Properties

Label 471.2.s.a.2.8
Level $471$
Weight $2$
Character 471.2
Analytic conductor $3.761$
Analytic rank $0$
Dimension $1200$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [471,2,Mod(2,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(52))
 
chi = DirichletCharacter(H, H._module([26, 47]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.s (of order \(52\), degree \(24\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(1200\)
Relative dimension: \(50\) over \(\Q(\zeta_{52})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label 2.8
Character \(\chi\) \(=\) 471.2
Dual form 471.2.s.a.236.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.14879 + 0.393780i) q^{2} +(-1.33115 - 1.10817i) q^{3} +(2.59219 - 0.983089i) q^{4} +(-0.374862 - 1.20298i) q^{5} +(3.29674 + 1.85703i) q^{6} +(3.78902 - 1.70530i) q^{7} +(-1.44392 + 0.872879i) q^{8} +(0.543937 + 2.95028i) q^{9} +O(q^{10})\) \(q+(-2.14879 + 0.393780i) q^{2} +(-1.33115 - 1.10817i) q^{3} +(2.59219 - 0.983089i) q^{4} +(-0.374862 - 1.20298i) q^{5} +(3.29674 + 1.85703i) q^{6} +(3.78902 - 1.70530i) q^{7} +(-1.44392 + 0.872879i) q^{8} +(0.543937 + 2.95028i) q^{9} +(1.27921 + 2.43733i) q^{10} +(1.70650 - 1.17791i) q^{11} +(-4.54003 - 1.56394i) q^{12} +0.232398i q^{13} +(-7.47028 + 5.15636i) q^{14} +(-0.834097 + 2.01675i) q^{15} +(-1.39132 + 1.23260i) q^{16} +(-2.51046 + 4.78328i) q^{17} +(-2.33056 - 6.12533i) q^{18} +(6.87660 + 1.69493i) q^{19} +(-2.15435 - 2.74982i) q^{20} +(-6.93351 - 1.92885i) q^{21} +(-3.20306 + 3.20306i) q^{22} +(0.0669838 - 1.10737i) q^{23} +(2.88937 + 0.438165i) q^{24} +(2.80829 - 1.93842i) q^{25} +(-0.0915138 - 0.499375i) q^{26} +(2.54533 - 4.53004i) q^{27} +(8.14540 - 8.14540i) q^{28} +(6.34815 + 1.97816i) q^{29} +(0.998140 - 4.66203i) q^{30} +(-3.42235 - 0.415548i) q^{31} +(4.58539 - 5.85282i) q^{32} +(-3.57693 - 0.323104i) q^{33} +(3.51088 - 11.2668i) q^{34} +(-3.47179 - 3.91884i) q^{35} +(4.31037 + 7.11294i) q^{36} +(-3.31110 + 1.73780i) q^{37} +(-15.4438 - 0.934176i) q^{38} +(0.257536 - 0.309358i) q^{39} +(1.59132 + 1.40979i) q^{40} +(0.151634 + 2.50681i) q^{41} +(15.6582 + 1.41440i) q^{42} +(-1.32995 - 0.598563i) q^{43} +(3.26558 - 4.73101i) q^{44} +(3.34521 - 1.76029i) q^{45} +(0.292128 + 2.40589i) q^{46} +(5.39611 - 10.2814i) q^{47} +(3.21798 - 0.0989683i) q^{48} +(6.80675 - 7.68323i) q^{49} +(-5.27111 + 5.27111i) q^{50} +(8.64247 - 3.58527i) q^{51} +(0.228468 + 0.602421i) q^{52} +(9.30295 - 5.62383i) q^{53} +(-3.68554 + 10.7364i) q^{54} +(-2.05670 - 1.61132i) q^{55} +(-3.98251 + 5.76966i) q^{56} +(-7.27554 - 9.87662i) q^{57} +(-14.4198 - 1.75088i) q^{58} +(0.956443 + 0.578190i) q^{59} +(-0.179492 + 6.04781i) q^{60} +(0.0243419 - 0.0147152i) q^{61} +(7.51753 - 0.454727i) q^{62} +(7.09209 + 10.2511i) q^{63} +(-5.82067 + 11.0904i) q^{64} +(0.279570 - 0.0871174i) q^{65} +(7.81330 - 0.714243i) q^{66} +(-6.99919 - 1.72515i) q^{67} +(-1.80520 + 14.8672i) q^{68} +(-1.31632 + 1.39986i) q^{69} +(9.00331 + 7.05364i) q^{70} +(0.285763 - 1.15939i) q^{71} +(-3.36064 - 3.78517i) q^{72} +(-5.06822 - 11.2611i) q^{73} +(6.43054 - 5.03800i) q^{74} +(-5.88636 - 0.531714i) q^{75} +(19.4917 - 2.36672i) q^{76} +(4.45726 - 7.37321i) q^{77} +(-0.431571 + 0.766157i) q^{78} +(-2.45265 + 13.3837i) q^{79} +(2.00434 + 1.21166i) q^{80} +(-8.40826 + 3.20953i) q^{81} +(-1.31296 - 5.32690i) q^{82} +(4.87109 + 6.21749i) q^{83} +(-19.8692 + 1.81632i) q^{84} +(6.69524 + 1.22695i) q^{85} +(3.09349 + 0.762476i) q^{86} +(-6.25823 - 9.66804i) q^{87} +(-1.43587 + 3.19037i) q^{88} +(-15.2536 - 1.85212i) q^{89} +(-6.49498 + 5.09977i) q^{90} +(0.396309 + 0.880561i) q^{91} +(-0.915012 - 2.93638i) q^{92} +(4.09517 + 4.34569i) q^{93} +(-7.54647 + 24.2175i) q^{94} +(-0.538819 - 8.90775i) q^{95} +(-12.5897 + 2.70962i) q^{96} +(-4.95077 - 15.8876i) q^{97} +(-11.6008 + 19.1900i) q^{98} +(4.40339 + 4.39393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{47}{52}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14879 + 0.393780i −1.51942 + 0.278444i −0.874206 0.485556i \(-0.838617\pi\)
−0.645216 + 0.764000i \(0.723233\pi\)
\(3\) −1.33115 1.10817i −0.768542 0.639800i
\(4\) 2.59219 0.983089i 1.29610 0.491544i
\(5\) −0.374862 1.20298i −0.167644 0.537987i 0.832221 0.554444i \(-0.187069\pi\)
−0.999865 + 0.0164569i \(0.994761\pi\)
\(6\) 3.29674 + 1.85703i 1.34589 + 0.758130i
\(7\) 3.78902 1.70530i 1.43211 0.644542i 0.461931 0.886916i \(-0.347157\pi\)
0.970183 + 0.242374i \(0.0779261\pi\)
\(8\) −1.44392 + 0.872879i −0.510502 + 0.308609i
\(9\) 0.543937 + 2.95028i 0.181312 + 0.983426i
\(10\) 1.27921 + 2.43733i 0.404521 + 0.770750i
\(11\) 1.70650 1.17791i 0.514529 0.355153i −0.282332 0.959317i \(-0.591108\pi\)
0.796861 + 0.604163i \(0.206493\pi\)
\(12\) −4.54003 1.56394i −1.31059 0.451470i
\(13\) 0.232398i 0.0644557i 0.999481 + 0.0322279i \(0.0102602\pi\)
−0.999481 + 0.0322279i \(0.989740\pi\)
\(14\) −7.47028 + 5.15636i −1.99652 + 1.37810i
\(15\) −0.834097 + 2.01675i −0.215363 + 0.520724i
\(16\) −1.39132 + 1.23260i −0.347829 + 0.308149i
\(17\) −2.51046 + 4.78328i −0.608875 + 1.16011i 0.364566 + 0.931178i \(0.381217\pi\)
−0.973441 + 0.228937i \(0.926475\pi\)
\(18\) −2.33056 6.12533i −0.549319 1.44375i
\(19\) 6.87660 + 1.69493i 1.57760 + 0.388843i 0.928343 0.371726i \(-0.121234\pi\)
0.649257 + 0.760569i \(0.275080\pi\)
\(20\) −2.15435 2.74982i −0.481727 0.614879i
\(21\) −6.93351 1.92885i −1.51302 0.420909i
\(22\) −3.20306 + 3.20306i −0.682896 + 0.682896i
\(23\) 0.0669838 1.10737i 0.0139671 0.230904i −0.984493 0.175425i \(-0.943870\pi\)
0.998460 0.0554785i \(-0.0176684\pi\)
\(24\) 2.88937 + 0.438165i 0.589790 + 0.0894401i
\(25\) 2.80829 1.93842i 0.561658 0.387685i
\(26\) −0.0915138 0.499375i −0.0179473 0.0979354i
\(27\) 2.54533 4.53004i 0.489849 0.871807i
\(28\) 8.14540 8.14540i 1.53934 1.53934i
\(29\) 6.34815 + 1.97816i 1.17882 + 0.367336i 0.823450 0.567389i \(-0.192046\pi\)
0.355372 + 0.934725i \(0.384354\pi\)
\(30\) 0.998140 4.66203i 0.182235 0.851166i
\(31\) −3.42235 0.415548i −0.614672 0.0746347i −0.192721 0.981254i \(-0.561731\pi\)
−0.421951 + 0.906619i \(0.638654\pi\)
\(32\) 4.58539 5.85282i 0.810590 1.03464i
\(33\) −3.57693 0.323104i −0.622664 0.0562451i
\(34\) 3.51088 11.2668i 0.602111 1.93224i
\(35\) −3.47179 3.91884i −0.586840 0.662405i
\(36\) 4.31037 + 7.11294i 0.718395 + 1.18549i
\(37\) −3.31110 + 1.73780i −0.544341 + 0.285692i −0.714395 0.699742i \(-0.753298\pi\)
0.170054 + 0.985435i \(0.445606\pi\)
\(38\) −15.4438 0.934176i −2.50531 0.151543i
\(39\) 0.257536 0.309358i 0.0412388 0.0495369i
\(40\) 1.59132 + 1.40979i 0.251610 + 0.222907i
\(41\) 0.151634 + 2.50681i 0.0236813 + 0.391498i 0.990634 + 0.136543i \(0.0435992\pi\)
−0.966953 + 0.254955i \(0.917939\pi\)
\(42\) 15.6582 + 1.41440i 2.41611 + 0.218247i
\(43\) −1.32995 0.598563i −0.202816 0.0912800i 0.306459 0.951884i \(-0.400856\pi\)
−0.509275 + 0.860604i \(0.670086\pi\)
\(44\) 3.26558 4.73101i 0.492305 0.713227i
\(45\) 3.34521 1.76029i 0.498674 0.262409i
\(46\) 0.292128 + 2.40589i 0.0430719 + 0.354729i
\(47\) 5.39611 10.2814i 0.787103 1.49970i −0.0773602 0.997003i \(-0.524649\pi\)
0.864463 0.502696i \(-0.167659\pi\)
\(48\) 3.21798 0.0989683i 0.464475 0.0142848i
\(49\) 6.80675 7.68323i 0.972393 1.09760i
\(50\) −5.27111 + 5.27111i −0.745447 + 0.745447i
\(51\) 8.64247 3.58527i 1.21019 0.502038i
\(52\) 0.228468 + 0.602421i 0.0316828 + 0.0835408i
\(53\) 9.30295 5.62383i 1.27786 0.772493i 0.294761 0.955571i \(-0.404760\pi\)
0.983098 + 0.183079i \(0.0586063\pi\)
\(54\) −3.68554 + 10.7364i −0.501538 + 1.46104i
\(55\) −2.05670 1.61132i −0.277325 0.217271i
\(56\) −3.98251 + 5.76966i −0.532186 + 0.771004i
\(57\) −7.27554 9.87662i −0.963669 1.30819i
\(58\) −14.4198 1.75088i −1.89341 0.229902i
\(59\) 0.956443 + 0.578190i 0.124518 + 0.0752739i 0.578226 0.815877i \(-0.303745\pi\)
−0.453708 + 0.891151i \(0.649899\pi\)
\(60\) −0.179492 + 6.04781i −0.0231723 + 0.780768i
\(61\) 0.0243419 0.0147152i 0.00311666 0.00188409i −0.515779 0.856722i \(-0.672497\pi\)
0.518895 + 0.854838i \(0.326343\pi\)
\(62\) 7.51753 0.454727i 0.954728 0.0577504i
\(63\) 7.09209 + 10.2511i 0.893519 + 1.29151i
\(64\) −5.82067 + 11.0904i −0.727584 + 1.38629i
\(65\) 0.279570 0.0871174i 0.0346764 0.0108056i
\(66\) 7.81330 0.714243i 0.961750 0.0879172i
\(67\) −6.99919 1.72515i −0.855087 0.210760i −0.212678 0.977122i \(-0.568219\pi\)
−0.642409 + 0.766362i \(0.722065\pi\)
\(68\) −1.80520 + 14.8672i −0.218913 + 1.80291i
\(69\) −1.31632 + 1.39986i −0.158466 + 0.168523i
\(70\) 9.00331 + 7.05364i 1.07610 + 0.843071i
\(71\) 0.285763 1.15939i 0.0339138 0.137594i −0.951545 0.307511i \(-0.900504\pi\)
0.985458 + 0.169917i \(0.0543501\pi\)
\(72\) −3.36064 3.78517i −0.396055 0.446086i
\(73\) −5.06822 11.2611i −0.593190 1.31802i −0.926889 0.375335i \(-0.877528\pi\)
0.333699 0.942680i \(-0.391703\pi\)
\(74\) 6.43054 5.03800i 0.747535 0.585656i
\(75\) −5.88636 0.531714i −0.679698 0.0613970i
\(76\) 19.4917 2.36672i 2.23585 0.271482i
\(77\) 4.45726 7.37321i 0.507952 0.840255i
\(78\) −0.431571 + 0.766157i −0.0488658 + 0.0867502i
\(79\) −2.45265 + 13.3837i −0.275945 + 1.50578i 0.495006 + 0.868890i \(0.335166\pi\)
−0.770951 + 0.636895i \(0.780219\pi\)
\(80\) 2.00434 + 1.21166i 0.224092 + 0.135468i
\(81\) −8.40826 + 3.20953i −0.934252 + 0.356614i
\(82\) −1.31296 5.32690i −0.144992 0.588257i
\(83\) 4.87109 + 6.21749i 0.534672 + 0.682458i 0.976716 0.214535i \(-0.0688237\pi\)
−0.442045 + 0.896993i \(0.645747\pi\)
\(84\) −19.8692 + 1.81632i −2.16791 + 0.198177i
\(85\) 6.69524 + 1.22695i 0.726201 + 0.133081i
\(86\) 3.09349 + 0.762476i 0.333579 + 0.0822199i
\(87\) −6.25823 9.66804i −0.670952 1.03652i
\(88\) −1.43587 + 3.19037i −0.153064 + 0.340095i
\(89\) −15.2536 1.85212i −1.61688 0.196324i −0.738487 0.674268i \(-0.764459\pi\)
−0.878391 + 0.477943i \(0.841382\pi\)
\(90\) −6.49498 + 5.09977i −0.684631 + 0.537563i
\(91\) 0.396309 + 0.880561i 0.0415444 + 0.0923079i
\(92\) −0.915012 2.93638i −0.0953966 0.306139i
\(93\) 4.09517 + 4.34569i 0.424650 + 0.450627i
\(94\) −7.54647 + 24.2175i −0.778359 + 2.49784i
\(95\) −0.538819 8.90775i −0.0552817 0.913916i
\(96\) −12.5897 + 2.70962i −1.28494 + 0.276550i
\(97\) −4.95077 15.8876i −0.502675 1.61314i −0.762157 0.647392i \(-0.775860\pi\)
0.259483 0.965748i \(-0.416448\pi\)
\(98\) −11.6008 + 19.1900i −1.17185 + 1.93848i
\(99\) 4.40339 + 4.39393i 0.442557 + 0.441607i
\(100\) 5.37399 7.78556i 0.537399 0.778556i
\(101\) 4.00434 + 2.76400i 0.398447 + 0.275028i 0.750393 0.660992i \(-0.229864\pi\)
−0.351946 + 0.936020i \(0.614480\pi\)
\(102\) −17.1590 + 11.1072i −1.69900 + 1.09978i
\(103\) 4.36231 + 5.56808i 0.429831 + 0.548639i 0.952755 0.303741i \(-0.0982356\pi\)
−0.522924 + 0.852380i \(0.675159\pi\)
\(104\) −0.202856 0.335564i −0.0198916 0.0329048i
\(105\) 0.278759 + 9.06390i 0.0272041 + 0.884546i
\(106\) −17.7755 + 15.7477i −1.72651 + 1.52955i
\(107\) 3.35857 + 3.35857i 0.324685 + 0.324685i 0.850561 0.525876i \(-0.176262\pi\)
−0.525876 + 0.850561i \(0.676262\pi\)
\(108\) 2.14456 14.2450i 0.206360 1.37073i
\(109\) −5.33201 14.0593i −0.510713 1.34664i −0.904121 0.427277i \(-0.859473\pi\)
0.393407 0.919364i \(-0.371296\pi\)
\(110\) 5.05392 + 2.65250i 0.481872 + 0.252906i
\(111\) 6.33335 + 1.35597i 0.601135 + 0.128703i
\(112\) −3.16977 + 7.04294i −0.299515 + 0.665495i
\(113\) −6.69600 4.62192i −0.629907 0.434793i 0.209867 0.977730i \(-0.432697\pi\)
−0.839774 + 0.542937i \(0.817312\pi\)
\(114\) 19.5228 + 18.3578i 1.82848 + 1.71937i
\(115\) −1.35725 + 0.334533i −0.126565 + 0.0311954i
\(116\) 18.4003 1.11301i 1.70843 0.103341i
\(117\) −0.685640 + 0.126410i −0.0633874 + 0.0116866i
\(118\) −2.28287 0.865779i −0.210155 0.0797015i
\(119\) −1.35525 + 22.4050i −0.124236 + 2.05386i
\(120\) −0.556014 3.64010i −0.0507569 0.332294i
\(121\) −2.37599 + 6.26497i −0.215999 + 0.569543i
\(122\) −0.0465110 + 0.0412051i −0.00421091 + 0.00373054i
\(123\) 2.57612 3.50499i 0.232281 0.316034i
\(124\) −9.27990 + 2.28729i −0.833360 + 0.205405i
\(125\) −8.34397 6.53708i −0.746307 0.584694i
\(126\) −19.2761 19.2347i −1.71725 1.71356i
\(127\) 3.30687 0.401527i 0.293438 0.0356298i 0.0275059 0.999622i \(-0.491244\pi\)
0.265932 + 0.963992i \(0.414320\pi\)
\(128\) 3.71627 11.9259i 0.328475 1.05411i
\(129\) 1.10706 + 2.27059i 0.0974715 + 0.199914i
\(130\) −0.566431 + 0.297286i −0.0496793 + 0.0260737i
\(131\) −6.51059 + 1.19311i −0.568833 + 0.104243i −0.456972 0.889481i \(-0.651066\pi\)
−0.111861 + 0.993724i \(0.535681\pi\)
\(132\) −9.58973 + 2.67889i −0.834679 + 0.233168i
\(133\) 28.9459 5.30453i 2.50993 0.459961i
\(134\) 15.7191 + 0.950830i 1.35792 + 0.0821392i
\(135\) −6.40368 1.36383i −0.551141 0.117380i
\(136\) −0.550327 9.09799i −0.0471901 0.780146i
\(137\) −0.699543 + 0.548057i −0.0597660 + 0.0468237i −0.646157 0.763204i \(-0.723625\pi\)
0.586391 + 0.810028i \(0.300548\pi\)
\(138\) 2.27726 3.52633i 0.193853 0.300181i
\(139\) 18.1706 + 10.9845i 1.54121 + 0.931693i 0.995605 + 0.0936501i \(0.0298535\pi\)
0.545604 + 0.838043i \(0.316300\pi\)
\(140\) −12.8521 6.74531i −1.08620 0.570083i
\(141\) −18.5766 + 7.70637i −1.56443 + 0.648993i
\(142\) −0.157501 + 2.60380i −0.0132172 + 0.218506i
\(143\) 0.273745 + 0.396588i 0.0228917 + 0.0331643i
\(144\) −4.39329 3.43431i −0.366108 0.286192i
\(145\) 8.37821i 0.695772i
\(146\) 15.3249 + 22.2020i 1.26830 + 1.83745i
\(147\) −17.5751 + 2.68455i −1.44957 + 0.221418i
\(148\) −6.87459 + 7.75981i −0.565088 + 0.637852i
\(149\) −5.18428 8.57585i −0.424713 0.702561i 0.568005 0.823025i \(-0.307716\pi\)
−0.992718 + 0.120464i \(0.961562\pi\)
\(150\) 12.8579 1.17539i 1.04984 0.0959702i
\(151\) −7.78511 1.42667i −0.633543 0.116101i −0.146120 0.989267i \(-0.546679\pi\)
−0.487423 + 0.873166i \(0.662063\pi\)
\(152\) −11.4087 + 3.55510i −0.925369 + 0.288357i
\(153\) −15.4775 4.80474i −1.25128 0.388440i
\(154\) −6.67429 + 17.5986i −0.537829 + 1.41814i
\(155\) 0.783015 + 4.27278i 0.0628933 + 0.343198i
\(156\) 0.363456 1.05510i 0.0290998 0.0844753i
\(157\) 4.32545 11.7597i 0.345209 0.938526i
\(158\) 29.7245i 2.36476i
\(159\) −18.6158 2.82303i −1.47633 0.223881i
\(160\) −8.75969 3.32211i −0.692514 0.262636i
\(161\) −1.63460 4.31009i −0.128825 0.339682i
\(162\) 16.8037 10.2076i 1.32023 0.801985i
\(163\) 0.0552299 0.301380i 0.00432594 0.0236059i −0.981386 0.192045i \(-0.938488\pi\)
0.985712 + 0.168439i \(0.0538727\pi\)
\(164\) 2.85748 + 6.34907i 0.223132 + 0.495779i
\(165\) 0.952171 + 4.42408i 0.0741264 + 0.344414i
\(166\) −12.9153 11.4419i −1.00242 0.888065i
\(167\) −13.0987 + 6.87475i −1.01361 + 0.531984i −0.887878 0.460080i \(-0.847821\pi\)
−0.125734 + 0.992064i \(0.540129\pi\)
\(168\) 11.6951 3.26702i 0.902295 0.252056i
\(169\) 12.9460 0.995845
\(170\) −14.8698 −1.14046
\(171\) −1.26007 + 21.2098i −0.0963602 + 1.62195i
\(172\) −4.03593 0.244129i −0.307737 0.0186147i
\(173\) 13.6402 + 15.3966i 1.03704 + 1.17058i 0.985109 + 0.171930i \(0.0550004\pi\)
0.0519350 + 0.998650i \(0.483461\pi\)
\(174\) 17.2547 + 18.3102i 1.30807 + 1.38809i
\(175\) 7.33507 12.1337i 0.554479 0.917221i
\(176\) −0.922387 + 3.74227i −0.0695275 + 0.282084i
\(177\) −0.632442 1.82956i −0.0475372 0.137518i
\(178\) 33.5060 2.02674i 2.51138 0.151911i
\(179\) −8.10644 8.10644i −0.605904 0.605904i 0.335969 0.941873i \(-0.390936\pi\)
−0.941873 + 0.335969i \(0.890936\pi\)
\(180\) 6.94090 7.85165i 0.517344 0.585227i
\(181\) 2.29272 + 12.5110i 0.170416 + 0.929932i 0.951992 + 0.306122i \(0.0990315\pi\)
−0.781576 + 0.623810i \(0.785584\pi\)
\(182\) −1.19833 1.73608i −0.0888261 0.128687i
\(183\) −0.0487096 0.00738668i −0.00360072 0.000546039i
\(184\) 0.869885 + 1.65743i 0.0641288 + 0.122187i
\(185\) 3.33174 + 3.33174i 0.244954 + 0.244954i
\(186\) −10.5109 7.72536i −0.770697 0.566451i
\(187\) 1.35018 + 11.1197i 0.0987351 + 0.813157i
\(188\) 3.88019 31.9563i 0.282992 2.33065i
\(189\) 1.91923 21.5050i 0.139604 1.56426i
\(190\) 4.66550 + 18.9287i 0.338471 + 1.37323i
\(191\) 21.1296 + 6.58425i 1.52888 + 0.476419i 0.942667 0.333735i \(-0.108309\pi\)
0.586217 + 0.810154i \(0.300617\pi\)
\(192\) 20.0382 8.31270i 1.44613 0.599917i
\(193\) 6.36648 + 2.41449i 0.458269 + 0.173799i 0.572927 0.819606i \(-0.305808\pi\)
−0.114658 + 0.993405i \(0.536577\pi\)
\(194\) 16.8944 + 32.1895i 1.21294 + 2.31107i
\(195\) −0.468691 0.193843i −0.0335636 0.0138814i
\(196\) 10.0911 26.6080i 0.720793 1.90057i
\(197\) 5.79430 6.54042i 0.412827 0.465985i −0.504911 0.863171i \(-0.668475\pi\)
0.917738 + 0.397186i \(0.130013\pi\)
\(198\) −11.1922 7.70766i −0.795394 0.547760i
\(199\) −5.65644 22.9491i −0.400975 1.62682i −0.730670 0.682731i \(-0.760792\pi\)
0.329695 0.944087i \(-0.393054\pi\)
\(200\) −2.36293 + 5.25022i −0.167085 + 0.371247i
\(201\) 7.40525 + 10.0527i 0.522326 + 0.709062i
\(202\) −9.69288 4.36241i −0.681989 0.306938i
\(203\) 27.4266 3.33019i 1.92497 0.233734i
\(204\) 18.8783 17.7900i 1.32174 1.24555i
\(205\) 2.95879 1.12212i 0.206651 0.0783724i
\(206\) −11.5663 10.2468i −0.805860 0.713930i
\(207\) 3.30350 0.404721i 0.229609 0.0281301i
\(208\) −0.286454 0.323339i −0.0198620 0.0224196i
\(209\) 13.7314 5.20763i 0.949819 0.360219i
\(210\) −4.16818 19.3666i −0.287631 1.33642i
\(211\) 0.778687 0.610062i 0.0536070 0.0419984i −0.589558 0.807726i \(-0.700698\pi\)
0.643165 + 0.765728i \(0.277621\pi\)
\(212\) 18.5863 23.7237i 1.27651 1.62935i
\(213\) −1.66518 + 1.22665i −0.114097 + 0.0840484i
\(214\) −8.53938 5.89431i −0.583740 0.402927i
\(215\) −0.221508 + 1.82428i −0.0151067 + 0.124415i
\(216\) 0.278927 + 8.76278i 0.0189786 + 0.596232i
\(217\) −13.6760 + 4.26160i −0.928385 + 0.289297i
\(218\) 16.9936 + 28.1109i 1.15095 + 1.90391i
\(219\) −5.73262 + 20.6067i −0.387374 + 1.39247i
\(220\) −6.91543 2.15494i −0.466238 0.145286i
\(221\) −1.11163 0.583426i −0.0747760 0.0392455i
\(222\) −14.1430 0.419747i −0.949214 0.0281715i
\(223\) −11.3914 + 5.12686i −0.762826 + 0.343320i −0.754202 0.656643i \(-0.771976\pi\)
−0.00862399 + 0.999963i \(0.502745\pi\)
\(224\) 7.39332 29.9959i 0.493987 2.00418i
\(225\) 7.24642 + 7.23085i 0.483094 + 0.482057i
\(226\) 16.2083 + 7.29476i 1.07816 + 0.485240i
\(227\) 2.71192 3.46151i 0.179997 0.229749i −0.688758 0.724991i \(-0.741844\pi\)
0.868755 + 0.495242i \(0.164921\pi\)
\(228\) −28.5692 18.4496i −1.89204 1.22185i
\(229\) −0.854679 + 4.66383i −0.0564788 + 0.308195i −0.999714 0.0239318i \(-0.992382\pi\)
0.943235 + 0.332127i \(0.107766\pi\)
\(230\) 2.78472 1.25330i 0.183619 0.0826402i
\(231\) −14.1040 + 4.87549i −0.927978 + 0.320784i
\(232\) −10.8929 + 2.68486i −0.715154 + 0.176270i
\(233\) 0.861679 + 7.09656i 0.0564505 + 0.464911i 0.993334 + 0.115270i \(0.0367734\pi\)
−0.936884 + 0.349641i \(0.886304\pi\)
\(234\) 1.42352 0.541620i 0.0930581 0.0354068i
\(235\) −14.3911 2.63727i −0.938772 0.172036i
\(236\) 3.04770 + 0.558511i 0.198388 + 0.0363560i
\(237\) 18.0962 15.0978i 1.17548 0.980708i
\(238\) −5.91049 48.6772i −0.383120 3.15528i
\(239\) 14.7468 3.63477i 0.953893 0.235113i 0.268494 0.963281i \(-0.413474\pi\)
0.685399 + 0.728168i \(0.259628\pi\)
\(240\) −1.32535 3.83405i −0.0855513 0.247487i
\(241\) −0.383893 + 0.172776i −0.0247287 + 0.0111295i −0.422739 0.906251i \(-0.638931\pi\)
0.398011 + 0.917381i \(0.369701\pi\)
\(242\) 2.63848 14.3977i 0.169608 0.925520i
\(243\) 14.7494 + 5.04538i 0.946173 + 0.323661i
\(244\) 0.0486325 0.0620748i 0.00311338 0.00397393i
\(245\) −11.7943 5.30820i −0.753512 0.339128i
\(246\) −4.15533 + 8.54590i −0.264934 + 0.544866i
\(247\) −0.393899 + 1.59811i −0.0250632 + 0.101685i
\(248\) 5.30432 2.38728i 0.336824 0.151592i
\(249\) 0.405840 13.6744i 0.0257191 0.866580i
\(250\) 20.5036 + 10.7611i 1.29676 + 0.680592i
\(251\) 13.6830 + 4.26379i 0.863662 + 0.269128i 0.697162 0.716914i \(-0.254446\pi\)
0.166500 + 0.986041i \(0.446753\pi\)
\(252\) 28.4618 + 19.6006i 1.79292 + 1.23472i
\(253\) −1.19008 1.96863i −0.0748197 0.123767i
\(254\) −6.94765 + 2.16498i −0.435935 + 0.135843i
\(255\) −7.55273 9.05269i −0.472970 0.566902i
\(256\) −0.269831 + 2.22226i −0.0168644 + 0.138891i
\(257\) −21.3241 14.7190i −1.33016 0.918145i −0.330491 0.943809i \(-0.607214\pi\)
−0.999671 + 0.0256644i \(0.991830\pi\)
\(258\) −3.27296 4.44307i −0.203765 0.276613i
\(259\) −9.58234 + 12.2310i −0.595418 + 0.759995i
\(260\) 0.639054 0.500667i 0.0396324 0.0310500i
\(261\) −2.38314 + 19.8048i −0.147512 + 1.22589i
\(262\) 13.5201 5.12748i 0.835272 0.316777i
\(263\) −1.58372 1.78764i −0.0976561 0.110231i 0.697651 0.716438i \(-0.254229\pi\)
−0.795307 + 0.606207i \(0.792690\pi\)
\(264\) 5.44683 2.65569i 0.335229 0.163447i
\(265\) −10.2527 9.08306i −0.629816 0.557968i
\(266\) −60.1098 + 22.7966i −3.68557 + 1.39775i
\(267\) 18.2524 + 19.3690i 1.11703 + 1.18536i
\(268\) −19.8392 + 2.40892i −1.21187 + 0.147148i
\(269\) −2.73514 1.23099i −0.166765 0.0750546i 0.325311 0.945607i \(-0.394531\pi\)
−0.492076 + 0.870552i \(0.663762\pi\)
\(270\) 14.2972 + 0.408941i 0.870100 + 0.0248873i
\(271\) −5.87405 + 13.0516i −0.356823 + 0.792828i 0.642818 + 0.766019i \(0.277765\pi\)
−0.999641 + 0.0268088i \(0.991465\pi\)
\(272\) −2.40302 9.74943i −0.145704 0.591146i
\(273\) 0.448261 1.61134i 0.0271300 0.0975226i
\(274\) 1.28736 1.45312i 0.0777720 0.0877864i
\(275\) 2.50905 6.61583i 0.151302 0.398950i
\(276\) −2.03597 + 4.92275i −0.122551 + 0.296315i
\(277\) 8.29809 + 15.8107i 0.498584 + 0.949973i 0.996567 + 0.0827859i \(0.0263818\pi\)
−0.497983 + 0.867187i \(0.665926\pi\)
\(278\) −43.3702 16.4481i −2.60117 0.986494i
\(279\) −0.635560 10.3229i −0.0380500 0.618016i
\(280\) 8.43366 + 2.62804i 0.504008 + 0.157055i
\(281\) 7.15982 + 29.0485i 0.427119 + 1.73289i 0.651740 + 0.758443i \(0.274040\pi\)
−0.224621 + 0.974446i \(0.572114\pi\)
\(282\) 36.8825 23.8744i 2.19632 1.42170i
\(283\) −3.30380 + 27.2093i −0.196391 + 1.61742i 0.477527 + 0.878617i \(0.341533\pi\)
−0.673918 + 0.738806i \(0.735390\pi\)
\(284\) −0.399026 3.28628i −0.0236779 0.195005i
\(285\) −9.15401 + 12.4547i −0.542237 + 0.737751i
\(286\) −0.744387 0.744387i −0.0440165 0.0440165i
\(287\) 4.84941 + 9.23977i 0.286251 + 0.545407i
\(288\) 19.7616 + 10.3446i 1.16446 + 0.609561i
\(289\) −6.92024 10.0257i −0.407073 0.589747i
\(290\) 3.29917 + 18.0030i 0.193734 + 1.05717i
\(291\) −11.0158 + 26.6351i −0.645760 + 1.56138i
\(292\) −24.2085 24.2085i −1.41669 1.41669i
\(293\) −24.1695 + 1.46199i −1.41200 + 0.0854101i −0.748682 0.662930i \(-0.769313\pi\)
−0.663316 + 0.748340i \(0.730851\pi\)
\(294\) 36.7081 12.6893i 2.14086 0.740052i
\(295\) 0.337014 1.36732i 0.0196217 0.0796084i
\(296\) 3.26407 5.39943i 0.189720 0.313835i
\(297\) −0.992381 10.7287i −0.0575838 0.622541i
\(298\) 14.5169 + 16.3862i 0.840943 + 0.949228i
\(299\) 0.257352 + 0.0155669i 0.0148831 + 0.000900259i
\(300\) −15.7813 + 4.40851i −0.911133 + 0.254525i
\(301\) −6.05994 −0.349289
\(302\) 17.2903 0.994947
\(303\) −2.26742 8.11678i −0.130260 0.466297i
\(304\) −11.6567 + 6.11790i −0.668557 + 0.350886i
\(305\) −0.0268269 0.0237665i −0.00153610 0.00136087i
\(306\) 35.1499 + 4.22963i 2.00939 + 0.241792i
\(307\) 1.00466 + 2.23227i 0.0573392 + 0.127403i 0.938342 0.345709i \(-0.112362\pi\)
−0.881003 + 0.473112i \(0.843131\pi\)
\(308\) 4.30556 23.4947i 0.245332 1.33873i
\(309\) 0.363450 12.2461i 0.0206760 0.696658i
\(310\) −3.36507 8.87295i −0.191123 0.503950i
\(311\) −29.2741 11.1022i −1.65998 0.629547i −0.666704 0.745323i \(-0.732295\pi\)
−0.993275 + 0.115775i \(0.963065\pi\)
\(312\) −0.101829 + 0.671485i −0.00576493 + 0.0380154i
\(313\) 3.06824i 0.173427i 0.996233 + 0.0867136i \(0.0276365\pi\)
−0.996233 + 0.0867136i \(0.972364\pi\)
\(314\) −4.66374 + 26.9724i −0.263190 + 1.52214i
\(315\) 9.67324 12.3744i 0.545025 0.697216i
\(316\) 6.79962 + 37.1043i 0.382508 + 2.08728i
\(317\) −5.39206 + 14.2177i −0.302848 + 0.798545i 0.694056 + 0.719921i \(0.255822\pi\)
−0.996904 + 0.0786238i \(0.974947\pi\)
\(318\) 41.1130 1.26442i 2.30550 0.0709054i
\(319\) 13.1632 4.10182i 0.736998 0.229658i
\(320\) 15.5234 + 2.84477i 0.867783 + 0.159027i
\(321\) −0.748918 8.19262i −0.0418005 0.457267i
\(322\) 5.20963 + 8.61779i 0.290322 + 0.480251i
\(323\) −25.3707 + 28.6376i −1.41166 + 1.59344i
\(324\) −18.6406 + 16.5858i −1.03559 + 0.921433i
\(325\) 0.450486 + 0.652642i 0.0249885 + 0.0362021i
\(326\) 0.669350i 0.0370719i
\(327\) −8.48237 + 24.6239i −0.469076 + 1.36170i
\(328\) −2.40709 3.48727i −0.132909 0.192553i
\(329\) 2.91305 48.1584i 0.160602 2.65506i
\(330\) −3.78813 9.13146i −0.208530 0.502671i
\(331\) −0.886551 0.465298i −0.0487292 0.0255751i 0.440183 0.897908i \(-0.354914\pi\)
−0.488912 + 0.872333i \(0.662606\pi\)
\(332\) 18.7391 + 11.3282i 1.02844 + 0.621716i
\(333\) −6.92801 8.82340i −0.379653 0.483519i
\(334\) 25.4393 19.9304i 1.39198 1.09054i
\(335\) 0.548425 + 9.06655i 0.0299637 + 0.495358i
\(336\) 12.0242 5.86260i 0.655974 0.319831i
\(337\) −10.2463 0.619787i −0.558152 0.0337620i −0.221105 0.975250i \(-0.570966\pi\)
−0.337046 + 0.941488i \(0.609428\pi\)
\(338\) −27.8182 + 5.09787i −1.51311 + 0.277288i
\(339\) 3.79155 + 13.5728i 0.205929 + 0.737171i
\(340\) 18.5616 3.40153i 1.00664 0.184474i
\(341\) −6.32971 + 3.32209i −0.342773 + 0.179901i
\(342\) −5.64436 46.0715i −0.305212 2.49126i
\(343\) 4.03564 12.9508i 0.217904 0.699279i
\(344\) 2.44282 0.296612i 0.131708 0.0159922i
\(345\) 2.17743 + 1.05875i 0.117229 + 0.0570011i
\(346\) −35.3727 27.7128i −1.90165 1.48985i
\(347\) 5.56485 1.37161i 0.298737 0.0736320i −0.0870984 0.996200i \(-0.527759\pi\)
0.385835 + 0.922568i \(0.373913\pi\)
\(348\) −25.7271 18.9090i −1.37912 1.01363i
\(349\) 6.97812 6.18208i 0.373530 0.330919i −0.455383 0.890295i \(-0.650498\pi\)
0.828914 + 0.559376i \(0.188959\pi\)
\(350\) −10.9835 + 28.9611i −0.587093 + 1.54804i
\(351\) 1.05277 + 0.591531i 0.0561930 + 0.0315736i
\(352\) 0.930863 15.3890i 0.0496152 0.820236i
\(353\) −18.4862 7.01089i −0.983922 0.373152i −0.190408 0.981705i \(-0.560981\pi\)
−0.793513 + 0.608553i \(0.791750\pi\)
\(354\) 2.07943 + 3.68229i 0.110520 + 0.195711i
\(355\) −1.50183 + 0.0908442i −0.0797091 + 0.00482151i
\(356\) −41.3610 + 10.1946i −2.19213 + 0.540312i
\(357\) 26.6325 28.3226i 1.40954 1.49899i
\(358\) 20.6112 + 14.2269i 1.08933 + 0.751913i
\(359\) 12.1886 27.0820i 0.643291 1.42933i −0.244758 0.969584i \(-0.578709\pi\)
0.888049 0.459749i \(-0.152061\pi\)
\(360\) −3.29369 + 5.46168i −0.173593 + 0.287856i
\(361\) 27.5912 + 14.4810i 1.45217 + 0.762155i
\(362\) −9.85312 25.9805i −0.517869 1.36551i
\(363\) 10.1054 5.70665i 0.530398 0.299521i
\(364\) 1.89298 + 1.89298i 0.0992190 + 0.0992190i
\(365\) −11.6470 + 10.3183i −0.609631 + 0.540086i
\(366\) 0.107575 0.00330846i 0.00562305 0.000172936i
\(367\) 0.437665 + 0.723987i 0.0228459 + 0.0377918i 0.866996 0.498316i \(-0.166048\pi\)
−0.844150 + 0.536108i \(0.819894\pi\)
\(368\) 1.27175 + 1.62327i 0.0662946 + 0.0846188i
\(369\) −7.31331 + 1.81091i −0.380716 + 0.0942723i
\(370\) −8.47116 5.84722i −0.440395 0.303983i
\(371\) 25.6587 37.1731i 1.33214 1.92993i
\(372\) 14.8877 + 7.23894i 0.771890 + 0.375321i
\(373\) 6.34549 10.4967i 0.328557 0.543500i −0.647210 0.762312i \(-0.724064\pi\)
0.975767 + 0.218812i \(0.0702181\pi\)
\(374\) −7.27999 23.3623i −0.376439 1.20804i
\(375\) 3.86293 + 17.9484i 0.199481 + 0.926849i
\(376\) 1.18290 + 19.5557i 0.0610034 + 1.00851i
\(377\) −0.459722 + 1.47530i −0.0236769 + 0.0759818i
\(378\) 4.34419 + 46.9653i 0.223441 + 2.41564i
\(379\) 10.0770 + 32.3382i 0.517621 + 1.66110i 0.729635 + 0.683837i \(0.239690\pi\)
−0.212014 + 0.977267i \(0.568002\pi\)
\(380\) −10.1538 22.5609i −0.520880 1.15735i
\(381\) −4.84691 3.13007i −0.248315 0.160358i
\(382\) −47.9957 5.82774i −2.45568 0.298173i
\(383\) −9.45501 + 21.0082i −0.483129 + 1.07347i 0.495645 + 0.868525i \(0.334932\pi\)
−0.978774 + 0.204943i \(0.934299\pi\)
\(384\) −18.1628 + 11.7570i −0.926868 + 0.599971i
\(385\) −10.5407 2.59804i −0.537202 0.132408i
\(386\) −14.6310 2.68123i −0.744698 0.136471i
\(387\) 1.04252 4.24931i 0.0529941 0.216005i
\(388\) −28.4522 36.3166i −1.44444 1.84370i
\(389\) 3.91693 + 15.8916i 0.198596 + 0.805736i 0.982715 + 0.185125i \(0.0592690\pi\)
−0.784119 + 0.620611i \(0.786885\pi\)
\(390\) 1.08345 + 0.231966i 0.0548625 + 0.0117461i
\(391\) 5.12872 + 3.10042i 0.259370 + 0.156795i
\(392\) −3.12186 + 17.0354i −0.157678 + 0.860419i
\(393\) 9.98876 + 5.62660i 0.503866 + 0.283825i
\(394\) −9.87524 + 16.3356i −0.497508 + 0.822978i
\(395\) 17.0197 2.06656i 0.856353 0.103980i
\(396\) 15.7341 + 7.06099i 0.790666 + 0.354828i
\(397\) 18.1202 14.1963i 0.909426 0.712490i −0.0487068 0.998813i \(-0.515510\pi\)
0.958133 + 0.286323i \(0.0924331\pi\)
\(398\) 21.1914 + 47.0853i 1.06223 + 2.36017i
\(399\) −44.4097 25.0157i −2.22327 1.25235i
\(400\) −1.51792 + 6.15845i −0.0758961 + 0.307922i
\(401\) 8.03072 + 6.29167i 0.401035 + 0.314191i 0.796892 0.604121i \(-0.206476\pi\)
−0.395858 + 0.918312i \(0.629553\pi\)
\(402\) −19.8708 18.6851i −0.991068 0.931926i
\(403\) 0.0965728 0.795348i 0.00481063 0.0396191i
\(404\) 13.0973 + 3.22819i 0.651614 + 0.160608i
\(405\) 7.01293 + 8.91181i 0.348475 + 0.442831i
\(406\) −57.6226 + 17.9559i −2.85976 + 0.891137i
\(407\) −3.60341 + 6.86573i −0.178615 + 0.340322i
\(408\) −9.34951 + 12.7207i −0.462870 + 0.629767i
\(409\) −38.3605 + 2.32039i −1.89681 + 0.114736i −0.967231 0.253896i \(-0.918288\pi\)
−0.929575 + 0.368632i \(0.879826\pi\)
\(410\) −5.91595 + 3.57632i −0.292168 + 0.176622i
\(411\) 1.53854 + 0.0456619i 0.0758904 + 0.00225234i
\(412\) 16.7819 + 10.1450i 0.826783 + 0.499808i
\(413\) 4.60997 + 0.559751i 0.226842 + 0.0275436i
\(414\) −6.93914 + 2.17051i −0.341040 + 0.106675i
\(415\) 5.65350 8.19051i 0.277519 0.402056i
\(416\) 1.36019 + 1.06564i 0.0666886 + 0.0522471i
\(417\) −12.0152 34.7581i −0.588386 1.70211i
\(418\) −27.4552 + 16.5972i −1.34288 + 0.811797i
\(419\) 8.33007 + 21.9646i 0.406950 + 1.07304i 0.969244 + 0.246102i \(0.0791499\pi\)
−0.562293 + 0.826938i \(0.690081\pi\)
\(420\) 9.63322 + 23.2213i 0.470053 + 1.13308i
\(421\) −10.1505 + 10.1505i −0.494703 + 0.494703i −0.909784 0.415081i \(-0.863753\pi\)
0.415081 + 0.909784i \(0.363753\pi\)
\(422\) −1.43300 + 1.61753i −0.0697575 + 0.0787399i
\(423\) 33.2682 + 10.3276i 1.61755 + 0.502143i
\(424\) −8.52378 + 16.2407i −0.413951 + 0.788718i
\(425\) 2.22192 + 18.2992i 0.107779 + 0.887639i
\(426\) 3.09510 3.29152i 0.149958 0.159475i
\(427\) 0.0671380 0.0972662i 0.00324904 0.00470704i
\(428\) 12.0078 + 5.40428i 0.580420 + 0.261226i
\(429\) 0.0750888 0.831273i 0.00362532 0.0401342i
\(430\) −0.242392 4.00721i −0.0116892 0.193245i
\(431\) −4.28130 3.79290i −0.206223 0.182698i 0.553689 0.832723i \(-0.313220\pi\)
−0.759912 + 0.650026i \(0.774758\pi\)
\(432\) 2.04236 + 9.44009i 0.0982631 + 0.454186i
\(433\) −22.2094 1.34342i −1.06731 0.0645606i −0.482632 0.875823i \(-0.660319\pi\)
−0.584682 + 0.811262i \(0.698781\pi\)
\(434\) 27.7086 14.5426i 1.33006 0.698067i
\(435\) −9.28445 + 11.1527i −0.445155 + 0.534730i
\(436\) −27.6432 31.2027i −1.32387 1.49434i
\(437\) 2.33754 7.50144i 0.111820 0.358842i
\(438\) 4.20366 46.5368i 0.200859 2.22362i
\(439\) 4.39383 5.60831i 0.209706 0.267670i −0.670870 0.741575i \(-0.734079\pi\)
0.880576 + 0.473905i \(0.157156\pi\)
\(440\) 4.37620 + 0.531366i 0.208627 + 0.0253319i
\(441\) 26.3701 + 15.9026i 1.25572 + 0.757266i
\(442\) 2.61839 + 0.815923i 0.124544 + 0.0388095i
\(443\) −4.74093 + 4.74093i −0.225249 + 0.225249i −0.810704 0.585456i \(-0.800916\pi\)
0.585456 + 0.810704i \(0.300916\pi\)
\(444\) 17.7503 2.71131i 0.842391 0.128673i
\(445\) 3.48994 + 19.0440i 0.165439 + 0.902772i
\(446\) 22.4589 15.5022i 1.06346 0.734052i
\(447\) −2.60239 + 17.1608i −0.123089 + 0.811679i
\(448\) −3.14225 + 51.9475i −0.148457 + 2.45429i
\(449\) −10.7824 + 10.7824i −0.508852 + 0.508852i −0.914174 0.405322i \(-0.867160\pi\)
0.405322 + 0.914174i \(0.367160\pi\)
\(450\) −18.4184 12.6841i −0.868250 0.597933i
\(451\) 3.21157 + 4.09926i 0.151227 + 0.193027i
\(452\) −21.9011 5.39813i −1.03014 0.253907i
\(453\) 8.78218 + 10.5263i 0.412623 + 0.494569i
\(454\) −4.46427 + 8.50596i −0.209519 + 0.399204i
\(455\) 0.910733 0.806839i 0.0426958 0.0378252i
\(456\) 19.1264 + 7.91037i 0.895675 + 0.370437i
\(457\) 33.9207 23.4137i 1.58674 1.09525i 0.642357 0.766406i \(-0.277957\pi\)
0.944385 0.328843i \(-0.106659\pi\)
\(458\) 10.3581i 0.484004i
\(459\) 15.2785 + 23.5475i 0.713139 + 1.09910i
\(460\) −3.18939 + 2.20148i −0.148706 + 0.102644i
\(461\) −12.6190 24.0434i −0.587724 1.11981i −0.979818 0.199890i \(-0.935942\pi\)
0.392094 0.919925i \(-0.371751\pi\)
\(462\) 28.3867 16.0303i 1.32067 0.745796i
\(463\) 3.90397 2.36003i 0.181433 0.109680i −0.423707 0.905799i \(-0.639271\pi\)
0.605139 + 0.796120i \(0.293117\pi\)
\(464\) −11.2706 + 5.07247i −0.523222 + 0.235483i
\(465\) 3.69263 6.55543i 0.171242 0.304001i
\(466\) −4.64605 14.9097i −0.215224 0.690678i
\(467\) −25.8220 + 9.79298i −1.19490 + 0.453165i −0.870222 0.492660i \(-0.836025\pi\)
−0.324676 + 0.945825i \(0.605255\pi\)
\(468\) −1.65304 + 1.00172i −0.0764117 + 0.0463047i
\(469\) −29.4619 + 5.39910i −1.36043 + 0.249307i
\(470\) 31.9619 1.47429
\(471\) −18.7895 + 10.8606i −0.865776 + 0.500432i
\(472\) −1.88572 −0.0867971
\(473\) −2.97462 + 0.545119i −0.136773 + 0.0250646i
\(474\) −32.9397 + 39.5679i −1.51297 + 1.81741i
\(475\) 22.5970 8.56990i 1.03682 0.393214i
\(476\) 18.5130 + 59.4104i 0.848543 + 2.72307i
\(477\) 21.6521 + 24.3873i 0.991381 + 1.11662i
\(478\) −30.2565 + 13.6173i −1.38390 + 0.622843i
\(479\) 29.4736 17.8174i 1.34668 0.814098i 0.354045 0.935228i \(-0.384806\pi\)
0.992637 + 0.121131i \(0.0386520\pi\)
\(480\) 7.97903 + 14.1294i 0.364191 + 0.644917i
\(481\) −0.403862 0.769494i −0.0184145 0.0350859i
\(482\) 0.756868 0.522428i 0.0344744 0.0237960i
\(483\) −2.60039 + 7.54879i −0.118322 + 0.343482i
\(484\) 18.5758i 0.844355i
\(485\) −17.2565 + 11.9113i −0.783578 + 0.540865i
\(486\) −33.6800 5.03343i −1.52776 0.228321i
\(487\) 7.86060 6.96388i 0.356198 0.315564i −0.465979 0.884796i \(-0.654298\pi\)
0.822177 + 0.569232i \(0.192759\pi\)
\(488\) −0.0223031 + 0.0424950i −0.00100961 + 0.00192366i
\(489\) −0.407498 + 0.339979i −0.0184277 + 0.0153744i
\(490\) 27.4338 + 6.76182i 1.23933 + 0.305468i
\(491\) −13.3584 17.0507i −0.602856 0.769488i 0.385325 0.922781i \(-0.374089\pi\)
−0.988181 + 0.153292i \(0.951012\pi\)
\(492\) 3.23207 11.6182i 0.145713 0.523787i
\(493\) −25.3989 + 25.3989i −1.14391 + 1.14391i
\(494\) 0.217101 3.58911i 0.00976784 0.161482i
\(495\) 3.63513 6.94429i 0.163387 0.312123i
\(496\) 5.27377 3.64022i 0.236799 0.163451i
\(497\) −0.894337 4.88024i −0.0401165 0.218909i
\(498\) 4.51264 + 29.5432i 0.202216 + 1.32386i
\(499\) 0.745464 0.745464i 0.0333715 0.0333715i −0.690224 0.723596i \(-0.742488\pi\)
0.723596 + 0.690224i \(0.242488\pi\)
\(500\) −28.0557 8.74251i −1.25469 0.390977i
\(501\) 25.0548 + 5.36424i 1.11937 + 0.239656i
\(502\) −31.0808 3.77389i −1.38720 0.168437i
\(503\) −14.5445 + 18.5647i −0.648507 + 0.827758i −0.993852 0.110718i \(-0.964685\pi\)
0.345345 + 0.938476i \(0.387762\pi\)
\(504\) −19.1883 8.61118i −0.854717 0.383572i
\(505\) 1.82394 5.85324i 0.0811645 0.260466i
\(506\) 3.33244 + 3.76154i 0.148145 + 0.167221i
\(507\) −17.2331 14.3463i −0.765349 0.637142i
\(508\) 8.17731 4.29178i 0.362810 0.190417i
\(509\) 28.6429 + 1.73258i 1.26957 + 0.0767951i 0.681383 0.731927i \(-0.261379\pi\)
0.588191 + 0.808722i \(0.299840\pi\)
\(510\) 19.7940 + 16.4782i 0.876492 + 0.729667i
\(511\) −38.4072 34.0258i −1.69903 1.50521i
\(512\) 1.21317 + 20.0561i 0.0536150 + 0.886361i
\(513\) 25.1813 26.8371i 1.11178 1.18489i
\(514\) 51.6170 + 23.2309i 2.27673 + 1.02467i
\(515\) 5.06300 7.33502i 0.223102 0.323219i
\(516\) 5.10191 + 4.79746i 0.224599 + 0.211196i
\(517\) −2.90215 23.9014i −0.127636 1.05118i
\(518\) 15.7741 30.0551i 0.693075 1.32054i
\(519\) −1.09520 35.6108i −0.0480741 1.56314i
\(520\) −0.327633 + 0.369821i −0.0143676 + 0.0162177i
\(521\) 15.0852 15.0852i 0.660894 0.660894i −0.294697 0.955591i \(-0.595219\pi\)
0.955591 + 0.294697i \(0.0952187\pi\)
\(522\) −2.67788 43.4947i −0.117208 1.90371i
\(523\) −8.30135 21.8889i −0.362993 0.957133i −0.984758 0.173930i \(-0.944353\pi\)
0.621765 0.783204i \(-0.286416\pi\)
\(524\) −15.7038 + 9.49326i −0.686022 + 0.414715i
\(525\) −23.2102 + 8.02332i −1.01298 + 0.350167i
\(526\) 4.10701 + 3.21763i 0.179074 + 0.140295i
\(527\) 10.5793 15.3268i 0.460843 0.667647i
\(528\) 5.37490 3.95938i 0.233912 0.172310i
\(529\) 21.6105 + 2.62399i 0.939588 + 0.114087i
\(530\) 25.6075 + 15.4803i 1.11232 + 0.672420i
\(531\) −1.18558 + 3.13627i −0.0514496 + 0.136103i
\(532\) 69.8185 42.2068i 3.02702 1.82990i
\(533\) −0.582579 + 0.0352396i −0.0252343 + 0.00152639i
\(534\) −46.8476 34.4324i −2.02730 1.49003i
\(535\) 2.78127 5.29928i 0.120245 0.229108i
\(536\) 11.6121 3.61848i 0.501566 0.156294i
\(537\) 1.80763 + 19.7742i 0.0780052 + 0.853320i
\(538\) 6.36198 + 1.56809i 0.274284 + 0.0676050i
\(539\) 2.56554 21.1292i 0.110506 0.910097i
\(540\) −17.9403 + 2.76008i −0.772029 + 0.118775i
\(541\) 18.2534 + 14.3006i 0.784774 + 0.614832i 0.927025 0.374999i \(-0.122357\pi\)
−0.142251 + 0.989831i \(0.545434\pi\)
\(542\) 7.48262 30.3582i 0.321406 1.30400i
\(543\) 10.8123 19.1947i 0.463998 0.823724i
\(544\) 16.4842 + 36.6264i 0.706755 + 1.57034i
\(545\) −14.9143 + 11.6846i −0.638858 + 0.500513i
\(546\) −0.328705 + 3.63894i −0.0140673 + 0.155732i
\(547\) 17.3567 2.10749i 0.742119 0.0901096i 0.259260 0.965808i \(-0.416521\pi\)
0.482859 + 0.875698i \(0.339598\pi\)
\(548\) −1.27456 + 2.10838i −0.0544465 + 0.0900656i
\(549\) 0.0566543 + 0.0638111i 0.00241795 + 0.00272339i
\(550\) −2.78624 + 15.2040i −0.118806 + 0.648302i
\(551\) 40.3008 + 24.3627i 1.71687 + 1.03789i
\(552\) 0.678754 3.17027i 0.0288897 0.134935i
\(553\) 13.5301 + 54.8936i 0.575356 + 2.33431i
\(554\) −24.0568 30.7062i −1.02207 1.30458i
\(555\) −0.742935 8.12717i −0.0315358 0.344979i
\(556\) 57.9004 + 10.6106i 2.45552 + 0.449991i
\(557\) −16.8643 4.15668i −0.714564 0.176124i −0.134757 0.990879i \(-0.543026\pi\)
−0.579806 + 0.814755i \(0.696872\pi\)
\(558\) 5.43064 + 21.9315i 0.229897 + 0.928433i
\(559\) 0.139105 0.309079i 0.00588352 0.0130726i
\(560\) 9.66072 + 1.17302i 0.408240 + 0.0495693i
\(561\) 10.5252 16.2983i 0.444375 0.688115i
\(562\) −26.8236 59.5997i −1.13149 2.51406i
\(563\) 1.52791 + 4.90322i 0.0643935 + 0.206646i 0.981310 0.192433i \(-0.0616377\pi\)
−0.916917 + 0.399079i \(0.869330\pi\)
\(564\) −40.5780 + 38.2388i −1.70864 + 1.61014i
\(565\) −3.04997 + 9.78771i −0.128313 + 0.411772i
\(566\) −3.61529 59.7679i −0.151962 2.51223i
\(567\) −26.3859 + 26.4996i −1.10810 + 1.11288i
\(568\) 0.599385 + 1.92349i 0.0251496 + 0.0807080i
\(569\) −0.208033 + 0.344129i −0.00872120 + 0.0144266i −0.860111 0.510106i \(-0.829606\pi\)
0.851390 + 0.524533i \(0.175760\pi\)
\(570\) 14.7656 30.3671i 0.618464 1.27194i
\(571\) 10.2550 14.8570i 0.429159 0.621744i −0.547432 0.836850i \(-0.684394\pi\)
0.976591 + 0.215106i \(0.0690097\pi\)
\(572\) 1.09948 + 0.758916i 0.0459715 + 0.0317319i
\(573\) −20.8303 32.1797i −0.870198 1.34433i
\(574\) −14.0588 17.9447i −0.586802 0.748998i
\(575\) −1.95845 3.23967i −0.0816730 0.135104i
\(576\) −35.8857 11.1401i −1.49524 0.464172i
\(577\) −14.6445 + 12.9739i −0.609658 + 0.540110i −0.910471 0.413573i \(-0.864281\pi\)
0.300813 + 0.953683i \(0.402742\pi\)
\(578\) 18.8180 + 18.8180i 0.782727 + 0.782727i
\(579\) −5.79911 10.2692i −0.241003 0.426772i
\(580\) −8.23652 21.7179i −0.342003 0.901788i
\(581\) 29.0593 + 15.2515i 1.20558 + 0.632739i
\(582\) 13.1823 61.5709i 0.546426 2.55220i
\(583\) 9.25110 20.5551i 0.383142 0.851306i
\(584\) 17.1477 + 11.8362i 0.709577 + 0.489786i
\(585\) 0.409089 + 0.777421i 0.0169137 + 0.0321424i
\(586\) 51.3594 12.6590i 2.12164 0.522937i
\(587\) −43.2687 + 2.61727i −1.78589 + 0.108026i −0.919929 0.392084i \(-0.871754\pi\)
−0.865962 + 0.500111i \(0.833293\pi\)
\(588\) −42.9189 + 24.2368i −1.76995 + 0.999507i
\(589\) −22.8298 8.65820i −0.940685 0.356755i
\(590\) −0.185749 + 3.07079i −0.00764714 + 0.126422i
\(591\) −14.9610 + 2.28525i −0.615412 + 0.0940025i
\(592\) 2.46477 6.49908i 0.101302 0.267110i
\(593\) 21.2882 18.8597i 0.874200 0.774474i −0.101211 0.994865i \(-0.532272\pi\)
0.975412 + 0.220391i \(0.0707334\pi\)
\(594\) 6.35715 + 22.6629i 0.260837 + 0.929869i
\(595\) 27.4607 6.76845i 1.12578 0.277480i
\(596\) −21.8695 17.1336i −0.895809 0.701821i
\(597\) −17.9018 + 36.8170i −0.732672 + 1.50682i
\(598\) −0.559125 + 0.0678900i −0.0228643 + 0.00277623i
\(599\) −0.119479 + 0.383422i −0.00488179 + 0.0156662i −0.957130 0.289660i \(-0.906458\pi\)
0.952248 + 0.305326i \(0.0987655\pi\)
\(600\) 8.96354 4.37033i 0.365935 0.178418i
\(601\) −27.8431 + 14.6132i −1.13575 + 0.596085i −0.924437 0.381334i \(-0.875465\pi\)
−0.211308 + 0.977420i \(0.567772\pi\)
\(602\) 13.0215 2.38628i 0.530718 0.0972576i
\(603\) 1.28254 21.5879i 0.0522289 0.879128i
\(604\) −21.5830 + 3.95524i −0.878202 + 0.160936i
\(605\) 8.42728 + 0.509757i 0.342618 + 0.0207246i
\(606\) 8.06843 + 16.5484i 0.327758 + 0.672231i
\(607\) 1.49399 + 24.6985i 0.0606390 + 1.00248i 0.893518 + 0.449027i \(0.148229\pi\)
−0.832879 + 0.553455i \(0.813309\pi\)
\(608\) 41.4520 32.4756i 1.68110 1.31706i
\(609\) −40.1994 25.9602i −1.62896 1.05196i
\(610\) 0.0670040 + 0.0405053i 0.00271291 + 0.00164001i
\(611\) 2.38939 + 1.25405i 0.0966642 + 0.0507333i
\(612\) −44.8442 + 2.76096i −1.81272 + 0.111605i
\(613\) −1.61910 + 26.7669i −0.0653948 + 1.08111i 0.806443 + 0.591311i \(0.201390\pi\)
−0.871838 + 0.489794i \(0.837072\pi\)
\(614\) −3.03784 4.40106i −0.122597 0.177613i
\(615\) −5.18210 1.78512i −0.208963 0.0719829i
\(616\) 14.5370i 0.585711i
\(617\) 12.8467 + 18.6117i 0.517190 + 0.749279i 0.991362 0.131153i \(-0.0418680\pi\)
−0.474172 + 0.880432i \(0.657253\pi\)
\(618\) 4.04130 + 26.4574i 0.162565 + 1.06427i
\(619\) 18.0382 20.3610i 0.725018 0.818376i −0.264255 0.964453i \(-0.585126\pi\)
0.989273 + 0.146077i \(0.0466646\pi\)
\(620\) 6.23024 + 10.3061i 0.250213 + 0.413902i
\(621\) −4.84596 3.12208i −0.194462 0.125285i
\(622\) 67.2755 + 12.3287i 2.69750 + 0.494336i
\(623\) −60.9545 + 18.9942i −2.44209 + 0.760987i
\(624\) 0.0230001 + 0.747853i 0.000920740 + 0.0299381i
\(625\) 1.31403 3.46481i 0.0525611 0.138592i
\(626\) −1.20821 6.59299i −0.0482898 0.263509i
\(627\) −24.0495 8.28450i −0.960444 0.330851i
\(628\) −0.348423 34.7357i −0.0139036 1.38610i
\(629\) 20.2006i 0.805449i
\(630\) −15.9130 + 30.3990i −0.633987 + 1.21112i
\(631\) 23.7544 + 9.00884i 0.945646 + 0.358636i 0.778747 0.627338i \(-0.215855\pi\)
0.166899 + 0.985974i \(0.446625\pi\)
\(632\) −8.14092 21.4658i −0.323828 0.853865i
\(633\) −1.71260 0.0508280i −0.0680698 0.00202023i
\(634\) 5.98774 32.6741i 0.237804 1.29765i
\(635\) −1.72265 3.82757i −0.0683613 0.151893i
\(636\) −51.0310 + 10.9831i −2.02351 + 0.435509i
\(637\) 1.78557 + 1.58188i 0.0707469 + 0.0626763i
\(638\) −26.6697 + 13.9973i −1.05586 + 0.554160i
\(639\) 3.57594 + 0.212447i 0.141462 + 0.00840426i
\(640\) −15.7397 −0.622166
\(641\) 43.8639 1.73252 0.866259 0.499594i \(-0.166518\pi\)
0.866259 + 0.499594i \(0.166518\pi\)
\(642\) 4.83535 + 17.3093i 0.190836 + 0.683143i
\(643\) −7.30356 0.441784i −0.288024 0.0174223i −0.0842654 0.996443i \(-0.526854\pi\)
−0.203759 + 0.979021i \(0.565316\pi\)
\(644\) −8.47440 9.56562i −0.333938 0.376938i
\(645\) 2.31647 2.18293i 0.0912107 0.0859527i
\(646\) 43.2394 71.5266i 1.70123 2.81418i
\(647\) 2.78064 11.2815i 0.109318 0.443521i −0.890619 0.454751i \(-0.849728\pi\)
0.999937 + 0.0112296i \(0.00357457\pi\)
\(648\) 9.33932 11.9737i 0.366883 0.470371i
\(649\) 2.31323 0.139924i 0.0908020 0.00549251i
\(650\) −1.22500 1.22500i −0.0480483 0.0480483i
\(651\) 22.9274 + 9.48239i 0.898595 + 0.371644i
\(652\) −0.153117 0.835530i −0.00599651 0.0327219i
\(653\) 27.9917 + 40.5529i 1.09540 + 1.58696i 0.766086 + 0.642738i \(0.222202\pi\)
0.329313 + 0.944221i \(0.393183\pi\)
\(654\) 8.53041 56.2517i 0.333566 2.19961i
\(655\) 3.87586 + 7.38483i 0.151442 + 0.288549i
\(656\) −3.30086 3.30086i −0.128877 0.128877i
\(657\) 30.4666 21.0780i 1.18862 0.822331i
\(658\) 12.7043 + 104.629i 0.495265 + 4.07888i
\(659\) 2.82328 23.2518i 0.109979 0.905760i −0.828396 0.560143i \(-0.810746\pi\)
0.938375 0.345618i \(-0.112331\pi\)
\(660\) 6.81747 + 10.5320i 0.265370 + 0.409957i
\(661\) −1.12528 4.56544i −0.0437683 0.177575i 0.944990 0.327101i \(-0.106072\pi\)
−0.988758 + 0.149525i \(0.952225\pi\)
\(662\) 2.08823 + 0.650720i 0.0811615 + 0.0252909i
\(663\) 0.833211 + 2.00850i 0.0323592 + 0.0780035i
\(664\) −12.4606 4.72567i −0.483564 0.183392i
\(665\) −17.2320 32.8328i −0.668227 1.27320i
\(666\) 18.3613 + 16.2315i 0.711486 + 0.628958i
\(667\) 2.61579 6.89727i 0.101284 0.267063i
\(668\) −27.1960 + 30.6979i −1.05224 + 1.18774i
\(669\) 20.8451 + 5.79894i 0.805919 + 0.224200i
\(670\) −4.74867 19.2661i −0.183457 0.744315i
\(671\) 0.0242062 0.0537840i 0.000934470 0.00207631i
\(672\) −43.0820 + 31.7361i −1.66193 + 1.22425i
\(673\) −39.5784 17.8128i −1.52563 0.686632i −0.537933 0.842987i \(-0.680795\pi\)
−0.987701 + 0.156355i \(0.950025\pi\)
\(674\) 22.2612 2.70300i 0.857469 0.104116i
\(675\) −1.63311 17.6556i −0.0628583 0.679565i
\(676\) 33.5585 12.7271i 1.29071 0.489502i
\(677\) 12.3679 + 10.9570i 0.475336 + 0.421111i 0.866475 0.499221i \(-0.166380\pi\)
−0.391139 + 0.920332i \(0.627919\pi\)
\(678\) −13.4919 27.6719i −0.518154 1.06273i
\(679\) −45.8516 51.7558i −1.75962 1.98620i
\(680\) −10.7384 + 4.07252i −0.411797 + 0.156174i
\(681\) −7.44592 + 1.60254i −0.285328 + 0.0614096i
\(682\) 12.2930 9.63097i 0.470724 0.368789i
\(683\) −17.7830 + 22.6984i −0.680449 + 0.868529i −0.996785 0.0801182i \(-0.974470\pi\)
0.316336 + 0.948647i \(0.397547\pi\)
\(684\) 17.5848 + 56.2186i 0.672370 + 2.14957i
\(685\) 0.921532 + 0.636087i 0.0352099 + 0.0243036i
\(686\) −3.57196 + 29.4177i −0.136378 + 1.12317i
\(687\) 6.30601 5.26115i 0.240589 0.200725i
\(688\) 2.58817 0.806507i 0.0986731 0.0307478i
\(689\) 1.30697 + 2.16199i 0.0497916 + 0.0823653i
\(690\) −5.09575 1.41760i −0.193992 0.0539669i
\(691\) 7.06713 + 2.20221i 0.268846 + 0.0837759i 0.428963 0.903322i \(-0.358879\pi\)
−0.160116 + 0.987098i \(0.551187\pi\)
\(692\) 50.4942 + 26.5014i 1.91950 + 1.00743i
\(693\) 24.1775 + 9.13959i 0.918427 + 0.347184i
\(694\) −11.4176 + 5.13863i −0.433405 + 0.195060i
\(695\) 6.40262 25.9765i 0.242865 0.985343i
\(696\) 17.4754 + 8.49719i 0.662403 + 0.322085i
\(697\) −12.3715 5.56794i −0.468602 0.210901i
\(698\) −12.5601 + 16.0318i −0.475408 + 0.606813i
\(699\) 6.71714 10.4015i 0.254066 0.393421i
\(700\) 7.08542 38.6639i 0.267804 1.46136i
\(701\) −15.9791 + 7.19162i −0.603524 + 0.271624i −0.689052 0.724712i \(-0.741973\pi\)
0.0855285 + 0.996336i \(0.472742\pi\)
\(702\) −2.49512 0.856513i −0.0941723 0.0323270i
\(703\) −25.7145 + 6.33806i −0.969842 + 0.239045i
\(704\) 3.13049 + 25.7819i 0.117985 + 0.971692i
\(705\) 16.2342 + 19.4583i 0.611416 + 0.732843i
\(706\) 42.4837 + 7.78542i 1.59889 + 0.293008i
\(707\) 19.8859 + 3.64424i 0.747888 + 0.137056i
\(708\) −3.43803 4.12082i −0.129209 0.154870i
\(709\) −0.615893 5.07233i −0.0231303 0.190495i 0.976564 0.215228i \(-0.0690496\pi\)
−0.999694 + 0.0247329i \(0.992126\pi\)
\(710\) 3.19135 0.786597i 0.119769 0.0295205i
\(711\) −40.8197 + 0.0438828i −1.53086 + 0.00164573i
\(712\) 23.6416 10.6402i 0.886007 0.398759i
\(713\) −0.689409 + 3.76199i −0.0258186 + 0.140887i
\(714\) −46.0747 + 71.3466i −1.72430 + 2.67008i
\(715\) 0.374469 0.477974i 0.0140043 0.0178752i
\(716\) −28.9828 13.0441i −1.08314 0.487481i
\(717\) −23.6582 11.5035i −0.883532 0.429606i
\(718\) −15.5264 + 62.9931i −0.579440 + 2.35088i
\(719\) −40.0829 + 18.0398i −1.49484 + 0.672773i −0.982543 0.186036i \(-0.940436\pi\)
−0.512297 + 0.858808i \(0.671205\pi\)
\(720\) −2.48451 + 6.57242i −0.0925923 + 0.244940i
\(721\) 26.0241 + 13.6585i 0.969188 + 0.508669i
\(722\) −64.9898 20.2516i −2.41867 0.753688i
\(723\) 0.702485 + 0.195425i 0.0261257 + 0.00726795i
\(724\) 18.2425 + 30.1768i 0.677979 + 1.12151i
\(725\) 21.6620 6.75014i 0.804505 0.250694i
\(726\) −19.4673 + 16.2417i −0.722498 + 0.602786i
\(727\) −2.85914 + 23.5471i −0.106040 + 0.873314i 0.838497 + 0.544907i \(0.183435\pi\)
−0.944536 + 0.328407i \(0.893488\pi\)
\(728\) −1.34086 0.925529i −0.0496956 0.0343024i
\(729\) −14.0426 23.0609i −0.520095 0.854108i
\(730\) 20.9637 26.7582i 0.775902 0.990366i
\(731\) 6.20188 4.85886i 0.229385 0.179712i
\(732\) −0.133526 + 0.0287382i −0.00493528 + 0.00106219i
\(733\) 32.3106 12.2538i 1.19342 0.452605i 0.323705 0.946158i \(-0.395071\pi\)
0.869716 + 0.493553i \(0.164302\pi\)
\(734\) −1.22554 1.38335i −0.0452355 0.0510604i
\(735\) 9.81770 + 20.1361i 0.362131 + 0.742731i
\(736\) −6.17411 5.46979i −0.227581 0.201619i
\(737\) −13.9762 + 5.30046i −0.514819 + 0.195245i
\(738\) 15.0017 6.77110i 0.552218 0.249248i
\(739\) 6.24765 0.758603i 0.229824 0.0279056i −0.00481456 0.999988i \(-0.501533\pi\)
0.234638 + 0.972083i \(0.424609\pi\)
\(740\) 11.9119 + 5.36111i 0.437890 + 0.197078i
\(741\) 2.29531 1.69082i 0.0843204 0.0621140i
\(742\) −40.4971 + 89.9810i −1.48670 + 3.30331i
\(743\) 10.4290 + 42.3122i 0.382604 + 1.55229i 0.774681 + 0.632353i \(0.217911\pi\)
−0.392077 + 0.919932i \(0.628243\pi\)
\(744\) −9.70636 2.70023i −0.355852 0.0989951i
\(745\) −8.37315 + 9.45133i −0.306769 + 0.346270i
\(746\) −9.50171 + 25.0540i −0.347882 + 0.917290i
\(747\) −15.6937 + 17.7530i −0.574204 + 0.649548i
\(748\) 14.4316 + 27.4972i 0.527673 + 1.00540i
\(749\) 18.4530 + 6.99831i 0.674259 + 0.255713i
\(750\) −15.3683 37.0461i −0.561171 1.35273i
\(751\) 28.8208 + 8.98093i 1.05169 + 0.327719i 0.774154 0.632997i \(-0.218176\pi\)
0.277533 + 0.960716i \(0.410483\pi\)
\(752\) 5.16517 + 20.9559i 0.188354 + 0.764184i
\(753\) −13.4892 20.8388i −0.491572 0.759407i
\(754\) 0.406901 3.35113i 0.0148185 0.122041i
\(755\) 1.20209 + 9.90010i 0.0437485 + 0.360302i
\(756\) −16.1663 57.6317i −0.587961 2.09605i
\(757\) 6.64791 + 6.64791i 0.241622 + 0.241622i 0.817521 0.575899i \(-0.195348\pi\)
−0.575899 + 0.817521i \(0.695348\pi\)
\(758\) −34.3875 65.5199i −1.24901 2.37979i
\(759\) −0.597393 + 3.93936i −0.0216840 + 0.142990i
\(760\) 8.55340 + 12.3917i 0.310264 + 0.449495i
\(761\) −8.08681 44.1283i −0.293147 1.59965i −0.719102 0.694905i \(-0.755446\pi\)
0.425955 0.904744i \(-0.359938\pi\)
\(762\) 11.6475 + 4.81724i 0.421946 + 0.174510i
\(763\) −44.1784 44.1784i −1.59937 1.59937i
\(764\) 61.2448 3.70463i 2.21576 0.134029i
\(765\) 0.0219525 + 20.4202i 0.000793695 + 0.738294i
\(766\) 12.0442 48.8653i 0.435175 1.76558i
\(767\) −0.134370 + 0.222276i −0.00485184 + 0.00802592i
\(768\) 2.82182 2.65915i 0.101824 0.0959538i
\(769\) −33.6802 38.0171i −1.21454 1.37093i −0.907944 0.419092i \(-0.862349\pi\)
−0.306596 0.951840i \(-0.599190\pi\)
\(770\) 23.6727 + 1.43193i 0.853104 + 0.0516033i
\(771\) 12.0746 + 43.2239i 0.434856 + 1.55667i
\(772\) 18.8768 0.679391
\(773\) −24.6795 −0.887659 −0.443829 0.896111i \(-0.646380\pi\)
−0.443829 + 0.896111i \(0.646380\pi\)
\(774\) −0.566853 + 9.54138i −0.0203751 + 0.342958i
\(775\) −10.4165 + 5.46698i −0.374170 + 0.196380i
\(776\) 21.0164 + 18.6189i 0.754447 + 0.668381i
\(777\) 26.3095 5.66245i 0.943848 0.203139i
\(778\) −14.6744 32.6052i −0.526104 1.16895i
\(779\) −3.20614 + 17.4954i −0.114872 + 0.626836i
\(780\) −1.40550 0.0417136i −0.0503250 0.00149359i
\(781\) −0.877999 2.31509i −0.0314173 0.0828405i
\(782\) −12.2414 4.64255i −0.437752 0.166017i
\(783\) 25.1193 23.7223i 0.897691 0.847766i
\(784\) 19.0798i 0.681421i
\(785\) −15.7681 0.795146i −0.562787 0.0283800i
\(786\) −23.6794 8.15700i −0.844615 0.290951i
\(787\) −4.89439 26.7078i −0.174466 0.952031i −0.947999 0.318275i \(-0.896897\pi\)
0.773532 0.633757i \(-0.218488\pi\)
\(788\) 8.59014 22.6503i 0.306011 0.806885i
\(789\) 0.127160 + 4.13465i 0.00452703 + 0.147197i
\(790\) −35.7579 + 11.1426i −1.27221 + 0.396436i
\(791\) −33.2530 6.09384i −1.18234 0.216672i
\(792\) −10.1935 2.50085i −0.362211 0.0888639i
\(793\) 0.00341978 + 0.00565701i 0.000121440 + 0.000200886i
\(794\) −33.3462 + 37.6401i −1.18341 + 1.33580i
\(795\) 3.58232 + 23.4526i 0.127052 + 0.831778i
\(796\) −37.2236 53.9277i −1.31935 1.91142i
\(797\) 21.5472i 0.763240i −0.924319 0.381620i \(-0.875366\pi\)
0.924319 0.381620i \(-0.124634\pi\)
\(798\) 105.278 + 36.2658i 3.72679 + 1.28380i
\(799\) 35.6322 + 51.6221i 1.26058 + 1.82626i
\(800\) 1.53187 25.3248i 0.0541598 0.895368i
\(801\) −2.83272 46.0098i −0.100089 1.62567i
\(802\) −19.7338 10.3571i −0.696826 0.365722i
\(803\) −21.9135 13.2472i −0.773311 0.467483i
\(804\) 29.0785 + 18.7785i 1.02552 + 0.662267i
\(805\) −4.57218 + 3.58207i −0.161148 + 0.126252i
\(806\) 0.105678 + 1.74706i 0.00372234 + 0.0615377i
\(807\) 2.27675 + 4.66962i 0.0801456 + 0.164379i
\(808\) −8.19457 0.495680i −0.288284 0.0174380i
\(809\) −43.3993 + 7.95321i −1.52584 + 0.279620i −0.876695 0.481047i \(-0.840257\pi\)
−0.649142 + 0.760667i \(0.724872\pi\)
\(810\) −18.5786 16.3880i −0.652785 0.575817i
\(811\) −7.34116 + 1.34532i −0.257783 + 0.0472405i −0.307592 0.951518i \(-0.599523\pi\)
0.0498093 + 0.998759i \(0.484139\pi\)
\(812\) 67.8211 35.5953i 2.38006 1.24915i
\(813\) 22.2826 10.8643i 0.781484 0.381026i
\(814\) 5.03938 16.1719i 0.176630 0.566826i
\(815\) −0.383256 + 0.0465357i −0.0134249 + 0.00163008i
\(816\) −7.60520 + 15.6409i −0.266235 + 0.547542i
\(817\) −8.13103 6.37025i −0.284469 0.222867i
\(818\) 81.5149 20.0916i 2.85010 0.702487i
\(819\) −2.38233 + 1.64819i −0.0832455 + 0.0575924i
\(820\) 6.56661 5.81751i 0.229316 0.203156i
\(821\) −6.85012 + 18.0623i −0.239071 + 0.630378i −0.999826 0.0186614i \(-0.994060\pi\)
0.760755 + 0.649039i \(0.224829\pi\)
\(822\) −3.32397 + 0.507727i −0.115937 + 0.0177090i
\(823\) −0.951390 + 15.7284i −0.0331634 + 0.548256i 0.943214 + 0.332185i \(0.107786\pi\)
−0.976378 + 0.216071i \(0.930676\pi\)
\(824\) −11.1591 4.23208i −0.388745 0.147431i
\(825\) −10.6714 + 6.02624i −0.371529 + 0.209807i
\(826\) −10.1263 + 0.612526i −0.352337 + 0.0213125i
\(827\) 11.0330 2.71938i 0.383654 0.0945623i −0.0427715 0.999085i \(-0.513619\pi\)
0.426426 + 0.904523i \(0.359773\pi\)
\(828\) 8.16542 4.29674i 0.283768 0.149322i
\(829\) −5.47798 3.78118i −0.190258 0.131326i 0.469128 0.883130i \(-0.344568\pi\)
−0.659386 + 0.751805i \(0.729184\pi\)
\(830\) −8.92291 + 19.8259i −0.309719 + 0.688167i
\(831\) 6.47484 30.2421i 0.224610 1.04909i
\(832\) −2.57738 1.35271i −0.0893546 0.0468969i
\(833\) 19.6630 + 51.8470i 0.681281 + 1.79639i
\(834\) 39.5051 + 69.9564i 1.36795 + 2.42239i
\(835\) 13.1804 + 13.1804i 0.456126 + 0.456126i
\(836\) 30.4748 26.9983i 1.05399 0.933757i
\(837\) −10.5935 + 14.4457i −0.366164 + 0.499316i
\(838\) −26.5488 43.9170i −0.917112 1.51709i
\(839\) −12.6925 16.2008i −0.438193 0.559312i 0.516736 0.856145i \(-0.327147\pi\)
−0.954930 + 0.296832i \(0.904070\pi\)
\(840\) −8.31420 12.8442i −0.286867 0.443167i
\(841\) 12.5193 + 8.64148i 0.431701 + 0.297982i
\(842\) 17.8141 25.8082i 0.613915 0.889410i
\(843\) 22.6598 46.6023i 0.780444 1.60507i
\(844\) 1.41876 2.34692i 0.0488358 0.0807842i
\(845\) −4.85297 15.5737i −0.166947 0.535752i
\(846\) −75.5530 9.09139i −2.59757 0.312568i
\(847\) 1.68098 + 27.7899i 0.0577590 + 0.954871i
\(848\) −6.01142 + 19.2913i −0.206433 + 0.662467i
\(849\) 34.5503 32.5586i 1.18576 1.11741i
\(850\) −11.9803 38.4460i −0.410920 1.31869i
\(851\) 1.70260 + 3.78303i 0.0583645 + 0.129681i
\(852\) −3.11058 + 4.81673i −0.106567 + 0.165018i
\(853\) −32.8591 3.98981i −1.12507 0.136609i −0.463221 0.886243i \(-0.653306\pi\)
−0.661852 + 0.749634i \(0.730229\pi\)
\(854\) −0.105964 + 0.235442i −0.00362601 + 0.00805666i
\(855\) 25.9872 6.43492i 0.888745 0.220070i
\(856\) −7.78112 1.91787i −0.265953 0.0655516i
\(857\) 3.12767 + 0.573167i 0.106839 + 0.0195790i 0.233409 0.972379i \(-0.425012\pi\)
−0.126569 + 0.991958i \(0.540397\pi\)
\(858\) 0.165989 + 1.81580i 0.00566677 + 0.0619903i
\(859\) 15.5017 + 19.7865i 0.528911 + 0.675105i 0.975593 0.219588i \(-0.0704712\pi\)
−0.446682 + 0.894693i \(0.647394\pi\)
\(860\) 1.21924 + 4.94664i 0.0415757 + 0.168679i
\(861\) 3.78390 17.6735i 0.128955 0.602311i
\(862\) 10.6932 + 6.46424i 0.364211 + 0.220173i
\(863\) −1.96589 + 10.7275i −0.0669198 + 0.365169i 0.933065 + 0.359707i \(0.117123\pi\)
−0.999985 + 0.00546236i \(0.998261\pi\)
\(864\) −14.8422 35.6694i −0.504941 1.21350i
\(865\) 13.4085 22.1804i 0.455904 0.754157i
\(866\) 48.2522 5.85888i 1.63968 0.199093i
\(867\) −1.89824 + 21.0145i −0.0644675 + 0.713690i
\(868\) −31.2612 + 24.4916i −1.06107 + 0.831299i
\(869\) 11.5794 + 25.7283i 0.392803 + 0.872772i
\(870\) 15.5586 27.6208i 0.527486 0.936432i
\(871\) 0.400921 1.62660i 0.0135847 0.0551153i
\(872\) 19.9711 + 15.6463i 0.676306 + 0.529852i
\(873\) 44.1799 23.2480i 1.49526 0.786825i
\(874\) −2.06897 + 17.0395i −0.0699838 + 0.576369i
\(875\) −42.7631 10.5402i −1.44566 0.356322i
\(876\) 5.39818 + 59.0522i 0.182388 + 1.99519i
\(877\) 10.6002 3.30317i 0.357945 0.111540i −0.113256 0.993566i \(-0.536128\pi\)
0.471201 + 0.882026i \(0.343820\pi\)
\(878\) −7.23297 + 13.7813i −0.244101 + 0.465096i
\(879\) 33.7934 + 24.8377i 1.13982 + 0.837754i
\(880\) 4.84763 0.293228i 0.163414 0.00988470i
\(881\) −1.04952 + 0.634459i −0.0353594 + 0.0213755i −0.534907 0.844911i \(-0.679653\pi\)
0.499548 + 0.866286i \(0.333500\pi\)
\(882\) −62.9259 23.7873i −2.11882 0.800959i
\(883\) 6.34579 + 3.83617i 0.213553 + 0.129097i 0.620072 0.784545i \(-0.287104\pi\)
−0.406519 + 0.913642i \(0.633257\pi\)
\(884\) −3.45511 0.419526i −0.116208 0.0141102i
\(885\) −1.96383 + 1.44664i −0.0660136 + 0.0486284i
\(886\) 8.32037 12.0541i 0.279528 0.404967i
\(887\) 17.1263 + 13.4176i 0.575044 + 0.450518i 0.861630 0.507536i \(-0.169444\pi\)
−0.286587 + 0.958054i \(0.592521\pi\)
\(888\) −10.3284 + 3.57034i −0.346600 + 0.119813i
\(889\) 11.8451 7.16060i 0.397271 0.240159i
\(890\) −14.9983 39.5472i −0.502744 1.32563i
\(891\) −10.5682 + 15.3812i −0.354046 + 0.515291i
\(892\) −24.4886 + 24.4886i −0.819938 + 0.819938i
\(893\) 54.5331 61.5552i 1.82488 2.05987i
\(894\) −1.16560 37.8997i −0.0389835 1.26756i
\(895\) −6.71306 + 12.7907i −0.224393 + 0.427545i
\(896\) −6.25625 51.5249i −0.209007 1.72132i
\(897\) −0.325324 0.305911i −0.0108623 0.0102141i
\(898\) 18.9232 27.4150i 0.631475 0.914849i
\(899\) −20.9036 9.40793i −0.697173 0.313772i
\(900\) 25.8927 + 11.6199i 0.863089 + 0.387330i
\(901\) 3.54567 + 58.6170i 0.118124 + 1.95281i
\(902\) −8.51518 7.54379i −0.283524 0.251181i
\(903\) 8.06671 + 6.71542i 0.268443 + 0.223475i
\(904\) 13.7029 + 0.828870i 0.455750 + 0.0275678i
\(905\) 14.1909 7.44797i 0.471722 0.247579i
\(906\) −23.0161 19.1606i −0.764658 0.636567i
\(907\) −13.3297 15.0462i −0.442606 0.499599i 0.484295 0.874905i \(-0.339076\pi\)
−0.926901 + 0.375306i \(0.877538\pi\)
\(908\) 3.62685 11.6390i 0.120361 0.386253i
\(909\) −5.97644 + 13.3174i −0.198226 + 0.441709i
\(910\) −1.63925 + 2.09235i −0.0543408 + 0.0693609i
\(911\) 4.46471 + 0.542113i 0.147922 + 0.0179610i 0.194163 0.980969i \(-0.437801\pi\)
−0.0462405 + 0.998930i \(0.514724\pi\)
\(912\) 22.2965 + 4.77368i 0.738310 + 0.158072i
\(913\) 15.6362 + 4.87242i 0.517481 + 0.161254i
\(914\) −63.6684 + 63.6684i −2.10596 + 2.10596i
\(915\) 0.00937341 + 0.0613655i 0.000309875 + 0.00202868i
\(916\) 2.36947 + 12.9298i 0.0782895 + 0.427212i
\(917\) −22.6341 + 15.6232i −0.747445 + 0.515924i
\(918\) −42.1028 44.5822i −1.38960 1.47143i
\(919\) 0.621824 10.2800i 0.0205121 0.339105i −0.973414 0.229054i \(-0.926437\pi\)
0.993926 0.110051i \(-0.0351015\pi\)
\(920\) 1.66776 1.66776i 0.0549843 0.0549843i
\(921\) 1.13637 4.08483i 0.0374446 0.134600i
\(922\) 36.5833 + 46.6951i 1.20481 + 1.53782i
\(923\) 0.269439 + 0.0664108i 0.00886870 + 0.00218594i
\(924\) −31.7673 + 26.5037i −1.04507 + 0.871908i
\(925\) −5.92994 + 11.2985i −0.194975 + 0.371494i
\(926\) −7.45946 + 6.60851i −0.245133 + 0.217169i
\(927\) −14.0545 + 15.8987i −0.461612 + 0.522182i
\(928\) 40.6866 28.0839i 1.33560 0.921899i
\(929\) 13.3546i 0.438149i 0.975708 + 0.219074i \(0.0703037\pi\)
−0.975708 + 0.219074i \(0.929696\pi\)
\(930\) −5.35328 + 15.5403i −0.175541 + 0.509587i
\(931\) 59.8298 41.2975i 1.96084 1.35347i
\(932\) 9.21019 + 17.5485i 0.301690 + 0.574822i
\(933\) 26.6652 + 47.2192i 0.872979 + 1.54589i
\(934\) 51.6296 31.2112i 1.68937 1.02126i
\(935\) 12.8707 5.79261i 0.420915 0.189439i
\(936\) 0.879667 0.781006i 0.0287528 0.0255280i
\(937\) 9.89006 + 31.7383i 0.323094 + 1.03685i 0.963251 + 0.268601i \(0.0865614\pi\)
−0.640157 + 0.768244i \(0.721131\pi\)
\(938\) 61.1814 23.2030i 1.99764 0.757606i
\(939\) 3.40012 4.08430i 0.110959 0.133286i
\(940\) −39.8972 + 7.31142i −1.30130 + 0.238472i
\(941\) −10.7389 −0.350077 −0.175039 0.984562i \(-0.556005\pi\)
−0.175039 + 0.984562i \(0.556005\pi\)
\(942\) 36.0980 30.7361i 1.17614 1.00144i
\(943\) 2.78614 0.0907291
\(944\) −2.04339 + 0.374465i −0.0665067 + 0.0121878i
\(945\) −26.5894 + 5.75261i −0.864953 + 0.187132i
\(946\) 6.17716 2.34269i 0.200837 0.0761674i
\(947\) −0.831639 2.66882i −0.0270247 0.0867252i 0.940223 0.340559i \(-0.110616\pi\)
−0.967248 + 0.253833i \(0.918308\pi\)
\(948\) 32.0664 56.9266i 1.04147 1.84889i
\(949\) 2.61707 1.17785i 0.0849536 0.0382345i
\(950\) −45.1814 + 27.3131i −1.46588 + 0.886155i
\(951\) 22.9332 12.9506i 0.743660 0.419953i
\(952\) −17.6000 33.5340i −0.570418 1.08684i
\(953\) −44.1495 + 30.4742i −1.43014 + 0.987157i −0.433864 + 0.900979i \(0.642850\pi\)
−0.996280 + 0.0861781i \(0.972535\pi\)
\(954\) −56.1289 43.8769i −1.81724 1.42057i
\(955\) 27.8866i 0.902388i
\(956\) 34.6533 23.9194i 1.12077 0.773610i
\(957\) −22.0677 9.12686i −0.713349 0.295030i
\(958\) −56.3163 + 49.8919i −1.81950 + 1.61193i
\(959\) −1.71598 + 3.26953i −0.0554119 + 0.105579i
\(960\) −17.5115 20.9893i −0.565182 0.677427i
\(961\) −18.5594 4.57448i −0.598691 0.147564i
\(962\) 1.17082 + 1.49445i 0.0377489 + 0.0481829i
\(963\) −8.08185 + 11.7356i −0.260434 + 0.378173i
\(964\) −0.825270 + 0.825270i −0.0265801 + 0.0265801i
\(965\) 0.518016 8.56382i 0.0166755 0.275679i
\(966\) 2.61512 17.2447i 0.0841400 0.554840i
\(967\) 1.67524 1.15633i 0.0538721 0.0371852i −0.540824 0.841136i \(-0.681888\pi\)
0.594696 + 0.803950i \(0.297272\pi\)
\(968\) −2.03783 11.1201i −0.0654982 0.357412i
\(969\) 65.5075 10.0061i 2.10441 0.321442i
\(970\) 32.3902 32.3902i 1.03999 1.03999i
\(971\) −36.5767 11.3978i −1.17380 0.365772i −0.352251 0.935905i \(-0.614584\pi\)
−0.821552 + 0.570134i \(0.806891\pi\)
\(972\) 43.1933 1.42136i 1.38542 0.0455903i
\(973\) 87.5805 + 10.6342i 2.80770 + 0.340917i
\(974\) −14.1485 + 18.0592i −0.453348 + 0.578656i
\(975\) 0.123569 1.36798i 0.00395739 0.0438104i
\(976\) −0.0157293 + 0.0504772i −0.000503484 + 0.00161574i
\(977\) −5.90939 6.67032i −0.189058 0.213402i 0.646338 0.763052i \(-0.276300\pi\)
−0.835396 + 0.549649i \(0.814761\pi\)
\(978\) 0.741750 0.891007i 0.0237186 0.0284913i
\(979\) −28.2119 + 14.8067i −0.901655 + 0.473225i
\(980\) −35.7916 2.16499i −1.14332 0.0691582i
\(981\) 38.5787 23.3783i 1.23172 0.746411i
\(982\) 35.4186 + 31.3781i 1.13025 + 1.00132i
\(983\) 3.01424 + 49.8313i 0.0961393 + 1.58937i 0.652080 + 0.758150i \(0.273897\pi\)
−0.555940 + 0.831222i \(0.687642\pi\)
\(984\) −0.660271 + 7.30955i −0.0210487 + 0.233020i
\(985\) −10.0400 4.51865i −0.319902 0.143976i
\(986\) 44.5752 64.5783i 1.41956 2.05659i
\(987\) −57.2453 + 60.8781i −1.82214 + 1.93777i
\(988\) 0.550023 + 4.52985i 0.0174986 + 0.144114i
\(989\) −0.751919 + 1.43266i −0.0239096 + 0.0455560i
\(990\) −5.07660 + 16.3532i −0.161345 + 0.519740i
\(991\) 2.44725 2.76238i 0.0777395 0.0877497i −0.708354 0.705857i \(-0.750562\pi\)
0.786093 + 0.618108i \(0.212100\pi\)
\(992\) −18.1249 + 18.1249i −0.575467 + 0.575467i
\(993\) 0.664508 + 1.60183i 0.0210875 + 0.0508325i
\(994\) 3.84348 + 10.1344i 0.121908 + 0.321444i
\(995\) −25.4868 + 15.4073i −0.807986 + 0.488445i
\(996\) −12.3911 35.8457i −0.392628 1.13581i
\(997\) −45.9036 35.9632i −1.45378 1.13896i −0.963601 0.267343i \(-0.913854\pi\)
−0.490179 0.871622i \(-0.663069\pi\)
\(998\) −1.30829 + 1.89539i −0.0414133 + 0.0599976i
\(999\) −0.555544 + 19.4227i −0.0175766 + 0.614507i
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 471.2.s.a.2.8 1200
3.2 odd 2 inner 471.2.s.a.2.43 yes 1200
157.79 odd 52 inner 471.2.s.a.236.43 yes 1200
471.236 even 52 inner 471.2.s.a.236.8 yes 1200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.s.a.2.8 1200 1.1 even 1 trivial
471.2.s.a.2.43 yes 1200 3.2 odd 2 inner
471.2.s.a.236.8 yes 1200 471.236 even 52 inner
471.2.s.a.236.43 yes 1200 157.79 odd 52 inner