Properties

Label 880.2.bo.d.401.2
Level $880$
Weight $2$
Character 880.401
Analytic conductor $7.027$
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] = [880,2,Mod(81,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, 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("880.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bo (of order \(5\), degree \(4\), 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: \(7.02683537787\)
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: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 401.2
Root \(-0.227943 - 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 880.401
Dual form 880.2.bo.d.801.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965584 + 0.701538i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.48685 + 1.08026i) q^{7} +(-0.486854 - 1.49838i) q^{9} +O(q^{10})\) \(q+(0.965584 + 0.701538i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.48685 + 1.08026i) q^{7} +(-0.486854 - 1.49838i) q^{9} +(1.96213 - 2.67395i) q^{11} +(-0.387959 - 1.19402i) q^{13} +(0.965584 - 0.701538i) q^{15} +(1.99285 - 6.13335i) q^{17} +(1.01224 + 0.735436i) q^{19} -2.19353 q^{21} +4.35567 q^{23} +(-0.809017 - 0.587785i) q^{25} +(1.68753 - 5.19370i) q^{27} +(0.587734 - 0.427014i) q^{29} +(3.42360 + 10.5368i) q^{31} +(3.77048 - 1.20541i) q^{33} +(0.567928 + 1.74790i) q^{35} +(9.31066 - 6.76459i) q^{37} +(0.463040 - 1.42509i) q^{39} +(-6.41087 - 4.65777i) q^{41} -0.606873 q^{43} -1.57549 q^{45} +(-3.22146 - 2.34053i) q^{47} +(-1.11935 + 3.44501i) q^{49} +(6.22704 - 4.52421i) q^{51} +(2.11148 + 6.49847i) q^{53} +(-1.93675 - 2.69240i) q^{55} +(0.461467 + 1.42025i) q^{57} +(-1.14234 + 0.829959i) q^{59} +(-3.01356 + 9.27478i) q^{61} +(2.34253 + 1.70195i) q^{63} -1.25546 q^{65} -12.5899 q^{67} +(4.20577 + 3.05567i) q^{69} +(2.10028 - 6.46400i) q^{71} +(8.14293 - 5.91618i) q^{73} +(-0.368820 - 1.13511i) q^{75} +(-0.0288358 + 6.09540i) q^{77} +(-2.01472 - 6.20066i) q^{79} +(1.44923 - 1.05292i) q^{81} +(-0.199108 + 0.612790i) q^{83} +(-5.21734 - 3.79062i) q^{85} +0.867073 q^{87} +9.39723 q^{89} +(1.86669 + 1.35623i) q^{91} +(-4.08616 + 12.5759i) q^{93} +(1.01224 - 0.735436i) q^{95} +(-1.44061 - 4.43374i) q^{97} +(-4.96188 - 1.63820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.965584 + 0.701538i 0.557480 + 0.405033i 0.830536 0.556965i \(-0.188034\pi\)
−0.273056 + 0.961998i \(0.588034\pi\)
\(4\) 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 \(-0.812909\pi\)
0.270204 + 0.962803i \(0.412909\pi\)
\(8\) 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 0.882732 0.469878i \(-0.155702\pi\)
−0.990332 + 0.138718i \(0.955702\pi\)
\(14\) 0 0
\(15\) 0.965584 0.701538i 0.249313 0.181136i
\(16\) 0 0
\(17\) 1.99285 6.13335i 0.483336 1.48756i −0.351039 0.936361i \(-0.614172\pi\)
0.834376 0.551196i \(-0.185828\pi\)
\(18\) 0 0
\(19\) 1.01224 + 0.735436i 0.232224 + 0.168721i 0.697812 0.716281i \(-0.254157\pi\)
−0.465588 + 0.885002i \(0.654157\pi\)
\(20\) 0 0
\(21\) −2.19353 −0.478667
\(22\) 0 0
\(23\) 4.35567 0.908221 0.454110 0.890945i \(-0.349957\pi\)
0.454110 + 0.890945i \(0.349957\pi\)
\(24\) 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 −0.531877 0.846822i \(-0.678513\pi\)
0.641016 + 0.767527i \(0.278513\pi\)
\(30\) 0 0
\(31\) 3.42360 + 10.5368i 0.614897 + 1.89246i 0.403149 + 0.915134i \(0.367916\pi\)
0.211748 + 0.977324i \(0.432084\pi\)
\(32\) 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 0.574793 0.818299i \(-0.305082\pi\)
0.955869 0.293793i \(-0.0949175\pi\)
\(38\) 0 0
\(39\) 0.463040 1.42509i 0.0741457 0.228197i
\(40\) 0 0
\(41\) −6.41087 4.65777i −1.00121 0.727421i −0.0388623 0.999245i \(-0.512373\pi\)
−0.962347 + 0.271823i \(0.912373\pi\)
\(42\) 0 0
\(43\) −0.606873 −0.0925473 −0.0462736 0.998929i \(-0.514735\pi\)
−0.0462736 + 0.998929i \(0.514735\pi\)
\(44\) 0 0
\(45\) −1.57549 −0.234861
\(46\) 0 0
\(47\) −3.22146 2.34053i −0.469898 0.341401i 0.327504 0.944850i \(-0.393793\pi\)
−0.797402 + 0.603449i \(0.793793\pi\)
\(48\) 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 0.984844 + 0.173441i \(0.0554884\pi\)
−0.694810 + 0.719193i \(0.744512\pi\)
\(54\) 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 \(-0.729299\pi\)
0.510937 + 0.859618i \(0.329299\pi\)
\(60\) 0 0
\(61\) −3.01356 + 9.27478i −0.385847 + 1.18751i 0.550018 + 0.835153i \(0.314621\pi\)
−0.935864 + 0.352361i \(0.885379\pi\)
\(62\) 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 \(-0.779272\pi\)
−0.769053 + 0.639186i \(0.779272\pi\)
\(68\) 0 0
\(69\) 4.20577 + 3.05567i 0.506315 + 0.367859i
\(70\) 0 0
\(71\) 2.10028 6.46400i 0.249257 0.767135i −0.745650 0.666338i \(-0.767861\pi\)
0.994907 0.100797i \(-0.0321393\pi\)
\(72\) 0 0
\(73\) 8.14293 5.91618i 0.953058 0.692437i 0.00152961 0.999999i \(-0.499513\pi\)
0.951528 + 0.307562i \(0.0995131\pi\)
\(74\) 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 −0.998117 0.0613320i \(-0.980465\pi\)
0.771444 0.636297i \(-0.219535\pi\)
\(80\) 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 \(-0.911258\pi\)
0.939534 + 0.342455i \(0.111258\pi\)
\(84\) 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 0.850901 0.525327i \(-0.176057\pi\)
−0.997172 + 0.0751486i \(0.976057\pi\)
\(98\) 0 0
\(99\) −4.96188 1.63820i −0.498688 0.164646i
\(100\) 0 0
\(101\) 3.12347 + 9.61305i 0.310797 + 0.956534i 0.977450 + 0.211166i \(0.0677261\pi\)
−0.666654 + 0.745368i \(0.732274\pi\)
\(102\) 0 0
\(103\) −3.00254 + 2.18148i −0.295849 + 0.214947i −0.725801 0.687905i \(-0.758531\pi\)
0.429951 + 0.902852i \(0.358531\pi\)
\(104\) 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 \(-0.421275\pi\)
−0.846467 + 0.532442i \(0.821275\pi\)
\(108\) 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 0.911030 0.412341i \(-0.135289\pi\)
−0.110636 + 0.993861i \(0.535289\pi\)
\(114\) 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 \(-0.814526\pi\)
0.998959 + 0.0456181i \(0.0145257\pi\)
\(128\) 0 0
\(129\) −0.585987 0.425744i −0.0515932 0.0374847i
\(130\) 0 0
\(131\) 9.13159 0.797831 0.398915 0.916988i \(-0.369387\pi\)
0.398915 + 0.916988i \(0.369387\pi\)
\(132\) 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 −0.852154 0.523291i \(-0.824704\pi\)
0.996990 + 0.0775326i \(0.0247042\pi\)
\(138\) 0 0
\(139\) −14.3608 + 10.4338i −1.21807 + 0.884979i −0.995938 0.0900374i \(-0.971301\pi\)
−0.222131 + 0.975017i \(0.571301\pi\)
\(140\) 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 0.543008 + 0.839727i \(0.317285\pi\)
−0.932882 + 0.360181i \(0.882715\pi\)
\(150\) 0 0
\(151\) −11.7220 8.51654i −0.953924 0.693067i −0.00219249 0.999998i \(-0.500698\pi\)
−0.951732 + 0.306931i \(0.900698\pi\)
\(152\) 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 0.734210 0.678923i \(-0.237553\pi\)
−0.418810 + 0.908074i \(0.637553\pi\)
\(158\) 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 0.687632 + 0.726059i \(0.258650\pi\)
−0.129539 + 0.991574i \(0.541350\pi\)
\(164\) 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 \(-0.140020\pi\)
−0.982299 + 0.187319i \(0.940020\pi\)
\(168\) 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 −0.109369 0.994001i \(-0.534883\pi\)
−0.979148 + 0.203147i \(0.934883\pi\)
\(174\) 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 \(-0.0713876\pi\)
0.0897674 + 0.995963i \(0.471388\pi\)
\(180\) 0 0
\(181\) −1.48239 + 4.56233i −0.110185 + 0.339116i −0.990912 0.134508i \(-0.957054\pi\)
0.880727 + 0.473624i \(0.157054\pi\)
\(182\) 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 \(-0.838226\pi\)
0.192853 + 0.981228i \(0.438226\pi\)
\(192\) 0 0
\(193\) 1.25252 3.85485i 0.0901581 0.277478i −0.895804 0.444450i \(-0.853399\pi\)
0.985962 + 0.166972i \(0.0533990\pi\)
\(194\) 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 \(-0.785401\pi\)
−0.781218 + 0.624259i \(0.785401\pi\)
\(200\) 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 \(-0.00809556\pi\)
−0.823703 + 0.567022i \(0.808096\pi\)
\(212\) 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 \(-0.181689\pi\)
−0.253826 + 0.967250i \(0.581689\pi\)
\(224\) 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 \(-0.757709\pi\)
0.432280 + 0.901740i \(0.357709\pi\)
\(228\) 0 0
\(229\) 6.45771 + 19.8748i 0.426738 + 1.31336i 0.901320 + 0.433153i \(0.142599\pi\)
−0.474583 + 0.880211i \(0.657401\pi\)
\(230\) 0 0
\(231\) −4.30400 + 5.86539i −0.283182 + 0.385914i
\(232\) 0 0
\(233\) 8.33463 + 25.6513i 0.546020 + 1.68048i 0.718553 + 0.695472i \(0.244805\pi\)
−0.172533 + 0.985004i \(0.555195\pi\)
\(234\) 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 \(-0.0288674\pi\)
0.221614 + 0.975134i \(0.428867\pi\)
\(240\) 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 0.959953 + 0.280163i \(0.0903884\pi\)
−0.611942 + 0.790902i \(0.709612\pi\)
\(252\) 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 0.416281 0.909236i \(-0.363333\pi\)
0.993373 0.114937i \(-0.0366668\pi\)
\(258\) 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 \(-0.348410\pi\)
0.458436 + 0.888728i \(0.348410\pi\)
\(264\) 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 −0.997662 0.0683464i \(-0.978228\pi\)
0.847298 + 0.531117i \(0.178228\pi\)
\(270\) 0 0
\(271\) −15.2170 + 11.0558i −0.924367 + 0.671592i −0.944607 0.328203i \(-0.893557\pi\)
0.0202404 + 0.999795i \(0.493557\pi\)
\(272\) 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 −0.999834 0.0182019i \(-0.994206\pi\)
0.798184 0.602414i \(-0.205794\pi\)
\(278\) 0 0
\(279\) 14.1213 10.2597i 0.845421 0.614234i
\(280\) 0 0
\(281\) −7.45024 + 22.9295i −0.444444 + 1.36786i 0.438648 + 0.898659i \(0.355457\pi\)
−0.883092 + 0.469199i \(0.844543\pi\)
\(282\) 0 0
\(283\) −7.37802 5.36045i −0.438578 0.318646i 0.346492 0.938053i \(-0.387373\pi\)
−0.785070 + 0.619407i \(0.787373\pi\)
\(284\) 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 −0.997576 0.0695907i \(-0.977831\pi\)
−0.242083 + 0.970256i \(0.577831\pi\)
\(294\) 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 \(-0.425189\pi\)
0.232868 + 0.972508i \(0.425189\pi\)
\(308\) 0 0
\(309\) −4.42960 −0.251991
\(310\) 0 0
\(311\) −10.9163 7.93119i −0.619009 0.449736i 0.233566 0.972341i \(-0.424960\pi\)
−0.852575 + 0.522605i \(0.824960\pi\)
\(312\) 0 0
\(313\) 2.42214 7.45457i 0.136907 0.421357i −0.858974 0.512018i \(-0.828898\pi\)
0.995882 + 0.0906610i \(0.0288980\pi\)
\(314\) 0 0
\(315\) 2.34253 1.70195i 0.131987 0.0958938i
\(316\) 0 0
\(317\) 1.95549 + 6.01836i 0.109831 + 0.338025i 0.990834 0.135086i \(-0.0431310\pi\)
−0.881003 + 0.473111i \(0.843131\pi\)
\(318\) 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 \(-0.474394\pi\)
0.0803566 + 0.996766i \(0.474394\pi\)
\(332\) 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 −0.958623 0.284680i \(-0.908113\pi\)
−0.0254842 + 0.999675i \(0.508113\pi\)
\(338\) 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 \(-0.948227\pi\)
0.893521 + 0.449021i \(0.148227\pi\)
\(348\) 0 0
\(349\) 3.34641 + 2.43131i 0.179129 + 0.130145i 0.673737 0.738972i \(-0.264688\pi\)
−0.494608 + 0.869116i \(0.664688\pi\)
\(350\) 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 \(-0.569845\pi\)
0.860989 + 0.508623i \(0.169845\pi\)
\(360\) 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 \(-0.742797\pi\)
0.474036 + 0.880505i \(0.342797\pi\)
\(368\) 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 −0.657604 0.753363i \(-0.728430\pi\)
0.974829 0.222954i \(-0.0715699\pi\)
\(380\) 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 \(-0.161149\pi\)
−0.992561 + 0.121752i \(0.961149\pi\)
\(384\) 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 0.00734201 0.999973i \(-0.497663\pi\)
0.953300 + 0.302026i \(0.0976629\pi\)
\(390\) 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 −0.865998 0.500048i \(-0.833316\pi\)
0.994528 + 0.104474i \(0.0333159\pi\)
\(402\) 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 0.960251 + 0.279137i \(0.0900482\pi\)
−0.612787 + 0.790248i \(0.709952\pi\)
\(410\) 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 \(-0.372657\pi\)
0.389473 + 0.921038i \(0.372657\pi\)
\(420\) 0 0
\(421\) 26.7782 + 19.4555i 1.30509 + 0.948203i 0.999992 0.00411867i \(-0.00131102\pi\)
0.305097 + 0.952321i \(0.401311\pi\)
\(422\) 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 −0.998273 0.0587513i \(-0.981288\pi\)
0.773086 0.634301i \(-0.218712\pi\)
\(432\) 0 0
\(433\) −8.67258 + 6.30100i −0.416778 + 0.302807i −0.776340 0.630314i \(-0.782926\pi\)
0.359562 + 0.933121i \(0.382926\pi\)
\(434\) 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 \(-0.171295\pi\)
0.858663 + 0.512540i \(0.171295\pi\)
\(440\) 0 0
\(441\) 5.70690 0.271757
\(442\) 0 0
\(443\) 2.96042 + 2.15087i 0.140654 + 0.102191i 0.655887 0.754859i \(-0.272295\pi\)
−0.515233 + 0.857050i \(0.672295\pi\)
\(444\) 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 0.990252 0.139287i \(-0.0444812\pi\)
−0.883002 + 0.469370i \(0.844481\pi\)
\(450\) 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 −0.415558 0.909567i \(-0.636414\pi\)
0.870823 0.491596i \(-0.163586\pi\)
\(458\) 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 \(-0.393705\pi\)
0.327764 + 0.944759i \(0.393705\pi\)
\(464\) 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 \(-0.938035\pi\)
0.907438 + 0.420186i \(0.138035\pi\)
\(468\) 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 0.770293 + 0.637690i \(0.220110\pi\)
−0.998005 + 0.0631353i \(0.979890\pi\)
\(480\) 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 \(-0.297071\pi\)
−0.580317 + 0.814391i \(0.697071\pi\)
\(488\) 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 \(-0.613943\pi\)
0.782502 + 0.622648i \(0.213943\pi\)
\(492\) 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 \(-0.490269\pi\)
0.960057 + 0.279804i \(0.0902695\pi\)
\(500\) 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 \(-0.437229\pi\)
−0.872079 + 0.489365i \(0.837229\pi\)
\(504\) 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 −0.271897 0.962326i \(-0.587651\pi\)
−0.999248 + 0.0387861i \(0.987651\pi\)
\(510\) 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 −0.162499 0.986709i \(-0.551956\pi\)
0.888201 + 0.459456i \(0.151956\pi\)
\(522\) 0 0
\(523\) 9.35067 28.7784i 0.408876 1.25839i −0.508739 0.860921i \(-0.669888\pi\)
0.917615 0.397471i \(-0.130112\pi\)
\(524\) 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 0.991487 0.130208i \(-0.0415646\pi\)
−0.878664 + 0.477440i \(0.841565\pi\)
\(542\) 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 \(-0.111997\pi\)
−0.0376810 + 0.999290i \(0.511997\pi\)
\(548\) 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 −0.772582 0.634915i \(-0.781035\pi\)
0.365099 + 0.930969i \(0.381035\pi\)
\(558\) 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 0.813195 + 0.581991i \(0.197726\pi\)
−0.315803 + 0.948825i \(0.602274\pi\)
\(564\) 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 −0.0495152 0.998773i \(-0.515768\pi\)
−0.965191 + 0.261546i \(0.915768\pi\)
\(570\) 0 0
\(571\) −34.1271 −1.42817 −0.714087 0.700057i \(-0.753158\pi\)
−0.714087 + 0.700057i \(0.753158\pi\)
\(572\) 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 −0.981451 0.191713i \(-0.938596\pi\)
0.906697 + 0.421783i \(0.138596\pi\)
\(578\) 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 \(-0.653468\pi\)
0.699360 + 0.714770i \(0.253468\pi\)
\(588\) 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 0.0709098 + 0.997483i \(0.477410\pi\)
−0.643673 + 0.765301i \(0.722590\pi\)
\(600\) 0 0
\(601\) −34.5915 + 25.1322i −1.41101 + 1.02516i −0.417841 + 0.908520i \(0.637213\pi\)
−0.993174 + 0.116642i \(0.962787\pi\)
\(602\) 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 0.811569 + 0.584257i \(0.198614\pi\)
−0.313155 + 0.949702i \(0.601386\pi\)
\(608\) 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 −0.942416 0.334444i \(-0.891452\pi\)
−0.609298 0.792942i \(-0.708548\pi\)
\(614\) 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 \(-0.497660\pi\)
−0.948759 + 0.316000i \(0.897660\pi\)
\(620\) 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 \(-0.636376\pi\)
0.736714 + 0.676204i \(0.236376\pi\)
\(632\) 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 0.996663 + 0.0816296i \(0.0260124\pi\)
0.385620 + 0.922658i \(0.373988\pi\)
\(642\) 0 0
\(643\) −3.20542 + 9.86526i −0.126409 + 0.389048i −0.994155 0.107960i \(-0.965568\pi\)
0.867746 + 0.497008i \(0.165568\pi\)
\(644\) 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 \(-0.156468\pi\)
−0.990663 + 0.136335i \(0.956468\pi\)
\(648\) 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 −0.451111 0.892468i \(-0.648972\pi\)
0.709386 + 0.704820i \(0.248972\pi\)
\(654\) 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 \(-0.576510\pi\)
−0.238055 + 0.971252i \(0.576510\pi\)
\(660\) 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 −0.999127 0.0417717i \(-0.986700\pi\)
0.783758 0.621066i \(-0.213300\pi\)
\(674\) 0 0
\(675\) −4.41802 + 3.20988i −0.170050 + 0.123548i
\(676\) 0 0
\(677\) 5.94644 18.3013i 0.228540 0.703375i −0.769372 0.638800i \(-0.779431\pi\)
0.997913 0.0645747i \(-0.0205691\pi\)
\(678\) 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 \(-0.718472\pi\)
−0.633717 + 0.773565i \(0.718472\pi\)
\(684\) 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 0.792156 + 0.610318i \(0.208958\pi\)
−0.282132 + 0.959376i \(0.591042\pi\)
\(692\) 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 0.708372 0.705840i \(-0.249430\pi\)
−0.452395 + 0.891818i \(0.649430\pi\)
\(702\) 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 −0.948260 0.317495i \(-0.897158\pi\)
0.953777 + 0.300514i \(0.0971582\pi\)
\(710\) 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 \(-0.709885\pi\)
0.562382 + 0.826878i \(0.309885\pi\)
\(720\) 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 \(-0.587065\pi\)
−0.270124 + 0.962826i \(0.587065\pi\)
\(728\) 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 0.278205 0.960522i \(-0.410261\pi\)
0.999481 + 0.0322289i \(0.0102605\pi\)
\(734\) 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 −0.788691 0.614790i \(-0.789241\pi\)
0.276700 0.960956i \(-0.410759\pi\)
\(740\) 0 0
\(741\) 1.51677 1.10200i 0.0557199 0.0404829i
\(742\) 0 0
\(743\) 6.70050 20.6220i 0.245818 0.756549i −0.749683 0.661797i \(-0.769794\pi\)
0.995501 0.0947520i \(-0.0302058\pi\)
\(744\) 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 \(-0.321046\pi\)
−0.639952 + 0.768415i \(0.721046\pi\)
\(752\) 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 0.950951 + 0.309343i \(0.100109\pi\)
−0.587508 + 0.809218i \(0.699891\pi\)
\(758\) 0 0
\(759\) 16.4230 5.25039i 0.596117 0.190577i
\(760\) 0 0
\(761\) −8.16887 25.1412i −0.296121 0.911367i −0.982843 0.184447i \(-0.940951\pi\)
0.686721 0.726921i \(-0.259049\pi\)
\(762\) 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 0.0925439 0.995709i \(-0.470500\pi\)
−0.918378 + 0.395705i \(0.870500\pi\)
\(774\) 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 0.651425 + 0.758713i \(0.274172\pi\)
−0.972974 + 0.230914i \(0.925828\pi\)
\(788\) 0