Properties

Label 171.2.g.c.106.1
Level $171$
Weight $2$
Character 171.106
Analytic conductor $1.365$
Analytic rank $0$
Dimension $32$
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] = [171,2,Mod(106,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.g (of order \(3\), degree \(2\), 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: \(1.36544187456\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 106.1
Character \(\chi\) \(=\) 171.106
Dual form 171.2.g.c.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23404 - 2.13742i) q^{2} +(1.62292 + 0.605076i) q^{3} +(-2.04570 + 3.54325i) q^{4} +1.91524 q^{5} +(-0.709450 - 4.21555i) q^{6} +(-0.324708 + 0.562412i) q^{7} +5.16173 q^{8} +(2.26777 + 1.96399i) q^{9} +O(q^{10})\) \(q+(-1.23404 - 2.13742i) q^{2} +(1.62292 + 0.605076i) q^{3} +(-2.04570 + 3.54325i) q^{4} +1.91524 q^{5} +(-0.709450 - 4.21555i) q^{6} +(-0.324708 + 0.562412i) q^{7} +5.16173 q^{8} +(2.26777 + 1.96399i) q^{9} +(-2.36348 - 4.09366i) q^{10} +(2.93240 - 5.07906i) q^{11} +(-5.46395 + 4.51263i) q^{12} +(0.327691 - 0.567577i) q^{13} +1.60281 q^{14} +(3.10829 + 1.15887i) q^{15} +(-2.27837 - 3.94625i) q^{16} +(-1.93700 + 3.35499i) q^{17} +(1.39935 - 7.27079i) q^{18} +(-4.28438 - 0.802530i) q^{19} +(-3.91800 + 6.78618i) q^{20} +(-0.867279 + 0.716278i) q^{21} -14.4748 q^{22} +(0.961768 - 1.66583i) q^{23} +(8.37709 + 3.12324i) q^{24} -1.33186 q^{25} -1.61753 q^{26} +(2.49205 + 4.55957i) q^{27} +(-1.32851 - 2.30105i) q^{28} -6.53639 q^{29} +(-1.35877 - 8.07379i) q^{30} +(1.54544 + 2.67678i) q^{31} +(-0.461461 + 0.799274i) q^{32} +(7.83228 - 6.46861i) q^{33} +9.56134 q^{34} +(-0.621894 + 1.07715i) q^{35} +(-11.5981 + 4.01755i) q^{36} +2.23125 q^{37} +(3.57175 + 10.1479i) q^{38} +(0.875245 - 0.722857i) q^{39} +9.88594 q^{40} -6.96810 q^{41} +(2.60124 + 0.969822i) q^{42} +(4.46940 + 7.74122i) q^{43} +(11.9976 + 20.7805i) q^{44} +(4.34331 + 3.76150i) q^{45} -4.74743 q^{46} +11.5497 q^{47} +(-1.30984 - 7.78305i) q^{48} +(3.28913 + 5.69694i) q^{49} +(1.64357 + 2.84674i) q^{50} +(-5.17363 + 4.27286i) q^{51} +(1.34071 + 2.32218i) q^{52} +(-6.35124 - 11.0007i) q^{53} +(6.67042 - 10.9532i) q^{54} +(5.61624 - 9.72762i) q^{55} +(-1.67606 + 2.90302i) q^{56} +(-6.46764 - 3.89482i) q^{57} +(8.06615 + 13.9710i) q^{58} -14.3346 q^{59} +(-10.4648 + 8.64276i) q^{60} -10.3431 q^{61} +(3.81426 - 6.60649i) q^{62} +(-1.84093 + 0.637695i) q^{63} -6.83564 q^{64} +(0.627606 - 1.08705i) q^{65} +(-23.4914 - 8.75834i) q^{66} +(-0.381945 + 0.661549i) q^{67} +(-7.92505 - 13.7266i) q^{68} +(2.56883 - 2.12157i) q^{69} +3.06976 q^{70} +(-0.299796 + 0.519263i) q^{71} +(11.7056 + 10.1376i) q^{72} +(1.75541 - 3.04046i) q^{73} +(-2.75345 - 4.76912i) q^{74} +(-2.16151 - 0.805878i) q^{75} +(11.6081 - 13.5389i) q^{76} +(1.90435 + 3.29843i) q^{77} +(-2.62513 - 0.978730i) q^{78} +(2.13479 + 3.69756i) q^{79} +(-4.36362 - 7.55801i) q^{80} +(1.28552 + 8.90772i) q^{81} +(8.59890 + 14.8937i) q^{82} +(-3.29968 + 5.71522i) q^{83} +(-0.763763 - 4.53828i) q^{84} +(-3.70982 + 6.42560i) q^{85} +(11.0308 - 19.1059i) q^{86} +(-10.6081 - 3.95501i) q^{87} +(15.1362 - 26.2167i) q^{88} +(2.41922 + 4.19022i) q^{89} +(2.68008 - 13.9253i) q^{90} +(0.212808 + 0.368594i) q^{91} +(3.93497 + 6.81558i) q^{92} +(0.888475 + 5.27932i) q^{93} +(-14.2528 - 24.6866i) q^{94} +(-8.20562 - 1.53704i) q^{95} +(-1.23254 + 1.01794i) q^{96} +(-1.19452 - 2.06897i) q^{97} +(8.11782 - 14.0605i) q^{98} +(16.6252 - 5.75894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + q^{2} - 2 q^{3} - 17 q^{4} - 6 q^{5} + 2 q^{6} + q^{7} - 36 q^{8} - 10 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} + q^{15} - 11 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 11 q^{21} + 16 q^{22} + 5 q^{23} + 27 q^{24} + 18 q^{25} - 4 q^{26} - 5 q^{27} - 10 q^{28} - 20 q^{29} - 5 q^{30} - 10 q^{31} + 17 q^{32} + 34 q^{33} + 26 q^{34} - 3 q^{35} - 16 q^{36} + 2 q^{37} + 38 q^{38} - 24 q^{40} - 12 q^{41} + 25 q^{42} + 7 q^{43} + 20 q^{44} - 35 q^{45} + 18 q^{47} - 33 q^{48} - 13 q^{49} + q^{50} - 28 q^{51} + 19 q^{52} + 16 q^{53} + 35 q^{54} + 15 q^{55} - 6 q^{56} + 6 q^{57} - 74 q^{59} + 50 q^{60} + 24 q^{61} + 54 q^{62} - 30 q^{63} - 64 q^{64} + 54 q^{65} + 4 q^{66} - 11 q^{67} - 2 q^{68} + 3 q^{69} - 48 q^{70} + 9 q^{71} - 10 q^{73} + 6 q^{74} - 76 q^{75} + 29 q^{76} + 46 q^{77} - 82 q^{78} - 8 q^{79} - 24 q^{80} + 26 q^{81} + 7 q^{82} + 3 q^{83} + 12 q^{84} - 27 q^{85} + 17 q^{86} - 9 q^{87} + 9 q^{88} + 30 q^{89} - 74 q^{90} - q^{91} - 17 q^{92} - 24 q^{93} - 18 q^{94} - 6 q^{95} - 5 q^{96} + 18 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23404 2.13742i −0.872597 1.51138i −0.859301 0.511470i \(-0.829101\pi\)
−0.0132953 0.999912i \(-0.504232\pi\)
\(3\) 1.62292 + 0.605076i 0.936996 + 0.349341i
\(4\) −2.04570 + 3.54325i −1.02285 + 1.77163i
\(5\) 1.91524 0.856521 0.428260 0.903655i \(-0.359127\pi\)
0.428260 + 0.903655i \(0.359127\pi\)
\(6\) −0.709450 4.21555i −0.289632 1.72099i
\(7\) −0.324708 + 0.562412i −0.122728 + 0.212572i −0.920843 0.389934i \(-0.872498\pi\)
0.798114 + 0.602506i \(0.205831\pi\)
\(8\) 5.16173 1.82495
\(9\) 2.26777 + 1.96399i 0.755922 + 0.654662i
\(10\) −2.36348 4.09366i −0.747397 1.29453i
\(11\) 2.93240 5.07906i 0.884151 1.53140i 0.0374684 0.999298i \(-0.488071\pi\)
0.846683 0.532097i \(-0.178596\pi\)
\(12\) −5.46395 + 4.51263i −1.57731 + 1.30268i
\(13\) 0.327691 0.567577i 0.0908851 0.157418i −0.816999 0.576639i \(-0.804364\pi\)
0.907884 + 0.419222i \(0.137697\pi\)
\(14\) 1.60281 0.428369
\(15\) 3.10829 + 1.15887i 0.802556 + 0.299218i
\(16\) −2.27837 3.94625i −0.569592 0.986563i
\(17\) −1.93700 + 3.35499i −0.469792 + 0.813704i −0.999403 0.0345362i \(-0.989005\pi\)
0.529611 + 0.848241i \(0.322338\pi\)
\(18\) 1.39935 7.27079i 0.329829 1.71374i
\(19\) −4.28438 0.802530i −0.982905 0.184113i
\(20\) −3.91800 + 6.78618i −0.876092 + 1.51744i
\(21\) −0.867279 + 0.716278i −0.189256 + 0.156305i
\(22\) −14.4748 −3.08603
\(23\) 0.961768 1.66583i 0.200542 0.347350i −0.748161 0.663517i \(-0.769063\pi\)
0.948703 + 0.316168i \(0.102396\pi\)
\(24\) 8.37709 + 3.12324i 1.70997 + 0.637528i
\(25\) −1.33186 −0.266372
\(26\) −1.61753 −0.317224
\(27\) 2.49205 + 4.55957i 0.479595 + 0.877490i
\(28\) −1.32851 2.30105i −0.251065 0.434857i
\(29\) −6.53639 −1.21378 −0.606888 0.794787i \(-0.707582\pi\)
−0.606888 + 0.794787i \(0.707582\pi\)
\(30\) −1.35877 8.07379i −0.248076 1.47406i
\(31\) 1.54544 + 2.67678i 0.277569 + 0.480764i 0.970780 0.239971i \(-0.0771380\pi\)
−0.693211 + 0.720735i \(0.743805\pi\)
\(32\) −0.461461 + 0.799274i −0.0815755 + 0.141293i
\(33\) 7.83228 6.46861i 1.36343 1.12604i
\(34\) 9.56134 1.63976
\(35\) −0.621894 + 1.07715i −0.105119 + 0.182072i
\(36\) −11.5981 + 4.01755i −1.93301 + 0.669591i
\(37\) 2.23125 0.366816 0.183408 0.983037i \(-0.441287\pi\)
0.183408 + 0.983037i \(0.441287\pi\)
\(38\) 3.57175 + 10.1479i 0.579415 + 1.64620i
\(39\) 0.875245 0.722857i 0.140151 0.115750i
\(40\) 9.88594 1.56310
\(41\) −6.96810 −1.08823 −0.544117 0.839009i \(-0.683135\pi\)
−0.544117 + 0.839009i \(0.683135\pi\)
\(42\) 2.60124 + 0.969822i 0.401380 + 0.149647i
\(43\) 4.46940 + 7.74122i 0.681576 + 1.18052i 0.974500 + 0.224389i \(0.0720386\pi\)
−0.292923 + 0.956136i \(0.594628\pi\)
\(44\) 11.9976 + 20.7805i 1.80871 + 3.13277i
\(45\) 4.34331 + 3.76150i 0.647463 + 0.560731i
\(46\) −4.74743 −0.699971
\(47\) 11.5497 1.68470 0.842352 0.538928i \(-0.181171\pi\)
0.842352 + 0.538928i \(0.181171\pi\)
\(48\) −1.30984 7.78305i −0.189059 1.12339i
\(49\) 3.28913 + 5.69694i 0.469876 + 0.813848i
\(50\) 1.64357 + 2.84674i 0.232436 + 0.402590i
\(51\) −5.17363 + 4.27286i −0.724454 + 0.598320i
\(52\) 1.34071 + 2.32218i 0.185923 + 0.322029i
\(53\) −6.35124 11.0007i −0.872409 1.51106i −0.859497 0.511141i \(-0.829223\pi\)
−0.0129124 0.999917i \(-0.504110\pi\)
\(54\) 6.67042 10.9532i 0.907729 1.49055i
\(55\) 5.61624 9.72762i 0.757294 1.31167i
\(56\) −1.67606 + 2.90302i −0.223972 + 0.387932i
\(57\) −6.46764 3.89482i −0.856660 0.515882i
\(58\) 8.06615 + 13.9710i 1.05914 + 1.83448i
\(59\) −14.3346 −1.86621 −0.933103 0.359609i \(-0.882910\pi\)
−0.933103 + 0.359609i \(0.882910\pi\)
\(60\) −10.4648 + 8.64276i −1.35100 + 1.11578i
\(61\) −10.3431 −1.32430 −0.662150 0.749372i \(-0.730356\pi\)
−0.662150 + 0.749372i \(0.730356\pi\)
\(62\) 3.81426 6.60649i 0.484411 0.839025i
\(63\) −1.84093 + 0.637695i −0.231935 + 0.0803420i
\(64\) −6.83564 −0.854455
\(65\) 0.627606 1.08705i 0.0778449 0.134831i
\(66\) −23.4914 8.75834i −2.89160 1.07808i
\(67\) −0.381945 + 0.661549i −0.0466620 + 0.0808210i −0.888413 0.459045i \(-0.848192\pi\)
0.841751 + 0.539866i \(0.181525\pi\)
\(68\) −7.92505 13.7266i −0.961054 1.66459i
\(69\) 2.56883 2.12157i 0.309251 0.255407i
\(70\) 3.06976 0.366907
\(71\) −0.299796 + 0.519263i −0.0355793 + 0.0616251i −0.883267 0.468871i \(-0.844661\pi\)
0.847687 + 0.530496i \(0.177994\pi\)
\(72\) 11.7056 + 10.1376i 1.37952 + 1.19472i
\(73\) 1.75541 3.04046i 0.205455 0.355859i −0.744822 0.667263i \(-0.767466\pi\)
0.950278 + 0.311404i \(0.100799\pi\)
\(74\) −2.75345 4.76912i −0.320082 0.554399i
\(75\) −2.16151 0.805878i −0.249590 0.0930548i
\(76\) 11.6081 13.5389i 1.33154 1.55302i
\(77\) 1.90435 + 3.29843i 0.217021 + 0.375891i
\(78\) −2.62513 0.978730i −0.297238 0.110819i
\(79\) 2.13479 + 3.69756i 0.240182 + 0.416008i 0.960766 0.277360i \(-0.0894594\pi\)
−0.720584 + 0.693368i \(0.756126\pi\)
\(80\) −4.36362 7.55801i −0.487868 0.845012i
\(81\) 1.28552 + 8.90772i 0.142836 + 0.989746i
\(82\) 8.59890 + 14.8937i 0.949590 + 1.64474i
\(83\) −3.29968 + 5.71522i −0.362187 + 0.627327i −0.988321 0.152389i \(-0.951303\pi\)
0.626133 + 0.779716i \(0.284637\pi\)
\(84\) −0.763763 4.53828i −0.0833334 0.495167i
\(85\) −3.70982 + 6.42560i −0.402387 + 0.696955i
\(86\) 11.0308 19.1059i 1.18948 2.06024i
\(87\) −10.6081 3.95501i −1.13730 0.424022i
\(88\) 15.1362 26.2167i 1.61353 2.79471i
\(89\) 2.41922 + 4.19022i 0.256437 + 0.444162i 0.965285 0.261200i \(-0.0841180\pi\)
−0.708848 + 0.705361i \(0.750785\pi\)
\(90\) 2.68008 13.9253i 0.282506 1.46786i
\(91\) 0.212808 + 0.368594i 0.0223083 + 0.0386392i
\(92\) 3.93497 + 6.81558i 0.410249 + 0.710573i
\(93\) 0.888475 + 5.27932i 0.0921305 + 0.547440i
\(94\) −14.2528 24.6866i −1.47007 2.54623i
\(95\) −8.20562 1.53704i −0.841879 0.157697i
\(96\) −1.23254 + 1.01794i −0.125795 + 0.103893i
\(97\) −1.19452 2.06897i −0.121285 0.210072i 0.798990 0.601345i \(-0.205368\pi\)
−0.920275 + 0.391273i \(0.872035\pi\)
\(98\) 8.11782 14.0605i 0.820024 1.42032i
\(99\) 16.6252 5.75894i 1.67090 0.578795i
\(100\) 2.72459 4.71912i 0.272459 0.471912i
\(101\) −7.44414 −0.740720 −0.370360 0.928888i \(-0.620766\pi\)
−0.370360 + 0.928888i \(0.620766\pi\)
\(102\) 15.5173 + 5.78534i 1.53645 + 0.572834i
\(103\) −0.709718 1.22927i −0.0699306 0.121123i 0.828940 0.559338i \(-0.188944\pi\)
−0.898871 + 0.438214i \(0.855611\pi\)
\(104\) 1.69145 2.92968i 0.165860 0.287279i
\(105\) −1.66105 + 1.37184i −0.162102 + 0.133878i
\(106\) −15.6753 + 27.1505i −1.52252 + 2.63709i
\(107\) 7.56837 0.731662 0.365831 0.930681i \(-0.380785\pi\)
0.365831 + 0.930681i \(0.380785\pi\)
\(108\) −21.2537 0.497542i −2.04514 0.0478760i
\(109\) 3.79611 6.57506i 0.363602 0.629776i −0.624949 0.780665i \(-0.714880\pi\)
0.988551 + 0.150889i \(0.0482136\pi\)
\(110\) −27.7226 −2.64325
\(111\) 3.62116 + 1.35008i 0.343705 + 0.128144i
\(112\) 2.95922 0.279620
\(113\) 2.44573 + 4.23613i 0.230075 + 0.398502i 0.957830 0.287335i \(-0.0927694\pi\)
−0.727755 + 0.685837i \(0.759436\pi\)
\(114\) −0.343550 + 18.6304i −0.0321764 + 1.74490i
\(115\) 1.84201 3.19046i 0.171769 0.297512i
\(116\) 13.3715 23.1601i 1.24151 2.15036i
\(117\) 1.85784 0.643552i 0.171757 0.0594964i
\(118\) 17.6894 + 30.6390i 1.62845 + 2.82055i
\(119\) −1.25792 2.17879i −0.115314 0.199729i
\(120\) 16.0441 + 5.98175i 1.46462 + 0.546056i
\(121\) −11.6979 20.2614i −1.06345 1.84195i
\(122\) 12.7638 + 22.1075i 1.15558 + 2.00152i
\(123\) −11.3087 4.21623i −1.01967 0.380165i
\(124\) −12.6460 −1.13565
\(125\) −12.1270 −1.08467
\(126\) 3.63480 + 3.14790i 0.323813 + 0.280437i
\(127\) −3.57756 6.19651i −0.317457 0.549852i 0.662500 0.749062i \(-0.269496\pi\)
−0.979957 + 0.199210i \(0.936162\pi\)
\(128\) 9.35836 + 16.2091i 0.827170 + 1.43270i
\(129\) 2.56946 + 15.2677i 0.226228 + 1.34425i
\(130\) −3.09796 −0.271709
\(131\) 6.82633 0.596419 0.298209 0.954500i \(-0.403611\pi\)
0.298209 + 0.954500i \(0.403611\pi\)
\(132\) 6.89744 + 40.9846i 0.600345 + 3.56725i
\(133\) 1.84253 2.14900i 0.159767 0.186342i
\(134\) 1.88534 0.162869
\(135\) 4.77287 + 8.73267i 0.410783 + 0.751588i
\(136\) −9.99829 + 17.3175i −0.857346 + 1.48497i
\(137\) 10.2964 0.879684 0.439842 0.898075i \(-0.355034\pi\)
0.439842 + 0.898075i \(0.355034\pi\)
\(138\) −7.70472 2.87256i −0.655869 0.244528i
\(139\) −1.43344 + 2.48279i −0.121583 + 0.210587i −0.920392 0.390997i \(-0.872130\pi\)
0.798809 + 0.601584i \(0.205464\pi\)
\(140\) −2.54442 4.40706i −0.215042 0.372464i
\(141\) 18.7444 + 6.98848i 1.57856 + 0.588536i
\(142\) 1.47984 0.124185
\(143\) −1.92184 3.32872i −0.160712 0.278362i
\(144\) 2.58357 13.4239i 0.215298 1.11865i
\(145\) −12.5187 −1.03962
\(146\) −8.66497 −0.717118
\(147\) 1.89092 + 11.2359i 0.155961 + 0.926719i
\(148\) −4.56447 + 7.90590i −0.375198 + 0.649861i
\(149\) −8.16603 −0.668987 −0.334493 0.942398i \(-0.608565\pi\)
−0.334493 + 0.942398i \(0.608565\pi\)
\(150\) 0.944889 + 5.61453i 0.0771499 + 0.458425i
\(151\) 10.2584 17.7681i 0.834818 1.44595i −0.0593605 0.998237i \(-0.518906\pi\)
0.894179 0.447711i \(-0.147761\pi\)
\(152\) −22.1148 4.14244i −1.79375 0.335996i
\(153\) −10.9818 + 3.80408i −0.887828 + 0.307542i
\(154\) 4.70008 8.14077i 0.378743 0.656002i
\(155\) 2.95988 + 5.12667i 0.237744 + 0.411784i
\(156\) 0.770778 + 4.57996i 0.0617116 + 0.366690i
\(157\) −1.46067 −0.116574 −0.0582869 0.998300i \(-0.518564\pi\)
−0.0582869 + 0.998300i \(0.518564\pi\)
\(158\) 5.26882 9.12586i 0.419165 0.726015i
\(159\) −3.65133 21.6962i −0.289570 1.72062i
\(160\) −0.883808 + 1.53080i −0.0698711 + 0.121020i
\(161\) 0.624588 + 1.08182i 0.0492244 + 0.0852592i
\(162\) 17.4531 13.7402i 1.37125 1.07953i
\(163\) 18.1874 1.42455 0.712274 0.701901i \(-0.247665\pi\)
0.712274 + 0.701901i \(0.247665\pi\)
\(164\) 14.2546 24.6897i 1.11310 1.92795i
\(165\) 15.0007 12.3889i 1.16780 0.964477i
\(166\) 16.2877 1.26417
\(167\) 4.44733 7.70301i 0.344145 0.596077i −0.641053 0.767497i \(-0.721502\pi\)
0.985198 + 0.171420i \(0.0548355\pi\)
\(168\) −4.47666 + 3.69723i −0.345382 + 0.285248i
\(169\) 6.28524 + 10.8864i 0.483480 + 0.837412i
\(170\) 18.3123 1.40449
\(171\) −8.13982 10.2344i −0.622468 0.782646i
\(172\) −36.5721 −2.78860
\(173\) −4.78285 8.28413i −0.363633 0.629831i 0.624923 0.780687i \(-0.285130\pi\)
−0.988556 + 0.150856i \(0.951797\pi\)
\(174\) 4.63724 + 27.5545i 0.351548 + 2.08890i
\(175\) 0.432467 0.749054i 0.0326914 0.0566232i
\(176\) −26.7244 −2.01442
\(177\) −23.2640 8.67353i −1.74863 0.651942i
\(178\) 5.97082 10.3418i 0.447532 0.775148i
\(179\) 0.464358 0.0347078 0.0173539 0.999849i \(-0.494476\pi\)
0.0173539 + 0.999849i \(0.494476\pi\)
\(180\) −22.2131 + 7.69456i −1.65566 + 0.573519i
\(181\) 4.32082 + 7.48388i 0.321164 + 0.556272i 0.980728 0.195376i \(-0.0625926\pi\)
−0.659564 + 0.751648i \(0.729259\pi\)
\(182\) 0.525226 0.909718i 0.0389324 0.0674328i
\(183\) −16.7861 6.25837i −1.24086 0.462632i
\(184\) 4.96438 8.59856i 0.365979 0.633895i
\(185\) 4.27338 0.314185
\(186\) 10.1877 8.41392i 0.746997 0.616938i
\(187\) 11.3601 + 19.6763i 0.830735 + 1.43888i
\(188\) −23.6273 + 40.9237i −1.72320 + 2.98467i
\(189\) −3.37354 0.0789736i −0.245389 0.00574448i
\(190\) 6.84076 + 19.4356i 0.496281 + 1.41001i
\(191\) 11.1012 19.2279i 0.803256 1.39128i −0.114206 0.993457i \(-0.536432\pi\)
0.917462 0.397823i \(-0.130234\pi\)
\(192\) −11.0937 4.13608i −0.800620 0.298496i
\(193\) −4.72110 −0.339832 −0.169916 0.985459i \(-0.554350\pi\)
−0.169916 + 0.985459i \(0.554350\pi\)
\(194\) −2.94817 + 5.10638i −0.211666 + 0.366616i
\(195\) 1.67630 1.38444i 0.120043 0.0991420i
\(196\) −26.9143 −1.92245
\(197\) 8.23403 0.586650 0.293325 0.956013i \(-0.405238\pi\)
0.293325 + 0.956013i \(0.405238\pi\)
\(198\) −32.8254 28.4282i −2.33280 2.02031i
\(199\) −1.32235 2.29038i −0.0937389 0.162361i 0.815343 0.578979i \(-0.196549\pi\)
−0.909082 + 0.416618i \(0.863215\pi\)
\(200\) −6.87471 −0.486115
\(201\) −1.02016 + 0.842537i −0.0719562 + 0.0594280i
\(202\) 9.18635 + 15.9112i 0.646349 + 1.11951i
\(203\) 2.12242 3.67614i 0.148965 0.258014i
\(204\) −4.55612 27.0725i −0.318992 1.89545i
\(205\) −13.3456 −0.932095
\(206\) −1.75164 + 3.03393i −0.122042 + 0.211384i
\(207\) 5.45273 1.88881i 0.378991 0.131282i
\(208\) −2.98640 −0.207070
\(209\) −16.6396 + 19.4073i −1.15099 + 1.34243i
\(210\) 4.98199 + 1.85744i 0.343790 + 0.128176i
\(211\) 16.5480 1.13921 0.569605 0.821919i \(-0.307096\pi\)
0.569605 + 0.821919i \(0.307096\pi\)
\(212\) 51.9709 3.56937
\(213\) −0.800741 + 0.661324i −0.0548658 + 0.0453132i
\(214\) −9.33966 16.1768i −0.638446 1.10582i
\(215\) 8.55996 + 14.8263i 0.583784 + 1.01114i
\(216\) 12.8633 + 23.5353i 0.875236 + 1.60137i
\(217\) −2.00727 −0.136262
\(218\) −18.7382 −1.26911
\(219\) 4.68861 3.87228i 0.316827 0.261664i
\(220\) 22.9783 + 39.7996i 1.54920 + 2.68329i
\(221\) 1.26948 + 2.19880i 0.0853942 + 0.147907i
\(222\) −1.58296 9.40597i −0.106242 0.631287i
\(223\) −4.62185 8.00529i −0.309502 0.536074i 0.668751 0.743486i \(-0.266829\pi\)
−0.978254 + 0.207413i \(0.933496\pi\)
\(224\) −0.299680 0.519062i −0.0200232 0.0346813i
\(225\) −3.02035 2.61576i −0.201357 0.174384i
\(226\) 6.03625 10.4551i 0.401526 0.695463i
\(227\) 5.24132 9.07823i 0.347879 0.602544i −0.637994 0.770042i \(-0.720235\pi\)
0.985872 + 0.167498i \(0.0535688\pi\)
\(228\) 27.0312 14.9488i 1.79018 0.990012i
\(229\) −8.81057 15.2604i −0.582219 1.00843i −0.995216 0.0977001i \(-0.968851\pi\)
0.412997 0.910732i \(-0.364482\pi\)
\(230\) −9.09246 −0.599539
\(231\) 1.09481 + 6.50538i 0.0720334 + 0.428022i
\(232\) −33.7391 −2.21508
\(233\) −3.40859 + 5.90385i −0.223304 + 0.386774i −0.955809 0.293987i \(-0.905018\pi\)
0.732505 + 0.680762i \(0.238351\pi\)
\(234\) −3.66818 3.17681i −0.239797 0.207674i
\(235\) 22.1205 1.44298
\(236\) 29.3243 50.7911i 1.90885 3.30622i
\(237\) 1.22729 + 7.29257i 0.0797212 + 0.473704i
\(238\) −3.10465 + 5.37741i −0.201245 + 0.348566i
\(239\) 6.77458 + 11.7339i 0.438211 + 0.759004i 0.997552 0.0699338i \(-0.0222788\pi\)
−0.559340 + 0.828938i \(0.688945\pi\)
\(240\) −2.50865 14.9064i −0.161933 0.962204i
\(241\) 7.48784 0.482334 0.241167 0.970484i \(-0.422470\pi\)
0.241167 + 0.970484i \(0.422470\pi\)
\(242\) −28.8714 + 50.0067i −1.85592 + 3.21455i
\(243\) −3.30355 + 15.2344i −0.211923 + 0.977286i
\(244\) 21.1589 36.6483i 1.35456 2.34616i
\(245\) 6.29947 + 10.9110i 0.402458 + 0.697078i
\(246\) 4.94352 + 29.3744i 0.315187 + 1.87284i
\(247\) −1.85945 + 2.16874i −0.118314 + 0.137993i
\(248\) 7.97713 + 13.8168i 0.506548 + 0.877368i
\(249\) −8.81328 + 7.27880i −0.558519 + 0.461275i
\(250\) 14.9652 + 25.9205i 0.946483 + 1.63936i
\(251\) −15.0975 26.1496i −0.952946 1.65055i −0.739001 0.673705i \(-0.764702\pi\)
−0.213945 0.976846i \(-0.568631\pi\)
\(252\) 1.50648 7.82742i 0.0948991 0.493081i
\(253\) −5.64057 9.76976i −0.354620 0.614219i
\(254\) −8.82969 + 15.2935i −0.554024 + 0.959597i
\(255\) −9.90874 + 8.18354i −0.620510 + 0.512473i
\(256\) 16.2615 28.1657i 1.01634 1.76036i
\(257\) −11.6494 + 20.1773i −0.726667 + 1.25862i 0.231617 + 0.972807i \(0.425598\pi\)
−0.958284 + 0.285817i \(0.907735\pi\)
\(258\) 29.4627 24.3330i 1.83427 1.51490i
\(259\) −0.724507 + 1.25488i −0.0450187 + 0.0779747i
\(260\) 2.56779 + 4.44754i 0.159247 + 0.275824i
\(261\) −14.8230 12.8374i −0.917520 0.794613i
\(262\) −8.42394 14.5907i −0.520433 0.901416i
\(263\) 7.65298 + 13.2553i 0.471903 + 0.817360i 0.999483 0.0321454i \(-0.0102340\pi\)
−0.527580 + 0.849505i \(0.676901\pi\)
\(264\) 40.4281 33.3892i 2.48818 2.05496i
\(265\) −12.1641 21.0689i −0.747237 1.29425i
\(266\) −6.86705 1.28630i −0.421046 0.0788683i
\(267\) 1.39081 + 8.26422i 0.0851164 + 0.505762i
\(268\) −1.56269 2.70666i −0.0954565 0.165335i
\(269\) 2.30201 3.98719i 0.140356 0.243103i −0.787275 0.616602i \(-0.788509\pi\)
0.927631 + 0.373499i \(0.121842\pi\)
\(270\) 12.7754 20.9780i 0.777488 1.27668i
\(271\) −3.67360 + 6.36286i −0.223155 + 0.386517i −0.955764 0.294133i \(-0.904969\pi\)
0.732609 + 0.680650i \(0.238302\pi\)
\(272\) 17.6528 1.07036
\(273\) 0.122344 + 0.726965i 0.00740457 + 0.0439979i
\(274\) −12.7062 22.0078i −0.767610 1.32954i
\(275\) −3.90555 + 6.76461i −0.235513 + 0.407921i
\(276\) 2.26222 + 13.4421i 0.136170 + 0.809121i
\(277\) 11.8834 20.5827i 0.714006 1.23669i −0.249336 0.968417i \(-0.580212\pi\)
0.963342 0.268278i \(-0.0864544\pi\)
\(278\) 7.07567 0.424371
\(279\) −1.75246 + 9.10552i −0.104917 + 0.545134i
\(280\) −3.21005 + 5.55997i −0.191837 + 0.332272i
\(281\) 12.8409 0.766025 0.383012 0.923743i \(-0.374887\pi\)
0.383012 + 0.923743i \(0.374887\pi\)
\(282\) −8.19396 48.6885i −0.487944 2.89936i
\(283\) 1.50733 0.0896015 0.0448007 0.998996i \(-0.485735\pi\)
0.0448007 + 0.998996i \(0.485735\pi\)
\(284\) −1.22659 2.12451i −0.0727845 0.126066i
\(285\) −12.3871 7.45952i −0.733747 0.441864i
\(286\) −4.74325 + 8.21554i −0.280474 + 0.485795i
\(287\) 2.26260 3.91894i 0.133557 0.231328i
\(288\) −2.61625 + 0.906263i −0.154164 + 0.0534020i
\(289\) 0.996032 + 1.72518i 0.0585901 + 0.101481i
\(290\) 15.4486 + 26.7578i 0.907173 + 1.57127i
\(291\) −0.686732 4.08056i −0.0402569 0.239207i
\(292\) 7.18208 + 12.4397i 0.420300 + 0.727980i
\(293\) 12.6882 + 21.9765i 0.741250 + 1.28388i 0.951926 + 0.306327i \(0.0990999\pi\)
−0.210677 + 0.977556i \(0.567567\pi\)
\(294\) 21.6823 17.9072i 1.26454 1.04437i
\(295\) −27.4542 −1.59844
\(296\) 11.5171 0.669419
\(297\) 30.4660 + 0.713200i 1.76782 + 0.0413841i
\(298\) 10.0772 + 17.4542i 0.583756 + 1.01109i
\(299\) −0.630325 1.09175i −0.0364526 0.0631378i
\(300\) 7.27723 6.01020i 0.420151 0.346999i
\(301\) −5.80500 −0.334595
\(302\) −50.6371 −2.91384
\(303\) −12.0813 4.50427i −0.694051 0.258764i
\(304\) 6.59442 + 18.7357i 0.378216 + 1.07457i
\(305\) −19.8095 −1.13429
\(306\) 21.6829 + 18.7783i 1.23953 + 1.07349i
\(307\) 4.18433 7.24746i 0.238812 0.413635i −0.721562 0.692350i \(-0.756575\pi\)
0.960374 + 0.278716i \(0.0899087\pi\)
\(308\) −15.5829 −0.887918
\(309\) −0.408018 2.42444i −0.0232113 0.137922i
\(310\) 7.30522 12.6530i 0.414908 0.718642i
\(311\) 3.63194 + 6.29071i 0.205949 + 0.356713i 0.950435 0.310925i \(-0.100639\pi\)
−0.744486 + 0.667638i \(0.767305\pi\)
\(312\) 4.51778 3.73119i 0.255769 0.211237i
\(313\) 14.7246 0.832283 0.416142 0.909300i \(-0.363382\pi\)
0.416142 + 0.909300i \(0.363382\pi\)
\(314\) 1.80252 + 3.12205i 0.101722 + 0.176187i
\(315\) −3.52582 + 1.22134i −0.198658 + 0.0688146i
\(316\) −17.4685 −0.982682
\(317\) −16.3354 −0.917488 −0.458744 0.888569i \(-0.651700\pi\)
−0.458744 + 0.888569i \(0.651700\pi\)
\(318\) −41.8680 + 34.5784i −2.34784 + 1.93906i
\(319\) −19.1673 + 33.1987i −1.07316 + 1.85877i
\(320\) −13.0919 −0.731858
\(321\) 12.2829 + 4.57944i 0.685564 + 0.255599i
\(322\) 1.54153 2.67001i 0.0859062 0.148794i
\(323\) 10.9913 12.8196i 0.611575 0.713299i
\(324\) −34.1921 13.6676i −1.89956 0.759310i
\(325\) −0.436439 + 0.755934i −0.0242093 + 0.0419317i
\(326\) −22.4440 38.8741i −1.24306 2.15304i
\(327\) 10.1392 8.37388i 0.560700 0.463077i
\(328\) −35.9674 −1.98597
\(329\) −3.75030 + 6.49571i −0.206761 + 0.358120i
\(330\) −44.9917 16.7743i −2.47671 0.923395i
\(331\) −13.5395 + 23.4510i −0.744195 + 1.28898i 0.206374 + 0.978473i \(0.433834\pi\)
−0.950570 + 0.310511i \(0.899500\pi\)
\(332\) −13.5003 23.3832i −0.740926 1.28332i
\(333\) 5.05996 + 4.38215i 0.277284 + 0.240140i
\(334\) −21.9527 −1.20120
\(335\) −0.731516 + 1.26702i −0.0399670 + 0.0692249i
\(336\) 4.80259 + 1.79056i 0.262003 + 0.0976828i
\(337\) 17.3361 0.944358 0.472179 0.881503i \(-0.343468\pi\)
0.472179 + 0.881503i \(0.343468\pi\)
\(338\) 15.5124 26.8683i 0.843766 1.46144i
\(339\) 1.40606 + 8.35478i 0.0763664 + 0.453769i
\(340\) −15.1784 26.2897i −0.823163 1.42576i
\(341\) 18.1274 0.981652
\(342\) −11.8304 + 30.0278i −0.639713 + 1.62372i
\(343\) −8.81795 −0.476125
\(344\) 23.0698 + 39.9581i 1.24384 + 2.15439i
\(345\) 4.91992 4.06332i 0.264880 0.218762i
\(346\) −11.8044 + 20.4459i −0.634610 + 1.09918i
\(347\) 1.51943 0.0815675 0.0407837 0.999168i \(-0.487015\pi\)
0.0407837 + 0.999168i \(0.487015\pi\)
\(348\) 35.7145 29.4963i 1.91450 1.58117i
\(349\) −4.35421 + 7.54171i −0.233075 + 0.403699i −0.958712 0.284380i \(-0.908212\pi\)
0.725636 + 0.688079i \(0.241546\pi\)
\(350\) −2.13472 −0.114106
\(351\) 3.40453 + 0.0796989i 0.181720 + 0.00425401i
\(352\) 2.70637 + 4.68758i 0.144250 + 0.249849i
\(353\) −4.15920 + 7.20395i −0.221372 + 0.383428i −0.955225 0.295881i \(-0.904387\pi\)
0.733853 + 0.679309i \(0.237720\pi\)
\(354\) 10.1697 + 60.4283i 0.540513 + 3.21173i
\(355\) −0.574182 + 0.994512i −0.0304744 + 0.0527832i
\(356\) −19.7960 −1.04919
\(357\) −0.723182 4.29714i −0.0382748 0.227429i
\(358\) −0.573036 0.992527i −0.0302859 0.0524567i
\(359\) 13.7180 23.7604i 0.724011 1.25402i −0.235369 0.971906i \(-0.575630\pi\)
0.959380 0.282118i \(-0.0910368\pi\)
\(360\) 22.4190 + 19.4158i 1.18158 + 1.02330i
\(361\) 17.7119 + 6.87669i 0.932205 + 0.361931i
\(362\) 10.6641 18.4708i 0.560493 0.970803i
\(363\) −6.72515 39.9608i −0.352979 2.09740i
\(364\) −1.74136 −0.0912723
\(365\) 3.36203 5.82321i 0.175977 0.304801i
\(366\) 7.33792 + 43.6019i 0.383559 + 2.27911i
\(367\) 23.3930 1.22111 0.610553 0.791976i \(-0.290947\pi\)
0.610553 + 0.791976i \(0.290947\pi\)
\(368\) −8.76505 −0.456910
\(369\) −15.8020 13.6852i −0.822620 0.712426i
\(370\) −5.27352 9.13400i −0.274157 0.474854i
\(371\) 8.24920 0.428277
\(372\) −20.5235 7.65180i −1.06409 0.396727i
\(373\) 1.89269 + 3.27823i 0.0979996 + 0.169740i 0.910857 0.412723i \(-0.135422\pi\)
−0.812857 + 0.582463i \(0.802089\pi\)
\(374\) 28.0377 48.5627i 1.44979 2.51112i
\(375\) −19.6812 7.33778i −1.01633 0.378921i
\(376\) 59.6166 3.07449
\(377\) −2.14191 + 3.70990i −0.110314 + 0.191070i
\(378\) 3.99428 + 7.30813i 0.205444 + 0.375889i
\(379\) −5.16755 −0.265439 −0.132720 0.991154i \(-0.542371\pi\)
−0.132720 + 0.991154i \(0.542371\pi\)
\(380\) 22.2323 25.9303i 1.14049 1.33019i
\(381\) −2.05674 12.2212i −0.105370 0.626109i
\(382\) −54.7973 −2.80367
\(383\) −9.00109 −0.459934 −0.229967 0.973198i \(-0.573862\pi\)
−0.229967 + 0.973198i \(0.573862\pi\)
\(384\) 5.38013 + 31.9687i 0.274554 + 1.63140i
\(385\) 3.64728 + 6.31728i 0.185883 + 0.321958i
\(386\) 5.82602 + 10.0910i 0.296537 + 0.513616i
\(387\) −5.06811 + 26.3331i −0.257626 + 1.33859i
\(388\) 9.77452 0.496226
\(389\) 20.7642 1.05279 0.526393 0.850241i \(-0.323544\pi\)
0.526393 + 0.850241i \(0.323544\pi\)
\(390\) −5.02775 1.87450i −0.254590 0.0949191i
\(391\) 3.72590 + 6.45344i 0.188427 + 0.326365i
\(392\) 16.9776 + 29.4060i 0.857498 + 1.48523i
\(393\) 11.0786 + 4.13045i 0.558842 + 0.208354i
\(394\) −10.1611 17.5996i −0.511909 0.886653i
\(395\) 4.08863 + 7.08171i 0.205721 + 0.356320i
\(396\) −13.6048 + 70.6884i −0.683666 + 3.55222i
\(397\) −2.69831 + 4.67361i −0.135424 + 0.234562i −0.925759 0.378113i \(-0.876573\pi\)
0.790335 + 0.612675i \(0.209906\pi\)
\(398\) −3.26366 + 5.65283i −0.163593 + 0.283351i
\(399\) 4.29059 2.37279i 0.214798 0.118788i
\(400\) 3.03447 + 5.25586i 0.151724 + 0.262793i
\(401\) 18.9266 0.945152 0.472576 0.881290i \(-0.343324\pi\)
0.472576 + 0.881290i \(0.343324\pi\)
\(402\) 3.05976 + 1.14077i 0.152607 + 0.0568966i
\(403\) 2.02570 0.100908
\(404\) 15.2285 26.3765i 0.757645 1.31228i
\(405\) 2.46208 + 17.0604i 0.122342 + 0.847738i
\(406\) −10.4766 −0.519944
\(407\) 6.54293 11.3327i 0.324321 0.561740i
\(408\) −26.7049 + 22.0553i −1.32209 + 1.09190i
\(409\) −14.3032 + 24.7740i −0.707250 + 1.22499i 0.258623 + 0.965978i \(0.416731\pi\)
−0.965873 + 0.259015i \(0.916602\pi\)
\(410\) 16.4689 + 28.5250i 0.813343 + 1.40875i
\(411\) 16.7103 + 6.23013i 0.824260 + 0.307310i
\(412\) 5.80748 0.286114
\(413\) 4.65457 8.06195i 0.229036 0.396702i
\(414\) −10.7661 9.32389i −0.529123 0.458244i
\(415\) −6.31968 + 10.9460i −0.310221 + 0.537318i
\(416\) 0.302433 + 0.523829i 0.0148280 + 0.0256828i
\(417\) −3.82864 + 3.16204i −0.187489 + 0.154846i
\(418\) 62.0154 + 11.6164i 3.03327 + 0.568178i
\(419\) −14.8913 25.7926i −0.727490 1.26005i −0.957941 0.286965i \(-0.907354\pi\)
0.230451 0.973084i \(-0.425980\pi\)
\(420\) −1.46279 8.69189i −0.0713767 0.424121i
\(421\) 0.316310 + 0.547865i 0.0154160 + 0.0267013i 0.873630 0.486590i \(-0.161759\pi\)
−0.858214 + 0.513291i \(0.828426\pi\)
\(422\) −20.4208 35.3699i −0.994071 1.72178i
\(423\) 26.1921 + 22.6835i 1.27350 + 1.10291i
\(424\) −32.7834 56.7824i −1.59210 2.75760i
\(425\) 2.57982 4.46838i 0.125140 0.216748i
\(426\) 2.40167 + 0.895417i 0.116361 + 0.0433831i
\(427\) 3.35849 5.81708i 0.162529 0.281508i
\(428\) −15.4826 + 26.8167i −0.748380 + 1.29623i
\(429\) −1.10487 6.56513i −0.0533435 0.316967i
\(430\) 21.1266 36.5924i 1.01882 1.76464i
\(431\) 11.9641 + 20.7224i 0.576289 + 0.998162i 0.995900 + 0.0904579i \(0.0288331\pi\)
−0.419611 + 0.907704i \(0.637834\pi\)
\(432\) 12.3154 20.2226i 0.592525 0.972962i
\(433\) −2.23079 3.86384i −0.107205 0.185684i 0.807432 0.589961i \(-0.200857\pi\)
−0.914637 + 0.404276i \(0.867523\pi\)
\(434\) 2.47704 + 4.29037i 0.118902 + 0.205944i
\(435\) −20.3170 7.57479i −0.974124 0.363184i
\(436\) 15.5314 + 26.9012i 0.743819 + 1.28833i
\(437\) −5.45746 + 6.36521i −0.261066 + 0.304489i
\(438\) −14.0626 5.24297i −0.671937 0.250519i
\(439\) −8.09331 14.0180i −0.386273 0.669044i 0.605672 0.795714i \(-0.292904\pi\)
−0.991945 + 0.126670i \(0.959571\pi\)
\(440\) 28.9895 50.2113i 1.38202 2.39373i
\(441\) −3.72973 + 19.3791i −0.177606 + 0.922815i
\(442\) 3.13316 5.42680i 0.149029 0.258127i
\(443\) −17.6492 −0.838540 −0.419270 0.907862i \(-0.637714\pi\)
−0.419270 + 0.907862i \(0.637714\pi\)
\(444\) −12.1915 + 10.0688i −0.578582 + 0.477845i
\(445\) 4.63339 + 8.02526i 0.219644 + 0.380434i
\(446\) −11.4071 + 19.7577i −0.540141 + 0.935552i
\(447\) −13.2528 4.94107i −0.626838 0.233705i
\(448\) 2.21959 3.84444i 0.104866 0.181633i
\(449\) −41.2241 −1.94548 −0.972742 0.231890i \(-0.925509\pi\)
−0.972742 + 0.231890i \(0.925509\pi\)
\(450\) −1.86374 + 9.68369i −0.0878574 + 0.456493i
\(451\) −20.4332 + 35.3914i −0.962164 + 1.66652i
\(452\) −20.0129 −0.941329
\(453\) 27.3997 22.6291i 1.28735 1.06321i
\(454\) −25.8720 −1.21423
\(455\) 0.407578 + 0.705946i 0.0191076 + 0.0330952i
\(456\) −33.3842 20.1040i −1.56336 0.941457i
\(457\) −2.05989 + 3.56784i −0.0963576 + 0.166896i −0.910174 0.414225i \(-0.864053\pi\)
0.813817 + 0.581122i \(0.197386\pi\)
\(458\) −21.7451 + 37.6637i −1.01608 + 1.75991i
\(459\) −20.1244 0.471106i −0.939328 0.0219893i
\(460\) 7.53641 + 13.0535i 0.351387 + 0.608620i
\(461\) 7.01095 + 12.1433i 0.326533 + 0.565571i 0.981821 0.189807i \(-0.0607864\pi\)
−0.655289 + 0.755378i \(0.727453\pi\)
\(462\) 12.5537 10.3680i 0.584049 0.482361i
\(463\) 12.4782 + 21.6129i 0.579912 + 1.00444i 0.995489 + 0.0948795i \(0.0302466\pi\)
−0.415576 + 0.909558i \(0.636420\pi\)
\(464\) 14.8923 + 25.7942i 0.691358 + 1.19747i
\(465\) 1.70164 + 10.1111i 0.0789117 + 0.468893i
\(466\) 16.8253 0.779418
\(467\) −23.0107 −1.06481 −0.532405 0.846490i \(-0.678712\pi\)
−0.532405 + 0.846490i \(0.678712\pi\)
\(468\) −1.52031 + 7.89931i −0.0702765 + 0.365146i
\(469\) −0.248042 0.429621i −0.0114535 0.0198380i
\(470\) −27.2976 47.2807i −1.25914 2.18090i
\(471\) −2.37055 0.883814i −0.109229 0.0407240i
\(472\) −73.9913 −3.40573
\(473\) 52.4242 2.41047
\(474\) 14.0727 11.6225i 0.646382 0.533841i
\(475\) 5.70621 + 1.06886i 0.261819 + 0.0490426i
\(476\) 10.2933 0.471794
\(477\) 7.20203 37.4207i 0.329758 1.71337i
\(478\) 16.7202 28.9602i 0.764763 1.32461i
\(479\) 3.83688 0.175311 0.0876557 0.996151i \(-0.472062\pi\)
0.0876557 + 0.996151i \(0.472062\pi\)
\(480\) −2.36060 + 1.94960i −0.107746 + 0.0889867i
\(481\) 0.731162 1.26641i 0.0333381 0.0577433i
\(482\) −9.24028 16.0046i −0.420883 0.728991i
\(483\) 0.359077 + 2.13363i 0.0163385 + 0.0970837i
\(484\) 95.7217 4.35099
\(485\) −2.28779 3.96257i −0.103883 0.179931i
\(486\) 36.6389 11.7388i 1.66198 0.532481i
\(487\) −30.9854 −1.40408 −0.702041 0.712136i \(-0.747728\pi\)
−0.702041 + 0.712136i \(0.747728\pi\)
\(488\) −53.3883 −2.41677
\(489\) 29.5168 + 11.0048i 1.33480 + 0.497653i
\(490\) 15.5476 26.9292i 0.702367 1.21654i
\(491\) −27.8047 −1.25481 −0.627405 0.778693i \(-0.715883\pi\)
−0.627405 + 0.778693i \(0.715883\pi\)
\(492\) 38.0734 31.4444i 1.71648 1.41763i
\(493\) 12.6610 21.9295i 0.570223 0.987655i
\(494\) 6.93013 + 1.29812i 0.311801 + 0.0584051i
\(495\) 31.8412 11.0297i 1.43116 0.495750i
\(496\) 7.04216 12.1974i 0.316202 0.547679i
\(497\) −0.194693 0.337218i −0.00873317 0.0151263i
\(498\) 26.4338 + 9.85532i 1.18452 + 0.441627i
\(499\) −21.6588 −0.969583 −0.484791 0.874630i \(-0.661104\pi\)
−0.484791 + 0.874630i \(0.661104\pi\)
\(500\) 24.8082 42.9691i 1.10946 1.92164i
\(501\) 11.8786 9.81042i 0.530696 0.438297i
\(502\) −37.2618 + 64.5393i −1.66307 + 2.88053i
\(503\) −15.3608 26.6057i −0.684903 1.18629i −0.973467 0.228827i \(-0.926511\pi\)
0.288564 0.957461i \(-0.406822\pi\)
\(504\) −9.50238 + 3.29161i −0.423270 + 0.146620i
\(505\) −14.2573 −0.634442
\(506\) −13.9214 + 24.1125i −0.618880 + 1.07193i
\(507\) 3.61339 + 21.4708i 0.160476 + 0.953550i
\(508\) 29.2744 1.29884
\(509\) 14.0153 24.2753i 0.621218 1.07598i −0.368041 0.929810i \(-0.619971\pi\)
0.989259 0.146172i \(-0.0466953\pi\)
\(510\) 29.7194 + 11.0803i 1.31600 + 0.490644i
\(511\) 1.13999 + 1.97453i 0.0504303 + 0.0873479i
\(512\) −42.8358 −1.89309
\(513\) −7.01771 21.5349i −0.309839 0.950789i
\(514\) 57.5030 2.53635
\(515\) −1.35928 2.35434i −0.0598970 0.103745i
\(516\) −59.3538 22.1289i −2.61291 0.974172i
\(517\) 33.8685 58.6619i 1.48953 2.57995i
\(518\) 3.57628 0.157133
\(519\) −2.74966 16.3385i −0.120697 0.717181i
\(520\) 3.23953 5.61103i 0.142063 0.246060i
\(521\) −11.7617 −0.515287 −0.257644 0.966240i \(-0.582946\pi\)
−0.257644 + 0.966240i \(0.582946\pi\)
\(522\) −9.14667 + 47.5247i −0.400339 + 2.08010i
\(523\) 12.3785 + 21.4402i 0.541275 + 0.937516i 0.998831 + 0.0483349i \(0.0153915\pi\)
−0.457556 + 0.889181i \(0.651275\pi\)
\(524\) −13.9646 + 24.1874i −0.610047 + 1.05663i
\(525\) 1.15510 0.953983i 0.0504125 0.0416352i
\(526\) 18.8881 32.7152i 0.823562 1.42645i
\(527\) −11.9741 −0.521599
\(528\) −43.3716 16.1703i −1.88751 0.703721i
\(529\) 9.65001 + 16.7143i 0.419565 + 0.726709i
\(530\) −30.0220 + 51.9996i −1.30407 + 2.25872i
\(531\) −32.5075 28.1530i −1.41071 1.22173i
\(532\) 3.84519 + 10.9247i 0.166710 + 0.473648i
\(533\) −2.28338 + 3.95493i −0.0989043 + 0.171307i
\(534\) 15.9478 13.1711i 0.690127 0.569969i
\(535\) 14.4952 0.626684
\(536\) −1.97150 + 3.41473i −0.0851557 + 0.147494i
\(537\) 0.753618 + 0.280972i 0.0325210 + 0.0121248i
\(538\) −11.3630 −0.489896
\(539\) 38.5801 1.66176
\(540\) −40.7059 0.952912i −1.75170 0.0410068i
\(541\) −18.6115 32.2361i −0.800171 1.38594i −0.919503 0.393083i \(-0.871409\pi\)
0.119332 0.992854i \(-0.461925\pi\)
\(542\) 18.1335 0.778899
\(543\) 2.48405 + 14.7602i 0.106601 + 0.633421i
\(544\) −1.78770 3.09639i −0.0766471 0.132757i
\(545\) 7.27046 12.5928i 0.311432 0.539417i
\(546\) 1.40285 1.15860i 0.0600365 0.0495836i
\(547\) −3.93869 −0.168406 −0.0842030 0.996449i \(-0.526834\pi\)
−0.0842030 + 0.996449i \(0.526834\pi\)
\(548\) −21.0634 + 36.4829i −0.899785 + 1.55847i
\(549\) −23.4557 20.3137i −1.00107 0.866968i
\(550\) 19.2784 0.822033
\(551\) 28.0044 + 5.24565i 1.19303 + 0.223472i
\(552\) 13.2596 10.9510i 0.564366 0.466105i
\(553\) −2.77274 −0.117909
\(554\) −58.6584 −2.49216
\(555\) 6.93538 + 2.58572i 0.294390 + 0.109758i
\(556\) −5.86477 10.1581i −0.248722 0.430798i
\(557\) 10.2612 + 17.7730i 0.434783 + 0.753066i 0.997278 0.0737345i \(-0.0234917\pi\)
−0.562495 + 0.826801i \(0.690158\pi\)
\(558\) 21.6249 7.49082i 0.915455 0.317112i
\(559\) 5.85832 0.247780
\(560\) 5.66762 0.239501
\(561\) 6.53096 + 38.8069i 0.275737 + 1.63843i
\(562\) −15.8462 27.4464i −0.668431 1.15776i
\(563\) −6.27581 10.8700i −0.264494 0.458117i 0.702937 0.711252i \(-0.251872\pi\)
−0.967431 + 0.253135i \(0.918538\pi\)
\(564\) −63.1073 + 52.1197i −2.65729 + 2.19464i
\(565\) 4.68416 + 8.11321i 0.197064 + 0.341325i
\(566\) −1.86010 3.22179i −0.0781860 0.135422i
\(567\) −5.42722 2.16942i −0.227922 0.0911071i
\(568\) −1.54747 + 2.68029i −0.0649303 + 0.112463i
\(569\) 3.79925 6.58050i 0.159273 0.275869i −0.775334 0.631552i \(-0.782418\pi\)
0.934607 + 0.355683i \(0.115752\pi\)
\(570\) −0.657981 + 35.6816i −0.0275598 + 1.49454i
\(571\) −0.502011 0.869508i −0.0210085 0.0363878i 0.855330 0.518084i \(-0.173354\pi\)
−0.876339 + 0.481696i \(0.840021\pi\)
\(572\) 15.7260 0.657538
\(573\) 29.6508 24.4883i 1.23868 1.02301i
\(574\) −11.1685 −0.466166
\(575\) −1.28094 + 2.21866i −0.0534190 + 0.0925243i
\(576\) −15.5016 13.4251i −0.645901 0.559379i
\(577\) −6.38475 −0.265801 −0.132900 0.991129i \(-0.542429\pi\)
−0.132900 + 0.991129i \(0.542429\pi\)
\(578\) 2.45828 4.25787i 0.102251 0.177104i
\(579\) −7.66199 2.85663i −0.318421 0.118717i
\(580\) 25.6096 44.3571i 1.06338 1.84183i
\(581\) −2.14287 3.71156i −0.0889012 0.153981i
\(582\) −7.87440 + 6.50340i −0.326404 + 0.269574i
\(583\) −74.4974 −3.08537
\(584\) 9.06095 15.6940i 0.374945 0.649424i
\(585\) 3.55821 1.23255i 0.147114 0.0509599i
\(586\) 31.3153 54.2397i 1.29362 2.24062i
\(587\) 11.8750 + 20.5681i 0.490133 + 0.848935i 0.999936 0.0113561i \(-0.00361482\pi\)
−0.509802 + 0.860292i \(0.670281\pi\)
\(588\) −43.6798 16.2852i −1.80133 0.671590i
\(589\) −4.47306 12.7086i −0.184309 0.523649i
\(590\) 33.8795 + 58.6810i 1.39480 + 2.41586i
\(591\) 13.3632 + 4.98222i 0.549689 + 0.204941i
\(592\) −5.08362 8.80509i −0.208936 0.361887i
\(593\) 4.39025 + 7.60414i 0.180286 + 0.312264i 0.941978 0.335675i \(-0.108964\pi\)
−0.761692 + 0.647939i \(0.775631\pi\)
\(594\) −36.0718 65.9987i −1.48005 2.70796i
\(595\) −2.40922 4.17290i −0.0987685 0.171072i
\(596\) 16.7052 28.9343i 0.684273 1.18520i
\(597\) −0.760221 4.51723i −0.0311138 0.184878i
\(598\) −1.55569 + 2.69453i −0.0636169 + 0.110188i
\(599\) 8.44874 14.6336i 0.345206 0.597915i −0.640185 0.768221i \(-0.721142\pi\)
0.985391 + 0.170306i \(0.0544757\pi\)
\(600\) −11.1571 4.15972i −0.455488 0.169820i
\(601\) −15.1537 + 26.2469i −0.618131 + 1.07063i 0.371696 + 0.928355i \(0.378776\pi\)
−0.989827 + 0.142279i \(0.954557\pi\)
\(602\) 7.16359 + 12.4077i 0.291966 + 0.505700i
\(603\) −2.16543 + 0.750102i −0.0881833 + 0.0305465i
\(604\) 41.9713 + 72.6963i 1.70779 + 2.95797i
\(605\) −22.4043 38.8054i −0.910865 1.57766i
\(606\) 5.28124 + 31.3812i 0.214536 + 1.27477i
\(607\) 23.8244 + 41.2651i 0.967003 + 1.67490i 0.704133 + 0.710068i \(0.251336\pi\)
0.262870 + 0.964831i \(0.415331\pi\)
\(608\) 2.61852 3.05406i 0.106195 0.123858i
\(609\) 5.66887 4.68187i 0.229714 0.189719i
\(610\) 24.4457 + 42.3412i 0.989777 + 1.71434i
\(611\) 3.78474 6.55537i 0.153114 0.265202i
\(612\) 8.98668 46.6934i 0.363265 1.88747i
\(613\) 10.7830 18.6767i 0.435521 0.754345i −0.561817 0.827262i \(-0.689897\pi\)
0.997338 + 0.0729168i \(0.0232308\pi\)
\(614\) −20.6545 −0.833546
\(615\) −21.6589 8.07509i −0.873369 0.325619i
\(616\) 9.82973 + 17.0256i 0.396051 + 0.685981i
\(617\) −1.42352 + 2.46561i −0.0573088 + 0.0992618i −0.893257 0.449547i \(-0.851585\pi\)
0.835948 + 0.548809i \(0.184919\pi\)
\(618\) −4.67853 + 3.86396i −0.188198 + 0.155431i
\(619\) −6.25245 + 10.8296i −0.251307 + 0.435277i −0.963886 0.266315i \(-0.914194\pi\)
0.712579 + 0.701592i \(0.247527\pi\)
\(620\) −24.2201 −0.972703
\(621\) 9.99225 + 0.233915i 0.400975 + 0.00938669i
\(622\) 8.96391 15.5259i 0.359420 0.622534i
\(623\) −3.14217 −0.125888
\(624\) −4.84671 1.80700i −0.194023 0.0723380i
\(625\) −16.5668 −0.662673
\(626\) −18.1707 31.4726i −0.726247 1.25790i
\(627\) −38.7478 + 21.4284i −1.54744 + 0.855767i
\(628\) 2.98808 5.17551i 0.119237 0.206525i
\(629\) −4.32195 + 7.48583i −0.172327 + 0.298480i
\(630\) 6.96150 + 6.02897i 0.277353 + 0.240200i
\(631\) 0.917741 + 1.58957i 0.0365347 + 0.0632799i 0.883715 0.468026i \(-0.155035\pi\)
−0.847180 + 0.531306i \(0.821701\pi\)
\(632\) 11.0192 + 19.0858i 0.438320 + 0.759193i
\(633\) 26.8561 + 10.0128i 1.06744 + 0.397973i
\(634\) 20.1585 + 34.9156i 0.800597 + 1.38667i
\(635\) −6.85188 11.8678i −0.271909 0.470959i
\(636\) 84.3448 + 31.4463i 3.34449 + 1.24693i
\(637\) 4.31127 0.170819
\(638\) 94.6127 3.74575
\(639\) −1.69969 + 0.588770i −0.0672388 + 0.0232914i
\(640\) 17.9235 + 31.0444i 0.708488 + 1.22714i
\(641\) −1.91192 3.31154i −0.0755163 0.130798i 0.825794 0.563971i \(-0.190727\pi\)
−0.901311 + 0.433173i \(0.857394\pi\)
\(642\) −5.36938 31.9049i −0.211913 1.25918i
\(643\) 40.1005 1.58141 0.790705 0.612198i \(-0.209714\pi\)
0.790705 + 0.612198i \(0.209714\pi\)
\(644\) −5.11088 −0.201397
\(645\) 4.92113 + 29.2414i 0.193769 + 1.15138i
\(646\) −40.9645 7.67326i −1.61173 0.301901i
\(647\) 5.93898 0.233486 0.116743 0.993162i \(-0.462755\pi\)
0.116743 + 0.993162i \(0.462755\pi\)
\(648\) 6.63550 + 45.9792i 0.260667 + 1.80623i
\(649\) −42.0348 + 72.8064i −1.65001 + 2.85790i
\(650\) 2.15433 0.0844997
\(651\) −3.25764 1.21455i −0.127677 0.0476020i
\(652\) −37.2060 + 64.4427i −1.45710 + 2.52377i
\(653\) −20.0130 34.6636i −0.783170 1.35649i −0.930086 0.367342i \(-0.880268\pi\)
0.146916 0.989149i \(-0.453065\pi\)
\(654\) −30.4107 11.3380i −1.18915 0.443352i
\(655\) 13.0740 0.510845
\(656\) 15.8759 + 27.4979i 0.619850 + 1.07361i
\(657\) 9.95228 3.44745i 0.388276 0.134498i
\(658\) 18.5120 0.721675
\(659\) 11.5467 0.449794 0.224897 0.974383i \(-0.427795\pi\)
0.224897 + 0.974383i \(0.427795\pi\)
\(660\) 13.2102 + 78.4953i 0.514208 + 3.05542i
\(661\) −10.4830 + 18.1571i −0.407741 + 0.706228i −0.994636 0.103435i \(-0.967017\pi\)
0.586895 + 0.809663i \(0.300350\pi\)
\(662\) 66.8328 2.59753
\(663\) 0.729824 + 4.33661i 0.0283440 + 0.168420i
\(664\) −17.0321 + 29.5004i −0.660972 + 1.14484i
\(665\) 3.52888 4.11585i 0.136844 0.159606i
\(666\) 3.12230 16.2230i 0.120987 0.628628i
\(667\) −6.28649 + 10.8885i −0.243414 + 0.421605i
\(668\) 18.1958 + 31.5161i 0.704017 + 1.21939i
\(669\) −2.65711 15.7885i −0.102730 0.610420i
\(670\) 3.61087 0.139500
\(671\) −30.3301 + 52.5333i −1.17088 + 2.02803i
\(672\) −0.172287 1.02373i −0.00664610 0.0394911i
\(673\) 16.9832 29.4157i 0.654654 1.13389i −0.327327 0.944911i \(-0.606148\pi\)
0.981981 0.188982i \(-0.0605188\pi\)
\(674\) −21.3934 37.0545i −0.824044 1.42729i
\(675\) −3.31907 6.07272i −0.127751 0.233739i
\(676\) −51.4308 −1.97811
\(677\) 1.77679 3.07750i 0.0682878 0.118278i −0.829860 0.557972i \(-0.811580\pi\)
0.898148 + 0.439694i \(0.144913\pi\)
\(678\) 16.1225 13.3154i 0.619181 0.511376i
\(679\) 1.55148 0.0595405
\(680\) −19.1491 + 33.1672i −0.734335 + 1.27190i
\(681\) 13.9993 11.5619i 0.536454 0.443052i
\(682\) −22.3699 38.7457i −0.856586 1.48365i
\(683\) −27.1146 −1.03751 −0.518757 0.854922i \(-0.673605\pi\)
−0.518757 + 0.854922i \(0.673605\pi\)
\(684\) 52.9148 7.90492i 2.02325 0.302252i
\(685\) 19.7201 0.753468
\(686\) 10.8817 + 18.8476i 0.415465 + 0.719606i
\(687\) −5.06521 30.0975i −0.193250 1.14829i
\(688\) 20.3659 35.2747i 0.776441 1.34484i
\(689\) −8.32497 −0.317156
\(690\) −14.7564 5.50163i −0.561766 0.209444i
\(691\) 20.9193 36.2333i 0.795807 1.37838i −0.126518 0.991964i \(-0.540380\pi\)
0.922325 0.386415i \(-0.126287\pi\)
\(692\) 39.1371 1.48777
\(693\) −2.15945 + 11.2202i −0.0820308 + 0.426219i
\(694\) −1.87504 3.24766i −0.0711755 0.123280i
\(695\) −2.74538 + 4.75513i −0.104138 + 0.180373i
\(696\) −54.7559 20.4147i −2.07552 0.773817i
\(697\) 13.4972 23.3779i 0.511244 0.885501i
\(698\) 21.4930 0.813523
\(699\) −9.10417 + 7.51905i −0.344351 + 0.284397i
\(700\) 1.76939 + 3.06468i 0.0668768 + 0.115834i
\(701\) −8.86597 + 15.3563i −0.334863 + 0.580000i −0.983459 0.181133i \(-0.942023\pi\)
0.648595 + 0.761133i \(0.275357\pi\)
\(702\) −4.03097 7.37525i −0.152139 0.278361i
\(703\) −9.55955 1.79065i −0.360545 0.0675356i
\(704\) −20.0448 + 34.7186i −0.755467 + 1.30851i
\(705\) 35.8999 + 13.3846i 1.35207 + 0.504093i
\(706\) 20.5305 0.772674
\(707\) 2.41718 4.18667i 0.0909072 0.157456i
\(708\) 78.3236 64.6867i 2.94358 2.43108i
\(709\) −7.38598 −0.277386 −0.138693 0.990335i \(-0.544290\pi\)
−0.138693 + 0.990335i \(0.544290\pi\)
\(710\) 2.83425 0.106367
\(711\) −2.42076 + 12.5779i −0.0907856 + 0.471708i
\(712\) 12.4874 + 21.6287i 0.467984 + 0.810572i
\(713\) 5.94541 0.222657
\(714\) −8.29235 + 6.84858i −0.310334 + 0.256302i
\(715\) −3.68078 6.37530i −0.137653 0.238423i
\(716\) −0.949937 + 1.64534i −0.0355008 + 0.0614892i
\(717\) 3.89472 + 23.1424i 0.145451 + 0.864269i
\(718\) −67.7144 −2.52708
\(719\) −4.79763 + 8.30974i −0.178921 + 0.309901i −0.941511 0.336981i \(-0.890594\pi\)
0.762590 + 0.646882i \(0.223927\pi\)
\(720\) 4.94816 25.7099i 0.184407 0.958151i
\(721\) 0.921806 0.0343299
\(722\) −7.15879 46.3438i −0.266423 1.72474i
\(723\) 12.1522 + 4.53072i 0.451945 + 0.168499i
\(724\) −35.3564 −1.31401
\(725\) 8.70556 0.323317
\(726\) −77.1139 + 63.6876i −2.86196 + 2.36367i
\(727\) −16.4424 28.4791i −0.609815 1.05623i −0.991271 0.131844i \(-0.957910\pi\)
0.381455 0.924387i \(-0.375423\pi\)
\(728\) 1.09846 + 1.90258i 0.0407115 + 0.0705144i
\(729\) −14.5794 + 22.7254i −0.539977 + 0.841680i
\(730\) −16.5955 −0.614227
\(731\) −34.6289 −1.28080
\(732\) 56.5143 46.6746i 2.08883 1.72514i
\(733\) −18.1159 31.3777i −0.669126 1.15896i −0.978149 0.207906i \(-0.933335\pi\)
0.309022 0.951055i \(-0.399998\pi\)
\(734\) −28.8679 50.0006i −1.06553 1.84556i
\(735\) 3.62157 + 21.5194i 0.133584 + 0.793754i
\(736\) 0.887636 + 1.53743i 0.0327187 + 0.0566705i
\(737\) 2.24003 + 3.87985i 0.0825126 + 0.142916i
\(738\) −9.75079 + 50.6636i −0.358931 + 1.86495i
\(739\) 12.0565 20.8825i 0.443507 0.768177i −0.554440 0.832224i \(-0.687067\pi\)
0.997947 + 0.0640471i \(0.0204008\pi\)
\(740\) −8.74206 + 15.1417i −0.321364 + 0.556620i
\(741\) −4.33000 + 2.39459i −0.159066 + 0.0879673i
\(742\) −10.1798 17.6320i −0.373713 0.647290i
\(743\) −24.3039 −0.891623 −0.445811 0.895127i \(-0.647085\pi\)
−0.445811 + 0.895127i \(0.647085\pi\)
\(744\) 4.58606 + 27.2504i 0.168133 + 0.999048i
\(745\) −15.6399 −0.573001
\(746\) 4.67129 8.09092i 0.171028 0.296230i
\(747\) −18.7075 + 6.48024i −0.684472 + 0.237100i
\(748\) −92.9577 −3.39887
\(749\) −2.45751 + 4.25654i −0.0897956 + 0.155531i
\(750\) 8.60352 + 51.1221i 0.314156 + 1.86672i
\(751\) 10.9678 18.9968i 0.400221 0.693204i −0.593531 0.804811i \(-0.702267\pi\)
0.993752 + 0.111607i \(0.0355999\pi\)
\(752\) −26.3146 45.5782i −0.959594 1.66207i
\(753\) −8.67957 51.5740i −0.316301 1.87946i
\(754\) 10.5728 0.385039
\(755\) 19.6473 34.0301i 0.715039 1.23848i
\(756\) 7.18108 11.7918i 0.261173 0.428863i
\(757\) −20.3751 + 35.2907i −0.740545 + 1.28266i 0.211702 + 0.977334i \(0.432099\pi\)
−0.952247 + 0.305328i \(0.901234\pi\)
\(758\) 6.37695 + 11.0452i 0.231621 + 0.401180i
\(759\) −3.24277 19.2686i −0.117705 0.699404i
\(760\) −42.3552 7.93376i −1.53638 0.287788i
\(761\) −6.54874 11.3427i −0.237391 0.411174i 0.722574 0.691294i \(-0.242959\pi\)
−0.959965 + 0.280120i \(0.909626\pi\)
\(762\) −23.5836 + 19.4775i −0.854345 + 0.705595i
\(763\) 2.46526 + 4.26995i 0.0892484 + 0.154583i
\(764\) 45.4195 + 78.6689i 1.64322 + 2.84614i
\(765\) −21.0328 + 7.28572i −0.760443 + 0.263416i
\(766\) 11.1077 + 19.2391i 0.401337 + 0.695136i
\(767\) −4.69732 + 8.13599i −0.169610 + 0.293774i
\(768\) 43.4336 35.8714i 1.56727 1.29440i
\(769\) −20.4459 + 35.4133i −0.737297 + 1.27704i 0.216411 + 0.976302i \(0.430565\pi\)
−0.953708 + 0.300734i \(0.902768\pi\)
\(770\) 9.00177 15.5915i 0.324401 0.561880i
\(771\) −31.1148 + 25.6975i −1.12057 + 0.925471i
\(772\) 9.65795 16.7281i 0.347597 0.602056i
\(773\) −9.81097 16.9931i −0.352876 0.611199i 0.633876 0.773435i \(-0.281463\pi\)
−0.986752 + 0.162235i \(0.948130\pi\)
\(774\) 62.5390 21.6634i 2.24792 0.778674i
\(775\) −2.05831 3.56510i −0.0739367 0.128062i
\(776\) −6.16579 10.6795i −0.221339 0.383370i
\(777\) −1.93512 + 1.59820i −0.0694221 + 0.0573350i
\(778\) −25.6238 44.3817i −0.918657 1.59116i
\(779\) 29.8540 + 5.59211i 1.06963 + 0.200358i
\(780\) 1.47622 + 8.77172i 0.0528573 + 0.314078i
\(781\) 1.75825 + 3.04537i 0.0629150 + 0.108972i
\(782\) 9.19579 15.9276i 0.328841 0.569569i
\(783\) −16.2890 29.8031i −0.582122 1.06508i
\(784\) 14.9877 25.9595i 0.535275 0.927124i
\(785\) −2.79752 −0.0998478
\(786\) −4.84294 28.7767i −0.172742 1.02643i
\(787\) −3.19894 5.54073i −0.114030 0.197506i 0.803362 0.595492i \(-0.203043\pi\)
−0.917392 + 0.397986i \(0.869709\pi\)
\(788\) −16.8443 + 29.1753i −0.600055 + 1.03933i
\(789\) 4.39971 + 26.1431i 0.156634 + 0.930718i
\(790\) 10.0910 17.4782i 0.359023 0.621847i
\(791\) −3.17660 −0.112947
\(792\) 85.8148 29.7261i 3.04929 1.05627i
\(793\) −3.38934 + 5.87051i −0.120359 + 0.208468i
\(794\) 13.3193 0.472683
\(795\) −6.99317 41.5534i −0.248022 1.47375i
\(796\) 10.8205 0.383523
\(797\) 23.8040 + 41.2297i 0.843179 + 1.46043i 0.887193 + 0.461399i \(0.152652\pi\)
−0.0440136 + 0.999031i \(0.514014\pi\)
\(798\) −10.3664 6.24266i −0.366966 0.220988i
\(799\) −22.3719 + 38.7493i −0.791461 + 1.37085i
\(800\) 0.614602 1.06452i 0.0217295 0.0376365i
\(801\) −2.74330 + 14.2537i −0.0969296 + 0.503631i
\(802\) −23.3562 40.4541i −0.824736 1.42848i
\(803\) −10.2951 17.8317i −0.363307 0.629267i
\(804\) −0.898392 5.33825i −0.0316839 0.188265i
\(805\) 1.19624 + 2.07194i 0.0421618 + 0.0730263i
\(806\) −2.49980 4.32977i −0.0880515 0.152510i
\(807\) 6.14854 5.07802i 0.216439 0.178755i
\(808\) −38.4246 −1.35177
\(809\) 4.09101 0.143832 0.0719160 0.997411i \(-0.477089\pi\)
0.0719160 + 0.997411i \(0.477089\pi\)
\(810\) 33.4269 26.3157i 1.17450 0.924638i
\(811\) 11.1310 + 19.2794i 0.390862 + 0.676993i 0.992563 0.121728i \(-0.0388437\pi\)
−0.601702 + 0.798721i \(0.705510\pi\)
\(812\) 8.68367 + 15.0405i 0.304737 + 0.527820i
\(813\) −9.81200 + 8.10364i −0.344122 + 0.284207i
\(814\) −32.2969 −1.13201
\(815\) 34.8332 1.22016
\(816\) 28.6492 + 10.6813i 1.00292 + 0.373921i
\(817\) −12.9360 36.7532i −0.452575 1.28583i
\(818\) 70.6030 2.46858
\(819\) −0.241315 + 1.25384i −0.00843224 + 0.0438126i
\(820\) 27.3010 47.2868i 0.953393 1.65133i
\(821\) 11.6491 0.406556 0.203278 0.979121i \(-0.434840\pi\)
0.203278 + 0.979121i \(0.434840\pi\)
\(822\) −7.30481 43.4052i −0.254784 1.51393i
\(823\) 6.75493 11.6999i 0.235462 0.407832i −0.723945 0.689858i \(-0.757673\pi\)
0.959407 + 0.282026i \(0.0910063\pi\)
\(824\) −3.66337 6.34515i −0.127620 0.221044i
\(825\) −10.4315 + 8.61529i −0.363179 + 0.299946i
\(826\) −22.9756 −0.799425
\(827\) −5.09722 8.82865i −0.177248 0.307002i 0.763689 0.645584i \(-0.223386\pi\)
−0.940937 + 0.338582i \(0.890053\pi\)
\(828\) −4.46209 + 23.1844i −0.155069 + 0.805712i
\(829\) 6.76339 0.234902 0.117451 0.993079i \(-0.462528\pi\)
0.117451 + 0.993079i \(0.462528\pi\)
\(830\) 31.1949 1.08279
\(831\) 31.7400 26.2138i 1.10105 0.909346i
\(832\) −2.23998 + 3.87975i −0.0776572 + 0.134506i
\(833\) −25.4842 −0.882976
\(834\) 11.4833 + 4.28132i 0.397633 + 0.148250i
\(835\) 8.51771 14.7531i 0.294767 0.510552i
\(836\) −34.7254 98.6599i −1.20100 3.41223i
\(837\) −8.35365 + 13.7172i −0.288744 + 0.474136i
\(838\) −36.7530 + 63.6580i −1.26961 + 2.19903i
\(839\) −1.11605 1.93306i −0.0385305 0.0667367i 0.846117 0.532997i \(-0.178934\pi\)
−0.884648 + 0.466260i \(0.845601\pi\)
\(840\) −8.57387 + 7.08108i −0.295827 + 0.244320i
\(841\) 13.7244 0.473254
\(842\) 0.780677 1.35217i 0.0269039 0.0465990i
\(843\) 20.8398 + 7.76973i 0.717762 + 0.267604i
\(844\) −33.8522 + 58.6337i −1.16524 + 2.01826i
\(845\) 12.0377 + 20.8500i 0.414110 + 0.717260i
\(846\) 16.1621 83.9758i 0.555664 2.88715i
\(847\) 15.1937 0.522060
\(848\) −28.9409 + 50.1272i −0.993835 + 1.72137i
\(849\) 2.44628 + 0.912050i 0.0839562 + 0.0313015i
\(850\) −12.7344 −0.436786
\(851\) 2.14595 3.71689i 0.0735622 0.127413i
\(852\) −0.705166 4.19010i −0.0241586 0.143550i
\(853\) −15.9885 27.6930i −0.547437 0.948189i −0.998449 0.0556710i \(-0.982270\pi\)
0.451012 0.892518i \(-0.351063\pi\)
\(854\) −16.5780 −0.567289
\(855\) −15.5897 19.6014i −0.533156 0.670352i
\(856\) 39.0659 1.33524
\(857\) 15.8658 + 27.4804i 0.541966 + 0.938712i 0.998791 + 0.0491556i \(0.0156530\pi\)
−0.456826 + 0.889556i \(0.651014\pi\)
\(858\) −12.6690 + 10.4632i −0.432511 + 0.357207i
\(859\) −2.92572 + 5.06749i −0.0998242 + 0.172901i −0.911612 0.411052i \(-0.865161\pi\)
0.811788 + 0.583953i \(0.198495\pi\)
\(860\) −70.0444 −2.38849
\(861\) 6.04329 4.99110i 0.205955 0.170096i
\(862\) 29.5282 51.1444i 1.00574 1.74199i
\(863\) 29.7096 1.01133 0.505664 0.862731i \(-0.331248\pi\)
0.505664 + 0.862731i \(0.331248\pi\)
\(864\) −4.79433 0.112234i −0.163106 0.00381827i
\(865\) −9.16029 15.8661i −0.311459 0.539463i
\(866\) −5.50575 + 9.53624i −0.187093 + 0.324055i
\(867\) 0.572620 + 3.40251i 0.0194472 + 0.115555i
\(868\) 4.10627 7.11226i 0.139376 0.241406i
\(869\) 25.0402 0.849431
\(870\) 8.88142 + 52.7734i 0.301108 + 1.78919i
\(871\) 0.250320 + 0.433567i 0.00848177 + 0.0146908i
\(872\) 19.5945 33.9387i 0.663553 1.14931i
\(873\) 1.35454 7.03796i 0.0458441 0.238199i
\(874\) 20.3398 + 3.80996i 0.688005 + 0.128874i
\(875\) 3.93775 6.82038i 0.133120 0.230571i
\(876\) 4.12899 + 24.5345i 0.139506 + 0.828942i
\(877\) 39.7375 1.34184 0.670920 0.741530i \(-0.265899\pi\)
0.670920 + 0.741530i \(0.265899\pi\)
\(878\) −19.9749 + 34.5975i −0.674120 + 1.16761i
\(879\) 7.29444 + 43.3435i 0.246035 + 1.46194i
\(880\) −51.1835 −1.72540
\(881\) −22.1976 −0.747855 −0.373927 0.927458i \(-0.621989\pi\)
−0.373927 + 0.927458i \(0.621989\pi\)
\(882\) 46.0239 15.9426i 1.54970 0.536815i
\(883\) 0.944299 + 1.63557i 0.0317782 + 0.0550414i 0.881477 0.472227i \(-0.156550\pi\)
−0.849699 + 0.527268i \(0.823216\pi\)
\(884\) −10.3879 −0.349382
\(885\) −44.5561 16.6119i −1.49774 0.558402i
\(886\) 21.7798 + 37.7237i 0.731707 + 1.26735i
\(887\) −15.6748 + 27.1496i −0.526309 + 0.911595i 0.473221 + 0.880944i \(0.343091\pi\)
−0.999530 + 0.0306507i \(0.990242\pi\)
\(888\) 18.6914 + 6.96874i 0.627243 + 0.233856i
\(889\) 4.64665 0.155844
\(890\) 11.4355 19.8070i 0.383320 0.663931i
\(891\) 49.0125 + 19.5917i 1.64198 + 0.656348i
\(892\) 37.8197 1.26630
\(893\) −49.4835 9.26901i −1.65590 0.310176i
\(894\) 5.79339 + 34.4243i 0.193760 + 1.15132i
\(895\) 0.889357 0.0297279
\(896\) −12.1550 −0.406068
\(897\) −0.362375 2.15323i −0.0120993 0.0718942i
\(898\) 50.8721 + 88.1130i 1.69762 + 2.94037i
\(899\) −10.1016 17.4965i −0.336907 0.583540i
\(900\) 15.4470 5.35082i 0.514901 0.178361i
\(901\) 49.2095 1.63941
\(902\) 100.862 3.35832
\(903\) −9.42108 3.51247i −0.313514 0.116888i
\(904\) 12.6242 + 21.8658i 0.419875 + 0.727245i
\(905\) 8.27540 + 14.3334i 0.275084 + 0.476459i
\(906\) −82.1802 30.6393i −2.73025 1.01792i
\(907\) −15.4376 26.7387i −0.512596 0.887843i −0.999893 0.0146063i \(-0.995350\pi\)
0.487297 0.873236i \(-0.337983\pi\)
\(908\) 21.4443 + 37.1427i 0.711655 + 1.23262i
\(909\) −16.8816 14.6202i −0.559926 0.484921i
\(910\) 1.00593 1.74233i 0.0333464 0.0577576i
\(911\) −18.4983 + 32.0401i −0.612877 + 1.06153i 0.377875 + 0.925856i \(0.376655\pi\)
−0.990753 + 0.135678i \(0.956679\pi\)
\(912\) −0.634287 + 34.3968i −0.0210033 + 1.13899i
\(913\) 19.3520 + 33.5186i 0.640457 + 1.10930i
\(914\) 10.1679 0.336325
\(915\) −32.1493 11.9863i −1.06282 0.396254i
\(916\) 72.0951 2.38209
\(917\) −2.21657 + 3.83920i −0.0731974 + 0.126782i
\(918\) 23.8273 + 43.5956i 0.786420 + 1.43887i
\(919\) 43.0561 1.42029 0.710146 0.704055i \(-0.248629\pi\)
0.710146 + 0.704055i \(0.248629\pi\)
\(920\) 9.50798 16.4683i 0.313469 0.542944i
\(921\) 11.1761 9.23025i 0.368265 0.304147i
\(922\) 17.3036 29.9706i 0.569862 0.987031i
\(923\) 0.196481 + 0.340315i 0.00646725 + 0.0112016i
\(924\) −25.2899 9.42884i −0.831975 0.310186i
\(925\) −2.97172 −0.0977096
\(926\) 30.7972 53.3423i 1.01206 1.75294i
\(927\) 0.804791 4.18157i 0.0264328 0.137341i
\(928\) 3.01629 5.22436i 0.0990145 0.171498i
\(929\) −22.1233 38.3187i −0.725841 1.25719i −0.958627 0.284666i \(-0.908117\pi\)
0.232785 0.972528i \(-0.425216\pi\)
\(930\) 19.5118 16.1147i 0.639819 0.528420i
\(931\) −9.51993 27.0475i −0.312003 0.886446i
\(932\) −13.9459 24.1550i −0.456813 0.791224i
\(933\) 2.08801 + 12.4069i 0.0683583 + 0.406185i
\(934\) 28.3961 + 49.1835i 0.929149 + 1.60933i
\(935\) 21.7574 + 37.6849i 0.711542 + 1.23243i
\(936\) 9.58966 3.32184i 0.313448 0.108578i
\(937\) 1.92051 + 3.32642i 0.0627402 + 0.108669i 0.895689 0.444680i \(-0.146683\pi\)
−0.832949 + 0.553350i \(0.813349\pi\)
\(938\) −0.612186 + 1.06034i −0.0199886 + 0.0346212i
\(939\) 23.8969 + 8.90950i 0.779846 + 0.290751i
\(940\) −45.2519 + 78.3786i −1.47595 + 2.55643i
\(941\) 13.5614 23.4891i 0.442090 0.765722i −0.555755 0.831346i \(-0.687571\pi\)
0.997844 + 0.0656247i \(0.0209040\pi\)
\(942\) 1.03627 + 6.15751i 0.0337635 + 0.200622i
\(943\) −6.70169 + 11.6077i −0.218237 + 0.377998i
\(944\) 32.6595 + 56.5680i 1.06298 + 1.84113i
\(945\) −6.46114 0.151253i −0.210181 0.00492027i
\(946\) −64.6934 112.052i −2.10337 3.64314i
\(947\) 5.77749 + 10.0069i 0.187743 + 0.325181i 0.944497 0.328519i \(-0.106549\pi\)
−0.756754 + 0.653699i \(0.773216\pi\)
\(948\) −28.3501 10.5698i −0.920769 0.343291i
\(949\) −1.15046 1.99266i −0.0373456 0.0646846i
\(950\) −4.75708 13.5156i −0.154340 0.438502i
\(951\) −26.5111 9.88417i −0.859682 0.320516i
\(952\) −6.49306 11.2463i −0.210441 0.364495i
\(953\) −19.4213 + 33.6388i −0.629119 + 1.08967i 0.358610 + 0.933488i \(0.383251\pi\)
−0.987729 + 0.156178i \(0.950082\pi\)
\(954\) −88.8711 + 30.7848i −2.87731 + 0.996694i
\(955\) 21.2615 36.8260i 0.688005 1.19166i
\(956\) −55.4350 −1.79290
\(957\) −51.1948 + 42.2813i −1.65489 + 1.36676i
\(958\) −4.73485 8.20100i −0.152976 0.264962i
\(959\) −3.34334 + 5.79084i −0.107962 + 0.186996i
\(960\) −21.2471 7.92158i −0.685748 0.255668i
\(961\) 10.7232 18.5732i 0.345911 0.599135i
\(962\) −3.60912 −0.116363
\(963\) 17.1633 + 14.8642i 0.553079 + 0.478991i
\(964\) −15.3179 + 26.5313i −0.493356 + 0.854517i
\(965\) −9.04204 −0.291073
\(966\) 4.11735 3.40048i 0.132473 0.109409i
\(967\) −44.3816 −1.42722 −0.713608 0.700545i \(-0.752940\pi\)
−0.713608 + 0.700545i \(0.752940\pi\)
\(968\) −60.3815 104.584i −1.94073 3.36145i
\(969\) 25.5949 14.1546i 0.822228 0.454710i
\(970\) −5.64644 + 9.77993i −0.181296 + 0.314015i
\(971\) 4.70379 8.14720i 0.150952 0.261456i −0.780626 0.624999i \(-0.785100\pi\)
0.931578 + 0.363543i \(0.118433\pi\)
\(972\) −47.2212 42.8703i −1.51462 1.37506i
\(973\) −0.930900 1.61237i −0.0298433 0.0516901i
\(974\) 38.2372 + 66.2287i 1.22520 + 2.12210i
\(975\) −1.16570 + 0.962745i −0.0373324 + 0.0308325i
\(976\) 23.5654 + 40.8165i 0.754311 + 1.30650i
\(977\) −2.98306 5.16682i −0.0954367 0.165301i 0.814354 0.580368i \(-0.197091\pi\)
−0.909791 + 0.415067i \(0.863758\pi\)
\(978\) −12.9031 76.6700i −0.412594 2.45164i
\(979\) 28.3765 0.906917
\(980\) −51.5472 −1.64662
\(981\) 21.5220 7.45518i 0.687145 0.238026i
\(982\) 34.3121 + 59.4303i 1.09494 + 1.89650i
\(983\) 26.2848 + 45.5267i 0.838356 + 1.45208i 0.891268 + 0.453477i \(0.149817\pi\)
−0.0529116 + 0.998599i \(0.516850\pi\)
\(984\) −58.3724 21.7630i −1.86084 0.693780i
\(985\) 15.7701 0.502478
\(986\) −62.4967 −1.99030
\(987\) −10.0169 + 8.27283i −0.318840 + 0.263327i
\(988\) −3.88051 11.0251i −0.123455 0.350755i
\(989\) 17.1941 0.546740
\(990\) −62.8684 54.4468i −1.99809 1.73043i
\(991\) 19.1553 33.1780i 0.608489 1.05393i −0.383000 0.923748i \(-0.625109\pi\)
0.991490 0.130186i \(-0.0415576\pi\)
\(992\) −2.85264 −0.0905713
\(993\) −36.1632 + 29.8668i −1.14760 + 0.947795i
\(994\) −0.480517 + 0.832280i −0.0152411 + 0.0263983i
\(995\) −2.53262 4.38662i −0.0802893 0.139065i
\(996\) −7.76135 46.1179i −0.245928 1.46130i
\(997\) 15.3279 0.485441 0.242720 0.970096i \(-0.421960\pi\)
0.242720 + 0.970096i \(0.421960\pi\)
\(998\) 26.7278 + 46.2939i 0.846054 + 1.46541i
\(999\) 5.56040 + 10.1736i 0.175923 + 0.321877i
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 171.2.g.c.106.1 32
3.2 odd 2 513.2.g.c.505.16 32
9.4 even 3 171.2.h.c.49.16 yes 32
9.5 odd 6 513.2.h.c.334.1 32
19.7 even 3 171.2.h.c.7.16 yes 32
57.26 odd 6 513.2.h.c.235.1 32
171.121 even 3 inner 171.2.g.c.121.1 yes 32
171.140 odd 6 513.2.g.c.64.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.2.g.c.106.1 32 1.1 even 1 trivial
171.2.g.c.121.1 yes 32 171.121 even 3 inner
171.2.h.c.7.16 yes 32 19.7 even 3
171.2.h.c.49.16 yes 32 9.4 even 3
513.2.g.c.64.16 32 171.140 odd 6
513.2.g.c.505.16 32 3.2 odd 2
513.2.h.c.235.1 32 57.26 odd 6
513.2.h.c.334.1 32 9.5 odd 6