Properties

Label 315.2.bf.b.289.7
Level $315$
Weight $2$
Character 315.289
Analytic conductor $2.515$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(109,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bf (of order \(6\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} - 630 x^{7} + 584 x^{6} - 800 x^{5} + 734 x^{4} - 188 x^{3} + 32 x^{2} - 8 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.7
Root \(0.202747 - 0.0543258i\) of defining polynomial
Character \(\chi\) \(=\) 315.289
Dual form 315.2.bf.b.109.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54296 + 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(0.881181 - 2.05512i) q^{5} +(2.40898 + 1.09398i) q^{7} -1.47113i q^{8} +O(q^{10})\) \(q+(1.54296 + 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(0.881181 - 2.05512i) q^{5} +(2.40898 + 1.09398i) q^{7} -1.47113i q^{8} +(3.19038 - 2.38598i) q^{10} +(-1.03925 - 1.80003i) q^{11} +3.13023i q^{13} +(2.74241 + 3.83396i) q^{14} +(2.48481 - 4.30382i) q^{16} +(-1.84483 + 1.06512i) q^{17} +(-3.86880 + 6.70095i) q^{19} +(2.60736 - 0.310523i) q^{20} -3.70316i q^{22} +(4.79479 + 2.76827i) q^{23} +(-3.44704 - 3.62187i) q^{25} +(-2.78849 + 4.82981i) q^{26} +(0.301877 + 3.09218i) q^{28} -4.01368 q^{29} +(-1.45594 - 2.52177i) q^{31} +(5.11984 - 2.95594i) q^{32} -3.79533 q^{34} +(4.37102 - 3.98675i) q^{35} +(3.04424 + 1.75759i) q^{37} +(-11.9388 + 6.89286i) q^{38} +(-3.02335 - 1.29633i) q^{40} -7.99038 q^{41} -4.99038i q^{43} +(1.22038 - 2.11376i) q^{44} +(4.93210 + 8.54266i) q^{46} +(-2.11376 - 1.22038i) q^{47} +(4.60639 + 5.27078i) q^{49} +(-2.09218 - 8.65910i) q^{50} +(-3.18333 + 1.83790i) q^{52} +(-8.58394 + 4.95594i) q^{53} +(-4.61504 + 0.549626i) q^{55} +(1.60939 - 3.54393i) q^{56} +(-6.19294 - 3.57549i) q^{58} +(-1.47797 - 2.55992i) q^{59} +(5.44729 - 9.43499i) q^{61} -5.18797i q^{62} +0.593684 q^{64} +(6.43300 + 2.75830i) q^{65} +(-3.32501 + 1.91970i) q^{67} +(-2.16637 - 1.25075i) q^{68} +(10.2958 - 2.25756i) q^{70} +15.0248 q^{71} +(-7.40771 + 4.27684i) q^{73} +(3.13142 + 5.42378i) q^{74} -9.08617 q^{76} +(-0.534324 - 5.47316i) q^{77} +(4.05677 - 7.02653i) q^{79} +(-6.65530 - 8.89903i) q^{80} +(-12.3288 - 7.11804i) q^{82} +8.75128i q^{83} +(0.563307 + 4.72992i) q^{85} +(4.44556 - 7.69994i) q^{86} +(-2.64808 + 1.52887i) q^{88} +(-0.309330 + 0.535776i) q^{89} +(-3.42443 + 7.54067i) q^{91} +6.50151i q^{92} +(-2.17429 - 3.76598i) q^{94} +(10.3622 + 13.8556i) q^{95} +0.296842i q^{97} +(2.41212 + 12.2361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54296 + 0.890827i 1.09104 + 0.629910i 0.933852 0.357660i \(-0.116425\pi\)
0.157184 + 0.987569i \(0.449759\pi\)
\(3\) 0 0
\(4\) 0.587145 + 1.01696i 0.293572 + 0.508482i
\(5\) 0.881181 2.05512i 0.394076 0.919078i
\(6\) 0 0
\(7\) 2.40898 + 1.09398i 0.910510 + 0.413487i
\(8\) 1.47113i 0.520123i
\(9\) 0 0
\(10\) 3.19038 2.38598i 1.00889 0.754514i
\(11\) −1.03925 1.80003i −0.313345 0.542729i 0.665739 0.746184i \(-0.268116\pi\)
−0.979084 + 0.203455i \(0.934783\pi\)
\(12\) 0 0
\(13\) 3.13023i 0.868170i 0.900872 + 0.434085i \(0.142928\pi\)
−0.900872 + 0.434085i \(0.857072\pi\)
\(14\) 2.74241 + 3.83396i 0.732939 + 1.02467i
\(15\) 0 0
\(16\) 2.48481 4.30382i 0.621203 1.07596i
\(17\) −1.84483 + 1.06512i −0.447438 + 0.258329i −0.706748 0.707466i \(-0.749838\pi\)
0.259310 + 0.965794i \(0.416505\pi\)
\(18\) 0 0
\(19\) −3.86880 + 6.70095i −0.887563 + 1.53730i −0.0448157 + 0.998995i \(0.514270\pi\)
−0.842747 + 0.538309i \(0.819063\pi\)
\(20\) 2.60736 0.310523i 0.583024 0.0694350i
\(21\) 0 0
\(22\) 3.70316i 0.789516i
\(23\) 4.79479 + 2.76827i 0.999783 + 0.577225i 0.908184 0.418571i \(-0.137469\pi\)
0.0915990 + 0.995796i \(0.470802\pi\)
\(24\) 0 0
\(25\) −3.44704 3.62187i −0.689408 0.724374i
\(26\) −2.78849 + 4.82981i −0.546869 + 0.947204i
\(27\) 0 0
\(28\) 0.301877 + 3.09218i 0.0570495 + 0.584366i
\(29\) −4.01368 −0.745322 −0.372661 0.927968i \(-0.621555\pi\)
−0.372661 + 0.927968i \(0.621555\pi\)
\(30\) 0 0
\(31\) −1.45594 2.52177i −0.261495 0.452923i 0.705144 0.709064i \(-0.250882\pi\)
−0.966639 + 0.256141i \(0.917549\pi\)
\(32\) 5.11984 2.95594i 0.905069 0.522542i
\(33\) 0 0
\(34\) −3.79533 −0.650894
\(35\) 4.37102 3.98675i 0.738837 0.673884i
\(36\) 0 0
\(37\) 3.04424 + 1.75759i 0.500470 + 0.288947i 0.728908 0.684612i \(-0.240028\pi\)
−0.228437 + 0.973559i \(0.573362\pi\)
\(38\) −11.9388 + 6.89286i −1.93673 + 1.11817i
\(39\) 0 0
\(40\) −3.02335 1.29633i −0.478034 0.204968i
\(41\) −7.99038 −1.24789 −0.623944 0.781469i \(-0.714471\pi\)
−0.623944 + 0.781469i \(0.714471\pi\)
\(42\) 0 0
\(43\) 4.99038i 0.761026i −0.924776 0.380513i \(-0.875747\pi\)
0.924776 0.380513i \(-0.124253\pi\)
\(44\) 1.22038 2.11376i 0.183979 0.318661i
\(45\) 0 0
\(46\) 4.93210 + 8.54266i 0.727199 + 1.25955i
\(47\) −2.11376 1.22038i −0.308323 0.178010i 0.337853 0.941199i \(-0.390299\pi\)
−0.646176 + 0.763189i \(0.723633\pi\)
\(48\) 0 0
\(49\) 4.60639 + 5.27078i 0.658056 + 0.752969i
\(50\) −2.09218 8.65910i −0.295878 1.22458i
\(51\) 0 0
\(52\) −3.18333 + 1.83790i −0.441449 + 0.254871i
\(53\) −8.58394 + 4.95594i −1.17910 + 0.680751i −0.955805 0.294001i \(-0.905013\pi\)
−0.223290 + 0.974752i \(0.571680\pi\)
\(54\) 0 0
\(55\) −4.61504 + 0.549626i −0.622292 + 0.0741116i
\(56\) 1.60939 3.54393i 0.215064 0.473577i
\(57\) 0 0
\(58\) −6.19294 3.57549i −0.813173 0.469485i
\(59\) −1.47797 2.55992i −0.192415 0.333273i 0.753635 0.657293i \(-0.228299\pi\)
−0.946050 + 0.324020i \(0.894965\pi\)
\(60\) 0 0
\(61\) 5.44729 9.43499i 0.697454 1.20803i −0.271892 0.962328i \(-0.587649\pi\)
0.969346 0.245699i \(-0.0790174\pi\)
\(62\) 5.18797i 0.658873i
\(63\) 0 0
\(64\) 0.593684 0.0742104
\(65\) 6.43300 + 2.75830i 0.797916 + 0.342125i
\(66\) 0 0
\(67\) −3.32501 + 1.91970i −0.406215 + 0.234528i −0.689162 0.724607i \(-0.742021\pi\)
0.282947 + 0.959135i \(0.408688\pi\)
\(68\) −2.16637 1.25075i −0.262711 0.151676i
\(69\) 0 0
\(70\) 10.2958 2.25756i 1.23058 0.269830i
\(71\) 15.0248 1.78312 0.891559 0.452905i \(-0.149612\pi\)
0.891559 + 0.452905i \(0.149612\pi\)
\(72\) 0 0
\(73\) −7.40771 + 4.27684i −0.867007 + 0.500567i −0.866352 0.499433i \(-0.833542\pi\)
−0.000654464 1.00000i \(0.500208\pi\)
\(74\) 3.13142 + 5.42378i 0.364021 + 0.630502i
\(75\) 0 0
\(76\) −9.08617 −1.04226
\(77\) −0.534324 5.47316i −0.0608919 0.623725i
\(78\) 0 0
\(79\) 4.05677 7.02653i 0.456422 0.790546i −0.542347 0.840155i \(-0.682464\pi\)
0.998769 + 0.0496086i \(0.0157974\pi\)
\(80\) −6.65530 8.89903i −0.744085 0.994942i
\(81\) 0 0
\(82\) −12.3288 7.11804i −1.36149 0.786056i
\(83\) 8.75128i 0.960577i 0.877110 + 0.480289i \(0.159468\pi\)
−0.877110 + 0.480289i \(0.840532\pi\)
\(84\) 0 0
\(85\) 0.563307 + 4.72992i 0.0610992 + 0.513032i
\(86\) 4.44556 7.69994i 0.479377 0.830306i
\(87\) 0 0
\(88\) −2.64808 + 1.52887i −0.282286 + 0.162978i
\(89\) −0.309330 + 0.535776i −0.0327890 + 0.0567921i −0.881954 0.471335i \(-0.843772\pi\)
0.849165 + 0.528127i \(0.177106\pi\)
\(90\) 0 0
\(91\) −3.42443 + 7.54067i −0.358977 + 0.790477i
\(92\) 6.50151i 0.677829i
\(93\) 0 0
\(94\) −2.17429 3.76598i −0.224261 0.388431i
\(95\) 10.3622 + 13.8556i 1.06313 + 1.42155i
\(96\) 0 0
\(97\) 0.296842i 0.0301397i 0.999886 + 0.0150699i \(0.00479707\pi\)
−0.999886 + 0.0150699i \(0.995203\pi\)
\(98\) 2.41212 + 12.2361i 0.243660 + 1.23603i
\(99\) 0 0
\(100\) 1.65940 5.63207i 0.165940 0.563207i
\(101\) 4.12939 + 7.15232i 0.410890 + 0.711682i 0.994987 0.100001i \(-0.0318847\pi\)
−0.584097 + 0.811684i \(0.698551\pi\)
\(102\) 0 0
\(103\) 14.7974 + 8.54331i 1.45804 + 0.841797i 0.998915 0.0465766i \(-0.0148312\pi\)
0.459121 + 0.888374i \(0.348164\pi\)
\(104\) 4.60498 0.451555
\(105\) 0 0
\(106\) −17.6595 −1.71525
\(107\) −5.46507 3.15526i −0.528329 0.305031i 0.212007 0.977268i \(-0.432000\pi\)
−0.740336 + 0.672238i \(0.765333\pi\)
\(108\) 0 0
\(109\) 1.22338 + 2.11895i 0.117178 + 0.202959i 0.918648 0.395076i \(-0.129282\pi\)
−0.801470 + 0.598035i \(0.795948\pi\)
\(110\) −7.61044 3.26315i −0.725627 0.311130i
\(111\) 0 0
\(112\) 10.6942 7.64948i 1.01051 0.722808i
\(113\) 10.1570i 0.955489i −0.878499 0.477745i \(-0.841454\pi\)
0.878499 0.477745i \(-0.158546\pi\)
\(114\) 0 0
\(115\) 9.91422 7.41452i 0.924505 0.691408i
\(116\) −2.35661 4.08177i −0.218806 0.378983i
\(117\) 0 0
\(118\) 5.26647i 0.484817i
\(119\) −5.60939 + 0.547624i −0.514212 + 0.0502006i
\(120\) 0 0
\(121\) 3.33993 5.78493i 0.303630 0.525902i
\(122\) 16.8099 9.70519i 1.52190 0.878667i
\(123\) 0 0
\(124\) 1.70970 2.96128i 0.153535 0.265931i
\(125\) −10.4808 + 3.89256i −0.937435 + 0.348161i
\(126\) 0 0
\(127\) 8.86977i 0.787065i −0.919311 0.393532i \(-0.871253\pi\)
0.919311 0.393532i \(-0.128747\pi\)
\(128\) −9.32366 5.38302i −0.824103 0.475796i
\(129\) 0 0
\(130\) 7.46868 + 9.98663i 0.655046 + 0.875886i
\(131\) 2.67075 4.62588i 0.233345 0.404165i −0.725446 0.688279i \(-0.758366\pi\)
0.958790 + 0.284115i \(0.0916997\pi\)
\(132\) 0 0
\(133\) −16.6506 + 11.9101i −1.44379 + 1.03273i
\(134\) −6.84047 −0.590926
\(135\) 0 0
\(136\) 1.56692 + 2.71399i 0.134363 + 0.232723i
\(137\) −11.3483 + 6.55196i −0.969553 + 0.559772i −0.899100 0.437744i \(-0.855778\pi\)
−0.0704529 + 0.997515i \(0.522444\pi\)
\(138\) 0 0
\(139\) −0.243164 −0.0206249 −0.0103125 0.999947i \(-0.503283\pi\)
−0.0103125 + 0.999947i \(0.503283\pi\)
\(140\) 6.62080 + 2.10437i 0.559560 + 0.177852i
\(141\) 0 0
\(142\) 23.1827 + 13.3845i 1.94544 + 1.12320i
\(143\) 5.63451 3.25309i 0.471181 0.272037i
\(144\) 0 0
\(145\) −3.53678 + 8.24860i −0.293714 + 0.685009i
\(146\) −15.2397 −1.26125
\(147\) 0 0
\(148\) 4.12785i 0.339307i
\(149\) −1.16864 + 2.02415i −0.0957388 + 0.165824i −0.909917 0.414791i \(-0.863855\pi\)
0.814178 + 0.580615i \(0.197188\pi\)
\(150\) 0 0
\(151\) 5.55677 + 9.62460i 0.452203 + 0.783239i 0.998523 0.0543378i \(-0.0173048\pi\)
−0.546319 + 0.837577i \(0.683971\pi\)
\(152\) 9.85798 + 5.69151i 0.799588 + 0.461642i
\(153\) 0 0
\(154\) 4.05120 8.92084i 0.326455 0.718862i
\(155\) −6.46548 + 0.770003i −0.519320 + 0.0618481i
\(156\) 0 0
\(157\) −9.80185 + 5.65910i −0.782273 + 0.451645i −0.837235 0.546843i \(-0.815829\pi\)
0.0549624 + 0.998488i \(0.482496\pi\)
\(158\) 12.5188 7.22775i 0.995945 0.575009i
\(159\) 0 0
\(160\) −1.56331 13.1266i −0.123590 1.03775i
\(161\) 8.52212 + 11.9142i 0.671637 + 0.938967i
\(162\) 0 0
\(163\) 1.82166 + 1.05174i 0.142683 + 0.0823783i 0.569642 0.821893i \(-0.307082\pi\)
−0.426959 + 0.904271i \(0.640415\pi\)
\(164\) −4.69151 8.12593i −0.366345 0.634529i
\(165\) 0 0
\(166\) −7.79587 + 13.5028i −0.605077 + 1.04802i
\(167\) 3.58600i 0.277493i −0.990328 0.138747i \(-0.955693\pi\)
0.990328 0.138747i \(-0.0443074\pi\)
\(168\) 0 0
\(169\) 3.20165 0.246281
\(170\) −3.34438 + 7.79987i −0.256502 + 0.598223i
\(171\) 0 0
\(172\) 5.07504 2.93007i 0.386968 0.223416i
\(173\) 13.4580 + 7.77000i 1.02320 + 0.590742i 0.915028 0.403390i \(-0.132168\pi\)
0.108168 + 0.994133i \(0.465502\pi\)
\(174\) 0 0
\(175\) −4.34159 12.4960i −0.328193 0.944611i
\(176\) −10.3293 −0.778603
\(177\) 0 0
\(178\) −0.954567 + 0.551120i −0.0715478 + 0.0413082i
\(179\) −7.86783 13.6275i −0.588069 1.01857i −0.994485 0.104877i \(-0.966555\pi\)
0.406416 0.913688i \(-0.366778\pi\)
\(180\) 0 0
\(181\) −4.98692 −0.370675 −0.185337 0.982675i \(-0.559338\pi\)
−0.185337 + 0.982675i \(0.559338\pi\)
\(182\) −12.0012 + 8.58437i −0.889586 + 0.636315i
\(183\) 0 0
\(184\) 4.07249 7.05376i 0.300228 0.520010i
\(185\) 6.29460 4.70752i 0.462788 0.346104i
\(186\) 0 0
\(187\) 3.83448 + 2.21384i 0.280405 + 0.161892i
\(188\) 2.86615i 0.209036i
\(189\) 0 0
\(190\) 3.64542 + 30.6095i 0.264467 + 2.22065i
\(191\) 5.90421 10.2264i 0.427213 0.739955i −0.569411 0.822053i \(-0.692829\pi\)
0.996624 + 0.0820978i \(0.0261620\pi\)
\(192\) 0 0
\(193\) 21.4238 12.3690i 1.54212 0.890342i 0.543412 0.839466i \(-0.317132\pi\)
0.998705 0.0508752i \(-0.0162011\pi\)
\(194\) −0.264435 + 0.458014i −0.0189853 + 0.0328835i
\(195\) 0 0
\(196\) −2.65558 + 7.77925i −0.189684 + 0.555661i
\(197\) 19.5526i 1.39307i 0.717525 + 0.696533i \(0.245275\pi\)
−0.717525 + 0.696533i \(0.754725\pi\)
\(198\) 0 0
\(199\) −11.1201 19.2605i −0.788281 1.36534i −0.927019 0.375014i \(-0.877638\pi\)
0.138738 0.990329i \(-0.455695\pi\)
\(200\) −5.32824 + 5.07104i −0.376764 + 0.358577i
\(201\) 0 0
\(202\) 14.7143i 1.03529i
\(203\) −9.66889 4.39091i −0.678623 0.308181i
\(204\) 0 0
\(205\) −7.04097 + 16.4212i −0.491763 + 1.14691i
\(206\) 15.2212 + 26.3639i 1.06051 + 1.83686i
\(207\) 0 0
\(208\) 13.4720 + 7.77804i 0.934112 + 0.539310i
\(209\) 16.0826 1.11245
\(210\) 0 0
\(211\) 23.6191 1.62601 0.813003 0.582259i \(-0.197831\pi\)
0.813003 + 0.582259i \(0.197831\pi\)
\(212\) −10.0800 5.81971i −0.692299 0.399699i
\(213\) 0 0
\(214\) −5.62158 9.73687i −0.384283 0.665598i
\(215\) −10.2558 4.39743i −0.699442 0.299902i
\(216\) 0 0
\(217\) −0.748566 7.66767i −0.0508159 0.520515i
\(218\) 4.35927i 0.295247i
\(219\) 0 0
\(220\) −3.26865 4.37062i −0.220372 0.294667i
\(221\) −3.33406 5.77476i −0.224273 0.388452i
\(222\) 0 0
\(223\) 25.1420i 1.68363i −0.539765 0.841815i \(-0.681487\pi\)
0.539765 0.841815i \(-0.318513\pi\)
\(224\) 15.5674 1.51978i 1.04014 0.101545i
\(225\) 0 0
\(226\) 9.04812 15.6718i 0.601872 1.04247i
\(227\) 20.4990 11.8351i 1.36057 0.785524i 0.370869 0.928685i \(-0.379060\pi\)
0.989699 + 0.143161i \(0.0457266\pi\)
\(228\) 0 0
\(229\) 0.203158 0.351880i 0.0134251 0.0232529i −0.859235 0.511581i \(-0.829060\pi\)
0.872660 + 0.488328i \(0.162393\pi\)
\(230\) 21.9023 2.60844i 1.44419 0.171995i
\(231\) 0 0
\(232\) 5.90465i 0.387659i
\(233\) −6.20531 3.58264i −0.406523 0.234706i 0.282772 0.959187i \(-0.408746\pi\)
−0.689295 + 0.724481i \(0.742080\pi\)
\(234\) 0 0
\(235\) −4.37062 + 3.26865i −0.285108 + 0.213223i
\(236\) 1.73557 3.00609i 0.112976 0.195680i
\(237\) 0 0
\(238\) −9.14289 4.15204i −0.592646 0.269137i
\(239\) 10.0922 0.652809 0.326404 0.945230i \(-0.394163\pi\)
0.326404 + 0.945230i \(0.394163\pi\)
\(240\) 0 0
\(241\) 2.30338 + 3.98957i 0.148374 + 0.256991i 0.930627 0.365970i \(-0.119263\pi\)
−0.782253 + 0.622961i \(0.785929\pi\)
\(242\) 10.3067 5.95060i 0.662542 0.382519i
\(243\) 0 0
\(244\) 12.7934 0.819013
\(245\) 14.8912 4.82218i 0.951361 0.308078i
\(246\) 0 0
\(247\) −20.9755 12.1102i −1.33464 0.770556i
\(248\) −3.70985 + 2.14188i −0.235576 + 0.136010i
\(249\) 0 0
\(250\) −19.6391 3.33057i −1.24208 0.210643i
\(251\) 0.311597 0.0196678 0.00983390 0.999952i \(-0.496870\pi\)
0.00983390 + 0.999952i \(0.496870\pi\)
\(252\) 0 0
\(253\) 11.5077i 0.723482i
\(254\) 7.90143 13.6857i 0.495780 0.858715i
\(255\) 0 0
\(256\) −10.1844 17.6398i −0.636522 1.10249i
\(257\) 2.16689 + 1.25106i 0.135167 + 0.0780387i 0.566059 0.824365i \(-0.308468\pi\)
−0.430892 + 0.902404i \(0.641801\pi\)
\(258\) 0 0
\(259\) 5.41075 + 7.56437i 0.336207 + 0.470027i
\(260\) 0.972008 + 8.16165i 0.0602814 + 0.506164i
\(261\) 0 0
\(262\) 8.24171 4.75835i 0.509174 0.293972i
\(263\) 4.00546 2.31255i 0.246987 0.142598i −0.371397 0.928474i \(-0.621121\pi\)
0.618384 + 0.785876i \(0.287788\pi\)
\(264\) 0 0
\(265\) 2.62105 + 22.0081i 0.161010 + 1.35195i
\(266\) −36.3010 + 3.54393i −2.22576 + 0.217292i
\(267\) 0 0
\(268\) −3.90452 2.25428i −0.238507 0.137702i
\(269\) −6.01165 10.4125i −0.366537 0.634860i 0.622485 0.782632i \(-0.286123\pi\)
−0.989022 + 0.147772i \(0.952790\pi\)
\(270\) 0 0
\(271\) 2.73467 4.73660i 0.166120 0.287728i −0.770933 0.636917i \(-0.780210\pi\)
0.937052 + 0.349189i \(0.113543\pi\)
\(272\) 10.5864i 0.641898i
\(273\) 0 0
\(274\) −23.3466 −1.41042
\(275\) −2.93714 + 9.96879i −0.177116 + 0.601141i
\(276\) 0 0
\(277\) −25.8162 + 14.9050i −1.55114 + 0.895553i −0.553093 + 0.833119i \(0.686553\pi\)
−0.998049 + 0.0624333i \(0.980114\pi\)
\(278\) −0.375192 0.216617i −0.0225025 0.0129918i
\(279\) 0 0
\(280\) −5.86503 6.43034i −0.350503 0.384287i
\(281\) −7.78511 −0.464421 −0.232210 0.972666i \(-0.574596\pi\)
−0.232210 + 0.972666i \(0.574596\pi\)
\(282\) 0 0
\(283\) −2.26417 + 1.30722i −0.134591 + 0.0777062i −0.565784 0.824554i \(-0.691426\pi\)
0.431193 + 0.902260i \(0.358093\pi\)
\(284\) 8.82174 + 15.2797i 0.523474 + 0.906683i
\(285\) 0 0
\(286\) 11.5917 0.685434
\(287\) −19.2487 8.74136i −1.13621 0.515986i
\(288\) 0 0
\(289\) −6.23106 + 10.7925i −0.366533 + 0.634853i
\(290\) −12.8052 + 9.57657i −0.751946 + 0.562356i
\(291\) 0 0
\(292\) −8.69879 5.02225i −0.509058 0.293905i
\(293\) 12.7559i 0.745210i −0.927990 0.372605i \(-0.878465\pi\)
0.927990 0.372605i \(-0.121535\pi\)
\(294\) 0 0
\(295\) −6.56331 + 0.781653i −0.382131 + 0.0455096i
\(296\) 2.58565 4.47848i 0.150288 0.260306i
\(297\) 0 0
\(298\) −3.60633 + 2.08211i −0.208909 + 0.120614i
\(299\) −8.66534 + 15.0088i −0.501129 + 0.867982i
\(300\) 0 0
\(301\) 5.45940 12.0217i 0.314675 0.692922i
\(302\) 19.8005i 1.13939i
\(303\) 0 0
\(304\) 19.2265 + 33.3012i 1.10271 + 1.90996i
\(305\) −14.5900 19.5088i −0.835420 1.11707i
\(306\) 0 0
\(307\) 13.1919i 0.752900i −0.926437 0.376450i \(-0.877145\pi\)
0.926437 0.376450i \(-0.122855\pi\)
\(308\) 5.25228 3.75693i 0.299277 0.214071i
\(309\) 0 0
\(310\) −10.6619 4.57154i −0.605555 0.259646i
\(311\) −7.14113 12.3688i −0.404937 0.701371i 0.589378 0.807858i \(-0.299373\pi\)
−0.994314 + 0.106487i \(0.966040\pi\)
\(312\) 0 0
\(313\) 4.13218 + 2.38572i 0.233565 + 0.134849i 0.612215 0.790691i \(-0.290279\pi\)
−0.378651 + 0.925540i \(0.623612\pi\)
\(314\) −20.1651 −1.13798
\(315\) 0 0
\(316\) 9.52764 0.535971
\(317\) −16.2854 9.40240i −0.914681 0.528091i −0.0327466 0.999464i \(-0.510425\pi\)
−0.881934 + 0.471372i \(0.843759\pi\)
\(318\) 0 0
\(319\) 4.17121 + 7.22474i 0.233543 + 0.404508i
\(320\) 0.523143 1.22009i 0.0292446 0.0682052i
\(321\) 0 0
\(322\) 2.53582 + 25.9748i 0.141316 + 1.44752i
\(323\) 16.4829i 0.917131i
\(324\) 0 0
\(325\) 11.3373 10.7900i 0.628879 0.598523i
\(326\) 1.87383 + 3.24557i 0.103782 + 0.179755i
\(327\) 0 0
\(328\) 11.7549i 0.649055i
\(329\) −3.75693 5.25228i −0.207126 0.289568i
\(330\) 0 0
\(331\) −8.88708 + 15.3929i −0.488478 + 0.846069i −0.999912 0.0132538i \(-0.995781\pi\)
0.511434 + 0.859322i \(0.329114\pi\)
\(332\) −8.89973 + 5.13826i −0.488436 + 0.281999i
\(333\) 0 0
\(334\) 3.19451 5.53305i 0.174796 0.302755i
\(335\) 1.01527 + 8.52490i 0.0554700 + 0.465765i
\(336\) 0 0
\(337\) 3.86675i 0.210635i 0.994439 + 0.105318i \(0.0335860\pi\)
−0.994439 + 0.105318i \(0.966414\pi\)
\(338\) 4.94001 + 2.85212i 0.268701 + 0.155135i
\(339\) 0 0
\(340\) −4.47941 + 3.35001i −0.242930 + 0.181680i
\(341\) −3.02617 + 5.24148i −0.163876 + 0.283842i
\(342\) 0 0
\(343\) 5.33057 + 17.7365i 0.287824 + 0.957683i
\(344\) −7.34150 −0.395827
\(345\) 0 0
\(346\) 13.8435 + 23.9776i 0.744229 + 1.28904i
\(347\) −8.89622 + 5.13623i −0.477574 + 0.275727i −0.719405 0.694591i \(-0.755585\pi\)
0.241831 + 0.970318i \(0.422252\pi\)
\(348\) 0 0
\(349\) −23.6180 −1.26424 −0.632122 0.774869i \(-0.717816\pi\)
−0.632122 + 0.774869i \(0.717816\pi\)
\(350\) 4.43291 23.1484i 0.236949 1.23734i
\(351\) 0 0
\(352\) −10.6416 6.14391i −0.567197 0.327472i
\(353\) 5.00354 2.88880i 0.266312 0.153755i −0.360899 0.932605i \(-0.617530\pi\)
0.627210 + 0.778850i \(0.284197\pi\)
\(354\) 0 0
\(355\) 13.2396 30.8778i 0.702685 1.63882i
\(356\) −0.726487 −0.0385037
\(357\) 0 0
\(358\) 28.0355i 1.48172i
\(359\) −15.6527 + 27.1113i −0.826118 + 1.43088i 0.0749437 + 0.997188i \(0.476122\pi\)
−0.901062 + 0.433691i \(0.857211\pi\)
\(360\) 0 0
\(361\) −20.4352 35.3948i −1.07554 1.86288i
\(362\) −7.69461 4.44248i −0.404420 0.233492i
\(363\) 0 0
\(364\) −9.67923 + 0.944946i −0.507329 + 0.0495286i
\(365\) 2.26189 + 18.9924i 0.118393 + 0.994108i
\(366\) 0 0
\(367\) 14.3344 8.27595i 0.748248 0.432001i −0.0768125 0.997046i \(-0.524474\pi\)
0.825061 + 0.565044i \(0.191141\pi\)
\(368\) 23.8283 13.7573i 1.24214 0.717148i
\(369\) 0 0
\(370\) 13.9059 1.65611i 0.722932 0.0860972i
\(371\) −26.1003 + 2.54807i −1.35506 + 0.132289i
\(372\) 0 0
\(373\) −27.8363 16.0713i −1.44131 0.832140i −0.443371 0.896338i \(-0.646218\pi\)
−0.997937 + 0.0641985i \(0.979551\pi\)
\(374\) 3.94429 + 6.83171i 0.203954 + 0.353260i
\(375\) 0 0
\(376\) −1.79533 + 3.10961i −0.0925873 + 0.160366i
\(377\) 12.5638i 0.647066i
\(378\) 0 0
\(379\) 4.98800 0.256216 0.128108 0.991760i \(-0.459110\pi\)
0.128108 + 0.991760i \(0.459110\pi\)
\(380\) −8.00657 + 18.6732i −0.410728 + 0.957914i
\(381\) 0 0
\(382\) 18.2199 10.5192i 0.932210 0.538212i
\(383\) 22.9123 + 13.2284i 1.17076 + 0.675940i 0.953860 0.300253i \(-0.0970711\pi\)
0.216903 + 0.976193i \(0.430404\pi\)
\(384\) 0 0
\(385\) −11.7188 3.72475i −0.597247 0.189831i
\(386\) 44.0746 2.24334
\(387\) 0 0
\(388\) −0.301877 + 0.174289i −0.0153255 + 0.00884818i
\(389\) 6.38580 + 11.0605i 0.323773 + 0.560791i 0.981263 0.192672i \(-0.0617154\pi\)
−0.657491 + 0.753463i \(0.728382\pi\)
\(390\) 0 0
\(391\) −11.7941 −0.596455
\(392\) 7.75401 6.77661i 0.391637 0.342270i
\(393\) 0 0
\(394\) −17.4180 + 30.1688i −0.877506 + 1.51988i
\(395\) −10.8656 14.5288i −0.546708 0.731023i
\(396\) 0 0
\(397\) −13.0954 7.56061i −0.657237 0.379456i 0.133986 0.990983i \(-0.457222\pi\)
−0.791223 + 0.611527i \(0.790556\pi\)
\(398\) 39.6242i 1.98618i
\(399\) 0 0
\(400\) −24.1531 + 5.83577i −1.20766 + 0.291789i
\(401\) 6.18029 10.7046i 0.308629 0.534561i −0.669434 0.742872i \(-0.733463\pi\)
0.978063 + 0.208311i \(0.0667965\pi\)
\(402\) 0 0
\(403\) 7.89371 4.55744i 0.393214 0.227022i
\(404\) −4.84910 + 8.39889i −0.241252 + 0.417860i
\(405\) 0 0
\(406\) −11.0071 15.3883i −0.546275 0.763708i
\(407\) 7.30630i 0.362160i
\(408\) 0 0
\(409\) −5.26435 9.11813i −0.260306 0.450863i 0.706017 0.708194i \(-0.250490\pi\)
−0.966323 + 0.257332i \(0.917157\pi\)
\(410\) −25.4924 + 19.0649i −1.25898 + 0.941549i
\(411\) 0 0
\(412\) 20.0646i 0.988513i
\(413\) −0.759892 7.78368i −0.0373918 0.383010i
\(414\) 0 0
\(415\) 17.9849 + 7.71146i 0.882845 + 0.378541i
\(416\) 9.25278 + 16.0263i 0.453655 + 0.785754i
\(417\) 0 0
\(418\) 24.8147 + 14.3268i 1.21373 + 0.700745i
\(419\) 13.3110 0.650283 0.325142 0.945665i \(-0.394588\pi\)
0.325142 + 0.945665i \(0.394588\pi\)
\(420\) 0 0
\(421\) 19.1520 0.933413 0.466707 0.884412i \(-0.345440\pi\)
0.466707 + 0.884412i \(0.345440\pi\)
\(422\) 36.4433 + 21.0405i 1.77403 + 1.02424i
\(423\) 0 0
\(424\) 7.29084 + 12.6281i 0.354074 + 0.613275i
\(425\) 10.2169 + 3.01025i 0.495594 + 0.146019i
\(426\) 0 0
\(427\) 23.4442 16.7695i 1.13454 0.811531i
\(428\) 7.41038i 0.358194i
\(429\) 0 0
\(430\) −11.9070 15.9212i −0.574205 0.767789i
\(431\) 5.44818 + 9.43653i 0.262430 + 0.454542i 0.966887 0.255205i \(-0.0821429\pi\)
−0.704457 + 0.709746i \(0.748810\pi\)
\(432\) 0 0
\(433\) 19.4869i 0.936482i 0.883601 + 0.468241i \(0.155112\pi\)
−0.883601 + 0.468241i \(0.844888\pi\)
\(434\) 5.67556 12.4977i 0.272436 0.599910i
\(435\) 0 0
\(436\) −1.43660 + 2.48826i −0.0688006 + 0.119166i
\(437\) −37.1002 + 21.4198i −1.77474 + 1.02465i
\(438\) 0 0
\(439\) 6.76549 11.7182i 0.322899 0.559278i −0.658186 0.752856i \(-0.728676\pi\)
0.981085 + 0.193578i \(0.0620091\pi\)
\(440\) 0.808572 + 6.78933i 0.0385471 + 0.323669i
\(441\) 0 0
\(442\) 11.8803i 0.565087i
\(443\) 24.9990 + 14.4332i 1.18774 + 0.685740i 0.957792 0.287463i \(-0.0928119\pi\)
0.229945 + 0.973204i \(0.426145\pi\)
\(444\) 0 0
\(445\) 0.828508 + 1.10783i 0.0392750 + 0.0525160i
\(446\) 22.3971 38.7930i 1.06054 1.83690i
\(447\) 0 0
\(448\) 1.43017 + 0.649481i 0.0675693 + 0.0306851i
\(449\) 23.4298 1.10572 0.552860 0.833274i \(-0.313536\pi\)
0.552860 + 0.833274i \(0.313536\pi\)
\(450\) 0 0
\(451\) 8.30398 + 14.3829i 0.391019 + 0.677265i
\(452\) 10.3293 5.96362i 0.485849 0.280505i
\(453\) 0 0
\(454\) 42.1722 1.97924
\(455\) 12.4794 + 13.6823i 0.585046 + 0.641437i
\(456\) 0 0
\(457\) 26.2298 + 15.1438i 1.22698 + 0.708396i 0.966397 0.257056i \(-0.0827524\pi\)
0.260582 + 0.965452i \(0.416086\pi\)
\(458\) 0.626929 0.361958i 0.0292945 0.0169132i
\(459\) 0 0
\(460\) 13.3614 + 5.72901i 0.622978 + 0.267116i
\(461\) 7.02196 0.327045 0.163523 0.986540i \(-0.447714\pi\)
0.163523 + 0.986540i \(0.447714\pi\)
\(462\) 0 0
\(463\) 2.97324i 0.138178i 0.997610 + 0.0690891i \(0.0220093\pi\)
−0.997610 + 0.0690891i \(0.977991\pi\)
\(464\) −9.97324 + 17.2742i −0.462996 + 0.801933i
\(465\) 0 0
\(466\) −6.38302 11.0557i −0.295687 0.512146i
\(467\) −20.5723 11.8774i −0.951974 0.549623i −0.0582807 0.998300i \(-0.518562\pi\)
−0.893694 + 0.448678i \(0.851895\pi\)
\(468\) 0 0
\(469\) −10.1100 + 0.987002i −0.466837 + 0.0455755i
\(470\) −9.65548 + 1.14991i −0.445374 + 0.0530416i
\(471\) 0 0
\(472\) −3.76598 + 2.17429i −0.173343 + 0.100080i
\(473\) −8.98283 + 5.18624i −0.413031 + 0.238464i
\(474\) 0 0
\(475\) 37.6059 9.08617i 1.72548 0.416902i
\(476\) −3.85044 5.38302i −0.176485 0.246730i
\(477\) 0 0
\(478\) 15.5718 + 8.99038i 0.712237 + 0.411210i
\(479\) 3.27211 + 5.66747i 0.149507 + 0.258953i 0.931045 0.364904i \(-0.118898\pi\)
−0.781539 + 0.623857i \(0.785565\pi\)
\(480\) 0 0
\(481\) −5.50168 + 9.52918i −0.250855 + 0.434493i
\(482\) 8.20765i 0.373848i
\(483\) 0 0
\(484\) 7.84408 0.356549
\(485\) 0.610046 + 0.261571i 0.0277007 + 0.0118773i
\(486\) 0 0
\(487\) −14.1395 + 8.16346i −0.640723 + 0.369922i −0.784893 0.619631i \(-0.787282\pi\)
0.144170 + 0.989553i \(0.453949\pi\)
\(488\) −13.8801 8.01368i −0.628323 0.362762i
\(489\) 0 0
\(490\) 27.2721 + 5.82503i 1.23203 + 0.263148i
\(491\) −24.9009 −1.12376 −0.561882 0.827218i \(-0.689922\pi\)
−0.561882 + 0.827218i \(0.689922\pi\)
\(492\) 0 0
\(493\) 7.40458 4.27503i 0.333485 0.192538i
\(494\) −21.5762 37.3711i −0.970761 1.68141i
\(495\) 0 0
\(496\) −14.4710 −0.649766
\(497\) 36.1945 + 16.4369i 1.62355 + 0.737297i
\(498\) 0 0
\(499\) −6.10197 + 10.5689i −0.273161 + 0.473130i −0.969670 0.244419i \(-0.921403\pi\)
0.696508 + 0.717549i \(0.254736\pi\)
\(500\) −10.1124 8.37315i −0.452238 0.374458i
\(501\) 0 0
\(502\) 0.480780 + 0.277579i 0.0214583 + 0.0123889i
\(503\) 27.8165i 1.24028i 0.784492 + 0.620139i \(0.212924\pi\)
−0.784492 + 0.620139i \(0.787076\pi\)
\(504\) 0 0
\(505\) 18.3376 2.18391i 0.816013 0.0971827i
\(506\) 10.2514 17.7559i 0.455728 0.789345i
\(507\) 0 0
\(508\) 9.02024 5.20784i 0.400208 0.231060i
\(509\) 13.9099 24.0927i 0.616547 1.06789i −0.373563 0.927605i \(-0.621864\pi\)
0.990111 0.140287i \(-0.0448025\pi\)
\(510\) 0 0
\(511\) −22.5238 + 2.19892i −0.996396 + 0.0972744i
\(512\) 14.7579i 0.652214i
\(513\) 0 0
\(514\) 2.22895 + 3.86065i 0.0983146 + 0.170286i
\(515\) 30.5968 22.8823i 1.34825 1.00832i
\(516\) 0 0
\(517\) 5.07310i 0.223115i
\(518\) 1.61001 + 16.4915i 0.0707396 + 0.724596i
\(519\) 0 0
\(520\) 4.05782 9.46379i 0.177947 0.415015i
\(521\) 16.7513 + 29.0141i 0.733887 + 1.27113i 0.955210 + 0.295929i \(0.0956291\pi\)
−0.221323 + 0.975200i \(0.571038\pi\)
\(522\) 0 0
\(523\) −11.0815 6.39790i −0.484560 0.279761i 0.237755 0.971325i \(-0.423588\pi\)
−0.722315 + 0.691564i \(0.756922\pi\)
\(524\) 6.27247 0.274014
\(525\) 0 0
\(526\) 8.24034 0.359296
\(527\) 5.37195 + 3.10149i 0.234006 + 0.135103i
\(528\) 0 0
\(529\) 3.82668 + 6.62801i 0.166377 + 0.288174i
\(530\) −15.5613 + 36.2925i −0.675938 + 1.57644i
\(531\) 0 0
\(532\) −21.8884 9.94014i −0.948984 0.430960i
\(533\) 25.0117i 1.08338i
\(534\) 0 0
\(535\) −11.3002 + 8.45102i −0.488549 + 0.365370i
\(536\) 2.82412 + 4.89153i 0.121984 + 0.211282i
\(537\) 0 0
\(538\) 21.4214i 0.923540i
\(539\) 4.70038 13.7693i 0.202460 0.593085i
\(540\) 0 0
\(541\) −12.6283 + 21.8728i −0.542933 + 0.940387i 0.455801 + 0.890082i \(0.349353\pi\)
−0.998734 + 0.0503053i \(0.983981\pi\)
\(542\) 8.43897 4.87224i 0.362485 0.209281i
\(543\) 0 0
\(544\) −6.29684 + 10.9064i −0.269975 + 0.467610i
\(545\) 5.43272 0.647007i 0.232712 0.0277147i
\(546\) 0 0
\(547\) 38.8743i 1.66214i 0.556165 + 0.831072i \(0.312272\pi\)
−0.556165 + 0.831072i \(0.687728\pi\)
\(548\) −13.3262 7.69389i −0.569268 0.328667i
\(549\) 0 0
\(550\) −13.4123 + 12.7649i −0.571904 + 0.544298i
\(551\) 15.5281 26.8955i 0.661520 1.14579i
\(552\) 0 0
\(553\) 17.4596 12.4887i 0.742458 0.531075i
\(554\) −53.1110 −2.25647
\(555\) 0 0
\(556\) −0.142773 0.247290i −0.00605491 0.0104874i
\(557\) −1.18106 + 0.681888i −0.0500433 + 0.0288925i −0.524813 0.851218i \(-0.675865\pi\)
0.474770 + 0.880110i \(0.342531\pi\)
\(558\) 0 0
\(559\) 15.6210 0.660700
\(560\) −6.29709 28.7184i −0.266101 1.21357i
\(561\) 0 0
\(562\) −12.0121 6.93519i −0.506700 0.292543i
\(563\) −9.15774 + 5.28722i −0.385953 + 0.222830i −0.680405 0.732836i \(-0.738196\pi\)
0.294452 + 0.955666i \(0.404863\pi\)
\(564\) 0 0
\(565\) −20.8738 8.95015i −0.878169 0.376536i
\(566\) −4.65803 −0.195791
\(567\) 0 0
\(568\) 22.1035i 0.927441i
\(569\) −18.9932 + 32.8973i −0.796238 + 1.37913i 0.125811 + 0.992054i \(0.459847\pi\)
−0.922050 + 0.387071i \(0.873487\pi\)
\(570\) 0 0
\(571\) 7.84550 + 13.5888i 0.328324 + 0.568674i 0.982179 0.187946i \(-0.0601829\pi\)
−0.653856 + 0.756619i \(0.726850\pi\)
\(572\) 6.61654 + 3.82006i 0.276652 + 0.159725i
\(573\) 0 0
\(574\) −21.9129 30.6348i −0.914625 1.27867i
\(575\) −6.50151 26.9084i −0.271132 1.12216i
\(576\) 0 0
\(577\) 2.98614 1.72405i 0.124315 0.0717730i −0.436553 0.899678i \(-0.643801\pi\)
0.560868 + 0.827905i \(0.310468\pi\)
\(578\) −19.2285 + 11.1016i −0.799800 + 0.461765i
\(579\) 0 0
\(580\) −10.4651 + 1.24634i −0.434541 + 0.0517514i
\(581\) −9.57377 + 21.0817i −0.397187 + 0.874615i
\(582\) 0 0
\(583\) 17.8417 + 10.3009i 0.738927 + 0.426620i
\(584\) 6.29180 + 10.8977i 0.260356 + 0.450950i
\(585\) 0 0
\(586\) 11.3633 19.6819i 0.469415 0.813051i
\(587\) 10.5983i 0.437441i 0.975788 + 0.218720i \(0.0701882\pi\)
−0.975788 + 0.218720i \(0.929812\pi\)
\(588\) 0 0
\(589\) 22.5310 0.928373
\(590\) −10.8232 4.64071i −0.445585 0.191055i
\(591\) 0 0
\(592\) 15.1287 8.73458i 0.621787 0.358989i
\(593\) −0.203007 0.117206i −0.00833648 0.00481307i 0.495826 0.868422i \(-0.334865\pi\)
−0.504162 + 0.863609i \(0.668199\pi\)
\(594\) 0 0
\(595\) −3.81746 + 12.0105i −0.156501 + 0.492384i
\(596\) −2.74464 −0.112425
\(597\) 0 0
\(598\) −26.7405 + 15.4386i −1.09350 + 0.631333i
\(599\) 12.9145 + 22.3686i 0.527673 + 0.913956i 0.999480 + 0.0322543i \(0.0102687\pi\)
−0.471807 + 0.881702i \(0.656398\pi\)
\(600\) 0 0
\(601\) −1.15592 −0.0471508 −0.0235754 0.999722i \(-0.507505\pi\)
−0.0235754 + 0.999722i \(0.507505\pi\)
\(602\) 19.1329 13.6856i 0.779799 0.557785i
\(603\) 0 0
\(604\) −6.52525 + 11.3021i −0.265509 + 0.459875i
\(605\) −8.94564 11.9615i −0.363692 0.486305i
\(606\) 0 0
\(607\) 20.1014 + 11.6056i 0.815891 + 0.471055i 0.848997 0.528397i \(-0.177207\pi\)
−0.0331064 + 0.999452i \(0.510540\pi\)
\(608\) 45.7438i 1.85516i
\(609\) 0 0
\(610\) −5.13278 43.0984i −0.207820 1.74500i
\(611\) 3.82006 6.61654i 0.154543 0.267677i
\(612\) 0 0
\(613\) 5.48319 3.16572i 0.221464 0.127862i −0.385164 0.922848i \(-0.625855\pi\)
0.606628 + 0.794986i \(0.292522\pi\)
\(614\) 11.7517 20.3545i 0.474259 0.821440i
\(615\) 0 0
\(616\) −8.05174 + 0.786061i −0.324414 + 0.0316713i
\(617\) 25.9546i 1.04489i −0.852672 0.522447i \(-0.825019\pi\)
0.852672 0.522447i \(-0.174981\pi\)
\(618\) 0 0
\(619\) −14.5481 25.1981i −0.584738 1.01280i −0.994908 0.100787i \(-0.967864\pi\)
0.410170 0.912009i \(-0.365469\pi\)
\(620\) −4.57924 6.12306i −0.183907 0.245908i
\(621\) 0 0
\(622\) 25.4460i 1.02029i
\(623\) −1.33130 + 0.952272i −0.0533375 + 0.0381520i
\(624\) 0 0
\(625\) −1.23585 + 24.9694i −0.0494341 + 0.998777i
\(626\) 4.25052 + 7.36211i 0.169885 + 0.294249i
\(627\) 0 0
\(628\) −11.5102 6.64542i −0.459307 0.265181i
\(629\) −7.48816 −0.298573
\(630\) 0 0
\(631\) −37.3609 −1.48731 −0.743657 0.668561i \(-0.766911\pi\)
−0.743657 + 0.668561i \(0.766911\pi\)
\(632\) −10.3369 5.96804i −0.411181 0.237396i
\(633\) 0 0
\(634\) −16.7518 29.0150i −0.665300 1.15233i
\(635\) −18.2284 7.81588i −0.723374 0.310164i
\(636\) 0 0
\(637\) −16.4988 + 14.4191i −0.653705 + 0.571305i
\(638\) 14.8633i 0.588443i
\(639\) 0 0
\(640\) −19.2786 + 14.4178i −0.762053 + 0.569914i
\(641\) −13.9268 24.1219i −0.550074 0.952756i −0.998269 0.0588199i \(-0.981266\pi\)
0.448195 0.893936i \(-0.352067\pi\)
\(642\) 0 0
\(643\) 20.3104i 0.800963i 0.916305 + 0.400481i \(0.131157\pi\)
−0.916305 + 0.400481i \(0.868843\pi\)
\(644\) −7.11255 + 15.6620i −0.280274 + 0.617170i
\(645\) 0 0
\(646\) 14.6834 25.4324i 0.577710 1.00062i
\(647\) −19.4275 + 11.2165i −0.763773 + 0.440964i −0.830649 0.556797i \(-0.812030\pi\)
0.0668759 + 0.997761i \(0.478697\pi\)
\(648\) 0 0
\(649\) −3.07196 + 5.32078i −0.120585 + 0.208859i
\(650\) 27.1050 6.54900i 1.06315 0.256873i
\(651\) 0 0
\(652\) 2.47008i 0.0967360i
\(653\) −17.1517 9.90257i −0.671200 0.387517i 0.125331 0.992115i \(-0.460001\pi\)
−0.796531 + 0.604598i \(0.793334\pi\)
\(654\) 0 0
\(655\) −7.15332 9.56495i −0.279503 0.373734i
\(656\) −19.8546 + 34.3892i −0.775192 + 1.34267i
\(657\) 0 0
\(658\) −1.11790 11.4508i −0.0435803 0.446399i
\(659\) 38.3567 1.49416 0.747082 0.664731i \(-0.231454\pi\)
0.747082 + 0.664731i \(0.231454\pi\)
\(660\) 0 0
\(661\) −1.48746 2.57635i −0.0578554 0.100209i 0.835647 0.549267i \(-0.185093\pi\)
−0.893503 + 0.449058i \(0.851760\pi\)
\(662\) −27.4248 + 15.8337i −1.06589 + 0.615394i
\(663\) 0 0
\(664\) 12.8743 0.499619
\(665\) 9.80443 + 44.7139i 0.380199 + 1.73393i
\(666\) 0 0
\(667\) −19.2448 11.1110i −0.745160 0.430218i
\(668\) 3.64684 2.10550i 0.141100 0.0814644i
\(669\) 0 0
\(670\) −6.02769 + 14.0580i −0.232870 + 0.543107i
\(671\) −22.6443 −0.874175
\(672\) 0 0
\(673\) 22.8397i 0.880407i 0.897898 + 0.440203i \(0.145094\pi\)
−0.897898 + 0.440203i \(0.854906\pi\)
\(674\) −3.44461 + 5.96624i −0.132681 + 0.229811i
\(675\) 0 0
\(676\) 1.87983 + 3.25596i 0.0723012 + 0.125229i
\(677\) 6.23200 + 3.59805i 0.239515 + 0.138284i 0.614954 0.788563i \(-0.289175\pi\)
−0.375439 + 0.926847i \(0.622508\pi\)
\(678\) 0 0
\(679\) −0.324740 + 0.715087i −0.0124624 + 0.0274425i
\(680\) 6.95833 0.828698i 0.266840 0.0317791i
\(681\) 0 0
\(682\) −9.33850 + 5.39159i −0.357590 + 0.206454i
\(683\) −3.94425 + 2.27721i −0.150922 + 0.0871351i −0.573559 0.819164i \(-0.694438\pi\)
0.422637 + 0.906299i \(0.361105\pi\)
\(684\) 0 0
\(685\) 3.46513 + 29.0956i 0.132396 + 1.11169i
\(686\) −7.57535 + 32.1153i −0.289228 + 1.22617i
\(687\) 0 0
\(688\) −21.4777 12.4002i −0.818830 0.472751i
\(689\) −15.5132 26.8697i −0.591008 1.02366i
\(690\) 0 0
\(691\) −1.76948 + 3.06483i −0.0673142 + 0.116592i −0.897718 0.440570i \(-0.854776\pi\)
0.830404 + 0.557162i \(0.188110\pi\)
\(692\) 18.2485i 0.693702i
\(693\) 0 0
\(694\) −18.3020 −0.694734
\(695\) −0.214272 + 0.499732i −0.00812780 + 0.0189559i
\(696\) 0 0
\(697\) 14.7409 8.51068i 0.558353 0.322365i
\(698\) −36.4416 21.0396i −1.37934 0.796360i
\(699\) 0 0
\(700\) 10.1589 11.7522i 0.383969 0.444192i
\(701\) 16.8111 0.634948 0.317474 0.948267i \(-0.397165\pi\)
0.317474 + 0.948267i \(0.397165\pi\)
\(702\) 0 0
\(703\) −23.5551 + 13.5996i −0.888398 + 0.512917i
\(704\) −0.616984 1.06865i −0.0232535 0.0402762i
\(705\) 0 0
\(706\) 10.2937 0.387407
\(707\) 2.12311 + 21.7473i 0.0798477 + 0.817892i
\(708\) 0 0
\(709\) 15.9088 27.5549i 0.597468 1.03484i −0.395726 0.918369i \(-0.629507\pi\)
0.993194 0.116476i \(-0.0371597\pi\)
\(710\) 47.9349 35.8490i 1.79896 1.34539i
\(711\) 0 0
\(712\) 0.788197 + 0.455066i 0.0295389 + 0.0170543i
\(713\) 16.1218i 0.603766i
\(714\) 0 0
\(715\) −1.72046 14.4462i −0.0643414 0.540256i
\(716\) 9.23910 16.0026i 0.345282 0.598045i
\(717\) 0 0
\(718\) −48.3029 + 27.8877i −1.80265 + 1.04076i
\(719\) −7.64037 + 13.2335i −0.284938 + 0.493527i −0.972594 0.232510i \(-0.925306\pi\)
0.687656 + 0.726036i \(0.258640\pi\)
\(720\) 0 0
\(721\) 26.3005 + 36.7689i 0.979483 + 1.36934i
\(722\) 72.8169i 2.70996i
\(723\) 0 0
\(724\) −2.92804 5.07152i −0.108820 0.188482i
\(725\) 13.8353 + 14.5370i 0.513831 + 0.539891i
\(726\) 0 0
\(727\) 19.1829i 0.711453i −0.934590 0.355726i \(-0.884234\pi\)
0.934590 0.355726i \(-0.115766\pi\)
\(728\) 11.0933 + 5.03778i 0.411146 + 0.186713i
\(729\) 0 0
\(730\) −13.4289 + 31.3194i −0.497028 + 1.15918i
\(731\) 5.31533 + 9.20643i 0.196595 + 0.340512i
\(732\) 0 0
\(733\) −42.1943 24.3609i −1.55848 0.899790i −0.997403 0.0720283i \(-0.977053\pi\)
−0.561080 0.827762i \(-0.689614\pi\)
\(734\) 29.4898 1.08849
\(735\) 0 0
\(736\) 32.7314 1.20650
\(737\) 6.91102 + 3.99008i 0.254571 + 0.146976i
\(738\) 0 0
\(739\) −4.74202 8.21343i −0.174438 0.302136i 0.765529 0.643402i \(-0.222478\pi\)
−0.939967 + 0.341266i \(0.889144\pi\)
\(740\) 8.48322 + 3.63738i 0.311849 + 0.133713i
\(741\) 0 0
\(742\) −42.5415 19.3193i −1.56175 0.709233i
\(743\) 30.2032i 1.10805i 0.832501 + 0.554023i \(0.186908\pi\)
−0.832501 + 0.554023i \(0.813092\pi\)
\(744\) 0 0
\(745\) 3.13008 + 4.18534i 0.114677 + 0.153339i
\(746\) −28.6335 49.5946i −1.04835 1.81579i
\(747\) 0 0
\(748\) 5.19937i 0.190108i
\(749\) −9.71346 13.5797i −0.354922 0.496191i
\(750\) 0 0
\(751\) 3.66467 6.34739i 0.133726 0.231620i −0.791384 0.611319i \(-0.790639\pi\)
0.925110 + 0.379699i \(0.123973\pi\)
\(752\) −10.5046 + 6.06481i −0.383062 + 0.221161i
\(753\) 0 0
\(754\) 11.1921 19.3853i 0.407593 0.705972i
\(755\) 24.6762 2.93880i 0.898060 0.106954i
\(756\) 0 0
\(757\) 14.1603i 0.514666i −0.966323 0.257333i \(-0.917156\pi\)
0.966323 0.257333i \(-0.0828438\pi\)
\(758\) 7.69626 + 4.44344i 0.279541 + 0.161393i
\(759\) 0 0
\(760\) 20.3834 15.2441i 0.739384 0.552961i
\(761\) −11.9592 + 20.7139i −0.433519 + 0.750878i −0.997173 0.0751333i \(-0.976062\pi\)
0.563654 + 0.826011i \(0.309395\pi\)
\(762\) 0 0
\(763\) 0.628994 + 6.44288i 0.0227711 + 0.233248i
\(764\) 13.8665 0.501672
\(765\) 0 0
\(766\) 23.5684 + 40.8217i 0.851562 + 1.47495i
\(767\) 8.01315 4.62639i 0.289338 0.167049i
\(768\) 0 0
\(769\) −14.1358 −0.509750 −0.254875 0.966974i \(-0.582034\pi\)
−0.254875 + 0.966974i \(0.582034\pi\)
\(770\) −14.7636 16.1866i −0.532042 0.583324i
\(771\) 0 0
\(772\) 25.1577 + 14.5248i 0.905445 + 0.522759i
\(773\) −5.85409 + 3.37986i −0.210557 + 0.121565i −0.601570 0.798820i \(-0.705458\pi\)
0.391013 + 0.920385i \(0.372125\pi\)
\(774\) 0 0
\(775\) −4.11481 + 13.9659i −0.147808 + 0.501668i
\(776\) 0.436693 0.0156764
\(777\) 0 0
\(778\) 22.7545i 0.815790i
\(779\) 30.9132 53.5432i 1.10758 1.91838i
\(780\) 0 0
\(781\) −15.6145 27.0451i −0.558731 0.967750i
\(782\) −18.1978 10.5065i −0.650753 0.375713i
\(783\) 0 0
\(784\) 34.1305 6.72819i 1.21895 0.240293i
\(785\) 2.99292 + 25.1307i 0.106822 + 0.896952i
\(786\) 0 0
\(787\) −13.3152 + 7.68754i −0.474636 + 0.274031i −0.718178 0.695859i \(-0.755024\pi\)
0.243543 + 0.969890i \(0.421690\pi\)
\(788\) −19.8843 + 11.4802i −0.708349 + 0.408966i
\(789\) 0 0
\(790\) −3.82254 32.0967i −0.136000 1.14195i
\(791\) 11.1116 24.4680i 0.395083 0.869982i
\(792\) 0 0
\(793\) 29.5337 + 17.0513i 1.04877 + 0.605509i
\(794\) −13.4704 23.3314i −0.478046 0.828000i
\(795\) 0 0
\(796\) 13.0582 22.6174i 0.462835 0.801654i
\(797\) 9.46785i 0.335369i −0.985841 0.167684i \(-0.946371\pi\)
0.985841 0.167684i \(-0.0536289\pi\)
\(798\) 0 0
\(799\) 5.19937 0.183941
\(800\) −28.3543 8.35415i −1.00248 0.295364i
\(801\) 0 0
\(802\) 19.0718 11.0111i 0.673450 0.388817i
\(803\) 15.3969 + 8.88940i 0.543344 + 0.313700i
\(804\) 0 0
\(805\) 31.9945 7.01545i 1.12766 0.247262i
\(806\) 16.2395 0.572014
\(807\) 0 0
\(808\) 10.5220 6.07488i 0.370163 0.213713i
\(809\) −2.81872 4.88217i −0.0991011 0.171648i 0.812212 0.583363i \(-0.198263\pi\)
−0.911313 + 0.411715i \(0.864930\pi\)
\(810\) 0 0
\(811\) 24.3625 0.855485 0.427742 0.903901i \(-0.359309\pi\)
0.427742 + 0.903901i \(0.359309\pi\)
\(812\) −1.21164 12.4110i −0.0425202 0.435541i
\(813\) 0 0
\(814\) 6.50865 11.2733i 0.228128 0.395129i
\(815\) 3.76666 2.81696i 0.131940 0.0986738i
\(816\) 0 0
\(817\) 33.4403 + 19.3068i 1.16993 + 0.675458i
\(818\) 18.7585i 0.655876i
\(819\) 0 0
\(820\) −20.8338 + 2.48119i −0.727549 + 0.0866471i
\(821\) −15.8731 + 27.4930i −0.553974 + 0.959512i 0.444008 + 0.896023i \(0.353556\pi\)
−0.997983 + 0.0634890i \(0.979777\pi\)
\(822\) 0 0
\(823\) −3.44299 + 1.98781i −0.120015 + 0.0692908i −0.558806 0.829299i \(-0.688740\pi\)
0.438791 + 0.898589i \(0.355407\pi\)
\(824\) 12.5683 21.7690i 0.437838 0.758358i
\(825\) 0 0
\(826\) 5.76143 12.6868i 0.200466 0.441431i
\(827\) 6.80348i 0.236580i 0.992979 + 0.118290i \(0.0377413\pi\)
−0.992979 + 0.118290i \(0.962259\pi\)
\(828\) 0 0
\(829\) 11.5303 + 19.9710i 0.400463 + 0.693623i 0.993782 0.111345i \(-0.0355159\pi\)
−0.593319 + 0.804968i \(0.702183\pi\)
\(830\) 20.8804 + 27.9199i 0.724769 + 0.969114i
\(831\) 0 0
\(832\) 1.85837i 0.0644273i
\(833\) −14.1120 4.81738i −0.488953 0.166912i
\(834\) 0 0
\(835\) −7.36967 3.15992i −0.255038 0.109354i
\(836\) 9.44278 + 16.3554i 0.326586 + 0.565663i
\(837\) 0 0
\(838\) 20.5383 + 11.8578i 0.709482 + 0.409620i
\(839\) −35.0723 −1.21083 −0.605415 0.795910i \(-0.706993\pi\)
−0.605415 + 0.795910i \(0.706993\pi\)
\(840\) 0 0
\(841\) −12.8904 −0.444495
\(842\) 29.5508 + 17.0611i 1.01839 + 0.587966i
\(843\) 0 0
\(844\) 13.8678 + 24.0198i 0.477350 + 0.826795i
\(845\) 2.82124 6.57978i 0.0970534 0.226351i
\(846\) 0 0
\(847\) 14.3745 10.2820i 0.493912 0.353292i
\(848\) 49.2583i 1.69154i
\(849\) 0 0
\(850\) 13.0827 + 13.7462i 0.448732 + 0.471491i
\(851\) 9.73100 + 16.8546i 0.333575 + 0.577768i
\(852\) 0 0
\(853\) 12.3125i 0.421571i −0.977532 0.210785i \(-0.932398\pi\)
0.977532 0.210785i \(-0.0676021\pi\)
\(854\) 51.1120 4.98987i 1.74902 0.170750i
\(855\) 0 0
\(856\) −4.64180 + 8.03984i −0.158654 + 0.274796i
\(857\) 28.7952 16.6249i 0.983624 0.567896i 0.0802617 0.996774i \(-0.474424\pi\)
0.903362 + 0.428878i \(0.141091\pi\)
\(858\) 0 0
\(859\) −1.50697 + 2.61015i −0.0514172 + 0.0890573i −0.890588 0.454810i \(-0.849707\pi\)
0.839171 + 0.543867i \(0.183041\pi\)
\(860\) −1.54963 13.0117i −0.0528418 0.443697i
\(861\) 0 0
\(862\) 19.4136i 0.661228i
\(863\) −19.2569 11.1180i −0.655513 0.378460i 0.135052 0.990838i \(-0.456880\pi\)
−0.790565 + 0.612378i \(0.790213\pi\)
\(864\) 0 0
\(865\) 27.8273 20.8111i 0.946155 0.707599i
\(866\) −17.3595 + 30.0675i −0.589899 + 1.02174i
\(867\) 0 0
\(868\) 7.35823 5.26329i 0.249755 0.178648i
\(869\) −16.8639 −0.572070
\(870\) 0 0
\(871\) −6.00909 10.4081i −0.203610 0.352663i
\(872\) 3.11726 1.79975i 0.105564 0.0609472i
\(873\) 0 0
\(874\) −76.3253 −2.58174
\(875\) −29.5066 2.08878i −0.997504 0.0706137i
\(876\) 0 0
\(877\) −12.4033 7.16105i −0.418830 0.241812i 0.275747 0.961230i \(-0.411075\pi\)
−0.694577 + 0.719419i \(0.744408\pi\)
\(878\) 20.8777 12.0538i 0.704589 0.406795i
\(879\) 0 0
\(880\) −9.10202 + 21.2280i −0.306829 + 0.715597i
\(881\) −49.9929 −1.68431 −0.842153 0.539239i \(-0.818712\pi\)
−0.842153 + 0.539239i \(0.818712\pi\)
\(882\) 0 0
\(883\) 44.3095i 1.49113i 0.666432 + 0.745566i \(0.267821\pi\)
−0.666432 + 0.745566i \(0.732179\pi\)
\(884\) 3.91515 6.78124i 0.131681 0.228078i
\(885\) 0 0
\(886\) 25.7149 + 44.5395i 0.863909 + 1.49633i
\(887\) 8.91878 + 5.14926i 0.299463 + 0.172895i 0.642202 0.766536i \(-0.278021\pi\)
−0.342738 + 0.939431i \(0.611354\pi\)
\(888\) 0 0
\(889\) 9.70339 21.3671i 0.325441 0.716630i
\(890\) 0.291470 + 2.44739i 0.00977010 + 0.0820366i
\(891\) 0 0
\(892\) 25.5685 14.7620i 0.856096 0.494267i
\(893\) 16.3554 9.44278i 0.547312 0.315991i
\(894\) 0 0
\(895\) −34.9391 + 4.16105i −1.16788 + 0.139089i
\(896\) −16.5716 23.1675i −0.553618 0.773973i
\(897\) 0 0
\(898\) 36.1512 + 20.8719i 1.20638 + 0.696504i
\(899\) 5.84369 + 10.1216i 0.194898 + 0.337573i
\(900\) 0 0
\(901\) 10.5573 18.2858i 0.351715 0.609188i
\(902\) 29.5896i 0.985227i
\(903\) 0 0
\(904\) −14.9423 −0.496972
\(905\) −4.39438 + 10.2487i −0.146074 + 0.340679i
\(906\) 0 0
\(907\) −25.4854 + 14.7140i −0.846228 + 0.488570i −0.859376 0.511344i \(-0.829148\pi\)
0.0131487 + 0.999914i \(0.495815\pi\)
\(908\) 24.0718 + 13.8979i 0.798850 + 0.461216i
\(909\) 0 0
\(910\) 7.06669 + 32.2282i 0.234258 + 1.06836i
\(911\) 24.8078 0.821918 0.410959 0.911654i \(-0.365194\pi\)
0.410959 + 0.911654i \(0.365194\pi\)
\(912\) 0 0
\(913\) 15.7526 9.09474i 0.521334 0.300992i
\(914\) 26.9810 + 46.7324i 0.892451 + 1.54577i
\(915\) 0 0
\(916\) 0.477133 0.0157649
\(917\) 11.4944 8.22189i 0.379580 0.271511i
\(918\) 0 0
\(919\) 6.50466 11.2664i 0.214569 0.371645i −0.738570 0.674177i \(-0.764499\pi\)
0.953139 + 0.302532i \(0.0978320\pi\)
\(920\) −10.9077 14.5851i −0.359617 0.480857i
\(921\) 0 0
\(922\) 10.8346 + 6.25535i 0.356818 + 0.206009i
\(923\) 47.0312i 1.54805i
\(924\) 0 0
\(925\) −4.12785 17.0843i −0.135723 0.561730i
\(926\) −2.64864 + 4.58758i −0.0870398 + 0.150757i
\(927\) 0 0
\(928\) −20.5494 + 11.8642i −0.674568 + 0.389462i
\(929\) −12.4592 + 21.5800i −0.408775 + 0.708018i −0.994753 0.102309i \(-0.967377\pi\)
0.585978 + 0.810327i \(0.300710\pi\)
\(930\) 0 0
\(931\) −53.1405 + 10.4756i −1.74161 + 0.343326i
\(932\) 8.41410i 0.275613i
\(933\) 0 0
\(934\) −21.1615 36.6528i −0.692425 1.19932i
\(935\) 7.92858 5.92952i 0.259292 0.193916i
\(936\) 0 0
\(937\) 55.1260i 1.80089i −0.434973 0.900444i \(-0.643242\pi\)
0.434973 0.900444i \(-0.356758\pi\)
\(938\) −16.4786 7.48337i −0.538044 0.244341i
\(939\) 0 0
\(940\) −5.89028 2.52560i −0.192120 0.0823760i
\(941\) 6.82233 + 11.8166i 0.222402 + 0.385211i 0.955537 0.294872i \(-0.0952771\pi\)
−0.733135 + 0.680083i \(0.761944\pi\)
\(942\) 0 0
\(943\) −38.3122 22.1196i −1.24762 0.720312i
\(944\) −14.6899 −0.478116
\(945\) 0 0
\(946\) −18.4802 −0.600842
\(947\) −0.773437 0.446544i −0.0251333 0.0145107i 0.487381 0.873190i \(-0.337952\pi\)
−0.512514 + 0.858679i \(0.671286\pi\)
\(948\) 0 0
\(949\) −13.3875 23.1878i −0.434577 0.752709i
\(950\) 66.1184 + 19.4807i 2.14517 + 0.632038i
\(951\) 0 0
\(952\) 0.805627 + 8.25215i 0.0261105 + 0.267454i
\(953\) 34.5636i 1.11963i 0.828619 + 0.559813i \(0.189127\pi\)
−0.828619 + 0.559813i \(0.810873\pi\)
\(954\) 0 0
\(955\) −15.8138 21.1452i −0.511722 0.684241i
\(956\) 5.92557 + 10.2634i 0.191646 + 0.331941i
\(957\) 0 0
\(958\) 11.6595i 0.376703i
\(959\) −34.5057 + 3.36866i −1.11425 + 0.108780i
\(960\) 0 0
\(961\) 11.2605 19.5037i 0.363241 0.629151i
\(962\) −16.9777 + 9.80208i −0.547383 + 0.316032i
\(963\) 0 0
\(964\) −2.70483 + 4.68491i −0.0871169 + 0.150891i
\(965\) −6.54159 54.9278i −0.210581 1.76819i
\(966\) 0 0
\(967\) 22.1811i 0.713296i 0.934239 + 0.356648i \(0.116080\pi\)
−0.934239 + 0.356648i \(0.883920\pi\)
\(968\) −8.51038 4.91347i −0.273534 0.157925i
\(969\) 0 0
\(970\) 0.708259 + 0.947038i 0.0227408 + 0.0304076i
\(971\) 0.0379659 0.0657589i 0.00121839 0.00211031i −0.865416 0.501055i \(-0.832946\pi\)
0.866634 + 0.498944i \(0.166279\pi\)
\(972\) 0 0
\(973\) −0.585779 0.266018i −0.0187792 0.00852815i
\(974\) −29.0889 −0.932069
\(975\) 0 0
\(976\) −27.0710 46.8883i −0.866521 1.50086i
\(977\) 37.4222 21.6057i 1.19724 0.691228i 0.237303 0.971436i \(-0.423737\pi\)
0.959940 + 0.280207i \(0.0904032\pi\)
\(978\) 0 0
\(979\) 1.28588 0.0410970
\(980\) 13.6472 + 12.3125i 0.435945 + 0.393307i
\(981\) 0 0
\(982\) −38.4211 22.1824i −1.22607 0.707869i
\(983\) −15.8663 + 9.16040i −0.506055 + 0.292171i −0.731211 0.682152i \(-0.761044\pi\)
0.225155 + 0.974323i \(0.427711\pi\)
\(984\) 0 0
\(985\) 40.1830 + 17.2294i 1.28034 + 0.548974i
\(986\) 15.2333 0.485126
\(987\) 0 0
\(988\) 28.4418i 0.904855i
\(989\) 13.8147 23.9278i 0.439283 0.760861i
\(990\) 0 0
\(991\) 15.7888 + 27.3470i 0.501548 + 0.868706i 0.999998 + 0.00178831i \(0.000569236\pi\)
−0.498450 + 0.866918i \(0.666097\pi\)
\(992\) −14.9084 8.60736i −0.473342 0.273284i
\(993\) 0 0
\(994\) 41.2041 + 57.6045i 1.30692 + 1.82710i
\(995\) −49.3815 + 5.88106i −1.56550 + 0.186442i
\(996\) 0 0
\(997\) 34.4085 19.8657i 1.08973 0.629154i 0.156223 0.987722i \(-0.450068\pi\)
0.933504 + 0.358568i \(0.116735\pi\)
\(998\) −18.8301 + 10.8716i −0.596058 + 0.344134i
\(999\) 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 315.2.bf.b.289.7 16
3.2 odd 2 105.2.q.a.79.2 yes 16
5.4 even 2 inner 315.2.bf.b.289.2 16
7.2 even 3 2205.2.d.s.1324.2 8
7.4 even 3 inner 315.2.bf.b.109.2 16
7.5 odd 6 2205.2.d.o.1324.2 8
12.11 even 2 1680.2.di.d.289.6 16
15.2 even 4 525.2.i.h.226.4 8
15.8 even 4 525.2.i.k.226.1 8
15.14 odd 2 105.2.q.a.79.7 yes 16
21.2 odd 6 735.2.d.d.589.7 8
21.5 even 6 735.2.d.e.589.7 8
21.11 odd 6 105.2.q.a.4.7 yes 16
21.17 even 6 735.2.q.g.214.7 16
21.20 even 2 735.2.q.g.79.2 16
35.4 even 6 inner 315.2.bf.b.109.7 16
35.9 even 6 2205.2.d.s.1324.7 8
35.19 odd 6 2205.2.d.o.1324.7 8
60.59 even 2 1680.2.di.d.289.2 16
84.11 even 6 1680.2.di.d.529.2 16
105.2 even 12 3675.2.a.bz.1.1 4
105.23 even 12 3675.2.a.bp.1.4 4
105.32 even 12 525.2.i.h.151.4 8
105.44 odd 6 735.2.d.d.589.2 8
105.47 odd 12 3675.2.a.cb.1.1 4
105.53 even 12 525.2.i.k.151.1 8
105.59 even 6 735.2.q.g.214.2 16
105.68 odd 12 3675.2.a.bn.1.4 4
105.74 odd 6 105.2.q.a.4.2 16
105.89 even 6 735.2.d.e.589.2 8
105.104 even 2 735.2.q.g.79.7 16
420.179 even 6 1680.2.di.d.529.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.q.a.4.2 16 105.74 odd 6
105.2.q.a.4.7 yes 16 21.11 odd 6
105.2.q.a.79.2 yes 16 3.2 odd 2
105.2.q.a.79.7 yes 16 15.14 odd 2
315.2.bf.b.109.2 16 7.4 even 3 inner
315.2.bf.b.109.7 16 35.4 even 6 inner
315.2.bf.b.289.2 16 5.4 even 2 inner
315.2.bf.b.289.7 16 1.1 even 1 trivial
525.2.i.h.151.4 8 105.32 even 12
525.2.i.h.226.4 8 15.2 even 4
525.2.i.k.151.1 8 105.53 even 12
525.2.i.k.226.1 8 15.8 even 4
735.2.d.d.589.2 8 105.44 odd 6
735.2.d.d.589.7 8 21.2 odd 6
735.2.d.e.589.2 8 105.89 even 6
735.2.d.e.589.7 8 21.5 even 6
735.2.q.g.79.2 16 21.20 even 2
735.2.q.g.79.7 16 105.104 even 2
735.2.q.g.214.2 16 105.59 even 6
735.2.q.g.214.7 16 21.17 even 6
1680.2.di.d.289.2 16 60.59 even 2
1680.2.di.d.289.6 16 12.11 even 2
1680.2.di.d.529.2 16 84.11 even 6
1680.2.di.d.529.6 16 420.179 even 6
2205.2.d.o.1324.2 8 7.5 odd 6
2205.2.d.o.1324.7 8 35.19 odd 6
2205.2.d.s.1324.2 8 7.2 even 3
2205.2.d.s.1324.7 8 35.9 even 6
3675.2.a.bn.1.4 4 105.68 odd 12
3675.2.a.bp.1.4 4 105.23 even 12
3675.2.a.bz.1.1 4 105.2 even 12
3675.2.a.cb.1.1 4 105.47 odd 12