Properties

Label 440.2.y.a.361.1
Level $440$
Weight $2$
Character 440.361
Analytic conductor $3.513$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [440,2,Mod(81,440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(440, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 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("440.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.y (of order \(5\), degree \(4\), 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: \(3.51341768894\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.1
Root \(-0.227943 + 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 440.361
Dual form 440.2.y.a.401.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965584 + 0.701538i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.48685 + 1.08026i) q^{7} +(-0.486854 + 1.49838i) q^{9} +O(q^{10})\) \(q+(-0.965584 + 0.701538i) q^{3} +(0.309017 + 0.951057i) q^{5} +(1.48685 + 1.08026i) q^{7} +(-0.486854 + 1.49838i) q^{9} +(-1.96213 - 2.67395i) q^{11} +(-0.387959 + 1.19402i) q^{13} +(-0.965584 - 0.701538i) q^{15} +(1.99285 + 6.13335i) q^{17} +(-1.01224 + 0.735436i) q^{19} -2.19353 q^{21} -4.35567 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.68753 - 5.19370i) q^{27} +(0.587734 + 0.427014i) q^{29} +(-3.42360 + 10.5368i) q^{31} +(3.77048 + 1.20541i) q^{33} +(-0.567928 + 1.74790i) q^{35} +(9.31066 + 6.76459i) q^{37} +(-0.463040 - 1.42509i) q^{39} +(-6.41087 + 4.65777i) q^{41} +0.606873 q^{43} -1.57549 q^{45} +(3.22146 - 2.34053i) q^{47} +(-1.11935 - 3.44501i) q^{49} +(-6.22704 - 4.52421i) q^{51} +(2.11148 - 6.49847i) q^{53} +(1.93675 - 2.69240i) q^{55} +(0.461467 - 1.42025i) q^{57} +(1.14234 + 0.829959i) q^{59} +(-3.01356 - 9.27478i) q^{61} +(-2.34253 + 1.70195i) q^{63} -1.25546 q^{65} +12.5899 q^{67} +(4.20577 - 3.05567i) q^{69} +(-2.10028 - 6.46400i) q^{71} +(8.14293 + 5.91618i) q^{73} +(0.368820 - 1.13511i) q^{75} +(-0.0288358 - 6.09540i) q^{77} +(2.01472 - 6.20066i) q^{79} +(1.44923 + 1.05292i) q^{81} +(0.199108 + 0.612790i) q^{83} +(-5.21734 + 3.79062i) q^{85} -0.867073 q^{87} +9.39723 q^{89} +(-1.86669 + 1.35623i) q^{91} +(-4.08616 - 12.5759i) q^{93} +(-1.01224 - 0.735436i) q^{95} +(-1.44061 + 4.43374i) q^{97} +(4.96188 - 1.63820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 3 q^{17} + 9 q^{19} - 4 q^{21} - 22 q^{23} - 2 q^{25} - 8 q^{27} - 17 q^{29} - 4 q^{31} + 21 q^{33} + 6 q^{35} + 24 q^{37} - 13 q^{39} - 4 q^{41} - 14 q^{43} - 8 q^{45} - 12 q^{47} - 15 q^{49} - 17 q^{51} + 35 q^{53} + 3 q^{55} - q^{57} + 21 q^{59} - 22 q^{61} + 5 q^{63} + 6 q^{65} + 14 q^{67} + 3 q^{69} + 40 q^{71} + 9 q^{73} + q^{75} - 4 q^{77} + 41 q^{79} + 24 q^{81} - 7 q^{83} - 8 q^{85} - 46 q^{87} - 24 q^{89} - 18 q^{91} + 3 q^{93} + 9 q^{95} + 4 q^{97} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(221\) \(321\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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
\(3\) −0.965584 + 0.701538i −0.557480 + 0.405033i −0.830536 0.556965i \(-0.811966\pi\)
0.273056 + 0.961998i \(0.411966\pi\)
\(4\) 0 0
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0 0
\(7\) 1.48685 + 1.08026i 0.561978 + 0.408301i 0.832182 0.554502i \(-0.187091\pi\)
−0.270204 + 0.962803i \(0.587091\pi\)
\(8\) 0 0
\(9\) −0.486854 + 1.49838i −0.162285 + 0.499461i
\(10\) 0 0
\(11\) −1.96213 2.67395i −0.591606 0.806227i
\(12\) 0 0
\(13\) −0.387959 + 1.19402i −0.107600 + 0.331160i −0.990332 0.138718i \(-0.955702\pi\)
0.882732 + 0.469878i \(0.155702\pi\)
\(14\) 0 0
\(15\) −0.965584 0.701538i −0.249313 0.181136i
\(16\) 0 0
\(17\) 1.99285 + 6.13335i 0.483336 + 1.48756i 0.834376 + 0.551196i \(0.185828\pi\)
−0.351039 + 0.936361i \(0.614172\pi\)
\(18\) 0 0
\(19\) −1.01224 + 0.735436i −0.232224 + 0.168721i −0.697812 0.716281i \(-0.745843\pi\)
0.465588 + 0.885002i \(0.345843\pi\)
\(20\) 0 0
\(21\) −2.19353 −0.478667
\(22\) 0 0
\(23\) −4.35567 −0.908221 −0.454110 0.890945i \(-0.650043\pi\)
−0.454110 + 0.890945i \(0.650043\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) 0 0
\(27\) −1.68753 5.19370i −0.324766 0.999527i
\(28\) 0 0
\(29\) 0.587734 + 0.427014i 0.109139 + 0.0792945i 0.641016 0.767527i \(-0.278513\pi\)
−0.531877 + 0.846822i \(0.678513\pi\)
\(30\) 0 0
\(31\) −3.42360 + 10.5368i −0.614897 + 1.89246i −0.211748 + 0.977324i \(0.567916\pi\)
−0.403149 + 0.915134i \(0.632084\pi\)
\(32\) 0 0
\(33\) 3.77048 + 1.20541i 0.656357 + 0.209836i
\(34\) 0 0
\(35\) −0.567928 + 1.74790i −0.0959973 + 0.295449i
\(36\) 0 0
\(37\) 9.31066 + 6.76459i 1.53066 + 1.11209i 0.955869 + 0.293793i \(0.0949175\pi\)
0.574793 + 0.818299i \(0.305082\pi\)
\(38\) 0 0
\(39\) −0.463040 1.42509i −0.0741457 0.228197i
\(40\) 0 0
\(41\) −6.41087 + 4.65777i −1.00121 + 0.727421i −0.962347 0.271823i \(-0.912373\pi\)
−0.0388623 + 0.999245i \(0.512373\pi\)
\(42\) 0 0
\(43\) 0.606873 0.0925473 0.0462736 0.998929i \(-0.485265\pi\)
0.0462736 + 0.998929i \(0.485265\pi\)
\(44\) 0 0
\(45\) −1.57549 −0.234861
\(46\) 0 0
\(47\) 3.22146 2.34053i 0.469898 0.341401i −0.327504 0.944850i \(-0.606207\pi\)
0.797402 + 0.603449i \(0.206207\pi\)
\(48\) 0 0
\(49\) −1.11935 3.44501i −0.159907 0.492144i
\(50\) 0 0
\(51\) −6.22704 4.52421i −0.871960 0.633516i
\(52\) 0 0
\(53\) 2.11148 6.49847i 0.290034 0.892634i −0.694810 0.719193i \(-0.744512\pi\)
0.984844 0.173441i \(-0.0554884\pi\)
\(54\) 0 0
\(55\) 1.93675 2.69240i 0.261151 0.363043i
\(56\) 0 0
\(57\) 0.461467 1.42025i 0.0611228 0.188117i
\(58\) 0 0
\(59\) 1.14234 + 0.829959i 0.148720 + 0.108051i 0.659657 0.751567i \(-0.270701\pi\)
−0.510937 + 0.859618i \(0.670701\pi\)
\(60\) 0 0
\(61\) −3.01356 9.27478i −0.385847 1.18751i −0.935864 0.352361i \(-0.885379\pi\)
0.550018 0.835153i \(-0.314621\pi\)
\(62\) 0 0
\(63\) −2.34253 + 1.70195i −0.295131 + 0.214425i
\(64\) 0 0
\(65\) −1.25546 −0.155721
\(66\) 0 0
\(67\) 12.5899 1.53811 0.769053 0.639186i \(-0.220728\pi\)
0.769053 + 0.639186i \(0.220728\pi\)
\(68\) 0 0
\(69\) 4.20577 3.05567i 0.506315 0.367859i
\(70\) 0 0
\(71\) −2.10028 6.46400i −0.249257 0.767135i −0.994907 0.100797i \(-0.967861\pi\)
0.745650 0.666338i \(-0.232139\pi\)
\(72\) 0 0
\(73\) 8.14293 + 5.91618i 0.953058 + 0.692437i 0.951528 0.307562i \(-0.0995131\pi\)
0.00152961 + 0.999999i \(0.499513\pi\)
\(74\) 0 0
\(75\) 0.368820 1.13511i 0.0425877 0.131071i
\(76\) 0 0
\(77\) −0.0288358 6.09540i −0.00328614 0.694635i
\(78\) 0 0
\(79\) 2.01472 6.20066i 0.226674 0.697629i −0.771444 0.636297i \(-0.780465\pi\)
0.998117 0.0613320i \(-0.0195348\pi\)
\(80\) 0 0
\(81\) 1.44923 + 1.05292i 0.161025 + 0.116992i
\(82\) 0 0
\(83\) 0.199108 + 0.612790i 0.0218549 + 0.0672625i 0.961389 0.275192i \(-0.0887416\pi\)
−0.939534 + 0.342455i \(0.888742\pi\)
\(84\) 0 0
\(85\) −5.21734 + 3.79062i −0.565900 + 0.411151i
\(86\) 0 0
\(87\) −0.867073 −0.0929600
\(88\) 0 0
\(89\) 9.39723 0.996104 0.498052 0.867147i \(-0.334049\pi\)
0.498052 + 0.867147i \(0.334049\pi\)
\(90\) 0 0
\(91\) −1.86669 + 1.35623i −0.195682 + 0.142171i
\(92\) 0 0
\(93\) −4.08616 12.5759i −0.423715 1.30406i
\(94\) 0 0
\(95\) −1.01224 0.735436i −0.103854 0.0754542i
\(96\) 0 0
\(97\) −1.44061 + 4.43374i −0.146272 + 0.450178i −0.997172 0.0751486i \(-0.976057\pi\)
0.850901 + 0.525327i \(0.176057\pi\)
\(98\) 0 0
\(99\) 4.96188 1.63820i 0.498688 0.164646i
\(100\) 0 0
\(101\) 3.12347 9.61305i 0.310797 0.956534i −0.666654 0.745368i \(-0.732274\pi\)
0.977450 0.211166i \(-0.0677261\pi\)
\(102\) 0 0
\(103\) 3.00254 + 2.18148i 0.295849 + 0.214947i 0.725801 0.687905i \(-0.241469\pi\)
−0.429951 + 0.902852i \(0.641469\pi\)
\(104\) 0 0
\(105\) −0.677837 2.08617i −0.0661501 0.203589i
\(106\) 0 0
\(107\) 6.22359 4.52170i 0.601657 0.437129i −0.244810 0.969571i \(-0.578725\pi\)
0.846467 + 0.532442i \(0.178725\pi\)
\(108\) 0 0
\(109\) −3.06569 −0.293640 −0.146820 0.989163i \(-0.546904\pi\)
−0.146820 + 0.989163i \(0.546904\pi\)
\(110\) 0 0
\(111\) −13.7358 −1.30375
\(112\) 0 0
\(113\) 8.50830 6.18164i 0.800394 0.581520i −0.110636 0.993861i \(-0.535289\pi\)
0.911030 + 0.412341i \(0.135289\pi\)
\(114\) 0 0
\(115\) −1.34598 4.14249i −0.125513 0.386289i
\(116\) 0 0
\(117\) −1.60021 1.16262i −0.147940 0.107484i
\(118\) 0 0
\(119\) −3.66256 + 11.2722i −0.335746 + 1.03332i
\(120\) 0 0
\(121\) −3.30005 + 10.4933i −0.300005 + 0.953938i
\(122\) 0 0
\(123\) 2.92263 8.99493i 0.263525 0.811046i
\(124\) 0 0
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0 0
\(127\) −1.84785 5.68711i −0.163971 0.504649i 0.834988 0.550268i \(-0.185474\pi\)
−0.998959 + 0.0456181i \(0.985474\pi\)
\(128\) 0 0
\(129\) −0.585987 + 0.425744i −0.0515932 + 0.0374847i
\(130\) 0 0
\(131\) −9.13159 −0.797831 −0.398915 0.916988i \(-0.630613\pi\)
−0.398915 + 0.916988i \(0.630613\pi\)
\(132\) 0 0
\(133\) −2.29952 −0.199394
\(134\) 0 0
\(135\) 4.41802 3.20988i 0.380243 0.276263i
\(136\) 0 0
\(137\) 1.69526 + 5.21746i 0.144836 + 0.445758i 0.996990 0.0775326i \(-0.0247042\pi\)
−0.852154 + 0.523291i \(0.824704\pi\)
\(138\) 0 0
\(139\) 14.3608 + 10.4338i 1.21807 + 0.884979i 0.995938 0.0900374i \(-0.0286986\pi\)
0.222131 + 0.975017i \(0.428699\pi\)
\(140\) 0 0
\(141\) −1.46862 + 4.51995i −0.123680 + 0.380648i
\(142\) 0 0
\(143\) 3.95397 1.30543i 0.330647 0.109166i
\(144\) 0 0
\(145\) −0.224494 + 0.690923i −0.0186432 + 0.0573780i
\(146\) 0 0
\(147\) 3.49763 + 2.54118i 0.288480 + 0.209593i
\(148\) 0 0
\(149\) −4.75902 14.6468i −0.389874 1.19991i −0.932882 0.360181i \(-0.882715\pi\)
0.543008 0.839727i \(-0.317285\pi\)
\(150\) 0 0
\(151\) 11.7220 8.51654i 0.953924 0.693067i 0.00219249 0.999998i \(-0.499302\pi\)
0.951732 + 0.306931i \(0.0993021\pi\)
\(152\) 0 0
\(153\) −10.1603 −0.821415
\(154\) 0 0
\(155\) −11.0790 −0.889887
\(156\) 0 0
\(157\) 3.95195 2.87126i 0.315400 0.229151i −0.418810 0.908074i \(-0.637553\pi\)
0.734210 + 0.678923i \(0.237553\pi\)
\(158\) 0 0
\(159\) 2.52011 + 7.75610i 0.199858 + 0.615099i
\(160\) 0 0
\(161\) −6.47625 4.70527i −0.510400 0.370827i
\(162\) 0 0
\(163\) −7.12525 + 21.9293i −0.558093 + 1.71763i 0.129539 + 0.991574i \(0.458650\pi\)
−0.687632 + 0.726059i \(0.741350\pi\)
\(164\) 0 0
\(165\) 0.0187264 + 3.95844i 0.00145785 + 0.308164i
\(166\) 0 0
\(167\) 1.00151 3.08232i 0.0774988 0.238517i −0.904800 0.425836i \(-0.859980\pi\)
0.982299 + 0.187319i \(0.0599800\pi\)
\(168\) 0 0
\(169\) 9.24206 + 6.71475i 0.710928 + 0.516519i
\(170\) 0 0
\(171\) −0.609151 1.87477i −0.0465830 0.143368i
\(172\) 0 0
\(173\) −14.3172 + 10.4021i −1.08852 + 0.790854i −0.979148 0.203147i \(-0.934883\pi\)
−0.109369 + 0.994001i \(0.534883\pi\)
\(174\) 0 0
\(175\) −1.83785 −0.138929
\(176\) 0 0
\(177\) −1.68527 −0.126673
\(178\) 0 0
\(179\) −14.2450 + 10.3496i −1.06472 + 0.773567i −0.974957 0.222396i \(-0.928612\pi\)
−0.0897674 + 0.995963i \(0.528612\pi\)
\(180\) 0 0
\(181\) −1.48239 4.56233i −0.110185 0.339116i 0.880727 0.473624i \(-0.157054\pi\)
−0.990912 + 0.134508i \(0.957054\pi\)
\(182\) 0 0
\(183\) 9.41645 + 6.84145i 0.696084 + 0.505735i
\(184\) 0 0
\(185\) −3.55635 + 10.9453i −0.261468 + 0.804717i
\(186\) 0 0
\(187\) 12.4901 17.3632i 0.913364 1.26973i
\(188\) 0 0
\(189\) 3.10144 9.54525i 0.225597 0.694315i
\(190\) 0 0
\(191\) 9.40822 + 6.83547i 0.680755 + 0.494597i 0.873608 0.486630i \(-0.161774\pi\)
−0.192853 + 0.981228i \(0.561774\pi\)
\(192\) 0 0
\(193\) 1.25252 + 3.85485i 0.0901581 + 0.277478i 0.985962 0.166972i \(-0.0533990\pi\)
−0.895804 + 0.444450i \(0.853399\pi\)
\(194\) 0 0
\(195\) 1.21225 0.880754i 0.0868113 0.0630721i
\(196\) 0 0
\(197\) −17.4066 −1.24017 −0.620084 0.784536i \(-0.712901\pi\)
−0.620084 + 0.784536i \(0.712901\pi\)
\(198\) 0 0
\(199\) 22.0409 1.56244 0.781218 0.624259i \(-0.214599\pi\)
0.781218 + 0.624259i \(0.214599\pi\)
\(200\) 0 0
\(201\) −12.1566 + 8.83231i −0.857463 + 0.622983i
\(202\) 0 0
\(203\) 0.412588 + 1.26981i 0.0289580 + 0.0891235i
\(204\) 0 0
\(205\) −6.41087 4.65777i −0.447754 0.325313i
\(206\) 0 0
\(207\) 2.12058 6.52647i 0.147390 0.453621i
\(208\) 0 0
\(209\) 3.95268 + 1.26366i 0.273412 + 0.0874092i
\(210\) 0 0
\(211\) −2.55617 + 7.86707i −0.175974 + 0.541591i −0.999677 0.0254302i \(-0.991904\pi\)
0.823703 + 0.567022i \(0.191904\pi\)
\(212\) 0 0
\(213\) 6.56273 + 4.76810i 0.449671 + 0.326705i
\(214\) 0 0
\(215\) 0.187534 + 0.577170i 0.0127897 + 0.0393627i
\(216\) 0 0
\(217\) −16.4729 + 11.9682i −1.11825 + 0.812457i
\(218\) 0 0
\(219\) −12.0131 −0.811770
\(220\) 0 0
\(221\) −8.09646 −0.544627
\(222\) 0 0
\(223\) −8.77544 + 6.37573i −0.587647 + 0.426951i −0.841473 0.540299i \(-0.818311\pi\)
0.253826 + 0.967250i \(0.418311\pi\)
\(224\) 0 0
\(225\) −0.486854 1.49838i −0.0324569 0.0998922i
\(226\) 0 0
\(227\) 4.39556 + 3.19356i 0.291744 + 0.211964i 0.724023 0.689775i \(-0.242291\pi\)
−0.432280 + 0.901740i \(0.642291\pi\)
\(228\) 0 0
\(229\) 6.45771 19.8748i 0.426738 1.31336i −0.474583 0.880211i \(-0.657401\pi\)
0.901320 0.433153i \(-0.142599\pi\)
\(230\) 0 0
\(231\) 4.30400 + 5.86539i 0.283182 + 0.385914i
\(232\) 0 0
\(233\) 8.33463 25.6513i 0.546020 1.68048i −0.172533 0.985004i \(-0.555195\pi\)
0.718553 0.695472i \(-0.244805\pi\)
\(234\) 0 0
\(235\) 3.22146 + 2.34053i 0.210145 + 0.152679i
\(236\) 0 0
\(237\) 2.40462 + 7.40066i 0.156197 + 0.480725i
\(238\) 0 0
\(239\) −18.8222 + 13.6751i −1.21750 + 0.884569i −0.995891 0.0905654i \(-0.971133\pi\)
−0.221614 + 0.975134i \(0.571133\pi\)
\(240\) 0 0
\(241\) 9.93604 0.640037 0.320018 0.947411i \(-0.396311\pi\)
0.320018 + 0.947411i \(0.396311\pi\)
\(242\) 0 0
\(243\) 14.2449 0.913811
\(244\) 0 0
\(245\) 2.93050 2.12913i 0.187223 0.136025i
\(246\) 0 0
\(247\) −0.485414 1.49395i −0.0308861 0.0950578i
\(248\) 0 0
\(249\) −0.622150 0.452019i −0.0394272 0.0286455i
\(250\) 0 0
\(251\) −5.51352 + 16.9689i −0.348010 + 1.07106i 0.611942 + 0.790902i \(0.290388\pi\)
−0.959953 + 0.280163i \(0.909612\pi\)
\(252\) 0 0
\(253\) 8.54642 + 11.6469i 0.537309 + 0.732232i
\(254\) 0 0
\(255\) 2.37852 7.32032i 0.148949 0.458416i
\(256\) 0 0
\(257\) 22.5985 + 16.4187i 1.40965 + 1.02417i 0.993373 + 0.114937i \(0.0366668\pi\)
0.416281 + 0.909236i \(0.363333\pi\)
\(258\) 0 0
\(259\) 6.53606 + 20.1159i 0.406131 + 1.24994i
\(260\) 0 0
\(261\) −0.925971 + 0.672757i −0.0573162 + 0.0416426i
\(262\) 0 0
\(263\) −14.8691 −0.916871 −0.458436 0.888728i \(-0.651590\pi\)
−0.458436 + 0.888728i \(0.651590\pi\)
\(264\) 0 0
\(265\) 6.83290 0.419742
\(266\) 0 0
\(267\) −9.07381 + 6.59251i −0.555308 + 0.403455i
\(268\) 0 0
\(269\) −2.46614 7.59001i −0.150363 0.462771i 0.847298 0.531117i \(-0.178228\pi\)
−0.997662 + 0.0683464i \(0.978228\pi\)
\(270\) 0 0
\(271\) 15.2170 + 11.0558i 0.924367 + 0.671592i 0.944607 0.328203i \(-0.106443\pi\)
−0.0202404 + 0.999795i \(0.506443\pi\)
\(272\) 0 0
\(273\) 0.850999 2.61910i 0.0515048 0.158515i
\(274\) 0 0
\(275\) 3.15911 + 1.00996i 0.190502 + 0.0609029i
\(276\) 0 0
\(277\) −3.35613 + 10.3291i −0.201650 + 0.620615i 0.798184 + 0.602414i \(0.205794\pi\)
−0.999834 + 0.0182019i \(0.994206\pi\)
\(278\) 0 0
\(279\) −14.1213 10.2597i −0.845421 0.614234i
\(280\) 0 0
\(281\) −7.45024 22.9295i −0.444444 1.36786i −0.883092 0.469199i \(-0.844543\pi\)
0.438648 0.898659i \(-0.355457\pi\)
\(282\) 0 0
\(283\) 7.37802 5.36045i 0.438578 0.318646i −0.346492 0.938053i \(-0.612627\pi\)
0.785070 + 0.619407i \(0.212627\pi\)
\(284\) 0 0
\(285\) 1.49334 0.0884578
\(286\) 0 0
\(287\) −14.5636 −0.859665
\(288\) 0 0
\(289\) −19.8933 + 14.4533i −1.17019 + 0.850195i
\(290\) 0 0
\(291\) −1.71941 5.29179i −0.100793 0.310210i
\(292\) 0 0
\(293\) −21.2195 15.4169i −1.23966 0.900665i −0.242083 0.970256i \(-0.577831\pi\)
−0.997576 + 0.0695907i \(0.977831\pi\)
\(294\) 0 0
\(295\) −0.436335 + 1.34290i −0.0254044 + 0.0781868i
\(296\) 0 0
\(297\) −10.5765 + 14.7031i −0.613713 + 0.853161i
\(298\) 0 0
\(299\) 1.68982 5.20074i 0.0977250 0.300767i
\(300\) 0 0
\(301\) 0.902332 + 0.655582i 0.0520095 + 0.0377871i
\(302\) 0 0
\(303\) 3.72794 + 11.4734i 0.214165 + 0.659131i
\(304\) 0 0
\(305\) 7.88960 5.73213i 0.451757 0.328221i
\(306\) 0 0
\(307\) −8.16034 −0.465735 −0.232868 0.972508i \(-0.574811\pi\)
−0.232868 + 0.972508i \(0.574811\pi\)
\(308\) 0 0
\(309\) −4.42960 −0.251991
\(310\) 0 0
\(311\) 10.9163 7.93119i 0.619009 0.449736i −0.233566 0.972341i \(-0.575040\pi\)
0.852575 + 0.522605i \(0.175040\pi\)
\(312\) 0 0
\(313\) 2.42214 + 7.45457i 0.136907 + 0.421357i 0.995882 0.0906610i \(-0.0288980\pi\)
−0.858974 + 0.512018i \(0.828898\pi\)
\(314\) 0 0
\(315\) −2.34253 1.70195i −0.131987 0.0958938i
\(316\) 0 0
\(317\) 1.95549 6.01836i 0.109831 0.338025i −0.881003 0.473111i \(-0.843131\pi\)
0.990834 + 0.135086i \(0.0431310\pi\)
\(318\) 0 0
\(319\) −0.0113984 2.40943i −0.000638189 0.134902i
\(320\) 0 0
\(321\) −2.83725 + 8.73216i −0.158360 + 0.487382i
\(322\) 0 0
\(323\) −6.52793 4.74282i −0.363224 0.263898i
\(324\) 0 0
\(325\) −0.387959 1.19402i −0.0215201 0.0662320i
\(326\) 0 0
\(327\) 2.96018 2.15070i 0.163698 0.118934i
\(328\) 0 0
\(329\) 7.31822 0.403467
\(330\) 0 0
\(331\) −2.92392 −0.160713 −0.0803566 0.996766i \(-0.525606\pi\)
−0.0803566 + 0.996766i \(0.525606\pi\)
\(332\) 0 0
\(333\) −14.6689 + 10.6576i −0.803849 + 0.584031i
\(334\) 0 0
\(335\) 3.89050 + 11.9737i 0.212561 + 0.654195i
\(336\) 0 0
\(337\) −18.0658 13.1256i −0.984107 0.714995i −0.0254842 0.999675i \(-0.508113\pi\)
−0.958623 + 0.284680i \(0.908113\pi\)
\(338\) 0 0
\(339\) −3.87882 + 11.9378i −0.210669 + 0.648371i
\(340\) 0 0
\(341\) 34.8924 11.5200i 1.88953 0.623843i
\(342\) 0 0
\(343\) 6.03270 18.5667i 0.325735 1.00251i
\(344\) 0 0
\(345\) 4.20577 + 3.05567i 0.226431 + 0.164512i
\(346\) 0 0
\(347\) 1.73763 + 5.34787i 0.0932808 + 0.287089i 0.986802 0.161933i \(-0.0517727\pi\)
−0.893521 + 0.449021i \(0.851773\pi\)
\(348\) 0 0
\(349\) 3.34641 2.43131i 0.179129 0.130145i −0.494608 0.869116i \(-0.664688\pi\)
0.673737 + 0.738972i \(0.264688\pi\)
\(350\) 0 0
\(351\) 6.85605 0.365949
\(352\) 0 0
\(353\) 17.3112 0.921380 0.460690 0.887561i \(-0.347602\pi\)
0.460690 + 0.887561i \(0.347602\pi\)
\(354\) 0 0
\(355\) 5.49860 3.99497i 0.291836 0.212031i
\(356\) 0 0
\(357\) −4.37136 13.4537i −0.231357 0.712044i
\(358\) 0 0
\(359\) −12.1892 8.85595i −0.643320 0.467399i 0.217669 0.976023i \(-0.430155\pi\)
−0.860989 + 0.508623i \(0.830155\pi\)
\(360\) 0 0
\(361\) −5.38756 + 16.5812i −0.283556 + 0.872695i
\(362\) 0 0
\(363\) −4.17498 12.4473i −0.219129 0.653313i
\(364\) 0 0
\(365\) −3.11032 + 9.57259i −0.162802 + 0.501052i
\(366\) 0 0
\(367\) 4.15499 + 3.01878i 0.216889 + 0.157579i 0.690925 0.722926i \(-0.257203\pi\)
−0.474036 + 0.880505i \(0.657203\pi\)
\(368\) 0 0
\(369\) −3.85796 11.8736i −0.200838 0.618114i
\(370\) 0 0
\(371\) 10.1595 7.38133i 0.527456 0.383219i
\(372\) 0 0
\(373\) −4.24462 −0.219778 −0.109889 0.993944i \(-0.535050\pi\)
−0.109889 + 0.993944i \(0.535050\pi\)
\(374\) 0 0
\(375\) 1.19353 0.0616335
\(376\) 0 0
\(377\) −0.737878 + 0.536100i −0.0380026 + 0.0276105i
\(378\) 0 0
\(379\) −6.17571 19.0069i −0.317225 0.976317i −0.974829 0.222954i \(-0.928430\pi\)
0.657604 0.753363i \(-0.271570\pi\)
\(380\) 0 0
\(381\) 5.77398 + 4.19504i 0.295810 + 0.214918i
\(382\) 0 0
\(383\) 2.30927 7.10721i 0.117998 0.363161i −0.874562 0.484913i \(-0.838851\pi\)
0.992561 + 0.121752i \(0.0388512\pi\)
\(384\) 0 0
\(385\) 5.78816 1.91101i 0.294992 0.0973939i
\(386\) 0 0
\(387\) −0.295459 + 0.909328i −0.0150190 + 0.0462237i
\(388\) 0 0
\(389\) 18.9468 + 13.7657i 0.960642 + 0.697947i 0.953300 0.302026i \(-0.0976629\pi\)
0.00734201 + 0.999973i \(0.497663\pi\)
\(390\) 0 0
\(391\) −8.68019 26.7149i −0.438976 1.35103i
\(392\) 0 0
\(393\) 8.81732 6.40616i 0.444775 0.323148i
\(394\) 0 0
\(395\) 6.51977 0.328045
\(396\) 0 0
\(397\) 13.2416 0.664578 0.332289 0.943178i \(-0.392179\pi\)
0.332289 + 0.943178i \(0.392179\pi\)
\(398\) 0 0
\(399\) 2.22038 1.61320i 0.111158 0.0807610i
\(400\) 0 0
\(401\) 2.57380 + 7.92136i 0.128530 + 0.395574i 0.994528 0.104474i \(-0.0333159\pi\)
−0.865998 + 0.500048i \(0.833316\pi\)
\(402\) 0 0
\(403\) −11.2528 8.17567i −0.560544 0.407259i
\(404\) 0 0
\(405\) −0.553555 + 1.70367i −0.0275064 + 0.0846559i
\(406\) 0 0
\(407\) −0.180569 38.1693i −0.00895049 1.89198i
\(408\) 0 0
\(409\) 7.02703 21.6270i 0.347464 1.06938i −0.612787 0.790248i \(-0.709952\pi\)
0.960251 0.279137i \(-0.0900482\pi\)
\(410\) 0 0
\(411\) −5.29716 3.84861i −0.261290 0.189838i
\(412\) 0 0
\(413\) 0.801920 + 2.46806i 0.0394599 + 0.121445i
\(414\) 0 0
\(415\) −0.521270 + 0.378725i −0.0255882 + 0.0185909i
\(416\) 0 0
\(417\) −21.1863 −1.03750
\(418\) 0 0
\(419\) −15.9446 −0.778946 −0.389473 0.921038i \(-0.627343\pi\)
−0.389473 + 0.921038i \(0.627343\pi\)
\(420\) 0 0
\(421\) 26.7782 19.4555i 1.30509 0.948203i 0.305097 0.952321i \(-0.401311\pi\)
0.999992 + 0.00411867i \(0.00131102\pi\)
\(422\) 0 0
\(423\) 1.93862 + 5.96647i 0.0942591 + 0.290100i
\(424\) 0 0
\(425\) −5.21734 3.79062i −0.253078 0.183872i
\(426\) 0 0
\(427\) 5.53848 17.0457i 0.268026 0.824898i
\(428\) 0 0
\(429\) −2.90208 + 4.03436i −0.140114 + 0.194781i
\(430\) 0 0
\(431\) 4.67499 14.3881i 0.225186 0.693052i −0.773086 0.634301i \(-0.781288\pi\)
0.998273 0.0587513i \(-0.0187119\pi\)
\(432\) 0 0
\(433\) −8.67258 6.30100i −0.416778 0.302807i 0.359562 0.933121i \(-0.382926\pi\)
−0.776340 + 0.630314i \(0.782926\pi\)
\(434\) 0 0
\(435\) −0.267940 0.824635i −0.0128467 0.0395382i
\(436\) 0 0
\(437\) 4.40899 3.20332i 0.210911 0.153236i
\(438\) 0 0
\(439\) −35.9820 −1.71733 −0.858663 0.512540i \(-0.828705\pi\)
−0.858663 + 0.512540i \(0.828705\pi\)
\(440\) 0 0
\(441\) 5.70690 0.271757
\(442\) 0 0
\(443\) −2.96042 + 2.15087i −0.140654 + 0.102191i −0.655887 0.754859i \(-0.727705\pi\)
0.515233 + 0.857050i \(0.327705\pi\)
\(444\) 0 0
\(445\) 2.90390 + 8.93730i 0.137658 + 0.423669i
\(446\) 0 0
\(447\) 14.8705 + 10.8040i 0.703350 + 0.511013i
\(448\) 0 0
\(449\) 2.27259 6.99431i 0.107250 0.330082i −0.883002 0.469370i \(-0.844481\pi\)
0.990252 + 0.139287i \(0.0444812\pi\)
\(450\) 0 0
\(451\) 25.0336 + 8.00319i 1.17879 + 0.376856i
\(452\) 0 0
\(453\) −5.34391 + 16.4469i −0.251079 + 0.772741i
\(454\) 0 0
\(455\) −1.86669 1.35623i −0.0875117 0.0635810i
\(456\) 0 0
\(457\) 9.73246 + 29.9534i 0.455265 + 1.40116i 0.870823 + 0.491596i \(0.163586\pi\)
−0.415558 + 0.909567i \(0.636414\pi\)
\(458\) 0 0
\(459\) 28.4918 20.7005i 1.32988 0.966216i
\(460\) 0 0
\(461\) 39.7866 1.85305 0.926523 0.376239i \(-0.122783\pi\)
0.926523 + 0.376239i \(0.122783\pi\)
\(462\) 0 0
\(463\) −14.1053 −0.655529 −0.327764 0.944759i \(-0.606295\pi\)
−0.327764 + 0.944759i \(0.606295\pi\)
\(464\) 0 0
\(465\) 10.6977 7.77234i 0.496094 0.360434i
\(466\) 0 0
\(467\) 1.59211 + 4.90002i 0.0736742 + 0.226746i 0.981112 0.193441i \(-0.0619647\pi\)
−0.907438 + 0.420186i \(0.861965\pi\)
\(468\) 0 0
\(469\) 18.7194 + 13.6004i 0.864381 + 0.628010i
\(470\) 0 0
\(471\) −1.80164 + 5.54488i −0.0830152 + 0.255494i
\(472\) 0 0
\(473\) −1.19077 1.62275i −0.0547515 0.0746141i
\(474\) 0 0
\(475\) 0.386642 1.18996i 0.0177403 0.0545991i
\(476\) 0 0
\(477\) 8.70922 + 6.32762i 0.398768 + 0.289722i
\(478\) 0 0
\(479\) 4.98372 + 15.3383i 0.227712 + 0.700825i 0.998005 + 0.0631353i \(0.0201100\pi\)
−0.770293 + 0.637690i \(0.779890\pi\)
\(480\) 0 0
\(481\) −11.6892 + 8.49268i −0.532980 + 0.387233i
\(482\) 0 0
\(483\) 9.55429 0.434735
\(484\) 0 0
\(485\) −4.66191 −0.211686
\(486\) 0 0
\(487\) −0.328540 + 0.238698i −0.0148876 + 0.0108165i −0.595204 0.803575i \(-0.702929\pi\)
0.580317 + 0.814391i \(0.302929\pi\)
\(488\) 0 0
\(489\) −8.50418 26.1732i −0.384572 1.18359i
\(490\) 0 0
\(491\) −9.57545 6.95697i −0.432134 0.313964i 0.350368 0.936612i \(-0.386057\pi\)
−0.782502 + 0.622648i \(0.786057\pi\)
\(492\) 0 0
\(493\) −1.44776 + 4.45575i −0.0652039 + 0.200677i
\(494\) 0 0
\(495\) 3.09133 + 4.21280i 0.138945 + 0.189351i
\(496\) 0 0
\(497\) 3.86000 11.8799i 0.173145 0.532885i
\(498\) 0 0
\(499\) −22.1288 16.0775i −0.990622 0.719729i −0.0305647 0.999533i \(-0.509731\pi\)
−0.960057 + 0.279804i \(0.909731\pi\)
\(500\) 0 0
\(501\) 1.19532 + 3.67883i 0.0534031 + 0.164358i
\(502\) 0 0
\(503\) 15.1645 11.0177i 0.676153 0.491254i −0.195927 0.980619i \(-0.562771\pi\)
0.872079 + 0.489365i \(0.162771\pi\)
\(504\) 0 0
\(505\) 10.1078 0.449789
\(506\) 0 0
\(507\) −13.6346 −0.605535
\(508\) 0 0
\(509\) −28.6783 + 20.8360i −1.27114 + 0.923540i −0.999248 0.0387861i \(-0.987651\pi\)
−0.271897 + 0.962326i \(0.587651\pi\)
\(510\) 0 0
\(511\) 5.71631 + 17.5930i 0.252875 + 0.778269i
\(512\) 0 0
\(513\) 5.52782 + 4.01620i 0.244059 + 0.177319i
\(514\) 0 0
\(515\) −1.14687 + 3.52970i −0.0505371 + 0.155537i
\(516\) 0 0
\(517\) −12.5794 4.02160i −0.553241 0.176870i
\(518\) 0 0
\(519\) 6.52703 20.0881i 0.286505 0.881771i
\(520\) 0 0
\(521\) 16.5644 + 12.0348i 0.725701 + 0.527253i 0.888201 0.459456i \(-0.151956\pi\)
−0.162499 + 0.986709i \(0.551956\pi\)
\(522\) 0 0
\(523\) −9.35067 28.7784i −0.408876 1.25839i −0.917615 0.397471i \(-0.869888\pi\)
0.508739 0.860921i \(-0.330112\pi\)
\(524\) 0 0
\(525\) 1.77460 1.28932i 0.0774499 0.0562707i
\(526\) 0 0
\(527\) −71.4484 −3.11234
\(528\) 0 0
\(529\) −4.02810 −0.175135
\(530\) 0 0
\(531\) −1.79975 + 1.30760i −0.0781025 + 0.0567448i
\(532\) 0 0
\(533\) −3.07429 9.46170i −0.133162 0.409832i
\(534\) 0 0
\(535\) 6.22359 + 4.52170i 0.269069 + 0.195490i
\(536\) 0 0
\(537\) 6.49412 19.9869i 0.280242 0.862497i
\(538\) 0 0
\(539\) −7.01548 + 9.75267i −0.302178 + 0.420077i
\(540\) 0 0
\(541\) 2.62418 8.07641i 0.112823 0.347232i −0.878664 0.477440i \(-0.841565\pi\)
0.991487 + 0.130208i \(0.0415646\pi\)
\(542\) 0 0
\(543\) 4.63202 + 3.36536i 0.198779 + 0.144421i
\(544\) 0 0
\(545\) −0.947350 2.91564i −0.0405800 0.124892i
\(546\) 0 0
\(547\) −21.0739 + 15.3111i −0.901056 + 0.654655i −0.938737 0.344634i \(-0.888003\pi\)
0.0376810 + 0.999290i \(0.488003\pi\)
\(548\) 0 0
\(549\) 15.3643 0.655734
\(550\) 0 0
\(551\) −0.908970 −0.0387234
\(552\) 0 0
\(553\) 9.69394 7.04306i 0.412228 0.299501i
\(554\) 0 0
\(555\) −4.24461 13.0636i −0.180173 0.554517i
\(556\) 0 0
\(557\) −9.61695 6.98713i −0.407483 0.296054i 0.365099 0.930969i \(-0.381035\pi\)
−0.772582 + 0.634915i \(0.781035\pi\)
\(558\) 0 0
\(559\) −0.235442 + 0.724616i −0.00995813 + 0.0306480i
\(560\) 0 0
\(561\) 0.120766 + 25.5279i 0.00509875 + 1.07779i
\(562\) 0 0
\(563\) −11.8019 + 36.3226i −0.497392 + 1.53082i 0.315803 + 0.948825i \(0.397726\pi\)
−0.813195 + 0.581991i \(0.802274\pi\)
\(564\) 0 0
\(565\) 8.50830 + 6.18164i 0.357947 + 0.260064i
\(566\) 0 0
\(567\) 1.01735 + 3.13109i 0.0427248 + 0.131493i
\(568\) 0 0
\(569\) −24.2045 + 17.5856i −1.01471 + 0.737227i −0.965191 0.261546i \(-0.915768\pi\)
−0.0495152 + 0.998773i \(0.515768\pi\)
\(570\) 0 0
\(571\) 34.1271 1.42817 0.714087 0.700057i \(-0.246842\pi\)
0.714087 + 0.700057i \(0.246842\pi\)
\(572\) 0 0
\(573\) −13.8798 −0.579835
\(574\) 0 0
\(575\) 3.52381 2.56020i 0.146953 0.106768i
\(576\) 0 0
\(577\) −1.79566 5.52647i −0.0747542 0.230070i 0.906697 0.421783i \(-0.138596\pi\)
−0.981451 + 0.191713i \(0.938596\pi\)
\(578\) 0 0
\(579\) −3.91373 2.84349i −0.162649 0.118171i
\(580\) 0 0
\(581\) −0.365930 + 1.12622i −0.0151814 + 0.0467234i
\(582\) 0 0
\(583\) −21.5196 + 7.10487i −0.891252 + 0.294254i
\(584\) 0 0
\(585\) 0.611227 1.88116i 0.0252711 0.0777765i
\(586\) 0 0
\(587\) −5.71027 4.14875i −0.235688 0.171237i 0.463672 0.886007i \(-0.346532\pi\)
−0.699360 + 0.714770i \(0.746532\pi\)
\(588\) 0 0
\(589\) −4.28361 13.1836i −0.176503 0.543220i
\(590\) 0 0
\(591\) 16.8075 12.2114i 0.691369 0.502309i
\(592\) 0 0
\(593\) 35.1649 1.44405 0.722024 0.691868i \(-0.243212\pi\)
0.722024 + 0.691868i \(0.243212\pi\)
\(594\) 0 0
\(595\) −11.8523 −0.485897
\(596\) 0 0
\(597\) −21.2823 + 15.4625i −0.871027 + 0.632838i
\(598\) 0 0
\(599\) 14.0181 + 43.1432i 0.572763 + 1.76278i 0.643673 + 0.765301i \(0.277410\pi\)
−0.0709098 + 0.997483i \(0.522590\pi\)
\(600\) 0 0
\(601\) −34.5915 25.1322i −1.41101 1.02516i −0.993174 0.116642i \(-0.962787\pi\)
−0.417841 0.908520i \(-0.637213\pi\)
\(602\) 0 0
\(603\) −6.12946 + 18.8645i −0.249611 + 0.768223i
\(604\) 0 0
\(605\) −10.9995 + 0.104074i −0.447194 + 0.00423121i
\(606\) 0 0
\(607\) −12.2796 + 37.7927i −0.498414 + 1.53396i 0.313155 + 0.949702i \(0.398614\pi\)
−0.811569 + 0.584257i \(0.801386\pi\)
\(608\) 0 0
\(609\) −1.28921 0.936666i −0.0522415 0.0379556i
\(610\) 0 0
\(611\) 1.54483 + 4.75450i 0.0624971 + 0.192346i
\(612\) 0 0
\(613\) −38.4186 + 27.9128i −1.55171 + 1.12739i −0.609298 + 0.792942i \(0.708548\pi\)
−0.942416 + 0.334444i \(0.891452\pi\)
\(614\) 0 0
\(615\) 9.45783 0.381377
\(616\) 0 0
\(617\) 16.6834 0.671649 0.335824 0.941925i \(-0.390985\pi\)
0.335824 + 0.941925i \(0.390985\pi\)
\(618\) 0 0
\(619\) 23.4220 17.0170i 0.941408 0.683973i −0.00735131 0.999973i \(-0.502340\pi\)
0.948759 + 0.316000i \(0.102340\pi\)
\(620\) 0 0
\(621\) 7.35035 + 22.6220i 0.294959 + 0.907791i
\(622\) 0 0
\(623\) 13.9723 + 10.1515i 0.559789 + 0.406710i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 0 0
\(627\) −4.70314 + 1.55278i −0.187825 + 0.0620121i
\(628\) 0 0
\(629\) −22.9349 + 70.5863i −0.914474 + 2.81446i
\(630\) 0 0
\(631\) −8.07004 5.86323i −0.321263 0.233411i 0.415451 0.909616i \(-0.363624\pi\)
−0.736714 + 0.676204i \(0.763624\pi\)
\(632\) 0 0
\(633\) −3.05085 9.38956i −0.121261 0.373202i
\(634\) 0 0
\(635\) 4.83774 3.51483i 0.191980 0.139482i
\(636\) 0 0
\(637\) 4.54766 0.180185
\(638\) 0 0
\(639\) 10.7081 0.423605
\(640\) 0 0
\(641\) 34.9966 25.4265i 1.38228 1.00429i 0.385620 0.922658i \(-0.373988\pi\)
0.996663 0.0816296i \(-0.0260124\pi\)
\(642\) 0 0
\(643\) 3.20542 + 9.86526i 0.126409 + 0.389048i 0.994155 0.107960i \(-0.0344319\pi\)
−0.867746 + 0.497008i \(0.834432\pi\)
\(644\) 0 0
\(645\) −0.585987 0.425744i −0.0230732 0.0167637i
\(646\) 0 0
\(647\) 2.77418 8.53804i 0.109064 0.335665i −0.881599 0.472000i \(-0.843532\pi\)
0.990663 + 0.136335i \(0.0435323\pi\)
\(648\) 0 0
\(649\) −0.0221544 4.68306i −0.000869635 0.183826i
\(650\) 0 0
\(651\) 7.50976 23.1127i 0.294331 0.905857i
\(652\) 0 0
\(653\) 6.59993 + 4.79513i 0.258275 + 0.187648i 0.709386 0.704820i \(-0.248972\pi\)
−0.451111 + 0.892468i \(0.648972\pi\)
\(654\) 0 0
\(655\) −2.82182 8.68466i −0.110258 0.339338i
\(656\) 0 0
\(657\) −12.8291 + 9.32091i −0.500512 + 0.363643i
\(658\) 0 0
\(659\) 12.2222 0.476111 0.238055 0.971252i \(-0.423490\pi\)
0.238055 + 0.971252i \(0.423490\pi\)
\(660\) 0 0
\(661\) −22.7382 −0.884412 −0.442206 0.896914i \(-0.645804\pi\)
−0.442206 + 0.896914i \(0.645804\pi\)
\(662\) 0 0
\(663\) 7.81781 5.67997i 0.303619 0.220592i
\(664\) 0 0
\(665\) −0.710590 2.18697i −0.0275555 0.0848072i
\(666\) 0 0
\(667\) −2.55998 1.85993i −0.0991228 0.0720169i
\(668\) 0 0
\(669\) 4.00061 12.3126i 0.154672 0.476033i
\(670\) 0 0
\(671\) −18.8873 + 26.2565i −0.729137 + 1.01362i
\(672\) 0 0
\(673\) −5.58716 + 17.1955i −0.215369 + 0.662838i 0.783758 + 0.621066i \(0.213300\pi\)
−0.999127 + 0.0417717i \(0.986700\pi\)
\(674\) 0 0
\(675\) 4.41802 + 3.20988i 0.170050 + 0.123548i
\(676\) 0 0
\(677\) 5.94644 + 18.3013i 0.228540 + 0.703375i 0.997913 + 0.0645747i \(0.0205691\pi\)
−0.769372 + 0.638800i \(0.779431\pi\)
\(678\) 0 0
\(679\) −6.93158 + 5.03609i −0.266010 + 0.193267i
\(680\) 0 0
\(681\) −6.48469 −0.248494
\(682\) 0 0
\(683\) 33.1235 1.26743 0.633717 0.773565i \(-0.281528\pi\)
0.633717 + 0.773565i \(0.281528\pi\)
\(684\) 0 0
\(685\) −4.43824 + 3.22457i −0.169576 + 0.123205i
\(686\) 0 0
\(687\) 7.70746 + 23.7211i 0.294058 + 0.905017i
\(688\) 0 0
\(689\) 6.94011 + 5.04228i 0.264397 + 0.192096i
\(690\) 0 0
\(691\) −13.4070 + 41.2624i −0.510024 + 1.56969i 0.282132 + 0.959376i \(0.408958\pi\)
−0.792156 + 0.610318i \(0.791042\pi\)
\(692\) 0 0
\(693\) 9.14728 + 2.92436i 0.347477 + 0.111087i
\(694\) 0 0
\(695\) −5.48535 + 16.8822i −0.208071 + 0.640377i
\(696\) 0 0
\(697\) −41.3436 30.0379i −1.56600 1.13777i
\(698\) 0 0
\(699\) 9.94760 + 30.6156i 0.376253 + 1.15799i
\(700\) 0 0
\(701\) 6.77735 4.92404i 0.255977 0.185978i −0.452395 0.891818i \(-0.649430\pi\)
0.708372 + 0.705840i \(0.249430\pi\)
\(702\) 0 0
\(703\) −14.3996 −0.543089
\(704\) 0 0
\(705\) −4.75255 −0.178992
\(706\) 0 0
\(707\) 15.0288 10.9190i 0.565215 0.410652i
\(708\) 0 0
\(709\) 0.146919 + 0.452171i 0.00551766 + 0.0169816i 0.953777 0.300514i \(-0.0971582\pi\)
−0.948260 + 0.317495i \(0.897158\pi\)
\(710\) 0 0
\(711\) 8.31010 + 6.03764i 0.311653 + 0.226429i
\(712\) 0 0
\(713\) 14.9121 45.8947i 0.558462 1.71877i
\(714\) 0 0
\(715\) 2.46339 + 3.35705i 0.0921254 + 0.125546i
\(716\) 0 0
\(717\) 8.58078 26.4089i 0.320455 0.986259i
\(718\) 0 0
\(719\) 1.34714 + 0.978752i 0.0502397 + 0.0365013i 0.612622 0.790376i \(-0.290115\pi\)
−0.562382 + 0.826878i \(0.690115\pi\)
\(720\) 0 0
\(721\) 2.10778 + 6.48707i 0.0784977 + 0.241591i
\(722\) 0 0
\(723\) −9.59408 + 6.97051i −0.356808 + 0.259236i
\(724\) 0 0
\(725\) −0.726479 −0.0269808
\(726\) 0 0
\(727\) 14.5667 0.540247 0.270124 0.962826i \(-0.412935\pi\)
0.270124 + 0.962826i \(0.412935\pi\)
\(728\) 0 0
\(729\) −18.1023 + 13.1521i −0.670457 + 0.487115i
\(730\) 0 0
\(731\) 1.20941 + 3.72217i 0.0447315 + 0.137669i
\(732\) 0 0
\(733\) 34.5920 + 25.1326i 1.27769 + 0.928293i 0.999481 0.0322289i \(-0.0102605\pi\)
0.278205 + 0.960522i \(0.410261\pi\)
\(734\) 0 0
\(735\) −1.33598 + 4.11171i −0.0492782 + 0.151663i
\(736\) 0 0
\(737\) −24.7031 33.6649i −0.909952 1.24006i
\(738\) 0 0
\(739\) 13.9182 42.8360i 0.511991 1.57575i −0.276700 0.960956i \(-0.589241\pi\)
0.788691 0.614790i \(-0.210759\pi\)
\(740\) 0 0
\(741\) 1.51677 + 1.10200i 0.0557199 + 0.0404829i
\(742\) 0 0
\(743\) −6.70050 20.6220i −0.245818 0.756549i −0.995501 0.0947520i \(-0.969794\pi\)
0.749683 0.661797i \(-0.230206\pi\)
\(744\) 0 0
\(745\) 12.4593 9.05219i 0.456472 0.331647i
\(746\) 0 0
\(747\) −1.01513 −0.0371417
\(748\) 0 0
\(749\) 14.1382 0.516598
\(750\) 0 0
\(751\) 2.92960 2.12848i 0.106902 0.0776692i −0.533050 0.846084i \(-0.678954\pi\)
0.639952 + 0.768415i \(0.278954\pi\)
\(752\) 0 0
\(753\) −6.58053 20.2528i −0.239808 0.738053i
\(754\) 0 0
\(755\) 11.7220 + 8.51654i 0.426608 + 0.309949i
\(756\) 0 0
\(757\) 9.99962 30.7757i 0.363443 1.11856i −0.587508 0.809218i \(-0.699891\pi\)
0.950951 0.309343i \(-0.100109\pi\)
\(758\) 0 0
\(759\) −16.4230 5.25039i −0.596117 0.190577i
\(760\) 0 0
\(761\) −8.16887 + 25.1412i −0.296121 + 0.911367i 0.686721 + 0.726921i \(0.259049\pi\)
−0.982843 + 0.184447i \(0.940951\pi\)
\(762\) 0 0
\(763\) −4.55823 3.31175i −0.165019 0.119893i
\(764\) 0 0
\(765\) −3.13972 9.66306i −0.113517 0.349368i
\(766\) 0 0
\(767\) −1.43417 + 1.04198i −0.0517847 + 0.0376238i
\(768\) 0 0
\(769\) −31.6062 −1.13975 −0.569874 0.821732i \(-0.693008\pi\)
−0.569874 + 0.821732i \(0.693008\pi\)
\(770\) 0 0
\(771\) −33.3391 −1.20068
\(772\) 0 0
\(773\) −22.9605 + 16.6818i −0.825834 + 0.600003i −0.918378 0.395705i \(-0.870500\pi\)
0.0925439 + 0.995709i \(0.470500\pi\)
\(774\) 0 0
\(775\) −3.42360 10.5368i −0.122979 0.378492i
\(776\) 0 0
\(777\) −20.4232 14.8383i −0.732677 0.532321i
\(778\) 0 0
\(779\) 3.06385 9.42957i 0.109774 0.337849i
\(780\) 0 0
\(781\) −13.1634 + 18.2993i −0.471023 + 0.654800i
\(782\) 0 0
\(783\) 1.22596 3.77311i 0.0438122 0.134840i
\(784\) 0 0
\(785\) 3.95195 + 2.87126i 0.141051 + 0.102480i
\(786\) 0 0
\(787\) 9.02059 + 27.7625i 0.321549 + 0.989627i 0.972974 + 0.230914i \(0.0741716\pi\)
−0.651425 + 0.758713i \(0.725828\pi\)
\(788\) 0 0