Properties

Label 1040.2.da.f.881.8
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 881.8
Root \(0.551543i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.f.641.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62367 + 2.81228i) q^{3} +1.00000i q^{5} +(-4.00640 - 2.31309i) q^{7} +(-3.77262 + 6.53437i) q^{9} +O(q^{10})\) \(q+(1.62367 + 2.81228i) q^{3} +1.00000i q^{5} +(-4.00640 - 2.31309i) q^{7} +(-3.77262 + 6.53437i) q^{9} +(2.79680 - 1.61473i) q^{11} +(-1.42742 + 3.31096i) q^{13} +(-2.81228 + 1.62367i) q^{15} +(-2.77825 + 4.81207i) q^{17} +(-1.72537 - 0.996140i) q^{19} -15.0228i q^{21} +(-2.20224 - 3.81440i) q^{23} -1.00000 q^{25} -14.7599 q^{27} +(-0.197974 - 0.342902i) q^{29} +7.20020i q^{31} +(9.08216 + 5.24359i) q^{33} +(2.31309 - 4.00640i) q^{35} +(0.708052 - 0.408794i) q^{37} +(-11.6290 + 1.36160i) q^{39} +(-2.79170 + 1.61179i) q^{41} +(-3.42488 + 5.93207i) q^{43} +(-6.53437 - 3.77262i) q^{45} -6.19979i q^{47} +(7.20081 + 12.4722i) q^{49} -18.0439 q^{51} -0.512700 q^{53} +(1.61473 + 2.79680i) q^{55} -6.46962i q^{57} +(6.82230 + 3.93886i) q^{59} +(3.08672 - 5.34635i) q^{61} +(30.2292 - 17.4528i) q^{63} +(-3.31096 - 1.42742i) q^{65} +(7.58286 - 4.37797i) q^{67} +(7.15144 - 12.3867i) q^{69} +(2.43415 + 1.40535i) q^{71} +5.03482i q^{73} +(-1.62367 - 2.81228i) q^{75} -14.9401 q^{77} +8.25143 q^{79} +(-12.6475 - 21.9060i) q^{81} +1.49741i q^{83} +(-4.81207 - 2.77825i) q^{85} +(0.642891 - 1.11352i) q^{87} +(14.1316 - 8.15887i) q^{89} +(13.3774 - 9.96326i) q^{91} +(-20.2490 + 11.6908i) q^{93} +(0.996140 - 1.72537i) q^{95} +(4.84132 + 2.79514i) q^{97} +24.3671i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 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
\(3\) 1.62367 + 2.81228i 0.937427 + 1.62367i 0.770247 + 0.637745i \(0.220133\pi\)
0.167180 + 0.985926i \(0.446534\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −4.00640 2.31309i −1.51428 0.874267i −0.999860 0.0167263i \(-0.994676\pi\)
−0.514415 0.857541i \(-0.671991\pi\)
\(8\) 0 0
\(9\) −3.77262 + 6.53437i −1.25754 + 2.17812i
\(10\) 0 0
\(11\) 2.79680 1.61473i 0.843266 0.486860i −0.0151073 0.999886i \(-0.504809\pi\)
0.858373 + 0.513026i \(0.171476\pi\)
\(12\) 0 0
\(13\) −1.42742 + 3.31096i −0.395896 + 0.918295i
\(14\) 0 0
\(15\) −2.81228 + 1.62367i −0.726128 + 0.419230i
\(16\) 0 0
\(17\) −2.77825 + 4.81207i −0.673825 + 1.16710i 0.302986 + 0.952995i \(0.402016\pi\)
−0.976811 + 0.214104i \(0.931317\pi\)
\(18\) 0 0
\(19\) −1.72537 0.996140i −0.395826 0.228530i 0.288855 0.957373i \(-0.406725\pi\)
−0.684681 + 0.728842i \(0.740059\pi\)
\(20\) 0 0
\(21\) 15.0228i 3.27825i
\(22\) 0 0
\(23\) −2.20224 3.81440i −0.459199 0.795357i 0.539719 0.841845i \(-0.318530\pi\)
−0.998919 + 0.0464882i \(0.985197\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −14.7599 −2.84055
\(28\) 0 0
\(29\) −0.197974 0.342902i −0.0367629 0.0636753i 0.847059 0.531500i \(-0.178371\pi\)
−0.883821 + 0.467824i \(0.845038\pi\)
\(30\) 0 0
\(31\) 7.20020i 1.29319i 0.762832 + 0.646597i \(0.223808\pi\)
−0.762832 + 0.646597i \(0.776192\pi\)
\(32\) 0 0
\(33\) 9.08216 + 5.24359i 1.58100 + 0.912791i
\(34\) 0 0
\(35\) 2.31309 4.00640i 0.390984 0.677205i
\(36\) 0 0
\(37\) 0.708052 0.408794i 0.116403 0.0672053i −0.440668 0.897670i \(-0.645258\pi\)
0.557071 + 0.830465i \(0.311925\pi\)
\(38\) 0 0
\(39\) −11.6290 + 1.36160i −1.86213 + 0.218030i
\(40\) 0 0
\(41\) −2.79170 + 1.61179i −0.435991 + 0.251719i −0.701896 0.712280i \(-0.747663\pi\)
0.265905 + 0.963999i \(0.414329\pi\)
\(42\) 0 0
\(43\) −3.42488 + 5.93207i −0.522290 + 0.904633i 0.477374 + 0.878700i \(0.341589\pi\)
−0.999664 + 0.0259325i \(0.991745\pi\)
\(44\) 0 0
\(45\) −6.53437 3.77262i −0.974086 0.562389i
\(46\) 0 0
\(47\) 6.19979i 0.904333i −0.891934 0.452166i \(-0.850651\pi\)
0.891934 0.452166i \(-0.149349\pi\)
\(48\) 0 0
\(49\) 7.20081 + 12.4722i 1.02869 + 1.78174i
\(50\) 0 0
\(51\) −18.0439 −2.52665
\(52\) 0 0
\(53\) −0.512700 −0.0704247 −0.0352124 0.999380i \(-0.511211\pi\)
−0.0352124 + 0.999380i \(0.511211\pi\)
\(54\) 0 0
\(55\) 1.61473 + 2.79680i 0.217730 + 0.377120i
\(56\) 0 0
\(57\) 6.46962i 0.856922i
\(58\) 0 0
\(59\) 6.82230 + 3.93886i 0.888188 + 0.512795i 0.873349 0.487094i \(-0.161943\pi\)
0.0148385 + 0.999890i \(0.495277\pi\)
\(60\) 0 0
\(61\) 3.08672 5.34635i 0.395214 0.684530i −0.597915 0.801560i \(-0.704004\pi\)
0.993128 + 0.117029i \(0.0373371\pi\)
\(62\) 0 0
\(63\) 30.2292 17.4528i 3.80852 2.19885i
\(64\) 0 0
\(65\) −3.31096 1.42742i −0.410674 0.177050i
\(66\) 0 0
\(67\) 7.58286 4.37797i 0.926394 0.534854i 0.0407246 0.999170i \(-0.487033\pi\)
0.885669 + 0.464317i \(0.153700\pi\)
\(68\) 0 0
\(69\) 7.15144 12.3867i 0.860932 1.49118i
\(70\) 0 0
\(71\) 2.43415 + 1.40535i 0.288880 + 0.166785i 0.637437 0.770503i \(-0.279995\pi\)
−0.348557 + 0.937288i \(0.613328\pi\)
\(72\) 0 0
\(73\) 5.03482i 0.589281i 0.955608 + 0.294640i \(0.0951998\pi\)
−0.955608 + 0.294640i \(0.904800\pi\)
\(74\) 0 0
\(75\) −1.62367 2.81228i −0.187485 0.324734i
\(76\) 0 0
\(77\) −14.9401 −1.70258
\(78\) 0 0
\(79\) 8.25143 0.928358 0.464179 0.885741i \(-0.346349\pi\)
0.464179 + 0.885741i \(0.346349\pi\)
\(80\) 0 0
\(81\) −12.6475 21.9060i −1.40527 2.43400i
\(82\) 0 0
\(83\) 1.49741i 0.164362i 0.996617 + 0.0821811i \(0.0261886\pi\)
−0.996617 + 0.0821811i \(0.973811\pi\)
\(84\) 0 0
\(85\) −4.81207 2.77825i −0.521942 0.301344i
\(86\) 0 0
\(87\) 0.642891 1.11352i 0.0689251 0.119382i
\(88\) 0 0
\(89\) 14.1316 8.15887i 1.49794 0.864838i 0.497947 0.867207i \(-0.334087\pi\)
0.999997 + 0.00236896i \(0.000754063\pi\)
\(90\) 0 0
\(91\) 13.3774 9.96326i 1.40233 1.04443i
\(92\) 0 0
\(93\) −20.2490 + 11.6908i −2.09972 + 1.21228i
\(94\) 0 0
\(95\) 0.996140 1.72537i 0.102202 0.177019i
\(96\) 0 0
\(97\) 4.84132 + 2.79514i 0.491561 + 0.283803i 0.725222 0.688515i \(-0.241737\pi\)
−0.233661 + 0.972318i \(0.575070\pi\)
\(98\) 0 0
\(99\) 24.3671i 2.44898i
\(100\) 0 0
\(101\) 8.14688 + 14.1108i 0.810645 + 1.40408i 0.912413 + 0.409270i \(0.134217\pi\)
−0.101769 + 0.994808i \(0.532450\pi\)
\(102\) 0 0
\(103\) −17.2764 −1.70229 −0.851146 0.524928i \(-0.824092\pi\)
−0.851146 + 0.524928i \(0.824092\pi\)
\(104\) 0 0
\(105\) 15.0228 1.46608
\(106\) 0 0
\(107\) 2.79797 + 4.84622i 0.270490 + 0.468502i 0.968987 0.247110i \(-0.0794810\pi\)
−0.698498 + 0.715612i \(0.746148\pi\)
\(108\) 0 0
\(109\) 7.58276i 0.726296i 0.931731 + 0.363148i \(0.118298\pi\)
−0.931731 + 0.363148i \(0.881702\pi\)
\(110\) 0 0
\(111\) 2.29929 + 1.32749i 0.218239 + 0.126000i
\(112\) 0 0
\(113\) −6.15234 + 10.6562i −0.578764 + 1.00245i 0.416858 + 0.908972i \(0.363131\pi\)
−0.995622 + 0.0934763i \(0.970202\pi\)
\(114\) 0 0
\(115\) 3.81440 2.20224i 0.355694 0.205360i
\(116\) 0 0
\(117\) −16.2499 21.8183i −1.50230 2.01710i
\(118\) 0 0
\(119\) 22.2615 12.8527i 2.04071 1.17821i
\(120\) 0 0
\(121\) −0.285288 + 0.494134i −0.0259353 + 0.0449213i
\(122\) 0 0
\(123\) −9.06562 5.23404i −0.817419 0.471937i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −1.91541 3.31759i −0.169965 0.294389i 0.768442 0.639919i \(-0.221032\pi\)
−0.938407 + 0.345531i \(0.887699\pi\)
\(128\) 0 0
\(129\) −22.2436 −1.95844
\(130\) 0 0
\(131\) −12.2733 −1.07233 −0.536163 0.844115i \(-0.680127\pi\)
−0.536163 + 0.844115i \(0.680127\pi\)
\(132\) 0 0
\(133\) 4.60833 + 7.98187i 0.399593 + 0.692116i
\(134\) 0 0
\(135\) 14.7599i 1.27033i
\(136\) 0 0
\(137\) 7.83794 + 4.52523i 0.669640 + 0.386617i 0.795940 0.605375i \(-0.206977\pi\)
−0.126300 + 0.991992i \(0.540310\pi\)
\(138\) 0 0
\(139\) 2.60293 4.50840i 0.220777 0.382398i −0.734267 0.678861i \(-0.762474\pi\)
0.955044 + 0.296463i \(0.0958072\pi\)
\(140\) 0 0
\(141\) 17.4356 10.0664i 1.46834 0.847746i
\(142\) 0 0
\(143\) 1.35410 + 11.5650i 0.113235 + 0.967113i
\(144\) 0 0
\(145\) 0.342902 0.197974i 0.0284764 0.0164409i
\(146\) 0 0
\(147\) −23.3835 + 40.5014i −1.92864 + 3.34050i
\(148\) 0 0
\(149\) −11.0988 6.40790i −0.909250 0.524956i −0.0290603 0.999578i \(-0.509251\pi\)
−0.880190 + 0.474622i \(0.842585\pi\)
\(150\) 0 0
\(151\) 17.8652i 1.45385i 0.686719 + 0.726923i \(0.259050\pi\)
−0.686719 + 0.726923i \(0.740950\pi\)
\(152\) 0 0
\(153\) −20.9626 36.3082i −1.69472 2.93535i
\(154\) 0 0
\(155\) −7.20020 −0.578334
\(156\) 0 0
\(157\) 13.7462 1.09707 0.548533 0.836129i \(-0.315186\pi\)
0.548533 + 0.836129i \(0.315186\pi\)
\(158\) 0 0
\(159\) −0.832456 1.44186i −0.0660180 0.114347i
\(160\) 0 0
\(161\) 20.3760i 1.60585i
\(162\) 0 0
\(163\) −4.26051 2.45980i −0.333709 0.192667i 0.323778 0.946133i \(-0.395047\pi\)
−0.657486 + 0.753466i \(0.728380\pi\)
\(164\) 0 0
\(165\) −5.24359 + 9.08216i −0.408213 + 0.707045i
\(166\) 0 0
\(167\) −17.3879 + 10.0389i −1.34552 + 0.776834i −0.987611 0.156924i \(-0.949842\pi\)
−0.357905 + 0.933758i \(0.616509\pi\)
\(168\) 0 0
\(169\) −8.92492 9.45229i −0.686533 0.727099i
\(170\) 0 0
\(171\) 13.0183 7.51612i 0.995534 0.574772i
\(172\) 0 0
\(173\) −1.48256 + 2.56787i −0.112717 + 0.195231i −0.916865 0.399198i \(-0.869289\pi\)
0.804148 + 0.594429i \(0.202622\pi\)
\(174\) 0 0
\(175\) 4.00640 + 2.31309i 0.302855 + 0.174853i
\(176\) 0 0
\(177\) 25.5816i 1.92283i
\(178\) 0 0
\(179\) 13.0457 + 22.5958i 0.975079 + 1.68889i 0.679674 + 0.733514i \(0.262121\pi\)
0.295404 + 0.955372i \(0.404546\pi\)
\(180\) 0 0
\(181\) 16.3302 1.21382 0.606909 0.794772i \(-0.292409\pi\)
0.606909 + 0.794772i \(0.292409\pi\)
\(182\) 0 0
\(183\) 20.0473 1.48194
\(184\) 0 0
\(185\) 0.408794 + 0.708052i 0.0300551 + 0.0520570i
\(186\) 0 0
\(187\) 17.9445i 1.31223i
\(188\) 0 0
\(189\) 59.1342 + 34.1412i 4.30138 + 2.48340i
\(190\) 0 0
\(191\) −5.06878 + 8.77939i −0.366764 + 0.635254i −0.989058 0.147530i \(-0.952868\pi\)
0.622293 + 0.782784i \(0.286201\pi\)
\(192\) 0 0
\(193\) 9.74200 5.62455i 0.701244 0.404864i −0.106566 0.994306i \(-0.533986\pi\)
0.807811 + 0.589442i \(0.200652\pi\)
\(194\) 0 0
\(195\) −1.36160 11.6290i −0.0975059 0.832772i
\(196\) 0 0
\(197\) −15.4235 + 8.90475i −1.09888 + 0.634437i −0.935926 0.352197i \(-0.885435\pi\)
−0.162951 + 0.986634i \(0.552101\pi\)
\(198\) 0 0
\(199\) 1.27617 2.21039i 0.0904652 0.156690i −0.817242 0.576295i \(-0.804498\pi\)
0.907707 + 0.419605i \(0.137831\pi\)
\(200\) 0 0
\(201\) 24.6242 + 14.2168i 1.73685 + 1.00277i
\(202\) 0 0
\(203\) 1.83173i 0.128562i
\(204\) 0 0
\(205\) −1.61179 2.79170i −0.112572 0.194981i
\(206\) 0 0
\(207\) 33.2329 2.30985
\(208\) 0 0
\(209\) −6.43399 −0.445049
\(210\) 0 0
\(211\) −8.82052 15.2776i −0.607230 1.05175i −0.991695 0.128613i \(-0.958947\pi\)
0.384465 0.923140i \(-0.374386\pi\)
\(212\) 0 0
\(213\) 9.12734i 0.625395i
\(214\) 0 0
\(215\) −5.93207 3.42488i −0.404564 0.233575i
\(216\) 0 0
\(217\) 16.6547 28.8469i 1.13060 1.95825i
\(218\) 0 0
\(219\) −14.1593 + 8.17489i −0.956798 + 0.552408i
\(220\) 0 0
\(221\) −11.9668 16.0675i −0.804977 1.08082i
\(222\) 0 0
\(223\) 2.63584 1.52181i 0.176509 0.101908i −0.409142 0.912471i \(-0.634172\pi\)
0.585652 + 0.810563i \(0.300839\pi\)
\(224\) 0 0
\(225\) 3.77262 6.53437i 0.251508 0.435625i
\(226\) 0 0
\(227\) −3.09823 1.78877i −0.205637 0.118725i 0.393645 0.919262i \(-0.371214\pi\)
−0.599282 + 0.800538i \(0.704547\pi\)
\(228\) 0 0
\(229\) 4.44560i 0.293774i 0.989153 + 0.146887i \(0.0469253\pi\)
−0.989153 + 0.146887i \(0.953075\pi\)
\(230\) 0 0
\(231\) −24.2578 42.0158i −1.59605 2.76443i
\(232\) 0 0
\(233\) −1.11772 −0.0732245 −0.0366122 0.999330i \(-0.511657\pi\)
−0.0366122 + 0.999330i \(0.511657\pi\)
\(234\) 0 0
\(235\) 6.19979 0.404430
\(236\) 0 0
\(237\) 13.3976 + 23.2053i 0.870268 + 1.50735i
\(238\) 0 0
\(239\) 1.69362i 0.109551i −0.998499 0.0547755i \(-0.982556\pi\)
0.998499 0.0547755i \(-0.0174443\pi\)
\(240\) 0 0
\(241\) −21.0402 12.1476i −1.35532 0.782494i −0.366331 0.930485i \(-0.619386\pi\)
−0.988989 + 0.147991i \(0.952719\pi\)
\(242\) 0 0
\(243\) 18.9307 32.7889i 1.21440 2.10341i
\(244\) 0 0
\(245\) −12.4722 + 7.20081i −0.796817 + 0.460043i
\(246\) 0 0
\(247\) 5.76101 4.29070i 0.366564 0.273011i
\(248\) 0 0
\(249\) −4.21114 + 2.43130i −0.266870 + 0.154078i
\(250\) 0 0
\(251\) 6.39028 11.0683i 0.403351 0.698624i −0.590777 0.806835i \(-0.701179\pi\)
0.994128 + 0.108211i \(0.0345122\pi\)
\(252\) 0 0
\(253\) −12.3184 7.11206i −0.774454 0.447131i
\(254\) 0 0
\(255\) 18.0439i 1.12995i
\(256\) 0 0
\(257\) −0.350393 0.606898i −0.0218569 0.0378573i 0.854890 0.518809i \(-0.173624\pi\)
−0.876747 + 0.480952i \(0.840291\pi\)
\(258\) 0 0
\(259\) −3.78232 −0.235022
\(260\) 0 0
\(261\) 2.98753 0.184923
\(262\) 0 0
\(263\) −2.97697 5.15626i −0.183568 0.317948i 0.759525 0.650478i \(-0.225431\pi\)
−0.943093 + 0.332529i \(0.892098\pi\)
\(264\) 0 0
\(265\) 0.512700i 0.0314949i
\(266\) 0 0
\(267\) 45.8901 + 26.4947i 2.80843 + 1.62145i
\(268\) 0 0
\(269\) −9.77151 + 16.9247i −0.595779 + 1.03192i 0.397657 + 0.917534i \(0.369823\pi\)
−0.993436 + 0.114386i \(0.963510\pi\)
\(270\) 0 0
\(271\) 20.1091 11.6100i 1.22154 0.705257i 0.256294 0.966599i \(-0.417498\pi\)
0.965246 + 0.261342i \(0.0841650\pi\)
\(272\) 0 0
\(273\) 49.7400 + 21.4439i 3.01040 + 1.29785i
\(274\) 0 0
\(275\) −2.79680 + 1.61473i −0.168653 + 0.0973719i
\(276\) 0 0
\(277\) 8.96861 15.5341i 0.538872 0.933353i −0.460094 0.887870i \(-0.652184\pi\)
0.998965 0.0454825i \(-0.0144825\pi\)
\(278\) 0 0
\(279\) −47.0488 27.1636i −2.81674 1.62624i
\(280\) 0 0
\(281\) 28.0370i 1.67254i −0.548314 0.836272i \(-0.684730\pi\)
0.548314 0.836272i \(-0.315270\pi\)
\(282\) 0 0
\(283\) 4.04936 + 7.01370i 0.240709 + 0.416921i 0.960917 0.276838i \(-0.0892866\pi\)
−0.720207 + 0.693759i \(0.755953\pi\)
\(284\) 0 0
\(285\) 6.46962 0.383227
\(286\) 0 0
\(287\) 14.9129 0.880280
\(288\) 0 0
\(289\) −6.93735 12.0158i −0.408079 0.706814i
\(290\) 0 0
\(291\) 18.1535i 1.06418i
\(292\) 0 0
\(293\) 6.35415 + 3.66857i 0.371213 + 0.214320i 0.673988 0.738742i \(-0.264580\pi\)
−0.302775 + 0.953062i \(0.597913\pi\)
\(294\) 0 0
\(295\) −3.93886 + 6.82230i −0.229329 + 0.397210i
\(296\) 0 0
\(297\) −41.2806 + 23.8333i −2.39534 + 1.38295i
\(298\) 0 0
\(299\) 15.7729 1.84678i 0.912168 0.106802i
\(300\) 0 0
\(301\) 27.4429 15.8442i 1.58178 0.913242i
\(302\) 0 0
\(303\) −26.4557 + 45.8226i −1.51984 + 2.63244i
\(304\) 0 0
\(305\) 5.34635 + 3.08672i 0.306131 + 0.176745i
\(306\) 0 0
\(307\) 19.4266i 1.10874i −0.832271 0.554369i \(-0.812960\pi\)
0.832271 0.554369i \(-0.187040\pi\)
\(308\) 0 0
\(309\) −28.0512 48.5861i −1.59578 2.76396i
\(310\) 0 0
\(311\) 5.69920 0.323172 0.161586 0.986859i \(-0.448339\pi\)
0.161586 + 0.986859i \(0.448339\pi\)
\(312\) 0 0
\(313\) 26.8426 1.51724 0.758618 0.651536i \(-0.225875\pi\)
0.758618 + 0.651536i \(0.225875\pi\)
\(314\) 0 0
\(315\) 17.4528 + 30.2292i 0.983356 + 1.70322i
\(316\) 0 0
\(317\) 10.2434i 0.575326i 0.957732 + 0.287663i \(0.0928782\pi\)
−0.957732 + 0.287663i \(0.907122\pi\)
\(318\) 0 0
\(319\) −1.10739 0.639351i −0.0620018 0.0357968i
\(320\) 0 0
\(321\) −9.08596 + 15.7373i −0.507129 + 0.878373i
\(322\) 0 0
\(323\) 9.58699 5.53505i 0.533435 0.307979i
\(324\) 0 0
\(325\) 1.42742 3.31096i 0.0791792 0.183659i
\(326\) 0 0
\(327\) −21.3248 + 12.3119i −1.17927 + 0.680850i
\(328\) 0 0
\(329\) −14.3407 + 24.8388i −0.790629 + 1.36941i
\(330\) 0 0
\(331\) −19.9111 11.4957i −1.09441 0.631861i −0.159666 0.987171i \(-0.551042\pi\)
−0.934748 + 0.355310i \(0.884375\pi\)
\(332\) 0 0
\(333\) 6.16890i 0.338053i
\(334\) 0 0
\(335\) 4.37797 + 7.58286i 0.239194 + 0.414296i
\(336\) 0 0
\(337\) −1.35010 −0.0735446 −0.0367723 0.999324i \(-0.511708\pi\)
−0.0367723 + 0.999324i \(0.511708\pi\)
\(338\) 0 0
\(339\) −39.9575 −2.17020
\(340\) 0 0
\(341\) 11.6264 + 20.1375i 0.629604 + 1.09051i
\(342\) 0 0
\(343\) 34.2413i 1.84885i
\(344\) 0 0
\(345\) 12.3867 + 7.15144i 0.666875 + 0.385021i
\(346\) 0 0
\(347\) 0.904069 1.56589i 0.0485330 0.0840615i −0.840738 0.541442i \(-0.817879\pi\)
0.889271 + 0.457380i \(0.151212\pi\)
\(348\) 0 0
\(349\) 11.5909 6.69200i 0.620446 0.358215i −0.156597 0.987663i \(-0.550052\pi\)
0.777043 + 0.629448i \(0.216719\pi\)
\(350\) 0 0
\(351\) 21.0687 48.8696i 1.12456 2.60847i
\(352\) 0 0
\(353\) 7.29102 4.20948i 0.388062 0.224048i −0.293258 0.956033i \(-0.594740\pi\)
0.681320 + 0.731986i \(0.261406\pi\)
\(354\) 0 0
\(355\) −1.40535 + 2.43415i −0.0745885 + 0.129191i
\(356\) 0 0
\(357\) 72.2909 + 41.7372i 3.82604 + 2.20896i
\(358\) 0 0
\(359\) 9.35788i 0.493890i 0.969029 + 0.246945i \(0.0794267\pi\)
−0.969029 + 0.246945i \(0.920573\pi\)
\(360\) 0 0
\(361\) −7.51541 13.0171i −0.395548 0.685109i
\(362\) 0 0
\(363\) −1.85286 −0.0972499
\(364\) 0 0
\(365\) −5.03482 −0.263534
\(366\) 0 0
\(367\) 14.4871 + 25.0924i 0.756219 + 1.30981i 0.944766 + 0.327746i \(0.106289\pi\)
−0.188547 + 0.982064i \(0.560378\pi\)
\(368\) 0 0
\(369\) 24.3227i 1.26619i
\(370\) 0 0
\(371\) 2.05408 + 1.18592i 0.106642 + 0.0615700i
\(372\) 0 0
\(373\) −8.76329 + 15.1785i −0.453746 + 0.785911i −0.998615 0.0526100i \(-0.983246\pi\)
0.544869 + 0.838521i \(0.316579\pi\)
\(374\) 0 0
\(375\) 2.81228 1.62367i 0.145226 0.0838460i
\(376\) 0 0
\(377\) 1.41793 0.166019i 0.0730270 0.00855044i
\(378\) 0 0
\(379\) −10.5841 + 6.11073i −0.543669 + 0.313887i −0.746564 0.665313i \(-0.768298\pi\)
0.202896 + 0.979200i \(0.434965\pi\)
\(380\) 0 0
\(381\) 6.22000 10.7734i 0.318660 0.551936i
\(382\) 0 0
\(383\) 4.41450 + 2.54871i 0.225570 + 0.130233i 0.608527 0.793533i \(-0.291761\pi\)
−0.382957 + 0.923766i \(0.625094\pi\)
\(384\) 0 0
\(385\) 14.9401i 0.761418i
\(386\) 0 0
\(387\) −25.8416 44.7589i −1.31360 2.27522i
\(388\) 0 0
\(389\) −15.3931 −0.780461 −0.390231 0.920717i \(-0.627605\pi\)
−0.390231 + 0.920717i \(0.627605\pi\)
\(390\) 0 0
\(391\) 24.4735 1.23768
\(392\) 0 0
\(393\) −19.9279 34.5161i −1.00523 1.74110i
\(394\) 0 0
\(395\) 8.25143i 0.415174i
\(396\) 0 0
\(397\) 8.37393 + 4.83469i 0.420276 + 0.242646i 0.695195 0.718821i \(-0.255318\pi\)
−0.274920 + 0.961467i \(0.588651\pi\)
\(398\) 0 0
\(399\) −14.9648 + 25.9199i −0.749179 + 1.29762i
\(400\) 0 0
\(401\) 24.7662 14.2988i 1.23676 0.714046i 0.268332 0.963326i \(-0.413527\pi\)
0.968431 + 0.249281i \(0.0801941\pi\)
\(402\) 0 0
\(403\) −23.8396 10.2777i −1.18753 0.511970i
\(404\) 0 0
\(405\) 21.9060 12.6475i 1.08852 0.628457i
\(406\) 0 0
\(407\) 1.32018 2.28663i 0.0654391 0.113344i
\(408\) 0 0
\(409\) 5.76401 + 3.32785i 0.285012 + 0.164552i 0.635690 0.771944i \(-0.280716\pi\)
−0.350678 + 0.936496i \(0.614049\pi\)
\(410\) 0 0
\(411\) 29.3900i 1.44970i
\(412\) 0 0
\(413\) −18.2219 31.5612i −0.896641 1.55303i
\(414\) 0 0
\(415\) −1.49741 −0.0735050
\(416\) 0 0
\(417\) 16.9052 0.827851
\(418\) 0 0
\(419\) 8.57883 + 14.8590i 0.419103 + 0.725909i 0.995850 0.0910150i \(-0.0290111\pi\)
−0.576746 + 0.816923i \(0.695678\pi\)
\(420\) 0 0
\(421\) 18.9638i 0.924237i −0.886818 0.462119i \(-0.847089\pi\)
0.886818 0.462119i \(-0.152911\pi\)
\(422\) 0 0
\(423\) 40.5117 + 23.3895i 1.96975 + 1.13723i
\(424\) 0 0
\(425\) 2.77825 4.81207i 0.134765 0.233420i
\(426\) 0 0
\(427\) −24.7332 + 14.2797i −1.19693 + 0.691045i
\(428\) 0 0
\(429\) −30.3254 + 22.5858i −1.46412 + 1.09045i
\(430\) 0 0
\(431\) 7.90265 4.56260i 0.380657 0.219773i −0.297447 0.954738i \(-0.596135\pi\)
0.678104 + 0.734966i \(0.262802\pi\)
\(432\) 0 0
\(433\) 15.0774 26.1149i 0.724575 1.25500i −0.234574 0.972098i \(-0.575370\pi\)
0.959149 0.282902i \(-0.0912970\pi\)
\(434\) 0 0
\(435\) 1.11352 + 0.642891i 0.0533892 + 0.0308243i
\(436\) 0 0
\(437\) 8.77497i 0.419764i
\(438\) 0 0
\(439\) −2.07643 3.59649i −0.0991028 0.171651i 0.812211 0.583364i \(-0.198264\pi\)
−0.911314 + 0.411713i \(0.864931\pi\)
\(440\) 0 0
\(441\) −108.664 −5.17446
\(442\) 0 0
\(443\) −33.0164 −1.56866 −0.784329 0.620345i \(-0.786993\pi\)
−0.784329 + 0.620345i \(0.786993\pi\)
\(444\) 0 0
\(445\) 8.15887 + 14.1316i 0.386768 + 0.669901i
\(446\) 0 0
\(447\) 41.6173i 1.96843i
\(448\) 0 0
\(449\) 17.9151 + 10.3433i 0.845466 + 0.488130i 0.859119 0.511777i \(-0.171012\pi\)
−0.0136523 + 0.999907i \(0.504346\pi\)
\(450\) 0 0
\(451\) −5.20522 + 9.01570i −0.245104 + 0.424533i
\(452\) 0 0
\(453\) −50.2419 + 29.0072i −2.36057 + 1.36287i
\(454\) 0 0
\(455\) 9.96326 + 13.3774i 0.467085 + 0.627142i
\(456\) 0 0
\(457\) −3.88255 + 2.24159i −0.181618 + 0.104857i −0.588053 0.808823i \(-0.700105\pi\)
0.406435 + 0.913680i \(0.366772\pi\)
\(458\) 0 0
\(459\) 41.0068 71.0259i 1.91403 3.31521i
\(460\) 0 0
\(461\) −19.8427 11.4562i −0.924167 0.533568i −0.0392048 0.999231i \(-0.512482\pi\)
−0.884962 + 0.465663i \(0.845816\pi\)
\(462\) 0 0
\(463\) 19.4119i 0.902148i 0.892486 + 0.451074i \(0.148959\pi\)
−0.892486 + 0.451074i \(0.851041\pi\)
\(464\) 0 0
\(465\) −11.6908 20.2490i −0.542146 0.939024i
\(466\) 0 0
\(467\) 2.90247 0.134310 0.0671552 0.997743i \(-0.478608\pi\)
0.0671552 + 0.997743i \(0.478608\pi\)
\(468\) 0 0
\(469\) −40.5066 −1.87042
\(470\) 0 0
\(471\) 22.3193 + 38.6582i 1.02842 + 1.78128i
\(472\) 0 0
\(473\) 22.1211i 1.01713i
\(474\) 0 0
\(475\) 1.72537 + 0.996140i 0.0791652 + 0.0457061i
\(476\) 0 0
\(477\) 1.93422 3.35017i 0.0885619 0.153394i
\(478\) 0 0
\(479\) 12.9896 7.49954i 0.593509 0.342663i −0.172975 0.984926i \(-0.555338\pi\)
0.766484 + 0.642264i \(0.222005\pi\)
\(480\) 0 0
\(481\) 0.342811 + 2.92786i 0.0156308 + 0.133499i
\(482\) 0 0
\(483\) −57.3030 + 33.0839i −2.60738 + 1.50537i
\(484\) 0 0
\(485\) −2.79514 + 4.84132i −0.126921 + 0.219833i
\(486\) 0 0
\(487\) 32.1131 + 18.5405i 1.45518 + 0.840149i 0.998768 0.0496185i \(-0.0158006\pi\)
0.456413 + 0.889768i \(0.349134\pi\)
\(488\) 0 0
\(489\) 15.9757i 0.722444i
\(490\) 0 0
\(491\) 4.83319 + 8.37133i 0.218119 + 0.377793i 0.954233 0.299065i \(-0.0966747\pi\)
−0.736114 + 0.676857i \(0.763341\pi\)
\(492\) 0 0
\(493\) 2.20009 0.0990871
\(494\) 0 0
\(495\) −24.3671 −1.09522
\(496\) 0 0
\(497\) −6.50143 11.2608i −0.291629 0.505117i
\(498\) 0 0
\(499\) 38.0637i 1.70397i −0.523570 0.851983i \(-0.675400\pi\)
0.523570 0.851983i \(-0.324600\pi\)
\(500\) 0 0
\(501\) −56.4645 32.5998i −2.52265 1.45645i
\(502\) 0 0
\(503\) 1.09655 1.89928i 0.0488927 0.0846846i −0.840543 0.541744i \(-0.817764\pi\)
0.889436 + 0.457060i \(0.151097\pi\)
\(504\) 0 0
\(505\) −14.1108 + 8.14688i −0.627923 + 0.362531i
\(506\) 0 0
\(507\) 12.0914 40.4468i 0.536996 1.79631i
\(508\) 0 0
\(509\) 21.5682 12.4524i 0.955992 0.551942i 0.0610551 0.998134i \(-0.480553\pi\)
0.894937 + 0.446192i \(0.147220\pi\)
\(510\) 0 0
\(511\) 11.6460 20.1715i 0.515189 0.892333i
\(512\) 0 0
\(513\) 25.4663 + 14.7030i 1.12436 + 0.649152i
\(514\) 0 0
\(515\) 17.2764i 0.761288i
\(516\) 0 0
\(517\) −10.0110 17.3396i −0.440283 0.762593i
\(518\) 0 0
\(519\) −9.62875 −0.422655
\(520\) 0 0
\(521\) 21.2273 0.929984 0.464992 0.885315i \(-0.346057\pi\)
0.464992 + 0.885315i \(0.346057\pi\)
\(522\) 0 0
\(523\) −11.1474 19.3079i −0.487444 0.844278i 0.512452 0.858716i \(-0.328737\pi\)
−0.999896 + 0.0144383i \(0.995404\pi\)
\(524\) 0 0
\(525\) 15.0228i 0.655650i
\(526\) 0 0
\(527\) −34.6479 20.0040i −1.50928 0.871386i
\(528\) 0 0
\(529\) 1.80025 3.11812i 0.0782717 0.135571i
\(530\) 0 0
\(531\) −51.4759 + 29.7196i −2.23386 + 1.28972i
\(532\) 0 0
\(533\) −1.35163 11.5439i −0.0585457 0.500023i
\(534\) 0 0
\(535\) −4.84622 + 2.79797i −0.209520 + 0.120967i
\(536\) 0 0
\(537\) −42.3638 + 73.3762i −1.82813 + 3.16642i
\(538\) 0 0
\(539\) 40.2784 + 23.2547i 1.73491 + 1.00165i
\(540\) 0 0
\(541\) 24.1110i 1.03661i 0.855194 + 0.518307i \(0.173438\pi\)
−0.855194 + 0.518307i \(0.826562\pi\)
\(542\) 0 0
\(543\) 26.5150 + 45.9252i 1.13787 + 1.97084i
\(544\) 0 0
\(545\) −7.58276 −0.324810
\(546\) 0 0
\(547\) 44.9078 1.92012 0.960060 0.279794i \(-0.0902662\pi\)
0.960060 + 0.279794i \(0.0902662\pi\)
\(548\) 0 0
\(549\) 23.2900 + 40.3395i 0.993994 + 1.72165i
\(550\) 0 0
\(551\) 0.788841i 0.0336058i
\(552\) 0 0
\(553\) −33.0585 19.0863i −1.40579 0.811633i
\(554\) 0 0
\(555\) −1.32749 + 2.29929i −0.0563490 + 0.0975993i
\(556\) 0 0
\(557\) 10.9799 6.33924i 0.465233 0.268602i −0.249009 0.968501i \(-0.580105\pi\)
0.714242 + 0.699899i \(0.246772\pi\)
\(558\) 0 0
\(559\) −14.7521 19.8072i −0.623948 0.837757i
\(560\) 0 0
\(561\) −50.4650 + 29.1360i −2.13063 + 1.23012i
\(562\) 0 0
\(563\) −8.99769 + 15.5845i −0.379208 + 0.656807i −0.990947 0.134252i \(-0.957137\pi\)
0.611740 + 0.791059i \(0.290470\pi\)
\(564\) 0 0
\(565\) −10.6562 6.15234i −0.448308 0.258831i
\(566\) 0 0
\(567\) 117.019i 4.91434i
\(568\) 0 0
\(569\) 3.59418 + 6.22530i 0.150676 + 0.260978i 0.931476 0.363803i \(-0.118522\pi\)
−0.780800 + 0.624781i \(0.785188\pi\)
\(570\) 0 0
\(571\) −36.5611 −1.53003 −0.765016 0.644011i \(-0.777269\pi\)
−0.765016 + 0.644011i \(0.777269\pi\)
\(572\) 0 0
\(573\) −32.9202 −1.37526
\(574\) 0 0
\(575\) 2.20224 + 3.81440i 0.0918399 + 0.159071i
\(576\) 0 0
\(577\) 6.37212i 0.265275i 0.991165 + 0.132637i \(0.0423446\pi\)
−0.991165 + 0.132637i \(0.957655\pi\)
\(578\) 0 0
\(579\) 31.6356 + 18.2648i 1.31473 + 0.759060i
\(580\) 0 0
\(581\) 3.46365 5.99922i 0.143697 0.248890i
\(582\) 0 0
\(583\) −1.43392 + 0.827872i −0.0593867 + 0.0342870i
\(584\) 0 0
\(585\) 21.8183 16.2499i 0.902076 0.671851i
\(586\) 0 0
\(587\) −15.1127 + 8.72530i −0.623767 + 0.360132i −0.778334 0.627850i \(-0.783935\pi\)
0.154567 + 0.987982i \(0.450602\pi\)
\(588\) 0 0
\(589\) 7.17241 12.4230i 0.295534 0.511880i
\(590\) 0 0
\(591\) −50.0853 28.9168i −2.06023 1.18948i
\(592\) 0 0
\(593\) 27.2584i 1.11937i 0.828705 + 0.559685i \(0.189078\pi\)
−0.828705 + 0.559685i \(0.810922\pi\)
\(594\) 0 0
\(595\) 12.8527 + 22.2615i 0.526910 + 0.912634i
\(596\) 0 0
\(597\) 8.28832 0.339218
\(598\) 0 0
\(599\) −39.1965 −1.60152 −0.800762 0.598982i \(-0.795572\pi\)
−0.800762 + 0.598982i \(0.795572\pi\)
\(600\) 0 0
\(601\) 19.8891 + 34.4489i 0.811294 + 1.40520i 0.911959 + 0.410282i \(0.134570\pi\)
−0.100665 + 0.994920i \(0.532097\pi\)
\(602\) 0 0
\(603\) 66.0656i 2.69040i
\(604\) 0 0
\(605\) −0.494134 0.285288i −0.0200894 0.0115986i
\(606\) 0 0
\(607\) 11.7281 20.3137i 0.476031 0.824509i −0.523592 0.851969i \(-0.675408\pi\)
0.999623 + 0.0274598i \(0.00874181\pi\)
\(608\) 0 0
\(609\) −5.15135 + 2.97413i −0.208743 + 0.120518i
\(610\) 0 0
\(611\) 20.5273 + 8.84973i 0.830444 + 0.358022i
\(612\) 0 0
\(613\) 7.81755 4.51346i 0.315748 0.182297i −0.333748 0.942662i \(-0.608313\pi\)
0.649496 + 0.760365i \(0.274980\pi\)
\(614\) 0 0
\(615\) 5.23404 9.06562i 0.211057 0.365561i
\(616\) 0 0
\(617\) −10.3281 5.96295i −0.415795 0.240060i 0.277481 0.960731i \(-0.410500\pi\)
−0.693277 + 0.720671i \(0.743834\pi\)
\(618\) 0 0
\(619\) 3.10815i 0.124927i 0.998047 + 0.0624636i \(0.0198957\pi\)
−0.998047 + 0.0624636i \(0.980104\pi\)
\(620\) 0 0
\(621\) 32.5050 + 56.3003i 1.30438 + 2.25925i
\(622\) 0 0
\(623\) −75.4889 −3.02440
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −10.4467 18.0942i −0.417201 0.722613i
\(628\) 0 0
\(629\) 4.54293i 0.181138i
\(630\) 0 0
\(631\) −37.6497 21.7371i −1.49881 0.865340i −0.498813 0.866709i \(-0.666231\pi\)
−0.999999 + 0.00136957i \(0.999564\pi\)
\(632\) 0 0
\(633\) 28.6433 49.6116i 1.13847 1.97188i
\(634\) 0 0
\(635\) 3.31759 1.91541i 0.131655 0.0760108i
\(636\) 0 0
\(637\) −51.5735 + 6.03853i −2.04341 + 0.239255i
\(638\) 0 0
\(639\) −18.3662 + 10.6037i −0.726556 + 0.419477i
\(640\) 0 0
\(641\) 10.9222 18.9178i 0.431401 0.747208i −0.565594 0.824684i \(-0.691353\pi\)
0.996994 + 0.0774765i \(0.0246863\pi\)
\(642\) 0 0
\(643\) 5.65668 + 3.26589i 0.223078 + 0.128794i 0.607375 0.794416i \(-0.292223\pi\)
−0.384297 + 0.923210i \(0.625556\pi\)
\(644\) 0 0
\(645\) 22.2436i 0.875839i
\(646\) 0 0
\(647\) −4.78738 8.29199i −0.188211 0.325992i 0.756442 0.654060i \(-0.226936\pi\)
−0.944654 + 0.328068i \(0.893602\pi\)
\(648\) 0 0
\(649\) 25.4408 0.998638
\(650\) 0 0
\(651\) 108.167 4.23941
\(652\) 0 0
\(653\) −15.9175 27.5699i −0.622900 1.07889i −0.988943 0.148296i \(-0.952621\pi\)
0.366043 0.930598i \(-0.380712\pi\)
\(654\) 0 0
\(655\) 12.2733i 0.479559i
\(656\) 0 0
\(657\) −32.8993 18.9944i −1.28353 0.741044i
\(658\) 0 0
\(659\) 2.84117 4.92106i 0.110676 0.191697i −0.805367 0.592777i \(-0.798032\pi\)
0.916043 + 0.401080i \(0.131365\pi\)
\(660\) 0 0
\(661\) 9.56664 5.52330i 0.372099 0.214832i −0.302276 0.953220i \(-0.597746\pi\)
0.674375 + 0.738389i \(0.264413\pi\)
\(662\) 0 0
\(663\) 25.7562 59.7425i 1.00029 2.32021i
\(664\) 0 0
\(665\) −7.98187 + 4.60833i −0.309523 + 0.178703i
\(666\) 0 0
\(667\) −0.871976 + 1.51031i −0.0337630 + 0.0584793i
\(668\) 0 0
\(669\) 8.55949 + 4.94182i 0.330929 + 0.191062i
\(670\) 0 0
\(671\) 19.9369i 0.769655i
\(672\) 0 0
\(673\) 12.0476 + 20.8671i 0.464403 + 0.804369i 0.999174 0.0406276i \(-0.0129357\pi\)
−0.534772 + 0.844997i \(0.679602\pi\)
\(674\) 0 0
\(675\) 14.7599 0.568111
\(676\) 0 0
\(677\) −16.1944 −0.622403 −0.311201 0.950344i \(-0.600731\pi\)
−0.311201 + 0.950344i \(0.600731\pi\)
\(678\) 0 0
\(679\) −12.9308 22.3968i −0.496240 0.859512i
\(680\) 0 0
\(681\) 11.6175i 0.445183i
\(682\) 0 0
\(683\) −30.8212 17.7946i −1.17934 0.680892i −0.223478 0.974709i \(-0.571741\pi\)
−0.955862 + 0.293817i \(0.905074\pi\)
\(684\) 0 0
\(685\) −4.52523 + 7.83794i −0.172900 + 0.299472i
\(686\) 0 0
\(687\) −12.5023 + 7.21820i −0.476992 + 0.275391i
\(688\) 0 0
\(689\) 0.731840 1.69753i 0.0278809 0.0646707i
\(690\) 0 0
\(691\) 33.0084 19.0574i 1.25570 0.724977i 0.283463 0.958983i \(-0.408517\pi\)
0.972235 + 0.234006i \(0.0751835\pi\)
\(692\) 0 0
\(693\) 56.3633 97.6241i 2.14106 3.70843i
\(694\) 0 0
\(695\) 4.50840 + 2.60293i 0.171013 + 0.0987347i
\(696\) 0 0
\(697\) 17.9118i 0.678459i
\(698\) 0 0
\(699\) −1.81482 3.14335i −0.0686426 0.118893i
\(700\) 0 0
\(701\) −10.5042 −0.396740 −0.198370 0.980127i \(-0.563565\pi\)
−0.198370 + 0.980127i \(0.563565\pi\)
\(702\) 0 0
\(703\) −1.62886 −0.0614338
\(704\) 0 0
\(705\) 10.0664 + 17.4356i 0.379124 + 0.656661i
\(706\) 0 0
\(707\) 75.3780i 2.83488i
\(708\) 0 0
\(709\) −36.0124 20.7918i −1.35247 0.780851i −0.363878 0.931447i \(-0.618548\pi\)
−0.988595 + 0.150596i \(0.951881\pi\)
\(710\) 0 0
\(711\) −31.1295 + 53.9179i −1.16745 + 2.02208i
\(712\) 0 0
\(713\) 27.4644 15.8566i 1.02855 0.593834i
\(714\) 0 0
\(715\) −11.5650 + 1.35410i −0.432506 + 0.0506404i
\(716\) 0 0
\(717\) 4.76293 2.74988i 0.177875 0.102696i
\(718\) 0 0
\(719\) −21.3994 + 37.0649i −0.798063 + 1.38229i 0.122813 + 0.992430i \(0.460809\pi\)
−0.920876 + 0.389856i \(0.872525\pi\)
\(720\) 0 0
\(721\) 69.2160 + 39.9619i 2.57774 + 1.48826i
\(722\) 0 0
\(723\) 78.8947i 2.93412i
\(724\) 0 0
\(725\) 0.197974 + 0.342902i 0.00735258 + 0.0127351i
\(726\) 0 0
\(727\) −1.06263 −0.0394108 −0.0197054 0.999806i \(-0.506273\pi\)
−0.0197054 + 0.999806i \(0.506273\pi\)
\(728\) 0 0
\(729\) 47.0642 1.74312
\(730\) 0 0
\(731\) −19.0304 32.9616i −0.703864 1.21913i
\(732\) 0 0
\(733\) 20.7272i 0.765577i 0.923836 + 0.382789i \(0.125036\pi\)
−0.923836 + 0.382789i \(0.874964\pi\)
\(734\) 0 0
\(735\) −40.5014 23.3835i −1.49392 0.862513i
\(736\) 0 0
\(737\) 14.1385 24.4886i 0.520797 0.902048i
\(738\) 0 0
\(739\) 11.5583 6.67319i 0.425179 0.245477i −0.272112 0.962266i \(-0.587722\pi\)
0.697291 + 0.716788i \(0.254389\pi\)
\(740\) 0 0
\(741\) 21.4207 + 9.23489i 0.786907 + 0.339252i
\(742\) 0 0
\(743\) 0.346740 0.200191i 0.0127207 0.00734428i −0.493626 0.869674i \(-0.664329\pi\)
0.506347 + 0.862330i \(0.330996\pi\)
\(744\) 0 0
\(745\) 6.40790 11.0988i 0.234767 0.406629i
\(746\) 0 0
\(747\) −9.78463 5.64916i −0.358001 0.206692i
\(748\) 0 0
\(749\) 25.8878i 0.945921i
\(750\) 0 0
\(751\) 25.0742 + 43.4298i 0.914971 + 1.58478i 0.806944 + 0.590628i \(0.201120\pi\)
0.108027 + 0.994148i \(0.465547\pi\)
\(752\) 0 0
\(753\) 41.5028 1.51245
\(754\) 0 0
\(755\) −17.8652 −0.650180
\(756\) 0 0
\(757\) 1.11832 + 1.93698i 0.0406459 + 0.0704008i 0.885633 0.464386i \(-0.153725\pi\)
−0.844987 + 0.534787i \(0.820392\pi\)
\(758\) 0 0
\(759\) 46.1906i 1.67661i
\(760\) 0 0
\(761\) −16.3704 9.45146i −0.593427 0.342615i 0.173025 0.984917i \(-0.444646\pi\)
−0.766451 + 0.642303i \(0.777979\pi\)
\(762\) 0 0
\(763\) 17.5396 30.3795i 0.634977 1.09981i
\(764\) 0 0
\(765\) 36.3082 20.9626i 1.31273 0.757903i
\(766\) 0 0
\(767\) −22.7797 + 16.9659i −0.822528 + 0.612605i
\(768\) 0 0
\(769\) −10.3046 + 5.94934i −0.371592 + 0.214539i −0.674154 0.738591i \(-0.735491\pi\)
0.302562 + 0.953130i \(0.402158\pi\)
\(770\) 0 0
\(771\) 1.13785 1.97081i 0.0409785 0.0709768i
\(772\) 0 0
\(773\) −12.3557 7.13356i −0.444403 0.256576i 0.261060 0.965322i \(-0.415928\pi\)
−0.705464 + 0.708746i \(0.749261\pi\)
\(774\) 0 0
\(775\) 7.20020i 0.258639i
\(776\) 0 0
\(777\) −6.14124 10.6369i −0.220316 0.381598i
\(778\) 0 0
\(779\) 6.42228 0.230102
\(780\) 0 0
\(781\) 9.07708 0.324803
\(782\) 0 0
\(783\) 2.92209 + 5.06121i 0.104427 + 0.180873i
\(784\) 0 0
\(785\) 13.7462i 0.490623i
\(786\) 0 0
\(787\) 30.7475 + 17.7521i 1.09603 + 0.632792i 0.935175 0.354186i \(-0.115242\pi\)
0.160853 + 0.986978i \(0.448575\pi\)
\(788\) 0 0
\(789\)