Properties

Label 770.2.l.c.573.5
Level $770$
Weight $2$
Character 770.573
Analytic conductor $6.148$
Analytic rank $0$
Dimension $40$
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] = [770,2,Mod(573,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.573");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.l (of order \(4\), 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: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 573.5
Character \(\chi\) \(=\) 770.573
Dual form 770.2.l.c.727.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0715208 + 0.0715208i) q^{3} -1.00000i q^{4} +(1.95282 - 1.08927i) q^{5} -0.101146i q^{6} +(2.63480 - 0.240478i) q^{7} +(0.707107 + 0.707107i) q^{8} +2.98977i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0715208 + 0.0715208i) q^{3} -1.00000i q^{4} +(1.95282 - 1.08927i) q^{5} -0.101146i q^{6} +(2.63480 - 0.240478i) q^{7} +(0.707107 + 0.707107i) q^{8} +2.98977i q^{9} +(-0.610623 + 2.15108i) q^{10} -1.00000 q^{11} +(0.0715208 + 0.0715208i) q^{12} +(-2.32898 + 2.32898i) q^{13} +(-1.69304 + 2.03313i) q^{14} +(-0.0617619 + 0.217572i) q^{15} -1.00000 q^{16} +(2.41391 + 2.41391i) q^{17} +(-2.11409 - 2.11409i) q^{18} +2.20465 q^{19} +(-1.08927 - 1.95282i) q^{20} +(-0.171244 + 0.205642i) q^{21} +(0.707107 - 0.707107i) q^{22} +(1.77734 + 1.77734i) q^{23} -0.101146 q^{24} +(2.62700 - 4.25428i) q^{25} -3.29368i q^{26} +(-0.428393 - 0.428393i) q^{27} +(-0.240478 - 2.63480i) q^{28} -5.97677i q^{29} +(-0.110175 - 0.197519i) q^{30} +4.99705i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.0715208 - 0.0715208i) q^{33} -3.41379 q^{34} +(4.88334 - 3.33961i) q^{35} +2.98977 q^{36} +(6.33137 - 6.33137i) q^{37} +(-1.55892 + 1.55892i) q^{38} -0.333142i q^{39} +(2.15108 + 0.610623i) q^{40} +8.47999i q^{41} +(-0.0243233 - 0.266498i) q^{42} +(-1.16231 - 1.16231i) q^{43} +1.00000i q^{44} +(3.25666 + 5.83848i) q^{45} -2.51354 q^{46} +(-4.80004 - 4.80004i) q^{47} +(0.0715208 - 0.0715208i) q^{48} +(6.88434 - 1.26722i) q^{49} +(1.15066 + 4.86580i) q^{50} -0.345290 q^{51} +(2.32898 + 2.32898i) q^{52} +(3.59950 + 3.59950i) q^{53} +0.605839 q^{54} +(-1.95282 + 1.08927i) q^{55} +(2.03313 + 1.69304i) q^{56} +(-0.157678 + 0.157678i) q^{57} +(4.22621 + 4.22621i) q^{58} +3.32581 q^{59} +(0.217572 + 0.0617619i) q^{60} +11.2082i q^{61} +(-3.53345 - 3.53345i) q^{62} +(0.718974 + 7.87744i) q^{63} +1.00000i q^{64} +(-2.01120 + 7.08497i) q^{65} +0.101146i q^{66} +(9.53332 - 9.53332i) q^{67} +(2.41391 - 2.41391i) q^{68} -0.254233 q^{69} +(-1.09158 + 5.81450i) q^{70} -8.78250 q^{71} +(-2.11409 + 2.11409i) q^{72} +(-2.07792 + 2.07792i) q^{73} +8.95391i q^{74} +(0.116384 + 0.492154i) q^{75} -2.20465i q^{76} +(-2.63480 + 0.240478i) q^{77} +(0.235567 + 0.235567i) q^{78} +2.87628i q^{79} +(-1.95282 + 1.08927i) q^{80} -8.90803 q^{81} +(-5.99626 - 5.99626i) q^{82} +(3.19625 - 3.19625i) q^{83} +(0.205642 + 0.171244i) q^{84} +(7.34333 + 2.08454i) q^{85} +1.64375 q^{86} +(0.427463 + 0.427463i) q^{87} +(-0.707107 - 0.707107i) q^{88} -10.6987 q^{89} +(-6.43123 - 1.82562i) q^{90} +(-5.57634 + 6.69648i) q^{91} +(1.77734 - 1.77734i) q^{92} +(-0.357393 - 0.357393i) q^{93} +6.78828 q^{94} +(4.30527 - 2.40145i) q^{95} +0.101146i q^{96} +(-3.29793 - 3.29793i) q^{97} +(-3.97190 + 5.76403i) q^{98} -2.98977i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.0715208 + 0.0715208i −0.0412925 + 0.0412925i −0.727452 0.686159i \(-0.759295\pi\)
0.686159 + 0.727452i \(0.259295\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 1.95282 1.08927i 0.873327 0.487135i
\(6\) 0.101146i 0.0412925i
\(7\) 2.63480 0.240478i 0.995861 0.0908922i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.98977i 0.996590i
\(10\) −0.610623 + 2.15108i −0.193096 + 0.680231i
\(11\) −1.00000 −0.301511
\(12\) 0.0715208 + 0.0715208i 0.0206463 + 0.0206463i
\(13\) −2.32898 + 2.32898i −0.645944 + 0.645944i −0.952010 0.306066i \(-0.900987\pi\)
0.306066 + 0.952010i \(0.400987\pi\)
\(14\) −1.69304 + 2.03313i −0.452484 + 0.543376i
\(15\) −0.0617619 + 0.217572i −0.0159468 + 0.0561769i
\(16\) −1.00000 −0.250000
\(17\) 2.41391 + 2.41391i 0.585460 + 0.585460i 0.936398 0.350939i \(-0.114137\pi\)
−0.350939 + 0.936398i \(0.614137\pi\)
\(18\) −2.11409 2.11409i −0.498295 0.498295i
\(19\) 2.20465 0.505780 0.252890 0.967495i \(-0.418619\pi\)
0.252890 + 0.967495i \(0.418619\pi\)
\(20\) −1.08927 1.95282i −0.243567 0.436663i
\(21\) −0.171244 + 0.205642i −0.0373684 + 0.0448748i
\(22\) 0.707107 0.707107i 0.150756 0.150756i
\(23\) 1.77734 + 1.77734i 0.370601 + 0.370601i 0.867696 0.497095i \(-0.165600\pi\)
−0.497095 + 0.867696i \(0.665600\pi\)
\(24\) −0.101146 −0.0206463
\(25\) 2.62700 4.25428i 0.525399 0.850856i
\(26\) 3.29368i 0.645944i
\(27\) −0.428393 0.428393i −0.0824442 0.0824442i
\(28\) −0.240478 2.63480i −0.0454461 0.497930i
\(29\) 5.97677i 1.10986i −0.831898 0.554929i \(-0.812745\pi\)
0.831898 0.554929i \(-0.187255\pi\)
\(30\) −0.110175 0.197519i −0.0201150 0.0360619i
\(31\) 4.99705i 0.897497i 0.893658 + 0.448748i \(0.148130\pi\)
−0.893658 + 0.448748i \(0.851870\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.0715208 0.0715208i 0.0124502 0.0124502i
\(34\) −3.41379 −0.585460
\(35\) 4.88334 3.33961i 0.825435 0.564497i
\(36\) 2.98977 0.498295
\(37\) 6.33137 6.33137i 1.04087 1.04087i 0.0417425 0.999128i \(-0.486709\pi\)
0.999128 0.0417425i \(-0.0132909\pi\)
\(38\) −1.55892 + 1.55892i −0.252890 + 0.252890i
\(39\) 0.333142i 0.0533453i
\(40\) 2.15108 + 0.610623i 0.340115 + 0.0965480i
\(41\) 8.47999i 1.32435i 0.749348 + 0.662176i \(0.230367\pi\)
−0.749348 + 0.662176i \(0.769633\pi\)
\(42\) −0.0243233 0.266498i −0.00375317 0.0411216i
\(43\) −1.16231 1.16231i −0.177250 0.177250i 0.612906 0.790156i \(-0.290000\pi\)
−0.790156 + 0.612906i \(0.790000\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 3.25666 + 5.83848i 0.485474 + 0.870349i
\(46\) −2.51354 −0.370601
\(47\) −4.80004 4.80004i −0.700158 0.700158i 0.264286 0.964444i \(-0.414864\pi\)
−0.964444 + 0.264286i \(0.914864\pi\)
\(48\) 0.0715208 0.0715208i 0.0103231 0.0103231i
\(49\) 6.88434 1.26722i 0.983477 0.181032i
\(50\) 1.15066 + 4.86580i 0.162728 + 0.688128i
\(51\) −0.345290 −0.0483502
\(52\) 2.32898 + 2.32898i 0.322972 + 0.322972i
\(53\) 3.59950 + 3.59950i 0.494430 + 0.494430i 0.909699 0.415269i \(-0.136312\pi\)
−0.415269 + 0.909699i \(0.636312\pi\)
\(54\) 0.605839 0.0824442
\(55\) −1.95282 + 1.08927i −0.263318 + 0.146877i
\(56\) 2.03313 + 1.69304i 0.271688 + 0.226242i
\(57\) −0.157678 + 0.157678i −0.0208850 + 0.0208850i
\(58\) 4.22621 + 4.22621i 0.554929 + 0.554929i
\(59\) 3.32581 0.432984 0.216492 0.976284i \(-0.430538\pi\)
0.216492 + 0.976284i \(0.430538\pi\)
\(60\) 0.217572 + 0.0617619i 0.0280885 + 0.00797342i
\(61\) 11.2082i 1.43507i 0.696524 + 0.717534i \(0.254729\pi\)
−0.696524 + 0.717534i \(0.745271\pi\)
\(62\) −3.53345 3.53345i −0.448748 0.448748i
\(63\) 0.718974 + 7.87744i 0.0905822 + 0.992465i
\(64\) 1.00000i 0.125000i
\(65\) −2.01120 + 7.08497i −0.249458 + 0.878782i
\(66\) 0.101146i 0.0124502i
\(67\) 9.53332 9.53332i 1.16468 1.16468i 0.181242 0.983439i \(-0.441988\pi\)
0.983439 0.181242i \(-0.0580116\pi\)
\(68\) 2.41391 2.41391i 0.292730 0.292730i
\(69\) −0.254233 −0.0306061
\(70\) −1.09158 + 5.81450i −0.130469 + 0.694966i
\(71\) −8.78250 −1.04229 −0.521146 0.853468i \(-0.674495\pi\)
−0.521146 + 0.853468i \(0.674495\pi\)
\(72\) −2.11409 + 2.11409i −0.249147 + 0.249147i
\(73\) −2.07792 + 2.07792i −0.243202 + 0.243202i −0.818174 0.574971i \(-0.805013\pi\)
0.574971 + 0.818174i \(0.305013\pi\)
\(74\) 8.95391i 1.04087i
\(75\) 0.116384 + 0.492154i 0.0134389 + 0.0568291i
\(76\) 2.20465i 0.252890i
\(77\) −2.63480 + 0.240478i −0.300263 + 0.0274050i
\(78\) 0.235567 + 0.235567i 0.0266727 + 0.0266727i
\(79\) 2.87628i 0.323607i 0.986823 + 0.161803i \(0.0517310\pi\)
−0.986823 + 0.161803i \(0.948269\pi\)
\(80\) −1.95282 + 1.08927i −0.218332 + 0.121784i
\(81\) −8.90803 −0.989781
\(82\) −5.99626 5.99626i −0.662176 0.662176i
\(83\) 3.19625 3.19625i 0.350834 0.350834i −0.509586 0.860420i \(-0.670201\pi\)
0.860420 + 0.509586i \(0.170201\pi\)
\(84\) 0.205642 + 0.171244i 0.0224374 + 0.0186842i
\(85\) 7.34333 + 2.08454i 0.796496 + 0.226100i
\(86\) 1.64375 0.177250
\(87\) 0.427463 + 0.427463i 0.0458289 + 0.0458289i
\(88\) −0.707107 0.707107i −0.0753778 0.0753778i
\(89\) −10.6987 −1.13406 −0.567029 0.823698i \(-0.691907\pi\)
−0.567029 + 0.823698i \(0.691907\pi\)
\(90\) −6.43123 1.82562i −0.677911 0.192438i
\(91\) −5.57634 + 6.69648i −0.584559 + 0.701982i
\(92\) 1.77734 1.77734i 0.185300 0.185300i
\(93\) −0.357393 0.357393i −0.0370599 0.0370599i
\(94\) 6.78828 0.700158
\(95\) 4.30527 2.40145i 0.441712 0.246383i
\(96\) 0.101146i 0.0103231i
\(97\) −3.29793 3.29793i −0.334854 0.334854i 0.519572 0.854426i \(-0.326091\pi\)
−0.854426 + 0.519572i \(0.826091\pi\)
\(98\) −3.97190 + 5.76403i −0.401223 + 0.582255i
\(99\) 2.98977i 0.300483i
\(100\) −4.25428 2.62700i −0.425428 0.262700i
\(101\) 10.9777i 1.09232i 0.837680 + 0.546162i \(0.183912\pi\)
−0.837680 + 0.546162i \(0.816088\pi\)
\(102\) 0.244157 0.244157i 0.0241751 0.0241751i
\(103\) 11.1782 11.1782i 1.10142 1.10142i 0.107181 0.994240i \(-0.465817\pi\)
0.994240 0.107181i \(-0.0341825\pi\)
\(104\) −3.29368 −0.322972
\(105\) −0.110409 + 0.588112i −0.0107748 + 0.0573938i
\(106\) −5.09047 −0.494430
\(107\) 6.05699 6.05699i 0.585551 0.585551i −0.350872 0.936423i \(-0.614115\pi\)
0.936423 + 0.350872i \(0.114115\pi\)
\(108\) −0.428393 + 0.428393i −0.0412221 + 0.0412221i
\(109\) 8.73699i 0.836852i 0.908251 + 0.418426i \(0.137418\pi\)
−0.908251 + 0.418426i \(0.862582\pi\)
\(110\) 0.610623 2.15108i 0.0582206 0.205097i
\(111\) 0.905649i 0.0859604i
\(112\) −2.63480 + 0.240478i −0.248965 + 0.0227230i
\(113\) −7.26910 7.26910i −0.683820 0.683820i 0.277039 0.960859i \(-0.410647\pi\)
−0.960859 + 0.277039i \(0.910647\pi\)
\(114\) 0.222990i 0.0208850i
\(115\) 5.40682 + 1.53482i 0.504188 + 0.143123i
\(116\) −5.97677 −0.554929
\(117\) −6.96313 6.96313i −0.643741 0.643741i
\(118\) −2.35170 + 2.35170i −0.216492 + 0.216492i
\(119\) 6.94067 + 5.77968i 0.636250 + 0.529823i
\(120\) −0.197519 + 0.110175i −0.0180309 + 0.0100575i
\(121\) 1.00000 0.0909091
\(122\) −7.92542 7.92542i −0.717534 0.717534i
\(123\) −0.606496 0.606496i −0.0546859 0.0546859i
\(124\) 4.99705 0.448748
\(125\) 0.496003 11.1693i 0.0443639 0.999015i
\(126\) −6.07859 5.06180i −0.541523 0.450941i
\(127\) 5.92401 5.92401i 0.525671 0.525671i −0.393608 0.919279i \(-0.628773\pi\)
0.919279 + 0.393608i \(0.128773\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0.166258 0.0146382
\(130\) −3.58770 6.43196i −0.314662 0.564120i
\(131\) 10.4059i 0.909169i −0.890704 0.454585i \(-0.849788\pi\)
0.890704 0.454585i \(-0.150212\pi\)
\(132\) −0.0715208 0.0715208i −0.00622508 0.00622508i
\(133\) 5.80880 0.530169i 0.503687 0.0459715i
\(134\) 13.4821i 1.16468i
\(135\) −1.30321 0.369939i −0.112162 0.0318393i
\(136\) 3.41379i 0.292730i
\(137\) −5.98561 + 5.98561i −0.511386 + 0.511386i −0.914951 0.403565i \(-0.867771\pi\)
0.403565 + 0.914951i \(0.367771\pi\)
\(138\) 0.179770 0.179770i 0.0153030 0.0153030i
\(139\) 5.22788 0.443423 0.221711 0.975112i \(-0.428836\pi\)
0.221711 + 0.975112i \(0.428836\pi\)
\(140\) −3.33961 4.88334i −0.282249 0.412718i
\(141\) 0.686605 0.0578226
\(142\) 6.21017 6.21017i 0.521146 0.521146i
\(143\) 2.32898 2.32898i 0.194760 0.194760i
\(144\) 2.98977i 0.249147i
\(145\) −6.51029 11.6715i −0.540651 0.969269i
\(146\) 2.93862i 0.243202i
\(147\) −0.401741 + 0.583006i −0.0331350 + 0.0480855i
\(148\) −6.33137 6.33137i −0.520435 0.520435i
\(149\) 2.62196i 0.214799i −0.994216 0.107400i \(-0.965748\pi\)
0.994216 0.107400i \(-0.0342524\pi\)
\(150\) −0.430302 0.265709i −0.0351340 0.0216951i
\(151\) 1.43640 0.116893 0.0584463 0.998291i \(-0.481385\pi\)
0.0584463 + 0.998291i \(0.481385\pi\)
\(152\) 1.55892 + 1.55892i 0.126445 + 0.126445i
\(153\) −7.21704 + 7.21704i −0.583463 + 0.583463i
\(154\) 1.69304 2.03313i 0.136429 0.163834i
\(155\) 5.44312 + 9.75833i 0.437202 + 0.783808i
\(156\) −0.333142 −0.0266727
\(157\) 12.9197 + 12.9197i 1.03110 + 1.03110i 0.999500 + 0.0316032i \(0.0100613\pi\)
0.0316032 + 0.999500i \(0.489939\pi\)
\(158\) −2.03384 2.03384i −0.161803 0.161803i
\(159\) −0.514879 −0.0408325
\(160\) 0.610623 2.15108i 0.0482740 0.170058i
\(161\) 5.11035 + 4.25552i 0.402752 + 0.335382i
\(162\) 6.29893 6.29893i 0.494891 0.494891i
\(163\) −17.2431 17.2431i −1.35058 1.35058i −0.885008 0.465576i \(-0.845847\pi\)
−0.465576 0.885008i \(-0.654153\pi\)
\(164\) 8.47999 0.662176
\(165\) 0.0617619 0.217572i 0.00480815 0.0169380i
\(166\) 4.52017i 0.350834i
\(167\) −14.8739 14.8739i −1.15098 1.15098i −0.986357 0.164620i \(-0.947360\pi\)
−0.164620 0.986357i \(-0.552640\pi\)
\(168\) −0.266498 + 0.0243233i −0.0205608 + 0.00187658i
\(169\) 2.15166i 0.165512i
\(170\) −6.66651 + 3.71853i −0.511298 + 0.285198i
\(171\) 6.59138i 0.504056i
\(172\) −1.16231 + 1.16231i −0.0886250 + 0.0886250i
\(173\) −10.7916 + 10.7916i −0.820470 + 0.820470i −0.986175 0.165706i \(-0.947010\pi\)
0.165706 + 0.986175i \(0.447010\pi\)
\(174\) −0.604524 −0.0458289
\(175\) 5.89855 11.8409i 0.445888 0.895089i
\(176\) 1.00000 0.0753778
\(177\) −0.237865 + 0.237865i −0.0178790 + 0.0178790i
\(178\) 7.56512 7.56512i 0.567029 0.567029i
\(179\) 7.88097i 0.589051i −0.955644 0.294526i \(-0.904838\pi\)
0.955644 0.294526i \(-0.0951616\pi\)
\(180\) 5.83848 3.25666i 0.435174 0.242737i
\(181\) 25.8379i 1.92052i −0.279112 0.960259i \(-0.590040\pi\)
0.279112 0.960259i \(-0.409960\pi\)
\(182\) −0.792058 8.67819i −0.0587113 0.643270i
\(183\) −0.801622 0.801622i −0.0592576 0.0592576i
\(184\) 2.51354i 0.185300i
\(185\) 5.46746 19.2606i 0.401976 1.41606i
\(186\) 0.505430 0.0370599
\(187\) −2.41391 2.41391i −0.176523 0.176523i
\(188\) −4.80004 + 4.80004i −0.350079 + 0.350079i
\(189\) −1.23175 1.02571i −0.0895965 0.0746095i
\(190\) −1.34621 + 4.74237i −0.0976642 + 0.344047i
\(191\) −23.4159 −1.69432 −0.847159 0.531339i \(-0.821689\pi\)
−0.847159 + 0.531339i \(0.821689\pi\)
\(192\) −0.0715208 0.0715208i −0.00516157 0.00516157i
\(193\) 12.0396 + 12.0396i 0.866632 + 0.866632i 0.992098 0.125465i \(-0.0400424\pi\)
−0.125465 + 0.992098i \(0.540042\pi\)
\(194\) 4.66398 0.334854
\(195\) −0.362880 0.650565i −0.0259864 0.0465879i
\(196\) −1.26722 6.88434i −0.0905160 0.491739i
\(197\) −12.7592 + 12.7592i −0.909057 + 0.909057i −0.996196 0.0871394i \(-0.972227\pi\)
0.0871394 + 0.996196i \(0.472227\pi\)
\(198\) 2.11409 + 2.11409i 0.150242 + 0.150242i
\(199\) −1.49431 −0.105929 −0.0529643 0.998596i \(-0.516867\pi\)
−0.0529643 + 0.998596i \(0.516867\pi\)
\(200\) 4.86580 1.15066i 0.344064 0.0813641i
\(201\) 1.36366i 0.0961852i
\(202\) −7.76242 7.76242i −0.546162 0.546162i
\(203\) −1.43728 15.7476i −0.100877 1.10526i
\(204\) 0.345290i 0.0241751i
\(205\) 9.23697 + 16.5599i 0.645138 + 1.15659i
\(206\) 15.8084i 1.10142i
\(207\) −5.31384 + 5.31384i −0.369337 + 0.369337i
\(208\) 2.32898 2.32898i 0.161486 0.161486i
\(209\) −2.20465 −0.152499
\(210\) −0.337787 0.493929i −0.0233095 0.0340843i
\(211\) −24.1976 −1.66583 −0.832916 0.553399i \(-0.813330\pi\)
−0.832916 + 0.553399i \(0.813330\pi\)
\(212\) 3.59950 3.59950i 0.247215 0.247215i
\(213\) 0.628131 0.628131i 0.0430389 0.0430389i
\(214\) 8.56588i 0.585551i
\(215\) −3.53583 1.00371i −0.241142 0.0684525i
\(216\) 0.605839i 0.0412221i
\(217\) 1.20168 + 13.1662i 0.0815754 + 0.893782i
\(218\) −6.17799 6.17799i −0.418426 0.418426i
\(219\) 0.297229i 0.0200849i
\(220\) 1.08927 + 1.95282i 0.0734383 + 0.131659i
\(221\) −11.2439 −0.756349
\(222\) −0.640391 0.640391i −0.0429802 0.0429802i
\(223\) 14.3774 14.3774i 0.962785 0.962785i −0.0365471 0.999332i \(-0.511636\pi\)
0.999332 + 0.0365471i \(0.0116359\pi\)
\(224\) 1.69304 2.03313i 0.113121 0.135844i
\(225\) 12.7193 + 7.85411i 0.847954 + 0.523608i
\(226\) 10.2801 0.683820
\(227\) 6.98271 + 6.98271i 0.463459 + 0.463459i 0.899787 0.436329i \(-0.143721\pi\)
−0.436329 + 0.899787i \(0.643721\pi\)
\(228\) 0.157678 + 0.157678i 0.0104425 + 0.0104425i
\(229\) −0.136302 −0.00900707 −0.00450354 0.999990i \(-0.501434\pi\)
−0.00450354 + 0.999990i \(0.501434\pi\)
\(230\) −4.90848 + 2.73791i −0.323656 + 0.180533i
\(231\) 0.171244 0.205642i 0.0112670 0.0135303i
\(232\) 4.22621 4.22621i 0.277465 0.277465i
\(233\) −16.2560 16.2560i −1.06496 1.06496i −0.997738 0.0672252i \(-0.978585\pi\)
−0.0672252 0.997738i \(-0.521415\pi\)
\(234\) 9.84735 0.643741
\(235\) −14.6021 4.14508i −0.952538 0.270395i
\(236\) 3.32581i 0.216492i
\(237\) −0.205714 0.205714i −0.0133625 0.0133625i
\(238\) −8.99465 + 0.820941i −0.583037 + 0.0532137i
\(239\) 5.90173i 0.381751i 0.981614 + 0.190876i \(0.0611327\pi\)
−0.981614 + 0.190876i \(0.938867\pi\)
\(240\) 0.0617619 0.217572i 0.00398671 0.0140442i
\(241\) 6.08298i 0.391839i −0.980620 0.195920i \(-0.937231\pi\)
0.980620 0.195920i \(-0.0627692\pi\)
\(242\) −0.707107 + 0.707107i −0.0454545 + 0.0454545i
\(243\) 1.92229 1.92229i 0.123315 0.123315i
\(244\) 11.2082 0.717534
\(245\) 12.0635 9.97354i 0.770710 0.637186i
\(246\) 0.857714 0.0546859
\(247\) −5.13459 + 5.13459i −0.326706 + 0.326706i
\(248\) −3.53345 + 3.53345i −0.224374 + 0.224374i
\(249\) 0.457196i 0.0289736i
\(250\) 7.54718 + 8.24864i 0.477326 + 0.521690i
\(251\) 13.3303i 0.841401i −0.907200 0.420700i \(-0.861784\pi\)
0.907200 0.420700i \(-0.138216\pi\)
\(252\) 7.87744 0.718974i 0.496232 0.0452911i
\(253\) −1.77734 1.77734i −0.111740 0.111740i
\(254\) 8.37782i 0.525671i
\(255\) −0.674288 + 0.376113i −0.0422256 + 0.0235531i
\(256\) 1.00000 0.0625000
\(257\) −12.1951 12.1951i −0.760708 0.760708i 0.215743 0.976450i \(-0.430783\pi\)
−0.976450 + 0.215743i \(0.930783\pi\)
\(258\) −0.117562 + 0.117562i −0.00731910 + 0.00731910i
\(259\) 15.1593 18.2045i 0.941955 1.13117i
\(260\) 7.08497 + 2.01120i 0.439391 + 0.124729i
\(261\) 17.8692 1.10607
\(262\) 7.35809 + 7.35809i 0.454585 + 0.454585i
\(263\) 1.13084 + 1.13084i 0.0697304 + 0.0697304i 0.741112 0.671382i \(-0.234299\pi\)
−0.671382 + 0.741112i \(0.734299\pi\)
\(264\) 0.101146 0.00622508
\(265\) 10.9500 + 3.10836i 0.672653 + 0.190945i
\(266\) −3.73256 + 4.48233i −0.228858 + 0.274829i
\(267\) 0.765178 0.765178i 0.0468282 0.0468282i
\(268\) −9.53332 9.53332i −0.582340 0.582340i
\(269\) −16.1191 −0.982799 −0.491400 0.870934i \(-0.663515\pi\)
−0.491400 + 0.870934i \(0.663515\pi\)
\(270\) 1.18309 0.659920i 0.0720008 0.0401615i
\(271\) 5.27398i 0.320372i −0.987087 0.160186i \(-0.948791\pi\)
0.987087 0.160186i \(-0.0512094\pi\)
\(272\) −2.41391 2.41391i −0.146365 0.146365i
\(273\) −0.0801133 0.877761i −0.00484867 0.0531245i
\(274\) 8.46494i 0.511386i
\(275\) −2.62700 + 4.25428i −0.158414 + 0.256543i
\(276\) 0.254233i 0.0153030i
\(277\) 6.53318 6.53318i 0.392541 0.392541i −0.483051 0.875592i \(-0.660471\pi\)
0.875592 + 0.483051i \(0.160471\pi\)
\(278\) −3.69667 + 3.69667i −0.221711 + 0.221711i
\(279\) −14.9400 −0.894436
\(280\) 5.81450 + 1.09158i 0.347483 + 0.0652345i
\(281\) 2.68515 0.160183 0.0800913 0.996788i \(-0.474479\pi\)
0.0800913 + 0.996788i \(0.474479\pi\)
\(282\) −0.485503 + 0.485503i −0.0289113 + 0.0289113i
\(283\) −19.3234 + 19.3234i −1.14866 + 1.14866i −0.161842 + 0.986817i \(0.551744\pi\)
−0.986817 + 0.161842i \(0.948256\pi\)
\(284\) 8.78250i 0.521146i
\(285\) −0.136163 + 0.479670i −0.00806560 + 0.0284132i
\(286\) 3.29368i 0.194760i
\(287\) 2.03925 + 22.3431i 0.120373 + 1.31887i
\(288\) 2.11409 + 2.11409i 0.124574 + 0.124574i
\(289\) 5.34605i 0.314473i
\(290\) 12.8565 + 3.64955i 0.754960 + 0.214309i
\(291\) 0.471741 0.0276539
\(292\) 2.07792 + 2.07792i 0.121601 + 0.121601i
\(293\) −16.0098 + 16.0098i −0.935304 + 0.935304i −0.998031 0.0627265i \(-0.980020\pi\)
0.0627265 + 0.998031i \(0.480020\pi\)
\(294\) −0.128174 0.696321i −0.00747527 0.0406103i
\(295\) 6.49471 3.62270i 0.378136 0.210922i
\(296\) 8.95391 0.520435
\(297\) 0.428393 + 0.428393i 0.0248579 + 0.0248579i
\(298\) 1.85400 + 1.85400i 0.107400 + 0.107400i
\(299\) −8.27879 −0.478775
\(300\) 0.492154 0.116384i 0.0284145 0.00671946i
\(301\) −3.34195 2.78294i −0.192627 0.160406i
\(302\) −1.01569 + 1.01569i −0.0584463 + 0.0584463i
\(303\) −0.785135 0.785135i −0.0451048 0.0451048i
\(304\) −2.20465 −0.126445
\(305\) 12.2088 + 21.8876i 0.699071 + 1.25328i
\(306\) 10.2064i 0.583463i
\(307\) −13.9838 13.9838i −0.798099 0.798099i 0.184697 0.982796i \(-0.440870\pi\)
−0.982796 + 0.184697i \(0.940870\pi\)
\(308\) 0.240478 + 2.63480i 0.0137025 + 0.150132i
\(309\) 1.59895i 0.0909609i
\(310\) −10.7490 3.05131i −0.610505 0.173303i
\(311\) 25.3533i 1.43765i 0.695188 + 0.718827i \(0.255321\pi\)
−0.695188 + 0.718827i \(0.744679\pi\)
\(312\) 0.235567 0.235567i 0.0133363 0.0133363i
\(313\) −19.7694 + 19.7694i −1.11744 + 1.11744i −0.125319 + 0.992117i \(0.539995\pi\)
−0.992117 + 0.125319i \(0.960005\pi\)
\(314\) −18.2712 −1.03110
\(315\) 9.98466 + 14.6001i 0.562572 + 0.822620i
\(316\) 2.87628 0.161803
\(317\) 8.97452 8.97452i 0.504059 0.504059i −0.408638 0.912697i \(-0.633996\pi\)
0.912697 + 0.408638i \(0.133996\pi\)
\(318\) 0.364074 0.364074i 0.0204163 0.0204163i
\(319\) 5.97677i 0.334635i
\(320\) 1.08927 + 1.95282i 0.0608919 + 0.109166i
\(321\) 0.866401i 0.0483578i
\(322\) −6.62267 + 0.604451i −0.369067 + 0.0336847i
\(323\) 5.32182 + 5.32182i 0.296114 + 0.296114i
\(324\) 8.90803i 0.494891i
\(325\) 3.78992 + 16.0264i 0.210227 + 0.888984i
\(326\) 24.3854 1.35058
\(327\) −0.624876 0.624876i −0.0345557 0.0345557i
\(328\) −5.99626 + 5.99626i −0.331088 + 0.331088i
\(329\) −13.8015 11.4928i −0.760899 0.633621i
\(330\) 0.110175 + 0.197519i 0.00606491 + 0.0108731i
\(331\) 16.0212 0.880607 0.440303 0.897849i \(-0.354871\pi\)
0.440303 + 0.897849i \(0.354871\pi\)
\(332\) −3.19625 3.19625i −0.175417 0.175417i
\(333\) 18.9293 + 18.9293i 1.03732 + 1.03732i
\(334\) 21.0349 1.15098
\(335\) 8.23251 29.0012i 0.449790 1.58450i
\(336\) 0.171244 0.205642i 0.00934211 0.0112187i
\(337\) 12.2483 12.2483i 0.667206 0.667206i −0.289862 0.957068i \(-0.593610\pi\)
0.957068 + 0.289862i \(0.0936096\pi\)
\(338\) −1.52145 1.52145i −0.0827561 0.0827561i
\(339\) 1.03978 0.0564733
\(340\) 2.08454 7.34333i 0.113050 0.398248i
\(341\) 4.99705i 0.270605i
\(342\) −4.66081 4.66081i −0.252028 0.252028i
\(343\) 17.8341 4.99441i 0.962952 0.269673i
\(344\) 1.64375i 0.0886250i
\(345\) −0.496471 + 0.276928i −0.0267291 + 0.0149093i
\(346\) 15.2616i 0.820470i
\(347\) 8.93061 8.93061i 0.479420 0.479420i −0.425526 0.904946i \(-0.639911\pi\)
0.904946 + 0.425526i \(0.139911\pi\)
\(348\) 0.427463 0.427463i 0.0229144 0.0229144i
\(349\) −14.1309 −0.756409 −0.378204 0.925722i \(-0.623458\pi\)
−0.378204 + 0.925722i \(0.623458\pi\)
\(350\) 4.20188 + 12.5437i 0.224600 + 0.670488i
\(351\) 1.99544 0.106509
\(352\) −0.707107 + 0.707107i −0.0376889 + 0.0376889i
\(353\) −11.7222 + 11.7222i −0.623912 + 0.623912i −0.946529 0.322617i \(-0.895437\pi\)
0.322617 + 0.946529i \(0.395437\pi\)
\(354\) 0.336391i 0.0178790i
\(355\) −17.1506 + 9.56649i −0.910261 + 0.507737i
\(356\) 10.6987i 0.567029i
\(357\) −0.909770 + 0.0830346i −0.0481501 + 0.00439466i
\(358\) 5.57268 + 5.57268i 0.294526 + 0.294526i
\(359\) 33.7189i 1.77962i 0.456334 + 0.889809i \(0.349162\pi\)
−0.456334 + 0.889809i \(0.650838\pi\)
\(360\) −1.82562 + 6.43123i −0.0962188 + 0.338956i
\(361\) −14.1395 −0.744186
\(362\) 18.2702 + 18.2702i 0.960259 + 0.960259i
\(363\) −0.0715208 + 0.0715208i −0.00375387 + 0.00375387i
\(364\) 6.69648 + 5.57634i 0.350991 + 0.292280i
\(365\) −1.79439 + 6.32121i −0.0939227 + 0.330867i
\(366\) 1.13366 0.0592576
\(367\) −14.3586 14.3586i −0.749510 0.749510i 0.224877 0.974387i \(-0.427802\pi\)
−0.974387 + 0.224877i \(0.927802\pi\)
\(368\) −1.77734 1.77734i −0.0926502 0.0926502i
\(369\) −25.3532 −1.31984
\(370\) 9.75320 + 17.4854i 0.507044 + 0.909020i
\(371\) 10.3496 + 8.61837i 0.537323 + 0.447444i
\(372\) −0.357393 + 0.357393i −0.0185300 + 0.0185300i
\(373\) 5.92772 + 5.92772i 0.306926 + 0.306926i 0.843716 0.536790i \(-0.180363\pi\)
−0.536790 + 0.843716i \(0.680363\pi\)
\(374\) 3.41379 0.176523
\(375\) 0.763365 + 0.834314i 0.0394200 + 0.0430838i
\(376\) 6.78828i 0.350079i
\(377\) 13.9198 + 13.9198i 0.716906 + 0.716906i
\(378\) 1.59626 0.145691i 0.0821030 0.00749354i
\(379\) 29.1754i 1.49864i −0.662207 0.749321i \(-0.730380\pi\)
0.662207 0.749321i \(-0.269620\pi\)
\(380\) −2.40145 4.30527i −0.123192 0.220856i
\(381\) 0.847380i 0.0434126i
\(382\) 16.5576 16.5576i 0.847159 0.847159i
\(383\) −6.25262 + 6.25262i −0.319494 + 0.319494i −0.848573 0.529079i \(-0.822538\pi\)
0.529079 + 0.848573i \(0.322538\pi\)
\(384\) 0.101146 0.00516157
\(385\) −4.88334 + 3.33961i −0.248878 + 0.170202i
\(386\) −17.0266 −0.866632
\(387\) 3.47503 3.47503i 0.176646 0.176646i
\(388\) −3.29793 + 3.29793i −0.167427 + 0.167427i
\(389\) 8.63838i 0.437983i −0.975727 0.218992i \(-0.929723\pi\)
0.975727 0.218992i \(-0.0702767\pi\)
\(390\) 0.716614 + 0.203424i 0.0362871 + 0.0103008i
\(391\) 8.58069i 0.433944i
\(392\) 5.76403 + 3.97190i 0.291127 + 0.200611i
\(393\) 0.744239 + 0.744239i 0.0375419 + 0.0375419i
\(394\) 18.0443i 0.909057i
\(395\) 3.13304 + 5.61685i 0.157640 + 0.282614i
\(396\) −2.98977 −0.150242
\(397\) 10.3438 + 10.3438i 0.519138 + 0.519138i 0.917311 0.398172i \(-0.130355\pi\)
−0.398172 + 0.917311i \(0.630355\pi\)
\(398\) 1.05663 1.05663i 0.0529643 0.0529643i
\(399\) −0.377532 + 0.453368i −0.0189002 + 0.0226968i
\(400\) −2.62700 + 4.25428i −0.131350 + 0.212714i
\(401\) 7.92538 0.395775 0.197887 0.980225i \(-0.436592\pi\)
0.197887 + 0.980225i \(0.436592\pi\)
\(402\) −0.964254 0.964254i −0.0480926 0.0480926i
\(403\) −11.6381 11.6381i −0.579733 0.579733i
\(404\) 10.9777 0.546162
\(405\) −17.3958 + 9.70322i −0.864402 + 0.482157i
\(406\) 12.1515 + 10.1189i 0.603071 + 0.502193i
\(407\) −6.33137 + 6.33137i −0.313834 + 0.313834i
\(408\) −0.244157 0.244157i −0.0120876 0.0120876i
\(409\) 29.7189 1.46950 0.734752 0.678336i \(-0.237299\pi\)
0.734752 + 0.678336i \(0.237299\pi\)
\(410\) −18.2411 5.17808i −0.900865 0.255727i
\(411\) 0.856191i 0.0422328i
\(412\) −11.1782 11.1782i −0.550710 0.550710i
\(413\) 8.76285 0.799785i 0.431192 0.0393548i
\(414\) 7.51490i 0.369337i
\(415\) 2.76012 9.72325i 0.135489 0.477296i
\(416\) 3.29368i 0.161486i
\(417\) −0.373902 + 0.373902i −0.0183100 + 0.0183100i
\(418\) 1.55892 1.55892i 0.0762493 0.0762493i
\(419\) −6.93525 −0.338809 −0.169405 0.985547i \(-0.554184\pi\)
−0.169405 + 0.985547i \(0.554184\pi\)
\(420\) 0.588112 + 0.110409i 0.0286969 + 0.00538740i
\(421\) 24.4211 1.19021 0.595106 0.803647i \(-0.297110\pi\)
0.595106 + 0.803647i \(0.297110\pi\)
\(422\) 17.1103 17.1103i 0.832916 0.832916i
\(423\) 14.3510 14.3510i 0.697770 0.697770i
\(424\) 5.09047i 0.247215i
\(425\) 16.6108 3.92812i 0.805742 0.190542i
\(426\) 0.888312i 0.0430389i
\(427\) 2.69534 + 29.5315i 0.130436 + 1.42913i
\(428\) −6.05699 6.05699i −0.292776 0.292776i
\(429\) 0.333142i 0.0160842i
\(430\) 3.20994 1.79048i 0.154797 0.0863447i
\(431\) −10.7599 −0.518288 −0.259144 0.965839i \(-0.583441\pi\)
−0.259144 + 0.965839i \(0.583441\pi\)
\(432\) 0.428393 + 0.428393i 0.0206111 + 0.0206111i
\(433\) 11.5614 11.5614i 0.555604 0.555604i −0.372449 0.928053i \(-0.621482\pi\)
0.928053 + 0.372449i \(0.121482\pi\)
\(434\) −10.1596 8.46021i −0.487679 0.406103i
\(435\) 1.30038 + 0.369136i 0.0623484 + 0.0176987i
\(436\) 8.73699 0.418426
\(437\) 3.91840 + 3.91840i 0.187443 + 0.187443i
\(438\) 0.210173 + 0.210173i 0.0100424 + 0.0100424i
\(439\) −12.4834 −0.595800 −0.297900 0.954597i \(-0.596286\pi\)
−0.297900 + 0.954597i \(0.596286\pi\)
\(440\) −2.15108 0.610623i −0.102549 0.0291103i
\(441\) 3.78871 + 20.5826i 0.180415 + 0.980123i
\(442\) 7.95066 7.95066i 0.378174 0.378174i
\(443\) 7.25752 + 7.25752i 0.344815 + 0.344815i 0.858174 0.513359i \(-0.171599\pi\)
−0.513359 + 0.858174i \(0.671599\pi\)
\(444\) 0.905649 0.0429802
\(445\) −20.8926 + 11.6537i −0.990404 + 0.552439i
\(446\) 20.3328i 0.962785i
\(447\) 0.187524 + 0.187524i 0.00886960 + 0.00886960i
\(448\) 0.240478 + 2.63480i 0.0113615 + 0.124483i
\(449\) 6.97090i 0.328977i 0.986379 + 0.164489i \(0.0525974\pi\)
−0.986379 + 0.164489i \(0.947403\pi\)
\(450\) −14.5476 + 3.44021i −0.685781 + 0.162173i
\(451\) 8.47999i 0.399307i
\(452\) −7.26910 + 7.26910i −0.341910 + 0.341910i
\(453\) −0.102732 + 0.102732i −0.00482679 + 0.00482679i
\(454\) −9.87504 −0.463459
\(455\) −3.59533 + 19.1511i −0.168551 + 0.897819i
\(456\) −0.222990 −0.0104425
\(457\) 12.4271 12.4271i 0.581314 0.581314i −0.353950 0.935264i \(-0.615162\pi\)
0.935264 + 0.353950i \(0.115162\pi\)
\(458\) 0.0963799 0.0963799i 0.00450354 0.00450354i
\(459\) 2.06821i 0.0965356i
\(460\) 1.53482 5.40682i 0.0715615 0.252094i
\(461\) 11.4215i 0.531951i −0.963980 0.265976i \(-0.914306\pi\)
0.963980 0.265976i \(-0.0856941\pi\)
\(462\) 0.0243233 + 0.266498i 0.00113162 + 0.0123986i
\(463\) 14.6778 + 14.6778i 0.682134 + 0.682134i 0.960481 0.278347i \(-0.0897865\pi\)
−0.278347 + 0.960481i \(0.589786\pi\)
\(464\) 5.97677i 0.277465i
\(465\) −1.08722 0.308627i −0.0504186 0.0143122i
\(466\) 22.9894 1.06496
\(467\) 10.4596 + 10.4596i 0.484011 + 0.484011i 0.906410 0.422399i \(-0.138812\pi\)
−0.422399 + 0.906410i \(0.638812\pi\)
\(468\) −6.96313 + 6.96313i −0.321871 + 0.321871i
\(469\) 22.8258 27.4109i 1.05400 1.26572i
\(470\) 13.2563 7.39425i 0.611467 0.341071i
\(471\) −1.84805 −0.0851538
\(472\) 2.35170 + 2.35170i 0.108246 + 0.108246i
\(473\) 1.16231 + 1.16231i 0.0534429 + 0.0534429i
\(474\) 0.290923 0.0133625
\(475\) 5.79160 9.37918i 0.265737 0.430346i
\(476\) 5.77968 6.94067i 0.264911 0.318125i
\(477\) −10.7617 + 10.7617i −0.492744 + 0.492744i
\(478\) −4.17315 4.17315i −0.190876 0.190876i
\(479\) 7.45211 0.340496 0.170248 0.985401i \(-0.445543\pi\)
0.170248 + 0.985401i \(0.445543\pi\)
\(480\) 0.110175 + 0.197519i 0.00502876 + 0.00901547i
\(481\) 29.4913i 1.34469i
\(482\) 4.30132 + 4.30132i 0.195920 + 0.195920i
\(483\) −0.669854 + 0.0611376i −0.0304794 + 0.00278186i
\(484\) 1.00000i 0.0454545i
\(485\) −10.0326 2.84793i −0.455556 0.129318i
\(486\) 2.71853i 0.123315i
\(487\) −9.32786 + 9.32786i −0.422686 + 0.422686i −0.886127 0.463442i \(-0.846614\pi\)
0.463442 + 0.886127i \(0.346614\pi\)
\(488\) −7.92542 + 7.92542i −0.358767 + 0.358767i
\(489\) 2.46648 0.111538
\(490\) −1.47784 + 15.5826i −0.0667620 + 0.703948i
\(491\) −22.9262 −1.03465 −0.517324 0.855790i \(-0.673072\pi\)
−0.517324 + 0.855790i \(0.673072\pi\)
\(492\) −0.606496 + 0.606496i −0.0273429 + 0.0273429i
\(493\) 14.4274 14.4274i 0.649777 0.649777i
\(494\) 7.26140i 0.326706i
\(495\) −3.25666 5.83848i −0.146376 0.262420i
\(496\) 4.99705i 0.224374i
\(497\) −23.1401 + 2.11200i −1.03798 + 0.0947362i
\(498\) −0.323286 0.323286i −0.0144868 0.0144868i
\(499\) 25.5090i 1.14194i 0.820971 + 0.570970i \(0.193433\pi\)
−0.820971 + 0.570970i \(0.806567\pi\)
\(500\) −11.1693 0.496003i −0.499508 0.0221819i
\(501\) 2.12759 0.0950535
\(502\) 9.42594 + 9.42594i 0.420700 + 0.420700i
\(503\) 16.9751 16.9751i 0.756884 0.756884i −0.218870 0.975754i \(-0.570237\pi\)
0.975754 + 0.218870i \(0.0702371\pi\)
\(504\) −5.06180 + 6.07859i −0.225471 + 0.270762i
\(505\) 11.9577 + 21.4375i 0.532109 + 0.953955i
\(506\) 2.51354 0.111740
\(507\) −0.153888 0.153888i −0.00683442 0.00683442i
\(508\) −5.92401 5.92401i −0.262836 0.262836i
\(509\) −12.2625 −0.543524 −0.271762 0.962364i \(-0.587606\pi\)
−0.271762 + 0.962364i \(0.587606\pi\)
\(510\) 0.210842 0.742746i 0.00933624 0.0328893i
\(511\) −4.97521 + 5.97460i −0.220090 + 0.264301i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −0.944454 0.944454i −0.0416987 0.0416987i
\(514\) 17.2464 0.760708
\(515\) 9.65295 34.0050i 0.425360 1.49844i
\(516\) 0.166258i 0.00731910i
\(517\) 4.80004 + 4.80004i 0.211106 + 0.211106i
\(518\) 2.15322 + 23.5918i 0.0946070 + 1.03656i
\(519\) 1.54365i 0.0677585i
\(520\) −6.43196 + 3.58770i −0.282060 + 0.157331i
\(521\) 14.7148i 0.644669i −0.946626 0.322335i \(-0.895532\pi\)
0.946626 0.322335i \(-0.104468\pi\)
\(522\) −12.6354 + 12.6354i −0.553037 + 0.553037i
\(523\) −13.1748 + 13.1748i −0.576092 + 0.576092i −0.933824 0.357732i \(-0.883550\pi\)
0.357732 + 0.933824i \(0.383550\pi\)
\(524\) −10.4059 −0.454585
\(525\) 0.425002 + 1.26874i 0.0185486 + 0.0553723i
\(526\) −1.59924 −0.0697304
\(527\) −12.0624 + 12.0624i −0.525448 + 0.525448i
\(528\) −0.0715208 + 0.0715208i −0.00311254 + 0.00311254i
\(529\) 16.6821i 0.725310i
\(530\) −9.94076 + 5.54488i −0.431799 + 0.240854i
\(531\) 9.94341i 0.431507i
\(532\) −0.530169 5.80880i −0.0229857 0.251843i
\(533\) −19.7498 19.7498i −0.855458 0.855458i
\(534\) 1.08213i 0.0468282i
\(535\) 5.23052 18.4259i 0.226135 0.796620i
\(536\) 13.4821 0.582340
\(537\) 0.563653 + 0.563653i 0.0243234 + 0.0243234i
\(538\) 11.3979 11.3979i 0.491400 0.491400i
\(539\) −6.88434 + 1.26722i −0.296530 + 0.0545832i
\(540\) −0.369939 + 1.30321i −0.0159197 + 0.0560811i
\(541\) −9.59555 −0.412545 −0.206272 0.978495i \(-0.566133\pi\)
−0.206272 + 0.978495i \(0.566133\pi\)
\(542\) 3.72927 + 3.72927i 0.160186 + 0.160186i
\(543\) 1.84795 + 1.84795i 0.0793030 + 0.0793030i
\(544\) 3.41379 0.146365
\(545\) 9.51692 + 17.0618i 0.407660 + 0.730846i
\(546\) 0.677320 + 0.564022i 0.0289866 + 0.0241379i
\(547\) 21.9557 21.9557i 0.938759 0.938759i −0.0594707 0.998230i \(-0.518941\pi\)
0.998230 + 0.0594707i \(0.0189413\pi\)
\(548\) 5.98561 + 5.98561i 0.255693 + 0.255693i
\(549\) −33.5100 −1.43017
\(550\) −1.15066 4.86580i −0.0490644 0.207478i
\(551\) 13.1767i 0.561344i
\(552\) −0.179770 0.179770i −0.00765152 0.00765152i
\(553\) 0.691682 + 7.57842i 0.0294133 + 0.322267i
\(554\) 9.23932i 0.392541i
\(555\) 0.986493 + 1.76857i 0.0418743 + 0.0750715i
\(556\) 5.22788i 0.221711i
\(557\) 1.77779 1.77779i 0.0753274 0.0753274i −0.668439 0.743767i \(-0.733037\pi\)
0.743767 + 0.668439i \(0.233037\pi\)
\(558\) 10.5642 10.5642i 0.447218 0.447218i
\(559\) 5.41399 0.228987
\(560\) −4.88334 + 3.33961i −0.206359 + 0.141124i
\(561\) 0.345290 0.0145781
\(562\) −1.89869 + 1.89869i −0.0800913 + 0.0800913i
\(563\) 10.4762 10.4762i 0.441521 0.441521i −0.451002 0.892523i \(-0.648933\pi\)
0.892523 + 0.451002i \(0.148933\pi\)
\(564\) 0.686605i 0.0289113i
\(565\) −22.1132 6.27725i −0.930311 0.264086i
\(566\) 27.3275i 1.14866i
\(567\) −23.4709 + 2.14219i −0.985684 + 0.0899634i
\(568\) −6.21017 6.21017i −0.260573 0.260573i
\(569\) 8.40769i 0.352469i 0.984348 + 0.176234i \(0.0563917\pi\)
−0.984348 + 0.176234i \(0.943608\pi\)
\(570\) −0.242896 0.435459i −0.0101738 0.0182394i
\(571\) 24.7017 1.03373 0.516867 0.856065i \(-0.327098\pi\)
0.516867 + 0.856065i \(0.327098\pi\)
\(572\) −2.32898 2.32898i −0.0973798 0.0973798i
\(573\) 1.67473 1.67473i 0.0699627 0.0699627i
\(574\) −17.2409 14.3570i −0.719622 0.599249i
\(575\) 12.2304 2.89223i 0.510041 0.120614i
\(576\) −2.98977 −0.124574
\(577\) −14.9572 14.9572i −0.622678 0.622678i 0.323537 0.946215i \(-0.395128\pi\)
−0.946215 + 0.323537i \(0.895128\pi\)
\(578\) 3.78023 + 3.78023i 0.157237 + 0.157237i
\(579\) −1.72217 −0.0715709
\(580\) −11.6715 + 6.51029i −0.484634 + 0.270325i
\(581\) 7.65284 9.19010i 0.317493 0.381269i
\(582\) −0.333571 + 0.333571i −0.0138270 + 0.0138270i
\(583\) −3.59950 3.59950i −0.149076 0.149076i
\(584\) −2.93862 −0.121601
\(585\) −21.1824 6.01302i −0.875786 0.248608i
\(586\) 22.6413i 0.935304i
\(587\) 13.4550 + 13.4550i 0.555346 + 0.555346i 0.927979 0.372633i \(-0.121545\pi\)
−0.372633 + 0.927979i \(0.621545\pi\)
\(588\) 0.583006 + 0.401741i 0.0240428 + 0.0165675i
\(589\) 11.0167i 0.453936i
\(590\) −2.03082 + 7.15408i −0.0836074 + 0.294529i
\(591\) 1.82510i 0.0750745i
\(592\) −6.33137 + 6.33137i −0.260218 + 0.260218i
\(593\) 12.6950 12.6950i 0.521322 0.521322i −0.396649 0.917970i \(-0.629827\pi\)
0.917970 + 0.396649i \(0.129827\pi\)
\(594\) −0.605839 −0.0248579
\(595\) 19.8495 + 3.72643i 0.813750 + 0.152769i
\(596\) −2.62196 −0.107400
\(597\) 0.106874 0.106874i 0.00437406 0.00437406i
\(598\) 5.85399 5.85399i 0.239388 0.239388i
\(599\) 35.9067i 1.46711i −0.679631 0.733554i \(-0.737860\pi\)
0.679631 0.733554i \(-0.262140\pi\)
\(600\) −0.265709 + 0.430302i −0.0108475 + 0.0175670i
\(601\) 23.5376i 0.960118i 0.877236 + 0.480059i \(0.159385\pi\)
−0.877236 + 0.480059i \(0.840615\pi\)
\(602\) 4.33095 0.395286i 0.176516 0.0161106i
\(603\) 28.5024 + 28.5024i 1.16071 + 1.16071i
\(604\) 1.43640i 0.0584463i
\(605\) 1.95282 1.08927i 0.0793933 0.0442850i
\(606\) 1.11035 0.0451048
\(607\) −19.9351 19.9351i −0.809143 0.809143i 0.175361 0.984504i \(-0.443891\pi\)
−0.984504 + 0.175361i \(0.943891\pi\)
\(608\) 1.55892 1.55892i 0.0632225 0.0632225i
\(609\) 1.22908 + 1.02348i 0.0498046 + 0.0414737i
\(610\) −24.1098 6.84401i −0.976177 0.277106i
\(611\) 22.3585 0.904526
\(612\) 7.21704 + 7.21704i 0.291732 + 0.291732i
\(613\) −24.4323 24.4323i −0.986809 0.986809i 0.0131047 0.999914i \(-0.495829\pi\)
−0.999914 + 0.0131047i \(0.995829\pi\)
\(614\) 19.7761 0.798099
\(615\) −1.84501 0.523740i −0.0743980 0.0211192i
\(616\) −2.03313 1.69304i −0.0819171 0.0682146i
\(617\) −1.92851 + 1.92851i −0.0776389 + 0.0776389i −0.744860 0.667221i \(-0.767484\pi\)
0.667221 + 0.744860i \(0.267484\pi\)
\(618\) −1.13063 1.13063i −0.0454805 0.0454805i
\(619\) 11.8647 0.476884 0.238442 0.971157i \(-0.423363\pi\)
0.238442 + 0.971157i \(0.423363\pi\)
\(620\) 9.75833 5.44312i 0.391904 0.218601i
\(621\) 1.52280i 0.0611078i
\(622\) −17.9275 17.9275i −0.718827 0.718827i
\(623\) −28.1889 + 2.57280i −1.12936 + 0.103077i
\(624\) 0.333142i 0.0133363i
\(625\) −11.1978 22.3520i −0.447911 0.894078i
\(626\) 27.9582i 1.11744i
\(627\) 0.157678 0.157678i 0.00629705 0.00629705i
\(628\) 12.9197 12.9197i 0.515552 0.515552i
\(629\) 30.5668 1.21878
\(630\) −17.3840 3.26358i −0.692596 0.130024i
\(631\) −47.5513 −1.89299 −0.946494 0.322721i \(-0.895402\pi\)
−0.946494 + 0.322721i \(0.895402\pi\)
\(632\) −2.03384 + 2.03384i −0.0809017 + 0.0809017i
\(633\) 1.73063 1.73063i 0.0687864 0.0687864i
\(634\) 12.6919i 0.504059i
\(635\) 5.11569 18.0213i 0.203010 0.715155i
\(636\) 0.514879i 0.0204163i
\(637\) −13.0822 + 18.9849i −0.518335 + 0.752208i
\(638\) −4.22621 4.22621i −0.167317 0.167317i
\(639\) 26.2577i 1.03874i
\(640\) −2.15108 0.610623i −0.0850288 0.0241370i
\(641\) 38.1531 1.50696 0.753478 0.657473i \(-0.228374\pi\)
0.753478 + 0.657473i \(0.228374\pi\)
\(642\) −0.612638 0.612638i −0.0241789 0.0241789i
\(643\) 12.3659 12.3659i 0.487664 0.487664i −0.419904 0.907568i \(-0.637936\pi\)
0.907568 + 0.419904i \(0.137936\pi\)
\(644\) 4.25552 5.11035i 0.167691 0.201376i
\(645\) 0.324672 0.181099i 0.0127839 0.00713078i
\(646\) −7.52619 −0.296114
\(647\) −26.3540 26.3540i −1.03608 1.03608i −0.999324 0.0367565i \(-0.988297\pi\)
−0.0367565 0.999324i \(-0.511703\pi\)
\(648\) −6.29893 6.29893i −0.247445 0.247445i
\(649\) −3.32581 −0.130550
\(650\) −14.0122 8.65249i −0.549605 0.339379i
\(651\) −1.02760 0.855713i −0.0402750 0.0335381i
\(652\) −17.2431 + 17.2431i −0.675292 + 0.675292i
\(653\) −7.24581 7.24581i −0.283550 0.283550i 0.550973 0.834523i \(-0.314257\pi\)
−0.834523 + 0.550973i \(0.814257\pi\)
\(654\) 0.883709 0.0345557
\(655\) −11.3348 20.3209i −0.442888 0.794002i
\(656\) 8.47999i 0.331088i
\(657\) −6.21250 6.21250i −0.242373 0.242373i
\(658\) 17.8858 1.63243i 0.697260 0.0636389i
\(659\) 27.4624i 1.06978i −0.844921 0.534891i \(-0.820353\pi\)
0.844921 0.534891i \(-0.179647\pi\)
\(660\) −0.217572 0.0617619i −0.00846899 0.00240408i
\(661\) 43.3288i 1.68530i −0.538464 0.842648i \(-0.680995\pi\)
0.538464 0.842648i \(-0.319005\pi\)
\(662\) −11.3287 + 11.3287i −0.440303 + 0.440303i
\(663\) 0.804175 0.804175i 0.0312316 0.0312316i
\(664\) 4.52017 0.175417
\(665\) 10.7660 7.36265i 0.417489 0.285512i
\(666\) −26.7701 −1.03732
\(667\) 10.6227 10.6227i 0.411314 0.411314i
\(668\) −14.8739 + 14.8739i −0.575489 + 0.575489i
\(669\) 2.05657i 0.0795116i
\(670\) 14.6857 + 26.3282i 0.567356 + 1.01715i
\(671\) 11.2082i 0.432689i
\(672\) 0.0243233 + 0.266498i 0.000938292 + 0.0102804i
\(673\) 18.0721 + 18.0721i 0.696628 + 0.696628i 0.963682 0.267054i \(-0.0860501\pi\)
−0.267054 + 0.963682i \(0.586050\pi\)
\(674\) 17.3217i 0.667206i
\(675\) −2.94789 + 0.697116i −0.113464 + 0.0268320i
\(676\) 2.15166 0.0827561
\(677\) 29.8145 + 29.8145i 1.14586 + 1.14586i 0.987358 + 0.158505i \(0.0506675\pi\)
0.158505 + 0.987358i \(0.449333\pi\)
\(678\) −0.735238 + 0.735238i −0.0282366 + 0.0282366i
\(679\) −9.48246 7.89630i −0.363904 0.303032i
\(680\) 3.71853 + 6.66651i 0.142599 + 0.255649i
\(681\) −0.998817 −0.0382748
\(682\) 3.53345 + 3.53345i 0.135303 + 0.135303i
\(683\) 10.0456 + 10.0456i 0.384383 + 0.384383i 0.872679 0.488295i \(-0.162381\pi\)
−0.488295 + 0.872679i \(0.662381\pi\)
\(684\) 6.59138 0.252028
\(685\) −5.16889 + 18.2087i −0.197493 + 0.695720i
\(686\) −9.07904 + 16.1422i −0.346640 + 0.616312i
\(687\) 0.00974840 0.00974840i 0.000371925 0.000371925i
\(688\) 1.16231 + 1.16231i 0.0443125 + 0.0443125i
\(689\) −16.7664 −0.638748
\(690\) 0.155241 0.546876i 0.00590992 0.0208192i
\(691\) 48.2925i 1.83713i 0.395268 + 0.918566i \(0.370652\pi\)
−0.395268 + 0.918566i \(0.629348\pi\)
\(692\) 10.7916 + 10.7916i 0.410235 + 0.410235i
\(693\) −0.718974 7.87744i −0.0273116 0.299239i
\(694\) 12.6298i 0.479420i
\(695\) 10.2091 5.69455i 0.387253 0.216007i
\(696\) 0.604524i 0.0229144i
\(697\) −20.4700 + 20.4700i −0.775355 + 0.775355i
\(698\) 9.99204 9.99204i 0.378204 0.378204i
\(699\) 2.32528 0.0879500
\(700\) −11.8409 5.89855i −0.447544 0.222944i
\(701\) −40.4290 −1.52698 −0.763491 0.645818i \(-0.776516\pi\)
−0.763491 + 0.645818i \(0.776516\pi\)
\(702\) −1.41099 + 1.41099i −0.0532544 + 0.0532544i
\(703\) 13.9584 13.9584i 0.526452 0.526452i
\(704\) 1.00000i 0.0376889i
\(705\) 1.34082 0.747896i 0.0504980 0.0281674i
\(706\) 16.5778i 0.623912i
\(707\) 2.63990 + 28.9241i 0.0992837 + 1.08780i
\(708\) 0.237865 + 0.237865i 0.00893950 + 0.00893950i
\(709\) 47.7680i 1.79396i 0.442066 + 0.896982i \(0.354246\pi\)
−0.442066 + 0.896982i \(0.645754\pi\)
\(710\) 5.36280 18.8919i 0.201262 0.708999i
\(711\) −8.59941 −0.322503
\(712\) −7.56512 7.56512i −0.283515 0.283515i
\(713\) −8.88145 + 8.88145i −0.332613 + 0.332613i
\(714\) 0.584590 0.702019i 0.0218777 0.0262724i
\(715\) 2.01120 7.08497i 0.0752146 0.264963i
\(716\) −7.88097 −0.294526
\(717\) −0.422096 0.422096i −0.0157635 0.0157635i
\(718\) −23.8429 23.8429i −0.889809 0.889809i
\(719\) 8.73237 0.325662 0.162831 0.986654i \(-0.447937\pi\)
0.162831 + 0.986654i \(0.447937\pi\)
\(720\) −3.25666 5.83848i −0.121368 0.217587i
\(721\) 26.7642 32.1404i 0.996751 1.19697i
\(722\) 9.99816 9.99816i 0.372093 0.372093i
\(723\) 0.435059 + 0.435059i 0.0161800 + 0.0161800i
\(724\) −25.8379 −0.960259
\(725\) −25.4268 15.7010i −0.944329 0.583119i
\(726\) 0.101146i 0.00375387i
\(727\) 7.82764 + 7.82764i 0.290311 + 0.290311i 0.837203 0.546892i \(-0.184189\pi\)
−0.546892 + 0.837203i \(0.684189\pi\)
\(728\) −8.67819 + 0.792058i −0.321635 + 0.0293556i
\(729\) 26.4491i 0.979597i
\(730\) −3.20094 5.73860i −0.118472 0.212395i
\(731\) 5.61141i 0.207546i
\(732\) −0.801622 + 0.801622i −0.0296288 + 0.0296288i
\(733\) −16.9468 + 16.9468i −0.625944 + 0.625944i −0.947045 0.321101i \(-0.895947\pi\)
0.321101 + 0.947045i \(0.395947\pi\)
\(734\) 20.3061 0.749510
\(735\) −0.149477 + 1.57611i −0.00551355 + 0.0581356i
\(736\) 2.51354 0.0926502
\(737\) −9.53332 + 9.53332i −0.351164 + 0.351164i
\(738\) 17.9274 17.9274i 0.659918 0.659918i
\(739\) 14.9605i 0.550331i 0.961397 + 0.275166i \(0.0887327\pi\)
−0.961397 + 0.275166i \(0.911267\pi\)
\(740\) −19.2606 5.46746i −0.708032 0.200988i
\(741\) 0.734459i 0.0269810i
\(742\) −13.4124 + 1.22415i −0.492383 + 0.0449398i
\(743\) −10.5859 10.5859i −0.388359 0.388359i 0.485743 0.874102i \(-0.338549\pi\)
−0.874102 + 0.485743i \(0.838549\pi\)
\(744\) 0.505430i 0.0185300i
\(745\) −2.85601 5.12021i −0.104636 0.187590i
\(746\) −8.38306 −0.306926
\(747\) 9.55604 + 9.55604i 0.349637 + 0.349637i
\(748\) −2.41391 + 2.41391i −0.0882614 + 0.0882614i
\(749\) 14.5024 17.4155i 0.529906 0.636350i
\(750\) −1.12973 0.0501686i −0.0412519 0.00183190i
\(751\) 5.62163 0.205136 0.102568 0.994726i \(-0.467294\pi\)
0.102568 + 0.994726i \(0.467294\pi\)
\(752\) 4.80004 + 4.80004i 0.175040 + 0.175040i
\(753\) 0.953393 + 0.953393i 0.0347436 + 0.0347436i
\(754\) −19.6856 −0.716906
\(755\) 2.80503 1.56462i 0.102085 0.0569425i
\(756\) −1.02571 + 1.23175i −0.0373047 + 0.0447983i
\(757\) −7.51547 + 7.51547i −0.273155 + 0.273155i −0.830369 0.557214i \(-0.811870\pi\)
0.557214 + 0.830369i \(0.311870\pi\)
\(758\) 20.6301 + 20.6301i 0.749321 + 0.749321i
\(759\) 0.254233 0.00922809
\(760\) 4.74237 + 1.34621i 0.172024 + 0.0488321i
\(761\) 41.6701i 1.51054i −0.655414 0.755270i \(-0.727506\pi\)
0.655414 0.755270i \(-0.272494\pi\)
\(762\) −0.599188 0.599188i −0.0217063 0.0217063i
\(763\) 2.10106 + 23.0202i 0.0760633 + 0.833388i
\(764\) 23.4159i 0.847159i
\(765\) −6.23229 + 21.9549i −0.225329 + 0.793780i
\(766\) 8.84254i 0.319494i
\(767\) −7.74577 + 7.74577i −0.279683 + 0.279683i
\(768\) −0.0715208 + 0.0715208i −0.00258078 + 0.00258078i
\(769\) −20.9854 −0.756755 −0.378377 0.925651i \(-0.623518\pi\)
−0.378377 + 0.925651i \(0.623518\pi\)
\(770\) 1.09158 5.81450i 0.0393379 0.209540i
\(771\) 1.74440 0.0628231
\(772\) 12.0396 12.0396i 0.433316 0.433316i
\(773\) 7.21149 7.21149i 0.259379 0.259379i −0.565422 0.824802i \(-0.691287\pi\)
0.824802 + 0.565422i \(0.191287\pi\)
\(774\) 4.91443i 0.176646i
\(775\) 21.2588 + 13.1272i 0.763640 + 0.471544i
\(776\) 4.66398i 0.167427i
\(777\) 0.217789 + 2.38620i 0.00781313 + 0.0856046i
\(778\) 6.10826 + 6.10826i 0.218992 + 0.218992i
\(779\) 18.6954i 0.669832i
\(780\) −0.650565 + 0.362880i −0.0232940 + 0.0129932i
\(781\) 8.78250 0.314263
\(782\) −6.06746 6.06746i −0.216972 0.216972i
\(783\) −2.56041 + 2.56041i −0.0915014 + 0.0915014i
\(784\) −6.88434 + 1.26722i −0.245869 + 0.0452580i
\(785\) 39.3028 + 11.1568i 1.40278 + 0.398204i
\(786\) −1.05251 −0.0375419
\(787\) 34.6798 + 34.6798i 1.23620 + 1.23620i 0.961541 + 0.274661i \(0.0885656\pi\)
0.274661 + 0.961541i \(0.411434\pi\)
\(788\) 12.7592 + 12.7592i 0.454528 + 0.454528i
\(789\) −0.161757 −0.00575869
\(790\) −6.18710 1.75632i −0.220127 0.0624872i
\(791\) −20.9007 17.4046i −0.743143 0.618835i
\(792\) 2.11409 2.11409i 0.0751208 0.0751208i
\(793\) −26.1038 26.1038i −0.926974 0.926974i
\(794\) −14.6283 −0.519138
\(795\) −1.00546 + 0.560840i −0.0356601 + 0.0198909i
\(796\) 1.49431i 0.0529643i
\(797\) 37.7255 + 37.7255i 1.33631 + 1.33631i 0.899607 + 0.436700i \(0.143853\pi\)
0.436700 + 0.899607i \(0.356147\pi\)
\(798\) −0.0536243 0.587535i −0.00189828 0.0207985i
\(799\) 23.1738i 0.819829i
\(800\) −1.15066 4.86580i −0.0406821 0.172032i
\(801\) 31.9866i 1.13019i
\(802\) −5.60409 + 5.60409i −0.197887 + 0.197887i
\(803\) 2.07792 2.07792i 0.0733282 0.0733282i
\(804\) 1.36366 0.0480926
\(805\) 14.6150 + 2.74373i 0.515110 + 0.0967039i
\(806\) 16.4587 0.579733
\(807\) 1.15285 1.15285i 0.0405823 0.0405823i
\(808\) −7.76242 + 7.76242i −0.273081 + 0.273081i
\(809\) 3.18549i 0.111996i 0.998431 + 0.0559979i \(0.0178340\pi\)
−0.998431 + 0.0559979i \(0.982166\pi\)
\(810\) 5.43945 19.1619i 0.191123 0.673280i
\(811\) 21.8060i 0.765711i −0.923808 0.382856i \(-0.874941\pi\)
0.923808 0.382856i \(-0.125059\pi\)
\(812\) −15.7476 + 1.43728i −0.552632 + 0.0504387i
\(813\) 0.377199 + 0.377199i 0.0132290 + 0.0132290i
\(814\) 8.95391i 0.313834i
\(815\) −52.4550 14.8903i −1.83742 0.521585i
\(816\) 0.345290 0.0120876
\(817\) −2.56247 2.56247i −0.0896496 0.0896496i
\(818\) −21.0144 + 21.0144i −0.734752 + 0.734752i
\(819\) −20.0209 16.6720i −0.699588 0.582566i
\(820\) 16.5599 9.23697i 0.578296 0.322569i
\(821\) 52.2377 1.82311 0.911554 0.411180i \(-0.134883\pi\)
0.911554 + 0.411180i \(0.134883\pi\)
\(822\) 0.605419 + 0.605419i 0.0211164 + 0.0211164i
\(823\) 23.7810 + 23.7810i 0.828954 + 0.828954i 0.987372 0.158418i \(-0.0506394\pi\)
−0.158418 + 0.987372i \(0.550639\pi\)
\(824\) 15.8084 0.550710
\(825\) −0.116384 0.492154i −0.00405199 0.0171346i
\(826\) −5.63074 + 6.76180i −0.195918 + 0.235273i
\(827\) 7.97578 7.97578i 0.277345 0.277345i −0.554703 0.832048i \(-0.687168\pi\)
0.832048 + 0.554703i \(0.187168\pi\)
\(828\) 5.31384 + 5.31384i 0.184669 + 0.184669i
\(829\) −44.2643 −1.53736 −0.768681 0.639633i \(-0.779086\pi\)
−0.768681 + 0.639633i \(0.779086\pi\)
\(830\) 4.92367 + 8.82708i 0.170903 + 0.306392i
\(831\) 0.934516i 0.0324180i
\(832\) −2.32898 2.32898i −0.0807430 0.0807430i
\(833\) 19.6772 + 13.5592i 0.681773 + 0.469800i
\(834\) 0.528777i 0.0183100i
\(835\) −45.2477 12.8444i −1.56586 0.444498i
\(836\) 2.20465i 0.0762493i
\(837\) 2.14070 2.14070i 0.0739934 0.0739934i
\(838\) 4.90397 4.90397i 0.169405 0.169405i
\(839\) 14.2746 0.492814 0.246407 0.969166i \(-0.420750\pi\)
0.246407 + 0.969166i \(0.420750\pi\)
\(840\) −0.493929 + 0.337787i −0.0170422 + 0.0116548i
\(841\) −6.72177 −0.231785
\(842\) −17.2683 + 17.2683i −0.595106 + 0.595106i
\(843\) −0.192044 + 0.192044i −0.00661434 + 0.00661434i
\(844\) 24.1976i 0.832916i
\(845\) 2.34373 + 4.20180i 0.0806267 + 0.144546i
\(846\) 20.2954i 0.697770i
\(847\) 2.63480 0.240478i 0.0905328 0.00826293i
\(848\) −3.59950 3.59950i −0.123608 0.123608i
\(849\) 2.76405i 0.0948621i
\(850\) −8.96801 + 14.5232i −0.307600 + 0.498142i
\(851\) 22.5060 0.771495
\(852\) −0.628131 0.628131i −0.0215194 0.0215194i
\(853\) 10.2914 10.2914i 0.352370 0.352370i −0.508621 0.860991i \(-0.669845\pi\)
0.860991 + 0.508621i \(0.169845\pi\)
\(854\) −22.7878 18.9760i −0.779782 0.649346i
\(855\) 7.17977 + 12.8718i 0.245543 + 0.440205i
\(856\) 8.56588 0.292776
\(857\) 4.63187 + 4.63187i 0.158222 + 0.158222i 0.781778 0.623557i \(-0.214313\pi\)
−0.623557 + 0.781778i \(0.714313\pi\)
\(858\) −0.235567 0.235567i −0.00804211 0.00804211i
\(859\) 17.4622 0.595802 0.297901 0.954597i \(-0.403713\pi\)
0.297901 + 0.954597i \(0.403713\pi\)
\(860\) −1.00371 + 3.53583i −0.0342263 + 0.120571i
\(861\) −1.74384 1.45215i −0.0594300 0.0494890i
\(862\) 7.60843 7.60843i 0.259144 0.259144i
\(863\) −12.3634 12.3634i −0.420854 0.420854i 0.464644 0.885498i \(-0.346182\pi\)
−0.885498 + 0.464644i \(0.846182\pi\)
\(864\) −0.605839 −0.0206111
\(865\) −9.31910 + 32.8289i −0.316859 + 1.11622i
\(866\) 16.3502i 0.555604i
\(867\) 0.382353 + 0.382353i 0.0129854 + 0.0129854i
\(868\) 13.1662 1.20168i 0.446891 0.0407877i
\(869\) 2.87628i 0.0975711i
\(870\) −1.18053 + 0.658488i −0.0400236 + 0.0223248i
\(871\) 44.4059i 1.50464i
\(872\) −6.17799 + 6.17799i −0.209213 + 0.209213i
\(873\) 9.86005 9.86005i 0.333712 0.333712i
\(874\) −5.54146 −0.187443
\(875\) −1.37911 29.5482i −0.0466225 0.998913i
\(876\) −0.297229 −0.0100424
\(877\) −21.8767 + 21.8767i −0.738722 + 0.738722i −0.972331 0.233609i \(-0.924947\pi\)
0.233609 + 0.972331i \(0.424947\pi\)
\(878\) 8.82709 8.82709i 0.297900 0.297900i
\(879\) 2.29007i 0.0772422i
\(880\) 1.95282 1.08927i 0.0658295 0.0367192i
\(881\) 42.6802i 1.43793i 0.695045 + 0.718966i \(0.255384\pi\)
−0.695045 + 0.718966i \(0.744616\pi\)
\(882\) −17.2331 11.8751i −0.580269 0.399854i
\(883\) 16.6870 + 16.6870i 0.561563 + 0.561563i 0.929751 0.368188i \(-0.120022\pi\)
−0.368188 + 0.929751i \(0.620022\pi\)
\(884\) 11.2439i 0.378174i
\(885\) −0.205408 + 0.723604i −0.00690473 + 0.0243237i
\(886\) −10.2637 −0.344815
\(887\) −16.6285 16.6285i −0.558331 0.558331i 0.370501 0.928832i \(-0.379186\pi\)
−0.928832 + 0.370501i \(0.879186\pi\)
\(888\) −0.640391 + 0.640391i −0.0214901 + 0.0214901i
\(889\) 14.1840 17.0332i 0.475716 0.571275i
\(890\) 6.53287 23.0137i 0.218982 0.771422i
\(891\) 8.90803 0.298430
\(892\) −14.3774 14.3774i −0.481392 0.481392i
\(893\) −10.5824 10.5824i −0.354126 0.354126i
\(894\) −0.265200 −0.00886960
\(895\) −8.58447 15.3901i −0.286947 0.514434i
\(896\) −2.03313 1.69304i −0.0679221 0.0565605i
\(897\) 0.592106 0.592106i 0.0197698 0.0197698i
\(898\) −4.92917 4.92917i −0.164489 0.164489i
\(899\) 29.8662 0.996094
\(900\) 7.85411 12.7193i 0.261804 0.423977i
\(901\) 17.3778i 0.578938i
\(902\) 5.99626 + 5.99626i 0.199654 + 0.199654i
\(903\) 0.438057 0.0399814i 0.0145776 0.00133050i
\(904\) 10.2801i 0.341910i
\(905\) −28.1444 50.4568i −0.935551 1.67724i
\(906\) 0.145286i 0.00482679i
\(907\) −12.2498 + 12.2498i −0.406748 + 0.406748i −0.880603 0.473855i \(-0.842862\pi\)
0.473855 + 0.880603i \(0.342862\pi\)
\(908\) 6.98271 6.98271i 0.231729 0.231729i
\(909\) −32.8208 −1.08860
\(910\) −10.9996 16.0842i −0.364634 0.533185i
\(911\) −5.64056 −0.186880 −0.0934401 0.995625i \(-0.529786\pi\)
−0.0934401 + 0.995625i \(0.529786\pi\)
\(912\) 0.157678 0.157678i 0.00522124 0.00522124i
\(913\) −3.19625 + 3.19625i −0.105780 + 0.105780i
\(914\) 17.5745i 0.581314i
\(915\) −2.43860 0.692242i −0.0806177 0.0228848i
\(916\) 0.136302i 0.00450354i
\(917\) −2.50239 27.4175i −0.0826364 0.905406i
\(918\) 1.46244 + 1.46244i 0.0482678 + 0.0482678i
\(919\) 36.5538i 1.20580i 0.797817 + 0.602900i \(0.205988\pi\)
−0.797817 + 0.602900i \(0.794012\pi\)
\(920\) 2.73791 + 4.90848i 0.0902663 + 0.161828i
\(921\) 2.00027 0.0659111
\(922\) 8.07620 + 8.07620i 0.265976 + 0.265976i
\(923\) 20.4543 20.4543i 0.673262 0.673262i
\(924\) −0.205642 0.171244i −0.00676513 0.00563350i
\(925\) −10.3029 43.5679i −0.338758 1.43250i
\(926\) −20.7575 −0.682134
\(927\) 33.4202 + 33.4202i 1.09766 + 1.09766i
\(928\) −4.22621 4.22621i −0.138732 0.138732i
\(929\) 27.8619 0.914121 0.457060 0.889436i \(-0.348902\pi\)
0.457060 + 0.889436i \(0.348902\pi\)
\(930\) 0.987012 0.550548i 0.0323654 0.0180532i
\(931\) 15.1775 2.79378i 0.497423 0.0915624i
\(932\) −16.2560 + 16.2560i −0.532481 + 0.532481i
\(933\) −1.81329 1.81329i −0.0593644 0.0593644i
\(934\) −14.7921 −0.484011
\(935\) −7.34333 2.08454i −0.240153 0.0681717i
\(936\) 9.84735i 0.321871i
\(937\) 18.9935 + 18.9935i 0.620491 + 0.620491i 0.945657 0.325166i \(-0.105420\pi\)
−0.325166 + 0.945657i \(0.605420\pi\)
\(938\) 3.24216 + 35.5228i 0.105860 + 1.15986i
\(939\) 2.82785i 0.0922835i
\(940\) −4.14508 + 14.6021i −0.135198 + 0.476269i
\(941\) 4.42718i 0.144322i 0.997393 + 0.0721609i \(0.0229895\pi\)
−0.997393 + 0.0721609i \(0.977010\pi\)
\(942\) 1.30677 1.30677i 0.0425769 0.0425769i
\(943\) −15.0718 + 15.0718i −0.490806 + 0.490806i
\(944\) −3.32581 −0.108246
\(945\) −3.52265 0.661323i −0.114592 0.0215128i
\(946\) −1.64375 −0.0534429
\(947\) 22.9444 22.9444i 0.745591 0.745591i −0.228057 0.973648i \(-0.573237\pi\)
0.973648 + 0.228057i \(0.0732371\pi\)
\(948\) −0.205714 + 0.205714i −0.00668127 + 0.00668127i
\(949\) 9.67889i 0.314190i
\(950\) 2.53680 + 10.7274i 0.0823047 + 0.348041i
\(951\) 1.28373i 0.0416277i
\(952\) 0.820941 + 8.99465i 0.0266069 + 0.291518i
\(953\) 9.18554 + 9.18554i 0.297549 + 0.297549i 0.840053 0.542504i \(-0.182524\pi\)
−0.542504 + 0.840053i \(0.682524\pi\)
\(954\) 15.2193i 0.492744i
\(955\) −45.7271 + 25.5062i −1.47969 + 0.825361i
\(956\) 5.90173 0.190876
\(957\) −0.427463 0.427463i −0.0138179 0.0138179i
\(958\) −5.26944 + 5.26944i −0.170248 + 0.170248i
\(959\) −14.3315 + 17.2103i −0.462788 + 0.555750i
\(960\) −0.217572 0.0617619i −0.00702211 0.00199336i
\(961\) 6.02949 0.194500
\(962\) −20.8535 20.8535i −0.672345 0.672345i
\(963\) 18.1090 + 18.1090i 0.583555 + 0.583555i
\(964\) −6.08298 −0.195920
\(965\) 36.6256 + 10.3969i 1.17902 + 0.334687i
\(966\) 0.430428 0.516889i 0.0138488 0.0166306i
\(967\) −3.13051 + 3.13051i −0.100670 + 0.100670i −0.755648 0.654978i \(-0.772678\pi\)
0.654978 + 0.755648i \(0.272678\pi\)
\(968\) 0.707107 + 0.707107i 0.0227273 + 0.0227273i
\(969\) −0.761242 −0.0244546
\(970\) 9.10790 5.08031i 0.292437 0.163119i
\(971\) 51.0803i 1.63924i −0.572905 0.819622i \(-0.694183\pi\)
0.572905 0.819622i \(-0.305817\pi\)
\(972\) −1.92229 1.92229i −0.0616574 0.0616574i
\(973\) 13.7744 1.25719i 0.441587 0.0403037i
\(974\) 13.1916i 0.422686i
\(975\) −1.41728 0.875162i −0.0453892 0.0280276i
\(976\) 11.2082i 0.358767i
\(977\) 9.99224 9.99224i 0.319680 0.319680i −0.528964 0.848644i \(-0.677419\pi\)
0.848644 + 0.528964i \(0.177419\pi\)
\(978\) −1.74406 + 1.74406i −0.0557690 + 0.0557690i
\(979\) 10.6987 0.341932
\(980\) −9.97354 12.0635i −0.318593 0.385355i
\(981\) −26.1216 −0.833998
\(982\) 16.2113 16.2113i 0.517324 0.517324i
\(983\) −27.4320 + 27.4320i −0.874943 + 0.874943i −0.993006 0.118063i \(-0.962332\pi\)
0.118063 + 0.993006i \(0.462332\pi\)
\(984\) 0.857714i 0.0273429i
\(985\) −11.0182 + 38.8146i −0.351070 + 1.23674i
\(986\) 20.4034i 0.649777i
\(987\) 1.80907 0.165114i 0.0575833 0.00525562i
\(988\) 5.13459 + 5.13459i 0.163353 + 0.163353i
\(989\) 4.13163i 0.131378i
\(990\) 6.43123 + 1.82562i 0.204398 + 0.0580221i
\(991\) −7.82123 −0.248449 −0.124225 0.992254i \(-0.539644\pi\)
−0.124225 + 0.992254i \(0.539644\pi\)
\(992\) 3.53345 + 3.53345i 0.112187 + 0.112187i
\(993\) −1.14585 + 1.14585i −0.0363625 + 0.0363625i
\(994\) 14.8691 17.8560i 0.471621 0.566357i
\(995\) −2.91811 + 1.62770i −0.0925102 + 0.0516015i
\(996\) 0.457196 0.0144868
\(997\) −35.2372 35.2372i −1.11597 1.11597i −0.992326 0.123649i \(-0.960540\pi\)
−0.123649 0.992326i \(-0.539460\pi\)
\(998\) −18.0376 18.0376i −0.570970 0.570970i
\(999\) −5.42463 −0.171628
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 770.2.l.c.573.5 40
5.2 odd 4 inner 770.2.l.c.727.6 yes 40
7.6 odd 2 inner 770.2.l.c.573.6 yes 40
35.27 even 4 inner 770.2.l.c.727.5 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.l.c.573.5 40 1.1 even 1 trivial
770.2.l.c.573.6 yes 40 7.6 odd 2 inner
770.2.l.c.727.5 yes 40 35.27 even 4 inner
770.2.l.c.727.6 yes 40 5.2 odd 4 inner