Properties

Label 770.2.l.c.573.6
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 573.6
Character \(\chi\) \(=\) 770.573
Dual form 770.2.l.c.727.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.0715208 - 0.0715208i) q^{3} -1.00000i q^{4} +(-1.95282 + 1.08927i) q^{5} +0.101146i q^{6} +(0.240478 - 2.63480i) q^{7} +(0.707107 + 0.707107i) q^{8} +2.98977i q^{9} +O(q^{10})\) \(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} +(0.240478 - 2.63480i) 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} +(-2.63480 - 0.240478i) 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} +(2.40039 + 5.40723i) 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} +(0.266498 + 0.0243233i) 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} +(7.87744 + 0.718974i) 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} +(-5.52082 - 2.12616i) 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} +(-0.240478 + 2.63480i) 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} +(5.76403 - 3.97190i) 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 −0.686159 0.727452i \(-0.740705\pi\)
0.727452 + 0.686159i \(0.240705\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −1.95282 + 1.08927i −0.873327 + 0.487135i
\(6\) 0.101146i 0.0412925i
\(7\) 0.240478 2.63480i 0.0908922 0.995861i
\(8\) 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 −0.306066 0.952010i \(-0.599013\pi\)
0.952010 + 0.306066i \(0.0990128\pi\)
\(14\) 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 0.350939 0.936398i \(-0.385863\pi\)
−0.936398 + 0.350939i \(0.885863\pi\)
\(18\) −2.11409 2.11409i −0.498295 0.498295i
\(19\) −2.20465 −0.505780 −0.252890 0.967495i \(-0.581381\pi\)
−0.252890 + 0.967495i \(0.581381\pi\)
\(20\) 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
\(28\) −2.63480 0.240478i −0.497930 0.0454461i
\(29\) 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 \(-0.851870\pi\)
0.893658 0.448748i \(-0.148130\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.0715208 + 0.0715208i −0.0124502 + 0.0124502i
\(34\) 3.41379 0.585460
\(35\) 2.40039 + 5.40723i 0.405740 + 0.913989i
\(36\) 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 \(-0.769633\pi\)
0.749348 0.662176i \(-0.230367\pi\)
\(42\) 0.266498 + 0.0243233i 0.0411216 + 0.00375317i
\(43\) −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 0.964444 0.264286i \(-0.0851364\pi\)
−0.264286 + 0.964444i \(0.585136\pi\)
\(48\) −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 \(-0.569462\pi\)
−0.216492 + 0.976284i \(0.569462\pi\)
\(60\) 0.217572 + 0.0617619i 0.0280885 + 0.00797342i
\(61\) 11.2082i 1.43507i −0.696524 0.717534i \(-0.745271\pi\)
0.696524 0.717534i \(-0.254729\pi\)
\(62\) 3.53345 + 3.53345i 0.448748 + 0.448748i
\(63\) 7.87744 + 0.718974i 0.992465 + 0.0905822i
\(64\) 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
\(70\) −5.52082 2.12616i −0.659864 0.254124i
\(71\) −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 −0.574971 0.818174i \(-0.694987\pi\)
0.818174 + 0.574971i \(0.194987\pi\)
\(74\) 8.95391i 1.04087i
\(75\) −0.116384 0.492154i −0.0134389 0.0568291i
\(76\) 2.20465i 0.252890i
\(77\) −0.240478 + 2.63480i −0.0274050 + 0.300263i
\(78\) 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 −0.860420 0.509586i \(-0.829799\pi\)
0.509586 + 0.860420i \(0.329799\pi\)
\(84\) −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 \(-0.308093\pi\)
0.567029 + 0.823698i \(0.308093\pi\)
\(90\) 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 0.854426 0.519572i \(-0.173909\pi\)
−0.519572 + 0.854426i \(0.673909\pi\)
\(98\) 5.76403 3.97190i 0.582255 0.401223i
\(99\) 2.98977i 0.300483i
\(100\) −4.25428 2.62700i −0.425428 0.262700i
\(101\) 10.9777i 1.09232i −0.837680 0.546162i \(-0.816088\pi\)
0.837680 0.546162i \(-0.183912\pi\)
\(102\) 0.244157 0.244157i 0.0241751 0.0241751i
\(103\) −11.1782 + 11.1782i −1.10142 + 1.10142i −0.107181 + 0.994240i \(0.534183\pi\)
−0.994240 + 0.107181i \(0.965817\pi\)
\(104\) 3.29368 0.322972
\(105\) 0.558407 + 0.215052i 0.0544949 + 0.0209869i
\(106\) −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
\(112\) −0.240478 + 2.63480i −0.0227230 + 0.248965i
\(113\) −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 \(0.150212\pi\)
−0.890704 + 0.454585i \(0.849788\pi\)
\(132\) 0.0715208 + 0.0715208i 0.00622508 + 0.00622508i
\(133\) −0.530169 + 5.80880i −0.0459715 + 0.503687i
\(134\) 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 \(-0.571164\pi\)
−0.221711 + 0.975112i \(0.571164\pi\)
\(140\) 5.40723 2.40039i 0.456994 0.202870i
\(141\) 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
\(147\) −0.583006 + 0.401741i −0.0480855 + 0.0331350i
\(148\) −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 \(-0.989939\pi\)
−0.0316032 0.999500i \(-0.510061\pi\)
\(158\) −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 \(0.0526399\pi\)
0.164620 + 0.986357i \(0.447360\pi\)
\(168\) 0.0243233 0.266498i 0.00187658 0.0205608i
\(169\) 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 −0.165706 0.986175i \(-0.552990\pi\)
0.986175 + 0.165706i \(0.0529901\pi\)
\(174\) 0.604524 0.0458289
\(175\) −10.5774 7.94467i −0.799579 0.600561i
\(176\) 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 \(0.409960\pi\)
−0.279112 + 0.960259i \(0.590040\pi\)
\(182\) 8.67819 + 0.792058i 0.643270 + 0.0587113i
\(183\) −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 \(-0.483133\pi\)
0.0529643 + 0.998596i \(0.483133\pi\)
\(200\) 4.86580 1.15066i 0.344064 0.0813641i
\(201\) 1.36366i 0.0961852i
\(202\) 7.76242 + 7.76242i 0.546162 + 0.546162i
\(203\) −15.7476 1.43728i −1.10526 0.100877i
\(204\) 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
\(210\) −0.546918 + 0.242789i −0.0377409 + 0.0167540i
\(211\) −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
\(217\) −13.1662 1.20168i −0.893782 0.0815754i
\(218\) −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 −0.999332 0.0365471i \(-0.988364\pi\)
0.0365471 + 0.999332i \(0.488364\pi\)
\(224\) −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 0.436329 0.899787i \(-0.356279\pi\)
−0.899787 + 0.436329i \(0.856279\pi\)
\(228\) 0.157678 + 0.157678i 0.0104425 + 0.0104425i
\(229\) 0.136302 0.00900707 0.00450354 0.999990i \(-0.498566\pi\)
0.00450354 + 0.999990i \(0.498566\pi\)
\(230\) 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
\(238\) 0.820941 8.99465i 0.0532137 0.583037i
\(239\) 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 \(0.0627692\pi\)
−0.980620 + 0.195920i \(0.937231\pi\)
\(242\) −0.707107 + 0.707107i −0.0454545 + 0.0454545i
\(243\) −1.92229 + 1.92229i −0.123315 + 0.123315i
\(244\) −11.2082 −0.717534
\(245\) 14.8242 5.02423i 0.947084 0.320986i
\(246\) 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 \(0.138216\pi\)
−0.907200 + 0.420700i \(0.861784\pi\)
\(252\) 0.718974 7.87744i 0.0452911 0.496232i
\(253\) −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 0.976450 0.215743i \(-0.0692172\pi\)
−0.215743 + 0.976450i \(0.569217\pi\)
\(258\) 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 \(-0.336485\pi\)
0.491400 + 0.870934i \(0.336485\pi\)
\(270\) 1.18309 0.659920i 0.0720008 0.0401615i
\(271\) 5.27398i 0.320372i 0.987087 + 0.160186i \(0.0512094\pi\)
−0.987087 + 0.160186i \(0.948791\pi\)
\(272\) 2.41391 + 2.41391i 0.146365 + 0.146365i
\(273\) −0.877761 0.0801133i −0.0531245 0.00484867i
\(274\) 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
\(280\) −2.12616 + 5.52082i −0.127062 + 0.329932i
\(281\) 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 \(-0.448256\pi\)
0.986817 0.161842i \(-0.0517436\pi\)
\(284\) 8.78250i 0.521146i
\(285\) 0.136163 0.479670i 0.00806560 0.0284132i
\(286\) 3.29368i 0.194760i
\(287\) −22.3431 2.03925i −1.31887 0.120373i
\(288\) 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 −0.0627265 0.998031i \(-0.519980\pi\)
0.998031 + 0.0627265i \(0.0199796\pi\)
\(294\) 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 0.982796 0.184697i \(-0.0591302\pi\)
−0.184697 + 0.982796i \(0.559130\pi\)
\(308\) 2.63480 + 0.240478i 0.150132 + 0.0137025i
\(309\) 1.59895i 0.0909609i
\(310\) −10.7490 3.05131i −0.610505 0.173303i
\(311\) 25.3533i 1.43765i −0.695188 0.718827i \(-0.744679\pi\)
0.695188 0.718827i \(-0.255321\pi\)
\(312\) 0.235567 0.235567i 0.0133363 0.0133363i
\(313\) 19.7694 19.7694i 1.11744 1.11744i 0.125319 0.992117i \(-0.460005\pi\)
0.992117 0.125319i \(-0.0399954\pi\)
\(314\) 18.2712 1.03110
\(315\) −16.1664 + 7.17661i −0.910872 + 0.404356i
\(316\) 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
\(322\) −0.604451 + 6.62267i −0.0336847 + 0.369067i
\(323\) 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
\(343\) −4.99441 + 17.8341i −0.269673 + 0.962952i
\(344\) 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 \(-0.376542\pi\)
0.378204 + 0.925722i \(0.376542\pi\)
\(350\) 13.0971 1.86165i 0.700070 0.0995092i
\(351\) 1.99544 0.106509
\(352\) −0.707107 + 0.707107i −0.0376889 + 0.0376889i
\(353\) 11.7222 11.7222i 0.623912 0.623912i −0.322617 0.946529i \(-0.604563\pi\)
0.946529 + 0.322617i \(0.104563\pi\)
\(354\) 0.336391i 0.0178790i
\(355\) 17.1506 9.56649i 0.910261 0.507737i
\(356\) 10.6987i 0.567029i
\(357\) −0.0830346 + 0.909770i −0.00439466 + 0.0481501i
\(358\) 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 0.974387 0.224877i \(-0.0721980\pi\)
−0.224877 + 0.974387i \(0.572198\pi\)
\(368\) −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
\(378\) −0.145691 + 1.59626i −0.00749354 + 0.0821030i
\(379\) 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 −0.529079 0.848573i \(-0.677462\pi\)
0.848573 + 0.529079i \(0.177462\pi\)
\(384\) −0.101146 −0.00516157
\(385\) −2.40039 5.40723i −0.122335 0.275578i
\(386\) −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
\(392\) −3.97190 5.76403i −0.200611 0.291127i
\(393\) 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 0.398172 0.917311i \(-0.369645\pi\)
−0.917311 + 0.398172i \(0.869645\pi\)
\(398\) −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 \(-0.762701\pi\)
−0.734752 + 0.678336i \(0.762701\pi\)
\(410\) −18.2411 5.17808i −0.900865 0.255727i
\(411\) 0.856191i 0.0422328i
\(412\) 11.1782 + 11.1782i 0.550710 + 0.550710i
\(413\) −0.799785 + 8.76285i −0.0393548 + 0.431192i
\(414\) 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 \(-0.445816\pi\)
0.169405 + 0.985547i \(0.445816\pi\)
\(420\) 0.215052 0.558407i 0.0104934 0.0272475i
\(421\) 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
\(427\) −29.5315 2.69534i −1.42913 0.130436i
\(428\) −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 −0.928053 0.372449i \(-0.878518\pi\)
0.372449 + 0.928053i \(0.378518\pi\)
\(434\) 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 \(-0.403714\pi\)
0.297900 + 0.954597i \(0.403714\pi\)
\(440\) 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
\(448\) 2.63480 + 0.240478i 0.124483 + 0.0113615i
\(449\) 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
\(455\) 18.1838 + 7.00289i 0.852471 + 0.328300i
\(456\) −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 \(0.0856941\pi\)
−0.963980 + 0.265976i \(0.914306\pi\)
\(462\) −0.266498 0.0243233i −0.0123986 0.00113162i
\(463\) 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 0.422399 0.906410i \(-0.361188\pi\)
−0.906410 + 0.422399i \(0.861188\pi\)
\(468\) 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 \(-0.554457\pi\)
−0.170248 + 0.985401i \(0.554457\pi\)
\(480\) 0.110175 + 0.197519i 0.00502876 + 0.00901547i
\(481\) 29.4913i 1.34469i
\(482\) −4.30132 4.30132i −0.195920 0.195920i
\(483\) 0.0611376 0.669854i 0.00278186 0.0304794i
\(484\) 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
\(490\) −6.92963 + 14.0350i −0.313049 + 0.634035i
\(491\) −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
\(497\) −2.11200 + 23.1401i −0.0947362 + 1.03798i
\(498\) −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 −0.975754 0.218870i \(-0.929763\pi\)
0.218870 + 0.975754i \(0.429763\pi\)
\(504\) 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 \(-0.412394\pi\)
0.271762 + 0.962364i \(0.412394\pi\)
\(510\) −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
\(518\) 23.5918 + 2.15322i 1.03656 + 0.0946070i
\(519\) 1.54365i 0.0677585i
\(520\) −6.43196 + 3.58770i −0.282060 + 0.157331i
\(521\) 14.7148i 0.644669i 0.946626 + 0.322335i \(0.104468\pi\)
−0.946626 + 0.322335i \(0.895532\pi\)
\(522\) −12.6354 + 12.6354i −0.553037 + 0.553037i
\(523\) 13.1748 13.1748i 0.576092 0.576092i −0.357732 0.933824i \(-0.616450\pi\)
0.933824 + 0.357732i \(0.116450\pi\)
\(524\) 10.4059 0.454585
\(525\) −1.32472 + 0.188297i −0.0578153 + 0.00821797i
\(526\) −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
\(532\) 5.80880 + 0.530169i 0.251843 + 0.0229857i
\(533\) −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
\(553\) 7.57842 + 0.691682i 0.322267 + 0.0294133i
\(554\) 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
\(560\) −2.40039 5.40723i −0.101435 0.228497i
\(561\) 0.345290 0.0145781
\(562\) −1.89869 + 1.89869i −0.0800913 + 0.0800913i
\(563\) −10.4762 + 10.4762i −0.441521 + 0.441521i −0.892523 0.451002i \(-0.851067\pi\)
0.451002 + 0.892523i \(0.351067\pi\)
\(564\) 0.686605i 0.0289113i
\(565\) 22.1132 + 6.27725i 0.930311 + 0.264086i
\(566\) 27.3275i 1.14866i
\(567\) −2.14219 + 23.4709i −0.0899634 + 0.985684i
\(568\) −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 0.946215 0.323537i \(-0.104872\pi\)
−0.323537 + 0.946215i \(0.604872\pi\)
\(578\) 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 0.372633 0.927979i \(-0.378455\pi\)
−0.927979 + 0.372633i \(0.878455\pi\)
\(588\) 0.401741 + 0.583006i 0.0165675 + 0.0240428i
\(589\) 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 −0.917970 0.396649i \(-0.870173\pi\)
0.396649 + 0.917970i \(0.370173\pi\)
\(594\) 0.605839 0.0248579
\(595\) 7.25825 18.8469i 0.297559 0.772648i
\(596\) −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 \(-0.840615\pi\)
0.877236 0.480059i \(-0.159385\pi\)
\(602\) 0.395286 4.33095i 0.0161106 0.176516i
\(603\) 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 0.984504 0.175361i \(-0.0561094\pi\)
−0.175361 + 0.984504i \(0.556109\pi\)
\(608\) −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 \(-0.576637\pi\)
−0.238442 + 0.971157i \(0.576637\pi\)
\(620\) 9.75833 5.44312i 0.391904 0.218601i
\(621\) 1.52280i 0.0611078i
\(622\) 17.9275 + 17.9275i 0.718827 + 0.718827i
\(623\) 2.57280 28.1889i 0.103077 1.12936i
\(624\) 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
\(630\) 6.35672 16.5060i 0.253258 0.657614i
\(631\) −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
\(637\) −18.9849 + 13.0822i −0.752208 + 0.518335i
\(638\) −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 −0.907568 0.419904i \(-0.862064\pi\)
0.419904 + 0.907568i \(0.362064\pi\)
\(644\) −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 \(0.0117026\pi\)
0.0367565 + 0.999324i \(0.488297\pi\)
\(648\) −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
\(658\) −1.63243 + 17.8858i −0.0636389 + 0.697260i
\(659\) 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 \(0.319005\pi\)
−0.538464 + 0.842648i \(0.680995\pi\)
\(662\) −11.3287 + 11.3287i −0.440303 + 0.440303i
\(663\) −0.804175 + 0.804175i −0.0312316 + 0.0312316i
\(664\) −4.52017 −0.175417
\(665\) −5.29201 11.9210i −0.205215 0.462278i
\(666\) −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
\(672\) −0.266498 0.0243233i −0.0102804 0.000938292i
\(673\) 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 \(-0.949333\pi\)
−0.158505 0.987358i \(-0.550667\pi\)
\(678\) 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 \(-0.629348\pi\)
0.395268 0.918566i \(-0.370652\pi\)
\(692\) −10.7916 10.7916i −0.410235 0.410235i
\(693\) −7.87744 0.718974i −0.299239 0.0273116i
\(694\) 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
\(700\) −7.94467 + 10.5774i −0.300280 + 0.399790i
\(701\) −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
\(707\) −28.9241 2.63990i −1.08780 0.0992837i
\(708\) 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 \(-0.552063\pi\)
−0.162831 + 0.986654i \(0.552063\pi\)
\(720\) 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 0.546892 0.837203i \(-0.315811\pi\)
−0.837203 + 0.546892i \(0.815811\pi\)
\(728\) 0.792058 8.67819i 0.0293556 0.321635i
\(729\) 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 −0.321101 0.947045i \(-0.604053\pi\)
0.947045 + 0.321101i \(0.104053\pi\)
\(734\) −20.3061 −0.749510
\(735\) 0.700902 1.41958i 0.0258532 0.0523618i
\(736\) 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
\(742\) −1.22415 + 13.4124i −0.0449398 + 0.492383i
\(743\) −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 \(0.272494\pi\)
−0.655414 + 0.755270i \(0.727506\pi\)
\(762\) 0.599188 + 0.599188i 0.0217063 + 0.0217063i
\(763\) 23.0202 + 2.10106i 0.833388 + 0.0760633i
\(764\) 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 \(-0.376482\pi\)
0.378377 + 0.925651i \(0.376482\pi\)
\(770\) 5.52082 + 2.12616i 0.198957 + 0.0766214i
\(771\) 1.74440 0.0628231
\(772\) 12.0396 12.0396i 0.433316 0.433316i
\(773\) −7.21149 + 7.21149i −0.259379 + 0.259379i −0.824802 0.565422i \(-0.808713\pi\)
0.565422 + 0.824802i \(0.308713\pi\)
\(774\) 4.91443i 0.176646i
\(775\) −21.2588 13.1272i −0.763640 0.471544i
\(776\) 4.66398i 0.167427i
\(777\) −2.38620 0.217789i −0.0856046 0.00781313i
\(778\) 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 \(-0.911434\pi\)
−0.274661 0.961541i \(-0.588566\pi\)
\(788\) 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 \(-0.856147\pi\)
−0.436700 0.899607i \(-0.643853\pi\)
\(798\) −0.587535 0.0536243i −0.0207985 0.00189828i
\(799\) 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
\(805\) −5.34418 + 13.8768i −0.188357 + 0.489093i
\(806\) 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 \(0.125059\pi\)
−0.923808 + 0.382856i \(0.874941\pi\)
\(812\) −1.43728 + 15.7476i −0.0504387 + 0.552632i
\(813\) 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 \(-0.220914\pi\)
0.768681 + 0.639633i \(0.220914\pi\)
\(830\) 4.92367 + 8.82708i 0.170903 + 0.306392i
\(831\) 0.934516i 0.0324180i
\(832\) 2.32898 + 2.32898i 0.0807430 + 0.0807430i
\(833\) 13.5592 + 19.6772i 0.469800 + 0.681773i
\(834\) 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 \(-0.579250\pi\)
−0.246407 + 0.969166i \(0.579250\pi\)
\(840\) 0.242789 + 0.546918i 0.00837701 + 0.0188705i
\(841\) −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
\(847\) 0.240478 2.63480i 0.00826293 0.0905328i
\(848\) −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 −0.860991 0.508621i \(-0.830155\pi\)
0.508621 + 0.860991i \(0.330155\pi\)
\(854\) 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 0.623557 0.781778i \(-0.285687\pi\)
−0.781778 + 0.623557i \(0.785687\pi\)
\(858\) −0.235567 0.235567i −0.00804211 0.00804211i
\(859\) −17.4622 −0.595802 −0.297901 0.954597i \(-0.596287\pi\)
−0.297901 + 0.954597i \(0.596287\pi\)
\(860\) 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
\(868\) −1.20168 + 13.1662i −0.0407877 + 0.446891i
\(869\) 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
\(875\) 29.3097 + 3.99285i 0.990848 + 0.134983i
\(876\) −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 \(-0.744616\pi\)
0.695045 0.718966i \(-0.255384\pi\)
\(882\) 11.8751 + 17.2331i 0.399854 + 0.580269i
\(883\) 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 0.928832 0.370501i \(-0.120814\pi\)
−0.370501 + 0.928832i \(0.620814\pi\)
\(888\) 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
\(903\) −0.0399814 + 0.438057i −0.00133050 + 0.0145776i
\(904\) 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
\(910\) −17.8097 + 7.90612i −0.590386 + 0.262085i
\(911\) −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
\(917\) 27.4175 + 2.50239i 0.905406 + 0.0826364i
\(918\) 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 \(-0.651098\pi\)
−0.457060 + 0.889436i \(0.651098\pi\)
\(930\) −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 0.325166 0.945657i \(-0.394580\pi\)
−0.945657 + 0.325166i \(0.894580\pi\)
\(938\) 35.5228 + 3.24216i 1.15986 + 0.105860i
\(939\) 2.82785i 0.0922835i
\(940\) −4.14508 + 14.6021i −0.135198 + 0.476269i
\(941\) 4.42718i 0.144322i −0.997393 0.0721609i \(-0.977010\pi\)
0.997393 0.0721609i \(-0.0229895\pi\)
\(942\) 1.30677 1.30677i 0.0425769 0.0425769i
\(943\) 15.0718 15.0718i 0.490806 0.490806i
\(944\) 3.32581 0.108246
\(945\) −1.28811 + 3.34473i −0.0419022 + 0.108804i
\(946\) −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
\(952\) −8.99465 0.820941i −0.291518 0.0266069i
\(953\) 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 \(0.305817\pi\)
−0.572905 + 0.819622i \(0.694183\pi\)
\(972\) 1.92229 + 1.92229i 0.0616574 + 0.0616574i
\(973\) −1.25719 + 13.7744i −0.0403037 + 0.441587i
\(974\) 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
\(980\) −5.02423 14.8242i −0.160493 0.473542i
\(981\) −26.1216 −0.833998
\(982\) 16.2113 16.2113i 0.517324 0.517324i
\(983\) 27.4320 27.4320i 0.874943 0.874943i −0.118063 0.993006i \(-0.537668\pi\)
0.993006 + 0.118063i \(0.0376684\pi\)
\(984\) 0.857714i 0.0273429i
\(985\) 11.0182 38.8146i 0.351070 1.23674i
\(986\) 20.4034i 0.649777i
\(987\) 0.165114 1.80907i 0.00525562 0.0575833i
\(988\) 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 \(0.0394595\pi\)
0.123649 + 0.992326i \(0.460540\pi\)
\(998\) −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.573.6 yes 40
5.2 odd 4 inner 770.2.l.c.727.5 yes 40
7.6 odd 2 inner 770.2.l.c.573.5 40
35.27 even 4 inner 770.2.l.c.727.6 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.l.c.573.5 40 7.6 odd 2 inner
770.2.l.c.573.6 yes 40 1.1 even 1 trivial
770.2.l.c.727.5 yes 40 5.2 odd 4 inner
770.2.l.c.727.6 yes 40 35.27 even 4 inner