Properties

Label 405.4.e.v.136.3
Level $405$
Weight $4$
Character 405.136
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: 6.0.84779568.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.3
Root \(0.327167 + 0.566669i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.v.271.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.72938 - 4.72742i) q^{2} +(-10.8990 - 18.8776i) q^{4} +(2.50000 + 4.33013i) q^{5} +(5.90326 - 10.2247i) q^{7} -75.3201 q^{8} +O(q^{10})\) \(q+(2.72938 - 4.72742i) q^{2} +(-10.8990 - 18.8776i) q^{4} +(2.50000 + 4.33013i) q^{5} +(5.90326 - 10.2247i) q^{7} -75.3201 q^{8} +27.2938 q^{10} +(-28.1188 + 48.7032i) q^{11} +(-17.2980 - 29.9611i) q^{13} +(-32.2245 - 55.8144i) q^{14} +(-118.385 + 205.049i) q^{16} -39.2675 q^{17} -146.561 q^{19} +(54.4951 - 94.3882i) q^{20} +(153.494 + 265.859i) q^{22} +(-11.7889 - 20.4189i) q^{23} +(-12.5000 + 21.6506i) q^{25} -188.851 q^{26} -257.359 q^{28} +(80.5013 - 139.432i) q^{29} +(14.7733 + 25.5880i) q^{31} +(344.954 + 597.478i) q^{32} +(-107.176 + 185.634i) q^{34} +59.0326 q^{35} -217.688 q^{37} +(-400.020 + 692.855i) q^{38} +(-188.300 - 326.146i) q^{40} +(71.1449 + 123.227i) q^{41} +(234.015 - 405.326i) q^{43} +1225.87 q^{44} -128.705 q^{46} +(197.159 - 341.490i) q^{47} +(101.803 + 176.328i) q^{49} +(68.2345 + 118.186i) q^{50} +(-377.063 + 653.092i) q^{52} +134.780 q^{53} -281.188 q^{55} +(-444.634 + 770.129i) q^{56} +(-439.437 - 761.128i) q^{58} +(-65.5977 - 113.619i) q^{59} +(-129.901 + 224.994i) q^{61} +161.287 q^{62} +1871.88 q^{64} +(86.4901 - 149.805i) q^{65} +(-222.622 - 385.593i) q^{67} +(427.977 + 741.278i) q^{68} +(161.122 - 279.072i) q^{70} -560.841 q^{71} -88.6681 q^{73} +(-594.152 + 1029.10i) q^{74} +(1597.37 + 2766.72i) q^{76} +(331.985 + 575.015i) q^{77} +(-225.171 + 390.008i) q^{79} -1183.85 q^{80} +776.726 q^{82} +(142.148 - 246.207i) q^{83} +(-98.1687 - 170.033i) q^{85} +(-1277.43 - 2212.57i) q^{86} +(2117.91 - 3668.33i) q^{88} -625.305 q^{89} -408.459 q^{91} +(-256.974 + 445.092i) q^{92} +(-1076.24 - 1864.11i) q^{94} +(-366.402 - 634.627i) q^{95} +(96.6307 - 167.369i) q^{97} +1111.44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 5 q^{2} - 17 q^{4} + 15 q^{5} + 4 q^{7} - 150 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 5 q^{2} - 17 q^{4} + 15 q^{5} + 4 q^{7} - 150 q^{8} + 50 q^{10} + 5 q^{11} - 7 q^{13} + 60 q^{14} - 161 q^{16} - 310 q^{17} - 100 q^{19} + 85 q^{20} + 229 q^{22} + 285 q^{23} - 75 q^{25} - 370 q^{26} - 668 q^{28} + 115 q^{29} + 115 q^{31} + 775 q^{32} - 413 q^{34} + 40 q^{35} - 768 q^{37} - 1150 q^{38} - 375 q^{40} + 580 q^{41} + 797 q^{43} + 2830 q^{44} - 570 q^{46} - 145 q^{47} - 577 q^{49} + 125 q^{50} - 825 q^{52} + 800 q^{53} + 50 q^{55} - 2190 q^{56} + 59 q^{58} + 380 q^{59} + 152 q^{61} + 2010 q^{62} + 5874 q^{64} + 35 q^{65} - 2 q^{67} + 475 q^{68} - 300 q^{70} - 80 q^{71} - 1960 q^{73} - 2720 q^{74} + 3276 q^{76} + 1950 q^{77} - 1013 q^{79} - 1610 q^{80} + 8 q^{82} + 270 q^{83} - 775 q^{85} - 1555 q^{86} + 5193 q^{88} - 2040 q^{89} - 1264 q^{91} - 1215 q^{92} - 3833 q^{94} - 250 q^{95} - 720 q^{97} + 610 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72938 4.72742i 0.964981 1.67140i 0.255315 0.966858i \(-0.417821\pi\)
0.709666 0.704538i \(-0.248846\pi\)
\(3\) 0 0
\(4\) −10.8990 18.8776i −1.36238 2.35971i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 5.90326 10.2247i 0.318746 0.552084i −0.661481 0.749962i \(-0.730072\pi\)
0.980227 + 0.197878i \(0.0634050\pi\)
\(8\) −75.3201 −3.32871
\(9\) 0 0
\(10\) 27.2938 0.863105
\(11\) −28.1188 + 48.7032i −0.770740 + 1.33496i 0.166418 + 0.986055i \(0.446780\pi\)
−0.937158 + 0.348905i \(0.886554\pi\)
\(12\) 0 0
\(13\) −17.2980 29.9611i −0.369047 0.639208i 0.620370 0.784309i \(-0.286983\pi\)
−0.989417 + 0.145101i \(0.953649\pi\)
\(14\) −32.2245 55.8144i −0.615168 1.06550i
\(15\) 0 0
\(16\) −118.385 + 205.049i −1.84976 + 3.20389i
\(17\) −39.2675 −0.560221 −0.280111 0.959968i \(-0.590371\pi\)
−0.280111 + 0.959968i \(0.590371\pi\)
\(18\) 0 0
\(19\) −146.561 −1.76965 −0.884825 0.465924i \(-0.845722\pi\)
−0.884825 + 0.465924i \(0.845722\pi\)
\(20\) 54.4951 94.3882i 0.609273 1.05529i
\(21\) 0 0
\(22\) 153.494 + 265.859i 1.48750 + 2.57642i
\(23\) −11.7889 20.4189i −0.106876 0.185115i 0.807627 0.589693i \(-0.200751\pi\)
−0.914503 + 0.404579i \(0.867418\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −188.851 −1.42449
\(27\) 0 0
\(28\) −257.359 −1.73701
\(29\) 80.5013 139.432i 0.515473 0.892826i −0.484365 0.874866i \(-0.660949\pi\)
0.999839 0.0179601i \(-0.00571719\pi\)
\(30\) 0 0
\(31\) 14.7733 + 25.5880i 0.0855921 + 0.148250i 0.905643 0.424040i \(-0.139388\pi\)
−0.820051 + 0.572290i \(0.806055\pi\)
\(32\) 344.954 + 597.478i 1.90562 + 3.30063i
\(33\) 0 0
\(34\) −107.176 + 185.634i −0.540603 + 0.936352i
\(35\) 59.0326 0.285095
\(36\) 0 0
\(37\) −217.688 −0.967233 −0.483617 0.875280i \(-0.660677\pi\)
−0.483617 + 0.875280i \(0.660677\pi\)
\(38\) −400.020 + 692.855i −1.70768 + 2.95779i
\(39\) 0 0
\(40\) −188.300 326.146i −0.744322 1.28920i
\(41\) 71.1449 + 123.227i 0.270999 + 0.469385i 0.969118 0.246597i \(-0.0793125\pi\)
−0.698119 + 0.715982i \(0.745979\pi\)
\(42\) 0 0
\(43\) 234.015 405.326i 0.829929 1.43748i −0.0681645 0.997674i \(-0.521714\pi\)
0.898093 0.439805i \(-0.144952\pi\)
\(44\) 1225.87 4.20015
\(45\) 0 0
\(46\) −128.705 −0.412533
\(47\) 197.159 341.490i 0.611886 1.05982i −0.379037 0.925382i \(-0.623745\pi\)
0.990922 0.134435i \(-0.0429220\pi\)
\(48\) 0 0
\(49\) 101.803 + 176.328i 0.296802 + 0.514076i
\(50\) 68.2345 + 118.186i 0.192996 + 0.334279i
\(51\) 0 0
\(52\) −377.063 + 653.092i −1.00556 + 1.74168i
\(53\) 134.780 0.349311 0.174655 0.984630i \(-0.444119\pi\)
0.174655 + 0.984630i \(0.444119\pi\)
\(54\) 0 0
\(55\) −281.188 −0.689371
\(56\) −444.634 + 770.129i −1.06101 + 1.83773i
\(57\) 0 0
\(58\) −439.437 761.128i −0.994844 1.72312i
\(59\) −65.5977 113.619i −0.144747 0.250710i 0.784531 0.620089i \(-0.212904\pi\)
−0.929279 + 0.369379i \(0.879570\pi\)
\(60\) 0 0
\(61\) −129.901 + 224.994i −0.272657 + 0.472255i −0.969541 0.244928i \(-0.921236\pi\)
0.696885 + 0.717183i \(0.254569\pi\)
\(62\) 161.287 0.330379
\(63\) 0 0
\(64\) 1871.88 3.65602
\(65\) 86.4901 149.805i 0.165043 0.285863i
\(66\) 0 0
\(67\) −222.622 385.593i −0.405935 0.703100i 0.588495 0.808501i \(-0.299721\pi\)
−0.994430 + 0.105401i \(0.966387\pi\)
\(68\) 427.977 + 741.278i 0.763233 + 1.32196i
\(69\) 0 0
\(70\) 161.122 279.072i 0.275111 0.476507i
\(71\) −560.841 −0.937459 −0.468729 0.883342i \(-0.655288\pi\)
−0.468729 + 0.883342i \(0.655288\pi\)
\(72\) 0 0
\(73\) −88.6681 −0.142162 −0.0710809 0.997471i \(-0.522645\pi\)
−0.0710809 + 0.997471i \(0.522645\pi\)
\(74\) −594.152 + 1029.10i −0.933362 + 1.61663i
\(75\) 0 0
\(76\) 1597.37 + 2766.72i 2.41093 + 4.17585i
\(77\) 331.985 + 575.015i 0.491340 + 0.851027i
\(78\) 0 0
\(79\) −225.171 + 390.008i −0.320680 + 0.555434i −0.980629 0.195877i \(-0.937245\pi\)
0.659948 + 0.751311i \(0.270578\pi\)
\(80\) −1183.85 −1.65448
\(81\) 0 0
\(82\) 776.726 1.04604
\(83\) 142.148 246.207i 0.187985 0.325599i −0.756594 0.653886i \(-0.773138\pi\)
0.944578 + 0.328286i \(0.106471\pi\)
\(84\) 0 0
\(85\) −98.1687 170.033i −0.125269 0.216973i
\(86\) −1277.43 2212.57i −1.60173 2.77428i
\(87\) 0 0
\(88\) 2117.91 3668.33i 2.56557 4.44369i
\(89\) −625.305 −0.744744 −0.372372 0.928083i \(-0.621455\pi\)
−0.372372 + 0.928083i \(0.621455\pi\)
\(90\) 0 0
\(91\) −408.459 −0.470529
\(92\) −256.974 + 445.092i −0.291211 + 0.504392i
\(93\) 0 0
\(94\) −1076.24 1864.11i −1.18092 2.04541i
\(95\) −366.402 634.627i −0.395706 0.685382i
\(96\) 0 0
\(97\) 96.6307 167.369i 0.101148 0.175193i −0.811010 0.585032i \(-0.801082\pi\)
0.912158 + 0.409839i \(0.134415\pi\)
\(98\) 1111.44 1.14563
\(99\) 0 0
\(100\) 544.951 0.544951
\(101\) 687.429 1190.66i 0.677245 1.17302i −0.298562 0.954390i \(-0.596507\pi\)
0.975807 0.218633i \(-0.0701596\pi\)
\(102\) 0 0
\(103\) −1014.80 1757.69i −0.970789 1.68146i −0.693184 0.720761i \(-0.743793\pi\)
−0.277605 0.960695i \(-0.589541\pi\)
\(104\) 1302.89 + 2256.67i 1.22845 + 2.12774i
\(105\) 0 0
\(106\) 367.866 637.162i 0.337078 0.583836i
\(107\) 823.062 0.743630 0.371815 0.928307i \(-0.378736\pi\)
0.371815 + 0.928307i \(0.378736\pi\)
\(108\) 0 0
\(109\) −829.868 −0.729238 −0.364619 0.931157i \(-0.618801\pi\)
−0.364619 + 0.931157i \(0.618801\pi\)
\(110\) −767.469 + 1329.29i −0.665230 + 1.15221i
\(111\) 0 0
\(112\) 1397.71 + 2420.91i 1.17921 + 2.04245i
\(113\) −751.683 1301.95i −0.625773 1.08387i −0.988391 0.151933i \(-0.951450\pi\)
0.362618 0.931938i \(-0.381883\pi\)
\(114\) 0 0
\(115\) 58.9443 102.095i 0.0477964 0.0827858i
\(116\) −3509.54 −2.80908
\(117\) 0 0
\(118\) −716.164 −0.558714
\(119\) −231.806 + 401.500i −0.178568 + 0.309289i
\(120\) 0 0
\(121\) −915.834 1586.27i −0.688080 1.19179i
\(122\) 709.095 + 1228.19i 0.526217 + 0.911435i
\(123\) 0 0
\(124\) 322.028 557.768i 0.233217 0.403944i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −576.348 −0.402698 −0.201349 0.979520i \(-0.564532\pi\)
−0.201349 + 0.979520i \(0.564532\pi\)
\(128\) 2349.44 4069.36i 1.62237 2.81003i
\(129\) 0 0
\(130\) −472.129 817.751i −0.318526 0.551704i
\(131\) 1195.02 + 2069.83i 0.797017 + 1.38047i 0.921551 + 0.388258i \(0.126923\pi\)
−0.124534 + 0.992215i \(0.539743\pi\)
\(132\) 0 0
\(133\) −865.186 + 1498.55i −0.564069 + 0.976996i
\(134\) −2430.48 −1.56688
\(135\) 0 0
\(136\) 2957.63 1.86481
\(137\) 501.230 868.155i 0.312576 0.541398i −0.666343 0.745645i \(-0.732141\pi\)
0.978919 + 0.204248i \(0.0654747\pi\)
\(138\) 0 0
\(139\) −65.9084 114.157i −0.0402178 0.0696593i 0.845216 0.534425i \(-0.179472\pi\)
−0.885434 + 0.464766i \(0.846139\pi\)
\(140\) −643.397 1114.40i −0.388407 0.672740i
\(141\) 0 0
\(142\) −1530.75 + 2651.33i −0.904630 + 1.56687i
\(143\) 1945.60 1.13776
\(144\) 0 0
\(145\) 805.013 0.461053
\(146\) −242.009 + 419.171i −0.137183 + 0.237609i
\(147\) 0 0
\(148\) 2372.58 + 4109.43i 1.31774 + 2.28239i
\(149\) 509.743 + 882.900i 0.280267 + 0.485436i 0.971450 0.237243i \(-0.0762438\pi\)
−0.691184 + 0.722679i \(0.742910\pi\)
\(150\) 0 0
\(151\) −1411.19 + 2444.25i −0.760537 + 1.31729i 0.182037 + 0.983292i \(0.441731\pi\)
−0.942574 + 0.333997i \(0.891603\pi\)
\(152\) 11039.0 5.89065
\(153\) 0 0
\(154\) 3624.45 1.89654
\(155\) −73.8663 + 127.940i −0.0382779 + 0.0662993i
\(156\) 0 0
\(157\) −238.250 412.661i −0.121111 0.209770i 0.799095 0.601205i \(-0.205312\pi\)
−0.920206 + 0.391434i \(0.871979\pi\)
\(158\) 1229.15 + 2128.96i 0.618900 + 1.07197i
\(159\) 0 0
\(160\) −1724.77 + 2987.39i −0.852219 + 1.47609i
\(161\) −278.371 −0.136265
\(162\) 0 0
\(163\) −2242.26 −1.07747 −0.538734 0.842476i \(-0.681097\pi\)
−0.538734 + 0.842476i \(0.681097\pi\)
\(164\) 1550.82 2686.10i 0.738406 1.27896i
\(165\) 0 0
\(166\) −775.949 1343.98i −0.362803 0.628394i
\(167\) 47.5195 + 82.3062i 0.0220190 + 0.0381380i 0.876825 0.480810i \(-0.159657\pi\)
−0.854806 + 0.518948i \(0.826324\pi\)
\(168\) 0 0
\(169\) 500.056 866.123i 0.227609 0.394230i
\(170\) −1071.76 −0.483530
\(171\) 0 0
\(172\) −10202.1 −4.52270
\(173\) −1066.88 + 1847.89i −0.468864 + 0.812096i −0.999367 0.0355875i \(-0.988670\pi\)
0.530503 + 0.847683i \(0.322003\pi\)
\(174\) 0 0
\(175\) 147.581 + 255.619i 0.0637492 + 0.110417i
\(176\) −6657.68 11531.4i −2.85137 4.93872i
\(177\) 0 0
\(178\) −1706.70 + 2956.08i −0.718664 + 1.24476i
\(179\) 1704.68 0.711808 0.355904 0.934523i \(-0.384173\pi\)
0.355904 + 0.934523i \(0.384173\pi\)
\(180\) 0 0
\(181\) −1360.98 −0.558902 −0.279451 0.960160i \(-0.590152\pi\)
−0.279451 + 0.960160i \(0.590152\pi\)
\(182\) −1114.84 + 1930.96i −0.454051 + 0.786440i
\(183\) 0 0
\(184\) 887.938 + 1537.95i 0.355759 + 0.616193i
\(185\) −544.219 942.615i −0.216280 0.374608i
\(186\) 0 0
\(187\) 1104.15 1912.45i 0.431785 0.747873i
\(188\) −8595.36 −3.33447
\(189\) 0 0
\(190\) −4000.20 −1.52739
\(191\) −548.421 + 949.892i −0.207761 + 0.359852i −0.951009 0.309164i \(-0.899951\pi\)
0.743248 + 0.669016i \(0.233284\pi\)
\(192\) 0 0
\(193\) 1433.63 + 2483.13i 0.534691 + 0.926111i 0.999178 + 0.0405316i \(0.0129052\pi\)
−0.464488 + 0.885580i \(0.653762\pi\)
\(194\) −527.483 913.628i −0.195212 0.338117i
\(195\) 0 0
\(196\) 2219.11 3843.61i 0.808712 1.40073i
\(197\) −724.139 −0.261892 −0.130946 0.991389i \(-0.541801\pi\)
−0.130946 + 0.991389i \(0.541801\pi\)
\(198\) 0 0
\(199\) −1693.65 −0.603315 −0.301658 0.953416i \(-0.597540\pi\)
−0.301658 + 0.953416i \(0.597540\pi\)
\(200\) 941.501 1630.73i 0.332871 0.576549i
\(201\) 0 0
\(202\) −3752.51 6499.53i −1.30706 2.26389i
\(203\) −950.440 1646.21i −0.328610 0.569169i
\(204\) 0 0
\(205\) −355.725 + 616.133i −0.121195 + 0.209915i
\(206\) −11079.1 −3.74717
\(207\) 0 0
\(208\) 8191.30 2.73060
\(209\) 4121.11 7137.98i 1.36394 2.36241i
\(210\) 0 0
\(211\) −473.726 820.517i −0.154562 0.267710i 0.778337 0.627846i \(-0.216063\pi\)
−0.932900 + 0.360137i \(0.882730\pi\)
\(212\) −1468.97 2544.33i −0.475893 0.824270i
\(213\) 0 0
\(214\) 2246.45 3890.96i 0.717589 1.24290i
\(215\) 2340.15 0.742311
\(216\) 0 0
\(217\) 348.841 0.109129
\(218\) −2265.02 + 3923.14i −0.703701 + 1.21885i
\(219\) 0 0
\(220\) 3064.67 + 5308.17i 0.939183 + 1.62671i
\(221\) 679.250 + 1176.50i 0.206748 + 0.358098i
\(222\) 0 0
\(223\) −55.9328 + 96.8784i −0.0167961 + 0.0290918i −0.874301 0.485384i \(-0.838680\pi\)
0.857505 + 0.514475i \(0.172013\pi\)
\(224\) 8145.41 2.42964
\(225\) 0 0
\(226\) −8206.51 −2.41544
\(227\) 600.350 1039.84i 0.175536 0.304037i −0.764811 0.644255i \(-0.777168\pi\)
0.940347 + 0.340218i \(0.110501\pi\)
\(228\) 0 0
\(229\) −411.190 712.202i −0.118656 0.205518i 0.800579 0.599227i \(-0.204525\pi\)
−0.919235 + 0.393709i \(0.871192\pi\)
\(230\) −321.763 557.309i −0.0922452 0.159773i
\(231\) 0 0
\(232\) −6063.37 + 10502.1i −1.71586 + 2.97196i
\(233\) 5329.21 1.49840 0.749202 0.662341i \(-0.230437\pi\)
0.749202 + 0.662341i \(0.230437\pi\)
\(234\) 0 0
\(235\) 1971.59 0.547287
\(236\) −1429.90 + 2476.66i −0.394401 + 0.683123i
\(237\) 0 0
\(238\) 1265.37 + 2191.69i 0.344630 + 0.596917i
\(239\) −3542.81 6136.32i −0.958850 1.66078i −0.725302 0.688431i \(-0.758300\pi\)
−0.233548 0.972345i \(-0.575034\pi\)
\(240\) 0 0
\(241\) 3280.05 5681.21i 0.876707 1.51850i 0.0217738 0.999763i \(-0.493069\pi\)
0.854933 0.518738i \(-0.173598\pi\)
\(242\) −9998.63 −2.65593
\(243\) 0 0
\(244\) 5663.15 1.48584
\(245\) −509.015 + 881.641i −0.132734 + 0.229902i
\(246\) 0 0
\(247\) 2535.21 + 4391.12i 0.653084 + 1.13117i
\(248\) −1112.72 1927.29i −0.284911 0.493481i
\(249\) 0 0
\(250\) −341.172 + 590.928i −0.0863105 + 0.149494i
\(251\) −714.222 −0.179607 −0.0898033 0.995960i \(-0.528624\pi\)
−0.0898033 + 0.995960i \(0.528624\pi\)
\(252\) 0 0
\(253\) 1325.95 0.329494
\(254\) −1573.07 + 2724.64i −0.388595 + 0.673067i
\(255\) 0 0
\(256\) −5337.51 9244.85i −1.30310 2.25704i
\(257\) 2198.29 + 3807.56i 0.533563 + 0.924159i 0.999231 + 0.0391993i \(0.0124807\pi\)
−0.465668 + 0.884959i \(0.654186\pi\)
\(258\) 0 0
\(259\) −1285.07 + 2225.80i −0.308302 + 0.533994i
\(260\) −3770.63 −0.899402
\(261\) 0 0
\(262\) 13046.6 3.07643
\(263\) −3775.15 + 6538.76i −0.885118 + 1.53307i −0.0395390 + 0.999218i \(0.512589\pi\)
−0.845579 + 0.533851i \(0.820744\pi\)
\(264\) 0 0
\(265\) 336.950 + 583.615i 0.0781082 + 0.135287i
\(266\) 4722.84 + 8180.20i 1.08863 + 1.88556i
\(267\) 0 0
\(268\) −4852.72 + 8405.17i −1.10607 + 1.91577i
\(269\) 5536.86 1.25497 0.627487 0.778627i \(-0.284083\pi\)
0.627487 + 0.778627i \(0.284083\pi\)
\(270\) 0 0
\(271\) 3058.25 0.685518 0.342759 0.939423i \(-0.388639\pi\)
0.342759 + 0.939423i \(0.388639\pi\)
\(272\) 4648.68 8051.75i 1.03628 1.79489i
\(273\) 0 0
\(274\) −2736.09 4739.05i −0.603260 1.04488i
\(275\) −702.970 1217.58i −0.154148 0.266992i
\(276\) 0 0
\(277\) 2035.09 3524.88i 0.441433 0.764584i −0.556363 0.830939i \(-0.687804\pi\)
0.997796 + 0.0663552i \(0.0211371\pi\)
\(278\) −719.556 −0.155238
\(279\) 0 0
\(280\) −4446.34 −0.948998
\(281\) 3723.09 6448.59i 0.790396 1.36901i −0.135326 0.990801i \(-0.543208\pi\)
0.925722 0.378204i \(-0.123458\pi\)
\(282\) 0 0
\(283\) 387.326 + 670.868i 0.0813573 + 0.140915i 0.903833 0.427885i \(-0.140741\pi\)
−0.822476 + 0.568800i \(0.807408\pi\)
\(284\) 6112.61 + 10587.4i 1.27717 + 2.21213i
\(285\) 0 0
\(286\) 5310.28 9197.67i 1.09791 1.90164i
\(287\) 1679.95 0.345520
\(288\) 0 0
\(289\) −3371.06 −0.686152
\(290\) 2197.19 3805.64i 0.444908 0.770603i
\(291\) 0 0
\(292\) 966.394 + 1673.84i 0.193678 + 0.335460i
\(293\) 3374.62 + 5845.01i 0.672857 + 1.16542i 0.977090 + 0.212825i \(0.0682665\pi\)
−0.304233 + 0.952598i \(0.598400\pi\)
\(294\) 0 0
\(295\) 327.989 568.093i 0.0647330 0.112121i
\(296\) 16396.3 3.21964
\(297\) 0 0
\(298\) 5565.12 1.08181
\(299\) −407.848 + 706.413i −0.0788845 + 0.136632i
\(300\) 0 0
\(301\) −2762.90 4785.48i −0.529073 0.916381i
\(302\) 7703.35 + 13342.6i 1.46781 + 2.54232i
\(303\) 0 0
\(304\) 17350.6 30052.1i 3.27343 5.66975i
\(305\) −1299.01 −0.243872
\(306\) 0 0
\(307\) −2204.39 −0.409808 −0.204904 0.978782i \(-0.565688\pi\)
−0.204904 + 0.978782i \(0.565688\pi\)
\(308\) 7236.62 12534.2i 1.33878 2.31884i
\(309\) 0 0
\(310\) 403.218 + 698.394i 0.0738750 + 0.127955i
\(311\) −3016.49 5224.71i −0.549998 0.952625i −0.998274 0.0587296i \(-0.981295\pi\)
0.448276 0.893895i \(-0.352038\pi\)
\(312\) 0 0
\(313\) 2886.48 4999.53i 0.521257 0.902844i −0.478437 0.878122i \(-0.658797\pi\)
0.999694 0.0247221i \(-0.00787008\pi\)
\(314\) −2601.09 −0.467479
\(315\) 0 0
\(316\) 9816.57 1.74755
\(317\) −1651.04 + 2859.68i −0.292528 + 0.506674i −0.974407 0.224791i \(-0.927830\pi\)
0.681879 + 0.731465i \(0.261163\pi\)
\(318\) 0 0
\(319\) 4527.20 + 7841.35i 0.794592 + 1.37627i
\(320\) 4679.71 + 8105.49i 0.817511 + 1.41597i
\(321\) 0 0
\(322\) −759.779 + 1315.98i −0.131493 + 0.227753i
\(323\) 5755.07 0.991395
\(324\) 0 0
\(325\) 864.901 0.147619
\(326\) −6119.97 + 10600.1i −1.03974 + 1.80087i
\(327\) 0 0
\(328\) −5358.64 9281.44i −0.902078 1.56244i
\(329\) −2327.76 4031.80i −0.390072 0.675625i
\(330\) 0 0
\(331\) −4026.58 + 6974.23i −0.668642 + 1.15812i 0.309642 + 0.950853i \(0.399791\pi\)
−0.978284 + 0.207269i \(0.933542\pi\)
\(332\) −6197.08 −1.02442
\(333\) 0 0
\(334\) 518.795 0.0849916
\(335\) 1113.11 1927.96i 0.181540 0.314436i
\(336\) 0 0
\(337\) −1730.16 2996.73i −0.279668 0.484398i 0.691635 0.722248i \(-0.256891\pi\)
−0.971302 + 0.237849i \(0.923558\pi\)
\(338\) −2729.69 4727.96i −0.439276 0.760849i
\(339\) 0 0
\(340\) −2139.88 + 3706.39i −0.341328 + 0.591197i
\(341\) −1661.62 −0.263877
\(342\) 0 0
\(343\) 6453.51 1.01591
\(344\) −17626.0 + 30529.2i −2.76259 + 4.78495i
\(345\) 0 0
\(346\) 5823.84 + 10087.2i 0.904889 + 1.56731i
\(347\) −4664.14 8078.52i −0.721568 1.24979i −0.960371 0.278724i \(-0.910089\pi\)
0.238804 0.971068i \(-0.423245\pi\)
\(348\) 0 0
\(349\) −4449.71 + 7707.13i −0.682486 + 1.18210i 0.291734 + 0.956499i \(0.405768\pi\)
−0.974220 + 0.225601i \(0.927566\pi\)
\(350\) 1611.22 0.246067
\(351\) 0 0
\(352\) −38798.8 −5.87495
\(353\) 1861.23 3223.74i 0.280632 0.486069i −0.690909 0.722942i \(-0.742789\pi\)
0.971541 + 0.236873i \(0.0761227\pi\)
\(354\) 0 0
\(355\) −1402.10 2428.51i −0.209622 0.363076i
\(356\) 6815.21 + 11804.3i 1.01462 + 1.75738i
\(357\) 0 0
\(358\) 4652.71 8058.73i 0.686881 1.18971i
\(359\) −11029.3 −1.62145 −0.810727 0.585425i \(-0.800928\pi\)
−0.810727 + 0.585425i \(0.800928\pi\)
\(360\) 0 0
\(361\) 14621.1 2.13166
\(362\) −3714.64 + 6433.95i −0.539330 + 0.934146i
\(363\) 0 0
\(364\) 4451.80 + 7710.74i 0.641038 + 1.11031i
\(365\) −221.670 383.944i −0.0317883 0.0550590i
\(366\) 0 0
\(367\) 2426.56 4202.92i 0.345137 0.597794i −0.640242 0.768173i \(-0.721166\pi\)
0.985379 + 0.170379i \(0.0544992\pi\)
\(368\) 5582.49 0.790781
\(369\) 0 0
\(370\) −5941.52 −0.834824
\(371\) 795.641 1378.09i 0.111341 0.192849i
\(372\) 0 0
\(373\) 6186.89 + 10716.0i 0.858834 + 1.48754i 0.873042 + 0.487645i \(0.162144\pi\)
−0.0142081 + 0.999899i \(0.504523\pi\)
\(374\) −6027.31 10439.6i −0.833328 1.44337i
\(375\) 0 0
\(376\) −14850.0 + 25721.0i −2.03679 + 3.52782i
\(377\) −5570.06 −0.760935
\(378\) 0 0
\(379\) 11150.6 1.51127 0.755634 0.654994i \(-0.227329\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(380\) −7986.84 + 13833.6i −1.07820 + 1.86750i
\(381\) 0 0
\(382\) 2993.69 + 5185.23i 0.400970 + 0.694501i
\(383\) 1099.80 + 1904.90i 0.146728 + 0.254141i 0.930016 0.367518i \(-0.119792\pi\)
−0.783288 + 0.621659i \(0.786459\pi\)
\(384\) 0 0
\(385\) −1659.93 + 2875.07i −0.219734 + 0.380591i
\(386\) 15651.7 2.06386
\(387\) 0 0
\(388\) −4212.72 −0.551207
\(389\) 4609.46 7983.82i 0.600794 1.04061i −0.391907 0.920005i \(-0.628185\pi\)
0.992701 0.120601i \(-0.0384821\pi\)
\(390\) 0 0
\(391\) 462.919 + 801.799i 0.0598742 + 0.103705i
\(392\) −7667.82 13281.1i −0.987968 1.71121i
\(393\) 0 0
\(394\) −1976.45 + 3423.31i −0.252721 + 0.437726i
\(395\) −2251.71 −0.286825
\(396\) 0 0
\(397\) 1119.36 0.141509 0.0707544 0.997494i \(-0.477459\pi\)
0.0707544 + 0.997494i \(0.477459\pi\)
\(398\) −4622.61 + 8006.60i −0.582188 + 1.00838i
\(399\) 0 0
\(400\) −2959.62 5126.22i −0.369953 0.640777i
\(401\) 6148.45 + 10649.4i 0.765683 + 1.32620i 0.939885 + 0.341491i \(0.110932\pi\)
−0.174202 + 0.984710i \(0.555735\pi\)
\(402\) 0 0
\(403\) 511.096 885.245i 0.0631750 0.109422i
\(404\) −29969.2 −3.69065
\(405\) 0 0
\(406\) −10376.4 −1.26841
\(407\) 6121.12 10602.1i 0.745485 1.29122i
\(408\) 0 0
\(409\) −1250.11 2165.25i −0.151134 0.261772i 0.780510 0.625143i \(-0.214959\pi\)
−0.931645 + 0.363370i \(0.881626\pi\)
\(410\) 1941.81 + 3363.32i 0.233901 + 0.405128i
\(411\) 0 0
\(412\) −22120.7 + 38314.1i −2.64516 + 4.58155i
\(413\) −1548.96 −0.184551
\(414\) 0 0
\(415\) 1421.48 0.168139
\(416\) 11934.1 20670.4i 1.40653 2.43618i
\(417\) 0 0
\(418\) −22496.2 38964.5i −2.63235 4.55937i
\(419\) −4166.49 7216.57i −0.485790 0.841414i 0.514076 0.857744i \(-0.328135\pi\)
−0.999867 + 0.0163308i \(0.994802\pi\)
\(420\) 0 0
\(421\) −5687.10 + 9850.35i −0.658367 + 1.14032i 0.322672 + 0.946511i \(0.395419\pi\)
−0.981038 + 0.193814i \(0.937914\pi\)
\(422\) −5171.91 −0.596598
\(423\) 0 0
\(424\) −10151.6 −1.16275
\(425\) 490.844 850.166i 0.0560221 0.0970332i
\(426\) 0 0
\(427\) 1533.67 + 2656.40i 0.173816 + 0.301059i
\(428\) −8970.56 15537.5i −1.01310 1.75475i
\(429\) 0 0
\(430\) 6387.15 11062.9i 0.716316 1.24070i
\(431\) 10030.2 1.12097 0.560484 0.828165i \(-0.310615\pi\)
0.560484 + 0.828165i \(0.310615\pi\)
\(432\) 0 0
\(433\) 7609.38 0.844535 0.422267 0.906471i \(-0.361234\pi\)
0.422267 + 0.906471i \(0.361234\pi\)
\(434\) 952.120 1649.12i 0.105307 0.182397i
\(435\) 0 0
\(436\) 9044.74 + 15666.0i 0.993497 + 1.72079i
\(437\) 1727.78 + 2992.61i 0.189133 + 0.327588i
\(438\) 0 0
\(439\) 6185.24 10713.2i 0.672450 1.16472i −0.304757 0.952430i \(-0.598575\pi\)
0.977207 0.212287i \(-0.0680913\pi\)
\(440\) 21179.1 2.29471
\(441\) 0 0
\(442\) 7415.72 0.798032
\(443\) −6042.21 + 10465.4i −0.648023 + 1.12241i 0.335572 + 0.942015i \(0.391071\pi\)
−0.983594 + 0.180394i \(0.942263\pi\)
\(444\) 0 0
\(445\) −1563.26 2707.65i −0.166530 0.288438i
\(446\) 305.324 + 528.836i 0.0324159 + 0.0561460i
\(447\) 0 0
\(448\) 11050.2 19139.5i 1.16534 2.01843i
\(449\) 625.550 0.0657495 0.0328747 0.999459i \(-0.489534\pi\)
0.0328747 + 0.999459i \(0.489534\pi\)
\(450\) 0 0
\(451\) −8002.04 −0.835480
\(452\) −16385.2 + 28380.0i −1.70508 + 2.95328i
\(453\) 0 0
\(454\) −3277.16 5676.22i −0.338777 0.586780i
\(455\) −1021.15 1768.68i −0.105213 0.182235i
\(456\) 0 0
\(457\) −905.611 + 1568.56i −0.0926974 + 0.160557i −0.908645 0.417569i \(-0.862882\pi\)
0.815948 + 0.578125i \(0.196216\pi\)
\(458\) −4489.17 −0.458003
\(459\) 0 0
\(460\) −2569.74 −0.260467
\(461\) −5812.49 + 10067.5i −0.587233 + 1.01712i 0.407359 + 0.913268i \(0.366450\pi\)
−0.994593 + 0.103850i \(0.966884\pi\)
\(462\) 0 0
\(463\) −3645.94 6314.96i −0.365964 0.633868i 0.622966 0.782249i \(-0.285927\pi\)
−0.988930 + 0.148380i \(0.952594\pi\)
\(464\) 19060.3 + 33013.4i 1.90701 + 3.30303i
\(465\) 0 0
\(466\) 14545.4 25193.4i 1.44593 2.50443i
\(467\) 11637.6 1.15316 0.576579 0.817042i \(-0.304387\pi\)
0.576579 + 0.817042i \(0.304387\pi\)
\(468\) 0 0
\(469\) −5256.78 −0.517560
\(470\) 5381.22 9320.55i 0.528122 0.914734i
\(471\) 0 0
\(472\) 4940.83 + 8557.76i 0.481822 + 0.834540i
\(473\) 13160.4 + 22794.5i 1.27932 + 2.21584i
\(474\) 0 0
\(475\) 1832.01 3173.13i 0.176965 0.306512i
\(476\) 10105.8 0.973109
\(477\) 0 0
\(478\) −38678.6 −3.70109
\(479\) 6020.72 10428.2i 0.574309 0.994732i −0.421807 0.906685i \(-0.638604\pi\)
0.996116 0.0880467i \(-0.0280625\pi\)
\(480\) 0 0
\(481\) 3765.57 + 6522.16i 0.356955 + 0.618263i
\(482\) −17905.0 31012.3i −1.69201 2.93065i
\(483\) 0 0
\(484\) −19963.4 + 34577.6i −1.87485 + 3.24733i
\(485\) 966.307 0.0904695
\(486\) 0 0
\(487\) 7037.81 0.654853 0.327427 0.944877i \(-0.393819\pi\)
0.327427 + 0.944877i \(0.393819\pi\)
\(488\) 9784.12 16946.6i 0.907595 1.57200i
\(489\) 0 0
\(490\) 2778.59 + 4812.66i 0.256171 + 0.443702i
\(491\) 3301.53 + 5718.42i 0.303454 + 0.525599i 0.976916 0.213624i \(-0.0685266\pi\)
−0.673462 + 0.739222i \(0.735193\pi\)
\(492\) 0 0
\(493\) −3161.09 + 5475.16i −0.288779 + 0.500180i
\(494\) 27678.2 2.52085
\(495\) 0 0
\(496\) −6995.72 −0.633301
\(497\) −3310.79 + 5734.46i −0.298811 + 0.517556i
\(498\) 0 0
\(499\) 18.3523 + 31.7872i 0.00164642 + 0.00285168i 0.866847 0.498573i \(-0.166143\pi\)
−0.865201 + 0.501425i \(0.832809\pi\)
\(500\) 1362.38 + 2359.71i 0.121855 + 0.211059i
\(501\) 0 0
\(502\) −1949.38 + 3376.43i −0.173317 + 0.300194i
\(503\) −21242.5 −1.88302 −0.941508 0.336990i \(-0.890591\pi\)
−0.941508 + 0.336990i \(0.890591\pi\)
\(504\) 0 0
\(505\) 6874.29 0.605746
\(506\) 3619.03 6268.35i 0.317956 0.550715i
\(507\) 0 0
\(508\) 6281.62 + 10880.1i 0.548626 + 0.950248i
\(509\) −5640.20 9769.12i −0.491155 0.850705i 0.508794 0.860889i \(-0.330092\pi\)
−0.999948 + 0.0101839i \(0.996758\pi\)
\(510\) 0 0
\(511\) −523.430 + 906.608i −0.0453135 + 0.0784853i
\(512\) −20681.3 −1.78514
\(513\) 0 0
\(514\) 23999.9 2.05951
\(515\) 5074.00 8788.43i 0.434150 0.751970i
\(516\) 0 0
\(517\) 11087.8 + 19204.6i 0.943209 + 1.63369i
\(518\) 7014.87 + 12150.1i 0.595011 + 1.03059i
\(519\) 0 0
\(520\) −6514.45 + 11283.4i −0.549379 + 0.951553i
\(521\) 10239.3 0.861023 0.430511 0.902585i \(-0.358333\pi\)
0.430511 + 0.902585i \(0.358333\pi\)
\(522\) 0 0
\(523\) −2822.00 −0.235942 −0.117971 0.993017i \(-0.537639\pi\)
−0.117971 + 0.993017i \(0.537639\pi\)
\(524\) 26049.0 45118.3i 2.17167 3.76145i
\(525\) 0 0
\(526\) 20607.6 + 35693.5i 1.70824 + 2.95876i
\(527\) −580.108 1004.78i −0.0479505 0.0830527i
\(528\) 0 0
\(529\) 5805.55 10055.5i 0.477155 0.826457i
\(530\) 3678.66 0.301492
\(531\) 0 0
\(532\) 37718.7 3.07390
\(533\) 2461.33 4263.16i 0.200023 0.346450i
\(534\) 0 0
\(535\) 2057.65 + 3563.96i 0.166281 + 0.288007i
\(536\) 16767.9 + 29042.9i 1.35124 + 2.34041i
\(537\) 0 0
\(538\) 15112.2 26175.1i 1.21103 2.09756i
\(539\) −11450.3 −0.915028
\(540\) 0 0
\(541\) −9409.63 −0.747785 −0.373892 0.927472i \(-0.621977\pi\)
−0.373892 + 0.927472i \(0.621977\pi\)
\(542\) 8347.12 14457.6i 0.661512 1.14577i
\(543\) 0 0
\(544\) −13545.5 23461.5i −1.06757 1.84908i
\(545\) −2074.67 3593.43i −0.163063 0.282433i
\(546\) 0 0
\(547\) 1918.21 3322.45i 0.149940 0.259703i −0.781265 0.624199i \(-0.785425\pi\)
0.931205 + 0.364496i \(0.118759\pi\)
\(548\) −21851.6 −1.70339
\(549\) 0 0
\(550\) −7674.69 −0.594999
\(551\) −11798.3 + 20435.3i −0.912207 + 1.57999i
\(552\) 0 0
\(553\) 2658.49 + 4604.63i 0.204431 + 0.354085i
\(554\) −11109.1 19241.5i −0.851948 1.47562i
\(555\) 0 0
\(556\) −1436.67 + 2488.39i −0.109584 + 0.189804i
\(557\) −6145.92 −0.467524 −0.233762 0.972294i \(-0.575104\pi\)
−0.233762 + 0.972294i \(0.575104\pi\)
\(558\) 0 0
\(559\) −16192.0 −1.22513
\(560\) −6988.57 + 12104.6i −0.527359 + 0.913412i
\(561\) 0 0
\(562\) −20323.5 35201.3i −1.52543 2.64213i
\(563\) 6623.93 + 11473.0i 0.495854 + 0.858844i 0.999989 0.00478126i \(-0.00152193\pi\)
−0.504135 + 0.863625i \(0.668189\pi\)
\(564\) 0 0
\(565\) 3758.41 6509.76i 0.279854 0.484722i
\(566\) 4228.63 0.314033
\(567\) 0 0
\(568\) 42242.6 3.12053
\(569\) 3272.45 5668.04i 0.241104 0.417604i −0.719925 0.694052i \(-0.755824\pi\)
0.961029 + 0.276448i \(0.0891572\pi\)
\(570\) 0 0
\(571\) −10181.0 17634.1i −0.746170 1.29241i −0.949646 0.313325i \(-0.898557\pi\)
0.203475 0.979080i \(-0.434776\pi\)
\(572\) −21205.1 36728.3i −1.55005 2.68477i
\(573\) 0 0
\(574\) 4585.21 7941.82i 0.333420 0.577500i
\(575\) 589.443 0.0427504
\(576\) 0 0
\(577\) −26247.4 −1.89375 −0.946876 0.321600i \(-0.895779\pi\)
−0.946876 + 0.321600i \(0.895779\pi\)
\(578\) −9200.91 + 15936.4i −0.662124 + 1.14683i
\(579\) 0 0
\(580\) −8773.85 15196.8i −0.628128 1.08795i
\(581\) −1678.27 2906.85i −0.119839 0.207567i
\(582\) 0 0
\(583\) −3789.85 + 6564.22i −0.269228 + 0.466316i
\(584\) 6678.49 0.473215
\(585\) 0 0
\(586\) 36842.4 2.59718
\(587\) −7049.08 + 12209.4i −0.495650 + 0.858492i −0.999987 0.00501514i \(-0.998404\pi\)
0.504337 + 0.863507i \(0.331737\pi\)
\(588\) 0 0
\(589\) −2165.18 3750.20i −0.151468 0.262350i
\(590\) −1790.41 3101.08i −0.124932 0.216389i
\(591\) 0 0
\(592\) 25770.9 44636.6i 1.78915 3.09891i
\(593\) −3476.71 −0.240761 −0.120380 0.992728i \(-0.538411\pi\)
−0.120380 + 0.992728i \(0.538411\pi\)
\(594\) 0 0
\(595\) −2318.06 −0.159716
\(596\) 11111.4 19245.5i 0.763658 1.32269i
\(597\) 0 0
\(598\) 2226.34 + 3856.14i 0.152244 + 0.263694i
\(599\) −8089.48 14011.4i −0.551798 0.955743i −0.998145 0.0608826i \(-0.980608\pi\)
0.446347 0.894860i \(-0.352725\pi\)
\(600\) 0 0
\(601\) −4056.08 + 7025.34i −0.275293 + 0.476821i −0.970209 0.242270i \(-0.922108\pi\)
0.694916 + 0.719091i \(0.255441\pi\)
\(602\) −30164.0 −2.04218
\(603\) 0 0
\(604\) 61522.3 4.14455
\(605\) 4579.17 7931.35i 0.307719 0.532984i
\(606\) 0 0
\(607\) −10569.6 18307.1i −0.706765 1.22415i −0.966051 0.258352i \(-0.916821\pi\)
0.259286 0.965800i \(-0.416513\pi\)
\(608\) −50556.7 87566.8i −3.37228 5.84096i
\(609\) 0 0
\(610\) −3545.48 + 6140.95i −0.235331 + 0.407606i
\(611\) −13641.9 −0.903258
\(612\) 0 0
\(613\) −11440.3 −0.753785 −0.376892 0.926257i \(-0.623007\pi\)
−0.376892 + 0.926257i \(0.623007\pi\)
\(614\) −6016.62 + 10421.1i −0.395457 + 0.684952i
\(615\) 0 0
\(616\) −25005.1 43310.2i −1.63553 2.83282i
\(617\) 10783.1 + 18676.9i 0.703584 + 1.21864i 0.967200 + 0.254016i \(0.0817514\pi\)
−0.263616 + 0.964628i \(0.584915\pi\)
\(618\) 0 0
\(619\) 7599.14 13162.1i 0.493433 0.854651i −0.506538 0.862218i \(-0.669075\pi\)
0.999971 + 0.00756612i \(0.00240839\pi\)
\(620\) 3220.28 0.208596
\(621\) 0 0
\(622\) −32932.6 −2.12295
\(623\) −3691.34 + 6393.59i −0.237384 + 0.411162i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −15756.6 27291.2i −1.00601 1.74245i
\(627\) 0 0
\(628\) −5193.37 + 8995.19i −0.329997 + 0.571572i
\(629\) 8548.05 0.541865
\(630\) 0 0
\(631\) −4929.66 −0.311009 −0.155504 0.987835i \(-0.549700\pi\)
−0.155504 + 0.987835i \(0.549700\pi\)
\(632\) 16959.9 29375.4i 1.06745 1.84888i
\(633\) 0 0
\(634\) 9012.61 + 15610.3i 0.564569 + 0.977862i
\(635\) −1440.87 2495.66i −0.0900459 0.155964i
\(636\) 0 0
\(637\) 3521.99 6100.26i 0.219068 0.379436i
\(638\) 49425.8 3.06706
\(639\) 0 0
\(640\) 23494.4 1.45109
\(641\) −3767.86 + 6526.13i −0.232171 + 0.402132i −0.958447 0.285271i \(-0.907916\pi\)
0.726276 + 0.687403i \(0.241250\pi\)
\(642\) 0 0
\(643\) 7998.62 + 13854.0i 0.490568 + 0.849688i 0.999941 0.0108576i \(-0.00345614\pi\)
−0.509373 + 0.860546i \(0.670123\pi\)
\(644\) 3033.97 + 5254.98i 0.185644 + 0.321546i
\(645\) 0 0
\(646\) 15707.8 27206.7i 0.956678 1.65701i
\(647\) −6020.46 −0.365825 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(648\) 0 0
\(649\) 7378.12 0.446250
\(650\) 2360.64 4088.75i 0.142449 0.246729i
\(651\) 0 0
\(652\) 24438.4 + 42328.5i 1.46792 + 2.54251i
\(653\) 5474.34 + 9481.84i 0.328067 + 0.568228i 0.982128 0.188213i \(-0.0602696\pi\)
−0.654062 + 0.756441i \(0.726936\pi\)
\(654\) 0 0
\(655\) −5975.09 + 10349.2i −0.356437 + 0.617367i
\(656\) −33690.0 −2.00514
\(657\) 0 0
\(658\) −25413.4 −1.50565
\(659\) −6169.14 + 10685.3i −0.364667 + 0.631622i −0.988723 0.149758i \(-0.952150\pi\)
0.624056 + 0.781380i \(0.285484\pi\)
\(660\) 0 0
\(661\) −10008.4 17335.0i −0.588928 1.02005i −0.994373 0.105934i \(-0.966217\pi\)
0.405445 0.914119i \(-0.367116\pi\)
\(662\) 21980.1 + 38070.6i 1.29045 + 2.23513i
\(663\) 0 0
\(664\) −10706.6 + 18544.3i −0.625746 + 1.08382i
\(665\) −8651.86 −0.504518
\(666\) 0 0
\(667\) −3796.08 −0.220367
\(668\) 1035.83 1794.11i 0.0599963 0.103917i
\(669\) 0 0
\(670\) −6076.20 10524.3i −0.350364 0.606849i
\(671\) −7305.29 12653.1i −0.420295 0.727972i
\(672\) 0 0
\(673\) 4209.61 7291.26i 0.241112 0.417619i −0.719919 0.694058i \(-0.755821\pi\)
0.961031 + 0.276439i \(0.0891544\pi\)
\(674\) −18889.1 −1.07950
\(675\) 0 0
\(676\) −21800.5 −1.24036
\(677\) −12853.5 + 22263.0i −0.729692 + 1.26386i 0.227321 + 0.973820i \(0.427003\pi\)
−0.957013 + 0.290044i \(0.906330\pi\)
\(678\) 0 0
\(679\) −1140.87 1976.05i −0.0644810 0.111684i
\(680\) 7394.08 + 12806.9i 0.416985 + 0.722239i
\(681\) 0 0
\(682\) −4535.20 + 7855.20i −0.254636 + 0.441043i
\(683\) −19624.3 −1.09942 −0.549708 0.835357i \(-0.685261\pi\)
−0.549708 + 0.835357i \(0.685261\pi\)
\(684\) 0 0
\(685\) 5012.30 0.279577
\(686\) 17614.1 30508.5i 0.980334 1.69799i
\(687\) 0 0
\(688\) 55407.7 + 95968.9i 3.07035 + 5.31799i
\(689\) −2331.43 4038.15i −0.128912 0.223282i
\(690\) 0 0
\(691\) −3636.61 + 6298.80i −0.200207 + 0.346769i −0.948595 0.316492i \(-0.897495\pi\)
0.748388 + 0.663261i \(0.230828\pi\)
\(692\) 46511.8 2.55508
\(693\) 0 0
\(694\) −50920.8 −2.78520
\(695\) 329.542 570.783i 0.0179860 0.0311526i
\(696\) 0 0
\(697\) −2793.68 4838.80i −0.151820 0.262959i
\(698\) 24289.9 + 42071.3i 1.31717 + 2.28141i
\(699\) 0 0
\(700\) 3216.98 5571.98i 0.173701 0.300859i
\(701\) 17644.3 0.950664 0.475332 0.879807i \(-0.342328\pi\)
0.475332 + 0.879807i \(0.342328\pi\)
\(702\) 0 0
\(703\) 31904.5 1.71166
\(704\) −52635.1 + 91166.7i −2.81784 + 4.88064i
\(705\) 0 0
\(706\) −10160.0 17597.6i −0.541609 0.938094i
\(707\) −8116.14 14057.6i −0.431738 0.747793i
\(708\) 0 0
\(709\) −12152.2 + 21048.2i −0.643703 + 1.11493i 0.340897 + 0.940101i \(0.389269\pi\)
−0.984600 + 0.174825i \(0.944064\pi\)
\(710\) −15307.5 −0.809126
\(711\) 0 0
\(712\) 47098.1 2.47904
\(713\) 348.320 603.307i 0.0182955 0.0316887i
\(714\) 0 0
\(715\) 4864.00 + 8424.69i 0.254410 + 0.440651i
\(716\) −18579.3 32180.3i −0.969751 1.67966i
\(717\) 0 0
\(718\) −30103.0 + 52139.9i −1.56467 + 2.71009i
\(719\) −15170.2 −0.786863 −0.393431 0.919354i \(-0.628712\pi\)
−0.393431 + 0.919354i \(0.628712\pi\)
\(720\) 0 0
\(721\) −23962.5 −1.23774
\(722\) 39906.4 69119.9i 2.05701 3.56285i
\(723\) 0 0
\(724\) 14833.4 + 25692.2i 0.761435 + 1.31884i
\(725\) 2012.53 + 3485.81i 0.103095 + 0.178565i
\(726\) 0 0
\(727\) 8743.52 15144.2i 0.446051 0.772583i −0.552074 0.833795i \(-0.686163\pi\)
0.998125 + 0.0612123i \(0.0194967\pi\)
\(728\) 30765.2 1.56625
\(729\) 0 0
\(730\) −2420.09 −0.122701
\(731\) −9189.18 + 15916.1i −0.464944 + 0.805306i
\(732\) 0 0
\(733\) −9349.02 16193.0i −0.471097 0.815964i 0.528357 0.849023i \(-0.322808\pi\)
−0.999453 + 0.0330590i \(0.989475\pi\)
\(734\) −13246.0 22942.7i −0.666101 1.15372i
\(735\) 0 0
\(736\) 8133.23 14087.2i 0.407330 0.705516i
\(737\) 25039.5 1.25148
\(738\) 0 0
\(739\) −35250.3 −1.75467 −0.877336 0.479876i \(-0.840682\pi\)
−0.877336 + 0.479876i \(0.840682\pi\)
\(740\) −11862.9 + 20547.2i −0.589310 + 1.02071i
\(741\) 0 0
\(742\) −4343.21 7522.67i −0.214885 0.372191i
\(743\) 5566.78 + 9641.94i 0.274866 + 0.476081i 0.970101 0.242701i \(-0.0780333\pi\)
−0.695236 + 0.718782i \(0.744700\pi\)
\(744\) 0 0
\(745\) −2548.71 + 4414.50i −0.125339 + 0.217094i
\(746\) 67545.5 3.31503
\(747\) 0 0
\(748\) −48136.8 −2.35301
\(749\) 4858.75 8415.59i 0.237029 0.410546i
\(750\) 0 0
\(751\) −8598.81 14893.6i −0.417809 0.723667i 0.577909 0.816101i \(-0.303869\pi\)
−0.995719 + 0.0924337i \(0.970535\pi\)
\(752\) 46681.3 + 80854.5i 2.26369 + 3.92082i
\(753\) 0 0
\(754\) −15202.8 + 26332.0i −0.734288 + 1.27182i
\(755\) −14111.9 −0.680245
\(756\) 0 0
\(757\) 804.647 0.0386333 0.0193166 0.999813i \(-0.493851\pi\)
0.0193166 + 0.999813i \(0.493851\pi\)
\(758\) 30434.3 52713.8i 1.45834 2.52593i
\(759\) 0 0
\(760\) 27597.4 + 47800.1i 1.31719 + 2.28144i
\(761\) 13104.4 + 22697.5i 0.624225 + 1.08119i 0.988690 + 0.149973i \(0.0479185\pi\)
−0.364465 + 0.931217i \(0.618748\pi\)
\(762\) 0 0
\(763\) −4898.93 + 8485.19i −0.232442 + 0.402601i
\(764\) 23909.0 1.13219
\(765\) 0 0
\(766\) 12007.0 0.566360
\(767\) −2269.42 + 3930.76i −0.106837 + 0.185047i
\(768\) 0 0
\(769\) −18272.1 31648.2i −0.856837 1.48409i −0.874930 0.484250i \(-0.839093\pi\)
0.0180924 0.999836i \(-0.494241\pi\)
\(770\) 9061.13 + 15694.3i 0.424078 + 0.734525i
\(771\) 0 0
\(772\) 31250.4 54127.3i 1.45690 2.52342i
\(773\) 42387.4 1.97228 0.986139 0.165923i \(-0.0530603\pi\)
0.986139 + 0.165923i \(0.0530603\pi\)
\(774\) 0 0
\(775\) −738.663 −0.0342368
\(776\) −7278.23 + 12606.3i −0.336692 + 0.583168i
\(777\) 0 0
\(778\) −25161.9 43581.7i −1.15951 2.00833i
\(779\) −10427.1 18060.2i −0.479574 0.830646i
\(780\) 0 0
\(781\) 15770.2 27314.7i 0.722537 1.25147i
\(782\) 5053.92 0.231110
\(783\) 0 0
\(784\) −48207.8 −2.19606
\(785\) 1191.25 2063.30i 0.0541624 0.0938120i
\(786\) 0 0
\(787\) −13424.7 23252.2i −0.608054 1.05318i −0.991561 0.129642i \(-0.958617\pi\)
0.383507 0.923538i \(-0.374716\pi\)
\(788\) 7892.40 + 13670.0i 0.356796 + 0.617988i
\(789\) 0 0
\(790\) −6145.77 + 10644.8i −0.276781 + 0.479398i
\(791\) −17749.5 −0.797851
\(792\) 0 0
\(793\) 8988.09 0.402492
\(794\) 3055.15 5291.68i 0.136553 0.236517i
\(795\) 0 0
\(796\) 18459.1 + 31972.1i 0.821943 + 1.42365i
\(797\) −15653.5 27112.7i −0.695704 1.20500i −0.969943 0.243333i \(-0.921759\pi\)
0.274238 0.961662i \(-0.411574\pi\)
\(798\) 0 0
\(799\) −7741.94 + 13409.4i −0.342791 + 0.593732i
\(800\) −17247.7 −0.762248
\(801\) 0 0
\(802\) 67125.7 2.95548
\(803\) 2493.24 4318.42i 0.109570 0.189780i
\(804\) 0 0
\(805\) −695.927 1205.38i −0.0304698 0.0527752i
\(806\) −2789.95 4832.34i −0.121925 0.211181i
\(807\) 0 0
\(808\) −51777.2 + 89680.8i −2.25435 + 3.90465i
\(809\) 10011.9 0.435106 0.217553 0.976049i \(-0.430193\pi\)
0.217553 + 0.976049i \(0.430193\pi\)
\(810\) 0 0
\(811\) 4603.68 0.199331 0.0996653 0.995021i \(-0.468223\pi\)
0.0996653 + 0.995021i \(0.468223\pi\)
\(812\) −20717.7 + 35884.2i −0.895381 + 1.55085i
\(813\) 0 0
\(814\) −33413.7 57874.2i −1.43876 2.49200i
\(815\) −5605.64 9709.26i −0.240929 0.417301i
\(816\) 0 0
\(817\) −34297.4 + 59404.8i −1.46868 + 2.54383i
\(818\) −13648.1 −0.583367
\(819\) 0 0
\(820\) 15508.2 0.660451
\(821\) −17714.5 + 30682.4i −0.753033 + 1.30429i 0.193313 + 0.981137i \(0.438077\pi\)
−0.946346 + 0.323154i \(0.895257\pi\)
\(822\) 0 0
\(823\) 14148.8 + 24506.4i 0.599265 + 1.03796i 0.992930 + 0.118704i \(0.0378739\pi\)
−0.393664 + 0.919254i \(0.628793\pi\)
\(824\) 76434.9 + 132389.i 3.23147 + 5.59708i
\(825\) 0 0
\(826\) −4227.70 + 7322.60i −0.178088 + 0.308457i
\(827\) −41059.9 −1.72647 −0.863236 0.504800i \(-0.831566\pi\)
−0.863236 + 0.504800i \(0.831566\pi\)
\(828\) 0 0
\(829\) 9030.68 0.378345 0.189173 0.981944i \(-0.439419\pi\)
0.189173 + 0.981944i \(0.439419\pi\)
\(830\) 3879.75 6719.92i 0.162251 0.281026i
\(831\) 0 0
\(832\) −32379.9 56083.6i −1.34924 2.33696i
\(833\) −3997.55 6923.96i −0.166275 0.287996i
\(834\) 0 0
\(835\) −237.598 + 411.531i −0.00984719 + 0.0170558i
\(836\) −179664. −7.43280
\(837\) 0 0
\(838\) −45487.7 −1.87511
\(839\) 2613.90 4527.41i 0.107559 0.186298i −0.807222 0.590248i \(-0.799030\pi\)
0.914781 + 0.403951i \(0.132363\pi\)
\(840\) 0 0
\(841\) −766.434 1327.50i −0.0314254 0.0544304i
\(842\) 31044.5 + 53770.7i 1.27062 + 2.20078i
\(843\) 0 0
\(844\) −10326.3 + 17885.7i −0.421144 + 0.729443i
\(845\) 5000.56 0.203579
\(846\) 0 0
\(847\) −21625.6 −0.877290
\(848\) −15955.9 + 27636.5i −0.646142 + 1.11915i
\(849\) 0 0
\(850\) −2679.40 4640.85i −0.108121 0.187270i
\(851\) 2566.29 + 4444.94i 0.103374 + 0.179049i
\(852\) 0 0
\(853\) 15001.5 25983.3i 0.602158 1.04297i −0.390336 0.920672i \(-0.627641\pi\)
0.992494 0.122295i \(-0.0390254\pi\)
\(854\) 16743.9 0.670918
\(855\) 0 0
\(856\) −61993.1 −2.47533
\(857\) 7835.86 13572.1i 0.312331 0.540973i −0.666535 0.745473i \(-0.732224\pi\)
0.978867 + 0.204500i \(0.0655568\pi\)
\(858\) 0 0
\(859\) 15653.4 + 27112.5i 0.621755 + 1.07691i 0.989159 + 0.146850i \(0.0469133\pi\)
−0.367404 + 0.930061i \(0.619753\pi\)
\(860\) −25505.3 44176.5i −1.01131 1.75164i
\(861\) 0 0
\(862\) 27376.2 47416.9i 1.08171 1.87358i
\(863\) −13212.3 −0.521150 −0.260575 0.965454i \(-0.583912\pi\)
−0.260575 + 0.965454i \(0.583912\pi\)
\(864\) 0 0
\(865\) −10668.8 −0.419364
\(866\) 20768.9 35972.8i 0.814960 1.41155i
\(867\) 0 0
\(868\) −3802.03 6585.30i −0.148674 0.257511i
\(869\) −12663.1 21933.1i −0.494322 0.856190i
\(870\) 0 0
\(871\) −7701.85 + 13340.0i −0.299618 + 0.518953i
\(872\) 62505.7 2.42742
\(873\) 0 0
\(874\) 18863.1 0.730039
\(875\) −737.907 + 1278.09i −0.0285095 + 0.0493799i
\(876\) 0 0
\(877\) −7720.32 13372.0i −0.297260 0.514869i 0.678248 0.734833i \(-0.262739\pi\)
−0.975508 + 0.219964i \(0.929406\pi\)
\(878\) −33763.7 58480.5i −1.29780 2.24786i
\(879\) 0 0
\(880\) 33288.4 57657.2i 1.27517 2.20866i
\(881\) 27563.1 1.05406 0.527029 0.849847i \(-0.323306\pi\)
0.527029 + 0.849847i \(0.323306\pi\)
\(882\) 0 0
\(883\) 19897.7 0.758337 0.379169 0.925328i \(-0.376210\pi\)
0.379169 + 0.925328i \(0.376210\pi\)
\(884\) 14806.3 25645.3i 0.563337 0.975729i
\(885\) 0 0
\(886\) 32983.0 + 57128.2i 1.25066 + 2.16621i
\(887\) 20030.8 + 34694.4i 0.758251 + 1.31333i 0.943742 + 0.330683i \(0.107279\pi\)
−0.185491 + 0.982646i \(0.559388\pi\)
\(888\) 0 0
\(889\) −3402.33 + 5893.01i −0.128358 + 0.222323i
\(890\) −17067.0 −0.642793
\(891\) 0 0
\(892\) 2438.45 0.0915306
\(893\) −28895.8 + 50049.0i −1.08282 + 1.87550i
\(894\) 0 0
\(895\) 4261.70 + 7381.47i 0.159165 + 0.275682i
\(896\) −27738.8 48044.9i −1.03425 1.79137i
\(897\) 0 0
\(898\) 1707.36 2957.24i 0.0634470 0.109893i
\(899\) 4757.07 0.176482
\(900\) 0 0
\(901\) −5292.47 −0.195691
\(902\) −21840.6 + 37829.0i −0.806222 + 1.39642i
\(903\) 0 0
\(904\) 56616.8 + 98063.2i 2.08302 + 3.60789i
\(905\) −3402.46 5893.24i −0.124974 0.216462i
\(906\) 0 0
\(907\) −13919.8 + 24109.8i −0.509591 + 0.882638i 0.490347 + 0.871527i \(0.336870\pi\)
−0.999938 + 0.0111107i \(0.996463\pi\)
\(908\) −26172.9 −0.956584
\(909\) 0 0
\(910\) −11148.4 −0.406116
\(911\) 11125.5 19270.0i 0.404616 0.700815i −0.589661 0.807651i \(-0.700739\pi\)
0.994277 + 0.106836i \(0.0340719\pi\)
\(912\) 0 0
\(913\) 7994.04 + 13846.1i 0.289775 + 0.501904i
\(914\) 4943.51 + 8562.41i 0.178902 + 0.309868i
\(915\) 0 0
\(916\) −8963.13 + 15524.6i −0.323308 + 0.559986i
\(917\) 28218.0 1.01618
\(918\) 0 0
\(919\) 29480.5 1.05819 0.529093 0.848564i \(-0.322532\pi\)
0.529093 + 0.848564i \(0.322532\pi\)
\(920\) −4439.69 + 7689.77i −0.159100 + 0.275570i
\(921\) 0 0
\(922\) 31729.0 + 54956.2i 1.13334 + 1.96300i
\(923\) 9701.44 + 16803.4i 0.345966 + 0.599231i
\(924\) 0 0
\(925\) 2721.10 4713.08i 0.0967233 0.167530i
\(926\) −39804.6 −1.41259
\(927\) 0 0
\(928\) 111077. 3.92919
\(929\) 21175.9 36677.7i 0.747857 1.29533i −0.200992 0.979593i \(-0.564416\pi\)
0.948848 0.315733i \(-0.102250\pi\)
\(930\) 0 0
\(931\) −14920.3 25842.8i −0.525236 0.909735i
\(932\) −58083.1 100603.i −2.04139 3.53579i
\(933\) 0 0
\(934\) 31763.4 55015.9i 1.11277 1.92738i
\(935\) 11041.5 0.386200
\(936\) 0 0
\(937\) −35930.6 −1.25272 −0.626362 0.779532i \(-0.715457\pi\)
−0.626362 + 0.779532i \(0.715457\pi\)
\(938\) −14347.8 + 24851.0i −0.499436 + 0.865048i
\(939\) 0 0
\(940\) −21488.4 37219.0i −0.745611 1.29144i
\(941\) −10782.0 18675.0i −0.373521 0.646957i 0.616584 0.787289i \(-0.288516\pi\)
−0.990104 + 0.140333i \(0.955183\pi\)
\(942\) 0 0
\(943\) 1677.44 2905.40i 0.0579266 0.100332i
\(944\) 31063.1 1.07099
\(945\) 0 0
\(946\) 143679. 4.93807
\(947\) −8316.19 + 14404.1i −0.285364 + 0.494265i −0.972697 0.232077i \(-0.925448\pi\)
0.687333 + 0.726342i \(0.258781\pi\)
\(948\) 0 0
\(949\) 1533.78 + 2656.59i 0.0524644 + 0.0908710i
\(950\) −10000.5 17321.4i −0.341536 0.591557i
\(951\) 0 0
\(952\) 17459.7 30241.0i 0.594402 1.02953i
\(953\) −39557.8 −1.34460 −0.672299 0.740279i \(-0.734693\pi\)
−0.672299 + 0.740279i \(0.734693\pi\)
\(954\) 0 0
\(955\) −5484.21 −0.185827
\(956\) −77226.2 + 133760.i −2.61263 + 4.52521i
\(957\) 0 0
\(958\) −32865.7 56925.0i −1.10839 1.91980i
\(959\) −5917.77 10249.9i −0.199265 0.345137i
\(960\) 0 0
\(961\) 14459.0 25043.7i 0.485348 0.840647i
\(962\) 41110.6 1.37782
\(963\) 0 0
\(964\) −142997. −4.77762
\(965\) −7168.17 + 12415.6i −0.239121 + 0.414170i
\(966\) 0 0
\(967\) 5333.10 + 9237.20i 0.177354 + 0.307185i 0.940973 0.338481i \(-0.109913\pi\)
−0.763620 + 0.645666i \(0.776580\pi\)
\(968\) 68980.7 + 119478.i 2.29042 + 3.96712i
\(969\) 0 0
\(970\) 2637.42 4568.14i 0.0873014 0.151210i
\(971\) −31821.8 −1.05171 −0.525855 0.850574i \(-0.676254\pi\)
−0.525855 + 0.850574i \(0.676254\pi\)
\(972\) 0 0
\(973\) −1556.30 −0.0512771
\(974\) 19208.8 33270.7i 0.631921 1.09452i
\(975\) 0 0
\(976\) −30756.5 53271.9i −1.00870 1.74712i
\(977\) 5563.23 + 9635.80i 0.182173 + 0.315534i 0.942620 0.333866i \(-0.108353\pi\)
−0.760447 + 0.649400i \(0.775020\pi\)
\(978\) 0 0
\(979\) 17582.8 30454.4i 0.574004 0.994204i
\(980\) 22191.1 0.723334
\(981\) 0 0
\(982\) 36044.5 1.17131
\(983\) −495.612 + 858.426i −0.0160810 + 0.0278530i −0.873954 0.486009i \(-0.838452\pi\)
0.857873 + 0.513862i \(0.171786\pi\)
\(984\) 0 0
\(985\) −1810.35 3135.61i −0.0585609 0.101430i
\(986\) 17255.6 + 29887.6i 0.557333 + 0.965329i
\(987\) 0 0
\(988\) 55262.6 95717.7i 1.77949 3.08217i
\(989\) −11035.1 −0.354798
\(990\) 0 0
\(991\) −48714.9 −1.56153 −0.780767 0.624822i \(-0.785171\pi\)
−0.780767 + 0.624822i \(0.785171\pi\)
\(992\) −10192.2 + 17653.4i −0.326212 + 0.565016i
\(993\) 0 0
\(994\) 18072.8 + 31303.0i 0.576694 + 0.998864i
\(995\) −4234.13 7333.72i −0.134905 0.233663i
\(996\) 0 0
\(997\) 21103.6 36552.5i 0.670369 1.16111i −0.307431 0.951570i \(-0.599469\pi\)
0.977800 0.209542i \(-0.0671974\pi\)
\(998\) 200.362 0.00635505
\(999\) 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.v.136.3 6
3.2 odd 2 405.4.e.q.136.1 6
9.2 odd 6 135.4.a.h.1.3 yes 3
9.4 even 3 inner 405.4.e.v.271.3 6
9.5 odd 6 405.4.e.q.271.1 6
9.7 even 3 135.4.a.e.1.1 3
36.7 odd 6 2160.4.a.bi.1.2 3
36.11 even 6 2160.4.a.bq.1.2 3
45.2 even 12 675.4.b.n.649.6 6
45.7 odd 12 675.4.b.m.649.1 6
45.29 odd 6 675.4.a.p.1.1 3
45.34 even 6 675.4.a.s.1.3 3
45.38 even 12 675.4.b.n.649.1 6
45.43 odd 12 675.4.b.m.649.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.4.a.e.1.1 3 9.7 even 3
135.4.a.h.1.3 yes 3 9.2 odd 6
405.4.e.q.136.1 6 3.2 odd 2
405.4.e.q.271.1 6 9.5 odd 6
405.4.e.v.136.3 6 1.1 even 1 trivial
405.4.e.v.271.3 6 9.4 even 3 inner
675.4.a.p.1.1 3 45.29 odd 6
675.4.a.s.1.3 3 45.34 even 6
675.4.b.m.649.1 6 45.7 odd 12
675.4.b.m.649.6 6 45.43 odd 12
675.4.b.n.649.1 6 45.38 even 12
675.4.b.n.649.6 6 45.2 even 12
2160.4.a.bi.1.2 3 36.7 odd 6
2160.4.a.bq.1.2 3 36.11 even 6