Properties

Label 1040.2.da.f.881.2
Level $1040$
Weight $2$
Character 1040.881
Analytic conductor $8.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(641,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1040.641");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 520)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.2
Root \(2.79253i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.f.641.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00284 - 1.73697i) q^{3} +1.00000i q^{5} +(-1.48627 - 0.858099i) q^{7} +(-0.511370 + 0.885719i) q^{9} +O(q^{10})\) \(q+(-1.00284 - 1.73697i) q^{3} +1.00000i q^{5} +(-1.48627 - 0.858099i) q^{7} +(-0.511370 + 0.885719i) q^{9} +(4.59199 - 2.65119i) q^{11} +(2.34769 + 2.73649i) q^{13} +(1.73697 - 1.00284i) q^{15} +(0.811344 - 1.40529i) q^{17} +(-1.96681 - 1.13554i) q^{19} +3.44214i q^{21} +(2.52585 + 4.37490i) q^{23} -1.00000 q^{25} -3.96574 q^{27} +(-2.08770 - 3.61600i) q^{29} -8.79183i q^{31} +(-9.21004 - 5.31742i) q^{33} +(0.858099 - 1.48627i) q^{35} +(-0.942563 + 0.544189i) q^{37} +(2.39884 - 6.82211i) q^{39} +(7.86992 - 4.54370i) q^{41} +(4.18560 - 7.24968i) q^{43} +(-0.885719 - 0.511370i) q^{45} +2.45297i q^{47} +(-2.02733 - 3.51144i) q^{49} -3.25459 q^{51} -5.54358 q^{53} +(2.65119 + 4.59199i) q^{55} +4.55505i q^{57} +(-8.57344 - 4.94988i) q^{59} +(0.373308 - 0.646589i) q^{61} +(1.52007 - 0.877612i) q^{63} +(-2.73649 + 2.34769i) q^{65} +(-13.5181 + 7.80468i) q^{67} +(5.06604 - 8.77464i) q^{69} +(-2.13260 - 1.23126i) q^{71} -12.7513i q^{73} +(1.00284 + 1.73697i) q^{75} -9.09991 q^{77} -0.702839 q^{79} +(5.51111 + 9.54553i) q^{81} +3.57032i q^{83} +(1.40529 + 0.811344i) q^{85} +(-4.18725 + 7.25253i) q^{87} +(9.93763 - 5.73750i) q^{89} +(-1.14112 - 6.08171i) q^{91} +(-15.2711 + 8.81679i) q^{93} +(1.13554 - 1.96681i) q^{95} +(12.1902 + 7.03799i) q^{97} +5.42295i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −1.00284 1.73697i −0.578989 1.00284i −0.995596 0.0937516i \(-0.970114\pi\)
0.416607 0.909087i \(-0.363219\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −1.48627 0.858099i −0.561757 0.324331i 0.192093 0.981377i \(-0.438472\pi\)
−0.753851 + 0.657046i \(0.771806\pi\)
\(8\) 0 0
\(9\) −0.511370 + 0.885719i −0.170457 + 0.295240i
\(10\) 0 0
\(11\) 4.59199 2.65119i 1.38454 0.799362i 0.391844 0.920032i \(-0.371837\pi\)
0.992693 + 0.120670i \(0.0385041\pi\)
\(12\) 0 0
\(13\) 2.34769 + 2.73649i 0.651132 + 0.758965i
\(14\) 0 0
\(15\) 1.73697 1.00284i 0.448483 0.258932i
\(16\) 0 0
\(17\) 0.811344 1.40529i 0.196780 0.340833i −0.750703 0.660640i \(-0.770285\pi\)
0.947483 + 0.319808i \(0.103618\pi\)
\(18\) 0 0
\(19\) −1.96681 1.13554i −0.451217 0.260510i 0.257127 0.966378i \(-0.417224\pi\)
−0.708344 + 0.705867i \(0.750557\pi\)
\(20\) 0 0
\(21\) 3.44214i 0.751136i
\(22\) 0 0
\(23\) 2.52585 + 4.37490i 0.526677 + 0.912230i 0.999517 + 0.0310823i \(0.00989541\pi\)
−0.472840 + 0.881148i \(0.656771\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −3.96574 −0.763208
\(28\) 0 0
\(29\) −2.08770 3.61600i −0.387676 0.671475i 0.604460 0.796635i \(-0.293389\pi\)
−0.992137 + 0.125161i \(0.960055\pi\)
\(30\) 0 0
\(31\) 8.79183i 1.57906i −0.613712 0.789530i \(-0.710324\pi\)
0.613712 0.789530i \(-0.289676\pi\)
\(32\) 0 0
\(33\) −9.21004 5.31742i −1.60326 0.925644i
\(34\) 0 0
\(35\) 0.858099 1.48627i 0.145045 0.251226i
\(36\) 0 0
\(37\) −0.942563 + 0.544189i −0.154956 + 0.0894641i −0.575473 0.817821i \(-0.695182\pi\)
0.420517 + 0.907285i \(0.361849\pi\)
\(38\) 0 0
\(39\) 2.39884 6.82211i 0.384121 1.09241i
\(40\) 0 0
\(41\) 7.86992 4.54370i 1.22908 0.709607i 0.262239 0.965003i \(-0.415539\pi\)
0.966837 + 0.255396i \(0.0822058\pi\)
\(42\) 0 0
\(43\) 4.18560 7.24968i 0.638299 1.10557i −0.347507 0.937677i \(-0.612972\pi\)
0.985806 0.167888i \(-0.0536948\pi\)
\(44\) 0 0
\(45\) −0.885719 0.511370i −0.132035 0.0762306i
\(46\) 0 0
\(47\) 2.45297i 0.357802i 0.983867 + 0.178901i \(0.0572542\pi\)
−0.983867 + 0.178901i \(0.942746\pi\)
\(48\) 0 0
\(49\) −2.02733 3.51144i −0.289619 0.501635i
\(50\) 0 0
\(51\) −3.25459 −0.455734
\(52\) 0 0
\(53\) −5.54358 −0.761470 −0.380735 0.924684i \(-0.624329\pi\)
−0.380735 + 0.924684i \(0.624329\pi\)
\(54\) 0 0
\(55\) 2.65119 + 4.59199i 0.357486 + 0.619183i
\(56\) 0 0
\(57\) 4.55505i 0.603331i
\(58\) 0 0
\(59\) −8.57344 4.94988i −1.11617 0.644419i −0.175747 0.984435i \(-0.556234\pi\)
−0.940420 + 0.340016i \(0.889567\pi\)
\(60\) 0 0
\(61\) 0.373308 0.646589i 0.0477972 0.0827872i −0.841137 0.540822i \(-0.818113\pi\)
0.888934 + 0.458035i \(0.151447\pi\)
\(62\) 0 0
\(63\) 1.52007 0.877612i 0.191511 0.110569i
\(64\) 0 0
\(65\) −2.73649 + 2.34769i −0.339419 + 0.291195i
\(66\) 0 0
\(67\) −13.5181 + 7.80468i −1.65150 + 0.953494i −0.675044 + 0.737778i \(0.735875\pi\)
−0.976456 + 0.215716i \(0.930791\pi\)
\(68\) 0 0
\(69\) 5.06604 8.77464i 0.609880 1.05634i
\(70\) 0 0
\(71\) −2.13260 1.23126i −0.253093 0.146123i 0.368087 0.929791i \(-0.380013\pi\)
−0.621180 + 0.783668i \(0.713346\pi\)
\(72\) 0 0
\(73\) 12.7513i 1.49243i −0.665705 0.746215i \(-0.731869\pi\)
0.665705 0.746215i \(-0.268131\pi\)
\(74\) 0 0
\(75\) 1.00284 + 1.73697i 0.115798 + 0.200568i
\(76\) 0 0
\(77\) −9.09991 −1.03703
\(78\) 0 0
\(79\) −0.702839 −0.0790756 −0.0395378 0.999218i \(-0.512589\pi\)
−0.0395378 + 0.999218i \(0.512589\pi\)
\(80\) 0 0
\(81\) 5.51111 + 9.54553i 0.612346 + 1.06061i
\(82\) 0 0
\(83\) 3.57032i 0.391893i 0.980615 + 0.195947i \(0.0627780\pi\)
−0.980615 + 0.195947i \(0.937222\pi\)
\(84\) 0 0
\(85\) 1.40529 + 0.811344i 0.152425 + 0.0880026i
\(86\) 0 0
\(87\) −4.18725 + 7.25253i −0.448920 + 0.777553i
\(88\) 0 0
\(89\) 9.93763 5.73750i 1.05339 0.608173i 0.129791 0.991541i \(-0.458569\pi\)
0.923596 + 0.383368i \(0.125236\pi\)
\(90\) 0 0
\(91\) −1.14112 6.08171i −0.119622 0.637536i
\(92\) 0 0
\(93\) −15.2711 + 8.81679i −1.58354 + 0.914258i
\(94\) 0 0
\(95\) 1.13554 1.96681i 0.116504 0.201790i
\(96\) 0 0
\(97\) 12.1902 + 7.03799i 1.23772 + 0.714600i 0.968628 0.248514i \(-0.0799421\pi\)
0.269095 + 0.963114i \(0.413275\pi\)
\(98\) 0 0
\(99\) 5.42295i 0.545027i
\(100\) 0 0
\(101\) −4.91897 8.51991i −0.489456 0.847763i 0.510470 0.859895i \(-0.329471\pi\)
−0.999926 + 0.0121325i \(0.996138\pi\)
\(102\) 0 0
\(103\) 9.24998 0.911427 0.455714 0.890126i \(-0.349384\pi\)
0.455714 + 0.890126i \(0.349384\pi\)
\(104\) 0 0
\(105\) −3.44214 −0.335918
\(106\) 0 0
\(107\) −0.260938 0.451957i −0.0252258 0.0436923i 0.853137 0.521687i \(-0.174697\pi\)
−0.878363 + 0.477995i \(0.841364\pi\)
\(108\) 0 0
\(109\) 5.45250i 0.522254i 0.965304 + 0.261127i \(0.0840942\pi\)
−0.965304 + 0.261127i \(0.915906\pi\)
\(110\) 0 0
\(111\) 1.89048 + 1.09147i 0.179436 + 0.103597i
\(112\) 0 0
\(113\) 6.02393 10.4338i 0.566684 0.981525i −0.430207 0.902730i \(-0.641559\pi\)
0.996891 0.0787949i \(-0.0251072\pi\)
\(114\) 0 0
\(115\) −4.37490 + 2.52585i −0.407962 + 0.235537i
\(116\) 0 0
\(117\) −3.62430 + 0.680035i −0.335066 + 0.0628693i
\(118\) 0 0
\(119\) −2.41175 + 1.39243i −0.221085 + 0.127644i
\(120\) 0 0
\(121\) 8.55756 14.8221i 0.777960 1.34747i
\(122\) 0 0
\(123\) −15.7845 9.11320i −1.42324 0.821710i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 2.46780 + 4.27436i 0.218982 + 0.379288i 0.954497 0.298220i \(-0.0963930\pi\)
−0.735515 + 0.677508i \(0.763060\pi\)
\(128\) 0 0
\(129\) −16.7899 −1.47827
\(130\) 0 0
\(131\) −11.9892 −1.04750 −0.523749 0.851872i \(-0.675467\pi\)
−0.523749 + 0.851872i \(0.675467\pi\)
\(132\) 0 0
\(133\) 1.94881 + 3.37543i 0.168983 + 0.292687i
\(134\) 0 0
\(135\) 3.96574i 0.341317i
\(136\) 0 0
\(137\) −6.49042 3.74724i −0.554514 0.320149i 0.196427 0.980518i \(-0.437066\pi\)
−0.750940 + 0.660370i \(0.770400\pi\)
\(138\) 0 0
\(139\) 0.720969 1.24876i 0.0611518 0.105918i −0.833829 0.552023i \(-0.813856\pi\)
0.894981 + 0.446105i \(0.147189\pi\)
\(140\) 0 0
\(141\) 4.26072 2.45993i 0.358818 0.207163i
\(142\) 0 0
\(143\) 18.0355 + 6.34175i 1.50820 + 0.530324i
\(144\) 0 0
\(145\) 3.61600 2.08770i 0.300293 0.173374i
\(146\) 0 0
\(147\) −4.06618 + 7.04282i −0.335373 + 0.580882i
\(148\) 0 0
\(149\) 2.05708 + 1.18765i 0.168522 + 0.0972964i 0.581889 0.813268i \(-0.302314\pi\)
−0.413367 + 0.910565i \(0.635647\pi\)
\(150\) 0 0
\(151\) 22.4022i 1.82307i 0.411226 + 0.911533i \(0.365101\pi\)
−0.411226 + 0.911533i \(0.634899\pi\)
\(152\) 0 0
\(153\) 0.829794 + 1.43725i 0.0670849 + 0.116194i
\(154\) 0 0
\(155\) 8.79183 0.706177
\(156\) 0 0
\(157\) 4.85797 0.387708 0.193854 0.981030i \(-0.437901\pi\)
0.193854 + 0.981030i \(0.437901\pi\)
\(158\) 0 0
\(159\) 5.55932 + 9.62902i 0.440883 + 0.763631i
\(160\) 0 0
\(161\) 8.66972i 0.683270i
\(162\) 0 0
\(163\) 18.7808 + 10.8431i 1.47103 + 0.849299i 0.999471 0.0325366i \(-0.0103585\pi\)
0.471558 + 0.881835i \(0.343692\pi\)
\(164\) 0 0
\(165\) 5.31742 9.21004i 0.413961 0.717001i
\(166\) 0 0
\(167\) 6.73636 3.88924i 0.521275 0.300958i −0.216181 0.976353i \(-0.569360\pi\)
0.737456 + 0.675395i \(0.236027\pi\)
\(168\) 0 0
\(169\) −1.97672 + 12.8488i −0.152055 + 0.988372i
\(170\) 0 0
\(171\) 2.01154 1.16136i 0.153826 0.0888115i
\(172\) 0 0
\(173\) 4.56690 7.91010i 0.347215 0.601394i −0.638539 0.769590i \(-0.720461\pi\)
0.985754 + 0.168196i \(0.0537942\pi\)
\(174\) 0 0
\(175\) 1.48627 + 0.858099i 0.112351 + 0.0648662i
\(176\) 0 0
\(177\) 19.8557i 1.49245i
\(178\) 0 0
\(179\) 6.19014 + 10.7216i 0.462673 + 0.801373i 0.999093 0.0425782i \(-0.0135572\pi\)
−0.536420 + 0.843951i \(0.680224\pi\)
\(180\) 0 0
\(181\) 25.9739 1.93062 0.965311 0.261101i \(-0.0840857\pi\)
0.965311 + 0.261101i \(0.0840857\pi\)
\(182\) 0 0
\(183\) −1.49747 −0.110696
\(184\) 0 0
\(185\) −0.544189 0.942563i −0.0400096 0.0692986i
\(186\) 0 0
\(187\) 8.60409i 0.629194i
\(188\) 0 0
\(189\) 5.89417 + 3.40300i 0.428738 + 0.247532i
\(190\) 0 0
\(191\) 4.32834 7.49691i 0.313188 0.542457i −0.665863 0.746074i \(-0.731936\pi\)
0.979051 + 0.203617i \(0.0652697\pi\)
\(192\) 0 0
\(193\) −10.7967 + 6.23348i −0.777164 + 0.448696i −0.835424 0.549606i \(-0.814778\pi\)
0.0582602 + 0.998301i \(0.481445\pi\)
\(194\) 0 0
\(195\) 6.82211 + 2.39884i 0.488542 + 0.171784i
\(196\) 0 0
\(197\) −18.7568 + 10.8292i −1.33637 + 0.771551i −0.986267 0.165162i \(-0.947185\pi\)
−0.350099 + 0.936713i \(0.613852\pi\)
\(198\) 0 0
\(199\) 10.1999 17.6668i 0.723052 1.25236i −0.236719 0.971578i \(-0.576072\pi\)
0.959771 0.280785i \(-0.0905947\pi\)
\(200\) 0 0
\(201\) 27.1130 + 15.6537i 1.91240 + 1.10413i
\(202\) 0 0
\(203\) 7.16581i 0.502941i
\(204\) 0 0
\(205\) 4.54370 + 7.86992i 0.317346 + 0.549659i
\(206\) 0 0
\(207\) −5.16658 −0.359102
\(208\) 0 0
\(209\) −12.0421 −0.832969
\(210\) 0 0
\(211\) 1.40805 + 2.43882i 0.0969345 + 0.167895i 0.910414 0.413698i \(-0.135763\pi\)
−0.813480 + 0.581593i \(0.802430\pi\)
\(212\) 0 0
\(213\) 4.93901i 0.338415i
\(214\) 0 0
\(215\) 7.24968 + 4.18560i 0.494424 + 0.285456i
\(216\) 0 0
\(217\) −7.54426 + 13.0670i −0.512138 + 0.887049i
\(218\) 0 0
\(219\) −22.1486 + 12.7875i −1.49667 + 0.864101i
\(220\) 0 0
\(221\) 5.75034 1.07895i 0.386810 0.0725780i
\(222\) 0 0
\(223\) −1.26128 + 0.728200i −0.0844615 + 0.0487639i −0.541636 0.840613i \(-0.682195\pi\)
0.457174 + 0.889377i \(0.348862\pi\)
\(224\) 0 0
\(225\) 0.511370 0.885719i 0.0340914 0.0590480i
\(226\) 0 0
\(227\) −2.55700 1.47629i −0.169714 0.0979845i 0.412737 0.910850i \(-0.364573\pi\)
−0.582451 + 0.812866i \(0.697906\pi\)
\(228\) 0 0
\(229\) 11.4087i 0.753906i 0.926232 + 0.376953i \(0.123028\pi\)
−0.926232 + 0.376953i \(0.876972\pi\)
\(230\) 0 0
\(231\) 9.12574 + 15.8063i 0.600430 + 1.03998i
\(232\) 0 0
\(233\) −20.9789 −1.37438 −0.687188 0.726480i \(-0.741155\pi\)
−0.687188 + 0.726480i \(0.741155\pi\)
\(234\) 0 0
\(235\) −2.45297 −0.160014
\(236\) 0 0
\(237\) 0.704834 + 1.22081i 0.0457839 + 0.0793001i
\(238\) 0 0
\(239\) 18.5331i 1.19881i −0.800447 0.599403i \(-0.795405\pi\)
0.800447 0.599403i \(-0.204595\pi\)
\(240\) 0 0
\(241\) 15.0668 + 8.69885i 0.970541 + 0.560342i 0.899401 0.437124i \(-0.144003\pi\)
0.0711396 + 0.997466i \(0.477336\pi\)
\(242\) 0 0
\(243\) 5.10489 8.84194i 0.327479 0.567211i
\(244\) 0 0
\(245\) 3.51144 2.02733i 0.224338 0.129522i
\(246\) 0 0
\(247\) −1.51007 8.04804i −0.0960836 0.512085i
\(248\) 0 0
\(249\) 6.20153 3.58045i 0.393006 0.226902i
\(250\) 0 0
\(251\) −2.59642 + 4.49713i −0.163885 + 0.283857i −0.936259 0.351311i \(-0.885736\pi\)
0.772374 + 0.635168i \(0.219069\pi\)
\(252\) 0 0
\(253\) 23.1974 + 13.3930i 1.45841 + 0.842011i
\(254\) 0 0
\(255\) 3.25459i 0.203810i
\(256\) 0 0
\(257\) −8.06865 13.9753i −0.503309 0.871756i −0.999993 0.00382494i \(-0.998782\pi\)
0.496684 0.867932i \(-0.334551\pi\)
\(258\) 0 0
\(259\) 1.86787 0.116064
\(260\) 0 0
\(261\) 4.27035 0.264328
\(262\) 0 0
\(263\) 2.08186 + 3.60589i 0.128373 + 0.222349i 0.923046 0.384689i \(-0.125691\pi\)
−0.794673 + 0.607037i \(0.792358\pi\)
\(264\) 0 0
\(265\) 5.54358i 0.340540i
\(266\) 0 0
\(267\) −19.9317 11.5076i −1.21980 0.704251i
\(268\) 0 0
\(269\) −14.1797 + 24.5599i −0.864550 + 1.49744i 0.00294289 + 0.999996i \(0.499063\pi\)
−0.867493 + 0.497449i \(0.834270\pi\)
\(270\) 0 0
\(271\) 17.1277 9.88867i 1.04043 0.600694i 0.120476 0.992716i \(-0.461558\pi\)
0.919956 + 0.392023i \(0.128224\pi\)
\(272\) 0 0
\(273\) −9.41936 + 8.08107i −0.570086 + 0.489088i
\(274\) 0 0
\(275\) −4.59199 + 2.65119i −0.276907 + 0.159872i
\(276\) 0 0
\(277\) 13.9236 24.1164i 0.836589 1.44901i −0.0561409 0.998423i \(-0.517880\pi\)
0.892730 0.450592i \(-0.148787\pi\)
\(278\) 0 0
\(279\) 7.78710 + 4.49588i 0.466201 + 0.269161i
\(280\) 0 0
\(281\) 23.0773i 1.37668i 0.725390 + 0.688338i \(0.241659\pi\)
−0.725390 + 0.688338i \(0.758341\pi\)
\(282\) 0 0
\(283\) −10.7995 18.7053i −0.641963 1.11191i −0.984994 0.172588i \(-0.944787\pi\)
0.343031 0.939324i \(-0.388546\pi\)
\(284\) 0 0
\(285\) −4.55505 −0.269818
\(286\) 0 0
\(287\) −15.5958 −0.920590
\(288\) 0 0
\(289\) 7.18344 + 12.4421i 0.422555 + 0.731887i
\(290\) 0 0
\(291\) 28.2319i 1.65498i
\(292\) 0 0
\(293\) 11.0994 + 6.40827i 0.648437 + 0.374375i 0.787857 0.615858i \(-0.211191\pi\)
−0.139420 + 0.990233i \(0.544524\pi\)
\(294\) 0 0
\(295\) 4.94988 8.57344i 0.288193 0.499165i
\(296\) 0 0
\(297\) −18.2106 + 10.5139i −1.05669 + 0.610080i
\(298\) 0 0
\(299\) −6.04195 + 17.1829i −0.349415 + 0.993711i
\(300\) 0 0
\(301\) −12.4419 + 7.18332i −0.717138 + 0.414040i
\(302\) 0 0
\(303\) −9.86587 + 17.0882i −0.566780 + 0.981691i
\(304\) 0 0
\(305\) 0.646589 + 0.373308i 0.0370236 + 0.0213756i
\(306\) 0 0
\(307\) 6.39172i 0.364795i 0.983225 + 0.182397i \(0.0583858\pi\)
−0.983225 + 0.182397i \(0.941614\pi\)
\(308\) 0 0
\(309\) −9.27623 16.0669i −0.527707 0.914014i
\(310\) 0 0
\(311\) 20.3701 1.15508 0.577540 0.816362i \(-0.304013\pi\)
0.577540 + 0.816362i \(0.304013\pi\)
\(312\) 0 0
\(313\) −1.16374 −0.0657786 −0.0328893 0.999459i \(-0.510471\pi\)
−0.0328893 + 0.999459i \(0.510471\pi\)
\(314\) 0 0
\(315\) 0.877612 + 1.52007i 0.0494479 + 0.0856462i
\(316\) 0 0
\(317\) 2.24705i 0.126207i 0.998007 + 0.0631033i \(0.0200998\pi\)
−0.998007 + 0.0631033i \(0.979900\pi\)
\(318\) 0 0
\(319\) −19.1734 11.0698i −1.07350 0.619787i
\(320\) 0 0
\(321\) −0.523356 + 0.906480i −0.0292109 + 0.0505948i
\(322\) 0 0
\(323\) −3.19152 + 1.84262i −0.177581 + 0.102526i
\(324\) 0 0
\(325\) −2.34769 2.73649i −0.130226 0.151793i
\(326\) 0 0
\(327\) 9.47081 5.46797i 0.523737 0.302380i
\(328\) 0 0
\(329\) 2.10489 3.64577i 0.116046 0.200998i
\(330\) 0 0
\(331\) 14.2060 + 8.20183i 0.780832 + 0.450813i 0.836725 0.547623i \(-0.184467\pi\)
−0.0558933 + 0.998437i \(0.517801\pi\)
\(332\) 0 0
\(333\) 1.11313i 0.0609990i
\(334\) 0 0
\(335\) −7.80468 13.5181i −0.426415 0.738573i
\(336\) 0 0
\(337\) 0.463522 0.0252497 0.0126248 0.999920i \(-0.495981\pi\)
0.0126248 + 0.999920i \(0.495981\pi\)
\(338\) 0 0
\(339\) −24.1641 −1.31241
\(340\) 0 0
\(341\) −23.3088 40.3720i −1.26224 2.18627i
\(342\) 0 0
\(343\) 18.9720i 1.02439i
\(344\) 0 0
\(345\) 8.77464 + 5.06604i 0.472411 + 0.272747i
\(346\) 0 0
\(347\) 8.94212 15.4882i 0.480038 0.831451i −0.519700 0.854349i \(-0.673956\pi\)
0.999738 + 0.0228985i \(0.00728947\pi\)
\(348\) 0 0
\(349\) −11.7299 + 6.77227i −0.627888 + 0.362511i −0.779934 0.625862i \(-0.784747\pi\)
0.152046 + 0.988373i \(0.451414\pi\)
\(350\) 0 0
\(351\) −9.31033 10.8522i −0.496949 0.579248i
\(352\) 0 0
\(353\) −30.3096 + 17.4992i −1.61322 + 0.931390i −0.624597 + 0.780947i \(0.714737\pi\)
−0.988619 + 0.150443i \(0.951930\pi\)
\(354\) 0 0
\(355\) 1.23126 2.13260i 0.0653483 0.113187i
\(356\) 0 0
\(357\) 4.83720 + 2.79276i 0.256012 + 0.147808i
\(358\) 0 0
\(359\) 32.9967i 1.74150i 0.491725 + 0.870750i \(0.336366\pi\)
−0.491725 + 0.870750i \(0.663634\pi\)
\(360\) 0 0
\(361\) −6.92110 11.9877i −0.364269 0.630932i
\(362\) 0 0
\(363\) −34.3274 −1.80172
\(364\) 0 0
\(365\) 12.7513 0.667435
\(366\) 0 0
\(367\) 13.5804 + 23.5219i 0.708889 + 1.22783i 0.965270 + 0.261256i \(0.0841367\pi\)
−0.256380 + 0.966576i \(0.582530\pi\)
\(368\) 0 0
\(369\) 9.29406i 0.483829i
\(370\) 0 0
\(371\) 8.23926 + 4.75694i 0.427761 + 0.246968i
\(372\) 0 0
\(373\) 6.94659 12.0319i 0.359681 0.622986i −0.628226 0.778031i \(-0.716219\pi\)
0.987907 + 0.155045i \(0.0495522\pi\)
\(374\) 0 0
\(375\) −1.73697 + 1.00284i −0.0896966 + 0.0517864i
\(376\) 0 0
\(377\) 4.99387 14.2022i 0.257197 0.731451i
\(378\) 0 0
\(379\) 7.37323 4.25694i 0.378738 0.218664i −0.298531 0.954400i \(-0.596497\pi\)
0.677269 + 0.735736i \(0.263163\pi\)
\(380\) 0 0
\(381\) 4.94962 8.57298i 0.253576 0.439207i
\(382\) 0 0
\(383\) −15.0492 8.68865i −0.768977 0.443969i 0.0635326 0.997980i \(-0.479763\pi\)
−0.832510 + 0.554011i \(0.813097\pi\)
\(384\) 0 0
\(385\) 9.09991i 0.463775i
\(386\) 0 0
\(387\) 4.28079 + 7.41454i 0.217605 + 0.376902i
\(388\) 0 0
\(389\) −0.820966 −0.0416246 −0.0208123 0.999783i \(-0.506625\pi\)
−0.0208123 + 0.999783i \(0.506625\pi\)
\(390\) 0 0
\(391\) 8.19734 0.414557
\(392\) 0 0
\(393\) 12.0232 + 20.8248i 0.606490 + 1.05047i
\(394\) 0 0
\(395\) 0.702839i 0.0353637i
\(396\) 0 0
\(397\) −27.9339 16.1276i −1.40196 0.809422i −0.407367 0.913265i \(-0.633553\pi\)
−0.994594 + 0.103842i \(0.966886\pi\)
\(398\) 0 0
\(399\) 3.90868 6.77003i 0.195679 0.338926i
\(400\) 0 0
\(401\) −31.9989 + 18.4746i −1.59795 + 0.922577i −0.606069 + 0.795412i \(0.707254\pi\)
−0.991882 + 0.127165i \(0.959412\pi\)
\(402\) 0 0
\(403\) 24.0587 20.6405i 1.19845 1.02818i
\(404\) 0 0
\(405\) −9.54553 + 5.51111i −0.474321 + 0.273849i
\(406\) 0 0
\(407\) −2.88549 + 4.99782i −0.143028 + 0.247733i
\(408\) 0 0
\(409\) 1.04612 + 0.603980i 0.0517275 + 0.0298649i 0.525641 0.850707i \(-0.323826\pi\)
−0.473913 + 0.880572i \(0.657159\pi\)
\(410\) 0 0
\(411\) 15.0315i 0.741450i
\(412\) 0 0
\(413\) 8.49497 + 14.7137i 0.418010 + 0.724015i
\(414\) 0 0
\(415\) −3.57032 −0.175260
\(416\) 0 0
\(417\) −2.89206 −0.141625
\(418\) 0 0
\(419\) 16.9479 + 29.3547i 0.827960 + 1.43407i 0.899636 + 0.436641i \(0.143832\pi\)
−0.0716752 + 0.997428i \(0.522835\pi\)
\(420\) 0 0
\(421\) 9.03483i 0.440330i −0.975463 0.220165i \(-0.929340\pi\)
0.975463 0.220165i \(-0.0706597\pi\)
\(422\) 0 0
\(423\) −2.17264 1.25437i −0.105637 0.0609898i
\(424\) 0 0
\(425\) −0.811344 + 1.40529i −0.0393560 + 0.0681665i
\(426\) 0 0
\(427\) −1.10967 + 0.640671i −0.0537009 + 0.0310042i
\(428\) 0 0
\(429\) −7.07126 37.6868i −0.341404 1.81954i
\(430\) 0 0
\(431\) 2.41688 1.39539i 0.116417 0.0672135i −0.440661 0.897674i \(-0.645256\pi\)
0.557078 + 0.830460i \(0.311922\pi\)
\(432\) 0 0
\(433\) 7.74573 13.4160i 0.372236 0.644731i −0.617673 0.786435i \(-0.711925\pi\)
0.989909 + 0.141703i \(0.0452579\pi\)
\(434\) 0 0
\(435\) −7.25253 4.18725i −0.347732 0.200763i
\(436\) 0 0
\(437\) 11.4728i 0.548819i
\(438\) 0 0
\(439\) −2.88191 4.99161i −0.137546 0.238236i 0.789021 0.614366i \(-0.210588\pi\)
−0.926567 + 0.376129i \(0.877255\pi\)
\(440\) 0 0
\(441\) 4.14687 0.197470
\(442\) 0 0
\(443\) 8.98705 0.426987 0.213494 0.976944i \(-0.431516\pi\)
0.213494 + 0.976944i \(0.431516\pi\)
\(444\) 0 0
\(445\) 5.73750 + 9.93763i 0.271983 + 0.471089i
\(446\) 0 0
\(447\) 4.76410i 0.225334i
\(448\) 0 0
\(449\) 23.9604 + 13.8336i 1.13076 + 0.652846i 0.944126 0.329584i \(-0.106908\pi\)
0.186635 + 0.982429i \(0.440242\pi\)
\(450\) 0 0
\(451\) 24.0924 41.7292i 1.13447 1.96495i
\(452\) 0 0
\(453\) 38.9119 22.4658i 1.82824 1.05554i
\(454\) 0 0
\(455\) 6.08171 1.14112i 0.285115 0.0534967i
\(456\) 0 0
\(457\) 33.8839 19.5629i 1.58502 0.915112i 0.590910 0.806737i \(-0.298769\pi\)
0.994110 0.108374i \(-0.0345645\pi\)
\(458\) 0 0
\(459\) −3.21758 + 5.57302i −0.150184 + 0.260126i
\(460\) 0 0
\(461\) −2.48917 1.43712i −0.115932 0.0669334i 0.440913 0.897550i \(-0.354655\pi\)
−0.556845 + 0.830617i \(0.687988\pi\)
\(462\) 0 0
\(463\) 21.5250i 1.00035i 0.865924 + 0.500176i \(0.166731\pi\)
−0.865924 + 0.500176i \(0.833269\pi\)
\(464\) 0 0
\(465\) −8.81679 15.2711i −0.408869 0.708181i
\(466\) 0 0
\(467\) −27.3600 −1.26607 −0.633035 0.774123i \(-0.718191\pi\)
−0.633035 + 0.774123i \(0.718191\pi\)
\(468\) 0 0
\(469\) 26.7888 1.23699
\(470\) 0 0
\(471\) −4.87176 8.43813i −0.224479 0.388809i
\(472\) 0 0
\(473\) 44.3872i 2.04093i
\(474\) 0 0
\(475\) 1.96681 + 1.13554i 0.0902435 + 0.0521021i
\(476\) 0 0
\(477\) 2.83482 4.91006i 0.129798 0.224816i
\(478\) 0 0
\(479\) 25.4251 14.6792i 1.16170 0.670708i 0.209990 0.977704i \(-0.432657\pi\)
0.951711 + 0.306995i \(0.0993236\pi\)
\(480\) 0 0
\(481\) −3.70201 1.30172i −0.168797 0.0593535i
\(482\) 0 0
\(483\) −15.0590 + 8.69433i −0.685209 + 0.395606i
\(484\) 0 0
\(485\) −7.03799 + 12.1902i −0.319579 + 0.553527i
\(486\) 0 0
\(487\) 5.39501 + 3.11481i 0.244471 + 0.141146i 0.617230 0.786783i \(-0.288255\pi\)
−0.372759 + 0.927928i \(0.621588\pi\)
\(488\) 0 0
\(489\) 43.4956i 1.96694i
\(490\) 0 0
\(491\) −7.30361 12.6502i −0.329607 0.570897i 0.652827 0.757507i \(-0.273583\pi\)
−0.982434 + 0.186611i \(0.940250\pi\)
\(492\) 0 0
\(493\) −6.77537 −0.305147
\(494\) 0 0
\(495\) −5.42295 −0.243743
\(496\) 0 0
\(497\) 2.11308 + 3.65996i 0.0947846 + 0.164172i
\(498\) 0 0
\(499\) 0.958620i 0.0429137i 0.999770 + 0.0214569i \(0.00683046\pi\)
−0.999770 + 0.0214569i \(0.993170\pi\)
\(500\) 0 0
\(501\) −13.5110 7.80055i −0.603625 0.348503i
\(502\) 0 0
\(503\) −10.8418 + 18.7786i −0.483413 + 0.837295i −0.999819 0.0190488i \(-0.993936\pi\)
0.516406 + 0.856344i \(0.327270\pi\)
\(504\) 0 0
\(505\) 8.51991 4.91897i 0.379131 0.218891i
\(506\) 0 0
\(507\) 24.3003 9.45181i 1.07922 0.419770i
\(508\) 0 0
\(509\) −24.6912 + 14.2554i −1.09442 + 0.631862i −0.934749 0.355309i \(-0.884376\pi\)
−0.159668 + 0.987171i \(0.551042\pi\)
\(510\) 0 0
\(511\) −10.9419 + 18.9519i −0.484041 + 0.838384i
\(512\) 0 0
\(513\) 7.79987 + 4.50325i 0.344373 + 0.198824i
\(514\) 0 0
\(515\) 9.24998i 0.407603i
\(516\) 0 0
\(517\) 6.50327 + 11.2640i 0.286013 + 0.495390i
\(518\) 0 0
\(519\) −18.3194 −0.804134
\(520\) 0 0
\(521\) 7.39789 0.324107 0.162054 0.986782i \(-0.448188\pi\)
0.162054 + 0.986782i \(0.448188\pi\)
\(522\) 0 0
\(523\) 5.27191 + 9.13121i 0.230524 + 0.399280i 0.957963 0.286893i \(-0.0926225\pi\)
−0.727438 + 0.686173i \(0.759289\pi\)
\(524\) 0 0
\(525\) 3.44214i 0.150227i
\(526\) 0 0
\(527\) −12.3551 7.13320i −0.538195 0.310727i
\(528\) 0 0
\(529\) −1.25985 + 2.18213i −0.0547763 + 0.0948753i
\(530\) 0 0
\(531\) 8.76841 5.06244i 0.380516 0.219691i
\(532\) 0 0
\(533\) 30.9099 + 10.8687i 1.33886 + 0.470777i
\(534\) 0 0
\(535\) 0.451957 0.260938i 0.0195398 0.0112813i
\(536\) 0 0
\(537\) 12.4154 21.5041i 0.535765 0.927972i
\(538\) 0 0
\(539\) −18.6190 10.7497i −0.801976 0.463021i
\(540\) 0 0
\(541\) 37.8467i 1.62715i 0.581457 + 0.813577i \(0.302483\pi\)
−0.581457 + 0.813577i \(0.697517\pi\)
\(542\) 0 0
\(543\) −26.0476 45.1158i −1.11781 1.93610i
\(544\) 0 0
\(545\) −5.45250 −0.233559
\(546\) 0 0
\(547\) −7.38183 −0.315624 −0.157812 0.987469i \(-0.550444\pi\)
−0.157812 + 0.987469i \(0.550444\pi\)
\(548\) 0 0
\(549\) 0.381798 + 0.661293i 0.0162947 + 0.0282233i
\(550\) 0 0
\(551\) 9.48265i 0.403975i
\(552\) 0 0
\(553\) 1.04461 + 0.603105i 0.0444213 + 0.0256467i
\(554\) 0 0
\(555\) −1.09147 + 1.89048i −0.0463302 + 0.0802462i
\(556\) 0 0
\(557\) 16.3597 9.44530i 0.693185 0.400210i −0.111619 0.993751i \(-0.535604\pi\)
0.804804 + 0.593541i \(0.202270\pi\)
\(558\) 0 0
\(559\) 29.6651 5.56614i 1.25470 0.235423i
\(560\) 0 0
\(561\) −14.9450 + 8.62852i −0.630980 + 0.364296i
\(562\) 0 0
\(563\) 0.984449 1.70512i 0.0414896 0.0718620i −0.844535 0.535500i \(-0.820123\pi\)
0.886024 + 0.463638i \(0.153456\pi\)
\(564\) 0 0
\(565\) 10.4338 + 6.02393i 0.438951 + 0.253429i
\(566\) 0 0
\(567\) 18.9163i 0.794410i
\(568\) 0 0
\(569\) 6.74724 + 11.6866i 0.282859 + 0.489926i 0.972088 0.234618i \(-0.0753838\pi\)
−0.689229 + 0.724544i \(0.742050\pi\)
\(570\) 0 0
\(571\) −11.8340 −0.495236 −0.247618 0.968858i \(-0.579648\pi\)
−0.247618 + 0.968858i \(0.579648\pi\)
\(572\) 0 0
\(573\) −17.3625 −0.725330
\(574\) 0 0
\(575\) −2.52585 4.37490i −0.105335 0.182446i
\(576\) 0 0
\(577\) 5.86318i 0.244087i −0.992525 0.122044i \(-0.961055\pi\)
0.992525 0.122044i \(-0.0389448\pi\)
\(578\) 0 0
\(579\) 21.6547 + 12.5024i 0.899939 + 0.519580i
\(580\) 0 0
\(581\) 3.06369 5.30646i 0.127103 0.220149i
\(582\) 0 0
\(583\) −25.4561 + 14.6971i −1.05428 + 0.608690i
\(584\) 0 0
\(585\) −0.680035 3.62430i −0.0281160 0.149846i
\(586\) 0 0
\(587\) 34.3418 19.8273i 1.41744 0.818359i 0.421366 0.906891i \(-0.361551\pi\)
0.996073 + 0.0885314i \(0.0282173\pi\)
\(588\) 0 0
\(589\) −9.98346 + 17.2919i −0.411361 + 0.712499i
\(590\) 0 0
\(591\) 37.6201 + 21.7199i 1.54748 + 0.893439i
\(592\) 0 0
\(593\) 9.39484i 0.385800i −0.981218 0.192900i \(-0.938211\pi\)
0.981218 0.192900i \(-0.0617893\pi\)
\(594\) 0 0
\(595\) −1.39243 2.41175i −0.0570839 0.0988722i
\(596\) 0 0
\(597\) −40.9154 −1.67456
\(598\) 0 0
\(599\) −40.7504 −1.66502 −0.832508 0.554013i \(-0.813096\pi\)
−0.832508 + 0.554013i \(0.813096\pi\)
\(600\) 0 0
\(601\) −11.9231 20.6514i −0.486353 0.842388i 0.513524 0.858075i \(-0.328340\pi\)
−0.999877 + 0.0156872i \(0.995006\pi\)
\(602\) 0 0
\(603\) 15.9643i 0.650118i
\(604\) 0 0
\(605\) 14.8221 + 8.55756i 0.602606 + 0.347914i
\(606\) 0 0
\(607\) −21.5955 + 37.4045i −0.876535 + 1.51820i −0.0214172 + 0.999771i \(0.506818\pi\)
−0.855118 + 0.518433i \(0.826516\pi\)
\(608\) 0 0
\(609\) 12.4468 7.18615i 0.504369 0.291197i
\(610\) 0 0
\(611\) −6.71251 + 5.75880i −0.271559 + 0.232976i
\(612\) 0 0
\(613\) −18.1727 + 10.4920i −0.733990 + 0.423769i −0.819880 0.572535i \(-0.805960\pi\)
0.0858899 + 0.996305i \(0.472627\pi\)
\(614\) 0 0
\(615\) 9.11320 15.7845i 0.367480 0.636494i
\(616\) 0 0
\(617\) −36.5250 21.0877i −1.47044 0.848960i −0.470992 0.882138i \(-0.656104\pi\)
−0.999449 + 0.0331780i \(0.989437\pi\)
\(618\) 0 0
\(619\) 0.238595i 0.00958994i 0.999989 + 0.00479497i \(0.00152629\pi\)
−0.999989 + 0.00479497i \(0.998474\pi\)
\(620\) 0 0
\(621\) −10.0169 17.3497i −0.401964 0.696221i
\(622\) 0 0
\(623\) −19.6933 −0.788997
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 12.0763 + 20.9167i 0.482280 + 0.835333i
\(628\) 0 0
\(629\) 1.76610i 0.0704189i
\(630\) 0 0
\(631\) −6.56681 3.79135i −0.261420 0.150931i 0.363562 0.931570i \(-0.381561\pi\)
−0.624982 + 0.780639i \(0.714894\pi\)
\(632\) 0 0
\(633\) 2.82410 4.89149i 0.112248 0.194419i
\(634\) 0 0
\(635\) −4.27436 + 2.46780i −0.169623 + 0.0979318i
\(636\) 0 0
\(637\) 4.84947 13.7915i 0.192143 0.546441i
\(638\) 0 0
\(639\) 2.18110 1.25926i 0.0862828 0.0498154i
\(640\) 0 0
\(641\) 18.0317 31.2318i 0.712210 1.23358i −0.251816 0.967775i \(-0.581028\pi\)
0.964026 0.265808i \(-0.0856388\pi\)
\(642\) 0 0
\(643\) −10.7462 6.20431i −0.423788 0.244674i 0.272909 0.962040i \(-0.412014\pi\)
−0.696697 + 0.717366i \(0.745348\pi\)
\(644\) 0 0
\(645\) 16.7899i 0.661103i
\(646\) 0 0
\(647\) −3.66854 6.35409i −0.144225 0.249805i 0.784858 0.619675i \(-0.212736\pi\)
−0.929084 + 0.369870i \(0.879402\pi\)
\(648\) 0 0
\(649\) −52.4922 −2.06050
\(650\) 0 0
\(651\) 30.2627 1.18609
\(652\) 0 0
\(653\) −6.04754 10.4746i −0.236659 0.409905i 0.723095 0.690749i \(-0.242719\pi\)
−0.959753 + 0.280844i \(0.909386\pi\)
\(654\) 0 0
\(655\) 11.9892i 0.468456i
\(656\) 0 0
\(657\) 11.2941 + 6.52065i 0.440625 + 0.254395i
\(658\) 0 0
\(659\) −10.9871 + 19.0302i −0.427997 + 0.741313i −0.996695 0.0812334i \(-0.974114\pi\)
0.568698 + 0.822547i \(0.307447\pi\)
\(660\) 0 0
\(661\) −28.2689 + 16.3211i −1.09953 + 0.634817i −0.936099 0.351737i \(-0.885591\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(662\) 0 0
\(663\) −7.64076 8.90614i −0.296743 0.345886i
\(664\) 0 0
\(665\) −3.37543 + 1.94881i −0.130894 + 0.0755715i
\(666\) 0 0
\(667\) 10.5464 18.2670i 0.408360 0.707300i
\(668\) 0 0
\(669\) 2.52972 + 1.46053i 0.0978046 + 0.0564675i
\(670\) 0 0
\(671\) 3.95884i 0.152829i
\(672\) 0 0
\(673\) 22.2921 + 38.6111i 0.859299 + 1.48835i 0.872599 + 0.488437i \(0.162433\pi\)
−0.0133002 + 0.999912i \(0.504234\pi\)
\(674\) 0 0
\(675\) 3.96574 0.152642
\(676\) 0 0
\(677\) 21.1348 0.812275 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(678\) 0 0
\(679\) −12.0786 20.9207i −0.463533 0.802864i
\(680\) 0 0
\(681\) 5.92190i 0.226928i
\(682\) 0 0
\(683\) 8.54278 + 4.93218i 0.326881 + 0.188725i 0.654455 0.756101i \(-0.272898\pi\)
−0.327575 + 0.944825i \(0.606231\pi\)
\(684\) 0 0
\(685\) 3.74724 6.49042i 0.143175 0.247986i
\(686\) 0 0
\(687\) 19.8165 11.4410i 0.756046 0.436503i
\(688\) 0 0
\(689\) −13.0146 15.1699i −0.495817 0.577929i
\(690\) 0 0
\(691\) 0.654092 0.377640i 0.0248828 0.0143661i −0.487507 0.873119i \(-0.662094\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(692\) 0 0
\(693\) 4.65343 8.05997i 0.176769 0.306173i
\(694\) 0 0
\(695\) 1.24876 + 0.720969i 0.0473680 + 0.0273479i
\(696\) 0 0
\(697\) 14.7460i 0.558545i
\(698\) 0 0
\(699\) 21.0385 + 36.4397i 0.795749 + 1.37828i
\(700\) 0 0
\(701\) −29.9381 −1.13075 −0.565373 0.824835i \(-0.691268\pi\)
−0.565373 + 0.824835i \(0.691268\pi\)
\(702\) 0 0
\(703\) 2.47179 0.0932253
\(704\) 0 0
\(705\) 2.45993 + 4.26072i 0.0926463 + 0.160468i
\(706\) 0 0
\(707\) 16.8839i 0.634983i
\(708\) 0 0
\(709\) 6.46114 + 3.73034i 0.242653 + 0.140096i 0.616395 0.787437i \(-0.288592\pi\)
−0.373742 + 0.927533i \(0.621926\pi\)
\(710\) 0 0
\(711\) 0.359411 0.622518i 0.0134790 0.0233463i
\(712\) 0 0
\(713\) 38.4634 22.2069i 1.44047 0.831654i
\(714\) 0 0
\(715\) −6.34175 + 18.0355i −0.237168 + 0.674489i
\(716\) 0 0
\(717\) −32.1914 + 18.5857i −1.20221 + 0.694095i
\(718\) 0 0
\(719\) 22.7263 39.3631i 0.847547 1.46799i −0.0358435 0.999357i \(-0.511412\pi\)
0.883391 0.468637i \(-0.155255\pi\)
\(720\) 0 0
\(721\) −13.7480 7.93739i −0.512001 0.295604i
\(722\) 0 0
\(723\) 34.8942i 1.29773i
\(724\) 0 0
\(725\) 2.08770 + 3.61600i 0.0775352 + 0.134295i
\(726\) 0 0
\(727\) −16.8996 −0.626770 −0.313385 0.949626i \(-0.601463\pi\)
−0.313385 + 0.949626i \(0.601463\pi\)
\(728\) 0 0
\(729\) 12.5891 0.466264
\(730\) 0 0
\(731\) −6.79193 11.7640i −0.251209 0.435106i
\(732\) 0 0
\(733\) 15.8306i 0.584716i 0.956309 + 0.292358i \(0.0944399\pi\)
−0.956309 + 0.292358i \(0.905560\pi\)
\(734\) 0 0
\(735\) −7.04282 4.06618i −0.259778 0.149983i
\(736\) 0 0
\(737\) −41.3833 + 71.6780i −1.52437 + 2.64029i
\(738\) 0 0
\(739\) 25.9335 14.9727i 0.953980 0.550781i 0.0596653 0.998218i \(-0.480997\pi\)
0.894315 + 0.447438i \(0.147663\pi\)
\(740\) 0 0
\(741\) −12.4648 + 10.6938i −0.457907 + 0.392848i
\(742\) 0 0
\(743\) 22.3811 12.9217i 0.821083 0.474052i −0.0297071 0.999559i \(-0.509457\pi\)
0.850790 + 0.525506i \(0.176124\pi\)
\(744\) 0 0
\(745\) −1.18765 + 2.05708i −0.0435123 + 0.0753655i
\(746\) 0 0
\(747\) −3.16230 1.82576i −0.115703 0.0668009i
\(748\) 0 0
\(749\) 0.895641i 0.0327260i
\(750\) 0 0
\(751\) 8.27217 + 14.3278i 0.301856 + 0.522830i 0.976556 0.215262i \(-0.0690605\pi\)
−0.674701 + 0.738092i \(0.735727\pi\)
\(752\) 0 0
\(753\) 10.4152 0.379550
\(754\) 0 0
\(755\) −22.4022 −0.815300
\(756\) 0 0
\(757\) 8.82115 + 15.2787i 0.320610 + 0.555313i 0.980614 0.195949i \(-0.0627787\pi\)
−0.660004 + 0.751262i \(0.729445\pi\)
\(758\) 0 0
\(759\) 53.7241i 1.95006i
\(760\) 0 0
\(761\) 28.8019 + 16.6288i 1.04407 + 0.602794i 0.920983 0.389602i \(-0.127387\pi\)
0.123086 + 0.992396i \(0.460721\pi\)
\(762\) 0 0
\(763\) 4.67878 8.10388i 0.169383 0.293380i
\(764\) 0 0
\(765\) −1.43725 + 0.829794i −0.0519637 + 0.0300013i
\(766\) 0 0
\(767\) −6.58249 35.0819i −0.237680 1.26673i
\(768\) 0 0
\(769\) 34.7652 20.0717i 1.25367 0.723804i 0.281830 0.959464i \(-0.409059\pi\)
0.971836 + 0.235660i \(0.0757252\pi\)
\(770\) 0 0
\(771\) −16.1831 + 28.0300i −0.582821 + 1.00948i
\(772\) 0 0
\(773\) 13.7243 + 7.92372i 0.493628 + 0.284996i 0.726078 0.687612i \(-0.241341\pi\)
−0.232450 + 0.972608i \(0.574674\pi\)
\(774\) 0 0
\(775\) 8.79183i 0.315812i
\(776\) 0 0
\(777\) −1.87317 3.24443i −0.0671997 0.116393i
\(778\) 0 0
\(779\) −20.6382 −0.739440
\(780\) 0 0
\(781\) −13.0572 −0.467222
\(782\) 0 0
\(783\) 8.27928 + 14.3401i 0.295877 + 0.512475i
\(784\) 0 0
\(785\) 4.85797i 0.173388i
\(786\) 0 0
\(787\) 1.79404 + 1.03579i 0.0639508 + 0.0369220i 0.531634 0.846974i \(-0.321578\pi\)
−0.467684 + 0.883896i \(0.654911\pi\)
\(788\) 0 0