Properties

Label 405.4.e.s.271.2
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
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] = [405,4,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not 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: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.148347072.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 29x^{4} + 223x^{2} + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.2
Root \(3.41374i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.s.136.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.663404 - 1.14905i) q^{2} +(3.11979 - 5.40363i) q^{4} +(2.50000 - 4.33013i) q^{5} +(12.0521 + 20.8749i) q^{7} -18.8932 q^{8} +O(q^{10})\) \(q+(-0.663404 - 1.14905i) q^{2} +(3.11979 - 5.40363i) q^{4} +(2.50000 - 4.33013i) q^{5} +(12.0521 + 20.8749i) q^{7} -18.8932 q^{8} -6.63404 q^{10} +(4.13810 + 7.16739i) q^{11} +(-43.5573 + 75.4434i) q^{13} +(15.9909 - 27.6970i) q^{14} +(-12.4245 - 21.5198i) q^{16} -51.9166 q^{17} -88.5107 q^{19} +(-15.5989 - 27.0182i) q^{20} +(5.49046 - 9.50976i) q^{22} +(-64.6224 + 111.929i) q^{23} +(-12.5000 - 21.6506i) q^{25} +115.584 q^{26} +150.400 q^{28} +(-135.554 - 234.787i) q^{29} +(-112.273 + 194.463i) q^{31} +(-92.0577 + 159.449i) q^{32} +(34.4417 + 59.6548i) q^{34} +120.521 q^{35} -70.5268 q^{37} +(58.7184 + 101.703i) q^{38} +(-47.2330 + 81.8099i) q^{40} +(183.469 - 317.778i) q^{41} +(97.7736 + 169.349i) q^{43} +51.6399 q^{44} +171.483 q^{46} +(-179.596 - 311.069i) q^{47} +(-119.008 + 206.128i) q^{49} +(-16.5851 + 28.7262i) q^{50} +(271.779 + 470.735i) q^{52} -29.4890 q^{53} +41.3810 q^{55} +(-227.703 - 394.394i) q^{56} +(-179.855 + 311.517i) q^{58} +(-429.052 + 743.140i) q^{59} +(278.406 + 482.213i) q^{61} +297.931 q^{62} +45.4941 q^{64} +(217.786 + 377.217i) q^{65} +(20.9493 - 36.2853i) q^{67} +(-161.969 + 280.538i) q^{68} +(-79.9544 - 138.485i) q^{70} +549.163 q^{71} -185.505 q^{73} +(46.7878 + 81.0388i) q^{74} +(-276.135 + 478.279i) q^{76} +(-99.7458 + 172.765i) q^{77} +(-40.2456 - 69.7075i) q^{79} -124.245 q^{80} -486.857 q^{82} +(-288.377 - 499.483i) q^{83} +(-129.792 + 224.806i) q^{85} +(129.727 - 224.694i) q^{86} +(-78.1818 - 135.415i) q^{88} -224.516 q^{89} -2099.83 q^{91} +(403.216 + 698.391i) q^{92} +(-238.290 + 412.730i) q^{94} +(-221.277 + 383.263i) q^{95} +(277.508 + 480.658i) q^{97} +315.801 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8} - 10 q^{10} - 58 q^{11} + 47 q^{13} - 159 q^{14} + 127 q^{16} + 68 q^{17} - 10 q^{19} + 25 q^{20} - 260 q^{22} + 51 q^{23} - 75 q^{25} + 506 q^{26} + 166 q^{28} - 350 q^{29} - 638 q^{31} - 245 q^{32} + 154 q^{34} + 250 q^{35} - 828 q^{37} - 397 q^{38} - 135 q^{40} - 179 q^{41} + 836 q^{43} + 664 q^{44} + 522 q^{46} - 235 q^{47} - 892 q^{49} - 25 q^{50} + 1335 q^{52} + 1010 q^{53} - 580 q^{55} - 15 q^{56} - 1876 q^{58} - 535 q^{59} + 104 q^{61} + 696 q^{62} - 606 q^{64} - 235 q^{65} + 40 q^{67} - 830 q^{68} + 795 q^{70} + 904 q^{71} - 1420 q^{73} - 1394 q^{74} - 849 q^{76} - 2148 q^{77} + 634 q^{79} + 1270 q^{80} + 1226 q^{82} - 1734 q^{83} + 170 q^{85} - 460 q^{86} + 768 q^{88} - 1704 q^{89} - 2458 q^{91} + 1839 q^{92} - 1751 q^{94} - 25 q^{95} + 76 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.663404 1.14905i −0.234549 0.406251i 0.724593 0.689177i \(-0.242028\pi\)
−0.959141 + 0.282927i \(0.908695\pi\)
\(3\) 0 0
\(4\) 3.11979 5.40363i 0.389974 0.675454i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) 12.0521 + 20.8749i 0.650754 + 1.12714i 0.982940 + 0.183925i \(0.0588804\pi\)
−0.332186 + 0.943214i \(0.607786\pi\)
\(8\) −18.8932 −0.834969
\(9\) 0 0
\(10\) −6.63404 −0.209787
\(11\) 4.13810 + 7.16739i 0.113426 + 0.196459i 0.917149 0.398544i \(-0.130484\pi\)
−0.803724 + 0.595003i \(0.797151\pi\)
\(12\) 0 0
\(13\) −43.5573 + 75.4434i −0.929278 + 1.60956i −0.144745 + 0.989469i \(0.546236\pi\)
−0.784533 + 0.620087i \(0.787097\pi\)
\(14\) 15.9909 27.6970i 0.305267 0.528738i
\(15\) 0 0
\(16\) −12.4245 21.5198i −0.194133 0.336248i
\(17\) −51.9166 −0.740684 −0.370342 0.928895i \(-0.620760\pi\)
−0.370342 + 0.928895i \(0.620760\pi\)
\(18\) 0 0
\(19\) −88.5107 −1.06872 −0.534362 0.845256i \(-0.679448\pi\)
−0.534362 + 0.845256i \(0.679448\pi\)
\(20\) −15.5989 27.0182i −0.174402 0.302072i
\(21\) 0 0
\(22\) 5.49046 9.50976i 0.0532077 0.0921585i
\(23\) −64.6224 + 111.929i −0.585856 + 1.01473i 0.408912 + 0.912574i \(0.365908\pi\)
−0.994768 + 0.102159i \(0.967425\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 115.584 0.871844
\(27\) 0 0
\(28\) 150.400 1.01511
\(29\) −135.554 234.787i −0.867993 1.50341i −0.864044 0.503416i \(-0.832076\pi\)
−0.00394885 0.999992i \(-0.501257\pi\)
\(30\) 0 0
\(31\) −112.273 + 194.463i −0.650481 + 1.12667i 0.332526 + 0.943094i \(0.392099\pi\)
−0.983006 + 0.183571i \(0.941234\pi\)
\(32\) −92.0577 + 159.449i −0.508552 + 0.880837i
\(33\) 0 0
\(34\) 34.4417 + 59.6548i 0.173727 + 0.300903i
\(35\) 120.521 0.582052
\(36\) 0 0
\(37\) −70.5268 −0.313366 −0.156683 0.987649i \(-0.550080\pi\)
−0.156683 + 0.987649i \(0.550080\pi\)
\(38\) 58.7184 + 101.703i 0.250668 + 0.434169i
\(39\) 0 0
\(40\) −47.2330 + 81.8099i −0.186705 + 0.323382i
\(41\) 183.469 317.778i 0.698855 1.21045i −0.270009 0.962858i \(-0.587027\pi\)
0.968864 0.247594i \(-0.0796401\pi\)
\(42\) 0 0
\(43\) 97.7736 + 169.349i 0.346752 + 0.600592i 0.985670 0.168682i \(-0.0539512\pi\)
−0.638918 + 0.769274i \(0.720618\pi\)
\(44\) 51.6399 0.176932
\(45\) 0 0
\(46\) 171.483 0.549648
\(47\) −179.596 311.069i −0.557378 0.965407i −0.997714 0.0675743i \(-0.978474\pi\)
0.440336 0.897833i \(-0.354859\pi\)
\(48\) 0 0
\(49\) −119.008 + 206.128i −0.346962 + 0.600955i
\(50\) −16.5851 + 28.7262i −0.0469098 + 0.0812501i
\(51\) 0 0
\(52\) 271.779 + 470.735i 0.724788 + 1.25537i
\(53\) −29.4890 −0.0764270 −0.0382135 0.999270i \(-0.512167\pi\)
−0.0382135 + 0.999270i \(0.512167\pi\)
\(54\) 0 0
\(55\) 41.3810 0.101451
\(56\) −227.703 394.394i −0.543360 0.941126i
\(57\) 0 0
\(58\) −179.855 + 311.517i −0.407174 + 0.705245i
\(59\) −429.052 + 743.140i −0.946743 + 1.63981i −0.194519 + 0.980899i \(0.562315\pi\)
−0.752224 + 0.658908i \(0.771019\pi\)
\(60\) 0 0
\(61\) 278.406 + 482.213i 0.584364 + 1.01215i 0.994954 + 0.100328i \(0.0319892\pi\)
−0.410591 + 0.911820i \(0.634677\pi\)
\(62\) 297.931 0.610278
\(63\) 0 0
\(64\) 45.4941 0.0888557
\(65\) 217.786 + 377.217i 0.415586 + 0.719815i
\(66\) 0 0
\(67\) 20.9493 36.2853i 0.0381995 0.0661635i −0.846294 0.532717i \(-0.821171\pi\)
0.884493 + 0.466553i \(0.154504\pi\)
\(68\) −161.969 + 280.538i −0.288847 + 0.500298i
\(69\) 0 0
\(70\) −79.9544 138.485i −0.136520 0.236459i
\(71\) 549.163 0.917939 0.458970 0.888452i \(-0.348219\pi\)
0.458970 + 0.888452i \(0.348219\pi\)
\(72\) 0 0
\(73\) −185.505 −0.297420 −0.148710 0.988881i \(-0.547512\pi\)
−0.148710 + 0.988881i \(0.547512\pi\)
\(74\) 46.7878 + 81.0388i 0.0734996 + 0.127305i
\(75\) 0 0
\(76\) −276.135 + 478.279i −0.416774 + 0.721874i
\(77\) −99.7458 + 172.765i −0.147624 + 0.255693i
\(78\) 0 0
\(79\) −40.2456 69.7075i −0.0573163 0.0992748i 0.835944 0.548815i \(-0.184921\pi\)
−0.893260 + 0.449541i \(0.851588\pi\)
\(80\) −124.245 −0.173637
\(81\) 0 0
\(82\) −486.857 −0.655663
\(83\) −288.377 499.483i −0.381367 0.660547i 0.609891 0.792485i \(-0.291213\pi\)
−0.991258 + 0.131939i \(0.957880\pi\)
\(84\) 0 0
\(85\) −129.792 + 224.806i −0.165622 + 0.286866i
\(86\) 129.727 224.694i 0.162661 0.281736i
\(87\) 0 0
\(88\) −78.1818 135.415i −0.0947070 0.164037i
\(89\) −224.516 −0.267401 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(90\) 0 0
\(91\) −2099.83 −2.41893
\(92\) 403.216 + 698.391i 0.456937 + 0.791438i
\(93\) 0 0
\(94\) −238.290 + 412.730i −0.261465 + 0.452870i
\(95\) −221.277 + 383.263i −0.238974 + 0.413915i
\(96\) 0 0
\(97\) 277.508 + 480.658i 0.290481 + 0.503128i 0.973924 0.226876i \(-0.0728513\pi\)
−0.683442 + 0.730005i \(0.739518\pi\)
\(98\) 315.801 0.325518
\(99\) 0 0
\(100\) −155.989 −0.155989
\(101\) 113.500 + 196.587i 0.111818 + 0.193675i 0.916503 0.400027i \(-0.130999\pi\)
−0.804685 + 0.593702i \(0.797666\pi\)
\(102\) 0 0
\(103\) −191.762 + 332.142i −0.183446 + 0.317737i −0.943052 0.332646i \(-0.892058\pi\)
0.759606 + 0.650383i \(0.225392\pi\)
\(104\) 822.936 1425.37i 0.775918 1.34393i
\(105\) 0 0
\(106\) 19.5632 + 33.8844i 0.0179259 + 0.0310485i
\(107\) 1775.32 1.60399 0.801993 0.597334i \(-0.203773\pi\)
0.801993 + 0.597334i \(0.203773\pi\)
\(108\) 0 0
\(109\) 1530.50 1.34491 0.672454 0.740139i \(-0.265240\pi\)
0.672454 + 0.740139i \(0.265240\pi\)
\(110\) −27.4523 47.5488i −0.0237952 0.0412145i
\(111\) 0 0
\(112\) 299.483 518.720i 0.252665 0.437629i
\(113\) −420.391 + 728.138i −0.349974 + 0.606173i −0.986244 0.165293i \(-0.947143\pi\)
0.636271 + 0.771466i \(0.280476\pi\)
\(114\) 0 0
\(115\) 323.112 + 559.646i 0.262003 + 0.453802i
\(116\) −1691.60 −1.35398
\(117\) 0 0
\(118\) 1138.54 0.888230
\(119\) −625.706 1083.75i −0.482003 0.834854i
\(120\) 0 0
\(121\) 631.252 1093.36i 0.474269 0.821458i
\(122\) 369.391 639.804i 0.274124 0.474796i
\(123\) 0 0
\(124\) 700.539 + 1213.37i 0.507341 + 0.878740i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1038.45 0.725572 0.362786 0.931873i \(-0.381826\pi\)
0.362786 + 0.931873i \(0.381826\pi\)
\(128\) 706.281 + 1223.31i 0.487711 + 0.844740i
\(129\) 0 0
\(130\) 288.961 500.495i 0.194950 0.337664i
\(131\) −401.705 + 695.774i −0.267917 + 0.464046i −0.968324 0.249698i \(-0.919669\pi\)
0.700407 + 0.713744i \(0.253002\pi\)
\(132\) 0 0
\(133\) −1066.74 1847.65i −0.695476 1.20460i
\(134\) −55.5915 −0.0358386
\(135\) 0 0
\(136\) 980.871 0.618449
\(137\) 434.576 + 752.707i 0.271010 + 0.469402i 0.969121 0.246587i \(-0.0793091\pi\)
−0.698111 + 0.715990i \(0.745976\pi\)
\(138\) 0 0
\(139\) 98.1990 170.086i 0.0599218 0.103788i −0.834508 0.550995i \(-0.814248\pi\)
0.894430 + 0.447208i \(0.147582\pi\)
\(140\) 376.001 651.253i 0.226985 0.393150i
\(141\) 0 0
\(142\) −364.317 631.016i −0.215302 0.372913i
\(143\) −720.976 −0.421616
\(144\) 0 0
\(145\) −1355.54 −0.776357
\(146\) 123.065 + 213.154i 0.0697596 + 0.120827i
\(147\) 0 0
\(148\) −220.029 + 381.101i −0.122204 + 0.211664i
\(149\) 377.142 653.228i 0.207360 0.359158i −0.743522 0.668711i \(-0.766846\pi\)
0.950882 + 0.309553i \(0.100180\pi\)
\(150\) 0 0
\(151\) −1028.82 1781.96i −0.554464 0.960359i −0.997945 0.0640756i \(-0.979590\pi\)
0.443481 0.896284i \(-0.353743\pi\)
\(152\) 1672.25 0.892351
\(153\) 0 0
\(154\) 264.687 0.138501
\(155\) 561.367 + 972.316i 0.290904 + 0.503860i
\(156\) 0 0
\(157\) 1679.29 2908.62i 0.853644 1.47855i −0.0242531 0.999706i \(-0.507721\pi\)
0.877897 0.478849i \(-0.158946\pi\)
\(158\) −53.3983 + 92.4885i −0.0268869 + 0.0465696i
\(159\) 0 0
\(160\) 460.289 + 797.243i 0.227431 + 0.393922i
\(161\) −3115.35 −1.52499
\(162\) 0 0
\(163\) −710.376 −0.341356 −0.170678 0.985327i \(-0.554596\pi\)
−0.170678 + 0.985327i \(0.554596\pi\)
\(164\) −1144.77 1982.80i −0.545070 0.944089i
\(165\) 0 0
\(166\) −382.621 + 662.718i −0.178898 + 0.309861i
\(167\) −574.134 + 994.430i −0.266035 + 0.460786i −0.967834 0.251589i \(-0.919047\pi\)
0.701799 + 0.712375i \(0.252380\pi\)
\(168\) 0 0
\(169\) −2695.97 4669.56i −1.22711 2.12542i
\(170\) 344.417 0.155386
\(171\) 0 0
\(172\) 1220.13 0.540897
\(173\) −1462.64 2533.37i −0.642790 1.11335i −0.984807 0.173652i \(-0.944443\pi\)
0.342017 0.939694i \(-0.388890\pi\)
\(174\) 0 0
\(175\) 301.303 521.873i 0.130151 0.225428i
\(176\) 102.827 178.102i 0.0440393 0.0762782i
\(177\) 0 0
\(178\) 148.945 + 257.980i 0.0627185 + 0.108632i
\(179\) −3422.02 −1.42890 −0.714452 0.699685i \(-0.753324\pi\)
−0.714452 + 0.699685i \(0.753324\pi\)
\(180\) 0 0
\(181\) −1151.58 −0.472907 −0.236454 0.971643i \(-0.575985\pi\)
−0.236454 + 0.971643i \(0.575985\pi\)
\(182\) 1393.04 + 2412.81i 0.567356 + 0.982690i
\(183\) 0 0
\(184\) 1220.92 2114.70i 0.489172 0.847271i
\(185\) −176.317 + 305.390i −0.0700707 + 0.121366i
\(186\) 0 0
\(187\) −214.836 372.107i −0.0840126 0.145514i
\(188\) −2241.21 −0.869451
\(189\) 0 0
\(190\) 587.184 0.224204
\(191\) 466.060 + 807.240i 0.176560 + 0.305811i 0.940700 0.339240i \(-0.110170\pi\)
−0.764140 + 0.645050i \(0.776836\pi\)
\(192\) 0 0
\(193\) 2136.41 3700.36i 0.796797 1.38009i −0.124894 0.992170i \(-0.539859\pi\)
0.921692 0.387923i \(-0.126807\pi\)
\(194\) 368.200 637.742i 0.136264 0.236016i
\(195\) 0 0
\(196\) 742.559 + 1286.15i 0.270612 + 0.468713i
\(197\) 1924.15 0.695888 0.347944 0.937515i \(-0.386880\pi\)
0.347944 + 0.937515i \(0.386880\pi\)
\(198\) 0 0
\(199\) 1738.84 0.619414 0.309707 0.950832i \(-0.399769\pi\)
0.309707 + 0.950832i \(0.399769\pi\)
\(200\) 236.165 + 409.050i 0.0834969 + 0.144621i
\(201\) 0 0
\(202\) 150.593 260.834i 0.0524537 0.0908525i
\(203\) 3267.44 5659.37i 1.12970 1.95670i
\(204\) 0 0
\(205\) −917.345 1588.89i −0.312537 0.541331i
\(206\) 508.864 0.172108
\(207\) 0 0
\(208\) 2164.71 0.721613
\(209\) −366.266 634.391i −0.121221 0.209960i
\(210\) 0 0
\(211\) −1601.17 + 2773.32i −0.522414 + 0.904848i 0.477246 + 0.878770i \(0.341635\pi\)
−0.999660 + 0.0260782i \(0.991698\pi\)
\(212\) −91.9996 + 159.348i −0.0298045 + 0.0516229i
\(213\) 0 0
\(214\) −1177.75 2039.93i −0.376213 0.651620i
\(215\) 977.736 0.310144
\(216\) 0 0
\(217\) −5412.54 −1.69321
\(218\) −1015.34 1758.62i −0.315447 0.546370i
\(219\) 0 0
\(220\) 129.100 223.608i 0.0395632 0.0685255i
\(221\) 2261.35 3916.77i 0.688301 1.19217i
\(222\) 0 0
\(223\) 702.494 + 1216.76i 0.210953 + 0.365381i 0.952013 0.306058i \(-0.0990100\pi\)
−0.741060 + 0.671439i \(0.765677\pi\)
\(224\) −4437.97 −1.32377
\(225\) 0 0
\(226\) 1115.56 0.328344
\(227\) 3119.17 + 5402.57i 0.912012 + 1.57965i 0.811218 + 0.584744i \(0.198805\pi\)
0.100794 + 0.994907i \(0.467862\pi\)
\(228\) 0 0
\(229\) −3315.15 + 5742.01i −0.956644 + 1.65696i −0.226084 + 0.974108i \(0.572592\pi\)
−0.730560 + 0.682848i \(0.760741\pi\)
\(230\) 428.708 742.543i 0.122905 0.212878i
\(231\) 0 0
\(232\) 2561.05 + 4435.88i 0.724747 + 1.25530i
\(233\) −2453.48 −0.689840 −0.344920 0.938632i \(-0.612094\pi\)
−0.344920 + 0.938632i \(0.612094\pi\)
\(234\) 0 0
\(235\) −1795.96 −0.498534
\(236\) 2677.10 + 4636.88i 0.738410 + 1.27896i
\(237\) 0 0
\(238\) −830.192 + 1437.94i −0.226107 + 0.391628i
\(239\) −3474.87 + 6018.65i −0.940463 + 1.62893i −0.175873 + 0.984413i \(0.556275\pi\)
−0.764590 + 0.644517i \(0.777058\pi\)
\(240\) 0 0
\(241\) −3167.60 5486.44i −0.846651 1.46644i −0.884180 0.467146i \(-0.845282\pi\)
0.0375294 0.999296i \(-0.488051\pi\)
\(242\) −1675.10 −0.444957
\(243\) 0 0
\(244\) 3474.27 0.911546
\(245\) 595.039 + 1030.64i 0.155166 + 0.268755i
\(246\) 0 0
\(247\) 3855.28 6677.55i 0.993141 1.72017i
\(248\) 2121.20 3674.03i 0.543131 0.940731i
\(249\) 0 0
\(250\) 82.9255 + 143.631i 0.0209787 + 0.0363362i
\(251\) 4022.65 1.01158 0.505792 0.862656i \(-0.331200\pi\)
0.505792 + 0.862656i \(0.331200\pi\)
\(252\) 0 0
\(253\) −1069.65 −0.265805
\(254\) −688.913 1193.23i −0.170182 0.294764i
\(255\) 0 0
\(256\) 1119.08 1938.30i 0.273212 0.473217i
\(257\) −2498.87 + 4328.17i −0.606519 + 1.05052i 0.385291 + 0.922795i \(0.374101\pi\)
−0.991809 + 0.127726i \(0.959232\pi\)
\(258\) 0 0
\(259\) −849.998 1472.24i −0.203924 0.353207i
\(260\) 2717.79 0.648270
\(261\) 0 0
\(262\) 1065.97 0.251359
\(263\) −1996.24 3457.58i −0.468035 0.810660i 0.531298 0.847185i \(-0.321704\pi\)
−0.999333 + 0.0365251i \(0.988371\pi\)
\(264\) 0 0
\(265\) −73.7226 + 127.691i −0.0170896 + 0.0296000i
\(266\) −1415.36 + 2451.48i −0.326246 + 0.565075i
\(267\) 0 0
\(268\) −130.715 226.405i −0.0297936 0.0516041i
\(269\) 2188.89 0.496131 0.248065 0.968743i \(-0.420205\pi\)
0.248065 + 0.968743i \(0.420205\pi\)
\(270\) 0 0
\(271\) 4280.26 0.959437 0.479718 0.877423i \(-0.340739\pi\)
0.479718 + 0.877423i \(0.340739\pi\)
\(272\) 645.038 + 1117.24i 0.143791 + 0.249053i
\(273\) 0 0
\(274\) 576.599 998.699i 0.127130 0.220196i
\(275\) 103.452 179.185i 0.0226851 0.0392918i
\(276\) 0 0
\(277\) 1939.98 + 3360.15i 0.420803 + 0.728852i 0.996018 0.0891502i \(-0.0284151\pi\)
−0.575215 + 0.818002i \(0.695082\pi\)
\(278\) −260.583 −0.0562184
\(279\) 0 0
\(280\) −2277.03 −0.485996
\(281\) −3198.72 5540.34i −0.679072 1.17619i −0.975261 0.221058i \(-0.929049\pi\)
0.296188 0.955130i \(-0.404284\pi\)
\(282\) 0 0
\(283\) 171.435 296.933i 0.0360096 0.0623705i −0.847459 0.530861i \(-0.821869\pi\)
0.883469 + 0.468490i \(0.155202\pi\)
\(284\) 1713.27 2967.48i 0.357972 0.620026i
\(285\) 0 0
\(286\) 478.299 + 828.438i 0.0988895 + 0.171282i
\(287\) 8844.78 1.81913
\(288\) 0 0
\(289\) −2217.66 −0.451387
\(290\) 899.273 + 1557.59i 0.182094 + 0.315395i
\(291\) 0 0
\(292\) −578.735 + 1002.40i −0.115986 + 0.200894i
\(293\) −3666.71 + 6350.94i −0.731098 + 1.26630i 0.225316 + 0.974286i \(0.427659\pi\)
−0.956414 + 0.292013i \(0.905675\pi\)
\(294\) 0 0
\(295\) 2145.26 + 3715.70i 0.423396 + 0.733344i
\(296\) 1332.48 0.261651
\(297\) 0 0
\(298\) −1000.79 −0.194544
\(299\) −5629.55 9750.66i −1.08885 1.88594i
\(300\) 0 0
\(301\) −2356.76 + 4082.03i −0.451300 + 0.781675i
\(302\) −1365.04 + 2364.33i −0.260098 + 0.450502i
\(303\) 0 0
\(304\) 1099.70 + 1904.74i 0.207474 + 0.359356i
\(305\) 2784.06 0.522671
\(306\) 0 0
\(307\) −7965.33 −1.48080 −0.740399 0.672167i \(-0.765364\pi\)
−0.740399 + 0.672167i \(0.765364\pi\)
\(308\) 622.372 + 1077.98i 0.115139 + 0.199427i
\(309\) 0 0
\(310\) 744.827 1290.08i 0.136462 0.236360i
\(311\) −1093.10 + 1893.30i −0.199305 + 0.345206i −0.948303 0.317366i \(-0.897202\pi\)
0.748998 + 0.662572i \(0.230535\pi\)
\(312\) 0 0
\(313\) −19.3152 33.4549i −0.00348805 0.00604147i 0.864276 0.503018i \(-0.167777\pi\)
−0.867764 + 0.496976i \(0.834444\pi\)
\(314\) −4456.20 −0.800885
\(315\) 0 0
\(316\) −502.232 −0.0894074
\(317\) 4767.91 + 8258.25i 0.844770 + 1.46319i 0.885820 + 0.464028i \(0.153596\pi\)
−0.0410499 + 0.999157i \(0.513070\pi\)
\(318\) 0 0
\(319\) 1121.87 1943.14i 0.196905 0.341050i
\(320\) 113.735 196.995i 0.0198687 0.0344137i
\(321\) 0 0
\(322\) 2066.74 + 3579.69i 0.357686 + 0.619530i
\(323\) 4595.18 0.791587
\(324\) 0 0
\(325\) 2177.86 0.371711
\(326\) 471.267 + 816.258i 0.0800645 + 0.138676i
\(327\) 0 0
\(328\) −3466.32 + 6003.84i −0.583522 + 1.01069i
\(329\) 4329.03 7498.10i 0.725432 1.25649i
\(330\) 0 0
\(331\) 1505.29 + 2607.24i 0.249964 + 0.432951i 0.963516 0.267652i \(-0.0862477\pi\)
−0.713551 + 0.700603i \(0.752914\pi\)
\(332\) −3598.70 −0.594892
\(333\) 0 0
\(334\) 1523.53 0.249593
\(335\) −104.747 181.427i −0.0170833 0.0295892i
\(336\) 0 0
\(337\) −1406.36 + 2435.89i −0.227327 + 0.393742i −0.957015 0.290038i \(-0.906332\pi\)
0.729688 + 0.683780i \(0.239665\pi\)
\(338\) −3577.04 + 6195.61i −0.575637 + 0.997032i
\(339\) 0 0
\(340\) 809.845 + 1402.69i 0.129176 + 0.223740i
\(341\) −1858.39 −0.295125
\(342\) 0 0
\(343\) 2530.57 0.398361
\(344\) −1847.26 3199.54i −0.289527 0.501476i
\(345\) 0 0
\(346\) −1940.65 + 3361.30i −0.301531 + 0.522268i
\(347\) −69.6769 + 120.684i −0.0107794 + 0.0186705i −0.871365 0.490636i \(-0.836765\pi\)
0.860585 + 0.509306i \(0.170098\pi\)
\(348\) 0 0
\(349\) 2605.14 + 4512.24i 0.399571 + 0.692077i 0.993673 0.112313i \(-0.0358259\pi\)
−0.594102 + 0.804390i \(0.702493\pi\)
\(350\) −799.544 −0.122107
\(351\) 0 0
\(352\) −1523.77 −0.230731
\(353\) −1705.23 2953.55i −0.257112 0.445330i 0.708355 0.705856i \(-0.249437\pi\)
−0.965467 + 0.260526i \(0.916104\pi\)
\(354\) 0 0
\(355\) 1372.91 2377.95i 0.205257 0.355516i
\(356\) −700.443 + 1213.20i −0.104279 + 0.180617i
\(357\) 0 0
\(358\) 2270.18 + 3932.07i 0.335148 + 0.580493i
\(359\) −8131.85 −1.19549 −0.597747 0.801685i \(-0.703937\pi\)
−0.597747 + 0.801685i \(0.703937\pi\)
\(360\) 0 0
\(361\) 975.143 0.142170
\(362\) 763.963 + 1323.22i 0.110920 + 0.192119i
\(363\) 0 0
\(364\) −6551.03 + 11346.7i −0.943317 + 1.63387i
\(365\) −463.762 + 803.259i −0.0665052 + 0.115190i
\(366\) 0 0
\(367\) −66.0757 114.447i −0.00939816 0.0162781i 0.861288 0.508117i \(-0.169658\pi\)
−0.870686 + 0.491839i \(0.836325\pi\)
\(368\) 3211.60 0.454935
\(369\) 0 0
\(370\) 467.878 0.0657400
\(371\) −355.406 615.581i −0.0497352 0.0861438i
\(372\) 0 0
\(373\) −4674.44 + 8096.37i −0.648883 + 1.12390i 0.334507 + 0.942393i \(0.391430\pi\)
−0.983390 + 0.181505i \(0.941903\pi\)
\(374\) −285.046 + 493.715i −0.0394101 + 0.0682603i
\(375\) 0 0
\(376\) 3393.14 + 5877.10i 0.465394 + 0.806085i
\(377\) 23617.5 3.22643
\(378\) 0 0
\(379\) 6164.17 0.835441 0.417720 0.908576i \(-0.362829\pi\)
0.417720 + 0.908576i \(0.362829\pi\)
\(380\) 1380.67 + 2391.40i 0.186387 + 0.322832i
\(381\) 0 0
\(382\) 618.373 1071.05i 0.0828238 0.143455i
\(383\) −1300.64 + 2252.77i −0.173523 + 0.300551i −0.939649 0.342139i \(-0.888849\pi\)
0.766126 + 0.642690i \(0.222182\pi\)
\(384\) 0 0
\(385\) 498.729 + 863.824i 0.0660197 + 0.114349i
\(386\) −5669.20 −0.747552
\(387\) 0 0
\(388\) 3463.07 0.453120
\(389\) −2125.29 3681.10i −0.277008 0.479793i 0.693631 0.720330i \(-0.256010\pi\)
−0.970640 + 0.240537i \(0.922676\pi\)
\(390\) 0 0
\(391\) 3354.98 5810.99i 0.433935 0.751597i
\(392\) 2248.44 3894.41i 0.289702 0.501779i
\(393\) 0 0
\(394\) −1276.49 2210.94i −0.163220 0.282705i
\(395\) −402.456 −0.0512653
\(396\) 0 0
\(397\) −6088.35 −0.769687 −0.384843 0.922982i \(-0.625745\pi\)
−0.384843 + 0.922982i \(0.625745\pi\)
\(398\) −1153.56 1998.02i −0.145283 0.251637i
\(399\) 0 0
\(400\) −310.612 + 537.996i −0.0388265 + 0.0672495i
\(401\) −3862.90 + 6690.73i −0.481057 + 0.833215i −0.999764 0.0217370i \(-0.993080\pi\)
0.518707 + 0.854952i \(0.326414\pi\)
\(402\) 0 0
\(403\) −9780.64 16940.6i −1.20895 2.09397i
\(404\) 1416.38 0.174425
\(405\) 0 0
\(406\) −8670.53 −1.05988
\(407\) −291.847 505.493i −0.0355437 0.0615635i
\(408\) 0 0
\(409\) −8160.57 + 14134.5i −0.986588 + 1.70882i −0.351930 + 0.936026i \(0.614475\pi\)
−0.634657 + 0.772794i \(0.718859\pi\)
\(410\) −1217.14 + 2108.15i −0.146611 + 0.253937i
\(411\) 0 0
\(412\) 1196.52 + 2072.43i 0.143078 + 0.247818i
\(413\) −20684.0 −2.46439
\(414\) 0 0
\(415\) −2883.77 −0.341105
\(416\) −8019.56 13890.3i −0.945172 1.63709i
\(417\) 0 0
\(418\) −485.964 + 841.715i −0.0568644 + 0.0984920i
\(419\) −576.228 + 998.055i −0.0671851 + 0.116368i −0.897661 0.440686i \(-0.854735\pi\)
0.830476 + 0.557054i \(0.188068\pi\)
\(420\) 0 0
\(421\) 1765.61 + 3058.13i 0.204396 + 0.354024i 0.949940 0.312432i \(-0.101144\pi\)
−0.745544 + 0.666456i \(0.767810\pi\)
\(422\) 4248.91 0.490127
\(423\) 0 0
\(424\) 557.142 0.0638142
\(425\) 648.958 + 1124.03i 0.0740684 + 0.128290i
\(426\) 0 0
\(427\) −6710.76 + 11623.4i −0.760554 + 1.31732i
\(428\) 5538.62 9593.17i 0.625512 1.08342i
\(429\) 0 0
\(430\) −648.634 1123.47i −0.0727440 0.125996i
\(431\) 10230.6 1.14337 0.571683 0.820475i \(-0.306291\pi\)
0.571683 + 0.820475i \(0.306291\pi\)
\(432\) 0 0
\(433\) −7311.31 −0.811453 −0.405726 0.913995i \(-0.632981\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(434\) 3590.70 + 6219.27i 0.397141 + 0.687868i
\(435\) 0 0
\(436\) 4774.83 8270.24i 0.524479 0.908424i
\(437\) 5719.77 9906.94i 0.626119 1.08447i
\(438\) 0 0
\(439\) −3526.59 6108.23i −0.383405 0.664077i 0.608141 0.793829i \(-0.291915\pi\)
−0.991547 + 0.129751i \(0.958582\pi\)
\(440\) −781.818 −0.0847085
\(441\) 0 0
\(442\) −6000.75 −0.645761
\(443\) 83.8952 + 145.311i 0.00899770 + 0.0155845i 0.870489 0.492188i \(-0.163803\pi\)
−0.861491 + 0.507772i \(0.830469\pi\)
\(444\) 0 0
\(445\) −561.290 + 972.183i −0.0597926 + 0.103564i
\(446\) 932.076 1614.40i 0.0989575 0.171399i
\(447\) 0 0
\(448\) 548.301 + 949.685i 0.0578232 + 0.100153i
\(449\) 3949.94 0.415165 0.207582 0.978218i \(-0.433440\pi\)
0.207582 + 0.978218i \(0.433440\pi\)
\(450\) 0 0
\(451\) 3036.85 0.317072
\(452\) 2623.06 + 4543.28i 0.272961 + 0.472783i
\(453\) 0 0
\(454\) 4138.55 7168.17i 0.427823 0.741011i
\(455\) −5249.58 + 9092.54i −0.540888 + 0.936846i
\(456\) 0 0
\(457\) 3723.80 + 6449.81i 0.381164 + 0.660195i 0.991229 0.132156i \(-0.0421900\pi\)
−0.610065 + 0.792351i \(0.708857\pi\)
\(458\) 8797.15 0.897519
\(459\) 0 0
\(460\) 4032.16 0.408697
\(461\) −5443.82 9428.98i −0.549987 0.952606i −0.998275 0.0587164i \(-0.981299\pi\)
0.448287 0.893889i \(-0.352034\pi\)
\(462\) 0 0
\(463\) 1585.63 2746.40i 0.159159 0.275672i −0.775407 0.631462i \(-0.782455\pi\)
0.934566 + 0.355791i \(0.115788\pi\)
\(464\) −3368.39 + 5834.21i −0.337012 + 0.583721i
\(465\) 0 0
\(466\) 1627.65 + 2819.17i 0.161801 + 0.280248i
\(467\) −16348.5 −1.61996 −0.809978 0.586461i \(-0.800521\pi\)
−0.809978 + 0.586461i \(0.800521\pi\)
\(468\) 0 0
\(469\) 1009.94 0.0994340
\(470\) 1191.45 + 2063.65i 0.116931 + 0.202530i
\(471\) 0 0
\(472\) 8106.17 14040.3i 0.790501 1.36919i
\(473\) −809.193 + 1401.56i −0.0786612 + 0.136245i
\(474\) 0 0
\(475\) 1106.38 + 1916.31i 0.106872 + 0.185108i
\(476\) −7808.29 −0.751874
\(477\) 0 0
\(478\) 9220.98 0.882338
\(479\) −4706.84 8152.49i −0.448980 0.777655i 0.549340 0.835599i \(-0.314879\pi\)
−0.998320 + 0.0579433i \(0.981546\pi\)
\(480\) 0 0
\(481\) 3071.95 5320.78i 0.291204 0.504380i
\(482\) −4202.79 + 7279.45i −0.397162 + 0.687905i
\(483\) 0 0
\(484\) −3938.75 6822.11i −0.369905 0.640694i
\(485\) 2775.08 0.259814
\(486\) 0 0
\(487\) 13482.3 1.25450 0.627250 0.778818i \(-0.284180\pi\)
0.627250 + 0.778818i \(0.284180\pi\)
\(488\) −5259.97 9110.54i −0.487926 0.845112i
\(489\) 0 0
\(490\) 789.503 1367.46i 0.0727880 0.126073i
\(491\) 4609.87 7984.53i 0.423708 0.733883i −0.572591 0.819841i \(-0.694062\pi\)
0.996299 + 0.0859577i \(0.0273950\pi\)
\(492\) 0 0
\(493\) 7037.52 + 12189.3i 0.642909 + 1.11355i
\(494\) −10230.4 −0.931760
\(495\) 0 0
\(496\) 5579.76 0.505118
\(497\) 6618.59 + 11463.7i 0.597353 + 1.03465i
\(498\) 0 0
\(499\) −52.1731 + 90.3665i −0.00468054 + 0.00810693i −0.868356 0.495941i \(-0.834823\pi\)
0.863676 + 0.504048i \(0.168157\pi\)
\(500\) −389.974 + 675.454i −0.0348803 + 0.0604145i
\(501\) 0 0
\(502\) −2668.64 4622.23i −0.237266 0.410956i
\(503\) 490.652 0.0434933 0.0217466 0.999764i \(-0.493077\pi\)
0.0217466 + 0.999764i \(0.493077\pi\)
\(504\) 0 0
\(505\) 1135.00 0.100013
\(506\) 709.613 + 1229.09i 0.0623442 + 0.107983i
\(507\) 0 0
\(508\) 3239.75 5611.41i 0.282954 0.490090i
\(509\) 1706.40 2955.58i 0.148595 0.257375i −0.782113 0.623136i \(-0.785858\pi\)
0.930709 + 0.365762i \(0.119192\pi\)
\(510\) 0 0
\(511\) −2235.73 3872.39i −0.193547 0.335234i
\(512\) 8330.89 0.719095
\(513\) 0 0
\(514\) 6631.05 0.569033
\(515\) 958.811 + 1660.71i 0.0820393 + 0.142096i
\(516\) 0 0
\(517\) 1486.37 2574.47i 0.126442 0.219004i
\(518\) −1127.79 + 1953.38i −0.0956603 + 0.165688i
\(519\) 0 0
\(520\) −4114.68 7126.83i −0.347001 0.601024i
\(521\) −3486.31 −0.293163 −0.146582 0.989199i \(-0.546827\pi\)
−0.146582 + 0.989199i \(0.546827\pi\)
\(522\) 0 0
\(523\) 14465.6 1.20943 0.604717 0.796440i \(-0.293286\pi\)
0.604717 + 0.796440i \(0.293286\pi\)
\(524\) 2506.47 + 4341.34i 0.208961 + 0.361932i
\(525\) 0 0
\(526\) −2648.62 + 4587.55i −0.219554 + 0.380279i
\(527\) 5828.86 10095.9i 0.481801 0.834503i
\(528\) 0 0
\(529\) −2268.60 3929.34i −0.186456 0.322950i
\(530\) 195.632 0.0160334
\(531\) 0 0
\(532\) −13312.1 −1.08487
\(533\) 15982.8 + 27683.1i 1.29886 + 2.24969i
\(534\) 0 0
\(535\) 4438.29 7687.35i 0.358662 0.621221i
\(536\) −395.800 + 685.545i −0.0318954 + 0.0552445i
\(537\) 0 0
\(538\) −1452.12 2515.15i −0.116367 0.201553i
\(539\) −1969.86 −0.157417
\(540\) 0 0
\(541\) 6602.78 0.524724 0.262362 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(542\) −2839.54 4918.23i −0.225035 0.389772i
\(543\) 0 0
\(544\) 4779.33 8278.03i 0.376676 0.652422i
\(545\) 3826.24 6627.24i 0.300731 0.520881i
\(546\) 0 0
\(547\) −3179.28 5506.67i −0.248512 0.430436i 0.714601 0.699532i \(-0.246608\pi\)
−0.963113 + 0.269096i \(0.913275\pi\)
\(548\) 5423.14 0.422746
\(549\) 0 0
\(550\) −274.523 −0.0212831
\(551\) 11998.0 + 20781.2i 0.927645 + 1.60673i
\(552\) 0 0
\(553\) 970.092 1680.25i 0.0745976 0.129207i
\(554\) 2573.99 4458.28i 0.197398 0.341903i
\(555\) 0 0
\(556\) −612.720 1061.26i −0.0467359 0.0809489i
\(557\) −20782.3 −1.58092 −0.790461 0.612513i \(-0.790159\pi\)
−0.790461 + 0.612513i \(0.790159\pi\)
\(558\) 0 0
\(559\) −17035.0 −1.28892
\(560\) −1497.42 2593.60i −0.112995 0.195714i
\(561\) 0 0
\(562\) −4244.08 + 7350.97i −0.318551 + 0.551747i
\(563\) −8234.98 + 14263.4i −0.616453 + 1.06773i 0.373675 + 0.927560i \(0.378098\pi\)
−0.990128 + 0.140168i \(0.955236\pi\)
\(564\) 0 0
\(565\) 2101.95 + 3640.69i 0.156513 + 0.271089i
\(566\) −454.922 −0.0337841
\(567\) 0 0
\(568\) −10375.4 −0.766451
\(569\) −2712.69 4698.52i −0.199863 0.346173i 0.748621 0.662998i \(-0.230716\pi\)
−0.948484 + 0.316825i \(0.897383\pi\)
\(570\) 0 0
\(571\) 7344.86 12721.7i 0.538306 0.932374i −0.460689 0.887561i \(-0.652398\pi\)
0.998995 0.0448121i \(-0.0142689\pi\)
\(572\) −2249.29 + 3895.89i −0.164419 + 0.284782i
\(573\) 0 0
\(574\) −5867.66 10163.1i −0.426675 0.739023i
\(575\) 3231.12 0.234343
\(576\) 0 0
\(577\) −17933.1 −1.29387 −0.646935 0.762545i \(-0.723949\pi\)
−0.646935 + 0.762545i \(0.723949\pi\)
\(578\) 1471.21 + 2548.21i 0.105872 + 0.183376i
\(579\) 0 0
\(580\) −4229.01 + 7324.86i −0.302759 + 0.524393i
\(581\) 6951.11 12039.7i 0.496352 0.859707i
\(582\) 0 0
\(583\) −122.028 211.359i −0.00866878 0.0150148i
\(584\) 3504.78 0.248337
\(585\) 0 0
\(586\) 9730.06 0.685913
\(587\) −2400.58 4157.92i −0.168795 0.292361i 0.769202 0.639006i \(-0.220654\pi\)
−0.937996 + 0.346645i \(0.887321\pi\)
\(588\) 0 0
\(589\) 9937.40 17212.1i 0.695184 1.20409i
\(590\) 2846.35 4930.02i 0.198614 0.344010i
\(591\) 0 0
\(592\) 876.259 + 1517.73i 0.0608345 + 0.105368i
\(593\) −16803.8 −1.16366 −0.581830 0.813311i \(-0.697663\pi\)
−0.581830 + 0.813311i \(0.697663\pi\)
\(594\) 0 0
\(595\) −6257.06 −0.431117
\(596\) −2353.20 4075.87i −0.161730 0.280124i
\(597\) 0 0
\(598\) −7469.33 + 12937.3i −0.510775 + 0.884689i
\(599\) 8610.08 14913.1i 0.587310 1.01725i −0.407274 0.913306i \(-0.633520\pi\)
0.994583 0.103944i \(-0.0331462\pi\)
\(600\) 0 0
\(601\) −10768.3 18651.3i −0.730865 1.26590i −0.956514 0.291687i \(-0.905784\pi\)
0.225649 0.974209i \(-0.427550\pi\)
\(602\) 6253.94 0.423408
\(603\) 0 0
\(604\) −12838.8 −0.864905
\(605\) −3156.26 5466.81i −0.212100 0.367367i
\(606\) 0 0
\(607\) 12025.5 20828.7i 0.804117 1.39277i −0.112769 0.993621i \(-0.535972\pi\)
0.916886 0.399150i \(-0.130695\pi\)
\(608\) 8148.09 14112.9i 0.543501 0.941372i
\(609\) 0 0
\(610\) −1846.96 3199.02i −0.122592 0.212335i
\(611\) 31290.8 2.07184
\(612\) 0 0
\(613\) −3554.49 −0.234200 −0.117100 0.993120i \(-0.537360\pi\)
−0.117100 + 0.993120i \(0.537360\pi\)
\(614\) 5284.23 + 9152.56i 0.347320 + 0.601575i
\(615\) 0 0
\(616\) 1884.52 3264.08i 0.123262 0.213496i
\(617\) −4873.71 + 8441.51i −0.318003 + 0.550798i −0.980071 0.198646i \(-0.936346\pi\)
0.662068 + 0.749444i \(0.269679\pi\)
\(618\) 0 0
\(619\) 10382.6 + 17983.2i 0.674171 + 1.16770i 0.976711 + 0.214561i \(0.0688321\pi\)
−0.302540 + 0.953137i \(0.597835\pi\)
\(620\) 7005.39 0.453779
\(621\) 0 0
\(622\) 2900.66 0.186987
\(623\) −2705.90 4686.75i −0.174012 0.301398i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −25.6275 + 44.3882i −0.00163623 + 0.00283404i
\(627\) 0 0
\(628\) −10478.1 18148.6i −0.665797 1.15320i
\(629\) 3661.51 0.232105
\(630\) 0 0
\(631\) 23740.6 1.49778 0.748890 0.662694i \(-0.230587\pi\)
0.748890 + 0.662694i \(0.230587\pi\)
\(632\) 760.369 + 1317.00i 0.0478574 + 0.0828914i
\(633\) 0 0
\(634\) 6326.10 10957.1i 0.396280 0.686377i
\(635\) 2596.13 4496.62i 0.162243 0.281013i
\(636\) 0 0
\(637\) −10367.3 17956.7i −0.644848 1.11691i
\(638\) −2977.02 −0.184736
\(639\) 0 0
\(640\) 7062.81 0.436222
\(641\) 13054.4 + 22610.8i 0.804394 + 1.39325i 0.916700 + 0.399577i \(0.130843\pi\)
−0.112306 + 0.993674i \(0.535824\pi\)
\(642\) 0 0
\(643\) 12008.9 20800.1i 0.736526 1.27570i −0.217525 0.976055i \(-0.569798\pi\)
0.954051 0.299646i \(-0.0968685\pi\)
\(644\) −9719.24 + 16834.2i −0.594707 + 1.03006i
\(645\) 0 0
\(646\) −3048.46 5280.09i −0.185666 0.321582i
\(647\) −18588.3 −1.12949 −0.564747 0.825264i \(-0.691026\pi\)
−0.564747 + 0.825264i \(0.691026\pi\)
\(648\) 0 0
\(649\) −7101.83 −0.429540
\(650\) −1444.80 2502.47i −0.0871844 0.151008i
\(651\) 0 0
\(652\) −2216.22 + 3838.61i −0.133120 + 0.230570i
\(653\) 6085.97 10541.2i 0.364721 0.631714i −0.624011 0.781416i \(-0.714498\pi\)
0.988731 + 0.149701i \(0.0478312\pi\)
\(654\) 0 0
\(655\) 2008.53 + 3478.87i 0.119816 + 0.207528i
\(656\) −9118.04 −0.542682
\(657\) 0 0
\(658\) −11487.6 −0.680597
\(659\) 4294.82 + 7438.84i 0.253873 + 0.439721i 0.964589 0.263758i \(-0.0849621\pi\)
−0.710716 + 0.703479i \(0.751629\pi\)
\(660\) 0 0
\(661\) −12497.7 + 21646.6i −0.735405 + 1.27376i 0.219140 + 0.975693i \(0.429675\pi\)
−0.954545 + 0.298066i \(0.903659\pi\)
\(662\) 1997.23 3459.31i 0.117258 0.203096i
\(663\) 0 0
\(664\) 5448.36 + 9436.83i 0.318430 + 0.551536i
\(665\) −10667.4 −0.622053
\(666\) 0 0
\(667\) 35039.4 2.03408
\(668\) 3582.36 + 6204.82i 0.207493 + 0.359389i
\(669\) 0 0
\(670\) −138.979 + 240.718i −0.00801376 + 0.0138802i
\(671\) −2304.14 + 3990.88i −0.132564 + 0.229607i
\(672\) 0 0
\(673\) 1270.08 + 2199.85i 0.0727461 + 0.126000i 0.900104 0.435675i \(-0.143490\pi\)
−0.827358 + 0.561675i \(0.810157\pi\)
\(674\) 3731.94 0.213277
\(675\) 0 0
\(676\) −33643.4 −1.91417
\(677\) 2098.89 + 3635.39i 0.119154 + 0.206380i 0.919433 0.393248i \(-0.128649\pi\)
−0.800279 + 0.599628i \(0.795315\pi\)
\(678\) 0 0
\(679\) −6689.13 + 11585.9i −0.378064 + 0.654826i
\(680\) 2452.18 4247.30i 0.138289 0.239524i
\(681\) 0 0
\(682\) 1232.87 + 2135.39i 0.0692212 + 0.119895i
\(683\) −8523.02 −0.477488 −0.238744 0.971083i \(-0.576736\pi\)
−0.238744 + 0.971083i \(0.576736\pi\)
\(684\) 0 0
\(685\) 4345.76 0.242398
\(686\) −1678.79 2907.75i −0.0934352 0.161834i
\(687\) 0 0
\(688\) 2429.57 4208.15i 0.134632 0.233189i
\(689\) 1284.46 2224.75i 0.0710219 0.123014i
\(690\) 0 0
\(691\) 10146.0 + 17573.4i 0.558571 + 0.967473i 0.997616 + 0.0690084i \(0.0219835\pi\)
−0.439045 + 0.898465i \(0.644683\pi\)
\(692\) −18252.6 −1.00269
\(693\) 0 0
\(694\) 184.896 0.0101132
\(695\) −490.995 850.428i −0.0267978 0.0464152i
\(696\) 0 0
\(697\) −9525.10 + 16498.0i −0.517631 + 0.896563i
\(698\) 3456.53 5986.88i 0.187438 0.324652i
\(699\) 0 0
\(700\) −1880.01 3256.27i −0.101511 0.175822i
\(701\) −11223.6 −0.604721 −0.302361 0.953194i \(-0.597775\pi\)
−0.302361 + 0.953194i \(0.597775\pi\)
\(702\) 0 0
\(703\) 6242.38 0.334901
\(704\) 188.259 + 326.074i 0.0100785 + 0.0174565i
\(705\) 0 0
\(706\) −2262.52 + 3918.79i −0.120610 + 0.208903i
\(707\) −2735.83 + 4738.60i −0.145533 + 0.252070i
\(708\) 0 0
\(709\) 9965.49 + 17260.7i 0.527873 + 0.914302i 0.999472 + 0.0324893i \(0.0103435\pi\)
−0.471600 + 0.881813i \(0.656323\pi\)
\(710\) −3643.17 −0.192572
\(711\) 0 0
\(712\) 4241.83 0.223271
\(713\) −14510.7 25133.4i −0.762177 1.32013i
\(714\) 0 0
\(715\) −1802.44 + 3121.92i −0.0942762 + 0.163291i
\(716\) −10676.0 + 18491.3i −0.557235 + 0.965159i
\(717\) 0 0
\(718\) 5394.70 + 9343.90i 0.280402 + 0.485670i
\(719\) −3186.13 −0.165261 −0.0826305 0.996580i \(-0.526332\pi\)
−0.0826305 + 0.996580i \(0.526332\pi\)
\(720\) 0 0
\(721\) −9244.58 −0.477512
\(722\) −646.914 1120.49i −0.0333458 0.0577566i
\(723\) 0 0
\(724\) −3592.69 + 6222.72i −0.184421 + 0.319427i
\(725\) −3388.86 + 5869.67i −0.173599 + 0.300682i
\(726\) 0 0
\(727\) 11544.1 + 19995.0i 0.588923 + 1.02004i 0.994374 + 0.105927i \(0.0337810\pi\)
−0.405451 + 0.914117i \(0.632886\pi\)
\(728\) 39672.5 2.01973
\(729\) 0 0
\(730\) 1230.65 0.0623949
\(731\) −5076.08 8792.02i −0.256834 0.444849i
\(732\) 0 0
\(733\) 14900.7 25808.8i 0.750846 1.30050i −0.196567 0.980490i \(-0.562979\pi\)
0.947413 0.320013i \(-0.103687\pi\)
\(734\) −87.6698 + 151.849i −0.00440866 + 0.00763602i
\(735\) 0 0
\(736\) −11898.0 20607.9i −0.595877 1.03209i
\(737\) 346.761 0.0173312
\(738\) 0 0
\(739\) 39741.5 1.97823 0.989117 0.147134i \(-0.0470047\pi\)
0.989117 + 0.147134i \(0.0470047\pi\)
\(740\) 1100.14 + 1905.50i 0.0546515 + 0.0946591i
\(741\) 0 0
\(742\) −471.555 + 816.758i −0.0233307 + 0.0404099i
\(743\) −4856.77 + 8412.17i −0.239808 + 0.415360i −0.960659 0.277730i \(-0.910418\pi\)
0.720851 + 0.693090i \(0.243751\pi\)
\(744\) 0 0
\(745\) −1885.71 3266.14i −0.0927342 0.160620i
\(746\) 12404.2 0.608779
\(747\) 0 0
\(748\) −2680.97 −0.131051
\(749\) 21396.4 + 37059.6i 1.04380 + 1.80791i
\(750\) 0 0
\(751\) 1254.64 2173.10i 0.0609619 0.105589i −0.833934 0.551865i \(-0.813917\pi\)
0.894896 + 0.446275i \(0.147250\pi\)
\(752\) −4462.78 + 7729.76i −0.216411 + 0.374834i
\(753\) 0 0
\(754\) −15667.9 27137.7i −0.756755 1.31074i
\(755\) −10288.2 −0.495927
\(756\) 0 0
\(757\) 9705.73 0.465998 0.232999 0.972477i \(-0.425146\pi\)
0.232999 + 0.972477i \(0.425146\pi\)
\(758\) −4089.34 7082.94i −0.195952 0.339398i
\(759\) 0 0
\(760\) 4180.62 7241.05i 0.199536 0.345606i
\(761\) 3889.22 6736.33i 0.185262 0.320883i −0.758403 0.651786i \(-0.774020\pi\)
0.943665 + 0.330903i \(0.107353\pi\)
\(762\) 0 0
\(763\) 18445.7 + 31949.0i 0.875204 + 1.51590i
\(764\) 5816.04 0.275415
\(765\) 0 0
\(766\) 3451.39 0.162799
\(767\) −37376.7 64738.3i −1.75957 3.04767i
\(768\) 0 0
\(769\) −693.951 + 1201.96i −0.0325416 + 0.0563638i −0.881838 0.471553i \(-0.843693\pi\)
0.849296 + 0.527917i \(0.177027\pi\)
\(770\) 661.718 1146.13i 0.0309697 0.0536410i
\(771\) 0 0
\(772\) −13330.3 23088.7i −0.621460 1.07640i
\(773\) 20692.0 0.962796 0.481398 0.876502i \(-0.340129\pi\)
0.481398 + 0.876502i \(0.340129\pi\)
\(774\) 0 0
\(775\) 5613.67 0.260192
\(776\) −5243.02 9081.17i −0.242543 0.420097i
\(777\) 0 0
\(778\) −2819.85 + 4884.12i −0.129944 + 0.225070i
\(779\) −16239.0 + 28126.7i −0.746883 + 1.29364i
\(780\) 0 0
\(781\) 2272.49 + 3936.07i 0.104118 + 0.180338i
\(782\) −8902.82 −0.407115
\(783\) 0 0
\(784\) 5914.45 0.269426
\(785\) −8396.46 14543.1i −0.381761 0.661230i
\(786\) 0 0
\(787\) −16948.4 + 29355.5i −0.767655 + 1.32962i 0.171176 + 0.985240i \(0.445243\pi\)
−0.938831 + 0.344377i \(0.888090\pi\)
\(788\) 6002.94 10397.4i 0.271378 0.470041i
\(789\) 0 0
\(790\) 266.991 + 462.443i 0.0120242 + 0.0208265i
\(791\) −20266.4 −0.910988
\(792\) 0 0
\(793\) −48506.4 −2.17215
\(794\) 4039.04 + 6995.82i 0.180529 + 0.312686i
\(795\) 0 0
\(796\) 5424.83 9396.07i 0.241555 0.418386i
\(797\) 5977.27 10352.9i 0.265653 0.460125i −0.702081 0.712097i \(-0.747746\pi\)
0.967735 + 0.251972i \(0.0810790\pi\)
\(798\) 0 0
\(799\) 9324.02 + 16149.7i 0.412841 + 0.715062i
\(800\) 4602.89 0.203421
\(801\) 0 0
\(802\) 10250.7 0.451325
\(803\) −767.636 1329.58i −0.0337351 0.0584309i
\(804\) 0 0
\(805\) −7788.38 + 13489.9i −0.340999 + 0.590628i
\(806\) −12977.0 + 22476.9i −0.567118 + 0.982277i
\(807\) 0 0
\(808\) −2144.37 3714.17i −0.0933649 0.161713i
\(809\) 27377.3 1.18978 0.594891 0.803807i \(-0.297195\pi\)
0.594891 + 0.803807i \(0.297195\pi\)
\(810\) 0 0
\(811\) −713.034 −0.0308730 −0.0154365 0.999881i \(-0.504914\pi\)
−0.0154365 + 0.999881i \(0.504914\pi\)
\(812\) −20387.4 35312.1i −0.881107 1.52612i
\(813\) 0 0
\(814\) −387.225 + 670.693i −0.0166735 + 0.0288793i
\(815\) −1775.94 + 3076.02i −0.0763294 + 0.132206i
\(816\) 0 0
\(817\) −8654.01 14989.2i −0.370582 0.641867i
\(818\) 21655.0 0.925612
\(819\) 0 0
\(820\) −11447.7 −0.487526
\(821\) −3192.06 5528.81i −0.135693 0.235026i 0.790169 0.612889i \(-0.209993\pi\)
−0.925862 + 0.377862i \(0.876659\pi\)
\(822\) 0 0
\(823\) −9818.14 + 17005.5i −0.415843 + 0.720261i −0.995517 0.0945876i \(-0.969847\pi\)
0.579674 + 0.814849i \(0.303180\pi\)
\(824\) 3623.00 6275.22i 0.153171 0.265301i
\(825\) 0 0
\(826\) 13721.8 + 23766.9i 0.578019 + 1.00116i
\(827\) 43578.4 1.83237 0.916185 0.400756i \(-0.131253\pi\)
0.916185 + 0.400756i \(0.131253\pi\)
\(828\) 0 0
\(829\) −20418.8 −0.855458 −0.427729 0.903907i \(-0.640686\pi\)
−0.427729 + 0.903907i \(0.640686\pi\)
\(830\) 1913.10 + 3313.59i 0.0800058 + 0.138574i
\(831\) 0 0
\(832\) −1981.60 + 3432.23i −0.0825716 + 0.143018i
\(833\) 6178.49 10701.5i 0.256989 0.445118i
\(834\) 0 0
\(835\) 2870.67 + 4972.15i 0.118974 + 0.206070i
\(836\) −4570.69 −0.189092
\(837\) 0 0
\(838\) 1529.09 0.0630328
\(839\) 5480.99 + 9493.36i 0.225536 + 0.390640i 0.956480 0.291797i \(-0.0942533\pi\)
−0.730944 + 0.682438i \(0.760920\pi\)
\(840\) 0 0
\(841\) −24555.4 + 42531.3i −1.00682 + 1.74387i
\(842\) 2342.63 4057.56i 0.0958817 0.166072i
\(843\) 0 0
\(844\) 9990.66 + 17304.3i 0.407456 + 0.705734i
\(845\) −26959.7 −1.09756
\(846\) 0 0
\(847\) 30431.8 1.23453
\(848\) 366.386 + 634.599i 0.0148370 + 0.0256984i
\(849\) 0 0
\(850\) 861.043 1491.37i 0.0347453 0.0601807i
\(851\) 4557.61 7894.01i 0.183587 0.317983i
\(852\) 0 0
\(853\) 2623.20 + 4543.52i 0.105295 + 0.182377i 0.913859 0.406032i \(-0.133088\pi\)
−0.808564 + 0.588409i \(0.799755\pi\)
\(854\) 17807.8 0.713548
\(855\) 0 0
\(856\) −33541.4 −1.33928
\(857\) 13641.5 + 23627.8i 0.543741 + 0.941787i 0.998685 + 0.0512671i \(0.0163260\pi\)
−0.454944 + 0.890520i \(0.650341\pi\)
\(858\) 0 0
\(859\) −1790.52 + 3101.28i −0.0711198 + 0.123183i −0.899392 0.437142i \(-0.855991\pi\)
0.828273 + 0.560325i \(0.189324\pi\)
\(860\) 3050.33 5283.33i 0.120948 0.209488i
\(861\) 0 0
\(862\) −6787.02 11755.5i −0.268175 0.464493i
\(863\) −41710.9 −1.64526 −0.822629 0.568579i \(-0.807493\pi\)
−0.822629 + 0.568579i \(0.807493\pi\)
\(864\) 0 0
\(865\) −14626.4 −0.574929
\(866\) 4850.35 + 8401.06i 0.190325 + 0.329653i
\(867\) 0 0
\(868\) −16886.0 + 29247.4i −0.660308 + 1.14369i
\(869\) 333.081 576.913i 0.0130023 0.0225206i
\(870\) 0 0
\(871\) 1824.99 + 3160.98i 0.0709959 + 0.122969i
\(872\) −28916.0 −1.12296
\(873\) 0 0
\(874\) −15178.1 −0.587422
\(875\) −1506.52 2609.36i −0.0582052 0.100814i
\(876\) 0 0
\(877\) −10766.8 + 18648.6i −0.414560 + 0.718038i −0.995382 0.0959919i \(-0.969398\pi\)
0.580822 + 0.814030i \(0.302731\pi\)
\(878\) −4679.11 + 8104.45i −0.179855 + 0.311517i
\(879\) 0 0
\(880\) −514.137 890.512i −0.0196950 0.0341127i
\(881\) −30919.1 −1.18240 −0.591199 0.806526i \(-0.701345\pi\)
−0.591199 + 0.806526i \(0.701345\pi\)
\(882\) 0 0
\(883\) 5341.72 0.203582 0.101791 0.994806i \(-0.467543\pi\)
0.101791 + 0.994806i \(0.467543\pi\)
\(884\) −14109.8 24439.0i −0.536839 0.929832i
\(885\) 0 0
\(886\) 111.313 192.799i 0.00422080 0.00731064i
\(887\) 5605.16 9708.42i 0.212179 0.367505i −0.740217 0.672368i \(-0.765277\pi\)
0.952396 + 0.304863i \(0.0986107\pi\)
\(888\) 0 0
\(889\) 12515.5 + 21677.6i 0.472169 + 0.817820i
\(890\) 1489.45 0.0560972
\(891\) 0 0
\(892\) 8766.54 0.329064
\(893\) 15896.2 + 27533.0i 0.595683 + 1.03175i
\(894\) 0 0
\(895\) −8555.05 + 14817.8i −0.319513 + 0.553412i
\(896\) −17024.4 + 29487.1i −0.634760 + 1.09944i
\(897\) 0 0
\(898\) −2620.41 4538.68i −0.0973765 0.168661i
\(899\) 60876.6 2.25845
\(900\) 0 0
\(901\) 1530.97 0.0566083
\(902\) −2014.66 3489.49i −0.0743690 0.128811i
\(903\) 0 0
\(904\) 7942.53 13756.9i 0.292217 0.506135i
\(905\) −2878.95 + 4986.49i −0.105745 + 0.183156i
\(906\) 0 0
\(907\) −10345.4 17918.8i −0.378737 0.655991i 0.612142 0.790748i \(-0.290308\pi\)
−0.990879 + 0.134757i \(0.956975\pi\)
\(908\) 38924.6 1.42264
\(909\) 0 0
\(910\) 13930.4 0.507459
\(911\) 9735.79 + 16862.9i 0.354073 + 0.613273i 0.986959 0.160972i \(-0.0514629\pi\)
−0.632885 + 0.774245i \(0.718130\pi\)
\(912\) 0 0
\(913\) 2386.66 4133.82i 0.0865136 0.149846i
\(914\) 4940.77 8557.66i 0.178803 0.309696i
\(915\) 0 0
\(916\) 20685.2 + 35827.8i 0.746132 + 1.29234i
\(917\) −19365.6 −0.697393
\(918\) 0 0
\(919\) −30002.0 −1.07690 −0.538452 0.842656i \(-0.680991\pi\)
−0.538452 + 0.842656i \(0.680991\pi\)
\(920\) −6104.62 10573.5i −0.218764 0.378911i
\(921\) 0 0
\(922\) −7222.91 + 12510.5i −0.257998 + 0.446865i
\(923\) −23920.0 + 41430.7i −0.853021 + 1.47747i
\(924\) 0 0
\(925\) 881.585 + 1526.95i 0.0313366 + 0.0542765i
\(926\) −4207.66 −0.149322
\(927\) 0 0
\(928\) 49915.3 1.76568
\(929\) 11131.4 + 19280.1i 0.393121 + 0.680905i 0.992859 0.119291i \(-0.0380621\pi\)
−0.599739 + 0.800196i \(0.704729\pi\)
\(930\) 0 0
\(931\) 10533.5 18244.5i 0.370806 0.642255i
\(932\) −7654.33 + 13257.7i −0.269019 + 0.465955i
\(933\) 0 0
\(934\) 10845.7 + 18785.3i 0.379959 + 0.658108i
\(935\) −2148.36 −0.0751432
\(936\) 0 0
\(937\) 23361.5 0.814500 0.407250 0.913317i \(-0.366488\pi\)
0.407250 + 0.913317i \(0.366488\pi\)
\(938\) −669.996 1160.47i −0.0233221 0.0403951i
\(939\) 0 0
\(940\) −5603.02 + 9704.71i −0.194415 + 0.336737i
\(941\) 19665.5 34061.6i 0.681271 1.18000i −0.293322 0.956014i \(-0.594761\pi\)
0.974593 0.223982i \(-0.0719058\pi\)
\(942\) 0 0
\(943\) 23712.4 + 41071.1i 0.818857 + 1.41830i
\(944\) 21323.0 0.735175
\(945\) 0 0
\(946\) 2147.29 0.0737995
\(947\) −13434.9 23270.0i −0.461011 0.798494i 0.538001 0.842944i \(-0.319180\pi\)
−0.999012 + 0.0444504i \(0.985846\pi\)
\(948\) 0 0
\(949\) 8080.07 13995.1i 0.276386 0.478715i
\(950\) 1467.96 2542.58i 0.0501336 0.0868339i
\(951\) 0 0
\(952\) 11821.6 + 20475.6i 0.402458 + 0.697078i
\(953\) −16422.6 −0.558218 −0.279109 0.960259i \(-0.590039\pi\)
−0.279109 + 0.960259i \(0.590039\pi\)
\(954\) 0 0
\(955\) 4660.60 0.157920
\(956\) 21681.7 + 37553.9i 0.733512 + 1.27048i
\(957\) 0 0
\(958\) −6245.08 + 10816.8i −0.210615 + 0.364796i
\(959\) −10475.1 + 18143.5i −0.352721 + 0.610931i
\(960\) 0 0
\(961\) −10315.1 17866.3i −0.346250 0.599723i
\(962\) −8151.79 −0.273206
\(963\) 0 0
\(964\) −39528.9 −1.32069
\(965\) −10682.0 18501.8i −0.356339 0.617197i
\(966\) 0 0
\(967\) −5152.22 + 8923.91i −0.171339 + 0.296767i −0.938888 0.344223i \(-0.888143\pi\)
0.767550 + 0.640990i \(0.221476\pi\)
\(968\) −11926.4 + 20657.1i −0.396000 + 0.685892i
\(969\) 0 0
\(970\) −1841.00 3188.71i −0.0609392 0.105550i
\(971\) 44153.1 1.45926 0.729630 0.683842i \(-0.239692\pi\)
0.729630 + 0.683842i \(0.239692\pi\)
\(972\) 0 0
\(973\) 4734.03 0.155977
\(974\) −8944.22 15491.9i −0.294242 0.509642i
\(975\) 0 0
\(976\) 6918.10 11982.5i 0.226888 0.392982i
\(977\) 8057.81 13956.5i 0.263861 0.457021i −0.703403 0.710791i \(-0.748337\pi\)
0.967265 + 0.253770i \(0.0816706\pi\)
\(978\) 0 0
\(979\) −929.069 1609.20i −0.0303301 0.0525333i
\(980\) 7425.59 0.242043
\(981\) 0 0
\(982\) −12232.8 −0.397521
\(983\) 19374.3 + 33557.2i 0.628630 + 1.08882i 0.987827 + 0.155558i \(0.0497174\pi\)
−0.359197 + 0.933262i \(0.616949\pi\)
\(984\) 0 0
\(985\) 4810.37 8331.81i 0.155605 0.269516i
\(986\) 9337.44 16172.9i 0.301587 0.522364i
\(987\) 0 0
\(988\) −24055.3 41665.1i −0.774598 1.34164i
\(989\) −25273.5 −0.812587
\(990\) 0 0
\(991\) −42906.4 −1.37534 −0.687672 0.726022i \(-0.741367\pi\)
−0.687672 + 0.726022i \(0.741367\pi\)
\(992\) −20671.3 35803.7i −0.661606 1.14594i
\(993\) 0 0
\(994\) 8781.60 15210.2i 0.280217 0.485350i
\(995\) 4347.11 7529.41i 0.138505 0.239898i
\(996\) 0 0
\(997\) 9697.66 + 16796.8i 0.308052 + 0.533562i 0.977936 0.208904i \(-0.0669895\pi\)
−0.669884 + 0.742466i \(0.733656\pi\)
\(998\) 138.447 0.00439126
\(999\) 0 0
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 405.4.e.s.271.2 6
3.2 odd 2 405.4.e.u.271.2 6
9.2 odd 6 405.4.e.u.136.2 6
9.4 even 3 405.4.a.i.1.2 yes 3
9.5 odd 6 405.4.a.g.1.2 3
9.7 even 3 inner 405.4.e.s.136.2 6
45.4 even 6 2025.4.a.p.1.2 3
45.14 odd 6 2025.4.a.r.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
405.4.a.g.1.2 3 9.5 odd 6
405.4.a.i.1.2 yes 3 9.4 even 3
405.4.e.s.136.2 6 9.7 even 3 inner
405.4.e.s.271.2 6 1.1 even 1 trivial
405.4.e.u.136.2 6 9.2 odd 6
405.4.e.u.271.2 6 3.2 odd 2
2025.4.a.p.1.2 3 45.4 even 6
2025.4.a.r.1.2 3 45.14 odd 6