Properties

Label 360.2.q.c.241.2
Level $360$
Weight $2$
Character 360.241
Analytic conductor $2.875$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(121,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.q (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 360.241
Dual form 360.2.q.c.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.72474 + 0.158919i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.724745 - 1.25529i) q^{7} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\) \(q+(1.72474 + 0.158919i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.724745 - 1.25529i) q^{7} +(2.94949 + 0.548188i) q^{9} +(0.724745 + 1.57313i) q^{15} -2.00000 q^{17} +2.89898 q^{19} +(1.44949 - 2.04989i) q^{21} +(1.27526 + 2.20881i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(5.00000 + 1.41421i) q^{27} +(-3.94949 + 6.84072i) q^{29} +(-5.44949 - 9.43879i) q^{31} +1.44949 q^{35} -6.00000 q^{37} +(0.0505103 + 0.0874863i) q^{41} +(3.89898 - 6.75323i) q^{43} +(1.00000 + 2.82843i) q^{45} +(2.27526 - 3.94086i) q^{47} +(2.44949 + 4.24264i) q^{49} +(-3.44949 - 0.317837i) q^{51} -11.7980 q^{53} +(5.00000 + 0.460702i) q^{57} +(5.44949 + 9.43879i) q^{59} +(1.50000 - 2.59808i) q^{61} +(2.82577 - 3.30518i) q^{63} +(-5.62372 - 9.74058i) q^{67} +(1.84847 + 4.01229i) q^{69} -9.79796 q^{71} -5.79796 q^{73} +(-1.00000 + 1.41421i) q^{75} +(-1.44949 + 2.51059i) q^{79} +(8.39898 + 3.23375i) q^{81} +(0.275255 - 0.476756i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(-7.89898 + 11.1708i) q^{87} -16.7980 q^{89} +(-7.89898 - 17.1455i) q^{93} +(1.44949 + 2.51059i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{7} + 2 q^{9} - 2 q^{15} - 8 q^{17} - 8 q^{19} - 4 q^{21} + 10 q^{23} - 2 q^{25} + 20 q^{27} - 6 q^{29} - 12 q^{31} - 4 q^{35} - 24 q^{37} + 10 q^{41} - 4 q^{43} + 4 q^{45} + 14 q^{47} - 4 q^{51} - 8 q^{53} + 20 q^{57} + 12 q^{59} + 6 q^{61} + 26 q^{63} + 2 q^{67} - 22 q^{69} + 16 q^{73} - 4 q^{75} + 4 q^{79} + 14 q^{81} + 6 q^{83} - 4 q^{85} - 12 q^{87} - 28 q^{89} - 12 q^{93} - 4 q^{95} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.72474 + 0.158919i 0.995782 + 0.0917517i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0.724745 1.25529i 0.273928 0.474457i −0.695936 0.718104i \(-0.745010\pi\)
0.969864 + 0.243647i \(0.0783437\pi\)
\(8\) 0 0
\(9\) 2.94949 + 0.548188i 0.983163 + 0.182729i
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0 0
\(15\) 0.724745 + 1.57313i 0.187128 + 0.406181i
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 2.89898 0.665072 0.332536 0.943091i \(-0.392096\pi\)
0.332536 + 0.943091i \(0.392096\pi\)
\(20\) 0 0
\(21\) 1.44949 2.04989i 0.316305 0.447322i
\(22\) 0 0
\(23\) 1.27526 + 2.20881i 0.265909 + 0.460568i 0.967801 0.251715i \(-0.0809946\pi\)
−0.701892 + 0.712283i \(0.747661\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) −3.94949 + 6.84072i −0.733402 + 1.27029i 0.222019 + 0.975042i \(0.428735\pi\)
−0.955421 + 0.295247i \(0.904598\pi\)
\(30\) 0 0
\(31\) −5.44949 9.43879i −0.978757 1.69526i −0.666933 0.745117i \(-0.732393\pi\)
−0.311824 0.950140i \(-0.600940\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.44949 0.245008
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.0505103 + 0.0874863i 0.00788838 + 0.0136631i 0.869943 0.493153i \(-0.164156\pi\)
−0.862054 + 0.506816i \(0.830822\pi\)
\(42\) 0 0
\(43\) 3.89898 6.75323i 0.594589 1.02986i −0.399016 0.916944i \(-0.630648\pi\)
0.993605 0.112914i \(-0.0360185\pi\)
\(44\) 0 0
\(45\) 1.00000 + 2.82843i 0.149071 + 0.421637i
\(46\) 0 0
\(47\) 2.27526 3.94086i 0.331880 0.574833i −0.651000 0.759077i \(-0.725650\pi\)
0.982880 + 0.184244i \(0.0589837\pi\)
\(48\) 0 0
\(49\) 2.44949 + 4.24264i 0.349927 + 0.606092i
\(50\) 0 0
\(51\) −3.44949 0.317837i −0.483025 0.0445061i
\(52\) 0 0
\(53\) −11.7980 −1.62057 −0.810287 0.586033i \(-0.800689\pi\)
−0.810287 + 0.586033i \(0.800689\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.00000 + 0.460702i 0.662266 + 0.0610214i
\(58\) 0 0
\(59\) 5.44949 + 9.43879i 0.709463 + 1.22883i 0.965057 + 0.262042i \(0.0843958\pi\)
−0.255593 + 0.966784i \(0.582271\pi\)
\(60\) 0 0
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) 0 0
\(63\) 2.82577 3.30518i 0.356013 0.416414i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −5.62372 9.74058i −0.687047 1.19000i −0.972789 0.231694i \(-0.925573\pi\)
0.285741 0.958307i \(-0.407760\pi\)
\(68\) 0 0
\(69\) 1.84847 + 4.01229i 0.222530 + 0.483023i
\(70\) 0 0
\(71\) −9.79796 −1.16280 −0.581402 0.813617i \(-0.697496\pi\)
−0.581402 + 0.813617i \(0.697496\pi\)
\(72\) 0 0
\(73\) −5.79796 −0.678600 −0.339300 0.940678i \(-0.610190\pi\)
−0.339300 + 0.940678i \(0.610190\pi\)
\(74\) 0 0
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.44949 + 2.51059i −0.163080 + 0.282463i −0.935972 0.352075i \(-0.885476\pi\)
0.772892 + 0.634538i \(0.218810\pi\)
\(80\) 0 0
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 0 0
\(83\) 0.275255 0.476756i 0.0302132 0.0523308i −0.850523 0.525937i \(-0.823715\pi\)
0.880737 + 0.473606i \(0.157048\pi\)
\(84\) 0 0
\(85\) −1.00000 1.73205i −0.108465 0.187867i
\(86\) 0 0
\(87\) −7.89898 + 11.1708i −0.846859 + 1.19764i
\(88\) 0 0
\(89\) −16.7980 −1.78058 −0.890290 0.455394i \(-0.849498\pi\)
−0.890290 + 0.455394i \(0.849498\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.89898 17.1455i −0.819086 1.77791i
\(94\) 0 0
\(95\) 1.44949 + 2.51059i 0.148715 + 0.257581i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) −5.00000 8.66025i −0.492665 0.853320i 0.507300 0.861770i \(-0.330644\pi\)
−0.999964 + 0.00844953i \(0.997310\pi\)
\(104\) 0 0
\(105\) 2.50000 + 0.230351i 0.243975 + 0.0224799i
\(106\) 0 0
\(107\) 2.34847 0.227035 0.113518 0.993536i \(-0.463788\pi\)
0.113518 + 0.993536i \(0.463788\pi\)
\(108\) 0 0
\(109\) 8.79796 0.842692 0.421346 0.906900i \(-0.361558\pi\)
0.421346 + 0.906900i \(0.361558\pi\)
\(110\) 0 0
\(111\) −10.3485 0.953512i −0.982233 0.0905033i
\(112\) 0 0
\(113\) −4.89898 8.48528i −0.460857 0.798228i 0.538147 0.842851i \(-0.319125\pi\)
−0.999004 + 0.0446231i \(0.985791\pi\)
\(114\) 0 0
\(115\) −1.27526 + 2.20881i −0.118918 + 0.205972i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.44949 + 2.51059i −0.132875 + 0.230145i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 0 0
\(123\) 0.0732141 + 0.158919i 0.00660149 + 0.0143292i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −14.3485 −1.27322 −0.636610 0.771186i \(-0.719664\pi\)
−0.636610 + 0.771186i \(0.719664\pi\)
\(128\) 0 0
\(129\) 7.79796 11.0280i 0.686572 0.970959i
\(130\) 0 0
\(131\) 3.44949 + 5.97469i 0.301383 + 0.522011i 0.976450 0.215746i \(-0.0692183\pi\)
−0.675066 + 0.737757i \(0.735885\pi\)
\(132\) 0 0
\(133\) 2.10102 3.63907i 0.182182 0.315548i
\(134\) 0 0
\(135\) 1.27526 + 5.03723i 0.109756 + 0.433536i
\(136\) 0 0
\(137\) 9.79796 16.9706i 0.837096 1.44989i −0.0552162 0.998474i \(-0.517585\pi\)
0.892312 0.451419i \(-0.149082\pi\)
\(138\) 0 0
\(139\) 9.79796 + 16.9706i 0.831052 + 1.43942i 0.897205 + 0.441615i \(0.145594\pi\)
−0.0661527 + 0.997810i \(0.521072\pi\)
\(140\) 0 0
\(141\) 4.55051 6.43539i 0.383222 0.541958i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −7.89898 −0.655975
\(146\) 0 0
\(147\) 3.55051 + 7.70674i 0.292841 + 0.635641i
\(148\) 0 0
\(149\) 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i \(0.162991\pi\)
−0.0115483 + 0.999933i \(0.503676\pi\)
\(150\) 0 0
\(151\) −6.00000 + 10.3923i −0.488273 + 0.845714i −0.999909 0.0134886i \(-0.995706\pi\)
0.511636 + 0.859202i \(0.329040\pi\)
\(152\) 0 0
\(153\) −5.89898 1.09638i −0.476904 0.0886368i
\(154\) 0 0
\(155\) 5.44949 9.43879i 0.437714 0.758142i
\(156\) 0 0
\(157\) 2.10102 + 3.63907i 0.167680 + 0.290430i 0.937604 0.347706i \(-0.113039\pi\)
−0.769924 + 0.638136i \(0.779706\pi\)
\(158\) 0 0
\(159\) −20.3485 1.87492i −1.61374 0.148690i
\(160\) 0 0
\(161\) 3.69694 0.291360
\(162\) 0 0
\(163\) 11.7980 0.924087 0.462044 0.886857i \(-0.347116\pi\)
0.462044 + 0.886857i \(0.347116\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.17423 + 5.49794i 0.245630 + 0.425443i 0.962308 0.271960i \(-0.0876720\pi\)
−0.716679 + 0.697403i \(0.754339\pi\)
\(168\) 0 0
\(169\) 6.50000 11.2583i 0.500000 0.866025i
\(170\) 0 0
\(171\) 8.55051 + 1.58919i 0.653874 + 0.121528i
\(172\) 0 0
\(173\) 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i \(-0.682554\pi\)
0.998755 + 0.0498898i \(0.0158870\pi\)
\(174\) 0 0
\(175\) 0.724745 + 1.25529i 0.0547856 + 0.0948914i
\(176\) 0 0
\(177\) 7.89898 + 17.1455i 0.593724 + 1.28874i
\(178\) 0 0
\(179\) 5.79796 0.433360 0.216680 0.976243i \(-0.430477\pi\)
0.216680 + 0.976243i \(0.430477\pi\)
\(180\) 0 0
\(181\) 19.6969 1.46406 0.732031 0.681271i \(-0.238573\pi\)
0.732031 + 0.681271i \(0.238573\pi\)
\(182\) 0 0
\(183\) 3.00000 4.24264i 0.221766 0.313625i
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.39898 5.25153i 0.392718 0.381993i
\(190\) 0 0
\(191\) 2.55051 4.41761i 0.184548 0.319647i −0.758876 0.651235i \(-0.774251\pi\)
0.943424 + 0.331588i \(0.107584\pi\)
\(192\) 0 0
\(193\) 10.8990 + 18.8776i 0.784526 + 1.35884i 0.929282 + 0.369371i \(0.120427\pi\)
−0.144756 + 0.989467i \(0.546240\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.5959 1.68114 0.840570 0.541703i \(-0.182220\pi\)
0.840570 + 0.541703i \(0.182220\pi\)
\(198\) 0 0
\(199\) 13.1010 0.928707 0.464353 0.885650i \(-0.346287\pi\)
0.464353 + 0.885650i \(0.346287\pi\)
\(200\) 0 0
\(201\) −8.15153 17.6937i −0.574965 1.24802i
\(202\) 0 0
\(203\) 5.72474 + 9.91555i 0.401798 + 0.695935i
\(204\) 0 0
\(205\) −0.0505103 + 0.0874863i −0.00352779 + 0.00611031i
\(206\) 0 0
\(207\) 2.55051 + 7.21393i 0.177273 + 0.501403i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −6.00000 10.3923i −0.413057 0.715436i 0.582165 0.813070i \(-0.302206\pi\)
−0.995222 + 0.0976347i \(0.968872\pi\)
\(212\) 0 0
\(213\) −16.8990 1.55708i −1.15790 0.106689i
\(214\) 0 0
\(215\) 7.79796 0.531816
\(216\) 0 0
\(217\) −15.7980 −1.07244
\(218\) 0 0
\(219\) −10.0000 0.921404i −0.675737 0.0622627i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.275255 + 0.476756i −0.0184324 + 0.0319259i −0.875094 0.483952i \(-0.839201\pi\)
0.856662 + 0.515878i \(0.172534\pi\)
\(224\) 0 0
\(225\) −1.94949 + 2.28024i −0.129966 + 0.152016i
\(226\) 0 0
\(227\) 13.8990 24.0737i 0.922508 1.59783i 0.126986 0.991904i \(-0.459470\pi\)
0.795521 0.605926i \(-0.207197\pi\)
\(228\) 0 0
\(229\) 6.94949 + 12.0369i 0.459235 + 0.795419i 0.998921 0.0464480i \(-0.0147902\pi\)
−0.539686 + 0.841867i \(0.681457\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.202041 −0.0132361 −0.00661807 0.999978i \(-0.502107\pi\)
−0.00661807 + 0.999978i \(0.502107\pi\)
\(234\) 0 0
\(235\) 4.55051 0.296843
\(236\) 0 0
\(237\) −2.89898 + 4.09978i −0.188309 + 0.266309i
\(238\) 0 0
\(239\) −10.8990 18.8776i −0.704996 1.22109i −0.966693 0.255939i \(-0.917615\pi\)
0.261696 0.965150i \(-0.415718\pi\)
\(240\) 0 0
\(241\) −12.8485 + 22.2542i −0.827643 + 1.43352i 0.0722401 + 0.997387i \(0.476985\pi\)
−0.899883 + 0.436132i \(0.856348\pi\)
\(242\) 0 0
\(243\) 13.9722 + 6.91215i 0.896317 + 0.443415i
\(244\) 0 0
\(245\) −2.44949 + 4.24264i −0.156492 + 0.271052i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.550510 0.778539i 0.0348872 0.0493379i
\(250\) 0 0
\(251\) −6.89898 −0.435460 −0.217730 0.976009i \(-0.569865\pi\)
−0.217730 + 0.976009i \(0.569865\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −1.44949 3.14626i −0.0907706 0.197027i
\(256\) 0 0
\(257\) −4.10102 7.10318i −0.255815 0.443084i 0.709302 0.704905i \(-0.249010\pi\)
−0.965116 + 0.261821i \(0.915677\pi\)
\(258\) 0 0
\(259\) −4.34847 + 7.53177i −0.270201 + 0.468001i
\(260\) 0 0
\(261\) −15.3990 + 18.0116i −0.953173 + 1.11489i
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) −5.89898 10.2173i −0.362371 0.627646i
\(266\) 0 0
\(267\) −28.9722 2.66951i −1.77307 0.163371i
\(268\) 0 0
\(269\) −16.5959 −1.01187 −0.505935 0.862571i \(-0.668853\pi\)
−0.505935 + 0.862571i \(0.668853\pi\)
\(270\) 0 0
\(271\) 21.1010 1.28180 0.640898 0.767626i \(-0.278562\pi\)
0.640898 + 0.767626i \(0.278562\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.00000 12.1244i 0.420589 0.728482i −0.575408 0.817867i \(-0.695157\pi\)
0.995997 + 0.0893846i \(0.0284900\pi\)
\(278\) 0 0
\(279\) −10.8990 30.8270i −0.652505 1.84556i
\(280\) 0 0
\(281\) 8.94949 15.5010i 0.533882 0.924710i −0.465335 0.885135i \(-0.654066\pi\)
0.999217 0.0395756i \(-0.0126006\pi\)
\(282\) 0 0
\(283\) 9.17423 + 15.8902i 0.545352 + 0.944577i 0.998585 + 0.0531847i \(0.0169372\pi\)
−0.453233 + 0.891392i \(0.649729\pi\)
\(284\) 0 0
\(285\) 2.10102 + 4.56048i 0.124454 + 0.270139i
\(286\) 0 0
\(287\) 0.146428 0.00864338
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −2.00000 + 2.82843i −0.117242 + 0.165805i
\(292\) 0 0
\(293\) 10.7980 + 18.7026i 0.630823 + 1.09262i 0.987384 + 0.158346i \(0.0506161\pi\)
−0.356560 + 0.934272i \(0.616051\pi\)
\(294\) 0 0
\(295\) −5.44949 + 9.43879i −0.317282 + 0.549548i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −5.65153 9.78874i −0.325749 0.564214i
\(302\) 0 0
\(303\) 2.00000 2.82843i 0.114897 0.162489i
\(304\) 0 0
\(305\) 3.00000 0.171780
\(306\) 0 0
\(307\) −29.2474 −1.66924 −0.834620 0.550826i \(-0.814313\pi\)
−0.834620 + 0.550826i \(0.814313\pi\)
\(308\) 0 0
\(309\) −7.24745 15.7313i −0.412293 0.894924i
\(310\) 0 0
\(311\) −1.44949 2.51059i −0.0821930 0.142362i 0.821999 0.569489i \(-0.192859\pi\)
−0.904192 + 0.427127i \(0.859526\pi\)
\(312\) 0 0
\(313\) −11.7980 + 20.4347i −0.666860 + 1.15504i 0.311917 + 0.950109i \(0.399029\pi\)
−0.978777 + 0.204926i \(0.934305\pi\)
\(314\) 0 0
\(315\) 4.27526 + 0.794593i 0.240883 + 0.0447703i
\(316\) 0 0
\(317\) 3.10102 5.37113i 0.174171 0.301672i −0.765703 0.643194i \(-0.777609\pi\)
0.939874 + 0.341522i \(0.110942\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 4.05051 + 0.373215i 0.226077 + 0.0208309i
\(322\) 0 0
\(323\) −5.79796 −0.322607
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 15.1742 + 1.39816i 0.839137 + 0.0773184i
\(328\) 0 0
\(329\) −3.29796 5.71223i −0.181822 0.314926i
\(330\) 0 0
\(331\) −1.44949 + 2.51059i −0.0796712 + 0.137994i −0.903108 0.429413i \(-0.858720\pi\)
0.823437 + 0.567408i \(0.192054\pi\)
\(332\) 0 0
\(333\) −17.6969 3.28913i −0.969786 0.180243i
\(334\) 0 0
\(335\) 5.62372 9.74058i 0.307257 0.532185i
\(336\) 0 0
\(337\) 5.10102 + 8.83523i 0.277870 + 0.481285i 0.970855 0.239667i \(-0.0770381\pi\)
−0.692985 + 0.720952i \(0.743705\pi\)
\(338\) 0 0
\(339\) −7.10102 15.4135i −0.385674 0.837146i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 17.2474 0.931275
\(344\) 0 0
\(345\) −2.55051 + 3.60697i −0.137315 + 0.194193i
\(346\) 0 0
\(347\) −6.79796 11.7744i −0.364934 0.632083i 0.623832 0.781559i \(-0.285575\pi\)
−0.988765 + 0.149475i \(0.952242\pi\)
\(348\) 0 0
\(349\) 15.8485 27.4504i 0.848349 1.46938i −0.0343315 0.999410i \(-0.510930\pi\)
0.882681 0.469973i \(-0.155736\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) 0 0
\(355\) −4.89898 8.48528i −0.260011 0.450352i
\(356\) 0 0
\(357\) −2.89898 + 4.09978i −0.153430 + 0.216983i
\(358\) 0 0
\(359\) −0.696938 −0.0367830 −0.0183915 0.999831i \(-0.505855\pi\)
−0.0183915 + 0.999831i \(0.505855\pi\)
\(360\) 0 0
\(361\) −10.5959 −0.557680
\(362\) 0 0
\(363\) 7.97219 + 17.3045i 0.418432 + 0.908248i
\(364\) 0 0
\(365\) −2.89898 5.02118i −0.151740 0.262821i
\(366\) 0 0
\(367\) −11.0000 + 19.0526i −0.574195 + 0.994535i 0.421933 + 0.906627i \(0.361352\pi\)
−0.996129 + 0.0879086i \(0.971982\pi\)
\(368\) 0 0
\(369\) 0.101021 + 0.285729i 0.00525892 + 0.0148745i
\(370\) 0 0
\(371\) −8.55051 + 14.8099i −0.443920 + 0.768893i
\(372\) 0 0
\(373\) 8.79796 + 15.2385i 0.455541 + 0.789020i 0.998719 0.0505973i \(-0.0161125\pi\)
−0.543178 + 0.839618i \(0.682779\pi\)
\(374\) 0 0
\(375\) −1.72474 0.158919i −0.0890654 0.00820652i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 17.1010 0.878420 0.439210 0.898384i \(-0.355258\pi\)
0.439210 + 0.898384i \(0.355258\pi\)
\(380\) 0 0
\(381\) −24.7474 2.28024i −1.26785 0.116820i
\(382\) 0 0
\(383\) −1.00000 1.73205i −0.0510976 0.0885037i 0.839345 0.543599i \(-0.182939\pi\)
−0.890443 + 0.455095i \(0.849605\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 15.2020 17.7812i 0.772763 0.903870i
\(388\) 0 0
\(389\) −11.2980 + 19.5686i −0.572829 + 0.992169i 0.423444 + 0.905922i \(0.360821\pi\)
−0.996274 + 0.0862473i \(0.972512\pi\)
\(390\) 0 0
\(391\) −2.55051 4.41761i −0.128985 0.223408i
\(392\) 0 0
\(393\) 5.00000 + 10.8530i 0.252217 + 0.547462i
\(394\) 0 0
\(395\) −2.89898 −0.145863
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 4.20204 5.94258i 0.210365 0.297501i
\(400\) 0 0
\(401\) 6.79796 + 11.7744i 0.339474 + 0.587986i 0.984334 0.176315i \(-0.0564177\pi\)
−0.644860 + 0.764301i \(0.723084\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.39898 + 8.89060i 0.0695158 + 0.441778i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −14.7980 25.6308i −0.731712 1.26736i −0.956151 0.292874i \(-0.905388\pi\)
0.224439 0.974488i \(-0.427945\pi\)
\(410\) 0 0
\(411\) 19.5959 27.7128i 0.966595 1.36697i
\(412\) 0 0
\(413\) 15.7980 0.777367
\(414\) 0 0
\(415\) 0.550510 0.0270235
\(416\) 0 0
\(417\) 14.2020 + 30.8270i 0.695477 + 1.50960i
\(418\) 0 0
\(419\) −10.0000 17.3205i −0.488532 0.846162i 0.511381 0.859354i \(-0.329134\pi\)
−0.999913 + 0.0131919i \(0.995801\pi\)
\(420\) 0 0
\(421\) 6.79796 11.7744i 0.331312 0.573850i −0.651457 0.758685i \(-0.725842\pi\)
0.982769 + 0.184836i \(0.0591753\pi\)
\(422\) 0 0
\(423\) 8.87117 10.3763i 0.431331 0.504511i
\(424\) 0 0
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) −2.17423 3.76588i −0.105219 0.182244i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.10102 0.245708 0.122854 0.992425i \(-0.460795\pi\)
0.122854 + 0.992425i \(0.460795\pi\)
\(432\) 0 0
\(433\) 7.79796 0.374746 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(434\) 0 0
\(435\) −13.6237 1.25529i −0.653208 0.0601868i
\(436\) 0 0
\(437\) 3.69694 + 6.40329i 0.176849 + 0.306311i
\(438\) 0 0
\(439\) −0.898979 + 1.55708i −0.0429059 + 0.0743153i −0.886681 0.462382i \(-0.846995\pi\)
0.843775 + 0.536697i \(0.180328\pi\)
\(440\) 0 0
\(441\) 4.89898 + 13.8564i 0.233285 + 0.659829i
\(442\) 0 0
\(443\) −13.0732 + 22.6435i −0.621127 + 1.07582i 0.368149 + 0.929767i \(0.379992\pi\)
−0.989276 + 0.146057i \(0.953342\pi\)
\(444\) 0 0
\(445\) −8.39898 14.5475i −0.398150 0.689616i
\(446\) 0 0
\(447\) 15.2196 + 33.0358i 0.719864 + 1.56254i
\(448\) 0 0
\(449\) −17.5959 −0.830403 −0.415201 0.909730i \(-0.636289\pi\)
−0.415201 + 0.909730i \(0.636289\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −12.0000 + 16.9706i −0.563809 + 0.797347i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.7980 18.7026i 0.505107 0.874871i −0.494875 0.868964i \(-0.664786\pi\)
0.999983 0.00590738i \(-0.00188039\pi\)
\(458\) 0 0
\(459\) −10.0000 2.82843i −0.466760 0.132020i
\(460\) 0 0
\(461\) −10.9495 + 18.9651i −0.509969 + 0.883291i 0.489965 + 0.871742i \(0.337010\pi\)
−0.999933 + 0.0115492i \(0.996324\pi\)
\(462\) 0 0
\(463\) −15.8990 27.5378i −0.738888 1.27979i −0.952996 0.302982i \(-0.902018\pi\)
0.214108 0.976810i \(-0.431316\pi\)
\(464\) 0 0
\(465\) 10.8990 15.4135i 0.505428 0.714783i
\(466\) 0 0
\(467\) −11.7980 −0.545944 −0.272972 0.962022i \(-0.588007\pi\)
−0.272972 + 0.962022i \(0.588007\pi\)
\(468\) 0 0
\(469\) −16.3031 −0.752805
\(470\) 0 0
\(471\) 3.04541 + 6.61037i 0.140325 + 0.304590i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.44949 + 2.51059i −0.0665072 + 0.115194i
\(476\) 0 0
\(477\) −34.7980 6.46750i −1.59329 0.296127i
\(478\) 0 0
\(479\) 9.24745 16.0171i 0.422527 0.731838i −0.573659 0.819094i \(-0.694477\pi\)
0.996186 + 0.0872564i \(0.0278099\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 6.37628 + 0.587512i 0.290131 + 0.0267327i
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) 25.5959 1.15986 0.579931 0.814666i \(-0.303080\pi\)
0.579931 + 0.814666i \(0.303080\pi\)
\(488\) 0 0
\(489\) 20.3485 + 1.87492i 0.920190 + 0.0847866i
\(490\) 0 0
\(491\) −2.89898 5.02118i −0.130829 0.226603i 0.793167 0.609004i \(-0.208431\pi\)
−0.923996 + 0.382401i \(0.875097\pi\)
\(492\) 0 0
\(493\) 7.89898 13.6814i 0.355752 0.616181i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.10102 + 12.2993i −0.318524 + 0.551700i
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 0 0
\(501\) 4.60102 + 9.98698i 0.205558 + 0.446185i
\(502\) 0 0
\(503\) −19.0454 −0.849193 −0.424596 0.905383i \(-0.639584\pi\)
−0.424596 + 0.905383i \(0.639584\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 13.0000 18.3848i 0.577350 0.816497i
\(508\) 0 0
\(509\) 6.94949 + 12.0369i 0.308031 + 0.533525i 0.977931 0.208926i \(-0.0669967\pi\)
−0.669901 + 0.742451i \(0.733663\pi\)
\(510\) 0 0
\(511\) −4.20204 + 7.27815i −0.185887 + 0.321966i
\(512\) 0 0
\(513\) 14.4949 + 4.09978i 0.639965 + 0.181010i
\(514\) 0 0
\(515\) 5.00000 8.66025i 0.220326 0.381616i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 12.0000 16.9706i 0.526742 0.744925i
\(520\) 0 0
\(521\) 28.7980 1.26166 0.630831 0.775920i \(-0.282714\pi\)
0.630831 + 0.775920i \(0.282714\pi\)
\(522\) 0 0
\(523\) −19.6515 −0.859301 −0.429651 0.902995i \(-0.641363\pi\)
−0.429651 + 0.902995i \(0.641363\pi\)
\(524\) 0 0
\(525\) 1.05051 + 2.28024i 0.0458480 + 0.0995178i
\(526\) 0 0
\(527\) 10.8990 + 18.8776i 0.474767 + 0.822321i
\(528\) 0 0
\(529\) 8.24745 14.2850i 0.358585 0.621087i
\(530\) 0 0
\(531\) 10.8990 + 30.8270i 0.472975 + 1.33778i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 1.17423 + 2.03383i 0.0507666 + 0.0879303i
\(536\) 0 0
\(537\) 10.0000 + 0.921404i 0.431532 + 0.0397615i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 21.8990 0.941511 0.470755 0.882264i \(-0.343981\pi\)
0.470755 + 0.882264i \(0.343981\pi\)
\(542\) 0 0
\(543\) 33.9722 + 3.13021i 1.45789 + 0.134330i
\(544\) 0 0
\(545\) 4.39898 + 7.61926i 0.188432 + 0.326373i
\(546\) 0 0
\(547\) 20.6237 35.7213i 0.881807 1.52733i 0.0324764 0.999473i \(-0.489661\pi\)
0.849330 0.527862i \(-0.177006\pi\)
\(548\) 0 0
\(549\) 5.84847 6.84072i 0.249607 0.291955i
\(550\) 0 0
\(551\) −11.4495 + 19.8311i −0.487765 + 0.844833i
\(552\) 0 0
\(553\) 2.10102 + 3.63907i 0.0893445 + 0.154749i
\(554\) 0 0
\(555\) −4.34847 9.43879i −0.184582 0.400654i
\(556\) 0 0
\(557\) 24.2020 1.02547 0.512737 0.858546i \(-0.328632\pi\)
0.512737 + 0.858546i \(0.328632\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.17423 3.76588i −0.0916331 0.158713i 0.816565 0.577253i \(-0.195875\pi\)
−0.908198 + 0.418540i \(0.862542\pi\)
\(564\) 0 0
\(565\) 4.89898 8.48528i 0.206102 0.356978i
\(566\) 0 0
\(567\) 10.1464 8.19955i 0.426110 0.344349i
\(568\) 0 0
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 0 0
\(571\) −3.10102 5.37113i −0.129774 0.224775i 0.793815 0.608159i \(-0.208092\pi\)
−0.923589 + 0.383385i \(0.874758\pi\)
\(572\) 0 0
\(573\) 5.10102 7.21393i 0.213098 0.301366i
\(574\) 0 0
\(575\) −2.55051 −0.106364
\(576\) 0 0
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 0 0
\(579\) 15.7980 + 34.2911i 0.656541 + 1.42509i
\(580\) 0 0
\(581\) −0.398979 0.691053i −0.0165525 0.0286697i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.1742 + 19.3543i −0.461210 + 0.798839i −0.999022 0.0442259i \(-0.985918\pi\)
0.537812 + 0.843065i \(0.319251\pi\)
\(588\) 0 0
\(589\) −15.7980 27.3629i −0.650944 1.12747i
\(590\) 0 0
\(591\) 40.6969 + 3.74983i 1.67405 + 0.154247i
\(592\) 0 0
\(593\) 27.3939 1.12493 0.562466 0.826821i \(-0.309853\pi\)
0.562466 + 0.826821i \(0.309853\pi\)
\(594\) 0 0
\(595\) −2.89898 −0.118847
\(596\) 0 0
\(597\) 22.5959 + 2.08200i 0.924789 + 0.0852104i
\(598\) 0 0
\(599\) −2.34847 4.06767i −0.0959559 0.166200i 0.814051 0.580793i \(-0.197257\pi\)
−0.910007 + 0.414593i \(0.863924\pi\)
\(600\) 0 0
\(601\) −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i \(-0.925505\pi\)
0.687203 + 0.726465i \(0.258838\pi\)
\(602\) 0 0
\(603\) −11.2474 31.8126i −0.458032 1.29551i
\(604\) 0 0
\(605\) −5.50000 + 9.52628i −0.223607 + 0.387298i
\(606\) 0 0
\(607\) 16.0732 + 27.8396i 0.652392 + 1.12998i 0.982541 + 0.186047i \(0.0595676\pi\)
−0.330149 + 0.943929i \(0.607099\pi\)
\(608\) 0 0
\(609\) 8.29796 + 18.0116i 0.336250 + 0.729865i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.59592 0.387575 0.193788 0.981043i \(-0.437923\pi\)
0.193788 + 0.981043i \(0.437923\pi\)
\(614\) 0 0
\(615\) −0.101021 + 0.142865i −0.00407354 + 0.00576086i
\(616\) 0 0
\(617\) −21.5959 37.4052i −0.869419 1.50588i −0.862592 0.505901i \(-0.831160\pi\)
−0.00682740 0.999977i \(-0.502173\pi\)
\(618\) 0 0
\(619\) −2.34847 + 4.06767i −0.0943929 + 0.163493i −0.909355 0.416021i \(-0.863424\pi\)
0.814962 + 0.579514i \(0.196758\pi\)
\(620\) 0 0
\(621\) 3.25255 + 12.8475i 0.130520 + 0.515553i
\(622\) 0 0
\(623\) −12.1742 + 21.0864i −0.487750 + 0.844808i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 23.5959 0.939339 0.469669 0.882842i \(-0.344373\pi\)
0.469669 + 0.882842i \(0.344373\pi\)
\(632\) 0 0
\(633\) −8.69694 18.8776i −0.345672 0.750317i
\(634\) 0 0
\(635\) −7.17423 12.4261i −0.284701 0.493116i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −28.8990 5.37113i −1.14323 0.212478i
\(640\) 0 0
\(641\) 2.05051 3.55159i 0.0809903 0.140279i −0.822685 0.568497i \(-0.807525\pi\)
0.903676 + 0.428218i \(0.140858\pi\)
\(642\) 0 0
\(643\) −7.07321 12.2512i −0.278940 0.483139i 0.692181 0.721724i \(-0.256650\pi\)
−0.971122 + 0.238585i \(0.923317\pi\)
\(644\) 0 0
\(645\) 13.4495 + 1.23924i 0.529573 + 0.0487951i
\(646\) 0 0
\(647\) 11.4495 0.450126 0.225063 0.974344i \(-0.427741\pi\)
0.225063 + 0.974344i \(0.427741\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −27.2474 2.51059i −1.06791 0.0983978i
\(652\) 0 0
\(653\) −4.10102 7.10318i −0.160485 0.277969i 0.774558 0.632503i \(-0.217973\pi\)
−0.935043 + 0.354535i \(0.884639\pi\)
\(654\) 0 0
\(655\) −3.44949 + 5.97469i −0.134783 + 0.233451i
\(656\) 0 0
\(657\) −17.1010 3.17837i −0.667174 0.124000i
\(658\) 0 0
\(659\) −14.8990 + 25.8058i −0.580382 + 1.00525i 0.415052 + 0.909798i \(0.363763\pi\)
−0.995434 + 0.0954532i \(0.969570\pi\)
\(660\) 0 0
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.20204 0.162948
\(666\) 0 0
\(667\) −20.1464 −0.780073
\(668\) 0 0
\(669\) −0.550510 + 0.778539i −0.0212840 + 0.0301001i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 8.00000 13.8564i 0.308377 0.534125i −0.669630 0.742695i \(-0.733547\pi\)
0.978008 + 0.208569i \(0.0668807\pi\)
\(674\) 0 0
\(675\) −3.72474 + 3.62302i −0.143365 + 0.139450i
\(676\) 0 0
\(677\) −16.8990 + 29.2699i −0.649481 + 1.12493i 0.333767 + 0.942656i \(0.391680\pi\)
−0.983247 + 0.182278i \(0.941653\pi\)
\(678\) 0 0
\(679\) 1.44949 + 2.51059i 0.0556263 + 0.0963476i
\(680\) 0 0
\(681\) 27.7980 39.3123i 1.06522 1.50645i
\(682\) 0 0
\(683\) −35.3939 −1.35431 −0.677155 0.735841i \(-0.736787\pi\)
−0.677155 + 0.735841i \(0.736787\pi\)
\(684\) 0 0
\(685\) 19.5959 0.748722
\(686\) 0 0
\(687\) 10.0732 + 21.8649i 0.384317 + 0.834199i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −14.5505 + 25.2022i −0.553527 + 0.958738i 0.444489 + 0.895784i \(0.353385\pi\)
−0.998016 + 0.0629534i \(0.979948\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.79796 + 16.9706i −0.371658 + 0.643730i
\(696\) 0 0
\(697\) −0.101021 0.174973i −0.00382642 0.00662756i
\(698\) 0 0
\(699\) −0.348469 0.0321081i −0.0131803 0.00121444i
\(700\) 0 0
\(701\) −28.3939 −1.07242 −0.536211 0.844084i \(-0.680145\pi\)
−0.536211 + 0.844084i \(0.680145\pi\)
\(702\) 0 0
\(703\) −17.3939 −0.656022
\(704\) 0 0
\(705\) 7.84847 + 0.723161i 0.295590 + 0.0272358i
\(706\) 0 0
\(707\) −1.44949 2.51059i −0.0545137 0.0944205i
\(708\) 0 0
\(709\) 9.84847 17.0580i 0.369867 0.640628i −0.619677 0.784857i \(-0.712737\pi\)
0.989544 + 0.144228i \(0.0460699\pi\)
\(710\) 0 0
\(711\) −5.65153 + 6.61037i −0.211949 + 0.247908i
\(712\) 0 0
\(713\) 13.8990 24.0737i 0.520521 0.901569i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −15.7980 34.2911i −0.589986 1.28062i
\(718\) 0 0
\(719\) 40.2929 1.50267 0.751335 0.659921i \(-0.229410\pi\)
0.751335 + 0.659921i \(0.229410\pi\)
\(720\) 0 0
\(721\) −14.4949 −0.539818
\(722\) 0 0
\(723\) −25.6969 + 36.3410i −0.955679 + 1.35153i
\(724\) 0 0
\(725\) −3.94949 6.84072i −0.146680 0.254058i
\(726\) 0 0
\(727\) 3.37628 5.84788i 0.125219 0.216886i −0.796599 0.604508i \(-0.793370\pi\)
0.921819 + 0.387622i \(0.126703\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) −7.79796 + 13.5065i −0.288418 + 0.499555i
\(732\) 0 0
\(733\) −4.79796 8.31031i −0.177217 0.306948i 0.763710 0.645560i \(-0.223376\pi\)
−0.940926 + 0.338612i \(0.890043\pi\)
\(734\) 0 0
\(735\) −4.89898 + 6.92820i −0.180702 + 0.255551i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −42.8990 −1.57806 −0.789032 0.614352i \(-0.789418\pi\)
−0.789032 + 0.614352i \(0.789418\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.5227 32.0823i −0.679532 1.17698i −0.975122 0.221669i \(-0.928849\pi\)
0.295590 0.955315i \(-0.404484\pi\)
\(744\) 0 0
\(745\) −10.5000 + 18.1865i −0.384690 + 0.666303i
\(746\) 0 0
\(747\) 1.07321 1.25529i 0.0392669 0.0459288i
\(748\) 0 0
\(749\) 1.70204 2.94802i 0.0621912 0.107718i
\(750\) 0 0
\(751\) −22.8990 39.6622i −0.835596 1.44729i −0.893545 0.448975i \(-0.851789\pi\)
0.0579489 0.998320i \(-0.481544\pi\)
\(752\) 0 0
\(753\) −11.8990 1.09638i −0.433623 0.0399542i
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) −7.59592 −0.276078 −0.138039 0.990427i \(-0.544080\pi\)
−0.138039 + 0.990427i \(0.544080\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.5000 30.3109i −0.634375 1.09877i −0.986647 0.162872i \(-0.947924\pi\)
0.352273 0.935897i \(-0.385409\pi\)
\(762\) 0 0
\(763\) 6.37628 11.0440i 0.230837 0.399821i
\(764\) 0 0
\(765\) −2.00000 5.65685i −0.0723102 0.204524i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 12.3990 + 21.4757i 0.447119 + 0.774432i 0.998197 0.0600212i \(-0.0191168\pi\)
−0.551078 + 0.834453i \(0.685784\pi\)
\(770\) 0 0
\(771\) −5.94439 12.9029i −0.214082 0.464686i
\(772\) 0 0
\(773\) 25.7980 0.927888 0.463944 0.885865i \(-0.346434\pi\)
0.463944 + 0.885865i \(0.346434\pi\)
\(774\) 0 0
\(775\) 10.8990 0.391503
\(776\) 0 0
\(777\) −8.69694 + 12.2993i −0.312001 + 0.441236i
\(778\) 0 0
\(779\) 0.146428 + 0.253621i 0.00524633 + 0.00908692i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −29.4217 + 28.6182i −1.05145 + 1.02273i
\(784\) 0 0
\(785\) −2.10102 + 3.63907i −0.0749886 + 0.129884i
\(786\) 0 0
\(787\) 5.20204 + 9.01020i 0.185433 + 0.321179i 0.943722 0.330739i \(-0.107298\pi\)
−0.758290 + 0.651918i \(0.773965\pi\)
\(788\) 0 0
\(789\) −18.0000 + 25.4558i −0.640817 + 0.906252i
\(790\) 0 0
\(791\) −14.2020 −0.504966
\(792\) 0 0