Properties

Label 882.2.y.a.571.16
Level $882$
Weight $2$
Character 882.571
Analytic conductor $7.043$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(193,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 22]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.y (of order \(21\), degree \(12\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 571.16
Character \(\chi\) \(=\) 882.571
Dual form 882.2.y.a.709.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.826239 + 0.563320i) q^{2} +(0.382088 + 1.68938i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.888346 - 3.89210i) q^{5} +(-1.26736 - 1.18059i) q^{6} +(-0.839750 - 2.50895i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.70802 + 1.29098i) q^{9} +O(q^{10})\) \(q+(-0.826239 + 0.563320i) q^{2} +(0.382088 + 1.68938i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.888346 - 3.89210i) q^{5} +(-1.26736 - 1.18059i) q^{6} +(-0.839750 - 2.50895i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-2.70802 + 1.29098i) q^{9} +(2.92648 + 2.71538i) q^{10} +(2.05428 + 0.989291i) q^{11} +(1.71219 + 0.261525i) q^{12} +(-3.47680 + 2.37044i) q^{13} +(2.10717 + 1.59994i) q^{14} +(6.23581 - 2.98788i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(1.93671 + 4.93466i) q^{17} +(1.51023 - 2.59214i) q^{18} +(-2.48033 - 4.29607i) q^{19} +(-3.94760 - 0.595005i) q^{20} +(3.91771 - 2.37730i) q^{21} +(-2.25462 + 0.339829i) q^{22} +(0.0537973 + 0.0674597i) q^{23} +(-1.56200 + 0.748431i) q^{24} +(-9.85441 + 4.74564i) q^{25} +(1.53735 - 3.91711i) q^{26} +(-3.21567 - 4.08160i) q^{27} +(-2.64231 - 0.134920i) q^{28} +(-6.91184 - 1.04179i) q^{29} +(-3.46914 + 5.98146i) q^{30} +(1.11649 + 1.93381i) q^{31} +(0.988831 + 0.149042i) q^{32} +(-0.886372 + 3.84846i) q^{33} +(-4.37998 - 2.98622i) q^{34} +(-9.01908 + 5.49720i) q^{35} +(0.212394 + 2.99247i) q^{36} +(-8.42858 - 1.27040i) q^{37} +(4.46941 + 2.15235i) q^{38} +(-5.33303 - 4.96793i) q^{39} +(3.59684 - 1.73215i) q^{40} +(7.29061 + 2.24886i) q^{41} +(-1.89779 + 4.17114i) q^{42} +(-8.26988 + 2.55092i) q^{43} +(1.67142 - 1.55085i) q^{44} +(7.43029 + 9.39303i) q^{45} +(-0.0824509 - 0.0254327i) q^{46} +(-1.41474 + 0.964556i) q^{47} +(0.868981 - 1.49829i) q^{48} +(-5.58964 + 4.21378i) q^{49} +(5.46879 - 9.47222i) q^{50} +(-7.59653 + 5.15732i) q^{51} +(0.936365 + 4.10249i) q^{52} +(0.470129 - 0.0708606i) q^{53} +(4.95616 + 1.56093i) q^{54} +(2.02550 - 8.87430i) q^{55} +(2.25918 - 1.37699i) q^{56} +(6.30999 - 5.83171i) q^{57} +(6.29769 - 3.03281i) q^{58} +(-7.68604 + 2.37083i) q^{59} +(-0.503140 - 6.89634i) q^{60} +(-5.51947 - 14.0634i) q^{61} +(-2.01184 - 0.968850i) q^{62} +(5.51307 + 5.71017i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(12.3146 + 11.4263i) q^{65} +(-1.43556 - 3.67906i) q^{66} +(4.96164 + 8.59382i) q^{67} +5.30111 q^{68} +(-0.0934099 + 0.116660i) q^{69} +(4.35523 - 9.62263i) q^{70} +(-6.27170 - 7.86446i) q^{71} +(-1.86121 - 2.35285i) q^{72} +(0.703177 - 9.38324i) q^{73} +(7.67967 - 3.69833i) q^{74} +(-11.7824 - 14.8346i) q^{75} +(-4.90526 + 0.739349i) q^{76} +(0.756994 - 5.98485i) q^{77} +(7.20489 + 1.10049i) q^{78} +(-2.06257 + 3.57248i) q^{79} +(-1.99609 + 3.45734i) q^{80} +(5.66672 - 6.99202i) q^{81} +(-7.29061 + 2.24886i) q^{82} +(6.73380 + 4.59103i) q^{83} +(-0.781663 - 4.51542i) q^{84} +(17.4857 - 11.9216i) q^{85} +(5.39591 - 6.76626i) q^{86} +(-0.880946 - 12.0748i) q^{87} +(-0.507366 + 2.22292i) q^{88} +(7.91088 + 5.39355i) q^{89} +(-11.4305 - 3.57525i) q^{90} +(8.86697 + 6.73254i) q^{91} +(0.0824509 - 0.0254327i) q^{92} +(-2.84035 + 2.62505i) q^{93} +(0.625562 - 1.59391i) q^{94} +(-14.5173 + 13.4701i) q^{95} +(0.126031 + 1.72746i) q^{96} +(-0.318936 - 0.552413i) q^{97} +(2.24467 - 6.63034i) q^{98} +(-6.84019 - 0.0269689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9} - 2 q^{10} + q^{12} - 23 q^{13} + q^{14} + q^{15} + 28 q^{16} + 7 q^{17} - q^{18} + 38 q^{19} + 2 q^{20} + 13 q^{21} + 21 q^{23} - q^{24} - 48 q^{25} + 9 q^{26} - 28 q^{27} + 2 q^{28} + 11 q^{29} - 7 q^{30} + 44 q^{31} - 28 q^{32} - 25 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} - 22 q^{38} - 51 q^{39} + 4 q^{40} + 3 q^{41} + 13 q^{42} + q^{43} - 75 q^{45} - 42 q^{46} - 33 q^{47} - 2 q^{48} - 41 q^{49} + 172 q^{50} + 4 q^{51} + 11 q^{52} - 78 q^{53} + 11 q^{54} + 23 q^{55} + q^{56} - 30 q^{57} - 13 q^{58} + 14 q^{59} - 8 q^{60} + 92 q^{61} - 24 q^{62} - 22 q^{63} - 56 q^{64} + 7 q^{65} + 29 q^{66} + 29 q^{67} + 42 q^{68} + 19 q^{69} - 34 q^{70} + 7 q^{71} - q^{72} - 8 q^{73} - 8 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{77} + 4 q^{78} - 9 q^{79} - 12 q^{80} + 45 q^{81} - 3 q^{82} - 109 q^{83} + 28 q^{84} + 93 q^{85} + 2 q^{86} - 15 q^{87} + 47 q^{89} - 3 q^{90} + 45 q^{91} + 42 q^{92} + 155 q^{93} - 9 q^{94} - 13 q^{95} - q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.826239 + 0.563320i −0.584239 + 0.398327i
\(3\) 0.382088 + 1.68938i 0.220599 + 0.975365i
\(4\) 0.365341 0.930874i 0.182671 0.465437i
\(5\) −0.888346 3.89210i −0.397280 1.74060i −0.638030 0.770011i \(-0.720251\pi\)
0.240750 0.970587i \(-0.422607\pi\)
\(6\) −1.26736 1.18059i −0.517397 0.481976i
\(7\) −0.839750 2.50895i −0.317396 0.948293i
\(8\) 0.222521 + 0.974928i 0.0786730 + 0.344689i
\(9\) −2.70802 + 1.29098i −0.902673 + 0.430328i
\(10\) 2.92648 + 2.71538i 0.925435 + 0.858678i
\(11\) 2.05428 + 0.989291i 0.619390 + 0.298282i 0.717141 0.696929i \(-0.245451\pi\)
−0.0977508 + 0.995211i \(0.531165\pi\)
\(12\) 1.71219 + 0.261525i 0.494268 + 0.0754957i
\(13\) −3.47680 + 2.37044i −0.964292 + 0.657443i −0.939608 0.342252i \(-0.888810\pi\)
−0.0246836 + 0.999695i \(0.507858\pi\)
\(14\) 2.10717 + 1.59994i 0.563166 + 0.427602i
\(15\) 6.23581 2.98788i 1.61008 0.771467i
\(16\) −0.733052 0.680173i −0.183263 0.170043i
\(17\) 1.93671 + 4.93466i 0.469722 + 1.19683i 0.947900 + 0.318569i \(0.103202\pi\)
−0.478178 + 0.878263i \(0.658703\pi\)
\(18\) 1.51023 2.59214i 0.355965 0.610974i
\(19\) −2.48033 4.29607i −0.569028 0.985585i −0.996662 0.0816334i \(-0.973986\pi\)
0.427635 0.903952i \(-0.359347\pi\)
\(20\) −3.94760 0.595005i −0.882710 0.133047i
\(21\) 3.91771 2.37730i 0.854915 0.518769i
\(22\) −2.25462 + 0.339829i −0.480686 + 0.0724517i
\(23\) 0.0537973 + 0.0674597i 0.0112175 + 0.0140663i 0.787409 0.616431i \(-0.211422\pi\)
−0.776191 + 0.630498i \(0.782851\pi\)
\(24\) −1.56200 + 0.748431i −0.318842 + 0.152773i
\(25\) −9.85441 + 4.74564i −1.97088 + 0.949127i
\(26\) 1.53735 3.91711i 0.301499 0.768208i
\(27\) −3.21567 4.08160i −0.618855 0.785505i
\(28\) −2.64231 0.134920i −0.499349 0.0254975i
\(29\) −6.91184 1.04179i −1.28350 0.193456i −0.528358 0.849022i \(-0.677192\pi\)
−0.755138 + 0.655566i \(0.772430\pi\)
\(30\) −3.46914 + 5.98146i −0.633375 + 1.09206i
\(31\) 1.11649 + 1.93381i 0.200527 + 0.347322i 0.948698 0.316183i \(-0.102401\pi\)
−0.748172 + 0.663505i \(0.769068\pi\)
\(32\) 0.988831 + 0.149042i 0.174802 + 0.0263472i
\(33\) −0.886372 + 3.84846i −0.154298 + 0.669932i
\(34\) −4.37998 2.98622i −0.751161 0.512133i
\(35\) −9.01908 + 5.49720i −1.52450 + 0.929197i
\(36\) 0.212394 + 2.99247i 0.0353989 + 0.498745i
\(37\) −8.42858 1.27040i −1.38565 0.208853i −0.586483 0.809962i \(-0.699488\pi\)
−0.799167 + 0.601108i \(0.794726\pi\)
\(38\) 4.46941 + 2.15235i 0.725034 + 0.349158i
\(39\) −5.33303 4.96793i −0.853968 0.795505i
\(40\) 3.59684 1.73215i 0.568710 0.273876i
\(41\) 7.29061 + 2.24886i 1.13860 + 0.351212i 0.806036 0.591867i \(-0.201609\pi\)
0.332567 + 0.943080i \(0.392085\pi\)
\(42\) −1.89779 + 4.17114i −0.292835 + 0.643621i
\(43\) −8.26988 + 2.55092i −1.26115 + 0.389012i −0.852041 0.523475i \(-0.824635\pi\)
−0.409105 + 0.912487i \(0.634159\pi\)
\(44\) 1.67142 1.55085i 0.251976 0.233799i
\(45\) 7.43029 + 9.39303i 1.10764 + 1.40023i
\(46\) −0.0824509 0.0254327i −0.0121567 0.00374985i
\(47\) −1.41474 + 0.964556i −0.206362 + 0.140695i −0.662091 0.749423i \(-0.730331\pi\)
0.455730 + 0.890118i \(0.349378\pi\)
\(48\) 0.868981 1.49829i 0.125427 0.216260i
\(49\) −5.58964 + 4.21378i −0.798520 + 0.601968i
\(50\) 5.46879 9.47222i 0.773403 1.33957i
\(51\) −7.59653 + 5.15732i −1.06373 + 0.722170i
\(52\) 0.936365 + 4.10249i 0.129851 + 0.568912i
\(53\) 0.470129 0.0708606i 0.0645772 0.00973345i −0.116674 0.993170i \(-0.537223\pi\)
0.181251 + 0.983437i \(0.441985\pi\)
\(54\) 4.95616 + 1.56093i 0.674448 + 0.212416i
\(55\) 2.02550 8.87430i 0.273119 1.19661i
\(56\) 2.25918 1.37699i 0.301896 0.184008i
\(57\) 6.30999 5.83171i 0.835778 0.772428i
\(58\) 6.29769 3.03281i 0.826927 0.398227i
\(59\) −7.68604 + 2.37083i −1.00064 + 0.308656i −0.751443 0.659798i \(-0.770642\pi\)
−0.249194 + 0.968454i \(0.580166\pi\)
\(60\) −0.503140 6.89634i −0.0649551 0.890314i
\(61\) −5.51947 14.0634i −0.706695 1.80063i −0.589904 0.807473i \(-0.700834\pi\)
−0.116791 0.993157i \(-0.537261\pi\)
\(62\) −2.01184 0.968850i −0.255504 0.123044i
\(63\) 5.51307 + 5.71017i 0.694582 + 0.719414i
\(64\) −0.900969 + 0.433884i −0.112621 + 0.0542355i
\(65\) 12.3146 + 11.4263i 1.52744 + 1.41726i
\(66\) −1.43556 3.67906i −0.176705 0.452861i
\(67\) 4.96164 + 8.59382i 0.606161 + 1.04990i 0.991867 + 0.127280i \(0.0406247\pi\)
−0.385706 + 0.922622i \(0.626042\pi\)
\(68\) 5.30111 0.642854
\(69\) −0.0934099 + 0.116660i −0.0112452 + 0.0140442i
\(70\) 4.35523 9.62263i 0.520549 1.15012i
\(71\) −6.27170 7.86446i −0.744313 0.933339i 0.255123 0.966909i \(-0.417884\pi\)
−0.999436 + 0.0335692i \(0.989313\pi\)
\(72\) −1.86121 2.35285i −0.219345 0.277286i
\(73\) 0.703177 9.38324i 0.0823006 1.09823i −0.791250 0.611493i \(-0.790569\pi\)
0.873551 0.486733i \(-0.161812\pi\)
\(74\) 7.67967 3.69833i 0.892743 0.429922i
\(75\) −11.7824 14.8346i −1.36052 1.71295i
\(76\) −4.90526 + 0.739349i −0.562672 + 0.0848092i
\(77\) 0.756994 5.98485i 0.0862675 0.682037i
\(78\) 7.20489 + 1.10049i 0.815793 + 0.124606i
\(79\) −2.06257 + 3.57248i −0.232058 + 0.401936i −0.958414 0.285383i \(-0.907879\pi\)
0.726356 + 0.687319i \(0.241213\pi\)
\(80\) −1.99609 + 3.45734i −0.223170 + 0.386542i
\(81\) 5.66672 6.99202i 0.629635 0.776891i
\(82\) −7.29061 + 2.24886i −0.805114 + 0.248345i
\(83\) 6.73380 + 4.59103i 0.739130 + 0.503931i 0.873394 0.487015i \(-0.161914\pi\)
−0.134263 + 0.990946i \(0.542867\pi\)
\(84\) −0.781663 4.51542i −0.0852864 0.492673i
\(85\) 17.4857 11.9216i 1.89659 1.29307i
\(86\) 5.39591 6.76626i 0.581856 0.729625i
\(87\) −0.880946 12.0748i −0.0944473 1.29455i
\(88\) −0.507366 + 2.22292i −0.0540854 + 0.236964i
\(89\) 7.91088 + 5.39355i 0.838551 + 0.571715i 0.904678 0.426097i \(-0.140112\pi\)
−0.0661263 + 0.997811i \(0.521064\pi\)
\(90\) −11.4305 3.57525i −1.20488 0.376864i
\(91\) 8.86697 + 6.73254i 0.929511 + 0.705762i
\(92\) 0.0824509 0.0254327i 0.00859610 0.00265155i
\(93\) −2.84035 + 2.62505i −0.294530 + 0.272205i
\(94\) 0.625562 1.59391i 0.0645218 0.164399i
\(95\) −14.5173 + 13.4701i −1.48944 + 1.38200i
\(96\) 0.126031 + 1.72746i 0.0128630 + 0.176308i
\(97\) −0.318936 0.552413i −0.0323830 0.0560891i 0.849380 0.527782i \(-0.176976\pi\)
−0.881763 + 0.471693i \(0.843643\pi\)
\(98\) 2.24467 6.63034i 0.226746 0.669766i
\(99\) −6.84019 0.0269689i −0.687465 0.00271048i
\(100\) 0.817366 + 10.9070i 0.0817366 + 1.09070i
\(101\) 1.49158 + 6.53505i 0.148418 + 0.650261i 0.993325 + 0.115348i \(0.0367985\pi\)
−0.844907 + 0.534913i \(0.820344\pi\)
\(102\) 3.37133 8.54046i 0.333811 0.845632i
\(103\) −1.15927 5.07909i −0.114226 0.500458i −0.999382 0.0351621i \(-0.988805\pi\)
0.885155 0.465295i \(-0.154052\pi\)
\(104\) −3.08467 2.86216i −0.302477 0.280658i
\(105\) −12.7330 13.1362i −1.24261 1.28197i
\(106\) −0.348522 + 0.323381i −0.0338514 + 0.0314095i
\(107\) −4.89130 3.33483i −0.472859 0.322390i 0.303335 0.952884i \(-0.401900\pi\)
−0.776194 + 0.630494i \(0.782852\pi\)
\(108\) −4.97427 + 1.50220i −0.478650 + 0.144549i
\(109\) 8.81296 6.00858i 0.844129 0.575517i −0.0622130 0.998063i \(-0.519816\pi\)
0.906342 + 0.422546i \(0.138863\pi\)
\(110\) 3.32552 + 8.47330i 0.317076 + 0.807897i
\(111\) −1.07426 14.7245i −0.101964 1.39759i
\(112\) −1.09094 + 2.41036i −0.103084 + 0.227758i
\(113\) −0.707097 + 9.43556i −0.0665181 + 0.887622i 0.859740 + 0.510732i \(0.170626\pi\)
−0.926258 + 0.376890i \(0.876993\pi\)
\(114\) −1.92844 + 8.37292i −0.180615 + 0.784196i
\(115\) 0.214769 0.269312i 0.0200273 0.0251135i
\(116\) −3.49495 + 6.05344i −0.324498 + 0.562048i
\(117\) 6.35504 10.9077i 0.587523 1.00842i
\(118\) 5.01497 6.28857i 0.461665 0.578910i
\(119\) 10.7545 9.00300i 0.985860 0.825303i
\(120\) 4.30056 + 5.41460i 0.392586 + 0.494283i
\(121\) −3.61700 4.53558i −0.328819 0.412325i
\(122\) 12.4826 + 8.51047i 1.13012 + 0.770502i
\(123\) −1.01352 + 13.1759i −0.0913860 + 1.18803i
\(124\) 2.20803 0.332807i 0.198287 0.0298870i
\(125\) 14.7791 + 18.5325i 1.32189 + 1.65759i
\(126\) −7.77177 1.61234i −0.692364 0.143639i
\(127\) −8.14428 + 10.2126i −0.722688 + 0.906222i −0.998487 0.0549933i \(-0.982486\pi\)
0.275799 + 0.961215i \(0.411058\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −7.46930 12.9963i −0.657635 1.14426i
\(130\) −16.6115 2.50377i −1.45692 0.219595i
\(131\) −1.73626 + 7.60705i −0.151698 + 0.664631i 0.840694 + 0.541510i \(0.182147\pi\)
−0.992392 + 0.123121i \(0.960710\pi\)
\(132\) 3.25861 + 2.23110i 0.283625 + 0.194193i
\(133\) −8.69574 + 9.83065i −0.754017 + 0.852426i
\(134\) −8.94057 4.30555i −0.772348 0.371943i
\(135\) −13.0294 + 16.1416i −1.12139 + 1.38924i
\(136\) −4.37998 + 2.98622i −0.375580 + 0.256066i
\(137\) 4.27052 18.7104i 0.364855 1.59853i −0.375835 0.926687i \(-0.622644\pi\)
0.740690 0.671847i \(-0.234499\pi\)
\(138\) 0.0114621 0.149008i 0.000975717 0.0126844i
\(139\) −3.93674 1.21432i −0.333910 0.102998i 0.123267 0.992374i \(-0.460663\pi\)
−0.457176 + 0.889376i \(0.651139\pi\)
\(140\) 1.82216 + 10.4040i 0.154001 + 0.879297i
\(141\) −2.17006 2.02150i −0.182752 0.170241i
\(142\) 9.61212 + 2.96495i 0.806632 + 0.248813i
\(143\) −9.48740 + 1.43000i −0.793376 + 0.119582i
\(144\) 2.86321 + 0.895561i 0.238601 + 0.0746301i
\(145\) 2.08535 + 27.8270i 0.173179 + 2.31091i
\(146\) 4.70478 + 8.14891i 0.389370 + 0.674409i
\(147\) −9.25441 7.83300i −0.763291 0.646055i
\(148\) −4.26189 + 7.38182i −0.350325 + 0.606781i
\(149\) −0.168991 0.0813819i −0.0138443 0.00666707i 0.426949 0.904276i \(-0.359588\pi\)
−0.440793 + 0.897609i \(0.645303\pi\)
\(150\) 18.0917 + 5.61965i 1.47718 + 0.458842i
\(151\) −2.32064 2.91000i −0.188851 0.236812i 0.678388 0.734704i \(-0.262679\pi\)
−0.867239 + 0.497892i \(0.834108\pi\)
\(152\) 3.63643 3.37411i 0.294953 0.273677i
\(153\) −11.6152 10.8629i −0.939036 0.878213i
\(154\) 2.74593 + 5.37134i 0.221273 + 0.432835i
\(155\) 6.53475 6.06336i 0.524884 0.487021i
\(156\) −6.57289 + 3.14939i −0.526252 + 0.252153i
\(157\) 12.1712 3.75431i 0.971365 0.299626i 0.231839 0.972754i \(-0.425526\pi\)
0.739526 + 0.673128i \(0.235050\pi\)
\(158\) −0.308273 4.11361i −0.0245249 0.327262i
\(159\) 0.299341 + 0.767152i 0.0237393 + 0.0608391i
\(160\) −0.298337 3.98103i −0.0235856 0.314728i
\(161\) 0.124077 0.191624i 0.00977861 0.0151021i
\(162\) −0.743319 + 8.96925i −0.0584007 + 0.704691i
\(163\) −16.8345 + 5.19276i −1.31858 + 0.406728i −0.872653 0.488341i \(-0.837602\pi\)
−0.445927 + 0.895069i \(0.647126\pi\)
\(164\) 4.75696 5.96504i 0.371456 0.465792i
\(165\) 15.7660 + 0.0310802i 1.22738 + 0.00241959i
\(166\) −8.14994 −0.632558
\(167\) −1.87396 4.77477i −0.145011 0.369483i 0.839852 0.542815i \(-0.182642\pi\)
−0.984863 + 0.173333i \(0.944546\pi\)
\(168\) 3.18947 + 3.29049i 0.246073 + 0.253867i
\(169\) 1.71972 4.38178i 0.132286 0.337060i
\(170\) −7.73172 + 19.7001i −0.592996 + 1.51093i
\(171\) 12.2629 + 8.43175i 0.937771 + 0.644792i
\(172\) −0.646742 + 8.63017i −0.0493136 + 0.658045i
\(173\) −5.65408 + 0.852216i −0.429872 + 0.0647928i −0.360415 0.932792i \(-0.617365\pi\)
−0.0694573 + 0.997585i \(0.522127\pi\)
\(174\) 7.52984 + 9.48040i 0.570836 + 0.718707i
\(175\) 20.1818 + 20.7391i 1.52560 + 1.56773i
\(176\) −0.833008 2.12247i −0.0627903 0.159987i
\(177\) −6.94198 12.0788i −0.521791 0.907898i
\(178\) −9.57457 −0.717644
\(179\) −6.95868 17.7304i −0.520116 1.32523i −0.913866 0.406017i \(-0.866917\pi\)
0.393749 0.919218i \(-0.371178\pi\)
\(180\) 11.4583 3.48501i 0.854052 0.259757i
\(181\) 11.1560 5.37246i 0.829222 0.399332i 0.0293984 0.999568i \(-0.490641\pi\)
0.799823 + 0.600236i \(0.204927\pi\)
\(182\) −11.1188 0.567742i −0.824181 0.0420839i
\(183\) 21.6495 14.6979i 1.60037 1.08650i
\(184\) −0.0537973 + 0.0674597i −0.00396599 + 0.00497320i
\(185\) 2.54296 + 33.9334i 0.186962 + 2.49483i
\(186\) 0.868058 3.76895i 0.0636491 0.276352i
\(187\) −0.903260 + 12.0532i −0.0660529 + 0.881415i
\(188\) 0.381016 + 1.66934i 0.0277884 + 0.121749i
\(189\) −7.54018 + 11.4955i −0.548467 + 0.836172i
\(190\) 4.40679 19.3074i 0.319702 1.40071i
\(191\) 6.66233 + 2.05506i 0.482070 + 0.148699i 0.526259 0.850324i \(-0.323594\pi\)
−0.0441893 + 0.999023i \(0.514070\pi\)
\(192\) −1.07724 1.35630i −0.0777434 0.0978824i
\(193\) −17.1848 + 15.9452i −1.23699 + 1.14776i −0.253394 + 0.967363i \(0.581547\pi\)
−0.983594 + 0.180395i \(0.942263\pi\)
\(194\) 0.574703 + 0.276762i 0.0412613 + 0.0198704i
\(195\) −14.5981 + 25.1699i −1.04539 + 1.80245i
\(196\) 1.88037 + 6.74271i 0.134312 + 0.481622i
\(197\) 23.5041 1.67460 0.837300 0.546744i \(-0.184133\pi\)
0.837300 + 0.546744i \(0.184133\pi\)
\(198\) 5.66683 3.83094i 0.402724 0.272253i
\(199\) 9.11687 + 2.81218i 0.646278 + 0.199350i 0.600529 0.799603i \(-0.294957\pi\)
0.0457485 + 0.998953i \(0.485433\pi\)
\(200\) −6.81947 8.55134i −0.482209 0.604671i
\(201\) −12.6225 + 11.6657i −0.890319 + 0.822835i
\(202\) −4.91373 4.55927i −0.345728 0.320789i
\(203\) 3.19042 + 18.2163i 0.223923 + 1.27853i
\(204\) 2.02549 + 8.95560i 0.141813 + 0.627017i
\(205\) 2.27618 30.3735i 0.158975 2.12138i
\(206\) 3.81899 + 3.54350i 0.266081 + 0.246887i
\(207\) −0.232774 0.113231i −0.0161789 0.00787007i
\(208\) 4.16099 + 0.627168i 0.288513 + 0.0434863i
\(209\) −0.845252 11.2791i −0.0584673 0.780192i
\(210\) 17.9204 + 3.68095i 1.23662 + 0.254010i
\(211\) 1.01539 13.5494i 0.0699020 0.932777i −0.846467 0.532442i \(-0.821275\pi\)
0.916369 0.400336i \(-0.131106\pi\)
\(212\) 0.105795 0.463519i 0.00726604 0.0318346i
\(213\) 10.8897 13.6002i 0.746152 0.931870i
\(214\) 5.91996 0.404680
\(215\) 17.2749 + 29.9211i 1.17814 + 2.04060i
\(216\) 3.26372 4.04328i 0.222068 0.275111i
\(217\) 3.91426 4.42512i 0.265717 0.300397i
\(218\) −3.89686 + 9.92904i −0.263929 + 0.672479i
\(219\) 16.1206 2.39729i 1.08933 0.161994i
\(220\) −7.52086 5.12763i −0.507056 0.345705i
\(221\) −18.4309 12.5660i −1.23980 0.845280i
\(222\) 9.18220 + 11.5608i 0.616269 + 0.775910i
\(223\) 5.83221 14.8602i 0.390553 0.995114i −0.591465 0.806330i \(-0.701450\pi\)
0.982019 0.188784i \(-0.0604544\pi\)
\(224\) −0.456432 2.60608i −0.0304966 0.174126i
\(225\) 20.5594 25.5732i 1.37063 1.70488i
\(226\) −4.73101 8.19434i −0.314702 0.545080i
\(227\) −17.2482 −1.14480 −0.572402 0.819973i \(-0.693988\pi\)
−0.572402 + 0.819973i \(0.693988\pi\)
\(228\) −3.12328 8.00436i −0.206845 0.530102i
\(229\) 0.943417 4.13338i 0.0623427 0.273141i −0.934144 0.356898i \(-0.883835\pi\)
0.996486 + 0.0837561i \(0.0266917\pi\)
\(230\) −0.0257418 + 0.343500i −0.00169736 + 0.0226497i
\(231\) 10.3999 1.00789i 0.684265 0.0663141i
\(232\) −0.522357 6.97036i −0.0342944 0.457627i
\(233\) 1.94748 + 0.293535i 0.127584 + 0.0192301i 0.212524 0.977156i \(-0.431832\pi\)
−0.0849400 + 0.996386i \(0.527070\pi\)
\(234\) 0.893750 + 12.5923i 0.0584262 + 0.823184i
\(235\) 5.01093 + 4.64946i 0.326877 + 0.303297i
\(236\) −0.601083 + 8.02090i −0.0391272 + 0.522116i
\(237\) −6.82337 2.11947i −0.443226 0.137674i
\(238\) −3.81418 + 13.4968i −0.247237 + 0.874870i
\(239\) −7.08966 6.57824i −0.458592 0.425511i 0.416746 0.909023i \(-0.363171\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(240\) −6.60344 2.05116i −0.426250 0.132402i
\(241\) 2.36596 + 2.96682i 0.152405 + 0.191110i 0.852173 0.523261i \(-0.175285\pi\)
−0.699768 + 0.714370i \(0.746713\pi\)
\(242\) 5.54349 + 1.70994i 0.356349 + 0.109919i
\(243\) 13.9774 + 6.90168i 0.896649 + 0.442743i
\(244\) −15.1077 −0.967172
\(245\) 21.3660 + 18.0121i 1.36502 + 1.15075i
\(246\) −6.58483 11.4574i −0.419834 0.730495i
\(247\) 18.8072 + 9.05708i 1.19667 + 0.576288i
\(248\) −1.63688 + 1.51881i −0.103942 + 0.0964443i
\(249\) −5.18309 + 13.1301i −0.328465 + 0.832088i
\(250\) −22.6508 6.98685i −1.43256 0.441887i
\(251\) 4.11695 18.0375i 0.259859 1.13852i −0.661542 0.749908i \(-0.730098\pi\)
0.921402 0.388611i \(-0.127045\pi\)
\(252\) 7.32960 3.04581i 0.461721 0.191868i
\(253\) 0.0437777 + 0.191803i 0.00275228 + 0.0120585i
\(254\) 0.976155 13.0259i 0.0612494 0.817317i
\(255\) 26.8211 + 24.9850i 1.67961 + 1.56462i
\(256\) 0.0747301 + 0.997204i 0.00467063 + 0.0623252i
\(257\) 13.3788 16.7764i 0.834545 1.04649i −0.163656 0.986518i \(-0.552329\pi\)
0.998200 0.0599684i \(-0.0191000\pi\)
\(258\) 13.4925 + 6.53045i 0.840007 + 0.406568i
\(259\) 3.89053 + 22.2137i 0.241746 + 1.38029i
\(260\) 15.1355 7.28885i 0.938661 0.452035i
\(261\) 20.0623 6.10188i 1.24183 0.377697i
\(262\) −2.85064 7.26331i −0.176113 0.448729i
\(263\) −14.5358 −0.896315 −0.448157 0.893955i \(-0.647920\pi\)
−0.448157 + 0.893955i \(0.647920\pi\)
\(264\) −3.94921 0.00778526i −0.243057 0.000479150i
\(265\) −0.693433 1.76684i −0.0425973 0.108536i
\(266\) 1.64696 13.0210i 0.100981 0.798366i
\(267\) −6.08910 + 15.4253i −0.372647 + 0.944013i
\(268\) 9.81245 1.47899i 0.599391 0.0903437i
\(269\) 0.875992 11.6893i 0.0534102 0.712710i −0.904652 0.426150i \(-0.859869\pi\)
0.958063 0.286559i \(-0.0925115\pi\)
\(270\) 1.67251 20.6765i 0.101786 1.25833i
\(271\) −2.69121 + 6.85709i −0.163479 + 0.416539i −0.989016 0.147810i \(-0.952777\pi\)
0.825536 + 0.564349i \(0.190873\pi\)
\(272\) 1.93671 4.93466i 0.117430 0.299208i
\(273\) −7.98586 + 17.5521i −0.483326 + 1.06230i
\(274\) 7.01145 + 17.8649i 0.423577 + 1.07926i
\(275\) −24.9386 −1.50385
\(276\) 0.0744691 + 0.129573i 0.00448251 + 0.00779940i
\(277\) −16.3011 + 20.4409i −0.979436 + 1.22817i −0.00581912 + 0.999983i \(0.501852\pi\)
−0.973617 + 0.228190i \(0.926719\pi\)
\(278\) 3.93674 1.21432i 0.236110 0.0728303i
\(279\) −5.51998 3.79542i −0.330473 0.227226i
\(280\) −7.36631 7.56971i −0.440221 0.452377i
\(281\) −0.912068 12.1707i −0.0544094 0.726043i −0.955984 0.293419i \(-0.905207\pi\)
0.901574 0.432624i \(-0.142412\pi\)
\(282\) 2.93174 + 0.447801i 0.174582 + 0.0266661i
\(283\) −1.01095 13.4902i −0.0600947 0.801908i −0.943093 0.332530i \(-0.892098\pi\)
0.882998 0.469377i \(-0.155521\pi\)
\(284\) −9.61212 + 2.96495i −0.570375 + 0.175937i
\(285\) −28.3030 19.3785i −1.67653 1.14788i
\(286\) 7.03331 6.52596i 0.415888 0.385888i
\(287\) −0.480031 20.1803i −0.0283353 1.19120i
\(288\) −2.87018 + 0.872956i −0.169127 + 0.0514394i
\(289\) −8.13817 + 7.55112i −0.478716 + 0.444184i
\(290\) −17.3985 21.8170i −1.02168 1.28114i
\(291\) 0.811375 0.749875i 0.0475637 0.0439585i
\(292\) −8.47772 4.08265i −0.496121 0.238919i
\(293\) 0.436161 0.755452i 0.0254808 0.0441340i −0.853004 0.521905i \(-0.825222\pi\)
0.878485 + 0.477771i \(0.158555\pi\)
\(294\) 12.0588 + 1.25873i 0.703286 + 0.0734106i
\(295\) 16.0554 + 27.8087i 0.934779 + 1.61909i
\(296\) −0.636983 8.49995i −0.0370239 0.494050i
\(297\) −2.56800 11.5660i −0.149010 0.671127i
\(298\) 0.185471 0.0279553i 0.0107441 0.00161941i
\(299\) −0.346952 0.107021i −0.0200648 0.00618916i
\(300\) −18.1138 + 5.54827i −1.04580 + 0.320330i
\(301\) 13.3448 + 18.6066i 0.769180 + 1.07247i
\(302\) 3.55666 + 1.09709i 0.204663 + 0.0631302i
\(303\) −10.4703 + 5.01681i −0.601501 + 0.288208i
\(304\) −1.10385 + 4.83629i −0.0633103 + 0.277381i
\(305\) −49.8328 + 33.9754i −2.85342 + 1.94543i
\(306\) 15.7162 + 2.43225i 0.898437 + 0.139043i
\(307\) 27.8663 + 13.4197i 1.59041 + 0.765903i 0.999176 0.0405939i \(-0.0129250\pi\)
0.591238 + 0.806497i \(0.298639\pi\)
\(308\) −5.29458 2.89118i −0.301686 0.164740i
\(309\) 8.13757 3.89911i 0.462930 0.221812i
\(310\) −1.98365 + 8.69094i −0.112664 + 0.493612i
\(311\) 4.31044 + 0.649694i 0.244423 + 0.0368408i 0.270111 0.962829i \(-0.412940\pi\)
−0.0256883 + 0.999670i \(0.508178\pi\)
\(312\) 3.65666 6.30479i 0.207018 0.356938i
\(313\) −7.43448 + 12.8769i −0.420222 + 0.727845i −0.995961 0.0897880i \(-0.971381\pi\)
0.575739 + 0.817633i \(0.304714\pi\)
\(314\) −7.94142 + 9.95822i −0.448160 + 0.561975i
\(315\) 17.3270 26.5300i 0.976267 1.49480i
\(316\) 2.57199 + 3.22517i 0.144686 + 0.181430i
\(317\) 16.9337 2.55234i 0.951091 0.143354i 0.344870 0.938650i \(-0.387923\pi\)
0.606221 + 0.795297i \(0.292685\pi\)
\(318\) −0.679479 0.465226i −0.0381033 0.0260886i
\(319\) −13.1682 8.97795i −0.737280 0.502669i
\(320\) 2.48909 + 3.12122i 0.139144 + 0.174481i
\(321\) 3.76489 9.53746i 0.210136 0.532329i
\(322\) 0.00542876 + 0.228222i 0.000302533 + 0.0127183i
\(323\) 16.3959 20.5599i 0.912295 1.14398i
\(324\) −4.43840 7.82947i −0.246578 0.434971i
\(325\) 23.0126 39.8590i 1.27651 2.21098i
\(326\) 10.9841 13.7737i 0.608355 0.762853i
\(327\) 13.5181 + 12.5926i 0.747553 + 0.696375i
\(328\) −0.570159 + 7.60824i −0.0314818 + 0.420095i
\(329\) 3.60805 + 2.73953i 0.198918 + 0.151035i
\(330\) −13.0440 + 8.85562i −0.718048 + 0.487486i
\(331\) −12.8558 32.7559i −0.706616 1.80043i −0.590247 0.807222i \(-0.700970\pi\)
−0.116369 0.993206i \(-0.537125\pi\)
\(332\) 6.73380 4.59103i 0.369565 0.251965i
\(333\) 24.4648 7.44089i 1.34066 0.407758i
\(334\) 4.23806 + 2.88946i 0.231896 + 0.158104i
\(335\) 29.0403 26.9455i 1.58664 1.47219i
\(336\) −4.48886 0.922038i −0.244887 0.0503013i
\(337\) 20.3075 + 18.8426i 1.10622 + 1.02642i 0.999483 + 0.0321372i \(0.0102313\pi\)
0.106739 + 0.994287i \(0.465959\pi\)
\(338\) 1.04744 + 4.58915i 0.0569734 + 0.249617i
\(339\) −16.2104 + 2.41066i −0.880429 + 0.130929i
\(340\) −4.70922 20.6324i −0.255393 1.11895i
\(341\) 0.380478 + 5.07712i 0.0206040 + 0.274942i
\(342\) −14.8819 0.0586750i −0.804721 0.00317278i
\(343\) 15.2661 + 10.4856i 0.824289 + 0.566169i
\(344\) −4.32719 7.49491i −0.233306 0.404098i
\(345\) 0.537031 + 0.259926i 0.0289128 + 0.0139940i
\(346\) 4.19155 3.88919i 0.225339 0.209084i
\(347\) 2.95507 7.52939i 0.158636 0.404199i −0.829352 0.558726i \(-0.811290\pi\)
0.987989 + 0.154527i \(0.0493855\pi\)
\(348\) −11.5619 3.59136i −0.619785 0.192517i
\(349\) −34.6777 + 10.6967i −1.85625 + 0.572579i −0.857991 + 0.513664i \(0.828288\pi\)
−0.998263 + 0.0589145i \(0.981236\pi\)
\(350\) −28.3577 5.76660i −1.51578 0.308238i
\(351\) 20.8555 + 6.56838i 1.11318 + 0.350594i
\(352\) 1.88389 + 1.28442i 0.100412 + 0.0684596i
\(353\) −0.673811 + 2.95216i −0.0358633 + 0.157127i −0.989689 0.143234i \(-0.954250\pi\)
0.953826 + 0.300361i \(0.0971071\pi\)
\(354\) 12.5400 + 6.06941i 0.666491 + 0.322585i
\(355\) −25.0378 + 31.3964i −1.32887 + 1.66635i
\(356\) 7.91088 5.39355i 0.419276 0.285857i
\(357\) 19.3186 + 14.7284i 1.02245 + 0.779512i
\(358\) 15.7374 + 10.7296i 0.831750 + 0.567077i
\(359\) −33.6907 + 10.3922i −1.77813 + 0.548480i −0.997106 0.0760221i \(-0.975778\pi\)
−0.781023 + 0.624502i \(0.785302\pi\)
\(360\) −7.50413 + 9.33414i −0.395502 + 0.491953i
\(361\) −2.80412 + 4.85688i −0.147585 + 0.255625i
\(362\) −6.19113 + 10.7234i −0.325399 + 0.563607i
\(363\) 6.28031 7.84349i 0.329631 0.411676i
\(364\) 9.50661 5.79436i 0.498282 0.303707i
\(365\) −37.1452 + 5.59873i −1.94427 + 0.293051i
\(366\) −9.60799 + 24.3396i −0.502218 + 1.27225i
\(367\) −0.481199 + 0.231733i −0.0251184 + 0.0120964i −0.446401 0.894833i \(-0.647294\pi\)
0.421282 + 0.906930i \(0.361580\pi\)
\(368\) 0.00644803 0.0860430i 0.000336127 0.00448530i
\(369\) −22.6464 + 3.32213i −1.17892 + 0.172943i
\(370\) −21.2165 26.6046i −1.10299 1.38311i
\(371\) −0.572576 1.12002i −0.0297267 0.0581488i
\(372\) 1.40590 + 3.60304i 0.0728925 + 0.186809i
\(373\) 17.2708 0.894250 0.447125 0.894471i \(-0.352448\pi\)
0.447125 + 0.894471i \(0.352448\pi\)
\(374\) −6.04348 10.4676i −0.312501 0.541268i
\(375\) −25.6615 + 32.0487i −1.32515 + 1.65499i
\(376\) −1.25518 1.16464i −0.0647311 0.0600617i
\(377\) 26.5006 12.7620i 1.36485 0.657277i
\(378\) −0.245640 13.7455i −0.0126344 0.706994i
\(379\) −13.6319 6.56479i −0.700225 0.337211i 0.0496714 0.998766i \(-0.484183\pi\)
−0.749897 + 0.661555i \(0.769897\pi\)
\(380\) 7.23519 + 18.4350i 0.371157 + 0.945693i
\(381\) −20.3648 9.85668i −1.04332 0.504973i
\(382\) −6.66233 + 2.05506i −0.340875 + 0.105146i
\(383\) −0.606594 + 0.292120i −0.0309955 + 0.0149266i −0.449317 0.893372i \(-0.648333\pi\)
0.418322 + 0.908299i \(0.362618\pi\)
\(384\) 1.65409 + 0.513793i 0.0844100 + 0.0262194i
\(385\) −23.9661 + 2.37032i −1.22142 + 0.120803i
\(386\) 5.21652 22.8550i 0.265514 1.16329i
\(387\) 19.1018 17.5842i 0.970999 0.893857i
\(388\) −0.630748 + 0.0950699i −0.0320214 + 0.00482644i
\(389\) 3.96739 + 17.3823i 0.201155 + 0.881316i 0.970235 + 0.242164i \(0.0778572\pi\)
−0.769081 + 0.639152i \(0.779286\pi\)
\(390\) −2.11721 29.0197i −0.107209 1.46947i
\(391\) −0.228701 + 0.396122i −0.0115659 + 0.0200328i
\(392\) −5.35194 4.51184i −0.270314 0.227882i
\(393\) −13.5146 0.0266420i −0.681722 0.00134391i
\(394\) −19.4200 + 13.2403i −0.978367 + 0.667039i
\(395\) 15.7367 + 4.85414i 0.791801 + 0.244238i
\(396\) −2.52411 + 6.35750i −0.126841 + 0.319477i
\(397\) 9.07447 8.41988i 0.455435 0.422582i −0.418805 0.908076i \(-0.637551\pi\)
0.874240 + 0.485495i \(0.161360\pi\)
\(398\) −9.11687 + 2.81218i −0.456987 + 0.140962i
\(399\) −19.9303 10.9343i −0.997761 0.547397i
\(400\) 10.4516 + 3.22391i 0.522582 + 0.161195i
\(401\) −2.78738 + 1.34233i −0.139195 + 0.0670327i −0.502185 0.864760i \(-0.667470\pi\)
0.362990 + 0.931793i \(0.381756\pi\)
\(402\) 3.85764 16.7491i 0.192401 0.835371i
\(403\) −8.46579 4.07691i −0.421711 0.203085i
\(404\) 6.62824 + 0.999046i 0.329767 + 0.0497044i
\(405\) −32.2476 15.8441i −1.60240 0.787299i
\(406\) −12.8976 13.2538i −0.640099 0.657774i
\(407\) −16.0579 10.9481i −0.795960 0.542677i
\(408\) −6.71841 6.25846i −0.332611 0.309840i
\(409\) −11.4045 1.71895i −0.563917 0.0849968i −0.139104 0.990278i \(-0.544422\pi\)
−0.424813 + 0.905281i \(0.639660\pi\)
\(410\) 15.2294 + 26.3780i 0.752124 + 1.30272i
\(411\) 33.2406 + 0.0655288i 1.63964 + 0.00323230i
\(412\) −5.15152 0.776467i −0.253797 0.0382538i
\(413\) 12.4026 + 17.2930i 0.610294 + 0.850932i
\(414\) 0.256112 0.0375705i 0.0125872 0.00184649i
\(415\) 11.8868 30.2870i 0.583499 1.48673i
\(416\) −3.79127 + 1.82578i −0.185882 + 0.0895161i
\(417\) 0.547274 7.11463i 0.0268001 0.348405i
\(418\) 7.05213 + 8.84309i 0.344931 + 0.432530i
\(419\) −20.0470 + 3.02161i −0.979362 + 0.147615i −0.619165 0.785261i \(-0.712529\pi\)
−0.360197 + 0.932876i \(0.617291\pi\)
\(420\) −16.8801 + 7.05356i −0.823662 + 0.344178i
\(421\) −11.8795 1.79055i −0.578972 0.0872660i −0.146974 0.989140i \(-0.546953\pi\)
−0.431998 + 0.901874i \(0.642191\pi\)
\(422\) 6.79368 + 11.7670i 0.330711 + 0.572809i
\(423\) 2.58592 4.43845i 0.125732 0.215805i
\(424\) 0.173697 + 0.442574i 0.00843550 + 0.0214933i
\(425\) −42.5033 39.4373i −2.06171 1.91299i
\(426\) −1.33625 + 17.3714i −0.0647415 + 0.841648i
\(427\) −30.6493 + 25.6578i −1.48322 + 1.24167i
\(428\) −4.89130 + 3.33483i −0.236430 + 0.161195i
\(429\) −6.04083 15.4814i −0.291654 0.747451i
\(430\) −31.1284 14.9906i −1.50114 0.722913i
\(431\) 11.5567 + 10.7231i 0.556668 + 0.516512i 0.907570 0.419900i \(-0.137935\pi\)
−0.350903 + 0.936412i \(0.614125\pi\)
\(432\) −0.418946 + 5.17924i −0.0201566 + 0.249186i
\(433\) 3.91559 + 17.1553i 0.188171 + 0.824431i 0.977580 + 0.210564i \(0.0675300\pi\)
−0.789409 + 0.613868i \(0.789613\pi\)
\(434\) −0.741353 + 5.86119i −0.0355861 + 0.281346i
\(435\) −46.2136 + 14.1553i −2.21577 + 0.678695i
\(436\) −2.37349 10.3989i −0.113669 0.498019i
\(437\) 0.156376 0.398440i 0.00748048 0.0190600i
\(438\) −11.9690 + 11.0618i −0.571900 + 0.528552i
\(439\) 28.4220 19.3778i 1.35651 0.924851i 0.356552 0.934276i \(-0.383952\pi\)
0.999956 + 0.00942438i \(0.00299992\pi\)
\(440\) 9.10252 0.433946
\(441\) 9.69692 18.6271i 0.461758 0.887006i
\(442\) 22.3070 1.06104
\(443\) −23.8443 + 16.2568i −1.13288 + 0.772383i −0.976543 0.215321i \(-0.930920\pi\)
−0.156335 + 0.987704i \(0.549968\pi\)
\(444\) −14.0991 4.37946i −0.669115 0.207840i
\(445\) 13.9646 35.5812i 0.661986 1.68671i
\(446\) 3.55226 + 15.5635i 0.168205 + 0.736953i
\(447\) 0.0729155 0.316586i 0.00344879 0.0149740i
\(448\) 1.84518 + 1.89613i 0.0871766 + 0.0895837i
\(449\) −0.617534 2.70559i −0.0291432 0.127685i 0.958264 0.285886i \(-0.0922878\pi\)
−0.987407 + 0.158201i \(0.949431\pi\)
\(450\) −2.58109 + 32.7110i −0.121674 + 1.54201i
\(451\) 12.7522 + 11.8323i 0.600478 + 0.557163i
\(452\) 8.52498 + 4.10541i 0.400981 + 0.193102i
\(453\) 4.02940 5.03233i 0.189318 0.236439i
\(454\) 14.2512 9.71627i 0.668840 0.456007i
\(455\) 18.3268 40.4919i 0.859171 1.89829i
\(456\) 7.08960 + 4.85411i 0.332001 + 0.227314i
\(457\) −9.08830 8.43271i −0.425133 0.394465i 0.438382 0.898789i \(-0.355552\pi\)
−0.863515 + 0.504323i \(0.831742\pi\)
\(458\) 1.54893 + 3.94660i 0.0723766 + 0.184413i
\(459\) 13.9135 23.7731i 0.649428 1.10963i
\(460\) −0.172232 0.298314i −0.00803034 0.0139089i
\(461\) −16.3546 2.46507i −0.761711 0.114810i −0.243312 0.969948i \(-0.578234\pi\)
−0.518400 + 0.855139i \(0.673472\pi\)
\(462\) −8.02506 + 6.69124i −0.373360 + 0.311305i
\(463\) −26.2724 + 3.95993i −1.22098 + 0.184033i −0.727737 0.685857i \(-0.759428\pi\)
−0.493246 + 0.869890i \(0.664190\pi\)
\(464\) 4.35814 + 5.46493i 0.202321 + 0.253703i
\(465\) 12.7402 + 8.72294i 0.590811 + 0.404517i
\(466\) −1.77444 + 0.854524i −0.0821992 + 0.0395850i
\(467\) −13.1315 + 33.4584i −0.607651 + 1.54827i 0.213128 + 0.977024i \(0.431635\pi\)
−0.820779 + 0.571246i \(0.806460\pi\)
\(468\) −7.83194 9.90077i −0.362031 0.457663i
\(469\) 17.3949 19.6652i 0.803222 0.908053i
\(470\) −6.75936 1.01881i −0.311786 0.0469942i
\(471\) 10.9929 + 19.1273i 0.506527 + 0.881338i
\(472\) −4.02169 6.96578i −0.185113 0.320626i
\(473\) −19.5123 2.94100i −0.897176 0.135228i
\(474\) 6.83168 2.09255i 0.313789 0.0961141i
\(475\) 44.8298 + 30.5644i 2.05693 + 1.40239i
\(476\) −4.45161 13.3002i −0.204039 0.609614i
\(477\) −1.18164 + 0.798821i −0.0541035 + 0.0365755i
\(478\) 9.56341 + 1.44145i 0.437420 + 0.0659305i
\(479\) 12.6521 + 6.09295i 0.578091 + 0.278394i 0.699995 0.714148i \(-0.253186\pi\)
−0.121904 + 0.992542i \(0.538900\pi\)
\(480\) 6.61148 2.02511i 0.301771 0.0924330i
\(481\) 32.3159 15.5625i 1.47348 0.709591i
\(482\) −3.62612 1.11851i −0.165165 0.0509467i
\(483\) 0.371134 + 0.136395i 0.0168872 + 0.00620621i
\(484\) −5.54349 + 1.70994i −0.251977 + 0.0777246i
\(485\) −1.86672 + 1.73206i −0.0847634 + 0.0786490i
\(486\) −15.4365 + 2.17129i −0.700214 + 0.0984919i
\(487\) 7.91626 + 2.44184i 0.358720 + 0.110651i 0.468876 0.883264i \(-0.344659\pi\)
−0.110156 + 0.993914i \(0.535135\pi\)
\(488\) 12.4826 8.51047i 0.565060 0.385251i
\(489\) −15.2048 26.4558i −0.687585 1.19637i
\(490\) −27.8000 2.84644i −1.25588 0.128589i
\(491\) −11.1969 + 19.3937i −0.505310 + 0.875223i 0.494671 + 0.869081i \(0.335289\pi\)
−0.999981 + 0.00614290i \(0.998045\pi\)
\(492\) 11.8948 + 5.75715i 0.536259 + 0.259552i
\(493\) −8.24535 36.1252i −0.371352 1.62700i
\(494\) −20.6413 + 3.11117i −0.928695 + 0.139978i
\(495\) 5.97149 + 26.6467i 0.268399 + 1.19768i
\(496\) 0.496883 2.17699i 0.0223107 0.0977495i
\(497\) −14.4649 + 22.3395i −0.648837 + 1.00207i
\(498\) −3.11399 13.7684i −0.139541 0.616975i
\(499\) 23.8987 11.5090i 1.06985 0.515214i 0.185793 0.982589i \(-0.440515\pi\)
0.884059 + 0.467375i \(0.154800\pi\)
\(500\) 22.6508 6.98685i 1.01298 0.312462i
\(501\) 7.35039 4.99021i 0.328391 0.222946i
\(502\) 6.75932 + 17.2225i 0.301683 + 0.768676i
\(503\) 24.7061 + 11.8978i 1.10159 + 0.530499i 0.894158 0.447751i \(-0.147775\pi\)
0.207433 + 0.978249i \(0.433489\pi\)
\(504\) −4.34023 + 6.64548i −0.193329 + 0.296013i
\(505\) 24.1100 11.6108i 1.07288 0.516672i
\(506\) −0.144217 0.133814i −0.00641123 0.00594875i
\(507\) 8.05957 + 1.23104i 0.357938 + 0.0546724i
\(508\) 6.53121 + 11.3124i 0.289775 + 0.501906i
\(509\) 3.87678 0.171835 0.0859177 0.996302i \(-0.472618\pi\)
0.0859177 + 0.996302i \(0.472618\pi\)
\(510\) −36.2352 5.53465i −1.60452 0.245079i
\(511\) −24.1326 + 6.11535i −1.06756 + 0.270527i
\(512\) −0.623490 0.781831i −0.0275546 0.0345524i
\(513\) −9.55891 + 23.9385i −0.422036 + 1.05691i
\(514\) −1.60355 + 21.3979i −0.0707295 + 0.943820i
\(515\) −18.7385 + 9.02397i −0.825716 + 0.397644i
\(516\) −14.8268 + 2.20489i −0.652712 + 0.0970649i
\(517\) −3.86051 + 0.581878i −0.169785 + 0.0255910i
\(518\) −15.7279 16.1622i −0.691045 0.710127i
\(519\) −3.60008 9.22628i −0.158026 0.404989i
\(520\) −8.39954 + 14.5484i −0.368344 + 0.637991i
\(521\) 20.3244 35.2029i 0.890428 1.54227i 0.0510653 0.998695i \(-0.483738\pi\)
0.839363 0.543572i \(-0.182928\pi\)
\(522\) −13.1389 + 16.3431i −0.575076 + 0.715319i
\(523\) 18.4612 5.69454i 0.807254 0.249005i 0.136457 0.990646i \(-0.456428\pi\)
0.670797 + 0.741641i \(0.265952\pi\)
\(524\) 6.44688 + 4.39541i 0.281633 + 0.192014i
\(525\) −27.3250 + 42.0189i −1.19256 + 1.83385i
\(526\) 12.0100 8.18830i 0.523662 0.357027i
\(527\) −7.38039 + 9.25471i −0.321495 + 0.403142i
\(528\) 3.26738 2.21824i 0.142194 0.0965364i
\(529\) 5.11632 22.4161i 0.222449 0.974612i
\(530\) 1.56824 + 1.06921i 0.0681199 + 0.0464433i
\(531\) 17.7532 16.3428i 0.770425 0.709218i
\(532\) 5.97418 + 11.6862i 0.259014 + 0.506660i
\(533\) −30.6788 + 9.46316i −1.32885 + 0.409895i
\(534\) −3.65833 16.1751i −0.158311 0.699965i
\(535\) −8.63432 + 21.9999i −0.373294 + 0.951138i
\(536\) −7.27428 + 6.74955i −0.314201 + 0.291536i
\(537\) 27.2946 18.5305i 1.17785 0.799648i
\(538\) 5.86104 + 10.1516i 0.252687 + 0.437667i
\(539\) −15.6514 + 3.12652i −0.674152 + 0.134669i
\(540\) 10.2656 + 18.0259i 0.441760 + 0.775710i
\(541\) −0.779741 10.4049i −0.0335237 0.447342i −0.988557 0.150845i \(-0.951801\pi\)
0.955034 0.296497i \(-0.0958185\pi\)
\(542\) −1.63915 7.18161i −0.0704077 0.308476i
\(543\) 13.3387 + 16.7940i 0.572420 + 0.720701i
\(544\) 1.17961 + 5.16820i 0.0505753 + 0.221585i
\(545\) −31.2149 28.9632i −1.33710 1.24065i
\(546\) −3.28923 19.0008i −0.140766 0.813160i
\(547\) 25.7375 23.8810i 1.10046 1.02108i 0.100800 0.994907i \(-0.467860\pi\)
0.999658 0.0261691i \(-0.00833083\pi\)
\(548\) −15.8568 10.8110i −0.677368 0.461822i
\(549\) 33.1024 + 30.9583i 1.41278 + 1.32127i
\(550\) 20.6052 14.0484i 0.878609 0.599026i
\(551\) 12.6681 + 32.2777i 0.539678 + 1.37508i
\(552\) −0.134521 0.0651087i −0.00572557 0.00277121i
\(553\) 10.6952 + 2.17490i 0.454807 + 0.0924861i
\(554\) 1.95381 26.0718i 0.0830094 1.10768i
\(555\) −56.3548 + 17.2616i −2.39213 + 0.732713i
\(556\) −2.56863 + 3.22096i −0.108934 + 0.136599i
\(557\) −5.67584 + 9.83084i −0.240493 + 0.416546i −0.960855 0.277052i \(-0.910642\pi\)
0.720362 + 0.693599i \(0.243976\pi\)
\(558\) 6.69886 + 0.0264116i 0.283585 + 0.00111809i
\(559\) 22.7059 28.4724i 0.960359 1.20425i
\(560\) 10.3505 + 2.10480i 0.437388 + 0.0889439i
\(561\) −20.7075 + 3.07942i −0.874272 + 0.130013i
\(562\) 7.60959 + 9.54212i 0.320991 + 0.402510i
\(563\) 7.81444 + 5.32780i 0.329340 + 0.224540i 0.716689 0.697393i \(-0.245657\pi\)
−0.387349 + 0.921933i \(0.626609\pi\)
\(564\) −2.67457 + 1.28152i −0.112620 + 0.0539615i
\(565\) 37.3522 5.62994i 1.57142 0.236854i
\(566\) 8.43457 + 10.5766i 0.354531 + 0.444568i
\(567\) −22.3012 8.34595i −0.936564 0.350497i
\(568\) 6.27170 7.86446i 0.263155 0.329985i
\(569\) 20.7111 35.8727i 0.868254 1.50386i 0.00447432 0.999990i \(-0.498576\pi\)
0.863780 0.503870i \(-0.168091\pi\)
\(570\) 34.3013 + 0.0676198i 1.43673 + 0.00283228i
\(571\) −40.0278 6.03322i −1.67511 0.252482i −0.758330 0.651871i \(-0.773984\pi\)
−0.916782 + 0.399389i \(0.869222\pi\)
\(572\) −2.13499 + 9.35400i −0.0892684 + 0.391111i
\(573\) −0.926178 + 12.0404i −0.0386917 + 0.502996i
\(574\) 11.7646 + 16.4033i 0.491043 + 0.684660i
\(575\) −0.850281 0.409474i −0.0354592 0.0170762i
\(576\) 1.87970 2.33810i 0.0783209 0.0974209i
\(577\) 34.2858 23.3756i 1.42733 0.973140i 0.429803 0.902923i \(-0.358583\pi\)
0.997532 0.0702174i \(-0.0223693\pi\)
\(578\) 2.47038 10.8234i 0.102754 0.450195i
\(579\) −33.5036 22.9392i −1.39236 0.953321i
\(580\) 26.6653 + 8.22515i 1.10722 + 0.341531i
\(581\) 5.86394 20.7501i 0.243277 0.860858i
\(582\) −0.247970 + 1.07664i −0.0102787 + 0.0446282i
\(583\) 1.03588 + 0.319527i 0.0429018 + 0.0132334i
\(584\) 9.30446 1.40242i 0.385021 0.0580326i
\(585\) −48.0993 15.0446i −1.98866 0.622018i
\(586\) 0.0651886 + 0.869882i 0.00269292 + 0.0359345i
\(587\) 2.30635 + 3.99472i 0.0951934 + 0.164880i 0.909689 0.415289i \(-0.136320\pi\)
−0.814496 + 0.580169i \(0.802986\pi\)
\(588\) −10.6725 + 5.75298i −0.440128 + 0.237249i
\(589\) 5.53851 9.59299i 0.228211 0.395272i
\(590\) −28.9308 13.9323i −1.19106 0.573585i
\(591\) 8.98065 + 39.7074i 0.369414 + 1.63335i
\(592\) 5.31449 + 6.66416i 0.218424 + 0.273895i
\(593\) 29.6924 27.5505i 1.21932 1.13137i 0.231986 0.972719i \(-0.425478\pi\)
0.987335 0.158646i \(-0.0507129\pi\)
\(594\) 8.63714 + 8.10967i 0.354386 + 0.332744i
\(595\) −44.5942 33.8596i −1.82818 1.38811i
\(596\) −0.137496 + 0.127577i −0.00563205 + 0.00522577i
\(597\) −1.26740 + 16.4764i −0.0518713 + 0.674333i
\(598\) 0.346952 0.107021i 0.0141879 0.00437640i
\(599\) −2.76669 36.9190i −0.113044 1.50847i −0.708861 0.705348i \(-0.750791\pi\)
0.595817 0.803120i \(-0.296828\pi\)
\(600\) 11.8408 14.7880i 0.483400 0.603719i
\(601\) 0.350804 + 4.68116i 0.0143096 + 0.190948i 0.999778 + 0.0210874i \(0.00671283\pi\)
−0.985468 + 0.169861i \(0.945668\pi\)
\(602\) −21.5074 7.85610i −0.876577 0.320191i
\(603\) −24.5307 16.8668i −0.998968 0.686870i
\(604\) −3.55666 + 1.09709i −0.144719 + 0.0446398i
\(605\) −14.4398 + 18.1069i −0.587060 + 0.736150i
\(606\) 5.82487 10.0432i 0.236619 0.407977i
\(607\) −40.9792 −1.66330 −0.831648 0.555303i \(-0.812602\pi\)
−0.831648 + 0.555303i \(0.812602\pi\)
\(608\) −1.81234 4.61776i −0.0734999 0.187275i
\(609\) −29.5552 + 12.3501i −1.19764 + 0.500449i
\(610\) 22.0347 56.1436i 0.892161 2.27319i
\(611\) 2.63236 6.70714i 0.106494 0.271342i
\(612\) −14.3555 + 6.84365i −0.580287 + 0.276638i
\(613\) 2.44943 32.6854i 0.0989316 1.32015i −0.698008 0.716090i \(-0.745930\pi\)
0.796939 0.604060i \(-0.206451\pi\)
\(614\) −30.5838 + 4.60977i −1.23426 + 0.186035i
\(615\) 52.1822 7.76002i 2.10419 0.312914i
\(616\) 6.00324 0.593739i 0.241877 0.0239224i
\(617\) 8.77741 + 22.3645i 0.353365 + 0.900360i 0.991461 + 0.130403i \(0.0416271\pi\)
−0.638096 + 0.769957i \(0.720278\pi\)
\(618\) −4.52714 + 7.80565i −0.182108 + 0.313989i
\(619\) −27.7485 −1.11531 −0.557654 0.830074i \(-0.688298\pi\)
−0.557654 + 0.830074i \(0.688298\pi\)
\(620\) −3.25681 8.29822i −0.130797 0.333265i
\(621\) 0.102350 0.436507i 0.00410715 0.0175164i
\(622\) −3.92744 + 1.89135i −0.157476 + 0.0758364i
\(623\) 6.88896 24.3772i 0.276000 0.976652i
\(624\) 0.530338 + 7.26913i 0.0212305 + 0.290998i
\(625\) 24.9038 31.2284i 0.996153 1.24914i
\(626\) −1.11116 14.8274i −0.0444109 0.592622i
\(627\) 18.7318 5.73756i 0.748074 0.229136i
\(628\) 0.951840 12.7014i 0.0379826 0.506842i
\(629\) −10.0547 44.0526i −0.400908 1.75649i
\(630\) 0.628629 + 31.6808i 0.0250452 + 1.26219i
\(631\) −5.82120 + 25.5043i −0.231738 + 1.01531i 0.716459 + 0.697629i \(0.245762\pi\)
−0.948197 + 0.317682i \(0.897095\pi\)
\(632\) −3.94188 1.21591i −0.156800 0.0483663i
\(633\) 23.2780 3.46168i 0.925218 0.137589i
\(634\) −12.5535 + 11.6479i −0.498563 + 0.462598i
\(635\) 46.9834 + 22.6260i 1.86448 + 0.897885i
\(636\) 0.823483 + 0.00162337i 0.0326532 + 6.43709e-5i
\(637\) 9.44555 27.9004i 0.374246 1.10545i
\(638\) 15.9376 0.630974
\(639\) 27.1368 + 13.2004i 1.07351 + 0.522201i
\(640\) −3.81483 1.17672i −0.150794 0.0465139i
\(641\) 13.9359 + 17.4750i 0.550434 + 0.690222i 0.976757 0.214349i \(-0.0687629\pi\)
−0.426323 + 0.904571i \(0.640191\pi\)
\(642\) 2.26194 + 10.0011i 0.0892718 + 0.394710i
\(643\) −3.33387 3.09338i −0.131475 0.121991i 0.611695 0.791094i \(-0.290488\pi\)
−0.743170 + 0.669103i \(0.766679\pi\)
\(644\) −0.133048 0.185508i −0.00524281 0.00731003i
\(645\) −43.9476 + 40.6165i −1.73043 + 1.59927i
\(646\) −1.96518 + 26.2235i −0.0773190 + 1.03175i
\(647\) −23.1479 21.4781i −0.910037 0.844391i 0.0782597 0.996933i \(-0.475064\pi\)
−0.988297 + 0.152542i \(0.951254\pi\)
\(648\) 8.07768 + 3.96877i 0.317321 + 0.155908i
\(649\) −18.1348 2.73337i −0.711851 0.107294i
\(650\) 3.43947 + 45.8965i 0.134907 + 1.80021i
\(651\) 8.97131 + 4.92189i 0.351613 + 0.192904i
\(652\) −1.31653 + 17.5679i −0.0515595 + 0.688013i
\(653\) 0.234612 1.02790i 0.00918108 0.0402249i −0.970130 0.242586i \(-0.922004\pi\)
0.979311 + 0.202361i \(0.0648615\pi\)
\(654\) −18.2629 2.78952i −0.714135 0.109079i
\(655\) 31.1498 1.21712
\(656\) −3.81479 6.60741i −0.148942 0.257976i
\(657\) 10.2094 + 26.3178i 0.398307 + 1.02675i
\(658\) −4.52435 0.231020i −0.176377 0.00900608i
\(659\) −11.1792 + 28.4841i −0.435479 + 1.10958i 0.529745 + 0.848157i \(0.322288\pi\)
−0.965224 + 0.261425i \(0.915807\pi\)
\(660\) 5.78890 14.6648i 0.225333 0.570827i
\(661\) −10.2349 6.97801i −0.398090 0.271413i 0.347684 0.937612i \(-0.386968\pi\)
−0.745775 + 0.666198i \(0.767920\pi\)
\(662\) 29.0740 + 19.8223i 1.12999 + 0.770416i
\(663\) 14.1865 35.9382i 0.550958 1.39572i
\(664\) −2.97751 + 7.58657i −0.115550 + 0.294416i
\(665\) 45.9867 + 25.1117i 1.78329 + 0.973788i
\(666\) −16.0222 + 19.9295i −0.620847 + 0.772252i
\(667\) −0.301559 0.522316i −0.0116764 0.0202242i
\(668\) −5.12934 −0.198460
\(669\) 27.3330 + 4.17491i 1.05675 + 0.161411i
\(670\) −8.81531 + 38.6224i −0.340565 + 1.49211i
\(671\) 2.57421 34.3505i 0.0993764 1.32609i
\(672\) 4.22827 1.76684i 0.163109 0.0681573i
\(673\) 2.24509 + 29.9586i 0.0865419 + 1.15482i 0.856298 + 0.516483i \(0.172759\pi\)
−0.769756 + 0.638338i \(0.779622\pi\)
\(674\) −27.3933 4.12888i −1.05515 0.159038i
\(675\) 51.0583 + 24.9614i 1.96524 + 0.960766i
\(676\) −3.45060 3.20168i −0.132715 0.123142i
\(677\) −1.94758 + 25.9887i −0.0748517 + 0.998826i 0.825709 + 0.564096i \(0.190775\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(678\) 12.0357 11.1234i 0.462229 0.427193i
\(679\) −1.11815 + 1.26408i −0.0429107 + 0.0485111i
\(680\) 15.5136 + 14.3945i 0.594920 + 0.552005i
\(681\) −6.59034 29.1388i −0.252542 1.11660i
\(682\) −3.17441 3.98058i −0.121554 0.152424i
\(683\) 19.5172 + 6.02025i 0.746804 + 0.230359i 0.644722 0.764417i \(-0.276973\pi\)
0.102083 + 0.994776i \(0.467449\pi\)
\(684\) 12.3290 8.33479i 0.471413 0.318689i
\(685\) −76.6162 −2.92736
\(686\) −18.5201 0.0639276i −0.707103 0.00244077i
\(687\) 7.34332 + 0.0144762i 0.280165 + 0.000552303i
\(688\) 7.79732 + 3.75499i 0.297270 + 0.143158i
\(689\) −1.46658 + 1.36078i −0.0558721 + 0.0518417i
\(690\) −0.590138 + 0.0877595i −0.0224662 + 0.00334095i
\(691\) 22.5505 + 6.95589i 0.857860 + 0.264615i 0.692322 0.721589i \(-0.256588\pi\)
0.165538 + 0.986203i \(0.447064\pi\)
\(692\) −1.27236 + 5.57459i −0.0483680 + 0.211914i
\(693\) 5.67639 + 17.1843i 0.215628 + 0.652779i
\(694\) 1.79987 + 7.88573i 0.0683220 + 0.299338i
\(695\) −1.22908 + 16.4009i −0.0466216 + 0.622122i
\(696\) 11.5760 3.54575i 0.438788 0.134401i
\(697\) 3.02248 + 40.3321i 0.114484 + 1.52769i
\(698\) 22.6264 28.3726i 0.856422 1.07392i
\(699\) 0.248215 + 3.40219i 0.00938837 + 0.128683i
\(700\) 26.6787 11.2099i 1.00836 0.423693i
\(701\) −31.8448 + 15.3357i −1.20276 + 0.579220i −0.924462 0.381274i \(-0.875485\pi\)
−0.278301 + 0.960494i \(0.589771\pi\)
\(702\) −20.9317 + 6.32125i −0.790015 + 0.238580i
\(703\) 15.4480 + 39.3608i 0.582631 + 1.48452i
\(704\) −2.28008 −0.0859338
\(705\) −5.94010 + 10.2419i −0.223717 + 0.385731i
\(706\) −1.10628 2.81876i −0.0416354 0.106085i
\(707\) 15.1435 9.23011i 0.569531 0.347134i
\(708\) −13.7800 + 2.04923i −0.517885 + 0.0770148i
\(709\) 31.0365 4.67800i 1.16560 0.175686i 0.462396 0.886674i \(-0.346990\pi\)
0.703205 + 0.710988i \(0.251752\pi\)
\(710\) 3.00097 40.0452i 0.112625 1.50287i
\(711\) 0.973467 12.3371i 0.0365079 0.462677i
\(712\) −3.49798 + 8.91271i −0.131092 + 0.334018i
\(713\) −0.0703903 + 0.179352i −0.00263614 + 0.00671677i
\(714\) −24.2586 1.28663i −0.907857 0.0481510i
\(715\) 13.9938 + 35.6555i 0.523337 + 1.33344i
\(716\) −19.0471 −0.711823
\(717\) 8.40429 14.4906i 0.313864 0.541162i
\(718\) 21.9824 27.5651i 0.820378 1.02872i
\(719\) −15.2904 + 4.71646i −0.570235 + 0.175894i −0.566447 0.824098i \(-0.691682\pi\)
−0.00378892 + 0.999993i \(0.501206\pi\)
\(720\) 0.942091 11.9395i 0.0351096 0.444957i
\(721\) −11.7697 + 7.17371i −0.438326 + 0.267163i
\(722\) −0.419104 5.59256i −0.0155974 0.208133i
\(723\) −4.10808 + 5.13059i −0.152781 + 0.190809i
\(724\) −0.925328 12.3476i −0.0343895 0.458897i
\(725\) 73.0561 22.5348i 2.71323 0.836922i
\(726\) −0.770640 + 10.0184i −0.0286011 + 0.371818i
\(727\) −10.9771 + 10.1852i −0.407118 + 0.377750i −0.856981 0.515347i \(-0.827663\pi\)
0.449864 + 0.893097i \(0.351472\pi\)
\(728\) −4.59065 + 10.1428i −0.170141 + 0.375917i
\(729\) −6.31899 + 26.2502i −0.234037 + 0.972228i
\(730\) 27.5369 25.5505i 1.01919 0.945667i
\(731\) −28.6043 35.8687i −1.05797 1.32665i
\(732\) −5.77247 25.5227i −0.213357 0.943345i
\(733\) 15.3551 + 7.39461i 0.567152 + 0.273126i 0.695408 0.718615i \(-0.255224\pi\)
−0.128256 + 0.991741i \(0.540938\pi\)
\(734\) 0.267045 0.462536i 0.00985683 0.0170725i
\(735\) −22.2657 + 42.9775i −0.821281 + 1.58525i
\(736\) 0.0431421 + 0.0747243i 0.00159024 + 0.00275438i
\(737\) 1.69084 + 22.5626i 0.0622828 + 0.831106i
\(738\) 16.8399 15.5020i 0.619884 0.570637i
\(739\) −15.1211 + 2.27915i −0.556240 + 0.0838398i −0.421146 0.906993i \(-0.638372\pi\)
−0.135095 + 0.990833i \(0.543134\pi\)
\(740\) 32.5168 + 10.0301i 1.19534 + 0.368714i
\(741\) −8.11485 + 35.2332i −0.298106 + 1.29432i
\(742\) 1.10402 + 0.602864i 0.0405297 + 0.0221318i
\(743\) −31.6442 9.76093i −1.16091 0.358094i −0.346313 0.938119i \(-0.612567\pi\)
−0.814599 + 0.580025i \(0.803043\pi\)
\(744\) −3.19128 2.18500i −0.116998 0.0801061i
\(745\) −0.166624 + 0.730026i −0.00610462 + 0.0267461i
\(746\) −14.2698 + 9.72901i −0.522456 + 0.356204i
\(747\) −24.1622 3.73935i −0.884048 0.136816i
\(748\) 10.8900 + 5.24434i 0.398177 + 0.191752i
\(749\) −4.25945 + 15.0724i −0.155637 + 0.550735i
\(750\) 3.14885 40.9355i 0.114980 1.49475i
\(751\) 1.85986 8.14857i 0.0678672 0.297346i −0.929592 0.368591i \(-0.879840\pi\)
0.997459 + 0.0712456i \(0.0226974\pi\)
\(752\) 1.69315 + 0.255201i 0.0617427 + 0.00930621i
\(753\) 32.0453 + 0.0631724i 1.16780 + 0.00230213i
\(754\) −14.7067 + 25.4728i −0.535587 + 0.927665i
\(755\) −9.26445 + 11.6173i −0.337168 + 0.422795i
\(756\) 7.94609 + 11.2187i 0.288997 + 0.408021i
\(757\) 8.91057 + 11.1735i 0.323860 + 0.406108i 0.916933 0.399041i \(-0.130657\pi\)
−0.593073 + 0.805149i \(0.702085\pi\)
\(758\) 14.9613 2.25506i 0.543419 0.0819073i
\(759\) −0.307301 + 0.147243i −0.0111543 + 0.00534457i
\(760\) −16.3628 11.1560i −0.593540 0.404669i
\(761\) 28.3434 + 35.5415i 1.02745 + 1.28838i 0.956759 + 0.290882i \(0.0939486\pi\)
0.0706898 + 0.997498i \(0.477480\pi\)
\(762\) 22.3787 3.32794i 0.810693 0.120558i
\(763\) −22.4759 17.0656i −0.813682 0.617815i
\(764\) 4.34702 5.45099i 0.157270 0.197210i
\(765\) −31.9611 + 54.8576i −1.15556 + 1.98338i
\(766\) 0.336634 0.583067i 0.0121631 0.0210671i
\(767\) 21.1029 26.4622i 0.761983 0.955496i
\(768\) −1.65610 + 0.507267i −0.0597595 + 0.0183044i
\(769\) −2.28130 + 30.4418i −0.0822656 + 1.09776i 0.791422 + 0.611271i \(0.209341\pi\)
−0.873687 + 0.486488i \(0.838278\pi\)
\(770\) 18.4665 15.4590i 0.665485 0.557104i
\(771\) 33.4537 + 16.1918i 1.20480 + 0.583132i
\(772\) 8.56462 + 21.8223i 0.308247 + 0.785402i
\(773\) 7.71016 5.25670i 0.277315 0.189070i −0.416673 0.909056i \(-0.636804\pi\)
0.693989 + 0.719986i \(0.255852\pi\)
\(774\) −5.87709 + 25.2892i −0.211248 + 0.909001i
\(775\) −20.1795 13.7581i −0.724868 0.494206i
\(776\) 0.467593 0.433863i 0.0167856 0.0155748i
\(777\) −36.0409 + 15.0602i −1.29296 + 0.540280i
\(778\) −13.0698 12.1270i −0.468575 0.434774i
\(779\) −8.42193 36.8989i −0.301747 1.32204i
\(780\) 18.0967 + 22.7846i 0.647966 + 0.815818i
\(781\) −5.10361 22.3604i −0.182621 0.800116i
\(782\) −0.0341817 0.456123i −0.00122234 0.0163109i
\(783\) 17.9740 + 31.5614i 0.642337 + 1.12791i
\(784\) 6.96359 + 0.713001i 0.248700 + 0.0254643i
\(785\) −25.4243 44.0363i −0.907434 1.57172i
\(786\) 11.1813 7.59104i 0.398824 0.270763i
\(787\) 17.1457 15.9089i 0.611180 0.567092i −0.312663 0.949864i \(-0.601221\pi\)
0.923843 + 0.382772i \(0.125031\pi\)
\(788\) 8.58702 21.8794i 0.305900 0.779421i
\(789\) −5.55395 24.5565i −0.197726 0.874234i
\(790\) −15.7367 + 4.85414i −0.559888 + 0.172703i
\(791\) 24.2671 6.14944i 0.862839 0.218649i
\(792\) −1.49579 6.67470i −0.0531507 0.237175i
\(793\) 52.5265 + 35.8120i 1.86527 + 1.27172i
\(794\) −2.75459 + 12.0687i −0.0977569 + 0.428301i
\(795\) 2.71991 1.84656i 0.0964653 0.0654908i
\(796\) 5.94855 7.45925i 0.210841 0.264386i
\(797\) −8.00391 + 5.45697i −0.283513 + 0.193296i −0.696724 0.717340i \(-0.745360\pi\)
0.413211 + 0.910635i \(0.364407\pi\)
\(798\) 22.6266 2.19281i 0.800974 0.0776247i
\(799\) −7.49971 5.11322i −0.265321 0.180893i
\(800\) −10.4516 + 3.22391i −0.369522 + 0.113982i
\(801\) −28.3858 4.39300i −1.00296 0.155219i
\(802\) 1.54688 2.67927i 0.0546221 0.0946083i
\(803\) 10.7273 18.5802i 0.378558 0.655681i
\(804\) 6.24780 + 16.0119i 0.220343 + 0.564695i
\(805\) −0.856042 0.312690i −0.0301715 0.0110209i
\(806\) 9.29137 1.40045i 0.327274 0.0493287i
\(807\) 20.0824 2.98646i 0.706934 0.105128i
\(808\) −6.03929 + 2.90837i −0.212462 + 0.102316i
\(809\) −3.49955 + 46.6982i −0.123037 + 1.64182i 0.504627 + 0.863337i \(0.331630\pi\)
−0.627665 + 0.778484i \(0.715989\pi\)
\(810\) 35.5695 5.07473i 1.24979 0.178308i
\(811\) 5.25832 + 6.59373i 0.184645 + 0.231537i 0.865535 0.500848i \(-0.166978\pi\)
−0.680890 + 0.732385i \(0.738407\pi\)
\(812\) 18.1226 + 3.68528i 0.635980 + 0.129328i
\(813\) −12.6125 1.92647i −0.442340 0.0675642i
\(814\) 19.4349 0.681194
\(815\) 35.1656 + 60.9086i 1.23180 + 2.13353i
\(816\) 9.07652 + 1.38637i 0.317742 + 0.0485327i
\(817\) 31.4710 + 29.2008i 1.10103 + 1.02161i
\(818\) 10.3912 5.00413i 0.363319 0.174965i
\(819\) −32.7035 6.78471i −1.14275 0.237077i
\(820\) −27.4423 13.2155i −0.958328 0.461507i
\(821\) −3.47360 8.85060i −0.121230 0.308888i 0.857357 0.514722i \(-0.172105\pi\)
−0.978587 + 0.205834i \(0.934009\pi\)
\(822\) −27.5016 + 18.6710i −0.959229 + 0.651225i
\(823\) −35.8871 + 11.0697i −1.25095 + 0.385865i −0.848312 0.529496i \(-0.822381\pi\)
−0.402633 + 0.915362i \(0.631905\pi\)
\(824\) 4.69378 2.26041i 0.163516 0.0787450i
\(825\) −9.52873 42.1308i −0.331748 1.46680i
\(826\) −19.9890 7.30147i −0.695507 0.254051i
\(827\) −6.59614 + 28.8996i −0.229370 + 1.00494i 0.720785 + 0.693159i \(0.243782\pi\)
−0.950155 + 0.311778i \(0.899076\pi\)
\(828\) −0.190445 + 0.175315i −0.00661843 + 0.00609262i
\(829\) −47.6519 + 7.18237i −1.65502 + 0.249454i −0.909098 0.416581i \(-0.863228\pi\)
−0.745920 + 0.666035i \(0.767990\pi\)
\(830\) 7.23997 + 31.7204i 0.251303 + 1.10103i
\(831\) −40.7609 19.7285i −1.41398 0.684374i
\(832\) 2.10399 3.64422i 0.0729429 0.126341i
\(833\) −31.6191 19.4221i −1.09554 0.672936i
\(834\) 3.55564 + 6.18667i 0.123122 + 0.214227i
\(835\) −16.9191 + 11.5353i −0.585511 + 0.399195i
\(836\) −10.8082 3.33390i −0.373810 0.115305i
\(837\) 4.30280 10.7755i 0.148727 0.372457i
\(838\) 14.8615 13.7895i 0.513382 0.476349i
\(839\) −2.85892 + 0.881861i −0.0987009 + 0.0304452i −0.343712 0.939075i \(-0.611684\pi\)
0.245011 + 0.969520i \(0.421208\pi\)
\(840\) 9.97355 15.3368i 0.344120 0.529170i
\(841\) 18.9765 + 5.85349i 0.654364 + 0.201844i
\(842\) 10.8240 5.21255i 0.373019 0.179636i
\(843\) 20.2125 6.19111i 0.696154 0.213233i
\(844\) −12.2418 5.89534i −0.421380 0.202926i
\(845\) −18.5820 2.80079i −0.639240 0.0963500i
\(846\) 0.363675 + 5.12392i 0.0125034 + 0.176164i
\(847\) −8.34215 + 12.8836i −0.286640 + 0.442687i
\(848\) −0.392826 0.267825i −0.0134897 0.00919713i
\(849\) 22.4038 6.86231i 0.768895 0.235514i
\(850\) 57.3337 + 8.64166i 1.96653 + 0.296407i
\(851\) −0.367734 0.636934i −0.0126058 0.0218338i
\(852\) −8.68160 15.1057i −0.297427 0.517512i
\(853\) −14.1080 2.12644i −0.483048 0.0728078i −0.0969960 0.995285i \(-0.530923\pi\)
−0.386052 + 0.922477i \(0.626161\pi\)
\(854\) 10.8701 38.4648i 0.371967 1.31624i
\(855\) 21.9234 55.2189i 0.749766 1.88845i
\(856\) 2.16280 5.51073i 0.0739231 0.188353i
\(857\) 7.11155 3.42474i 0.242926 0.116987i −0.308460 0.951237i \(-0.599814\pi\)
0.551386 + 0.834250i \(0.314099\pi\)
\(858\) 13.7122 + 9.38845i 0.468126 + 0.320516i
\(859\) −19.8672 24.9126i −0.677859 0.850008i 0.317296 0.948326i \(-0.397225\pi\)
−0.995155 + 0.0983187i \(0.968654\pi\)
\(860\) 34.1640 5.14940i 1.16498 0.175593i
\(861\) 33.9087 8.52159i 1.15561 0.290415i
\(862\) −15.5891 2.34968i −0.530968 0.0800305i
\(863\) −17.6783 30.6197i −0.601776 1.04231i −0.992552 0.121820i \(-0.961127\pi\)
0.390776 0.920486i \(-0.372207\pi\)
\(864\) −2.57142 4.51529i −0.0874814 0.153613i
\(865\) 8.33969 + 21.2492i 0.283558 + 0.722494i
\(866\) −12.8991 11.9686i −0.438331 0.406711i
\(867\) −15.8662 10.8633i −0.538845 0.368937i
\(868\) −2.68919 5.26036i −0.0912770 0.178548i
\(869\) −7.77134 + 5.29841i −0.263625 + 0.179736i
\(870\) 30.2095 37.7287i 1.02420 1.27912i
\(871\) −37.6218 18.1177i −1.27477 0.613895i
\(872\) 7.81900 + 7.25497i 0.264785 + 0.245684i
\(873\) 1.57684 + 1.08420i 0.0533680 + 0.0366947i
\(874\) 0.0952451 + 0.417296i 0.00322171 + 0.0141152i
\(875\) 34.0862 52.6428i 1.15232 1.77965i
\(876\) 3.65792 15.8820i 0.123590 0.536604i
\(877\) 2.95115 + 12.9298i 0.0996533 + 0.436610i 0.999999 + 0.00143429i \(0.000456550\pi\)
−0.900346 + 0.435176i \(0.856686\pi\)
\(878\) −12.5675 + 32.0214i −0.424131 + 1.08067i
\(879\) 1.44290 + 0.448192i 0.0486678 + 0.0151172i
\(880\) −7.52086 + 5.12763i −0.253528 + 0.172852i
\(881\) −8.11075 −0.273258 −0.136629 0.990622i \(-0.543627\pi\)
−0.136629 + 0.990622i \(0.543627\pi\)
\(882\) 2.48106 + 20.8529i 0.0835418 + 0.702154i
\(883\) −19.5765 −0.658801 −0.329400 0.944190i \(-0.606847\pi\)
−0.329400 + 0.944190i \(0.606847\pi\)
\(884\) −18.4309 + 12.5660i −0.619899 + 0.422640i
\(885\) −40.8449 + 37.7490i −1.37299 + 1.26892i
\(886\) 10.5433 26.8640i 0.354210 0.902513i
\(887\) 3.08003 + 13.4945i 0.103417 + 0.453101i 0.999949 + 0.0101206i \(0.00322155\pi\)
−0.896532 + 0.442980i \(0.853921\pi\)
\(888\) 14.1163 4.32384i 0.473711 0.145098i
\(889\) 32.4621 + 11.8575i 1.08874 + 0.397689i
\(890\) 8.50552 + 37.2651i 0.285106 + 1.24913i
\(891\) 18.5582 8.75755i 0.621723 0.293389i
\(892\) −11.7022 10.8581i −0.391820 0.363556i
\(893\) 7.65283 + 3.68541i 0.256092 + 0.123328i
\(894\) 0.118093 + 0.302650i 0.00394964 + 0.0101221i
\(895\) −62.8269 + 42.8346i −2.10007 + 1.43180i
\(896\) −2.59269 0.527229i −0.0866156 0.0176135i
\(897\) 0.0482323 0.627026i 0.00161043 0.0209358i
\(898\) 2.03434 + 1.88760i 0.0678869 + 0.0629899i
\(899\) −5.70234 14.5293i −0.190184 0.484580i
\(900\) −16.2942 28.4811i −0.543140 0.949370i
\(901\) 1.26018 + 2.18269i 0.0419826 + 0.0727160i
\(902\) −17.2018 2.59275i −0.572756 0.0863291i
\(903\) −26.3347 + 29.6537i −0.876365 + 0.986815i
\(904\) −9.35633 + 1.41024i −0.311187 + 0.0469039i
\(905\) −30.8206 38.6478i −1.02451 1.28470i
\(906\) −0.494437 + 6.42775i −0.0164266 + 0.213548i
\(907\) −27.4035 + 13.1969i −0.909920 + 0.438194i −0.829462 0.558564i \(-0.811353\pi\)
−0.0804582 + 0.996758i \(0.525638\pi\)
\(908\) −6.30148 + 16.0559i −0.209122 + 0.532834i
\(909\) −12.4759 15.7714i −0.413799 0.523105i
\(910\) 7.66763 + 43.7798i 0.254180 + 1.45129i
\(911\) 13.5025 + 2.03517i 0.447358 + 0.0674283i 0.368858 0.929486i \(-0.379749\pi\)
0.0784999 + 0.996914i \(0.474987\pi\)
\(912\) −8.59211 0.0169380i −0.284513 0.000560874i
\(913\) 9.29127 + 16.0930i 0.307496 + 0.532599i
\(914\) 12.2594 + 1.84781i 0.405506 + 0.0611201i
\(915\) −76.4380 71.2050i −2.52696 2.35396i
\(916\) −3.50299 2.38829i −0.115742 0.0789115i
\(917\) 20.5437 2.03184i 0.678413 0.0670972i
\(918\) 1.89598 + 27.4800i 0.0625768 + 0.906977i
\(919\) −42.2745 6.37186i −1.39451 0.210188i −0.591571 0.806253i \(-0.701492\pi\)
−0.802936 + 0.596065i \(0.796730\pi\)
\(920\) 0.310350 + 0.149457i 0.0102320 + 0.00492745i
\(921\) −12.0236 + 52.2043i −0.396192 + 1.72019i
\(922\) 14.9015 7.17616i 0.490753 0.236334i
\(923\) 40.4477 + 12.4765i 1.33135 + 0.410668i
\(924\) 2.86130 10.0492i 0.0941300 0.330596i
\(925\) 89.0876 27.4799i 2.92918 0.903533i
\(926\) 19.4766 18.0716i 0.640040 0.593870i
\(927\) 9.69635 + 12.2577i 0.318470 + 0.402595i
\(928\) −6.67937 2.06031i −0.219261 0.0676330i
\(929\) −9.26180 + 6.31459i −0.303870 + 0.207175i −0.705649 0.708562i \(-0.749344\pi\)
0.401779 + 0.915737i \(0.368392\pi\)
\(930\) −15.4402 0.0304381i −0.506305 0.000998103i
\(931\) 31.9668 + 13.5619i 1.04767 + 0.444472i
\(932\) 0.984738 1.70562i 0.0322562 0.0558693i
\(933\) 0.549386 + 7.53022i 0.0179861 + 0.246528i
\(934\) −7.99807 35.0418i −0.261705 1.14660i
\(935\) 47.7145 7.19181i 1.56043 0.235197i
\(936\) 12.0484 + 3.76851i 0.393813 + 0.123178i
\(937\) −5.18080 + 22.6986i −0.169249 + 0.741530i 0.817050 + 0.576566i \(0.195608\pi\)
−0.986300 + 0.164963i \(0.947249\pi\)
\(938\) −3.29456 + 26.0470i −0.107571 + 0.850465i
\(939\) −24.5946 7.63957i −0.802615 0.249308i
\(940\) 6.15876 2.96590i 0.200877 0.0967370i
\(941\) −14.1722 + 4.37155i −0.462001 + 0.142508i −0.517013 0.855977i \(-0.672956\pi\)
0.0550126 + 0.998486i \(0.482480\pi\)
\(942\) −19.8576 9.61116i −0.646994 0.313149i
\(943\) 0.240508 + 0.612805i 0.00783203 + 0.0199557i
\(944\) 7.24684 + 3.48990i 0.235865 + 0.113586i
\(945\) 51.4397 + 19.1351i 1.67334 + 0.622466i
\(946\) 17.7785 8.56169i 0.578030 0.278365i
\(947\) −5.57029 5.16848i −0.181010 0.167953i 0.584464 0.811420i \(-0.301305\pi\)
−0.765474 + 0.643467i \(0.777495\pi\)
\(948\) −4.46582 + 5.57737i −0.145043 + 0.181145i
\(949\) 19.7976 + 34.2905i 0.642659 + 1.11312i
\(950\) −54.2577 −1.76035
\(951\) 10.7820 + 27.6322i 0.349632 + 0.896037i
\(952\) 11.1704 + 8.48147i 0.362034 + 0.274886i
\(953\) −21.8888 27.4477i −0.709047 0.889117i 0.288616 0.957445i \(-0.406805\pi\)
−0.997663 + 0.0683279i \(0.978234\pi\)
\(954\) 0.526323 1.32566i 0.0170403 0.0429197i
\(955\) 2.08003 27.7560i 0.0673081 0.898165i
\(956\) −8.71366 + 4.19628i −0.281820 + 0.135717i
\(957\) 10.1358 25.6765i 0.327643 0.830005i
\(958\) −13.8860 + 2.09297i −0.448635 + 0.0676209i
\(959\) −50.5295 + 4.99752i −1.63168 + 0.161378i
\(960\) −4.32188 + 5.39760i −0.139488 + 0.174207i
\(961\) 13.0069 22.5286i 0.419578 0.726731i
\(962\) −17.9340 + 31.0626i −0.578215 + 1.00150i
\(963\) 17.5509 + 2.71619i 0.565571 + 0.0875280i
\(964\) 3.62612 1.11851i 0.116789 0.0360247i
\(965\) 77.3261 + 52.7201i 2.48922 + 1.69712i
\(966\) −0.383480 + 0.0963722i −0.0123383 + 0.00310072i
\(967\) −35.7252 + 24.3570i −1.14884 + 0.783268i −0.979332 0.202260i \(-0.935171\pi\)
−0.169512 + 0.985528i \(0.554219\pi\)
\(968\) 3.61700 4.53558i 0.116255 0.145779i
\(969\) 40.9981 + 19.8433i 1.31705 + 0.637459i
\(970\) 0.566651 2.48266i 0.0181941 0.0797134i
\(971\) −17.0657 11.6352i −0.547664 0.373391i 0.257651 0.966238i \(-0.417051\pi\)
−0.805315 + 0.592847i \(0.798004\pi\)
\(972\) 11.5311 10.4897i 0.369860 0.336457i
\(973\) 0.259204 + 10.8968i 0.00830970 + 0.349335i
\(974\) −7.91626 + 2.44184i −0.253653 + 0.0782417i
\(975\) 76.1298 + 23.6474i 2.43811 + 0.757323i
\(976\) −5.51947 + 14.0634i −0.176674 + 0.450157i
\(977\) 3.88828 3.60780i 0.124397 0.115424i −0.615521 0.788120i \(-0.711055\pi\)
0.739919 + 0.672697i \(0.234864\pi\)
\(978\) 27.4659 + 13.2936i 0.878262 + 0.425084i
\(979\) 10.9154 + 18.9060i 0.348858 + 0.604239i
\(980\) 24.5729 13.3085i 0.784952 0.425123i
\(981\) −16.1087 + 27.6487i −0.514310 + 0.882756i
\(982\) −1.67350 22.3312i −0.0534034 0.712619i
\(983\) 4.02415 + 17.6310i 0.128351 + 0.562340i 0.997678 + 0.0681043i \(0.0216951\pi\)
−0.869328 + 0.494236i \(0.835448\pi\)
\(984\) −13.0711 + 1.94380i −0.416691 + 0.0619661i
\(985\) −20.8798 91.4803i −0.665286 2.91481i
\(986\) 27.1627 + 25.2033i 0.865037 + 0.802637i
\(987\) −3.24952 + 7.14212i −0.103433 + 0.227336i
\(988\) 15.3020 14.1982i 0.486823 0.451706i
\(989\) −0.616982 0.420651i −0.0196189 0.0133759i
\(990\) −19.9445 18.6526i −0.633877 0.592820i
\(991\) −19.6475 + 13.3954i −0.624123 + 0.425520i −0.833658 0.552281i \(-0.813757\pi\)
0.209535 + 0.977801i \(0.432805\pi\)
\(992\) 0.815796 + 2.07861i 0.0259015 + 0.0659961i
\(993\) 50.4252 34.2339i 1.60020 1.08638i
\(994\) −0.632885 26.6061i −0.0200739 0.843895i
\(995\) 2.84635 37.9819i 0.0902354 1.20411i
\(996\) 10.3289 + 9.62178i 0.327284 + 0.304878i
\(997\) −20.4628 + 25.6596i −0.648064 + 0.812646i −0.991985 0.126352i \(-0.959673\pi\)
0.343922 + 0.938998i \(0.388245\pi\)
\(998\) −13.2628 + 22.9718i −0.419826 + 0.727159i
\(999\) 21.9182 + 38.4873i 0.693462 + 1.21769i
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 882.2.y.a.571.16 336
9.7 even 3 882.2.bb.b.277.21 yes 336
49.23 even 21 882.2.bb.b.121.21 yes 336
441.268 even 21 inner 882.2.y.a.709.16 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.y.a.571.16 336 1.1 even 1 trivial
882.2.y.a.709.16 yes 336 441.268 even 21 inner
882.2.bb.b.121.21 yes 336 49.23 even 21
882.2.bb.b.277.21 yes 336 9.7 even 3