Properties

Label 160.2.u.a.43.10
Level $160$
Weight $2$
Character 160.43
Analytic conductor $1.278$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [160,2,Mod(43,160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(160, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("160.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.u (of order \(8\), 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: \(1.27760643234\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 43.10
Character \(\chi\) \(=\) 160.43
Dual form 160.2.u.a.67.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.458371 + 1.33787i) q^{2} +(0.218753 - 0.528116i) q^{3} +(-1.57979 - 1.22648i) q^{4} +(1.03318 + 1.98306i) q^{5} +(0.606280 + 0.534736i) q^{6} +0.814088i q^{7} +(2.36500 - 1.55137i) q^{8} +(1.89027 + 1.89027i) q^{9} +O(q^{10})\) \(q+(-0.458371 + 1.33787i) q^{2} +(0.218753 - 0.528116i) q^{3} +(-1.57979 - 1.22648i) q^{4} +(1.03318 + 1.98306i) q^{5} +(0.606280 + 0.534736i) q^{6} +0.814088i q^{7} +(2.36500 - 1.55137i) q^{8} +(1.89027 + 1.89027i) q^{9} +(-3.12666 + 0.473287i) q^{10} +(-2.18824 + 5.28289i) q^{11} +(-0.993308 + 0.566017i) q^{12} +(1.29817 - 3.13405i) q^{13} +(-1.08914 - 0.373154i) q^{14} +(1.27330 - 0.111840i) q^{15} +(0.991489 + 3.87517i) q^{16} +(1.06141 + 1.06141i) q^{17} +(-3.39537 + 1.66249i) q^{18} +(-1.35555 - 3.27259i) q^{19} +(0.799973 - 4.40000i) q^{20} +(0.429932 + 0.178084i) q^{21} +(-6.06479 - 5.34911i) q^{22} -7.06624i q^{23} +(-0.301954 - 1.58836i) q^{24} +(-2.86507 + 4.09773i) q^{25} +(3.59791 + 3.17334i) q^{26} +(2.99613 - 1.24104i) q^{27} +(0.998463 - 1.28609i) q^{28} +(1.28483 + 3.10185i) q^{29} +(-0.434015 + 1.75477i) q^{30} -3.96241i q^{31} +(-5.63894 - 0.449781i) q^{32} +(2.31129 + 2.31129i) q^{33} +(-1.90655 + 0.933511i) q^{34} +(-1.61439 + 0.841101i) q^{35} +(-0.667853 - 5.30461i) q^{36} +(-1.68376 - 4.06496i) q^{37} +(4.99965 - 0.313492i) q^{38} +(-1.37117 - 1.37117i) q^{39} +(5.51995 + 3.08709i) q^{40} +(7.46225 - 7.46225i) q^{41} +(-0.435322 + 0.493565i) q^{42} +(-3.40086 + 1.40868i) q^{43} +(9.93633 - 5.66203i) q^{44} +(-1.79553 + 5.70151i) q^{45} +(9.45371 + 3.23896i) q^{46} +(5.53756 - 5.53756i) q^{47} +(2.26343 + 0.324083i) q^{48} +6.33726 q^{49} +(-4.16897 - 5.71137i) q^{50} +(0.792735 - 0.328362i) q^{51} +(-5.89469 + 3.35898i) q^{52} +(-1.74894 - 4.22232i) q^{53} +(0.287009 + 4.57729i) q^{54} +(-12.7371 + 1.11876i) q^{55} +(1.26295 + 1.92532i) q^{56} -2.02484 q^{57} +(-4.73880 + 0.297136i) q^{58} +(-2.42524 + 5.85504i) q^{59} +(-2.14872 - 1.38499i) q^{60} +(-14.3773 + 5.95527i) q^{61} +(5.30118 + 1.81625i) q^{62} +(-1.53884 + 1.53884i) q^{63} +(3.18648 - 7.33801i) q^{64} +(7.55626 - 0.663703i) q^{65} +(-4.15164 + 2.03278i) q^{66} +(-0.0299831 - 0.0124194i) q^{67} +(-0.375009 - 2.97861i) q^{68} +(-3.73179 - 1.54576i) q^{69} +(-0.385297 - 2.54537i) q^{70} +(-3.37479 + 3.37479i) q^{71} +(7.40300 + 1.53798i) q^{72} -6.66157 q^{73} +(6.21017 - 0.389395i) q^{74} +(1.53733 + 2.40948i) q^{75} +(-1.87228 + 6.83258i) q^{76} +(-4.30073 - 1.78142i) q^{77} +(2.46294 - 1.20594i) q^{78} -3.45823i q^{79} +(-6.66031 + 5.96994i) q^{80} +6.16594i q^{81} +(6.56304 + 13.4040i) q^{82} +(-3.60660 - 1.49390i) q^{83} +(-0.460788 - 0.808640i) q^{84} +(-1.00821 + 3.20148i) q^{85} +(-0.325779 - 5.19561i) q^{86} +1.91919 q^{87} +(3.02053 + 15.8888i) q^{88} +(-0.670113 + 0.670113i) q^{89} +(-6.80486 - 5.01558i) q^{90} +(2.55139 + 1.05682i) q^{91} +(-8.66661 + 11.1632i) q^{92} +(-2.09261 - 0.866787i) q^{93} +(4.87028 + 9.94680i) q^{94} +(5.08922 - 6.06933i) q^{95} +(-1.47107 + 2.87962i) q^{96} +(6.31432 - 6.31432i) q^{97} +(-2.90482 + 8.47843i) q^{98} +(-14.1224 + 5.84970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.458371 + 1.33787i −0.324117 + 0.946017i
\(3\) 0.218753 0.528116i 0.126297 0.304908i −0.848066 0.529891i \(-0.822233\pi\)
0.974363 + 0.224983i \(0.0722328\pi\)
\(4\) −1.57979 1.22648i −0.789896 0.613240i
\(5\) 1.03318 + 1.98306i 0.462053 + 0.886852i
\(6\) 0.606280 + 0.534736i 0.247513 + 0.218305i
\(7\) 0.814088i 0.307696i 0.988095 + 0.153848i \(0.0491666\pi\)
−0.988095 + 0.153848i \(0.950833\pi\)
\(8\) 2.36500 1.55137i 0.836155 0.548494i
\(9\) 1.89027 + 1.89027i 0.630089 + 0.630089i
\(10\) −3.12666 + 0.473287i −0.988737 + 0.149666i
\(11\) −2.18824 + 5.28289i −0.659780 + 1.59285i 0.138362 + 0.990382i \(0.455816\pi\)
−0.798142 + 0.602469i \(0.794184\pi\)
\(12\) −0.993308 + 0.566017i −0.286743 + 0.163395i
\(13\) 1.29817 3.13405i 0.360047 0.869230i −0.635245 0.772310i \(-0.719101\pi\)
0.995292 0.0969195i \(-0.0308989\pi\)
\(14\) −1.08914 0.373154i −0.291086 0.0997296i
\(15\) 1.27330 0.111840i 0.328764 0.0288769i
\(16\) 0.991489 + 3.87517i 0.247872 + 0.968793i
\(17\) 1.06141 + 1.06141i 0.257430 + 0.257430i 0.824008 0.566578i \(-0.191733\pi\)
−0.566578 + 0.824008i \(0.691733\pi\)
\(18\) −3.39537 + 1.66249i −0.800297 + 0.391852i
\(19\) −1.35555 3.27259i −0.310985 0.750785i −0.999669 0.0257229i \(-0.991811\pi\)
0.688684 0.725062i \(-0.258189\pi\)
\(20\) 0.799973 4.40000i 0.178879 0.983871i
\(21\) 0.429932 + 0.178084i 0.0938190 + 0.0388611i
\(22\) −6.06479 5.34911i −1.29302 1.14043i
\(23\) 7.06624i 1.47341i −0.676213 0.736707i \(-0.736380\pi\)
0.676213 0.736707i \(-0.263620\pi\)
\(24\) −0.301954 1.58836i −0.0616362 0.324223i
\(25\) −2.86507 + 4.09773i −0.573014 + 0.819546i
\(26\) 3.59791 + 3.17334i 0.705609 + 0.622343i
\(27\) 2.99613 1.24104i 0.576605 0.238838i
\(28\) 0.998463 1.28609i 0.188692 0.243048i
\(29\) 1.28483 + 3.10185i 0.238586 + 0.575999i 0.997137 0.0756156i \(-0.0240922\pi\)
−0.758551 + 0.651614i \(0.774092\pi\)
\(30\) −0.434015 + 1.75477i −0.0792400 + 0.320376i
\(31\) 3.96241i 0.711669i −0.934549 0.355834i \(-0.884197\pi\)
0.934549 0.355834i \(-0.115803\pi\)
\(32\) −5.63894 0.449781i −0.996834 0.0795109i
\(33\) 2.31129 + 2.31129i 0.402344 + 0.402344i
\(34\) −1.90655 + 0.933511i −0.326971 + 0.160096i
\(35\) −1.61439 + 0.841101i −0.272881 + 0.142172i
\(36\) −0.667853 5.30461i −0.111309 0.884101i
\(37\) −1.68376 4.06496i −0.276809 0.668275i 0.722935 0.690916i \(-0.242793\pi\)
−0.999744 + 0.0226409i \(0.992793\pi\)
\(38\) 4.99965 0.313492i 0.811051 0.0508552i
\(39\) −1.37117 1.37117i −0.219562 0.219562i
\(40\) 5.51995 + 3.08709i 0.872781 + 0.488112i
\(41\) 7.46225 7.46225i 1.16541 1.16541i 0.182133 0.983274i \(-0.441700\pi\)
0.983274 0.182133i \(-0.0583002\pi\)
\(42\) −0.435322 + 0.493565i −0.0671716 + 0.0761588i
\(43\) −3.40086 + 1.40868i −0.518626 + 0.214822i −0.626613 0.779330i \(-0.715559\pi\)
0.107987 + 0.994152i \(0.465559\pi\)
\(44\) 9.93633 5.66203i 1.49796 0.853583i
\(45\) −1.79553 + 5.70151i −0.267661 + 0.849930i
\(46\) 9.45371 + 3.23896i 1.39387 + 0.477558i
\(47\) 5.53756 5.53756i 0.807737 0.807737i −0.176554 0.984291i \(-0.556495\pi\)
0.984291 + 0.176554i \(0.0564951\pi\)
\(48\) 2.26343 + 0.324083i 0.326698 + 0.0467774i
\(49\) 6.33726 0.905323
\(50\) −4.16897 5.71137i −0.589581 0.807709i
\(51\) 0.792735 0.328362i 0.111005 0.0459798i
\(52\) −5.89469 + 3.35898i −0.817446 + 0.465806i
\(53\) −1.74894 4.22232i −0.240236 0.579981i 0.757070 0.653334i \(-0.226630\pi\)
−0.997306 + 0.0733529i \(0.976630\pi\)
\(54\) 0.287009 + 4.57729i 0.0390569 + 0.622890i
\(55\) −12.7371 + 1.11876i −1.71748 + 0.150854i
\(56\) 1.26295 + 1.92532i 0.168769 + 0.257282i
\(57\) −2.02484 −0.268197
\(58\) −4.73880 + 0.297136i −0.622234 + 0.0390158i
\(59\) −2.42524 + 5.85504i −0.315739 + 0.762261i 0.683732 + 0.729733i \(0.260356\pi\)
−0.999471 + 0.0325278i \(0.989644\pi\)
\(60\) −2.14872 1.38499i −0.277398 0.178802i
\(61\) −14.3773 + 5.95527i −1.84083 + 0.762495i −0.887291 + 0.461211i \(0.847415\pi\)
−0.953534 + 0.301284i \(0.902585\pi\)
\(62\) 5.30118 + 1.81625i 0.673251 + 0.230664i
\(63\) −1.53884 + 1.53884i −0.193876 + 0.193876i
\(64\) 3.18648 7.33801i 0.398310 0.917251i
\(65\) 7.55626 0.663703i 0.937239 0.0823222i
\(66\) −4.15164 + 2.03278i −0.511031 + 0.250218i
\(67\) −0.0299831 0.0124194i −0.00366302 0.00151727i 0.380851 0.924636i \(-0.375631\pi\)
−0.384514 + 0.923119i \(0.625631\pi\)
\(68\) −0.375009 2.97861i −0.0454765 0.361210i
\(69\) −3.73179 1.54576i −0.449255 0.186088i
\(70\) −0.385297 2.54537i −0.0460518 0.304230i
\(71\) −3.37479 + 3.37479i −0.400514 + 0.400514i −0.878414 0.477900i \(-0.841398\pi\)
0.477900 + 0.878414i \(0.341398\pi\)
\(72\) 7.40300 + 1.53798i 0.872452 + 0.181252i
\(73\) −6.66157 −0.779677 −0.389839 0.920883i \(-0.627469\pi\)
−0.389839 + 0.920883i \(0.627469\pi\)
\(74\) 6.21017 0.389395i 0.721918 0.0452663i
\(75\) 1.53733 + 2.40948i 0.177516 + 0.278222i
\(76\) −1.87228 + 6.83258i −0.214765 + 0.783751i
\(77\) −4.30073 1.78142i −0.490114 0.203012i
\(78\) 2.46294 1.20594i 0.278873 0.136546i
\(79\) 3.45823i 0.389081i −0.980895 0.194540i \(-0.937678\pi\)
0.980895 0.194540i \(-0.0623215\pi\)
\(80\) −6.66031 + 5.96994i −0.744646 + 0.667460i
\(81\) 6.16594i 0.685104i
\(82\) 6.56304 + 13.4040i 0.724767 + 1.48022i
\(83\) −3.60660 1.49390i −0.395876 0.163977i 0.175859 0.984415i \(-0.443730\pi\)
−0.571735 + 0.820438i \(0.693730\pi\)
\(84\) −0.460788 0.808640i −0.0502761 0.0882298i
\(85\) −1.00821 + 3.20148i −0.109356 + 0.347249i
\(86\) −0.325779 5.19561i −0.0351297 0.560257i
\(87\) 1.91919 0.205759
\(88\) 3.02053 + 15.8888i 0.321990 + 1.69375i
\(89\) −0.670113 + 0.670113i −0.0710319 + 0.0710319i −0.741730 0.670698i \(-0.765995\pi\)
0.670698 + 0.741730i \(0.265995\pi\)
\(90\) −6.80486 5.01558i −0.717295 0.528689i
\(91\) 2.55139 + 1.05682i 0.267459 + 0.110785i
\(92\) −8.66661 + 11.1632i −0.903557 + 1.16384i
\(93\) −2.09261 0.866787i −0.216993 0.0898816i
\(94\) 4.87028 + 9.94680i 0.502331 + 1.02593i
\(95\) 5.08922 6.06933i 0.522143 0.622700i
\(96\) −1.47107 + 2.87962i −0.150141 + 0.293900i
\(97\) 6.31432 6.31432i 0.641122 0.641122i −0.309709 0.950831i \(-0.600232\pi\)
0.950831 + 0.309709i \(0.100232\pi\)
\(98\) −2.90482 + 8.47843i −0.293431 + 0.856451i
\(99\) −14.1224 + 5.84970i −1.41936 + 0.587917i
\(100\) 9.55200 2.95961i 0.955200 0.295961i
\(101\) 3.71176 8.96097i 0.369334 0.891650i −0.624526 0.781004i \(-0.714708\pi\)
0.993860 0.110646i \(-0.0352921\pi\)
\(102\) 0.0759386 + 1.21109i 0.00751904 + 0.119916i
\(103\) 11.8642 1.16901 0.584507 0.811388i \(-0.301288\pi\)
0.584507 + 0.811388i \(0.301288\pi\)
\(104\) −1.79192 9.42599i −0.175712 0.924294i
\(105\) 0.0910475 + 1.03658i 0.00888532 + 0.101159i
\(106\) 6.45058 0.404470i 0.626536 0.0392856i
\(107\) 6.96510 + 16.8153i 0.673342 + 1.62559i 0.775894 + 0.630864i \(0.217299\pi\)
−0.102551 + 0.994728i \(0.532701\pi\)
\(108\) −6.25537 1.71411i −0.601923 0.164941i
\(109\) 7.10157 2.94157i 0.680207 0.281751i −0.0157062 0.999877i \(-0.505000\pi\)
0.695914 + 0.718126i \(0.255000\pi\)
\(110\) 4.34157 17.5535i 0.413953 1.67366i
\(111\) −2.51510 −0.238722
\(112\) −3.15473 + 0.807159i −0.298094 + 0.0762693i
\(113\) −6.45581 + 6.45581i −0.607311 + 0.607311i −0.942243 0.334931i \(-0.891287\pi\)
0.334931 + 0.942243i \(0.391287\pi\)
\(114\) 0.928127 2.70897i 0.0869271 0.253718i
\(115\) 14.0128 7.30072i 1.30670 0.680795i
\(116\) 1.77460 6.47609i 0.164767 0.601290i
\(117\) 8.37808 3.47031i 0.774554 0.320831i
\(118\) −6.72162 5.92843i −0.618776 0.545756i
\(119\) −0.864082 + 0.864082i −0.0792103 + 0.0792103i
\(120\) 2.83785 2.23986i 0.259059 0.204471i
\(121\) −15.3423 15.3423i −1.39476 1.39476i
\(122\) −1.37725 21.9647i −0.124690 1.98859i
\(123\) −2.30854 5.57332i −0.208154 0.502529i
\(124\) −4.85981 + 6.25978i −0.436424 + 0.562145i
\(125\) −11.0862 1.44790i −0.991579 0.129504i
\(126\) −1.35341 2.76413i −0.120571 0.246248i
\(127\) 5.63123 + 5.63123i 0.499691 + 0.499691i 0.911342 0.411651i \(-0.135048\pi\)
−0.411651 + 0.911342i \(0.635048\pi\)
\(128\) 8.35671 + 7.62662i 0.738636 + 0.674104i
\(129\) 2.10420i 0.185264i
\(130\) −2.57562 + 10.4135i −0.225897 + 0.913326i
\(131\) 0.886992 + 2.14139i 0.0774969 + 0.187094i 0.957880 0.287170i \(-0.0927143\pi\)
−0.880383 + 0.474264i \(0.842714\pi\)
\(132\) −0.816606 6.48612i −0.0710765 0.564544i
\(133\) 2.66418 1.10354i 0.231014 0.0956889i
\(134\) 0.0303589 0.0344208i 0.00262261 0.00297351i
\(135\) 5.55660 + 4.65929i 0.478236 + 0.401008i
\(136\) 4.15689 + 0.863595i 0.356450 + 0.0740527i
\(137\) 2.52984i 0.216139i −0.994143 0.108069i \(-0.965533\pi\)
0.994143 0.108069i \(-0.0344669\pi\)
\(138\) 3.77857 4.28412i 0.321653 0.364689i
\(139\) −3.32332 1.37656i −0.281880 0.116759i 0.237264 0.971445i \(-0.423749\pi\)
−0.519144 + 0.854687i \(0.673749\pi\)
\(140\) 3.58199 + 0.651248i 0.302733 + 0.0550405i
\(141\) −1.71312 4.13583i −0.144271 0.348300i
\(142\) −2.96813 6.06194i −0.249080 0.508707i
\(143\) 13.7161 + 13.7161i 1.14700 + 1.14700i
\(144\) −5.45093 + 9.19929i −0.454244 + 0.766607i
\(145\) −4.82369 + 5.75267i −0.400586 + 0.477733i
\(146\) 3.05347 8.91231i 0.252707 0.737588i
\(147\) 1.38629 3.34681i 0.114340 0.276040i
\(148\) −2.32560 + 8.48689i −0.191163 + 0.697618i
\(149\) 3.35125 8.09064i 0.274545 0.662811i −0.725122 0.688621i \(-0.758217\pi\)
0.999667 + 0.0258101i \(0.00821651\pi\)
\(150\) −3.92824 + 0.952320i −0.320739 + 0.0777566i
\(151\) −3.49423 3.49423i −0.284357 0.284357i 0.550487 0.834844i \(-0.314442\pi\)
−0.834844 + 0.550487i \(0.814442\pi\)
\(152\) −8.28290 5.63672i −0.671832 0.457199i
\(153\) 4.01270i 0.324408i
\(154\) 4.35464 4.93727i 0.350907 0.397857i
\(155\) 7.85769 4.09389i 0.631145 0.328829i
\(156\) 0.484449 + 3.84786i 0.0387869 + 0.308076i
\(157\) −2.87473 + 6.94022i −0.229429 + 0.553890i −0.996108 0.0881404i \(-0.971908\pi\)
0.766679 + 0.642030i \(0.221908\pi\)
\(158\) 4.62666 + 1.58515i 0.368077 + 0.126108i
\(159\) −2.61246 −0.207182
\(160\) −4.93412 11.6471i −0.390076 0.920783i
\(161\) 5.75254 0.453364
\(162\) −8.24923 2.82629i −0.648120 0.222054i
\(163\) 7.78578 18.7965i 0.609829 1.47226i −0.253358 0.967373i \(-0.581535\pi\)
0.863187 0.504885i \(-0.168465\pi\)
\(164\) −20.9411 + 2.63650i −1.63523 + 0.205876i
\(165\) −2.19545 + 6.97142i −0.170915 + 0.542724i
\(166\) 3.65181 4.14040i 0.283435 0.321358i
\(167\) 9.46735i 0.732605i 0.930496 + 0.366303i \(0.119377\pi\)
−0.930496 + 0.366303i \(0.880623\pi\)
\(168\) 1.29307 0.245817i 0.0997622 0.0189652i
\(169\) 1.05534 + 1.05534i 0.0811800 + 0.0811800i
\(170\) −3.82103 2.81632i −0.293059 0.216002i
\(171\) 3.62372 8.74843i 0.277113 0.669009i
\(172\) 7.10037 + 1.94566i 0.541398 + 0.148355i
\(173\) −2.33654 + 5.64090i −0.177644 + 0.428870i −0.987471 0.157798i \(-0.949561\pi\)
0.809828 + 0.586668i \(0.199561\pi\)
\(174\) −0.879702 + 2.56763i −0.0666901 + 0.194652i
\(175\) −3.33591 2.33242i −0.252171 0.176314i
\(176\) −22.6417 3.24189i −1.70668 0.244367i
\(177\) 2.56161 + 2.56161i 0.192542 + 0.192542i
\(178\) −0.589364 1.20368i −0.0441747 0.0902200i
\(179\) 7.90631 + 19.0875i 0.590945 + 1.42667i 0.882591 + 0.470141i \(0.155797\pi\)
−0.291646 + 0.956526i \(0.594203\pi\)
\(180\) 9.82935 6.80502i 0.732636 0.507216i
\(181\) 6.59835 + 2.73313i 0.490451 + 0.203152i 0.614182 0.789164i \(-0.289486\pi\)
−0.123731 + 0.992316i \(0.539486\pi\)
\(182\) −2.58337 + 2.92902i −0.191492 + 0.217113i
\(183\) 8.89561i 0.657583i
\(184\) −10.9624 16.7117i −0.808158 1.23200i
\(185\) 6.32143 7.53885i 0.464761 0.554267i
\(186\) 2.11884 2.40233i 0.155361 0.176147i
\(187\) −7.92995 + 3.28469i −0.579895 + 0.240200i
\(188\) −15.5399 + 1.95649i −1.13336 + 0.142691i
\(189\) 1.01031 + 2.43911i 0.0734894 + 0.177419i
\(190\) 5.78723 + 9.59072i 0.419850 + 0.695784i
\(191\) 13.1291i 0.949988i 0.879989 + 0.474994i \(0.157550\pi\)
−0.879989 + 0.474994i \(0.842450\pi\)
\(192\) −3.17827 3.28804i −0.229372 0.237294i
\(193\) −11.7096 11.7096i −0.842875 0.842875i 0.146357 0.989232i \(-0.453245\pi\)
−0.989232 + 0.146357i \(0.953245\pi\)
\(194\) 5.55344 + 11.3420i 0.398714 + 0.814311i
\(195\) 1.30244 4.13577i 0.0932697 0.296169i
\(196\) −10.0116 7.77253i −0.715111 0.555181i
\(197\) −8.13349 19.6360i −0.579487 1.39901i −0.893274 0.449512i \(-0.851598\pi\)
0.313787 0.949493i \(-0.398402\pi\)
\(198\) −1.35283 21.5753i −0.0961416 1.53329i
\(199\) −8.06864 8.06864i −0.571971 0.571971i 0.360708 0.932679i \(-0.382535\pi\)
−0.932679 + 0.360708i \(0.882535\pi\)
\(200\) −0.418781 + 14.1359i −0.0296123 + 0.999561i
\(201\) −0.0131178 + 0.0131178i −0.000925257 + 0.000925257i
\(202\) 10.2873 + 9.07330i 0.723809 + 0.638395i
\(203\) −2.52518 + 1.04596i −0.177233 + 0.0734121i
\(204\) −1.65509 0.453531i −0.115879 0.0317535i
\(205\) 22.5080 + 7.08823i 1.57202 + 0.495064i
\(206\) −5.43820 + 15.8728i −0.378898 + 1.10591i
\(207\) 13.3571 13.3571i 0.928381 0.928381i
\(208\) 13.4321 + 1.92324i 0.931349 + 0.133353i
\(209\) 20.2550 1.40107
\(210\) −1.42854 0.353326i −0.0985784 0.0243818i
\(211\) −13.7348 + 5.68914i −0.945542 + 0.391656i −0.801554 0.597923i \(-0.795993\pi\)
−0.143989 + 0.989579i \(0.545993\pi\)
\(212\) −2.41563 + 8.81544i −0.165906 + 0.605447i
\(213\) 1.04404 + 2.52053i 0.0715362 + 0.172704i
\(214\) −25.6892 + 1.61079i −1.75608 + 0.110111i
\(215\) −6.30721 5.28869i −0.430148 0.360685i
\(216\) 5.16054 7.58317i 0.351130 0.515969i
\(217\) 3.22574 0.218978
\(218\) 0.680282 + 10.8493i 0.0460745 + 0.734808i
\(219\) −1.45724 + 3.51808i −0.0984709 + 0.237730i
\(220\) 21.4942 + 13.8545i 1.44914 + 0.934067i
\(221\) 4.70441 1.94863i 0.316453 0.131079i
\(222\) 1.15285 3.36487i 0.0773740 0.225835i
\(223\) −2.21049 + 2.21049i −0.148025 + 0.148025i −0.777235 0.629210i \(-0.783379\pi\)
0.629210 + 0.777235i \(0.283379\pi\)
\(224\) 0.366161 4.59059i 0.0244652 0.306722i
\(225\) −13.1615 + 2.33006i −0.877436 + 0.155337i
\(226\) −5.67788 11.5962i −0.377687 0.771367i
\(227\) −9.30656 3.85490i −0.617698 0.255859i 0.0518179 0.998657i \(-0.483498\pi\)
−0.669516 + 0.742798i \(0.733498\pi\)
\(228\) 3.19883 + 2.48343i 0.211847 + 0.164469i
\(229\) −2.85613 1.18305i −0.188738 0.0781780i 0.286313 0.958136i \(-0.407570\pi\)
−0.475051 + 0.879958i \(0.657570\pi\)
\(230\) 3.34436 + 22.0937i 0.220520 + 1.45682i
\(231\) −1.88159 + 1.88159i −0.123800 + 0.123800i
\(232\) 7.85075 + 5.34263i 0.515427 + 0.350761i
\(233\) −19.3641 −1.26858 −0.634291 0.773095i \(-0.718708\pi\)
−0.634291 + 0.773095i \(0.718708\pi\)
\(234\) 0.802563 + 12.7995i 0.0524652 + 0.836727i
\(235\) 16.7026 + 5.26002i 1.08956 + 0.343126i
\(236\) 11.0125 6.27524i 0.716850 0.408483i
\(237\) −1.82634 0.756496i −0.118634 0.0491397i
\(238\) −0.759960 1.55210i −0.0492609 0.100608i
\(239\) 1.09143i 0.0705985i −0.999377 0.0352993i \(-0.988762\pi\)
0.999377 0.0352993i \(-0.0112384\pi\)
\(240\) 1.69586 + 4.82336i 0.109467 + 0.311346i
\(241\) 0.331423i 0.0213488i 0.999943 + 0.0106744i \(0.00339784\pi\)
−0.999943 + 0.0106744i \(0.996602\pi\)
\(242\) 27.5585 13.4936i 1.77153 0.867399i
\(243\) 12.2447 + 5.07193i 0.785499 + 0.325364i
\(244\) 30.0172 + 8.22539i 1.92165 + 0.526577i
\(245\) 6.54755 + 12.5672i 0.418307 + 0.802888i
\(246\) 8.51454 0.533886i 0.542867 0.0340393i
\(247\) −12.0162 −0.764573
\(248\) −6.14717 9.37110i −0.390346 0.595065i
\(249\) −1.57791 + 1.57791i −0.0999959 + 0.0999959i
\(250\) 7.01869 14.1682i 0.443901 0.896076i
\(251\) 17.7733 + 7.36194i 1.12184 + 0.464681i 0.865000 0.501773i \(-0.167319\pi\)
0.256840 + 0.966454i \(0.417319\pi\)
\(252\) 4.31841 0.543691i 0.272034 0.0342493i
\(253\) 37.3302 + 15.4627i 2.34693 + 0.972129i
\(254\) −10.1150 + 4.95266i −0.634674 + 0.310758i
\(255\) 1.47020 + 1.23279i 0.0920676 + 0.0772000i
\(256\) −14.0339 + 7.68438i −0.877119 + 0.480274i
\(257\) −18.6648 + 18.6648i −1.16428 + 1.16428i −0.180746 + 0.983530i \(0.557851\pi\)
−0.983530 + 0.180746i \(0.942149\pi\)
\(258\) −2.81515 0.964504i −0.175263 0.0600474i
\(259\) 3.30923 1.37073i 0.205626 0.0851729i
\(260\) −12.7513 8.21910i −0.790805 0.509727i
\(261\) −3.43465 + 8.29198i −0.212600 + 0.513261i
\(262\) −3.27147 + 0.205131i −0.202112 + 0.0126730i
\(263\) −22.8147 −1.40681 −0.703407 0.710788i \(-0.748339\pi\)
−0.703407 + 0.710788i \(0.748339\pi\)
\(264\) 9.05189 + 1.88053i 0.557105 + 0.115739i
\(265\) 6.56615 7.83069i 0.403355 0.481036i
\(266\) 0.255210 + 4.07015i 0.0156479 + 0.249557i
\(267\) 0.207308 + 0.500486i 0.0126871 + 0.0306293i
\(268\) 0.0321349 + 0.0563938i 0.00196295 + 0.00344480i
\(269\) −25.2576 + 10.4620i −1.53998 + 0.637882i −0.981471 0.191613i \(-0.938628\pi\)
−0.558514 + 0.829495i \(0.688628\pi\)
\(270\) −8.78051 + 5.29833i −0.534365 + 0.322446i
\(271\) −2.59431 −0.157593 −0.0787965 0.996891i \(-0.525108\pi\)
−0.0787965 + 0.996891i \(0.525108\pi\)
\(272\) −3.06077 + 5.16553i −0.185587 + 0.313206i
\(273\) 1.11625 1.11625i 0.0675584 0.0675584i
\(274\) 3.38460 + 1.15960i 0.204471 + 0.0700543i
\(275\) −15.3784 24.1027i −0.927351 1.45345i
\(276\) 3.99962 + 7.01895i 0.240749 + 0.422491i
\(277\) −14.3113 + 5.92794i −0.859883 + 0.356175i −0.768662 0.639655i \(-0.779077\pi\)
−0.0912215 + 0.995831i \(0.529077\pi\)
\(278\) 3.36498 3.81519i 0.201818 0.228820i
\(279\) 7.49000 7.49000i 0.448415 0.448415i
\(280\) −2.51316 + 4.49372i −0.150190 + 0.268551i
\(281\) −10.7050 10.7050i −0.638609 0.638609i 0.311603 0.950212i \(-0.399134\pi\)
−0.950212 + 0.311603i \(0.899134\pi\)
\(282\) 6.31845 0.396185i 0.376258 0.0235924i
\(283\) −6.62305 15.9895i −0.393700 0.950475i −0.989127 0.147066i \(-0.953017\pi\)
0.595427 0.803409i \(-0.296983\pi\)
\(284\) 9.47060 1.19235i 0.561977 0.0707532i
\(285\) −2.09203 4.01538i −0.123921 0.237851i
\(286\) −24.6375 + 12.0633i −1.45685 + 0.713320i
\(287\) 6.07492 + 6.07492i 0.358591 + 0.358591i
\(288\) −9.80890 11.5093i −0.577995 0.678193i
\(289\) 14.7468i 0.867459i
\(290\) −5.48528 9.09033i −0.322107 0.533802i
\(291\) −1.95342 4.71597i −0.114511 0.276455i
\(292\) 10.5239 + 8.17028i 0.615864 + 0.478130i
\(293\) 11.2873 4.67536i 0.659412 0.273137i −0.0277793 0.999614i \(-0.508844\pi\)
0.687191 + 0.726477i \(0.258844\pi\)
\(294\) 3.84216 + 3.38876i 0.224079 + 0.197636i
\(295\) −14.1166 + 1.23993i −0.821901 + 0.0721915i
\(296\) −10.2884 7.00149i −0.597999 0.406954i
\(297\) 18.5439i 1.07603i
\(298\) 9.28810 + 8.19205i 0.538045 + 0.474553i
\(299\) −22.1460 9.17316i −1.28073 0.530498i
\(300\) 0.526508 5.69199i 0.0303980 0.328627i
\(301\) −1.14679 2.76860i −0.0660999 0.159579i
\(302\) 6.27648 3.07317i 0.361171 0.176841i
\(303\) −3.92047 3.92047i −0.225225 0.225225i
\(304\) 11.3378 8.49774i 0.650270 0.487379i
\(305\) −26.6641 22.3582i −1.52678 1.28023i
\(306\) −5.36848 1.83931i −0.306895 0.105146i
\(307\) 6.02953 14.5566i 0.344124 0.830788i −0.653166 0.757215i \(-0.726560\pi\)
0.997290 0.0735732i \(-0.0234403\pi\)
\(308\) 4.60939 + 8.08904i 0.262644 + 0.460916i
\(309\) 2.59533 6.26567i 0.147643 0.356442i
\(310\) 1.87535 + 12.3891i 0.106513 + 0.703653i
\(311\) 18.4513 + 18.4513i 1.04628 + 1.04628i 0.998876 + 0.0474028i \(0.0150944\pi\)
0.0474028 + 0.998876i \(0.484906\pi\)
\(312\) −5.37000 1.11562i −0.304016 0.0631595i
\(313\) 30.4836i 1.72304i 0.507726 + 0.861519i \(0.330486\pi\)
−0.507726 + 0.861519i \(0.669514\pi\)
\(314\) −7.96742 7.02721i −0.449627 0.396568i
\(315\) −4.64153 1.46171i −0.261520 0.0823583i
\(316\) −4.24145 + 5.46328i −0.238600 + 0.307333i
\(317\) 9.39280 22.6762i 0.527552 1.27362i −0.405570 0.914064i \(-0.632927\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(318\) 1.19748 3.49513i 0.0671511 0.195997i
\(319\) −19.1982 −1.07489
\(320\) 17.8439 1.26252i 0.997506 0.0705772i
\(321\) 10.4040 0.580697
\(322\) −2.63680 + 7.69615i −0.146943 + 0.428890i
\(323\) 2.03477 4.91237i 0.113218 0.273332i
\(324\) 7.56241 9.74091i 0.420134 0.541161i
\(325\) 9.12316 + 14.2988i 0.506062 + 0.793155i
\(326\) 21.5785 + 19.0321i 1.19512 + 1.05409i
\(327\) 4.39393i 0.242985i
\(328\) 6.07150 29.2250i 0.335242 1.61368i
\(329\) 4.50806 + 4.50806i 0.248537 + 0.248537i
\(330\) −8.32053 6.13272i −0.458030 0.337595i
\(331\) 6.75682 16.3124i 0.371388 0.896611i −0.622127 0.782916i \(-0.713731\pi\)
0.993516 0.113695i \(-0.0362686\pi\)
\(332\) 3.86544 + 6.78349i 0.212144 + 0.372292i
\(333\) 4.50110 10.8666i 0.246659 0.595487i
\(334\) −12.6661 4.33956i −0.693057 0.237450i
\(335\) −0.00634957 0.0722899i −0.000346914 0.00394962i
\(336\) −0.263832 + 1.84263i −0.0143932 + 0.100524i
\(337\) −11.1980 11.1980i −0.609996 0.609996i 0.332949 0.942945i \(-0.391956\pi\)
−0.942945 + 0.332949i \(0.891956\pi\)
\(338\) −1.89565 + 0.928171i −0.103110 + 0.0504858i
\(339\) 1.99719 + 4.82164i 0.108472 + 0.261875i
\(340\) 5.51932 3.82112i 0.299327 0.207229i
\(341\) 20.9329 + 8.67071i 1.13358 + 0.469545i
\(342\) 10.0433 + 8.85809i 0.543077 + 0.478991i
\(343\) 10.8577i 0.586261i
\(344\) −5.85765 + 8.60754i −0.315823 + 0.464087i
\(345\) −0.790288 8.99743i −0.0425477 0.484405i
\(346\) −6.47579 5.71161i −0.348141 0.307058i
\(347\) −29.3103 + 12.1407i −1.57346 + 0.651748i −0.987360 0.158493i \(-0.949337\pi\)
−0.586098 + 0.810240i \(0.699337\pi\)
\(348\) −3.03193 2.35385i −0.162528 0.126180i
\(349\) 2.08028 + 5.02224i 0.111355 + 0.268834i 0.969726 0.244194i \(-0.0785234\pi\)
−0.858371 + 0.513029i \(0.828523\pi\)
\(350\) 4.64955 3.39390i 0.248529 0.181412i
\(351\) 11.0011i 0.587195i
\(352\) 14.7155 28.8057i 0.784340 1.53535i
\(353\) 7.92828 + 7.92828i 0.421980 + 0.421980i 0.885885 0.463905i \(-0.153552\pi\)
−0.463905 + 0.885885i \(0.653552\pi\)
\(354\) −4.60127 + 2.25294i −0.244555 + 0.119742i
\(355\) −10.1792 3.20565i −0.540256 0.170138i
\(356\) 1.88052 0.236759i 0.0996674 0.0125482i
\(357\) 0.267315 + 0.645356i 0.0141478 + 0.0341558i
\(358\) −29.1606 + 1.82845i −1.54119 + 0.0966368i
\(359\) 1.49806 + 1.49806i 0.0790646 + 0.0790646i 0.745533 0.666469i \(-0.232195\pi\)
−0.666469 + 0.745533i \(0.732195\pi\)
\(360\) 4.59875 + 16.2696i 0.242375 + 0.857484i
\(361\) 4.56268 4.56268i 0.240141 0.240141i
\(362\) −6.68106 + 7.57495i −0.351149 + 0.398130i
\(363\) −11.4587 + 4.74635i −0.601425 + 0.249119i
\(364\) −2.73450 4.79879i −0.143327 0.251525i
\(365\) −6.88261 13.2103i −0.360252 0.691459i
\(366\) −11.9012 4.07749i −0.622084 0.213134i
\(367\) −14.1446 + 14.1446i −0.738341 + 0.738341i −0.972257 0.233916i \(-0.924846\pi\)
0.233916 + 0.972257i \(0.424846\pi\)
\(368\) 27.3829 7.00610i 1.42743 0.365218i
\(369\) 28.2113 1.46862
\(370\) 7.18844 + 11.9128i 0.373709 + 0.619319i
\(371\) 3.43734 1.42379i 0.178458 0.0739196i
\(372\) 2.24279 + 3.93589i 0.116283 + 0.204066i
\(373\) −0.896464 2.16426i −0.0464172 0.112061i 0.898970 0.438009i \(-0.144316\pi\)
−0.945388 + 0.325949i \(0.894316\pi\)
\(374\) −0.759635 12.1148i −0.0392798 0.626444i
\(375\) −3.18979 + 5.53806i −0.164720 + 0.285984i
\(376\) 4.50552 21.6872i 0.232354 1.11843i
\(377\) 11.3893 0.586577
\(378\) −3.72631 + 0.233650i −0.191661 + 0.0120177i
\(379\) 10.1581 24.5237i 0.521785 1.25970i −0.415009 0.909817i \(-0.636222\pi\)
0.936794 0.349882i \(-0.113778\pi\)
\(380\) −15.4838 + 3.34645i −0.794304 + 0.171669i
\(381\) 4.20579 1.74209i 0.215469 0.0892502i
\(382\) −17.5650 6.01799i −0.898705 0.307907i
\(383\) −15.2971 + 15.2971i −0.781643 + 0.781643i −0.980108 0.198465i \(-0.936404\pi\)
0.198465 + 0.980108i \(0.436404\pi\)
\(384\) 5.85579 2.74497i 0.298827 0.140079i
\(385\) −0.910773 10.3692i −0.0464173 0.528461i
\(386\) 21.0333 10.2986i 1.07056 0.524184i
\(387\) −9.09131 3.76575i −0.462137 0.191424i
\(388\) −17.7197 + 2.23092i −0.899582 + 0.113258i
\(389\) 7.41607 + 3.07184i 0.376010 + 0.155748i 0.562681 0.826674i \(-0.309770\pi\)
−0.186671 + 0.982422i \(0.559770\pi\)
\(390\) 4.93612 + 3.63821i 0.249950 + 0.184228i
\(391\) 7.50019 7.50019i 0.379301 0.379301i
\(392\) 14.9876 9.83146i 0.756990 0.496564i
\(393\) 1.32493 0.0668341
\(394\) 29.9985 1.88099i 1.51130 0.0947631i
\(395\) 6.85787 3.57298i 0.345057 0.179776i
\(396\) 29.4851 + 8.07958i 1.48168 + 0.406014i
\(397\) 0.409833 + 0.169758i 0.0205689 + 0.00851993i 0.392944 0.919562i \(-0.371457\pi\)
−0.372375 + 0.928082i \(0.621457\pi\)
\(398\) 14.4932 7.09636i 0.726480 0.355709i
\(399\) 1.64840i 0.0825230i
\(400\) −18.7201 7.03977i −0.936004 0.351989i
\(401\) 16.5372i 0.825828i 0.910770 + 0.412914i \(0.135489\pi\)
−0.910770 + 0.412914i \(0.864511\pi\)
\(402\) −0.0115371 0.0235627i −0.000575417 0.00117520i
\(403\) −12.4184 5.14386i −0.618604 0.256234i
\(404\) −16.8543 + 9.60408i −0.838531 + 0.477821i
\(405\) −12.2274 + 6.37054i −0.607586 + 0.316555i
\(406\) −0.241895 3.85779i −0.0120050 0.191459i
\(407\) 25.1592 1.24710
\(408\) 1.36541 2.00640i 0.0675978 0.0993318i
\(409\) −0.392350 + 0.392350i −0.0194005 + 0.0194005i −0.716740 0.697340i \(-0.754367\pi\)
0.697340 + 0.716740i \(0.254367\pi\)
\(410\) −19.8001 + 26.8637i −0.977858 + 1.32670i
\(411\) −1.33605 0.553410i −0.0659024 0.0272977i
\(412\) −18.7430 14.5512i −0.923401 0.716887i
\(413\) −4.76651 1.97435i −0.234545 0.0971516i
\(414\) 11.7475 + 23.9925i 0.577360 + 1.17917i
\(415\) −0.763776 8.69559i −0.0374923 0.426850i
\(416\) −8.72993 + 17.0889i −0.428020 + 0.837850i
\(417\) −1.45397 + 1.45397i −0.0712013 + 0.0712013i
\(418\) −9.28431 + 27.0986i −0.454110 + 1.32544i
\(419\) 25.8254 10.6972i 1.26166 0.522595i 0.351238 0.936286i \(-0.385761\pi\)
0.910417 + 0.413692i \(0.135761\pi\)
\(420\) 1.12750 1.74924i 0.0550166 0.0853543i
\(421\) 1.04149 2.51437i 0.0507590 0.122543i −0.896466 0.443112i \(-0.853874\pi\)
0.947225 + 0.320569i \(0.103874\pi\)
\(422\) −1.31570 20.9831i −0.0640473 1.02144i
\(423\) 20.9349 1.01789
\(424\) −10.6867 7.27254i −0.518990 0.353186i
\(425\) −7.39040 + 1.30836i −0.358487 + 0.0634649i
\(426\) −3.85069 + 0.241449i −0.186567 + 0.0116983i
\(427\) −4.84811 11.7044i −0.234617 0.566415i
\(428\) 9.62016 35.1072i 0.465008 1.69697i
\(429\) 10.2442 4.24327i 0.494592 0.204867i
\(430\) 9.96662 6.01405i 0.480633 0.290023i
\(431\) −40.5492 −1.95319 −0.976593 0.215096i \(-0.930994\pi\)
−0.976593 + 0.215096i \(0.930994\pi\)
\(432\) 7.77986 + 10.3800i 0.374309 + 0.499410i
\(433\) −3.57791 + 3.57791i −0.171943 + 0.171943i −0.787833 0.615889i \(-0.788797\pi\)
0.615889 + 0.787833i \(0.288797\pi\)
\(434\) −1.47859 + 4.31563i −0.0709744 + 0.207157i
\(435\) 1.98288 + 3.80588i 0.0950717 + 0.182478i
\(436\) −14.8268 4.06288i −0.710074 0.194577i
\(437\) −23.1249 + 9.57866i −1.10622 + 0.458210i
\(438\) −4.03878 3.56218i −0.192980 0.170207i
\(439\) 24.2044 24.2044i 1.15521 1.15521i 0.169720 0.985492i \(-0.445714\pi\)
0.985492 0.169720i \(-0.0542864\pi\)
\(440\) −28.3878 + 22.4060i −1.35333 + 1.06816i
\(441\) 11.9791 + 11.9791i 0.570434 + 0.570434i
\(442\) 0.450651 + 7.18708i 0.0214353 + 0.341855i
\(443\) −1.58086 3.81653i −0.0751088 0.181329i 0.881866 0.471501i \(-0.156288\pi\)
−0.956975 + 0.290172i \(0.906288\pi\)
\(444\) 3.97333 + 3.08472i 0.188566 + 0.146394i
\(445\) −2.02123 0.636527i −0.0958153 0.0301743i
\(446\) −1.94413 3.97057i −0.0920570 0.188012i
\(447\) −3.53970 3.53970i −0.167422 0.167422i
\(448\) 5.97378 + 2.59407i 0.282235 + 0.122558i
\(449\) 19.5593i 0.923061i 0.887124 + 0.461531i \(0.152700\pi\)
−0.887124 + 0.461531i \(0.847300\pi\)
\(450\) 2.91555 18.6765i 0.137440 0.880417i
\(451\) 23.0930 + 55.7514i 1.08741 + 2.62523i
\(452\) 18.1168 2.28091i 0.852141 0.107285i
\(453\) −2.60973 + 1.08099i −0.122616 + 0.0507892i
\(454\) 9.42322 10.6840i 0.442253 0.501425i
\(455\) 0.540312 + 6.15146i 0.0253302 + 0.288385i
\(456\) −4.78875 + 3.14128i −0.224254 + 0.147104i
\(457\) 18.8259i 0.880638i 0.897841 + 0.440319i \(0.145135\pi\)
−0.897841 + 0.440319i \(0.854865\pi\)
\(458\) 2.89193 3.27885i 0.135131 0.153211i
\(459\) 4.49738 + 1.86287i 0.209920 + 0.0869515i
\(460\) −31.0915 5.65280i −1.44965 0.263563i
\(461\) 10.5085 + 25.3698i 0.489430 + 1.18159i 0.955008 + 0.296582i \(0.0958467\pi\)
−0.465577 + 0.885007i \(0.654153\pi\)
\(462\) −1.65486 3.37980i −0.0769911 0.157242i
\(463\) 27.5223 + 27.5223i 1.27907 + 1.27907i 0.941189 + 0.337881i \(0.109710\pi\)
0.337881 + 0.941189i \(0.390290\pi\)
\(464\) −10.7463 + 8.05437i −0.498884 + 0.373915i
\(465\) −0.443155 5.04532i −0.0205508 0.233971i
\(466\) 8.87592 25.9066i 0.411169 1.20010i
\(467\) −14.3518 + 34.6483i −0.664122 + 1.60333i 0.127160 + 0.991882i \(0.459414\pi\)
−0.791282 + 0.611451i \(0.790586\pi\)
\(468\) −17.4919 4.79318i −0.808563 0.221565i
\(469\) 0.0101105 0.0244089i 0.000466859 0.00112710i
\(470\) −14.6932 + 19.9349i −0.677748 + 0.919530i
\(471\) 3.03638 + 3.03638i 0.139909 + 0.139909i
\(472\) 3.34766 + 17.6096i 0.154089 + 0.810549i
\(473\) 21.0489i 0.967829i
\(474\) 1.84924 2.09665i 0.0849382 0.0963025i
\(475\) 17.2940 + 3.82151i 0.793501 + 0.175343i
\(476\) 2.42485 0.305290i 0.111143 0.0139930i
\(477\) 4.67535 11.2873i 0.214069 0.516809i
\(478\) 1.46019 + 0.500278i 0.0667874 + 0.0228822i
\(479\) 23.0553 1.05342 0.526711 0.850044i \(-0.323425\pi\)
0.526711 + 0.850044i \(0.323425\pi\)
\(480\) −7.23036 + 0.0579533i −0.330019 + 0.00264520i
\(481\) −14.9256 −0.680549
\(482\) −0.443401 0.151915i −0.0201964 0.00691952i
\(483\) 1.25838 3.03801i 0.0572584 0.138234i
\(484\) 5.42062 + 43.0547i 0.246392 + 1.95703i
\(485\) 19.0455 + 5.99784i 0.864813 + 0.272348i
\(486\) −12.3982 + 14.0570i −0.562394 + 0.637639i
\(487\) 7.07071i 0.320404i −0.987084 0.160202i \(-0.948785\pi\)
0.987084 0.160202i \(-0.0512146\pi\)
\(488\) −24.7635 + 36.3888i −1.12099 + 1.64724i
\(489\) −8.22358 8.22358i −0.371883 0.371883i
\(490\) −19.8145 + 2.99934i −0.895126 + 0.135496i
\(491\) 10.6204 25.6398i 0.479290 1.15711i −0.480652 0.876911i \(-0.659600\pi\)
0.959942 0.280198i \(-0.0904000\pi\)
\(492\) −3.18855 + 11.6361i −0.143751 + 0.524595i
\(493\) −1.92861 + 4.65607i −0.0868601 + 0.209699i
\(494\) 5.50788 16.0761i 0.247811 0.723300i
\(495\) −26.1914 21.9618i −1.17721 0.987111i
\(496\) 15.3550 3.92868i 0.689460 0.176403i
\(497\) −2.74738 2.74738i −0.123237 0.123237i
\(498\) −1.38777 2.83430i −0.0621874 0.127008i
\(499\) 2.84790 + 6.87545i 0.127490 + 0.307787i 0.974717 0.223443i \(-0.0717298\pi\)
−0.847227 + 0.531231i \(0.821730\pi\)
\(500\) 15.7381 + 15.8844i 0.703827 + 0.710371i
\(501\) 4.99986 + 2.07101i 0.223377 + 0.0925258i
\(502\) −17.9961 + 20.4039i −0.803204 + 0.910669i
\(503\) 19.9623i 0.890075i −0.895512 0.445038i \(-0.853190\pi\)
0.895512 0.445038i \(-0.146810\pi\)
\(504\) −1.25205 + 6.02669i −0.0557706 + 0.268450i
\(505\) 21.6051 1.89768i 0.961414 0.0844456i
\(506\) −37.7981 + 42.8553i −1.68033 + 1.90515i
\(507\) 0.788200 0.326483i 0.0350052 0.0144996i
\(508\) −1.98958 15.8028i −0.0882732 0.701134i
\(509\) −6.53636 15.7802i −0.289719 0.699444i 0.710271 0.703928i \(-0.248572\pi\)
−0.999990 + 0.00448484i \(0.998572\pi\)
\(510\) −2.32320 + 1.40187i −0.102873 + 0.0620757i
\(511\) 5.42310i 0.239904i
\(512\) −3.84797 22.2978i −0.170058 0.985434i
\(513\) −8.12282 8.12282i −0.358631 0.358631i
\(514\) −16.4156 33.5264i −0.724063 1.47879i
\(515\) 12.2579 + 23.5275i 0.540147 + 1.03674i
\(516\) 2.58076 3.32420i 0.113612 0.146340i
\(517\) 17.1368 + 41.3719i 0.753675 + 1.81953i
\(518\) 0.317002 + 5.05562i 0.0139283 + 0.222131i
\(519\) 2.46793 + 2.46793i 0.108330 + 0.108330i
\(520\) 16.8409 13.2923i 0.738524 0.582904i
\(521\) 12.1901 12.1901i 0.534059 0.534059i −0.387719 0.921778i \(-0.626737\pi\)
0.921778 + 0.387719i \(0.126737\pi\)
\(522\) −9.51925 8.39592i −0.416646 0.367480i
\(523\) 11.7545 4.86887i 0.513988 0.212901i −0.110586 0.993867i \(-0.535273\pi\)
0.624574 + 0.780966i \(0.285273\pi\)
\(524\) 1.22511 4.47083i 0.0535191 0.195309i
\(525\) −1.96153 + 1.25152i −0.0856080 + 0.0546210i
\(526\) 10.4576 30.5231i 0.455972 1.33087i
\(527\) 4.20574 4.20574i 0.183205 0.183205i
\(528\) −6.66503 + 11.2483i −0.290058 + 0.489518i
\(529\) −26.9318 −1.17095
\(530\) 7.46672 + 12.3740i 0.324334 + 0.537493i
\(531\) −15.6519 + 6.48324i −0.679236 + 0.281349i
\(532\) −5.56232 1.52420i −0.241157 0.0660825i
\(533\) −13.6998 33.0743i −0.593406 1.43261i
\(534\) −0.764610 + 0.0479432i −0.0330879 + 0.00207471i
\(535\) −26.1495 + 31.1855i −1.13054 + 1.34826i
\(536\) −0.0901773 + 0.0171431i −0.00389507 + 0.000740469i
\(537\) 11.8099 0.509637
\(538\) −2.41951 38.5869i −0.104312 1.66360i
\(539\) −13.8675 + 33.4790i −0.597314 + 1.44204i
\(540\) −3.06375 14.1758i −0.131843 0.610028i
\(541\) −31.1777 + 12.9142i −1.34043 + 0.555226i −0.933614 0.358282i \(-0.883363\pi\)
−0.406821 + 0.913508i \(0.633363\pi\)
\(542\) 1.18915 3.47085i 0.0510786 0.149086i
\(543\) 2.88681 2.88681i 0.123885 0.123885i
\(544\) −5.50784 6.46265i −0.236147 0.277084i
\(545\) 13.1705 + 11.0437i 0.564164 + 0.473059i
\(546\) 0.981740 + 2.00505i 0.0420146 + 0.0858083i
\(547\) 13.2471 + 5.48713i 0.566406 + 0.234613i 0.647463 0.762097i \(-0.275830\pi\)
−0.0810579 + 0.996709i \(0.525830\pi\)
\(548\) −3.10280 + 3.99662i −0.132545 + 0.170727i
\(549\) −38.4340 15.9199i −1.64032 0.679444i
\(550\) 39.2952 9.52632i 1.67555 0.406204i
\(551\) 8.40943 8.40943i 0.358254 0.358254i
\(552\) −11.2238 + 2.13368i −0.477715 + 0.0908156i
\(553\) 2.81530 0.119719
\(554\) −1.37093 21.8639i −0.0582451 0.928907i
\(555\) −2.59855 4.98759i −0.110302 0.211711i
\(556\) 3.56183 + 6.25067i 0.151055 + 0.265088i
\(557\) −3.20913 1.32926i −0.135975 0.0563227i 0.313658 0.949536i \(-0.398445\pi\)
−0.449633 + 0.893213i \(0.648445\pi\)
\(558\) 6.58745 + 13.4538i 0.278869 + 0.569547i
\(559\) 12.4872i 0.528151i
\(560\) −4.86006 5.42208i −0.205375 0.229125i
\(561\) 4.90647i 0.207151i
\(562\) 19.2288 9.41507i 0.811119 0.397151i
\(563\) 6.50253 + 2.69344i 0.274049 + 0.113515i 0.515476 0.856904i \(-0.327615\pi\)
−0.241427 + 0.970419i \(0.577615\pi\)
\(564\) −2.36615 + 8.63486i −0.0996328 + 0.363593i
\(565\) −19.4723 6.13224i −0.819205 0.257985i
\(566\) 24.4276 1.53168i 1.02677 0.0643814i
\(567\) −5.01961 −0.210804
\(568\) −2.74583 + 13.2170i −0.115212 + 0.554572i
\(569\) −3.51818 + 3.51818i −0.147490 + 0.147490i −0.776996 0.629506i \(-0.783257\pi\)
0.629506 + 0.776996i \(0.283257\pi\)
\(570\) 6.33098 0.958329i 0.265176 0.0401400i
\(571\) 2.80418 + 1.16153i 0.117351 + 0.0486085i 0.440587 0.897710i \(-0.354771\pi\)
−0.323235 + 0.946319i \(0.604771\pi\)
\(572\) −4.84607 38.4912i −0.202624 1.60940i
\(573\) 6.93368 + 2.87203i 0.289659 + 0.119981i
\(574\) −10.9120 + 5.34289i −0.455459 + 0.223008i
\(575\) 28.9555 + 20.2453i 1.20753 + 0.844286i
\(576\) 19.8941 7.84750i 0.828920 0.326979i
\(577\) 13.9476 13.9476i 0.580648 0.580648i −0.354434 0.935081i \(-0.615326\pi\)
0.935081 + 0.354434i \(0.115326\pi\)
\(578\) 19.7293 + 6.75951i 0.820631 + 0.281158i
\(579\) −8.74553 + 3.62252i −0.363452 + 0.150547i
\(580\) 14.6760 3.17185i 0.609386 0.131704i
\(581\) 1.21617 2.93609i 0.0504552 0.121810i
\(582\) 7.20474 0.451757i 0.298646 0.0187259i
\(583\) 26.1332 1.08233
\(584\) −15.7546 + 10.3346i −0.651931 + 0.427648i
\(585\) 15.5379 + 13.0288i 0.642414 + 0.538674i
\(586\) 1.08125 + 17.2440i 0.0446659 + 0.712343i
\(587\) −3.45809 8.34857i −0.142731 0.344583i 0.836307 0.548261i \(-0.184710\pi\)
−0.979038 + 0.203679i \(0.934710\pi\)
\(588\) −6.29485 + 3.58700i −0.259595 + 0.147925i
\(589\) −12.9673 + 5.37125i −0.534310 + 0.221318i
\(590\) 4.81178 19.4545i 0.198098 0.800931i
\(591\) −12.1493 −0.499755
\(592\) 14.0830 10.5552i 0.578807 0.433817i
\(593\) 26.7663 26.7663i 1.09916 1.09916i 0.104650 0.994509i \(-0.466628\pi\)
0.994509 0.104650i \(-0.0333722\pi\)
\(594\) −24.8093 8.49998i −1.01794 0.348758i
\(595\) −2.60628 0.820774i −0.106847 0.0336484i
\(596\) −15.2173 + 8.67128i −0.623325 + 0.355189i
\(597\) −6.02621 + 2.49614i −0.246637 + 0.102160i
\(598\) 22.4236 25.4237i 0.916968 1.03965i
\(599\) 8.14906 8.14906i 0.332961 0.332961i −0.520749 0.853710i \(-0.674347\pi\)
0.853710 + 0.520749i \(0.174347\pi\)
\(600\) 7.37380 + 3.31344i 0.301034 + 0.135271i
\(601\) 13.1584 + 13.1584i 0.536742 + 0.536742i 0.922570 0.385829i \(-0.126084\pi\)
−0.385829 + 0.922570i \(0.626084\pi\)
\(602\) 4.22968 0.265213i 0.172389 0.0108093i
\(603\) −0.0332001 0.0801521i −0.00135201 0.00326405i
\(604\) 1.23455 + 9.80577i 0.0502332 + 0.398991i
\(605\) 14.5733 46.2762i 0.592491 1.88139i
\(606\) 7.04212 3.44806i 0.286066 0.140068i
\(607\) −22.6421 22.6421i −0.919015 0.919015i 0.0779425 0.996958i \(-0.475165\pi\)
−0.996958 + 0.0779425i \(0.975165\pi\)
\(608\) 6.17194 + 19.0637i 0.250305 + 0.773134i
\(609\) 1.56239i 0.0633113i
\(610\) 42.1344 25.4247i 1.70597 1.02942i
\(611\) −10.1663 24.5437i −0.411286 0.992932i
\(612\) 4.92150 6.33924i 0.198940 0.256249i
\(613\) −26.0495 + 10.7901i −1.05213 + 0.435807i −0.840652 0.541576i \(-0.817828\pi\)
−0.211479 + 0.977383i \(0.567828\pi\)
\(614\) 16.7110 + 14.7390i 0.674403 + 0.594819i
\(615\) 8.66709 10.3362i 0.349491 0.416797i
\(616\) −12.9349 + 2.45898i −0.521162 + 0.0990751i
\(617\) 3.20102i 0.128868i −0.997922 0.0644342i \(-0.979476\pi\)
0.997922 0.0644342i \(-0.0205243\pi\)
\(618\) 7.19304 + 6.34421i 0.289346 + 0.255202i
\(619\) 19.1073 + 7.91452i 0.767989 + 0.318111i 0.732057 0.681243i \(-0.238560\pi\)
0.0359314 + 0.999354i \(0.488560\pi\)
\(620\) −17.4346 3.16982i −0.700190 0.127303i
\(621\) −8.76947 21.1714i −0.351907 0.849578i
\(622\) −33.1430 + 16.2279i −1.32891 + 0.650681i
\(623\) −0.545531 0.545531i −0.0218562 0.0218562i
\(624\) 3.95400 6.67299i 0.158287 0.267134i
\(625\) −8.58278 23.4805i −0.343311 0.939222i
\(626\) −40.7831 13.9728i −1.63002 0.558466i
\(627\) 4.43084 10.6970i 0.176951 0.427197i
\(628\) 13.0535 7.43830i 0.520892 0.296821i
\(629\) 2.52743 6.10176i 0.100775 0.243293i
\(630\) 4.08312 5.53975i 0.162676 0.220709i
\(631\) 23.6372 + 23.6372i 0.940983 + 0.940983i 0.998353 0.0573701i \(-0.0182715\pi\)
−0.0573701 + 0.998353i \(0.518272\pi\)
\(632\) −5.36500 8.17871i −0.213408 0.325332i
\(633\) 8.49808i 0.337768i
\(634\) 26.0324 + 22.9605i 1.03388 + 0.911876i
\(635\) −5.34898 + 16.9852i −0.212268 + 0.674035i
\(636\) 4.12715 + 3.20413i 0.163652 + 0.127052i
\(637\) 8.22682 19.8613i 0.325959 0.786934i
\(638\) 8.79990 25.6847i 0.348392 1.01687i
\(639\) −12.7585 −0.504719
\(640\) −6.49004 + 24.4516i −0.256542 + 0.966533i
\(641\) −12.6311 −0.498898 −0.249449 0.968388i \(-0.580250\pi\)
−0.249449 + 0.968388i \(0.580250\pi\)
\(642\) −4.76891 + 13.9192i −0.188214 + 0.549349i
\(643\) −13.1896 + 31.8424i −0.520145 + 1.25574i 0.417667 + 0.908600i \(0.362848\pi\)
−0.937813 + 0.347142i \(0.887152\pi\)
\(644\) −9.08782 7.05538i −0.358110 0.278021i
\(645\) −4.17276 + 2.17402i −0.164302 + 0.0856021i
\(646\) 5.63943 + 4.97394i 0.221881 + 0.195697i
\(647\) 34.2449i 1.34631i −0.739503 0.673154i \(-0.764939\pi\)
0.739503 0.673154i \(-0.235061\pi\)
\(648\) 9.56568 + 14.5825i 0.375775 + 0.572853i
\(649\) −25.6245 25.6245i −1.00585 1.00585i
\(650\) −23.3117 + 5.65145i −0.914362 + 0.221668i
\(651\) 0.705640 1.70357i 0.0276562 0.0667680i
\(652\) −35.3535 + 20.1455i −1.38455 + 0.788959i
\(653\) 6.24144 15.0682i 0.244246 0.589663i −0.753450 0.657506i \(-0.771612\pi\)
0.997696 + 0.0678426i \(0.0216116\pi\)
\(654\) 5.87851 + 2.01405i 0.229868 + 0.0787555i
\(655\) −3.33008 + 3.97141i −0.130117 + 0.155176i
\(656\) 36.3162 + 21.5187i 1.41791 + 0.840166i
\(657\) −12.5921 12.5921i −0.491266 0.491266i
\(658\) −8.09756 + 3.96484i −0.315676 + 0.154565i
\(659\) 2.76171 + 6.66735i 0.107581 + 0.259723i 0.968498 0.249023i \(-0.0801093\pi\)
−0.860917 + 0.508746i \(0.830109\pi\)
\(660\) 12.0187 8.32072i 0.467826 0.323884i
\(661\) −8.77278 3.63380i −0.341222 0.141339i 0.205491 0.978659i \(-0.434121\pi\)
−0.546712 + 0.837320i \(0.684121\pi\)
\(662\) 18.7267 + 16.5169i 0.727836 + 0.641946i
\(663\) 2.91074i 0.113044i
\(664\) −10.8472 + 2.06210i −0.420954 + 0.0800251i
\(665\) 4.94097 + 4.14307i 0.191603 + 0.160661i
\(666\) 12.4749 + 11.0028i 0.483394 + 0.426351i
\(667\) 21.9184 9.07890i 0.848684 0.351536i
\(668\) 11.6115 14.9564i 0.449263 0.578682i
\(669\) 0.683844 + 1.65095i 0.0264390 + 0.0638293i
\(670\) 0.0996250 + 0.0246407i 0.00384885 + 0.000951952i
\(671\) 88.9853i 3.43524i
\(672\) −2.34427 1.19758i −0.0904321 0.0461977i
\(673\) 5.53925 + 5.53925i 0.213522 + 0.213522i 0.805762 0.592240i \(-0.201756\pi\)
−0.592240 + 0.805762i \(0.701756\pi\)
\(674\) 20.1144 9.84867i 0.774777 0.379357i
\(675\) −3.49868 + 15.8330i −0.134664 + 0.609412i
\(676\) −0.372864 2.96157i −0.0143409 0.113907i
\(677\) 10.8146 + 26.1088i 0.415639 + 1.00344i 0.983596 + 0.180383i \(0.0577338\pi\)
−0.567957 + 0.823058i \(0.692266\pi\)
\(678\) −7.36618 + 0.461880i −0.282896 + 0.0177384i
\(679\) 5.14041 + 5.14041i 0.197271 + 0.197271i
\(680\) 2.58226 + 9.13562i 0.0990253 + 0.350335i
\(681\) −4.07167 + 4.07167i −0.156027 + 0.156027i
\(682\) −21.1953 + 24.0312i −0.811611 + 0.920200i
\(683\) −36.7383 + 15.2175i −1.40575 + 0.582281i −0.951238 0.308459i \(-0.900187\pi\)
−0.454513 + 0.890740i \(0.650187\pi\)
\(684\) −16.4545 + 9.37629i −0.629154 + 0.358511i
\(685\) 5.01683 2.61379i 0.191683 0.0998677i
\(686\) −14.5262 4.97685i −0.554613 0.190017i
\(687\) −1.24957 + 1.24957i −0.0476741 + 0.0476741i
\(688\) −8.83080 11.7822i −0.336671 0.449193i
\(689\) −15.5034 −0.590633
\(690\) 12.3996 + 3.06686i 0.472046 + 0.116753i
\(691\) −5.74794 + 2.38088i −0.218662 + 0.0905728i −0.489325 0.872101i \(-0.662757\pi\)
0.270663 + 0.962674i \(0.412757\pi\)
\(692\) 10.6097 6.04573i 0.403320 0.229824i
\(693\) −4.76217 11.4969i −0.180900 0.436731i
\(694\) −2.80772 44.7783i −0.106580 1.69976i
\(695\) −0.703785 8.01259i −0.0266961 0.303935i
\(696\) 4.53890 2.97739i 0.172047 0.112858i
\(697\) 15.8410 0.600022
\(698\) −7.67265 + 0.481097i −0.290414 + 0.0182098i
\(699\) −4.23594 + 10.2265i −0.160218 + 0.386800i
\(700\) 2.40938 + 7.77616i 0.0910661 + 0.293911i
\(701\) −23.9645 + 9.92644i −0.905129 + 0.374917i −0.786190 0.617985i \(-0.787949\pi\)
−0.118939 + 0.992902i \(0.537949\pi\)
\(702\) 14.7180 + 5.04258i 0.555497 + 0.190320i
\(703\) −11.0205 + 11.0205i −0.415647 + 0.415647i
\(704\) 31.7931 + 32.8911i 1.19825 + 1.23963i
\(705\) 6.43165 7.67029i 0.242230 0.288880i
\(706\) −14.2411 + 6.97292i −0.535971 + 0.262429i
\(707\) 7.29502 + 3.02170i 0.274357 + 0.113643i
\(708\) −0.905047 7.18858i −0.0340137 0.270163i
\(709\) −17.4586 7.23159i −0.655671 0.271588i 0.0299445 0.999552i \(-0.490467\pi\)
−0.685616 + 0.727964i \(0.740467\pi\)
\(710\) 8.95459 12.1491i 0.336060 0.455947i
\(711\) 6.53697 6.53697i 0.245155 0.245155i
\(712\) −0.545223 + 2.62442i −0.0204331 + 0.0983541i
\(713\) −27.9993 −1.04858
\(714\) −0.985932 + 0.0618207i −0.0368976 + 0.00231358i
\(715\) −13.0287 + 41.3712i −0.487245 + 1.54720i
\(716\) 10.9201 39.8512i 0.408105 1.48931i
\(717\) −0.576400 0.238752i −0.0215260 0.00891638i
\(718\) −2.69088 + 1.31754i −0.100423 + 0.0491703i
\(719\) 42.0594i 1.56855i 0.620413 + 0.784276i \(0.286965\pi\)
−0.620413 + 0.784276i \(0.713035\pi\)
\(720\) −23.8746 1.30499i −0.889752 0.0486339i
\(721\) 9.65850i 0.359701i
\(722\) 4.01288 + 8.19567i 0.149344 + 0.305011i
\(723\) 0.175030 + 0.0724997i 0.00650942 + 0.00269629i
\(724\) −7.07190 12.4105i −0.262825 0.461233i
\(725\) −16.3916 3.62213i −0.608770 0.134522i
\(726\) −1.09766 17.5058i −0.0407382 0.649702i
\(727\) −22.6419 −0.839742 −0.419871 0.907584i \(-0.637925\pi\)
−0.419871 + 0.907584i \(0.637925\pi\)
\(728\) 7.67358 1.45878i 0.284402 0.0540660i
\(729\) −7.72280 + 7.72280i −0.286030 + 0.286030i
\(730\) 20.8284 3.15283i 0.770895 0.116691i
\(731\) −5.10490 2.11452i −0.188812 0.0782083i
\(732\) 10.9103 14.0532i 0.403256 0.519422i
\(733\) 19.7248 + 8.17030i 0.728554 + 0.301777i 0.715958 0.698144i \(-0.245990\pi\)
0.0125963 + 0.999921i \(0.495990\pi\)
\(734\) −12.4401 25.4071i −0.459174 0.937791i
\(735\) 8.06922 0.708759i 0.297638 0.0261430i
\(736\) −3.17826 + 39.8461i −0.117152 + 1.46875i
\(737\) 0.131221 0.131221i 0.00483358 0.00483358i
\(738\) −12.9312 + 37.7430i −0.476005 + 1.38934i
\(739\) 18.1749 7.52830i 0.668575 0.276933i −0.0224667 0.999748i \(-0.507152\pi\)
0.691042 + 0.722815i \(0.257152\pi\)
\(740\) −19.2328 + 4.15670i −0.707012 + 0.152803i
\(741\) −2.62858 + 6.34595i −0.0965633 + 0.233124i
\(742\) 0.329274 + 5.25134i 0.0120880 + 0.192783i
\(743\) −46.0431 −1.68916 −0.844578 0.535432i \(-0.820149\pi\)
−0.844578 + 0.535432i \(0.820149\pi\)
\(744\) −6.29374 + 1.19647i −0.230740 + 0.0438646i
\(745\) 19.5067 1.71337i 0.714670 0.0627729i
\(746\) 3.30641 0.207321i 0.121056 0.00759056i
\(747\) −3.99356 9.64132i −0.146117 0.352757i
\(748\) 16.5563 + 4.53680i 0.605358 + 0.165882i
\(749\) −13.6891 + 5.67021i −0.500188 + 0.207185i
\(750\) −5.94709 6.80601i −0.217157 0.248521i
\(751\) −30.7636 −1.12258 −0.561290 0.827619i \(-0.689695\pi\)
−0.561290 + 0.827619i \(0.689695\pi\)
\(752\) 26.9494 + 15.9686i 0.982745 + 0.582314i
\(753\) 7.77591 7.77591i 0.283370 0.283370i
\(754\) −5.22051 + 15.2374i −0.190120 + 0.554912i
\(755\) 3.31910 10.5395i 0.120794 0.383570i
\(756\) 1.39544 5.09242i 0.0507516 0.185209i
\(757\) 21.2098 8.78539i 0.770884 0.319311i 0.0376534 0.999291i \(-0.488012\pi\)
0.733230 + 0.679980i \(0.238012\pi\)
\(758\) 28.1534 + 24.8311i 1.02258 + 0.901907i
\(759\) 16.3321 16.3321i 0.592819 0.592819i
\(760\) 2.62022 22.2493i 0.0950454 0.807066i
\(761\) −5.27029 5.27029i −0.191048 0.191048i 0.605101 0.796149i \(-0.293133\pi\)
−0.796149 + 0.605101i \(0.793133\pi\)
\(762\) 0.402886 + 6.42532i 0.0145950 + 0.232765i
\(763\) 2.39469 + 5.78130i 0.0866937 + 0.209297i
\(764\) 16.1026 20.7412i 0.582571 0.750392i
\(765\) −7.95744 + 4.14585i −0.287702 + 0.149894i
\(766\) −13.4537 27.4772i −0.486104 0.992791i
\(767\) 15.2016 + 15.2016i 0.548899 + 0.548899i
\(768\) 0.988288 + 9.09250i 0.0356618 + 0.328097i
\(769\) 17.7291i 0.639328i 0.947531 + 0.319664i \(0.103570\pi\)
−0.947531 + 0.319664i \(0.896430\pi\)
\(770\) 14.2901 + 3.53442i 0.514978 + 0.127372i
\(771\) 5.77419 + 13.9401i 0.207952 + 0.502041i
\(772\) 4.13714 + 32.8603i 0.148899 + 1.18267i
\(773\) −9.20330 + 3.81213i −0.331020 + 0.137113i −0.542002 0.840377i \(-0.682334\pi\)
0.210983 + 0.977490i \(0.432334\pi\)
\(774\) 9.20527 10.4369i 0.330877 0.375146i
\(775\) 16.2369 + 11.3526i 0.583245 + 0.407796i
\(776\) 5.13751 24.7293i 0.184426 0.887728i
\(777\) 2.04751i 0.0734540i
\(778\) −7.50903 + 8.51370i −0.269212 + 0.305231i
\(779\) −34.5364 14.3054i −1.23739 0.512545i
\(780\) −7.13003 + 4.93624i −0.255296 + 0.176746i
\(781\) −10.4438 25.2135i −0.373708 0.902211i
\(782\) 6.59641 + 13.4722i 0.235887 + 0.481763i
\(783\) 7.69901 + 7.69901i 0.275140 + 0.275140i
\(784\) 6.28333 + 24.5580i 0.224404 + 0.877070i
\(785\) −16.7330 + 1.46974i −0.597227 + 0.0524573i
\(786\) −0.607311 + 1.77259i −0.0216621 + 0.0632262i
\(787\) −4.91656 + 11.8696i −0.175256 + 0.423106i −0.986961 0.160963i \(-0.948540\pi\)
0.811704 + 0.584069i \(0.198540\pi\)
\(788\) −11.2339 + 40.9963i −0.400192 + 1.46043i
\(789\) −4.99077 + 12.0488i −0.177676 + 0.428948i
\(790\) 1.63673 + 10.8127i 0.0582323 + 0.384698i
\(791\) −5.25559 5.25559i −0.186867 0.186867i
\(792\) −24.3245 + 35.7437i −0.864334 + 1.27010i
\(793\) 52.7902i 1.87463i
\(794\) −0.414970 + 0.470491i −0.0147267 + 0.0166971i
\(795\) −2.69915 5.18067i −0.0957290 0.183740i
\(796\) 2.85074 + 22.6428i 0.101042 + 0.802553i
\(797\) −3.32856 + 8.03586i −0.117904 + 0.284645i −0.971803 0.235793i \(-0.924231\pi\)
0.853900 + 0.520438i \(0.174231\pi\)
\(798\) 2.20534 + 0.755577i 0.0780682 + 0.0267471i
\(799\) 11.7553 0.415872
\(800\) 17.9990 21.8182i 0.636362 0.771390i
\(801\) −2.53339 −0.0895128
\(802\) −22.1246 7.58016i −0.781247 0.267665i
\(803\) 14.5771 35.1923i 0.514416 1.24191i
\(804\) 0.0368121 0.00463466i 0.00129826 0.000163452i
\(805\) 5.94342 + 11.4076i 0.209478 + 0.402067i
\(806\) 12.5740 14.2564i 0.442902 0.502160i
\(807\) 15.6275i 0.550116i
\(808\) −5.12351 26.9511i −0.180244 0.948135i
\(809\) 30.6872 + 30.6872i 1.07890 + 1.07890i 0.996608 + 0.0822955i \(0.0262251\pi\)
0.0822955 + 0.996608i \(0.473775\pi\)
\(810\) −2.91826 19.2788i −0.102537 0.677388i
\(811\) 7.16488 17.2976i 0.251593 0.607399i −0.746740 0.665116i \(-0.768382\pi\)
0.998333 + 0.0577168i \(0.0183820\pi\)
\(812\) 5.27211 + 1.44468i 0.185015 + 0.0506982i
\(813\) −0.567512 + 1.37010i −0.0199035 + 0.0480513i
\(814\) −11.5322 + 33.6597i −0.404205 + 1.17977i
\(815\) 45.3188 3.98057i 1.58745 0.139433i
\(816\) 2.05845 + 2.74642i 0.0720600 + 0.0961438i
\(817\) 9.22009 + 9.22009i 0.322570 + 0.322570i
\(818\) −0.345072 0.704755i −0.0120652 0.0246412i
\(819\) 2.82514 + 6.82049i 0.0987183 + 0.238327i
\(820\) −26.8643 38.8035i −0.938143 1.35508i
\(821\) −3.39391 1.40580i −0.118448 0.0490628i 0.322672 0.946511i \(-0.395419\pi\)
−0.441120 + 0.897448i \(0.645419\pi\)
\(822\) 1.35280 1.53379i 0.0471842 0.0534972i
\(823\) 20.6060i 0.718280i −0.933284 0.359140i \(-0.883070\pi\)
0.933284 0.359140i \(-0.116930\pi\)
\(824\) 28.0589 18.4058i 0.977477 0.641197i
\(825\) −16.0931 + 2.84904i −0.560288 + 0.0991909i
\(826\) 4.82626 5.47199i 0.167927 0.190395i
\(827\) 27.0603 11.2088i 0.940980 0.389767i 0.141147 0.989989i \(-0.454921\pi\)
0.799833 + 0.600222i \(0.204921\pi\)
\(828\) −37.4836 + 4.71921i −1.30265 + 0.164004i
\(829\) 7.90537 + 19.0853i 0.274565 + 0.662858i 0.999668 0.0257824i \(-0.00820769\pi\)
−0.725103 + 0.688641i \(0.758208\pi\)
\(830\) 11.9837 + 2.96397i 0.415959 + 0.102881i
\(831\) 8.85478i 0.307169i
\(832\) −18.8611 19.5125i −0.653892 0.676476i
\(833\) 6.72644 + 6.72644i 0.233057 + 0.233057i
\(834\) −1.27877 2.61168i −0.0442801 0.0904351i
\(835\) −18.7743 + 9.78150i −0.649713 + 0.338503i
\(836\) −31.9987 24.8424i −1.10670 0.859192i
\(837\) −4.91749 11.8719i −0.169973 0.410352i
\(838\) 2.47390 + 39.4544i 0.0854595 + 1.36293i
\(839\) −0.0728146 0.0728146i −0.00251384 0.00251384i 0.705849 0.708363i \(-0.250566\pi\)
−0.708363 + 0.705849i \(0.750566\pi\)
\(840\) 1.82344 + 2.31026i 0.0629148 + 0.0797114i
\(841\) 12.5354 12.5354i 0.432256 0.432256i
\(842\) 2.88652 + 2.54589i 0.0994760 + 0.0877372i
\(843\) −7.99526 + 3.31174i −0.275371 + 0.114062i
\(844\) 28.6757 + 7.85781i 0.987060 + 0.270477i
\(845\) −1.00245 + 3.18316i −0.0344852 + 0.109504i
\(846\) −9.59597 + 28.0082i −0.329916 + 0.962943i
\(847\) 12.4900 12.4900i 0.429161 0.429161i
\(848\) 14.6282 10.9638i 0.502333 0.376500i
\(849\) −9.89310 −0.339530
\(850\) 1.63712 10.4871i 0.0561528 0.359705i
\(851\) −28.7240 + 11.8979i −0.984645 + 0.407853i
\(852\) 1.44202 5.26240i 0.0494027 0.180287i
\(853\) −1.52090 3.67178i −0.0520747 0.125719i 0.895701 0.444656i \(-0.146674\pi\)
−0.947776 + 0.318937i \(0.896674\pi\)
\(854\) 17.8812 1.12120i 0.611881 0.0383667i
\(855\) 21.0926 1.85267i 0.721353 0.0633599i
\(856\) 42.5592 + 28.9626i 1.45464 + 0.989922i
\(857\) 51.2513 1.75071 0.875355 0.483481i \(-0.160628\pi\)
0.875355 + 0.483481i \(0.160628\pi\)
\(858\) 0.981320 + 15.6503i 0.0335017 + 0.534294i
\(859\) 16.9377 40.8912i 0.577907 1.39519i −0.316781 0.948499i \(-0.602602\pi\)
0.894688 0.446692i \(-0.147398\pi\)
\(860\) 3.47761 + 16.0907i 0.118586 + 0.548688i
\(861\) 4.53717 1.87936i 0.154626 0.0640483i
\(862\) 18.5866 54.2495i 0.633061 1.84775i
\(863\) 7.14958 7.14958i 0.243374 0.243374i −0.574870 0.818245i \(-0.694947\pi\)
0.818245 + 0.574870i \(0.194947\pi\)
\(864\) −17.4532 + 5.65054i −0.593770 + 0.192235i
\(865\) −13.6003 + 1.19458i −0.462425 + 0.0406170i
\(866\) −3.14677 6.42679i −0.106932 0.218391i
\(867\) −7.78802 3.22590i −0.264495 0.109557i
\(868\) −5.09601 3.95631i −0.172970 0.134286i
\(869\) 18.2694 + 7.56744i 0.619748 + 0.256708i
\(870\) −6.00067 + 0.908329i −0.203442 + 0.0307952i
\(871\) −0.0778462 + 0.0778462i −0.00263772 + 0.00263772i
\(872\) 12.2318 17.9740i 0.414220 0.608677i
\(873\) 23.8715 0.807928
\(874\) −2.21521 35.3287i −0.0749307 1.19501i
\(875\) 1.17872 9.02513i 0.0398480 0.305105i
\(876\) 6.61699 3.77056i 0.223567 0.127395i
\(877\) 40.6235 + 16.8268i 1.37176 + 0.568201i 0.942265 0.334868i \(-0.108692\pi\)
0.429495 + 0.903069i \(0.358692\pi\)
\(878\) 21.2877 + 43.4769i 0.718427 + 1.46727i
\(879\) 6.98375i 0.235556i
\(880\) −16.9641 48.2494i −0.571861 1.62649i
\(881\) 1.07314i 0.0361548i −0.999837 0.0180774i \(-0.994245\pi\)
0.999837 0.0180774i \(-0.00575454\pi\)
\(882\) −21.5174 + 10.5356i −0.724528 + 0.354753i
\(883\) 24.6570 + 10.2132i 0.829773 + 0.343703i 0.756813 0.653632i \(-0.226755\pi\)
0.0729599 + 0.997335i \(0.476755\pi\)
\(884\) −9.82195 2.69144i −0.330348 0.0905228i
\(885\) −2.43322 + 7.72644i −0.0817918 + 0.259722i
\(886\) 5.83064 0.365598i 0.195884 0.0122825i
\(887\) −13.6649 −0.458823 −0.229411 0.973330i \(-0.573680\pi\)
−0.229411 + 0.973330i \(0.573680\pi\)
\(888\) −5.94821 + 3.90186i −0.199609 + 0.130938i
\(889\) −4.58431 + 4.58431i −0.153753 + 0.153753i
\(890\) 1.77806 2.41237i 0.0596007 0.0808629i
\(891\) −32.5740 13.4926i −1.09127 0.452018i
\(892\) 6.20324 0.780992i 0.207700 0.0261496i
\(893\) −25.6287 10.6157i −0.857630 0.355242i
\(894\) 6.35815 3.11316i 0.212648 0.104120i
\(895\) −29.6831 + 35.3996i −0.992195 + 1.18328i
\(896\) −6.20874 + 6.80310i −0.207419 + 0.227276i
\(897\) −9.68898 + 9.68898i −0.323506 + 0.323506i
\(898\) −26.1678 8.96542i −0.873232 0.299180i
\(899\) 12.2908 5.09101i 0.409920 0.169795i
\(900\) 23.6503 + 12.4614i 0.788343 + 0.415379i
\(901\) 2.62527 6.33797i 0.0874606 0.211148i
\(902\) −85.1733 + 5.34061i −2.83596 + 0.177823i
\(903\) −1.71300 −0.0570052
\(904\) −5.25263 + 25.2834i −0.174700 + 0.840912i
\(905\) 1.39734 + 15.9087i 0.0464492 + 0.528825i
\(906\) −0.249995 3.98697i −0.00830551 0.132458i
\(907\) −0.640513 1.54634i −0.0212679 0.0513452i 0.912889 0.408208i \(-0.133846\pi\)
−0.934157 + 0.356863i \(0.883846\pi\)
\(908\) 9.97447 + 17.5043i 0.331014 + 0.580900i
\(909\) 23.9548 9.92242i 0.794532 0.329106i
\(910\) −8.47752 2.09678i −0.281027 0.0695076i
\(911\) 24.6293 0.816007 0.408003 0.912980i \(-0.366225\pi\)
0.408003 + 0.912980i \(0.366225\pi\)
\(912\) −2.00761 7.84660i −0.0664785 0.259827i
\(913\) 15.7842 15.7842i 0.522382 0.522382i
\(914\) −25.1866 8.62923i −0.833098 0.285430i
\(915\) −17.6406 + 9.19079i −0.583179 + 0.303838i
\(916\) 3.06111 + 5.37196i 0.101142 + 0.177494i
\(917\) −1.74328 + 0.722090i −0.0575681 + 0.0238455i
\(918\) −4.55375 + 5.16302i −0.150296 + 0.170405i
\(919\) −25.5224 + 25.5224i −0.841905 + 0.841905i −0.989106 0.147202i \(-0.952973\pi\)
0.147202 + 0.989106i \(0.452973\pi\)
\(920\) 21.8142 39.0053i 0.719191 1.28597i
\(921\) −6.36858 6.36858i −0.209852 0.209852i
\(922\) −38.7583 + 2.43025i −1.27644 + 0.0800361i
\(923\) 6.19574 + 14.9578i 0.203935 + 0.492343i
\(924\) 5.28027 0.664789i 0.173708 0.0218700i
\(925\) 21.4812 + 4.74678i 0.706297 + 0.156073i
\(926\) −49.4367 + 24.2058i −1.62459 + 0.795453i
\(927\) 22.4265 + 22.4265i 0.736583 + 0.736583i
\(928\) −5.84992 18.0690i −0.192033 0.593145i
\(929\) 10.3638i 0.340027i −0.985442 0.170013i \(-0.945619\pi\)
0.985442 0.170013i \(-0.0543811\pi\)
\(930\) 6.95311 + 1.71974i 0.228002 + 0.0563926i
\(931\) −8.59049 20.7393i −0.281542 0.679703i
\(932\) 30.5912 + 23.7496i 1.00205 + 0.777945i
\(933\) 13.7807 5.70816i 0.451160 0.186877i
\(934\) −39.7765 35.0826i −1.30153 1.14794i
\(935\) −14.7068 12.3319i −0.480965 0.403296i
\(936\) 14.4304 21.2048i 0.471673 0.693102i
\(937\) 38.9474i 1.27235i −0.771543 0.636177i \(-0.780515\pi\)
0.771543 0.636177i \(-0.219485\pi\)
\(938\) 0.0280216 + 0.0247148i 0.000914936 + 0.000806968i
\(939\) 16.0989 + 6.66838i 0.525367 + 0.217614i
\(940\) −19.9354 28.7952i −0.650221 0.939196i
\(941\) 7.92882 + 19.1419i 0.258472 + 0.624007i 0.998838 0.0481976i \(-0.0153477\pi\)
−0.740366 + 0.672204i \(0.765348\pi\)
\(942\) −5.45408 + 2.67050i −0.177703 + 0.0870095i
\(943\) −52.7300 52.7300i −1.71713 1.71713i
\(944\) −25.0939 3.59300i −0.816736 0.116942i
\(945\) −3.79307 + 4.52356i −0.123389 + 0.147151i
\(946\) 28.1607 + 9.64819i 0.915583 + 0.313690i
\(947\) 18.6394 44.9994i 0.605698 1.46228i −0.261938 0.965085i \(-0.584362\pi\)
0.867636 0.497200i \(-0.165638\pi\)
\(948\) 1.95742 + 3.43508i 0.0635739 + 0.111566i
\(949\) −8.64783 + 20.8777i −0.280720 + 0.677719i
\(950\) −13.0397 + 21.3854i −0.423065 + 0.693834i
\(951\) −9.92097 9.92097i −0.321709 0.321709i
\(952\) −0.703042 + 3.38407i −0.0227857 + 0.109678i
\(953\) 43.1213i 1.39684i −0.715690 0.698418i \(-0.753888\pi\)
0.715690 0.698418i \(-0.246112\pi\)
\(954\) 12.9579 + 11.4288i 0.419527 + 0.370020i
\(955\) −26.0358 + 13.5648i −0.842499 + 0.438945i
\(956\) −1.33861 + 1.72423i −0.0432939 + 0.0557655i
\(957\) −4.19966 + 10.1389i −0.135756 + 0.327744i
\(958\) −10.5679 + 30.8449i −0.341432 + 0.996555i
\(959\) 2.05951 0.0665051
\(960\) 3.23665 9.69984i 0.104462 0.313061i
\(961\) 15.2993 0.493527
\(962\) 6.84146 19.9685i 0.220577 0.643811i
\(963\) −18.6194 + 44.9512i −0.600002 + 1.44853i
\(964\) 0.406484 0.523579i 0.0130920 0.0168634i
\(965\) 11.1227 35.3190i 0.358052 1.13696i
\(966\) 3.48765 + 3.07609i 0.112213 + 0.0989715i
\(967\) 19.8075i 0.636967i 0.947928 + 0.318483i \(0.103173\pi\)
−0.947928 + 0.318483i \(0.896827\pi\)
\(968\) −60.0863 12.4829i −1.93125 0.401217i
\(969\) −2.14919 2.14919i −0.0690419 0.0690419i
\(970\) −16.7542 + 22.7312i −0.537946 + 0.729855i
\(971\) 6.68117 16.1298i 0.214409 0.517629i −0.779682 0.626175i \(-0.784619\pi\)
0.994091 + 0.108546i \(0.0346195\pi\)
\(972\) −13.1235 23.0305i −0.420936 0.738704i
\(973\) 1.12064 2.70547i 0.0359262 0.0867335i
\(974\) 9.45969 + 3.24100i 0.303108 + 0.103848i
\(975\) 9.54714 1.69018i 0.305753 0.0541292i
\(976\) −37.3326 49.8099i −1.19499 1.59438i
\(977\) 34.4766 + 34.4766i 1.10300 + 1.10300i 0.994046 + 0.108958i \(0.0347513\pi\)
0.108958 + 0.994046i \(0.465249\pi\)
\(978\) 14.7715 7.23264i 0.472342 0.231274i
\(979\) −2.07376 5.00650i −0.0662777 0.160009i
\(980\) 5.06964 27.8840i 0.161944 0.890721i
\(981\) 18.9842 + 7.86352i 0.606119 + 0.251063i
\(982\) 29.4347 + 25.9612i 0.939298 + 0.828455i
\(983\) 22.1834i 0.707539i −0.935333 0.353770i \(-0.884900\pi\)
0.935333 0.353770i \(-0.115100\pi\)
\(984\) −14.1060 9.59950i −0.449683 0.306021i
\(985\) 30.5360 36.4168i 0.972957 1.16033i
\(986\) −5.34520 4.71443i −0.170226 0.150138i
\(987\) 3.36693 1.39463i 0.107171 0.0443915i
\(988\) 18.9831 + 14.7377i 0.603934 + 0.468867i
\(989\) 9.95409 + 24.0313i 0.316521 + 0.764150i
\(990\) 41.3874 24.9740i 1.31538 0.793725i
\(991\) 21.8010i 0.692531i 0.938136 + 0.346266i \(0.112550\pi\)
−0.938136 + 0.346266i \(0.887450\pi\)
\(992\) −1.78222 + 22.3438i −0.0565854 + 0.709416i
\(993\) −7.13677 7.13677i −0.226478 0.226478i
\(994\) 4.93495 2.41632i 0.156527 0.0766409i
\(995\) 7.66423 24.3370i 0.242973 0.771535i
\(996\) 4.42804 0.557493i 0.140308 0.0176649i
\(997\) −5.31872 12.8405i −0.168446 0.406664i 0.817004 0.576632i \(-0.195633\pi\)
−0.985450 + 0.169968i \(0.945633\pi\)
\(998\) −10.5039 + 0.658621i −0.332494 + 0.0208483i
\(999\) −10.0895 10.0895i −0.319219 0.319219i
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 160.2.u.a.43.10 88
4.3 odd 2 640.2.u.a.463.10 88
5.2 odd 4 160.2.ba.a.107.2 yes 88
5.3 odd 4 800.2.bb.b.107.21 88
5.4 even 2 800.2.v.b.43.13 88
20.7 even 4 640.2.ba.a.207.13 88
32.3 odd 8 160.2.ba.a.3.2 yes 88
32.29 even 8 640.2.ba.a.303.13 88
160.3 even 8 800.2.v.b.707.13 88
160.67 even 8 inner 160.2.u.a.67.10 yes 88
160.99 odd 8 800.2.bb.b.643.21 88
160.157 odd 8 640.2.u.a.47.10 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.u.a.43.10 88 1.1 even 1 trivial
160.2.u.a.67.10 yes 88 160.67 even 8 inner
160.2.ba.a.3.2 yes 88 32.3 odd 8
160.2.ba.a.107.2 yes 88 5.2 odd 4
640.2.u.a.47.10 88 160.157 odd 8
640.2.u.a.463.10 88 4.3 odd 2
640.2.ba.a.207.13 88 20.7 even 4
640.2.ba.a.303.13 88 32.29 even 8
800.2.v.b.43.13 88 5.4 even 2
800.2.v.b.707.13 88 160.3 even 8
800.2.bb.b.107.21 88 5.3 odd 4
800.2.bb.b.643.21 88 160.99 odd 8