Properties

Label 138.3.h.a.7.8
Level $138$
Weight $3$
Character 138.7
Analytic conductor $3.760$
Analytic rank $0$
Dimension $80$
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] = [138,3,Mod(7,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 138.h (of order \(22\), degree \(10\), 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: \(3.76022764817\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 7.8
Character \(\chi\) \(=\) 138.7
Dual form 138.3.h.a.79.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.926113 - 1.06879i) q^{2} +(1.45709 - 0.936417i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(4.69832 - 2.14565i) q^{5} +(0.348599 - 2.42456i) q^{6} +(1.48393 + 5.05379i) q^{7} +(-2.37942 - 1.52916i) q^{8} +(1.24625 - 2.72890i) q^{9} +O(q^{10})\) \(q+(0.926113 - 1.06879i) q^{2} +(1.45709 - 0.936417i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(4.69832 - 2.14565i) q^{5} +(0.348599 - 2.42456i) q^{6} +(1.48393 + 5.05379i) q^{7} +(-2.37942 - 1.52916i) q^{8} +(1.24625 - 2.72890i) q^{9} +(2.05792 - 7.00863i) q^{10} +(1.33809 - 1.15946i) q^{11} +(-2.26850 - 2.61799i) q^{12} +(-11.1767 - 3.28179i) q^{13} +(6.77574 + 3.09438i) q^{14} +(4.83667 - 7.52600i) q^{15} +(-3.83797 + 1.12693i) q^{16} +(-9.71450 - 1.39673i) q^{17} +(-1.76246 - 3.85924i) q^{18} +(9.43233 - 1.35616i) q^{19} +(-5.58490 - 8.69027i) q^{20} +(6.89468 + 5.97428i) q^{21} -2.50393i q^{22} +(20.9101 + 9.57950i) q^{23} -4.89898 q^{24} +(1.09885 - 1.26815i) q^{25} +(-13.8585 + 8.90630i) q^{26} +(-0.739490 - 5.14326i) q^{27} +(9.58234 - 4.37611i) q^{28} +(-6.28278 + 43.6977i) q^{29} +(-3.56442 - 12.1393i) q^{30} +(-22.8567 - 14.6891i) q^{31} +(-2.34994 + 5.14566i) q^{32} +(0.863982 - 2.94245i) q^{33} +(-10.4895 + 9.08924i) q^{34} +(17.8156 + 20.5603i) q^{35} +(-5.75696 - 1.69040i) q^{36} +(-28.2773 - 12.9138i) q^{37} +(7.28595 - 11.3372i) q^{38} +(-19.3587 + 5.68422i) q^{39} +(-14.4603 - 2.07908i) q^{40} +(28.6907 + 62.8238i) q^{41} +(12.7705 - 1.83612i) q^{42} +(7.93792 + 12.3517i) q^{43} +(-2.67618 - 2.31892i) q^{44} -15.4952i q^{45} +(29.6036 - 13.4769i) q^{46} +12.7189 q^{47} +(-4.53701 + 5.23599i) q^{48} +(17.8826 - 11.4925i) q^{49} +(-0.337720 - 2.34889i) q^{50} +(-15.4629 + 7.06165i) q^{51} +(-3.31553 + 23.0600i) q^{52} +(10.6235 + 36.1803i) q^{53} +(-6.18193 - 3.97288i) q^{54} +(3.79897 - 8.31858i) q^{55} +(4.19718 - 14.2943i) q^{56} +(12.4739 - 10.8087i) q^{57} +(40.8851 + 47.1840i) q^{58} +(-42.8710 - 12.5881i) q^{59} +(-16.2754 - 7.43275i) q^{60} +(-38.9315 + 60.5786i) q^{61} +(-36.8674 + 10.8253i) q^{62} +(15.6406 + 2.24878i) q^{63} +(3.32332 + 7.27706i) q^{64} +(-59.5534 + 8.56249i) q^{65} +(-2.34472 - 3.64846i) q^{66} +(-30.7485 - 26.6437i) q^{67} +19.6288i q^{68} +(39.4384 - 5.62237i) q^{69} +38.4740 q^{70} +(20.2185 - 23.3334i) q^{71} +(-7.13827 + 4.58749i) q^{72} +(-10.7362 - 74.6718i) q^{73} +(-39.9901 + 18.2629i) q^{74} +(0.413620 - 2.87679i) q^{75} +(-5.36944 - 18.2866i) q^{76} +(7.84530 + 5.04187i) q^{77} +(-11.8531 + 25.9546i) q^{78} +(42.4878 - 144.700i) q^{79} +(-15.6140 + 13.5296i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(93.7163 + 27.5176i) q^{82} +(39.0161 + 17.8180i) q^{83} +(9.86450 - 15.3495i) q^{84} +(-48.6387 + 14.2816i) q^{85} +(20.5528 + 2.95504i) q^{86} +(31.7647 + 69.5549i) q^{87} +(-4.95689 + 0.712693i) q^{88} +(-58.2826 - 90.6895i) q^{89} +(-16.5612 - 14.3503i) q^{90} -61.3549i q^{91} +(13.0124 - 44.1212i) q^{92} -47.0594 q^{93} +(11.7792 - 13.5939i) q^{94} +(41.4062 - 26.6102i) q^{95} +(1.39439 + 9.69823i) q^{96} +(-20.8578 + 9.52543i) q^{97} +(4.27828 - 29.7561i) q^{98} +(-1.49646 - 5.09648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 16 q^{4} - 24 q^{9} - 16 q^{13} - 32 q^{16} + 220 q^{17} + 132 q^{19} + 88 q^{20} - 104 q^{23} - 336 q^{25} - 208 q^{26} - 264 q^{28} - 164 q^{29} - 268 q^{31} + 552 q^{35} - 48 q^{36} + 352 q^{37} + 216 q^{39} + 192 q^{41} + 88 q^{43} + 80 q^{46} - 64 q^{47} - 40 q^{49} + 160 q^{50} - 264 q^{51} - 32 q^{52} - 352 q^{53} + 196 q^{55} - 528 q^{57} + 312 q^{58} - 696 q^{59} + 616 q^{61} + 96 q^{62} - 64 q^{64} + 44 q^{67} + 72 q^{69} - 32 q^{70} - 32 q^{71} - 284 q^{73} - 48 q^{75} - 224 q^{77} + 144 q^{78} - 440 q^{79} - 72 q^{81} - 616 q^{82} + 352 q^{83} - 532 q^{85} - 96 q^{87} + 88 q^{89} - 32 q^{92} - 192 q^{93} + 16 q^{94} + 372 q^{95} - 264 q^{97} + 1184 q^{98} + 660 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.926113 1.06879i 0.463056 0.534396i
\(3\) 1.45709 0.936417i 0.485698 0.312139i
\(4\) −0.284630 1.97964i −0.0711574 0.494911i
\(5\) 4.69832 2.14565i 0.939663 0.429130i 0.114119 0.993467i \(-0.463595\pi\)
0.825544 + 0.564337i \(0.190868\pi\)
\(6\) 0.348599 2.42456i 0.0580998 0.404093i
\(7\) 1.48393 + 5.05379i 0.211990 + 0.721971i 0.994992 + 0.0999522i \(0.0318690\pi\)
−0.783003 + 0.622019i \(0.786313\pi\)
\(8\) −2.37942 1.52916i −0.297428 0.191145i
\(9\) 1.24625 2.72890i 0.138472 0.303211i
\(10\) 2.05792 7.00863i 0.205792 0.700863i
\(11\) 1.33809 1.15946i 0.121644 0.105406i −0.591914 0.806001i \(-0.701628\pi\)
0.713559 + 0.700595i \(0.247082\pi\)
\(12\) −2.26850 2.61799i −0.189042 0.218166i
\(13\) −11.1767 3.28179i −0.859749 0.252445i −0.177999 0.984031i \(-0.556962\pi\)
−0.681750 + 0.731586i \(0.738781\pi\)
\(14\) 6.77574 + 3.09438i 0.483981 + 0.221027i
\(15\) 4.83667 7.52600i 0.322444 0.501733i
\(16\) −3.83797 + 1.12693i −0.239873 + 0.0704331i
\(17\) −9.71450 1.39673i −0.571441 0.0821608i −0.149464 0.988767i \(-0.547755\pi\)
−0.421977 + 0.906606i \(0.638664\pi\)
\(18\) −1.76246 3.85924i −0.0979143 0.214402i
\(19\) 9.43233 1.35616i 0.496438 0.0713771i 0.110452 0.993881i \(-0.464770\pi\)
0.385987 + 0.922504i \(0.373861\pi\)
\(20\) −5.58490 8.69027i −0.279245 0.434514i
\(21\) 6.89468 + 5.97428i 0.328318 + 0.284489i
\(22\) 2.50393i 0.113815i
\(23\) 20.9101 + 9.57950i 0.909136 + 0.416500i
\(24\) −4.89898 −0.204124
\(25\) 1.09885 1.26815i 0.0439542 0.0507258i
\(26\) −13.8585 + 8.90630i −0.533018 + 0.342550i
\(27\) −0.739490 5.14326i −0.0273885 0.190491i
\(28\) 9.58234 4.37611i 0.342226 0.156290i
\(29\) −6.28278 + 43.6977i −0.216648 + 1.50682i 0.533644 + 0.845709i \(0.320822\pi\)
−0.750291 + 0.661107i \(0.770087\pi\)
\(30\) −3.56442 12.1393i −0.118814 0.404644i
\(31\) −22.8567 14.6891i −0.737312 0.473842i 0.117308 0.993096i \(-0.462574\pi\)
−0.854620 + 0.519254i \(0.826210\pi\)
\(32\) −2.34994 + 5.14566i −0.0734357 + 0.160802i
\(33\) 0.863982 2.94245i 0.0261813 0.0891652i
\(34\) −10.4895 + 9.08924i −0.308516 + 0.267331i
\(35\) 17.8156 + 20.5603i 0.509018 + 0.587438i
\(36\) −5.75696 1.69040i −0.159915 0.0469554i
\(37\) −28.2773 12.9138i −0.764251 0.349022i −0.00514309 0.999987i \(-0.501637\pi\)
−0.759108 + 0.650965i \(0.774364\pi\)
\(38\) 7.28595 11.3372i 0.191735 0.298346i
\(39\) −19.3587 + 5.68422i −0.496376 + 0.145749i
\(40\) −14.4603 2.07908i −0.361508 0.0519771i
\(41\) 28.6907 + 62.8238i 0.699772 + 1.53229i 0.840247 + 0.542203i \(0.182410\pi\)
−0.140475 + 0.990084i \(0.544863\pi\)
\(42\) 12.7705 1.83612i 0.304060 0.0437172i
\(43\) 7.93792 + 12.3517i 0.184603 + 0.287248i 0.921204 0.389080i \(-0.127207\pi\)
−0.736601 + 0.676327i \(0.763571\pi\)
\(44\) −2.67618 2.31892i −0.0608222 0.0527028i
\(45\) 15.4952i 0.344338i
\(46\) 29.6036 13.4769i 0.643557 0.292975i
\(47\) 12.7189 0.270616 0.135308 0.990804i \(-0.456798\pi\)
0.135308 + 0.990804i \(0.456798\pi\)
\(48\) −4.53701 + 5.23599i −0.0945210 + 0.109083i
\(49\) 17.8826 11.4925i 0.364951 0.234540i
\(50\) −0.337720 2.34889i −0.00675439 0.0469778i
\(51\) −15.4629 + 7.06165i −0.303193 + 0.138464i
\(52\) −3.31553 + 23.0600i −0.0637603 + 0.443462i
\(53\) 10.6235 + 36.1803i 0.200443 + 0.682647i 0.996952 + 0.0780195i \(0.0248597\pi\)
−0.796509 + 0.604627i \(0.793322\pi\)
\(54\) −6.18193 3.97288i −0.114480 0.0735719i
\(55\) 3.79897 8.31858i 0.0690722 0.151247i
\(56\) 4.19718 14.2943i 0.0749497 0.255255i
\(57\) 12.4739 10.8087i 0.218840 0.189626i
\(58\) 40.8851 + 47.1840i 0.704916 + 0.813517i
\(59\) −42.8710 12.5881i −0.726627 0.213357i −0.102559 0.994727i \(-0.532703\pi\)
−0.624068 + 0.781370i \(0.714521\pi\)
\(60\) −16.2754 7.43275i −0.271257 0.123879i
\(61\) −38.9315 + 60.5786i −0.638221 + 0.993091i 0.359970 + 0.932964i \(0.382787\pi\)
−0.998191 + 0.0601271i \(0.980849\pi\)
\(62\) −36.8674 + 10.8253i −0.594636 + 0.174601i
\(63\) 15.6406 + 2.24878i 0.248264 + 0.0356949i
\(64\) 3.32332 + 7.27706i 0.0519269 + 0.113704i
\(65\) −59.5534 + 8.56249i −0.916206 + 0.131731i
\(66\) −2.34472 3.64846i −0.0355261 0.0552797i
\(67\) −30.7485 26.6437i −0.458933 0.397668i 0.394479 0.918905i \(-0.370925\pi\)
−0.853412 + 0.521237i \(0.825471\pi\)
\(68\) 19.6288i 0.288659i
\(69\) 39.4384 5.62237i 0.571571 0.0814836i
\(70\) 38.4740 0.549629
\(71\) 20.2185 23.3334i 0.284768 0.328639i −0.595286 0.803514i \(-0.702961\pi\)
0.880053 + 0.474875i \(0.157507\pi\)
\(72\) −7.13827 + 4.58749i −0.0991427 + 0.0637151i
\(73\) −10.7362 74.6718i −0.147071 1.02290i −0.920981 0.389607i \(-0.872611\pi\)
0.773910 0.633295i \(-0.218298\pi\)
\(74\) −39.9901 + 18.2629i −0.540407 + 0.246796i
\(75\) 0.413620 2.87679i 0.00551494 0.0383572i
\(76\) −5.36944 18.2866i −0.0706505 0.240614i
\(77\) 7.84530 + 5.04187i 0.101887 + 0.0654788i
\(78\) −11.8531 + 25.9546i −0.151963 + 0.332751i
\(79\) 42.4878 144.700i 0.537820 1.83165i −0.0172621 0.999851i \(-0.505495\pi\)
0.555082 0.831796i \(-0.312687\pi\)
\(80\) −15.6140 + 13.5296i −0.195175 + 0.169120i
\(81\) −5.89375 6.80175i −0.0727623 0.0839722i
\(82\) 93.7163 + 27.5176i 1.14288 + 0.335580i
\(83\) 39.0161 + 17.8180i 0.470073 + 0.214675i 0.636345 0.771405i \(-0.280446\pi\)
−0.166272 + 0.986080i \(0.553173\pi\)
\(84\) 9.86450 15.3495i 0.117435 0.182732i
\(85\) −48.6387 + 14.2816i −0.572220 + 0.168019i
\(86\) 20.5528 + 2.95504i 0.238986 + 0.0343609i
\(87\) 31.7647 + 69.5549i 0.365111 + 0.799482i
\(88\) −4.95689 + 0.712693i −0.0563283 + 0.00809878i
\(89\) −58.2826 90.6895i −0.654861 1.01898i −0.996852 0.0792805i \(-0.974738\pi\)
0.341991 0.939703i \(-0.388899\pi\)
\(90\) −16.5612 14.3503i −0.184013 0.159448i
\(91\) 61.3549i 0.674229i
\(92\) 13.0124 44.1212i 0.141439 0.479578i
\(93\) −47.0594 −0.506015
\(94\) 11.7792 13.5939i 0.125310 0.144616i
\(95\) 41.4062 26.6102i 0.435855 0.280107i
\(96\) 1.39439 + 9.69823i 0.0145249 + 0.101023i
\(97\) −20.8578 + 9.52543i −0.215029 + 0.0982003i −0.520017 0.854156i \(-0.674075\pi\)
0.304989 + 0.952356i \(0.401347\pi\)
\(98\) 4.27828 29.7561i 0.0436559 0.303634i
\(99\) −1.49646 5.09648i −0.0151158 0.0514796i
\(100\) −2.82324 1.81439i −0.0282324 0.0181439i
\(101\) 39.9595 87.4991i 0.395639 0.866328i −0.602055 0.798454i \(-0.705651\pi\)
0.997694 0.0678735i \(-0.0216214\pi\)
\(102\) −6.77292 + 23.0665i −0.0664012 + 0.226142i
\(103\) −2.14938 + 1.86245i −0.0208678 + 0.0180821i −0.665232 0.746637i \(-0.731667\pi\)
0.644364 + 0.764719i \(0.277122\pi\)
\(104\) 21.5758 + 24.8998i 0.207460 + 0.239421i
\(105\) 45.2121 + 13.2755i 0.430592 + 0.126433i
\(106\) 48.5077 + 22.1527i 0.457620 + 0.208988i
\(107\) 60.3917 93.9714i 0.564409 0.878237i −0.435349 0.900262i \(-0.643375\pi\)
0.999757 + 0.0220249i \(0.00701129\pi\)
\(108\) −9.97134 + 2.92785i −0.0923273 + 0.0271097i
\(109\) −77.0498 11.0781i −0.706878 0.101634i −0.220506 0.975386i \(-0.570771\pi\)
−0.486372 + 0.873752i \(0.661680\pi\)
\(110\) −5.37256 11.7643i −0.0488414 0.106948i
\(111\) −53.2953 + 7.66271i −0.480138 + 0.0690335i
\(112\) −11.3905 17.7240i −0.101701 0.158250i
\(113\) −96.9713 84.0261i −0.858153 0.743594i 0.110006 0.993931i \(-0.464913\pi\)
−0.968159 + 0.250337i \(0.919458\pi\)
\(114\) 23.3420i 0.204754i
\(115\) 118.797 + 0.141742i 1.03301 + 0.00123254i
\(116\) 88.2941 0.761156
\(117\) −22.8846 + 26.4102i −0.195595 + 0.225729i
\(118\) −53.1574 + 34.1622i −0.450486 + 0.289510i
\(119\) −7.35681 51.1677i −0.0618219 0.429981i
\(120\) −23.0170 + 10.5115i −0.191808 + 0.0875958i
\(121\) −16.7740 + 116.665i −0.138628 + 0.964177i
\(122\) 28.6909 + 97.7122i 0.235171 + 0.800920i
\(123\) 100.634 + 64.6737i 0.818165 + 0.525803i
\(124\) −22.5735 + 49.4290i −0.182044 + 0.398621i
\(125\) −33.9375 + 115.580i −0.271500 + 0.924643i
\(126\) 16.8885 14.6339i 0.134035 0.116142i
\(127\) −18.3267 21.1502i −0.144305 0.166537i 0.678996 0.734142i \(-0.262415\pi\)
−0.823301 + 0.567605i \(0.807870\pi\)
\(128\) 10.8554 + 3.18744i 0.0848080 + 0.0249019i
\(129\) 23.1326 + 10.5643i 0.179323 + 0.0818938i
\(130\) −46.0017 + 71.5800i −0.353859 + 0.550615i
\(131\) 140.559 41.2718i 1.07297 0.315052i 0.302906 0.953020i \(-0.402043\pi\)
0.770062 + 0.637969i \(0.220225\pi\)
\(132\) −6.07092 0.872867i −0.0459918 0.00661263i
\(133\) 20.8507 + 45.6566i 0.156772 + 0.343283i
\(134\) −56.9532 + 8.18863i −0.425024 + 0.0611092i
\(135\) −14.5100 22.5780i −0.107481 0.167244i
\(136\) 20.9791 + 18.1785i 0.154258 + 0.133665i
\(137\) 221.153i 1.61426i −0.590377 0.807128i \(-0.701021\pi\)
0.590377 0.807128i \(-0.298979\pi\)
\(138\) 30.5153 47.3584i 0.221125 0.343177i
\(139\) −82.0604 −0.590362 −0.295181 0.955441i \(-0.595380\pi\)
−0.295181 + 0.955441i \(0.595380\pi\)
\(140\) 35.6313 41.1207i 0.254509 0.293719i
\(141\) 18.5327 11.9102i 0.131438 0.0844698i
\(142\) −6.21391 43.2187i −0.0437599 0.304357i
\(143\) −18.7606 + 8.56767i −0.131193 + 0.0599138i
\(144\) −1.70778 + 11.8779i −0.0118596 + 0.0824851i
\(145\) 64.2414 + 218.786i 0.443044 + 1.50887i
\(146\) −89.7515 57.6798i −0.614736 0.395067i
\(147\) 15.2949 33.4912i 0.104047 0.227831i
\(148\) −17.5162 + 59.6546i −0.118352 + 0.403071i
\(149\) −17.6689 + 15.3102i −0.118583 + 0.102753i −0.712134 0.702044i \(-0.752271\pi\)
0.593551 + 0.804797i \(0.297726\pi\)
\(150\) −2.69163 3.10631i −0.0179442 0.0207087i
\(151\) 231.710 + 68.0363i 1.53450 + 0.450571i 0.936426 0.350866i \(-0.114113\pi\)
0.598079 + 0.801437i \(0.295931\pi\)
\(152\) −24.5173 11.1967i −0.161298 0.0736624i
\(153\) −15.9182 + 24.7692i −0.104040 + 0.161890i
\(154\) 12.6543 3.71565i 0.0821711 0.0241276i
\(155\) −138.906 19.9716i −0.896165 0.128849i
\(156\) 16.7628 + 36.7054i 0.107454 + 0.235291i
\(157\) −291.637 + 41.9310i −1.85756 + 0.267077i −0.977984 0.208682i \(-0.933083\pi\)
−0.879576 + 0.475759i \(0.842174\pi\)
\(158\) −115.306 179.419i −0.729783 1.13556i
\(159\) 49.3592 + 42.7700i 0.310436 + 0.268994i
\(160\) 29.2181i 0.182613i
\(161\) −17.3837 + 119.891i −0.107973 + 0.744663i
\(162\) −12.7279 −0.0785674
\(163\) −120.229 + 138.752i −0.737602 + 0.851238i −0.993306 0.115517i \(-0.963148\pi\)
0.255703 + 0.966755i \(0.417693\pi\)
\(164\) 116.202 74.6788i 0.708551 0.455358i
\(165\) −2.25421 15.6784i −0.0136619 0.0950205i
\(166\) 55.1771 25.1985i 0.332392 0.151798i
\(167\) −7.24905 + 50.4182i −0.0434075 + 0.301905i 0.956539 + 0.291603i \(0.0941886\pi\)
−0.999947 + 0.0103026i \(0.996721\pi\)
\(168\) −7.26973 24.7584i −0.0432722 0.147372i
\(169\) −28.0225 18.0090i −0.165814 0.106562i
\(170\) −29.7809 + 65.2110i −0.175182 + 0.383594i
\(171\) 8.05416 27.4300i 0.0471004 0.160409i
\(172\) 22.1925 19.2299i 0.129026 0.111802i
\(173\) 14.0669 + 16.2340i 0.0813114 + 0.0938384i 0.794947 0.606678i \(-0.207498\pi\)
−0.713636 + 0.700517i \(0.752953\pi\)
\(174\) 103.757 + 30.4659i 0.596307 + 0.175091i
\(175\) 8.03957 + 3.67155i 0.0459404 + 0.0209803i
\(176\) −3.82892 + 5.95791i −0.0217552 + 0.0338518i
\(177\) −74.2547 + 21.8032i −0.419518 + 0.123182i
\(178\) −150.904 21.6968i −0.847778 0.121892i
\(179\) 64.0658 + 140.285i 0.357910 + 0.783713i 0.999856 + 0.0169634i \(0.00539986\pi\)
−0.641946 + 0.766749i \(0.721873\pi\)
\(180\) −30.6750 + 4.41040i −0.170417 + 0.0245022i
\(181\) 84.1022 + 130.866i 0.464653 + 0.723014i 0.991945 0.126670i \(-0.0404290\pi\)
−0.527292 + 0.849684i \(0.676793\pi\)
\(182\) −65.5756 56.8215i −0.360305 0.312206i
\(183\) 124.725i 0.681556i
\(184\) −35.1054 54.7687i −0.190790 0.297656i
\(185\) −160.564 −0.867914
\(186\) −43.5824 + 50.2967i −0.234314 + 0.270412i
\(187\) −14.6183 + 9.39463i −0.0781728 + 0.0502386i
\(188\) −3.62019 25.1790i −0.0192563 0.133931i
\(189\) 24.8956 11.3695i 0.131723 0.0601559i
\(190\) 9.90613 68.8986i 0.0521375 0.362624i
\(191\) 46.3104 + 157.719i 0.242463 + 0.825753i 0.987349 + 0.158561i \(0.0506856\pi\)
−0.744886 + 0.667192i \(0.767496\pi\)
\(192\) 11.6568 + 7.49134i 0.0607122 + 0.0390174i
\(193\) −116.892 + 255.957i −0.605657 + 1.32620i 0.319848 + 0.947469i \(0.396368\pi\)
−0.925505 + 0.378735i \(0.876359\pi\)
\(194\) −9.13597 + 31.1142i −0.0470926 + 0.160383i
\(195\) −78.7569 + 68.2432i −0.403881 + 0.349965i
\(196\) −27.8409 32.1301i −0.142045 0.163929i
\(197\) 241.277 + 70.8454i 1.22476 + 0.359621i 0.829269 0.558849i \(-0.188757\pi\)
0.395489 + 0.918471i \(0.370575\pi\)
\(198\) −6.83296 3.12051i −0.0345099 0.0157602i
\(199\) 90.2376 140.412i 0.453455 0.705590i −0.536976 0.843598i \(-0.680433\pi\)
0.990431 + 0.138007i \(0.0440698\pi\)
\(200\) −4.55384 + 1.33713i −0.0227692 + 0.00668564i
\(201\) −69.7531 10.0290i −0.347030 0.0498954i
\(202\) −56.5113 123.742i −0.279759 0.612586i
\(203\) −230.162 + 33.0923i −1.13380 + 0.163016i
\(204\) 18.3807 + 28.6010i 0.0901017 + 0.140201i
\(205\) 269.596 + 233.606i 1.31510 + 1.13954i
\(206\) 4.02209i 0.0195247i
\(207\) 52.2006 45.1231i 0.252177 0.217986i
\(208\) 46.5943 0.224011
\(209\) 11.0489 12.7511i 0.0528654 0.0610100i
\(210\) 56.0602 36.0277i 0.266954 0.171561i
\(211\) −53.9343 375.121i −0.255613 1.77782i −0.563216 0.826310i \(-0.690436\pi\)
0.307603 0.951515i \(-0.400473\pi\)
\(212\) 68.6003 31.3287i 0.323586 0.147777i
\(213\) 7.61046 52.9319i 0.0357298 0.248507i
\(214\) −44.5062 151.574i −0.207973 0.708291i
\(215\) 63.7972 + 41.0000i 0.296731 + 0.190698i
\(216\) −6.10533 + 13.3688i −0.0282654 + 0.0618926i
\(217\) 40.3180 137.311i 0.185797 0.632767i
\(218\) −83.1969 + 72.0905i −0.381637 + 0.330691i
\(219\) −85.5676 98.7503i −0.390720 0.450915i
\(220\) −17.5491 5.15289i −0.0797688 0.0234222i
\(221\) 103.993 + 47.4918i 0.470555 + 0.214895i
\(222\) −41.1677 + 64.0581i −0.185440 + 0.288550i
\(223\) 352.673 103.554i 1.58149 0.464368i 0.631172 0.775643i \(-0.282574\pi\)
0.950320 + 0.311275i \(0.100756\pi\)
\(224\) −29.4922 4.24034i −0.131662 0.0189301i
\(225\) −2.09120 4.57908i −0.00929420 0.0203515i
\(226\) −179.613 + 25.8244i −0.794746 + 0.114267i
\(227\) −142.941 222.421i −0.629696 0.979826i −0.998729 0.0504096i \(-0.983947\pi\)
0.369033 0.929416i \(-0.379689\pi\)
\(228\) −24.9477 21.6173i −0.109420 0.0948128i
\(229\) 359.267i 1.56885i −0.620222 0.784426i \(-0.712958\pi\)
0.620222 0.784426i \(-0.287042\pi\)
\(230\) 110.171 126.838i 0.479003 0.551468i
\(231\) 16.1526 0.0699249
\(232\) 81.7703 94.3679i 0.352458 0.406758i
\(233\) 260.561 167.452i 1.11829 0.718678i 0.155202 0.987883i \(-0.450397\pi\)
0.963083 + 0.269204i \(0.0867607\pi\)
\(234\) 7.03331 + 48.9177i 0.0300569 + 0.209050i
\(235\) 59.7576 27.2904i 0.254288 0.116129i
\(236\) −12.7175 + 88.4522i −0.0538877 + 0.374797i
\(237\) −73.5910 250.628i −0.310510 1.05750i
\(238\) −61.5009 39.5242i −0.258407 0.166068i
\(239\) −135.825 + 297.416i −0.568306 + 1.24442i 0.379388 + 0.925237i \(0.376134\pi\)
−0.947694 + 0.319179i \(0.896593\pi\)
\(240\) −10.0817 + 34.3352i −0.0420071 + 0.143063i
\(241\) 142.390 123.382i 0.590830 0.511957i −0.307344 0.951599i \(-0.599440\pi\)
0.898173 + 0.439642i \(0.144895\pi\)
\(242\) 109.156 + 125.973i 0.451060 + 0.520551i
\(243\) −14.9570 4.39178i −0.0615515 0.0180732i
\(244\) 131.005 + 59.8280i 0.536906 + 0.245197i
\(245\) 59.3594 92.3651i 0.242283 0.377000i
\(246\) 162.321 47.6619i 0.659843 0.193747i
\(247\) −109.873 15.7974i −0.444831 0.0639571i
\(248\) 31.9237 + 69.9032i 0.128725 + 0.281868i
\(249\) 73.5352 10.5728i 0.295322 0.0424609i
\(250\) 92.1014 + 143.313i 0.368406 + 0.573250i
\(251\) −44.8846 38.8928i −0.178823 0.154951i 0.560850 0.827917i \(-0.310474\pi\)
−0.739673 + 0.672966i \(0.765020\pi\)
\(252\) 31.6029i 0.125408i
\(253\) 39.0867 11.4262i 0.154493 0.0451630i
\(254\) −39.5778 −0.155818
\(255\) −57.4976 + 66.3558i −0.225481 + 0.260219i
\(256\) 13.4601 8.65025i 0.0525783 0.0337901i
\(257\) −42.5056 295.633i −0.165391 1.15032i −0.888261 0.459339i \(-0.848086\pi\)
0.722870 0.690984i \(-0.242823\pi\)
\(258\) 32.7144 14.9402i 0.126800 0.0579077i
\(259\) 23.3022 162.071i 0.0899701 0.625756i
\(260\) 33.9013 + 115.457i 0.130390 + 0.444067i
\(261\) 111.417 + 71.6031i 0.426883 + 0.274341i
\(262\) 86.0624 188.450i 0.328483 0.719276i
\(263\) −73.5371 + 250.444i −0.279609 + 0.952260i 0.693218 + 0.720728i \(0.256192\pi\)
−0.972827 + 0.231532i \(0.925626\pi\)
\(264\) −6.55527 + 5.68017i −0.0248306 + 0.0215158i
\(265\) 127.543 + 147.192i 0.481293 + 0.555442i
\(266\) 68.1075 + 19.9982i 0.256043 + 0.0751810i
\(267\) −169.847 77.5663i −0.636129 0.290510i
\(268\) −43.9931 + 68.4546i −0.164153 + 0.255428i
\(269\) 307.612 90.3229i 1.14354 0.335773i 0.345523 0.938410i \(-0.387702\pi\)
0.798015 + 0.602637i \(0.205883\pi\)
\(270\) −37.5691 5.40162i −0.139145 0.0200060i
\(271\) 209.571 + 458.897i 0.773326 + 1.69335i 0.719190 + 0.694813i \(0.244513\pi\)
0.0541356 + 0.998534i \(0.482760\pi\)
\(272\) 38.8580 5.58694i 0.142860 0.0205402i
\(273\) −57.4538 89.3998i −0.210453 0.327472i
\(274\) −236.366 204.813i −0.862651 0.747491i
\(275\) 2.97097i 0.0108035i
\(276\) −22.3556 76.4737i −0.0809986 0.277079i
\(277\) −43.5771 −0.157318 −0.0786590 0.996902i \(-0.525064\pi\)
−0.0786590 + 0.996902i \(0.525064\pi\)
\(278\) −75.9972 + 87.7054i −0.273371 + 0.315487i
\(279\) −68.5700 + 44.0673i −0.245771 + 0.157947i
\(280\) −10.9508 76.1648i −0.0391102 0.272017i
\(281\) 65.6547 29.9835i 0.233646 0.106703i −0.295152 0.955450i \(-0.595370\pi\)
0.528798 + 0.848748i \(0.322643\pi\)
\(282\) 4.43381 30.8378i 0.0157227 0.109354i
\(283\) −117.258 399.344i −0.414339 1.41111i −0.857416 0.514625i \(-0.827931\pi\)
0.443077 0.896484i \(-0.353887\pi\)
\(284\) −51.9466 33.3840i −0.182910 0.117549i
\(285\) 35.4145 77.5470i 0.124262 0.272095i
\(286\) −8.21736 + 27.9858i −0.0287320 + 0.0978523i
\(287\) −274.924 + 238.223i −0.957922 + 0.830044i
\(288\) 11.1134 + 12.8255i 0.0385880 + 0.0445330i
\(289\) −184.873 54.2836i −0.639698 0.187832i
\(290\) 293.332 + 133.960i 1.01149 + 0.461931i
\(291\) −21.4720 + 33.4110i −0.0737868 + 0.114815i
\(292\) −144.768 + 42.5076i −0.495780 + 0.145574i
\(293\) −193.651 27.8428i −0.660924 0.0950265i −0.196313 0.980541i \(-0.562897\pi\)
−0.464611 + 0.885515i \(0.653806\pi\)
\(294\) −21.6303 47.3637i −0.0735724 0.161101i
\(295\) −228.431 + 32.8434i −0.774343 + 0.111334i
\(296\) 47.5363 + 73.9680i 0.160596 + 0.249892i
\(297\) −6.95291 6.02473i −0.0234105 0.0202853i
\(298\) 33.0634i 0.110951i
\(299\) −202.269 175.690i −0.676485 0.587592i
\(300\) −5.81275 −0.0193758
\(301\) −50.6434 + 58.4456i −0.168251 + 0.194171i
\(302\) 287.306 184.641i 0.951346 0.611393i
\(303\) −23.7109 164.913i −0.0782539 0.544268i
\(304\) −34.6727 + 15.8345i −0.114055 + 0.0520872i
\(305\) −52.9321 + 368.151i −0.173548 + 1.20705i
\(306\) 11.7310 + 39.9523i 0.0383368 + 0.130563i
\(307\) −262.518 168.710i −0.855108 0.549545i 0.0380560 0.999276i \(-0.487883\pi\)
−0.893164 + 0.449731i \(0.851520\pi\)
\(308\) 7.74810 16.9660i 0.0251562 0.0550843i
\(309\) −1.38782 + 4.72649i −0.00449134 + 0.0152961i
\(310\) −149.988 + 129.965i −0.483831 + 0.419242i
\(311\) 244.704 + 282.404i 0.786831 + 0.908051i 0.997583 0.0694885i \(-0.0221367\pi\)
−0.210752 + 0.977540i \(0.567591\pi\)
\(312\) 54.7546 + 16.0774i 0.175496 + 0.0515301i
\(313\) 416.211 + 190.077i 1.32975 + 0.607276i 0.948377 0.317146i \(-0.102725\pi\)
0.381372 + 0.924422i \(0.375452\pi\)
\(314\) −225.273 + 350.532i −0.717430 + 1.11634i
\(315\) 78.3097 22.9938i 0.248602 0.0729962i
\(316\) −298.548 42.9247i −0.944771 0.135838i
\(317\) −55.1507 120.763i −0.173977 0.380956i 0.802477 0.596683i \(-0.203515\pi\)
−0.976454 + 0.215727i \(0.930788\pi\)
\(318\) 91.4245 13.1449i 0.287498 0.0413360i
\(319\) 42.2588 + 65.7560i 0.132473 + 0.206132i
\(320\) 31.2280 + 27.0592i 0.0975876 + 0.0845601i
\(321\) 193.477i 0.602732i
\(322\) 112.039 + 129.612i 0.347947 + 0.402522i
\(323\) −93.5245 −0.289550
\(324\) −11.7875 + 13.6035i −0.0363812 + 0.0419861i
\(325\) −16.4434 + 10.5675i −0.0505950 + 0.0325155i
\(326\) 36.9510 + 257.000i 0.113347 + 0.788343i
\(327\) −122.642 + 56.0089i −0.375053 + 0.171281i
\(328\) 27.8006 193.357i 0.0847578 0.589503i
\(329\) 18.8740 + 64.2789i 0.0573678 + 0.195377i
\(330\) −18.8446 12.1107i −0.0571048 0.0366990i
\(331\) −150.105 + 328.685i −0.453490 + 0.993006i 0.535433 + 0.844578i \(0.320149\pi\)
−0.988923 + 0.148428i \(0.952579\pi\)
\(332\) 24.1682 82.3094i 0.0727959 0.247920i
\(333\) −70.4808 + 61.0720i −0.211654 + 0.183399i
\(334\) 47.1731 + 54.4407i 0.141237 + 0.162996i
\(335\) −201.634 59.2052i −0.601893 0.176732i
\(336\) −33.1942 15.1593i −0.0987923 0.0451169i
\(337\) 69.9146 108.789i 0.207462 0.322817i −0.721893 0.692005i \(-0.756728\pi\)
0.929355 + 0.369188i \(0.120364\pi\)
\(338\) −45.1998 + 13.2719i −0.133727 + 0.0392659i
\(339\) −219.980 31.6283i −0.648908 0.0932988i
\(340\) 42.1165 + 92.2223i 0.123872 + 0.271242i
\(341\) −47.6157 + 6.84610i −0.139635 + 0.0200765i
\(342\) −21.8578 34.0115i −0.0639118 0.0994487i
\(343\) 279.669 + 242.334i 0.815361 + 0.706514i
\(344\) 41.5282i 0.120722i
\(345\) 173.231 111.037i 0.502118 0.321846i
\(346\) 30.3783 0.0877986
\(347\) −318.425 + 367.482i −0.917652 + 1.05903i 0.0804076 + 0.996762i \(0.474378\pi\)
−0.998060 + 0.0622648i \(0.980168\pi\)
\(348\) 128.653 82.6801i 0.369692 0.237587i
\(349\) 3.37877 + 23.4998i 0.00968128 + 0.0673348i 0.994089 0.108565i \(-0.0346256\pi\)
−0.984408 + 0.175900i \(0.943716\pi\)
\(350\) 11.3697 5.19235i 0.0324848 0.0148353i
\(351\) −8.61401 + 59.9117i −0.0245413 + 0.170689i
\(352\) 2.82175 + 9.61001i 0.00801635 + 0.0273012i
\(353\) −83.3773 53.5833i −0.236196 0.151794i 0.417189 0.908820i \(-0.363015\pi\)
−0.653385 + 0.757026i \(0.726652\pi\)
\(354\) −45.4652 + 99.5550i −0.128433 + 0.281229i
\(355\) 44.9276 153.009i 0.126557 0.431013i
\(356\) −162.944 + 141.192i −0.457708 + 0.396606i
\(357\) −58.6339 67.6671i −0.164241 0.189544i
\(358\) 209.267 + 61.4464i 0.584545 + 0.171638i
\(359\) 390.604 + 178.383i 1.08803 + 0.496889i 0.876951 0.480579i \(-0.159574\pi\)
0.211083 + 0.977468i \(0.432301\pi\)
\(360\) −23.6947 + 36.8697i −0.0658187 + 0.102416i
\(361\) −259.247 + 76.1219i −0.718137 + 0.210864i
\(362\) 217.756 + 31.3086i 0.601536 + 0.0864878i
\(363\) 84.8063 + 185.700i 0.233626 + 0.511570i
\(364\) −121.461 + 17.4634i −0.333683 + 0.0479764i
\(365\) −210.662 327.796i −0.577155 0.898071i
\(366\) 133.305 + 115.509i 0.364221 + 0.315599i
\(367\) 299.504i 0.816087i −0.912962 0.408044i \(-0.866211\pi\)
0.912962 0.408044i \(-0.133789\pi\)
\(368\) −91.0479 13.2016i −0.247413 0.0358739i
\(369\) 207.195 0.561505
\(370\) −148.700 + 171.610i −0.401893 + 0.463809i
\(371\) −167.083 + 107.378i −0.450359 + 0.289428i
\(372\) 13.3945 + 93.1609i 0.0360068 + 0.250432i
\(373\) −543.906 + 248.394i −1.45819 + 0.665935i −0.977496 0.210952i \(-0.932344\pi\)
−0.480697 + 0.876887i \(0.659616\pi\)
\(374\) −3.49732 + 24.3244i −0.00935113 + 0.0650386i
\(375\) 58.7814 + 200.191i 0.156750 + 0.533843i
\(376\) −30.2638 19.4493i −0.0804887 0.0517270i
\(377\) 213.627 467.779i 0.566651 1.24079i
\(378\) 10.9046 37.1377i 0.0288481 0.0982478i
\(379\) 301.791 261.504i 0.796283 0.689983i −0.158476 0.987363i \(-0.550658\pi\)
0.954759 + 0.297379i \(0.0961126\pi\)
\(380\) −64.4641 74.3955i −0.169642 0.195778i
\(381\) −46.5092 13.6563i −0.122071 0.0358434i
\(382\) 211.457 + 96.5693i 0.553553 + 0.252799i
\(383\) 162.123 252.269i 0.423298 0.658665i −0.562462 0.826823i \(-0.690146\pi\)
0.985760 + 0.168158i \(0.0537820\pi\)
\(384\) 18.8021 5.52081i 0.0489639 0.0143771i
\(385\) 47.6778 + 6.85504i 0.123838 + 0.0178053i
\(386\) 165.310 + 361.978i 0.428264 + 0.937768i
\(387\) 43.5990 6.26859i 0.112659 0.0161979i
\(388\) 24.7937 + 38.5797i 0.0639013 + 0.0994323i
\(389\) 543.024 + 470.533i 1.39595 + 1.20960i 0.949095 + 0.314991i \(0.102001\pi\)
0.446855 + 0.894607i \(0.352544\pi\)
\(390\) 147.376i 0.377886i
\(391\) −189.751 122.266i −0.485297 0.312701i
\(392\) −60.1242 −0.153378
\(393\) 166.160 191.759i 0.422799 0.487935i
\(394\) 299.169 192.264i 0.759312 0.487980i
\(395\) −110.855 771.011i −0.280645 1.95193i
\(396\) −9.66327 + 4.41307i −0.0244022 + 0.0111441i
\(397\) 44.4568 309.204i 0.111982 0.778851i −0.854006 0.520263i \(-0.825834\pi\)
0.965988 0.258588i \(-0.0832570\pi\)
\(398\) −66.5014 226.483i −0.167089 0.569053i
\(399\) 73.1350 + 47.0010i 0.183296 + 0.117797i
\(400\) −2.78826 + 6.10544i −0.00697065 + 0.0152636i
\(401\) −136.229 + 463.953i −0.339723 + 1.15699i 0.595626 + 0.803262i \(0.296904\pi\)
−0.935349 + 0.353727i \(0.884914\pi\)
\(402\) −75.3181 + 65.2635i −0.187359 + 0.162347i
\(403\) 207.257 + 239.187i 0.514284 + 0.593516i
\(404\) −184.591 54.2007i −0.456908 0.134160i
\(405\) −42.2849 19.3108i −0.104407 0.0476811i
\(406\) −177.787 + 276.643i −0.437900 + 0.681386i
\(407\) −52.8106 + 15.5066i −0.129756 + 0.0380997i
\(408\) 47.5911 + 6.84257i 0.116645 + 0.0167710i
\(409\) 138.171 + 302.553i 0.337827 + 0.739738i 0.999953 0.00965449i \(-0.00307317\pi\)
−0.662127 + 0.749392i \(0.730346\pi\)
\(410\) 499.352 71.7960i 1.21793 0.175112i
\(411\) −207.091 322.241i −0.503872 0.784041i
\(412\) 4.29877 + 3.72491i 0.0104339 + 0.00904103i
\(413\) 235.341i 0.569833i
\(414\) 0.116429 97.5807i 0.000281228 0.235702i
\(415\) 221.541 0.533834
\(416\) 43.1516 49.7996i 0.103730 0.119711i
\(417\) −119.570 + 76.8428i −0.286738 + 0.184275i
\(418\) −3.39574 23.6179i −0.00812378 0.0565021i
\(419\) 127.825 58.3758i 0.305072 0.139322i −0.256997 0.966412i \(-0.582733\pi\)
0.562069 + 0.827091i \(0.310006\pi\)
\(420\) 13.4120 93.2824i 0.0319333 0.222101i
\(421\) 97.3761 + 331.633i 0.231297 + 0.787726i 0.990576 + 0.136961i \(0.0437335\pi\)
−0.759279 + 0.650765i \(0.774448\pi\)
\(422\) −450.875 289.760i −1.06842 0.686635i
\(423\) 15.8509 34.7087i 0.0374726 0.0820536i
\(424\) 30.0478 102.333i 0.0708673 0.241352i
\(425\) −12.4461 + 10.7846i −0.0292849 + 0.0253755i
\(426\) −49.5250 57.1549i −0.116256 0.134166i
\(427\) −363.923 106.857i −0.852279 0.250252i
\(428\) −203.219 92.8070i −0.474811 0.216839i
\(429\) −19.3130 + 30.0516i −0.0450187 + 0.0700504i
\(430\) 102.904 30.2153i 0.239311 0.0702681i
\(431\) 651.687 + 93.6985i 1.51204 + 0.217398i 0.847877 0.530194i \(-0.177881\pi\)
0.664159 + 0.747592i \(0.268790\pi\)
\(432\) 8.63424 + 18.9063i 0.0199867 + 0.0437647i
\(433\) 7.71894 1.10982i 0.0178267 0.00256309i −0.133396 0.991063i \(-0.542588\pi\)
0.151222 + 0.988500i \(0.451679\pi\)
\(434\) −109.417 170.257i −0.252113 0.392296i
\(435\) 298.481 + 258.635i 0.686163 + 0.594564i
\(436\) 155.684i 0.357074i
\(437\) 210.223 + 61.9995i 0.481058 + 0.141875i
\(438\) −184.789 −0.421892
\(439\) −380.536 + 439.162i −0.866824 + 1.00037i 0.133133 + 0.991098i \(0.457496\pi\)
−0.999957 + 0.00927053i \(0.997049\pi\)
\(440\) −21.7598 + 13.9842i −0.0494542 + 0.0317823i
\(441\) −9.07561 63.1222i −0.0205796 0.143134i
\(442\) 147.068 67.1636i 0.332732 0.151954i
\(443\) −53.0862 + 369.222i −0.119833 + 0.833459i 0.837905 + 0.545817i \(0.183781\pi\)
−0.957738 + 0.287642i \(0.907129\pi\)
\(444\) 30.3389 + 103.325i 0.0683308 + 0.232713i
\(445\) −468.418 301.034i −1.05263 0.676481i
\(446\) 215.937 472.836i 0.484164 1.06017i
\(447\) −11.4085 + 38.8539i −0.0255225 + 0.0869215i
\(448\) −31.8452 + 27.5940i −0.0710830 + 0.0615938i
\(449\) −466.156 537.972i −1.03821 1.19816i −0.979824 0.199862i \(-0.935951\pi\)
−0.0583842 0.998294i \(-0.518595\pi\)
\(450\) −6.83076 2.00569i −0.0151795 0.00445710i
\(451\) 111.232 + 50.7981i 0.246635 + 0.112634i
\(452\) −138.741 + 215.885i −0.306948 + 0.477621i
\(453\) 401.334 117.842i 0.885947 0.260137i
\(454\) −370.101 53.2124i −0.815200 0.117208i
\(455\) −131.646 288.265i −0.289332 0.633549i
\(456\) −46.2088 + 6.64382i −0.101335 + 0.0145698i
\(457\) 31.6891 + 49.3092i 0.0693415 + 0.107898i 0.874193 0.485579i \(-0.161391\pi\)
−0.804851 + 0.593477i \(0.797755\pi\)
\(458\) −383.982 332.722i −0.838388 0.726467i
\(459\) 50.9971i 0.111105i
\(460\) −33.5324 235.215i −0.0728966 0.511338i
\(461\) −86.3486 −0.187307 −0.0936535 0.995605i \(-0.529855\pi\)
−0.0936535 + 0.995605i \(0.529855\pi\)
\(462\) 14.9592 17.2638i 0.0323792 0.0373675i
\(463\) −299.264 + 192.325i −0.646358 + 0.415389i −0.822334 0.569005i \(-0.807328\pi\)
0.175976 + 0.984394i \(0.443692\pi\)
\(464\) −25.1311 174.791i −0.0541619 0.376704i
\(465\) −221.100 + 100.973i −0.475484 + 0.217146i
\(466\) 62.3371 433.564i 0.133771 0.930396i
\(467\) −171.835 585.216i −0.367955 1.25314i −0.910639 0.413203i \(-0.864410\pi\)
0.542684 0.839937i \(-0.317408\pi\)
\(468\) 58.7965 + 37.7862i 0.125634 + 0.0807398i
\(469\) 89.0234 194.934i 0.189815 0.415637i
\(470\) 26.1746 89.1424i 0.0556906 0.189665i
\(471\) −385.677 + 334.191i −0.818848 + 0.709536i
\(472\) 82.7591 + 95.5091i 0.175337 + 0.202350i
\(473\) 24.9429 + 7.32390i 0.0527334 + 0.0154839i
\(474\) −336.022 153.456i −0.708908 0.323748i
\(475\) 8.64494 13.4518i 0.0181999 0.0283196i
\(476\) −99.1999 + 29.1277i −0.208403 + 0.0611927i
\(477\) 111.972 + 16.0991i 0.234741 + 0.0337507i
\(478\) 192.086 + 420.609i 0.401853 + 0.879935i
\(479\) 110.504 15.8881i 0.230698 0.0331693i −0.0259964 0.999662i \(-0.508276\pi\)
0.256694 + 0.966493i \(0.417367\pi\)
\(480\) 27.3603 + 42.5735i 0.0570007 + 0.0886947i
\(481\) 273.667 + 237.134i 0.568955 + 0.493002i
\(482\) 266.450i 0.552802i
\(483\) 86.9381 + 190.970i 0.179996 + 0.395384i
\(484\) 235.730 0.487046
\(485\) −77.5582 + 89.5070i −0.159914 + 0.184550i
\(486\) −18.5458 + 11.9186i −0.0381600 + 0.0245240i
\(487\) 49.2723 + 342.696i 0.101175 + 0.703688i 0.975764 + 0.218824i \(0.0702219\pi\)
−0.874589 + 0.484864i \(0.838869\pi\)
\(488\) 185.269 84.6095i 0.379650 0.173380i
\(489\) −45.2555 + 314.759i −0.0925471 + 0.643679i
\(490\) −43.7455 148.983i −0.0892764 0.304048i
\(491\) 495.408 + 318.379i 1.00898 + 0.648430i 0.937128 0.348986i \(-0.113474\pi\)
0.0718486 + 0.997416i \(0.477110\pi\)
\(492\) 99.3874 217.628i 0.202007 0.442333i
\(493\) 122.068 415.726i 0.247603 0.843257i
\(494\) −118.639 + 102.801i −0.240160 + 0.208100i
\(495\) −17.9661 20.7340i −0.0362952 0.0418868i
\(496\) 104.277 + 30.6184i 0.210236 + 0.0617307i
\(497\) 147.925 + 67.5551i 0.297636 + 0.135926i
\(498\) 56.8018 88.3854i 0.114060 0.177481i
\(499\) −138.277 + 40.6019i −0.277109 + 0.0813665i −0.417334 0.908753i \(-0.637035\pi\)
0.140225 + 0.990120i \(0.455217\pi\)
\(500\) 238.468 + 34.2865i 0.476935 + 0.0685729i
\(501\) 36.6500 + 80.2522i 0.0731536 + 0.160184i
\(502\) −83.1365 + 11.9532i −0.165611 + 0.0238112i
\(503\) −115.729 180.078i −0.230078 0.358008i 0.706950 0.707264i \(-0.250071\pi\)
−0.937027 + 0.349256i \(0.886434\pi\)
\(504\) −33.7769 29.2679i −0.0670177 0.0580712i
\(505\) 496.838i 0.983837i
\(506\) 23.9864 52.3575i 0.0474039 0.103473i
\(507\) −57.6953 −0.113798
\(508\) −36.6535 + 42.3004i −0.0721526 + 0.0832685i
\(509\) 243.236 156.318i 0.477870 0.307109i −0.279441 0.960163i \(-0.590149\pi\)
0.757311 + 0.653054i \(0.226513\pi\)
\(510\) 17.6712 + 122.906i 0.0346494 + 0.240992i
\(511\) 361.444 165.066i 0.707328 0.323026i
\(512\) 3.22022 22.3971i 0.00628949 0.0437443i
\(513\) −13.9502 47.5101i −0.0271934 0.0926122i
\(514\) −355.335 228.360i −0.691313 0.444280i
\(515\) −6.10232 + 13.3622i −0.0118492 + 0.0259461i
\(516\) 14.3293 48.8012i 0.0277700 0.0945760i
\(517\) 17.0191 14.7471i 0.0329189 0.0285244i
\(518\) −151.639 175.001i −0.292740 0.337840i
\(519\) 35.6986 + 10.4821i 0.0687834 + 0.0201966i
\(520\) 154.796 + 70.6931i 0.297685 + 0.135948i
\(521\) 50.3624 78.3654i 0.0966648 0.150413i −0.789553 0.613683i \(-0.789687\pi\)
0.886218 + 0.463269i \(0.153324\pi\)
\(522\) 179.713 52.7685i 0.344278 0.101089i
\(523\) 407.479 + 58.5866i 0.779118 + 0.112020i 0.520389 0.853930i \(-0.325787\pi\)
0.258729 + 0.965950i \(0.416696\pi\)
\(524\) −121.711 266.509i −0.232272 0.508605i
\(525\) 15.1525 2.17860i 0.0288619 0.00414972i
\(526\) 199.569 + 310.536i 0.379409 + 0.590372i
\(527\) 201.524 + 174.622i 0.382399 + 0.331351i
\(528\) 12.2667i 0.0232324i
\(529\) 345.466 + 400.617i 0.653055 + 0.757310i
\(530\) 275.437 0.519692
\(531\) −87.7793 + 101.303i −0.165309 + 0.190777i
\(532\) 84.4491 54.2721i 0.158739 0.102015i
\(533\) −114.494 796.322i −0.214810 1.49404i
\(534\) −240.199 + 109.695i −0.449811 + 0.205422i
\(535\) 82.1099 571.087i 0.153476 1.06745i
\(536\) 32.4211 + 110.416i 0.0604872 + 0.206000i
\(537\) 224.715 + 144.415i 0.418463 + 0.268930i
\(538\) 188.347 412.422i 0.350087 0.766583i
\(539\) 10.6035 36.1121i 0.0196725 0.0669984i
\(540\) −40.5664 + 35.1510i −0.0751230 + 0.0650944i
\(541\) 422.926 + 488.082i 0.781748 + 0.902186i 0.997234 0.0743213i \(-0.0236791\pi\)
−0.215486 + 0.976507i \(0.569134\pi\)
\(542\) 684.552 + 201.003i 1.26301 + 0.370853i
\(543\) 245.090 + 111.929i 0.451362 + 0.206130i
\(544\) 30.0156 46.7052i 0.0551758 0.0858552i
\(545\) −385.774 + 113.273i −0.707842 + 0.207841i
\(546\) −148.758 21.3882i −0.272451 0.0391726i
\(547\) −273.288 598.417i −0.499612 1.09400i −0.976595 0.215086i \(-0.930997\pi\)
0.476983 0.878913i \(-0.341730\pi\)
\(548\) −437.804 + 62.9467i −0.798912 + 0.114866i
\(549\) 116.794 + 181.736i 0.212740 + 0.331030i
\(550\) −3.17535 2.75145i −0.00577336 0.00500264i
\(551\) 420.691i 0.763505i
\(552\) −102.438 46.9298i −0.185577 0.0850177i
\(553\) 794.333 1.43641
\(554\) −40.3573 + 46.5748i −0.0728471 + 0.0840701i
\(555\) −233.957 + 150.355i −0.421544 + 0.270910i
\(556\) 23.3568 + 162.450i 0.0420087 + 0.292177i
\(557\) −521.912 + 238.349i −0.937006 + 0.427916i −0.824581 0.565744i \(-0.808589\pi\)
−0.112425 + 0.993660i \(0.535862\pi\)
\(558\) −16.4049 + 114.098i −0.0293994 + 0.204477i
\(559\) −48.1846 164.102i −0.0861979 0.293563i
\(560\) −91.5460 58.8330i −0.163475 0.105059i
\(561\) −12.5030 + 27.3777i −0.0222869 + 0.0488016i
\(562\) 28.7575 97.9392i 0.0511700 0.174269i
\(563\) −451.236 + 390.998i −0.801485 + 0.694490i −0.955957 0.293507i \(-0.905178\pi\)
0.154472 + 0.987997i \(0.450632\pi\)
\(564\) −28.8530 33.2981i −0.0511578 0.0590392i
\(565\) −635.892 186.715i −1.12547 0.330469i
\(566\) −535.409 244.513i −0.945952 0.432002i
\(567\) 25.6287 39.8791i 0.0452006 0.0703335i
\(568\) −83.7890 + 24.6027i −0.147516 + 0.0433145i
\(569\) 601.644 + 86.5033i 1.05737 + 0.152027i 0.648999 0.760789i \(-0.275188\pi\)
0.408371 + 0.912816i \(0.366097\pi\)
\(570\) −50.0837 109.668i −0.0878662 0.192400i
\(571\) −618.843 + 88.9761i −1.08379 + 0.155825i −0.660987 0.750398i \(-0.729862\pi\)
−0.422801 + 0.906223i \(0.638953\pi\)
\(572\) 22.3007 + 34.7006i 0.0389873 + 0.0606654i
\(573\) 215.169 + 186.445i 0.375514 + 0.325384i
\(574\) 514.457i 0.896267i
\(575\) 35.1254 15.9906i 0.0610876 0.0278097i
\(576\) 24.0000 0.0416667
\(577\) −242.341 + 279.676i −0.420001 + 0.484707i −0.925837 0.377922i \(-0.876639\pi\)
0.505836 + 0.862630i \(0.331184\pi\)
\(578\) −229.231 + 147.318i −0.396593 + 0.254875i
\(579\) 69.3606 + 482.413i 0.119794 + 0.833184i
\(580\) 414.834 189.448i 0.715230 0.326635i
\(581\) −32.1517 + 223.620i −0.0553385 + 0.384888i
\(582\) 15.8240 + 53.8914i 0.0271889 + 0.0925970i
\(583\) 56.1648 + 36.0949i 0.0963375 + 0.0619124i
\(584\) −88.6395 + 194.093i −0.151780 + 0.332352i
\(585\) −50.8520 + 173.186i −0.0869265 + 0.296045i
\(586\) −209.101 + 181.187i −0.356827 + 0.309192i
\(587\) 0.128787 + 0.148628i 0.000219398 + 0.000253199i 0.755859 0.654734i \(-0.227219\pi\)
−0.755640 + 0.654987i \(0.772674\pi\)
\(588\) −70.6540 20.7459i −0.120160 0.0352821i
\(589\) −235.512 107.555i −0.399851 0.182606i
\(590\) −176.450 + 274.562i −0.299068 + 0.465359i
\(591\) 417.905 122.708i 0.707114 0.207628i
\(592\) 123.080 + 17.6963i 0.207906 + 0.0298924i
\(593\) −153.140 335.329i −0.258246 0.565479i 0.735452 0.677577i \(-0.236970\pi\)
−0.993697 + 0.112098i \(0.964243\pi\)
\(594\) −12.8784 + 1.85163i −0.0216808 + 0.00311722i
\(595\) −144.353 224.617i −0.242610 0.377508i
\(596\) 35.3379 + 30.6204i 0.0592917 + 0.0513765i
\(597\) 289.094i 0.484245i
\(598\) −375.100 + 53.4745i −0.627258 + 0.0894223i
\(599\) −760.607 −1.26979 −0.634897 0.772597i \(-0.718958\pi\)
−0.634897 + 0.772597i \(0.718958\pi\)
\(600\) −5.38327 + 6.21262i −0.00897211 + 0.0103544i
\(601\) −87.6798 + 56.3484i −0.145890 + 0.0937577i −0.611549 0.791206i \(-0.709453\pi\)
0.465660 + 0.884964i \(0.345817\pi\)
\(602\) 15.5646 + 108.254i 0.0258549 + 0.179825i
\(603\) −111.028 + 50.7048i −0.184126 + 0.0840876i
\(604\) 68.7359 478.069i 0.113801 0.791504i
\(605\) 171.514 + 584.122i 0.283494 + 0.965492i
\(606\) −198.217 127.386i −0.327090 0.210208i
\(607\) −420.419 + 920.590i −0.692618 + 1.51662i 0.156079 + 0.987745i \(0.450114\pi\)
−0.848698 + 0.528878i \(0.822613\pi\)
\(608\) −15.1871 + 51.7224i −0.0249787 + 0.0850698i
\(609\) −304.380 + 263.747i −0.499803 + 0.433082i
\(610\) 344.455 + 397.522i 0.564680 + 0.651676i
\(611\) −142.156 41.7408i −0.232662 0.0683156i
\(612\) 53.5649 + 24.4623i 0.0875244 + 0.0399710i
\(613\) −63.1236 + 98.2222i −0.102975 + 0.160232i −0.888917 0.458068i \(-0.848542\pi\)
0.785943 + 0.618300i \(0.212178\pi\)
\(614\) −423.437 + 124.332i −0.689637 + 0.202496i
\(615\) 611.579 + 87.9318i 0.994437 + 0.142978i
\(616\) −10.9575 23.9935i −0.0177881 0.0389505i
\(617\) −589.483 + 84.7548i −0.955402 + 0.137366i −0.602345 0.798236i \(-0.705767\pi\)
−0.353057 + 0.935602i \(0.614858\pi\)
\(618\) 3.76635 + 5.86056i 0.00609442 + 0.00948310i
\(619\) −206.962 179.334i −0.334350 0.289716i 0.471463 0.881886i \(-0.343726\pi\)
−0.805813 + 0.592170i \(0.798271\pi\)
\(620\) 280.668i 0.452690i
\(621\) 33.8071 114.630i 0.0544397 0.184590i
\(622\) 528.455 0.849606
\(623\) 371.839 429.125i 0.596852 0.688804i
\(624\) 67.8923 43.6318i 0.108802 0.0699227i
\(625\) 94.5162 + 657.374i 0.151226 + 1.05180i
\(626\) 588.612 268.810i 0.940274 0.429409i
\(627\) 4.15891 28.9259i 0.00663304 0.0461338i
\(628\) 166.017 + 565.402i 0.264358 + 0.900322i
\(629\) 256.662 + 164.947i 0.408048 + 0.262237i
\(630\) 47.9480 104.992i 0.0761080 0.166653i
\(631\) 13.9634 47.5551i 0.0221291 0.0753647i −0.947688 0.319198i \(-0.896587\pi\)
0.969817 + 0.243833i \(0.0784048\pi\)
\(632\) −322.366 + 279.332i −0.510074 + 0.441981i
\(633\) −429.857 496.082i −0.679079 0.783699i
\(634\) −180.146 52.8957i −0.284142 0.0834317i
\(635\) −131.486 60.0476i −0.207064 0.0945631i
\(636\) 70.6203 109.887i 0.111038 0.172779i
\(637\) −237.585 + 69.7613i −0.372975 + 0.109515i
\(638\) 109.416 + 15.7316i 0.171498 + 0.0246577i
\(639\) −38.4772 84.2533i −0.0602147 0.131852i
\(640\) 57.8414 8.31633i 0.0903771 0.0129943i
\(641\) 542.595 + 844.295i 0.846482 + 1.31715i 0.946677 + 0.322184i \(0.104417\pi\)
−0.100195 + 0.994968i \(0.531947\pi\)
\(642\) −206.786 179.182i −0.322097 0.279099i
\(643\) 580.393i 0.902634i −0.892364 0.451317i \(-0.850954\pi\)
0.892364 0.451317i \(-0.149046\pi\)
\(644\) 242.289 + 0.289087i 0.376225 + 0.000448893i
\(645\) 131.352 0.203646
\(646\) −86.6143 + 99.9582i −0.134078 + 0.154734i
\(647\) 813.648 522.900i 1.25757 0.808191i 0.269620 0.962967i \(-0.413102\pi\)
0.987950 + 0.154775i \(0.0494654\pi\)
\(648\) 3.62274 + 25.1967i 0.00559065 + 0.0388839i
\(649\) −71.9606 + 32.8633i −0.110879 + 0.0506368i
\(650\) −3.93396 + 27.3613i −0.00605224 + 0.0420943i
\(651\) −69.8328 237.829i −0.107270 0.365328i
\(652\) 308.900 + 198.518i 0.473773 + 0.304475i
\(653\) 88.0865 192.883i 0.134895 0.295379i −0.830115 0.557593i \(-0.811725\pi\)
0.965010 + 0.262213i \(0.0844525\pi\)
\(654\) −53.7189 + 182.950i −0.0821390 + 0.279740i
\(655\) 571.835 495.498i 0.873031 0.756486i
\(656\) −180.912 208.784i −0.275780 0.318268i
\(657\) −217.152 63.7615i −0.330520 0.0970494i
\(658\) 86.1802 + 39.3572i 0.130973 + 0.0598133i
\(659\) −3.82691 + 5.95479i −0.00580715 + 0.00903610i −0.844145 0.536115i \(-0.819891\pi\)
0.838338 + 0.545151i \(0.183528\pi\)
\(660\) −30.3960 + 8.92506i −0.0460545 + 0.0135228i
\(661\) −1015.33 145.983i −1.53606 0.220852i −0.678253 0.734829i \(-0.737262\pi\)
−0.857804 + 0.513977i \(0.828172\pi\)
\(662\) 212.281 + 464.831i 0.320666 + 0.702161i
\(663\) 195.999 28.1804i 0.295625 0.0425044i
\(664\) −65.5891 102.059i −0.0987788 0.153703i
\(665\) 195.926 + 169.771i 0.294626 + 0.255295i
\(666\) 131.889i 0.198031i
\(667\) −549.976 + 853.538i −0.824551 + 1.27967i
\(668\) 101.873 0.152505
\(669\) 416.908 481.137i 0.623180 0.719188i
\(670\) −250.014 + 160.674i −0.373155 + 0.239812i
\(671\) 18.1447 + 126.199i 0.0270413 + 0.188076i
\(672\) −46.9437 + 21.4385i −0.0698567 + 0.0319025i
\(673\) −39.0105 + 271.324i −0.0579651 + 0.403156i 0.940096 + 0.340911i \(0.110735\pi\)
−0.998061 + 0.0622457i \(0.980174\pi\)
\(674\) −51.5242 175.475i −0.0764454 0.260349i
\(675\) −7.33500 4.71392i −0.0108667 0.00698358i
\(676\) −27.6753 + 60.6004i −0.0409398 + 0.0896456i
\(677\) −227.986 + 776.451i −0.336760 + 1.14690i 0.600894 + 0.799329i \(0.294811\pi\)
−0.937654 + 0.347570i \(0.887007\pi\)
\(678\) −237.530 + 205.821i −0.350339 + 0.303571i
\(679\) −79.0910 91.2759i −0.116482 0.134427i
\(680\) 137.571 + 40.3945i 0.202310 + 0.0594037i
\(681\) −416.557 190.235i −0.611684 0.279347i
\(682\) −36.7805 + 57.2315i −0.0539303 + 0.0839172i
\(683\) 20.2029 5.93211i 0.0295797 0.00868537i −0.266909 0.963722i \(-0.586002\pi\)
0.296489 + 0.955036i \(0.404184\pi\)
\(684\) −56.5940 8.13699i −0.0827397 0.0118962i
\(685\) −474.517 1039.05i −0.692725 1.51686i
\(686\) 518.010 74.4786i 0.755116 0.108569i
\(687\) −336.424 523.486i −0.489700 0.761988i
\(688\) −44.3850 38.4598i −0.0645131 0.0559009i
\(689\) 439.241i 0.637506i
\(690\) 41.7560 287.980i 0.0605160 0.417362i
\(691\) 399.341 0.577917 0.288959 0.957342i \(-0.406691\pi\)
0.288959 + 0.957342i \(0.406691\pi\)
\(692\) 28.1338 32.4681i 0.0406557 0.0469192i
\(693\) 23.5359 15.1256i 0.0339624 0.0218263i
\(694\) 97.8642 + 680.660i 0.141015 + 0.980779i
\(695\) −385.546 + 176.073i −0.554742 + 0.253342i
\(696\) 30.7792 214.074i 0.0442230 0.307578i
\(697\) −190.967 650.375i −0.273985 0.933106i
\(698\) 28.2456 + 18.1523i 0.0404664 + 0.0260062i
\(699\) 222.856 487.987i 0.318821 0.698121i
\(700\) 4.98005 16.9605i 0.00711436 0.0242293i
\(701\) 868.957 752.956i 1.23960 1.07412i 0.245084 0.969502i \(-0.421185\pi\)
0.994513 0.104615i \(-0.0333609\pi\)
\(702\) 56.0556 + 64.6916i 0.0798513 + 0.0921533i
\(703\) −284.234 83.4586i −0.404316 0.118718i
\(704\) 12.8844 + 5.88409i 0.0183016 + 0.00835808i
\(705\) 61.5173 95.7227i 0.0872585 0.135777i
\(706\) −134.486 + 39.4887i −0.190490 + 0.0559330i
\(707\) 501.500 + 72.1048i 0.709335 + 0.101987i
\(708\) 64.2976 + 140.792i 0.0908158 + 0.198859i
\(709\) −680.755 + 97.8778i −0.960162 + 0.138050i −0.604536 0.796578i \(-0.706641\pi\)
−0.355626 + 0.934628i \(0.615732\pi\)
\(710\) −121.927 189.722i −0.171728 0.267215i
\(711\) −341.921 296.276i −0.480902 0.416704i
\(712\) 304.913i 0.428248i
\(713\) −337.222 526.106i −0.472962 0.737877i
\(714\) −126.624 −0.177344
\(715\) −69.7599 + 80.5072i −0.0975663 + 0.112598i
\(716\) 259.478 166.757i 0.362400 0.232900i
\(717\) 80.5951 + 560.551i 0.112406 + 0.781801i
\(718\) 552.398 252.272i 0.769357 0.351353i
\(719\) −130.383 + 906.837i −0.181340 + 1.26125i 0.672259 + 0.740316i \(0.265324\pi\)
−0.853599 + 0.520931i \(0.825585\pi\)
\(720\) 17.4620 + 59.4702i 0.0242528 + 0.0825975i
\(721\) −12.6020 8.09880i −0.0174785 0.0112327i
\(722\) −158.734 + 347.579i −0.219853 + 0.481411i
\(723\) 91.9388 313.115i 0.127163 0.433077i
\(724\) 235.129 203.740i 0.324764 0.281410i
\(725\) 48.5112 + 55.9849i 0.0669120 + 0.0772205i
\(726\) 277.015 + 81.3389i 0.381563 + 0.112037i
\(727\) −163.719 74.7681i −0.225198 0.102845i 0.299621 0.954058i \(-0.403140\pi\)
−0.524819 + 0.851214i \(0.675867\pi\)
\(728\) −93.8216 + 145.989i −0.128876 + 0.200535i
\(729\) −25.9063 + 7.60678i −0.0355368 + 0.0104345i
\(730\) −545.442 78.4227i −0.747180 0.107428i
\(731\) −59.8610 131.077i −0.0818892 0.179312i
\(732\) 246.910 35.5004i 0.337309 0.0484978i
\(733\) 676.936 + 1053.33i 0.923514 + 1.43702i 0.899312 + 0.437308i \(0.144068\pi\)
0.0242021 + 0.999707i \(0.492295\pi\)
\(734\) −320.107 277.375i −0.436113 0.377894i
\(735\) 190.170i 0.258734i
\(736\) −98.4304 + 85.0850i −0.133737 + 0.115605i
\(737\) −72.0366 −0.0977430
\(738\) 191.886 221.448i 0.260008 0.300066i
\(739\) 451.129 289.923i 0.610459 0.392318i −0.198570 0.980087i \(-0.563630\pi\)
0.809029 + 0.587768i \(0.199993\pi\)
\(740\) 45.7013 + 317.860i 0.0617585 + 0.429540i
\(741\) −174.889 + 79.8690i −0.236017 + 0.107785i
\(742\) −39.9734 + 278.021i −0.0538725 + 0.374691i
\(743\) −223.208 760.178i −0.300415 1.02312i −0.961955 0.273209i \(-0.911915\pi\)
0.661540 0.749910i \(-0.269903\pi\)
\(744\) 111.974 + 71.9616i 0.150503 + 0.0967225i
\(745\) −50.1639 + 109.844i −0.0673341 + 0.147441i
\(746\) −238.238 + 811.363i −0.319353 + 1.08762i
\(747\) 97.2472 84.2651i 0.130184 0.112805i
\(748\) 22.7588 + 26.2651i 0.0304262 + 0.0351137i
\(749\) 564.529 + 165.761i 0.753710 + 0.221309i
\(750\) 268.401 + 122.575i 0.357868 + 0.163433i
\(751\) 720.924 1121.78i 0.959952 1.49371i 0.0927919 0.995686i \(-0.470421\pi\)
0.867160 0.498029i \(-0.165943\pi\)
\(752\) −48.8149 + 14.3334i −0.0649135 + 0.0190603i
\(753\) −101.821 14.6396i −0.135220 0.0194418i
\(754\) −302.115 661.539i −0.400683 0.877373i
\(755\) 1234.63 177.513i 1.63527 0.235117i
\(756\) −29.5935 46.0484i −0.0391449 0.0609106i
\(757\) −497.653 431.218i −0.657401 0.569641i 0.260977 0.965345i \(-0.415955\pi\)
−0.918378 + 0.395704i \(0.870501\pi\)
\(758\) 564.734i 0.745032i
\(759\) 46.2532 53.2505i 0.0609397 0.0701588i
\(760\) −139.214 −0.183177
\(761\) −393.068 + 453.625i −0.516515 + 0.596091i −0.952755 0.303740i \(-0.901765\pi\)
0.436240 + 0.899831i \(0.356310\pi\)
\(762\) −57.6685 + 37.0613i −0.0756805 + 0.0486369i
\(763\) −58.3499 405.833i −0.0764744 0.531891i
\(764\) 299.046 136.570i 0.391421 0.178756i
\(765\) −21.6427 + 150.528i −0.0282911 + 0.196769i
\(766\) −119.478 406.905i −0.155977 0.531208i
\(767\) 437.846 + 281.387i 0.570856 + 0.366867i
\(768\) 11.5123 25.2085i 0.0149900 0.0328235i
\(769\) 354.339 1206.77i 0.460779 1.56927i −0.321857 0.946788i \(-0.604307\pi\)
0.782636 0.622480i \(-0.213875\pi\)
\(770\) 51.4816 44.6091i 0.0668593 0.0579339i
\(771\) −338.771 390.962i −0.439391 0.507084i
\(772\) 539.975 + 158.551i 0.699450 + 0.205377i
\(773\) −937.490 428.137i −1.21279 0.553864i −0.296755 0.954954i \(-0.595904\pi\)
−0.916039 + 0.401089i \(0.868632\pi\)
\(774\) 33.6778 52.4036i 0.0435113 0.0677049i
\(775\) −43.7441 + 12.8444i −0.0564440 + 0.0165734i
\(776\) 64.1955 + 9.22991i 0.0827261 + 0.0118942i
\(777\) −117.812 257.973i −0.151625 0.332011i
\(778\) 1005.80 144.613i 1.29281 0.185878i
\(779\) 355.819 + 553.665i 0.456764 + 0.710739i
\(780\) 157.514 + 136.486i 0.201941 + 0.174983i
\(781\) 54.6647i 0.0699932i
\(782\) −306.408 + 89.5725i −0.391826 + 0.114543i
\(783\) 229.395 0.292969
\(784\) −55.6818 + 64.2602i −0.0710227 + 0.0819646i
\(785\) −1280.23 + 822.756i −1.63087 + 1.04810i
\(786\) −51.0672 355.180i −0.0649710 0.451883i
\(787\) 1027.02 469.025i 1.30498 0.595966i 0.363051 0.931769i \(-0.381735\pi\)
0.941932 + 0.335803i \(0.109008\pi\)
\(788\) 71.5739 497.808i 0.0908299 0.631736i
\(789\) 127.370 + 433.782i 0.161432 + 0.549788i
\(790\) −926.713 595.563i −1.17306 0.753877i
\(791\) 280.752 614.761i 0.354933 0.777195i
\(792\) −4.23263 + 14.4150i −0.00534423 + 0.0182008i
\(793\) 633.933 549.306i 0.799411 0.692693i
\(794\) −289.302 333.873i −0.364361 0.420494i
\(795\) 323.675 + 95.0395i 0.407138 + 0.119547i
\(796\) −303.651 138.673i −0.381471 0.174212i
\(797\) 130.412 202.925i 0.163629 0.254611i −0.749751 0.661720i \(-0.769827\pi\)
0.913380 + 0.407109i \(0.133463\pi\)
\(798\) 117.966 34.6378i 0.147827 0.0434058i
\(799\) −123.558 17.7650i −0.154641 0.0222340i
\(800\) 3.94320 + 8.63440i 0.00492900 + 0.0107930i
\(801\) −320.117 + 46.0258i −0.399646 + 0.0574605i
\(802\) 369.705 + 575.273i 0.460979 + 0.717297i
\(803\) −100.945 87.4694i −0.125710 0.108928i
\(804\) 140.941i 0.175299i
\(805\) 175.569 + 600.584i 0.218099 + 0.746067i
\(806\) 447.584 0.555315
\(807\) 363.639 419.662i 0.450606 0.520027i
\(808\) −228.881 + 147.093i −0.283269 + 0.182046i
\(809\) 138.503 + 963.311i 0.171203 + 1.19074i 0.876348 + 0.481679i \(0.159973\pi\)
−0.705145 + 0.709063i \(0.749118\pi\)
\(810\) −59.7998 + 27.3097i −0.0738269 + 0.0337156i
\(811\) 116.841 812.645i 0.144070 1.00203i −0.781623 0.623752i \(-0.785608\pi\)
0.925693 0.378277i \(-0.123483\pi\)
\(812\) 131.022 + 446.220i 0.161357 + 0.549532i
\(813\) 735.084 + 472.410i 0.904163 + 0.581070i
\(814\) −32.3352 + 70.8043i −0.0397239 + 0.0869832i
\(815\) −267.162 + 909.870i −0.327806 + 1.11640i
\(816\) 51.3880 44.5280i 0.0629755 0.0545686i
\(817\) 91.6240 + 105.740i 0.112147 + 0.129424i
\(818\) 451.328 + 132.522i 0.551745 + 0.162007i
\(819\) −167.431 76.4632i −0.204434 0.0933617i
\(820\) 385.721 600.194i 0.470392 0.731944i
\(821\) 78.9888 23.1932i 0.0962105 0.0282500i −0.233273 0.972411i \(-0.574944\pi\)
0.329484 + 0.944161i \(0.393125\pi\)
\(822\) −536.198 77.0936i −0.652309 0.0937879i
\(823\) 378.346 + 828.461i 0.459715 + 1.00664i 0.987552 + 0.157290i \(0.0502758\pi\)
−0.527837 + 0.849345i \(0.676997\pi\)
\(824\) 7.96229 1.14480i 0.00966298 0.00138933i
\(825\) −2.78207 4.32898i −0.00337220 0.00524725i
\(826\) −251.530 217.952i −0.304516 0.263865i
\(827\) 670.369i 0.810603i 0.914183 + 0.405302i \(0.132834\pi\)
−0.914183 + 0.405302i \(0.867166\pi\)
\(828\) −104.186 90.4952i −0.125828 0.109294i
\(829\) 62.8068 0.0757622 0.0378811 0.999282i \(-0.487939\pi\)
0.0378811 + 0.999282i \(0.487939\pi\)
\(830\) 205.172 236.781i 0.247195 0.285279i
\(831\) −63.4959 + 40.8063i −0.0764090 + 0.0491051i
\(832\) −13.2621 92.2402i −0.0159401 0.110866i
\(833\) −189.773 + 86.6663i −0.227818 + 0.104041i
\(834\) −28.6061 + 198.960i −0.0342999 + 0.238561i
\(835\) 74.1215 + 252.435i 0.0887683 + 0.302317i
\(836\) −28.3874 18.2435i −0.0339563 0.0218224i
\(837\) −58.6476 + 128.420i −0.0700688 + 0.153429i
\(838\) 55.9890 190.681i 0.0668127 0.227543i
\(839\) 603.136 522.621i 0.718875 0.622909i −0.216617 0.976257i \(-0.569502\pi\)
0.935492 + 0.353348i \(0.114957\pi\)
\(840\) −87.2784 100.725i −0.103903 0.119910i
\(841\) −1063.08 312.149i −1.26407 0.371164i
\(842\) 444.627 + 203.054i 0.528061 + 0.241157i
\(843\) 67.5879 105.169i 0.0801755 0.124756i
\(844\) −727.254 + 213.541i −0.861676 + 0.253011i
\(845\) −170.300 24.4854i −0.201538 0.0289768i
\(846\) −22.4166 49.0855i −0.0264971 0.0580207i
\(847\) −614.495 + 88.3510i −0.725496 + 0.104311i
\(848\) −81.5453 126.887i −0.0961619 0.149631i
\(849\) −544.808 472.079i −0.641706 0.556041i
\(850\) 23.2900i 0.0274000i
\(851\) −467.573 540.911i −0.549440 0.635618i
\(852\) −106.952 −0.125531
\(853\) 195.538 225.663i 0.229236 0.264552i −0.629466 0.777028i \(-0.716726\pi\)
0.858702 + 0.512476i \(0.171272\pi\)
\(854\) −451.242 + 289.996i −0.528387 + 0.339573i
\(855\) −21.0141 146.156i −0.0245779 0.170943i
\(856\) −287.395 + 131.249i −0.335742 + 0.153328i
\(857\) −70.4370 + 489.900i −0.0821902 + 0.571645i 0.906561 + 0.422075i \(0.138698\pi\)
−0.988751 + 0.149570i \(0.952211\pi\)
\(858\) 14.2329 + 48.4728i 0.0165884 + 0.0564951i
\(859\) 1096.58 + 704.727i 1.27657 + 0.820404i 0.990461 0.137793i \(-0.0440008\pi\)
0.286112 + 0.958196i \(0.407637\pi\)
\(860\) 63.0067 137.965i 0.0732636 0.160425i
\(861\) −177.514 + 604.556i −0.206172 + 0.702156i
\(862\) 703.680 609.742i 0.816334 0.707358i
\(863\) −85.2890 98.4288i −0.0988286 0.114054i 0.704181 0.710021i \(-0.251315\pi\)
−0.803009 + 0.595967i \(0.796769\pi\)
\(864\) 28.2032 + 8.28121i 0.0326426 + 0.00958474i
\(865\) 100.923 + 46.0901i 0.116674 + 0.0532833i
\(866\) 5.96245 9.27776i 0.00688505 0.0107133i
\(867\) −320.209 + 94.0219i −0.369330 + 0.108445i
\(868\) −283.301 40.7326i −0.326384 0.0469270i
\(869\) −110.922 242.885i −0.127643 0.279499i
\(870\) 552.854 79.4884i 0.635465 0.0913660i
\(871\) 256.229 + 398.700i 0.294178 + 0.457750i
\(872\) 166.394 + 144.181i 0.190819 + 0.165345i
\(873\) 68.7897i 0.0787970i
\(874\) 260.954 167.266i 0.298575 0.191379i
\(875\) −634.480 −0.725121
\(876\) −171.135 + 197.501i −0.195360 + 0.225457i
\(877\) −336.177 + 216.048i −0.383326 + 0.246349i −0.718085 0.695955i \(-0.754981\pi\)
0.334759 + 0.942304i \(0.391345\pi\)
\(878\) 116.953 + 813.427i 0.133204 + 0.926454i
\(879\) −308.240 + 140.768i −0.350671 + 0.160146i
\(880\) −5.20588 + 36.2077i −0.00591577 + 0.0411451i
\(881\) 56.9624 + 193.996i 0.0646565 + 0.220200i 0.985483 0.169772i \(-0.0543030\pi\)
−0.920827 + 0.389972i \(0.872485\pi\)
\(882\) −75.8695 48.7584i −0.0860199 0.0552816i
\(883\) −636.186 + 1393.05i −0.720483 + 1.57764i 0.0927438 + 0.995690i \(0.470436\pi\)
−0.813227 + 0.581947i \(0.802291\pi\)
\(884\) 64.4175 219.386i 0.0728705 0.248174i
\(885\) −302.090 + 261.763i −0.341345 + 0.295777i
\(886\) 345.458 + 398.680i 0.389907 + 0.449977i
\(887\) −1279.37 375.657i −1.44236 0.423514i −0.535350 0.844630i \(-0.679820\pi\)
−0.907007 + 0.421116i \(0.861639\pi\)
\(888\) 138.530 + 63.2644i 0.156002 + 0.0712437i
\(889\) 79.6932 124.005i 0.0896436 0.139488i
\(890\) −755.551 + 221.850i −0.848934 + 0.249269i
\(891\) −15.7727 2.26777i −0.0177023 0.00254520i
\(892\) −305.381 668.692i −0.342356 0.749654i
\(893\) 119.969 17.2490i 0.134344 0.0193158i
\(894\) 30.9611 + 48.1764i 0.0346321 + 0.0538886i
\(895\) 602.003 + 521.639i 0.672629 + 0.582837i
\(896\) 59.5910i 0.0665078i
\(897\) −459.244 66.5887i −0.511978 0.0742349i
\(898\) −1006.69 −1.12104
\(899\) 785.483 906.495i 0.873729 1.00834i
\(900\) −8.46973 + 5.44316i −0.00941081 + 0.00604796i
\(901\) −52.6676 366.311i −0.0584546 0.406561i
\(902\) 157.306 71.8394i 0.174397 0.0796446i
\(903\) −19.0627 + 132.584i −0.0211104 + 0.146826i
\(904\) 102.246 + 348.219i 0.113104 + 0.385198i
\(905\) 675.930 + 434.394i 0.746884 + 0.479993i
\(906\) 245.732 538.077i 0.271227 0.593904i
\(907\) 7.26633 24.7468i 0.00801139 0.0272843i −0.955390 0.295346i \(-0.904565\pi\)
0.963402 + 0.268062i \(0.0863832\pi\)
\(908\) −399.628 + 346.280i −0.440119 + 0.381365i
\(909\) −188.977 218.091i −0.207895 0.239924i
\(910\) −430.014 126.263i −0.472543 0.138751i
\(911\) −796.163 363.595i −0.873944 0.399117i −0.0726284 0.997359i \(-0.523139\pi\)
−0.801315 + 0.598242i \(0.795866\pi\)
\(912\) −35.6937 + 55.5405i −0.0391378 + 0.0608996i
\(913\) 72.8663 21.3955i 0.0798097 0.0234343i
\(914\) 82.0489 + 11.7969i 0.0897690 + 0.0129068i
\(915\) 267.616 + 585.996i 0.292476 + 0.640433i
\(916\) −711.221 + 102.258i −0.776442 + 0.111635i
\(917\) 417.158 + 649.111i 0.454917 + 0.707864i
\(918\) 54.5052 + 47.2291i 0.0593739 + 0.0514478i
\(919\) 960.745i 1.04542i 0.852509 + 0.522712i \(0.175080\pi\)
−0.852509 + 0.522712i \(0.824920\pi\)
\(920\) −282.451 181.997i −0.307012 0.197823i
\(921\) −540.497 −0.586859
\(922\) −79.9685 + 92.2886i −0.0867337 + 0.100096i
\(923\) −302.552 + 194.438i −0.327792 + 0.210659i
\(924\) −4.59752 31.9765i −0.00497567 0.0346066i
\(925\) −47.4492 + 21.6693i −0.0512964 + 0.0234263i
\(926\) −71.5966 + 497.965i −0.0773181 + 0.537759i
\(927\) 2.40378 + 8.18652i 0.00259307 + 0.00883120i
\(928\) −210.089 135.016i −0.226389 0.145491i
\(929\) 243.623 533.460i 0.262242 0.574230i −0.732010 0.681294i \(-0.761418\pi\)
0.994252 + 0.107064i \(0.0341448\pi\)
\(930\) −96.8446 + 329.822i −0.104134 + 0.354648i
\(931\) 153.089 132.652i 0.164435 0.142484i
\(932\) −405.659 468.155i −0.435256 0.502312i
\(933\) 621.005 + 182.344i 0.665600 + 0.195438i
\(934\) −784.613 358.321i −0.840056 0.383641i
\(935\) −48.5239 + 75.5047i −0.0518973 + 0.0807537i
\(936\) 94.8378 27.8469i 0.101322 0.0297509i
\(937\) 1099.08 + 158.023i 1.17297 + 0.168648i 0.701130 0.713034i \(-0.252679\pi\)
0.471844 + 0.881682i \(0.343588\pi\)
\(938\) −125.898 275.678i −0.134220 0.293900i
\(939\) 784.450 112.787i 0.835411 0.120114i
\(940\) −71.0340 110.531i −0.0755681 0.117586i
\(941\) −1015.17 879.653i −1.07882 0.934807i −0.0807440 0.996735i \(-0.525730\pi\)
−0.998081 + 0.0619280i \(0.980275\pi\)
\(942\) 721.707i 0.766144i
\(943\) −1.89532 + 1588.50i −0.00200988 + 1.68451i
\(944\) 178.723 0.189326
\(945\) 92.5728 106.835i 0.0979606 0.113053i
\(946\) 30.9277 19.8760i 0.0326931 0.0210106i
\(947\) 2.49738 + 17.3696i 0.00263715 + 0.0183418i 0.991098 0.133138i \(-0.0425053\pi\)
−0.988460 + 0.151480i \(0.951596\pi\)
\(948\) −475.208 + 217.020i −0.501274 + 0.228924i
\(949\) −125.061 + 869.821i −0.131782 + 0.916566i
\(950\) −6.37097 21.6975i −0.00670628 0.0228395i
\(951\) −193.444 124.319i −0.203411 0.130725i
\(952\) −60.7388 + 133.000i −0.0638013 + 0.139705i
\(953\) 261.161 889.434i 0.274041 0.933299i −0.701350 0.712817i \(-0.747419\pi\)
0.975391 0.220482i \(-0.0707630\pi\)
\(954\) 120.905 104.765i 0.126735 0.109816i
\(955\) 555.990 + 641.647i 0.582189 + 0.671882i
\(956\) 627.436 + 184.232i 0.656314 + 0.192711i
\(957\) 123.150 + 56.2408i 0.128684 + 0.0587678i
\(958\) 85.3583 132.820i 0.0891005 0.138643i
\(959\) 1117.66 328.175i 1.16545 0.342206i
\(960\) 70.8409 + 10.1854i 0.0737926 + 0.0106098i
\(961\) −92.5557 202.669i −0.0963119 0.210894i
\(962\) 506.894 72.8803i 0.526917 0.0757592i
\(963\) −181.175 281.914i −0.188136 0.292746i
\(964\) −284.780 246.763i −0.295415 0.255978i
\(965\) 1453.38i 1.50609i
\(966\) 284.622 + 83.9416i 0.294640 + 0.0868961i
\(967\) −555.630 −0.574592 −0.287296 0.957842i \(-0.592756\pi\)
−0.287296 + 0.957842i \(0.592756\pi\)
\(968\) 218.313 251.947i 0.225530 0.260275i
\(969\) −136.274 + 87.5780i −0.140634 + 0.0903798i
\(970\) 23.8366 + 165.787i 0.0245738 + 0.170915i
\(971\) −988.931 + 451.630i −1.01847 + 0.465118i −0.853451 0.521173i \(-0.825495\pi\)
−0.165016 + 0.986291i \(0.552767\pi\)
\(972\) −4.43694 + 30.8596i −0.00456475 + 0.0317485i
\(973\) −121.772 414.716i −0.125151 0.426224i
\(974\) 411.902 + 264.714i 0.422898 + 0.271780i
\(975\) −14.0639 + 30.7958i −0.0144246 + 0.0315854i
\(976\) 81.1501 276.372i 0.0831456 0.283168i
\(977\) −612.524 + 530.755i −0.626943 + 0.543250i −0.909343 0.416047i \(-0.863415\pi\)
0.282400 + 0.959297i \(0.408870\pi\)
\(978\) 294.500 + 339.871i 0.301125 + 0.347517i
\(979\) −183.138 53.7743i −0.187067 0.0549277i
\(980\) −199.745 91.2206i −0.203822 0.0930823i
\(981\) −126.254 + 196.455i −0.128699 + 0.200260i
\(982\) 799.084 234.632i 0.813731 0.238933i
\(983\) −55.9351 8.04225i −0.0569024 0.00818133i 0.113805 0.993503i \(-0.463696\pi\)
−0.170707 + 0.985322i \(0.554605\pi\)
\(984\) −140.555 307.772i −0.142840 0.312777i
\(985\) 1285.61 184.842i 1.30518 0.187657i
\(986\) −331.275 515.474i −0.335979 0.522793i
\(987\) 87.6931 + 75.9865i 0.0888481 + 0.0769873i
\(988\) 222.006i 0.224703i
\(989\) 47.6603 + 334.316i 0.0481904 + 0.338034i
\(990\) −38.7989 −0.0391909
\(991\) 630.959 728.166i 0.636689 0.734779i −0.342096 0.939665i \(-0.611137\pi\)
0.978786 + 0.204886i \(0.0656824\pi\)
\(992\) 129.297 83.0941i 0.130340 0.0837642i
\(993\) 89.0686 + 619.486i 0.0896965 + 0.623853i
\(994\) 209.198 95.5373i 0.210460 0.0961140i
\(995\) 122.689 853.320i 0.123305 0.857608i
\(996\) −41.8606 142.564i −0.0420287 0.143137i
\(997\) −220.660 141.809i −0.221324 0.142236i 0.425281 0.905061i \(-0.360175\pi\)
−0.646605 + 0.762825i \(0.723812\pi\)
\(998\) −84.6654 + 185.391i −0.0848351 + 0.185763i
\(999\) −45.5083 + 154.987i −0.0455539 + 0.155142i
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 138.3.h.a.7.8 80
3.2 odd 2 414.3.l.b.145.1 80
23.10 odd 22 inner 138.3.h.a.79.8 yes 80
69.56 even 22 414.3.l.b.217.1 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.3.h.a.7.8 80 1.1 even 1 trivial
138.3.h.a.79.8 yes 80 23.10 odd 22 inner
414.3.l.b.145.1 80 3.2 odd 2
414.3.l.b.217.1 80 69.56 even 22