Properties

Label 378.4.k.c.269.3
Level $378$
Weight $4$
Character 378.269
Analytic conductor $22.303$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,4,Mod(215,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.215");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 178 x^{14} + 23185 x^{12} - 1395488 x^{10} + 61706754 x^{8} - 468877357 x^{6} + 2731971910 x^{4} - 4899926507 x^{2} + 6975757441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.3
Root \(2.11897 - 1.22339i\) of defining polynomial
Character \(\chi\) \(=\) 378.269
Dual form 378.4.k.c.215.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.89811 + 6.75173i) q^{5} +(15.4219 - 10.2550i) q^{7} +8.00000i q^{8} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.89811 + 6.75173i) q^{5} +(15.4219 - 10.2550i) q^{7} +8.00000i q^{8} +(-13.5035 - 7.79622i) q^{10} +(-44.0180 - 25.4138i) q^{11} -50.9038i q^{13} +(-16.4565 + 33.1841i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(4.37255 - 7.57348i) q^{17} +(-87.9687 + 50.7888i) q^{19} +31.1849 q^{20} +101.655 q^{22} +(-36.9867 + 21.3543i) q^{23} +(32.1094 - 55.6152i) q^{25} +(50.9038 + 88.1679i) q^{26} +(-4.68064 - 73.9330i) q^{28} +218.184i q^{29} +(-87.6221 - 50.5886i) q^{31} +(27.7128 + 16.0000i) q^{32} +17.4902i q^{34} +(129.355 + 64.1492i) q^{35} +(-137.147 - 237.545i) q^{37} +(101.578 - 175.937i) q^{38} +(-54.0138 + 31.1849i) q^{40} -6.40338 q^{41} -262.501 q^{43} +(-176.072 + 101.655i) q^{44} +(42.7085 - 73.9733i) q^{46} +(-53.2835 - 92.2898i) q^{47} +(132.669 - 316.303i) q^{49} +128.438i q^{50} +(-176.336 - 101.808i) q^{52} +(-555.867 - 320.930i) q^{53} -396.263i q^{55} +(82.0401 + 123.375i) q^{56} +(-218.184 - 377.906i) q^{58} +(-52.5654 + 91.0459i) q^{59} +(471.522 - 272.233i) q^{61} +202.354 q^{62} -64.0000 q^{64} +(343.688 - 198.429i) q^{65} +(109.449 - 189.572i) q^{67} +(-17.4902 - 30.2939i) q^{68} +(-288.199 + 18.2457i) q^{70} -542.115i q^{71} +(-778.156 - 449.268i) q^{73} +(475.090 + 274.293i) q^{74} +406.310i q^{76} +(-939.460 + 59.4764i) q^{77} +(561.113 + 971.876i) q^{79} +(62.3698 - 108.028i) q^{80} +(11.0910 - 6.40338i) q^{82} +855.676 q^{83} +68.1788 q^{85} +(454.665 - 262.501i) q^{86} +(203.310 - 352.144i) q^{88} +(-658.192 - 1140.02i) q^{89} +(-522.019 - 785.032i) q^{91} +170.834i q^{92} +(184.580 + 106.567i) q^{94} +(-685.824 - 395.961i) q^{95} -1240.73i q^{97} +(86.5135 + 680.523i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} + 50 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} + 50 q^{7} + 60 q^{10} - 128 q^{16} - 498 q^{19} - 240 q^{22} - 470 q^{25} + 160 q^{28} - 582 q^{31} + 40 q^{37} + 240 q^{40} + 1900 q^{43} - 456 q^{46} - 1634 q^{49} - 720 q^{52} + 1200 q^{58} - 1302 q^{61} - 1024 q^{64} - 100 q^{67} - 1620 q^{70} - 5280 q^{73} + 590 q^{79} - 480 q^{82} + 2580 q^{85} - 480 q^{88} - 2382 q^{91} - 3396 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 3.89811 + 6.75173i 0.348658 + 0.603893i 0.986011 0.166679i \(-0.0533042\pi\)
−0.637354 + 0.770572i \(0.719971\pi\)
\(6\) 0 0
\(7\) 15.4219 10.2550i 0.832704 0.553719i
\(8\) 8.00000i 0.353553i
\(9\) 0 0
\(10\) −13.5035 7.79622i −0.427017 0.246538i
\(11\) −44.0180 25.4138i −1.20654 0.696595i −0.244537 0.969640i \(-0.578636\pi\)
−0.962001 + 0.273045i \(0.911969\pi\)
\(12\) 0 0
\(13\) 50.9038i 1.08601i −0.839729 0.543006i \(-0.817286\pi\)
0.839729 0.543006i \(-0.182714\pi\)
\(14\) −16.4565 + 33.1841i −0.314156 + 0.633487i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 4.37255 7.57348i 0.0623823 0.108049i −0.833148 0.553051i \(-0.813464\pi\)
0.895530 + 0.445001i \(0.146797\pi\)
\(18\) 0 0
\(19\) −87.9687 + 50.7888i −1.06218 + 0.613250i −0.926034 0.377439i \(-0.876805\pi\)
−0.136145 + 0.990689i \(0.543471\pi\)
\(20\) 31.1849 0.348658
\(21\) 0 0
\(22\) 101.655 0.985135
\(23\) −36.9867 + 21.3543i −0.335315 + 0.193594i −0.658198 0.752844i \(-0.728681\pi\)
0.322883 + 0.946439i \(0.395348\pi\)
\(24\) 0 0
\(25\) 32.1094 55.6152i 0.256876 0.444921i
\(26\) 50.9038 + 88.1679i 0.383964 + 0.665044i
\(27\) 0 0
\(28\) −4.68064 73.9330i −0.0315914 0.499001i
\(29\) 218.184i 1.39710i 0.715563 + 0.698548i \(0.246170\pi\)
−0.715563 + 0.698548i \(0.753830\pi\)
\(30\) 0 0
\(31\) −87.6221 50.5886i −0.507658 0.293096i 0.224213 0.974540i \(-0.428019\pi\)
−0.731870 + 0.681444i \(0.761352\pi\)
\(32\) 27.7128 + 16.0000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 17.4902i 0.0882219i
\(35\) 129.355 + 64.1492i 0.624715 + 0.309806i
\(36\) 0 0
\(37\) −137.147 237.545i −0.609373 1.05546i −0.991344 0.131290i \(-0.958088\pi\)
0.381971 0.924174i \(-0.375245\pi\)
\(38\) 101.578 175.937i 0.433633 0.751074i
\(39\) 0 0
\(40\) −54.0138 + 31.1849i −0.213508 + 0.123269i
\(41\) −6.40338 −0.0243912 −0.0121956 0.999926i \(-0.503882\pi\)
−0.0121956 + 0.999926i \(0.503882\pi\)
\(42\) 0 0
\(43\) −262.501 −0.930955 −0.465477 0.885060i \(-0.654117\pi\)
−0.465477 + 0.885060i \(0.654117\pi\)
\(44\) −176.072 + 101.655i −0.603269 + 0.348298i
\(45\) 0 0
\(46\) 42.7085 73.9733i 0.136892 0.237104i
\(47\) −53.2835 92.2898i −0.165366 0.286422i 0.771419 0.636327i \(-0.219547\pi\)
−0.936785 + 0.349905i \(0.886214\pi\)
\(48\) 0 0
\(49\) 132.669 316.303i 0.386791 0.922167i
\(50\) 128.438i 0.363277i
\(51\) 0 0
\(52\) −176.336 101.808i −0.470257 0.271503i
\(53\) −555.867 320.930i −1.44065 0.831758i −0.442754 0.896643i \(-0.645998\pi\)
−0.997893 + 0.0648858i \(0.979332\pi\)
\(54\) 0 0
\(55\) 396.263i 0.971494i
\(56\) 82.0401 + 123.375i 0.195769 + 0.294405i
\(57\) 0 0
\(58\) −218.184 377.906i −0.493948 0.855543i
\(59\) −52.5654 + 91.0459i −0.115990 + 0.200901i −0.918175 0.396175i \(-0.870338\pi\)
0.802185 + 0.597076i \(0.203671\pi\)
\(60\) 0 0
\(61\) 471.522 272.233i 0.989707 0.571408i 0.0845205 0.996422i \(-0.473064\pi\)
0.905187 + 0.425014i \(0.139731\pi\)
\(62\) 202.354 0.414501
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) 343.688 198.429i 0.655835 0.378647i
\(66\) 0 0
\(67\) 109.449 189.572i 0.199572 0.345670i −0.748817 0.662776i \(-0.769378\pi\)
0.948390 + 0.317107i \(0.102711\pi\)
\(68\) −17.4902 30.2939i −0.0311912 0.0540247i
\(69\) 0 0
\(70\) −288.199 + 18.2457i −0.492091 + 0.0311539i
\(71\) 542.115i 0.906158i −0.891470 0.453079i \(-0.850326\pi\)
0.891470 0.453079i \(-0.149674\pi\)
\(72\) 0 0
\(73\) −778.156 449.268i −1.24762 0.720314i −0.276986 0.960874i \(-0.589335\pi\)
−0.970634 + 0.240561i \(0.922669\pi\)
\(74\) 475.090 + 274.293i 0.746326 + 0.430891i
\(75\) 0 0
\(76\) 406.310i 0.613250i
\(77\) −939.460 + 59.4764i −1.39041 + 0.0880256i
\(78\) 0 0
\(79\) 561.113 + 971.876i 0.799115 + 1.38411i 0.920193 + 0.391465i \(0.128032\pi\)
−0.121078 + 0.992643i \(0.538635\pi\)
\(80\) 62.3698 108.028i 0.0871644 0.150973i
\(81\) 0 0
\(82\) 11.0910 6.40338i 0.0149365 0.00862360i
\(83\) 855.676 1.13160 0.565799 0.824543i \(-0.308568\pi\)
0.565799 + 0.824543i \(0.308568\pi\)
\(84\) 0 0
\(85\) 68.1788 0.0870003
\(86\) 454.665 262.501i 0.570091 0.329142i
\(87\) 0 0
\(88\) 203.310 352.144i 0.246284 0.426576i
\(89\) −658.192 1140.02i −0.783913 1.35778i −0.929646 0.368453i \(-0.879888\pi\)
0.145733 0.989324i \(-0.453446\pi\)
\(90\) 0 0
\(91\) −522.019 785.032i −0.601346 0.904327i
\(92\) 170.834i 0.193594i
\(93\) 0 0
\(94\) 184.580 + 106.567i 0.202531 + 0.116931i
\(95\) −685.824 395.961i −0.740674 0.427628i
\(96\) 0 0
\(97\) 1240.73i 1.29873i −0.760475 0.649367i \(-0.775034\pi\)
0.760475 0.649367i \(-0.224966\pi\)
\(98\) 86.5135 + 680.523i 0.0891753 + 0.701461i
\(99\) 0 0
\(100\) −128.438 222.461i −0.128438 0.222461i
\(101\) 250.942 434.645i 0.247225 0.428206i −0.715530 0.698582i \(-0.753815\pi\)
0.962755 + 0.270376i \(0.0871480\pi\)
\(102\) 0 0
\(103\) −305.111 + 176.156i −0.291878 + 0.168516i −0.638789 0.769382i \(-0.720564\pi\)
0.346910 + 0.937898i \(0.387231\pi\)
\(104\) 407.230 0.383964
\(105\) 0 0
\(106\) 1283.72 1.17628
\(107\) −935.207 + 539.942i −0.844952 + 0.487833i −0.858944 0.512069i \(-0.828879\pi\)
0.0139923 + 0.999902i \(0.495546\pi\)
\(108\) 0 0
\(109\) −242.598 + 420.192i −0.213180 + 0.369239i −0.952708 0.303887i \(-0.901716\pi\)
0.739528 + 0.673126i \(0.235049\pi\)
\(110\) 396.263 + 686.348i 0.343475 + 0.594916i
\(111\) 0 0
\(112\) −265.473 131.652i −0.223972 0.111071i
\(113\) 1686.83i 1.40428i −0.712038 0.702140i \(-0.752228\pi\)
0.712038 0.702140i \(-0.247772\pi\)
\(114\) 0 0
\(115\) −288.356 166.483i −0.233821 0.134996i
\(116\) 755.812 + 436.368i 0.604960 + 0.349274i
\(117\) 0 0
\(118\) 210.262i 0.164035i
\(119\) −10.2332 161.638i −0.00788297 0.124515i
\(120\) 0 0
\(121\) 626.222 + 1084.65i 0.470490 + 0.814913i
\(122\) −544.466 + 943.043i −0.404046 + 0.699829i
\(123\) 0 0
\(124\) −350.488 + 202.354i −0.253829 + 0.146548i
\(125\) 1475.19 1.05556
\(126\) 0 0
\(127\) 1425.59 0.996070 0.498035 0.867157i \(-0.334055\pi\)
0.498035 + 0.867157i \(0.334055\pi\)
\(128\) 110.851 64.0000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −396.857 + 687.377i −0.267744 + 0.463746i
\(131\) −576.837 999.111i −0.384721 0.666357i 0.607009 0.794695i \(-0.292369\pi\)
−0.991730 + 0.128338i \(0.959036\pi\)
\(132\) 0 0
\(133\) −835.804 + 1685.38i −0.544913 + 1.09880i
\(134\) 437.797i 0.282238i
\(135\) 0 0
\(136\) 60.5878 + 34.9804i 0.0382012 + 0.0220555i
\(137\) 1704.44 + 984.057i 1.06292 + 0.613676i 0.926238 0.376939i \(-0.123023\pi\)
0.136681 + 0.990615i \(0.456357\pi\)
\(138\) 0 0
\(139\) 821.420i 0.501237i 0.968086 + 0.250619i \(0.0806340\pi\)
−0.968086 + 0.250619i \(0.919366\pi\)
\(140\) 480.930 319.802i 0.290329 0.193058i
\(141\) 0 0
\(142\) 542.115 + 938.971i 0.320375 + 0.554906i
\(143\) −1293.66 + 2240.68i −0.756511 + 1.31032i
\(144\) 0 0
\(145\) −1473.12 + 850.506i −0.843696 + 0.487108i
\(146\) 1797.07 1.01868
\(147\) 0 0
\(148\) −1097.17 −0.609373
\(149\) −2337.37 + 1349.48i −1.28513 + 0.741971i −0.977782 0.209626i \(-0.932775\pi\)
−0.307350 + 0.951597i \(0.599442\pi\)
\(150\) 0 0
\(151\) −636.455 + 1102.37i −0.343007 + 0.594105i −0.984990 0.172614i \(-0.944779\pi\)
0.641983 + 0.766719i \(0.278112\pi\)
\(152\) −406.310 703.750i −0.216816 0.375537i
\(153\) 0 0
\(154\) 1567.72 1042.48i 0.820325 0.545488i
\(155\) 788.800i 0.408761i
\(156\) 0 0
\(157\) 2684.88 + 1550.11i 1.36482 + 0.787979i 0.990261 0.139225i \(-0.0444611\pi\)
0.374558 + 0.927203i \(0.377794\pi\)
\(158\) −1943.75 1122.23i −0.978712 0.565060i
\(159\) 0 0
\(160\) 249.479i 0.123269i
\(161\) −351.416 + 708.622i −0.172021 + 0.346877i
\(162\) 0 0
\(163\) 1415.80 + 2452.24i 0.680333 + 1.17837i 0.974879 + 0.222735i \(0.0714983\pi\)
−0.294546 + 0.955637i \(0.595168\pi\)
\(164\) −12.8068 + 22.1820i −0.00609780 + 0.0105617i
\(165\) 0 0
\(166\) −1482.07 + 855.676i −0.692959 + 0.400080i
\(167\) −3845.26 −1.78177 −0.890883 0.454234i \(-0.849913\pi\)
−0.890883 + 0.454234i \(0.849913\pi\)
\(168\) 0 0
\(169\) −394.194 −0.179424
\(170\) −118.089 + 68.1788i −0.0532766 + 0.0307593i
\(171\) 0 0
\(172\) −525.002 + 909.331i −0.232739 + 0.403115i
\(173\) 1098.40 + 1902.48i 0.482714 + 0.836084i 0.999803 0.0198470i \(-0.00631791\pi\)
−0.517090 + 0.855931i \(0.672985\pi\)
\(174\) 0 0
\(175\) −75.1464 1186.97i −0.0324602 0.512725i
\(176\) 813.242i 0.348298i
\(177\) 0 0
\(178\) 2280.05 + 1316.38i 0.960093 + 0.554310i
\(179\) −2000.24 1154.84i −0.835222 0.482216i 0.0204150 0.999792i \(-0.493501\pi\)
−0.855637 + 0.517576i \(0.826835\pi\)
\(180\) 0 0
\(181\) 3240.23i 1.33063i 0.746561 + 0.665317i \(0.231704\pi\)
−0.746561 + 0.665317i \(0.768296\pi\)
\(182\) 1689.20 + 837.697i 0.687975 + 0.341177i
\(183\) 0 0
\(184\) −170.834 295.893i −0.0684459 0.118552i
\(185\) 1069.23 1851.95i 0.424925 0.735992i
\(186\) 0 0
\(187\) −384.942 + 222.246i −0.150533 + 0.0869105i
\(188\) −426.268 −0.165366
\(189\) 0 0
\(190\) 1583.84 0.604758
\(191\) −95.2419 + 54.9879i −0.0360809 + 0.0208313i −0.517932 0.855422i \(-0.673298\pi\)
0.481851 + 0.876253i \(0.339965\pi\)
\(192\) 0 0
\(193\) 2499.43 4329.13i 0.932190 1.61460i 0.152621 0.988285i \(-0.451229\pi\)
0.779569 0.626316i \(-0.215438\pi\)
\(194\) 1240.73 + 2149.01i 0.459172 + 0.795308i
\(195\) 0 0
\(196\) −830.369 1092.19i −0.302612 0.398027i
\(197\) 508.689i 0.183973i −0.995760 0.0919863i \(-0.970678\pi\)
0.995760 0.0919863i \(-0.0293216\pi\)
\(198\) 0 0
\(199\) −1043.93 602.713i −0.371871 0.214700i 0.302405 0.953180i \(-0.402211\pi\)
−0.674275 + 0.738480i \(0.735544\pi\)
\(200\) 444.921 + 256.876i 0.157304 + 0.0908192i
\(201\) 0 0
\(202\) 1003.77i 0.349629i
\(203\) 2237.48 + 3364.81i 0.773598 + 1.16337i
\(204\) 0 0
\(205\) −24.9611 43.2339i −0.00850419 0.0147297i
\(206\) 352.311 610.221i 0.119159 0.206389i
\(207\) 0 0
\(208\) −705.343 + 407.230i −0.235129 + 0.135752i
\(209\) 5162.94 1.70875
\(210\) 0 0
\(211\) 3127.48 1.02040 0.510200 0.860056i \(-0.329571\pi\)
0.510200 + 0.860056i \(0.329571\pi\)
\(212\) −2223.47 + 1283.72i −0.720323 + 0.415879i
\(213\) 0 0
\(214\) 1079.88 1870.41i 0.344950 0.597471i
\(215\) −1023.26 1772.34i −0.324585 0.562197i
\(216\) 0 0
\(217\) −1870.08 + 118.394i −0.585021 + 0.0370372i
\(218\) 970.391i 0.301483i
\(219\) 0 0
\(220\) −1372.70 792.527i −0.420669 0.242873i
\(221\) −385.519 222.579i −0.117343 0.0677480i
\(222\) 0 0
\(223\) 1206.04i 0.362164i 0.983468 + 0.181082i \(0.0579599\pi\)
−0.983468 + 0.181082i \(0.942040\pi\)
\(224\) 591.464 37.4451i 0.176423 0.0111692i
\(225\) 0 0
\(226\) 1686.83 + 2921.68i 0.496488 + 0.859943i
\(227\) −236.529 + 409.681i −0.0691586 + 0.119786i −0.898531 0.438910i \(-0.855365\pi\)
0.829373 + 0.558696i \(0.188698\pi\)
\(228\) 0 0
\(229\) −1774.94 + 1024.76i −0.512188 + 0.295712i −0.733733 0.679438i \(-0.762223\pi\)
0.221545 + 0.975150i \(0.428890\pi\)
\(230\) 665.930 0.190914
\(231\) 0 0
\(232\) −1745.47 −0.493948
\(233\) 1548.92 894.267i 0.435506 0.251439i −0.266184 0.963922i \(-0.585763\pi\)
0.701689 + 0.712483i \(0.252429\pi\)
\(234\) 0 0
\(235\) 415.410 719.512i 0.115312 0.199727i
\(236\) 210.262 + 364.184i 0.0579952 + 0.100451i
\(237\) 0 0
\(238\) 179.362 + 269.732i 0.0488501 + 0.0734627i
\(239\) 4369.08i 1.18248i −0.806496 0.591239i \(-0.798639\pi\)
0.806496 0.591239i \(-0.201361\pi\)
\(240\) 0 0
\(241\) 2425.16 + 1400.17i 0.648208 + 0.374243i 0.787769 0.615970i \(-0.211236\pi\)
−0.139561 + 0.990213i \(0.544569\pi\)
\(242\) −2169.30 1252.44i −0.576230 0.332687i
\(243\) 0 0
\(244\) 2177.86i 0.571408i
\(245\) 2652.75 337.239i 0.691748 0.0879405i
\(246\) 0 0
\(247\) 2585.34 + 4477.94i 0.665997 + 1.15354i
\(248\) 404.709 700.976i 0.103625 0.179484i
\(249\) 0 0
\(250\) −2555.11 + 1475.19i −0.646397 + 0.373198i
\(251\) −3078.51 −0.774159 −0.387080 0.922046i \(-0.626516\pi\)
−0.387080 + 0.922046i \(0.626516\pi\)
\(252\) 0 0
\(253\) 2170.77 0.539428
\(254\) −2469.20 + 1425.59i −0.609966 + 0.352164i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −4.62749 8.01505i −0.00112317 0.00194539i 0.865463 0.500972i \(-0.167024\pi\)
−0.866586 + 0.499027i \(0.833691\pi\)
\(258\) 0 0
\(259\) −4551.09 2256.95i −1.09186 0.541468i
\(260\) 1587.43i 0.378647i
\(261\) 0 0
\(262\) 1998.22 + 1153.67i 0.471185 + 0.272039i
\(263\) 650.240 + 375.416i 0.152454 + 0.0880196i 0.574287 0.818654i \(-0.305280\pi\)
−0.421832 + 0.906674i \(0.638613\pi\)
\(264\) 0 0
\(265\) 5004.09i 1.15999i
\(266\) −237.724 3754.97i −0.0547962 0.865533i
\(267\) 0 0
\(268\) −437.797 758.287i −0.0997862 0.172835i
\(269\) −332.781 + 576.394i −0.0754276 + 0.130644i −0.901272 0.433253i \(-0.857365\pi\)
0.825845 + 0.563898i \(0.190699\pi\)
\(270\) 0 0
\(271\) −2885.66 + 1666.04i −0.646832 + 0.373449i −0.787242 0.616645i \(-0.788491\pi\)
0.140409 + 0.990094i \(0.455158\pi\)
\(272\) −139.922 −0.0311912
\(273\) 0 0
\(274\) −3936.23 −0.867870
\(275\) −2826.79 + 1632.05i −0.619861 + 0.357877i
\(276\) 0 0
\(277\) 2828.26 4898.68i 0.613478 1.06258i −0.377171 0.926144i \(-0.623103\pi\)
0.990649 0.136432i \(-0.0435635\pi\)
\(278\) −821.420 1422.74i −0.177214 0.306944i
\(279\) 0 0
\(280\) −513.194 + 1034.84i −0.109533 + 0.220870i
\(281\) 4156.44i 0.882392i −0.897411 0.441196i \(-0.854554\pi\)
0.897411 0.441196i \(-0.145446\pi\)
\(282\) 0 0
\(283\) −5249.78 3030.96i −1.10271 0.636650i −0.165779 0.986163i \(-0.553014\pi\)
−0.936932 + 0.349512i \(0.886347\pi\)
\(284\) −1877.94 1084.23i −0.392378 0.226540i
\(285\) 0 0
\(286\) 5174.63i 1.06987i
\(287\) −98.7522 + 65.6668i −0.0203107 + 0.0135059i
\(288\) 0 0
\(289\) 2418.26 + 4188.55i 0.492217 + 0.852545i
\(290\) 1701.01 2946.24i 0.344438 0.596583i
\(291\) 0 0
\(292\) −3112.62 + 1797.07i −0.623810 + 0.360157i
\(293\) 5099.64 1.01681 0.508403 0.861119i \(-0.330236\pi\)
0.508403 + 0.861119i \(0.330236\pi\)
\(294\) 0 0
\(295\) −819.623 −0.161764
\(296\) 1900.36 1097.17i 0.373163 0.215446i
\(297\) 0 0
\(298\) 2698.96 4674.73i 0.524653 0.908725i
\(299\) 1087.01 + 1882.76i 0.210246 + 0.364157i
\(300\) 0 0
\(301\) −4048.26 + 2691.95i −0.775210 + 0.515487i
\(302\) 2545.82i 0.485085i
\(303\) 0 0
\(304\) 1407.50 + 812.620i 0.265545 + 0.153312i
\(305\) 3676.09 + 2122.39i 0.690138 + 0.398451i
\(306\) 0 0
\(307\) 4775.43i 0.887778i −0.896082 0.443889i \(-0.853598\pi\)
0.896082 0.443889i \(-0.146402\pi\)
\(308\) −1672.89 + 3373.34i −0.309486 + 0.624070i
\(309\) 0 0
\(310\) 788.800 + 1366.24i 0.144519 + 0.250314i
\(311\) −5031.96 + 8715.62i −0.917481 + 1.58912i −0.114253 + 0.993452i \(0.536447\pi\)
−0.803228 + 0.595672i \(0.796886\pi\)
\(312\) 0 0
\(313\) −8486.84 + 4899.88i −1.53260 + 0.884848i −0.533361 + 0.845888i \(0.679071\pi\)
−0.999241 + 0.0389605i \(0.987595\pi\)
\(314\) −6200.46 −1.11437
\(315\) 0 0
\(316\) 4488.90 0.799115
\(317\) 3218.25 1858.06i 0.570205 0.329208i −0.187026 0.982355i \(-0.559885\pi\)
0.757231 + 0.653147i \(0.226552\pi\)
\(318\) 0 0
\(319\) 5544.89 9604.03i 0.973211 1.68565i
\(320\) −249.479 432.111i −0.0435822 0.0754866i
\(321\) 0 0
\(322\) −99.9516 1578.78i −0.0172984 0.273237i
\(323\) 888.306i 0.153024i
\(324\) 0 0
\(325\) −2831.02 1634.49i −0.483190 0.278970i
\(326\) −4904.49 2831.61i −0.833235 0.481068i
\(327\) 0 0
\(328\) 51.2270i 0.00862360i
\(329\) −1768.17 876.859i −0.296298 0.146939i
\(330\) 0 0
\(331\) −3354.20 5809.64i −0.556989 0.964734i −0.997746 0.0671070i \(-0.978623\pi\)
0.440757 0.897627i \(-0.354710\pi\)
\(332\) 1711.35 2964.15i 0.282899 0.489996i
\(333\) 0 0
\(334\) 6660.18 3845.26i 1.09110 0.629949i
\(335\) 1706.58 0.278330
\(336\) 0 0
\(337\) −735.278 −0.118852 −0.0594260 0.998233i \(-0.518927\pi\)
−0.0594260 + 0.998233i \(0.518927\pi\)
\(338\) 682.764 394.194i 0.109874 0.0634359i
\(339\) 0 0
\(340\) 136.358 236.178i 0.0217501 0.0376722i
\(341\) 2571.30 + 4453.62i 0.408339 + 0.707264i
\(342\) 0 0
\(343\) −1197.69 6238.52i −0.188539 0.982066i
\(344\) 2100.01i 0.329142i
\(345\) 0 0
\(346\) −3804.95 2196.79i −0.591201 0.341330i
\(347\) 9227.87 + 5327.71i 1.42760 + 0.824226i 0.996931 0.0782826i \(-0.0249437\pi\)
0.430671 + 0.902509i \(0.358277\pi\)
\(348\) 0 0
\(349\) 10961.2i 1.68120i −0.541653 0.840602i \(-0.682201\pi\)
0.541653 0.840602i \(-0.317799\pi\)
\(350\) 1317.13 + 1980.75i 0.201153 + 0.302502i
\(351\) 0 0
\(352\) −813.242 1408.58i −0.123142 0.213288i
\(353\) −1529.90 + 2649.87i −0.230676 + 0.399542i −0.958007 0.286744i \(-0.907427\pi\)
0.727331 + 0.686286i \(0.240760\pi\)
\(354\) 0 0
\(355\) 3660.21 2113.23i 0.547223 0.315939i
\(356\) −5265.54 −0.783913
\(357\) 0 0
\(358\) 4619.35 0.681956
\(359\) 5412.09 3124.67i 0.795653 0.459370i −0.0462959 0.998928i \(-0.514742\pi\)
0.841949 + 0.539557i \(0.181408\pi\)
\(360\) 0 0
\(361\) 1729.50 2995.58i 0.252150 0.436736i
\(362\) −3240.23 5612.25i −0.470450 0.814844i
\(363\) 0 0
\(364\) −3763.47 + 238.262i −0.541921 + 0.0343086i
\(365\) 7005.19i 1.00457i
\(366\) 0 0
\(367\) 10383.2 + 5994.76i 1.47684 + 0.852654i 0.999658 0.0261512i \(-0.00832512\pi\)
0.477181 + 0.878805i \(0.341658\pi\)
\(368\) 591.787 + 341.668i 0.0838288 + 0.0483986i
\(369\) 0 0
\(370\) 4276.91i 0.600935i
\(371\) −11863.7 + 751.079i −1.66019 + 0.105105i
\(372\) 0 0
\(373\) 1431.68 + 2479.73i 0.198738 + 0.344225i 0.948120 0.317914i \(-0.102982\pi\)
−0.749381 + 0.662139i \(0.769649\pi\)
\(374\) 444.493 769.884i 0.0614550 0.106443i
\(375\) 0 0
\(376\) 738.318 426.268i 0.101266 0.0584657i
\(377\) 11106.4 1.51726
\(378\) 0 0
\(379\) −7545.36 −1.02264 −0.511318 0.859392i \(-0.670843\pi\)
−0.511318 + 0.859392i \(0.670843\pi\)
\(380\) −2743.30 + 1583.84i −0.370337 + 0.213814i
\(381\) 0 0
\(382\) 109.976 190.484i 0.0147300 0.0255131i
\(383\) 1640.98 + 2842.25i 0.218929 + 0.379197i 0.954481 0.298272i \(-0.0964102\pi\)
−0.735552 + 0.677469i \(0.763077\pi\)
\(384\) 0 0
\(385\) −4063.69 6111.13i −0.537934 0.808966i
\(386\) 9997.71i 1.31832i
\(387\) 0 0
\(388\) −4298.02 2481.46i −0.562368 0.324683i
\(389\) 1010.94 + 583.664i 0.131765 + 0.0760744i 0.564433 0.825479i \(-0.309095\pi\)
−0.432669 + 0.901553i \(0.642428\pi\)
\(390\) 0 0
\(391\) 373.490i 0.0483075i
\(392\) 2530.43 + 1061.35i 0.326035 + 0.136751i
\(393\) 0 0
\(394\) 508.689 + 881.076i 0.0650441 + 0.112660i
\(395\) −4374.56 + 7576.96i −0.557235 + 0.965160i
\(396\) 0 0
\(397\) −11853.7 + 6843.75i −1.49854 + 0.865183i −0.999999 0.00168199i \(-0.999465\pi\)
−0.498543 + 0.866865i \(0.666131\pi\)
\(398\) 2410.85 0.303631
\(399\) 0 0
\(400\) −1027.50 −0.128438
\(401\) 3691.74 2131.42i 0.459742 0.265432i −0.252194 0.967677i \(-0.581152\pi\)
0.711936 + 0.702245i \(0.247819\pi\)
\(402\) 0 0
\(403\) −2575.15 + 4460.29i −0.318306 + 0.551323i
\(404\) −1003.77 1738.58i −0.123612 0.214103i
\(405\) 0 0
\(406\) −7240.25 3590.54i −0.885043 0.438906i
\(407\) 13941.7i 1.69794i
\(408\) 0 0
\(409\) 9296.72 + 5367.46i 1.12394 + 0.648909i 0.942405 0.334474i \(-0.108559\pi\)
0.181539 + 0.983384i \(0.441892\pi\)
\(410\) 86.4678 + 49.9222i 0.0104155 + 0.00601337i
\(411\) 0 0
\(412\) 1409.25i 0.168516i
\(413\) 123.020 + 1943.16i 0.0146572 + 0.231517i
\(414\) 0 0
\(415\) 3335.52 + 5777.29i 0.394540 + 0.683364i
\(416\) 814.460 1410.69i 0.0959909 0.166261i
\(417\) 0 0
\(418\) −8942.48 + 5162.94i −1.04639 + 0.604133i
\(419\) 894.104 0.104248 0.0521239 0.998641i \(-0.483401\pi\)
0.0521239 + 0.998641i \(0.483401\pi\)
\(420\) 0 0
\(421\) 4275.53 0.494956 0.247478 0.968893i \(-0.420398\pi\)
0.247478 + 0.968893i \(0.420398\pi\)
\(422\) −5416.95 + 3127.48i −0.624865 + 0.360766i
\(423\) 0 0
\(424\) 2567.44 4446.94i 0.294071 0.509345i
\(425\) −280.800 486.360i −0.0320490 0.0555105i
\(426\) 0 0
\(427\) 4480.00 9033.81i 0.507734 1.02383i
\(428\) 4319.54i 0.487833i
\(429\) 0 0
\(430\) 3544.67 + 2046.52i 0.397533 + 0.229516i
\(431\) −4324.96 2497.01i −0.483355 0.279065i 0.238459 0.971153i \(-0.423358\pi\)
−0.721813 + 0.692088i \(0.756691\pi\)
\(432\) 0 0
\(433\) 2469.93i 0.274128i −0.990562 0.137064i \(-0.956233\pi\)
0.990562 0.137064i \(-0.0437666\pi\)
\(434\) 3120.69 2075.15i 0.345156 0.229517i
\(435\) 0 0
\(436\) 970.391 + 1680.77i 0.106590 + 0.184620i
\(437\) 2169.11 3757.01i 0.237443 0.411264i
\(438\) 0 0
\(439\) −7186.67 + 4149.22i −0.781323 + 0.451097i −0.836899 0.547357i \(-0.815634\pi\)
0.0555758 + 0.998454i \(0.482301\pi\)
\(440\) 3170.11 0.343475
\(441\) 0 0
\(442\) 890.317 0.0958101
\(443\) −10784.7 + 6226.57i −1.15666 + 0.667795i −0.950500 0.310724i \(-0.899428\pi\)
−0.206155 + 0.978519i \(0.566095\pi\)
\(444\) 0 0
\(445\) 5131.42 8887.87i 0.546635 0.946799i
\(446\) −1206.04 2088.93i −0.128044 0.221779i
\(447\) 0 0
\(448\) −987.001 + 656.321i −0.104088 + 0.0692149i
\(449\) 7411.31i 0.778979i 0.921031 + 0.389489i \(0.127348\pi\)
−0.921031 + 0.389489i \(0.872652\pi\)
\(450\) 0 0
\(451\) 281.864 + 162.734i 0.0294289 + 0.0169908i
\(452\) −5843.36 3373.66i −0.608072 0.351070i
\(453\) 0 0
\(454\) 946.118i 0.0978051i
\(455\) 3265.44 6584.67i 0.336453 0.678449i
\(456\) 0 0
\(457\) 6156.75 + 10663.8i 0.630198 + 1.09154i 0.987511 + 0.157551i \(0.0503597\pi\)
−0.357313 + 0.933985i \(0.616307\pi\)
\(458\) 2049.52 3549.87i 0.209100 0.362171i
\(459\) 0 0
\(460\) −1153.43 + 665.930i −0.116910 + 0.0674982i
\(461\) −16338.5 −1.65067 −0.825334 0.564645i \(-0.809013\pi\)
−0.825334 + 0.564645i \(0.809013\pi\)
\(462\) 0 0
\(463\) 13862.3 1.39144 0.695720 0.718313i \(-0.255086\pi\)
0.695720 + 0.718313i \(0.255086\pi\)
\(464\) 3023.25 1745.47i 0.302480 0.174637i
\(465\) 0 0
\(466\) −1788.53 + 3097.83i −0.177794 + 0.307949i
\(467\) −8822.10 15280.3i −0.874172 1.51411i −0.857643 0.514246i \(-0.828072\pi\)
−0.0165291 0.999863i \(-0.505262\pi\)
\(468\) 0 0
\(469\) −256.146 4045.96i −0.0252191 0.398347i
\(470\) 1661.64i 0.163076i
\(471\) 0 0
\(472\) −728.368 420.523i −0.0710293 0.0410088i
\(473\) 11554.8 + 6671.15i 1.12323 + 0.648499i
\(474\) 0 0
\(475\) 6523.20i 0.630115i
\(476\) −580.397 287.827i −0.0558875 0.0277154i
\(477\) 0 0
\(478\) 4369.08 + 7567.47i 0.418069 + 0.724117i
\(479\) 2801.64 4852.59i 0.267245 0.462882i −0.700904 0.713255i \(-0.747220\pi\)
0.968149 + 0.250373i \(0.0805534\pi\)
\(480\) 0 0
\(481\) −12091.9 + 6981.29i −1.14625 + 0.661786i
\(482\) −5600.66 −0.529260
\(483\) 0 0
\(484\) 5009.78 0.470490
\(485\) 8377.08 4836.51i 0.784296 0.452813i
\(486\) 0 0
\(487\) 733.532 1270.51i 0.0682536 0.118219i −0.829879 0.557943i \(-0.811591\pi\)
0.898133 + 0.439725i \(0.144924\pi\)
\(488\) 2177.86 + 3772.17i 0.202023 + 0.349914i
\(489\) 0 0
\(490\) −4257.47 + 3236.87i −0.392516 + 0.298422i
\(491\) 379.554i 0.0348860i 0.999848 + 0.0174430i \(0.00555256\pi\)
−0.999848 + 0.0174430i \(0.994447\pi\)
\(492\) 0 0
\(493\) 1652.41 + 954.021i 0.150955 + 0.0871541i
\(494\) −8955.88 5170.68i −0.815676 0.470931i
\(495\) 0 0
\(496\) 1618.84i 0.146548i
\(497\) −5559.40 8360.44i −0.501757 0.754561i
\(498\) 0 0
\(499\) 6499.43 + 11257.3i 0.583075 + 1.00992i 0.995112 + 0.0987491i \(0.0314841\pi\)
−0.412037 + 0.911167i \(0.635183\pi\)
\(500\) 2950.39 5110.22i 0.263891 0.457072i
\(501\) 0 0
\(502\) 5332.14 3078.51i 0.474074 0.273707i
\(503\) 10899.0 0.966129 0.483064 0.875585i \(-0.339524\pi\)
0.483064 + 0.875585i \(0.339524\pi\)
\(504\) 0 0
\(505\) 3912.81 0.344787
\(506\) −3759.89 + 2170.77i −0.330331 + 0.190717i
\(507\) 0 0
\(508\) 2851.19 4938.40i 0.249018 0.431311i
\(509\) 8142.34 + 14103.0i 0.709043 + 1.22810i 0.965212 + 0.261467i \(0.0842062\pi\)
−0.256169 + 0.966632i \(0.582460\pi\)
\(510\) 0 0
\(511\) −16607.9 + 1051.43i −1.43775 + 0.0910227i
\(512\) 512.000i 0.0441942i
\(513\) 0 0
\(514\) 16.0301 + 9.25498i 0.00137560 + 0.000794201i
\(515\) −2378.71 1373.35i −0.203531 0.117509i
\(516\) 0 0
\(517\) 5416.55i 0.460773i
\(518\) 10139.7 641.935i 0.860061 0.0544498i
\(519\) 0 0
\(520\) 1587.43 + 2749.51i 0.133872 + 0.231873i
\(521\) 7475.64 12948.2i 0.628626 1.08881i −0.359202 0.933260i \(-0.616951\pi\)
0.987828 0.155552i \(-0.0497155\pi\)
\(522\) 0 0
\(523\) −11840.7 + 6836.22i −0.989975 + 0.571562i −0.905267 0.424844i \(-0.860329\pi\)
−0.0847081 + 0.996406i \(0.526996\pi\)
\(524\) −4614.70 −0.384721
\(525\) 0 0
\(526\) −1501.66 −0.124478
\(527\) −766.264 + 442.403i −0.0633377 + 0.0365680i
\(528\) 0 0
\(529\) −5171.49 + 8957.29i −0.425042 + 0.736195i
\(530\) 5004.09 + 8667.33i 0.410120 + 0.710349i
\(531\) 0 0
\(532\) 4166.72 + 6266.07i 0.339568 + 0.510655i
\(533\) 325.956i 0.0264892i
\(534\) 0 0
\(535\) −7291.08 4209.51i −0.589198 0.340174i
\(536\) 1516.57 + 875.594i 0.122213 + 0.0705595i
\(537\) 0 0
\(538\) 1331.12i 0.106671i
\(539\) −13878.3 + 10551.4i −1.10906 + 0.843194i
\(540\) 0 0
\(541\) −3105.32 5378.57i −0.246780 0.427436i 0.715850 0.698254i \(-0.246039\pi\)
−0.962631 + 0.270818i \(0.912706\pi\)
\(542\) 3332.08 5771.33i 0.264068 0.457379i
\(543\) 0 0
\(544\) 242.351 139.922i 0.0191006 0.0110277i
\(545\) −3782.69 −0.297308
\(546\) 0 0
\(547\) 10396.4 0.812649 0.406324 0.913729i \(-0.366810\pi\)
0.406324 + 0.913729i \(0.366810\pi\)
\(548\) 6817.75 3936.23i 0.531459 0.306838i
\(549\) 0 0
\(550\) 3264.09 5653.57i 0.253057 0.438308i
\(551\) −11081.3 19193.4i −0.856768 1.48397i
\(552\) 0 0
\(553\) 18620.0 + 9233.94i 1.43183 + 0.710067i
\(554\) 11313.0i 0.867589i
\(555\) 0 0
\(556\) 2845.48 + 1642.84i 0.217042 + 0.125309i
\(557\) 11076.9 + 6395.26i 0.842628 + 0.486492i 0.858157 0.513388i \(-0.171610\pi\)
−0.0155285 + 0.999879i \(0.504943\pi\)
\(558\) 0 0
\(559\) 13362.3i 1.01103i
\(560\) −145.965 2305.59i −0.0110146 0.173981i
\(561\) 0 0
\(562\) 4156.44 + 7199.16i 0.311973 + 0.540353i
\(563\) −3100.58 + 5370.36i −0.232103 + 0.402014i −0.958427 0.285339i \(-0.907894\pi\)
0.726324 + 0.687353i \(0.241227\pi\)
\(564\) 0 0
\(565\) 11389.0 6575.46i 0.848035 0.489613i
\(566\) 12123.9 0.900360
\(567\) 0 0
\(568\) 4336.92 0.320375
\(569\) 22006.0 12705.2i 1.62134 0.936079i 0.634774 0.772698i \(-0.281093\pi\)
0.986563 0.163381i \(-0.0522401\pi\)
\(570\) 0 0
\(571\) −4142.12 + 7174.37i −0.303577 + 0.525811i −0.976944 0.213498i \(-0.931514\pi\)
0.673366 + 0.739309i \(0.264848\pi\)
\(572\) 5174.63 + 8962.73i 0.378256 + 0.655158i
\(573\) 0 0
\(574\) 105.377 212.490i 0.00766264 0.0154515i
\(575\) 2742.69i 0.198919i
\(576\) 0 0
\(577\) −1424.66 822.525i −0.102789 0.0593452i 0.447724 0.894172i \(-0.352235\pi\)
−0.550513 + 0.834826i \(0.685568\pi\)
\(578\) −8377.10 4836.52i −0.602840 0.348050i
\(579\) 0 0
\(580\) 6804.05i 0.487108i
\(581\) 13196.1 8774.97i 0.942286 0.626587i
\(582\) 0 0
\(583\) 16312.1 + 28253.4i 1.15880 + 2.00710i
\(584\) 3594.15 6225.25i 0.254669 0.441100i
\(585\) 0 0
\(586\) −8832.83 + 5099.64i −0.622664 + 0.359495i
\(587\) −21115.2 −1.48470 −0.742350 0.670013i \(-0.766289\pi\)
−0.742350 + 0.670013i \(0.766289\pi\)
\(588\) 0 0
\(589\) 10277.3 0.718964
\(590\) 1419.63 819.623i 0.0990597 0.0571921i
\(591\) 0 0
\(592\) −2194.35 + 3800.72i −0.152343 + 0.263866i
\(593\) −6622.57 11470.6i −0.458611 0.794338i 0.540277 0.841488i \(-0.318320\pi\)
−0.998888 + 0.0471494i \(0.984986\pi\)
\(594\) 0 0
\(595\) 1051.45 699.174i 0.0724455 0.0481737i
\(596\) 10795.8i 0.741971i
\(597\) 0 0
\(598\) −3765.52 2174.02i −0.257498 0.148666i
\(599\) −11800.0 6812.73i −0.804900 0.464709i 0.0402819 0.999188i \(-0.487174\pi\)
−0.845182 + 0.534479i \(0.820508\pi\)
\(600\) 0 0
\(601\) 15150.8i 1.02831i −0.857697 0.514156i \(-0.828105\pi\)
0.857697 0.514156i \(-0.171895\pi\)
\(602\) 4319.85 8710.87i 0.292465 0.589748i
\(603\) 0 0
\(604\) 2545.82 + 4409.49i 0.171503 + 0.297052i
\(605\) −4882.17 + 8456.17i −0.328080 + 0.568251i
\(606\) 0 0
\(607\) −3988.38 + 2302.69i −0.266694 + 0.153976i −0.627384 0.778710i \(-0.715875\pi\)
0.360690 + 0.932686i \(0.382541\pi\)
\(608\) −3250.48 −0.216816
\(609\) 0 0
\(610\) −8489.56 −0.563495
\(611\) −4697.90 + 2712.33i −0.311058 + 0.179590i
\(612\) 0 0
\(613\) 2333.08 4041.01i 0.153723 0.266256i −0.778870 0.627185i \(-0.784207\pi\)
0.932593 + 0.360929i \(0.117540\pi\)
\(614\) 4775.43 + 8271.28i 0.313877 + 0.543651i
\(615\) 0 0
\(616\) −475.811 7515.68i −0.0311217 0.491583i
\(617\) 16316.4i 1.06463i −0.846548 0.532313i \(-0.821323\pi\)
0.846548 0.532313i \(-0.178677\pi\)
\(618\) 0 0
\(619\) 4523.82 + 2611.83i 0.293744 + 0.169593i 0.639629 0.768684i \(-0.279088\pi\)
−0.345885 + 0.938277i \(0.612421\pi\)
\(620\) −2732.48 1577.60i −0.176999 0.102190i
\(621\) 0 0
\(622\) 20127.9i 1.29751i
\(623\) −21841.5 10831.5i −1.40459 0.696559i
\(624\) 0 0
\(625\) 1736.79 + 3008.20i 0.111154 + 0.192525i
\(626\) 9799.76 16973.7i 0.625682 1.08371i
\(627\) 0 0
\(628\) 10739.5 6200.46i 0.682409 0.393989i
\(629\) −2398.72 −0.152056
\(630\) 0 0
\(631\) −12467.8 −0.786584 −0.393292 0.919414i \(-0.628664\pi\)
−0.393292 + 0.919414i \(0.628664\pi\)
\(632\) −7775.00 + 4488.90i −0.489356 + 0.282530i
\(633\) 0 0
\(634\) −3716.11 + 6436.50i −0.232785 + 0.403196i
\(635\) 5557.12 + 9625.22i 0.347288 + 0.601520i
\(636\) 0 0
\(637\) −16101.0 6753.37i −1.00149 0.420060i
\(638\) 22179.6i 1.37633i
\(639\) 0 0
\(640\) 864.221 + 498.958i 0.0533771 + 0.0308173i
\(641\) 5896.71 + 3404.47i 0.363348 + 0.209779i 0.670548 0.741866i \(-0.266059\pi\)
−0.307200 + 0.951645i \(0.599392\pi\)
\(642\) 0 0
\(643\) 8746.71i 0.536449i 0.963356 + 0.268224i \(0.0864369\pi\)
−0.963356 + 0.268224i \(0.913563\pi\)
\(644\) 1751.91 + 2634.58i 0.107197 + 0.161207i
\(645\) 0 0
\(646\) −888.306 1538.59i −0.0541020 0.0937075i
\(647\) −5728.79 + 9922.55i −0.348102 + 0.602930i −0.985912 0.167263i \(-0.946507\pi\)
0.637810 + 0.770193i \(0.279840\pi\)
\(648\) 0 0
\(649\) 4627.65 2671.77i 0.279894 0.161597i
\(650\) 6537.97 0.394523
\(651\) 0 0
\(652\) 11326.4 0.680333
\(653\) 19349.2 11171.3i 1.15956 0.669472i 0.208361 0.978052i \(-0.433187\pi\)
0.951198 + 0.308580i \(0.0998537\pi\)
\(654\) 0 0
\(655\) 4497.15 7789.29i 0.268272 0.464661i
\(656\) 51.2270 + 88.7278i 0.00304890 + 0.00528085i
\(657\) 0 0
\(658\) 3939.41 249.401i 0.233395 0.0147761i
\(659\) 6944.96i 0.410527i −0.978707 0.205263i \(-0.934195\pi\)
0.978707 0.205263i \(-0.0658051\pi\)
\(660\) 0 0
\(661\) −16338.1 9432.82i −0.961391 0.555059i −0.0647898 0.997899i \(-0.520638\pi\)
−0.896601 + 0.442840i \(0.853971\pi\)
\(662\) 11619.3 + 6708.40i 0.682170 + 0.393851i
\(663\) 0 0
\(664\) 6845.41i 0.400080i
\(665\) −14637.3 + 926.675i −0.853548 + 0.0540374i
\(666\) 0 0
\(667\) −4659.16 8069.90i −0.270470 0.468468i
\(668\) −7690.51 + 13320.4i −0.445441 + 0.771527i
\(669\) 0 0
\(670\) −2955.89 + 1706.58i −0.170442 + 0.0984045i
\(671\) −27673.9 −1.59216
\(672\) 0 0
\(673\) 5622.15 0.322018 0.161009 0.986953i \(-0.448525\pi\)
0.161009 + 0.986953i \(0.448525\pi\)
\(674\) 1273.54 735.278i 0.0727817 0.0420206i
\(675\) 0 0
\(676\) −788.388 + 1365.53i −0.0448560 + 0.0776928i
\(677\) −13723.5 23769.8i −0.779081 1.34941i −0.932472 0.361243i \(-0.882353\pi\)
0.153391 0.988166i \(-0.450981\pi\)
\(678\) 0 0
\(679\) −12723.7 19134.4i −0.719133 1.08146i
\(680\) 545.430i 0.0307593i
\(681\) 0 0
\(682\) −8907.24 5142.60i −0.500111 0.288739i
\(683\) 27472.6 + 15861.3i 1.53911 + 0.888604i 0.998891 + 0.0470784i \(0.0149911\pi\)
0.540217 + 0.841526i \(0.318342\pi\)
\(684\) 0 0
\(685\) 15343.9i 0.855852i
\(686\) 8312.97 + 9607.75i 0.462669 + 0.534731i
\(687\) 0 0
\(688\) 2100.01 + 3637.32i 0.116369 + 0.201558i
\(689\) −16336.6 + 28295.7i −0.903299 + 1.56456i
\(690\) 0 0
\(691\) 6896.96 3981.96i 0.379700 0.219220i −0.297988 0.954570i \(-0.596315\pi\)
0.677688 + 0.735350i \(0.262982\pi\)
\(692\) 8787.16 0.482714
\(693\) 0 0
\(694\) −21310.8 −1.16563
\(695\) −5546.01 + 3201.99i −0.302694 + 0.174760i
\(696\) 0 0
\(697\) −27.9991 + 48.4959i −0.00152158 + 0.00263545i
\(698\) 10961.2 + 18985.4i 0.594395 + 1.02952i
\(699\) 0 0
\(700\) −4262.09 2113.63i −0.230131 0.114125i
\(701\) 21374.8i 1.15166i −0.817568 0.575831i \(-0.804678\pi\)
0.817568 0.575831i \(-0.195322\pi\)
\(702\) 0 0
\(703\) 24129.2 + 13931.0i 1.29453 + 0.747395i
\(704\) 2817.15 + 1626.48i 0.150817 + 0.0870744i
\(705\) 0 0
\(706\) 6119.61i 0.326225i
\(707\) −587.286 9276.47i −0.0312407 0.493462i
\(708\) 0 0
\(709\) −3514.63 6087.51i −0.186170 0.322456i 0.757800 0.652487i \(-0.226274\pi\)
−0.943970 + 0.330031i \(0.892941\pi\)
\(710\) −4226.45 + 7320.43i −0.223403 + 0.386945i
\(711\) 0 0
\(712\) 9120.18 5265.54i 0.480047 0.277155i
\(713\) 4321.13 0.226967
\(714\) 0 0
\(715\) −20171.3 −1.05505
\(716\) −8000.95 + 4619.35i −0.417611 + 0.241108i
\(717\) 0 0
\(718\) −6249.35 + 10824.2i −0.324824 + 0.562612i
\(719\) 5369.20 + 9299.72i 0.278494 + 0.482366i 0.971011 0.239036i \(-0.0768314\pi\)
−0.692517 + 0.721402i \(0.743498\pi\)
\(720\) 0 0
\(721\) −2898.90 + 5845.57i −0.149738 + 0.301942i
\(722\) 6917.98i 0.356594i
\(723\) 0 0
\(724\) 11224.5 + 6480.47i 0.576181 + 0.332658i
\(725\) 12134.4 + 7005.77i 0.621598 + 0.358880i
\(726\) 0 0
\(727\) 15722.6i 0.802092i −0.916058 0.401046i \(-0.868647\pi\)
0.916058 0.401046i \(-0.131353\pi\)
\(728\) 6280.26 4176.15i 0.319728 0.212608i
\(729\) 0 0
\(730\) 7005.19 + 12133.4i 0.355170 + 0.615172i
\(731\) −1147.80 + 1988.05i −0.0580751 + 0.100589i
\(732\) 0 0
\(733\) −14966.9 + 8641.17i −0.754184 + 0.435428i −0.827204 0.561902i \(-0.810070\pi\)
0.0730197 + 0.997331i \(0.476736\pi\)
\(734\) −23979.0 −1.20583
\(735\) 0 0
\(736\) −1366.67 −0.0684459
\(737\) −9635.47 + 5563.04i −0.481584 + 0.278043i
\(738\) 0 0
\(739\) 17235.3 29852.5i 0.857932 1.48598i −0.0159660 0.999873i \(-0.505082\pi\)
0.873898 0.486109i \(-0.161584\pi\)
\(740\) −4276.91 7407.82i −0.212462 0.367996i
\(741\) 0 0
\(742\) 19797.4 13164.6i 0.979495 0.651330i
\(743\) 33600.2i 1.65904i −0.558474 0.829522i \(-0.688613\pi\)
0.558474 0.829522i \(-0.311387\pi\)
\(744\) 0 0
\(745\) −18222.6 10520.8i −0.896142 0.517388i
\(746\) −4959.47 2863.35i −0.243404 0.140529i
\(747\) 0 0
\(748\) 1777.97i 0.0869105i
\(749\) −8885.55 + 17917.5i −0.433472 + 0.874087i
\(750\) 0 0
\(751\) −17479.2 30274.9i −0.849303 1.47104i −0.881831 0.471565i \(-0.843689\pi\)
0.0325279 0.999471i \(-0.489644\pi\)
\(752\) −852.536 + 1476.64i −0.0413415 + 0.0716056i
\(753\) 0 0
\(754\) −19236.8 + 11106.4i −0.929131 + 0.536434i
\(755\) −9923.90 −0.478368
\(756\) 0 0
\(757\) 38297.1 1.83875 0.919374 0.393386i \(-0.128696\pi\)
0.919374 + 0.393386i \(0.128696\pi\)
\(758\) 13068.9 7545.36i 0.626234 0.361556i
\(759\) 0 0
\(760\) 3167.68 5486.59i 0.151189 0.261868i
\(761\) 9539.02 + 16522.1i 0.454388 + 0.787023i 0.998653 0.0518907i \(-0.0165247\pi\)
−0.544265 + 0.838913i \(0.683191\pi\)
\(762\) 0 0
\(763\) 567.757 + 8967.99i 0.0269386 + 0.425509i
\(764\) 439.903i 0.0208313i
\(765\) 0 0
\(766\) −5684.51 3281.95i −0.268133 0.154806i
\(767\) 4634.58 + 2675.78i 0.218181 + 0.125967i
\(768\) 0 0
\(769\) 12553.3i 0.588667i 0.955703 + 0.294334i \(0.0950977\pi\)
−0.955703 + 0.294334i \(0.904902\pi\)
\(770\) 13149.6 + 6521.10i 0.615429 + 0.305200i
\(771\) 0 0
\(772\) −9997.71 17316.5i −0.466095 0.807300i
\(773\) 4533.66 7852.53i 0.210950 0.365376i −0.741062 0.671437i \(-0.765678\pi\)
0.952012 + 0.306060i \(0.0990109\pi\)
\(774\) 0 0
\(775\) −5626.99 + 3248.74i −0.260810 + 0.150579i
\(776\) 9925.85 0.459172
\(777\) 0 0
\(778\) −2334.66 −0.107585
\(779\) 563.297 325.220i 0.0259078 0.0149579i
\(780\) 0 0
\(781\) −13777.2 + 23862.8i −0.631226 + 1.09331i
\(782\) −373.490 646.904i −0.0170793 0.0295822i
\(783\) 0 0
\(784\) −5444.18 + 692.108i −0.248004 + 0.0315282i
\(785\) 24170.1i 1.09894i
\(786\) 0 0
\(787\) 1848.67 + 1067.33i 0.0837333 + 0.0483435i 0.541282 0.840841i \(-0.317939\pi\)
−0.457549 + 0.889185i \(0.651272\pi\)
\(788\) −1762.15 1017.38i −0.0796625 0.0459932i
\(789\) 0 0
\(790\) 17498.2i 0.788050i
\(791\) −17298.5 26014.1i −0.777577 1.16935i
\(792\) 0 0
\(793\) −13857.7 24002.2i −0.620556 1.07483i
\(794\) 13687.5 23707.4i 0.611777 1.05963i
\(795\) 0 0
\(796\) −4175.72 + 2410.85i −0.185935 + 0.107350i
\(797\) −16730.6 −0.743574 −0.371787 0.928318i \(-0.621255\pi\)
−0.371787 + 0.928318i \(0.621255\pi\)
\(798\) 0 0
\(799\) −931.939 −0.0412636
\(800\) 1779.69 1027.50i 0.0786518 0.0454096i
\(801\) 0 0
\(802\) −4262.85 + 7383.47i −0.187689 + 0.325087i
\(803\) 22835.2 + 39551.8i 1.00353 + 1.73817i
\(804\) 0 0
\(805\) −6154.28 + 389.623i −0.269453 + 0.0170589i
\(806\) 10300.6i 0.450153i
\(807\) 0 0
\(808\) 3477.16 + 2007.54i 0.151394 + 0.0874072i
\(809\) −21928.9 12660.6i −0.953001 0.550215i −0.0589890 0.998259i \(-0.518788\pi\)
−0.894012 + 0.448043i \(0.852121\pi\)
\(810\) 0 0
\(811\) 23863.6i 1.03325i −0.856212 0.516625i \(-0.827188\pi\)
0.856212 0.516625i \(-0.172812\pi\)
\(812\) 16131.0 1021.24i 0.697152 0.0441362i
\(813\) 0 0
\(814\) −13941.7 24147.7i −0.600314 1.03977i
\(815\) −11037.9 + 19118.3i −0.474407 + 0.821697i
\(816\) 0 0
\(817\) 23091.9 13332.1i 0.988841 0.570908i
\(818\) −21469.8 −0.917696
\(819\) 0 0
\(820\) −199.689 −0.00850419
\(821\) 20798.2 12007.9i 0.884121 0.510447i 0.0121059 0.999927i \(-0.496146\pi\)
0.872015 + 0.489479i \(0.162813\pi\)
\(822\) 0 0
\(823\) 16008.0 27726.6i 0.678011 1.17435i −0.297569 0.954700i \(-0.596176\pi\)
0.975579 0.219648i \(-0.0704910\pi\)
\(824\) −1409.25 2440.89i −0.0595794 0.103195i
\(825\) 0 0
\(826\) −2156.24 3242.63i −0.0908294 0.136593i
\(827\) 33661.4i 1.41538i 0.706522 + 0.707691i \(0.250263\pi\)
−0.706522 + 0.707691i \(0.749737\pi\)
\(828\) 0 0
\(829\) 2750.33 + 1587.90i 0.115227 + 0.0665261i 0.556506 0.830844i \(-0.312142\pi\)
−0.441279 + 0.897370i \(0.645475\pi\)
\(830\) −11554.6 6671.04i −0.483211 0.278982i
\(831\) 0 0
\(832\) 3257.84i 0.135752i
\(833\) −1815.41 2387.82i −0.0755107 0.0993194i
\(834\) 0 0
\(835\) −14989.2 25962.1i −0.621226 1.07600i
\(836\) 10325.9 17885.0i 0.427187 0.739909i
\(837\) 0 0
\(838\) −1548.63 + 894.104i −0.0638385 + 0.0368572i
\(839\) 40349.4 1.66033 0.830165 0.557518i \(-0.188246\pi\)
0.830165 + 0.557518i \(0.188246\pi\)
\(840\) 0 0
\(841\) −23215.3 −0.951877
\(842\) −7405.43 + 4275.53i −0.303097 + 0.174993i
\(843\) 0 0
\(844\) 6254.96 10833.9i 0.255100 0.441846i
\(845\) −1536.61 2661.49i −0.0625575 0.108353i
\(846\) 0 0
\(847\) 20780.6 + 10305.4i 0.843012 + 0.418062i
\(848\) 10269.8i 0.415879i
\(849\) 0 0
\(850\) 972.721 + 561.601i 0.0392518 + 0.0226621i
\(851\) 10145.2 + 5857.33i 0.408664 + 0.235942i
\(852\) 0 0
\(853\) 46022.2i 1.84733i −0.383204 0.923664i \(-0.625179\pi\)
0.383204 0.923664i \(-0.374821\pi\)
\(854\) 1274.23 + 20127.0i 0.0510575 + 0.806478i
\(855\) 0 0
\(856\) −4319.54 7481.66i −0.172475 0.298736i
\(857\) −7564.70 + 13102.4i −0.301523 + 0.522253i −0.976481 0.215603i \(-0.930828\pi\)
0.674958 + 0.737856i \(0.264162\pi\)
\(858\) 0 0
\(859\) 39374.0 22732.6i 1.56394 0.902941i 0.567087 0.823658i \(-0.308070\pi\)
0.996852 0.0792832i \(-0.0252631\pi\)
\(860\) −8186.07 −0.324585
\(861\) 0 0
\(862\) 9988.06 0.394657
\(863\) 5596.89 3231.36i 0.220765 0.127459i −0.385539 0.922691i \(-0.625985\pi\)
0.606304 + 0.795233i \(0.292651\pi\)
\(864\) 0 0
\(865\) −8563.34 + 14832.1i −0.336604 + 0.583015i
\(866\) 2469.93 + 4278.05i 0.0969189 + 0.167868i
\(867\) 0 0
\(868\) −3330.04 + 6714.95i −0.130218 + 0.262581i
\(869\) 57040.0i 2.22664i
\(870\) 0 0
\(871\) −9649.91 5571.38i −0.375402 0.216738i
\(872\) −3361.53 1940.78i −0.130546 0.0753706i
\(873\) 0 0
\(874\) 8676.45i 0.335796i
\(875\) 22750.3 15128.1i 0.878970 0.584485i
\(876\) 0 0
\(877\) 16030.7 + 27766.0i 0.617240 + 1.06909i 0.989987 + 0.141158i \(0.0450826\pi\)
−0.372747 + 0.927933i \(0.621584\pi\)
\(878\) 8298.45 14373.3i 0.318974 0.552479i
\(879\) 0 0
\(880\) −5490.79 + 3170.11i −0.210335 + 0.121437i
\(881\) 17364.4 0.664042 0.332021 0.943272i \(-0.392270\pi\)
0.332021 + 0.943272i \(0.392270\pi\)
\(882\) 0 0
\(883\) −22921.5 −0.873578 −0.436789 0.899564i \(-0.643884\pi\)
−0.436789 + 0.899564i \(0.643884\pi\)
\(884\) −1542.07 + 890.317i −0.0586715 + 0.0338740i
\(885\) 0 0
\(886\) 12453.1 21569.5i 0.472202 0.817879i
\(887\) −19471.0 33724.7i −0.737058 1.27662i −0.953814 0.300397i \(-0.902881\pi\)
0.216756 0.976226i \(-0.430452\pi\)
\(888\) 0 0
\(889\) 21985.3 14619.5i 0.829432 0.551543i
\(890\) 20525.7i 0.773058i
\(891\) 0 0
\(892\) 4177.85 + 2412.08i 0.156822 + 0.0905410i
\(893\) 9374.56 + 5412.41i 0.351297 + 0.202821i
\(894\) 0 0
\(895\) 18006.8i 0.672513i
\(896\) 1053.21 2123.78i 0.0392695 0.0791859i
\(897\) 0 0
\(898\) −7411.31 12836.8i −0.275411 0.477025i
\(899\) 11037.6 19117.7i 0.409484 0.709246i
\(900\) 0 0
\(901\) −4861.12 + 2806.57i −0.179742 + 0.103774i
\(902\) −650.937 −0.0240286
\(903\) 0 0
\(904\) 13494.7 0.496488
\(905\) −21877.2 + 12630.8i −0.803560 + 0.463936i
\(906\) 0 0
\(907\) −19008.5 + 32923.6i −0.695882 + 1.20530i 0.274000 + 0.961730i \(0.411653\pi\)
−0.969882 + 0.243574i \(0.921680\pi\)
\(908\) 946.118 + 1638.72i 0.0345793 + 0.0598931i
\(909\) 0 0
\(910\) 928.773 + 14670.4i 0.0338335 + 0.534418i
\(911\) 22877.1i 0.832000i −0.909365 0.416000i \(-0.863432\pi\)
0.909365 0.416000i \(-0.136568\pi\)
\(912\) 0 0
\(913\) −37665.1 21746.0i −1.36532 0.788266i
\(914\) −21327.6 12313.5i −0.771832 0.445617i
\(915\) 0 0
\(916\) 8198.07i 0.295712i
\(917\) −19141.8 9492.70i −0.689333 0.341850i
\(918\) 0 0
\(919\) 314.315 + 544.409i 0.0112821 + 0.0195412i 0.871611 0.490198i \(-0.163075\pi\)
−0.860329 + 0.509739i \(0.829742\pi\)
\(920\) 1331.86 2306.85i 0.0477284 0.0826680i
\(921\) 0 0
\(922\) 28299.0 16338.5i 1.01082 0.583599i
\(923\) −27595.7 −0.984099
\(924\) 0 0
\(925\) −17614.8 −0.626132
\(926\) −24010.2 + 13862.3i −0.852079 + 0.491948i
\(927\) 0 0
\(928\) −3490.95 + 6046.50i −0.123487 + 0.213886i
\(929\) −21843.2 37833.5i −0.771423 1.33614i −0.936783 0.349911i \(-0.886212\pi\)
0.165359 0.986233i \(-0.447122\pi\)
\(930\) 0 0
\(931\) 4393.91 + 34562.9i 0.154677 + 1.21671i
\(932\) 7154.13i 0.251439i
\(933\) 0 0
\(934\) 30560.7 + 17644.2i 1.07064 + 0.618133i
\(935\) −3001.09 1732.68i −0.104969 0.0606040i
\(936\) 0 0
\(937\) 27163.5i 0.947059i 0.880778 + 0.473529i \(0.157020\pi\)
−0.880778 + 0.473529i \(0.842980\pi\)
\(938\) 4489.62 + 6751.66i 0.156281 + 0.235021i
\(939\) 0 0
\(940\) −1661.64 2878.05i −0.0576561 0.0998633i
\(941\) −13299.2 + 23034.9i −0.460725 + 0.797999i −0.998997 0.0447721i \(-0.985744\pi\)
0.538272 + 0.842771i \(0.319077\pi\)
\(942\) 0 0
\(943\) 236.840 136.739i 0.00817875 0.00472200i
\(944\) 1682.09 0.0579952
\(945\) 0 0
\(946\) −26684.6 −0.917116
\(947\) −17614.5 + 10169.7i −0.604429 + 0.348967i −0.770782 0.637099i \(-0.780134\pi\)
0.166353 + 0.986066i \(0.446801\pi\)
\(948\) 0 0
\(949\) −22869.5 + 39611.1i −0.782270 + 1.35493i
\(950\) −6523.20 11298.5i −0.222779 0.385865i
\(951\) 0 0
\(952\) 1293.10 81.8654i 0.0440228 0.00278705i
\(953\) 45566.5i 1.54884i 0.632673 + 0.774419i \(0.281958\pi\)
−0.632673 + 0.774419i \(0.718042\pi\)
\(954\) 0 0
\(955\) −742.527 428.698i −0.0251598 0.0145260i
\(956\) −15134.9 8738.16i −0.512028 0.295620i
\(957\) 0 0
\(958\) 11206.6i 0.377942i
\(959\) 36377.2 2303.01i 1.22490 0.0775475i
\(960\) 0 0
\(961\) −9777.08 16934.4i −0.328189 0.568440i
\(962\) 13962.6 24183.9i 0.467954 0.810519i
\(963\) 0 0
\(964\) 9700.63 5600.66i 0.324104 0.187121i
\(965\) 38972.2 1.30006
\(966\) 0 0
\(967\) −34217.5 −1.13791 −0.568955 0.822368i \(-0.692652\pi\)
−0.568955 + 0.822368i \(0.692652\pi\)
\(968\) −8677.19 + 5009.78i −0.288115 + 0.166343i
\(969\) 0 0
\(970\) −9673.02 + 16754.2i −0.320187 + 0.554581i
\(971\) −16355.4 28328.5i −0.540547 0.936255i −0.998873 0.0474705i \(-0.984884\pi\)
0.458326 0.888784i \(-0.348449\pi\)
\(972\) 0 0
\(973\) 8423.68 + 12667.9i 0.277544 + 0.417382i
\(974\) 2934.13i 0.0965252i
\(975\) 0 0
\(976\) −7544.34 4355.73i −0.247427 0.142852i
\(977\) −14095.0 8137.73i −0.461554 0.266478i 0.251144 0.967950i \(-0.419193\pi\)
−0.712697 + 0.701472i \(0.752527\pi\)
\(978\) 0 0
\(979\) 66908.7i 2.18428i
\(980\) 4137.28 9863.89i 0.134858 0.321521i
\(981\) 0 0
\(982\) −379.554 657.406i −0.0123341 0.0213632i
\(983\) 16406.9 28417.6i 0.532349 0.922056i −0.466938 0.884290i \(-0.654643\pi\)
0.999287 0.0377653i \(-0.0120239\pi\)
\(984\) 0 0
\(985\) 3434.53 1982.93i 0.111100 0.0641435i
\(986\) −3816.09 −0.123254
\(987\) 0 0
\(988\) 20682.7 0.665997
\(989\) 9709.04 5605.52i 0.312163 0.180228i
\(990\) 0 0
\(991\) 4299.83 7447.52i 0.137829 0.238727i −0.788846 0.614591i \(-0.789321\pi\)
0.926675 + 0.375865i \(0.122654\pi\)
\(992\) −1618.84 2803.91i −0.0518126 0.0897420i
\(993\) 0 0
\(994\) 17989.6 + 8921.31i 0.574040 + 0.284675i
\(995\) 9397.78i 0.299427i
\(996\) 0 0
\(997\) 27178.0 + 15691.2i 0.863326 + 0.498441i 0.865125 0.501557i \(-0.167239\pi\)
−0.00179867 + 0.999998i \(0.500573\pi\)
\(998\) −22514.7 12998.9i −0.714119 0.412297i
\(999\) 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 378.4.k.c.269.3 yes 16
3.2 odd 2 inner 378.4.k.c.269.6 yes 16
7.5 odd 6 inner 378.4.k.c.215.6 yes 16
21.5 even 6 inner 378.4.k.c.215.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.4.k.c.215.3 16 21.5 even 6 inner
378.4.k.c.215.6 yes 16 7.5 odd 6 inner
378.4.k.c.269.3 yes 16 1.1 even 1 trivial
378.4.k.c.269.6 yes 16 3.2 odd 2 inner