Properties

Label 507.2.k.k.80.15
Level $507$
Weight $2$
Character 507.80
Analytic conductor $4.048$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $16$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(80,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.80");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\), degree \(4\), not 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.15
Character \(\chi\) \(=\) 507.80
Dual form 507.2.k.k.488.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.197759 - 0.738045i) q^{2} +(-1.54108 + 0.790622i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(0.278754 + 1.29374i) q^{6} +(-2.46232 + 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.74983 - 2.43682i) q^{9} +O(q^{10})\) \(q+(0.197759 - 0.738045i) q^{2} +(-1.54108 + 0.790622i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(0.278754 + 1.29374i) q^{6} +(-2.46232 + 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.74983 - 2.43682i) q^{9} +(-0.932193 + 0.538202i) q^{10} +(-4.58925 - 1.22969i) q^{11} +(-2.44988 - 0.121564i) q^{12} +1.94778i q^{14} +(2.32270 + 0.747558i) q^{15} +(0.418964 + 0.725666i) q^{16} +(2.90210 - 5.02659i) q^{17} +(-1.45244 - 1.77336i) q^{18} +(-0.877888 - 3.27632i) q^{19} +(-0.516358 - 1.92707i) q^{20} +(3.27298 - 2.96353i) q^{21} +(-1.81513 + 3.14390i) q^{22} +(-1.69879 - 2.94240i) q^{23} +(-1.38513 + 4.30366i) q^{24} -3.01541i q^{25} +(-0.770022 + 5.13878i) q^{27} +(-3.48708 - 0.934361i) q^{28} +(-5.69796 + 3.28972i) q^{29} +(1.01107 - 1.56642i) q^{30} +(-0.386730 + 0.386730i) q^{31} +(5.66102 - 1.51687i) q^{32} +(8.04461 - 1.73333i) q^{33} +(-3.13593 - 3.13593i) q^{34} +(3.11004 + 1.79558i) q^{35} +(3.87157 - 1.74959i) q^{36} +(2.17320 - 8.11049i) q^{37} -2.59169 q^{38} -3.67719 q^{40} +(0.268848 - 1.00336i) q^{41} +(-1.53996 - 3.00167i) q^{42} +(-6.55422 - 3.78408i) q^{43} +(-4.75775 - 4.75775i) q^{44} +(-4.17050 + 0.684336i) q^{45} +(-2.50757 + 0.671902i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(-1.21938 - 0.787065i) q^{48} +(-0.434484 + 0.250850i) q^{49} +(-2.22551 - 0.596323i) q^{50} +(-0.498228 + 10.0408i) q^{51} -2.07223i q^{53} +(3.64038 + 1.58455i) q^{54} +(3.34660 + 5.79649i) q^{55} +(-3.32698 + 5.76250i) q^{56} +(3.94323 + 4.35499i) q^{57} +(1.30114 + 4.85592i) q^{58} +(1.30332 + 4.86406i) q^{59} +(2.31933 + 2.56152i) q^{60} +(-3.52415 + 6.10401i) q^{61} +(0.208945 + 0.361904i) q^{62} +(-2.70089 + 7.15471i) q^{63} -2.80221i q^{64} +(0.311618 - 6.28007i) q^{66} +(-6.20237 - 1.66192i) q^{67} +(7.11855 - 4.10990i) q^{68} +(4.94429 + 3.19135i) q^{69} +(1.94026 - 1.94026i) q^{70} +(-9.27862 + 2.48620i) q^{71} +(-1.26798 - 7.72737i) q^{72} +(6.04700 + 6.04700i) q^{73} +(-5.55614 - 3.20784i) q^{74} +(2.38405 + 4.64697i) q^{75} +(1.24325 - 4.63986i) q^{76} +12.1115 q^{77} +8.77426 q^{79} +(0.305519 - 1.14021i) q^{80} +(-2.87617 - 8.52805i) q^{81} +(-0.687355 - 0.396845i) q^{82} +(8.31849 + 8.31849i) q^{83} +(6.11259 - 1.31704i) q^{84} +(-7.89810 + 2.11629i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(6.18006 - 9.57464i) q^{87} +(-10.7401 + 6.20081i) q^{88} +(13.1488 + 3.52321i) q^{89} +(-0.319681 + 3.21335i) q^{90} -4.81159i q^{92} +(0.290223 - 0.901738i) q^{93} +(0.131592 + 0.227923i) q^{94} +(-2.38918 + 4.13818i) q^{95} +(-7.52480 + 6.81334i) q^{96} +(0.491207 + 1.83321i) q^{97} +(0.0992154 + 0.370277i) q^{98} +(-11.0270 + 9.03143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.197759 0.738045i 0.139837 0.521877i −0.860095 0.510135i \(-0.829596\pi\)
0.999931 0.0117423i \(-0.00373778\pi\)
\(3\) −1.54108 + 0.790622i −0.889741 + 0.456466i
\(4\) 1.22645 + 0.708090i 0.613224 + 0.354045i
\(5\) −0.996141 0.996141i −0.445488 0.445488i 0.448363 0.893851i \(-0.352007\pi\)
−0.893851 + 0.448363i \(0.852007\pi\)
\(6\) 0.278754 + 1.29374i 0.113801 + 0.528166i
\(7\) −2.46232 + 0.659775i −0.930668 + 0.249372i −0.692139 0.721764i \(-0.743332\pi\)
−0.238528 + 0.971136i \(0.576665\pi\)
\(8\) 1.84572 1.84572i 0.652560 0.652560i
\(9\) 1.74983 2.43682i 0.583277 0.812273i
\(10\) −0.932193 + 0.538202i −0.294785 + 0.170194i
\(11\) −4.58925 1.22969i −1.38371 0.370765i −0.511244 0.859436i \(-0.670815\pi\)
−0.872468 + 0.488671i \(0.837482\pi\)
\(12\) −2.44988 0.121564i −0.707220 0.0350924i
\(13\) 0 0
\(14\) 1.94778i 0.520565i
\(15\) 2.32270 + 0.747558i 0.599719 + 0.193019i
\(16\) 0.418964 + 0.725666i 0.104741 + 0.181417i
\(17\) 2.90210 5.02659i 0.703863 1.21913i −0.263237 0.964731i \(-0.584790\pi\)
0.967100 0.254395i \(-0.0818765\pi\)
\(18\) −1.45244 1.77336i −0.342343 0.417985i
\(19\) −0.877888 3.27632i −0.201401 0.751640i −0.990516 0.137395i \(-0.956127\pi\)
0.789115 0.614245i \(-0.210539\pi\)
\(20\) −0.516358 1.92707i −0.115461 0.430907i
\(21\) 3.27298 2.96353i 0.714223 0.646694i
\(22\) −1.81513 + 3.14390i −0.386987 + 0.670281i
\(23\) −1.69879 2.94240i −0.354223 0.613532i 0.632762 0.774346i \(-0.281921\pi\)
−0.986985 + 0.160815i \(0.948588\pi\)
\(24\) −1.38513 + 4.30366i −0.282738 + 0.878480i
\(25\) 3.01541i 0.603081i
\(26\) 0 0
\(27\) −0.770022 + 5.13878i −0.148191 + 0.988959i
\(28\) −3.48708 0.934361i −0.658997 0.176578i
\(29\) −5.69796 + 3.28972i −1.05808 + 0.610885i −0.924902 0.380206i \(-0.875853\pi\)
−0.133183 + 0.991092i \(0.542520\pi\)
\(30\) 1.01107 1.56642i 0.184595 0.285988i
\(31\) −0.386730 + 0.386730i −0.0694587 + 0.0694587i −0.740983 0.671524i \(-0.765640\pi\)
0.671524 + 0.740983i \(0.265640\pi\)
\(32\) 5.66102 1.51687i 1.00074 0.268147i
\(33\) 8.04461 1.73333i 1.40039 0.301733i
\(34\) −3.13593 3.13593i −0.537808 0.537808i
\(35\) 3.11004 + 1.79558i 0.525693 + 0.303509i
\(36\) 3.87157 1.74959i 0.645261 0.291599i
\(37\) 2.17320 8.11049i 0.357272 1.33336i −0.520330 0.853965i \(-0.674191\pi\)
0.877602 0.479391i \(-0.159142\pi\)
\(38\) −2.59169 −0.420427
\(39\) 0 0
\(40\) −3.67719 −0.581415
\(41\) 0.268848 1.00336i 0.0419871 0.156698i −0.941750 0.336315i \(-0.890819\pi\)
0.983737 + 0.179617i \(0.0574859\pi\)
\(42\) −1.53996 3.00167i −0.237620 0.463168i
\(43\) −6.55422 3.78408i −0.999509 0.577067i −0.0914058 0.995814i \(-0.529136\pi\)
−0.908103 + 0.418747i \(0.862469\pi\)
\(44\) −4.75775 4.75775i −0.717258 0.717258i
\(45\) −4.17050 + 0.684336i −0.621701 + 0.102015i
\(46\) −2.50757 + 0.671902i −0.369721 + 0.0990666i
\(47\) −0.243559 + 0.243559i −0.0355267 + 0.0355267i −0.724647 0.689120i \(-0.757997\pi\)
0.689120 + 0.724647i \(0.257997\pi\)
\(48\) −1.21938 0.787065i −0.176003 0.113603i
\(49\) −0.434484 + 0.250850i −0.0620692 + 0.0358357i
\(50\) −2.22551 0.596323i −0.314734 0.0843327i
\(51\) −0.498228 + 10.0408i −0.0697658 + 1.40600i
\(52\) 0 0
\(53\) 2.07223i 0.284642i −0.989821 0.142321i \(-0.954543\pi\)
0.989821 0.142321i \(-0.0454566\pi\)
\(54\) 3.64038 + 1.58455i 0.495392 + 0.215630i
\(55\) 3.34660 + 5.79649i 0.451256 + 0.781598i
\(56\) −3.32698 + 5.76250i −0.444586 + 0.770046i
\(57\) 3.94323 + 4.35499i 0.522293 + 0.576832i
\(58\) 1.30114 + 4.85592i 0.170848 + 0.637614i
\(59\) 1.30332 + 4.86406i 0.169678 + 0.633247i 0.997397 + 0.0721043i \(0.0229715\pi\)
−0.827719 + 0.561143i \(0.810362\pi\)
\(60\) 2.31933 + 2.56152i 0.299425 + 0.330691i
\(61\) −3.52415 + 6.10401i −0.451222 + 0.781539i −0.998462 0.0554367i \(-0.982345\pi\)
0.547241 + 0.836975i \(0.315678\pi\)
\(62\) 0.208945 + 0.361904i 0.0265361 + 0.0459618i
\(63\) −2.70089 + 7.15471i −0.340280 + 0.901409i
\(64\) 2.80221i 0.350276i
\(65\) 0 0
\(66\) 0.311618 6.28007i 0.0383575 0.773023i
\(67\) −6.20237 1.66192i −0.757740 0.203036i −0.140791 0.990039i \(-0.544965\pi\)
−0.616948 + 0.787004i \(0.711631\pi\)
\(68\) 7.11855 4.10990i 0.863252 0.498399i
\(69\) 4.94429 + 3.19135i 0.595223 + 0.384194i
\(70\) 1.94026 1.94026i 0.231906 0.231906i
\(71\) −9.27862 + 2.48620i −1.10117 + 0.295057i −0.763241 0.646114i \(-0.776393\pi\)
−0.337929 + 0.941172i \(0.609726\pi\)
\(72\) −1.26798 7.72737i −0.149433 0.910680i
\(73\) 6.04700 + 6.04700i 0.707748 + 0.707748i 0.966061 0.258313i \(-0.0831666\pi\)
−0.258313 + 0.966061i \(0.583167\pi\)
\(74\) −5.55614 3.20784i −0.645888 0.372904i
\(75\) 2.38405 + 4.64697i 0.275286 + 0.536586i
\(76\) 1.24325 4.63986i 0.142610 0.532229i
\(77\) 12.1115 1.38023
\(78\) 0 0
\(79\) 8.77426 0.987182 0.493591 0.869694i \(-0.335684\pi\)
0.493591 + 0.869694i \(0.335684\pi\)
\(80\) 0.305519 1.14021i 0.0341581 0.127480i
\(81\) −2.87617 8.52805i −0.319575 0.947561i
\(82\) −0.687355 0.396845i −0.0759057 0.0438242i
\(83\) 8.31849 + 8.31849i 0.913073 + 0.913073i 0.996513 0.0834395i \(-0.0265905\pi\)
−0.0834395 + 0.996513i \(0.526591\pi\)
\(84\) 6.11259 1.31704i 0.666938 0.143701i
\(85\) −7.89810 + 2.11629i −0.856669 + 0.229544i
\(86\) −4.08898 + 4.08898i −0.440926 + 0.440926i
\(87\) 6.18006 9.57464i 0.662572 1.02651i
\(88\) −10.7401 + 6.20081i −1.14490 + 0.661009i
\(89\) 13.1488 + 3.52321i 1.39377 + 0.373460i 0.876104 0.482123i \(-0.160134\pi\)
0.517667 + 0.855582i \(0.326801\pi\)
\(90\) −0.319681 + 3.21335i −0.0336974 + 0.338717i
\(91\) 0 0
\(92\) 4.81159i 0.501643i
\(93\) 0.290223 0.901738i 0.0300947 0.0935058i
\(94\) 0.131592 + 0.227923i 0.0135726 + 0.0235085i
\(95\) −2.38918 + 4.13818i −0.245125 + 0.424568i
\(96\) −7.52480 + 6.81334i −0.767996 + 0.695383i
\(97\) 0.491207 + 1.83321i 0.0498746 + 0.186134i 0.986369 0.164548i \(-0.0526164\pi\)
−0.936495 + 0.350682i \(0.885950\pi\)
\(98\) 0.0992154 + 0.370277i 0.0100223 + 0.0374036i
\(99\) −11.0270 + 9.03143i −1.10825 + 0.907693i
\(100\) 2.13518 3.69824i 0.213518 0.369824i
\(101\) 1.03384 + 1.79066i 0.102871 + 0.178178i 0.912866 0.408258i \(-0.133864\pi\)
−0.809995 + 0.586436i \(0.800530\pi\)
\(102\) 7.31205 + 2.35337i 0.724001 + 0.233019i
\(103\) 13.3818i 1.31854i −0.751905 0.659272i \(-0.770865\pi\)
0.751905 0.659272i \(-0.229135\pi\)
\(104\) 0 0
\(105\) −6.21244 0.308263i −0.606272 0.0300834i
\(106\) −1.52940 0.409801i −0.148548 0.0398034i
\(107\) 6.51440 3.76109i 0.629771 0.363599i −0.150892 0.988550i \(-0.548215\pi\)
0.780663 + 0.624952i \(0.214881\pi\)
\(108\) −4.58311 + 5.75720i −0.441010 + 0.553987i
\(109\) 2.10533 2.10533i 0.201654 0.201654i −0.599054 0.800709i \(-0.704457\pi\)
0.800709 + 0.599054i \(0.204457\pi\)
\(110\) 4.93989 1.32364i 0.471000 0.126204i
\(111\) 3.06327 + 14.2171i 0.290753 + 1.34942i
\(112\) −1.51040 1.51040i −0.142719 0.142719i
\(113\) 1.64175 + 0.947866i 0.154443 + 0.0891677i 0.575230 0.817992i \(-0.304913\pi\)
−0.420787 + 0.907160i \(0.638246\pi\)
\(114\) 3.99398 2.04904i 0.374071 0.191911i
\(115\) −1.23880 + 4.62328i −0.115519 + 0.431123i
\(116\) −9.31767 −0.865124
\(117\) 0 0
\(118\) 3.84764 0.354204
\(119\) −3.82947 + 14.2918i −0.351047 + 1.31013i
\(120\) 5.66683 2.90727i 0.517308 0.265396i
\(121\) 10.0228 + 5.78669i 0.911168 + 0.526063i
\(122\) 3.80811 + 3.80811i 0.344770 + 0.344770i
\(123\) 0.378960 + 1.75881i 0.0341696 + 0.158586i
\(124\) −0.748144 + 0.200465i −0.0671853 + 0.0180022i
\(125\) −7.98448 + 7.98448i −0.714153 + 0.714153i
\(126\) 4.74638 + 3.40828i 0.422841 + 0.303634i
\(127\) 6.16154 3.55737i 0.546748 0.315665i −0.201061 0.979579i \(-0.564439\pi\)
0.747810 + 0.663913i \(0.231106\pi\)
\(128\) 9.25388 + 2.47957i 0.817936 + 0.219165i
\(129\) 13.0923 + 0.649644i 1.15272 + 0.0571980i
\(130\) 0 0
\(131\) 5.36072i 0.468368i −0.972192 0.234184i \(-0.924758\pi\)
0.972192 0.234184i \(-0.0752419\pi\)
\(132\) 11.0936 + 3.57047i 0.965578 + 0.310770i
\(133\) 4.32327 + 7.48813i 0.374875 + 0.649303i
\(134\) −2.45314 + 4.24897i −0.211919 + 0.367055i
\(135\) 5.88600 4.35190i 0.506586 0.374552i
\(136\) −3.92120 14.6341i −0.336240 1.25487i
\(137\) −1.25278 4.67544i −0.107032 0.399450i 0.891536 0.452951i \(-0.149629\pi\)
−0.998568 + 0.0535011i \(0.982962\pi\)
\(138\) 3.33314 3.01800i 0.283736 0.256909i
\(139\) −5.89404 + 10.2088i −0.499926 + 0.865897i −1.00000 8.58189e-5i \(-0.999973\pi\)
0.500074 + 0.865982i \(0.333306\pi\)
\(140\) 2.54287 + 4.40438i 0.214912 + 0.372238i
\(141\) 0.182780 0.567905i 0.0153928 0.0478263i
\(142\) 7.33971i 0.615935i
\(143\) 0 0
\(144\) 2.50143 + 0.248856i 0.208453 + 0.0207380i
\(145\) 8.95300 + 2.39895i 0.743506 + 0.199222i
\(146\) 5.65881 3.26712i 0.468327 0.270389i
\(147\) 0.471246 0.730091i 0.0388677 0.0602169i
\(148\) 8.40827 8.40827i 0.691156 0.691156i
\(149\) −6.65319 + 1.78272i −0.545050 + 0.146046i −0.520829 0.853661i \(-0.674377\pi\)
−0.0242209 + 0.999707i \(0.507711\pi\)
\(150\) 3.90114 0.840556i 0.318527 0.0686311i
\(151\) −12.2053 12.2053i −0.993251 0.993251i 0.00672628 0.999977i \(-0.497859\pi\)
−0.999977 + 0.00672628i \(0.997859\pi\)
\(152\) −7.66750 4.42683i −0.621916 0.359063i
\(153\) −7.17069 15.8676i −0.579716 1.28282i
\(154\) 2.39516 8.93884i 0.193007 0.720313i
\(155\) 0.770475 0.0618861
\(156\) 0 0
\(157\) −13.4410 −1.07271 −0.536355 0.843993i \(-0.680199\pi\)
−0.536355 + 0.843993i \(0.680199\pi\)
\(158\) 1.73519 6.47580i 0.138044 0.515187i
\(159\) 1.63835 + 3.19346i 0.129930 + 0.253258i
\(160\) −7.15019 4.12816i −0.565272 0.326360i
\(161\) 6.12428 + 6.12428i 0.482661 + 0.482661i
\(162\) −6.86288 + 0.436250i −0.539199 + 0.0342751i
\(163\) 6.14766 1.64726i 0.481522 0.129023i −0.00988942 0.999951i \(-0.503148\pi\)
0.491411 + 0.870928i \(0.336481\pi\)
\(164\) 1.04019 1.04019i 0.0812256 0.0812256i
\(165\) −9.74020 6.28693i −0.758274 0.489437i
\(166\) 7.78448 4.49437i 0.604193 0.348831i
\(167\) −4.23233 1.13405i −0.327507 0.0877553i 0.0913190 0.995822i \(-0.470892\pi\)
−0.418826 + 0.908066i \(0.637558\pi\)
\(168\) 0.571170 11.5108i 0.0440667 0.888080i
\(169\) 0 0
\(170\) 6.24767i 0.479174i
\(171\) −9.51996 3.59376i −0.728010 0.274822i
\(172\) −5.35894 9.28195i −0.408615 0.707742i
\(173\) 2.16677 3.75296i 0.164737 0.285332i −0.771825 0.635835i \(-0.780656\pi\)
0.936562 + 0.350503i \(0.113989\pi\)
\(174\) −5.84436 6.45464i −0.443060 0.489325i
\(175\) 1.98949 + 7.42488i 0.150391 + 0.561268i
\(176\) −1.03039 3.84546i −0.0776685 0.289863i
\(177\) −5.85416 6.46546i −0.440025 0.485974i
\(178\) 5.20058 9.00767i 0.389800 0.675153i
\(179\) 6.99613 + 12.1177i 0.522916 + 0.905716i 0.999644 + 0.0266660i \(0.00848906\pi\)
−0.476729 + 0.879050i \(0.658178\pi\)
\(180\) −5.59947 2.11379i −0.417360 0.157552i
\(181\) 0.976007i 0.0725460i 0.999342 + 0.0362730i \(0.0115486\pi\)
−0.999342 + 0.0362730i \(0.988451\pi\)
\(182\) 0 0
\(183\) 0.605020 12.1930i 0.0447244 0.901334i
\(184\) −8.56632 2.29534i −0.631518 0.169215i
\(185\) −10.2440 + 5.91438i −0.753154 + 0.434834i
\(186\) −0.608129 0.392524i −0.0445902 0.0287813i
\(187\) −19.4996 + 19.4996i −1.42595 + 1.42595i
\(188\) −0.471174 + 0.126251i −0.0343639 + 0.00920777i
\(189\) −1.49440 13.1613i −0.108702 0.957347i
\(190\) 2.58168 + 2.58168i 0.187295 + 0.187295i
\(191\) 14.8153 + 8.55364i 1.07200 + 0.618920i 0.928727 0.370763i \(-0.120904\pi\)
0.143273 + 0.989683i \(0.454237\pi\)
\(192\) 2.21549 + 4.31842i 0.159889 + 0.311655i
\(193\) −0.657172 + 2.45260i −0.0473043 + 0.176542i −0.985536 0.169465i \(-0.945796\pi\)
0.938232 + 0.346007i \(0.112463\pi\)
\(194\) 1.45013 0.104114
\(195\) 0 0
\(196\) −0.710497 −0.0507498
\(197\) 4.62128 17.2469i 0.329253 1.22879i −0.580714 0.814108i \(-0.697227\pi\)
0.909967 0.414681i \(-0.136107\pi\)
\(198\) 4.48493 + 9.92444i 0.318730 + 0.705299i
\(199\) −2.26011 1.30487i −0.160215 0.0925001i 0.417749 0.908563i \(-0.362819\pi\)
−0.577964 + 0.816062i \(0.696153\pi\)
\(200\) −5.56558 5.56558i −0.393546 0.393546i
\(201\) 10.8723 2.34259i 0.766871 0.165233i
\(202\) 1.52604 0.408902i 0.107372 0.0287702i
\(203\) 11.8597 11.8597i 0.832387 0.832387i
\(204\) −7.72086 + 11.9618i −0.540568 + 0.837491i
\(205\) −1.26730 + 0.731673i −0.0885117 + 0.0511023i
\(206\) −9.87634 2.64636i −0.688117 0.184381i
\(207\) −10.1427 1.00905i −0.704965 0.0701337i
\(208\) 0 0
\(209\) 16.1154i 1.11473i
\(210\) −1.45608 + 4.52410i −0.100479 + 0.312193i
\(211\) −6.77213 11.7297i −0.466213 0.807504i 0.533042 0.846088i \(-0.321049\pi\)
−0.999255 + 0.0385841i \(0.987715\pi\)
\(212\) 1.46732 2.54148i 0.100776 0.174550i
\(213\) 12.3334 11.1673i 0.845072 0.765171i
\(214\) −1.48758 5.55172i −0.101689 0.379507i
\(215\) 2.75945 + 10.2984i 0.188193 + 0.702345i
\(216\) 8.06349 + 10.9060i 0.548651 + 0.742058i
\(217\) 0.697096 1.20741i 0.0473220 0.0819641i
\(218\) −1.13748 1.97018i −0.0770402 0.133437i
\(219\) −14.0998 4.53800i −0.952776 0.306650i
\(220\) 9.47879i 0.639060i
\(221\) 0 0
\(222\) 11.0986 + 0.550716i 0.744891 + 0.0369616i
\(223\) 10.0034 + 2.68041i 0.669879 + 0.179494i 0.577700 0.816249i \(-0.303950\pi\)
0.0921788 + 0.995742i \(0.470617\pi\)
\(224\) −12.9384 + 7.47001i −0.864485 + 0.499111i
\(225\) −7.34800 5.27645i −0.489866 0.351764i
\(226\) 1.02424 1.02424i 0.0681314 0.0681314i
\(227\) 0.0638035 0.0170961i 0.00423478 0.00113471i −0.256701 0.966491i \(-0.582636\pi\)
0.260936 + 0.965356i \(0.415969\pi\)
\(228\) 1.75244 + 8.13332i 0.116058 + 0.538643i
\(229\) 19.2246 + 19.2246i 1.27040 + 1.27040i 0.945880 + 0.324517i \(0.105202\pi\)
0.324517 + 0.945880i \(0.394798\pi\)
\(230\) 3.16721 + 1.82859i 0.208839 + 0.120573i
\(231\) −18.6648 + 9.57563i −1.22805 + 0.630030i
\(232\) −4.44493 + 16.5887i −0.291824 + 1.08910i
\(233\) −16.5148 −1.08192 −0.540961 0.841047i \(-0.681939\pi\)
−0.540961 + 0.841047i \(0.681939\pi\)
\(234\) 0 0
\(235\) 0.485238 0.0316534
\(236\) −1.84574 + 6.88839i −0.120147 + 0.448396i
\(237\) −13.5218 + 6.93713i −0.878336 + 0.450615i
\(238\) 9.79067 + 5.65265i 0.634635 + 0.366407i
\(239\) −18.7548 18.7548i −1.21315 1.21315i −0.969985 0.243165i \(-0.921814\pi\)
−0.243165 0.969985i \(-0.578186\pi\)
\(240\) 0.430650 + 1.99871i 0.0277983 + 0.129016i
\(241\) −4.55333 + 1.22006i −0.293306 + 0.0785911i −0.402472 0.915432i \(-0.631849\pi\)
0.109166 + 0.994024i \(0.465182\pi\)
\(242\) 6.25295 6.25295i 0.401955 0.401955i
\(243\) 11.1749 + 10.8684i 0.716868 + 0.697209i
\(244\) −8.64438 + 4.99084i −0.553400 + 0.319506i
\(245\) 0.682689 + 0.182926i 0.0436154 + 0.0116867i
\(246\) 1.37302 + 0.0681296i 0.0875406 + 0.00434378i
\(247\) 0 0
\(248\) 1.42759i 0.0906519i
\(249\) −19.3962 6.24265i −1.22919 0.395612i
\(250\) 4.31391 + 7.47191i 0.272835 + 0.472565i
\(251\) 7.02308 12.1643i 0.443293 0.767806i −0.554638 0.832091i \(-0.687143\pi\)
0.997932 + 0.0642852i \(0.0204767\pi\)
\(252\) −8.37868 + 6.86241i −0.527807 + 0.432291i
\(253\) 4.17797 + 15.5924i 0.262666 + 0.980285i
\(254\) −1.40700 5.25100i −0.0882831 0.329477i
\(255\) 10.4984 9.50577i 0.657434 0.595275i
\(256\) 6.46228 11.1930i 0.403893 0.699563i
\(257\) −9.76740 16.9176i −0.609274 1.05529i −0.991360 0.131167i \(-0.958128\pi\)
0.382087 0.924127i \(-0.375206\pi\)
\(258\) 3.06859 9.53426i 0.191042 0.593577i
\(259\) 21.4044i 1.33000i
\(260\) 0 0
\(261\) −1.95403 + 19.6413i −0.120951 + 1.21577i
\(262\) −3.95646 1.06013i −0.244431 0.0654950i
\(263\) 1.13335 0.654340i 0.0698854 0.0403484i −0.464650 0.885494i \(-0.653820\pi\)
0.534536 + 0.845146i \(0.320487\pi\)
\(264\) 11.6488 18.0473i 0.716937 1.11073i
\(265\) −2.06423 + 2.06423i −0.126805 + 0.126805i
\(266\) 6.38155 1.70993i 0.391278 0.104843i
\(267\) −23.0488 + 4.96620i −1.41057 + 0.303927i
\(268\) −6.43009 6.43009i −0.392780 0.392780i
\(269\) −24.4901 14.1394i −1.49319 0.862093i −0.493219 0.869905i \(-0.664180\pi\)
−0.999969 + 0.00781215i \(0.997513\pi\)
\(270\) −2.04789 5.20476i −0.124631 0.316752i
\(271\) −1.84107 + 6.87097i −0.111837 + 0.417382i −0.999031 0.0440153i \(-0.985985\pi\)
0.887194 + 0.461397i \(0.152652\pi\)
\(272\) 4.86350 0.294893
\(273\) 0 0
\(274\) −3.69843 −0.223431
\(275\) −3.70800 + 13.8385i −0.223601 + 0.834491i
\(276\) 3.80415 + 7.41503i 0.228983 + 0.446333i
\(277\) −10.6104 6.12593i −0.637518 0.368071i 0.146140 0.989264i \(-0.453315\pi\)
−0.783658 + 0.621193i \(0.786648\pi\)
\(278\) 6.36894 + 6.36894i 0.381984 + 0.381984i
\(279\) 0.265678 + 1.61910i 0.0159057 + 0.0969332i
\(280\) 9.05440 2.42612i 0.541104 0.144988i
\(281\) 17.0443 17.0443i 1.01678 1.01678i 0.0169217 0.999857i \(-0.494613\pi\)
0.999857 0.0169217i \(-0.00538659\pi\)
\(282\) −0.382994 0.247208i −0.0228070 0.0147210i
\(283\) 10.6763 6.16394i 0.634638 0.366408i −0.147908 0.989001i \(-0.547254\pi\)
0.782546 + 0.622593i \(0.213921\pi\)
\(284\) −13.1402 3.52091i −0.779727 0.208927i
\(285\) 0.410170 8.26619i 0.0242964 0.489647i
\(286\) 0 0
\(287\) 2.64796i 0.156304i
\(288\) 6.20951 16.4491i 0.365899 0.969275i
\(289\) −8.34439 14.4529i −0.490846 0.850171i
\(290\) 3.54107 6.13331i 0.207939 0.360160i
\(291\) −2.20637 2.43676i −0.129339 0.142845i
\(292\) 3.13451 + 11.6982i 0.183434 + 0.684583i
\(293\) −4.06923 15.1866i −0.237727 0.887209i −0.976901 0.213694i \(-0.931450\pi\)
0.739174 0.673515i \(-0.235216\pi\)
\(294\) −0.445648 0.492183i −0.0259907 0.0287047i
\(295\) 3.54700 6.14359i 0.206514 0.357693i
\(296\) −10.9586 18.9808i −0.636953 1.10324i
\(297\) 9.85292 22.6363i 0.571724 1.31349i
\(298\) 5.26290i 0.304872i
\(299\) 0 0
\(300\) −0.366564 + 7.38739i −0.0211636 + 0.426511i
\(301\) 18.6352 + 4.99328i 1.07411 + 0.287808i
\(302\) −11.4217 + 6.59435i −0.657248 + 0.379462i
\(303\) −3.00897 1.94217i −0.172861 0.111575i
\(304\) 2.00971 2.00971i 0.115265 0.115265i
\(305\) 9.59101 2.56990i 0.549180 0.147152i
\(306\) −13.1291 + 2.15434i −0.750539 + 0.123156i
\(307\) 1.83038 + 1.83038i 0.104465 + 0.104465i 0.757408 0.652942i \(-0.226466\pi\)
−0.652942 + 0.757408i \(0.726466\pi\)
\(308\) 14.8541 + 8.57604i 0.846393 + 0.488665i
\(309\) 10.5799 + 20.6223i 0.601870 + 1.17316i
\(310\) 0.152368 0.568646i 0.00865393 0.0322969i
\(311\) −15.2844 −0.866701 −0.433350 0.901226i \(-0.642669\pi\)
−0.433350 + 0.901226i \(0.642669\pi\)
\(312\) 0 0
\(313\) 31.4063 1.77519 0.887593 0.460628i \(-0.152376\pi\)
0.887593 + 0.460628i \(0.152376\pi\)
\(314\) −2.65808 + 9.92008i −0.150004 + 0.559823i
\(315\) 9.81757 4.43664i 0.553157 0.249976i
\(316\) 10.7612 + 6.21297i 0.605364 + 0.349507i
\(317\) −11.8144 11.8144i −0.663565 0.663565i 0.292654 0.956219i \(-0.405462\pi\)
−0.956219 + 0.292654i \(0.905462\pi\)
\(318\) 2.68092 0.577642i 0.150338 0.0323925i
\(319\) 30.1947 8.09065i 1.69058 0.452989i
\(320\) −2.79140 + 2.79140i −0.156044 + 0.156044i
\(321\) −7.06559 + 10.9466i −0.394363 + 0.610978i
\(322\) 5.73113 3.30887i 0.319383 0.184396i
\(323\) −19.0164 5.09544i −1.05810 0.283518i
\(324\) 2.51115 12.4958i 0.139508 0.694211i
\(325\) 0 0
\(326\) 4.86301i 0.269337i
\(327\) −1.57996 + 4.90901i −0.0873718 + 0.271469i
\(328\) −1.35569 2.34813i −0.0748556 0.129654i
\(329\) 0.439024 0.760412i 0.0242042 0.0419229i
\(330\) −6.56625 + 5.94542i −0.361460 + 0.327285i
\(331\) −5.81579 21.7048i −0.319665 1.19300i −0.919568 0.392932i \(-0.871461\pi\)
0.599903 0.800073i \(-0.295206\pi\)
\(332\) 4.31196 + 16.0924i 0.236649 + 0.883188i
\(333\) −15.9611 19.4877i −0.874660 1.06792i
\(334\) −1.67396 + 2.89938i −0.0915949 + 0.158647i
\(335\) 4.52293 + 7.83394i 0.247114 + 0.428014i
\(336\) 3.52179 + 1.13348i 0.192130 + 0.0618366i
\(337\) 9.19516i 0.500892i −0.968131 0.250446i \(-0.919423\pi\)
0.968131 0.250446i \(-0.0805773\pi\)
\(338\) 0 0
\(339\) −3.27947 0.162728i −0.178116 0.00883817i
\(340\) −11.1851 2.99705i −0.606599 0.162538i
\(341\) 2.25036 1.29925i 0.121864 0.0703581i
\(342\) −4.53501 + 6.31547i −0.245226 + 0.341501i
\(343\) 13.5221 13.5221i 0.730125 0.730125i
\(344\) −19.0816 + 5.11289i −1.02881 + 0.275669i
\(345\) −1.74618 8.10425i −0.0940110 0.436318i
\(346\) −2.34136 2.34136i −0.125872 0.125872i
\(347\) 9.72982 + 5.61751i 0.522324 + 0.301564i 0.737885 0.674926i \(-0.235825\pi\)
−0.215561 + 0.976490i \(0.569158\pi\)
\(348\) 14.3592 7.36676i 0.769736 0.394900i
\(349\) −9.02423 + 33.6789i −0.483056 + 1.80279i 0.105605 + 0.994408i \(0.466322\pi\)
−0.588660 + 0.808380i \(0.700344\pi\)
\(350\) 5.87334 0.313943
\(351\) 0 0
\(352\) −27.8451 −1.48415
\(353\) 8.33550 31.1085i 0.443654 1.65574i −0.275812 0.961212i \(-0.588947\pi\)
0.719466 0.694528i \(-0.244387\pi\)
\(354\) −5.92951 + 3.04203i −0.315150 + 0.161682i
\(355\) 11.7194 + 6.76621i 0.622002 + 0.359113i
\(356\) 13.6316 + 13.6316i 0.722472 + 0.722472i
\(357\) −5.39789 25.0524i −0.285687 1.32591i
\(358\) 10.3269 2.76709i 0.545795 0.146245i
\(359\) −20.8500 + 20.8500i −1.10042 + 1.10042i −0.106064 + 0.994359i \(0.533825\pi\)
−0.994359 + 0.106064i \(0.966175\pi\)
\(360\) −6.43447 + 8.96065i −0.339126 + 0.472268i
\(361\) 6.49088 3.74751i 0.341625 0.197237i
\(362\) 0.720338 + 0.193014i 0.0378601 + 0.0101446i
\(363\) −20.0211 0.993449i −1.05083 0.0521425i
\(364\) 0 0
\(365\) 12.0473i 0.630587i
\(366\) −8.87936 2.85781i −0.464131 0.149380i
\(367\) 10.6590 + 18.4619i 0.556395 + 0.963705i 0.997794 + 0.0663937i \(0.0211493\pi\)
−0.441398 + 0.897311i \(0.645517\pi\)
\(368\) 1.42347 2.46551i 0.0742032 0.128524i
\(369\) −1.97456 2.41084i −0.102791 0.125503i
\(370\) 2.33924 + 8.73016i 0.121611 + 0.453859i
\(371\) 1.36720 + 5.10248i 0.0709817 + 0.264907i
\(372\) 0.994455 0.900431i 0.0515601 0.0466851i
\(373\) 6.95177 12.0408i 0.359949 0.623450i −0.628003 0.778211i \(-0.716127\pi\)
0.987952 + 0.154761i \(0.0494607\pi\)
\(374\) 10.5354 + 18.2478i 0.544772 + 0.943572i
\(375\) 5.99198 18.6174i 0.309425 0.961398i
\(376\) 0.899081i 0.0463666i
\(377\) 0 0
\(378\) −10.0092 1.49983i −0.514818 0.0771430i
\(379\) 33.5805 + 8.99786i 1.72491 + 0.462189i 0.979001 0.203855i \(-0.0653471\pi\)
0.745912 + 0.666044i \(0.232014\pi\)
\(380\) −5.86041 + 3.38351i −0.300633 + 0.173570i
\(381\) −6.68287 + 10.3536i −0.342374 + 0.530432i
\(382\) 9.24284 9.24284i 0.472905 0.472905i
\(383\) 16.2968 4.36672i 0.832729 0.223129i 0.182825 0.983145i \(-0.441476\pi\)
0.649904 + 0.760016i \(0.274809\pi\)
\(384\) −16.2213 + 3.49512i −0.827792 + 0.178360i
\(385\) −12.0648 12.0648i −0.614878 0.614878i
\(386\) 1.68017 + 0.970045i 0.0855183 + 0.0493740i
\(387\) −20.6899 + 9.34994i −1.05173 + 0.475284i
\(388\) −0.695638 + 2.59616i −0.0353157 + 0.131800i
\(389\) 35.0012 1.77463 0.887315 0.461164i \(-0.152568\pi\)
0.887315 + 0.461164i \(0.152568\pi\)
\(390\) 0 0
\(391\) −19.7203 −0.997297
\(392\) −0.338938 + 1.26493i −0.0171189 + 0.0638887i
\(393\) 4.23831 + 8.26128i 0.213794 + 0.416727i
\(394\) −11.8151 6.82144i −0.595235 0.343659i
\(395\) −8.74040 8.74040i −0.439777 0.439777i
\(396\) −19.9191 + 3.26851i −1.00097 + 0.164249i
\(397\) −1.28080 + 0.343188i −0.0642813 + 0.0172241i −0.290816 0.956779i \(-0.593927\pi\)
0.226535 + 0.974003i \(0.427260\pi\)
\(398\) −1.41001 + 1.41001i −0.0706776 + 0.0706776i
\(399\) −12.5828 8.12170i −0.629927 0.406594i
\(400\) 2.18818 1.26335i 0.109409 0.0631673i
\(401\) 25.6759 + 6.87983i 1.28219 + 0.343562i 0.834689 0.550721i \(-0.185647\pi\)
0.447502 + 0.894283i \(0.352314\pi\)
\(402\) 0.421151 8.48750i 0.0210051 0.423318i
\(403\) 0 0
\(404\) 2.92821i 0.145684i
\(405\) −5.63007 + 11.3602i −0.279760 + 0.564494i
\(406\) −6.40764 11.0984i −0.318006 0.550802i
\(407\) −19.9467 + 34.5487i −0.988722 + 1.71252i
\(408\) 17.6129 + 19.4521i 0.871970 + 0.963023i
\(409\) −2.43275 9.07916i −0.120292 0.448936i 0.879336 0.476201i \(-0.157987\pi\)
−0.999628 + 0.0272657i \(0.991320\pi\)
\(410\) 0.289389 + 1.08002i 0.0142919 + 0.0533382i
\(411\) 5.62713 + 6.21473i 0.277566 + 0.306550i
\(412\) 9.47549 16.4120i 0.466824 0.808563i
\(413\) −6.41838 11.1170i −0.315828 0.547030i
\(414\) −2.75053 + 7.28622i −0.135181 + 0.358098i
\(415\) 16.5728i 0.813526i
\(416\) 0 0
\(417\) 1.01188 20.3925i 0.0495519 0.998623i
\(418\) 11.8939 + 3.18696i 0.581750 + 0.155879i
\(419\) 27.6079 15.9394i 1.34873 0.778692i 0.360664 0.932696i \(-0.382550\pi\)
0.988070 + 0.154003i \(0.0492166\pi\)
\(420\) −7.40096 4.77704i −0.361130 0.233096i
\(421\) −19.6414 + 19.6414i −0.957263 + 0.957263i −0.999123 0.0418609i \(-0.986671\pi\)
0.0418609 + 0.999123i \(0.486671\pi\)
\(422\) −9.99628 + 2.67850i −0.486612 + 0.130387i
\(423\) 0.167322 + 1.01970i 0.00813545 + 0.0495793i
\(424\) −3.82475 3.82475i −0.185746 0.185746i
\(425\) −15.1572 8.75101i −0.735232 0.424486i
\(426\) −5.80294 11.3111i −0.281153 0.548022i
\(427\) 4.65030 17.3552i 0.225044 0.839875i
\(428\) 10.6528 0.514921
\(429\) 0 0
\(430\) 8.14640 0.392854
\(431\) 1.23002 4.59049i 0.0592479 0.221116i −0.929954 0.367676i \(-0.880154\pi\)
0.989202 + 0.146560i \(0.0468202\pi\)
\(432\) −4.05165 + 1.59418i −0.194935 + 0.0767002i
\(433\) 1.78345 + 1.02968i 0.0857072 + 0.0494831i 0.542241 0.840223i \(-0.317576\pi\)
−0.456534 + 0.889706i \(0.650909\pi\)
\(434\) −0.753264 0.753264i −0.0361578 0.0361578i
\(435\) −15.6939 + 3.38148i −0.752465 + 0.162129i
\(436\) 4.07285 1.09132i 0.195054 0.0522646i
\(437\) −8.14889 + 8.14889i −0.389814 + 0.389814i
\(438\) −6.13761 + 9.50886i −0.293266 + 0.454351i
\(439\) 11.1416 6.43260i 0.531759 0.307011i −0.209973 0.977707i \(-0.567338\pi\)
0.741733 + 0.670696i \(0.234004\pi\)
\(440\) 16.8756 + 4.52179i 0.804511 + 0.215568i
\(441\) −0.149000 + 1.49770i −0.00709522 + 0.0713193i
\(442\) 0 0
\(443\) 14.4060i 0.684449i −0.939618 0.342224i \(-0.888820\pi\)
0.939618 0.342224i \(-0.111180\pi\)
\(444\) −6.31002 + 19.6056i −0.299460 + 0.930438i
\(445\) −9.58845 16.6077i −0.454536 0.787280i
\(446\) 3.95653 6.85291i 0.187347 0.324495i
\(447\) 8.84361 8.00746i 0.418288 0.378740i
\(448\) 1.84883 + 6.89992i 0.0873490 + 0.325991i
\(449\) −4.24760 15.8522i −0.200456 0.748113i −0.990787 0.135432i \(-0.956758\pi\)
0.790330 0.612681i \(-0.209909\pi\)
\(450\) −5.34739 + 4.37969i −0.252079 + 0.206461i
\(451\) −2.46763 + 4.27406i −0.116196 + 0.201257i
\(452\) 1.34235 + 2.32502i 0.0631388 + 0.109360i
\(453\) 28.4590 + 9.15950i 1.33712 + 0.430351i
\(454\) 0.0504707i 0.00236871i
\(455\) 0 0
\(456\) 15.3162 + 0.759991i 0.717245 + 0.0355898i
\(457\) −22.0326 5.90361i −1.03064 0.276159i −0.296411 0.955061i \(-0.595790\pi\)
−0.734230 + 0.678901i \(0.762456\pi\)
\(458\) 17.9905 10.3868i 0.840639 0.485343i
\(459\) 23.5959 + 18.7838i 1.10136 + 0.876755i
\(460\) −4.79303 + 4.79303i −0.223476 + 0.223476i
\(461\) 28.5168 7.64107i 1.32816 0.355880i 0.476132 0.879374i \(-0.342038\pi\)
0.852030 + 0.523494i \(0.175372\pi\)
\(462\) 3.37613 + 15.6691i 0.157072 + 0.728993i
\(463\) 25.6118 + 25.6118i 1.19028 + 1.19028i 0.976988 + 0.213295i \(0.0684197\pi\)
0.213295 + 0.976988i \(0.431580\pi\)
\(464\) −4.77448 2.75654i −0.221649 0.127969i
\(465\) −1.18736 + 0.609155i −0.0550626 + 0.0282489i
\(466\) −3.26595 + 12.1887i −0.151292 + 0.564631i
\(467\) −14.0544 −0.650361 −0.325180 0.945652i \(-0.605425\pi\)
−0.325180 + 0.945652i \(0.605425\pi\)
\(468\) 0 0
\(469\) 16.3687 0.755835
\(470\) 0.0959600 0.358128i 0.00442630 0.0165192i
\(471\) 20.7136 10.6268i 0.954434 0.489656i
\(472\) 11.3832 + 6.57212i 0.523956 + 0.302506i
\(473\) 25.4257 + 25.4257i 1.16908 + 1.16908i
\(474\) 2.44586 + 11.3516i 0.112342 + 0.521396i
\(475\) −9.87944 + 2.64719i −0.453300 + 0.121461i
\(476\) −14.8165 + 14.8165i −0.679114 + 0.679114i
\(477\) −5.04964 3.62605i −0.231207 0.166025i
\(478\) −17.5509 + 10.1330i −0.802758 + 0.463472i
\(479\) −12.4179 3.32737i −0.567389 0.152031i −0.0362900 0.999341i \(-0.511554\pi\)
−0.531099 + 0.847310i \(0.678221\pi\)
\(480\) 14.2828 + 0.708716i 0.651918 + 0.0323483i
\(481\) 0 0
\(482\) 3.60185i 0.164060i
\(483\) −14.2800 4.59599i −0.649762 0.209125i
\(484\) 8.19500 + 14.1942i 0.372500 + 0.645189i
\(485\) 1.33683 2.31545i 0.0607021 0.105139i
\(486\) 10.2313 6.09824i 0.464102 0.276622i
\(487\) 7.01541 + 26.1819i 0.317898 + 1.18641i 0.921261 + 0.388946i \(0.127161\pi\)
−0.603362 + 0.797467i \(0.706173\pi\)
\(488\) 4.76169 + 17.7709i 0.215552 + 0.804449i
\(489\) −8.17165 + 7.39903i −0.369535 + 0.334596i
\(490\) 0.270016 0.467681i 0.0121981 0.0211277i
\(491\) 6.27068 + 10.8611i 0.282992 + 0.490156i 0.972120 0.234483i \(-0.0753398\pi\)
−0.689128 + 0.724639i \(0.742006\pi\)
\(492\) −0.780618 + 2.42542i −0.0351930 + 0.109346i
\(493\) 38.1884i 1.71992i
\(494\) 0 0
\(495\) 19.9810 + 1.98782i 0.898079 + 0.0893457i
\(496\) −0.442663 0.118611i −0.0198761 0.00532580i
\(497\) 21.2066 12.2436i 0.951244 0.549201i
\(498\) −8.44313 + 13.0808i −0.378346 + 0.586163i
\(499\) 5.98039 5.98039i 0.267719 0.267719i −0.560461 0.828180i \(-0.689376\pi\)
0.828180 + 0.560461i \(0.189376\pi\)
\(500\) −15.4463 + 4.13882i −0.690778 + 0.185094i
\(501\) 7.41894 1.59852i 0.331454 0.0714165i
\(502\) −7.58896 7.58896i −0.338712 0.338712i
\(503\) 16.0716 + 9.27897i 0.716599 + 0.413729i 0.813500 0.581565i \(-0.197560\pi\)
−0.0969004 + 0.995294i \(0.530893\pi\)
\(504\) 8.22050 + 18.1906i 0.366170 + 0.810276i
\(505\) 0.753904 2.81361i 0.0335483 0.125204i
\(506\) 12.3341 0.548318
\(507\) 0 0
\(508\) 10.0757 0.447039
\(509\) −9.47229 + 35.3511i −0.419852 + 1.56691i 0.355063 + 0.934842i \(0.384459\pi\)
−0.774915 + 0.632066i \(0.782207\pi\)
\(510\) −4.93955 9.62813i −0.218727 0.426341i
\(511\) −18.8793 10.9000i −0.835171 0.482186i
\(512\) 6.56566 + 6.56566i 0.290164 + 0.290164i
\(513\) 17.5123 1.98843i 0.773187 0.0877915i
\(514\) −14.4176 + 3.86318i −0.635932 + 0.170397i
\(515\) −13.3301 + 13.3301i −0.587395 + 0.587395i
\(516\) 15.5971 + 10.0673i 0.686622 + 0.443188i
\(517\) 1.41725 0.818252i 0.0623307 0.0359867i
\(518\) 15.7974 + 4.23291i 0.694099 + 0.185983i
\(519\) −0.371988 + 7.49670i −0.0163285 + 0.329069i
\(520\) 0 0
\(521\) 32.0270i 1.40313i −0.712605 0.701565i \(-0.752485\pi\)
0.712605 0.701565i \(-0.247515\pi\)
\(522\) 14.1098 + 5.32641i 0.617568 + 0.233131i
\(523\) −8.20295 14.2079i −0.358690 0.621269i 0.629052 0.777363i \(-0.283443\pi\)
−0.987742 + 0.156094i \(0.950110\pi\)
\(524\) 3.79587 6.57465i 0.165824 0.287215i
\(525\) −8.93623 9.86937i −0.390009 0.430735i
\(526\) −0.258803 0.965866i −0.0112843 0.0421138i
\(527\) 0.821602 + 3.06626i 0.0357896 + 0.133568i
\(528\) 4.62822 + 5.11150i 0.201417 + 0.222450i
\(529\) 5.72821 9.92154i 0.249052 0.431372i
\(530\) 1.11528 + 1.93172i 0.0484445 + 0.0839084i
\(531\) 14.1334 + 5.33534i 0.613339 + 0.231534i
\(532\) 12.2451i 0.530891i
\(533\) 0 0
\(534\) −0.892826 + 17.9932i −0.0386364 + 0.778642i
\(535\) −10.2358 2.74269i −0.442534 0.118577i
\(536\) −14.5152 + 8.38038i −0.626963 + 0.361977i
\(537\) −20.3621 13.1429i −0.878688 0.567160i
\(538\) −15.2786 + 15.2786i −0.658709 + 0.658709i
\(539\) 2.30243 0.616933i 0.0991725 0.0265732i
\(540\) 10.3004 1.16956i 0.443259 0.0503299i
\(541\) 10.4088 + 10.4088i 0.447508 + 0.447508i 0.894525 0.447017i \(-0.147514\pi\)
−0.447017 + 0.894525i \(0.647514\pi\)
\(542\) 4.70700 + 2.71759i 0.202183 + 0.116730i
\(543\) −0.771653 1.50410i −0.0331148 0.0645472i
\(544\) 8.80420 32.8577i 0.377477 1.40876i
\(545\) −4.19442 −0.179669
\(546\) 0 0
\(547\) −18.0787 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(548\) 1.77416 6.62126i 0.0757884 0.282846i
\(549\) 8.70769 + 19.2687i 0.371635 + 0.822369i
\(550\) 9.48012 + 5.47335i 0.404234 + 0.233384i
\(551\) 15.7803 + 15.7803i 0.672265 + 0.672265i
\(552\) 15.0161 3.23543i 0.639128 0.137709i
\(553\) −21.6050 + 5.78904i −0.918738 + 0.246175i
\(554\) −6.61952 + 6.61952i −0.281236 + 0.281236i
\(555\) 11.1108 17.2136i 0.471625 0.730679i
\(556\) −14.4575 + 8.34702i −0.613133 + 0.353992i
\(557\) 12.4314 + 3.33099i 0.526736 + 0.141138i 0.512381 0.858759i \(-0.328764\pi\)
0.0143553 + 0.999897i \(0.495430\pi\)
\(558\) 1.24751 + 0.124109i 0.0528114 + 0.00525396i
\(559\) 0 0
\(560\) 3.00914i 0.127159i
\(561\) 14.6336 45.4672i 0.617829 1.91963i
\(562\) −9.20882 15.9501i −0.388451 0.672816i
\(563\) −13.9437 + 24.1513i −0.587659 + 1.01785i 0.406880 + 0.913482i \(0.366617\pi\)
−0.994538 + 0.104373i \(0.966716\pi\)
\(564\) 0.626298 0.567082i 0.0263719 0.0238785i
\(565\) −0.691209 2.57963i −0.0290794 0.108526i
\(566\) −2.43795 9.09854i −0.102475 0.382440i
\(567\) 12.7086 + 19.1011i 0.533713 + 0.802172i
\(568\) −12.5369 + 21.7145i −0.526036 + 0.911121i
\(569\) 0.877082 + 1.51915i 0.0367692 + 0.0636861i 0.883824 0.467819i \(-0.154960\pi\)
−0.847055 + 0.531505i \(0.821627\pi\)
\(570\) −6.01971 1.93744i −0.252138 0.0811502i
\(571\) 13.1497i 0.550300i −0.961401 0.275150i \(-0.911273\pi\)
0.961401 0.275150i \(-0.0887275\pi\)
\(572\) 0 0
\(573\) −29.5943 1.46847i −1.23632 0.0613464i
\(574\) 1.95431 + 0.523657i 0.0815715 + 0.0218570i
\(575\) −8.87251 + 5.12255i −0.370009 + 0.213625i
\(576\) −6.82848 4.90340i −0.284520 0.204308i
\(577\) −2.17547 + 2.17547i −0.0905662 + 0.0905662i −0.750938 0.660372i \(-0.770399\pi\)
0.660372 + 0.750938i \(0.270399\pi\)
\(578\) −12.3171 + 3.30035i −0.512323 + 0.137277i
\(579\) −0.926327 4.29922i −0.0384969 0.178669i
\(580\) 9.28171 + 9.28171i 0.385402 + 0.385402i
\(581\) −25.9711 14.9944i −1.07746 0.622073i
\(582\) −2.23477 + 1.14651i −0.0926341 + 0.0475243i
\(583\) −2.54819 + 9.50998i −0.105535 + 0.393863i
\(584\) 22.3221 0.923696
\(585\) 0 0
\(586\) −12.0131 −0.496257
\(587\) −3.89820 + 14.5483i −0.160896 + 0.600472i 0.837632 + 0.546235i \(0.183939\pi\)
−0.998528 + 0.0542369i \(0.982727\pi\)
\(588\) 1.09493 0.561735i 0.0451541 0.0231655i
\(589\) 1.60656 + 0.927547i 0.0661971 + 0.0382189i
\(590\) −3.83280 3.83280i −0.157794 0.157794i
\(591\) 6.51401 + 30.2324i 0.267950 + 1.24360i
\(592\) 6.79600 1.82098i 0.279314 0.0748419i
\(593\) 18.1461 18.1461i 0.745171 0.745171i −0.228397 0.973568i \(-0.573348\pi\)
0.973568 + 0.228397i \(0.0733483\pi\)
\(594\) −14.7581 11.7484i −0.605532 0.482044i
\(595\) 18.0513 10.4219i 0.740032 0.427258i
\(596\) −9.42211 2.52465i −0.385945 0.103414i
\(597\) 4.51467 + 0.224019i 0.184773 + 0.00916847i
\(598\) 0 0
\(599\) 19.9578i 0.815455i 0.913104 + 0.407728i \(0.133679\pi\)
−0.913104 + 0.407728i \(0.866321\pi\)
\(600\) 12.9773 + 4.17672i 0.529795 + 0.170514i
\(601\) 23.4640 + 40.6409i 0.957118 + 1.65778i 0.729444 + 0.684040i \(0.239779\pi\)
0.227674 + 0.973737i \(0.426888\pi\)
\(602\) 7.37054 12.7662i 0.300401 0.520310i
\(603\) −14.9029 + 12.2060i −0.606893 + 0.497065i
\(604\) −6.32670 23.6116i −0.257430 0.960741i
\(605\) −4.21981 15.7485i −0.171560 0.640269i
\(606\) −2.02846 + 1.83667i −0.0824006 + 0.0746097i
\(607\) −16.7800 + 29.0639i −0.681081 + 1.17967i 0.293570 + 0.955938i \(0.405157\pi\)
−0.974651 + 0.223730i \(0.928177\pi\)
\(608\) −9.93949 17.2157i −0.403099 0.698189i
\(609\) −8.90016 + 27.6532i −0.360653 + 1.12057i
\(610\) 7.58682i 0.307182i
\(611\) 0 0
\(612\) 2.44120 24.5383i 0.0986796 0.991901i
\(613\) −29.7615 7.97457i −1.20206 0.322090i −0.398415 0.917205i \(-0.630440\pi\)
−0.803640 + 0.595115i \(0.797106\pi\)
\(614\) 1.71288 0.988929i 0.0691261 0.0399099i
\(615\) 1.37452 2.12952i 0.0554260 0.0858704i
\(616\) 22.3544 22.3544i 0.900685 0.900685i
\(617\) −28.0366 + 7.51239i −1.12871 + 0.302437i −0.774404 0.632691i \(-0.781950\pi\)
−0.354308 + 0.935129i \(0.615283\pi\)
\(618\) 17.3125 3.73022i 0.696410 0.150051i
\(619\) −28.5202 28.5202i −1.14633 1.14633i −0.987270 0.159056i \(-0.949155\pi\)
−0.159056 0.987270i \(-0.550845\pi\)
\(620\) 0.944948 + 0.545566i 0.0379500 + 0.0219105i
\(621\) 16.4284 6.46401i 0.659250 0.259392i
\(622\) −3.02263 + 11.2806i −0.121196 + 0.452311i
\(623\) −34.7010 −1.39027
\(624\) 0 0
\(625\) 0.830307 0.0332123
\(626\) 6.21086 23.1792i 0.248236 0.926429i
\(627\) −12.7412 24.8351i −0.508835 0.991817i
\(628\) −16.4847 9.51745i −0.657812 0.379788i
\(629\) −34.4612 34.4612i −1.37406 1.37406i
\(630\) −1.33293 8.12320i −0.0531053 0.323636i
\(631\) 23.4553 6.28482i 0.933740 0.250195i 0.240291 0.970701i \(-0.422757\pi\)
0.693449 + 0.720506i \(0.256090\pi\)
\(632\) 16.1948 16.1948i 0.644195 0.644195i
\(633\) 19.7101 + 12.7221i 0.783407 + 0.505659i
\(634\) −11.0560 + 6.38318i −0.439090 + 0.253509i
\(635\) −9.68141 2.59413i −0.384195 0.102945i
\(636\) −0.251907 + 5.07671i −0.00998878 + 0.201305i
\(637\) 0 0
\(638\) 23.8851i 0.945619i
\(639\) −10.1776 + 26.9607i −0.402620 + 1.06655i
\(640\) −6.74817 11.6882i −0.266745 0.462016i
\(641\) −4.70367 + 8.14700i −0.185784 + 0.321787i −0.943840 0.330402i \(-0.892816\pi\)
0.758056 + 0.652189i \(0.226149\pi\)
\(642\) 6.68178 + 7.37951i 0.263709 + 0.291246i
\(643\) −11.8390 44.1838i −0.466885 1.74244i −0.650563 0.759453i \(-0.725467\pi\)
0.183677 0.982987i \(-0.441200\pi\)
\(644\) 3.17457 + 11.8477i 0.125096 + 0.466863i
\(645\) −12.3947 13.6889i −0.488040 0.539002i
\(646\) −7.52133 + 13.0273i −0.295923 + 0.512554i
\(647\) 4.40379 + 7.62760i 0.173131 + 0.299872i 0.939513 0.342514i \(-0.111278\pi\)
−0.766382 + 0.642385i \(0.777945\pi\)
\(648\) −21.0490 10.4318i −0.826882 0.409798i
\(649\) 23.9251i 0.939142i
\(650\) 0 0
\(651\) −0.119676 + 2.41184i −0.00469048 + 0.0945276i
\(652\) 8.70619 + 2.33282i 0.340961 + 0.0913602i
\(653\) −14.0573 + 8.11599i −0.550105 + 0.317603i −0.749164 0.662384i \(-0.769545\pi\)
0.199059 + 0.979987i \(0.436211\pi\)
\(654\) 3.31062 + 2.13688i 0.129455 + 0.0835586i
\(655\) −5.34004 + 5.34004i −0.208653 + 0.208653i
\(656\) 0.840739 0.225275i 0.0328254 0.00879553i
\(657\) 25.3167 4.15421i 0.987699 0.162071i
\(658\) −0.474398 0.474398i −0.0184940 0.0184940i
\(659\) −16.1496 9.32398i −0.629099 0.363211i 0.151304 0.988487i \(-0.451653\pi\)
−0.780403 + 0.625277i \(0.784986\pi\)
\(660\) −7.49414 14.6075i −0.291709 0.568598i
\(661\) 7.32011 27.3190i 0.284719 1.06259i −0.664325 0.747444i \(-0.731281\pi\)
0.949044 0.315143i \(-0.102052\pi\)
\(662\) −17.1693 −0.667303
\(663\) 0 0
\(664\) 30.7072 1.19167
\(665\) 3.15264 11.7658i 0.122254 0.456259i
\(666\) −17.5392 + 7.92613i −0.679632 + 0.307131i
\(667\) 19.3593 + 11.1771i 0.749595 + 0.432779i
\(668\) −4.38772 4.38772i −0.169766 0.169766i
\(669\) −17.5352 + 3.77822i −0.677952 + 0.146074i
\(670\) 6.67625 1.78890i 0.257926 0.0691111i
\(671\) 23.6793 23.6793i 0.914128 0.914128i
\(672\) 14.0332 21.7413i 0.541341 0.838687i
\(673\) −21.3639 + 12.3345i −0.823519 + 0.475459i −0.851629 0.524146i \(-0.824385\pi\)
0.0281092 + 0.999605i \(0.491051\pi\)
\(674\) −6.78645 1.81842i −0.261404 0.0700430i
\(675\) 15.4955 + 2.32193i 0.596422 + 0.0893710i
\(676\) 0 0
\(677\) 48.4537i 1.86223i 0.364727 + 0.931114i \(0.381162\pi\)
−0.364727 + 0.931114i \(0.618838\pi\)
\(678\) −0.768644 + 2.38822i −0.0295196 + 0.0917189i
\(679\) −2.41902 4.18986i −0.0928333 0.160792i
\(680\) −10.6716 + 18.4837i −0.409236 + 0.708818i
\(681\) −0.0848094 + 0.0767908i −0.00324990 + 0.00294263i
\(682\) −0.513874 1.91780i −0.0196773 0.0734365i
\(683\) 4.74192 + 17.6971i 0.181445 + 0.677161i 0.995364 + 0.0961824i \(0.0306632\pi\)
−0.813919 + 0.580978i \(0.802670\pi\)
\(684\) −9.13103 11.1486i −0.349134 0.426276i
\(685\) −3.40945 + 5.90534i −0.130268 + 0.225632i
\(686\) −7.30582 12.6540i −0.278937 0.483134i
\(687\) −44.8260 14.4272i −1.71022 0.550431i
\(688\) 6.34157i 0.241770i
\(689\) 0 0
\(690\) −6.32663 0.313929i −0.240851 0.0119511i
\(691\) −9.99134 2.67717i −0.380089 0.101844i 0.0637158 0.997968i \(-0.479705\pi\)
−0.443805 + 0.896124i \(0.646372\pi\)
\(692\) 5.31487 3.06854i 0.202041 0.116648i
\(693\) 21.1931 29.5136i 0.805060 1.12113i
\(694\) 6.07014 6.07014i 0.230419 0.230419i
\(695\) 16.0407 4.29809i 0.608457 0.163036i
\(696\) −6.26543 29.0787i −0.237490 1.10223i
\(697\) −4.26323 4.26323i −0.161481 0.161481i
\(698\) 23.0719 + 13.3206i 0.873285 + 0.504191i
\(699\) 25.4506 13.0570i 0.962631 0.493861i
\(700\) −2.81748 + 10.5150i −0.106491 + 0.397428i
\(701\) −1.23945 −0.0468132 −0.0234066 0.999726i \(-0.507451\pi\)
−0.0234066 + 0.999726i \(0.507451\pi\)
\(702\) 0 0
\(703\) −28.4804 −1.07416
\(704\) −3.44584 + 12.8601i −0.129870 + 0.484682i
\(705\) −0.747788 + 0.383640i −0.0281633 + 0.0144487i
\(706\) −21.3111 12.3040i −0.802053 0.463066i
\(707\) −3.72708 3.72708i −0.140171 0.140171i
\(708\) −2.60169 12.0748i −0.0977776 0.453799i
\(709\) −26.1123 + 6.99678i −0.980670 + 0.262770i −0.713327 0.700832i \(-0.752812\pi\)
−0.267343 + 0.963601i \(0.586146\pi\)
\(710\) 7.31139 7.31139i 0.274392 0.274392i
\(711\) 15.3535 21.3813i 0.575801 0.801861i
\(712\) 30.7718 17.7661i 1.15322 0.665814i
\(713\) 1.79489 + 0.480938i 0.0672190 + 0.0180113i
\(714\) −19.5573 0.970436i −0.731913 0.0363177i
\(715\) 0 0
\(716\) 19.8156i 0.740543i
\(717\) 43.7306 + 14.0746i 1.63315 + 0.525627i
\(718\) 11.2650 + 19.5116i 0.420406 + 0.728165i
\(719\) 19.0678 33.0264i 0.711109 1.23168i −0.253332 0.967379i \(-0.581527\pi\)
0.964441 0.264298i \(-0.0851401\pi\)
\(720\) −2.24389 2.73968i −0.0836247 0.102102i
\(721\) 8.82895 + 32.9501i 0.328807 + 1.22713i
\(722\) −1.48221 5.53167i −0.0551620 0.205867i
\(723\) 6.05243 5.48018i 0.225092 0.203810i
\(724\) −0.691101 + 1.19702i −0.0256846 + 0.0444870i
\(725\) 9.91983 + 17.1817i 0.368413 + 0.638111i
\(726\) −4.69255 + 14.5800i −0.174157 + 0.541114i
\(727\) 15.5870i 0.578091i −0.957315 0.289046i \(-0.906662\pi\)
0.957315 0.289046i \(-0.0933379\pi\)
\(728\) 0 0
\(729\) −25.8141 7.91395i −0.956079 0.293109i
\(730\) −8.89149 2.38247i −0.329089 0.0881791i
\(731\) −38.0420 + 21.9636i −1.40703 + 0.812352i
\(732\) 9.37578 14.5257i 0.346539 0.536885i
\(733\) −0.240557 + 0.240557i −0.00888518 + 0.00888518i −0.711535 0.702650i \(-0.752000\pi\)
0.702650 + 0.711535i \(0.252000\pi\)
\(734\) 15.7337 4.21582i 0.580740 0.155609i
\(735\) −1.19670 + 0.257847i −0.0441410 + 0.00951081i
\(736\) −14.0801 14.0801i −0.519000 0.519000i
\(737\) 26.4206 + 15.2539i 0.973215 + 0.561886i
\(738\) −2.16979 + 0.980548i −0.0798713 + 0.0360945i
\(739\) 8.76818 32.7233i 0.322543 1.20375i −0.594216 0.804305i \(-0.702538\pi\)
0.916759 0.399441i \(-0.130796\pi\)
\(740\) −16.7517 −0.615803
\(741\) 0 0
\(742\) 4.03624 0.148175
\(743\) 8.56404 31.9614i 0.314184 1.17255i −0.610563 0.791968i \(-0.709057\pi\)
0.924747 0.380583i \(-0.124277\pi\)
\(744\) −1.12868 2.20002i −0.0413795 0.0806567i
\(745\) 8.40335 + 4.85168i 0.307875 + 0.177752i
\(746\) −7.51190 7.51190i −0.275030 0.275030i
\(747\) 34.8266 5.71469i 1.27424 0.209090i
\(748\) −37.7227 + 10.1078i −1.37928 + 0.369577i
\(749\) −13.5590 + 13.5590i −0.495437 + 0.495437i
\(750\) −12.5555 8.10411i −0.458463 0.295920i
\(751\) −4.65403 + 2.68701i −0.169828 + 0.0980503i −0.582505 0.812827i \(-0.697927\pi\)
0.412677 + 0.910878i \(0.364594\pi\)
\(752\) −0.278785 0.0747001i −0.0101662 0.00272403i
\(753\) −1.20571 + 24.2988i −0.0439385 + 0.885497i
\(754\) 0 0
\(755\) 24.3164i 0.884963i
\(756\) 7.48661 17.1999i 0.272285 0.625553i
\(757\) 20.8335 + 36.0847i 0.757207 + 1.31152i 0.944270 + 0.329173i \(0.106770\pi\)
−0.187062 + 0.982348i \(0.559897\pi\)
\(758\) 13.2817 23.0045i 0.482412 0.835562i
\(759\) −18.7663 20.7259i −0.681172 0.752301i
\(760\) 3.22816 + 12.0477i 0.117098 + 0.437015i
\(761\) −1.76325 6.58054i −0.0639177 0.238544i 0.926575 0.376110i \(-0.122739\pi\)
−0.990493 + 0.137566i \(0.956072\pi\)
\(762\) 6.31985 + 6.97978i 0.228944 + 0.252851i
\(763\) −3.79495 + 6.57305i −0.137386 + 0.237960i
\(764\) 12.1135 + 20.9812i 0.438251 + 0.759073i
\(765\) −8.66333 + 22.9494i −0.313223 + 0.829736i
\(766\) 12.8914i 0.465784i
\(767\) 0 0
\(768\) −1.10943 + 22.3585i −0.0400332 + 0.806793i
\(769\) 20.8122 + 5.57662i 0.750508 + 0.201098i 0.613744 0.789505i \(-0.289663\pi\)
0.136765 + 0.990604i \(0.456330\pi\)
\(770\) −11.2903 + 6.51844i −0.406873 + 0.234908i
\(771\) 28.4278 + 18.3490i 1.02380 + 0.660825i
\(772\) −2.54265 + 2.54265i −0.0915119 + 0.0915119i
\(773\) −2.72302 + 0.729632i −0.0979403 + 0.0262430i −0.307456 0.951562i \(-0.599478\pi\)
0.209516 + 0.977805i \(0.432811\pi\)
\(774\) 2.80907 + 17.1191i 0.100970 + 0.615334i
\(775\) 1.16615 + 1.16615i 0.0418893 + 0.0418893i
\(776\) 4.29022 + 2.47696i 0.154010 + 0.0889176i
\(777\) −16.9228 32.9858i −0.607102 1.18336i
\(778\) 6.92179 25.8325i 0.248158 0.926138i
\(779\) −3.52334 −0.126237
\(780\) 0 0
\(781\) 45.6392 1.63310
\(782\) −3.89986 + 14.5545i −0.139459 + 0.520467i
\(783\) −12.5176 31.8137i −0.447342 1.13693i
\(784\) −0.364066 0.210194i −0.0130024 0.00750692i
\(785\) 13.3892 + 13.3892i 0.477879 + 0.477879i
\(786\) 6.93536 1.49432i 0.247376 0.0533007i
\(787\) −20.7925 + 5.57134i −0.741173 + 0.198597i −0.609599 0.792710i \(-0.708670\pi\)
−0.131574 + 0.991306i \(0.542003\pi\)
\(788\) 17.8801 17.8801i 0.636952 0.636952i
\(789\) −1.22924 + 1.90444i −0.0437622 + 0.0677999i
\(790\) −8.17931 + 4.72233i −0.291007 + 0.168013i
\(791\) −4.66789 1.25076i −0.165971 0.0444718i
\(792\) −3.68316 + 37.0221i −0.130875 + 1.31552i
\(793\) 0 0
\(794\) 1.01315i 0.0359555i
\(795\) 1.54911 4.81317i 0.0549413 0.170705i
\(796\) −1.84794 3.20072i −0.0654984 0.113447i
\(797\) 18.7764 32.5217i 0.665095 1.15198i −0.314165 0.949368i \(-0.601725\pi\)
0.979260 0.202609i \(-0.0649422\pi\)
\(798\) −8.48254 + 7.68053i −0.300279 + 0.271888i
\(799\) 0.517437 + 1.93110i 0.0183056 + 0.0683175i
\(800\) −4.57397 17.0703i −0.161714 0.603525i
\(801\) 31.5936 25.8762i 1.11631 0.914292i
\(802\) 10.1552 17.5894i 0.358594 0.621104i
\(803\) −20.3153 35.1872i −0.716912 1.24173i
\(804\) 14.9930 + 4.82549i 0.528764 + 0.170182i
\(805\) 12.2013i 0.430039i
\(806\) 0 0
\(807\) 48.9200 + 2.42742i 1.72207 + 0.0854493i
\(808\) 5.21324 + 1.39688i 0.183401 + 0.0491422i
\(809\) −28.0985 + 16.2227i −0.987889 + 0.570358i −0.904643 0.426171i \(-0.859862\pi\)
−0.0832467 + 0.996529i \(0.526529\pi\)
\(810\) 7.27096 + 6.40183i 0.255476 + 0.224937i
\(811\) 26.3972 26.3972i 0.926930 0.926930i −0.0705768 0.997506i \(-0.522484\pi\)
0.997506 + 0.0705768i \(0.0224840\pi\)
\(812\) 22.9430 6.14757i 0.805143 0.215737i
\(813\) −2.59511 12.0443i −0.0910145 0.422411i
\(814\) 21.5539 + 21.5539i 0.755464 + 0.755464i
\(815\) −7.76484 4.48303i −0.271990 0.157034i
\(816\) −7.49503 + 3.84519i −0.262378 + 0.134609i
\(817\) −6.64400 + 24.7957i −0.232444 + 0.867493i
\(818\) −7.18193 −0.251110
\(819\) 0 0
\(820\) −2.07236 −0.0723700
\(821\) −5.11709 + 19.0972i −0.178588 + 0.666498i 0.817325 + 0.576177i \(0.195456\pi\)
−0.995913 + 0.0903214i \(0.971211\pi\)
\(822\) 5.69957 2.92406i 0.198795 0.101988i
\(823\) −2.12522 1.22700i −0.0740806 0.0427704i 0.462502 0.886618i \(-0.346952\pi\)
−0.536583 + 0.843848i \(0.680285\pi\)
\(824\) −24.6989 24.6989i −0.860428 0.860428i
\(825\) −5.22668 24.2578i −0.181970 0.844547i
\(826\) −9.47411 + 2.53858i −0.329646 + 0.0883285i
\(827\) 12.7904 12.7904i 0.444765 0.444765i −0.448845 0.893610i \(-0.648164\pi\)
0.893610 + 0.448845i \(0.148164\pi\)
\(828\) −11.7250 8.41948i −0.407471 0.292597i
\(829\) −40.7956 + 23.5534i −1.41689 + 0.818042i −0.996024 0.0890809i \(-0.971607\pi\)
−0.420866 + 0.907123i \(0.638274\pi\)
\(830\) −12.2315 3.27741i −0.424561 0.113761i
\(831\) 21.1948 + 1.05169i 0.735238 + 0.0364827i
\(832\) 0 0
\(833\) 2.91196i 0.100894i
\(834\) −14.8505 4.77960i −0.514229 0.165504i
\(835\) 3.08632 + 5.34567i 0.106807 + 0.184994i
\(836\) −11.4112 + 19.7647i −0.394663 + 0.683577i
\(837\) −1.68953 2.28511i −0.0583987 0.0789850i
\(838\) −6.30432 23.5281i −0.217779 0.812763i
\(839\) 1.56504 + 5.84081i 0.0540312 + 0.201647i 0.987665 0.156582i \(-0.0500474\pi\)
−0.933634 + 0.358229i \(0.883381\pi\)
\(840\) −12.0354 + 10.8974i −0.415260 + 0.375998i
\(841\) 7.14449 12.3746i 0.246362 0.426711i
\(842\) 10.6120 + 18.3805i 0.365713 + 0.633434i
\(843\) −12.7910 + 39.7422i −0.440544 + 1.36879i
\(844\) 19.1811i 0.660242i
\(845\) 0 0
\(846\) 0.785671 + 0.0781627i 0.0270119 + 0.00268729i
\(847\) −28.4973 7.63583i −0.979179 0.262370i
\(848\) 1.50375 0.868188i 0.0516388 0.0298137i
\(849\) −11.5796 + 17.9400i −0.397410 + 0.615699i
\(850\) −9.45611 + 9.45611i −0.324342 + 0.324342i
\(851\) −27.5561 + 7.38363i −0.944610 + 0.253107i
\(852\) 23.0338 4.96295i 0.789123 0.170028i
\(853\) −13.7031 13.7031i −0.469185 0.469185i 0.432466 0.901650i \(-0.357644\pi\)
−0.901650 + 0.432466i \(0.857644\pi\)
\(854\) −11.8893 6.86426i −0.406842 0.234890i
\(855\) 5.90333 + 13.0631i 0.201890 + 0.446749i
\(856\) 5.08183 18.9657i 0.173694 0.648233i
\(857\) −15.1228 −0.516585 −0.258292 0.966067i \(-0.583160\pi\)
−0.258292 + 0.966067i \(0.583160\pi\)
\(858\) 0 0
\(859\) −5.35366 −0.182665 −0.0913323 0.995820i \(-0.529113\pi\)
−0.0913323 + 0.995820i \(0.529113\pi\)
\(860\) −3.90788 + 14.5844i −0.133258 + 0.497324i
\(861\) −2.09353 4.08071i −0.0713475 0.139070i
\(862\) −3.14474 1.81562i −0.107110 0.0618402i
\(863\) 18.3335 + 18.3335i 0.624080 + 0.624080i 0.946572 0.322492i \(-0.104521\pi\)
−0.322492 + 0.946572i \(0.604521\pi\)
\(864\) 3.43573 + 30.2588i 0.116886 + 1.02942i
\(865\) −5.89689 + 1.58007i −0.200500 + 0.0537239i
\(866\) 1.11264 1.11264i 0.0378091 0.0378091i
\(867\) 24.2861 + 15.6758i 0.824800 + 0.532377i
\(868\) 1.70990 0.987214i 0.0580379 0.0335082i
\(869\) −40.2673 10.7896i −1.36598 0.366012i
\(870\) −0.607924 + 12.2515i −0.0206105 + 0.415366i
\(871\) 0 0
\(872\) 7.77170i 0.263183i
\(873\) 5.32673 + 2.01083i 0.180283 + 0.0680562i
\(874\) 4.40274 + 7.62576i 0.148925 + 0.257945i
\(875\) 14.3923 24.9283i 0.486550 0.842729i
\(876\) −14.0794 15.5495i −0.475697 0.525370i
\(877\) 7.23433 + 26.9989i 0.244286 + 0.911688i 0.973741 + 0.227659i \(0.0731071\pi\)
−0.729455 + 0.684029i \(0.760226\pi\)
\(878\) −2.54421 9.49511i −0.0858628 0.320444i
\(879\) 18.2778 + 20.1865i 0.616496 + 0.680872i
\(880\) −2.80421 + 4.85704i −0.0945299 + 0.163731i
\(881\) −10.9976 19.0483i −0.370517 0.641755i 0.619128 0.785290i \(-0.287486\pi\)
−0.989645 + 0.143535i \(0.954153\pi\)
\(882\) 1.07591 + 0.406153i 0.0362277 + 0.0136759i
\(883\) 11.7640i 0.395889i −0.980213 0.197945i \(-0.936573\pi\)
0.980213 0.197945i \(-0.0634266\pi\)
\(884\) 0 0
\(885\) −0.608943 + 12.2721i −0.0204694 + 0.412521i
\(886\) −10.6323 2.84891i −0.357198 0.0957109i
\(887\) 26.4142 15.2503i 0.886903 0.512054i 0.0139750 0.999902i \(-0.495551\pi\)
0.872928 + 0.487848i \(0.162218\pi\)
\(888\) 31.8946 + 20.5867i 1.07031 + 0.690846i
\(889\) −12.8246 + 12.8246i −0.430123 + 0.430123i
\(890\) −14.1534 + 3.79240i −0.474424 + 0.127122i
\(891\) 2.71266 + 42.6742i 0.0908774 + 1.42964i
\(892\) 10.3707 + 10.3707i 0.347237 + 0.347237i
\(893\) 1.01179 + 0.584160i 0.0338584 + 0.0195482i
\(894\) −4.16097 8.11053i −0.139164 0.271257i
\(895\) 5.10176 19.0400i 0.170533 0.636438i
\(896\) −24.4219 −0.815880
\(897\) 0 0
\(898\) −12.5397 −0.418454
\(899\) 0.931339 3.47580i 0.0310619 0.115925i
\(900\) −5.27573 11.6743i −0.175858 0.389145i
\(901\) −10.4162 6.01381i −0.347015 0.200349i
\(902\) 2.66645 + 2.66645i 0.0887832 + 0.0887832i
\(903\) −32.6661 + 7.03837i −1.08706 + 0.234222i
\(904\) 4.77970 1.28072i 0.158971 0.0425960i
\(905\) 0.972241 0.972241i 0.0323184 0.0323184i
\(906\) 12.3881 19.1927i 0.411569 0.637634i
\(907\) −16.3002 + 9.41095i −0.541241 + 0.312485i −0.745582 0.666414i \(-0.767828\pi\)
0.204341 + 0.978900i \(0.434495\pi\)
\(908\) 0.0903572 + 0.0242111i 0.00299861 + 0.000803475i
\(909\) 6.17257 + 0.614081i 0.204731 + 0.0203678i
\(910\) 0 0
\(911\) 52.2340i 1.73059i −0.501262 0.865296i \(-0.667131\pi\)
0.501262 0.865296i \(-0.332869\pi\)
\(912\) −1.50820 + 4.68605i −0.0499414 + 0.155171i
\(913\) −27.9465 48.4048i −0.924895 1.60197i
\(914\) −8.71427 + 15.0936i −0.288242 + 0.499250i
\(915\) −12.7487 + 11.5433i −0.421458 + 0.381609i
\(916\) 9.96522 + 37.1907i 0.329260 + 1.22882i
\(917\) 3.53687 + 13.1998i 0.116798 + 0.435895i
\(918\) 18.5296 13.7001i 0.611569 0.452172i
\(919\) −1.44027 + 2.49462i −0.0475102 + 0.0822901i −0.888803 0.458290i \(-0.848462\pi\)
0.841292 + 0.540580i \(0.181795\pi\)
\(920\) 6.24678 + 10.8197i 0.205950 + 0.356716i
\(921\) −4.26789 1.37361i −0.140632 0.0452621i
\(922\) 22.5578i 0.742902i
\(923\) 0 0
\(924\) −29.6718 1.47232i −0.976129 0.0484357i
\(925\) −24.4564 6.55307i −0.804122 0.215464i
\(926\) 23.9677 13.8377i 0.787626 0.454736i
\(927\) −32.6089 23.4158i −1.07102 0.769077i
\(928\) −27.2662 + 27.2662i −0.895057 + 0.895057i
\(929\) −7.02107 + 1.88129i −0.230354 + 0.0617232i −0.372149 0.928173i \(-0.621379\pi\)
0.141796 + 0.989896i \(0.454712\pi\)
\(930\) 0.214773 + 0.996792i 0.00704269 + 0.0326861i
\(931\) 1.20329 + 1.20329i 0.0394363 + 0.0394363i
\(932\) −20.2546 11.6940i −0.663461 0.383049i
\(933\) 23.5545 12.0842i 0.771139 0.395620i
\(934\) −2.77938 + 10.3728i −0.0909442 + 0.339408i
\(935\) 38.8487 1.27049
\(936\) 0 0
\(937\) 3.76482 0.122991 0.0614957 0.998107i \(-0.480413\pi\)
0.0614957 + 0.998107i \(0.480413\pi\)
\(938\) 3.23705 12.0808i 0.105693 0.394453i
\(939\) −48.3994 + 24.8305i −1.57946 + 0.810312i
\(940\) 0.595119 + 0.343592i 0.0194106 + 0.0112067i
\(941\) 10.0291 + 10.0291i 0.326941 + 0.326941i 0.851422 0.524481i \(-0.175741\pi\)
−0.524481 + 0.851422i \(0.675741\pi\)
\(942\) −3.74674 17.3891i −0.122075 0.566569i
\(943\) −3.40899 + 0.913435i −0.111012 + 0.0297455i
\(944\) −2.98364 + 2.98364i −0.0971093 + 0.0971093i
\(945\) −11.6219 + 14.5992i −0.378061 + 0.474912i
\(946\) 23.7935 13.7372i 0.773594 0.446635i
\(947\) 17.4329 + 4.67114i 0.566494 + 0.151792i 0.530688 0.847567i \(-0.321934\pi\)
0.0358059 + 0.999359i \(0.488600\pi\)
\(948\) −21.4959 1.06663i −0.698155 0.0346426i
\(949\) 0 0
\(950\) 7.81498i 0.253551i
\(951\) 27.5477 + 8.86619i 0.893296 + 0.287506i
\(952\) 19.3105 + 33.4467i 0.625856 + 1.08401i
\(953\) −28.1061 + 48.6812i −0.910445 + 1.57694i −0.0970089 + 0.995284i \(0.530928\pi\)
−0.813436 + 0.581654i \(0.802406\pi\)
\(954\) −3.67480 + 3.00978i −0.118976 + 0.0974453i
\(955\) −6.23754 23.2788i −0.201842 0.753285i
\(956\) −9.72172 36.2820i −0.314423 1.17344i
\(957\) −40.1357 + 36.3409i −1.29740 + 1.17473i
\(958\) −4.91150 + 8.50696i −0.158683 + 0.274848i
\(959\) 6.16948 + 10.6858i 0.199223 + 0.345064i
\(960\) 2.09481 6.50870i 0.0676099 0.210067i
\(961\) 30.7009i 0.990351i
\(962\) 0 0
\(963\) 2.23401 22.4557i 0.0719901 0.723625i
\(964\) −6.44834 1.72783i −0.207687 0.0556496i
\(965\) 3.09777 1.78850i 0.0997208 0.0575738i
\(966\) −6.21604 + 9.63038i −0.199998 + 0.309852i
\(967\) 29.9079 29.9079i 0.961772 0.961772i −0.0375237 0.999296i \(-0.511947\pi\)
0.999296 + 0.0375237i \(0.0119470\pi\)
\(968\) 29.1799 7.81874i 0.937878 0.251304i
\(969\) 33.3344 7.18236i 1.07085 0.230731i
\(970\) −1.44454 1.44454i −0.0463813 0.0463813i
\(971\) −2.69565 1.55634i −0.0865077 0.0499452i 0.456122 0.889917i \(-0.349238\pi\)
−0.542630 + 0.839972i \(0.682571\pi\)
\(972\) 6.00958 + 21.2424i 0.192757 + 0.681349i
\(973\) 7.77748 29.0260i 0.249335 0.930529i
\(974\) 20.7108 0.663616
\(975\) 0 0
\(976\) −5.90597 −0.189045
\(977\) 8.18145 30.5336i 0.261748 0.976856i −0.702463 0.711720i \(-0.747916\pi\)
0.964211 0.265136i \(-0.0854168\pi\)
\(978\) 3.84480 + 7.49427i 0.122943 + 0.239640i
\(979\) −56.0108 32.3378i −1.79011 1.03352i
\(980\) 0.707755 + 0.707755i 0.0226084 + 0.0226084i
\(981\) −1.44634 8.81430i −0.0461780 0.281419i
\(982\) 9.25609 2.48016i 0.295374 0.0791451i
\(983\) −19.2933 + 19.2933i −0.615360 + 0.615360i −0.944338 0.328978i \(-0.893296\pi\)
0.328978 + 0.944338i \(0.393296\pi\)
\(984\) 3.94571 + 2.54680i 0.125785 + 0.0811892i
\(985\) −21.7838 + 12.5769i −0.694089 + 0.400732i
\(986\) 28.1848 + 7.55209i 0.897586 + 0.240507i
\(987\) −0.0753709 + 1.51896i −0.00239908 + 0.0483489i
\(988\) 0 0
\(989\) 25.7135i 0.817641i
\(990\) 5.41851 14.3538i 0.172212 0.456193i
\(991\) 15.1976 + 26.3230i 0.482767 + 0.836176i 0.999804 0.0197863i \(-0.00629859\pi\)
−0.517038 + 0.855963i \(0.672965\pi\)
\(992\) −1.60267 + 2.77590i −0.0508848 + 0.0881350i
\(993\) 26.1229 + 28.8507i 0.828985 + 0.915549i
\(994\) −4.84256 18.0727i −0.153597 0.573231i
\(995\) 0.951549 + 3.55123i 0.0301661 + 0.112582i
\(996\) −19.3681 21.3906i −0.613702 0.677786i
\(997\) −19.6231 + 33.9882i −0.621470 + 1.07642i 0.367742 + 0.929928i \(0.380131\pi\)
−0.989212 + 0.146490i \(0.953203\pi\)
\(998\) −3.23113 5.59647i −0.102279 0.177153i
\(999\) 40.0046 + 17.4128i 1.26569 + 0.550918i
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 507.2.k.k.80.15 96
3.2 odd 2 inner 507.2.k.k.80.10 96
13.2 odd 12 507.2.f.g.437.15 yes 48
13.3 even 3 507.2.f.g.239.15 yes 48
13.4 even 6 inner 507.2.k.k.188.16 96
13.5 odd 4 inner 507.2.k.k.89.9 96
13.6 odd 12 inner 507.2.k.k.488.16 96
13.7 odd 12 inner 507.2.k.k.488.10 96
13.8 odd 4 inner 507.2.k.k.89.15 96
13.9 even 3 inner 507.2.k.k.188.10 96
13.10 even 6 507.2.f.g.239.9 48
13.11 odd 12 507.2.f.g.437.9 yes 48
13.12 even 2 inner 507.2.k.k.80.9 96
39.2 even 12 507.2.f.g.437.10 yes 48
39.5 even 4 inner 507.2.k.k.89.16 96
39.8 even 4 inner 507.2.k.k.89.10 96
39.11 even 12 507.2.f.g.437.16 yes 48
39.17 odd 6 inner 507.2.k.k.188.9 96
39.20 even 12 inner 507.2.k.k.488.15 96
39.23 odd 6 507.2.f.g.239.16 yes 48
39.29 odd 6 507.2.f.g.239.10 yes 48
39.32 even 12 inner 507.2.k.k.488.9 96
39.35 odd 6 inner 507.2.k.k.188.15 96
39.38 odd 2 inner 507.2.k.k.80.16 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.f.g.239.9 48 13.10 even 6
507.2.f.g.239.10 yes 48 39.29 odd 6
507.2.f.g.239.15 yes 48 13.3 even 3
507.2.f.g.239.16 yes 48 39.23 odd 6
507.2.f.g.437.9 yes 48 13.11 odd 12
507.2.f.g.437.10 yes 48 39.2 even 12
507.2.f.g.437.15 yes 48 13.2 odd 12
507.2.f.g.437.16 yes 48 39.11 even 12
507.2.k.k.80.9 96 13.12 even 2 inner
507.2.k.k.80.10 96 3.2 odd 2 inner
507.2.k.k.80.15 96 1.1 even 1 trivial
507.2.k.k.80.16 96 39.38 odd 2 inner
507.2.k.k.89.9 96 13.5 odd 4 inner
507.2.k.k.89.10 96 39.8 even 4 inner
507.2.k.k.89.15 96 13.8 odd 4 inner
507.2.k.k.89.16 96 39.5 even 4 inner
507.2.k.k.188.9 96 39.17 odd 6 inner
507.2.k.k.188.10 96 13.9 even 3 inner
507.2.k.k.188.15 96 39.35 odd 6 inner
507.2.k.k.188.16 96 13.4 even 6 inner
507.2.k.k.488.9 96 39.32 even 12 inner
507.2.k.k.488.10 96 13.7 odd 12 inner
507.2.k.k.488.15 96 39.20 even 12 inner
507.2.k.k.488.16 96 13.6 odd 12 inner