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 | 77.2 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.a.533.2 |
$q$-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 | ||||
\(3\) | −1.35438 | − | 1.07966i | −0.781950 | − | 0.623341i | ||||
\(4\) | − | 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 | \(0.168606\pi\) | ||||
−0.862964 | + | 0.505266i | \(0.831394\pi\) | |||||||
\(12\) | −1.07966 | + | 1.35438i | −0.311670 | + | 0.390975i | ||||
\(13\) | 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 | ||||||||
\(15\) | 0.298918 | − | 3.86143i | 0.0771802 | − | 0.997017i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.534673 | − | 0.534673i | 0.129677 | − | 0.129677i | −0.639289 | − | 0.768966i | \(-0.720771\pi\) |
0.768966 | + | 0.639289i | \(0.220771\pi\) | |||||||
\(18\) | −2.54078 | − | 1.59513i | −0.598868 | − | 0.375975i | ||||
\(19\) | 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 | 0.986751 | − | 0.162245i | \(-0.0518734\pi\) |
−0.162245 | + | 0.986751i | \(0.551873\pi\) | |||||||
\(24\) | −0.194257 | − | 1.72112i | −0.0396525 | − | 0.351323i | ||||
\(25\) | −1.85133 | + | 4.64463i | −0.370266 | + | 0.928926i | ||||
\(26\) | 1.07345i | 0.210521i | ||||||||
\(27\) | 2.25184 | − | 4.68286i | 0.433368 | − | 0.901217i | ||||
\(28\) | −3.56316 | + | 3.56316i | −0.673374 | + | 0.673374i | ||||
\(29\) | −3.01104 | −0.559137 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(30\) | 2.51908 | + | 2.94181i | 0.459918 | + | 0.537099i | ||||
\(31\) | 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 | ||||
\(33\) | 3.61853 | − | 4.53927i | 0.629906 | − | 0.790186i | ||||
\(34\) | 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 | \(0.228777\pi\) | ||||
−0.752647 | + | 0.658425i | \(0.771223\pi\) | |||||||
\(42\) | −6.82480 | − | 5.44047i | −1.05309 | − | 0.839483i | ||||
\(43\) | 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 | ||||||||
\(45\) | −4.57387 | + | 4.90711i | −0.681832 | + | 0.731509i | ||||
\(46\) | −5.59207 | −0.824506 | ||||||||
\(47\) | −8.00851 | + | 8.00851i | −1.16816 | + | 1.16816i | −0.185522 | + | 0.982640i | \(0.559397\pi\) |
−0.982640 | + | 0.185522i | \(0.940603\pi\) | |||||||
\(48\) | 1.35438 | + | 1.07966i | 0.195488 | + | 0.155835i | ||||
\(49\) | 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 | 0.999506 | − | 0.0314411i | \(-0.0100097\pi\) |
−0.0314411 | + | 0.999506i | \(0.510010\pi\) | |||||||
\(54\) | 1.71899 | + | 4.90358i | 0.233925 | + | 0.667292i | ||||
\(55\) | −6.20325 | + | 4.20528i | −0.836446 | + | 0.567040i | ||||
\(56\) | − | 5.03907i | − | 0.673374i | ||||||
\(57\) | 1.07966 | − | 1.35438i | 0.143004 | − | 0.179392i | ||||
\(58\) | 2.12913 | − | 2.12913i | 0.279568 | − | 0.279568i | ||||
\(59\) | −4.32394 | −0.562928 | −0.281464 | − | 0.959572i | \(-0.590820\pi\) | ||||
−0.281464 | + | 0.959572i | \(0.590820\pi\) | |||||||
\(60\) | −3.86143 | − | 0.298918i | −0.498509 | − | 0.0385901i | ||||
\(61\) | 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 | ||||
\(63\) | 8.03795 | − | 12.8032i | 1.01269 | − | 1.61305i | ||||
\(64\) | 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 | \(-0.909096\pi\) | ||
0.959498 | − | 0.281716i | \(-0.0909038\pi\) | |||||||
\(72\) | −1.59513 | + | 2.54078i | −0.187987 | + | 0.299434i | ||||
\(73\) | −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 | ||||||||
\(75\) | 7.52201 | − | 4.29178i | 0.868567 | − | 0.495572i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 11.9421 | − | 11.9421i | 1.36093 | − | 1.36093i | ||||
\(78\) | 1.15896 | − | 1.45386i | 0.131226 | − | 0.164617i | ||||
\(79\) | 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 | 0.397947 | − | 0.917408i | \(-0.369723\pi\) |
−0.917408 | + | 0.397947i | \(0.869723\pi\) | |||||||
\(84\) | 8.67286 | − | 0.978873i | 0.946286 | − | 0.106804i | ||||
\(85\) | 1.66047 | + | 0.318735i | 0.180103 | + | 0.0345716i | ||||
\(86\) | 6.07639i | 0.655234i | ||||||||
\(87\) | 4.07809 | + | 3.25089i | 0.437217 | + | 0.348533i | ||||
\(88\) | −2.36991 | + | 2.36991i | −0.252633 | + | 0.252633i | ||||
\(89\) | 15.2064 | 1.61188 | 0.805938 | − | 0.592000i | \(-0.201662\pi\) | ||||
0.805938 | + | 0.592000i | \(0.201662\pi\) | |||||||
\(90\) | −0.235635 | − | 6.70406i | −0.0248381 | − | 0.706670i | ||||
\(91\) | −5.40919 | −0.567037 | ||||||||
\(92\) | 3.95419 | − | 3.95419i | 0.412253 | − | 0.412253i | ||||
\(93\) | −11.0853 | − | 8.83678i | −1.14949 | − | 0.916332i | ||||
\(94\) | − | 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 | \(-0.790018\pi\) | ||
0.790189 | − | 0.612863i | \(-0.209982\pi\) | |||||||
\(102\) | 0.816374 | − | 1.02410i | 0.0808331 | − | 0.101401i | ||||
\(103\) | 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 | ||||||||
\(105\) | −14.8240 | + | 12.6938i | −1.44667 | + | 1.23879i | ||||
\(106\) | −9.96683 | −0.968064 | ||||||||
\(107\) | −2.15869 | + | 2.15869i | −0.208688 | + | 0.208688i | −0.803710 | − | 0.595022i | \(-0.797143\pi\) |
0.595022 | + | 0.803710i | \(0.297143\pi\) | |||||||
\(108\) | −4.68286 | − | 2.25184i | −0.450609 | − | 0.216684i | ||||
\(109\) | − | 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 | 0.747946 | − | 0.663760i | \(-0.231040\pi\) |
−0.663760 | + | 0.747946i | \(0.731040\pi\) | |||||||
\(114\) | 0.194257 | + | 1.72112i | 0.0181938 | + | 0.161198i | ||||
\(115\) | −2.35721 | + | 12.2801i | −0.219811 | + | 1.14512i | ||||
\(116\) | 3.01104i | 0.279568i | ||||||||
\(117\) | 2.72740 | + | 1.71229i | 0.252149 | + | 0.158301i | ||||
\(118\) | 3.05748 | − | 3.05748i | 0.281464 | − | 0.281464i | ||||
\(119\) | −3.81025 | −0.349285 | ||||||||
\(120\) | 2.94181 | − | 2.51908i | 0.268549 | − | 0.229959i | ||||
\(121\) | −0.232932 | −0.0211757 | ||||||||
\(122\) | −0.959995 | + | 0.959995i | −0.0869138 | + | 0.0869138i | ||||
\(123\) | 9.10362 | − | 11.4200i | 0.820846 | − | 1.02971i | ||||
\(124\) | − | 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 | \(0.0213112\pi\) | ||||
−0.997760 | + | 0.0669011i | \(0.978689\pi\) | |||||||
\(132\) | −4.53927 | − | 3.61853i | −0.395093 | − | 0.314953i | ||||
\(133\) | 3.56316 | − | 3.56316i | 0.308965 | − | 0.308965i | ||||
\(134\) | −7.39695 | −0.639000 | ||||||||
\(135\) | 11.4927 | − | 1.70787i | 0.989138 | − | 0.146990i | ||||
\(136\) | 0.756142 | 0.0648386 | ||||||||
\(137\) | −4.76164 | + | 4.76164i | −0.406814 | + | 0.406814i | −0.880626 | − | 0.473812i | \(-0.842878\pi\) |
0.473812 | + | 0.880626i | \(0.342878\pi\) | |||||||
\(138\) | 7.57378 | + | 6.03752i | 0.644723 | + | 0.513948i | ||||
\(139\) | − | 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 | ||||||
\(147\) | 19.8573 | − | 24.9100i | 1.63780 | − | 2.05454i | ||||
\(148\) | 5.57606 | − | 5.57606i | 0.458350 | − | 0.458350i | ||||
\(149\) | 1.98019 | 0.162224 | 0.0811118 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811118 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(150\) | −2.28412 | + | 8.35361i | −0.186497 | + | 0.682069i | ||||
\(151\) | 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 | ||||
\(153\) | 1.92119 | + | 1.20614i | 0.155319 | + | 0.0975108i | ||||
\(154\) | 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 | ||||||
\(162\) | 2.96602 | − | 8.49722i | 0.233033 | − | 0.667604i | ||||
\(163\) | −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 | ||||||||
\(165\) | 12.9418 | + | 1.00184i | 1.00752 | + | 0.0779931i | ||||
\(166\) | 6.69279 | 0.519462 | ||||||||
\(167\) | −6.15920 | + | 6.15920i | −0.476613 | + | 0.476613i | −0.904047 | − | 0.427434i | \(-0.859418\pi\) |
0.427434 | + | 0.904047i | \(0.359418\pi\) | |||||||
\(168\) | −5.44047 | + | 6.82480i | −0.419741 | + | 0.526545i | ||||
\(169\) | 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 | 0.768633 | − | 0.639690i | \(-0.220937\pi\) |
−0.639690 | + | 0.768633i | \(0.720937\pi\) | |||||||
\(174\) | −5.18237 | + | 0.584915i | −0.392875 | + | 0.0443423i | ||||
\(175\) | 23.1461 | − | 9.95297i | 1.74968 | − | 0.752374i | ||||
\(176\) | − | 3.35156i | − | 0.252633i | ||||||
\(177\) | 5.85624 | + | 4.66837i | 0.440182 | + | 0.350896i | ||||
\(178\) | −10.7526 | + | 10.7526i | −0.805938 | + | 0.805938i | ||||
\(179\) | −11.4970 | −0.859323 | −0.429662 | − | 0.902990i | \(-0.641367\pi\) | ||||
−0.429662 | + | 0.902990i | \(0.641367\pi\) | |||||||
\(180\) | 4.90711 | + | 4.57387i | 0.365754 | + | 0.340916i | ||||
\(181\) | 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 | ||||
\(183\) | −1.83875 | − | 1.46578i | −0.135925 | − | 0.108354i | ||||
\(184\) | 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 | \(0.0926048\pi\) | ||||
−0.957978 | + | 0.286840i | \(0.907395\pi\) | |||||||
\(192\) | 1.07966 | − | 1.35438i | 0.0779176 | − | 0.0977438i | ||||
\(193\) | 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 | ||||||||
\(195\) | −2.70410 | − | 3.15789i | −0.193645 | − | 0.226141i | ||||
\(196\) | 18.3922 | 1.31373 | ||||||||
\(197\) | −4.72215 | + | 4.72215i | −0.336439 | + | 0.336439i | −0.855025 | − | 0.518586i | \(-0.826459\pi\) |
0.518586 | + | 0.855025i | \(0.326459\pi\) | |||||||
\(198\) | 5.34616 | − | 8.51557i | 0.379935 | − | 0.605176i | ||||
\(199\) | 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 | ||||||||
\(207\) | −8.92006 | + | 14.2082i | −0.619987 | + | 0.987540i | ||||
\(208\) | −0.759044 | + | 0.759044i | −0.0526302 | + | 0.0526302i | ||||
\(209\) | −3.35156 | −0.231832 | ||||||||
\(210\) | 1.50627 | − | 19.4580i | 0.103942 | − | 1.34273i | ||||
\(211\) | 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 | ||||
\(213\) | −5.12575 | + | 6.43000i | −0.351211 | + | 0.440577i | ||||
\(214\) | − | 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 | ||||||
\(222\) | 10.6803 | + | 8.51390i | 0.716813 | + | 0.571416i | ||||
\(223\) | −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 | ||||||||
\(225\) | −14.8213 | − | 2.30850i | −0.988086 | − | 0.153900i | ||||
\(226\) | −1.26560 | −0.0841865 | ||||||||
\(227\) | −15.0913 | + | 15.0913i | −1.00164 | + | 1.00164i | −0.00164481 | + | 0.999999i | \(0.500524\pi\) |
−0.999999 | + | 0.00164481i | \(0.999476\pi\) | |||||||
\(228\) | −1.35438 | − | 1.07966i | −0.0896959 | − | 0.0715021i | ||||
\(229\) | 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 | \(-0.942085\pi\) |
−0.180943 | − | 0.983494i | \(-0.557915\pi\) | |||||||
\(234\) | −3.13934 | + | 0.717794i | −0.205225 | + | 0.0469237i | ||||
\(235\) | −24.8711 | − | 4.77412i | −1.62241 | − | 0.311429i | ||||
\(236\) | 4.32394i | 0.281464i | ||||||||
\(237\) | 0.276879 | − | 0.347331i | 0.0179852 | − | 0.0225616i | ||||
\(238\) | 2.69425 | − | 2.69425i | 0.174643 | − | 0.174643i | ||||
\(239\) | −8.08746 | −0.523134 | −0.261567 | − | 0.965185i | \(-0.584239\pi\) | ||||
−0.261567 | + | 0.965185i | \(0.584239\pi\) | |||||||
\(240\) | −0.298918 | + | 3.86143i | −0.0192950 | + | 0.249254i | ||||
\(241\) | 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 | ||||
\(243\) | 15.2009 | + | 3.45425i | 0.975140 | + | 0.221590i | ||||
\(244\) | − | 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 | \(-0.977881\pi\) | ||
0.997587 | − | 0.0694333i | \(-0.0221191\pi\) | |||||||
\(252\) | −12.8032 | − | 8.03795i | −0.806524 | − | 0.506343i | ||||
\(253\) | −13.2527 | + | 13.2527i | −0.833190 | + | 0.833190i | ||||
\(254\) | 9.48196 | 0.594951 | ||||||||
\(255\) | −1.90478 | − | 2.22443i | −0.119282 | − | 0.139299i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.3829 | − | 18.3829i | 1.14670 | − | 1.14670i | 0.159499 | − | 0.987198i | \(-0.449012\pi\) |
0.987198 | − | 0.159499i | \(-0.0509877\pi\) | |||||||
\(258\) | 6.56042 | − | 8.22972i | 0.408434 | − | 0.512360i | ||||
\(259\) | − | 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 | \(0.0294573\pi\) |
0.0924109 | + | 0.995721i | \(0.470543\pi\) | |||||||
\(264\) | 5.76844 | − | 0.651062i | 0.355023 | − | 0.0400701i | ||||
\(265\) | −4.20130 | + | 21.8869i | −0.258084 | + | 1.34450i | ||||
\(266\) | 5.03907i | 0.308965i | ||||||||
\(267\) | −20.5952 | − | 16.4177i | −1.26041 | − | 1.00475i | ||||
\(268\) | 5.23044 | − | 5.23044i | 0.319500 | − | 0.319500i | ||||
\(269\) | −12.7863 | −0.779593 | −0.389796 | − | 0.920901i | \(-0.627455\pi\) | ||||
−0.389796 | + | 0.920901i | \(0.627455\pi\) | |||||||
\(270\) | −6.91895 | + | 9.33424i | −0.421074 | + | 0.568064i | ||||
\(271\) | −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 | ||||
\(273\) | 7.32609 | + | 5.84007i | 0.443395 | + | 0.353457i | ||||
\(274\) | − | 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 | \(-0.893368\pi\) | ||
0.944412 | − | 0.328765i | \(-0.106632\pi\) | |||||||
\(282\) | −12.2279 | + | 15.3393i | −0.728163 | + | 0.913445i | ||||
\(283\) | −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 | ||||||||
\(285\) | 3.86143 | + | 0.298918i | 0.228731 | + | 0.0177063i | ||||
\(286\) | −3.59773 | −0.212738 | ||||||||
\(287\) | 30.0444 | − | 30.0444i | 1.77346 | − | 1.77346i | ||||
\(288\) | 2.54078 | + | 1.59513i | 0.149717 | + | 0.0939937i | ||||
\(289\) | 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 | \(0.00632920\pi\) |
0.0198825 | + | 0.999802i | \(0.493671\pi\) | |||||||
\(294\) | 3.57281 | + | 31.6553i | 0.208371 | + | 1.84617i | ||||
\(295\) | −5.42535 | − | 8.00298i | −0.315876 | − | 0.465951i | ||||
\(296\) | 7.88574i | 0.458350i | ||||||||
\(297\) | 15.6949 | + | 7.54718i | 0.910709 | + | 0.437932i | ||||
\(298\) | −1.40021 | + | 1.40021i | −0.0811118 | + | 0.0811118i | ||||
\(299\) | 6.00281 | 0.347151 | ||||||||
\(300\) | −4.29178 | − | 7.52201i | −0.247786 | − | 0.434283i | ||||
\(301\) | −30.6193 | −1.76487 | ||||||||
\(302\) | −14.5835 | + | 14.5835i | −0.839185 | + | 0.839185i | ||||
\(303\) | −13.2997 | + | 16.6838i | −0.764045 | + | 0.958458i | ||||
\(304\) | − | 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 | \(0.132035\pi\) | ||||
−0.915197 | + | 0.403008i | \(0.867965\pi\) | |||||||
\(312\) | −1.45386 | − | 1.15896i | −0.0823085 | − | 0.0656131i | ||||
\(313\) | 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 | ||||||||
\(315\) | 33.7822 | − | 1.18738i | 1.90341 | − | 0.0669014i | ||||
\(316\) | 0.256451 | 0.0144265 | ||||||||
\(317\) | 9.99115 | − | 9.99115i | 0.561159 | − | 0.561159i | −0.368478 | − | 0.929637i | \(-0.620121\pi\) |
0.929637 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(318\) | 13.4989 | + | 10.7608i | 0.756978 | + | 0.603434i | ||||
\(319\) | − | 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 | ||||||
\(327\) | −3.19669 | + | 4.01009i | −0.176777 | + | 0.221759i | ||||
\(328\) | −5.96229 | + | 5.96229i | −0.329212 | + | 0.329212i | ||||
\(329\) | 57.0712 | 3.14644 | ||||||||
\(330\) | −9.85964 | + | 8.44283i | −0.542756 | + | 0.464763i | ||||
\(331\) | −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 | ||||
\(333\) | −12.5788 | + | 20.0360i | −0.689312 | + | 1.09796i | ||||
\(334\) | − | 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 | ||||||||
\(342\) | 1.59513 | − | 2.54078i | 0.0862546 | − | 0.137390i | ||||
\(343\) | 40.5923 | − | 40.5923i | 2.19178 | − | 2.19178i | ||||
\(344\) | 6.07639 | 0.327617 | ||||||||
\(345\) | 16.4508 | − | 14.0869i | 0.885682 | − | 0.758411i | ||||
\(346\) | −2.39849 | −0.128944 | ||||||||
\(347\) | −5.40165 | + | 5.40165i | −0.289976 | + | 0.289976i | −0.837071 | − | 0.547095i | \(-0.815734\pi\) |
0.547095 | + | 0.837071i | \(0.315734\pi\) | |||||||
\(348\) | 3.25089 | − | 4.07809i | 0.174266 | − | 0.218609i | ||||
\(349\) | − | 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 | 0.697288 | − | 0.716791i | \(-0.254390\pi\) |
−0.716791 | + | 0.697288i | \(0.754390\pi\) | |||||||
\(354\) | −7.44203 | + | 0.839954i | −0.395539 | + | 0.0446430i | ||||
\(355\) | 8.78707 | − | 5.95690i | 0.466369 | − | 0.316159i | ||||
\(356\) | − | 15.2064i | − | 0.805938i | ||||||
\(357\) | 5.16052 | + | 4.11377i | 0.273124 | + | 0.217724i | ||||
\(358\) | 8.12958 | − | 8.12958i | 0.429662 | − | 0.429662i | ||||
\(359\) | −16.4393 | −0.867631 | −0.433815 | − | 0.901002i | \(-0.642833\pi\) | ||||
−0.433815 | + | 0.901002i | \(0.642833\pi\) | |||||||
\(360\) | −6.70406 | + | 0.235635i | −0.353335 | + | 0.0124191i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −15.7893 | + | 15.7893i | −0.829867 | + | 0.829867i | ||||
\(363\) | 0.315478 | + | 0.251487i | 0.0165583 | + | 0.0131996i | ||||
\(364\) | 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 | ||||||
\(372\) | −8.83678 | + | 11.0853i | −0.458166 | + | 0.574747i | ||||
\(373\) | −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 | ||||||||
\(375\) | 17.3815 | + | 8.53714i | 0.897578 | + | 0.440856i | ||||
\(376\) | −11.3257 | −0.584081 | ||||||||
\(377\) | −2.28551 | + | 2.28551i | −0.117710 | + | 0.117710i | ||||
\(378\) | 11.3472 | − | 23.5973i | 0.583637 | − | 1.21371i | ||||
\(379\) | − | 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 | 0.686725 | − | 0.726917i | \(-0.259047\pi\) |
−0.726917 | + | 0.686725i | \(0.759047\pi\) | |||||||
\(384\) | 0.194257 | + | 1.72112i | 0.00991312 | + | 0.0878307i | ||||
\(385\) | 37.0873 | + | 7.11906i | 1.89014 | + | 0.362821i | ||||
\(386\) | 6.63236i | 0.337578i | ||||||||
\(387\) | 15.4388 | + | 9.69260i | 0.784797 | + | 0.492703i | ||||
\(388\) | −9.73496 | + | 9.73496i | −0.494218 | + | 0.494218i | ||||
\(389\) | 1.39333 | 0.0706444 | 0.0353222 | − | 0.999376i | \(-0.488754\pi\) | ||||
0.0353222 | + | 0.999376i | \(0.488754\pi\) | |||||||
\(390\) | 4.14505 | + | 0.320873i | 0.209893 | + | 0.0162480i | ||||
\(391\) | 4.22840 | 0.213839 | ||||||||
\(392\) | −13.0053 | + | 13.0053i | −0.656865 | + | 0.656865i | ||||
\(393\) | 1.65343 | − | 2.07414i | 0.0834043 | − | 0.104627i | ||||
\(394\) | − | 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 | \(-0.836852\pi\) | ||
0.871500 | − | 0.490396i | \(-0.163148\pi\) | |||||||
\(402\) | 10.0183 | + | 7.98618i | 0.499666 | + | 0.398314i | ||||
\(403\) | 6.21263 | − | 6.21263i | 0.309473 | − | 0.309473i | ||||
\(404\) | −12.3184 | −0.612863 | ||||||||
\(405\) | −17.4094 | − | 10.0951i | −0.865082 | − | 0.501631i | ||||
\(406\) | −15.1729 | −0.753016 | ||||||||
\(407\) | −18.6885 | + | 18.6885i | −0.926354 | + | 0.926354i | ||||
\(408\) | −1.02410 | − | 0.816374i | −0.0507006 | − | 0.0404165i | ||||
\(409\) | − | 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 | ||||||
\(417\) | −10.6283 | + | 13.3327i | −0.520471 | + | 0.652906i | ||||
\(418\) | 2.36991 | − | 2.36991i | 0.115916 | − | 0.115916i | ||||
\(419\) | −0.0254108 | −0.00124140 | −0.000620699 | − | 1.00000i | \(-0.500198\pi\) | ||||
−0.000620699 | 1.00000i | \(0.500198\pi\) | ||||||||
\(420\) | 12.6938 | + | 14.8240i | 0.619394 | + | 0.723337i | ||||
\(421\) | 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 | ||||
\(423\) | −28.7763 | − | 18.0660i | −1.39915 | − | 0.878399i | ||||
\(424\) | 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 | \(0.0215085\pi\) | ||||
−0.997718 | + | 0.0675195i | \(0.978491\pi\) | |||||||
\(432\) | −2.25184 | + | 4.68286i | −0.108342 | + | 0.225304i | ||||
\(433\) | −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 | ||||||||
\(435\) | −0.900054 | + | 11.6269i | −0.0431543 | + | 0.557469i | ||||
\(436\) | −2.96084 | −0.141798 | ||||||||
\(437\) | −3.95419 | + | 3.95419i | −0.189155 | + | 0.189155i | ||||
\(438\) | −7.82817 | + | 9.82006i | −0.374044 | + | 0.469221i | ||||
\(439\) | 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 | 0.453119 | − | 0.891450i | \(-0.350311\pi\) |
−0.891450 | + | 0.453119i | \(0.850311\pi\) | |||||||
\(444\) | −13.5723 | + | 1.53186i | −0.644115 | + | 0.0726988i | ||||
\(445\) | 19.0799 | + | 28.1448i | 0.904472 | + | 1.33419i | ||||
\(446\) | − | 9.31094i | − | 0.440886i | ||||||
\(447\) | −2.68193 | − | 2.13793i | −0.126851 | − | 0.101120i | ||||
\(448\) | 3.56316 | − | 3.56316i | 0.168343 | − | 0.168343i | ||||
\(449\) | 8.74214 | 0.412567 | 0.206283 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206283 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(450\) | 12.1126 | − | 8.84788i | 0.570993 | − | 0.417093i | ||||
\(451\) | −28.2602 | −1.33072 | ||||||||
\(452\) | 0.894915 | − | 0.894915i | 0.0420933 | − | 0.0420933i | ||||
\(453\) | −27.9329 | − | 22.2670i | −1.31240 | − | 1.04620i | ||||
\(454\) | − | 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 | \(-0.881170\pi\) | ||
0.931124 | − | 0.364704i | \(-0.118830\pi\) | |||||||
\(462\) | 18.2340 | − | 22.8737i | 0.848324 | − | 1.06418i | ||||
\(463\) | −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 | ||||||||
\(465\) | 2.44658 | − | 31.6050i | 0.113457 | − | 1.46565i | ||||
\(466\) | 25.1367 | 1.16444 | ||||||||
\(467\) | 26.4385 | − | 26.4385i | 1.22343 | − | 1.22343i | 0.257025 | − | 0.966405i | \(-0.417258\pi\) |
0.966405 | − | 0.257025i | \(-0.0827421\pi\) | |||||||
\(468\) | 1.71229 | − | 2.72740i | 0.0791506 | − | 0.126074i | ||||
\(469\) | − | 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 | ||||||||
\(477\) | −15.8984 | + | 25.3236i | −0.727936 | + | 1.15949i | ||||
\(478\) | 5.71869 | − | 5.71869i | 0.261567 | − | 0.261567i | ||||
\(479\) | 22.6245 | 1.03374 | 0.516871 | − | 0.856063i | \(-0.327097\pi\) | ||||
0.516871 | + | 0.856063i | \(0.327097\pi\) | |||||||
\(480\) | −2.51908 | − | 2.94181i | −0.114980 | − | 0.134275i | ||||
\(481\) | 8.46495 | 0.385969 | ||||||||
\(482\) | −12.3459 | + | 12.3459i | −0.562341 | + | 0.562341i | ||||
\(483\) | −30.4235 | + | 38.1648i | −1.38432 | + | 1.73656i | ||||
\(484\) | 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 | \(0.0521045\pi\) | ||||
−0.986632 | + | 0.162961i | \(0.947895\pi\) | |||||||
\(492\) | −11.4200 | − | 9.10362i | −0.514856 | − | 0.410423i | ||||
\(493\) | −1.60992 | + | 1.60992i | −0.0725073 | + | 0.0725073i | ||||
\(494\) | −1.07345 | −0.0482968 | ||||||||
\(495\) | −16.4465 | − | 15.3296i | −0.739213 | − | 0.689014i | ||||
\(496\) | −8.18480 | −0.367508 | ||||||||
\(497\) | −16.9164 | + | 16.9164i | −0.758802 | + | 0.758802i | ||||
\(498\) | −9.06457 | − | 7.22593i | −0.406193 | − | 0.323801i | ||||
\(499\) | 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 | \(0.0136392\pi\) |
0.0428359 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(504\) | 14.7369 | − | 3.36952i | 0.656434 | − | 0.150090i | ||||
\(505\) | 22.7996 | − | 15.4562i | 1.01457 | − | 0.687792i | ||||
\(506\) | − | 18.7421i | − | 0.833190i | ||||||
\(507\) | 12.7915 | − | 16.0463i | 0.568089 | − | 0.712640i | ||||
\(508\) | −6.70476 | + | 6.70476i | −0.297475 | + | 0.297475i | ||||
\(509\) | 15.9405 | 0.706550 | 0.353275 | − | 0.935520i | \(-0.385068\pi\) | ||||
0.353275 | + | 0.935520i | \(0.385068\pi\) | |||||||
\(510\) | 2.91979 | + | 0.226024i | 0.129290 | + | 0.0100085i | ||||
\(511\) | 36.5363 | 1.61627 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.68286 | + | 2.25184i | 0.206753 | + | 0.0994214i | ||||
\(514\) | 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 | \(-0.670236\pi\) | ||
0.509679 | − | 0.860365i | \(-0.329764\pi\) | |||||||
\(522\) | 7.65040 | + | 4.80299i | 0.334849 | + | 0.210221i | ||||
\(523\) | −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 | ||||||||
\(525\) | −42.0944 | − | 11.5098i | −1.83715 | − | 0.502330i | ||||
\(526\) | −24.9560 | −1.08813 | ||||||||
\(527\) | 4.37619 | − | 4.37619i | 0.190630 | − | 0.190630i | ||||
\(528\) | −3.61853 | + | 4.53927i | −0.157476 | + | 0.197547i | ||||
\(529\) | 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 | ||||||||
\(537\) | 15.5712 | + | 12.4128i | 0.671948 | + | 0.535651i | ||||
\(538\) | 9.04126 | − | 9.04126i | 0.389796 | − | 0.389796i | ||||
\(539\) | −61.6426 | −2.65513 | ||||||||
\(540\) | −1.70787 | − | 11.4927i | −0.0734949 | − | 0.494569i | ||||
\(541\) | −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 | ||||
\(543\) | −30.2425 | − | 24.1081i | −1.29783 | − | 1.03458i | ||||
\(544\) | − | 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 | ||||||
\(552\) | 6.03752 | − | 7.57378i | 0.256974 | − | 0.322361i | ||||
\(553\) | 0.913774 | − | 0.913774i | 0.0388576 | − | 0.0388576i | ||||
\(554\) | −6.12299 | −0.260141 | ||||||||
\(555\) | 23.1984 | − | 19.8648i | 0.984716 | − | 0.843214i | ||||
\(556\) | −9.84417 | −0.417486 | ||||||||
\(557\) | 12.9276 | − | 12.9276i | 0.547758 | − | 0.547758i | −0.378034 | − | 0.925792i | \(-0.623400\pi\) |
0.925792 | + | 0.378034i | \(0.123400\pi\) | |||||||
\(558\) | −20.7958 | − | 13.0558i | −0.880356 | − | 0.552696i | ||||
\(559\) | − | 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 | \(-0.952670\pi\) |
−0.148145 | − | 0.988966i | \(-0.547330\pi\) | |||||||
\(564\) | −2.20010 | − | 19.4930i | −0.0926410 | − | 0.820804i | ||||
\(565\) | −0.533486 | + | 2.77923i | −0.0224439 | + | 0.116923i | ||||
\(566\) | − | 17.1605i | − | 0.721309i | ||||||
\(567\) | 42.8181 | + | 14.9460i | 1.79819 | + | 0.627673i | ||||
\(568\) | 3.35704 | − | 3.35704i | 0.140858 | − | 0.140858i | ||||
\(569\) | −30.1015 | −1.26192 | −0.630961 | − | 0.775814i | \(-0.717339\pi\) | ||||
−0.630961 | + | 0.775814i | \(0.717339\pi\) | |||||||
\(570\) | −2.94181 | + | 2.51908i | −0.123219 | + | 0.105513i | ||||
\(571\) | −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 | ||||
\(573\) | 8.55997 | − | 10.7381i | 0.357598 | − | 0.448589i | ||||
\(574\) | 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 | ||||||||
\(582\) | −18.6461 | − | 14.8640i | −0.772908 | − | 0.616132i | ||||
\(583\) | −23.6205 | + | 23.6205i | −0.978260 | + | 0.978260i | ||||
\(584\) | −7.25060 | −0.300032 | ||||||||
\(585\) | 0.252943 | + | 7.19648i | 0.0104579 | + | 0.297538i | ||||
\(586\) | −24.6840 | −1.01968 | ||||||||
\(587\) | 9.92177 | − | 9.92177i | 0.409515 | − | 0.409515i | −0.472054 | − | 0.881569i | \(-0.656487\pi\) |
0.881569 | + | 0.472054i | \(0.156487\pi\) | |||||||
\(588\) | −24.9100 | − | 19.8573i | −1.02727 | − | 0.818901i | ||||
\(589\) | 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 | 0.689399 | − | 0.724382i | \(-0.257875\pi\) |
−0.724382 | + | 0.689399i | \(0.757875\pi\) | |||||||
\(594\) | −16.4346 | + | 5.76129i | −0.674321 | + | 0.236389i | ||||
\(595\) | −4.78082 | − | 7.05222i | −0.195994 | − | 0.289113i | ||||
\(596\) | − | 1.98019i | − | 0.0811118i | ||||||
\(597\) | 10.8017 | − | 13.5502i | 0.442084 | − | 0.554573i | ||||
\(598\) | −4.24463 | + | 4.24463i | −0.173576 | + | 0.173576i | ||||
\(599\) | −3.99004 | −0.163028 | −0.0815142 | − | 0.996672i | \(-0.525976\pi\) | ||||
−0.0815142 | + | 0.996672i | \(0.525976\pi\) | |||||||
\(600\) | 8.35361 | + | 2.28412i | 0.341035 | + | 0.0932486i | ||||
\(601\) | 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 | ||||
\(603\) | −11.7991 | + | 18.7940i | −0.480496 | + | 0.765353i | ||||
\(604\) | − | 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 | ||||||||
\(612\) | 1.20614 | − | 1.92119i | 0.0487554 | − | 0.0776596i | ||||
\(613\) | −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 | ||||||||
\(615\) | 32.5594 | + | 2.52046i | 1.31292 | + | 0.101635i | ||||
\(616\) | 16.8887 | 0.680466 | ||||||||
\(617\) | −27.8433 | + | 27.8433i | −1.12093 | + | 1.12093i | −0.129329 | + | 0.991602i | \(0.541282\pi\) |
−0.991602 | + | 0.129329i | \(0.958718\pi\) | |||||||
\(618\) | 0.545230 | − | 0.683965i | 0.0219324 | − | 0.0275131i | ||||
\(619\) | − | 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 | ||||||||
\(627\) | 4.53927 | + | 3.61853i | 0.181281 | + | 0.144510i | ||||
\(628\) | −16.6468 | + | 16.6468i | −0.664282 | + | 0.664282i | ||||
\(629\) | 5.96274 | 0.237750 | ||||||||
\(630\) | −23.0480 | + | 24.7273i | −0.918256 | + | 0.985158i | ||||
\(631\) | 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 | ||||
\(633\) | −0.458636 | − | 0.365606i | −0.0182291 | − | 0.0145316i | ||||
\(634\) | 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 | \(-0.624056\pi\) | ||
0.379943 | − | 0.925010i | \(-0.375944\pi\) | |||||||
\(642\) | −3.29602 | + | 4.13470i | −0.130084 | + | 0.163184i | ||||
\(643\) | 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 | ||||||||
\(645\) | −15.3069 | − | 17.8756i | −0.602708 | − | 0.703850i | ||||
\(646\) | −0.756142 | −0.0297500 | ||||||||
\(647\) | 10.8816 | − | 10.8816i | 0.427801 | − | 0.427801i | −0.460078 | − | 0.887879i | \(-0.652179\pi\) |
0.887879 | + | 0.460078i | \(0.152179\pi\) | |||||||
\(648\) | −8.49722 | − | 2.96602i | −0.333802 | − | 0.116516i | ||||
\(649\) | − | 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 | 0.709011 | − | 0.705197i | \(-0.249142\pi\) |
−0.705197 | + | 0.709011i | \(0.749142\pi\) | |||||||
\(654\) | −0.575163 | − | 5.09597i | −0.0224906 | − | 0.199268i | ||||
\(655\) | −2.83447 | + | 1.92153i | −0.110752 | + | 0.0750804i | ||||
\(656\) | − | 8.43195i | − | 0.329212i | ||||||
\(657\) | −18.4222 | − | 11.5656i | −0.718719 | − | 0.451218i | ||||
\(658\) | −40.3555 | + | 40.3555i | −1.57322 | + | 1.57322i | ||||
\(659\) | 4.39566 | 0.171231 | 0.0856153 | − | 0.996328i | \(-0.472714\pi\) | ||||
0.0856153 | + | 0.996328i | \(0.472714\pi\) | |||||||
\(660\) | 1.00184 | − | 12.9418i | 0.0389965 | − | 0.503759i | ||||
\(661\) | −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 | ||||
\(663\) | −0.876337 | + | 1.09932i | −0.0340341 | + | 0.0426941i | ||||
\(664\) | − | 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 | ||||||||
\(672\) | 6.82480 | + | 5.44047i | 0.263273 | + | 0.209871i | ||||
\(673\) | 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 | ||||||||
\(675\) | 17.5812 | + | 19.1285i | 0.676703 | + | 0.736256i | ||||
\(676\) | 11.8477 | 0.455681 | ||||||||
\(677\) | −21.1304 | + | 21.1304i | −0.812109 | + | 0.812109i | −0.984950 | − | 0.172841i | \(-0.944705\pi\) |
0.172841 | + | 0.984950i | \(0.444705\pi\) | |||||||
\(678\) | 1.71410 | + | 1.36642i | 0.0658297 | + | 0.0524769i | ||||
\(679\) | 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 | 0.497638 | − | 0.867385i | \(-0.334201\pi\) |
−0.867385 | + | 0.497638i | \(0.834201\pi\) | |||||||
\(684\) | 0.668679 | + | 2.92453i | 0.0255676 | + | 0.111822i | ||||
\(685\) | −14.7877 | − | 2.83856i | −0.565007 | − | 0.108456i | ||||
\(686\) | 57.4062i | 2.19178i | ||||||||
\(687\) | 14.2571 | − | 17.8849i | 0.543943 | − | 0.682350i | ||||
\(688\) | −4.29665 | + | 4.29665i | −0.163808 | + | 0.163808i | ||||
\(689\) | 10.6989 | 0.407596 | ||||||||
\(690\) | −1.67157 | + | 21.5934i | −0.0636355 | + | 0.822046i | ||||
\(691\) | −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 | ||||
\(693\) | 42.9106 | + | 26.9397i | 1.63004 | + | 1.02335i | ||||
\(694\) | − | 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 | \(-0.965778\pi\) | ||
0.994226 | − | 0.107305i | \(-0.0342221\pi\) | |||||||
\(702\) | 5.02682 | + | 2.41724i | 0.189725 | + | 0.0912330i | ||||
\(703\) | −5.57606 | + | 5.57606i | −0.210305 | + | 0.210305i | ||||
\(704\) | −3.35156 | −0.126317 | ||||||||
\(705\) | 28.5304 | + | 33.3182i | 1.07452 | + | 1.25484i | ||||
\(706\) | 0.518226 | 0.0195037 | ||||||||
\(707\) | −43.8924 | + | 43.8924i | −1.65075 | + | 1.65075i | ||||
\(708\) | 4.66837 | − | 5.85624i | 0.175448 | − | 0.220091i | ||||
\(709\) | 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 | ||||||||
\(717\) | 10.9535 | + | 8.73168i | 0.409065 | + | 0.326091i | ||||
\(718\) | 11.6243 | − | 11.6243i | 0.433815 | − | 0.433815i | ||||
\(719\) | 38.3623 | 1.43067 | 0.715337 | − | 0.698780i | \(-0.246273\pi\) | ||||
0.715337 | + | 0.698780i | \(0.246273\pi\) | |||||||
\(720\) | 4.57387 | − | 4.90711i | 0.170458 | − | 0.182877i | ||||
\(721\) | −2.54474 | −0.0947712 | ||||||||
\(722\) | 0.707107 | − | 0.707107i | 0.0263158 | − | 0.0263158i | ||||
\(723\) | −23.6471 | − | 18.8506i | −0.879446 | − | 0.701060i | ||||
\(724\) | − | 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 | ||||||
\(732\) | −1.46578 | + | 1.83875i | −0.0541769 | + | 0.0679623i | ||||
\(733\) | 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 | ||||||||
\(735\) | 71.0203 | + | 5.49776i | 2.61962 | + | 0.202788i | ||||
\(736\) | 5.59207 | 0.206126 | ||||||||
\(737\) | −17.5301 | + | 17.5301i | −0.645730 | + | 0.645730i | ||||
\(738\) | 13.4500 | − | 21.4237i | 0.495102 | − | 0.788619i | ||||
\(739\) | 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 | 0.620169 | − | 0.784468i | \(-0.287064\pi\) |
−0.784468 | + | 0.620169i | \(0.787064\pi\) | |||||||
\(744\) | −1.58995 | − | 14.0871i | −0.0582905 | − | 0.516456i | ||||
\(745\) | 2.48459 | + | 3.66505i | 0.0910285 | + | 0.134277i | ||||
\(746\) | − | 3.96766i | − | 0.145266i | ||||||
\(747\) | 10.6759 | − | 17.0049i | 0.390609 | − | 0.622178i | ||||
\(748\) | 1.79199 | − | 1.79199i | 0.0655215 | − | 0.0655215i | ||||
\(749\) | 15.3835 | 0.562100 | ||||||||
\(750\) | −18.3273 | + | 6.25392i | −0.669217 | + | 0.228361i | ||||
\(751\) | −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 | ||||
\(753\) | −2.37531 | + | 2.97971i | −0.0865612 | + | 0.108587i | ||||
\(754\) | − | 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 | \(-0.871382\pi\) | ||
0.919471 | − | 0.393159i | \(-0.128618\pi\) | |||||||
\(762\) | −12.8422 | − | 10.2373i | −0.465222 | − | 0.370857i | ||||
\(763\) | −10.5499 | + | 10.5499i | −0.381933 | + | 0.381933i | ||||
\(764\) | 7.92842 | 0.286840 | ||||||||
\(765\) | 0.178174 | + | 5.06922i | 0.00644188 | + | 0.183278i | ||||
\(766\) | 1.11237 | 0.0401914 | ||||||||
\(767\) | −3.28206 | + | 3.28206i | −0.118508 | + | 0.118508i | ||||
\(768\) | −1.35438 | − | 1.07966i | −0.0488719 | − | 0.0389588i | ||||
\(769\) | 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 | 0.765053 | − | 0.643968i | \(-0.222713\pi\) |
−0.643968 | + | 0.765053i | \(0.722713\pi\) | |||||||
\(774\) | −17.7706 | + | 4.06315i | −0.638750 | + | 0.146047i | ||||
\(775\) | −15.1528 | + | 38.0154i | −0.544303 | + | 1.36555i | ||||
\(776\) | − | 13.7673i | − | 0.494218i | ||||||
\(777\) | −42.9021 | + | 53.8187i | −1.53911 | + | 1.93073i | ||||
\(778\) | −0.985230 | + | 0.985230i | −0.0353222 | + | 0.0353222i | ||||
\(779\) | −8.43195 | −0.302106 | ||||||||
\(780\) | −3.15789 | + | 2.70410i | −0.113071 | + | 0.0968225i | ||||
\(781\) | 15.9118 | 0.569367 | ||||||||
\(782\) | −2.98993 | + | 2.98993i | −0.106920 | + | 0.106920i | ||||
\(783\) | −6.78040 | + | 14.1003i | −0.242312 | + | 0.503904i | ||||
\(784\) | − | 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 | ||||||
\(792\) | −8.51557 | − | 5.34616i | −0.302588 | − | 0.189967i | ||||
\(793\) | 1.03051 | − | 1.03051i | 0.0365944 | − | 0.0365944i | ||||
\(794\) | 14.8510 | 0.527041 | ||||||||
\(795\) | 29.3205 | − | 25.1072i | 1.03989 | − | 0.890462i | ||||
\(796\) | 10.0047 | 0.354609 | ||||||||
\(797\) | 29.5421 | − | 29.5421i | 1.04644 | − | 1.04644i | 0.0475679 | − | 0.998868i | \(-0.484853\pi\) |
0.998868 | − | 0.0475679i | \(-0.0151470\pi\) | |||||||
\(798\) | 5.44047 | − | 6.82480i | 0.192591 | − | 0.241595i | ||||
\(799\) | 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 | ||||||||
\(807\) | 17.3174 | + | 13.8048i | 0.609603 | + | 0.485952i | ||||
\(808\) | 8.71043 | − | 8.71043i | 0.306432 | − | 0.306432i | ||||
\(809\) | −56.0263 | −1.96978 | −0.984889 | − | 0.173186i | \(-0.944594\pi\) | ||||
−0.984889 | + | 0.173186i | \(0.944594\pi\) | |||||||
\(810\) | 19.4487 | − | 5.17199i | 0.683356 | − | 0.181725i | ||||
\(811\) | −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 | ||||
\(813\) | 11.1233 | + | 8.86709i | 0.390112 | + | 0.310982i | ||||
\(814\) | − | 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 | \(-0.895853\pi\) | ||
0.946950 | − | 0.321382i | \(-0.104147\pi\) | |||||||
\(822\) | −7.27039 | + | 9.12035i | −0.253584 | + | 0.318109i | ||||
\(823\) | 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 | ||||||||
\(825\) | 14.3841 | + | 25.2104i | 0.500792 | + | 0.877715i | ||||
\(826\) | −21.7886 | −0.758123 | ||||||||
\(827\) | −30.1536 | + | 30.1536i | −1.04854 | + | 1.04854i | −0.0497825 | + | 0.998760i | \(0.515853\pi\) |
−0.998760 | + | 0.0497825i | \(0.984147\pi\) | |||||||
\(828\) | 14.2082 | + | 8.92006i | 0.493770 | + | 0.309993i | ||||
\(829\) | − | 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 | ||||||||
\(837\) | 18.4309 | − | 38.3283i | 0.637065 | − | 1.32482i | ||||
\(838\) | 0.0179681 | − | 0.0179681i | 0.000620699 | − | 0.000620699i | ||||
\(839\) | −29.3705 | −1.01398 | −0.506991 | − | 0.861952i | \(-0.669242\pi\) | ||||
−0.506991 | + | 0.861952i | \(0.669242\pi\) | |||||||
\(840\) | −19.4580 | − | 1.50627i | −0.671365 | − | 0.0519711i | ||||
\(841\) | −19.9336 | −0.687366 | ||||||||
\(842\) | −3.86056 | + | 3.86056i | −0.133044 | + | 0.133044i | ||||
\(843\) | −11.9002 | + | 14.9283i | −0.409865 | + | 0.514156i | ||||
\(844\) | − | 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 | ||||||||
\(852\) | 6.43000 | + | 5.12575i | 0.220288 | + | 0.175605i | ||||
\(853\) | 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 | ||||||||
\(855\) | −4.90711 | − | 4.57387i | −0.167820 | − | 0.156423i | ||||
\(856\) | −3.05284 | −0.104344 | ||||||||
\(857\) | −18.0497 | + | 18.0497i | −0.616565 | + | 0.616565i | −0.944649 | − | 0.328084i | \(-0.893597\pi\) |
0.328084 | + | 0.944649i | \(0.393597\pi\) | |||||||
\(858\) | 4.87269 | + | 3.88432i | 0.166351 | + | 0.132608i | ||||
\(859\) | − | 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 | 0.787368 | − | 0.616483i | \(-0.211443\pi\) |
−0.616483 | + | 0.787368i | \(0.711443\pi\) | |||||||
\(864\) | −1.71899 | − | 4.90358i | −0.0584812 | − | 0.166823i | ||||
\(865\) | −1.01103 | + | 5.26703i | −0.0343760 | + | 0.179084i | ||||
\(866\) | − | 11.7849i | − | 0.400466i | ||||||
\(867\) | 17.7369 | − | 22.2501i | 0.602376 | − | 0.755652i | ||||
\(868\) | −29.1638 | + | 29.1638i | −0.989883 | + | 0.989883i | ||||
\(869\) | −0.859509 | −0.0291568 | ||||||||
\(870\) | −7.58505 | − | 8.85792i | −0.257157 | − | 0.300312i | ||||
\(871\) | 7.94026 | 0.269046 | ||||||||
\(872\) | 2.09363 | − | 2.09363i | 0.0708992 | − | 0.0708992i | ||||
\(873\) | 21.9606 | − | 34.9797i | 0.743254 | − | 1.18388i | ||||
\(874\) | − | 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 | \(0.0192020\pi\) | ||||
−0.998181 | + | 0.0602882i | \(0.980798\pi\) | |||||||
\(882\) | 29.3379 | − | 46.7306i | 0.987859 | − | 1.57350i | ||||
\(883\) | 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 | ||||||||
\(885\) | −1.29250 | + | 16.6966i | −0.0434469 | + | 0.561249i | ||||
\(886\) | 13.0473 | 0.438331 | ||||||||
\(887\) | 31.7609 | − | 31.7609i | 1.06643 | − | 1.06643i | 0.0687967 | − | 0.997631i | \(-0.478084\pi\) |
0.997631 | − | 0.0687967i | \(-0.0219160\pi\) | |||||||
\(888\) | 8.51390 | − | 10.6803i | 0.285708 | − | 0.358407i | ||||
\(889\) | 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 | ||||||||
\(897\) | −8.13007 | − | 6.48098i | −0.271455 | − | 0.216394i | ||||
\(898\) | −6.18162 | + | 6.18162i | −0.206283 | + | 0.206283i | ||||
\(899\) | −24.6448 | −0.821950 | ||||||||
\(900\) | −2.30850 | + | 14.8213i | −0.0769500 | + | 0.494043i | ||||
\(901\) | 7.53634 | 0.251072 | ||||||||
\(902\) | 19.9830 | − | 19.9830i | 0.665360 | − | 0.665360i | ||||
\(903\) | 41.4702 | + | 33.0584i | 1.38004 | + | 1.10011i | ||||
\(904\) | 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 | \(0.109907\pi\) | ||||
−0.940979 | + | 0.338464i | \(0.890093\pi\) | |||||||
\(912\) | −1.07966 | + | 1.35438i | −0.0357510 | + | 0.0448479i | ||||
\(913\) | 15.8613 | − | 15.8613i | 0.524933 | − | 0.524933i | ||||
\(914\) | −14.7700 | −0.488549 | ||||||||
\(915\) | 0.405822 | − | 5.24242i | 0.0134160 | − | 0.173309i | ||||
\(916\) | 13.2052 | 0.436313 | ||||||||
\(917\) | 5.45675 | − | 5.45675i | 0.180198 | − | 0.180198i | ||||
\(918\) | 3.54091 | + | 1.70271i | 0.116867 | + | 0.0561979i | ||||
\(919\) | − | 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 | ||||||
\(927\) | 1.28310 | + | 0.805543i | 0.0421426 | + | 0.0264575i | ||||
\(928\) | −2.12913 | + | 2.12913i | −0.0698921 | + | 0.0698921i | ||||
\(929\) | 32.3526 | 1.06145 | 0.530727 | − | 0.847543i | \(-0.321919\pi\) | ||||
0.530727 | + | 0.847543i | \(0.321919\pi\) | |||||||
\(930\) | 20.6181 | + | 24.0781i | 0.676096 | + | 0.789553i | ||||
\(931\) | −18.3922 | −0.602781 | ||||||||
\(932\) | −17.7744 | + | 17.7744i | −0.582218 | + | 0.582218i | ||||
\(933\) | 15.3465 | − | 19.2514i | 0.502422 | − | 0.630264i | ||||
\(934\) | 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 | \(-0.999010\pi\) | ||
0.999995 | − | 0.00311010i | \(-0.000989976\pi\) | |||||||
\(942\) | −31.8850 | − | 25.4175i | −1.03887 | − | 0.828147i | ||||
\(943\) | −33.3415 | + | 33.3415i | −1.08575 | + | 1.08575i | ||||
\(944\) | 4.32394 | 0.140732 | ||||||||
\(945\) | −47.0359 | − | 34.8651i | −1.53008 | − | 1.13416i | ||||
\(946\) | −20.3654 | −0.662135 | ||||||||
\(947\) | 16.3696 | − | 16.3696i | 0.531942 | − | 0.531942i | −0.389208 | − | 0.921150i | \(-0.627251\pi\) |
0.921150 | + | 0.389208i | \(0.127251\pi\) | |||||||
\(948\) | −0.347331 | − | 0.276879i | −0.0112808 | − | 0.00899260i | ||||
\(949\) | 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 | 0.562669 | − | 0.826682i | \(-0.309774\pi\) |
−0.826682 | + | 0.562669i | \(0.809774\pi\) | |||||||
\(954\) | −6.66462 | − | 29.1483i | −0.215775 | − | 0.943711i | ||||
\(955\) | −14.6744 | + | 9.94798i | −0.474851 | + | 0.321909i | ||||
\(956\) | 8.08746i | 0.261567i | ||||||||
\(957\) | −10.8956 | + | 13.6679i | −0.352203 | + | 0.441822i | ||||
\(958\) | −15.9980 | + | 15.9980i | −0.516871 | + | 0.516871i | ||||
\(959\) | 33.9330 | 1.09575 | ||||||||
\(960\) | 3.86143 | + | 0.298918i | 0.124627 | + | 0.00964752i | ||||
\(961\) | 35.9910 | 1.16100 | ||||||||
\(962\) | −5.98563 | + | 5.98563i | −0.192984 | + | 0.192984i | ||||
\(963\) | −7.75661 | − | 4.86967i | −0.249953 | − | 0.156923i | ||||
\(964\) | − | 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 | \(0.197922\pi\) | ||||
−0.812838 | + | 0.582490i | \(0.802078\pi\) | |||||||
\(972\) | 3.45425 | − | 15.2009i | 0.110795 | − | 0.487570i | ||||
\(973\) | −35.0763 | + | 35.0763i | −1.12450 | + | 1.12450i | ||||
\(974\) | −27.7724 | −0.889884 | ||||||||
\(975\) | 2.45188 | − | 8.96719i | 0.0785232 | − | 0.287180i | ||||
\(976\) | −1.35764 | −0.0434569 | ||||||||
\(977\) | 12.2667 | − | 12.2667i | 0.392448 | − | 0.392448i | −0.483111 | − | 0.875559i | \(-0.660493\pi\) |
0.875559 | + | 0.483111i | \(0.160493\pi\) | |||||||
\(978\) | −15.3105 | + | 19.2063i | −0.489575 | + | 0.614149i | ||||
\(979\) | 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 | 0.766940 | − | 0.641719i | \(-0.221778\pi\) |
−0.641719 | + | 0.766940i | \(0.721778\pi\) | |||||||
\(984\) | 14.5124 | − | 1.63796i | 0.462639 | − | 0.0522164i | ||||
\(985\) | −14.6650 | − | 2.81502i | −0.467267 | − | 0.0896939i | ||||
\(986\) | − | 2.27678i | − | 0.0725073i | ||||||
\(987\) | −77.2960 | − | 61.6174i | −2.46036 | − | 1.96130i | ||||
\(988\) | 0.759044 | − | 0.759044i | 0.0241484 | − | 0.0241484i | ||||
\(989\) | 33.9796 | 1.08049 | ||||||||
\(990\) | 22.4691 | − | 0.789744i | 0.714113 | − | 0.0250997i | ||||
\(991\) | −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 | ||||
\(993\) | 11.8344 | + | 9.43390i | 0.375552 | + | 0.299376i | ||||
\(994\) | − | 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.77.2 | ✓ | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.77.16 | yes | 36 | |
5.3 | odd | 4 | inner | 570.2.k.a.533.16 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.a.533.2 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.2 | ✓ | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.77.16 | yes | 36 | 3.2 | odd | 2 | inner | |
570.2.k.a.533.2 | yes | 36 | 15.8 | even | 4 | inner | |
570.2.k.a.533.16 | yes | 36 | 5.3 | odd | 4 | inner |