Properties

Label 1050.2.b.e.251.12
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,2,Mod(251,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.12
Root \(1.68439 - 0.403509i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.e.251.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.68439 + 0.403509i) q^{3} -1.00000 q^{4} +(-0.403509 + 1.68439i) q^{6} +(2.31502 + 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 + 1.35934i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.68439 + 0.403509i) q^{3} -1.00000 q^{4} +(-0.403509 + 1.68439i) q^{6} +(2.31502 + 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 + 1.35934i) q^{9} -5.34872i q^{11} +(-1.68439 - 0.403509i) q^{12} -3.95617i q^{13} +(-1.28088 + 2.31502i) q^{14} +1.00000 q^{16} +7.32496 q^{17} +(-1.35934 + 2.67436i) q^{18} -0.807019i q^{19} +(3.38256 + 3.09165i) q^{21} +5.34872 q^{22} -0.281327i q^{23} +(0.403509 - 1.68439i) q^{24} +3.95617 q^{26} +(3.95617 + 3.36879i) q^{27} +(-2.31502 - 1.28088i) q^{28} +0.281327i q^{29} +9.07971i q^{31} +1.00000i q^{32} +(2.15826 - 9.00935i) q^{33} +7.32496i q^{34} +(-2.67436 - 1.35934i) q^{36} -6.06739 q^{37} +0.807019 q^{38} +(1.59635 - 6.66375i) q^{39} -6.15019 q^{41} +(-3.09165 + 3.38256i) q^{42} -6.34872 q^{43} +5.34872i q^{44} +0.281327 q^{46} -5.78984 q^{47} +(1.68439 + 0.403509i) q^{48} +(3.71867 + 5.93055i) q^{49} +(12.3381 + 2.95569i) q^{51} +3.95617i q^{52} -10.9788i q^{53} +(-3.36879 + 3.95617i) q^{54} +(1.28088 - 2.31502i) q^{56} +(0.325639 - 1.35934i) q^{57} -0.281327 q^{58} +4.90390 q^{59} +13.2555i q^{61} -9.07971 q^{62} +(4.45006 + 6.57244i) q^{63} -1.00000 q^{64} +(9.00935 + 2.15826i) q^{66} +6.71867 q^{67} -7.32496 q^{68} +(0.113518 - 0.473865i) q^{69} +3.36995i q^{71} +(1.35934 - 2.67436i) q^{72} +4.98282i q^{73} -6.06739i q^{74} +0.807019i q^{76} +(6.85109 - 12.3824i) q^{77} +(6.66375 + 1.59635i) q^{78} -3.26010 q^{79} +(5.30441 + 7.27071i) q^{81} -6.15019i q^{82} -1.53511 q^{83} +(-3.38256 - 3.09165i) q^{84} -6.34872i q^{86} +(-0.113518 + 0.473865i) q^{87} -5.34872 q^{88} +4.31652 q^{89} +(5.06739 - 9.15863i) q^{91} +0.281327i q^{92} +(-3.66375 + 15.2938i) q^{93} -5.78984i q^{94} +(-0.403509 + 1.68439i) q^{96} +15.0892i q^{97} +(-5.93055 + 3.71867i) q^{98} +(7.27071 - 14.3044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{4} + 4 q^{7} + 12 q^{16} - 8 q^{18} + 14 q^{21} - 4 q^{28} + 8 q^{37} + 12 q^{39} - 14 q^{42} - 12 q^{43} + 20 q^{46} + 28 q^{49} + 28 q^{51} + 36 q^{57} - 20 q^{58} + 22 q^{63} - 12 q^{64} + 64 q^{67} + 8 q^{72} - 8 q^{78} + 56 q^{79} - 16 q^{81} - 14 q^{84} - 20 q^{91} + 44 q^{93} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.68439 + 0.403509i 0.972485 + 0.232966i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −0.403509 + 1.68439i −0.164732 + 0.687651i
\(7\) 2.31502 + 1.28088i 0.874997 + 0.484129i
\(8\) 1.00000i 0.353553i
\(9\) 2.67436 + 1.35934i 0.891454 + 0.453112i
\(10\) 0 0
\(11\) 5.34872i 1.61270i −0.591439 0.806350i \(-0.701440\pi\)
0.591439 0.806350i \(-0.298560\pi\)
\(12\) −1.68439 0.403509i −0.486242 0.116483i
\(13\) 3.95617i 1.09724i −0.836070 0.548622i \(-0.815153\pi\)
0.836070 0.548622i \(-0.184847\pi\)
\(14\) −1.28088 + 2.31502i −0.342331 + 0.618716i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.32496 1.77656 0.888281 0.459300i \(-0.151900\pi\)
0.888281 + 0.459300i \(0.151900\pi\)
\(18\) −1.35934 + 2.67436i −0.320399 + 0.630353i
\(19\) 0.807019i 0.185143i −0.995706 0.0925714i \(-0.970491\pi\)
0.995706 0.0925714i \(-0.0295086\pi\)
\(20\) 0 0
\(21\) 3.38256 + 3.09165i 0.738136 + 0.674652i
\(22\) 5.34872 1.14035
\(23\) 0.281327i 0.0586607i −0.999570 0.0293304i \(-0.990663\pi\)
0.999570 0.0293304i \(-0.00933749\pi\)
\(24\) 0.403509 1.68439i 0.0823660 0.343825i
\(25\) 0 0
\(26\) 3.95617 0.775869
\(27\) 3.95617 + 3.36879i 0.761365 + 0.648323i
\(28\) −2.31502 1.28088i −0.437498 0.242064i
\(29\) 0.281327i 0.0522411i 0.999659 + 0.0261206i \(0.00831538\pi\)
−0.999659 + 0.0261206i \(0.991685\pi\)
\(30\) 0 0
\(31\) 9.07971i 1.63076i 0.578924 + 0.815382i \(0.303473\pi\)
−0.578924 + 0.815382i \(0.696527\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.15826 9.00935i 0.375705 1.56833i
\(34\) 7.32496i 1.25622i
\(35\) 0 0
\(36\) −2.67436 1.35934i −0.445727 0.226556i
\(37\) −6.06739 −0.997473 −0.498737 0.866754i \(-0.666203\pi\)
−0.498737 + 0.866754i \(0.666203\pi\)
\(38\) 0.807019 0.130916
\(39\) 1.59635 6.66375i 0.255621 1.06705i
\(40\) 0 0
\(41\) −6.15019 −0.960498 −0.480249 0.877132i \(-0.659454\pi\)
−0.480249 + 0.877132i \(0.659454\pi\)
\(42\) −3.09165 + 3.38256i −0.477051 + 0.521941i
\(43\) −6.34872 −0.968171 −0.484085 0.875021i \(-0.660848\pi\)
−0.484085 + 0.875021i \(0.660848\pi\)
\(44\) 5.34872i 0.806350i
\(45\) 0 0
\(46\) 0.281327 0.0414794
\(47\) −5.78984 −0.844535 −0.422268 0.906471i \(-0.638766\pi\)
−0.422268 + 0.906471i \(0.638766\pi\)
\(48\) 1.68439 + 0.403509i 0.243121 + 0.0582415i
\(49\) 3.71867 + 5.93055i 0.531239 + 0.847222i
\(50\) 0 0
\(51\) 12.3381 + 2.95569i 1.72768 + 0.413879i
\(52\) 3.95617i 0.548622i
\(53\) 10.9788i 1.50805i −0.656846 0.754025i \(-0.728110\pi\)
0.656846 0.754025i \(-0.271890\pi\)
\(54\) −3.36879 + 3.95617i −0.458434 + 0.538367i
\(55\) 0 0
\(56\) 1.28088 2.31502i 0.171165 0.309358i
\(57\) 0.325639 1.35934i 0.0431320 0.180049i
\(58\) −0.281327 −0.0369401
\(59\) 4.90390 0.638433 0.319217 0.947682i \(-0.396580\pi\)
0.319217 + 0.947682i \(0.396580\pi\)
\(60\) 0 0
\(61\) 13.2555i 1.69719i 0.529040 + 0.848597i \(0.322552\pi\)
−0.529040 + 0.848597i \(0.677448\pi\)
\(62\) −9.07971 −1.15312
\(63\) 4.45006 + 6.57244i 0.560654 + 0.828050i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 9.00935 + 2.15826i 1.10897 + 0.265663i
\(67\) 6.71867 0.820817 0.410408 0.911902i \(-0.365386\pi\)
0.410408 + 0.911902i \(0.365386\pi\)
\(68\) −7.32496 −0.888281
\(69\) 0.113518 0.473865i 0.0136660 0.0570467i
\(70\) 0 0
\(71\) 3.36995i 0.399940i 0.979802 + 0.199970i \(0.0640844\pi\)
−0.979802 + 0.199970i \(0.935916\pi\)
\(72\) 1.35934 2.67436i 0.160199 0.315176i
\(73\) 4.98282i 0.583195i 0.956541 + 0.291598i \(0.0941868\pi\)
−0.956541 + 0.291598i \(0.905813\pi\)
\(74\) 6.06739i 0.705320i
\(75\) 0 0
\(76\) 0.807019i 0.0925714i
\(77\) 6.85109 12.3824i 0.780754 1.41111i
\(78\) 6.66375 + 1.59635i 0.754521 + 0.180751i
\(79\) −3.26010 −0.366789 −0.183395 0.983039i \(-0.558709\pi\)
−0.183395 + 0.983039i \(0.558709\pi\)
\(80\) 0 0
\(81\) 5.30441 + 7.27071i 0.589379 + 0.807857i
\(82\) 6.15019i 0.679175i
\(83\) −1.53511 −0.168501 −0.0842503 0.996445i \(-0.526850\pi\)
−0.0842503 + 0.996445i \(0.526850\pi\)
\(84\) −3.38256 3.09165i −0.369068 0.337326i
\(85\) 0 0
\(86\) 6.34872i 0.684600i
\(87\) −0.113518 + 0.473865i −0.0121704 + 0.0508037i
\(88\) −5.34872 −0.570176
\(89\) 4.31652 0.457550 0.228775 0.973479i \(-0.426528\pi\)
0.228775 + 0.973479i \(0.426528\pi\)
\(90\) 0 0
\(91\) 5.06739 9.15863i 0.531207 0.960085i
\(92\) 0.281327i 0.0293304i
\(93\) −3.66375 + 15.2938i −0.379913 + 1.58589i
\(94\) 5.78984i 0.597177i
\(95\) 0 0
\(96\) −0.403509 + 1.68439i −0.0411830 + 0.171913i
\(97\) 15.0892i 1.53207i 0.642796 + 0.766037i \(0.277774\pi\)
−0.642796 + 0.766037i \(0.722226\pi\)
\(98\) −5.93055 + 3.71867i −0.599076 + 0.375643i
\(99\) 7.27071 14.3044i 0.730734 1.43765i
\(100\) 0 0
\(101\) 5.78984 0.576111 0.288055 0.957614i \(-0.406991\pi\)
0.288055 + 0.957614i \(0.406991\pi\)
\(102\) −2.95569 + 12.3381i −0.292657 + 1.22165i
\(103\) 6.95721i 0.685514i −0.939424 0.342757i \(-0.888639\pi\)
0.939424 0.342757i \(-0.111361\pi\)
\(104\) −3.95617 −0.387934
\(105\) 0 0
\(106\) 10.9788 1.06635
\(107\) 10.6088i 1.02559i −0.858510 0.512797i \(-0.828610\pi\)
0.858510 0.512797i \(-0.171390\pi\)
\(108\) −3.95617 3.36879i −0.380683 0.324162i
\(109\) −18.1348 −1.73700 −0.868499 0.495691i \(-0.834915\pi\)
−0.868499 + 0.495691i \(0.834915\pi\)
\(110\) 0 0
\(111\) −10.2199 2.44825i −0.970028 0.232378i
\(112\) 2.31502 + 1.28088i 0.218749 + 0.121032i
\(113\) 8.54142i 0.803510i −0.915747 0.401755i \(-0.868400\pi\)
0.915747 0.401755i \(-0.131600\pi\)
\(114\) 1.35934 + 0.325639i 0.127314 + 0.0304989i
\(115\) 0 0
\(116\) 0.281327i 0.0261206i
\(117\) 5.37777 10.5802i 0.497175 0.978142i
\(118\) 4.90390i 0.451441i
\(119\) 16.9574 + 9.38242i 1.55449 + 0.860085i
\(120\) 0 0
\(121\) −17.6088 −1.60080
\(122\) −13.2555 −1.20010
\(123\) −10.3593 2.48166i −0.934070 0.223764i
\(124\) 9.07971i 0.815382i
\(125\) 0 0
\(126\) −6.57244 + 4.45006i −0.585520 + 0.396443i
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −10.6937 2.56177i −0.941532 0.225551i
\(130\) 0 0
\(131\) −16.5454 −1.44558 −0.722788 0.691070i \(-0.757140\pi\)
−0.722788 + 0.691070i \(0.757140\pi\)
\(132\) −2.15826 + 9.00935i −0.187852 + 0.784163i
\(133\) 1.03370 1.86827i 0.0896329 0.161999i
\(134\) 6.71867i 0.580405i
\(135\) 0 0
\(136\) 7.32496i 0.628110i
\(137\) 7.41612i 0.633601i 0.948492 + 0.316801i \(0.102609\pi\)
−0.948492 + 0.316801i \(0.897391\pi\)
\(138\) 0.473865 + 0.113518i 0.0403381 + 0.00966330i
\(139\) 6.36982i 0.540281i 0.962821 + 0.270141i \(0.0870702\pi\)
−0.962821 + 0.270141i \(0.912930\pi\)
\(140\) 0 0
\(141\) −9.75237 2.33625i −0.821298 0.196748i
\(142\) −3.36995 −0.282800
\(143\) −21.1604 −1.76953
\(144\) 2.67436 + 1.35934i 0.222863 + 0.113278i
\(145\) 0 0
\(146\) −4.98282 −0.412381
\(147\) 3.87067 + 11.4899i 0.319248 + 0.947671i
\(148\) 6.06739 0.498737
\(149\) 7.60882i 0.623339i 0.950191 + 0.311669i \(0.100888\pi\)
−0.950191 + 0.311669i \(0.899112\pi\)
\(150\) 0 0
\(151\) −4.63005 −0.376788 −0.188394 0.982094i \(-0.560328\pi\)
−0.188394 + 0.982094i \(0.560328\pi\)
\(152\) −0.807019 −0.0654578
\(153\) 19.5896 + 9.95708i 1.58372 + 0.804982i
\(154\) 12.3824 + 6.85109i 0.997804 + 0.552077i
\(155\) 0 0
\(156\) −1.59635 + 6.66375i −0.127810 + 0.533527i
\(157\) 15.3162i 1.22237i −0.791489 0.611184i \(-0.790694\pi\)
0.791489 0.611184i \(-0.209306\pi\)
\(158\) 3.26010i 0.259359i
\(159\) 4.43004 18.4926i 0.351325 1.46656i
\(160\) 0 0
\(161\) 0.360347 0.651279i 0.0283993 0.0513280i
\(162\) −7.27071 + 5.30441i −0.571241 + 0.416754i
\(163\) 3.06739 0.240257 0.120128 0.992758i \(-0.461669\pi\)
0.120128 + 0.992758i \(0.461669\pi\)
\(164\) 6.15019 0.480249
\(165\) 0 0
\(166\) 1.53511i 0.119148i
\(167\) −1.89546 −0.146675 −0.0733376 0.997307i \(-0.523365\pi\)
−0.0733376 + 0.997307i \(0.523365\pi\)
\(168\) 3.09165 3.38256i 0.238526 0.260970i
\(169\) −2.65128 −0.203945
\(170\) 0 0
\(171\) 1.09701 2.15826i 0.0838904 0.165046i
\(172\) 6.34872 0.484085
\(173\) 8.86007 0.673619 0.336809 0.941573i \(-0.390652\pi\)
0.336809 + 0.941573i \(0.390652\pi\)
\(174\) −0.473865 0.113518i −0.0359236 0.00860578i
\(175\) 0 0
\(176\) 5.34872i 0.403175i
\(177\) 8.26010 + 1.97877i 0.620867 + 0.148733i
\(178\) 4.31652i 0.323537i
\(179\) 11.3487i 0.848243i −0.905605 0.424122i \(-0.860583\pi\)
0.905605 0.424122i \(-0.139417\pi\)
\(180\) 0 0
\(181\) 8.63303i 0.641688i −0.947132 0.320844i \(-0.896033\pi\)
0.947132 0.320844i \(-0.103967\pi\)
\(182\) 9.15863 + 5.06739i 0.678883 + 0.375620i
\(183\) −5.34872 + 22.3275i −0.395389 + 1.65050i
\(184\) −0.281327 −0.0207397
\(185\) 0 0
\(186\) −15.2938 3.66375i −1.12140 0.268639i
\(187\) 39.1791i 2.86506i
\(188\) 5.78984 0.422268
\(189\) 4.84360 + 12.8662i 0.352320 + 0.935879i
\(190\) 0 0
\(191\) 7.78607i 0.563380i 0.959505 + 0.281690i \(0.0908950\pi\)
−0.959505 + 0.281690i \(0.909105\pi\)
\(192\) −1.68439 0.403509i −0.121561 0.0291208i
\(193\) 25.1715 1.81188 0.905941 0.423404i \(-0.139165\pi\)
0.905941 + 0.423404i \(0.139165\pi\)
\(194\) −15.0892 −1.08334
\(195\) 0 0
\(196\) −3.71867 5.93055i −0.265619 0.423611i
\(197\) 2.52597i 0.179968i 0.995943 + 0.0899840i \(0.0286816\pi\)
−0.995943 + 0.0899840i \(0.971318\pi\)
\(198\) 14.3044 + 7.27071i 1.01657 + 0.516707i
\(199\) 0.947731i 0.0671828i −0.999436 0.0335914i \(-0.989306\pi\)
0.999436 0.0335914i \(-0.0106945\pi\)
\(200\) 0 0
\(201\) 11.3169 + 2.71105i 0.798232 + 0.191222i
\(202\) 5.78984i 0.407372i
\(203\) −0.360347 + 0.651279i −0.0252914 + 0.0457108i
\(204\) −12.3381 2.95569i −0.863840 0.206940i
\(205\) 0 0
\(206\) 6.95721 0.484732
\(207\) 0.382418 0.752370i 0.0265799 0.0522933i
\(208\) 3.95617i 0.274311i
\(209\) −4.31652 −0.298580
\(210\) 0 0
\(211\) −12.8901 −0.887394 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(212\) 10.9788i 0.754025i
\(213\) −1.35981 + 5.67632i −0.0931724 + 0.388935i
\(214\) 10.6088 0.725204
\(215\) 0 0
\(216\) 3.36879 3.95617i 0.229217 0.269183i
\(217\) −11.6300 + 21.0197i −0.789499 + 1.42691i
\(218\) 18.1348i 1.22824i
\(219\) −2.01062 + 8.39303i −0.135865 + 0.567149i
\(220\) 0 0
\(221\) 28.9788i 1.94932i
\(222\) 2.44825 10.2199i 0.164316 0.685913i
\(223\) 23.7296i 1.58905i 0.607230 + 0.794526i \(0.292281\pi\)
−0.607230 + 0.794526i \(0.707719\pi\)
\(224\) −1.28088 + 2.31502i −0.0855827 + 0.154679i
\(225\) 0 0
\(226\) 8.54142 0.568167
\(227\) 10.4667 0.694700 0.347350 0.937736i \(-0.387082\pi\)
0.347350 + 0.937736i \(0.387082\pi\)
\(228\) −0.325639 + 1.35934i −0.0215660 + 0.0900243i
\(229\) 16.4762i 1.08878i −0.838833 0.544388i \(-0.816762\pi\)
0.838833 0.544388i \(-0.183238\pi\)
\(230\) 0 0
\(231\) 16.5364 18.0924i 1.08801 1.19039i
\(232\) 0.281327 0.0184700
\(233\) 27.9575i 1.83156i −0.401681 0.915780i \(-0.631574\pi\)
0.401681 0.915780i \(-0.368426\pi\)
\(234\) 10.5802 + 5.37777i 0.691651 + 0.351556i
\(235\) 0 0
\(236\) −4.90390 −0.319217
\(237\) −5.49128 1.31548i −0.356697 0.0854495i
\(238\) −9.38242 + 16.9574i −0.608172 + 1.09919i
\(239\) 17.2601i 1.11646i 0.829685 + 0.558231i \(0.188520\pi\)
−0.829685 + 0.558231i \(0.811480\pi\)
\(240\) 0 0
\(241\) 19.1935i 1.23636i −0.786037 0.618180i \(-0.787870\pi\)
0.786037 0.618180i \(-0.212130\pi\)
\(242\) 17.6088i 1.13194i
\(243\) 6.00091 + 14.3871i 0.384959 + 0.922934i
\(244\) 13.2555i 0.848597i
\(245\) 0 0
\(246\) 2.48166 10.3593i 0.158225 0.660487i
\(247\) −3.19270 −0.203147
\(248\) 9.07971 0.576562
\(249\) −2.58574 0.619433i −0.163864 0.0392550i
\(250\) 0 0
\(251\) −21.0271 −1.32722 −0.663611 0.748078i \(-0.730977\pi\)
−0.663611 + 0.748078i \(0.730977\pi\)
\(252\) −4.45006 6.57244i −0.280327 0.414025i
\(253\) −1.50474 −0.0946022
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.5881 −0.909982 −0.454991 0.890496i \(-0.650358\pi\)
−0.454991 + 0.890496i \(0.650358\pi\)
\(258\) 2.56177 10.6937i 0.159489 0.665763i
\(259\) −14.0462 7.77163i −0.872786 0.482905i
\(260\) 0 0
\(261\) −0.382418 + 0.752370i −0.0236711 + 0.0465705i
\(262\) 16.5454i 1.02218i
\(263\) 8.91138i 0.549499i 0.961516 + 0.274749i \(0.0885949\pi\)
−0.961516 + 0.274749i \(0.911405\pi\)
\(264\) −9.00935 2.15826i −0.554487 0.132832i
\(265\) 0 0
\(266\) 1.86827 + 1.03370i 0.114551 + 0.0633800i
\(267\) 7.27071 + 1.74175i 0.444960 + 0.106594i
\(268\) −6.71867 −0.410408
\(269\) −22.3352 −1.36180 −0.680901 0.732375i \(-0.738412\pi\)
−0.680901 + 0.732375i \(0.738412\pi\)
\(270\) 0 0
\(271\) 7.17684i 0.435962i 0.975953 + 0.217981i \(0.0699471\pi\)
−0.975953 + 0.217981i \(0.930053\pi\)
\(272\) 7.32496 0.444141
\(273\) 12.2311 13.3820i 0.740258 0.809915i
\(274\) −7.41612 −0.448024
\(275\) 0 0
\(276\) −0.113518 + 0.473865i −0.00683298 + 0.0285233i
\(277\) −9.32749 −0.560435 −0.280217 0.959937i \(-0.590407\pi\)
−0.280217 + 0.959937i \(0.590407\pi\)
\(278\) −6.36982 −0.382037
\(279\) −12.3424 + 24.2824i −0.738919 + 1.45375i
\(280\) 0 0
\(281\) 17.4373i 1.04022i 0.854098 + 0.520112i \(0.174110\pi\)
−0.854098 + 0.520112i \(0.825890\pi\)
\(282\) 2.33625 9.75237i 0.139122 0.580745i
\(283\) 16.1776i 0.961660i −0.876814 0.480830i \(-0.840335\pi\)
0.876814 0.480830i \(-0.159665\pi\)
\(284\) 3.36995i 0.199970i
\(285\) 0 0
\(286\) 21.1604i 1.25124i
\(287\) −14.2378 7.87768i −0.840433 0.465005i
\(288\) −1.35934 + 2.67436i −0.0800997 + 0.157588i
\(289\) 36.6550 2.15618
\(290\) 0 0
\(291\) −6.08862 + 25.4161i −0.356922 + 1.48992i
\(292\) 4.98282i 0.291598i
\(293\) 22.5623 1.31810 0.659050 0.752099i \(-0.270958\pi\)
0.659050 + 0.752099i \(0.270958\pi\)
\(294\) −11.4899 + 3.87067i −0.670105 + 0.225742i
\(295\) 0 0
\(296\) 6.06739i 0.352660i
\(297\) 18.0187 21.1604i 1.04555 1.22785i
\(298\) −7.60882 −0.440767
\(299\) −1.11298 −0.0643652
\(300\) 0 0
\(301\) −14.6974 8.13197i −0.847146 0.468719i
\(302\) 4.63005i 0.266429i
\(303\) 9.75237 + 2.33625i 0.560259 + 0.134214i
\(304\) 0.807019i 0.0462857i
\(305\) 0 0
\(306\) −9.95708 + 19.5896i −0.569208 + 1.11986i
\(307\) 19.4057i 1.10754i 0.832669 + 0.553771i \(0.186812\pi\)
−0.832669 + 0.553771i \(0.813188\pi\)
\(308\) −6.85109 + 12.3824i −0.390377 + 0.705554i
\(309\) 2.80730 11.7187i 0.159702 0.666652i
\(310\) 0 0
\(311\) −6.73757 −0.382053 −0.191026 0.981585i \(-0.561182\pi\)
−0.191026 + 0.981585i \(0.561182\pi\)
\(312\) −6.66375 1.59635i −0.377260 0.0903756i
\(313\) 21.3875i 1.20889i −0.796646 0.604446i \(-0.793394\pi\)
0.796646 0.604446i \(-0.206606\pi\)
\(314\) 15.3162 0.864344
\(315\) 0 0
\(316\) 3.26010 0.183395
\(317\) 3.47403i 0.195121i 0.995230 + 0.0975605i \(0.0311039\pi\)
−0.995230 + 0.0975605i \(0.968896\pi\)
\(318\) 18.4926 + 4.43004i 1.03701 + 0.248424i
\(319\) 1.50474 0.0842493
\(320\) 0 0
\(321\) 4.28076 17.8694i 0.238929 0.997374i
\(322\) 0.651279 + 0.360347i 0.0362944 + 0.0200814i
\(323\) 5.91138i 0.328918i
\(324\) −5.30441 7.27071i −0.294689 0.403928i
\(325\) 0 0
\(326\) 3.06739i 0.169887i
\(327\) −30.5461 7.31755i −1.68920 0.404662i
\(328\) 6.15019i 0.339587i
\(329\) −13.4036 7.41612i −0.738966 0.408864i
\(330\) 0 0
\(331\) −8.93261 −0.490980 −0.245490 0.969399i \(-0.578949\pi\)
−0.245490 + 0.969399i \(0.578949\pi\)
\(332\) 1.53511 0.0842503
\(333\) −16.2264 8.24763i −0.889201 0.451967i
\(334\) 1.89546i 0.103715i
\(335\) 0 0
\(336\) 3.38256 + 3.09165i 0.184534 + 0.168663i
\(337\) −34.2176 −1.86395 −0.931977 0.362518i \(-0.881917\pi\)
−0.931977 + 0.362518i \(0.881917\pi\)
\(338\) 2.65128i 0.144211i
\(339\) 3.44654 14.3871i 0.187191 0.781401i
\(340\) 0 0
\(341\) 48.5648 2.62993
\(342\) 2.15826 + 1.09701i 0.116705 + 0.0593195i
\(343\) 1.01247 + 18.4926i 0.0546680 + 0.998505i
\(344\) 6.34872i 0.342300i
\(345\) 0 0
\(346\) 8.86007i 0.476320i
\(347\) 11.5260i 0.618747i −0.950941 0.309373i \(-0.899881\pi\)
0.950941 0.309373i \(-0.100119\pi\)
\(348\) 0.113518 0.473865i 0.00608521 0.0254018i
\(349\) 21.8342i 1.16876i 0.811482 + 0.584378i \(0.198661\pi\)
−0.811482 + 0.584378i \(0.801339\pi\)
\(350\) 0 0
\(351\) 13.3275 15.6513i 0.711369 0.835403i
\(352\) 5.34872 0.285088
\(353\) −4.84211 −0.257720 −0.128860 0.991663i \(-0.541132\pi\)
−0.128860 + 0.991663i \(0.541132\pi\)
\(354\) −1.97877 + 8.26010i −0.105170 + 0.439019i
\(355\) 0 0
\(356\) −4.31652 −0.228775
\(357\) 24.7771 + 22.6462i 1.31134 + 1.19856i
\(358\) 11.3487 0.599799
\(359\) 30.3063i 1.59950i −0.600331 0.799752i \(-0.704965\pi\)
0.600331 0.799752i \(-0.295035\pi\)
\(360\) 0 0
\(361\) 18.3487 0.965722
\(362\) 8.63303 0.453742
\(363\) −29.6602 7.10532i −1.55676 0.372933i
\(364\) −5.06739 + 9.15863i −0.265604 + 0.480043i
\(365\) 0 0
\(366\) −22.3275 5.34872i −1.16708 0.279582i
\(367\) 13.9910i 0.730325i 0.930944 + 0.365162i \(0.118987\pi\)
−0.930944 + 0.365162i \(0.881013\pi\)
\(368\) 0.281327i 0.0146652i
\(369\) −16.4478 8.36018i −0.856239 0.435213i
\(370\) 0 0
\(371\) 14.0625 25.4161i 0.730090 1.31954i
\(372\) 3.66375 15.2938i 0.189956 0.792946i
\(373\) −4.24464 −0.219779 −0.109890 0.993944i \(-0.535050\pi\)
−0.109890 + 0.993944i \(0.535050\pi\)
\(374\) 39.1791 2.02591
\(375\) 0 0
\(376\) 5.78984i 0.298588i
\(377\) 1.11298 0.0573213
\(378\) −12.8662 + 4.84360i −0.661767 + 0.249128i
\(379\) −1.63005 −0.0837299 −0.0418650 0.999123i \(-0.513330\pi\)
−0.0418650 + 0.999123i \(0.513330\pi\)
\(380\) 0 0
\(381\) −3.36879 0.807019i −0.172588 0.0413448i
\(382\) −7.78607 −0.398370
\(383\) −16.9994 −0.868631 −0.434316 0.900761i \(-0.643010\pi\)
−0.434316 + 0.900761i \(0.643010\pi\)
\(384\) 0.403509 1.68439i 0.0205915 0.0859563i
\(385\) 0 0
\(386\) 25.1715i 1.28119i
\(387\) −16.9788 8.63005i −0.863079 0.438690i
\(388\) 15.0892i 0.766037i
\(389\) 29.4623i 1.49380i 0.664938 + 0.746898i \(0.268458\pi\)
−0.664938 + 0.746898i \(0.731542\pi\)
\(390\) 0 0
\(391\) 2.06071i 0.104214i
\(392\) 5.93055 3.71867i 0.299538 0.187821i
\(393\) −27.8689 6.67621i −1.40580 0.336770i
\(394\) −2.52597 −0.127257
\(395\) 0 0
\(396\) −7.27071 + 14.3044i −0.365367 + 0.718824i
\(397\) 17.8706i 0.896899i −0.893808 0.448449i \(-0.851976\pi\)
0.893808 0.448449i \(-0.148024\pi\)
\(398\) 0.947731 0.0475054
\(399\) 2.49502 2.72979i 0.124907 0.136660i
\(400\) 0 0
\(401\) 12.6762i 0.633020i −0.948589 0.316510i \(-0.897489\pi\)
0.948589 0.316510i \(-0.102511\pi\)
\(402\) −2.71105 + 11.3169i −0.135215 + 0.564435i
\(403\) 35.9209 1.78935
\(404\) −5.78984 −0.288055
\(405\) 0 0
\(406\) −0.651279 0.360347i −0.0323224 0.0178837i
\(407\) 32.4528i 1.60863i
\(408\) 2.95569 12.3381i 0.146328 0.610827i
\(409\) 5.26425i 0.260300i −0.991494 0.130150i \(-0.958454\pi\)
0.991494 0.130150i \(-0.0415459\pi\)
\(410\) 0 0
\(411\) −2.99247 + 12.4917i −0.147608 + 0.616168i
\(412\) 6.95721i 0.342757i
\(413\) 11.3526 + 6.28133i 0.558627 + 0.309084i
\(414\) 0.752370 + 0.382418i 0.0369770 + 0.0187948i
\(415\) 0 0
\(416\) 3.95617 0.193967
\(417\) −2.57028 + 10.7293i −0.125867 + 0.525416i
\(418\) 4.31652i 0.211128i
\(419\) 13.1148 0.640700 0.320350 0.947299i \(-0.396200\pi\)
0.320350 + 0.947299i \(0.396200\pi\)
\(420\) 0 0
\(421\) 3.86521 0.188379 0.0941895 0.995554i \(-0.469974\pi\)
0.0941895 + 0.995554i \(0.469974\pi\)
\(422\) 12.8901i 0.627482i
\(423\) −15.4841 7.87034i −0.752864 0.382669i
\(424\) −10.9788 −0.533176
\(425\) 0 0
\(426\) −5.67632 1.35981i −0.275019 0.0658829i
\(427\) −16.9788 + 30.6868i −0.821660 + 1.48504i
\(428\) 10.6088i 0.512797i
\(429\) −35.6425 8.53844i −1.72084 0.412240i
\(430\) 0 0
\(431\) 10.2389i 0.493189i 0.969119 + 0.246594i \(0.0793115\pi\)
−0.969119 + 0.246594i \(0.920688\pi\)
\(432\) 3.95617 + 3.36879i 0.190341 + 0.162081i
\(433\) 22.7030i 1.09103i −0.838099 0.545517i \(-0.816333\pi\)
0.838099 0.545517i \(-0.183667\pi\)
\(434\) −21.0197 11.6300i −1.00898 0.558260i
\(435\) 0 0
\(436\) 18.1348 0.868499
\(437\) −0.227036 −0.0108606
\(438\) −8.39303 2.01062i −0.401035 0.0960709i
\(439\) 26.4492i 1.26235i −0.775639 0.631176i \(-0.782572\pi\)
0.775639 0.631176i \(-0.217428\pi\)
\(440\) 0 0
\(441\) 1.88345 + 20.9154i 0.0896883 + 0.995970i
\(442\) 28.9788 1.37838
\(443\) 27.8689i 1.32409i 0.749463 + 0.662046i \(0.230312\pi\)
−0.749463 + 0.662046i \(0.769688\pi\)
\(444\) 10.2199 + 2.44825i 0.485014 + 0.116189i
\(445\) 0 0
\(446\) −23.7296 −1.12363
\(447\) −3.07023 + 12.8162i −0.145217 + 0.606187i
\(448\) −2.31502 1.28088i −0.109375 0.0605161i
\(449\) 9.45858i 0.446378i 0.974775 + 0.223189i \(0.0716467\pi\)
−0.974775 + 0.223189i \(0.928353\pi\)
\(450\) 0 0
\(451\) 32.8956i 1.54900i
\(452\) 8.54142i 0.401755i
\(453\) −7.79882 1.86827i −0.366421 0.0877789i
\(454\) 10.4667i 0.491227i
\(455\) 0 0
\(456\) −1.35934 0.325639i −0.0636568 0.0152495i
\(457\) 31.8322 1.48905 0.744524 0.667595i \(-0.232676\pi\)
0.744524 + 0.667595i \(0.232676\pi\)
\(458\) 16.4762 0.769881
\(459\) 28.9788 + 24.6762i 1.35261 + 1.15179i
\(460\) 0 0
\(461\) −10.6320 −0.495179 −0.247590 0.968865i \(-0.579638\pi\)
−0.247590 + 0.968865i \(0.579638\pi\)
\(462\) 18.0924 + 16.5364i 0.841734 + 0.769341i
\(463\) 12.8322 0.596364 0.298182 0.954509i \(-0.403620\pi\)
0.298182 + 0.954509i \(0.403620\pi\)
\(464\) 0.281327i 0.0130603i
\(465\) 0 0
\(466\) 27.9575 1.29511
\(467\) −20.8716 −0.965824 −0.482912 0.875669i \(-0.660421\pi\)
−0.482912 + 0.875669i \(0.660421\pi\)
\(468\) −5.37777 + 10.5802i −0.248587 + 0.489071i
\(469\) 15.5539 + 8.60584i 0.718212 + 0.397381i
\(470\) 0 0
\(471\) 6.18024 25.7985i 0.284770 1.18873i
\(472\) 4.90390i 0.225720i
\(473\) 33.9575i 1.56137i
\(474\) 1.31548 5.49128i 0.0604220 0.252223i
\(475\) 0 0
\(476\) −16.9574 9.38242i −0.777243 0.430042i
\(477\) 14.9238 29.3612i 0.683316 1.34436i
\(478\) −17.2601 −0.789458
\(479\) −33.6879 −1.53924 −0.769619 0.638504i \(-0.779554\pi\)
−0.769619 + 0.638504i \(0.779554\pi\)
\(480\) 0 0
\(481\) 24.0036i 1.09447i
\(482\) 19.1935 0.874238
\(483\) 0.869764 0.951606i 0.0395756 0.0432996i
\(484\) 17.6088 0.800401
\(485\) 0 0
\(486\) −14.3871 + 6.00091i −0.652613 + 0.272207i
\(487\) 33.3524 1.51134 0.755671 0.654951i \(-0.227311\pi\)
0.755671 + 0.654951i \(0.227311\pi\)
\(488\) 13.2555 0.600049
\(489\) 5.16670 + 1.23772i 0.233646 + 0.0559717i
\(490\) 0 0
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) 10.3593 + 2.48166i 0.467035 + 0.111882i
\(493\) 2.06071i 0.0928096i
\(494\) 3.19270i 0.143646i
\(495\) 0 0
\(496\) 9.07971i 0.407691i
\(497\) −4.31652 + 7.80152i −0.193622 + 0.349946i
\(498\) 0.619433 2.58574i 0.0277574 0.115870i
\(499\) −19.1810 −0.858657 −0.429329 0.903148i \(-0.641250\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(500\) 0 0
\(501\) −3.19270 0.764836i −0.142639 0.0341704i
\(502\) 21.0271i 0.938487i
\(503\) −36.9851 −1.64909 −0.824543 0.565800i \(-0.808568\pi\)
−0.824543 + 0.565800i \(0.808568\pi\)
\(504\) 6.57244 4.45006i 0.292760 0.198221i
\(505\) 0 0
\(506\) 1.50474i 0.0668938i
\(507\) −4.46580 1.06982i −0.198333 0.0475122i
\(508\) 2.00000 0.0887357
\(509\) 36.0374 1.59733 0.798665 0.601776i \(-0.205540\pi\)
0.798665 + 0.601776i \(0.205540\pi\)
\(510\) 0 0
\(511\) −6.38242 + 11.5354i −0.282342 + 0.510294i
\(512\) 1.00000i 0.0441942i
\(513\) 2.71867 3.19270i 0.120032 0.140961i
\(514\) 14.5881i 0.643455i
\(515\) 0 0
\(516\) 10.6937 + 2.56177i 0.470766 + 0.112776i
\(517\) 30.9682i 1.36198i
\(518\) 7.77163 14.0462i 0.341466 0.617153i
\(519\) 14.9238 + 3.57512i 0.655084 + 0.156930i
\(520\) 0 0
\(521\) 3.65761 0.160243 0.0801214 0.996785i \(-0.474469\pi\)
0.0801214 + 0.996785i \(0.474469\pi\)
\(522\) −0.752370 0.382418i −0.0329303 0.0167380i
\(523\) 2.26321i 0.0989633i 0.998775 + 0.0494816i \(0.0157569\pi\)
−0.998775 + 0.0494816i \(0.984243\pi\)
\(524\) 16.5454 0.722788
\(525\) 0 0
\(526\) −8.91138 −0.388554
\(527\) 66.5084i 2.89715i
\(528\) 2.15826 9.00935i 0.0939261 0.392082i
\(529\) 22.9209 0.996559
\(530\) 0 0
\(531\) 13.1148 + 6.66605i 0.569134 + 0.289282i
\(532\) −1.03370 + 1.86827i −0.0448164 + 0.0809997i
\(533\) 24.3312i 1.05390i
\(534\) −1.74175 + 7.27071i −0.0753731 + 0.314634i
\(535\) 0 0
\(536\) 6.71867i 0.290202i
\(537\) 4.57931 19.1157i 0.197612 0.824904i
\(538\) 22.3352i 0.962940i
\(539\) 31.7209 19.8901i 1.36632 0.856729i
\(540\) 0 0
\(541\) 15.1502 0.651360 0.325680 0.945480i \(-0.394407\pi\)
0.325680 + 0.945480i \(0.394407\pi\)
\(542\) −7.17684 −0.308272
\(543\) 3.48351 14.5414i 0.149492 0.624032i
\(544\) 7.32496i 0.314055i
\(545\) 0 0
\(546\) 13.3820 + 12.2311i 0.572696 + 0.523442i
\(547\) 2.89014 0.123574 0.0617868 0.998089i \(-0.480320\pi\)
0.0617868 + 0.998089i \(0.480320\pi\)
\(548\) 7.41612i 0.316801i
\(549\) −18.0187 + 35.4500i −0.769019 + 1.51297i
\(550\) 0 0
\(551\) 0.227036 0.00967206
\(552\) −0.473865 0.113518i −0.0201690 0.00483165i
\(553\) −7.54720 4.17580i −0.320940 0.177573i
\(554\) 9.32749i 0.396287i
\(555\) 0 0
\(556\) 6.36982i 0.270141i
\(557\) 32.4777i 1.37613i −0.725651 0.688063i \(-0.758461\pi\)
0.725651 0.688063i \(-0.241539\pi\)
\(558\) −24.2824 12.3424i −1.02796 0.522494i
\(559\) 25.1166i 1.06232i
\(560\) 0 0
\(561\) 15.8091 65.9931i 0.667463 2.78623i
\(562\) −17.4373 −0.735550
\(563\) −10.9208 −0.460256 −0.230128 0.973160i \(-0.573914\pi\)
−0.230128 + 0.973160i \(0.573914\pi\)
\(564\) 9.75237 + 2.33625i 0.410649 + 0.0983741i
\(565\) 0 0
\(566\) 16.1776 0.679996
\(567\) 2.96690 + 23.6262i 0.124598 + 0.992207i
\(568\) 3.36995 0.141400
\(569\) 4.58388i 0.192166i 0.995373 + 0.0960832i \(0.0306315\pi\)
−0.995373 + 0.0960832i \(0.969369\pi\)
\(570\) 0 0
\(571\) 5.82853 0.243916 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(572\) 21.1604 0.884763
\(573\) −3.14175 + 13.1148i −0.131248 + 0.547879i
\(574\) 7.87768 14.2378i 0.328808 0.594276i
\(575\) 0 0
\(576\) −2.67436 1.35934i −0.111432 0.0566390i
\(577\) 9.82493i 0.409017i −0.978865 0.204509i \(-0.934440\pi\)
0.978865 0.204509i \(-0.0655597\pi\)
\(578\) 36.6550i 1.52465i
\(579\) 42.3987 + 10.1569i 1.76203 + 0.422107i
\(580\) 0 0
\(581\) −3.55383 1.96630i −0.147438 0.0815760i
\(582\) −25.4161 6.08862i −1.05353 0.252382i
\(583\) −58.7224 −2.43203
\(584\) 4.98282 0.206191
\(585\) 0 0
\(586\) 22.5623i 0.932038i
\(587\) 27.3106 1.12723 0.563615 0.826037i \(-0.309410\pi\)
0.563615 + 0.826037i \(0.309410\pi\)
\(588\) −3.87067 11.4899i −0.159624 0.473836i
\(589\) 7.32749 0.301924
\(590\) 0 0
\(591\) −1.01925 + 4.25473i −0.0419264 + 0.175016i
\(592\) −6.06739 −0.249368
\(593\) 26.8788 1.10378 0.551889 0.833917i \(-0.313907\pi\)
0.551889 + 0.833917i \(0.313907\pi\)
\(594\) 21.1604 + 18.0187i 0.868224 + 0.739316i
\(595\) 0 0
\(596\) 7.60882i 0.311669i
\(597\) 0.382418 1.59635i 0.0156513 0.0653343i
\(598\) 1.11298i 0.0455130i
\(599\) 6.45858i 0.263890i −0.991257 0.131945i \(-0.957878\pi\)
0.991257 0.131945i \(-0.0421223\pi\)
\(600\) 0 0
\(601\) 1.31548i 0.0536595i 0.999640 + 0.0268298i \(0.00854120\pi\)
−0.999640 + 0.0268298i \(0.991459\pi\)
\(602\) 8.13197 14.6974i 0.331435 0.599023i
\(603\) 17.9682 + 9.13294i 0.731720 + 0.371922i
\(604\) 4.63005 0.188394
\(605\) 0 0
\(606\) −2.33625 + 9.75237i −0.0949039 + 0.396163i
\(607\) 26.9651i 1.09448i 0.836976 + 0.547240i \(0.184321\pi\)
−0.836976 + 0.547240i \(0.815679\pi\)
\(608\) 0.807019 0.0327289
\(609\) −0.869764 + 0.951606i −0.0352446 + 0.0385610i
\(610\) 0 0
\(611\) 22.9056i 0.926661i
\(612\) −19.5896 9.95708i −0.791862 0.402491i
\(613\) −33.9151 −1.36982 −0.684909 0.728629i \(-0.740158\pi\)
−0.684909 + 0.728629i \(0.740158\pi\)
\(614\) −19.4057 −0.783150
\(615\) 0 0
\(616\) −12.3824 6.85109i −0.498902 0.276038i
\(617\) 13.1253i 0.528405i 0.964467 + 0.264203i \(0.0851087\pi\)
−0.964467 + 0.264203i \(0.914891\pi\)
\(618\) 11.7187 + 2.80730i 0.471394 + 0.112926i
\(619\) 38.0907i 1.53099i 0.643439 + 0.765497i \(0.277507\pi\)
−0.643439 + 0.765497i \(0.722493\pi\)
\(620\) 0 0
\(621\) 0.947731 1.11298i 0.0380311 0.0446623i
\(622\) 6.73757i 0.270152i
\(623\) 9.99284 + 5.52896i 0.400355 + 0.221513i
\(624\) 1.59635 6.66375i 0.0639052 0.266763i
\(625\) 0 0
\(626\) 21.3875 0.854816
\(627\) −7.27071 1.74175i −0.290364 0.0695590i
\(628\) 15.3162i 0.611184i
\(629\) −44.4434 −1.77207
\(630\) 0 0
\(631\) −12.0674 −0.480395 −0.240198 0.970724i \(-0.577212\pi\)
−0.240198 + 0.970724i \(0.577212\pi\)
\(632\) 3.26010i 0.129680i
\(633\) −21.7121 5.20129i −0.862977 0.206733i
\(634\) −3.47403 −0.137971
\(635\) 0 0
\(636\) −4.43004 + 18.4926i −0.175662 + 0.733278i
\(637\) 23.4623 14.7117i 0.929609 0.582899i
\(638\) 1.50474i 0.0595732i
\(639\) −4.58090 + 9.01247i −0.181218 + 0.356528i
\(640\) 0 0
\(641\) 17.4373i 0.688734i −0.938835 0.344367i \(-0.888094\pi\)
0.938835 0.344367i \(-0.111906\pi\)
\(642\) 17.8694 + 4.28076i 0.705250 + 0.168948i
\(643\) 6.01688i 0.237283i 0.992937 + 0.118641i \(0.0378538\pi\)
−0.992937 + 0.118641i \(0.962146\pi\)
\(644\) −0.360347 + 0.651279i −0.0141997 + 0.0256640i
\(645\) 0 0
\(646\) 5.91138 0.232580
\(647\) −36.7581 −1.44511 −0.722555 0.691314i \(-0.757032\pi\)
−0.722555 + 0.691314i \(0.757032\pi\)
\(648\) 7.27071 5.30441i 0.285621 0.208377i
\(649\) 26.2296i 1.02960i
\(650\) 0 0
\(651\) −28.0712 + 30.7127i −1.10020 + 1.20372i
\(652\) −3.06739 −0.120128
\(653\) 14.8073i 0.579454i −0.957109 0.289727i \(-0.906435\pi\)
0.957109 0.289727i \(-0.0935646\pi\)
\(654\) 7.31755 30.5461i 0.286139 1.19445i
\(655\) 0 0
\(656\) −6.15019 −0.240125
\(657\) −6.77333 + 13.3259i −0.264253 + 0.519892i
\(658\) 7.41612 13.4036i 0.289110 0.522528i
\(659\) 11.3487i 0.442083i −0.975264 0.221042i \(-0.929054\pi\)
0.975264 0.221042i \(-0.0709457\pi\)
\(660\) 0 0
\(661\) 19.7043i 0.766407i 0.923664 + 0.383203i \(0.125179\pi\)
−0.923664 + 0.383203i \(0.874821\pi\)
\(662\) 8.93261i 0.347176i
\(663\) 11.6932 48.8116i 0.454126 1.89569i
\(664\) 1.53511i 0.0595740i
\(665\) 0 0
\(666\) 8.24763 16.2264i 0.319589 0.628760i
\(667\) 0.0791449 0.00306450
\(668\) 1.89546 0.0733376
\(669\) −9.57512 + 39.9700i −0.370196 + 1.54533i
\(670\) 0 0
\(671\) 70.9000 2.73707
\(672\) −3.09165 + 3.38256i −0.119263 + 0.130485i
\(673\) 21.7861 0.839791 0.419896 0.907572i \(-0.362067\pi\)
0.419896 + 0.907572i \(0.362067\pi\)
\(674\) 34.2176i 1.31801i
\(675\) 0 0
\(676\) 2.65128 0.101972
\(677\) 15.3706 0.590740 0.295370 0.955383i \(-0.404557\pi\)
0.295370 + 0.955383i \(0.404557\pi\)
\(678\) 14.3871 + 3.44654i 0.552534 + 0.132364i
\(679\) −19.3275 + 34.9318i −0.741721 + 1.34056i
\(680\) 0 0
\(681\) 17.6300 + 4.22341i 0.675585 + 0.161842i
\(682\) 48.5648i 1.85964i
\(683\) 22.0462i 0.843573i 0.906695 + 0.421786i \(0.138597\pi\)
−0.906695 + 0.421786i \(0.861403\pi\)
\(684\) −1.09701 + 2.15826i −0.0419452 + 0.0825231i
\(685\) 0 0
\(686\) −18.4926 + 1.01247i −0.706049 + 0.0386561i
\(687\) 6.64829 27.7524i 0.253648 1.05882i
\(688\) −6.34872 −0.242043
\(689\) −43.4339 −1.65470
\(690\) 0 0
\(691\) 31.7209i 1.20672i 0.797469 + 0.603360i \(0.206172\pi\)
−0.797469 + 0.603360i \(0.793828\pi\)
\(692\) −8.86007 −0.336809
\(693\) 35.1542 23.8021i 1.33540 0.904168i
\(694\) 11.5260 0.437520
\(695\) 0 0
\(696\) 0.473865 + 0.113518i 0.0179618 + 0.00430289i
\(697\) −45.0499 −1.70639
\(698\) −21.8342 −0.826435
\(699\) 11.2811 47.0915i 0.426691 1.78116i
\(700\) 0 0
\(701\) 49.4316i 1.86700i 0.358571 + 0.933502i \(0.383264\pi\)
−0.358571 + 0.933502i \(0.616736\pi\)
\(702\) 15.6513 + 13.3275i 0.590719 + 0.503014i
\(703\) 4.89650i 0.184675i
\(704\) 5.34872i 0.201588i
\(705\) 0 0
\(706\) 4.84211i 0.182235i
\(707\) 13.4036 + 7.41612i 0.504095 + 0.278912i
\(708\) −8.26010 1.97877i −0.310433 0.0743667i
\(709\) −0.697442 −0.0261930 −0.0130965 0.999914i \(-0.504169\pi\)
−0.0130965 + 0.999914i \(0.504169\pi\)
\(710\) 0 0
\(711\) −8.71867 4.43157i −0.326976 0.166197i
\(712\) 4.31652i 0.161768i
\(713\) 2.55437 0.0956618
\(714\) −22.6462 + 24.7771i −0.847512 + 0.927260i
\(715\) 0 0
\(716\) 11.3487i 0.424122i
\(717\) −6.96461 + 29.0728i −0.260098 + 1.08574i
\(718\) 30.3063 1.13102
\(719\) −32.1430 −1.19873 −0.599366 0.800475i \(-0.704581\pi\)
−0.599366 + 0.800475i \(0.704581\pi\)
\(720\) 0 0
\(721\) 8.91138 16.1061i 0.331877 0.599823i
\(722\) 18.3487i 0.682869i
\(723\) 7.74474 32.3293i 0.288030 1.20234i
\(724\) 8.63303i 0.320844i
\(725\) 0 0
\(726\) 7.10532 29.6602i 0.263703 1.10079i
\(727\) 27.3970i 1.01610i −0.861328 0.508049i \(-0.830367\pi\)
0.861328 0.508049i \(-0.169633\pi\)
\(728\) −9.15863 5.06739i −0.339441 0.187810i
\(729\) 4.30256 + 26.6550i 0.159354 + 0.987222i
\(730\) 0 0
\(731\) −46.5041 −1.72002
\(732\) 5.34872 22.3275i 0.197694 0.825248i
\(733\) 0.0617893i 0.00228224i −0.999999 0.00114112i \(-0.999637\pi\)
0.999999 0.00114112i \(-0.000363230\pi\)
\(734\) −13.9910 −0.516417
\(735\) 0 0
\(736\) 0.281327 0.0103699
\(737\) 35.9363i 1.32373i
\(738\) 8.36018 16.4478i 0.307742 0.605453i
\(739\) −45.0037 −1.65549 −0.827744 0.561106i \(-0.810376\pi\)
−0.827744 + 0.561106i \(0.810376\pi\)
\(740\) 0 0
\(741\) −5.37777 1.28828i −0.197557 0.0473263i
\(742\) 25.4161 + 14.0625i 0.933055 + 0.516252i
\(743\) 38.1655i 1.40016i −0.714066 0.700078i \(-0.753148\pi\)
0.714066 0.700078i \(-0.246852\pi\)
\(744\) 15.2938 + 3.66375i 0.560698 + 0.134319i
\(745\) 0 0
\(746\) 4.24464i 0.155407i
\(747\) −4.10545 2.08674i −0.150211 0.0763497i
\(748\) 39.1791i 1.43253i
\(749\) 13.5887 24.5597i 0.496519 0.897391i
\(750\) 0 0
\(751\) −27.8901 −1.01773 −0.508863 0.860848i \(-0.669934\pi\)
−0.508863 + 0.860848i \(0.669934\pi\)
\(752\) −5.78984 −0.211134
\(753\) −35.4180 8.48464i −1.29070 0.309198i
\(754\) 1.11298i 0.0405323i
\(755\) 0 0
\(756\) −4.84360 12.8662i −0.176160 0.467940i
\(757\) 38.5876 1.40249 0.701245 0.712921i \(-0.252628\pi\)
0.701245 + 0.712921i \(0.252628\pi\)
\(758\) 1.63005i 0.0592060i
\(759\) −2.53457 0.607177i −0.0919992 0.0220391i
\(760\) 0 0
\(761\) 28.9173 1.04825 0.524125 0.851641i \(-0.324392\pi\)
0.524125 + 0.851641i \(0.324392\pi\)
\(762\) 0.807019 3.36879i 0.0292352 0.122038i
\(763\) −41.9825 23.2286i −1.51987 0.840930i
\(764\) 7.78607i 0.281690i
\(765\) 0 0
\(766\) 16.9994i 0.614215i
\(767\) 19.4007i 0.700517i
\(768\) 1.68439 + 0.403509i 0.0607803 + 0.0145604i
\(769\) 30.3191i 1.09333i −0.837350 0.546667i \(-0.815896\pi\)
0.837350 0.546667i \(-0.184104\pi\)
\(770\) 0 0
\(771\) −24.5721 5.88644i −0.884944 0.211995i
\(772\) −25.1715 −0.905941
\(773\) 23.7370 0.853761 0.426881 0.904308i \(-0.359612\pi\)
0.426881 + 0.904308i \(0.359612\pi\)
\(774\) 8.63005 16.9788i 0.310201 0.610289i
\(775\) 0 0
\(776\) 15.0892 0.541670
\(777\) −20.5233 18.7582i −0.736271 0.672948i
\(778\) −29.4623 −1.05627
\(779\) 4.96332i 0.177829i
\(780\) 0 0
\(781\) 18.0249 0.644983
\(782\) 2.06071 0.0736908
\(783\) −0.947731 + 1.11298i −0.0338691 + 0.0397746i
\(784\) 3.71867 + 5.93055i 0.132810 + 0.211806i
\(785\) 0 0
\(786\) 6.67621 27.8689i 0.238133 0.994051i
\(787\) 30.7560i 1.09633i −0.836369 0.548167i \(-0.815326\pi\)
0.836369 0.548167i \(-0.184674\pi\)
\(788\) 2.52597i 0.0899840i
\(789\) −3.59582 + 15.0103i −0.128015 + 0.534379i
\(790\) 0 0
\(791\) 10.9406 19.7736i 0.389002 0.703068i
\(792\) −14.3044 7.27071i −0.508285 0.258353i
\(793\) 52.4410 1.86224
\(794\) 17.8706 0.634203
\(795\) 0 0
\(796\) 0.947731i 0.0335914i
\(797\) 14.1958 0.502842 0.251421 0.967878i \(-0.419102\pi\)
0.251421 + 0.967878i \(0.419102\pi\)
\(798\) 2.72979 + 2.49502i 0.0966335 + 0.0883226i
\(799\) −42.4103 −1.50037
\(800\) 0 0
\(801\) 11.5439 + 5.86760i 0.407884 + 0.207321i
\(802\) 12.6762 0.447613
\(803\) 26.6517 0.940519
\(804\) −11.3169 2.71105i −0.399116 0.0956112i
\(805\) 0 0
\(806\) 35.9209i 1.26526i
\(807\) −37.6213 9.01247i −1.32433 0.317254i
\(808\) 5.78984i 0.203686i
\(809\) 39.0404i 1.37259i −0.727325 0.686293i \(-0.759237\pi\)
0.727325 0.686293i \(-0.240763\pi\)
\(810\) 0 0
\(811\) 42.9328i 1.50758i −0.657118 0.753788i \(-0.728225\pi\)
0.657118 0.753788i \(-0.271775\pi\)
\(812\) 0.360347 0.651279i 0.0126457 0.0228554i
\(813\) −2.89592 + 12.0886i −0.101564 + 0.423967i
\(814\) −32.4528 −1.13747
\(815\) 0 0
\(816\) 12.3381 + 2.95569i 0.431920 + 0.103470i
\(817\) 5.12354i 0.179250i
\(818\) 5.26425 0.184060
\(819\) 26.0017 17.6052i 0.908573 0.615175i
\(820\) 0 0
\(821\) 2.45280i 0.0856033i −0.999084 0.0428016i \(-0.986372\pi\)
0.999084 0.0428016i \(-0.0136283\pi\)
\(822\) −12.4917 2.99247i −0.435696 0.104374i
\(823\) 30.6300 1.06770 0.533848 0.845580i \(-0.320745\pi\)
0.533848 + 0.845580i \(0.320745\pi\)
\(824\) −6.95721 −0.242366
\(825\) 0 0
\(826\) −6.28133 + 11.3526i −0.218555 + 0.395009i
\(827\) 37.8265i 1.31535i −0.753300 0.657677i \(-0.771539\pi\)
0.753300 0.657677i \(-0.228461\pi\)
\(828\) −0.382418 + 0.752370i −0.0132899 + 0.0261467i
\(829\) 18.6605i 0.648105i −0.946039 0.324052i \(-0.894955\pi\)
0.946039 0.324052i \(-0.105045\pi\)
\(830\) 0 0
\(831\) −15.7112 3.76373i −0.545014 0.130562i
\(832\) 3.95617i 0.137156i
\(833\) 27.2391 + 43.4410i 0.943779 + 1.50514i
\(834\) −10.7293 2.57028i −0.371525 0.0890016i
\(835\) 0 0
\(836\) 4.31652 0.149290
\(837\) −30.5876 + 35.9209i −1.05726 + 1.24161i
\(838\) 13.1148i 0.453043i
\(839\) 21.1604 0.730540 0.365270 0.930902i \(-0.380977\pi\)
0.365270 + 0.930902i \(0.380977\pi\)
\(840\) 0 0
\(841\) 28.9209 0.997271
\(842\) 3.86521i 0.133204i
\(843\) −7.03613 + 29.3713i −0.242337 + 1.01160i
\(844\) 12.8901 0.443697
\(845\) 0 0
\(846\) 7.87034 15.4841i 0.270588 0.532355i
\(847\) −40.7648 22.5549i −1.40070 0.774994i
\(848\) 10.9788i 0.377012i
\(849\) 6.52782 27.2495i 0.224034 0.935200i
\(850\) 0 0
\(851\) 1.70692i 0.0585125i
\(852\) 1.35981 5.67632i 0.0465862 0.194468i
\(853\) 18.3790i 0.629287i 0.949210 + 0.314643i \(0.101885\pi\)
−0.949210 + 0.314643i \(0.898115\pi\)
\(854\) −30.6868 16.9788i −1.05008 0.581002i
\(855\) 0 0
\(856\) −10.6088 −0.362602
\(857\) 47.0915 1.60861 0.804307 0.594214i \(-0.202537\pi\)
0.804307 + 0.594214i \(0.202537\pi\)
\(858\) 8.53844 35.6425i 0.291497 1.21682i
\(859\) 30.5313i 1.04171i 0.853644 + 0.520857i \(0.174388\pi\)
−0.853644 + 0.520857i \(0.825612\pi\)
\(860\) 0 0
\(861\) −20.8034 19.0142i −0.708978 0.648002i
\(862\) −10.2389 −0.348737
\(863\) 32.2696i 1.09847i 0.835668 + 0.549235i \(0.185081\pi\)
−0.835668 + 0.549235i \(0.814919\pi\)
\(864\) −3.36879 + 3.95617i −0.114608 + 0.134592i
\(865\) 0 0
\(866\) 22.7030 0.771478
\(867\) 61.7414 + 14.7906i 2.09685 + 0.502316i
\(868\) 11.6300 21.0197i 0.394750 0.713456i
\(869\) 17.4373i 0.591521i
\(870\) 0 0
\(871\) 26.5802i 0.900636i
\(872\) 18.1348i 0.614121i
\(873\) −20.5113 + 40.3539i −0.694202 + 1.36577i
\(874\) 0.227036i 0.00767961i
\(875\) 0 0
\(876\) 2.01062 8.39303i 0.0679324 0.283574i
\(877\) 9.61460 0.324662 0.162331 0.986736i \(-0.448099\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(878\) 26.4492 0.892618
\(879\) 38.0037 + 9.10408i 1.28183 + 0.307073i
\(880\) 0 0
\(881\) 22.0464 0.742762 0.371381 0.928481i \(-0.378884\pi\)
0.371381 + 0.928481i \(0.378884\pi\)
\(882\) −20.9154 + 1.88345i −0.704257 + 0.0634192i
\(883\) −31.5876 −1.06301 −0.531503 0.847056i \(-0.678373\pi\)
−0.531503 + 0.847056i \(0.678373\pi\)
\(884\) 28.9788i 0.974661i
\(885\) 0 0
\(886\) −27.8689 −0.936274
\(887\) −17.9472 −0.602607 −0.301304 0.953528i \(-0.597422\pi\)
−0.301304 + 0.953528i \(0.597422\pi\)
\(888\) −2.44825 + 10.2199i −0.0821579 + 0.342957i
\(889\) −4.63005 2.56177i −0.155287 0.0859189i
\(890\) 0 0
\(891\) 38.8890 28.3718i 1.30283 0.950491i
\(892\) 23.7296i 0.794526i
\(893\) 4.67251i 0.156360i
\(894\) −12.8162 3.07023i −0.428639 0.102684i
\(895\) 0 0
\(896\) 1.28088 2.31502i 0.0427913 0.0773395i
\(897\) −1.87469 0.449097i −0.0625941 0.0149949i
\(898\) −9.45858 −0.315637
\(899\) −2.55437 −0.0851929
\(900\) 0 0
\(901\) 80.4190i 2.67915i
\(902\) −32.8956 −1.09531
\(903\) −21.4749 19.6280i −0.714641 0.653179i
\(904\) −8.54142 −0.284084
\(905\) 0 0
\(906\) 1.86827 7.79882i 0.0620690 0.259098i
\(907\) 39.9942 1.32799 0.663993 0.747739i \(-0.268860\pi\)
0.663993 + 0.747739i \(0.268860\pi\)
\(908\) −10.4667 −0.347350
\(909\) 15.4841 + 7.87034i 0.513576 + 0.261043i
\(910\) 0 0
\(911\) 15.4740i 0.512677i 0.966587 + 0.256339i \(0.0825163\pi\)
−0.966587 + 0.256339i \(0.917484\pi\)
\(912\) 0.325639 1.35934i 0.0107830 0.0450121i
\(913\) 8.21090i 0.271741i
\(914\) 31.8322i 1.05292i
\(915\) 0 0
\(916\) 16.4762i 0.544388i
\(917\) −38.3029 21.1927i −1.26487 0.699845i
\(918\) −24.6762 + 28.9788i −0.814436 + 0.956442i
\(919\) 25.5721 0.843547 0.421773 0.906701i \(-0.361408\pi\)
0.421773 + 0.906701i \(0.361408\pi\)
\(920\) 0 0
\(921\) −7.83038 + 32.6868i −0.258020 + 1.07707i
\(922\) 10.6320i 0.350145i
\(923\) 13.3321 0.438831
\(924\) −16.5364 + 18.0924i −0.544006 + 0.595196i
\(925\) 0 0
\(926\) 12.8322i 0.421693i
\(927\) 9.45719 18.6061i 0.310615 0.611104i
\(928\) −0.281327 −0.00923501
\(929\) 27.6092 0.905828 0.452914 0.891554i \(-0.350384\pi\)
0.452914 + 0.891554i \(0.350384\pi\)
\(930\) 0 0
\(931\) 4.78607 3.00104i 0.156857 0.0983550i
\(932\) 27.9575i 0.915780i
\(933\) −11.3487 2.71867i −0.371540 0.0890054i
\(934\) 20.8716i 0.682940i
\(935\) 0 0
\(936\) −10.5802 5.37777i −0.345825 0.175778i
\(937\) 36.8988i 1.20543i −0.797956 0.602716i \(-0.794085\pi\)
0.797956 0.602716i \(-0.205915\pi\)
\(938\) −8.60584 + 15.5539i −0.280991 + 0.507852i
\(939\) 8.63005 36.0249i 0.281631 1.17563i
\(940\) 0 0
\(941\) −45.1245 −1.47102 −0.735508 0.677516i \(-0.763057\pi\)
−0.735508 + 0.677516i \(0.763057\pi\)
\(942\) 25.7985 + 6.18024i 0.840562 + 0.201363i
\(943\) 1.73021i 0.0563435i
\(944\) 4.90390 0.159608
\(945\) 0 0
\(946\) −33.9575 −1.10405
\(947\) 13.3524i 0.433895i 0.976183 + 0.216948i \(0.0696101\pi\)
−0.976183 + 0.216948i \(0.930390\pi\)
\(948\) 5.49128 + 1.31548i 0.178349 + 0.0427248i
\(949\) 19.7129 0.639908
\(950\) 0 0
\(951\) −1.40180 + 5.85163i −0.0454566 + 0.189752i
\(952\) 9.38242 16.9574i 0.304086 0.549594i
\(953\) 52.2483i 1.69249i −0.532794 0.846245i \(-0.678858\pi\)
0.532794 0.846245i \(-0.321142\pi\)
\(954\) 29.3612 + 14.9238i 0.950604 + 0.483177i
\(955\) 0 0
\(956\) 17.2601i 0.558231i
\(957\) 2.53457 + 0.607177i 0.0819311 + 0.0196272i
\(958\) 33.6879i 1.08841i
\(959\) −9.49918 + 17.1685i −0.306745 + 0.554399i
\(960\) 0 0
\(961\) −51.4410 −1.65939
\(962\) −24.0036 −0.773908
\(963\) 14.4210 28.3718i 0.464709 0.914269i
\(964\) 19.1935i 0.618180i
\(965\) 0 0
\(966\) 0.951606 + 0.869764i 0.0306174 + 0.0279842i
\(967\) 3.46228 0.111339 0.0556697 0.998449i \(-0.482271\pi\)
0.0556697 + 0.998449i \(0.482271\pi\)
\(968\) 17.6088i 0.565969i
\(969\) 2.38529 9.95708i 0.0766267 0.319867i
\(970\) 0 0
\(971\) −42.3528 −1.35917 −0.679584 0.733598i \(-0.737839\pi\)
−0.679584 + 0.733598i \(0.737839\pi\)
\(972\) −6.00091 14.3871i −0.192479 0.461467i
\(973\) −8.15901 + 14.7463i −0.261566 + 0.472745i
\(974\) 33.3524i 1.06868i
\(975\) 0 0
\(976\) 13.2555i 0.424299i
\(977\) 16.2483i 0.519831i 0.965631 + 0.259915i \(0.0836947\pi\)
−0.965631 + 0.259915i \(0.916305\pi\)
\(978\) −1.23772 + 5.16670i −0.0395780 + 0.165213i
\(979\) 23.0878i 0.737891i
\(980\) 0 0
\(981\) −48.4990 24.6513i −1.54845 0.787055i
\(982\) −30.0000 −0.957338
\(983\) 33.9149 1.08172 0.540859 0.841114i \(-0.318099\pi\)
0.540859 + 0.841114i \(0.318099\pi\)
\(984\) −2.48166 + 10.3593i −0.0791124 + 0.330244i
\(985\) 0 0
\(986\) −2.06071 −0.0656263
\(987\) −19.5845 17.9001i −0.623382 0.569768i
\(988\) 3.19270 0.101573
\(989\) 1.78607i 0.0567936i
\(990\) 0 0
\(991\) −41.5971 −1.32137 −0.660687 0.750661i \(-0.729735\pi\)
−0.660687 + 0.750661i \(0.729735\pi\)
\(992\) −9.07971 −0.288281
\(993\) −15.0460 3.60439i −0.477471 0.114382i
\(994\) −7.80152 4.31652i −0.247449 0.136912i
\(995\) 0 0
\(996\) 2.58574 + 0.619433i 0.0819322 + 0.0196275i
\(997\) 9.45719i 0.299512i 0.988723 + 0.149756i \(0.0478488\pi\)
−0.988723 + 0.149756i \(0.952151\pi\)
\(998\) 19.1810i 0.607162i
\(999\) −24.0036 20.4398i −0.759442 0.646685i
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 1050.2.b.e.251.12 yes 12
3.2 odd 2 inner 1050.2.b.e.251.1 yes 12
5.2 odd 4 1050.2.d.g.1049.7 12
5.3 odd 4 1050.2.d.h.1049.6 12
5.4 even 2 1050.2.b.d.251.1 12
7.6 odd 2 inner 1050.2.b.e.251.7 yes 12
15.2 even 4 1050.2.d.h.1049.8 12
15.8 even 4 1050.2.d.g.1049.5 12
15.14 odd 2 1050.2.b.d.251.12 yes 12
21.20 even 2 inner 1050.2.b.e.251.6 yes 12
35.13 even 4 1050.2.d.h.1049.7 12
35.27 even 4 1050.2.d.g.1049.6 12
35.34 odd 2 1050.2.b.d.251.6 yes 12
105.62 odd 4 1050.2.d.h.1049.5 12
105.83 odd 4 1050.2.d.g.1049.8 12
105.104 even 2 1050.2.b.d.251.7 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.b.d.251.1 12 5.4 even 2
1050.2.b.d.251.6 yes 12 35.34 odd 2
1050.2.b.d.251.7 yes 12 105.104 even 2
1050.2.b.d.251.12 yes 12 15.14 odd 2
1050.2.b.e.251.1 yes 12 3.2 odd 2 inner
1050.2.b.e.251.6 yes 12 21.20 even 2 inner
1050.2.b.e.251.7 yes 12 7.6 odd 2 inner
1050.2.b.e.251.12 yes 12 1.1 even 1 trivial
1050.2.d.g.1049.5 12 15.8 even 4
1050.2.d.g.1049.6 12 35.27 even 4
1050.2.d.g.1049.7 12 5.2 odd 4
1050.2.d.g.1049.8 12 105.83 odd 4
1050.2.d.h.1049.5 12 105.62 odd 4
1050.2.d.h.1049.6 12 5.3 odd 4
1050.2.d.h.1049.7 12 35.13 even 4
1050.2.d.h.1049.8 12 15.2 even 4