Properties

Label 35.5.g.a.8.4
Level $35$
Weight $5$
Character 35.8
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,5,Mod(8,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.8");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.4
Character \(\chi\) \(=\) 35.8
Dual form 35.5.g.a.22.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.97419 + 2.97419i) q^{2} +(-1.22954 - 1.22954i) q^{3} -1.69164i q^{4} +(-22.1755 - 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 - 13.0958i) q^{7} +(-42.5558 - 42.5558i) q^{8} -77.9765i q^{9} +O(q^{10})\) \(q+(-2.97419 + 2.97419i) q^{2} +(-1.22954 - 1.22954i) q^{3} -1.69164i q^{4} +(-22.1755 - 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 - 13.0958i) q^{7} +(-42.5558 - 42.5558i) q^{8} -77.9765i q^{9} +(100.286 - 31.6225i) q^{10} +17.6226 q^{11} +(-2.07994 + 2.07994i) q^{12} +(-160.405 - 160.405i) q^{13} +77.8989i q^{14} +(13.0728 + 41.4585i) q^{15} +280.205 q^{16} +(-324.451 + 324.451i) q^{17} +(231.917 + 231.917i) q^{18} +468.403i q^{19} +(-19.5270 + 37.5130i) q^{20} -32.2036 q^{21} +(-52.4131 + 52.4131i) q^{22} +(-625.505 - 625.505i) q^{23} +104.648i q^{24} +(358.508 + 511.954i) q^{25} +954.152 q^{26} +(-195.468 + 195.468i) q^{27} +(-22.1534 - 22.1534i) q^{28} -755.645i q^{29} +(-162.187 - 84.4243i) q^{30} +553.934 q^{31} +(-152.489 + 152.489i) q^{32} +(-21.6677 - 21.6677i) q^{33} -1929.96i q^{34} +(-441.574 + 139.239i) q^{35} -131.908 q^{36} +(555.586 - 555.586i) q^{37} +(-1393.12 - 1393.12i) q^{38} +394.449i q^{39} +(452.467 + 1434.93i) q^{40} -1685.09 q^{41} +(95.7796 - 95.7796i) q^{42} +(-416.902 - 416.902i) q^{43} -29.8112i q^{44} +(-900.099 + 1729.17i) q^{45} +3720.74 q^{46} +(-319.293 + 319.293i) q^{47} +(-344.522 - 344.522i) q^{48} -343.000i q^{49} +(-2588.92 - 456.377i) q^{50} +797.849 q^{51} +(-271.348 + 271.348i) q^{52} +(3352.34 + 3352.34i) q^{53} -1162.72i q^{54} +(-390.791 - 203.422i) q^{55} -1114.60 q^{56} +(575.920 - 575.920i) q^{57} +(2247.43 + 2247.43i) q^{58} -4679.64i q^{59} +(70.1329 - 22.1145i) q^{60} +848.263 q^{61} +(-1647.51 + 1647.51i) q^{62} +(-1021.16 - 1021.16i) q^{63} +3576.21i q^{64} +(1705.48 + 5408.66i) q^{65} +128.888 q^{66} +(2472.93 - 2472.93i) q^{67} +(548.854 + 548.854i) q^{68} +1538.16i q^{69} +(899.203 - 1727.45i) q^{70} -2453.67 q^{71} +(-3318.35 + 3318.35i) q^{72} +(-2349.08 - 2349.08i) q^{73} +3304.84i q^{74} +(188.667 - 1070.27i) q^{75} +792.371 q^{76} +(230.782 - 230.782i) q^{77} +(-1173.17 - 1173.17i) q^{78} -1766.38i q^{79} +(-6213.69 - 3234.46i) q^{80} -5835.43 q^{81} +(5011.77 - 5011.77i) q^{82} +(-885.758 - 885.758i) q^{83} +54.4769i q^{84} +(10940.1 - 3449.66i) q^{85} +2479.89 q^{86} +(-929.094 + 929.094i) q^{87} +(-749.945 - 749.945i) q^{88} +3514.86i q^{89} +(-2465.81 - 7819.95i) q^{90} -4201.27 q^{91} +(-1058.13 + 1058.13i) q^{92} +(-681.083 - 681.083i) q^{93} -1899.28i q^{94} +(5406.88 - 10387.1i) q^{95} +374.983 q^{96} +(421.287 - 421.287i) q^{97} +(1020.15 + 1020.15i) q^{98} -1374.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.97419 + 2.97419i −0.743548 + 0.743548i −0.973259 0.229711i \(-0.926222\pi\)
0.229711 + 0.973259i \(0.426222\pi\)
\(3\) −1.22954 1.22954i −0.136615 0.136615i 0.635492 0.772107i \(-0.280797\pi\)
−0.772107 + 0.635492i \(0.780797\pi\)
\(4\) 1.69164i 0.105728i
\(5\) −22.1755 11.5432i −0.887021 0.461729i
\(6\) 7.31376 0.203160
\(7\) 13.0958 13.0958i 0.267261 0.267261i
\(8\) −42.5558 42.5558i −0.664935 0.664935i
\(9\) 77.9765i 0.962673i
\(10\) 100.286 31.6225i 1.00286 0.316225i
\(11\) 17.6226 0.145642 0.0728208 0.997345i \(-0.476800\pi\)
0.0728208 + 0.997345i \(0.476800\pi\)
\(12\) −2.07994 + 2.07994i −0.0144440 + 0.0144440i
\(13\) −160.405 160.405i −0.949144 0.949144i 0.0496243 0.998768i \(-0.484198\pi\)
−0.998768 + 0.0496243i \(0.984198\pi\)
\(14\) 77.8989i 0.397443i
\(15\) 13.0728 + 41.4585i 0.0581015 + 0.184260i
\(16\) 280.205 1.09455
\(17\) −324.451 + 324.451i −1.12267 + 1.12267i −0.131328 + 0.991339i \(0.541924\pi\)
−0.991339 + 0.131328i \(0.958076\pi\)
\(18\) 231.917 + 231.917i 0.715793 + 0.715793i
\(19\) 468.403i 1.29752i 0.760995 + 0.648758i \(0.224711\pi\)
−0.760995 + 0.648758i \(0.775289\pi\)
\(20\) −19.5270 + 37.5130i −0.0488175 + 0.0937826i
\(21\) −32.2036 −0.0730239
\(22\) −52.4131 + 52.4131i −0.108291 + 0.108291i
\(23\) −625.505 625.505i −1.18243 1.18243i −0.979113 0.203315i \(-0.934828\pi\)
−0.203315 0.979113i \(-0.565172\pi\)
\(24\) 104.648i 0.181680i
\(25\) 358.508 + 511.954i 0.573613 + 0.819126i
\(26\) 954.152 1.41147
\(27\) −195.468 + 195.468i −0.268131 + 0.268131i
\(28\) −22.1534 22.1534i −0.0282569 0.0282569i
\(29\) 755.645i 0.898508i −0.893404 0.449254i \(-0.851690\pi\)
0.893404 0.449254i \(-0.148310\pi\)
\(30\) −162.187 84.4243i −0.180207 0.0938048i
\(31\) 553.934 0.576414 0.288207 0.957568i \(-0.406941\pi\)
0.288207 + 0.957568i \(0.406941\pi\)
\(32\) −152.489 + 152.489i −0.148915 + 0.148915i
\(33\) −21.6677 21.6677i −0.0198969 0.0198969i
\(34\) 1929.96i 1.66951i
\(35\) −441.574 + 139.239i −0.360469 + 0.113664i
\(36\) −131.908 −0.101781
\(37\) 555.586 555.586i 0.405834 0.405834i −0.474449 0.880283i \(-0.657353\pi\)
0.880283 + 0.474449i \(0.157353\pi\)
\(38\) −1393.12 1393.12i −0.964766 0.964766i
\(39\) 394.449i 0.259335i
\(40\) 452.467 + 1434.93i 0.282792 + 0.896830i
\(41\) −1685.09 −1.00243 −0.501215 0.865323i \(-0.667113\pi\)
−0.501215 + 0.865323i \(0.667113\pi\)
\(42\) 95.7796 95.7796i 0.0542968 0.0542968i
\(43\) −416.902 416.902i −0.225474 0.225474i 0.585325 0.810799i \(-0.300967\pi\)
−0.810799 + 0.585325i \(0.800967\pi\)
\(44\) 29.8112i 0.0153983i
\(45\) −900.099 + 1729.17i −0.444493 + 0.853911i
\(46\) 3720.74 1.75839
\(47\) −319.293 + 319.293i −0.144542 + 0.144542i −0.775675 0.631133i \(-0.782590\pi\)
0.631133 + 0.775675i \(0.282590\pi\)
\(48\) −344.522 344.522i −0.149532 0.149532i
\(49\) 343.000i 0.142857i
\(50\) −2588.92 456.377i −1.03557 0.182551i
\(51\) 797.849 0.306747
\(52\) −271.348 + 271.348i −0.100351 + 0.100351i
\(53\) 3352.34 + 3352.34i 1.19343 + 1.19343i 0.976098 + 0.217329i \(0.0697345\pi\)
0.217329 + 0.976098i \(0.430266\pi\)
\(54\) 1162.72i 0.398737i
\(55\) −390.791 203.422i −0.129187 0.0672469i
\(56\) −1114.60 −0.355422
\(57\) 575.920 575.920i 0.177261 0.177261i
\(58\) 2247.43 + 2247.43i 0.668084 + 0.668084i
\(59\) 4679.64i 1.34434i −0.740398 0.672168i \(-0.765363\pi\)
0.740398 0.672168i \(-0.234637\pi\)
\(60\) 70.1329 22.1145i 0.0194813 0.00614293i
\(61\) 848.263 0.227966 0.113983 0.993483i \(-0.463639\pi\)
0.113983 + 0.993483i \(0.463639\pi\)
\(62\) −1647.51 + 1647.51i −0.428592 + 0.428592i
\(63\) −1021.16 1021.16i −0.257285 0.257285i
\(64\) 3576.21i 0.873098i
\(65\) 1705.48 + 5408.66i 0.403664 + 1.28016i
\(66\) 128.888 0.0295885
\(67\) 2472.93 2472.93i 0.550886 0.550886i −0.375811 0.926696i \(-0.622636\pi\)
0.926696 + 0.375811i \(0.122636\pi\)
\(68\) 548.854 + 548.854i 0.118697 + 0.118697i
\(69\) 1538.16i 0.323076i
\(70\) 899.203 1727.45i 0.183511 0.352541i
\(71\) −2453.67 −0.486743 −0.243371 0.969933i \(-0.578253\pi\)
−0.243371 + 0.969933i \(0.578253\pi\)
\(72\) −3318.35 + 3318.35i −0.640114 + 0.640114i
\(73\) −2349.08 2349.08i −0.440811 0.440811i 0.451474 0.892284i \(-0.350898\pi\)
−0.892284 + 0.451474i \(0.850898\pi\)
\(74\) 3304.84i 0.603514i
\(75\) 188.667 1070.27i 0.0335408 0.190270i
\(76\) 792.371 0.137183
\(77\) 230.782 230.782i 0.0389243 0.0389243i
\(78\) −1173.17 1173.17i −0.192828 0.192828i
\(79\) 1766.38i 0.283028i −0.989936 0.141514i \(-0.954803\pi\)
0.989936 0.141514i \(-0.0451970\pi\)
\(80\) −6213.69 3234.46i −0.970888 0.505385i
\(81\) −5835.43 −0.889411
\(82\) 5011.77 5011.77i 0.745355 0.745355i
\(83\) −885.758 885.758i −0.128576 0.128576i 0.639890 0.768466i \(-0.278980\pi\)
−0.768466 + 0.639890i \(0.778980\pi\)
\(84\) 54.4769i 0.00772065i
\(85\) 10940.1 3449.66i 1.51420 0.477462i
\(86\) 2479.89 0.335302
\(87\) −929.094 + 929.094i −0.122750 + 0.122750i
\(88\) −749.945 749.945i −0.0968421 0.0968421i
\(89\) 3514.86i 0.443740i 0.975076 + 0.221870i \(0.0712160\pi\)
−0.975076 + 0.221870i \(0.928784\pi\)
\(90\) −2465.81 7819.95i −0.304422 0.965426i
\(91\) −4201.27 −0.507339
\(92\) −1058.13 + 1058.13i −0.125015 + 0.125015i
\(93\) −681.083 681.083i −0.0787470 0.0787470i
\(94\) 1899.28i 0.214948i
\(95\) 5406.88 10387.1i 0.599101 1.15092i
\(96\) 374.983 0.0406883
\(97\) 421.287 421.287i 0.0447748 0.0447748i −0.684365 0.729140i \(-0.739920\pi\)
0.729140 + 0.684365i \(0.239920\pi\)
\(98\) 1020.15 + 1020.15i 0.106221 + 0.106221i
\(99\) 1374.15i 0.140205i
\(100\) 866.042 606.468i 0.0866042 0.0606468i
\(101\) 9326.25 0.914249 0.457124 0.889403i \(-0.348879\pi\)
0.457124 + 0.889403i \(0.348879\pi\)
\(102\) −2372.96 + 2372.96i −0.228081 + 0.228081i
\(103\) −3554.31 3554.31i −0.335028 0.335028i 0.519464 0.854492i \(-0.326132\pi\)
−0.854492 + 0.519464i \(0.826132\pi\)
\(104\) 13652.4i 1.26224i
\(105\) 714.131 + 371.733i 0.0647738 + 0.0337172i
\(106\) −19941.0 −1.77474
\(107\) 5312.92 5312.92i 0.464051 0.464051i −0.435930 0.899981i \(-0.643580\pi\)
0.899981 + 0.435930i \(0.143580\pi\)
\(108\) 330.661 + 330.661i 0.0283489 + 0.0283489i
\(109\) 9313.69i 0.783915i 0.919983 + 0.391957i \(0.128202\pi\)
−0.919983 + 0.391957i \(0.871798\pi\)
\(110\) 1767.30 557.272i 0.146058 0.0460556i
\(111\) −1366.23 −0.110886
\(112\) 3669.50 3669.50i 0.292531 0.292531i
\(113\) 10930.8 + 10930.8i 0.856043 + 0.856043i 0.990869 0.134826i \(-0.0430477\pi\)
−0.134826 + 0.990869i \(0.543048\pi\)
\(114\) 3425.79i 0.263604i
\(115\) 6650.56 + 21091.2i 0.502878 + 1.59480i
\(116\) −1278.28 −0.0949971
\(117\) −12507.8 + 12507.8i −0.913714 + 0.913714i
\(118\) 13918.1 + 13918.1i 0.999579 + 0.999579i
\(119\) 8497.89i 0.600091i
\(120\) 1207.97 2320.62i 0.0838871 0.161154i
\(121\) −14330.4 −0.978789
\(122\) −2522.90 + 2522.90i −0.169504 + 0.169504i
\(123\) 2071.88 + 2071.88i 0.136947 + 0.136947i
\(124\) 937.058i 0.0609429i
\(125\) −2040.52 15491.2i −0.130593 0.991436i
\(126\) 6074.28 0.382608
\(127\) 14279.3 14279.3i 0.885318 0.885318i −0.108751 0.994069i \(-0.534685\pi\)
0.994069 + 0.108751i \(0.0346852\pi\)
\(128\) −13076.2 13076.2i −0.798106 0.798106i
\(129\) 1025.19i 0.0616064i
\(130\) −21158.8 11014.0i −1.25200 0.651715i
\(131\) −9187.71 −0.535383 −0.267692 0.963505i \(-0.586261\pi\)
−0.267692 + 0.963505i \(0.586261\pi\)
\(132\) −36.6539 + 36.6539i −0.00210365 + 0.00210365i
\(133\) 6134.12 + 6134.12i 0.346776 + 0.346776i
\(134\) 14709.9i 0.819220i
\(135\) 6590.92 2078.27i 0.361642 0.114034i
\(136\) 27614.5 1.49300
\(137\) −2649.32 + 2649.32i −0.141154 + 0.141154i −0.774153 0.632999i \(-0.781824\pi\)
0.632999 + 0.774153i \(0.281824\pi\)
\(138\) −4574.79 4574.79i −0.240222 0.240222i
\(139\) 29935.3i 1.54937i −0.632349 0.774684i \(-0.717909\pi\)
0.632349 0.774684i \(-0.282091\pi\)
\(140\) 235.542 + 746.985i 0.0120174 + 0.0381115i
\(141\) 785.166 0.0394933
\(142\) 7297.69 7297.69i 0.361917 0.361917i
\(143\) −2826.76 2826.76i −0.138235 0.138235i
\(144\) 21849.4i 1.05369i
\(145\) −8722.58 + 16756.8i −0.414867 + 0.796996i
\(146\) 13973.2 0.655528
\(147\) −421.731 + 421.731i −0.0195165 + 0.0195165i
\(148\) −939.853 939.853i −0.0429078 0.0429078i
\(149\) 35767.7i 1.61108i −0.592538 0.805542i \(-0.701874\pi\)
0.592538 0.805542i \(-0.298126\pi\)
\(150\) 2622.04 + 3744.31i 0.116535 + 0.166414i
\(151\) −41532.5 −1.82152 −0.910760 0.412936i \(-0.864503\pi\)
−0.910760 + 0.412936i \(0.864503\pi\)
\(152\) 19933.3 19933.3i 0.862764 0.862764i
\(153\) 25299.5 + 25299.5i 1.08076 + 1.08076i
\(154\) 1372.78i 0.0578842i
\(155\) −12283.8 6394.18i −0.511291 0.266147i
\(156\) 667.266 0.0274189
\(157\) −20305.2 + 20305.2i −0.823774 + 0.823774i −0.986647 0.162873i \(-0.947924\pi\)
0.162873 + 0.986647i \(0.447924\pi\)
\(158\) 5253.55 + 5253.55i 0.210445 + 0.210445i
\(159\) 8243.65i 0.326081i
\(160\) 5141.75 1621.32i 0.200850 0.0633326i
\(161\) −16383.0 −0.632035
\(162\) 17355.7 17355.7i 0.661320 0.661320i
\(163\) −24246.0 24246.0i −0.912567 0.912567i 0.0839065 0.996474i \(-0.473260\pi\)
−0.996474 + 0.0839065i \(0.973260\pi\)
\(164\) 2850.56i 0.105985i
\(165\) 230.378 + 730.607i 0.00846199 + 0.0268359i
\(166\) 5268.83 0.191204
\(167\) −29647.0 + 29647.0i −1.06303 + 1.06303i −0.0651591 + 0.997875i \(0.520755\pi\)
−0.997875 + 0.0651591i \(0.979245\pi\)
\(168\) 1370.45 + 1370.45i 0.0485561 + 0.0485561i
\(169\) 22898.7i 0.801747i
\(170\) −22277.9 + 42797.9i −0.770863 + 1.48089i
\(171\) 36524.4 1.24908
\(172\) −705.248 + 705.248i −0.0238388 + 0.0238388i
\(173\) −4080.56 4080.56i −0.136341 0.136341i 0.635642 0.771984i \(-0.280735\pi\)
−0.771984 + 0.635642i \(0.780735\pi\)
\(174\) 5526.61i 0.182541i
\(175\) 11399.4 + 2009.49i 0.372225 + 0.0656161i
\(176\) 4937.94 0.159412
\(177\) −5753.79 + 5753.79i −0.183657 + 0.183657i
\(178\) −10453.9 10453.9i −0.329942 0.329942i
\(179\) 20997.6i 0.655335i −0.944793 0.327668i \(-0.893737\pi\)
0.944793 0.327668i \(-0.106263\pi\)
\(180\) 2925.14 + 1522.65i 0.0902819 + 0.0469952i
\(181\) 22890.3 0.698705 0.349352 0.936991i \(-0.386402\pi\)
0.349352 + 0.936991i \(0.386402\pi\)
\(182\) 12495.4 12495.4i 0.377231 0.377231i
\(183\) −1042.97 1042.97i −0.0311437 0.0311437i
\(184\) 53237.7i 1.57248i
\(185\) −18733.7 + 5907.17i −0.547368 + 0.172598i
\(186\) 4051.34 0.117104
\(187\) −5717.68 + 5717.68i −0.163507 + 0.163507i
\(188\) 540.130 + 540.130i 0.0152821 + 0.0152821i
\(189\) 5119.61i 0.143322i
\(190\) 14812.1 + 46974.3i 0.410308 + 1.30123i
\(191\) 57786.8 1.58402 0.792012 0.610506i \(-0.209034\pi\)
0.792012 + 0.610506i \(0.209034\pi\)
\(192\) 4397.08 4397.08i 0.119278 0.119278i
\(193\) −10258.8 10258.8i −0.275412 0.275412i 0.555863 0.831274i \(-0.312388\pi\)
−0.831274 + 0.555863i \(0.812388\pi\)
\(194\) 2505.97i 0.0665845i
\(195\) 4553.21 8747.11i 0.119742 0.230036i
\(196\) −580.233 −0.0151039
\(197\) 14590.3 14590.3i 0.375951 0.375951i −0.493688 0.869639i \(-0.664351\pi\)
0.869639 + 0.493688i \(0.164351\pi\)
\(198\) 4086.99 + 4086.99i 0.104249 + 0.104249i
\(199\) 50015.5i 1.26299i −0.775381 0.631493i \(-0.782442\pi\)
0.775381 0.631493i \(-0.217558\pi\)
\(200\) 6530.00 37043.2i 0.163250 0.926081i
\(201\) −6081.11 −0.150519
\(202\) −27738.1 + 27738.1i −0.679788 + 0.679788i
\(203\) −9895.78 9895.78i −0.240136 0.240136i
\(204\) 1349.67i 0.0324316i
\(205\) 37367.7 + 19451.3i 0.889177 + 0.462851i
\(206\) 21142.4 0.498219
\(207\) −48774.7 + 48774.7i −1.13829 + 1.13829i
\(208\) −44946.3 44946.3i −1.03888 1.03888i
\(209\) 8254.50i 0.188972i
\(210\) −3229.57 + 1018.36i −0.0732328 + 0.0230920i
\(211\) −37327.4 −0.838422 −0.419211 0.907889i \(-0.637693\pi\)
−0.419211 + 0.907889i \(0.637693\pi\)
\(212\) 5670.95 5670.95i 0.126178 0.126178i
\(213\) 3016.88 + 3016.88i 0.0664965 + 0.0664965i
\(214\) 31603.3i 0.690089i
\(215\) 4432.63 + 14057.4i 0.0958925 + 0.304108i
\(216\) 16636.6 0.356579
\(217\) 7254.21 7254.21i 0.154053 0.154053i
\(218\) −27700.7 27700.7i −0.582878 0.582878i
\(219\) 5776.57i 0.120443i
\(220\) −344.117 + 661.078i −0.00710985 + 0.0136586i
\(221\) 104087. 2.13114
\(222\) 4063.43 4063.43i 0.0824492 0.0824492i
\(223\) 9094.35 + 9094.35i 0.182878 + 0.182878i 0.792609 0.609731i \(-0.208722\pi\)
−0.609731 + 0.792609i \(0.708722\pi\)
\(224\) 3993.94i 0.0795987i
\(225\) 39920.4 27955.2i 0.788550 0.552202i
\(226\) −65020.7 −1.27302
\(227\) −30816.0 + 30816.0i −0.598032 + 0.598032i −0.939789 0.341757i \(-0.888978\pi\)
0.341757 + 0.939789i \(0.388978\pi\)
\(228\) −974.250 974.250i −0.0187413 0.0187413i
\(229\) 13976.7i 0.266522i −0.991081 0.133261i \(-0.957455\pi\)
0.991081 0.133261i \(-0.0425448\pi\)
\(230\) −82509.5 42949.3i −1.55973 0.811897i
\(231\) −567.511 −0.0106353
\(232\) −32157.1 + 32157.1i −0.597449 + 0.597449i
\(233\) 6660.07 + 6660.07i 0.122678 + 0.122678i 0.765780 0.643102i \(-0.222353\pi\)
−0.643102 + 0.765780i \(0.722353\pi\)
\(234\) 74401.4i 1.35878i
\(235\) 10766.2 3394.83i 0.194951 0.0614727i
\(236\) −7916.26 −0.142133
\(237\) −2171.83 + 2171.83i −0.0386660 + 0.0386660i
\(238\) −25274.4 25274.4i −0.446196 0.446196i
\(239\) 7840.64i 0.137264i −0.997642 0.0686318i \(-0.978137\pi\)
0.997642 0.0686318i \(-0.0218634\pi\)
\(240\) 3663.07 + 11616.9i 0.0635949 + 0.201681i
\(241\) −79730.7 −1.37275 −0.686375 0.727247i \(-0.740799\pi\)
−0.686375 + 0.727247i \(0.740799\pi\)
\(242\) 42621.5 42621.5i 0.727776 0.727776i
\(243\) 23007.7 + 23007.7i 0.389638 + 0.389638i
\(244\) 1434.96i 0.0241023i
\(245\) −3959.32 + 7606.21i −0.0659612 + 0.126717i
\(246\) −12324.3 −0.203654
\(247\) 75134.4 75134.4i 1.23153 1.23153i
\(248\) −23573.1 23573.1i −0.383278 0.383278i
\(249\) 2178.15i 0.0351308i
\(250\) 52142.7 + 40004.9i 0.834283 + 0.640078i
\(251\) 55697.0 0.884065 0.442032 0.896999i \(-0.354258\pi\)
0.442032 + 0.896999i \(0.354258\pi\)
\(252\) −1727.44 + 1727.44i −0.0272021 + 0.0272021i
\(253\) −11023.0 11023.0i −0.172211 0.172211i
\(254\) 84938.7i 1.31655i
\(255\) −17692.7 9209.74i −0.272091 0.141634i
\(256\) 20562.7 0.313762
\(257\) 53468.3 53468.3i 0.809525 0.809525i −0.175037 0.984562i \(-0.556005\pi\)
0.984562 + 0.175037i \(0.0560046\pi\)
\(258\) −3049.12 3049.12i −0.0458073 0.0458073i
\(259\) 14551.7i 0.216927i
\(260\) 9149.52 2885.06i 0.135348 0.0426784i
\(261\) −58922.6 −0.864969
\(262\) 27326.0 27326.0i 0.398083 0.398083i
\(263\) 78703.8 + 78703.8i 1.13785 + 1.13785i 0.988835 + 0.149013i \(0.0476097\pi\)
0.149013 + 0.988835i \(0.452390\pi\)
\(264\) 1844.17i 0.0264602i
\(265\) −35643.1 113037.i −0.507556 1.60964i
\(266\) −36488.1 −0.515689
\(267\) 4321.66 4321.66i 0.0606216 0.0606216i
\(268\) −4183.31 4183.31i −0.0582438 0.0582438i
\(269\) 83582.2i 1.15507i 0.816365 + 0.577536i \(0.195986\pi\)
−0.816365 + 0.577536i \(0.804014\pi\)
\(270\) −13421.5 + 25783.8i −0.184108 + 0.353688i
\(271\) 32293.6 0.439721 0.219861 0.975531i \(-0.429440\pi\)
0.219861 + 0.975531i \(0.429440\pi\)
\(272\) −90912.6 + 90912.6i −1.22881 + 1.22881i
\(273\) 5165.62 + 5165.62i 0.0693102 + 0.0693102i
\(274\) 15759.2i 0.209910i
\(275\) 6317.86 + 9021.97i 0.0835419 + 0.119299i
\(276\) 2602.02 0.0341580
\(277\) −58656.0 + 58656.0i −0.764456 + 0.764456i −0.977124 0.212668i \(-0.931785\pi\)
0.212668 + 0.977124i \(0.431785\pi\)
\(278\) 89033.5 + 89033.5i 1.15203 + 1.15203i
\(279\) 43193.8i 0.554898i
\(280\) 24717.0 + 12866.1i 0.315267 + 0.164109i
\(281\) −60425.2 −0.765254 −0.382627 0.923903i \(-0.624980\pi\)
−0.382627 + 0.923903i \(0.624980\pi\)
\(282\) −2335.24 + 2335.24i −0.0293652 + 0.0293652i
\(283\) 72566.2 + 72566.2i 0.906070 + 0.906070i 0.995952 0.0898824i \(-0.0286491\pi\)
−0.0898824 + 0.995952i \(0.528649\pi\)
\(284\) 4150.73i 0.0514622i
\(285\) −19419.3 + 6123.36i −0.239080 + 0.0753876i
\(286\) 16814.7 0.205568
\(287\) −22067.5 + 22067.5i −0.267911 + 0.267911i
\(288\) 11890.6 + 11890.6i 0.143357 + 0.143357i
\(289\) 127016.i 1.52076i
\(290\) −23895.4 75780.7i −0.284131 0.901078i
\(291\) −1035.98 −0.0122339
\(292\) −3973.80 + 3973.80i −0.0466059 + 0.0466059i
\(293\) −15395.9 15395.9i −0.179336 0.179336i 0.611730 0.791067i \(-0.290474\pi\)
−0.791067 + 0.611730i \(0.790474\pi\)
\(294\) 2508.62i 0.0290229i
\(295\) −54018.0 + 103773.i −0.620719 + 1.19245i
\(296\) −47286.8 −0.539706
\(297\) −3444.65 + 3444.65i −0.0390510 + 0.0390510i
\(298\) 106380. + 106380.i 1.19792 + 1.19792i
\(299\) 200669.i 2.24459i
\(300\) −1810.51 319.157i −0.0201167 0.00354619i
\(301\) −10919.3 −0.120521
\(302\) 123526. 123526.i 1.35439 1.35439i
\(303\) −11467.0 11467.0i −0.124900 0.124900i
\(304\) 131249.i 1.42020i
\(305\) −18810.7 9791.68i −0.202211 0.105259i
\(306\) −150491. −1.60720
\(307\) 40854.0 40854.0i 0.433469 0.433469i −0.456338 0.889807i \(-0.650839\pi\)
0.889807 + 0.456338i \(0.150839\pi\)
\(308\) −390.401 390.401i −0.00411538 0.00411538i
\(309\) 8740.32i 0.0915399i
\(310\) 55551.8 17516.8i 0.578063 0.182277i
\(311\) −124994. −1.29231 −0.646157 0.763205i \(-0.723625\pi\)
−0.646157 + 0.763205i \(0.723625\pi\)
\(312\) 16786.1 16786.1i 0.172441 0.172441i
\(313\) −27798.6 27798.6i −0.283749 0.283749i 0.550853 0.834602i \(-0.314302\pi\)
−0.834602 + 0.550853i \(0.814302\pi\)
\(314\) 120783.i 1.22503i
\(315\) 10857.3 + 34432.4i 0.109421 + 0.347013i
\(316\) −2988.08 −0.0299239
\(317\) 83808.0 83808.0i 0.834002 0.834002i −0.154060 0.988062i \(-0.549235\pi\)
0.988062 + 0.154060i \(0.0492348\pi\)
\(318\) 24518.2 + 24518.2i 0.242457 + 0.242457i
\(319\) 13316.5i 0.130860i
\(320\) 41280.9 79304.3i 0.403134 0.774456i
\(321\) −13064.9 −0.126793
\(322\) 48726.1 48726.1i 0.469948 0.469948i
\(323\) −151974. 151974.i −1.45668 1.45668i
\(324\) 9871.45i 0.0940353i
\(325\) 24613.5 139627.i 0.233027 1.32191i
\(326\) 144225. 1.35708
\(327\) 11451.5 11451.5i 0.107095 0.107095i
\(328\) 71710.2 + 71710.2i 0.666551 + 0.666551i
\(329\) 8362.81i 0.0772610i
\(330\) −2858.15 1487.78i −0.0262457 0.0136619i
\(331\) −37373.1 −0.341117 −0.170558 0.985348i \(-0.554557\pi\)
−0.170558 + 0.985348i \(0.554557\pi\)
\(332\) −1498.38 + 1498.38i −0.0135940 + 0.0135940i
\(333\) −43322.7 43322.7i −0.390685 0.390685i
\(334\) 176352.i 1.58083i
\(335\) −83384.0 + 26292.9i −0.743007 + 0.234288i
\(336\) −9023.59 −0.0799283
\(337\) −7169.19 + 7169.19i −0.0631263 + 0.0631263i −0.737965 0.674839i \(-0.764213\pi\)
0.674839 + 0.737965i \(0.264213\pi\)
\(338\) −68105.1 68105.1i −0.596138 0.596138i
\(339\) 26879.7i 0.233897i
\(340\) −5835.59 18506.7i −0.0504809 0.160092i
\(341\) 9761.77 0.0839498
\(342\) −108631. + 108631.i −0.928754 + 0.928754i
\(343\) −4491.86 4491.86i −0.0381802 0.0381802i
\(344\) 35483.2i 0.299851i
\(345\) 17755.4 34109.6i 0.149173 0.286575i
\(346\) 24272.7 0.202753
\(347\) 9680.63 9680.63i 0.0803979 0.0803979i −0.665764 0.746162i \(-0.731894\pi\)
0.746162 + 0.665764i \(0.231894\pi\)
\(348\) 1571.69 + 1571.69i 0.0129781 + 0.0129781i
\(349\) 72057.7i 0.591602i −0.955250 0.295801i \(-0.904413\pi\)
0.955250 0.295801i \(-0.0955866\pi\)
\(350\) −39880.6 + 27927.4i −0.325556 + 0.227979i
\(351\) 62708.0 0.508990
\(352\) −2687.26 + 2687.26i −0.0216883 + 0.0216883i
\(353\) 52704.4 + 52704.4i 0.422958 + 0.422958i 0.886221 0.463263i \(-0.153321\pi\)
−0.463263 + 0.886221i \(0.653321\pi\)
\(354\) 34225.7i 0.273115i
\(355\) 54411.5 + 28323.3i 0.431751 + 0.224743i
\(356\) 5945.89 0.0469155
\(357\) 10448.5 10448.5i 0.0819816 0.0819816i
\(358\) 62450.9 + 62450.9i 0.487273 + 0.487273i
\(359\) 232709.i 1.80561i 0.430046 + 0.902807i \(0.358497\pi\)
−0.430046 + 0.902807i \(0.641503\pi\)
\(360\) 111891. 35281.8i 0.863354 0.272236i
\(361\) −89080.8 −0.683549
\(362\) −68080.0 + 68080.0i −0.519520 + 0.519520i
\(363\) 17619.8 + 17619.8i 0.133717 + 0.133717i
\(364\) 7107.04i 0.0536397i
\(365\) 24976.2 + 79208.1i 0.187474 + 0.594543i
\(366\) 6203.99 0.0463137
\(367\) −44132.8 + 44132.8i −0.327664 + 0.327664i −0.851698 0.524033i \(-0.824427\pi\)
0.524033 + 0.851698i \(0.324427\pi\)
\(368\) −175269. 175269.i −1.29423 1.29423i
\(369\) 131397.i 0.965012i
\(370\) 38148.5 73286.6i 0.278660 0.535329i
\(371\) 87803.1 0.637914
\(372\) −1152.15 + 1152.15i −0.00832573 + 0.00832573i
\(373\) 90918.1 + 90918.1i 0.653480 + 0.653480i 0.953829 0.300349i \(-0.0971031\pi\)
−0.300349 + 0.953829i \(0.597103\pi\)
\(374\) 34010.9i 0.243151i
\(375\) −16538.1 + 21555.9i −0.117604 + 0.153286i
\(376\) 27175.6 0.192222
\(377\) −121210. + 121210.i −0.852813 + 0.852813i
\(378\) −15226.7 15226.7i −0.106567 0.106567i
\(379\) 90612.2i 0.630824i 0.948955 + 0.315412i \(0.102143\pi\)
−0.948955 + 0.315412i \(0.897857\pi\)
\(380\) −17571.2 9146.51i −0.121684 0.0633415i
\(381\) −35113.8 −0.241896
\(382\) −171869. + 171869.i −1.17780 + 1.17780i
\(383\) −178249. 178249.i −1.21515 1.21515i −0.969310 0.245840i \(-0.920936\pi\)
−0.245840 0.969310i \(-0.579064\pi\)
\(384\) 32155.3i 0.218067i
\(385\) −7781.69 + 2453.75i −0.0524992 + 0.0165542i
\(386\) 61023.4 0.409564
\(387\) −32508.5 + 32508.5i −0.217058 + 0.217058i
\(388\) −712.666 712.666i −0.00473394 0.00473394i
\(389\) 125379.i 0.828564i −0.910149 0.414282i \(-0.864033\pi\)
0.910149 0.414282i \(-0.135967\pi\)
\(390\) 12473.5 + 39557.7i 0.0820084 + 0.260077i
\(391\) 405891. 2.65495
\(392\) −14596.6 + 14596.6i −0.0949907 + 0.0949907i
\(393\) 11296.6 + 11296.6i 0.0731415 + 0.0731415i
\(394\) 86788.7i 0.559076i
\(395\) −20389.7 + 39170.4i −0.130682 + 0.251052i
\(396\) −2324.57 −0.0148235
\(397\) 187283. 187283.i 1.18828 1.18828i 0.210735 0.977543i \(-0.432414\pi\)
0.977543 0.210735i \(-0.0675858\pi\)
\(398\) 148756. + 148756.i 0.939091 + 0.939091i
\(399\) 15084.3i 0.0947498i
\(400\) 100456. + 143452.i 0.627848 + 0.896574i
\(401\) −159884. −0.994296 −0.497148 0.867666i \(-0.665619\pi\)
−0.497148 + 0.867666i \(0.665619\pi\)
\(402\) 18086.4 18086.4i 0.111918 0.111918i
\(403\) −88853.9 88853.9i −0.547100 0.547100i
\(404\) 15776.7i 0.0966613i
\(405\) 129404. + 67359.6i 0.788926 + 0.410667i
\(406\) 58863.9 0.357106
\(407\) 9790.89 9790.89i 0.0591062 0.0591062i
\(408\) −33953.1 33953.1i −0.203967 0.203967i
\(409\) 99389.4i 0.594146i 0.954855 + 0.297073i \(0.0960105\pi\)
−0.954855 + 0.297073i \(0.903989\pi\)
\(410\) −168991. + 53286.7i −1.00530 + 0.316994i
\(411\) 6514.89 0.0385676
\(412\) −6012.62 + 6012.62i −0.0354217 + 0.0354217i
\(413\) −61283.6 61283.6i −0.359289 0.359289i
\(414\) 290130.i 1.69275i
\(415\) 9417.66 + 29866.6i 0.0546823 + 0.173416i
\(416\) 48920.2 0.282684
\(417\) −36806.6 + 36806.6i −0.211667 + 0.211667i
\(418\) −24550.5 24550.5i −0.140510 0.140510i
\(419\) 155849.i 0.887721i 0.896096 + 0.443860i \(0.146391\pi\)
−0.896096 + 0.443860i \(0.853609\pi\)
\(420\) 628.838 1208.05i 0.00356484 0.00684838i
\(421\) 150890. 0.851325 0.425663 0.904882i \(-0.360041\pi\)
0.425663 + 0.904882i \(0.360041\pi\)
\(422\) 111019. 111019.i 0.623407 0.623407i
\(423\) 24897.4 + 24897.4i 0.139147 + 0.139147i
\(424\) 285323.i 1.58710i
\(425\) −282422. 49785.5i −1.56358 0.275629i
\(426\) −17945.6 −0.0988867
\(427\) 11108.7 11108.7i 0.0609266 0.0609266i
\(428\) −8987.56 8987.56i −0.0490630 0.0490630i
\(429\) 6951.22i 0.0377700i
\(430\) −54992.9 28625.9i −0.297420 0.154818i
\(431\) 39190.3 0.210972 0.105486 0.994421i \(-0.466360\pi\)
0.105486 + 0.994421i \(0.466360\pi\)
\(432\) −54770.9 + 54770.9i −0.293483 + 0.293483i
\(433\) −132917. 132917.i −0.708933 0.708933i 0.257378 0.966311i \(-0.417142\pi\)
−0.966311 + 0.257378i \(0.917142\pi\)
\(434\) 43150.8i 0.229092i
\(435\) 31327.9 9878.42i 0.165559 0.0522046i
\(436\) 15755.4 0.0828814
\(437\) 292989. 292989.i 1.53422 1.53422i
\(438\) −17180.6 17180.6i −0.0895551 0.0895551i
\(439\) 163837.i 0.850124i −0.905164 0.425062i \(-0.860252\pi\)
0.905164 0.425062i \(-0.139748\pi\)
\(440\) 7973.65 + 25287.2i 0.0411862 + 0.130616i
\(441\) −26745.9 −0.137525
\(442\) −309575. + 309575.i −1.58461 + 1.58461i
\(443\) 27337.1 + 27337.1i 0.139298 + 0.139298i 0.773317 0.634019i \(-0.218596\pi\)
−0.634019 + 0.773317i \(0.718596\pi\)
\(444\) 2311.17i 0.0117237i
\(445\) 40572.8 77943.9i 0.204887 0.393607i
\(446\) −54096.7 −0.271957
\(447\) −43977.7 + 43977.7i −0.220099 + 0.220099i
\(448\) 46833.3 + 46833.3i 0.233345 + 0.233345i
\(449\) 160196.i 0.794617i 0.917685 + 0.397308i \(0.130056\pi\)
−0.917685 + 0.397308i \(0.869944\pi\)
\(450\) −35586.6 + 201875.i −0.175737 + 0.996914i
\(451\) −29695.6 −0.145995
\(452\) 18491.0 18491.0i 0.0905073 0.0905073i
\(453\) 51065.7 + 51065.7i 0.248847 + 0.248847i
\(454\) 183305.i 0.889331i
\(455\) 93165.4 + 48496.2i 0.450020 + 0.234253i
\(456\) −49017.5 −0.235733
\(457\) −106963. + 106963.i −0.512153 + 0.512153i −0.915186 0.403033i \(-0.867956\pi\)
0.403033 + 0.915186i \(0.367956\pi\)
\(458\) 41569.3 + 41569.3i 0.198172 + 0.198172i
\(459\) 126839.i 0.602044i
\(460\) 35678.8 11250.4i 0.168614 0.0531681i
\(461\) −23815.9 −0.112064 −0.0560318 0.998429i \(-0.517845\pi\)
−0.0560318 + 0.998429i \(0.517845\pi\)
\(462\) 1687.89 1687.89i 0.00790787 0.00790787i
\(463\) −122436. 122436.i −0.571147 0.571147i 0.361302 0.932449i \(-0.382332\pi\)
−0.932449 + 0.361302i \(0.882332\pi\)
\(464\) 211735.i 0.983462i
\(465\) 7241.48 + 22965.2i 0.0334905 + 0.106210i
\(466\) −39616.7 −0.182434
\(467\) 37772.5 37772.5i 0.173198 0.173198i −0.615185 0.788383i \(-0.710919\pi\)
0.788383 + 0.615185i \(0.210919\pi\)
\(468\) 21158.8 + 21158.8i 0.0966048 + 0.0966048i
\(469\) 64769.9i 0.294461i
\(470\) −21923.8 + 42117.5i −0.0992476 + 0.190663i
\(471\) 49932.0 0.225080
\(472\) −199146. + 199146.i −0.893896 + 0.893896i
\(473\) −7346.90 7346.90i −0.0328384 0.0328384i
\(474\) 12918.9i 0.0575000i
\(475\) −239801. + 167927.i −1.06283 + 0.744273i
\(476\) 14375.4 0.0634462
\(477\) 261403. 261403.i 1.14888 1.14888i
\(478\) 23319.6 + 23319.6i 0.102062 + 0.102062i
\(479\) 181209.i 0.789787i −0.918727 0.394893i \(-0.870782\pi\)
0.918727 0.394893i \(-0.129218\pi\)
\(480\) −8315.45 4328.51i −0.0360914 0.0187869i
\(481\) −178238. −0.770389
\(482\) 237135. 237135.i 1.02071 1.02071i
\(483\) 20143.5 + 20143.5i 0.0863456 + 0.0863456i
\(484\) 24242.0i 0.103485i
\(485\) −14205.3 + 4479.25i −0.0603901 + 0.0190424i
\(486\) −136859. −0.579429
\(487\) 38680.6 38680.6i 0.163093 0.163093i −0.620842 0.783935i \(-0.713209\pi\)
0.783935 + 0.620842i \(0.213209\pi\)
\(488\) −36098.5 36098.5i −0.151583 0.151583i
\(489\) 59622.7i 0.249341i
\(490\) −10846.5 34398.1i −0.0451751 0.143266i
\(491\) 281643. 1.16825 0.584126 0.811663i \(-0.301437\pi\)
0.584126 + 0.811663i \(0.301437\pi\)
\(492\) 3504.87 3504.87i 0.0144791 0.0144791i
\(493\) 245170. + 245170.i 1.00873 + 1.00873i
\(494\) 446928.i 1.83140i
\(495\) −15862.1 + 30472.5i −0.0647367 + 0.124365i
\(496\) 155215. 0.630914
\(497\) −32132.8 + 32132.8i −0.130088 + 0.130088i
\(498\) −6478.22 6478.22i −0.0261214 0.0261214i
\(499\) 460535.i 1.84953i −0.380536 0.924766i \(-0.624260\pi\)
0.380536 0.924766i \(-0.375740\pi\)
\(500\) −26205.5 + 3451.82i −0.104822 + 0.0138073i
\(501\) 72904.1 0.290453
\(502\) −165653. + 165653.i −0.657345 + 0.657345i
\(503\) 51536.3 + 51536.3i 0.203694 + 0.203694i 0.801580 0.597887i \(-0.203993\pi\)
−0.597887 + 0.801580i \(0.703993\pi\)
\(504\) 86913.0i 0.342155i
\(505\) −206815. 107655.i −0.810958 0.422135i
\(506\) 65569.3 0.256094
\(507\) 28154.8 28154.8i 0.109531 0.109531i
\(508\) −24155.4 24155.4i −0.0936025 0.0936025i
\(509\) 159178.i 0.614395i 0.951646 + 0.307198i \(0.0993912\pi\)
−0.951646 + 0.307198i \(0.900609\pi\)
\(510\) 80013.1 25230.0i 0.307624 0.0970012i
\(511\) −61526.2 −0.235623
\(512\) 148061. 148061.i 0.564808 0.564808i
\(513\) −91557.7 91557.7i −0.347904 0.347904i
\(514\) 318050.i 1.20384i
\(515\) 37790.6 + 119847.i 0.142485 + 0.451869i
\(516\) 1734.26 0.00651350
\(517\) −5626.79 + 5626.79i −0.0210513 + 0.0210513i
\(518\) 43279.5 + 43279.5i 0.161296 + 0.161296i
\(519\) 10034.4i 0.0372526i
\(520\) 157592. 302748.i 0.582811 1.11963i
\(521\) 302546. 1.11459 0.557295 0.830314i \(-0.311839\pi\)
0.557295 + 0.830314i \(0.311839\pi\)
\(522\) 175247. 175247.i 0.643146 0.643146i
\(523\) 286177. + 286177.i 1.04624 + 1.04624i 0.998878 + 0.0473640i \(0.0150821\pi\)
0.0473640 + 0.998878i \(0.484918\pi\)
\(524\) 15542.3i 0.0566048i
\(525\) −11545.2 16486.7i −0.0418875 0.0598158i
\(526\) −468161. −1.69209
\(527\) −179724. + 179724.i −0.647121 + 0.647121i
\(528\) −6071.38 6071.38i −0.0217781 0.0217781i
\(529\) 502672.i 1.79628i
\(530\) 442202. + 230183.i 1.57423 + 0.819449i
\(531\) −364901. −1.29416
\(532\) 10376.7 10376.7i 0.0366638 0.0366638i
\(533\) 270297. + 270297.i 0.951450 + 0.951450i
\(534\) 25706.9i 0.0901502i
\(535\) −179145. + 56488.6i −0.625889 + 0.197357i
\(536\) −210475. −0.732606
\(537\) −25817.3 + 25817.3i −0.0895288 + 0.0895288i
\(538\) −248589. 248589.i −0.858852 0.858852i
\(539\) 6044.56i 0.0208059i
\(540\) −3515.69 11149.5i −0.0120566 0.0382355i
\(541\) −266396. −0.910192 −0.455096 0.890442i \(-0.650395\pi\)
−0.455096 + 0.890442i \(0.650395\pi\)
\(542\) −96047.3 + 96047.3i −0.326954 + 0.326954i
\(543\) −28144.4 28144.4i −0.0954537 0.0954537i
\(544\) 98950.7i 0.334365i
\(545\) 107510. 206536.i 0.361956 0.695349i
\(546\) −30727.1 −0.103071
\(547\) −243105. + 243105.i −0.812492 + 0.812492i −0.985007 0.172515i \(-0.944811\pi\)
0.172515 + 0.985007i \(0.444811\pi\)
\(548\) 4481.71 + 4481.71i 0.0149239 + 0.0149239i
\(549\) 66144.5i 0.219457i
\(550\) −45623.6 8042.56i −0.150822 0.0265870i
\(551\) 353947. 1.16583
\(552\) 65457.8 65457.8i 0.214824 0.214824i
\(553\) −23132.1 23132.1i −0.0756425 0.0756425i
\(554\) 348908.i 1.13682i
\(555\) 30296.8 + 15770.7i 0.0983584 + 0.0511993i
\(556\) −50639.9 −0.163811
\(557\) −22586.2 + 22586.2i −0.0728003 + 0.0728003i −0.742569 0.669769i \(-0.766393\pi\)
0.669769 + 0.742569i \(0.266393\pi\)
\(558\) 128467. + 128467.i 0.412593 + 0.412593i
\(559\) 133746.i 0.428015i
\(560\) −123731. + 39015.3i −0.394551 + 0.124411i
\(561\) 14060.2 0.0446751
\(562\) 179716. 179716.i 0.569003 0.569003i
\(563\) −422208. 422208.i −1.33202 1.33202i −0.903565 0.428451i \(-0.859059\pi\)
−0.428451 0.903565i \(-0.640941\pi\)
\(564\) 1328.22i 0.00417553i
\(565\) −116220. 368573.i −0.364069 1.15459i
\(566\) −431652. −1.34741
\(567\) −76419.6 + 76419.6i −0.237705 + 0.237705i
\(568\) 104418. + 104418.i 0.323652 + 0.323652i
\(569\) 400419.i 1.23677i 0.785874 + 0.618387i \(0.212213\pi\)
−0.785874 + 0.618387i \(0.787787\pi\)
\(570\) 39544.7 75968.7i 0.121713 0.233822i
\(571\) 281832. 0.864406 0.432203 0.901776i \(-0.357736\pi\)
0.432203 + 0.901776i \(0.357736\pi\)
\(572\) −4781.87 + 4781.87i −0.0146152 + 0.0146152i
\(573\) −71051.0 71051.0i −0.216402 0.216402i
\(574\) 131266.i 0.398409i
\(575\) 95980.9 544478.i 0.290302 1.64682i
\(576\) 278860. 0.840507
\(577\) −112269. + 112269.i −0.337215 + 0.337215i −0.855318 0.518103i \(-0.826638\pi\)
0.518103 + 0.855318i \(0.326638\pi\)
\(578\) 377769. + 377769.i 1.13076 + 1.13076i
\(579\) 25227.2i 0.0752509i
\(580\) 28346.6 + 14755.5i 0.0842645 + 0.0438629i
\(581\) −23199.4 −0.0687266
\(582\) 3081.19 3081.19i 0.00909646 0.00909646i
\(583\) 59077.0 + 59077.0i 0.173813 + 0.173813i
\(584\) 199934.i 0.586221i
\(585\) 421749. 132987.i 1.23237 0.388596i
\(586\) 91580.5 0.266691
\(587\) 154399. 154399.i 0.448094 0.448094i −0.446627 0.894720i \(-0.647375\pi\)
0.894720 + 0.446627i \(0.147375\pi\)
\(588\) 713.418 + 713.418i 0.00206343 + 0.00206343i
\(589\) 259465.i 0.747907i
\(590\) −147982. 469302.i −0.425113 1.34818i
\(591\) −35878.6 −0.102721
\(592\) 155678. 155678.i 0.444205 0.444205i
\(593\) −202843. 202843.i −0.576835 0.576835i 0.357195 0.934030i \(-0.383733\pi\)
−0.934030 + 0.357195i \(0.883733\pi\)
\(594\) 20490.1i 0.0580726i
\(595\) 98092.9 188445.i 0.277079 0.532293i
\(596\) −60506.1 −0.170336
\(597\) −61496.0 + 61496.0i −0.172543 + 0.172543i
\(598\) −596827. 596827.i −1.66896 1.66896i
\(599\) 495814.i 1.38186i −0.722921 0.690931i \(-0.757201\pi\)
0.722921 0.690931i \(-0.242799\pi\)
\(600\) −53574.9 + 37517.2i −0.148819 + 0.104214i
\(601\) −552708. −1.53020 −0.765098 0.643914i \(-0.777309\pi\)
−0.765098 + 0.643914i \(0.777309\pi\)
\(602\) 32476.2 32476.2i 0.0896132 0.0896132i
\(603\) −192830. 192830.i −0.530323 0.530323i
\(604\) 70258.0i 0.192585i
\(605\) 317785. + 165419.i 0.868206 + 0.451935i
\(606\) 68210.0 0.185739
\(607\) 60231.6 60231.6i 0.163473 0.163473i −0.620630 0.784103i \(-0.713123\pi\)
0.784103 + 0.620630i \(0.213123\pi\)
\(608\) −71426.6 71426.6i −0.193220 0.193220i
\(609\) 24334.5i 0.0656126i
\(610\) 85068.9 26824.2i 0.228618 0.0720888i
\(611\) 102433. 0.274382
\(612\) 42797.7 42797.7i 0.114266 0.114266i
\(613\) 376210. + 376210.i 1.00117 + 1.00117i 0.999999 + 0.00117501i \(0.000374018\pi\)
0.00117501 + 0.999999i \(0.499626\pi\)
\(614\) 243016.i 0.644610i
\(615\) −22028.8 69861.1i −0.0582427 0.184708i
\(616\) −19642.3 −0.0517643
\(617\) −127411. + 127411.i −0.334685 + 0.334685i −0.854363 0.519677i \(-0.826052\pi\)
0.519677 + 0.854363i \(0.326052\pi\)
\(618\) −25995.4 25995.4i −0.0680643 0.0680643i
\(619\) 527739.i 1.37733i −0.725080 0.688665i \(-0.758197\pi\)
0.725080 0.688665i \(-0.241803\pi\)
\(620\) −10816.7 + 20779.7i −0.0281391 + 0.0540576i
\(621\) 244532. 0.634092
\(622\) 371756. 371756.i 0.960898 0.960898i
\(623\) 46029.9 + 46029.9i 0.118594 + 0.118594i
\(624\) 110526.i 0.283855i
\(625\) −133569. + 367079.i −0.341936 + 0.939723i
\(626\) 165357. 0.421962
\(627\) 10149.2 10149.2i 0.0258165 0.0258165i
\(628\) 34349.1 + 34349.1i 0.0870956 + 0.0870956i
\(629\) 360521.i 0.911232i
\(630\) −134700. 70116.7i −0.339381 0.176661i
\(631\) −594356. −1.49275 −0.746376 0.665524i \(-0.768208\pi\)
−0.746376 + 0.665524i \(0.768208\pi\)
\(632\) −75169.7 + 75169.7i −0.188195 + 0.188195i
\(633\) 45895.4 + 45895.4i 0.114541 + 0.114541i
\(634\) 498522.i 1.24024i
\(635\) −481480. + 151822.i −1.19407 + 0.376519i
\(636\) −13945.3 −0.0344757
\(637\) −55019.0 + 55019.0i −0.135592 + 0.135592i
\(638\) 39605.7 + 39605.7i 0.0973008 + 0.0973008i
\(639\) 191329.i 0.468574i
\(640\) 139030. + 440912.i 0.339428 + 1.07644i
\(641\) −720768. −1.75420 −0.877100 0.480307i \(-0.840525\pi\)
−0.877100 + 0.480307i \(0.840525\pi\)
\(642\) 38857.4 38857.4i 0.0942767 0.0942767i
\(643\) 22321.8 + 22321.8i 0.0539892 + 0.0539892i 0.733586 0.679597i \(-0.237845\pi\)
−0.679597 + 0.733586i \(0.737845\pi\)
\(644\) 27714.1i 0.0668235i
\(645\) 11834.0 22734.2i 0.0284455 0.0546462i
\(646\) 903999. 2.16622
\(647\) 61507.7 61507.7i 0.146934 0.146934i −0.629813 0.776747i \(-0.716869\pi\)
0.776747 + 0.629813i \(0.216869\pi\)
\(648\) 248331. + 248331.i 0.591400 + 0.591400i
\(649\) 82467.5i 0.195791i
\(650\) 342072. + 488482.i 0.809637 + 1.15617i
\(651\) −17838.6 −0.0420920
\(652\) −41015.5 + 41015.5i −0.0964835 + 0.0964835i
\(653\) 406395. + 406395.i 0.953064 + 0.953064i 0.998947 0.0458828i \(-0.0146101\pi\)
−0.0458828 + 0.998947i \(0.514610\pi\)
\(654\) 68118.1i 0.159260i
\(655\) 203742. + 106056.i 0.474896 + 0.247202i
\(656\) −472169. −1.09721
\(657\) −183173. + 183173.i −0.424356 + 0.424356i
\(658\) −24872.6 24872.6i −0.0574473 0.0574473i
\(659\) 128094.i 0.294956i −0.989065 0.147478i \(-0.952884\pi\)
0.989065 0.147478i \(-0.0471156\pi\)
\(660\) 1235.93 389.716i 0.00283729 0.000894665i
\(661\) −328592. −0.752062 −0.376031 0.926607i \(-0.622711\pi\)
−0.376031 + 0.926607i \(0.622711\pi\)
\(662\) 111155. 111155.i 0.253637 0.253637i
\(663\) −127979. 127979.i −0.291147 0.291147i
\(664\) 75388.3i 0.170989i
\(665\) −65219.9 206835.i −0.147481 0.467714i
\(666\) 257700. 0.580986
\(667\) −472660. + 472660.i −1.06242 + 1.06242i
\(668\) 50152.0 + 50152.0i 0.112392 + 0.112392i
\(669\) 22363.7i 0.0499679i
\(670\) 169800. 326200.i 0.378257 0.726666i
\(671\) 14948.6 0.0332014
\(672\) 4910.70 4910.70i 0.0108744 0.0108744i
\(673\) 595757. + 595757.i 1.31534 + 1.31534i 0.917417 + 0.397927i \(0.130270\pi\)
0.397927 + 0.917417i \(0.369730\pi\)
\(674\) 42645.1i 0.0938749i
\(675\) −170147. 29993.6i −0.373437 0.0658296i
\(676\) 38736.4 0.0847668
\(677\) −249719. + 249719.i −0.544846 + 0.544846i −0.924946 0.380099i \(-0.875890\pi\)
0.380099 + 0.924946i \(0.375890\pi\)
\(678\) 79945.4 + 79945.4i 0.173914 + 0.173914i
\(679\) 11034.2i 0.0239332i
\(680\) −612367. 318761.i −1.32432 0.689361i
\(681\) 75778.8 0.163401
\(682\) −29033.4 + 29033.4i −0.0624207 + 0.0624207i
\(683\) −392090. 392090.i −0.840512 0.840512i 0.148413 0.988925i \(-0.452583\pi\)
−0.988925 + 0.148413i \(0.952583\pi\)
\(684\) 61786.3i 0.132063i
\(685\) 89331.9 28168.4i 0.190382 0.0600318i
\(686\) 26719.3 0.0567776
\(687\) −17184.8 + 17184.8i −0.0364109 + 0.0364109i
\(688\) −116818. 116818.i −0.246793 0.246793i
\(689\) 1.07547e6i 2.26547i
\(690\) 48640.6 + 154256.i 0.102165 + 0.324000i
\(691\) 905394. 1.89619 0.948094 0.317990i \(-0.103008\pi\)
0.948094 + 0.317990i \(0.103008\pi\)
\(692\) −6902.84 + 6902.84i −0.0144150 + 0.0144150i
\(693\) −17995.6 17995.6i −0.0374714 0.0374714i
\(694\) 57584.1i 0.119559i
\(695\) −345550. + 663832.i −0.715388 + 1.37432i
\(696\) 79076.7 0.163241
\(697\) 546727. 546727.i 1.12540 1.12540i
\(698\) 214314. + 214314.i 0.439885 + 0.439885i
\(699\) 16377.6i 0.0335194i
\(700\) 3399.34 19283.7i 0.00693743 0.0393545i
\(701\) 528653. 1.07581 0.537904 0.843006i \(-0.319216\pi\)
0.537904 + 0.843006i \(0.319216\pi\)
\(702\) −186506. + 186506.i −0.378458 + 0.378458i
\(703\) 260239. + 260239.i 0.526576 + 0.526576i
\(704\) 63022.2i 0.127159i
\(705\) −17411.5 9063.35i −0.0350314 0.0182352i
\(706\) −313506. −0.628980
\(707\) 122135. 122135.i 0.244343 0.244343i
\(708\) 9733.34 + 9733.34i 0.0194176 + 0.0194176i
\(709\) 684824.i 1.36234i −0.732124 0.681172i \(-0.761471\pi\)
0.732124 0.681172i \(-0.238529\pi\)
\(710\) −246069. + 77591.3i −0.488135 + 0.153921i
\(711\) −137736. −0.272463
\(712\) 149578. 149578.i 0.295058 0.295058i
\(713\) −346488. 346488.i −0.681569 0.681569i
\(714\) 62151.5i 0.121915i
\(715\) 30055.0 + 95314.9i 0.0587902 + 0.186444i
\(716\) −35520.4 −0.0692870
\(717\) −9640.36 + 9640.36i −0.0187523 + 0.0187523i
\(718\) −692122. 692122.i −1.34256 1.34256i
\(719\) 485616.i 0.939367i −0.882835 0.469683i \(-0.844368\pi\)
0.882835 0.469683i \(-0.155632\pi\)
\(720\) −252212. + 484521.i −0.486520 + 0.934648i
\(721\) −93093.1 −0.179080
\(722\) 264943. 264943.i 0.508252 0.508252i
\(723\) 98031.9 + 98031.9i 0.187539 + 0.187539i
\(724\) 38722.1i 0.0738724i
\(725\) 386856. 270905.i 0.735992 0.515396i
\(726\) −104809. −0.198851
\(727\) 650933. 650933.i 1.23159 1.23159i 0.268243 0.963351i \(-0.413557\pi\)
0.963351 0.268243i \(-0.0864428\pi\)
\(728\) 178788. + 178788.i 0.337347 + 0.337347i
\(729\) 416092.i 0.782950i
\(730\) −309864. 161296.i −0.581467 0.302676i
\(731\) 270528. 0.506265
\(732\) −1764.33 + 1764.33i −0.00329275 + 0.00329275i
\(733\) 34579.8 + 34579.8i 0.0643599 + 0.0643599i 0.738554 0.674194i \(-0.235509\pi\)
−0.674194 + 0.738554i \(0.735509\pi\)
\(734\) 262519.i 0.487268i
\(735\) 14220.3 4483.98i 0.0263228 0.00830021i
\(736\) 190766. 0.352164
\(737\) 43579.5 43579.5i 0.0802319 0.0802319i
\(738\) −390800. 390800.i −0.717533 0.717533i
\(739\) 206401.i 0.377941i 0.981983 + 0.188970i \(0.0605150\pi\)
−0.981983 + 0.188970i \(0.939485\pi\)
\(740\) 9992.81 + 31690.7i 0.0182484 + 0.0578719i
\(741\) −184761. −0.336491
\(742\) −261143. + 261143.i −0.474320 + 0.474320i
\(743\) −601192. 601192.i −1.08902 1.08902i −0.995630 0.0933899i \(-0.970230\pi\)
−0.0933899 0.995630i \(-0.529770\pi\)
\(744\) 57968.0i 0.104723i
\(745\) −412874. + 793167.i −0.743884 + 1.42907i
\(746\) −540816. −0.971788
\(747\) −69068.3 + 69068.3i −0.123776 + 0.123776i
\(748\) 9672.26 + 9672.26i 0.0172872 + 0.0172872i
\(749\) 139154.i 0.248046i
\(750\) −14923.9 113299.i −0.0265313 0.201420i
\(751\) 565097. 1.00194 0.500972 0.865463i \(-0.332976\pi\)
0.500972 + 0.865463i \(0.332976\pi\)
\(752\) −89467.5 + 89467.5i −0.158208 + 0.158208i
\(753\) −68481.5 68481.5i −0.120777 0.120777i
\(754\) 721001.i 1.26822i
\(755\) 921005. + 479418.i 1.61573 + 0.841048i
\(756\) 8660.54 0.0151531
\(757\) −282485. + 282485.i −0.492951 + 0.492951i −0.909235 0.416284i \(-0.863332\pi\)
0.416284 + 0.909235i \(0.363332\pi\)
\(758\) −269498. 269498.i −0.469048 0.469048i
\(759\) 27106.5i 0.0470532i
\(760\) −672126. + 211937.i −1.16365 + 0.366927i
\(761\) −157487. −0.271942 −0.135971 0.990713i \(-0.543415\pi\)
−0.135971 + 0.990713i \(0.543415\pi\)
\(762\) 104435. 104435.i 0.179861 0.179861i
\(763\) 121970. + 121970.i 0.209510 + 0.209510i
\(764\) 97754.5i 0.167475i
\(765\) −268993. 853068.i −0.459640 1.45768i
\(766\) 1.06030e6 1.80705
\(767\) −750638. + 750638.i −1.27597 + 1.27597i
\(768\) −25282.6 25282.6i −0.0428647 0.0428647i
\(769\) 801382.i 1.35515i 0.735455 + 0.677574i \(0.236969\pi\)
−0.735455 + 0.677574i \(0.763031\pi\)
\(770\) 15846.3 30442.2i 0.0267268 0.0513445i
\(771\) −131483. −0.221187
\(772\) −17354.2 + 17354.2i −0.0291186 + 0.0291186i
\(773\) 407066. + 407066.i 0.681249 + 0.681249i 0.960282 0.279033i \(-0.0900139\pi\)
−0.279033 + 0.960282i \(0.590014\pi\)
\(774\) 193373.i 0.322786i
\(775\) 198590. + 283589.i 0.330639 + 0.472156i
\(776\) −35856.4 −0.0595447
\(777\) −17891.9 + 17891.9i −0.0296356 + 0.0296356i
\(778\) 372902. + 372902.i 0.616077 + 0.616077i
\(779\) 789300.i 1.30067i
\(780\) −14797.0 7702.39i −0.0243211 0.0126601i
\(781\) −43240.1 −0.0708900
\(782\) −1.20720e6 + 1.20720e6i −1.97408 + 1.97408i
\(783\) 147704. + 147704.i 0.240918 + 0.240918i
\(784\) 96110.2i 0.156364i
\(785\) 684666. 215891.i 1.11106 0.350345i
\(786\) −67196.7 −0.108768
\(787\) 384677. 384677.i 0.621079 0.621079i −0.324728 0.945807i \(-0.605273\pi\)
0.945807 + 0.324728i \(0.105273\pi\)
\(788\) −24681.6 24681.6i −0.0397484 0.0397484i
\(789\) 193539.i 0.310895i
\(790\) −55857.4 177143.i −0.0895007 0.283838i
\(791\) 286295. 0.457574
\(792\) −58478.1 + 58478.1i −0.0932272 + 0.0932272i
\(793\) −136066. 136066.i −0.216373 0.216373i
\(794\) 1.11403e6i 1.76708i
\(795\) −95158.2 + 182807.i −0.150561 + 0.289241i
\(796\) −84608.3 −0.133533
\(797\) 168513. 168513.i 0.265287 0.265287i −0.561911 0.827198i \(-0.689933\pi\)
0.827198 + 0.561911i \(0.189933\pi\)
\(798\) 44863.5 + 44863.5i 0.0704510 + 0.0704510i
\(799\) 207190.i 0.324545i
\(800\) −132736. 23398.8i −0.207400 0.0365607i
\(801\) 274077. 0.427176
\(802\) 475525. 475525.i 0.739307 0.739307i
\(803\) −41397.0 41397.0i −0.0642004 0.0642004i
\(804\) 10287.1i 0.0159140i
\(805\) 363301. + 189112.i 0.560628 + 0.291829i
\(806\) 528537. 0.813590
\(807\) 102767. 102767.i 0.157801 0.157801i
\(808\) −396886. 396886.i −0.607916 0.607916i
\(809\) 154337.i 0.235816i −0.993025 0.117908i \(-0.962381\pi\)
0.993025 0.117908i \(-0.0376188\pi\)
\(810\) −585212. + 184531.i −0.891955 + 0.281254i
\(811\) 196780. 0.299185 0.149592 0.988748i \(-0.452204\pi\)
0.149592 + 0.988748i \(0.452204\pi\)
\(812\) −16740.1 + 16740.1i −0.0253890 + 0.0253890i
\(813\) −39706.1 39706.1i −0.0600726 0.0600726i
\(814\) 58240.0i 0.0878967i
\(815\) 257791. + 817545.i 0.388108 + 1.23082i
\(816\) 223561. 0.335750
\(817\) 195278. 195278.i 0.292556 0.292556i
\(818\) −295603. 295603.i −0.441776 0.441776i
\(819\) 327600.i 0.488401i
\(820\) 32904.6 63212.7i 0.0489361 0.0940105i
\(821\) −392342. −0.582074 −0.291037 0.956712i \(-0.594000\pi\)
−0.291037 + 0.956712i \(0.594000\pi\)
\(822\) −19376.5 + 19376.5i −0.0286769 + 0.0286769i
\(823\) −292221. 292221.i −0.431432 0.431432i 0.457683 0.889115i \(-0.348679\pi\)
−0.889115 + 0.457683i \(0.848679\pi\)
\(824\) 302513.i 0.445543i
\(825\) 3324.81 18860.9i 0.00488494 0.0277111i
\(826\) 364538. 0.534297
\(827\) −652551. + 652551.i −0.954122 + 0.954122i −0.998993 0.0448712i \(-0.985712\pi\)
0.0448712 + 0.998993i \(0.485712\pi\)
\(828\) 82509.2 + 82509.2i 0.120349 + 0.120349i
\(829\) 604523.i 0.879637i 0.898087 + 0.439819i \(0.144957\pi\)
−0.898087 + 0.439819i \(0.855043\pi\)
\(830\) −116839. 60819.2i −0.169602 0.0882846i
\(831\) 144239. 0.208873
\(832\) 573643. 573643.i 0.828695 0.828695i
\(833\) 111287. + 111287.i 0.160381 + 0.160381i
\(834\) 218940.i 0.314770i
\(835\) 999658. 315216.i 1.43377 0.452100i
\(836\) 13963.7 0.0199796
\(837\) −108276. + 108276.i −0.154555 + 0.154555i
\(838\) −463525. 463525.i −0.660063 0.660063i
\(839\) 61209.4i 0.0869549i 0.999054 + 0.0434775i \(0.0138437\pi\)
−0.999054 + 0.0434775i \(0.986156\pi\)
\(840\) −14571.0 46209.8i −0.0206506 0.0654901i
\(841\) 136281. 0.192683
\(842\) −448775. + 448775.i −0.633001 + 0.633001i
\(843\) 74295.0 + 74295.0i 0.104545 + 0.104545i
\(844\) 63144.5i 0.0886443i
\(845\) 264325. 507791.i 0.370190 0.711167i
\(846\) −148099. −0.206924
\(847\) −187669. + 187669.i −0.261592 + 0.261592i
\(848\) 939341. + 939341.i 1.30627 + 1.30627i
\(849\) 178446.i 0.247566i
\(850\) 988050. 691906.i 1.36754 0.957656i
\(851\) −695044. −0.959739
\(852\) 5103.48 5103.48i 0.00703052 0.00703052i
\(853\) −587656. 587656.i −0.807654 0.807654i 0.176625 0.984278i \(-0.443482\pi\)
−0.984278 + 0.176625i \(0.943482\pi\)
\(854\) 66078.7i 0.0906037i
\(855\) −809949. 421610.i −1.10796 0.576738i
\(856\) −452191. −0.617127
\(857\) −162064. + 162064.i −0.220661 + 0.220661i −0.808777 0.588116i \(-0.799870\pi\)
0.588116 + 0.808777i \(0.299870\pi\)
\(858\) −20674.3 20674.3i −0.0280838 0.0280838i
\(859\) 1.21163e6i 1.64204i 0.570897 + 0.821022i \(0.306596\pi\)
−0.570897 + 0.821022i \(0.693404\pi\)
\(860\) 23780.1 7498.42i 0.0321526 0.0101385i
\(861\) 54265.7 0.0732014
\(862\) −116560. + 116560.i −0.156868 + 0.156868i
\(863\) 199163. + 199163.i 0.267416 + 0.267416i 0.828058 0.560642i \(-0.189446\pi\)
−0.560642 + 0.828058i \(0.689446\pi\)
\(864\) 59613.5i 0.0798577i
\(865\) 43385.8 + 137591.i 0.0579849 + 0.183890i
\(866\) 790643. 1.05425
\(867\) −156171. + 156171.i −0.207760 + 0.207760i
\(868\) −12271.5 12271.5i −0.0162877 0.0162877i
\(869\) 31128.2i 0.0412207i
\(870\) −63794.9 + 122556.i −0.0842844 + 0.161918i
\(871\) −793341. −1.04574
\(872\) 396352. 396352.i 0.521252 0.521252i
\(873\) −32850.4 32850.4i −0.0431035 0.0431035i
\(874\) 1.74281e6i 2.28153i
\(875\) −229592. 176147.i −0.299875 0.230070i
\(876\) 9771.88 0.0127341
\(877\) −67773.5 + 67773.5i −0.0881172 + 0.0881172i −0.749791 0.661674i \(-0.769846\pi\)
0.661674 + 0.749791i \(0.269846\pi\)
\(878\) 487282. + 487282.i 0.632108 + 0.632108i
\(879\) 37859.6i 0.0490002i
\(880\) −109501. 56999.7i −0.141402 0.0736050i
\(881\) 623471. 0.803276 0.401638 0.915799i \(-0.368441\pi\)
0.401638 + 0.915799i \(0.368441\pi\)
\(882\) 79547.5 79547.5i 0.102256 0.102256i
\(883\) −660163. 660163.i −0.846701 0.846701i 0.143019 0.989720i \(-0.454319\pi\)
−0.989720 + 0.143019i \(0.954319\pi\)
\(884\) 176078.i 0.225321i
\(885\) 194010. 61176.1i 0.247707 0.0781079i
\(886\) −162612. −0.207150
\(887\) 846037. 846037.i 1.07533 1.07533i 0.0784092 0.996921i \(-0.475016\pi\)
0.996921 0.0784092i \(-0.0249841\pi\)
\(888\) 58141.0 + 58141.0i 0.0737320 + 0.0737320i
\(889\) 373997.i 0.473222i
\(890\) 111149. + 352492.i 0.140322 + 0.445009i
\(891\) −102836. −0.129535
\(892\) 15384.4 15384.4i 0.0193353 0.0193353i
\(893\) −149558. 149558.i −0.187546 0.187546i
\(894\) 261596.i 0.327308i
\(895\) −242380. + 465633.i −0.302587 + 0.581296i
\(896\) −342486. −0.426605
\(897\) 246730. 246730.i 0.306645 0.306645i
\(898\) −476452. 476452.i −0.590836 0.590836i
\(899\) 418578.i 0.517913i
\(900\) −47290.2 67530.9i −0.0583830 0.0833715i
\(901\) −2.17534e6 −2.67964
\(902\) 88320.5 88320.5i 0.108555 0.108555i
\(903\) 13425.7 + 13425.7i 0.0164650 + 0.0164650i
\(904\) 930339.i 1.13842i
\(905\) −507604. 264227.i −0.619766 0.322612i
\(906\) −303759. −0.370060
\(907\) −67185.8 + 67185.8i −0.0816701 + 0.0816701i −0.746762 0.665092i \(-0.768392\pi\)
0.665092 + 0.746762i \(0.268392\pi\)
\(908\) 52129.6 + 52129.6i 0.0632285 + 0.0632285i
\(909\) 727228.i 0.880122i
\(910\) −421329. + 132855.i −0.508790 + 0.160433i
\(911\) −286850. −0.345635 −0.172818 0.984954i \(-0.555287\pi\)
−0.172818 + 0.984954i \(0.555287\pi\)
\(912\) 161375. 161375.i 0.194020 0.194020i
\(913\) −15609.4 15609.4i −0.0187260 0.0187260i
\(914\) 636255.i 0.761621i
\(915\) 11089.2 + 35167.7i 0.0132452 + 0.0420050i
\(916\) −23643.5 −0.0281787
\(917\) −120320. + 120320.i −0.143087 + 0.143087i
\(918\) 377244. + 377244.i 0.447649 + 0.447649i
\(919\) 184400.i 0.218339i −0.994023 0.109169i \(-0.965181\pi\)
0.994023 0.109169i \(-0.0348191\pi\)
\(920\) 614535. 1.18057e6i 0.726057 1.39482i
\(921\) −100463. −0.118437
\(922\) 70833.0 70833.0i 0.0833247 0.0833247i
\(923\) 393582. + 393582.i 0.461989 + 0.461989i
\(924\) 960.026i 0.00112445i
\(925\) 483617. + 85252.3i 0.565221 + 0.0996374i
\(926\) 728297. 0.849350
\(927\) −277153. + 277153.i −0.322522 + 0.322522i
\(928\) 115228. + 115228.i 0.133802 + 0.133802i
\(929\) 223434.i 0.258891i −0.991587 0.129446i \(-0.958680\pi\)
0.991587 0.129446i \(-0.0413198\pi\)
\(930\) −89840.6 46765.5i −0.103874 0.0540704i
\(931\) 160662. 0.185359
\(932\) 11266.5 11266.5i 0.0129705 0.0129705i
\(933\) 153685. + 153685.i 0.176550 + 0.176550i
\(934\) 224685.i 0.257562i
\(935\) 192793. 60792.1i 0.220530 0.0695383i
\(936\) 1.06456e6 1.21512
\(937\) 799998. 799998.i 0.911192 0.911192i −0.0851740 0.996366i \(-0.527145\pi\)
0.996366 + 0.0851740i \(0.0271446\pi\)
\(938\) 192638. + 192638.i 0.218946 + 0.218946i
\(939\) 68358.9i 0.0775289i
\(940\) −5742.83 18212.5i −0.00649936 0.0206117i
\(941\) −1.67631e6 −1.89311 −0.946554 0.322545i \(-0.895462\pi\)
−0.946554 + 0.322545i \(0.895462\pi\)
\(942\) −148507. + 148507.i −0.167358 + 0.167358i
\(943\) 1.05403e6 + 1.05403e6i 1.18530 + 1.18530i
\(944\) 1.31126e6i 1.47144i
\(945\) 59096.7 113530.i 0.0661759 0.127130i
\(946\) 43702.2 0.0488339
\(947\) 45066.2 45066.2i 0.0502517 0.0502517i −0.681534 0.731786i \(-0.738687\pi\)
0.731786 + 0.681534i \(0.238687\pi\)
\(948\) 3673.96 + 3673.96i 0.00408806 + 0.00408806i
\(949\) 753610.i 0.836785i
\(950\) 213768. 1.21266e6i 0.236862 1.34367i
\(951\) −206090. −0.227875
\(952\) 361634. 361634.i 0.399021 0.399021i
\(953\) 148966. + 148966.i 0.164022 + 0.164022i 0.784346 0.620324i \(-0.212999\pi\)
−0.620324 + 0.784346i \(0.712999\pi\)
\(954\) 1.55493e6i 1.70849i
\(955\) −1.28145e6 667045.i −1.40506 0.731389i
\(956\) −13263.5 −0.0145126
\(957\) −16373.1 + 16373.1i −0.0178775 + 0.0178775i
\(958\) 538952. + 538952.i 0.587245 + 0.587245i
\(959\) 69390.0i 0.0754501i
\(960\) −148264. + 46751.2i −0.160877 + 0.0507283i
\(961\) −616678. −0.667747
\(962\) 530114. 530114.i 0.572821 0.572821i
\(963\) −414283. 414283.i −0.446729 0.446729i
\(964\) 134876.i 0.145138i
\(965\) 109075. + 345914.i 0.117131 + 0.371462i
\(966\) −119821. −0.128404
\(967\) 205113. 205113.i 0.219352 0.219352i −0.588874 0.808225i \(-0.700428\pi\)
0.808225 + 0.588874i \(0.200428\pi\)
\(968\) 609844. + 609844.i 0.650830 + 0.650830i
\(969\) 373715.i 0.398009i
\(970\) 28927.0 55571.3i 0.0307440 0.0590619i
\(971\) −57664.8 −0.0611606 −0.0305803 0.999532i \(-0.509736\pi\)
−0.0305803 + 0.999532i \(0.509736\pi\)
\(972\) 38920.9 38920.9i 0.0411955 0.0411955i
\(973\) −392027. 392027.i −0.414086 0.414086i
\(974\) 230087.i 0.242535i
\(975\) −201940. + 141413.i −0.212428 + 0.148758i
\(976\) 237687. 0.249520
\(977\) 161161. 161161.i 0.168838 0.168838i −0.617630 0.786469i \(-0.711907\pi\)
0.786469 + 0.617630i \(0.211907\pi\)
\(978\) −177329. 177329.i −0.185397 0.185397i
\(979\) 61941.1i 0.0646269i
\(980\) 12867.0 + 6697.76i 0.0133975 + 0.00697392i
\(981\) 726249. 0.754653
\(982\) −837662. + 837662.i −0.868652 + 0.868652i
\(983\) 392165. + 392165.i 0.405847 + 0.405847i 0.880287 0.474441i \(-0.157350\pi\)
−0.474441 + 0.880287i \(0.657350\pi\)
\(984\) 176341.i 0.182122i
\(985\) −491967. + 155129.i −0.507064 + 0.159889i
\(986\) −1.45836e6 −1.50007
\(987\) 10282.4 10282.4i 0.0105550 0.0105550i
\(988\) −127100. 127100.i −0.130207 0.130207i
\(989\) 521548.i 0.533214i
\(990\) −43454.1 137808.i −0.0443364 0.140606i
\(991\) 988822. 1.00686 0.503432 0.864035i \(-0.332070\pi\)
0.503432 + 0.864035i \(0.332070\pi\)
\(992\) −84469.1 + 84469.1i −0.0858370 + 0.0858370i
\(993\) 45951.6 + 45951.6i 0.0466018 + 0.0466018i
\(994\) 191138.i 0.193453i
\(995\) −577340. + 1.10912e6i −0.583157 + 1.12030i
\(996\) 3684.64 0.00371430
\(997\) 952325. 952325.i 0.958064 0.958064i −0.0410911 0.999155i \(-0.513083\pi\)
0.999155 + 0.0410911i \(0.0130834\pi\)
\(998\) 1.36972e6 + 1.36972e6i 1.37522 + 1.37522i
\(999\) 217198.i 0.217633i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 35.5.g.a.8.4 24
5.2 odd 4 inner 35.5.g.a.22.4 yes 24
5.3 odd 4 175.5.g.c.57.9 24
5.4 even 2 175.5.g.c.43.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.g.a.8.4 24 1.1 even 1 trivial
35.5.g.a.22.4 yes 24 5.2 odd 4 inner
175.5.g.c.43.9 24 5.4 even 2
175.5.g.c.57.9 24 5.3 odd 4