Properties

Label 527.2.h.c.35.8
Level $527$
Weight $2$
Character 527.35
Analytic conductor $4.208$
Analytic rank $0$
Dimension $96$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [527,2,Mod(35,527)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(527, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("527.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 527 = 17 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 527.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.20811618652\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 35.8
Character \(\chi\) \(=\) 527.35
Dual form 527.2.h.c.256.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +O(q^{10})\) \(q+(-0.376285 - 1.15809i) q^{2} +(-0.0739502 + 0.227595i) q^{3} +(0.418458 - 0.304028i) q^{4} -1.77800 q^{5} +0.291402 q^{6} +(-0.161608 + 0.117415i) q^{7} +(-2.47981 - 1.80168i) q^{8} +(2.38072 + 1.72969i) q^{9} +(0.669036 + 2.05908i) q^{10} +(4.41639 - 3.20870i) q^{11} +(0.0382502 + 0.117722i) q^{12} +(0.455967 - 1.40332i) q^{13} +(0.196788 + 0.142975i) q^{14} +(0.131483 - 0.404664i) q^{15} +(-0.833720 + 2.56593i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.10731 - 3.40794i) q^{18} +(-1.73093 - 5.32725i) q^{19} +(-0.744018 + 0.540561i) q^{20} +(-0.0147722 - 0.0454642i) q^{21} +(-5.37778 - 3.90718i) q^{22} +(-7.23855 - 5.25912i) q^{23} +(0.593437 - 0.431157i) q^{24} -1.83872 q^{25} -1.79674 q^{26} +(-1.15054 + 0.835914i) q^{27} +(-0.0319288 + 0.0982668i) q^{28} +(1.55371 + 4.78184i) q^{29} -0.518112 q^{30} +(4.57132 - 3.17853i) q^{31} -2.84513 q^{32} +(0.403691 + 1.24243i) q^{33} +(-0.376285 + 1.15809i) q^{34} +(0.287340 - 0.208765i) q^{35} +1.52211 q^{36} +10.4793 q^{37} +(-5.51810 + 4.00913i) q^{38} +(0.285670 + 0.207552i) q^{39} +(4.40910 + 3.20340i) q^{40} +(-3.45554 - 10.6350i) q^{41} +(-0.0470929 + 0.0342150i) q^{42} +(0.499597 + 1.53760i) q^{43} +(0.872542 - 2.68541i) q^{44} +(-4.23292 - 3.07540i) q^{45} +(-3.36676 + 10.3618i) q^{46} +(0.491048 - 1.51129i) q^{47} +(-0.522339 - 0.379501i) q^{48} +(-2.15079 + 6.61944i) q^{49} +(0.691882 + 2.12939i) q^{50} +(0.193604 - 0.140662i) q^{51} +(-0.235845 - 0.725857i) q^{52} +(-4.61935 - 3.35616i) q^{53} +(1.40099 + 1.01788i) q^{54} +(-7.85235 + 5.70506i) q^{55} +0.612303 q^{56} +1.34046 q^{57} +(4.95315 - 3.59867i) q^{58} +(-0.428033 + 1.31735i) q^{59} +(-0.0680088 - 0.209310i) q^{60} +3.71271 q^{61} +(-5.40113 - 4.09796i) q^{62} -0.587837 q^{63} +(2.73802 + 8.42677i) q^{64} +(-0.810709 + 2.49511i) q^{65} +(1.28694 - 0.935019i) q^{66} -2.38128 q^{67} -0.517242 q^{68} +(1.73224 - 1.25855i) q^{69} +(-0.349889 - 0.254210i) q^{70} +(5.86105 + 4.25830i) q^{71} +(-2.78736 - 8.57861i) q^{72} +(0.160910 - 0.116908i) q^{73} +(-3.94322 - 12.1360i) q^{74} +(0.135973 - 0.418483i) q^{75} +(-2.34395 - 1.70298i) q^{76} +(-0.336976 + 1.03710i) q^{77} +(0.132869 - 0.408930i) q^{78} +(11.3142 + 8.22025i) q^{79} +(1.48235 - 4.56222i) q^{80} +(2.62289 + 8.07244i) q^{81} +(-11.0161 + 8.00363i) q^{82} +(-0.432705 - 1.33173i) q^{83} +(-0.0200039 - 0.0145337i) q^{84} +(1.43843 + 1.04508i) q^{85} +(1.59269 - 1.15715i) q^{86} -1.20322 q^{87} -16.7329 q^{88} +(8.62465 - 6.26618i) q^{89} +(-1.96879 + 6.05932i) q^{90} +(0.0910834 + 0.280326i) q^{91} -4.62795 q^{92} +(0.385367 + 1.27546i) q^{93} -1.93498 q^{94} +(3.07759 + 9.47185i) q^{95} +(0.210398 - 0.647539i) q^{96} +(5.17845 - 3.76236i) q^{97} +8.47521 q^{98} +16.0643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/527\mathbb{Z}\right)^\times\).

\(n\) \(156\) \(375\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.376285 1.15809i −0.266074 0.818892i −0.991444 0.130532i \(-0.958331\pi\)
0.725370 0.688359i \(-0.241669\pi\)
\(3\) −0.0739502 + 0.227595i −0.0426952 + 0.131402i −0.970132 0.242578i \(-0.922007\pi\)
0.927437 + 0.373980i \(0.122007\pi\)
\(4\) 0.418458 0.304028i 0.209229 0.152014i
\(5\) −1.77800 −0.795146 −0.397573 0.917571i \(-0.630147\pi\)
−0.397573 + 0.917571i \(0.630147\pi\)
\(6\) 0.291402 0.118964
\(7\) −0.161608 + 0.117415i −0.0610822 + 0.0443788i −0.617907 0.786251i \(-0.712019\pi\)
0.556825 + 0.830630i \(0.312019\pi\)
\(8\) −2.47981 1.80168i −0.876744 0.636992i
\(9\) 2.38072 + 1.72969i 0.793573 + 0.576565i
\(10\) 0.669036 + 2.05908i 0.211568 + 0.651138i
\(11\) 4.41639 3.20870i 1.33159 0.967459i 0.331884 0.943320i \(-0.392316\pi\)
0.999709 0.0241383i \(-0.00768421\pi\)
\(12\) 0.0382502 + 0.117722i 0.0110419 + 0.0339834i
\(13\) 0.455967 1.40332i 0.126462 0.389211i −0.867702 0.497084i \(-0.834404\pi\)
0.994165 + 0.107873i \(0.0344040\pi\)
\(14\) 0.196788 + 0.142975i 0.0525939 + 0.0382117i
\(15\) 0.131483 0.404664i 0.0339489 0.104484i
\(16\) −0.833720 + 2.56593i −0.208430 + 0.641482i
\(17\) −0.809017 0.587785i −0.196215 0.142559i
\(18\) 1.10731 3.40794i 0.260995 0.803259i
\(19\) −1.73093 5.32725i −0.397102 1.22215i −0.927312 0.374288i \(-0.877887\pi\)
0.530210 0.847866i \(-0.322113\pi\)
\(20\) −0.744018 + 0.540561i −0.166368 + 0.120873i
\(21\) −0.0147722 0.0454642i −0.00322356 0.00992110i
\(22\) −5.37778 3.90718i −1.14655 0.833014i
\(23\) −7.23855 5.25912i −1.50934 1.09660i −0.966468 0.256788i \(-0.917336\pi\)
−0.542875 0.839814i \(-0.682664\pi\)
\(24\) 0.593437 0.431157i 0.121135 0.0880096i
\(25\) −1.83872 −0.367743
\(26\) −1.79674 −0.352370
\(27\) −1.15054 + 0.835914i −0.221421 + 0.160872i
\(28\) −0.0319288 + 0.0982668i −0.00603398 + 0.0185707i
\(29\) 1.55371 + 4.78184i 0.288517 + 0.887965i 0.985322 + 0.170704i \(0.0546043\pi\)
−0.696805 + 0.717261i \(0.745396\pi\)
\(30\) −0.518112 −0.0945939
\(31\) 4.57132 3.17853i 0.821033 0.570880i
\(32\) −2.84513 −0.502953
\(33\) 0.403691 + 1.24243i 0.0702736 + 0.216280i
\(34\) −0.376285 + 1.15809i −0.0645324 + 0.198610i
\(35\) 0.287340 0.208765i 0.0485693 0.0352877i
\(36\) 1.52211 0.253684
\(37\) 10.4793 1.72279 0.861396 0.507933i \(-0.169590\pi\)
0.861396 + 0.507933i \(0.169590\pi\)
\(38\) −5.51810 + 4.00913i −0.895153 + 0.650367i
\(39\) 0.285670 + 0.207552i 0.0457439 + 0.0332349i
\(40\) 4.40910 + 3.20340i 0.697139 + 0.506501i
\(41\) −3.45554 10.6350i −0.539664 1.66092i −0.733349 0.679852i \(-0.762044\pi\)
0.193685 0.981064i \(-0.437956\pi\)
\(42\) −0.0470929 + 0.0342150i −0.00726660 + 0.00527949i
\(43\) 0.499597 + 1.53760i 0.0761878 + 0.234482i 0.981896 0.189419i \(-0.0606605\pi\)
−0.905709 + 0.423901i \(0.860660\pi\)
\(44\) 0.872542 2.68541i 0.131541 0.404841i
\(45\) −4.23292 3.07540i −0.631007 0.458453i
\(46\) −3.36676 + 10.3618i −0.496401 + 1.52777i
\(47\) 0.491048 1.51129i 0.0716267 0.220444i −0.908834 0.417157i \(-0.863027\pi\)
0.980461 + 0.196712i \(0.0630265\pi\)
\(48\) −0.522339 0.379501i −0.0753931 0.0547763i
\(49\) −2.15079 + 6.61944i −0.307255 + 0.945635i
\(50\) 0.691882 + 2.12939i 0.0978469 + 0.301142i
\(51\) 0.193604 0.140662i 0.0271100 0.0196966i
\(52\) −0.235845 0.725857i −0.0327059 0.100658i
\(53\) −4.61935 3.35616i −0.634517 0.461004i 0.223445 0.974717i \(-0.428270\pi\)
−0.857962 + 0.513713i \(0.828270\pi\)
\(54\) 1.40099 + 1.01788i 0.190651 + 0.138516i
\(55\) −7.85235 + 5.70506i −1.05881 + 0.769271i
\(56\) 0.612303 0.0818224
\(57\) 1.34046 0.177548
\(58\) 4.95315 3.59867i 0.650380 0.472529i
\(59\) −0.428033 + 1.31735i −0.0557252 + 0.171505i −0.975045 0.222006i \(-0.928740\pi\)
0.919320 + 0.393511i \(0.128740\pi\)
\(60\) −0.0680088 0.209310i −0.00877990 0.0270218i
\(61\) 3.71271 0.475364 0.237682 0.971343i \(-0.423612\pi\)
0.237682 + 0.971343i \(0.423612\pi\)
\(62\) −5.40113 4.09796i −0.685945 0.520441i
\(63\) −0.587837 −0.0740605
\(64\) 2.73802 + 8.42677i 0.342253 + 1.05335i
\(65\) −0.810709 + 2.49511i −0.100556 + 0.309480i
\(66\) 1.28694 0.935019i 0.158412 0.115093i
\(67\) −2.38128 −0.290920 −0.145460 0.989364i \(-0.546466\pi\)
−0.145460 + 0.989364i \(0.546466\pi\)
\(68\) −0.517242 −0.0627249
\(69\) 1.73224 1.25855i 0.208537 0.151511i
\(70\) −0.349889 0.254210i −0.0418198 0.0303839i
\(71\) 5.86105 + 4.25830i 0.695579 + 0.505368i 0.878489 0.477762i \(-0.158552\pi\)
−0.182910 + 0.983130i \(0.558552\pi\)
\(72\) −2.78736 8.57861i −0.328494 1.01100i
\(73\) 0.160910 0.116908i 0.0188331 0.0136830i −0.578329 0.815804i \(-0.696295\pi\)
0.597162 + 0.802121i \(0.296295\pi\)
\(74\) −3.94322 12.1360i −0.458390 1.41078i
\(75\) 0.135973 0.418483i 0.0157008 0.0483222i
\(76\) −2.34395 1.70298i −0.268870 0.195345i
\(77\) −0.336976 + 1.03710i −0.0384020 + 0.118189i
\(78\) 0.132869 0.408930i 0.0150445 0.0463022i
\(79\) 11.3142 + 8.22025i 1.27295 + 0.924850i 0.999316 0.0369842i \(-0.0117751\pi\)
0.273631 + 0.961835i \(0.411775\pi\)
\(80\) 1.48235 4.56222i 0.165732 0.510072i
\(81\) 2.62289 + 8.07244i 0.291433 + 0.896938i
\(82\) −11.0161 + 8.00363i −1.21652 + 0.883853i
\(83\) −0.432705 1.33173i −0.0474955 0.146176i 0.924496 0.381191i \(-0.124486\pi\)
−0.971992 + 0.235015i \(0.924486\pi\)
\(84\) −0.0200039 0.0145337i −0.00218261 0.00158576i
\(85\) 1.43843 + 1.04508i 0.156020 + 0.113355i
\(86\) 1.59269 1.15715i 0.171744 0.124779i
\(87\) −1.20322 −0.128999
\(88\) −16.7329 −1.78373
\(89\) 8.62465 6.26618i 0.914211 0.664213i −0.0278651 0.999612i \(-0.508871\pi\)
0.942076 + 0.335398i \(0.108871\pi\)
\(90\) −1.96879 + 6.05932i −0.207529 + 0.638708i
\(91\) 0.0910834 + 0.280326i 0.00954814 + 0.0293861i
\(92\) −4.62795 −0.482497
\(93\) 0.385367 + 1.27546i 0.0399607 + 0.132259i
\(94\) −1.93498 −0.199578
\(95\) 3.07759 + 9.47185i 0.315754 + 0.971791i
\(96\) 0.210398 0.647539i 0.0214737 0.0660892i
\(97\) 5.17845 3.76236i 0.525791 0.382010i −0.292990 0.956116i \(-0.594650\pi\)
0.818781 + 0.574106i \(0.194650\pi\)
\(98\) 8.47521 0.856125
\(99\) 16.0643 1.61452
\(100\) −0.769425 + 0.559020i −0.0769425 + 0.0559020i
\(101\) −4.91332 3.56974i −0.488894 0.355202i 0.315865 0.948804i \(-0.397705\pi\)
−0.804759 + 0.593602i \(0.797705\pi\)
\(102\) −0.235749 0.171282i −0.0233426 0.0169594i
\(103\) 0.132155 + 0.406731i 0.0130216 + 0.0400764i 0.957356 0.288910i \(-0.0932929\pi\)
−0.944335 + 0.328987i \(0.893293\pi\)
\(104\) −3.65905 + 2.65846i −0.358799 + 0.260683i
\(105\) 0.0262650 + 0.0808353i 0.00256320 + 0.00788872i
\(106\) −2.14853 + 6.61249i −0.208684 + 0.642262i
\(107\) 5.38236 + 3.91051i 0.520332 + 0.378044i 0.816729 0.577021i \(-0.195785\pi\)
−0.296397 + 0.955065i \(0.595785\pi\)
\(108\) −0.227311 + 0.699590i −0.0218730 + 0.0673181i
\(109\) −5.50617 + 16.9463i −0.527396 + 1.62316i 0.232133 + 0.972684i \(0.425429\pi\)
−0.759529 + 0.650473i \(0.774571\pi\)
\(110\) 9.56169 + 6.94697i 0.911671 + 0.662368i
\(111\) −0.774949 + 2.38505i −0.0735549 + 0.226379i
\(112\) −0.166543 0.512567i −0.0157368 0.0484330i
\(113\) 4.17928 3.03642i 0.393153 0.285643i −0.373593 0.927593i \(-0.621874\pi\)
0.766746 + 0.641950i \(0.221874\pi\)
\(114\) −0.504395 1.55237i −0.0472409 0.145393i
\(115\) 12.8701 + 9.35071i 1.20015 + 0.871958i
\(116\) 2.10397 + 1.52863i 0.195349 + 0.141929i
\(117\) 3.51285 2.55223i 0.324763 0.235954i
\(118\) 1.68667 0.155271
\(119\) 0.199759 0.0183119
\(120\) −1.05513 + 0.766598i −0.0963198 + 0.0699805i
\(121\) 5.80960 17.8801i 0.528145 1.62546i
\(122\) −1.39704 4.29964i −0.126482 0.389271i
\(123\) 2.67602 0.241289
\(124\) 0.946546 2.71989i 0.0850024 0.244253i
\(125\) 12.1592 1.08756
\(126\) 0.221195 + 0.680767i 0.0197056 + 0.0606475i
\(127\) −0.781318 + 2.40465i −0.0693308 + 0.213378i −0.979719 0.200377i \(-0.935783\pi\)
0.910388 + 0.413756i \(0.135783\pi\)
\(128\) 4.12513 2.99709i 0.364614 0.264907i
\(129\) −0.386896 −0.0340643
\(130\) 3.19461 0.280186
\(131\) 5.15658 3.74647i 0.450532 0.327331i −0.339274 0.940688i \(-0.610181\pi\)
0.789806 + 0.613357i \(0.210181\pi\)
\(132\) 0.546662 + 0.397173i 0.0475808 + 0.0345695i
\(133\) 0.905233 + 0.657690i 0.0784937 + 0.0570290i
\(134\) 0.896043 + 2.75774i 0.0774063 + 0.238232i
\(135\) 2.04565 1.48626i 0.176062 0.127916i
\(136\) 0.947202 + 2.91519i 0.0812219 + 0.249975i
\(137\) −5.70366 + 17.5541i −0.487297 + 1.49975i 0.341329 + 0.939944i \(0.389123\pi\)
−0.828626 + 0.559802i \(0.810877\pi\)
\(138\) −2.10933 1.53251i −0.179558 0.130456i
\(139\) 4.85167 14.9319i 0.411513 1.26651i −0.503819 0.863809i \(-0.668072\pi\)
0.915333 0.402699i \(-0.131928\pi\)
\(140\) 0.0567694 0.174718i 0.00479789 0.0147664i
\(141\) 0.307650 + 0.223520i 0.0259088 + 0.0188238i
\(142\) 2.72606 8.38995i 0.228766 0.704069i
\(143\) −2.48910 7.66068i −0.208149 0.640618i
\(144\) −6.42312 + 4.66667i −0.535260 + 0.388889i
\(145\) −2.76250 8.50211i −0.229413 0.706061i
\(146\) −0.195937 0.142357i −0.0162159 0.0117815i
\(147\) −1.34750 0.979018i −0.111140 0.0807481i
\(148\) 4.38516 3.18601i 0.360458 0.261888i
\(149\) −16.1260 −1.32109 −0.660545 0.750786i \(-0.729675\pi\)
−0.660545 + 0.750786i \(0.729675\pi\)
\(150\) −0.535805 −0.0437483
\(151\) −7.22653 + 5.25038i −0.588087 + 0.427270i −0.841630 0.540054i \(-0.818404\pi\)
0.253544 + 0.967324i \(0.418404\pi\)
\(152\) −5.30566 + 16.3291i −0.430345 + 1.32447i
\(153\) −0.909354 2.79870i −0.0735169 0.226262i
\(154\) 1.32786 0.107002
\(155\) −8.12781 + 5.65142i −0.652841 + 0.453933i
\(156\) 0.182642 0.0146231
\(157\) 6.36067 + 19.5761i 0.507637 + 1.56234i 0.796292 + 0.604912i \(0.206792\pi\)
−0.288656 + 0.957433i \(0.593208\pi\)
\(158\) 5.26240 16.1960i 0.418654 1.28848i
\(159\) 1.10545 0.803155i 0.0876677 0.0636943i
\(160\) 5.05865 0.399921
\(161\) 1.78731 0.140860
\(162\) 8.36164 6.07508i 0.656952 0.477304i
\(163\) 14.6234 + 10.6245i 1.14539 + 0.832174i 0.987861 0.155340i \(-0.0496473\pi\)
0.157529 + 0.987514i \(0.449647\pi\)
\(164\) −4.67934 3.39974i −0.365395 0.265475i
\(165\) −0.717763 2.20905i −0.0558778 0.171974i
\(166\) −1.37944 + 1.00222i −0.107065 + 0.0777874i
\(167\) 1.42820 + 4.39554i 0.110517 + 0.340137i 0.990986 0.133968i \(-0.0427719\pi\)
−0.880469 + 0.474105i \(0.842772\pi\)
\(168\) −0.0452799 + 0.139357i −0.00349342 + 0.0107516i
\(169\) 8.75582 + 6.36147i 0.673524 + 0.489344i
\(170\) 0.669036 2.05908i 0.0513127 0.157924i
\(171\) 5.09366 15.6767i 0.389522 1.19882i
\(172\) 0.676533 + 0.491530i 0.0515852 + 0.0374788i
\(173\) −4.19524 + 12.9116i −0.318958 + 0.981653i 0.655136 + 0.755511i \(0.272611\pi\)
−0.974094 + 0.226142i \(0.927389\pi\)
\(174\) 0.452754 + 1.39343i 0.0343232 + 0.105636i
\(175\) 0.297152 0.215893i 0.0224626 0.0163200i
\(176\) 4.55125 + 14.0073i 0.343063 + 1.05584i
\(177\) −0.268170 0.194837i −0.0201569 0.0146448i
\(178\) −10.5021 7.63023i −0.787167 0.571910i
\(179\) 12.4747 9.06339i 0.932402 0.677429i −0.0141780 0.999899i \(-0.504513\pi\)
0.946580 + 0.322470i \(0.104513\pi\)
\(180\) −2.70630 −0.201716
\(181\) −23.8252 −1.77091 −0.885457 0.464722i \(-0.846154\pi\)
−0.885457 + 0.464722i \(0.846154\pi\)
\(182\) 0.290369 0.210965i 0.0215236 0.0156378i
\(183\) −0.274556 + 0.844995i −0.0202957 + 0.0624638i
\(184\) 8.47494 + 26.0832i 0.624781 + 1.92288i
\(185\) −18.6323 −1.36987
\(186\) 1.33209 0.926227i 0.0976736 0.0679143i
\(187\) −5.45896 −0.399199
\(188\) −0.253991 0.781704i −0.0185242 0.0570116i
\(189\) 0.0877873 0.270181i 0.00638559 0.0196528i
\(190\) 9.81118 7.12824i 0.711778 0.517137i
\(191\) 11.3763 0.823163 0.411581 0.911373i \(-0.364977\pi\)
0.411581 + 0.911373i \(0.364977\pi\)
\(192\) −2.12037 −0.153024
\(193\) 18.1802 13.2087i 1.30864 0.950780i 0.308637 0.951180i \(-0.400127\pi\)
1.00000 0.000399665i \(0.000127217\pi\)
\(194\) −6.30572 4.58137i −0.452724 0.328923i
\(195\) −0.507922 0.369027i −0.0363730 0.0264266i
\(196\) 1.11248 + 3.42386i 0.0794628 + 0.244561i
\(197\) −9.72309 + 7.06424i −0.692741 + 0.503306i −0.877560 0.479466i \(-0.840830\pi\)
0.184819 + 0.982773i \(0.440830\pi\)
\(198\) −6.04475 18.6038i −0.429581 1.32212i
\(199\) 0.546738 1.68269i 0.0387572 0.119282i −0.929806 0.368050i \(-0.880026\pi\)
0.968563 + 0.248768i \(0.0800255\pi\)
\(200\) 4.55966 + 3.31279i 0.322417 + 0.234249i
\(201\) 0.176096 0.541969i 0.0124209 0.0382275i
\(202\) −2.28526 + 7.03330i −0.160790 + 0.494861i
\(203\) −0.812554 0.590355i −0.0570301 0.0414348i
\(204\) 0.0382502 0.117722i 0.00267805 0.00824218i
\(205\) 6.14395 + 18.9091i 0.429112 + 1.32067i
\(206\) 0.421302 0.306094i 0.0293535 0.0213266i
\(207\) −8.13630 25.0410i −0.565512 1.74047i
\(208\) 3.22067 + 2.33995i 0.223313 + 0.162247i
\(209\) −24.7380 17.9732i −1.71116 1.24323i
\(210\) 0.0837313 0.0608343i 0.00577801 0.00419797i
\(211\) −5.65487 −0.389297 −0.194649 0.980873i \(-0.562357\pi\)
−0.194649 + 0.980873i \(0.562357\pi\)
\(212\) −2.95337 −0.202838
\(213\) −1.40260 + 1.01905i −0.0961043 + 0.0698238i
\(214\) 2.50341 7.70471i 0.171130 0.526683i
\(215\) −0.888283 2.73385i −0.0605804 0.186447i
\(216\) 4.35916 0.296603
\(217\) −0.365556 + 1.05042i −0.0248156 + 0.0713071i
\(218\) 21.6971 1.46952
\(219\) 0.0147083 + 0.0452676i 0.000993898 + 0.00305890i
\(220\) −1.55138 + 4.77466i −0.104594 + 0.321907i
\(221\) −1.19374 + 0.867300i −0.0802994 + 0.0583409i
\(222\) 3.05370 0.204951
\(223\) −7.32415 −0.490461 −0.245231 0.969465i \(-0.578864\pi\)
−0.245231 + 0.969465i \(0.578864\pi\)
\(224\) 0.459797 0.334062i 0.0307215 0.0223205i
\(225\) −4.37747 3.18042i −0.291831 0.212028i
\(226\) −5.08904 3.69741i −0.338518 0.245948i
\(227\) 2.73057 + 8.40382i 0.181234 + 0.557781i 0.999863 0.0165414i \(-0.00526554\pi\)
−0.818629 + 0.574323i \(0.805266\pi\)
\(228\) 0.560926 0.407536i 0.0371482 0.0269897i
\(229\) 2.09978 + 6.46245i 0.138757 + 0.427051i 0.996155 0.0876027i \(-0.0279206\pi\)
−0.857398 + 0.514653i \(0.827921\pi\)
\(230\) 5.98609 18.4233i 0.394711 1.21480i
\(231\) −0.211121 0.153388i −0.0138907 0.0100922i
\(232\) 4.76246 14.6573i 0.312670 0.962301i
\(233\) 5.90586 18.1764i 0.386906 1.19077i −0.548182 0.836359i \(-0.684680\pi\)
0.935088 0.354415i \(-0.115320\pi\)
\(234\) −4.27754 3.10781i −0.279632 0.203164i
\(235\) −0.873084 + 2.68708i −0.0569537 + 0.175285i
\(236\) 0.221397 + 0.681390i 0.0144117 + 0.0443547i
\(237\) −2.70758 + 1.96717i −0.175876 + 0.127781i
\(238\) −0.0751664 0.231338i −0.00487231 0.0149954i
\(239\) 2.34985 + 1.70726i 0.151999 + 0.110434i 0.661185 0.750223i \(-0.270054\pi\)
−0.509187 + 0.860656i \(0.670054\pi\)
\(240\) 0.928719 + 0.674754i 0.0599485 + 0.0435552i
\(241\) −12.1666 + 8.83958i −0.783722 + 0.569408i −0.906094 0.423077i \(-0.860950\pi\)
0.122371 + 0.992484i \(0.460950\pi\)
\(242\) −22.8928 −1.47161
\(243\) −6.29764 −0.403994
\(244\) 1.55361 1.12877i 0.0994599 0.0722618i
\(245\) 3.82410 11.7694i 0.244313 0.751918i
\(246\) −1.00695 3.09907i −0.0642007 0.197590i
\(247\) −8.26508 −0.525895
\(248\) −17.0627 0.353951i −1.08348 0.0224759i
\(249\) 0.335094 0.0212357
\(250\) −4.57534 14.0815i −0.289370 0.890590i
\(251\) −7.70800 + 23.7228i −0.486525 + 1.49737i 0.343236 + 0.939249i \(0.388477\pi\)
−0.829761 + 0.558120i \(0.811523\pi\)
\(252\) −0.245985 + 0.178719i −0.0154956 + 0.0112582i
\(253\) −48.8432 −3.07075
\(254\) 3.07879 0.193181
\(255\) −0.344228 + 0.250096i −0.0215564 + 0.0156616i
\(256\) 9.31336 + 6.76655i 0.582085 + 0.422909i
\(257\) −16.7731 12.1863i −1.04627 0.760163i −0.0747739 0.997201i \(-0.523823\pi\)
−0.971500 + 0.237038i \(0.923823\pi\)
\(258\) 0.145583 + 0.448059i 0.00906362 + 0.0278949i
\(259\) −1.69355 + 1.23044i −0.105232 + 0.0764555i
\(260\) 0.419333 + 1.29057i 0.0260059 + 0.0800380i
\(261\) −4.57216 + 14.0717i −0.283010 + 0.871014i
\(262\) −6.27909 4.56203i −0.387924 0.281843i
\(263\) −4.32462 + 13.3098i −0.266667 + 0.820717i 0.724637 + 0.689130i \(0.242007\pi\)
−0.991305 + 0.131587i \(0.957993\pi\)
\(264\) 1.23740 3.80832i 0.0761566 0.234386i
\(265\) 8.21321 + 5.96725i 0.504534 + 0.366565i
\(266\) 0.421037 1.29582i 0.0258154 0.0794517i
\(267\) 0.788357 + 2.42631i 0.0482467 + 0.148488i
\(268\) −0.996467 + 0.723976i −0.0608689 + 0.0442239i
\(269\) 6.69581 + 20.6076i 0.408251 + 1.25647i 0.918150 + 0.396233i \(0.129683\pi\)
−0.509899 + 0.860234i \(0.670317\pi\)
\(270\) −2.49096 1.80979i −0.151595 0.110140i
\(271\) −25.7994 18.7444i −1.56720 1.13864i −0.929774 0.368132i \(-0.879998\pi\)
−0.637430 0.770508i \(-0.720002\pi\)
\(272\) 2.18271 1.58583i 0.132346 0.0961551i
\(273\) −0.0705365 −0.00426906
\(274\) 22.4754 1.35779
\(275\) −8.12049 + 5.89988i −0.489684 + 0.355776i
\(276\) 0.342237 1.05330i 0.0206003 0.0634011i
\(277\) −4.06760 12.5188i −0.244398 0.752180i −0.995735 0.0922613i \(-0.970591\pi\)
0.751337 0.659919i \(-0.229409\pi\)
\(278\) −19.1181 −1.14663
\(279\) 16.3809 + 0.339808i 0.980700 + 0.0203438i
\(280\) −1.08867 −0.0650608
\(281\) −8.04158 24.7494i −0.479721 1.47643i −0.839484 0.543385i \(-0.817143\pi\)
0.359763 0.933044i \(-0.382857\pi\)
\(282\) 0.143092 0.440393i 0.00852102 0.0262250i
\(283\) 21.5688 15.6706i 1.28213 0.931523i 0.282516 0.959263i \(-0.408831\pi\)
0.999615 + 0.0277396i \(0.00883094\pi\)
\(284\) 3.74725 0.222358
\(285\) −2.38334 −0.141177
\(286\) −7.93512 + 5.76520i −0.469213 + 0.340904i
\(287\) 1.80716 + 1.31298i 0.106673 + 0.0775028i
\(288\) −6.77347 4.92121i −0.399130 0.289985i
\(289\) 0.309017 + 0.951057i 0.0181775 + 0.0559445i
\(290\) −8.80669 + 6.39844i −0.517147 + 0.375729i
\(291\) 0.473348 + 1.45682i 0.0277482 + 0.0854001i
\(292\) 0.0317908 0.0978420i 0.00186042 0.00572577i
\(293\) 20.3866 + 14.8117i 1.19100 + 0.865309i 0.993369 0.114969i \(-0.0366768\pi\)
0.197626 + 0.980277i \(0.436677\pi\)
\(294\) −0.626743 + 1.92892i −0.0365524 + 0.112497i
\(295\) 0.761043 2.34225i 0.0443097 0.136371i
\(296\) −25.9867 18.8805i −1.51045 1.09740i
\(297\) −2.39903 + 7.38345i −0.139206 + 0.428431i
\(298\) 6.06796 + 18.6753i 0.351508 + 1.08183i
\(299\) −10.6808 + 7.76003i −0.617685 + 0.448774i
\(300\) −0.0703312 0.216457i −0.00406057 0.0124972i
\(301\) −0.261277 0.189829i −0.0150598 0.0109416i
\(302\) 8.79964 + 6.39331i 0.506362 + 0.367894i
\(303\) 1.17580 0.854266i 0.0675477 0.0490763i
\(304\) 15.1124 0.866758
\(305\) −6.60120 −0.377984
\(306\) −2.89897 + 2.10622i −0.165723 + 0.120405i
\(307\) 6.18208 19.0265i 0.352830 1.08590i −0.604427 0.796660i \(-0.706598\pi\)
0.957257 0.289238i \(-0.0934020\pi\)
\(308\) 0.174298 + 0.536435i 0.00993156 + 0.0305662i
\(309\) −0.102343 −0.00582208
\(310\) 9.60321 + 7.28617i 0.545426 + 0.413827i
\(311\) 2.88523 0.163607 0.0818033 0.996648i \(-0.473932\pi\)
0.0818033 + 0.996648i \(0.473932\pi\)
\(312\) −0.334464 1.02938i −0.0189353 0.0582769i
\(313\) 5.41701 16.6718i 0.306187 0.942348i −0.673044 0.739602i \(-0.735014\pi\)
0.979231 0.202746i \(-0.0649865\pi\)
\(314\) 20.2774 14.7324i 1.14432 0.831399i
\(315\) 1.04517 0.0588889
\(316\) 7.23370 0.406927
\(317\) −13.4919 + 9.80247i −0.757783 + 0.550561i −0.898229 0.439527i \(-0.855146\pi\)
0.140447 + 0.990088i \(0.455146\pi\)
\(318\) −1.34609 0.977990i −0.0754848 0.0548429i
\(319\) 22.2053 + 16.1331i 1.24326 + 0.903279i
\(320\) −4.86820 14.9828i −0.272141 0.837564i
\(321\) −1.28804 + 0.935816i −0.0718914 + 0.0522322i
\(322\) −0.672540 2.06986i −0.0374792 0.115349i
\(323\) −1.73093 + 5.32725i −0.0963114 + 0.296416i
\(324\) 3.55181 + 2.58054i 0.197323 + 0.143364i
\(325\) −0.838393 + 2.58031i −0.0465057 + 0.143130i
\(326\) 6.80153 20.9330i 0.376702 1.15937i
\(327\) −3.44971 2.50636i −0.190769 0.138602i
\(328\) −10.5919 + 32.5987i −0.584842 + 1.79996i
\(329\) 0.0980913 + 0.301894i 0.00540795 + 0.0166440i
\(330\) −2.28819 + 1.66246i −0.125961 + 0.0915157i
\(331\) 3.12470 + 9.61684i 0.171749 + 0.528589i 0.999470 0.0325506i \(-0.0103630\pi\)
−0.827721 + 0.561140i \(0.810363\pi\)
\(332\) −0.585951 0.425718i −0.0321582 0.0233643i
\(333\) 24.9484 + 18.1261i 1.36716 + 0.993302i
\(334\) 4.55301 3.30795i 0.249129 0.181003i
\(335\) 4.23392 0.231324
\(336\) 0.128974 0.00703609
\(337\) 0.137700 0.100045i 0.00750101 0.00544980i −0.584028 0.811733i \(-0.698524\pi\)
0.591529 + 0.806283i \(0.298524\pi\)
\(338\) 4.07246 12.5337i 0.221512 0.681745i
\(339\) 0.382017 + 1.17573i 0.0207483 + 0.0638567i
\(340\) 0.919657 0.0498754
\(341\) 9.98982 28.7056i 0.540979 1.55450i
\(342\) −20.0716 −1.08535
\(343\) −0.861742 2.65217i −0.0465297 0.143204i
\(344\) 1.53137 4.71307i 0.0825659 0.254112i
\(345\) −3.07993 + 2.23770i −0.165818 + 0.120474i
\(346\) 16.5314 0.888734
\(347\) 15.4448 0.829120 0.414560 0.910022i \(-0.363936\pi\)
0.414560 + 0.910022i \(0.363936\pi\)
\(348\) −0.503497 + 0.365812i −0.0269903 + 0.0196096i
\(349\) −5.12666 3.72474i −0.274424 0.199381i 0.442058 0.896987i \(-0.354249\pi\)
−0.716482 + 0.697606i \(0.754249\pi\)
\(350\) −0.361837 0.262890i −0.0193410 0.0140521i
\(351\) 0.648449 + 1.99572i 0.0346117 + 0.106524i
\(352\) −12.5652 + 9.12917i −0.669729 + 0.486586i
\(353\) 0.581150 + 1.78859i 0.0309315 + 0.0951973i 0.965330 0.261031i \(-0.0840625\pi\)
−0.934399 + 0.356228i \(0.884063\pi\)
\(354\) −0.124730 + 0.383878i −0.00662930 + 0.0204029i
\(355\) −10.4210 7.57127i −0.553087 0.401841i
\(356\) 1.70396 5.24426i 0.0903099 0.277945i
\(357\) −0.0147722 + 0.0454642i −0.000781828 + 0.00240622i
\(358\) −15.1902 11.0364i −0.802829 0.583289i
\(359\) 6.21907 19.1403i 0.328230 1.01019i −0.641731 0.766930i \(-0.721784\pi\)
0.969961 0.243259i \(-0.0782164\pi\)
\(360\) 4.95593 + 15.2528i 0.261200 + 0.803892i
\(361\) −10.0121 + 7.27424i −0.526954 + 0.382855i
\(362\) 8.96508 + 27.5917i 0.471194 + 1.45019i
\(363\) 3.63981 + 2.64447i 0.191040 + 0.138799i
\(364\) 0.123341 + 0.0896128i 0.00646485 + 0.00469699i
\(365\) −0.286098 + 0.207862i −0.0149750 + 0.0108800i
\(366\) 1.08189 0.0565513
\(367\) −20.6712 −1.07903 −0.539513 0.841977i \(-0.681392\pi\)
−0.539513 + 0.841977i \(0.681392\pi\)
\(368\) 19.5294 14.1890i 1.01804 0.739651i
\(369\) 10.1687 31.2961i 0.529362 1.62921i
\(370\) 7.01105 + 21.5778i 0.364487 + 1.12178i
\(371\) 1.14059 0.0592165
\(372\) 0.549036 + 0.416566i 0.0284662 + 0.0215979i
\(373\) −17.0920 −0.884991 −0.442496 0.896771i \(-0.645907\pi\)
−0.442496 + 0.896771i \(0.645907\pi\)
\(374\) 2.05413 + 6.32196i 0.106216 + 0.326901i
\(375\) −0.899178 + 2.76738i −0.0464333 + 0.142907i
\(376\) −3.94057 + 2.86300i −0.203220 + 0.147648i
\(377\) 7.41889 0.382092
\(378\) −0.345927 −0.0177926
\(379\) 21.5113 15.6289i 1.10496 0.802801i 0.123098 0.992394i \(-0.460717\pi\)
0.981863 + 0.189593i \(0.0607169\pi\)
\(380\) 4.16754 + 3.02790i 0.213790 + 0.155328i
\(381\) −0.489508 0.355649i −0.0250783 0.0182204i
\(382\) −4.28075 13.1748i −0.219022 0.674081i
\(383\) −4.49859 + 3.26841i −0.229867 + 0.167008i −0.696757 0.717307i \(-0.745374\pi\)
0.466890 + 0.884315i \(0.345374\pi\)
\(384\) 0.377068 + 1.16050i 0.0192422 + 0.0592213i
\(385\) 0.599143 1.84397i 0.0305352 0.0939775i
\(386\) −22.1377 16.0840i −1.12678 0.818654i
\(387\) −1.47018 + 4.52475i −0.0747334 + 0.230006i
\(388\) 1.02310 3.14878i 0.0519401 0.159855i
\(389\) −2.78238 2.02152i −0.141072 0.102495i 0.515011 0.857184i \(-0.327788\pi\)
−0.656083 + 0.754689i \(0.727788\pi\)
\(390\) −0.236242 + 0.727078i −0.0119626 + 0.0368170i
\(391\) 2.76488 + 8.50943i 0.139826 + 0.430340i
\(392\) 17.2597 12.5399i 0.871746 0.633361i
\(393\) 0.471350 + 1.45067i 0.0237764 + 0.0731764i
\(394\) 11.8397 + 8.60202i 0.596474 + 0.433363i
\(395\) −20.1167 14.6156i −1.01218 0.735391i
\(396\) 6.72222 4.88398i 0.337804 0.245429i
\(397\) −13.9725 −0.701259 −0.350629 0.936514i \(-0.614032\pi\)
−0.350629 + 0.936514i \(0.614032\pi\)
\(398\) −2.15443 −0.107992
\(399\) −0.216629 + 0.157390i −0.0108450 + 0.00787938i
\(400\) 1.53297 4.71801i 0.0766487 0.235900i
\(401\) 5.12275 + 15.7662i 0.255818 + 0.787326i 0.993667 + 0.112361i \(0.0358414\pi\)
−0.737850 + 0.674965i \(0.764159\pi\)
\(402\) −0.693910 −0.0346091
\(403\) −2.37612 7.86433i −0.118363 0.391750i
\(404\) −3.14132 −0.156286
\(405\) −4.66351 14.3528i −0.231732 0.713196i
\(406\) −0.377931 + 1.16315i −0.0187564 + 0.0577262i
\(407\) 46.2809 33.6250i 2.29406 1.66673i
\(408\) −0.733528 −0.0363151
\(409\) −8.15547 −0.403262 −0.201631 0.979462i \(-0.564624\pi\)
−0.201631 + 0.979462i \(0.564624\pi\)
\(410\) 19.5865 14.2305i 0.967310 0.702792i
\(411\) −3.57344 2.59625i −0.176265 0.128064i
\(412\) 0.178959 + 0.130021i 0.00881666 + 0.00640568i
\(413\) −0.0855035 0.263153i −0.00420735 0.0129489i
\(414\) −25.9381 + 18.8451i −1.27479 + 0.926186i
\(415\) 0.769349 + 2.36781i 0.0377659 + 0.116231i
\(416\) −1.29729 + 3.99264i −0.0636047 + 0.195755i
\(417\) 3.03965 + 2.20843i 0.148852 + 0.108147i
\(418\) −11.5060 + 35.4118i −0.562776 + 1.73205i
\(419\) 4.70716 14.4872i 0.229960 0.707744i −0.767790 0.640701i \(-0.778644\pi\)
0.997750 0.0670425i \(-0.0213563\pi\)
\(420\) 0.0355670 + 0.0258409i 0.00173549 + 0.00126091i
\(421\) 1.15327 3.54940i 0.0562070 0.172987i −0.919012 0.394230i \(-0.871011\pi\)
0.975219 + 0.221243i \(0.0710113\pi\)
\(422\) 2.12784 + 6.54883i 0.103582 + 0.318792i
\(423\) 3.78312 2.74860i 0.183942 0.133641i
\(424\) 5.40837 + 16.6452i 0.262653 + 0.808364i
\(425\) 1.48755 + 1.08077i 0.0721569 + 0.0524250i
\(426\) 1.70792 + 1.24088i 0.0827490 + 0.0601207i
\(427\) −0.600005 + 0.435929i −0.0290363 + 0.0210961i
\(428\) 3.44119 0.166336
\(429\) 1.92760 0.0930655
\(430\) −2.83179 + 2.05742i −0.136561 + 0.0992176i
\(431\) −5.55882 + 17.1083i −0.267759 + 0.824077i 0.723286 + 0.690548i \(0.242631\pi\)
−0.991045 + 0.133528i \(0.957369\pi\)
\(432\) −1.18567 3.64911i −0.0570455 0.175568i
\(433\) 16.8123 0.807945 0.403973 0.914771i \(-0.367629\pi\)
0.403973 + 0.914771i \(0.367629\pi\)
\(434\) 1.35403 + 0.0280883i 0.0649956 + 0.00134828i
\(435\) 2.13933 0.102573
\(436\) 2.84803 + 8.76533i 0.136396 + 0.419783i
\(437\) −15.4872 + 47.6647i −0.740854 + 2.28011i
\(438\) 0.0468894 0.0340671i 0.00224046 0.00162779i
\(439\) 23.2212 1.10829 0.554144 0.832421i \(-0.313046\pi\)
0.554144 + 0.832421i \(0.313046\pi\)
\(440\) 29.7510 1.41832
\(441\) −16.5700 + 12.0388i −0.789050 + 0.573278i
\(442\) 1.45360 + 1.05610i 0.0691405 + 0.0502335i
\(443\) −6.26858 4.55439i −0.297829 0.216386i 0.428827 0.903386i \(-0.358927\pi\)
−0.726657 + 0.687001i \(0.758927\pi\)
\(444\) 0.400836 + 1.23365i 0.0190229 + 0.0585463i
\(445\) −15.3346 + 11.1413i −0.726931 + 0.528147i
\(446\) 2.75597 + 8.48200i 0.130499 + 0.401635i
\(447\) 1.19252 3.67019i 0.0564041 0.173594i
\(448\) −1.43192 1.04035i −0.0676518 0.0491519i
\(449\) −1.59431 + 4.90679i −0.0752402 + 0.231566i −0.981603 0.190936i \(-0.938848\pi\)
0.906362 + 0.422501i \(0.138848\pi\)
\(450\) −2.03602 + 6.26623i −0.0959790 + 0.295393i
\(451\) −49.3857 35.8808i −2.32548 1.68956i
\(452\) 0.825696 2.54123i 0.0388375 0.119529i
\(453\) −0.660559 2.03299i −0.0310358 0.0955182i
\(454\) 8.70489 6.32447i 0.408541 0.296822i
\(455\) −0.161946 0.498420i −0.00759216 0.0233663i
\(456\) −3.32408 2.41508i −0.155664 0.113097i
\(457\) 19.4922 + 14.1619i 0.911807 + 0.662467i 0.941471 0.337093i \(-0.109444\pi\)
−0.0296642 + 0.999560i \(0.509444\pi\)
\(458\) 6.69397 4.86345i 0.312789 0.227254i
\(459\) 1.42214 0.0663799
\(460\) 8.22849 0.383655
\(461\) 16.1297 11.7189i 0.751233 0.545803i −0.144976 0.989435i \(-0.546310\pi\)
0.896209 + 0.443632i \(0.146310\pi\)
\(462\) −0.0981953 + 0.302214i −0.00456846 + 0.0140603i
\(463\) 3.89284 + 11.9809i 0.180916 + 0.556802i 0.999854 0.0170799i \(-0.00543698\pi\)
−0.818938 + 0.573882i \(0.805437\pi\)
\(464\) −13.5652 −0.629749
\(465\) −0.685183 2.26777i −0.0317746 0.105166i
\(466\) −23.2721 −1.07806
\(467\) 0.536439 + 1.65099i 0.0248234 + 0.0763986i 0.962701 0.270568i \(-0.0872116\pi\)
−0.937877 + 0.346967i \(0.887212\pi\)
\(468\) 0.694030 2.13600i 0.0320815 0.0987368i
\(469\) 0.384836 0.279599i 0.0177701 0.0129107i
\(470\) 3.44040 0.158694
\(471\) −4.92580 −0.226969
\(472\) 3.43489 2.49559i 0.158104 0.114869i
\(473\) 7.14011 + 5.18759i 0.328303 + 0.238526i
\(474\) 3.29698 + 2.39539i 0.151435 + 0.110024i
\(475\) 3.18268 + 9.79529i 0.146032 + 0.449439i
\(476\) 0.0835907 0.0607322i 0.00383137 0.00278366i
\(477\) −5.19226 15.9801i −0.237737 0.731680i
\(478\) 1.09295 3.36375i 0.0499902 0.153854i
\(479\) 33.6753 + 24.4665i 1.53866 + 1.11790i 0.951168 + 0.308675i \(0.0998855\pi\)
0.587494 + 0.809228i \(0.300115\pi\)
\(480\) −0.374088 + 1.15132i −0.0170747 + 0.0525505i
\(481\) 4.77823 14.7059i 0.217868 0.670530i
\(482\) 14.8151 + 10.7638i 0.674811 + 0.490279i
\(483\) −0.132172 + 0.406784i −0.00601404 + 0.0185093i
\(484\) −3.00497 9.24835i −0.136590 0.420380i
\(485\) −9.20728 + 6.68948i −0.418081 + 0.303754i
\(486\) 2.36971 + 7.29322i 0.107492 + 0.330827i
\(487\) 0.0580922 + 0.0422065i 0.00263241 + 0.00191256i 0.589101 0.808060i \(-0.299482\pi\)
−0.586468 + 0.809972i \(0.699482\pi\)
\(488\) −9.20680 6.68913i −0.416772 0.302803i
\(489\) −3.49948 + 2.54252i −0.158252 + 0.114977i
\(490\) −15.0689 −0.680744
\(491\) 28.2983 1.27708 0.638542 0.769587i \(-0.279538\pi\)
0.638542 + 0.769587i \(0.279538\pi\)
\(492\) 1.11980 0.813585i 0.0504846 0.0366792i
\(493\) 1.55371 4.78184i 0.0699757 0.215363i
\(494\) 3.11003 + 9.57169i 0.139927 + 0.430651i
\(495\) −28.5623 −1.28378
\(496\) 4.34466 + 14.3797i 0.195081 + 0.645667i
\(497\) −1.44719 −0.0649152
\(498\) −0.126091 0.388068i −0.00565027 0.0173897i
\(499\) 7.54410 23.2184i 0.337720 1.03940i −0.627646 0.778499i \(-0.715981\pi\)
0.965366 0.260898i \(-0.0840186\pi\)
\(500\) 5.08813 3.69674i 0.227548 0.165323i
\(501\) −1.10602 −0.0494133
\(502\) 30.3735 1.35563
\(503\) 30.5047 22.1630i 1.36014 0.988197i 0.361701 0.932294i \(-0.382196\pi\)
0.998436 0.0559030i \(-0.0178038\pi\)
\(504\) 1.45772 + 1.05910i 0.0649321 + 0.0471759i
\(505\) 8.73589 + 6.34699i 0.388742 + 0.282438i
\(506\) 18.3790 + 56.5647i 0.817046 + 2.51461i
\(507\) −2.09534 + 1.52235i −0.0930571 + 0.0676099i
\(508\) 0.404131 + 1.24379i 0.0179304 + 0.0551841i
\(509\) −8.63231 + 26.5675i −0.382620 + 1.17758i 0.555571 + 0.831469i \(0.312500\pi\)
−0.938192 + 0.346116i \(0.887500\pi\)
\(510\) 0.419161 + 0.304539i 0.0185608 + 0.0134852i
\(511\) −0.0122776 + 0.0377866i −0.000543129 + 0.00167158i
\(512\) 7.48310 23.0306i 0.330709 1.01782i
\(513\) 6.44462 + 4.68229i 0.284537 + 0.206728i
\(514\) −7.80139 + 24.0102i −0.344104 + 1.05904i
\(515\) −0.234971 0.723167i −0.0103541 0.0318666i
\(516\) −0.161900 + 0.117627i −0.00712723 + 0.00517824i
\(517\) −2.68061 8.25008i −0.117893 0.362838i
\(518\) 2.06221 + 1.49828i 0.0906083 + 0.0658308i
\(519\) −2.62839 1.90963i −0.115373 0.0838237i
\(520\) 6.50579 4.72674i 0.285298 0.207281i
\(521\) −17.7074 −0.775774 −0.387887 0.921707i \(-0.626795\pi\)
−0.387887 + 0.921707i \(0.626795\pi\)
\(522\) 18.0167 0.788568
\(523\) 3.89900 2.83279i 0.170491 0.123869i −0.499267 0.866448i \(-0.666397\pi\)
0.669759 + 0.742579i \(0.266397\pi\)
\(524\) 1.01878 3.13548i 0.0445056 0.136974i
\(525\) 0.0271619 + 0.0835957i 0.00118544 + 0.00364842i
\(526\) 17.0412 0.743032
\(527\) −5.56657 0.115474i −0.242483 0.00503012i
\(528\) −3.52456 −0.153387
\(529\) 17.6310 + 54.2625i 0.766563 + 2.35924i
\(530\) 3.82008 11.7570i 0.165934 0.510692i
\(531\) −3.29764 + 2.39588i −0.143106 + 0.103972i
\(532\) 0.578758 0.0250923
\(533\) −16.5000 −0.714694
\(534\) 2.51324 1.82597i 0.108758 0.0790176i
\(535\) −9.56984 6.95289i −0.413740 0.300600i
\(536\) 5.90512 + 4.29032i 0.255063 + 0.185314i
\(537\) 1.14028 + 3.50942i 0.0492067 + 0.151443i
\(538\) 21.3459 15.5087i 0.920286 0.668627i
\(539\) 11.7411 + 36.1353i 0.505724 + 1.55646i
\(540\) 0.404158 1.24387i 0.0173922 0.0535277i
\(541\) −9.16307 6.65736i −0.393951 0.286222i 0.373122 0.927782i \(-0.378287\pi\)
−0.767073 + 0.641560i \(0.778287\pi\)
\(542\) −11.9997 + 36.9312i −0.515431 + 1.58633i
\(543\) 1.76188 5.42250i 0.0756094 0.232702i
\(544\) 2.30176 + 1.67233i 0.0986872 + 0.0717005i
\(545\) 9.78998 30.1305i 0.419357 1.29065i
\(546\) 0.0265419 + 0.0816874i 0.00113589 + 0.00349590i
\(547\) −30.7609 + 22.3491i −1.31524 + 0.955579i −0.315263 + 0.949004i \(0.602093\pi\)
−0.999978 + 0.00657462i \(0.997907\pi\)
\(548\) 2.95018 + 9.07971i 0.126025 + 0.387866i
\(549\) 8.83892 + 6.42185i 0.377236 + 0.274078i
\(550\) 9.88820 + 7.18420i 0.421634 + 0.306335i
\(551\) 22.7847 16.5540i 0.970659 0.705225i
\(552\) −6.56313 −0.279345
\(553\) −2.79365 −0.118798
\(554\) −12.9673 + 9.42127i −0.550926 + 0.400271i
\(555\) 1.37786 4.24061i 0.0584869 0.180004i
\(556\) −2.50949 7.72342i −0.106426 0.327546i
\(557\) −42.6565 −1.80741 −0.903707 0.428151i \(-0.859165\pi\)
−0.903707 + 0.428151i \(0.859165\pi\)
\(558\) −5.77037 19.0984i −0.244279 0.808500i
\(559\) 2.38555 0.100898
\(560\) 0.296114 + 0.911344i 0.0125131 + 0.0385113i
\(561\) 0.403691 1.24243i 0.0170439 0.0524556i
\(562\) −25.6361 + 18.6257i −1.08139 + 0.785678i
\(563\) −26.8921 −1.13337 −0.566683 0.823936i \(-0.691773\pi\)
−0.566683 + 0.823936i \(0.691773\pi\)
\(564\) 0.196695 0.00828234
\(565\) −7.43075 + 5.39876i −0.312614 + 0.227128i
\(566\) −26.2640 19.0819i −1.10396 0.802072i
\(567\) −1.37171 0.996606i −0.0576064 0.0418535i
\(568\) −6.86215 21.1195i −0.287930 0.886156i
\(569\) −21.6052 + 15.6971i −0.905739 + 0.658058i −0.939934 0.341358i \(-0.889113\pi\)
0.0341949 + 0.999415i \(0.489113\pi\)
\(570\) 0.896814 + 2.76011i 0.0375634 + 0.115608i
\(571\) −3.20136 + 9.85277i −0.133973 + 0.412326i −0.995429 0.0955064i \(-0.969553\pi\)
0.861456 + 0.507832i \(0.169553\pi\)
\(572\) −3.37064 2.44891i −0.140934 0.102394i
\(573\) −0.841282 + 2.58920i −0.0351451 + 0.108165i
\(574\) 0.840537 2.58691i 0.0350833 0.107975i
\(575\) 13.3096 + 9.67002i 0.555050 + 0.403268i
\(576\) −8.05727 + 24.7977i −0.335719 + 1.03324i
\(577\) 11.2257 + 34.5492i 0.467333 + 1.43830i 0.856024 + 0.516936i \(0.172927\pi\)
−0.388691 + 0.921368i \(0.627073\pi\)
\(578\) 0.985128 0.715737i 0.0409759 0.0297708i
\(579\) 1.66180 + 5.11450i 0.0690621 + 0.212551i
\(580\) −3.74086 2.71790i −0.155331 0.112855i
\(581\) 0.226294 + 0.164412i 0.00938826 + 0.00682097i
\(582\) 1.50901 1.09636i 0.0625504 0.0454455i
\(583\) −31.1698 −1.29092
\(584\) −0.609656 −0.0252277
\(585\) −6.24584 + 4.53787i −0.258234 + 0.187618i
\(586\) 9.48208 29.1828i 0.391701 1.20553i
\(587\) 8.85084 + 27.2401i 0.365313 + 1.12432i 0.949785 + 0.312904i \(0.101302\pi\)
−0.584471 + 0.811414i \(0.698698\pi\)
\(588\) −0.861522 −0.0355286
\(589\) −24.8454 18.8508i −1.02374 0.776732i
\(590\) −2.99890 −0.123463
\(591\) −0.888763 2.73533i −0.0365588 0.112516i
\(592\) −8.73684 + 26.8892i −0.359082 + 1.10514i
\(593\) 32.1665 23.3703i 1.32092 0.959705i 0.321001 0.947079i \(-0.395981\pi\)
0.999920 0.0126262i \(-0.00401915\pi\)
\(594\) 9.45340 0.387878
\(595\) −0.355171 −0.0145606
\(596\) −6.74804 + 4.90274i −0.276410 + 0.200824i
\(597\) 0.342540 + 0.248870i 0.0140192 + 0.0101856i
\(598\) 13.0058 + 9.44928i 0.531847 + 0.386410i
\(599\) 0.0942623 + 0.290110i 0.00385145 + 0.0118536i 0.952964 0.303084i \(-0.0980163\pi\)
−0.949112 + 0.314938i \(0.898016\pi\)
\(600\) −1.09116 + 0.792775i −0.0445465 + 0.0323649i
\(601\) −11.3033 34.7881i −0.461072 1.41903i −0.863856 0.503739i \(-0.831957\pi\)
0.402784 0.915295i \(-0.368043\pi\)
\(602\) −0.121524 + 0.374011i −0.00495294 + 0.0152436i
\(603\) −5.66917 4.11889i −0.230867 0.167734i
\(604\) −1.42774 + 4.39413i −0.0580939 + 0.178795i
\(605\) −10.3295 + 31.7908i −0.419953 + 1.29248i
\(606\) −1.43175 1.04023i −0.0581609 0.0422563i
\(607\) 7.87786 24.2456i 0.319752 0.984097i −0.654002 0.756493i \(-0.726911\pi\)
0.973754 0.227603i \(-0.0730890\pi\)
\(608\) 4.92472 + 15.1567i 0.199724 + 0.614687i
\(609\) 0.194451 0.141277i 0.00787953 0.00572482i
\(610\) 2.48394 + 7.64477i 0.100572 + 0.309528i
\(611\) −1.89693 1.37820i −0.0767414 0.0557559i
\(612\) −1.23141 0.894671i −0.0497768 0.0361649i
\(613\) −1.60620 + 1.16697i −0.0648737 + 0.0471335i −0.619749 0.784800i \(-0.712766\pi\)
0.554876 + 0.831933i \(0.312766\pi\)
\(614\) −24.3606 −0.983112
\(615\) −4.75797 −0.191860
\(616\) 2.70417 1.96470i 0.108954 0.0791598i
\(617\) 2.32028 7.14110i 0.0934111 0.287490i −0.893425 0.449212i \(-0.851705\pi\)
0.986836 + 0.161722i \(0.0517048\pi\)
\(618\) 0.0385101 + 0.118522i 0.00154910 + 0.00476765i
\(619\) −25.3824 −1.02020 −0.510102 0.860114i \(-0.670392\pi\)
−0.510102 + 0.860114i \(0.670392\pi\)
\(620\) −1.68296 + 4.83596i −0.0675893 + 0.194217i
\(621\) 12.7244 0.510612
\(622\) −1.08567 3.34135i −0.0435315 0.133976i
\(623\) −0.658071 + 2.02533i −0.0263650 + 0.0811433i
\(624\) −0.770732 + 0.559969i −0.0308540 + 0.0224167i
\(625\) −12.4255 −0.497022
\(626\) −21.3458 −0.853149
\(627\) 5.91999 4.30113i 0.236422 0.171770i
\(628\) 8.61335 + 6.25797i 0.343710 + 0.249720i
\(629\) −8.47796 6.15960i −0.338039 0.245599i
\(630\) −0.393284 1.21040i −0.0156688 0.0482236i
\(631\) 33.6782 24.4686i 1.34071 0.974081i 0.341290 0.939958i \(-0.389136\pi\)
0.999418 0.0341228i \(-0.0108637\pi\)
\(632\) −13.2467 40.7693i −0.526927 1.62171i
\(633\) 0.418178 1.28702i 0.0166211 0.0511545i
\(634\) 16.4289 + 11.9363i 0.652476 + 0.474052i
\(635\) 1.38918 4.27547i 0.0551281 0.169667i
\(636\) 0.218402 0.672173i 0.00866021 0.0266534i
\(637\) 8.30852 + 6.03649i 0.329196 + 0.239175i
\(638\) 10.3280 31.7863i 0.408889 1.25843i
\(639\) 6.58796 + 20.2757i 0.260616 + 0.802093i
\(640\) −7.33449 + 5.32882i −0.289921 + 0.210640i
\(641\) −14.8672 45.7566i −0.587220 1.80728i −0.590166 0.807282i \(-0.700938\pi\)
0.00294610 0.999996i \(-0.499062\pi\)
\(642\) 1.56843 + 1.13953i 0.0619009 + 0.0449736i
\(643\) −23.8302 17.3137i −0.939772 0.682784i 0.00859384 0.999963i \(-0.497264\pi\)
−0.948366 + 0.317179i \(0.897264\pi\)
\(644\) 0.747915 0.543392i 0.0294720 0.0214126i
\(645\) 0.687901 0.0270861
\(646\) 6.82074 0.268359
\(647\) 16.2427 11.8010i 0.638568 0.463947i −0.220790 0.975321i \(-0.570864\pi\)
0.859358 + 0.511375i \(0.170864\pi\)
\(648\) 8.03972 24.7437i 0.315830 0.972025i
\(649\) 2.33662 + 7.19137i 0.0917203 + 0.282286i
\(650\) 3.30370 0.129582
\(651\) −0.212038 0.160878i −0.00831041 0.00630529i
\(652\) 9.34940 0.366151
\(653\) 9.08720 + 27.9675i 0.355610 + 1.09445i 0.955655 + 0.294488i \(0.0951490\pi\)
−0.600046 + 0.799966i \(0.704851\pi\)
\(654\) −1.60451 + 4.93817i −0.0627412 + 0.193098i
\(655\) −9.16840 + 6.66123i −0.358239 + 0.260276i
\(656\) 30.1697 1.17793
\(657\) 0.585296 0.0228346
\(658\) 0.312709 0.227197i 0.0121907 0.00885705i
\(659\) 14.5674 + 10.5838i 0.567465 + 0.412288i 0.834184 0.551487i \(-0.185939\pi\)
−0.266718 + 0.963775i \(0.585939\pi\)
\(660\) −0.971965 0.706174i −0.0378337 0.0274878i
\(661\) −1.68569 5.18803i −0.0655658 0.201791i 0.912907 0.408169i \(-0.133832\pi\)
−0.978472 + 0.206378i \(0.933832\pi\)
\(662\) 9.96136 7.23735i 0.387159 0.281288i
\(663\) −0.109116 0.335826i −0.00423773 0.0130424i
\(664\) −1.32633 + 4.08203i −0.0514716 + 0.158413i
\(665\) −1.60950 1.16937i −0.0624139 0.0453464i
\(666\) 11.6038 35.7130i 0.449640 1.38385i
\(667\) 13.9016 42.7847i 0.538272 1.65663i
\(668\) 1.93400 + 1.40514i 0.0748289 + 0.0543664i
\(669\) 0.541622 1.66694i 0.0209403 0.0644477i
\(670\) −1.59316 4.90325i −0.0615493 0.189429i
\(671\) 16.3968 11.9130i 0.632991 0.459895i
\(672\) 0.0420289 + 0.129352i 0.00162130 + 0.00498985i
\(673\) −18.2484 13.2582i −0.703422 0.511066i 0.177623 0.984099i \(-0.443159\pi\)
−0.881045 + 0.473032i \(0.843159\pi\)
\(674\) −0.167676 0.121823i −0.00645862 0.00469246i
\(675\) 2.11551 1.53701i 0.0814260 0.0591595i
\(676\) 5.59800 0.215308
\(677\) −23.4823 −0.902499 −0.451250 0.892398i \(-0.649022\pi\)
−0.451250 + 0.892398i \(0.649022\pi\)
\(678\) 1.21785 0.884818i 0.0467712 0.0339812i
\(679\) −0.395121 + 1.21606i −0.0151634 + 0.0466680i
\(680\) −1.68412 5.18320i −0.0645832 0.198767i
\(681\) −2.11460 −0.0810315
\(682\) −37.0026 0.767589i −1.41690 0.0293925i
\(683\) −9.42895 −0.360789 −0.180394 0.983594i \(-0.557737\pi\)
−0.180394 + 0.983594i \(0.557737\pi\)
\(684\) −2.63466 8.10863i −0.100739 0.310041i
\(685\) 10.1411 31.2111i 0.387472 1.19252i
\(686\) −2.74718 + 1.99594i −0.104888 + 0.0762055i
\(687\) −1.62610 −0.0620396
\(688\) −4.36189 −0.166296
\(689\) −6.81604 + 4.95214i −0.259670 + 0.188662i
\(690\) 3.75038 + 2.72481i 0.142775 + 0.103732i
\(691\) 14.9873 + 10.8889i 0.570143 + 0.414233i 0.835157 0.550011i \(-0.185377\pi\)
−0.265014 + 0.964245i \(0.585377\pi\)
\(692\) 2.16996 + 6.67844i 0.0824894 + 0.253876i
\(693\) −2.59612 + 1.88619i −0.0986184 + 0.0716505i
\(694\) −5.81165 17.8864i −0.220607 0.678959i
\(695\) −8.62627 + 26.5489i −0.327213 + 1.00706i
\(696\) 2.98375 + 2.16782i 0.113099 + 0.0821712i
\(697\) −3.45554 + 10.6350i −0.130888 + 0.402831i
\(698\) −2.38448 + 7.33868i −0.0902540 + 0.277773i
\(699\) 3.70012 + 2.68829i 0.139951 + 0.101681i
\(700\) 0.0587080 0.180685i 0.00221895 0.00682924i
\(701\) −2.78210 8.56241i −0.105078 0.323398i 0.884671 0.466217i \(-0.154383\pi\)
−0.989749 + 0.142819i \(0.954383\pi\)
\(702\) 2.06722 1.50192i 0.0780221 0.0566864i
\(703\) −18.1390 55.8260i −0.684124 2.10552i
\(704\) 39.1311 + 28.4304i 1.47481 + 1.07151i
\(705\) −0.547001 0.397419i −0.0206012 0.0149677i
\(706\) 1.85267 1.34604i 0.0697262 0.0506590i
\(707\) 1.21318 0.0456262
\(708\) −0.171453 −0.00644362
\(709\) −6.79383 + 4.93601i −0.255148 + 0.185376i −0.708005 0.706207i \(-0.750405\pi\)
0.452857 + 0.891583i \(0.350405\pi\)
\(710\) −4.84694 + 14.9173i −0.181902 + 0.559838i
\(711\) 12.7174 + 39.1402i 0.476941 + 1.46787i
\(712\) −32.6771 −1.22463
\(713\) −49.8060 1.03318i −1.86525 0.0386930i
\(714\) 0.0582101 0.00217846
\(715\) 4.42563 + 13.6207i 0.165509 + 0.509385i
\(716\) 2.46461 7.58529i 0.0921069 0.283476i
\(717\) −0.562336 + 0.408561i −0.0210008 + 0.0152580i
\(718\) −24.5063 −0.914568
\(719\) 46.9970 1.75269 0.876345 0.481683i \(-0.159974\pi\)
0.876345 + 0.481683i \(0.159974\pi\)
\(720\) 11.4203 8.29734i 0.425610 0.309224i
\(721\) −0.0691138 0.0502141i −0.00257393 0.00187007i
\(722\) 12.1916 + 8.85774i 0.453725 + 0.329651i
\(723\) −1.11212 3.42276i −0.0413603 0.127294i
\(724\) −9.96985 + 7.24352i −0.370526 + 0.269203i
\(725\) −2.85684 8.79244i −0.106100 0.326543i
\(726\) 1.69293 5.21029i 0.0628304 0.193372i
\(727\) −21.7076 15.7715i −0.805092 0.584933i 0.107312 0.994225i \(-0.465776\pi\)
−0.912403 + 0.409292i \(0.865776\pi\)
\(728\) 0.279190 0.859258i 0.0103475 0.0318462i
\(729\) −7.40297 + 22.7840i −0.274184 + 0.843852i
\(730\) 0.348377 + 0.253111i 0.0128940 + 0.00936804i
\(731\) 0.499597 1.53760i 0.0184783 0.0568702i
\(732\) 0.142012 + 0.437067i 0.00524891 + 0.0161545i
\(733\) 8.33003 6.05212i 0.307677 0.223540i −0.423222 0.906026i \(-0.639101\pi\)
0.730899 + 0.682486i \(0.239101\pi\)
\(734\) 7.77826 + 23.9390i 0.287101 + 0.883605i
\(735\) 2.39586 + 1.74069i 0.0883726 + 0.0642065i
\(736\) 20.5947 + 14.9629i 0.759129 + 0.551539i
\(737\) −10.5167 + 7.64082i −0.387387 + 0.281453i
\(738\) −40.0700 −1.47500
\(739\) 11.7142 0.430912 0.215456 0.976514i \(-0.430876\pi\)
0.215456 + 0.976514i \(0.430876\pi\)
\(740\) −7.79682 + 5.66472i −0.286617 + 0.208239i
\(741\) 0.611204 1.88109i 0.0224532 0.0691037i
\(742\) −0.429188 1.32090i −0.0157560 0.0484919i
\(743\) 39.0027 1.43087 0.715434 0.698680i \(-0.246229\pi\)
0.715434 + 0.698680i \(0.246229\pi\)
\(744\) 1.34235 3.85721i 0.0492128 0.141412i
\(745\) 28.6720 1.05046
\(746\) 6.43148 + 19.7941i 0.235473 + 0.724712i
\(747\) 1.27333 3.91892i 0.0465889 0.143386i
\(748\) −2.28435 + 1.65967i −0.0835240 + 0.0606837i
\(749\) −1.32899 −0.0485602
\(750\) 3.54322 0.129380
\(751\) 8.28352 6.01833i 0.302270 0.219612i −0.426303 0.904581i \(-0.640184\pi\)
0.728573 + 0.684969i \(0.240184\pi\)
\(752\) 3.46847 + 2.51999i 0.126482 + 0.0918945i
\(753\) −4.82918 3.50861i −0.175985 0.127861i
\(754\) −2.79162 8.59173i −0.101665 0.312892i
\(755\) 12.8488 9.33518i 0.467615 0.339742i
\(756\) −0.0454073 0.139749i −0.00165145 0.00508263i
\(757\) 13.0225 40.0791i 0.473311 1.45670i −0.374911 0.927061i \(-0.622327\pi\)
0.848222 0.529641i \(-0.177673\pi\)
\(758\) −26.1940 19.0311i −0.951409 0.691239i
\(759\) 3.61196 11.1165i 0.131106 0.403503i
\(760\) 9.43346 29.0332i 0.342187 1.05314i
\(761\) 29.2235 + 21.2321i 1.05935 + 0.769662i 0.973968 0.226686i \(-0.0727891\pi\)
0.0853814 + 0.996348i \(0.472789\pi\)
\(762\) −0.227677 + 0.700719i −0.00824788 + 0.0253844i
\(763\) −1.09991 3.38517i −0.0398193 0.122551i
\(764\) 4.76052 3.45872i 0.172229 0.125132i
\(765\) 1.61683 + 4.97610i 0.0584567 + 0.179911i
\(766\) 5.47786 + 3.97990i 0.197923 + 0.143800i
\(767\) 1.65350 + 1.20134i 0.0597043 + 0.0433777i
\(768\) −2.22876 + 1.61929i −0.0804234 + 0.0584310i
\(769\) 29.8738 1.07728 0.538638 0.842537i \(-0.318939\pi\)
0.538638 + 0.842537i \(0.318939\pi\)
\(770\) −2.36093 −0.0850820
\(771\) 4.01392 2.91629i 0.144558 0.105027i
\(772\) 3.59184 11.0545i 0.129273 0.397862i
\(773\) −1.55429 4.78360i −0.0559038 0.172054i 0.919206 0.393777i \(-0.128832\pi\)
−0.975110 + 0.221723i \(0.928832\pi\)
\(774\) 5.79326 0.208234
\(775\) −8.40536 + 5.84440i −0.301929 + 0.209937i
\(776\) −19.6201 −0.704322
\(777\) −0.154803 0.476435i −0.00555353 0.0170920i
\(778\) −1.29413 + 3.98291i −0.0463967 + 0.142794i
\(779\) −50.6743 + 36.8170i −1.81559 + 1.31911i
\(780\) −0.324738 −0.0116275
\(781\) 39.5483 1.41515
\(782\) 8.81428 6.40395i 0.315198 0.229005i
\(783\) −5.78481 4.20291i −0.206732 0.150200i
\(784\) −15.1919 11.0375i −0.542566 0.394198i
\(785\) −11.3093 34.8063i −0.403645 1.24229i
\(786\) 1.50264 1.09173i 0.0535972 0.0389407i
\(787\) 5.62690 + 17.3178i 0.200577 + 0.617313i 0.999866 + 0.0163662i \(0.00520975\pi\)
−0.799289 + 0.600947i \(0.794790\pi\)
\(788\) −1.92098 + 5.91217i −0.0684321 + 0.210612i
\(789\) −2.70944 1.96852i −0.0964587 0.0700813i
\(790\) −9.35655 + 28.7965i −0.332891 + 1.02453i
\(791\) −0.318884 + 0.981423i −0.0113382 + 0.0348954i
\(792\) −39.8363 28.9427i −1.41552 1.02844i
\(793\) 1.69287 5.21012i 0.0601156 0.185017i
\(794\) 5.25764 + 16.1814i 0.186587 + 0.574255i
\(795\) −1.96549 + 1.42801i −0.0697086 + 0.0506463i
\(796\) −0.282796 0.870357i −0.0100234 0.0308490i
\(797\) −3.39850 2.46915i −0.120381 0.0874618i 0.525966 0.850506i \(-0.323704\pi\)
−0.646347 + 0.763044i \(0.723704\pi\)
\(798\) 0.263786 + 0.191652i 0.00933794 + 0.00678441i
\(799\) −1.28558 + 0.934029i −0.0454806 + 0.0330436i
\(800\) 5.23139 0.184958
\(801\) 31.3715 1.10846
\(802\) 16.3310 11.8652i 0.576668 0.418974i
\(803\) 0.335519 1.03262i 0.0118402 0.0364404i
\(804\) −0.0910845 0.280329i −0.00321230 0.00988646i
\(805\) −3.17784 −0.112004
\(806\) −8.21349 + 5.71099i −0.289308 + 0.201161i
\(807\) −5.18535 −0.182533
\(808\) 5.75255 + 17.7045i 0.202374 + 0.622843i
\(809\) 3.68437 11.3393i 0.129535 0.398669i −0.865165 0.501488i \(-0.832786\pi\)
0.994700 + 0.102819i \(0.0327862\pi\)
\(810\) −14.8670 + 10.8015i −0.522373 + 0.379526i
\(811\) −1.88461 −0.0661775 −0.0330888 0.999452i \(-0.510534\pi\)
−0.0330888 + 0.999452i \(0.510534\pi\)
\(812\) −0.519504 −0.0182310
\(813\) 6.17400 4.48568i 0.216532 0.157320i
\(814\) −56.3555 40.9447i −1.97526 1.43511i
\(815\) −26.0003 18.8903i −0.910752 0.661700i
\(816\) 0.199516 + 0.614046i 0.00698445 + 0.0214959i
\(817\) 7.32641 5.32295i 0.256319 0.186226i
\(818\) 3.06878 + 9.44475i 0.107298 + 0.330228i
\(819\) −0.268034 + 0.824924i −0.00936587 + 0.0288252i
\(820\) 8.31988 + 6.04474i 0.290543 + 0.211092i
\(821\) −2.25465 + 6.93910i −0.0786878 + 0.242176i −0.982660 0.185414i \(-0.940637\pi\)
0.903973 + 0.427590i \(0.140637\pi\)
\(822\) −1.66206 + 5.11528i −0.0579709 + 0.178416i
\(823\) 4.35320 + 3.16279i 0.151743 + 0.110248i 0.661066 0.750328i \(-0.270104\pi\)
−0.509323 + 0.860575i \(0.670104\pi\)
\(824\) 0.405082 1.24671i 0.0141117 0.0434314i
\(825\) −0.742273 2.28448i −0.0258426 0.0795355i
\(826\) −0.272580 + 0.198041i −0.00948428 + 0.00689073i
\(827\) 0.825976 + 2.54209i 0.0287220 + 0.0883972i 0.964390 0.264485i \(-0.0852018\pi\)
−0.935668 + 0.352882i \(0.885202\pi\)
\(828\) −11.0178 8.00493i −0.382897 0.278191i
\(829\) 8.10596 + 5.88933i 0.281532 + 0.204545i 0.719585 0.694404i \(-0.244332\pi\)
−0.438054 + 0.898949i \(0.644332\pi\)
\(830\) 2.45264 1.78195i 0.0851324 0.0618523i
\(831\) 3.15001 0.109273
\(832\) 13.0739 0.453256
\(833\) 5.63084 4.09104i 0.195097 0.141746i
\(834\) 1.41378 4.35118i 0.0489553 0.150669i
\(835\) −2.53933 7.81526i −0.0878773 0.270458i
\(836\) −15.8161 −0.547013
\(837\) −2.60250 + 7.47824i −0.0899555 + 0.258486i
\(838\) −18.5486 −0.640752
\(839\) 3.66837 + 11.2901i 0.126646 + 0.389777i 0.994197 0.107571i \(-0.0343073\pi\)
−0.867551 + 0.497348i \(0.834307\pi\)
\(840\) 0.0805077 0.247777i 0.00277778 0.00854913i
\(841\) 3.00955 2.18657i 0.103778 0.0753989i
\(842\) −4.54448 −0.156613
\(843\) 6.22753 0.214488
\(844\) −2.36632 + 1.71923i −0.0814522 + 0.0591785i
\(845\) −15.5678 11.3107i −0.535550 0.389100i
\(846\) −4.60665 3.34693i −0.158380 0.115070i
\(847\) 1.16052 + 3.57171i 0.0398759 + 0.122725i
\(848\) 12.4629 9.05483i 0.427978 0.310944i
\(849\) 1.97155 + 6.06780i 0.0676633 + 0.208246i
\(850\) 0.691882 2.12939i 0.0237314 0.0730376i
\(851\) −75.8552 55.1121i −2.60028 1.88922i
\(852\) −0.277109 + 0.852855i −0.00949361 + 0.0292183i
\(853\) −1.42040 + 4.37153i −0.0486335 + 0.149678i −0.972424 0.233220i \(-0.925074\pi\)
0.923791 + 0.382898i \(0.125074\pi\)
\(854\) 0.730617 + 0.530825i 0.0250012 + 0.0181644i
\(855\) −9.05652 + 27.8731i −0.309726 + 0.953240i
\(856\) −6.30170 19.3946i −0.215388 0.662895i
\(857\) −12.4143 + 9.01949i −0.424063 + 0.308100i −0.779271 0.626688i \(-0.784410\pi\)
0.355208 + 0.934787i \(0.384410\pi\)
\(858\) −0.725329 2.23233i −0.0247623 0.0762106i
\(859\) −42.6265 30.9700i −1.45440 1.05668i −0.984779 0.173814i \(-0.944391\pi\)
−0.469620 0.882869i \(-0.655609\pi\)
\(860\) −1.20288 0.873940i −0.0410177 0.0298011i
\(861\) −0.432468 + 0.314206i −0.0147385 + 0.0107081i
\(862\) 21.9046 0.746073
\(863\) −52.3577 −1.78228 −0.891139 0.453731i \(-0.850093\pi\)
−0.891139 + 0.453731i \(0.850093\pi\)
\(864\) 3.27343 2.37829i 0.111364 0.0809110i
\(865\) 7.45914 22.9569i 0.253618 0.780557i
\(866\) −6.32621 19.4701i −0.214973 0.661620i
\(867\) −0.239308 −0.00812732
\(868\) 0.166387 + 0.550696i 0.00564753 + 0.0186918i
\(869\) 76.3443 2.58980
\(870\) −0.804997 2.47753i −0.0272920 0.0839960i
\(871\) −1.08579 + 3.34171i −0.0367905 + 0.113229i
\(872\) 44.1861 32.1031i 1.49633 1.08715i
\(873\) 18.8362 0.637508
\(874\) 61.0275 2.06429
\(875\) −1.96503 + 1.42768i −0.0664303 + 0.0482644i
\(876\) 0.0199174 + 0.0144709i 0.000672948 + 0.000488925i
\(877\) 9.38770 + 6.82056i 0.317000 + 0.230314i 0.734894 0.678182i \(-0.237232\pi\)
−0.417894 + 0.908496i \(0.637232\pi\)
\(878\) −8.73781 26.8922i −0.294887 0.907568i
\(879\) −4.87866 + 3.54455i −0.164553 + 0.119555i
\(880\) −8.09212 24.9050i −0.272785 0.839547i
\(881\) 0.157970 0.486180i 0.00532213 0.0163798i −0.948360 0.317195i \(-0.897259\pi\)
0.953682 + 0.300816i \(0.0972589\pi\)
\(882\) 20.1771 + 14.6595i 0.679398 + 0.493612i
\(883\) −4.53642 + 13.9617i −0.152663 + 0.469848i −0.997917 0.0645173i \(-0.979449\pi\)
0.845254 + 0.534365i \(0.179449\pi\)
\(884\) −0.235845 + 0.725857i −0.00793234 + 0.0244132i
\(885\) 0.476806 + 0.346420i 0.0160277 + 0.0116448i
\(886\) −2.91561 + 8.97331i −0.0979517 + 0.301464i
\(887\) −8.98206 27.6439i −0.301588 0.928192i −0.980928 0.194369i \(-0.937734\pi\)
0.679341 0.733823i \(-0.262266\pi\)
\(888\) 6.21883 4.51824i 0.208690 0.151622i
\(889\) −0.156075 0.480351i −0.00523460 0.0161104i
\(890\) 18.6728 + 13.5666i 0.625912 + 0.454752i
\(891\) 37.4857 + 27.2350i 1.25582 + 0.912406i
\(892\) −3.06485 + 2.22674i −0.102619 + 0.0745568i
\(893\) −8.90099 −0.297860
\(894\) −4.69913 −0.157162
\(895\) −22.1800 + 16.1147i −0.741395 + 0.538655i
\(896\) −0.314752 + 0.968708i −0.0105151 + 0.0323623i
\(897\) −0.976302 3.00475i −0.0325978 0.100326i
\(898\) 6.28241 0.209647
\(899\) 22.3017 + 16.9208i 0.743804 + 0.564340i
\(900\) −2.79872 −0.0932907
\(901\) 1.76444 + 5.43038i 0.0587819 + 0.180912i
\(902\) −22.9700 + 70.6943i −0.764817 + 2.35386i
\(903\) 0.0625256 0.0454275i 0.00208072 0.00151173i
\(904\) −15.8345 −0.526647
\(905\) 42.3612 1.40813
\(906\) −2.10582 + 1.52997i −0.0699613 + 0.0508298i
\(907\) 16.4368 + 11.9420i 0.545774 + 0.396528i 0.826225 0.563340i \(-0.190484\pi\)
−0.280451 + 0.959868i \(0.590484\pi\)
\(908\) 3.69762 + 2.68648i 0.122710 + 0.0891539i
\(909\) −5.52269 16.9971i −0.183176 0.563758i
\(910\) −0.516276 + 0.375096i −0.0171144 + 0.0124343i
\(911\) 9.03153 + 27.7962i 0.299228 + 0.920929i 0.981768 + 0.190081i \(0.0608751\pi\)
−0.682540 + 0.730848i \(0.739125\pi\)
\(912\) −1.11757 + 3.43952i −0.0370064 + 0.113894i
\(913\) −6.18411 4.49302i −0.204664 0.148697i
\(914\) 9.06611 27.9026i 0.299880 0.922936i
\(915\) 0.488160 1.50240i 0.0161381 0.0496679i
\(916\) 2.84343 + 2.06587i 0.0939496 + 0.0682584i
\(917\) −0.393453 + 1.21092i −0.0129930 + 0.0399882i
\(918\) −0.535131 1.64696i −0.0176620 0.0543579i
\(919\) −24.7421 + 17.9762i −0.816166 + 0.592979i −0.915612 0.402064i \(-0.868293\pi\)
0.0994455 + 0.995043i \(0.468293\pi\)
\(920\) −15.0684 46.3759i −0.496792 1.52897i
\(921\) 3.87317 + 2.81402i 0.127625 + 0.0927252i
\(922\) −19.6408 14.2699i −0.646837 0.469954i
\(923\) 8.64821 6.28329i 0.284659 0.206817i
\(924\) −0.134979 −0.00444049
\(925\) −19.2685 −0.633545
\(926\) 12.4102 9.01651i 0.407823 0.296301i
\(927\) −0.388896 + 1.19690i −0.0127730 + 0.0393113i
\(928\) −4.42052 13.6050i −0.145111 0.446605i
\(929\) 12.1310 0.398006 0.199003 0.979999i \(-0.436230\pi\)
0.199003 + 0.979999i \(0.436230\pi\)
\(930\) −2.36846 + 1.64683i −0.0776647 + 0.0540018i
\(931\) 38.9863 1.27772
\(932\) −3.05476 9.40159i −0.100062 0.307959i
\(933\) −0.213364 + 0.656666i −0.00698521 + 0.0214983i
\(934\) 1.71014 1.24249i 0.0559573 0.0406554i
\(935\) 9.70603 0.317421
\(936\) −13.3095 −0.435034
\(937\) 13.8325 10.0499i 0.451887 0.328315i −0.338453 0.940983i \(-0.609904\pi\)
0.790340 + 0.612668i \(0.209904\pi\)
\(938\) −0.468609 0.340464i −0.0153006 0.0111165i
\(939\) 3.39384 + 2.46577i 0.110754 + 0.0804674i
\(940\) 0.451596 + 1.38987i 0.0147294 + 0.0453326i
\(941\) −43.7488 + 31.7854i −1.42617 + 1.03617i −0.435458 + 0.900209i \(0.643413\pi\)
−0.990714 + 0.135965i \(0.956587\pi\)
\(942\) 1.85351 + 5.70451i 0.0603906 + 0.185863i
\(943\) −30.9179 + 95.1555i −1.00682 + 3.09869i
\(944\) −3.02337 2.19660i −0.0984022 0.0714934i
\(945\) −0.156086 + 0.480383i −0.00507747 + 0.0156269i
\(946\) 3.32097 10.2209i 0.107974 0.332310i
\(947\) −3.76957 2.73875i −0.122495 0.0889975i 0.524851 0.851194i \(-0.324121\pi\)
−0.647346 + 0.762197i \(0.724121\pi\)
\(948\) −0.534933 + 1.64636i −0.0173738 + 0.0534711i
\(949\) −0.0906897 0.279114i −0.00294391 0.00906043i
\(950\) 10.1462 7.37165i 0.329186 0.239168i
\(951\) −1.23326 3.79559i −0.0399913 0.123081i
\(952\) −0.495364 0.359903i −0.0160548 0.0116645i
\(953\) −13.2486 9.62568i −0.429164 0.311806i 0.352150 0.935943i \(-0.385451\pi\)
−0.781315 + 0.624137i \(0.785451\pi\)
\(954\) −16.5526 + 12.0262i −0.535911 + 0.389362i
\(955\) −20.2271 −0.654534
\(956\) 1.50237 0.0485900
\(957\) −5.31389 + 3.86077i −0.171774 + 0.124801i
\(958\) 15.6628 48.2053i 0.506044 1.55744i
\(959\) −1.13936 3.50658i −0.0367918 0.113234i
\(960\) 3.77002 0.121677
\(961\) 10.7940 29.0601i 0.348192 0.937423i
\(962\) −18.8287 −0.607061
\(963\) 6.04990 + 18.6197i 0.194955 + 0.600011i
\(964\) −2.40375 + 7.39799i −0.0774196 + 0.238273i
\(965\) −32.3243 + 23.4850i −1.04056 + 0.756009i
\(966\) 0.520826 0.0167573
\(967\) 57.6946 1.85533 0.927667 0.373409i \(-0.121811\pi\)
0.927667 + 0.373409i \(0.121811\pi\)
\(968\) −46.6210 + 33.8721i −1.49846 + 1.08869i
\(969\) −1.08445 0.787902i −0.0348377 0.0253111i
\(970\) 11.2116 + 8.14568i 0.359982 + 0.261542i
\(971\) 12.0699 + 37.1472i 0.387340 + 1.19211i 0.934768 + 0.355258i \(0.115607\pi\)
−0.547428 + 0.836853i \(0.684393\pi\)
\(972\) −2.63530 + 1.91466i −0.0845272 + 0.0614126i
\(973\) 0.969165 + 2.98278i 0.0310700 + 0.0956236i
\(974\) 0.0270195 0.0831575i 0.000865761 0.00266454i
\(975\) −0.525267 0.381628i −0.0168220 0.0122219i
\(976\) −3.09536 + 9.52654i −0.0990801 + 0.304937i
\(977\) 8.72001 26.8374i 0.278978 0.858605i −0.709162 0.705046i \(-0.750926\pi\)
0.988139 0.153559i \(-0.0490736\pi\)
\(978\) 4.26127 + 3.09599i 0.136260 + 0.0989990i
\(979\) 17.9836 55.3478i 0.574758 1.76892i
\(980\) −1.97799 6.08762i −0.0631845 0.194462i
\(981\) −42.4205 + 30.8203i −1.35438 + 0.984017i
\(982\) −10.6482 32.7719i −0.339799 1.04579i
\(983\) 4.66913 + 3.39232i 0.148922 + 0.108198i 0.659751 0.751484i \(-0.270662\pi\)
−0.510829 + 0.859682i \(0.670662\pi\)
\(984\) −6.63602 4.82135i −0.211549 0.153699i
\(985\) 17.2877 12.5602i 0.550831 0.400202i
\(986\) −6.12243 −0.194978
\(987\) −0.0759635 −0.00241794
\(988\) −3.45859 + 2.51281i −0.110032 + 0.0799432i
\(989\) 4.47006 13.7574i 0.142140 0.437461i
\(990\) 10.7476 + 33.0776i 0.341580 + 1.05127i
\(991\) −6.30092 −0.200155 −0.100078 0.994980i \(-0.531909\pi\)
−0.100078 + 0.994980i \(0.531909\pi\)
\(992\) −13.0060 + 9.04333i −0.412942 + 0.287126i
\(993\) −2.41982 −0.0767906
\(994\) 0.544555 + 1.67597i 0.0172722 + 0.0531585i
\(995\) −0.972100 + 2.99182i −0.0308176 + 0.0948469i
\(996\) 0.140223 0.101878i 0.00444312 0.00322812i
\(997\) 28.6119 0.906147 0.453073 0.891473i \(-0.350328\pi\)
0.453073 + 0.891473i \(0.350328\pi\)
\(998\) −29.7276 −0.941012
\(999\) −12.0569 + 8.75983i −0.381462 + 0.277149i
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 527.2.h.c.35.8 96
31.8 even 5 inner 527.2.h.c.256.8 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
527.2.h.c.35.8 96 1.1 even 1 trivial
527.2.h.c.256.8 yes 96 31.8 even 5 inner