Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(37,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.v (of order \(12\), 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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 88.15 | ||
Character | \(\chi\) | \(=\) | 105.88 |
Dual form | 105.3.v.a.37.15 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.41166 | + | 0.914152i | 1.70583 | + | 0.457076i | 0.974397 | − | 0.224836i | \(-0.0721845\pi\) |
0.731435 | + | 0.681912i | \(0.238851\pi\) | |||||||
\(3\) | 1.67303 | − | 0.448288i | 0.557678 | − | 0.149429i | ||||
\(4\) | 7.33966 | + | 4.23756i | 1.83492 | + | 1.05939i | ||||
\(5\) | −4.98672 | − | 0.364163i | −0.997344 | − | 0.0728326i | ||||
\(6\) | 6.11763 | 1.01960 | ||||||||
\(7\) | −6.35750 | + | 2.92953i | −0.908215 | + | 0.418505i | ||||
\(8\) | 11.1766 | + | 11.1766i | 1.39708 | + | 1.39708i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.288675 | − | 0.166667i | ||||
\(10\) | −16.6801 | − | 5.80102i | −1.66801 | − | 0.580102i | ||||
\(11\) | 8.72135 | − | 15.1058i | 0.792850 | − | 1.37326i | −0.131345 | − | 0.991337i | \(-0.541930\pi\) |
0.924195 | − | 0.381920i | \(-0.124737\pi\) | |||||||
\(12\) | 14.1791 | + | 3.79929i | 1.18160 | + | 0.316608i | ||||
\(13\) | −8.72144 | − | 8.72144i | −0.670880 | − | 0.670880i | 0.287039 | − | 0.957919i | \(-0.407329\pi\) |
−0.957919 | + | 0.287039i | \(0.907329\pi\) | |||||||
\(14\) | −24.3677 | + | 4.18286i | −1.74055 | + | 0.298776i | ||||
\(15\) | −8.50620 | + | 1.62623i | −0.567080 | + | 0.108415i | ||||
\(16\) | 10.9636 | + | 18.9894i | 0.685222 | + | 1.18684i | ||||
\(17\) | 3.02215 | + | 11.2788i | 0.177774 | + | 0.663461i | 0.996063 | + | 0.0886535i | \(0.0282564\pi\) |
−0.818289 | + | 0.574807i | \(0.805077\pi\) | |||||||
\(18\) | 10.2350 | − | 2.74246i | 0.568610 | − | 0.152359i | ||||
\(19\) | −3.12903 | + | 1.80655i | −0.164686 | + | 0.0950814i | −0.580078 | − | 0.814561i | \(-0.696978\pi\) |
0.415392 | + | 0.909643i | \(0.363644\pi\) | |||||||
\(20\) | −35.0577 | − | 23.8044i | −1.75288 | − | 1.19022i | ||||
\(21\) | −9.32303 | + | 7.75120i | −0.443954 | + | 0.369105i | ||||
\(22\) | 43.5633 | − | 43.5633i | 1.98015 | − | 1.98015i | ||||
\(23\) | −6.21349 | + | 23.1890i | −0.270152 | + | 1.00822i | 0.688870 | + | 0.724885i | \(0.258107\pi\) |
−0.959021 | + | 0.283334i | \(0.908559\pi\) | |||||||
\(24\) | 23.7092 | + | 13.6885i | 0.987885 | + | 0.570356i | ||||
\(25\) | 24.7348 | + | 3.63196i | 0.989391 | + | 0.145278i | ||||
\(26\) | −21.7819 | − | 37.7273i | −0.837765 | − | 1.45105i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −59.0760 | − | 5.43848i | −2.10986 | − | 0.194231i | ||||
\(29\) | 46.5831i | 1.60631i | 0.595767 | + | 0.803157i | \(0.296848\pi\) | ||||
−0.595767 | + | 0.803157i | \(0.703152\pi\) | |||||||
\(30\) | −30.5069 | − | 2.22781i | −1.01690 | − | 0.0742605i | ||||
\(31\) | −1.10507 | + | 1.91403i | −0.0356474 | + | 0.0617430i | −0.883299 | − | 0.468811i | \(-0.844683\pi\) |
0.847651 | + | 0.530554i | \(0.178016\pi\) | |||||||
\(32\) | 3.68097 | + | 13.7376i | 0.115030 | + | 0.429300i | ||||
\(33\) | 7.81935 | − | 29.1822i | 0.236950 | − | 0.884310i | ||||
\(34\) | 41.2423i | 1.21301i | ||||||||
\(35\) | 32.7699 | − | 12.2936i | 0.936283 | − | 0.351246i | ||||
\(36\) | 25.4253 | 0.706260 | ||||||||
\(37\) | −29.3791 | − | 7.87211i | −0.794030 | − | 0.212760i | −0.161069 | − | 0.986943i | \(-0.551494\pi\) |
−0.632961 | + | 0.774183i | \(0.718161\pi\) | |||||||
\(38\) | −12.3266 | + | 3.30292i | −0.324386 | + | 0.0869188i | ||||
\(39\) | −18.5010 | − | 10.6815i | −0.474384 | − | 0.273886i | ||||
\(40\) | −51.6647 | − | 59.8049i | −1.29162 | − | 1.49512i | ||||
\(41\) | 29.9435 | 0.730329 | 0.365165 | − | 0.930943i | \(-0.381013\pi\) | ||||
0.365165 | + | 0.930943i | \(0.381013\pi\) | |||||||
\(42\) | −38.8928 | + | 17.9218i | −0.926019 | + | 0.426709i | ||||
\(43\) | −19.6771 | − | 19.6771i | −0.457608 | − | 0.457608i | 0.440262 | − | 0.897869i | \(-0.354886\pi\) |
−0.897869 | + | 0.440262i | \(0.854886\pi\) | |||||||
\(44\) | 128.024 | − | 73.9145i | 2.90963 | − | 1.67987i | ||||
\(45\) | −13.5021 | + | 6.53396i | −0.300047 | + | 0.145199i | ||||
\(46\) | −42.3966 | + | 73.4331i | −0.921666 | + | 1.59637i | ||||
\(47\) | 79.1503 | + | 21.2083i | 1.68405 | + | 0.451240i | 0.968844 | − | 0.247674i | \(-0.0796661\pi\) |
0.715206 | + | 0.698913i | \(0.246333\pi\) | |||||||
\(48\) | 26.8551 | + | 26.8551i | 0.559482 | + | 0.559482i | ||||
\(49\) | 31.8357 | − | 37.2490i | 0.649707 | − | 0.760185i | ||||
\(50\) | 81.0665 | + | 35.0024i | 1.62133 | + | 0.700047i | ||||
\(51\) | 10.1123 | + | 17.5151i | 0.198281 | + | 0.343433i | ||||
\(52\) | −27.0549 | − | 100.970i | −0.520286 | − | 1.94173i | ||||
\(53\) | 1.63190 | − | 0.437265i | 0.0307905 | − | 0.00825028i | −0.243391 | − | 0.969928i | \(-0.578260\pi\) |
0.274181 | + | 0.961678i | \(0.411593\pi\) | |||||||
\(54\) | 15.8941 | − | 9.17644i | 0.294334 | − | 0.169934i | ||||
\(55\) | −48.9919 | + | 72.1526i | −0.890763 | + | 1.31186i | ||||
\(56\) | −103.798 | − | 38.3132i | −1.85353 | − | 0.684164i | ||||
\(57\) | −4.42512 | + | 4.42512i | −0.0776336 | + | 0.0776336i | ||||
\(58\) | −42.5841 | + | 158.926i | −0.734208 | + | 2.74010i | ||||
\(59\) | −76.5567 | − | 44.2000i | −1.29757 | − | 0.749153i | −0.317587 | − | 0.948229i | \(-0.602873\pi\) |
−0.979984 | + | 0.199076i | \(0.936206\pi\) | |||||||
\(60\) | −69.3239 | − | 24.1095i | −1.15540 | − | 0.401825i | ||||
\(61\) | −23.4309 | − | 40.5836i | −0.384114 | − | 0.665305i | 0.607532 | − | 0.794295i | \(-0.292160\pi\) |
−0.991646 | + | 0.128990i | \(0.958826\pi\) | |||||||
\(62\) | −5.51984 | + | 5.51984i | −0.0890296 | + | 0.0890296i | ||||
\(63\) | −12.1230 | + | 17.1474i | −0.192428 | + | 0.272181i | ||||
\(64\) | − | 37.4755i | − | 0.585554i | ||||||
\(65\) | 40.3154 | + | 46.6674i | 0.620236 | + | 0.717960i | ||||
\(66\) | 53.3540 | − | 92.4118i | 0.808394 | − | 1.40018i | ||||
\(67\) | 3.01836 | + | 11.2647i | 0.0450501 | + | 0.168129i | 0.984786 | − | 0.173772i | \(-0.0555957\pi\) |
−0.939736 | + | 0.341902i | \(0.888929\pi\) | |||||||
\(68\) | −25.6131 | + | 95.5894i | −0.376663 | + | 1.40573i | ||||
\(69\) | 41.5815i | 0.602630i | ||||||||
\(70\) | 123.038 | − | 11.9849i | 1.75769 | − | 0.171213i | ||||
\(71\) | 67.1402 | 0.945636 | 0.472818 | − | 0.881160i | \(-0.343237\pi\) | ||||
0.472818 | + | 0.881160i | \(0.343237\pi\) | |||||||
\(72\) | 45.8027 | + | 12.2728i | 0.636149 | + | 0.170456i | ||||
\(73\) | −17.6525 | + | 4.72997i | −0.241815 | + | 0.0647941i | −0.377691 | − | 0.925932i | \(-0.623282\pi\) |
0.135876 | + | 0.990726i | \(0.456615\pi\) | |||||||
\(74\) | −93.0353 | − | 53.7140i | −1.25723 | − | 0.725865i | ||||
\(75\) | 43.0102 | − | 5.01191i | 0.573470 | − | 0.0668254i | ||||
\(76\) | −30.6214 | −0.402913 | ||||||||
\(77\) | −11.1930 | + | 121.585i | −0.145363 | + | 1.57902i | ||||
\(78\) | −53.3545 | − | 53.3545i | −0.684032 | − | 0.684032i | ||||
\(79\) | 19.4021 | − | 11.2018i | 0.245596 | − | 0.141795i | −0.372150 | − | 0.928173i | \(-0.621379\pi\) |
0.617746 | + | 0.786378i | \(0.288046\pi\) | |||||||
\(80\) | −47.7569 | − | 98.6876i | −0.596962 | − | 1.23359i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 102.157 | + | 27.3729i | 1.24582 | + | 0.333816i | ||||
\(83\) | 52.4430 | + | 52.4430i | 0.631844 | + | 0.631844i | 0.948530 | − | 0.316686i | \(-0.102570\pi\) |
−0.316686 | + | 0.948530i | \(0.602570\pi\) | |||||||
\(84\) | −101.274 | + | 17.3843i | −1.20564 | + | 0.206956i | ||||
\(85\) | −10.9633 | − | 57.3450i | −0.128980 | − | 0.674647i | ||||
\(86\) | −49.1438 | − | 85.1196i | −0.571440 | − | 0.989763i | ||||
\(87\) | 20.8826 | + | 77.9351i | 0.240030 | + | 0.895805i | ||||
\(88\) | 266.308 | − | 71.3570i | 3.02623 | − | 0.810875i | ||||
\(89\) | 44.2757 | − | 25.5626i | 0.497480 | − | 0.287220i | −0.230192 | − | 0.973145i | \(-0.573935\pi\) |
0.727672 | + | 0.685925i | \(0.240602\pi\) | |||||||
\(90\) | −52.0377 | + | 9.94866i | −0.578197 | + | 0.110541i | ||||
\(91\) | 80.9964 | + | 29.8968i | 0.890070 | + | 0.328536i | ||||
\(92\) | −143.870 | + | 143.870i | −1.56380 | + | 1.56380i | ||||
\(93\) | −0.990777 | + | 3.69763i | −0.0106535 | + | 0.0397595i | ||||
\(94\) | 250.647 | + | 144.711i | 2.66645 | + | 1.53948i | ||||
\(95\) | 16.2615 | − | 7.86926i | 0.171173 | − | 0.0828343i | ||||
\(96\) | 12.3168 | + | 21.3333i | 0.128300 | + | 0.222222i | ||||
\(97\) | 9.15031 | − | 9.15031i | 0.0943331 | − | 0.0943331i | −0.658365 | − | 0.752698i | \(-0.728752\pi\) |
0.752698 | + | 0.658365i | \(0.228752\pi\) | |||||||
\(98\) | 142.664 | − | 97.9785i | 1.45575 | − | 0.999781i | ||||
\(99\) | − | 52.3281i | − | 0.528567i | ||||||
\(100\) | 166.154 | + | 131.472i | 1.66154 | + | 1.31472i | ||||
\(101\) | 42.1642 | − | 73.0305i | 0.417467 | − | 0.723074i | −0.578217 | − | 0.815883i | \(-0.696251\pi\) |
0.995684 | + | 0.0928089i | \(0.0295846\pi\) | |||||||
\(102\) | 18.4884 | + | 68.9997i | 0.181259 | + | 0.676468i | ||||
\(103\) | −30.3411 | + | 113.235i | −0.294574 | + | 1.09937i | 0.646981 | + | 0.762506i | \(0.276031\pi\) |
−0.941555 | + | 0.336859i | \(0.890635\pi\) | |||||||
\(104\) | − | 194.953i | − | 1.87455i | ||||||
\(105\) | 49.3141 | − | 35.2579i | 0.469658 | − | 0.335790i | ||||
\(106\) | 5.96720 | 0.0562944 | ||||||||
\(107\) | −138.045 | − | 36.9890i | −1.29014 | − | 0.345691i | −0.452425 | − | 0.891802i | \(-0.649441\pi\) |
−0.837713 | + | 0.546111i | \(0.816108\pi\) | |||||||
\(108\) | 42.5374 | − | 11.3979i | 0.393865 | − | 0.105536i | ||||
\(109\) | −140.724 | − | 81.2472i | −1.29105 | − | 0.745387i | −0.312208 | − | 0.950014i | \(-0.601069\pi\) |
−0.978840 | + | 0.204627i | \(0.934402\pi\) | |||||||
\(110\) | −233.102 | + | 201.374i | −2.11911 | + | 1.83067i | ||||
\(111\) | −52.6812 | −0.474605 | ||||||||
\(112\) | −125.331 | − | 88.6073i | −1.11903 | − | 0.791136i | ||||
\(113\) | −3.09464 | − | 3.09464i | −0.0273862 | − | 0.0273862i | 0.693281 | − | 0.720667i | \(-0.256164\pi\) |
−0.720667 | + | 0.693281i | \(0.756164\pi\) | |||||||
\(114\) | −19.1422 | + | 11.0518i | −0.167914 | + | 0.0969454i | ||||
\(115\) | 39.4295 | − | 113.375i | 0.342865 | − | 0.985866i | ||||
\(116\) | −197.399 | + | 341.904i | −1.70171 | + | 2.94745i | ||||
\(117\) | −35.7411 | − | 9.57681i | −0.305480 | − | 0.0818531i | ||||
\(118\) | −220.780 | − | 220.780i | −1.87102 | − | 1.87102i | ||||
\(119\) | −52.2551 | − | 62.8517i | −0.439118 | − | 0.528166i | ||||
\(120\) | −113.247 | − | 76.8950i | −0.943721 | − | 0.640791i | ||||
\(121\) | −91.6240 | − | 158.697i | −0.757223 | − | 1.31155i | ||||
\(122\) | −42.8389 | − | 159.877i | −0.351139 | − | 1.31047i | ||||
\(123\) | 50.0965 | − | 13.4233i | 0.407288 | − | 0.109133i | ||||
\(124\) | −16.2217 | + | 9.36558i | −0.130820 | + | 0.0755289i | ||||
\(125\) | −122.023 | − | 27.1191i | −0.976182 | − | 0.216953i | ||||
\(126\) | −57.0348 | + | 47.4189i | −0.452657 | + | 0.376341i | ||||
\(127\) | −117.674 | + | 117.674i | −0.926571 | + | 0.926571i | −0.997483 | − | 0.0709120i | \(-0.977409\pi\) |
0.0709120 | + | 0.997483i | \(0.477409\pi\) | |||||||
\(128\) | 48.9822 | − | 182.804i | 0.382673 | − | 1.42816i | ||||
\(129\) | −41.7415 | − | 24.0995i | −0.323578 | − | 0.186818i | ||||
\(130\) | 94.8813 | + | 196.068i | 0.729856 | + | 1.50821i | ||||
\(131\) | 81.6255 | + | 141.379i | 0.623095 | + | 1.07923i | 0.988906 | + | 0.148543i | \(0.0474584\pi\) |
−0.365811 | + | 0.930689i | \(0.619208\pi\) | |||||||
\(132\) | 181.053 | − | 181.053i | 1.37161 | − | 1.37161i | ||||
\(133\) | 14.6005 | − | 20.6517i | 0.109778 | − | 0.155276i | ||||
\(134\) | 41.1905i | 0.307392i | ||||||||
\(135\) | −19.6604 | + | 16.9844i | −0.145633 | + | 0.125810i | ||||
\(136\) | −92.2820 | + | 159.837i | −0.678544 | + | 1.17527i | ||||
\(137\) | −38.2623 | − | 142.797i | −0.279287 | − | 1.04231i | −0.952914 | − | 0.303241i | \(-0.901931\pi\) |
0.673627 | − | 0.739072i | \(-0.264735\pi\) | |||||||
\(138\) | −38.0118 | + | 141.862i | −0.275448 | + | 1.02798i | ||||
\(139\) | 101.553i | 0.730596i | 0.930891 | + | 0.365298i | \(0.119033\pi\) | ||||
−0.930891 | + | 0.365298i | \(0.880967\pi\) | |||||||
\(140\) | 292.615 | + | 48.6335i | 2.09011 | + | 0.347382i | ||||
\(141\) | 141.929 | 1.00659 | ||||||||
\(142\) | 229.060 | + | 61.3763i | 1.61310 | + | 0.432228i | ||||
\(143\) | −207.807 | + | 55.6818i | −1.45320 | + | 0.389383i | ||||
\(144\) | 56.9683 | + | 32.8907i | 0.395613 | + | 0.228407i | ||||
\(145\) | 16.9639 | − | 232.297i | 0.116992 | − | 1.60205i | ||||
\(146\) | −64.5483 | −0.442112 | ||||||||
\(147\) | 36.5638 | − | 76.5904i | 0.248733 | − | 0.521023i | ||||
\(148\) | −182.274 | − | 182.274i | −1.23158 | − | 1.23158i | ||||
\(149\) | 91.7653 | − | 52.9807i | 0.615874 | − | 0.355575i | −0.159387 | − | 0.987216i | \(-0.550952\pi\) |
0.775261 | + | 0.631641i | \(0.217618\pi\) | |||||||
\(150\) | 151.318 | + | 22.2190i | 1.00879 | + | 0.148126i | ||||
\(151\) | 80.5845 | − | 139.576i | 0.533672 | − | 0.924347i | −0.465554 | − | 0.885019i | \(-0.654145\pi\) |
0.999226 | − | 0.0393279i | \(-0.0125217\pi\) | |||||||
\(152\) | −55.1632 | − | 14.7809i | −0.362916 | − | 0.0972429i | ||||
\(153\) | 24.7700 | + | 24.7700i | 0.161896 | + | 0.161896i | ||||
\(154\) | −149.334 | + | 404.574i | −0.969699 | + | 2.62711i | ||||
\(155\) | 6.20769 | − | 9.14233i | 0.0400496 | − | 0.0589828i | ||||
\(156\) | −90.5273 | − | 156.798i | −0.580303 | − | 1.00511i | ||||
\(157\) | −35.5563 | − | 132.698i | −0.226473 | − | 0.845210i | −0.981809 | − | 0.189872i | \(-0.939193\pi\) |
0.755336 | − | 0.655338i | \(-0.227474\pi\) | |||||||
\(158\) | 76.4335 | − | 20.4803i | 0.483756 | − | 0.129622i | ||||
\(159\) | 2.53419 | − | 1.46312i | 0.0159383 | − | 0.00920200i | ||||
\(160\) | −13.3533 | − | 69.8460i | −0.0834579 | − | 0.436537i | ||||
\(161\) | −28.4309 | − | 165.627i | −0.176589 | − | 1.02874i | ||||
\(162\) | 22.4776 | − | 22.4776i | 0.138751 | − | 0.138751i | ||||
\(163\) | −48.8824 | + | 182.431i | −0.299892 | + | 1.11921i | 0.637362 | + | 0.770564i | \(0.280025\pi\) |
−0.937254 | + | 0.348647i | \(0.886641\pi\) | |||||||
\(164\) | 219.775 | + | 126.887i | 1.34009 | + | 0.773703i | ||||
\(165\) | −49.6200 | + | 142.676i | −0.300727 | + | 0.864703i | ||||
\(166\) | 130.977 | + | 226.859i | 0.789018 | + | 1.36662i | ||||
\(167\) | −114.153 | + | 114.153i | −0.683552 | + | 0.683552i | −0.960799 | − | 0.277247i | \(-0.910578\pi\) |
0.277247 | + | 0.960799i | \(0.410578\pi\) | |||||||
\(168\) | −190.833 | − | 17.5679i | −1.13591 | − | 0.104571i | ||||
\(169\) | − | 16.8729i | − | 0.0998396i | ||||||
\(170\) | 15.0189 | − | 205.664i | 0.0883466 | − | 1.20979i | ||||
\(171\) | −5.41964 | + | 9.38709i | −0.0316938 | + | 0.0548952i | ||||
\(172\) | −61.0406 | − | 227.807i | −0.354887 | − | 1.32446i | ||||
\(173\) | 53.9511 | − | 201.348i | 0.311856 | − | 1.16386i | −0.615025 | − | 0.788508i | \(-0.710854\pi\) |
0.926881 | − | 0.375355i | \(-0.122479\pi\) | |||||||
\(174\) | 284.978i | 1.63780i | ||||||||
\(175\) | −167.891 | + | 49.3712i | −0.959379 | + | 0.282121i | ||||
\(176\) | 382.468 | 2.17312 | ||||||||
\(177\) | −147.896 | − | 39.6287i | −0.835572 | − | 0.223891i | ||||
\(178\) | 174.422 | − | 46.7362i | 0.979899 | − | 0.262563i | ||||
\(179\) | −102.967 | − | 59.4481i | −0.575235 | − | 0.332112i | 0.184002 | − | 0.982926i | \(-0.441095\pi\) |
−0.759238 | + | 0.650814i | \(0.774428\pi\) | |||||||
\(180\) | −126.789 | − | 9.25897i | −0.704384 | − | 0.0514387i | ||||
\(181\) | −2.13381 | −0.0117890 | −0.00589449 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589449 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(182\) | 249.002 | + | 176.041i | 1.36814 | + | 0.967257i | ||||
\(183\) | −57.3939 | − | 57.3939i | −0.313628 | − | 0.313628i | ||||
\(184\) | −328.622 | + | 189.730i | −1.78599 | + | 1.03114i | ||||
\(185\) | 143.639 | + | 49.9548i | 0.776426 | + | 0.270026i | ||||
\(186\) | −6.76039 | + | 11.7093i | −0.0363462 | + | 0.0629535i | ||||
\(187\) | 196.733 | + | 52.7146i | 1.05205 | + | 0.281896i | ||||
\(188\) | 491.066 | + | 491.066i | 2.61205 | + | 2.61205i | ||||
\(189\) | −12.5952 | + | 34.1227i | −0.0666410 | + | 0.180544i | ||||
\(190\) | 62.6724 | − | 11.9818i | 0.329855 | − | 0.0630621i | ||||
\(191\) | 85.4671 | + | 148.033i | 0.447472 | + | 0.775044i | 0.998221 | − | 0.0596272i | \(-0.0189912\pi\) |
−0.550749 | + | 0.834671i | \(0.685658\pi\) | |||||||
\(192\) | −16.7998 | − | 62.6977i | −0.0874990 | − | 0.326551i | ||||
\(193\) | 80.0626 | − | 21.4527i | 0.414832 | − | 0.111154i | −0.0453656 | − | 0.998970i | \(-0.514445\pi\) |
0.460197 | + | 0.887817i | \(0.347779\pi\) | |||||||
\(194\) | 39.5825 | − | 22.8530i | 0.204034 | − | 0.117799i | ||||
\(195\) | 88.3694 | + | 60.0032i | 0.453176 | + | 0.307709i | ||||
\(196\) | 391.508 | − | 138.490i | 1.99749 | − | 0.706582i | ||||
\(197\) | 32.0391 | − | 32.0391i | 0.162635 | − | 0.162635i | −0.621098 | − | 0.783733i | \(-0.713313\pi\) |
0.783733 | + | 0.621098i | \(0.213313\pi\) | |||||||
\(198\) | 47.8359 | − | 178.526i | 0.241595 | − | 0.901646i | ||||
\(199\) | 22.0307 | + | 12.7194i | 0.110707 | + | 0.0639167i | 0.554331 | − | 0.832296i | \(-0.312974\pi\) |
−0.443624 | + | 0.896213i | \(0.646307\pi\) | |||||||
\(200\) | 235.859 | + | 317.045i | 1.17929 | + | 1.58522i | ||||
\(201\) | 10.0996 | + | 17.4931i | 0.0502469 | + | 0.0870302i | ||||
\(202\) | 210.611 | − | 210.611i | 1.04263 | − | 1.04263i | ||||
\(203\) | −136.467 | − | 296.152i | −0.672250 | − | 1.45888i | ||||
\(204\) | 171.406i | 0.840227i | ||||||||
\(205\) | −149.320 | − | 10.9043i | −0.728390 | − | 0.0531918i | ||||
\(206\) | −207.027 | + | 358.582i | −1.00499 | + | 1.74069i | ||||
\(207\) | 18.6405 | + | 69.5671i | 0.0900505 | + | 0.336073i | ||||
\(208\) | 69.9973 | − | 261.233i | 0.336525 | − | 1.25593i | ||||
\(209\) | 63.0221i | 0.301541i | ||||||||
\(210\) | 200.474 | − | 75.2077i | 0.954638 | − | 0.358132i | ||||
\(211\) | 139.996 | 0.663487 | 0.331744 | − | 0.943370i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943370i | \(0.392363\pi\) | |||||||
\(212\) | 13.8305 | + | 3.70587i | 0.0652382 | + | 0.0174805i | ||||
\(213\) | 112.328 | − | 30.0981i | 0.527360 | − | 0.141306i | ||||
\(214\) | −437.148 | − | 252.388i | −2.04275 | − | 1.17938i | ||||
\(215\) | 90.9587 | + | 105.290i | 0.423064 | + | 0.489721i | ||||
\(216\) | 82.1312 | 0.380237 | ||||||||
\(217\) | 1.41824 | − | 15.4058i | 0.00653568 | − | 0.0709945i | ||||
\(218\) | −405.831 | − | 405.831i | −1.86161 | − | 1.86161i | ||||
\(219\) | −27.4128 | + | 15.8268i | −0.125173 | + | 0.0722685i | ||||
\(220\) | −665.335 | + | 321.969i | −3.02425 | + | 1.46350i | ||||
\(221\) | 72.0102 | − | 124.725i | 0.325838 | − | 0.564368i | ||||
\(222\) | −179.730 | − | 48.1586i | −0.809597 | − | 0.216931i | ||||
\(223\) | 132.643 | + | 132.643i | 0.594809 | + | 0.594809i | 0.938927 | − | 0.344117i | \(-0.111822\pi\) |
−0.344117 | + | 0.938927i | \(0.611822\pi\) | |||||||
\(224\) | −63.6465 | − | 76.5532i | −0.284136 | − | 0.341755i | ||||
\(225\) | 69.7108 | − | 27.6660i | 0.309826 | − | 0.122960i | ||||
\(226\) | −7.72888 | − | 13.3868i | −0.0341986 | − | 0.0592337i | ||||
\(227\) | 63.5422 | + | 237.143i | 0.279922 | + | 1.04468i | 0.952471 | + | 0.304629i | \(0.0985326\pi\) |
−0.672549 | + | 0.740052i | \(0.734801\pi\) | |||||||
\(228\) | −51.2305 | + | 13.7272i | −0.224695 | + | 0.0602069i | ||||
\(229\) | 217.561 | − | 125.609i | 0.950047 | − | 0.548510i | 0.0569516 | − | 0.998377i | \(-0.481862\pi\) |
0.893096 | + | 0.449867i | \(0.148529\pi\) | |||||||
\(230\) | 238.162 | − | 350.751i | 1.03549 | − | 1.52501i | ||||
\(231\) | 35.7788 | + | 208.433i | 0.154886 | + | 0.902308i | ||||
\(232\) | −520.643 | + | 520.643i | −2.24415 | + | 2.24415i | ||||
\(233\) | −76.4808 | + | 285.430i | −0.328244 | + | 1.22502i | 0.582767 | + | 0.812640i | \(0.301970\pi\) |
−0.911010 | + | 0.412383i | \(0.864696\pi\) | |||||||
\(234\) | −113.182 | − | 65.3457i | −0.483684 | − | 0.279255i | ||||
\(235\) | −386.977 | − | 134.583i | −1.64671 | − | 0.572695i | ||||
\(236\) | −374.600 | − | 648.827i | −1.58729 | − | 2.74927i | ||||
\(237\) | 27.4387 | − | 27.4387i | 0.115775 | − | 0.115775i | ||||
\(238\) | −120.821 | − | 262.198i | −0.507650 | − | 1.10167i | ||||
\(239\) | 100.831i | 0.421885i | 0.977498 | + | 0.210943i | \(0.0676533\pi\) | ||||
−0.977498 | + | 0.210943i | \(0.932347\pi\) | |||||||
\(240\) | −124.139 | − | 143.699i | −0.517247 | − | 0.598744i | ||||
\(241\) | −179.672 | + | 311.201i | −0.745527 | + | 1.29129i | 0.204421 | + | 0.978883i | \(0.434469\pi\) |
−0.949948 | + | 0.312408i | \(0.898865\pi\) | |||||||
\(242\) | −167.517 | − | 625.181i | −0.692217 | − | 2.58339i | ||||
\(243\) | 4.03459 | − | 15.0573i | 0.0166032 | − | 0.0619642i | ||||
\(244\) | − | 397.160i | − | 1.62770i | ||||||
\(245\) | −172.320 | + | 174.157i | −0.703348 | + | 0.710846i | ||||
\(246\) | 183.183 | 0.744647 | ||||||||
\(247\) | 43.0453 | + | 11.5340i | 0.174273 | + | 0.0466962i | ||||
\(248\) | −33.7434 | + | 9.04153i | −0.136062 | + | 0.0364578i | ||||
\(249\) | 111.248 | + | 64.2293i | 0.446781 | + | 0.257949i | ||||
\(250\) | −391.510 | − | 204.068i | −1.56604 | − | 0.816274i | ||||
\(251\) | 17.4715 | 0.0696075 | 0.0348038 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348038 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(252\) | −161.642 | + | 74.4844i | −0.641435 | + | 0.295573i | ||||
\(253\) | 296.100 | + | 296.100i | 1.17035 | + | 1.17035i | ||||
\(254\) | −509.038 | + | 293.893i | −2.00409 | + | 1.15706i | ||||
\(255\) | −44.0490 | − | 91.0253i | −0.172741 | − | 0.356962i | ||||
\(256\) | 259.270 | − | 449.070i | 1.01278 | − | 1.75418i | ||||
\(257\) | 77.1706 | + | 20.6778i | 0.300275 | + | 0.0804583i | 0.405811 | − | 0.913957i | \(-0.366989\pi\) |
−0.105536 | + | 0.994415i | \(0.533656\pi\) | |||||||
\(258\) | −120.377 | − | 120.377i | −0.466579 | − | 0.466579i | ||||
\(259\) | 209.839 | − | 36.0202i | 0.810191 | − | 0.139074i | ||||
\(260\) | 98.1454 | + | 513.362i | 0.377482 | + | 1.97447i | ||||
\(261\) | 69.8747 | + | 121.026i | 0.267719 | + | 0.463703i | ||||
\(262\) | 149.236 | + | 556.957i | 0.569604 | + | 2.12579i | ||||
\(263\) | 167.452 | − | 44.8686i | 0.636699 | − | 0.170603i | 0.0739911 | − | 0.997259i | \(-0.476426\pi\) |
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(264\) | 413.553 | − | 238.765i | 1.56649 | − | 0.904414i | ||||
\(265\) | −8.29704 | + | 1.58624i | −0.0313096 | + | 0.00598582i | ||||
\(266\) | 68.6907 | − | 57.1096i | 0.258236 | − | 0.214698i | ||||
\(267\) | 62.6154 | − | 62.6154i | 0.234514 | − | 0.234514i | ||||
\(268\) | −25.5809 | + | 95.4694i | −0.0954513 | + | 0.356229i | ||||
\(269\) | −160.485 | − | 92.6559i | −0.596597 | − | 0.344446i | 0.171104 | − | 0.985253i | \(-0.445266\pi\) |
−0.767702 | + | 0.640807i | \(0.778600\pi\) | |||||||
\(270\) | −82.6010 | + | 39.9723i | −0.305929 | + | 0.148046i | ||||
\(271\) | −182.223 | − | 315.620i | −0.672410 | − | 1.16465i | −0.977219 | − | 0.212235i | \(-0.931926\pi\) |
0.304808 | − | 0.952414i | \(-0.401408\pi\) | |||||||
\(272\) | −181.045 | + | 181.045i | −0.665607 | + | 0.665607i | ||||
\(273\) | 148.912 | + | 13.7087i | 0.545465 | + | 0.0502149i | ||||
\(274\) | − | 522.152i | − | 1.90567i | ||||||
\(275\) | 270.584 | − | 341.964i | 0.983943 | − | 1.24350i | ||||
\(276\) | −176.204 | + | 305.194i | −0.638420 | + | 1.10578i | ||||
\(277\) | 125.143 | + | 467.038i | 0.451778 | + | 1.68606i | 0.697391 | + | 0.716691i | \(0.254344\pi\) |
−0.245613 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(278\) | −92.8347 | + | 346.464i | −0.333938 | + | 1.24627i | ||||
\(279\) | 6.63041i | 0.0237649i | ||||||||
\(280\) | 503.659 | + | 228.856i | 1.79878 | + | 0.817345i | ||||
\(281\) | −472.914 | −1.68297 | −0.841484 | − | 0.540282i | \(-0.818318\pi\) | ||||
−0.841484 | + | 0.540282i | \(0.818318\pi\) | |||||||
\(282\) | 484.212 | + | 129.744i | 1.71706 | + | 0.460086i | ||||
\(283\) | −239.837 | + | 64.2640i | −0.847479 | + | 0.227081i | −0.656324 | − | 0.754479i | \(-0.727890\pi\) |
−0.191154 | + | 0.981560i | \(0.561223\pi\) | |||||||
\(284\) | 492.786 | + | 284.510i | 1.73516 | + | 1.00180i | ||||
\(285\) | 23.6783 | − | 20.4554i | 0.0830817 | − | 0.0717732i | ||||
\(286\) | −759.870 | −2.65689 | ||||||||
\(287\) | −190.366 | + | 87.7205i | −0.663296 | + | 0.305646i | ||||
\(288\) | 30.1698 | + | 30.1698i | 0.104756 | + | 0.104756i | ||||
\(289\) | 132.203 | − | 76.3272i | 0.457449 | − | 0.264108i | ||||
\(290\) | 270.230 | − | 777.011i | 0.931827 | − | 2.67935i | ||||
\(291\) | 11.2068 | − | 19.4107i | 0.0385113 | − | 0.0667036i | ||||
\(292\) | −149.607 | − | 40.0871i | −0.512353 | − | 0.137284i | ||||
\(293\) | 61.1515 | + | 61.1515i | 0.208708 | + | 0.208708i | 0.803718 | − | 0.595010i | \(-0.202852\pi\) |
−0.595010 | + | 0.803718i | \(0.702852\pi\) | |||||||
\(294\) | 194.759 | − | 227.876i | 0.662444 | − | 0.775087i | ||||
\(295\) | 365.671 | + | 248.292i | 1.23956 | + | 0.841669i | ||||
\(296\) | −240.376 | − | 416.344i | −0.812082 | − | 1.40657i | ||||
\(297\) | −23.4581 | − | 87.5467i | −0.0789834 | − | 0.294770i | ||||
\(298\) | 361.505 | − | 96.8649i | 1.21310 | − | 0.325050i | ||||
\(299\) | 256.433 | − | 148.051i | 0.857634 | − | 0.495155i | ||||
\(300\) | 336.919 | + | 145.473i | 1.12306 | + | 0.484909i | ||||
\(301\) | 182.742 | + | 67.4526i | 0.607117 | + | 0.224095i | ||||
\(302\) | 402.521 | − | 402.521i | 1.33285 | − | 1.33285i | ||||
\(303\) | 37.8034 | − | 141.084i | 0.124764 | − | 0.465624i | ||||
\(304\) | −68.6106 | − | 39.6123i | −0.225693 | − | 0.130304i | ||||
\(305\) | 102.065 | + | 210.912i | 0.334638 | + | 0.691514i | ||||
\(306\) | 61.8634 | + | 107.151i | 0.202168 | + | 0.350165i | ||||
\(307\) | −36.7448 | + | 36.7448i | −0.119690 | + | 0.119690i | −0.764415 | − | 0.644725i | \(-0.776972\pi\) |
0.644725 | + | 0.764415i | \(0.276972\pi\) | |||||||
\(308\) | −597.375 | + | 844.961i | −1.93953 | + | 2.74338i | ||||
\(309\) | 203.047i | 0.657110i | ||||||||
\(310\) | 29.5360 | − | 25.5158i | 0.0952775 | − | 0.0823089i | ||||
\(311\) | −44.4761 | + | 77.0348i | −0.143010 | + | 0.247700i | −0.928629 | − | 0.371010i | \(-0.879011\pi\) |
0.785619 | + | 0.618711i | \(0.212345\pi\) | |||||||
\(312\) | −87.3950 | − | 326.163i | −0.280112 | − | 1.04539i | ||||
\(313\) | 47.5609 | − | 177.500i | 0.151952 | − | 0.567092i | −0.847395 | − | 0.530962i | \(-0.821831\pi\) |
0.999347 | − | 0.0361293i | \(-0.0115028\pi\) | |||||||
\(314\) | − | 485.224i | − | 1.54530i | ||||||
\(315\) | 66.6983 | − | 81.0946i | 0.211741 | − | 0.257443i | ||||
\(316\) | 189.873 | 0.600864 | ||||||||
\(317\) | −356.038 | − | 95.4002i | −1.12315 | − | 0.300947i | −0.350992 | − | 0.936378i | \(-0.614156\pi\) |
−0.772157 | + | 0.635431i | \(0.780822\pi\) | |||||||
\(318\) | 9.98333 | − | 2.67502i | 0.0313941 | − | 0.00841203i | ||||
\(319\) | 703.676 | + | 406.268i | 2.20588 | + | 1.27357i | ||||
\(320\) | −13.6472 | + | 186.880i | −0.0426475 | + | 0.583999i | ||||
\(321\) | −247.535 | −0.771137 | ||||||||
\(322\) | 54.4118 | − | 591.054i | 0.168981 | − | 1.83557i | ||||
\(323\) | −29.8321 | − | 29.8321i | −0.0923596 | − | 0.0923596i | ||||
\(324\) | 66.0570 | − | 38.1380i | 0.203880 | − | 0.117710i | ||||
\(325\) | −184.047 | − | 247.399i | −0.566298 | − | 0.761227i | ||||
\(326\) | −333.540 | + | 577.709i | −1.02313 | + | 1.77211i | ||||
\(327\) | −271.858 | − | 72.8442i | −0.831371 | − | 0.222765i | ||||
\(328\) | 334.668 | + | 334.668i | 1.02033 | + | 1.02033i | ||||
\(329\) | −565.329 | + | 97.0420i | −1.71832 | + | 0.294961i | ||||
\(330\) | −299.714 | + | 441.402i | −0.908225 | + | 1.33758i | ||||
\(331\) | 224.992 | + | 389.697i | 0.679734 | + | 1.17733i | 0.975061 | + | 0.221937i | \(0.0712381\pi\) |
−0.295327 | + | 0.955396i | \(0.595429\pi\) | |||||||
\(332\) | 162.684 | + | 607.145i | 0.490012 | + | 1.82875i | ||||
\(333\) | −88.1374 | + | 23.6163i | −0.264677 | + | 0.0709199i | ||||
\(334\) | −493.805 | + | 285.099i | −1.47846 | + | 0.853589i | ||||
\(335\) | −10.9495 | − | 57.2729i | −0.0326852 | − | 0.170964i | ||||
\(336\) | −249.404 | − | 92.0585i | −0.742275 | − | 0.273984i | ||||
\(337\) | −9.37231 | + | 9.37231i | −0.0278110 | + | 0.0278110i | −0.720876 | − | 0.693065i | \(-0.756260\pi\) |
0.693065 | + | 0.720876i | \(0.256260\pi\) | |||||||
\(338\) | 15.4244 | − | 57.5646i | 0.0456343 | − | 0.170309i | ||||
\(339\) | −6.56471 | − | 3.79014i | −0.0193649 | − | 0.0111804i | ||||
\(340\) | 162.536 | − | 467.350i | 0.478046 | − | 1.37456i | ||||
\(341\) | 19.2754 | + | 33.3859i | 0.0565260 | + | 0.0979060i | ||||
\(342\) | −27.0712 | + | 27.0712i | −0.0791556 | + | 0.0791556i | ||||
\(343\) | −93.2729 | + | 330.074i | −0.271933 | + | 0.962316i | ||||
\(344\) | − | 439.849i | − | 1.27863i | ||||||
\(345\) | 15.1424 | − | 207.355i | 0.0438911 | − | 0.601029i | ||||
\(346\) | 368.126 | − | 637.613i | 1.06395 | − | 1.84281i | ||||
\(347\) | −101.459 | − | 378.650i | −0.292389 | − | 1.09121i | −0.943269 | − | 0.332029i | \(-0.892267\pi\) |
0.650880 | − | 0.759180i | \(-0.274400\pi\) | |||||||
\(348\) | −176.983 | + | 660.509i | −0.508571 | + | 1.89801i | ||||
\(349\) | − | 480.726i | − | 1.37744i | −0.725028 | − | 0.688720i | \(-0.758173\pi\) | ||
0.725028 | − | 0.688720i | \(-0.241827\pi\) | |||||||
\(350\) | −617.921 | + | 14.9596i | −1.76549 | + | 0.0427416i | ||||
\(351\) | −64.0893 | −0.182590 | ||||||||
\(352\) | 239.621 | + | 64.2062i | 0.680741 | + | 0.182404i | ||||
\(353\) | 535.395 | − | 143.459i | 1.51670 | − | 0.406398i | 0.598045 | − | 0.801462i | \(-0.295944\pi\) |
0.918654 | + | 0.395064i | \(0.129278\pi\) | |||||||
\(354\) | −468.345 | − | 270.399i | −1.32301 | − | 0.763840i | ||||
\(355\) | −334.809 | − | 24.4500i | −0.943125 | − | 0.0688732i | ||||
\(356\) | 433.292 | 1.21711 | ||||||||
\(357\) | −115.600 | − | 81.7276i | −0.323810 | − | 0.228929i | ||||
\(358\) | −296.944 | − | 296.944i | −0.829454 | − | 0.829454i | ||||
\(359\) | −87.7247 | + | 50.6479i | −0.244359 | + | 0.141080i | −0.617178 | − | 0.786823i | \(-0.711724\pi\) |
0.372820 | + | 0.927904i | \(0.378391\pi\) | |||||||
\(360\) | −223.936 | − | 77.8807i | −0.622045 | − | 0.216335i | ||||
\(361\) | −173.973 | + | 301.330i | −0.481919 | + | 0.834708i | ||||
\(362\) | −7.27983 | − | 1.95062i | −0.0201100 | − | 0.00538846i | ||||
\(363\) | −224.432 | − | 224.432i | −0.618270 | − | 0.618270i | ||||
\(364\) | 467.797 | + | 562.659i | 1.28516 | + | 1.54577i | ||||
\(365\) | 89.7506 | − | 17.1587i | 0.245892 | − | 0.0470100i | ||||
\(366\) | −143.342 | − | 248.275i | −0.391644 | − | 0.678348i | ||||
\(367\) | −78.8661 | − | 294.332i | −0.214894 | − | 0.801996i | −0.986204 | − | 0.165536i | \(-0.947065\pi\) |
0.771310 | − | 0.636460i | \(-0.219602\pi\) | |||||||
\(368\) | −508.469 | + | 136.244i | −1.38171 | + | 0.370228i | ||||
\(369\) | 77.7955 | − | 44.9153i | 0.210828 | − | 0.121722i | ||||
\(370\) | 444.381 | + | 301.737i | 1.20103 | + | 0.815505i | ||||
\(371\) | −9.09379 | + | 7.56061i | −0.0245116 | + | 0.0203790i | ||||
\(372\) | −22.9409 | + | 22.9409i | −0.0616691 | + | 0.0616691i | ||||
\(373\) | 27.7530 | − | 103.576i | 0.0744048 | − | 0.277682i | −0.918693 | − | 0.394973i | \(-0.870754\pi\) |
0.993098 | + | 0.117290i | \(0.0374208\pi\) | |||||||
\(374\) | 622.999 | + | 359.689i | 1.66577 | + | 0.961734i | ||||
\(375\) | −216.305 | + | 9.33023i | −0.576814 | + | 0.0248806i | ||||
\(376\) | 647.598 | + | 1121.67i | 1.72234 | + | 2.98317i | ||||
\(377\) | 406.272 | − | 406.272i | 1.07764 | − | 1.07764i | ||||
\(378\) | −74.1638 | + | 104.901i | −0.196201 | + | 0.277517i | ||||
\(379\) | 0 | 5.00789e-5i | 0 | 1.32134e-7i | −1.00000 | 6.60672e-8i | \(-1.00000\pi\) | |||
1.00000 | 6.60672e-8i | \(-2.10298e-8\pi\) | ||||||||
\(380\) | 152.700 | + | 11.1512i | 0.401843 | + | 0.0293452i | ||||
\(381\) | −144.121 | + | 249.625i | −0.378271 | + | 0.655184i | ||||
\(382\) | 156.260 | + | 583.170i | 0.409057 | + | 1.52662i | ||||
\(383\) | 48.7638 | − | 181.989i | 0.127321 | − | 0.475167i | −0.872591 | − | 0.488451i | \(-0.837562\pi\) |
0.999912 | + | 0.0132843i | \(0.00422864\pi\) | |||||||
\(384\) | − | 327.795i | − | 0.853633i | ||||||
\(385\) | 100.093 | − | 602.234i | 0.259982 | − | 1.56424i | ||||
\(386\) | 292.757 | 0.758439 | ||||||||
\(387\) | −80.6384 | − | 21.6070i | −0.208368 | − | 0.0558320i | ||||
\(388\) | 105.935 | − | 28.3852i | 0.273029 | − | 0.0731578i | ||||
\(389\) | 182.547 | + | 105.394i | 0.469273 | + | 0.270935i | 0.715935 | − | 0.698166i | \(-0.246000\pi\) |
−0.246662 | + | 0.969102i | \(0.579334\pi\) | |||||||
\(390\) | 246.634 | + | 285.494i | 0.632396 | + | 0.732036i | ||||
\(391\) | −280.324 | −0.716940 | ||||||||
\(392\) | 772.135 | − | 60.5035i | 1.96973 | − | 0.154346i | ||||
\(393\) | 199.941 | + | 199.941i | 0.508755 | + | 0.508755i | ||||
\(394\) | 138.595 | − | 80.0181i | 0.351765 | − | 0.203092i | ||||
\(395\) | −100.832 | + | 48.7947i | −0.255271 | + | 0.123531i | ||||
\(396\) | 221.743 | − | 384.071i | 0.559958 | − | 0.969876i | ||||
\(397\) | −242.295 | − | 64.9229i | −0.610316 | − | 0.163534i | −0.0595944 | − | 0.998223i | \(-0.518981\pi\) |
−0.550722 | + | 0.834689i | \(0.685647\pi\) | |||||||
\(398\) | 63.5338 | + | 63.5338i | 0.159633 | + | 0.159633i | ||||
\(399\) | 15.1692 | − | 41.0962i | 0.0380179 | − | 0.102998i | ||||
\(400\) | 202.212 | + | 509.519i | 0.505530 | + | 1.27380i | ||||
\(401\) | 172.876 | + | 299.430i | 0.431113 | + | 0.746709i | 0.996969 | − | 0.0777947i | \(-0.0247879\pi\) |
−0.565857 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(402\) | 18.4652 | + | 68.9130i | 0.0459333 | + | 0.171425i | ||||
\(403\) | 26.3309 | − | 7.05535i | 0.0653373 | − | 0.0175071i | ||||
\(404\) | 618.942 | − | 357.346i | 1.53203 | − | 0.884520i | ||||
\(405\) | −25.2786 | + | 37.2289i | −0.0624163 | + | 0.0919232i | ||||
\(406\) | −194.851 | − | 1135.12i | −0.479928 | − | 2.79587i | ||||
\(407\) | −375.141 | + | 375.141i | −0.921721 | + | 0.921721i | ||||
\(408\) | −82.7378 | + | 308.782i | −0.202789 | + | 0.756818i | ||||
\(409\) | −98.4923 | − | 56.8646i | −0.240812 | − | 0.139033i | 0.374738 | − | 0.927131i | \(-0.377733\pi\) |
−0.615550 | + | 0.788098i | \(0.711066\pi\) | |||||||
\(410\) | −499.461 | − | 173.703i | −1.21820 | − | 0.423666i | ||||
\(411\) | −128.028 | − | 221.751i | −0.311504 | − | 0.539541i | ||||
\(412\) | −702.532 | + | 702.532i | −1.70518 | + | 1.70518i | ||||
\(413\) | 616.195 | + | 56.7263i | 1.49200 | + | 0.137352i | ||||
\(414\) | 254.380i | 0.614444i | ||||||||
\(415\) | −242.421 | − | 280.617i | −0.584147 | − | 0.676185i | ||||
\(416\) | 87.7081 | − | 151.915i | 0.210837 | − | 0.365180i | ||||
\(417\) | 45.5249 | + | 169.901i | 0.109172 | + | 0.407437i | ||||
\(418\) | −57.6118 | + | 215.010i | −0.137827 | + | 0.514378i | ||||
\(419\) | 220.394i | 0.526000i | 0.964796 | + | 0.263000i | \(0.0847120\pi\) | ||||
−0.964796 | + | 0.263000i | \(0.915288\pi\) | |||||||
\(420\) | 511.356 | − | 49.8103i | 1.21751 | − | 0.118596i | ||||
\(421\) | −611.981 | −1.45364 | −0.726818 | − | 0.686830i | \(-0.759002\pi\) | ||||
−0.726818 | + | 0.686830i | \(0.759002\pi\) | |||||||
\(422\) | 477.618 | + | 127.977i | 1.13180 | + | 0.303264i | ||||
\(423\) | 237.451 | − | 63.6248i | 0.561350 | − | 0.150413i | ||||
\(424\) | 23.1263 | + | 13.3520i | 0.0545431 | + | 0.0314905i | ||||
\(425\) | 33.7880 | + | 289.956i | 0.0795012 | + | 0.682249i | ||||
\(426\) | 410.739 | 0.964175 | ||||||||
\(427\) | 267.853 | + | 189.368i | 0.627291 | + | 0.443486i | ||||
\(428\) | −856.459 | − | 856.459i | −2.00107 | − | 2.00107i | ||||
\(429\) | −322.707 | + | 186.315i | −0.752231 | + | 0.434301i | ||||
\(430\) | 214.069 | + | 442.364i | 0.497835 | + | 1.02875i | ||||
\(431\) | 362.392 | − | 627.681i | 0.840816 | − | 1.45634i | −0.0483893 | − | 0.998829i | \(-0.515409\pi\) |
0.889206 | − | 0.457508i | \(-0.151258\pi\) | |||||||
\(432\) | 110.054 | + | 29.4890i | 0.254755 | + | 0.0682615i | ||||
\(433\) | −152.433 | − | 152.433i | −0.352038 | − | 0.352038i | 0.508829 | − | 0.860867i | \(-0.330078\pi\) |
−0.860867 | + | 0.508829i | \(0.830078\pi\) | |||||||
\(434\) | 18.9218 | − | 51.2629i | 0.0435987 | − | 0.118117i | ||||
\(435\) | −75.7548 | − | 396.245i | −0.174149 | − | 0.910908i | ||||
\(436\) | −688.579 | − | 1192.65i | −1.57931 | − | 2.73545i | ||||
\(437\) | −22.4499 | − | 83.7842i | −0.0513728 | − | 0.191726i | ||||
\(438\) | −107.991 | + | 28.9362i | −0.246556 | + | 0.0660644i | ||||
\(439\) | −719.426 | + | 415.361i | −1.63878 | + | 0.946152i | −0.657530 | + | 0.753428i | \(0.728399\pi\) |
−0.981253 | + | 0.192723i | \(0.938268\pi\) | |||||||
\(440\) | −1353.99 | + | 258.858i | −3.07725 | + | 0.588313i | ||||
\(441\) | 26.8379 | − | 144.529i | 0.0608569 | − | 0.327731i | ||||
\(442\) | 359.692 | − | 359.692i | 0.813783 | − | 0.813783i | ||||
\(443\) | −86.1258 | + | 321.426i | −0.194415 | + | 0.725566i | 0.798003 | + | 0.602654i | \(0.205890\pi\) |
−0.992418 | + | 0.122912i | \(0.960777\pi\) | |||||||
\(444\) | −386.662 | − | 223.240i | −0.870861 | − | 0.502792i | ||||
\(445\) | −230.100 | + | 111.350i | −0.517078 | + | 0.250225i | ||||
\(446\) | 331.276 | + | 573.787i | 0.742771 | + | 1.28652i | ||||
\(447\) | 129.776 | − | 129.776i | 0.290326 | − | 0.290326i | ||||
\(448\) | 109.786 | + | 238.250i | 0.245057 | + | 0.531809i | ||||
\(449\) | − | 20.5616i | − | 0.0457943i | −0.999738 | − | 0.0228971i | \(-0.992711\pi\) | ||
0.999738 | − | 0.0228971i | \(-0.00728902\pi\) | |||||||
\(450\) | 263.121 | − | 30.6610i | 0.584712 | − | 0.0681355i | ||||
\(451\) | 261.148 | − | 452.321i | 0.579042 | − | 1.00293i | ||||
\(452\) | −9.59989 | − | 35.8273i | −0.0212387 | − | 0.0792639i | ||||
\(453\) | 72.2501 | − | 269.641i | 0.159492 | − | 0.595234i | ||||
\(454\) | 867.138i | 1.91000i | ||||||||
\(455\) | −393.019 | − | 178.583i | −0.863778 | − | 0.392490i | ||||
\(456\) | −98.9159 | −0.216921 | ||||||||
\(457\) | 521.445 | + | 139.721i | 1.14102 | + | 0.305734i | 0.779360 | − | 0.626577i | \(-0.215545\pi\) |
0.361657 | + | 0.932311i | \(0.382211\pi\) | |||||||
\(458\) | 857.070 | − | 229.651i | 1.87133 | − | 0.501422i | ||||
\(459\) | 52.5452 | + | 30.3370i | 0.114478 | + | 0.0660936i | ||||
\(460\) | 769.831 | − | 665.047i | 1.67355 | − | 1.44575i | ||||
\(461\) | 650.544 | 1.41116 | 0.705579 | − | 0.708632i | \(-0.250687\pi\) | ||||
0.705579 | + | 0.708632i | \(0.250687\pi\) | |||||||
\(462\) | −68.4744 | + | 743.811i | −0.148213 | + | 1.60998i | ||||
\(463\) | 229.971 | + | 229.971i | 0.496697 | + | 0.496697i | 0.910408 | − | 0.413711i | \(-0.135768\pi\) |
−0.413711 | + | 0.910408i | \(0.635768\pi\) | |||||||
\(464\) | −884.587 | + | 510.717i | −1.90644 | + | 1.10068i | ||||
\(465\) | 6.28727 | − | 18.0782i | 0.0135210 | − | 0.0388779i | ||||
\(466\) | −521.854 | + | 903.877i | −1.11986 | + | 1.93965i | ||||
\(467\) | 564.037 | + | 151.133i | 1.20779 | + | 0.323626i | 0.805894 | − | 0.592060i | \(-0.201685\pi\) |
0.401895 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(468\) | −221.746 | − | 221.746i | −0.473816 | − | 0.473816i | ||||
\(469\) | −52.1895 | − | 62.7728i | −0.111278 | − | 0.133844i | ||||
\(470\) | −1197.21 | − | 812.909i | −2.54725 | − | 1.72959i | ||||
\(471\) | −118.974 | − | 206.069i | −0.252598 | − | 0.437513i | ||||
\(472\) | −361.639 | − | 1349.66i | −0.766184 | − | 2.85944i | ||||
\(473\) | −468.851 | + | 125.628i | −0.991228 | + | 0.265599i | ||||
\(474\) | 118.695 | − | 68.5284i | 0.250411 | − | 0.144575i | ||||
\(475\) | −83.9571 | + | 33.3200i | −0.176752 | + | 0.0701473i | ||||
\(476\) | −117.197 | − | 682.744i | −0.246212 | − | 1.43434i | ||||
\(477\) | 3.58389 | − | 3.58389i | 0.00751340 | − | 0.00751340i | ||||
\(478\) | −92.1745 | + | 344.000i | −0.192834 | + | 0.719665i | ||||
\(479\) | 255.740 | + | 147.651i | 0.533904 | + | 0.308249i | 0.742605 | − | 0.669730i | \(-0.233590\pi\) |
−0.208701 | + | 0.977980i | \(0.566924\pi\) | |||||||
\(480\) | −53.6516 | − | 110.868i | −0.111774 | − | 0.230976i | ||||
\(481\) | 187.572 | + | 324.885i | 0.389963 | + | 0.675436i | ||||
\(482\) | −897.465 | + | 897.465i | −1.86196 | + | 1.86196i | ||||
\(483\) | −121.814 | − | 264.354i | −0.252204 | − | 0.547317i | ||||
\(484\) | − | 1553.05i | − | 3.20878i | ||||||
\(485\) | −48.9622 | + | 42.2978i | −0.100953 | + | 0.0872120i | ||||
\(486\) | 27.5293 | − | 47.6822i | 0.0566447 | − | 0.0981115i | ||||
\(487\) | −8.56814 | − | 31.9767i | −0.0175937 | − | 0.0656606i | 0.956571 | − | 0.291500i | \(-0.0941543\pi\) |
−0.974165 | + | 0.225839i | \(0.927488\pi\) | |||||||
\(488\) | 191.709 | − | 715.468i | 0.392846 | − | 1.46612i | ||||
\(489\) | 327.127i | 0.668972i | ||||||||
\(490\) | −747.105 | + | 436.639i | −1.52470 | + | 0.891099i | ||||
\(491\) | 602.433 | 1.22695 | 0.613476 | − | 0.789713i | \(-0.289771\pi\) | ||||
0.613476 | + | 0.789713i | \(0.289771\pi\) | |||||||
\(492\) | 424.573 | + | 113.764i | 0.862954 | + | 0.231228i | ||||
\(493\) | −525.403 | + | 140.781i | −1.06573 | + | 0.285561i | ||||
\(494\) | 136.312 | + | 78.7000i | 0.275936 | + | 0.159312i | ||||
\(495\) | −19.0560 | + | 260.946i | −0.0384969 | + | 0.527163i | ||||
\(496\) | −48.4619 | −0.0977055 | ||||||||
\(497\) | −426.844 | + | 196.689i | −0.858841 | + | 0.395754i | ||||
\(498\) | 320.827 | + | 320.827i | 0.644231 | + | 0.644231i | ||||
\(499\) | 712.187 | − | 411.181i | 1.42723 | − | 0.824010i | 0.430326 | − | 0.902673i | \(-0.358398\pi\) |
0.996901 | + | 0.0786631i | \(0.0250651\pi\) | |||||||
\(500\) | −780.688 | − | 716.123i | −1.56138 | − | 1.43225i | ||||
\(501\) | −139.808 | + | 242.155i | −0.279059 | + | 0.483344i | ||||
\(502\) | 59.6068 | + | 15.9716i | 0.118739 | + | 0.0318159i | ||||
\(503\) | −494.995 | − | 494.995i | −0.984086 | − | 0.984086i | 0.0157893 | − | 0.999875i | \(-0.494974\pi\) |
−0.999875 | + | 0.0157893i | \(0.994974\pi\) | |||||||
\(504\) | −327.145 | + | 56.1563i | −0.649097 | + | 0.111421i | ||||
\(505\) | −236.856 | + | 348.828i | −0.469022 | + | 0.690749i | ||||
\(506\) | 739.512 | + | 1280.87i | 1.46149 | + | 2.53137i | ||||
\(507\) | −7.56391 | − | 28.2289i | −0.0149190 | − | 0.0556783i | ||||
\(508\) | −1362.34 | + | 365.039i | −2.68178 | + | 0.718580i | ||||
\(509\) | −503.114 | + | 290.473i | −0.988437 | + | 0.570674i | −0.904807 | − | 0.425823i | \(-0.859985\pi\) |
−0.0836299 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(510\) | −67.0694 | − | 350.815i | −0.131509 | − | 0.687873i | ||||
\(511\) | 98.3692 | − | 81.7844i | 0.192503 | − | 0.160048i | ||||
\(512\) | 759.774 | − | 759.774i | 1.48393 | − | 1.48393i | ||||
\(513\) | −4.85911 | + | 18.1345i | −0.00947196 | + | 0.0353498i | ||||
\(514\) | 244.377 | + | 141.091i | 0.475442 | + | 0.274497i | ||||
\(515\) | 192.539 | − | 553.621i | 0.373861 | − | 1.07499i | ||||
\(516\) | −204.246 | − | 353.764i | −0.395825 | − | 0.685589i | ||||
\(517\) | 1010.67 | − | 1010.67i | 1.95487 | − | 1.95487i | ||||
\(518\) | 748.829 | + | 68.9365i | 1.44562 | + | 0.133082i | ||||
\(519\) | − | 361.048i | − | 0.695660i | ||||||
\(520\) | −70.9947 | + | 972.176i | −0.136528 | + | 1.86957i | ||||
\(521\) | −274.035 | + | 474.643i | −0.525979 | + | 0.911023i | 0.473563 | + | 0.880760i | \(0.342968\pi\) |
−0.999542 | + | 0.0302629i | \(0.990366\pi\) | |||||||
\(522\) | 127.752 | + | 476.778i | 0.244736 | + | 0.913367i | ||||
\(523\) | 60.8889 | − | 227.240i | 0.116422 | − | 0.434494i | −0.882967 | − | 0.469435i | \(-0.844458\pi\) |
0.999389 | + | 0.0349409i | \(0.0111243\pi\) | |||||||
\(524\) | 1383.57i | 2.64040i | ||||||||
\(525\) | −258.755 | + | 157.863i | −0.492867 | + | 0.300692i | ||||
\(526\) | 612.306 | 1.16408 | ||||||||
\(527\) | −24.9278 | − | 6.67937i | −0.0473013 | − | 0.0126743i | ||||
\(528\) | 639.882 | − | 171.456i | 1.21190 | − | 0.324727i | ||||
\(529\) | −40.9971 | − | 23.6697i | −0.0774992 | − | 0.0447442i | ||||
\(530\) | −29.7568 | − | 2.17304i | −0.0561449 | − | 0.00410007i | ||||
\(531\) | −265.200 | −0.499435 | ||||||||
\(532\) | 194.675 | − | 89.7064i | 0.365931 | − | 0.168621i | ||||
\(533\) | −261.151 | − | 261.151i | −0.489964 | − | 0.489964i | ||||
\(534\) | 270.862 | − | 156.382i | 0.507233 | − | 0.292851i | ||||
\(535\) | 674.921 | + | 234.725i | 1.26153 | + | 0.438737i | ||||
\(536\) | −92.1661 | + | 159.636i | −0.171952 | + | 0.297829i | ||||
\(537\) | −198.917 | − | 53.2997i | −0.370423 | − | 0.0992546i | ||||
\(538\) | −462.818 | − | 462.818i | −0.860256 | − | 0.860256i | ||||
\(539\) | −285.028 | − | 805.766i | −0.528808 | − | 1.49493i | ||||
\(540\) | −216.273 | + | 41.3474i | −0.400506 | + | 0.0765693i | ||||
\(541\) | 261.735 | + | 453.339i | 0.483799 | + | 0.837965i | 0.999827 | − | 0.0186072i | \(-0.00592319\pi\) |
−0.516028 | + | 0.856572i | \(0.672590\pi\) | |||||||
\(542\) | −333.159 | − | 1243.37i | −0.614685 | − | 2.29404i | ||||
\(543\) | −3.56993 | + | 0.956559i | −0.00657445 | + | 0.00176162i | ||||
\(544\) | −143.819 | + | 83.0342i | −0.264374 | + | 0.152636i | ||||
\(545\) | 672.165 | + | 456.404i | 1.23333 | + | 0.837438i | ||||
\(546\) | 495.505 | + | 182.898i | 0.907519 | + | 0.334977i | ||||
\(547\) | −201.681 | + | 201.681i | −0.368703 | + | 0.368703i | −0.867004 | − | 0.498301i | \(-0.833958\pi\) |
0.498301 | + | 0.867004i | \(0.333958\pi\) | |||||||
\(548\) | 324.277 | − | 1210.22i | 0.591747 | − | 2.20843i | ||||
\(549\) | −121.751 | − | 70.2928i | −0.221768 | − | 0.128038i | ||||
\(550\) | 1235.75 | − | 919.309i | 2.24682 | − | 1.67147i | ||||
\(551\) | −84.1545 | − | 145.760i | −0.152731 | − | 0.264537i | ||||
\(552\) | −464.741 | + | 464.741i | −0.841923 | + | 0.841923i | ||||
\(553\) | −90.5327 | + | 128.054i | −0.163712 | + | 0.231563i | ||||
\(554\) | 1707.78i | 3.08263i | ||||||||
\(555\) | 262.706 | + | 19.1846i | 0.473345 | + | 0.0345668i | ||||
\(556\) | −430.336 | + | 745.364i | −0.773985 | + | 1.34058i | ||||
\(557\) | 178.472 | + | 666.065i | 0.320416 | + | 1.19581i | 0.918841 | + | 0.394629i | \(0.129127\pi\) |
−0.598425 | + | 0.801179i | \(0.704207\pi\) | |||||||
\(558\) | −6.06120 | + | 22.6207i | −0.0108624 | + | 0.0405389i | ||||
\(559\) | 343.226i | 0.614000i | ||||||||
\(560\) | 592.723 | + | 487.501i | 1.05843 | + | 0.870537i | ||||
\(561\) | 352.773 | 0.628828 | ||||||||
\(562\) | −1613.42 | − | 432.315i | −2.87086 | − | 0.769244i | ||||
\(563\) | −739.166 | + | 198.059i | −1.31291 | + | 0.351792i | −0.846315 | − | 0.532682i | \(-0.821184\pi\) |
−0.466590 | + | 0.884474i | \(0.654517\pi\) | |||||||
\(564\) | 1041.71 | + | 601.430i | 1.84700 | + | 1.06637i | ||||
\(565\) | 14.3051 | + | 16.5590i | 0.0253188 | + | 0.0293080i | ||||
\(566\) | −876.988 | −1.54945 | ||||||||
\(567\) | −5.77530 | + | 62.7347i | −0.0101857 | + | 0.110643i | ||||
\(568\) | 750.402 | + | 750.402i | 1.32113 | + | 1.32113i | ||||
\(569\) | −116.121 | + | 67.0425i | −0.204079 | + | 0.117825i | −0.598557 | − | 0.801080i | \(-0.704259\pi\) |
0.394478 | + | 0.918906i | \(0.370926\pi\) | |||||||
\(570\) | 99.4816 | − | 48.1412i | 0.174529 | − | 0.0844583i | ||||
\(571\) | −286.520 | + | 496.267i | −0.501786 | + | 0.869119i | 0.498212 | + | 0.867055i | \(0.333990\pi\) |
−0.999998 | + | 0.00206333i | \(0.999343\pi\) | |||||||
\(572\) | −1761.19 | − | 471.910i | −3.07901 | − | 0.825017i | ||||
\(573\) | 209.351 | + | 209.351i | 0.365359 | + | 0.365359i | ||||
\(574\) | −729.654 | + | 125.249i | −1.27117 | + | 0.218205i | ||||
\(575\) | −237.911 | + | 551.009i | −0.413758 | + | 0.958276i | ||||
\(576\) | −56.2132 | − | 97.3642i | −0.0975924 | − | 0.169035i | ||||
\(577\) | −178.653 | − | 666.742i | −0.309624 | − | 1.15553i | −0.928891 | − | 0.370352i | \(-0.879237\pi\) |
0.619268 | − | 0.785180i | \(-0.287430\pi\) | |||||||
\(578\) | 520.805 | − | 139.549i | 0.901048 | − | 0.241435i | ||||
\(579\) | 124.330 | − | 71.7821i | 0.214733 | − | 0.123976i | ||||
\(580\) | 1108.88 | − | 1633.10i | 1.91186 | − | 2.81568i | ||||
\(581\) | −487.040 | − | 179.773i | −0.838280 | − | 0.309420i | ||||
\(582\) | 55.9782 | − | 55.9782i | 0.0961824 | − | 0.0961824i | ||||
\(583\) | 7.62709 | − | 28.4647i | 0.0130825 | − | 0.0488245i | ||||
\(584\) | −250.161 | − | 144.430i | −0.428358 | − | 0.247312i | ||||
\(585\) | 174.744 | + | 60.7725i | 0.298707 | + | 0.103885i | ||||
\(586\) | 152.726 | + | 264.530i | 0.260625 | + | 0.451416i | ||||
\(587\) | 688.633 | − | 688.633i | 1.17314 | − | 1.17314i | 0.191682 | − | 0.981457i | \(-0.438606\pi\) |
0.981457 | − | 0.191682i | \(-0.0613942\pi\) | |||||||
\(588\) | 592.922 | − | 407.207i | 1.00837 | − | 0.692528i | ||||
\(589\) | − | 7.98542i | − | 0.0135576i | ||||||
\(590\) | 1020.57 | + | 1181.37i | 1.72978 | + | 2.00232i | ||||
\(591\) | 39.2398 | − | 67.9653i | 0.0663955 | − | 0.115000i | ||||
\(592\) | −172.613 | − | 644.199i | −0.291576 | − | 1.08817i | ||||
\(593\) | −100.681 | + | 375.748i | −0.169783 | + | 0.633640i | 0.827598 | + | 0.561321i | \(0.189707\pi\) |
−0.997382 | + | 0.0723188i | \(0.976960\pi\) | |||||||
\(594\) | − | 320.124i | − | 0.538929i | ||||||
\(595\) | 237.693 | + | 332.453i | 0.399484 | + | 0.558745i | ||||
\(596\) | 898.035 | 1.50677 | ||||||||
\(597\) | 42.5600 | + | 11.4039i | 0.0712898 | + | 0.0191021i | ||||
\(598\) | 1010.20 | − | 270.683i | 1.68930 | − | 0.452647i | ||||
\(599\) | 223.139 | + | 128.830i | 0.372520 | + | 0.215074i | 0.674559 | − | 0.738221i | \(-0.264334\pi\) |
−0.302039 | + | 0.953296i | \(0.597667\pi\) | |||||||
\(600\) | 536.727 | + | 424.694i | 0.894544 | + | 0.707823i | ||||
\(601\) | 91.8404 | 0.152813 | 0.0764064 | − | 0.997077i | \(-0.475655\pi\) | ||||
0.0764064 | + | 0.997077i | \(0.475655\pi\) | |||||||
\(602\) | 561.793 | + | 397.180i | 0.933211 | + | 0.659767i | ||||
\(603\) | 24.7389 | + | 24.7389i | 0.0410264 | + | 0.0410264i | ||||
\(604\) | 1182.93 | − | 682.963i | 1.95849 | − | 1.13073i | ||||
\(605\) | 399.112 | + | 824.746i | 0.659689 | + | 1.36322i | ||||
\(606\) | 257.945 | − | 446.773i | 0.425651 | − | 0.737250i | ||||
\(607\) | 759.412 | + | 203.484i | 1.25109 | + | 0.335229i | 0.822757 | − | 0.568393i | \(-0.192435\pi\) |
0.428333 | + | 0.903621i | \(0.359101\pi\) | |||||||
\(608\) | −36.3355 | − | 36.3355i | −0.0597623 | − | 0.0597623i | ||||
\(609\) | −361.075 | − | 434.296i | −0.592898 | − | 0.713130i | ||||
\(610\) | 155.404 | + | 812.862i | 0.254761 | + | 1.33256i | ||||
\(611\) | −505.338 | − | 875.272i | −0.827068 | − | 1.43252i | ||||
\(612\) | 76.8393 | + | 286.768i | 0.125554 | + | 0.468576i | ||||
\(613\) | 407.928 | − | 109.304i | 0.665461 | − | 0.178310i | 0.0897518 | − | 0.995964i | \(-0.471393\pi\) |
0.575709 | + | 0.817654i | \(0.304726\pi\) | |||||||
\(614\) | −158.951 | + | 91.7706i | −0.258878 | + | 0.149464i | ||||
\(615\) | −254.705 | + | 48.6950i | −0.414155 | + | 0.0791789i | ||||
\(616\) | −1484.01 | + | 1233.81i | −2.40911 | + | 2.00294i | ||||
\(617\) | 174.640 | − | 174.640i | 0.283047 | − | 0.283047i | −0.551276 | − | 0.834323i | \(-0.685859\pi\) |
0.834323 | + | 0.551276i | \(0.185859\pi\) | |||||||
\(618\) | −185.616 | + | 692.727i | −0.300349 | + | 1.12092i | ||||
\(619\) | 408.198 | + | 235.673i | 0.659448 | + | 0.380732i | 0.792066 | − | 0.610435i | \(-0.209005\pi\) |
−0.132619 | + | 0.991167i | \(0.542339\pi\) | |||||||
\(620\) | 84.3035 | − | 40.7962i | 0.135973 | − | 0.0658003i | ||||
\(621\) | 62.3722 | + | 108.032i | 0.100438 | + | 0.173964i | ||||
\(622\) | −222.159 | + | 222.159i | −0.357169 | + | 0.357169i | ||||
\(623\) | −206.597 | + | 292.222i | −0.331616 | + | 0.469056i | ||||
\(624\) | − | 468.431i | − | 0.750690i | ||||||
\(625\) | 598.618 | + | 179.671i | 0.957788 | + | 0.287474i | ||||
\(626\) | 324.524 | − | 562.091i | 0.518408 | − | 0.897909i | ||||
\(627\) | 28.2520 | + | 105.438i | 0.0450591 | + | 0.168163i | ||||
\(628\) | 301.344 | − | 1124.63i | 0.479847 | − | 1.79081i | ||||
\(629\) | − | 355.153i | − | 0.564631i | ||||||
\(630\) | 301.685 | − | 215.695i | 0.478865 | − | 0.342373i | ||||
\(631\) | −670.413 | −1.06246 | −0.531230 | − | 0.847227i | \(-0.678270\pi\) | ||||
−0.531230 | + | 0.847227i | \(0.678270\pi\) | |||||||
\(632\) | 342.049 | + | 91.6516i | 0.541216 | + | 0.145018i | ||||
\(633\) | 234.218 | − | 62.7584i | 0.370012 | − | 0.0991444i | ||||
\(634\) | −1127.47 | − | 650.947i | −1.77835 | − | 1.02673i | ||||
\(635\) | 629.662 | − | 543.957i | 0.991594 | − | 0.856625i | ||||
\(636\) | 24.8002 | 0.0389940 | ||||||||
\(637\) | −602.518 | + | 47.2125i | −0.945868 | + | 0.0741170i | ||||
\(638\) | 2029.32 | + | 2029.32i | 3.18075 | + | 3.18075i | ||||
\(639\) | 174.435 | − | 100.710i | 0.272982 | − | 0.157606i | ||||
\(640\) | −310.831 | + | 893.755i | −0.485673 | + | 1.39649i | ||||
\(641\) | 617.665 | − | 1069.83i | 0.963596 | − | 1.66900i | 0.250256 | − | 0.968180i | \(-0.419485\pi\) |
0.713341 | − | 0.700818i | \(-0.247181\pi\) | |||||||
\(642\) | −844.506 | − | 226.285i | −1.31543 | − | 0.352468i | ||||
\(643\) | −504.796 | − | 504.796i | −0.785064 | − | 0.785064i | 0.195617 | − | 0.980680i | \(-0.437329\pi\) |
−0.980680 | + | 0.195617i | \(0.937329\pi\) | |||||||
\(644\) | 493.181 | − | 1336.12i | 0.765809 | − | 2.07473i | ||||
\(645\) | 199.377 | + | 135.378i | 0.309112 | + | 0.209888i | ||||
\(646\) | −74.5061 | − | 129.048i | −0.115334 | − | 0.199765i | ||||
\(647\) | 27.8251 | + | 103.845i | 0.0430064 | + | 0.160502i | 0.984090 | − | 0.177673i | \(-0.0568570\pi\) |
−0.941083 | + | 0.338175i | \(0.890190\pi\) | |||||||
\(648\) | 137.408 | − | 36.8184i | 0.212050 | − | 0.0568186i | ||||
\(649\) | −1335.36 | + | 770.968i | −2.05756 | + | 1.18793i | ||||
\(650\) | −401.746 | − | 1012.29i | −0.618071 | − | 1.55737i | ||||
\(651\) | −4.53347 | − | 26.4102i | −0.00696385 | − | 0.0405687i | ||||
\(652\) | −1131.84 | + | 1131.84i | −1.73596 | + | 1.73596i | ||||
\(653\) | 79.6877 | − | 297.399i | 0.122033 | − | 0.455434i | −0.877683 | − | 0.479241i | \(-0.840912\pi\) |
0.999717 | + | 0.0238067i | \(0.00757864\pi\) | |||||||
\(654\) | −860.898 | − | 497.040i | −1.31636 | − | 0.760000i | ||||
\(655\) | −355.558 | − | 734.745i | −0.542837 | − | 1.12175i | ||||
\(656\) | 328.287 | + | 568.610i | 0.500438 | + | 0.866784i | ||||
\(657\) | −38.7676 | + | 38.7676i | −0.0590070 | + | 0.0590070i | ||||
\(658\) | −2017.42 | − | 185.722i | −3.06599 | − | 0.282252i | ||||
\(659\) | − | 590.013i | − | 0.895315i | −0.894205 | − | 0.447658i | \(-0.852258\pi\) | ||
0.894205 | − | 0.447658i | \(-0.147742\pi\) | |||||||
\(660\) | −968.792 | + | 836.927i | −1.46787 | + | 1.26807i | ||||
\(661\) | −1.19346 | + | 2.06714i | −0.00180554 | + | 0.00312729i | −0.866927 | − | 0.498436i | \(-0.833908\pi\) |
0.865121 | + | 0.501563i | \(0.167241\pi\) | |||||||
\(662\) | 411.354 | + | 1535.19i | 0.621380 | + | 2.31902i | ||||
\(663\) | 64.5625 | − | 240.951i | 0.0973794 | − | 0.363425i | ||||
\(664\) | 1172.27i | 1.76547i | ||||||||
\(665\) | −80.3291 | + | 97.6674i | −0.120796 | + | 0.146868i | ||||
\(666\) | −322.284 | −0.483910 | ||||||||
\(667\) | −1080.22 | − | 289.444i | −1.61952 | − | 0.433948i | ||||
\(668\) | −1321.58 | + | 354.115i | −1.97841 | + | 0.530113i | ||||
\(669\) | 281.377 | + | 162.453i | 0.420594 | + | 0.242830i | ||||
\(670\) | 15.0001 | − | 205.405i | 0.0223882 | − | 0.306575i | ||||
\(671\) | −817.398 | −1.21818 | ||||||||
\(672\) | −140.801 | − | 99.5440i | −0.209525 | − | 0.148131i | ||||
\(673\) | −50.3354 | − | 50.3354i | −0.0747925 | − | 0.0747925i | 0.668721 | − | 0.743513i | \(-0.266842\pi\) |
−0.743513 | + | 0.668721i | \(0.766842\pi\) | |||||||
\(674\) | −40.5429 | + | 23.4075i | −0.0601527 | + | 0.0347292i | ||||
\(675\) | 104.226 | − | 77.5367i | 0.154409 | − | 0.114869i | ||||
\(676\) | 71.4998 | − | 123.841i | 0.105769 | − | 0.183197i | ||||
\(677\) | −500.800 | − | 134.189i | −0.739734 | − | 0.198211i | −0.130774 | − | 0.991412i | \(-0.541746\pi\) |
−0.608960 | + | 0.793201i | \(0.708413\pi\) | |||||||
\(678\) | −18.9318 | − | 18.9318i | −0.0279230 | − | 0.0279230i | ||||
\(679\) | −31.3670 | + | 84.9793i | −0.0461958 | + | 0.125154i | ||||
\(680\) | 518.391 | − | 763.457i | 0.762340 | − | 1.12273i | ||||
\(681\) | 212.616 | + | 368.262i | 0.312212 | + | 0.540767i | ||||
\(682\) | 35.2413 | + | 131.522i | 0.0516734 | + | 0.192848i | ||||
\(683\) | −97.0866 | + | 26.0143i | −0.142147 | + | 0.0380883i | −0.329191 | − | 0.944263i | \(-0.606776\pi\) |
0.187044 | + | 0.982352i | \(0.440109\pi\) | |||||||
\(684\) | −79.5566 | + | 45.9321i | −0.116311 | + | 0.0671521i | ||||
\(685\) | 138.802 | + | 726.022i | 0.202631 | + | 1.05989i | ||||
\(686\) | −619.954 | + | 1040.84i | −0.903723 | + | 1.51726i | ||||
\(687\) | 307.677 | − | 307.677i | 0.447857 | − | 0.447857i | ||||
\(688\) | 157.926 | − | 589.389i | 0.229544 | − | 0.856670i | ||||
\(689\) | −18.0461 | − | 10.4189i | −0.0261917 | − | 0.0151218i | ||||
\(690\) | 241.215 | − | 693.583i | 0.349587 | − | 1.00519i | ||||
\(691\) | 0.723424 | + | 1.25301i | 0.00104692 | + | 0.00181332i | 0.866548 | − | 0.499093i | \(-0.166333\pi\) |
−0.865501 | + | 0.500906i | \(0.833000\pi\) | |||||||
\(692\) | 1249.21 | − | 1249.21i | 1.80521 | − | 1.80521i | ||||
\(693\) | 153.297 | + | 332.676i | 0.221208 | + | 0.480052i | ||||
\(694\) | − | 1384.57i | − | 1.99506i | ||||||
\(695\) | 36.9818 | − | 506.416i | 0.0532112 | − | 0.728655i | ||||
\(696\) | −637.655 | + | 1104.45i | −0.916171 | + | 1.58685i | ||||
\(697\) | 90.4939 | + | 337.728i | 0.129833 | + | 0.484545i | ||||
\(698\) | 439.457 | − | 1640.08i | 0.629595 | − | 2.34968i | ||||
\(699\) | 511.820i | 0.732217i | ||||||||
\(700\) | −1441.48 | − | 349.081i | −2.05926 | − | 0.498687i | ||||
\(701\) | −230.081 | −0.328218 | −0.164109 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164109 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(702\) | −218.651 | − | 58.5873i | −0.311469 | − | 0.0834577i | ||||
\(703\) | 106.149 | − | 28.4427i | 0.150995 | − | 0.0404590i | ||||
\(704\) | −566.098 | − | 326.837i | −0.804117 | − | 0.464257i | ||||
\(705\) | −707.758 | − | 51.6851i | −1.00391 | − | 0.0733122i | ||||
\(706\) | 1957.73 | 2.77299 | ||||||||
\(707\) | −54.1135 | + | 587.813i | −0.0765396 | + | 0.831419i | ||||
\(708\) | −917.580 | − | 917.580i | −1.29602 | − | 1.29602i | ||||
\(709\) | 383.431 | − | 221.374i | 0.540805 | − | 0.312234i | −0.204600 | − | 0.978846i | \(-0.565589\pi\) |
0.745405 | + | 0.666612i | \(0.232256\pi\) | |||||||
\(710\) | −1119.91 | − | 389.482i | −1.57733 | − | 0.548566i | ||||
\(711\) | 33.6054 | − | 58.2062i | 0.0472649 | − | 0.0818653i | ||||
\(712\) | 780.559 | + | 209.150i | 1.09629 | + | 0.293750i | ||||
\(713\) | −37.5183 | − | 37.5183i | −0.0526203 | − | 0.0526203i | ||||
\(714\) | −319.677 | − | 384.503i | −0.447727 | − | 0.538520i | ||||
\(715\) | 1056.55 | − | 201.994i | 1.47770 | − | 0.282509i | ||||
\(716\) | −503.829 | − | 872.658i | −0.703672 | − | 1.21880i | ||||
\(717\) | 45.2011 | + | 168.693i | 0.0630420 | + | 0.235276i | ||||
\(718\) | −345.587 | + | 92.5998i | −0.481319 | + | 0.128969i | ||||
\(719\) | −446.525 | + | 257.801i | −0.621036 | + | 0.358555i | −0.777272 | − | 0.629164i | \(-0.783397\pi\) |
0.156236 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(720\) | −272.108 | − | 184.762i | −0.377927 | − | 0.256614i | ||||
\(721\) | −138.831 | − | 808.775i | −0.192553 | − | 1.12174i | ||||
\(722\) | −868.998 | + | 868.998i | −1.20360 | + | 1.20360i | ||||
\(723\) | −161.090 | + | 601.194i | −0.222807 | + | 0.831527i | ||||
\(724\) | −15.6614 | − | 9.04213i | −0.0216318 | − | 0.0124891i | ||||
\(725\) | −169.188 | + | 1152.22i | −0.233363 | + | 1.58927i | ||||
\(726\) | −560.522 | − | 970.852i | −0.772068 | − | 1.33726i | ||||
\(727\) | −829.146 | + | 829.146i | −1.14050 | + | 1.14050i | −0.152145 | + | 0.988358i | \(0.548618\pi\) |
−0.988358 | + | 0.152145i | \(0.951382\pi\) | |||||||
\(728\) | 571.121 | + | 1239.41i | 0.784507 | + | 1.70249i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 321.884 | + | 23.5061i | 0.440937 | + | 0.0322001i | ||||
\(731\) | 162.468 | − | 281.402i | 0.222254 | − | 0.384956i | ||||
\(732\) | −178.042 | − | 664.462i | −0.243227 | − | 0.907734i | ||||
\(733\) | 266.886 | − | 996.034i | 0.364102 | − | 1.35885i | −0.504533 | − | 0.863392i | \(-0.668335\pi\) |
0.868635 | − | 0.495453i | \(-0.164998\pi\) | |||||||
\(734\) | − | 1076.26i | − | 1.46629i | ||||||
\(735\) | −210.225 | + | 368.620i | −0.286020 | + | 0.501523i | ||||
\(736\) | −341.433 | −0.463904 | ||||||||
\(737\) | 196.486 | + | 52.6484i | 0.266603 | + | 0.0714360i | ||||
\(738\) | 306.471 | − | 82.1188i | 0.415273 | − | 0.111272i | ||||
\(739\) | −287.660 | − | 166.081i | −0.389256 | − | 0.224737i | 0.292582 | − | 0.956241i | \(-0.405486\pi\) |
−0.681838 | + | 0.731503i | \(0.738819\pi\) | |||||||
\(740\) | 842.574 | + | 975.329i | 1.13861 | + | 1.31801i | ||||
\(741\) | 77.1868 | 0.104166 | ||||||||
\(742\) | −37.9365 | + | 17.4811i | −0.0511274 | + | 0.0235595i | ||||
\(743\) | −764.980 | − | 764.980i | −1.02958 | − | 1.02958i | −0.999549 | − | 0.0300340i | \(-0.990438\pi\) |
−0.0300340 | − | 0.999549i | \(-0.509562\pi\) | |||||||
\(744\) | −52.4007 | + | 30.2535i | −0.0704310 | + | 0.0406634i | ||||
\(745\) | −476.902 | + | 230.783i | −0.640136 | + | 0.309775i | ||||
\(746\) | 189.368 | − | 327.994i | 0.253844 | − | 0.439671i | ||||
\(747\) | 214.916 | + | 57.5865i | 0.287705 | + | 0.0770903i | ||||
\(748\) | 1220.58 | + | 1220.58i | 1.63179 | + | 1.63179i | ||||
\(749\) | 985.980 | − | 169.249i | 1.31640 | − | 0.225967i | ||||
\(750\) | −746.490 | − | 165.904i | −0.995320 | − | 0.221206i | ||||
\(751\) | −66.3561 | − | 114.932i | −0.0883570 | − | 0.153039i | 0.818460 | − | 0.574564i | \(-0.194828\pi\) |
−0.906817 | + | 0.421525i | \(0.861495\pi\) | |||||||
\(752\) | 465.036 | + | 1735.54i | 0.618399 | + | 2.30790i | ||||
\(753\) | 29.2304 | − | 7.83225i | 0.0388185 | − | 0.0104014i | ||||
\(754\) | 1757.46 | − | 1014.67i | 2.33084 | − | 1.34571i | ||||
\(755\) | −452.681 | + | 666.683i | −0.599577 | + | 0.883024i | ||||
\(756\) | −237.041 | + | 197.077i | −0.313547 | + | 0.260684i | ||||
\(757\) | 705.876 | − | 705.876i | 0.932465 | − | 0.932465i | −0.0653945 | − | 0.997859i | \(-0.520831\pi\) |
0.997859 | + | 0.0653945i | \(0.0208306\pi\) | |||||||
\(758\) | 4.57797e−5 | 0 | 0.000170852i | 6.03954e−8 | 0 | 2.25399e-7i | ||||
\(759\) | 628.122 | + | 362.647i | 0.827566 | + | 0.477795i | ||||
\(760\) | 269.701 | + | 93.7968i | 0.354869 | + | 0.123417i | ||||
\(761\) | −21.9538 | − | 38.0250i | −0.0288486 | − | 0.0499672i | 0.851241 | − | 0.524776i | \(-0.175851\pi\) |
−0.880089 | + | 0.474808i | \(0.842517\pi\) | |||||||
\(762\) | −719.888 | + | 719.888i | −0.944735 | + | 0.944735i | ||||
\(763\) | 1132.67 | + | 104.273i | 1.48450 | + | 0.136661i | ||||
\(764\) | 1448.69i | 1.89619i | ||||||||
\(765\) | −114.501 | − | 132.542i | −0.149674 | − | 0.173257i | ||||
\(766\) | 332.731 | − | 576.308i | 0.434375 | − | 0.752360i | ||||
\(767\) | 282.197 | + | 1053.17i | 0.367923 | + | 1.37311i | ||||
\(768\) | 232.456 | − | 867.536i | 0.302676 | − | 1.12960i | ||||
\(769\) | − | 317.954i | − | 0.413464i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) | ||
0.978398 | − | 0.206732i | \(-0.0662829\pi\) | |||||||
\(770\) | 892.017 | − | 1963.12i | 1.15846 | − | 2.54950i | ||||
\(771\) | 138.378 | 0.179479 | ||||||||
\(772\) | 678.539 | + | 181.814i | 0.878937 | + | 0.235510i | ||||
\(773\) | −681.538 | + | 182.617i | −0.881679 | + | 0.236245i | −0.671131 | − | 0.741339i | \(-0.734191\pi\) |
−0.210547 | + | 0.977584i | \(0.567525\pi\) | |||||||
\(774\) | −255.359 | − | 147.432i | −0.329921 | − | 0.190480i | ||||
\(775\) | −34.2853 | + | 43.3296i | −0.0442391 | + | 0.0559092i | ||||
\(776\) | 204.540 | 0.263582 | ||||||||
\(777\) | 334.921 | − | 154.331i | 0.431044 | − | 0.198625i | ||||
\(778\) | 526.444 | + | 526.444i | 0.676663 | + | 0.676663i | ||||
\(779\) | −93.6941 | + | 54.0943i | −0.120275 | + | 0.0694407i | ||||
\(780\) | 394.334 | + | 814.874i | 0.505557 | + | 1.04471i | ||||
\(781\) | 585.553 | − | 1014.21i | 0.749748 | − | 1.29860i | ||||
\(782\) | −956.369 | − | 256.258i | −1.22298 | − | 0.327696i | ||||
\(783\) | 171.157 | + | 171.157i | 0.218592 | + | 0.218592i | ||||
\(784\) | 1056.37 | + | 196.159i | 1.34741 | + | 0.250203i | ||||
\(785\) | 128.986 | + | 674.676i | 0.164313 | + | 0.859460i | ||||
\(786\) | 499.354 | + | 864.907i | 0.635311 | + | 1.10039i | ||||
\(787\) | −81.4498 | − | 303.975i | −0.103494 | − | 0.386245i | 0.894676 | − | 0.446716i | \(-0.147406\pi\) |
−0.998170 | + | 0.0604708i | \(0.980740\pi\) | |||||||
\(788\) | 370.924 | − | 99.3888i | 0.470716 | − | 0.126128i | ||||
\(789\) | 260.038 | − | 150.133i | 0.329580 | − | 0.190283i | ||||
\(790\) | −388.611 | + | 74.2952i | −0.491912 | + | 0.0940446i | ||||
\(791\) | 28.7400 | + | 10.6083i | 0.0363337 | + | 0.0134113i | ||||
\(792\) | 584.853 | − | 584.853i | 0.738451 | − | 0.738451i | ||||
\(793\) | −149.596 | + | 558.299i | −0.188645 | + | 0.704034i | ||||
\(794\) | −767.281 | − | 442.990i | −0.966349 | − | 0.557922i | ||||
\(795\) | −13.1701 | + | 6.37330i | −0.0165662 | + | 0.00801673i | ||||
\(796\) | 107.799 | + | 186.713i | 0.135425 | + | 0.234564i | ||||
\(797\) | 298.666 | − | 298.666i | 0.374738 | − | 0.374738i | −0.494461 | − | 0.869200i | \(-0.664635\pi\) |
0.869200 | + | 0.494461i | \(0.164635\pi\) | |||||||
\(798\) | 89.3202 | − | 126.339i | 0.111930 | − | 0.158320i | ||||
\(799\) | 956.818i | 1.19752i | ||||||||
\(800\) | 41.1537 | + | 353.165i | 0.0514421 | + | 0.441456i | ||||
\(801\) | 76.6878 | − | 132.827i | 0.0957401 | − | 0.165827i | ||||
\(802\) | 316.070 | + | 1179.59i | 0.394102 | + | 1.47081i | ||||
\(803\) | −82.5035 | + | 307.907i | −0.102744 | + | 0.383446i | ||||
\(804\) | 171.191i | 0.212924i | ||||||||
\(805\) | 81.4615 | + | 836.289i | 0.101194 | + | 1.03887i | ||||
\(806\) | 96.2819 | 0.119456 | ||||||||
\(807\) | −310.033 | − | 83.0730i | −0.384179 | − | 0.102940i | ||||
\(808\) | 1287.49 | − | 344.982i | 1.59343 | − | 0.426958i | ||||
\(809\) | −1146.88 | − | 662.154i | −1.41766 | − | 0.818485i | −0.421564 | − | 0.906798i | \(-0.638519\pi\) |
−0.996093 | + | 0.0883137i | \(0.971852\pi\) | |||||||
\(810\) | −120.275 | + | 103.904i | −0.148488 | + | 0.128277i | ||||
\(811\) | 238.488 | 0.294067 | 0.147033 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147033 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(812\) | 253.341 | − | 2751.94i | 0.311997 | − | 3.38909i | ||||
\(813\) | −446.354 | − | 446.354i | −0.549021 | − | 0.549021i | ||||
\(814\) | −1622.79 | + | 936.917i | −1.99360 | + | 1.15100i | ||||
\(815\) | 310.197 | − | 891.933i | 0.380610 | − | 1.09440i | ||||
\(816\) | −221.734 | + | 384.055i | −0.271733 | + | 0.470655i | ||||
\(817\) | 97.1180 | + | 26.0227i | 0.118871 | + | 0.0318515i | ||||
\(818\) | −284.040 | − | 284.040i | −0.347237 | − | 0.347237i | ||||
\(819\) | 255.280 | − | 43.8203i | 0.311697 | − | 0.0535047i | ||||
\(820\) | −1049.75 | − | 712.786i | −1.28018 | − | 0.869251i | ||||
\(821\) | 276.005 | + | 478.055i | 0.336182 | + | 0.582284i | 0.983711 | − | 0.179756i | \(-0.0575310\pi\) |
−0.647529 | + | 0.762041i | \(0.724198\pi\) | |||||||
\(822\) | −234.074 | − | 873.578i | −0.284762 | − | 1.06275i | ||||
\(823\) | −700.442 | + | 187.683i | −0.851084 | + | 0.228047i | −0.657891 | − | 0.753113i | \(-0.728551\pi\) |
−0.193194 | + | 0.981161i | \(0.561885\pi\) | |||||||
\(824\) | −1604.70 | + | 926.472i | −1.94745 | + | 1.12436i | ||||
\(825\) | 299.399 | − | 693.416i | 0.362907 | − | 0.840504i | ||||
\(826\) | 2050.39 | + | 756.827i | 2.48231 | + | 0.916255i | ||||
\(827\) | 403.921 | − | 403.921i | 0.488417 | − | 0.488417i | −0.419389 | − | 0.907807i | \(-0.637756\pi\) |
0.907807 | + | 0.419389i | \(0.137756\pi\) | |||||||
\(828\) | −157.980 | + | 589.590i | −0.190797 | + | 0.712065i | ||||
\(829\) | 292.544 | + | 168.900i | 0.352887 | + | 0.203740i | 0.665956 | − | 0.745991i | \(-0.268024\pi\) |
−0.313069 | + | 0.949730i | \(0.601357\pi\) | |||||||
\(830\) | −570.532 | − | 1178.98i | −0.687388 | − | 1.42046i | ||||
\(831\) | 418.735 | + | 725.270i | 0.503893 | + | 0.872768i | ||||
\(832\) | −326.840 | + | 326.840i | −0.392837 | + | 0.392837i | ||||
\(833\) | 516.338 | + | 246.497i | 0.619854 | + | 0.295914i | ||||
\(834\) | 621.262i | 0.744919i | ||||||||
\(835\) | 610.820 | − | 527.679i | 0.731521 | − | 0.631951i | ||||
\(836\) | −267.060 | + | 462.561i | −0.319449 | + | 0.553303i | ||||
\(837\) | 2.97233 | + | 11.0929i | 0.00355117 | + | 0.0132532i | ||||
\(838\) | −201.474 | + | 751.910i | −0.240422 | + | 0.897268i | ||||
\(839\) | 1419.09i | 1.69141i | 0.533649 | + | 0.845706i | \(0.320820\pi\) | ||||
−0.533649 | + | 0.845706i | \(0.679180\pi\) | |||||||
\(840\) | 945.231 | + | 157.100i | 1.12528 | + | 0.187024i | ||||
\(841\) | −1328.99 | −1.58025 | ||||||||
\(842\) | −2087.87 | − | 559.444i | −2.47966 | − | 0.664423i | ||||
\(843\) | −791.201 | + | 212.002i | −0.938553 | + | 0.251485i | ||||
\(844\) | 1027.52 | + | 593.240i | 1.21744 | + | 0.702891i | ||||
\(845\) | −6.14448 | + | 84.1404i | −0.00727158 | + | 0.0995744i | ||||
\(846\) | 868.265 | 1.02632 | ||||||||
\(847\) | 1047.41 | + | 740.504i | 1.23661 | + | 0.874266i | ||||
\(848\) | 26.1948 | + | 26.1948i | 0.0308901 | + | 0.0308901i | ||||
\(849\) | −372.446 | + | 215.032i | −0.438687 | + | 0.253276i | ||||
\(850\) | −149.790 | + | 1020.12i | −0.176224 | + | 1.20014i | ||||
\(851\) | 365.094 | − | 632.361i | 0.429017 | − | 0.743080i | ||||
\(852\) | 951.990 | + | 255.085i | 1.11736 | + | 0.299396i | ||||
\(853\) | −104.379 | − | 104.379i | −0.122367 | − | 0.122367i | 0.643271 | − | 0.765638i | \(-0.277577\pi\) |
−0.765638 | + | 0.643271i | \(0.777577\pi\) | |||||||
\(854\) | 740.713 | + | 890.920i | 0.867346 | + | 1.04323i | ||||
\(855\) | 30.4447 | − | 44.8372i | 0.0356078 | − | 0.0524411i | ||||
\(856\) | −1129.46 | − | 1956.29i | −1.31947 | − | 2.28539i | ||||
\(857\) | 306.801 | + | 1145.00i | 0.357995 | + | 1.33605i | 0.876674 | + | 0.481085i | \(0.159757\pi\) |
−0.518679 | + | 0.854969i | \(0.673576\pi\) | |||||||
\(858\) | −1271.29 | + | 340.641i | −1.48169 | + | 0.397017i | ||||
\(859\) | −70.8786 | + | 40.9218i | −0.0825129 | + | 0.0476388i | −0.540689 | − | 0.841223i | \(-0.681836\pi\) |
0.458176 | + | 0.888862i | \(0.348503\pi\) | |||||||
\(860\) | 221.434 | + | 1158.24i | 0.257481 | + | 1.34679i | ||||
\(861\) | −279.164 | + | 232.098i | −0.324233 | + | 0.269568i | ||||
\(862\) | 1810.15 | − | 1810.15i | 2.09995 | − | 2.09995i | ||||
\(863\) | −148.450 | + | 554.024i | −0.172016 | + | 0.641974i | 0.825024 | + | 0.565097i | \(0.191161\pi\) |
−0.997041 | + | 0.0768766i | \(0.975505\pi\) | |||||||
\(864\) | 63.9999 | + | 36.9503i | 0.0740739 | + | 0.0427666i | ||||
\(865\) | −342.363 | + | 984.420i | −0.395795 | + | 1.13806i | ||||
\(866\) | −380.702 | − | 659.395i | −0.439609 | − | 0.761426i | ||||
\(867\) | 186.963 | − | 186.963i | 0.215643 | − | 0.215643i | ||||
\(868\) | 75.6924 | − | 107.064i | 0.0872033 | − | 0.123345i | ||||
\(869\) | − | 390.779i | − | 0.449688i | ||||||
\(870\) | 103.779 | − | 1421.11i | 0.119286 | − | 1.63346i | ||||
\(871\) | 71.9197 | − | 124.569i | 0.0825714 | − | 0.143018i | ||||
\(872\) | −664.754 | − | 2480.90i | −0.762333 | − | 2.84506i | ||||
\(873\) | 10.0477 | − | 37.4987i | 0.0115094 | − | 0.0429538i | ||||
\(874\) | − | 306.366i | − | 0.350533i | ||||||
\(875\) | 855.206 | − | 185.060i | 0.977379 | − | 0.211498i | ||||
\(876\) | −268.268 | −0.306242 | ||||||||
\(877\) | −1061.54 | − | 284.440i | −1.21043 | − | 0.324333i | −0.403497 | − | 0.914981i | \(-0.632206\pi\) |
−0.806929 | + | 0.590648i | \(0.798872\pi\) | |||||||
\(878\) | −2834.14 | + | 759.406i | −3.22795 | + | 0.864927i | ||||
\(879\) | 129.722 | + | 74.8950i | 0.147579 | + | 0.0852047i | ||||
\(880\) | −1907.26 | − | 139.281i | −2.16734 | − | 0.158274i | ||||
\(881\) | −791.292 | −0.898175 | −0.449087 | − | 0.893488i | \(-0.648251\pi\) | ||||
−0.449087 | + | 0.893488i | \(0.648251\pi\) | |||||||
\(882\) | 223.684 | − | 468.551i | 0.253610 | − | 0.531237i | ||||
\(883\) | −364.152 | − | 364.152i | −0.412403 | − | 0.412403i | 0.470172 | − | 0.882575i | \(-0.344192\pi\) |
−0.882575 | + | 0.470172i | \(0.844192\pi\) | |||||||
\(884\) | 1057.06 | − | 610.294i | 1.19577 | − | 0.690378i | ||||
\(885\) | 723.086 | + | 251.475i | 0.817046 | + | 0.284153i | ||||
\(886\) | −587.664 | + | 1017.86i | −0.663278 | + | 1.14883i | ||||
\(887\) | 651.280 | + | 174.510i | 0.734250 | + | 0.196742i | 0.606521 | − | 0.795067i | \(-0.292565\pi\) |
0.127729 | + | 0.991809i | \(0.459231\pi\) | |||||||
\(888\) | −588.799 | − | 588.799i | −0.663062 | − | 0.663062i | ||||
\(889\) | 403.384 | − | 1092.85i | 0.453751 | − | 1.22930i | ||||
\(890\) | −886.813 | + | 169.542i | −0.996420 | + | 0.190497i | ||||
\(891\) | −78.4922 | − | 135.952i | −0.0880945 | − | 0.152584i | ||||
\(892\) | 411.471 | + | 1535.63i | 0.461291 | + | 1.72156i | ||||
\(893\) | −285.977 | + | 76.6274i | −0.320243 | + | 0.0858090i | ||||
\(894\) | 561.386 | − | 324.116i | 0.627948 | − | 0.362546i | ||||
\(895\) | 491.819 | + | 333.948i | 0.549519 | + | 0.373126i | ||||
\(896\) | 224.126 | + | 1305.67i | 0.250141 | + | 1.45722i | ||||
\(897\) | 362.650 | − | 362.650i | 0.404292 | − | 0.404292i | ||||
\(898\) | 18.7965 | − | 70.1493i | 0.0209315 | − | 0.0781173i | ||||
\(899\) | −89.1617 | − | 51.4775i | −0.0991787 | − | 0.0572609i | ||||
\(900\) | 628.890 | + | 92.3438i | 0.698767 | + | 0.102604i | ||||
\(901\) | 9.86368 | + | 17.0844i | 0.0109475 | + | 0.0189616i | ||||
\(902\) | 1304.44 | − | 1304.44i | 1.44616 | − | 1.44616i | ||||
\(903\) | 335.972 | + | 30.9292i | 0.372062 | + | 0.0342516i | ||||
\(904\) | − | 69.1753i | − | 0.0765213i | ||||||
\(905\) | 10.6407 | + | 0.777054i | 0.0117577 | + | 0.000858623i | ||||
\(906\) | 492.986 | − | 853.876i | 0.544134 | − | 0.942468i | ||||
\(907\) | −254.987 | − | 951.626i | −0.281133 | − | 1.04920i | −0.951619 | − | 0.307280i | \(-0.900581\pi\) |
0.670486 | − | 0.741922i | \(-0.266086\pi\) | |||||||
\(908\) | −538.528 | + | 2009.81i | −0.593092 | + | 2.21345i | ||||
\(909\) | − | 252.985i | − | 0.278311i | ||||||
\(910\) | −1177.60 | − | 968.544i | −1.29406 | − | 1.06433i | ||||
\(911\) | 395.990 | 0.434676 | 0.217338 | − | 0.976096i | \(-0.430263\pi\) | ||||
0.217338 | + | 0.976096i | \(0.430263\pi\) | |||||||
\(912\) | −132.545 | − | 35.5154i | −0.145335 | − | 0.0389424i | ||||
\(913\) | 1249.57 | − | 334.821i | 1.36864 | − | 0.366726i | ||||
\(914\) | 1651.27 | + | 953.359i | 1.80664 | + | 1.04306i | ||||
\(915\) | 265.306 | + | 307.108i | 0.289952 | + | 0.335637i | ||||
\(916\) | 2129.10 | 2.32434 | ||||||||
\(917\) | −933.110 | − | 659.696i | −1.01757 | − | 0.719406i | ||||
\(918\) | 151.534 | + | 151.534i | 0.165070 | + | 0.165070i | ||||
\(919\) | −967.833 | + | 558.779i | −1.05314 | + | 0.608029i | −0.923526 | − | 0.383536i | \(-0.874706\pi\) |
−0.129612 | + | 0.991565i | \(0.541373\pi\) | |||||||
\(920\) | 1707.84 | − | 826.458i | 1.85634 | − | 0.898324i | ||||
\(921\) | −45.0031 | + | 77.9476i | −0.0488633 | + | 0.0846336i | ||||
\(922\) | 2219.43 | + | 594.696i | 2.40720 | + | 0.645006i | ||||
\(923\) | −585.559 | − | 585.559i | −0.634409 | − | 0.634409i | ||||
\(924\) | −620.643 | + | 1681.44i | −0.671691 | + | 1.81974i | ||||
\(925\) | −698.095 | − | 301.419i | −0.754697 | − | 0.325858i | ||||
\(926\) | 574.354 | + | 994.811i | 0.620253 | + | 1.07431i | ||||
\(927\) | 91.0234 | + | 339.704i | 0.0981914 | + | 0.366455i | ||||
\(928\) | −639.939 | + | 171.471i | −0.689590 | + | 0.184775i | ||||
\(929\) | 724.522 | − | 418.303i | 0.779894 | − | 0.450272i | −0.0564987 | − | 0.998403i | \(-0.517994\pi\) |
0.836393 | + | 0.548131i | \(0.184660\pi\) | |||||||
\(930\) | 37.9763 | − | 55.9293i | 0.0408347 | − | 0.0601391i | ||||
\(931\) | −32.3226 | + | 174.066i | −0.0347181 | + | 0.186967i | ||||
\(932\) | −1770.87 | + | 1770.87i | −1.90008 | + | 1.90008i | ||||
\(933\) | −39.8762 | + | 148.820i | −0.0427397 | + | 0.159507i | ||||
\(934\) | 1786.15 | + | 1031.23i | 1.91236 | + | 1.10410i | ||||
\(935\) | −961.858 | − | 334.516i | −1.02873 | − | 0.357771i | ||||
\(936\) | −292.429 | − | 506.503i | −0.312425 | − | 0.541135i | ||||
\(937\) | −406.918 | + | 406.918i | −0.434277 | + | 0.434277i | −0.890081 | − | 0.455803i | \(-0.849352\pi\) |
0.455803 | + | 0.890081i | \(0.349352\pi\) | |||||||
\(938\) | −120.669 | − | 261.869i | −0.128645 | − | 0.279178i | ||||
\(939\) | − | 318.284i | − | 0.338960i | ||||||
\(940\) | −2269.98 | − | 2627.64i | −2.41487 | − | 2.79536i | ||||
\(941\) | 75.9717 | − | 131.587i | 0.0807350 | − | 0.139837i | −0.822831 | − | 0.568286i | \(-0.807607\pi\) |
0.903566 | + | 0.428449i | \(0.140940\pi\) | |||||||
\(942\) | −217.520 | − | 811.796i | −0.230913 | − | 0.861780i | ||||
\(943\) | −186.054 | + | 694.361i | −0.197300 | + | 0.736332i | ||||
\(944\) | − | 1938.36i | − | 2.05335i | ||||||
\(945\) | 75.2348 | − | 165.574i | 0.0796135 | − | 0.175211i | ||||
\(946\) | −1714.40 | −1.81227 | ||||||||
\(947\) | 532.138 | + | 142.586i | 0.561920 | + | 0.150566i | 0.528588 | − | 0.848878i | \(-0.322722\pi\) |
0.0333318 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(948\) | 317.664 | − | 85.1177i | 0.335088 | − | 0.0897866i | ||||
\(949\) | 195.207 | + | 112.703i | 0.205698 | + | 0.118760i | ||||
\(950\) | −316.893 | + | 36.9270i | −0.333571 | + | 0.0388705i | ||||
\(951\) | −638.431 | −0.671326 | ||||||||
\(952\) | 118.435 | − | 1286.51i | 0.124406 | − | 1.35137i | ||||
\(953\) | 12.6759 | + | 12.6759i | 0.0133010 | + | 0.0133010i | 0.713726 | − | 0.700425i | \(-0.247006\pi\) |
−0.700425 | + | 0.713726i | \(0.747006\pi\) | |||||||
\(954\) | 15.5032 | − | 8.95080i | 0.0162508 | − | 0.00938240i | ||||
\(955\) | −372.292 | − | 769.325i | −0.389835 | − | 0.805576i | ||||
\(956\) | −427.275 | + | 740.063i | −0.446941 | + | 0.774124i | ||||
\(957\) | 1359.40 | + | 364.250i | 1.42048 | + | 0.380616i | ||||
\(958\) | 737.522 | + | 737.522i | 0.769856 | + | 0.769856i | ||||
\(959\) | 661.581 | + | 795.741i | 0.689865 | + | 0.829761i | ||||
\(960\) | 60.9437 | + | 318.774i | 0.0634830 | + | 0.332056i | ||||
\(961\) | 478.058 | + | 828.020i | 0.497459 | + | 0.861623i | ||||
\(962\) | 342.939 | + | 1279.87i | 0.356485 | + | 1.33042i | ||||
\(963\) | −414.134 | + | 110.967i | −0.430046 | + | 0.115230i | ||||
\(964\) | −2637.46 | + | 1522.74i | −2.73596 | + | 1.57961i | ||||
\(965\) | −407.062 | + | 77.8228i | −0.421826 | + | 0.0806454i | ||||
\(966\) | −173.929 | − | 1013.24i | −0.180051 | − | 1.04891i | ||||
\(967\) | −674.724 | + | 674.724i | −0.697750 | + | 0.697750i | −0.963925 | − | 0.266175i | \(-0.914240\pi\) |
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(968\) | 749.656 | − | 2797.75i | 0.774438 | − | 2.89024i | ||||
\(969\) | −63.2835 | − | 36.5368i | −0.0653081 | − | 0.0377056i | ||||
\(970\) | −205.709 | + | 99.5470i | −0.212071 | + | 0.102626i | ||||
\(971\) | 876.594 | + | 1518.30i | 0.902774 | + | 1.56365i | 0.823878 | + | 0.566768i | \(0.191806\pi\) |
0.0788965 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(972\) | 93.4187 | − | 93.4187i | 0.0961098 | − | 0.0961098i | ||||
\(973\) | −297.502 | − | 645.622i | −0.305758 | − | 0.663538i | ||||
\(974\) | − | 116.926i | − | 0.120048i | ||||||
\(975\) | −418.822 | − | 331.400i | −0.429561 | − | 0.339898i | ||||
\(976\) | 513.773 | − | 889.881i | 0.526407 | − | 0.911763i | ||||
\(977\) | −320.764 | − | 1197.11i | −0.328315 | − | 1.22529i | −0.910937 | − | 0.412546i | \(-0.864640\pi\) |
0.582621 | − | 0.812744i | \(-0.302027\pi\) | |||||||
\(978\) | −299.044 | + | 1116.05i | −0.305771 | + | 1.14115i | ||||
\(979\) | − | 891.762i | − | 0.910891i | ||||||
\(980\) | −2002.77 | + | 548.038i | −2.04365 | + | 0.559223i | ||||
\(981\) | −487.483 | −0.496925 | ||||||||
\(982\) | 2055.30 | + | 550.716i | 2.09297 | + | 0.560810i | ||||
\(983\) | 1036.06 | − | 277.611i | 1.05398 | − | 0.282412i | 0.310083 | − | 0.950710i | \(-0.399643\pi\) |
0.743894 | + | 0.668297i | \(0.232977\pi\) | |||||||
\(984\) | 709.938 | + | 409.883i | 0.721482 | + | 0.416548i | ||||
\(985\) | −171.438 | + | 148.103i | −0.174048 | + | 0.150358i | ||||
\(986\) | −1921.19 | −1.94847 | ||||||||
\(987\) | −902.311 | + | 415.784i | −0.914195 | + | 0.421261i | ||||
\(988\) | 267.062 | + | 267.062i | 0.270306 | + | 0.270306i | ||||
\(989\) | 578.558 | − | 334.030i | 0.584992 | − | 0.337746i | ||||
\(990\) | −303.557 | + | 872.839i | −0.306623 | + | 0.881655i | ||||
\(991\) | 128.143 | − | 221.951i | 0.129307 | − | 0.223966i | −0.794101 | − | 0.607785i | \(-0.792058\pi\) |
0.923408 | + | 0.383819i | \(0.125391\pi\) | |||||||
\(992\) | −30.3619 | − | 8.13546i | −0.0306068 | − | 0.00820106i | ||||
\(993\) | 551.115 | + | 551.115i | 0.555000 | + | 0.555000i | ||||
\(994\) | −1636.05 | + | 280.838i | −1.64593 | + | 0.282533i | ||||
\(995\) | −105.229 | − | 71.4510i | −0.105758 | − | 0.0718101i | ||||
\(996\) | 544.351 | + | 942.844i | 0.546537 | + | 0.946630i | ||||
\(997\) | −374.016 | − | 1395.85i | −0.375141 | − | 1.40005i | −0.853138 | − | 0.521685i | \(-0.825304\pi\) |
0.477997 | − | 0.878362i | \(-0.341363\pi\) | |||||||
\(998\) | 2805.62 | − | 751.764i | 2.81124 | − | 0.753271i | ||||
\(999\) | −136.870 | + | 79.0218i | −0.137007 | + | 0.0791009i |
(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 | 105.3.v.a.88.15 | yes | 64 | |
3.2 | odd | 2 | 315.3.ca.b.298.2 | 64 | |||
5.2 | odd | 4 | inner | 105.3.v.a.67.2 | yes | 64 | |
7.2 | even | 3 | inner | 105.3.v.a.58.2 | yes | 64 | |
15.2 | even | 4 | 315.3.ca.b.172.15 | 64 | |||
21.2 | odd | 6 | 315.3.ca.b.163.15 | 64 | |||
35.2 | odd | 12 | inner | 105.3.v.a.37.15 | ✓ | 64 | |
105.2 | even | 12 | 315.3.ca.b.37.2 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.15 | ✓ | 64 | 35.2 | odd | 12 | inner | |
105.3.v.a.58.2 | yes | 64 | 7.2 | even | 3 | inner | |
105.3.v.a.67.2 | yes | 64 | 5.2 | odd | 4 | inner | |
105.3.v.a.88.15 | yes | 64 | 1.1 | even | 1 | trivial | |
315.3.ca.b.37.2 | 64 | 105.2 | even | 12 | |||
315.3.ca.b.163.15 | 64 | 21.2 | odd | 6 | |||
315.3.ca.b.172.15 | 64 | 15.2 | even | 4 | |||
315.3.ca.b.298.2 | 64 | 3.2 | odd | 2 |