Properties

Label 819.2.fy.a.344.11
Level $819$
Weight $2$
Character 819.344
Analytic conductor $6.540$
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] = [819,2,Mod(50,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.50");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fy (of order \(12\), degree \(4\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 344.11
Character \(\chi\) \(=\) 819.344
Dual form 819.2.fy.a.50.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.585079 + 2.18354i) q^{2} +(0.305712 - 1.70486i) q^{3} +(-2.69350 - 1.55509i) q^{4} +(0.0226908 - 0.0846831i) q^{5} +(3.54377 + 1.66501i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.77459 - 1.77459i) q^{8} +(-2.81308 - 1.04239i) q^{9} +O(q^{10})\) \(q+(-0.585079 + 2.18354i) q^{2} +(0.305712 - 1.70486i) q^{3} +(-2.69350 - 1.55509i) q^{4} +(0.0226908 - 0.0846831i) q^{5} +(3.54377 + 1.66501i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.77459 - 1.77459i) q^{8} +(-2.81308 - 1.04239i) q^{9} +(0.171633 + 0.0990926i) q^{10} +(1.90998 + 0.511778i) q^{11} +(-3.47464 + 4.11662i) q^{12} +(-3.58230 + 0.408798i) q^{13} +(1.95771 - 1.13029i) q^{14} +(-0.137436 - 0.0645732i) q^{15} +(-0.273568 - 0.473834i) q^{16} +(1.55787 + 2.69831i) q^{17} +(3.92198 - 5.53260i) q^{18} +(-2.44324 - 0.654663i) q^{19} +(-0.192807 + 0.192807i) q^{20} +(-1.42169 + 0.989346i) q^{21} +(-2.23498 + 3.87110i) q^{22} -2.36546 q^{23} +(-2.48290 - 3.56793i) q^{24} +(4.32347 + 2.49616i) q^{25} +(1.20330 - 8.06129i) q^{26} +(-2.63712 + 4.47723i) q^{27} +(0.804974 + 3.00420i) q^{28} +(-7.62726 + 4.40360i) q^{29} +(0.221409 - 0.262317i) q^{30} +(-6.17174 - 1.65371i) q^{31} +(6.04295 - 1.61920i) q^{32} +(1.45641 - 3.09979i) q^{33} +(-6.80335 + 1.82295i) q^{34} +(-0.0759248 + 0.0438352i) q^{35} +(5.95601 + 7.18227i) q^{36} +(-7.44049 + 1.99367i) q^{37} +(2.85897 - 4.95188i) q^{38} +(-0.398209 + 6.23229i) q^{39} +(-0.110011 - 0.190544i) q^{40} +(-5.12248 - 5.12248i) q^{41} +(-1.32848 - 3.68316i) q^{42} +5.94738i q^{43} +(-4.34867 - 4.34867i) q^{44} +(-0.152104 + 0.214568i) q^{45} +(1.38398 - 5.16508i) q^{46} +(0.0184044 + 0.0686863i) q^{47} +(-0.891453 + 0.321538i) q^{48} +1.00000i q^{49} +(-7.98004 + 7.98004i) q^{50} +(5.07649 - 1.83104i) q^{51} +(10.2846 + 4.46971i) q^{52} -7.25132i q^{53} +(-8.23331 - 8.37780i) q^{54} +(0.0866779 - 0.150131i) q^{55} -2.50964 q^{56} +(-1.86303 + 3.96523i) q^{57} +(-5.15291 - 19.2309i) q^{58} +(-0.992812 - 3.70523i) q^{59} +(0.269766 + 0.387653i) q^{60} -5.39486 q^{61} +(7.22191 - 12.5087i) q^{62} +(1.25207 + 2.72623i) q^{63} +13.0481i q^{64} +(-0.0466669 + 0.312636i) q^{65} +(5.91641 + 4.99376i) q^{66} +(-4.62147 + 4.62147i) q^{67} -9.69051i q^{68} +(-0.723148 + 4.03277i) q^{69} +(-0.0512941 - 0.191432i) q^{70} +(3.39106 - 12.6556i) q^{71} +(-6.84186 + 3.14224i) q^{72} +(-8.77428 - 8.77428i) q^{73} -17.4131i q^{74} +(5.57733 - 6.60780i) q^{75} +(5.56278 + 5.56278i) q^{76} +(-0.988679 - 1.71244i) q^{77} +(-13.3755 - 4.51589i) q^{78} +(-8.51984 + 14.7568i) q^{79} +(-0.0463332 + 0.0124150i) q^{80} +(6.82684 + 5.86466i) q^{81} +(14.1822 - 8.18810i) q^{82} +(10.8032 - 2.89471i) q^{83} +(5.36783 - 0.453946i) q^{84} +(0.263850 - 0.0706985i) q^{85} +(-12.9864 - 3.47969i) q^{86} +(5.17577 + 14.3496i) q^{87} +(4.29762 - 2.48123i) q^{88} +(1.29962 + 4.85023i) q^{89} +(-0.379525 - 0.457664i) q^{90} +(2.82213 + 2.24401i) q^{91} +(6.37135 + 3.67850i) q^{92} +(-4.70612 + 10.0164i) q^{93} -0.160748 q^{94} +(-0.110878 + 0.192046i) q^{95} +(-0.913111 - 10.7974i) q^{96} +(1.28086 - 1.28086i) q^{97} +(-2.18354 - 0.585079i) q^{98} +(-4.83946 - 3.43062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.585079 + 2.18354i −0.413713 + 1.54400i 0.373686 + 0.927555i \(0.378094\pi\)
−0.787399 + 0.616443i \(0.788573\pi\)
\(3\) 0.305712 1.70486i 0.176503 0.984300i
\(4\) −2.69350 1.55509i −1.34675 0.777545i
\(5\) 0.0226908 0.0846831i 0.0101476 0.0378714i −0.960666 0.277705i \(-0.910426\pi\)
0.970814 + 0.239834i \(0.0770929\pi\)
\(6\) 3.54377 + 1.66501i 1.44674 + 0.679738i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 1.77459 1.77459i 0.627411 0.627411i
\(9\) −2.81308 1.04239i −0.937694 0.347463i
\(10\) 0.171633 + 0.0990926i 0.0542753 + 0.0313358i
\(11\) 1.90998 + 0.511778i 0.575881 + 0.154307i 0.534993 0.844857i \(-0.320314\pi\)
0.0408887 + 0.999164i \(0.486981\pi\)
\(12\) −3.47464 + 4.11662i −1.00304 + 1.18837i
\(13\) −3.58230 + 0.408798i −0.993552 + 0.113380i
\(14\) 1.95771 1.13029i 0.523220 0.302081i
\(15\) −0.137436 0.0645732i −0.0354858 0.0166727i
\(16\) −0.273568 0.473834i −0.0683921 0.118459i
\(17\) 1.55787 + 2.69831i 0.377839 + 0.654436i 0.990748 0.135718i \(-0.0433341\pi\)
−0.612909 + 0.790154i \(0.710001\pi\)
\(18\) 3.92198 5.53260i 0.924419 1.30405i
\(19\) −2.44324 0.654663i −0.560517 0.150190i −0.0325730 0.999469i \(-0.510370\pi\)
−0.527944 + 0.849279i \(0.677037\pi\)
\(20\) −0.192807 + 0.192807i −0.0431130 + 0.0431130i
\(21\) −1.42169 + 0.989346i −0.310238 + 0.215893i
\(22\) −2.23498 + 3.87110i −0.476499 + 0.825321i
\(23\) −2.36546 −0.493232 −0.246616 0.969113i \(-0.579319\pi\)
−0.246616 + 0.969113i \(0.579319\pi\)
\(24\) −2.48290 3.56793i −0.506821 0.728300i
\(25\) 4.32347 + 2.49616i 0.864694 + 0.499231i
\(26\) 1.20330 8.06129i 0.235987 1.58095i
\(27\) −2.63712 + 4.47723i −0.507514 + 0.861644i
\(28\) 0.804974 + 3.00420i 0.152126 + 0.567741i
\(29\) −7.62726 + 4.40360i −1.41635 + 0.817728i −0.995976 0.0896240i \(-0.971433\pi\)
−0.420371 + 0.907352i \(0.638100\pi\)
\(30\) 0.221409 0.262317i 0.0404236 0.0478923i
\(31\) −6.17174 1.65371i −1.10848 0.297016i −0.342265 0.939603i \(-0.611194\pi\)
−0.766212 + 0.642588i \(0.777861\pi\)
\(32\) 6.04295 1.61920i 1.06825 0.286238i
\(33\) 1.45641 3.09979i 0.253529 0.539604i
\(34\) −6.80335 + 1.82295i −1.16676 + 0.312634i
\(35\) −0.0759248 + 0.0438352i −0.0128336 + 0.00740950i
\(36\) 5.95601 + 7.18227i 0.992668 + 1.19704i
\(37\) −7.44049 + 1.99367i −1.22321 + 0.327758i −0.811932 0.583752i \(-0.801584\pi\)
−0.411278 + 0.911510i \(0.634917\pi\)
\(38\) 2.85897 4.95188i 0.463786 0.803301i
\(39\) −0.398209 + 6.23229i −0.0637645 + 0.997965i
\(40\) −0.110011 0.190544i −0.0173942 0.0301277i
\(41\) −5.12248 5.12248i −0.799997 0.799997i 0.183098 0.983095i \(-0.441387\pi\)
−0.983095 + 0.183098i \(0.941387\pi\)
\(42\) −1.32848 3.68316i −0.204989 0.568324i
\(43\) 5.94738i 0.906967i 0.891265 + 0.453483i \(0.149819\pi\)
−0.891265 + 0.453483i \(0.850181\pi\)
\(44\) −4.34867 4.34867i −0.655586 0.655586i
\(45\) −0.152104 + 0.214568i −0.0226743 + 0.0319859i
\(46\) 1.38398 5.16508i 0.204057 0.761550i
\(47\) 0.0184044 + 0.0686863i 0.00268456 + 0.0100189i 0.967255 0.253806i \(-0.0816825\pi\)
−0.964571 + 0.263825i \(0.915016\pi\)
\(48\) −0.891453 + 0.321538i −0.128670 + 0.0464101i
\(49\) 1.00000i 0.142857i
\(50\) −7.98004 + 7.98004i −1.12855 + 1.12855i
\(51\) 5.07649 1.83104i 0.710851 0.256397i
\(52\) 10.2846 + 4.46971i 1.42622 + 0.619837i
\(53\) 7.25132i 0.996045i −0.867164 0.498023i \(-0.834060\pi\)
0.867164 0.498023i \(-0.165940\pi\)
\(54\) −8.23331 8.37780i −1.12041 1.14007i
\(55\) 0.0866779 0.150131i 0.0116877 0.0202436i
\(56\) −2.50964 −0.335365
\(57\) −1.86303 + 3.96523i −0.246765 + 0.525208i
\(58\) −5.15291 19.2309i −0.676610 2.52514i
\(59\) −0.992812 3.70523i −0.129253 0.482379i 0.870702 0.491810i \(-0.163665\pi\)
−0.999956 + 0.00943103i \(0.996998\pi\)
\(60\) 0.269766 + 0.387653i 0.0348266 + 0.0500458i
\(61\) −5.39486 −0.690741 −0.345371 0.938466i \(-0.612247\pi\)
−0.345371 + 0.938466i \(0.612247\pi\)
\(62\) 7.22191 12.5087i 0.917183 1.58861i
\(63\) 1.25207 + 2.72623i 0.157746 + 0.343473i
\(64\) 13.0481i 1.63102i
\(65\) −0.0466669 + 0.312636i −0.00578832 + 0.0387778i
\(66\) 5.91641 + 4.99376i 0.728260 + 0.614690i
\(67\) −4.62147 + 4.62147i −0.564603 + 0.564603i −0.930611 0.366009i \(-0.880724\pi\)
0.366009 + 0.930611i \(0.380724\pi\)
\(68\) 9.69051i 1.17515i
\(69\) −0.723148 + 4.03277i −0.0870568 + 0.485488i
\(70\) −0.0512941 0.191432i −0.00613082 0.0228805i
\(71\) 3.39106 12.6556i 0.402445 1.50195i −0.406274 0.913751i \(-0.633172\pi\)
0.808719 0.588195i \(-0.200161\pi\)
\(72\) −6.84186 + 3.14224i −0.806321 + 0.370317i
\(73\) −8.77428 8.77428i −1.02695 1.02695i −0.999627 0.0273256i \(-0.991301\pi\)
−0.0273256 0.999627i \(-0.508699\pi\)
\(74\) 17.4131i 2.02423i
\(75\) 5.57733 6.60780i 0.644014 0.763003i
\(76\) 5.56278 + 5.56278i 0.638095 + 0.638095i
\(77\) −0.988679 1.71244i −0.112670 0.195151i
\(78\) −13.3755 4.51589i −1.51448 0.511324i
\(79\) −8.51984 + 14.7568i −0.958557 + 1.66027i −0.232547 + 0.972585i \(0.574706\pi\)
−0.726010 + 0.687684i \(0.758627\pi\)
\(80\) −0.0463332 + 0.0124150i −0.00518021 + 0.00138803i
\(81\) 6.82684 + 5.86466i 0.758538 + 0.651628i
\(82\) 14.1822 8.18810i 1.56616 0.904225i
\(83\) 10.8032 2.89471i 1.18581 0.317736i 0.388579 0.921415i \(-0.372966\pi\)
0.797227 + 0.603679i \(0.206299\pi\)
\(84\) 5.36783 0.453946i 0.585678 0.0495295i
\(85\) 0.263850 0.0706985i 0.0286186 0.00766833i
\(86\) −12.9864 3.47969i −1.40036 0.375224i
\(87\) 5.17577 + 14.3496i 0.554901 + 1.53844i
\(88\) 4.29762 2.48123i 0.458128 0.264500i
\(89\) 1.29962 + 4.85023i 0.137759 + 0.514124i 0.999971 + 0.00757652i \(0.00241170\pi\)
−0.862212 + 0.506547i \(0.830922\pi\)
\(90\) −0.379525 0.457664i −0.0400055 0.0482421i
\(91\) 2.82213 + 2.24401i 0.295840 + 0.235236i
\(92\) 6.37135 + 3.67850i 0.664259 + 0.383510i
\(93\) −4.70612 + 10.0164i −0.488002 + 1.03865i
\(94\) −0.160748 −0.0165798
\(95\) −0.110878 + 0.192046i −0.0113758 + 0.0197035i
\(96\) −0.913111 10.7974i −0.0931940 1.10200i
\(97\) 1.28086 1.28086i 0.130051 0.130051i −0.639085 0.769136i \(-0.720687\pi\)
0.769136 + 0.639085i \(0.220687\pi\)
\(98\) −2.18354 0.585079i −0.220571 0.0591019i
\(99\) −4.83946 3.43062i −0.486384 0.344790i
\(100\) −7.76350 13.4468i −0.776350 1.34468i
\(101\) 8.55549 + 14.8185i 0.851303 + 1.47450i 0.880033 + 0.474913i \(0.157521\pi\)
−0.0287295 + 0.999587i \(0.509146\pi\)
\(102\) 1.02801 + 12.1560i 0.101788 + 1.20363i
\(103\) 15.2918 8.82874i 1.50675 0.869922i 0.506780 0.862075i \(-0.330836\pi\)
0.999969 0.00784662i \(-0.00249768\pi\)
\(104\) −5.63165 + 7.08255i −0.552229 + 0.694501i
\(105\) 0.0515217 + 0.142842i 0.00502800 + 0.0139399i
\(106\) 15.8336 + 4.24259i 1.53789 + 0.412077i
\(107\) −1.85310 1.06989i −0.179146 0.103430i 0.407745 0.913096i \(-0.366315\pi\)
−0.586891 + 0.809666i \(0.699648\pi\)
\(108\) 14.0656 7.95844i 1.35346 0.765802i
\(109\) −4.68158 + 4.68158i −0.448414 + 0.448414i −0.894827 0.446413i \(-0.852701\pi\)
0.446413 + 0.894827i \(0.352701\pi\)
\(110\) 0.277103 + 0.277103i 0.0264208 + 0.0264208i
\(111\) 1.12428 + 13.2945i 0.106712 + 1.26186i
\(112\) −0.141609 + 0.528493i −0.0133808 + 0.0499379i
\(113\) 5.40533 + 3.12077i 0.508491 + 0.293577i 0.732213 0.681076i \(-0.238488\pi\)
−0.223722 + 0.974653i \(0.571821\pi\)
\(114\) −7.56823 6.38799i −0.708830 0.598290i
\(115\) −0.0536741 + 0.200314i −0.00500513 + 0.0186794i
\(116\) 27.3920 2.54328
\(117\) 10.5034 + 2.58417i 0.971042 + 0.238907i
\(118\) 8.67139 0.798267
\(119\) 0.806412 3.00957i 0.0739237 0.275887i
\(120\) −0.358482 + 0.129301i −0.0327248 + 0.0118035i
\(121\) −6.14017 3.54503i −0.558197 0.322275i
\(122\) 3.15642 11.7799i 0.285769 1.06650i
\(123\) −10.2991 + 7.16709i −0.928639 + 0.646235i
\(124\) 14.0519 + 14.0519i 1.26190 + 1.26190i
\(125\) 0.619447 0.619447i 0.0554050 0.0554050i
\(126\) −6.68540 + 1.13888i −0.595583 + 0.101460i
\(127\) 0.491066 + 0.283517i 0.0435750 + 0.0251581i 0.521629 0.853172i \(-0.325324\pi\)
−0.478054 + 0.878330i \(0.658658\pi\)
\(128\) −16.4053 4.39578i −1.45004 0.388536i
\(129\) 10.1394 + 1.81818i 0.892728 + 0.160082i
\(130\) −0.655352 0.284816i −0.0574781 0.0249800i
\(131\) 5.62317 3.24654i 0.491298 0.283651i −0.233815 0.972281i \(-0.575121\pi\)
0.725113 + 0.688630i \(0.241788\pi\)
\(132\) −8.74330 + 6.08442i −0.761006 + 0.529581i
\(133\) 1.26471 + 2.19054i 0.109664 + 0.189944i
\(134\) −7.38726 12.7951i −0.638162 1.10533i
\(135\) 0.319308 + 0.324911i 0.0274816 + 0.0279639i
\(136\) 7.55295 + 2.02381i 0.647660 + 0.173540i
\(137\) 7.96257 7.96257i 0.680288 0.680288i −0.279777 0.960065i \(-0.590260\pi\)
0.960065 + 0.279777i \(0.0902605\pi\)
\(138\) −8.38263 3.93851i −0.713577 0.335269i
\(139\) 5.80681 10.0577i 0.492527 0.853082i −0.507436 0.861690i \(-0.669407\pi\)
0.999963 + 0.00860748i \(0.00273988\pi\)
\(140\) 0.272671 0.0230449
\(141\) 0.122727 0.0103787i 0.0103355 0.000874047i
\(142\) 25.6501 + 14.8091i 2.15251 + 1.24275i
\(143\) −7.05135 1.05255i −0.589663 0.0880184i
\(144\) 0.275649 + 1.61810i 0.0229708 + 0.134842i
\(145\) 0.199842 + 0.745821i 0.0165960 + 0.0619371i
\(146\) 24.2927 14.0254i 2.01048 1.16075i
\(147\) 1.70486 + 0.305712i 0.140614 + 0.0252147i
\(148\) 23.1413 + 6.20069i 1.90220 + 0.509693i
\(149\) −11.1182 + 2.97911i −0.910839 + 0.244058i −0.683665 0.729796i \(-0.739615\pi\)
−0.227173 + 0.973854i \(0.572948\pi\)
\(150\) 11.1652 + 16.0444i 0.911638 + 1.31002i
\(151\) 6.88461 1.84472i 0.560261 0.150122i 0.0324349 0.999474i \(-0.489674\pi\)
0.527826 + 0.849352i \(0.323007\pi\)
\(152\) −5.49748 + 3.17397i −0.445905 + 0.257443i
\(153\) −1.56972 9.21446i −0.126904 0.744945i
\(154\) 4.31765 1.15691i 0.347926 0.0932265i
\(155\) −0.280083 + 0.485118i −0.0224968 + 0.0389656i
\(156\) 10.7643 16.1674i 0.861838 1.29443i
\(157\) −6.99918 12.1229i −0.558596 0.967516i −0.997614 0.0690378i \(-0.978007\pi\)
0.439019 0.898478i \(-0.355326\pi\)
\(158\) −27.2373 27.2373i −2.16689 2.16689i
\(159\) −12.3625 2.21681i −0.980408 0.175805i
\(160\) 0.548477i 0.0433609i
\(161\) 1.67263 + 1.67263i 0.131822 + 0.131822i
\(162\) −16.8000 + 11.4754i −1.31993 + 0.901595i
\(163\) −0.0941290 + 0.351294i −0.00737275 + 0.0275155i −0.969514 0.245035i \(-0.921201\pi\)
0.962141 + 0.272551i \(0.0878672\pi\)
\(164\) 5.83146 + 21.7633i 0.455360 + 1.69943i
\(165\) −0.229453 0.193670i −0.0178629 0.0150772i
\(166\) 25.2829i 1.96233i
\(167\) −6.97223 + 6.97223i −0.539527 + 0.539527i −0.923390 0.383863i \(-0.874593\pi\)
0.383863 + 0.923390i \(0.374593\pi\)
\(168\) −0.767227 + 4.27858i −0.0591929 + 0.330100i
\(169\) 12.6658 2.92888i 0.974290 0.225298i
\(170\) 0.617493i 0.0473596i
\(171\) 6.19060 + 4.38842i 0.473407 + 0.335591i
\(172\) 9.24871 16.0192i 0.705208 1.22146i
\(173\) −6.44720 −0.490171 −0.245086 0.969501i \(-0.578816\pi\)
−0.245086 + 0.969501i \(0.578816\pi\)
\(174\) −34.3613 + 2.90586i −2.60492 + 0.220292i
\(175\) −1.29211 4.82220i −0.0976740 0.364524i
\(176\) −0.280013 1.04502i −0.0211067 0.0787714i
\(177\) −6.62040 + 0.559872i −0.497619 + 0.0420826i
\(178\) −11.3511 −0.850799
\(179\) −6.02414 + 10.4341i −0.450266 + 0.779883i −0.998402 0.0565059i \(-0.982004\pi\)
0.548137 + 0.836389i \(0.315337\pi\)
\(180\) 0.743363 0.341402i 0.0554070 0.0254466i
\(181\) 9.52948i 0.708320i 0.935185 + 0.354160i \(0.115233\pi\)
−0.935185 + 0.354160i \(0.884767\pi\)
\(182\) −6.55106 + 4.84933i −0.485597 + 0.359456i
\(183\) −1.64927 + 9.19747i −0.121918 + 0.679897i
\(184\) −4.19771 + 4.19771i −0.309459 + 0.309459i
\(185\) 0.675322i 0.0496507i
\(186\) −19.1177 16.1364i −1.40178 1.18318i
\(187\) 1.59457 + 5.95100i 0.116606 + 0.435180i
\(188\) 0.0572411 0.213627i 0.00417474 0.0155803i
\(189\) 5.03061 1.30116i 0.365923 0.0946451i
\(190\) −0.354469 0.354469i −0.0257159 0.0257159i
\(191\) 24.1986i 1.75095i 0.483265 + 0.875474i \(0.339451\pi\)
−0.483265 + 0.875474i \(0.660549\pi\)
\(192\) 22.2452 + 3.98897i 1.60541 + 0.287879i
\(193\) 6.28304 + 6.28304i 0.452263 + 0.452263i 0.896105 0.443842i \(-0.146385\pi\)
−0.443842 + 0.896105i \(0.646385\pi\)
\(194\) 2.04740 + 3.54621i 0.146995 + 0.254603i
\(195\) 0.518734 + 0.175137i 0.0371473 + 0.0125418i
\(196\) 1.55509 2.69350i 0.111078 0.192393i
\(197\) −3.75223 + 1.00541i −0.267336 + 0.0716323i −0.389997 0.920816i \(-0.627524\pi\)
0.122661 + 0.992449i \(0.460857\pi\)
\(198\) 10.3224 8.55999i 0.733579 0.608332i
\(199\) 12.6432 7.29957i 0.896255 0.517453i 0.0202714 0.999795i \(-0.493547\pi\)
0.875983 + 0.482342i \(0.160214\pi\)
\(200\) 12.1020 3.24272i 0.855741 0.229295i
\(201\) 6.46612 + 9.29180i 0.456085 + 0.655393i
\(202\) −37.3626 + 10.0113i −2.62882 + 0.704391i
\(203\) 8.50710 + 2.27947i 0.597082 + 0.159988i
\(204\) −16.5209 2.96250i −1.15670 0.207417i
\(205\) −0.550020 + 0.317554i −0.0384151 + 0.0221790i
\(206\) 10.3310 + 38.5559i 0.719796 + 2.68632i
\(207\) 6.65422 + 2.46573i 0.462501 + 0.171380i
\(208\) 1.17371 + 1.58558i 0.0813819 + 0.109940i
\(209\) −4.33149 2.50079i −0.299616 0.172983i
\(210\) −0.342046 + 0.0289261i −0.0236034 + 0.00199609i
\(211\) −23.8468 −1.64168 −0.820842 0.571155i \(-0.806496\pi\)
−0.820842 + 0.571155i \(0.806496\pi\)
\(212\) −11.2765 + 19.5314i −0.774470 + 1.34142i
\(213\) −20.5394 9.65026i −1.40733 0.661225i
\(214\) 3.42036 3.42036i 0.233811 0.233811i
\(215\) 0.503643 + 0.134951i 0.0343481 + 0.00920356i
\(216\) 3.26544 + 12.6250i 0.222185 + 0.859024i
\(217\) 3.19473 + 5.53343i 0.216872 + 0.375634i
\(218\) −7.48334 12.9615i −0.506836 0.877865i
\(219\) −17.6413 + 12.2765i −1.19209 + 0.829569i
\(220\) −0.466933 + 0.269584i −0.0314806 + 0.0181754i
\(221\) −6.68382 9.02930i −0.449602 0.607376i
\(222\) −29.6869 5.32339i −1.99245 0.357283i
\(223\) −21.5109 5.76383i −1.44048 0.385974i −0.547776 0.836625i \(-0.684525\pi\)
−0.892700 + 0.450651i \(0.851192\pi\)
\(224\) −5.41796 3.12806i −0.362003 0.209003i
\(225\) −9.56030 11.5286i −0.637353 0.768576i
\(226\) −9.97688 + 9.97688i −0.663652 + 0.663652i
\(227\) 11.3980 + 11.3980i 0.756515 + 0.756515i 0.975686 0.219171i \(-0.0703354\pi\)
−0.219171 + 0.975686i \(0.570335\pi\)
\(228\) 11.1844 7.78315i 0.740703 0.515451i
\(229\) 4.05899 15.1484i 0.268226 1.00103i −0.692021 0.721878i \(-0.743279\pi\)
0.960246 0.279154i \(-0.0900540\pi\)
\(230\) −0.405992 0.234399i −0.0267703 0.0154558i
\(231\) −3.22172 + 1.16204i −0.211974 + 0.0764569i
\(232\) −5.72066 + 21.3498i −0.375580 + 1.40168i
\(233\) −7.39188 −0.484258 −0.242129 0.970244i \(-0.577846\pi\)
−0.242129 + 0.970244i \(0.577846\pi\)
\(234\) −11.7880 + 21.4228i −0.770605 + 1.40045i
\(235\) 0.00623418 0.000406673
\(236\) −3.08783 + 11.5239i −0.201000 + 0.750143i
\(237\) 22.5536 + 19.0364i 1.46502 + 1.23655i
\(238\) 6.09972 + 3.52167i 0.395386 + 0.228276i
\(239\) 2.65725 9.91699i 0.171883 0.641477i −0.825178 0.564872i \(-0.808925\pi\)
0.997062 0.0766046i \(-0.0244079\pi\)
\(240\) 0.00700111 + 0.0827870i 0.000451920 + 0.00534388i
\(241\) −9.92762 9.92762i −0.639494 0.639494i 0.310936 0.950431i \(-0.399357\pi\)
−0.950431 + 0.310936i \(0.899357\pi\)
\(242\) 11.3332 11.3332i 0.728526 0.728526i
\(243\) 12.0855 9.84590i 0.775282 0.631615i
\(244\) 14.5310 + 8.38950i 0.930254 + 0.537082i
\(245\) 0.0846831 + 0.0226908i 0.00541021 + 0.00144966i
\(246\) −9.62388 26.6819i −0.613596 1.70117i
\(247\) 9.02003 + 1.34641i 0.573931 + 0.0856700i
\(248\) −13.8869 + 8.01762i −0.881821 + 0.509120i
\(249\) −1.63240 19.3029i −0.103449 1.22327i
\(250\) 0.990164 + 1.71501i 0.0626235 + 0.108467i
\(251\) 5.77140 + 9.99635i 0.364287 + 0.630964i 0.988662 0.150161i \(-0.0479793\pi\)
−0.624374 + 0.781125i \(0.714646\pi\)
\(252\) 0.867097 9.29017i 0.0546220 0.585225i
\(253\) −4.51798 1.21059i −0.284043 0.0761091i
\(254\) −0.906384 + 0.906384i −0.0568716 + 0.0568716i
\(255\) −0.0398687 0.471441i −0.00249668 0.0295228i
\(256\) 6.14863 10.6497i 0.384289 0.665608i
\(257\) 7.72844 0.482087 0.241043 0.970514i \(-0.422510\pi\)
0.241043 + 0.970514i \(0.422510\pi\)
\(258\) −9.90245 + 21.0761i −0.616500 + 1.31214i
\(259\) 6.67096 + 3.85148i 0.414514 + 0.239320i
\(260\) 0.611875 0.769514i 0.0379469 0.0477232i
\(261\) 26.0464 4.43710i 1.61223 0.274650i
\(262\) 3.79896 + 14.1779i 0.234700 + 0.875914i
\(263\) −6.00298 + 3.46582i −0.370160 + 0.213712i −0.673528 0.739162i \(-0.735222\pi\)
0.303369 + 0.952873i \(0.401889\pi\)
\(264\) −2.91631 8.08537i −0.179487 0.497620i
\(265\) −0.614064 0.164538i −0.0377217 0.0101075i
\(266\) −5.52311 + 1.47991i −0.338643 + 0.0907392i
\(267\) 8.66627 0.732887i 0.530367 0.0448520i
\(268\) 19.6347 5.26111i 1.19938 0.321373i
\(269\) 0.299119 0.172697i 0.0182376 0.0105295i −0.490853 0.871242i \(-0.663315\pi\)
0.509091 + 0.860713i \(0.329982\pi\)
\(270\) −0.896278 + 0.507123i −0.0545458 + 0.0308626i
\(271\) −13.3856 + 3.58667i −0.813120 + 0.217875i −0.641336 0.767260i \(-0.721620\pi\)
−0.171784 + 0.985135i \(0.554953\pi\)
\(272\) 0.852367 1.47634i 0.0516823 0.0895164i
\(273\) 4.68847 4.12532i 0.283759 0.249676i
\(274\) 12.7279 + 22.0453i 0.768920 + 1.33181i
\(275\) 6.98027 + 6.98027i 0.420926 + 0.420926i
\(276\) 8.21912 9.73769i 0.494733 0.586140i
\(277\) 30.8361i 1.85276i −0.376588 0.926381i \(-0.622903\pi\)
0.376588 0.926381i \(-0.377097\pi\)
\(278\) 18.5640 + 18.5640i 1.11339 + 1.11339i
\(279\) 15.6378 + 11.0854i 0.936210 + 0.663665i
\(280\) −0.0569457 + 0.212524i −0.00340316 + 0.0127008i
\(281\) −0.0627560 0.234209i −0.00374371 0.0139717i 0.964029 0.265798i \(-0.0856355\pi\)
−0.967772 + 0.251826i \(0.918969\pi\)
\(282\) −0.0491424 + 0.274052i −0.00292639 + 0.0163195i
\(283\) 11.8324i 0.703365i 0.936119 + 0.351682i \(0.114390\pi\)
−0.936119 + 0.351682i \(0.885610\pi\)
\(284\) −28.8145 + 28.8145i −1.70982 + 1.70982i
\(285\) 0.293514 + 0.247742i 0.0173863 + 0.0146749i
\(286\) 6.42387 14.7811i 0.379852 0.874025i
\(287\) 7.24428i 0.427616i
\(288\) −18.6872 1.74416i −1.10115 0.102776i
\(289\) 3.64609 6.31521i 0.214476 0.371483i
\(290\) −1.74546 −0.102497
\(291\) −1.79210 2.57525i −0.105055 0.150964i
\(292\) 9.98869 + 37.2783i 0.584544 + 2.18155i
\(293\) 0.456027 + 1.70192i 0.0266414 + 0.0994270i 0.977966 0.208763i \(-0.0669436\pi\)
−0.951325 + 0.308190i \(0.900277\pi\)
\(294\) −1.66501 + 3.54377i −0.0971054 + 0.206677i
\(295\) −0.336298 −0.0195800
\(296\) −9.66585 + 16.7417i −0.561816 + 0.973094i
\(297\) −7.32820 + 7.20181i −0.425225 + 0.417891i
\(298\) 26.0201i 1.50730i
\(299\) 8.47378 0.966995i 0.490052 0.0559228i
\(300\) −25.2982 + 9.12482i −1.46059 + 0.526822i
\(301\) 4.20543 4.20543i 0.242397 0.242397i
\(302\) 16.1121i 0.927150i
\(303\) 27.8790 10.0557i 1.60161 0.577684i
\(304\) 0.358190 + 1.33678i 0.0205436 + 0.0766698i
\(305\) −0.122414 + 0.456854i −0.00700938 + 0.0261594i
\(306\) 21.0386 + 1.96364i 1.20270 + 0.112254i
\(307\) 17.8862 + 17.8862i 1.02082 + 1.02082i 0.999779 + 0.0210412i \(0.00669811\pi\)
0.0210412 + 0.999779i \(0.493302\pi\)
\(308\) 6.14994i 0.350426i
\(309\) −10.3769 28.7695i −0.590319 1.63664i
\(310\) −0.895406 0.895406i −0.0508556 0.0508556i
\(311\) −0.905589 1.56853i −0.0513513 0.0889430i 0.839207 0.543812i \(-0.183019\pi\)
−0.890558 + 0.454869i \(0.849686\pi\)
\(312\) 10.3531 + 11.7664i 0.586127 + 0.666140i
\(313\) 6.00459 10.4003i 0.339399 0.587857i −0.644920 0.764250i \(-0.723110\pi\)
0.984320 + 0.176393i \(0.0564429\pi\)
\(314\) 30.5660 8.19015i 1.72494 0.462197i
\(315\) 0.259276 0.0441687i 0.0146085 0.00248862i
\(316\) 45.8963 26.4982i 2.58187 1.49064i
\(317\) 29.0154 7.77466i 1.62967 0.436668i 0.675847 0.737042i \(-0.263778\pi\)
0.953822 + 0.300373i \(0.0971113\pi\)
\(318\) 12.0735 25.6970i 0.677050 1.44102i
\(319\) −16.8216 + 4.50733i −0.941829 + 0.252362i
\(320\) 1.10496 + 0.296072i 0.0617690 + 0.0165510i
\(321\) −2.39052 + 2.83220i −0.133426 + 0.158078i
\(322\) −4.63089 + 2.67364i −0.258069 + 0.148996i
\(323\) −2.03976 7.61248i −0.113495 0.423570i
\(324\) −9.26800 26.4128i −0.514889 1.46738i
\(325\) −16.5084 7.17456i −0.915721 0.397973i
\(326\) −0.711993 0.411069i −0.0394337 0.0227670i
\(327\) 6.55021 + 9.41264i 0.362227 + 0.520520i
\(328\) −18.1805 −1.00385
\(329\) 0.0355546 0.0615824i 0.00196019 0.00339515i
\(330\) 0.557135 0.387708i 0.0306693 0.0213426i
\(331\) −7.29804 + 7.29804i −0.401137 + 0.401137i −0.878633 0.477497i \(-0.841544\pi\)
0.477497 + 0.878633i \(0.341544\pi\)
\(332\) −33.5999 9.00308i −1.84404 0.494108i
\(333\) 23.0089 + 2.14753i 1.26088 + 0.117684i
\(334\) −11.1449 19.3035i −0.609820 1.05624i
\(335\) 0.286496 + 0.496226i 0.0156529 + 0.0271117i
\(336\) 0.857714 + 0.402991i 0.0467922 + 0.0219849i
\(337\) −12.8631 + 7.42650i −0.700696 + 0.404547i −0.807607 0.589722i \(-0.799237\pi\)
0.106911 + 0.994269i \(0.465904\pi\)
\(338\) −1.01514 + 29.3699i −0.0552165 + 1.59751i
\(339\) 6.97294 8.26126i 0.378718 0.448690i
\(340\) −0.820622 0.219885i −0.0445045 0.0119249i
\(341\) −10.9416 6.31712i −0.592520 0.342091i
\(342\) −13.2043 + 10.9499i −0.714007 + 0.592102i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 10.5541 + 10.5541i 0.569041 + 0.569041i
\(345\) 0.325099 + 0.152745i 0.0175027 + 0.00822352i
\(346\) 3.77212 14.0777i 0.202790 0.756824i
\(347\) 23.9646 + 13.8360i 1.28649 + 0.742754i 0.978026 0.208483i \(-0.0668526\pi\)
0.308462 + 0.951237i \(0.400186\pi\)
\(348\) 8.37406 46.6995i 0.448897 2.50335i
\(349\) 0.931805 3.47754i 0.0498784 0.186149i −0.936492 0.350689i \(-0.885947\pi\)
0.986370 + 0.164540i \(0.0526141\pi\)
\(350\) 11.2855 0.603234
\(351\) 7.61667 17.1168i 0.406548 0.913629i
\(352\) 12.3706 0.659356
\(353\) 5.39162 20.1218i 0.286967 1.07098i −0.660423 0.750894i \(-0.729623\pi\)
0.947390 0.320082i \(-0.103710\pi\)
\(354\) 2.65095 14.7835i 0.140896 0.785734i
\(355\) −0.994772 0.574332i −0.0527970 0.0304824i
\(356\) 4.04204 15.0851i 0.214228 0.799509i
\(357\) −4.88436 2.29488i −0.258508 0.121458i
\(358\) −19.2588 19.2588i −1.01786 1.01786i
\(359\) −9.96897 + 9.96897i −0.526142 + 0.526142i −0.919420 0.393278i \(-0.871341\pi\)
0.393278 + 0.919420i \(0.371341\pi\)
\(360\) 0.110848 + 0.650690i 0.00584218 + 0.0342944i
\(361\) −10.9137 6.30101i −0.574404 0.331632i
\(362\) −20.8080 5.57550i −1.09365 0.293042i
\(363\) −7.92089 + 9.38435i −0.415739 + 0.492551i
\(364\) −4.11177 10.4329i −0.215515 0.546832i
\(365\) −0.942129 + 0.543938i −0.0493133 + 0.0284710i
\(366\) −19.1181 8.98250i −0.999320 0.469523i
\(367\) −7.43645 12.8803i −0.388180 0.672347i 0.604025 0.796965i \(-0.293563\pi\)
−0.992205 + 0.124619i \(0.960229\pi\)
\(368\) 0.647114 + 1.12083i 0.0337332 + 0.0584276i
\(369\) 9.07032 + 19.7496i 0.472182 + 1.02812i
\(370\) −1.47460 0.395117i −0.0766606 0.0205411i
\(371\) −5.12746 + 5.12746i −0.266204 + 0.266204i
\(372\) 28.2523 19.6606i 1.46481 1.01936i
\(373\) 11.6008 20.0932i 0.600667 1.04039i −0.392053 0.919942i \(-0.628235\pi\)
0.992720 0.120443i \(-0.0384315\pi\)
\(374\) −13.9272 −0.720159
\(375\) −0.866697 1.24544i −0.0447560 0.0643143i
\(376\) 0.154550 + 0.0892294i 0.00797030 + 0.00460166i
\(377\) 25.5230 18.8930i 1.31450 0.973041i
\(378\) −0.102170 + 11.7458i −0.00525508 + 0.604140i
\(379\) 4.87506 + 18.1940i 0.250415 + 0.934561i 0.970584 + 0.240763i \(0.0773976\pi\)
−0.720169 + 0.693799i \(0.755936\pi\)
\(380\) 0.597298 0.344850i 0.0306407 0.0176904i
\(381\) 0.633481 0.750523i 0.0324542 0.0384505i
\(382\) −52.8387 14.1581i −2.70346 0.724390i
\(383\) 16.7798 4.49615i 0.857410 0.229742i 0.196774 0.980449i \(-0.436953\pi\)
0.660636 + 0.750706i \(0.270287\pi\)
\(384\) −12.5095 + 26.6248i −0.638372 + 1.35869i
\(385\) −0.167449 + 0.0448678i −0.00853399 + 0.00228667i
\(386\) −17.3954 + 10.0432i −0.885400 + 0.511186i
\(387\) 6.19949 16.7305i 0.315138 0.850457i
\(388\) −5.44183 + 1.45813i −0.276267 + 0.0740255i
\(389\) 12.2562 21.2284i 0.621416 1.07632i −0.367806 0.929903i \(-0.619891\pi\)
0.989222 0.146422i \(-0.0467757\pi\)
\(390\) −0.685920 + 1.03021i −0.0347329 + 0.0521667i
\(391\) −3.68507 6.38273i −0.186362 0.322789i
\(392\) 1.77459 + 1.77459i 0.0896301 + 0.0896301i
\(393\) −3.81581 10.5792i −0.192482 0.533650i
\(394\) 8.78141i 0.442401i
\(395\) 1.05633 + 1.05633i 0.0531497 + 0.0531497i
\(396\) 7.70014 + 16.7662i 0.386947 + 0.842531i
\(397\) −0.887952 + 3.31388i −0.0445650 + 0.166319i −0.984622 0.174699i \(-0.944105\pi\)
0.940057 + 0.341018i \(0.110772\pi\)
\(398\) 8.54165 + 31.8779i 0.428154 + 1.59789i
\(399\) 4.12121 1.48648i 0.206318 0.0744170i
\(400\) 2.73148i 0.136574i
\(401\) −17.5933 + 17.5933i −0.878566 + 0.878566i −0.993386 0.114820i \(-0.963371\pi\)
0.114820 + 0.993386i \(0.463371\pi\)
\(402\) −24.0722 + 8.68262i −1.20061 + 0.433050i
\(403\) 22.7851 + 3.40110i 1.13500 + 0.169421i
\(404\) 53.2183i 2.64771i
\(405\) 0.651544 0.445045i 0.0323755 0.0221145i
\(406\) −9.95465 + 17.2420i −0.494041 + 0.855704i
\(407\) −15.2315 −0.754999
\(408\) 5.75933 12.2580i 0.285129 0.606862i
\(409\) −7.04501 26.2924i −0.348354 1.30007i −0.888645 0.458595i \(-0.848353\pi\)
0.540292 0.841478i \(-0.318314\pi\)
\(410\) −0.371589 1.38679i −0.0183515 0.0684886i
\(411\) −11.1408 16.0093i −0.549535 0.789681i
\(412\) −54.9180 −2.70561
\(413\) −1.91797 + 3.32201i −0.0943769 + 0.163466i
\(414\) −9.27728 + 13.0871i −0.455953 + 0.643198i
\(415\) 0.980533i 0.0481325i
\(416\) −20.9858 + 8.27083i −1.02891 + 0.405511i
\(417\) −15.3717 12.9745i −0.752756 0.635366i
\(418\) 7.99485 7.99485i 0.391041 0.391041i
\(419\) 11.3138i 0.552716i −0.961055 0.276358i \(-0.910873\pi\)
0.961055 0.276358i \(-0.0891275\pi\)
\(420\) 0.0833587 0.464865i 0.00406749 0.0226831i
\(421\) 8.52615 + 31.8200i 0.415539 + 1.55081i 0.783754 + 0.621072i \(0.213302\pi\)
−0.368215 + 0.929741i \(0.620031\pi\)
\(422\) 13.9523 52.0706i 0.679187 2.53476i
\(423\) 0.0198248 0.212405i 0.000963913 0.0103275i
\(424\) −12.8681 12.8681i −0.624930 0.624930i
\(425\) 15.5547i 0.754516i
\(426\) 33.0889 39.2024i 1.60316 1.89936i
\(427\) 3.81474 + 3.81474i 0.184608 + 0.184608i
\(428\) 3.32755 + 5.76348i 0.160843 + 0.278589i
\(429\) −3.95012 + 11.6998i −0.190714 + 0.564870i
\(430\) −0.589341 + 1.02077i −0.0284206 + 0.0492258i
\(431\) −4.13746 + 1.10863i −0.199295 + 0.0534008i −0.357085 0.934072i \(-0.616229\pi\)
0.157791 + 0.987473i \(0.449563\pi\)
\(432\) 2.84290 + 0.0247288i 0.136779 + 0.00118976i
\(433\) 1.32891 0.767247i 0.0638634 0.0368716i −0.467728 0.883872i \(-0.654927\pi\)
0.531592 + 0.847001i \(0.321594\pi\)
\(434\) −13.9517 + 3.73833i −0.669701 + 0.179446i
\(435\) 1.33261 0.112696i 0.0638939 0.00540337i
\(436\) 19.8901 5.32953i 0.952562 0.255238i
\(437\) 5.77937 + 1.54858i 0.276465 + 0.0740785i
\(438\) −16.4847 45.7033i −0.787671 2.18379i
\(439\) 0.468303 0.270375i 0.0223509 0.0129043i −0.488783 0.872405i \(-0.662559\pi\)
0.511134 + 0.859501i \(0.329226\pi\)
\(440\) −0.112602 0.420237i −0.00536810 0.0200340i
\(441\) 1.04239 2.81308i 0.0496376 0.133956i
\(442\) 23.6264 9.31156i 1.12379 0.442906i
\(443\) 1.14873 + 0.663219i 0.0545778 + 0.0315105i 0.527041 0.849840i \(-0.323302\pi\)
−0.472463 + 0.881351i \(0.656635\pi\)
\(444\) 17.6459 37.5570i 0.837435 1.78238i
\(445\) 0.440222 0.0208685
\(446\) 25.1711 43.5977i 1.19189 2.06441i
\(447\) 1.68000 + 19.8657i 0.0794612 + 0.939616i
\(448\) 9.22643 9.22643i 0.435908 0.435908i
\(449\) −27.4540 7.35629i −1.29564 0.347165i −0.455837 0.890063i \(-0.650660\pi\)
−0.839798 + 0.542898i \(0.817327\pi\)
\(450\) 30.7668 14.1302i 1.45036 0.666103i
\(451\) −7.16227 12.4054i −0.337258 0.584148i
\(452\) −9.70615 16.8116i −0.456539 0.790749i
\(453\) −1.04029 12.3012i −0.0488770 0.577962i
\(454\) −31.5569 + 18.2194i −1.48104 + 0.855078i
\(455\) 0.254066 0.188069i 0.0119108 0.00881680i
\(456\) 3.73053 + 10.3428i 0.174698 + 0.484344i
\(457\) 6.14339 + 1.64612i 0.287376 + 0.0770020i 0.399627 0.916678i \(-0.369140\pi\)
−0.112252 + 0.993680i \(0.535806\pi\)
\(458\) 30.7023 + 17.7260i 1.43462 + 0.828280i
\(459\) −16.1892 0.140821i −0.755649 0.00657297i
\(460\) 0.456078 0.456078i 0.0212647 0.0212647i
\(461\) 26.3227 + 26.3227i 1.22597 + 1.22597i 0.965475 + 0.260497i \(0.0838864\pi\)
0.260497 + 0.965475i \(0.416114\pi\)
\(462\) −0.652412 7.71466i −0.0303529 0.358918i
\(463\) 6.06685 22.6418i 0.281951 1.05225i −0.669088 0.743183i \(-0.733315\pi\)
0.951039 0.309071i \(-0.100018\pi\)
\(464\) 4.17315 + 2.40937i 0.193734 + 0.111852i
\(465\) 0.741433 + 0.625808i 0.0343831 + 0.0290212i
\(466\) 4.32483 16.1405i 0.200344 0.747694i
\(467\) −9.06324 −0.419397 −0.209698 0.977766i \(-0.567248\pi\)
−0.209698 + 0.977766i \(0.567248\pi\)
\(468\) −24.2723 23.2942i −1.12199 1.07678i
\(469\) 6.53575 0.301793
\(470\) −0.00364749 + 0.0136126i −0.000168246 + 0.000627903i
\(471\) −22.8076 + 8.22648i −1.05092 + 0.379056i
\(472\) −8.33707 4.81341i −0.383745 0.221555i
\(473\) −3.04374 + 11.3594i −0.139951 + 0.522305i
\(474\) −54.7626 + 38.1090i −2.51533 + 1.75040i
\(475\) −8.92912 8.92912i −0.409696 0.409696i
\(476\) −6.85222 + 6.85222i −0.314071 + 0.314071i
\(477\) −7.55871 + 20.3985i −0.346089 + 0.933985i
\(478\) 20.0995 + 11.6044i 0.919329 + 0.530775i
\(479\) −40.6315 10.8872i −1.85650 0.497448i −0.856670 0.515865i \(-0.827471\pi\)
−0.999830 + 0.0184174i \(0.994137\pi\)
\(480\) −0.935076 0.167676i −0.0426802 0.00765333i
\(481\) 25.8391 10.1836i 1.17816 0.464332i
\(482\) 27.4858 15.8690i 1.25195 0.722811i
\(483\) 3.36294 2.34026i 0.153019 0.106485i
\(484\) 11.0257 + 19.0970i 0.501167 + 0.868047i
\(485\) −0.0794032 0.137530i −0.00360552 0.00624494i
\(486\) 14.4280 + 32.1497i 0.654468 + 1.45834i
\(487\) −0.839487 0.224940i −0.0380408 0.0101930i 0.239748 0.970835i \(-0.422935\pi\)
−0.277789 + 0.960642i \(0.589602\pi\)
\(488\) −9.57364 + 9.57364i −0.433378 + 0.433378i
\(489\) 0.570130 + 0.267871i 0.0257822 + 0.0121136i
\(490\) −0.0990926 + 0.171633i −0.00447655 + 0.00775361i
\(491\) 15.6661 0.706999 0.353500 0.935435i \(-0.384992\pi\)
0.353500 + 0.935435i \(0.384992\pi\)
\(492\) 38.8861 3.28851i 1.75312 0.148257i
\(493\) −23.7645 13.7205i −1.07030 0.617939i
\(494\) −8.21737 + 18.9079i −0.369717 + 0.850706i
\(495\) −0.400327 + 0.331977i −0.0179933 + 0.0149213i
\(496\) 0.904807 + 3.37678i 0.0406270 + 0.151622i
\(497\) −11.3467 + 6.55103i −0.508970 + 0.293854i
\(498\) 43.1038 + 7.72929i 1.93153 + 0.346358i
\(499\) 11.6828 + 3.13040i 0.522995 + 0.140136i 0.510652 0.859788i \(-0.329404\pi\)
0.0123435 + 0.999924i \(0.496071\pi\)
\(500\) −2.63177 + 0.705182i −0.117697 + 0.0315367i
\(501\) 9.75516 + 14.0181i 0.435829 + 0.626285i
\(502\) −25.2042 + 6.75344i −1.12492 + 0.301421i
\(503\) −24.6430 + 14.2276i −1.09878 + 0.634378i −0.935899 0.352268i \(-0.885410\pi\)
−0.162876 + 0.986646i \(0.552077\pi\)
\(504\) 7.05983 + 2.61603i 0.314470 + 0.116527i
\(505\) 1.44901 0.388261i 0.0644802 0.0172774i
\(506\) 5.28675 9.15692i 0.235025 0.407075i
\(507\) −1.12124 22.4887i −0.0497961 0.998759i
\(508\) −0.881789 1.52730i −0.0391231 0.0677631i
\(509\) −11.4868 11.4868i −0.509144 0.509144i 0.405120 0.914264i \(-0.367230\pi\)
−0.914264 + 0.405120i \(0.867230\pi\)
\(510\) 1.05274 + 0.188775i 0.0466160 + 0.00835909i
\(511\) 12.4087i 0.548929i
\(512\) −4.36228 4.36228i −0.192787 0.192787i
\(513\) 9.37418 9.21251i 0.413880 0.406742i
\(514\) −4.52174 + 16.8754i −0.199446 + 0.744341i
\(515\) −0.400662 1.49529i −0.0176553 0.0658904i
\(516\) −24.4831 20.6650i −1.07781 0.909726i
\(517\) 0.140609i 0.00618396i
\(518\) −12.3129 + 12.3129i −0.540999 + 0.540999i
\(519\) −1.97098 + 10.9916i −0.0865166 + 0.482476i
\(520\) 0.471986 + 0.637614i 0.0206979 + 0.0279612i
\(521\) 8.84438i 0.387479i 0.981053 + 0.193740i \(0.0620617\pi\)
−0.981053 + 0.193740i \(0.937938\pi\)
\(522\) −5.55057 + 59.4694i −0.242942 + 2.60291i
\(523\) −13.5855 + 23.5308i −0.594054 + 1.02893i 0.399626 + 0.916678i \(0.369140\pi\)
−0.993680 + 0.112253i \(0.964193\pi\)
\(524\) −20.1946 −0.882207
\(525\) −8.61619 + 0.728652i −0.376041 + 0.0318010i
\(526\) −4.05556 15.1355i −0.176831 0.659941i
\(527\) −5.15253 19.2295i −0.224448 0.837651i
\(528\) −1.86722 + 0.157906i −0.0812601 + 0.00687199i
\(529\) −17.4046 −0.756722
\(530\) 0.718552 1.24457i 0.0312119 0.0540606i
\(531\) −1.06943 + 11.4580i −0.0464093 + 0.497235i
\(532\) 7.86696i 0.341076i
\(533\) 20.4443 + 16.2562i 0.885542 + 0.704134i
\(534\) −3.47016 + 19.3520i −0.150168 + 0.837441i
\(535\) −0.132650 + 0.132650i −0.00573496 + 0.00573496i
\(536\) 16.4024i 0.708476i
\(537\) 15.9470 + 13.4601i 0.688166 + 0.580848i
\(538\) 0.202082 + 0.754181i 0.00871238 + 0.0325150i
\(539\) −0.511778 + 1.90998i −0.0220438 + 0.0822687i
\(540\) −0.354787 1.37170i −0.0152676 0.0590286i
\(541\) −30.1892 30.1892i −1.29794 1.29794i −0.929753 0.368183i \(-0.879980\pi\)
−0.368183 0.929753i \(-0.620020\pi\)
\(542\) 31.3266i 1.34559i
\(543\) 16.2464 + 2.91327i 0.697200 + 0.125021i
\(544\) 13.7832 + 13.7832i 0.590952 + 0.590952i
\(545\) 0.290222 + 0.502679i 0.0124317 + 0.0215324i
\(546\) 6.26469 + 12.6511i 0.268104 + 0.541418i
\(547\) −7.01579 + 12.1517i −0.299973 + 0.519569i −0.976130 0.217189i \(-0.930311\pi\)
0.676156 + 0.736758i \(0.263644\pi\)
\(548\) −33.8297 + 9.06463i −1.44513 + 0.387222i
\(549\) 15.1762 + 5.62355i 0.647704 + 0.240007i
\(550\) −19.3257 + 11.1577i −0.824052 + 0.475767i
\(551\) 21.5181 5.76575i 0.916701 0.245629i
\(552\) 5.87321 + 8.43978i 0.249980 + 0.359221i
\(553\) 16.4591 4.41019i 0.699911 0.187541i
\(554\) 67.3320 + 18.0415i 2.86066 + 0.766512i
\(555\) 1.15133 + 0.206454i 0.0488712 + 0.00876348i
\(556\) −31.2812 + 18.0602i −1.32662 + 0.765924i
\(557\) 2.94048 + 10.9740i 0.124592 + 0.464984i 0.999825 0.0187180i \(-0.00595846\pi\)
−0.875233 + 0.483702i \(0.839292\pi\)
\(558\) −33.3548 + 27.6600i −1.41202 + 1.17094i
\(559\) −2.43128 21.3053i −0.102832 0.901118i
\(560\) 0.0415412 + 0.0239838i 0.00175544 + 0.00101350i
\(561\) 10.6331 0.899217i 0.448929 0.0379650i
\(562\) 0.548122 0.0231211
\(563\) −5.58335 + 9.67065i −0.235310 + 0.407569i −0.959363 0.282176i \(-0.908944\pi\)
0.724053 + 0.689745i \(0.242277\pi\)
\(564\) −0.346704 0.162896i −0.0145989 0.00685917i
\(565\) 0.386927 0.386927i 0.0162782 0.0162782i
\(566\) −25.8366 6.92290i −1.08599 0.290991i
\(567\) −0.680370 8.97425i −0.0285728 0.376883i
\(568\) −16.4408 28.4762i −0.689839 1.19484i
\(569\) 9.15646 + 15.8595i 0.383859 + 0.664863i 0.991610 0.129264i \(-0.0412616\pi\)
−0.607751 + 0.794127i \(0.707928\pi\)
\(570\) −0.712684 + 0.495953i −0.0298510 + 0.0207732i
\(571\) 13.8623 8.00340i 0.580119 0.334932i −0.181062 0.983472i \(-0.557953\pi\)
0.761181 + 0.648540i \(0.224620\pi\)
\(572\) 17.3560 + 13.8005i 0.725689 + 0.577028i
\(573\) 41.2551 + 7.39779i 1.72346 + 0.309047i
\(574\) −15.8182 4.23847i −0.660239 0.176910i
\(575\) −10.2270 5.90455i −0.426495 0.246237i
\(576\) 13.6013 36.7055i 0.566719 1.52940i
\(577\) −16.9330 + 16.9330i −0.704931 + 0.704931i −0.965465 0.260534i \(-0.916101\pi\)
0.260534 + 0.965465i \(0.416101\pi\)
\(578\) 11.6563 + 11.6563i 0.484838 + 0.484838i
\(579\) 12.6325 8.79088i 0.524988 0.365337i
\(580\) 0.621546 2.31964i 0.0258083 0.0963178i
\(581\) −9.68589 5.59215i −0.401839 0.232002i
\(582\) 6.67169 2.40641i 0.276551 0.0997491i
\(583\) 3.71107 13.8499i 0.153697 0.573604i
\(584\) −31.1414 −1.28864
\(585\) 0.457167 0.830826i 0.0189015 0.0343504i
\(586\) −3.98302 −0.164537
\(587\) 9.77558 36.4830i 0.403481 1.50581i −0.403358 0.915042i \(-0.632157\pi\)
0.806839 0.590771i \(-0.201176\pi\)
\(588\) −4.11662 3.47464i −0.169766 0.143292i
\(589\) 13.9964 + 8.08082i 0.576711 + 0.332964i
\(590\) 0.196761 0.734321i 0.00810051 0.0302315i
\(591\) 0.566975 + 6.70439i 0.0233223 + 0.275782i
\(592\) 2.98015 + 2.98015i 0.122484 + 0.122484i
\(593\) 23.4781 23.4781i 0.964130 0.964130i −0.0352488 0.999379i \(-0.511222\pi\)
0.999379 + 0.0352488i \(0.0112224\pi\)
\(594\) −11.4379 20.2151i −0.469303 0.829434i
\(595\) −0.236562 0.136579i −0.00969809 0.00559919i
\(596\) 34.5796 + 9.26558i 1.41644 + 0.379533i
\(597\) −8.57955 23.7865i −0.351137 0.973515i
\(598\) −2.84636 + 19.0686i −0.116396 + 0.779775i
\(599\) 15.9023 9.18118i 0.649749 0.375133i −0.138611 0.990347i \(-0.544264\pi\)
0.788360 + 0.615214i \(0.210930\pi\)
\(600\) −1.82866 21.6235i −0.0746546 0.882778i
\(601\) −6.40795 11.0989i −0.261386 0.452733i 0.705225 0.708984i \(-0.250846\pi\)
−0.966610 + 0.256250i \(0.917513\pi\)
\(602\) 6.72224 + 11.6433i 0.273978 + 0.474544i
\(603\) 17.8180 8.18320i 0.725603 0.333246i
\(604\) −21.4124 5.73743i −0.871257 0.233453i
\(605\) −0.439529 + 0.439529i −0.0178694 + 0.0178694i
\(606\) 5.64562 + 66.7585i 0.229337 + 2.71188i
\(607\) −19.6339 + 34.0070i −0.796917 + 1.38030i 0.124698 + 0.992195i \(0.460204\pi\)
−0.921615 + 0.388106i \(0.873129\pi\)
\(608\) −15.8244 −0.641764
\(609\) 6.48690 13.8065i 0.262862 0.559469i
\(610\) −0.925938 0.534591i −0.0374902 0.0216449i
\(611\) −0.0940090 0.238531i −0.00380320 0.00964994i
\(612\) −10.1013 + 27.2602i −0.408321 + 1.10193i
\(613\) −3.79080 14.1475i −0.153109 0.571411i −0.999260 0.0384671i \(-0.987753\pi\)
0.846151 0.532943i \(-0.178914\pi\)
\(614\) −49.5202 + 28.5905i −1.99847 + 1.15382i
\(615\) 0.373237 + 1.03479i 0.0150504 + 0.0417266i
\(616\) −4.79337 1.28438i −0.193130 0.0517492i
\(617\) −31.9546 + 8.56220i −1.28644 + 0.344701i −0.836308 0.548259i \(-0.815291\pi\)
−0.450135 + 0.892961i \(0.648624\pi\)
\(618\) 68.8906 5.82593i 2.77119 0.234353i
\(619\) −10.8960 + 2.91956i −0.437945 + 0.117347i −0.471054 0.882105i \(-0.656126\pi\)
0.0331080 + 0.999452i \(0.489459\pi\)
\(620\) 1.50880 0.871109i 0.0605951 0.0349846i
\(621\) 6.23800 10.5907i 0.250322 0.424990i
\(622\) 3.95479 1.05968i 0.158573 0.0424894i
\(623\) 2.51067 4.34860i 0.100588 0.174223i
\(624\) 3.06201 1.51627i 0.122578 0.0606994i
\(625\) 12.4424 + 21.5508i 0.497695 + 0.862034i
\(626\) 19.1962 + 19.1962i 0.767236 + 0.767236i
\(627\) −5.58768 + 6.62006i −0.223150 + 0.264380i
\(628\) 43.5374i 1.73733i
\(629\) −16.9709 16.9709i −0.676672 0.676672i
\(630\) −0.0552526 + 0.591983i −0.00220132 + 0.0235852i
\(631\) −8.42144 + 31.4292i −0.335252 + 1.25118i 0.568343 + 0.822792i \(0.307585\pi\)
−0.903595 + 0.428387i \(0.859082\pi\)
\(632\) 11.0680 + 41.3064i 0.440262 + 1.64308i
\(633\) −7.29026 + 40.6555i −0.289762 + 1.61591i
\(634\) 67.9052i 2.69686i
\(635\) 0.0351518 0.0351518i 0.00139496 0.00139496i
\(636\) 29.8509 + 25.1957i 1.18367 + 0.999076i
\(637\) −0.408798 3.58230i −0.0161972 0.141936i
\(638\) 39.3678i 1.55859i
\(639\) −22.7314 + 32.0665i −0.899242 + 1.26853i
\(640\) −0.744497 + 1.28951i −0.0294288 + 0.0509722i
\(641\) −38.7291 −1.52971 −0.764853 0.644205i \(-0.777189\pi\)
−0.764853 + 0.644205i \(0.777189\pi\)
\(642\) −4.78559 6.87688i −0.188872 0.271409i
\(643\) 4.85286 + 18.1111i 0.191378 + 0.714234i 0.993175 + 0.116636i \(0.0372112\pi\)
−0.801796 + 0.597597i \(0.796122\pi\)
\(644\) −1.90413 7.10632i −0.0750333 0.280028i
\(645\) 0.384041 0.817383i 0.0151216 0.0321844i
\(646\) 17.8156 0.700946
\(647\) 23.4153 40.5564i 0.920549 1.59444i 0.121982 0.992532i \(-0.461075\pi\)
0.798567 0.601906i \(-0.205592\pi\)
\(648\) 22.5222 1.70748i 0.884754 0.0670763i
\(649\) 7.58501i 0.297738i
\(650\) 25.3247 31.8491i 0.993316 1.24923i
\(651\) 10.4104 3.75492i 0.408015 0.147167i
\(652\) 0.799830 0.799830i 0.0313238 0.0313238i
\(653\) 3.05664i 0.119616i 0.998210 + 0.0598078i \(0.0190488\pi\)
−0.998210 + 0.0598078i \(0.980951\pi\)
\(654\) −24.3853 + 8.79554i −0.953541 + 0.343933i
\(655\) −0.147333 0.549854i −0.00575677 0.0214846i
\(656\) −1.02586 + 3.82855i −0.0400530 + 0.149480i
\(657\) 15.5365 + 33.8290i 0.606138 + 1.31979i
\(658\) 0.113666 + 0.113666i 0.00443115 + 0.00443115i
\(659\) 38.9037i 1.51547i 0.652560 + 0.757737i \(0.273695\pi\)
−0.652560 + 0.757737i \(0.726305\pi\)
\(660\) 0.316855 + 0.878470i 0.0123336 + 0.0341944i
\(661\) 3.27339 + 3.27339i 0.127320 + 0.127320i 0.767895 0.640575i \(-0.221304\pi\)
−0.640575 + 0.767895i \(0.721304\pi\)
\(662\) −11.6657 20.2055i −0.453399 0.785310i
\(663\) −17.4370 + 8.63460i −0.677197 + 0.335340i
\(664\) 14.0343 24.3081i 0.544637 0.943338i
\(665\) 0.214199 0.0573946i 0.00830630 0.00222567i
\(666\) −18.1512 + 48.9845i −0.703347 + 1.89811i
\(667\) 18.0420 10.4165i 0.698588 0.403330i
\(668\) 29.6221 7.93722i 1.14611 0.307100i
\(669\) −16.4026 + 34.9110i −0.634163 + 1.34974i
\(670\) −1.25115 + 0.335245i −0.0483363 + 0.0129517i
\(671\) −10.3041 2.76097i −0.397785 0.106586i
\(672\) −6.98924 + 8.28057i −0.269616 + 0.319430i
\(673\) −11.9301 + 6.88784i −0.459871 + 0.265507i −0.711990 0.702190i \(-0.752206\pi\)
0.252119 + 0.967696i \(0.418873\pi\)
\(674\) −8.69017 32.4322i −0.334733 1.24924i
\(675\) −22.5774 + 12.7745i −0.869004 + 0.491691i
\(676\) −38.6699 11.8075i −1.48730 0.454135i
\(677\) −16.1061 9.29888i −0.619009 0.357385i 0.157474 0.987523i \(-0.449665\pi\)
−0.776483 + 0.630138i \(0.782998\pi\)
\(678\) 13.9591 + 20.0592i 0.536096 + 0.770369i
\(679\) −1.81140 −0.0695153
\(680\) 0.342764 0.593686i 0.0131444 0.0227668i
\(681\) 22.9166 15.9475i 0.878165 0.611111i
\(682\) 20.1954 20.1954i 0.773322 0.773322i
\(683\) −14.9180 3.99726i −0.570820 0.152951i −0.0381474 0.999272i \(-0.512146\pi\)
−0.532673 + 0.846321i \(0.678812\pi\)
\(684\) −9.84997 21.4472i −0.376623 0.820052i
\(685\) −0.493618 0.854972i −0.0188602 0.0326668i
\(686\) 1.13029 + 1.95771i 0.0431545 + 0.0747458i
\(687\) −24.5849 11.5510i −0.937973 0.440699i
\(688\) 2.81807 1.62701i 0.107438 0.0620293i
\(689\) 2.96433 + 25.9764i 0.112932 + 0.989623i
\(690\) −0.523734 + 0.620499i −0.0199382 + 0.0236220i
\(691\) −38.7792 10.3909i −1.47523 0.395287i −0.570510 0.821291i \(-0.693254\pi\)
−0.904721 + 0.426004i \(0.859921\pi\)
\(692\) 17.3655 + 10.0260i 0.660137 + 0.381130i
\(693\) 0.996201 + 5.84783i 0.0378425 + 0.222141i
\(694\) −44.2326 + 44.2326i −1.67905 + 1.67905i
\(695\) −0.719956 0.719956i −0.0273095 0.0273095i
\(696\) 34.6495 + 16.2798i 1.31339 + 0.617084i
\(697\) 5.84187 21.8022i 0.221277 0.825816i
\(698\) 7.04819 + 4.06927i 0.266778 + 0.154024i
\(699\) −2.25978 + 12.6021i −0.0854729 + 0.476655i
\(700\) −4.01868 + 14.9979i −0.151892 + 0.566868i
\(701\) −38.7123 −1.46214 −0.731071 0.682302i \(-0.760979\pi\)
−0.731071 + 0.682302i \(0.760979\pi\)
\(702\) 32.9190 + 26.6460i 1.24245 + 1.00569i
\(703\) 19.4841 0.734855
\(704\) −6.67775 + 24.9217i −0.251677 + 0.939273i
\(705\) 0.00190586 0.0106284i 7.17789e−5 0.000400288i
\(706\) 40.7823 + 23.5457i 1.53486 + 0.886154i
\(707\) 4.42865 16.5279i 0.166556 0.621597i
\(708\) 18.7027 + 8.78730i 0.702889 + 0.330247i
\(709\) −17.7853 17.7853i −0.667942 0.667942i 0.289297 0.957239i \(-0.406578\pi\)
−0.957239 + 0.289297i \(0.906578\pi\)
\(710\) 1.83610 1.83610i 0.0689076 0.0689076i
\(711\) 39.3493 32.6311i 1.47572 1.22376i
\(712\) 10.9134 + 6.30087i 0.408998 + 0.236135i
\(713\) 14.5990 + 3.91179i 0.546736 + 0.146498i
\(714\) 7.86871 9.32253i 0.294479 0.348887i
\(715\) −0.249133 + 0.573247i −0.00931706 + 0.0214382i
\(716\) 32.4520 18.7362i 1.21279 0.700204i
\(717\) −16.0947 7.56197i −0.601068 0.282407i
\(718\) −15.9350 27.6003i −0.594691 1.03003i
\(719\) 18.9210 + 32.7721i 0.705634 + 1.22219i 0.966462 + 0.256809i \(0.0826711\pi\)
−0.260828 + 0.965385i \(0.583996\pi\)
\(720\) 0.143280 + 0.0133731i 0.00533974 + 0.000498384i
\(721\) −17.0558 4.57009i −0.635192 0.170199i
\(722\) 20.1439 20.1439i 0.749678 0.749678i
\(723\) −19.9602 + 13.8902i −0.742327 + 0.516582i
\(724\) 14.8192 25.6676i 0.550751 0.953929i
\(725\) −43.9683 −1.63294
\(726\) −15.8568 22.7862i −0.588501 0.845675i
\(727\) −34.0851 19.6790i −1.26414 0.729854i −0.290271 0.956945i \(-0.593745\pi\)
−0.973874 + 0.227090i \(0.927079\pi\)
\(728\) 8.99030 1.02594i 0.333203 0.0380238i
\(729\) −13.0912 23.6140i −0.484859 0.874592i
\(730\) −0.636494 2.37543i −0.0235577 0.0879185i
\(731\) −16.0479 + 9.26524i −0.593551 + 0.342687i
\(732\) 18.7452 22.2086i 0.692843 0.820853i
\(733\) 29.3171 + 7.85548i 1.08285 + 0.290149i 0.755763 0.654845i \(-0.227266\pi\)
0.327087 + 0.944994i \(0.393933\pi\)
\(734\) 32.4756 8.70182i 1.19870 0.321190i
\(735\) 0.0645732 0.137436i 0.00238182 0.00506940i
\(736\) −14.2944 + 3.83016i −0.526897 + 0.141182i
\(737\) −11.1921 + 6.46176i −0.412266 + 0.238022i
\(738\) −48.4309 + 8.25039i −1.78277 + 0.303701i
\(739\) −31.5833 + 8.46272i −1.16181 + 0.311306i −0.787689 0.616073i \(-0.788723\pi\)
−0.374122 + 0.927380i \(0.622056\pi\)
\(740\) 1.05019 1.81898i 0.0386056 0.0668669i
\(741\) 5.05297 14.9663i 0.185625 0.549799i
\(742\) −8.19606 14.1960i −0.300887 0.521151i
\(743\) −13.7383 13.7383i −0.504009 0.504009i 0.408672 0.912681i \(-0.365992\pi\)
−0.912681 + 0.408672i \(0.865992\pi\)
\(744\) 9.42351 + 26.1263i 0.345483 + 0.957838i
\(745\) 1.00912i 0.0369714i
\(746\) 37.0870 + 37.0870i 1.35785 + 1.35785i
\(747\) −33.4077 3.11811i −1.22232 0.114086i
\(748\) 4.95939 18.5087i 0.181333 0.676745i
\(749\) 0.553815 + 2.06687i 0.0202360 + 0.0755217i
\(750\) 3.22656 1.16379i 0.117817 0.0424956i
\(751\) 34.1075i 1.24460i 0.782779 + 0.622299i \(0.213801\pi\)
−0.782779 + 0.622299i \(0.786199\pi\)
\(752\) 0.0275110 0.0275110i 0.00100322 0.00100322i
\(753\) 18.8067 6.78341i 0.685356 0.247201i
\(754\) 26.3208 + 66.7844i 0.958548 + 2.43215i
\(755\) 0.624868i 0.0227413i
\(756\) −15.5733 4.31839i −0.566397 0.157058i
\(757\) −4.67131 + 8.09095i −0.169782 + 0.294071i −0.938343 0.345706i \(-0.887640\pi\)
0.768561 + 0.639776i \(0.220973\pi\)
\(758\) −42.5796 −1.54656
\(759\) −3.44508 + 7.33243i −0.125049 + 0.266150i
\(760\) 0.144040 + 0.537564i 0.00522488 + 0.0194995i
\(761\) −6.06026 22.6172i −0.219684 0.819873i −0.984465 0.175582i \(-0.943819\pi\)
0.764781 0.644291i \(-0.222847\pi\)
\(762\) 1.26816 + 1.82235i 0.0459407 + 0.0660167i
\(763\) 6.62075 0.239687
\(764\) 37.6310 65.1788i 1.36144 2.35809i
\(765\) −0.815928 0.0761545i −0.0294999 0.00275337i
\(766\) 39.2701i 1.41889i
\(767\) 5.07124 + 12.8674i 0.183112 + 0.464614i
\(768\) −16.2766 13.7383i −0.587330 0.495738i
\(769\) 27.4212 27.4212i 0.988835 0.988835i −0.0111038 0.999938i \(-0.503535\pi\)
0.999938 + 0.0111038i \(0.00353452\pi\)
\(770\) 0.391883i 0.0141225i
\(771\) 2.36267 13.1759i 0.0850896 0.474518i
\(772\) −7.15264 26.6940i −0.257429 0.960739i
\(773\) 6.03203 22.5119i 0.216957 0.809695i −0.768511 0.639836i \(-0.779002\pi\)
0.985468 0.169859i \(-0.0543312\pi\)
\(774\) 32.9045 + 23.3255i 1.18273 + 0.838418i
\(775\) −22.5554 22.5554i −0.810214 0.810214i
\(776\) 4.54598i 0.163191i
\(777\) 8.60562 10.1956i 0.308725 0.365765i
\(778\) 39.1824 + 39.1824i 1.40476 + 1.40476i
\(779\) 9.16192 + 15.8689i 0.328260 + 0.568563i
\(780\) −1.12485 1.27841i −0.0402762 0.0457744i
\(781\) 12.9537 22.4365i 0.463521 0.802843i
\(782\) 16.0930 4.31212i 0.575486 0.154201i
\(783\) 0.398057 45.7618i 0.0142254 1.63539i
\(784\) 0.473834 0.273568i 0.0169227 0.00977030i
\(785\) −1.18543 + 0.317634i −0.0423096 + 0.0113368i
\(786\) 25.3327 2.14233i 0.903588 0.0764144i
\(787\) 8.43826 2.26103i 0.300792 0.0805969i −0.105267 0.994444i \(-0.533570\pi\)
0.406058 + 0.913847i \(0.366903\pi\)
\(788\) 11.6701 + 3.12700i 0.415731 + 0.111395i
\(789\) 4.07355 + 11.2938i 0.145022 + 0.402069i
\(790\) −2.92458 + 1.68851i −0.104052 + 0.0600744i
\(791\) −1.61543 6.02886i −0.0574380 0.214362i
\(792\) −14.6760 + 2.50011i −0.521488 + 0.0888375i
\(793\) 19.3260 2.20541i 0.686287 0.0783164i
\(794\) −6.71648 3.87776i −0.238359 0.137617i
\(795\) −0.468241 + 0.996591i −0.0166068 + 0.0353455i
\(796\) −45.4060 −1.60937
\(797\) −0.864344 + 1.49709i −0.0306166 + 0.0530296i −0.880928 0.473251i \(-0.843080\pi\)
0.850311 + 0.526280i \(0.176414\pi\)
\(798\) 0.834561 + 9.86854i 0.0295431 + 0.349342i
\(799\) −0.156665 + 0.156665i −0.00554241 + 0.00554241i
\(800\) 30.1683 + 8.08358i 1.06661 + 0.285798i
\(801\) 1.39991 14.9988i 0.0494634 0.529957i
\(802\) −28.1222 48.7091i −0.993031 1.71998i
\(803\) −12.2682 21.2492i −0.432937 0.749868i
\(804\) −2.96688 35.0828i −0.104634 1.23728i
\(805\) 0.179597 0.103690i 0.00632996 0.00365460i
\(806\) −20.7575 + 47.7623i −0.731152 + 1.68235i
\(807\) −0.202979 0.562751i −0.00714519 0.0198098i
\(808\) 41.4792 + 11.1143i 1.45923 + 0.391001i
\(809\) 11.5815 + 6.68658i 0.407184 + 0.235088i 0.689579 0.724211i \(-0.257796\pi\)
−0.282395 + 0.959298i \(0.591129\pi\)
\(810\) 0.590571 + 1.68306i 0.0207505 + 0.0591367i
\(811\) −19.7534 + 19.7534i −0.693634 + 0.693634i −0.963030 0.269396i \(-0.913176\pi\)
0.269396 + 0.963030i \(0.413176\pi\)
\(812\) −19.3691 19.3691i −0.679721 0.679721i
\(813\) 2.02262 + 23.9171i 0.0709363 + 0.838810i
\(814\) 8.91164 33.2587i 0.312353 1.16572i
\(815\) 0.0276128 + 0.0159423i 0.000967235 + 0.000558433i
\(816\) −2.25638 1.90450i −0.0789890 0.0666708i
\(817\) 3.89353 14.5308i 0.136217 0.508370i
\(818\) 61.5324 2.15143
\(819\) −5.59976 9.25433i −0.195671 0.323373i
\(820\) 1.97530 0.0689806
\(821\) −0.468800 + 1.74959i −0.0163612 + 0.0610610i −0.973624 0.228159i \(-0.926729\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(822\) 41.4753 14.9597i 1.44662 0.521780i
\(823\) −36.2557 20.9323i −1.26380 0.729652i −0.289989 0.957030i \(-0.593651\pi\)
−0.973807 + 0.227378i \(0.926985\pi\)
\(824\) 11.4693 42.8040i 0.399552 1.49115i
\(825\) 14.0343 9.76642i 0.488612 0.340023i
\(826\) −6.13160 6.13160i −0.213346 0.213346i
\(827\) 6.73892 6.73892i 0.234335 0.234335i −0.580164 0.814499i \(-0.697012\pi\)
0.814499 + 0.580164i \(0.197012\pi\)
\(828\) −14.0887 16.9894i −0.489616 0.590421i
\(829\) −1.79323 1.03532i −0.0622813 0.0359581i 0.468536 0.883444i \(-0.344782\pi\)
−0.530817 + 0.847486i \(0.678115\pi\)
\(830\) 2.14104 + 0.573689i 0.0743165 + 0.0199130i
\(831\) −52.5712 9.42696i −1.82367 0.327018i
\(832\) −5.33406 46.7424i −0.184925 1.62050i
\(833\) −2.69831 + 1.55787i −0.0934908 + 0.0539770i
\(834\) 37.3241 25.9737i 1.29243 0.899396i
\(835\) 0.432225 + 0.748635i 0.0149578 + 0.0259076i
\(836\) 7.77791 + 13.4717i 0.269004 + 0.465929i
\(837\) 23.6797 23.2713i 0.818489 0.804373i
\(838\) 24.7042 + 6.61947i 0.853392 + 0.228666i
\(839\) −8.20551 + 8.20551i −0.283286 + 0.283286i −0.834418 0.551132i \(-0.814196\pi\)
0.551132 + 0.834418i \(0.314196\pi\)
\(840\) 0.344915 + 0.162056i 0.0119007 + 0.00559145i
\(841\) 24.2834 42.0601i 0.837359 1.45035i
\(842\) −74.4689 −2.56637
\(843\) −0.418477 + 0.0353897i −0.0144131 + 0.00121889i
\(844\) 64.2314 + 37.0840i 2.21094 + 1.27648i
\(845\) 0.0393697 1.13904i 0.00135436 0.0391840i
\(846\) 0.452196 + 0.167562i 0.0155468 + 0.00576089i
\(847\) 1.83504 + 6.84846i 0.0630527 + 0.235316i
\(848\) −3.43592 + 1.98373i −0.117990 + 0.0681216i
\(849\) 20.1726 + 3.61731i 0.692322 + 0.124146i
\(850\) −33.9645 9.10075i −1.16497 0.312153i
\(851\) 17.6002 4.71595i 0.603326 0.161661i
\(852\) 40.3156 + 57.9335i 1.38119 + 1.98477i
\(853\) −34.8760 + 9.34499i −1.19413 + 0.319966i −0.800517 0.599309i \(-0.795442\pi\)
−0.393614 + 0.919276i \(0.628775\pi\)
\(854\) −10.5616 + 6.09773i −0.361410 + 0.208660i
\(855\) 0.512095 0.424663i 0.0175133 0.0145232i
\(856\) −5.18710 + 1.38988i −0.177291 + 0.0475051i
\(857\) 15.2129 26.3495i 0.519663 0.900083i −0.480075 0.877227i \(-0.659391\pi\)
0.999739 0.0228561i \(-0.00727596\pi\)
\(858\) −23.2358 15.4705i −0.793258 0.528156i
\(859\) 18.2735 + 31.6506i 0.623483 + 1.07991i 0.988832 + 0.149034i \(0.0476165\pi\)
−0.365349 + 0.930871i \(0.619050\pi\)
\(860\) −1.14670 1.14670i −0.0391021 0.0391021i
\(861\) 12.3505 + 2.21466i 0.420903 + 0.0754755i
\(862\) 9.68297i 0.329803i
\(863\) −20.5837 20.5837i −0.700676 0.700676i 0.263879 0.964556i \(-0.414998\pi\)
−0.964556 + 0.263879i \(0.914998\pi\)
\(864\) −8.68644 + 31.3257i −0.295519 + 1.06572i
\(865\) −0.146292 + 0.545969i −0.00497407 + 0.0185635i
\(866\) 0.897800 + 3.35064i 0.0305085 + 0.113859i
\(867\) −9.65189 8.14670i −0.327795 0.276676i
\(868\) 19.8724i 0.674512i
\(869\) −23.8249 + 23.8249i −0.808206 + 0.808206i
\(870\) −0.533607 + 2.97576i −0.0180910 + 0.100888i
\(871\) 14.6663 18.4448i 0.496947 0.624977i
\(872\) 16.6157i 0.562679i
\(873\) −4.93830 + 2.26800i −0.167136 + 0.0767601i
\(874\) −6.76277 + 11.7135i −0.228754 + 0.396214i
\(875\) −0.876030 −0.0296152
\(876\) 66.6079 5.63288i 2.25047 0.190317i
\(877\) 1.31742 + 4.91667i 0.0444860 + 0.166024i 0.984595 0.174849i \(-0.0559439\pi\)
−0.940109 + 0.340874i \(0.889277\pi\)
\(878\) 0.316381 + 1.18075i 0.0106773 + 0.0398484i
\(879\) 3.04094 0.257165i 0.102568 0.00867397i
\(880\) −0.0948493 −0.00319737
\(881\) −20.1440 + 34.8904i −0.678668 + 1.17549i 0.296714 + 0.954966i \(0.404109\pi\)
−0.975382 + 0.220522i \(0.929224\pi\)
\(882\) 5.53260 + 3.92198i 0.186292 + 0.132060i
\(883\) 8.02363i 0.270017i −0.990844 0.135008i \(-0.956894\pi\)
0.990844 0.135008i \(-0.0431061\pi\)
\(884\) 3.96146 + 34.7143i 0.133238 + 1.16757i
\(885\) −0.102810 + 0.573340i −0.00345593 + 0.0192726i
\(886\) −2.12026 + 2.12026i −0.0712317 + 0.0712317i
\(887\) 12.2583i 0.411595i 0.978595 + 0.205797i \(0.0659788\pi\)
−0.978595 + 0.205797i \(0.934021\pi\)
\(888\) 25.5873 + 21.5970i 0.858654 + 0.724749i
\(889\) −0.146759 0.547713i −0.00492215 0.0183697i
\(890\) −0.257565 + 0.961244i −0.00863359 + 0.0322210i
\(891\) 10.0377 + 14.6952i 0.336277 + 0.492308i
\(892\) 48.9762 + 48.9762i 1.63985 + 1.63985i
\(893\) 0.179865i 0.00601897i
\(894\) −44.3606 7.95465i −1.48364 0.266043i
\(895\) 0.746901 + 0.746901i 0.0249662 + 0.0249662i
\(896\) 8.49200 + 14.7086i 0.283698 + 0.491379i
\(897\) 0.941947 14.7422i 0.0314507 0.492228i
\(898\) 32.1255 55.6431i 1.07204 1.85683i
\(899\) 54.3558 14.5646i 1.81287 0.485756i
\(900\) 7.82256 + 45.9195i 0.260752 + 1.53065i
\(901\) 19.5663 11.2966i 0.651848 0.376344i
\(902\) 31.2783 8.38098i 1.04145 0.279056i
\(903\) −5.88401 8.45531i −0.195808 0.281375i
\(904\) 15.1303 4.05415i 0.503226 0.134839i
\(905\) 0.806986 + 0.216231i 0.0268251 + 0.00718777i
\(906\) 27.4689 + 4.92567i 0.912594 + 0.163645i
\(907\) −4.41396 + 2.54840i −0.146563 + 0.0846182i −0.571488 0.820610i \(-0.693634\pi\)
0.424925 + 0.905228i \(0.360300\pi\)
\(908\) −12.9756 48.4256i −0.430610 1.60706i
\(909\) −8.62058 50.6039i −0.285926 1.67843i
\(910\) 0.262008 + 0.664799i 0.00868548 + 0.0220379i
\(911\) 12.6395 + 7.29742i 0.418765 + 0.241774i 0.694549 0.719445i \(-0.255604\pi\)
−0.275784 + 0.961220i \(0.588937\pi\)
\(912\) 2.38853 0.201993i 0.0790921 0.00668864i
\(913\) 22.1154 0.731912
\(914\) −7.18873 + 12.4512i −0.237782 + 0.411851i
\(915\) 0.741447 + 0.348363i 0.0245115 + 0.0115165i
\(916\) −34.4899 + 34.4899i −1.13958 + 1.13958i
\(917\) −6.27183 1.68053i −0.207114 0.0554960i
\(918\) 9.77947 35.2675i 0.322771 1.16400i
\(919\) 24.8027 + 42.9596i 0.818167 + 1.41711i 0.907032 + 0.421062i \(0.138343\pi\)
−0.0888652 + 0.996044i \(0.528324\pi\)
\(920\) 0.260226 + 0.450724i 0.00857939 + 0.0148599i
\(921\) 35.9615 25.0254i 1.18497 0.824616i
\(922\) −72.8777 + 42.0760i −2.40010 + 1.38570i
\(923\) −6.97422 + 46.7225i −0.229559 + 1.53789i
\(924\) 10.4848 + 1.88011i 0.344924 + 0.0618511i
\(925\) −37.1453 9.95305i −1.22133 0.327254i
\(926\) 45.8898 + 26.4945i 1.50803 + 0.870663i
\(927\) −52.2202 + 8.89591i −1.71514 + 0.292180i
\(928\) −38.9609 + 38.9609i −1.27895 + 1.27895i
\(929\) 32.7091 + 32.7091i 1.07315 + 1.07315i 0.997104 + 0.0760451i \(0.0242293\pi\)
0.0760451 + 0.997104i \(0.475771\pi\)
\(930\) −1.80028 + 1.25280i −0.0590334 + 0.0410810i
\(931\) 0.654663 2.44324i 0.0214557 0.0800738i
\(932\) 19.9100 + 11.4950i 0.652173 + 0.376532i
\(933\) −2.95096 + 1.06438i −0.0966102 + 0.0348464i
\(934\) 5.30271 19.7900i 0.173510 0.647548i
\(935\) 0.540131 0.0176642
\(936\) 23.2251 14.0534i 0.759135 0.459350i
\(937\) 5.16848 0.168847 0.0844235 0.996430i \(-0.473095\pi\)
0.0844235 + 0.996430i \(0.473095\pi\)
\(938\) −3.82393 + 14.2711i −0.124856 + 0.465968i
\(939\) −15.8953 13.4164i −0.518723 0.437829i
\(940\) −0.0167917 0.00969471i −0.000547686 0.000316207i
\(941\) −1.68411 + 6.28519i −0.0549004 + 0.204891i −0.987928 0.154914i \(-0.950490\pi\)
0.933028 + 0.359805i \(0.117157\pi\)
\(942\) −4.61863 54.6146i −0.150483 1.77944i
\(943\) 12.1170 + 12.1170i 0.394584 + 0.394584i
\(944\) −1.48406 + 1.48406i −0.0483021 + 0.0483021i
\(945\) 0.00396242 0.455532i 0.000128897 0.0148184i
\(946\) −23.0229 13.2923i −0.748539 0.432169i
\(947\) 52.1450 + 13.9722i 1.69449 + 0.454036i 0.971541 0.236870i \(-0.0761215\pi\)
0.722945 + 0.690906i \(0.242788\pi\)
\(948\) −31.1447 86.3475i −1.01153 2.80444i
\(949\) 35.0190 + 27.8452i 1.13677 + 0.903894i
\(950\) 24.7214 14.2729i 0.802067 0.463073i
\(951\) −4.38433 51.8440i −0.142172 1.68116i
\(952\) −3.90969 6.77179i −0.126714 0.219475i
\(953\) 23.1715 + 40.1342i 0.750598 + 1.30007i 0.947533 + 0.319658i \(0.103568\pi\)
−0.196935 + 0.980417i \(0.563099\pi\)
\(954\) −40.1187 28.4395i −1.29889 0.920764i
\(955\) 2.04921 + 0.549085i 0.0663109 + 0.0177680i
\(956\) −22.5791 + 22.5791i −0.730261 + 0.730261i
\(957\) 2.54180 + 30.0564i 0.0821648 + 0.971585i
\(958\) 47.5452 82.3508i 1.53612 2.66063i
\(959\) −11.2608 −0.363629
\(960\) 0.842560 1.79328i 0.0271935 0.0578780i
\(961\) 8.50881 + 4.91256i 0.274478 + 0.158470i
\(962\) 7.11844 + 62.3790i 0.229508 + 2.01118i
\(963\) 4.09768 + 4.94134i 0.132046 + 0.159233i
\(964\) 11.3017 + 42.1784i 0.364002 + 1.35847i
\(965\) 0.674634 0.389500i 0.0217172 0.0125385i
\(966\) 3.14246 + 8.71237i 0.101107 + 0.280316i
\(967\) 40.4891 + 10.8490i 1.30204 + 0.348881i 0.842222 0.539131i \(-0.181247\pi\)
0.459820 + 0.888012i \(0.347914\pi\)
\(968\) −17.1872 + 4.60530i −0.552417 + 0.148020i
\(969\) −13.6018 + 1.15027i −0.436952 + 0.0369521i
\(970\) 0.346761 0.0929143i 0.0111338 0.00298330i
\(971\) 16.4936 9.52259i 0.529305 0.305594i −0.211428 0.977393i \(-0.567812\pi\)
0.740733 + 0.671799i \(0.234478\pi\)
\(972\) −47.8634 + 7.72593i −1.53522 + 0.247809i
\(973\) −11.2179 + 3.00583i −0.359629 + 0.0963624i
\(974\) 0.982332 1.70145i 0.0314759 0.0545179i
\(975\) −17.2784 + 25.9511i −0.553352 + 0.831101i
\(976\) 1.47586 + 2.55627i 0.0472412 + 0.0818242i
\(977\) −24.7669 24.7669i −0.792362 0.792362i 0.189515 0.981878i \(-0.439308\pi\)
−0.981878 + 0.189515i \(0.939308\pi\)
\(978\) −0.918480 + 1.08818i −0.0293697 + 0.0347961i
\(979\) 9.92897i 0.317331i
\(980\) −0.192807 0.192807i −0.00615901 0.00615901i
\(981\) 18.0497 8.28962i 0.576282 0.264667i
\(982\) −9.16588 + 34.2075i −0.292495 + 1.09161i
\(983\) 1.30973 + 4.88798i 0.0417739 + 0.155902i 0.983662 0.180024i \(-0.0576174\pi\)
−0.941888 + 0.335926i \(0.890951\pi\)
\(984\) −5.55801 + 30.9953i −0.177183 + 0.988093i
\(985\) 0.340564i 0.0108513i
\(986\) 43.8634 43.8634i 1.39689 1.39689i
\(987\) −0.0941198 0.0794421i −0.00299587 0.00252867i
\(988\) −22.2016 17.6535i −0.706328 0.561633i
\(989\) 14.0683i 0.447345i
\(990\) −0.490664 1.06836i −0.0155943 0.0339548i
\(991\) −4.96704 + 8.60316i −0.157783 + 0.273288i −0.934069 0.357093i \(-0.883768\pi\)
0.776286 + 0.630381i \(0.217101\pi\)
\(992\) −39.9732 −1.26915
\(993\) 10.2110 + 14.6732i 0.324037 + 0.465641i
\(994\) −7.66574 28.6089i −0.243143 0.907420i
\(995\) −0.331266 1.23630i −0.0105018 0.0391934i
\(996\) −25.6209 + 54.5308i −0.811828 + 1.72787i
\(997\) −23.3262 −0.738750 −0.369375 0.929281i \(-0.620428\pi\)
−0.369375 + 0.929281i \(0.620428\pi\)
\(998\) −13.6707 + 23.6784i −0.432740 + 0.749528i
\(999\) 10.6953 38.5704i 0.338385 1.22031i
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 819.2.fy.a.344.11 yes 336
9.5 odd 6 819.2.ew.a.617.74 yes 336
13.11 odd 12 819.2.ew.a.596.74 336
117.50 even 12 inner 819.2.fy.a.50.11 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.596.74 336 13.11 odd 12
819.2.ew.a.617.74 yes 336 9.5 odd 6
819.2.fy.a.50.11 yes 336 117.50 even 12 inner
819.2.fy.a.344.11 yes 336 1.1 even 1 trivial