Properties

Label 690.2.m.b.331.1
Level $690$
Weight $2$
Character 690.331
Analytic conductor $5.510$
Analytic rank $0$
Dimension $10$
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] = [690,2,Mod(31,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\), degree \(10\), 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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 331.1
Root \(0.654861 - 0.755750i\) of defining polynomial
Character \(\chi\) \(=\) 690.331
Dual form 690.2.m.b.271.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.24302 - 2.72183i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.24302 - 2.72183i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(1.52977 + 0.449181i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-0.404992 - 0.886808i) q^{13} +(0.425839 - 2.96177i) q^{14} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-0.675969 - 0.434419i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-1.37491 + 0.883600i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-2.87102 + 0.843008i) q^{21} +1.59435 q^{22} +(-4.04911 - 2.56996i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(-0.638429 - 0.736786i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.425839 - 2.96177i) q^{28} +(-1.50468 - 0.966997i) q^{29} +(-0.415415 + 0.909632i) q^{30} +(3.90897 - 4.51120i) q^{31} +(0.142315 - 0.989821i) q^{32} +(-0.662317 - 1.45027i) q^{33} +(-0.770978 - 0.226380i) q^{34} +(-2.87102 - 0.843008i) q^{35} +(0.415415 + 0.909632i) q^{36} +(0.999396 - 6.95095i) q^{37} +(-1.07028 + 1.23516i) q^{38} +(-0.404992 + 0.886808i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.899209 + 6.25413i) q^{41} +(-2.51722 + 1.61772i) q^{42} +(-1.02231 - 1.17981i) q^{43} +(1.52977 - 0.449181i) q^{44} +1.00000 q^{45} +(-4.60914 - 1.32509i) q^{46} +4.24399 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-1.27923 - 1.47631i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(0.114354 + 0.795348i) q^{51} +(-0.820145 - 0.527075i) q^{52} +(-0.819203 + 1.79380i) q^{53} +(0.654861 - 0.755750i) q^{54} +(0.226900 - 1.57812i) q^{55} +(-1.24302 - 2.72183i) q^{56} +(1.56815 + 0.460451i) q^{57} +(-1.71616 - 0.503910i) q^{58} +(2.74441 + 6.00941i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(-1.52177 + 1.75622i) q^{61} +(2.47968 - 5.42975i) q^{62} +(2.51722 + 1.61772i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.820145 + 0.527075i) q^{65} +(-1.04408 - 1.20493i) q^{66} +(10.7115 - 3.14518i) q^{67} -0.803526 q^{68} +(0.709362 + 4.74308i) q^{69} -2.99223 q^{70} +(4.80594 - 1.41115i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-3.34748 + 2.15129i) q^{73} +(-0.999396 - 6.95095i) q^{74} +(0.841254 + 0.540641i) q^{75} +(-0.678936 + 1.48666i) q^{76} +(3.12412 - 3.60543i) q^{77} +(-0.138744 + 0.964985i) q^{78} +(0.632393 + 1.38475i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(2.62478 + 5.74746i) q^{82} +(-1.99366 + 13.8662i) q^{83} +(-1.95949 + 2.26138i) q^{84} +(-0.333797 + 0.730913i) q^{85} +(-1.31329 - 0.844002i) q^{86} +(0.254546 + 1.77041i) q^{87} +(1.34125 - 0.861971i) q^{88} +(3.91232 + 4.51506i) q^{89} +(0.959493 - 0.281733i) q^{90} -2.91715 q^{91} +(-4.79575 + 0.0271313i) q^{92} -5.96917 q^{93} +(4.07208 - 1.19567i) q^{94} +(1.07028 + 1.23516i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.0304261 + 0.211618i) q^{97} +(-1.64333 - 1.05610i) q^{98} +(-0.662317 + 1.45027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.959493 0.281733i 0.678464 0.199215i
\(3\) −0.654861 0.755750i −0.378084 0.436332i
\(4\) 0.841254 0.540641i 0.420627 0.270320i
\(5\) −0.142315 0.989821i −0.0636451 0.442662i
\(6\) −0.841254 0.540641i −0.343440 0.220716i
\(7\) 1.24302 2.72183i 0.469816 1.02875i −0.515323 0.856996i \(-0.672328\pi\)
0.985139 0.171758i \(-0.0549447\pi\)
\(8\) 0.654861 0.755750i 0.231528 0.267198i
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) −0.415415 0.909632i −0.131366 0.287651i
\(11\) 1.52977 + 0.449181i 0.461243 + 0.135433i 0.504095 0.863648i \(-0.331826\pi\)
−0.0428521 + 0.999081i \(0.513644\pi\)
\(12\) −0.959493 0.281733i −0.276982 0.0813292i
\(13\) −0.404992 0.886808i −0.112324 0.245956i 0.845118 0.534579i \(-0.179530\pi\)
−0.957443 + 0.288623i \(0.906803\pi\)
\(14\) 0.425839 2.96177i 0.113810 0.791567i
\(15\) −0.654861 + 0.755750i −0.169084 + 0.195134i
\(16\) 0.415415 0.909632i 0.103854 0.227408i
\(17\) −0.675969 0.434419i −0.163947 0.105362i 0.456095 0.889931i \(-0.349248\pi\)
−0.620041 + 0.784569i \(0.712884\pi\)
\(18\) 0.142315 + 0.989821i 0.0335439 + 0.233303i
\(19\) −1.37491 + 0.883600i −0.315426 + 0.202712i −0.688768 0.724982i \(-0.741848\pi\)
0.373342 + 0.927694i \(0.378212\pi\)
\(20\) −0.654861 0.755750i −0.146431 0.168991i
\(21\) −2.87102 + 0.843008i −0.626508 + 0.183959i
\(22\) 1.59435 0.339917
\(23\) −4.04911 2.56996i −0.844299 0.535873i
\(24\) −1.00000 −0.204124
\(25\) −0.959493 + 0.281733i −0.191899 + 0.0563465i
\(26\) −0.638429 0.736786i −0.125206 0.144496i
\(27\) 0.841254 0.540641i 0.161899 0.104046i
\(28\) −0.425839 2.96177i −0.0804759 0.559722i
\(29\) −1.50468 0.966997i −0.279411 0.179567i 0.393428 0.919355i \(-0.371289\pi\)
−0.672839 + 0.739789i \(0.734925\pi\)
\(30\) −0.415415 + 0.909632i −0.0758441 + 0.166075i
\(31\) 3.90897 4.51120i 0.702073 0.810235i −0.286958 0.957943i \(-0.592644\pi\)
0.989031 + 0.147708i \(0.0471896\pi\)
\(32\) 0.142315 0.989821i 0.0251579 0.174977i
\(33\) −0.662317 1.45027i −0.115295 0.252460i
\(34\) −0.770978 0.226380i −0.132222 0.0388238i
\(35\) −2.87102 0.843008i −0.485291 0.142494i
\(36\) 0.415415 + 0.909632i 0.0692358 + 0.151605i
\(37\) 0.999396 6.95095i 0.164300 1.14273i −0.726113 0.687575i \(-0.758675\pi\)
0.890413 0.455154i \(-0.150416\pi\)
\(38\) −1.07028 + 1.23516i −0.173622 + 0.200370i
\(39\) −0.404992 + 0.886808i −0.0648505 + 0.142003i
\(40\) −0.841254 0.540641i −0.133014 0.0854828i
\(41\) 0.899209 + 6.25413i 0.140433 + 0.976731i 0.931172 + 0.364579i \(0.118787\pi\)
−0.790740 + 0.612153i \(0.790304\pi\)
\(42\) −2.51722 + 1.61772i −0.388416 + 0.249620i
\(43\) −1.02231 1.17981i −0.155901 0.179919i 0.672426 0.740165i \(-0.265252\pi\)
−0.828327 + 0.560245i \(0.810707\pi\)
\(44\) 1.52977 0.449181i 0.230621 0.0677165i
\(45\) 1.00000 0.149071
\(46\) −4.60914 1.32509i −0.679580 0.195374i
\(47\) 4.24399 0.619050 0.309525 0.950891i \(-0.399830\pi\)
0.309525 + 0.950891i \(0.399830\pi\)
\(48\) −0.959493 + 0.281733i −0.138491 + 0.0406646i
\(49\) −1.27923 1.47631i −0.182747 0.210901i
\(50\) −0.841254 + 0.540641i −0.118971 + 0.0764582i
\(51\) 0.114354 + 0.795348i 0.0160127 + 0.111371i
\(52\) −0.820145 0.527075i −0.113734 0.0730922i
\(53\) −0.819203 + 1.79380i −0.112526 + 0.246398i −0.957514 0.288388i \(-0.906881\pi\)
0.844987 + 0.534786i \(0.179608\pi\)
\(54\) 0.654861 0.755750i 0.0891153 0.102844i
\(55\) 0.226900 1.57812i 0.0305952 0.212794i
\(56\) −1.24302 2.72183i −0.166105 0.363719i
\(57\) 1.56815 + 0.460451i 0.207707 + 0.0609883i
\(58\) −1.71616 0.503910i −0.225343 0.0661667i
\(59\) 2.74441 + 6.00941i 0.357291 + 0.782359i 0.999870 + 0.0161390i \(0.00513744\pi\)
−0.642578 + 0.766220i \(0.722135\pi\)
\(60\) −0.142315 + 0.989821i −0.0183728 + 0.127785i
\(61\) −1.52177 + 1.75622i −0.194843 + 0.224861i −0.844761 0.535143i \(-0.820258\pi\)
0.649918 + 0.760004i \(0.274803\pi\)
\(62\) 2.47968 5.42975i 0.314920 0.689579i
\(63\) 2.51722 + 1.61772i 0.317140 + 0.203814i
\(64\) −0.142315 0.989821i −0.0177894 0.123728i
\(65\) −0.820145 + 0.527075i −0.101726 + 0.0653756i
\(66\) −1.04408 1.20493i −0.128517 0.148317i
\(67\) 10.7115 3.14518i 1.30862 0.384245i 0.448245 0.893911i \(-0.352049\pi\)
0.860372 + 0.509666i \(0.170231\pi\)
\(68\) −0.803526 −0.0974419
\(69\) 0.709362 + 4.74308i 0.0853972 + 0.571000i
\(70\) −2.99223 −0.357640
\(71\) 4.80594 1.41115i 0.570360 0.167473i 0.0161791 0.999869i \(-0.494850\pi\)
0.554181 + 0.832396i \(0.313032\pi\)
\(72\) 0.654861 + 0.755750i 0.0771761 + 0.0890659i
\(73\) −3.34748 + 2.15129i −0.391792 + 0.251790i −0.721675 0.692232i \(-0.756627\pi\)
0.329882 + 0.944022i \(0.392991\pi\)
\(74\) −0.999396 6.95095i −0.116177 0.808032i
\(75\) 0.841254 + 0.540641i 0.0971396 + 0.0624278i
\(76\) −0.678936 + 1.48666i −0.0778793 + 0.170532i
\(77\) 3.12412 3.60543i 0.356027 0.410876i
\(78\) −0.138744 + 0.964985i −0.0157097 + 0.109263i
\(79\) 0.632393 + 1.38475i 0.0711498 + 0.155796i 0.941865 0.335991i \(-0.109071\pi\)
−0.870715 + 0.491787i \(0.836344\pi\)
\(80\) −0.959493 0.281733i −0.107275 0.0314987i
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 2.62478 + 5.74746i 0.289858 + 0.634701i
\(83\) −1.99366 + 13.8662i −0.218833 + 1.52202i 0.523524 + 0.852011i \(0.324617\pi\)
−0.742357 + 0.670005i \(0.766292\pi\)
\(84\) −1.95949 + 2.26138i −0.213798 + 0.246736i
\(85\) −0.333797 + 0.730913i −0.0362054 + 0.0792787i
\(86\) −1.31329 0.844002i −0.141616 0.0910111i
\(87\) 0.254546 + 1.77041i 0.0272902 + 0.189808i
\(88\) 1.34125 0.861971i 0.142978 0.0918864i
\(89\) 3.91232 + 4.51506i 0.414705 + 0.478595i 0.924217 0.381869i \(-0.124719\pi\)
−0.509511 + 0.860464i \(0.670174\pi\)
\(90\) 0.959493 0.281733i 0.101139 0.0296972i
\(91\) −2.91715 −0.305800
\(92\) −4.79575 + 0.0271313i −0.499992 + 0.00282863i
\(93\) −5.96917 −0.618974
\(94\) 4.07208 1.19567i 0.420003 0.123324i
\(95\) 1.07028 + 1.23516i 0.109808 + 0.126725i
\(96\) −0.841254 + 0.540641i −0.0858601 + 0.0551789i
\(97\) 0.0304261 + 0.211618i 0.00308930 + 0.0214865i 0.991308 0.131563i \(-0.0419996\pi\)
−0.988218 + 0.153050i \(0.951091\pi\)
\(98\) −1.64333 1.05610i −0.166002 0.106683i
\(99\) −0.662317 + 1.45027i −0.0665654 + 0.145758i
\(100\) −0.654861 + 0.755750i −0.0654861 + 0.0755750i
\(101\) −1.36495 + 9.49344i −0.135818 + 0.944632i 0.801956 + 0.597384i \(0.203793\pi\)
−0.937773 + 0.347248i \(0.887116\pi\)
\(102\) 0.333797 + 0.730913i 0.0330508 + 0.0723712i
\(103\) 17.1438 + 5.03387i 1.68923 + 0.496002i 0.978288 0.207252i \(-0.0664518\pi\)
0.710939 + 0.703253i \(0.248270\pi\)
\(104\) −0.935418 0.274663i −0.0917252 0.0269330i
\(105\) 1.24302 + 2.72183i 0.121306 + 0.265623i
\(106\) −0.280646 + 1.95194i −0.0272588 + 0.189589i
\(107\) 4.62525 5.33783i 0.447140 0.516027i −0.486772 0.873529i \(-0.661826\pi\)
0.933913 + 0.357502i \(0.116371\pi\)
\(108\) 0.415415 0.909632i 0.0399733 0.0875294i
\(109\) −9.32818 5.99485i −0.893477 0.574203i 0.0113719 0.999935i \(-0.496380\pi\)
−0.904849 + 0.425732i \(0.860016\pi\)
\(110\) −0.226900 1.57812i −0.0216340 0.150468i
\(111\) −5.90764 + 3.79661i −0.560729 + 0.360358i
\(112\) −1.95949 2.26138i −0.185155 0.213680i
\(113\) −6.20687 + 1.82250i −0.583893 + 0.171447i −0.560321 0.828276i \(-0.689322\pi\)
−0.0235724 + 0.999722i \(0.507504\pi\)
\(114\) 1.63436 0.153071
\(115\) −1.96755 + 4.37364i −0.183475 + 0.407844i
\(116\) −1.78861 −0.166069
\(117\) 0.935418 0.274663i 0.0864794 0.0253926i
\(118\) 4.32629 + 4.99280i 0.398267 + 0.459625i
\(119\) −2.02265 + 1.29988i −0.185416 + 0.119160i
\(120\) 0.142315 + 0.989821i 0.0129915 + 0.0903579i
\(121\) −7.11536 4.57276i −0.646851 0.415706i
\(122\) −0.965346 + 2.11381i −0.0873983 + 0.191376i
\(123\) 4.13770 4.77516i 0.373084 0.430562i
\(124\) 0.849501 5.90841i 0.0762875 0.530591i
\(125\) 0.415415 + 0.909632i 0.0371558 + 0.0813600i
\(126\) 2.87102 + 0.843008i 0.255771 + 0.0751011i
\(127\) 12.4270 + 3.64889i 1.10271 + 0.323786i 0.781930 0.623366i \(-0.214235\pi\)
0.320784 + 0.947152i \(0.396053\pi\)
\(128\) −0.415415 0.909632i −0.0367178 0.0804009i
\(129\) −0.222170 + 1.54522i −0.0195609 + 0.136049i
\(130\) −0.638429 + 0.736786i −0.0559939 + 0.0646204i
\(131\) −6.67755 + 14.6218i −0.583420 + 1.27751i 0.355918 + 0.934517i \(0.384168\pi\)
−0.939338 + 0.342994i \(0.888559\pi\)
\(132\) −1.34125 0.861971i −0.116741 0.0750250i
\(133\) 0.695972 + 4.84059i 0.0603484 + 0.419732i
\(134\) 9.39150 6.03555i 0.811302 0.521392i
\(135\) −0.654861 0.755750i −0.0563614 0.0650446i
\(136\) −0.770978 + 0.226380i −0.0661108 + 0.0194119i
\(137\) 12.5301 1.07052 0.535259 0.844688i \(-0.320214\pi\)
0.535259 + 0.844688i \(0.320214\pi\)
\(138\) 2.01691 + 4.35110i 0.171691 + 0.370390i
\(139\) 6.13485 0.520351 0.260176 0.965561i \(-0.416220\pi\)
0.260176 + 0.965561i \(0.416220\pi\)
\(140\) −2.87102 + 0.843008i −0.242646 + 0.0712472i
\(141\) −2.77923 3.20740i −0.234053 0.270112i
\(142\) 4.21370 2.70798i 0.353606 0.227248i
\(143\) −0.221207 1.53853i −0.0184982 0.128658i
\(144\) 0.841254 + 0.540641i 0.0701045 + 0.0450534i
\(145\) −0.743017 + 1.62698i −0.0617042 + 0.135113i
\(146\) −2.60579 + 3.00724i −0.215657 + 0.248881i
\(147\) −0.278002 + 1.93355i −0.0229292 + 0.159476i
\(148\) −2.91722 6.38783i −0.239794 0.525076i
\(149\) 12.3772 + 3.63429i 1.01398 + 0.297732i 0.746182 0.665742i \(-0.231885\pi\)
0.267801 + 0.963474i \(0.413703\pi\)
\(150\) 0.959493 + 0.281733i 0.0783423 + 0.0230034i
\(151\) 2.40145 + 5.25844i 0.195427 + 0.427926i 0.981823 0.189797i \(-0.0607829\pi\)
−0.786396 + 0.617722i \(0.788056\pi\)
\(152\) −0.232593 + 1.61772i −0.0188658 + 0.131214i
\(153\) 0.526198 0.607265i 0.0425406 0.0490944i
\(154\) 1.98181 4.33955i 0.159698 0.349691i
\(155\) −5.02158 3.22718i −0.403343 0.259213i
\(156\) 0.138744 + 0.964985i 0.0111084 + 0.0772606i
\(157\) 5.68077 3.65081i 0.453375 0.291366i −0.293955 0.955819i \(-0.594972\pi\)
0.747330 + 0.664453i \(0.231335\pi\)
\(158\) 0.996905 + 1.15049i 0.0793095 + 0.0915281i
\(159\) 1.89213 0.555580i 0.150056 0.0440603i
\(160\) −1.00000 −0.0790569
\(161\) −12.0281 + 7.82649i −0.947946 + 0.616814i
\(162\) −1.00000 −0.0785674
\(163\) 16.1904 4.75393i 1.26813 0.372357i 0.422616 0.906309i \(-0.361112\pi\)
0.845515 + 0.533952i \(0.179294\pi\)
\(164\) 4.13770 + 4.77516i 0.323100 + 0.372878i
\(165\) −1.34125 + 0.861971i −0.104416 + 0.0671044i
\(166\) 1.99366 + 13.8662i 0.154738 + 1.07623i
\(167\) 4.35503 + 2.79881i 0.337002 + 0.216578i 0.698186 0.715916i \(-0.253991\pi\)
−0.361184 + 0.932495i \(0.617627\pi\)
\(168\) −1.24302 + 2.72183i −0.0959008 + 0.209993i
\(169\) 7.89078 9.10645i 0.606983 0.700496i
\(170\) −0.114354 + 0.795348i −0.00877053 + 0.0610004i
\(171\) −0.678936 1.48666i −0.0519195 0.113688i
\(172\) −1.49788 0.439817i −0.114212 0.0335357i
\(173\) −22.7443 6.67834i −1.72922 0.507745i −0.742455 0.669896i \(-0.766338\pi\)
−0.986766 + 0.162152i \(0.948157\pi\)
\(174\) 0.743017 + 1.62698i 0.0563279 + 0.123341i
\(175\) −0.425839 + 2.96177i −0.0321904 + 0.223889i
\(176\) 1.04408 1.20493i 0.0787003 0.0908250i
\(177\) 2.74441 6.00941i 0.206282 0.451695i
\(178\) 5.02588 + 3.22994i 0.376706 + 0.242094i
\(179\) 2.83821 + 19.7402i 0.212138 + 1.47545i 0.765998 + 0.642842i \(0.222245\pi\)
−0.553861 + 0.832609i \(0.686846\pi\)
\(180\) 0.841254 0.540641i 0.0627033 0.0402970i
\(181\) −13.2089 15.2438i −0.981807 1.13307i −0.991101 0.133109i \(-0.957504\pi\)
0.00929406 0.999957i \(-0.497042\pi\)
\(182\) −2.79898 + 0.821856i −0.207474 + 0.0609200i
\(183\) 2.32381 0.171781
\(184\) −4.59385 + 1.37715i −0.338663 + 0.101525i
\(185\) −7.02243 −0.516299
\(186\) −5.72738 + 1.68171i −0.419952 + 0.123309i
\(187\) −0.838944 0.968193i −0.0613497 0.0708013i
\(188\) 3.57028 2.29448i 0.260389 0.167342i
\(189\) −0.425839 2.96177i −0.0309752 0.215437i
\(190\) 1.37491 + 0.883600i 0.0997463 + 0.0641031i
\(191\) 0.412044 0.902250i 0.0298144 0.0652845i −0.894139 0.447790i \(-0.852211\pi\)
0.923953 + 0.382505i \(0.124939\pi\)
\(192\) −0.654861 + 0.755750i −0.0472605 + 0.0545415i
\(193\) −0.594966 + 4.13808i −0.0428266 + 0.297865i 0.957140 + 0.289627i \(0.0935314\pi\)
−0.999966 + 0.00823798i \(0.997378\pi\)
\(194\) 0.0888133 + 0.194474i 0.00637642 + 0.0139624i
\(195\) 0.935418 + 0.274663i 0.0669866 + 0.0196691i
\(196\) −1.87430 0.550345i −0.133879 0.0393104i
\(197\) 2.07307 + 4.53939i 0.147700 + 0.323418i 0.968993 0.247089i \(-0.0794740\pi\)
−0.821293 + 0.570507i \(0.806747\pi\)
\(198\) −0.226900 + 1.57812i −0.0161251 + 0.112152i
\(199\) 0.481050 0.555161i 0.0341007 0.0393544i −0.738443 0.674316i \(-0.764439\pi\)
0.772544 + 0.634962i \(0.218984\pi\)
\(200\) −0.415415 + 0.909632i −0.0293743 + 0.0643207i
\(201\) −9.39150 6.03555i −0.662425 0.425715i
\(202\) 1.36495 + 9.49344i 0.0960375 + 0.667956i
\(203\) −4.50234 + 2.89348i −0.316002 + 0.203082i
\(204\) 0.526198 + 0.607265i 0.0368412 + 0.0425170i
\(205\) 6.06250 1.78011i 0.423424 0.124328i
\(206\) 17.8675 1.24489
\(207\) 3.12005 3.64216i 0.216858 0.253147i
\(208\) −0.974908 −0.0675977
\(209\) −2.50019 + 0.734121i −0.172942 + 0.0507802i
\(210\) 1.95949 + 2.26138i 0.135218 + 0.156050i
\(211\) −8.04246 + 5.16857i −0.553665 + 0.355819i −0.787363 0.616490i \(-0.788554\pi\)
0.233697 + 0.972309i \(0.424918\pi\)
\(212\) 0.280646 + 1.95194i 0.0192749 + 0.134060i
\(213\) −4.21370 2.70798i −0.288718 0.185548i
\(214\) 2.93406 6.42469i 0.200568 0.439183i
\(215\) −1.02231 + 1.17981i −0.0697211 + 0.0804624i
\(216\) 0.142315 0.989821i 0.00968330 0.0673488i
\(217\) −7.41978 16.2470i −0.503687 1.10292i
\(218\) −10.6393 3.12397i −0.720582 0.211582i
\(219\) 3.81797 + 1.12106i 0.257994 + 0.0757540i
\(220\) −0.662317 1.45027i −0.0446534 0.0977774i
\(221\) −0.111484 + 0.775391i −0.00749925 + 0.0521584i
\(222\) −4.59871 + 5.30720i −0.308645 + 0.356196i
\(223\) 0.766671 1.67878i 0.0513401 0.112419i −0.882224 0.470831i \(-0.843954\pi\)
0.933564 + 0.358412i \(0.116682\pi\)
\(224\) −2.51722 1.61772i −0.168189 0.108089i
\(225\) −0.142315 0.989821i −0.00948766 0.0659881i
\(226\) −5.44199 + 3.49736i −0.361996 + 0.232641i
\(227\) 0.462908 + 0.534225i 0.0307243 + 0.0354577i 0.770904 0.636952i \(-0.219805\pi\)
−0.740179 + 0.672409i \(0.765259\pi\)
\(228\) 1.56815 0.460451i 0.103853 0.0304941i
\(229\) 0.634910 0.0419560 0.0209780 0.999780i \(-0.493322\pi\)
0.0209780 + 0.999780i \(0.493322\pi\)
\(230\) −0.655652 + 4.75080i −0.0432324 + 0.313259i
\(231\) −4.77066 −0.313887
\(232\) −1.71616 + 0.503910i −0.112672 + 0.0330833i
\(233\) −5.18417 5.98285i −0.339626 0.391949i 0.560085 0.828435i \(-0.310768\pi\)
−0.899711 + 0.436486i \(0.856223\pi\)
\(234\) 0.820145 0.527075i 0.0536146 0.0344560i
\(235\) −0.603983 4.20080i −0.0393995 0.274030i
\(236\) 5.55768 + 3.57170i 0.361774 + 0.232498i
\(237\) 0.632393 1.38475i 0.0410784 0.0899490i
\(238\) −1.57450 + 1.81707i −0.102060 + 0.117783i
\(239\) 0.918852 6.39076i 0.0594356 0.413384i −0.938283 0.345869i \(-0.887584\pi\)
0.997718 0.0675144i \(-0.0215069\pi\)
\(240\) 0.415415 + 0.909632i 0.0268149 + 0.0587165i
\(241\) 13.5447 + 3.97707i 0.872488 + 0.256186i 0.687173 0.726494i \(-0.258851\pi\)
0.185315 + 0.982679i \(0.440670\pi\)
\(242\) −8.11543 2.38291i −0.521680 0.153179i
\(243\) 0.415415 + 0.909632i 0.0266489 + 0.0583529i
\(244\) −0.330713 + 2.30016i −0.0211717 + 0.147252i
\(245\) −1.27923 + 1.47631i −0.0817267 + 0.0943177i
\(246\) 2.62478 5.74746i 0.167350 0.366445i
\(247\) 1.34041 + 0.861429i 0.0852882 + 0.0548114i
\(248\) −0.849501 5.90841i −0.0539434 0.375185i
\(249\) 11.7850 7.57374i 0.746842 0.479966i
\(250\) 0.654861 + 0.755750i 0.0414170 + 0.0477978i
\(251\) −2.28317 + 0.670400i −0.144113 + 0.0423153i −0.352993 0.935626i \(-0.614836\pi\)
0.208881 + 0.977941i \(0.433018\pi\)
\(252\) 2.99223 0.188493
\(253\) −5.03983 5.75022i −0.316852 0.361513i
\(254\) 12.9516 0.812655
\(255\) 0.770978 0.226380i 0.0482805 0.0141764i
\(256\) −0.654861 0.755750i −0.0409288 0.0472343i
\(257\) 6.10744 3.92501i 0.380972 0.244836i −0.336113 0.941822i \(-0.609112\pi\)
0.717085 + 0.696986i \(0.245476\pi\)
\(258\) 0.222170 + 1.54522i 0.0138317 + 0.0962014i
\(259\) −17.6770 11.3603i −1.09840 0.705897i
\(260\) −0.404992 + 0.886808i −0.0251165 + 0.0549975i
\(261\) 1.17129 1.35174i 0.0725012 0.0836708i
\(262\) −2.28763 + 15.9108i −0.141330 + 0.982972i
\(263\) −12.1342 26.5701i −0.748225 1.63838i −0.769529 0.638611i \(-0.779509\pi\)
0.0213044 0.999773i \(-0.493218\pi\)
\(264\) −1.52977 0.449181i −0.0941508 0.0276452i
\(265\) 1.89213 + 0.555580i 0.116233 + 0.0341290i
\(266\) 2.03153 + 4.44843i 0.124561 + 0.272751i
\(267\) 0.850228 5.91347i 0.0520331 0.361898i
\(268\) 7.31067 8.43696i 0.446570 0.515369i
\(269\) −11.3388 + 24.8285i −0.691338 + 1.51382i 0.158830 + 0.987306i \(0.449228\pi\)
−0.850168 + 0.526512i \(0.823499\pi\)
\(270\) −0.841254 0.540641i −0.0511971 0.0329024i
\(271\) −0.153611 1.06838i −0.00933118 0.0648998i 0.984624 0.174688i \(-0.0558917\pi\)
−0.993955 + 0.109788i \(0.964983\pi\)
\(272\) −0.675969 + 0.434419i −0.0409867 + 0.0263405i
\(273\) 1.91033 + 2.20463i 0.115618 + 0.133430i
\(274\) 12.0225 3.53014i 0.726308 0.213263i
\(275\) −1.59435 −0.0961430
\(276\) 3.16106 + 3.60662i 0.190273 + 0.217093i
\(277\) −18.3184 −1.10065 −0.550323 0.834952i \(-0.685496\pi\)
−0.550323 + 0.834952i \(0.685496\pi\)
\(278\) 5.88635 1.72839i 0.353040 0.103662i
\(279\) 3.90897 + 4.51120i 0.234024 + 0.270078i
\(280\) −2.51722 + 1.61772i −0.150433 + 0.0966773i
\(281\) −0.787000 5.47371i −0.0469485 0.326534i −0.999738 0.0229015i \(-0.992710\pi\)
0.952789 0.303633i \(-0.0981995\pi\)
\(282\) −3.57028 2.29448i −0.212607 0.136634i
\(283\) 2.15676 4.72265i 0.128206 0.280733i −0.834634 0.550806i \(-0.814321\pi\)
0.962840 + 0.270073i \(0.0870478\pi\)
\(284\) 3.28009 3.78542i 0.194637 0.224623i
\(285\) 0.232593 1.61772i 0.0137776 0.0958255i
\(286\) −0.645699 1.41388i −0.0381810 0.0836046i
\(287\) 18.1404 + 5.32650i 1.07079 + 0.314413i
\(288\) 0.959493 + 0.281733i 0.0565387 + 0.0166013i
\(289\) −6.79384 14.8764i −0.399638 0.875084i
\(290\) −0.254546 + 1.77041i −0.0149475 + 0.103962i
\(291\) 0.140005 0.161575i 0.00820726 0.00947168i
\(292\) −1.65300 + 3.61956i −0.0967345 + 0.211819i
\(293\) −11.0859 7.12446i −0.647644 0.416215i 0.175161 0.984540i \(-0.443955\pi\)
−0.822804 + 0.568325i \(0.807592\pi\)
\(294\) 0.278002 + 1.93355i 0.0162134 + 0.112767i
\(295\) 5.55768 3.57170i 0.323580 0.207953i
\(296\) −4.59871 5.30720i −0.267295 0.308475i
\(297\) 1.52977 0.449181i 0.0887662 0.0260641i
\(298\) 12.8998 0.747264
\(299\) −0.639200 + 4.63160i −0.0369659 + 0.267852i
\(300\) 1.00000 0.0577350
\(301\) −4.48199 + 1.31603i −0.258338 + 0.0758548i
\(302\) 3.78565 + 4.36887i 0.217839 + 0.251400i
\(303\) 8.06851 5.18532i 0.463524 0.297889i
\(304\) 0.232593 + 1.61772i 0.0133401 + 0.0927827i
\(305\) 1.95491 + 1.25635i 0.111938 + 0.0719382i
\(306\) 0.333797 0.730913i 0.0190819 0.0417835i
\(307\) −4.81572 + 5.55763i −0.274848 + 0.317191i −0.876345 0.481684i \(-0.840025\pi\)
0.601498 + 0.798875i \(0.294571\pi\)
\(308\) 0.678936 4.72210i 0.0386860 0.269067i
\(309\) −7.42245 16.2529i −0.422248 0.924595i
\(310\) −5.72738 1.68171i −0.325293 0.0955147i
\(311\) −22.9076 6.72628i −1.29897 0.381412i −0.442111 0.896961i \(-0.645770\pi\)
−0.856861 + 0.515548i \(0.827588\pi\)
\(312\) 0.404992 + 0.886808i 0.0229281 + 0.0502056i
\(313\) −3.13670 + 21.8163i −0.177297 + 1.23313i 0.685687 + 0.727897i \(0.259502\pi\)
−0.862984 + 0.505231i \(0.831407\pi\)
\(314\) 4.42211 5.10338i 0.249554 0.288001i
\(315\) 1.24302 2.72183i 0.0700361 0.153358i
\(316\) 1.28065 + 0.823027i 0.0720424 + 0.0462989i
\(317\) 1.04694 + 7.28165i 0.0588022 + 0.408978i 0.997869 + 0.0652443i \(0.0207827\pi\)
−0.939067 + 0.343734i \(0.888308\pi\)
\(318\) 1.65896 1.06615i 0.0930299 0.0597867i
\(319\) −1.86745 2.15515i −0.104557 0.120665i
\(320\) −0.959493 + 0.281733i −0.0536373 + 0.0157493i
\(321\) −7.06296 −0.394216
\(322\) −9.33589 + 10.8982i −0.520269 + 0.607331i
\(323\) 1.31325 0.0730711
\(324\) −0.959493 + 0.281733i −0.0533052 + 0.0156518i
\(325\) 0.638429 + 0.736786i 0.0354137 + 0.0408696i
\(326\) 14.1953 9.12273i 0.786202 0.505261i
\(327\) 1.57805 + 10.9756i 0.0872662 + 0.606950i
\(328\) 5.31541 + 3.41601i 0.293495 + 0.188618i
\(329\) 5.27536 11.5514i 0.290840 0.636850i
\(330\) −1.04408 + 1.20493i −0.0574746 + 0.0663292i
\(331\) −0.708989 + 4.93113i −0.0389696 + 0.271039i −0.999985 0.00545498i \(-0.998264\pi\)
0.961016 + 0.276494i \(0.0891727\pi\)
\(332\) 5.81947 + 12.7429i 0.319385 + 0.699356i
\(333\) 6.73797 + 1.97845i 0.369239 + 0.108418i
\(334\) 4.96714 + 1.45848i 0.271790 + 0.0798046i
\(335\) −4.63757 10.1549i −0.253377 0.554819i
\(336\) −0.425839 + 2.96177i −0.0232314 + 0.161578i
\(337\) 15.1970 17.5383i 0.827833 0.955370i −0.171724 0.985145i \(-0.554934\pi\)
0.999557 + 0.0297754i \(0.00947920\pi\)
\(338\) 5.00557 10.9607i 0.272267 0.596181i
\(339\) 5.44199 + 3.49736i 0.295568 + 0.189950i
\(340\) 0.114354 + 0.795348i 0.00620170 + 0.0431338i
\(341\) 8.00617 5.14525i 0.433558 0.278631i
\(342\) −1.07028 1.23516i −0.0578739 0.0667900i
\(343\) 14.4888 4.25430i 0.782322 0.229711i
\(344\) −1.56111 −0.0841696
\(345\) 4.59385 1.37715i 0.247325 0.0741434i
\(346\) −23.7045 −1.27436
\(347\) −8.41884 + 2.47199i −0.451947 + 0.132704i −0.499781 0.866152i \(-0.666586\pi\)
0.0478343 + 0.998855i \(0.484768\pi\)
\(348\) 1.17129 + 1.35174i 0.0627879 + 0.0724611i
\(349\) −15.8606 + 10.1930i −0.848998 + 0.545618i −0.891262 0.453489i \(-0.850179\pi\)
0.0422642 + 0.999106i \(0.486543\pi\)
\(350\) 0.425839 + 2.96177i 0.0227620 + 0.158313i
\(351\) −0.820145 0.527075i −0.0437761 0.0281332i
\(352\) 0.662317 1.45027i 0.0353016 0.0772998i
\(353\) −6.68945 + 7.72003i −0.356043 + 0.410896i −0.905310 0.424751i \(-0.860362\pi\)
0.549267 + 0.835647i \(0.314907\pi\)
\(354\) 0.940192 6.53918i 0.0499706 0.347553i
\(355\) −2.08074 4.55619i −0.110434 0.241818i
\(356\) 5.73228 + 1.68315i 0.303810 + 0.0892067i
\(357\) 2.30694 + 0.677379i 0.122096 + 0.0358507i
\(358\) 8.28470 + 18.1410i 0.437860 + 0.958780i
\(359\) 1.25988 8.76264i 0.0664938 0.462474i −0.929185 0.369614i \(-0.879490\pi\)
0.995679 0.0928604i \(-0.0296010\pi\)
\(360\) 0.654861 0.755750i 0.0345142 0.0398315i
\(361\) −6.78326 + 14.8533i −0.357014 + 0.781751i
\(362\) −16.9685 10.9050i −0.891845 0.573154i
\(363\) 1.20371 + 8.37195i 0.0631781 + 0.439414i
\(364\) −2.45406 + 1.57713i −0.128628 + 0.0826640i
\(365\) 2.60579 + 3.00724i 0.136393 + 0.157406i
\(366\) 2.22968 0.654693i 0.116547 0.0342214i
\(367\) 10.3255 0.538986 0.269493 0.963002i \(-0.413144\pi\)
0.269493 + 0.963002i \(0.413144\pi\)
\(368\) −4.01978 + 2.61561i −0.209545 + 0.136348i
\(369\) −6.31845 −0.328925
\(370\) −6.73797 + 1.97845i −0.350290 + 0.102855i
\(371\) 3.86414 + 4.45946i 0.200616 + 0.231523i
\(372\) −5.02158 + 3.22718i −0.260357 + 0.167321i
\(373\) 5.09538 + 35.4392i 0.263829 + 1.83497i 0.503354 + 0.864081i \(0.332099\pi\)
−0.239525 + 0.970890i \(0.576992\pi\)
\(374\) −1.07773 0.692617i −0.0557282 0.0358144i
\(375\) 0.415415 0.909632i 0.0214519 0.0469732i
\(376\) 2.77923 3.20740i 0.143328 0.165409i
\(377\) −0.248159 + 1.72598i −0.0127808 + 0.0888927i
\(378\) −1.24302 2.72183i −0.0639339 0.139996i
\(379\) −16.1303 4.73627i −0.828556 0.243286i −0.160160 0.987091i \(-0.551201\pi\)
−0.668397 + 0.743805i \(0.733019\pi\)
\(380\) 1.56815 + 0.460451i 0.0804446 + 0.0236207i
\(381\) −5.38029 11.7812i −0.275640 0.603568i
\(382\) 0.141160 0.981789i 0.00722237 0.0502327i
\(383\) 16.2021 18.6982i 0.827887 0.955432i −0.171671 0.985154i \(-0.554917\pi\)
0.999558 + 0.0297220i \(0.00946219\pi\)
\(384\) −0.415415 + 0.909632i −0.0211991 + 0.0464195i
\(385\) −4.01334 2.57922i −0.204539 0.131449i
\(386\) 0.594966 + 4.13808i 0.0302830 + 0.210623i
\(387\) 1.31329 0.844002i 0.0667584 0.0429030i
\(388\) 0.140005 + 0.161575i 0.00710769 + 0.00820272i
\(389\) −22.6578 + 6.65294i −1.14880 + 0.337318i −0.800070 0.599906i \(-0.795204\pi\)
−0.348728 + 0.937224i \(0.613386\pi\)
\(390\) 0.974908 0.0493664
\(391\) 1.62064 + 3.49622i 0.0819592 + 0.176812i
\(392\) −1.95343 −0.0986632
\(393\) 15.4233 4.52868i 0.778001 0.228442i
\(394\) 3.26799 + 3.77146i 0.164639 + 0.190003i
\(395\) 1.28065 0.823027i 0.0644367 0.0414110i
\(396\) 0.226900 + 1.57812i 0.0114021 + 0.0793037i
\(397\) −22.0616 14.1781i −1.10724 0.711580i −0.146550 0.989203i \(-0.546817\pi\)
−0.960690 + 0.277623i \(0.910453\pi\)
\(398\) 0.305157 0.668201i 0.0152961 0.0334939i
\(399\) 3.20251 3.69589i 0.160326 0.185026i
\(400\) −0.142315 + 0.989821i −0.00711574 + 0.0494911i
\(401\) −4.59087 10.0526i −0.229257 0.502003i 0.759687 0.650288i \(-0.225352\pi\)
−0.988945 + 0.148285i \(0.952625\pi\)
\(402\) −10.7115 3.14518i −0.534241 0.156867i
\(403\) −5.58367 1.63951i −0.278142 0.0816699i
\(404\) 3.98427 + 8.72433i 0.198225 + 0.434052i
\(405\) −0.142315 + 0.989821i −0.00707168 + 0.0491846i
\(406\) −3.50477 + 4.04473i −0.173939 + 0.200736i
\(407\) 4.65108 10.1844i 0.230545 0.504824i
\(408\) 0.675969 + 0.434419i 0.0334655 + 0.0215069i
\(409\) 1.95444 + 13.5934i 0.0966409 + 0.672152i 0.979341 + 0.202216i \(0.0648142\pi\)
−0.882700 + 0.469937i \(0.844277\pi\)
\(410\) 5.31541 3.41601i 0.262510 0.168705i
\(411\) −8.20547 9.46962i −0.404746 0.467102i
\(412\) 17.1438 5.03387i 0.844614 0.248001i
\(413\) 19.7679 0.972716
\(414\) 1.96755 4.37364i 0.0966998 0.214953i
\(415\) 14.0088 0.687666
\(416\) −0.935418 + 0.274663i −0.0458626 + 0.0134665i
\(417\) −4.01747 4.63641i −0.196737 0.227046i
\(418\) −2.19209 + 1.40877i −0.107218 + 0.0689051i
\(419\) −1.70342 11.8476i −0.0832177 0.578792i −0.988180 0.153300i \(-0.951010\pi\)
0.904962 0.425492i \(-0.139899\pi\)
\(420\) 2.51722 + 1.61772i 0.122828 + 0.0789367i
\(421\) 7.84603 17.1804i 0.382392 0.837322i −0.616364 0.787461i \(-0.711395\pi\)
0.998756 0.0498609i \(-0.0158778\pi\)
\(422\) −6.26052 + 7.22503i −0.304758 + 0.351709i
\(423\) −0.603983 + 4.20080i −0.0293667 + 0.204250i
\(424\) 0.819203 + 1.79380i 0.0397840 + 0.0871148i
\(425\) 0.770978 + 0.226380i 0.0373979 + 0.0109810i
\(426\) −4.80594 1.41115i −0.232848 0.0683705i
\(427\) 2.88853 + 6.32501i 0.139786 + 0.306089i
\(428\) 1.00516 6.99107i 0.0485864 0.337926i
\(429\) −1.01788 + 1.17470i −0.0491437 + 0.0567149i
\(430\) −0.648510 + 1.42004i −0.0312739 + 0.0684804i
\(431\) 21.3786 + 13.7392i 1.02977 + 0.661793i 0.942436 0.334386i \(-0.108529\pi\)
0.0873340 + 0.996179i \(0.472165\pi\)
\(432\) −0.142315 0.989821i −0.00684713 0.0476228i
\(433\) 8.88803 5.71199i 0.427131 0.274501i −0.309363 0.950944i \(-0.600116\pi\)
0.736495 + 0.676443i \(0.236480\pi\)
\(434\) −11.6965 13.4985i −0.561452 0.647950i
\(435\) 1.71616 0.503910i 0.0822836 0.0241607i
\(436\) −11.0884 −0.531039
\(437\) 7.83797 0.0443422i 0.374941 0.00212118i
\(438\) 3.97915 0.190131
\(439\) −29.0861 + 8.54044i −1.38820 + 0.407613i −0.888616 0.458651i \(-0.848333\pi\)
−0.499586 + 0.866264i \(0.666515\pi\)
\(440\) −1.04408 1.20493i −0.0497745 0.0574428i
\(441\) 1.64333 1.05610i 0.0782539 0.0502907i
\(442\) 0.111484 + 0.775391i 0.00530277 + 0.0368816i
\(443\) −26.0760 16.7580i −1.23891 0.796198i −0.253654 0.967295i \(-0.581632\pi\)
−0.985254 + 0.171097i \(0.945269\pi\)
\(444\) −2.91722 + 6.38783i −0.138445 + 0.303153i
\(445\) 3.91232 4.51506i 0.185462 0.214034i
\(446\) 0.262650 1.82677i 0.0124368 0.0865001i
\(447\) −5.35876 11.7340i −0.253461 0.555002i
\(448\) −2.87102 0.843008i −0.135643 0.0398284i
\(449\) −6.11055 1.79422i −0.288375 0.0846745i 0.134346 0.990935i \(-0.457107\pi\)
−0.422721 + 0.906260i \(0.638925\pi\)
\(450\) −0.415415 0.909632i −0.0195829 0.0428805i
\(451\) −1.43365 + 9.97128i −0.0675081 + 0.469529i
\(452\) −4.23623 + 4.88887i −0.199256 + 0.229953i
\(453\) 2.40145 5.25844i 0.112830 0.247063i
\(454\) 0.594666 + 0.382169i 0.0279091 + 0.0179361i
\(455\) 0.415153 + 2.88746i 0.0194627 + 0.135366i
\(456\) 1.37491 0.883600i 0.0643860 0.0413783i
\(457\) −23.8425 27.5157i −1.11531 1.28713i −0.953860 0.300250i \(-0.902930\pi\)
−0.161446 0.986882i \(-0.551616\pi\)
\(458\) 0.609191 0.178875i 0.0284656 0.00835827i
\(459\) −0.803526 −0.0375054
\(460\) 0.709362 + 4.74308i 0.0330742 + 0.221147i
\(461\) 6.45146 0.300474 0.150237 0.988650i \(-0.451996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(462\) −4.57742 + 1.34405i −0.212961 + 0.0625309i
\(463\) 11.3031 + 13.0445i 0.525300 + 0.606229i 0.954950 0.296767i \(-0.0959084\pi\)
−0.429650 + 0.902996i \(0.641363\pi\)
\(464\) −1.50468 + 0.966997i −0.0698529 + 0.0448917i
\(465\) 0.849501 + 5.90841i 0.0393947 + 0.273996i
\(466\) −6.65974 4.27995i −0.308506 0.198265i
\(467\) 12.0366 26.3565i 0.556989 1.21964i −0.396452 0.918055i \(-0.629759\pi\)
0.953441 0.301580i \(-0.0975141\pi\)
\(468\) 0.638429 0.736786i 0.0295114 0.0340580i
\(469\) 4.75393 33.0643i 0.219516 1.52677i
\(470\) −1.76302 3.86047i −0.0813220 0.178070i
\(471\) −6.47921 1.90247i −0.298546 0.0876611i
\(472\) 6.33882 + 1.86124i 0.291768 + 0.0856707i
\(473\) −1.03395 2.26404i −0.0475412 0.104101i
\(474\) 0.216648 1.50682i 0.00995098 0.0692106i
\(475\) 1.07028 1.23516i 0.0491076 0.0566732i
\(476\) −0.998797 + 2.18706i −0.0457798 + 0.100244i
\(477\) −1.65896 1.06615i −0.0759586 0.0488156i
\(478\) −0.918852 6.39076i −0.0420273 0.292306i
\(479\) 27.0720 17.3981i 1.23695 0.794940i 0.251992 0.967729i \(-0.418914\pi\)
0.984959 + 0.172789i \(0.0552778\pi\)
\(480\) 0.654861 + 0.755750i 0.0298902 + 0.0344951i
\(481\) −6.56890 + 1.92880i −0.299516 + 0.0879459i
\(482\) 14.1165 0.642987
\(483\) 13.7916 + 3.96497i 0.627539 + 0.180412i
\(484\) −8.45804 −0.384457
\(485\) 0.205134 0.0602328i 0.00931465 0.00273503i
\(486\) 0.654861 + 0.755750i 0.0297051 + 0.0342815i
\(487\) −22.2751 + 14.3153i −1.00938 + 0.648689i −0.937232 0.348705i \(-0.886621\pi\)
−0.0721471 + 0.997394i \(0.522985\pi\)
\(488\) 0.330713 + 2.30016i 0.0149707 + 0.104123i
\(489\) −14.1953 9.12273i −0.641931 0.412544i
\(490\) −0.811485 + 1.77690i −0.0366591 + 0.0802723i
\(491\) 19.1837 22.1391i 0.865746 0.999125i −0.134220 0.990952i \(-0.542853\pi\)
0.999967 0.00817303i \(-0.00260159\pi\)
\(492\) 0.899209 6.25413i 0.0405395 0.281958i
\(493\) 0.597033 + 1.30732i 0.0268890 + 0.0588788i
\(494\) 1.52881 + 0.448898i 0.0687842 + 0.0201969i
\(495\) 1.52977 + 0.449181i 0.0687580 + 0.0201892i
\(496\) −2.47968 5.42975i −0.111341 0.243803i
\(497\) 2.13295 14.8350i 0.0956760 0.665441i
\(498\) 9.17382 10.5872i 0.411089 0.474422i
\(499\) −14.3457 + 31.4127i −0.642202 + 1.40623i 0.256015 + 0.966673i \(0.417590\pi\)
−0.898217 + 0.439553i \(0.855137\pi\)
\(500\) 0.841254 + 0.540641i 0.0376220 + 0.0241782i
\(501\) −0.736740 5.12414i −0.0329151 0.228930i
\(502\) −2.00181 + 1.28649i −0.0893453 + 0.0574188i
\(503\) 0.0815619 + 0.0941275i 0.00363667 + 0.00419694i 0.757565 0.652760i \(-0.226389\pi\)
−0.753928 + 0.656957i \(0.771843\pi\)
\(504\) 2.87102 0.843008i 0.127885 0.0375506i
\(505\) 9.59106 0.426797
\(506\) −6.45571 4.09741i −0.286991 0.182152i
\(507\) −12.0496 −0.535139
\(508\) 12.4270 3.64889i 0.551357 0.161893i
\(509\) 0.478832 + 0.552602i 0.0212239 + 0.0244936i 0.766262 0.642528i \(-0.222114\pi\)
−0.745038 + 0.667022i \(0.767569\pi\)
\(510\) 0.675969 0.434419i 0.0299324 0.0192364i
\(511\) 1.69448 + 11.7853i 0.0749592 + 0.521353i
\(512\) −0.841254 0.540641i −0.0371785 0.0238932i
\(513\) −0.678936 + 1.48666i −0.0299758 + 0.0656378i
\(514\) 4.75424 5.48669i 0.209701 0.242007i
\(515\) 2.54282 17.6857i 0.112050 0.779324i
\(516\) 0.648510 + 1.42004i 0.0285491 + 0.0625137i
\(517\) 6.49233 + 1.90632i 0.285532 + 0.0838399i
\(518\) −20.1616 5.91997i −0.885848 0.260108i
\(519\) 9.84722 + 21.5624i 0.432245 + 0.946485i
\(520\) −0.138744 + 0.964985i −0.00608432 + 0.0423174i
\(521\) 6.49754 7.49856i 0.284662 0.328518i −0.595352 0.803465i \(-0.702987\pi\)
0.880014 + 0.474947i \(0.157533\pi\)
\(522\) 0.743017 1.62698i 0.0325210 0.0712110i
\(523\) −10.1093 6.49685i −0.442049 0.284088i 0.300623 0.953743i \(-0.402805\pi\)
−0.742672 + 0.669655i \(0.766442\pi\)
\(524\) 2.28763 + 15.9108i 0.0999354 + 0.695066i
\(525\) 2.51722 1.61772i 0.109861 0.0706031i
\(526\) −19.1283 22.0753i −0.834035 0.962527i
\(527\) −4.60210 + 1.35130i −0.200470 + 0.0588634i
\(528\) −1.59435 −0.0693852
\(529\) 9.79065 + 20.8121i 0.425680 + 0.904874i
\(530\) 1.97201 0.0856587
\(531\) −6.33882 + 1.86124i −0.275081 + 0.0807711i
\(532\) 3.20251 + 3.69589i 0.138846 + 0.160237i
\(533\) 5.18204 3.33030i 0.224459 0.144251i
\(534\) −0.850228 5.91347i −0.0367930 0.255901i
\(535\) −5.94174 3.81852i −0.256884 0.165089i
\(536\) 4.63757 10.1549i 0.200312 0.438623i
\(537\) 13.0600 15.0721i 0.563581 0.650407i
\(538\) −3.88449 + 27.0172i −0.167472 + 1.16480i
\(539\) −1.29379 2.83301i −0.0557276 0.122026i
\(540\) −0.959493 0.281733i −0.0412900 0.0121238i
\(541\) 11.4828 + 3.37165i 0.493684 + 0.144959i 0.519092 0.854718i \(-0.326270\pi\)
−0.0254078 + 0.999677i \(0.508088\pi\)
\(542\) −0.448387 0.981831i −0.0192599 0.0421732i
\(543\) −2.87056 + 19.9652i −0.123188 + 0.856788i
\(544\) −0.526198 + 0.607265i −0.0225605 + 0.0260363i
\(545\) −4.60630 + 10.0864i −0.197312 + 0.432053i
\(546\) 2.45406 + 1.57713i 0.105024 + 0.0674949i
\(547\) 3.05397 + 21.2408i 0.130578 + 0.908192i 0.944802 + 0.327641i \(0.106254\pi\)
−0.814224 + 0.580551i \(0.802837\pi\)
\(548\) 10.5410 6.77428i 0.450289 0.289383i
\(549\) −1.52177 1.75622i −0.0649476 0.0749536i
\(550\) −1.52977 + 0.449181i −0.0652296 + 0.0191531i
\(551\) 2.92323 0.124534
\(552\) 4.04911 + 2.56996i 0.172342 + 0.109385i
\(553\) 4.55512 0.193703
\(554\) −17.5764 + 5.16089i −0.746749 + 0.219265i
\(555\) 4.59871 + 5.30720i 0.195205 + 0.225278i
\(556\) 5.16097 3.31675i 0.218874 0.140662i
\(557\) 4.21110 + 29.2888i 0.178430 + 1.24101i 0.860397 + 0.509625i \(0.170216\pi\)
−0.681967 + 0.731383i \(0.738875\pi\)
\(558\) 5.02158 + 3.22718i 0.212581 + 0.136617i
\(559\) −0.632238 + 1.38441i −0.0267408 + 0.0585542i
\(560\) −1.95949 + 2.26138i −0.0828037 + 0.0955606i
\(561\) −0.182320 + 1.26806i −0.00769755 + 0.0535377i
\(562\) −2.29724 5.03026i −0.0969033 0.212189i
\(563\) −18.7711 5.51170i −0.791108 0.232290i −0.138876 0.990310i \(-0.544349\pi\)
−0.652232 + 0.758019i \(0.726167\pi\)
\(564\) −4.07208 1.19567i −0.171466 0.0503469i
\(565\) 2.68728 + 5.88433i 0.113055 + 0.247555i
\(566\) 0.738874 5.13898i 0.0310572 0.216008i
\(567\) −1.95949 + 2.26138i −0.0822910 + 0.0949688i
\(568\) 2.08074 4.55619i 0.0873061 0.191174i
\(569\) −7.50745 4.82475i −0.314729 0.202264i 0.373733 0.927536i \(-0.378078\pi\)
−0.688462 + 0.725272i \(0.741714\pi\)
\(570\) −0.232593 1.61772i −0.00974225 0.0677589i
\(571\) −12.2307 + 7.86019i −0.511838 + 0.328939i −0.770936 0.636913i \(-0.780211\pi\)
0.259098 + 0.965851i \(0.416575\pi\)
\(572\) −1.01788 1.17470i −0.0425597 0.0491165i
\(573\) −0.951706 + 0.279446i −0.0397581 + 0.0116740i
\(574\) 18.9062 0.789131
\(575\) 4.60914 + 1.32509i 0.192214 + 0.0552600i
\(576\) 1.00000 0.0416667
\(577\) −38.1822 + 11.2113i −1.58955 + 0.466733i −0.952613 0.304185i \(-0.901616\pi\)
−0.636934 + 0.770918i \(0.719798\pi\)
\(578\) −10.7098 12.3598i −0.445470 0.514099i
\(579\) 3.51697 2.26022i 0.146160 0.0939315i
\(580\) 0.254546 + 1.77041i 0.0105695 + 0.0735122i
\(581\) 35.2633 + 22.6623i 1.46297 + 0.940193i
\(582\) 0.0888133 0.194474i 0.00368143 0.00806120i
\(583\) −2.05893 + 2.37614i −0.0852723 + 0.0984095i
\(584\) −0.566293 + 3.93865i −0.0234334 + 0.162983i
\(585\) −0.404992 0.886808i −0.0167443 0.0366650i
\(586\) −12.6440 3.71262i −0.522319 0.153367i
\(587\) −31.2889 9.18725i −1.29143 0.379198i −0.437328 0.899302i \(-0.644075\pi\)
−0.854103 + 0.520104i \(0.825893\pi\)
\(588\) 0.811485 + 1.77690i 0.0334651 + 0.0732783i
\(589\) −1.38839 + 9.65645i −0.0572075 + 0.397887i
\(590\) 4.32629 4.99280i 0.178110 0.205550i
\(591\) 2.07307 4.53939i 0.0852747 0.186726i
\(592\) −5.90764 3.79661i −0.242803 0.156040i
\(593\) 2.70197 + 18.7926i 0.110957 + 0.771721i 0.966993 + 0.254804i \(0.0820111\pi\)
−0.856036 + 0.516916i \(0.827080\pi\)
\(594\) 1.34125 0.861971i 0.0550323 0.0353671i
\(595\) 1.57450 + 1.81707i 0.0645484 + 0.0744928i
\(596\) 12.3772 3.63429i 0.506992 0.148866i
\(597\) −0.734584 −0.0300645
\(598\) 0.691563 + 4.62407i 0.0282801 + 0.189092i
\(599\) 44.7599 1.82884 0.914419 0.404768i \(-0.132648\pi\)
0.914419 + 0.404768i \(0.132648\pi\)
\(600\) 0.959493 0.281733i 0.0391711 0.0115017i
\(601\) 10.7600 + 12.4177i 0.438910 + 0.506529i 0.931505 0.363730i \(-0.118497\pi\)
−0.492594 + 0.870259i \(0.663951\pi\)
\(602\) −3.92967 + 2.52545i −0.160161 + 0.102930i
\(603\) 1.58876 + 11.0501i 0.0646993 + 0.449994i
\(604\) 4.86315 + 3.12536i 0.197879 + 0.127169i
\(605\) −3.51360 + 7.69371i −0.142848 + 0.312794i
\(606\) 6.28081 7.24844i 0.255140 0.294448i
\(607\) −3.64058 + 25.3208i −0.147767 + 1.02774i 0.772098 + 0.635504i \(0.219208\pi\)
−0.919864 + 0.392236i \(0.871702\pi\)
\(608\) 0.678936 + 1.48666i 0.0275345 + 0.0602921i
\(609\) 5.13515 + 1.50782i 0.208087 + 0.0610998i
\(610\) 2.22968 + 0.654693i 0.0902771 + 0.0265077i
\(611\) −1.71878 3.76361i −0.0695345 0.152259i
\(612\) 0.114354 0.795348i 0.00462247 0.0321500i
\(613\) −13.6896 + 15.7986i −0.552917 + 0.638101i −0.961560 0.274594i \(-0.911457\pi\)
0.408643 + 0.912694i \(0.366002\pi\)
\(614\) −3.05488 + 6.68926i −0.123285 + 0.269956i
\(615\) −5.31541 3.41601i −0.214338 0.137747i
\(616\) −0.678936 4.72210i −0.0273551 0.190259i
\(617\) 22.5638 14.5009i 0.908385 0.583784i −0.000880605 1.00000i \(-0.500280\pi\)
0.909266 + 0.416216i \(0.136644\pi\)
\(618\) −11.7008 13.5034i −0.470673 0.543186i
\(619\) −47.2663 + 13.8786i −1.89979 + 0.557829i −0.910147 + 0.414285i \(0.864032\pi\)
−0.989644 + 0.143544i \(0.954150\pi\)
\(620\) −5.96917 −0.239728
\(621\) −4.79575 + 0.0271313i −0.192447 + 0.00108874i
\(622\) −23.8747 −0.957288
\(623\) 17.1523 5.03637i 0.687192 0.201778i
\(624\) 0.638429 + 0.736786i 0.0255576 + 0.0294951i
\(625\) 0.841254 0.540641i 0.0336501 0.0216256i
\(626\) 3.13670 + 21.8163i 0.125368 + 0.871953i
\(627\) 2.19209 + 1.40877i 0.0875435 + 0.0562608i
\(628\) 2.80519 6.14251i 0.111939 0.245113i
\(629\) −3.69519 + 4.26447i −0.147337 + 0.170036i
\(630\) 0.425839 2.96177i 0.0169658 0.118000i
\(631\) 4.41587 + 9.66940i 0.175793 + 0.384933i 0.976934 0.213543i \(-0.0685005\pi\)
−0.801141 + 0.598476i \(0.795773\pi\)
\(632\) 1.46065 + 0.428886i 0.0581016 + 0.0170602i
\(633\) 9.17283 + 2.69339i 0.364587 + 0.107053i
\(634\) 3.05601 + 6.69173i 0.121370 + 0.265763i
\(635\) 1.84320 12.8198i 0.0731453 0.508737i
\(636\) 1.29139 1.49035i 0.0512070 0.0590961i
\(637\) −0.791123 + 1.73232i −0.0313454 + 0.0686369i
\(638\) −2.39898 1.54173i −0.0949767 0.0610378i
\(639\) 0.712831 + 4.95785i 0.0281992 + 0.196129i
\(640\) −0.841254 + 0.540641i −0.0332535 + 0.0213707i
\(641\) −3.79664 4.38156i −0.149958 0.173061i 0.675800 0.737085i \(-0.263798\pi\)
−0.825759 + 0.564024i \(0.809253\pi\)
\(642\) −6.77686 + 1.98987i −0.267461 + 0.0785337i
\(643\) 6.66779 0.262952 0.131476 0.991319i \(-0.458028\pi\)
0.131476 + 0.991319i \(0.458028\pi\)
\(644\) −5.88736 + 13.0869i −0.231994 + 0.515698i
\(645\) 1.56111 0.0614688
\(646\) 1.26005 0.369985i 0.0495761 0.0145569i
\(647\) 32.4120 + 37.4054i 1.27425 + 1.47056i 0.811829 + 0.583896i \(0.198472\pi\)
0.462417 + 0.886662i \(0.346982\pi\)
\(648\) −0.841254 + 0.540641i −0.0330476 + 0.0212384i
\(649\) 1.49900 + 10.4257i 0.0588407 + 0.409246i
\(650\) 0.820145 + 0.527075i 0.0321687 + 0.0206736i
\(651\) −7.41978 + 16.2470i −0.290804 + 0.636772i
\(652\) 11.0501 12.7525i 0.432754 0.499425i
\(653\) −5.13536 + 35.7172i −0.200962 + 1.39772i 0.600475 + 0.799643i \(0.294978\pi\)
−0.801438 + 0.598079i \(0.795931\pi\)
\(654\) 4.60630 + 10.0864i 0.180120 + 0.394409i
\(655\) 15.4233 + 4.52868i 0.602637 + 0.176950i
\(656\) 6.06250 + 1.78011i 0.236701 + 0.0695017i
\(657\) −1.65300 3.61956i −0.0644897 0.141213i
\(658\) 1.80726 12.5697i 0.0704542 0.490020i
\(659\) −14.8580 + 17.1470i −0.578784 + 0.667953i −0.967343 0.253471i \(-0.918428\pi\)
0.388559 + 0.921424i \(0.372973\pi\)
\(660\) −0.662317 + 1.45027i −0.0257807 + 0.0564518i
\(661\) 24.0004 + 15.4241i 0.933506 + 0.599928i 0.916547 0.399928i \(-0.130965\pi\)
0.0169598 + 0.999856i \(0.494601\pi\)
\(662\) 0.708989 + 4.93113i 0.0275557 + 0.191654i
\(663\) 0.659008 0.423519i 0.0255938 0.0164481i
\(664\) 9.17382 + 10.5872i 0.356013 + 0.410861i
\(665\) 4.69227 1.37778i 0.181959 0.0534279i
\(666\) 7.02243 0.272114
\(667\) 3.60747 + 7.78244i 0.139682 + 0.301337i
\(668\) 5.17683 0.200298
\(669\) −1.77080 + 0.519953i −0.0684630 + 0.0201025i
\(670\) −7.31067 8.43696i −0.282436 0.325948i
\(671\) −3.11682 + 2.00306i −0.120323 + 0.0773272i
\(672\) 0.425839 + 2.96177i 0.0164271 + 0.114253i
\(673\) −27.7781 17.8519i −1.07077 0.688141i −0.118362 0.992971i \(-0.537764\pi\)
−0.952407 + 0.304829i \(0.901401\pi\)
\(674\) 9.64030 21.1093i 0.371331 0.813101i
\(675\) −0.654861 + 0.755750i −0.0252056 + 0.0290888i
\(676\) 1.71483 11.9269i 0.0659550 0.458727i
\(677\) −7.73997 16.9482i −0.297471 0.651371i 0.700593 0.713561i \(-0.252919\pi\)
−0.998064 + 0.0621897i \(0.980192\pi\)
\(678\) 6.20687 + 1.82250i 0.238373 + 0.0699928i
\(679\) 0.613808 + 0.180230i 0.0235558 + 0.00691660i
\(680\) 0.333797 + 0.730913i 0.0128005 + 0.0280292i
\(681\) 0.100600 0.699686i 0.00385499 0.0268120i
\(682\) 6.23228 7.19243i 0.238646 0.275412i
\(683\) −6.58520 + 14.4196i −0.251976 + 0.551750i −0.992777 0.119974i \(-0.961719\pi\)
0.740801 + 0.671724i \(0.234446\pi\)
\(684\) −1.37491 0.883600i −0.0525709 0.0337853i
\(685\) −1.78322 12.4026i −0.0681333 0.473878i
\(686\) 12.7033 8.16394i 0.485016 0.311701i
\(687\) −0.415777 0.479833i −0.0158629 0.0183068i
\(688\) −1.49788 + 0.439817i −0.0571060 + 0.0167678i
\(689\) 1.92253 0.0732426
\(690\) 4.01978 2.61561i 0.153030 0.0995744i
\(691\) 42.3686 1.61178 0.805888 0.592068i \(-0.201688\pi\)
0.805888 + 0.592068i \(0.201688\pi\)
\(692\) −22.7443 + 6.67834i −0.864610 + 0.253872i
\(693\) 3.12412 + 3.60543i 0.118676 + 0.136959i
\(694\) −7.38137 + 4.74372i −0.280193 + 0.180069i
\(695\) −0.873081 6.07241i −0.0331178 0.230340i
\(696\) 1.50468 + 0.966997i 0.0570346 + 0.0366539i
\(697\) 2.10908 4.61824i 0.0798870 0.174928i
\(698\) −12.3464 + 14.2485i −0.467319 + 0.539315i
\(699\) −1.12663 + 7.83586i −0.0426130 + 0.296380i
\(700\) 1.24302 + 2.72183i 0.0469816 + 0.102875i
\(701\) 46.4592 + 13.6416i 1.75474 + 0.515238i 0.991412 0.130776i \(-0.0417468\pi\)
0.763326 + 0.646013i \(0.223565\pi\)
\(702\) −0.935418 0.274663i −0.0353051 0.0103665i
\(703\) 4.76778 + 10.4400i 0.179820 + 0.393751i
\(704\) 0.226900 1.57812i 0.00855161 0.0594777i
\(705\) −2.77923 + 3.20740i −0.104672 + 0.120798i
\(706\) −4.24349 + 9.29195i −0.159706 + 0.349707i
\(707\) 24.1428 + 15.5157i 0.907985 + 0.583526i
\(708\) −0.940192 6.53918i −0.0353346 0.245757i
\(709\) 25.7210 16.5299i 0.965974 0.620794i 0.0403286 0.999186i \(-0.487160\pi\)
0.925645 + 0.378393i \(0.123523\pi\)
\(710\) −3.28009 3.78542i −0.123099 0.142064i
\(711\) −1.46065 + 0.428886i −0.0547787 + 0.0160845i
\(712\) 5.97428 0.223896
\(713\) −27.4215 + 8.22046i −1.02694 + 0.307859i
\(714\) 2.40433 0.0899799
\(715\) −1.49138 + 0.437910i −0.0557746 + 0.0163769i
\(716\) 13.0600 + 15.0721i 0.488076 + 0.563269i
\(717\) −5.43153 + 3.49063i −0.202844 + 0.130360i
\(718\) −1.25988 8.76264i −0.0470182 0.327019i
\(719\) −5.34597 3.43565i −0.199371 0.128128i 0.437146 0.899390i \(-0.355989\pi\)
−0.636517 + 0.771262i \(0.719626\pi\)
\(720\) 0.415415 0.909632i 0.0154816 0.0339000i
\(721\) 35.0113 40.4052i 1.30389 1.50477i
\(722\) −2.32384 + 16.1627i −0.0864844 + 0.601512i
\(723\) −5.86419 12.8408i −0.218092 0.477554i
\(724\) −19.3535 5.68269i −0.719265 0.211195i
\(725\) 1.71616 + 0.503910i 0.0637366 + 0.0187148i
\(726\) 3.51360 + 7.69371i 0.130402 + 0.285540i
\(727\) −3.49170 + 24.2853i −0.129500 + 0.900692i 0.816689 + 0.577078i \(0.195807\pi\)
−0.946189 + 0.323614i \(0.895102\pi\)
\(728\) −1.91033 + 2.20463i −0.0708014 + 0.0817092i
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 3.34748 + 2.15129i 0.123896 + 0.0796229i
\(731\) 0.178519 + 1.24163i 0.00660277 + 0.0459233i
\(732\) 1.95491 1.25635i 0.0722557 0.0464359i
\(733\) 2.74147 + 3.16383i 0.101259 + 0.116859i 0.804117 0.594471i \(-0.202639\pi\)
−0.702858 + 0.711330i \(0.748093\pi\)
\(734\) 9.90723 2.90902i 0.365682 0.107374i
\(735\) 1.95343 0.0720534
\(736\) −3.12005 + 3.64216i −0.115006 + 0.134252i
\(737\) 17.7989 0.655629
\(738\) −6.06250 + 1.78011i −0.223164 + 0.0655268i
\(739\) 22.7481 + 26.2527i 0.836802 + 0.965722i 0.999781 0.0209080i \(-0.00665571\pi\)
−0.162979 + 0.986630i \(0.552110\pi\)
\(740\) −5.90764 + 3.79661i −0.217169 + 0.139566i
\(741\) −0.226757 1.57713i −0.00833013 0.0579373i
\(742\) 4.96399 + 3.19016i 0.182234 + 0.117115i
\(743\) 6.40427 14.0234i 0.234950 0.514468i −0.755028 0.655693i \(-0.772377\pi\)
0.989978 + 0.141225i \(0.0451040\pi\)
\(744\) −3.90897 + 4.51120i −0.143310 + 0.165389i
\(745\) 1.83583 12.7685i 0.0672596 0.467801i
\(746\) 14.8734 + 32.5681i 0.544552 + 1.19240i
\(747\) −13.4414 3.94674i −0.491794 0.144404i
\(748\) −1.22921 0.360928i −0.0449443 0.0131969i
\(749\) −8.77937 19.2241i −0.320791 0.702435i
\(750\) 0.142315 0.989821i 0.00519660 0.0361432i
\(751\) 12.8195 14.7945i 0.467791 0.539859i −0.472005 0.881596i \(-0.656470\pi\)
0.939796 + 0.341737i \(0.111015\pi\)
\(752\) 1.76302 3.86047i 0.0642907 0.140777i
\(753\) 2.00181 + 1.28649i 0.0729502 + 0.0468822i
\(754\) 0.248159 + 1.72598i 0.00903742 + 0.0628567i
\(755\) 4.86315 3.12536i 0.176988 0.113743i
\(756\) −1.95949 2.26138i −0.0712661 0.0822454i
\(757\) −31.9428 + 9.37925i −1.16098 + 0.340895i −0.804813 0.593528i \(-0.797735\pi\)
−0.356167 + 0.934422i \(0.615917\pi\)
\(758\) −16.8112 −0.610612
\(759\) −1.04534 + 7.57445i −0.0379434 + 0.274935i
\(760\) 1.63436 0.0592843
\(761\) 12.2802 3.60578i 0.445156 0.130709i −0.0514696 0.998675i \(-0.516391\pi\)
0.496625 + 0.867965i \(0.334572\pi\)
\(762\) −8.48149 9.78816i −0.307252 0.354588i
\(763\) −27.9120 + 17.9380i −1.01048 + 0.649398i
\(764\) −0.141160 0.981789i −0.00510699 0.0355199i
\(765\) −0.675969 0.434419i −0.0244397 0.0157065i
\(766\) 10.2779 22.5054i 0.371355 0.813154i
\(767\) 4.21773 4.86752i 0.152293 0.175756i
\(768\) −0.142315 + 0.989821i −0.00513534 + 0.0357171i
\(769\) 20.9349 + 45.8410i 0.754931 + 1.65307i 0.757297 + 0.653070i \(0.226519\pi\)
−0.00236655 + 0.999997i \(0.500753\pi\)
\(770\) −4.57742 1.34405i −0.164959 0.0484362i
\(771\) −6.96585 2.04536i −0.250869 0.0736618i
\(772\) 1.73670 + 3.80283i 0.0625051 + 0.136867i
\(773\) −5.15554 + 35.8576i −0.185432 + 1.28971i 0.658224 + 0.752822i \(0.271308\pi\)
−0.843656 + 0.536884i \(0.819601\pi\)
\(774\) 1.02231 1.17981i 0.0367462 0.0424074i
\(775\) −2.47968 + 5.42975i −0.0890728 + 0.195042i
\(776\) 0.179855 + 0.115586i 0.00645642 + 0.00414929i
\(777\) 2.99042 + 20.7988i 0.107281 + 0.746154i
\(778\) −19.8657 + 12.7669i −0.712219 + 0.457716i
\(779\) −6.76248 7.80432i −0.242291 0.279619i
\(780\) 0.935418 0.274663i 0.0334933 0.00983453i
\(781\) 7.98584 0.285756
\(782\) 2.53999 + 2.89802i 0.0908299 + 0.103633i
\(783\) −1.78861 −0.0639198
\(784\) −1.87430 + 0.550345i −0.0669394 + 0.0196552i
\(785\) −4.42211 5.10338i −0.157832 0.182148i
\(786\) 13.5226 8.69048i 0.482337 0.309979i
\(787\) −0.813375 5.65715i −0.0289937 0.201656i 0.970176 0.242402i \(-0.0779354\pi\)
−0.999170 + 0.0407467i \(0.987026\pi\)
\(788\) 4.19816 + 2.69799i 0.149553 + 0.0961120i
\(789\) −12.1342 + 26.5701i −0.431988 + 0.945922i
\(790\) 0.996905 1.15049i 0.0354683 0.0409326i
\(791\) −2.75471 + 19.1594i −0.0979462 + 0.681231i
\(792\) 0.662317 + 1.45027i 0.0235344 + 0.0515332i
\(793\) 2.17373 + 0.638266i 0.0771915 + 0.0226655i
\(794\) −25.1624 7.38835i −0.892980 0.262203i
\(795\) −0.819203 1.79380i −0.0290541 0.0636197i
\(796\) 0.104542 0.727107i 0.00370540 0.0257716i
\(797\) −22.9351 + 26.4685i −0.812403 + 0.937563i −0.998993 0.0448747i \(-0.985711\pi\)
0.186589 + 0.982438i \(0.440257\pi\)
\(798\) 2.03153 4.44843i 0.0719155 0.157473i
\(799\) −2.86881 1.84367i −0.101491 0.0652244i
\(800\) 0.142315 + 0.989821i 0.00503159 + 0.0349955i
\(801\) −5.02588 + 3.22994i −0.177581 + 0.114124i
\(802\) −7.23706 8.35201i −0.255549 0.294920i
\(803\) −6.08718 + 1.78736i −0.214812 + 0.0630745i
\(804\) −11.1637 −0.393713
\(805\) 9.45860 + 10.7918i 0.333372 + 0.380362i
\(806\) −5.81939 −0.204979
\(807\) 26.1894 7.68991i 0.921911 0.270698i
\(808\) 6.28081 + 7.24844i 0.220958 + 0.254999i
\(809\) −11.5316 + 7.41089i −0.405428 + 0.260553i −0.727424 0.686188i \(-0.759283\pi\)
0.321996 + 0.946741i \(0.395646\pi\)
\(810\) 0.142315 + 0.989821i 0.00500043 + 0.0347788i
\(811\) 6.42281 + 4.12769i 0.225535 + 0.144943i 0.648529 0.761190i \(-0.275384\pi\)
−0.422994 + 0.906133i \(0.639021\pi\)
\(812\) −2.22328 + 4.86829i −0.0780217 + 0.170844i
\(813\) −0.706838 + 0.815734i −0.0247899 + 0.0286091i
\(814\) 1.59339 11.0823i 0.0558482 0.388433i
\(815\) −7.00968 15.3491i −0.245538 0.537654i
\(816\) 0.770978 + 0.226380i 0.0269896 + 0.00792487i
\(817\) 2.44807 + 0.718817i 0.0856470 + 0.0251482i
\(818\) 5.70499 + 12.4922i 0.199470 + 0.436779i
\(819\) 0.415153 2.88746i 0.0145066 0.100896i
\(820\) 4.13770 4.77516i 0.144495 0.166756i
\(821\) 13.3546 29.2424i 0.466077 1.02057i −0.519983 0.854177i \(-0.674062\pi\)
0.986060 0.166390i \(-0.0532111\pi\)
\(822\) −10.5410 6.77428i −0.367659 0.236280i
\(823\) −4.23608 29.4626i −0.147661 1.02700i −0.920035 0.391835i \(-0.871840\pi\)
0.772375 0.635167i \(-0.219069\pi\)
\(824\) 15.0311 9.65992i 0.523634 0.336519i
\(825\) 1.04408 + 1.20493i 0.0363501 + 0.0419503i
\(826\) 18.9672 5.56927i 0.659953 0.193780i
\(827\) −18.0791 −0.628673 −0.314337 0.949312i \(-0.601782\pi\)
−0.314337 + 0.949312i \(0.601782\pi\)
\(828\) 0.655652 4.75080i 0.0227855 0.165102i
\(829\) −6.45333 −0.224133 −0.112067 0.993701i \(-0.535747\pi\)
−0.112067 + 0.993701i \(0.535747\pi\)
\(830\) 13.4414 3.94674i 0.466556 0.136993i
\(831\) 11.9960 + 13.8441i 0.416137 + 0.480248i
\(832\) −0.820145 + 0.527075i −0.0284334 + 0.0182730i
\(833\) 0.223382 + 1.55366i 0.00773973 + 0.0538310i
\(834\) −5.16097 3.31675i −0.178710 0.114850i
\(835\) 2.15053 4.70901i 0.0744223 0.162962i
\(836\) −1.70640 + 1.96929i −0.0590169 + 0.0681092i
\(837\) 0.849501 5.90841i 0.0293631 0.204225i
\(838\) −4.97227 10.8878i −0.171764 0.376111i
\(839\) −22.0997 6.48905i −0.762965 0.224027i −0.122975 0.992410i \(-0.539244\pi\)
−0.639990 + 0.768383i \(0.721062\pi\)
\(840\) 2.87102 + 0.843008i 0.0990597 + 0.0290865i
\(841\) −10.7181 23.4693i −0.369588 0.809286i
\(842\) 2.68793 18.6950i 0.0926322 0.644271i
\(843\) −3.62138 + 4.17929i −0.124727 + 0.143942i
\(844\) −3.97140 + 8.69616i −0.136701 + 0.299334i
\(845\) −10.1367 6.51448i −0.348714 0.224105i
\(846\) 0.603983 + 4.20080i 0.0207654 + 0.144426i
\(847\) −21.2908 + 13.6828i −0.731560 + 0.470145i
\(848\) 1.29139 + 1.49035i 0.0443466 + 0.0511787i
\(849\) −4.98152 + 1.46271i −0.170965 + 0.0502000i
\(850\) 0.803526 0.0275607
\(851\) −21.9103 + 25.5768i −0.751076 + 0.876761i
\(852\) −5.00883 −0.171600
\(853\) 33.6935 9.89329i 1.15364 0.338740i 0.351683 0.936119i \(-0.385609\pi\)
0.801959 + 0.597379i \(0.203791\pi\)
\(854\) 4.55349 + 5.25501i 0.155817 + 0.179823i
\(855\) −1.37491 + 0.883600i −0.0470209 + 0.0302185i
\(856\) −1.00516 6.99107i −0.0343558 0.238950i
\(857\) −9.14115 5.87466i −0.312256 0.200674i 0.375121 0.926976i \(-0.377601\pi\)
−0.687376 + 0.726302i \(0.741238\pi\)
\(858\) −0.645699 + 1.41388i −0.0220438 + 0.0482692i
\(859\) 16.0892 18.5679i 0.548955 0.633528i −0.411684 0.911327i \(-0.635059\pi\)
0.960639 + 0.277799i \(0.0896048\pi\)
\(860\) −0.222170 + 1.54522i −0.00757592 + 0.0526917i
\(861\) −7.85393 17.1977i −0.267661 0.586097i
\(862\) 24.3834 + 7.15961i 0.830501 + 0.243857i
\(863\) −51.2557 15.0500i −1.74476 0.512309i −0.755087 0.655624i \(-0.772406\pi\)
−0.989677 + 0.143315i \(0.954224\pi\)
\(864\) −0.415415 0.909632i −0.0141327 0.0309463i
\(865\) −3.37351 + 23.4633i −0.114703 + 0.797775i
\(866\) 6.91875 7.98466i 0.235109 0.271330i
\(867\) −6.79384 + 14.8764i −0.230731 + 0.505230i
\(868\) −15.0257 9.65645i −0.510007 0.327761i
\(869\) 0.345413 + 2.40240i 0.0117173 + 0.0814959i
\(870\) 1.50468 0.966997i 0.0510133 0.0327843i
\(871\) −7.12723 8.22526i −0.241497 0.278702i
\(872\) −10.6393 + 3.12397i −0.360291 + 0.105791i
\(873\) −0.213794 −0.00723583
\(874\) 7.50799 2.25076i 0.253961 0.0761330i
\(875\) 2.99223 0.101156
\(876\) 3.81797 1.12106i 0.128997 0.0378770i
\(877\) −6.91551 7.98093i −0.233520 0.269497i 0.626880 0.779116i \(-0.284332\pi\)
−0.860400 + 0.509619i \(0.829786\pi\)
\(878\) −25.5018 + 16.3890i −0.860643 + 0.553102i
\(879\) 1.87540 + 13.0437i 0.0632556 + 0.439952i
\(880\) −1.34125 0.861971i −0.0452136 0.0290570i
\(881\) −1.70826 + 3.74057i −0.0575529 + 0.126023i −0.936223 0.351406i \(-0.885704\pi\)
0.878670 + 0.477429i \(0.158431\pi\)
\(882\) 1.27923 1.47631i 0.0430738 0.0497098i
\(883\) 5.69348 39.5990i 0.191601 1.33261i −0.636171 0.771548i \(-0.719483\pi\)
0.827772 0.561065i \(-0.189608\pi\)
\(884\) 0.325421 + 0.712573i 0.0109451 + 0.0239664i
\(885\) −6.33882 1.86124i −0.213077 0.0625650i
\(886\) −29.7410 8.73275i −0.999169 0.293382i
\(887\) −13.3943 29.3295i −0.449738 0.984789i −0.989708 0.143104i \(-0.954292\pi\)
0.539969 0.841685i \(-0.318436\pi\)
\(888\) −0.999396 + 6.95095i −0.0335375 + 0.233259i
\(889\) 25.3786 29.2884i 0.851169 0.982302i
\(890\) 2.48181 5.43439i 0.0831903 0.182161i
\(891\) −1.34125 0.861971i −0.0449337 0.0288771i
\(892\) −0.262650 1.82677i −0.00879417 0.0611648i
\(893\) −5.83510 + 3.74999i −0.195264 + 0.125489i
\(894\) −8.44756 9.74900i −0.282529 0.326055i
\(895\) 19.1354 5.61865i 0.639624 0.187811i
\(896\) −2.99223 −0.0999633
\(897\) 3.91891 2.54997i 0.130849 0.0851412i
\(898\) −6.36852 −0.212520
\(899\) −10.2441 + 3.00793i −0.341658 + 0.100320i
\(900\) −0.654861 0.755750i −0.0218287 0.0251917i
\(901\) 1.33302 0.856679i 0.0444093 0.0285401i
\(902\) 1.43365 + 9.97128i 0.0477355 + 0.332007i
\(903\) 3.92967 + 2.52545i 0.130771 + 0.0840416i
\(904\) −2.68728 + 5.88433i −0.0893777 + 0.195710i
\(905\) −13.2089 + 15.2438i −0.439078 + 0.506723i
\(906\) 0.822700 5.72200i 0.0273324 0.190101i
\(907\) −16.0389 35.1202i −0.532562 1.16615i −0.964461 0.264226i \(-0.914883\pi\)
0.431899 0.901922i \(-0.357844\pi\)
\(908\) 0.678247 + 0.199151i 0.0225084 + 0.00660907i
\(909\) −9.20255 2.70211i −0.305229 0.0896235i
\(910\) 1.21183 + 2.65353i 0.0401717 + 0.0879637i
\(911\) 4.72731 32.8792i 0.156623 1.08934i −0.748177 0.663499i \(-0.769071\pi\)
0.904800 0.425837i \(-0.140020\pi\)
\(912\) 1.07028 1.23516i 0.0354404 0.0409004i
\(913\) −9.27828 + 20.3166i −0.307066 + 0.672381i
\(914\) −30.6288 19.6839i −1.01311 0.651087i
\(915\) −0.330713 2.30016i −0.0109330 0.0760409i
\(916\) 0.534120 0.343258i 0.0176478 0.0113416i
\(917\) 31.4977 + 36.3503i 1.04014 + 1.20039i
\(918\) −0.770978 + 0.226380i −0.0254461 + 0.00747164i
\(919\) 39.5537 1.30475 0.652377 0.757894i \(-0.273772\pi\)
0.652377 + 0.757894i \(0.273772\pi\)
\(920\) 2.01691 + 4.35110i 0.0664955 + 0.143452i
\(921\) 7.35380 0.242316
\(922\) 6.19013 1.81759i 0.203861 0.0598590i
\(923\) −3.19778 3.69044i −0.105256 0.121472i
\(924\) −4.01334 + 2.57922i −0.132029 + 0.0848499i
\(925\) 0.999396 + 6.95095i 0.0328599 + 0.228546i
\(926\) 14.5203 + 9.33164i 0.477167 + 0.306657i
\(927\) −7.42245 + 16.2529i −0.243785 + 0.533815i
\(928\) −1.17129 + 1.35174i −0.0384496 + 0.0443732i
\(929\) 1.59483 11.0923i 0.0523246 0.363925i −0.946790 0.321852i \(-0.895695\pi\)
0.999115 0.0420732i \(-0.0133963\pi\)
\(930\) 2.47968 + 5.42975i 0.0813120 + 0.178048i
\(931\) 3.06328 + 0.899460i 0.100395 + 0.0294786i
\(932\) −7.59577 2.23032i −0.248808 0.0730565i
\(933\) 9.91791 + 21.7172i 0.324698 + 0.710989i
\(934\) 4.12357 28.6800i 0.134927 0.938439i
\(935\) −0.838944 + 0.968193i −0.0274364 + 0.0316633i
\(936\) 0.404992 0.886808i 0.0132376 0.0289862i
\(937\) 3.89353 + 2.50222i 0.127196 + 0.0817440i 0.602692 0.797974i \(-0.294095\pi\)
−0.475496 + 0.879718i \(0.657731\pi\)
\(938\) −4.75393 33.0643i −0.155221 1.07959i
\(939\) 18.5417 11.9160i 0.605087 0.388866i
\(940\) −2.77923 3.20740i −0.0906483 0.104614i
\(941\) 17.8144 5.23079i 0.580734 0.170519i 0.0218448 0.999761i \(-0.493046\pi\)
0.558889 + 0.829243i \(0.311228\pi\)
\(942\) −6.75275 −0.220016
\(943\) 12.4319 27.6346i 0.404837 0.899907i
\(944\) 6.60642 0.215021
\(945\) −2.87102 + 0.843008i −0.0933944 + 0.0274231i
\(946\) −1.62992 1.88103i −0.0529934 0.0611577i
\(947\) −51.1922 + 32.8992i −1.66352 + 1.06908i −0.750778 + 0.660555i \(0.770321\pi\)
−0.912746 + 0.408527i \(0.866043\pi\)
\(948\) −0.216648 1.50682i −0.00703641 0.0489393i
\(949\) 3.26348 + 2.09731i 0.105937 + 0.0680817i
\(950\) 0.678936 1.48666i 0.0220276 0.0482337i
\(951\) 4.81750 5.55969i 0.156218 0.180285i
\(952\) −0.342172 + 2.37986i −0.0110899 + 0.0771318i
\(953\) −14.3892 31.5079i −0.466111 1.02064i −0.986052 0.166438i \(-0.946773\pi\)
0.519941 0.854202i \(-0.325954\pi\)
\(954\) −1.89213 0.555580i −0.0612600 0.0179876i
\(955\) −0.951706 0.279446i −0.0307965 0.00904267i
\(956\) −2.68212 5.87302i −0.0867458 0.189947i
\(957\) −0.405836 + 2.82265i −0.0131188 + 0.0912434i
\(958\) 21.0738 24.3204i 0.680863 0.785758i
\(959\) 15.5751 34.1048i 0.502947 1.10130i
\(960\) 0.841254 + 0.540641i 0.0271513 + 0.0174491i
\(961\) −0.659058 4.58385i −0.0212599 0.147866i
\(962\) −5.75941 + 3.70135i −0.185691 + 0.119336i
\(963\) 4.62525 + 5.33783i 0.149047 + 0.172009i
\(964\) 13.5447 3.97707i 0.436244 0.128093i
\(965\) 4.18063 0.134579
\(966\) 14.3500 0.0811830i 0.461703 0.00261202i
\(967\) 40.3627 1.29798 0.648988 0.760798i \(-0.275192\pi\)
0.648988 + 0.760798i \(0.275192\pi\)
\(968\) −8.11543 + 2.38291i −0.260840 + 0.0765895i
\(969\) −0.859995 0.992487i −0.0276270 0.0318833i
\(970\) 0.179855 0.115586i 0.00577480 0.00371124i
\(971\) −1.51896 10.5646i −0.0487457 0.339034i −0.999571 0.0293048i \(-0.990671\pi\)
0.950825 0.309729i \(-0.100238\pi\)
\(972\) 0.841254 + 0.540641i 0.0269832 + 0.0173411i
\(973\) 7.62572 16.6980i 0.244469 0.535313i
\(974\) −17.3397 + 20.0111i −0.555599 + 0.641196i
\(975\) 0.138744 0.964985i 0.00444336 0.0309043i
\(976\) 0.965346 + 2.11381i 0.0309000 + 0.0676615i
\(977\) 1.99916 + 0.587005i 0.0639587 + 0.0187800i 0.313555 0.949570i \(-0.398480\pi\)
−0.249597 + 0.968350i \(0.580298\pi\)
\(978\) −16.1904 4.75393i −0.517712 0.152014i
\(979\) 3.95687 + 8.66433i 0.126462 + 0.276913i
\(980\) −0.278002 + 1.93355i −0.00888046 + 0.0617649i
\(981\) 7.26137 8.38007i 0.231838 0.267555i
\(982\) 12.1693 26.6470i 0.388337 0.850340i
\(983\) −40.1650 25.8125i −1.28106 0.823289i −0.290045 0.957013i \(-0.593670\pi\)
−0.991019 + 0.133724i \(0.957307\pi\)
\(984\) −0.899209 6.25413i −0.0286657 0.199374i
\(985\) 4.19816 2.69799i 0.133764 0.0859651i
\(986\) 0.941164 + 1.08616i 0.0299728 + 0.0345904i
\(987\) −12.1846 + 3.57772i −0.387840 + 0.113880i
\(988\) 1.59335 0.0506911
\(989\) 1.10740 + 7.40449i 0.0352131 + 0.235449i
\(990\) 1.59435 0.0506718
\(991\) 14.5653 4.27675i 0.462681 0.135856i −0.0420803 0.999114i \(-0.513399\pi\)
0.504762 + 0.863259i \(0.331580\pi\)
\(992\) −3.90897 4.51120i −0.124110 0.143231i
\(993\) 4.19099 2.69338i 0.132997 0.0854720i
\(994\) −2.13295 14.8350i −0.0676532 0.470538i
\(995\) −0.617971 0.397146i −0.0195910 0.0125904i
\(996\) 5.81947 12.7429i 0.184397 0.403773i
\(997\) 5.86834 6.77243i 0.185852 0.214485i −0.655176 0.755476i \(-0.727405\pi\)
0.841028 + 0.540992i \(0.181951\pi\)
\(998\) −4.91462 + 34.1819i −0.155570 + 1.08201i
\(999\) −2.91722 6.38783i −0.0922968 0.202102i
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 690.2.m.b.331.1 yes 10
23.18 even 11 inner 690.2.m.b.271.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.b.271.1 10 23.18 even 11 inner
690.2.m.b.331.1 yes 10 1.1 even 1 trivial