Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.12 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.j.508.12 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29430 | − | 2.24179i | 0.915209 | − | 1.58519i | 0.108613 | − | 0.994084i | \(-0.465359\pi\) |
0.806596 | − | 0.591104i | \(-0.201308\pi\) | |||||||
\(3\) | −0.259233 | − | 0.449005i | −0.149668 | − | 0.259233i | 0.781437 | − | 0.623985i | \(-0.214487\pi\) |
−0.931105 | + | 0.364752i | \(0.881154\pi\) | |||||||
\(4\) | −2.35043 | − | 4.07106i | −1.17521 | − | 2.03553i | ||||
\(5\) | 0.806027 | − | 1.39608i | 0.360466 | − | 0.624346i | −0.627571 | − | 0.778559i | \(-0.715951\pi\) |
0.988038 | + | 0.154213i | \(0.0492843\pi\) | |||||||
\(6\) | −1.34210 | −0.547910 | ||||||||
\(7\) | −2.13104 | − | 1.56802i | −0.805457 | − | 0.592654i | ||||
\(8\) | −6.99143 | −2.47184 | ||||||||
\(9\) | 1.36560 | − | 2.36528i | 0.455199 | − | 0.788428i | ||||
\(10\) | −2.08648 | − | 3.61389i | −0.659803 | − | 1.14281i | ||||
\(11\) | 1.35248 | + | 2.34256i | 0.407788 | + | 0.706309i | 0.994642 | − | 0.103384i | \(-0.0329670\pi\) |
−0.586854 | + | 0.809693i | \(0.699634\pi\) | |||||||
\(12\) | −1.21862 | + | 2.11070i | −0.351784 | + | 0.609308i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.27337 | + | 2.74787i | −1.67663 | + | 0.734398i | ||||
\(15\) | −0.835795 | −0.215801 | ||||||||
\(16\) | −4.34816 | + | 7.53123i | −1.08704 | + | 1.88281i | ||||
\(17\) | −1.56330 | − | 2.70772i | −0.379157 | − | 0.656719i | 0.611783 | − | 0.791026i | \(-0.290453\pi\) |
−0.990940 | + | 0.134307i | \(0.957119\pi\) | |||||||
\(18\) | −3.53498 | − | 6.12277i | −0.833204 | − | 1.44315i | ||||
\(19\) | 1.84075 | − | 3.18828i | 0.422297 | − | 0.731441i | −0.573866 | − | 0.818949i | \(-0.694557\pi\) |
0.996164 | + | 0.0875083i | \(0.0278904\pi\) | |||||||
\(20\) | −7.57803 | −1.69450 | ||||||||
\(21\) | −0.151611 | + | 1.36333i | −0.0330842 | + | 0.297502i | ||||
\(22\) | 7.00205 | 1.49284 | ||||||||
\(23\) | −0.993019 | + | 1.71996i | −0.207059 | + | 0.358636i | −0.950787 | − | 0.309846i | \(-0.899722\pi\) |
0.743728 | + | 0.668482i | \(0.233056\pi\) | |||||||
\(24\) | 1.81241 | + | 3.13918i | 0.369956 | + | 0.640783i | ||||
\(25\) | 1.20064 | + | 2.07957i | 0.240128 | + | 0.415914i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.97143 | −0.571852 | ||||||||
\(28\) | −1.37463 | + | 12.3611i | −0.259781 | + | 2.33603i | ||||
\(29\) | −5.37271 | −0.997687 | −0.498844 | − | 0.866692i | \(-0.666242\pi\) | ||||
−0.498844 | + | 0.866692i | \(0.666242\pi\) | |||||||
\(30\) | −1.08177 | + | 1.87368i | −0.197503 | + | 0.342086i | ||||
\(31\) | 5.23902 | + | 9.07425i | 0.940956 | + | 1.62978i | 0.763653 | + | 0.645627i | \(0.223404\pi\) |
0.177303 | + | 0.984156i | \(0.443263\pi\) | |||||||
\(32\) | 4.26421 | + | 7.38583i | 0.753813 | + | 1.30564i | ||||
\(33\) | 0.701214 | − | 1.21454i | 0.122066 | − | 0.211424i | ||||
\(34\) | −8.09354 | −1.38803 | ||||||||
\(35\) | −3.90675 | + | 1.71124i | −0.660361 | + | 0.289252i | ||||
\(36\) | −12.8389 | −2.13982 | ||||||||
\(37\) | 2.97673 | − | 5.15585i | 0.489371 | − | 0.847616i | −0.510554 | − | 0.859846i | \(-0.670560\pi\) |
0.999925 | + | 0.0122297i | \(0.00389292\pi\) | |||||||
\(38\) | −4.76497 | − | 8.25317i | −0.772981 | − | 1.33884i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.63528 | + | 9.76059i | −0.891016 | + | 1.54329i | ||||
\(41\) | 7.70150 | 1.20277 | 0.601386 | − | 0.798958i | \(-0.294615\pi\) | ||||
0.601386 | + | 0.798958i | \(0.294615\pi\) | |||||||
\(42\) | 2.86007 | + | 2.10444i | 0.441318 | + | 0.324721i | ||||
\(43\) | −3.35600 | −0.511785 | −0.255892 | − | 0.966705i | \(-0.582369\pi\) | ||||
−0.255892 | + | 0.966705i | \(0.582369\pi\) | |||||||
\(44\) | 6.35780 | − | 11.0120i | 0.958475 | − | 1.66013i | ||||
\(45\) | −2.20141 | − | 3.81296i | −0.328168 | − | 0.568403i | ||||
\(46\) | 2.57053 | + | 4.45229i | 0.379004 | + | 0.656454i | ||||
\(47\) | 0.527542 | − | 0.913730i | 0.0769500 | − | 0.133281i | −0.824983 | − | 0.565158i | \(-0.808815\pi\) |
0.901933 | + | 0.431877i | \(0.142148\pi\) | |||||||
\(48\) | 4.50874 | 0.650781 | ||||||||
\(49\) | 2.08265 | + | 6.68300i | 0.297522 | + | 0.954715i | ||||
\(50\) | 6.21596 | 0.879070 | ||||||||
\(51\) | −0.810520 | + | 1.40386i | −0.113495 | + | 0.196580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.63284 | − | 6.29226i | −0.499009 | − | 0.864308i | 0.500991 | − | 0.865453i | \(-0.332969\pi\) |
−0.999999 | + | 0.00114437i | \(0.999636\pi\) | |||||||
\(54\) | −3.84592 | + | 6.66133i | −0.523363 | + | 0.906492i | ||||
\(55\) | 4.36054 | 0.587975 | ||||||||
\(56\) | 14.8990 | + | 10.9627i | 1.99096 | + | 1.46495i | ||||
\(57\) | −1.90873 | −0.252818 | ||||||||
\(58\) | −6.95390 | + | 12.0445i | −0.913092 | + | 1.58152i | ||||
\(59\) | 5.71203 | + | 9.89352i | 0.743643 | + | 1.28803i | 0.950826 | + | 0.309725i | \(0.100237\pi\) |
−0.207183 | + | 0.978302i | \(0.566430\pi\) | |||||||
\(60\) | 1.96447 | + | 3.40257i | 0.253613 | + | 0.439270i | ||||
\(61\) | 1.46254 | − | 2.53319i | 0.187259 | − | 0.324341i | −0.757077 | − | 0.653326i | \(-0.773373\pi\) |
0.944335 | + | 0.328985i | \(0.106706\pi\) | |||||||
\(62\) | 27.1235 | 3.44468 | ||||||||
\(63\) | −6.61894 | + | 2.89923i | −0.833908 | + | 0.365269i | ||||
\(64\) | 4.68406 | 0.585507 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.81516 | − | 3.14395i | −0.223431 | − | 0.386994i | ||||
\(67\) | −6.79091 | − | 11.7622i | −0.829642 | − | 1.43698i | −0.898320 | − | 0.439343i | \(-0.855211\pi\) |
0.0686778 | − | 0.997639i | \(-0.478122\pi\) | |||||||
\(68\) | −7.34886 | + | 12.7286i | −0.891180 | + | 1.54357i | ||||
\(69\) | 1.02969 | 0.123960 | ||||||||
\(70\) | −1.22027 | + | 10.9730i | −0.145850 | + | 1.31152i | ||||
\(71\) | 1.35111 | 0.160347 | 0.0801736 | − | 0.996781i | \(-0.474453\pi\) | ||||
0.0801736 | + | 0.996781i | \(0.474453\pi\) | |||||||
\(72\) | −9.54747 | + | 16.5367i | −1.12518 | + | 1.94887i | ||||
\(73\) | 4.55168 | + | 7.88374i | 0.532733 | + | 0.922721i | 0.999269 | + | 0.0382192i | \(0.0121685\pi\) |
−0.466536 | + | 0.884502i | \(0.654498\pi\) | |||||||
\(74\) | −7.70557 | − | 13.3464i | −0.895754 | − | 1.55149i | ||||
\(75\) | 0.622492 | − | 1.07819i | 0.0718791 | − | 0.124498i | ||||
\(76\) | −17.3062 | −1.98516 | ||||||||
\(77\) | 0.790989 | − | 7.11280i | 0.0901416 | − | 0.810578i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.10289 | − | 5.37436i | 0.349102 | − | 0.604663i | −0.636988 | − | 0.770874i | \(-0.719820\pi\) |
0.986090 | + | 0.166211i | \(0.0531532\pi\) | |||||||
\(80\) | 7.00946 | + | 12.1407i | 0.783682 | + | 1.35738i | ||||
\(81\) | −3.32650 | − | 5.76166i | −0.369611 | − | 0.640185i | ||||
\(82\) | 9.96806 | − | 17.2652i | 1.10079 | − | 1.90662i | ||||
\(83\) | 2.69672 | 0.296003 | 0.148002 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148002 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(84\) | 5.90654 | − | 2.58718i | 0.644456 | − | 0.282285i | ||||
\(85\) | −5.04026 | −0.546693 | ||||||||
\(86\) | −4.34367 | + | 7.52346i | −0.468390 | + | 0.811275i | ||||
\(87\) | 1.39278 | + | 2.41237i | 0.149322 | + | 0.258633i | ||||
\(88\) | −9.45576 | − | 16.3779i | −1.00799 | − | 1.74589i | ||||
\(89\) | 0.879938 | − | 1.52410i | 0.0932732 | − | 0.161554i | −0.815613 | − | 0.578597i | \(-0.803600\pi\) |
0.908887 | + | 0.417043i | \(0.136934\pi\) | |||||||
\(90\) | −11.3972 | −1.20137 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.33607 | 0.973353 | ||||||||
\(93\) | 2.71625 | − | 4.70469i | 0.281662 | − | 0.487853i | ||||
\(94\) | −1.36560 | − | 2.36528i | −0.140851 | − | 0.243960i | ||||
\(95\) | −2.96739 | − | 5.13967i | −0.304448 | − | 0.527319i | ||||
\(96\) | 2.21085 | − | 3.82930i | 0.225644 | − | 0.390827i | ||||
\(97\) | −15.4820 | −1.57196 | −0.785981 | − | 0.618250i | \(-0.787842\pi\) | ||||
−0.785981 | + | 0.618250i | \(0.787842\pi\) | |||||||
\(98\) | 17.6775 | + | 3.98094i | 1.78570 | + | 0.402135i | ||||
\(99\) | 7.38776 | 0.742498 | ||||||||
\(100\) | 5.64404 | − | 9.77576i | 0.564404 | − | 0.977576i | ||||
\(101\) | 0.639651 | + | 1.10791i | 0.0636477 | + | 0.110241i | 0.896093 | − | 0.443866i | \(-0.146393\pi\) |
−0.832446 | + | 0.554107i | \(0.813060\pi\) | |||||||
\(102\) | 2.09811 | + | 3.63404i | 0.207744 | + | 0.359823i | ||||
\(103\) | 5.73367 | − | 9.93101i | 0.564956 | − | 0.978532i | −0.432098 | − | 0.901827i | \(-0.642227\pi\) |
0.997054 | − | 0.0767054i | \(-0.0244401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.78111 | + | 1.31054i | 0.173819 | + | 0.127896i | ||||
\(106\) | −18.8079 | −1.82679 | ||||||||
\(107\) | 2.56763 | − | 4.44726i | 0.248222 | − | 0.429933i | −0.714811 | − | 0.699318i | \(-0.753487\pi\) |
0.963033 | + | 0.269385i | \(0.0868205\pi\) | |||||||
\(108\) | 6.98412 | + | 12.0969i | 0.672048 | + | 1.16402i | ||||
\(109\) | 0.863916 | + | 1.49635i | 0.0827481 | + | 0.143324i | 0.904429 | − | 0.426623i | \(-0.140297\pi\) |
−0.821681 | + | 0.569947i | \(0.806964\pi\) | |||||||
\(110\) | 5.64384 | − | 9.77542i | 0.538119 | − | 0.932050i | ||||
\(111\) | −3.08667 | −0.292973 | ||||||||
\(112\) | 21.0752 | − | 9.23136i | 1.99142 | − | 0.872282i | ||||
\(113\) | −8.59113 | −0.808185 | −0.404093 | − | 0.914718i | \(-0.632413\pi\) | ||||
−0.404093 | + | 0.914718i | \(0.632413\pi\) | |||||||
\(114\) | −2.47048 | + | 4.27899i | −0.231381 | + | 0.400764i | ||||
\(115\) | 1.60080 | + | 2.77267i | 0.149275 | + | 0.258552i | ||||
\(116\) | 12.6282 | + | 21.8726i | 1.17250 | + | 2.03082i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.5723 | 2.72235 | ||||||||
\(119\) | −0.914289 | + | 8.22154i | −0.0838127 | + | 0.753668i | ||||
\(120\) | 5.84340 | 0.533427 | ||||||||
\(121\) | 1.84160 | − | 3.18975i | 0.167419 | − | 0.289977i | ||||
\(122\) | −3.78592 | − | 6.55741i | −0.342761 | − | 0.593680i | ||||
\(123\) | −1.99648 | − | 3.45801i | −0.180017 | − | 0.311798i | ||||
\(124\) | 24.6279 | − | 42.6567i | 2.21165 | − | 3.83069i | ||||
\(125\) | 11.9313 | 1.06716 | ||||||||
\(126\) | −2.06741 | + | 18.5908i | −0.184180 | + | 1.65620i | ||||
\(127\) | −3.12412 | −0.277221 | −0.138610 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138610 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(128\) | −2.46585 | + | 4.27097i | −0.217952 | + | 0.377504i | ||||
\(129\) | 0.869985 | + | 1.50686i | 0.0765979 | + | 0.132671i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.10460 | + | 8.84142i | −0.445991 | + | 0.772479i | −0.998121 | − | 0.0612793i | \(-0.980482\pi\) |
0.552130 | + | 0.833758i | \(0.313815\pi\) | |||||||
\(132\) | −6.59261 | −0.573813 | ||||||||
\(133\) | −8.92198 | + | 3.90801i | −0.773634 | + | 0.338868i | ||||
\(134\) | −35.1579 | −3.03718 | ||||||||
\(135\) | −2.39505 | + | 4.14835i | −0.206133 | + | 0.357033i | ||||
\(136\) | 10.9297 | + | 18.9308i | 0.937216 | + | 1.62331i | ||||
\(137\) | −4.99630 | − | 8.65385i | −0.426863 | − | 0.739348i | 0.569729 | − | 0.821832i | \(-0.307048\pi\) |
−0.996592 | + | 0.0824839i | \(0.973715\pi\) | |||||||
\(138\) | 1.33273 | − | 2.30836i | 0.113450 | − | 0.196501i | ||||
\(139\) | −1.66420 | −0.141156 | −0.0705778 | − | 0.997506i | \(-0.522484\pi\) | ||||
−0.0705778 | + | 0.997506i | \(0.522484\pi\) | |||||||
\(140\) | 16.1491 | + | 11.8825i | 1.36485 | + | 1.00425i | ||||
\(141\) | −0.547025 | −0.0460679 | ||||||||
\(142\) | 1.74874 | − | 3.02891i | 0.146751 | − | 0.254180i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 11.8757 | + | 20.5692i | 0.989638 | + | 1.71410i | ||||
\(145\) | −4.33055 | + | 7.50073i | −0.359633 | + | 0.622902i | ||||
\(146\) | 23.5649 | 1.95025 | ||||||||
\(147\) | 2.46081 | − | 2.66758i | 0.202964 | − | 0.220018i | ||||
\(148\) | −27.9863 | −2.30046 | ||||||||
\(149\) | 9.89902 | − | 17.1456i | 0.810959 | − | 1.40462i | −0.101234 | − | 0.994863i | \(-0.532279\pi\) |
0.912193 | − | 0.409760i | \(-0.134387\pi\) | |||||||
\(150\) | −1.61138 | − | 2.79100i | −0.131569 | − | 0.227884i | ||||
\(151\) | 3.76746 | + | 6.52544i | 0.306592 | + | 0.531033i | 0.977614 | − | 0.210404i | \(-0.0674780\pi\) |
−0.671023 | + | 0.741437i | \(0.734145\pi\) | |||||||
\(152\) | −12.8695 | + | 22.2906i | −1.04385 | + | 1.80801i | ||||
\(153\) | −8.53937 | −0.690367 | ||||||||
\(154\) | −14.9216 | − | 10.9793i | −1.20242 | − | 0.884740i | ||||
\(155\) | 16.8912 | 1.35673 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00223 | − | 12.1282i | −0.558839 | − | 0.967938i | −0.997594 | − | 0.0693309i | \(-0.977914\pi\) |
0.438755 | − | 0.898607i | \(-0.355420\pi\) | |||||||
\(158\) | −8.03214 | − | 13.9121i | −0.639003 | − | 1.10679i | ||||
\(159\) | −1.88350 | + | 3.26232i | −0.149371 | + | 0.258719i | ||||
\(160\) | 13.7483 | 1.08690 | ||||||||
\(161\) | 4.81308 | − | 2.10823i | 0.379324 | − | 0.166152i | ||||
\(162\) | −17.2219 | −1.35308 | ||||||||
\(163\) | −3.58498 | + | 6.20936i | −0.280797 | + | 0.486355i | −0.971581 | − | 0.236706i | \(-0.923932\pi\) |
0.690784 | + | 0.723061i | \(0.257265\pi\) | |||||||
\(164\) | −18.1018 | − | 31.3533i | −1.41351 | − | 2.44828i | ||||
\(165\) | −1.13039 | − | 1.95790i | −0.0880011 | − | 0.152422i | ||||
\(166\) | 3.49036 | − | 6.04548i | 0.270904 | − | 0.469220i | ||||
\(167\) | 17.9805 | 1.39138 | 0.695688 | − | 0.718344i | \(-0.255099\pi\) | ||||
0.695688 | + | 0.718344i | \(0.255099\pi\) | |||||||
\(168\) | 1.05998 | − | 9.53161i | 0.0817790 | − | 0.735380i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.52361 | + | 11.2992i | −0.500338 | + | 0.866611i | ||||
\(171\) | −5.02745 | − | 8.70780i | −0.384459 | − | 0.665902i | ||||
\(172\) | 7.88803 | + | 13.6625i | 0.601456 | + | 1.04175i | ||||
\(173\) | 6.40579 | − | 11.0952i | 0.487023 | − | 0.843549i | −0.512865 | − | 0.858469i | \(-0.671416\pi\) |
0.999889 | + | 0.0149198i | \(0.00474930\pi\) | |||||||
\(174\) | 7.21072 | 0.546643 | ||||||||
\(175\) | 0.702188 | − | 6.31427i | 0.0530804 | − | 0.477314i | ||||
\(176\) | −23.5232 | −1.77312 | ||||||||
\(177\) | 2.96149 | − | 5.12945i | 0.222599 | − | 0.385553i | ||||
\(178\) | −2.27781 | − | 3.94528i | −0.170729 | − | 0.295711i | ||||
\(179\) | −0.920110 | − | 1.59368i | −0.0687723 | − | 0.119117i | 0.829589 | − | 0.558375i | \(-0.188575\pi\) |
−0.898361 | + | 0.439258i | \(0.855242\pi\) | |||||||
\(180\) | −10.3485 | + | 17.9242i | −0.771334 | + | 1.33599i | ||||
\(181\) | 3.29928 | 0.245234 | 0.122617 | − | 0.992454i | \(-0.460871\pi\) | ||||
0.122617 | + | 0.992454i | \(0.460871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51655 | −0.112107 | ||||||||
\(184\) | 6.94262 | − | 12.0250i | 0.511817 | − | 0.886493i | ||||
\(185\) | −4.79865 | − | 8.31150i | −0.352804 | − | 0.611074i | ||||
\(186\) | −7.03129 | − | 12.1786i | −0.515560 | − | 0.892975i | ||||
\(187\) | 4.22867 | − | 7.32427i | 0.309231 | − | 0.535604i | ||||
\(188\) | −4.95980 | −0.361731 | ||||||||
\(189\) | 6.33223 | + | 4.65925i | 0.460602 | + | 0.338910i | ||||
\(190\) | −15.3628 | −1.11453 | ||||||||
\(191\) | −2.44807 | + | 4.24018i | −0.177136 | + | 0.306809i | −0.940898 | − | 0.338689i | \(-0.890017\pi\) |
0.763762 | + | 0.645498i | \(0.223350\pi\) | |||||||
\(192\) | −1.21426 | − | 2.10316i | −0.0876318 | − | 0.151783i | ||||
\(193\) | 1.50955 | + | 2.61462i | 0.108660 | + | 0.188204i | 0.915228 | − | 0.402937i | \(-0.132011\pi\) |
−0.806568 | + | 0.591142i | \(0.798677\pi\) | |||||||
\(194\) | −20.0384 | + | 34.7075i | −1.43867 | + | 2.49186i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.3118 | − | 24.1865i | 1.59370 | − | 1.72761i | ||||
\(197\) | −4.64991 | −0.331292 | −0.165646 | − | 0.986185i | \(-0.552971\pi\) | ||||
−0.165646 | + | 0.986185i | \(0.552971\pi\) | |||||||
\(198\) | 9.56198 | − | 16.5618i | 0.679540 | − | 1.17700i | ||||
\(199\) | −0.205360 | − | 0.355694i | −0.0145576 | − | 0.0252145i | 0.858655 | − | 0.512554i | \(-0.171301\pi\) |
−0.873212 | + | 0.487340i | \(0.837967\pi\) | |||||||
\(200\) | −8.39420 | − | 14.5392i | −0.593560 | − | 1.02808i | ||||
\(201\) | −3.52085 | + | 6.09830i | −0.248342 | + | 0.430141i | ||||
\(202\) | 3.31160 | 0.233004 | ||||||||
\(203\) | 11.4495 | + | 8.42450i | 0.803594 | + | 0.591284i | ||||
\(204\) | 7.62027 | 0.533525 | ||||||||
\(205\) | 6.20762 | − | 10.7519i | 0.433559 | − | 0.750946i | ||||
\(206\) | −14.8422 | − | 25.7074i | −1.03410 | − | 1.79112i | ||||
\(207\) | 2.71213 | + | 4.69754i | 0.188506 | + | 0.326502i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.95831 | 0.688831 | ||||||||
\(210\) | 5.24325 | − | 2.29665i | 0.361819 | − | 0.158484i | ||||
\(211\) | −7.51600 | −0.517423 | −0.258711 | − | 0.965955i | \(-0.583298\pi\) | ||||
−0.258711 | + | 0.965955i | \(0.583298\pi\) | |||||||
\(212\) | −17.0774 | + | 29.5790i | −1.17288 | + | 2.03149i | ||||
\(213\) | −0.350252 | − | 0.606654i | −0.0239989 | − | 0.0415672i | ||||
\(214\) | −6.64656 | − | 11.5122i | −0.454349 | − | 0.786956i | ||||
\(215\) | −2.70502 | + | 4.68524i | −0.184481 | + | 0.319531i | ||||
\(216\) | 20.7745 | 1.41353 | ||||||||
\(217\) | 3.06401 | − | 27.5524i | 0.207999 | − | 1.87038i | ||||
\(218\) | 4.47267 | 0.302927 | ||||||||
\(219\) | 2.35989 | − | 4.08745i | 0.159467 | − | 0.276204i | ||||
\(220\) | −10.2491 | − | 17.7520i | −0.690996 | − | 1.19684i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.99507 | + | 6.91967i | −0.268132 | + | 0.464418i | ||||
\(223\) | 22.5794 | 1.51203 | 0.756016 | − | 0.654553i | \(-0.227143\pi\) | ||||
0.756016 | + | 0.654553i | \(0.227143\pi\) | |||||||
\(224\) | 2.49390 | − | 22.4259i | 0.166631 | − | 1.49839i | ||||
\(225\) | 6.55837 | 0.437225 | ||||||||
\(226\) | −11.1195 | + | 19.2595i | −0.739658 | + | 1.28113i | ||||
\(227\) | 6.83586 | + | 11.8401i | 0.453712 | + | 0.785853i | 0.998613 | − | 0.0526478i | \(-0.0167661\pi\) |
−0.544901 | + | 0.838500i | \(0.683433\pi\) | |||||||
\(228\) | 4.48634 | + | 7.77057i | 0.297115 | + | 0.514618i | ||||
\(229\) | 3.96543 | − | 6.86832i | 0.262043 | − | 0.453872i | −0.704742 | − | 0.709464i | \(-0.748937\pi\) |
0.966785 | + | 0.255592i | \(0.0822705\pi\) | |||||||
\(230\) | 8.28766 | 0.546472 | ||||||||
\(231\) | −3.39873 | + | 1.48871i | −0.223620 | + | 0.0979502i | ||||
\(232\) | 37.5629 | 2.46613 | ||||||||
\(233\) | 3.28585 | − | 5.69127i | 0.215263 | − | 0.372847i | −0.738091 | − | 0.674702i | \(-0.764272\pi\) |
0.953354 | + | 0.301854i | \(0.0976056\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.850427 | − | 1.47298i | −0.0554757 | − | 0.0960868i | ||||
\(236\) | 26.8514 | − | 46.5080i | 1.74788 | − | 3.02741i | ||||
\(237\) | −3.21749 | −0.208998 | ||||||||
\(238\) | 17.2476 | + | 12.6908i | 1.11800 | + | 0.822622i | ||||
\(239\) | 9.39284 | 0.607572 | 0.303786 | − | 0.952740i | \(-0.401749\pi\) | ||||
0.303786 | + | 0.952740i | \(0.401749\pi\) | |||||||
\(240\) | 3.63417 | − | 6.29456i | 0.234584 | − | 0.406312i | ||||
\(241\) | −5.04292 | − | 8.73460i | −0.324843 | − | 0.562645i | 0.656637 | − | 0.754206i | \(-0.271978\pi\) |
−0.981481 | + | 0.191562i | \(0.938645\pi\) | |||||||
\(242\) | −4.76718 | − | 8.25699i | −0.306446 | − | 0.530780i | ||||
\(243\) | −6.18182 | + | 10.7072i | −0.396564 | + | 0.686869i | ||||
\(244\) | −13.7503 | −0.880275 | ||||||||
\(245\) | 11.0087 | + | 2.47913i | 0.703319 | + | 0.158386i | ||||
\(246\) | −10.3362 | −0.659012 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −36.6282 | − | 63.4420i | −2.32590 | − | 4.02857i | ||||
\(249\) | −0.699078 | − | 1.21084i | −0.0443022 | − | 0.0767337i | ||||
\(250\) | 15.4426 | − | 26.7474i | 0.976678 | − | 1.69166i | ||||
\(251\) | −10.3485 | −0.653194 | −0.326597 | − | 0.945164i | \(-0.605902\pi\) | ||||
−0.326597 | + | 0.945164i | \(0.605902\pi\) | |||||||
\(252\) | 27.3603 | + | 20.1317i | 1.72354 | + | 1.26818i | ||||
\(253\) | −5.37215 | −0.337744 | ||||||||
\(254\) | −4.04355 | + | 7.00363i | −0.253715 | + | 0.439447i | ||||
\(255\) | 1.30660 | + | 2.26310i | 0.0818225 | + | 0.141721i | ||||
\(256\) | 11.0672 | + | 19.1689i | 0.691697 | + | 1.19805i | ||||
\(257\) | −3.99329 | + | 6.91658i | −0.249095 | + | 0.431445i | −0.963275 | − | 0.268517i | \(-0.913466\pi\) |
0.714180 | + | 0.699962i | \(0.246800\pi\) | |||||||
\(258\) | 4.50409 | 0.280412 | ||||||||
\(259\) | −14.4280 | + | 6.31975i | −0.896511 | + | 0.392690i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.33696 | + | 12.7080i | −0.454146 | + | 0.786604i | ||||
\(262\) | 13.2138 | + | 22.8869i | 0.816349 | + | 1.41396i | ||||
\(263\) | −2.52967 | − | 4.38152i | −0.155986 | − | 0.270176i | 0.777431 | − | 0.628968i | \(-0.216522\pi\) |
−0.933418 | + | 0.358792i | \(0.883189\pi\) | |||||||
\(264\) | −4.90249 | + | 8.49136i | −0.301727 | + | 0.522607i | ||||
\(265\) | −11.7127 | −0.719503 | ||||||||
\(266\) | −2.78677 | + | 25.0594i | −0.170868 | + | 1.53649i | ||||
\(267\) | −0.912435 | −0.0558401 | ||||||||
\(268\) | −31.9231 | + | 55.2924i | −1.95001 | + | 3.37752i | ||||
\(269\) | −6.94512 | − | 12.0293i | −0.423451 | − | 0.733439i | 0.572823 | − | 0.819679i | \(-0.305848\pi\) |
−0.996274 | + | 0.0862400i | \(0.972515\pi\) | |||||||
\(270\) | 6.19983 | + | 10.7384i | 0.377310 | + | 0.653519i | ||||
\(271\) | −4.16361 | + | 7.21158i | −0.252921 | + | 0.438072i | −0.964329 | − | 0.264707i | \(-0.914725\pi\) |
0.711408 | + | 0.702780i | \(0.248058\pi\) | |||||||
\(272\) | 27.1900 | 1.64863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | −3.24768 | + | 5.62515i | −0.195843 | + | 0.339210i | ||||
\(276\) | −2.42022 | − | 4.19194i | −0.145680 | − | 0.252325i | ||||
\(277\) | 11.6058 | + | 20.1018i | 0.697325 | + | 1.20780i | 0.969391 | + | 0.245523i | \(0.0789598\pi\) |
−0.272066 | + | 0.962279i | \(0.587707\pi\) | |||||||
\(278\) | −2.15398 | + | 3.73080i | −0.129187 | + | 0.223758i | ||||
\(279\) | 28.6176 | 1.71329 | ||||||||
\(280\) | 27.3138 | − | 11.9640i | 1.63231 | − | 0.714985i | ||||
\(281\) | −27.1595 | −1.62020 | −0.810100 | − | 0.586292i | \(-0.800587\pi\) | ||||
−0.810100 | + | 0.586292i | \(0.800587\pi\) | |||||||
\(282\) | −0.708015 | + | 1.22632i | −0.0421617 | + | 0.0730262i | ||||
\(283\) | 8.07563 | + | 13.9874i | 0.480046 | + | 0.831464i | 0.999738 | − | 0.0228894i | \(-0.00728654\pi\) |
−0.519692 | + | 0.854354i | \(0.673953\pi\) | |||||||
\(284\) | −3.17568 | − | 5.50044i | −0.188442 | − | 0.326391i | ||||
\(285\) | −1.53849 | + | 2.66474i | −0.0911323 | + | 0.157846i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.4122 | − | 12.0761i | −0.968782 | − | 0.712828i | ||||
\(288\) | 23.2928 | 1.37254 | ||||||||
\(289\) | 3.61216 | − | 6.25645i | 0.212480 | − | 0.368027i | ||||
\(290\) | 11.2101 | + | 19.4164i | 0.658278 | + | 1.14017i | ||||
\(291\) | 4.01345 | + | 6.95151i | 0.235273 | + | 0.407504i | ||||
\(292\) | 21.3968 | − | 37.0603i | 1.25215 | − | 2.16879i | ||||
\(293\) | 14.6452 | 0.855582 | 0.427791 | − | 0.903878i | \(-0.359292\pi\) | ||||
0.427791 | + | 0.903878i | \(0.359292\pi\) | |||||||
\(294\) | −2.79513 | − | 8.96927i | −0.163015 | − | 0.523098i | ||||
\(295\) | 18.4162 | 1.07223 | ||||||||
\(296\) | −20.8116 | + | 36.0468i | −1.20965 | + | 2.09517i | ||||
\(297\) | −4.01879 | − | 6.96075i | −0.233194 | − | 0.403904i | ||||
\(298\) | −25.6246 | − | 44.3831i | −1.48439 | − | 2.57104i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.85248 | −0.337893 | ||||||||
\(301\) | 7.15176 | + | 5.26226i | 0.412221 | + | 0.303311i | ||||
\(302\) | 19.5049 | 1.12238 | ||||||||
\(303\) | 0.331637 | − | 0.574412i | 0.0190521 | − | 0.0329991i | ||||
\(304\) | 16.0078 | + | 27.7263i | 0.918108 | + | 1.59021i | ||||
\(305\) | −2.35769 | − | 4.08363i | −0.135001 | − | 0.233828i | ||||
\(306\) | −11.0525 | + | 19.1435i | −0.631830 | + | 1.09436i | ||||
\(307\) | 8.97844 | 0.512427 | 0.256213 | − | 0.966620i | \(-0.417525\pi\) | ||||
0.256213 | + | 0.966620i | \(0.417525\pi\) | |||||||
\(308\) | −30.8158 | + | 13.4979i | −1.75589 | + | 0.769117i | ||||
\(309\) | −5.94543 | −0.338224 | ||||||||
\(310\) | 21.8622 | − | 37.8665i | 1.24169 | − | 2.15067i | ||||
\(311\) | −6.09080 | − | 10.5496i | −0.345378 | − | 0.598212i | 0.640045 | − | 0.768338i | \(-0.278916\pi\) |
−0.985422 | + | 0.170126i | \(0.945583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.56198 | + | 11.3657i | −0.370905 | + | 0.642427i | −0.989705 | − | 0.143122i | \(-0.954286\pi\) |
0.618800 | + | 0.785549i | \(0.287619\pi\) | |||||||
\(314\) | −36.2520 | −2.04582 | ||||||||
\(315\) | −1.28748 | + | 11.5774i | −0.0725415 | + | 0.652314i | ||||
\(316\) | −29.1725 | −1.64108 | ||||||||
\(317\) | −8.35775 | + | 14.4761i | −0.469418 | + | 0.813056i | −0.999389 | − | 0.0349599i | \(-0.988870\pi\) |
0.529971 | + | 0.848016i | \(0.322203\pi\) | |||||||
\(318\) | 4.87563 | + | 8.44485i | 0.273412 | + | 0.473564i | ||||
\(319\) | −7.26648 | − | 12.5859i | −0.406845 | − | 0.704675i | ||||
\(320\) | 3.77548 | − | 6.53932i | 0.211056 | − | 0.365559i | ||||
\(321\) | −2.66245 | −0.148604 | ||||||||
\(322\) | 1.50336 | − | 13.5186i | 0.0837789 | − | 0.753364i | ||||
\(323\) | −11.5106 | −0.640468 | ||||||||
\(324\) | −15.6374 | + | 27.0847i | −0.868743 | + | 1.50471i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.28007 | + | 16.0736i | 0.513976 | + | 0.890232i | ||||
\(327\) | 0.447911 | − | 0.775804i | 0.0247695 | − | 0.0429021i | ||||
\(328\) | −53.8445 | −2.97307 | ||||||||
\(329\) | −2.55696 | + | 1.12000i | −0.140970 | + | 0.0617476i | ||||
\(330\) | −5.85228 | −0.322157 | ||||||||
\(331\) | −1.98332 | + | 3.43522i | −0.109013 | + | 0.188817i | −0.915371 | − | 0.402612i | \(-0.868102\pi\) |
0.806357 | + | 0.591428i | \(0.201436\pi\) | |||||||
\(332\) | −6.33843 | − | 10.9785i | −0.347867 | − | 0.602523i | ||||
\(333\) | −8.13002 | − | 14.0816i | −0.445523 | − | 0.771668i | ||||
\(334\) | 23.2722 | − | 40.3087i | 1.27340 | − | 2.20559i | ||||
\(335\) | −21.8946 | −1.19623 | ||||||||
\(336\) | −9.60831 | − | 7.06978i | −0.524176 | − | 0.385688i | ||||
\(337\) | 13.7032 | 0.746461 | 0.373230 | − | 0.927739i | \(-0.378250\pi\) | ||||
0.373230 | + | 0.927739i | \(0.378250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.22710 | + | 3.85746i | 0.120960 | + | 0.209508i | ||||
\(340\) | 11.8468 | + | 20.5192i | 0.642481 | + | 1.11281i | ||||
\(341\) | −14.1713 | + | 24.5455i | −0.767420 | + | 1.32921i | ||||
\(342\) | −26.0281 | −1.40744 | ||||||||
\(343\) | 6.04084 | − | 17.5074i | 0.326175 | − | 0.945309i | ||||
\(344\) | 23.4632 | 1.26505 | ||||||||
\(345\) | 0.829960 | − | 1.43753i | 0.0446835 | − | 0.0773942i | ||||
\(346\) | −16.5820 | − | 28.7209i | −0.891456 | − | 1.54405i | ||||
\(347\) | 13.1989 | + | 22.8612i | 0.708556 | + | 1.22725i | 0.965393 | + | 0.260800i | \(0.0839863\pi\) |
−0.256837 | + | 0.966455i | \(0.582680\pi\) | |||||||
\(348\) | 6.54727 | − | 11.3402i | 0.350971 | − | 0.607899i | ||||
\(349\) | −4.89024 | −0.261769 | −0.130884 | − | 0.991398i | \(-0.541782\pi\) | ||||
−0.130884 | + | 0.991398i | \(0.541782\pi\) | |||||||
\(350\) | −13.2465 | − | 9.74673i | −0.708053 | − | 0.520984i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.5345 | + | 19.9784i | −0.614792 | + | 1.06485i | ||||
\(353\) | 6.77886 | + | 11.7413i | 0.360802 | + | 0.624928i | 0.988093 | − | 0.153857i | \(-0.0491696\pi\) |
−0.627291 | + | 0.778785i | \(0.715836\pi\) | |||||||
\(354\) | −7.66612 | − | 13.2781i | −0.407450 | − | 0.705724i | ||||
\(355\) | 1.08903 | − | 1.88626i | 0.0577997 | − | 0.100112i | ||||
\(356\) | −8.27291 | −0.438464 | ||||||||
\(357\) | 3.92852 | − | 1.72077i | 0.207920 | − | 0.0910731i | ||||
\(358\) | −4.76360 | −0.251764 | ||||||||
\(359\) | 4.29284 | − | 7.43541i | 0.226567 | − | 0.392426i | −0.730221 | − | 0.683211i | \(-0.760583\pi\) |
0.956789 | + | 0.290785i | \(0.0939163\pi\) | |||||||
\(360\) | 15.3910 | + | 26.6581i | 0.811179 | + | 1.40500i | ||||
\(361\) | 2.72326 | + | 4.71683i | 0.143330 | + | 0.248254i | ||||
\(362\) | 4.27026 | − | 7.39632i | 0.224440 | − | 0.388742i | ||||
\(363\) | −1.90962 | −0.100229 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6751 | 0.768130 | ||||||||
\(366\) | −1.96287 | + | 3.39979i | −0.102601 | + | 0.177710i | ||||
\(367\) | 0.831612 | + | 1.44039i | 0.0434098 | + | 0.0751880i | 0.886914 | − | 0.461935i | \(-0.152845\pi\) |
−0.843504 | + | 0.537123i | \(0.819511\pi\) | |||||||
\(368\) | −8.63560 | − | 14.9573i | −0.450162 | − | 0.779703i | ||||
\(369\) | 10.5171 | − | 18.2162i | 0.547501 | − | 0.948299i | ||||
\(370\) | −24.8436 | −1.29156 | ||||||||
\(371\) | −2.12464 | + | 19.1054i | −0.110306 | + | 0.991903i | ||||
\(372\) | −25.5374 | −1.32405 | ||||||||
\(373\) | −6.98174 | + | 12.0927i | −0.361501 | + | 0.626138i | −0.988208 | − | 0.153117i | \(-0.951069\pi\) |
0.626707 | + | 0.779255i | \(0.284402\pi\) | |||||||
\(374\) | −10.9463 | − | 18.9596i | −0.566022 | − | 0.980378i | ||||
\(375\) | −3.09298 | − | 5.35719i | −0.159721 | − | 0.276644i | ||||
\(376\) | −3.68828 | + | 6.38828i | −0.190208 | + | 0.329450i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 18.6409 | − | 8.16509i | 0.958783 | − | 0.419967i | ||||
\(379\) | 31.5758 | 1.62194 | 0.810969 | − | 0.585089i | \(-0.198941\pi\) | ||||
0.810969 | + | 0.585089i | \(0.198941\pi\) | |||||||
\(380\) | −13.9493 | + | 24.1608i | −0.715582 | + | 1.23943i | ||||
\(381\) | 0.809874 | + | 1.40274i | 0.0414911 | + | 0.0718647i | ||||
\(382\) | 6.33707 | + | 10.9761i | 0.324233 | + | 0.561588i | ||||
\(383\) | −15.9541 | + | 27.6333i | −0.815217 | + | 1.41200i | 0.0939554 | + | 0.995576i | \(0.470049\pi\) |
−0.909172 | + | 0.416420i | \(0.863284\pi\) | |||||||
\(384\) | 2.55692 | 0.130482 | ||||||||
\(385\) | −9.29247 | − | 6.83739i | −0.473588 | − | 0.348466i | ||||
\(386\) | 7.81525 | 0.397786 | ||||||||
\(387\) | −4.58294 | + | 7.93788i | −0.232964 | + | 0.403505i | ||||
\(388\) | 36.3894 | + | 63.0283i | 1.84739 | + | 3.19978i | ||||
\(389\) | 12.7075 | + | 22.0100i | 0.644296 | + | 1.11595i | 0.984464 | + | 0.175589i | \(0.0561829\pi\) |
−0.340168 | + | 0.940365i | \(0.610484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.20956 | 0.314031 | ||||||||
\(392\) | −14.5607 | − | 46.7238i | −0.735428 | − | 2.35991i | ||||
\(393\) | 5.29312 | 0.267003 | ||||||||
\(394\) | −6.01838 | + | 10.4241i | −0.303202 | + | 0.525161i | ||||
\(395\) | −5.00203 | − | 8.66376i | −0.251679 | − | 0.435921i | ||||
\(396\) | −17.3644 | − | 30.0760i | −0.872593 | − | 1.51138i | ||||
\(397\) | 2.07949 | − | 3.60178i | 0.104366 | − | 0.180768i | −0.809113 | − | 0.587653i | \(-0.800052\pi\) |
0.913479 | + | 0.406885i | \(0.133385\pi\) | |||||||
\(398\) | −1.06319 | −0.0532930 | ||||||||
\(399\) | 4.06759 | + | 2.99293i | 0.203634 | + | 0.149834i | ||||
\(400\) | −20.8823 | −1.04412 | ||||||||
\(401\) | −9.80067 | + | 16.9753i | −0.489422 | + | 0.847704i | −0.999926 | − | 0.0121716i | \(-0.996126\pi\) |
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(402\) | 9.11409 | + | 15.7861i | 0.454569 | + | 0.787337i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.00691 | − | 5.20811i | 0.149599 | − | 0.259113i | ||||
\(405\) | −10.7250 | −0.532929 | ||||||||
\(406\) | 33.7050 | − | 14.7635i | 1.67275 | − | 0.732700i | ||||
\(407\) | 16.1039 | 0.798238 | ||||||||
\(408\) | 5.66669 | − | 9.81500i | 0.280543 | − | 0.485915i | ||||
\(409\) | −8.81685 | − | 15.2712i | −0.435965 | − | 0.755114i | 0.561409 | − | 0.827539i | \(-0.310260\pi\) |
−0.997374 | + | 0.0724249i | \(0.976926\pi\) | |||||||
\(410\) | −16.0690 | − | 27.8324i | −0.793594 | − | 1.37454i | ||||
\(411\) | −2.59041 | + | 4.48673i | −0.127776 | + | 0.221314i | ||||
\(412\) | −53.9063 | −2.65577 | ||||||||
\(413\) | 3.34065 | − | 30.0400i | 0.164382 | − | 1.47817i | ||||
\(414\) | 14.0412 | 0.690088 | ||||||||
\(415\) | 2.17363 | − | 3.76483i | 0.106699 | − | 0.184808i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.431416 | + | 0.747234i | 0.0211265 | + | 0.0365922i | ||||
\(418\) | 12.8890 | − | 22.3245i | 0.630424 | − | 1.09193i | ||||
\(419\) | 29.8911 | 1.46027 | 0.730137 | − | 0.683301i | \(-0.239456\pi\) | ||||
0.730137 | + | 0.683301i | \(0.239456\pi\) | |||||||
\(420\) | 1.14891 | − | 10.3313i | 0.0560611 | − | 0.504117i | ||||
\(421\) | 12.8528 | 0.626407 | 0.313203 | − | 0.949686i | \(-0.398598\pi\) | ||||
0.313203 | + | 0.949686i | \(0.398598\pi\) | |||||||
\(422\) | −9.72796 | + | 16.8493i | −0.473550 | + | 0.820212i | ||||
\(423\) | −1.44082 | − | 2.49557i | −0.0700551 | − | 0.121339i | ||||
\(424\) | 25.3987 | + | 43.9919i | 1.23347 | + | 2.13644i | ||||
\(425\) | 3.75393 | − | 6.50200i | 0.182093 | − | 0.315394i | ||||
\(426\) | −1.81332 | −0.0878559 | ||||||||
\(427\) | −7.08880 | + | 3.10504i | −0.343051 | + | 0.150263i | ||||
\(428\) | −24.1401 | −1.16685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.00223 | + | 12.1282i | 0.337677 | + | 0.584874i | ||||
\(431\) | −4.48530 | − | 7.76876i | −0.216049 | − | 0.374208i | 0.737547 | − | 0.675295i | \(-0.235984\pi\) |
−0.953597 | + | 0.301087i | \(0.902650\pi\) | |||||||
\(432\) | 12.9202 | − | 22.3785i | 0.621625 | − | 1.07669i | ||||
\(433\) | −3.45062 | −0.165826 | −0.0829132 | − | 0.996557i | \(-0.526422\pi\) | ||||
−0.0829132 | + | 0.996557i | \(0.526422\pi\) | |||||||
\(434\) | −57.8012 | − | 42.5300i | −2.77454 | − | 2.04151i | ||||
\(435\) | 4.49048 | 0.215302 | ||||||||
\(436\) | 4.06114 | − | 7.03410i | 0.194493 | − | 0.336872i | ||||
\(437\) | 3.65580 | + | 6.33204i | 0.174881 | + | 0.302902i | ||||
\(438\) | −6.10881 | − | 10.5808i | −0.291890 | − | 0.505569i | ||||
\(439\) | 19.2572 | − | 33.3544i | 0.919096 | − | 1.59192i | 0.118304 | − | 0.992977i | \(-0.462254\pi\) |
0.800792 | − | 0.598943i | \(-0.204412\pi\) | |||||||
\(440\) | −30.4864 | −1.45338 | ||||||||
\(441\) | 18.6513 | + | 4.20023i | 0.888155 | + | 0.200011i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.51997 | − | 13.0250i | 0.357284 | − | 0.618835i | −0.630222 | − | 0.776415i | \(-0.717036\pi\) |
0.987506 | + | 0.157580i | \(0.0503693\pi\) | |||||||
\(444\) | 7.25498 | + | 12.5660i | 0.344306 | + | 0.596356i | ||||
\(445\) | −1.41851 | − | 2.45693i | −0.0672437 | − | 0.116469i | ||||
\(446\) | 29.2246 | − | 50.6185i | 1.38382 | − | 2.39685i | ||||
\(447\) | −10.2646 | −0.485499 | ||||||||
\(448\) | −9.98191 | − | 7.34468i | −0.471601 | − | 0.347003i | ||||
\(449\) | −38.9235 | −1.83691 | −0.918456 | − | 0.395522i | \(-0.870564\pi\) | ||||
−0.918456 | + | 0.395522i | \(0.870564\pi\) | |||||||
\(450\) | 8.48850 | − | 14.7025i | 0.400152 | − | 0.693083i | ||||
\(451\) | 10.4161 | + | 18.0412i | 0.490476 | + | 0.849529i | ||||
\(452\) | 20.1928 | + | 34.9750i | 0.949790 | + | 1.64509i | ||||
\(453\) | 1.95330 | − | 3.38322i | 0.0917741 | − | 0.158957i | ||||
\(454\) | 35.3906 | 1.66097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3448 | 0.624927 | ||||||||
\(457\) | 6.96982 | − | 12.0721i | 0.326034 | − | 0.564708i | −0.655687 | − | 0.755033i | \(-0.727621\pi\) |
0.981721 | + | 0.190325i | \(0.0609541\pi\) | |||||||
\(458\) | −10.2649 | − | 17.7793i | −0.479648 | − | 0.830774i | ||||
\(459\) | 4.64524 | + | 8.04580i | 0.216821 | + | 0.375546i | ||||
\(460\) | 7.52512 | − | 13.0339i | 0.350861 | − | 0.607709i | ||||
\(461\) | 37.4635 | 1.74485 | 0.872424 | − | 0.488749i | \(-0.162547\pi\) | ||||
0.872424 | + | 0.488749i | \(0.162547\pi\) | |||||||
\(462\) | −1.06159 | + | 9.54609i | −0.0493895 | + | 0.444124i | ||||
\(463\) | 6.75275 | 0.313827 | 0.156913 | − | 0.987612i | \(-0.449846\pi\) | ||||
0.156913 | + | 0.987612i | \(0.449846\pi\) | |||||||
\(464\) | 23.3614 | − | 40.4631i | 1.08453 | − | 1.87845i | ||||
\(465\) | −4.37875 | − | 7.58421i | −0.203059 | − | 0.351709i | ||||
\(466\) | −8.50576 | − | 14.7324i | −0.394022 | − | 0.682466i | ||||
\(467\) | −2.52516 | + | 4.37371i | −0.116851 | + | 0.202391i | −0.918518 | − | 0.395379i | \(-0.870613\pi\) |
0.801667 | + | 0.597770i | \(0.203947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.97162 | + | 35.7140i | −0.183393 | + | 1.64912i | ||||
\(470\) | −4.40283 | −0.203087 | ||||||||
\(471\) | −3.63042 | + | 6.28807i | −0.167281 | + | 0.289739i | ||||
\(472\) | −39.9353 | − | 69.1699i | −1.83817 | − | 3.18380i | ||||
\(473\) | −4.53892 | − | 7.86163i | −0.208700 | − | 0.361478i | ||||
\(474\) | −4.16439 | + | 7.21294i | −0.191277 | + | 0.331301i | ||||
\(475\) | 8.84033 | 0.405622 | ||||||||
\(476\) | 35.6194 | − | 15.6020i | 1.63261 | − | 0.715117i | ||||
\(477\) | −19.8440 | −0.908593 | ||||||||
\(478\) | 12.1572 | − | 21.0568i | 0.556055 | − | 0.963116i | ||||
\(479\) | 4.72659 | + | 8.18670i | 0.215964 | + | 0.374060i | 0.953570 | − | 0.301171i | \(-0.0973774\pi\) |
−0.737607 | + | 0.675231i | \(0.764044\pi\) | |||||||
\(480\) | −3.56401 | − | 6.17304i | −0.162674 | − | 0.281759i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26.1082 | −1.18920 | ||||||||
\(483\) | −2.19432 | − | 1.61457i | −0.0998448 | − | 0.0734657i | ||||
\(484\) | −17.3142 | −0.787010 | ||||||||
\(485\) | −12.4789 | + | 21.6142i | −0.566639 | + | 0.981448i | ||||
\(486\) | 16.0023 | + | 27.7167i | 0.725877 | + | 1.25726i | ||||
\(487\) | 19.9998 | + | 34.6407i | 0.906277 | + | 1.56972i | 0.819194 | + | 0.573517i | \(0.194421\pi\) |
0.0870831 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(488\) | −10.2252 | + | 17.7106i | −0.462874 | + | 0.801721i | ||||
\(489\) | 3.71737 | 0.168105 | ||||||||
\(490\) | 19.8062 | − | 21.4705i | 0.894755 | − | 0.969936i | ||||
\(491\) | −6.76097 | −0.305118 | −0.152559 | − | 0.988294i | \(-0.548751\pi\) | ||||
−0.152559 | + | 0.988294i | \(0.548751\pi\) | |||||||
\(492\) | −9.38518 | + | 16.2556i | −0.423116 | + | 0.732859i | ||||
\(493\) | 8.39918 | + | 14.5478i | 0.378280 | + | 0.655200i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.95473 | − | 10.3139i | 0.267645 | − | 0.463575i | ||||
\(496\) | −91.1203 | −4.09142 | ||||||||
\(497\) | −2.87927 | − | 2.11856i | −0.129153 | − | 0.0950304i | ||||
\(498\) | −3.61927 | −0.162183 | ||||||||
\(499\) | 5.67877 | − | 9.83591i | 0.254217 | − | 0.440316i | −0.710466 | − | 0.703732i | \(-0.751516\pi\) |
0.964682 | + | 0.263416i | \(0.0848491\pi\) | |||||||
\(500\) | −28.0436 | − | 48.5729i | −1.25415 | − | 2.17225i | ||||
\(501\) | −4.66115 | − | 8.07335i | −0.208245 | − | 0.360691i | ||||
\(502\) | −13.3941 | + | 23.1993i | −0.597808 | + | 1.03543i | ||||
\(503\) | −13.9285 | −0.621040 | −0.310520 | − | 0.950567i | \(-0.600503\pi\) | ||||
−0.310520 | + | 0.950567i | \(0.600503\pi\) | |||||||
\(504\) | 46.2759 | − | 20.2698i | 2.06129 | − | 0.902888i | ||||
\(505\) | 2.06230 | 0.0917713 | ||||||||
\(506\) | −6.95317 | + | 12.0432i | −0.309106 | + | 0.535388i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34301 | + | 12.7185i | 0.325793 | + | 0.564290i | ||||
\(509\) | −9.90746 | + | 17.1602i | −0.439141 | + | 0.760614i | −0.997623 | − | 0.0689022i | \(-0.978050\pi\) |
0.558483 | + | 0.829516i | \(0.311384\pi\) | |||||||
\(510\) | 6.76454 | 0.299539 | ||||||||
\(511\) | 2.66202 | − | 23.9376i | 0.117761 | − | 1.05894i | ||||
\(512\) | 47.4335 | 2.09628 | ||||||||
\(513\) | −5.46966 | + | 9.47373i | −0.241491 | + | 0.418276i | ||||
\(514\) | 10.3370 | + | 17.9043i | 0.455947 | + | 0.789724i | ||||
\(515\) | −9.24299 | − | 16.0093i | −0.407295 | − | 0.705455i | ||||
\(516\) | 4.08967 | − | 7.08352i | 0.180038 | − | 0.311835i | ||||
\(517\) | 2.85396 | 0.125517 | ||||||||
\(518\) | −4.50655 | + | 40.5242i | −0.198007 | + | 1.78053i | ||||
\(519\) | −6.64237 | −0.291568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5476 | + | 26.9292i | 0.681151 | + | 1.17979i | 0.974630 | + | 0.223823i | \(0.0718537\pi\) |
−0.293479 | + | 0.955966i | \(0.594813\pi\) | |||||||
\(522\) | 18.9924 | + | 32.8959i | 0.831277 | + | 1.43981i | ||||
\(523\) | −11.3601 | + | 19.6763i | −0.496742 | + | 0.860383i | −0.999993 | − | 0.00375758i | \(-0.998804\pi\) |
0.503251 | + | 0.864140i | \(0.332137\pi\) | |||||||
\(524\) | 47.9919 | 2.09654 | ||||||||
\(525\) | −3.01717 | + | 1.32158i | −0.131680 | + | 0.0576786i | ||||
\(526\) | −13.0966 | −0.571040 | ||||||||
\(527\) | 16.3804 | − | 28.3716i | 0.713540 | − | 1.23589i | ||||
\(528\) | 6.09798 | + | 10.5620i | 0.265380 | + | 0.459652i | ||||
\(529\) | 9.52783 | + | 16.5027i | 0.414253 | + | 0.717508i | ||||
\(530\) | −15.1597 | + | 26.2574i | −0.658495 | + | 1.14055i | ||||
\(531\) | 31.2013 | 1.35402 | ||||||||
\(532\) | 36.8802 | + | 27.1364i | 1.59896 | + | 1.17651i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.18097 | + | 2.04549i | −0.0511054 | + | 0.0885171i | ||||
\(535\) | −4.13915 | − | 7.16922i | −0.178951 | − | 0.309952i | ||||
\(536\) | 47.4782 | + | 82.2346i | 2.05074 | + | 3.55199i | ||||
\(537\) | −0.477046 | + | 0.826267i | −0.0205860 | + | 0.0356561i | ||||
\(538\) | −35.9563 | −1.55018 | ||||||||
\(539\) | −12.8386 | + | 13.9174i | −0.552998 | + | 0.599463i | ||||
\(540\) | 22.5176 | 0.969002 | ||||||||
\(541\) | 1.04936 | − | 1.81754i | 0.0451155 | − | 0.0781423i | −0.842586 | − | 0.538562i | \(-0.818968\pi\) |
0.887701 | + | 0.460420i | \(0.152301\pi\) | |||||||
\(542\) | 10.7779 | + | 18.6679i | 0.462951 | + | 0.801855i | ||||
\(543\) | −0.855283 | − | 1.48139i | −0.0367037 | − | 0.0635727i | ||||
\(544\) | 13.3325 | − | 23.0926i | 0.571627 | − | 0.990087i | ||||
\(545\) | 2.78536 | 0.119312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3770 | 1.08504 | 0.542521 | − | 0.840042i | \(-0.317470\pi\) | ||||
0.542521 | + | 0.840042i | \(0.317470\pi\) | |||||||
\(548\) | −23.4869 | + | 40.6805i | −1.00331 | + | 1.73778i | ||||
\(549\) | −3.99447 | − | 6.91862i | −0.170480 | − | 0.295280i | ||||
\(550\) | 8.40696 | + | 14.5613i | 0.358474 | + | 0.620895i | ||||
\(551\) | −9.88983 | + | 17.1297i | −0.421321 | + | 0.729749i | ||||
\(552\) | −7.19902 | −0.306411 | ||||||||
\(553\) | −15.0395 | + | 6.58760i | −0.639543 | + | 0.280133i | ||||
\(554\) | 60.0855 | 2.55279 | ||||||||
\(555\) | −2.48794 | + | 4.30923i | −0.105607 | + | 0.182917i | ||||
\(556\) | 3.91158 | + | 6.77506i | 0.165888 | + | 0.287327i | ||||
\(557\) | −22.1252 | − | 38.3219i | −0.937473 | − | 1.62375i | −0.770164 | − | 0.637846i | \(-0.779826\pi\) |
−0.167309 | − | 0.985904i | \(-0.553508\pi\) | |||||||
\(558\) | 37.0397 | − | 64.1547i | 1.56802 | − | 2.71588i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.09944 | − | 36.8634i | 0.173233 | − | 1.55776i | ||||
\(561\) | −4.38484 | −0.185128 | ||||||||
\(562\) | −35.1526 | + | 60.8860i | −1.48282 | + | 2.56832i | ||||
\(563\) | 19.4453 | + | 33.6803i | 0.819523 | + | 1.41946i | 0.906034 | + | 0.423205i | \(0.139095\pi\) |
−0.0865108 | + | 0.996251i | \(0.527572\pi\) | |||||||
\(564\) | 1.28574 | + | 2.22697i | 0.0541396 | + | 0.0937725i | ||||
\(565\) | −6.92468 | + | 11.9939i | −0.291324 | + | 0.504587i | ||||
\(566\) | 41.8092 | 1.75737 | ||||||||
\(567\) | −1.94548 | + | 17.4943i | −0.0817026 | + | 0.734693i | ||||
\(568\) | −9.44618 | −0.396353 | ||||||||
\(569\) | −23.0789 | + | 39.9739i | −0.967520 | + | 1.67579i | −0.264832 | + | 0.964294i | \(0.585317\pi\) |
−0.702687 | + | 0.711499i | \(0.748017\pi\) | |||||||
\(570\) | 3.98254 | + | 6.89796i | 0.166810 | + | 0.288924i | ||||
\(571\) | −10.5684 | − | 18.3050i | −0.442274 | − | 0.766041i | 0.555584 | − | 0.831461i | \(-0.312495\pi\) |
−0.997858 | + | 0.0654194i | \(0.979161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.53848 | 0.106047 | ||||||||
\(574\) | −48.3144 | + | 21.1627i | −2.01660 | + | 0.883314i | ||||
\(575\) | −4.76904 | −0.198883 | ||||||||
\(576\) | 6.39653 | − | 11.0791i | 0.266522 | − | 0.461630i | ||||
\(577\) | 12.6652 | + | 21.9368i | 0.527259 | + | 0.913239i | 0.999495 | + | 0.0317671i | \(0.0101135\pi\) |
−0.472237 | + | 0.881472i | \(0.656553\pi\) | |||||||
\(578\) | −9.35045 | − | 16.1955i | −0.388927 | − | 0.673642i | ||||
\(579\) | 0.782650 | − | 1.35559i | 0.0325258 | − | 0.0563364i | ||||
\(580\) | 40.7146 | 1.69058 | ||||||||
\(581\) | −5.74681 | − | 4.22849i | −0.238418 | − | 0.175427i | ||||
\(582\) | 20.7785 | 0.861295 | ||||||||
\(583\) | 9.82667 | − | 17.0203i | 0.406979 | − | 0.704908i | ||||
\(584\) | −31.8227 | − | 55.1186i | −1.31683 | − | 2.28082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.9553 | − | 32.8315i | 0.783036 | − | 1.35626i | ||||
\(587\) | −3.56287 | −0.147056 | −0.0735278 | − | 0.997293i | \(-0.523426\pi\) | ||||
−0.0735278 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(588\) | −16.6438 | − | 3.74815i | −0.686379 | − | 0.154571i | ||||
\(589\) | 38.5749 | 1.58945 | ||||||||
\(590\) | 23.8361 | − | 41.2853i | 0.981316 | − | 1.69969i | ||||
\(591\) | 1.20541 | + | 2.08783i | 0.0495839 | + | 0.0858819i | ||||
\(592\) | 25.8866 | + | 44.8369i | 1.06393 | + | 1.84278i | ||||
\(593\) | 12.6768 | − | 21.9568i | 0.520573 | − | 0.901659i | −0.479141 | − | 0.877738i | \(-0.659052\pi\) |
0.999714 | − | 0.0239212i | \(-0.00761509\pi\) | |||||||
\(594\) | −20.8061 | −0.853685 | ||||||||
\(595\) | 10.7410 | + | 7.90320i | 0.440338 | + | 0.324000i | ||||
\(596\) | −93.0677 | −3.81220 | ||||||||
\(597\) | −0.106472 | + | 0.184415i | −0.00435762 | + | 0.00754762i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.46078 | − | 9.45835i | −0.223122 | − | 0.386458i | 0.732633 | − | 0.680624i | \(-0.238291\pi\) |
−0.955754 | + | 0.294166i | \(0.904958\pi\) | |||||||
\(600\) | −4.35211 | + | 7.53807i | −0.177674 | + | 0.307740i | ||||
\(601\) | 24.2564 | 0.989439 | 0.494720 | − | 0.869053i | \(-0.335271\pi\) | ||||
0.494720 | + | 0.869053i | \(0.335271\pi\) | |||||||
\(602\) | 21.0534 | − | 9.22183i | 0.858074 | − | 0.375854i | ||||
\(603\) | −37.0946 | −1.51061 | ||||||||
\(604\) | 17.7103 | − | 30.6751i | 0.720621 | − | 1.24815i | ||||
\(605\) | −2.96876 | − | 5.14205i | −0.120697 | − | 0.209054i | ||||
\(606\) | −0.858476 | − | 1.48692i | −0.0348732 | − | 0.0604022i | ||||
\(607\) | 4.92724 | − | 8.53422i | 0.199990 | − | 0.346393i | −0.748535 | − | 0.663096i | \(-0.769242\pi\) |
0.948525 | + | 0.316702i | \(0.102576\pi\) | |||||||
\(608\) | 31.3974 | 1.27333 | ||||||||
\(609\) | 0.814561 | − | 7.32476i | 0.0330077 | − | 0.296814i | ||||
\(610\) | −12.2062 | −0.494215 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 20.0712 | + | 34.7643i | 0.811328 | + | 1.40526i | ||||
\(613\) | 1.83844 | + | 3.18428i | 0.0742540 | + | 0.128612i | 0.900762 | − | 0.434314i | \(-0.143009\pi\) |
−0.826508 | + | 0.562926i | \(0.809676\pi\) | |||||||
\(614\) | 11.6208 | − | 20.1278i | 0.468977 | − | 0.812293i | ||||
\(615\) | −6.43688 | −0.259560 | ||||||||
\(616\) | −5.53015 | + | 49.7286i | −0.222816 | + | 2.00362i | ||||
\(617\) | 18.7468 | 0.754718 | 0.377359 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377359 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(618\) | −7.69517 | + | 13.3284i | −0.309545 | + | 0.536148i | ||||
\(619\) | −7.94725 | − | 13.7650i | −0.319427 | − | 0.553264i | 0.660942 | − | 0.750437i | \(-0.270157\pi\) |
−0.980369 | + | 0.197174i | \(0.936824\pi\) | |||||||
\(620\) | −39.7014 | − | 68.7649i | −1.59445 | − | 2.76167i | ||||
\(621\) | 2.95068 | − | 5.11073i | 0.118407 | − | 0.205087i | ||||
\(622\) | −31.5333 | −1.26437 | ||||||||
\(623\) | −4.26499 | + | 1.86815i | −0.170873 | + | 0.0748460i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.61371 | − | 6.25913i | 0.144549 | − | 0.250365i | ||||
\(626\) | 16.9864 | + | 29.4212i | 0.678911 | + | 1.17591i | ||||
\(627\) | −2.58152 | − | 4.47133i | −0.103096 | − | 0.178568i | ||||
\(628\) | −32.9165 | + | 57.0130i | −1.31351 | + | 2.27507i | ||||
\(629\) | −18.6141 | −0.742194 | ||||||||
\(630\) | 24.2878 | + | 17.8709i | 0.967649 | + | 0.711995i | ||||
\(631\) | 19.7451 | 0.786040 | 0.393020 | − | 0.919530i | \(-0.371430\pi\) | ||||
0.393020 | + | 0.919530i | \(0.371430\pi\) | |||||||
\(632\) | −21.6936 | + | 37.5745i | −0.862927 | + | 1.49463i | ||||
\(633\) | 1.94839 | + | 3.37472i | 0.0774417 | + | 0.134133i | ||||
\(634\) | 21.6349 | + | 37.4727i | 0.859231 | + | 1.48823i | ||||
\(635\) | −2.51812 | + | 4.36151i | −0.0999286 | + | 0.173081i | ||||
\(636\) | 17.7081 | 0.702173 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.6200 | −1.48939 | ||||||||
\(639\) | 1.84507 | − | 3.19575i | 0.0729898 | − | 0.126422i | ||||
\(640\) | 3.97508 | + | 6.88504i | 0.157129 | + | 0.272155i | ||||
\(641\) | 14.8893 | + | 25.7890i | 0.588092 | + | 1.01860i | 0.994482 | + | 0.104905i | \(0.0334539\pi\) |
−0.406390 | + | 0.913699i | \(0.633213\pi\) | |||||||
\(642\) | −3.44601 | + | 5.96867i | −0.136003 | + | 0.235565i | ||||
\(643\) | 11.5725 | 0.456373 | 0.228187 | − | 0.973617i | \(-0.426720\pi\) | ||||
0.228187 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(644\) | −19.8955 | − | 14.6391i | −0.783994 | − | 0.576862i | ||||
\(645\) | 2.80493 | 0.110444 | ||||||||
\(646\) | −14.8982 | + | 25.8044i | −0.586162 | + | 1.01526i | ||||
\(647\) | −12.7533 | − | 22.0893i | −0.501382 | − | 0.868420i | −0.999999 | − | 0.00159698i | \(-0.999492\pi\) |
0.498616 | − | 0.866823i | \(-0.333842\pi\) | |||||||
\(648\) | 23.2570 | + | 40.2823i | 0.913620 | + | 1.58244i | ||||
\(649\) | −15.4508 | + | 26.7616i | −0.606497 | + | 1.05048i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.1655 | + | 5.76675i | −0.515995 | + | 0.226017i | ||||
\(652\) | 33.7049 | 1.31999 | ||||||||
\(653\) | 22.4146 | − | 38.8233i | 0.877152 | − | 1.51927i | 0.0227004 | − | 0.999742i | \(-0.492774\pi\) |
0.854452 | − | 0.519530i | \(-0.173893\pi\) | |||||||
\(654\) | −1.15946 | − | 2.00825i | −0.0453386 | − | 0.0785287i | ||||
\(655\) | 8.22889 | + | 14.2529i | 0.321529 | + | 0.556905i | ||||
\(656\) | −33.4874 | + | 58.0018i | −1.30746 | + | 2.26459i | ||||
\(657\) | 24.8630 | 0.969999 | ||||||||
\(658\) | −0.798661 | + | 7.18179i | −0.0311350 | + | 0.279975i | ||||
\(659\) | 41.1734 | 1.60389 | 0.801944 | − | 0.597399i | \(-0.203799\pi\) | ||||
0.801944 | + | 0.597399i | \(0.203799\pi\) | |||||||
\(660\) | −5.31382 | + | 9.20380i | −0.206840 | + | 0.358258i | ||||
\(661\) | −10.9469 | − | 18.9606i | −0.425785 | − | 0.737481i | 0.570709 | − | 0.821153i | \(-0.306669\pi\) |
−0.996493 | + | 0.0836719i | \(0.973335\pi\) | |||||||
\(662\) | 5.13404 | + | 8.89241i | 0.199540 | + | 0.345613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.8539 | −0.731673 | ||||||||
\(665\) | −1.73546 | + | 15.6058i | −0.0672983 | + | 0.605165i | ||||
\(666\) | −42.0908 | −1.63098 | ||||||||
\(667\) | 5.33520 | − | 9.24084i | 0.206580 | − | 0.357807i | ||||
\(668\) | −42.2620 | − | 73.1999i | −1.63516 | − | 2.83219i | ||||
\(669\) | −5.85334 | − | 10.1383i | −0.226303 | − | 0.391968i | ||||
\(670\) | −28.3382 | + | 49.0832i | −1.09480 | + | 1.89625i | ||||
\(671\) | 7.91219 | 0.305447 | ||||||||
\(672\) | −10.7158 | + | 4.69375i | −0.413371 | + | 0.181065i | ||||
\(673\) | 35.6688 | 1.37493 | 0.687466 | − | 0.726217i | \(-0.258723\pi\) | ||||
0.687466 | + | 0.726217i | \(0.258723\pi\) | |||||||
\(674\) | 17.7361 | − | 30.7197i | 0.683167 | − | 1.18328i | ||||
\(675\) | −3.56762 | − | 6.17930i | −0.137318 | − | 0.237841i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.27766 | + | 2.21297i | −0.0491044 | + | 0.0850514i | −0.889533 | − | 0.456871i | \(-0.848970\pi\) |
0.840428 | + | 0.541923i | \(0.182303\pi\) | |||||||
\(678\) | 11.5302 | 0.442813 | ||||||||
\(679\) | 32.9928 | + | 24.2761i | 1.26615 | + | 0.931630i | ||||
\(680\) | 35.2386 | 1.35134 | ||||||||
\(681\) | 3.54416 | − | 6.13867i | 0.135813 | − | 0.235234i | ||||
\(682\) | 36.6839 | + | 63.5384i | 1.40470 | + | 2.43301i | ||||
\(683\) | 17.8700 | + | 30.9517i | 0.683775 | + | 1.18433i | 0.973820 | + | 0.227320i | \(0.0729962\pi\) |
−0.290045 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(684\) | −23.6333 | + | 40.9341i | −0.903642 | + | 1.56515i | ||||
\(685\) | −16.1086 | −0.615479 | ||||||||
\(686\) | −31.4293 | − | 36.2021i | −1.19997 | − | 1.38220i | ||||
\(687\) | −4.11188 | −0.156878 | ||||||||
\(688\) | 14.5924 | − | 25.2748i | 0.556330 | − | 0.963592i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.14843 | − | 3.72120i | −0.0817895 | − | 0.141664i | ||||
\(691\) | −13.0146 | + | 22.5419i | −0.495099 | + | 0.857536i | −0.999984 | − | 0.00565028i | \(-0.998201\pi\) |
0.504885 | + | 0.863186i | \(0.331535\pi\) | |||||||
\(692\) | −60.2254 | −2.28943 | ||||||||
\(693\) | −15.7436 | − | 11.5841i | −0.598050 | − | 0.440045i | ||||
\(694\) | 68.3335 | 2.59391 | ||||||||
\(695\) | −1.34139 | + | 2.32336i | −0.0508818 | + | 0.0881299i | ||||
\(696\) | −9.73755 | − | 16.8659i | −0.369101 | − | 0.639301i | ||||
\(697\) | −12.0398 | − | 20.8535i | −0.456040 | − | 0.789884i | ||||
\(698\) | −6.32944 | + | 10.9629i | −0.239573 | + | 0.414952i | ||||
\(699\) | −3.40721 | −0.128872 | ||||||||
\(700\) | −27.3562 | + | 11.9826i | −1.03397 | + | 0.452899i | ||||
\(701\) | 1.12731 | 0.0425779 | 0.0212890 | − | 0.999773i | \(-0.493223\pi\) | ||||
0.0212890 | + | 0.999773i | \(0.493223\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9588 | − | 18.9813i | −0.413321 | − | 0.715892i | ||||
\(704\) | 6.33509 | + | 10.9727i | 0.238763 | + | 0.413549i | ||||
\(705\) | −0.440917 | + | 0.763691i | −0.0166059 | + | 0.0287623i | ||||
\(706\) | 35.0955 | 1.32084 | ||||||||
\(707\) | 0.374096 | − | 3.36398i | 0.0140693 | − | 0.126515i | ||||
\(708\) | −27.8431 | −1.04641 | ||||||||
\(709\) | 3.02515 | − | 5.23972i | 0.113612 | − | 0.196782i | −0.803612 | − | 0.595153i | \(-0.797091\pi\) |
0.917224 | + | 0.398372i | \(0.130425\pi\) | |||||||
\(710\) | −2.81906 | − | 4.88276i | −0.105798 | − | 0.183247i | ||||
\(711\) | −8.47459 | − | 14.6784i | −0.317822 | − | 0.550484i | ||||
\(712\) | −6.15202 | + | 10.6556i | −0.230557 | + | 0.399336i | ||||
\(713\) | −20.8098 | −0.779332 | ||||||||
\(714\) | 1.22707 | − | 11.0341i | 0.0459219 | − | 0.412942i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.32530 | + | 7.49164i | −0.161644 | + | 0.279976i | ||||
\(717\) | −2.43493 | − | 4.21743i | −0.0909342 | − | 0.157503i | ||||
\(718\) | −11.1124 | − | 19.2473i | −0.414713 | − | 0.718304i | ||||
\(719\) | −23.5589 | + | 40.8052i | −0.878597 | + | 1.52178i | −0.0257170 | + | 0.999669i | \(0.508187\pi\) |
−0.852880 | + | 0.522106i | \(0.825146\pi\) | |||||||
\(720\) | 38.2884 | 1.42692 | ||||||||
\(721\) | −27.7907 | + | 12.1729i | −1.03498 | + | 0.453342i | ||||
\(722\) | 14.0989 | 0.524706 | ||||||||
\(723\) | −2.61458 | + | 4.52859i | −0.0972374 | + | 0.168420i | ||||
\(724\) | −7.75473 | − | 13.4316i | −0.288202 | − | 0.499181i | ||||
\(725\) | −6.45070 | − | 11.1729i | −0.239573 | − | 0.414953i | ||||
\(726\) | −2.47162 | + | 4.28097i | −0.0917303 | + | 0.158882i | ||||
\(727\) | −17.9215 | −0.664671 | −0.332335 | − | 0.943161i | \(-0.607837\pi\) | ||||
−0.332335 | + | 0.943161i | \(0.607837\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.5489 | −0.501810 | ||||||||
\(730\) | 18.9940 | − | 32.8985i | 0.702999 | − | 1.21763i | ||||
\(731\) | 5.24644 | + | 9.08711i | 0.194047 | + | 0.336099i | ||||
\(732\) | 3.56454 | + | 6.17396i | 0.131749 | + | 0.228196i | ||||
\(733\) | 22.6343 | − | 39.2037i | 0.836016 | − | 1.44802i | −0.0571848 | − | 0.998364i | \(-0.518212\pi\) |
0.893201 | − | 0.449658i | \(-0.148454\pi\) | |||||||
\(734\) | 4.30542 | 0.158916 | ||||||||
\(735\) | −1.74067 | − | 5.58562i | −0.0642056 | − | 0.206029i | ||||
\(736\) | −16.9378 | −0.624335 | ||||||||
\(737\) | 18.3691 | − | 31.8163i | 0.676635 | − | 1.17197i | ||||
\(738\) | −27.2247 | − | 47.1546i | −1.00215 | − | 1.73578i | ||||
\(739\) | 9.63066 | + | 16.6808i | 0.354270 | + | 0.613613i | 0.986993 | − | 0.160765i | \(-0.0513962\pi\) |
−0.632723 | + | 0.774378i | \(0.718063\pi\) | |||||||
\(740\) | −22.5577 | + | 39.0712i | −0.829239 | + | 1.43628i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.0804 | + | 29.4911i | 1.47140 | + | 1.08265i | ||||
\(743\) | −34.8853 | −1.27982 | −0.639908 | − | 0.768452i | \(-0.721028\pi\) | ||||
−0.639908 | + | 0.768452i | \(0.721028\pi\) | |||||||
\(744\) | −18.9905 | + | 32.8925i | −0.696225 | + | 1.20590i | ||||
\(745\) | −15.9577 | − | 27.6396i | −0.584647 | − | 1.01264i | ||||
\(746\) | 18.0729 | + | 31.3032i | 0.661697 | + | 1.14609i | ||||
\(747\) | 3.68263 | − | 6.37850i | 0.134740 | − | 0.233377i | ||||
\(748\) | −39.7567 | −1.45365 | ||||||||
\(749\) | −12.4451 | + | 5.45120i | −0.454733 | + | 0.199183i | ||||
\(750\) | −16.0130 | −0.584711 | ||||||||
\(751\) | 12.4834 | − | 21.6219i | 0.455526 | − | 0.788993i | −0.543193 | − | 0.839608i | \(-0.682785\pi\) |
0.998718 | + | 0.0506146i | \(0.0161180\pi\) | |||||||
\(752\) | 4.58767 | + | 7.94609i | 0.167295 | + | 0.289764i | ||||
\(753\) | 2.68268 | + | 4.64654i | 0.0977623 | + | 0.169329i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1467 | 0.442064 | ||||||||
\(756\) | 4.08462 | − | 36.7301i | 0.148556 | − | 1.33586i | ||||
\(757\) | −10.6049 | −0.385440 | −0.192720 | − | 0.981254i | \(-0.561731\pi\) | ||||
−0.192720 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(758\) | 40.8685 | − | 70.7863i | 1.48441 | − | 2.57108i | ||||
\(759\) | 1.39264 | + | 2.41212i | 0.0505495 | + | 0.0875543i | ||||
\(760\) | 20.7463 | + | 35.9337i | 0.752548 | + | 1.30345i | ||||
\(761\) | −16.3194 | + | 28.2660i | −0.591578 | + | 1.02464i | 0.402442 | + | 0.915446i | \(0.368162\pi\) |
−0.994020 | + | 0.109198i | \(0.965172\pi\) | |||||||
\(762\) | 4.19288 | 0.151892 | ||||||||
\(763\) | 0.505256 | − | 4.54340i | 0.0182915 | − | 0.164482i | ||||
\(764\) | 23.0160 | 0.832691 | ||||||||
\(765\) | −6.88296 | + | 11.9216i | −0.248854 | + | 0.431028i | ||||
\(766\) | 41.2988 | + | 71.5316i | 1.49219 | + | 2.58454i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.73794 | − | 9.93841i | 0.207050 | − | 0.358621i | ||||
\(769\) | 52.1752 | 1.88149 | 0.940744 | − | 0.339119i | \(-0.110129\pi\) | ||||
0.940744 | + | 0.339119i | \(0.110129\pi\) | |||||||
\(770\) | −27.3553 | + | 11.9822i | −0.985815 | + | 0.431807i | ||||
\(771\) | 4.14077 | 0.149126 | ||||||||
\(772\) | 7.09618 | − | 12.2909i | 0.255397 | − | 0.442360i | ||||
\(773\) | −17.8529 | − | 30.9221i | −0.642123 | − | 1.11219i | −0.984958 | − | 0.172794i | \(-0.944721\pi\) |
0.342835 | − | 0.939396i | \(-0.388613\pi\) | |||||||
\(774\) | 11.8634 | + | 20.5480i | 0.426421 | + | 0.738583i | ||||
\(775\) | −12.5804 | + | 21.7898i | −0.451900 | + | 0.782714i | ||||
\(776\) | 108.242 | 3.88565 | ||||||||
\(777\) | 6.57780 | + | 4.83994i | 0.235977 | + | 0.173632i | ||||
\(778\) | 65.7893 | 2.35866 | ||||||||
\(779\) | 14.1766 | − | 24.5545i | 0.507928 | − | 0.879757i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.82735 | + | 3.16506i | 0.0653876 | + | 0.113255i | ||||
\(782\) | 8.03703 | − | 13.9206i | 0.287404 | − | 0.497798i | ||||
\(783\) | 15.9646 | 0.570529 | ||||||||
\(784\) | −59.3870 | − | 13.3738i | −2.12096 | − | 0.477636i | ||||
\(785\) | −22.5760 | −0.805770 | ||||||||
\(786\) | 6.85089 | − | 11.8661i | 0.244363 | − | 0.423249i | ||||
\(787\) | −3.05310 | − | 5.28813i | −0.108831 | − | 0.188501i | 0.806466 | − | 0.591281i | \(-0.201378\pi\) |
−0.915297 | + | 0.402779i | \(0.868044\pi\) | |||||||
\(788\) | 10.9293 | + | 18.9301i | 0.389339 | + | 0.674356i | ||||
\(789\) | −1.31155 | + | 2.27167i | −0.0466923 | + | 0.0808735i | ||||
\(790\) | −25.8965 | −0.921356 | ||||||||
\(791\) | 18.3080 | + | 13.4710i | 0.650959 | + | 0.478975i | ||||
\(792\) | −51.6510 | −1.83534 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.38296 | − | 9.32356i | −0.191034 | − | 0.330881i | ||||
\(795\) | 3.03631 | + | 5.25904i | 0.107687 | + | 0.186519i | ||||
\(796\) | −0.965369 | + | 1.67207i | −0.0342166 | + | 0.0592649i | ||||
\(797\) | −46.2299 | −1.63755 | −0.818773 | − | 0.574117i | \(-0.805346\pi\) | ||||
−0.818773 | + | 0.574117i | \(0.805346\pi\) | |||||||
\(798\) | 11.9742 | − | 5.24495i | 0.423882 | − | 0.185669i | ||||
\(799\) | −3.29884 | −0.116704 | ||||||||
\(800\) | −10.2396 | + | 17.7355i | −0.362024 | + | 0.627044i | ||||
\(801\) | −2.40328 | − | 4.16260i | −0.0849157 | − | 0.147078i | ||||
\(802\) | 25.3700 | + | 43.9422i | 0.895847 | + | 1.55165i | ||||
\(803\) | −12.3121 | + | 21.3252i | −0.434484 | + | 0.752549i | ||||
\(804\) | 33.1020 | 1.16742 | ||||||||
\(805\) | 0.936218 | − | 8.41874i | 0.0329974 | − | 0.296722i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.60080 | + | 6.23678i | −0.126754 | + | 0.219545i | ||||
\(808\) | −4.47208 | − | 7.74586i | −0.157327 | − | 0.272498i | ||||
\(809\) | −19.6439 | − | 34.0243i | −0.690644 | − | 1.19623i | −0.971627 | − | 0.236518i | \(-0.923994\pi\) |
0.280983 | − | 0.959713i | \(-0.409339\pi\) | |||||||
\(810\) | −13.8814 | + | 24.0432i | −0.487741 | + | 0.844792i | ||||
\(811\) | 6.90664 | 0.242525 | 0.121262 | − | 0.992620i | \(-0.461306\pi\) | ||||
0.121262 | + | 0.992620i | \(0.461306\pi\) | |||||||
\(812\) | 7.38551 | − | 66.4126i | 0.259180 | − | 2.33062i | ||||
\(813\) | 4.31738 | 0.151417 | ||||||||
\(814\) | 20.8432 | − | 36.1015i | 0.730555 | − | 1.26536i | ||||
\(815\) | 5.77917 | + | 10.0098i | 0.202436 | + | 0.350629i | ||||
\(816\) | −7.04853 | − | 12.2084i | −0.246748 | − | 0.427380i | ||||
\(817\) | −6.17756 | + | 10.6998i | −0.216125 | + | 0.374340i | ||||
\(818\) | −45.6466 | −1.59600 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.3622 | −2.03810 | ||||||||
\(821\) | 0.955244 | − | 1.65453i | 0.0333382 | − | 0.0577435i | −0.848875 | − | 0.528594i | \(-0.822719\pi\) |
0.882213 | + | 0.470850i | \(0.156053\pi\) | |||||||
\(822\) | 6.70554 | + | 11.6143i | 0.233883 | + | 0.405097i | ||||
\(823\) | −0.789844 | − | 1.36805i | −0.0275322 | − | 0.0476872i | 0.851931 | − | 0.523654i | \(-0.175432\pi\) |
−0.879463 | + | 0.475967i | \(0.842098\pi\) | |||||||
\(824\) | −40.0866 | + | 69.4320i | −1.39648 | + | 2.41878i | ||||
\(825\) | 3.36763 | 0.117246 | ||||||||
\(826\) | −63.0198 | − | 46.3699i | −2.19274 | − | 1.61341i | ||||
\(827\) | −32.5050 | −1.13031 | −0.565155 | − | 0.824985i | \(-0.691184\pi\) | ||||
−0.565155 | + | 0.824985i | \(0.691184\pi\) | |||||||
\(828\) | 12.7493 | − | 22.0824i | 0.443069 | − | 0.767418i | ||||
\(829\) | 17.5269 | + | 30.3575i | 0.608735 | + | 1.05436i | 0.991449 | + | 0.130493i | \(0.0416561\pi\) |
−0.382714 | + | 0.923867i | \(0.625011\pi\) | |||||||
\(830\) | −5.62665 | − | 9.74564i | −0.195304 | − | 0.338276i | ||||
\(831\) | 6.01721 | − | 10.4221i | 0.208735 | − | 0.361539i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8399 | − | 16.0868i | 0.514172 | − | 0.557375i | ||||
\(834\) | 2.23353 | 0.0773407 | ||||||||
\(835\) | 14.4928 | − | 25.1023i | 0.501544 | − | 0.868700i | ||||
\(836\) | −23.4063 | − | 40.5409i | −0.809523 | − | 1.40214i | ||||
\(837\) | −15.5674 | − | 26.9635i | −0.538087 | − | 0.931994i | ||||
\(838\) | 38.6880 | − | 67.0096i | 1.33645 | − | 2.31481i | ||||
\(839\) | −5.35487 | −0.184871 | −0.0924354 | − | 0.995719i | \(-0.529465\pi\) | ||||
−0.0924354 | + | 0.995719i | \(0.529465\pi\) | |||||||
\(840\) | −12.4525 | − | 9.16254i | −0.429653 | − | 0.316138i | ||||
\(841\) | −0.133978 | −0.00461993 | ||||||||
\(842\) | 16.6354 | − | 28.8133i | 0.573293 | − | 0.992973i | ||||
\(843\) | 7.04064 | + | 12.1947i | 0.242492 | + | 0.420009i | ||||
\(844\) | 17.6658 | + | 30.5981i | 0.608082 | + | 1.05323i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.45942 | −0.256460 | ||||||||
\(847\) | −8.92611 | + | 3.90982i | −0.306705 | + | 0.134343i | ||||
\(848\) | 63.1846 | 2.16977 | ||||||||
\(849\) | 4.18694 | − | 7.25199i | 0.143695 | − | 0.248888i | ||||
\(850\) | −9.71744 | − | 16.8311i | −0.333305 | − | 0.577302i | ||||
\(851\) | 5.91190 | + | 10.2397i | 0.202657 | + | 0.351013i | ||||
\(852\) | −1.64648 | + | 2.85179i | −0.0564076 | + | 0.0977008i | ||||
\(853\) | −49.6270 | −1.69920 | −0.849598 | − | 0.527431i | \(-0.823155\pi\) | ||||
−0.849598 | + | 0.527431i | \(0.823155\pi\) | |||||||
\(854\) | −2.21417 | + | 19.9105i | −0.0757675 | + | 0.681322i | ||||
\(855\) | −16.2090 | −0.554337 | ||||||||
\(856\) | −17.9514 | + | 31.0927i | −0.613566 | + | 1.06273i | ||||
\(857\) | −2.94196 | − | 5.09563i | −0.100496 | − | 0.174063i | 0.811393 | − | 0.584500i | \(-0.198709\pi\) |
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6931 | + | 37.5735i | −0.740159 | + | 1.28199i | 0.212264 | + | 0.977212i | \(0.431916\pi\) |
−0.952423 | + | 0.304780i | \(0.901417\pi\) | |||||||
\(860\) | 25.4318 | 0.867219 | ||||||||
\(861\) | −1.16763 | + | 10.4997i | −0.0397928 | + | 0.357828i | ||||
\(862\) | −23.2213 | −0.790920 | ||||||||
\(863\) | −15.5636 | + | 26.9570i | −0.529792 | + | 0.917626i | 0.469604 | + | 0.882877i | \(0.344397\pi\) |
−0.999396 | + | 0.0347490i | \(0.988937\pi\) | |||||||
\(864\) | −12.6708 | − | 21.9465i | −0.431069 | − | 0.746634i | ||||
\(865\) | −10.3265 | − | 17.8860i | −0.351111 | − | 0.608142i | ||||
\(866\) | −4.46614 | + | 7.73558i | −0.151766 | + | 0.262866i | ||||
\(867\) | −3.74557 | −0.127206 | ||||||||
\(868\) | −119.369 | + | 52.2862i | −4.05166 | + | 1.77471i | ||||
\(869\) | 16.7864 | 0.569439 | ||||||||
\(870\) | 5.81203 | − | 10.0667i | 0.197046 | − | 0.341294i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.04001 | − | 10.4616i | −0.204540 | − | 0.354274i | ||||
\(873\) | −21.1422 | + | 36.6194i | −0.715556 | + | 1.23938i | ||||
\(874\) | 18.9268 | 0.640209 | ||||||||
\(875\) | −25.4260 | − | 18.7084i | −0.859555 | − | 0.632460i | ||||
\(876\) | −22.1870 | −0.749629 | ||||||||
\(877\) | 14.9553 | − | 25.9033i | 0.505004 | − | 0.874693i | −0.494979 | − | 0.868905i | \(-0.664824\pi\) |
0.999983 | − | 0.00578807i | \(-0.00184241\pi\) | |||||||
\(878\) | −49.8492 | − | 86.3413i | −1.68233 | − | 2.91388i | ||||
\(879\) | −3.79652 | − | 6.57576i | −0.128053 | − | 0.221795i | ||||
\(880\) | −18.9603 | + | 32.8402i | −0.639152 | + | 1.10704i | ||||
\(881\) | 14.5695 | 0.490860 | 0.245430 | − | 0.969414i | \(-0.421071\pi\) | ||||
0.245430 | + | 0.969414i | \(0.421071\pi\) | |||||||
\(882\) | 33.5564 | − | 36.3759i | 1.12990 | − | 1.22484i | ||||
\(883\) | −48.9296 | −1.64661 | −0.823307 | − | 0.567597i | \(-0.807873\pi\) | ||||
−0.823307 | + | 0.567597i | \(0.807873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.77408 | − | 8.26896i | −0.160479 | − | 0.277958i | ||||
\(886\) | −19.4662 | − | 33.7164i | −0.653980 | − | 1.13273i | ||||
\(887\) | −27.2951 | + | 47.2765i | −0.916480 | + | 1.58739i | −0.111761 | + | 0.993735i | \(0.535649\pi\) |
−0.804719 | + | 0.593655i | \(0.797684\pi\) | |||||||
\(888\) | 21.5802 | 0.724184 | ||||||||
\(889\) | 6.65761 | + | 4.89866i | 0.223289 | + | 0.164296i | ||||
\(890\) | −7.34389 | −0.246168 | ||||||||
\(891\) | 8.99803 | − | 15.5851i | 0.301445 | − | 0.522119i | ||||
\(892\) | −53.0713 | − | 91.9222i | −1.77696 | − | 3.07778i | ||||
\(893\) | −1.94215 | − | 3.36390i | −0.0649916 | − | 0.112569i | ||||
\(894\) | −13.2855 | + | 23.0111i | −0.444333 | + | 0.769607i | ||||
\(895\) | −2.96653 | −0.0991603 | ||||||||
\(896\) | 11.9518 | − | 5.23512i | 0.399281 | − | 0.174893i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50.3787 | + | 87.2584i | −1.68116 | + | 2.91185i | ||||
\(899\) | −28.1477 | − | 48.7533i | −0.938780 | − | 1.62601i | ||||
\(900\) | −15.4150 | − | 26.6995i | −0.513832 | − | 0.889983i | ||||
\(901\) | −11.3585 | + | 19.6734i | −0.378405 | + | 0.655417i | ||||
\(902\) | 53.9263 | 1.79555 | ||||||||
\(903\) | 0.508806 | − | 4.57532i | 0.0169320 | − | 0.152257i | ||||
\(904\) | 60.0643 | 1.99771 | ||||||||
\(905\) | 2.65931 | − | 4.60606i | 0.0883985 | − | 0.153111i | ||||
\(906\) | −5.05632 | − | 8.75780i | −0.167985 | − | 0.290958i | ||||
\(907\) | −11.3628 | − | 19.6809i | −0.377295 | − | 0.653494i | 0.613373 | − | 0.789793i | \(-0.289812\pi\) |
−0.990668 | + | 0.136300i | \(0.956479\pi\) | |||||||
\(908\) | 32.1344 | − | 55.6584i | 1.06642 | − | 1.84709i | ||||
\(909\) | 3.49402 | 0.115889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2359 | −1.39934 | −0.699669 | − | 0.714467i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714467i | \(0.746669\pi\) | |||||||
\(912\) | 8.29948 | − | 14.3751i | 0.274823 | − | 0.476008i | ||||
\(913\) | 3.64725 | + | 6.31722i | 0.120706 | + | 0.209070i | ||||
\(914\) | −18.0421 | − | 31.2498i | −0.596779 | − | 1.03365i | ||||
\(915\) | −1.22238 | + | 2.11722i | −0.0404106 | + | 0.0699933i | ||||
\(916\) | −37.2818 | −1.23182 | ||||||||
\(917\) | 24.7416 | − | 10.8373i | 0.817039 | − | 0.357880i | ||||
\(918\) | 24.0494 | 0.793747 | ||||||||
\(919\) | −15.3470 | + | 26.5818i | −0.506251 | + | 0.876853i | 0.493722 | + | 0.869620i | \(0.335636\pi\) |
−0.999974 | + | 0.00723365i | \(0.997697\pi\) | |||||||
\(920\) | −11.1919 | − | 19.3849i | −0.368985 | − | 0.639101i | ||||
\(921\) | −2.32751 | − | 4.03136i | −0.0766940 | − | 0.132838i | ||||
\(922\) | 48.4890 | − | 83.9854i | 1.59690 | − | 2.76591i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 14.0491 | + | 10.3373i | 0.462182 | + | 0.340073i | ||||
\(925\) | 14.2959 | 0.470048 | ||||||||
\(926\) | 8.74009 | − | 15.1383i | 0.287217 | − | 0.497474i | ||||
\(927\) | −15.6598 | − | 27.1235i | −0.514334 | − | 0.890853i | ||||
\(928\) | −22.9104 | − | 39.6819i | −0.752070 | − | 1.30262i | ||||
\(929\) | −18.7125 | + | 32.4110i | −0.613936 | + | 1.06337i | 0.376634 | + | 0.926362i | \(0.377082\pi\) |
−0.990570 | + | 0.137007i | \(0.956252\pi\) | |||||||
\(930\) | −22.6696 | −0.743367 | ||||||||
\(931\) | 25.1409 | + | 5.66168i | 0.823960 | + | 0.185554i | ||||
\(932\) | −30.8926 | −1.01192 | ||||||||
\(933\) | −3.15787 | + | 5.46960i | −0.103384 | + | 0.179067i | ||||
\(934\) | 6.53663 | + | 11.3218i | 0.213885 | + | 0.370460i | ||||
\(935\) | −6.81684 | − | 11.8071i | −0.222935 | − | 0.386134i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.3386 | 1.44848 | 0.724239 | − | 0.689549i | \(-0.242191\pi\) | ||||
0.724239 | + | 0.689549i | \(0.242191\pi\) | |||||||
\(938\) | 74.9229 | + | 55.1282i | 2.44632 | + | 1.80000i | ||||
\(939\) | 6.80433 | 0.222051 | ||||||||
\(940\) | −3.99773 | + | 6.92427i | −0.130392 | + | 0.225845i | ||||
\(941\) | −13.7526 | − | 23.8202i | −0.448323 | − | 0.776518i | 0.549954 | − | 0.835195i | \(-0.314645\pi\) |
−0.998277 | + | 0.0586770i | \(0.981312\pi\) | |||||||
\(942\) | 9.39771 | + | 16.2773i | 0.306194 | + | 0.530343i | ||||
\(943\) | −7.64774 | + | 13.2463i | −0.249045 | + | 0.431358i | ||||
\(944\) | −99.3472 | −3.23348 | ||||||||
\(945\) | 11.6086 | − | 5.08482i | 0.377629 | − | 0.165409i | ||||
\(946\) | −23.4989 | −0.764014 | ||||||||
\(947\) | 2.54165 | − | 4.40226i | 0.0825925 | − | 0.143054i | −0.821770 | − | 0.569819i | \(-0.807013\pi\) |
0.904363 | + | 0.426765i | \(0.140347\pi\) | |||||||
\(948\) | 7.56246 | + | 13.0986i | 0.245617 | + | 0.425422i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 11.4420 | − | 19.8182i | 0.371229 | − | 0.642987i | ||||
\(951\) | 8.66642 | 0.281028 | ||||||||
\(952\) | 6.39219 | − | 57.4804i | 0.207172 | − | 1.86295i | ||||
\(953\) | 9.81437 | 0.317919 | 0.158959 | − | 0.987285i | \(-0.449186\pi\) | ||||
0.158959 | + | 0.987285i | \(0.449186\pi\) | |||||||
\(954\) | −25.6840 | + | 44.4861i | −0.831552 | + | 1.44029i | ||||
\(955\) | 3.94642 | + | 6.83540i | 0.127703 | + | 0.221188i | ||||
\(956\) | −22.0772 | − | 38.2388i | −0.714027 | − | 1.23673i | ||||
\(957\) | −3.76742 | + | 6.52536i | −0.121783 | + | 0.210935i | ||||
\(958\) | 24.4705 | 0.790607 | ||||||||
\(959\) | −2.92206 | + | 26.2760i | −0.0943582 | + | 0.848496i | ||||
\(960\) | −3.91491 | −0.126353 | ||||||||
\(961\) | −39.3947 | + | 68.2336i | −1.27080 | + | 2.20108i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.01268 | − | 12.1463i | −0.225981 | − | 0.391410i | ||||
\(964\) | −23.7060 | + | 41.0601i | −0.763520 | + | 1.32246i | ||||
\(965\) | 4.86695 | 0.156673 | ||||||||
\(966\) | −6.45965 | + | 2.82946i | −0.207836 | + | 0.0910363i | ||||
\(967\) | 2.69619 | 0.0867036 | 0.0433518 | − | 0.999060i | \(-0.486196\pi\) | ||||
0.0433518 | + | 0.999060i | \(0.486196\pi\) | |||||||
\(968\) | −12.8754 | + | 22.3009i | −0.413832 | + | 0.716779i | ||||
\(969\) | 2.98393 | + | 5.16832i | 0.0958577 | + | 0.166030i | ||||
\(970\) | 32.3030 | + | 55.9504i | 1.03719 | + | 1.79646i | ||||
\(971\) | −12.4620 | + | 21.5848i | −0.399925 | + | 0.692691i | −0.993716 | − | 0.111929i | \(-0.964297\pi\) |
0.593791 | + | 0.804619i | \(0.297631\pi\) | |||||||
\(972\) | 58.1196 | 1.86419 | ||||||||
\(973\) | 3.54648 | + | 2.60949i | 0.113695 | + | 0.0836565i | ||||
\(974\) | 103.543 | 3.31773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7187 | + | 22.0294i | 0.407115 | + | 0.705144i | ||||
\(977\) | −14.1565 | − | 24.5197i | −0.452906 | − | 0.784456i | 0.545659 | − | 0.838007i | \(-0.316279\pi\) |
−0.998565 | + | 0.0535514i | \(0.982946\pi\) | |||||||
\(978\) | 4.81140 | − | 8.33359i | 0.153852 | − | 0.266479i | ||||
\(979\) | 4.76039 | 0.152143 | ||||||||
\(980\) | −15.7824 | − | 50.6440i | −0.504150 | − | 1.61776i | ||||
\(981\) | 4.71904 | 0.150667 | ||||||||
\(982\) | −8.75073 | + | 15.1567i | −0.279247 | + | 0.483670i | ||||
\(983\) | 18.9258 | + | 32.7805i | 0.603641 | + | 1.04554i | 0.992265 | + | 0.124140i | \(0.0396172\pi\) |
−0.388624 | + | 0.921396i | \(0.627049\pi\) | |||||||
\(984\) | 13.9583 | + | 24.1764i | 0.444974 | + | 0.770717i | ||||
\(985\) | −3.74795 | + | 6.49165i | −0.119420 | + | 0.206841i | ||||
\(986\) | 43.4842 | 1.38482 | ||||||||
\(987\) | 1.16573 | + | 0.857744i | 0.0371057 | + | 0.0273023i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.33257 | − | 5.77218i | 0.105970 | − | 0.183545i | ||||
\(990\) | −15.4144 | − | 26.6986i | −0.489903 | − | 0.848536i | ||||
\(991\) | −29.2079 | − | 50.5896i | −0.927820 | − | 1.60703i | −0.786962 | − | 0.617001i | \(-0.788347\pi\) |
−0.140858 | − | 0.990030i | \(-0.544986\pi\) | |||||||
\(992\) | −44.6806 | + | 77.3891i | −1.41861 | + | 2.45711i | ||||
\(993\) | 2.05657 | 0.0652633 | ||||||||
\(994\) | −8.47601 | + | 3.71267i | −0.268843 | + | 0.117759i | ||||
\(995\) | −0.662104 | −0.0209901 | ||||||||
\(996\) | −3.28626 | + | 5.69197i | −0.104129 | + | 0.180357i | ||||
\(997\) | −14.0294 | − | 24.2997i | −0.444316 | − | 0.769578i | 0.553688 | − | 0.832724i | \(-0.313220\pi\) |
−0.998004 | + | 0.0631462i | \(0.979887\pi\) | |||||||
\(998\) | −14.7001 | − | 25.4613i | −0.465322 | − | 0.805962i | ||||
\(999\) | −8.84514 | + | 15.3202i | −0.279848 | + | 0.484711i |
(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 | 1183.2.e.j.170.12 | 24 | ||
7.2 | even | 3 | 8281.2.a.cp.1.1 | 12 | |||
7.4 | even | 3 | inner | 1183.2.e.j.508.12 | 24 | ||
7.5 | odd | 6 | 8281.2.a.co.1.1 | 12 | |||
13.6 | odd | 12 | 91.2.k.b.23.6 | yes | 12 | ||
13.11 | odd | 12 | 91.2.u.b.30.1 | yes | 12 | ||
13.12 | even | 2 | inner | 1183.2.e.j.170.1 | 24 | ||
39.11 | even | 12 | 819.2.do.e.667.6 | 12 | |||
39.32 | even | 12 | 819.2.bm.f.478.1 | 12 | |||
91.6 | even | 12 | 637.2.k.i.569.6 | 12 | |||
91.11 | odd | 12 | 91.2.k.b.4.1 | ✓ | 12 | ||
91.12 | odd | 6 | 8281.2.a.co.1.12 | 12 | |||
91.19 | even | 12 | 637.2.q.i.491.6 | 12 | |||
91.24 | even | 12 | 637.2.k.i.459.1 | 12 | |||
91.25 | even | 6 | inner | 1183.2.e.j.508.1 | 24 | ||
91.32 | odd | 12 | 91.2.u.b.88.1 | yes | 12 | ||
91.37 | odd | 12 | 637.2.q.g.589.6 | 12 | |||
91.45 | even | 12 | 637.2.u.g.361.1 | 12 | |||
91.51 | even | 6 | 8281.2.a.cp.1.12 | 12 | |||
91.58 | odd | 12 | 637.2.q.g.491.6 | 12 | |||
91.76 | even | 12 | 637.2.u.g.30.1 | 12 | |||
91.89 | even | 12 | 637.2.q.i.589.6 | 12 | |||
273.11 | even | 12 | 819.2.bm.f.550.6 | 12 | |||
273.32 | even | 12 | 819.2.do.e.361.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.1 | ✓ | 12 | 91.11 | odd | 12 | ||
91.2.k.b.23.6 | yes | 12 | 13.6 | odd | 12 | ||
91.2.u.b.30.1 | yes | 12 | 13.11 | odd | 12 | ||
91.2.u.b.88.1 | yes | 12 | 91.32 | odd | 12 | ||
637.2.k.i.459.1 | 12 | 91.24 | even | 12 | |||
637.2.k.i.569.6 | 12 | 91.6 | even | 12 | |||
637.2.q.g.491.6 | 12 | 91.58 | odd | 12 | |||
637.2.q.g.589.6 | 12 | 91.37 | odd | 12 | |||
637.2.q.i.491.6 | 12 | 91.19 | even | 12 | |||
637.2.q.i.589.6 | 12 | 91.89 | even | 12 | |||
637.2.u.g.30.1 | 12 | 91.76 | even | 12 | |||
637.2.u.g.361.1 | 12 | 91.45 | even | 12 | |||
819.2.bm.f.478.1 | 12 | 39.32 | even | 12 | |||
819.2.bm.f.550.6 | 12 | 273.11 | even | 12 | |||
819.2.do.e.361.6 | 12 | 273.32 | even | 12 | |||
819.2.do.e.667.6 | 12 | 39.11 | even | 12 | |||
1183.2.e.j.170.1 | 24 | 13.12 | even | 2 | inner | ||
1183.2.e.j.170.12 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.e.j.508.1 | 24 | 91.25 | even | 6 | inner | ||
1183.2.e.j.508.12 | 24 | 7.4 | even | 3 | inner | ||
8281.2.a.co.1.1 | 12 | 7.5 | odd | 6 | |||
8281.2.a.co.1.12 | 12 | 91.12 | odd | 6 | |||
8281.2.a.cp.1.1 | 12 | 7.2 | even | 3 | |||
8281.2.a.cp.1.12 | 12 | 91.51 | even | 6 |