Properties

Label 605.2.j.k.9.3
Level $605$
Weight $2$
Character 605.9
Analytic conductor $4.831$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 605.9
Dual form 605.2.j.k.269.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.92380 - 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) q^{5} +(1.82196 + 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +O(q^{10})\) \(q+(-1.92380 - 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) q^{5} +(1.82196 + 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +(-3.81402 - 2.43146i) q^{10} -6.09692i q^{12} +(-0.617001 - 0.200476i) q^{13} +(5.25521 - 3.81813i) q^{14} +(-2.38682 - 6.06482i) q^{15} +(-1.17677 - 3.62171i) q^{16} +(1.13030 - 0.367258i) q^{17} +(6.53436 - 8.99378i) q^{18} +(1.52982 - 1.11148i) q^{19} +(2.97400 + 3.61003i) q^{20} +9.36008 q^{21} -4.35986i q^{23} +(-0.167155 + 0.514449i) q^{24} +(4.37159 + 2.42676i) q^{25} +(1.06168 + 0.771352i) q^{26} +(6.91857 - 2.24798i) q^{27} +(-6.38841 + 2.07572i) q^{28} +(-3.36869 - 2.44750i) q^{29} +(0.800770 + 13.1595i) q^{30} +(2.44118 - 7.51319i) q^{31} +8.07420i q^{32} -2.40405 q^{34} +(-5.54217 + 4.56573i) q^{35} +(-9.30029 + 6.75706i) q^{36} +(-1.20995 + 1.66536i) q^{37} +(-3.63783 + 1.18200i) q^{38} +(0.584338 + 1.79841i) q^{39} +(-0.151968 - 0.386145i) q^{40} +(2.67396 - 1.94275i) q^{41} +(-18.0070 - 5.85081i) q^{42} -10.9313i q^{43} +(-6.60607 + 10.3624i) q^{45} +(-2.72527 + 8.38752i) q^{46} +(-1.71325 - 2.35809i) q^{47} +(-6.52422 + 8.97981i) q^{48} +(-1.02356 - 3.15019i) q^{49} +(-6.89316 - 7.40121i) q^{50} +(-2.80252 - 2.03615i) q^{51} +(-0.797640 - 1.09786i) q^{52} +(6.10422 + 1.98338i) q^{53} -14.7151 q^{54} +0.595953 q^{56} +(-5.24191 - 1.70320i) q^{57} +(4.95081 + 6.81421i) q^{58} +(-3.00659 - 2.18442i) q^{59} +(3.41756 - 13.1978i) q^{60} +(-2.40630 - 7.40582i) q^{61} +(-9.39272 + 12.9280i) q^{62} +(-10.3735 - 14.2779i) q^{63} +(2.69350 - 8.28974i) q^{64} +(-1.22323 - 0.779817i) q^{65} -2.37993i q^{67} +(2.36431 + 0.768210i) q^{68} +(-10.2809 + 7.46954i) q^{69} +(13.5160 - 5.31925i) q^{70} +(4.85662 + 14.9471i) q^{71} +(0.969998 - 0.315171i) q^{72} +(3.35877 - 4.62295i) q^{73} +(3.36869 - 2.44750i) q^{74} +(-1.76712 - 14.4662i) q^{75} +3.95540 q^{76} -3.82504i q^{78} +(4.71438 - 14.5094i) q^{79} +(-0.517201 - 8.49944i) q^{80} +(-3.81561 - 2.77220i) q^{81} +(-6.35854 + 2.06602i) q^{82} +(-10.1161 + 3.28693i) q^{83} +(15.8397 + 11.5082i) q^{84} +(2.65260 - 0.161414i) q^{85} +(-6.83298 + 21.0297i) q^{86} +12.1368i q^{87} -9.00000 q^{89} +(19.1861 - 15.8058i) q^{90} +(1.68545 - 1.22455i) q^{91} +(5.36044 - 7.37801i) q^{92} +(-21.8991 + 7.11545i) q^{93} +(1.82196 + 5.60741i) q^{94} +(3.93457 - 1.54846i) q^{95} +(19.0397 - 13.8331i) q^{96} +(14.3972 + 4.67793i) q^{97} +6.70015i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92380 0.625081i −1.36033 0.441999i −0.464179 0.885741i \(-0.653651\pi\)
−0.896155 + 0.443742i \(0.853651\pi\)
\(3\) −1.71325 2.35809i −0.989145 1.36144i −0.931754 0.363090i \(-0.881722\pi\)
−0.0573908 0.998352i \(-0.518278\pi\)
\(4\) 1.69226 + 1.22950i 0.846128 + 0.614748i
\(5\) 2.16467 + 0.560538i 0.968070 + 0.250680i
\(6\) 1.82196 + 5.60741i 0.743812 + 2.28922i
\(7\) −1.88754 + 2.59798i −0.713424 + 0.981943i 0.286293 + 0.958142i \(0.407577\pi\)
−0.999717 + 0.0238013i \(0.992423\pi\)
\(8\) −0.109082 0.150138i −0.0385663 0.0530819i
\(9\) −1.69829 + 5.22681i −0.566098 + 1.74227i
\(10\) −3.81402 2.43146i −1.20610 0.768895i
\(11\) 0 0
\(12\) 6.09692i 1.76003i
\(13\) −0.617001 0.200476i −0.171125 0.0556020i 0.222201 0.975001i \(-0.428676\pi\)
−0.393327 + 0.919399i \(0.628676\pi\)
\(14\) 5.25521 3.81813i 1.40451 1.02044i
\(15\) −2.38682 6.06482i −0.616275 1.56593i
\(16\) −1.17677 3.62171i −0.294191 0.905428i
\(17\) 1.13030 0.367258i 0.274139 0.0890731i −0.168721 0.985664i \(-0.553964\pi\)
0.442860 + 0.896591i \(0.353964\pi\)
\(18\) 6.53436 8.99378i 1.54016 2.11985i
\(19\) 1.52982 1.11148i 0.350964 0.254990i −0.398309 0.917251i \(-0.630403\pi\)
0.749273 + 0.662261i \(0.230403\pi\)
\(20\) 2.97400 + 3.61003i 0.665006 + 0.807227i
\(21\) 9.36008 2.04254
\(22\) 0 0
\(23\) 4.35986i 0.909095i −0.890723 0.454547i \(-0.849801\pi\)
0.890723 0.454547i \(-0.150199\pi\)
\(24\) −0.167155 + 0.514449i −0.0341203 + 0.105011i
\(25\) 4.37159 + 2.42676i 0.874319 + 0.485352i
\(26\) 1.06168 + 0.771352i 0.208212 + 0.151275i
\(27\) 6.91857 2.24798i 1.33148 0.432624i
\(28\) −6.38841 + 2.07572i −1.20730 + 0.392274i
\(29\) −3.36869 2.44750i −0.625550 0.454489i 0.229306 0.973354i \(-0.426355\pi\)
−0.854856 + 0.518866i \(0.826355\pi\)
\(30\) 0.800770 + 13.1595i 0.146200 + 2.40258i
\(31\) 2.44118 7.51319i 0.438450 1.34941i −0.451060 0.892493i \(-0.648954\pi\)
0.889510 0.456916i \(-0.151046\pi\)
\(32\) 8.07420i 1.42733i
\(33\) 0 0
\(34\) −2.40405 −0.412291
\(35\) −5.54217 + 4.56573i −0.936798 + 0.771749i
\(36\) −9.30029 + 6.75706i −1.55005 + 1.12618i
\(37\) −1.20995 + 1.66536i −0.198915 + 0.273783i −0.896809 0.442418i \(-0.854121\pi\)
0.697894 + 0.716201i \(0.254121\pi\)
\(38\) −3.63783 + 1.18200i −0.590134 + 0.191746i
\(39\) 0.584338 + 1.79841i 0.0935689 + 0.287976i
\(40\) −0.151968 0.386145i −0.0240283 0.0610548i
\(41\) 2.67396 1.94275i 0.417602 0.303406i −0.359070 0.933311i \(-0.616906\pi\)
0.776672 + 0.629905i \(0.216906\pi\)
\(42\) −18.0070 5.85081i −2.77853 0.902800i
\(43\) 10.9313i 1.66701i −0.552509 0.833507i \(-0.686330\pi\)
0.552509 0.833507i \(-0.313670\pi\)
\(44\) 0 0
\(45\) −6.60607 + 10.3624i −0.984775 + 1.54473i
\(46\) −2.72527 + 8.38752i −0.401819 + 1.23667i
\(47\) −1.71325 2.35809i −0.249903 0.343962i 0.665574 0.746332i \(-0.268187\pi\)
−0.915477 + 0.402370i \(0.868187\pi\)
\(48\) −6.52422 + 8.97981i −0.941689 + 1.29612i
\(49\) −1.02356 3.15019i −0.146223 0.450027i
\(50\) −6.89316 7.40121i −0.974840 1.04669i
\(51\) −2.80252 2.03615i −0.392431 0.285118i
\(52\) −0.797640 1.09786i −0.110613 0.152245i
\(53\) 6.10422 + 1.98338i 0.838479 + 0.272438i 0.696613 0.717447i \(-0.254690\pi\)
0.141866 + 0.989886i \(0.454690\pi\)
\(54\) −14.7151 −2.00248
\(55\) 0 0
\(56\) 0.595953 0.0796376
\(57\) −5.24191 1.70320i −0.694308 0.225594i
\(58\) 4.95081 + 6.81421i 0.650074 + 0.894750i
\(59\) −3.00659 2.18442i −0.391425 0.284387i 0.374614 0.927181i \(-0.377775\pi\)
−0.766039 + 0.642794i \(0.777775\pi\)
\(60\) 3.41756 13.1978i 0.441205 1.70383i
\(61\) −2.40630 7.40582i −0.308095 0.948218i −0.978504 0.206227i \(-0.933882\pi\)
0.670410 0.741991i \(-0.266118\pi\)
\(62\) −9.39272 + 12.9280i −1.19288 + 1.64185i
\(63\) −10.3735 14.2779i −1.30694 1.79885i
\(64\) 2.69350 8.28974i 0.336688 1.03622i
\(65\) −1.22323 0.779817i −0.151723 0.0967244i
\(66\) 0 0
\(67\) 2.37993i 0.290755i −0.989376 0.145377i \(-0.953560\pi\)
0.989376 0.145377i \(-0.0464396\pi\)
\(68\) 2.36431 + 0.768210i 0.286714 + 0.0931591i
\(69\) −10.2809 + 7.46954i −1.23768 + 0.899226i
\(70\) 13.5160 5.31925i 1.61547 0.635772i
\(71\) 4.85662 + 14.9471i 0.576375 + 1.77390i 0.631450 + 0.775417i \(0.282460\pi\)
−0.0550754 + 0.998482i \(0.517540\pi\)
\(72\) 0.969998 0.315171i 0.114315 0.0371433i
\(73\) 3.35877 4.62295i 0.393114 0.541075i −0.565885 0.824484i \(-0.691465\pi\)
0.958999 + 0.283409i \(0.0914653\pi\)
\(74\) 3.36869 2.44750i 0.391602 0.284516i
\(75\) −1.76712 14.4662i −0.204049 1.67042i
\(76\) 3.95540 0.453715
\(77\) 0 0
\(78\) 3.82504i 0.433100i
\(79\) 4.71438 14.5094i 0.530410 1.63243i −0.222954 0.974829i \(-0.571570\pi\)
0.753364 0.657604i \(-0.228430\pi\)
\(80\) −0.517201 8.49944i −0.0578248 0.950266i
\(81\) −3.81561 2.77220i −0.423956 0.308022i
\(82\) −6.35854 + 2.06602i −0.702184 + 0.228153i
\(83\) −10.1161 + 3.28693i −1.11039 + 0.360787i −0.806092 0.591790i \(-0.798421\pi\)
−0.304297 + 0.952577i \(0.598421\pi\)
\(84\) 15.8397 + 11.5082i 1.72825 + 1.25565i
\(85\) 2.65260 0.161414i 0.287714 0.0175078i
\(86\) −6.83298 + 21.0297i −0.736819 + 2.26770i
\(87\) 12.1368i 1.30121i
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 19.1861 15.8058i 2.02239 1.66608i
\(91\) 1.68545 1.22455i 0.176683 0.128368i
\(92\) 5.36044 7.37801i 0.558864 0.769211i
\(93\) −21.8991 + 7.11545i −2.27083 + 0.737838i
\(94\) 1.82196 + 5.60741i 0.187921 + 0.578360i
\(95\) 3.93457 1.54846i 0.403679 0.158869i
\(96\) 19.0397 13.8331i 1.94323 1.41184i
\(97\) 14.3972 + 4.67793i 1.46181 + 0.474971i 0.928623 0.371025i \(-0.120994\pi\)
0.533189 + 0.845996i \(0.320994\pi\)
\(98\) 6.70015i 0.676817i
\(99\) 0 0
\(100\) 4.41416 + 9.48156i 0.441416 + 0.948156i
\(101\) −1.72375 + 5.30516i −0.171519 + 0.527883i −0.999457 0.0329370i \(-0.989514\pi\)
0.827938 + 0.560820i \(0.189514\pi\)
\(102\) 4.11873 + 5.66895i 0.407815 + 0.561310i
\(103\) 1.87043 2.57443i 0.184299 0.253666i −0.706864 0.707350i \(-0.749891\pi\)
0.891163 + 0.453684i \(0.149891\pi\)
\(104\) 0.0372046 + 0.114504i 0.00364821 + 0.0112280i
\(105\) 20.2615 + 5.24669i 1.97732 + 0.512024i
\(106\) −10.5035 7.63127i −1.02019 0.741214i
\(107\) −2.33296 3.21104i −0.225536 0.310423i 0.681221 0.732078i \(-0.261449\pi\)
−0.906756 + 0.421655i \(0.861449\pi\)
\(108\) 14.4719 + 4.70220i 1.39256 + 0.452470i
\(109\) 15.4150 1.47649 0.738243 0.674535i \(-0.235656\pi\)
0.738243 + 0.674535i \(0.235656\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 11.6303 + 3.77892i 1.09896 + 0.357074i
\(113\) −5.95741 8.19967i −0.560426 0.771360i 0.430955 0.902374i \(-0.358177\pi\)
−0.991381 + 0.131014i \(0.958177\pi\)
\(114\) 9.01977 + 6.55325i 0.844779 + 0.613768i
\(115\) 2.44387 9.43767i 0.227892 0.880067i
\(116\) −2.69150 8.28359i −0.249900 0.769112i
\(117\) 2.09570 2.88448i 0.193747 0.266670i
\(118\) 4.41865 + 6.08175i 0.406770 + 0.559870i
\(119\) −1.17937 + 3.62972i −0.108112 + 0.332736i
\(120\) −0.650203 + 1.01992i −0.0593552 + 0.0931052i
\(121\) 0 0
\(122\) 15.7515i 1.42607i
\(123\) −9.16232 2.97702i −0.826138 0.268429i
\(124\) 13.3686 9.71282i 1.20053 0.872237i
\(125\) 8.10277 + 7.70358i 0.724733 + 0.689029i
\(126\) 11.0318 + 33.9523i 0.982787 + 3.02471i
\(127\) 15.6382 5.08117i 1.38767 0.450881i 0.482486 0.875904i \(-0.339734\pi\)
0.905183 + 0.425023i \(0.139734\pi\)
\(128\) −0.871737 + 1.19984i −0.0770514 + 0.106052i
\(129\) −25.7770 + 18.7281i −2.26954 + 1.64892i
\(130\) 1.86580 + 2.26483i 0.163642 + 0.198639i
\(131\) −14.0007 −1.22325 −0.611625 0.791148i \(-0.709484\pi\)
−0.611625 + 0.791148i \(0.709484\pi\)
\(132\) 0 0
\(133\) 6.07239i 0.526543i
\(134\) −1.48765 + 4.57851i −0.128513 + 0.395523i
\(135\) 16.2365 0.988011i 1.39742 0.0850345i
\(136\) −0.178435 0.129641i −0.0153007 0.0111166i
\(137\) 13.0975 4.25564i 1.11900 0.363584i 0.309611 0.950863i \(-0.399801\pi\)
0.809384 + 0.587280i \(0.199801\pi\)
\(138\) 24.4476 7.94349i 2.08111 0.676195i
\(139\) −5.46468 3.97032i −0.463508 0.336758i 0.331398 0.943491i \(-0.392480\pi\)
−0.794906 + 0.606733i \(0.792480\pi\)
\(140\) −14.9923 + 0.912301i −1.26708 + 0.0771035i
\(141\) −2.62534 + 8.07998i −0.221094 + 0.680457i
\(142\) 31.7911i 2.66785i
\(143\) 0 0
\(144\) 20.9285 1.74404
\(145\) −5.92019 7.18631i −0.491645 0.596790i
\(146\) −9.35133 + 6.79414i −0.773922 + 0.562287i
\(147\) −5.67480 + 7.81069i −0.468050 + 0.644215i
\(148\) −4.09510 + 1.33058i −0.336615 + 0.109373i
\(149\) −5.93216 18.2573i −0.485982 1.49570i −0.830554 0.556938i \(-0.811976\pi\)
0.344572 0.938760i \(-0.388024\pi\)
\(150\) −5.64299 + 28.9348i −0.460748 + 2.36252i
\(151\) −2.66216 + 1.93418i −0.216644 + 0.157401i −0.690815 0.723032i \(-0.742748\pi\)
0.474171 + 0.880433i \(0.342748\pi\)
\(152\) −0.333751 0.108442i −0.0270708 0.00879582i
\(153\) 6.53159i 0.528048i
\(154\) 0 0
\(155\) 9.49579 14.8952i 0.762720 1.19641i
\(156\) −1.22229 + 3.76181i −0.0978612 + 0.301186i
\(157\) −8.23746 11.3379i −0.657421 0.904863i 0.341971 0.939710i \(-0.388905\pi\)
−0.999393 + 0.0348477i \(0.988905\pi\)
\(158\) −18.1391 + 24.9663i −1.44307 + 1.98621i
\(159\) −5.78107 17.7923i −0.458469 1.41102i
\(160\) −4.52590 + 17.4780i −0.357804 + 1.38176i
\(161\) 11.3268 + 8.22942i 0.892679 + 0.648570i
\(162\) 5.60762 + 7.71823i 0.440577 + 0.606402i
\(163\) −9.81676 3.18966i −0.768908 0.249833i −0.101811 0.994804i \(-0.532464\pi\)
−0.667097 + 0.744970i \(0.732464\pi\)
\(164\) 6.91362 0.539863
\(165\) 0 0
\(166\) 21.5160 1.66997
\(167\) 13.8909 + 4.51344i 1.07491 + 0.349260i 0.792399 0.610003i \(-0.208832\pi\)
0.282513 + 0.959263i \(0.408832\pi\)
\(168\) −1.02102 1.40531i −0.0787731 0.108422i
\(169\) −10.1767 7.39382i −0.782825 0.568755i
\(170\) −5.20397 1.34756i −0.399126 0.103353i
\(171\) 3.21140 + 9.88367i 0.245582 + 0.755823i
\(172\) 13.4400 18.4986i 1.02479 1.41051i
\(173\) 1.29806 + 1.78662i 0.0986895 + 0.135834i 0.855506 0.517793i \(-0.173246\pi\)
−0.756816 + 0.653628i \(0.773246\pi\)
\(174\) 7.58651 23.3489i 0.575132 1.77007i
\(175\) −14.5562 + 6.77669i −1.10035 + 0.512270i
\(176\) 0 0
\(177\) 10.8322i 0.814201i
\(178\) 17.3142 + 5.62573i 1.29776 + 0.421667i
\(179\) 8.74393 6.35284i 0.653552 0.474833i −0.210927 0.977502i \(-0.567648\pi\)
0.864479 + 0.502668i \(0.167648\pi\)
\(180\) −23.9197 + 9.41363i −1.78287 + 0.701651i
\(181\) −1.04045 3.20219i −0.0773363 0.238017i 0.904913 0.425596i \(-0.139936\pi\)
−0.982249 + 0.187580i \(0.939936\pi\)
\(182\) −4.00791 + 1.30225i −0.297086 + 0.0965291i
\(183\) −13.3410 + 18.3623i −0.986193 + 1.35738i
\(184\) −0.654583 + 0.475582i −0.0482565 + 0.0350604i
\(185\) −3.55264 + 2.92672i −0.261195 + 0.215177i
\(186\) 46.5773 3.41521
\(187\) 0 0
\(188\) 6.09692i 0.444664i
\(189\) −7.21889 + 22.2175i −0.525097 + 1.61608i
\(190\) −8.53726 + 0.519502i −0.619358 + 0.0376887i
\(191\) −7.50382 5.45185i −0.542957 0.394482i 0.282225 0.959348i \(-0.408928\pi\)
−0.825182 + 0.564867i \(0.808928\pi\)
\(192\) −24.1626 + 7.85089i −1.74378 + 0.566589i
\(193\) −4.62491 + 1.50273i −0.332908 + 0.108169i −0.470702 0.882293i \(-0.655999\pi\)
0.137793 + 0.990461i \(0.455999\pi\)
\(194\) −24.7732 17.9988i −1.77862 1.29224i
\(195\) 0.256823 + 4.22050i 0.0183914 + 0.302236i
\(196\) 2.14102 6.58939i 0.152930 0.470670i
\(197\) 11.8747i 0.846038i 0.906121 + 0.423019i \(0.139030\pi\)
−0.906121 + 0.423019i \(0.860970\pi\)
\(198\) 0 0
\(199\) 4.99158 0.353844 0.176922 0.984225i \(-0.443386\pi\)
0.176922 + 0.984225i \(0.443386\pi\)
\(200\) −0.112512 0.921060i −0.00795579 0.0651288i
\(201\) −5.61208 + 4.07741i −0.395845 + 0.287598i
\(202\) 6.63231 9.12859i 0.466648 0.642285i
\(203\) 12.7171 4.13203i 0.892565 0.290012i
\(204\) −2.23914 6.89137i −0.156771 0.482492i
\(205\) 6.87722 2.70655i 0.480326 0.189033i
\(206\) −5.20757 + 3.78352i −0.362828 + 0.263610i
\(207\) 22.7882 + 7.40433i 1.58389 + 0.514636i
\(208\) 2.47051i 0.171299i
\(209\) 0 0
\(210\) −35.6995 22.7587i −2.46350 1.57050i
\(211\) −0.486128 + 1.49615i −0.0334665 + 0.102999i −0.966394 0.257064i \(-0.917245\pi\)
0.932928 + 0.360063i \(0.117245\pi\)
\(212\) 7.89135 + 10.8615i 0.541980 + 0.745971i
\(213\) 26.9260 37.0605i 1.84494 2.53934i
\(214\) 2.48099 + 7.63570i 0.169597 + 0.521966i
\(215\) 6.12743 23.6627i 0.417888 1.61379i
\(216\) −1.09220 0.793530i −0.0743148 0.0539928i
\(217\) 14.9113 + 20.5236i 1.01224 + 1.39323i
\(218\) −29.6554 9.63561i −2.00852 0.652606i
\(219\) −16.6557 −1.12549
\(220\) 0 0
\(221\) −0.771025 −0.0518647
\(222\) −11.5428 3.75049i −0.774703 0.251716i
\(223\) −1.94836 2.68169i −0.130472 0.179579i 0.738783 0.673943i \(-0.235401\pi\)
−0.869255 + 0.494364i \(0.835401\pi\)
\(224\) −20.9766 15.2404i −1.40156 1.01829i
\(225\) −20.1085 + 18.7281i −1.34056 + 1.24854i
\(226\) 6.33542 + 19.4984i 0.421426 + 1.29702i
\(227\) 1.66938 2.29770i 0.110800 0.152504i −0.750015 0.661421i \(-0.769954\pi\)
0.860816 + 0.508917i \(0.169954\pi\)
\(228\) −6.77658 9.32717i −0.448790 0.617707i
\(229\) 0.615433 1.89411i 0.0406690 0.125166i −0.928661 0.370930i \(-0.879039\pi\)
0.969330 + 0.245764i \(0.0790389\pi\)
\(230\) −10.6008 + 16.6286i −0.698999 + 1.09646i
\(231\) 0 0
\(232\) 0.772748i 0.0507334i
\(233\) 19.2623 + 6.25868i 1.26191 + 0.410020i 0.862175 0.506610i \(-0.169102\pi\)
0.399737 + 0.916630i \(0.369102\pi\)
\(234\) −5.83474 + 4.23919i −0.381429 + 0.277125i
\(235\) −2.38682 6.06482i −0.155699 0.395625i
\(236\) −2.40219 7.39318i −0.156369 0.481255i
\(237\) −42.2913 + 13.7413i −2.74711 + 0.892591i
\(238\) 4.53774 6.24566i 0.294138 0.404846i
\(239\) 1.52982 1.11148i 0.0989556 0.0718954i −0.537207 0.843450i \(-0.680521\pi\)
0.636163 + 0.771555i \(0.280521\pi\)
\(240\) −19.1563 + 15.7813i −1.23653 + 1.01868i
\(241\) 4.00503 0.257986 0.128993 0.991645i \(-0.458825\pi\)
0.128993 + 0.991645i \(0.458825\pi\)
\(242\) 0 0
\(243\) 8.07686i 0.518131i
\(244\) 5.03336 15.4911i 0.322228 0.991715i
\(245\) −0.449864 7.39286i −0.0287408 0.472312i
\(246\) 15.7656 + 11.4544i 1.00518 + 0.730305i
\(247\) −1.16672 + 0.379091i −0.0742368 + 0.0241210i
\(248\) −1.39431 + 0.453038i −0.0885386 + 0.0287680i
\(249\) 25.0823 + 18.2234i 1.58953 + 1.15486i
\(250\) −10.7728 19.8851i −0.681329 1.25764i
\(251\) 7.01714 21.5965i 0.442918 1.36316i −0.441833 0.897097i \(-0.645672\pi\)
0.884751 0.466064i \(-0.154328\pi\)
\(252\) 36.9162i 2.32550i
\(253\) 0 0
\(254\) −33.2610 −2.08698
\(255\) −4.92519 5.97851i −0.308427 0.374389i
\(256\) −11.6763 + 8.48333i −0.729769 + 0.530208i
\(257\) 2.38815 3.28701i 0.148969 0.205038i −0.728011 0.685566i \(-0.759555\pi\)
0.876979 + 0.480528i \(0.159555\pi\)
\(258\) 61.2965 19.9164i 3.81616 1.23994i
\(259\) −2.04272 6.28686i −0.126929 0.390646i
\(260\) −1.11124 2.82361i −0.0689160 0.175113i
\(261\) 18.5136 13.4509i 1.14596 0.832592i
\(262\) 26.9347 + 8.75160i 1.66403 + 0.540676i
\(263\) 12.3054i 0.758783i −0.925236 0.379391i \(-0.876133\pi\)
0.925236 0.379391i \(-0.123867\pi\)
\(264\) 0 0
\(265\) 12.1019 + 7.71502i 0.743411 + 0.473930i
\(266\) 3.79574 11.6821i 0.232732 0.716274i
\(267\) 15.4192 + 21.2228i 0.943642 + 1.29881i
\(268\) 2.92611 4.02745i 0.178741 0.246016i
\(269\) 2.38188 + 7.33068i 0.145226 + 0.446959i 0.997040 0.0768848i \(-0.0244974\pi\)
−0.851814 + 0.523844i \(0.824497\pi\)
\(270\) −31.8534 8.24840i −1.93854 0.501982i
\(271\) −12.5995 9.15410i −0.765367 0.556072i 0.135185 0.990820i \(-0.456837\pi\)
−0.900552 + 0.434749i \(0.856837\pi\)
\(272\) −2.66020 3.66146i −0.161299 0.222008i
\(273\) −5.77518 1.87647i −0.349530 0.113569i
\(274\) −27.8571 −1.68291
\(275\) 0 0
\(276\) −26.5817 −1.60003
\(277\) −19.3093 6.27399i −1.16019 0.376967i −0.335215 0.942142i \(-0.608809\pi\)
−0.824971 + 0.565175i \(0.808809\pi\)
\(278\) 8.03120 + 11.0540i 0.481679 + 0.662974i
\(279\) 35.1242 + 25.5192i 2.10283 + 1.52779i
\(280\) 1.29004 + 0.334055i 0.0770947 + 0.0199636i
\(281\) 7.48425 + 23.0342i 0.446473 + 1.37410i 0.880860 + 0.473377i \(0.156965\pi\)
−0.434387 + 0.900726i \(0.643035\pi\)
\(282\) 10.1013 13.9032i 0.601523 0.827925i
\(283\) 8.48599 + 11.6800i 0.504440 + 0.694302i 0.982969 0.183770i \(-0.0588300\pi\)
−0.478529 + 0.878072i \(0.658830\pi\)
\(284\) −10.1588 + 31.2656i −0.602814 + 1.85527i
\(285\) −10.3923 6.62516i −0.615587 0.392441i
\(286\) 0 0
\(287\) 10.6139i 0.626519i
\(288\) −42.2023 13.7124i −2.48679 0.808008i
\(289\) −12.6106 + 9.16212i −0.741799 + 0.538948i
\(290\) 6.89725 + 17.5256i 0.405021 + 1.02914i
\(291\) −13.6350 41.9642i −0.799298 2.45999i
\(292\) 11.3678 3.69362i 0.665250 0.216153i
\(293\) −8.91231 + 12.2667i −0.520663 + 0.716631i −0.985672 0.168675i \(-0.946051\pi\)
0.465009 + 0.885306i \(0.346051\pi\)
\(294\) 15.7995 11.4790i 0.921447 0.669470i
\(295\) −5.28383 6.41385i −0.307636 0.373429i
\(296\) 0.382018 0.0222043
\(297\) 0 0
\(298\) 38.8316i 2.24945i
\(299\) −0.874048 + 2.69004i −0.0505475 + 0.155569i
\(300\) 14.7958 26.6533i 0.854234 1.53883i
\(301\) 28.3994 + 20.6334i 1.63691 + 1.18929i
\(302\) 6.33050 2.05690i 0.364279 0.118361i
\(303\) 15.4632 5.02431i 0.888339 0.288639i
\(304\) −5.82568 4.23261i −0.334126 0.242757i
\(305\) −1.05759 17.3800i −0.0605576 0.995175i
\(306\) 4.08278 12.5655i 0.233397 0.718321i
\(307\) 8.04171i 0.458965i 0.973313 + 0.229482i \(0.0737033\pi\)
−0.973313 + 0.229482i \(0.926297\pi\)
\(308\) 0 0
\(309\) −9.27523 −0.527650
\(310\) −27.5787 + 22.7198i −1.56637 + 1.29040i
\(311\) −18.0142 + 13.0881i −1.02149 + 0.742158i −0.966588 0.256333i \(-0.917486\pi\)
−0.0549049 + 0.998492i \(0.517486\pi\)
\(312\) 0.206269 0.283905i 0.0116777 0.0160730i
\(313\) −2.23540 + 0.726326i −0.126352 + 0.0410543i −0.371511 0.928429i \(-0.621160\pi\)
0.245158 + 0.969483i \(0.421160\pi\)
\(314\) 8.76015 + 26.9610i 0.494364 + 1.52150i
\(315\) −14.4519 36.7218i −0.814275 2.06904i
\(316\) 25.8172 18.7573i 1.45233 1.05518i
\(317\) −17.1412 5.56952i −0.962747 0.312815i −0.214863 0.976644i \(-0.568930\pi\)
−0.747885 + 0.663829i \(0.768930\pi\)
\(318\) 37.8425i 2.12210i
\(319\) 0 0
\(320\) 10.4773 16.4347i 0.585696 0.918730i
\(321\) −3.57497 + 11.0026i −0.199535 + 0.614107i
\(322\) −16.6465 22.9120i −0.927675 1.27683i
\(323\) 1.32096 1.81814i 0.0735001 0.101164i
\(324\) −3.04858 9.38255i −0.169365 0.521253i
\(325\) −2.21077 2.37371i −0.122632 0.131670i
\(326\) 16.8917 + 12.2726i 0.935546 + 0.679714i
\(327\) −26.4097 36.3498i −1.46046 2.01015i
\(328\) −0.583361 0.189546i −0.0322107 0.0104659i
\(329\) 9.36008 0.516038
\(330\) 0 0
\(331\) −3.09174 −0.169938 −0.0849688 0.996384i \(-0.527079\pi\)
−0.0849688 + 0.996384i \(0.527079\pi\)
\(332\) −21.1603 6.87541i −1.16132 0.377337i
\(333\) −6.64964 9.15245i −0.364398 0.501551i
\(334\) −23.9021 17.3659i −1.30787 0.950221i
\(335\) 1.33404 5.15176i 0.0728865 0.281471i
\(336\) −11.0146 33.8995i −0.600897 1.84937i
\(337\) 21.1284 29.0807i 1.15094 1.58413i 0.410719 0.911762i \(-0.365278\pi\)
0.740218 0.672367i \(-0.234722\pi\)
\(338\) 14.9563 + 20.5855i 0.813514 + 1.11971i
\(339\) −9.12900 + 28.0962i −0.495819 + 1.52597i
\(340\) 4.68733 + 2.98820i 0.254206 + 0.162058i
\(341\) 0 0
\(342\) 21.0216i 1.13672i
\(343\) −11.2626 3.65945i −0.608124 0.197592i
\(344\) −1.64121 + 1.19241i −0.0884883 + 0.0642905i
\(345\) −26.4418 + 10.4062i −1.42358 + 0.560252i
\(346\) −1.38042 4.24850i −0.0742119 0.228401i
\(347\) −11.6627 + 3.78944i −0.626087 + 0.203428i −0.604841 0.796346i \(-0.706763\pi\)
−0.0212460 + 0.999774i \(0.506763\pi\)
\(348\) −14.9222 + 20.5386i −0.799914 + 1.10099i
\(349\) 14.2981 10.3881i 0.765357 0.556065i −0.135192 0.990819i \(-0.543165\pi\)
0.900549 + 0.434755i \(0.143165\pi\)
\(350\) 32.2393 3.93819i 1.72326 0.210505i
\(351\) −4.71943 −0.251905
\(352\) 0 0
\(353\) 18.7202i 0.996378i −0.867068 0.498189i \(-0.833999\pi\)
0.867068 0.498189i \(-0.166001\pi\)
\(354\) 6.77104 20.8391i 0.359876 1.10759i
\(355\) 2.13454 + 35.0779i 0.113289 + 1.86174i
\(356\) −15.2303 11.0655i −0.807205 0.586469i
\(357\) 10.5797 3.43756i 0.559939 0.181935i
\(358\) −20.7926 + 6.75594i −1.09893 + 0.357062i
\(359\) 30.1495 + 21.9049i 1.59123 + 1.15610i 0.902159 + 0.431403i \(0.141981\pi\)
0.689071 + 0.724694i \(0.258019\pi\)
\(360\) 2.27639 0.138521i 0.119976 0.00730071i
\(361\) −4.76637 + 14.6694i −0.250861 + 0.772072i
\(362\) 6.81074i 0.357965i
\(363\) 0 0
\(364\) 4.35779 0.228410
\(365\) 9.86197 8.12444i 0.516199 0.425253i
\(366\) 37.1433 26.9862i 1.94151 1.41059i
\(367\) −10.5794 + 14.5613i −0.552242 + 0.760096i −0.990314 0.138844i \(-0.955661\pi\)
0.438072 + 0.898940i \(0.355661\pi\)
\(368\) −15.7902 + 5.13054i −0.823120 + 0.267448i
\(369\) 5.61319 + 17.2756i 0.292211 + 0.899333i
\(370\) 8.66402 3.40974i 0.450421 0.177264i
\(371\) −16.6748 + 12.1149i −0.865710 + 0.628975i
\(372\) −45.8073 14.8837i −2.37500 0.771684i
\(373\) 0.202607i 0.0104906i −0.999986 0.00524531i \(-0.998330\pi\)
0.999986 0.00524531i \(-0.00166964\pi\)
\(374\) 0 0
\(375\) 4.28365 32.3052i 0.221207 1.66823i
\(376\) −0.167155 + 0.514449i −0.00862034 + 0.0265307i
\(377\) 1.58782 + 2.18545i 0.0817770 + 0.112556i
\(378\) 27.7754 38.2296i 1.42861 1.96632i
\(379\) 10.5014 + 32.3199i 0.539419 + 1.66016i 0.733901 + 0.679256i \(0.237697\pi\)
−0.194482 + 0.980906i \(0.562303\pi\)
\(380\) 8.56213 + 2.21715i 0.439228 + 0.113738i
\(381\) −38.7740 28.1710i −1.98645 1.44324i
\(382\) 11.0280 + 15.1788i 0.564243 + 0.776614i
\(383\) −6.79248 2.20701i −0.347080 0.112773i 0.130289 0.991476i \(-0.458409\pi\)
−0.477369 + 0.878703i \(0.658409\pi\)
\(384\) 4.32284 0.220599
\(385\) 0 0
\(386\) 9.83675 0.500677
\(387\) 57.1360 + 18.5646i 2.90439 + 0.943692i
\(388\) 18.6122 + 25.6175i 0.944893 + 1.30053i
\(389\) 10.7331 + 7.79804i 0.544189 + 0.395376i 0.825638 0.564200i \(-0.190815\pi\)
−0.281450 + 0.959576i \(0.590815\pi\)
\(390\) 2.14408 8.27995i 0.108570 0.419271i
\(391\) −1.60119 4.92797i −0.0809759 0.249218i
\(392\) −0.361312 + 0.497304i −0.0182490 + 0.0251176i
\(393\) 23.9867 + 33.0149i 1.20997 + 1.66538i
\(394\) 7.42266 22.8446i 0.373948 1.15089i
\(395\) 18.3382 28.7654i 0.922692 1.44735i
\(396\) 0 0
\(397\) 33.5614i 1.68440i −0.539165 0.842200i \(-0.681260\pi\)
0.539165 0.842200i \(-0.318740\pi\)
\(398\) −9.60282 3.12015i −0.481346 0.156399i
\(399\) 14.3192 10.4035i 0.716857 0.520827i
\(400\) 3.64469 18.6884i 0.182235 0.934419i
\(401\) 10.3802 + 31.9469i 0.518361 + 1.59535i 0.777082 + 0.629399i \(0.216699\pi\)
−0.258721 + 0.965952i \(0.583301\pi\)
\(402\) 13.3452 4.33613i 0.665600 0.216267i
\(403\) −3.01243 + 4.14625i −0.150060 + 0.206539i
\(404\) −9.43970 + 6.85834i −0.469642 + 0.341215i
\(405\) −6.70561 8.13969i −0.333204 0.404465i
\(406\) −27.0480 −1.34237
\(407\) 0 0
\(408\) 0.642872i 0.0318269i
\(409\) −2.52435 + 7.76914i −0.124821 + 0.384159i −0.993868 0.110569i \(-0.964733\pi\)
0.869048 + 0.494729i \(0.164733\pi\)
\(410\) −14.9222 + 0.908036i −0.736957 + 0.0448447i
\(411\) −32.4745 23.5941i −1.60185 1.16381i
\(412\) 6.33050 2.05690i 0.311881 0.101336i
\(413\) 11.3501 3.68788i 0.558503 0.181469i
\(414\) −39.2117 28.4889i −1.92715 1.40015i
\(415\) −23.7405 + 1.44464i −1.16538 + 0.0709146i
\(416\) 1.61868 4.98179i 0.0793624 0.244252i
\(417\) 19.6883i 0.964142i
\(418\) 0 0
\(419\) −19.5329 −0.954243 −0.477121 0.878837i \(-0.658320\pi\)
−0.477121 + 0.878837i \(0.658320\pi\)
\(420\) 27.8369 + 33.7902i 1.35830 + 1.64879i
\(421\) 19.3422 14.0529i 0.942680 0.684897i −0.00638396 0.999980i \(-0.502032\pi\)
0.949064 + 0.315082i \(0.102032\pi\)
\(422\) 1.87043 2.57443i 0.0910511 0.125321i
\(423\) 15.2349 4.95011i 0.740744 0.240682i
\(424\) −0.368078 1.13283i −0.0178755 0.0550150i
\(425\) 5.83247 + 1.13747i 0.282917 + 0.0551756i
\(426\) −74.9662 + 54.4661i −3.63212 + 2.63889i
\(427\) 23.7821 + 7.72729i 1.15090 + 0.373950i
\(428\) 8.30227i 0.401306i
\(429\) 0 0
\(430\) −26.5791 + 41.6923i −1.28176 + 2.01058i
\(431\) −2.33735 + 7.19363i −0.112586 + 0.346505i −0.991436 0.130594i \(-0.958312\pi\)
0.878850 + 0.477099i \(0.158312\pi\)
\(432\) −16.2831 22.4117i −0.783420 1.07829i
\(433\) −15.0587 + 20.7265i −0.723675 + 0.996054i 0.275718 + 0.961238i \(0.411084\pi\)
−0.999394 + 0.0348152i \(0.988916\pi\)
\(434\) −15.8574 48.8041i −0.761181 2.34267i
\(435\) −6.80316 + 26.2722i −0.326187 + 1.25966i
\(436\) 26.0861 + 18.9527i 1.24930 + 0.907668i
\(437\) −4.84589 6.66979i −0.231810 0.319059i
\(438\) 32.0423 + 10.4112i 1.53104 + 0.497466i
\(439\) 20.4668 0.976827 0.488413 0.872612i \(-0.337576\pi\)
0.488413 + 0.872612i \(0.337576\pi\)
\(440\) 0 0
\(441\) 18.2037 0.866844
\(442\) 1.48330 + 0.481953i 0.0705534 + 0.0229242i
\(443\) 5.97474 + 8.22353i 0.283869 + 0.390712i 0.927010 0.375035i \(-0.122369\pi\)
−0.643142 + 0.765747i \(0.722369\pi\)
\(444\) 10.1535 + 7.37698i 0.481866 + 0.350096i
\(445\) −19.4820 5.04485i −0.923537 0.239149i
\(446\) 2.07199 + 6.37692i 0.0981114 + 0.301956i
\(447\) −32.8891 + 45.2679i −1.55560 + 2.14110i
\(448\) 16.4525 + 22.6449i 0.777306 + 1.06987i
\(449\) 4.54240 13.9801i 0.214369 0.659760i −0.784829 0.619713i \(-0.787249\pi\)
0.999198 0.0400475i \(-0.0127509\pi\)
\(450\) 50.3913 23.4598i 2.37547 1.10591i
\(451\) 0 0
\(452\) 21.2006i 0.997190i
\(453\) 9.12191 + 2.96389i 0.428584 + 0.139256i
\(454\) −4.64780 + 3.37683i −0.218132 + 0.158482i
\(455\) 4.33484 1.70599i 0.203221 0.0799779i
\(456\) 0.316082 + 0.972801i 0.0148019 + 0.0455556i
\(457\) −3.19822 + 1.03916i −0.149606 + 0.0486101i −0.382863 0.923805i \(-0.625062\pi\)
0.233256 + 0.972415i \(0.425062\pi\)
\(458\) −2.36794 + 3.25919i −0.110647 + 0.152292i
\(459\) 6.99450 5.08180i 0.326475 0.237198i
\(460\) 15.7392 12.9662i 0.733846 0.604553i
\(461\) −1.41424 −0.0658677 −0.0329338 0.999458i \(-0.510485\pi\)
−0.0329338 + 0.999458i \(0.510485\pi\)
\(462\) 0 0
\(463\) 15.4595i 0.718465i 0.933248 + 0.359232i \(0.116961\pi\)
−0.933248 + 0.359232i \(0.883039\pi\)
\(464\) −4.89997 + 15.0806i −0.227475 + 0.700098i
\(465\) −51.3928 + 3.12732i −2.38329 + 0.145026i
\(466\) −33.1446 24.0810i −1.53539 1.11553i
\(467\) −17.7760 + 5.77576i −0.822574 + 0.267270i −0.689914 0.723891i \(-0.742352\pi\)
−0.132660 + 0.991162i \(0.542352\pi\)
\(468\) 7.09292 2.30463i 0.327870 0.106531i
\(469\) 6.18300 + 4.49221i 0.285505 + 0.207431i
\(470\) 0.800770 + 13.1595i 0.0369368 + 0.607001i
\(471\) −12.6229 + 38.8493i −0.581633 + 1.79008i
\(472\) 0.689685i 0.0317453i
\(473\) 0 0
\(474\) 89.9495 4.13152
\(475\) 9.38502 1.14643i 0.430614 0.0526016i
\(476\) −6.45852 + 4.69239i −0.296026 + 0.215075i
\(477\) −20.7335 + 28.5372i −0.949322 + 1.30663i
\(478\) −3.63783 + 1.18200i −0.166390 + 0.0540635i
\(479\) 9.23235 + 28.4142i 0.421837 + 1.29828i 0.905991 + 0.423297i \(0.139127\pi\)
−0.484154 + 0.874983i \(0.660873\pi\)
\(480\) 48.9686 19.2717i 2.23510 0.879628i
\(481\) 1.08041 0.784960i 0.0492622 0.0357911i
\(482\) −7.70488 2.50347i −0.350948 0.114030i
\(483\) 40.8087i 1.85686i
\(484\) 0 0
\(485\) 28.5430 + 18.1963i 1.29607 + 0.826253i
\(486\) −5.04869 + 15.5383i −0.229013 + 0.704831i
\(487\) −0.549473 0.756284i −0.0248990 0.0342705i 0.796386 0.604789i \(-0.206742\pi\)
−0.821285 + 0.570518i \(0.806742\pi\)
\(488\) −0.849414 + 1.16912i −0.0384512 + 0.0529235i
\(489\) 9.29707 + 28.6134i 0.420428 + 1.29394i
\(490\) −3.75569 + 14.5036i −0.169665 + 0.655206i
\(491\) 26.6121 + 19.3348i 1.20099 + 0.872569i 0.994382 0.105855i \(-0.0337580\pi\)
0.206607 + 0.978424i \(0.433758\pi\)
\(492\) −11.8448 16.3029i −0.534003 0.734992i
\(493\) −4.70651 1.52924i −0.211970 0.0688733i
\(494\) 2.48151 0.111648
\(495\) 0 0
\(496\) −30.0833 −1.35078
\(497\) −47.9994 15.5960i −2.15307 0.699574i
\(498\) −36.8623 50.7366i −1.65184 2.27356i
\(499\) 7.27434 + 5.28512i 0.325644 + 0.236594i 0.738580 0.674166i \(-0.235497\pi\)
−0.412936 + 0.910760i \(0.635497\pi\)
\(500\) 4.24043 + 22.9988i 0.189638 + 1.02854i
\(501\) −13.1556 40.4886i −0.587747 1.80890i
\(502\) −26.9992 + 37.1612i −1.20503 + 1.65858i
\(503\) −0.717663 0.987779i −0.0319990 0.0440429i 0.792718 0.609589i \(-0.208665\pi\)
−0.824717 + 0.565546i \(0.808665\pi\)
\(504\) −1.01210 + 3.11493i −0.0450826 + 0.138750i
\(505\) −6.70509 + 10.5177i −0.298373 + 0.468031i
\(506\) 0 0
\(507\) 36.6650i 1.62835i
\(508\) 32.7112 + 10.6285i 1.45132 + 0.471564i
\(509\) 19.5744 14.2216i 0.867621 0.630363i −0.0623268 0.998056i \(-0.519852\pi\)
0.929947 + 0.367692i \(0.119852\pi\)
\(510\) 5.73803 + 14.5801i 0.254084 + 0.645618i
\(511\) 5.67051 + 17.4520i 0.250848 + 0.772032i
\(512\) 30.5867 9.93821i 1.35175 0.439211i
\(513\) 8.08557 11.1288i 0.356987 0.491350i
\(514\) −6.64897 + 4.83076i −0.293274 + 0.213076i
\(515\) 5.49193 4.52434i 0.242003 0.199366i
\(516\) −66.6475 −2.93399
\(517\) 0 0
\(518\) 13.3715i 0.587512i
\(519\) 1.98911 6.12186i 0.0873124 0.268720i
\(520\) 0.0163518 + 0.268718i 0.000717074 + 0.0117841i
\(521\) 3.92663 + 2.85286i 0.172029 + 0.124986i 0.670468 0.741938i \(-0.266093\pi\)
−0.498439 + 0.866925i \(0.666093\pi\)
\(522\) −44.0245 + 14.3044i −1.92690 + 0.626088i
\(523\) −6.97451 + 2.26616i −0.304974 + 0.0990921i −0.457506 0.889206i \(-0.651257\pi\)
0.152532 + 0.988299i \(0.451257\pi\)
\(524\) −23.6928 17.2139i −1.03503 0.751991i
\(525\) 40.9185 + 22.7147i 1.78583 + 0.991350i
\(526\) −7.69187 + 23.6731i −0.335382 + 1.03220i
\(527\) 9.38873i 0.408980i
\(528\) 0 0
\(529\) 3.99158 0.173547
\(530\) −18.4591 22.4068i −0.801811 0.973290i
\(531\) 16.5236 12.0051i 0.717063 0.520977i
\(532\) −7.46598 + 10.2760i −0.323691 + 0.445523i
\(533\) −2.03931 + 0.662612i −0.0883323 + 0.0287009i
\(534\) −16.3976 50.4667i −0.709595 2.18391i
\(535\) −3.25017 8.25856i −0.140517 0.357049i
\(536\) −0.357319 + 0.259607i −0.0154338 + 0.0112133i
\(537\) −29.9611 9.73494i −1.29292 0.420094i
\(538\) 15.5917i 0.672204i
\(539\) 0 0
\(540\) 28.6911 + 18.2908i 1.23467 + 0.787109i
\(541\) 8.67728 26.7059i 0.373065 1.14818i −0.571710 0.820456i \(-0.693720\pi\)
0.944775 0.327720i \(-0.106280\pi\)
\(542\) 18.5170 + 25.4864i 0.795372 + 1.09474i
\(543\) −5.76847 + 7.93962i −0.247549 + 0.340722i
\(544\) 2.96531 + 9.12629i 0.127137 + 0.391287i
\(545\) 33.3683 + 8.64068i 1.42934 + 0.370126i
\(546\) 9.93737 + 7.21992i 0.425280 + 0.308984i
\(547\) 13.7323 + 18.9009i 0.587151 + 0.808144i 0.994457 0.105148i \(-0.0335316\pi\)
−0.407306 + 0.913292i \(0.633532\pi\)
\(548\) 27.3966 + 8.90171i 1.17033 + 0.380262i
\(549\) 42.7954 1.82646
\(550\) 0 0
\(551\) −7.87382 −0.335436
\(552\) 2.24293 + 0.728772i 0.0954654 + 0.0310186i
\(553\) 28.7965 + 39.6349i 1.22455 + 1.68545i
\(554\) 33.2256 + 24.1398i 1.41162 + 1.02560i
\(555\) 12.9880 + 3.36323i 0.551311 + 0.142761i
\(556\) −4.36615 13.4376i −0.185166 0.569882i
\(557\) −0.0200153 + 0.0275487i −0.000848077 + 0.00116728i −0.809441 0.587201i \(-0.800230\pi\)
0.808593 + 0.588369i \(0.200230\pi\)
\(558\) −51.6204 71.0494i −2.18527 3.00776i
\(559\) −2.19147 + 6.74465i −0.0926893 + 0.285268i
\(560\) 23.0576 + 14.6994i 0.974361 + 0.621161i
\(561\) 0 0
\(562\) 48.9915i 2.06658i
\(563\) 22.4995 + 7.31054i 0.948242 + 0.308103i 0.742001 0.670399i \(-0.233877\pi\)
0.206241 + 0.978501i \(0.433877\pi\)
\(564\) −14.3771 + 10.4455i −0.605383 + 0.439837i
\(565\) −8.29960 21.0889i −0.349167 0.887218i
\(566\) −9.02445 27.7744i −0.379326 1.16744i
\(567\) 14.4042 4.68022i 0.604921 0.196551i
\(568\) 1.71437 2.35963i 0.0719334 0.0990078i
\(569\) 24.8653 18.0657i 1.04241 0.757355i 0.0716547 0.997429i \(-0.477172\pi\)
0.970754 + 0.240075i \(0.0771720\pi\)
\(570\) 15.8515 + 19.2415i 0.663945 + 0.805940i
\(571\) −28.4768 −1.19172 −0.595860 0.803089i \(-0.703188\pi\)
−0.595860 + 0.803089i \(0.703188\pi\)
\(572\) 0 0
\(573\) 27.0350i 1.12940i
\(574\) 6.63455 20.4191i 0.276921 0.852275i
\(575\) 10.5803 19.0596i 0.441231 0.794838i
\(576\) 38.7545 + 28.1568i 1.61477 + 1.17320i
\(577\) 36.7234 11.9321i 1.52881 0.496742i 0.580550 0.814225i \(-0.302838\pi\)
0.948264 + 0.317483i \(0.102838\pi\)
\(578\) 29.9873 9.74348i 1.24731 0.405275i
\(579\) 11.4672 + 8.33140i 0.476560 + 0.346241i
\(580\) −1.18294 19.4399i −0.0491190 0.807199i
\(581\) 10.5552 32.4857i 0.437905 1.34773i
\(582\) 89.2539i 3.69969i
\(583\) 0 0
\(584\) −1.06046 −0.0438823
\(585\) 6.15336 5.06923i 0.254410 0.209587i
\(586\) 24.8132 18.0279i 1.02503 0.744725i
\(587\) 8.39465 11.5542i 0.346484 0.476894i −0.599837 0.800122i \(-0.704768\pi\)
0.946321 + 0.323228i \(0.104768\pi\)
\(588\) −19.2064 + 6.24055i −0.792060 + 0.257356i
\(589\) −4.61617 14.2071i −0.190206 0.585394i
\(590\) 6.15586 + 15.6418i 0.253433 + 0.643963i
\(591\) 28.0016 20.3443i 1.15183 0.836854i
\(592\) 7.45527 + 2.42236i 0.306410 + 0.0995585i
\(593\) 36.4700i 1.49764i 0.662771 + 0.748822i \(0.269380\pi\)
−0.662771 + 0.748822i \(0.730620\pi\)
\(594\) 0 0
\(595\) −4.58754 + 7.19606i −0.188071 + 0.295010i
\(596\) 12.4086 38.1897i 0.508275 1.56431i
\(597\) −8.55183 11.7706i −0.350003 0.481738i
\(598\) 3.36299 4.62876i 0.137523 0.189284i
\(599\) −9.37587 28.8560i −0.383088 1.17902i −0.937858 0.347019i \(-0.887194\pi\)
0.554770 0.832004i \(-0.312806\pi\)
\(600\) −1.97918 + 1.84332i −0.0807996 + 0.0752531i
\(601\) −30.5989 22.2314i −1.24816 0.906839i −0.250043 0.968235i \(-0.580445\pi\)
−0.998113 + 0.0613962i \(0.980445\pi\)
\(602\) −41.7373 57.4464i −1.70108 2.34134i
\(603\) 12.4394 + 4.04182i 0.506573 + 0.164595i
\(604\) −6.88313 −0.280071
\(605\) 0 0
\(606\) −32.8888 −1.33602
\(607\) 29.5616 + 9.60513i 1.19987 + 0.389860i 0.839712 0.543032i \(-0.182724\pi\)
0.360155 + 0.932893i \(0.382724\pi\)
\(608\) 8.97428 + 12.3520i 0.363955 + 0.500941i
\(609\) −31.5312 22.9088i −1.27771 0.928311i
\(610\) −8.82930 + 34.0967i −0.357488 + 1.38054i
\(611\) 0.584338 + 1.79841i 0.0236398 + 0.0727558i
\(612\) −8.03057 + 11.0531i −0.324616 + 0.446796i
\(613\) −21.3175 29.3410i −0.861004 1.18507i −0.981329 0.192336i \(-0.938394\pi\)
0.120325 0.992735i \(-0.461606\pi\)
\(614\) 5.02672 15.4707i 0.202862 0.624345i
\(615\) −18.1647 11.5801i −0.732470 0.466954i
\(616\) 0 0
\(617\) 1.28079i 0.0515626i −0.999668 0.0257813i \(-0.991793\pi\)
0.999668 0.0257813i \(-0.00820735\pi\)
\(618\) 17.8437 + 5.79778i 0.717780 + 0.233221i
\(619\) 6.66694 4.84382i 0.267967 0.194689i −0.445685 0.895190i \(-0.647040\pi\)
0.713652 + 0.700500i \(0.247040\pi\)
\(620\) 34.3829 13.5315i 1.38085 0.543437i
\(621\) −9.80089 30.1640i −0.393296 1.21044i
\(622\) 42.8370 13.9186i 1.71761 0.558084i
\(623\) 16.9879 23.3818i 0.680605 0.936772i
\(624\) 5.82568 4.23261i 0.233214 0.169440i
\(625\) 13.2217 + 21.2176i 0.528866 + 0.848705i
\(626\) 4.75448 0.190027
\(627\) 0 0
\(628\) 29.3146i 1.16978i
\(629\) −0.755998 + 2.32672i −0.0301436 + 0.0927725i
\(630\) 4.84857 + 79.6792i 0.193172 + 3.17449i
\(631\) 10.0378 + 7.29291i 0.399600 + 0.290326i 0.769378 0.638794i \(-0.220566\pi\)
−0.369778 + 0.929120i \(0.620566\pi\)
\(632\) −2.69267 + 0.874901i −0.107109 + 0.0348017i
\(633\) 4.36091 1.41694i 0.173331 0.0563185i
\(634\) 29.4949 + 21.4293i 1.17139 + 0.851067i
\(635\) 36.6998 2.23323i 1.45639 0.0886229i
\(636\) 12.0925 37.2169i 0.479500 1.47575i
\(637\) 2.14887i 0.0851412i
\(638\) 0 0
\(639\) −86.3738 −3.41689
\(640\) −2.55958 + 2.10862i −0.101176 + 0.0833507i
\(641\) 4.39239 3.19126i 0.173489 0.126047i −0.497652 0.867377i \(-0.665804\pi\)
0.671141 + 0.741329i \(0.265804\pi\)
\(642\) 13.7551 18.9322i 0.542870 0.747196i
\(643\) −1.98579 + 0.645222i −0.0783119 + 0.0254451i −0.347911 0.937528i \(-0.613109\pi\)
0.269599 + 0.962973i \(0.413109\pi\)
\(644\) 9.04986 + 27.8526i 0.356614 + 1.09755i
\(645\) −66.2966 + 26.0912i −2.61043 + 1.02734i
\(646\) −3.67775 + 2.67204i −0.144699 + 0.105130i
\(647\) −23.5511 7.65223i −0.925891 0.300840i −0.193010 0.981197i \(-0.561825\pi\)
−0.732881 + 0.680357i \(0.761825\pi\)
\(648\) 0.875266i 0.0343837i
\(649\) 0 0
\(650\) 2.76932 + 5.94847i 0.108622 + 0.233318i
\(651\) 22.8497 70.3241i 0.895550 2.75622i
\(652\) −12.6908 17.4674i −0.497010 0.684076i
\(653\) −4.05522 + 5.58154i −0.158693 + 0.218422i −0.880958 0.473194i \(-0.843101\pi\)
0.722265 + 0.691616i \(0.243101\pi\)
\(654\) 28.0854 + 86.4381i 1.09823 + 3.38000i
\(655\) −30.3070 7.84795i −1.18419 0.306645i
\(656\) −10.1827 7.39816i −0.397567 0.288849i
\(657\) 18.4591 + 25.4068i 0.720158 + 0.991213i
\(658\) −18.0070 5.85081i −0.701984 0.228089i
\(659\) 12.4567 0.485246 0.242623 0.970121i \(-0.421992\pi\)
0.242623 + 0.970121i \(0.421992\pi\)
\(660\) 0 0
\(661\) 17.8173 0.693012 0.346506 0.938048i \(-0.387368\pi\)
0.346506 + 0.938048i \(0.387368\pi\)
\(662\) 5.94791 + 1.93259i 0.231172 + 0.0751123i
\(663\) 1.32096 + 1.81814i 0.0513018 + 0.0706108i
\(664\) 1.59698 + 1.16027i 0.0619749 + 0.0450274i
\(665\) −3.40381 + 13.1447i −0.131994 + 0.509730i
\(666\) 7.07158 + 21.7641i 0.274018 + 0.843341i
\(667\) −10.6708 + 14.6870i −0.413173 + 0.568684i
\(668\) 17.9578 + 24.7167i 0.694807 + 0.956320i
\(669\) −2.98562 + 9.18880i −0.115431 + 0.355259i
\(670\) −5.78670 + 9.07709i −0.223560 + 0.350679i
\(671\) 0 0
\(672\) 75.5752i 2.91538i
\(673\) −27.6539 8.98531i −1.06598 0.346358i −0.277060 0.960853i \(-0.589360\pi\)
−0.788921 + 0.614494i \(0.789360\pi\)
\(674\) −58.8247 + 42.7386i −2.26584 + 1.64623i
\(675\) 35.7005 + 6.96247i 1.37411 + 0.267985i
\(676\) −8.13095 25.0245i −0.312729 0.962480i
\(677\) −38.8680 + 12.6290i −1.49382 + 0.485371i −0.938208 0.346072i \(-0.887515\pi\)
−0.555610 + 0.831443i \(0.687515\pi\)
\(678\) 35.1248 48.3451i 1.34896 1.85668i
\(679\) −39.3284 + 28.5738i −1.50929 + 1.09656i
\(680\) −0.313585 0.380649i −0.0120254 0.0145972i
\(681\) −8.27824 −0.317223
\(682\) 0 0
\(683\) 17.2211i 0.658948i 0.944165 + 0.329474i \(0.106871\pi\)
−0.944165 + 0.329474i \(0.893129\pi\)
\(684\) −6.71743 + 20.6741i −0.256847 + 0.790494i
\(685\) 30.7372 1.87040i 1.17441 0.0714642i
\(686\) 19.3796 + 14.0801i 0.739917 + 0.537581i
\(687\) −5.52086 + 1.79384i −0.210634 + 0.0684391i
\(688\) −39.5902 + 12.8636i −1.50936 + 0.490421i
\(689\) −3.36869 2.44750i −0.128337 0.0932422i
\(690\) 57.3735 3.49125i 2.18417 0.132910i
\(691\) 6.22380 19.1549i 0.236764 0.728686i −0.760118 0.649785i \(-0.774859\pi\)
0.996882 0.0789009i \(-0.0251411\pi\)
\(692\) 4.61938i 0.175603i
\(693\) 0 0
\(694\) 24.8055 0.941603
\(695\) −9.60372 11.6576i −0.364290 0.442198i
\(696\) 1.82221 1.32391i 0.0690705 0.0501827i
\(697\) 2.30890 3.17792i 0.0874557 0.120372i
\(698\) −34.0001 + 11.0473i −1.28692 + 0.418146i
\(699\) −18.2425 56.1447i −0.689996 2.12359i
\(700\) −32.9648 6.42894i −1.24595 0.242991i
\(701\) −17.1242 + 12.4414i −0.646771 + 0.469906i −0.862170 0.506620i \(-0.830895\pi\)
0.215399 + 0.976526i \(0.430895\pi\)
\(702\) 9.07926 + 2.95003i 0.342675 + 0.111342i
\(703\) 3.89252i 0.146809i
\(704\) 0 0
\(705\) −10.2121 + 16.0189i −0.384611 + 0.603306i
\(706\) −11.7017 + 36.0141i −0.440398 + 1.35541i
\(707\) −10.5290 14.4920i −0.395985 0.545026i
\(708\) −13.3182 + 18.3309i −0.500529 + 0.688919i
\(709\) −6.35410 19.5559i −0.238633 0.734437i −0.996619 0.0821658i \(-0.973816\pi\)
0.757986 0.652271i \(-0.226184\pi\)
\(710\) 17.8201 68.8173i 0.668778 2.58267i
\(711\) 67.8313 + 49.2824i 2.54387 + 1.84823i
\(712\) 0.981738 + 1.35125i 0.0367922 + 0.0506401i
\(713\) −32.7565 10.6432i −1.22674 0.398592i
\(714\) −22.5021 −0.842119
\(715\) 0 0
\(716\) 22.6078 0.844892
\(717\) −5.24191 1.70320i −0.195763 0.0636072i
\(718\) −44.3094 60.9866i −1.65361 2.27600i
\(719\) −14.7645 10.7271i −0.550625 0.400052i 0.277391 0.960757i \(-0.410530\pi\)
−0.828016 + 0.560705i \(0.810530\pi\)
\(720\) 45.3033 + 11.7312i 1.68835 + 0.437197i
\(721\) 3.15779 + 9.71868i 0.117602 + 0.361942i
\(722\) 18.3391 25.2416i 0.682510 0.939395i
\(723\) −6.86161 9.44419i −0.255186 0.351233i
\(724\) 2.17636 6.69816i 0.0808839 0.248935i
\(725\) −8.78706 18.8745i −0.326343 0.700980i
\(726\) 0 0
\(727\) 0.218345i 0.00809798i −0.999992 0.00404899i \(-0.998711\pi\)
0.999992 0.00404899i \(-0.00128884\pi\)
\(728\) −0.367704 0.119474i −0.0136280 0.00442801i
\(729\) −30.4927 + 22.1543i −1.12936 + 0.820529i
\(730\) −24.0509 + 9.46529i −0.890165 + 0.350326i
\(731\) −4.01462 12.3557i −0.148486 0.456993i
\(732\) −45.1527 + 14.6710i −1.66889 + 0.542256i
\(733\) 1.02489 1.41065i 0.0378553 0.0521034i −0.789670 0.613532i \(-0.789748\pi\)
0.827525 + 0.561429i \(0.189748\pi\)
\(734\) 29.4548 21.4002i 1.08720 0.789894i
\(735\) −16.6623 + 13.7266i −0.614597 + 0.506314i
\(736\) 35.2024 1.29758
\(737\) 0 0
\(738\) 36.7436i 1.35255i
\(739\) −9.38909 + 28.8966i −0.345383 + 1.06298i 0.615995 + 0.787750i \(0.288754\pi\)
−0.961378 + 0.275230i \(0.911246\pi\)
\(740\) −9.61038 + 0.584803i −0.353284 + 0.0214978i
\(741\) 2.89282 + 2.10175i 0.106270 + 0.0772099i
\(742\) 39.6517 12.8836i 1.45566 0.472973i
\(743\) −32.9687 + 10.7122i −1.20950 + 0.392991i −0.843249 0.537524i \(-0.819360\pi\)
−0.366254 + 0.930515i \(0.619360\pi\)
\(744\) 3.45710 + 2.51173i 0.126743 + 0.0920845i
\(745\) −2.60725 42.8463i −0.0955222 1.56977i
\(746\) −0.126646 + 0.389777i −0.00463684 + 0.0142707i
\(747\) 58.4572i 2.13884i
\(748\) 0 0
\(749\) 12.7458 0.465720
\(750\) −28.4343 + 59.4712i −1.03827 + 2.17158i
\(751\) −7.73330 + 5.61857i −0.282192 + 0.205025i −0.719873 0.694106i \(-0.755800\pi\)
0.437681 + 0.899130i \(0.355800\pi\)
\(752\) −6.52422 + 8.97981i −0.237914 + 0.327460i
\(753\) −62.9486 + 20.4532i −2.29397 + 0.745357i
\(754\) −1.68857 5.19689i −0.0614942 0.189260i
\(755\) −6.84689 + 2.69461i −0.249184 + 0.0980668i
\(756\) −39.5325 + 28.7220i −1.43778 + 1.04461i
\(757\) −5.95480 1.93483i −0.216431 0.0703226i 0.198795 0.980041i \(-0.436297\pi\)
−0.415225 + 0.909719i \(0.636297\pi\)
\(758\) 68.7414i 2.49680i
\(759\) 0 0
\(760\) −0.661674 0.421822i −0.0240014 0.0153011i
\(761\) 8.24025 25.3609i 0.298709 0.919331i −0.683241 0.730193i \(-0.739430\pi\)
0.981950 0.189139i \(-0.0605696\pi\)
\(762\) 56.9844 + 78.4324i 2.06433 + 2.84130i
\(763\) −29.0964 + 40.0478i −1.05336 + 1.44983i
\(764\) −5.99537 18.4518i −0.216905 0.667564i
\(765\) −3.66121 + 14.1387i −0.132371 + 0.511187i
\(766\) 11.6878 + 8.49171i 0.422299 + 0.306818i
\(767\) 1.41715 + 1.95054i 0.0511702 + 0.0704298i
\(768\) 40.0088 + 12.9997i 1.44369 + 0.469085i
\(769\) −42.2399 −1.52321 −0.761605 0.648042i \(-0.775588\pi\)
−0.761605 + 0.648042i \(0.775588\pi\)
\(770\) 0 0
\(771\) −11.8425 −0.426498
\(772\) −9.67414 3.14332i −0.348180 0.113130i
\(773\) −27.2115 37.4535i −0.978731 1.34711i −0.937510 0.347958i \(-0.886875\pi\)
−0.0412213 0.999150i \(-0.513125\pi\)
\(774\) −98.3140 71.4293i −3.53382 2.56747i
\(775\) 28.9046 26.9205i 1.03828 0.967011i
\(776\) −0.868135 2.67185i −0.0311642 0.0959137i
\(777\) −11.3252 + 15.5879i −0.406291 + 0.559212i
\(778\) −15.7739 21.7109i −0.565522 0.778375i
\(779\) 1.93135 5.94409i 0.0691978 0.212969i
\(780\) −4.75448 + 7.45793i −0.170238 + 0.267037i
\(781\) 0 0
\(782\) 10.4813i 0.374811i
\(783\) −28.8085 9.36044i −1.02953 0.334515i
\(784\) −10.2046 + 7.41406i −0.364449 + 0.264788i
\(785\) −11.4761 29.1602i −0.409598 1.04077i
\(786\) −25.5088 78.5079i −0.909867 2.80028i
\(787\) 46.7397 15.1866i 1.66609 0.541345i 0.683955 0.729524i \(-0.260258\pi\)
0.982135 + 0.188178i \(0.0602583\pi\)
\(788\) −14.5999 + 20.0951i −0.520100 + 0.715857i
\(789\) −29.0172 + 21.0822i −1.03304 + 0.750546i
\(790\) −53.2597 + 43.8762i −1.89490 + 1.56104i
\(791\) 32.5474 1.15725
\(792\) 0 0
\(793\) 5.05180i 0.179395i
\(794\) −20.9786 + 64.5656i −0.744504 + 2.29135i
\(795\) −2.54084 41.7550i −0.0901143 1.48090i
\(796\) 8.44704 + 6.13713i 0.299397 + 0.217525i
\(797\) −41.5326 + 13.4948i −1.47116 + 0.478009i −0.931459 0.363847i \(-0.881463\pi\)
−0.539702 + 0.841856i \(0.681463\pi\)
\(798\) −34.0504 + 11.0636i −1.20537 + 0.391649i
\(799\) −2.80252 2.03615i −0.0991459 0.0720337i
\(800\) −19.5942 + 35.2971i −0.692758 + 1.24794i
\(801\) 15.2846 47.0413i 0.540056 1.66212i
\(802\) 67.9480i 2.39933i
\(803\) 0 0
\(804\) −14.5102 −0.511737
\(805\) 19.9059 + 24.1631i 0.701592 + 0.851638i
\(806\) 8.38706 6.09356i 0.295422 0.214636i
\(807\) 13.2056 18.1760i 0.464860 0.639824i
\(808\) 0.984538 0.319896i 0.0346359 0.0112539i
\(809\) 12.2076 + 37.5713i 0.429198 + 1.32094i 0.898917 + 0.438120i \(0.144355\pi\)
−0.469719 + 0.882816i \(0.655645\pi\)
\(810\) 7.81229 + 19.8507i 0.274496 + 0.697483i
\(811\) −37.6818 + 27.3775i −1.32319 + 0.961352i −0.323302 + 0.946296i \(0.604793\pi\)
−0.999887 + 0.0150565i \(0.995207\pi\)
\(812\) 26.6009 + 8.64316i 0.933509 + 0.303315i
\(813\) 45.3940i 1.59204i
\(814\) 0 0
\(815\) −19.4621 12.4072i −0.681728 0.434606i
\(816\) −4.07644 + 12.5460i −0.142704 + 0.439197i
\(817\) −12.1499 16.7229i −0.425072 0.585062i
\(818\) 9.71269 13.3684i 0.339596 0.467414i
\(819\) 3.53810 + 10.8892i 0.123631 + 0.380498i
\(820\) 14.9657 + 3.87535i 0.522625 + 0.135333i
\(821\) −23.6291 17.1675i −0.824661 0.599151i 0.0933826 0.995630i \(-0.470232\pi\)
−0.918044 + 0.396479i \(0.870232\pi\)
\(822\) 47.7262 + 65.6895i 1.66464 + 2.29119i
\(823\) −13.2024 4.28972i −0.460207 0.149530i 0.0697326 0.997566i \(-0.477785\pi\)
−0.529940 + 0.848035i \(0.677785\pi\)
\(824\) −0.590551 −0.0205728
\(825\) 0 0
\(826\) −24.1406 −0.839960
\(827\) 9.08284 + 2.95119i 0.315841 + 0.102623i 0.462648 0.886542i \(-0.346899\pi\)
−0.146806 + 0.989165i \(0.546899\pi\)
\(828\) 29.4599 + 40.5480i 1.02380 + 1.40914i
\(829\) 30.1958 + 21.9386i 1.04875 + 0.761958i 0.971973 0.235091i \(-0.0755387\pi\)
0.0767717 + 0.997049i \(0.475539\pi\)
\(830\) 46.5751 + 12.0606i 1.61665 + 0.418628i
\(831\) 18.2871 + 56.2820i 0.634373 + 1.95240i
\(832\) −3.32379 + 4.57480i −0.115232 + 0.158603i
\(833\) −2.31386 3.18476i −0.0801706 0.110345i
\(834\) 12.3068 37.8765i 0.426150 1.31156i
\(835\) 27.5393 + 17.5565i 0.953038 + 0.607568i
\(836\) 0 0
\(837\) 57.4683i 1.98640i
\(838\) 37.5774 + 12.2096i 1.29809 + 0.421775i
\(839\) −1.15908 + 0.842119i −0.0400158 + 0.0290732i −0.607613 0.794233i \(-0.707873\pi\)
0.567598 + 0.823306i \(0.307873\pi\)
\(840\) −1.42243 3.61435i −0.0490786 0.124707i
\(841\) −3.60366 11.0909i −0.124264 0.382445i
\(842\) −45.9948 + 14.9446i −1.58508 + 0.515025i
\(843\) 41.4941 57.1118i 1.42913 1.96703i
\(844\) −2.66216 + 1.93418i −0.0916355 + 0.0665771i
\(845\) −17.8847 21.7096i −0.615253 0.746834i
\(846\) −32.4031 −1.11404
\(847\) 0 0
\(848\) 24.4417i 0.839332i
\(849\) 13.0037 40.0214i 0.446287 1.37353i
\(850\) −10.5095 5.83405i −0.360473 0.200106i
\(851\) 7.26072 + 5.27523i 0.248894 + 0.180832i
\(852\) 91.1315 29.6104i 3.12211 1.01444i
\(853\) 26.7648 8.69640i 0.916408 0.297759i 0.187416 0.982281i \(-0.439989\pi\)
0.728993 + 0.684522i \(0.239989\pi\)
\(854\) −40.9220 29.7315i −1.40032 1.01739i
\(855\) 1.41144 + 23.1950i 0.0482703 + 0.793252i
\(856\) −0.227617 + 0.700533i −0.00777979 + 0.0239437i
\(857\) 4.04561i 0.138195i 0.997610 + 0.0690977i \(0.0220120\pi\)
−0.997610 + 0.0690977i \(0.977988\pi\)
\(858\) 0 0
\(859\) 55.2064 1.88362 0.941808 0.336151i \(-0.109125\pi\)
0.941808 + 0.336151i \(0.109125\pi\)
\(860\) 39.4625 32.5098i 1.34566 1.10857i
\(861\) 25.0285 18.1843i 0.852968 0.619718i
\(862\) 8.99321 12.3781i 0.306310 0.421599i
\(863\) 28.7149 9.33004i 0.977467 0.317598i 0.223641 0.974672i \(-0.428206\pi\)
0.753827 + 0.657073i \(0.228206\pi\)
\(864\) 18.1506 + 55.8619i 0.617497 + 1.90046i
\(865\) 1.80840 + 4.59506i 0.0614873 + 0.156237i
\(866\) 41.9258 30.4608i 1.42470 1.03510i
\(867\) 43.2101 + 14.0398i 1.46749 + 0.476818i
\(868\) 53.0646i 1.80113i
\(869\) 0 0
\(870\) 29.5102 46.2901i 1.00049 1.56938i
\(871\) −0.477118 + 1.46842i −0.0161665 + 0.0497555i
\(872\) −1.68150 2.31438i −0.0569426 0.0783748i
\(873\) −48.9012 + 67.3068i −1.65506 + 2.27799i
\(874\) 5.15337 + 15.8604i 0.174315 + 0.536487i
\(875\) −35.3080 + 6.50997i −1.19363 + 0.220077i
\(876\) −28.1858 20.4782i −0.952309 0.691893i
\(877\) 18.1859 + 25.0308i 0.614096 + 0.845230i 0.996906 0.0785967i \(-0.0250439\pi\)
−0.382811 + 0.923827i \(0.625044\pi\)
\(878\) −39.3741 12.7934i −1.32881 0.431757i
\(879\) 44.1951 1.49066
\(880\) 0 0
\(881\) −8.25840 −0.278233 −0.139116 0.990276i \(-0.544426\pi\)
−0.139116 + 0.990276i \(0.544426\pi\)
\(882\) −35.0204 11.3788i −1.17920 0.383144i
\(883\) 23.5284 + 32.3840i 0.791793 + 1.08981i 0.993883 + 0.110442i \(0.0352267\pi\)
−0.202090 + 0.979367i \(0.564773\pi\)
\(884\) −1.30477 0.947972i −0.0438842 0.0318838i
\(885\) −6.07189 + 23.4482i −0.204104 + 0.788204i
\(886\) −6.35385 19.5551i −0.213462 0.656968i
\(887\) 22.1801 30.5283i 0.744735 1.02504i −0.253597 0.967310i \(-0.581614\pi\)
0.998332 0.0577299i \(-0.0183862\pi\)
\(888\) −0.654492 0.900831i −0.0219633 0.0302299i
\(889\) −16.3170 + 50.2187i −0.547256 + 1.68428i
\(890\) 34.3261 + 21.8831i 1.15062 + 0.733525i
\(891\) 0 0
\(892\) 6.93360i 0.232154i
\(893\) −5.24191 1.70320i −0.175414 0.0569955i
\(894\) 91.5682 66.5282i 3.06250 2.22504i
\(895\) 22.4887 8.85049i 0.751716 0.295839i
\(896\) −1.47173 4.52951i −0.0491669 0.151320i
\(897\) 7.84081 2.54763i 0.261797 0.0850630i
\(898\) −17.4774 + 24.0555i −0.583227 + 0.802743i
\(899\) −26.6121 + 19.3348i −0.887564 + 0.644853i
\(900\) −57.0549 + 6.96952i −1.90183 + 0.232317i
\(901\) 7.62803 0.254127
\(902\) 0 0
\(903\) 102.318i 3.40494i
\(904\) −0.581240 + 1.78887i −0.0193317 + 0.0594970i
\(905\) −0.457290 7.51489i −0.0152008 0.249803i
\(906\) −15.6961 11.4039i −0.521467 0.378868i
\(907\) −31.8908 + 10.3619i −1.05892 + 0.344063i −0.786161 0.618021i \(-0.787935\pi\)
−0.272754 + 0.962084i \(0.587935\pi\)
\(908\) 5.65003 1.83581i 0.187503 0.0609234i
\(909\) −24.8016 18.0194i −0.822617 0.597666i
\(910\) −9.40577 + 0.572352i −0.311798 + 0.0189733i
\(911\) −4.25913 + 13.1083i −0.141111 + 0.434296i −0.996490 0.0837064i \(-0.973324\pi\)
0.855379 + 0.518003i \(0.173324\pi\)
\(912\) 20.9890i 0.695014i
\(913\) 0 0
\(914\) 6.80231 0.225000
\(915\) −39.1716 + 32.2701i −1.29497 + 1.06682i
\(916\) 3.37027 2.44864i 0.111357 0.0809055i
\(917\) 26.4270 36.3736i 0.872695 1.20116i
\(918\) −16.6326 + 5.40425i −0.548957 + 0.178367i
\(919\) −12.9209 39.7663i −0.426220 1.31177i −0.901821 0.432109i \(-0.857769\pi\)
0.475601 0.879661i \(-0.342231\pi\)
\(920\) −1.68354 + 0.662560i −0.0555046 + 0.0218440i
\(921\) 18.9630 13.7775i 0.624853 0.453982i
\(922\) 2.72072 + 0.884014i 0.0896020 + 0.0291135i
\(923\) 10.1960i 0.335607i
\(924\) 0 0
\(925\) −9.33084 + 4.34399i −0.306796 + 0.142830i
\(926\) 9.66346 29.7411i 0.317561 0.977352i
\(927\) 10.2795 + 14.1485i 0.337623 + 0.464698i
\(928\) 19.7616 27.1995i 0.648706 0.892867i
\(929\) −4.04898 12.4615i −0.132843 0.408848i 0.862405 0.506218i \(-0.168957\pi\)
−0.995248 + 0.0973699i \(0.968957\pi\)
\(930\) 100.825 + 26.1084i 3.30617 + 0.856127i
\(931\) −5.06721 3.68155i −0.166071 0.120658i
\(932\) 24.9016 + 34.2742i 0.815680 + 1.12269i
\(933\) 61.7258 + 20.0559i 2.02081 + 0.656601i
\(934\) 37.8078 1.23711
\(935\) 0 0
\(936\) −0.661674 −0.0216275
\(937\) −8.32692 2.70558i −0.272029 0.0883875i 0.169826 0.985474i \(-0.445679\pi\)
−0.441855 + 0.897087i \(0.645679\pi\)
\(938\) −9.08688 12.5070i −0.296697 0.408369i
\(939\) 5.54254 + 4.02689i 0.180874 + 0.131413i
\(940\) 3.41756 13.1978i 0.111468 0.430466i
\(941\) −5.45505 16.7889i −0.177829 0.547303i 0.821922 0.569600i \(-0.192902\pi\)
−0.999751 + 0.0222975i \(0.992902\pi\)
\(942\) 48.5679 66.8480i 1.58243 2.17803i
\(943\) −8.47011 11.6581i −0.275825 0.379640i
\(944\) −4.37327 + 13.4595i −0.142338 + 0.438071i
\(945\) −28.0803 + 44.0470i −0.913451 + 1.43285i
\(946\) 0 0
\(947\) 56.2415i 1.82760i 0.406159 + 0.913802i \(0.366868\pi\)
−0.406159 + 0.913802i \(0.633132\pi\)
\(948\) −88.4625 28.7432i −2.87313 0.933537i
\(949\) −2.99916 + 2.17901i −0.0973567 + 0.0707338i
\(950\) −18.7715 3.66091i −0.609029 0.118776i
\(951\) 16.2338 + 49.9625i 0.526417 + 1.62014i
\(952\) 0.673608 0.218868i 0.0218318 0.00709357i
\(953\) 2.78838 3.83788i 0.0903246 0.124321i −0.761463 0.648208i \(-0.775519\pi\)
0.851788 + 0.523887i \(0.175519\pi\)
\(954\) 57.7253 41.9399i 1.86892 1.35785i
\(955\) −13.1873 16.0076i −0.426732 0.517995i
\(956\) 3.95540 0.127927
\(957\) 0 0
\(958\) 60.4344i 1.95255i
\(959\) −13.6660 + 42.0597i −0.441299 + 1.35818i
\(960\) −56.7047 + 3.45055i −1.83014 + 0.111366i
\(961\) −25.4092 18.4608i −0.819650 0.595511i
\(962\) −2.56915 + 0.834768i −0.0828327 + 0.0269140i
\(963\) 20.7456 6.74064i 0.668516 0.217214i
\(964\) 6.77753 + 4.92416i 0.218290 + 0.158597i
\(965\) −10.8537 + 0.660464i −0.349394 + 0.0212611i
\(966\) −25.5088 + 78.5079i −0.820731 + 2.52595i
\(967\) 33.8619i 1.08892i 0.838785 + 0.544462i \(0.183266\pi\)
−0.838785 + 0.544462i \(0.816734\pi\)
\(968\) 0 0
\(969\) −6.55047 −0.210431
\(970\) −43.5369 52.8478i −1.39788 1.69684i
\(971\) 16.0047 11.6281i 0.513614 0.373162i −0.300579 0.953757i \(-0.597180\pi\)
0.814193 + 0.580595i \(0.197180\pi\)
\(972\) 9.93047 13.6681i 0.318520 0.438405i
\(973\) 20.6296 6.70297i 0.661356 0.214887i
\(974\) 0.584338 + 1.79841i 0.0187234 + 0.0576247i
\(975\) −1.80982 + 9.27995i −0.0579605 + 0.297196i
\(976\) −23.9901 + 17.4298i −0.767904 + 0.557915i
\(977\) −6.33521 2.05844i −0.202681 0.0658552i 0.205917 0.978569i \(-0.433982\pi\)
−0.408598 + 0.912714i \(0.633982\pi\)
\(978\) 60.8581i 1.94603i
\(979\) 0 0
\(980\) 8.32821 13.0637i 0.266035 0.417305i
\(981\) −26.1791 + 80.5711i −0.835836 + 2.57244i
\(982\) −39.1106 53.8312i −1.24807 1.71782i
\(983\) 3.03421 4.17623i 0.0967762 0.133201i −0.757883 0.652391i \(-0.773766\pi\)
0.854659 + 0.519190i \(0.173766\pi\)
\(984\) 0.552479 + 1.70035i 0.0176124 + 0.0542053i
\(985\) −6.65623 + 25.7048i −0.212085 + 0.819024i
\(986\) 8.09849 + 5.88390i 0.257909 + 0.187382i
\(987\) −16.0362 22.0719i −0.510437 0.702556i
\(988\) −2.44049 0.792962i −0.0776422 0.0252275i
\(989\) −47.6592 −1.51547
\(990\) 0 0
\(991\) −23.8830 −0.758669 −0.379334 0.925260i \(-0.623847\pi\)
−0.379334 + 0.925260i \(0.623847\pi\)
\(992\) 60.6630 + 19.7106i 1.92605 + 0.625812i
\(993\) 5.29693 + 7.29060i 0.168093 + 0.231360i
\(994\) 82.5926 + 60.0071i 2.61968 + 1.90331i
\(995\) 10.8051 + 2.79797i 0.342546 + 0.0887017i
\(996\) 20.0401 + 61.6772i 0.634996 + 1.95432i
\(997\) 17.4233 23.9811i 0.551801 0.759489i −0.438454 0.898753i \(-0.644474\pi\)
0.990255 + 0.139265i \(0.0444739\pi\)
\(998\) −10.6908 14.7146i −0.338410 0.465782i
\(999\) −4.62745 + 14.2418i −0.146406 + 0.450592i
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 605.2.j.k.9.3 48
5.4 even 2 inner 605.2.j.k.9.10 48
11.2 odd 10 inner 605.2.j.k.124.3 48
11.3 even 5 inner 605.2.j.k.444.4 48
11.4 even 5 605.2.b.h.364.4 yes 12
11.5 even 5 inner 605.2.j.k.269.10 48
11.6 odd 10 inner 605.2.j.k.269.4 48
11.7 odd 10 605.2.b.h.364.10 yes 12
11.8 odd 10 inner 605.2.j.k.444.10 48
11.9 even 5 inner 605.2.j.k.124.9 48
11.10 odd 2 inner 605.2.j.k.9.9 48
55.4 even 10 605.2.b.h.364.9 yes 12
55.7 even 20 3025.2.a.bo.1.4 12
55.9 even 10 inner 605.2.j.k.124.4 48
55.14 even 10 inner 605.2.j.k.444.9 48
55.18 even 20 3025.2.a.bo.1.9 12
55.19 odd 10 inner 605.2.j.k.444.3 48
55.24 odd 10 inner 605.2.j.k.124.10 48
55.29 odd 10 605.2.b.h.364.3 12
55.37 odd 20 3025.2.a.bo.1.10 12
55.39 odd 10 inner 605.2.j.k.269.9 48
55.48 odd 20 3025.2.a.bo.1.3 12
55.49 even 10 inner 605.2.j.k.269.3 48
55.54 odd 2 inner 605.2.j.k.9.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.h.364.3 12 55.29 odd 10
605.2.b.h.364.4 yes 12 11.4 even 5
605.2.b.h.364.9 yes 12 55.4 even 10
605.2.b.h.364.10 yes 12 11.7 odd 10
605.2.j.k.9.3 48 1.1 even 1 trivial
605.2.j.k.9.4 48 55.54 odd 2 inner
605.2.j.k.9.9 48 11.10 odd 2 inner
605.2.j.k.9.10 48 5.4 even 2 inner
605.2.j.k.124.3 48 11.2 odd 10 inner
605.2.j.k.124.4 48 55.9 even 10 inner
605.2.j.k.124.9 48 11.9 even 5 inner
605.2.j.k.124.10 48 55.24 odd 10 inner
605.2.j.k.269.3 48 55.49 even 10 inner
605.2.j.k.269.4 48 11.6 odd 10 inner
605.2.j.k.269.9 48 55.39 odd 10 inner
605.2.j.k.269.10 48 11.5 even 5 inner
605.2.j.k.444.3 48 55.19 odd 10 inner
605.2.j.k.444.4 48 11.3 even 5 inner
605.2.j.k.444.9 48 55.14 even 10 inner
605.2.j.k.444.10 48 11.8 odd 10 inner
3025.2.a.bo.1.3 12 55.48 odd 20
3025.2.a.bo.1.4 12 55.7 even 20
3025.2.a.bo.1.9 12 55.18 even 20
3025.2.a.bo.1.10 12 55.37 odd 20