Properties

Label 261.3.s.a.118.4
Level $261$
Weight $3$
Character 261.118
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
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] = [261,3,Mod(10,261)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(261, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([0, 23]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("261.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 118.4
Character \(\chi\) \(=\) 261.118
Dual form 261.3.s.a.73.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.56136 + 0.401269i) q^{2} +(8.62256 + 1.96804i) q^{4} +(-5.24106 + 4.17960i) q^{5} +(2.11977 + 9.28734i) q^{7} +(16.3872 + 5.73413i) q^{8} +O(q^{10})\) \(q+(3.56136 + 0.401269i) q^{2} +(8.62256 + 1.96804i) q^{4} +(-5.24106 + 4.17960i) q^{5} +(2.11977 + 9.28734i) q^{7} +(16.3872 + 5.73413i) q^{8} +(-20.3424 + 12.7820i) q^{10} +(0.700768 - 0.245209i) q^{11} +(3.39382 - 7.04735i) q^{13} +(3.82256 + 33.9262i) q^{14} +(24.1861 + 11.6474i) q^{16} +(17.4730 - 17.4730i) q^{17} +(-7.96846 - 12.6817i) q^{19} +(-53.4169 + 25.7242i) q^{20} +(2.59408 - 0.592082i) q^{22} +(11.9732 - 15.0139i) q^{23} +(4.43656 - 19.4379i) q^{25} +(14.9145 - 23.7363i) q^{26} +84.2524i q^{28} +(19.7681 + 21.2184i) q^{29} +(0.327624 + 0.0369143i) q^{31} +(22.6600 + 14.2382i) q^{32} +(69.2390 - 55.2162i) q^{34} +(-49.9272 - 39.8156i) q^{35} +(-15.2693 - 5.34296i) q^{37} +(-23.2898 - 48.3617i) q^{38} +(-109.853 + 38.4391i) q^{40} +(-28.0484 - 28.0484i) q^{41} +(0.679170 + 6.02780i) q^{43} +(6.52499 - 0.735190i) q^{44} +(48.6656 - 48.6656i) q^{46} +(-1.43620 - 4.10443i) q^{47} +(-37.6137 + 18.1138i) q^{49} +(23.6000 - 67.4450i) q^{50} +(43.1329 - 54.0870i) q^{52} +(37.6082 + 47.1592i) q^{53} +(-2.64789 + 4.21408i) q^{55} +(-18.5176 + 164.349i) q^{56} +(61.8871 + 83.4988i) q^{58} -91.1542 q^{59} +(6.43745 + 4.04492i) q^{61} +(1.15197 + 0.262930i) q^{62} +(-8.96447 - 7.14893i) q^{64} +(11.6679 + 51.1204i) q^{65} +(29.8663 + 62.0180i) q^{67} +(185.049 - 116.274i) q^{68} +(-161.832 - 161.832i) q^{70} +(38.1572 - 79.2343i) q^{71} +(-29.1293 + 3.28209i) q^{73} +(-52.2355 - 25.1553i) q^{74} +(-43.7503 - 125.031i) q^{76} +(3.76281 + 5.98848i) q^{77} +(7.28322 - 20.8142i) q^{79} +(-175.442 + 40.0435i) q^{80} +(-88.6354 - 111.145i) q^{82} +(-9.19165 + 40.2713i) q^{83} +(-18.5468 + 164.607i) q^{85} +21.7397i q^{86} +12.8897 q^{88} +(-98.0089 - 11.0429i) q^{89} +(72.6452 + 16.5808i) q^{91} +(132.788 - 105.895i) q^{92} +(-3.46785 - 15.1936i) q^{94} +(94.7678 + 33.1607i) q^{95} +(136.891 - 86.0143i) q^{97} +(-141.224 + 49.4166i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{1}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.56136 + 0.401269i 1.78068 + 0.200634i 0.940064 0.340997i \(-0.110765\pi\)
0.840616 + 0.541632i \(0.182193\pi\)
\(3\) 0 0
\(4\) 8.62256 + 1.96804i 2.15564 + 0.492011i
\(5\) −5.24106 + 4.17960i −1.04821 + 0.835920i −0.986760 0.162190i \(-0.948144\pi\)
−0.0614515 + 0.998110i \(0.519573\pi\)
\(6\) 0 0
\(7\) 2.11977 + 9.28734i 0.302825 + 1.32676i 0.865842 + 0.500317i \(0.166783\pi\)
−0.563017 + 0.826445i \(0.690360\pi\)
\(8\) 16.3872 + 5.73413i 2.04840 + 0.716766i
\(9\) 0 0
\(10\) −20.3424 + 12.7820i −2.03424 + 1.27820i
\(11\) 0.700768 0.245209i 0.0637061 0.0222917i −0.298238 0.954492i \(-0.596399\pi\)
0.361944 + 0.932200i \(0.382113\pi\)
\(12\) 0 0
\(13\) 3.39382 7.04735i 0.261063 0.542104i −0.728698 0.684835i \(-0.759874\pi\)
0.989761 + 0.142731i \(0.0455885\pi\)
\(14\) 3.82256 + 33.9262i 0.273040 + 2.42330i
\(15\) 0 0
\(16\) 24.1861 + 11.6474i 1.51163 + 0.727962i
\(17\) 17.4730 17.4730i 1.02782 1.02782i 0.0282209 0.999602i \(-0.491016\pi\)
0.999602 0.0282209i \(-0.00898419\pi\)
\(18\) 0 0
\(19\) −7.96846 12.6817i −0.419393 0.667460i 0.568485 0.822694i \(-0.307530\pi\)
−0.987878 + 0.155234i \(0.950387\pi\)
\(20\) −53.4169 + 25.7242i −2.67085 + 1.28621i
\(21\) 0 0
\(22\) 2.59408 0.592082i 0.117913 0.0269128i
\(23\) 11.9732 15.0139i 0.520575 0.652780i −0.450156 0.892950i \(-0.648632\pi\)
0.970731 + 0.240170i \(0.0772031\pi\)
\(24\) 0 0
\(25\) 4.43656 19.4379i 0.177463 0.777514i
\(26\) 14.9145 23.7363i 0.573635 0.912935i
\(27\) 0 0
\(28\) 84.2524i 3.00901i
\(29\) 19.7681 + 21.2184i 0.681659 + 0.731670i
\(30\) 0 0
\(31\) 0.327624 + 0.0369143i 0.0105685 + 0.00119078i 0.117247 0.993103i \(-0.462593\pi\)
−0.106679 + 0.994294i \(0.534022\pi\)
\(32\) 22.6600 + 14.2382i 0.708124 + 0.444944i
\(33\) 0 0
\(34\) 69.2390 55.2162i 2.03644 1.62401i
\(35\) −49.9272 39.8156i −1.42649 1.13759i
\(36\) 0 0
\(37\) −15.2693 5.34296i −0.412684 0.144404i 0.115949 0.993255i \(-0.463009\pi\)
−0.528632 + 0.848851i \(0.677295\pi\)
\(38\) −23.2898 48.3617i −0.612889 1.27268i
\(39\) 0 0
\(40\) −109.853 + 38.4391i −2.74632 + 0.960978i
\(41\) −28.0484 28.0484i −0.684106 0.684106i 0.276816 0.960923i \(-0.410721\pi\)
−0.960923 + 0.276816i \(0.910721\pi\)
\(42\) 0 0
\(43\) 0.679170 + 6.02780i 0.0157947 + 0.140181i 0.999135 0.0415949i \(-0.0132439\pi\)
−0.983340 + 0.181776i \(0.941815\pi\)
\(44\) 6.52499 0.735190i 0.148295 0.0167089i
\(45\) 0 0
\(46\) 48.6656 48.6656i 1.05795 1.05795i
\(47\) −1.43620 4.10443i −0.0305575 0.0873282i 0.927594 0.373590i \(-0.121873\pi\)
−0.958152 + 0.286261i \(0.907587\pi\)
\(48\) 0 0
\(49\) −37.6137 + 18.1138i −0.767627 + 0.369670i
\(50\) 23.6000 67.4450i 0.472000 1.34890i
\(51\) 0 0
\(52\) 43.1329 54.0870i 0.829479 1.04013i
\(53\) 37.6082 + 47.1592i 0.709589 + 0.889797i 0.997699 0.0678006i \(-0.0215982\pi\)
−0.288110 + 0.957597i \(0.593027\pi\)
\(54\) 0 0
\(55\) −2.64789 + 4.21408i −0.0481434 + 0.0766197i
\(56\) −18.5176 + 164.349i −0.330672 + 2.93480i
\(57\) 0 0
\(58\) 61.8871 + 83.4988i 1.06702 + 1.43963i
\(59\) −91.1542 −1.54499 −0.772493 0.635023i \(-0.780991\pi\)
−0.772493 + 0.635023i \(0.780991\pi\)
\(60\) 0 0
\(61\) 6.43745 + 4.04492i 0.105532 + 0.0663101i 0.583764 0.811923i \(-0.301579\pi\)
−0.478232 + 0.878234i \(0.658722\pi\)
\(62\) 1.15197 + 0.262930i 0.0185802 + 0.00424081i
\(63\) 0 0
\(64\) −8.96447 7.14893i −0.140070 0.111702i
\(65\) 11.6679 + 51.1204i 0.179506 + 0.786467i
\(66\) 0 0
\(67\) 29.8663 + 62.0180i 0.445766 + 0.925642i 0.995891 + 0.0905598i \(0.0288656\pi\)
−0.550125 + 0.835082i \(0.685420\pi\)
\(68\) 185.049 116.274i 2.72131 1.70992i
\(69\) 0 0
\(70\) −161.832 161.832i −2.31189 2.31189i
\(71\) 38.1572 79.2343i 0.537426 1.11598i −0.438672 0.898647i \(-0.644551\pi\)
0.976098 0.217329i \(-0.0697346\pi\)
\(72\) 0 0
\(73\) −29.1293 + 3.28209i −0.399032 + 0.0449601i −0.309200 0.950997i \(-0.600061\pi\)
−0.0898315 + 0.995957i \(0.528633\pi\)
\(74\) −52.2355 25.1553i −0.705885 0.339936i
\(75\) 0 0
\(76\) −43.7503 125.031i −0.575662 1.64515i
\(77\) 3.76281 + 5.98848i 0.0488677 + 0.0777724i
\(78\) 0 0
\(79\) 7.28322 20.8142i 0.0921927 0.263472i −0.888549 0.458782i \(-0.848286\pi\)
0.980741 + 0.195311i \(0.0625715\pi\)
\(80\) −175.442 + 40.0435i −2.19302 + 0.500543i
\(81\) 0 0
\(82\) −88.6354 111.145i −1.08092 1.35543i
\(83\) −9.19165 + 40.2713i −0.110743 + 0.485196i 0.888891 + 0.458120i \(0.151477\pi\)
−0.999633 + 0.0270764i \(0.991380\pi\)
\(84\) 0 0
\(85\) −18.5468 + 164.607i −0.218197 + 1.93655i
\(86\) 21.7397i 0.252787i
\(87\) 0 0
\(88\) 12.8897 0.146474
\(89\) −98.0089 11.0429i −1.10122 0.124078i −0.457407 0.889258i \(-0.651222\pi\)
−0.643817 + 0.765180i \(0.722650\pi\)
\(90\) 0 0
\(91\) 72.6452 + 16.5808i 0.798299 + 0.182207i
\(92\) 132.788 105.895i 1.44335 1.15103i
\(93\) 0 0
\(94\) −3.46785 15.1936i −0.0368920 0.161635i
\(95\) 94.7678 + 33.1607i 0.997556 + 0.349060i
\(96\) 0 0
\(97\) 136.891 86.0143i 1.41125 0.886745i 0.411551 0.911387i \(-0.364987\pi\)
0.999696 + 0.0246414i \(0.00784441\pi\)
\(98\) −141.224 + 49.4166i −1.44107 + 0.504251i
\(99\) 0 0
\(100\) 76.5091 158.873i 0.765091 1.58873i
\(101\) −0.930887 8.26185i −0.00921670 0.0818005i 0.988262 0.152770i \(-0.0488193\pi\)
−0.997478 + 0.0709693i \(0.977391\pi\)
\(102\) 0 0
\(103\) −65.6998 31.6393i −0.637862 0.307178i 0.0868590 0.996221i \(-0.472317\pi\)
−0.724721 + 0.689043i \(0.758031\pi\)
\(104\) 96.0257 96.0257i 0.923324 0.923324i
\(105\) 0 0
\(106\) 115.013 + 183.042i 1.08503 + 1.72681i
\(107\) 73.2735 35.2867i 0.684799 0.329782i −0.0589308 0.998262i \(-0.518769\pi\)
0.743730 + 0.668480i \(0.233055\pi\)
\(108\) 0 0
\(109\) 119.739 27.3296i 1.09852 0.250730i 0.365415 0.930845i \(-0.380927\pi\)
0.733106 + 0.680114i \(0.238070\pi\)
\(110\) −11.1211 + 13.9454i −0.101100 + 0.126776i
\(111\) 0 0
\(112\) −56.9043 + 249.314i −0.508074 + 2.22602i
\(113\) −84.5371 + 134.540i −0.748116 + 1.19062i 0.228062 + 0.973647i \(0.426761\pi\)
−0.976178 + 0.216973i \(0.930382\pi\)
\(114\) 0 0
\(115\) 128.732i 1.11941i
\(116\) 128.693 + 221.862i 1.10942 + 1.91260i
\(117\) 0 0
\(118\) −324.633 36.5773i −2.75113 0.309977i
\(119\) 199.316 + 125.239i 1.67493 + 1.05243i
\(120\) 0 0
\(121\) −94.1707 + 75.0986i −0.778270 + 0.620650i
\(122\) 21.3030 + 16.9886i 0.174615 + 0.139250i
\(123\) 0 0
\(124\) 2.75231 + 0.963073i 0.0221960 + 0.00776672i
\(125\) −14.7239 30.5745i −0.117791 0.244596i
\(126\) 0 0
\(127\) 91.0577 31.8625i 0.716990 0.250886i 0.0529652 0.998596i \(-0.483133\pi\)
0.664025 + 0.747711i \(0.268847\pi\)
\(128\) −104.751 104.751i −0.818369 0.818369i
\(129\) 0 0
\(130\) 21.0405 + 186.740i 0.161850 + 1.43646i
\(131\) −75.6558 + 8.52436i −0.577525 + 0.0650714i −0.395895 0.918296i \(-0.629566\pi\)
−0.181630 + 0.983367i \(0.558137\pi\)
\(132\) 0 0
\(133\) 100.888 100.888i 0.758558 0.758558i
\(134\) 81.4787 + 232.853i 0.608050 + 1.73771i
\(135\) 0 0
\(136\) 386.526 186.141i 2.84210 1.36868i
\(137\) 50.4454 144.165i 0.368215 1.05230i −0.599528 0.800354i \(-0.704645\pi\)
0.967742 0.251943i \(-0.0810695\pi\)
\(138\) 0 0
\(139\) −84.2699 + 105.671i −0.606258 + 0.760224i −0.986339 0.164729i \(-0.947325\pi\)
0.380080 + 0.924953i \(0.375896\pi\)
\(140\) −352.142 441.572i −2.51530 3.15408i
\(141\) 0 0
\(142\) 167.686 266.871i 1.18089 1.87937i
\(143\) 0.650207 5.77075i 0.00454690 0.0403549i
\(144\) 0 0
\(145\) −192.290 28.5841i −1.32614 0.197132i
\(146\) −105.057 −0.719569
\(147\) 0 0
\(148\) −121.145 76.1206i −0.818549 0.514328i
\(149\) −58.0928 13.2593i −0.389885 0.0889886i 0.0230848 0.999734i \(-0.492651\pi\)
−0.412969 + 0.910745i \(0.635508\pi\)
\(150\) 0 0
\(151\) −203.074 161.946i −1.34486 1.07249i −0.990519 0.137373i \(-0.956134\pi\)
−0.354340 0.935117i \(-0.615294\pi\)
\(152\) −57.8621 253.510i −0.380672 1.66783i
\(153\) 0 0
\(154\) 10.9977 + 22.8370i 0.0714138 + 0.148292i
\(155\) −1.87138 + 1.17587i −0.0120734 + 0.00758624i
\(156\) 0 0
\(157\) −132.437 132.437i −0.843550 0.843550i 0.145769 0.989319i \(-0.453434\pi\)
−0.989319 + 0.145769i \(0.953434\pi\)
\(158\) 34.2903 71.2045i 0.217027 0.450661i
\(159\) 0 0
\(160\) −178.272 + 20.0865i −1.11420 + 0.125540i
\(161\) 164.820 + 79.3732i 1.02373 + 0.493001i
\(162\) 0 0
\(163\) 84.1241 + 240.413i 0.516098 + 1.47492i 0.847171 + 0.531320i \(0.178304\pi\)
−0.331073 + 0.943605i \(0.607411\pi\)
\(164\) −186.648 297.049i −1.13810 1.81127i
\(165\) 0 0
\(166\) −48.8944 + 139.732i −0.294545 + 0.841760i
\(167\) 37.5325 8.56655i 0.224746 0.0512967i −0.108665 0.994078i \(-0.534658\pi\)
0.333411 + 0.942782i \(0.391800\pi\)
\(168\) 0 0
\(169\) 67.2227 + 84.2946i 0.397768 + 0.498785i
\(170\) −132.103 + 578.783i −0.777079 + 3.40460i
\(171\) 0 0
\(172\) −6.00679 + 53.3117i −0.0349232 + 0.309952i
\(173\) 38.3828i 0.221866i −0.993828 0.110933i \(-0.964616\pi\)
0.993828 0.110933i \(-0.0353839\pi\)
\(174\) 0 0
\(175\) 189.930 1.08532
\(176\) 19.8048 + 2.23147i 0.112528 + 0.0126788i
\(177\) 0 0
\(178\) −344.614 78.6558i −1.93603 0.441887i
\(179\) −136.077 + 108.518i −0.760206 + 0.606244i −0.924949 0.380092i \(-0.875892\pi\)
0.164742 + 0.986337i \(0.447321\pi\)
\(180\) 0 0
\(181\) 37.8882 + 165.999i 0.209327 + 0.917122i 0.965016 + 0.262191i \(0.0844451\pi\)
−0.755689 + 0.654931i \(0.772698\pi\)
\(182\) 252.062 + 88.2005i 1.38496 + 0.484618i
\(183\) 0 0
\(184\) 282.300 177.381i 1.53424 0.964025i
\(185\) 102.359 35.8168i 0.553290 0.193605i
\(186\) 0 0
\(187\) 7.95997 16.5290i 0.0425667 0.0883906i
\(188\) −4.30604 38.2172i −0.0229045 0.203283i
\(189\) 0 0
\(190\) 324.196 + 156.124i 1.70629 + 0.821708i
\(191\) 20.1345 20.1345i 0.105416 0.105416i −0.652431 0.757848i \(-0.726251\pi\)
0.757848 + 0.652431i \(0.226251\pi\)
\(192\) 0 0
\(193\) −157.961 251.393i −0.818449 1.30255i −0.950316 0.311287i \(-0.899240\pi\)
0.131867 0.991267i \(-0.457903\pi\)
\(194\) 522.033 251.398i 2.69089 1.29587i
\(195\) 0 0
\(196\) −359.975 + 82.1620i −1.83661 + 0.419194i
\(197\) −152.105 + 190.734i −0.772108 + 0.968192i −0.999985 0.00549749i \(-0.998250\pi\)
0.227877 + 0.973690i \(0.426822\pi\)
\(198\) 0 0
\(199\) −70.5672 + 309.175i −0.354609 + 1.55364i 0.411789 + 0.911279i \(0.364904\pi\)
−0.766399 + 0.642365i \(0.777953\pi\)
\(200\) 184.162 293.092i 0.920811 1.46546i
\(201\) 0 0
\(202\) 29.7970i 0.147510i
\(203\) −155.159 + 228.571i −0.764329 + 1.12597i
\(204\) 0 0
\(205\) 264.234 + 29.7720i 1.28895 + 0.145229i
\(206\) −221.285 139.042i −1.07420 0.674963i
\(207\) 0 0
\(208\) 164.166 130.918i 0.789261 0.629415i
\(209\) −8.69372 6.93301i −0.0415967 0.0331723i
\(210\) 0 0
\(211\) 353.376 + 123.652i 1.67477 + 0.586027i 0.989789 0.142537i \(-0.0455259\pi\)
0.684978 + 0.728563i \(0.259812\pi\)
\(212\) 231.468 + 480.648i 1.09183 + 2.26721i
\(213\) 0 0
\(214\) 275.113 96.2661i 1.28557 0.449842i
\(215\) −28.7534 28.7534i −0.133737 0.133737i
\(216\) 0 0
\(217\) 0.351652 + 3.12100i 0.00162052 + 0.0143825i
\(218\) 437.400 49.2831i 2.00642 0.226069i
\(219\) 0 0
\(220\) −31.1250 + 31.1250i −0.141477 + 0.141477i
\(221\) −63.8380 182.438i −0.288860 0.825513i
\(222\) 0 0
\(223\) −249.428 + 120.118i −1.11851 + 0.538647i −0.899432 0.437061i \(-0.856020\pi\)
−0.219079 + 0.975707i \(0.570305\pi\)
\(224\) −84.2010 + 240.633i −0.375897 + 1.07425i
\(225\) 0 0
\(226\) −355.054 + 445.223i −1.57103 + 1.97001i
\(227\) 163.809 + 205.410i 0.721624 + 0.904888i 0.998429 0.0560385i \(-0.0178470\pi\)
−0.276805 + 0.960926i \(0.589276\pi\)
\(228\) 0 0
\(229\) 164.093 261.153i 0.716564 1.14040i −0.267667 0.963512i \(-0.586253\pi\)
0.984230 0.176893i \(-0.0566046\pi\)
\(230\) −51.6562 + 458.462i −0.224592 + 1.99331i
\(231\) 0 0
\(232\) 202.275 + 461.064i 0.871875 + 1.98734i
\(233\) −92.4111 −0.396614 −0.198307 0.980140i \(-0.563544\pi\)
−0.198307 + 0.980140i \(0.563544\pi\)
\(234\) 0 0
\(235\) 24.6821 + 15.5088i 0.105030 + 0.0659948i
\(236\) −785.982 179.395i −3.33043 0.760150i
\(237\) 0 0
\(238\) 659.583 + 526.000i 2.77136 + 2.21008i
\(239\) 91.6570 + 401.575i 0.383502 + 1.68023i 0.686412 + 0.727213i \(0.259185\pi\)
−0.302910 + 0.953019i \(0.597958\pi\)
\(240\) 0 0
\(241\) −53.8613 111.844i −0.223491 0.464084i 0.758830 0.651289i \(-0.225771\pi\)
−0.982321 + 0.187205i \(0.940057\pi\)
\(242\) −365.510 + 229.665i −1.51037 + 0.949031i
\(243\) 0 0
\(244\) 47.5467 + 47.5467i 0.194864 + 0.194864i
\(245\) 121.427 252.146i 0.495621 1.02917i
\(246\) 0 0
\(247\) −116.416 + 13.1169i −0.471320 + 0.0531051i
\(248\) 5.15717 + 2.48356i 0.0207950 + 0.0100144i
\(249\) 0 0
\(250\) −40.1686 114.795i −0.160674 0.459181i
\(251\) −17.8330 28.3810i −0.0710477 0.113072i 0.809311 0.587381i \(-0.199841\pi\)
−0.880358 + 0.474309i \(0.842698\pi\)
\(252\) 0 0
\(253\) 4.70889 13.4572i 0.0186122 0.0531906i
\(254\) 337.075 76.9351i 1.32707 0.302894i
\(255\) 0 0
\(256\) −302.428 379.233i −1.18136 1.48138i
\(257\) 60.1375 263.480i 0.233998 1.02521i −0.712289 0.701886i \(-0.752342\pi\)
0.946287 0.323327i \(-0.104801\pi\)
\(258\) 0 0
\(259\) 17.2544 153.137i 0.0666193 0.591262i
\(260\) 463.751i 1.78366i
\(261\) 0 0
\(262\) −272.858 −1.04144
\(263\) −177.612 20.0120i −0.675329 0.0760914i −0.232362 0.972629i \(-0.574646\pi\)
−0.442967 + 0.896538i \(0.646074\pi\)
\(264\) 0 0
\(265\) −394.214 89.9767i −1.48760 0.339535i
\(266\) 399.783 318.816i 1.50294 1.19856i
\(267\) 0 0
\(268\) 135.470 + 593.532i 0.505484 + 2.21467i
\(269\) 369.061 + 129.140i 1.37197 + 0.480074i 0.912849 0.408298i \(-0.133878\pi\)
0.459124 + 0.888372i \(0.348163\pi\)
\(270\) 0 0
\(271\) 28.6724 18.0161i 0.105802 0.0664799i −0.478092 0.878310i \(-0.658671\pi\)
0.583894 + 0.811830i \(0.301528\pi\)
\(272\) 626.117 219.088i 2.30190 0.805470i
\(273\) 0 0
\(274\) 237.503 493.180i 0.866799 1.79993i
\(275\) −1.65734 14.7093i −0.00602669 0.0534884i
\(276\) 0 0
\(277\) −106.776 51.4207i −0.385473 0.185634i 0.231103 0.972929i \(-0.425767\pi\)
−0.616576 + 0.787295i \(0.711481\pi\)
\(278\) −342.518 + 342.518i −1.23208 + 1.23208i
\(279\) 0 0
\(280\) −589.860 938.756i −2.10664 3.35270i
\(281\) −257.658 + 124.081i −0.916932 + 0.441571i −0.831975 0.554814i \(-0.812790\pi\)
−0.0849569 + 0.996385i \(0.527075\pi\)
\(282\) 0 0
\(283\) −221.399 + 50.5329i −0.782329 + 0.178561i −0.594989 0.803734i \(-0.702844\pi\)
−0.187340 + 0.982295i \(0.559986\pi\)
\(284\) 484.950 608.108i 1.70757 2.14122i
\(285\) 0 0
\(286\) 4.63124 20.2908i 0.0161932 0.0709469i
\(287\) 201.038 319.951i 0.700482 1.11481i
\(288\) 0 0
\(289\) 321.610i 1.11284i
\(290\) −673.345 178.958i −2.32188 0.617098i
\(291\) 0 0
\(292\) −257.629 29.0278i −0.882290 0.0994102i
\(293\) 160.239 + 100.685i 0.546891 + 0.343634i 0.776970 0.629538i \(-0.216756\pi\)
−0.230079 + 0.973172i \(0.573899\pi\)
\(294\) 0 0
\(295\) 477.744 380.988i 1.61947 1.29149i
\(296\) −219.584 175.112i −0.741837 0.591595i
\(297\) 0 0
\(298\) −201.569 70.5320i −0.676405 0.236685i
\(299\) −65.1735 135.334i −0.217971 0.452622i
\(300\) 0 0
\(301\) −54.5425 + 19.0853i −0.181204 + 0.0634062i
\(302\) −658.235 658.235i −2.17959 2.17959i
\(303\) 0 0
\(304\) −45.0165 399.533i −0.148081 1.31425i
\(305\) −50.6452 + 5.70634i −0.166050 + 0.0187093i
\(306\) 0 0
\(307\) −287.766 + 287.766i −0.937349 + 0.937349i −0.998150 0.0608010i \(-0.980634\pi\)
0.0608010 + 0.998150i \(0.480634\pi\)
\(308\) 20.6595 + 59.0414i 0.0670762 + 0.191693i
\(309\) 0 0
\(310\) −7.13650 + 3.43676i −0.0230210 + 0.0110863i
\(311\) 7.89034 22.5493i 0.0253709 0.0725058i −0.930501 0.366288i \(-0.880628\pi\)
0.955872 + 0.293782i \(0.0949141\pi\)
\(312\) 0 0
\(313\) 256.380 321.491i 0.819107 1.02713i −0.179949 0.983676i \(-0.557593\pi\)
0.999056 0.0434514i \(-0.0138354\pi\)
\(314\) −418.514 524.800i −1.33285 1.67134i
\(315\) 0 0
\(316\) 103.763 165.138i 0.328365 0.522590i
\(317\) 53.9274 478.619i 0.170118 1.50984i −0.561131 0.827727i \(-0.689633\pi\)
0.731248 0.682111i \(-0.238938\pi\)
\(318\) 0 0
\(319\) 19.0558 + 10.0219i 0.0597361 + 0.0314165i
\(320\) 76.8630 0.240197
\(321\) 0 0
\(322\) 555.134 + 348.814i 1.72402 + 1.08327i
\(323\) −360.821 82.3550i −1.11709 0.254969i
\(324\) 0 0
\(325\) −121.928 97.2347i −0.375164 0.299184i
\(326\) 203.126 + 889.953i 0.623086 + 2.72992i
\(327\) 0 0
\(328\) −298.801 620.467i −0.910980 1.89167i
\(329\) 35.0748 22.0389i 0.106610 0.0669877i
\(330\) 0 0
\(331\) −253.593 253.593i −0.766142 0.766142i 0.211283 0.977425i \(-0.432236\pi\)
−0.977425 + 0.211283i \(0.932236\pi\)
\(332\) −158.511 + 329.152i −0.477443 + 0.991421i
\(333\) 0 0
\(334\) 137.104 15.4479i 0.410492 0.0462513i
\(335\) −415.742 200.211i −1.24102 0.597644i
\(336\) 0 0
\(337\) 7.65449 + 21.8753i 0.0227136 + 0.0649118i 0.954682 0.297628i \(-0.0961955\pi\)
−0.931968 + 0.362540i \(0.881910\pi\)
\(338\) 205.580 + 327.178i 0.608223 + 0.967982i
\(339\) 0 0
\(340\) −483.874 + 1382.83i −1.42316 + 4.06716i
\(341\) 0.238640 0.0544680i 0.000699823 0.000159730i
\(342\) 0 0
\(343\) 43.0726 + 54.0114i 0.125576 + 0.157468i
\(344\) −23.4345 + 102.673i −0.0681236 + 0.298469i
\(345\) 0 0
\(346\) 15.4018 136.695i 0.0445139 0.395072i
\(347\) 307.231i 0.885393i −0.896672 0.442696i \(-0.854022\pi\)
0.896672 0.442696i \(-0.145978\pi\)
\(348\) 0 0
\(349\) 81.9545 0.234827 0.117413 0.993083i \(-0.462540\pi\)
0.117413 + 0.993083i \(0.462540\pi\)
\(350\) 676.411 + 76.2132i 1.93260 + 0.217752i
\(351\) 0 0
\(352\) 19.3707 + 4.42124i 0.0550305 + 0.0125603i
\(353\) −34.5942 + 27.5880i −0.0980006 + 0.0781529i −0.671264 0.741218i \(-0.734248\pi\)
0.573264 + 0.819371i \(0.305677\pi\)
\(354\) 0 0
\(355\) 131.184 + 574.754i 0.369532 + 1.61902i
\(356\) −823.354 288.104i −2.31279 0.809281i
\(357\) 0 0
\(358\) −528.164 + 331.867i −1.47532 + 0.927004i
\(359\) 329.635 115.344i 0.918204 0.321294i 0.170525 0.985353i \(-0.445454\pi\)
0.747680 + 0.664060i \(0.231168\pi\)
\(360\) 0 0
\(361\) 59.3020 123.142i 0.164271 0.341113i
\(362\) 68.3233 + 606.386i 0.188738 + 1.67510i
\(363\) 0 0
\(364\) 593.756 + 285.938i 1.63120 + 0.785543i
\(365\) 138.951 138.951i 0.380687 0.380687i
\(366\) 0 0
\(367\) 117.163 + 186.464i 0.319246 + 0.508076i 0.967340 0.253484i \(-0.0815765\pi\)
−0.648094 + 0.761560i \(0.724434\pi\)
\(368\) 464.458 223.671i 1.26211 0.607802i
\(369\) 0 0
\(370\) 378.908 86.4833i 1.02408 0.233739i
\(371\) −358.263 + 449.247i −0.965668 + 1.21091i
\(372\) 0 0
\(373\) 58.3911 255.828i 0.156545 0.685867i −0.834351 0.551234i \(-0.814157\pi\)
0.990896 0.134633i \(-0.0429855\pi\)
\(374\) 34.9809 55.6718i 0.0935318 0.148855i
\(375\) 0 0
\(376\) 75.4955i 0.200786i
\(377\) 216.623 67.3012i 0.574597 0.178518i
\(378\) 0 0
\(379\) −224.710 25.3187i −0.592901 0.0668039i −0.189584 0.981864i \(-0.560714\pi\)
−0.403317 + 0.915061i \(0.632143\pi\)
\(380\) 751.879 + 472.437i 1.97863 + 1.24326i
\(381\) 0 0
\(382\) 79.7857 63.6270i 0.208863 0.166563i
\(383\) −106.140 84.6436i −0.277127 0.221002i 0.475056 0.879956i \(-0.342428\pi\)
−0.752183 + 0.658954i \(0.770999\pi\)
\(384\) 0 0
\(385\) −44.7505 15.6589i −0.116235 0.0406724i
\(386\) −461.679 958.686i −1.19606 2.48364i
\(387\) 0 0
\(388\) 1349.63 472.256i 3.47843 1.21715i
\(389\) 11.0445 + 11.0445i 0.0283920 + 0.0283920i 0.721160 0.692768i \(-0.243609\pi\)
−0.692768 + 0.721160i \(0.743609\pi\)
\(390\) 0 0
\(391\) −53.1305 471.546i −0.135884 1.20600i
\(392\) −720.251 + 81.1528i −1.83737 + 0.207022i
\(393\) 0 0
\(394\) −618.237 + 618.237i −1.56913 + 1.56913i
\(395\) 48.8235 + 139.530i 0.123604 + 0.353240i
\(396\) 0 0
\(397\) −258.406 + 124.442i −0.650896 + 0.313455i −0.730036 0.683409i \(-0.760497\pi\)
0.0791405 + 0.996863i \(0.474782\pi\)
\(398\) −375.378 + 1072.77i −0.943160 + 2.69540i
\(399\) 0 0
\(400\) 333.703 418.451i 0.834258 1.04613i
\(401\) −94.6371 118.671i −0.236003 0.295938i 0.649700 0.760191i \(-0.274894\pi\)
−0.885703 + 0.464253i \(0.846323\pi\)
\(402\) 0 0
\(403\) 1.37204 2.18360i 0.00340458 0.00541835i
\(404\) 8.23305 73.0703i 0.0203788 0.180867i
\(405\) 0 0
\(406\) −644.295 + 751.765i −1.58693 + 1.85164i
\(407\) −12.0104 −0.0295095
\(408\) 0 0
\(409\) −138.561 87.0640i −0.338781 0.212870i 0.351886 0.936043i \(-0.385540\pi\)
−0.690668 + 0.723172i \(0.742683\pi\)
\(410\) 929.086 + 212.058i 2.26606 + 0.517214i
\(411\) 0 0
\(412\) −504.233 402.112i −1.22387 0.976000i
\(413\) −193.226 846.580i −0.467860 2.04983i
\(414\) 0 0
\(415\) −120.144 249.481i −0.289503 0.601160i
\(416\) 177.246 111.371i 0.426071 0.267718i
\(417\) 0 0
\(418\) −28.1795 28.1795i −0.0674150 0.0674150i
\(419\) 14.3641 29.8274i 0.0342819 0.0711870i −0.883125 0.469139i \(-0.844564\pi\)
0.917406 + 0.397952i \(0.130279\pi\)
\(420\) 0 0
\(421\) −442.876 + 49.9001i −1.05196 + 0.118528i −0.620974 0.783831i \(-0.713263\pi\)
−0.430986 + 0.902358i \(0.641834\pi\)
\(422\) 1208.88 + 582.167i 2.86465 + 1.37954i
\(423\) 0 0
\(424\) 345.877 + 988.459i 0.815747 + 2.33127i
\(425\) −262.117 417.157i −0.616747 0.981547i
\(426\) 0 0
\(427\) −23.9206 + 68.3611i −0.0560201 + 0.160096i
\(428\) 701.251 160.056i 1.63844 0.373962i
\(429\) 0 0
\(430\) −90.8633 113.939i −0.211310 0.264974i
\(431\) −56.6584 + 248.237i −0.131458 + 0.575955i 0.865696 + 0.500569i \(0.166876\pi\)
−0.997154 + 0.0753857i \(0.975981\pi\)
\(432\) 0 0
\(433\) 41.5408 368.685i 0.0959371 0.851465i −0.849927 0.526901i \(-0.823354\pi\)
0.945864 0.324564i \(-0.105218\pi\)
\(434\) 11.2561i 0.0259358i
\(435\) 0 0
\(436\) 1086.24 2.49138
\(437\) −285.811 32.2032i −0.654030 0.0736915i
\(438\) 0 0
\(439\) 472.512 + 107.848i 1.07634 + 0.245667i 0.723715 0.690099i \(-0.242433\pi\)
0.352622 + 0.935766i \(0.385290\pi\)
\(440\) −67.5556 + 53.8738i −0.153535 + 0.122440i
\(441\) 0 0
\(442\) −154.143 675.345i −0.348740 1.52793i
\(443\) 133.331 + 46.6547i 0.300974 + 0.105315i 0.476541 0.879152i \(-0.341890\pi\)
−0.175567 + 0.984467i \(0.556176\pi\)
\(444\) 0 0
\(445\) 559.825 351.761i 1.25803 0.790475i
\(446\) −936.503 + 327.696i −2.09978 + 0.734745i
\(447\) 0 0
\(448\) 47.3918 98.4102i 0.105785 0.219666i
\(449\) −55.2993 490.795i −0.123161 1.09309i −0.891493 0.453034i \(-0.850342\pi\)
0.768332 0.640051i \(-0.221087\pi\)
\(450\) 0 0
\(451\) −26.5331 12.7777i −0.0588317 0.0283319i
\(452\) −993.706 + 993.706i −2.19847 + 2.19847i
\(453\) 0 0
\(454\) 500.957 + 797.269i 1.10343 + 1.75610i
\(455\) −450.039 + 216.727i −0.989096 + 0.476324i
\(456\) 0 0
\(457\) 890.248 203.193i 1.94803 0.444624i 0.964373 0.264547i \(-0.0852225\pi\)
0.983653 0.180077i \(-0.0576347\pi\)
\(458\) 689.187 864.213i 1.50478 1.88693i
\(459\) 0 0
\(460\) −253.351 + 1110.00i −0.550762 + 2.41305i
\(461\) 70.6093 112.374i 0.153166 0.243762i −0.761323 0.648372i \(-0.775450\pi\)
0.914489 + 0.404611i \(0.132593\pi\)
\(462\) 0 0
\(463\) 36.6184i 0.0790895i −0.999218 0.0395447i \(-0.987409\pi\)
0.999218 0.0395447i \(-0.0125908\pi\)
\(464\) 230.973 + 743.437i 0.497788 + 1.60223i
\(465\) 0 0
\(466\) −329.109 37.0817i −0.706243 0.0795745i
\(467\) −125.291 78.7258i −0.268290 0.168578i 0.391168 0.920319i \(-0.372071\pi\)
−0.659458 + 0.751742i \(0.729214\pi\)
\(468\) 0 0
\(469\) −512.672 + 408.843i −1.09312 + 0.871733i
\(470\) 81.6786 + 65.1365i 0.173784 + 0.138588i
\(471\) 0 0
\(472\) −1493.76 522.690i −3.16475 1.10739i
\(473\) 1.95401 + 4.05755i 0.00413111 + 0.00857833i
\(474\) 0 0
\(475\) −281.858 + 98.6265i −0.593386 + 0.207635i
\(476\) 1472.14 + 1472.14i 3.09273 + 3.09273i
\(477\) 0 0
\(478\) 165.284 + 1466.93i 0.345782 + 3.06890i
\(479\) 541.118 60.9693i 1.12968 0.127285i 0.472723 0.881211i \(-0.343271\pi\)
0.656959 + 0.753926i \(0.271842\pi\)
\(480\) 0 0
\(481\) −89.4749 + 89.4749i −0.186019 + 0.186019i
\(482\) −146.940 419.930i −0.304855 0.871225i
\(483\) 0 0
\(484\) −959.789 + 462.210i −1.98304 + 0.954980i
\(485\) −357.948 + 1022.96i −0.738036 + 2.10919i
\(486\) 0 0
\(487\) −143.770 + 180.282i −0.295216 + 0.370190i −0.907214 0.420670i \(-0.861795\pi\)
0.611997 + 0.790860i \(0.290366\pi\)
\(488\) 82.2977 + 103.198i 0.168643 + 0.211471i
\(489\) 0 0
\(490\) 533.624 849.257i 1.08903 1.73318i
\(491\) −55.3414 + 491.168i −0.112712 + 1.00034i 0.802302 + 0.596919i \(0.203608\pi\)
−0.915013 + 0.403424i \(0.867820\pi\)
\(492\) 0 0
\(493\) 716.157 + 25.3412i 1.45265 + 0.0514020i
\(494\) −419.863 −0.849926
\(495\) 0 0
\(496\) 7.49397 + 4.70877i 0.0151088 + 0.00949349i
\(497\) 816.761 + 186.420i 1.64338 + 0.375091i
\(498\) 0 0
\(499\) 116.986 + 93.2931i 0.234441 + 0.186960i 0.733663 0.679514i \(-0.237809\pi\)
−0.499222 + 0.866474i \(0.666381\pi\)
\(500\) −66.7859 292.608i −0.133572 0.585216i
\(501\) 0 0
\(502\) −52.1212 108.231i −0.103827 0.215599i
\(503\) 579.852 364.345i 1.15279 0.724344i 0.186664 0.982424i \(-0.440233\pi\)
0.966124 + 0.258080i \(0.0830897\pi\)
\(504\) 0 0
\(505\) 39.4101 + 39.4101i 0.0780398 + 0.0780398i
\(506\) 22.1700 46.0365i 0.0438143 0.0909813i
\(507\) 0 0
\(508\) 847.857 95.5305i 1.66901 0.188052i
\(509\) 285.063 + 137.279i 0.560046 + 0.269704i 0.692419 0.721496i \(-0.256545\pi\)
−0.132372 + 0.991200i \(0.542259\pi\)
\(510\) 0 0
\(511\) −92.2295 263.577i −0.180488 0.515806i
\(512\) −609.618 970.201i −1.19066 1.89492i
\(513\) 0 0
\(514\) 319.898 914.215i 0.622369 1.77863i
\(515\) 476.576 108.775i 0.925390 0.211214i
\(516\) 0 0
\(517\) −2.01289 2.52408i −0.00389340 0.00488217i
\(518\) 122.898 538.452i 0.237255 1.03948i
\(519\) 0 0
\(520\) −101.927 + 904.625i −0.196013 + 1.73966i
\(521\) 561.548i 1.07783i 0.842361 + 0.538914i \(0.181165\pi\)
−0.842361 + 0.538914i \(0.818835\pi\)
\(522\) 0 0
\(523\) −649.609 −1.24208 −0.621041 0.783778i \(-0.713290\pi\)
−0.621041 + 0.783778i \(0.713290\pi\)
\(524\) −669.123 75.3920i −1.27695 0.143878i
\(525\) 0 0
\(526\) −624.509 142.540i −1.18728 0.270989i
\(527\) 6.36957 5.07956i 0.0120865 0.00963863i
\(528\) 0 0
\(529\) 35.6531 + 156.206i 0.0673971 + 0.295286i
\(530\) −1367.83 478.625i −2.58082 0.903066i
\(531\) 0 0
\(532\) 1068.47 671.362i 2.00840 1.26196i
\(533\) −292.858 + 102.475i −0.549452 + 0.192261i
\(534\) 0 0
\(535\) −236.546 + 491.193i −0.442143 + 0.918119i
\(536\) 133.806 + 1187.56i 0.249638 + 2.21560i
\(537\) 0 0
\(538\) 1262.54 + 608.006i 2.34672 + 1.13012i
\(539\) −21.9168 + 21.9168i −0.0406620 + 0.0406620i
\(540\) 0 0
\(541\) 412.119 + 655.884i 0.761774 + 1.21236i 0.972064 + 0.234717i \(0.0754162\pi\)
−0.210290 + 0.977639i \(0.567441\pi\)
\(542\) 109.342 52.6563i 0.201738 0.0971519i
\(543\) 0 0
\(544\) 644.722 147.153i 1.18515 0.270503i
\(545\) −513.331 + 643.697i −0.941892 + 1.18109i
\(546\) 0 0
\(547\) −116.423 + 510.082i −0.212839 + 0.932508i 0.749788 + 0.661678i \(0.230155\pi\)
−0.962627 + 0.270830i \(0.912702\pi\)
\(548\) 718.691 1143.79i 1.31148 2.08721i
\(549\) 0 0
\(550\) 53.0502i 0.0964549i
\(551\) 111.565 419.772i 0.202477 0.761837i
\(552\) 0 0
\(553\) 208.748 + 23.5202i 0.377482 + 0.0425320i
\(554\) −359.635 225.973i −0.649160 0.407894i
\(555\) 0 0
\(556\) −934.588 + 745.309i −1.68091 + 1.34048i
\(557\) 133.141 + 106.177i 0.239033 + 0.190622i 0.735678 0.677331i \(-0.236864\pi\)
−0.496645 + 0.867954i \(0.665435\pi\)
\(558\) 0 0
\(559\) 44.7850 + 15.6709i 0.0801163 + 0.0280339i
\(560\) −743.794 1544.50i −1.32820 2.75804i
\(561\) 0 0
\(562\) −967.402 + 338.509i −1.72136 + 0.602329i
\(563\) 622.112 + 622.112i 1.10499 + 1.10499i 0.993799 + 0.111195i \(0.0354679\pi\)
0.111195 + 0.993799i \(0.464532\pi\)
\(564\) 0 0
\(565\) −119.260 1058.46i −0.211080 1.87339i
\(566\) −808.759 + 91.1252i −1.42890 + 0.160999i
\(567\) 0 0
\(568\) 1079.63 1079.63i 1.90076 1.90076i
\(569\) −62.1379 177.580i −0.109205 0.312091i 0.876292 0.481780i \(-0.160010\pi\)
−0.985498 + 0.169689i \(0.945724\pi\)
\(570\) 0 0
\(571\) 485.208 233.664i 0.849751 0.409218i 0.0422657 0.999106i \(-0.486542\pi\)
0.807485 + 0.589888i \(0.200828\pi\)
\(572\) 16.9635 48.4790i 0.0296565 0.0847535i
\(573\) 0 0
\(574\) 844.356 1058.79i 1.47100 1.84458i
\(575\) −238.719 299.344i −0.415163 0.520599i
\(576\) 0 0
\(577\) −276.433 + 439.941i −0.479087 + 0.762462i −0.995589 0.0938238i \(-0.970091\pi\)
0.516502 + 0.856286i \(0.327234\pi\)
\(578\) 129.052 1145.37i 0.223274 1.98161i
\(579\) 0 0
\(580\) −1601.78 624.904i −2.76169 1.07742i
\(581\) −393.497 −0.677276
\(582\) 0 0
\(583\) 37.9185 + 23.8258i 0.0650403 + 0.0408675i
\(584\) −496.168 113.247i −0.849603 0.193916i
\(585\) 0 0
\(586\) 530.267 + 422.874i 0.904893 + 0.721628i
\(587\) 235.013 + 1029.66i 0.400363 + 1.75411i 0.625931 + 0.779878i \(0.284719\pi\)
−0.225568 + 0.974227i \(0.572424\pi\)
\(588\) 0 0
\(589\) −2.14252 4.44899i −0.00363755 0.00755346i
\(590\) 1854.30 1165.13i 3.14288 1.97480i
\(591\) 0 0
\(592\) −307.072 307.072i −0.518703 0.518703i
\(593\) −85.9928 + 178.566i −0.145013 + 0.301123i −0.960806 0.277221i \(-0.910587\pi\)
0.815793 + 0.578344i \(0.196301\pi\)
\(594\) 0 0
\(595\) −1568.08 + 176.680i −2.63542 + 0.296941i
\(596\) −474.814 228.658i −0.796667 0.383655i
\(597\) 0 0
\(598\) −177.801 508.126i −0.297326 0.849708i
\(599\) 154.573 + 246.002i 0.258052 + 0.410687i 0.950473 0.310806i \(-0.100599\pi\)
−0.692421 + 0.721493i \(0.743456\pi\)
\(600\) 0 0
\(601\) −168.543 + 481.670i −0.280438 + 0.801447i 0.714378 + 0.699760i \(0.246710\pi\)
−0.994816 + 0.101687i \(0.967576\pi\)
\(602\) −201.904 + 46.0833i −0.335389 + 0.0765503i
\(603\) 0 0
\(604\) −1432.30 1796.05i −2.37136 2.97359i
\(605\) 179.671 787.192i 0.296978 1.30114i
\(606\) 0 0
\(607\) 2.33822 20.7523i 0.00385209 0.0341883i −0.991639 0.129042i \(-0.958810\pi\)
0.995491 + 0.0948538i \(0.0302384\pi\)
\(608\) 400.825i 0.659251i
\(609\) 0 0
\(610\) −182.656 −0.299435
\(611\) −33.7995 3.80829i −0.0553184 0.00623289i
\(612\) 0 0
\(613\) −480.301 109.626i −0.783525 0.178835i −0.187998 0.982169i \(-0.560200\pi\)
−0.595527 + 0.803335i \(0.703057\pi\)
\(614\) −1140.31 + 909.367i −1.85718 + 1.48105i
\(615\) 0 0
\(616\) 27.3232 + 119.711i 0.0443559 + 0.194336i
\(617\) −814.785 285.105i −1.32056 0.462083i −0.424262 0.905539i \(-0.639467\pi\)
−0.896296 + 0.443456i \(0.853752\pi\)
\(618\) 0 0
\(619\) −111.989 + 70.3677i −0.180920 + 0.113680i −0.619447 0.785038i \(-0.712643\pi\)
0.438527 + 0.898718i \(0.355500\pi\)
\(620\) −18.4502 + 6.45602i −0.0297585 + 0.0104129i
\(621\) 0 0
\(622\) 37.1487 77.1400i 0.0597245 0.124019i
\(623\) −105.197 933.650i −0.168856 1.49864i
\(624\) 0 0
\(625\) 654.040 + 314.969i 1.04646 + 0.503951i
\(626\) 1042.07 1042.07i 1.66464 1.66464i
\(627\) 0 0
\(628\) −881.306 1402.59i −1.40335 2.23342i
\(629\) −360.157 + 173.443i −0.572587 + 0.275744i
\(630\) 0 0
\(631\) 901.413 205.742i 1.42855 0.326056i 0.562822 0.826578i \(-0.309716\pi\)
0.865724 + 0.500522i \(0.166858\pi\)
\(632\) 238.703 299.324i 0.377695 0.473615i
\(633\) 0 0
\(634\) 384.110 1682.89i 0.605851 2.65441i
\(635\) −344.066 + 547.578i −0.541836 + 0.862327i
\(636\) 0 0
\(637\) 326.552i 0.512640i
\(638\) 63.8431 + 43.3380i 0.100068 + 0.0679278i
\(639\) 0 0
\(640\) 986.826 + 111.189i 1.54192 + 0.173732i
\(641\) 836.101 + 525.357i 1.30437 + 0.819590i 0.991488 0.130202i \(-0.0415625\pi\)
0.312883 + 0.949792i \(0.398705\pi\)
\(642\) 0 0
\(643\) 597.523 476.509i 0.929274 0.741071i −0.0368040 0.999323i \(-0.511718\pi\)
0.966078 + 0.258251i \(0.0831463\pi\)
\(644\) 1264.96 + 1008.77i 1.96423 + 1.56642i
\(645\) 0 0
\(646\) −1251.97 438.082i −1.93803 0.678145i
\(647\) 530.613 + 1101.83i 0.820112 + 1.70298i 0.704520 + 0.709684i \(0.251162\pi\)
0.115593 + 0.993297i \(0.463123\pi\)
\(648\) 0 0
\(649\) −63.8779 + 22.3518i −0.0984251 + 0.0344404i
\(650\) −395.214 395.214i −0.608021 0.608021i
\(651\) 0 0
\(652\) 252.222 + 2238.53i 0.386844 + 3.43333i
\(653\) −1154.35 + 130.064i −1.76777 + 0.199179i −0.935049 0.354520i \(-0.884644\pi\)
−0.832717 + 0.553699i \(0.813216\pi\)
\(654\) 0 0
\(655\) 360.888 360.888i 0.550974 0.550974i
\(656\) −351.689 1005.07i −0.536111 1.53212i
\(657\) 0 0
\(658\) 133.757 64.4142i 0.203279 0.0978939i
\(659\) 103.295 295.200i 0.156745 0.447951i −0.838552 0.544821i \(-0.816597\pi\)
0.995297 + 0.0968701i \(0.0308831\pi\)
\(660\) 0 0
\(661\) −741.803 + 930.192i −1.12224 + 1.40725i −0.220281 + 0.975436i \(0.570697\pi\)
−0.901963 + 0.431813i \(0.857874\pi\)
\(662\) −801.377 1004.90i −1.21054 1.51797i
\(663\) 0 0
\(664\) −381.546 + 607.228i −0.574618 + 0.914499i
\(665\) −107.088 + 950.433i −0.161035 + 1.42922i
\(666\) 0 0
\(667\) 555.260 42.7445i 0.832474 0.0640847i
\(668\) 340.486 0.509709
\(669\) 0 0
\(670\) −1400.27 879.846i −2.08995 1.31320i
\(671\) 5.50301 + 1.25603i 0.00820120 + 0.00187187i
\(672\) 0 0
\(673\) −444.801 354.717i −0.660922 0.527068i 0.234596 0.972093i \(-0.424623\pi\)
−0.895518 + 0.445025i \(0.853195\pi\)
\(674\) 18.4825 + 80.9772i 0.0274221 + 0.120144i
\(675\) 0 0
\(676\) 413.736 + 859.133i 0.612036 + 1.27091i
\(677\) −157.955 + 99.2497i −0.233316 + 0.146602i −0.643616 0.765348i \(-0.722567\pi\)
0.410300 + 0.911950i \(0.365424\pi\)
\(678\) 0 0
\(679\) 1089.02 + 1089.02i 1.60386 + 1.60386i
\(680\) −1247.81 + 2591.10i −1.83501 + 3.81044i
\(681\) 0 0
\(682\) 0.871738 0.0982213i 0.00127821 0.000144020i
\(683\) −102.817 49.5142i −0.150538 0.0724951i 0.357098 0.934067i \(-0.383766\pi\)
−0.507636 + 0.861572i \(0.669480\pi\)
\(684\) 0 0
\(685\) 338.164 + 966.417i 0.493670 + 1.41083i
\(686\) 131.724 + 209.638i 0.192018 + 0.305594i
\(687\) 0 0
\(688\) −53.7817 + 153.699i −0.0781711 + 0.223400i
\(689\) 459.983 104.988i 0.667610 0.152378i
\(690\) 0 0
\(691\) −301.568 378.155i −0.436423 0.547257i 0.514174 0.857686i \(-0.328099\pi\)
−0.950597 + 0.310429i \(0.899527\pi\)
\(692\) 75.5389 330.958i 0.109160 0.478263i
\(693\) 0 0
\(694\) 123.282 1094.16i 0.177640 1.57660i
\(695\) 906.043i 1.30366i
\(696\) 0 0
\(697\) −980.177 −1.40628
\(698\) 291.870 + 32.8858i 0.418151 + 0.0471143i
\(699\) 0 0
\(700\) 1637.69 + 373.791i 2.33955 + 0.533988i
\(701\) 382.725 305.213i 0.545969 0.435396i −0.311264 0.950323i \(-0.600752\pi\)
0.857234 + 0.514927i \(0.172181\pi\)
\(702\) 0 0
\(703\) 53.9148 + 236.216i 0.0766925 + 0.336012i
\(704\) −8.03499 2.81157i −0.0114133 0.00399370i
\(705\) 0 0
\(706\) −134.273 + 84.3691i −0.190188 + 0.119503i
\(707\) 74.7573 26.1587i 0.105739 0.0369996i
\(708\) 0 0
\(709\) 461.431 958.172i 0.650820 1.35144i −0.270531 0.962711i \(-0.587199\pi\)
0.921351 0.388731i \(-0.127086\pi\)
\(710\) 236.562 + 2099.54i 0.333186 + 2.95711i
\(711\) 0 0
\(712\) −1542.77 742.959i −2.16681 1.04348i
\(713\) 4.47694 4.47694i 0.00627902 0.00627902i
\(714\) 0 0
\(715\) 20.7117 + 32.9624i 0.0289674 + 0.0461013i
\(716\) −1386.90 + 667.895i −1.93701 + 0.932815i
\(717\) 0 0
\(718\) 1220.23 278.511i 1.69949 0.387898i
\(719\) 465.243 583.396i 0.647069 0.811399i −0.344798 0.938677i \(-0.612053\pi\)
0.991867 + 0.127278i \(0.0406240\pi\)
\(720\) 0 0
\(721\) 154.577 677.244i 0.214392 0.939312i
\(722\) 260.609 414.757i 0.360954 0.574455i
\(723\) 0 0
\(724\) 1505.90i 2.07998i
\(725\) 500.143 290.113i 0.689853 0.400156i
\(726\) 0 0
\(727\) 137.483 + 15.4906i 0.189110 + 0.0213076i 0.206012 0.978550i \(-0.433952\pi\)
−0.0169014 + 0.999857i \(0.505380\pi\)
\(728\) 1095.38 + 688.270i 1.50464 + 0.945426i
\(729\) 0 0
\(730\) 550.610 439.097i 0.754260 0.601502i
\(731\) 117.191 + 93.4566i 0.160316 + 0.127848i
\(732\) 0 0
\(733\) −96.2298 33.6723i −0.131282 0.0459376i 0.263838 0.964567i \(-0.415011\pi\)
−0.395121 + 0.918629i \(0.629297\pi\)
\(734\) 342.438 + 711.079i 0.466537 + 0.968773i
\(735\) 0 0
\(736\) 485.085 169.738i 0.659082 0.230623i
\(737\) 36.1367 + 36.1367i 0.0490322 + 0.0490322i
\(738\) 0 0
\(739\) 77.8075 + 690.560i 0.105288 + 0.934452i 0.929663 + 0.368410i \(0.120098\pi\)
−0.824376 + 0.566043i \(0.808474\pi\)
\(740\) 953.082 107.387i 1.28795 0.145117i
\(741\) 0 0
\(742\) −1456.17 + 1456.17i −1.96250 + 1.96250i
\(743\) 213.456 + 610.021i 0.287289 + 0.821024i 0.993583 + 0.113106i \(0.0360799\pi\)
−0.706294 + 0.707918i \(0.749634\pi\)
\(744\) 0 0
\(745\) 359.886 173.312i 0.483069 0.232634i
\(746\) 310.608 887.666i 0.416364 1.18990i
\(747\) 0 0
\(748\) 101.165 126.857i 0.135247 0.169595i
\(749\) 483.042 + 605.716i 0.644916 + 0.808700i
\(750\) 0 0
\(751\) 203.554 323.954i 0.271044 0.431364i −0.683272 0.730164i \(-0.739444\pi\)
0.954316 + 0.298800i \(0.0965865\pi\)
\(752\) 13.0698 115.998i 0.0173801 0.154253i
\(753\) 0 0
\(754\) 798.479 152.760i 1.05899 0.202599i
\(755\) 1741.19 2.30621
\(756\) 0 0
\(757\) −572.593 359.784i −0.756397 0.475276i 0.0978121 0.995205i \(-0.468816\pi\)
−0.854210 + 0.519929i \(0.825958\pi\)
\(758\) −790.112 180.338i −1.04236 0.237913i
\(759\) 0 0
\(760\) 1362.83 + 1086.82i 1.79320 + 1.43003i
\(761\) −139.727 612.184i −0.183610 0.804447i −0.979893 0.199523i \(-0.936061\pi\)
0.796283 0.604924i \(-0.206796\pi\)
\(762\) 0 0
\(763\) 507.639 + 1054.12i 0.665319 + 1.38155i
\(764\) 213.237 133.986i 0.279106 0.175374i
\(765\) 0 0
\(766\) −344.037 344.037i −0.449134 0.449134i
\(767\) −309.361 + 642.395i −0.403339 + 0.837543i
\(768\) 0 0
\(769\) −322.552 + 36.3428i −0.419443 + 0.0472599i −0.319164 0.947700i \(-0.603402\pi\)
−0.100279 + 0.994959i \(0.531974\pi\)
\(770\) −153.089 73.7240i −0.198817 0.0957454i
\(771\) 0 0
\(772\) −867.273 2478.52i −1.12341 3.21052i
\(773\) 246.656 + 392.551i 0.319089 + 0.507828i 0.967301 0.253633i \(-0.0816255\pi\)
−0.648211 + 0.761461i \(0.724483\pi\)
\(774\) 0 0
\(775\) 2.17106 6.20453i 0.00280137 0.00800585i
\(776\) 2736.48 624.583i 3.52639 0.804875i
\(777\) 0 0
\(778\) 34.9016 + 43.7652i 0.0448606 + 0.0562534i
\(779\) −132.200 + 579.204i −0.169704 + 0.743523i
\(780\) 0 0
\(781\) 7.31037 64.8814i 0.00936027 0.0830747i
\(782\) 1700.67i 2.17476i
\(783\) 0 0
\(784\) −1120.71 −1.42947
\(785\) 1247.65 + 140.576i 1.58936 + 0.179078i
\(786\) 0 0
\(787\) 1295.68 + 295.731i 1.64636 + 0.375770i 0.942404 0.334476i \(-0.108559\pi\)
0.703953 + 0.710246i \(0.251416\pi\)
\(788\) −1686.91 + 1345.26i −2.14075 + 1.70719i
\(789\) 0 0
\(790\) 117.889 + 516.507i 0.149227 + 0.653806i
\(791\) −1428.72 499.930i −1.80622 0.632023i
\(792\) 0 0
\(793\) 50.3535 31.6392i 0.0634975 0.0398981i
\(794\) −970.210 + 339.491i −1.22193 + 0.427571i
\(795\) 0 0
\(796\) −1216.94 + 2527.00i −1.52882 + 3.17463i
\(797\) 29.7161 + 263.738i 0.0372849 + 0.330913i 0.998483 + 0.0550550i \(0.0175334\pi\)
−0.961198 + 0.275858i \(0.911038\pi\)
\(798\) 0 0
\(799\) −96.8113 46.6219i −0.121166 0.0583503i
\(800\) 377.293 377.293i 0.471616 0.471616i
\(801\) 0 0
\(802\) −289.418 460.606i −0.360870 0.574321i
\(803\) −19.6081 + 9.44276i −0.0244185 + 0.0117594i
\(804\) 0 0
\(805\) −1195.58 + 272.883i −1.48519 + 0.338985i
\(806\) 5.76256 7.22602i 0.00714957 0.00896528i
\(807\) 0 0
\(808\) 32.1199 140.727i 0.0397524 0.174166i
\(809\) 617.736 983.122i 0.763580 1.21523i −0.207909 0.978148i \(-0.566666\pi\)
0.971489 0.237083i \(-0.0761913\pi\)
\(810\) 0 0
\(811\) 321.059i 0.395880i 0.980214 + 0.197940i \(0.0634252\pi\)
−0.980214 + 0.197940i \(0.936575\pi\)
\(812\) −1787.70 + 1665.51i −2.20161 + 2.05112i
\(813\) 0 0
\(814\) −42.7732 4.81939i −0.0525470 0.00592062i
\(815\) −1445.73 908.411i −1.77390 1.11462i
\(816\) 0 0
\(817\) 71.0311 56.6454i 0.0869413 0.0693334i
\(818\) −458.531 365.667i −0.560552 0.447025i
\(819\) 0 0
\(820\) 2219.78 + 776.735i 2.70705 + 0.947238i
\(821\) −286.021 593.929i −0.348381 0.723421i 0.650982 0.759093i \(-0.274357\pi\)
−0.999364 + 0.0356719i \(0.988643\pi\)
\(822\) 0 0
\(823\) −1135.65 + 397.380i −1.37989 + 0.482843i −0.915331 0.402702i \(-0.868071\pi\)
−0.464555 + 0.885545i \(0.653786\pi\)
\(824\) −895.212 895.212i −1.08642 1.08642i
\(825\) 0 0
\(826\) −348.442 3092.51i −0.421843 3.74396i
\(827\) −935.574 + 105.414i −1.13129 + 0.127465i −0.657699 0.753281i \(-0.728470\pi\)
−0.473588 + 0.880747i \(0.657041\pi\)
\(828\) 0 0
\(829\) 445.070 445.070i 0.536876 0.536876i −0.385734 0.922610i \(-0.626052\pi\)
0.922610 + 0.385734i \(0.126052\pi\)
\(830\) −327.767 936.703i −0.394900 1.12856i
\(831\) 0 0
\(832\) −80.8048 + 38.9135i −0.0971212 + 0.0467711i
\(833\) −340.722 + 973.726i −0.409029 + 1.16894i
\(834\) 0 0
\(835\) −160.905 + 201.769i −0.192701 + 0.241639i
\(836\) −61.3176 76.8899i −0.0733465 0.0919736i
\(837\) 0 0
\(838\) 63.1245 100.462i 0.0753276 0.119883i
\(839\) 112.137 995.248i 0.133656 1.18623i −0.730466 0.682949i \(-0.760697\pi\)
0.864122 0.503282i \(-0.167874\pi\)
\(840\) 0 0
\(841\) −59.4431 + 838.897i −0.0706814 + 0.997499i
\(842\) −1597.26 −1.89699
\(843\) 0 0
\(844\) 2803.65 + 1761.65i 3.32186 + 2.08727i
\(845\) −704.636 160.829i −0.833889 0.190330i
\(846\) 0 0
\(847\) −897.087 715.403i −1.05913 0.844631i
\(848\) 360.313 + 1578.63i 0.424897 + 1.86160i
\(849\) 0 0
\(850\) −766.102 1590.83i −0.901297 1.87156i
\(851\) −263.041 + 165.280i −0.309097 + 0.194218i
\(852\) 0 0
\(853\) −187.887 187.887i −0.220266 0.220266i 0.588345 0.808610i \(-0.299780\pi\)
−0.808610 + 0.588345i \(0.799780\pi\)
\(854\) −112.621 + 233.860i −0.131875 + 0.273841i
\(855\) 0 0
\(856\) 1403.09 158.090i 1.63912 0.184684i
\(857\) −391.026 188.308i −0.456273 0.219729i 0.191608 0.981472i \(-0.438630\pi\)
−0.647880 + 0.761742i \(0.724344\pi\)
\(858\) 0 0
\(859\) −188.502 538.706i −0.219443 0.627132i −0.999998 0.00204487i \(-0.999349\pi\)
0.780555 0.625087i \(-0.214937\pi\)
\(860\) −191.340 304.516i −0.222488 0.354088i
\(861\) 0 0
\(862\) −301.391 + 861.325i −0.349641 + 0.999217i
\(863\) −1118.53 + 255.297i −1.29610 + 0.295826i −0.814293 0.580454i \(-0.802875\pi\)
−0.481803 + 0.876279i \(0.660018\pi\)
\(864\) 0 0
\(865\) 160.425 + 201.166i 0.185462 + 0.232562i
\(866\) 295.883 1296.35i 0.341667 1.49694i
\(867\) 0 0
\(868\) −3.11012 + 27.6031i −0.00358309 + 0.0318008i
\(869\) 16.3719i 0.0188399i
\(870\) 0 0
\(871\) 538.423 0.618167
\(872\) 2118.90 + 238.742i 2.42993 + 0.273787i
\(873\) 0 0
\(874\) −1004.95 229.374i −1.14983 0.262442i
\(875\) 252.745 201.557i 0.288851 0.230351i
\(876\) 0 0
\(877\) −242.063 1060.55i −0.276012 1.20929i −0.902787 0.430088i \(-0.858483\pi\)
0.626775 0.779200i \(-0.284375\pi\)
\(878\) 1639.51 + 573.689i 1.86732 + 0.653404i
\(879\) 0 0
\(880\) −113.125 + 71.0811i −0.128551 + 0.0807740i
\(881\) 775.831 271.475i 0.880625 0.308144i 0.148172 0.988962i \(-0.452661\pi\)
0.732453 + 0.680817i \(0.238375\pi\)
\(882\) 0 0
\(883\) −143.552 + 298.089i −0.162573 + 0.337587i −0.966303 0.257408i \(-0.917132\pi\)
0.803730 + 0.594995i \(0.202846\pi\)
\(884\) −191.400 1698.72i −0.216516 1.92163i
\(885\) 0 0
\(886\) 456.120 + 219.656i 0.514809 + 0.247919i
\(887\) −629.240 + 629.240i −0.709402 + 0.709402i −0.966410 0.257007i \(-0.917264\pi\)
0.257007 + 0.966410i \(0.417264\pi\)
\(888\) 0 0
\(889\) 488.939 + 778.142i 0.549988 + 0.875301i
\(890\) 2134.89 1028.11i 2.39875 1.15518i
\(891\) 0 0
\(892\) −2387.10 + 544.841i −2.67613 + 0.610808i
\(893\) −40.6070 + 50.9195i −0.0454725 + 0.0570207i
\(894\) 0 0
\(895\) 259.626 1137.50i 0.290085 1.27094i
\(896\) 750.811 1194.91i 0.837959 1.33360i
\(897\) 0 0
\(898\) 1770.09i 1.97115i
\(899\) 5.69324 + 7.68138i 0.00633286 + 0.00854437i
\(900\) 0 0
\(901\) 1481.14 + 166.884i 1.64389 + 0.185221i
\(902\) −89.3666 56.1528i −0.0990761 0.0622536i
\(903\) 0 0
\(904\) −2156.80 + 1719.99i −2.38584 + 1.90264i
\(905\) −892.384 711.653i −0.986060 0.786356i
\(906\) 0 0
\(907\) 142.031 + 49.6988i 0.156594 + 0.0547947i 0.407438 0.913233i \(-0.366422\pi\)
−0.250844 + 0.968028i \(0.580708\pi\)
\(908\) 1008.19 + 2093.54i 1.11035 + 2.30566i
\(909\) 0 0
\(910\) −1689.72 + 591.257i −1.85683 + 0.649733i
\(911\) 396.137 + 396.137i 0.434837 + 0.434837i 0.890270 0.455433i \(-0.150515\pi\)
−0.455433 + 0.890270i \(0.650515\pi\)
\(912\) 0 0
\(913\) 3.43367 + 30.4747i 0.00376087 + 0.0333786i
\(914\) 3252.03 366.415i 3.55802 0.400892i
\(915\) 0 0
\(916\) 1928.86 1928.86i 2.10574 2.10574i
\(917\) −239.542 684.571i −0.261223 0.746533i
\(918\) 0 0
\(919\) 84.8857 40.8788i 0.0923675 0.0444818i −0.387130 0.922025i \(-0.626533\pi\)
0.479497 + 0.877543i \(0.340819\pi\)
\(920\) −738.168 + 2109.56i −0.802356 + 2.29300i
\(921\) 0 0
\(922\) 296.558 371.871i 0.321646 0.403331i
\(923\) −428.893 537.815i −0.464673 0.582681i
\(924\) 0 0
\(925\) −171.599 + 273.098i −0.185512 + 0.295241i
\(926\) 14.6938 130.411i 0.0158681 0.140833i
\(927\) 0 0
\(928\) 145.833 + 762.272i 0.157147 + 0.821413i
\(929\) −426.924 −0.459552 −0.229776 0.973243i \(-0.573799\pi\)
−0.229776 + 0.973243i \(0.573799\pi\)
\(930\) 0 0
\(931\) 529.438 + 332.668i 0.568677 + 0.357323i
\(932\) −796.820 181.869i −0.854957 0.195138i
\(933\) 0 0
\(934\) −414.618 330.647i −0.443916 0.354011i
\(935\) 27.3662 + 119.899i 0.0292686 + 0.128234i
\(936\) 0 0
\(937\) 495.268 + 1028.43i 0.528568 + 1.09758i 0.978828 + 0.204685i \(0.0656169\pi\)
−0.450260 + 0.892897i \(0.648669\pi\)
\(938\) −1989.87 + 1250.32i −2.12139 + 1.33296i
\(939\) 0 0
\(940\) 182.301 + 182.301i 0.193937 + 0.193937i
\(941\) −54.6779 + 113.540i −0.0581062 + 0.120659i −0.928000 0.372581i \(-0.878473\pi\)
0.869894 + 0.493239i \(0.164187\pi\)
\(942\) 0 0
\(943\) −756.946 + 85.2873i −0.802700 + 0.0904425i
\(944\) −2204.66 1061.71i −2.33544 1.12469i
\(945\) 0 0
\(946\) 5.33078 + 15.2345i 0.00563507 + 0.0161041i
\(947\) 220.220 + 350.478i 0.232545 + 0.370093i 0.942529 0.334125i \(-0.108441\pi\)
−0.709984 + 0.704218i \(0.751298\pi\)
\(948\) 0 0
\(949\) −75.7298 + 216.423i −0.0797996 + 0.228054i
\(950\) −1043.38 + 238.144i −1.09829 + 0.250677i
\(951\) 0 0
\(952\) 2548.10 + 3195.22i 2.67658 + 3.35632i
\(953\) −151.639 + 664.374i −0.159117 + 0.697139i 0.830927 + 0.556382i \(0.187811\pi\)
−0.990044 + 0.140757i \(0.955046\pi\)
\(954\) 0 0
\(955\) −21.3719 + 189.681i −0.0223789 + 0.198618i
\(956\) 3642.99i 3.81066i
\(957\) 0 0
\(958\) 1951.58 2.03714
\(959\) 1445.84 + 162.907i 1.50765 + 0.169872i
\(960\) 0 0
\(961\) −936.800 213.818i −0.974818 0.222496i
\(962\) −354.556 + 282.749i −0.368561 + 0.293918i
\(963\) 0 0
\(964\) −244.308 1070.38i −0.253432 1.11036i
\(965\) 1878.60 + 657.352i 1.94674 + 0.681193i
\(966\) 0 0
\(967\) 253.964 159.576i 0.262631 0.165022i −0.394280 0.918990i \(-0.629006\pi\)
0.656910 + 0.753969i \(0.271863\pi\)
\(968\) −1973.82 + 690.669i −2.03907 + 0.713501i
\(969\) 0 0
\(970\) −1685.26 + 3499.48i −1.73738 + 3.60771i
\(971\) −154.759 1373.53i −0.159381 1.41455i −0.777708 0.628626i \(-0.783618\pi\)
0.618327 0.785921i \(-0.287811\pi\)
\(972\) 0 0
\(973\) −1160.04 558.644i −1.19223 0.574146i
\(974\) −584.360 + 584.360i −0.599959 + 0.599959i
\(975\) 0 0
\(976\) 108.584 + 172.810i 0.111254 + 0.177059i
\(977\) 1397.72 673.106i 1.43062 0.688952i 0.451510 0.892266i \(-0.350885\pi\)
0.979114 + 0.203314i \(0.0651712\pi\)
\(978\) 0 0
\(979\) −71.3893 + 16.2941i −0.0729206 + 0.0166437i
\(980\) 1543.25 1935.17i 1.57474 1.97466i
\(981\) 0 0
\(982\) −394.181 + 1727.02i −0.401406 + 1.75868i
\(983\) −582.106 + 926.416i −0.592173 + 0.942438i 0.407401 + 0.913249i \(0.366435\pi\)
−0.999574 + 0.0291883i \(0.990708\pi\)
\(984\) 0 0
\(985\) 1635.39i 1.66029i
\(986\) 2540.33 + 377.621i 2.57639 + 0.382983i
\(987\) 0 0
\(988\) −1029.62 116.010i −1.04213 0.117419i
\(989\) 98.6330 + 61.9752i 0.0997300 + 0.0626645i
\(990\) 0 0
\(991\) 75.5485 60.2479i 0.0762346 0.0607951i −0.584631 0.811299i \(-0.698761\pi\)
0.660866 + 0.750504i \(0.270189\pi\)
\(992\) 6.89835 + 5.50125i 0.00695398 + 0.00554562i
\(993\) 0 0
\(994\) 2833.97 + 991.651i 2.85108 + 0.997636i
\(995\) −922.383 1915.35i −0.927018 1.92497i
\(996\) 0 0
\(997\) 937.382 328.004i 0.940203 0.328991i 0.183700 0.982982i \(-0.441192\pi\)
0.756502 + 0.653991i \(0.226907\pi\)
\(998\) 379.193 + 379.193i 0.379953 + 0.379953i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 261.3.s.a.118.4 48
3.2 odd 2 29.3.f.a.2.1 48
29.15 odd 28 inner 261.3.s.a.73.4 48
87.44 even 28 29.3.f.a.15.1 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.3.f.a.2.1 48 3.2 odd 2
29.3.f.a.15.1 yes 48 87.44 even 28
261.3.s.a.73.4 48 29.15 odd 28 inner
261.3.s.a.118.4 48 1.1 even 1 trivial