Properties

Label 287.3.p.a.146.14
Level $287$
Weight $3$
Character 287.146
Analytic conductor $7.820$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,3,Mod(146,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.146");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.p (of order \(10\), 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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(54\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 146.14
Character \(\chi\) \(=\) 287.146
Dual form 287.3.p.a.230.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707080 - 2.17617i) q^{2} +3.12138 q^{3} +(-0.999682 + 0.726311i) q^{4} +(-4.21845 - 5.80620i) q^{5} +(-2.20707 - 6.79266i) q^{6} +(2.87524 - 6.38224i) q^{7} +(-5.11721 - 3.71787i) q^{8} +0.743042 q^{9} +O(q^{10})\) \(q+(-0.707080 - 2.17617i) q^{2} +3.12138 q^{3} +(-0.999682 + 0.726311i) q^{4} +(-4.21845 - 5.80620i) q^{5} +(-2.20707 - 6.79266i) q^{6} +(2.87524 - 6.38224i) q^{7} +(-5.11721 - 3.71787i) q^{8} +0.743042 q^{9} +(-9.65249 + 13.2855i) q^{10} +(4.73855 - 6.52206i) q^{11} +(-3.12039 + 2.26710i) q^{12} +(5.27470 + 16.2338i) q^{13} +(-15.9219 - 1.74426i) q^{14} +(-13.1674 - 18.1234i) q^{15} +(-5.99981 + 18.4655i) q^{16} +(11.4999 + 8.35520i) q^{17} +(-0.525390 - 1.61699i) q^{18} +(-7.42948 + 22.8656i) q^{19} +(8.43422 + 2.74044i) q^{20} +(8.97474 - 19.9214i) q^{21} +(-17.5436 - 5.70027i) q^{22} +(-9.34359 - 28.7566i) q^{23} +(-15.9728 - 11.6049i) q^{24} +(-8.19120 + 25.2099i) q^{25} +(31.5980 - 22.9573i) q^{26} -25.7731 q^{27} +(1.76116 + 8.46853i) q^{28} +(-7.18636 - 9.89118i) q^{29} +(-30.1291 + 41.4692i) q^{30} +(20.0676 - 27.6206i) q^{31} +19.1256 q^{32} +(14.7908 - 20.3579i) q^{33} +(10.0509 - 30.9336i) q^{34} +(-49.1856 + 10.2289i) q^{35} +(-0.742806 + 0.539680i) q^{36} +(26.3352 - 19.1337i) q^{37} +55.0126 q^{38} +(16.4644 + 50.6721i) q^{39} +45.3952i q^{40} +(4.80798 - 40.7171i) q^{41} +(-49.6982 - 5.44452i) q^{42} +(-17.5904 - 54.1377i) q^{43} +9.96165i q^{44} +(-3.13449 - 4.31425i) q^{45} +(-55.9726 + 40.6665i) q^{46} +(18.6462 + 57.3871i) q^{47} +(-18.7277 + 57.6380i) q^{48} +(-32.4659 - 36.7010i) q^{49} +60.6529 q^{50} +(35.8957 + 26.0798i) q^{51} +(-17.0639 - 12.3976i) q^{52} +(31.8821 + 43.8820i) q^{53} +(18.2237 + 56.0867i) q^{54} -57.8577 q^{55} +(-38.4416 + 21.9695i) q^{56} +(-23.1903 + 71.3723i) q^{57} +(-16.4436 + 22.6326i) q^{58} +(5.60564 - 1.82138i) q^{59} +(26.3264 + 8.55398i) q^{60} +(42.0865 + 13.6747i) q^{61} +(-74.2966 - 24.1404i) q^{62} +(2.13643 - 4.74227i) q^{63} +(10.4759 + 32.2416i) q^{64} +(72.0059 - 99.1076i) q^{65} +(-54.7604 - 17.7927i) q^{66} +(-7.76223 - 10.6838i) q^{67} -17.5648 q^{68} +(-29.1649 - 89.7604i) q^{69} +(57.0380 + 99.8036i) q^{70} +(79.3547 - 109.222i) q^{71} +(-3.80230 - 2.76253i) q^{72} -25.7234i q^{73} +(-60.2592 - 43.7809i) q^{74} +(-25.5679 + 78.6898i) q^{75} +(-9.18042 - 28.2544i) q^{76} +(-28.0008 - 48.9951i) q^{77} +(98.6294 - 71.6585i) q^{78} +64.9134i q^{79} +(132.524 - 43.0598i) q^{80} -87.1353 q^{81} +(-92.0070 + 18.3273i) q^{82} +112.227i q^{83} +(5.49727 + 26.4335i) q^{84} -102.017i q^{85} +(-105.375 + 76.5595i) q^{86} +(-22.4314 - 30.8742i) q^{87} +(-48.4963 + 15.7574i) q^{88} +(16.9232 - 52.0844i) q^{89} +(-7.17220 + 9.87169i) q^{90} +(118.774 + 13.0119i) q^{91} +(30.2269 + 21.9611i) q^{92} +(62.6386 - 86.2147i) q^{93} +(111.700 - 81.1546i) q^{94} +(164.103 - 53.3203i) q^{95} +59.6983 q^{96} +(119.705 - 86.9706i) q^{97} +(-56.9115 + 96.6019i) q^{98} +(3.52094 - 4.84616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 6 q^{2} - 110 q^{4} - 5 q^{7} + 22 q^{8} + 552 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 6 q^{2} - 110 q^{4} - 5 q^{7} + 22 q^{8} + 552 q^{9} - 10 q^{11} - 100 q^{15} - 182 q^{16} - 84 q^{18} - 61 q^{21} + 30 q^{22} + 54 q^{23} + 204 q^{25} + 90 q^{28} - 390 q^{29} - 300 q^{30} + 152 q^{32} + 180 q^{35} - 556 q^{36} - 28 q^{37} - 160 q^{39} - 180 q^{42} - 44 q^{43} - 480 q^{46} - 11 q^{49} - 20 q^{50} + 246 q^{51} - 460 q^{53} + 525 q^{56} + 152 q^{57} - 10 q^{58} + 690 q^{60} - 215 q^{63} - 850 q^{64} - 580 q^{65} - 370 q^{67} - 425 q^{70} + 700 q^{71} + 234 q^{72} + 632 q^{74} + 378 q^{77} + 350 q^{78} + 1096 q^{81} - 160 q^{84} + 184 q^{86} - 600 q^{88} + 838 q^{91} + 534 q^{92} - 780 q^{93} + 1430 q^{95} - 5 q^{98} - 1110 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707080 2.17617i −0.353540 1.08808i −0.956851 0.290579i \(-0.906152\pi\)
0.603311 0.797506i \(-0.293848\pi\)
\(3\) 3.12138 1.04046 0.520231 0.854026i \(-0.325846\pi\)
0.520231 + 0.854026i \(0.325846\pi\)
\(4\) −0.999682 + 0.726311i −0.249920 + 0.181578i
\(5\) −4.21845 5.80620i −0.843690 1.16124i −0.985218 0.171306i \(-0.945201\pi\)
0.141528 0.989934i \(-0.454799\pi\)
\(6\) −2.20707 6.79266i −0.367845 1.13211i
\(7\) 2.87524 6.38224i 0.410749 0.911748i
\(8\) −5.11721 3.71787i −0.639651 0.464734i
\(9\) 0.743042 0.0825602
\(10\) −9.65249 + 13.2855i −0.965249 + 1.32855i
\(11\) 4.73855 6.52206i 0.430778 0.592914i −0.537354 0.843357i \(-0.680576\pi\)
0.968131 + 0.250442i \(0.0805761\pi\)
\(12\) −3.12039 + 2.26710i −0.260033 + 0.188925i
\(13\) 5.27470 + 16.2338i 0.405746 + 1.24876i 0.920271 + 0.391282i \(0.127968\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(14\) −15.9219 1.74426i −1.13728 0.124590i
\(15\) −13.1674 18.1234i −0.877827 1.20823i
\(16\) −5.99981 + 18.4655i −0.374988 + 1.15410i
\(17\) 11.4999 + 8.35520i 0.676467 + 0.491482i 0.872184 0.489178i \(-0.162703\pi\)
−0.195717 + 0.980661i \(0.562703\pi\)
\(18\) −0.525390 1.61699i −0.0291884 0.0898325i
\(19\) −7.42948 + 22.8656i −0.391025 + 1.20345i 0.540989 + 0.841030i \(0.318050\pi\)
−0.932014 + 0.362422i \(0.881950\pi\)
\(20\) 8.43422 + 2.74044i 0.421711 + 0.137022i
\(21\) 8.97474 19.9214i 0.427369 0.948639i
\(22\) −17.5436 5.70027i −0.797438 0.259103i
\(23\) −9.34359 28.7566i −0.406243 1.25029i −0.919853 0.392264i \(-0.871692\pi\)
0.513610 0.858024i \(-0.328308\pi\)
\(24\) −15.9728 11.6049i −0.665532 0.483538i
\(25\) −8.19120 + 25.2099i −0.327648 + 1.00840i
\(26\) 31.5980 22.9573i 1.21531 0.882972i
\(27\) −25.7731 −0.954561
\(28\) 1.76116 + 8.46853i 0.0628987 + 0.302448i
\(29\) −7.18636 9.89118i −0.247806 0.341075i 0.666936 0.745115i \(-0.267606\pi\)
−0.914741 + 0.404040i \(0.867606\pi\)
\(30\) −30.1291 + 41.4692i −1.00430 + 1.38231i
\(31\) 20.0676 27.6206i 0.647341 0.890989i −0.351639 0.936136i \(-0.614376\pi\)
0.998980 + 0.0451469i \(0.0143756\pi\)
\(32\) 19.1256 0.597675
\(33\) 14.7908 20.3579i 0.448207 0.616905i
\(34\) 10.0509 30.9336i 0.295616 0.909812i
\(35\) −49.1856 + 10.2289i −1.40530 + 0.292255i
\(36\) −0.742806 + 0.539680i −0.0206335 + 0.0149911i
\(37\) 26.3352 19.1337i 0.711762 0.517126i −0.171979 0.985101i \(-0.555016\pi\)
0.883742 + 0.467975i \(0.155016\pi\)
\(38\) 55.0126 1.44770
\(39\) 16.4644 + 50.6721i 0.422163 + 1.29928i
\(40\) 45.3952i 1.13488i
\(41\) 4.80798 40.7171i 0.117268 0.993100i
\(42\) −49.6982 5.44452i −1.18329 0.129631i
\(43\) −17.5904 54.1377i −0.409079 1.25902i −0.917440 0.397873i \(-0.869748\pi\)
0.508361 0.861144i \(-0.330252\pi\)
\(44\) 9.96165i 0.226401i
\(45\) −3.13449 4.31425i −0.0696552 0.0958722i
\(46\) −55.9726 + 40.6665i −1.21680 + 0.884054i
\(47\) 18.6462 + 57.3871i 0.396728 + 1.22100i 0.927608 + 0.373556i \(0.121862\pi\)
−0.530880 + 0.847447i \(0.678138\pi\)
\(48\) −18.7277 + 57.6380i −0.390161 + 1.20079i
\(49\) −32.4659 36.7010i −0.662570 0.749000i
\(50\) 60.6529 1.21306
\(51\) 35.8957 + 26.0798i 0.703838 + 0.511368i
\(52\) −17.0639 12.3976i −0.328151 0.238416i
\(53\) 31.8821 + 43.8820i 0.601550 + 0.827962i 0.995849 0.0910200i \(-0.0290127\pi\)
−0.394299 + 0.918982i \(0.629013\pi\)
\(54\) 18.2237 + 56.0867i 0.337476 + 1.03864i
\(55\) −57.8577 −1.05196
\(56\) −38.4416 + 21.9695i −0.686456 + 0.392312i
\(57\) −23.1903 + 71.3723i −0.406847 + 1.25215i
\(58\) −16.4436 + 22.6326i −0.283509 + 0.390217i
\(59\) 5.60564 1.82138i 0.0950109 0.0308709i −0.261126 0.965305i \(-0.584094\pi\)
0.356137 + 0.934434i \(0.384094\pi\)
\(60\) 26.3264 + 8.55398i 0.438774 + 0.142566i
\(61\) 42.0865 + 13.6747i 0.689942 + 0.224176i 0.632943 0.774198i \(-0.281847\pi\)
0.0569991 + 0.998374i \(0.481847\pi\)
\(62\) −74.2966 24.1404i −1.19833 0.389362i
\(63\) 2.13643 4.74227i 0.0339115 0.0752742i
\(64\) 10.4759 + 32.2416i 0.163686 + 0.503775i
\(65\) 72.0059 99.1076i 1.10778 1.52473i
\(66\) −54.7604 17.7927i −0.829704 0.269587i
\(67\) −7.76223 10.6838i −0.115854 0.159460i 0.747152 0.664654i \(-0.231421\pi\)
−0.863006 + 0.505194i \(0.831421\pi\)
\(68\) −17.5648 −0.258305
\(69\) −29.1649 89.7604i −0.422680 1.30088i
\(70\) 57.0380 + 99.8036i 0.814829 + 1.42577i
\(71\) 79.3547 109.222i 1.11767 1.53834i 0.308072 0.951363i \(-0.400316\pi\)
0.809601 0.586981i \(-0.199684\pi\)
\(72\) −3.80230 2.76253i −0.0528097 0.0383685i
\(73\) 25.7234i 0.352375i −0.984357 0.176188i \(-0.943623\pi\)
0.984357 0.176188i \(-0.0563766\pi\)
\(74\) −60.2592 43.7809i −0.814313 0.591633i
\(75\) −25.5679 + 78.6898i −0.340905 + 1.04920i
\(76\) −9.18042 28.2544i −0.120795 0.371769i
\(77\) −28.0008 48.9951i −0.363647 0.636300i
\(78\) 98.6294 71.6585i 1.26448 0.918698i
\(79\) 64.9134i 0.821689i 0.911705 + 0.410844i \(0.134766\pi\)
−0.911705 + 0.410844i \(0.865234\pi\)
\(80\) 132.524 43.0598i 1.65656 0.538248i
\(81\) −87.1353 −1.07574
\(82\) −92.0070 + 18.3273i −1.12204 + 0.223503i
\(83\) 112.227i 1.35213i 0.736841 + 0.676066i \(0.236317\pi\)
−0.736841 + 0.676066i \(0.763683\pi\)
\(84\) 5.49727 + 26.4335i 0.0654437 + 0.314685i
\(85\) 102.017i 1.20020i
\(86\) −105.375 + 76.5595i −1.22529 + 0.890226i
\(87\) −22.4314 30.8742i −0.257832 0.354876i
\(88\) −48.4963 + 15.7574i −0.551095 + 0.179061i
\(89\) 16.9232 52.0844i 0.190149 0.585218i −0.809850 0.586637i \(-0.800452\pi\)
0.999999 + 0.00141887i \(0.000451641\pi\)
\(90\) −7.17220 + 9.87169i −0.0796912 + 0.109685i
\(91\) 118.774 + 13.0119i 1.30521 + 0.142988i
\(92\) 30.2269 + 21.9611i 0.328553 + 0.238708i
\(93\) 62.6386 86.2147i 0.673534 0.927039i
\(94\) 111.700 81.1546i 1.18830 0.863347i
\(95\) 164.103 53.3203i 1.72740 0.561266i
\(96\) 59.6983 0.621858
\(97\) 119.705 86.9706i 1.23407 0.896604i 0.236881 0.971539i \(-0.423875\pi\)
0.997188 + 0.0749350i \(0.0238749\pi\)
\(98\) −56.9115 + 96.6019i −0.580730 + 0.985734i
\(99\) 3.52094 4.84616i 0.0355651 0.0489511i
\(100\) −10.1217 31.1513i −0.101217 0.311513i
\(101\) 1.33917 4.12154i 0.0132591 0.0408073i −0.944208 0.329350i \(-0.893171\pi\)
0.957467 + 0.288542i \(0.0931706\pi\)
\(102\) 31.3729 96.5557i 0.307577 0.946625i
\(103\) 118.853 + 38.6177i 1.15391 + 0.374929i 0.822616 0.568597i \(-0.192514\pi\)
0.331298 + 0.943526i \(0.392514\pi\)
\(104\) 33.3636 102.683i 0.320804 0.987333i
\(105\) −153.527 + 31.9284i −1.46216 + 0.304080i
\(106\) 72.9514 100.409i 0.688221 0.947255i
\(107\) 38.3054 117.892i 0.357995 1.10179i −0.596258 0.802793i \(-0.703346\pi\)
0.954253 0.299001i \(-0.0966535\pi\)
\(108\) 25.7649 18.7193i 0.238564 0.173327i
\(109\) 58.1426i 0.533419i 0.963777 + 0.266709i \(0.0859363\pi\)
−0.963777 + 0.266709i \(0.914064\pi\)
\(110\) 40.9101 + 125.908i 0.371910 + 1.14462i
\(111\) 82.2023 59.7235i 0.740561 0.538049i
\(112\) 100.600 + 91.3852i 0.898219 + 0.815939i
\(113\) −25.9487 18.8528i −0.229634 0.166839i 0.467018 0.884248i \(-0.345328\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(114\) 171.716 1.50628
\(115\) −127.551 + 175.559i −1.10914 + 1.52660i
\(116\) 14.3682 + 4.66850i 0.123863 + 0.0402457i
\(117\) 3.91932 + 12.0624i 0.0334985 + 0.103098i
\(118\) −7.92728 10.9110i −0.0671803 0.0924658i
\(119\) 86.3900 49.3722i 0.725967 0.414892i
\(120\) 141.696i 1.18080i
\(121\) 17.3077 + 53.2676i 0.143039 + 0.440228i
\(122\) 101.256i 0.829970i
\(123\) 15.0076 127.094i 0.122013 1.03328i
\(124\) 42.1872i 0.340219i
\(125\) 10.2880 3.34279i 0.0823043 0.0267423i
\(126\) −11.8306 1.29606i −0.0938937 0.0102862i
\(127\) −205.457 + 149.273i −1.61777 + 1.17538i −0.798292 + 0.602270i \(0.794263\pi\)
−0.819479 + 0.573109i \(0.805737\pi\)
\(128\) 124.648 90.5617i 0.973809 0.707514i
\(129\) −54.9065 168.985i −0.425631 1.30996i
\(130\) −266.589 86.6200i −2.05068 0.666308i
\(131\) −24.8290 + 34.1742i −0.189535 + 0.260872i −0.893200 0.449659i \(-0.851545\pi\)
0.703665 + 0.710531i \(0.251545\pi\)
\(132\) 31.0941i 0.235562i
\(133\) 124.572 + 113.161i 0.936632 + 0.850833i
\(134\) −17.7612 + 24.4462i −0.132546 + 0.182435i
\(135\) 108.723 + 149.644i 0.805354 + 1.10847i
\(136\) −27.7841 85.5106i −0.204295 0.628754i
\(137\) 38.7505i 0.282850i 0.989949 + 0.141425i \(0.0451684\pi\)
−0.989949 + 0.141425i \(0.954832\pi\)
\(138\) −174.712 + 126.936i −1.26603 + 0.919824i
\(139\) −128.567 41.7741i −0.924945 0.300533i −0.192451 0.981307i \(-0.561644\pi\)
−0.732494 + 0.680774i \(0.761644\pi\)
\(140\) 41.7406 45.9497i 0.298147 0.328212i
\(141\) 58.2020 + 179.127i 0.412780 + 1.27041i
\(142\) −293.797 95.4603i −2.06899 0.672256i
\(143\) 130.873 + 42.5231i 0.915193 + 0.297364i
\(144\) −4.45811 + 13.7207i −0.0309591 + 0.0952824i
\(145\) −27.1149 + 83.4509i −0.186999 + 0.575524i
\(146\) −55.9785 + 18.1885i −0.383414 + 0.124579i
\(147\) −101.339 114.558i −0.689379 0.779305i
\(148\) −12.4298 + 38.2551i −0.0839854 + 0.258481i
\(149\) −9.08442 12.5036i −0.0609692 0.0839170i 0.777444 0.628953i \(-0.216516\pi\)
−0.838413 + 0.545036i \(0.816516\pi\)
\(150\) 189.321 1.26214
\(151\) 187.511 60.9259i 1.24179 0.403483i 0.386820 0.922155i \(-0.373574\pi\)
0.854973 + 0.518672i \(0.173574\pi\)
\(152\) 123.029 89.3861i 0.809404 0.588067i
\(153\) 8.54494 + 6.20826i 0.0558493 + 0.0405769i
\(154\) −86.8228 + 95.5780i −0.563784 + 0.620636i
\(155\) −245.025 −1.58081
\(156\) −53.2628 38.6977i −0.341428 0.248062i
\(157\) 40.6160 125.003i 0.258701 0.796200i −0.734377 0.678742i \(-0.762526\pi\)
0.993078 0.117458i \(-0.0374745\pi\)
\(158\) 141.263 45.8990i 0.894067 0.290500i
\(159\) 99.5164 + 136.973i 0.625889 + 0.861463i
\(160\) −80.6804 111.047i −0.504252 0.694044i
\(161\) −210.397 23.0493i −1.30681 0.143163i
\(162\) 61.6116 + 189.621i 0.380319 + 1.17050i
\(163\) −265.648 −1.62974 −0.814870 0.579644i \(-0.803192\pi\)
−0.814870 + 0.579644i \(0.803192\pi\)
\(164\) 24.7669 + 44.1963i 0.151017 + 0.269489i
\(165\) −180.596 −1.09452
\(166\) 244.225 79.3535i 1.47123 0.478033i
\(167\) −147.329 −0.882213 −0.441106 0.897455i \(-0.645414\pi\)
−0.441106 + 0.897455i \(0.645414\pi\)
\(168\) −119.991 + 68.5751i −0.714231 + 0.408185i
\(169\) −98.9916 + 71.9216i −0.585749 + 0.425571i
\(170\) −222.006 + 72.1342i −1.30592 + 0.424319i
\(171\) −5.52041 + 16.9901i −0.0322831 + 0.0993573i
\(172\) 56.9057 + 41.3444i 0.330847 + 0.240374i
\(173\) 151.624i 0.876442i 0.898867 + 0.438221i \(0.144391\pi\)
−0.898867 + 0.438221i \(0.855609\pi\)
\(174\) −51.3266 + 70.6451i −0.294981 + 0.406006i
\(175\) 137.344 + 124.763i 0.784823 + 0.712931i
\(176\) 92.0028 + 126.631i 0.522743 + 0.719494i
\(177\) 17.4974 5.68524i 0.0988552 0.0321200i
\(178\) −125.311 −0.703992
\(179\) 135.969 + 187.146i 0.759605 + 1.04551i 0.997247 + 0.0741535i \(0.0236255\pi\)
−0.237642 + 0.971353i \(0.576375\pi\)
\(180\) 6.26698 + 2.03626i 0.0348165 + 0.0113126i
\(181\) 85.9561 + 62.4508i 0.474896 + 0.345032i 0.799346 0.600871i \(-0.205179\pi\)
−0.324451 + 0.945903i \(0.605179\pi\)
\(182\) −55.6669 267.674i −0.305862 1.47073i
\(183\) 131.368 + 42.6841i 0.717858 + 0.233246i
\(184\) −59.1002 + 181.892i −0.321197 + 0.988543i
\(185\) −222.188 72.1931i −1.20101 0.390233i
\(186\) −231.908 75.3516i −1.24682 0.405116i
\(187\) 108.986 35.4118i 0.582814 0.189368i
\(188\) −60.3212 43.8259i −0.320858 0.233117i
\(189\) −74.1041 + 164.490i −0.392085 + 0.870319i
\(190\) −232.068 319.414i −1.22141 1.68113i
\(191\) 248.975i 1.30353i −0.758420 0.651766i \(-0.774028\pi\)
0.758420 0.651766i \(-0.225972\pi\)
\(192\) 32.6994 + 100.638i 0.170309 + 0.524158i
\(193\) 134.127 + 184.610i 0.694960 + 0.956530i 0.999991 + 0.00418804i \(0.00133310\pi\)
−0.305031 + 0.952342i \(0.598667\pi\)
\(194\) −273.903 199.003i −1.41187 1.02579i
\(195\) 224.758 309.353i 1.15261 1.58643i
\(196\) 59.1120 + 13.1089i 0.301592 + 0.0668823i
\(197\) 0.484813 + 0.352237i 0.00246098 + 0.00178801i 0.589015 0.808122i \(-0.299516\pi\)
−0.586554 + 0.809910i \(0.699516\pi\)
\(198\) −13.0357 4.23554i −0.0658367 0.0213916i
\(199\) 25.4205 + 78.2362i 0.127741 + 0.393147i 0.994391 0.105771i \(-0.0337310\pi\)
−0.866649 + 0.498918i \(0.833731\pi\)
\(200\) 135.643 98.5506i 0.678216 0.492753i
\(201\) −24.2289 33.3482i −0.120542 0.165912i
\(202\) −9.91607 −0.0490895
\(203\) −83.7904 + 17.4255i −0.412761 + 0.0858401i
\(204\) −54.8264 −0.268757
\(205\) −256.694 + 143.847i −1.25217 + 0.701693i
\(206\) 285.950i 1.38811i
\(207\) −6.94268 21.3674i −0.0335395 0.103224i
\(208\) −331.414 −1.59334
\(209\) 113.926 + 156.805i 0.545099 + 0.750264i
\(210\) 178.038 + 311.525i 0.847798 + 1.48345i
\(211\) 157.301 51.1103i 0.745504 0.242229i 0.0884586 0.996080i \(-0.471806\pi\)
0.657046 + 0.753851i \(0.271806\pi\)
\(212\) −63.7440 20.7117i −0.300679 0.0976966i
\(213\) 247.697 340.925i 1.16290 1.60059i
\(214\) −283.638 −1.32541
\(215\) −240.130 + 330.511i −1.11688 + 1.53726i
\(216\) 131.887 + 95.8212i 0.610586 + 0.443617i
\(217\) −118.582 207.492i −0.546463 0.956185i
\(218\) 126.528 41.1115i 0.580404 0.188585i
\(219\) 80.2927i 0.366633i
\(220\) 57.8393 42.0227i 0.262906 0.191012i
\(221\) −74.9783 + 230.759i −0.339268 + 1.04416i
\(222\) −188.092 136.657i −0.847261 0.615572i
\(223\) 92.7518 30.1369i 0.415928 0.135143i −0.0935749 0.995612i \(-0.529829\pi\)
0.509502 + 0.860469i \(0.329829\pi\)
\(224\) 54.9908 122.064i 0.245494 0.544929i
\(225\) −6.08640 + 18.7320i −0.0270507 + 0.0832534i
\(226\) −22.6791 + 69.7992i −0.100350 + 0.308846i
\(227\) −11.5219 + 35.4607i −0.0507572 + 0.156214i −0.973222 0.229866i \(-0.926171\pi\)
0.922465 + 0.386080i \(0.126171\pi\)
\(228\) −28.6556 88.1929i −0.125683 0.386811i
\(229\) 75.0672 + 54.5395i 0.327804 + 0.238164i 0.739498 0.673158i \(-0.235063\pi\)
−0.411694 + 0.911322i \(0.635063\pi\)
\(230\) 472.235 + 153.439i 2.05320 + 0.667124i
\(231\) −87.4014 152.933i −0.378361 0.662045i
\(232\) 77.3332i 0.333333i
\(233\) 316.130 102.717i 1.35678 0.440845i 0.461815 0.886976i \(-0.347199\pi\)
0.894968 + 0.446131i \(0.147199\pi\)
\(234\) 23.4786 17.0582i 0.100336 0.0728984i
\(235\) 254.543 350.348i 1.08316 1.49084i
\(236\) −4.28097 + 5.89225i −0.0181397 + 0.0249672i
\(237\) 202.620i 0.854936i
\(238\) −168.527 153.089i −0.708096 0.643232i
\(239\) 80.9816 + 26.3125i 0.338835 + 0.110094i 0.473492 0.880798i \(-0.342993\pi\)
−0.134657 + 0.990892i \(0.542993\pi\)
\(240\) 413.660 134.406i 1.72358 0.560026i
\(241\) 230.722 + 317.561i 0.957352 + 1.31768i 0.948183 + 0.317724i \(0.102919\pi\)
0.00916883 + 0.999958i \(0.497081\pi\)
\(242\) 103.681 75.3289i 0.428435 0.311277i
\(243\) −40.0244 −0.164709
\(244\) −52.0052 + 16.8975i −0.213136 + 0.0692521i
\(245\) −76.1373 + 343.325i −0.310764 + 1.40133i
\(246\) −287.189 + 57.2065i −1.16744 + 0.232547i
\(247\) −410.385 −1.66148
\(248\) −205.380 + 66.7320i −0.828145 + 0.269081i
\(249\) 350.304i 1.40684i
\(250\) −14.5489 20.0249i −0.0581958 0.0800996i
\(251\) −95.7580 131.800i −0.381506 0.525098i 0.574477 0.818521i \(-0.305206\pi\)
−0.955983 + 0.293423i \(0.905206\pi\)
\(252\) 1.30862 + 6.29247i 0.00519293 + 0.0249701i
\(253\) −231.827 75.3253i −0.916314 0.297728i
\(254\) 470.118 + 341.561i 1.85086 + 1.34473i
\(255\) 318.434i 1.24876i
\(256\) −175.508 127.514i −0.685579 0.498102i
\(257\) −170.665 123.995i −0.664065 0.482472i 0.203968 0.978978i \(-0.434616\pi\)
−0.868033 + 0.496506i \(0.834616\pi\)
\(258\) −328.916 + 238.972i −1.27487 + 0.926246i
\(259\) −46.3954 223.092i −0.179133 0.861357i
\(260\) 151.375i 0.582211i
\(261\) −5.33977 7.34956i −0.0204589 0.0281593i
\(262\) 91.9250 + 29.8683i 0.350859 + 0.114001i
\(263\) −198.223 + 272.830i −0.753699 + 1.03738i 0.244014 + 0.969772i \(0.421536\pi\)
−0.997712 + 0.0676053i \(0.978464\pi\)
\(264\) −151.376 + 49.1849i −0.573393 + 0.186307i
\(265\) 120.294 370.228i 0.453941 1.39709i
\(266\) 158.175 351.104i 0.594642 1.31994i
\(267\) 52.8240 162.575i 0.197843 0.608897i
\(268\) 15.5195 + 5.04260i 0.0579087 + 0.0188157i
\(269\) 246.039 79.9428i 0.914642 0.297185i 0.186375 0.982479i \(-0.440326\pi\)
0.728267 + 0.685293i \(0.240326\pi\)
\(270\) 248.775 342.409i 0.921389 1.26818i
\(271\) −295.351 95.9653i −1.08986 0.354115i −0.291665 0.956521i \(-0.594209\pi\)
−0.798190 + 0.602405i \(0.794209\pi\)
\(272\) −223.281 + 162.223i −0.820885 + 0.596408i
\(273\) 370.740 + 40.6152i 1.35802 + 0.148773i
\(274\) 84.3276 27.3997i 0.307765 0.0999989i
\(275\) 125.606 + 172.882i 0.456750 + 0.628662i
\(276\) 94.3497 + 68.5491i 0.341847 + 0.248366i
\(277\) 8.33397 + 6.05498i 0.0300865 + 0.0218591i 0.602727 0.797948i \(-0.294081\pi\)
−0.572640 + 0.819807i \(0.694081\pi\)
\(278\) 309.322i 1.11267i
\(279\) 14.9111 20.5233i 0.0534446 0.0735602i
\(280\) 289.723 + 130.522i 1.03472 + 0.466151i
\(281\) 283.716 92.1848i 1.00966 0.328060i 0.242944 0.970040i \(-0.421887\pi\)
0.766721 + 0.641980i \(0.221887\pi\)
\(282\) 348.658 253.315i 1.23638 0.898280i
\(283\) −268.729 369.873i −0.949571 1.30697i −0.951718 0.306975i \(-0.900683\pi\)
0.00214613 0.999998i \(-0.499317\pi\)
\(284\) 166.824i 0.587408i
\(285\) 512.229 166.433i 1.79729 0.583976i
\(286\) 314.868i 1.10094i
\(287\) −246.042 147.757i −0.857290 0.514834i
\(288\) 14.2111 0.0493442
\(289\) −26.8665 82.6867i −0.0929638 0.286113i
\(290\) 200.776 0.692330
\(291\) 373.644 271.469i 1.28400 0.932882i
\(292\) 18.6832 + 25.7152i 0.0639836 + 0.0880659i
\(293\) 103.685 + 319.110i 0.353874 + 1.08911i 0.956660 + 0.291208i \(0.0940573\pi\)
−0.602786 + 0.797903i \(0.705943\pi\)
\(294\) −177.643 + 301.532i −0.604227 + 1.02562i
\(295\) −34.2225 24.8641i −0.116008 0.0842850i
\(296\) −205.899 −0.695605
\(297\) −122.127 + 168.094i −0.411203 + 0.565973i
\(298\) −20.7866 + 28.6103i −0.0697537 + 0.0960077i
\(299\) 417.546 303.365i 1.39647 1.01460i
\(300\) −31.5936 97.2351i −0.105312 0.324117i
\(301\) −396.097 43.3930i −1.31594 0.144163i
\(302\) −265.170 364.976i −0.878047 1.20853i
\(303\) 4.18006 12.8649i 0.0137956 0.0424585i
\(304\) −377.650 274.379i −1.24227 0.902561i
\(305\) −98.1415 302.048i −0.321775 0.990323i
\(306\) 7.46827 22.9850i 0.0244061 0.0751143i
\(307\) 194.406 + 63.1664i 0.633245 + 0.205754i 0.608012 0.793928i \(-0.291967\pi\)
0.0252328 + 0.999682i \(0.491967\pi\)
\(308\) 63.5776 + 28.6422i 0.206421 + 0.0929941i
\(309\) 370.986 + 120.541i 1.20060 + 0.390100i
\(310\) 173.252 + 533.216i 0.558879 + 1.72005i
\(311\) 30.4851 + 22.1487i 0.0980229 + 0.0712178i 0.635717 0.771922i \(-0.280704\pi\)
−0.537694 + 0.843140i \(0.680704\pi\)
\(312\) 104.141 320.512i 0.333784 1.02728i
\(313\) −369.346 + 268.345i −1.18002 + 0.857334i −0.992174 0.124865i \(-0.960150\pi\)
−0.187845 + 0.982199i \(0.560150\pi\)
\(314\) −300.747 −0.957794
\(315\) −36.5470 + 7.60052i −0.116022 + 0.0241286i
\(316\) −47.1474 64.8928i −0.149200 0.205357i
\(317\) −122.207 + 168.203i −0.385510 + 0.530609i −0.957034 0.289977i \(-0.906352\pi\)
0.571524 + 0.820585i \(0.306352\pi\)
\(318\) 227.709 313.415i 0.716067 0.985582i
\(319\) −98.5638 −0.308978
\(320\) 143.009 196.835i 0.446903 0.615109i
\(321\) 119.566 367.986i 0.372480 1.14637i
\(322\) 98.6082 + 474.156i 0.306237 + 1.47254i
\(323\) −276.485 + 200.878i −0.855991 + 0.621914i
\(324\) 87.1076 63.2873i 0.268850 0.195331i
\(325\) −452.460 −1.39218
\(326\) 187.834 + 578.094i 0.576178 + 1.77329i
\(327\) 181.485i 0.555001i
\(328\) −175.984 + 190.483i −0.536538 + 0.580739i
\(329\) 419.871 + 45.9975i 1.27620 + 0.139810i
\(330\) 127.696 + 393.008i 0.386958 + 1.19093i
\(331\) 362.614i 1.09551i 0.836639 + 0.547755i \(0.184517\pi\)
−0.836639 + 0.547755i \(0.815483\pi\)
\(332\) −81.5118 112.191i −0.245517 0.337926i
\(333\) 19.5682 14.2171i 0.0587633 0.0426940i
\(334\) 104.174 + 320.614i 0.311898 + 0.959922i
\(335\) −29.2877 + 90.1381i −0.0874258 + 0.269069i
\(336\) 314.013 + 285.248i 0.934562 + 0.848953i
\(337\) −134.165 −0.398117 −0.199059 0.979988i \(-0.563788\pi\)
−0.199059 + 0.979988i \(0.563788\pi\)
\(338\) 226.508 + 164.568i 0.670143 + 0.486888i
\(339\) −80.9958 58.8469i −0.238926 0.173590i
\(340\) 74.0961 + 101.985i 0.217930 + 0.299954i
\(341\) −85.0522 261.764i −0.249420 0.767636i
\(342\) 40.8767 0.119522
\(343\) −327.582 + 101.681i −0.955050 + 0.296446i
\(344\) −111.263 + 342.433i −0.323440 + 0.995445i
\(345\) −398.136 + 547.987i −1.15402 + 1.58837i
\(346\) 329.961 107.211i 0.953643 0.309857i
\(347\) −146.555 47.6185i −0.422347 0.137229i 0.0901293 0.995930i \(-0.471272\pi\)
−0.512477 + 0.858701i \(0.671272\pi\)
\(348\) 44.8485 + 14.5722i 0.128875 + 0.0418741i
\(349\) 502.995 + 163.433i 1.44125 + 0.468289i 0.922286 0.386509i \(-0.126319\pi\)
0.518960 + 0.854798i \(0.326319\pi\)
\(350\) 174.392 387.101i 0.498262 1.10600i
\(351\) −135.946 418.397i −0.387309 1.19202i
\(352\) 90.6277 124.738i 0.257465 0.354370i
\(353\) −324.043 105.288i −0.917968 0.298266i −0.188335 0.982105i \(-0.560309\pi\)
−0.729633 + 0.683839i \(0.760309\pi\)
\(354\) −24.7441 34.0573i −0.0698986 0.0962071i
\(355\) −968.921 −2.72936
\(356\) 20.9116 + 64.3594i 0.0587405 + 0.180785i
\(357\) 269.656 154.109i 0.755340 0.431679i
\(358\) 311.119 428.219i 0.869049 1.19614i
\(359\) −193.756 140.772i −0.539709 0.392122i 0.284268 0.958745i \(-0.408250\pi\)
−0.823977 + 0.566623i \(0.808250\pi\)
\(360\) 33.7305i 0.0936959i
\(361\) −175.583 127.568i −0.486379 0.353375i
\(362\) 75.1256 231.213i 0.207529 0.638709i
\(363\) 54.0240 + 166.269i 0.148826 + 0.458040i
\(364\) −128.187 + 73.2594i −0.352163 + 0.201262i
\(365\) −149.355 + 108.513i −0.409192 + 0.297296i
\(366\) 316.060i 0.863552i
\(367\) 250.320 81.3341i 0.682072 0.221619i 0.0525698 0.998617i \(-0.483259\pi\)
0.629502 + 0.776999i \(0.283259\pi\)
\(368\) 587.066 1.59529
\(369\) 3.57253 30.2545i 0.00968166 0.0819906i
\(370\) 534.564i 1.44477i
\(371\) 371.734 77.3079i 1.00198 0.208377i
\(372\) 131.682i 0.353985i
\(373\) 473.389 343.937i 1.26914 0.922084i 0.269971 0.962868i \(-0.412986\pi\)
0.999168 + 0.0407847i \(0.0129858\pi\)
\(374\) −154.124 212.133i −0.412096 0.567202i
\(375\) 32.1129 10.4341i 0.0856345 0.0278243i
\(376\) 117.941 362.986i 0.313674 0.965389i
\(377\) 122.666 168.835i 0.325374 0.447839i
\(378\) 410.356 + 44.9551i 1.08560 + 0.118929i
\(379\) 424.925 + 308.726i 1.12117 + 0.814581i 0.984387 0.176019i \(-0.0563221\pi\)
0.136788 + 0.990600i \(0.456322\pi\)
\(380\) −125.324 + 172.493i −0.329799 + 0.453930i
\(381\) −641.310 + 465.939i −1.68323 + 1.22294i
\(382\) −541.811 + 176.045i −1.41835 + 0.460851i
\(383\) 9.41924 0.0245933 0.0122967 0.999924i \(-0.496086\pi\)
0.0122967 + 0.999924i \(0.496086\pi\)
\(384\) 389.073 282.678i 1.01321 0.736141i
\(385\) −166.355 + 369.262i −0.432091 + 0.959122i
\(386\) 306.905 422.418i 0.795090 1.09435i
\(387\) −13.0704 40.2266i −0.0337737 0.103945i
\(388\) −56.4989 + 173.886i −0.145616 + 0.448159i
\(389\) −187.527 + 577.149i −0.482075 + 1.48367i 0.354098 + 0.935208i \(0.384788\pi\)
−0.836173 + 0.548466i \(0.815212\pi\)
\(390\) −832.127 270.374i −2.13366 0.693268i
\(391\) 132.816 408.767i 0.339684 1.04544i
\(392\) 29.6855 + 308.511i 0.0757283 + 0.787017i
\(393\) −77.5010 + 106.671i −0.197203 + 0.271427i
\(394\) 0.423726 1.30410i 0.00107545 0.00330989i
\(395\) 376.900 273.834i 0.954178 0.693251i
\(396\) 7.40192i 0.0186917i
\(397\) 101.747 + 313.144i 0.256289 + 0.788775i 0.993573 + 0.113193i \(0.0361078\pi\)
−0.737284 + 0.675583i \(0.763892\pi\)
\(398\) 152.281 110.639i 0.382616 0.277986i
\(399\) 388.837 + 353.219i 0.974530 + 0.885259i
\(400\) −416.369 302.510i −1.04092 0.756274i
\(401\) −794.689 −1.98177 −0.990884 0.134718i \(-0.956987\pi\)
−0.990884 + 0.134718i \(0.956987\pi\)
\(402\) −55.4396 + 76.3061i −0.137910 + 0.189816i
\(403\) 554.240 + 180.083i 1.37529 + 0.446857i
\(404\) 1.65478 + 5.09288i 0.00409599 + 0.0126061i
\(405\) 367.576 + 505.925i 0.907595 + 1.24920i
\(406\) 97.1675 + 170.021i 0.239329 + 0.418771i
\(407\) 262.426i 0.644780i
\(408\) −86.7248 266.911i −0.212561 0.654195i
\(409\) 522.060i 1.27643i 0.769858 + 0.638215i \(0.220327\pi\)
−0.769858 + 0.638215i \(0.779673\pi\)
\(410\) 494.539 + 456.898i 1.20619 + 1.11439i
\(411\) 120.955i 0.294295i
\(412\) −146.864 + 47.7189i −0.356466 + 0.115823i
\(413\) 4.49309 41.0135i 0.0108791 0.0993063i
\(414\) −41.5900 + 30.2169i −0.100459 + 0.0729877i
\(415\) 651.612 473.424i 1.57015 1.14078i
\(416\) 100.882 + 310.482i 0.242504 + 0.746351i
\(417\) −401.308 130.393i −0.962370 0.312693i
\(418\) 260.680 358.796i 0.623637 0.858362i
\(419\) 644.080i 1.53718i 0.639740 + 0.768592i \(0.279042\pi\)
−0.639740 + 0.768592i \(0.720958\pi\)
\(420\) 130.288 143.427i 0.310211 0.341492i
\(421\) −175.666 + 241.783i −0.417258 + 0.574307i −0.964970 0.262360i \(-0.915499\pi\)
0.547712 + 0.836667i \(0.315499\pi\)
\(422\) −222.449 306.175i −0.527131 0.725534i
\(423\) 13.8549 + 42.6411i 0.0327539 + 0.100806i
\(424\) 343.087i 0.809167i
\(425\) −304.832 + 221.474i −0.717252 + 0.521114i
\(426\) −917.052 297.968i −2.15271 0.699456i
\(427\) 208.284 229.288i 0.487785 0.536973i
\(428\) 47.3331 + 145.676i 0.110591 + 0.340365i
\(429\) 408.504 + 132.731i 0.952223 + 0.309396i
\(430\) 889.039 + 288.866i 2.06753 + 0.671782i
\(431\) 23.3126 71.7487i 0.0540895 0.166470i −0.920362 0.391066i \(-0.872106\pi\)
0.974452 + 0.224596i \(0.0721063\pi\)
\(432\) 154.634 475.915i 0.357949 1.10165i
\(433\) −300.924 + 97.7762i −0.694975 + 0.225811i −0.635140 0.772397i \(-0.719058\pi\)
−0.0598353 + 0.998208i \(0.519058\pi\)
\(434\) −367.691 + 404.769i −0.847214 + 0.932647i
\(435\) −84.6359 + 260.482i −0.194565 + 0.598810i
\(436\) −42.2297 58.1241i −0.0968570 0.133312i
\(437\) 726.955 1.66351
\(438\) −174.730 + 56.7734i −0.398928 + 0.129620i
\(439\) 130.322 94.6843i 0.296860 0.215682i −0.429378 0.903125i \(-0.641267\pi\)
0.726238 + 0.687443i \(0.241267\pi\)
\(440\) 296.070 + 215.107i 0.672886 + 0.488881i
\(441\) −24.1236 27.2704i −0.0547019 0.0618376i
\(442\) 555.187 1.25608
\(443\) −70.7253 51.3850i −0.159651 0.115993i 0.505092 0.863066i \(-0.331459\pi\)
−0.664742 + 0.747073i \(0.731459\pi\)
\(444\) −38.7983 + 119.409i −0.0873836 + 0.268939i
\(445\) −373.802 + 121.456i −0.840005 + 0.272934i
\(446\) −131.166 180.535i −0.294094 0.404786i
\(447\) −28.3560 39.0286i −0.0634362 0.0873124i
\(448\) 235.894 + 25.8426i 0.526550 + 0.0576843i
\(449\) −14.1181 43.4511i −0.0314435 0.0967731i 0.934103 0.357003i \(-0.116202\pi\)
−0.965547 + 0.260230i \(0.916202\pi\)
\(450\) 45.0676 0.100150
\(451\) −242.777 224.298i −0.538307 0.497335i
\(452\) 39.6335 0.0876846
\(453\) 585.293 190.173i 1.29204 0.419809i
\(454\) 85.3153 0.187919
\(455\) −425.494 744.518i −0.935152 1.63630i
\(456\) 384.022 279.008i 0.842154 0.611861i
\(457\) 374.177 121.577i 0.818768 0.266034i 0.130461 0.991453i \(-0.458354\pi\)
0.688307 + 0.725420i \(0.258354\pi\)
\(458\) 65.6087 201.923i 0.143250 0.440879i
\(459\) −296.390 215.340i −0.645729 0.469150i
\(460\) 268.145i 0.582924i
\(461\) −136.320 + 187.629i −0.295706 + 0.407004i −0.930857 0.365384i \(-0.880938\pi\)
0.635151 + 0.772388i \(0.280938\pi\)
\(462\) −271.007 + 298.336i −0.586596 + 0.645748i
\(463\) −246.907 339.838i −0.533276 0.733992i 0.454349 0.890824i \(-0.349872\pi\)
−0.987625 + 0.156832i \(0.949872\pi\)
\(464\) 225.763 73.3548i 0.486558 0.158092i
\(465\) −764.818 −1.64477
\(466\) −447.059 615.324i −0.959354 1.32044i
\(467\) −354.048 115.037i −0.758132 0.246332i −0.0956554 0.995415i \(-0.530495\pi\)
−0.662477 + 0.749082i \(0.730495\pi\)
\(468\) −12.6792 9.21195i −0.0270922 0.0196836i
\(469\) −90.5049 + 18.8219i −0.192974 + 0.0401320i
\(470\) −942.400 306.204i −2.00511 0.651499i
\(471\) 126.778 390.183i 0.269168 0.828415i
\(472\) −35.4569 11.5207i −0.0751206 0.0244082i
\(473\) −436.443 141.809i −0.922712 0.299807i
\(474\) 440.935 143.268i 0.930242 0.302254i
\(475\) −515.583 374.593i −1.08544 0.788617i
\(476\) −50.5030 + 112.103i −0.106099 + 0.235509i
\(477\) 23.6898 + 32.6062i 0.0496641 + 0.0683567i
\(478\) 194.835i 0.407604i
\(479\) 251.737 + 774.765i 0.525546 + 1.61746i 0.763234 + 0.646123i \(0.223611\pi\)
−0.237688 + 0.971342i \(0.576389\pi\)
\(480\) −251.835 346.620i −0.524655 0.722126i
\(481\) 449.523 + 326.598i 0.934559 + 0.678997i
\(482\) 527.928 726.631i 1.09529 1.50753i
\(483\) −656.729 71.9456i −1.35969 0.148956i
\(484\) −55.9911 40.6799i −0.115684 0.0840494i
\(485\) −1009.94 328.148i −2.08234 0.676595i
\(486\) 28.3005 + 87.0999i 0.0582314 + 0.179218i
\(487\) 26.6415 19.3562i 0.0547053 0.0397457i −0.560097 0.828427i \(-0.689236\pi\)
0.614802 + 0.788682i \(0.289236\pi\)
\(488\) −164.524 226.448i −0.337140 0.464034i
\(489\) −829.188 −1.69568
\(490\) 800.969 77.0707i 1.63463 0.157287i
\(491\) 317.261 0.646153 0.323077 0.946373i \(-0.395283\pi\)
0.323077 + 0.946373i \(0.395283\pi\)
\(492\) 77.3069 + 137.954i 0.157128 + 0.280393i
\(493\) 173.792i 0.352518i
\(494\) 290.175 + 893.067i 0.587399 + 1.80783i
\(495\) −42.9907 −0.0868499
\(496\) 389.628 + 536.277i 0.785541 + 1.08120i
\(497\) −468.919 820.502i −0.943500 1.65091i
\(498\) 762.320 247.693i 1.53076 0.497375i
\(499\) −126.377 41.0624i −0.253260 0.0822893i 0.179635 0.983733i \(-0.442508\pi\)
−0.432896 + 0.901444i \(0.642508\pi\)
\(500\) −7.85686 + 10.8140i −0.0157137 + 0.0216281i
\(501\) −459.872 −0.917908
\(502\) −219.110 + 301.578i −0.436473 + 0.600754i
\(503\) 330.020 + 239.773i 0.656102 + 0.476686i 0.865344 0.501178i \(-0.167100\pi\)
−0.209242 + 0.977864i \(0.567100\pi\)
\(504\) −28.5637 + 16.3242i −0.0566740 + 0.0323894i
\(505\) −29.5797 + 9.61103i −0.0585737 + 0.0190317i
\(506\) 557.757i 1.10229i
\(507\) −308.991 + 224.495i −0.609449 + 0.442791i
\(508\) 96.9728 298.451i 0.190891 0.587503i
\(509\) −370.375 269.093i −0.727652 0.528670i 0.161168 0.986927i \(-0.448474\pi\)
−0.888820 + 0.458257i \(0.848474\pi\)
\(510\) −692.967 + 225.158i −1.35876 + 0.441487i
\(511\) −164.173 73.9611i −0.321278 0.144738i
\(512\) 37.0505 114.030i 0.0723642 0.222714i
\(513\) 191.481 589.318i 0.373257 1.14877i
\(514\) −149.161 + 459.070i −0.290196 + 0.893132i
\(515\) −277.154 852.992i −0.538163 1.65629i
\(516\) 177.625 + 129.052i 0.344234 + 0.250100i
\(517\) 462.638 + 150.320i 0.894852 + 0.290755i
\(518\) −452.680 + 258.708i −0.873899 + 0.499436i
\(519\) 473.278i 0.911904i
\(520\) −736.938 + 239.446i −1.41719 + 0.460473i
\(521\) −399.640 + 290.355i −0.767063 + 0.557304i −0.901068 0.433677i \(-0.857216\pi\)
0.134006 + 0.990981i \(0.457216\pi\)
\(522\) −12.2182 + 16.8170i −0.0234066 + 0.0322164i
\(523\) 336.872 463.665i 0.644115 0.886548i −0.354712 0.934976i \(-0.615421\pi\)
0.998827 + 0.0484276i \(0.0154210\pi\)
\(524\) 52.1970i 0.0996126i
\(525\) 428.703 + 389.433i 0.816578 + 0.741777i
\(526\) 733.884 + 238.453i 1.39522 + 0.453333i
\(527\) 461.552 149.967i 0.875810 0.284568i
\(528\) 287.176 + 395.264i 0.543894 + 0.748606i
\(529\) −311.670 + 226.442i −0.589168 + 0.428056i
\(530\) −890.737 −1.68064
\(531\) 4.16523 1.35336i 0.00784412 0.00254871i
\(532\) −206.722 22.6467i −0.388576 0.0425691i
\(533\) 686.356 136.718i 1.28772 0.256507i
\(534\) −391.142 −0.732476
\(535\) −846.094 + 274.913i −1.58148 + 0.513855i
\(536\) 83.5302i 0.155840i
\(537\) 424.412 + 584.154i 0.790340 + 1.08781i
\(538\) −347.938 478.896i −0.646725 0.890141i
\(539\) −393.208 + 37.8352i −0.729513 + 0.0701952i
\(540\) −217.376 70.6298i −0.402549 0.130796i
\(541\) 388.833 + 282.504i 0.718730 + 0.522188i 0.885978 0.463727i \(-0.153488\pi\)
−0.167248 + 0.985915i \(0.553488\pi\)
\(542\) 710.588i 1.31105i
\(543\) 268.302 + 194.933i 0.494111 + 0.358992i
\(544\) 219.943 + 159.798i 0.404308 + 0.293747i
\(545\) 337.588 245.272i 0.619427 0.450040i
\(546\) −173.758 835.512i −0.318238 1.53024i
\(547\) 659.626i 1.20590i −0.797780 0.602949i \(-0.793992\pi\)
0.797780 0.602949i \(-0.206008\pi\)
\(548\) −28.1449 38.7382i −0.0513593 0.0706901i
\(549\) 31.2720 + 10.1609i 0.0569618 + 0.0185080i
\(550\) 287.407 395.582i 0.522558 0.719239i
\(551\) 279.559 90.8341i 0.507366 0.164853i
\(552\) −184.475 + 567.754i −0.334193 + 1.02854i
\(553\) 414.293 + 186.642i 0.749173 + 0.337508i
\(554\) 7.28388 22.4175i 0.0131478 0.0404648i
\(555\) −693.533 225.343i −1.24961 0.406023i
\(556\) 158.867 51.6192i 0.285733 0.0928402i
\(557\) −342.280 + 471.107i −0.614506 + 0.845794i −0.996939 0.0781889i \(-0.975086\pi\)
0.382433 + 0.923983i \(0.375086\pi\)
\(558\) −55.2055 17.9374i −0.0989346 0.0321458i
\(559\) 786.080 571.120i 1.40623 1.02168i
\(560\) 106.222 969.610i 0.189683 1.73145i
\(561\) 340.188 110.534i 0.606395 0.197030i
\(562\) −401.220 552.231i −0.713914 0.982618i
\(563\) 476.148 + 345.942i 0.845733 + 0.614461i 0.923966 0.382474i \(-0.124928\pi\)
−0.0782330 + 0.996935i \(0.524928\pi\)
\(564\) −188.286 136.798i −0.333840 0.242549i
\(565\) 230.193i 0.407421i
\(566\) −614.894 + 846.329i −1.08639 + 1.49528i
\(567\) −250.535 + 556.118i −0.441861 + 0.980808i
\(568\) −812.150 + 263.883i −1.42984 + 0.464583i
\(569\) −638.652 + 464.008i −1.12241 + 0.815480i −0.984573 0.174975i \(-0.944016\pi\)
−0.137839 + 0.990455i \(0.544016\pi\)
\(570\) −724.374 997.015i −1.27083 1.74915i
\(571\) 748.366i 1.31062i 0.755358 + 0.655312i \(0.227463\pi\)
−0.755358 + 0.655312i \(0.772537\pi\)
\(572\) −161.716 + 52.5447i −0.282720 + 0.0918613i
\(573\) 777.146i 1.35628i
\(574\) −147.573 + 639.906i −0.257096 + 1.11482i
\(575\) 801.487 1.39389
\(576\) 7.78405 + 23.9569i 0.0135140 + 0.0415918i
\(577\) −80.6643 −0.139799 −0.0698997 0.997554i \(-0.522268\pi\)
−0.0698997 + 0.997554i \(0.522268\pi\)
\(578\) −160.943 + 116.932i −0.278449 + 0.202305i
\(579\) 418.663 + 576.240i 0.723079 + 0.995233i
\(580\) −33.5051 103.118i −0.0577675 0.177790i
\(581\) 716.259 + 322.680i 1.23280 + 0.555387i
\(582\) −854.958 621.163i −1.46900 1.06729i
\(583\) 437.276 0.750045
\(584\) −95.6363 + 131.632i −0.163761 + 0.225397i
\(585\) 53.5034 73.6411i 0.0914588 0.125882i
\(586\) 621.123 451.272i 1.05994 0.770089i
\(587\) −282.134 868.320i −0.480638 1.47925i −0.838201 0.545362i \(-0.816392\pi\)
0.357563 0.933889i \(-0.383608\pi\)
\(588\) 184.511 + 40.9180i 0.313795 + 0.0695885i
\(589\) 482.471 + 664.064i 0.819135 + 1.12744i
\(590\) −29.9104 + 92.0547i −0.0506956 + 0.156025i
\(591\) 1.51329 + 1.09947i 0.00256056 + 0.00186035i
\(592\) 195.307 + 601.092i 0.329910 + 1.01536i
\(593\) −81.6774 + 251.377i −0.137736 + 0.423907i −0.996006 0.0892915i \(-0.971540\pi\)
0.858270 + 0.513199i \(0.171540\pi\)
\(594\) 452.155 + 146.914i 0.761203 + 0.247330i
\(595\) −651.097 293.324i −1.09428 0.492981i
\(596\) 18.1631 + 5.90153i 0.0304749 + 0.00990190i
\(597\) 79.3472 + 244.205i 0.132910 + 0.409054i
\(598\) −955.412 694.147i −1.59768 1.16078i
\(599\) −226.330 + 696.572i −0.377846 + 1.16289i 0.563692 + 0.825985i \(0.309380\pi\)
−0.941538 + 0.336906i \(0.890620\pi\)
\(600\) 423.395 307.614i 0.705658 0.512690i
\(601\) −259.603 −0.431952 −0.215976 0.976399i \(-0.569293\pi\)
−0.215976 + 0.976399i \(0.569293\pi\)
\(602\) 185.642 + 892.656i 0.308375 + 1.48282i
\(603\) −5.76766 7.93851i −0.00956495 0.0131650i
\(604\) −143.200 + 197.098i −0.237086 + 0.326321i
\(605\) 236.271 325.199i 0.390530 0.537518i
\(606\) −30.9519 −0.0510757
\(607\) 676.754 931.472i 1.11492 1.53455i 0.300948 0.953641i \(-0.402697\pi\)
0.813968 0.580910i \(-0.197303\pi\)
\(608\) −142.093 + 437.318i −0.233706 + 0.719273i
\(609\) −261.542 + 54.3918i −0.429462 + 0.0893133i
\(610\) −587.915 + 427.145i −0.963795 + 0.700238i
\(611\) −833.261 + 605.400i −1.36377 + 0.990834i
\(612\) −13.0514 −0.0213257
\(613\) −116.240 357.749i −0.189624 0.583603i 0.810373 0.585914i \(-0.199264\pi\)
−0.999997 + 0.00231082i \(0.999264\pi\)
\(614\) 467.724i 0.761766i
\(615\) −801.240 + 449.002i −1.30283 + 0.730084i
\(616\) −38.8712 + 354.822i −0.0631026 + 0.576009i
\(617\) 44.6077 + 137.288i 0.0722977 + 0.222510i 0.980676 0.195641i \(-0.0626786\pi\)
−0.908378 + 0.418150i \(0.862679\pi\)
\(618\) 892.561i 1.44427i
\(619\) −100.721 138.630i −0.162715 0.223958i 0.719872 0.694107i \(-0.244200\pi\)
−0.882587 + 0.470148i \(0.844200\pi\)
\(620\) 244.947 177.965i 0.395076 0.287040i
\(621\) 240.814 + 741.148i 0.387784 + 1.19348i
\(622\) 26.6440 82.0017i 0.0428360 0.131836i
\(623\) −283.757 257.764i −0.455468 0.413746i
\(624\) −1034.47 −1.65780
\(625\) 473.312 + 343.882i 0.757300 + 0.550211i
\(626\) 845.122 + 614.017i 1.35004 + 0.980858i
\(627\) 355.606 + 489.450i 0.567155 + 0.780621i
\(628\) 50.1882 + 154.463i 0.0799176 + 0.245961i
\(629\) 462.719 0.735642
\(630\) 42.3817 + 74.1582i 0.0672725 + 0.117712i
\(631\) 75.6271 232.756i 0.119853 0.368869i −0.873075 0.487585i \(-0.837878\pi\)
0.992928 + 0.118716i \(0.0378779\pi\)
\(632\) 241.340 332.175i 0.381866 0.525594i
\(633\) 490.998 159.535i 0.775668 0.252030i
\(634\) 452.448 + 147.009i 0.713640 + 0.231876i
\(635\) 1733.42 + 563.222i 2.72980 + 0.886964i
\(636\) −198.969 64.6491i −0.312845 0.101650i
\(637\) 424.550 720.634i 0.666484 1.13129i
\(638\) 69.6925 + 214.492i 0.109236 + 0.336194i
\(639\) 58.9639 81.1569i 0.0922753 0.127006i
\(640\) −1051.64 341.698i −1.64319 0.533904i
\(641\) 278.342 + 383.105i 0.434231 + 0.597667i 0.968918 0.247383i \(-0.0795705\pi\)
−0.534687 + 0.845050i \(0.679571\pi\)
\(642\) −885.343 −1.37904
\(643\) −305.636 940.650i −0.475328 1.46291i −0.845515 0.533952i \(-0.820706\pi\)
0.370187 0.928957i \(-0.379294\pi\)
\(644\) 227.071 129.772i 0.352594 0.201509i
\(645\) −749.539 + 1031.65i −1.16208 + 1.59946i
\(646\) 632.642 + 459.641i 0.979322 + 0.711519i
\(647\) 740.879i 1.14510i 0.819870 + 0.572550i \(0.194046\pi\)
−0.819870 + 0.572550i \(0.805954\pi\)
\(648\) 445.889 + 323.958i 0.688101 + 0.499934i
\(649\) 14.6835 45.1911i 0.0226248 0.0696318i
\(650\) 319.926 + 984.630i 0.492193 + 1.51481i
\(651\) −370.141 647.663i −0.568573 0.994874i
\(652\) 265.563 192.943i 0.407305 0.295925i
\(653\) 771.976i 1.18220i −0.806599 0.591099i \(-0.798694\pi\)
0.806599 0.591099i \(-0.201306\pi\)
\(654\) 394.943 128.325i 0.603889 0.196215i
\(655\) 303.162 0.462843
\(656\) 723.016 + 333.077i 1.10216 + 0.507739i
\(657\) 19.1136i 0.0290922i
\(658\) −196.784 946.234i −0.299064 1.43805i
\(659\) 1043.93i 1.58412i −0.610445 0.792059i \(-0.709009\pi\)
0.610445 0.792059i \(-0.290991\pi\)
\(660\) 180.539 131.169i 0.273544 0.198741i
\(661\) 337.064 + 463.929i 0.509931 + 0.701860i 0.983908 0.178678i \(-0.0571819\pi\)
−0.473977 + 0.880537i \(0.657182\pi\)
\(662\) 789.108 256.397i 1.19201 0.387306i
\(663\) −234.036 + 720.289i −0.352996 + 1.08641i
\(664\) 417.245 574.289i 0.628382 0.864893i
\(665\) 131.533 1200.65i 0.197795 1.80549i
\(666\) −44.7751 32.5310i −0.0672299 0.0488454i
\(667\) −217.290 + 299.075i −0.325773 + 0.448388i
\(668\) 147.283 107.007i 0.220483 0.160190i
\(669\) 289.514 94.0689i 0.432757 0.140611i
\(670\) 216.865 0.323678
\(671\) 288.616 209.692i 0.430129 0.312507i
\(672\) 171.647 381.009i 0.255428 0.566978i
\(673\) −560.312 + 771.204i −0.832559 + 1.14592i 0.154882 + 0.987933i \(0.450500\pi\)
−0.987441 + 0.157986i \(0.949500\pi\)
\(674\) 94.8657 + 291.967i 0.140750 + 0.433185i
\(675\) 211.113 649.739i 0.312760 0.962576i
\(676\) 46.7226 143.797i 0.0691163 0.212718i
\(677\) −844.573 274.418i −1.24752 0.405345i −0.390490 0.920607i \(-0.627694\pi\)
−0.857032 + 0.515263i \(0.827694\pi\)
\(678\) −70.7903 + 217.870i −0.104410 + 0.321342i
\(679\) −210.887 1014.05i −0.310584 1.49344i
\(680\) −379.286 + 522.042i −0.557773 + 0.767709i
\(681\) −35.9642 + 110.686i −0.0528109 + 0.162535i
\(682\) −509.504 + 370.176i −0.747073 + 0.542780i
\(683\) 947.992i 1.38798i −0.719983 0.693991i \(-0.755851\pi\)
0.719983 0.693991i \(-0.244149\pi\)
\(684\) −6.82144 20.9942i −0.00997286 0.0306933i
\(685\) 224.993 163.467i 0.328457 0.238638i
\(686\) 452.902 + 640.977i 0.660207 + 0.934369i
\(687\) 234.314 + 170.239i 0.341068 + 0.247800i
\(688\) 1105.22 1.60643
\(689\) −544.205 + 749.034i −0.789848 + 1.08713i
\(690\) 1474.03 + 478.941i 2.13627 + 0.694117i
\(691\) 276.910 + 852.242i 0.400738 + 1.23335i 0.924402 + 0.381421i \(0.124565\pi\)
−0.523663 + 0.851925i \(0.675435\pi\)
\(692\) −110.127 151.576i −0.159142 0.219041i
\(693\) −20.8058 36.4054i −0.0300228 0.0525331i
\(694\) 352.598i 0.508066i
\(695\) 299.807 + 922.710i 0.431376 + 1.32764i
\(696\) 241.387i 0.346820i
\(697\) 395.491 428.073i 0.567419 0.614165i
\(698\) 1210.16i 1.73376i
\(699\) 986.764 320.619i 1.41168 0.458683i
\(700\) −227.917 24.9686i −0.325596 0.0356695i
\(701\) −5.91320 + 4.29619i −0.00843538 + 0.00612866i −0.591995 0.805942i \(-0.701659\pi\)
0.583560 + 0.812070i \(0.301659\pi\)
\(702\) −814.379 + 591.681i −1.16008 + 0.842850i
\(703\) 241.845 + 744.323i 0.344019 + 1.05878i
\(704\) 259.922 + 84.4538i 0.369208 + 0.119963i
\(705\) 794.527 1093.57i 1.12699 1.55117i
\(706\) 779.618i 1.10428i
\(707\) −22.4542 20.3973i −0.0317599 0.0288505i
\(708\) −13.3626 + 18.3920i −0.0188737 + 0.0259774i
\(709\) −114.025 156.942i −0.160825 0.221356i 0.720998 0.692937i \(-0.243684\pi\)
−0.881823 + 0.471581i \(0.843684\pi\)
\(710\) 685.105 + 2108.54i 0.964937 + 2.96977i
\(711\) 48.2334i 0.0678388i
\(712\) −280.243 + 203.608i −0.393599 + 0.285967i
\(713\) −981.780 319.000i −1.37697 0.447405i
\(714\) −526.037 477.850i −0.736747 0.669258i
\(715\) −305.182 939.253i −0.426828 1.31364i
\(716\) −271.852 88.3301i −0.379682 0.123366i
\(717\) 252.775 + 82.1315i 0.352545 + 0.114549i
\(718\) −169.342 + 521.182i −0.235853 + 0.725880i
\(719\) 40.6720 125.175i 0.0565674 0.174097i −0.918781 0.394768i \(-0.870825\pi\)
0.975348 + 0.220672i \(0.0708249\pi\)
\(720\) 98.4712 31.9952i 0.136766 0.0444378i
\(721\) 588.199 647.514i 0.815810 0.898077i
\(722\) −153.459 + 472.299i −0.212547 + 0.654153i
\(723\) 720.172 + 991.231i 0.996088 + 1.37100i
\(724\) −131.287 −0.181336
\(725\) 308.221 100.147i 0.425132 0.138134i
\(726\) 323.629 235.131i 0.445771 0.323871i
\(727\) −148.272 107.726i −0.203950 0.148178i 0.481122 0.876654i \(-0.340229\pi\)
−0.685072 + 0.728475i \(0.740229\pi\)
\(728\) −559.417 508.172i −0.768429 0.698039i
\(729\) 659.286 0.904370
\(730\) 341.749 + 248.295i 0.468149 + 0.340130i
\(731\) 250.043 769.552i 0.342056 1.05274i
\(732\) −162.328 + 52.7436i −0.221760 + 0.0720541i
\(733\) −75.2727 103.604i −0.102691 0.141342i 0.754579 0.656210i \(-0.227841\pi\)
−0.857270 + 0.514867i \(0.827841\pi\)
\(734\) −353.993 487.230i −0.482280 0.663801i
\(735\) −237.654 + 1071.65i −0.323338 + 1.45803i
\(736\) −178.702 549.987i −0.242801 0.747266i
\(737\) −106.462 −0.144453
\(738\) −68.3650 + 13.6179i −0.0926355 + 0.0184525i
\(739\) 1169.03 1.58190 0.790952 0.611878i \(-0.209586\pi\)
0.790952 + 0.611878i \(0.209586\pi\)
\(740\) 274.552 89.2072i 0.371016 0.120550i
\(741\) −1280.97 −1.72870
\(742\) −431.081 754.294i −0.580972 1.01657i
\(743\) 270.872 196.800i 0.364566 0.264873i −0.390388 0.920650i \(-0.627659\pi\)
0.754954 + 0.655778i \(0.227659\pi\)
\(744\) −641.070 + 208.296i −0.861653 + 0.279968i
\(745\) −34.2764 + 105.492i −0.0460086 + 0.141600i
\(746\) −1083.19 786.983i −1.45200 1.05494i
\(747\) 83.3894i 0.111632i
\(748\) −83.2316 + 114.558i −0.111272 + 0.153153i
\(749\) −642.277 583.443i −0.857513 0.778962i
\(750\) −45.4128 62.5054i −0.0605505 0.0833405i
\(751\) 924.511 300.392i 1.23104 0.399989i 0.379949 0.925007i \(-0.375942\pi\)
0.851091 + 0.525018i \(0.175942\pi\)
\(752\) −1171.56 −1.55792
\(753\) −298.898 411.397i −0.396942 0.546344i
\(754\) −454.149 147.562i −0.602320 0.195706i
\(755\) −1144.75 831.712i −1.51623 1.10160i
\(756\) −45.3907 218.261i −0.0600406 0.288705i
\(757\) 493.483 + 160.342i 0.651892 + 0.211813i 0.616248 0.787552i \(-0.288652\pi\)
0.0356440 + 0.999365i \(0.488652\pi\)
\(758\) 371.384 1143.00i 0.489953 1.50792i
\(759\) −723.622 235.119i −0.953389 0.309775i
\(760\) −1037.99 337.263i −1.36577 0.443766i
\(761\) −720.033 + 233.953i −0.946167 + 0.307428i −0.741157 0.671332i \(-0.765723\pi\)
−0.205010 + 0.978760i \(0.565723\pi\)
\(762\) 1467.42 + 1066.14i 1.92575 + 1.39914i
\(763\) 371.080 + 167.174i 0.486343 + 0.219101i
\(764\) 180.833 + 248.895i 0.236693 + 0.325779i
\(765\) 75.8029i 0.0990887i
\(766\) −6.66016 20.4979i −0.00869473 0.0267596i
\(767\) 59.1362 + 81.3939i 0.0771006 + 0.106120i
\(768\) −547.829 398.021i −0.713318 0.518256i
\(769\) 140.969 194.027i 0.183314 0.252311i −0.707463 0.706750i \(-0.750160\pi\)
0.890778 + 0.454440i \(0.150160\pi\)
\(770\) 921.202 + 100.919i 1.19637 + 0.131064i
\(771\) −532.710 387.037i −0.690934 0.501993i
\(772\) −268.169 87.1335i −0.347369 0.112867i
\(773\) 72.2115 + 222.244i 0.0934172 + 0.287508i 0.986838 0.161712i \(-0.0517017\pi\)
−0.893421 + 0.449221i \(0.851702\pi\)
\(774\) −78.2981 + 56.8869i −0.101160 + 0.0734973i
\(775\) 531.937 + 732.148i 0.686370 + 0.944707i
\(776\) −935.899 −1.20606
\(777\) −144.818 696.354i −0.186381 0.896209i
\(778\) 1388.57 1.78480
\(779\) 895.300 + 412.444i 1.14929 + 0.529453i
\(780\) 472.499i 0.605768i
\(781\) −336.328 1035.11i −0.430638 1.32537i
\(782\) −983.458 −1.25762
\(783\) 185.215 + 254.927i 0.236546 + 0.325577i
\(784\) 872.493 379.302i 1.11287 0.483803i
\(785\) −897.131 + 291.496i −1.14284 + 0.371332i
\(786\) 286.933 + 93.2303i 0.365055 + 0.118614i
\(787\) −708.612 + 975.320i −0.900396 + 1.23929i 0.0699458 + 0.997551i \(0.477717\pi\)
−0.970342 + 0.241738i \(0.922283\pi\)
\(788\) −0.740493 −0.000939712
\(789\) −618.729 + 851.608i −0.784194 + 1.07935i
\(790\) −862.408 626.576i −1.09166 0.793134i
\(791\) −194.932 + 111.404i −0.246437 + 0.140840i
\(792\) −36.0348 + 11.7084i −0.0454985 + 0.0147834i
\(793\) 755.355i 0.952529i
\(794\) 609.511 442.836i 0.767646 0.557727i
\(795\) 375.485 1155.62i 0.472308 1.45362i
\(796\) −82.2363 59.7482i −0.103312 0.0750605i
\(797\) −428.509 + 139.231i −0.537652 + 0.174694i −0.565241 0.824926i \(-0.691217\pi\)
0.0275894 + 0.999619i \(0.491217\pi\)
\(798\) 493.724 1095.93i 0.618702 1.37335i
\(799\) −265.051 + 815.742i −0.331728 + 1.02095i
\(800\) −156.662 + 482.155i −0.195827 + 0.602693i
\(801\) 12.5747 38.7009i 0.0156987 0.0483157i
\(802\) 561.909 + 1729.38i 0.700634 + 2.15633i
\(803\) −167.770 121.892i −0.208929 0.151795i
\(804\) 48.4424 + 15.7399i 0.0602518 + 0.0195770i
\(805\) 753.719 + 1318.84i 0.936297 + 1.63831i
\(806\) 1333.45i 1.65441i
\(807\) 767.982 249.532i 0.951650 0.309210i
\(808\) −22.1762 + 16.1119i −0.0274457 + 0.0199405i
\(809\) 454.457 625.506i 0.561751 0.773184i −0.429797 0.902926i \(-0.641415\pi\)
0.991548 + 0.129742i \(0.0414148\pi\)
\(810\) 841.072 1157.64i 1.03836 1.42918i
\(811\) 1200.01i 1.47967i 0.672788 + 0.739835i \(0.265097\pi\)
−0.672788 + 0.739835i \(0.734903\pi\)
\(812\) 71.1074 78.2779i 0.0875707 0.0964014i
\(813\) −921.903 299.545i −1.13395 0.368443i
\(814\) −571.083 + 185.556i −0.701576 + 0.227956i
\(815\) 1120.62 + 1542.40i 1.37500 + 1.89252i
\(816\) −696.945 + 506.360i −0.854099 + 0.620539i
\(817\) 1368.58 1.67513
\(818\) 1136.09 369.138i 1.38886 0.451269i
\(819\) 88.2543 + 9.66839i 0.107759 + 0.0118051i
\(820\) 152.135 330.241i 0.185530 0.402733i
\(821\) 1016.78 1.23846 0.619232 0.785208i \(-0.287444\pi\)
0.619232 + 0.785208i \(0.287444\pi\)
\(822\) 263.219 85.5250i 0.320218 0.104045i
\(823\) 952.384i 1.15721i −0.815608 0.578605i \(-0.803597\pi\)
0.815608 0.578605i \(-0.196403\pi\)
\(824\) −464.621 639.495i −0.563860 0.776086i
\(825\) 392.065 + 539.631i 0.475230 + 0.654098i
\(826\) −92.4293 + 19.2221i −0.111900 + 0.0232713i
\(827\) 1420.06 + 461.404i 1.71712 + 0.557925i 0.991492 0.130167i \(-0.0415512\pi\)
0.725624 + 0.688091i \(0.241551\pi\)
\(828\) 22.4598 + 16.3180i 0.0271254 + 0.0197078i
\(829\) 1287.44i 1.55301i −0.630113 0.776504i \(-0.716991\pi\)
0.630113 0.776504i \(-0.283009\pi\)
\(830\) −1490.99 1083.27i −1.79638 1.30514i
\(831\) 26.0135 + 18.8999i 0.0313039 + 0.0227436i
\(832\) −468.148 + 340.129i −0.562677 + 0.408809i
\(833\) −66.7125 693.319i −0.0800870 0.832315i
\(834\) 965.513i 1.15769i
\(835\) 621.502 + 855.424i 0.744314 + 1.02446i
\(836\) −227.779 74.0099i −0.272463 0.0885285i
\(837\) −517.205 + 711.871i −0.617927 + 0.850503i
\(838\) 1401.63 455.416i 1.67259 0.543456i
\(839\) −314.424 + 967.698i −0.374761 + 1.15339i 0.568879 + 0.822421i \(0.307377\pi\)
−0.943640 + 0.330974i \(0.892623\pi\)
\(840\) 904.337 + 407.410i 1.07659 + 0.485012i
\(841\) 213.692 657.675i 0.254092 0.782016i
\(842\) 650.371 + 211.318i 0.772412 + 0.250972i
\(843\) 885.586 287.744i 1.05052 0.341334i
\(844\) −120.129 + 165.344i −0.142333 + 0.195905i
\(845\) 835.182 + 271.367i 0.988381 + 0.321144i
\(846\) 82.9976 60.3013i 0.0981059 0.0712781i
\(847\) 389.730 + 42.6955i 0.460130 + 0.0504079i
\(848\) −1001.59 + 325.437i −1.18112 + 0.383770i
\(849\) −838.806 1154.52i −0.987993 1.35986i
\(850\) 697.505 + 506.767i 0.820594 + 0.596196i
\(851\) −796.284 578.535i −0.935704 0.679829i
\(852\) 520.722i 0.611176i
\(853\) −675.255 + 929.409i −0.791624 + 1.08958i 0.202280 + 0.979328i \(0.435165\pi\)
−0.993904 + 0.110249i \(0.964835\pi\)
\(854\) −646.242 291.137i −0.756724 0.340910i
\(855\) 121.935 39.6192i 0.142615 0.0463383i
\(856\) −634.324 + 460.863i −0.741033 + 0.538392i
\(857\) −396.692 545.999i −0.462884 0.637105i 0.512220 0.858855i \(-0.328823\pi\)
−0.975104 + 0.221749i \(0.928823\pi\)
\(858\) 982.824i 1.14548i
\(859\) −224.152 + 72.8315i −0.260946 + 0.0847864i −0.436568 0.899671i \(-0.643806\pi\)
0.175622 + 0.984458i \(0.443806\pi\)
\(860\) 504.815i 0.586994i
\(861\) −767.992 461.207i −0.891977 0.535665i
\(862\) −172.621 −0.200257
\(863\) −260.621 802.109i −0.301994 0.929443i −0.980782 0.195108i \(-0.937494\pi\)
0.678788 0.734335i \(-0.262506\pi\)
\(864\) −492.927 −0.570517
\(865\) 880.362 639.620i 1.01776 0.739446i
\(866\) 425.555 + 585.726i 0.491403 + 0.676359i
\(867\) −83.8608 258.097i −0.0967253 0.297690i
\(868\) 269.249 + 121.298i 0.310194 + 0.139745i
\(869\) 423.369 + 307.596i 0.487191 + 0.353965i
\(870\) 626.698 0.720343
\(871\) 132.496 182.365i 0.152119 0.209374i
\(872\) 216.167 297.528i 0.247898 0.341202i
\(873\) 88.9456 64.6228i 0.101885 0.0740238i
\(874\) −514.015 1581.98i −0.588118 1.81004i
\(875\) 8.24616 75.2721i 0.00942419 0.0860252i
\(876\) 58.3175 + 80.2671i 0.0665725 + 0.0916291i
\(877\) −100.883 + 310.486i −0.115032 + 0.354032i −0.991954 0.126601i \(-0.959593\pi\)
0.876922 + 0.480633i \(0.159593\pi\)
\(878\) −298.197 216.653i −0.339632 0.246757i
\(879\) 323.641 + 996.064i 0.368192 + 1.13318i
\(880\) 347.136 1068.37i 0.394472 1.21406i
\(881\) −543.264 176.517i −0.616644 0.200360i −0.0159945 0.999872i \(-0.505091\pi\)
−0.600650 + 0.799512i \(0.705091\pi\)
\(882\) −42.2877 + 71.7793i −0.0479452 + 0.0813824i
\(883\) −369.067 119.917i −0.417970 0.135807i 0.0924793 0.995715i \(-0.470521\pi\)
−0.510449 + 0.859908i \(0.670521\pi\)
\(884\) −92.6488 285.144i −0.104806 0.322561i
\(885\) −106.821 77.6103i −0.120702 0.0876953i
\(886\) −61.8139 + 190.244i −0.0697674 + 0.214722i
\(887\) 146.926 106.748i 0.165644 0.120347i −0.501875 0.864940i \(-0.667356\pi\)
0.667519 + 0.744593i \(0.267356\pi\)
\(888\) −642.691 −0.723751
\(889\) 361.958 + 1740.47i 0.407152 + 1.95779i
\(890\) 528.616 + 727.578i 0.593951 + 0.817503i
\(891\) −412.895 + 568.301i −0.463406 + 0.637824i
\(892\) −70.8336 + 97.4940i −0.0794098 + 0.109298i
\(893\) −1450.72 −1.62455
\(894\) −64.8830 + 89.3037i −0.0725760 + 0.0998923i
\(895\) 513.025 1578.93i 0.573213 1.76417i
\(896\) −219.595 1055.92i −0.245083 1.17848i
\(897\) 1303.32 946.918i 1.45298 1.05565i
\(898\) −84.5743 + 61.4469i −0.0941808 + 0.0684263i
\(899\) −417.414 −0.464309
\(900\) −7.52082 23.1467i −0.00835646 0.0257185i
\(901\) 771.022i 0.855740i
\(902\) −316.448 + 686.920i −0.350830 + 0.761552i
\(903\) −1236.37 135.446i −1.36918 0.149996i
\(904\) 62.6925 + 192.948i 0.0693501 + 0.213438i
\(905\) 762.524i 0.842568i
\(906\) −827.698 1139.23i −0.913574 1.25743i
\(907\) −512.511 + 372.361i −0.565062 + 0.410541i −0.833308 0.552809i \(-0.813556\pi\)
0.268246 + 0.963350i \(0.413556\pi\)
\(908\) −14.2373 43.8179i −0.0156798 0.0482576i
\(909\) 0.995059 3.06248i 0.00109467 0.00336906i
\(910\) −1319.34 + 1452.38i −1.44982 + 1.59602i
\(911\) −1416.39 −1.55476 −0.777382 0.629028i \(-0.783453\pi\)
−0.777382 + 0.629028i \(0.783453\pi\)
\(912\) −1178.79 856.441i −1.29253 0.939080i
\(913\) 731.951 + 531.794i 0.801699 + 0.582468i
\(914\) −529.146 728.307i −0.578934 0.796835i
\(915\) −306.337 942.810i −0.334795 1.03039i
\(916\) −114.656 −0.125170
\(917\) 146.719 + 256.724i 0.159998 + 0.279961i
\(918\) −259.044 + 797.257i −0.282183 + 0.868471i
\(919\) 107.164 147.498i 0.116609 0.160499i −0.746722 0.665136i \(-0.768374\pi\)
0.863332 + 0.504637i \(0.168374\pi\)
\(920\) 1305.41 424.154i 1.41893 0.461037i
\(921\) 606.816 + 197.167i 0.658867 + 0.214079i
\(922\) 504.702 + 163.987i 0.547399 + 0.177861i
\(923\) 2191.67 + 712.118i 2.37451 + 0.771525i
\(924\) 198.450 + 89.4032i 0.214773 + 0.0967568i
\(925\) 266.641 + 820.636i 0.288260 + 0.887174i
\(926\) −564.962 + 777.604i −0.610110 + 0.839745i
\(927\) 88.3129 + 28.6946i 0.0952674 + 0.0309542i
\(928\) −137.444 189.175i −0.148107 0.203852i
\(929\) −255.050 −0.274542 −0.137271 0.990534i \(-0.543833\pi\)
−0.137271 + 0.990534i \(0.543833\pi\)
\(930\) 540.787 + 1664.37i 0.581492 + 1.78965i
\(931\) 1080.39 469.684i 1.16047 0.504494i
\(932\) −241.425 + 332.293i −0.259040 + 0.356538i
\(933\) 95.1558 + 69.1348i 0.101989 + 0.0740994i
\(934\) 851.808i 0.912000i
\(935\) −665.361 483.413i −0.711616 0.517019i
\(936\) 24.7906 76.2975i 0.0264856 0.0815144i
\(937\) −193.174 594.530i −0.206163 0.634504i −0.999664 0.0259346i \(-0.991744\pi\)
0.793501 0.608569i \(-0.208256\pi\)
\(938\) 104.954 + 183.645i 0.111891 + 0.195784i
\(939\) −1152.87 + 837.609i −1.22776 + 0.892023i
\(940\) 535.115i 0.569271i
\(941\) 1246.97 405.167i 1.32516 0.430570i 0.440895 0.897559i \(-0.354661\pi\)
0.884263 + 0.466988i \(0.154661\pi\)
\(942\) −938.748 −0.996547
\(943\) −1215.81 + 242.183i −1.28930 + 0.256822i
\(944\) 114.439i 0.121228i
\(945\) 1267.67 263.631i 1.34145 0.278975i
\(946\) 1050.04i 1.10998i
\(947\) −352.074 + 255.797i −0.371778 + 0.270113i −0.757948 0.652315i \(-0.773798\pi\)
0.386170 + 0.922428i \(0.373798\pi\)
\(948\) −147.165 202.555i −0.155237 0.213666i
\(949\) 417.590 135.683i 0.440032 0.142975i
\(950\) −450.619 + 1386.86i −0.474336 + 1.45986i
\(951\) −381.454 + 525.026i −0.401108 + 0.552078i
\(952\) −625.635 68.5392i −0.657180 0.0719950i
\(953\) −673.809 489.551i −0.707040 0.513694i 0.175178 0.984537i \(-0.443950\pi\)
−0.882217 + 0.470842i \(0.843950\pi\)
\(954\) 54.2060 74.6081i 0.0568197 0.0782056i
\(955\) −1445.60 + 1050.29i −1.51371 + 1.09978i
\(956\) −100.067 + 32.5137i −0.104673 + 0.0340102i
\(957\) −307.656 −0.321479
\(958\) 1508.02 1095.64i 1.57414 1.14368i
\(959\) 247.315 + 111.417i 0.257888 + 0.116181i
\(960\) 446.386 614.397i 0.464985 0.639997i
\(961\) −63.2273 194.594i −0.0657933 0.202491i
\(962\) 392.883 1209.17i 0.408402 1.25693i
\(963\) 28.4625 87.5987i 0.0295561 0.0909644i
\(964\) −461.297 149.884i −0.478524 0.155482i
\(965\) 506.075 1557.54i 0.524430 1.61403i
\(966\) 307.794 + 1480.02i 0.318628 + 1.53212i
\(967\) 810.545 1115.62i 0.838206 1.15369i −0.148133 0.988967i \(-0.547326\pi\)
0.986340 0.164725i \(-0.0526735\pi\)
\(968\) 109.475 336.929i 0.113094 0.348067i
\(969\) −863.016 + 627.018i −0.890626 + 0.647077i
\(970\) 2429.82i 2.50497i
\(971\) −202.104 622.012i −0.208140 0.640589i −0.999570 0.0293291i \(-0.990663\pi\)
0.791430 0.611260i \(-0.209337\pi\)
\(972\) 40.0117 29.0702i 0.0411643 0.0299076i
\(973\) −636.275 + 700.437i −0.653931 + 0.719874i
\(974\) −60.9600 44.2900i −0.0625873 0.0454723i
\(975\) −1412.30 −1.44851
\(976\) −505.022 + 695.103i −0.517440 + 0.712196i
\(977\) −883.189 286.966i −0.903981 0.293721i −0.180102 0.983648i \(-0.557643\pi\)
−0.723879 + 0.689927i \(0.757643\pi\)
\(978\) 586.303 + 1804.45i 0.599492 + 1.84505i
\(979\) −259.506 357.179i −0.265072 0.364841i
\(980\) −173.248 398.515i −0.176784 0.406648i
\(981\) 43.2024i 0.0440392i
\(982\) −224.329 690.414i −0.228441 0.703069i
\(983\) 725.111i 0.737651i −0.929499 0.368825i \(-0.879760\pi\)
0.929499 0.368825i \(-0.120240\pi\)
\(984\) −549.315 + 594.569i −0.558247 + 0.604237i
\(985\) 4.30082i 0.00436631i
\(986\) −378.200 + 122.885i −0.383570 + 0.124629i
\(987\) 1310.58 + 143.576i 1.32784 + 0.145467i
\(988\) 410.254 298.067i 0.415237 0.301687i
\(989\) −1392.46 + 1011.68i −1.40795 + 1.02293i
\(990\) 30.3979 + 93.5551i 0.0307049 + 0.0945001i
\(991\) 85.0074 + 27.6206i 0.0857794 + 0.0278714i 0.351592 0.936153i \(-0.385640\pi\)
−0.265813 + 0.964025i \(0.585640\pi\)
\(992\) 383.804 528.261i 0.386900 0.532522i
\(993\) 1131.86i 1.13984i
\(994\) −1453.99 + 1600.61i −1.46276 + 1.61027i
\(995\) 347.020 477.632i 0.348764 0.480032i
\(996\) −254.430 350.192i −0.255451 0.351599i
\(997\) −129.483 398.507i −0.129872 0.399706i 0.864885 0.501970i \(-0.167391\pi\)
−0.994757 + 0.102264i \(0.967391\pi\)
\(998\) 304.052i 0.304661i
\(999\) −678.741 + 493.134i −0.679421 + 0.493628i
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 287.3.p.a.146.14 yes 216
7.6 odd 2 inner 287.3.p.a.146.13 216
41.25 even 10 inner 287.3.p.a.230.13 yes 216
287.230 odd 10 inner 287.3.p.a.230.14 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.p.a.146.13 216 7.6 odd 2 inner
287.3.p.a.146.14 yes 216 1.1 even 1 trivial
287.3.p.a.230.13 yes 216 41.25 even 10 inner
287.3.p.a.230.14 yes 216 287.230 odd 10 inner