Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(111,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.k (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.151 |
Dual form | 170.2.k.a.161.1 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | ||||
\(3\) | 0.548594 | + | 1.32442i | 0.316731 | + | 0.764656i | 0.999424 | + | 0.0339504i | \(0.0108088\pi\) |
−0.682693 | + | 0.730706i | \(0.739191\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.923880 | + | 0.382683i | −0.413171 | + | 0.171141i | ||||
\(6\) | −0.548594 | + | 1.32442i | −0.223963 | + | 0.540694i | ||||
\(7\) | 0.599456 | + | 0.248303i | 0.226573 | + | 0.0938497i | 0.493082 | − | 0.869983i | \(-0.335870\pi\) |
−0.266509 | + | 0.963832i | \(0.585870\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0.668179 | − | 0.668179i | 0.222726 | − | 0.222726i | ||||
\(10\) | −0.923880 | − | 0.382683i | −0.292156 | − | 0.121015i | ||||
\(11\) | −1.42788 | + | 3.44722i | −0.430523 | + | 1.03937i | 0.548596 | + | 0.836087i | \(0.315162\pi\) |
−0.979119 | + | 0.203287i | \(0.934838\pi\) | |||||||
\(12\) | −1.32442 | + | 0.548594i | −0.382328 | + | 0.158365i | ||||
\(13\) | − | 4.08239i | − | 1.13225i | −0.824319 | − | 0.566126i | \(-0.808442\pi\) | ||
0.824319 | − | 0.566126i | \(-0.191558\pi\) | |||||||
\(14\) | 0.248303 | + | 0.599456i | 0.0663617 | + | 0.160211i | ||||
\(15\) | −1.01367 | − | 1.01367i | −0.261728 | − | 0.261728i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.85403 | + | 1.46508i | 0.934740 | + | 0.355333i | ||||
\(18\) | 0.944947 | 0.222726 | ||||||||
\(19\) | −3.03300 | − | 3.03300i | −0.695818 | − | 0.695818i | 0.267687 | − | 0.963506i | \(-0.413741\pi\) |
−0.963506 | + | 0.267687i | \(0.913741\pi\) | |||||||
\(20\) | −0.382683 | − | 0.923880i | −0.0855706 | − | 0.206586i | ||||
\(21\) | 0.930151i | 0.202976i | ||||||||
\(22\) | −3.44722 | + | 1.42788i | −0.734949 | + | 0.304426i | ||||
\(23\) | 2.78470 | − | 6.72286i | 0.580650 | − | 1.40181i | −0.311575 | − | 0.950222i | \(-0.600857\pi\) |
0.892225 | − | 0.451591i | \(-0.149143\pi\) | |||||||
\(24\) | −1.32442 | − | 0.548594i | −0.270347 | − | 0.111981i | ||||
\(25\) | 0.707107 | − | 0.707107i | 0.141421 | − | 0.141421i | ||||
\(26\) | 2.88669 | − | 2.88669i | 0.566126 | − | 0.566126i | ||||
\(27\) | 5.22478 | + | 2.16417i | 1.00551 | + | 0.416496i | ||||
\(28\) | −0.248303 | + | 0.599456i | −0.0469248 | + | 0.113287i | ||||
\(29\) | −1.66399 | + | 0.689246i | −0.308995 | + | 0.127990i | −0.531792 | − | 0.846875i | \(-0.678481\pi\) |
0.222797 | + | 0.974865i | \(0.428481\pi\) | |||||||
\(30\) | − | 1.43355i | − | 0.261728i | ||||||
\(31\) | 1.90342 | + | 4.59527i | 0.341865 | + | 0.825334i | 0.997527 | + | 0.0702802i | \(0.0223893\pi\) |
−0.655663 | + | 0.755054i | \(0.727611\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −5.34890 | −0.931124 | ||||||||
\(34\) | 1.68925 | + | 3.76118i | 0.289703 | + | 0.645036i | ||||
\(35\) | −0.648847 | −0.109675 | ||||||||
\(36\) | 0.668179 | + | 0.668179i | 0.111363 | + | 0.111363i | ||||
\(37\) | −3.12132 | − | 7.53553i | −0.513142 | − | 1.23883i | −0.942046 | − | 0.335484i | \(-0.891100\pi\) |
0.428904 | − | 0.903350i | \(-0.358900\pi\) | |||||||
\(38\) | − | 4.28931i | − | 0.695818i | ||||||
\(39\) | 5.40682 | − | 2.23958i | 0.865783 | − | 0.358619i | ||||
\(40\) | 0.382683 | − | 0.923880i | 0.0605076 | − | 0.146078i | ||||
\(41\) | 1.78950 | + | 0.741235i | 0.279473 | + | 0.115761i | 0.518017 | − | 0.855370i | \(-0.326670\pi\) |
−0.238544 | + | 0.971132i | \(0.576670\pi\) | |||||||
\(42\) | −0.657716 | + | 0.657716i | −0.101488 | + | 0.101488i | ||||
\(43\) | 0.740108 | − | 0.740108i | 0.112865 | − | 0.112865i | −0.648419 | − | 0.761284i | \(-0.724569\pi\) |
0.761284 | + | 0.648419i | \(0.224569\pi\) | |||||||
\(44\) | −3.44722 | − | 1.42788i | −0.519687 | − | 0.215262i | ||||
\(45\) | −0.361616 | + | 0.873017i | −0.0539065 | + | 0.130142i | ||||
\(46\) | 6.72286 | − | 2.78470i | 0.991231 | − | 0.410581i | ||||
\(47\) | 4.71031i | 0.687070i | 0.939140 | + | 0.343535i | \(0.111624\pi\) | ||||
−0.939140 | + | 0.343535i | \(0.888376\pi\) | |||||||
\(48\) | −0.548594 | − | 1.32442i | −0.0791827 | − | 0.191164i | ||||
\(49\) | −4.65205 | − | 4.65205i | −0.664579 | − | 0.664579i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0.173918 | + | 5.90810i | 0.0243534 | + | 0.827300i | ||||
\(52\) | 4.08239 | 0.566126 | ||||||||
\(53\) | −6.16799 | − | 6.16799i | −0.847239 | − | 0.847239i | 0.142549 | − | 0.989788i | \(-0.454470\pi\) |
−0.989788 | + | 0.142549i | \(0.954470\pi\) | |||||||
\(54\) | 2.16417 | + | 5.22478i | 0.294507 | + | 0.711003i | ||||
\(55\) | − | 3.73124i | − | 0.503120i | ||||||
\(56\) | −0.599456 | + | 0.248303i | −0.0801057 | + | 0.0331809i | ||||
\(57\) | 2.35309 | − | 5.68087i | 0.311675 | − | 0.752449i | ||||
\(58\) | −1.66399 | − | 0.689246i | −0.218492 | − | 0.0905025i | ||||
\(59\) | −7.34549 | + | 7.34549i | −0.956301 | + | 0.956301i | −0.999084 | − | 0.0427829i | \(-0.986378\pi\) |
0.0427829 | + | 0.999084i | \(0.486378\pi\) | |||||||
\(60\) | 1.01367 | − | 1.01367i | 0.130864 | − | 0.130864i | ||||
\(61\) | −3.27209 | − | 1.35534i | −0.418948 | − | 0.173534i | 0.163243 | − | 0.986586i | \(-0.447805\pi\) |
−0.582191 | + | 0.813052i | \(0.697805\pi\) | |||||||
\(62\) | −1.90342 | + | 4.59527i | −0.241735 | + | 0.583599i | ||||
\(63\) | 0.566454 | − | 0.234633i | 0.0713666 | − | 0.0295610i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.56226 | + | 3.77164i | 0.193775 | + | 0.467814i | ||||
\(66\) | −3.78224 | − | 3.78224i | −0.465562 | − | 0.465562i | ||||
\(67\) | −3.48022 | −0.425176 | −0.212588 | − | 0.977142i | \(-0.568189\pi\) | ||||
−0.212588 | + | 0.977142i | \(0.568189\pi\) | |||||||
\(68\) | −1.46508 | + | 3.85403i | −0.177667 | + | 0.467370i | ||||
\(69\) | 10.4316 | 1.25581 | ||||||||
\(70\) | −0.458804 | − | 0.458804i | −0.0548376 | − | 0.0548376i | ||||
\(71\) | 5.07933 | + | 12.2626i | 0.602805 | + | 1.45530i | 0.870681 | + | 0.491847i | \(0.163678\pi\) |
−0.267876 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(72\) | 0.944947i | 0.111363i | ||||||||
\(73\) | −5.53701 | + | 2.29350i | −0.648057 | + | 0.268434i | −0.682403 | − | 0.730976i | \(-0.739065\pi\) |
0.0343459 | + | 0.999410i | \(0.489065\pi\) | |||||||
\(74\) | 3.12132 | − | 7.53553i | 0.362846 | − | 0.875988i | ||||
\(75\) | 1.32442 | + | 0.548594i | 0.152931 | + | 0.0633462i | ||||
\(76\) | 3.03300 | − | 3.03300i | 0.347909 | − | 0.347909i | ||||
\(77\) | −1.71191 | + | 1.71191i | −0.195090 | + | 0.195090i | ||||
\(78\) | 5.40682 | + | 2.23958i | 0.612201 | + | 0.253582i | ||||
\(79\) | −0.112187 | + | 0.270842i | −0.0126220 | + | 0.0304721i | −0.930065 | − | 0.367395i | \(-0.880250\pi\) |
0.917443 | + | 0.397867i | \(0.130250\pi\) | |||||||
\(80\) | 0.923880 | − | 0.382683i | 0.103293 | − | 0.0427853i | ||||
\(81\) | 5.27223i | 0.585804i | ||||||||
\(82\) | 0.741235 | + | 1.78950i | 0.0818557 | + | 0.197617i | ||||
\(83\) | 1.75650 | + | 1.75650i | 0.192801 | + | 0.192801i | 0.796905 | − | 0.604104i | \(-0.206469\pi\) |
−0.604104 | + | 0.796905i | \(0.706469\pi\) | |||||||
\(84\) | −0.930151 | −0.101488 | ||||||||
\(85\) | −4.12132 | + | 0.121320i | −0.447020 | + | 0.0131590i | ||||
\(86\) | 1.04667 | 0.112865 | ||||||||
\(87\) | −1.82571 | − | 1.82571i | −0.195736 | − | 0.195736i | ||||
\(88\) | −1.42788 | − | 3.44722i | −0.152213 | − | 0.367474i | ||||
\(89\) | 3.59539i | 0.381110i | 0.981676 | + | 0.190555i | \(0.0610288\pi\) | ||||
−0.981676 | + | 0.190555i | \(0.938971\pi\) | |||||||
\(90\) | −0.873017 | + | 0.361616i | −0.0920241 | + | 0.0381176i | ||||
\(91\) | 1.01367 | − | 2.44722i | 0.106261 | − | 0.256538i | ||||
\(92\) | 6.72286 | + | 2.78470i | 0.700906 | + | 0.290325i | ||||
\(93\) | −5.04187 | + | 5.04187i | −0.522818 | + | 0.522818i | ||||
\(94\) | −3.33070 | + | 3.33070i | −0.343535 | + | 0.343535i | ||||
\(95\) | 3.96281 | + | 1.64145i | 0.406575 | + | 0.168409i | ||||
\(96\) | 0.548594 | − | 1.32442i | 0.0559907 | − | 0.135173i | ||||
\(97\) | −17.7713 | + | 7.36110i | −1.80440 | + | 0.747406i | −0.819782 | + | 0.572675i | \(0.805906\pi\) |
−0.984616 | + | 0.174731i | \(0.944094\pi\) | |||||||
\(98\) | − | 6.57900i | − | 0.664579i | ||||||
\(99\) | 1.34927 | + | 3.25744i | 0.135607 | + | 0.327385i | ||||
\(100\) | 0.707107 | + | 0.707107i | 0.0707107 | + | 0.0707107i | ||||
\(101\) | −9.83938 | −0.979055 | −0.489527 | − | 0.871988i | \(-0.662831\pi\) | ||||
−0.489527 | + | 0.871988i | \(0.662831\pi\) | |||||||
\(102\) | −4.05468 | + | 4.30064i | −0.401473 | + | 0.425826i | ||||
\(103\) | 5.96722 | 0.587968 | 0.293984 | − | 0.955810i | \(-0.405019\pi\) | ||||
0.293984 | + | 0.955810i | \(0.405019\pi\) | |||||||
\(104\) | 2.88669 | + | 2.88669i | 0.283063 | + | 0.283063i | ||||
\(105\) | −0.355953 | − | 0.859348i | −0.0347375 | − | 0.0838637i | ||||
\(106\) | − | 8.72286i | − | 0.847239i | ||||||
\(107\) | 5.02349 | − | 2.08080i | 0.485640 | − | 0.201158i | −0.126410 | − | 0.991978i | \(-0.540345\pi\) |
0.612049 | + | 0.790820i | \(0.290345\pi\) | |||||||
\(108\) | −2.16417 | + | 5.22478i | −0.208248 | + | 0.502755i | ||||
\(109\) | 15.0972 | + | 6.25345i | 1.44605 | + | 0.598972i | 0.961256 | − | 0.275659i | \(-0.0888960\pi\) |
0.484790 | + | 0.874631i | \(0.338896\pi\) | |||||||
\(110\) | 2.63838 | − | 2.63838i | 0.251560 | − | 0.251560i | ||||
\(111\) | 8.26790 | − | 8.26790i | 0.784754 | − | 0.784754i | ||||
\(112\) | −0.599456 | − | 0.248303i | −0.0566433 | − | 0.0234624i | ||||
\(113\) | −0.953472 | + | 2.30188i | −0.0896951 | + | 0.216543i | −0.962361 | − | 0.271775i | \(-0.912389\pi\) |
0.872666 | + | 0.488318i | \(0.162389\pi\) | |||||||
\(114\) | 5.68087 | − | 2.35309i | 0.532062 | − | 0.220387i | ||||
\(115\) | 7.27677i | 0.678562i | ||||||||
\(116\) | −0.689246 | − | 1.66399i | −0.0639949 | − | 0.154497i | ||||
\(117\) | −2.72777 | − | 2.72777i | −0.252182 | − | 0.252182i | ||||
\(118\) | −10.3881 | −0.956301 | ||||||||
\(119\) | 1.94654 | + | 1.83522i | 0.178439 | + | 0.168234i | ||||
\(120\) | 1.43355 | 0.130864 | ||||||||
\(121\) | −2.06627 | − | 2.06627i | −0.187843 | − | 0.187843i | ||||
\(122\) | −1.35534 | − | 3.27209i | −0.122707 | − | 0.296241i | ||||
\(123\) | 2.77669i | 0.250366i | ||||||||
\(124\) | −4.59527 | + | 1.90342i | −0.412667 | + | 0.170932i | ||||
\(125\) | −0.382683 | + | 0.923880i | −0.0342282 | + | 0.0826343i | ||||
\(126\) | 0.566454 | + | 0.234633i | 0.0504638 | + | 0.0209028i | ||||
\(127\) | 6.36642 | − | 6.36642i | 0.564928 | − | 0.564928i | −0.365775 | − | 0.930703i | \(-0.619196\pi\) |
0.930703 | + | 0.365775i | \(0.119196\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 1.38624 | + | 0.574198i | 0.122051 | + | 0.0505553i | ||||
\(130\) | −1.56226 | + | 3.77164i | −0.137020 | + | 0.330795i | ||||
\(131\) | −14.6940 | + | 6.08646i | −1.28382 | + | 0.531777i | −0.917138 | − | 0.398569i | \(-0.869507\pi\) |
−0.366684 | + | 0.930346i | \(0.619507\pi\) | |||||||
\(132\) | − | 5.34890i | − | 0.465562i | ||||||
\(133\) | −1.06505 | − | 2.57125i | −0.0923514 | − | 0.222956i | ||||
\(134\) | −2.46088 | − | 2.46088i | −0.212588 | − | 0.212588i | ||||
\(135\) | −5.65526 | −0.486727 | ||||||||
\(136\) | −3.76118 | + | 1.68925i | −0.322518 | + | 0.144852i | ||||
\(137\) | 22.9252 | 1.95864 | 0.979318 | − | 0.202328i | \(-0.0648507\pi\) | ||||
0.979318 | + | 0.202328i | \(0.0648507\pi\) | |||||||
\(138\) | 7.37624 | + | 7.37624i | 0.627907 | + | 0.627907i | ||||
\(139\) | −4.40508 | − | 10.6348i | −0.373634 | − | 0.902032i | −0.993128 | − | 0.117031i | \(-0.962662\pi\) |
0.619494 | − | 0.785001i | \(-0.287338\pi\) | |||||||
\(140\) | − | 0.648847i | − | 0.0548376i | ||||||
\(141\) | −6.23845 | + | 2.58405i | −0.525372 | + | 0.217616i | ||||
\(142\) | −5.07933 | + | 12.2626i | −0.426248 | + | 1.02905i | ||||
\(143\) | 14.0729 | + | 5.82918i | 1.17683 | + | 0.487460i | ||||
\(144\) | −0.668179 | + | 0.668179i | −0.0556816 | + | 0.0556816i | ||||
\(145\) | 1.27356 | − | 1.27356i | 0.105764 | − | 0.105764i | ||||
\(146\) | −5.53701 | − | 2.29350i | −0.458246 | − | 0.189812i | ||||
\(147\) | 3.60920 | − | 8.71338i | 0.297682 | − | 0.718667i | ||||
\(148\) | 7.53553 | − | 3.12132i | 0.619417 | − | 0.256571i | ||||
\(149\) | − | 13.8251i | − | 1.13260i | −0.824200 | − | 0.566299i | \(-0.808375\pi\) | ||
0.824200 | − | 0.566299i | \(-0.191625\pi\) | |||||||
\(150\) | 0.548594 | + | 1.32442i | 0.0447925 | + | 0.108139i | ||||
\(151\) | −12.9700 | − | 12.9700i | −1.05549 | − | 1.05549i | −0.998367 | − | 0.0571190i | \(-0.981809\pi\) |
−0.0571190 | − | 0.998367i | \(-0.518191\pi\) | |||||||
\(152\) | 4.28931 | 0.347909 | ||||||||
\(153\) | 3.55411 | − | 1.59625i | 0.287333 | − | 0.129049i | ||||
\(154\) | −2.42100 | −0.195090 | ||||||||
\(155\) | −3.51706 | − | 3.51706i | −0.282497 | − | 0.282497i | ||||
\(156\) | 2.23958 | + | 5.40682i | 0.179310 | + | 0.432892i | ||||
\(157\) | − | 17.5326i | − | 1.39926i | −0.714507 | − | 0.699629i | \(-0.753349\pi\) | ||
0.714507 | − | 0.699629i | \(-0.246651\pi\) | |||||||
\(158\) | −0.270842 | + | 0.112187i | −0.0215470 | + | 0.00892508i | ||||
\(159\) | 4.78531 | − | 11.5528i | 0.379500 | − | 0.916193i | ||||
\(160\) | 0.923880 | + | 0.382683i | 0.0730391 | + | 0.0302538i | ||||
\(161\) | 3.33861 | − | 3.33861i | 0.263119 | − | 0.263119i | ||||
\(162\) | −3.72803 | + | 3.72803i | −0.292902 | + | 0.292902i | ||||
\(163\) | 7.95590 | + | 3.29544i | 0.623154 | + | 0.258119i | 0.671841 | − | 0.740695i | \(-0.265504\pi\) |
−0.0486872 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(164\) | −0.741235 | + | 1.78950i | −0.0578807 | + | 0.139736i | ||||
\(165\) | 4.94174 | − | 2.04694i | 0.384714 | − | 0.159354i | ||||
\(166\) | 2.48406i | 0.192801i | ||||||||
\(167\) | −4.24877 | − | 10.2574i | −0.328780 | − | 0.793744i | −0.998683 | − | 0.0512964i | \(-0.983665\pi\) |
0.669904 | − | 0.742448i | \(-0.266335\pi\) | |||||||
\(168\) | −0.657716 | − | 0.657716i | −0.0507439 | − | 0.0507439i | ||||
\(169\) | −3.66593 | −0.281994 | ||||||||
\(170\) | −3.00000 | − | 2.82843i | −0.230089 | − | 0.216930i | ||||
\(171\) | −4.05317 | −0.309954 | ||||||||
\(172\) | 0.740108 | + | 0.740108i | 0.0564327 | + | 0.0564327i | ||||
\(173\) | 5.86377 | + | 14.1564i | 0.445814 | + | 1.07629i | 0.973875 | + | 0.227085i | \(0.0729194\pi\) |
−0.528061 | + | 0.849207i | \(0.677081\pi\) | |||||||
\(174\) | − | 2.58194i | − | 0.195736i | ||||||
\(175\) | 0.599456 | − | 0.248303i | 0.0453146 | − | 0.0187699i | ||||
\(176\) | 1.42788 | − | 3.44722i | 0.107631 | − | 0.259844i | ||||
\(177\) | −13.7582 | − | 5.69885i | −1.03413 | − | 0.428352i | ||||
\(178\) | −2.54232 | + | 2.54232i | −0.190555 | + | 0.190555i | ||||
\(179\) | −7.20533 | + | 7.20533i | −0.538551 | + | 0.538551i | −0.923103 | − | 0.384552i | \(-0.874356\pi\) |
0.384552 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(180\) | −0.873017 | − | 0.361616i | −0.0650709 | − | 0.0269532i | ||||
\(181\) | 5.00086 | − | 12.0731i | 0.371711 | − | 0.897390i | −0.621750 | − | 0.783216i | \(-0.713578\pi\) |
0.993461 | − | 0.114174i | \(-0.0364221\pi\) | |||||||
\(182\) | 2.44722 | − | 1.01367i | 0.181400 | − | 0.0751382i | ||||
\(183\) | − | 5.07717i | − | 0.375315i | ||||||
\(184\) | 2.78470 | + | 6.72286i | 0.205291 | + | 0.495616i | ||||
\(185\) | 5.76745 | + | 5.76745i | 0.424031 | + | 0.424031i | ||||
\(186\) | −7.13028 | −0.522818 | ||||||||
\(187\) | −10.5535 | + | 11.1937i | −0.771751 | + | 0.818566i | ||||
\(188\) | −4.71031 | −0.343535 | ||||||||
\(189\) | 2.59466 | + | 2.59466i | 0.188733 | + | 0.188733i | ||||
\(190\) | 1.64145 | + | 3.96281i | 0.119083 | + | 0.287492i | ||||
\(191\) | − | 19.7531i | − | 1.42929i | −0.699489 | − | 0.714644i | \(-0.746589\pi\) | ||
0.699489 | − | 0.714644i | \(-0.253411\pi\) | |||||||
\(192\) | 1.32442 | − | 0.548594i | 0.0955820 | − | 0.0395914i | ||||
\(193\) | 3.96501 | − | 9.57238i | 0.285408 | − | 0.689035i | −0.714537 | − | 0.699598i | \(-0.753362\pi\) |
0.999944 | + | 0.0105631i | \(0.00336239\pi\) | |||||||
\(194\) | −17.7713 | − | 7.36110i | −1.27590 | − | 0.528496i | ||||
\(195\) | −4.13820 | + | 4.13820i | −0.296342 | + | 0.296342i | ||||
\(196\) | 4.65205 | − | 4.65205i | 0.332290 | − | 0.332290i | ||||
\(197\) | 15.4145 | + | 6.38489i | 1.09824 | + | 0.454904i | 0.856871 | − | 0.515530i | \(-0.172405\pi\) |
0.241365 | + | 0.970434i | \(0.422405\pi\) | |||||||
\(198\) | −1.34927 | + | 3.25744i | −0.0958888 | + | 0.231496i | ||||
\(199\) | −8.75167 | + | 3.62506i | −0.620389 | + | 0.256974i | −0.670663 | − | 0.741762i | \(-0.733991\pi\) |
0.0502741 | + | 0.998735i | \(0.483991\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −1.90923 | − | 4.60928i | −0.134666 | − | 0.325114i | ||||
\(202\) | −6.95749 | − | 6.95749i | −0.489527 | − | 0.489527i | ||||
\(203\) | −1.16863 | −0.0820217 | ||||||||
\(204\) | −5.90810 | + | 0.173918i | −0.413650 | + | 0.0121767i | ||||
\(205\) | −1.93694 | −0.135282 | ||||||||
\(206\) | 4.21946 | + | 4.21946i | 0.293984 | + | 0.293984i | ||||
\(207\) | −2.63139 | − | 6.35275i | −0.182894 | − | 0.441546i | ||||
\(208\) | 4.08239i | 0.283063i | ||||||||
\(209\) | 14.7862 | − | 6.12464i | 1.02278 | − | 0.423650i | ||||
\(210\) | 0.355953 | − | 0.859348i | 0.0245631 | − | 0.0593006i | ||||
\(211\) | 23.2236 | + | 9.61954i | 1.59878 | + | 0.662236i | 0.991242 | − | 0.132054i | \(-0.0421573\pi\) |
0.607538 | + | 0.794291i | \(0.292157\pi\) | |||||||
\(212\) | 6.16799 | − | 6.16799i | 0.423619 | − | 0.423619i | ||||
\(213\) | −13.4544 | + | 13.4544i | −0.921878 | + | 0.921878i | ||||
\(214\) | 5.02349 | + | 2.08080i | 0.343399 | + | 0.142241i | ||||
\(215\) | −0.400544 | + | 0.966998i | −0.0273169 | + | 0.0659487i | ||||
\(216\) | −5.22478 | + | 2.16417i | −0.355501 | + | 0.147253i | ||||
\(217\) | 3.22729i | 0.219082i | ||||||||
\(218\) | 6.25345 | + | 15.0972i | 0.423537 | + | 1.02251i | ||||
\(219\) | −6.07514 | − | 6.07514i | −0.410520 | − | 0.410520i | ||||
\(220\) | 3.73124 | 0.251560 | ||||||||
\(221\) | 5.98101 | − | 15.7337i | 0.402326 | − | 1.05836i | ||||
\(222\) | 11.6926 | 0.784754 | ||||||||
\(223\) | 13.4826 | + | 13.4826i | 0.902859 | + | 0.902859i | 0.995683 | − | 0.0928234i | \(-0.0295892\pi\) |
−0.0928234 | + | 0.995683i | \(0.529589\pi\) | |||||||
\(224\) | −0.248303 | − | 0.599456i | −0.0165904 | − | 0.0400529i | ||||
\(225\) | − | 0.944947i | − | 0.0629965i | ||||||
\(226\) | −2.30188 | + | 0.953472i | −0.153119 | + | 0.0634240i | ||||
\(227\) | −1.53539 | + | 3.70676i | −0.101907 | + | 0.246026i | −0.966607 | − | 0.256263i | \(-0.917509\pi\) |
0.864700 | + | 0.502289i | \(0.167509\pi\) | |||||||
\(228\) | 5.68087 | + | 2.35309i | 0.376224 | + | 0.155837i | ||||
\(229\) | −12.1237 | + | 12.1237i | −0.801154 | + | 0.801154i | −0.983276 | − | 0.182122i | \(-0.941704\pi\) |
0.182122 | + | 0.983276i | \(0.441704\pi\) | |||||||
\(230\) | −5.14545 | + | 5.14545i | −0.339281 | + | 0.339281i | ||||
\(231\) | −3.20643 | − | 1.32815i | −0.210968 | − | 0.0873857i | ||||
\(232\) | 0.689246 | − | 1.66399i | 0.0452512 | − | 0.109246i | ||||
\(233\) | −17.4907 | + | 7.24486i | −1.14585 | + | 0.474627i | −0.873140 | − | 0.487469i | \(-0.837920\pi\) |
−0.272710 | + | 0.962096i | \(0.587920\pi\) | |||||||
\(234\) | − | 3.85765i | − | 0.252182i | ||||||
\(235\) | −1.80256 | − | 4.35176i | −0.117586 | − | 0.283878i | ||||
\(236\) | −7.34549 | − | 7.34549i | −0.478151 | − | 0.478151i | ||||
\(237\) | −0.420255 | −0.0272985 | ||||||||
\(238\) | 0.0787183 | + | 2.67411i | 0.00510255 | + | 0.173336i | ||||
\(239\) | −25.1215 | −1.62498 | −0.812488 | − | 0.582978i | \(-0.801888\pi\) | ||||
−0.812488 | + | 0.582978i | \(0.801888\pi\) | |||||||
\(240\) | 1.01367 | + | 1.01367i | 0.0654321 | + | 0.0654321i | ||||
\(241\) | 2.29117 | + | 5.53137i | 0.147587 | + | 0.356307i | 0.980334 | − | 0.197348i | \(-0.0632328\pi\) |
−0.832746 | + | 0.553655i | \(0.813233\pi\) | |||||||
\(242\) | − | 2.92214i | − | 0.187843i | ||||||
\(243\) | 8.69167 | − | 3.60021i | 0.557571 | − | 0.230953i | ||||
\(244\) | 1.35534 | − | 3.27209i | 0.0867670 | − | 0.209474i | ||||
\(245\) | 6.07820 | + | 2.51767i | 0.388322 | + | 0.160848i | ||||
\(246\) | −1.96342 | + | 1.96342i | −0.125183 | + | 0.125183i | ||||
\(247\) | −12.3819 | + | 12.3819i | −0.787842 | + | 0.787842i | ||||
\(248\) | −4.59527 | − | 1.90342i | −0.291800 | − | 0.120867i | ||||
\(249\) | −1.36274 | + | 3.28995i | −0.0863603 | + | 0.208492i | ||||
\(250\) | −0.923880 | + | 0.382683i | −0.0584313 | + | 0.0242030i | ||||
\(251\) | 25.4489i | 1.60632i | 0.595763 | + | 0.803160i | \(0.296850\pi\) | ||||
−0.595763 | + | 0.803160i | \(0.703150\pi\) | |||||||
\(252\) | 0.234633 | + | 0.566454i | 0.0147805 | + | 0.0356833i | ||||
\(253\) | 19.1989 | + | 19.1989i | 1.20703 | + | 1.20703i | ||||
\(254\) | 9.00347 | 0.564928 | ||||||||
\(255\) | −2.42161 | − | 5.39182i | −0.151647 | − | 0.337649i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.5824 | + | 17.5824i | 1.09676 | + | 1.09676i | 0.994787 | + | 0.101975i | \(0.0325161\pi\) |
0.101975 | + | 0.994787i | \(0.467484\pi\) | |||||||
\(258\) | 0.574198 | + | 1.38624i | 0.0357480 | + | 0.0863033i | ||||
\(259\) | − | 5.29226i | − | 0.328845i | ||||||
\(260\) | −3.77164 | + | 1.56226i | −0.233907 | + | 0.0968875i | ||||
\(261\) | −0.651302 | + | 1.57238i | −0.0403146 | + | 0.0973279i | ||||
\(262\) | −14.6940 | − | 6.08646i | −0.907799 | − | 0.376023i | ||||
\(263\) | 3.88755 | − | 3.88755i | 0.239717 | − | 0.239717i | −0.577016 | − | 0.816733i | \(-0.695783\pi\) |
0.816733 | + | 0.577016i | \(0.195783\pi\) | |||||||
\(264\) | 3.78224 | − | 3.78224i | 0.232781 | − | 0.232781i | ||||
\(265\) | 8.05887 | + | 3.33809i | 0.495052 | + | 0.205057i | ||||
\(266\) | 1.06505 | − | 2.57125i | 0.0653023 | − | 0.157654i | ||||
\(267\) | −4.76181 | + | 1.97241i | −0.291418 | + | 0.120709i | ||||
\(268\) | − | 3.48022i | − | 0.212588i | ||||||
\(269\) | 3.47034 | + | 8.37815i | 0.211591 | + | 0.510825i | 0.993668 | − | 0.112357i | \(-0.0358399\pi\) |
−0.782077 | + | 0.623181i | \(0.785840\pi\) | |||||||
\(270\) | −3.99887 | − | 3.99887i | −0.243364 | − | 0.243364i | ||||
\(271\) | 26.0766 | 1.58404 | 0.792020 | − | 0.610496i | \(-0.209030\pi\) | ||||
0.792020 | + | 0.610496i | \(0.209030\pi\) | |||||||
\(272\) | −3.85403 | − | 1.46508i | −0.233685 | − | 0.0888333i | ||||
\(273\) | 3.79724 | 0.229820 | ||||||||
\(274\) | 16.2106 | + | 16.2106i | 0.979318 | + | 0.979318i | ||||
\(275\) | 1.42788 | + | 3.44722i | 0.0861046 | + | 0.207875i | ||||
\(276\) | 10.4316i | 0.627907i | ||||||||
\(277\) | −2.31159 | + | 0.957491i | −0.138890 | + | 0.0575300i | −0.451046 | − | 0.892501i | \(-0.648949\pi\) |
0.312156 | + | 0.950031i | \(0.398949\pi\) | |||||||
\(278\) | 4.40508 | − | 10.6348i | 0.264199 | − | 0.637833i | ||||
\(279\) | 4.34228 | + | 1.79863i | 0.259966 | + | 0.107681i | ||||
\(280\) | 0.458804 | − | 0.458804i | 0.0274188 | − | 0.0274188i | ||||
\(281\) | 8.22652 | − | 8.22652i | 0.490753 | − | 0.490753i | −0.417791 | − | 0.908543i | \(-0.637195\pi\) |
0.908543 | + | 0.417791i | \(0.137195\pi\) | |||||||
\(282\) | −6.23845 | − | 2.58405i | −0.371494 | − | 0.153878i | ||||
\(283\) | −10.3720 | + | 25.0401i | −0.616549 | + | 1.48848i | 0.239137 | + | 0.970986i | \(0.423135\pi\) |
−0.855686 | + | 0.517495i | \(0.826865\pi\) | |||||||
\(284\) | −12.2626 | + | 5.07933i | −0.727650 | + | 0.301403i | ||||
\(285\) | 6.14892i | 0.364231i | ||||||||
\(286\) | 5.82918 | + | 14.0729i | 0.344687 | + | 0.832147i | ||||
\(287\) | 0.888676 | + | 0.888676i | 0.0524569 | + | 0.0524569i | ||||
\(288\) | −0.944947 | −0.0556816 | ||||||||
\(289\) | 12.7071 | + | 11.2929i | 0.747477 | + | 0.664288i | ||||
\(290\) | 1.80109 | 0.105764 | ||||||||
\(291\) | −19.4984 | − | 19.4984i | −1.14302 | − | 1.14302i | ||||
\(292\) | −2.29350 | − | 5.53701i | −0.134217 | − | 0.324029i | ||||
\(293\) | − | 19.1754i | − | 1.12024i | −0.828413 | − | 0.560118i | \(-0.810756\pi\) | ||
0.828413 | − | 0.560118i | \(-0.189244\pi\) | |||||||
\(294\) | 8.71338 | − | 3.60920i | 0.508175 | − | 0.210493i | ||||
\(295\) | 3.97535 | − | 9.59735i | 0.231454 | − | 0.558779i | ||||
\(296\) | 7.53553 | + | 3.12132i | 0.437994 | + | 0.181423i | ||||
\(297\) | −14.9208 | + | 14.9208i | −0.865790 | + | 0.865790i | ||||
\(298\) | 9.77583 | − | 9.77583i | 0.566299 | − | 0.566299i | ||||
\(299\) | −27.4453 | − | 11.3682i | −1.58721 | − | 0.657442i | ||||
\(300\) | −0.548594 | + | 1.32442i | −0.0316731 | + | 0.0764656i | ||||
\(301\) | 0.627434 | − | 0.259892i | 0.0361647 | − | 0.0149799i | ||||
\(302\) | − | 18.3424i | − | 1.05549i | ||||||
\(303\) | −5.39782 | − | 13.0315i | −0.310097 | − | 0.748640i | ||||
\(304\) | 3.03300 | + | 3.03300i | 0.173955 | + | 0.173955i | ||||
\(305\) | 3.54168 | 0.202796 | ||||||||
\(306\) | 3.64186 | + | 1.38442i | 0.208191 | + | 0.0791420i | ||||
\(307\) | 8.72029 | 0.497693 | 0.248847 | − | 0.968543i | \(-0.419949\pi\) | ||||
0.248847 | + | 0.968543i | \(0.419949\pi\) | |||||||
\(308\) | −1.71191 | − | 1.71191i | −0.0975450 | − | 0.0975450i | ||||
\(309\) | 3.27358 | + | 7.90313i | 0.186228 | + | 0.449593i | ||||
\(310\) | − | 4.97388i | − | 0.282497i | ||||||
\(311\) | −15.5804 | + | 6.45361i | −0.883483 | + | 0.365951i | −0.777847 | − | 0.628454i | \(-0.783688\pi\) |
−0.105636 | + | 0.994405i | \(0.533688\pi\) | |||||||
\(312\) | −2.23958 | + | 5.40682i | −0.126791 | + | 0.306101i | ||||
\(313\) | −6.87302 | − | 2.84690i | −0.388486 | − | 0.160916i | 0.179887 | − | 0.983687i | \(-0.442427\pi\) |
−0.568373 | + | 0.822771i | \(0.692427\pi\) | |||||||
\(314\) | 12.3975 | − | 12.3975i | 0.699629 | − | 0.699629i | ||||
\(315\) | −0.433546 | + | 0.433546i | −0.0244275 | + | 0.0244275i | ||||
\(316\) | −0.270842 | − | 0.112187i | −0.0152361 | − | 0.00631098i | ||||
\(317\) | −0.493794 | + | 1.19212i | −0.0277342 | + | 0.0669563i | −0.937140 | − | 0.348954i | \(-0.886537\pi\) |
0.909406 | + | 0.415910i | \(0.136537\pi\) | |||||||
\(318\) | 11.5528 | − | 4.78531i | 0.647846 | − | 0.268347i | ||||
\(319\) | − | 6.72029i | − | 0.376264i | ||||||
\(320\) | 0.382683 | + | 0.923880i | 0.0213927 | + | 0.0516464i | ||||
\(321\) | 5.51172 | + | 5.51172i | 0.307634 | + | 0.307634i | ||||
\(322\) | 4.72151 | 0.263119 | ||||||||
\(323\) | −7.24571 | − | 16.1329i | −0.403162 | − | 0.897656i | ||||
\(324\) | −5.27223 | −0.292902 | ||||||||
\(325\) | −2.88669 | − | 2.88669i | −0.160125 | − | 0.160125i | ||||
\(326\) | 3.29544 | + | 7.95590i | 0.182518 | + | 0.440636i | ||||
\(327\) | 23.4256i | 1.29544i | ||||||||
\(328\) | −1.78950 | + | 0.741235i | −0.0988086 | + | 0.0409278i | ||||
\(329\) | −1.16958 | + | 2.82363i | −0.0644813 | + | 0.155672i | ||||
\(330\) | 4.94174 | + | 2.04694i | 0.272034 | + | 0.112680i | ||||
\(331\) | −5.13820 | + | 5.13820i | −0.282421 | + | 0.282421i | −0.834074 | − | 0.551653i | \(-0.813997\pi\) |
0.551653 | + | 0.834074i | \(0.313997\pi\) | |||||||
\(332\) | −1.75650 | + | 1.75650i | −0.0964003 | + | 0.0964003i | ||||
\(333\) | −7.12068 | − | 2.94948i | −0.390211 | − | 0.161631i | ||||
\(334\) | 4.24877 | − | 10.2574i | 0.232482 | − | 0.561262i | ||||
\(335\) | 3.21530 | − | 1.33182i | 0.175671 | − | 0.0727652i | ||||
\(336\) | − | 0.930151i | − | 0.0507439i | ||||||
\(337\) | −6.69206 | − | 16.1561i | −0.364540 | − | 0.880077i | −0.994624 | − | 0.103550i | \(-0.966980\pi\) |
0.630085 | − | 0.776526i | \(-0.283020\pi\) | |||||||
\(338\) | −2.59220 | − | 2.59220i | −0.140997 | − | 0.140997i | ||||
\(339\) | −3.57174 | −0.193990 | ||||||||
\(340\) | −0.121320 | − | 4.12132i | −0.00657952 | − | 0.223510i | ||||
\(341\) | −18.5587 | −1.00501 | ||||||||
\(342\) | −2.86603 | − | 2.86603i | −0.154977 | − | 0.154977i | ||||
\(343\) | −3.37170 | − | 8.14001i | −0.182055 | − | 0.439519i | ||||
\(344\) | 1.04667i | 0.0564327i | ||||||||
\(345\) | −9.63752 | + | 3.99199i | −0.518867 | + | 0.214922i | ||||
\(346\) | −5.86377 | + | 14.1564i | −0.315238 | + | 0.761053i | ||||
\(347\) | −20.1394 | − | 8.34203i | −1.08114 | − | 0.447824i | −0.230232 | − | 0.973136i | \(-0.573949\pi\) |
−0.850910 | + | 0.525312i | \(0.823949\pi\) | |||||||
\(348\) | 1.82571 | − | 1.82571i | 0.0978682 | − | 0.0978682i | ||||
\(349\) | 9.34399 | − | 9.34399i | 0.500172 | − | 0.500172i | −0.411319 | − | 0.911491i | \(-0.634932\pi\) |
0.911491 | + | 0.411319i | \(0.134932\pi\) | |||||||
\(350\) | 0.599456 | + | 0.248303i | 0.0320423 | + | 0.0132723i | ||||
\(351\) | 8.83501 | − | 21.3296i | 0.471578 | − | 1.13849i | ||||
\(352\) | 3.44722 | − | 1.42788i | 0.183737 | − | 0.0761064i | ||||
\(353\) | − | 29.5181i | − | 1.57109i | −0.618803 | − | 0.785546i | \(-0.712382\pi\) | ||
0.618803 | − | 0.785546i | \(-0.287618\pi\) | |||||||
\(354\) | −5.69885 | − | 13.7582i | −0.302890 | − | 0.731242i | ||||
\(355\) | −9.38537 | − | 9.38537i | −0.498124 | − | 0.498124i | ||||
\(356\) | −3.59539 | −0.190555 | ||||||||
\(357\) | −1.36274 | + | 3.58483i | −0.0721240 | + | 0.189729i | ||||
\(358\) | −10.1899 | −0.538551 | ||||||||
\(359\) | −5.80701 | − | 5.80701i | −0.306482 | − | 0.306482i | 0.537061 | − | 0.843543i | \(-0.319535\pi\) |
−0.843543 | + | 0.537061i | \(0.819535\pi\) | |||||||
\(360\) | −0.361616 | − | 0.873017i | −0.0190588 | − | 0.0460121i | ||||
\(361\) | − | 0.601802i | − | 0.0316738i | ||||||
\(362\) | 12.0731 | − | 5.00086i | 0.634551 | − | 0.262839i | ||||
\(363\) | 1.60307 | − | 3.87016i | 0.0841394 | − | 0.203130i | ||||
\(364\) | 2.44722 | + | 1.01367i | 0.128269 | + | 0.0531307i | ||||
\(365\) | 4.23784 | − | 4.23784i | 0.221819 | − | 0.221819i | ||||
\(366\) | 3.59010 | − | 3.59010i | 0.187657 | − | 0.187657i | ||||
\(367\) | 10.0984 | + | 4.18290i | 0.527133 | + | 0.218345i | 0.630347 | − | 0.776314i | \(-0.282913\pi\) |
−0.103214 | + | 0.994659i | \(0.532913\pi\) | |||||||
\(368\) | −2.78470 | + | 6.72286i | −0.145162 | + | 0.350453i | ||||
\(369\) | 1.69098 | − | 0.700428i | 0.0880290 | − | 0.0364628i | ||||
\(370\) | 8.15640i | 0.424031i | ||||||||
\(371\) | −2.16591 | − | 5.22897i | −0.112448 | − | 0.271475i | ||||
\(372\) | −5.04187 | − | 5.04187i | −0.261409 | − | 0.261409i | ||||
\(373\) | −4.57353 | −0.236808 | −0.118404 | − | 0.992965i | \(-0.537778\pi\) | ||||
−0.118404 | + | 0.992965i | \(0.537778\pi\) | |||||||
\(374\) | −15.3776 | + | 0.452675i | −0.795158 | + | 0.0234073i | ||||
\(375\) | −1.43355 | −0.0740280 | ||||||||
\(376\) | −3.33070 | − | 3.33070i | −0.171767 | − | 0.171767i | ||||
\(377\) | 2.81377 | + | 6.79305i | 0.144917 | + | 0.349860i | ||||
\(378\) | 3.66940i | 0.188733i | ||||||||
\(379\) | 6.69098 | − | 2.77150i | 0.343693 | − | 0.142362i | −0.204159 | − | 0.978938i | \(-0.565446\pi\) |
0.547851 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(380\) | −1.64145 | + | 3.96281i | −0.0842045 | + | 0.203288i | ||||
\(381\) | 11.9244 | + | 4.93925i | 0.610906 | + | 0.253046i | ||||
\(382\) | 13.9676 | − | 13.9676i | 0.714644 | − | 0.714644i | ||||
\(383\) | −25.0497 | + | 25.0497i | −1.27998 | + | 1.27998i | −0.339303 | + | 0.940677i | \(0.610191\pi\) |
−0.940677 | + | 0.339303i | \(0.889809\pi\) | |||||||
\(384\) | 1.32442 | + | 0.548594i | 0.0675867 | + | 0.0279953i | ||||
\(385\) | 0.926477 | − | 2.23671i | 0.0472177 | − | 0.113994i | ||||
\(386\) | 9.57238 | − | 3.96501i | 0.487221 | − | 0.201814i | ||||
\(387\) | − | 0.989049i | − | 0.0502762i | ||||||
\(388\) | −7.36110 | − | 17.7713i | −0.373703 | − | 0.902199i | ||||
\(389\) | 23.5600 | + | 23.5600i | 1.19454 | + | 1.19454i | 0.975779 | + | 0.218760i | \(0.0702011\pi\) |
0.218760 | + | 0.975779i | \(0.429799\pi\) | |||||||
\(390\) | −5.85229 | −0.296342 | ||||||||
\(391\) | 20.5818 | − | 21.8303i | 1.04087 | − | 1.10401i | ||||
\(392\) | 6.57900 | 0.332290 | ||||||||
\(393\) | −16.1221 | − | 16.1221i | −0.813253 | − | 0.813253i | ||||
\(394\) | 6.38489 | + | 15.4145i | 0.321666 | + | 0.776570i | ||||
\(395\) | − | 0.293157i | − | 0.0147504i | ||||||
\(396\) | −3.25744 | + | 1.34927i | −0.163692 | + | 0.0678036i | ||||
\(397\) | −5.13254 | + | 12.3910i | −0.257595 | + | 0.621888i | −0.998778 | − | 0.0494138i | \(-0.984265\pi\) |
0.741184 | + | 0.671302i | \(0.234265\pi\) | |||||||
\(398\) | −8.75167 | − | 3.62506i | −0.438682 | − | 0.181708i | ||||
\(399\) | 2.82115 | − | 2.82115i | 0.141234 | − | 0.141234i | ||||
\(400\) | −0.707107 | + | 0.707107i | −0.0353553 | + | 0.0353553i | ||||
\(401\) | −31.7817 | − | 13.1644i | −1.58710 | − | 0.657399i | −0.597584 | − | 0.801806i | \(-0.703873\pi\) |
−0.989518 | + | 0.144407i | \(0.953873\pi\) | |||||||
\(402\) | 1.90923 | − | 4.60928i | 0.0952236 | − | 0.229890i | ||||
\(403\) | 18.7597 | − | 7.77051i | 0.934486 | − | 0.387077i | ||||
\(404\) | − | 9.83938i | − | 0.489527i | ||||||
\(405\) | −2.01760 | − | 4.87091i | −0.100255 | − | 0.242037i | ||||
\(406\) | −0.826346 | − | 0.826346i | −0.0410109 | − | 0.0410109i | ||||
\(407\) | 30.4335 | 1.50853 | ||||||||
\(408\) | −4.30064 | − | 4.05468i | −0.212913 | − | 0.200737i | ||||
\(409\) | 37.6365 | 1.86101 | 0.930503 | − | 0.366283i | \(-0.119370\pi\) | ||||
0.930503 | + | 0.366283i | \(0.119370\pi\) | |||||||
\(410\) | −1.36962 | − | 1.36962i | −0.0676409 | − | 0.0676409i | ||||
\(411\) | 12.5767 | + | 30.3627i | 0.620361 | + | 1.49768i | ||||
\(412\) | 5.96722i | 0.293984i | ||||||||
\(413\) | −6.22721 | + | 2.57939i | −0.306421 | + | 0.126924i | ||||
\(414\) | 2.63139 | − | 6.35275i | 0.129326 | − | 0.312220i | ||||
\(415\) | −2.29497 | − | 0.950609i | −0.112656 | − | 0.0466636i | ||||
\(416\) | −2.88669 | + | 2.88669i | −0.141531 | + | 0.141531i | ||||
\(417\) | 11.6684 | − | 11.6684i | 0.571403 | − | 0.571403i | ||||
\(418\) | 14.7862 | + | 6.12464i | 0.723216 | + | 0.299566i | ||||
\(419\) | −0.774034 | + | 1.86868i | −0.0378140 | + | 0.0912912i | −0.941658 | − | 0.336570i | \(-0.890733\pi\) |
0.903844 | + | 0.427862i | \(0.140733\pi\) | |||||||
\(420\) | 0.859348 | − | 0.355953i | 0.0419319 | − | 0.0173688i | ||||
\(421\) | 34.7424i | 1.69324i | 0.532198 | + | 0.846620i | \(0.321366\pi\) | ||||
−0.532198 | + | 0.846620i | \(0.678634\pi\) | |||||||
\(422\) | 9.61954 | + | 23.2236i | 0.468272 | + | 1.13051i | ||||
\(423\) | 3.14733 | + | 3.14733i | 0.153028 | + | 0.153028i | ||||
\(424\) | 8.72286 | 0.423619 | ||||||||
\(425\) | 3.76118 | − | 1.68925i | 0.182444 | − | 0.0819405i | ||||
\(426\) | −19.0273 | −0.921878 | ||||||||
\(427\) | −1.62494 | − | 1.62494i | −0.0786363 | − | 0.0786363i | ||||
\(428\) | 2.08080 | + | 5.02349i | 0.100579 | + | 0.242820i | ||||
\(429\) | 21.8363i | 1.05427i | ||||||||
\(430\) | −0.966998 | + | 0.400544i | −0.0466328 | + | 0.0193159i | ||||
\(431\) | 9.13585 | − | 22.0559i | 0.440059 | − | 1.06240i | −0.535869 | − | 0.844301i | \(-0.680016\pi\) |
0.975928 | − | 0.218094i | \(-0.0699840\pi\) | |||||||
\(432\) | −5.22478 | − | 2.16417i | −0.251377 | − | 0.104124i | ||||
\(433\) | −0.816086 | + | 0.816086i | −0.0392186 | + | 0.0392186i | −0.726444 | − | 0.687226i | \(-0.758828\pi\) |
0.687226 | + | 0.726444i | \(0.258828\pi\) | |||||||
\(434\) | −2.28204 | + | 2.28204i | −0.109541 | + | 0.109541i | ||||
\(435\) | 2.38540 | + | 0.988066i | 0.114371 | + | 0.0473741i | ||||
\(436\) | −6.25345 | + | 15.0972i | −0.299486 | + | 0.723023i | ||||
\(437\) | −28.8364 | + | 11.9444i | −1.37943 | + | 0.571380i | ||||
\(438\) | − | 8.59154i | − | 0.410520i | ||||||
\(439\) | −0.151207 | − | 0.365047i | −0.00721674 | − | 0.0174227i | 0.920230 | − | 0.391378i | \(-0.128001\pi\) |
−0.927447 | + | 0.373955i | \(0.878001\pi\) | |||||||
\(440\) | 2.63838 | + | 2.63838i | 0.125780 | + | 0.125780i | ||||
\(441\) | −6.21681 | −0.296038 | ||||||||
\(442\) | 15.3546 | − | 6.89617i | 0.730344 | − | 0.328017i | ||||
\(443\) | −17.8435 | −0.847772 | −0.423886 | − | 0.905716i | \(-0.639334\pi\) | ||||
−0.423886 | + | 0.905716i | \(0.639334\pi\) | |||||||
\(444\) | 8.26790 | + | 8.26790i | 0.392377 | + | 0.392377i | ||||
\(445\) | −1.37589 | − | 3.32170i | −0.0652237 | − | 0.157464i | ||||
\(446\) | 19.0672i | 0.902859i | ||||||||
\(447\) | 18.3103 | − | 7.58437i | 0.866047 | − | 0.358729i | ||||
\(448\) | 0.248303 | − | 0.599456i | 0.0117312 | − | 0.0283216i | ||||
\(449\) | −27.9884 | − | 11.5932i | −1.32085 | − | 0.547115i | −0.392820 | − | 0.919615i | \(-0.628500\pi\) |
−0.928032 | + | 0.372500i | \(0.878500\pi\) | |||||||
\(450\) | 0.668179 | − | 0.668179i | 0.0314982 | − | 0.0314982i | ||||
\(451\) | −5.11039 | + | 5.11039i | −0.240639 | + | 0.240639i | ||||
\(452\) | −2.30188 | − | 0.953472i | −0.108272 | − | 0.0448475i | ||||
\(453\) | 10.0625 | − | 24.2931i | 0.472779 | − | 1.14139i | ||||
\(454\) | −3.70676 | + | 1.53539i | −0.173967 | + | 0.0720595i | ||||
\(455\) | 2.64885i | 0.124180i | ||||||||
\(456\) | 2.35309 | + | 5.68087i | 0.110194 | + | 0.266031i | ||||
\(457\) | 24.8070 | + | 24.8070i | 1.16042 | + | 1.16042i | 0.984384 | + | 0.176037i | \(0.0563278\pi\) |
0.176037 | + | 0.984384i | \(0.443672\pi\) | |||||||
\(458\) | −17.1455 | −0.801154 | ||||||||
\(459\) | 16.9658 | + | 15.9955i | 0.791895 | + | 0.746606i | ||||
\(460\) | −7.27677 | −0.339281 | ||||||||
\(461\) | 28.4656 | + | 28.4656i | 1.32577 | + | 1.32577i | 0.909019 | + | 0.416755i | \(0.136833\pi\) |
0.416755 | + | 0.909019i | \(0.363167\pi\) | |||||||
\(462\) | −1.32815 | − | 3.20643i | −0.0617910 | − | 0.149177i | ||||
\(463\) | − | 1.74763i | − | 0.0812191i | −0.999175 | − | 0.0406096i | \(-0.987070\pi\) | ||
0.999175 | − | 0.0406096i | \(-0.0129300\pi\) | |||||||
\(464\) | 1.66399 | − | 0.689246i | 0.0772487 | − | 0.0319975i | ||||
\(465\) | 2.72864 | − | 6.58752i | 0.126538 | − | 0.305489i | ||||
\(466\) | −17.4907 | − | 7.24486i | −0.810239 | − | 0.335612i | ||||
\(467\) | 12.0812 | − | 12.0812i | 0.559049 | − | 0.559049i | −0.369987 | − | 0.929037i | \(-0.620638\pi\) |
0.929037 | + | 0.369987i | \(0.120638\pi\) | |||||||
\(468\) | 2.72777 | − | 2.72777i | 0.126091 | − | 0.126091i | ||||
\(469\) | −2.08624 | − | 0.864148i | −0.0963335 | − | 0.0399026i | ||||
\(470\) | 1.80256 | − | 4.35176i | 0.0831459 | − | 0.200732i | ||||
\(471\) | 23.2206 | − | 9.61830i | 1.06995 | − | 0.443188i | ||||
\(472\) | − | 10.3881i | − | 0.478151i | ||||||
\(473\) | 1.49452 | + | 3.60810i | 0.0687183 | + | 0.165901i | ||||
\(474\) | −0.297165 | − | 0.297165i | −0.0136492 | − | 0.0136492i | ||||
\(475\) | −4.28931 | −0.196807 | ||||||||
\(476\) | −1.83522 | + | 1.94654i | −0.0841170 | + | 0.0892195i | ||||
\(477\) | −8.24264 | −0.377405 | ||||||||
\(478\) | −17.7636 | − | 17.7636i | −0.812488 | − | 0.812488i | ||||
\(479\) | −8.00249 | − | 19.3197i | −0.365643 | − | 0.882740i | −0.994453 | − | 0.105181i | \(-0.966458\pi\) |
0.628810 | − | 0.777559i | \(-0.283542\pi\) | |||||||
\(480\) | 1.43355i | 0.0654321i | ||||||||
\(481\) | −30.7630 | + | 12.7425i | −1.40267 | + | 0.581006i | ||||
\(482\) | −2.29117 | + | 5.53137i | −0.104360 | + | 0.251947i | ||||
\(483\) | 6.25327 | + | 2.59019i | 0.284534 | + | 0.117858i | ||||
\(484\) | 2.06627 | − | 2.06627i | 0.0939213 | − | 0.0939213i | ||||
\(485\) | 13.6015 | − | 13.6015i | 0.617614 | − | 0.617614i | ||||
\(486\) | 8.69167 | + | 3.60021i | 0.394262 | + | 0.163309i | ||||
\(487\) | −6.21937 | + | 15.0149i | −0.281827 | + | 0.680390i | −0.999878 | − | 0.0156002i | \(-0.995034\pi\) |
0.718052 | + | 0.695990i | \(0.245034\pi\) | |||||||
\(488\) | 3.27209 | − | 1.35534i | 0.148121 | − | 0.0613535i | ||||
\(489\) | 12.3448i | 0.558253i | ||||||||
\(490\) | 2.51767 | + | 6.07820i | 0.113737 | + | 0.274585i | ||||
\(491\) | −11.5317 | − | 11.5317i | −0.520420 | − | 0.520420i | 0.397278 | − | 0.917698i | \(-0.369955\pi\) |
−0.917698 | + | 0.397278i | \(0.869955\pi\) | |||||||
\(492\) | −2.77669 | −0.125183 | ||||||||
\(493\) | −7.42286 | + | 0.218509i | −0.334309 | + | 0.00984113i | ||||
\(494\) | −17.5107 | −0.787842 | ||||||||
\(495\) | −2.49313 | − | 2.49313i | −0.112058 | − | 0.112058i | ||||
\(496\) | −1.90342 | − | 4.59527i | −0.0854661 | − | 0.206334i | ||||
\(497\) | 8.61209i | 0.386305i | ||||||||
\(498\) | −3.28995 | + | 1.36274i | −0.147426 | + | 0.0610659i | ||||
\(499\) | −12.5137 | + | 30.2109i | −0.560192 | + | 1.35242i | 0.349420 | + | 0.936966i | \(0.386379\pi\) |
−0.909613 | + | 0.415458i | \(0.863621\pi\) | |||||||
\(500\) | −0.923880 | − | 0.382683i | −0.0413171 | − | 0.0171141i | ||||
\(501\) | 11.2543 | − | 11.2543i | 0.502807 | − | 0.502807i | ||||
\(502\) | −17.9951 | + | 17.9951i | −0.803160 | + | 0.803160i | ||||
\(503\) | −16.2893 | − | 6.74725i | −0.726305 | − | 0.300845i | −0.0112721 | − | 0.999936i | \(-0.503588\pi\) |
−0.715032 | + | 0.699091i | \(0.753588\pi\) | |||||||
\(504\) | −0.234633 | + | 0.566454i | −0.0104514 | + | 0.0252319i | ||||
\(505\) | 9.09040 | − | 3.76537i | 0.404517 | − | 0.167557i | ||||
\(506\) | 27.1514i | 1.20703i | ||||||||
\(507\) | −2.01111 | − | 4.85524i | −0.0893163 | − | 0.215629i | ||||
\(508\) | 6.36642 | + | 6.36642i | 0.282464 | + | 0.282464i | ||||
\(509\) | 18.7525 | 0.831189 | 0.415595 | − | 0.909550i | \(-0.363574\pi\) | ||||
0.415595 | + | 0.909550i | \(0.363574\pi\) | |||||||
\(510\) | 2.10025 | − | 5.52493i | 0.0930007 | − | 0.244648i | ||||
\(511\) | −3.88868 | −0.172025 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −9.28282 | − | 22.4107i | −0.409847 | − | 0.989457i | ||||
\(514\) | 24.8653i | 1.09676i | ||||||||
\(515\) | −5.51299 | + | 2.28356i | −0.242932 | + | 0.100626i | ||||
\(516\) | −0.574198 | + | 1.38624i | −0.0252776 | + | 0.0610256i | ||||
\(517\) | −16.2375 | − | 6.72578i | −0.714123 | − | 0.295799i | ||||
\(518\) | 3.74219 | − | 3.74219i | 0.164422 | − | 0.164422i | ||||
\(519\) | −15.5322 | + | 15.5322i | −0.681790 | + | 0.681790i | ||||
\(520\) | −3.77164 | − | 1.56226i | −0.165397 | − | 0.0685098i | ||||
\(521\) | 7.60180 | − | 18.3524i | 0.333041 | − | 0.804032i | −0.665307 | − | 0.746570i | \(-0.731699\pi\) |
0.998348 | − | 0.0574619i | \(-0.0183008\pi\) | |||||||
\(522\) | −1.57238 | + | 0.651302i | −0.0688212 | + | 0.0285067i | ||||
\(523\) | 16.9141i | 0.739601i | 0.929111 | + | 0.369801i | \(0.120574\pi\) | ||||
−0.929111 | + | 0.369801i | \(0.879426\pi\) | |||||||
\(524\) | −6.08646 | − | 14.6940i | −0.265888 | − | 0.641911i | ||||
\(525\) | 0.657716 | + | 0.657716i | 0.0287051 | + | 0.0287051i | ||||
\(526\) | 5.49782 | 0.239717 | ||||||||
\(527\) | 0.603433 | + | 20.4990i | 0.0262859 | + | 0.892948i | ||||
\(528\) | 5.34890 | 0.232781 | ||||||||
\(529\) | −21.1788 | − | 21.1788i | −0.920818 | − | 0.920818i | ||||
\(530\) | 3.33809 | + | 8.05887i | 0.144997 | + | 0.350055i | ||||
\(531\) | 9.81620i | 0.425987i | ||||||||
\(532\) | 2.57125 | − | 1.06505i | 0.111478 | − | 0.0461757i | ||||
\(533\) | 3.02601 | − | 7.30544i | 0.131071 | − | 0.316434i | ||||
\(534\) | −4.76181 | − | 1.97241i | −0.206064 | − | 0.0853544i | ||||
\(535\) | −3.84482 | + | 3.84482i | −0.166226 | + | 0.166226i | ||||
\(536\) | 2.46088 | − | 2.46088i | 0.106294 | − | 0.106294i | ||||
\(537\) | −13.4957 | − | 5.59010i | −0.582383 | − | 0.241231i | ||||
\(538\) | −3.47034 | + | 8.37815i | −0.149617 | + | 0.361208i | ||||
\(539\) | 22.6792 | − | 9.39404i | 0.976863 | − | 0.404630i | ||||
\(540\) | − | 5.65526i | − | 0.243364i | ||||||
\(541\) | 8.46190 | + | 20.4288i | 0.363806 | + | 0.878304i | 0.994737 | + | 0.102465i | \(0.0326731\pi\) |
−0.630931 | + | 0.775839i | \(0.717327\pi\) | |||||||
\(542\) | 18.4389 | + | 18.4389i | 0.792020 | + | 0.792020i | ||||
\(543\) | 18.7334 | 0.803927 | ||||||||
\(544\) | −1.68925 | − | 3.76118i | −0.0724258 | − | 0.161259i | ||||
\(545\) | −16.3410 | −0.699974 | ||||||||
\(546\) | 2.68506 | + | 2.68506i | 0.114910 | + | 0.114910i | ||||
\(547\) | −13.5956 | − | 32.8227i | −0.581307 | − | 1.40340i | −0.891629 | − | 0.452767i | \(-0.850437\pi\) |
0.310322 | − | 0.950632i | \(-0.399563\pi\) | |||||||
\(548\) | 22.9252i | 0.979318i | ||||||||
\(549\) | −3.09195 | + | 1.28073i | −0.131961 | + | 0.0546602i | ||||
\(550\) | −1.42788 | + | 3.44722i | −0.0608851 | + | 0.146990i | ||||
\(551\) | 7.13736 | + | 2.95639i | 0.304062 | + | 0.125947i | ||||
\(552\) | −7.37624 | + | 7.37624i | −0.313954 | + | 0.313954i | ||||
\(553\) | −0.134502 | + | 0.134502i | −0.00571960 | + | 0.00571960i | ||||
\(554\) | −2.31159 | − | 0.957491i | −0.0982099 | − | 0.0406799i | ||||
\(555\) | −4.47455 | + | 10.8025i | −0.189934 | + | 0.458542i | ||||
\(556\) | 10.6348 | − | 4.40508i | 0.451016 | − | 0.186817i | ||||
\(557\) | − | 5.78242i | − | 0.245009i | −0.992468 | − | 0.122504i | \(-0.960907\pi\) | ||
0.992468 | − | 0.122504i | \(-0.0390926\pi\) | |||||||
\(558\) | 1.79863 | + | 4.34228i | 0.0761422 | + | 0.183824i | ||||
\(559\) | −3.02141 | − | 3.02141i | −0.127792 | − | 0.127792i | ||||
\(560\) | 0.648847 | 0.0274188 | ||||||||
\(561\) | −20.6148 | − | 7.83654i | −0.870359 | − | 0.330859i | ||||
\(562\) | 11.6341 | 0.490753 | ||||||||
\(563\) | 0.624450 | + | 0.624450i | 0.0263174 | + | 0.0263174i | 0.720143 | − | 0.693826i | \(-0.244076\pi\) |
−0.693826 | + | 0.720143i | \(0.744076\pi\) | |||||||
\(564\) | −2.58405 | − | 6.23845i | −0.108808 | − | 0.262686i | ||||
\(565\) | − | 2.49154i | − | 0.104820i | ||||||
\(566\) | −25.0401 | + | 10.3720i | −1.05251 | + | 0.435966i | ||||
\(567\) | −1.30911 | + | 3.16047i | −0.0549775 | + | 0.132727i | ||||
\(568\) | −12.2626 | − | 5.07933i | −0.514527 | − | 0.213124i | ||||
\(569\) | −4.28648 | + | 4.28648i | −0.179699 | + | 0.179699i | −0.791224 | − | 0.611526i | \(-0.790556\pi\) |
0.611526 | + | 0.791224i | \(0.290556\pi\) | |||||||
\(570\) | −4.34795 | + | 4.34795i | −0.182115 | + | 0.182115i | ||||
\(571\) | 20.4305 | + | 8.46257i | 0.854988 | + | 0.354148i | 0.766745 | − | 0.641951i | \(-0.221875\pi\) |
0.0882426 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(572\) | −5.82918 | + | 14.0729i | −0.243730 | + | 0.588417i | ||||
\(573\) | 26.1615 | − | 10.8365i | 1.09291 | − | 0.452699i | ||||
\(574\) | 1.25678i | 0.0524569i | ||||||||
\(575\) | −2.78470 | − | 6.72286i | −0.116130 | − | 0.280363i | ||||
\(576\) | −0.668179 | − | 0.668179i | −0.0278408 | − | 0.0278408i | ||||
\(577\) | 11.1949 | 0.466051 | 0.233026 | − | 0.972471i | \(-0.425137\pi\) | ||||
0.233026 | + | 0.972471i | \(0.425137\pi\) | |||||||
\(578\) | 1.00000 | + | 16.9706i | 0.0415945 | + | 0.705882i | ||||
\(579\) | 14.8531 | 0.617272 | ||||||||
\(580\) | 1.27356 | + | 1.27356i | 0.0528818 | + | 0.0528818i | ||||
\(581\) | 0.616800 | + | 1.48909i | 0.0255892 | + | 0.0617777i | ||||
\(582\) | − | 27.5749i | − | 1.14302i | ||||||
\(583\) | 30.0696 | − | 12.4552i | 1.24535 | − | 0.515843i | ||||
\(584\) | 2.29350 | − | 5.53701i | 0.0949058 | − | 0.229123i | ||||
\(585\) | 3.56400 | + | 1.47626i | 0.147353 | + | 0.0610357i | ||||
\(586\) | 13.5590 | − | 13.5590i | 0.560118 | − | 0.560118i | ||||
\(587\) | 9.94683 | − | 9.94683i | 0.410549 | − | 0.410549i | −0.471380 | − | 0.881930i | \(-0.656244\pi\) |
0.881930 | + | 0.471380i | \(0.156244\pi\) | |||||||
\(588\) | 8.71338 | + | 3.60920i | 0.359334 | + | 0.148841i | ||||
\(589\) | 8.16437 | − | 19.7105i | 0.336407 | − | 0.812158i | ||||
\(590\) | 9.59735 | − | 3.97535i | 0.395117 | − | 0.163663i | ||||
\(591\) | 23.9180i | 0.983855i | ||||||||
\(592\) | 3.12132 | + | 7.53553i | 0.128285 | + | 0.309709i | ||||
\(593\) | 7.06788 | + | 7.06788i | 0.290243 | + | 0.290243i | 0.837176 | − | 0.546933i | \(-0.184205\pi\) |
−0.546933 | + | 0.837176i | \(0.684205\pi\) | |||||||
\(594\) | −21.1011 | −0.865790 | ||||||||
\(595\) | −2.50068 | − | 0.950609i | −0.102518 | − | 0.0389712i | ||||
\(596\) | 13.8251 | 0.566299 | ||||||||
\(597\) | −9.60223 | − | 9.60223i | −0.392993 | − | 0.392993i | ||||
\(598\) | −11.3682 | − | 27.4453i | −0.464882 | − | 1.12232i | ||||
\(599\) | 17.8658i | 0.729976i | 0.931012 | + | 0.364988i | \(0.118927\pi\) | ||||
−0.931012 | + | 0.364988i | \(0.881073\pi\) | |||||||
\(600\) | −1.32442 | + | 0.548594i | −0.0540694 | + | 0.0223963i | ||||
\(601\) | −8.37878 | + | 20.2282i | −0.341778 | + | 0.825124i | 0.655759 | + | 0.754971i | \(0.272349\pi\) |
−0.997536 | + | 0.0701534i | \(0.977651\pi\) | |||||||
\(602\) | 0.627434 | + | 0.259892i | 0.0255723 | + | 0.0105924i | ||||
\(603\) | −2.32541 | + | 2.32541i | −0.0946979 | + | 0.0946979i | ||||
\(604\) | 12.9700 | − | 12.9700i | 0.527743 | − | 0.527743i | ||||
\(605\) | 2.69971 | + | 1.11826i | 0.109759 | + | 0.0454636i | ||||
\(606\) | 5.39782 | − | 13.0315i | 0.219272 | − | 0.529369i | ||||
\(607\) | −15.5502 | + | 6.44109i | −0.631161 | + | 0.261436i | −0.675246 | − | 0.737592i | \(-0.735963\pi\) |
0.0440850 | + | 0.999028i | \(0.485963\pi\) | |||||||
\(608\) | 4.28931i | 0.173955i | ||||||||
\(609\) | −0.641103 | − | 1.54776i | −0.0259788 | − | 0.0627184i | ||||
\(610\) | 2.50435 | + | 2.50435i | 0.101398 | + | 0.101398i | ||||
\(611\) | 19.2293 | 0.777936 | ||||||||
\(612\) | 1.59625 | + | 3.55411i | 0.0645245 | + | 0.143667i | ||||
\(613\) | −16.8709 | −0.681408 | −0.340704 | − | 0.940171i | \(-0.610665\pi\) | ||||
−0.340704 | + | 0.940171i | \(0.610665\pi\) | |||||||
\(614\) | 6.16617 | + | 6.16617i | 0.248847 | + | 0.248847i | ||||
\(615\) | −1.06259 | − | 2.56533i | −0.0428479 | − | 0.103444i | ||||
\(616\) | − | 2.42100i | − | 0.0975450i | ||||||
\(617\) | 28.6140 | − | 11.8523i | 1.15196 | − | 0.477156i | 0.276767 | − | 0.960937i | \(-0.410737\pi\) |
0.875189 | + | 0.483781i | \(0.160737\pi\) | |||||||
\(618\) | −3.27358 | + | 7.90313i | −0.131683 | + | 0.317910i | ||||
\(619\) | −8.34821 | − | 3.45794i | −0.335543 | − | 0.138986i | 0.208549 | − | 0.978012i | \(-0.433126\pi\) |
−0.544092 | + | 0.839025i | \(0.683126\pi\) | |||||||
\(620\) | 3.51706 | − | 3.51706i | 0.141249 | − | 0.141249i | ||||
\(621\) | 29.0989 | − | 29.0989i | 1.16770 | − | 1.16770i | ||||
\(622\) | −15.5804 | − | 6.45361i | −0.624717 | − | 0.258766i | ||||
\(623\) | −0.892745 | + | 2.15528i | −0.0357671 | + | 0.0863493i | ||||
\(624\) | −5.40682 | + | 2.23958i | −0.216446 | + | 0.0896548i | ||||
\(625\) | − | 1.00000i | − | 0.0400000i | ||||||
\(626\) | −2.84690 | − | 6.87302i | −0.113785 | − | 0.274701i | ||||
\(627\) | 16.2232 | + | 16.2232i | 0.647893 | + | 0.647893i | ||||
\(628\) | 17.5326 | 0.699629 | ||||||||
\(629\) | −0.989538 | − | 33.6152i | −0.0394554 | − | 1.34032i | ||||
\(630\) | −0.613126 | −0.0244275 | ||||||||
\(631\) | −17.5159 | − | 17.5159i | −0.697298 | − | 0.697298i | 0.266529 | − | 0.963827i | \(-0.414123\pi\) |
−0.963827 | + | 0.266529i | \(0.914123\pi\) | |||||||
\(632\) | −0.112187 | − | 0.270842i | −0.00446254 | − | 0.0107735i | ||||
\(633\) | 36.0351i | 1.43227i | ||||||||
\(634\) | −1.19212 | + | 0.493794i | −0.0473453 | + | 0.0196111i | ||||
\(635\) | −3.44548 | + | 8.31812i | −0.136730 | + | 0.330095i | ||||
\(636\) | 11.5528 | + | 4.78531i | 0.458097 | + | 0.189750i | ||||
\(637\) | −18.9915 | + | 18.9915i | −0.752471 | + | 0.752471i | ||||
\(638\) | 4.75196 | − | 4.75196i | 0.188132 | − | 0.188132i | ||||
\(639\) | 11.5875 | + | 4.79970i | 0.458394 | + | 0.189873i | ||||
\(640\) | −0.382683 | + | 0.923880i | −0.0151269 | + | 0.0365195i | ||||
\(641\) | 28.3008 | − | 11.7226i | 1.11781 | − | 0.463014i | 0.254192 | − | 0.967154i | \(-0.418190\pi\) |
0.863622 | + | 0.504140i | \(0.168190\pi\) | |||||||
\(642\) | 7.79475i | 0.307634i | ||||||||
\(643\) | −0.913274 | − | 2.20484i | −0.0360160 | − | 0.0869504i | 0.904848 | − | 0.425735i | \(-0.139984\pi\) |
−0.940864 | + | 0.338784i | \(0.889984\pi\) | |||||||
\(644\) | 3.33861 | + | 3.33861i | 0.131560 | + | 0.131560i | ||||
\(645\) | −1.50045 | −0.0590802 | ||||||||
\(646\) | 6.28417 | − | 16.5311i | 0.247247 | − | 0.650409i | ||||
\(647\) | −25.0527 | −0.984924 | −0.492462 | − | 0.870334i | \(-0.663903\pi\) | ||||
−0.492462 | + | 0.870334i | \(0.663903\pi\) | |||||||
\(648\) | −3.72803 | − | 3.72803i | −0.146451 | − | 0.146451i | ||||
\(649\) | −14.8330 | − | 35.8100i | −0.582246 | − | 1.40567i | ||||
\(650\) | − | 4.08239i | − | 0.160125i | ||||||
\(651\) | −4.27429 | + | 1.77047i | −0.167523 | + | 0.0693902i | ||||
\(652\) | −3.29544 | + | 7.95590i | −0.129059 | + | 0.311577i | ||||
\(653\) | −14.3005 | − | 5.92347i | −0.559623 | − | 0.231803i | 0.0848986 | − | 0.996390i | \(-0.472943\pi\) |
−0.644521 | + | 0.764586i | \(0.722943\pi\) | |||||||
\(654\) | −16.5644 | + | 16.5644i | −0.647720 | + | 0.647720i | ||||
\(655\) | 11.2463 | − | 11.2463i | 0.439430 | − | 0.439430i | ||||
\(656\) | −1.78950 | − | 0.741235i | −0.0698682 | − | 0.0289404i | ||||
\(657\) | −2.16724 | + | 5.23218i | −0.0845521 | + | 0.204127i | ||||
\(658\) | −2.82363 | + | 1.16958i | −0.110076 | + | 0.0455952i | ||||
\(659\) | − | 8.19841i | − | 0.319365i | −0.987168 | − | 0.159682i | \(-0.948953\pi\) | ||
0.987168 | − | 0.159682i | \(-0.0510470\pi\) | |||||||
\(660\) | 2.04694 | + | 4.94174i | 0.0796769 | + | 0.192357i | ||||
\(661\) | −31.9638 | − | 31.9638i | −1.24325 | − | 1.24325i | −0.958646 | − | 0.284601i | \(-0.908139\pi\) |
−0.284601 | − | 0.958646i | \(-0.591861\pi\) | |||||||
\(662\) | −7.26651 | −0.282421 | ||||||||
\(663\) | 24.1192 | − | 0.710002i | 0.936711 | − | 0.0275742i | ||||
\(664\) | −2.48406 | −0.0964003 | ||||||||
\(665\) | 1.96795 | + | 1.96795i | 0.0763139 | + | 0.0763139i | ||||
\(666\) | −2.94948 | − | 7.12068i | −0.114290 | − | 0.275921i | ||||
\(667\) | 13.1061i | 0.507470i | ||||||||
\(668\) | 10.2574 | − | 4.24877i | 0.396872 | − | 0.164390i | ||||
\(669\) | −10.4602 | + | 25.2531i | −0.404413 | + | 0.976340i | ||||
\(670\) | 3.21530 | + | 1.33182i | 0.124218 | + | 0.0514527i | ||||
\(671\) | 9.34432 | − | 9.34432i | 0.360734 | − | 0.360734i | ||||
\(672\) | 0.657716 | − | 0.657716i | 0.0253720 | − | 0.0253720i | ||||
\(673\) | 16.2917 | + | 6.74826i | 0.628000 | + | 0.260126i | 0.673903 | − | 0.738820i | \(-0.264616\pi\) |
−0.0459028 | + | 0.998946i | \(0.514616\pi\) | |||||||
\(674\) | 6.69206 | − | 16.1561i | 0.257768 | − | 0.622308i | ||||
\(675\) | 5.22478 | − | 2.16417i | 0.201102 | − | 0.0832991i | ||||
\(676\) | − | 3.66593i | − | 0.140997i | ||||||
\(677\) | −16.1407 | − | 38.9670i | −0.620336 | − | 1.49762i | −0.851310 | − | 0.524663i | \(-0.824191\pi\) |
0.230974 | − | 0.972960i | \(-0.425809\pi\) | |||||||
\(678\) | −2.52560 | − | 2.52560i | −0.0969951 | − | 0.0969951i | ||||
\(679\) | −12.4809 | −0.478972 | ||||||||
\(680\) | 2.82843 | − | 3.00000i | 0.108465 | − | 0.115045i | ||||
\(681\) | −5.75163 | −0.220403 | ||||||||
\(682\) | −13.1230 | − | 13.1230i | −0.502506 | − | 0.502506i | ||||
\(683\) | 4.61287 | + | 11.1365i | 0.176507 | + | 0.426125i | 0.987229 | − | 0.159306i | \(-0.0509255\pi\) |
−0.810723 | + | 0.585430i | \(0.800926\pi\) | |||||||
\(684\) | − | 4.05317i | − | 0.154977i | ||||||
\(685\) | −21.1802 | + | 8.77311i | −0.809252 | + | 0.335203i | ||||
\(686\) | 3.37170 | − | 8.14001i | 0.128732 | − | 0.310787i | ||||
\(687\) | −22.7078 | − | 9.40589i | −0.866358 | − | 0.358857i | ||||
\(688\) | −0.740108 | + | 0.740108i | −0.0282164 | + | 0.0282164i | ||||
\(689\) | −25.1802 | + | 25.1802i | −0.959288 | + | 0.959288i | ||||
\(690\) | −9.63752 | − | 3.99199i | −0.366894 | − | 0.151973i | ||||
\(691\) | −12.0484 | + | 29.0873i | −0.458341 | + | 1.10653i | 0.510728 | + | 0.859743i | \(0.329376\pi\) |
−0.969069 | + | 0.246791i | \(0.920624\pi\) | |||||||
\(692\) | −14.1564 | + | 5.86377i | −0.538146 | + | 0.222907i | ||||
\(693\) | 2.28772i | 0.0869033i | ||||||||
\(694\) | −8.34203 | − | 20.1394i | −0.316659 | − | 0.764483i | ||||
\(695\) | 8.13953 | + | 8.13953i | 0.308750 | + | 0.308750i | ||||
\(696\) | 2.58194 | 0.0978682 | ||||||||
\(697\) | 5.81082 | + | 5.47849i | 0.220100 | + | 0.207513i | ||||
\(698\) | 13.2144 | 0.500172 | ||||||||
\(699\) | −19.1905 | − | 19.1905i | −0.725853 | − | 0.725853i | ||||
\(700\) | 0.248303 | + | 0.599456i | 0.00938497 | + | 0.0226573i | ||||
\(701\) | 7.86897i | 0.297207i | 0.988897 | + | 0.148603i | \(0.0474778\pi\) | ||||
−0.988897 | + | 0.148603i | \(0.952522\pi\) | |||||||
\(702\) | 21.3296 | − | 8.83501i | 0.805034 | − | 0.333456i | ||||
\(703\) | −13.3883 | + | 32.3223i | −0.504950 | + | 1.21906i | ||||
\(704\) | 3.44722 | + | 1.42788i | 0.129922 | + | 0.0538154i | ||||
\(705\) | 4.77470 | − | 4.77470i | 0.179826 | − | 0.179826i | ||||
\(706\) | 20.8725 | − | 20.8725i | 0.785546 | − | 0.785546i | ||||
\(707\) | −5.89828 | − | 2.44315i | −0.221827 | − | 0.0918840i | ||||
\(708\) | 5.69885 | − | 13.7582i | 0.214176 | − | 0.517066i | ||||
\(709\) | −14.8176 | + | 6.13766i | −0.556487 | + | 0.230505i | −0.643159 | − | 0.765732i | \(-0.722377\pi\) |
0.0866721 | + | 0.996237i | \(0.472377\pi\) | |||||||
\(710\) | − | 13.2729i | − | 0.498124i | ||||||
\(711\) | 0.106010 | + | 0.255932i | 0.00397570 | + | 0.00959818i | ||||
\(712\) | −2.54232 | − | 2.54232i | −0.0952776 | − | 0.0952776i | ||||
\(713\) | 36.1938 | 1.35547 | ||||||||
\(714\) | −3.49846 | + | 1.57125i | −0.130927 | + | 0.0588027i | ||||
\(715\) | −15.2324 | −0.569659 | ||||||||
\(716\) | −7.20533 | − | 7.20533i | −0.269276 | − | 0.269276i | ||||
\(717\) | −13.7815 | − | 33.2715i | −0.514680 | − | 1.24255i | ||||
\(718\) | − | 8.21236i | − | 0.306482i | ||||||
\(719\) | −1.04991 | + | 0.434886i | −0.0391549 | + | 0.0162185i | −0.402175 | − | 0.915563i | \(-0.631746\pi\) |
0.363020 | + | 0.931781i | \(0.381746\pi\) | |||||||
\(720\) | 0.361616 | − | 0.873017i | 0.0134766 | − | 0.0325354i | ||||
\(721\) | 3.57709 | + | 1.48168i | 0.133218 | + | 0.0551806i | ||||
\(722\) | 0.425538 | − | 0.425538i | 0.0158369 | − | 0.0158369i | ||||
\(723\) | −6.06896 | + | 6.06896i | −0.225707 | + | 0.225707i | ||||
\(724\) | 12.0731 | + | 5.00086i | 0.448695 | + | 0.185856i | ||||
\(725\) | −0.689246 | + | 1.66399i | −0.0255980 | + | 0.0617990i | ||||
\(726\) | 3.87016 | − | 1.60307i | 0.143635 | − | 0.0594955i | ||||
\(727\) | − | 16.5261i | − | 0.612918i | −0.951884 | − | 0.306459i | \(-0.900856\pi\) | ||
0.951884 | − | 0.306459i | \(-0.0991442\pi\) | |||||||
\(728\) | 1.01367 | + | 2.44722i | 0.0375691 | + | 0.0906998i | ||||
\(729\) | 20.7205 | + | 20.7205i | 0.767426 | + | 0.767426i | ||||
\(730\) | 5.99321 | 0.221819 | ||||||||
\(731\) | 3.93672 | − | 1.76809i | 0.145605 | − | 0.0653950i | ||||
\(732\) | 5.07717 | 0.187657 | ||||||||
\(733\) | 3.39332 | + | 3.39332i | 0.125335 | + | 0.125335i | 0.766992 | − | 0.641657i | \(-0.221753\pi\) |
−0.641657 | + | 0.766992i | \(0.721753\pi\) | |||||||
\(734\) | 4.18290 | + | 10.0984i | 0.154394 | + | 0.372739i | ||||
\(735\) | 9.43129i | 0.347878i | ||||||||
\(736\) | −6.72286 | + | 2.78470i | −0.247808 | + | 0.102645i | ||||
\(737\) | 4.96934 | − | 11.9971i | 0.183048 | − | 0.441917i | ||||
\(738\) | 1.69098 | + | 0.700428i | 0.0622459 | + | 0.0257831i | ||||
\(739\) | 34.0696 | − | 34.0696i | 1.25327 | − | 1.25327i | 0.299024 | − | 0.954246i | \(-0.403339\pi\) |
0.954246 | − | 0.299024i | \(-0.0966609\pi\) | |||||||
\(740\) | −5.76745 | + | 5.76745i | −0.212016 | + | 0.212016i | ||||
\(741\) | −23.1915 | − | 9.60624i | −0.851962 | − | 0.352894i | ||||
\(742\) | 2.16591 | − | 5.22897i | 0.0795131 | − | 0.191962i | ||||
\(743\) | −18.2530 | + | 7.56064i | −0.669637 | + | 0.277373i | −0.691488 | − | 0.722388i | \(-0.743044\pi\) |
0.0218502 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(744\) | − | 7.13028i | − | 0.261409i | ||||||
\(745\) | 5.29064 | + | 12.7727i | 0.193834 | + | 0.467957i | ||||
\(746\) | −3.23397 | − | 3.23397i | −0.118404 | − | 0.118404i | ||||
\(747\) | 2.34731 | 0.0858835 | ||||||||
\(748\) | −11.1937 | − | 10.5535i | −0.409283 | − | 0.385876i | ||||
\(749\) | 3.52803 | 0.128912 | ||||||||
\(750\) | −1.01367 | − | 1.01367i | −0.0370140 | − | 0.0370140i | ||||
\(751\) | −6.23471 | − | 15.0519i | −0.227508 | − | 0.549253i | 0.768365 | − | 0.640012i | \(-0.221071\pi\) |
−0.995873 | + | 0.0907592i | \(0.971071\pi\) | |||||||
\(752\) | − | 4.71031i | − | 0.171767i | ||||||
\(753\) | −33.7051 | + | 13.9611i | −1.22828 | + | 0.508771i | ||||
\(754\) | −2.81377 | + | 6.79305i | −0.102472 | + | 0.247388i | ||||
\(755\) | 16.9462 | + | 7.01933i | 0.616734 | + | 0.255460i | ||||
\(756\) | −2.59466 | + | 2.59466i | −0.0943667 | + | 0.0943667i | ||||
\(757\) | 11.3255 | − | 11.3255i | 0.411631 | − | 0.411631i | −0.470676 | − | 0.882306i | \(-0.655990\pi\) |
0.882306 | + | 0.470676i | \(0.155990\pi\) | |||||||
\(758\) | 6.69098 | + | 2.77150i | 0.243027 | + | 0.100665i | ||||
\(759\) | −14.8951 | + | 35.9599i | −0.540657 | + | 1.30526i | ||||
\(760\) | −3.96281 | + | 1.64145i | −0.143746 | + | 0.0595416i | ||||
\(761\) | − | 14.4363i | − | 0.523314i | −0.965161 | − | 0.261657i | \(-0.915731\pi\) | ||
0.965161 | − | 0.261657i | \(-0.0842690\pi\) | |||||||
\(762\) | 4.93925 | + | 11.9244i | 0.178930 | + | 0.431976i | ||||
\(763\) | 7.49734 | + | 7.49734i | 0.271422 | + | 0.271422i | ||||
\(764\) | 19.7531 | 0.714644 | ||||||||
\(765\) | −2.67271 | + | 2.83484i | −0.0966322 | + | 0.102494i | ||||
\(766\) | −35.4256 | −1.27998 | ||||||||
\(767\) | 29.9872 | + | 29.9872i | 1.08277 | + | 1.08277i | ||||
\(768\) | 0.548594 | + | 1.32442i | 0.0197957 | + | 0.0477910i | ||||
\(769\) | − | 55.2022i | − | 1.99064i | −0.0966274 | − | 0.995321i | \(-0.530806\pi\) | ||
0.0966274 | − | 0.995321i | \(-0.469194\pi\) | |||||||
\(770\) | 2.23671 | − | 0.926477i | 0.0806056 | − | 0.0333879i | ||||
\(771\) | −13.6410 | + | 32.9322i | −0.491267 | + | 1.18602i | ||||
\(772\) | 9.57238 | + | 3.96501i | 0.344518 | + | 0.142704i | ||||
\(773\) | 0.0691582 | − | 0.0691582i | 0.00248745 | − | 0.00248745i | −0.705862 | − | 0.708349i | \(-0.749440\pi\) |
0.708349 | + | 0.705862i | \(0.249440\pi\) | |||||||
\(774\) | 0.699363 | − | 0.699363i | 0.0251381 | − | 0.0251381i | ||||
\(775\) | 4.59527 | + | 1.90342i | 0.165067 | + | 0.0683729i | ||||
\(776\) | 7.36110 | − | 17.7713i | 0.264248 | − | 0.637951i | ||||
\(777\) | 7.00919 | − | 2.90330i | 0.251453 | − | 0.104155i | ||||
\(778\) | 33.3188i | 1.19454i | ||||||||
\(779\) | −3.17939 | − | 7.67572i | −0.113913 | − | 0.275011i | ||||
\(780\) | −4.13820 | − | 4.13820i | −0.148171 | − | 0.148171i | ||||
\(781\) | −49.5244 | −1.77212 | ||||||||
\(782\) | 29.9899 | − | 0.882820i | 1.07244 | − | 0.0315696i | ||||
\(783\) | −10.1856 | −0.364004 | ||||||||
\(784\) | 4.65205 | + | 4.65205i | 0.166145 | + | 0.166145i | ||||
\(785\) | 6.70945 | + | 16.1981i | 0.239471 | + | 0.578133i | ||||
\(786\) | − | 22.8001i | − | 0.813253i | ||||||
\(787\) | 34.6262 | − | 14.3427i | 1.23429 | − | 0.511260i | 0.332365 | − | 0.943151i | \(-0.392153\pi\) |
0.901926 | + | 0.431890i | \(0.142153\pi\) | |||||||
\(788\) | −6.38489 | + | 15.4145i | −0.227452 | + | 0.549118i | ||||
\(789\) | 7.28145 | + | 3.01607i | 0.259226 | + | 0.107375i | ||||
\(790\) | 0.207294 | − | 0.207294i | 0.00737518 | − | 0.00737518i | ||||
\(791\) | −1.14313 | + | 1.14313i | −0.0406450 | + | 0.0406450i | ||||
\(792\) | −3.25744 | − | 1.34927i | −0.115748 | − | 0.0479444i | ||||
\(793\) | −5.53305 | + | 13.3580i | −0.196484 | + | 0.474355i | ||||
\(794\) | −12.3910 | + | 5.13254i | −0.439741 | + | 0.182147i | ||||
\(795\) | 12.5046i | 0.443493i | ||||||||
\(796\) | −3.62506 | − | 8.75167i | −0.128487 | − | 0.310195i | ||||
\(797\) | 18.9951 | + | 18.9951i | 0.672841 | + | 0.672841i | 0.958370 | − | 0.285529i | \(-0.0921694\pi\) |
−0.285529 | + | 0.958370i | \(0.592169\pi\) | |||||||
\(798\) | 3.98971 | 0.141234 | ||||||||
\(799\) | −6.90097 | + | 18.1537i | −0.244139 | + | 0.642232i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 2.40236 | + | 2.40236i | 0.0848832 | + | 0.0848832i | ||||
\(802\) | −13.1644 | − | 31.7817i | −0.464852 | − | 1.12225i | ||||
\(803\) | − | 22.3621i | − | 0.789142i | ||||||
\(804\) | 4.60928 | − | 1.90923i | 0.162557 | − | 0.0673332i | ||||
\(805\) | −1.80684 | + | 4.36210i | −0.0636828 | + | 0.153744i | ||||
\(806\) | 18.7597 | + | 7.77051i | 0.660781 | + | 0.273705i | ||||
\(807\) | −9.19240 | + | 9.19240i | −0.323588 | + | 0.323588i | ||||
\(808\) | 6.95749 | − | 6.95749i | 0.244764 | − | 0.244764i | ||||
\(809\) | 29.5789 | + | 12.2520i | 1.03994 | + | 0.430757i | 0.836290 | − | 0.548288i | \(-0.184720\pi\) |
0.203648 | + | 0.979044i | \(0.434720\pi\) | |||||||
\(810\) | 2.01760 | − | 4.87091i | 0.0708911 | − | 0.171146i | ||||
\(811\) | 29.5923 | − | 12.2575i | 1.03913 | − | 0.430420i | 0.203128 | − | 0.979152i | \(-0.434889\pi\) |
0.835998 | + | 0.548732i | \(0.184889\pi\) | |||||||
\(812\) | − | 1.16863i | − | 0.0410109i | ||||||
\(813\) | 14.3055 | + | 34.5364i | 0.501714 | + | 1.21125i | ||||
\(814\) | 21.5197 | + | 21.5197i | 0.754266 | + | 0.754266i | ||||
\(815\) | −8.61140 | −0.301644 | ||||||||
\(816\) | −0.173918 | − | 5.90810i | −0.00608836 | − | 0.206825i | ||||
\(817\) | −4.48950 | −0.157068 | ||||||||
\(818\) | 26.6130 | + | 26.6130i | 0.930503 | + | 0.930503i | ||||
\(819\) | −0.957864 | − | 2.31249i | −0.0334705 | − | 0.0808049i | ||||
\(820\) | − | 1.93694i | − | 0.0676409i | ||||||
\(821\) | −3.57138 | + | 1.47931i | −0.124642 | + | 0.0516284i | −0.444133 | − | 0.895961i | \(-0.646488\pi\) |
0.319491 | + | 0.947589i | \(0.396488\pi\) | |||||||
\(822\) | −12.5767 | + | 30.3627i | −0.438661 | + | 1.05902i | ||||
\(823\) | 3.90191 | + | 1.61622i | 0.136012 | + | 0.0563380i | 0.449651 | − | 0.893204i | \(-0.351548\pi\) |
−0.313639 | + | 0.949542i | \(0.601548\pi\) | |||||||
\(824\) | −4.21946 | + | 4.21946i | −0.146992 | + | 0.146992i | ||||
\(825\) | −3.78224 | + | 3.78224i | −0.131681 | + | 0.131681i | ||||
\(826\) | −6.22721 | − | 2.57939i | −0.216672 | − | 0.0897486i | ||||
\(827\) | 16.2655 | − | 39.2683i | 0.565606 | − | 1.36549i | −0.339620 | − | 0.940563i | \(-0.610298\pi\) |
0.905226 | − | 0.424931i | \(-0.139702\pi\) | |||||||
\(828\) | 6.35275 | − | 2.63139i | 0.220773 | − | 0.0914472i | ||||
\(829\) | − | 10.9929i | − | 0.381798i | −0.981610 | − | 0.190899i | \(-0.938860\pi\) | ||
0.981610 | − | 0.190899i | \(-0.0611403\pi\) | |||||||
\(830\) | −0.950609 | − | 2.29497i | −0.0329961 | − | 0.0796597i | ||||
\(831\) | −2.53625 | − | 2.53625i | −0.0879814 | − | 0.0879814i | ||||
\(832\) | −4.08239 | −0.141531 | ||||||||
\(833\) | −11.1135 | − | 24.7448i | −0.385062 | − | 0.857355i | ||||
\(834\) | 16.5016 | 0.571403 | ||||||||
\(835\) | 7.85070 | + | 7.85070i | 0.271685 | + | 0.271685i | ||||
\(836\) | 6.12464 | + | 14.7862i | 0.211825 | + | 0.511391i | ||||
\(837\) | 28.1286i | 0.972266i | ||||||||
\(838\) | −1.86868 | + | 0.774034i | −0.0645526 | + | 0.0267386i | ||||
\(839\) | −12.8714 | + | 31.0742i | −0.444369 | + | 1.07280i | 0.530030 | + | 0.847979i | \(0.322181\pi\) |
−0.974400 | + | 0.224823i | \(0.927819\pi\) | |||||||
\(840\) | 0.859348 | + | 0.355953i | 0.0296503 | + | 0.0122816i | ||||
\(841\) | −18.2123 | + | 18.2123i | −0.628010 | + | 0.628010i | ||||
\(842\) | −24.5666 | + | 24.5666i | −0.846620 | + | 0.846620i | ||||
\(843\) | 15.4084 | + | 6.38237i | 0.530694 | + | 0.219821i | ||||
\(844\) | −9.61954 | + | 23.2236i | −0.331118 | + | 0.799390i | ||||
\(845\) | 3.38687 | − | 1.40289i | 0.116512 | − | 0.0482609i | ||||
\(846\) | 4.45100i | 0.153028i | ||||||||
\(847\) | −0.725577 | − | 1.75170i | −0.0249311 | − | 0.0601890i | ||||
\(848\) | 6.16799 | + | 6.16799i | 0.211810 | + | 0.211810i | ||||
\(849\) | −38.8537 | −1.33346 | ||||||||
\(850\) | 3.85403 | + | 1.46508i | 0.132192 | + | 0.0502517i | ||||
\(851\) | −59.3523 | −2.03457 | ||||||||
\(852\) | −13.4544 | − | 13.4544i | −0.460939 | − | 0.460939i | ||||
\(853\) | 4.07881 | + | 9.84712i | 0.139656 | + | 0.337159i | 0.978197 | − | 0.207679i | \(-0.0665910\pi\) |
−0.838541 | + | 0.544838i | \(0.816591\pi\) | |||||||
\(854\) | − | 2.29801i | − | 0.0786363i | ||||||
\(855\) | 3.74464 | − | 1.55108i | 0.128064 | − | 0.0530459i | ||||
\(856\) | −2.08080 | + | 5.02349i | −0.0711203 | + | 0.171699i | ||||
\(857\) | −22.3523 | − | 9.25864i | −0.763542 | − | 0.316269i | −0.0332883 | − | 0.999446i | \(-0.510598\pi\) |
−0.730253 | + | 0.683177i | \(0.760598\pi\) | |||||||
\(858\) | −15.4406 | + | 15.4406i | −0.527134 | + | 0.527134i | ||||
\(859\) | 13.6445 | − | 13.6445i | 0.465546 | − | 0.465546i | −0.434922 | − | 0.900468i | \(-0.643224\pi\) |
0.900468 | + | 0.434922i | \(0.143224\pi\) | |||||||
\(860\) | −0.966998 | − | 0.400544i | −0.0329744 | − | 0.0136584i | ||||
\(861\) | −0.689460 | + | 1.66450i | −0.0234967 | + | 0.0567262i | ||||
\(862\) | 22.0559 | − | 9.13585i | 0.751227 | − | 0.311168i | ||||
\(863\) | 31.7534i | 1.08090i | 0.841377 | + | 0.540449i | \(0.181746\pi\) | ||||
−0.841377 | + | 0.540449i | \(0.818254\pi\) | |||||||
\(864\) | −2.16417 | − | 5.22478i | −0.0736267 | − | 0.177751i | ||||
\(865\) | −10.8348 | − | 10.8348i | −0.368396 | − | 0.368396i | ||||
\(866\) | −1.15412 | −0.0392186 | ||||||||
\(867\) | −7.98553 | + | 23.0248i | −0.271203 | + | 0.781963i | ||||
\(868\) | −3.22729 | −0.109541 | ||||||||
\(869\) | −0.773462 | − | 0.773462i | −0.0262379 | − | 0.0262379i | ||||
\(870\) | 0.988066 | + | 2.38540i | 0.0334986 | + | 0.0808727i | ||||
\(871\) | 14.2076i | 0.481407i | ||||||||
\(872\) | −15.0972 | + | 6.25345i | −0.511254 | + | 0.211768i | ||||
\(873\) | −6.95585 | + | 16.7929i | −0.235420 | + | 0.568354i | ||||
\(874\) | −28.8364 | − | 11.9444i | −0.975407 | − | 0.404027i | ||||
\(875\) | −0.458804 | + | 0.458804i | −0.0155104 | + | 0.0155104i | ||||
\(876\) | 6.07514 | − | 6.07514i | 0.205260 | − | 0.205260i | ||||
\(877\) | 34.2435 | + | 14.1841i | 1.15632 | + | 0.478964i | 0.876649 | − | 0.481131i | \(-0.159774\pi\) |
0.279673 | + | 0.960095i | \(0.409774\pi\) | |||||||
\(878\) | 0.151207 | − | 0.365047i | 0.00510300 | − | 0.0123197i | ||||
\(879\) | 25.3963 | − | 10.5195i | 0.856596 | − | 0.354814i | ||||
\(880\) | 3.73124i | 0.125780i | ||||||||
\(881\) | 12.6307 | + | 30.4933i | 0.425540 | + | 1.02735i | 0.980685 | + | 0.195592i | \(0.0626627\pi\) |
−0.555145 | + | 0.831753i | \(0.687337\pi\) | |||||||
\(882\) | −4.39595 | − | 4.39595i | −0.148019 | − | 0.148019i | ||||
\(883\) | −25.4716 | −0.857188 | −0.428594 | − | 0.903497i | \(-0.640991\pi\) | ||||
−0.428594 | + | 0.903497i | \(0.640991\pi\) | |||||||
\(884\) | 15.7337 | + | 5.98101i | 0.529180 | + | 0.201163i | ||||
\(885\) | 14.8918 | 0.500583 | ||||||||
\(886\) | −12.6173 | − | 12.6173i | −0.423886 | − | 0.423886i | ||||
\(887\) | 11.1926 | + | 27.0213i | 0.375810 | + | 0.907287i | 0.992741 | + | 0.120269i | \(0.0383758\pi\) |
−0.616931 | + | 0.787017i | \(0.711624\pi\) | |||||||
\(888\) | 11.6926i | 0.392377i | ||||||||
\(889\) | 5.39719 | − | 2.23559i | 0.181016 | − | 0.0749792i | ||||
\(890\) | 1.37589 | − | 3.32170i | 0.0461201 | − | 0.111344i | ||||
\(891\) | −18.1745 | − | 7.52813i | −0.608869 | − | 0.252202i | ||||
\(892\) | −13.4826 | + | 13.4826i | −0.451430 | + | 0.451430i | ||||
\(893\) | 14.2864 | − | 14.2864i | 0.478076 | − | 0.478076i | ||||
\(894\) | 18.3103 | + | 7.58437i | 0.612388 | + | 0.253659i | ||||
\(895\) | 3.89949 | − | 9.41421i | 0.130346 | − | 0.314682i | ||||
\(896\) | 0.599456 | − | 0.248303i | 0.0200264 | − | 0.00829522i | ||||
\(897\) | − | 42.5858i | − | 1.42190i | ||||||
\(898\) | −11.5932 | − | 27.9884i | −0.386869 | − | 0.933983i | ||||
\(899\) | −6.33454 | − | 6.33454i | −0.211269 | − | 0.211269i | ||||
\(900\) | 0.944947 | 0.0314982 | ||||||||
\(901\) | −14.7351 | − | 32.8082i | −0.490896 | − | 1.09300i | ||||
\(902\) | −7.22718 | −0.240639 | ||||||||
\(903\) | 0.688413 | + | 0.688413i | 0.0229089 | + | 0.0229089i | ||||
\(904\) | −0.953472 | − | 2.30188i | −0.0317120 | − | 0.0765595i | ||||
\(905\) | 13.0679i | 0.434391i | ||||||||
\(906\) | 24.2931 | − | 10.0625i | 0.807084 | − | 0.334305i | ||||
\(907\) | 15.9140 | − | 38.4199i | 0.528417 | − | 1.27571i | −0.404143 | − | 0.914696i | \(-0.632430\pi\) |
0.932560 | − | 0.361016i | \(-0.117570\pi\) | |||||||
\(908\) | −3.70676 | − | 1.53539i | −0.123013 | − | 0.0509537i | ||||
\(909\) | −6.57446 | + | 6.57446i | −0.218061 | + | 0.218061i | ||||
\(910\) | −1.87302 | + | 1.87302i | −0.0620899 | + | 0.0620899i | ||||
\(911\) | 0.0576221 | + | 0.0238679i | 0.00190911 | + | 0.000790777i | 0.383638 | − | 0.923484i | \(-0.374671\pi\) |
−0.381729 | + | 0.924274i | \(0.624671\pi\) | |||||||
\(912\) | −2.35309 | + | 5.68087i | −0.0779186 | + | 0.188112i | ||||
\(913\) | −8.56310 | + | 3.54695i | −0.283397 | + | 0.117387i | ||||
\(914\) | 35.0823i | 1.16042i | ||||||||
\(915\) | 1.94295 | + | 4.69069i | 0.0642319 | + | 0.155069i | ||||
\(916\) | −12.1237 | − | 12.1237i | −0.400577 | − | 0.400577i | ||||
\(917\) | −10.3197 | −0.340787 | ||||||||
\(918\) | 0.686098 | + | 23.3071i | 0.0226446 | + | 0.769250i | ||||
\(919\) | 17.0376 | 0.562019 | 0.281009 | − | 0.959705i | \(-0.409331\pi\) | ||||
0.281009 | + | 0.959705i | \(0.409331\pi\) | |||||||
\(920\) | −5.14545 | − | 5.14545i | −0.169641 | − | 0.169641i | ||||
\(921\) | 4.78390 | + | 11.5494i | 0.157635 | + | 0.380564i | ||||
\(922\) | 40.2564i | 1.32577i | ||||||||
\(923\) | 50.0607 | − | 20.7358i | 1.64777 | − | 0.682527i | ||||
\(924\) | 1.32815 | − | 3.20643i | 0.0436928 | − | 0.105484i | ||||
\(925\) | −7.53553 | − | 3.12132i | −0.247767 | − | 0.102628i | ||||
\(926\) | 1.23576 | − | 1.23576i | 0.0406096 | − | 0.0406096i | ||||
\(927\) | 3.98717 | − | 3.98717i | 0.130956 | − | 0.130956i | ||||
\(928\) | 1.66399 | + | 0.689246i | 0.0546231 | + | 0.0226256i | ||||
\(929\) | 2.63169 | − | 6.35346i | 0.0863429 | − | 0.208450i | −0.874810 | − | 0.484466i | \(-0.839014\pi\) |
0.961153 | + | 0.276015i | \(0.0890141\pi\) | |||||||
\(930\) | 6.58752 | − | 2.72864i | 0.216013 | − | 0.0894757i | ||||
\(931\) | 28.2194i | 0.924853i | ||||||||
\(932\) | −7.24486 | − | 17.4907i | −0.237313 | − | 0.572925i | ||||
\(933\) | −17.0946 | − | 17.0946i | −0.559653 | − | 0.559653i | ||||
\(934\) | 17.0853 | 0.559049 | ||||||||
\(935\) | 5.46655 | − | 14.3803i | 0.178775 | − | 0.470286i | ||||
\(936\) | 3.85765 | 0.126091 | ||||||||
\(937\) | 13.4652 | + | 13.4652i | 0.439890 | + | 0.439890i | 0.891975 | − | 0.452085i | \(-0.149320\pi\) |
−0.452085 | + | 0.891975i | \(0.649320\pi\) | |||||||
\(938\) | −0.864148 | − | 2.08624i | −0.0282154 | − | 0.0681181i | ||||
\(939\) | − | 10.6646i | − | 0.348025i | ||||||
\(940\) | 4.35176 | − | 1.80256i | 0.141939 | − | 0.0587930i | ||||
\(941\) | 0.996369 | − | 2.40545i | 0.0324807 | − | 0.0784153i | −0.906807 | − | 0.421546i | \(-0.861487\pi\) |
0.939288 | + | 0.343131i | \(0.111487\pi\) | |||||||
\(942\) | 23.2206 | + | 9.61830i | 0.756569 | + | 0.313381i | ||||
\(943\) | 9.96643 | − | 9.96643i | 0.324552 | − | 0.324552i | ||||
\(944\) | 7.34549 | − | 7.34549i | 0.239075 | − | 0.239075i | ||||
\(945\) | −3.39008 | − | 1.40422i | −0.110279 | − | 0.0456792i | ||||
\(946\) | −1.49452 | + | 3.60810i | −0.0485912 | + | 0.117310i | ||||
\(947\) | 6.85990 | − | 2.84147i | 0.222917 | − | 0.0923352i | −0.268430 | − | 0.963299i | \(-0.586505\pi\) |
0.491347 | + | 0.870964i | \(0.336505\pi\) | |||||||
\(948\) | − | 0.420255i | − | 0.0136492i | ||||||
\(949\) | 9.36298 | + | 22.6042i | 0.303935 | + | 0.733764i | ||||
\(950\) | −3.03300 | − | 3.03300i | −0.0984036 | − | 0.0984036i | ||||
\(951\) | −1.84977 | −0.0599829 | ||||||||
\(952\) | −2.67411 | + | 0.0787183i | −0.0866682 | + | 0.00255127i | ||||
\(953\) | 37.5558 | 1.21655 | 0.608277 | − | 0.793725i | \(-0.291861\pi\) | ||||
0.608277 | + | 0.793725i | \(0.291861\pi\) | |||||||
\(954\) | −5.82843 | − | 5.82843i | −0.188702 | − | 0.188702i | ||||
\(955\) | 7.55920 | + | 18.2495i | 0.244610 | + | 0.590541i | ||||
\(956\) | − | 25.1215i | − | 0.812488i | ||||||
\(957\) | 8.90051 | − | 3.68671i | 0.287713 | − | 0.119174i | ||||
\(958\) | 8.00249 | − | 19.3197i | 0.258549 | − | 0.624192i | ||||
\(959\) | 13.7427 | + | 5.69240i | 0.443774 | + | 0.183817i | ||||
\(960\) | −1.01367 | + | 1.01367i | −0.0327161 | + | 0.0327161i | ||||
\(961\) | 4.42686 | − | 4.42686i | 0.142802 | − | 0.142802i | ||||
\(962\) | −30.7630 | − | 12.7425i | −0.991839 | − | 0.410833i | ||||
\(963\) | 1.96625 | − | 4.74694i | 0.0633614 | − | 0.152968i | ||||
\(964\) | −5.53137 | + | 2.29117i | −0.178153 | + | 0.0737936i | ||||
\(965\) | 10.3611i | 0.333535i | ||||||||
\(966\) | 2.59019 | + | 6.25327i | 0.0833380 | + | 0.201196i | ||||
\(967\) | −34.7364 | − | 34.7364i | −1.11705 | − | 1.11705i | −0.992173 | − | 0.124874i | \(-0.960147\pi\) |
−0.124874 | − | 0.992173i | \(-0.539853\pi\) | |||||||
\(968\) | 2.92214 | 0.0939213 | ||||||||
\(969\) | 17.3918 | − | 18.4468i | 0.558705 | − | 0.592596i | ||||
\(970\) | 19.2355 | 0.617614 | ||||||||
\(971\) | −14.1996 | − | 14.1996i | −0.455688 | − | 0.455688i | 0.441549 | − | 0.897237i | \(-0.354429\pi\) |
−0.897237 | + | 0.441549i | \(0.854429\pi\) | |||||||
\(972\) | 3.60021 | + | 8.69167i | 0.115477 | + | 0.278786i | ||||
\(973\) | − | 7.46889i | − | 0.239442i | ||||||
\(974\) | −15.0149 | + | 6.21937i | −0.481108 | + | 0.199281i | ||||
\(975\) | 2.23958 | − | 5.40682i | 0.0717238 | − | 0.173157i | ||||
\(976\) | 3.27209 | + | 1.35534i | 0.104737 | + | 0.0433835i | ||||
\(977\) | −27.5071 | + | 27.5071i | −0.880029 | + | 0.880029i | −0.993537 | − | 0.113508i | \(-0.963791\pi\) |
0.113508 | + | 0.993537i | \(0.463791\pi\) | |||||||
\(978\) | −8.72912 | + | 8.72912i | −0.279126 | + | 0.279126i | ||||
\(979\) | −12.3941 | − | 5.13379i | −0.396116 | − | 0.164077i | ||||
\(980\) | −2.51767 | + | 6.07820i | −0.0804241 | + | 0.194161i | ||||
\(981\) | 14.2660 | − | 5.90918i | 0.455479 | − | 0.188666i | ||||
\(982\) | − | 16.3083i | − | 0.520420i | ||||||
\(983\) | 1.69233 | + | 4.08564i | 0.0539769 | + | 0.130312i | 0.948568 | − | 0.316575i | \(-0.102533\pi\) |
−0.894591 | + | 0.446886i | \(0.852533\pi\) | |||||||
\(984\) | −1.96342 | − | 1.96342i | −0.0625915 | − | 0.0625915i | ||||
\(985\) | −16.6845 | −0.531613 | ||||||||
\(986\) | −5.40326 | − | 5.09425i | −0.172075 | − | 0.162234i | ||||
\(987\) | −4.38130 | −0.139458 | ||||||||
\(988\) | −12.3819 | − | 12.3819i | −0.393921 | − | 0.393921i | ||||
\(989\) | −2.91466 | − | 7.03662i | −0.0926809 | − | 0.223752i | ||||
\(990\) | − | 3.52582i | − | 0.112058i | ||||||
\(991\) | −15.2551 | + | 6.31887i | −0.484594 | + | 0.200726i | −0.611586 | − | 0.791178i | \(-0.709468\pi\) |
0.126991 | + | 0.991904i | \(0.459468\pi\) | |||||||
\(992\) | 1.90342 | − | 4.59527i | 0.0604337 | − | 0.145900i | ||||
\(993\) | −9.62393 | − | 3.98636i | −0.305406 | − | 0.126503i | ||||
\(994\) | −6.08967 | + | 6.08967i | −0.193153 | + | 0.193153i | ||||
\(995\) | 6.69824 | − | 6.69824i | 0.212348 | − | 0.212348i | ||||
\(996\) | −3.28995 | − | 1.36274i | −0.104246 | − | 0.0431801i | ||||
\(997\) | 21.5733 | − | 52.0826i | 0.683234 | − | 1.64947i | −0.0747525 | − | 0.997202i | \(-0.523817\pi\) |
0.757986 | − | 0.652270i | \(-0.226183\pi\) | |||||||
\(998\) | −30.2109 | + | 12.5137i | −0.956308 | + | 0.396116i | ||||
\(999\) | − | 46.1266i | − | 1.45938i |
(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 | 170.2.k.a.151.1 | ✓ | 8 | |
5.2 | odd | 4 | 850.2.o.f.49.1 | 8 | |||
5.3 | odd | 4 | 850.2.o.c.49.2 | 8 | |||
5.4 | even | 2 | 850.2.l.d.151.2 | 8 | |||
17.3 | odd | 16 | 2890.2.b.p.2311.5 | 8 | |||
17.5 | odd | 16 | 2890.2.a.bc.1.3 | 4 | |||
17.8 | even | 8 | inner | 170.2.k.a.161.1 | yes | 8 | |
17.12 | odd | 16 | 2890.2.a.bf.1.2 | 4 | |||
17.14 | odd | 16 | 2890.2.b.p.2311.4 | 8 | |||
85.8 | odd | 8 | 850.2.o.f.399.1 | 8 | |||
85.42 | odd | 8 | 850.2.o.c.399.2 | 8 | |||
85.59 | even | 8 | 850.2.l.d.501.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.k.a.151.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
170.2.k.a.161.1 | yes | 8 | 17.8 | even | 8 | inner | |
850.2.l.d.151.2 | 8 | 5.4 | even | 2 | |||
850.2.l.d.501.2 | 8 | 85.59 | even | 8 | |||
850.2.o.c.49.2 | 8 | 5.3 | odd | 4 | |||
850.2.o.c.399.2 | 8 | 85.42 | odd | 8 | |||
850.2.o.f.49.1 | 8 | 5.2 | odd | 4 | |||
850.2.o.f.399.1 | 8 | 85.8 | odd | 8 | |||
2890.2.a.bc.1.3 | 4 | 17.5 | odd | 16 | |||
2890.2.a.bf.1.2 | 4 | 17.12 | odd | 16 | |||
2890.2.b.p.2311.4 | 8 | 17.14 | odd | 16 | |||
2890.2.b.p.2311.5 | 8 | 17.3 | odd | 16 |