Properties

Label 675.2.k.c.199.1
Level $675$
Weight $2$
Character 675.199
Analytic conductor $5.390$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(199,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.1
Root \(-2.28087 + 1.31686i\) of defining polynomial
Character \(\chi\) \(=\) 675.199
Dual form 675.2.k.c.424.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.28087 + 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(-1.55662 + 0.898714i) q^{7} +7.73393i q^{8} +O(q^{10})\) \(q+(-2.28087 + 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(-1.55662 + 0.898714i) q^{7} +7.73393i q^{8} +(0.904062 + 1.56588i) q^{11} +(1.70765 + 0.985914i) q^{13} +(2.36696 - 4.09970i) q^{14} +(-5.24801 - 9.08982i) q^{16} -4.80812i q^{17} -2.96467 q^{19} +(-4.12410 - 2.38105i) q^{22} +(1.50162 + 0.866963i) q^{23} -5.19325 q^{26} +8.87300i q^{28} +(3.68382 + 6.38057i) q^{29} +(1.31151 - 2.27161i) q^{31} +(10.5445 + 6.08789i) q^{32} +(6.33163 + 10.9667i) q^{34} +11.6351i q^{37} +(6.76203 - 3.90406i) q^{38} +(-1.23324 + 2.13603i) q^{41} +(6.30306 - 3.63907i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(-5.44910 + 3.14604i) q^{47} +(-1.88463 + 3.26427i) q^{49} +(8.42983 - 4.86696i) q^{52} +1.72540i q^{53} +(-6.95059 - 12.0388i) q^{56} +(-16.8047 - 9.70218i) q^{58} +(-5.51300 + 9.54880i) q^{59} +(6.33521 + 10.9729i) q^{61} +6.90833i q^{62} -11.0756 q^{64} +(-7.88407 - 4.55187i) q^{67} +(-20.5554 - 11.8676i) q^{68} -1.27460 q^{71} +3.58770i q^{73} +(-15.3218 - 26.5382i) q^{74} +(-7.31755 + 12.6744i) q^{76} +(-2.81456 - 1.62499i) q^{77} +(1.05545 + 1.82809i) q^{79} -6.49602i q^{82} +(0.951614 - 0.549415i) q^{83} +(-9.58431 + 16.6005i) q^{86} +(-12.1104 + 6.99195i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(7.41277 - 4.27976i) q^{92} +(8.28580 - 14.3514i) q^{94} +(-3.31926 + 1.91638i) q^{97} -9.92718i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28087 + 1.31686i −1.61282 + 0.931162i −0.624107 + 0.781339i \(0.714537\pi\)
−0.988713 + 0.149823i \(0.952130\pi\)
\(3\) 0 0
\(4\) 2.46825 4.27513i 1.23412 2.13757i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.55662 + 0.898714i −0.588346 + 0.339682i −0.764443 0.644691i \(-0.776986\pi\)
0.176097 + 0.984373i \(0.443653\pi\)
\(8\) 7.73393i 2.73436i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.904062 + 1.56588i 0.272585 + 0.472131i 0.969523 0.245000i \(-0.0787881\pi\)
−0.696938 + 0.717131i \(0.745455\pi\)
\(12\) 0 0
\(13\) 1.70765 + 0.985914i 0.473618 + 0.273443i 0.717753 0.696298i \(-0.245171\pi\)
−0.244135 + 0.969741i \(0.578504\pi\)
\(14\) 2.36696 4.09970i 0.632598 1.09569i
\(15\) 0 0
\(16\) −5.24801 9.08982i −1.31200 2.27246i
\(17\) 4.80812i 1.16614i −0.812421 0.583071i \(-0.801851\pi\)
0.812421 0.583071i \(-0.198149\pi\)
\(18\) 0 0
\(19\) −2.96467 −0.680142 −0.340071 0.940400i \(-0.610451\pi\)
−0.340071 + 0.940400i \(0.610451\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.12410 2.38105i −0.879261 0.507641i
\(23\) 1.50162 + 0.866963i 0.313110 + 0.180774i 0.648317 0.761370i \(-0.275473\pi\)
−0.335207 + 0.942144i \(0.608806\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −5.19325 −1.01848
\(27\) 0 0
\(28\) 8.87300i 1.67684i
\(29\) 3.68382 + 6.38057i 0.684069 + 1.18484i 0.973728 + 0.227713i \(0.0731247\pi\)
−0.289659 + 0.957130i \(0.593542\pi\)
\(30\) 0 0
\(31\) 1.31151 2.27161i 0.235555 0.407993i −0.723879 0.689927i \(-0.757643\pi\)
0.959434 + 0.281934i \(0.0909760\pi\)
\(32\) 10.5445 + 6.08789i 1.86403 + 1.07620i
\(33\) 0 0
\(34\) 6.33163 + 10.9667i 1.08587 + 1.88078i
\(35\) 0 0
\(36\) 0 0
\(37\) 11.6351i 1.91280i 0.292063 + 0.956399i \(0.405658\pi\)
−0.292063 + 0.956399i \(0.594342\pi\)
\(38\) 6.76203 3.90406i 1.09695 0.633322i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.23324 + 2.13603i −0.192600 + 0.333592i −0.946111 0.323842i \(-0.895025\pi\)
0.753511 + 0.657435i \(0.228359\pi\)
\(42\) 0 0
\(43\) 6.30306 3.63907i 0.961207 0.554953i 0.0646628 0.997907i \(-0.479403\pi\)
0.896544 + 0.442954i \(0.146069\pi\)
\(44\) 8.92580 1.34562
\(45\) 0 0
\(46\) −4.56668 −0.673321
\(47\) −5.44910 + 3.14604i −0.794833 + 0.458897i −0.841661 0.540006i \(-0.818422\pi\)
0.0468283 + 0.998903i \(0.485089\pi\)
\(48\) 0 0
\(49\) −1.88463 + 3.26427i −0.269233 + 0.466324i
\(50\) 0 0
\(51\) 0 0
\(52\) 8.42983 4.86696i 1.16901 0.674926i
\(53\) 1.72540i 0.237001i 0.992954 + 0.118501i \(0.0378088\pi\)
−0.992954 + 0.118501i \(0.962191\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −6.95059 12.0388i −0.928811 1.60875i
\(57\) 0 0
\(58\) −16.8047 9.70218i −2.20656 1.27396i
\(59\) −5.51300 + 9.54880i −0.717732 + 1.24315i 0.244165 + 0.969734i \(0.421486\pi\)
−0.961896 + 0.273414i \(0.911847\pi\)
\(60\) 0 0
\(61\) 6.33521 + 10.9729i 0.811141 + 1.40494i 0.912066 + 0.410043i \(0.134486\pi\)
−0.100925 + 0.994894i \(0.532180\pi\)
\(62\) 6.90833i 0.877358i
\(63\) 0 0
\(64\) −11.0756 −1.38445
\(65\) 0 0
\(66\) 0 0
\(67\) −7.88407 4.55187i −0.963193 0.556100i −0.0660386 0.997817i \(-0.521036\pi\)
−0.897154 + 0.441717i \(0.854369\pi\)
\(68\) −20.5554 11.8676i −2.49271 1.43916i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.27460 −0.151268 −0.0756338 0.997136i \(-0.524098\pi\)
−0.0756338 + 0.997136i \(0.524098\pi\)
\(72\) 0 0
\(73\) 3.58770i 0.419908i 0.977711 + 0.209954i \(0.0673315\pi\)
−0.977711 + 0.209954i \(0.932669\pi\)
\(74\) −15.3218 26.5382i −1.78112 3.08500i
\(75\) 0 0
\(76\) −7.31755 + 12.6744i −0.839380 + 1.45385i
\(77\) −2.81456 1.62499i −0.320749 0.185184i
\(78\) 0 0
\(79\) 1.05545 + 1.82809i 0.118747 + 0.205676i 0.919272 0.393624i \(-0.128779\pi\)
−0.800524 + 0.599300i \(0.795445\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 6.49602i 0.717366i
\(83\) 0.951614 0.549415i 0.104453 0.0603061i −0.446863 0.894602i \(-0.647459\pi\)
0.551317 + 0.834296i \(0.314126\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −9.58431 + 16.6005i −1.03350 + 1.79008i
\(87\) 0 0
\(88\) −12.1104 + 6.99195i −1.29097 + 0.745344i
\(89\) −13.2935 −1.40910 −0.704552 0.709653i \(-0.748852\pi\)
−0.704552 + 0.709653i \(0.748852\pi\)
\(90\) 0 0
\(91\) −3.54422 −0.371535
\(92\) 7.41277 4.27976i 0.772834 0.446196i
\(93\) 0 0
\(94\) 8.28580 14.3514i 0.854615 1.48024i
\(95\) 0 0
\(96\) 0 0
\(97\) −3.31926 + 1.91638i −0.337020 + 0.194579i −0.658954 0.752184i \(-0.729001\pi\)
0.321933 + 0.946762i \(0.395667\pi\)
\(98\) 9.92718i 1.00280i
\(99\) 0 0
\(100\) 0 0
\(101\) 3.27618 + 5.67452i 0.325993 + 0.564636i 0.981713 0.190368i \(-0.0609682\pi\)
−0.655720 + 0.755004i \(0.727635\pi\)
\(102\) 0 0
\(103\) −6.99365 4.03779i −0.689105 0.397855i 0.114172 0.993461i \(-0.463579\pi\)
−0.803277 + 0.595606i \(0.796912\pi\)
\(104\) −7.62499 + 13.2069i −0.747691 + 1.29504i
\(105\) 0 0
\(106\) −2.27211 3.93541i −0.220687 0.382241i
\(107\) 8.97674i 0.867814i 0.900958 + 0.433907i \(0.142865\pi\)
−0.900958 + 0.433907i \(0.857135\pi\)
\(108\) 0 0
\(109\) 6.34164 0.607419 0.303710 0.952765i \(-0.401775\pi\)
0.303710 + 0.952765i \(0.401775\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 16.3383 + 9.43292i 1.54382 + 0.891327i
\(113\) 12.9060 + 7.45127i 1.21409 + 0.700957i 0.963648 0.267174i \(-0.0860899\pi\)
0.250444 + 0.968131i \(0.419423\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 36.3704 3.37691
\(117\) 0 0
\(118\) 29.0394i 2.67330i
\(119\) 4.32113 + 7.48441i 0.396117 + 0.686095i
\(120\) 0 0
\(121\) 3.86534 6.69497i 0.351395 0.608634i
\(122\) −28.8996 16.6852i −2.61645 1.51061i
\(123\) 0 0
\(124\) −6.47428 11.2138i −0.581408 1.00703i
\(125\) 0 0
\(126\) 0 0
\(127\) 3.62303i 0.321492i 0.986996 + 0.160746i \(0.0513899\pi\)
−0.986996 + 0.160746i \(0.948610\pi\)
\(128\) 4.17289 2.40922i 0.368835 0.212947i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.64673 6.31631i 0.318616 0.551859i −0.661584 0.749871i \(-0.730115\pi\)
0.980200 + 0.198012i \(0.0634486\pi\)
\(132\) 0 0
\(133\) 4.61486 2.66439i 0.400159 0.231032i
\(134\) 23.9767 2.07127
\(135\) 0 0
\(136\) 37.1857 3.18865
\(137\) 6.17148 3.56310i 0.527265 0.304417i −0.212637 0.977131i \(-0.568205\pi\)
0.739902 + 0.672715i \(0.234872\pi\)
\(138\) 0 0
\(139\) −7.35533 + 12.7398i −0.623871 + 1.08058i 0.364887 + 0.931052i \(0.381108\pi\)
−0.988758 + 0.149525i \(0.952226\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.90721 1.67848i 0.243967 0.140855i
\(143\) 3.56531i 0.298146i
\(144\) 0 0
\(145\) 0 0
\(146\) −4.72450 8.18308i −0.391003 0.677236i
\(147\) 0 0
\(148\) 49.7416 + 28.7183i 4.08873 + 2.36063i
\(149\) 0.282655 0.489572i 0.0231560 0.0401073i −0.854215 0.519920i \(-0.825962\pi\)
0.877371 + 0.479812i \(0.159295\pi\)
\(150\) 0 0
\(151\) −0.0766925 0.132835i −0.00624115 0.0108100i 0.862888 0.505395i \(-0.168653\pi\)
−0.869129 + 0.494585i \(0.835320\pi\)
\(152\) 22.9285i 1.85975i
\(153\) 0 0
\(154\) 8.55953 0.689746
\(155\) 0 0
\(156\) 0 0
\(157\) 9.92525 + 5.73035i 0.792121 + 0.457332i 0.840709 0.541487i \(-0.182139\pi\)
−0.0485874 + 0.998819i \(0.515472\pi\)
\(158\) −4.81469 2.77976i −0.383036 0.221146i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.11661 −0.245623
\(162\) 0 0
\(163\) 22.0595i 1.72783i 0.503637 + 0.863915i \(0.331995\pi\)
−0.503637 + 0.863915i \(0.668005\pi\)
\(164\) 6.08789 + 10.5445i 0.475384 + 0.823389i
\(165\) 0 0
\(166\) −1.44701 + 2.50629i −0.112310 + 0.194526i
\(167\) 14.7817 + 8.53421i 1.14384 + 0.660397i 0.947379 0.320115i \(-0.103721\pi\)
0.196462 + 0.980511i \(0.437055\pi\)
\(168\) 0 0
\(169\) −4.55595 7.89113i −0.350457 0.607010i
\(170\) 0 0
\(171\) 0 0
\(172\) 35.9285i 2.73953i
\(173\) 10.3444 5.97233i 0.786468 0.454067i −0.0522497 0.998634i \(-0.516639\pi\)
0.838718 + 0.544567i \(0.183306\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.48906 16.4355i 0.715265 1.23887i
\(177\) 0 0
\(178\) 30.3207 17.5056i 2.27263 1.31210i
\(179\) 8.54921 0.638998 0.319499 0.947587i \(-0.396485\pi\)
0.319499 + 0.947587i \(0.396485\pi\)
\(180\) 0 0
\(181\) −10.5524 −0.784351 −0.392176 0.919890i \(-0.628277\pi\)
−0.392176 + 0.919890i \(0.628277\pi\)
\(182\) 8.08390 4.66724i 0.599219 0.345959i
\(183\) 0 0
\(184\) −6.70503 + 11.6135i −0.494301 + 0.856155i
\(185\) 0 0
\(186\) 0 0
\(187\) 7.52895 4.34684i 0.550571 0.317873i
\(188\) 31.0608i 2.26534i
\(189\) 0 0
\(190\) 0 0
\(191\) −8.66862 15.0145i −0.627239 1.08641i −0.988103 0.153792i \(-0.950852\pi\)
0.360864 0.932618i \(-0.382482\pi\)
\(192\) 0 0
\(193\) 1.35059 + 0.779763i 0.0972175 + 0.0561286i 0.547821 0.836596i \(-0.315458\pi\)
−0.450603 + 0.892724i \(0.648791\pi\)
\(194\) 5.04721 8.74202i 0.362369 0.627641i
\(195\) 0 0
\(196\) 9.30346 + 16.1141i 0.664533 + 1.15100i
\(197\) 17.9767i 1.28079i −0.768046 0.640395i \(-0.778771\pi\)
0.768046 0.640395i \(-0.221229\pi\)
\(198\) 0 0
\(199\) −11.0225 −0.781362 −0.390681 0.920526i \(-0.627760\pi\)
−0.390681 + 0.920526i \(0.627760\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −14.9451 8.62856i −1.05153 0.607104i
\(203\) −11.4686 6.62141i −0.804939 0.464732i
\(204\) 0 0
\(205\) 0 0
\(206\) 21.2688 1.48187
\(207\) 0 0
\(208\) 20.6964i 1.43503i
\(209\) −2.68025 4.64232i −0.185397 0.321116i
\(210\) 0 0
\(211\) 11.9643 20.7227i 0.823655 1.42661i −0.0792886 0.996852i \(-0.525265\pi\)
0.902943 0.429760i \(-0.141402\pi\)
\(212\) 7.37630 + 4.25871i 0.506606 + 0.292489i
\(213\) 0 0
\(214\) −11.8211 20.4748i −0.808076 1.39963i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.71470i 0.320055i
\(218\) −14.4645 + 8.35107i −0.979658 + 0.565606i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.74040 8.21061i 0.318874 0.552305i
\(222\) 0 0
\(223\) −18.8020 + 10.8553i −1.25907 + 0.726927i −0.972895 0.231249i \(-0.925719\pi\)
−0.286180 + 0.958176i \(0.592385\pi\)
\(224\) −21.8851 −1.46226
\(225\) 0 0
\(226\) −39.2492 −2.61082
\(227\) −12.2111 + 7.05010i −0.810481 + 0.467932i −0.847123 0.531397i \(-0.821667\pi\)
0.0366416 + 0.999328i \(0.488334\pi\)
\(228\) 0 0
\(229\) 1.83879 3.18488i 0.121511 0.210463i −0.798853 0.601526i \(-0.794559\pi\)
0.920364 + 0.391064i \(0.127893\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −49.3469 + 28.4904i −3.23978 + 1.87049i
\(233\) 5.34164i 0.349943i −0.984574 0.174971i \(-0.944017\pi\)
0.984574 0.174971i \(-0.0559833\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 27.2149 + 47.1376i 1.77154 + 3.06840i
\(237\) 0 0
\(238\) −19.7119 11.3807i −1.27773 0.737698i
\(239\) 11.0167 19.0815i 0.712613 1.23428i −0.251260 0.967920i \(-0.580845\pi\)
0.963873 0.266362i \(-0.0858218\pi\)
\(240\) 0 0
\(241\) 9.32358 + 16.1489i 0.600585 + 1.04024i 0.992733 + 0.120341i \(0.0383988\pi\)
−0.392148 + 0.919902i \(0.628268\pi\)
\(242\) 20.3605i 1.30882i
\(243\) 0 0
\(244\) 62.5475 4.00420
\(245\) 0 0
\(246\) 0 0
\(247\) −5.06263 2.92291i −0.322127 0.185980i
\(248\) 17.5684 + 10.1431i 1.11560 + 0.644091i
\(249\) 0 0
\(250\) 0 0
\(251\) −14.6929 −0.927407 −0.463704 0.885990i \(-0.653480\pi\)
−0.463704 + 0.885990i \(0.653480\pi\)
\(252\) 0 0
\(253\) 3.13515i 0.197105i
\(254\) −4.77103 8.26366i −0.299361 0.518508i
\(255\) 0 0
\(256\) 4.73035 8.19320i 0.295647 0.512075i
\(257\) 19.2335 + 11.1045i 1.19975 + 0.692678i 0.960500 0.278280i \(-0.0897642\pi\)
0.239253 + 0.970957i \(0.423098\pi\)
\(258\) 0 0
\(259\) −10.4566 18.1114i −0.649743 1.12539i
\(260\) 0 0
\(261\) 0 0
\(262\) 19.2089i 1.18673i
\(263\) 4.97100 2.87001i 0.306525 0.176972i −0.338846 0.940842i \(-0.610036\pi\)
0.645370 + 0.763870i \(0.276703\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −7.01727 + 12.1543i −0.430256 + 0.745226i
\(267\) 0 0
\(268\) −38.9197 + 22.4703i −2.37740 + 1.37259i
\(269\) −15.6162 −0.952139 −0.476070 0.879408i \(-0.657939\pi\)
−0.476070 + 0.879408i \(0.657939\pi\)
\(270\) 0 0
\(271\) −6.75315 −0.410225 −0.205112 0.978738i \(-0.565756\pi\)
−0.205112 + 0.978738i \(0.565756\pi\)
\(272\) −43.7050 + 25.2331i −2.65000 + 1.52998i
\(273\) 0 0
\(274\) −9.38423 + 16.2540i −0.566922 + 0.981938i
\(275\) 0 0
\(276\) 0 0
\(277\) 26.2376 15.1483i 1.57646 0.910172i 0.581118 0.813820i \(-0.302616\pi\)
0.995347 0.0963529i \(-0.0307177\pi\)
\(278\) 38.7438i 2.32370i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.31755 + 16.1385i 0.555838 + 0.962740i 0.997838 + 0.0657249i \(0.0209360\pi\)
−0.441999 + 0.897015i \(0.645731\pi\)
\(282\) 0 0
\(283\) −4.91354 2.83683i −0.292079 0.168632i 0.346800 0.937939i \(-0.387268\pi\)
−0.638879 + 0.769307i \(0.720602\pi\)
\(284\) −3.14604 + 5.44910i −0.186683 + 0.323345i
\(285\) 0 0
\(286\) −4.69502 8.13201i −0.277622 0.480856i
\(287\) 4.43332i 0.261690i
\(288\) 0 0
\(289\) −6.11806 −0.359886
\(290\) 0 0
\(291\) 0 0
\(292\) 15.3379 + 8.85533i 0.897582 + 0.518219i
\(293\) −15.8286 9.13867i −0.924720 0.533887i −0.0395819 0.999216i \(-0.512603\pi\)
−0.885138 + 0.465329i \(0.845936\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −89.9850 −5.23027
\(297\) 0 0
\(298\) 1.48887i 0.0862478i
\(299\) 1.70950 + 2.96094i 0.0988631 + 0.171236i
\(300\) 0 0
\(301\) −6.54097 + 11.3293i −0.377015 + 0.653009i
\(302\) 0.349852 + 0.201987i 0.0201317 + 0.0116230i
\(303\) 0 0
\(304\) 15.5586 + 26.9483i 0.892349 + 1.54559i
\(305\) 0 0
\(306\) 0 0
\(307\) 15.5050i 0.884915i −0.896789 0.442458i \(-0.854107\pi\)
0.896789 0.442458i \(-0.145893\pi\)
\(308\) −13.8941 + 8.02174i −0.791688 + 0.457081i
\(309\) 0 0
\(310\) 0 0
\(311\) 15.2232 26.3673i 0.863228 1.49515i −0.00556798 0.999984i \(-0.501772\pi\)
0.868796 0.495170i \(-0.164894\pi\)
\(312\) 0 0
\(313\) 6.01832 3.47468i 0.340176 0.196401i −0.320174 0.947359i \(-0.603741\pi\)
0.660350 + 0.750958i \(0.270408\pi\)
\(314\) −30.1843 −1.70340
\(315\) 0 0
\(316\) 10.4205 0.586196
\(317\) 13.9820 8.07253i 0.785309 0.453398i −0.0529995 0.998595i \(-0.516878\pi\)
0.838308 + 0.545196i \(0.183545\pi\)
\(318\) 0 0
\(319\) −6.66081 + 11.5369i −0.372934 + 0.645940i
\(320\) 0 0
\(321\) 0 0
\(322\) 7.10858 4.10414i 0.396146 0.228715i
\(323\) 14.2545i 0.793142i
\(324\) 0 0
\(325\) 0 0
\(326\) −29.0493 50.3148i −1.60889 2.78668i
\(327\) 0 0
\(328\) −16.5199 9.53779i −0.912160 0.526636i
\(329\) 5.65478 9.79436i 0.311758 0.539981i
\(330\) 0 0
\(331\) −6.31112 10.9312i −0.346890 0.600832i 0.638805 0.769369i \(-0.279429\pi\)
−0.985695 + 0.168537i \(0.946096\pi\)
\(332\) 5.42437i 0.297701i
\(333\) 0 0
\(334\) −44.9535 −2.45975
\(335\) 0 0
\(336\) 0 0
\(337\) 5.99324 + 3.46020i 0.326473 + 0.188489i 0.654274 0.756258i \(-0.272974\pi\)
−0.327801 + 0.944747i \(0.606308\pi\)
\(338\) 20.7831 + 11.9991i 1.13045 + 0.652665i
\(339\) 0 0
\(340\) 0 0
\(341\) 4.74276 0.256835
\(342\) 0 0
\(343\) 19.3570i 1.04518i
\(344\) 28.1443 + 48.7474i 1.51744 + 2.62828i
\(345\) 0 0
\(346\) −15.7295 + 27.2442i −0.845621 + 1.46466i
\(347\) 11.9566 + 6.90317i 0.641866 + 0.370581i 0.785333 0.619074i \(-0.212492\pi\)
−0.143467 + 0.989655i \(0.545825\pi\)
\(348\) 0 0
\(349\) 3.28384 + 5.68778i 0.175780 + 0.304460i 0.940431 0.339985i \(-0.110422\pi\)
−0.764651 + 0.644445i \(0.777089\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 22.0153i 1.17342i
\(353\) −3.05273 + 1.76250i −0.162481 + 0.0938082i −0.579035 0.815302i \(-0.696571\pi\)
0.416555 + 0.909111i \(0.363237\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −32.8116 + 56.8313i −1.73901 + 3.01205i
\(357\) 0 0
\(358\) −19.4996 + 11.2581i −1.03059 + 0.595010i
\(359\) 22.9285 1.21012 0.605061 0.796179i \(-0.293149\pi\)
0.605061 + 0.796179i \(0.293149\pi\)
\(360\) 0 0
\(361\) −10.2107 −0.537407
\(362\) 24.0686 13.8960i 1.26502 0.730358i
\(363\) 0 0
\(364\) −8.74801 + 15.1520i −0.458520 + 0.794181i
\(365\) 0 0
\(366\) 0 0
\(367\) 3.61939 2.08966i 0.188931 0.109079i −0.402551 0.915397i \(-0.631876\pi\)
0.591482 + 0.806318i \(0.298543\pi\)
\(368\) 18.1993i 0.948706i
\(369\) 0 0
\(370\) 0 0
\(371\) −1.55064 2.68578i −0.0805051 0.139439i
\(372\) 0 0
\(373\) 5.92440 + 3.42045i 0.306754 + 0.177104i 0.645473 0.763783i \(-0.276660\pi\)
−0.338719 + 0.940888i \(0.609994\pi\)
\(374\) −11.4484 + 19.8292i −0.591982 + 1.02534i
\(375\) 0 0
\(376\) −24.3312 42.1429i −1.25479 2.17336i
\(377\) 14.5277i 0.748217i
\(378\) 0 0
\(379\) 12.7764 0.656280 0.328140 0.944629i \(-0.393578\pi\)
0.328140 + 0.944629i \(0.393578\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 39.5440 + 22.8307i 2.02325 + 1.16812i
\(383\) −6.52515 3.76730i −0.333420 0.192500i 0.323939 0.946078i \(-0.394993\pi\)
−0.657358 + 0.753578i \(0.728326\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.10736 −0.209059
\(387\) 0 0
\(388\) 18.9204i 0.960538i
\(389\) −2.72588 4.72135i −0.138207 0.239382i 0.788611 0.614893i \(-0.210801\pi\)
−0.926818 + 0.375511i \(0.877467\pi\)
\(390\) 0 0
\(391\) 4.16847 7.22000i 0.210808 0.365131i
\(392\) −25.2456 14.5756i −1.27510 0.736177i
\(393\) 0 0
\(394\) 23.6729 + 41.0026i 1.19262 + 2.06568i
\(395\) 0 0
\(396\) 0 0
\(397\) 5.64549i 0.283339i −0.989914 0.141670i \(-0.954753\pi\)
0.989914 0.141670i \(-0.0452470\pi\)
\(398\) 25.1408 14.5151i 1.26020 0.727574i
\(399\) 0 0
\(400\) 0 0
\(401\) −2.75209 + 4.76676i −0.137433 + 0.238040i −0.926524 0.376235i \(-0.877218\pi\)
0.789091 + 0.614276i \(0.210552\pi\)
\(402\) 0 0
\(403\) 4.47922 2.58608i 0.223126 0.128822i
\(404\) 32.3458 1.60926
\(405\) 0 0
\(406\) 34.8779 1.73096
\(407\) −18.2192 + 10.5188i −0.903091 + 0.521400i
\(408\) 0 0
\(409\) 16.4265 28.4515i 0.812238 1.40684i −0.0990570 0.995082i \(-0.531583\pi\)
0.911295 0.411755i \(-0.135084\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −34.5241 + 19.9325i −1.70088 + 0.982005i
\(413\) 19.8184i 0.975202i
\(414\) 0 0
\(415\) 0 0
\(416\) 12.0043 + 20.7920i 0.588558 + 1.01941i
\(417\) 0 0
\(418\) 12.2266 + 7.05903i 0.598022 + 0.345268i
\(419\) −11.4295 + 19.7965i −0.558369 + 0.967124i 0.439264 + 0.898358i \(0.355239\pi\)
−0.997633 + 0.0687656i \(0.978094\pi\)
\(420\) 0 0
\(421\) −8.97071 15.5377i −0.437205 0.757262i 0.560267 0.828312i \(-0.310698\pi\)
−0.997473 + 0.0710498i \(0.977365\pi\)
\(422\) 63.0212i 3.06782i
\(423\) 0 0
\(424\) −13.3441 −0.648046
\(425\) 0 0
\(426\) 0 0
\(427\) −19.7230 11.3871i −0.954463 0.551060i
\(428\) 38.3768 + 22.1568i 1.85501 + 1.07099i
\(429\) 0 0
\(430\) 0 0
\(431\) 6.18871 0.298100 0.149050 0.988830i \(-0.452378\pi\)
0.149050 + 0.988830i \(0.452378\pi\)
\(432\) 0 0
\(433\) 3.11806i 0.149844i 0.997189 + 0.0749221i \(0.0238708\pi\)
−0.997189 + 0.0749221i \(0.976129\pi\)
\(434\) −6.20861 10.7536i −0.298023 0.516190i
\(435\) 0 0
\(436\) 15.6528 27.1114i 0.749631 1.29840i
\(437\) −4.45182 2.57026i −0.212960 0.122952i
\(438\) 0 0
\(439\) 6.75494 + 11.6999i 0.322396 + 0.558406i 0.980982 0.194100i \(-0.0621785\pi\)
−0.658586 + 0.752505i \(0.728845\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 24.9698i 1.18769i
\(443\) −21.0248 + 12.1387i −0.998918 + 0.576726i −0.907928 0.419126i \(-0.862337\pi\)
−0.0909904 + 0.995852i \(0.529003\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 28.5899 49.5192i 1.35377 2.34480i
\(447\) 0 0
\(448\) 17.2404 9.95377i 0.814534 0.470271i
\(449\) −24.1437 −1.13941 −0.569705 0.821849i \(-0.692943\pi\)
−0.569705 + 0.821849i \(0.692943\pi\)
\(450\) 0 0
\(451\) −4.45970 −0.209999
\(452\) 63.7104 36.7832i 2.99668 1.73014i
\(453\) 0 0
\(454\) 18.5680 32.1607i 0.871440 1.50938i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.44355 + 1.41078i −0.114304 + 0.0659937i −0.556062 0.831141i \(-0.687688\pi\)
0.441758 + 0.897134i \(0.354355\pi\)
\(458\) 9.68573i 0.452585i
\(459\) 0 0
\(460\) 0 0
\(461\) 10.7286 + 18.5825i 0.499681 + 0.865474i 1.00000 0.000367761i \(-0.000117062\pi\)
−0.500318 + 0.865841i \(0.666784\pi\)
\(462\) 0 0
\(463\) −17.1502 9.90167i −0.797037 0.460170i 0.0453970 0.998969i \(-0.485545\pi\)
−0.842434 + 0.538799i \(0.818878\pi\)
\(464\) 38.6655 66.9706i 1.79500 3.10903i
\(465\) 0 0
\(466\) 7.03421 + 12.1836i 0.325853 + 0.564395i
\(467\) 22.7210i 1.05140i −0.850669 0.525701i \(-0.823803\pi\)
0.850669 0.525701i \(-0.176197\pi\)
\(468\) 0 0
\(469\) 16.3633 0.755588
\(470\) 0 0
\(471\) 0 0
\(472\) −73.8497 42.6372i −3.39921 1.96253i
\(473\) 11.3967 + 6.57989i 0.524021 + 0.302544i
\(474\) 0 0
\(475\) 0 0
\(476\) 42.6625 1.95543
\(477\) 0 0
\(478\) 58.0300i 2.65423i
\(479\) −10.6440 18.4359i −0.486336 0.842359i 0.513541 0.858065i \(-0.328334\pi\)
−0.999877 + 0.0157065i \(0.995000\pi\)
\(480\) 0 0
\(481\) −11.4712 + 19.8687i −0.523042 + 0.905935i
\(482\) −42.5318 24.5557i −1.93727 1.11848i
\(483\) 0 0
\(484\) −19.0813 33.0497i −0.867330 1.50226i
\(485\) 0 0
\(486\) 0 0
\(487\) 9.58690i 0.434424i −0.976124 0.217212i \(-0.930304\pi\)
0.976124 0.217212i \(-0.0696963\pi\)
\(488\) −84.8637 + 48.9961i −3.84160 + 2.21795i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.9222 + 32.7742i −0.853945 + 1.47908i 0.0236745 + 0.999720i \(0.492463\pi\)
−0.877620 + 0.479357i \(0.840870\pi\)
\(492\) 0 0
\(493\) 30.6786 17.7123i 1.38169 0.797721i
\(494\) 15.3963 0.692711
\(495\) 0 0
\(496\) −27.5314 −1.23619
\(497\) 1.98407 1.14550i 0.0889977 0.0513829i
\(498\) 0 0
\(499\) 8.46266 14.6577i 0.378840 0.656171i −0.612053 0.790816i \(-0.709656\pi\)
0.990894 + 0.134646i \(0.0429896\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 33.5126 19.3485i 1.49574 0.863566i
\(503\) 40.4168i 1.80210i 0.433719 + 0.901048i \(0.357201\pi\)
−0.433719 + 0.901048i \(0.642799\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.12856 7.15088i −0.183537 0.317896i
\(507\) 0 0
\(508\) 15.4889 + 8.94253i 0.687210 + 0.396761i
\(509\) 20.7034 35.8593i 0.917660 1.58943i 0.114701 0.993400i \(-0.463409\pi\)
0.802959 0.596034i \(-0.203258\pi\)
\(510\) 0 0
\(511\) −3.22431 5.58467i −0.142635 0.247051i
\(512\) 34.5537i 1.52707i
\(513\) 0 0
\(514\) −58.4922 −2.57998
\(515\) 0 0
\(516\) 0 0
\(517\) −9.85265 5.68843i −0.433319 0.250177i
\(518\) 47.7004 + 27.5398i 2.09584 + 1.21003i
\(519\) 0 0
\(520\) 0 0
\(521\) 17.0301 0.746103 0.373052 0.927811i \(-0.378311\pi\)
0.373052 + 0.927811i \(0.378311\pi\)
\(522\) 0 0
\(523\) 9.57651i 0.418751i −0.977835 0.209376i \(-0.932857\pi\)
0.977835 0.209376i \(-0.0671432\pi\)
\(524\) −18.0021 31.1805i −0.786424 1.36213i
\(525\) 0 0
\(526\) −7.55880 + 13.0922i −0.329579 + 0.570848i
\(527\) −10.9222 6.30592i −0.475777 0.274690i
\(528\) 0 0
\(529\) −9.99675 17.3149i −0.434641 0.752821i
\(530\) 0 0
\(531\) 0 0
\(532\) 26.3055i 1.14049i
\(533\) −4.21189 + 2.43174i −0.182437 + 0.105330i
\(534\) 0 0
\(535\) 0 0
\(536\) 35.2038 60.9748i 1.52057 2.63371i
\(537\) 0 0
\(538\) 35.6187 20.5644i 1.53563 0.886596i
\(539\) −6.81528 −0.293555
\(540\) 0 0
\(541\) −0.833751 −0.0358458 −0.0179229 0.999839i \(-0.505705\pi\)
−0.0179229 + 0.999839i \(0.505705\pi\)
\(542\) 15.4031 8.89297i 0.661619 0.381986i
\(543\) 0 0
\(544\) 29.2713 50.6994i 1.25500 2.17372i
\(545\) 0 0
\(546\) 0 0
\(547\) −24.5319 + 14.1635i −1.04891 + 0.605587i −0.922343 0.386371i \(-0.873728\pi\)
−0.126565 + 0.991958i \(0.540395\pi\)
\(548\) 35.1785i 1.50275i
\(549\) 0 0
\(550\) 0 0
\(551\) −10.9213 18.9163i −0.465264 0.805861i
\(552\) 0 0
\(553\) −3.28586 1.89709i −0.139729 0.0806727i
\(554\) −39.8964 + 69.1026i −1.69504 + 2.93589i
\(555\) 0 0
\(556\) 36.3096 + 62.8901i 1.53987 + 2.66713i
\(557\) 11.5042i 0.487448i −0.969845 0.243724i \(-0.921631\pi\)
0.969845 0.243724i \(-0.0783690\pi\)
\(558\) 0 0
\(559\) 14.3512 0.606993
\(560\) 0 0
\(561\) 0 0
\(562\) −42.5043 24.5398i −1.79293 1.03515i
\(563\) −28.5840 16.5030i −1.20467 0.695517i −0.243080 0.970006i \(-0.578158\pi\)
−0.961590 + 0.274490i \(0.911491\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.9429 0.628095
\(567\) 0 0
\(568\) 9.85769i 0.413619i
\(569\) 13.5044 + 23.3903i 0.566135 + 0.980574i 0.996943 + 0.0781305i \(0.0248951\pi\)
−0.430809 + 0.902443i \(0.641772\pi\)
\(570\) 0 0
\(571\) 12.2122 21.1521i 0.511064 0.885189i −0.488854 0.872366i \(-0.662585\pi\)
0.999918 0.0128232i \(-0.00408185\pi\)
\(572\) 15.2422 + 8.80007i 0.637307 + 0.367950i
\(573\) 0 0
\(574\) 5.83807 + 10.1118i 0.243676 + 0.422060i
\(575\) 0 0
\(576\) 0 0
\(577\) 14.7976i 0.616033i 0.951381 + 0.308017i \(0.0996653\pi\)
−0.951381 + 0.308017i \(0.900335\pi\)
\(578\) 13.9545 8.05663i 0.580431 0.335112i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.987533 + 1.71046i −0.0409698 + 0.0709617i
\(582\) 0 0
\(583\) −2.70177 + 1.55987i −0.111896 + 0.0646030i
\(584\) −27.7470 −1.14818
\(585\) 0 0
\(586\) 48.1375 1.98854
\(587\) −26.4813 + 15.2890i −1.09300 + 0.631044i −0.934374 0.356295i \(-0.884040\pi\)
−0.158626 + 0.987339i \(0.550706\pi\)
\(588\) 0 0
\(589\) −3.88821 + 6.73457i −0.160211 + 0.277493i
\(590\) 0 0
\(591\) 0 0
\(592\) 105.761 61.0611i 4.34675 2.50960i
\(593\) 5.09990i 0.209428i −0.994502 0.104714i \(-0.966607\pi\)
0.994502 0.104714i \(-0.0333927\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.39532 2.41677i −0.0571547 0.0989949i
\(597\) 0 0
\(598\) −7.79831 4.50236i −0.318897 0.184115i
\(599\) 0.282655 0.489572i 0.0115490 0.0200034i −0.860193 0.509968i \(-0.829657\pi\)
0.871742 + 0.489965i \(0.162990\pi\)
\(600\) 0 0
\(601\) 5.50480 + 9.53459i 0.224546 + 0.388924i 0.956183 0.292770i \(-0.0945769\pi\)
−0.731637 + 0.681694i \(0.761244\pi\)
\(602\) 34.4542i 1.40425i
\(603\) 0 0
\(604\) −0.757185 −0.0308094
\(605\) 0 0
\(606\) 0 0
\(607\) 16.5396 + 9.54913i 0.671321 + 0.387587i 0.796577 0.604537i \(-0.206642\pi\)
−0.125256 + 0.992124i \(0.539975\pi\)
\(608\) −31.2611 18.0486i −1.26780 0.731967i
\(609\) 0 0
\(610\) 0 0
\(611\) −12.4069 −0.501929
\(612\) 0 0
\(613\) 9.33918i 0.377206i −0.982053 0.188603i \(-0.939604\pi\)
0.982053 0.188603i \(-0.0603959\pi\)
\(614\) 20.4179 + 35.3648i 0.823999 + 1.42721i
\(615\) 0 0
\(616\) 12.5675 21.7676i 0.506360 0.877041i
\(617\) −21.1444 12.2077i −0.851241 0.491464i 0.00982861 0.999952i \(-0.496871\pi\)
−0.861069 + 0.508488i \(0.830205\pi\)
\(618\) 0 0
\(619\) 19.7431 + 34.1961i 0.793544 + 1.37446i 0.923760 + 0.382973i \(0.125100\pi\)
−0.130216 + 0.991486i \(0.541567\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 80.1874i 3.21522i
\(623\) 20.6928 11.9470i 0.829040 0.478647i
\(624\) 0 0
\(625\) 0 0
\(626\) −9.15135 + 15.8506i −0.365761 + 0.633517i
\(627\) 0 0
\(628\) 48.9960 28.2879i 1.95515 1.12881i
\(629\) 55.9430 2.23059
\(630\) 0 0
\(631\) 42.1634 1.67850 0.839249 0.543747i \(-0.182995\pi\)
0.839249 + 0.543747i \(0.182995\pi\)
\(632\) −14.1383 + 8.16277i −0.562393 + 0.324698i
\(633\) 0 0
\(634\) −21.2608 + 36.8248i −0.844375 + 1.46250i
\(635\) 0 0
\(636\) 0 0
\(637\) −6.43658 + 3.71616i −0.255027 + 0.147240i
\(638\) 35.0855i 1.38905i
\(639\) 0 0
\(640\) 0 0
\(641\) 17.6577 + 30.5841i 0.697438 + 1.20800i 0.969352 + 0.245677i \(0.0790103\pi\)
−0.271913 + 0.962322i \(0.587656\pi\)
\(642\) 0 0
\(643\) 12.2936 + 7.09771i 0.484812 + 0.279906i 0.722420 0.691455i \(-0.243030\pi\)
−0.237608 + 0.971361i \(0.576363\pi\)
\(644\) −7.69256 + 13.3239i −0.303129 + 0.525036i
\(645\) 0 0
\(646\) −18.7712 32.5127i −0.738544 1.27919i
\(647\) 17.4897i 0.687593i −0.939044 0.343796i \(-0.888287\pi\)
0.939044 0.343796i \(-0.111713\pi\)
\(648\) 0 0
\(649\) −19.9364 −0.782572
\(650\) 0 0
\(651\) 0 0
\(652\) 94.3072 + 54.4483i 3.69335 + 2.13236i
\(653\) 9.50650 + 5.48858i 0.372018 + 0.214785i 0.674340 0.738421i \(-0.264428\pi\)
−0.302322 + 0.953206i \(0.597762\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 25.8882 1.01077
\(657\) 0 0
\(658\) 29.7862i 1.16119i
\(659\) 7.89381 + 13.6725i 0.307499 + 0.532604i 0.977815 0.209472i \(-0.0671746\pi\)
−0.670316 + 0.742076i \(0.733841\pi\)
\(660\) 0 0
\(661\) −24.9466 + 43.2088i −0.970311 + 1.68063i −0.275697 + 0.961245i \(0.588909\pi\)
−0.694614 + 0.719383i \(0.744425\pi\)
\(662\) 28.7897 + 16.6217i 1.11894 + 0.646022i
\(663\) 0 0
\(664\) 4.24913 + 7.35972i 0.164898 + 0.285612i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.7750i 0.494649i
\(668\) 72.9698 42.1291i 2.82328 1.63002i
\(669\) 0 0
\(670\) 0 0
\(671\) −11.4549 + 19.8404i −0.442210 + 0.765929i
\(672\) 0 0
\(673\) −24.9757 + 14.4197i −0.962743 + 0.555840i −0.897016 0.441998i \(-0.854270\pi\)
−0.0657266 + 0.997838i \(0.520937\pi\)
\(674\) −18.2264 −0.702055
\(675\) 0 0
\(676\) −44.9809 −1.73003
\(677\) −9.06176 + 5.23181i −0.348272 + 0.201075i −0.663924 0.747800i \(-0.731110\pi\)
0.315652 + 0.948875i \(0.397777\pi\)
\(678\) 0 0
\(679\) 3.44455 5.96614i 0.132190 0.228959i
\(680\) 0 0
\(681\) 0 0
\(682\) −10.8176 + 6.24556i −0.414228 + 0.239155i
\(683\) 16.1875i 0.619396i −0.950835 0.309698i \(-0.899772\pi\)
0.950835 0.309698i \(-0.100228\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 25.4904 + 44.1507i 0.973229 + 1.68568i
\(687\) 0 0
\(688\) −66.1570 38.1958i −2.52221 1.45620i
\(689\) −1.70109 + 2.94638i −0.0648065 + 0.112248i
\(690\) 0 0
\(691\) −4.94181 8.55946i −0.187995 0.325617i 0.756586 0.653894i \(-0.226866\pi\)
−0.944582 + 0.328276i \(0.893532\pi\)
\(692\) 58.9648i 2.24150i
\(693\) 0 0
\(694\) −36.3621 −1.38029
\(695\) 0 0
\(696\) 0 0
\(697\) 10.2703 + 5.92957i 0.389016 + 0.224598i
\(698\) −14.9800 8.64872i −0.567002 0.327359i
\(699\) 0 0
\(700\) 0 0
\(701\) −43.9692 −1.66069 −0.830346 0.557248i \(-0.811857\pi\)
−0.830346 + 0.557248i \(0.811857\pi\)
\(702\) 0 0
\(703\) 34.4942i 1.30097i
\(704\) −10.0130 17.3430i −0.377379 0.653640i
\(705\) 0 0
\(706\) 4.64193 8.04005i 0.174701 0.302591i
\(707\) −10.1995 5.88870i −0.383593 0.221467i
\(708\) 0 0
\(709\) 12.6130 + 21.8464i 0.473692 + 0.820458i 0.999546 0.0301162i \(-0.00958774\pi\)
−0.525855 + 0.850574i \(0.676254\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 102.811i 3.85299i
\(713\) 3.93880 2.27407i 0.147509 0.0851645i
\(714\) 0 0
\(715\) 0 0
\(716\) 21.1016 36.5490i 0.788603 1.36590i
\(717\) 0 0
\(718\) −52.2971 + 30.1937i −1.95171 + 1.12682i
\(719\) −36.8600 −1.37465 −0.687323 0.726352i \(-0.741214\pi\)
−0.687323 + 0.726352i \(0.741214\pi\)
\(720\) 0 0
\(721\) 14.5153 0.540576
\(722\) 23.2893 13.4461i 0.866740 0.500412i
\(723\) 0 0
\(724\) −26.0459 + 45.1128i −0.967988 + 1.67660i
\(725\) 0 0
\(726\) 0 0
\(727\) −33.1213 + 19.1226i −1.22840 + 0.709217i −0.966695 0.255931i \(-0.917618\pi\)
−0.261705 + 0.965148i \(0.584285\pi\)
\(728\) 27.4107i 1.01591i
\(729\) 0 0
\(730\) 0 0
\(731\) −17.4971 30.3059i −0.647154 1.12090i
\(732\) 0 0
\(733\) 34.2801 + 19.7916i 1.26616 + 0.731020i 0.974260 0.225428i \(-0.0723781\pi\)
0.291903 + 0.956448i \(0.405711\pi\)
\(734\) −5.50358 + 9.53248i −0.203141 + 0.351850i
\(735\) 0 0
\(736\) 10.5559 + 18.2834i 0.389097 + 0.673936i
\(737\) 16.4607i 0.606338i
\(738\) 0 0
\(739\) 8.24773 0.303398 0.151699 0.988427i \(-0.451526\pi\)
0.151699 + 0.988427i \(0.451526\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 7.07361 + 4.08395i 0.259680 + 0.149927i
\(743\) −1.13292 0.654091i −0.0415627 0.0239963i 0.479075 0.877774i \(-0.340972\pi\)
−0.520637 + 0.853778i \(0.674306\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −18.0171 −0.659651
\(747\) 0 0
\(748\) 42.9164i 1.56918i
\(749\) −8.06752 13.9734i −0.294781 0.510575i
\(750\) 0 0
\(751\) −14.2234 + 24.6357i −0.519020 + 0.898969i 0.480736 + 0.876866i \(0.340370\pi\)
−0.999756 + 0.0221034i \(0.992964\pi\)
\(752\) 57.1939 + 33.0209i 2.08565 + 1.20415i
\(753\) 0 0
\(754\) −19.1310 33.1359i −0.696711 1.20674i
\(755\) 0 0
\(756\) 0 0
\(757\) 38.2012i 1.38845i −0.719760 0.694223i \(-0.755748\pi\)
0.719760 0.694223i \(-0.244252\pi\)
\(758\) −29.1414 + 16.8248i −1.05846 + 0.611103i
\(759\) 0 0
\(760\) 0 0
\(761\) 11.0952 19.2174i 0.402200 0.696632i −0.591791 0.806092i \(-0.701579\pi\)
0.993991 + 0.109460i \(0.0349121\pi\)
\(762\) 0 0
\(763\) −9.87152 + 5.69932i −0.357373 + 0.206329i
\(764\) −85.5852 −3.09637
\(765\) 0 0
\(766\) 19.8440 0.716994
\(767\) −18.8286 + 10.8707i −0.679861 + 0.392518i
\(768\) 0 0
\(769\) −8.45652 + 14.6471i −0.304950 + 0.528189i −0.977250 0.212090i \(-0.931973\pi\)
0.672300 + 0.740279i \(0.265306\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.66718 3.84930i 0.239957 0.138539i
\(773\) 38.6464i 1.39001i −0.719003 0.695007i \(-0.755401\pi\)
0.719003 0.695007i \(-0.244599\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.8211 25.6709i −0.532047 0.921533i
\(777\) 0 0
\(778\) 12.4347 + 7.17920i 0.445807 + 0.257387i
\(779\) 3.65615 6.33264i 0.130995 0.226890i
\(780\) 0 0
\(781\) −1.15232 1.99588i −0.0412333 0.0714181i
\(782\) 21.9572i 0.785187i
\(783\) 0 0
\(784\) 39.5622 1.41294
\(785\) 0 0
\(786\) 0 0
\(787\) −9.45240 5.45734i −0.336942 0.194533i 0.321977 0.946747i \(-0.395653\pi\)
−0.658919 + 0.752214i \(0.728986\pi\)
\(788\) −76.8530 44.3711i −2.73777 1.58065i