Properties

Label 855.2.k.i.406.3
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.3
Root \(0.145349 - 0.251751i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.i.676.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.145349 - 0.251751i) q^{2} +(0.957748 - 1.65887i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.486575 q^{7} -1.13822 q^{8} +(0.145349 - 0.251751i) q^{10} -5.34764 q^{11} +(1.24329 - 2.15344i) q^{13} +(0.0707229 + 0.122496i) q^{14} +(-1.75006 - 3.03119i) q^{16} +(-1.70780 - 2.95800i) q^{17} +(-2.46291 - 3.59640i) q^{19} +1.91550 q^{20} +(0.777272 + 1.34627i) q^{22} +(3.20619 - 5.55329i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.722840 q^{26} +(-0.466016 + 0.807163i) q^{28} +(1.38312 - 2.39564i) q^{29} +4.83099 q^{31} +(-1.64696 + 2.85262i) q^{32} +(-0.496454 + 0.859883i) q^{34} +(-0.243287 - 0.421386i) q^{35} -6.31756 q^{37} +(-0.547418 + 1.14277i) q^{38} +(-0.569112 - 0.985730i) q^{40} +(1.29070 + 2.23555i) q^{41} +(1.24329 + 2.15344i) q^{43} +(-5.12169 + 8.87102i) q^{44} -1.86406 q^{46} +(5.55533 - 9.62211i) q^{47} -6.76325 q^{49} +0.290697 q^{50} +(-2.38151 - 4.12490i) q^{52} +(1.49839 - 2.59529i) q^{53} +(-2.67382 - 4.63119i) q^{55} +0.553831 q^{56} -0.804139 q^{58} +(6.36659 + 11.0273i) q^{59} +(-5.92742 + 10.2666i) q^{61} +(-0.702178 - 1.21621i) q^{62} -6.04269 q^{64} +2.48657 q^{65} +(7.58770 - 13.1423i) q^{67} -6.54258 q^{68} +(-0.0707229 + 0.122496i) q^{70} +(-4.96452 - 8.59879i) q^{71} +(5.50642 + 9.53740i) q^{73} +(0.918249 + 1.59045i) q^{74} +(-8.32479 + 0.641189i) q^{76} +2.60202 q^{77} +(-4.06636 - 7.04314i) q^{79} +(1.75006 - 3.03119i) q^{80} +(0.375202 - 0.649869i) q^{82} +5.86106 q^{83} +(1.70780 - 2.95800i) q^{85} +(0.361420 - 0.625998i) q^{86} +6.08681 q^{88} +(-3.25521 + 5.63820i) q^{89} +(-0.604952 + 1.04781i) q^{91} +(-6.14145 - 10.6373i) q^{92} -3.22984 q^{94} +(1.88312 - 3.93114i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(0.983028 + 1.70265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.145349 0.251751i −0.102777 0.178015i 0.810051 0.586360i \(-0.199439\pi\)
−0.912828 + 0.408345i \(0.866106\pi\)
\(3\) 0 0
\(4\) 0.957748 1.65887i 0.478874 0.829434i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −0.486575 −0.183908 −0.0919539 0.995763i \(-0.529311\pi\)
−0.0919539 + 0.995763i \(0.529311\pi\)
\(8\) −1.13822 −0.402423
\(9\) 0 0
\(10\) 0.145349 0.251751i 0.0459633 0.0796107i
\(11\) −5.34764 −1.61237 −0.806187 0.591661i \(-0.798472\pi\)
−0.806187 + 0.591661i \(0.798472\pi\)
\(12\) 0 0
\(13\) 1.24329 2.15344i 0.344826 0.597256i −0.640496 0.767961i \(-0.721271\pi\)
0.985322 + 0.170705i \(0.0546046\pi\)
\(14\) 0.0707229 + 0.122496i 0.0189015 + 0.0327384i
\(15\) 0 0
\(16\) −1.75006 3.03119i −0.437514 0.757796i
\(17\) −1.70780 2.95800i −0.414203 0.717421i 0.581141 0.813803i \(-0.302606\pi\)
−0.995344 + 0.0963817i \(0.969273\pi\)
\(18\) 0 0
\(19\) −2.46291 3.59640i −0.565029 0.825071i
\(20\) 1.91550 0.428318
\(21\) 0 0
\(22\) 0.777272 + 1.34627i 0.165715 + 0.287027i
\(23\) 3.20619 5.55329i 0.668537 1.15794i −0.309776 0.950810i \(-0.600254\pi\)
0.978313 0.207131i \(-0.0664126\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.722840 −0.141761
\(27\) 0 0
\(28\) −0.466016 + 0.807163i −0.0880687 + 0.152539i
\(29\) 1.38312 2.39564i 0.256839 0.444859i −0.708554 0.705656i \(-0.750652\pi\)
0.965393 + 0.260798i \(0.0839856\pi\)
\(30\) 0 0
\(31\) 4.83099 0.867671 0.433836 0.900992i \(-0.357160\pi\)
0.433836 + 0.900992i \(0.357160\pi\)
\(32\) −1.64696 + 2.85262i −0.291144 + 0.504276i
\(33\) 0 0
\(34\) −0.496454 + 0.859883i −0.0851411 + 0.147469i
\(35\) −0.243287 0.421386i −0.0411231 0.0712272i
\(36\) 0 0
\(37\) −6.31756 −1.03860 −0.519301 0.854592i \(-0.673808\pi\)
−0.519301 + 0.854592i \(0.673808\pi\)
\(38\) −0.547418 + 1.14277i −0.0888030 + 0.185382i
\(39\) 0 0
\(40\) −0.569112 0.985730i −0.0899845 0.155858i
\(41\) 1.29070 + 2.23555i 0.201573 + 0.349135i 0.949035 0.315169i \(-0.102061\pi\)
−0.747462 + 0.664304i \(0.768728\pi\)
\(42\) 0 0
\(43\) 1.24329 + 2.15344i 0.189600 + 0.328396i 0.945117 0.326733i \(-0.105948\pi\)
−0.755517 + 0.655129i \(0.772614\pi\)
\(44\) −5.12169 + 8.87102i −0.772123 + 1.33736i
\(45\) 0 0
\(46\) −1.86406 −0.274841
\(47\) 5.55533 9.62211i 0.810328 1.40353i −0.102306 0.994753i \(-0.532622\pi\)
0.912634 0.408777i \(-0.134044\pi\)
\(48\) 0 0
\(49\) −6.76325 −0.966178
\(50\) 0.290697 0.0411108
\(51\) 0 0
\(52\) −2.38151 4.12490i −0.330256 0.572020i
\(53\) 1.49839 2.59529i 0.205820 0.356490i −0.744574 0.667540i \(-0.767347\pi\)
0.950394 + 0.311050i \(0.100681\pi\)
\(54\) 0 0
\(55\) −2.67382 4.63119i −0.360538 0.624470i
\(56\) 0.553831 0.0740087
\(57\) 0 0
\(58\) −0.804139 −0.105589
\(59\) 6.36659 + 11.0273i 0.828859 + 1.43563i 0.898934 + 0.438084i \(0.144343\pi\)
−0.0700752 + 0.997542i \(0.522324\pi\)
\(60\) 0 0
\(61\) −5.92742 + 10.2666i −0.758929 + 1.31450i 0.184469 + 0.982838i \(0.440944\pi\)
−0.943397 + 0.331664i \(0.892390\pi\)
\(62\) −0.702178 1.21621i −0.0891767 0.154458i
\(63\) 0 0
\(64\) −6.04269 −0.755336
\(65\) 2.48657 0.308422
\(66\) 0 0
\(67\) 7.58770 13.1423i 0.926985 1.60559i 0.138649 0.990342i \(-0.455724\pi\)
0.788336 0.615244i \(-0.210943\pi\)
\(68\) −6.54258 −0.793404
\(69\) 0 0
\(70\) −0.0707229 + 0.122496i −0.00845301 + 0.0146410i
\(71\) −4.96452 8.59879i −0.589180 1.02049i −0.994340 0.106244i \(-0.966118\pi\)
0.405160 0.914246i \(-0.367216\pi\)
\(72\) 0 0
\(73\) 5.50642 + 9.53740i 0.644478 + 1.11627i 0.984422 + 0.175823i \(0.0562585\pi\)
−0.339944 + 0.940446i \(0.610408\pi\)
\(74\) 0.918249 + 1.59045i 0.106744 + 0.184887i
\(75\) 0 0
\(76\) −8.32479 + 0.641189i −0.954919 + 0.0735494i
\(77\) 2.60202 0.296528
\(78\) 0 0
\(79\) −4.06636 7.04314i −0.457501 0.792415i 0.541327 0.840812i \(-0.317922\pi\)
−0.998828 + 0.0483971i \(0.984589\pi\)
\(80\) 1.75006 3.03119i 0.195662 0.338897i
\(81\) 0 0
\(82\) 0.375202 0.649869i 0.0414341 0.0717660i
\(83\) 5.86106 0.643335 0.321668 0.946853i \(-0.395757\pi\)
0.321668 + 0.946853i \(0.395757\pi\)
\(84\) 0 0
\(85\) 1.70780 2.95800i 0.185237 0.320840i
\(86\) 0.361420 0.625998i 0.0389729 0.0675031i
\(87\) 0 0
\(88\) 6.08681 0.648856
\(89\) −3.25521 + 5.63820i −0.345052 + 0.597647i −0.985363 0.170468i \(-0.945472\pi\)
0.640311 + 0.768116i \(0.278805\pi\)
\(90\) 0 0
\(91\) −0.604952 + 1.04781i −0.0634162 + 0.109840i
\(92\) −6.14145 10.6373i −0.640290 1.10901i
\(93\) 0 0
\(94\) −3.22984 −0.333132
\(95\) 1.88312 3.93114i 0.193204 0.403326i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 0.983028 + 1.70265i 0.0993008 + 0.171994i
\(99\) 0 0
\(100\) 0.957748 + 1.65887i 0.0957748 + 0.165887i
\(101\) 0.758324 1.31346i 0.0754561 0.130694i −0.825828 0.563921i \(-0.809292\pi\)
0.901285 + 0.433228i \(0.142625\pi\)
\(102\) 0 0
\(103\) −9.15478 −0.902047 −0.451023 0.892512i \(-0.648941\pi\)
−0.451023 + 0.892512i \(0.648941\pi\)
\(104\) −1.41514 + 2.45109i −0.138766 + 0.240349i
\(105\) 0 0
\(106\) −0.871155 −0.0846140
\(107\) −0.138936 −0.0134315 −0.00671574 0.999977i \(-0.502138\pi\)
−0.00671574 + 0.999977i \(0.502138\pi\)
\(108\) 0 0
\(109\) 7.86497 + 13.6225i 0.753328 + 1.30480i 0.946201 + 0.323579i \(0.104886\pi\)
−0.192873 + 0.981224i \(0.561781\pi\)
\(110\) −0.777272 + 1.34627i −0.0741099 + 0.128362i
\(111\) 0 0
\(112\) 0.851533 + 1.47490i 0.0804623 + 0.139365i
\(113\) −14.8011 −1.39237 −0.696187 0.717860i \(-0.745122\pi\)
−0.696187 + 0.717860i \(0.745122\pi\)
\(114\) 0 0
\(115\) 6.41238 0.597958
\(116\) −2.64936 4.58883i −0.245987 0.426062i
\(117\) 0 0
\(118\) 1.85075 3.20559i 0.170375 0.295099i
\(119\) 0.830974 + 1.43929i 0.0761752 + 0.131939i
\(120\) 0 0
\(121\) 17.5972 1.59975
\(122\) 3.44617 0.312002
\(123\) 0 0
\(124\) 4.62687 8.01397i 0.415505 0.719676i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.91550 8.51389i 0.436180 0.755485i −0.561211 0.827672i \(-0.689665\pi\)
0.997391 + 0.0721871i \(0.0229979\pi\)
\(128\) 4.17222 + 7.22649i 0.368775 + 0.638738i
\(129\) 0 0
\(130\) −0.361420 0.625998i −0.0316986 0.0549037i
\(131\) 7.11459 + 12.3228i 0.621605 + 1.07665i 0.989187 + 0.146660i \(0.0468524\pi\)
−0.367582 + 0.929991i \(0.619814\pi\)
\(132\) 0 0
\(133\) 1.19839 + 1.74992i 0.103913 + 0.151737i
\(134\) −4.41145 −0.381091
\(135\) 0 0
\(136\) 1.94386 + 3.36687i 0.166685 + 0.288707i
\(137\) 3.29220 5.70225i 0.281271 0.487176i −0.690427 0.723402i \(-0.742577\pi\)
0.971698 + 0.236226i \(0.0759106\pi\)
\(138\) 0 0
\(139\) −0.116878 + 0.202439i −0.00991347 + 0.0171706i −0.870940 0.491390i \(-0.836489\pi\)
0.861026 + 0.508561i \(0.169822\pi\)
\(140\) −0.932031 −0.0787710
\(141\) 0 0
\(142\) −1.44317 + 2.49965i −0.121108 + 0.209766i
\(143\) −6.64865 + 11.5158i −0.555988 + 0.963000i
\(144\) 0 0
\(145\) 2.76624 0.229724
\(146\) 1.60070 2.77250i 0.132475 0.229453i
\(147\) 0 0
\(148\) −6.05063 + 10.4800i −0.497359 + 0.861451i
\(149\) −1.33650 2.31488i −0.109490 0.189642i 0.806074 0.591815i \(-0.201588\pi\)
−0.915564 + 0.402173i \(0.868255\pi\)
\(150\) 0 0
\(151\) 5.95266 0.484421 0.242210 0.970224i \(-0.422128\pi\)
0.242210 + 0.970224i \(0.422128\pi\)
\(152\) 2.80334 + 4.09351i 0.227381 + 0.332027i
\(153\) 0 0
\(154\) −0.378201 0.655063i −0.0304763 0.0527865i
\(155\) 2.41550 + 4.18376i 0.194017 + 0.336048i
\(156\) 0 0
\(157\) 3.60424 + 6.24273i 0.287650 + 0.498224i 0.973248 0.229756i \(-0.0737928\pi\)
−0.685599 + 0.727980i \(0.740459\pi\)
\(158\) −1.18208 + 2.04742i −0.0940411 + 0.162884i
\(159\) 0 0
\(160\) −3.29392 −0.260407
\(161\) −1.56005 + 2.70209i −0.122949 + 0.212954i
\(162\) 0 0
\(163\) 14.1756 1.11032 0.555161 0.831743i \(-0.312657\pi\)
0.555161 + 0.831743i \(0.312657\pi\)
\(164\) 4.94465 0.386112
\(165\) 0 0
\(166\) −0.851897 1.47553i −0.0661201 0.114523i
\(167\) 6.27817 10.8741i 0.485819 0.841464i −0.514048 0.857762i \(-0.671855\pi\)
0.999867 + 0.0162977i \(0.00518794\pi\)
\(168\) 0 0
\(169\) 3.40847 + 5.90365i 0.262190 + 0.454127i
\(170\) −0.992907 −0.0761525
\(171\) 0 0
\(172\) 4.76302 0.363177
\(173\) 1.09482 + 1.89628i 0.0832376 + 0.144172i 0.904639 0.426179i \(-0.140141\pi\)
−0.821401 + 0.570351i \(0.806807\pi\)
\(174\) 0 0
\(175\) 0.243287 0.421386i 0.0183908 0.0318538i
\(176\) 9.35867 + 16.2097i 0.705436 + 1.22185i
\(177\) 0 0
\(178\) 1.89256 0.141854
\(179\) −7.50421 −0.560891 −0.280445 0.959870i \(-0.590482\pi\)
−0.280445 + 0.959870i \(0.590482\pi\)
\(180\) 0 0
\(181\) 6.33260 10.9684i 0.470699 0.815274i −0.528740 0.848784i \(-0.677335\pi\)
0.999438 + 0.0335101i \(0.0106686\pi\)
\(182\) 0.351716 0.0260709
\(183\) 0 0
\(184\) −3.64936 + 6.32088i −0.269035 + 0.465982i
\(185\) −3.15878 5.47117i −0.232238 0.402249i
\(186\) 0 0
\(187\) 9.13272 + 15.8183i 0.667850 + 1.15675i
\(188\) −10.6412 18.4311i −0.776090 1.34423i
\(189\) 0 0
\(190\) −1.26338 + 0.0973074i −0.0916551 + 0.00705942i
\(191\) −8.15777 −0.590276 −0.295138 0.955455i \(-0.595366\pi\)
−0.295138 + 0.955455i \(0.595366\pi\)
\(192\) 0 0
\(193\) 1.68252 + 2.91422i 0.121111 + 0.209770i 0.920206 0.391435i \(-0.128021\pi\)
−0.799095 + 0.601204i \(0.794688\pi\)
\(194\) −0.290697 + 0.503502i −0.0208708 + 0.0361494i
\(195\) 0 0
\(196\) −6.47748 + 11.2193i −0.462677 + 0.801381i
\(197\) −3.83399 −0.273160 −0.136580 0.990629i \(-0.543611\pi\)
−0.136580 + 0.990629i \(0.543611\pi\)
\(198\) 0 0
\(199\) −6.34925 + 10.9972i −0.450086 + 0.779572i −0.998391 0.0567063i \(-0.981940\pi\)
0.548305 + 0.836279i \(0.315273\pi\)
\(200\) 0.569112 0.985730i 0.0402423 0.0697017i
\(201\) 0 0
\(202\) −0.440885 −0.0310206
\(203\) −0.672992 + 1.16566i −0.0472348 + 0.0818130i
\(204\) 0 0
\(205\) −1.29070 + 2.23555i −0.0901462 + 0.156138i
\(206\) 1.33063 + 2.30473i 0.0927097 + 0.160578i
\(207\) 0 0
\(208\) −8.70329 −0.603465
\(209\) 13.1707 + 19.2323i 0.911038 + 1.33032i
\(210\) 0 0
\(211\) 4.57828 + 7.92982i 0.315182 + 0.545911i 0.979476 0.201560i \(-0.0646011\pi\)
−0.664294 + 0.747471i \(0.731268\pi\)
\(212\) −2.87016 4.97126i −0.197123 0.341427i
\(213\) 0 0
\(214\) 0.0201942 + 0.0349774i 0.00138045 + 0.00239100i
\(215\) −1.24329 + 2.15344i −0.0847915 + 0.146863i
\(216\) 0 0
\(217\) −2.35064 −0.159572
\(218\) 2.28633 3.96003i 0.154850 0.268207i
\(219\) 0 0
\(220\) −10.2434 −0.690608
\(221\) −8.49316 −0.571312
\(222\) 0 0
\(223\) −5.44877 9.43754i −0.364876 0.631984i 0.623880 0.781520i \(-0.285555\pi\)
−0.988756 + 0.149536i \(0.952222\pi\)
\(224\) 0.801369 1.38801i 0.0535437 0.0927404i
\(225\) 0 0
\(226\) 2.15133 + 3.72620i 0.143104 + 0.247863i
\(227\) 24.6351 1.63509 0.817545 0.575864i \(-0.195334\pi\)
0.817545 + 0.575864i \(0.195334\pi\)
\(228\) 0 0
\(229\) 17.1676 1.13447 0.567234 0.823557i \(-0.308013\pi\)
0.567234 + 0.823557i \(0.308013\pi\)
\(230\) −0.932031 1.61433i −0.0614563 0.106445i
\(231\) 0 0
\(232\) −1.57430 + 2.72677i −0.103358 + 0.179021i
\(233\) 14.2316 + 24.6498i 0.932341 + 1.61486i 0.779309 + 0.626640i \(0.215570\pi\)
0.153032 + 0.988221i \(0.451096\pi\)
\(234\) 0 0
\(235\) 11.1107 0.724780
\(236\) 24.3903 1.58768
\(237\) 0 0
\(238\) 0.241562 0.418397i 0.0156581 0.0271207i
\(239\) −4.07741 −0.263746 −0.131873 0.991267i \(-0.542099\pi\)
−0.131873 + 0.991267i \(0.542099\pi\)
\(240\) 0 0
\(241\) 6.33421 10.9712i 0.408023 0.706716i −0.586646 0.809844i \(-0.699552\pi\)
0.994668 + 0.103128i \(0.0328852\pi\)
\(242\) −2.55773 4.43012i −0.164417 0.284779i
\(243\) 0 0
\(244\) 11.3539 + 19.6656i 0.726862 + 1.25896i
\(245\) −3.38162 5.85714i −0.216044 0.374199i
\(246\) 0 0
\(247\) −10.8067 + 0.832351i −0.687615 + 0.0529612i
\(248\) −5.49875 −0.349171
\(249\) 0 0
\(250\) 0.145349 + 0.251751i 0.00919265 + 0.0159221i
\(251\) −5.81204 + 10.0668i −0.366853 + 0.635408i −0.989072 0.147436i \(-0.952898\pi\)
0.622219 + 0.782843i \(0.286231\pi\)
\(252\) 0 0
\(253\) −17.1456 + 29.6970i −1.07793 + 1.86703i
\(254\) −2.85784 −0.179317
\(255\) 0 0
\(256\) −4.82984 + 8.36553i −0.301865 + 0.522845i
\(257\) 5.27416 9.13512i 0.328993 0.569833i −0.653319 0.757083i \(-0.726624\pi\)
0.982312 + 0.187250i \(0.0599574\pi\)
\(258\) 0 0
\(259\) 3.07397 0.191007
\(260\) 2.38151 4.12490i 0.147695 0.255815i
\(261\) 0 0
\(262\) 2.06819 3.58221i 0.127773 0.221310i
\(263\) 11.8967 + 20.6058i 0.733585 + 1.27061i 0.955341 + 0.295504i \(0.0954876\pi\)
−0.221757 + 0.975102i \(0.571179\pi\)
\(264\) 0 0
\(265\) 2.99678 0.184091
\(266\) 0.266360 0.556043i 0.0163316 0.0340932i
\(267\) 0 0
\(268\) −14.5342 25.1740i −0.887818 1.53775i
\(269\) −2.11377 3.66115i −0.128879 0.223224i 0.794364 0.607442i \(-0.207804\pi\)
−0.923242 + 0.384218i \(0.874471\pi\)
\(270\) 0 0
\(271\) −15.5736 26.9742i −0.946027 1.63857i −0.753682 0.657239i \(-0.771724\pi\)
−0.192344 0.981328i \(-0.561609\pi\)
\(272\) −5.97750 + 10.3533i −0.362439 + 0.627763i
\(273\) 0 0
\(274\) −1.91406 −0.115633
\(275\) 2.67382 4.63119i 0.161237 0.279271i
\(276\) 0 0
\(277\) 1.05393 0.0633243 0.0316621 0.999499i \(-0.489920\pi\)
0.0316621 + 0.999499i \(0.489920\pi\)
\(278\) 0.0679523 0.00407551
\(279\) 0 0
\(280\) 0.276915 + 0.479631i 0.0165489 + 0.0286635i
\(281\) 12.8177 22.2009i 0.764638 1.32439i −0.175799 0.984426i \(-0.556251\pi\)
0.940437 0.339967i \(-0.110416\pi\)
\(282\) 0 0
\(283\) −14.7056 25.4708i −0.874157 1.51408i −0.857658 0.514220i \(-0.828082\pi\)
−0.0164983 0.999864i \(-0.505252\pi\)
\(284\) −19.0190 −1.12857
\(285\) 0 0
\(286\) 3.86549 0.228571
\(287\) −0.628020 1.08776i −0.0370709 0.0642086i
\(288\) 0 0
\(289\) 2.66681 4.61906i 0.156871 0.271709i
\(290\) −0.402070 0.696405i −0.0236103 0.0408943i
\(291\) 0 0
\(292\) 21.0950 1.23449
\(293\) 10.8548 0.634147 0.317073 0.948401i \(-0.397300\pi\)
0.317073 + 0.948401i \(0.397300\pi\)
\(294\) 0 0
\(295\) −6.36659 + 11.0273i −0.370677 + 0.642031i
\(296\) 7.19080 0.417957
\(297\) 0 0
\(298\) −0.388516 + 0.672929i −0.0225061 + 0.0389817i
\(299\) −7.97244 13.8087i −0.461058 0.798576i
\(300\) 0 0
\(301\) −0.604952 1.04781i −0.0348688 0.0603946i
\(302\) −0.865211 1.49859i −0.0497873 0.0862341i
\(303\) 0 0
\(304\) −6.59114 + 13.7594i −0.378028 + 0.789157i
\(305\) −11.8548 −0.678806
\(306\) 0 0
\(307\) −16.8445 29.1756i −0.961368 1.66514i −0.719072 0.694936i \(-0.755433\pi\)
−0.242296 0.970202i \(-0.577901\pi\)
\(308\) 2.49208 4.31641i 0.142000 0.245950i
\(309\) 0 0
\(310\) 0.702178 1.21621i 0.0398810 0.0690759i
\(311\) 11.7221 0.664701 0.332350 0.943156i \(-0.392158\pi\)
0.332350 + 0.943156i \(0.392158\pi\)
\(312\) 0 0
\(313\) −2.23928 + 3.87855i −0.126572 + 0.219229i −0.922346 0.386364i \(-0.873731\pi\)
0.795775 + 0.605593i \(0.207064\pi\)
\(314\) 1.04774 1.81474i 0.0591275 0.102412i
\(315\) 0 0
\(316\) −15.5782 −0.876341
\(317\) 6.19367 10.7277i 0.347871 0.602530i −0.638000 0.770036i \(-0.720238\pi\)
0.985871 + 0.167506i \(0.0535714\pi\)
\(318\) 0 0
\(319\) −7.39644 + 12.8110i −0.414121 + 0.717278i
\(320\) −3.02135 5.23312i −0.168898 0.292541i
\(321\) 0 0
\(322\) 0.907005 0.0505454
\(323\) −6.43200 + 13.4272i −0.357886 + 0.747111i
\(324\) 0 0
\(325\) 1.24329 + 2.15344i 0.0689652 + 0.119451i
\(326\) −2.06041 3.56873i −0.114115 0.197654i
\(327\) 0 0
\(328\) −1.46910 2.54456i −0.0811176 0.140500i
\(329\) −2.70308 + 4.68188i −0.149026 + 0.258120i
\(330\) 0 0
\(331\) 24.5058 1.34696 0.673480 0.739206i \(-0.264799\pi\)
0.673480 + 0.739206i \(0.264799\pi\)
\(332\) 5.61342 9.72273i 0.308076 0.533604i
\(333\) 0 0
\(334\) −3.65009 −0.199724
\(335\) 15.1754 0.829121
\(336\) 0 0
\(337\) −5.25038 9.09392i −0.286006 0.495378i 0.686846 0.726803i \(-0.258995\pi\)
−0.972853 + 0.231425i \(0.925661\pi\)
\(338\) 0.990834 1.71617i 0.0538942 0.0933476i
\(339\) 0 0
\(340\) −3.27129 5.66604i −0.177411 0.307284i
\(341\) −25.8344 −1.39901
\(342\) 0 0
\(343\) 6.69684 0.361596
\(344\) −1.41514 2.45109i −0.0762992 0.132154i
\(345\) 0 0
\(346\) 0.318261 0.551244i 0.0171098 0.0296351i
\(347\) −0.727562 1.26017i −0.0390576 0.0676497i 0.845836 0.533443i \(-0.179102\pi\)
−0.884893 + 0.465794i \(0.845769\pi\)
\(348\) 0 0
\(349\) 23.7332 1.27041 0.635204 0.772345i \(-0.280916\pi\)
0.635204 + 0.772345i \(0.280916\pi\)
\(350\) −0.141446 −0.00756060
\(351\) 0 0
\(352\) 8.80735 15.2548i 0.469433 0.813082i
\(353\) 7.39055 0.393359 0.196680 0.980468i \(-0.436984\pi\)
0.196680 + 0.980468i \(0.436984\pi\)
\(354\) 0 0
\(355\) 4.96452 8.59879i 0.263489 0.456377i
\(356\) 6.23535 + 10.7999i 0.330473 + 0.572395i
\(357\) 0 0
\(358\) 1.09073 + 1.88919i 0.0576467 + 0.0998469i
\(359\) 1.17934 + 2.04268i 0.0622433 + 0.107808i 0.895468 0.445126i \(-0.146841\pi\)
−0.833225 + 0.552935i \(0.813508\pi\)
\(360\) 0 0
\(361\) −6.86820 + 17.7152i −0.361484 + 0.932378i
\(362\) −3.68174 −0.193508
\(363\) 0 0
\(364\) 1.15878 + 2.00707i 0.0607367 + 0.105199i
\(365\) −5.50642 + 9.53740i −0.288219 + 0.499210i
\(366\) 0 0
\(367\) 11.0743 19.1812i 0.578073 1.00125i −0.417628 0.908618i \(-0.637138\pi\)
0.995700 0.0926329i \(-0.0295283\pi\)
\(368\) −22.4441 −1.16998
\(369\) 0 0
\(370\) −0.918249 + 1.59045i −0.0477375 + 0.0826838i
\(371\) −0.729078 + 1.26280i −0.0378518 + 0.0655613i
\(372\) 0 0
\(373\) 31.1738 1.61412 0.807060 0.590469i \(-0.201057\pi\)
0.807060 + 0.590469i \(0.201057\pi\)
\(374\) 2.65485 4.59834i 0.137279 0.237775i
\(375\) 0 0
\(376\) −6.32321 + 10.9521i −0.326094 + 0.564812i
\(377\) −3.43924 5.95693i −0.177130 0.306798i
\(378\) 0 0
\(379\) −26.0349 −1.33732 −0.668662 0.743567i \(-0.733132\pi\)
−0.668662 + 0.743567i \(0.733132\pi\)
\(380\) −4.71768 6.88889i −0.242012 0.353393i
\(381\) 0 0
\(382\) 1.18572 + 2.05373i 0.0606668 + 0.105078i
\(383\) −1.06647 1.84718i −0.0544941 0.0943865i 0.837492 0.546450i \(-0.184021\pi\)
−0.891986 + 0.452064i \(0.850688\pi\)
\(384\) 0 0
\(385\) 1.30101 + 2.25342i 0.0663057 + 0.114845i
\(386\) 0.489105 0.847154i 0.0248948 0.0431190i
\(387\) 0 0
\(388\) −3.83099 −0.194489
\(389\) −6.52135 + 11.2953i −0.330645 + 0.572695i −0.982639 0.185530i \(-0.940600\pi\)
0.651993 + 0.758225i \(0.273933\pi\)
\(390\) 0 0
\(391\) −21.9022 −1.10764
\(392\) 7.69808 0.388812
\(393\) 0 0
\(394\) 0.557265 + 0.965211i 0.0280746 + 0.0486266i
\(395\) 4.06636 7.04314i 0.204601 0.354379i
\(396\) 0 0
\(397\) −0.0143214 0.0248054i −0.000718770 0.00124495i 0.865666 0.500622i \(-0.166895\pi\)
−0.866385 + 0.499377i \(0.833562\pi\)
\(398\) 3.69142 0.185034
\(399\) 0 0
\(400\) 3.50011 0.175006
\(401\) −13.6596 23.6591i −0.682126 1.18148i −0.974331 0.225122i \(-0.927722\pi\)
0.292204 0.956356i \(-0.405611\pi\)
\(402\) 0 0
\(403\) 6.00631 10.4032i 0.299196 0.518222i
\(404\) −1.45257 2.51592i −0.0722679 0.125172i
\(405\) 0 0
\(406\) 0.391274 0.0194186
\(407\) 33.7841 1.67461
\(408\) 0 0
\(409\) 3.36958 5.83629i 0.166615 0.288586i −0.770612 0.637304i \(-0.780050\pi\)
0.937228 + 0.348718i \(0.113383\pi\)
\(410\) 0.750404 0.0370598
\(411\) 0 0
\(412\) −8.76796 + 15.1866i −0.431967 + 0.748188i
\(413\) −3.09782 5.36558i −0.152434 0.264023i
\(414\) 0 0
\(415\) 2.93053 + 5.07583i 0.143854 + 0.249163i
\(416\) 4.09529 + 7.09325i 0.200788 + 0.347775i
\(417\) 0 0
\(418\) 2.92739 6.11113i 0.143184 0.298905i
\(419\) −26.4076 −1.29010 −0.645048 0.764142i \(-0.723163\pi\)
−0.645048 + 0.764142i \(0.723163\pi\)
\(420\) 0 0
\(421\) −18.9448 32.8133i −0.923311 1.59922i −0.794255 0.607584i \(-0.792139\pi\)
−0.129056 0.991637i \(-0.541195\pi\)
\(422\) 1.33089 2.30518i 0.0647869 0.112214i
\(423\) 0 0
\(424\) −1.70550 + 2.95401i −0.0828265 + 0.143460i
\(425\) 3.41561 0.165681
\(426\) 0 0
\(427\) 2.88413 4.99546i 0.139573 0.241747i
\(428\) −0.133066 + 0.230477i −0.00643198 + 0.0111405i
\(429\) 0 0
\(430\) 0.722840 0.0348585
\(431\) −9.60285 + 16.6326i −0.462553 + 0.801165i −0.999087 0.0427131i \(-0.986400\pi\)
0.536534 + 0.843879i \(0.319733\pi\)
\(432\) 0 0
\(433\) −8.47562 + 14.6802i −0.407312 + 0.705485i −0.994588 0.103902i \(-0.966867\pi\)
0.587275 + 0.809387i \(0.300201\pi\)
\(434\) 0.341662 + 0.591776i 0.0164003 + 0.0284061i
\(435\) 0 0
\(436\) 30.1306 1.44300
\(437\) −27.8684 + 2.14647i −1.33313 + 0.102680i
\(438\) 0 0
\(439\) −5.55143 9.61536i −0.264955 0.458916i 0.702597 0.711588i \(-0.252024\pi\)
−0.967552 + 0.252672i \(0.918691\pi\)
\(440\) 3.04340 + 5.27133i 0.145089 + 0.251301i
\(441\) 0 0
\(442\) 1.23447 + 2.13816i 0.0587177 + 0.101702i
\(443\) −6.94708 + 12.0327i −0.330066 + 0.571691i −0.982524 0.186133i \(-0.940404\pi\)
0.652459 + 0.757824i \(0.273738\pi\)
\(444\) 0 0
\(445\) −6.51043 −0.308624
\(446\) −1.58394 + 2.74347i −0.0750018 + 0.129907i
\(447\) 0 0
\(448\) 2.94022 0.138912
\(449\) −27.8675 −1.31515 −0.657573 0.753391i \(-0.728417\pi\)
−0.657573 + 0.753391i \(0.728417\pi\)
\(450\) 0 0
\(451\) −6.90218 11.9549i −0.325011 0.562936i
\(452\) −14.1758 + 24.5531i −0.666772 + 1.15488i
\(453\) 0 0
\(454\) −3.58068 6.20192i −0.168050 0.291071i
\(455\) −1.20990 −0.0567212
\(456\) 0 0
\(457\) −36.5660 −1.71048 −0.855242 0.518229i \(-0.826591\pi\)
−0.855242 + 0.518229i \(0.826591\pi\)
\(458\) −2.49529 4.32197i −0.116597 0.201952i
\(459\) 0 0
\(460\) 6.14145 10.6373i 0.286346 0.495966i
\(461\) 10.9590 + 18.9816i 0.510412 + 0.884059i 0.999927 + 0.0120646i \(0.00384039\pi\)
−0.489515 + 0.871995i \(0.662826\pi\)
\(462\) 0 0
\(463\) −14.0255 −0.651821 −0.325910 0.945401i \(-0.605671\pi\)
−0.325910 + 0.945401i \(0.605671\pi\)
\(464\) −9.68216 −0.449483
\(465\) 0 0
\(466\) 4.13707 7.16562i 0.191646 0.331941i
\(467\) −33.9294 −1.57007 −0.785033 0.619453i \(-0.787354\pi\)
−0.785033 + 0.619453i \(0.787354\pi\)
\(468\) 0 0
\(469\) −3.69198 + 6.39470i −0.170480 + 0.295280i
\(470\) −1.61492 2.79712i −0.0744906 0.129022i
\(471\) 0 0
\(472\) −7.24660 12.5515i −0.333552 0.577728i
\(473\) −6.64865 11.5158i −0.305705 0.529497i
\(474\) 0 0
\(475\) 4.34603 0.334738i 0.199409 0.0153588i
\(476\) 3.18345 0.145913
\(477\) 0 0
\(478\) 0.592646 + 1.02649i 0.0271070 + 0.0469507i
\(479\) 15.9748 27.6692i 0.729909 1.26424i −0.227012 0.973892i \(-0.572896\pi\)
0.956921 0.290348i \(-0.0937711\pi\)
\(480\) 0 0
\(481\) −7.85455 + 13.6045i −0.358137 + 0.620311i
\(482\) −3.68268 −0.167741
\(483\) 0 0
\(484\) 16.8537 29.1915i 0.766078 1.32689i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 37.6229 1.70486 0.852428 0.522844i \(-0.175129\pi\)
0.852428 + 0.522844i \(0.175129\pi\)
\(488\) 6.74673 11.6857i 0.305410 0.528986i
\(489\) 0 0
\(490\) −0.983028 + 1.70265i −0.0444087 + 0.0769181i
\(491\) −20.0421 34.7139i −0.904487 1.56662i −0.821604 0.570059i \(-0.806920\pi\)
−0.0828838 0.996559i \(-0.526413\pi\)
\(492\) 0 0
\(493\) −9.44840 −0.425535
\(494\) 1.78029 + 2.59962i 0.0800989 + 0.116963i
\(495\) 0 0
\(496\) −8.45450 14.6436i −0.379618 0.657518i
\(497\) 2.41561 + 4.18395i 0.108355 + 0.187676i
\(498\) 0 0
\(499\) 15.1533 + 26.2464i 0.678357 + 1.17495i 0.975475 + 0.220108i \(0.0706410\pi\)
−0.297118 + 0.954841i \(0.596026\pi\)
\(500\) −0.957748 + 1.65887i −0.0428318 + 0.0741868i
\(501\) 0 0
\(502\) 3.37909 0.150816
\(503\) −8.64393 + 14.9717i −0.385414 + 0.667556i −0.991827 0.127594i \(-0.959275\pi\)
0.606413 + 0.795150i \(0.292608\pi\)
\(504\) 0 0
\(505\) 1.51665 0.0674899
\(506\) 9.96833 0.443146
\(507\) 0 0
\(508\) −9.41561 16.3083i −0.417750 0.723564i
\(509\) 2.80412 4.85688i 0.124291 0.215278i −0.797165 0.603762i \(-0.793668\pi\)
0.921455 + 0.388484i \(0.127001\pi\)
\(510\) 0 0
\(511\) −2.67928 4.64066i −0.118525 0.205291i
\(512\) 19.4969 0.861650
\(513\) 0 0
\(514\) −3.06637 −0.135252
\(515\) −4.57739 7.92827i −0.201704 0.349361i
\(516\) 0 0
\(517\) −29.7079 + 51.4556i −1.30655 + 2.26301i
\(518\) −0.446797 0.773874i −0.0196311 0.0340021i
\(519\) 0 0
\(520\) −2.83028 −0.124116
\(521\) −13.7128 −0.600767 −0.300384 0.953818i \(-0.597115\pi\)
−0.300384 + 0.953818i \(0.597115\pi\)
\(522\) 0 0
\(523\) 17.6171 30.5137i 0.770341 1.33427i −0.167035 0.985951i \(-0.553419\pi\)
0.937376 0.348319i \(-0.113247\pi\)
\(524\) 27.2559 1.19068
\(525\) 0 0
\(526\) 3.45835 5.99004i 0.150791 0.261178i
\(527\) −8.25038 14.2901i −0.359392 0.622486i
\(528\) 0 0
\(529\) −9.05934 15.6912i −0.393884 0.682228i
\(530\) −0.435577 0.754442i −0.0189203 0.0327709i
\(531\) 0 0
\(532\) 4.05063 0.311986i 0.175617 0.0135263i
\(533\) 6.41883 0.278030
\(534\) 0 0
\(535\) −0.0694682 0.120322i −0.00300337 0.00520199i
\(536\) −8.63650 + 14.9589i −0.373040 + 0.646124i
\(537\) 0 0
\(538\) −0.614466 + 1.06429i −0.0264915 + 0.0458847i
\(539\) 36.1674 1.55784
\(540\) 0 0
\(541\) −15.1179 + 26.1849i −0.649968 + 1.12578i 0.333162 + 0.942869i \(0.391884\pi\)
−0.983130 + 0.182908i \(0.941449\pi\)
\(542\) −4.52719 + 7.84133i −0.194460 + 0.336814i
\(543\) 0 0
\(544\) 11.2507 0.482371
\(545\) −7.86497 + 13.6225i −0.336899 + 0.583525i
\(546\) 0 0
\(547\) −17.4766 + 30.2703i −0.747244 + 1.29426i 0.201895 + 0.979407i \(0.435290\pi\)
−0.949139 + 0.314858i \(0.898043\pi\)
\(548\) −6.30619 10.9226i −0.269387 0.466592i
\(549\) 0 0
\(550\) −1.55454 −0.0662860
\(551\) −12.0222 + 0.925967i −0.512162 + 0.0394475i
\(552\) 0 0
\(553\) 1.97859 + 3.42701i 0.0841380 + 0.145731i
\(554\) −0.153187 0.265327i −0.00650828 0.0112727i
\(555\) 0 0
\(556\) 0.223879 + 0.387771i 0.00949460 + 0.0164451i
\(557\) 1.58139 2.73906i 0.0670058 0.116058i −0.830576 0.556905i \(-0.811989\pi\)
0.897582 + 0.440848i \(0.145322\pi\)
\(558\) 0 0
\(559\) 6.18305 0.261515
\(560\) −0.851533 + 1.47490i −0.0359838 + 0.0623258i
\(561\) 0 0
\(562\) −7.45213 −0.314349
\(563\) 29.0570 1.22460 0.612302 0.790624i \(-0.290244\pi\)
0.612302 + 0.790624i \(0.290244\pi\)
\(564\) 0 0
\(565\) −7.40057 12.8182i −0.311344 0.539264i
\(566\) −4.27487 + 7.40430i −0.179686 + 0.311226i
\(567\) 0 0
\(568\) 5.65073 + 9.78735i 0.237099 + 0.410668i
\(569\) 31.3398 1.31383 0.656916 0.753964i \(-0.271861\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(570\) 0 0
\(571\) 2.56556 0.107365 0.0536827 0.998558i \(-0.482904\pi\)
0.0536827 + 0.998558i \(0.482904\pi\)
\(572\) 12.7355 + 22.0585i 0.532496 + 0.922311i
\(573\) 0 0
\(574\) −0.182564 + 0.316210i −0.00762006 + 0.0131983i
\(575\) 3.20619 + 5.55329i 0.133707 + 0.231588i
\(576\) 0 0
\(577\) 3.12153 0.129951 0.0649755 0.997887i \(-0.479303\pi\)
0.0649755 + 0.997887i \(0.479303\pi\)
\(578\) −1.55047 −0.0644911
\(579\) 0 0
\(580\) 2.64936 4.58883i 0.110009 0.190541i
\(581\) −2.85184 −0.118314
\(582\) 0 0
\(583\) −8.01284 + 13.8786i −0.331858 + 0.574795i
\(584\) −6.26754 10.8557i −0.259353 0.449212i
\(585\) 0 0
\(586\) −1.57774 2.73272i −0.0651757 0.112888i
\(587\) −4.63985 8.03646i −0.191507 0.331700i 0.754243 0.656596i \(-0.228004\pi\)
−0.945750 + 0.324896i \(0.894671\pi\)
\(588\) 0 0
\(589\) −11.8983 17.3742i −0.490260 0.715891i
\(590\) 3.70150 0.152388
\(591\) 0 0
\(592\) 11.0561 + 19.1497i 0.454403 + 0.787048i
\(593\) 17.0224 29.4836i 0.699025 1.21075i −0.269780 0.962922i \(-0.586951\pi\)
0.968805 0.247825i \(-0.0797157\pi\)
\(594\) 0 0
\(595\) −0.830974 + 1.43929i −0.0340666 + 0.0590051i
\(596\) −5.12010 −0.209728
\(597\) 0 0
\(598\) −2.31756 + 4.01414i −0.0947723 + 0.164150i
\(599\) 12.5366 21.7140i 0.512231 0.887210i −0.487669 0.873029i \(-0.662153\pi\)
0.999899 0.0141810i \(-0.00451411\pi\)
\(600\) 0 0
\(601\) −26.0225 −1.06148 −0.530739 0.847535i \(-0.678086\pi\)
−0.530739 + 0.847535i \(0.678086\pi\)
\(602\) −0.175858 + 0.304595i −0.00716743 + 0.0124144i
\(603\) 0 0
\(604\) 5.70115 9.87468i 0.231976 0.401795i
\(605\) 8.79862 + 15.2397i 0.357715 + 0.619580i
\(606\) 0 0
\(607\) −7.54650 −0.306303 −0.153151 0.988203i \(-0.548942\pi\)
−0.153151 + 0.988203i \(0.548942\pi\)
\(608\) 14.3155 1.10260i 0.580569 0.0447163i
\(609\) 0 0
\(610\) 1.72308 + 2.98447i 0.0697657 + 0.120838i
\(611\) −13.8137 23.9261i −0.558844 0.967946i
\(612\) 0 0
\(613\) 19.1345 + 33.1419i 0.772836 + 1.33859i 0.936003 + 0.351992i \(0.114496\pi\)
−0.163167 + 0.986598i \(0.552171\pi\)
\(614\) −4.89666 + 8.48126i −0.197613 + 0.342276i
\(615\) 0 0
\(616\) −2.96169 −0.119330
\(617\) −5.82540 + 10.0899i −0.234522 + 0.406203i −0.959134 0.282954i \(-0.908686\pi\)
0.724612 + 0.689157i \(0.242019\pi\)
\(618\) 0 0
\(619\) −2.47710 −0.0995630 −0.0497815 0.998760i \(-0.515852\pi\)
−0.0497815 + 0.998760i \(0.515852\pi\)
\(620\) 9.25374 0.371639
\(621\) 0 0
\(622\) −1.70379 2.95106i −0.0683159 0.118327i
\(623\) 1.58390 2.74340i 0.0634578 0.109912i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 1.30191 0.0520346
\(627\) 0 0
\(628\) 13.8078 0.550991
\(629\) 10.7892 + 18.6874i 0.430192 + 0.745114i
\(630\) 0 0
\(631\) 21.8279 37.8070i 0.868954 1.50507i 0.00588756 0.999983i \(-0.498126\pi\)
0.863067 0.505090i \(-0.168541\pi\)
\(632\) 4.62842 + 8.01666i 0.184109 + 0.318886i
\(633\) 0 0
\(634\) −3.60096 −0.143012
\(635\) 9.83099 0.390131
\(636\) 0 0
\(637\) −8.40866 + 14.5642i −0.333163 + 0.577055i
\(638\) 4.30025 0.170248
\(639\) 0 0
\(640\) −4.17222 + 7.22649i −0.164921 + 0.285652i
\(641\) 12.1163 + 20.9860i 0.478564 + 0.828897i 0.999698 0.0245776i \(-0.00782407\pi\)
−0.521134 + 0.853475i \(0.674491\pi\)
\(642\) 0 0
\(643\) −4.15878 7.20322i −0.164006 0.284067i 0.772296 0.635263i \(-0.219108\pi\)
−0.936302 + 0.351196i \(0.885775\pi\)
\(644\) 2.98827 + 5.17584i 0.117754 + 0.203957i
\(645\) 0 0
\(646\) 4.31520 0.332364i 0.169779 0.0130767i
\(647\) 10.9164 0.429170 0.214585 0.976705i \(-0.431160\pi\)
0.214585 + 0.976705i \(0.431160\pi\)
\(648\) 0 0
\(649\) −34.0462 58.9697i −1.33643 2.31476i
\(650\) 0.361420 0.625998i 0.0141761 0.0245537i
\(651\) 0 0
\(652\) 13.5767 23.5155i 0.531704 0.920938i
\(653\) 21.8452 0.854868 0.427434 0.904047i \(-0.359418\pi\)
0.427434 + 0.904047i \(0.359418\pi\)
\(654\) 0 0
\(655\) −7.11459 + 12.3228i −0.277990 + 0.481493i
\(656\) 4.51758 7.82469i 0.176382 0.305503i
\(657\) 0 0
\(658\) 1.57156 0.0612657
\(659\) −13.2094 + 22.8794i −0.514566 + 0.891254i 0.485291 + 0.874352i \(0.338714\pi\)
−0.999857 + 0.0169015i \(0.994620\pi\)
\(660\) 0 0
\(661\) −9.30721 + 16.1206i −0.362008 + 0.627017i −0.988291 0.152579i \(-0.951242\pi\)
0.626283 + 0.779596i \(0.284576\pi\)
\(662\) −3.56188 6.16936i −0.138436 0.239779i
\(663\) 0 0
\(664\) −6.67120 −0.258893
\(665\) −0.916279 + 1.91279i −0.0355318 + 0.0741749i
\(666\) 0 0
\(667\) −8.86911 15.3617i −0.343413 0.594809i
\(668\) −12.0258 20.8293i −0.465292 0.805910i
\(669\) 0 0
\(670\) −2.20572 3.82043i −0.0852146 0.147596i
\(671\) 31.6977 54.9020i 1.22368 2.11947i
\(672\) 0 0
\(673\) 5.98693 0.230779 0.115390 0.993320i \(-0.463188\pi\)
0.115390 + 0.993320i \(0.463188\pi\)
\(674\) −1.52627 + 2.64358i −0.0587898 + 0.101827i
\(675\) 0 0
\(676\) 13.0578 0.502224
\(677\) −33.7287 −1.29630 −0.648150 0.761512i \(-0.724457\pi\)
−0.648150 + 0.761512i \(0.724457\pi\)
\(678\) 0 0
\(679\) 0.486575 + 0.842772i 0.0186730 + 0.0323426i
\(680\) −1.94386 + 3.36687i −0.0745437 + 0.129113i
\(681\) 0 0
\(682\) 3.75499 + 6.50384i 0.143786 + 0.249045i
\(683\) −11.4959 −0.439880 −0.219940 0.975513i \(-0.570586\pi\)
−0.219940 + 0.975513i \(0.570586\pi\)
\(684\) 0 0
\(685\) 6.58439 0.251577
\(686\) −0.973377 1.68594i −0.0371637 0.0643694i
\(687\) 0 0
\(688\) 4.35164 7.53727i 0.165905 0.287356i
\(689\) −3.72586 6.45337i −0.141944 0.245854i
\(690\) 0 0
\(691\) 36.3039 1.38107 0.690533 0.723301i \(-0.257376\pi\)
0.690533 + 0.723301i \(0.257376\pi\)
\(692\) 4.19424 0.159441
\(693\) 0 0
\(694\) −0.211500 + 0.366329i −0.00802844 + 0.0139057i
\(695\) −0.233756 −0.00886688
\(696\) 0 0
\(697\) 4.40851 7.63577i 0.166984 0.289225i
\(698\) −3.44958 5.97485i −0.130569 0.226152i
\(699\) 0 0
\(700\) −0.466016 0.807163i −0.0176137 0.0305079i
\(701\) 6.76373 + 11.7151i 0.255463 + 0.442474i 0.965021 0.262172i \(-0.0844389\pi\)
−0.709558 + 0.704647i \(0.751106\pi\)
\(702\) 0 0
\(703\) 15.5596 + 22.7205i 0.586840 + 0.856920i
\(704\) 32.3141 1.21788
\(705\) 0 0
\(706\) −1.07421 1.86058i −0.0404283 0.0700239i
\(707\) −0.368981 + 0.639094i −0.0138770 + 0.0240356i
\(708\) 0 0
\(709\) 0.496778 0.860444i 0.0186569 0.0323147i −0.856546 0.516070i \(-0.827394\pi\)
0.875203 + 0.483756i \(0.160728\pi\)
\(710\) −2.88634 −0.108322
\(711\) 0 0
\(712\) 3.70516 6.41753i 0.138857 0.240507i
\(713\) 15.4891 26.8279i 0.580071 1.00471i
\(714\) 0 0
\(715\) −13.2973 −0.497291
\(716\) −7.18714 + 12.4485i −0.268596 + 0.465222i
\(717\) 0 0
\(718\) 0.342831 0.593801i 0.0127943 0.0221605i
\(719\) −0.700670 1.21360i −0.0261306 0.0452595i 0.852664 0.522459i \(-0.174985\pi\)
−0.878795 + 0.477200i \(0.841652\pi\)
\(720\) 0 0
\(721\) 4.45448 0.165894
\(722\) 5.45810 0.845801i 0.203130 0.0314775i
\(723\) 0 0
\(724\) −12.1301 21.0099i −0.450810 0.780827i
\(725\) 1.38312 + 2.39564i 0.0513679 + 0.0889717i
\(726\) 0 0
\(727\) 23.4834 + 40.6745i 0.870953 + 1.50853i 0.861013 + 0.508584i \(0.169831\pi\)
0.00993990 + 0.999951i \(0.496836\pi\)
\(728\) 0.688570 1.19264i 0.0255201 0.0442021i
\(729\) 0 0
\(730\) 3.20140 0.118489
\(731\) 4.24658 7.35529i 0.157065 0.272045i
\(732\) 0 0
\(733\) −21.6068 −0.798066 −0.399033 0.916937i \(-0.630654\pi\)
−0.399033 + 0.916937i \(0.630654\pi\)
\(734\) −6.43852 −0.237650
\(735\) 0 0
\(736\) 10.5609 + 18.2921i 0.389281 + 0.674255i
\(737\) −40.5763 + 70.2802i −1.49465 + 2.58880i
\(738\) 0 0
\(739\) 15.4063 + 26.6845i 0.566729 + 0.981603i 0.996887 + 0.0788496i \(0.0251247\pi\)
−0.430158 + 0.902754i \(0.641542\pi\)
\(740\) −12.1013 −0.444851
\(741\) 0 0
\(742\) 0.423882 0.0155612
\(743\) 22.2143 + 38.4763i 0.814964 + 1.41156i 0.909354 + 0.416024i \(0.136577\pi\)
−0.0943897 + 0.995535i \(0.530090\pi\)
\(744\) 0 0
\(745\) 1.33650 2.31488i 0.0489654 0.0848106i
\(746\) −4.53107 7.84805i −0.165894 0.287338i
\(747\) 0 0
\(748\) 34.9873 1.27926
\(749\) 0.0676029 0.00247016
\(750\) 0 0
\(751\) −7.43935 + 12.8853i −0.271466 + 0.470192i −0.969237 0.246128i \(-0.920842\pi\)
0.697772 + 0.716320i \(0.254175\pi\)
\(752\) −38.8886 −1.41812
\(753\) 0 0
\(754\) −0.999776 + 1.73166i −0.0364097 + 0.0630634i
\(755\) 2.97633 + 5.15516i 0.108320 + 0.187615i
\(756\) 0 0
\(757\) −11.7204 20.3004i −0.425986 0.737829i 0.570526 0.821279i \(-0.306739\pi\)
−0.996512 + 0.0834503i \(0.973406\pi\)
\(758\) 3.78414 + 6.55432i 0.137446 + 0.238063i
\(759\) 0 0
\(760\) −2.14341 + 4.47451i −0.0777498 + 0.162308i
\(761\) −36.3224 −1.31669 −0.658344 0.752717i \(-0.728743\pi\)
−0.658344 + 0.752717i \(0.728743\pi\)
\(762\) 0 0
\(763\) −3.82690 6.62838i −0.138543 0.239963i
\(764\) −7.81309 + 13.5327i −0.282668 + 0.489595i
\(765\) 0 0
\(766\) −0.310020 + 0.536970i −0.0112015 + 0.0194015i
\(767\) 31.6620 1.14325
\(768\) 0 0
\(769\) −10.4052 + 18.0223i −0.375220 + 0.649901i −0.990360 0.138517i \(-0.955766\pi\)
0.615140 + 0.788418i \(0.289100\pi\)
\(770\) 0.378201 0.655063i 0.0136294 0.0236068i
\(771\) 0 0
\(772\) 6.44573 0.231987
\(773\) 1.78351 3.08913i 0.0641484 0.111108i −0.832168 0.554524i \(-0.812900\pi\)
0.896316 + 0.443416i \(0.146234\pi\)
\(774\) 0 0
\(775\) −2.41550 + 4.18376i −0.0867671 + 0.150285i
\(776\) 1.13822 + 1.97146i 0.0408598 + 0.0707713i
\(777\) 0 0
\(778\) 3.79147 0.135931
\(779\) 4.86108 10.1478i 0.174166 0.363583i
\(780\) 0 0
\(781\) 26.5484 + 45.9832i 0.949978 + 1.64541i
\(782\) 3.18345 + 5.51390i 0.113840 + 0.197177i
\(783\) 0 0
\(784\) 11.8361 + 20.5007i 0.422716 + 0.732166i
\(785\) −3.60424 + 6.24273i −0.128641 + 0.222812i
\(786\) 0 0
\(787\) 44.5660 1.58860 0.794302 0.607523i \(-0.207837\pi\)
0.794302 + 0.607523i \(0.207837\pi\)
\(788\) −3.67199 + 6.36008i −0.130809 + 0.226568i
\(789\) 0 0
\(790\) −2.36416 −0.0841129
\(791\) 7.20186 0.256069
\(792\) 0 0
\(793\) 14.7390 + 25.5287i 0.523396 + 0.906549i
\(794\) −0.00416319 + 0.00721085i −0.000147746 + 0.000255904i
\(795\) 0 0
\(796\) 12.1620 + 21.0651i 0.431069 + 0.746634i
\(797\) 44.7396 1.58476 0.792378 0.610030i \(-0.208843\pi\)
0.792378 + 0.610030i \(0.208843\pi\)
\(798\) 0 0
\(799\) −37.9496 −1.34256
\(800\) −1.64696 2.85262i −0.0582288 0.100855i
\(801\) 0 0
\(802\) −3.97080 + 6.87762i −0.140214 + 0.242857i
\(803\) −29.4463 51.0026i −1.03914 1.79984i
\(804\) 0 0
\(805\) −3.12010 −0.109969
\(806\) −3.49203 −0.123002
\(807\) 0 0
\(808\) −0.863142 + 1.49501i −0.0303652 + 0.0525941i
\(809\) −8.67442 −0.304976 −0.152488 0.988305i \(-0.548729\pi\)
−0.152488 + 0.988305i \(0.548729\pi\)
\(810\) 0 0
\(811\) −13.3651 + 23.1490i −0.469312 + 0.812872i −0.999384 0.0350805i \(-0.988831\pi\)
0.530073 + 0.847952i \(0.322165\pi\)
\(812\) 1.28911 + 2.23281i 0.0452390 + 0.0783562i
\(813\) 0 0
\(814\) −4.91046 8.50517i −0.172112 0.298106i
\(815\) 7.08781 + 12.2765i 0.248275 + 0.430025i
\(816\) 0 0
\(817\) 4.68252 9.77507i 0.163821 0.341986i
\(818\) −1.95906 −0.0684968
\(819\) 0 0
\(820\) 2.47232 + 4.28219i 0.0863373 + 0.149541i
\(821\) −4.72432 + 8.18275i −0.164880 + 0.285580i −0.936613 0.350367i \(-0.886057\pi\)
0.771733 + 0.635947i \(0.219390\pi\)
\(822\) 0 0
\(823\) 9.73340 16.8587i 0.339285 0.587659i −0.645014 0.764171i \(-0.723148\pi\)
0.984298 + 0.176513i \(0.0564816\pi\)
\(824\) 10.4202 0.363004
\(825\) 0 0
\(826\) −0.900527 + 1.55976i −0.0313333 + 0.0542709i
\(827\) −18.5009 + 32.0445i −0.643340 + 1.11430i 0.341342 + 0.939939i \(0.389118\pi\)
−0.984682 + 0.174358i \(0.944215\pi\)
\(828\) 0 0
\(829\) 20.5418 0.713448 0.356724 0.934210i \(-0.383894\pi\)
0.356724 + 0.934210i \(0.383894\pi\)
\(830\) 0.851897 1.47553i 0.0295698 0.0512164i
\(831\) 0 0
\(832\) −7.51280 + 13.0126i −0.260459 + 0.451129i
\(833\) 11.5503 + 20.0057i 0.400194 + 0.693156i
\(834\) 0 0
\(835\) 12.5563 0.434530
\(836\) 44.5180 3.42885i 1.53969 0.118589i
\(837\) 0 0
\(838\) 3.83831 + 6.64814i 0.132592 + 0.229656i
\(839\) −23.8946 41.3866i −0.824932 1.42882i −0.901972 0.431795i \(-0.857880\pi\)
0.0770401 0.997028i \(-0.475453\pi\)
\(840\) 0 0
\(841\) 10.6739 + 18.4878i 0.368067 + 0.637511i
\(842\) −5.50719 + 9.53873i −0.189790 + 0.328726i
\(843\) 0 0
\(844\) 17.5394 0.603730
\(845\) −3.40847 + 5.90365i −0.117255 + 0.203092i
\(846\) 0 0
\(847\) −8.56237 −0.294206
\(848\) −10.4891 −0.360196
\(849\) 0 0
\(850\) −0.496454 0.859883i −0.0170282 0.0294937i
\(851\) −20.2553 + 35.0833i −0.694344 + 1.20264i
\(852\) 0 0
\(853\) −5.71632 9.90096i −0.195723 0.339003i 0.751414 0.659831i \(-0.229372\pi\)
−0.947137 + 0.320828i \(0.896039\pi\)
\(854\) −1.67682 −0.0573795
\(855\) 0 0
\(856\) 0.158141 0.00540513
\(857\) 2.78522 + 4.82414i 0.0951412 + 0.164789i 0.909668 0.415337i \(-0.136336\pi\)
−0.814526 + 0.580127i \(0.803003\pi\)
\(858\) 0 0
\(859\) 8.50709 14.7347i 0.290258 0.502742i −0.683612 0.729845i \(-0.739592\pi\)
0.973871 + 0.227103i \(0.0729255\pi\)
\(860\) 2.38151 + 4.12490i 0.0812088 + 0.140658i
\(861\) 0 0
\(862\) 5.58304 0.190159
\(863\) −46.8850 −1.59598 −0.797992 0.602668i \(-0.794104\pi\)
−0.797992 + 0.602668i \(0.794104\pi\)
\(864\) 0 0
\(865\) −1.09482 + 1.89628i −0.0372250 + 0.0644756i
\(866\) 4.92768 0.167449
\(867\) 0 0
\(868\) −2.25132 + 3.89939i −0.0764147 + 0.132354i
\(869\) 21.7454 + 37.6642i 0.737662 + 1.27767i
\(870\) 0 0
\(871\) −18.8674 32.6793i −0.639297 1.10730i
\(872\) −8.95210 15.5055i −0.303156 0.525082i
\(873\) 0 0
\(874\) 4.59101 + 6.70391i 0.155293 + 0.226763i
\(875\) 0.486575 0.0164492
\(876\) 0 0
\(877\) 14.8922 + 25.7940i 0.502873 + 0.871002i 0.999994 + 0.00332078i \(0.00105704\pi\)
−0.497121 + 0.867681i \(0.665610\pi\)
\(878\) −1.61379 + 2.79516i −0.0544626 + 0.0943321i
\(879\) 0 0
\(880\) −9.35867 + 16.2097i −0.315481 + 0.546428i
\(881\) 20.4884 0.690271 0.345135 0.938553i \(-0.387833\pi\)
0.345135 + 0.938553i \(0.387833\pi\)
\(882\) 0 0
\(883\) −15.7402 + 27.2628i −0.529699 + 0.917466i 0.469701 + 0.882826i \(0.344362\pi\)
−0.999400 + 0.0346401i \(0.988972\pi\)
\(884\) −8.13430 + 14.0890i −0.273586 + 0.473865i
\(885\) 0 0
\(886\) 4.03900 0.135693
\(887\) −16.8051 + 29.1074i −0.564262 + 0.977330i 0.432856 + 0.901463i \(0.357506\pi\)
−0.997118 + 0.0758670i \(0.975828\pi\)
\(888\) 0 0
\(889\) −2.39175 + 4.14264i −0.0802169 + 0.138940i
\(890\) 0.946281 + 1.63901i 0.0317194 + 0.0549397i
\(891\) 0 0
\(892\) −20.8742 −0.698919
\(893\) −48.2872 + 3.71916i −1.61587 + 0.124457i
\(894\) 0 0
\(895\) −3.75210 6.49883i −0.125419 0.217232i
\(896\) −2.03009 3.51623i −0.0678207 0.117469i
\(897\) 0 0
\(898\) 4.05050 + 7.01567i 0.135167 + 0.234116i
\(899\) 6.68185 11.5733i 0.222852 0.385991i
\(900\) 0 0
\(901\) −10.2358 −0.341004
\(902\) −2.00644 + 3.47526i −0.0668073 + 0.115714i
\(903\) 0 0
\(904\) 16.8470 0.560323
\(905\) 12.6652 0.421006
\(906\) 0 0
\(907\) −10.9747 19.0088i −0.364410 0.631176i 0.624272 0.781207i \(-0.285396\pi\)
−0.988681 + 0.150031i \(0.952063\pi\)
\(908\) 23.5942 40.8664i 0.783002 1.35620i
\(909\) 0 0
\(910\) 0.175858 + 0.304595i 0.00582963 + 0.0100972i
\(911\) −21.2865 −0.705253 −0.352626 0.935764i \(-0.614711\pi\)
−0.352626 + 0.935764i \(0.614711\pi\)
\(912\) 0 0
\(913\) −31.3428 −1.03730
\(914\) 5.31481 + 9.20552i 0.175798 + 0.304492i
\(915\) 0 0
\(916\) 16.4422 28.4788i 0.543267 0.940966i
\(917\) −3.46178 5.99598i −0.114318 0.198005i
\(918\) 0 0
\(919\) −2.61948 −0.0864087 −0.0432043 0.999066i \(-0.513757\pi\)
−0.0432043 + 0.999066i \(0.513757\pi\)
\(920\) −7.29873 −0.240632
\(921\) 0 0
\(922\) 3.18575 5.51789i 0.104917 0.181722i
\(923\) −24.6893 −0.812658
\(924\) 0 0
\(925\) 3.15878 5.47117i 0.103860 0.179891i
\(926\) 2.03859 + 3.53094i 0.0669921 + 0.116034i
\(927\) 0 0
\(928\) 4.55589 + 7.89104i 0.149554 + 0.259036i
\(929\) 1.91237 + 3.31232i 0.0627428 + 0.108674i 0.895691 0.444678i \(-0.146682\pi\)
−0.832948 + 0.553352i \(0.813349\pi\)
\(930\) 0 0
\(931\) 16.6572 + 24.3233i 0.545919 + 0.797165i
\(932\) 54.5210 1.78589
\(933\) 0 0
\(934\) 4.93160 + 8.54177i 0.161367 + 0.279495i
\(935\) −9.13272 + 15.8183i −0.298672 + 0.517315i
\(936\) 0 0
\(937\) 3.69584 6.40138i 0.120738 0.209124i −0.799321 0.600904i \(-0.794807\pi\)
0.920059 + 0.391780i \(0.128141\pi\)
\(938\) 2.14650 0.0700856
\(939\) 0 0
\(940\) 10.6412 18.4311i 0.347078 0.601157i
\(941\) 24.3057 42.0988i 0.792344 1.37238i −0.132168 0.991227i \(-0.542194\pi\)
0.924512 0.381153i \(-0.124473\pi\)
\(942\) 0 0
\(943\) 16.5529 0.539036
\(944\) 22.2838 38.5966i 0.725275 1.25621i
\(945\) 0 0
\(946\) −1.93274 + 3.34761i −0.0628389 + 0.108840i
\(947\) −18.0103 31.1948i −0.585257 1.01370i −0.994843 0.101424i \(-0.967660\pi\)
0.409586 0.912271i \(-0.365673\pi\)
\(948\) 0 0
\(949\) 27.3843 0.888930
\(950\) −0.715960 1.04546i −0.0232288 0.0339193i
\(951\) 0 0
\(952\) −0.945834 1.63823i −0.0306546 0.0530954i
\(953\) 5.60605 + 9.70996i 0.181598 + 0.314537i 0.942425 0.334418i \(-0.108540\pi\)
−0.760827 + 0.648955i \(0.775206\pi\)
\(954\) 0 0
\(955\) −4.07889 7.06484i −0.131990 0.228613i
\(956\) −3.90513 + 6.76389i −0.126301 + 0.218760i
\(957\) 0 0
\(958\) −9.28769 −0.300072
\(959\) −1.60190 + 2.77457i −0.0517280 + 0.0895955i
\(960\) 0 0
\(961\) −7.66153 −0.247146
\(962\) 4.56659 0.147233
\(963\) 0 0
\(964\) −12.1332 21.0152i −0.390783 0.676855i
\(965\) −1.68252 + 2.91422i −0.0541623 + 0.0938119i
\(966\) 0 0
\(967\) 5.02307 + 8.70021i 0.161531 + 0.279780i 0.935418 0.353544i \(-0.115023\pi\)
−0.773887 + 0.633324i \(0.781690\pi\)
\(968\) −20.0296 −0.643775
\(969\) 0 0
\(970\) −0.581394 −0.0186674
\(971\) −18.9495 32.8214i −0.608117 1.05329i −0.991551 0.129721i \(-0.958592\pi\)
0.383434 0.923568i \(-0.374742\pi\)
\(972\) 0 0
\(973\) 0.0568699 0.0985016i 0.00182317 0.00315782i
\(974\) −5.46844 9.47161i −0.175220 0.303490i
\(975\) 0 0
\(976\) 41.4933 1.32817
\(977\) −44.6435 −1.42827 −0.714135 0.700008i \(-0.753180\pi\)
−0.714135 + 0.700008i \(0.753180\pi\)
\(978\) 0 0
\(979\) 17.4077 30.1510i 0.556353 0.963631i
\(980\) −12.9550 −0.413831
\(981\) 0 0
\(982\) −5.82618 + 10.0912i −0.185921 + 0.322025i
\(983\) −6.25454 10.8332i −0.199489 0.345525i 0.748874 0.662712i \(-0.230595\pi\)
−0.948363 + 0.317188i \(0.897262\pi\)
\(984\) 0 0
\(985\) −1.91699 3.32033i −0.0610805 0.105795i
\(986\) 1.37331 + 2.37865i 0.0437352 + 0.0757515i
\(987\) 0 0
\(988\) −8.96935 + 18.7241i −0.285353 + 0.595693i
\(989\) 15.9449 0.507017
\(990\) 0 0
\(991\) −25.1503 43.5617i −0.798927 1.38378i −0.920315 0.391177i \(-0.872068\pi\)
0.121388 0.992605i \(-0.461265\pi\)
\(992\) −7.95645 + 13.7810i −0.252617 + 0.437546i
\(993\) 0 0
\(994\) 0.702210 1.21626i 0.0222728 0.0385775i
\(995\) −12.6985 −0.402569
\(996\) 0 0
\(997\) −6.46875 + 11.2042i −0.204867 + 0.354841i −0.950090 0.311975i \(-0.899010\pi\)
0.745223 + 0.666815i \(0.232343\pi\)
\(998\) 4.40504 7.62975i 0.139439 0.241515i
\(999\) 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 855.2.k.i.406.3 10
3.2 odd 2 285.2.i.f.121.3 yes 10
19.11 even 3 inner 855.2.k.i.676.3 10
57.11 odd 6 285.2.i.f.106.3 10
57.26 odd 6 5415.2.a.y.1.3 5
57.50 even 6 5415.2.a.z.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.3 10 57.11 odd 6
285.2.i.f.121.3 yes 10 3.2 odd 2
855.2.k.i.406.3 10 1.1 even 1 trivial
855.2.k.i.676.3 10 19.11 even 3 inner
5415.2.a.y.1.3 5 57.26 odd 6
5415.2.a.z.1.3 5 57.50 even 6