Properties

Label 378.4.g.f.109.1
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
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] = [378,4,Mod(109,378)]
 
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([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.109");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), 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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(-0.338925 - 0.587036i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.f.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-8.05411 - 13.9501i) q^{5} +(6.77345 - 17.2372i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-8.05411 - 13.9501i) q^{5} +(6.77345 - 17.2372i) q^{7} -8.00000 q^{8} +(16.1082 - 27.9003i) q^{10} +(-6.04111 + 10.4635i) q^{11} -39.7518 q^{13} +(36.6291 - 5.50523i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-62.7914 + 108.758i) q^{17} +(62.5108 + 108.272i) q^{19} +64.4329 q^{20} -24.1645 q^{22} +(24.1212 + 41.7792i) q^{23} +(-67.2373 + 116.458i) q^{25} +(-39.7518 - 68.8521i) q^{26} +(46.1645 + 57.9383i) q^{28} -93.0461 q^{29} +(-11.3809 + 19.7123i) q^{31} +(16.0000 - 27.7128i) q^{32} -251.166 q^{34} +(-295.015 + 44.3397i) q^{35} +(200.361 + 347.035i) q^{37} +(-125.022 + 216.544i) q^{38} +(64.4329 + 111.601i) q^{40} -354.070 q^{41} +225.918 q^{43} +(-24.1645 - 41.8541i) q^{44} +(-48.2424 + 83.5583i) q^{46} +(-124.107 - 214.960i) q^{47} +(-251.241 - 233.510i) q^{49} -268.949 q^{50} +(79.5036 - 137.704i) q^{52} +(-167.460 + 290.050i) q^{53} +194.623 q^{55} +(-54.1876 + 137.897i) q^{56} +(-93.0461 - 161.161i) q^{58} +(91.4364 - 158.373i) q^{59} +(-304.912 - 528.123i) q^{61} -45.5237 q^{62} +64.0000 q^{64} +(320.165 + 554.542i) q^{65} +(-59.1898 + 102.520i) q^{67} +(-251.166 - 435.032i) q^{68} +(-371.814 - 466.641i) q^{70} -81.4905 q^{71} +(489.415 - 847.692i) q^{73} +(-400.721 + 694.069i) q^{74} -500.086 q^{76} +(139.442 + 175.006i) q^{77} +(346.714 + 600.527i) q^{79} +(-128.866 + 223.202i) q^{80} +(-354.070 - 613.268i) q^{82} -1409.05 q^{83} +2022.92 q^{85} +(225.918 + 391.301i) q^{86} +(48.3289 - 83.7081i) q^{88} +(605.706 + 1049.11i) q^{89} +(-269.256 + 685.209i) q^{91} -192.970 q^{92} +(248.215 - 429.921i) q^{94} +(1006.94 - 1744.07i) q^{95} -1336.50 q^{97} +(153.211 - 668.672i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8} + 4 q^{10} + 32 q^{11} - 4 q^{13} + 36 q^{14} - 64 q^{16} - 58 q^{17} + 70 q^{19} + 16 q^{20} + 128 q^{22} + 86 q^{23} - 156 q^{25} - 4 q^{26} + 48 q^{28} - 212 q^{29} - 64 q^{31} + 128 q^{32} - 232 q^{34} + 8 q^{35} - 146 q^{37} - 140 q^{38} + 16 q^{40} - 780 q^{41} + 880 q^{43} + 128 q^{44} - 172 q^{46} - 306 q^{47} + 50 q^{49} - 624 q^{50} + 8 q^{52} - 90 q^{53} - 64 q^{55} - 48 q^{56} - 212 q^{58} + 148 q^{59} - 364 q^{61} - 256 q^{62} + 512 q^{64} + 1296 q^{65} - 954 q^{67} - 232 q^{68} + 20 q^{70} - 1360 q^{71} - 54 q^{73} + 292 q^{74} - 560 q^{76} + 2224 q^{77} - 226 q^{79} - 32 q^{80} - 780 q^{82} - 3136 q^{83} + 3920 q^{85} + 880 q^{86} - 256 q^{88} - 1458 q^{89} + 3836 q^{91} - 688 q^{92} + 612 q^{94} + 1310 q^{95} - 4344 q^{97} + 776 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −8.05411 13.9501i −0.720381 1.24774i −0.960847 0.277080i \(-0.910633\pi\)
0.240466 0.970658i \(-0.422700\pi\)
\(6\) 0 0
\(7\) 6.77345 17.2372i 0.365732 0.930720i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 16.1082 27.9003i 0.509387 0.882283i
\(11\) −6.04111 + 10.4635i −0.165588 + 0.286806i −0.936864 0.349694i \(-0.886285\pi\)
0.771276 + 0.636501i \(0.219619\pi\)
\(12\) 0 0
\(13\) −39.7518 −0.848089 −0.424045 0.905641i \(-0.639390\pi\)
−0.424045 + 0.905641i \(0.639390\pi\)
\(14\) 36.6291 5.50523i 0.699253 0.105095i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −62.7914 + 108.758i −0.895833 + 1.55163i −0.0630630 + 0.998010i \(0.520087\pi\)
−0.832770 + 0.553619i \(0.813246\pi\)
\(18\) 0 0
\(19\) 62.5108 + 108.272i 0.754787 + 1.30733i 0.945480 + 0.325680i \(0.105593\pi\)
−0.190693 + 0.981650i \(0.561073\pi\)
\(20\) 64.4329 0.720381
\(21\) 0 0
\(22\) −24.1645 −0.234176
\(23\) 24.1212 + 41.7792i 0.218679 + 0.378763i 0.954404 0.298517i \(-0.0964919\pi\)
−0.735725 + 0.677280i \(0.763159\pi\)
\(24\) 0 0
\(25\) −67.2373 + 116.458i −0.537899 + 0.931668i
\(26\) −39.7518 68.8521i −0.299845 0.519346i
\(27\) 0 0
\(28\) 46.1645 + 57.9383i 0.311581 + 0.391047i
\(29\) −93.0461 −0.595801 −0.297900 0.954597i \(-0.596286\pi\)
−0.297900 + 0.954597i \(0.596286\pi\)
\(30\) 0 0
\(31\) −11.3809 + 19.7123i −0.0659379 + 0.114208i −0.897110 0.441808i \(-0.854337\pi\)
0.831172 + 0.556016i \(0.187671\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −251.166 −1.26690
\(35\) −295.015 + 44.3397i −1.42476 + 0.214137i
\(36\) 0 0
\(37\) 200.361 + 347.035i 0.890245 + 1.54195i 0.839581 + 0.543234i \(0.182800\pi\)
0.0506642 + 0.998716i \(0.483866\pi\)
\(38\) −125.022 + 216.544i −0.533715 + 0.924422i
\(39\) 0 0
\(40\) 64.4329 + 111.601i 0.254693 + 0.441142i
\(41\) −354.070 −1.34870 −0.674348 0.738414i \(-0.735575\pi\)
−0.674348 + 0.738414i \(0.735575\pi\)
\(42\) 0 0
\(43\) 225.918 0.801212 0.400606 0.916250i \(-0.368800\pi\)
0.400606 + 0.916250i \(0.368800\pi\)
\(44\) −24.1645 41.8541i −0.0827938 0.143403i
\(45\) 0 0
\(46\) −48.2424 + 83.5583i −0.154630 + 0.267826i
\(47\) −124.107 214.960i −0.385169 0.667132i 0.606624 0.794989i \(-0.292523\pi\)
−0.991793 + 0.127857i \(0.959190\pi\)
\(48\) 0 0
\(49\) −251.241 233.510i −0.732481 0.680788i
\(50\) −268.949 −0.760704
\(51\) 0 0
\(52\) 79.5036 137.704i 0.212022 0.367233i
\(53\) −167.460 + 290.050i −0.434008 + 0.751724i −0.997214 0.0745926i \(-0.976234\pi\)
0.563206 + 0.826316i \(0.309568\pi\)
\(54\) 0 0
\(55\) 194.623 0.477145
\(56\) −54.1876 + 137.897i −0.129306 + 0.329059i
\(57\) 0 0
\(58\) −93.0461 161.161i −0.210647 0.364852i
\(59\) 91.4364 158.373i 0.201763 0.349464i −0.747334 0.664449i \(-0.768666\pi\)
0.949097 + 0.314985i \(0.102000\pi\)
\(60\) 0 0
\(61\) −304.912 528.123i −0.639999 1.10851i −0.985432 0.170068i \(-0.945601\pi\)
0.345433 0.938443i \(-0.387732\pi\)
\(62\) −45.5237 −0.0932502
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 320.165 + 554.542i 0.610948 + 1.05819i
\(66\) 0 0
\(67\) −59.1898 + 102.520i −0.107928 + 0.186937i −0.914931 0.403611i \(-0.867755\pi\)
0.807003 + 0.590548i \(0.201088\pi\)
\(68\) −251.166 435.032i −0.447917 0.775814i
\(69\) 0 0
\(70\) −371.814 466.641i −0.634860 0.796775i
\(71\) −81.4905 −0.136213 −0.0681066 0.997678i \(-0.521696\pi\)
−0.0681066 + 0.997678i \(0.521696\pi\)
\(72\) 0 0
\(73\) 489.415 847.692i 0.784681 1.35911i −0.144508 0.989504i \(-0.546160\pi\)
0.929189 0.369604i \(-0.120507\pi\)
\(74\) −400.721 + 694.069i −0.629498 + 1.09032i
\(75\) 0 0
\(76\) −500.086 −0.754787
\(77\) 139.442 + 175.006i 0.206376 + 0.259010i
\(78\) 0 0
\(79\) 346.714 + 600.527i 0.493777 + 0.855247i 0.999974 0.00717076i \(-0.00228254\pi\)
−0.506197 + 0.862418i \(0.668949\pi\)
\(80\) −128.866 + 223.202i −0.180095 + 0.311934i
\(81\) 0 0
\(82\) −354.070 613.268i −0.476836 0.825904i
\(83\) −1409.05 −1.86341 −0.931707 0.363212i \(-0.881680\pi\)
−0.931707 + 0.363212i \(0.881680\pi\)
\(84\) 0 0
\(85\) 2022.92 2.58137
\(86\) 225.918 + 391.301i 0.283271 + 0.490640i
\(87\) 0 0
\(88\) 48.3289 83.7081i 0.0585441 0.101401i
\(89\) 605.706 + 1049.11i 0.721401 + 1.24950i 0.960438 + 0.278493i \(0.0898348\pi\)
−0.239037 + 0.971010i \(0.576832\pi\)
\(90\) 0 0
\(91\) −269.256 + 685.209i −0.310173 + 0.789334i
\(92\) −192.970 −0.218679
\(93\) 0 0
\(94\) 248.215 429.921i 0.272355 0.471733i
\(95\) 1006.94 1744.07i 1.08747 1.88355i
\(96\) 0 0
\(97\) −1336.50 −1.39898 −0.699492 0.714641i \(-0.746590\pi\)
−0.699492 + 0.714641i \(0.746590\pi\)
\(98\) 153.211 668.672i 0.157925 0.689246i
\(99\) 0 0
\(100\) −268.949 465.834i −0.268949 0.465834i
\(101\) −103.208 + 178.762i −0.101679 + 0.176114i −0.912377 0.409352i \(-0.865755\pi\)
0.810697 + 0.585465i \(0.199088\pi\)
\(102\) 0 0
\(103\) 344.223 + 596.212i 0.329294 + 0.570354i 0.982372 0.186936i \(-0.0598559\pi\)
−0.653078 + 0.757291i \(0.726523\pi\)
\(104\) 318.014 0.299845
\(105\) 0 0
\(106\) −669.841 −0.613780
\(107\) −226.713 392.678i −0.204833 0.354781i 0.745247 0.666789i \(-0.232332\pi\)
−0.950079 + 0.312008i \(0.898998\pi\)
\(108\) 0 0
\(109\) −685.492 + 1187.31i −0.602369 + 1.04333i 0.390093 + 0.920776i \(0.372443\pi\)
−0.992461 + 0.122558i \(0.960890\pi\)
\(110\) 194.623 + 337.097i 0.168696 + 0.292191i
\(111\) 0 0
\(112\) −293.033 + 44.0418i −0.247223 + 0.0371568i
\(113\) −1807.69 −1.50489 −0.752446 0.658654i \(-0.771126\pi\)
−0.752446 + 0.658654i \(0.771126\pi\)
\(114\) 0 0
\(115\) 388.550 672.988i 0.315065 0.545708i
\(116\) 186.092 322.321i 0.148950 0.257989i
\(117\) 0 0
\(118\) 365.746 0.285336
\(119\) 1449.37 + 1819.01i 1.11650 + 1.40125i
\(120\) 0 0
\(121\) 592.510 + 1026.26i 0.445161 + 0.771042i
\(122\) 609.824 1056.25i 0.452548 0.783836i
\(123\) 0 0
\(124\) −45.5237 78.8493i −0.0329689 0.0571039i
\(125\) 152.620 0.109206
\(126\) 0 0
\(127\) −196.476 −0.137279 −0.0686394 0.997642i \(-0.521866\pi\)
−0.0686394 + 0.997642i \(0.521866\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −640.330 + 1109.08i −0.432005 + 0.748255i
\(131\) −753.242 1304.65i −0.502374 0.870138i −0.999996 0.00274396i \(-0.999127\pi\)
0.497622 0.867394i \(-0.334207\pi\)
\(132\) 0 0
\(133\) 2289.71 344.136i 1.49281 0.224364i
\(134\) −236.759 −0.152634
\(135\) 0 0
\(136\) 502.332 870.064i 0.316725 0.548583i
\(137\) 157.673 273.097i 0.0983277 0.170309i −0.812665 0.582731i \(-0.801984\pi\)
0.910993 + 0.412423i \(0.135317\pi\)
\(138\) 0 0
\(139\) −324.501 −0.198013 −0.0990064 0.995087i \(-0.531566\pi\)
−0.0990064 + 0.995087i \(0.531566\pi\)
\(140\) 436.433 1110.64i 0.263466 0.670474i
\(141\) 0 0
\(142\) −81.4905 141.146i −0.0481587 0.0834132i
\(143\) 240.145 415.943i 0.140433 0.243237i
\(144\) 0 0
\(145\) 749.403 + 1298.00i 0.429204 + 0.743403i
\(146\) 1957.66 1.10971
\(147\) 0 0
\(148\) −1602.88 −0.890245
\(149\) −638.745 1106.34i −0.351195 0.608287i 0.635264 0.772295i \(-0.280891\pi\)
−0.986459 + 0.164008i \(0.947558\pi\)
\(150\) 0 0
\(151\) −258.424 + 447.604i −0.139273 + 0.241228i −0.927222 0.374513i \(-0.877810\pi\)
0.787948 + 0.615741i \(0.211143\pi\)
\(152\) −500.086 866.175i −0.266858 0.462211i
\(153\) 0 0
\(154\) −163.677 + 416.527i −0.0856457 + 0.217953i
\(155\) 366.653 0.190002
\(156\) 0 0
\(157\) 649.320 1124.66i 0.330073 0.571702i −0.652453 0.757829i \(-0.726260\pi\)
0.982526 + 0.186127i \(0.0595935\pi\)
\(158\) −693.428 + 1201.05i −0.349153 + 0.604751i
\(159\) 0 0
\(160\) −515.463 −0.254693
\(161\) 883.539 132.793i 0.432501 0.0650034i
\(162\) 0 0
\(163\) −1487.02 2575.60i −0.714556 1.23765i −0.963130 0.269035i \(-0.913295\pi\)
0.248574 0.968613i \(-0.420038\pi\)
\(164\) 708.141 1226.54i 0.337174 0.584002i
\(165\) 0 0
\(166\) −1409.05 2440.55i −0.658816 1.14110i
\(167\) 3607.22 1.67147 0.835733 0.549135i \(-0.185043\pi\)
0.835733 + 0.549135i \(0.185043\pi\)
\(168\) 0 0
\(169\) −616.796 −0.280745
\(170\) 2022.92 + 3503.79i 0.912651 + 1.58076i
\(171\) 0 0
\(172\) −451.835 + 782.602i −0.200303 + 0.346935i
\(173\) 1263.21 + 2187.94i 0.555143 + 0.961536i 0.997892 + 0.0648904i \(0.0206698\pi\)
−0.442749 + 0.896645i \(0.645997\pi\)
\(174\) 0 0
\(175\) 1551.99 + 1947.81i 0.670396 + 0.841374i
\(176\) 193.316 0.0827938
\(177\) 0 0
\(178\) −1211.41 + 2098.23i −0.510108 + 0.883532i
\(179\) 711.221 1231.87i 0.296979 0.514382i −0.678465 0.734633i \(-0.737354\pi\)
0.975443 + 0.220251i \(0.0706877\pi\)
\(180\) 0 0
\(181\) 2494.29 1.02431 0.512153 0.858894i \(-0.328848\pi\)
0.512153 + 0.858894i \(0.328848\pi\)
\(182\) −1456.07 + 218.843i −0.593029 + 0.0891302i
\(183\) 0 0
\(184\) −192.970 334.233i −0.0773148 0.133913i
\(185\) 3227.45 5590.11i 1.28263 2.22158i
\(186\) 0 0
\(187\) −758.661 1314.04i −0.296678 0.513861i
\(188\) 992.859 0.385169
\(189\) 0 0
\(190\) 4027.75 1.53791
\(191\) 1846.91 + 3198.94i 0.699674 + 1.21187i 0.968580 + 0.248704i \(0.0800047\pi\)
−0.268906 + 0.963167i \(0.586662\pi\)
\(192\) 0 0
\(193\) 38.5601 66.7881i 0.0143815 0.0249094i −0.858745 0.512403i \(-0.828755\pi\)
0.873127 + 0.487494i \(0.162089\pi\)
\(194\) −1336.50 2314.89i −0.494615 0.856699i
\(195\) 0 0
\(196\) 1311.38 403.304i 0.477910 0.146977i
\(197\) 1259.96 0.455679 0.227839 0.973699i \(-0.426834\pi\)
0.227839 + 0.973699i \(0.426834\pi\)
\(198\) 0 0
\(199\) −2725.37 + 4720.48i −0.970837 + 1.68154i −0.277796 + 0.960640i \(0.589604\pi\)
−0.693041 + 0.720898i \(0.743729\pi\)
\(200\) 537.899 931.668i 0.190176 0.329394i
\(201\) 0 0
\(202\) −412.833 −0.143796
\(203\) −630.242 + 1603.85i −0.217903 + 0.554524i
\(204\) 0 0
\(205\) 2851.72 + 4939.33i 0.971575 + 1.68282i
\(206\) −688.446 + 1192.42i −0.232846 + 0.403301i
\(207\) 0 0
\(208\) 318.014 + 550.817i 0.106011 + 0.183617i
\(209\) −1510.54 −0.499934
\(210\) 0 0
\(211\) 326.412 0.106498 0.0532492 0.998581i \(-0.483042\pi\)
0.0532492 + 0.998581i \(0.483042\pi\)
\(212\) −669.841 1160.20i −0.217004 0.375862i
\(213\) 0 0
\(214\) 453.425 785.355i 0.144839 0.250868i
\(215\) −1819.57 3151.58i −0.577178 0.999702i
\(216\) 0 0
\(217\) 262.697 + 329.695i 0.0821799 + 0.103139i
\(218\) −2741.97 −0.851878
\(219\) 0 0
\(220\) −389.246 + 674.195i −0.119286 + 0.206610i
\(221\) 2496.07 4323.32i 0.759746 1.31592i
\(222\) 0 0
\(223\) −3095.25 −0.929477 −0.464738 0.885448i \(-0.653852\pi\)
−0.464738 + 0.885448i \(0.653852\pi\)
\(224\) −369.316 463.506i −0.110160 0.138256i
\(225\) 0 0
\(226\) −1807.69 3131.01i −0.532060 0.921555i
\(227\) −313.357 + 542.750i −0.0916221 + 0.158694i −0.908194 0.418550i \(-0.862539\pi\)
0.816572 + 0.577244i \(0.195872\pi\)
\(228\) 0 0
\(229\) −3333.25 5773.36i −0.961867 1.66600i −0.717808 0.696241i \(-0.754854\pi\)
−0.244059 0.969760i \(-0.578479\pi\)
\(230\) 1554.20 0.445569
\(231\) 0 0
\(232\) 744.369 0.210647
\(233\) 1750.26 + 3031.53i 0.492117 + 0.852371i 0.999959 0.00907927i \(-0.00289006\pi\)
−0.507842 + 0.861450i \(0.669557\pi\)
\(234\) 0 0
\(235\) −1999.15 + 3462.63i −0.554937 + 0.961179i
\(236\) 365.746 + 633.490i 0.100881 + 0.174732i
\(237\) 0 0
\(238\) −1701.26 + 4329.39i −0.463345 + 1.17913i
\(239\) 119.098 0.0322335 0.0161168 0.999870i \(-0.494870\pi\)
0.0161168 + 0.999870i \(0.494870\pi\)
\(240\) 0 0
\(241\) −635.903 + 1101.42i −0.169967 + 0.294392i −0.938408 0.345529i \(-0.887699\pi\)
0.768441 + 0.639921i \(0.221033\pi\)
\(242\) −1185.02 + 2052.51i −0.314777 + 0.545209i
\(243\) 0 0
\(244\) 2439.29 0.639999
\(245\) −1233.98 + 5385.56i −0.321779 + 1.40437i
\(246\) 0 0
\(247\) −2484.91 4304.00i −0.640127 1.10873i
\(248\) 91.0474 157.699i 0.0233126 0.0403785i
\(249\) 0 0
\(250\) 152.620 + 264.346i 0.0386102 + 0.0668748i
\(251\) −330.354 −0.0830749 −0.0415374 0.999137i \(-0.513226\pi\)
−0.0415374 + 0.999137i \(0.513226\pi\)
\(252\) 0 0
\(253\) −582.876 −0.144842
\(254\) −196.476 340.306i −0.0485354 0.0840658i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1260.40 2183.08i −0.305921 0.529870i 0.671545 0.740964i \(-0.265631\pi\)
−0.977466 + 0.211093i \(0.932298\pi\)
\(258\) 0 0
\(259\) 7339.03 1103.03i 1.76072 0.264629i
\(260\) −2561.32 −0.610948
\(261\) 0 0
\(262\) 1506.48 2609.31i 0.355232 0.615281i
\(263\) −713.729 + 1236.21i −0.167340 + 0.289841i −0.937484 0.348029i \(-0.886851\pi\)
0.770144 + 0.637870i \(0.220184\pi\)
\(264\) 0 0
\(265\) 5394.97 1.25061
\(266\) 2885.78 + 3621.77i 0.665182 + 0.834830i
\(267\) 0 0
\(268\) −236.759 410.079i −0.0539641 0.0934686i
\(269\) 4094.93 7092.63i 0.928151 1.60760i 0.141737 0.989904i \(-0.454731\pi\)
0.786414 0.617700i \(-0.211935\pi\)
\(270\) 0 0
\(271\) −3197.35 5537.98i −0.716699 1.24136i −0.962301 0.271988i \(-0.912319\pi\)
0.245602 0.969371i \(-0.421014\pi\)
\(272\) 2009.33 0.447917
\(273\) 0 0
\(274\) 630.691 0.139056
\(275\) −812.377 1407.08i −0.178139 0.308545i
\(276\) 0 0
\(277\) 3319.70 5749.90i 0.720078 1.24721i −0.240890 0.970553i \(-0.577439\pi\)
0.960968 0.276660i \(-0.0892275\pi\)
\(278\) −324.501 562.052i −0.0700081 0.121258i
\(279\) 0 0
\(280\) 2360.12 354.718i 0.503729 0.0757087i
\(281\) −4929.95 −1.04661 −0.523303 0.852147i \(-0.675300\pi\)
−0.523303 + 0.852147i \(0.675300\pi\)
\(282\) 0 0
\(283\) −1391.39 + 2409.96i −0.292261 + 0.506210i −0.974344 0.225064i \(-0.927741\pi\)
0.682083 + 0.731274i \(0.261074\pi\)
\(284\) 162.981 282.291i 0.0340533 0.0589821i
\(285\) 0 0
\(286\) 960.580 0.198602
\(287\) −2398.28 + 6103.18i −0.493261 + 1.25526i
\(288\) 0 0
\(289\) −5429.03 9403.36i −1.10503 1.91397i
\(290\) −1498.81 + 2596.01i −0.303493 + 0.525665i
\(291\) 0 0
\(292\) 1957.66 + 3390.77i 0.392341 + 0.679554i
\(293\) −1639.57 −0.326910 −0.163455 0.986551i \(-0.552264\pi\)
−0.163455 + 0.986551i \(0.552264\pi\)
\(294\) 0 0
\(295\) −2945.76 −0.581385
\(296\) −1602.88 2776.28i −0.314749 0.545162i
\(297\) 0 0
\(298\) 1277.49 2212.68i 0.248332 0.430124i
\(299\) −958.861 1660.80i −0.185459 0.321225i
\(300\) 0 0
\(301\) 1530.24 3894.18i 0.293029 0.745705i
\(302\) −1033.70 −0.196962
\(303\) 0 0
\(304\) 1000.17 1732.35i 0.188697 0.326832i
\(305\) −4911.59 + 8507.12i −0.922087 + 1.59710i
\(306\) 0 0
\(307\) −10332.5 −1.92087 −0.960436 0.278502i \(-0.910162\pi\)
−0.960436 + 0.278502i \(0.910162\pi\)
\(308\) −885.123 + 133.031i −0.163749 + 0.0246108i
\(309\) 0 0
\(310\) 366.653 + 635.061i 0.0671757 + 0.116352i
\(311\) −4626.39 + 8013.14i −0.843532 + 1.46104i 0.0433584 + 0.999060i \(0.486194\pi\)
−0.886890 + 0.461980i \(0.847139\pi\)
\(312\) 0 0
\(313\) 1238.89 + 2145.82i 0.223726 + 0.387504i 0.955936 0.293574i \(-0.0948447\pi\)
−0.732211 + 0.681078i \(0.761511\pi\)
\(314\) 2597.28 0.466793
\(315\) 0 0
\(316\) −2773.71 −0.493777
\(317\) −1441.61 2496.94i −0.255422 0.442404i 0.709588 0.704617i \(-0.248881\pi\)
−0.965010 + 0.262213i \(0.915548\pi\)
\(318\) 0 0
\(319\) 562.102 973.589i 0.0986573 0.170879i
\(320\) −515.463 892.808i −0.0900477 0.155967i
\(321\) 0 0
\(322\) 1113.54 + 1397.54i 0.192718 + 0.241869i
\(323\) −15700.6 −2.70465
\(324\) 0 0
\(325\) 2672.80 4629.43i 0.456186 0.790137i
\(326\) 2974.05 5151.20i 0.505267 0.875149i
\(327\) 0 0
\(328\) 2832.56 0.476836
\(329\) −4545.95 + 683.240i −0.761782 + 0.114493i
\(330\) 0 0
\(331\) 248.565 + 430.528i 0.0412761 + 0.0714923i 0.885925 0.463828i \(-0.153524\pi\)
−0.844649 + 0.535320i \(0.820191\pi\)
\(332\) 2818.10 4881.09i 0.465853 0.806882i
\(333\) 0 0
\(334\) 3607.22 + 6247.89i 0.590953 + 1.02356i
\(335\) 1906.89 0.310998
\(336\) 0 0
\(337\) 6711.07 1.08479 0.542397 0.840123i \(-0.317517\pi\)
0.542397 + 0.840123i \(0.317517\pi\)
\(338\) −616.796 1068.32i −0.0992583 0.171920i
\(339\) 0 0
\(340\) −4045.83 + 7007.59i −0.645341 + 1.11776i
\(341\) −137.507 238.169i −0.0218370 0.0378228i
\(342\) 0 0
\(343\) −5726.82 + 2749.02i −0.901514 + 0.432749i
\(344\) −1807.34 −0.283271
\(345\) 0 0
\(346\) −2526.41 + 4375.87i −0.392545 + 0.679908i
\(347\) 80.8131 139.972i 0.0125022 0.0216545i −0.859707 0.510788i \(-0.829354\pi\)
0.872209 + 0.489134i \(0.162687\pi\)
\(348\) 0 0
\(349\) −3970.85 −0.609040 −0.304520 0.952506i \(-0.598496\pi\)
−0.304520 + 0.952506i \(0.598496\pi\)
\(350\) −1821.71 + 4635.93i −0.278213 + 0.708002i
\(351\) 0 0
\(352\) 193.316 + 334.833i 0.0292720 + 0.0507007i
\(353\) 5777.83 10007.5i 0.871169 1.50891i 0.0103815 0.999946i \(-0.496695\pi\)
0.860788 0.508964i \(-0.169971\pi\)
\(354\) 0 0
\(355\) 656.333 + 1136.80i 0.0981255 + 0.169958i
\(356\) −4845.65 −0.721401
\(357\) 0 0
\(358\) 2844.88 0.419991
\(359\) 4270.56 + 7396.82i 0.627831 + 1.08744i 0.987986 + 0.154543i \(0.0493904\pi\)
−0.360155 + 0.932892i \(0.617276\pi\)
\(360\) 0 0
\(361\) −4385.70 + 7596.25i −0.639407 + 1.10749i
\(362\) 2494.29 + 4320.24i 0.362147 + 0.627257i
\(363\) 0 0
\(364\) −1835.12 2303.15i −0.264248 0.331642i
\(365\) −15767.2 −2.26108
\(366\) 0 0
\(367\) −1901.32 + 3293.18i −0.270431 + 0.468400i −0.968972 0.247170i \(-0.920499\pi\)
0.698541 + 0.715570i \(0.253833\pi\)
\(368\) 385.939 668.467i 0.0546698 0.0946908i
\(369\) 0 0
\(370\) 12909.8 1.81392
\(371\) 3865.35 + 4851.18i 0.540914 + 0.678869i
\(372\) 0 0
\(373\) 4296.45 + 7441.66i 0.596412 + 1.03302i 0.993346 + 0.115168i \(0.0367407\pi\)
−0.396934 + 0.917847i \(0.629926\pi\)
\(374\) 1517.32 2628.08i 0.209783 0.363355i
\(375\) 0 0
\(376\) 992.859 + 1719.68i 0.136178 + 0.235867i
\(377\) 3698.75 0.505292
\(378\) 0 0
\(379\) −9415.95 −1.27616 −0.638080 0.769970i \(-0.720271\pi\)
−0.638080 + 0.769970i \(0.720271\pi\)
\(380\) 4027.75 + 6976.27i 0.543735 + 0.941776i
\(381\) 0 0
\(382\) −3693.82 + 6397.88i −0.494744 + 0.856922i
\(383\) 4618.37 + 7999.25i 0.616156 + 1.06721i 0.990181 + 0.139795i \(0.0446442\pi\)
−0.374025 + 0.927419i \(0.622022\pi\)
\(384\) 0 0
\(385\) 1318.27 3354.76i 0.174507 0.444089i
\(386\) 154.241 0.0203384
\(387\) 0 0
\(388\) 2673.01 4629.78i 0.349746 0.605777i
\(389\) −1003.96 + 1738.90i −0.130855 + 0.226648i −0.924006 0.382377i \(-0.875106\pi\)
0.793151 + 0.609025i \(0.208439\pi\)
\(390\) 0 0
\(391\) −6058.42 −0.783600
\(392\) 2009.93 + 1868.08i 0.258971 + 0.240695i
\(393\) 0 0
\(394\) 1259.96 + 2182.32i 0.161107 + 0.279045i
\(395\) 5584.95 9673.41i 0.711416 1.23221i
\(396\) 0 0
\(397\) −635.532 1100.77i −0.0803437 0.139159i 0.823054 0.567963i \(-0.192268\pi\)
−0.903398 + 0.428804i \(0.858935\pi\)
\(398\) −10901.5 −1.37297
\(399\) 0 0
\(400\) 2151.59 0.268949
\(401\) 7512.71 + 13012.4i 0.935578 + 1.62047i 0.773600 + 0.633674i \(0.218454\pi\)
0.161978 + 0.986794i \(0.448213\pi\)
\(402\) 0 0
\(403\) 452.412 783.600i 0.0559212 0.0968583i
\(404\) −412.833 715.048i −0.0508396 0.0880568i
\(405\) 0 0
\(406\) −3408.20 + 512.240i −0.416616 + 0.0626159i
\(407\) −4841.61 −0.589655
\(408\) 0 0
\(409\) −239.226 + 414.352i −0.0289217 + 0.0500939i −0.880124 0.474744i \(-0.842541\pi\)
0.851202 + 0.524838i \(0.175874\pi\)
\(410\) −5703.44 + 9878.66i −0.687007 + 1.18993i
\(411\) 0 0
\(412\) −2753.78 −0.329294
\(413\) −2110.56 2648.83i −0.251462 0.315595i
\(414\) 0 0
\(415\) 11348.6 + 19656.4i 1.34237 + 2.32505i
\(416\) −636.028 + 1101.63i −0.0749612 + 0.129837i
\(417\) 0 0
\(418\) −1510.54 2616.33i −0.176753 0.306146i
\(419\) 11608.0 1.35343 0.676715 0.736245i \(-0.263403\pi\)
0.676715 + 0.736245i \(0.263403\pi\)
\(420\) 0 0
\(421\) −3833.92 −0.443833 −0.221917 0.975066i \(-0.571231\pi\)
−0.221917 + 0.975066i \(0.571231\pi\)
\(422\) 326.412 + 565.363i 0.0376529 + 0.0652167i
\(423\) 0 0
\(424\) 1339.68 2320.40i 0.153445 0.265775i
\(425\) −8443.86 14625.2i −0.963735 1.66924i
\(426\) 0 0
\(427\) −11168.7 + 1678.61i −1.26578 + 0.190243i
\(428\) 1813.70 0.204833
\(429\) 0 0
\(430\) 3639.13 6303.16i 0.408127 0.706896i
\(431\) 499.024 864.334i 0.0557706 0.0965975i −0.836792 0.547521i \(-0.815572\pi\)
0.892563 + 0.450923i \(0.148905\pi\)
\(432\) 0 0
\(433\) 1298.17 0.144079 0.0720396 0.997402i \(-0.477049\pi\)
0.0720396 + 0.997402i \(0.477049\pi\)
\(434\) −308.352 + 784.700i −0.0341046 + 0.0867899i
\(435\) 0 0
\(436\) −2741.97 4749.23i −0.301184 0.521667i
\(437\) −3015.67 + 5223.30i −0.330112 + 0.571772i
\(438\) 0 0
\(439\) 966.704 + 1674.38i 0.105099 + 0.182036i 0.913778 0.406213i \(-0.133151\pi\)
−0.808680 + 0.588249i \(0.799818\pi\)
\(440\) −1556.99 −0.168696
\(441\) 0 0
\(442\) 9984.29 1.07444
\(443\) −7267.01 12586.8i −0.779382 1.34993i −0.932299 0.361690i \(-0.882200\pi\)
0.152917 0.988239i \(-0.451133\pi\)
\(444\) 0 0
\(445\) 9756.84 16899.3i 1.03937 1.80024i
\(446\) −3095.25 5361.13i −0.328620 0.569186i
\(447\) 0 0
\(448\) 433.500 1103.18i 0.0457165 0.116340i
\(449\) 4799.65 0.504476 0.252238 0.967665i \(-0.418833\pi\)
0.252238 + 0.967665i \(0.418833\pi\)
\(450\) 0 0
\(451\) 2138.98 3704.82i 0.223327 0.386814i
\(452\) 3615.37 6262.01i 0.376223 0.651638i
\(453\) 0 0
\(454\) −1253.43 −0.129573
\(455\) 11727.4 1762.58i 1.20832 0.181607i
\(456\) 0 0
\(457\) −2367.14 4100.00i −0.242297 0.419671i 0.719071 0.694937i \(-0.244568\pi\)
−0.961368 + 0.275265i \(0.911234\pi\)
\(458\) 6666.50 11546.7i 0.680142 1.17804i
\(459\) 0 0
\(460\) 1554.20 + 2691.95i 0.157532 + 0.272854i
\(461\) 8137.41 0.822119 0.411060 0.911608i \(-0.365159\pi\)
0.411060 + 0.911608i \(0.365159\pi\)
\(462\) 0 0
\(463\) 8671.77 0.870435 0.435218 0.900325i \(-0.356671\pi\)
0.435218 + 0.900325i \(0.356671\pi\)
\(464\) 744.369 + 1289.28i 0.0744751 + 0.128995i
\(465\) 0 0
\(466\) −3500.51 + 6063.07i −0.347979 + 0.602717i
\(467\) −7794.04 13499.7i −0.772303 1.33767i −0.936298 0.351206i \(-0.885772\pi\)
0.163995 0.986461i \(-0.447562\pi\)
\(468\) 0 0
\(469\) 1366.23 + 1714.68i 0.134513 + 0.168820i
\(470\) −7996.60 −0.784799
\(471\) 0 0
\(472\) −731.492 + 1266.98i −0.0713340 + 0.123554i
\(473\) −1364.79 + 2363.89i −0.132671 + 0.229793i
\(474\) 0 0
\(475\) −16812.2 −1.62400
\(476\) −9199.98 + 1382.73i −0.885883 + 0.133145i
\(477\) 0 0
\(478\) 119.098 + 206.284i 0.0113963 + 0.0197389i
\(479\) 4767.04 8256.76i 0.454722 0.787601i −0.543951 0.839117i \(-0.683072\pi\)
0.998672 + 0.0515163i \(0.0164054\pi\)
\(480\) 0 0
\(481\) −7964.69 13795.2i −0.755007 1.30771i
\(482\) −2543.61 −0.240370
\(483\) 0 0
\(484\) −4740.08 −0.445161
\(485\) 10764.3 + 18644.4i 1.00780 + 1.74556i
\(486\) 0 0
\(487\) 4398.55 7618.51i 0.409276 0.708887i −0.585533 0.810649i \(-0.699115\pi\)
0.994809 + 0.101762i \(0.0324480\pi\)
\(488\) 2439.29 + 4224.98i 0.226274 + 0.391918i
\(489\) 0 0
\(490\) −10562.0 + 3248.25i −0.973764 + 0.299471i
\(491\) −15749.6 −1.44760 −0.723799 0.690010i \(-0.757606\pi\)
−0.723799 + 0.690010i \(0.757606\pi\)
\(492\) 0 0
\(493\) 5842.50 10119.5i 0.533738 0.924461i
\(494\) 4969.83 8608.00i 0.452638 0.783992i
\(495\) 0 0
\(496\) 364.190 0.0329689
\(497\) −551.971 + 1404.67i −0.0498175 + 0.126776i
\(498\) 0 0
\(499\) 6490.60 + 11242.0i 0.582283 + 1.00854i 0.995208 + 0.0977783i \(0.0311736\pi\)
−0.412926 + 0.910765i \(0.635493\pi\)
\(500\) −305.240 + 528.692i −0.0273015 + 0.0472876i
\(501\) 0 0
\(502\) −330.354 572.191i −0.0293714 0.0508727i
\(503\) 13047.4 1.15657 0.578284 0.815836i \(-0.303723\pi\)
0.578284 + 0.815836i \(0.303723\pi\)
\(504\) 0 0
\(505\) 3325.00 0.292991
\(506\) −582.876 1009.57i −0.0512095 0.0886974i
\(507\) 0 0
\(508\) 392.952 680.612i 0.0343197 0.0594435i
\(509\) 381.720 + 661.159i 0.0332406 + 0.0575744i 0.882167 0.470937i \(-0.156084\pi\)
−0.848927 + 0.528511i \(0.822751\pi\)
\(510\) 0 0
\(511\) −11296.8 14177.9i −0.977967 1.22739i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2520.80 4366.15i 0.216319 0.374675i
\(515\) 5544.82 9603.91i 0.474435 0.821745i
\(516\) 0 0
\(517\) 2998.99 0.255117
\(518\) 9249.54 + 11608.5i 0.784559 + 0.984653i
\(519\) 0 0
\(520\) −2561.32 4436.34i −0.216003 0.374127i
\(521\) 1015.38 1758.68i 0.0853829 0.147887i −0.820171 0.572118i \(-0.806122\pi\)
0.905554 + 0.424230i \(0.139455\pi\)
\(522\) 0 0
\(523\) 6482.87 + 11228.7i 0.542019 + 0.938805i 0.998788 + 0.0492192i \(0.0156733\pi\)
−0.456769 + 0.889585i \(0.650993\pi\)
\(524\) 6025.94 0.502374
\(525\) 0 0
\(526\) −2854.91 −0.236654
\(527\) −1429.25 2475.53i −0.118139 0.204622i
\(528\) 0 0
\(529\) 4919.83 8521.40i 0.404359 0.700370i
\(530\) 5394.97 + 9344.36i 0.442156 + 0.765836i
\(531\) 0 0
\(532\) −3387.31 + 8620.08i −0.276050 + 0.702496i
\(533\) 14074.9 1.14381
\(534\) 0 0
\(535\) −3651.93 + 6325.34i −0.295116 + 0.511155i
\(536\) 473.519 820.158i 0.0381584 0.0660923i
\(537\) 0 0
\(538\) 16379.7 1.31260
\(539\) 3961.11 1218.20i 0.316544 0.0973500i
\(540\) 0 0
\(541\) 7812.43 + 13531.5i 0.620855 + 1.07535i 0.989327 + 0.145714i \(0.0465479\pi\)
−0.368471 + 0.929639i \(0.620119\pi\)
\(542\) 6394.70 11076.0i 0.506782 0.877773i
\(543\) 0 0
\(544\) 2009.33 + 3480.26i 0.158362 + 0.274292i
\(545\) 22084.1 1.73574
\(546\) 0 0
\(547\) −14437.8 −1.12855 −0.564273 0.825588i \(-0.690843\pi\)
−0.564273 + 0.825588i \(0.690843\pi\)
\(548\) 630.691 + 1092.39i 0.0491639 + 0.0851543i
\(549\) 0 0
\(550\) 1624.75 2814.16i 0.125963 0.218175i
\(551\) −5816.38 10074.3i −0.449703 0.778908i
\(552\) 0 0
\(553\) 12699.8 1908.74i 0.976586 0.146777i
\(554\) 13278.8 1.01834
\(555\) 0 0
\(556\) 649.001 1124.10i 0.0495032 0.0857421i
\(557\) 8242.53 14276.5i 0.627015 1.08602i −0.361133 0.932514i \(-0.617610\pi\)
0.988148 0.153507i \(-0.0490567\pi\)
\(558\) 0 0
\(559\) −8980.63 −0.679499
\(560\) 2974.51 + 3733.13i 0.224457 + 0.281703i
\(561\) 0 0
\(562\) −4929.95 8538.92i −0.370031 0.640912i
\(563\) −8366.91 + 14491.9i −0.626329 + 1.08483i 0.361954 + 0.932196i \(0.382110\pi\)
−0.988282 + 0.152637i \(0.951223\pi\)
\(564\) 0 0
\(565\) 14559.3 + 25217.5i 1.08410 + 1.87771i
\(566\) −5565.57 −0.413319
\(567\) 0 0
\(568\) 651.924 0.0481587
\(569\) 7508.37 + 13004.9i 0.553194 + 0.958160i 0.998042 + 0.0625539i \(0.0199245\pi\)
−0.444848 + 0.895606i \(0.646742\pi\)
\(570\) 0 0
\(571\) −3236.25 + 5605.35i −0.237186 + 0.410817i −0.959906 0.280323i \(-0.909558\pi\)
0.722720 + 0.691141i \(0.242892\pi\)
\(572\) 960.580 + 1663.77i 0.0702166 + 0.121619i
\(573\) 0 0
\(574\) −12969.3 + 1949.24i −0.943080 + 0.141742i
\(575\) −6487.38 −0.470509
\(576\) 0 0
\(577\) −4955.10 + 8582.48i −0.357510 + 0.619226i −0.987544 0.157342i \(-0.949708\pi\)
0.630034 + 0.776567i \(0.283041\pi\)
\(578\) 10858.1 18806.7i 0.781377 1.35338i
\(579\) 0 0
\(580\) −5995.23 −0.429204
\(581\) −9544.12 + 24288.0i −0.681509 + 1.73432i
\(582\) 0 0
\(583\) −2023.29 3504.45i −0.143733 0.248952i
\(584\) −3915.32 + 6781.54i −0.277427 + 0.480517i
\(585\) 0 0
\(586\) −1639.57 2839.81i −0.115580 0.200191i
\(587\) −1112.26 −0.0782079 −0.0391039 0.999235i \(-0.512450\pi\)
−0.0391039 + 0.999235i \(0.512450\pi\)
\(588\) 0 0
\(589\) −2845.72 −0.199076
\(590\) −2945.76 5102.20i −0.205551 0.356024i
\(591\) 0 0
\(592\) 3205.77 5552.56i 0.222561 0.385488i
\(593\) 379.191 + 656.778i 0.0262589 + 0.0454817i 0.878856 0.477087i \(-0.158307\pi\)
−0.852597 + 0.522568i \(0.824974\pi\)
\(594\) 0 0
\(595\) 13702.1 34869.4i 0.944087 2.40253i
\(596\) 5109.96 0.351195
\(597\) 0 0
\(598\) 1917.72 3321.59i 0.131140 0.227140i
\(599\) 8957.35 15514.6i 0.610997 1.05828i −0.380076 0.924955i \(-0.624102\pi\)
0.991073 0.133323i \(-0.0425646\pi\)
\(600\) 0 0
\(601\) 19337.1 1.31244 0.656221 0.754569i \(-0.272154\pi\)
0.656221 + 0.754569i \(0.272154\pi\)
\(602\) 8275.17 1243.73i 0.560250 0.0842037i
\(603\) 0 0
\(604\) −1033.70 1790.42i −0.0696366 0.120614i
\(605\) 9544.28 16531.2i 0.641372 1.11089i
\(606\) 0 0
\(607\) −787.211 1363.49i −0.0526391 0.0911736i 0.838505 0.544894i \(-0.183430\pi\)
−0.891144 + 0.453720i \(0.850097\pi\)
\(608\) 4000.69 0.266858
\(609\) 0 0
\(610\) −19646.3 −1.30403
\(611\) 4933.49 + 8545.06i 0.326657 + 0.565787i
\(612\) 0 0
\(613\) 2597.21 4498.49i 0.171126 0.296399i −0.767688 0.640824i \(-0.778593\pi\)
0.938814 + 0.344425i \(0.111926\pi\)
\(614\) −10332.5 17896.4i −0.679131 1.17629i
\(615\) 0 0
\(616\) −1115.54 1400.05i −0.0729649 0.0915739i
\(617\) −1699.80 −0.110910 −0.0554550 0.998461i \(-0.517661\pi\)
−0.0554550 + 0.998461i \(0.517661\pi\)
\(618\) 0 0
\(619\) 6362.04 11019.4i 0.413105 0.715518i −0.582123 0.813101i \(-0.697778\pi\)
0.995227 + 0.0975825i \(0.0311110\pi\)
\(620\) −733.305 + 1270.12i −0.0475004 + 0.0822731i
\(621\) 0 0
\(622\) −18505.6 −1.19293
\(623\) 22186.5 3334.55i 1.42678 0.214440i
\(624\) 0 0
\(625\) 7175.45 + 12428.2i 0.459229 + 0.795407i
\(626\) −2477.78 + 4291.63i −0.158198 + 0.274007i
\(627\) 0 0
\(628\) 2597.28 + 4498.62i 0.165036 + 0.285851i
\(629\) −50323.7 −3.19004
\(630\) 0 0
\(631\) −14921.6 −0.941392 −0.470696 0.882295i \(-0.655997\pi\)
−0.470696 + 0.882295i \(0.655997\pi\)
\(632\) −2773.71 4804.21i −0.174577 0.302375i
\(633\) 0 0
\(634\) 2883.22 4993.88i 0.180611 0.312827i
\(635\) 1582.44 + 2740.86i 0.0988931 + 0.171288i
\(636\) 0 0
\(637\) 9987.27 + 9282.45i 0.621209 + 0.577369i
\(638\) 2248.41 0.139522
\(639\) 0 0
\(640\) 1030.93 1785.62i 0.0636733 0.110285i
\(641\) −13483.7 + 23354.5i −0.830850 + 1.43907i 0.0665155 + 0.997785i \(0.478812\pi\)
−0.897365 + 0.441289i \(0.854522\pi\)
\(642\) 0 0
\(643\) 12146.2 0.744947 0.372473 0.928043i \(-0.378510\pi\)
0.372473 + 0.928043i \(0.378510\pi\)
\(644\) −1307.07 + 3326.25i −0.0799779 + 0.203529i
\(645\) 0 0
\(646\) −15700.6 27194.2i −0.956239 1.65626i
\(647\) 13575.9 23514.1i 0.824919 1.42880i −0.0770625 0.997026i \(-0.524554\pi\)
0.901981 0.431775i \(-0.142113\pi\)
\(648\) 0 0
\(649\) 1104.76 + 1913.49i 0.0668189 + 0.115734i
\(650\) 10691.2 0.645144
\(651\) 0 0
\(652\) 11896.2 0.714556
\(653\) 6320.52 + 10947.5i 0.378776 + 0.656060i 0.990884 0.134714i \(-0.0430117\pi\)
−0.612108 + 0.790774i \(0.709678\pi\)
\(654\) 0 0
\(655\) −12133.4 + 21015.6i −0.723802 + 1.25366i
\(656\) 2832.56 + 4906.14i 0.168587 + 0.292001i
\(657\) 0 0
\(658\) −5729.35 7190.57i −0.339443 0.426015i
\(659\) −11360.0 −0.671506 −0.335753 0.941950i \(-0.608991\pi\)
−0.335753 + 0.941950i \(0.608991\pi\)
\(660\) 0 0
\(661\) −2078.99 + 3600.91i −0.122335 + 0.211890i −0.920688 0.390300i \(-0.872371\pi\)
0.798353 + 0.602189i \(0.205705\pi\)
\(662\) −497.131 + 861.056i −0.0291866 + 0.0505527i
\(663\) 0 0
\(664\) 11272.4 0.658816
\(665\) −23242.4 29170.1i −1.35534 1.70100i
\(666\) 0 0
\(667\) −2244.38 3887.39i −0.130289 0.225668i
\(668\) −7214.44 + 12495.8i −0.417867 + 0.723766i
\(669\) 0 0
\(670\) 1906.89 + 3302.82i 0.109954 + 0.190447i
\(671\) 7368.03 0.423904
\(672\) 0 0
\(673\) 8753.81 0.501389 0.250694 0.968066i \(-0.419341\pi\)
0.250694 + 0.968066i \(0.419341\pi\)
\(674\) 6711.07 + 11623.9i 0.383532 + 0.664297i
\(675\) 0 0
\(676\) 1233.59 2136.65i 0.0701862 0.121566i
\(677\) −5802.61 10050.4i −0.329413 0.570560i 0.652983 0.757373i \(-0.273517\pi\)
−0.982395 + 0.186813i \(0.940184\pi\)
\(678\) 0 0
\(679\) −9052.73 + 23037.6i −0.511652 + 1.30206i
\(680\) −16183.3 −0.912651
\(681\) 0 0
\(682\) 275.014 476.338i 0.0154411 0.0267448i
\(683\) −9199.15 + 15933.4i −0.515367 + 0.892642i 0.484474 + 0.874806i \(0.339011\pi\)
−0.999841 + 0.0178364i \(0.994322\pi\)
\(684\) 0 0
\(685\) −5079.66 −0.283334
\(686\) −10488.3 7170.13i −0.583737 0.399063i
\(687\) 0 0
\(688\) −1807.34 3130.41i −0.100152 0.173468i
\(689\) 6656.84 11530.0i 0.368077 0.637529i
\(690\) 0 0
\(691\) 20.7919 + 36.0127i 0.00114466 + 0.00198261i 0.866597 0.499008i \(-0.166302\pi\)
−0.865453 + 0.500991i \(0.832969\pi\)
\(692\) −10105.6 −0.555143
\(693\) 0 0
\(694\) 323.252 0.0176808
\(695\) 2613.56 + 4526.83i 0.142645 + 0.247068i
\(696\) 0 0
\(697\) 22232.6 38508.0i 1.20821 2.09267i
\(698\) −3970.85 6877.72i −0.215328 0.372959i
\(699\) 0 0
\(700\) −9851.38 + 1480.63i −0.531924 + 0.0799464i
\(701\) 29655.0 1.59779 0.798896 0.601469i \(-0.205418\pi\)
0.798896 + 0.601469i \(0.205418\pi\)
\(702\) 0 0
\(703\) −25049.4 + 43386.8i −1.34389 + 2.32769i
\(704\) −386.631 + 669.665i −0.0206985 + 0.0358508i
\(705\) 0 0
\(706\) 23111.3 1.23202
\(707\) 2382.28 + 2989.85i 0.126725 + 0.159045i
\(708\) 0 0
\(709\) 4375.23 + 7578.13i 0.231757 + 0.401414i 0.958325 0.285680i \(-0.0922194\pi\)
−0.726569 + 0.687094i \(0.758886\pi\)
\(710\) −1312.67 + 2273.60i −0.0693852 + 0.120179i
\(711\) 0 0
\(712\) −4845.65 8392.91i −0.255054 0.441766i
\(713\) −1098.09 −0.0576769
\(714\) 0 0
\(715\) −7736.62 −0.404662
\(716\) 2844.88 + 4927.48i 0.148489 + 0.257191i
\(717\) 0 0
\(718\) −8541.11 + 14793.6i −0.443944 + 0.768933i
\(719\) 9541.72 + 16526.8i 0.494918 + 0.857224i 0.999983 0.00585789i \(-0.00186464\pi\)
−0.505065 + 0.863082i \(0.668531\pi\)
\(720\) 0 0
\(721\) 12608.6 1895.03i 0.651274 0.0978842i
\(722\) −17542.8 −0.904259
\(723\) 0 0
\(724\) −4988.59 + 8640.49i −0.256076 + 0.443537i
\(725\) 6256.17 10836.0i 0.320480 0.555088i
\(726\) 0 0
\(727\) 15050.9 0.767821 0.383910 0.923370i \(-0.374577\pi\)
0.383910 + 0.923370i \(0.374577\pi\)
\(728\) 2154.05 5481.67i 0.109663 0.279072i
\(729\) 0 0
\(730\) −15767.2 27309.6i −0.799412 1.38462i
\(731\) −14185.7 + 24570.4i −0.717752 + 1.24318i
\(732\) 0 0
\(733\) −5279.02 9143.53i −0.266010 0.460742i 0.701818 0.712356i \(-0.252372\pi\)
−0.967828 + 0.251614i \(0.919039\pi\)
\(734\) −7605.28 −0.382447
\(735\) 0 0
\(736\) 1543.76 0.0773148
\(737\) −715.145 1238.67i −0.0357432 0.0619090i
\(738\) 0 0
\(739\) 16623.4 28792.5i 0.827470 1.43322i −0.0725462 0.997365i \(-0.523112\pi\)
0.900017 0.435856i \(-0.143554\pi\)
\(740\) 12909.8 + 22360.4i 0.641316 + 1.11079i
\(741\) 0 0
\(742\) −4537.13 + 11546.2i −0.224479 + 0.571258i
\(743\) −32799.7 −1.61952 −0.809761 0.586760i \(-0.800403\pi\)
−0.809761 + 0.586760i \(0.800403\pi\)
\(744\) 0 0
\(745\) −10289.0 + 17821.1i −0.505988 + 0.876397i
\(746\) −8592.89 + 14883.3i −0.421727 + 0.730452i
\(747\) 0 0
\(748\) 6069.29 0.296678
\(749\) −8304.28 + 1248.10i −0.405116 + 0.0608875i
\(750\) 0 0
\(751\) 12113.3 + 20980.8i 0.588574 + 1.01944i 0.994419 + 0.105499i \(0.0336439\pi\)
−0.405845 + 0.913942i \(0.633023\pi\)
\(752\) −1985.72 + 3439.37i −0.0962922 + 0.166783i
\(753\) 0 0
\(754\) 3698.75 + 6406.42i 0.178648 + 0.309427i
\(755\) 8325.51 0.401319
\(756\) 0 0
\(757\) −3116.97 −0.149654 −0.0748271 0.997197i \(-0.523840\pi\)
−0.0748271 + 0.997197i \(0.523840\pi\)
\(758\) −9415.95 16308.9i −0.451191 0.781485i
\(759\) 0 0
\(760\) −8055.50 + 13952.5i −0.384478 + 0.665936i
\(761\) 4355.33 + 7543.65i 0.207464 + 0.359339i 0.950915 0.309452i \(-0.100146\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(762\) 0 0
\(763\) 15822.7 + 19858.1i 0.750746 + 0.942217i
\(764\) −14775.3 −0.699674
\(765\) 0 0
\(766\) −9236.74 + 15998.5i −0.435688 + 0.754634i
\(767\) −3634.76 + 6295.59i −0.171113 + 0.296376i
\(768\) 0 0
\(769\) −14498.2 −0.679868 −0.339934 0.940449i \(-0.610405\pi\)
−0.339934 + 0.940449i \(0.610405\pi\)
\(770\) 7128.88 1071.45i 0.333645 0.0501457i
\(771\) 0 0
\(772\) 154.241 + 267.153i 0.00719073 + 0.0124547i
\(773\) 7418.91 12849.9i 0.345200 0.597904i −0.640190 0.768217i \(-0.721144\pi\)
0.985390 + 0.170312i \(0.0544777\pi\)
\(774\) 0 0
\(775\) −1530.45 2650.81i −0.0709358 0.122864i
\(776\) 10692.0 0.494615
\(777\) 0 0
\(778\) −4015.82 −0.185057
\(779\) −22133.2 38335.9i −1.01798 1.76319i
\(780\) 0 0
\(781\) 492.293 852.677i 0.0225552 0.0390668i
\(782\) −6058.42 10493.5i −0.277044 0.479855i
\(783\) 0 0
\(784\) −1225.69 + 5349.38i −0.0558348 + 0.243685i
\(785\) −20918.8 −0.951112
\(786\) 0 0
\(787\) −22013.0 + 38127.6i −0.997050 + 1.72694i −0.432059 + 0.901845i \(0.642213\pi\)
−0.564991 + 0.825097i \(0.691120\pi\)
\(788\) −2519.93 + 4364.64i −0.113920 + 0.197315i
\(789\) 0 0
\(790\) 22339.8 1.00609
\(791\) −12244.3 + 31159.4i −0.550387 + 1.40063i
\(792\) 0 0
\(793\) 12120.8 + 20993.8i 0.542776 + 0.940116i
\(794\) 1271.06 2201.55i 0.0568116 0.0984005i
\(795\) 0 0
\(796\) −10901.5 18881.9i −0.485418 0.840769i
\(797\) −14499.6 −0.644419 −0.322209 0.946668i \(-0.604426\pi\)
−0.322209 + 0.946668i \(0.604426\pi\)
\(798\) 0 0
\(799\) 31171.5 1.38019
\(800\) 2151.59 + 3726.67i 0.0950880 + 0.164697i
\(801\) 0 0
\(802\) −15025.4 + 26024.8i −0.661553 + 1.14584i
\(803\) 5913.23 + 10242.0i 0.259867 + 0.450103i
\(804\) 0 0
\(805\) −8968.59 11255.9i −0.392673 0.492820i
\(806\) 1809.65 0.0790845
\(807\) 0 0
\(808\) 825.666 1430.10i 0.0359490 0.0622656i
\(809\) −8965.81 + 15529.2i −0.389643 + 0.674881i −0.992401 0.123042i \(-0.960735\pi\)
0.602758 + 0.797924i \(0.294068\pi\)
\(810\) 0 0
\(811\) 7961.18 0.344704 0.172352 0.985035i \(-0.444863\pi\)
0.172352 + 0.985035i \(0.444863\pi\)
\(812\) −4295.42 5390.93i −0.185640 0.232986i
\(813\) 0 0
\(814\) −4841.61 8385.91i −0.208474 0.361088i
\(815\) −23953.3 + 41488.3i −1.02951 + 1.78316i
\(816\) 0 0
\(817\) 14122.3 + 24460.5i 0.604745 + 1.04745i
\(818\) −956.906 −0.0409015
\(819\) 0 0
\(820\) −22813.8 −0.971575
\(821\) −3354.32 5809.86i −0.142590 0.246974i 0.785881 0.618378i \(-0.212210\pi\)
−0.928471 + 0.371404i \(0.878877\pi\)
\(822\) 0 0
\(823\) 279.982 484.944i 0.0118585 0.0205396i −0.860035 0.510235i \(-0.829559\pi\)
0.871894 + 0.489695i \(0.162892\pi\)
\(824\) −2753.78 4769.70i −0.116423 0.201651i
\(825\) 0 0
\(826\) 2477.36 6304.43i 0.104356 0.265568i
\(827\) 41169.0 1.73106 0.865530 0.500858i \(-0.166982\pi\)
0.865530 + 0.500858i \(0.166982\pi\)
\(828\) 0 0
\(829\) 2086.87 3614.57i 0.0874308 0.151435i −0.818994 0.573803i \(-0.805468\pi\)
0.906424 + 0.422368i \(0.138801\pi\)
\(830\) −22697.3 + 39312.8i −0.949198 + 1.64406i
\(831\) 0 0
\(832\) −2544.11 −0.106011
\(833\) 41171.9 12662.0i 1.71251 0.526666i
\(834\) 0 0
\(835\) −29052.9 50321.2i −1.20409 2.08555i
\(836\) 3021.08 5232.66i 0.124983 0.216478i
\(837\) 0 0
\(838\) 11608.0 + 20105.6i 0.478510 + 0.828803i
\(839\) −9010.93 −0.370789 −0.185394 0.982664i \(-0.559356\pi\)
−0.185394 + 0.982664i \(0.559356\pi\)
\(840\) 0 0
\(841\) −15731.4 −0.645021
\(842\) −3833.92 6640.55i −0.156919 0.271791i
\(843\) 0 0
\(844\) −652.825 + 1130.73i −0.0266246 + 0.0461152i
\(845\) 4967.75 + 8604.39i 0.202243 + 0.350296i
\(846\) 0 0
\(847\) 21703.1 3261.90i 0.880434 0.132326i
\(848\) 5358.73 0.217004
\(849\) 0 0
\(850\) 16887.7 29250.4i 0.681463 1.18033i
\(851\) −9665.88 + 16741.8i −0.389356 + 0.674385i
\(852\) 0 0
\(853\) −24474.7 −0.982411 −0.491205 0.871044i \(-0.663444\pi\)
−0.491205 + 0.871044i \(0.663444\pi\)
\(854\) −14076.1 17666.1i −0.564021 0.707869i
\(855\) 0 0
\(856\) 1813.70 + 3141.42i 0.0724194 + 0.125434i
\(857\) −14742.4 + 25534.5i −0.587619 + 1.01779i 0.406925 + 0.913462i \(0.366601\pi\)
−0.994543 + 0.104324i \(0.966732\pi\)
\(858\) 0 0
\(859\) −3986.84 6905.41i −0.158358 0.274284i 0.775919 0.630833i \(-0.217287\pi\)
−0.934277 + 0.356549i \(0.883953\pi\)
\(860\) 14556.5 0.577178
\(861\) 0 0
\(862\) 1996.09 0.0788715
\(863\) −13792.0 23888.4i −0.544015 0.942261i −0.998668 0.0515928i \(-0.983570\pi\)
0.454653 0.890668i \(-0.349763\pi\)
\(864\) 0 0
\(865\) 20348.0 35243.7i 0.799829 1.38535i
\(866\) 1298.17 + 2248.50i 0.0509397 + 0.0882301i
\(867\) 0 0
\(868\) −1667.49 + 250.618i −0.0652055 + 0.00980017i
\(869\) −8378.16 −0.327054
\(870\) 0 0
\(871\) 2352.90 4075.34i 0.0915327 0.158539i
\(872\) 5483.93 9498.45i 0.212970 0.368874i
\(873\) 0 0
\(874\) −12062.7 −0.466849
\(875\) 1033.76 2630.74i 0.0399401 0.101640i
\(876\) 0 0
\(877\) −7078.94 12261.1i −0.272564 0.472095i 0.696954 0.717116i \(-0.254538\pi\)
−0.969518 + 0.245021i \(0.921205\pi\)
\(878\) −1933.41 + 3348.76i −0.0743159 + 0.128719i
\(879\) 0 0
\(880\) −1556.99 2696.78i −0.0596431 0.103305i
\(881\) −31107.6 −1.18960 −0.594802 0.803873i \(-0.702769\pi\)
−0.594802 + 0.803873i \(0.702769\pi\)
\(882\) 0 0
\(883\) 9141.04 0.348381 0.174190 0.984712i \(-0.444269\pi\)
0.174190 + 0.984712i \(0.444269\pi\)
\(884\) 9984.29 + 17293.3i 0.379873 + 0.657960i
\(885\) 0 0
\(886\) 14534.0 25173.7i 0.551106 0.954544i
\(887\) −17902.3 31007.8i −0.677680 1.17378i −0.975678 0.219209i \(-0.929652\pi\)
0.297998 0.954567i \(-0.403681\pi\)
\(888\) 0 0
\(889\) −1330.82 + 3386.69i −0.0502072 + 0.127768i
\(890\) 39027.4 1.46989
\(891\) 0 0
\(892\) 6190.50 10722.3i 0.232369 0.402475i
\(893\) 15516.1 26874.7i 0.581441 1.00709i
\(894\) 0 0
\(895\) −22913.0 −0.855751
\(896\) 2344.26 352.335i 0.0874066 0.0131369i
\(897\) 0 0
\(898\) 4799.65 + 8313.24i 0.178359 + 0.308927i
\(899\) 1058.95 1834.16i 0.0392858 0.0680451i
\(900\) 0 0
\(901\) −21030.1 36425.3i −0.777597 1.34684i
\(902\) 8555.92 0.315833
\(903\) 0 0
\(904\) 14461.5 0.532060
\(905\) −20089.3 34795.7i −0.737891 1.27806i
\(906\) 0 0
\(907\) 11155.9 19322.6i 0.408407 0.707382i −0.586304 0.810091i \(-0.699418\pi\)
0.994711 + 0.102709i \(0.0327511\pi\)
\(908\) −1253.43 2171.00i −0.0458110 0.0793470i
\(909\) 0 0
\(910\) 14780.2 + 18549.8i 0.538418 + 0.675737i
\(911\) −11553.9 −0.420195 −0.210097 0.977680i \(-0.567378\pi\)
−0.210097 + 0.977680i \(0.567378\pi\)
\(912\) 0 0
\(913\) 8512.23 14743.6i 0.308558 0.534439i
\(914\) 4734.27 8200.00i 0.171330 0.296753i
\(915\) 0 0
\(916\) 26666.0 0.961867
\(917\) −27590.6 + 4146.77i −0.993589 + 0.149333i
\(918\) 0 0
\(919\) 13687.1 + 23706.8i 0.491291 + 0.850942i 0.999950 0.0100269i \(-0.00319171\pi\)
−0.508658 + 0.860968i \(0.669858\pi\)
\(920\) −3108.40 + 5383.90i −0.111392 + 0.192937i
\(921\) 0 0
\(922\) 8137.41 + 14094.4i 0.290663 + 0.503443i
\(923\) 3239.39 0.115521
\(924\) 0 0
\(925\) −53886.8 −1.91545
\(926\) 8671.77 + 15020.0i 0.307745 + 0.533031i
\(927\) 0 0
\(928\) −1488.74 + 2578.57i −0.0526618 + 0.0912130i
\(929\) 18587.1 + 32193.7i 0.656428 + 1.13697i 0.981534 + 0.191289i \(0.0612669\pi\)
−0.325105 + 0.945678i \(0.605400\pi\)
\(930\) 0 0
\(931\) 9577.32 41799.2i 0.337147 1.47144i
\(932\) −14002.1 −0.492117
\(933\) 0 0
\(934\) 15588.1 26999.4i 0.546100 0.945874i
\(935\) −12220.7 + 21166.8i −0.427442 + 0.740352i
\(936\) 0 0
\(937\) 603.266 0.0210329 0.0105165 0.999945i \(-0.496652\pi\)
0.0105165 + 0.999945i \(0.496652\pi\)
\(938\) −1603.68 + 4081.06i −0.0558229 + 0.142059i
\(939\) 0 0
\(940\) −7996.60 13850.5i −0.277468 0.480589i
\(941\) −8075.89 + 13987.9i −0.279773 + 0.484581i −0.971328 0.237742i \(-0.923593\pi\)
0.691555 + 0.722324i \(0.256926\pi\)
\(942\) 0 0
\(943\) −8540.61 14792.8i −0.294932 0.510837i
\(944\) −2925.97 −0.100881
\(945\) 0 0
\(946\) −5459.18 −0.187625
\(947\) 8506.64 + 14733.9i 0.291899 + 0.505585i 0.974259 0.225432i \(-0.0723794\pi\)
−0.682359 + 0.731017i \(0.739046\pi\)
\(948\) 0 0
\(949\) −19455.1 + 33697.3i −0.665480 + 1.15264i
\(950\) −16812.2 29119.6i −0.574169 0.994491i
\(951\) 0 0
\(952\) −11594.9 14552.1i −0.394742 0.495417i
\(953\) −5233.67 −0.177896 −0.0889482 0.996036i \(-0.528351\pi\)
−0.0889482 + 0.996036i \(0.528351\pi\)
\(954\) 0 0
\(955\) 29750.4 51529.2i 1.00806 1.74602i
\(956\) −238.196 + 412.568i −0.00805838 + 0.0139575i
\(957\) 0 0
\(958\) 19068.2 0.643074
\(959\) −3639.44 4567.65i −0.122548 0.153803i
\(960\) 0 0
\(961\) 14636.4 + 25351.1i 0.491304 + 0.850964i
\(962\) 15929.4 27590.5i 0.533871 0.924691i
\(963\) 0 0
\(964\) −2543.61 4405.66i −0.0849836 0.147196i
\(965\) −1242.27 −0.0414405
\(966\) 0 0
\(967\) 16834.4 0.559832 0.279916 0.960024i \(-0.409693\pi\)
0.279916 + 0.960024i \(0.409693\pi\)
\(968\) −4740.08 8210.06i −0.157388 0.272605i
\(969\) 0 0
\(970\) −21528.7 + 37288.8i −0.712623 + 1.23430i
\(971\) 26609.2 + 46088.5i 0.879434 + 1.52322i 0.851963 + 0.523602i \(0.175412\pi\)
0.0274708 + 0.999623i \(0.491255\pi\)
\(972\) 0 0
\(973\) −2197.99 + 5593.48i −0.0724196 + 0.184295i
\(974\) 17594.2 0.578803
\(975\) 0 0
\(976\) −4878.59 + 8449.96i −0.160000 + 0.277128i
\(977\) 27579.9 47769.9i 0.903133 1.56427i 0.0797279 0.996817i \(-0.474595\pi\)
0.823405 0.567455i \(-0.192072\pi\)
\(978\) 0 0
\(979\) −14636.6 −0.477821
\(980\) −16188.2 15045.7i −0.527665 0.490427i
\(981\) 0 0
\(982\) −15749.6 27279.2i −0.511804 0.886470i
\(983\) −25566.4 + 44282.2i −0.829542 + 1.43681i 0.0688555 + 0.997627i \(0.478065\pi\)
−0.898398 + 0.439183i \(0.855268\pi\)
\(984\) 0 0
\(985\) −10147.9 17576.6i −0.328262 0.568567i
\(986\) 23370.0 0.754820
\(987\) 0 0
\(988\) 19879.3 0.640127
\(989\) 5449.41 + 9438.65i 0.175208 + 0.303470i
\(990\) 0 0
\(991\) −18879.1 + 32699.6i −0.605161 + 1.04817i 0.386865 + 0.922136i \(0.373558\pi\)
−0.992026 + 0.126033i \(0.959776\pi\)
\(992\) 364.190 + 630.795i 0.0116563 + 0.0201893i
\(993\) 0 0
\(994\) −2984.92 + 448.624i −0.0952475 + 0.0143154i
\(995\) 87801.8 2.79749
\(996\) 0 0
\(997\) 12028.9 20834.6i 0.382105 0.661825i −0.609258 0.792972i \(-0.708533\pi\)
0.991363 + 0.131147i \(0.0418660\pi\)
\(998\) −12981.2 + 22484.1i −0.411736 + 0.713148i
\(999\) 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.g.f.109.1 yes 8
3.2 odd 2 378.4.g.c.109.4 8
7.2 even 3 inner 378.4.g.f.163.1 yes 8
21.2 odd 6 378.4.g.c.163.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.4.g.c.109.4 8 3.2 odd 2
378.4.g.c.163.4 yes 8 21.2 odd 6
378.4.g.f.109.1 yes 8 1.1 even 1 trivial
378.4.g.f.163.1 yes 8 7.2 even 3 inner