.136322\pi\)
−0.251022 + 0.967981i \(0.580767\pi\)
\(308\) 0 0
\(309\) −1.64769 + 0.599711i −0.0937340 + 0.0341164i
\(310\) 0 0
\(311\) 8.77503 + 15.1988i 0.497586 + 0.861845i 0.999996 0.00278480i \(-0.000886430\pi\)
−0.502410 + 0.864630i \(0.667553\pi\)
\(312\) 0 0
\(313\) −2.35274 13.3430i −0.132985 0.754194i −0.976242 0.216683i \(-0.930476\pi\)
0.843257 0.537510i \(-0.180635\pi\)
\(314\) 0 0
\(315\) −4.62018 + 8.00239i −0.260318 + 0.450884i
\(316\) 0 0
\(317\) −20.4370 + 17.1487i −1.14786 + 0.963165i −0.999667 0.0257936i \(-0.991789\pi\)
−0.148189 + 0.988959i \(0.547344\pi\)
\(318\) 0 0
\(319\) 0.340036 + 0.123763i 0.0190384 + 0.00692940i
\(320\) 0 0
\(321\) 0.140731 0.798123i 0.00785482 0.0445469i
\(322\) 0 0
\(323\) 22.2181 + 1.19838i 1.23625 + 0.0666796i
\(324\) 0 0
\(325\) 0.331316 1.87898i 0.0183781 0.104227i
\(326\) 0 0
\(327\) 2.50625 + 0.912199i 0.138596 + 0.0504447i
\(328\) 0 0
\(329\) −20.4749 + 17.1804i −1.12882 + 0.947189i
\(330\) 0 0
\(331\) 5.91678 10.2482i 0.325215 0.563290i −0.656340 0.754465i \(-0.727897\pi\)
0.981556 + 0.191175i \(0.0612298\pi\)
\(332\) 0 0
\(333\) −3.12074 17.6986i −0.171016 0.969878i
\(334\) 0 0
\(335\) 1.28859 + 2.23191i 0.0704034 + 0.121942i
\(336\) 0 0
\(337\) −9.66454 + 3.51760i −0.526461 + 0.191616i −0.591557 0.806263i \(-0.701487\pi\)
0.0650965 + 0.997879i \(0.479264\pi\)
\(338\) 0 0
\(339\) 0.971866 + 0.815492i 0.0527845 + 0.0442915i
\(340\) 0 0
\(341\) −0.179123 −0.00970004
\(342\) 0 0
\(343\) −13.4087 −0.724004
\(344\) 0 0
\(345\) 0.378651 + 0.317726i 0.0203859 + 0.0171058i
\(346\) 0 0
\(347\) −27.3527 + 9.95559i −1.46837 + 0.534444i −0.947658 0.319287i \(-0.896557\pi\)
−0.520714 + 0.853731i \(0.674334\pi\)
\(348\) 0 0
\(349\) −8.10052 14.0305i −0.433611 0.751036i 0.563570 0.826068i \(-0.309427\pi\)
−0.997181 + 0.0750319i \(0.976094\pi\)
\(350\) 0 0
\(351\) −0.354022 2.00776i −0.0188963 0.107166i
\(352\) 0 0
\(353\) −6.83410 + 11.8370i −0.363742 + 0.630020i −0.988573 0.150740i \(-0.951834\pi\)
0.624831 + 0.780760i \(0.285168\pi\)
\(354\) 0 0
\(355\) −5.17335 + 4.34096i −0.274573 + 0.230394i
\(356\) 0 0
\(357\) −2.67390 0.973220i −0.141518 0.0515082i
\(358\) 0 0
\(359\) 3.32554 18.8601i 0.175515 0.995396i −0.762032 0.647539i \(-0.775798\pi\)
0.937548 0.347857i \(-0.113091\pi\)
\(360\) 0 0
\(361\) −18.4496 + 4.54027i −0.971029 + 0.238961i
\(362\) 0 0
\(363\) −0.339815 + 1.92719i −0.0178357 + 0.101151i
\(364\) 0 0
\(365\) 10.0067 + 3.64214i 0.523774 + 0.190638i
\(366\) 0 0
\(367\) −7.94360 + 6.66547i −0.414652 + 0.347935i −0.826124 0.563488i \(-0.809459\pi\)
0.411472 + 0.911422i \(0.365015\pi\)
\(368\) 0 0
\(369\) 2.50172 4.33311i 0.130235 0.225573i
\(370\) 0 0
\(371\) 1.27991 + 7.25872i 0.0664495 + 0.376854i
\(372\) 0 0
\(373\) 4.04511 + 7.00634i 0.209448 + 0.362774i 0.951541 0.307523i \(-0.0995000\pi\)
−0.742093 + 0.670297i \(0.766167\pi\)
\(374\) 0 0
\(375\) 0.168248 0.0612373i 0.00868830 0.00316228i
\(376\) 0 0
\(377\) 1.99465 + 1.67371i 0.102730 + 0.0862004i
\(378\) 0 0
\(379\) 2.89627 0.148771 0.0743857 0.997230i \(-0.476300\pi\)
0.0743857 + 0.997230i \(0.476300\pi\)
\(380\) 0 0
\(381\) 1.41816 0.0726545
\(382\) 0 0
\(383\) 9.28938 + 7.79471i 0.474665 + 0.398291i 0.848493 0.529207i \(-0.177510\pi\)
−0.373828 + 0.927498i \(0.621955\pi\)
\(384\) 0 0
\(385\) −0.775743 + 0.282347i −0.0395355 + 0.0143898i
\(386\) 0 0
\(387\) 9.85136 + 17.0630i 0.500773 + 0.867364i
\(388\) 0 0
\(389\) −5.88197 33.3583i −0.298227 1.69133i −0.653787 0.756678i \(-0.726821\pi\)
0.355560 0.934654i \(-0.384290\pi\)
\(390\) 0 0
\(391\) 7.04615 12.2043i 0.356339 0.617197i
\(392\) 0 0
\(393\) 0.272334 0.228515i 0.0137374 0.0115271i
\(394\) 0 0
\(395\) 10.1683 + 3.70096i 0.511622 + 0.186215i
\(396\) 0 0
\(397\) −5.04822 + 28.6299i −0.253363 + 1.43689i 0.546878 + 0.837212i \(0.315816\pi\)
−0.800241 + 0.599679i \(0.795295\pi\)
\(398\) 0 0
\(399\) 2.42630 + 0.130867i 0.121467 + 0.00655156i
\(400\) 0 0
\(401\) −4.63072 + 26.2621i −0.231247 + 1.31147i 0.619128 + 0.785290i \(0.287486\pi\)
−0.850375 + 0.526177i \(0.823625\pi\)
\(402\) 0 0
\(403\) −1.21118 0.440835i −0.0603333 0.0219595i
\(404\) 0 0
\(405\) −6.67417 + 5.60029i −0.331642 + 0.278281i
\(406\) 0 0
\(407\) 0.802787 1.39047i 0.0397927 0.0689230i
\(408\) 0 0
\(409\) 4.38604 + 24.8745i 0.216876 + 1.22996i 0.877622 + 0.479353i \(0.159129\pi\)
−0.660746 + 0.750609i \(0.729760\pi\)
\(410\) 0 0
\(411\) −1.39559 2.41723i −0.0688392 0.119233i
\(412\) 0 0
\(413\) 37.7918 13.7551i 1.85962 0.676845i
\(414\) 0 0
\(415\) 2.54443 + 2.13503i 0.124901 + 0.104804i
\(416\) 0 0
\(417\) −0.956446 −0.0468374
\(418\) 0 0
\(419\) 10.8366 0.529401 0.264701 0.964331i \(-0.414727\pi\)
0.264701 + 0.964331i \(0.414727\pi\)
\(420\) 0 0
\(421\) 22.8967 + 19.2126i 1.11592 + 0.936365i 0.998391 0.0567046i \(-0.0180593\pi\)
0.117526 + 0.993070i \(0.462504\pi\)
\(422\) 0 0
\(423\) −23.9428 + 8.71446i −1.16414 + 0.423711i
\(424\) 0 0
\(425\) −2.55230 4.42071i −0.123805 0.214436i
\(426\) 0 0
\(427\) −2.25735 12.8021i −0.109241 0.619535i
\(428\) 0 0
\(429\) 0.0452902 0.0784450i 0.00218663 0.00378736i
\(430\) 0 0
\(431\) 1.26927 1.06505i 0.0611387 0.0513015i −0.611706 0.791085i \(-0.709517\pi\)
0.672845 + 0.739784i \(0.265072\pi\)
\(432\) 0 0
\(433\) −26.2816 9.56572i −1.26301 0.459699i −0.378234 0.925710i \(-0.623469\pi\)
−0.884779 + 0.466011i \(0.845691\pi\)
\(434\) 0 0
\(435\) −0.0424302 + 0.240634i −0.00203437 + 0.0115375i
\(436\) 0 0
\(437\) −2.72486 + 11.7211i −0.130348 + 0.560696i
\(438\) 0 0
\(439\) 2.76255 15.6672i 0.131849 0.747755i −0.845153 0.534525i \(-0.820490\pi\)
0.977002 0.213230i \(-0.0683984\pi\)
\(440\) 0 0
\(441\) 7.51123 + 2.73386i 0.357678 + 0.130184i
\(442\) 0 0
\(443\) −13.5410 + 11.3622i −0.643350 + 0.539835i −0.905045 0.425316i \(-0.860163\pi\)
0.261695 + 0.965151i \(0.415719\pi\)
\(444\) 0 0
\(445\) −8.15994 + 14.1334i −0.386818 + 0.669988i
\(446\) 0 0
\(447\) 0.181075 + 1.02693i 0.00856454 + 0.0485719i
\(448\) 0 0
\(449\) −19.4043 33.6092i −0.915744 1.58611i −0.805809 0.592176i \(-0.798269\pi\)
−0.109935 0.993939i \(-0.535064\pi\)
\(450\) 0 0
\(451\) 0.420047 0.152885i 0.0197792 0.00719906i
\(452\) 0 0
\(453\) 2.59005 + 2.17331i 0.121691 + 0.102111i
\(454\) 0 0
\(455\) −5.94026 −0.278484
\(456\) 0 0
\(457\) 20.7093 0.968738 0.484369 0.874864i \(-0.339049\pi\)
0.484369 + 0.874864i \(0.339049\pi\)
\(458\) 0 0
\(459\) −4.17834 3.50605i −0.195028 0.163648i
\(460\) 0 0
\(461\) −12.6137 + 4.59101i −0.587478 + 0.213824i −0.618620 0.785691i \(-0.712308\pi\)
0.0311419 + 0.999515i \(0.490086\pi\)
\(462\) 0 0
\(463\) −19.7557 34.2178i −0.918124 1.59024i −0.802262 0.596973i \(-0.796370\pi\)
−0.115863 0.993265i \(-0.536963\pi\)
\(464\) 0 0
\(465\) −0.0210033 0.119115i −0.000974003 0.00552385i
\(466\) 0 0
\(467\) −1.87193 + 3.24228i −0.0866228 + 0.150035i −0.906082 0.423103i \(-0.860941\pi\)
0.819459 + 0.573138i \(0.194274\pi\)
\(468\) 0 0
\(469\) 6.14659 5.15760i 0.283823 0.238156i
\(470\) 0 0
\(471\) 2.55437 + 0.929715i 0.117699 + 0.0428390i
\(472\) 0 0
\(473\) −0.305660 + 1.73349i −0.0140543 + 0.0797058i
\(474\) 0 0
\(475\) 3.18336 + 2.97762i 0.146063 + 0.136623i
\(476\) 0 0
\(477\) −1.22011 + 6.91961i −0.0558652 + 0.316827i
\(478\) 0 0
\(479\) 23.0700 + 8.39679i 1.05409 + 0.383659i 0.810207 0.586144i \(-0.199355\pi\)
0.243888 + 0.969803i \(0.421577\pi\)
\(480\) 0 0
\(481\) 8.85029 7.42628i 0.403539 0.338609i
\(482\) 0 0
\(483\) 0.769465 1.33275i 0.0350119 0.0606423i
\(484\) 0 0
\(485\) −2.07945 11.7931i −0.0944228 0.535498i
\(486\) 0 0
\(487\) −1.89990 3.29072i −0.0860927 0.149117i 0.819764 0.572702i \(-0.194105\pi\)
−0.905856 + 0.423585i \(0.860771\pi\)
\(488\) 0 0
\(489\) −2.74714 + 0.999876i −0.124230 + 0.0452160i
\(490\) 0 0
\(491\) −13.1947 11.0716i −0.595466 0.499656i 0.294518 0.955646i \(-0.404841\pi\)
−0.889985 + 0.455990i \(0.849285\pi\)
\(492\) 0 0
\(493\) 6.96629 0.313746
\(494\) 0 0
\(495\) −0.786962 −0.0353713
\(496\) 0 0
\(497\) 16.1067 + 13.5151i 0.722483 + 0.606235i
\(498\) 0 0
\(499\) 6.09378 2.21795i 0.272795 0.0992892i −0.202001 0.979385i \(-0.564744\pi\)
0.474795 + 0.880096i \(0.342522\pi\)
\(500\) 0 0
\(501\) −0.594001 1.02884i −0.0265380 0.0459652i
\(502\) 0 0
\(503\) −3.73168 21.1634i −0.166387 0.943630i −0.947622 0.319393i \(-0.896521\pi\)
0.781235 0.624237i \(-0.214590\pi\)
\(504\) 0 0
\(505\) −1.96724 + 3.40737i −0.0875412 + 0.151626i
\(506\) 0 0
\(507\) −1.28374 + 1.07719i −0.0570130 + 0.0478396i
\(508\) 0 0
\(509\) −0.301747 0.109827i −0.0133747 0.00486799i 0.335324 0.942103i \(-0.391154\pi\)
−0.348699 + 0.937235i \(0.613376\pi\)
\(510\) 0 0
\(511\) 5.75717 32.6505i 0.254682 1.44437i
\(512\) 0 0
\(513\) 4.28460 + 1.82642i 0.189170 + 0.0806384i
\(514\) 0 0
\(515\) −1.70058 + 9.64446i −0.0749364 + 0.424986i
\(516\) 0 0
\(517\) −2.13903 0.778544i −0.0940746 0.0342403i
\(518\) 0 0
\(519\) 3.43638 2.88347i 0.150840 0.126570i
\(520\) 0 0
\(521\) −2.12082 + 3.67337i −0.0929148 + 0.160933i −0.908736 0.417370i \(-0.862952\pi\)
0.815822 + 0.578304i \(0.196285\pi\)
\(522\) 0 0
\(523\) −3.24517 18.4043i −0.141901 0.804763i −0.969803 0.243890i \(-0.921577\pi\)
0.827902 0.560874i \(-0.189535\pi\)
\(524\) 0 0
\(525\) −0.278720 0.482757i −0.0121643 0.0210693i
\(526\) 0 0
\(527\) −3.24040 + 1.17941i −0.141154 + 0.0513759i
\(528\) 0 0
\(529\) −11.7806 9.88510i −0.512200 0.429787i
\(530\) 0 0
\(531\) 38.3384 1.66374
\(532\) 0 0
\(533\) 3.21651 0.139323
\(534\) 0 0
\(535\) −3.46743 2.90952i −0.149910 0.125790i
\(536\) 0 0
\(537\) 3.76577 1.37063i 0.162505 0.0591469i
\(538\) 0 0
\(539\) 0.357057 + 0.618442i 0.0153796 + 0.0266382i
\(540\) 0 0
\(541\) −4.08726 23.1800i −0.175725 0.996585i −0.937304 0.348513i \(-0.886687\pi\)
0.761579 0.648072i \(-0.224424\pi\)
\(542\) 0 0
\(543\) −1.33486 + 2.31205i −0.0572845 + 0.0992197i
\(544\) 0 0
\(545\) 11.4111 9.57505i 0.488798 0.410150i
\(546\) 0 0
\(547\) −21.1791 7.70857i −0.905554 0.329595i −0.153078 0.988214i \(-0.548919\pi\)
−0.752476 + 0.658619i \(0.771141\pi\)
\(548\) 0 0
\(549\) 2.15189 12.2040i 0.0918405 0.520853i
\(550\) 0 0
\(551\) −5.69136 + 1.73054i −0.242460 + 0.0737233i
\(552\) 0 0
\(553\) 5.85014 33.1778i 0.248773 1.41086i
\(554\) 0 0
\(555\) 1.01878 + 0.370807i 0.0432450 + 0.0157399i
\(556\) 0 0
\(557\) −2.22292 + 1.86525i −0.0941880 + 0.0790331i −0.688666 0.725079i \(-0.741803\pi\)
0.594478 + 0.804112i \(0.297359\pi\)
\(558\) 0 0
\(559\) −6.33304 + 10.9691i −0.267859 + 0.463945i
\(560\) 0 0
\(561\) −0.0420818 0.238658i −0.00177669 0.0100761i
\(562\) 0 0
\(563\) 20.9940 + 36.3626i 0.884790 + 1.53250i 0.845954 + 0.533255i \(0.179031\pi\)
0.0388353 + 0.999246i \(0.487635\pi\)
\(564\) 0 0
\(565\) 6.65846 2.42348i 0.280123 0.101957i
\(566\) 0 0
\(567\) 20.7793 + 17.4359i 0.872649 + 0.732239i
\(568\) 0 0
\(569\) 20.8503 0.874089 0.437044 0.899440i \(-0.356025\pi\)
0.437044 + 0.899440i \(0.356025\pi\)
\(570\) 0 0
\(571\) −6.25450 −0.261743 −0.130871 0.991399i \(-0.541778\pi\)
−0.130871 + 0.991399i \(0.541778\pi\)
\(572\) 0 0
\(573\) −0.893580 0.749802i −0.0373298 0.0313234i
\(574\) 0 0
\(575\) 2.59422 0.944218i 0.108186 0.0393766i
\(576\) 0 0
\(577\) 7.15843 + 12.3988i 0.298009 + 0.516167i 0.975680 0.219198i \(-0.0703441\pi\)
−0.677671 + 0.735365i \(0.737011\pi\)
\(578\) 0 0
\(579\) −0.145633 0.825926i −0.00605230 0.0343243i
\(580\) 0 0
\(581\) 5.17058 8.95571i 0.214512 0.371545i
\(582\) 0 0
\(583\) −0.480869 + 0.403497i −0.0199156 + 0.0167112i
\(584\) 0 0
\(585\) −5.32124 1.93677i −0.220006 0.0800757i
\(586\) 0 0
\(587\) 3.44990 19.5654i 0.142393 0.807550i −0.827031 0.562157i \(-0.809972\pi\)
0.969424 0.245393i \(-0.0789171\pi\)
\(588\) 0 0
\(589\) 2.35438 1.76853i 0.0970104 0.0728709i
\(590\) 0 0
\(591\) 0.0471286 0.267280i 0.00193861 0.0109944i
\(592\) 0 0
\(593\) 16.0951 + 5.85814i 0.660947 + 0.240565i 0.650645 0.759382i \(-0.274499\pi\)
0.0103018 + 0.999947i \(0.496721\pi\)
\(594\) 0 0
\(595\) −12.1744 + 10.2156i −0.499103 + 0.418797i
\(596\) 0 0
\(597\) 1.20282 2.08334i 0.0492281 0.0852656i
\(598\) 0 0
\(599\) −1.40409 7.96299i −0.0573695 0.325359i 0.942594 0.333942i \(-0.108379\pi\)
−0.999963 + 0.00858318i \(0.997268\pi\)
\(600\) 0 0
\(601\) −4.79952 8.31302i −0.195777 0.339095i 0.751378 0.659872i \(-0.229389\pi\)
−0.947155 + 0.320777i \(0.896056\pi\)
\(602\) 0 0
\(603\) 7.18766 2.61609i 0.292704 0.106536i
\(604\) 0 0
\(605\) 8.37263 + 7.02547i 0.340396 + 0.285626i
\(606\) 0 0
\(607\) 13.5088 0.548307 0.274153 0.961686i \(-0.411602\pi\)
0.274153 + 0.961686i \(0.411602\pi\)
\(608\) 0 0
\(609\) 0.760745 0.0308269
\(610\) 0 0
\(611\) −12.5475 10.5286i −0.507619 0.425943i
\(612\) 0 0
\(613\) 20.3672 7.41304i 0.822622 0.299410i 0.103795 0.994599i \(-0.466901\pi\)
0.718827 + 0.695189i \(0.244679\pi\)
\(614\) 0 0
\(615\) 0.150920 + 0.261402i 0.00608570 + 0.0105407i
\(616\) 0 0
\(617\) −2.08734 11.8379i −0.0840330 0.476575i −0.997561 0.0697991i \(-0.977764\pi\)
0.913528 0.406776i \(-0.133347\pi\)
\(618\) 0 0
\(619\) −4.00380 + 6.93478i −0.160926 + 0.278732i −0.935201 0.354117i \(-0.884781\pi\)
0.774275 + 0.632849i \(0.218115\pi\)
\(620\) 0 0
\(621\) 2.25977 1.89617i 0.0906813 0.0760907i
\(622\) 0 0
\(623\) 47.7459 + 17.3781i 1.91290 + 0.696239i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) 0.0936665 + 0.184526i 0.00374068 + 0.00736926i
\(628\) 0 0
\(629\) 5.36739 30.4400i 0.214012 1.21372i
\(630\) 0 0
\(631\) −37.9863 13.8259i −1.51221 0.550400i −0.553023 0.833166i \(-0.686526\pi\)
−0.959189 + 0.282766i \(0.908748\pi\)
\(632\) 0 0
\(633\) 3.60410 3.02420i 0.143250 0.120201i
\(634\) 0 0
\(635\) 3.96032 6.85948i 0.157161 0.272210i
\(636\) 0 0
\(637\) 0.892301 + 5.06049i 0.0353543 + 0.200504i
\(638\) 0 0
\(639\) 10.0217 + 17.3582i 0.396454 + 0.686679i
\(640\) 0 0
\(641\) −32.8766 + 11.9661i −1.29855 + 0.472632i −0.896523 0.442997i \(-0.853915\pi\)
−0.402024 + 0.915629i \(0.631693\pi\)
\(642\) 0 0
\(643\) −23.8674 20.0271i −0.941237 0.789791i 0.0365634 0.999331i \(-0.488359\pi\)
−0.977800 + 0.209540i \(0.932803\pi\)
\(644\) 0 0
\(645\) −1.18860 −0.0468010
\(646\) 0 0
\(647\) −22.9037 −0.900437 −0.450218 0.892919i \(-0.648654\pi\)
−0.450218 + 0.892919i \(0.648654\pi\)
\(648\) 0 0
\(649\) 2.62380 + 2.20163i 0.102993 + 0.0864216i
\(650\) 0 0
\(651\) −0.353864 + 0.128796i −0.0138690 + 0.00504791i
\(652\) 0 0
\(653\) −17.5309 30.3644i −0.686038 1.18825i −0.973110 0.230343i \(-0.926015\pi\)
0.287072 0.957909i \(-0.407318\pi\)
\(654\) 0 0
\(655\) −0.344789 1.95540i −0.0134720 0.0764037i
\(656\) 0 0
\(657\) 15.8027 27.3710i 0.616521 1.06784i
\(658\) 0 0
\(659\) 0.178893 0.150109i 0.00696869 0.00584742i −0.639297 0.768960i \(-0.720774\pi\)
0.646265 + 0.763113i \(0.276330\pi\)
\(660\) 0 0
\(661\) −32.3499 11.7744i −1.25827 0.457971i −0.375079 0.926993i \(-0.622385\pi\)
−0.883187 + 0.469021i \(0.844607\pi\)
\(662\) 0 0
\(663\) 0.302808 1.71731i 0.0117601 0.0666948i
\(664\) 0 0
\(665\) 7.40862 11.3703i 0.287294 0.440921i
\(666\) 0 0
\(667\) −0.654232 + 3.71033i −0.0253320 + 0.143665i
\(668\) 0 0
\(669\) 1.88702 + 0.686819i 0.0729564 + 0.0265539i
\(670\) 0 0
\(671\) 0.848100 0.711640i 0.0327405 0.0274726i
\(672\) 0 0
\(673\) −14.0851 + 24.3961i −0.542941 + 0.940402i 0.455792 + 0.890086i \(0.349356\pi\)
−0.998733 + 0.0503154i \(0.983977\pi\)
\(674\) 0 0
\(675\) −0.185549 1.05230i −0.00714179 0.0405031i
\(676\) 0 0
\(677\) −4.48115 7.76158i −0.172225 0.298302i 0.766973 0.641680i \(-0.221762\pi\)
−0.939197 + 0.343378i \(0.888429\pi\)
\(678\) 0 0
\(679\) −35.0346 + 12.7516i −1.34450 + 0.489360i
\(680\) 0 0
\(681\) 3.48551 + 2.92469i 0.133565 + 0.112074i
\(682\) 0 0
\(683\) −12.5097 −0.478672 −0.239336 0.970937i \(-0.576930\pi\)
−0.239336 + 0.970937i \(0.576930\pi\)
\(684\) 0 0
\(685\) −15.5892 −0.595631
\(686\) 0 0
\(687\) 2.66162 + 2.23336i 0.101547 + 0.0852081i
\(688\) 0 0
\(689\) −4.24455 + 1.54489i −0.161705 + 0.0588557i
\(690\) 0 0
\(691\) 15.2624 + 26.4352i 0.580607 + 1.00564i 0.995407 + 0.0957287i \(0.0305181\pi\)
−0.414800 + 0.909912i \(0.636149\pi\)
\(692\) 0 0
\(693\) 0.425459 + 2.41290i 0.0161619 + 0.0916585i
\(694\) 0 0
\(695\) −2.67095 + 4.62623i −0.101315 + 0.175483i
\(696\) 0 0
\(697\) 6.59218 5.53149i 0.249696 0.209520i
\(698\) 0 0
\(699\) 0.0747890 + 0.0272210i 0.00282878 + 0.00102959i
\(700\) 0 0
\(701\) 0.606258 3.43826i 0.0228980 0.129861i −0.971216 0.238201i \(-0.923442\pi\)
0.994114 + 0.108340i \(0.0345534\pi\)
\(702\) 0 0
\(703\) 3.17669 + 26.2024i 0.119811 + 0.988241i
\(704\) 0 0
\(705\) 0.266912 1.51373i 0.0100525 0.0570105i
\(706\) 0 0
\(707\) 11.5109 + 4.18961i 0.432910 + 0.157566i
\(708\) 0 0
\(709\) 10.5028 8.81289i 0.394441 0.330975i −0.423899 0.905709i \(-0.639339\pi\)
0.818340 + 0.574734i \(0.194895\pi\)
\(710\) 0 0
\(711\) 16.0579 27.8130i 0.602217 1.04307i
\(712\) 0 0
\(713\) −0.323849 1.83664i −0.0121283 0.0687828i
\(714\) 0 0
\(715\) −0.252953 0.438128i −0.00945991 0.0163850i
\(716\) 0 0
\(717\) 1.21459 0.442074i 0.0453597 0.0165096i
\(718\) 0 0
\(719\) 18.4686 + 15.4970i 0.688763 + 0.577940i 0.918552 0.395300i \(-0.129359\pi\)
−0.229790 + 0.973240i \(0.573804\pi\)
\(720\) 0 0
\(721\) 30.4902 1.13551
\(722\) 0 0
\(723\) −3.96838 −0.147586
\(724\) 0 0
\(725\) 1.04543 + 0.877219i 0.0388263 + 0.0325791i
\(726\) 0 0
\(727\) −22.7710 + 8.28797i −0.844531 + 0.307384i −0.727808 0.685781i \(-0.759461\pi\)
−0.116722 + 0.993165i \(0.537239\pi\)
\(728\) 0 0
\(729\) 12.6421 + 21.8968i 0.468227 + 0.810994i
\(730\) 0 0
\(731\) 5.88439 + 33.3721i 0.217642 + 1.23431i
\(732\) 0 0
\(733\) −25.5971 + 44.3354i −0.945449 + 1.63757i −0.190601 + 0.981668i \(0.561044\pi\)
−0.754849 + 0.655899i \(0.772290\pi\)
\(734\) 0 0
\(735\) −0.369392 + 0.309957i −0.0136252 + 0.0114329i
\(736\) 0 0
\(737\) 0.642141 + 0.233720i 0.0236536 + 0.00860920i
\(738\) 0 0
\(739\) 1.75933 9.97766i 0.0647180 0.367034i −0.935199 0.354124i \(-0.884779\pi\)
0.999917 0.0129105i \(-0.00410967\pi\)
\(740\) 0 0
\(741\) 0.179217 + 1.47824i 0.00658370 + 0.0543044i
\(742\) 0 0
\(743\) −4.71509 + 26.7406i −0.172980 + 0.981017i 0.767470 + 0.641085i \(0.221515\pi\)
−0.940450 + 0.339932i \(0.889596\pi\)
\(744\) 0 0
\(745\) 5.47280 + 1.99193i 0.200508 + 0.0729788i
\(746\) 0 0
\(747\) 7.55171 6.33663i 0.276303 0.231845i
\(748\) 0 0
\(749\) −7.04624 + 12.2045i −0.257464 + 0.445941i
\(750\) 0 0
\(751\) 9.11495 + 51.6934i 0.332609 + 1.88632i 0.449669 + 0.893195i \(0.351542\pi\)
−0.117060 + 0.993125i \(0.537347\pi\)
\(752\) 0 0
\(753\) −1.55987 2.70177i −0.0568448 0.0984580i
\(754\) 0 0
\(755\) 17.7450 6.45864i 0.645805 0.235054i
\(756\) 0 0
\(757\) −16.8839 14.1673i −0.613656 0.514919i 0.282146 0.959371i \(-0.408954\pi\)
−0.895802 + 0.444453i \(0.853398\pi\)
\(758\) 0 0
\(759\) 0.131064 0.00475732
\(760\) 0 0
\(761\) 19.8303 0.718849 0.359424 0.933174i \(-0.382973\pi\)
0.359424 + 0.933174i \(0.382973\pi\)
\(762\) 0 0
\(763\) −35.5272 29.8109i −1.28617 1.07923i
\(764\) 0 0
\(765\) −14.2365 + 5.18165i −0.514721 + 0.187343i
\(766\) 0 0
\(767\) 12.3231 + 21.3442i 0.444962 + 0.770696i
\(768\) 0 0
\(769\) 5.49699 + 31.1750i 0.198226 + 1.12420i 0.907749 + 0.419515i \(0.137800\pi\)
−0.709522 + 0.704683i \(0.751089\pi\)
\(770\) 0 0
\(771\) −2.50116 + 4.33214i −0.0900772 + 0.156018i
\(772\) 0 0
\(773\) 30.5314 25.6189i 1.09814 0.921448i 0.100841 0.994903i \(-0.467847\pi\)
0.997299 + 0.0734542i \(0.0234023\pi\)
\(774\) 0 0
\(775\) −0.634802 0.231049i −0.0228028 0.00829952i
\(776\) 0 0
\(777\) 0.586139 3.32416i 0.0210276 0.119254i
\(778\) 0 0
\(779\) −4.01160 + 6.15674i −0.143730 + 0.220588i
\(780\) 0 0
\(781\) −0.310947 + 1.76347i −0.0111266 + 0.0631019i
\(782\) 0 0
\(783\) 1.37030 + 0.498748i 0.0489705 + 0.0178238i
\(784\) 0 0
\(785\) 11.6302 9.75891i 0.415100 0.348310i
\(786\) 0 0
\(787\) 6.60318 11.4370i 0.235378 &m