Properties

Label 930.4.d.c.559.19
Level $930$
Weight $4$
Character 930.559
Analytic conductor $54.872$
Analytic rank $0$
Dimension $20$
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] = [930,4,Mod(559,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.559");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\), degree \(1\), 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: \(54.8717763053\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.19
Root \(22.4343i\) of defining polynomial
Character \(\chi\) \(=\) 930.559
Dual form 930.4.d.c.559.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(10.6574 - 3.37922i) q^{5} +6.00000 q^{6} +22.4343i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(10.6574 - 3.37922i) q^{5} +6.00000 q^{6} +22.4343i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(6.75844 + 21.3149i) q^{10} -57.5594 q^{11} +12.0000i q^{12} -41.6653i q^{13} -44.8686 q^{14} +(-10.1377 - 31.9723i) q^{15} +16.0000 q^{16} -41.4957i q^{17} -18.0000i q^{18} +55.8008 q^{19} +(-42.6297 + 13.5169i) q^{20} +67.3030 q^{21} -115.119i q^{22} +115.808i q^{23} -24.0000 q^{24} +(102.162 - 72.0276i) q^{25} +83.3306 q^{26} +27.0000i q^{27} -89.7373i q^{28} +220.538 q^{29} +(63.9446 - 20.2753i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +172.678i q^{33} +82.9914 q^{34} +(75.8105 + 239.092i) q^{35} +36.0000 q^{36} -40.0489i q^{37} +111.602i q^{38} -124.996 q^{39} +(-27.0338 - 85.2595i) q^{40} +236.222 q^{41} +134.606i q^{42} -52.3815i q^{43} +230.238 q^{44} +(-95.9169 + 30.4130i) q^{45} -231.616 q^{46} +3.59556i q^{47} -48.0000i q^{48} -160.299 q^{49} +(144.055 + 204.323i) q^{50} -124.487 q^{51} +166.661i q^{52} -263.196i q^{53} -54.0000 q^{54} +(-613.435 + 194.506i) q^{55} +179.475 q^{56} -167.402i q^{57} +441.075i q^{58} +212.525 q^{59} +(40.5507 + 127.889i) q^{60} +678.688 q^{61} -62.0000i q^{62} -201.909i q^{63} -64.0000 q^{64} +(-140.796 - 444.045i) q^{65} -345.356 q^{66} -736.794i q^{67} +165.983i q^{68} +347.423 q^{69} +(-478.184 + 151.621i) q^{70} -379.090 q^{71} +72.0000i q^{72} +1076.93i q^{73} +80.0977 q^{74} +(-216.083 - 306.485i) q^{75} -223.203 q^{76} -1291.31i q^{77} -249.992i q^{78} +288.554 q^{79} +(170.519 - 54.0675i) q^{80} +81.0000 q^{81} +472.444i q^{82} +876.288i q^{83} -269.212 q^{84} +(-140.223 - 442.238i) q^{85} +104.763 q^{86} -661.613i q^{87} +460.475i q^{88} +1116.75 q^{89} +(-60.8260 - 191.834i) q^{90} +934.733 q^{91} -463.231i q^{92} +93.0000i q^{93} -7.19111 q^{94} +(594.693 - 188.563i) q^{95} +96.0000 q^{96} -1308.93i q^{97} -320.597i q^{98} +518.034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 3.00000i 0.577350i
\(4\) −4.00000 −0.500000
\(5\) 10.6574 3.37922i 0.953230 0.302247i
\(6\) 6.00000 0.408248
\(7\) 22.4343i 1.21134i 0.795716 + 0.605670i \(0.207095\pi\)
−0.795716 + 0.605670i \(0.792905\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) 6.75844 + 21.3149i 0.213721 + 0.674035i
\(11\) −57.5594 −1.57771 −0.788855 0.614580i \(-0.789326\pi\)
−0.788855 + 0.614580i \(0.789326\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 41.6653i 0.888914i −0.895800 0.444457i \(-0.853397\pi\)
0.895800 0.444457i \(-0.146603\pi\)
\(14\) −44.8686 −0.856546
\(15\) −10.1377 31.9723i −0.174502 0.550347i
\(16\) 16.0000 0.250000
\(17\) 41.4957i 0.592011i −0.955186 0.296005i \(-0.904345\pi\)
0.955186 0.296005i \(-0.0956546\pi\)
\(18\) 18.0000i 0.235702i
\(19\) 55.8008 0.673768 0.336884 0.941546i \(-0.390627\pi\)
0.336884 + 0.941546i \(0.390627\pi\)
\(20\) −42.6297 + 13.5169i −0.476615 + 0.151123i
\(21\) 67.3030 0.699367
\(22\) 115.119i 1.11561i
\(23\) 115.808i 1.04990i 0.851134 + 0.524948i \(0.175915\pi\)
−0.851134 + 0.524948i \(0.824085\pi\)
\(24\) −24.0000 −0.204124
\(25\) 102.162 72.0276i 0.817294 0.576221i
\(26\) 83.3306 0.628557
\(27\) 27.0000i 0.192450i
\(28\) 89.7373i 0.605670i
\(29\) 220.538 1.41217 0.706083 0.708129i \(-0.250460\pi\)
0.706083 + 0.708129i \(0.250460\pi\)
\(30\) 63.9446 20.2753i 0.389154 0.123392i
\(31\) −31.0000 −0.179605
\(32\) 32.0000i 0.176777i
\(33\) 172.678i 0.910891i
\(34\) 82.9914 0.418615
\(35\) 75.8105 + 239.092i 0.366123 + 1.15468i
\(36\) 36.0000 0.166667
\(37\) 40.0489i 0.177946i −0.996034 0.0889729i \(-0.971642\pi\)
0.996034 0.0889729i \(-0.0283584\pi\)
\(38\) 111.602i 0.476426i
\(39\) −124.996 −0.513215
\(40\) −27.0338 85.2595i −0.106860 0.337018i
\(41\) 236.222 0.899797 0.449898 0.893080i \(-0.351460\pi\)
0.449898 + 0.893080i \(0.351460\pi\)
\(42\) 134.606i 0.494527i
\(43\) 52.3815i 0.185770i −0.995677 0.0928849i \(-0.970391\pi\)
0.995677 0.0928849i \(-0.0296089\pi\)
\(44\) 230.238 0.788855
\(45\) −95.9169 + 30.4130i −0.317743 + 0.100749i
\(46\) −231.616 −0.742388
\(47\) 3.59556i 0.0111588i 0.999984 + 0.00557942i \(0.00177599\pi\)
−0.999984 + 0.00557942i \(0.998224\pi\)
\(48\) 48.0000i 0.144338i
\(49\) −160.299 −0.467343
\(50\) 144.055 + 204.323i 0.407450 + 0.577914i
\(51\) −124.487 −0.341798
\(52\) 166.661i 0.444457i
\(53\) 263.196i 0.682127i −0.940040 0.341063i \(-0.889213\pi\)
0.940040 0.341063i \(-0.110787\pi\)
\(54\) −54.0000 −0.136083
\(55\) −613.435 + 194.506i −1.50392 + 0.476858i
\(56\) 179.475 0.428273
\(57\) 167.402i 0.389000i
\(58\) 441.075i 0.998552i
\(59\) 212.525 0.468957 0.234478 0.972121i \(-0.424662\pi\)
0.234478 + 0.972121i \(0.424662\pi\)
\(60\) 40.5507 + 127.889i 0.0872511 + 0.275174i
\(61\) 678.688 1.42454 0.712271 0.701904i \(-0.247667\pi\)
0.712271 + 0.701904i \(0.247667\pi\)
\(62\) 62.0000i 0.127000i
\(63\) 201.909i 0.403780i
\(64\) −64.0000 −0.125000
\(65\) −140.796 444.045i −0.268671 0.847339i
\(66\) −345.356 −0.644097
\(67\) 736.794i 1.34349i −0.740783 0.671744i \(-0.765545\pi\)
0.740783 0.671744i \(-0.234455\pi\)
\(68\) 165.983i 0.296005i
\(69\) 347.423 0.606158
\(70\) −478.184 + 151.621i −0.816485 + 0.258888i
\(71\) −379.090 −0.633658 −0.316829 0.948483i \(-0.602618\pi\)
−0.316829 + 0.948483i \(0.602618\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 1076.93i 1.72665i 0.504652 + 0.863323i \(0.331621\pi\)
−0.504652 + 0.863323i \(0.668379\pi\)
\(74\) 80.0977 0.125827
\(75\) −216.083 306.485i −0.332681 0.471865i
\(76\) −223.203 −0.336884
\(77\) 1291.31i 1.91114i
\(78\) 249.992i 0.362898i
\(79\) 288.554 0.410947 0.205473 0.978663i \(-0.434127\pi\)
0.205473 + 0.978663i \(0.434127\pi\)
\(80\) 170.519 54.0675i 0.238307 0.0755617i
\(81\) 81.0000 0.111111
\(82\) 472.444i 0.636253i
\(83\) 876.288i 1.15886i 0.815023 + 0.579428i \(0.196724\pi\)
−0.815023 + 0.579428i \(0.803276\pi\)
\(84\) −269.212 −0.349684
\(85\) −140.223 442.238i −0.178933 0.564322i
\(86\) 104.763 0.131359
\(87\) 661.613i 0.815315i
\(88\) 460.475i 0.557805i
\(89\) 1116.75 1.33006 0.665032 0.746814i \(-0.268418\pi\)
0.665032 + 0.746814i \(0.268418\pi\)
\(90\) −60.8260 191.834i −0.0712402 0.224678i
\(91\) 934.733 1.07678
\(92\) 463.231i 0.524948i
\(93\) 93.0000i 0.103695i
\(94\) −7.19111 −0.00789050
\(95\) 594.693 188.563i 0.642255 0.203644i
\(96\) 96.0000 0.102062
\(97\) 1308.93i 1.37012i −0.728488 0.685058i \(-0.759777\pi\)
0.728488 0.685058i \(-0.240223\pi\)
\(98\) 320.597i 0.330461i
\(99\) 518.034 0.525903
\(100\) −408.647 + 288.111i −0.408647 + 0.288111i
\(101\) 450.901 0.444221 0.222110 0.975022i \(-0.428705\pi\)
0.222110 + 0.975022i \(0.428705\pi\)
\(102\) 248.974i 0.241687i
\(103\) 212.078i 0.202880i 0.994842 + 0.101440i \(0.0323450\pi\)
−0.994842 + 0.101440i \(0.967655\pi\)
\(104\) −333.323 −0.314279
\(105\) 717.277 227.432i 0.666657 0.211381i
\(106\) 526.391 0.482336
\(107\) 1111.74i 1.00445i −0.864737 0.502224i \(-0.832515\pi\)
0.864737 0.502224i \(-0.167485\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 1200.10 1.05458 0.527288 0.849687i \(-0.323209\pi\)
0.527288 + 0.849687i \(0.323209\pi\)
\(110\) −389.012 1226.87i −0.337189 1.06343i
\(111\) −120.147 −0.102737
\(112\) 358.949i 0.302835i
\(113\) 771.438i 0.642219i 0.947042 + 0.321109i \(0.104056\pi\)
−0.947042 + 0.321109i \(0.895944\pi\)
\(114\) 334.805 0.275064
\(115\) 391.340 + 1234.21i 0.317328 + 1.00079i
\(116\) −882.151 −0.706083
\(117\) 374.988i 0.296305i
\(118\) 425.051i 0.331603i
\(119\) 930.928 0.717126
\(120\) −255.778 + 81.1013i −0.194577 + 0.0616959i
\(121\) 1982.08 1.48917
\(122\) 1357.38i 1.00730i
\(123\) 708.666i 0.519498i
\(124\) 124.000 0.0898027
\(125\) 845.384 1112.86i 0.604908 0.796296i
\(126\) 403.818 0.285515
\(127\) 2103.35i 1.46962i 0.678272 + 0.734811i \(0.262729\pi\)
−0.678272 + 0.734811i \(0.737271\pi\)
\(128\) 128.000i 0.0883883i
\(129\) −157.144 −0.107254
\(130\) 888.091 281.593i 0.599159 0.189979i
\(131\) 1698.77 1.13299 0.566497 0.824064i \(-0.308298\pi\)
0.566497 + 0.824064i \(0.308298\pi\)
\(132\) 690.713i 0.455446i
\(133\) 1251.85i 0.816161i
\(134\) 1473.59 0.949990
\(135\) 91.2390 + 287.751i 0.0581674 + 0.183449i
\(136\) −331.966 −0.209307
\(137\) 1289.18i 0.803955i 0.915650 + 0.401978i \(0.131677\pi\)
−0.915650 + 0.401978i \(0.868323\pi\)
\(138\) 694.847i 0.428618i
\(139\) −724.171 −0.441895 −0.220947 0.975286i \(-0.570915\pi\)
−0.220947 + 0.975286i \(0.570915\pi\)
\(140\) −303.242 956.369i −0.183062 0.577342i
\(141\) 10.7867 0.00644256
\(142\) 758.180i 0.448064i
\(143\) 2398.23i 1.40245i
\(144\) −144.000 −0.0833333
\(145\) 2350.37 745.246i 1.34612 0.426823i
\(146\) −2153.86 −1.22092
\(147\) 480.896i 0.269821i
\(148\) 160.195i 0.0889729i
\(149\) −5.97522 −0.00328529 −0.00164265 0.999999i \(-0.500523\pi\)
−0.00164265 + 0.999999i \(0.500523\pi\)
\(150\) 612.970 432.166i 0.333659 0.235241i
\(151\) 959.441 0.517074 0.258537 0.966001i \(-0.416760\pi\)
0.258537 + 0.966001i \(0.416760\pi\)
\(152\) 446.406i 0.238213i
\(153\) 373.461i 0.197337i
\(154\) 2582.61 1.35138
\(155\) −330.380 + 104.756i −0.171205 + 0.0542851i
\(156\) 499.984 0.256607
\(157\) 2298.66i 1.16849i −0.811577 0.584246i \(-0.801390\pi\)
0.811577 0.584246i \(-0.198610\pi\)
\(158\) 577.107i 0.290583i
\(159\) −789.587 −0.393826
\(160\) 108.135 + 341.038i 0.0534302 + 0.168509i
\(161\) −2598.07 −1.27178
\(162\) 162.000i 0.0785674i
\(163\) 4055.96i 1.94900i −0.224386 0.974500i \(-0.572038\pi\)
0.224386 0.974500i \(-0.427962\pi\)
\(164\) −944.888 −0.449898
\(165\) 583.518 + 1840.31i 0.275314 + 0.868288i
\(166\) −1752.58 −0.819436
\(167\) 430.521i 0.199489i −0.995013 0.0997446i \(-0.968197\pi\)
0.995013 0.0997446i \(-0.0318026\pi\)
\(168\) 538.424i 0.247264i
\(169\) 461.001 0.209832
\(170\) 884.475 280.446i 0.399036 0.126525i
\(171\) −502.207 −0.224589
\(172\) 209.526i 0.0928849i
\(173\) 2264.40i 0.995141i 0.867423 + 0.497571i \(0.165774\pi\)
−0.867423 + 0.497571i \(0.834226\pi\)
\(174\) 1323.23 0.576514
\(175\) 1615.89 + 2291.93i 0.697999 + 0.990020i
\(176\) −920.950 −0.394427
\(177\) 637.576i 0.270752i
\(178\) 2233.51i 0.940498i
\(179\) 480.399 0.200596 0.100298 0.994957i \(-0.468020\pi\)
0.100298 + 0.994957i \(0.468020\pi\)
\(180\) 383.668 121.652i 0.158872 0.0503745i
\(181\) 2389.42 0.981239 0.490619 0.871374i \(-0.336771\pi\)
0.490619 + 0.871374i \(0.336771\pi\)
\(182\) 1869.47i 0.761396i
\(183\) 2036.06i 0.822460i
\(184\) 926.463 0.371194
\(185\) −135.334 426.818i −0.0537835 0.169623i
\(186\) −186.000 −0.0733236
\(187\) 2388.47i 0.934021i
\(188\) 14.3822i 0.00557942i
\(189\) −605.727 −0.233122
\(190\) 377.127 + 1189.39i 0.143998 + 0.454143i
\(191\) −386.040 −0.146246 −0.0731228 0.997323i \(-0.523296\pi\)
−0.0731228 + 0.997323i \(0.523296\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 2832.74i 1.05650i −0.849088 0.528251i \(-0.822848\pi\)
0.849088 0.528251i \(-0.177152\pi\)
\(194\) 2617.85 0.968819
\(195\) −1332.14 + 422.389i −0.489211 + 0.155117i
\(196\) 641.194 0.233671
\(197\) 95.0624i 0.0343803i −0.999852 0.0171901i \(-0.994528\pi\)
0.999852 0.0171901i \(-0.00547206\pi\)
\(198\) 1036.07i 0.371870i
\(199\) −424.470 −0.151205 −0.0756027 0.997138i \(-0.524088\pi\)
−0.0756027 + 0.997138i \(0.524088\pi\)
\(200\) −576.221 817.294i −0.203725 0.288957i
\(201\) −2210.38 −0.775663
\(202\) 901.801i 0.314111i
\(203\) 4947.61i 1.71061i
\(204\) 497.948 0.170899
\(205\) 2517.52 798.246i 0.857713 0.271961i
\(206\) −424.156 −0.143458
\(207\) 1042.27i 0.349965i
\(208\) 666.645i 0.222228i
\(209\) −3211.86 −1.06301
\(210\) 454.863 + 1434.55i 0.149469 + 0.471398i
\(211\) −4889.26 −1.59522 −0.797608 0.603176i \(-0.793902\pi\)
−0.797608 + 0.603176i \(0.793902\pi\)
\(212\) 1052.78i 0.341063i
\(213\) 1137.27i 0.365843i
\(214\) 2223.48 0.710252
\(215\) −177.009 558.252i −0.0561483 0.177081i
\(216\) 216.000 0.0680414
\(217\) 695.464i 0.217563i
\(218\) 2400.20i 0.745698i
\(219\) 3230.79 0.996879
\(220\) 2453.74 778.023i 0.751960 0.238429i
\(221\) −1728.93 −0.526247
\(222\) 240.293i 0.0726461i
\(223\) 233.543i 0.0701309i 0.999385 + 0.0350655i \(0.0111640\pi\)
−0.999385 + 0.0350655i \(0.988836\pi\)
\(224\) −717.898 −0.214137
\(225\) −919.456 + 648.249i −0.272431 + 0.192074i
\(226\) −1542.88 −0.454117
\(227\) 1432.11i 0.418734i 0.977837 + 0.209367i \(0.0671403\pi\)
−0.977837 + 0.209367i \(0.932860\pi\)
\(228\) 669.610i 0.194500i
\(229\) 1142.48 0.329683 0.164842 0.986320i \(-0.447289\pi\)
0.164842 + 0.986320i \(0.447289\pi\)
\(230\) −2468.43 + 782.681i −0.707667 + 0.224384i
\(231\) −3873.92 −1.10340
\(232\) 1764.30i 0.499276i
\(233\) 1546.92i 0.434943i −0.976067 0.217472i \(-0.930219\pi\)
0.976067 0.217472i \(-0.0697810\pi\)
\(234\) −749.976 −0.209519
\(235\) 12.1502 + 38.3194i 0.00337273 + 0.0106369i
\(236\) −850.102 −0.234478
\(237\) 865.661i 0.237260i
\(238\) 1861.86i 0.507085i
\(239\) −822.195 −0.222525 −0.111262 0.993791i \(-0.535489\pi\)
−0.111262 + 0.993791i \(0.535489\pi\)
\(240\) −162.203 511.557i −0.0436256 0.137587i
\(241\) 3862.11 1.03228 0.516142 0.856503i \(-0.327368\pi\)
0.516142 + 0.856503i \(0.327368\pi\)
\(242\) 3964.16i 1.05300i
\(243\) 243.000i 0.0641500i
\(244\) −2714.75 −0.712271
\(245\) −1708.37 + 541.685i −0.445485 + 0.141253i
\(246\) 1417.33 0.367341
\(247\) 2324.96i 0.598921i
\(248\) 248.000i 0.0635001i
\(249\) 2628.86 0.669066
\(250\) 2225.71 + 1690.77i 0.563066 + 0.427734i
\(251\) 2133.84 0.536602 0.268301 0.963335i \(-0.413538\pi\)
0.268301 + 0.963335i \(0.413538\pi\)
\(252\) 807.635i 0.201890i
\(253\) 6665.83i 1.65643i
\(254\) −4206.70 −1.03918
\(255\) −1326.71 + 420.669i −0.325812 + 0.103307i
\(256\) 256.000 0.0625000
\(257\) 3083.52i 0.748423i −0.927343 0.374212i \(-0.877913\pi\)
0.927343 0.374212i \(-0.122087\pi\)
\(258\) 314.289i 0.0758402i
\(259\) 898.469 0.215553
\(260\) 563.185 + 1776.18i 0.134336 + 0.423670i
\(261\) −1984.84 −0.470722
\(262\) 3397.54i 0.801147i
\(263\) 3582.39i 0.839922i 0.907542 + 0.419961i \(0.137956\pi\)
−0.907542 + 0.419961i \(0.862044\pi\)
\(264\) 1381.43 0.322049
\(265\) −889.397 2804.99i −0.206171 0.650223i
\(266\) −2503.71 −0.577113
\(267\) 3350.26i 0.767913i
\(268\) 2947.18i 0.671744i
\(269\) −2132.95 −0.483450 −0.241725 0.970345i \(-0.577713\pi\)
−0.241725 + 0.970345i \(0.577713\pi\)
\(270\) −575.501 + 182.478i −0.129718 + 0.0411306i
\(271\) 4909.37 1.10045 0.550227 0.835015i \(-0.314541\pi\)
0.550227 + 0.835015i \(0.314541\pi\)
\(272\) 663.931i 0.148003i
\(273\) 2804.20i 0.621677i
\(274\) −2578.35 −0.568482
\(275\) −5880.37 + 4145.87i −1.28945 + 0.909110i
\(276\) −1389.69 −0.303079
\(277\) 2781.01i 0.603231i 0.953430 + 0.301615i \(0.0975258\pi\)
−0.953430 + 0.301615i \(0.902474\pi\)
\(278\) 1448.34i 0.312467i
\(279\) 279.000 0.0598684
\(280\) 1912.74 606.484i 0.408243 0.129444i
\(281\) −4183.11 −0.888054 −0.444027 0.896013i \(-0.646451\pi\)
−0.444027 + 0.896013i \(0.646451\pi\)
\(282\) 21.5733i 0.00455558i
\(283\) 5911.48i 1.24170i −0.783929 0.620850i \(-0.786788\pi\)
0.783929 0.620850i \(-0.213212\pi\)
\(284\) 1516.36 0.316829
\(285\) −565.690 1784.08i −0.117574 0.370806i
\(286\) −4796.46 −0.991680
\(287\) 5299.48i 1.08996i
\(288\) 288.000i 0.0589256i
\(289\) 3191.11 0.649523
\(290\) 1490.49 + 4700.73i 0.301809 + 0.951850i
\(291\) −3926.78 −0.791037
\(292\) 4307.72i 0.863323i
\(293\) 9034.01i 1.80127i 0.434576 + 0.900635i \(0.356898\pi\)
−0.434576 + 0.900635i \(0.643102\pi\)
\(294\) −961.792 −0.190792
\(295\) 2264.98 718.171i 0.447024 0.141741i
\(296\) −320.391 −0.0629133
\(297\) 1554.10i 0.303630i
\(298\) 11.9504i 0.00232305i
\(299\) 4825.17 0.933267
\(300\) 864.332 + 1225.94i 0.166341 + 0.235932i
\(301\) 1175.14 0.225030
\(302\) 1918.88i 0.365627i
\(303\) 1352.70i 0.256471i
\(304\) 892.813 0.168442
\(305\) 7233.07 2293.44i 1.35792 0.430563i
\(306\) −746.923 −0.139538
\(307\) 6256.30i 1.16308i −0.813517 0.581541i \(-0.802450\pi\)
0.813517 0.581541i \(-0.197550\pi\)
\(308\) 5165.22i 0.955571i
\(309\) 636.234 0.117133
\(310\) −209.512 660.761i −0.0383854 0.121060i
\(311\) 635.997 0.115962 0.0579809 0.998318i \(-0.481534\pi\)
0.0579809 + 0.998318i \(0.481534\pi\)
\(312\) 999.968i 0.181449i
\(313\) 3035.48i 0.548164i 0.961706 + 0.274082i \(0.0883740\pi\)
−0.961706 + 0.274082i \(0.911626\pi\)
\(314\) 4597.33 0.826249
\(315\) −682.295 2151.83i −0.122041 0.384895i
\(316\) −1154.21 −0.205473
\(317\) 6984.39i 1.23748i −0.785594 0.618742i \(-0.787643\pi\)
0.785594 0.618742i \(-0.212357\pi\)
\(318\) 1579.17i 0.278477i
\(319\) −12694.0 −2.22799
\(320\) −682.076 + 216.270i −0.119154 + 0.0377808i
\(321\) −3335.22 −0.579919
\(322\) 5196.14i 0.899284i
\(323\) 2315.49i 0.398878i
\(324\) −324.000 −0.0555556
\(325\) −3001.05 4256.60i −0.512211 0.726504i
\(326\) 8111.91 1.37815
\(327\) 3600.30i 0.608860i
\(328\) 1889.78i 0.318126i
\(329\) −80.6639 −0.0135171
\(330\) −3680.61 + 1167.04i −0.613973 + 0.194676i
\(331\) 6327.31 1.05070 0.525348 0.850887i \(-0.323935\pi\)
0.525348 + 0.850887i \(0.323935\pi\)
\(332\) 3505.15i 0.579428i
\(333\) 360.440i 0.0593153i
\(334\) 861.041 0.141060
\(335\) −2489.79 7852.33i −0.406065 1.28065i
\(336\) 1076.85 0.174842
\(337\) 501.049i 0.0809907i 0.999180 + 0.0404954i \(0.0128936\pi\)
−0.999180 + 0.0404954i \(0.987106\pi\)
\(338\) 922.002i 0.148374i
\(339\) 2314.31 0.370785
\(340\) 560.893 + 1768.95i 0.0894667 + 0.282161i
\(341\) 1784.34 0.283365
\(342\) 1004.41i 0.158809i
\(343\) 4098.78i 0.645228i
\(344\) −419.052 −0.0656795
\(345\) 3702.64 1174.02i 0.577807 0.183209i
\(346\) −4528.81 −0.703671
\(347\) 1157.28i 0.179038i −0.995985 0.0895191i \(-0.971467\pi\)
0.995985 0.0895191i \(-0.0285330\pi\)
\(348\) 2646.45i 0.407657i
\(349\) −3980.30 −0.610489 −0.305245 0.952274i \(-0.598738\pi\)
−0.305245 + 0.952274i \(0.598738\pi\)
\(350\) −4583.86 + 3231.78i −0.700050 + 0.493560i
\(351\) 1124.96 0.171072
\(352\) 1841.90i 0.278902i
\(353\) 4029.24i 0.607521i 0.952748 + 0.303761i \(0.0982423\pi\)
−0.952748 + 0.303761i \(0.901758\pi\)
\(354\) 1275.15 0.191451
\(355\) −4040.13 + 1281.03i −0.604021 + 0.191521i
\(356\) −4467.02 −0.665032
\(357\) 2792.78i 0.414033i
\(358\) 960.798i 0.141843i
\(359\) 2100.54 0.308809 0.154404 0.988008i \(-0.450654\pi\)
0.154404 + 0.988008i \(0.450654\pi\)
\(360\) 243.304 + 767.335i 0.0356201 + 0.112339i
\(361\) −3745.27 −0.546037
\(362\) 4778.84i 0.693840i
\(363\) 5946.25i 0.859771i
\(364\) −3738.93 −0.538388
\(365\) 3639.19 + 11477.3i 0.521873 + 1.64589i
\(366\) 4072.13 0.581567
\(367\) 6519.16i 0.927241i 0.886034 + 0.463620i \(0.153450\pi\)
−0.886034 + 0.463620i \(0.846550\pi\)
\(368\) 1852.93i 0.262474i
\(369\) −2126.00 −0.299932
\(370\) 853.636 270.668i 0.119942 0.0380307i
\(371\) 5904.62 0.826287
\(372\) 372.000i 0.0518476i
\(373\) 157.218i 0.0218242i −0.999940 0.0109121i \(-0.996527\pi\)
0.999940 0.0109121i \(-0.00347350\pi\)
\(374\) −4776.93 −0.660453
\(375\) −3338.57 2536.15i −0.459741 0.349244i
\(376\) 28.7644 0.00394525
\(377\) 9188.77i 1.25529i
\(378\) 1211.45i 0.164842i
\(379\) 10091.4 1.36770 0.683851 0.729622i \(-0.260304\pi\)
0.683851 + 0.729622i \(0.260304\pi\)
\(380\) −2378.77 + 754.253i −0.321128 + 0.101822i
\(381\) 6310.04 0.848487
\(382\) 772.081i 0.103411i
\(383\) 186.982i 0.0249460i −0.999922 0.0124730i \(-0.996030\pi\)
0.999922 0.0124730i \(-0.00397039\pi\)
\(384\) −384.000 −0.0510310
\(385\) −4363.61 13762.0i −0.577636 1.82176i
\(386\) 5665.48 0.747060
\(387\) 471.433i 0.0619233i
\(388\) 5235.71i 0.685058i
\(389\) −8164.80 −1.06419 −0.532097 0.846683i \(-0.678596\pi\)
−0.532097 + 0.846683i \(0.678596\pi\)
\(390\) −844.778 2664.27i −0.109685 0.345925i
\(391\) 4805.53 0.621550
\(392\) 1282.39i 0.165231i
\(393\) 5096.31i 0.654134i
\(394\) 190.125 0.0243105
\(395\) 3075.24 975.086i 0.391727 0.124207i
\(396\) −2072.14 −0.262952
\(397\) 3031.44i 0.383233i 0.981470 + 0.191617i \(0.0613730\pi\)
−0.981470 + 0.191617i \(0.938627\pi\)
\(398\) 848.940i 0.106918i
\(399\) 3755.56 0.471211
\(400\) 1634.59 1152.44i 0.204323 0.144055i
\(401\) −14669.2 −1.82679 −0.913395 0.407075i \(-0.866549\pi\)
−0.913395 + 0.407075i \(0.866549\pi\)
\(402\) 4420.76i 0.548477i
\(403\) 1291.62i 0.159654i
\(404\) −1803.60 −0.222110
\(405\) 863.252 273.717i 0.105914 0.0335830i
\(406\) −9895.23 −1.20959
\(407\) 2305.19i 0.280747i
\(408\) 995.897i 0.120844i
\(409\) −10988.9 −1.32852 −0.664260 0.747502i \(-0.731253\pi\)
−0.664260 + 0.747502i \(0.731253\pi\)
\(410\) 1596.49 + 5035.04i 0.192305 + 0.606495i
\(411\) 3867.53 0.464164
\(412\) 848.312i 0.101440i
\(413\) 4767.86i 0.568066i
\(414\) 2084.54 0.247463
\(415\) 2961.17 + 9338.98i 0.350261 + 1.10466i
\(416\) 1333.29 0.157139
\(417\) 2172.51i 0.255128i
\(418\) 6423.72i 0.751661i
\(419\) 4258.01 0.496462 0.248231 0.968701i \(-0.420151\pi\)
0.248231 + 0.968701i \(0.420151\pi\)
\(420\) −2869.11 + 909.726i −0.333329 + 0.105691i
\(421\) 1538.19 0.178068 0.0890339 0.996029i \(-0.471622\pi\)
0.0890339 + 0.996029i \(0.471622\pi\)
\(422\) 9778.52i 1.12799i
\(423\) 32.3600i 0.00371962i
\(424\) −2105.57 −0.241168
\(425\) −2988.84 4239.27i −0.341129 0.483847i
\(426\) −2274.54 −0.258690
\(427\) 15225.9i 1.72560i
\(428\) 4446.96i 0.502224i
\(429\) 7194.69 0.809704
\(430\) 1116.50 354.017i 0.125215 0.0397028i
\(431\) −3432.85 −0.383653 −0.191826 0.981429i \(-0.561441\pi\)
−0.191826 + 0.981429i \(0.561441\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 4646.46i 0.515692i −0.966186 0.257846i \(-0.916987\pi\)
0.966186 0.257846i \(-0.0830128\pi\)
\(434\) 1390.93 0.153840
\(435\) −2235.74 7051.10i −0.246426 0.777182i
\(436\) −4800.40 −0.527288
\(437\) 6462.17i 0.707386i
\(438\) 6461.58i 0.704900i
\(439\) 3080.19 0.334873 0.167437 0.985883i \(-0.446451\pi\)
0.167437 + 0.985883i \(0.446451\pi\)
\(440\) 1556.05 + 4907.48i 0.168595 + 0.531716i
\(441\) 1442.69 0.155781
\(442\) 3457.86i 0.372113i
\(443\) 10840.0i 1.16259i −0.813695 0.581293i \(-0.802547\pi\)
0.813695 0.581293i \(-0.197453\pi\)
\(444\) 480.586 0.0513685
\(445\) 11901.7 3773.76i 1.26786 0.402008i
\(446\) −467.086 −0.0495901
\(447\) 17.9256i 0.00189676i
\(448\) 1435.80i 0.151417i
\(449\) −9724.20 −1.02208 −0.511039 0.859557i \(-0.670739\pi\)
−0.511039 + 0.859557i \(0.670739\pi\)
\(450\) −1296.50 1838.91i −0.135817 0.192638i
\(451\) −13596.8 −1.41962
\(452\) 3085.75i 0.321109i
\(453\) 2878.32i 0.298533i
\(454\) −2864.22 −0.296090
\(455\) 9961.85 3158.67i 1.02642 0.325452i
\(456\) −1339.22 −0.137532
\(457\) 15252.2i 1.56120i −0.625030 0.780601i \(-0.714913\pi\)
0.625030 0.780601i \(-0.285087\pi\)
\(458\) 2284.97i 0.233121i
\(459\) 1120.38 0.113933
\(460\) −1565.36 4936.86i −0.158664 0.500396i
\(461\) −18790.6 −1.89841 −0.949203 0.314663i \(-0.898108\pi\)
−0.949203 + 0.314663i \(0.898108\pi\)
\(462\) 7747.83i 0.780220i
\(463\) 6086.94i 0.610980i −0.952195 0.305490i \(-0.901180\pi\)
0.952195 0.305490i \(-0.0988203\pi\)
\(464\) 3528.60 0.353042
\(465\) 314.268 + 991.141i 0.0313415 + 0.0988453i
\(466\) 3093.83 0.307551
\(467\) 981.191i 0.0972250i −0.998818 0.0486125i \(-0.984520\pi\)
0.998818 0.0486125i \(-0.0154799\pi\)
\(468\) 1499.95i 0.148152i
\(469\) 16529.5 1.62742
\(470\) −76.6388 + 24.3004i −0.00752146 + 0.00238488i
\(471\) −6895.99 −0.674629
\(472\) 1700.20i 0.165801i
\(473\) 3015.04i 0.293091i
\(474\) 1731.32 0.167768
\(475\) 5700.71 4019.20i 0.550666 0.388239i
\(476\) −3723.71 −0.358563
\(477\) 2368.76i 0.227376i
\(478\) 1644.39i 0.157349i
\(479\) −20392.2 −1.94519 −0.972593 0.232513i \(-0.925305\pi\)
−0.972593 + 0.232513i \(0.925305\pi\)
\(480\) 1023.11 324.405i 0.0972886 0.0308479i
\(481\) −1668.65 −0.158178
\(482\) 7724.23i 0.729936i
\(483\) 7794.21i 0.734262i
\(484\) −7928.33 −0.744584
\(485\) −4423.15 13949.8i −0.414113 1.30604i
\(486\) 486.000 0.0453609
\(487\) 8755.86i 0.814714i 0.913269 + 0.407357i \(0.133550\pi\)
−0.913269 + 0.407357i \(0.866450\pi\)
\(488\) 5429.50i 0.503652i
\(489\) −12167.9 −1.12526
\(490\) −1083.37 3416.74i −0.0998809 0.315006i
\(491\) −9788.68 −0.899709 −0.449855 0.893102i \(-0.648524\pi\)
−0.449855 + 0.893102i \(0.648524\pi\)
\(492\) 2834.66i 0.259749i
\(493\) 9151.37i 0.836018i
\(494\) 4649.92 0.423501
\(495\) 5520.92 1750.55i 0.501307 0.158953i
\(496\) −496.000 −0.0449013
\(497\) 8504.63i 0.767575i
\(498\) 5257.73i 0.473101i
\(499\) 9506.90 0.852880 0.426440 0.904516i \(-0.359768\pi\)
0.426440 + 0.904516i \(0.359768\pi\)
\(500\) −3381.54 + 4451.43i −0.302454 + 0.398148i
\(501\) −1291.56 −0.115175
\(502\) 4267.69i 0.379435i
\(503\) 3358.96i 0.297751i 0.988856 + 0.148875i \(0.0475654\pi\)
−0.988856 + 0.148875i \(0.952435\pi\)
\(504\) −1615.27 −0.142758
\(505\) 4805.44 1523.69i 0.423444 0.134264i
\(506\) 13331.7 1.17127
\(507\) 1383.00i 0.121147i
\(508\) 8413.39i 0.734811i
\(509\) −22834.6 −1.98846 −0.994230 0.107274i \(-0.965788\pi\)
−0.994230 + 0.107274i \(0.965788\pi\)
\(510\) −841.339 2653.43i −0.0730492 0.230384i
\(511\) −24160.2 −2.09155
\(512\) 512.000i 0.0441942i
\(513\) 1506.62i 0.129667i
\(514\) 6167.04 0.529215
\(515\) 716.659 + 2260.21i 0.0613199 + 0.193392i
\(516\) 628.578 0.0536271
\(517\) 206.958i 0.0176054i
\(518\) 1796.94i 0.152419i
\(519\) 6793.21 0.574545
\(520\) −3552.36 + 1126.37i −0.299580 + 0.0949897i
\(521\) −18524.1 −1.55769 −0.778845 0.627217i \(-0.784194\pi\)
−0.778845 + 0.627217i \(0.784194\pi\)
\(522\) 3969.68i 0.332851i
\(523\) 5652.88i 0.472626i −0.971677 0.236313i \(-0.924061\pi\)
0.971677 0.236313i \(-0.0759391\pi\)
\(524\) −6795.08 −0.566497
\(525\) 6875.79 4847.67i 0.571588 0.402990i
\(526\) −7164.77 −0.593914
\(527\) 1286.37i 0.106328i
\(528\) 2762.85i 0.227723i
\(529\) −1244.45 −0.102281
\(530\) 5609.98 1778.79i 0.459777 0.145785i
\(531\) −1912.73 −0.156319
\(532\) 5007.41i 0.408081i
\(533\) 9842.26i 0.799842i
\(534\) 6700.53 0.542997
\(535\) −3756.82 11848.3i −0.303591 0.957470i
\(536\) −5894.35 −0.474995
\(537\) 1441.20i 0.115814i
\(538\) 4265.89i 0.341851i
\(539\) 9226.69 0.737331
\(540\) −364.956 1151.00i −0.0290837 0.0917246i
\(541\) 14341.3 1.13970 0.569852 0.821748i \(-0.307001\pi\)
0.569852 + 0.821748i \(0.307001\pi\)
\(542\) 9818.74i 0.778138i
\(543\) 7168.26i 0.566518i
\(544\) 1327.86 0.104654
\(545\) 12790.0 4055.40i 1.00525 0.318742i
\(546\) 5608.40 0.439592
\(547\) 3284.64i 0.256747i 0.991726 + 0.128374i \(0.0409757\pi\)
−0.991726 + 0.128374i \(0.959024\pi\)
\(548\) 5156.71i 0.401978i
\(549\) −6108.19 −0.474848
\(550\) −8291.73 11760.7i −0.642838 0.911780i
\(551\) 12306.2 0.951472
\(552\) 2779.39i 0.214309i
\(553\) 6473.50i 0.497796i
\(554\) −5562.03 −0.426548
\(555\) −1280.45 + 406.002i −0.0979320 + 0.0310519i
\(556\) 2896.68 0.220947
\(557\) 2529.86i 0.192448i −0.995360 0.0962240i \(-0.969323\pi\)
0.995360 0.0962240i \(-0.0306765\pi\)
\(558\) 558.000i 0.0423334i
\(559\) −2182.49 −0.165133
\(560\) 1212.97 + 3825.48i 0.0915308 + 0.288671i
\(561\) 7165.40 0.539257
\(562\) 8366.22i 0.627949i
\(563\) 1728.05i 0.129358i 0.997906 + 0.0646792i \(0.0206024\pi\)
−0.997906 + 0.0646792i \(0.979398\pi\)
\(564\) −43.1467 −0.00322128
\(565\) 2606.86 + 8221.54i 0.194109 + 0.612182i
\(566\) 11823.0 0.878015
\(567\) 1817.18i 0.134593i
\(568\) 3032.72i 0.224032i
\(569\) 7481.61 0.551222 0.275611 0.961269i \(-0.411120\pi\)
0.275611 + 0.961269i \(0.411120\pi\)
\(570\) 3568.16 1131.38i 0.262200 0.0831373i
\(571\) −14370.7 −1.05323 −0.526616 0.850103i \(-0.676539\pi\)
−0.526616 + 0.850103i \(0.676539\pi\)
\(572\) 9592.92i 0.701224i
\(573\) 1158.12i 0.0844349i
\(574\) −10599.0 −0.770718
\(575\) 8341.37 + 11831.1i 0.604972 + 0.858073i
\(576\) 576.000 0.0416667
\(577\) 19900.0i 1.43578i −0.696155 0.717891i \(-0.745108\pi\)
0.696155 0.717891i \(-0.254892\pi\)
\(578\) 6382.21i 0.459282i
\(579\) −8498.21 −0.609972
\(580\) −9401.46 + 2980.98i −0.673059 + 0.213411i
\(581\) −19658.9 −1.40377
\(582\) 7853.56i 0.559348i
\(583\) 15149.4i 1.07620i
\(584\) 8615.44 0.610462
\(585\) 1267.17 + 3996.41i 0.0895571 + 0.282446i
\(586\) −18068.0 −1.27369
\(587\) 11044.9i 0.776614i 0.921530 + 0.388307i \(0.126940\pi\)
−0.921530 + 0.388307i \(0.873060\pi\)
\(588\) 1923.58i 0.134910i
\(589\) −1729.82 −0.121012
\(590\) 1436.34 + 4529.95i 0.100226 + 0.316093i
\(591\) −285.187 −0.0198495
\(592\) 640.782i 0.0444864i
\(593\) 5730.49i 0.396835i 0.980118 + 0.198417i \(0.0635801\pi\)
−0.980118 + 0.198417i \(0.936420\pi\)
\(594\) 3108.21 0.214699
\(595\) 9921.30 3145.81i 0.683586 0.216749i
\(596\) 23.9009 0.00164265
\(597\) 1273.41i 0.0872985i
\(598\) 9650.34i 0.659919i
\(599\) −18192.0 −1.24091 −0.620456 0.784241i \(-0.713053\pi\)
−0.620456 + 0.784241i \(0.713053\pi\)
\(600\) −2451.88 + 1728.66i −0.166829 + 0.117621i
\(601\) −27821.7 −1.88831 −0.944154 0.329506i \(-0.893118\pi\)
−0.944154 + 0.329506i \(0.893118\pi\)
\(602\) 2350.29i 0.159120i
\(603\) 6631.15i 0.447829i
\(604\) −3837.76 −0.258537
\(605\) 21123.9 6697.89i 1.41952 0.450096i
\(606\) 2705.40 0.181352
\(607\) 20709.7i 1.38481i 0.721509 + 0.692405i \(0.243449\pi\)
−0.721509 + 0.692405i \(0.756551\pi\)
\(608\) 1785.63i 0.119106i
\(609\) 14842.8 0.987623
\(610\) 4586.87 + 14466.1i 0.304454 + 0.960192i
\(611\) 149.810 0.00991925
\(612\) 1493.85i 0.0986685i
\(613\) 21571.2i 1.42129i 0.703550 + 0.710646i \(0.251597\pi\)
−0.703550 + 0.710646i \(0.748403\pi\)
\(614\) 12512.6 0.822423
\(615\) −2394.74 7552.56i −0.157017 0.495201i
\(616\) −10330.4 −0.675691
\(617\) 15924.1i 1.03903i −0.854461 0.519515i \(-0.826113\pi\)
0.854461 0.519515i \(-0.173887\pi\)
\(618\) 1272.47i 0.0828255i
\(619\) −21362.2 −1.38711 −0.693554 0.720405i \(-0.743956\pi\)
−0.693554 + 0.720405i \(0.743956\pi\)
\(620\) 1321.52 419.023i 0.0856026 0.0271426i
\(621\) −3126.81 −0.202053
\(622\) 1271.99i 0.0819973i
\(623\) 25053.6i 1.61116i
\(624\) −1999.94 −0.128304
\(625\) 5249.04 14716.9i 0.335938 0.941884i
\(626\) −6070.96 −0.387611
\(627\) 9635.58i 0.613729i
\(628\) 9194.65i 0.584246i
\(629\) −1661.86 −0.105346
\(630\) 4303.66 1364.59i 0.272162 0.0862961i
\(631\) 29763.6 1.87777 0.938883 0.344237i \(-0.111862\pi\)
0.938883 + 0.344237i \(0.111862\pi\)
\(632\) 2308.43i 0.145292i
\(633\) 14667.8i 0.920999i
\(634\) 13968.8 0.875033
\(635\) 7107.68 + 22416.3i 0.444188 + 1.40089i
\(636\) 3158.35 0.196913
\(637\) 6678.89i 0.415428i
\(638\) 25388.0i 1.57543i
\(639\) 3411.81 0.211219
\(640\) −432.540 1364.15i −0.0267151 0.0842544i
\(641\) 20950.0 1.29091 0.645456 0.763797i \(-0.276667\pi\)
0.645456 + 0.763797i \(0.276667\pi\)
\(642\) 6670.44i 0.410064i
\(643\) 21161.2i 1.29785i −0.760853 0.648925i \(-0.775219\pi\)
0.760853 0.648925i \(-0.224781\pi\)
\(644\) 10392.3 0.635890
\(645\) −1674.76 + 531.026i −0.102238 + 0.0324172i
\(646\) 4630.99 0.282049
\(647\) 27929.0i 1.69707i 0.529140 + 0.848535i \(0.322515\pi\)
−0.529140 + 0.848535i \(0.677485\pi\)
\(648\) 648.000i 0.0392837i
\(649\) −12232.8 −0.739878
\(650\) 8513.20 6002.11i 0.513716 0.362188i
\(651\) −2086.39 −0.125610
\(652\) 16223.8i 0.974500i
\(653\) 24990.7i 1.49764i 0.662772 + 0.748821i \(0.269380\pi\)
−0.662772 + 0.748821i \(0.730620\pi\)
\(654\) 7200.60 0.430529
\(655\) 18104.5 5740.52i 1.08000 0.342444i
\(656\) 3779.55 0.224949
\(657\) 9692.37i 0.575549i
\(658\) 161.328i 0.00955807i
\(659\) 31126.7 1.83995 0.919973 0.391983i \(-0.128211\pi\)
0.919973 + 0.391983i \(0.128211\pi\)
\(660\) −2334.07 7361.22i −0.137657 0.434144i
\(661\) −14724.6 −0.866446 −0.433223 0.901287i \(-0.642624\pi\)
−0.433223 + 0.901287i \(0.642624\pi\)
\(662\) 12654.6i 0.742955i
\(663\) 5186.79i 0.303829i
\(664\) 7010.31 0.409718
\(665\) 4230.29 + 13341.5i 0.246682 + 0.777989i
\(666\) −720.880 −0.0419422
\(667\) 25540.0i 1.48263i
\(668\) 1722.08i 0.0997446i
\(669\) 700.629 0.0404901
\(670\) 15704.7 4979.58i 0.905559 0.287131i
\(671\) −39064.9 −2.24751
\(672\) 2153.69i 0.123632i
\(673\) 29919.4i 1.71368i 0.515581 + 0.856841i \(0.327576\pi\)
−0.515581 + 0.856841i \(0.672424\pi\)
\(674\) −1002.10 −0.0572691
\(675\) 1944.75 + 2758.37i 0.110894 + 0.157288i
\(676\) −1844.00 −0.104916
\(677\) 14987.8i 0.850856i 0.904992 + 0.425428i \(0.139876\pi\)
−0.904992 + 0.425428i \(0.860124\pi\)
\(678\) 4628.63i 0.262185i
\(679\) 29364.9 1.65968
\(680\) −3537.90 + 1121.79i −0.199518 + 0.0632625i
\(681\) 4296.33 0.241756
\(682\) 3568.68i 0.200369i
\(683\) 18606.8i 1.04242i 0.853429 + 0.521208i \(0.174519\pi\)
−0.853429 + 0.521208i \(0.825481\pi\)
\(684\) 2008.83 0.112295
\(685\) 4356.42 + 13739.3i 0.242993 + 0.766354i
\(686\) −8197.56 −0.456245
\(687\) 3427.45i 0.190343i
\(688\) 838.104i 0.0464424i
\(689\) −10966.1 −0.606352
\(690\) 2348.04 + 7405.28i 0.129548 + 0.408572i
\(691\) −18534.0 −1.02036 −0.510178 0.860069i \(-0.670421\pi\)
−0.510178 + 0.860069i \(0.670421\pi\)
\(692\) 9057.62i 0.497571i
\(693\) 11621.7i 0.637047i
\(694\) 2314.57 0.126599
\(695\) −7717.80 + 2447.13i −0.421227 + 0.133561i
\(696\) −5292.90 −0.288257
\(697\) 9802.19i 0.532690i
\(698\) 7960.60i 0.431681i
\(699\) −4640.75 −0.251115
\(700\) −6463.56 9167.71i −0.349000 0.495010i
\(701\) −18960.0 −1.02156 −0.510778 0.859713i \(-0.670642\pi\)
−0.510778 + 0.859713i \(0.670642\pi\)
\(702\) 2249.93i 0.120966i
\(703\) 2234.76i 0.119894i
\(704\) 3683.80 0.197214
\(705\) 114.958 36.4505i 0.00614124 0.00194724i
\(706\) −8058.49 −0.429582
\(707\) 10115.6i 0.538102i
\(708\) 2550.31i 0.135376i
\(709\) 28218.1 1.49472 0.747358 0.664422i \(-0.231322\pi\)
0.747358 + 0.664422i \(0.231322\pi\)
\(710\) −2562.06 8080.25i −0.135426 0.427108i
\(711\) −2596.98 −0.136982
\(712\) 8934.04i 0.470249i
\(713\) 3590.04i 0.188567i
\(714\) 5585.57 0.292765
\(715\) 8104.15 + 25559.0i 0.423885 + 1.33686i
\(716\) −1921.60 −0.100298
\(717\) 2466.59i 0.128475i
\(718\) 4201.09i 0.218361i
\(719\) 12392.6 0.642792 0.321396 0.946945i \(-0.395848\pi\)
0.321396 + 0.946945i \(0.395848\pi\)
\(720\) −1534.67 + 486.608i −0.0794358 + 0.0251872i
\(721\) −4757.83 −0.245757
\(722\) 7490.54i 0.386107i
\(723\) 11586.3i 0.595990i
\(724\) −9557.68 −0.490619
\(725\) 22530.5 15884.8i 1.15415 0.813720i
\(726\) 11892.5 0.607950
\(727\) 31895.4i 1.62714i −0.581464 0.813572i \(-0.697520\pi\)
0.581464 0.813572i \(-0.302480\pi\)
\(728\) 7477.86i 0.380698i
\(729\) −729.000 −0.0370370
\(730\) −22954.6 + 7278.37i −1.16382 + 0.369020i
\(731\) −2173.61 −0.109978
\(732\) 8144.26i 0.411230i
\(733\) 24622.5i 1.24073i −0.784315 0.620363i \(-0.786985\pi\)
0.784315 0.620363i \(-0.213015\pi\)
\(734\) −13038.3 −0.655658
\(735\) 1625.05 + 5125.12i 0.0815524 + 0.257201i
\(736\) −3705.85 −0.185597
\(737\) 42409.4i 2.11963i
\(738\) 4252.00i 0.212084i
\(739\) 33118.3 1.64855 0.824274 0.566191i \(-0.191584\pi\)
0.824274 + 0.566191i \(0.191584\pi\)
\(740\) 541.336 + 1707.27i 0.0268918 + 0.0848116i
\(741\) −6974.88 −0.345787
\(742\) 11809.2i 0.584273i
\(743\) 3339.76i 0.164905i −0.996595 0.0824523i \(-0.973725\pi\)
0.996595 0.0824523i \(-0.0262752\pi\)
\(744\) 744.000 0.0366618
\(745\) −63.6805 + 20.1916i −0.00313164 + 0.000992969i
\(746\) 314.435 0.0154320
\(747\) 7886.59i 0.386286i
\(748\) 9553.87i 0.467011i
\(749\) 24941.1 1.21673
\(750\) 5072.31 6677.14i 0.246953 0.325086i
\(751\) −28779.3 −1.39837 −0.699183 0.714943i \(-0.746453\pi\)
−0.699183 + 0.714943i \(0.746453\pi\)
\(752\) 57.5289i 0.00278971i
\(753\) 6401.53i 0.309807i
\(754\) 18377.5 0.887627
\(755\) 10225.2 3242.16i 0.492890 0.156284i
\(756\) 2422.91 0.116561
\(757\) 518.139i 0.0248772i 0.999923 + 0.0124386i \(0.00395944\pi\)
−0.999923 + 0.0124386i \(0.996041\pi\)
\(758\) 20182.7i 0.967111i
\(759\) −19997.5 −0.956341
\(760\) −1508.51 4757.55i −0.0719990 0.227072i
\(761\) 33119.3 1.57762 0.788812 0.614634i \(-0.210696\pi\)
0.788812 + 0.614634i \(0.210696\pi\)
\(762\) 12620.1i 0.599971i
\(763\) 26923.4i 1.27745i
\(764\) 1544.16 0.0731228
\(765\) 1262.01 + 3980.14i 0.0596445 + 0.188107i
\(766\) 373.964 0.0176395
\(767\) 8854.94i 0.416862i
\(768\) 768.000i 0.0360844i
\(769\) 6074.22 0.284840 0.142420 0.989806i \(-0.454512\pi\)
0.142420 + 0.989806i \(0.454512\pi\)
\(770\) 27524.0 8727.21i 1.28818 0.408451i
\(771\) −9250.57 −0.432102
\(772\) 11331.0i 0.528251i
\(773\) 2650.10i 0.123309i −0.998098 0.0616544i \(-0.980362\pi\)
0.998098 0.0616544i \(-0.0196376\pi\)
\(774\) −942.866 −0.0437864
\(775\) −3167.01 + 2232.86i −0.146790 + 0.103492i
\(776\) −10471.4 −0.484409
\(777\) 2695.41i 0.124449i
\(778\) 16329.6i 0.752499i
\(779\) 13181.4 0.606254
\(780\) 5328.54 1689.56i 0.244606 0.0775587i
\(781\) 21820.2 0.999728
\(782\) 9611.05i 0.439502i
\(783\) 5954.52i 0.271772i
\(784\) −2564.78 −0.116836
\(785\) −7767.69 24497.8i −0.353173 1.11384i
\(786\) 10192.6 0.462543
\(787\) 12990.2i 0.588376i 0.955748 + 0.294188i \(0.0950492\pi\)
−0.955748 + 0.294188i \(0.904951\pi\)
\(788\) 380.249i 0.0171901i
\(789\) 10747.2 0.484929
\(790\) 1950.17 + 6150.48i 0.0878279 + 0.276993i
\(791\) −17306.7 −0.777945
\(792\) 4144.28i 0.185935i
\(793\) 28277.8i 1.26630i
\(794\) −6062.88 −0.270987
\(795\) −8414.97 + 2668.19i −0.375407 + 0.119033i
\(796\) 1697.88 0.0756027
\(797\) 22872.5i 1.01654i 0.861197 + 0.508272i \(0.169715\pi\)
−0.861197 + 0.508272i \(0.830285\pi\)
\(798\) 7511.12i 0.333196i
\(799\) 149.200 0.00660616
\(800\) 2304.88 + 3269.18i 0.101862 + 0.144478i
\(801\) −10050.8 −0.443355
\(802\) 29338.3i 1.29173i
\(803\) 61987.4i 2.72415i
\(804\) 8841.53 0.387832
\(805\) −27688.8 + 8779.45i −1.21230 + 0.384391i
\(806\) −2583.25 −0.112892
\(807\) 6398.84i 0.279120i
\(808\) 3607.20i 0.157056i
\(809\) 10880.8 0.472866 0.236433 0.971648i \(-0.424022\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(810\) 547.434 + 1726.50i 0.0237467 + 0.0748928i
\(811\) 44284.1 1.91742 0.958709 0.284388i \(-0.0917903\pi\)
0.958709 + 0.284388i \(0.0917903\pi\)
\(812\) 19790.5i 0.855306i
\(813\) 14728.1i 0.635347i
\(814\) −4610.38 −0.198518
\(815\) −13706.0 43226.1i −0.589079 1.85785i
\(816\) −1991.79 −0.0854494
\(817\) 2922.93i 0.125166i
\(818\) 21977.7i 0.939405i
\(819\) −8412.60 −0.358925
\(820\) −10070.1 + 3192.99i −0.428857 + 0.135980i
\(821\) 20401.3 0.867249 0.433624 0.901094i \(-0.357234\pi\)
0.433624 + 0.901094i \(0.357234\pi\)
\(822\) 7735.06i 0.328213i
\(823\) 31905.5i 1.35134i −0.737203 0.675671i \(-0.763854\pi\)
0.737203 0.675671i \(-0.236146\pi\)
\(824\) 1696.62 0.0717290
\(825\) 12437.6 + 17641.1i 0.524875 + 0.744466i
\(826\) −9535.73 −0.401683
\(827\) 11424.3i 0.480364i 0.970728 + 0.240182i \(0.0772072\pi\)
−0.970728 + 0.240182i \(0.922793\pi\)
\(828\) 4169.08i 0.174983i
\(829\) 21995.0 0.921494 0.460747 0.887532i \(-0.347582\pi\)
0.460747 + 0.887532i \(0.347582\pi\)
\(830\) −18678.0 + 5922.34i −0.781110 + 0.247672i
\(831\) 8343.04 0.348275
\(832\) 2666.58i 0.111114i
\(833\) 6651.70i 0.276672i
\(834\) −4345.03 −0.180403
\(835\) −1454.82 4588.25i −0.0602950 0.190159i
\(836\) 12847.4 0.531505
\(837\) 837.000i 0.0345651i
\(838\) 8516.03i 0.351052i
\(839\) −17674.3 −0.727278 −0.363639 0.931540i \(-0.618466\pi\)
−0.363639 + 0.931540i \(0.618466\pi\)
\(840\) −1819.45 5738.21i −0.0747346 0.235699i
\(841\) 24247.9 0.994214
\(842\) 3076.37i 0.125913i
\(843\) 12549.3i 0.512718i
\(844\) 19557.0 0.797608
\(845\) 4913.09 1557.82i 0.200018 0.0634211i
\(846\) 64.7200 0.00263017
\(847\) 44466.7i 1.80389i
\(848\) 4211.13i 0.170532i
\(849\) −17734.5 −0.716896
\(850\) 8478.54 5977.67i 0.342131 0.241215i
\(851\) 4637.97 0.186825
\(852\) 4549.08i 0.182921i
\(853\) 36566.9i 1.46779i −0.679262 0.733896i \(-0.737700\pi\)
0.679262 0.733896i \(-0.262300\pi\)
\(854\) −30451.8 −1.22019
\(855\) −5352.24 + 1697.07i −0.214085 + 0.0678813i
\(856\) −8893.92 −0.355126
\(857\) 10794.9i 0.430278i −0.976583 0.215139i \(-0.930980\pi\)
0.976583 0.215139i \(-0.0690204\pi\)
\(858\) 14389.4i 0.572547i
\(859\) 31664.1 1.25770 0.628851 0.777526i \(-0.283526\pi\)
0.628851 + 0.777526i \(0.283526\pi\)
\(860\) 708.034 + 2233.01i 0.0280742 + 0.0885406i
\(861\) 15898.4 0.629288
\(862\) 6865.69i 0.271283i
\(863\) 26769.7i 1.05591i 0.849273 + 0.527955i \(0.177041\pi\)
−0.849273 + 0.527955i \(0.822959\pi\)
\(864\) −864.000 −0.0340207
\(865\) 7651.92 + 24132.7i 0.300778 + 0.948598i
\(866\) 9292.93 0.364650
\(867\) 9573.32i 0.375002i
\(868\) 2781.86i 0.108781i
\(869\) −16609.0 −0.648355
\(870\) 14102.2 4471.47i 0.549551 0.174250i
\(871\) −30698.8 −1.19425
\(872\) 9600.80i 0.372849i
\(873\) 11780.3i 0.456706i
\(874\) −12924.3 −0.500197
\(875\) 24966.2 + 18965.6i 0.964584 + 0.732749i
\(876\) −12923.2 −0.498440
\(877\) 29225.9i 1.12530i 0.826695 + 0.562650i \(0.190218\pi\)
−0.826695 + 0.562650i \(0.809782\pi\)
\(878\) 6160.38i 0.236791i
\(879\) 27102.0 1.03996
\(880\) −9814.96 + 3112.09i −0.375980 + 0.119214i
\(881\) 7606.81 0.290897 0.145448 0.989366i \(-0.453538\pi\)
0.145448 + 0.989366i \(0.453538\pi\)
\(882\) 2885.38i 0.110154i
\(883\) 49912.4i 1.90225i −0.308806 0.951125i \(-0.599929\pi\)
0.308806 0.951125i \(-0.400071\pi\)
\(884\) 6915.73 0.263123
\(885\) −2154.51 6794.93i −0.0818340 0.258089i
\(886\) 21680.1 0.822072
\(887\) 5775.46i 0.218626i −0.994007 0.109313i \(-0.965135\pi\)
0.994007 0.109313i \(-0.0348651\pi\)
\(888\) 961.173i 0.0363230i
\(889\) −47187.2 −1.78021
\(890\) 7547.52 + 23803.5i 0.284262 + 0.896511i
\(891\) −4662.31 −0.175301
\(892\) 934.172i 0.0350655i
\(893\) 200.635i 0.00751847i
\(894\) −35.8513 −0.00134122
\(895\) 5119.82 1623.38i 0.191214 0.0606296i
\(896\) 2871.59 0.107068
\(897\) 14475.5i 0.538822i
\(898\) 19448.4i 0.722719i
\(899\) −6836.67 −0.253633
\(900\) 3677.82 2593.00i 0.136216 0.0960369i
\(901\) −10921.5 −0.403826
\(902\) 27193.6i 1.00382i
\(903\) 3525.43i 0.129921i
\(904\) 6171.50 0.227059
\(905\) 25465.1 8074.38i 0.935346 0.296576i
\(906\) 5756.65 0.211095
\(907\) 34185.5i 1.25150i −0.780024 0.625750i \(-0.784793\pi\)
0.780024 0.625750i \(-0.215207\pi\)
\(908\) 5728.45i 0.209367i
\(909\) −4058.11 −0.148074
\(910\) 6317.34 + 19923.7i 0.230129 + 0.725785i
\(911\) 17367.6 0.631629 0.315814 0.948821i \(-0.397722\pi\)
0.315814 + 0.948821i \(0.397722\pi\)
\(912\) 2678.44i 0.0972500i
\(913\) 50438.6i 1.82834i
\(914\) 30504.5 1.10394
\(915\) −6880.31 21699.2i −0.248586 0.783993i
\(916\) −4569.93 −0.164842
\(917\) 38110.7i 1.37244i
\(918\) 2240.77i 0.0805625i
\(919\) 38445.5 1.37998 0.689989 0.723820i \(-0.257615\pi\)
0.689989 + 0.723820i \(0.257615\pi\)
\(920\) 9873.71 3130.72i 0.353833 0.112192i
\(921\) −18768.9 −0.671506
\(922\) 37581.2i 1.34238i
\(923\) 15794.9i 0.563267i
\(924\) 15495.7 0.551699
\(925\) −2884.63 4091.46i −0.102536 0.145434i
\(926\) 12173.9 0.432028
\(927\) 1908.70i 0.0676268i
\(928\) 7057.21i 0.249638i
\(929\) −44008.6 −1.55422 −0.777112 0.629362i \(-0.783316\pi\)
−0.777112 + 0.629362i \(0.783316\pi\)
\(930\) −1982.28 + 628.535i −0.0698942 + 0.0221618i
\(931\) −8944.79 −0.314880
\(932\) 6187.66i 0.217472i
\(933\) 1907.99i 0.0669506i
\(934\) 1962.38 0.0687485
\(935\) 8071.16 + 25454.9i 0.282305 + 0.890337i
\(936\) 2999.90 0.104760
\(937\) 56605.9i 1.97357i 0.162037 + 0.986785i \(0.448194\pi\)
−0.162037 + 0.986785i \(0.551806\pi\)
\(938\) 33058.9i 1.15076i
\(939\) 9106.44 0.316483
\(940\) −48.6007 153.278i −0.00168636 0.00531847i
\(941\) 48627.9 1.68462 0.842309 0.538995i \(-0.181196\pi\)
0.842309 + 0.538995i \(0.181196\pi\)
\(942\) 13792.0i 0.477035i
\(943\) 27356.4i 0.944693i
\(944\) 3400.41 0.117239
\(945\) −6455.49 + 2046.88i −0.222219 + 0.0704605i
\(946\) −6030.09 −0.207246
\(947\) 34717.9i 1.19132i −0.803237 0.595659i \(-0.796891\pi\)
0.803237 0.595659i \(-0.203109\pi\)
\(948\) 3462.64i 0.118630i
\(949\) 44870.6 1.53484
\(950\) 8038.40 + 11401.4i 0.274527 + 0.389380i
\(951\) −20953.2 −0.714461
\(952\) 7447.42i 0.253542i
\(953\) 27703.8i 0.941674i −0.882220 0.470837i \(-0.843952\pi\)
0.882220 0.470837i \(-0.156048\pi\)
\(954\) −4737.52 −0.160779
\(955\) −4114.20 + 1304.52i −0.139406 + 0.0442022i
\(956\) 3288.78 0.111262
\(957\) 38082.0i 1.28633i
\(958\) 40784.4i 1.37545i
\(959\) −28921.8 −0.973862
\(960\) 648.811 + 2046.23i 0.0218128 + 0.0687934i
\(961\) 961.000 0.0322581
\(962\) 3337.30i 0.111849i
\(963\) 10005.7i 0.334816i
\(964\) −15448.5 −0.516142
\(965\) −9572.45 30189.7i −0.319324 1.00709i
\(966\) −15588.4 −0.519202
\(967\) 42653.7i 1.41846i 0.704977 + 0.709230i \(0.250957\pi\)
−0.704977 + 0.709230i \(0.749043\pi\)
\(968\) 15856.7i 0.526500i
\(969\) −6946.48 −0.230292
\(970\) 27899.6 8846.30i 0.923507 0.292822i
\(971\) −22521.7 −0.744343 −0.372172 0.928164i \(-0.621387\pi\)
−0.372172 + 0.928164i \(0.621387\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 16246.3i 0.535285i
\(974\) −17511.7 −0.576090
\(975\) −12769.8 + 9003.16i −0.419447 + 0.295725i
\(976\) 10859.0 0.356136
\(977\) 5033.46i 0.164826i 0.996598 + 0.0824128i \(0.0262626\pi\)
−0.996598 + 0.0824128i \(0.973737\pi\)
\(978\) 24335.7i 0.795676i
\(979\) −64279.7 −2.09846
\(980\) 6833.49 2166.74i 0.222743 0.0706264i
\(981\) −10800.9 −0.351525
\(982\) 19577.4i 0.636190i
\(983\) 11793.2i 0.382649i −0.981527 0.191325i \(-0.938722\pi\)
0.981527 0.191325i \(-0.0612783\pi\)
\(984\) −5669.33 −0.183670
\(985\) −321.237 1013.12i −0.0103913 0.0327723i
\(986\) 18302.7 0.591154
\(987\) 241.992i 0.00780413i
\(988\) 9299.83i 0.299461i
\(989\) 6066.18 0.195039
\(990\) 3501.11 + 11041.8i 0.112396 + 0.354477i
\(991\) 38245.7 1.22595 0.612974 0.790103i \(-0.289973\pi\)
0.612974 + 0.790103i \(0.289973\pi\)
\(992\) 992.000i 0.0317500i
\(993\) 18981.9i 0.606620i
\(994\) 17009.3 0.542757
\(995\) −4523.76 + 1434.38i −0.144134 + 0.0457013i
\(996\) −10515.5 −0.334533
\(997\) 6791.48i 0.215736i 0.994165 + 0.107868i \(0.0344023\pi\)
−0.994165 + 0.107868i \(0.965598\pi\)
\(998\) 19013.8i 0.603077i
\(999\) 1081.32 0.0342457
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 930.4.d.c.559.19 yes 20
5.4 even 2 inner 930.4.d.c.559.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.4.d.c.559.9 20 5.4 even 2 inner
930.4.d.c.559.19 yes 20 1.1 even 1 trivial