Properties

Label 380.2.u.a.301.3
Level $380$
Weight $2$
Character 380.301
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 301.3
Root \(-0.443867 - 2.51729i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.a.101.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +O(q^{10})\) \(q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +(2.60901 - 4.51894i) q^{11} +(-1.93810 - 0.705410i) q^{13} +(0.443867 + 2.51729i) q^{15} +(4.62527 + 3.88107i) q^{17} +(1.86541 + 3.93958i) q^{19} +(-0.462280 - 0.387899i) q^{21} +(-0.685398 - 3.88708i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(0.682201 - 1.18161i) q^{27} +(-6.90607 + 5.79488i) q^{29} +(-1.86652 - 3.23290i) q^{31} +(2.31611 - 13.1353i) q^{33} +(0.221847 - 0.0807459i) q^{35} +1.73098 q^{37} -5.27196 q^{39} +(-11.1003 + 4.04019i) q^{41} +(-0.0112258 + 0.0636649i) q^{43} +(1.76689 + 3.06034i) q^{45} +(-6.65712 + 5.58599i) q^{47} +(3.47213 - 6.01391i) q^{49} +(14.5028 + 5.27858i) q^{51} +(0.300841 + 1.70615i) q^{53} +(3.99724 + 3.35408i) q^{55} +(7.92481 + 7.83193i) q^{57} +(0.134661 + 0.112994i) q^{59} +(-1.78040 - 10.0971i) q^{61} +(-0.783959 - 0.285338i) q^{63} +(1.03124 - 1.78616i) q^{65} +(-0.759172 + 0.637021i) q^{67} +(-5.04458 - 8.73746i) q^{69} +(-0.860306 + 4.87904i) q^{71} +(-2.27800 + 0.829123i) q^{73} -2.55613 q^{75} -1.23190 q^{77} +(6.14146 - 2.23531i) q^{79} +(-1.23529 + 7.00568i) q^{81} +(2.39473 + 4.14780i) q^{83} +(-4.62527 + 3.88107i) q^{85} +(-11.5220 + 19.9568i) q^{87} +(-5.51716 - 2.00808i) q^{89} +(0.0845529 + 0.479523i) q^{91} +(-7.30968 - 6.13355i) q^{93} +(-4.20365 + 1.15297i) q^{95} +(-2.70875 - 2.27291i) q^{97} +(-3.20196 - 18.1592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

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
\(3\) 2.40197 0.874246i 1.38678 0.504746i 0.462553 0.886592i \(-0.346933\pi\)
0.924226 + 0.381845i \(0.124711\pi\)
\(4\) 0 0
\(5\) −0.173648 + 0.984808i −0.0776578 + 0.440419i
\(6\) 0 0
\(7\) −0.118043 0.204456i −0.0446159 0.0772770i 0.842855 0.538141i \(-0.180873\pi\)
−0.887471 + 0.460864i \(0.847540\pi\)
\(8\) 0 0
\(9\) 2.70703 2.27147i 0.902344 0.757156i
\(10\) 0 0
\(11\) 2.60901 4.51894i 0.786646 1.36251i −0.141364 0.989958i \(-0.545149\pi\)
0.928011 0.372554i \(-0.121518\pi\)
\(12\) 0 0
\(13\) −1.93810 0.705410i −0.537532 0.195645i 0.0589666 0.998260i \(-0.481219\pi\)
−0.596498 + 0.802614i \(0.703442\pi\)
\(14\) 0 0
\(15\) 0.443867 + 2.51729i 0.114606 + 0.649962i
\(16\) 0 0
\(17\) 4.62527 + 3.88107i 1.12179 + 0.941297i 0.998694 0.0510977i \(-0.0162720\pi\)
0.123100 + 0.992394i \(0.460716\pi\)
\(18\) 0 0
\(19\) 1.86541 + 3.93958i 0.427953 + 0.903801i
\(20\) 0 0
\(21\) −0.462280 0.387899i −0.100878 0.0846464i
\(22\) 0 0
\(23\) −0.685398 3.88708i −0.142915 0.810513i −0.969017 0.246993i \(-0.920558\pi\)
0.826102 0.563521i \(-0.190553\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) 0.682201 1.18161i 0.131290 0.227400i
\(28\) 0 0
\(29\) −6.90607 + 5.79488i −1.28243 + 1.07608i −0.289520 + 0.957172i \(0.593496\pi\)
−0.992905 + 0.118911i \(0.962060\pi\)
\(30\) 0 0
\(31\) −1.86652 3.23290i −0.335237 0.580647i 0.648294 0.761390i \(-0.275483\pi\)
−0.983530 + 0.180744i \(0.942150\pi\)
\(32\) 0 0
\(33\) 2.31611 13.1353i 0.403182 2.28656i
\(34\) 0 0
\(35\) 0.221847 0.0807459i 0.0374991 0.0136485i
\(36\) 0 0
\(37\) 1.73098 0.284572 0.142286 0.989826i \(-0.454555\pi\)
0.142286 + 0.989826i \(0.454555\pi\)
\(38\) 0 0
\(39\) −5.27196 −0.844189
\(40\) 0 0
\(41\) −11.1003 + 4.04019i −1.73358 + 0.630972i −0.998875 0.0474136i \(-0.984902\pi\)
−0.734706 + 0.678386i \(0.762680\pi\)
\(42\) 0 0
\(43\) −0.0112258 + 0.0636649i −0.00171193 + 0.00970881i −0.985652 0.168792i \(-0.946013\pi\)
0.983940 + 0.178500i \(0.0571246\pi\)
\(44\) 0 0
\(45\) 1.76689 + 3.06034i 0.263392 + 0.456209i
\(46\) 0 0
\(47\) −6.65712 + 5.58599i −0.971041 + 0.814800i −0.982714 0.185132i \(-0.940729\pi\)
0.0116727 + 0.999932i \(0.496284\pi\)
\(48\) 0 0
\(49\) 3.47213 6.01391i 0.496019 0.859130i
\(50\) 0 0
\(51\) 14.5028 + 5.27858i 2.03080 + 0.739149i
\(52\) 0 0
\(53\) 0.300841 + 1.70615i 0.0413237 + 0.234358i 0.998473 0.0552354i \(-0.0175909\pi\)
−0.957150 + 0.289594i \(0.906480\pi\)
\(54\) 0 0
\(55\) 3.99724 + 3.35408i 0.538987 + 0.452264i
\(56\) 0 0
\(57\) 7.92481 + 7.83193i 1.04967 + 1.03736i
\(58\) 0 0
\(59\) 0.134661 + 0.112994i 0.0175313 + 0.0147105i 0.651511 0.758639i \(-0.274135\pi\)
−0.633980 + 0.773350i \(0.718580\pi\)
\(60\) 0 0
\(61\) −1.78040 10.0971i −0.227956 1.29280i −0.856952 0.515396i \(-0.827645\pi\)
0.628996 0.777409i \(-0.283466\pi\)
\(62\) 0 0
\(63\) −0.783959 0.285338i −0.0987696 0.0359492i
\(64\) 0 0
\(65\) 1.03124 1.78616i 0.127910 0.221546i
\(66\) 0 0
\(67\) −0.759172 + 0.637021i −0.0927477 + 0.0778245i −0.687983 0.725727i \(-0.741503\pi\)
0.595235 + 0.803552i \(0.297059\pi\)
\(68\) 0 0
\(69\) −5.04458 8.73746i −0.607296 1.05187i
\(70\) 0 0
\(71\) −0.860306 + 4.87904i −0.102099 + 0.579035i 0.890240 + 0.455492i \(0.150537\pi\)
−0.992339 + 0.123543i \(0.960574\pi\)
\(72\) 0 0
\(73\) −2.27800 + 0.829123i −0.266619 + 0.0970415i −0.471871 0.881668i \(-0.656421\pi\)
0.205251 + 0.978709i \(0.434199\pi\)
\(74\) 0 0
\(75\) −2.55613 −0.295156
\(76\) 0 0
\(77\) −1.23190 −0.140388
\(78\) 0 0
\(79\) 6.14146 2.23531i 0.690968 0.251492i 0.0274184 0.999624i \(-0.491271\pi\)
0.663550 + 0.748132i \(0.269049\pi\)
\(80\) 0 0
\(81\) −1.23529 + 7.00568i −0.137254 + 0.778408i
\(82\) 0 0
\(83\) 2.39473 + 4.14780i 0.262856 + 0.455280i 0.967000 0.254777i \(-0.0820022\pi\)
−0.704143 + 0.710058i \(0.748669\pi\)
\(84\) 0 0
\(85\) −4.62527 + 3.88107i −0.501681 + 0.420961i
\(86\) 0 0
\(87\) −11.5220 + 19.9568i −1.23529 + 2.13959i
\(88\) 0 0
\(89\) −5.51716 2.00808i −0.584818 0.212856i 0.0326309 0.999467i \(-0.489611\pi\)
−0.617449 + 0.786611i \(0.711834\pi\)
\(90\) 0 0
\(91\) 0.0845529 + 0.479523i 0.00886355 + 0.0502677i
\(92\) 0 0
\(93\) −7.30968 6.13355i −0.757978 0.636019i
\(94\) 0 0
\(95\) −4.20365 + 1.15297i −0.431285 + 0.118292i
\(96\) 0 0
\(97\) −2.70875 2.27291i −0.275032 0.230780i 0.494830 0.868990i \(-0.335230\pi\)
−0.769862 + 0.638211i \(0.779675\pi\)
\(98\) 0 0
\(99\) −3.20196 18.1592i −0.321809 1.82507i
\(100\) 0 0
\(101\) −10.9459 3.98397i −1.08915 0.396420i −0.265847 0.964015i \(-0.585651\pi\)
−0.823307 + 0.567596i \(0.807874\pi\)
\(102\) 0 0
\(103\) −4.76990 + 8.26171i −0.469992 + 0.814050i −0.999411 0.0343103i \(-0.989077\pi\)
0.529419 + 0.848360i \(0.322410\pi\)
\(104\) 0 0
\(105\) 0.462280 0.387899i 0.0451139 0.0378550i
\(106\) 0 0
\(107\) 9.94308 + 17.2219i 0.961234 + 1.66491i 0.719411 + 0.694585i \(0.244412\pi\)
0.241823 + 0.970320i \(0.422255\pi\)
\(108\) 0 0
\(109\) 2.26241 12.8308i 0.216700 1.22896i −0.661233 0.750180i \(-0.729967\pi\)
0.877933 0.478784i \(-0.158922\pi\)
\(110\) 0 0
\(111\) 4.15777 1.51330i 0.394638 0.143636i
\(112\) 0 0
\(113\) 6.57342 0.618376 0.309188 0.951001i \(-0.399943\pi\)
0.309188 + 0.951001i \(0.399943\pi\)
\(114\) 0 0
\(115\) 3.94705 0.368064
\(116\) 0 0
\(117\) −6.84880 + 2.49276i −0.633172 + 0.230456i
\(118\) 0 0
\(119\) 0.247527 1.40379i 0.0226907 0.128686i
\(120\) 0 0
\(121\) −8.11387 14.0536i −0.737625 1.27760i
\(122\) 0 0
\(123\) −23.1306 + 19.4089i −2.08561 + 1.75004i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) 11.4305 + 4.16037i 1.01429 + 0.369173i 0.795080 0.606504i \(-0.207429\pi\)
0.219214 + 0.975677i \(0.429651\pi\)
\(128\) 0 0
\(129\) 0.0286947 + 0.162736i 0.00252643 + 0.0143281i
\(130\) 0 0
\(131\) −0.637106 0.534596i −0.0556642 0.0467078i 0.614531 0.788893i \(-0.289345\pi\)
−0.670195 + 0.742185i \(0.733790\pi\)
\(132\) 0 0
\(133\) 0.585272 0.846431i 0.0507495 0.0733948i
\(134\) 0 0
\(135\) 1.04519 + 0.877021i 0.0899558 + 0.0754819i
\(136\) 0 0
\(137\) −3.09683 17.5630i −0.264580 1.50051i −0.770227 0.637770i \(-0.779857\pi\)
0.505647 0.862741i \(-0.331254\pi\)
\(138\) 0 0
\(139\) −13.7175 4.99275i −1.16350 0.423480i −0.313154 0.949702i \(-0.601386\pi\)
−0.850347 + 0.526222i \(0.823608\pi\)
\(140\) 0 0
\(141\) −11.1067 + 19.2374i −0.935352 + 1.62008i
\(142\) 0 0
\(143\) −8.24422 + 6.91772i −0.689416 + 0.578489i
\(144\) 0 0
\(145\) −4.50762 7.80742i −0.374337 0.648371i
\(146\) 0 0
\(147\) 3.08233 17.4807i 0.254226 1.44179i
\(148\) 0 0
\(149\) 11.8453 4.31134i 0.970406 0.353199i 0.192303 0.981336i \(-0.438404\pi\)
0.778103 + 0.628137i \(0.216182\pi\)
\(150\) 0 0
\(151\) 19.6626 1.60012 0.800059 0.599922i \(-0.204802\pi\)
0.800059 + 0.599922i \(0.204802\pi\)
\(152\) 0 0
\(153\) 21.3365 1.72495
\(154\) 0 0
\(155\) 3.50791 1.27677i 0.281762 0.102553i
\(156\) 0 0
\(157\) −3.00747 + 17.0562i −0.240022 + 1.36123i 0.591752 + 0.806120i \(0.298437\pi\)
−0.831774 + 0.555114i \(0.812675\pi\)
\(158\) 0 0
\(159\) 2.21421 + 3.83513i 0.175598 + 0.304145i
\(160\) 0 0
\(161\) −0.713830 + 0.598975i −0.0562577 + 0.0472058i
\(162\) 0 0
\(163\) 5.89573 10.2117i 0.461789 0.799843i −0.537261 0.843416i \(-0.680541\pi\)
0.999050 + 0.0435735i \(0.0138743\pi\)
\(164\) 0 0
\(165\) 12.5335 + 4.56184i 0.975735 + 0.355138i
\(166\) 0 0
\(167\) −0.0232720 0.131982i −0.00180084 0.0102131i 0.983894 0.178752i \(-0.0572061\pi\)
−0.985695 + 0.168539i \(0.946095\pi\)
\(168\) 0 0
\(169\) −6.69996 5.62193i −0.515381 0.432456i
\(170\) 0 0
\(171\) 13.9983 + 6.42734i 1.07048 + 0.491511i
\(172\) 0 0
\(173\) 18.3629 + 15.4083i 1.39610 + 1.17147i 0.962798 + 0.270221i \(0.0870968\pi\)
0.433304 + 0.901248i \(0.357348\pi\)
\(174\) 0 0
\(175\) 0.0409957 + 0.232498i 0.00309899 + 0.0175752i
\(176\) 0 0
\(177\) 0.422236 + 0.153681i 0.0317372 + 0.0115514i
\(178\) 0 0
\(179\) 5.89792 10.2155i 0.440831 0.763542i −0.556920 0.830566i \(-0.688017\pi\)
0.997751 + 0.0670239i \(0.0213504\pi\)
\(180\) 0 0
\(181\) −0.682360 + 0.572568i −0.0507194 + 0.0425586i −0.667795 0.744345i \(-0.732762\pi\)
0.617076 + 0.786904i \(0.288317\pi\)
\(182\) 0 0
\(183\) −13.1038 22.6965i −0.968664 1.67777i
\(184\) 0 0
\(185\) −0.300582 + 1.70468i −0.0220992 + 0.125331i
\(186\) 0 0
\(187\) 29.6057 10.7756i 2.16498 0.787989i
\(188\) 0 0
\(189\) −0.322115 −0.0234304
\(190\) 0 0
\(191\) 5.07774 0.367412 0.183706 0.982981i \(-0.441191\pi\)
0.183706 + 0.982981i \(0.441191\pi\)
\(192\) 0 0
\(193\) 8.33614 3.03411i 0.600049 0.218400i −0.0240946 0.999710i \(-0.507670\pi\)
0.624143 + 0.781310i \(0.285448\pi\)
\(194\) 0 0
\(195\) 0.915466 5.19187i 0.0655579 0.371797i
\(196\) 0 0
\(197\) 11.4388 + 19.8126i 0.814983 + 1.41159i 0.909340 + 0.416054i \(0.136587\pi\)
−0.0943565 + 0.995538i \(0.530079\pi\)
\(198\) 0 0
\(199\) 5.20879 4.37069i 0.369241 0.309830i −0.439220 0.898379i \(-0.644745\pi\)
0.808461 + 0.588549i \(0.200301\pi\)
\(200\) 0 0
\(201\) −1.26660 + 2.19381i −0.0893389 + 0.154739i
\(202\) 0 0
\(203\) 2.00001 + 0.727943i 0.140373 + 0.0510916i
\(204\) 0 0
\(205\) −2.05126 11.6333i −0.143266 0.812503i
\(206\) 0 0
\(207\) −10.6848 8.96560i −0.742644 0.623152i
\(208\) 0 0
\(209\) 22.6696 + 1.84874i 1.56809 + 0.127880i
\(210\) 0 0
\(211\) 8.29874 + 6.96347i 0.571309 + 0.479385i 0.882080 0.471100i \(-0.156143\pi\)
−0.310771 + 0.950485i \(0.600587\pi\)
\(212\) 0 0
\(213\) 2.19905 + 12.4714i 0.150676 + 0.854528i
\(214\) 0 0
\(215\) −0.0607484 0.0221106i −0.00414301 0.00150793i
\(216\) 0 0
\(217\) −0.440657 + 0.763241i −0.0299138 + 0.0518121i
\(218\) 0 0
\(219\) −4.74682 + 3.98306i −0.320761 + 0.269150i
\(220\) 0 0
\(221\) −6.22649 10.7846i −0.418839 0.725450i
\(222\) 0 0
\(223\) 4.17205 23.6609i 0.279381 1.58445i −0.445311 0.895376i \(-0.646907\pi\)
0.724692 0.689073i \(-0.241982\pi\)
\(224\) 0 0
\(225\) −3.32066 + 1.20862i −0.221378 + 0.0805749i
\(226\) 0 0
\(227\) −20.0082 −1.32799 −0.663995 0.747737i \(-0.731141\pi\)
−0.663995 + 0.747737i \(0.731141\pi\)
\(228\) 0 0
\(229\) 6.88943 0.455266 0.227633 0.973747i \(-0.426901\pi\)
0.227633 + 0.973747i \(0.426901\pi\)
\(230\) 0 0
\(231\) −2.95898 + 1.07698i −0.194687 + 0.0708602i
\(232\) 0 0
\(233\) 1.40492 7.96771i 0.0920396 0.521982i −0.903575 0.428430i \(-0.859067\pi\)
0.995614 0.0935520i \(-0.0298221\pi\)
\(234\) 0 0
\(235\) −4.34513 7.52598i −0.283445 0.490941i
\(236\) 0 0
\(237\) 12.7974 10.7383i 0.831281 0.697527i
\(238\) 0 0
\(239\) −6.11728 + 10.5954i −0.395694 + 0.685362i −0.993189 0.116510i \(-0.962829\pi\)
0.597496 + 0.801872i \(0.296162\pi\)
\(240\) 0 0
\(241\) 0.885693 + 0.322366i 0.0570525 + 0.0207654i 0.370389 0.928877i \(-0.379224\pi\)
−0.313336 + 0.949642i \(0.601447\pi\)
\(242\) 0 0
\(243\) 3.86833 + 21.9384i 0.248154 + 1.40735i
\(244\) 0 0
\(245\) 5.31961 + 4.46369i 0.339858 + 0.285174i
\(246\) 0 0
\(247\) −0.836322 8.95116i −0.0532139 0.569549i
\(248\) 0 0
\(249\) 9.37829 + 7.86932i 0.594325 + 0.498698i
\(250\) 0 0
\(251\) −3.01716 17.1112i −0.190442 1.08005i −0.918762 0.394811i \(-0.870810\pi\)
0.728321 0.685236i \(-0.240301\pi\)
\(252\) 0 0
\(253\) −19.3537 7.04417i −1.21676 0.442863i
\(254\) 0 0
\(255\) −7.71677 + 13.3658i −0.483243 + 0.837001i
\(256\) 0 0
\(257\) −3.34243 + 2.80463i −0.208495 + 0.174948i −0.741055 0.671444i \(-0.765674\pi\)
0.532560 + 0.846392i \(0.321230\pi\)
\(258\) 0 0
\(259\) −0.204329 0.353909i −0.0126964 0.0219908i
\(260\) 0 0
\(261\) −5.53206 + 31.3738i −0.342426 + 1.94199i
\(262\) 0 0
\(263\) 9.63727 3.50768i 0.594260 0.216293i −0.0273423 0.999626i \(-0.508704\pi\)
0.621602 + 0.783333i \(0.286482\pi\)
\(264\) 0 0
\(265\) −1.73247 −0.106425
\(266\) 0 0
\(267\) −15.0076 −0.918451
\(268\) 0 0
\(269\) −21.2011 + 7.71658i −1.29266 + 0.470488i −0.894598 0.446872i \(-0.852538\pi\)
−0.398058 + 0.917360i \(0.630316\pi\)
\(270\) 0 0
\(271\) 4.86690 27.6016i 0.295643 1.67667i −0.368934 0.929455i \(-0.620277\pi\)
0.664577 0.747220i \(-0.268612\pi\)
\(272\) 0 0
\(273\) 0.622315 + 1.07788i 0.0376642 + 0.0652364i
\(274\) 0 0
\(275\) −3.99724 + 3.35408i −0.241042 + 0.202259i
\(276\) 0 0
\(277\) −5.33746 + 9.24475i −0.320697 + 0.555463i −0.980632 0.195859i \(-0.937250\pi\)
0.659935 + 0.751323i \(0.270584\pi\)
\(278\) 0 0
\(279\) −12.3962 4.51183i −0.742139 0.270116i
\(280\) 0 0
\(281\) −3.29343 18.6780i −0.196469 1.11423i −0.910311 0.413926i \(-0.864157\pi\)
0.713841 0.700308i \(-0.246954\pi\)
\(282\) 0 0
\(283\) 1.96247 + 1.64670i 0.116656 + 0.0978864i 0.699250 0.714877i \(-0.253518\pi\)
−0.582593 + 0.812764i \(0.697962\pi\)
\(284\) 0 0
\(285\) −9.08907 + 6.44442i −0.538390 + 0.381734i
\(286\) 0 0
\(287\) 2.13635 + 1.79261i 0.126105 + 0.105815i
\(288\) 0 0
\(289\) 3.37847 + 19.1602i 0.198733 + 1.12707i
\(290\) 0 0
\(291\) −8.49344 3.09136i −0.497894 0.181219i
\(292\) 0 0
\(293\) 1.40995 2.44211i 0.0823704 0.142670i −0.821897 0.569636i \(-0.807084\pi\)
0.904268 + 0.426966i \(0.140418\pi\)
\(294\) 0 0
\(295\) −0.134661 + 0.112994i −0.00784025 + 0.00657875i
\(296\) 0 0
\(297\) −3.55974 6.16565i −0.206557 0.357767i
\(298\) 0 0
\(299\) −1.41362 + 8.01703i −0.0817517 + 0.463637i
\(300\) 0 0
\(301\) 0.0143418 0.00521998i 0.000826647 0.000300875i
\(302\) 0 0
\(303\) −29.7746 −1.71051
\(304\) 0 0
\(305\) 10.2529 0.587079
\(306\) 0 0
\(307\) −10.2154 + 3.71810i −0.583023 + 0.212203i −0.616658 0.787231i \(-0.711514\pi\)
0.0336350 + 0.999434i \(0.489292\pi\)
\(308\) 0 0
\(309\) −4.23440 + 24.0145i −0.240886 + 1.36613i
\(310\) 0 0
\(311\) −14.8848 25.7812i −0.844039 1.46192i −0.886454 0.462818i \(-0.846839\pi\)
0.0424150 0.999100i \(-0.486495\pi\)
\(312\) 0 0
\(313\) 26.9762 22.6357i 1.52478 1.27944i 0.699692 0.714444i \(-0.253320\pi\)
0.825090 0.565001i \(-0.191124\pi\)
\(314\) 0 0
\(315\) 0.417136 0.722501i 0.0235030 0.0407083i
\(316\) 0 0
\(317\) −27.7278 10.0921i −1.55735 0.566829i −0.587223 0.809425i \(-0.699779\pi\)
−0.970127 + 0.242596i \(0.922001\pi\)
\(318\) 0 0
\(319\) 8.16870 + 46.3270i 0.457360 + 2.59382i
\(320\) 0 0
\(321\) 38.9392 + 32.6739i 2.17337 + 1.82368i
\(322\) 0 0
\(323\) −6.66174 + 25.4614i −0.370669 + 1.41671i
\(324\) 0 0
\(325\) 1.57995 + 1.32574i 0.0876399 + 0.0735386i
\(326\) 0 0
\(327\) −5.78300 32.7970i −0.319801 1.81368i
\(328\) 0 0
\(329\) 1.92791 + 0.701702i 0.106289 + 0.0386861i
\(330\) 0 0
\(331\) −5.69418 + 9.86261i −0.312981 + 0.542098i −0.979006 0.203831i \(-0.934661\pi\)
0.666026 + 0.745929i \(0.267994\pi\)
\(332\) 0 0
\(333\) 4.68582 3.93187i 0.256781 0.215465i
\(334\) 0 0
\(335\) −0.495515 0.858256i −0.0270728 0.0468916i
\(336\) 0 0
\(337\) 4.72558 26.8001i 0.257419 1.45989i −0.532369 0.846512i \(-0.678698\pi\)
0.789788 0.613381i \(-0.210191\pi\)
\(338\) 0 0
\(339\) 15.7892 5.74679i 0.857551 0.312123i
\(340\) 0 0
\(341\) −19.4791 −1.05485
\(342\) 0 0
\(343\) −3.29203 −0.177753
\(344\) 0 0
\(345\) 9.48070 3.45069i 0.510424 0.185779i
\(346\) 0 0
\(347\) 4.30641 24.4229i 0.231180 1.31109i −0.619330 0.785130i \(-0.712596\pi\)
0.850511 0.525958i \(-0.176293\pi\)
\(348\) 0 0
\(349\) 5.63267 + 9.75608i 0.301510 + 0.522231i 0.976478 0.215616i \(-0.0691760\pi\)
−0.674968 + 0.737847i \(0.735843\pi\)
\(350\) 0 0
\(351\) −2.15569 + 1.80884i −0.115062 + 0.0965486i
\(352\) 0 0
\(353\) −13.1589 + 22.7920i −0.700380 + 1.21309i 0.267953 + 0.963432i \(0.413653\pi\)
−0.968333 + 0.249662i \(0.919681\pi\)
\(354\) 0 0
\(355\) −4.65552 1.69447i −0.247089 0.0899332i
\(356\) 0 0
\(357\) −0.632710 3.58827i −0.0334865 0.189912i
\(358\) 0 0
\(359\) 1.03308 + 0.866856i 0.0545238 + 0.0457509i 0.669642 0.742684i \(-0.266447\pi\)
−0.615119 + 0.788435i \(0.710892\pi\)
\(360\) 0 0
\(361\) −12.0405 + 14.6978i −0.633712 + 0.773569i
\(362\) 0 0
\(363\) −31.7756 26.6629i −1.66779 1.39944i
\(364\) 0 0
\(365\) −0.420957 2.38736i −0.0220339 0.124960i
\(366\) 0 0
\(367\) 27.2974 + 9.93543i 1.42491 + 0.518625i 0.935469 0.353410i \(-0.114978\pi\)
0.489443 + 0.872035i \(0.337200\pi\)
\(368\) 0 0
\(369\) −20.8718 + 36.1510i −1.08654 + 1.88195i
\(370\) 0 0
\(371\) 0.313321 0.262907i 0.0162668 0.0136495i
\(372\) 0 0
\(373\) 1.77239 + 3.06988i 0.0917711 + 0.158952i 0.908256 0.418414i \(-0.137414\pi\)
−0.816485 + 0.577366i \(0.804081\pi\)
\(374\) 0 0
\(375\) 0.443867 2.51729i 0.0229212 0.129992i
\(376\) 0 0
\(377\) 17.4724 6.35944i 0.899875 0.327528i
\(378\) 0 0
\(379\) −15.3268 −0.787286 −0.393643 0.919263i \(-0.628785\pi\)
−0.393643 + 0.919263i \(0.628785\pi\)
\(380\) 0 0
\(381\) 31.0930 1.59294
\(382\) 0 0
\(383\) 13.1607 4.79009i 0.672479 0.244762i 0.0168642 0.999858i \(-0.494632\pi\)
0.655615 + 0.755095i \(0.272409\pi\)
\(384\) 0 0
\(385\) 0.213917 1.21318i 0.0109022 0.0618295i
\(386\) 0 0
\(387\) 0.114224 + 0.197842i 0.00580634 + 0.0100569i
\(388\) 0 0
\(389\) −15.3712 + 12.8979i −0.779349 + 0.653952i −0.943085 0.332553i \(-0.892090\pi\)
0.163735 + 0.986504i \(0.447646\pi\)
\(390\) 0 0
\(391\) 11.9159 20.6389i 0.602612 1.04375i
\(392\) 0 0
\(393\) −1.99768 0.727096i −0.100770 0.0366771i
\(394\) 0 0
\(395\) 1.13490 + 6.43631i 0.0571028 + 0.323846i
\(396\) 0 0
\(397\) 6.64859 + 5.57883i 0.333683 + 0.279993i 0.794199 0.607658i \(-0.207891\pi\)
−0.460516 + 0.887652i \(0.652335\pi\)
\(398\) 0 0
\(399\) 0.665817 2.54477i 0.0333326 0.127398i
\(400\) 0 0
\(401\) 12.0981 + 10.1515i 0.604149 + 0.506941i 0.892776 0.450500i \(-0.148754\pi\)
−0.288627 + 0.957442i \(0.593199\pi\)
\(402\) 0 0
\(403\) 1.33697 + 7.58234i 0.0665993 + 0.377703i
\(404\) 0 0
\(405\) −6.68474 2.43305i −0.332167 0.120899i
\(406\) 0 0
\(407\) 4.51615 7.82220i 0.223857 0.387732i
\(408\) 0 0
\(409\) 9.76460 8.19347i 0.482829 0.405141i −0.368619 0.929580i \(-0.620169\pi\)
0.851448 + 0.524439i \(0.175725\pi\)
\(410\) 0 0
\(411\) −22.7929 39.4785i −1.12429 1.94733i
\(412\) 0 0
\(413\) 0.00720652 0.0408702i 0.000354610 0.00201109i
\(414\) 0 0
\(415\) −4.50063 + 1.63809i −0.220927 + 0.0804109i
\(416\) 0 0
\(417\) −37.3139 −1.82727
\(418\) 0 0
\(419\) 1.77915 0.0869172 0.0434586 0.999055i \(-0.486162\pi\)
0.0434586 + 0.999055i \(0.486162\pi\)
\(420\) 0 0
\(421\) −30.1320 + 10.9671i −1.46854 + 0.534506i −0.947704 0.319150i \(-0.896603\pi\)
−0.520838 + 0.853655i \(0.674381\pi\)
\(422\) 0 0
\(423\) −5.33264 + 30.2429i −0.259282 + 1.47046i
\(424\) 0 0
\(425\) −3.01893 5.22895i −0.146440 0.253641i
\(426\) 0 0
\(427\) −1.85425 + 1.55590i −0.0897336 + 0.0752954i
\(428\) 0 0
\(429\) −13.7546 + 23.8237i −0.664078 + 1.15022i
\(430\) 0 0
\(431\) 12.8374 + 4.67243i 0.618356 + 0.225063i 0.632155 0.774842i \(-0.282170\pi\)
−0.0137993 + 0.999905i \(0.504393\pi\)
\(432\) 0 0
\(433\) −2.36578 13.4170i −0.113692 0.644781i −0.987389 0.158311i \(-0.949395\pi\)
0.873697 0.486471i \(-0.161716\pi\)
\(434\) 0 0
\(435\) −17.6528 14.8124i −0.846386 0.710202i
\(436\) 0 0
\(437\) 14.0349 9.95117i 0.671381 0.476029i
\(438\) 0 0
\(439\) 9.83630 + 8.25363i 0.469461 + 0.393924i 0.846598 0.532233i \(-0.178647\pi\)
−0.377137 + 0.926157i \(0.623091\pi\)
\(440\) 0 0
\(441\) −4.26124 24.1667i −0.202916 1.15079i
\(442\) 0 0
\(443\) 38.9124 + 14.1630i 1.84878 + 0.672902i 0.985860 + 0.167568i \(0.0535915\pi\)
0.862924 + 0.505334i \(0.168631\pi\)
\(444\) 0 0
\(445\) 2.93562 5.08464i 0.139162 0.241035i
\(446\) 0 0
\(447\) 24.6829 20.7114i 1.16746 0.979618i
\(448\) 0 0
\(449\) 4.19525 + 7.26638i 0.197986 + 0.342922i 0.947875 0.318642i \(-0.103227\pi\)
−0.749889 + 0.661563i \(0.769893\pi\)
\(450\) 0 0
\(451\) −10.7035 + 60.7027i −0.504009 + 2.85838i
\(452\) 0 0
\(453\) 47.2290 17.1899i 2.21901 0.807654i
\(454\) 0 0
\(455\) −0.486921 −0.0228272
\(456\) 0 0
\(457\) −40.4467 −1.89202 −0.946008 0.324145i \(-0.894924\pi\)
−0.946008 + 0.324145i \(0.894924\pi\)
\(458\) 0 0
\(459\) 7.74126 2.81759i 0.361331 0.131514i
\(460\) 0 0
\(461\) 5.11750 29.0228i 0.238346 1.35173i −0.597106 0.802162i \(-0.703683\pi\)
0.835452 0.549564i \(-0.185206\pi\)
\(462\) 0 0
\(463\) −3.75782 6.50873i −0.174641 0.302486i 0.765396 0.643559i \(-0.222543\pi\)
−0.940037 + 0.341073i \(0.889210\pi\)
\(464\) 0 0
\(465\) 7.30968 6.13355i 0.338978 0.284437i
\(466\) 0 0
\(467\) −15.4358 + 26.7355i −0.714282 + 1.23717i 0.248954 + 0.968515i \(0.419913\pi\)
−0.963236 + 0.268657i \(0.913420\pi\)
\(468\) 0 0
\(469\) 0.219857 + 0.0800215i 0.0101521 + 0.00369505i
\(470\) 0 0
\(471\) 7.68747 + 43.5978i 0.354220 + 2.00888i
\(472\) 0 0
\(473\) 0.258410 + 0.216831i 0.0118817 + 0.00996992i
\(474\) 0 0
\(475\) −0.405494 4.34000i −0.0186053 0.199133i
\(476\) 0 0
\(477\) 4.68986 + 3.93526i 0.214734 + 0.180183i
\(478\) 0 0
\(479\) 4.58448 + 25.9999i 0.209470 + 1.18796i 0.890249 + 0.455474i \(0.150530\pi\)
−0.680779 + 0.732489i \(0.738359\pi\)
\(480\) 0 0
\(481\) −3.35481 1.22105i −0.152966 0.0556751i
\(482\) 0 0
\(483\) −1.19095 + 2.06278i −0.0541901 + 0.0938599i
\(484\) 0 0
\(485\) 2.70875 2.27291i 0.122998 0.103208i
\(486\) 0 0
\(487\) −15.5999 27.0197i −0.706897 1.22438i −0.966003 0.258533i \(-0.916761\pi\)
0.259105 0.965849i \(-0.416572\pi\)
\(488\) 0 0
\(489\) 5.23384 29.6826i 0.236682 1.34229i
\(490\) 0 0
\(491\) −24.9835 + 9.09324i −1.12749 + 0.410372i −0.837380 0.546622i \(-0.815914\pi\)
−0.290109 + 0.956994i \(0.593691\pi\)
\(492\) 0 0
\(493\) −54.4328 −2.45153
\(494\) 0 0
\(495\) 18.4393 0.828786
\(496\) 0 0
\(497\) 1.09910 0.400039i 0.0493013 0.0179442i
\(498\) 0 0
\(499\) 5.92353 33.5940i 0.265173 1.50387i −0.503367 0.864072i \(-0.667906\pi\)
0.768541 0.639801i \(-0.220983\pi\)
\(500\) 0 0
\(501\) −0.171283 0.296671i −0.00765237 0.0132543i
\(502\) 0 0
\(503\) 10.0478 8.43114i 0.448011 0.375926i −0.390686 0.920524i \(-0.627762\pi\)
0.838697 + 0.544598i \(0.183318\pi\)
\(504\) 0 0
\(505\) 5.82417 10.0878i 0.259172 0.448899i
\(506\) 0 0
\(507\) −21.0081 7.64631i −0.933001 0.339585i
\(508\) 0 0
\(509\) −4.69483 26.6257i −0.208095 1.18016i −0.892495 0.451057i \(-0.851047\pi\)
0.684401 0.729106i \(-0.260064\pi\)
\(510\) 0 0
\(511\) 0.438419 + 0.367877i 0.0193945 + 0.0162739i
\(512\) 0 0
\(513\) 5.92761 + 0.483407i 0.261710 + 0.0213429i
\(514\) 0 0
\(515\) −7.30791 6.13206i −0.322025 0.270211i
\(516\) 0 0
\(517\) 7.87424 + 44.6570i 0.346309 + 1.96401i
\(518\) 0 0
\(519\) 57.5777 + 20.9566i 2.52738 + 0.919891i
\(520\) 0 0
\(521\) −14.5020 + 25.1182i −0.635344 + 1.10045i 0.351098 + 0.936339i \(0.385808\pi\)
−0.986442 + 0.164109i \(0.947525\pi\)
\(522\) 0 0
\(523\) −32.5685 + 27.3283i −1.42412 + 1.19498i −0.475037 + 0.879966i \(0.657565\pi\)
−0.949087 + 0.315015i \(0.897990\pi\)
\(524\) 0 0
\(525\) 0.301732 + 0.522614i 0.0131686 + 0.0228088i
\(526\) 0 0
\(527\) 3.91396 22.1971i 0.170495 0.966923i
\(528\) 0 0
\(529\) 6.97328 2.53807i 0.303186 0.110351i
\(530\) 0 0
\(531\) 0.621193 0.0269575
\(532\) 0 0
\(533\) 24.3635 1.05530
\(534\) 0 0
\(535\) −18.6869 + 6.80147i −0.807904 + 0.294053i
\(536\) 0 0
\(537\) 5.23578 29.6936i 0.225941 1.28137i
\(538\) 0 0
\(539\) −18.1177 31.3807i −0.780383 1.35166i
\(540\) 0 0
\(541\) 6.62959 5.56288i 0.285028 0.239167i −0.489052 0.872255i \(-0.662657\pi\)
0.774080 + 0.633088i \(0.218213\pi\)
\(542\) 0 0
\(543\) −1.13844 + 1.97184i −0.0488553 + 0.0846199i
\(544\) 0 0
\(545\) 12.2430 + 4.45608i 0.524431 + 0.190877i
\(546\) 0 0
\(547\) 5.39244 + 30.5820i 0.230564 + 1.30759i 0.851757 + 0.523936i \(0.175537\pi\)
−0.621193 + 0.783657i \(0.713352\pi\)
\(548\) 0 0
\(549\) −27.7549 23.2891i −1.18455 0.993956i
\(550\) 0 0
\(551\) −35.7120 16.3972i −1.52138 0.698544i
\(552\) 0 0
\(553\) −1.18198 0.991795i −0.0502627 0.0421754i
\(554\) 0 0
\(555\) 0.768325 + 4.35738i 0.0326136 + 0.184961i
\(556\) 0 0
\(557\) −15.0627 5.48237i −0.638227 0.232296i 0.00258113 0.999997i \(-0.499178\pi\)
−0.640808 + 0.767701i \(0.721401\pi\)
\(558\) 0 0
\(559\) 0.0666667 0.115470i 0.00281970 0.00488386i
\(560\) 0 0
\(561\) 61.6915 51.7653i 2.60462 2.18553i
\(562\) 0 0
\(563\) 7.28944 + 12.6257i 0.307213 + 0.532109i 0.977752 0.209766i \(-0.0672701\pi\)
−0.670538 + 0.741875i \(0.733937\pi\)
\(564\) 0 0
\(565\) −1.14146 + 6.47356i −0.0480217 + 0.272345i
\(566\) 0 0
\(567\) 1.57817 0.574406i 0.0662768 0.0241228i
\(568\) 0 0
\(569\) 11.4134 0.478474 0.239237 0.970961i \(-0.423103\pi\)
0.239237 + 0.970961i \(0.423103\pi\)
\(570\) 0 0
\(571\) 42.2764 1.76921 0.884606 0.466340i \(-0.154428\pi\)
0.884606 + 0.466340i \(0.154428\pi\)
\(572\) 0 0
\(573\) 12.1966 4.43919i 0.509520 0.185450i
\(574\) 0 0
\(575\) −0.685398 + 3.88708i −0.0285831 + 0.162103i
\(576\) 0 0
\(577\) −6.88137 11.9189i −0.286475 0.496189i 0.686491 0.727139i \(-0.259150\pi\)
−0.972966 + 0.230949i \(0.925817\pi\)
\(578\) 0 0
\(579\) 17.3706 14.5757i 0.721899 0.605745i
\(580\) 0 0
\(581\) 0.565361 0.979234i 0.0234551 0.0406255i
\(582\) 0 0
\(583\) 8.49491 + 3.09189i 0.351823 + 0.128053i
\(584\) 0 0
\(585\) −1.26561 7.17762i −0.0523264 0.296758i
\(586\) 0 0
\(587\) −16.7949 14.0926i −0.693201 0.581664i 0.226630 0.973981i \(-0.427229\pi\)
−0.919830 + 0.392317i \(0.871674\pi\)
\(588\) 0 0
\(589\) 9.25446 13.3840i 0.381323 0.551477i
\(590\) 0 0
\(591\) 44.7969 + 37.5891i 1.84270 + 1.54621i
\(592\) 0 0
\(593\) 7.48981 + 42.4768i 0.307570 + 1.74432i 0.611155 + 0.791511i \(0.290705\pi\)
−0.303585 + 0.952804i \(0.598184\pi\)
\(594\) 0 0
\(595\) 1.33949 + 0.487533i 0.0549135 + 0.0199869i
\(596\) 0 0
\(597\) 8.69030 15.0520i 0.355670 0.616039i
\(598\) 0 0
\(599\) 0.277780 0.233085i 0.0113498 0.00952360i −0.637095 0.770785i \(-0.719864\pi\)
0.648445 + 0.761262i \(0.275420\pi\)
\(600\) 0 0
\(601\) 8.61809 + 14.9270i 0.351539 + 0.608884i 0.986519 0.163645i \(-0.0523251\pi\)
−0.634980 + 0.772528i \(0.718992\pi\)
\(602\) 0 0
\(603\) −0.608129 + 3.44887i −0.0247649 + 0.140449i
\(604\) 0 0
\(605\) 15.2491 5.55022i 0.619964 0.225648i
\(606\) 0 0
\(607\) 43.4646 1.76417 0.882086 0.471088i \(-0.156139\pi\)
0.882086 + 0.471088i \(0.156139\pi\)
\(608\) 0 0
\(609\) 5.44036 0.220455
\(610\) 0 0
\(611\) 16.8426 6.13019i 0.681377 0.248001i
\(612\) 0 0
\(613\) −3.33887 + 18.9357i −0.134856 + 0.764805i 0.840104 + 0.542425i \(0.182494\pi\)
−0.974960 + 0.222380i \(0.928617\pi\)
\(614\) 0 0
\(615\) −15.0974 26.1495i −0.608786 1.05445i
\(616\) 0 0
\(617\) 15.8140 13.2695i 0.636647 0.534210i −0.266340 0.963879i \(-0.585814\pi\)
0.902986 + 0.429669i \(0.141370\pi\)
\(618\) 0 0
\(619\) −12.2404 + 21.2011i −0.491985 + 0.852143i −0.999957 0.00923061i \(-0.997062\pi\)
0.507973 + 0.861373i \(0.330395\pi\)
\(620\) 0 0
\(621\) −5.06058 1.84190i −0.203074 0.0739130i
\(622\) 0 0
\(623\) 0.240696 + 1.36505i 0.00964327 + 0.0546897i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) 56.0679 15.3782i 2.23914 0.614145i
\(628\) 0 0
\(629\) 8.00626 + 6.71805i 0.319231 + 0.267866i
\(630\) 0 0
\(631\) −5.95880 33.7940i −0.237216 1.34532i −0.837896 0.545829i \(-0.816215\pi\)
0.600680 0.799489i \(-0.294896\pi\)
\(632\) 0 0
\(633\) 26.0211 + 9.47092i 1.03425 + 0.376435i
\(634\) 0 0
\(635\) −6.08205 + 10.5344i −0.241359 + 0.418046i
\(636\) 0 0
\(637\) −10.9716 + 9.20627i −0.434711 + 0.364766i
\(638\) 0 0
\(639\) 8.75370 + 15.1619i 0.346291 + 0.599794i
\(640\) 0 0
\(641\) 0.820906 4.65559i 0.0324238 0.183885i −0.964295 0.264832i \(-0.914683\pi\)
0.996718 + 0.0809474i \(0.0257946\pi\)
\(642\) 0 0
\(643\) −3.58886 + 1.30624i −0.141531 + 0.0515130i −0.411814 0.911268i \(-0.635105\pi\)
0.270284 + 0.962781i \(0.412883\pi\)
\(644\) 0 0
\(645\) −0.165246 −0.00650656
\(646\) 0 0
\(647\) 7.12252 0.280015 0.140008 0.990150i \(-0.455287\pi\)
0.140008 + 0.990150i \(0.455287\pi\)
\(648\) 0 0
\(649\) 0.861943 0.313722i 0.0338342 0.0123147i
\(650\) 0 0
\(651\) −0.391186 + 2.21853i −0.0153318 + 0.0869509i
\(652\) 0 0
\(653\) −5.16829 8.95175i −0.202251 0.350309i 0.747002 0.664821i \(-0.231492\pi\)
−0.949253 + 0.314512i \(0.898159\pi\)
\(654\) 0 0
\(655\) 0.637106 0.534596i 0.0248938 0.0208884i
\(656\) 0 0
\(657\) −4.28328 + 7.41885i −0.167107 + 0.289437i
\(658\) 0 0
\(659\) −1.81962 0.662288i −0.0708824 0.0257991i 0.306336 0.951924i \(-0.400897\pi\)
−0.377218 + 0.926124i \(0.623119\pi\)
\(660\) 0 0
\(661\) 6.66418 + 37.7945i 0.259207 + 1.47003i 0.785039 + 0.619446i \(0.212643\pi\)
−0.525832 + 0.850588i \(0.676246\pi\)
\(662\) 0 0
\(663\) −24.3842 20.4608i −0.947006 0.794632i
\(664\) 0 0
\(665\) 0.731940 + 0.723361i 0.0283834 + 0.0280507i
\(666\) 0 0
\(667\) 27.2586 + 22.8727i 1.05546 + 0.885634i
\(668\) 0 0
\(669\) −10.6643 60.4802i −0.412305 2.33830i
\(670\) 0 0
\(671\) −50.2734 18.2980i −1.94078 0.706387i
\(672\) 0 0
\(673\) −20.6769 + 35.8134i −0.797035 + 1.38050i 0.124504 + 0.992219i \(0.460266\pi\)
−0.921539 + 0.388286i \(0.873067\pi\)
\(674\) 0 0
\(675\) −1.04519 + 0.877021i −0.0402295 + 0.0337565i
\(676\) 0 0
\(677\) 6.63593 + 11.4938i 0.255039 + 0.441741i 0.964906 0.262595i \(-0.0845782\pi\)
−0.709867 + 0.704336i \(0.751245\pi\)
\(678\) 0 0
\(679\) −0.144962 + 0.822121i −0.00556313 + 0.0315501i
\(680\) 0 0
\(681\) −48.0591 + 17.4921i −1.84163 + 0.670299i
\(682\) 0 0
\(683\) 8.82787 0.337789 0.168894 0.985634i \(-0.445980\pi\)
0.168894 + 0.985634i \(0.445980\pi\)
\(684\) 0 0
\(685\) 17.8340 0.681401
\(686\) 0 0
\(687\) 16.5482 6.02306i 0.631354 0.229794i
\(688\) 0 0
\(689\) 0.620479 3.51891i 0.0236384 0.134060i
\(690\) 0 0
\(691\) −0.657277 1.13844i −0.0250040 0.0433082i 0.853253 0.521498i \(-0.174627\pi\)
−0.878257 + 0.478190i \(0.841293\pi\)
\(692\) 0 0
\(693\) −3.33478 + 2.79822i −0.126678 + 0.106295i
\(694\) 0 0
\(695\) 7.29892 12.6421i 0.276864 0.479542i
\(696\) 0 0
\(697\) −67.0223 24.3941i −2.53865 0.923994i
\(698\) 0 0
\(699\) −3.59116 20.3665i −0.135830 0.770331i
\(700\) 0 0
\(701\) 10.7483 + 9.01893i 0.405959 + 0.340640i 0.822792 0.568343i \(-0.192415\pi\)
−0.416832 + 0.908983i \(0.636860\pi\)
\(702\) 0 0
\(703\) 3.22898 + 6.81933i 0.121783 + 0.257196i
\(704\) 0 0
\(705\) −17.0164 14.2785i −0.640876 0.537759i
\(706\) 0 0
\(707\) 0.477533 + 2.70822i 0.0179595 + 0.101853i
\(708\) 0 0
\(709\) −29.7957 10.8447i −1.11900 0.407283i −0.284713 0.958613i \(-0.591898\pi\)
−0.834287 + 0.551330i \(0.814121\pi\)
\(710\) 0 0
\(711\) 11.5477 20.0012i 0.433072 0.750103i
\(712\) 0 0
\(713\) −11.2873 + 9.47114i −0.422711 + 0.354697i
\(714\) 0 0
\(715\) −5.38103 9.32022i −0.201239 0.348557i
\(716\) 0 0
\(717\) −5.43051 + 30.7979i −0.202806 + 1.15017i
\(718\) 0 0
\(719\) 21.2941 7.75043i 0.794137 0.289042i 0.0870823 0.996201i \(-0.472246\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(720\) 0 0
\(721\) 2.25220 0.0838764
\(722\) 0 0
\(723\) 2.40924 0.0896005
\(724\) 0 0
\(725\) 8.47155 3.08339i 0.314625 0.114514i
\(726\) 0 0
\(727\) −6.03930 + 34.2506i −0.223985 + 1.27028i 0.640630 + 0.767850i \(0.278673\pi\)
−0.864615 + 0.502434i \(0.832438\pi\)
\(728\) 0 0
\(729\) 17.8006 + 30.8315i 0.659281 + 1.14191i
\(730\) 0 0
\(731\) −0.299010 + 0.250900i −0.0110593 + 0.00927985i
\(732\) 0 0
\(733\) 2.83708 4.91397i 0.104790 0.181502i −0.808862 0.587998i \(-0.799916\pi\)
0.913652 + 0.406496i \(0.133250\pi\)
\(734\) 0 0
\(735\) 16.6799 + 6.07100i 0.615248 + 0.223932i
\(736\) 0 0
\(737\) 0.897971 + 5.09265i 0.0330772 + 0.187590i
\(738\) 0 0
\(739\) 19.8424 + 16.6497i 0.729913 + 0.612470i 0.930108 0.367286i \(-0.119713\pi\)
−0.200195 + 0.979756i \(0.564158\pi\)
\(740\) 0 0
\(741\) −9.83434 20.7693i −0.361274 0.762979i
\(742\) 0 0
\(743\) −19.7891 16.6050i −0.725992 0.609179i 0.203044 0.979170i \(-0.434917\pi\)
−0.929036 + 0.369990i \(0.879361\pi\)
\(744\) 0 0
\(745\) 2.18893 + 12.4140i 0.0801960 + 0.454814i
\(746\) 0 0
\(747\) 15.9042 + 5.78866i 0.581905 + 0.211796i
\(748\) 0 0
\(749\) 2.34741 4.06584i 0.0857726 0.148562i
\(750\) 0 0
\(751\) −22.1536 + 18.5891i −0.808397 + 0.678325i −0.950225 0.311566i \(-0.899147\pi\)
0.141828 + 0.989891i \(0.454702\pi\)
\(752\) 0 0
\(753\) −22.2065 38.4628i −0.809250 1.40166i
\(754\) 0 0
\(755\) −3.41437 + 19.3639i −0.124262 + 0.704723i
\(756\) 0 0
\(757\) −0.0387621 + 0.0141082i −0.00140883 + 0.000512773i −0.342724 0.939436i \(-0.611350\pi\)
0.341316 + 0.939949i \(0.389128\pi\)
\(758\) 0 0
\(759\) −52.6454 −1.91091
\(760\) 0 0
\(761\) −18.9666 −0.687538 −0.343769 0.939054i \(-0.611704\pi\)
−0.343769 + 0.939054i \(0.611704\pi\)
\(762\) 0 0
\(763\) −2.89038 + 1.05201i −0.104639 + 0.0380854i
\(764\) 0 0
\(765\) −3.70504 + 21.0123i −0.133956 + 0.759702i
\(766\) 0 0
\(767\) −0.181279 0.313984i −0.00654559 0.0113373i
\(768\) 0 0
\(769\) −22.9870 + 19.2883i −0.828931 + 0.695556i −0.955045 0.296460i \(-0.904194\pi\)
0.126114 + 0.992016i \(0.459749\pi\)
\(770\) 0 0
\(771\) −5.57648 + 9.65874i −0.200832 + 0.347851i
\(772\) 0 0
\(773\) 46.8749 + 17.0611i 1.68597 + 0.613644i 0.994109 0.108383i \(-0.0345674\pi\)
0.691864 + 0.722028i \(0.256790\pi\)
\(774\) 0 0
\(775\) 0.648235 + 3.67632i 0.0232853 + 0.132057i
\(776\) 0 0
\(777\) −0.800197 0.671445i −0.0287069 0.0240880i
\(778\) 0 0
\(779\) −36.6233 36.1940i −1.31217 1.29679i
\(780\) 0 0
\(781\) 19.8035 + 16.6171i 0.708626 + 0.594607i
\(782\) 0 0
\(783\) 2.13594 + 12.1135i 0.0763324 + 0.432902i
\(784\) 0 0
\(785\) −16.2749 5.92356i −0.580874 0.211421i
\(786\) 0 0
\(787\) 6.07584 10.5237i 0.216580 0.375128i −0.737180