Properties

Label 1040.2.da.f.881.3
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 881.3
Root \(-2.44974i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.f.641.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.275748 - 0.477609i) q^{3} -1.00000i q^{5} +(1.57306 + 0.908206i) q^{7} +(1.34793 - 2.33468i) q^{9} +O(q^{10})\) \(q+(-0.275748 - 0.477609i) q^{3} -1.00000i q^{5} +(1.57306 + 0.908206i) q^{7} +(1.34793 - 2.33468i) q^{9} +(-0.759545 + 0.438523i) q^{11} +(-2.94577 - 2.07905i) q^{13} +(-0.477609 + 0.275748i) q^{15} +(2.47282 - 4.28305i) q^{17} +(-3.18017 - 1.83607i) q^{19} -1.00174i q^{21} +(2.69554 + 4.66881i) q^{23} -1.00000 q^{25} -3.14124 q^{27} +(0.214596 + 0.371692i) q^{29} -2.36449i q^{31} +(0.418885 + 0.241844i) q^{33} +(0.908206 - 1.57306i) q^{35} +(7.40500 - 4.27528i) q^{37} +(-0.180686 + 1.98022i) q^{39} +(1.03931 - 0.600045i) q^{41} +(-1.00825 + 1.74634i) q^{43} +(-2.33468 - 1.34793i) q^{45} -8.92633i q^{47} +(-1.85032 - 3.20485i) q^{49} -2.72750 q^{51} -5.45025 q^{53} +(0.438523 + 0.759545i) q^{55} +2.02517i q^{57} +(-3.96683 - 2.29025i) q^{59} +(-0.952525 + 1.64982i) q^{61} +(4.24074 - 2.44839i) q^{63} +(-2.07905 + 2.94577i) q^{65} +(4.42293 - 2.55358i) q^{67} +(1.48658 - 2.57483i) q^{69} +(-13.4521 - 7.76656i) q^{71} -10.7435i q^{73} +(0.275748 + 0.477609i) q^{75} -1.59308 q^{77} +11.2334 q^{79} +(-3.17759 - 5.50375i) q^{81} -2.60910i q^{83} +(-4.28305 - 2.47282i) q^{85} +(0.118349 - 0.204986i) q^{87} +(0.645218 - 0.372517i) q^{89} +(-2.74566 - 5.94584i) q^{91} +(-1.12930 + 0.652003i) q^{93} +(-1.83607 + 3.18017i) q^{95} +(8.46798 + 4.88899i) q^{97} +2.36439i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 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
\(3\) −0.275748 0.477609i −0.159203 0.275748i 0.775379 0.631497i \(-0.217559\pi\)
−0.934582 + 0.355749i \(0.884226\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.57306 + 0.908206i 0.594561 + 0.343270i 0.766899 0.641768i \(-0.221799\pi\)
−0.172338 + 0.985038i \(0.555132\pi\)
\(8\) 0 0
\(9\) 1.34793 2.33468i 0.449309 0.778226i
\(10\) 0 0
\(11\) −0.759545 + 0.438523i −0.229011 + 0.132220i −0.610116 0.792312i \(-0.708877\pi\)
0.381105 + 0.924532i \(0.375544\pi\)
\(12\) 0 0
\(13\) −2.94577 2.07905i −0.817009 0.576625i
\(14\) 0 0
\(15\) −0.477609 + 0.275748i −0.123318 + 0.0711977i
\(16\) 0 0
\(17\) 2.47282 4.28305i 0.599748 1.03879i −0.393111 0.919491i \(-0.628601\pi\)
0.992858 0.119302i \(-0.0380657\pi\)
\(18\) 0 0
\(19\) −3.18017 1.83607i −0.729581 0.421224i 0.0886879 0.996059i \(-0.471733\pi\)
−0.818269 + 0.574836i \(0.805066\pi\)
\(20\) 0 0
\(21\) 1.00174i 0.218598i
\(22\) 0 0
\(23\) 2.69554 + 4.66881i 0.562058 + 0.973513i 0.997317 + 0.0732079i \(0.0233237\pi\)
−0.435258 + 0.900306i \(0.643343\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −3.14124 −0.604531
\(28\) 0 0
\(29\) 0.214596 + 0.371692i 0.0398496 + 0.0690215i 0.885262 0.465092i \(-0.153979\pi\)
−0.845413 + 0.534114i \(0.820645\pi\)
\(30\) 0 0
\(31\) 2.36449i 0.424675i −0.977196 0.212338i \(-0.931892\pi\)
0.977196 0.212338i \(-0.0681077\pi\)
\(32\) 0 0
\(33\) 0.418885 + 0.241844i 0.0729186 + 0.0420996i
\(34\) 0 0
\(35\) 0.908206 1.57306i 0.153515 0.265896i
\(36\) 0 0
\(37\) 7.40500 4.27528i 1.21737 0.702851i 0.253019 0.967461i \(-0.418577\pi\)
0.964355 + 0.264610i \(0.0852432\pi\)
\(38\) 0 0
\(39\) −0.180686 + 1.98022i −0.0289329 + 0.317089i
\(40\) 0 0
\(41\) 1.03931 0.600045i 0.162313 0.0937113i −0.416643 0.909070i \(-0.636794\pi\)
0.578956 + 0.815359i \(0.303460\pi\)
\(42\) 0 0
\(43\) −1.00825 + 1.74634i −0.153757 + 0.266315i −0.932606 0.360897i \(-0.882471\pi\)
0.778849 + 0.627212i \(0.215804\pi\)
\(44\) 0 0
\(45\) −2.33468 1.34793i −0.348033 0.200937i
\(46\) 0 0
\(47\) 8.92633i 1.30204i −0.759061 0.651020i \(-0.774341\pi\)
0.759061 0.651020i \(-0.225659\pi\)
\(48\) 0 0
\(49\) −1.85032 3.20485i −0.264332 0.457836i
\(50\) 0 0
\(51\) −2.72750 −0.381926
\(52\) 0 0
\(53\) −5.45025 −0.748650 −0.374325 0.927298i \(-0.622126\pi\)
−0.374325 + 0.927298i \(0.622126\pi\)
\(54\) 0 0
\(55\) 0.438523 + 0.759545i 0.0591305 + 0.102417i
\(56\) 0 0
\(57\) 2.02517i 0.268240i
\(58\) 0 0
\(59\) −3.96683 2.29025i −0.516437 0.298165i 0.219039 0.975716i \(-0.429708\pi\)
−0.735476 + 0.677551i \(0.763041\pi\)
\(60\) 0 0
\(61\) −0.952525 + 1.64982i −0.121958 + 0.211238i −0.920540 0.390649i \(-0.872251\pi\)
0.798582 + 0.601887i \(0.205584\pi\)
\(62\) 0 0
\(63\) 4.24074 2.44839i 0.534283 0.308468i
\(64\) 0 0
\(65\) −2.07905 + 2.94577i −0.257875 + 0.365377i
\(66\) 0 0
\(67\) 4.42293 2.55358i 0.540347 0.311970i −0.204872 0.978789i \(-0.565678\pi\)
0.745220 + 0.666819i \(0.232345\pi\)
\(68\) 0 0
\(69\) 1.48658 2.57483i 0.178963 0.309973i
\(70\) 0 0
\(71\) −13.4521 7.76656i −1.59647 0.921721i −0.992161 0.124969i \(-0.960117\pi\)
−0.604306 0.796752i \(-0.706550\pi\)
\(72\) 0 0
\(73\) 10.7435i 1.25743i −0.777635 0.628716i \(-0.783581\pi\)
0.777635 0.628716i \(-0.216419\pi\)
\(74\) 0 0
\(75\) 0.275748 + 0.477609i 0.0318406 + 0.0551495i
\(76\) 0 0
\(77\) −1.59308 −0.181548
\(78\) 0 0
\(79\) 11.2334 1.26386 0.631929 0.775026i \(-0.282263\pi\)
0.631929 + 0.775026i \(0.282263\pi\)
\(80\) 0 0
\(81\) −3.17759 5.50375i −0.353066 0.611528i
\(82\) 0 0
\(83\) 2.60910i 0.286386i −0.989695 0.143193i \(-0.954263\pi\)
0.989695 0.143193i \(-0.0457369\pi\)
\(84\) 0 0
\(85\) −4.28305 2.47282i −0.464562 0.268215i
\(86\) 0 0
\(87\) 0.118349 0.204986i 0.0126883 0.0219768i
\(88\) 0 0
\(89\) 0.645218 0.372517i 0.0683930 0.0394867i −0.465414 0.885093i \(-0.654094\pi\)
0.533807 + 0.845607i \(0.320761\pi\)
\(90\) 0 0
\(91\) −2.74566 5.94584i −0.287823 0.623293i
\(92\) 0 0
\(93\) −1.12930 + 0.652003i −0.117103 + 0.0676096i
\(94\) 0 0
\(95\) −1.83607 + 3.18017i −0.188377 + 0.326279i
\(96\) 0 0
\(97\) 8.46798 + 4.88899i 0.859794 + 0.496402i 0.863943 0.503589i \(-0.167988\pi\)
−0.00414956 + 0.999991i \(0.501321\pi\)
\(98\) 0 0
\(99\) 2.36439i 0.237630i
\(100\) 0 0
\(101\) 3.45444 + 5.98327i 0.343730 + 0.595358i 0.985122 0.171855i \(-0.0549761\pi\)
−0.641392 + 0.767213i \(0.721643\pi\)
\(102\) 0 0
\(103\) 17.4021 1.71468 0.857342 0.514747i \(-0.172114\pi\)
0.857342 + 0.514747i \(0.172114\pi\)
\(104\) 0 0
\(105\) −1.00174 −0.0977601
\(106\) 0 0
\(107\) −3.84562 6.66080i −0.371770 0.643924i 0.618068 0.786124i \(-0.287916\pi\)
−0.989838 + 0.142201i \(0.954582\pi\)
\(108\) 0 0
\(109\) 11.1587i 1.06881i 0.845229 + 0.534404i \(0.179464\pi\)
−0.845229 + 0.534404i \(0.820536\pi\)
\(110\) 0 0
\(111\) −4.08382 2.35780i −0.387619 0.223792i
\(112\) 0 0
\(113\) −6.84621 + 11.8580i −0.644038 + 1.11551i 0.340485 + 0.940250i \(0.389409\pi\)
−0.984523 + 0.175256i \(0.943925\pi\)
\(114\) 0 0
\(115\) 4.66881 2.69554i 0.435368 0.251360i
\(116\) 0 0
\(117\) −8.82459 + 4.07500i −0.815834 + 0.376734i
\(118\) 0 0
\(119\) 7.77979 4.49167i 0.713172 0.411750i
\(120\) 0 0
\(121\) −5.11539 + 8.86012i −0.465036 + 0.805466i
\(122\) 0 0
\(123\) −0.573174 0.330922i −0.0516814 0.0298383i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.56497 + 11.3709i 0.582547 + 1.00900i 0.995176 + 0.0981016i \(0.0312770\pi\)
−0.412630 + 0.910899i \(0.635390\pi\)
\(128\) 0 0
\(129\) 1.11209 0.0979143
\(130\) 0 0
\(131\) −19.2978 −1.68606 −0.843030 0.537866i \(-0.819230\pi\)
−0.843030 + 0.537866i \(0.819230\pi\)
\(132\) 0 0
\(133\) −3.33506 5.77650i −0.289187 0.500886i
\(134\) 0 0
\(135\) 3.14124i 0.270355i
\(136\) 0 0
\(137\) 3.90390 + 2.25392i 0.333533 + 0.192565i 0.657408 0.753534i \(-0.271653\pi\)
−0.323876 + 0.946100i \(0.604986\pi\)
\(138\) 0 0
\(139\) 4.78060 8.28024i 0.405485 0.702321i −0.588893 0.808211i \(-0.700436\pi\)
0.994378 + 0.105890i \(0.0337692\pi\)
\(140\) 0 0
\(141\) −4.26330 + 2.46142i −0.359034 + 0.207289i
\(142\) 0 0
\(143\) 3.14915 + 0.287346i 0.263346 + 0.0240291i
\(144\) 0 0
\(145\) 0.371692 0.214596i 0.0308673 0.0178213i
\(146\) 0 0
\(147\) −1.02044 + 1.76746i −0.0841649 + 0.145778i
\(148\) 0 0
\(149\) 13.7633 + 7.94624i 1.12753 + 0.650981i 0.943313 0.331904i \(-0.107691\pi\)
0.184220 + 0.982885i \(0.441024\pi\)
\(150\) 0 0
\(151\) 13.4356i 1.09338i 0.837336 + 0.546689i \(0.184112\pi\)
−0.837336 + 0.546689i \(0.815888\pi\)
\(152\) 0 0
\(153\) −6.66637 11.5465i −0.538944 0.933478i
\(154\) 0 0
\(155\) −2.36449 −0.189921
\(156\) 0 0
\(157\) 21.8879 1.74685 0.873424 0.486960i \(-0.161894\pi\)
0.873424 + 0.486960i \(0.161894\pi\)
\(158\) 0 0
\(159\) 1.50289 + 2.60309i 0.119187 + 0.206438i
\(160\) 0 0
\(161\) 9.79241i 0.771750i
\(162\) 0 0
\(163\) 3.25507 + 1.87932i 0.254957 + 0.147199i 0.622032 0.782992i \(-0.286307\pi\)
−0.367075 + 0.930191i \(0.619641\pi\)
\(164\) 0 0
\(165\) 0.241844 0.418885i 0.0188275 0.0326102i
\(166\) 0 0
\(167\) 13.3492 7.70716i 1.03299 0.596398i 0.115151 0.993348i \(-0.463265\pi\)
0.917840 + 0.396950i \(0.129931\pi\)
\(168\) 0 0
\(169\) 4.35508 + 12.2488i 0.335006 + 0.942216i
\(170\) 0 0
\(171\) −8.57327 + 4.94978i −0.655614 + 0.378519i
\(172\) 0 0
\(173\) 0.430549 0.745733i 0.0327340 0.0566970i −0.849194 0.528081i \(-0.822912\pi\)
0.881928 + 0.471384i \(0.156245\pi\)
\(174\) 0 0
\(175\) −1.57306 0.908206i −0.118912 0.0686539i
\(176\) 0 0
\(177\) 2.52612i 0.189875i
\(178\) 0 0
\(179\) −3.90073 6.75627i −0.291554 0.504987i 0.682623 0.730771i \(-0.260839\pi\)
−0.974177 + 0.225784i \(0.927506\pi\)
\(180\) 0 0
\(181\) 5.70152 0.423791 0.211895 0.977292i \(-0.432036\pi\)
0.211895 + 0.977292i \(0.432036\pi\)
\(182\) 0 0
\(183\) 1.05063 0.0776645
\(184\) 0 0
\(185\) −4.27528 7.40500i −0.314325 0.544426i
\(186\) 0 0
\(187\) 4.33756i 0.317194i
\(188\) 0 0
\(189\) −4.94135 2.85289i −0.359430 0.207517i
\(190\) 0 0
\(191\) 0.926061 1.60398i 0.0670074 0.116060i −0.830575 0.556906i \(-0.811988\pi\)
0.897583 + 0.440846i \(0.145322\pi\)
\(192\) 0 0
\(193\) −7.47772 + 4.31726i −0.538258 + 0.310763i −0.744373 0.667765i \(-0.767251\pi\)
0.206115 + 0.978528i \(0.433918\pi\)
\(194\) 0 0
\(195\) 1.98022 + 0.180686i 0.141806 + 0.0129392i
\(196\) 0 0
\(197\) 3.66599 2.11656i 0.261191 0.150799i −0.363687 0.931521i \(-0.618482\pi\)
0.624878 + 0.780723i \(0.285149\pi\)
\(198\) 0 0
\(199\) −13.8668 + 24.0179i −0.982988 + 1.70259i −0.332432 + 0.943127i \(0.607869\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(200\) 0 0
\(201\) −2.43923 1.40829i −0.172050 0.0993330i
\(202\) 0 0
\(203\) 0.779591i 0.0547166i
\(204\) 0 0
\(205\) −0.600045 1.03931i −0.0419090 0.0725885i
\(206\) 0 0
\(207\) 14.5335 1.01015
\(208\) 0 0
\(209\) 3.22064 0.222776
\(210\) 0 0
\(211\) −0.0728649 0.126206i −0.00501623 0.00868836i 0.863506 0.504338i \(-0.168263\pi\)
−0.868523 + 0.495650i \(0.834930\pi\)
\(212\) 0 0
\(213\) 8.56644i 0.586963i
\(214\) 0 0
\(215\) 1.74634 + 1.00825i 0.119100 + 0.0687622i
\(216\) 0 0
\(217\) 2.14745 3.71949i 0.145778 0.252495i
\(218\) 0 0
\(219\) −5.13119 + 2.96250i −0.346734 + 0.200187i
\(220\) 0 0
\(221\) −16.1891 + 7.47575i −1.08899 + 0.502873i
\(222\) 0 0
\(223\) 4.24045 2.44822i 0.283961 0.163945i −0.351254 0.936280i \(-0.614245\pi\)
0.635215 + 0.772335i \(0.280911\pi\)
\(224\) 0 0
\(225\) −1.34793 + 2.33468i −0.0898618 + 0.155645i
\(226\) 0 0
\(227\) −11.9441 6.89595i −0.792760 0.457700i 0.0481730 0.998839i \(-0.484660\pi\)
−0.840933 + 0.541139i \(0.817993\pi\)
\(228\) 0 0
\(229\) 12.6453i 0.835628i −0.908533 0.417814i \(-0.862796\pi\)
0.908533 0.417814i \(-0.137204\pi\)
\(230\) 0 0
\(231\) 0.439288 + 0.760869i 0.0289030 + 0.0500615i
\(232\) 0 0
\(233\) 10.2878 0.673975 0.336987 0.941509i \(-0.390592\pi\)
0.336987 + 0.941509i \(0.390592\pi\)
\(234\) 0 0
\(235\) −8.92633 −0.582290
\(236\) 0 0
\(237\) −3.09759 5.36518i −0.201210 0.348506i
\(238\) 0 0
\(239\) 20.1730i 1.30489i 0.757838 + 0.652443i \(0.226256\pi\)
−0.757838 + 0.652443i \(0.773744\pi\)
\(240\) 0 0
\(241\) 0.798945 + 0.461271i 0.0514645 + 0.0297131i 0.525512 0.850786i \(-0.323874\pi\)
−0.474047 + 0.880500i \(0.657207\pi\)
\(242\) 0 0
\(243\) −6.46428 + 11.1965i −0.414684 + 0.718253i
\(244\) 0 0
\(245\) −3.20485 + 1.85032i −0.204751 + 0.118213i
\(246\) 0 0
\(247\) 5.55075 + 12.0204i 0.353186 + 0.764838i
\(248\) 0 0
\(249\) −1.24613 + 0.719453i −0.0789702 + 0.0455935i
\(250\) 0 0
\(251\) −8.13425 + 14.0889i −0.513430 + 0.889286i 0.486449 + 0.873709i \(0.338292\pi\)
−0.999879 + 0.0155772i \(0.995041\pi\)
\(252\) 0 0
\(253\) −4.09476 2.36411i −0.257435 0.148630i
\(254\) 0 0
\(255\) 2.72750i 0.170803i
\(256\) 0 0
\(257\) 8.50538 + 14.7318i 0.530551 + 0.918941i 0.999365 + 0.0356442i \(0.0113483\pi\)
−0.468814 + 0.883297i \(0.655318\pi\)
\(258\) 0 0
\(259\) 15.5313 0.965070
\(260\) 0 0
\(261\) 1.15704 0.0716190
\(262\) 0 0
\(263\) 9.66899 + 16.7472i 0.596215 + 1.03268i 0.993374 + 0.114925i \(0.0366629\pi\)
−0.397159 + 0.917750i \(0.630004\pi\)
\(264\) 0 0
\(265\) 5.45025i 0.334806i
\(266\) 0 0
\(267\) −0.355835 0.205441i −0.0217767 0.0125728i
\(268\) 0 0
\(269\) 0.285151 0.493896i 0.0173860 0.0301134i −0.857202 0.514981i \(-0.827799\pi\)
0.874587 + 0.484868i \(0.161132\pi\)
\(270\) 0 0
\(271\) −20.3837 + 11.7686i −1.23822 + 0.714889i −0.968731 0.248113i \(-0.920190\pi\)
−0.269493 + 0.963002i \(0.586856\pi\)
\(272\) 0 0
\(273\) −2.08268 + 2.95090i −0.126049 + 0.178597i
\(274\) 0 0
\(275\) 0.759545 0.438523i 0.0458023 0.0264440i
\(276\) 0 0
\(277\) 7.23659 12.5341i 0.434804 0.753103i −0.562475 0.826814i \(-0.690151\pi\)
0.997280 + 0.0737109i \(0.0234842\pi\)
\(278\) 0 0
\(279\) −5.52033 3.18716i −0.330493 0.190810i
\(280\) 0 0
\(281\) 24.4795i 1.46033i −0.683273 0.730163i \(-0.739444\pi\)
0.683273 0.730163i \(-0.260556\pi\)
\(282\) 0 0
\(283\) 8.89924 + 15.4139i 0.529005 + 0.916263i 0.999428 + 0.0338224i \(0.0107681\pi\)
−0.470423 + 0.882441i \(0.655899\pi\)
\(284\) 0 0
\(285\) 2.02517 0.119961
\(286\) 0 0
\(287\) 2.17986 0.128673
\(288\) 0 0
\(289\) −3.72970 6.46003i −0.219394 0.380002i
\(290\) 0 0
\(291\) 5.39251i 0.316115i
\(292\) 0 0
\(293\) 17.5760 + 10.1475i 1.02680 + 0.592824i 0.916067 0.401026i \(-0.131346\pi\)
0.110735 + 0.993850i \(0.464680\pi\)
\(294\) 0 0
\(295\) −2.29025 + 3.96683i −0.133344 + 0.230958i
\(296\) 0 0
\(297\) 2.38591 1.37751i 0.138445 0.0799310i
\(298\) 0 0
\(299\) 1.76627 19.3574i 0.102146 1.11947i
\(300\) 0 0
\(301\) −3.17208 + 1.83140i −0.182836 + 0.105560i
\(302\) 0 0
\(303\) 1.90511 3.29975i 0.109446 0.189566i
\(304\) 0 0
\(305\) 1.64982 + 0.952525i 0.0944685 + 0.0545414i
\(306\) 0 0
\(307\) 9.55636i 0.545410i 0.962098 + 0.272705i \(0.0879184\pi\)
−0.962098 + 0.272705i \(0.912082\pi\)
\(308\) 0 0
\(309\) −4.79860 8.31142i −0.272983 0.472820i
\(310\) 0 0
\(311\) −0.151461 −0.00858856 −0.00429428 0.999991i \(-0.501367\pi\)
−0.00429428 + 0.999991i \(0.501367\pi\)
\(312\) 0 0
\(313\) 28.5006 1.61095 0.805475 0.592630i \(-0.201910\pi\)
0.805475 + 0.592630i \(0.201910\pi\)
\(314\) 0 0
\(315\) −2.44839 4.24074i −0.137951 0.238938i
\(316\) 0 0
\(317\) 20.0004i 1.12333i 0.827363 + 0.561667i \(0.189840\pi\)
−0.827363 + 0.561667i \(0.810160\pi\)
\(318\) 0 0
\(319\) −0.325991 0.188211i −0.0182520 0.0105378i
\(320\) 0 0
\(321\) −2.12084 + 3.67340i −0.118374 + 0.205029i
\(322\) 0 0
\(323\) −15.7280 + 9.08056i −0.875129 + 0.505256i
\(324\) 0 0
\(325\) 2.94577 + 2.07905i 0.163402 + 0.115325i
\(326\) 0 0
\(327\) 5.32949 3.07698i 0.294721 0.170157i
\(328\) 0 0
\(329\) 8.10695 14.0417i 0.446951 0.774141i
\(330\) 0 0
\(331\) −8.73156 5.04117i −0.479930 0.277088i 0.240457 0.970660i \(-0.422703\pi\)
−0.720387 + 0.693572i \(0.756036\pi\)
\(332\) 0 0
\(333\) 23.0510i 1.26319i
\(334\) 0 0
\(335\) −2.55358 4.42293i −0.139517 0.241651i
\(336\) 0 0
\(337\) −9.00198 −0.490369 −0.245185 0.969476i \(-0.578849\pi\)
−0.245185 + 0.969476i \(0.578849\pi\)
\(338\) 0 0
\(339\) 7.55131 0.410131
\(340\) 0 0
\(341\) 1.03689 + 1.79594i 0.0561505 + 0.0972555i
\(342\) 0 0
\(343\) 19.4368i 1.04949i
\(344\) 0 0
\(345\) −2.57483 1.48658i −0.138624 0.0800346i
\(346\) 0 0
\(347\) −0.686627 + 1.18927i −0.0368601 + 0.0638435i −0.883867 0.467738i \(-0.845069\pi\)
0.847007 + 0.531582i \(0.178402\pi\)
\(348\) 0 0
\(349\) −17.6180 + 10.1717i −0.943069 + 0.544481i −0.890921 0.454158i \(-0.849940\pi\)
−0.0521480 + 0.998639i \(0.516607\pi\)
\(350\) 0 0
\(351\) 9.25335 + 6.53079i 0.493907 + 0.348588i
\(352\) 0 0
\(353\) −6.13858 + 3.54411i −0.326724 + 0.188634i −0.654386 0.756161i \(-0.727073\pi\)
0.327662 + 0.944795i \(0.393739\pi\)
\(354\) 0 0
\(355\) −7.76656 + 13.4521i −0.412206 + 0.713962i
\(356\) 0 0
\(357\) −4.29052 2.47713i −0.227078 0.131104i
\(358\) 0 0
\(359\) 4.81284i 0.254012i −0.991902 0.127006i \(-0.959463\pi\)
0.991902 0.127006i \(-0.0405368\pi\)
\(360\) 0 0
\(361\) −2.75768 4.77644i −0.145141 0.251392i
\(362\) 0 0
\(363\) 5.64223 0.296140
\(364\) 0 0
\(365\) −10.7435 −0.562341
\(366\) 0 0
\(367\) 4.57841 + 7.93004i 0.238991 + 0.413945i 0.960425 0.278538i \(-0.0898499\pi\)
−0.721434 + 0.692483i \(0.756517\pi\)
\(368\) 0 0
\(369\) 3.23527i 0.168421i
\(370\) 0 0
\(371\) −8.57357 4.94995i −0.445118 0.256989i
\(372\) 0 0
\(373\) −5.88828 + 10.1988i −0.304884 + 0.528074i −0.977235 0.212158i \(-0.931951\pi\)
0.672352 + 0.740232i \(0.265284\pi\)
\(374\) 0 0
\(375\) 0.477609 0.275748i 0.0246636 0.0142395i
\(376\) 0 0
\(377\) 0.140616 1.54107i 0.00724209 0.0793694i
\(378\) 0 0
\(379\) 31.9745 18.4605i 1.64242 0.948253i 0.662453 0.749104i \(-0.269516\pi\)
0.979969 0.199149i \(-0.0638178\pi\)
\(380\) 0 0
\(381\) 3.62055 6.27098i 0.185486 0.321272i
\(382\) 0 0
\(383\) −19.1140 11.0355i −0.976679 0.563886i −0.0754134 0.997152i \(-0.524028\pi\)
−0.901266 + 0.433266i \(0.857361\pi\)
\(384\) 0 0
\(385\) 1.59308i 0.0811908i
\(386\) 0 0
\(387\) 2.71810 + 4.70788i 0.138169 + 0.239315i
\(388\) 0 0
\(389\) 35.1523 1.78229 0.891146 0.453716i \(-0.149902\pi\)
0.891146 + 0.453716i \(0.149902\pi\)
\(390\) 0 0
\(391\) 26.6623 1.34837
\(392\) 0 0
\(393\) 5.32133 + 9.21682i 0.268426 + 0.464927i
\(394\) 0 0
\(395\) 11.2334i 0.565214i
\(396\) 0 0
\(397\) 8.03921 + 4.64144i 0.403476 + 0.232947i 0.687983 0.725727i \(-0.258496\pi\)
−0.284506 + 0.958674i \(0.591830\pi\)
\(398\) 0 0
\(399\) −1.83927 + 3.18571i −0.0920788 + 0.159485i
\(400\) 0 0
\(401\) −24.6221 + 14.2156i −1.22957 + 0.709893i −0.966940 0.255004i \(-0.917923\pi\)
−0.262630 + 0.964897i \(0.584590\pi\)
\(402\) 0 0
\(403\) −4.91590 + 6.96524i −0.244879 + 0.346963i
\(404\) 0 0
\(405\) −5.50375 + 3.17759i −0.273483 + 0.157896i
\(406\) 0 0
\(407\) −3.74962 + 6.49453i −0.185862 + 0.321922i
\(408\) 0 0
\(409\) 17.5634 + 10.1402i 0.868452 + 0.501401i 0.866834 0.498598i \(-0.166151\pi\)
0.00161856 + 0.999999i \(0.499485\pi\)
\(410\) 0 0
\(411\) 2.48605i 0.122628i
\(412\) 0 0
\(413\) −4.16004 7.20540i −0.204702 0.354554i
\(414\) 0 0
\(415\) −2.60910 −0.128076
\(416\) 0 0
\(417\) −5.27296 −0.258218
\(418\) 0 0
\(419\) −14.6625 25.3962i −0.716309 1.24068i −0.962452 0.271450i \(-0.912497\pi\)
0.246143 0.969233i \(-0.420837\pi\)
\(420\) 0 0
\(421\) 2.92975i 0.142787i 0.997448 + 0.0713936i \(0.0227447\pi\)
−0.997448 + 0.0713936i \(0.977255\pi\)
\(422\) 0 0
\(423\) −20.8401 12.0320i −1.01328 0.585018i
\(424\) 0 0
\(425\) −2.47282 + 4.28305i −0.119950 + 0.207759i
\(426\) 0 0
\(427\) −2.99676 + 1.73018i −0.145023 + 0.0837292i
\(428\) 0 0
\(429\) −0.731133 1.58330i −0.0352994 0.0764424i
\(430\) 0 0
\(431\) 30.4786 17.5968i 1.46810 0.847609i 0.468741 0.883336i \(-0.344708\pi\)
0.999362 + 0.0357266i \(0.0113746\pi\)
\(432\) 0 0
\(433\) −10.3241 + 17.8819i −0.496147 + 0.859351i −0.999990 0.00444359i \(-0.998586\pi\)
0.503843 + 0.863795i \(0.331919\pi\)
\(434\) 0 0
\(435\) −0.204986 0.118349i −0.00982834 0.00567440i
\(436\) 0 0
\(437\) 19.7968i 0.947009i
\(438\) 0 0
\(439\) 4.98217 + 8.62936i 0.237786 + 0.411857i 0.960079 0.279730i \(-0.0902450\pi\)
−0.722293 + 0.691587i \(0.756912\pi\)
\(440\) 0 0
\(441\) −9.97640 −0.475067
\(442\) 0 0
\(443\) −35.1084 −1.66805 −0.834025 0.551727i \(-0.813969\pi\)
−0.834025 + 0.551727i \(0.813969\pi\)
\(444\) 0 0
\(445\) −0.372517 0.645218i −0.0176590 0.0305863i
\(446\) 0 0
\(447\) 8.76463i 0.414553i
\(448\) 0 0
\(449\) −27.9768 16.1524i −1.32031 0.762280i −0.336531 0.941673i \(-0.609254\pi\)
−0.983778 + 0.179392i \(0.942587\pi\)
\(450\) 0 0
\(451\) −0.526268 + 0.911523i −0.0247810 + 0.0429219i
\(452\) 0 0
\(453\) 6.41698 3.70485i 0.301496 0.174069i
\(454\) 0 0
\(455\) −5.94584 + 2.74566i −0.278745 + 0.128718i
\(456\) 0 0
\(457\) 17.3917 10.0411i 0.813550 0.469703i −0.0346373 0.999400i \(-0.511028\pi\)
0.848187 + 0.529697i \(0.177694\pi\)
\(458\) 0 0
\(459\) −7.76772 + 13.4541i −0.362566 + 0.627983i
\(460\) 0 0
\(461\) −18.1537 10.4810i −0.845502 0.488151i 0.0136287 0.999907i \(-0.495662\pi\)
−0.859131 + 0.511756i \(0.828995\pi\)
\(462\) 0 0
\(463\) 35.1142i 1.63189i −0.578127 0.815947i \(-0.696216\pi\)
0.578127 0.815947i \(-0.303784\pi\)
\(464\) 0 0
\(465\) 0.652003 + 1.12930i 0.0302359 + 0.0523702i
\(466\) 0 0
\(467\) 31.6858 1.46625 0.733123 0.680096i \(-0.238062\pi\)
0.733123 + 0.680096i \(0.238062\pi\)
\(468\) 0 0
\(469\) 9.27672 0.428359
\(470\) 0 0
\(471\) −6.03555 10.4539i −0.278103 0.481689i
\(472\) 0 0
\(473\) 1.76857i 0.0813188i
\(474\) 0 0
\(475\) 3.18017 + 1.83607i 0.145916 + 0.0842448i
\(476\) 0 0
\(477\) −7.34654 + 12.7246i −0.336375 + 0.582619i
\(478\) 0 0
\(479\) 3.42202 1.97570i 0.156356 0.0902721i −0.419781 0.907626i \(-0.637893\pi\)
0.576137 + 0.817353i \(0.304560\pi\)
\(480\) 0 0
\(481\) −30.7019 2.80141i −1.39989 0.127733i
\(482\) 0 0
\(483\) 4.67694 2.70023i 0.212808 0.122865i
\(484\) 0 0
\(485\) 4.88899 8.46798i 0.221998 0.384511i
\(486\) 0 0
\(487\) −15.6267 9.02205i −0.708111 0.408828i 0.102250 0.994759i \(-0.467396\pi\)
−0.810361 + 0.585931i \(0.800729\pi\)
\(488\) 0 0
\(489\) 2.07287i 0.0937383i
\(490\) 0 0
\(491\) 5.77834 + 10.0084i 0.260773 + 0.451672i 0.966448 0.256864i \(-0.0826892\pi\)
−0.705675 + 0.708536i \(0.749356\pi\)
\(492\) 0 0
\(493\) 2.12264 0.0955987
\(494\) 0 0
\(495\) 2.36439 0.106271
\(496\) 0 0
\(497\) −14.1073 24.4345i −0.632798 1.09604i
\(498\) 0 0
\(499\) 2.01039i 0.0899973i 0.998987 + 0.0449987i \(0.0143284\pi\)
−0.998987 + 0.0449987i \(0.985672\pi\)
\(500\) 0 0
\(501\) −7.36202 4.25046i −0.328911 0.189897i
\(502\) 0 0
\(503\) 16.8145 29.1236i 0.749721 1.29856i −0.198235 0.980155i \(-0.563521\pi\)
0.947956 0.318401i \(-0.103146\pi\)
\(504\) 0 0
\(505\) 5.98327 3.45444i 0.266252 0.153721i
\(506\) 0 0
\(507\) 4.64924 5.45761i 0.206480 0.242381i
\(508\) 0 0
\(509\) −18.8008 + 10.8547i −0.833333 + 0.481125i −0.854992 0.518640i \(-0.826438\pi\)
0.0216596 + 0.999765i \(0.493105\pi\)
\(510\) 0 0
\(511\) 9.75732 16.9002i 0.431638 0.747620i
\(512\) 0 0
\(513\) 9.98967 + 5.76754i 0.441054 + 0.254643i
\(514\) 0 0
\(515\) 17.4021i 0.766830i
\(516\) 0 0
\(517\) 3.91441 + 6.77995i 0.172155 + 0.298182i
\(518\) 0 0
\(519\) −0.474892 −0.0208454
\(520\) 0 0
\(521\) 22.8718 1.00203 0.501016 0.865438i \(-0.332960\pi\)
0.501016 + 0.865438i \(0.332960\pi\)
\(522\) 0 0
\(523\) −3.36726 5.83226i −0.147240 0.255027i 0.782966 0.622064i \(-0.213706\pi\)
−0.930206 + 0.367037i \(0.880372\pi\)
\(524\) 0 0
\(525\) 1.00174i 0.0437196i
\(526\) 0 0
\(527\) −10.1272 5.84697i −0.441150 0.254698i
\(528\) 0 0
\(529\) −3.03183 + 5.25129i −0.131819 + 0.228317i
\(530\) 0 0
\(531\) −10.6940 + 6.17418i −0.464080 + 0.267936i
\(532\) 0 0
\(533\) −4.30909 0.393184i −0.186647 0.0170307i
\(534\) 0 0
\(535\) −6.66080 + 3.84562i −0.287972 + 0.166260i
\(536\) 0 0
\(537\) −2.15124 + 3.72605i −0.0928327 + 0.160791i
\(538\) 0 0
\(539\) 2.81081 + 1.62282i 0.121070 + 0.0698998i
\(540\) 0 0
\(541\) 11.2559i 0.483927i 0.970285 + 0.241964i \(0.0777915\pi\)
−0.970285 + 0.241964i \(0.922209\pi\)
\(542\) 0 0
\(543\) −1.57218 2.72310i −0.0674688 0.116859i
\(544\) 0 0
\(545\) 11.1587 0.477985
\(546\) 0 0
\(547\) 10.1685 0.434774 0.217387 0.976086i \(-0.430247\pi\)
0.217387 + 0.976086i \(0.430247\pi\)
\(548\) 0 0
\(549\) 2.56787 + 4.44768i 0.109594 + 0.189822i
\(550\) 0 0
\(551\) 1.57606i 0.0671423i
\(552\) 0 0
\(553\) 17.6708 + 10.2023i 0.751440 + 0.433844i
\(554\) 0 0
\(555\) −2.35780 + 4.08382i −0.100083 + 0.173349i
\(556\) 0 0
\(557\) −16.3299 + 9.42807i −0.691920 + 0.399480i −0.804331 0.594181i \(-0.797476\pi\)
0.112411 + 0.993662i \(0.464143\pi\)
\(558\) 0 0
\(559\) 6.60081 3.04811i 0.279185 0.128921i
\(560\) 0 0
\(561\) 2.07166 1.19607i 0.0874655 0.0504982i
\(562\) 0 0
\(563\) −9.22434 + 15.9770i −0.388760 + 0.673351i −0.992283 0.123994i \(-0.960430\pi\)
0.603523 + 0.797345i \(0.293763\pi\)
\(564\) 0 0
\(565\) 11.8580 + 6.84621i 0.498869 + 0.288022i
\(566\) 0 0
\(567\) 11.5436i 0.484787i
\(568\) 0 0
\(569\) 12.8990 + 22.3417i 0.540753 + 0.936612i 0.998861 + 0.0477153i \(0.0151940\pi\)
−0.458108 + 0.888897i \(0.651473\pi\)
\(570\) 0 0
\(571\) 46.0810 1.92843 0.964216 0.265118i \(-0.0854110\pi\)
0.964216 + 0.265118i \(0.0854110\pi\)
\(572\) 0 0
\(573\) −1.02144 −0.0426711
\(574\) 0 0
\(575\) −2.69554 4.66881i −0.112412 0.194703i
\(576\) 0 0
\(577\) 9.69085i 0.403435i −0.979444 0.201718i \(-0.935348\pi\)
0.979444 0.201718i \(-0.0646524\pi\)
\(578\) 0 0
\(579\) 4.12393 + 2.38095i 0.171385 + 0.0989489i
\(580\) 0 0
\(581\) 2.36960 4.10427i 0.0983075 0.170274i
\(582\) 0 0
\(583\) 4.13971 2.39006i 0.171449 0.0989863i
\(584\) 0 0
\(585\) 4.07500 + 8.82459i 0.168481 + 0.364852i
\(586\) 0 0
\(587\) 32.4680 18.7454i 1.34010 0.773705i 0.353275 0.935520i \(-0.385068\pi\)
0.986821 + 0.161815i \(0.0517348\pi\)
\(588\) 0 0
\(589\) −4.34138 + 7.51949i −0.178883 + 0.309835i
\(590\) 0 0
\(591\) −2.02178 1.16727i −0.0831648 0.0480152i
\(592\) 0 0
\(593\) 20.6021i 0.846027i −0.906123 0.423013i \(-0.860972\pi\)
0.906123 0.423013i \(-0.139028\pi\)
\(594\) 0 0
\(595\) −4.49167 7.77979i −0.184140 0.318940i
\(596\) 0 0
\(597\) 15.2949 0.625979
\(598\) 0 0
\(599\) −1.39843 −0.0571382 −0.0285691 0.999592i \(-0.509095\pi\)
−0.0285691 + 0.999592i \(0.509095\pi\)
\(600\) 0 0
\(601\) −19.2004 33.2561i −0.783201 1.35654i −0.930068 0.367387i \(-0.880252\pi\)
0.146867 0.989156i \(-0.453081\pi\)
\(602\) 0 0
\(603\) 13.7682i 0.560683i
\(604\) 0 0
\(605\) 8.86012 + 5.11539i 0.360215 + 0.207970i
\(606\) 0 0
\(607\) −3.33388 + 5.77446i −0.135318 + 0.234378i −0.925719 0.378212i \(-0.876539\pi\)
0.790401 + 0.612590i \(0.209872\pi\)
\(608\) 0 0
\(609\) 0.372340 0.214970i 0.0150880 0.00871104i
\(610\) 0 0
\(611\) −18.5583 + 26.2949i −0.750789 + 1.06378i
\(612\) 0 0
\(613\) 35.3895 20.4322i 1.42937 0.825247i 0.432299 0.901730i \(-0.357703\pi\)
0.997071 + 0.0764834i \(0.0243692\pi\)
\(614\) 0 0
\(615\) −0.330922 + 0.573174i −0.0133441 + 0.0231126i
\(616\) 0 0
\(617\) −10.1135 5.83904i −0.407155 0.235071i 0.282412 0.959293i \(-0.408866\pi\)
−0.689566 + 0.724222i \(0.742199\pi\)
\(618\) 0 0
\(619\) 23.9724i 0.963534i −0.876299 0.481767i \(-0.839995\pi\)
0.876299 0.481767i \(-0.160005\pi\)
\(620\) 0 0
\(621\) −8.46732 14.6658i −0.339782 0.588519i
\(622\) 0 0
\(623\) 1.35329 0.0542183
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.888085 1.53821i −0.0354667 0.0614301i
\(628\) 0 0
\(629\) 42.2880i 1.68613i
\(630\) 0 0
\(631\) −5.83169 3.36693i −0.232156 0.134035i 0.379410 0.925228i \(-0.376127\pi\)
−0.611566 + 0.791193i \(0.709460\pi\)
\(632\) 0 0
\(633\) −0.0401846 + 0.0696019i −0.00159720 + 0.00276643i
\(634\) 0 0
\(635\) 11.3709 6.56497i 0.451239 0.260523i
\(636\) 0 0
\(637\) −1.21244 + 13.2877i −0.0480385 + 0.526477i
\(638\) 0 0
\(639\) −36.2648 + 20.9375i −1.43461 + 0.828275i
\(640\) 0 0
\(641\) −0.320045 + 0.554334i −0.0126410 + 0.0218949i −0.872277 0.489013i \(-0.837357\pi\)
0.859636 + 0.510907i \(0.170691\pi\)
\(642\) 0 0
\(643\) 26.2562 + 15.1590i 1.03544 + 0.597814i 0.918540 0.395329i \(-0.129369\pi\)
0.116905 + 0.993143i \(0.462703\pi\)
\(644\) 0 0
\(645\) 1.11209i 0.0437886i
\(646\) 0 0
\(647\) −3.22347 5.58321i −0.126728 0.219499i 0.795679 0.605718i \(-0.207114\pi\)
−0.922407 + 0.386219i \(0.873781\pi\)
\(648\) 0 0
\(649\) 4.01731 0.157693
\(650\) 0 0
\(651\) −2.36861 −0.0928333
\(652\) 0 0
\(653\) 0.154888 + 0.268274i 0.00606124 + 0.0104984i 0.869040 0.494742i \(-0.164737\pi\)
−0.862979 + 0.505240i \(0.831404\pi\)
\(654\) 0 0
\(655\) 19.2978i 0.754029i
\(656\) 0 0
\(657\) −25.0826 14.4815i −0.978566 0.564975i
\(658\) 0 0
\(659\) 2.55240 4.42088i 0.0994273 0.172213i −0.812020 0.583629i \(-0.801632\pi\)
0.911448 + 0.411416i \(0.134966\pi\)
\(660\) 0 0
\(661\) 17.1957 9.92794i 0.668835 0.386152i −0.126800 0.991928i \(-0.540471\pi\)
0.795635 + 0.605776i \(0.207137\pi\)
\(662\) 0 0
\(663\) 8.03458 + 5.67062i 0.312037 + 0.220228i
\(664\) 0 0
\(665\) −5.77650 + 3.33506i −0.224003 + 0.129328i
\(666\) 0 0
\(667\) −1.15690 + 2.00382i −0.0447955 + 0.0775881i
\(668\) 0 0
\(669\) −2.33859 1.35018i −0.0904150 0.0522011i
\(670\) 0 0
\(671\) 1.67082i 0.0645012i
\(672\) 0 0
\(673\) 0.192547 + 0.333501i 0.00742213 + 0.0128555i 0.869713 0.493558i \(-0.164304\pi\)
−0.862290 + 0.506414i \(0.830971\pi\)
\(674\) 0 0
\(675\) 3.14124 0.120906
\(676\) 0 0
\(677\) −14.8350 −0.570157 −0.285078 0.958504i \(-0.592020\pi\)
−0.285078 + 0.958504i \(0.592020\pi\)
\(678\) 0 0
\(679\) 8.88043 + 15.3814i 0.340800 + 0.590282i
\(680\) 0 0
\(681\) 7.60617i 0.291469i
\(682\) 0 0
\(683\) −35.9469 20.7540i −1.37547 0.794129i −0.383861 0.923391i \(-0.625406\pi\)
−0.991610 + 0.129263i \(0.958739\pi\)
\(684\) 0 0
\(685\) 2.25392 3.90390i 0.0861178 0.149160i
\(686\) 0 0
\(687\) −6.03953 + 3.48692i −0.230422 + 0.133034i
\(688\) 0 0
\(689\) 16.0552 + 11.3314i 0.611653 + 0.431690i
\(690\) 0 0
\(691\) 9.55411 5.51607i 0.363455 0.209841i −0.307140 0.951664i \(-0.599372\pi\)
0.670595 + 0.741823i \(0.266039\pi\)
\(692\) 0 0
\(693\) −2.14735 + 3.71932i −0.0815712 + 0.141285i
\(694\) 0 0
\(695\) −8.28024 4.78060i −0.314087 0.181338i
\(696\) 0 0
\(697\) 5.93522i 0.224813i
\(698\) 0 0
\(699\) −2.83683 4.91353i −0.107299 0.185847i
\(700\) 0 0
\(701\) −29.7358 −1.12311 −0.561554 0.827440i \(-0.689796\pi\)
−0.561554 + 0.827440i \(0.689796\pi\)
\(702\) 0 0
\(703\) −31.3989 −1.18423
\(704\) 0 0
\(705\) 2.46142 + 4.26330i 0.0927023 + 0.160565i
\(706\) 0 0
\(707\) 12.5494i 0.471968i
\(708\) 0 0
\(709\) −39.3547 22.7214i −1.47800 0.853321i −0.478305 0.878194i \(-0.658749\pi\)
−0.999691 + 0.0248726i \(0.992082\pi\)
\(710\) 0 0
\(711\) 15.1418 26.2264i 0.567862 0.983567i
\(712\) 0 0
\(713\) 11.0394 6.37358i 0.413427 0.238692i
\(714\) 0 0
\(715\) 0.287346 3.14915i 0.0107461 0.117772i
\(716\) 0 0
\(717\) 9.63483 5.56267i 0.359819 0.207742i
\(718\) 0 0
\(719\) −26.1218 + 45.2443i −0.974179 + 1.68733i −0.291563 + 0.956552i \(0.594175\pi\)
−0.682617 + 0.730777i \(0.739158\pi\)
\(720\) 0 0
\(721\) 27.3746 + 15.8047i 1.01948 + 0.588599i
\(722\) 0 0
\(723\) 0.508777i 0.0189216i
\(724\) 0 0
\(725\) −0.214596 0.371692i −0.00796991 0.0138043i
\(726\) 0 0
\(727\) −46.9248 −1.74035 −0.870173 0.492747i \(-0.835993\pi\)
−0.870173 + 0.492747i \(0.835993\pi\)
\(728\) 0 0
\(729\) −11.9355 −0.442056
\(730\) 0 0
\(731\) 4.98645 + 8.63679i 0.184431 + 0.319443i
\(732\) 0 0
\(733\) 36.6313i 1.35301i 0.736439 + 0.676504i \(0.236506\pi\)
−0.736439 + 0.676504i \(0.763494\pi\)
\(734\) 0 0
\(735\) 1.76746 + 1.02044i 0.0651938 + 0.0376397i
\(736\) 0 0
\(737\) −2.23961 + 3.87912i −0.0824971 + 0.142889i
\(738\) 0 0
\(739\) 36.1588 20.8763i 1.33012 0.767947i 0.344805 0.938674i \(-0.387945\pi\)
0.985318 + 0.170727i \(0.0546116\pi\)
\(740\) 0 0
\(741\) 4.21043 5.96568i 0.154674 0.219155i
\(742\) 0 0
\(743\) −24.4237 + 14.1011i −0.896020 + 0.517318i −0.875907 0.482480i \(-0.839736\pi\)
−0.0201134 + 0.999798i \(0.506403\pi\)
\(744\) 0 0
\(745\) 7.94624 13.7633i 0.291128 0.504248i
\(746\) 0 0
\(747\) −6.09140 3.51687i −0.222873 0.128676i
\(748\) 0 0
\(749\) 13.9704i 0.510469i
\(750\) 0 0
\(751\) 15.9708 + 27.6623i 0.582784 + 1.00941i 0.995148 + 0.0983921i \(0.0313699\pi\)
−0.412364 + 0.911019i \(0.635297\pi\)
\(752\) 0 0
\(753\) 8.97201 0.326958
\(754\) 0 0
\(755\) 13.4356 0.488973
\(756\) 0 0
\(757\) −5.36247 9.28807i −0.194902 0.337581i 0.751966 0.659202i \(-0.229106\pi\)
−0.946868 + 0.321621i \(0.895772\pi\)
\(758\) 0 0
\(759\) 2.60759i 0.0946496i
\(760\) 0 0
\(761\) 0.389260 + 0.224739i 0.0141107 + 0.00814679i 0.507039 0.861923i \(-0.330740\pi\)
−0.492928 + 0.870070i \(0.664073\pi\)
\(762\) 0 0
\(763\) −10.1344 + 17.5533i −0.366889 + 0.635471i
\(764\) 0 0
\(765\) −11.5465 + 6.66637i −0.417464 + 0.241023i
\(766\) 0 0
\(767\) 6.92381 + 14.9938i 0.250004 + 0.541394i
\(768\) 0 0
\(769\) −11.7839 + 6.80346i −0.424940 + 0.245339i −0.697188 0.716888i \(-0.745566\pi\)
0.272249 + 0.962227i \(0.412233\pi\)
\(770\) 0 0
\(771\) 4.69068 8.12449i 0.168931 0.292596i
\(772\) 0 0
\(773\) 1.70461 + 0.984159i 0.0613107 + 0.0353977i 0.530342 0.847784i \(-0.322064\pi\)
−0.469031 + 0.883182i \(0.655397\pi\)
\(774\) 0 0
\(775\) 2.36449i 0.0849351i
\(776\) 0 0
\(777\) −4.28273 7.41791i −0.153642 0.266116i
\(778\) 0 0
\(779\) −4.40691 −0.157894
\(780\) 0 0
\(781\) 13.6233 0.487479
\(782\) 0 0
\(783\) −0.674098 1.16757i −0.0240903 0.0417256i
\(784\) 0 0
\(785\) 21.8879i 0.781214i
\(786\) 0 0
\(787\) −14.3743 8.29901i −0.512389 0.295828i 0.221426 0.975177i \(-0.428929\pi\)
−0.733815 + 0.679349i \(0.762262\pi\)
\(788\) 0 0