Properties

Label 225.2.h.d.181.3
Level $225$
Weight $2$
Character 225.181
Analytic conductor $1.797$
Analytic rank $0$
Dimension $12$
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] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.3
Root \(-2.17386 + 1.57940i\) of defining polynomial
Character \(\chi\) \(=\) 225.181
Dual form 225.2.h.d.46.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.830342 + 2.55553i) q^{2} +(-4.22323 + 3.06835i) q^{4} +(1.34843 + 1.78375i) q^{5} +1.68704 q^{7} +(-7.00026 - 5.08599i) q^{8} +O(q^{10})\) \(q+(0.830342 + 2.55553i) q^{2} +(-4.22323 + 3.06835i) q^{4} +(1.34843 + 1.78375i) q^{5} +1.68704 q^{7} +(-7.00026 - 5.08599i) q^{8} +(-3.43876 + 4.92706i) q^{10} +(-0.333373 - 1.02602i) q^{11} +(0.827310 - 2.54620i) q^{13} +(1.40082 + 4.31129i) q^{14} +(3.95852 - 12.1831i) q^{16} +(-3.18079 - 2.31098i) q^{17} +(0.952655 + 0.692144i) q^{19} +(-11.1679 - 3.39571i) q^{20} +(2.34520 - 1.70389i) q^{22} +(1.25552 + 3.86409i) q^{23} +(-1.36350 + 4.81050i) q^{25} +7.19384 q^{26} +(-7.12476 + 5.17644i) q^{28} +(4.81846 - 3.50082i) q^{29} +(5.74653 + 4.17510i) q^{31} +17.1155 q^{32} +(3.26463 - 10.0475i) q^{34} +(2.27485 + 3.00925i) q^{35} +(-1.41587 + 4.35761i) q^{37} +(-0.977766 + 3.00925i) q^{38} +(-0.367227 - 19.3448i) q^{40} +(3.47998 - 10.7103i) q^{41} +2.58587 q^{43} +(4.55609 + 3.31019i) q^{44} +(-8.83229 + 6.41703i) q^{46} +(-1.55155 + 1.12727i) q^{47} -4.15389 q^{49} +(-13.4255 + 0.509905i) q^{50} +(4.31872 + 13.2917i) q^{52} +(-2.06187 + 1.49803i) q^{53} +(1.38062 - 1.97816i) q^{55} +(-11.8097 - 8.58028i) q^{56} +(12.9474 + 9.40685i) q^{58} +(-0.412843 + 1.27060i) q^{59} +(-2.24997 - 6.92470i) q^{61} +(-5.89800 + 18.1522i) q^{62} +(6.29470 + 19.3731i) q^{64} +(5.65734 - 1.95765i) q^{65} +(-10.0683 - 7.31502i) q^{67} +20.5241 q^{68} +(-5.80133 + 8.31216i) q^{70} +(-4.84181 + 3.51778i) q^{71} +(-1.01996 - 3.13911i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(-0.562414 - 1.73093i) q^{77} +(3.23934 - 2.35351i) q^{79} +(27.0693 - 9.36699i) q^{80} +30.2600 q^{82} +(7.17988 + 5.21649i) q^{83} +(-0.166861 - 8.78989i) q^{85} +(2.14716 + 6.60827i) q^{86} +(-2.88461 + 8.87792i) q^{88} +(-4.77234 - 14.6877i) q^{89} +(1.39571 - 4.29555i) q^{91} +(-17.1587 - 12.4666i) q^{92} +(-4.16908 - 3.02901i) q^{94} +(0.0499753 + 2.63260i) q^{95} +(-8.71166 + 6.32939i) q^{97} +(-3.44915 - 10.6154i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.830342 + 2.55553i 0.587140 + 1.80703i 0.590500 + 0.807038i \(0.298931\pi\)
−0.00335992 + 0.999994i \(0.501069\pi\)
\(3\) 0 0
\(4\) −4.22323 + 3.06835i −2.11161 + 1.53418i
\(5\) 1.34843 + 1.78375i 0.603034 + 0.797715i
\(6\) 0 0
\(7\) 1.68704 0.637642 0.318821 0.947815i \(-0.396713\pi\)
0.318821 + 0.947815i \(0.396713\pi\)
\(8\) −7.00026 5.08599i −2.47497 1.79817i
\(9\) 0 0
\(10\) −3.43876 + 4.92706i −1.08743 + 1.55807i
\(11\) −0.333373 1.02602i −0.100516 0.309356i 0.888136 0.459581i \(-0.152000\pi\)
−0.988652 + 0.150225i \(0.952000\pi\)
\(12\) 0 0
\(13\) 0.827310 2.54620i 0.229455 0.706189i −0.768354 0.640025i \(-0.778924\pi\)
0.997809 0.0661638i \(-0.0210760\pi\)
\(14\) 1.40082 + 4.31129i 0.374385 + 1.15224i
\(15\) 0 0
\(16\) 3.95852 12.1831i 0.989631 3.04577i
\(17\) −3.18079 2.31098i −0.771454 0.560494i 0.130948 0.991389i \(-0.458198\pi\)
−0.902402 + 0.430895i \(0.858198\pi\)
\(18\) 0 0
\(19\) 0.952655 + 0.692144i 0.218554 + 0.158789i 0.691676 0.722208i \(-0.256873\pi\)
−0.473121 + 0.880997i \(0.656873\pi\)
\(20\) −11.1679 3.39571i −2.49721 0.759305i
\(21\) 0 0
\(22\) 2.34520 1.70389i 0.499999 0.363270i
\(23\) 1.25552 + 3.86409i 0.261794 + 0.805719i 0.992415 + 0.122935i \(0.0392307\pi\)
−0.730621 + 0.682783i \(0.760769\pi\)
\(24\) 0 0
\(25\) −1.36350 + 4.81050i −0.272699 + 0.962099i
\(26\) 7.19384 1.41083
\(27\) 0 0
\(28\) −7.12476 + 5.17644i −1.34645 + 0.978256i
\(29\) 4.81846 3.50082i 0.894766 0.650086i −0.0423500 0.999103i \(-0.513484\pi\)
0.937116 + 0.349017i \(0.113484\pi\)
\(30\) 0 0
\(31\) 5.74653 + 4.17510i 1.03211 + 0.749870i 0.968729 0.248120i \(-0.0798128\pi\)
0.0633776 + 0.997990i \(0.479813\pi\)
\(32\) 17.1155 3.02563
\(33\) 0 0
\(34\) 3.26463 10.0475i 0.559879 1.72313i
\(35\) 2.27485 + 3.00925i 0.384520 + 0.508657i
\(36\) 0 0
\(37\) −1.41587 + 4.35761i −0.232768 + 0.716387i 0.764641 + 0.644456i \(0.222916\pi\)
−0.997410 + 0.0719311i \(0.977084\pi\)
\(38\) −0.977766 + 3.00925i −0.158615 + 0.488165i
\(39\) 0 0
\(40\) −0.367227 19.3448i −0.0580637 3.05868i
\(41\) 3.47998 10.7103i 0.543481 1.67266i −0.181093 0.983466i \(-0.557963\pi\)
0.724574 0.689197i \(-0.242037\pi\)
\(42\) 0 0
\(43\) 2.58587 0.394342 0.197171 0.980369i \(-0.436825\pi\)
0.197171 + 0.980369i \(0.436825\pi\)
\(44\) 4.55609 + 3.31019i 0.686857 + 0.499031i
\(45\) 0 0
\(46\) −8.83229 + 6.41703i −1.30225 + 0.946140i
\(47\) −1.55155 + 1.12727i −0.226317 + 0.164429i −0.695166 0.718850i \(-0.744669\pi\)
0.468849 + 0.883278i \(0.344669\pi\)
\(48\) 0 0
\(49\) −4.15389 −0.593413
\(50\) −13.4255 + 0.509905i −1.89866 + 0.0721114i
\(51\) 0 0
\(52\) 4.31872 + 13.2917i 0.598899 + 1.84322i
\(53\) −2.06187 + 1.49803i −0.283219 + 0.205771i −0.720320 0.693642i \(-0.756005\pi\)
0.437101 + 0.899412i \(0.356005\pi\)
\(54\) 0 0
\(55\) 1.38062 1.97816i 0.186163 0.266735i
\(56\) −11.8097 8.58028i −1.57814 1.14659i
\(57\) 0 0
\(58\) 12.9474 + 9.40685i 1.70008 + 1.23518i
\(59\) −0.412843 + 1.27060i −0.0537476 + 0.165418i −0.974327 0.225137i \(-0.927717\pi\)
0.920579 + 0.390555i \(0.127717\pi\)
\(60\) 0 0
\(61\) −2.24997 6.92470i −0.288079 0.886617i −0.985459 0.169915i \(-0.945651\pi\)
0.697379 0.716702i \(-0.254349\pi\)
\(62\) −5.89800 + 18.1522i −0.749047 + 2.30533i
\(63\) 0 0
\(64\) 6.29470 + 19.3731i 0.786838 + 2.42164i
\(65\) 5.65734 1.95765i 0.701706 0.242817i
\(66\) 0 0
\(67\) −10.0683 7.31502i −1.23003 0.893672i −0.233141 0.972443i \(-0.574900\pi\)
−0.996893 + 0.0787711i \(0.974900\pi\)
\(68\) 20.5241 2.48891
\(69\) 0 0
\(70\) −5.80133 + 8.31216i −0.693392 + 0.993493i
\(71\) −4.84181 + 3.51778i −0.574617 + 0.417484i −0.836779 0.547540i \(-0.815564\pi\)
0.262162 + 0.965024i \(0.415564\pi\)
\(72\) 0 0
\(73\) −1.01996 3.13911i −0.119377 0.367405i 0.873458 0.486900i \(-0.161872\pi\)
−0.992835 + 0.119495i \(0.961872\pi\)
\(74\) −12.3117 −1.43120
\(75\) 0 0
\(76\) −6.14702 −0.705112
\(77\) −0.562414 1.73093i −0.0640931 0.197258i
\(78\) 0 0
\(79\) 3.23934 2.35351i 0.364454 0.264791i −0.390454 0.920623i \(-0.627682\pi\)
0.754907 + 0.655831i \(0.227682\pi\)
\(80\) 27.0693 9.36699i 3.02644 1.04726i
\(81\) 0 0
\(82\) 30.2600 3.34166
\(83\) 7.17988 + 5.21649i 0.788094 + 0.572584i 0.907397 0.420274i \(-0.138066\pi\)
−0.119303 + 0.992858i \(0.538066\pi\)
\(84\) 0 0
\(85\) −0.166861 8.78989i −0.0180986 0.953398i
\(86\) 2.14716 + 6.60827i 0.231534 + 0.712588i
\(87\) 0 0
\(88\) −2.88461 + 8.87792i −0.307501 + 0.946389i
\(89\) −4.77234 14.6877i −0.505867 1.55690i −0.799309 0.600920i \(-0.794801\pi\)
0.293442 0.955977i \(-0.405199\pi\)
\(90\) 0 0
\(91\) 1.39571 4.29555i 0.146310 0.450296i
\(92\) −17.1587 12.4666i −1.78892 1.29973i
\(93\) 0 0
\(94\) −4.16908 3.02901i −0.430008 0.312419i
\(95\) 0.0499753 + 2.63260i 0.00512736 + 0.270099i
\(96\) 0 0
\(97\) −8.71166 + 6.32939i −0.884535 + 0.642652i −0.934447 0.356101i \(-0.884106\pi\)
0.0499122 + 0.998754i \(0.484106\pi\)
\(98\) −3.44915 10.6154i −0.348416 1.07232i
\(99\) 0 0
\(100\) −9.00196 24.4995i −0.900196 2.44995i
\(101\) 13.5654 1.34981 0.674905 0.737905i \(-0.264185\pi\)
0.674905 + 0.737905i \(0.264185\pi\)
\(102\) 0 0
\(103\) −1.10757 + 0.804700i −0.109133 + 0.0792894i −0.641013 0.767530i \(-0.721486\pi\)
0.531880 + 0.846819i \(0.321486\pi\)
\(104\) −18.7413 + 13.6164i −1.83774 + 1.33520i
\(105\) 0 0
\(106\) −5.54032 4.02528i −0.538124 0.390970i
\(107\) −11.0115 −1.06452 −0.532262 0.846579i \(-0.678658\pi\)
−0.532262 + 0.846579i \(0.678658\pi\)
\(108\) 0 0
\(109\) 1.06577 3.28010i 0.102082 0.314176i −0.886952 0.461861i \(-0.847182\pi\)
0.989035 + 0.147684i \(0.0471820\pi\)
\(110\) 6.20163 + 1.88568i 0.591303 + 0.179792i
\(111\) 0 0
\(112\) 6.67820 20.5534i 0.631030 1.94211i
\(113\) −1.87015 + 5.75574i −0.175929 + 0.541455i −0.999675 0.0255053i \(-0.991881\pi\)
0.823745 + 0.566960i \(0.191881\pi\)
\(114\) 0 0
\(115\) −5.19958 + 7.44997i −0.484863 + 0.694713i
\(116\) −9.60772 + 29.5695i −0.892054 + 2.74546i
\(117\) 0 0
\(118\) −3.58986 −0.330473
\(119\) −5.36612 3.89872i −0.491912 0.357395i
\(120\) 0 0
\(121\) 7.95761 5.78155i 0.723419 0.525595i
\(122\) 15.8280 11.4997i 1.43300 1.04114i
\(123\) 0 0
\(124\) −37.0796 −3.32984
\(125\) −10.4193 + 4.05447i −0.931928 + 0.362643i
\(126\) 0 0
\(127\) −6.25332 19.2457i −0.554893 1.70778i −0.696227 0.717822i \(-0.745139\pi\)
0.141334 0.989962i \(-0.454861\pi\)
\(128\) −16.5882 + 12.0521i −1.46621 + 1.06526i
\(129\) 0 0
\(130\) 9.70036 + 12.8320i 0.850778 + 1.12544i
\(131\) −2.46759 1.79281i −0.215595 0.156639i 0.474747 0.880122i \(-0.342540\pi\)
−0.690341 + 0.723484i \(0.742540\pi\)
\(132\) 0 0
\(133\) 1.60717 + 1.16768i 0.139359 + 0.101250i
\(134\) 10.3336 31.8037i 0.892691 2.74742i
\(135\) 0 0
\(136\) 10.5127 + 32.3549i 0.901460 + 2.77441i
\(137\) 6.33795 19.5062i 0.541487 1.66653i −0.187711 0.982224i \(-0.560107\pi\)
0.729199 0.684302i \(-0.239893\pi\)
\(138\) 0 0
\(139\) 5.66068 + 17.4218i 0.480133 + 1.47770i 0.838908 + 0.544273i \(0.183194\pi\)
−0.358775 + 0.933424i \(0.616806\pi\)
\(140\) −18.8407 5.72871i −1.59233 0.484165i
\(141\) 0 0
\(142\) −13.0101 9.45242i −1.09179 0.793230i
\(143\) −2.88825 −0.241527
\(144\) 0 0
\(145\) 12.7419 + 3.87432i 1.05816 + 0.321745i
\(146\) 7.17517 5.21306i 0.593821 0.431436i
\(147\) 0 0
\(148\) −7.39114 22.7476i −0.607548 1.86984i
\(149\) −0.705938 −0.0578327 −0.0289163 0.999582i \(-0.509206\pi\)
−0.0289163 + 0.999582i \(0.509206\pi\)
\(150\) 0 0
\(151\) 7.04538 0.573345 0.286673 0.958029i \(-0.407451\pi\)
0.286673 + 0.958029i \(0.407451\pi\)
\(152\) −3.14860 9.69039i −0.255385 0.785994i
\(153\) 0 0
\(154\) 3.95645 2.87453i 0.318820 0.231636i
\(155\) 0.301457 + 15.8802i 0.0242136 + 1.27552i
\(156\) 0 0
\(157\) −5.12880 −0.409323 −0.204662 0.978833i \(-0.565609\pi\)
−0.204662 + 0.978833i \(0.565609\pi\)
\(158\) 8.70423 + 6.32399i 0.692471 + 0.503110i
\(159\) 0 0
\(160\) 23.0790 + 30.5298i 1.82456 + 2.41359i
\(161\) 2.11811 + 6.51888i 0.166931 + 0.513760i
\(162\) 0 0
\(163\) −7.49715 + 23.0739i −0.587222 + 1.80728i 0.00293441 + 0.999996i \(0.499066\pi\)
−0.590157 + 0.807289i \(0.700934\pi\)
\(164\) 18.1662 + 55.9097i 1.41854 + 4.36581i
\(165\) 0 0
\(166\) −7.36913 + 22.6799i −0.571955 + 1.76030i
\(167\) 3.68013 + 2.67377i 0.284777 + 0.206903i 0.720998 0.692937i \(-0.243683\pi\)
−0.436221 + 0.899840i \(0.643683\pi\)
\(168\) 0 0
\(169\) 4.71853 + 3.42821i 0.362964 + 0.263709i
\(170\) 22.3243 7.72503i 1.71219 0.592483i
\(171\) 0 0
\(172\) −10.9207 + 7.93437i −0.832697 + 0.604990i
\(173\) 0.827327 + 2.54625i 0.0629005 + 0.193588i 0.977568 0.210618i \(-0.0675478\pi\)
−0.914668 + 0.404206i \(0.867548\pi\)
\(174\) 0 0
\(175\) −2.30027 + 8.11551i −0.173884 + 0.613475i
\(176\) −13.8197 −1.04170
\(177\) 0 0
\(178\) 33.5723 24.3917i 2.51635 1.82823i
\(179\) −12.6422 + 9.18511i −0.944924 + 0.686528i −0.949601 0.313461i \(-0.898511\pi\)
0.00467674 + 0.999989i \(0.498511\pi\)
\(180\) 0 0
\(181\) −0.164103 0.119228i −0.0121977 0.00886215i 0.581670 0.813425i \(-0.302400\pi\)
−0.593867 + 0.804563i \(0.702400\pi\)
\(182\) 12.1363 0.899603
\(183\) 0 0
\(184\) 10.8638 33.4352i 0.800887 2.46488i
\(185\) −9.68207 + 3.35036i −0.711840 + 0.246323i
\(186\) 0 0
\(187\) −1.31071 + 4.03396i −0.0958488 + 0.294992i
\(188\) 3.09369 9.52141i 0.225631 0.694420i
\(189\) 0 0
\(190\) −6.68619 + 2.31367i −0.485067 + 0.167851i
\(191\) 2.44734 7.53213i 0.177083 0.545006i −0.822639 0.568563i \(-0.807499\pi\)
0.999722 + 0.0235578i \(0.00749937\pi\)
\(192\) 0 0
\(193\) −16.4269 −1.18243 −0.591216 0.806513i \(-0.701352\pi\)
−0.591216 + 0.806513i \(0.701352\pi\)
\(194\) −23.4086 17.0073i −1.68064 1.22106i
\(195\) 0 0
\(196\) 17.5428 12.7456i 1.25306 0.910400i
\(197\) −13.8640 + 10.0728i −0.987770 + 0.717657i −0.959432 0.281942i \(-0.909022\pi\)
−0.0283382 + 0.999598i \(0.509022\pi\)
\(198\) 0 0
\(199\) −2.01848 −0.143086 −0.0715430 0.997438i \(-0.522792\pi\)
−0.0715430 + 0.997438i \(0.522792\pi\)
\(200\) 34.0110 26.7400i 2.40494 1.89081i
\(201\) 0 0
\(202\) 11.2639 + 34.6668i 0.792528 + 2.43915i
\(203\) 8.12895 5.90603i 0.570541 0.414522i
\(204\) 0 0
\(205\) 23.7969 8.23461i 1.66205 0.575130i
\(206\) −2.97610 2.16226i −0.207355 0.150652i
\(207\) 0 0
\(208\) −27.7456 20.1584i −1.92381 1.39773i
\(209\) 0.392562 1.20818i 0.0271541 0.0835717i
\(210\) 0 0
\(211\) −7.36119 22.6554i −0.506765 1.55966i −0.797783 0.602945i \(-0.793994\pi\)
0.291018 0.956718i \(-0.406006\pi\)
\(212\) 4.11123 12.6531i 0.282361 0.869017i
\(213\) 0 0
\(214\) −9.14333 28.1403i −0.625025 1.92363i
\(215\) 3.48686 + 4.61254i 0.237802 + 0.314572i
\(216\) 0 0
\(217\) 9.69463 + 7.04356i 0.658115 + 0.478148i
\(218\) 9.26733 0.627663
\(219\) 0 0
\(220\) 0.239008 + 12.5905i 0.0161139 + 0.848849i
\(221\) −8.51571 + 6.18702i −0.572828 + 0.416184i
\(222\) 0 0
\(223\) 4.05158 + 12.4695i 0.271314 + 0.835017i 0.990171 + 0.139860i \(0.0446653\pi\)
−0.718858 + 0.695157i \(0.755335\pi\)
\(224\) 28.8746 1.92927
\(225\) 0 0
\(226\) −16.2618 −1.08172
\(227\) 8.12118 + 24.9944i 0.539022 + 1.65894i 0.734795 + 0.678289i \(0.237278\pi\)
−0.195774 + 0.980649i \(0.562722\pi\)
\(228\) 0 0
\(229\) −1.61484 + 1.17325i −0.106711 + 0.0775304i −0.639861 0.768490i \(-0.721008\pi\)
0.533150 + 0.846021i \(0.321008\pi\)
\(230\) −23.3560 7.10166i −1.54005 0.468269i
\(231\) 0 0
\(232\) −51.5357 −3.38348
\(233\) −0.425178 0.308910i −0.0278543 0.0202373i 0.573771 0.819016i \(-0.305480\pi\)
−0.601625 + 0.798778i \(0.705480\pi\)
\(234\) 0 0
\(235\) −4.10291 1.24753i −0.267644 0.0813801i
\(236\) −2.15512 6.63278i −0.140286 0.431757i
\(237\) 0 0
\(238\) 5.50757 16.9505i 0.357002 1.09874i
\(239\) 2.16612 + 6.66663i 0.140115 + 0.431229i 0.996350 0.0853565i \(-0.0272029\pi\)
−0.856236 + 0.516585i \(0.827203\pi\)
\(240\) 0 0
\(241\) 0.715542 2.20221i 0.0460921 0.141857i −0.925362 0.379085i \(-0.876239\pi\)
0.971454 + 0.237228i \(0.0762388\pi\)
\(242\) 21.3824 + 15.5353i 1.37452 + 0.998644i
\(243\) 0 0
\(244\) 30.7496 + 22.3409i 1.96854 + 1.43023i
\(245\) −5.60121 7.40948i −0.357848 0.473374i
\(246\) 0 0
\(247\) 2.55048 1.85303i 0.162283 0.117906i
\(248\) −18.9927 58.4536i −1.20604 3.71180i
\(249\) 0 0
\(250\) −19.0129 23.2602i −1.20248 1.47110i
\(251\) 6.17885 0.390005 0.195003 0.980803i \(-0.437528\pi\)
0.195003 + 0.980803i \(0.437528\pi\)
\(252\) 0 0
\(253\) 3.54607 2.57637i 0.222939 0.161975i
\(254\) 43.9907 31.9611i 2.76022 2.00542i
\(255\) 0 0
\(256\) −11.6138 8.43794i −0.725864 0.527371i
\(257\) −13.2239 −0.824882 −0.412441 0.910984i \(-0.635324\pi\)
−0.412441 + 0.910984i \(0.635324\pi\)
\(258\) 0 0
\(259\) −2.38864 + 7.35148i −0.148423 + 0.456799i
\(260\) −17.8855 + 25.6263i −1.10921 + 1.58928i
\(261\) 0 0
\(262\) 2.53264 7.79465i 0.156467 0.481555i
\(263\) 2.15583 6.63498i 0.132934 0.409130i −0.862329 0.506349i \(-0.830995\pi\)
0.995263 + 0.0972190i \(0.0309947\pi\)
\(264\) 0 0
\(265\) −5.45239 1.65786i −0.334937 0.101841i
\(266\) −1.64953 + 5.07674i −0.101139 + 0.311275i
\(267\) 0 0
\(268\) 64.9656 3.96841
\(269\) 19.1898 + 13.9422i 1.17002 + 0.850070i 0.991011 0.133777i \(-0.0427107\pi\)
0.179010 + 0.983847i \(0.442711\pi\)
\(270\) 0 0
\(271\) −23.4542 + 17.0405i −1.42474 + 1.03514i −0.433775 + 0.901021i \(0.642819\pi\)
−0.990966 + 0.134114i \(0.957181\pi\)
\(272\) −40.7460 + 29.6037i −2.47059 + 1.79499i
\(273\) 0 0
\(274\) 55.1113 3.32940
\(275\) 5.39020 0.204721i 0.325041 0.0123451i
\(276\) 0 0
\(277\) −2.65343 8.16641i −0.159429 0.490672i 0.839154 0.543894i \(-0.183051\pi\)
−0.998583 + 0.0532223i \(0.983051\pi\)
\(278\) −39.8216 + 28.9321i −2.38834 + 1.73523i
\(279\) 0 0
\(280\) −0.619527 32.6354i −0.0370238 1.95034i
\(281\) 13.8877 + 10.0900i 0.828471 + 0.601919i 0.919126 0.393963i \(-0.128896\pi\)
−0.0906557 + 0.995882i \(0.528896\pi\)
\(282\) 0 0
\(283\) 7.78278 + 5.65452i 0.462638 + 0.336126i 0.794565 0.607179i \(-0.207699\pi\)
−0.331927 + 0.943305i \(0.607699\pi\)
\(284\) 9.65426 29.7128i 0.572875 1.76313i
\(285\) 0 0
\(286\) −2.39823 7.38100i −0.141810 0.436447i
\(287\) 5.87087 18.0687i 0.346546 1.06656i
\(288\) 0 0
\(289\) −0.476498 1.46651i −0.0280293 0.0862654i
\(290\) 0.679209 + 35.7793i 0.0398845 + 2.10104i
\(291\) 0 0
\(292\) 13.9394 + 10.1276i 0.815742 + 0.592671i
\(293\) −16.8202 −0.982649 −0.491324 0.870977i \(-0.663487\pi\)
−0.491324 + 0.870977i \(0.663487\pi\)
\(294\) 0 0
\(295\) −2.82312 + 0.976903i −0.164368 + 0.0568775i
\(296\) 32.0743 23.3033i 1.86428 1.35448i
\(297\) 0 0
\(298\) −0.586170 1.80404i −0.0339559 0.104505i
\(299\) 10.8775 0.629059
\(300\) 0 0
\(301\) 4.36247 0.251449
\(302\) 5.85008 + 18.0047i 0.336634 + 1.03605i
\(303\) 0 0
\(304\) 12.2036 8.86641i 0.699922 0.508523i
\(305\) 9.31799 13.3508i 0.533546 0.764466i
\(306\) 0 0
\(307\) 11.3212 0.646134 0.323067 0.946376i \(-0.395286\pi\)
0.323067 + 0.946376i \(0.395286\pi\)
\(308\) 7.68632 + 5.58444i 0.437969 + 0.318203i
\(309\) 0 0
\(310\) −40.3319 + 13.9563i −2.29070 + 0.792667i
\(311\) −5.73642 17.6549i −0.325283 1.00112i −0.971313 0.237805i \(-0.923572\pi\)
0.646030 0.763312i \(-0.276428\pi\)
\(312\) 0 0
\(313\) −2.99731 + 9.22478i −0.169418 + 0.521416i −0.999335 0.0364720i \(-0.988388\pi\)
0.829916 + 0.557888i \(0.188388\pi\)
\(314\) −4.25866 13.1068i −0.240330 0.739660i
\(315\) 0 0
\(316\) −6.45903 + 19.8789i −0.363349 + 1.11827i
\(317\) 6.04859 + 4.39456i 0.339723 + 0.246823i 0.744545 0.667573i \(-0.232667\pi\)
−0.404822 + 0.914395i \(0.632667\pi\)
\(318\) 0 0
\(319\) −5.19825 3.77675i −0.291046 0.211457i
\(320\) −26.0688 + 37.3514i −1.45729 + 2.08800i
\(321\) 0 0
\(322\) −14.9004 + 10.8258i −0.830369 + 0.603298i
\(323\) −1.43066 4.40313i −0.0796042 0.244997i
\(324\) 0 0
\(325\) 11.1205 + 7.45150i 0.616852 + 0.413335i
\(326\) −65.1911 −3.61060
\(327\) 0 0
\(328\) −78.8331 + 57.2756i −4.35283 + 3.16252i
\(329\) −2.61753 + 1.90175i −0.144309 + 0.104847i
\(330\) 0 0
\(331\) 20.4333 + 14.8457i 1.12312 + 0.815993i 0.984679 0.174378i \(-0.0557914\pi\)
0.138439 + 0.990371i \(0.455791\pi\)
\(332\) −46.3283 −2.54259
\(333\) 0 0
\(334\) −3.77714 + 11.6248i −0.206676 + 0.636083i
\(335\) −0.528171 27.8230i −0.0288571 1.52013i
\(336\) 0 0
\(337\) −4.02464 + 12.3866i −0.219236 + 0.674739i 0.779590 + 0.626291i \(0.215428\pi\)
−0.998826 + 0.0484485i \(0.984572\pi\)
\(338\) −4.84291 + 14.9049i −0.263419 + 0.810721i
\(339\) 0 0
\(340\) 27.6752 + 36.6097i 1.50090 + 1.98544i
\(341\) 2.36798 7.28790i 0.128233 0.394662i
\(342\) 0 0
\(343\) −18.8171 −1.01603
\(344\) −18.1018 13.1517i −0.975983 0.709093i
\(345\) 0 0
\(346\) −5.82005 + 4.22852i −0.312888 + 0.227326i
\(347\) −4.85531 + 3.52759i −0.260647 + 0.189371i −0.710432 0.703766i \(-0.751500\pi\)
0.449785 + 0.893137i \(0.351500\pi\)
\(348\) 0 0
\(349\) −22.7183 −1.21608 −0.608042 0.793905i \(-0.708045\pi\)
−0.608042 + 0.793905i \(0.708045\pi\)
\(350\) −22.6494 + 0.860231i −1.21066 + 0.0459813i
\(351\) 0 0
\(352\) −5.70586 17.5608i −0.304123 0.935996i
\(353\) −3.92772 + 2.85366i −0.209052 + 0.151885i −0.687385 0.726294i \(-0.741241\pi\)
0.478333 + 0.878179i \(0.341241\pi\)
\(354\) 0 0
\(355\) −12.8036 3.89309i −0.679547 0.206624i
\(356\) 65.2218 + 47.3864i 3.45675 + 2.51148i
\(357\) 0 0
\(358\) −33.9702 24.6808i −1.79538 1.30442i
\(359\) −8.92780 + 27.4769i −0.471191 + 1.45018i 0.379835 + 0.925054i \(0.375981\pi\)
−0.851026 + 0.525123i \(0.824019\pi\)
\(360\) 0 0
\(361\) −5.44284 16.7513i −0.286465 0.881649i
\(362\) 0.168429 0.518371i 0.00885242 0.0272450i
\(363\) 0 0
\(364\) 7.28587 + 22.4236i 0.381883 + 1.17532i
\(365\) 4.22403 6.05220i 0.221096 0.316787i
\(366\) 0 0
\(367\) 11.8998 + 8.64570i 0.621163 + 0.451302i 0.853328 0.521375i \(-0.174581\pi\)
−0.232164 + 0.972677i \(0.574581\pi\)
\(368\) 52.0465 2.71311
\(369\) 0 0
\(370\) −16.6014 21.9609i −0.863064 1.14169i
\(371\) −3.47846 + 2.52725i −0.180592 + 0.131208i
\(372\) 0 0
\(373\) −10.2096 31.4220i −0.528635 1.62697i −0.757013 0.653399i \(-0.773342\pi\)
0.228378 0.973572i \(-0.426658\pi\)
\(374\) −11.3972 −0.589337
\(375\) 0 0
\(376\) 16.5945 0.855797
\(377\) −4.92742 15.1650i −0.253775 0.781039i
\(378\) 0 0
\(379\) 12.2612 8.90826i 0.629814 0.457587i −0.226522 0.974006i \(-0.572735\pi\)
0.856336 + 0.516419i \(0.172735\pi\)
\(380\) −8.28880 10.9647i −0.425207 0.562478i
\(381\) 0 0
\(382\) 21.2807 1.08882
\(383\) −6.47870 4.70705i −0.331046 0.240519i 0.409828 0.912163i \(-0.365589\pi\)
−0.740874 + 0.671644i \(0.765589\pi\)
\(384\) 0 0
\(385\) 2.32917 3.33724i 0.118706 0.170081i
\(386\) −13.6399 41.9793i −0.694253 2.13669i
\(387\) 0 0
\(388\) 17.3705 53.4609i 0.881854 2.71407i
\(389\) −0.332078 1.02203i −0.0168370 0.0518191i 0.942285 0.334812i \(-0.108673\pi\)
−0.959122 + 0.282993i \(0.908673\pi\)
\(390\) 0 0
\(391\) 4.93629 15.1923i 0.249639 0.768309i
\(392\) 29.0783 + 21.1266i 1.46868 + 1.06706i
\(393\) 0 0
\(394\) −37.2532 27.0660i −1.87679 1.36357i
\(395\) 8.56607 + 2.60461i 0.431006 + 0.131052i
\(396\) 0 0
\(397\) 19.5894 14.2326i 0.983166 0.714312i 0.0247517 0.999694i \(-0.492120\pi\)
0.958414 + 0.285382i \(0.0921205\pi\)
\(398\) −1.67603 5.15828i −0.0840116 0.258561i
\(399\) 0 0
\(400\) 53.2093 + 35.6540i 2.66046 + 1.78270i
\(401\) 1.99317 0.0995340 0.0497670 0.998761i \(-0.484152\pi\)
0.0497670 + 0.998761i \(0.484152\pi\)
\(402\) 0 0
\(403\) 15.3848 11.1777i 0.766371 0.556801i
\(404\) −57.2899 + 41.6235i −2.85028 + 2.07085i
\(405\) 0 0
\(406\) 21.8428 + 15.8698i 1.08404 + 0.787603i
\(407\) 4.94300 0.245015
\(408\) 0 0
\(409\) 2.05953 6.33858i 0.101837 0.313423i −0.887138 0.461504i \(-0.847310\pi\)
0.988975 + 0.148082i \(0.0473098\pi\)
\(410\) 40.8033 + 53.9761i 2.01513 + 2.66569i
\(411\) 0 0
\(412\) 2.20843 6.79686i 0.108802 0.334857i
\(413\) −0.696484 + 2.14356i −0.0342717 + 0.105477i
\(414\) 0 0
\(415\) 0.376649 + 19.8411i 0.0184890 + 0.973962i
\(416\) 14.1599 43.5796i 0.694245 2.13667i
\(417\) 0 0
\(418\) 3.41351 0.166960
\(419\) 17.2758 + 12.5516i 0.843977 + 0.613185i 0.923479 0.383650i \(-0.125333\pi\)
−0.0795021 + 0.996835i \(0.525333\pi\)
\(420\) 0 0
\(421\) −18.0708 + 13.1292i −0.880717 + 0.639878i −0.933441 0.358731i \(-0.883210\pi\)
0.0527243 + 0.998609i \(0.483210\pi\)
\(422\) 51.7842 37.6235i 2.52082 1.83148i
\(423\) 0 0
\(424\) 22.0526 1.07097
\(425\) 15.4539 12.1502i 0.749626 0.589369i
\(426\) 0 0
\(427\) −3.79580 11.6823i −0.183692 0.565344i
\(428\) 46.5042 33.7873i 2.24786 1.63317i
\(429\) 0 0
\(430\) −8.89219 + 12.7407i −0.428819 + 0.614413i
\(431\) −24.6046 17.8763i −1.18516 0.861070i −0.192416 0.981313i \(-0.561632\pi\)
−0.992744 + 0.120244i \(0.961632\pi\)
\(432\) 0 0
\(433\) −0.466511 0.338940i −0.0224191 0.0162884i 0.576519 0.817084i \(-0.304411\pi\)
−0.598938 + 0.800795i \(0.704411\pi\)
\(434\) −9.95017 + 30.6235i −0.477624 + 1.46997i
\(435\) 0 0
\(436\) 5.56352 + 17.1227i 0.266444 + 0.820031i
\(437\) −1.47843 + 4.55015i −0.0707230 + 0.217663i
\(438\) 0 0
\(439\) 3.95681 + 12.1778i 0.188848 + 0.581215i 0.999993 0.00363006i \(-0.00115549\pi\)
−0.811145 + 0.584845i \(0.801155\pi\)
\(440\) −19.7256 + 6.82580i −0.940383 + 0.325407i
\(441\) 0 0
\(442\) −22.8821 16.6248i −1.08839 0.790761i
\(443\) −14.3147 −0.680110 −0.340055 0.940405i \(-0.610446\pi\)
−0.340055 + 0.940405i \(0.610446\pi\)
\(444\) 0 0
\(445\) 19.7640 28.3180i 0.936906 1.34240i
\(446\) −28.5019 + 20.7078i −1.34960 + 0.980545i
\(447\) 0 0
\(448\) 10.6194 + 32.6833i 0.501721 + 1.54414i
\(449\) 11.9663 0.564724 0.282362 0.959308i \(-0.408882\pi\)
0.282362 + 0.959308i \(0.408882\pi\)
\(450\) 0 0
\(451\) −12.1490 −0.572076
\(452\) −9.76257 30.0461i −0.459193 1.41325i
\(453\) 0 0
\(454\) −57.1306 + 41.5078i −2.68127 + 1.94806i
\(455\) 9.54417 3.30264i 0.447438 0.154830i
\(456\) 0 0
\(457\) −8.22154 −0.384587 −0.192294 0.981337i \(-0.561593\pi\)
−0.192294 + 0.981337i \(0.561593\pi\)
\(458\) −4.33913 3.15257i −0.202754 0.147310i
\(459\) 0 0
\(460\) −0.900131 47.4171i −0.0419688 2.21083i
\(461\) −0.393120 1.20990i −0.0183094 0.0563506i 0.941484 0.337057i \(-0.109431\pi\)
−0.959794 + 0.280706i \(0.909431\pi\)
\(462\) 0 0
\(463\) 10.0976 31.0771i 0.469273 1.44428i −0.384254 0.923227i \(-0.625541\pi\)
0.853527 0.521048i \(-0.174459\pi\)
\(464\) −23.5768 72.5618i −1.09452 3.36860i
\(465\) 0 0
\(466\) 0.436385 1.34305i 0.0202151 0.0622158i
\(467\) 11.6779 + 8.48450i 0.540389 + 0.392616i 0.824230 0.566256i \(-0.191609\pi\)
−0.283840 + 0.958872i \(0.591609\pi\)
\(468\) 0 0
\(469\) −16.9856 12.3407i −0.784321 0.569843i
\(470\) −0.218706 11.5210i −0.0100881 0.531423i
\(471\) 0 0
\(472\) 9.35227 6.79482i 0.430473 0.312757i
\(473\) −0.862060 2.65315i −0.0396375 0.121992i
\(474\) 0 0
\(475\) −4.62850 + 3.63901i −0.212370 + 0.166969i
\(476\) 34.6250 1.58703
\(477\) 0 0
\(478\) −15.2382 + 11.0712i −0.696977 + 0.506383i
\(479\) −13.6415 + 9.91113i −0.623296 + 0.452851i −0.854071 0.520156i \(-0.825874\pi\)
0.230775 + 0.973007i \(0.425874\pi\)
\(480\) 0 0
\(481\) 9.92398 + 7.21020i 0.452495 + 0.328757i
\(482\) 6.22196 0.283403
\(483\) 0 0
\(484\) −15.8670 + 48.8336i −0.721227 + 2.21971i
\(485\) −23.0371 7.00467i −1.04606 0.318066i
\(486\) 0 0
\(487\) 12.3061 37.8744i 0.557644 1.71625i −0.131212 0.991354i \(-0.541887\pi\)
0.688856 0.724898i \(-0.258113\pi\)
\(488\) −19.4686 + 59.9181i −0.881301 + 2.71236i
\(489\) 0 0
\(490\) 14.2842 20.4665i 0.645295 0.924580i
\(491\) −4.33411 + 13.3390i −0.195596 + 0.601981i 0.804374 + 0.594124i \(0.202501\pi\)
−0.999969 + 0.00785739i \(0.997499\pi\)
\(492\) 0 0
\(493\) −23.4168 −1.05464
\(494\) 6.85324 + 4.97917i 0.308342 + 0.224024i
\(495\) 0 0
\(496\) 73.6133 53.4832i 3.30534 2.40147i
\(497\) −8.16834 + 5.93464i −0.366400 + 0.266205i
\(498\) 0 0
\(499\) 15.2315 0.681857 0.340929 0.940089i \(-0.389259\pi\)
0.340929 + 0.940089i \(0.389259\pi\)
\(500\) 31.5624 49.0930i 1.41151 2.19550i
\(501\) 0 0
\(502\) 5.13055 + 15.7902i 0.228988 + 0.704752i
\(503\) 19.2004 13.9499i 0.856104 0.621996i −0.0707185 0.997496i \(-0.522529\pi\)
0.926822 + 0.375501i \(0.122529\pi\)
\(504\) 0 0
\(505\) 18.2920 + 24.1973i 0.813982 + 1.07676i
\(506\) 9.52843 + 6.92281i 0.423590 + 0.307756i
\(507\) 0 0
\(508\) 85.4620 + 62.0918i 3.79176 + 2.75488i
\(509\) 3.86570 11.8974i 0.171344 0.527343i −0.828103 0.560575i \(-0.810580\pi\)
0.999448 + 0.0332320i \(0.0105800\pi\)
\(510\) 0 0
\(511\) −1.72071 5.29581i −0.0761198 0.234273i
\(512\) −0.752345 + 2.31548i −0.0332493 + 0.102331i
\(513\) 0 0
\(514\) −10.9803 33.7940i −0.484321 1.49059i
\(515\) −2.92886 0.890552i −0.129061 0.0392424i
\(516\) 0 0
\(517\) 1.67384 + 1.21612i 0.0736154 + 0.0534847i
\(518\) −20.7703 −0.912595
\(519\) 0 0
\(520\) −49.5594 15.0691i −2.17333 0.660823i
\(521\) −22.6232 + 16.4367i −0.991141 + 0.720106i −0.960171 0.279414i \(-0.909860\pi\)
−0.0309702 + 0.999520i \(0.509860\pi\)
\(522\) 0 0
\(523\) 4.85196 + 14.9328i 0.212162 + 0.652966i 0.999343 + 0.0362446i \(0.0115395\pi\)
−0.787181 + 0.616722i \(0.788460\pi\)
\(524\) 15.9222 0.695564
\(525\) 0 0
\(526\) 18.7460 0.817362
\(527\) −8.62993 26.5602i −0.375926 1.15698i
\(528\) 0 0
\(529\) 5.25252 3.81618i 0.228370 0.165921i
\(530\) −0.290640 15.3103i −0.0126246 0.665038i
\(531\) 0 0
\(532\) −10.3703 −0.449609
\(533\) −24.3915 17.7214i −1.05651 0.767601i
\(534\) 0 0
\(535\) −14.8482 19.6418i −0.641945 0.849187i
\(536\) 33.2764 + 102.414i 1.43732 + 4.42362i
\(537\) 0 0
\(538\) −19.6956 + 60.6168i −0.849137 + 2.61338i
\(539\) 1.38479 + 4.26196i 0.0596473 + 0.183576i
\(540\) 0 0
\(541\) −7.40971 + 22.8048i −0.318569 + 0.980453i 0.655692 + 0.755028i \(0.272377\pi\)
−0.974261 + 0.225425i \(0.927623\pi\)
\(542\) −63.0224 45.7885i −2.70705 1.96678i
\(543\) 0 0
\(544\) −54.4409 39.5536i −2.33413 1.69585i
\(545\) 7.28796 2.52191i 0.312182 0.108027i
\(546\) 0 0
\(547\) 4.55219 3.30736i 0.194637 0.141412i −0.486198 0.873848i \(-0.661617\pi\)
0.680836 + 0.732436i \(0.261617\pi\)
\(548\) 33.0853 + 101.826i 1.41333 + 4.34980i
\(549\) 0 0
\(550\) 4.99888 + 13.6048i 0.213153 + 0.580112i
\(551\) 7.01341 0.298781
\(552\) 0 0
\(553\) 5.46490 3.97048i 0.232391 0.168842i
\(554\) 18.6663 13.5618i 0.793053 0.576187i
\(555\) 0 0
\(556\) −77.3626 56.2072i −3.28090 2.38372i
\(557\) 42.4247 1.79759 0.898796 0.438366i \(-0.144443\pi\)
0.898796 + 0.438366i \(0.144443\pi\)
\(558\) 0 0
\(559\) 2.13932 6.58414i 0.0904835 0.278480i
\(560\) 45.6670 15.8025i 1.92978 0.667778i
\(561\) 0 0
\(562\) −14.2538 + 43.8686i −0.601259 + 1.85048i
\(563\) −1.78796 + 5.50279i −0.0753537 + 0.231915i −0.981638 0.190754i \(-0.938907\pi\)
0.906284 + 0.422669i \(0.138907\pi\)
\(564\) 0 0
\(565\) −12.7885 + 4.42531i −0.538018 + 0.186174i
\(566\) −7.98793 + 24.5843i −0.335758 + 1.03336i
\(567\) 0 0
\(568\) 51.7853 2.17286
\(569\) −17.8029 12.9346i −0.746336 0.542245i 0.148353 0.988934i \(-0.452603\pi\)
−0.894689 + 0.446690i \(0.852603\pi\)
\(570\) 0 0
\(571\) −27.1946 + 19.7580i −1.13806 + 0.826847i −0.986847 0.161654i \(-0.948317\pi\)
−0.151210 + 0.988502i \(0.548317\pi\)
\(572\) 12.1977 8.86216i 0.510012 0.370546i
\(573\) 0 0
\(574\) 51.0499 2.13078
\(575\) −20.3001 + 0.771002i −0.846572 + 0.0321530i
\(576\) 0 0
\(577\) 12.4333 + 38.2658i 0.517605 + 1.59303i 0.778491 + 0.627656i \(0.215985\pi\)
−0.260886 + 0.965370i \(0.584015\pi\)
\(578\) 3.35205 2.43541i 0.139427 0.101300i
\(579\) 0 0
\(580\) −65.6998 + 22.7346i −2.72803 + 0.944002i
\(581\) 12.1128 + 8.80043i 0.502522 + 0.365103i
\(582\) 0 0
\(583\) 2.22438 + 1.61611i 0.0921243 + 0.0669323i
\(584\) −8.82549 + 27.1621i −0.365201 + 1.12397i
\(585\) 0 0
\(586\) −13.9665 42.9846i −0.576952 1.77568i
\(587\) 0.872353 2.68483i 0.0360059 0.110815i −0.931438 0.363899i \(-0.881445\pi\)
0.967444 + 0.253085i \(0.0814452\pi\)
\(588\) 0 0
\(589\) 2.58469 + 7.95485i 0.106500 + 0.327774i
\(590\) −4.84066 6.40339i −0.199287 0.263623i
\(591\) 0 0
\(592\) 47.4844 + 34.4994i 1.95160 + 1.41792i
\(593\) 24.6805 1.01351 0.506754 0.862091i \(-0.330845\pi\)
0.506754 + 0.862091i \(0.330845\pi\)
\(594\) 0 0
\(595\) −0.281501 14.8289i −0.0115404 0.607927i
\(596\) 2.98134 2.16607i 0.122120 0.0887256i
\(597\) 0 0
\(598\) 9.03200 + 27.7976i 0.369346 + 1.13673i
\(599\) 7.71547 0.315245 0.157623 0.987499i \(-0.449617\pi\)
0.157623 + 0.987499i \(0.449617\pi\)
\(600\) 0 0
\(601\) 22.6506 0.923938 0.461969 0.886896i \(-0.347143\pi\)
0.461969 + 0.886896i \(0.347143\pi\)
\(602\) 3.62234 + 11.1484i 0.147636 + 0.454376i
\(603\) 0 0
\(604\) −29.7543 + 21.6177i −1.21068 + 0.879613i
\(605\) 21.0431 + 6.39837i 0.855522 + 0.260131i
\(606\) 0 0
\(607\) −24.6423 −1.00020 −0.500099 0.865968i \(-0.666703\pi\)
−0.500099 + 0.865968i \(0.666703\pi\)
\(608\) 16.3052 + 11.8464i 0.661264 + 0.480436i
\(609\) 0 0
\(610\) 41.8555 + 12.7266i 1.69468 + 0.515286i
\(611\) 1.58663 + 4.88315i 0.0641883 + 0.197551i
\(612\) 0 0
\(613\) −12.9180 + 39.7574i −0.521751 + 1.60579i 0.248901 + 0.968529i \(0.419931\pi\)
−0.770652 + 0.637256i \(0.780069\pi\)
\(614\) 9.40045 + 28.9316i 0.379371 + 1.16758i
\(615\) 0 0
\(616\) −4.86646 + 14.9774i −0.196075 + 0.603458i
\(617\) 12.8949 + 9.36871i 0.519130 + 0.377170i 0.816276 0.577662i \(-0.196035\pi\)
−0.297146 + 0.954832i \(0.596035\pi\)
\(618\) 0 0
\(619\) 38.1613 + 27.7258i 1.53383 + 1.11440i 0.954059 + 0.299619i \(0.0968595\pi\)
0.579775 + 0.814777i \(0.303141\pi\)
\(620\) −49.9990 66.1405i −2.00801 2.65627i
\(621\) 0 0
\(622\) 40.3544 29.3192i 1.61806 1.17559i
\(623\) −8.05113 24.7788i −0.322562 0.992743i
\(624\) 0 0
\(625\) −21.2818 13.1182i −0.851270 0.524727i
\(626\) −26.0630 −1.04169
\(627\) 0 0
\(628\) 21.6601 15.7370i 0.864332 0.627974i
\(629\) 14.5739 10.5886i 0.581101 0.422195i
\(630\) 0 0
\(631\) −26.1825 19.0227i −1.04231 0.757282i −0.0715741 0.997435i \(-0.522802\pi\)
−0.970735 + 0.240153i \(0.922802\pi\)
\(632\) −34.6462 −1.37815
\(633\) 0 0
\(634\) −6.20802 + 19.1063i −0.246552 + 0.758809i
\(635\) 25.8974 37.1058i 1.02771 1.47250i
\(636\) 0 0
\(637\) −3.43656 + 10.5766i −0.136161 + 0.419061i
\(638\) 5.33526 16.4203i 0.211225 0.650084i
\(639\) 0 0
\(640\) −43.8658 13.3379i −1.73395 0.527226i
\(641\) −5.56360 + 17.1230i −0.219749 + 0.676317i 0.779033 + 0.626982i \(0.215710\pi\)
−0.998782 + 0.0493350i \(0.984290\pi\)
\(642\) 0 0
\(643\) 21.8891 0.863224 0.431612 0.902059i \(-0.357945\pi\)
0.431612 + 0.902059i \(0.357945\pi\)
\(644\) −28.9475 21.0316i −1.14069 0.828761i
\(645\) 0 0
\(646\) 10.0644 7.31220i 0.395978 0.287695i
\(647\) 15.3926 11.1834i 0.605147 0.439665i −0.242555 0.970138i \(-0.577985\pi\)
0.847702 + 0.530473i \(0.177985\pi\)
\(648\) 0 0
\(649\) 1.44129 0.0565755
\(650\) −9.80876 + 34.6059i −0.384731 + 1.35736i
\(651\) 0 0
\(652\) −39.1366 120.450i −1.53271 4.71719i
\(653\) −1.87669 + 1.36349i −0.0734405 + 0.0533576i −0.623900 0.781504i \(-0.714453\pi\)
0.550459 + 0.834862i \(0.314453\pi\)
\(654\) 0 0
\(655\) −0.129447 6.81903i −0.00505793 0.266442i
\(656\) −116.709 84.7937i −4.55670 3.31064i
\(657\) 0 0
\(658\) −7.03341 5.11007i −0.274191 0.199211i
\(659\) −2.22239 + 6.83980i −0.0865719 + 0.266441i −0.984966 0.172750i \(-0.944735\pi\)
0.898394 + 0.439191i \(0.144735\pi\)
\(660\) 0 0
\(661\) 13.2943 + 40.9158i 0.517090 + 1.59144i 0.779447 + 0.626468i \(0.215500\pi\)
−0.262358 + 0.964971i \(0.584500\pi\)
\(662\) −20.9719 + 64.5450i −0.815098 + 2.50861i
\(663\) 0 0
\(664\) −23.7300 73.0336i −0.920904 2.83425i
\(665\) 0.0843105 + 4.44131i 0.00326942 + 0.172226i
\(666\) 0 0
\(667\) 19.5772 + 14.2236i 0.758031 + 0.550742i
\(668\) −23.7461 −0.918765
\(669\) 0 0
\(670\) 70.6639 24.4523i 2.72998 0.944676i
\(671\) −6.35478 + 4.61702i −0.245324 + 0.178238i
\(672\) 0 0
\(673\) −9.20966 28.3444i −0.355006 1.09260i −0.956006 0.293348i \(-0.905231\pi\)
0.600999 0.799250i \(-0.294769\pi\)
\(674\) −34.9961 −1.34800
\(675\) 0 0
\(676\) −30.4464 −1.17102
\(677\) 8.26144 + 25.4261i 0.317513 + 0.977204i 0.974708 + 0.223483i \(0.0717428\pi\)
−0.657195 + 0.753721i \(0.728257\pi\)
\(678\) 0 0
\(679\) −14.6969 + 10.6780i −0.564017 + 0.409782i
\(680\) −43.5372 + 62.3802i −1.66958 + 2.39217i
\(681\) 0 0
\(682\) 20.5907 0.788457
\(683\) 23.0529 + 16.7489i 0.882096 + 0.640880i 0.933805 0.357782i \(-0.116467\pi\)
−0.0517093 + 0.998662i \(0.516467\pi\)
\(684\) 0 0
\(685\) 43.3403 14.9974i 1.65595 0.573020i
\(686\) −15.6246 48.0876i −0.596550 1.83599i
\(687\) 0 0
\(688\) 10.2362 31.5039i 0.390253 1.20107i
\(689\) 2.10849 + 6.48926i 0.0803270 + 0.247221i
\(690\) 0 0
\(691\) 10.7065 32.9512i 0.407294 1.25352i −0.511671 0.859182i \(-0.670973\pi\)
0.918965 0.394340i \(-0.129027\pi\)
\(692\) −11.3068 8.21486i −0.429820 0.312282i
\(693\) 0 0
\(694\) −13.0464 9.47878i −0.495235 0.359810i
\(695\) −23.4430 + 33.5892i −0.889245 + 1.27411i
\(696\) 0 0
\(697\) −35.8203 + 26.0249i −1.35679 + 0.985765i
\(698\) −18.8640 58.0574i −0.714012 2.19750i
\(699\) 0 0
\(700\) −15.1867 41.3317i −0.574003 1.56219i
\(701\) −0.973305 −0.0367612 −0.0183806 0.999831i \(-0.505851\pi\)
−0.0183806 + 0.999831i \(0.505851\pi\)
\(702\) 0 0
\(703\) −4.36494 + 3.17131i −0.164627 + 0.119608i
\(704\) 17.7786 12.9169i 0.670058 0.486826i
\(705\) 0 0
\(706\) −10.5540 7.66790i −0.397204 0.288585i
\(707\) 22.8854 0.860696
\(708\) 0 0
\(709\) −3.49938 + 10.7700i −0.131422 + 0.404475i −0.995016 0.0997119i \(-0.968208\pi\)
0.863594 + 0.504187i \(0.168208\pi\)
\(710\) −0.682499 35.9527i −0.0256137 1.34928i
\(711\) 0 0
\(712\) −41.2941 + 127.090i −1.54756 + 4.76290i
\(713\) −8.91808 + 27.4470i −0.333985 + 1.02790i
\(714\) 0 0
\(715\) −3.89459 5.15190i −0.145649 0.192670i
\(716\) 25.2078 77.5816i 0.942060 2.89936i
\(717\) 0 0
\(718\) −77.6312 −2.89717
\(719\) −24.8627 18.0638i −0.927224 0.673667i 0.0180878 0.999836i \(-0.494242\pi\)
−0.945311 + 0.326169i \(0.894242\pi\)
\(720\) 0 0
\(721\) −1.86852 + 1.35756i −0.0695875 + 0.0505583i
\(722\) 38.2891 27.8186i 1.42497 1.03530i
\(723\) 0 0
\(724\) 1.05888 0.0393529
\(725\) 10.2707 + 27.9526i 0.381445 + 1.03813i
\(726\) 0 0
\(727\) −2.02973 6.24688i −0.0752787 0.231684i 0.906336 0.422558i \(-0.138868\pi\)
−0.981615 + 0.190874i \(0.938868\pi\)
\(728\) −31.6174 + 22.9714i −1.17182 + 0.851377i
\(729\) 0 0
\(730\) 18.9740 + 5.76924i 0.702258 + 0.213529i
\(731\) −8.22510 5.97589i −0.304216 0.221026i
\(732\) 0 0
\(733\) 25.8300 + 18.7666i 0.954051 + 0.693159i 0.951762 0.306838i \(-0.0992711\pi\)
0.00228977 + 0.999997i \(0.499271\pi\)
\(734\) −12.2134 + 37.5891i −0.450806 + 1.38744i
\(735\) 0 0
\(736\) 21.4889 + 66.1360i 0.792091 + 2.43781i
\(737\) −4.14885 + 12.7688i −0.152825 + 0.470346i
\(738\) 0 0
\(739\) −4.73017 14.5580i −0.174002 0.535524i 0.825584 0.564279i \(-0.190846\pi\)
−0.999586 + 0.0287550i \(0.990846\pi\)
\(740\) 30.6095 43.8574i 1.12523 1.61223i
\(741\) 0 0
\(742\) −9.34676 6.79082i −0.343130 0.249299i
\(743\) −16.5455 −0.606995 −0.303498 0.952832i \(-0.598154\pi\)
−0.303498 + 0.952832i \(0.598154\pi\)
\(744\) 0 0
\(745\) −0.951905 1.25921i −0.0348751 0.0461340i
\(746\) 71.8225 52.1821i 2.62961 1.91052i
\(747\) 0 0
\(748\) −6.84217 21.0580i −0.250175 0.769959i
\(749\) −18.5769 −0.678786
\(750\) 0 0
\(751\) 46.0279 1.67958 0.839791 0.542911i \(-0.182678\pi\)
0.839791 + 0.542911i \(0.182678\pi\)
\(752\) 7.59174 + 23.3650i 0.276842 + 0.852033i
\(753\) 0 0
\(754\) 34.6632 25.1843i 1.26236 0.917159i
\(755\) 9.50018 + 12.5672i 0.345747 + 0.457366i
\(756\) 0 0
\(757\) −26.5282 −0.964184 −0.482092 0.876121i \(-0.660123\pi\)
−0.482092 + 0.876121i \(0.660123\pi\)
\(758\) 32.9463 + 23.9369i 1.19666 + 0.869427i
\(759\) 0 0
\(760\) 13.0395 18.6831i 0.472994 0.677706i
\(761\) 8.78353 + 27.0329i 0.318403 + 0.979943i 0.974331 + 0.225120i \(0.0722774\pi\)
−0.655928 + 0.754823i \(0.727723\pi\)
\(762\) 0 0
\(763\) 1.79800 5.53366i 0.0650918 0.200332i
\(764\) 12.7756 + 39.3192i 0.462204 + 1.42252i
\(765\) 0 0
\(766\) 6.64947 20.4650i 0.240255 0.739429i
\(767\) 2.89365 + 2.10236i 0.104484 + 0.0759119i
\(768\) 0 0
\(769\) 7.24841 + 5.26628i 0.261384 + 0.189907i 0.710757 0.703438i \(-0.248353\pi\)
−0.449373 + 0.893344i \(0.648353\pi\)
\(770\) 10.4624 + 3.18121i 0.377039 + 0.114643i
\(771\) 0 0
\(772\) 69.3744 50.4034i 2.49684 1.81406i
\(773\) −7.13959 21.9734i −0.256793 0.790329i −0.993471 0.114085i \(-0.963607\pi\)
0.736678 0.676244i \(-0.236393\pi\)
\(774\) 0 0
\(775\) −27.9197 + 21.9509i −1.00290 + 0.788501i
\(776\) 93.1752 3.34479
\(777\) 0 0
\(778\) 2.33609 1.69727i 0.0837530 0.0608501i
\(779\) 10.7283 7.79455i 0.384380 0.279269i
\(780\) 0 0
\(781\) 5.22343 + 3.79504i 0.186909 + 0.135797i
\(782\) 42.9232 1.53493
\(783\) 0 0
\(784\) −16.4433 + 50.6072i −0.587260 + 1.80740i
\(785\) −6.91581 9.14848i −0.246836 0.326523i
\(786\) 0 0
\(787\) −0.628511 + 1.93436i −0.0224040 + 0.0689524i −0.961633 0.274338i \(-0.911541\pi\)
0.939229 + 0.343290i \(0.111541\pi\)
\(788\) 27.6440 85.0794i 0.984776 3.03083i
\(789\) 0 0
\(790\) 0.456615 + 24.0536i 0.0162456 + 0.855788i
\(791\) −3.15503 + 9.71018i −0.112180 + 0.345254i
\(792\) 0 0
\(793\) −19.4931 −0.692220
\(794\) 52.6376 + 38.2435i 1.86804 + 1.35721i
\(795\) 0 0
\(796\) 8.52449 6.19340i 0.302142 0.219519i
\(797\) −9.86379 + 7.16646i −0.349393 + 0.253849i −0.748614 0.663006i \(-0.769281\pi\)
0.399221 + 0.916855i \(0.369281\pi\)
\(798\) 0 0
\(799\) 7.54024 0.266754
\(800\) −23.3370 + 82.3343i −0.825086 + 2.91096i
\(801\) 0 0
\(802\) 1.65501 + 5.09359i 0.0584404 + 0.179861i
\(803\) −2.88075 + 2.09299i −0.101659 + 0.0738599i
\(804\) 0 0
\(805\) −8.77191 + 12.5684i −0.309169 + 0.442978i
\(806\) 41.3396 + 30.0350i 1.45612 + 1.05794i
\(807\) 0 0
\(808\) −94.9616 68.9936i −3.34074 2.42719i
\(809\) −2.72972 + 8.40121i −0.0959718 + 0.295371i −0.987506 0.157583i \(-0.949630\pi\)
0.891534 + 0.452954i \(0.149630\pi\)
\(810\) 0 0
\(811\) −4.30102 13.2372i −0.151029 0.464820i 0.846708 0.532058i \(-0.178581\pi\)
−0.997737 + 0.0672381i \(0.978581\pi\)
\(812\) −16.2086 + 49.8850i −0.568811 + 1.75062i
\(813\) 0 0
\(814\) 4.10438 + 12.6320i 0.143858 + 0.442750i
\(815\) −51.2673 + 17.7404i −1.79581 + 0.621419i
\(816\) 0 0
\(817\) 2.46344 + 1.78980i 0.0861850 + 0.0626170i
\(818\) 17.9085 0.626158
\(819\) 0 0
\(820\) −75.2330 + 107.794i −2.62725 + 3.76433i
\(821\) −23.8603 + 17.3355i −0.832731 + 0.605015i −0.920331 0.391141i \(-0.872080\pi\)
0.0875994 + 0.996156i \(0.472080\pi\)
\(822\) 0 0
\(823\) −12.9682 39.9121i −0.452044 1.39125i −0.874571 0.484898i \(-0.838857\pi\)
0.422527 0.906350i \(-0.361143\pi\)
\(824\) 11.8460 0.412675
\(825\) 0 0
\(826\) −6.05624 −0.210724
\(827\) −11.5781 35.6336i −0.402609 1.23910i −0.922875 0.385099i \(-0.874167\pi\)
0.520266 0.854004i \(-0.325833\pi\)
\(828\) 0 0
\(829\) 7.73108 5.61696i 0.268512 0.195085i −0.445379 0.895342i \(-0.646931\pi\)
0.713891 + 0.700257i \(0.246931\pi\)
\(830\) −50.3918 + 17.4374i −1.74913 + 0.605263i
\(831\) 0 0
\(832\) 54.5355 1.89068
\(833\) 13.2126 + 9.59954i 0.457791 + 0.332604i
\(834\) 0 0
\(835\) 0.193056 + 10.1698i 0.00668099 + 0.351941i
\(836\) 2.04925 + 6.30695i 0.0708748 + 0.218130i
\(837\) 0 0
\(838\) −17.7311 + 54.5708i −0.612512 + 1.88512i
\(839\) −16.9128 52.0522i −0.583895 1.79704i −0.603665 0.797238i \(-0.706293\pi\)
0.0197702 0.999805i \(-0.493707\pi\)
\(840\) 0 0
\(841\) 2.00037 6.15651i 0.0689783 0.212294i
\(842\) −48.5570 35.2787i −1.67338 1.21579i
\(843\) 0 0
\(844\) 100.603 + 73.0922i 3.46289 + 2.51594i
\(845\) 0.247529 + 13.0394i 0.00851527 + 0.448567i
\(846\) 0 0
\(847\) 13.4248 9.75371i 0.461283 0.335141i
\(848\) 10.0887 + 31.0499i 0.346448 + 1.06626i
\(849\) 0 0
\(850\) 43.8821 + 29.4042i 1.50514 + 1.00856i
\(851\) −18.6159 −0.638144
\(852\) 0 0
\(853\) 12.3834 8.99706i 0.423999 0.308053i −0.355246 0.934773i \(-0.615603\pi\)
0.779245 + 0.626720i \(0.215603\pi\)
\(854\) 26.7026 19.4005i 0.913743 0.663873i
\(855\) 0 0
\(856\) 77.0836 + 56.0045i 2.63466 + 1.91419i
\(857\) 8.66910 0.296131 0.148065 0.988978i \(-0.452695\pi\)
0.148065 + 0.988978i \(0.452695\pi\)
\(858\) 0 0
\(859\) −9.39653 + 28.9195i −0.320605 + 0.986722i 0.652780 + 0.757547i \(0.273603\pi\)
−0.973385 + 0.229174i \(0.926397\pi\)
\(860\) −28.8787 8.78088i −0.984755 0.299425i
\(861\) 0 0
\(862\) 25.2531 77.7211i 0.860125 2.64719i
\(863\) 5.57545 17.1595i 0.189791 0.584115i −0.810207 0.586143i \(-0.800646\pi\)
0.999998 + 0.00202803i \(0.000645543\pi\)
\(864\) 0 0
\(865\) −3.42627 + 4.90917i −0.116497 + 0.166917i
\(866\) 0.478808 1.47362i 0.0162706 0.0500756i
\(867\) 0 0
\(868\) −62.5548 −2.12325
\(869\) −3.49465 2.53901i −0.118548 0.0861301i
\(870\) 0 0
\(871\) −26.9551 + 19.5840i −0.913338 + 0.663579i
\(872\) −24.1432 + 17.5411i −0.817591 + 0.594015i
\(873\) 0 0
\(874\) −12.8556 −0.434848
\(875\) −17.5778 + 6.84006i −0.594237 + 0.231236i
\(876\) 0 0
\(877\) 6.89285 + 21.2140i 0.232755 + 0.716346i 0.997411 + 0.0719076i \(0.0229087\pi\)
−0.764656 + 0.644438i \(0.777091\pi\)
\(878\) −27.8352 + 20.2235i −0.939393 + 0.682509i
\(879\) 0 0
\(880\) −18.6349 24.6508i −0.628181 0.830980i
\(881\) 6.27761 + 4.56095i 0.211498 + 0.153662i 0.688491 0.725245i \(-0.258273\pi\)
−0.476993 + 0.878907i \(0.658273\pi\)
\(882\) 0 0
\(883\) 16.1421 + 11.7279i 0.543224 + 0.394675i 0.825281 0.564722i \(-0.191017\pi\)
−0.282057 + 0.959398i \(0.591017\pi\)
\(884\) 16.9798 52.2584i 0.571092 1.75764i
\(885\) 0 0
\(886\) −11.8861 36.5816i −0.399320 1.22898i
\(887\) −2.65844 + 8.18183i −0.0892616 + 0.274719i −0.985716 0.168418i \(-0.946134\pi\)
0.896454 + 0.443137i \(0.146134\pi\)
\(888\) 0 0
\(889\) −10.5496 32.4684i −0.353823 1.08895i
\(890\) 88.7783 + 26.9940i 2.97585 + 0.904841i
\(891\) 0 0
\(892\) −55.3715 40.2297i −1.85397 1.34699i
\(893\) −2.25832 −0.0755719
\(894\) 0 0
\(895\) −33.4310 10.1651i −1.11748 0.339781i
\(896\) −27.9851 + 20.3323i −0.934916 + 0.679256i
\(897\) 0 0
\(898\) 9.93611 + 30.5802i 0.331572 + 1.02047i
\(899\) 42.3057 1.41097
\(900\) 0 0
\(901\) 10.0203 0.333824
\(902\) −10.0879 31.0472i −0.335889 1.03376i
\(903\) 0 0
\(904\) 42.3652 30.7801i 1.40905 1.02373i
\(905\) −0.00860869 0.453488i −0.000286163 0.0150745i
\(906\) 0 0
\(907\) 6.26125 0.207902 0.103951 0.994582i \(-0.466852\pi\)
0.103951 + 0.994582i \(0.466852\pi\)
\(908\) −110.989 80.6385i −3.68331 2.67608i
\(909\) 0 0
\(910\) 16.3649 + 21.6481i 0.542491 + 0.717627i
\(911\) −0.279838 0.861253i −0.00927145 0.0285346i 0.946314 0.323250i \(-0.104775\pi\)
−0.955585 + 0.294715i \(0.904775\pi\)
\(912\) 0 0
\(913\) 2.95862 9.10571i 0.0979162 0.301355i
\(914\) −6.82669 21.0104i −0.225807 0.694962i
\(915\) 0 0
\(916\) 3.21988 9.90978i 0.106388 0.327428i
\(917\) −4.16293 3.02455i −0.137472 0.0998794i
\(918\) 0 0
\(919\) −35.5913 25.8586i −1.17405 0.852997i −0.182561 0.983194i \(-0.558439\pi\)
−0.991488 + 0.130198i \(0.958439\pi\)
\(920\) 74.2889 25.7067i 2.44923 0.847526i
\(921\) 0 0
\(922\) 2.76551 2.00926i 0.0910771 0.0661714i
\(923\) 4.95129 + 15.2385i 0.162974 + 0.501582i
\(924\) 0 0
\(925\) −19.0317 12.7526i −0.625760 0.419304i
\(926\) 87.8029 2.88538
\(927\) 0 0
\(928\) 82.4707 59.9184i 2.70723 1.96692i
\(929\) −29.7271 + 21.5980i −0.975313 + 0.708606i −0.956656 0.291220i \(-0.905939\pi\)
−0.0186568 + 0.999826i \(0.505939\pi\)
\(930\) 0 0
\(931\) −3.95722 2.87509i −0.129693 0.0942273i
\(932\) 2.74347 0.0898652
\(933\) 0 0
\(934\) −11.9857 + 36.8883i −0.392185 + 1.20702i
\(935\) −8.96295 + 3.10152i −0.293120 + 0.101430i
\(936\) 0 0
\(937\) 7.61696 23.4426i 0.248835 0.765836i −0.746147 0.665782i \(-0.768098\pi\)
0.994982 0.100055i \(-0.0319017\pi\)
\(938\) 17.4333 53.6542i 0.569217 1.75187i
\(939\) 0 0
\(940\) 21.1554 7.32055i 0.690012 0.238770i
\(941\) 18.2777 56.2530i 0.595836 1.83379i 0.0453159 0.998973i \(-0.485571\pi\)
0.550520 0.834822i \(-0.314429\pi\)
\(942\) 0 0
\(943\) 45.7546 1.48998
\(944\) 13.8456 + 10.0594i 0.450635 + 0.327406i
\(945\) 0 0
\(946\) 6.06439 4.40604i 0.197170 0.143253i
\(947\) −24.3482 + 17.6900i −0.791210 + 0.574848i −0.908322 0.418271i \(-0.862636\pi\)
0.117112 + 0.993119i \(0.462636\pi\)
\(948\) 0 0
\(949\) −8.83661 −0.286849
\(950\) −13.1428 8.80664i −0.426410 0.285725i
\(951\) 0 0
\(952\) 17.7354 + 54.5841i 0.574809 + 1.76908i
\(953\) −16.6975 + 12.1315i −0.540886 + 0.392977i −0.824414 0.565987i \(-0.808495\pi\)
0.283528 + 0.958964i \(0.408495\pi\)
\(954\) 0 0
\(955\) 16.7355 5.79109i 0.541547 0.187395i
\(956\) −29.6036 21.5083i −0.957449 0.695628i
\(957\) 0 0
\(958\) −36.6553 26.6316i −1.18428 0.860429i
\(959\) 10.6924 32.9078i 0.345275 1.06265i
\(960\) 0 0
\(961\) 6.01162 + 18.5019i 0.193923 + 0.596834i
\(962\) −10.1856 + 31.3480i −0.328396 + 1.01070i
\(963\) 0 0
\(964\) 3.73527 + 11.4960i 0.120305 + 0.370260i
\(965\) −22.1504 29.3013i −0.713047 0.943244i
\(966\) 0 0
\(967\) 18.2850 + 13.2849i 0.588007 + 0.427212i 0.841602 0.540098i \(-0.181613\pi\)
−0.253595 + 0.967311i \(0.581613\pi\)
\(968\) −85.1103 −2.73555
\(969\) 0 0
\(970\) −1.22799 64.6881i −0.0394284 2.07701i
\(971\) 19.5281 14.1880i 0.626687 0.455315i −0.228564 0.973529i \(-0.573403\pi\)
0.855251 + 0.518214i \(0.173403\pi\)
\(972\) 0 0
\(973\) 9.54981 + 29.3913i 0.306153 + 0.942242i
\(974\) 107.007 3.42874
\(975\) 0 0
\(976\) −93.2708 −2.98553
\(977\) −7.12302 21.9224i −0.227886 0.701360i −0.997986 0.0634371i \(-0.979794\pi\)
0.770100 0.637923i \(-0.220206\pi\)
\(978\) 0 0
\(979\) −13.4789 + 9.79299i −0.430787 + 0.312985i
\(980\) 46.3901 + 14.1054i 1.48188 + 0.450581i
\(981\) 0 0
\(982\) −37.6870 −1.20264
\(983\) 24.1664 + 17.5579i 0.770787 + 0.560010i 0.902200 0.431318i \(-0.141951\pi\)
−0.131413 + 0.991328i \(0.541951\pi\)
\(984\) 0 0
\(985\) −36.6619 11.1474i −1.16814 0.355187i
\(986\) −19.4440 59.8424i −0.619222 1.90577i
\(987\) 0 0
\(988\) −5.08550 + 15.6515i −0.161791 + 0.497942i
\(989\) 3.24661 + 9.99204i 0.103236 + 0.317728i
\(990\) 0 0
\(991\) 5.14700 15.8408i 0.163500 0.503201i −0.835423 0.549608i \(-0.814777\pi\)
0.998923 + 0.0464072i \(0.0147772\pi\)
\(992\) 98.3550 + 71.4591i 3.12277 + 2.26883i
\(993\) 0 0
\(994\) −21.9487 15.9466i −0.696169 0.505797i
\(995\) −2.72177 3.60045i −0.0862858 0.114142i
\(996\) 0 0
\(997\) −10.1074 + 7.34343i −0.320103 + 0.232569i −0.736220 0.676743i \(-0.763391\pi\)
0.416116 + 0.909311i \(0.363391\pi\)
\(998\) 12.6474 + 38.9246i 0.400346 + 1.23214i
\(999\) 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 225.2.h.d.181.3 12
3.2 odd 2 75.2.g.c.31.1 12
15.2 even 4 375.2.i.d.349.6 24
15.8 even 4 375.2.i.d.349.1 24
15.14 odd 2 375.2.g.c.151.3 12
25.11 even 5 5625.2.a.p.1.6 6
25.14 even 10 5625.2.a.q.1.1 6
25.21 even 5 inner 225.2.h.d.46.3 12
75.2 even 20 1875.2.b.f.1249.1 12
75.11 odd 10 1875.2.a.j.1.1 6
75.14 odd 10 1875.2.a.k.1.6 6
75.23 even 20 1875.2.b.f.1249.12 12
75.29 odd 10 375.2.g.c.226.3 12
75.47 even 20 375.2.i.d.274.1 24
75.53 even 20 375.2.i.d.274.6 24
75.71 odd 10 75.2.g.c.46.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.c.31.1 12 3.2 odd 2
75.2.g.c.46.1 yes 12 75.71 odd 10
225.2.h.d.46.3 12 25.21 even 5 inner
225.2.h.d.181.3 12 1.1 even 1 trivial
375.2.g.c.151.3 12 15.14 odd 2
375.2.g.c.226.3 12 75.29 odd 10
375.2.i.d.274.1 24 75.47 even 20
375.2.i.d.274.6 24 75.53 even 20
375.2.i.d.349.1 24 15.8 even 4
375.2.i.d.349.6 24 15.2 even 4
1875.2.a.j.1.1 6 75.11 odd 10
1875.2.a.k.1.6 6 75.14 odd 10
1875.2.b.f.1249.1 12 75.2 even 20
1875.2.b.f.1249.12 12 75.23 even 20
5625.2.a.p.1.6 6 25.11 even 5
5625.2.a.q.1.1 6 25.14 even 10