Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.16 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.a.533.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.07966 | + | 1.35438i | 0.623341 | + | 0.781950i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.25473 | − | 1.85086i | −0.561130 | − | 0.827728i | ||||
\(6\) | 1.72112 | + | 0.194257i | 0.702646 | + | 0.0793050i | ||||
\(7\) | −3.56316 | − | 3.56316i | −1.34675 | − | 1.34675i | −0.889169 | − | 0.457579i | \(-0.848717\pi\) |
−0.457579 | − | 0.889169i | \(-0.651283\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −0.668679 | + | 2.92453i | −0.222893 | + | 0.974843i | ||||
\(10\) | −2.19598 | − | 0.421528i | −0.694429 | − | 0.133299i | ||||
\(11\) | − | 3.35156i | − | 1.01053i | −0.862964 | − | 0.505266i | \(-0.831394\pi\) | ||
0.862964 | − | 0.505266i | \(-0.168606\pi\) | |||||||
\(12\) | 1.35438 | − | 1.07966i | 0.390975 | − | 0.311670i | ||||
\(13\) | 0.759044 | − | 0.759044i | 0.210521 | − | 0.210521i | −0.593968 | − | 0.804489i | \(-0.702439\pi\) |
0.804489 | + | 0.593968i | \(0.202439\pi\) | |||||||
\(14\) | −5.03907 | −1.34675 | ||||||||
\(15\) | 1.15208 | − | 3.69766i | 0.297467 | − | 0.954732i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.534673 | + | 0.534673i | −0.129677 | + | 0.129677i | −0.768966 | − | 0.639289i | \(-0.779229\pi\) |
0.639289 | + | 0.768966i | \(0.279229\pi\) | |||||||
\(18\) | 1.59513 | + | 2.54078i | 0.375975 | + | 0.598868i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | −1.85086 | + | 1.25473i | −0.413864 | + | 0.280565i | ||||
\(21\) | 0.978873 | − | 8.67286i | 0.213608 | − | 1.89257i | ||||
\(22\) | −2.36991 | − | 2.36991i | −0.505266 | − | 0.505266i | ||||
\(23\) | −3.95419 | − | 3.95419i | −0.824506 | − | 0.824506i | 0.162245 | − | 0.986751i | \(-0.448127\pi\) |
−0.986751 | + | 0.162245i | \(0.948127\pi\) | |||||||
\(24\) | 0.194257 | − | 1.72112i | 0.0396525 | − | 0.351323i | ||||
\(25\) | −1.85133 | + | 4.64463i | −0.370266 | + | 0.928926i | ||||
\(26\) | − | 1.07345i | − | 0.210521i | ||||||
\(27\) | −4.68286 | + | 2.25184i | −0.901217 | + | 0.433368i | ||||
\(28\) | −3.56316 | + | 3.56316i | −0.673374 | + | 0.673374i | ||||
\(29\) | 3.01104 | 0.559137 | 0.279568 | − | 0.960126i | \(-0.409809\pi\) | ||||
0.279568 | + | 0.960126i | \(0.409809\pi\) | |||||||
\(30\) | −1.80000 | − | 3.42929i | −0.328633 | − | 0.626099i | ||||
\(31\) | 8.18480 | 1.47003 | 0.735017 | − | 0.678049i | \(-0.237174\pi\) | ||||
0.735017 | + | 0.678049i | \(0.237174\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 4.53927 | − | 3.61853i | 0.790186 | − | 0.629906i | ||||
\(34\) | 0.756142i | 0.129677i | ||||||||
\(35\) | −2.12411 | + | 11.0657i | −0.359040 | + | 1.87044i | ||||
\(36\) | 2.92453 | + | 0.668679i | 0.487421 | + | 0.111447i | ||||
\(37\) | 5.57606 | + | 5.57606i | 0.916699 | + | 0.916699i | 0.996788 | − | 0.0800886i | \(-0.0255203\pi\) |
−0.0800886 | + | 0.996788i | \(0.525520\pi\) | |||||||
\(38\) | 0.707107 | + | 0.707107i | 0.114708 | + | 0.114708i | ||||
\(39\) | 1.84754 | + | 0.208525i | 0.295843 | + | 0.0333907i | ||||
\(40\) | −0.421528 | + | 2.19598i | −0.0666494 | + | 0.347214i | ||||
\(41\) | − | 8.43195i | − | 1.31685i | −0.752647 | − | 0.658425i | \(-0.771223\pi\) | ||
0.752647 | − | 0.658425i | \(-0.228777\pi\) | |||||||
\(42\) | −5.44047 | − | 6.82480i | −0.839483 | − | 1.05309i | ||||
\(43\) | 4.29665 | − | 4.29665i | 0.655234 | − | 0.655234i | −0.299015 | − | 0.954248i | \(-0.596658\pi\) |
0.954248 | + | 0.299015i | \(0.0966580\pi\) | |||||||
\(44\) | −3.35156 | −0.505266 | ||||||||
\(45\) | 6.25189 | − | 2.43185i | 0.931976 | − | 0.362519i | ||||
\(46\) | −5.59207 | −0.824506 | ||||||||
\(47\) | 8.00851 | − | 8.00851i | 1.16816 | − | 1.16816i | 0.185522 | − | 0.982640i | \(-0.440603\pi\) |
0.982640 | − | 0.185522i | \(-0.0593975\pi\) | |||||||
\(48\) | −1.07966 | − | 1.35438i | −0.155835 | − | 0.195488i | ||||
\(49\) | 18.3922i | 2.62746i | ||||||||
\(50\) | 1.97516 | + | 4.59334i | 0.279330 | + | 0.649596i | ||||
\(51\) | −1.30141 | − | 0.146886i | −0.182234 | − | 0.0205681i | ||||
\(52\) | −0.759044 | − | 0.759044i | −0.105260 | − | 0.105260i | ||||
\(53\) | −7.04762 | − | 7.04762i | −0.968064 | − | 0.968064i | 0.0314411 | − | 0.999506i | \(-0.489990\pi\) |
−0.999506 | + | 0.0314411i | \(0.989990\pi\) | |||||||
\(54\) | −1.71899 | + | 4.90358i | −0.233925 | + | 0.667292i | ||||
\(55\) | −6.20325 | + | 4.20528i | −0.836446 | + | 0.567040i | ||||
\(56\) | 5.03907i | 0.673374i | ||||||||
\(57\) | −1.35438 | + | 1.07966i | −0.179392 | + | 0.143004i | ||||
\(58\) | 2.12913 | − | 2.12913i | 0.279568 | − | 0.279568i | ||||
\(59\) | 4.32394 | 0.562928 | 0.281464 | − | 0.959572i | \(-0.409180\pi\) | ||||
0.281464 | + | 0.959572i | \(0.409180\pi\) | |||||||
\(60\) | −3.69766 | − | 1.15208i | −0.477366 | − | 0.148733i | ||||
\(61\) | 1.35764 | 0.173828 | 0.0869138 | − | 0.996216i | \(-0.472300\pi\) | ||||
0.0869138 | + | 0.996216i | \(0.472300\pi\) | |||||||
\(62\) | 5.78753 | − | 5.78753i | 0.735017 | − | 0.735017i | ||||
\(63\) | 12.8032 | − | 8.03795i | 1.61305 | − | 1.01269i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.35727 | − | 0.452489i | −0.292384 | − | 0.0561243i | ||||
\(66\) | 0.651062 | − | 5.76844i | 0.0801402 | − | 0.710046i | ||||
\(67\) | 5.23044 | + | 5.23044i | 0.639000 | + | 0.639000i | 0.950309 | − | 0.311309i | \(-0.100767\pi\) |
−0.311309 | + | 0.950309i | \(0.600767\pi\) | |||||||
\(68\) | 0.534673 | + | 0.534673i | 0.0648386 | + | 0.0648386i | ||||
\(69\) | 1.08630 | − | 9.62464i | 0.130775 | − | 1.15867i | ||||
\(70\) | 6.32265 | + | 9.32659i | 0.755701 | + | 1.11474i | ||||
\(71\) | 4.74757i | 0.563433i | 0.959498 | + | 0.281716i | \(0.0909038\pi\) | ||||
−0.959498 | + | 0.281716i | \(0.909096\pi\) | |||||||
\(72\) | 2.54078 | − | 1.59513i | 0.299434 | − | 0.187987i | ||||
\(73\) | −5.12695 | + | 5.12695i | −0.600064 | + | 0.600064i | −0.940330 | − | 0.340265i | \(-0.889483\pi\) |
0.340265 | + | 0.940330i | \(0.389483\pi\) | |||||||
\(74\) | 7.88574 | 0.916699 | ||||||||
\(75\) | −8.28939 | + | 2.50721i | −0.957176 | + | 0.289507i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −11.9421 | + | 11.9421i | −1.36093 | + | 1.36093i | ||||
\(78\) | 1.45386 | − | 1.15896i | 0.164617 | − | 0.131226i | ||||
\(79\) | 0.256451i | 0.0288529i | 0.999896 | + | 0.0144265i | \(0.00459225\pi\) | ||||
−0.999896 | + | 0.0144265i | \(0.995408\pi\) | |||||||
\(80\) | 1.25473 | + | 1.85086i | 0.140283 | + | 0.206932i | ||||
\(81\) | −8.10574 | − | 3.91114i | −0.900637 | − | 0.434572i | ||||
\(82\) | −5.96229 | − | 5.96229i | −0.658425 | − | 0.658425i | ||||
\(83\) | 4.73252 | + | 4.73252i | 0.519462 | + | 0.519462i | 0.917408 | − | 0.397947i | \(-0.130277\pi\) |
−0.397947 | + | 0.917408i | \(0.630277\pi\) | |||||||
\(84\) | −8.67286 | − | 0.978873i | −0.946286 | − | 0.106804i | ||||
\(85\) | 1.66047 | + | 0.318735i | 0.180103 | + | 0.0345716i | ||||
\(86\) | − | 6.07639i | − | 0.655234i | ||||||
\(87\) | 3.25089 | + | 4.07809i | 0.348533 | + | 0.437217i | ||||
\(88\) | −2.36991 | + | 2.36991i | −0.252633 | + | 0.252633i | ||||
\(89\) | −15.2064 | −1.61188 | −0.805938 | − | 0.592000i | \(-0.798338\pi\) | ||||
−0.805938 | + | 0.592000i | \(0.798338\pi\) | |||||||
\(90\) | 2.70117 | − | 6.14033i | 0.284729 | − | 0.647248i | ||||
\(91\) | −5.40919 | −0.567037 | ||||||||
\(92\) | −3.95419 | + | 3.95419i | −0.412253 | + | 0.412253i | ||||
\(93\) | 8.83678 | + | 11.0853i | 0.916332 | + | 1.14949i | ||||
\(94\) | − | 11.3257i | − | 1.16816i | ||||||
\(95\) | 1.85086 | − | 1.25473i | 0.189894 | − | 0.128732i | ||||
\(96\) | −1.72112 | − | 0.194257i | −0.175661 | − | 0.0198262i | ||||
\(97\) | −9.73496 | − | 9.73496i | −0.988435 | − | 0.988435i | 0.0114985 | − | 0.999934i | \(-0.496340\pi\) |
−0.999934 | + | 0.0114985i | \(0.996340\pi\) | |||||||
\(98\) | 13.0053 | + | 13.0053i | 1.31373 | + | 1.31373i | ||||
\(99\) | 9.80172 | + | 2.24112i | 0.985110 | + | 0.225241i | ||||
\(100\) | 4.64463 | + | 1.85133i | 0.464463 | + | 0.185133i | ||||
\(101\) | 12.3184i | 1.22573i | 0.790189 | + | 0.612863i | \(0.209982\pi\) | ||||
−0.790189 | + | 0.612863i | \(0.790018\pi\) | |||||||
\(102\) | −1.02410 | + | 0.816374i | −0.101401 | + | 0.0808331i | ||||
\(103\) | 0.357091 | − | 0.357091i | 0.0351852 | − | 0.0351852i | −0.689295 | − | 0.724481i | \(-0.742080\pi\) |
0.724481 | + | 0.689295i | \(0.242080\pi\) | |||||||
\(104\) | −1.07345 | −0.105260 | ||||||||
\(105\) | −17.2804 | + | 9.07030i | −1.68640 | + | 0.885171i | ||||
\(106\) | −9.96683 | −0.968064 | ||||||||
\(107\) | 2.15869 | − | 2.15869i | 0.208688 | − | 0.208688i | −0.595022 | − | 0.803710i | \(-0.702857\pi\) |
0.803710 | + | 0.595022i | \(0.202857\pi\) | |||||||
\(108\) | 2.25184 | + | 4.68286i | 0.216684 | + | 0.450609i | ||||
\(109\) | − | 2.96084i | − | 0.283597i | −0.989896 | − | 0.141798i | \(-0.954712\pi\) | ||
0.989896 | − | 0.141798i | \(-0.0452885\pi\) | |||||||
\(110\) | −1.41277 | + | 7.35994i | −0.134703 | + | 0.701743i | ||||
\(111\) | −1.53186 | + | 13.5723i | −0.145398 | + | 1.28823i | ||||
\(112\) | 3.56316 | + | 3.56316i | 0.336687 | + | 0.336687i | ||||
\(113\) | −0.894915 | − | 0.894915i | −0.0841865 | − | 0.0841865i | 0.663760 | − | 0.747946i | \(-0.268960\pi\) |
−0.747946 | + | 0.663760i | \(0.768960\pi\) | |||||||
\(114\) | −0.194257 | + | 1.72112i | −0.0181938 | + | 0.161198i | ||||
\(115\) | −2.35721 | + | 12.2801i | −0.219811 | + | 1.14512i | ||||
\(116\) | − | 3.01104i | − | 0.279568i | ||||||
\(117\) | 1.71229 | + | 2.72740i | 0.158301 | + | 0.252149i | ||||
\(118\) | 3.05748 | − | 3.05748i | 0.281464 | − | 0.281464i | ||||
\(119\) | 3.81025 | 0.349285 | ||||||||
\(120\) | −3.42929 | + | 1.80000i | −0.313050 | + | 0.164316i | ||||
\(121\) | −0.232932 | −0.0211757 | ||||||||
\(122\) | 0.959995 | − | 0.959995i | 0.0869138 | − | 0.0869138i | ||||
\(123\) | 11.4200 | − | 9.10362i | 1.02971 | − | 0.820846i | ||||
\(124\) | − | 8.18480i | − | 0.735017i | ||||||
\(125\) | 10.9194 | − | 2.40119i | 0.976665 | − | 0.214769i | ||||
\(126\) | 3.36952 | − | 14.7369i | 0.300181 | − | 1.31287i | ||||
\(127\) | −6.70476 | − | 6.70476i | −0.594951 | − | 0.594951i | 0.344014 | − | 0.938965i | \(-0.388213\pi\) |
−0.938965 | + | 0.344014i | \(0.888213\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 10.4582 | + | 1.18038i | 0.920794 | + | 0.103927i | ||||
\(130\) | −1.98680 | + | 1.34689i | −0.174254 | + | 0.118130i | ||||
\(131\) | − | 1.53144i | − | 0.133802i | −0.997760 | − | 0.0669011i | \(-0.978689\pi\) | ||
0.997760 | − | 0.0669011i | \(-0.0213112\pi\) | |||||||
\(132\) | −3.61853 | − | 4.53927i | −0.314953 | − | 0.395093i | ||||
\(133\) | 3.56316 | − | 3.56316i | 0.308965 | − | 0.308965i | ||||
\(134\) | 7.39695 | 0.639000 | ||||||||
\(135\) | 10.0435 | + | 5.84185i | 0.864411 | + | 0.502787i | ||||
\(136\) | 0.756142 | 0.0648386 | ||||||||
\(137\) | 4.76164 | − | 4.76164i | 0.406814 | − | 0.406814i | −0.473812 | − | 0.880626i | \(-0.657122\pi\) |
0.880626 | + | 0.473812i | \(0.157122\pi\) | |||||||
\(138\) | −6.03752 | − | 7.57378i | −0.513948 | − | 0.644723i | ||||
\(139\) | − | 9.84417i | − | 0.834971i | −0.908684 | − | 0.417486i | \(-0.862911\pi\) | ||
0.908684 | − | 0.417486i | \(-0.137089\pi\) | |||||||
\(140\) | 11.0657 | + | 2.12411i | 0.935221 | + | 0.179520i | ||||
\(141\) | 19.4930 | + | 2.20010i | 1.64161 | + | 0.185282i | ||||
\(142\) | 3.35704 | + | 3.35704i | 0.281716 | + | 0.281716i | ||||
\(143\) | −2.54398 | − | 2.54398i | −0.212738 | − | 0.212738i | ||||
\(144\) | 0.668679 | − | 2.92453i | 0.0557233 | − | 0.243711i | ||||
\(145\) | −3.77803 | − | 5.57300i | −0.313748 | − | 0.462813i | ||||
\(146\) | 7.25060i | 0.600064i | ||||||||
\(147\) | −24.9100 | + | 19.8573i | −2.05454 | + | 1.63780i | ||||
\(148\) | 5.57606 | − | 5.57606i | 0.458350 | − | 0.458350i | ||||
\(149\) | −1.98019 | −0.162224 | −0.0811118 | − | 0.996705i | \(-0.525847\pi\) | ||||
−0.0811118 | + | 0.996705i | \(0.525847\pi\) | |||||||
\(150\) | −4.08862 | + | 7.63434i | −0.333834 | + | 0.623342i | ||||
\(151\) | 20.6241 | 1.67837 | 0.839185 | − | 0.543847i | \(-0.183033\pi\) | ||||
0.839185 | + | 0.543847i | \(0.183033\pi\) | |||||||
\(152\) | 0.707107 | − | 0.707107i | 0.0573539 | − | 0.0573539i | ||||
\(153\) | −1.20614 | − | 1.92119i | −0.0975108 | − | 0.155319i | ||||
\(154\) | 16.8887i | 1.36093i | ||||||||
\(155\) | −10.2697 | − | 15.1489i | −0.824880 | − | 1.21679i | ||||
\(156\) | 0.208525 | − | 1.84754i | 0.0166954 | − | 0.147922i | ||||
\(157\) | −16.6468 | − | 16.6468i | −1.32856 | − | 1.32856i | −0.906624 | − | 0.421939i | \(-0.861350\pi\) |
−0.421939 | − | 0.906624i | \(-0.638650\pi\) | |||||||
\(158\) | 0.181338 | + | 0.181338i | 0.0144265 | + | 0.0144265i | ||||
\(159\) | 1.93612 | − | 17.1541i | 0.153545 | − | 1.36041i | ||||
\(160\) | 2.19598 | + | 0.421528i | 0.173607 | + | 0.0333247i | ||||
\(161\) | 28.1788i | 2.22080i | ||||||||
\(162\) | −8.49722 | + | 2.96602i | −0.667604 | + | 0.233033i | ||||
\(163\) | −10.0274 | + | 10.0274i | −0.785406 | + | 0.785406i | −0.980737 | − | 0.195331i | \(-0.937422\pi\) |
0.195331 | + | 0.980737i | \(0.437422\pi\) | |||||||
\(164\) | −8.43195 | −0.658425 | ||||||||
\(165\) | −12.3929 | − | 3.86128i | −0.964788 | − | 0.300600i | ||||
\(166\) | 6.69279 | 0.519462 | ||||||||
\(167\) | 6.15920 | − | 6.15920i | 0.476613 | − | 0.476613i | −0.427434 | − | 0.904047i | \(-0.640582\pi\) |
0.904047 | + | 0.427434i | \(0.140582\pi\) | |||||||
\(168\) | −6.82480 | + | 5.44047i | −0.526545 | + | 0.419741i | ||||
\(169\) | 11.8477i | 0.911362i | ||||||||
\(170\) | 1.39951 | − | 0.948750i | 0.107337 | − | 0.0727658i | ||||
\(171\) | −2.92453 | − | 0.668679i | −0.223644 | − | 0.0511352i | ||||
\(172\) | −4.29665 | − | 4.29665i | −0.327617 | − | 0.327617i | ||||
\(173\) | −1.69599 | − | 1.69599i | −0.128944 | − | 0.128944i | 0.639690 | − | 0.768633i | \(-0.279063\pi\) |
−0.768633 | + | 0.639690i | \(0.779063\pi\) | |||||||
\(174\) | 5.18237 | + | 0.584915i | 0.392875 | + | 0.0443423i | ||||
\(175\) | 23.1461 | − | 9.95297i | 1.74968 | − | 0.752374i | ||||
\(176\) | 3.35156i | 0.252633i | ||||||||
\(177\) | 4.66837 | + | 5.85624i | 0.350896 | + | 0.440182i | ||||
\(178\) | −10.7526 | + | 10.7526i | −0.805938 | + | 0.805938i | ||||
\(179\) | 11.4970 | 0.859323 | 0.429662 | − | 0.902990i | \(-0.358633\pi\) | ||||
0.429662 | + | 0.902990i | \(0.358633\pi\) | |||||||
\(180\) | −2.43185 | − | 6.25189i | −0.181259 | − | 0.465988i | ||||
\(181\) | 22.3294 | 1.65973 | 0.829867 | − | 0.557961i | \(-0.188416\pi\) | ||||
0.829867 | + | 0.557961i | \(0.188416\pi\) | |||||||
\(182\) | −3.82488 | + | 3.82488i | −0.283519 | + | 0.283519i | ||||
\(183\) | 1.46578 | + | 1.83875i | 0.108354 | + | 0.135925i | ||||
\(184\) | 5.59207i | 0.412253i | ||||||||
\(185\) | 3.32406 | − | 17.3169i | 0.244390 | − | 1.27316i | ||||
\(186\) | 14.0871 | + | 1.58995i | 1.03291 | + | 0.116581i | ||||
\(187\) | 1.79199 | + | 1.79199i | 0.131043 | + | 0.131043i | ||||
\(188\) | −8.00851 | − | 8.00851i | −0.584081 | − | 0.584081i | ||||
\(189\) | 24.7095 | + | 8.66210i | 1.79735 | + | 0.630075i | ||||
\(190\) | 0.421528 | − | 2.19598i | 0.0305808 | − | 0.159313i | ||||
\(191\) | − | 7.92842i | − | 0.573680i | −0.957978 | − | 0.286840i | \(-0.907395\pi\) | ||
0.957978 | − | 0.286840i | \(-0.0926048\pi\) | |||||||
\(192\) | −1.35438 | + | 1.07966i | −0.0977438 | + | 0.0779176i | ||||
\(193\) | 4.68979 | − | 4.68979i | 0.337578 | − | 0.337578i | −0.517877 | − | 0.855455i | \(-0.673277\pi\) |
0.855455 | + | 0.517877i | \(0.173277\pi\) | |||||||
\(194\) | −13.7673 | −0.988435 | ||||||||
\(195\) | −1.93221 | − | 3.68117i | −0.138368 | − | 0.263614i | ||||
\(196\) | 18.3922 | 1.31373 | ||||||||
\(197\) | 4.72215 | − | 4.72215i | 0.336439 | − | 0.336439i | −0.518586 | − | 0.855025i | \(-0.673541\pi\) |
0.855025 | + | 0.518586i | \(0.173541\pi\) | |||||||
\(198\) | 8.51557 | − | 5.34616i | 0.605176 | − | 0.379935i | ||||
\(199\) | 10.0047i | 0.709217i | 0.935015 | + | 0.354609i | \(0.115386\pi\) | ||||
−0.935015 | + | 0.354609i | \(0.884614\pi\) | |||||||
\(200\) | 4.59334 | − | 1.97516i | 0.324798 | − | 0.139665i | ||||
\(201\) | −1.43691 | + | 12.7311i | −0.101352 | + | 0.897980i | ||||
\(202\) | 8.71043 | + | 8.71043i | 0.612863 | + | 0.612863i | ||||
\(203\) | −10.7288 | − | 10.7288i | −0.753016 | − | 0.753016i | ||||
\(204\) | −0.146886 | + | 1.30141i | −0.0102841 | + | 0.0911171i | ||||
\(205\) | −15.6063 | + | 10.5798i | −1.08999 | + | 0.738924i | ||||
\(206\) | − | 0.505003i | − | 0.0351852i | ||||||
\(207\) | 14.2082 | − | 8.92006i | 0.987540 | − | 0.619987i | ||||
\(208\) | −0.759044 | + | 0.759044i | −0.0526302 | + | 0.0526302i | ||||
\(209\) | 3.35156 | 0.231832 | ||||||||
\(210\) | −5.80543 | + | 18.6328i | −0.400613 | + | 1.28578i | ||||
\(211\) | 0.338632 | 0.0233124 | 0.0116562 | − | 0.999932i | \(-0.496290\pi\) | ||||
0.0116562 | + | 0.999932i | \(0.496290\pi\) | |||||||
\(212\) | −7.04762 | + | 7.04762i | −0.484032 | + | 0.484032i | ||||
\(213\) | −6.43000 | + | 5.12575i | −0.440577 | + | 0.351211i | ||||
\(214\) | − | 3.05284i | − | 0.208688i | ||||||
\(215\) | −13.3436 | − | 2.56136i | −0.910026 | − | 0.174684i | ||||
\(216\) | 4.90358 | + | 1.71899i | 0.333646 | + | 0.116962i | ||||
\(217\) | −29.1638 | − | 29.1638i | −1.97977 | − | 1.97977i | ||||
\(218\) | −2.09363 | − | 2.09363i | −0.141798 | − | 0.141798i | ||||
\(219\) | −12.4792 | − | 1.40848i | −0.843265 | − | 0.0951762i | ||||
\(220\) | 4.20528 | + | 6.20325i | 0.283520 | + | 0.418223i | ||||
\(221\) | 0.811681i | 0.0545996i | ||||||||
\(222\) | 8.51390 | + | 10.6803i | 0.571416 | + | 0.716813i | ||||
\(223\) | −6.58383 | + | 6.58383i | −0.440886 | + | 0.440886i | −0.892310 | − | 0.451424i | \(-0.850916\pi\) |
0.451424 | + | 0.892310i | \(0.350916\pi\) | |||||||
\(224\) | 5.03907 | 0.336687 | ||||||||
\(225\) | −12.3454 | − | 8.52003i | −0.823027 | − | 0.568002i | ||||
\(226\) | −1.26560 | −0.0841865 | ||||||||
\(227\) | 15.0913 | − | 15.0913i | 1.00164 | − | 1.00164i | 0.00164481 | − | 0.999999i | \(-0.499476\pi\) |
0.999999 | − | 0.00164481i | \(-0.000523559\pi\) | |||||||
\(228\) | 1.07966 | + | 1.35438i | 0.0715021 | + | 0.0896959i | ||||
\(229\) | 13.2052i | 0.872626i | 0.899795 | + | 0.436313i | \(0.143716\pi\) | ||||
−0.899795 | + | 0.436313i | \(0.856284\pi\) | |||||||
\(230\) | 7.01651 | + | 10.3501i | 0.462655 | + | 0.682466i | ||||
\(231\) | −29.0676 | − | 3.28075i | −1.91251 | − | 0.215857i | ||||
\(232\) | −2.12913 | − | 2.12913i | −0.139784 | − | 0.139784i | ||||
\(233\) | 17.7744 | + | 17.7744i | 1.16444 | + | 1.16444i | 0.983494 | + | 0.180943i | \(0.0579149\pi\) |
0.180943 | + | 0.983494i | \(0.442085\pi\) | |||||||
\(234\) | 3.13934 | + | 0.717794i | 0.205225 | + | 0.0469237i | ||||
\(235\) | −24.8711 | − | 4.77412i | −1.62241 | − | 0.311429i | ||||
\(236\) | − | 4.32394i | − | 0.281464i | ||||||
\(237\) | −0.347331 | + | 0.276879i | −0.0225616 | + | 0.0179852i | ||||
\(238\) | 2.69425 | − | 2.69425i | 0.174643 | − | 0.174643i | ||||
\(239\) | 8.08746 | 0.523134 | 0.261567 | − | 0.965185i | \(-0.415761\pi\) | ||||
0.261567 | + | 0.965185i | \(0.415761\pi\) | |||||||
\(240\) | −1.15208 | + | 3.69766i | −0.0743667 | + | 0.238683i | ||||
\(241\) | 17.4598 | 1.12468 | 0.562341 | − | 0.826905i | \(-0.309901\pi\) | ||||
0.562341 | + | 0.826905i | \(0.309901\pi\) | |||||||
\(242\) | −0.164708 | + | 0.164708i | −0.0105878 | + | 0.0105878i | ||||
\(243\) | −3.45425 | − | 15.2009i | −0.221590 | − | 0.975140i | ||||
\(244\) | − | 1.35764i | − | 0.0869138i | ||||||
\(245\) | 34.0413 | − | 23.0772i | 2.17482 | − | 1.47435i | ||||
\(246\) | 1.63796 | − | 14.5124i | 0.104433 | − | 0.925278i | ||||
\(247\) | 0.759044 | + | 0.759044i | 0.0482968 | + | 0.0482968i | ||||
\(248\) | −5.78753 | − | 5.78753i | −0.367508 | − | 0.367508i | ||||
\(249\) | −1.30012 | + | 11.5191i | −0.0823918 | + | 0.729995i | ||||
\(250\) | 6.02332 | − | 9.41911i | 0.380948 | − | 0.595717i | ||||
\(251\) | 2.20006i | 0.138867i | 0.997587 | + | 0.0694333i | \(0.0221191\pi\) | ||||
−0.997587 | + | 0.0694333i | \(0.977881\pi\) | |||||||
\(252\) | −8.03795 | − | 12.8032i | −0.506343 | − | 0.806524i | ||||
\(253\) | −13.2527 | + | 13.2527i | −0.833190 | + | 0.833190i | ||||
\(254\) | −9.48196 | −0.594951 | ||||||||
\(255\) | 1.36105 | + | 2.59303i | 0.0852324 | + | 0.162382i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.3829 | + | 18.3829i | −1.14670 | + | 1.14670i | −0.159499 | + | 0.987198i | \(0.550988\pi\) |
−0.987198 | + | 0.159499i | \(0.949012\pi\) | |||||||
\(258\) | 8.22972 | − | 6.56042i | 0.512360 | − | 0.408434i | ||||
\(259\) | − | 39.7368i | − | 2.46913i | ||||||
\(260\) | −0.452489 | + | 2.35727i | −0.0280622 | + | 0.146192i | ||||
\(261\) | −2.01342 | + | 8.80588i | −0.124628 | + | 0.545070i | ||||
\(262\) | −1.08289 | − | 1.08289i | −0.0669011 | − | 0.0669011i | ||||
\(263\) | −17.6465 | − | 17.6465i | −1.08813 | − | 1.08813i | −0.995721 | − | 0.0924109i | \(-0.970543\pi\) |
−0.0924109 | − | 0.995721i | \(-0.529457\pi\) | |||||||
\(264\) | −5.76844 | − | 0.651062i | −0.355023 | − | 0.0400701i | ||||
\(265\) | −4.20130 | + | 21.8869i | −0.258084 | + | 1.34450i | ||||
\(266\) | − | 5.03907i | − | 0.308965i | ||||||
\(267\) | −16.4177 | − | 20.5952i | −1.00475 | − | 1.26041i | ||||
\(268\) | 5.23044 | − | 5.23044i | 0.319500 | − | 0.319500i | ||||
\(269\) | 12.7863 | 0.779593 | 0.389796 | − | 0.920901i | \(-0.372545\pi\) | ||||
0.389796 | + | 0.920901i | \(0.372545\pi\) | |||||||
\(270\) | 11.2327 | − | 2.97104i | 0.683599 | − | 0.180812i | ||||
\(271\) | −8.21287 | −0.498897 | −0.249448 | − | 0.968388i | \(-0.580249\pi\) | ||||
−0.249448 | + | 0.968388i | \(0.580249\pi\) | |||||||
\(272\) | 0.534673 | − | 0.534673i | 0.0324193 | − | 0.0324193i | ||||
\(273\) | −5.84007 | − | 7.32609i | −0.353457 | − | 0.443395i | ||||
\(274\) | − | 6.73398i | − | 0.406814i | ||||||
\(275\) | 15.5667 | + | 6.20484i | 0.938710 | + | 0.374166i | ||||
\(276\) | −9.62464 | − | 1.08630i | −0.579335 | − | 0.0653874i | ||||
\(277\) | 4.32961 | + | 4.32961i | 0.260141 | + | 0.260141i | 0.825111 | − | 0.564970i | \(-0.191112\pi\) |
−0.564970 | + | 0.825111i | \(0.691112\pi\) | |||||||
\(278\) | −6.96088 | − | 6.96088i | −0.417486 | − | 0.417486i | ||||
\(279\) | −5.47301 | + | 23.9367i | −0.327660 | + | 1.43305i | ||||
\(280\) | 9.32659 | − | 6.32265i | 0.557370 | − | 0.377850i | ||||
\(281\) | 11.0222i | 0.657530i | 0.944412 | + | 0.328765i | \(0.106632\pi\) | ||||
−0.944412 | + | 0.328765i | \(0.893368\pi\) | |||||||
\(282\) | 15.3393 | − | 12.2279i | 0.913445 | − | 0.728163i | ||||
\(283\) | −12.1343 | + | 12.1343i | −0.721309 | + | 0.721309i | −0.968872 | − | 0.247563i | \(-0.920370\pi\) |
0.247563 | + | 0.968872i | \(0.420370\pi\) | |||||||
\(284\) | 4.74757 | 0.281716 | ||||||||
\(285\) | 3.69766 | + | 1.15208i | 0.219031 | + | 0.0682436i | ||||
\(286\) | −3.59773 | −0.212738 | ||||||||
\(287\) | −30.0444 | + | 30.0444i | −1.77346 | + | 1.77346i | ||||
\(288\) | −1.59513 | − | 2.54078i | −0.0939937 | − | 0.149717i | ||||
\(289\) | 16.4282i | 0.966368i | ||||||||
\(290\) | −6.61218 | − | 1.26924i | −0.388281 | − | 0.0745322i | ||||
\(291\) | 2.67439 | − | 23.6952i | 0.156776 | − | 1.38904i | ||||
\(292\) | 5.12695 | + | 5.12695i | 0.300032 | + | 0.300032i | ||||
\(293\) | −17.4542 | − | 17.4542i | −1.01968 | − | 1.01968i | −0.999802 | − | 0.0198825i | \(-0.993671\pi\) |
−0.0198825 | − | 0.999802i | \(-0.506329\pi\) | |||||||
\(294\) | −3.57281 | + | 31.6553i | −0.208371 | + | 1.84617i | ||||
\(295\) | −5.42535 | − | 8.00298i | −0.315876 | − | 0.465951i | ||||
\(296\) | − | 7.88574i | − | 0.458350i | ||||||
\(297\) | 7.54718 | + | 15.6949i | 0.437932 | + | 0.910709i | ||||
\(298\) | −1.40021 | + | 1.40021i | −0.0811118 | + | 0.0811118i | ||||
\(299\) | −6.00281 | −0.347151 | ||||||||
\(300\) | 2.50721 | + | 8.28939i | 0.144754 | + | 0.478588i | ||||
\(301\) | −30.6193 | −1.76487 | ||||||||
\(302\) | 14.5835 | − | 14.5835i | 0.839185 | − | 0.839185i | ||||
\(303\) | −16.6838 | + | 13.2997i | −0.958458 | + | 0.764045i | ||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | −1.70346 | − | 2.51279i | −0.0975399 | − | 0.143882i | ||||
\(306\) | −2.21136 | − | 0.505616i | −0.126415 | − | 0.0289042i | ||||
\(307\) | −5.85378 | − | 5.85378i | −0.334093 | − | 0.334093i | 0.520046 | − | 0.854138i | \(-0.325915\pi\) |
−0.854138 | + | 0.520046i | \(0.825915\pi\) | |||||||
\(308\) | 11.9421 | + | 11.9421i | 0.680466 | + | 0.680466i | ||||
\(309\) | 0.869172 | + | 0.0981002i | 0.0494455 | + | 0.00558073i | ||||
\(310\) | −17.9736 | − | 3.45012i | −1.02083 | − | 0.195954i | ||||
\(311\) | − | 14.2142i | − | 0.806015i | −0.915197 | − | 0.403008i | \(-0.867965\pi\) | ||
0.915197 | − | 0.403008i | \(-0.132035\pi\) | |||||||
\(312\) | −1.15896 | − | 1.45386i | −0.0656131 | − | 0.0823085i | ||||
\(313\) | 23.2992 | − | 23.2992i | 1.31695 | − | 1.31695i | 0.400766 | − | 0.916180i | \(-0.368744\pi\) |
0.916180 | − | 0.400766i | \(-0.131256\pi\) | |||||||
\(314\) | −23.5422 | −1.32856 | ||||||||
\(315\) | −30.9416 | − | 13.6114i | −1.74336 | − | 0.766916i | ||||
\(316\) | 0.256451 | 0.0144265 | ||||||||
\(317\) | −9.99115 | + | 9.99115i | −0.561159 | + | 0.561159i | −0.929637 | − | 0.368478i | \(-0.879879\pi\) |
0.368478 | + | 0.929637i | \(0.379879\pi\) | |||||||
\(318\) | −10.7608 | − | 13.4989i | −0.603434 | − | 0.756978i | ||||
\(319\) | − | 10.0917i | − | 0.565026i | ||||||
\(320\) | 1.85086 | − | 1.25473i | 0.103466 | − | 0.0701413i | ||||
\(321\) | 5.25432 | + | 0.593035i | 0.293267 | + | 0.0331000i | ||||
\(322\) | 19.9254 | + | 19.9254i | 1.11040 | + | 1.11040i | ||||
\(323\) | −0.534673 | − | 0.534673i | −0.0297500 | − | 0.0297500i | ||||
\(324\) | −3.91114 | + | 8.10574i | −0.217286 | + | 0.450319i | ||||
\(325\) | 2.12024 | + | 4.93072i | 0.117610 | + | 0.273507i | ||||
\(326\) | 14.1809i | 0.785406i | ||||||||
\(327\) | 4.01009 | − | 3.19669i | 0.221759 | − | 0.176777i | ||||
\(328\) | −5.96229 | + | 5.96229i | −0.329212 | + | 0.329212i | ||||
\(329\) | −57.0712 | −3.14644 | ||||||||
\(330\) | −11.4935 | + | 6.03279i | −0.632694 | + | 0.332094i | ||||
\(331\) | −8.73786 | −0.480276 | −0.240138 | − | 0.970739i | \(-0.577193\pi\) | ||||
−0.240138 | + | 0.970739i | \(0.577193\pi\) | |||||||
\(332\) | 4.73252 | − | 4.73252i | 0.259731 | − | 0.259731i | ||||
\(333\) | −20.0360 | + | 12.5788i | −1.09796 | + | 0.689312i | ||||
\(334\) | − | 8.71042i | − | 0.476613i | ||||||
\(335\) | 3.11802 | − | 16.2435i | 0.170356 | − | 0.887479i | ||||
\(336\) | −0.978873 | + | 8.67286i | −0.0534019 | + | 0.473143i | ||||
\(337\) | 18.7714 | + | 18.7714i | 1.02254 | + | 1.02254i | 0.999740 | + | 0.0228016i | \(0.00725861\pi\) |
0.0228016 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(338\) | 8.37759 | + | 8.37759i | 0.455681 | + | 0.455681i | ||||
\(339\) | 0.245851 | − | 2.17825i | 0.0133528 | − | 0.118307i | ||||
\(340\) | 0.318735 | − | 1.66047i | 0.0172858 | − | 0.0900516i | ||||
\(341\) | − | 27.4318i | − | 1.48552i | ||||||
\(342\) | −2.54078 | + | 1.59513i | −0.137390 | + | 0.0862546i | ||||
\(343\) | 40.5923 | − | 40.5923i | 2.19178 | − | 2.19178i | ||||
\(344\) | −6.07639 | −0.327617 | ||||||||
\(345\) | −19.1768 | + | 10.0657i | −1.03245 | + | 0.541919i | ||||
\(346\) | −2.39849 | −0.128944 | ||||||||
\(347\) | 5.40165 | − | 5.40165i | 0.289976 | − | 0.289976i | −0.547095 | − | 0.837071i | \(-0.684266\pi\) |
0.837071 | + | 0.547095i | \(0.184266\pi\) | |||||||
\(348\) | 4.07809 | − | 3.25089i | 0.218609 | − | 0.174266i | ||||
\(349\) | − | 19.1590i | − | 1.02556i | −0.858521 | − | 0.512778i | \(-0.828616\pi\) | ||
0.858521 | − | 0.512778i | \(-0.171384\pi\) | |||||||
\(350\) | 9.32898 | − | 23.4046i | 0.498655 | − | 1.25103i | ||||
\(351\) | −1.84525 | + | 5.26375i | −0.0984921 | + | 0.280958i | ||||
\(352\) | 2.36991 | + | 2.36991i | 0.126317 | + | 0.126317i | ||||
\(353\) | 0.366441 | + | 0.366441i | 0.0195037 | + | 0.0195037i | 0.716791 | − | 0.697288i | \(-0.245610\pi\) |
−0.697288 | + | 0.716791i | \(0.745610\pi\) | |||||||
\(354\) | 7.44203 | + | 0.839954i | 0.395539 | + | 0.0446430i | ||||
\(355\) | 8.78707 | − | 5.95690i | 0.466369 | − | 0.316159i | ||||
\(356\) | 15.2064i | 0.805938i | ||||||||
\(357\) | 4.11377 | + | 5.16052i | 0.217724 | + | 0.273124i | ||||
\(358\) | 8.12958 | − | 8.12958i | 0.429662 | − | 0.429662i | ||||
\(359\) | 16.4393 | 0.867631 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(360\) | −6.14033 | − | 2.70117i | −0.323624 | − | 0.142364i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 15.7893 | − | 15.7893i | 0.829867 | − | 0.829867i | ||||
\(363\) | −0.251487 | − | 0.315478i | −0.0131996 | − | 0.0165583i | ||||
\(364\) | 5.40919i | 0.283519i | ||||||||
\(365\) | 15.9222 | + | 3.05633i | 0.833404 | + | 0.159976i | ||||
\(366\) | 2.33666 | + | 0.263730i | 0.122139 | + | 0.0137854i | ||||
\(367\) | 13.3725 | + | 13.3725i | 0.698039 | + | 0.698039i | 0.963987 | − | 0.265948i | \(-0.0856851\pi\) |
−0.265948 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(368\) | 3.95419 | + | 3.95419i | 0.206126 | + | 0.206126i | ||||
\(369\) | 24.6595 | + | 5.63827i | 1.28372 | + | 0.293517i | ||||
\(370\) | −9.89444 | − | 14.5954i | −0.514387 | − | 0.758777i | ||||
\(371\) | 50.2236i | 2.60748i | ||||||||
\(372\) | 11.0853 | − | 8.83678i | 0.574747 | − | 0.458166i | ||||
\(373\) | −2.80556 | + | 2.80556i | −0.145266 | + | 0.145266i | −0.776000 | − | 0.630733i | \(-0.782754\pi\) |
0.630733 | + | 0.776000i | \(0.282754\pi\) | |||||||
\(374\) | 2.53425 | 0.131043 | ||||||||
\(375\) | 15.0414 | + | 12.1966i | 0.776733 | + | 0.629829i | ||||
\(376\) | −11.3257 | −0.584081 | ||||||||
\(377\) | 2.28551 | − | 2.28551i | 0.117710 | − | 0.117710i | ||||
\(378\) | 23.5973 | − | 11.3472i | 1.21371 | − | 0.583637i | ||||
\(379\) | − | 35.0537i | − | 1.80059i | −0.435284 | − | 0.900293i | \(-0.643352\pi\) | ||
0.435284 | − | 0.900293i | \(-0.356648\pi\) | |||||||
\(380\) | −1.25473 | − | 1.85086i | −0.0643660 | − | 0.0949469i | ||||
\(381\) | 1.84193 | − | 16.3196i | 0.0943651 | − | 0.836079i | ||||
\(382\) | −5.60624 | − | 5.60624i | −0.286840 | − | 0.286840i | ||||
\(383\) | 0.786561 | + | 0.786561i | 0.0401914 | + | 0.0401914i | 0.726917 | − | 0.686725i | \(-0.240953\pi\) |
−0.686725 | + | 0.726917i | \(0.740953\pi\) | |||||||
\(384\) | −0.194257 | + | 1.72112i | −0.00991312 | + | 0.0878307i | ||||
\(385\) | 37.0873 | + | 7.11906i | 1.89014 | + | 0.362821i | ||||
\(386\) | − | 6.63236i | − | 0.337578i | ||||||
\(387\) | 9.69260 | + | 15.4388i | 0.492703 | + | 0.784797i | ||||
\(388\) | −9.73496 | + | 9.73496i | −0.494218 | + | 0.494218i | ||||
\(389\) | −1.39333 | −0.0706444 | −0.0353222 | − | 0.999376i | \(-0.511246\pi\) | ||||
−0.0353222 | + | 0.999376i | \(0.511246\pi\) | |||||||
\(390\) | −3.96926 | − | 1.23671i | −0.200991 | − | 0.0626230i | ||||
\(391\) | 4.22840 | 0.213839 | ||||||||
\(392\) | 13.0053 | − | 13.0053i | 0.656865 | − | 0.656865i | ||||
\(393\) | 2.07414 | − | 1.65343i | 0.104627 | − | 0.0834043i | ||||
\(394\) | − | 6.67813i | − | 0.336439i | ||||||
\(395\) | 0.474653 | − | 0.321775i | 0.0238824 | − | 0.0161903i | ||||
\(396\) | 2.24112 | − | 9.80172i | 0.112620 | − | 0.492555i | ||||
\(397\) | −10.5012 | − | 10.5012i | −0.527041 | − | 0.527041i | 0.392648 | − | 0.919689i | \(-0.371559\pi\) |
−0.919689 | + | 0.392648i | \(0.871559\pi\) | |||||||
\(398\) | 7.07442 | + | 7.07442i | 0.354609 | + | 0.354609i | ||||
\(399\) | 8.67286 | + | 0.978873i | 0.434186 | + | 0.0490049i | ||||
\(400\) | 1.85133 | − | 4.64463i | 0.0925665 | − | 0.232231i | ||||
\(401\) | 19.6404i | 0.980792i | 0.871500 | + | 0.490396i | \(0.163148\pi\) | ||||
−0.871500 | + | 0.490396i | \(0.836852\pi\) | |||||||
\(402\) | 7.98618 | + | 10.0183i | 0.398314 | + | 0.499666i | ||||
\(403\) | 6.21263 | − | 6.21263i | 0.309473 | − | 0.309473i | ||||
\(404\) | 12.3184 | 0.612863 | ||||||||
\(405\) | 2.93151 | + | 19.9100i | 0.145668 | + | 0.989334i | ||||
\(406\) | −15.1729 | −0.753016 | ||||||||
\(407\) | 18.6885 | − | 18.6885i | 0.926354 | − | 0.926354i | ||||
\(408\) | 0.816374 | + | 1.02410i | 0.0404165 | + | 0.0507006i | ||||
\(409\) | − | 8.61457i | − | 0.425963i | −0.977056 | − | 0.212981i | \(-0.931683\pi\) | ||
0.977056 | − | 0.212981i | \(-0.0683174\pi\) | |||||||
\(410\) | −3.55430 | + | 18.5164i | −0.175534 | + | 0.914458i | ||||
\(411\) | 11.5900 | + | 1.30812i | 0.571693 | + | 0.0645248i | ||||
\(412\) | −0.357091 | − | 0.357091i | −0.0175926 | − | 0.0175926i | ||||
\(413\) | −15.4069 | − | 15.4069i | −0.758123 | − | 0.758123i | ||||
\(414\) | 3.73930 | − | 16.3542i | 0.183777 | − | 0.803764i | ||||
\(415\) | 2.82120 | − | 14.6972i | 0.138487 | − | 0.721458i | ||||
\(416\) | 1.07345i | 0.0526302i | ||||||||
\(417\) | 13.3327 | − | 10.6283i | 0.652906 | − | 0.520471i | ||||
\(418\) | 2.36991 | − | 2.36991i | 0.115916 | − | 0.115916i | ||||
\(419\) | 0.0254108 | 0.00124140 | 0.000620699 | − | 1.00000i | \(-0.499802\pi\) | ||||
0.000620699 | 1.00000i | \(0.499802\pi\) | ||||||||
\(420\) | 9.07030 | + | 17.2804i | 0.442585 | + | 0.843198i | ||||
\(421\) | 5.45966 | 0.266087 | 0.133044 | − | 0.991110i | \(-0.457525\pi\) | ||||
0.133044 | + | 0.991110i | \(0.457525\pi\) | |||||||
\(422\) | 0.239449 | − | 0.239449i | 0.0116562 | − | 0.0116562i | ||||
\(423\) | 18.0660 | + | 28.7763i | 0.878399 | + | 1.39915i | ||||
\(424\) | 9.96683i | 0.484032i | ||||||||
\(425\) | −1.49350 | − | 3.47321i | −0.0724455 | − | 0.168476i | ||||
\(426\) | −0.922247 | + | 8.17115i | −0.0446830 | + | 0.395894i | ||||
\(427\) | −4.83748 | − | 4.83748i | −0.234102 | − | 0.234102i | ||||
\(428\) | −2.15869 | − | 2.15869i | −0.104344 | − | 0.104344i | ||||
\(429\) | 0.698883 | − | 6.19214i | 0.0337424 | − | 0.298959i | ||||
\(430\) | −11.2465 | + | 7.62419i | −0.542355 | + | 0.367671i | ||||
\(431\) | − | 2.80348i | − | 0.135039i | −0.997718 | − | 0.0675195i | \(-0.978491\pi\) | ||
0.997718 | − | 0.0675195i | \(-0.0215085\pi\) | |||||||
\(432\) | 4.68286 | − | 2.25184i | 0.225304 | − | 0.108342i | ||||
\(433\) | −8.33316 | + | 8.33316i | −0.400466 | + | 0.400466i | −0.878397 | − | 0.477931i | \(-0.841387\pi\) |
0.477931 | + | 0.878397i | \(0.341387\pi\) | |||||||
\(434\) | −41.2438 | −1.97977 | ||||||||
\(435\) | 3.46897 | − | 11.1338i | 0.166325 | − | 0.533826i | ||||
\(436\) | −2.96084 | −0.141798 | ||||||||
\(437\) | 3.95419 | − | 3.95419i | 0.189155 | − | 0.189155i | ||||
\(438\) | −9.82006 | + | 7.82817i | −0.469221 | + | 0.374044i | ||||
\(439\) | 12.5841i | 0.600607i | 0.953844 | + | 0.300304i | \(0.0970880\pi\) | ||||
−0.953844 | + | 0.300304i | \(0.902912\pi\) | |||||||
\(440\) | 7.35994 | + | 1.41277i | 0.350871 | + | 0.0673513i | ||||
\(441\) | −53.7886 | − | 12.2985i | −2.56136 | − | 0.585643i | ||||
\(442\) | 0.573945 | + | 0.573945i | 0.0272998 | + | 0.0272998i | ||||
\(443\) | 9.22581 | + | 9.22581i | 0.438331 | + | 0.438331i | 0.891450 | − | 0.453119i | \(-0.149689\pi\) |
−0.453119 | + | 0.891450i | \(0.649689\pi\) | |||||||
\(444\) | 13.5723 | + | 1.53186i | 0.644115 | + | 0.0726988i | ||||
\(445\) | 19.0799 | + | 28.1448i | 0.904472 | + | 1.33419i | ||||
\(446\) | 9.31094i | 0.440886i | ||||||||
\(447\) | −2.13793 | − | 2.68193i | −0.101120 | − | 0.126851i | ||||
\(448\) | 3.56316 | − | 3.56316i | 0.168343 | − | 0.168343i | ||||
\(449\) | −8.74214 | −0.412567 | −0.206283 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206283 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(450\) | −14.7541 | + | 2.70494i | −0.695515 | + | 0.127512i | ||||
\(451\) | −28.2602 | −1.33072 | ||||||||
\(452\) | −0.894915 | + | 0.894915i | −0.0420933 | + | 0.0420933i | ||||
\(453\) | 22.2670 | + | 27.9329i | 1.04620 | + | 1.31240i | ||||
\(454\) | − | 21.3423i | − | 1.00164i | ||||||
\(455\) | 6.78705 | + | 10.0116i | 0.318182 | + | 0.469352i | ||||
\(456\) | 1.72112 | + | 0.194257i | 0.0805990 | + | 0.00909690i | ||||
\(457\) | 10.4440 | + | 10.4440i | 0.488549 | + | 0.488549i | 0.907848 | − | 0.419299i | \(-0.137724\pi\) |
−0.419299 | + | 0.907848i | \(0.637724\pi\) | |||||||
\(458\) | 9.33750 | + | 9.33750i | 0.436313 | + | 0.436313i | ||||
\(459\) | 1.29980 | − | 3.70780i | 0.0606694 | − | 0.173065i | ||||
\(460\) | 12.2801 | + | 2.35721i | 0.572561 | + | 0.109906i | ||||
\(461\) | 15.6610i | 0.729407i | 0.931124 | + | 0.364704i | \(0.118830\pi\) | ||||
−0.931124 | + | 0.364704i | \(0.881170\pi\) | |||||||
\(462\) | −22.8737 | + | 18.2340i | −1.06418 | + | 0.848324i | ||||
\(463\) | −3.40622 | + | 3.40622i | −0.158301 | + | 0.158301i | −0.781813 | − | 0.623513i | \(-0.785705\pi\) |
0.623513 | + | 0.781813i | \(0.285705\pi\) | |||||||
\(464\) | −3.01104 | −0.139784 | ||||||||
\(465\) | 9.42958 | − | 30.2646i | 0.437286 | − | 1.40349i | ||||
\(466\) | 25.1367 | 1.16444 | ||||||||
\(467\) | −26.4385 | + | 26.4385i | −1.22343 | + | 1.22343i | −0.257025 | + | 0.966405i | \(0.582742\pi\) |
−0.966405 | + | 0.257025i | \(0.917258\pi\) | |||||||
\(468\) | 2.72740 | − | 1.71229i | 0.126074 | − | 0.0791506i | ||||
\(469\) | − | 37.2738i | − | 1.72114i | ||||||
\(470\) | −20.9623 | + | 14.2107i | −0.966920 | + | 0.655491i | ||||
\(471\) | 4.57323 | − | 40.5190i | 0.210723 | − | 1.86702i | ||||
\(472\) | −3.05748 | − | 3.05748i | −0.140732 | − | 0.140732i | ||||
\(473\) | −14.4005 | − | 14.4005i | −0.662135 | − | 0.662135i | ||||
\(474\) | −0.0498172 | + | 0.441383i | −0.00228818 | + | 0.0202734i | ||||
\(475\) | −4.64463 | − | 1.85133i | −0.213110 | − | 0.0849448i | ||||
\(476\) | − | 3.81025i | − | 0.174643i | ||||||
\(477\) | 25.3236 | − | 15.8984i | 1.15949 | − | 0.727936i | ||||
\(478\) | 5.71869 | − | 5.71869i | 0.261567 | − | 0.261567i | ||||
\(479\) | −22.6245 | −1.03374 | −0.516871 | − | 0.856063i | \(-0.672903\pi\) | ||||
−0.516871 | + | 0.856063i | \(0.672903\pi\) | |||||||
\(480\) | 1.80000 | + | 3.42929i | 0.0821582 | + | 0.156525i | ||||
\(481\) | 8.46495 | 0.385969 | ||||||||
\(482\) | 12.3459 | − | 12.3459i | 0.562341 | − | 0.562341i | ||||
\(483\) | −38.1648 | + | 30.4235i | −1.73656 | + | 1.38432i | ||||
\(484\) | 0.232932i | 0.0105878i | ||||||||
\(485\) | −5.80330 | + | 30.2327i | −0.263514 | + | 1.37280i | ||||
\(486\) | −13.1912 | − | 8.30615i | −0.598365 | − | 0.376775i | ||||
\(487\) | 19.6380 | + | 19.6380i | 0.889884 | + | 0.889884i | 0.994511 | − | 0.104627i | \(-0.0333650\pi\) |
−0.104627 | + | 0.994511i | \(0.533365\pi\) | |||||||
\(488\) | −0.959995 | − | 0.959995i | −0.0434569 | − | 0.0434569i | ||||
\(489\) | −24.4070 | − | 2.75473i | −1.10372 | − | 0.124573i | ||||
\(490\) | 7.75283 | − | 40.3889i | 0.350237 | − | 1.82458i | ||||
\(491\) | − | 7.22196i | − | 0.325922i | −0.986632 | − | 0.162961i | \(-0.947895\pi\) | ||
0.986632 | − | 0.162961i | \(-0.0521045\pi\) | |||||||
\(492\) | −9.10362 | − | 11.4200i | −0.410423 | − | 0.514856i | ||||
\(493\) | −1.60992 | + | 1.60992i | −0.0725073 | + | 0.0725073i | ||||
\(494\) | 1.07345 | 0.0482968 | ||||||||
\(495\) | −8.15049 | − | 20.9536i | −0.366337 | − | 0.941792i | ||||
\(496\) | −8.18480 | −0.367508 | ||||||||
\(497\) | 16.9164 | − | 16.9164i | 0.758802 | − | 0.758802i | ||||
\(498\) | 7.22593 | + | 9.06457i | 0.323801 | + | 0.406193i | ||||
\(499\) | 29.0605i | 1.30093i | 0.759538 | + | 0.650463i | \(0.225425\pi\) | ||||
−0.759538 | + | 0.650463i | \(0.774575\pi\) | |||||||
\(500\) | −2.40119 | − | 10.9194i | −0.107384 | − | 0.488332i | ||||
\(501\) | 14.9917 | + | 1.69206i | 0.669780 | + | 0.0755956i | ||||
\(502\) | 1.55568 | + | 1.55568i | 0.0694333 | + | 0.0694333i | ||||
\(503\) | −23.3678 | − | 23.3678i | −1.04192 | − | 1.04192i | −0.999082 | − | 0.0428359i | \(-0.986361\pi\) |
−0.0428359 | − | 0.999082i | \(-0.513639\pi\) | |||||||
\(504\) | −14.7369 | − | 3.36952i | −0.656434 | − | 0.150090i | ||||
\(505\) | 22.7996 | − | 15.4562i | 1.01457 | − | 0.687792i | ||||
\(506\) | 18.7421i | 0.833190i | ||||||||
\(507\) | −16.0463 | + | 12.7915i | −0.712640 | + | 0.568089i | ||||
\(508\) | −6.70476 | + | 6.70476i | −0.297475 | + | 0.297475i | ||||
\(509\) | −15.9405 | −0.706550 | −0.353275 | − | 0.935520i | \(-0.614932\pi\) | ||||
−0.353275 | + | 0.935520i | \(0.614932\pi\) | |||||||
\(510\) | 2.79596 | + | 0.871139i | 0.123807 | + | 0.0385747i | ||||
\(511\) | 36.5363 | 1.61627 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.25184 | − | 4.68286i | −0.0994214 | − | 0.206753i | ||||
\(514\) | 25.9974i | 1.14670i | ||||||||
\(515\) | −1.10897 | − | 0.212873i | −0.0488673 | − | 0.00938029i | ||||
\(516\) | 1.18038 | − | 10.4582i | 0.0519633 | − | 0.460397i | ||||
\(517\) | −26.8410 | − | 26.8410i | −1.18047 | − | 1.18047i | ||||
\(518\) | −28.0982 | − | 28.0982i | −1.23456 | − | 1.23456i | ||||
\(519\) | 0.465923 | − | 4.12810i | 0.0204517 | − | 0.181203i | ||||
\(520\) | 1.34689 | + | 1.98680i | 0.0590648 | + | 0.0871270i | ||||
\(521\) | 39.2764i | 1.72073i | 0.509679 | + | 0.860365i | \(0.329764\pi\) | ||||
−0.509679 | + | 0.860365i | \(0.670236\pi\) | |||||||
\(522\) | 4.80299 | + | 7.65040i | 0.210221 | + | 0.334849i | ||||
\(523\) | −7.29624 | + | 7.29624i | −0.319042 | + | 0.319042i | −0.848399 | − | 0.529357i | \(-0.822433\pi\) |
0.529357 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(524\) | −1.53144 | −0.0669011 | ||||||||
\(525\) | 38.4700 | + | 20.6028i | 1.67897 | + | 0.899181i | ||||
\(526\) | −24.9560 | −1.08813 | ||||||||
\(527\) | −4.37619 | + | 4.37619i | −0.190630 | + | 0.190630i | ||||
\(528\) | −4.53927 | + | 3.61853i | −0.197547 | + | 0.157476i | ||||
\(529\) | 8.27125i | 0.359620i | ||||||||
\(530\) | 12.5056 | + | 18.4472i | 0.543210 | + | 0.801294i | ||||
\(531\) | −2.89133 | + | 12.6455i | −0.125473 | + | 0.548767i | ||||
\(532\) | −3.56316 | − | 3.56316i | −0.154483 | − | 0.154483i | ||||
\(533\) | −6.40022 | − | 6.40022i | −0.277224 | − | 0.277224i | ||||
\(534\) | −26.1721 | − | 2.95395i | −1.13258 | − | 0.127830i | ||||
\(535\) | −6.70397 | − | 1.28686i | −0.289838 | − | 0.0556357i | ||||
\(536\) | − | 7.39695i | − | 0.319500i | ||||||
\(537\) | 12.4128 | + | 15.5712i | 0.535651 | + | 0.671948i | ||||
\(538\) | 9.04126 | − | 9.04126i | 0.389796 | − | 0.389796i | ||||
\(539\) | 61.6426 | 2.65513 | ||||||||
\(540\) | 5.84185 | − | 10.0435i | 0.251393 | − | 0.432205i | ||||
\(541\) | −18.2326 | −0.783881 | −0.391940 | − | 0.919991i | \(-0.628196\pi\) | ||||
−0.391940 | + | 0.919991i | \(0.628196\pi\) | |||||||
\(542\) | −5.80738 | + | 5.80738i | −0.249448 | + | 0.249448i | ||||
\(543\) | 24.1081 | + | 30.2425i | 1.03458 | + | 1.29783i | ||||
\(544\) | − | 0.756142i | − | 0.0324193i | ||||||
\(545\) | −5.48008 | + | 3.71504i | −0.234741 | + | 0.159135i | ||||
\(546\) | −9.30988 | − | 1.05077i | −0.398426 | − | 0.0449689i | ||||
\(547\) | 15.9706 | + | 15.9706i | 0.682854 | + | 0.682854i | 0.960642 | − | 0.277788i | \(-0.0896013\pi\) |
−0.277788 | + | 0.960642i | \(0.589601\pi\) | |||||||
\(548\) | −4.76164 | − | 4.76164i | −0.203407 | − | 0.203407i | ||||
\(549\) | −0.907824 | + | 3.97045i | −0.0387450 | + | 0.169455i | ||||
\(550\) | 15.3948 | − | 6.61986i | 0.656438 | − | 0.282272i | ||||
\(551\) | 3.01104i | 0.128275i | ||||||||
\(552\) | −7.57378 | + | 6.03752i | −0.322361 | + | 0.256974i | ||||
\(553\) | 0.913774 | − | 0.913774i | 0.0388576 | − | 0.0388576i | ||||
\(554\) | 6.12299 | 0.260141 | ||||||||
\(555\) | 27.0425 | − | 14.1943i | 1.14789 | − | 0.602515i | ||||
\(556\) | −9.84417 | −0.417486 | ||||||||
\(557\) | −12.9276 | + | 12.9276i | −0.547758 | + | 0.547758i | −0.925792 | − | 0.378034i | \(-0.876600\pi\) |
0.378034 | + | 0.925792i | \(0.376600\pi\) | |||||||
\(558\) | 13.0558 | + | 20.7958i | 0.552696 | + | 0.880356i | ||||
\(559\) | − | 6.52270i | − | 0.275881i | ||||||
\(560\) | 2.12411 | − | 11.0657i | 0.0897599 | − | 0.467610i | ||||
\(561\) | −0.492296 | + | 4.36176i | −0.0207847 | + | 0.184154i | ||||
\(562\) | 7.79389 | + | 7.79389i | 0.328765 | + | 0.328765i | ||||
\(563\) | 26.9809 | + | 26.9809i | 1.13711 | + | 1.13711i | 0.988966 | + | 0.148145i | \(0.0473302\pi\) |
0.148145 | + | 0.988966i | \(0.452670\pi\) | |||||||
\(564\) | 2.20010 | − | 19.4930i | 0.0926410 | − | 0.820804i | ||||
\(565\) | −0.533486 | + | 2.77923i | −0.0224439 | + | 0.116923i | ||||
\(566\) | 17.1605i | 0.721309i | ||||||||
\(567\) | 14.9460 | + | 42.8181i | 0.627673 | + | 1.79819i | ||||
\(568\) | 3.35704 | − | 3.35704i | 0.140858 | − | 0.140858i | ||||
\(569\) | 30.1015 | 1.26192 | 0.630961 | − | 0.775814i | \(-0.282661\pi\) | ||||
0.630961 | + | 0.775814i | \(0.282661\pi\) | |||||||
\(570\) | 3.42929 | − | 1.80000i | 0.143637 | − | 0.0753935i | ||||
\(571\) | −2.85189 | −0.119348 | −0.0596740 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596740 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(572\) | −2.54398 | + | 2.54398i | −0.106369 | + | 0.106369i | ||||
\(573\) | 10.7381 | − | 8.55997i | 0.448589 | − | 0.357598i | ||||
\(574\) | 42.4892i | 1.77346i | ||||||||
\(575\) | 25.6863 | − | 11.0452i | 1.07119 | − | 0.460618i | ||||
\(576\) | −2.92453 | − | 0.668679i | −0.121855 | − | 0.0278616i | ||||
\(577\) | −2.60285 | − | 2.60285i | −0.108358 | − | 0.108358i | 0.650849 | − | 0.759207i | \(-0.274413\pi\) |
−0.759207 | + | 0.650849i | \(0.774413\pi\) | |||||||
\(578\) | 11.6165 | + | 11.6165i | 0.483184 | + | 0.483184i | ||||
\(579\) | 11.4151 | + | 1.28838i | 0.474396 | + | 0.0535433i | ||||
\(580\) | −5.57300 | + | 3.77803i | −0.231406 | + | 0.156874i | ||||
\(581\) | − | 33.7255i | − | 1.39917i | ||||||
\(582\) | −14.8640 | − | 18.6461i | −0.616132 | − | 0.772908i | ||||
\(583\) | −23.6205 | + | 23.6205i | −0.978260 | + | 0.978260i | ||||
\(584\) | 7.25060 | 0.300032 | ||||||||
\(585\) | 2.89958 | − | 6.59134i | 0.119883 | − | 0.272518i | ||||
\(586\) | −24.6840 | −1.01968 | ||||||||
\(587\) | −9.92177 | + | 9.92177i | −0.409515 | + | 0.409515i | −0.881569 | − | 0.472054i | \(-0.843513\pi\) |
0.472054 | + | 0.881569i | \(0.343513\pi\) | |||||||
\(588\) | 19.8573 | + | 24.9100i | 0.818901 | + | 1.02727i | ||||
\(589\) | 8.18480i | 0.337249i | ||||||||
\(590\) | −9.49526 | − | 1.82266i | −0.390914 | − | 0.0750377i | ||||
\(591\) | 11.4939 | + | 1.29727i | 0.472795 | + | 0.0533626i | ||||
\(592\) | −5.57606 | − | 5.57606i | −0.229175 | − | 0.229175i | ||||
\(593\) | 0.851881 | + | 0.851881i | 0.0349826 | + | 0.0349826i | 0.724382 | − | 0.689399i | \(-0.242125\pi\) |
−0.689399 | + | 0.724382i | \(0.742125\pi\) | |||||||
\(594\) | 16.4346 | + | 5.76129i | 0.674321 | + | 0.236389i | ||||
\(595\) | −4.78082 | − | 7.05222i | −0.195994 | − | 0.289113i | ||||
\(596\) | 1.98019i | 0.0811118i | ||||||||
\(597\) | −13.5502 | + | 10.8017i | −0.554573 | + | 0.442084i | ||||
\(598\) | −4.24463 | + | 4.24463i | −0.173576 | + | 0.173576i | ||||
\(599\) | 3.99004 | 0.163028 | 0.0815142 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815142 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(600\) | 7.63434 | + | 4.08862i | 0.311671 | + | 0.166917i | ||||
\(601\) | 6.42813 | 0.262209 | 0.131104 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131104 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(602\) | −21.6511 | + | 21.6511i | −0.882435 | + | 0.882435i | ||||
\(603\) | −18.7940 | + | 11.7991i | −0.765353 | + | 0.480496i | ||||
\(604\) | − | 20.6241i | − | 0.839185i | ||||||
\(605\) | 0.292266 | + | 0.431124i | 0.0118823 | + | 0.0175277i | ||||
\(606\) | −2.39293 | + | 21.2015i | −0.0972062 | + | 0.861252i | ||||
\(607\) | 18.0117 | + | 18.0117i | 0.731071 | + | 0.731071i | 0.970832 | − | 0.239761i | \(-0.0770690\pi\) |
−0.239761 | + | 0.970832i | \(0.577069\pi\) | |||||||
\(608\) | −0.707107 | − | 0.707107i | −0.0286770 | − | 0.0286770i | ||||
\(609\) | 2.94743 | − | 26.1143i | 0.119436 | − | 1.05821i | ||||
\(610\) | −2.98134 | − | 0.572282i | −0.120711 | − | 0.0231710i | ||||
\(611\) | − | 12.1576i | − | 0.491845i | ||||||
\(612\) | −1.92119 | + | 1.20614i | −0.0776596 | + | 0.0487554i | ||||
\(613\) | −24.1414 | + | 24.1414i | −0.975063 | + | 0.975063i | −0.999697 | − | 0.0246339i | \(-0.992158\pi\) |
0.0246339 | + | 0.999697i | \(0.492158\pi\) | |||||||
\(614\) | −8.27850 | −0.334093 | ||||||||
\(615\) | −31.1785 | − | 9.71432i | −1.25724 | − | 0.391719i | ||||
\(616\) | 16.8887 | 0.680466 | ||||||||
\(617\) | 27.8433 | − | 27.8433i | 1.12093 | − | 1.12093i | 0.129329 | − | 0.991602i | \(-0.458718\pi\) |
0.991602 | − | 0.129329i | \(-0.0412824\pi\) | |||||||
\(618\) | 0.683965 | − | 0.545230i | 0.0275131 | − | 0.0219324i | ||||
\(619\) | − | 26.3475i | − | 1.05899i | −0.848312 | − | 0.529497i | \(-0.822381\pi\) | ||
0.848312 | − | 0.529497i | \(-0.177619\pi\) | |||||||
\(620\) | −15.1489 | + | 10.2697i | −0.608394 | + | 0.412440i | ||||
\(621\) | 27.4212 | + | 9.61271i | 1.10037 | + | 0.385745i | ||||
\(622\) | −10.0510 | − | 10.0510i | −0.403008 | − | 0.403008i | ||||
\(623\) | 54.1828 | + | 54.1828i | 2.17079 | + | 2.17079i | ||||
\(624\) | −1.84754 | − | 0.208525i | −0.0739608 | − | 0.00834768i | ||||
\(625\) | −18.1452 | − | 17.1975i | −0.725806 | − | 0.687899i | ||||
\(626\) | − | 32.9500i | − | 1.31695i | ||||||
\(627\) | 3.61853 | + | 4.53927i | 0.144510 | + | 0.181281i | ||||
\(628\) | −16.6468 | + | 16.6468i | −0.664282 | + | 0.664282i | ||||
\(629\) | −5.96274 | −0.237750 | ||||||||
\(630\) | −31.5037 | + | 12.2543i | −1.25514 | + | 0.488222i | ||||
\(631\) | 34.9462 | 1.39119 | 0.695593 | − | 0.718436i | \(-0.255142\pi\) | ||||
0.695593 | + | 0.718436i | \(0.255142\pi\) | |||||||
\(632\) | 0.181338 | − | 0.181338i | 0.00721324 | − | 0.00721324i | ||||
\(633\) | 0.365606 | + | 0.458636i | 0.0145316 | + | 0.0182291i | ||||
\(634\) | 14.1296i | 0.561159i | ||||||||
\(635\) | −3.99691 | + | 20.8222i | −0.158612 | + | 0.826302i | ||||
\(636\) | −17.1541 | − | 1.93612i | −0.680206 | − | 0.0767723i | ||||
\(637\) | 13.9605 | + | 13.9605i | 0.553135 | + | 0.553135i | ||||
\(638\) | −7.13590 | − | 7.13590i | −0.282513 | − | 0.282513i | ||||
\(639\) | −13.8844 | − | 3.17460i | −0.549259 | − | 0.125585i | ||||
\(640\) | 0.421528 | − | 2.19598i | 0.0166623 | − | 0.0868036i | ||||
\(641\) | 46.8388i | 1.85002i | 0.379943 | + | 0.925010i | \(0.375944\pi\) | ||||
−0.379943 | + | 0.925010i | \(0.624056\pi\) | |||||||
\(642\) | 4.13470 | − | 3.29602i | 0.163184 | − | 0.130084i | ||||
\(643\) | 22.8114 | − | 22.8114i | 0.899592 | − | 0.899592i | −0.0958078 | − | 0.995400i | \(-0.530543\pi\) |
0.995400 | + | 0.0958078i | \(0.0305434\pi\) | |||||||
\(644\) | 28.1788 | 1.11040 | ||||||||
\(645\) | −10.9375 | − | 20.8377i | −0.430662 | − | 0.820483i | ||||
\(646\) | −0.756142 | −0.0297500 | ||||||||
\(647\) | −10.8816 | + | 10.8816i | −0.427801 | + | 0.427801i | −0.887879 | − | 0.460078i | \(-0.847821\pi\) |
0.460078 | + | 0.887879i | \(0.347821\pi\) | |||||||
\(648\) | 2.96602 | + | 8.49722i | 0.116516 | + | 0.333802i | ||||
\(649\) | − | 14.4919i | − | 0.568857i | ||||||
\(650\) | 4.98578 | + | 1.98731i | 0.195558 | + | 0.0779487i | ||||
\(651\) | 8.01188 | − | 70.9856i | 0.314010 | − | 2.78215i | ||||
\(652\) | 10.0274 | + | 10.0274i | 0.392703 | + | 0.392703i | ||||
\(653\) | −0.0974665 | − | 0.0974665i | −0.00381416 | − | 0.00381416i | 0.705197 | − | 0.709011i | \(-0.250858\pi\) |
−0.709011 | + | 0.705197i | \(0.750858\pi\) | |||||||
\(654\) | 0.575163 | − | 5.09597i | 0.0224906 | − | 0.199268i | ||||
\(655\) | −2.83447 | + | 1.92153i | −0.110752 | + | 0.0750804i | ||||
\(656\) | 8.43195i | 0.329212i | ||||||||
\(657\) | −11.5656 | − | 18.4222i | −0.451218 | − | 0.718719i | ||||
\(658\) | −40.3555 | + | 40.3555i | −1.57322 | + | 1.57322i | ||||
\(659\) | −4.39566 | −0.171231 | −0.0856153 | − | 0.996328i | \(-0.527286\pi\) | ||||
−0.0856153 | + | 0.996328i | \(0.527286\pi\) | |||||||
\(660\) | −3.86128 | + | 12.3929i | −0.150300 | + | 0.482394i | ||||
\(661\) | −36.4313 | −1.41701 | −0.708507 | − | 0.705704i | \(-0.750631\pi\) | ||||
−0.708507 | + | 0.705704i | \(0.750631\pi\) | |||||||
\(662\) | −6.17860 | + | 6.17860i | −0.240138 | + | 0.240138i | ||||
\(663\) | −1.09932 | + | 0.876337i | −0.0426941 | + | 0.0340341i | ||||
\(664\) | − | 6.69279i | − | 0.259731i | ||||||
\(665\) | −11.0657 | − | 2.12411i | −0.429109 | − | 0.0823693i | ||||
\(666\) | −5.27303 | + | 23.0621i | −0.204326 | + | 0.893638i | ||||
\(667\) | −11.9062 | − | 11.9062i | −0.461011 | − | 0.461011i | ||||
\(668\) | −6.15920 | − | 6.15920i | −0.238307 | − | 0.238307i | ||||
\(669\) | −16.0253 | − | 1.80871i | −0.619573 | − | 0.0699289i | ||||
\(670\) | −9.28114 | − | 13.6907i | −0.358562 | − | 0.528918i | ||||
\(671\) | − | 4.55020i | − | 0.175658i | ||||||
\(672\) | 5.44047 | + | 6.82480i | 0.209871 | + | 0.263273i | ||||
\(673\) | 12.9562 | − | 12.9562i | 0.499425 | − | 0.499425i | −0.411834 | − | 0.911259i | \(-0.635112\pi\) |
0.911259 | + | 0.411834i | \(0.135112\pi\) | |||||||
\(674\) | 26.5467 | 1.02254 | ||||||||
\(675\) | −1.78946 | − | 25.9191i | −0.0688764 | − | 0.997625i | ||||
\(676\) | 11.8477 | 0.455681 | ||||||||
\(677\) | 21.1304 | − | 21.1304i | 0.812109 | − | 0.812109i | −0.172841 | − | 0.984950i | \(-0.555295\pi\) |
0.984950 | + | 0.172841i | \(0.0552947\pi\) | |||||||
\(678\) | −1.36642 | − | 1.71410i | −0.0524769 | − | 0.0658297i | ||||
\(679\) | 69.3744i | 2.66235i | ||||||||
\(680\) | −0.948750 | − | 1.39951i | −0.0363829 | − | 0.0536687i | ||||
\(681\) | 36.7327 | + | 4.14588i | 1.40760 | + | 0.158871i | ||||
\(682\) | −19.3972 | − | 19.3972i | −0.742758 | − | 0.742758i | ||||
\(683\) | 9.66304 | + | 9.66304i | 0.369746 | + | 0.369746i | 0.867385 | − | 0.497638i | \(-0.165799\pi\) |
−0.497638 | + | 0.867385i | \(0.665799\pi\) | |||||||
\(684\) | −0.668679 | + | 2.92453i | −0.0255676 | + | 0.111822i | ||||
\(685\) | −14.7877 | − | 2.83856i | −0.565007 | − | 0.108456i | ||||
\(686\) | − | 57.4062i | − | 2.19178i | ||||||
\(687\) | −17.8849 | + | 14.2571i | −0.682350 | + | 0.543943i | ||||
\(688\) | −4.29665 | + | 4.29665i | −0.163808 | + | 0.163808i | ||||
\(689\) | −10.6989 | −0.407596 | ||||||||
\(690\) | −6.44254 | + | 20.6776i | −0.245263 | + | 0.787182i | ||||
\(691\) | −5.64130 | −0.214605 | −0.107303 | − | 0.994226i | \(-0.534221\pi\) | ||||
−0.107303 | + | 0.994226i | \(0.534221\pi\) | |||||||
\(692\) | −1.69599 | + | 1.69599i | −0.0644718 | + | 0.0644718i | ||||
\(693\) | −26.9397 | − | 42.9106i | −1.02335 | − | 1.63004i | ||||
\(694\) | − | 7.63909i | − | 0.289976i | ||||||
\(695\) | −18.2201 | + | 12.3517i | −0.691129 | + | 0.468527i | ||||
\(696\) | 0.584915 | − | 5.18237i | 0.0221712 | − | 0.196437i | ||||
\(697\) | 4.50834 | + | 4.50834i | 0.170765 | + | 0.170765i | ||||
\(698\) | −13.5474 | − | 13.5474i | −0.512778 | − | 0.512778i | ||||
\(699\) | −4.88298 | + | 43.2634i | −0.184691 | + | 1.63637i | ||||
\(700\) | −9.95297 | − | 23.1461i | −0.376187 | − | 0.874842i | ||||
\(701\) | 5.68210i | 0.214610i | 0.994226 | + | 0.107305i | \(0.0342221\pi\) | ||||
−0.994226 | + | 0.107305i | \(0.965778\pi\) | |||||||
\(702\) | 2.41724 | + | 5.02682i | 0.0912330 | + | 0.189725i | ||||
\(703\) | −5.57606 | + | 5.57606i | −0.210305 | + | 0.210305i | ||||
\(704\) | 3.35156 | 0.126317 | ||||||||
\(705\) | −20.3863 | − | 38.8393i | −0.767792 | − | 1.46277i | ||||
\(706\) | 0.518226 | 0.0195037 | ||||||||
\(707\) | 43.8924 | − | 43.8924i | 1.65075 | − | 1.65075i | ||||
\(708\) | 5.85624 | − | 4.66837i | 0.220091 | − | 0.175448i | ||||
\(709\) | 29.4977i | 1.10781i | 0.832580 | + | 0.553906i | \(0.186863\pi\) | ||||
−0.832580 | + | 0.553906i | \(0.813137\pi\) | |||||||
\(710\) | 2.00123 | − | 10.4256i | 0.0751049 | − | 0.391264i | ||||
\(711\) | −0.749997 | − | 0.171483i | −0.0281271 | − | 0.00643112i | ||||
\(712\) | 10.7526 | + | 10.7526i | 0.402969 | + | 0.402969i | ||||
\(713\) | −32.3643 | − | 32.3643i | −1.21205 | − | 1.21205i | ||||
\(714\) | 6.55791 | + | 0.740167i | 0.245424 | + | 0.0277000i | ||||
\(715\) | −1.51654 | + | 7.90053i | −0.0567155 | + | 0.295463i | ||||
\(716\) | − | 11.4970i | − | 0.429662i | ||||||
\(717\) | 8.73168 | + | 10.9535i | 0.326091 | + | 0.409065i | ||||
\(718\) | 11.6243 | − | 11.6243i | 0.433815 | − | 0.433815i | ||||
\(719\) | −38.3623 | −1.43067 | −0.715337 | − | 0.698780i | \(-0.753727\pi\) | ||||
−0.715337 | + | 0.698780i | \(0.753727\pi\) | |||||||
\(720\) | −6.25189 | + | 2.43185i | −0.232994 | + | 0.0906297i | ||||
\(721\) | −2.54474 | −0.0947712 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | 18.8506 | + | 23.6471i | 0.701060 | + | 0.879446i | ||||
\(724\) | − | 22.3294i | − | 0.829867i | ||||||
\(725\) | −5.57443 | + | 13.9852i | −0.207029 | + | 0.519396i | ||||
\(726\) | −0.400905 | − | 0.0452486i | −0.0148790 | − | 0.00167933i | ||||
\(727\) | −12.1887 | − | 12.1887i | −0.452054 | − | 0.452054i | 0.443982 | − | 0.896036i | \(-0.353565\pi\) |
−0.896036 | + | 0.443982i | \(0.853565\pi\) | |||||||
\(728\) | 3.82488 | + | 3.82488i | 0.141759 | + | 0.141759i | ||||
\(729\) | 16.8584 | − | 21.0902i | 0.624385 | − | 0.781117i | ||||
\(730\) | 13.4198 | − | 9.09752i | 0.496690 | − | 0.336714i | ||||
\(731\) | 4.59461i | 0.169938i | ||||||||
\(732\) | 1.83875 | − | 1.46578i | 0.0679623 | − | 0.0541769i | ||||
\(733\) | 21.4518 | − | 21.4518i | 0.792340 | − | 0.792340i | −0.189534 | − | 0.981874i | \(-0.560698\pi\) |
0.981874 | + | 0.189534i | \(0.0606977\pi\) | |||||||
\(734\) | 18.9116 | 0.698039 | ||||||||
\(735\) | 68.0082 | + | 21.1894i | 2.50852 | + | 0.781582i | ||||
\(736\) | 5.59207 | 0.206126 | ||||||||
\(737\) | 17.5301 | − | 17.5301i | 0.645730 | − | 0.645730i | ||||
\(738\) | 21.4237 | − | 13.4500i | 0.788619 | − | 0.495102i | ||||
\(739\) | 1.62124i | 0.0596381i | 0.999555 | + | 0.0298191i | \(0.00949311\pi\) | ||||
−0.999555 | + | 0.0298191i | \(0.990507\pi\) | |||||||
\(740\) | −17.3169 | − | 3.32406i | −0.636582 | − | 0.122195i | ||||
\(741\) | −0.208525 | + | 1.84754i | −0.00766036 | + | 0.0678711i | ||||
\(742\) | 35.5134 | + | 35.5134i | 1.30374 | + | 1.30374i | ||||
\(743\) | 4.47847 | + | 4.47847i | 0.164299 | + | 0.164299i | 0.784468 | − | 0.620169i | \(-0.212936\pi\) |
−0.620169 | + | 0.784468i | \(0.712936\pi\) | |||||||
\(744\) | 1.58995 | − | 14.0871i | 0.0582905 | − | 0.516456i | ||||
\(745\) | 2.48459 | + | 3.66505i | 0.0910285 | + | 0.134277i | ||||
\(746\) | 3.96766i | 0.145266i | ||||||||
\(747\) | −17.0049 | + | 10.6759i | −0.622178 | + | 0.390609i | ||||
\(748\) | 1.79199 | − | 1.79199i | 0.0655215 | − | 0.0655215i | ||||
\(749\) | −15.3835 | −0.562100 | ||||||||
\(750\) | 19.2602 | − | 2.01157i | 0.703281 | − | 0.0734520i | ||||
\(751\) | −21.5949 | −0.788010 | −0.394005 | − | 0.919108i | \(-0.628911\pi\) | ||||
−0.394005 | + | 0.919108i | \(0.628911\pi\) | |||||||
\(752\) | −8.00851 | + | 8.00851i | −0.292040 | + | 0.292040i | ||||
\(753\) | −2.97971 | + | 2.37531i | −0.108587 | + | 0.0865612i | ||||
\(754\) | − | 3.23220i | − | 0.117710i | ||||||
\(755\) | −25.8776 | − | 38.1723i | −0.941784 | − | 1.38923i | ||||
\(756\) | 8.66210 | − | 24.7095i | 0.315038 | − | 0.898675i | ||||
\(757\) | −11.6792 | − | 11.6792i | −0.424488 | − | 0.424488i | 0.462258 | − | 0.886746i | \(-0.347040\pi\) |
−0.886746 | + | 0.462258i | \(0.847040\pi\) | |||||||
\(758\) | −24.7867 | − | 24.7867i | −0.900293 | − | 0.900293i | ||||
\(759\) | −32.2575 | − | 3.64079i | −1.17087 | − | 0.132152i | ||||
\(760\) | −2.19598 | − | 0.421528i | −0.0796565 | − | 0.0152904i | ||||
\(761\) | 21.6915i | 0.786317i | 0.919471 | + | 0.393159i | \(0.128618\pi\) | ||||
−0.919471 | + | 0.393159i | \(0.871382\pi\) | |||||||
\(762\) | −10.2373 | − | 12.8422i | −0.370857 | − | 0.465222i | ||||
\(763\) | −10.5499 | + | 10.5499i | −0.381933 | + | 0.381933i | ||||
\(764\) | −7.92842 | −0.286840 | ||||||||
\(765\) | −2.04247 | + | 4.64296i | −0.0738457 | + | 0.167867i | ||||
\(766\) | 1.11237 | 0.0401914 | ||||||||
\(767\) | 3.28206 | − | 3.28206i | 0.118508 | − | 0.118508i | ||||
\(768\) | 1.07966 | + | 1.35438i | 0.0389588 | + | 0.0488719i | ||||
\(769\) | 24.6155i | 0.887659i | 0.896111 | + | 0.443830i | \(0.146380\pi\) | ||||
−0.896111 | + | 0.443830i | \(0.853620\pi\) | |||||||
\(770\) | 31.2586 | − | 21.1907i | 1.12648 | − | 0.763660i | ||||
\(771\) | −44.7447 | − | 5.05017i | −1.61144 | − | 0.181878i | ||||
\(772\) | −4.68979 | − | 4.68979i | −0.168789 | − | 0.168789i | ||||
\(773\) | −3.36652 | − | 3.36652i | −0.121085 | − | 0.121085i | 0.643968 | − | 0.765053i | \(-0.277287\pi\) |
−0.765053 | + | 0.643968i | \(0.777287\pi\) | |||||||
\(774\) | 17.7706 | + | 4.06315i | 0.638750 | + | 0.146047i | ||||
\(775\) | −15.1528 | + | 38.0154i | −0.544303 | + | 1.36555i | ||||
\(776\) | 13.7673i | 0.494218i | ||||||||
\(777\) | 53.8187 | − | 42.9021i | 1.93073 | − | 1.53911i | ||||
\(778\) | −0.985230 | + | 0.985230i | −0.0353222 | + | 0.0353222i | ||||
\(779\) | 8.43195 | 0.302106 | ||||||||
\(780\) | −3.68117 | + | 1.93221i | −0.131807 | + | 0.0691841i | ||||
\(781\) | 15.9118 | 0.569367 | ||||||||
\(782\) | 2.98993 | − | 2.98993i | 0.106920 | − | 0.106920i | ||||
\(783\) | −14.1003 | + | 6.78040i | −0.503904 | + | 0.242312i | ||||
\(784\) | − | 18.3922i | − | 0.656865i | ||||||
\(785\) | −9.92369 | + | 51.6981i | −0.354192 | + | 1.84519i | ||||
\(786\) | 0.297492 | − | 2.63579i | 0.0106112 | − | 0.0940155i | ||||
\(787\) | 6.46976 | + | 6.46976i | 0.230622 | + | 0.230622i | 0.812952 | − | 0.582330i | \(-0.197859\pi\) |
−0.582330 | + | 0.812952i | \(0.697859\pi\) | |||||||
\(788\) | −4.72215 | − | 4.72215i | −0.168220 | − | 0.168220i | ||||
\(789\) | 4.84786 | − | 42.9523i | 0.172589 | − | 1.52914i | ||||
\(790\) | 0.108101 | − | 0.563159i | 0.00384606 | − | 0.0200363i | ||||
\(791\) | 6.37745i | 0.226756i | ||||||||
\(792\) | −5.34616 | − | 8.51557i | −0.189967 | − | 0.302588i | ||||
\(793\) | 1.03051 | − | 1.03051i | 0.0365944 | − | 0.0365944i | ||||
\(794\) | −14.8510 | −0.527041 | ||||||||
\(795\) | −34.1791 | + | 17.9403i | −1.21221 | + | 0.636275i | ||||
\(796\) | 10.0047 | 0.354609 | ||||||||
\(797\) | −29.5421 | + | 29.5421i | −1.04644 | + | 1.04644i | −0.0475679 | + | 0.998868i | \(0.515147\pi\) |
−0.998868 | + | 0.0475679i | \(0.984853\pi\) | |||||||
\(798\) | 6.82480 | − | 5.44047i | 0.241595 | − | 0.192591i | ||||
\(799\) | 8.56387i | 0.302968i | ||||||||
\(800\) | −1.97516 | − | 4.59334i | −0.0698325 | − | 0.162399i | ||||
\(801\) | 10.1682 | − | 44.4716i | 0.359276 | − | 1.57133i | ||||
\(802\) | 13.8878 | + | 13.8878i | 0.490396 | + | 0.490396i | ||||
\(803\) | 17.1833 | + | 17.1833i | 0.606384 | + | 0.606384i | ||||
\(804\) | 12.7311 | + | 1.43691i | 0.448990 | + | 0.0506758i | ||||
\(805\) | 52.1549 | − | 35.3567i | 1.83822 | − | 1.24616i | ||||
\(806\) | − | 8.78598i | − | 0.309473i | ||||||
\(807\) | 13.8048 | + | 17.3174i | 0.485952 | + | 0.609603i | ||||
\(808\) | 8.71043 | − | 8.71043i | 0.306432 | − | 0.306432i | ||||
\(809\) | 56.0263 | 1.96978 | 0.984889 | − | 0.173186i | \(-0.0554063\pi\) | ||||
0.984889 | + | 0.173186i | \(0.0554063\pi\) | |||||||
\(810\) | 16.1514 | + | 12.0056i | 0.567501 | + | 0.421833i | ||||
\(811\) | −50.7816 | −1.78318 | −0.891591 | − | 0.452842i | \(-0.850410\pi\) | ||||
−0.891591 | + | 0.452842i | \(0.850410\pi\) | |||||||
\(812\) | −10.7288 | + | 10.7288i | −0.376508 | + | 0.376508i | ||||
\(813\) | −8.86709 | − | 11.1233i | −0.310982 | − | 0.390112i | ||||
\(814\) | − | 26.4295i | − | 0.926354i | ||||||
\(815\) | 31.1409 | + | 5.97763i | 1.09082 | + | 0.209387i | ||||
\(816\) | 1.30141 | + | 0.146886i | 0.0455586 | + | 0.00514203i | ||||
\(817\) | 4.29665 | + | 4.29665i | 0.150321 | + | 0.150321i | ||||
\(818\) | −6.09142 | − | 6.09142i | −0.212981 | − | 0.212981i | ||||
\(819\) | 3.61701 | − | 15.8193i | 0.126389 | − | 0.552772i | ||||
\(820\) | 10.5798 | + | 15.6063i | 0.369462 | + | 0.544996i | ||||
\(821\) | 18.4172i | 0.642764i | 0.946950 | + | 0.321382i | \(0.104147\pi\) | ||||
−0.946950 | + | 0.321382i | \(0.895853\pi\) | |||||||
\(822\) | 9.12035 | − | 7.27039i | 0.318109 | − | 0.253584i | ||||
\(823\) | 14.3557 | − | 14.3557i | 0.500409 | − | 0.500409i | −0.411156 | − | 0.911565i | \(-0.634875\pi\) |
0.911565 | + | 0.411156i | \(0.134875\pi\) | |||||||
\(824\) | −0.505003 | −0.0175926 | ||||||||
\(825\) | 8.40305 | + | 27.7823i | 0.292557 | + | 0.967257i | ||||
\(826\) | −21.7886 | −0.758123 | ||||||||
\(827\) | 30.1536 | − | 30.1536i | 1.04854 | − | 1.04854i | 0.0497825 | − | 0.998760i | \(-0.484147\pi\) |
0.998760 | − | 0.0497825i | \(-0.0158528\pi\) | |||||||
\(828\) | −8.92006 | − | 14.2082i | −0.309993 | − | 0.493770i | ||||
\(829\) | − | 14.0610i | − | 0.488357i | −0.969730 | − | 0.244179i | \(-0.921482\pi\) | ||
0.969730 | − | 0.244179i | \(-0.0785183\pi\) | |||||||
\(830\) | −8.39762 | − | 12.3874i | −0.291486 | − | 0.429973i | ||||
\(831\) | −1.18943 | + | 10.5384i | −0.0412610 | + | 0.365574i | ||||
\(832\) | 0.759044 | + | 0.759044i | 0.0263151 | + | 0.0263151i | ||||
\(833\) | −9.83382 | − | 9.83382i | −0.340722 | − | 0.340722i | ||||
\(834\) | 1.91230 | − | 16.9430i | 0.0662174 | − | 0.586689i | ||||
\(835\) | −19.1279 | − | 3.67168i | −0.661948 | − | 0.127064i | ||||
\(836\) | − | 3.35156i | − | 0.115916i | ||||||
\(837\) | −38.3283 | + | 18.4309i | −1.32482 | + | 0.637065i | ||||
\(838\) | 0.0179681 | − | 0.0179681i | 0.000620699 | − | 0.000620699i | ||||
\(839\) | 29.3705 | 1.01398 | 0.506991 | − | 0.861952i | \(-0.330758\pi\) | ||||
0.506991 | + | 0.861952i | \(0.330758\pi\) | |||||||
\(840\) | 18.6328 | + | 5.80543i | 0.642892 | + | 0.200306i | ||||
\(841\) | −19.9336 | −0.687366 | ||||||||
\(842\) | 3.86056 | − | 3.86056i | 0.133044 | − | 0.133044i | ||||
\(843\) | −14.9283 | + | 11.9002i | −0.514156 | + | 0.409865i | ||||
\(844\) | − | 0.338632i | − | 0.0116562i | ||||||
\(845\) | 21.9284 | − | 14.8656i | 0.754359 | − | 0.511393i | ||||
\(846\) | 33.1225 | + | 7.57330i | 1.13877 | + | 0.260375i | ||||
\(847\) | 0.829975 | + | 0.829975i | 0.0285183 | + | 0.0285183i | ||||
\(848\) | 7.04762 | + | 7.04762i | 0.242016 | + | 0.242016i | ||||
\(849\) | −29.5353 | − | 3.33354i | −1.01365 | − | 0.114407i | ||||
\(850\) | −3.51200 | − | 1.39987i | −0.120461 | − | 0.0480151i | ||||
\(851\) | − | 44.0976i | − | 1.51165i | ||||||
\(852\) | 5.12575 | + | 6.43000i | 0.175605 | + | 0.220288i | ||||
\(853\) | 0.0597623 | − | 0.0597623i | 0.00204622 | − | 0.00204622i | −0.706083 | − | 0.708129i | \(-0.749539\pi\) |
0.708129 | + | 0.706083i | \(0.249539\pi\) | |||||||
\(854\) | −6.84123 | −0.234102 | ||||||||
\(855\) | 2.43185 | + | 6.25189i | 0.0831675 | + | 0.213810i | ||||
\(856\) | −3.05284 | −0.104344 | ||||||||
\(857\) | 18.0497 | − | 18.0497i | 0.616565 | − | 0.616565i | −0.328084 | − | 0.944649i | \(-0.606403\pi\) |
0.944649 | + | 0.328084i | \(0.106403\pi\) | |||||||
\(858\) | −3.88432 | − | 4.87269i | −0.132608 | − | 0.166351i | ||||
\(859\) | − | 46.1834i | − | 1.57576i | −0.615831 | − | 0.787878i | \(-0.711180\pi\) | ||
0.615831 | − | 0.787878i | \(-0.288820\pi\) | |||||||
\(860\) | −2.56136 | + | 13.3436i | −0.0873418 | + | 0.455013i | ||||
\(861\) | −73.1291 | − | 8.25381i | −2.49223 | − | 0.281289i | ||||
\(862\) | −1.98236 | − | 1.98236i | −0.0675195 | − | 0.0675195i | ||||
\(863\) | −5.02007 | − | 5.02007i | −0.170885 | − | 0.170885i | 0.616483 | − | 0.787368i | \(-0.288557\pi\) |
−0.787368 | + | 0.616483i | \(0.788557\pi\) | |||||||
\(864\) | 1.71899 | − | 4.90358i | 0.0584812 | − | 0.166823i | ||||
\(865\) | −1.01103 | + | 5.26703i | −0.0343760 | + | 0.179084i | ||||
\(866\) | 11.7849i | 0.400466i | ||||||||
\(867\) | −22.2501 | + | 17.7369i | −0.755652 | + | 0.602376i | ||||
\(868\) | −29.1638 | + | 29.1638i | −0.989883 | + | 0.989883i | ||||
\(869\) | 0.859509 | 0.0291568 | ||||||||
\(870\) | −5.41986 | − | 10.3257i | −0.183751 | − | 0.350075i | ||||
\(871\) | 7.94026 | 0.269046 | ||||||||
\(872\) | −2.09363 | + | 2.09363i | −0.0708992 | + | 0.0708992i | ||||
\(873\) | 34.9797 | − | 21.9606i | 1.18388 | − | 0.743254i | ||||
\(874\) | − | 5.59207i | − | 0.189155i | ||||||
\(875\) | −47.4636 | − | 30.3519i | −1.60456 | − | 1.02608i | ||||
\(876\) | −1.40848 | + | 12.4792i | −0.0475881 | + | 0.421633i | ||||
\(877\) | 40.9594 | + | 40.9594i | 1.38310 | + | 1.38310i | 0.839058 | + | 0.544041i | \(0.183107\pi\) |
0.544041 | + | 0.839058i | \(0.316893\pi\) | |||||||
\(878\) | 8.89831 | + | 8.89831i | 0.300304 | + | 0.300304i | ||||
\(879\) | 4.79502 | − | 42.4841i | 0.161732 | − | 1.43295i | ||||
\(880\) | 6.20325 | − | 4.20528i | 0.209111 | − | 0.141760i | ||||
\(881\) | − | 3.57891i | − | 0.120576i | −0.998181 | − | 0.0602882i | \(-0.980798\pi\) | ||
0.998181 | − | 0.0602882i | \(-0.0192020\pi\) | |||||||
\(882\) | −46.7306 | + | 29.3379i | −1.57350 | + | 0.987859i | ||||
\(883\) | 25.5096 | − | 25.5096i | 0.858468 | − | 0.858468i | −0.132690 | − | 0.991158i | \(-0.542361\pi\) |
0.991158 | + | 0.132690i | \(0.0423614\pi\) | |||||||
\(884\) | 0.811681 | 0.0272998 | ||||||||
\(885\) | 4.98154 | − | 15.9885i | 0.167453 | − | 0.537446i | ||||
\(886\) | 13.0473 | 0.438331 | ||||||||
\(887\) | −31.7609 | + | 31.7609i | −1.06643 | + | 1.06643i | −0.0687967 | + | 0.997631i | \(0.521916\pi\) |
−0.997631 | + | 0.0687967i | \(0.978084\pi\) | |||||||
\(888\) | 10.6803 | − | 8.51390i | 0.358407 | − | 0.285708i | ||||
\(889\) | 47.7802i | 1.60250i | ||||||||
\(890\) | 33.3929 | + | 6.40992i | 1.11933 | + | 0.214861i | ||||
\(891\) | −13.1084 | + | 27.1668i | −0.439149 | + | 0.910123i | ||||
\(892\) | 6.58383 | + | 6.58383i | 0.220443 | + | 0.220443i | ||||
\(893\) | 8.00851 | + | 8.00851i | 0.267995 | + | 0.267995i | ||||
\(894\) | −3.40815 | − | 0.384665i | −0.113986 | − | 0.0128651i | ||||
\(895\) | −14.4255 | − | 21.2792i | −0.482192 | − | 0.711286i | ||||
\(896\) | − | 5.03907i | − | 0.168343i | ||||||
\(897\) | −6.48098 | − | 8.13007i | −0.216394 | − | 0.271455i | ||||
\(898\) | −6.18162 | + | 6.18162i | −0.206283 | + | 0.206283i | ||||
\(899\) | 24.6448 | 0.821950 | ||||||||
\(900\) | −8.52003 | + | 12.3454i | −0.284001 | + | 0.411513i | ||||
\(901\) | 7.53634 | 0.251072 | ||||||||
\(902\) | −19.9830 | + | 19.9830i | −0.665360 | + | 0.665360i | ||||
\(903\) | −33.0584 | − | 41.4702i | −1.10011 | − | 1.38004i | ||||
\(904\) | 1.26560i | 0.0420933i | ||||||||
\(905\) | −28.0173 | − | 41.3286i | −0.931327 | − | 1.37381i | ||||
\(906\) | 35.4967 | + | 4.00638i | 1.17930 | + | 0.133103i | ||||
\(907\) | −2.13634 | − | 2.13634i | −0.0709361 | − | 0.0709361i | 0.670749 | − | 0.741685i | \(-0.265973\pi\) |
−0.741685 | + | 0.670749i | \(0.765973\pi\) | |||||||
\(908\) | −15.0913 | − | 15.0913i | −0.500822 | − | 0.500822i | ||||
\(909\) | −36.0255 | − | 8.23706i | −1.19489 | − | 0.273206i | ||||
\(910\) | 11.8785 | + | 2.28012i | 0.393767 | + | 0.0755853i | ||||
\(911\) | − | 20.4315i | − | 0.676927i | −0.940979 | − | 0.338464i | \(-0.890093\pi\) | ||
0.940979 | − | 0.338464i | \(-0.109907\pi\) | |||||||
\(912\) | 1.35438 | − | 1.07966i | 0.0448479 | − | 0.0357510i | ||||
\(913\) | 15.8613 | − | 15.8613i | 0.524933 | − | 0.524933i | ||||
\(914\) | 14.7700 | 0.488549 | ||||||||
\(915\) | 1.56411 | − | 5.02008i | 0.0517080 | − | 0.165959i | ||||
\(916\) | 13.2052 | 0.436313 | ||||||||
\(917\) | −5.45675 | + | 5.45675i | −0.180198 | + | 0.180198i | ||||
\(918\) | −1.70271 | − | 3.54091i | −0.0561979 | − | 0.116867i | ||||
\(919\) | − | 33.7641i | − | 1.11377i | −0.830588 | − | 0.556887i | \(-0.811996\pi\) | ||
0.830588 | − | 0.556887i | \(-0.188004\pi\) | |||||||
\(920\) | 10.3501 | − | 7.01651i | 0.341233 | − | 0.231328i | ||||
\(921\) | 1.60815 | − | 14.2483i | 0.0529905 | − | 0.469498i | ||||
\(922\) | 11.0740 | + | 11.0740i | 0.364704 | + | 0.364704i | ||||
\(923\) | 3.60361 | + | 3.60361i | 0.118614 | + | 0.118614i | ||||
\(924\) | −3.28075 | + | 29.0676i | −0.107929 | + | 0.956253i | ||||
\(925\) | −36.2219 | + | 15.5756i | −1.19097 | + | 0.512123i | ||||
\(926\) | 4.81712i | 0.158301i | ||||||||
\(927\) | 0.805543 | + | 1.28310i | 0.0264575 | + | 0.0421426i | ||||
\(928\) | −2.12913 | + | 2.12913i | −0.0698921 | + | 0.0698921i | ||||
\(929\) | −32.3526 | −1.06145 | −0.530727 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530727 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(930\) | −14.7326 | − | 28.0680i | −0.483101 | − | 0.920387i | ||||
\(931\) | −18.3922 | −0.602781 | ||||||||
\(932\) | 17.7744 | − | 17.7744i | 0.582218 | − | 0.582218i | ||||
\(933\) | 19.2514 | − | 15.3465i | 0.630264 | − | 0.502422i | ||||
\(934\) | 37.3897i | 1.22343i | ||||||||
\(935\) | 1.06826 | − | 5.56516i | 0.0349357 | − | 0.182000i | ||||
\(936\) | 0.717794 | − | 3.13934i | 0.0234618 | − | 0.102612i | ||||
\(937\) | 32.7981 | + | 32.7981i | 1.07147 | + | 1.07147i | 0.997241 | + | 0.0742254i | \(0.0236484\pi\) |
0.0742254 | + | 0.997241i | \(0.476352\pi\) | |||||||
\(938\) | −26.3565 | − | 26.3565i | −0.860571 | − | 0.860571i | ||||
\(939\) | 56.7110 | + | 6.40076i | 1.85069 | + | 0.208881i | ||||
\(940\) | −4.77412 | + | 24.8711i | −0.155714 | + | 0.811205i | ||||
\(941\) | 0.190809i | 0.00622019i | 0.999995 | + | 0.00311010i | \(0.000989976\pi\) | ||||
−0.999995 | + | 0.00311010i | \(0.999010\pi\) | |||||||
\(942\) | −25.4175 | − | 31.8850i | −0.828147 | − | 1.03887i | ||||
\(943\) | −33.3415 | + | 33.3415i | −1.08575 | + | 1.08575i | ||||
\(944\) | −4.32394 | −0.140732 | ||||||||
\(945\) | −14.9713 | − | 56.6022i | −0.487016 | − | 1.84127i | ||||
\(946\) | −20.3654 | −0.662135 | ||||||||
\(947\) | −16.3696 | + | 16.3696i | −0.531942 | + | 0.531942i | −0.921150 | − | 0.389208i | \(-0.872749\pi\) |
0.389208 | + | 0.921150i | \(0.372749\pi\) | |||||||
\(948\) | 0.276879 | + | 0.347331i | 0.00899260 | + | 0.0112808i | ||||
\(949\) | 7.78316i | 0.252652i | ||||||||
\(950\) | −4.59334 | + | 1.97516i | −0.149028 | + | 0.0640827i | ||||
\(951\) | −24.3188 | − | 2.74477i | −0.788592 | − | 0.0890054i | ||||
\(952\) | −2.69425 | − | 2.69425i | −0.0873213 | − | 0.0873213i | ||||
\(953\) | 8.15026 | + | 8.15026i | 0.264013 | + | 0.264013i | 0.826682 | − | 0.562669i | \(-0.190226\pi\) |
−0.562669 | + | 0.826682i | \(0.690226\pi\) | |||||||
\(954\) | 6.66462 | − | 29.1483i | 0.215775 | − | 0.943711i | ||||
\(955\) | −14.6744 | + | 9.94798i | −0.474851 | + | 0.321909i | ||||
\(956\) | − | 8.08746i | − | 0.261567i | ||||||
\(957\) | 13.6679 | − | 10.8956i | 0.441822 | − | 0.352203i | ||||
\(958\) | −15.9980 | + | 15.9980i | −0.516871 | + | 0.516871i | ||||
\(959\) | −33.9330 | −1.09575 | ||||||||
\(960\) | 3.69766 | + | 1.15208i | 0.119342 | + | 0.0371834i | ||||
\(961\) | 35.9910 | 1.16100 | ||||||||
\(962\) | 5.98563 | − | 5.98563i | 0.192984 | − | 0.192984i | ||||
\(963\) | 4.86967 | + | 7.75661i | 0.156923 | + | 0.249953i | ||||
\(964\) | − | 17.4598i | − | 0.562341i | ||||||
\(965\) | −14.5645 | − | 2.79572i | −0.468848 | − | 0.0899976i | ||||
\(966\) | −5.47393 | + | 48.4992i | −0.176121 | + | 1.56044i | ||||
\(967\) | 24.7969 | + | 24.7969i | 0.797414 | + | 0.797414i | 0.982687 | − | 0.185273i | \(-0.0593169\pi\) |
−0.185273 | + | 0.982687i | \(0.559317\pi\) | |||||||
\(968\) | 0.164708 | + | 0.164708i | 0.00529391 | + | 0.00529391i | ||||
\(969\) | 0.146886 | − | 1.30141i | 0.00471865 | − | 0.0418074i | ||||
\(970\) | 17.2742 | + | 25.4813i | 0.554641 | + | 0.818155i | ||||
\(971\) | − | 36.3018i | − | 1.16498i | −0.812838 | − | 0.582490i | \(-0.802078\pi\) | ||
0.812838 | − | 0.582490i | \(-0.197922\pi\) | |||||||
\(972\) | −15.2009 | + | 3.45425i | −0.487570 | + | 0.110795i | ||||
\(973\) | −35.0763 | + | 35.0763i | −1.12450 | + | 1.12450i | ||||
\(974\) | 27.7724 | 0.889884 | ||||||||
\(975\) | −4.38893 | + | 8.19509i | −0.140558 | + | 0.262453i | ||||
\(976\) | −1.35764 | −0.0434569 | ||||||||
\(977\) | −12.2667 | + | 12.2667i | −0.392448 | + | 0.392448i | −0.875559 | − | 0.483111i | \(-0.839507\pi\) |
0.483111 | + | 0.875559i | \(0.339507\pi\) | |||||||
\(978\) | −19.2063 | + | 15.3105i | −0.614149 | + | 0.489575i | ||||
\(979\) | 50.9651i | 1.62885i | ||||||||
\(980\) | −23.0772 | − | 34.0413i | −0.737173 | − | 1.08741i | ||||
\(981\) | 8.65905 | + | 1.97985i | 0.276462 | + | 0.0632118i | ||||
\(982\) | −5.10669 | − | 5.10669i | −0.162961 | − | 0.162961i | ||||
\(983\) | −3.92604 | − | 3.92604i | −0.125221 | − | 0.125221i | 0.641719 | − | 0.766940i | \(-0.278222\pi\) |
−0.766940 | + | 0.641719i | \(0.778222\pi\) | |||||||
\(984\) | −14.5124 | − | 1.63796i | −0.462639 | − | 0.0522164i | ||||
\(985\) | −14.6650 | − | 2.81502i | −0.467267 | − | 0.0896939i | ||||
\(986\) | 2.27678i | 0.0725073i | ||||||||
\(987\) | −61.6174 | − | 77.2960i | −1.96130 | − | 2.46036i | ||||
\(988\) | 0.759044 | − | 0.759044i | 0.0241484 | − | 0.0241484i | ||||
\(989\) | −33.9796 | −1.08049 | ||||||||
\(990\) | −20.5797 | − | 9.05314i | −0.654065 | − | 0.287728i | ||||
\(991\) | −13.2000 | −0.419313 | −0.209656 | − | 0.977775i | \(-0.567235\pi\) | ||||
−0.209656 | + | 0.977775i | \(0.567235\pi\) | |||||||
\(992\) | −5.78753 | + | 5.78753i | −0.183754 | + | 0.183754i | ||||
\(993\) | −9.43390 | − | 11.8344i | −0.299376 | − | 0.375552i | ||||
\(994\) | − | 23.9233i | − | 0.758802i | ||||||
\(995\) | 18.5173 | − | 12.5532i | 0.587039 | − | 0.397963i | ||||
\(996\) | 11.5191 | + | 1.30012i | 0.364997 | + | 0.0411959i | ||||
\(997\) | −31.6834 | − | 31.6834i | −1.00342 | − | 1.00342i | −0.999994 | − | 0.00342936i | \(-0.998908\pi\) |
−0.00342936 | − | 0.999994i | \(-0.501092\pi\) | |||||||
\(998\) | 20.5489 | + | 20.5489i | 0.650463 | + | 0.650463i | ||||
\(999\) | −38.6684 | − | 13.5555i | −1.22341 | − | 0.428877i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 570.2.k.a.77.16 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.77.2 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.a.533.2 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.a.533.16 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.2 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.a.77.16 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.533.2 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.a.533.16 | yes | 36 | 15.8 | even | 4 | inner |