Properties

Label 418.2.n.c.235.1
Level $418$
Weight $2$
Character 418.235
Analytic conductor $3.338$
Analytic rank $0$
Dimension $8$
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] = [418,2,Mod(49,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([12, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.n (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 235.1
Root \(0.913545 - 0.406737i\) of defining polynomial
Character \(\chi\) \(=\) 418.235
Dual form 418.2.n.c.201.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.104528 + 0.994522i) q^{2} +(-1.95630 + 0.415823i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.348943 - 0.155360i) q^{5} +(-0.209057 - 1.98904i) q^{6} +(1.30902 + 4.02874i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\) \(q+(-0.104528 + 0.994522i) q^{2} +(-1.95630 + 0.415823i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.348943 - 0.155360i) q^{5} +(-0.209057 - 1.98904i) q^{6} +(1.30902 + 4.02874i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.190983 - 0.330792i) q^{10} +(-2.54508 - 2.12663i) q^{11} +2.00000 q^{12} +(-1.69381 + 0.754131i) q^{13} +(-4.14350 + 0.880728i) q^{14} +(0.747238 + 0.158830i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-4.91667 - 2.18904i) q^{17} +(0.309017 + 0.951057i) q^{18} +(4.30146 - 0.705295i) q^{19} +(0.309017 + 0.224514i) q^{20} +(-4.23607 - 7.33708i) q^{21} +(2.38101 - 2.30885i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.209057 + 1.98904i) q^{24} +(-3.24803 - 3.60730i) q^{25} +(-0.572949 - 1.76336i) q^{26} +(3.23607 - 2.35114i) q^{27} +(-0.442790 - 4.21286i) q^{28} +(-2.18720 - 0.464905i) q^{29} +(-0.236068 + 0.726543i) q^{30} +(-7.97214 - 5.79210i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.86324 + 3.10200i) q^{33} +(2.69098 - 4.66092i) q^{34} +(0.169131 - 1.60917i) q^{35} +(-0.978148 + 0.207912i) q^{36} +(-1.04508 - 3.21644i) q^{37} +(0.251807 + 4.35162i) q^{38} +(3.00000 - 2.17963i) q^{39} +(-0.255585 + 0.283856i) q^{40} +(-9.72697 + 2.06753i) q^{41} +(7.73968 - 3.44593i) q^{42} +(5.35410 + 9.27358i) q^{43} +(2.04732 + 2.60931i) q^{44} -0.381966 q^{45} +(0.809017 + 0.587785i) q^{46} +(0.669131 + 0.743145i) q^{47} +(-1.95630 - 0.415823i) q^{48} +(-8.85410 + 6.43288i) q^{49} +(3.92705 - 2.85317i) q^{50} +(10.5287 + 2.23795i) q^{51} +(1.81359 - 0.385489i) q^{52} +(6.17916 - 2.75114i) q^{53} +(2.00000 + 3.46410i) q^{54} +(0.557699 + 1.13748i) q^{55} +4.23607 q^{56} +(-8.12165 + 3.16841i) q^{57} +(0.690983 - 2.12663i) q^{58} +(5.82693 - 6.47146i) q^{59} +(-0.697887 - 0.310719i) q^{60} +(0.746950 + 7.10675i) q^{61} +(6.59368 - 7.32302i) q^{62} +(2.83448 + 3.14801i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.708204 q^{65} +(-3.69789 + 5.50687i) q^{66} +(-6.16312 + 10.6748i) q^{67} +(4.35410 + 3.16344i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(1.58268 + 0.336408i) q^{70} +(-5.77931 - 2.57311i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-7.51840 + 8.35003i) q^{73} +(3.30806 - 0.703150i) q^{74} +(7.85410 + 5.70634i) q^{75} +(-4.35410 - 0.204441i) q^{76} +(5.23607 - 13.0373i) q^{77} +(1.85410 + 3.21140i) q^{78} +(-0.387613 + 3.68789i) q^{79} +(-0.255585 - 0.283856i) q^{80} +(-7.36044 + 8.17459i) q^{81} +(-1.03946 - 9.88980i) q^{82} +(-9.28115 + 6.74315i) q^{83} +(2.61803 + 8.05748i) q^{84} +(1.37555 + 1.52770i) q^{85} +(-9.78243 + 4.35542i) q^{86} +4.47214 q^{87} +(-2.80902 + 1.76336i) q^{88} +(-7.35410 + 12.7377i) q^{89} +(0.0399263 - 0.379874i) q^{90} +(-5.25542 - 5.83674i) q^{91} +(-0.669131 + 0.743145i) q^{92} +(18.0043 + 8.01605i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(-1.61054 - 0.422165i) q^{95} +(0.618034 - 1.90211i) q^{96} +(1.69131 - 16.0917i) q^{97} +(-5.47214 - 9.47802i) q^{98} +(-3.19003 - 0.907591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9} + 6 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} - 3 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} - 18 q^{26} + 8 q^{27} + 7 q^{28} - 5 q^{29} + 16 q^{30} - 28 q^{31} - 4 q^{32} + 18 q^{33} + 26 q^{34} - 3 q^{35} + q^{36} + 14 q^{37} - 13 q^{38} + 24 q^{39} - 4 q^{40} - 19 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} - 12 q^{45} + 2 q^{46} + q^{47} + 2 q^{48} - 44 q^{49} + 18 q^{50} - 18 q^{51} + 9 q^{52} + 4 q^{53} + 16 q^{54} + 14 q^{55} + 16 q^{56} - 26 q^{57} + 10 q^{58} - 13 q^{59} + 2 q^{60} - 3 q^{61} - q^{62} - 3 q^{63} - 2 q^{64} - 48 q^{65} - 22 q^{66} - 18 q^{67} + 8 q^{68} + 4 q^{69} + 2 q^{70} - 16 q^{71} + q^{72} - 4 q^{73} - 7 q^{74} + 36 q^{75} - 8 q^{76} + 24 q^{77} - 12 q^{78} + 12 q^{79} - 4 q^{80} - 11 q^{81} + 21 q^{82} - 34 q^{83} + 12 q^{84} + 31 q^{85} - 19 q^{86} - 18 q^{88} - 32 q^{89} + q^{90} + 3 q^{91} - q^{92} + 28 q^{93} - 2 q^{94} - 38 q^{95} - 4 q^{96} - 30 q^{97} - 8 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.104528 + 0.994522i −0.0739128 + 0.703233i
\(3\) −1.95630 + 0.415823i −1.12947 + 0.240076i −0.734493 0.678616i \(-0.762580\pi\)
−0.394975 + 0.918692i \(0.629247\pi\)
\(4\) −0.978148 0.207912i −0.489074 0.103956i
\(5\) −0.348943 0.155360i −0.156052 0.0694789i 0.327224 0.944947i \(-0.393887\pi\)
−0.483276 + 0.875468i \(0.660553\pi\)
\(6\) −0.209057 1.98904i −0.0853471 0.812024i
\(7\) 1.30902 + 4.02874i 0.494762 + 1.52272i 0.817327 + 0.576173i \(0.195455\pi\)
−0.322566 + 0.946547i \(0.604545\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 0.913545 0.406737i 0.304515 0.135579i
\(10\) 0.190983 0.330792i 0.0603941 0.104606i
\(11\) −2.54508 2.12663i −0.767372 0.641202i
\(12\) 2.00000 0.577350
\(13\) −1.69381 + 0.754131i −0.469777 + 0.209158i −0.627951 0.778253i \(-0.716106\pi\)
0.158174 + 0.987411i \(0.449439\pi\)
\(14\) −4.14350 + 0.880728i −1.10740 + 0.235384i
\(15\) 0.747238 + 0.158830i 0.192936 + 0.0410098i
\(16\) 0.913545 + 0.406737i 0.228386 + 0.101684i
\(17\) −4.91667 2.18904i −1.19247 0.530921i −0.288069 0.957610i \(-0.593013\pi\)
−0.904399 + 0.426689i \(0.859680\pi\)
\(18\) 0.309017 + 0.951057i 0.0728360 + 0.224166i
\(19\) 4.30146 0.705295i 0.986823 0.161806i
\(20\) 0.309017 + 0.224514i 0.0690983 + 0.0502029i
\(21\) −4.23607 7.33708i −0.924386 1.60108i
\(22\) 2.38101 2.30885i 0.507633 0.492248i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) −0.209057 + 1.98904i −0.0426736 + 0.406012i
\(25\) −3.24803 3.60730i −0.649606 0.721460i
\(26\) −0.572949 1.76336i −0.112365 0.345823i
\(27\) 3.23607 2.35114i 0.622782 0.452477i
\(28\) −0.442790 4.21286i −0.0836794 0.796156i
\(29\) −2.18720 0.464905i −0.406154 0.0863306i 0.000304639 1.00000i \(-0.499903\pi\)
−0.406458 + 0.913669i \(0.633236\pi\)
\(30\) −0.236068 + 0.726543i −0.0430999 + 0.132648i
\(31\) −7.97214 5.79210i −1.43184 1.04029i −0.989671 0.143358i \(-0.954210\pi\)
−0.442167 0.896933i \(-0.645790\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 5.86324 + 3.10200i 1.02066 + 0.539990i
\(34\) 2.69098 4.66092i 0.461500 0.799341i
\(35\) 0.169131 1.60917i 0.0285883 0.271999i
\(36\) −0.978148 + 0.207912i −0.163025 + 0.0346519i
\(37\) −1.04508 3.21644i −0.171811 0.528780i 0.827663 0.561226i \(-0.189670\pi\)
−0.999473 + 0.0324464i \(0.989670\pi\)
\(38\) 0.251807 + 4.35162i 0.0408484 + 0.705926i
\(39\) 3.00000 2.17963i 0.480384 0.349020i
\(40\) −0.255585 + 0.283856i −0.0404116 + 0.0448816i
\(41\) −9.72697 + 2.06753i −1.51910 + 0.322894i −0.890553 0.454880i \(-0.849682\pi\)
−0.628544 + 0.777774i \(0.716349\pi\)
\(42\) 7.73968 3.44593i 1.19426 0.531718i
\(43\) 5.35410 + 9.27358i 0.816493 + 1.41421i 0.908251 + 0.418426i \(0.137418\pi\)
−0.0917581 + 0.995781i \(0.529249\pi\)
\(44\) 2.04732 + 2.60931i 0.308645 + 0.393368i
\(45\) −0.381966 −0.0569401
\(46\) 0.809017 + 0.587785i 0.119283 + 0.0866642i
\(47\) 0.669131 + 0.743145i 0.0976027 + 0.108399i 0.789967 0.613149i \(-0.210098\pi\)
−0.692364 + 0.721548i \(0.743431\pi\)
\(48\) −1.95630 0.415823i −0.282367 0.0600189i
\(49\) −8.85410 + 6.43288i −1.26487 + 0.918983i
\(50\) 3.92705 2.85317i 0.555369 0.403499i
\(51\) 10.5287 + 2.23795i 1.47431 + 0.313375i
\(52\) 1.81359 0.385489i 0.251499 0.0534578i
\(53\) 6.17916 2.75114i 0.848773 0.377898i 0.0642018 0.997937i \(-0.479550\pi\)
0.784571 + 0.620039i \(0.212883\pi\)
\(54\) 2.00000 + 3.46410i 0.272166 + 0.471405i
\(55\) 0.557699 + 1.13748i 0.0752001 + 0.153377i
\(56\) 4.23607 0.566068
\(57\) −8.12165 + 3.16841i −1.07574 + 0.419667i
\(58\) 0.690983 2.12663i 0.0907305 0.279240i
\(59\) 5.82693 6.47146i 0.758601 0.842512i −0.232915 0.972497i \(-0.574826\pi\)
0.991516 + 0.129985i \(0.0414930\pi\)
\(60\) −0.697887 0.310719i −0.0900968 0.0401137i
\(61\) 0.746950 + 7.10675i 0.0956371 + 0.909926i 0.932173 + 0.362014i \(0.117911\pi\)
−0.836536 + 0.547913i \(0.815423\pi\)
\(62\) 6.59368 7.32302i 0.837398 0.930025i
\(63\) 2.83448 + 3.14801i 0.357111 + 0.396612i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 0.708204 0.0878419
\(66\) −3.69789 + 5.50687i −0.455178 + 0.677849i
\(67\) −6.16312 + 10.6748i −0.752945 + 1.30414i 0.193445 + 0.981111i \(0.438034\pi\)
−0.946390 + 0.323028i \(0.895299\pi\)
\(68\) 4.35410 + 3.16344i 0.528012 + 0.383623i
\(69\) −0.618034 + 1.90211i −0.0744025 + 0.228988i
\(70\) 1.58268 + 0.336408i 0.189166 + 0.0402085i
\(71\) −5.77931 2.57311i −0.685877 0.305372i 0.0340515 0.999420i \(-0.489159\pi\)
−0.719929 + 0.694048i \(0.755826\pi\)
\(72\) −0.104528 0.994522i −0.0123188 0.117206i
\(73\) −7.51840 + 8.35003i −0.879962 + 0.977297i −0.999880 0.0154872i \(-0.995070\pi\)
0.119918 + 0.992784i \(0.461737\pi\)
\(74\) 3.30806 0.703150i 0.384554 0.0817396i
\(75\) 7.85410 + 5.70634i 0.906914 + 0.658911i
\(76\) −4.35410 0.204441i −0.499450 0.0234510i
\(77\) 5.23607 13.0373i 0.596705 1.48574i
\(78\) 1.85410 + 3.21140i 0.209936 + 0.363619i
\(79\) −0.387613 + 3.68789i −0.0436099 + 0.414920i 0.950838 + 0.309689i \(0.100225\pi\)
−0.994448 + 0.105231i \(0.966442\pi\)
\(80\) −0.255585 0.283856i −0.0285753 0.0317361i
\(81\) −7.36044 + 8.17459i −0.817826 + 0.908288i
\(82\) −1.03946 9.88980i −0.114789 1.09215i
\(83\) −9.28115 + 6.74315i −1.01874 + 0.740157i −0.966024 0.258452i \(-0.916787\pi\)
−0.0527149 + 0.998610i \(0.516787\pi\)
\(84\) 2.61803 + 8.05748i 0.285651 + 0.879143i
\(85\) 1.37555 + 1.52770i 0.149199 + 0.165703i
\(86\) −9.78243 + 4.35542i −1.05487 + 0.469657i
\(87\) 4.47214 0.479463
\(88\) −2.80902 + 1.76336i −0.299442 + 0.187974i
\(89\) −7.35410 + 12.7377i −0.779533 + 1.35019i 0.152678 + 0.988276i \(0.451210\pi\)
−0.932211 + 0.361915i \(0.882123\pi\)
\(90\) 0.0399263 0.379874i 0.00420860 0.0400422i
\(91\) −5.25542 5.83674i −0.550918 0.611856i
\(92\) −0.669131 + 0.743145i −0.0697617 + 0.0774782i
\(93\) 18.0043 + 8.01605i 1.86696 + 0.831226i
\(94\) −0.809017 + 0.587785i −0.0834437 + 0.0606254i
\(95\) −1.61054 0.422165i −0.165238 0.0433132i
\(96\) 0.618034 1.90211i 0.0630778 0.194134i
\(97\) 1.69131 16.0917i 0.171726 1.63386i −0.481319 0.876546i \(-0.659842\pi\)
0.653045 0.757319i \(-0.273491\pi\)
\(98\) −5.47214 9.47802i −0.552769 0.957424i
\(99\) −3.19003 0.907591i −0.320610 0.0912163i
\(100\) 2.42705 + 4.20378i 0.242705 + 0.420378i
\(101\) 2.52498 1.12419i 0.251245 0.111861i −0.277250 0.960798i \(-0.589423\pi\)
0.528495 + 0.848936i \(0.322756\pi\)
\(102\) −3.32624 + 10.2371i −0.329347 + 1.01362i
\(103\) 2.76393 + 8.50651i 0.272338 + 0.838171i 0.989911 + 0.141688i \(0.0452529\pi\)
−0.717573 + 0.696483i \(0.754747\pi\)
\(104\) 0.193806 + 1.84395i 0.0190043 + 0.180814i
\(105\) 0.338261 + 3.21834i 0.0330109 + 0.314078i
\(106\) 2.09017 + 6.43288i 0.203015 + 0.624817i
\(107\) 1.88197 5.79210i 0.181937 0.559943i −0.817946 0.575296i \(-0.804887\pi\)
0.999882 + 0.0153525i \(0.00488705\pi\)
\(108\) −3.65418 + 1.62695i −0.351624 + 0.156553i
\(109\) −3.95492 6.85011i −0.378812 0.656122i 0.612078 0.790798i \(-0.290334\pi\)
−0.990890 + 0.134676i \(0.957001\pi\)
\(110\) −1.18954 + 0.435745i −0.113418 + 0.0415466i
\(111\) 3.38197 + 5.85774i 0.321002 + 0.555992i
\(112\) −0.442790 + 4.21286i −0.0418397 + 0.398078i
\(113\) 3.40983 10.4944i 0.320770 0.987228i −0.652544 0.757751i \(-0.726298\pi\)
0.973314 0.229477i \(-0.0737017\pi\)
\(114\) −2.30211 8.40835i −0.215613 0.787514i
\(115\) −0.309017 + 0.224514i −0.0288160 + 0.0209360i
\(116\) 2.04275 + 0.909491i 0.189665 + 0.0844441i
\(117\) −1.24064 + 1.37787i −0.114697 + 0.127384i
\(118\) 5.82693 + 6.47146i 0.536412 + 0.595746i
\(119\) 2.38308 22.6735i 0.218456 2.07847i
\(120\) 0.381966 0.661585i 0.0348686 0.0603941i
\(121\) 1.95492 + 10.8249i 0.177720 + 0.984081i
\(122\) −7.14590 −0.646959
\(123\) 18.1691 8.08940i 1.63825 0.729397i
\(124\) 6.59368 + 7.32302i 0.592130 + 0.657627i
\(125\) 1.16312 + 3.57971i 0.104033 + 0.320179i
\(126\) −3.42705 + 2.48990i −0.305306 + 0.221818i
\(127\) 0.0587770 + 0.559226i 0.00521561 + 0.0496232i 0.996820 0.0796843i \(-0.0253912\pi\)
−0.991605 + 0.129308i \(0.958725\pi\)
\(128\) 0.669131 0.743145i 0.0591433 0.0656853i
\(129\) −14.3304 15.9155i −1.26172 1.40128i
\(130\) −0.0740275 + 0.704324i −0.00649264 + 0.0617733i
\(131\) −1.73607 3.00696i −0.151681 0.262719i 0.780165 0.625574i \(-0.215135\pi\)
−0.931846 + 0.362855i \(0.881802\pi\)
\(132\) −5.09017 4.25325i −0.443042 0.370198i
\(133\) 8.47214 + 16.4062i 0.734627 + 1.42260i
\(134\) −9.97214 7.24518i −0.861461 0.625888i
\(135\) −1.49448 + 0.317661i −0.128624 + 0.0273399i
\(136\) −3.60124 + 3.99958i −0.308804 + 0.342961i
\(137\) 1.15341 + 10.9740i 0.0985427 + 0.937572i 0.926377 + 0.376598i \(0.122906\pi\)
−0.827834 + 0.560973i \(0.810427\pi\)
\(138\) −1.82709 0.813473i −0.155532 0.0692474i
\(139\) 10.1888 + 2.16569i 0.864201 + 0.183692i 0.618626 0.785686i \(-0.287690\pi\)
0.245576 + 0.969377i \(0.421023\pi\)
\(140\) −0.500000 + 1.53884i −0.0422577 + 0.130056i
\(141\) −1.61803 1.17557i −0.136263 0.0990009i
\(142\) 3.16312 5.47868i 0.265443 0.459761i
\(143\) 5.91464 + 1.68277i 0.494607 + 0.140720i
\(144\) 1.00000 0.0833333
\(145\) 0.690983 + 0.502029i 0.0573830 + 0.0416912i
\(146\) −7.51840 8.35003i −0.622227 0.691053i
\(147\) 14.6463 16.2664i 1.20801 1.34163i
\(148\) 0.353512 + 3.36344i 0.0290585 + 0.276473i
\(149\) −8.30428 3.69731i −0.680313 0.302895i 0.0373328 0.999303i \(-0.488114\pi\)
−0.717646 + 0.696408i \(0.754780\pi\)
\(150\) −6.49606 + 7.21460i −0.530401 + 0.589070i
\(151\) 2.39919 7.38394i 0.195243 0.600896i −0.804731 0.593640i \(-0.797690\pi\)
0.999974 0.00725620i \(-0.00230974\pi\)
\(152\) 0.658449 4.30888i 0.0534072 0.349496i
\(153\) −5.38197 −0.435106
\(154\) 12.4185 + 6.57015i 1.00071 + 0.529438i
\(155\) 1.88197 + 3.25966i 0.151163 + 0.261822i
\(156\) −3.38761 + 1.50826i −0.271226 + 0.120758i
\(157\) −8.42971 + 1.79179i −0.672764 + 0.143000i −0.531613 0.846988i \(-0.678414\pi\)
−0.141151 + 0.989988i \(0.545080\pi\)
\(158\) −3.62717 0.770979i −0.288562 0.0613358i
\(159\) −10.9443 + 7.95148i −0.867937 + 0.630593i
\(160\) 0.309017 0.224514i 0.0244299 0.0177494i
\(161\) 4.14350 + 0.880728i 0.326554 + 0.0694111i
\(162\) −7.36044 8.17459i −0.578291 0.642257i
\(163\) 4.00000 + 2.90617i 0.313304 + 0.227629i 0.733313 0.679891i \(-0.237973\pi\)
−0.420009 + 0.907520i \(0.637973\pi\)
\(164\) 9.94427 0.776517
\(165\) −1.56401 1.99333i −0.121758 0.155181i
\(166\) −5.73607 9.93516i −0.445205 0.771118i
\(167\) 15.5303 6.91452i 1.20177 0.535062i 0.294515 0.955647i \(-0.404842\pi\)
0.907253 + 0.420585i \(0.138175\pi\)
\(168\) −8.28700 + 1.76146i −0.639356 + 0.135899i
\(169\) −6.39843 + 7.10618i −0.492187 + 0.546629i
\(170\) −1.66312 + 1.20833i −0.127555 + 0.0926744i
\(171\) 3.64271 2.39388i 0.278565 0.183065i
\(172\) −3.30902 10.1841i −0.252310 0.776531i
\(173\) −20.6630 + 4.39205i −1.57098 + 0.333922i −0.909390 0.415946i \(-0.863451\pi\)
−0.661588 + 0.749867i \(0.730117\pi\)
\(174\) −0.467465 + 4.44764i −0.0354385 + 0.337175i
\(175\) 10.2812 17.8075i 0.777182 1.34612i
\(176\) −1.46007 2.97795i −0.110057 0.224471i
\(177\) −8.70820 + 15.0831i −0.654549 + 1.13371i
\(178\) −11.8992 8.64527i −0.891882 0.647990i
\(179\) −0.527864 + 1.62460i −0.0394544 + 0.121428i −0.968844 0.247673i \(-0.920334\pi\)
0.929389 + 0.369101i \(0.120334\pi\)
\(180\) 0.373619 + 0.0794152i 0.0278479 + 0.00591926i
\(181\) −1.12514 10.7050i −0.0836308 0.795694i −0.953293 0.302047i \(-0.902330\pi\)
0.869662 0.493647i \(-0.164337\pi\)
\(182\) 6.35410 4.61653i 0.470997 0.342200i
\(183\) −4.41641 13.5923i −0.326470 1.00477i
\(184\) −0.669131 0.743145i −0.0493290 0.0547854i
\(185\) −0.135029 + 1.28472i −0.00992756 + 0.0944545i
\(186\) −9.85410 + 17.0678i −0.722538 + 1.25147i
\(187\) 7.85807 + 16.0272i 0.574639 + 1.17203i
\(188\) −0.500000 0.866025i −0.0364662 0.0631614i
\(189\) 13.7082 + 9.95959i 0.997125 + 0.724454i
\(190\) 0.588200 1.55759i 0.0426725 0.112999i
\(191\) −0.0901699 0.277515i −0.00652447 0.0200802i 0.947741 0.319040i \(-0.103360\pi\)
−0.954266 + 0.298960i \(0.903360\pi\)
\(192\) 1.82709 + 0.813473i 0.131859 + 0.0587074i
\(193\) 7.68877 + 3.42326i 0.553450 + 0.246412i 0.664352 0.747420i \(-0.268707\pi\)
−0.110902 + 0.993831i \(0.535374\pi\)
\(194\) 15.8268 + 3.36408i 1.13630 + 0.241527i
\(195\) −1.38546 + 0.294488i −0.0992146 + 0.0210887i
\(196\) 9.99809 4.45144i 0.714149 0.317960i
\(197\) 25.5623 1.82124 0.910619 0.413246i \(-0.135605\pi\)
0.910619 + 0.413246i \(0.135605\pi\)
\(198\) 1.23607 3.07768i 0.0878435 0.218721i
\(199\) −10.4271 + 18.0602i −0.739154 + 1.28025i 0.213723 + 0.976894i \(0.431441\pi\)
−0.952877 + 0.303358i \(0.901892\pi\)
\(200\) −4.43444 + 1.97434i −0.313562 + 0.139607i
\(201\) 7.61803 23.4459i 0.537335 1.65375i
\(202\) 0.854102 + 2.62866i 0.0600944 + 0.184952i
\(203\) −0.990108 9.42025i −0.0694919 0.661172i
\(204\) −9.83334 4.37809i −0.688472 0.306527i
\(205\) 3.71537 + 0.789726i 0.259493 + 0.0551569i
\(206\) −8.74882 + 1.85962i −0.609559 + 0.129566i
\(207\) 0.104528 0.994522i 0.00726523 0.0691241i
\(208\) −1.85410 −0.128559
\(209\) −12.4475 7.35256i −0.861010 0.508588i
\(210\) −3.23607 −0.223310
\(211\) −0.931331 + 8.86102i −0.0641155 + 0.610018i 0.914538 + 0.404500i \(0.132554\pi\)
−0.978653 + 0.205518i \(0.934112\pi\)
\(212\) −6.61612 + 1.40630i −0.454397 + 0.0965851i
\(213\) 12.3760 + 2.63060i 0.847989 + 0.180246i
\(214\) 5.56365 + 2.47710i 0.380323 + 0.169331i
\(215\) −0.427539 4.06776i −0.0291579 0.277419i
\(216\) −1.23607 3.80423i −0.0841038 0.258845i
\(217\) 12.8992 39.6996i 0.875654 2.69499i
\(218\) 7.22599 3.21722i 0.489406 0.217897i
\(219\) 11.2361 19.4614i 0.759263 1.31508i
\(220\) −0.309017 1.22857i −0.0208339 0.0828302i
\(221\) 9.97871 0.671241
\(222\) −6.17916 + 2.75114i −0.414718 + 0.184644i
\(223\) −20.0248 + 4.25640i −1.34096 + 0.285029i −0.821862 0.569687i \(-0.807065\pi\)
−0.519096 + 0.854716i \(0.673731\pi\)
\(224\) −4.14350 0.880728i −0.276849 0.0588461i
\(225\) −4.43444 1.97434i −0.295630 0.131623i
\(226\) 10.0805 + 4.48811i 0.670543 + 0.298545i
\(227\) 2.16312 + 6.65740i 0.143571 + 0.441867i 0.996824 0.0796299i \(-0.0253739\pi\)
−0.853253 + 0.521497i \(0.825374\pi\)
\(228\) 8.60292 1.41059i 0.569742 0.0934187i
\(229\) −15.1353 10.9964i −1.00017 0.726663i −0.0380421 0.999276i \(-0.512112\pi\)
−0.962124 + 0.272613i \(0.912112\pi\)
\(230\) −0.190983 0.330792i −0.0125930 0.0218118i
\(231\) −4.82209 + 27.6820i −0.317270 + 1.82134i
\(232\) −1.11803 + 1.93649i −0.0734025 + 0.127137i
\(233\) 1.06054 10.0903i 0.0694780 0.661039i −0.903254 0.429106i \(-0.858829\pi\)
0.972732 0.231932i \(-0.0745048\pi\)
\(234\) −1.24064 1.37787i −0.0811029 0.0900739i
\(235\) −0.118034 0.363271i −0.00769969 0.0236972i
\(236\) −7.04508 + 5.11855i −0.458596 + 0.333189i
\(237\) −0.775226 7.37578i −0.0503563 0.479108i
\(238\) 22.3002 + 4.74005i 1.44551 + 0.307252i
\(239\) −7.82624 + 24.0867i −0.506237 + 1.55804i 0.292443 + 0.956283i \(0.405532\pi\)
−0.798681 + 0.601755i \(0.794468\pi\)
\(240\) 0.618034 + 0.449028i 0.0398939 + 0.0289846i
\(241\) 2.66312 4.61266i 0.171547 0.297127i −0.767414 0.641152i \(-0.778457\pi\)
0.938961 + 0.344024i \(0.111790\pi\)
\(242\) −10.9699 + 0.812696i −0.705174 + 0.0522421i
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 0.746950 7.10675i 0.0478186 0.454963i
\(245\) 4.08899 0.869142i 0.261236 0.0555274i
\(246\) 6.14590 + 18.9151i 0.391848 + 1.20598i
\(247\) −6.75396 + 4.43850i −0.429744 + 0.282415i
\(248\) −7.97214 + 5.79210i −0.506231 + 0.367798i
\(249\) 15.3527 17.0509i 0.972939 1.08056i
\(250\) −3.68168 + 0.782565i −0.232850 + 0.0494938i
\(251\) −19.0512 + 8.48213i −1.20250 + 0.535387i −0.907476 0.420103i \(-0.861994\pi\)
−0.295023 + 0.955490i \(0.595327\pi\)
\(252\) −2.11803 3.66854i −0.133424 0.231096i
\(253\) −3.11426 + 1.14079i −0.195792 + 0.0717212i
\(254\) −0.562306 −0.0352822
\(255\) −3.32624 2.41665i −0.208297 0.151337i
\(256\) 0.669131 + 0.743145i 0.0418207 + 0.0464466i
\(257\) −13.6941 2.91076i −0.854212 0.181568i −0.240062 0.970758i \(-0.577168\pi\)
−0.614150 + 0.789189i \(0.710501\pi\)
\(258\) 17.3262 12.5882i 1.07868 0.783710i
\(259\) 11.5902 8.42075i 0.720178 0.523240i
\(260\) −0.692728 0.147244i −0.0429612 0.00913168i
\(261\) −2.18720 + 0.464905i −0.135385 + 0.0287769i
\(262\) 3.17195 1.41224i 0.195964 0.0872488i
\(263\) −8.39919 14.5478i −0.517916 0.897057i −0.999783 0.0208127i \(-0.993375\pi\)
0.481867 0.876244i \(-0.339959\pi\)
\(264\) 4.76202 4.61770i 0.293082 0.284200i
\(265\) −2.58359 −0.158709
\(266\) −17.2019 + 6.71081i −1.05472 + 0.411466i
\(267\) 9.09017 27.9767i 0.556309 1.71214i
\(268\) 8.24786 9.16018i 0.503818 0.559547i
\(269\) −14.0012 6.23374i −0.853669 0.380078i −0.0672238 0.997738i \(-0.521414\pi\)
−0.786445 + 0.617660i \(0.788081\pi\)
\(270\) −0.159705 1.51949i −0.00971935 0.0924735i
\(271\) 1.75181 1.94558i 0.106415 0.118185i −0.687584 0.726105i \(-0.741329\pi\)
0.793999 + 0.607919i \(0.207995\pi\)
\(272\) −3.60124 3.99958i −0.218357 0.242510i
\(273\) 12.7082 + 9.23305i 0.769135 + 0.558810i
\(274\) −11.0344 −0.666615
\(275\) 0.595124 + 16.0882i 0.0358874 + 0.970157i
\(276\) 1.00000 1.73205i 0.0601929 0.104257i
\(277\) 10.0451 + 7.29818i 0.603551 + 0.438505i 0.847137 0.531374i \(-0.178324\pi\)
−0.243587 + 0.969879i \(0.578324\pi\)
\(278\) −3.21885 + 9.90659i −0.193054 + 0.594158i
\(279\) −9.63877 2.04878i −0.577058 0.122657i
\(280\) −1.47815 0.658114i −0.0883362 0.0393298i
\(281\) 0.372362 + 3.54279i 0.0222133 + 0.211345i 0.999998 + 0.00173588i \(0.000552548\pi\)
−0.977785 + 0.209609i \(0.932781\pi\)
\(282\) 1.33826 1.48629i 0.0796923 0.0885073i
\(283\) −15.4195 + 3.27751i −0.916591 + 0.194827i −0.641974 0.766726i \(-0.721884\pi\)
−0.274617 + 0.961554i \(0.588551\pi\)
\(284\) 5.11803 + 3.71847i 0.303699 + 0.220651i
\(285\) 3.32624 + 0.156179i 0.197029 + 0.00925124i
\(286\) −2.29180 + 5.70634i −0.135517 + 0.337423i
\(287\) −21.0623 36.4810i −1.24327 2.15340i
\(288\) −0.104528 + 0.994522i −0.00615940 + 0.0586028i
\(289\) 8.00652 + 8.89214i 0.470972 + 0.523067i
\(290\) −0.571506 + 0.634721i −0.0335600 + 0.0372721i
\(291\) 3.38261 + 32.1834i 0.198292 + 1.88662i
\(292\) 9.09017 6.60440i 0.531962 0.386493i
\(293\) −5.69098 17.5150i −0.332471 1.02324i −0.967955 0.251126i \(-0.919199\pi\)
0.635484 0.772114i \(-0.280801\pi\)
\(294\) 14.6463 + 16.2664i 0.854189 + 0.948673i
\(295\) −3.03867 + 1.35290i −0.176918 + 0.0787690i
\(296\) −3.38197 −0.196573
\(297\) −13.2361 0.898056i −0.768035 0.0521105i
\(298\) 4.54508 7.87232i 0.263290 0.456031i
\(299\) −0.193806 + 1.84395i −0.0112081 + 0.106638i
\(300\) −6.49606 7.21460i −0.375050 0.416535i
\(301\) −30.3522 + 33.7096i −1.74947 + 1.94299i
\(302\) 7.09270 + 3.15788i 0.408139 + 0.181715i
\(303\) −4.47214 + 3.24920i −0.256917 + 0.186661i
\(304\) 4.21645 + 1.10524i 0.241830 + 0.0633900i
\(305\) 0.843459 2.59590i 0.0482963 0.148641i
\(306\) 0.562569 5.35248i 0.0321599 0.305981i
\(307\) −4.13525 7.16247i −0.236011 0.408784i 0.723555 0.690267i \(-0.242507\pi\)
−0.959566 + 0.281483i \(0.909174\pi\)
\(308\) −7.83225 + 11.6637i −0.446284 + 0.664603i
\(309\) −8.94427 15.4919i −0.508822 0.881305i
\(310\) −3.43852 + 1.53093i −0.195295 + 0.0869509i
\(311\) −4.80902 + 14.8006i −0.272694 + 0.839267i 0.717126 + 0.696944i \(0.245457\pi\)
−0.989820 + 0.142323i \(0.954543\pi\)
\(312\) −1.14590 3.52671i −0.0648737 0.199661i
\(313\) 0.528467 + 5.02803i 0.0298707 + 0.284201i 0.999253 + 0.0386446i \(0.0123040\pi\)
−0.969382 + 0.245557i \(0.921029\pi\)
\(314\) −0.900830 8.57082i −0.0508368 0.483680i
\(315\) −0.500000 1.53884i −0.0281718 0.0867039i
\(316\) 1.14590 3.52671i 0.0644618 0.198393i
\(317\) −1.18011 + 0.525421i −0.0662818 + 0.0295106i −0.439610 0.898189i \(-0.644883\pi\)
0.373328 + 0.927699i \(0.378217\pi\)
\(318\) −6.76393 11.7155i −0.379302 0.656971i
\(319\) 4.57794 + 5.83459i 0.256316 + 0.326674i
\(320\) 0.190983 + 0.330792i 0.0106763 + 0.0184919i
\(321\) −1.27319 + 12.1136i −0.0710627 + 0.676116i
\(322\) −1.30902 + 4.02874i −0.0729487 + 0.224513i
\(323\) −22.6928 5.94838i −1.26266 0.330976i
\(324\) 8.89919 6.46564i 0.494399 0.359202i
\(325\) 8.22191 + 3.66063i 0.456069 + 0.203055i
\(326\) −3.30836 + 3.67431i −0.183233 + 0.203501i
\(327\) 10.5854 + 11.7563i 0.585375 + 0.650125i
\(328\) −1.03946 + 9.88980i −0.0573945 + 0.546073i
\(329\) −2.11803 + 3.66854i −0.116771 + 0.202253i
\(330\) 2.14590 1.34708i 0.118128 0.0741545i
\(331\) 12.0344 0.661473 0.330736 0.943723i \(-0.392703\pi\)
0.330736 + 0.943723i \(0.392703\pi\)
\(332\) 10.4803 4.66614i 0.575182 0.256088i
\(333\) −2.26298 2.51329i −0.124010 0.137727i
\(334\) 5.25329 + 16.1680i 0.287447 + 0.884671i
\(335\) 3.80902 2.76741i 0.208109 0.151200i
\(336\) −0.885579 8.42572i −0.0483123 0.459661i
\(337\) 15.3900 17.0923i 0.838347 0.931079i −0.160082 0.987104i \(-0.551176\pi\)
0.998429 + 0.0560251i \(0.0178427\pi\)
\(338\) −6.39843 7.10618i −0.348029 0.386525i
\(339\) −2.30683 + 21.9480i −0.125290 + 1.19205i
\(340\) −1.02786 1.78031i −0.0557438 0.0965510i
\(341\) 7.97214 + 31.6951i 0.431715 + 1.71639i
\(342\) 2.00000 + 3.87298i 0.108148 + 0.209427i
\(343\) −13.5172 9.82084i −0.729861 0.530275i
\(344\) 10.4742 2.22636i 0.564731 0.120037i
\(345\) 0.511170 0.567712i 0.0275205 0.0305646i
\(346\) −2.20812 21.0089i −0.118709 1.12944i
\(347\) 4.78339 + 2.12970i 0.256786 + 0.114328i 0.531092 0.847314i \(-0.321782\pi\)
−0.274307 + 0.961642i \(0.588448\pi\)
\(348\) −4.37441 0.929809i −0.234493 0.0498430i
\(349\) 5.34346 16.4455i 0.286029 0.880306i −0.700060 0.714084i \(-0.746843\pi\)
0.986088 0.166222i \(-0.0531567\pi\)
\(350\) 16.6353 + 12.0862i 0.889192 + 0.646036i
\(351\) −3.70820 + 6.42280i −0.197929 + 0.342824i
\(352\) 3.11426 1.14079i 0.165990 0.0608046i
\(353\) 4.00000 0.212899 0.106449 0.994318i \(-0.466052\pi\)
0.106449 + 0.994318i \(0.466052\pi\)
\(354\) −14.0902 10.2371i −0.748884 0.544096i
\(355\) 1.61689 + 1.79574i 0.0858157 + 0.0953080i
\(356\) 9.84171 10.9303i 0.521610 0.579306i
\(357\) 4.76616 + 45.3470i 0.252252 + 2.40002i
\(358\) −1.56052 0.694789i −0.0824761 0.0367207i
\(359\) 15.5107 17.2263i 0.818622 0.909172i −0.178580 0.983925i \(-0.557150\pi\)
0.997202 + 0.0747534i \(0.0238170\pi\)
\(360\) −0.118034 + 0.363271i −0.00622094 + 0.0191461i
\(361\) 18.0051 6.06760i 0.947638 0.319347i
\(362\) 10.7639 0.565740
\(363\) −8.32563 20.3638i −0.436982 1.06882i
\(364\) 3.92705 + 6.80185i 0.205833 + 0.356514i
\(365\) 3.92075 1.74563i 0.205221 0.0913705i
\(366\) 13.9795 2.97143i 0.730719 0.155319i
\(367\) 26.6201 + 5.65827i 1.38956 + 0.295359i 0.841127 0.540837i \(-0.181893\pi\)
0.548429 + 0.836197i \(0.315226\pi\)
\(368\) 0.809017 0.587785i 0.0421729 0.0306404i
\(369\) −8.04508 + 5.84510i −0.418810 + 0.304284i
\(370\) −1.26357 0.268580i −0.0656897 0.0139628i
\(371\) 19.1722 + 21.2929i 0.995374 + 1.10547i
\(372\) −15.9443 11.5842i −0.826672 0.600612i
\(373\) −15.3607 −0.795346 −0.397673 0.917527i \(-0.630182\pi\)
−0.397673 + 0.917527i \(0.630182\pi\)
\(374\) −16.7608 + 6.13972i −0.866681 + 0.317477i
\(375\) −3.76393 6.51932i −0.194369 0.336656i
\(376\) 0.913545 0.406737i 0.0471125 0.0209758i
\(377\) 4.05530 0.861981i 0.208859 0.0443943i
\(378\) −11.3379 + 12.5920i −0.583160 + 0.647665i
\(379\) 13.2082 9.59632i 0.678460 0.492930i −0.194387 0.980925i \(-0.562272\pi\)
0.872846 + 0.487995i \(0.162272\pi\)
\(380\) 1.48757 + 0.747790i 0.0763109 + 0.0383608i
\(381\) −0.347524 1.06957i −0.0178042 0.0547957i
\(382\) 0.285420 0.0606678i 0.0146033 0.00310404i
\(383\) −2.63789 + 25.0978i −0.134790 + 1.28244i 0.692810 + 0.721120i \(0.256372\pi\)
−0.827600 + 0.561319i \(0.810294\pi\)
\(384\) −1.00000 + 1.73205i −0.0510310 + 0.0883883i
\(385\) −3.85256 + 3.73580i −0.196344 + 0.190394i
\(386\) −4.20820 + 7.28882i −0.214192 + 0.370991i
\(387\) 8.66312 + 6.29412i 0.440371 + 0.319948i
\(388\) −5.00000 + 15.3884i −0.253837 + 0.781229i
\(389\) 13.4968 + 2.86884i 0.684317 + 0.145456i 0.536935 0.843624i \(-0.319582\pi\)
0.147382 + 0.989080i \(0.452915\pi\)
\(390\) −0.148055 1.40865i −0.00749705 0.0713297i
\(391\) −4.35410 + 3.16344i −0.220196 + 0.159982i
\(392\) 3.38197 + 10.4086i 0.170815 + 0.525715i
\(393\) 4.64662 + 5.16060i 0.234391 + 0.260318i
\(394\) −2.67199 + 25.4223i −0.134613 + 1.28076i
\(395\) 0.708204 1.22665i 0.0356336 0.0617192i
\(396\) 2.93162 + 1.55100i 0.147319 + 0.0779408i
\(397\) 0.527864 + 0.914287i 0.0264927 + 0.0458868i 0.878968 0.476881i \(-0.158233\pi\)
−0.852475 + 0.522768i \(0.824899\pi\)
\(398\) −16.8713 12.2577i −0.845683 0.614425i
\(399\) −23.3961 28.5725i −1.17127 1.43041i
\(400\) −1.50000 4.61653i −0.0750000 0.230826i
\(401\) 17.3065 + 7.70533i 0.864243 + 0.384786i 0.790478 0.612490i \(-0.209832\pi\)
0.0737646 + 0.997276i \(0.476499\pi\)
\(402\) 22.5212 + 10.0271i 1.12325 + 0.500105i
\(403\) 17.8713 + 3.79865i 0.890231 + 0.189224i
\(404\) −2.70353 + 0.574654i −0.134506 + 0.0285901i
\(405\) 3.83838 1.70896i 0.190730 0.0849187i
\(406\) 9.47214 0.470094
\(407\) −4.18034 + 10.4086i −0.207212 + 0.515936i
\(408\) 5.38197 9.32184i 0.266447 0.461500i
\(409\) −20.6117 + 9.17692i −1.01918 + 0.453769i −0.847168 0.531325i \(-0.821694\pi\)
−0.172015 + 0.985094i \(0.555028\pi\)
\(410\) −1.17376 + 3.61247i −0.0579680 + 0.178407i
\(411\) −6.81966 20.9888i −0.336389 1.03530i
\(412\) −0.934931 8.89527i −0.0460607 0.438239i
\(413\) 33.6994 + 15.0039i 1.65824 + 0.738295i
\(414\) 0.978148 + 0.207912i 0.0480733 + 0.0102183i
\(415\) 4.28621 0.911062i 0.210402 0.0447223i
\(416\) 0.193806 1.84395i 0.00950214 0.0904068i
\(417\) −20.8328 −1.02019
\(418\) 8.61340 11.6107i 0.421295 0.567900i
\(419\) −33.6525 −1.64403 −0.822016 0.569465i \(-0.807150\pi\)
−0.822016 + 0.569465i \(0.807150\pi\)
\(420\) 0.338261 3.21834i 0.0165055 0.157039i
\(421\) −2.47262 + 0.525572i −0.120508 + 0.0256148i −0.267771 0.963483i \(-0.586287\pi\)
0.147263 + 0.989097i \(0.452954\pi\)
\(422\) −8.71513 1.85246i −0.424246 0.0901762i
\(423\) 0.913545 + 0.406737i 0.0444181 + 0.0197762i
\(424\) −0.707023 6.72688i −0.0343361 0.326686i
\(425\) 8.07295 + 24.8460i 0.391596 + 1.20521i
\(426\) −3.90983 + 12.0332i −0.189432 + 0.583011i
\(427\) −27.6535 + 12.3121i −1.33825 + 0.595826i
\(428\) −3.04508 + 5.27424i −0.147190 + 0.254940i
\(429\) −12.2705 0.832544i −0.592426 0.0401956i
\(430\) 4.09017 0.197246
\(431\) −19.6158 + 8.73350i −0.944859 + 0.420678i −0.820556 0.571566i \(-0.806336\pi\)
−0.124303 + 0.992244i \(0.539669\pi\)
\(432\) 3.91259 0.831647i 0.188245 0.0400126i
\(433\) 2.61533 + 0.555906i 0.125685 + 0.0267152i 0.270325 0.962769i \(-0.412869\pi\)
−0.144640 + 0.989484i \(0.546202\pi\)
\(434\) 38.1338 + 16.9783i 1.83048 + 0.814983i
\(435\) −1.56052 0.694789i −0.0748213 0.0333126i
\(436\) 2.44427 + 7.52270i 0.117059 + 0.360272i
\(437\) 1.53993 4.07782i 0.0736647 0.195069i
\(438\) 18.1803 + 13.2088i 0.868690 + 0.631140i
\(439\) 17.9164 + 31.0321i 0.855103 + 1.48108i 0.876549 + 0.481313i \(0.159840\pi\)
−0.0214455 + 0.999770i \(0.506827\pi\)
\(440\) 1.25414 0.178904i 0.0597889 0.00852889i
\(441\) −5.47214 + 9.47802i −0.260578 + 0.451334i
\(442\) −1.04306 + 9.92405i −0.0496133 + 0.472039i
\(443\) 8.17328 + 9.07735i 0.388324 + 0.431278i 0.905333 0.424702i \(-0.139621\pi\)
−0.517009 + 0.855980i \(0.672955\pi\)
\(444\) −2.09017 6.43288i −0.0991951 0.305291i
\(445\) 4.54508 3.30220i 0.215458 0.156539i
\(446\) −2.13992 20.3600i −0.101328 0.964073i
\(447\) 17.7831 + 3.77991i 0.841110 + 0.178783i
\(448\) 1.30902 4.02874i 0.0618452 0.190340i
\(449\) −4.11803 2.99193i −0.194342 0.141198i 0.486359 0.873759i \(-0.338325\pi\)
−0.680701 + 0.732561i \(0.738325\pi\)
\(450\) 2.42705 4.20378i 0.114412 0.198168i
\(451\) 29.1528 + 15.4236i 1.37275 + 0.726268i
\(452\) −5.51722 + 9.55611i −0.259508 + 0.449481i
\(453\) −1.62310 + 15.4428i −0.0762601 + 0.725566i
\(454\) −6.84703 + 1.45538i −0.321347 + 0.0683045i
\(455\) 0.927051 + 2.85317i 0.0434608 + 0.133759i
\(456\) 0.503613 + 8.70324i 0.0235839 + 0.407567i
\(457\) −8.80902 + 6.40013i −0.412068 + 0.299385i −0.774439 0.632649i \(-0.781968\pi\)
0.362370 + 0.932034i \(0.381968\pi\)
\(458\) 12.5182 13.9029i 0.584939 0.649640i
\(459\) −21.0574 + 4.47589i −0.982877 + 0.208917i
\(460\) 0.348943 0.155360i 0.0162696 0.00724368i
\(461\) −1.82624 3.16314i −0.0850564 0.147322i 0.820359 0.571849i \(-0.193774\pi\)
−0.905415 + 0.424527i \(0.860440\pi\)
\(462\) −27.0264 7.68924i −1.25738 0.357736i
\(463\) 10.7082 0.497652 0.248826 0.968548i \(-0.419955\pi\)
0.248826 + 0.968548i \(0.419955\pi\)
\(464\) −1.80902 1.31433i −0.0839815 0.0610161i
\(465\) −5.03712 5.59429i −0.233591 0.259429i
\(466\) 9.92419 + 2.10945i 0.459729 + 0.0977184i
\(467\) 14.8541 10.7921i 0.687366 0.499401i −0.188427 0.982087i \(-0.560339\pi\)
0.875793 + 0.482687i \(0.160339\pi\)
\(468\) 1.50000 1.08981i 0.0693375 0.0503767i
\(469\) −51.0738 10.8561i −2.35837 0.501286i
\(470\) 0.373619 0.0794152i 0.0172338 0.00366315i
\(471\) 15.7459 7.01054i 0.725534 0.323029i
\(472\) −4.35410 7.54153i −0.200414 0.347127i
\(473\) 6.09479 34.9882i 0.280239 1.60876i
\(474\) 7.41641 0.340647
\(475\) −16.5155 13.2258i −0.757782 0.606843i
\(476\) −7.04508 + 21.6825i −0.322911 + 0.993818i
\(477\) 4.52595 5.02658i 0.207229 0.230151i
\(478\) −23.1367 10.3011i −1.05825 0.471162i
\(479\) −3.32744 31.6584i −0.152034 1.44651i −0.758641 0.651509i \(-0.774136\pi\)
0.606607 0.795002i \(-0.292530\pi\)
\(480\) −0.511170 + 0.567712i −0.0233316 + 0.0259124i
\(481\) 4.19579 + 4.65990i 0.191312 + 0.212473i
\(482\) 4.30902 + 3.13068i 0.196270 + 0.142599i
\(483\) −8.47214 −0.385496
\(484\) 0.338426 10.9948i 0.0153830 0.499763i
\(485\) −3.09017 + 5.35233i −0.140317 + 0.243037i
\(486\) 8.09017 + 5.87785i 0.366978 + 0.266625i
\(487\) 4.34346 13.3678i 0.196821 0.605752i −0.803130 0.595804i \(-0.796833\pi\)
0.999951 0.00994811i \(-0.00316663\pi\)
\(488\) 6.98974 + 1.48572i 0.316411 + 0.0672552i
\(489\) −9.03363 4.02203i −0.408515 0.181883i
\(490\) 0.436965 + 4.15744i 0.0197400 + 0.187814i
\(491\) 7.44382 8.26720i 0.335935 0.373093i −0.551383 0.834252i \(-0.685900\pi\)
0.887318 + 0.461159i \(0.152566\pi\)
\(492\) −19.4539 + 4.13506i −0.877051 + 0.186423i
\(493\) 9.73607 + 7.07367i 0.438490 + 0.318582i
\(494\) −3.70820 7.18091i −0.166840 0.323084i
\(495\) 0.972136 + 0.812299i 0.0436943 + 0.0365101i
\(496\) −4.92705 8.53390i −0.221231 0.383184i
\(497\) 2.80119 26.6516i 0.125651 1.19549i
\(498\) 15.3527 + 17.0509i 0.687972 + 0.764070i
\(499\) 28.2099 31.3303i 1.26285 1.40254i 0.385483 0.922715i \(-0.374035\pi\)
0.877366 0.479821i \(-0.159298\pi\)
\(500\) −0.393438 3.74331i −0.0175951 0.167406i
\(501\) −27.5066 + 19.9847i −1.22890 + 0.892850i
\(502\) −6.44427 19.8334i −0.287622 0.885209i
\(503\) −12.0301 13.3608i −0.536396 0.595728i 0.412641 0.910894i \(-0.364607\pi\)
−0.949037 + 0.315166i \(0.897940\pi\)
\(504\) 3.86984 1.72296i 0.172376 0.0767469i
\(505\) −1.05573 −0.0469793
\(506\) −0.809017 3.21644i −0.0359652 0.142988i
\(507\) 9.56231 16.5624i 0.424677 0.735562i
\(508\) 0.0587770 0.559226i 0.00260781 0.0248116i
\(509\) 16.6537 + 18.4958i 0.738162 + 0.819812i 0.988953 0.148230i \(-0.0473575\pi\)
−0.250791 + 0.968041i \(0.580691\pi\)
\(510\) 2.75110 3.05541i 0.121821 0.135296i
\(511\) −43.4818 19.3593i −1.92352 0.856407i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 12.2616 12.3957i 0.541361 0.547285i
\(514\) 4.32624 13.3148i 0.190822 0.587290i
\(515\) 0.357112 3.39769i 0.0157362 0.149720i
\(516\) 10.7082 + 18.5472i 0.471402 + 0.816493i
\(517\) −0.122602 3.31436i −0.00539205 0.145765i
\(518\) 7.16312 + 12.4069i 0.314729 + 0.545127i
\(519\) 38.5966 17.1843i 1.69420 0.754307i
\(520\) 0.218847 0.673542i 0.00959708 0.0295368i
\(521\) −7.07295 21.7683i −0.309872 0.953686i −0.977814 0.209474i \(-0.932825\pi\)
0.667943 0.744213i \(-0.267175\pi\)
\(522\) −0.233733 2.22382i −0.0102302 0.0973339i
\(523\) 2.06367 + 19.6345i 0.0902379 + 0.858556i 0.942222 + 0.334989i \(0.108733\pi\)
−0.851984 + 0.523568i \(0.824601\pi\)
\(524\) 1.07295 + 3.30220i 0.0468720 + 0.144257i
\(525\) −12.7082 + 39.1118i −0.554631 + 1.70698i
\(526\) 15.3461 6.83251i 0.669121 0.297912i
\(527\) 26.5172 + 45.9292i 1.15511 + 2.00071i
\(528\) 4.09464 + 5.21862i 0.178196 + 0.227111i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0.270059 2.56944i 0.0117306 0.111609i
\(531\) 2.69098 8.28199i 0.116779 0.359408i
\(532\) −4.87595 17.8092i −0.211399 0.772125i
\(533\) 14.9164 10.8374i 0.646101 0.469420i
\(534\) 26.8732 + 11.9647i 1.16292 + 0.517765i
\(535\) −1.55656 + 1.72873i −0.0672958 + 0.0747396i
\(536\) 8.24786 + 9.16018i 0.356253 + 0.395660i
\(537\) 0.357112 3.39769i 0.0154105 0.146621i
\(538\) 7.66312 13.2729i 0.330381 0.572236i
\(539\) 36.2148 + 2.45714i 1.55988 + 0.105837i
\(540\) 1.52786 0.0657488
\(541\) 26.4734 11.7867i 1.13818 0.506750i 0.250914 0.968009i \(-0.419269\pi\)
0.887265 + 0.461259i \(0.152602\pi\)
\(542\) 1.75181 + 1.94558i 0.0752465 + 0.0835697i
\(543\) 6.65248 + 20.4742i 0.285485 + 0.878633i
\(544\) 4.35410 3.16344i 0.186681 0.135631i
\(545\) 0.315810 + 3.00474i 0.0135278 + 0.128709i
\(546\) −10.5108 + 11.6735i −0.449822 + 0.499578i
\(547\) 5.19508 + 5.76973i 0.222126 + 0.246696i 0.843900 0.536501i \(-0.180254\pi\)
−0.621774 + 0.783197i \(0.713588\pi\)
\(548\) 1.15341 10.9740i 0.0492714 0.468786i
\(549\) 3.57295 + 6.18853i 0.152490 + 0.264120i
\(550\) −16.0623 1.08981i −0.684899 0.0464698i
\(551\) −9.73607 0.457144i −0.414770 0.0194750i
\(552\) 1.61803 + 1.17557i 0.0688681 + 0.0500356i
\(553\) −15.3649 + 3.26592i −0.653384 + 0.138881i
\(554\) −8.30820 + 9.22719i −0.352982 + 0.392026i
\(555\) −0.270059 2.56944i −0.0114634 0.109067i
\(556\) −9.51586 4.23673i −0.403562 0.179678i
\(557\) 26.0155 + 5.52977i 1.10231 + 0.234304i 0.722920 0.690931i \(-0.242799\pi\)
0.379394 + 0.925235i \(0.376133\pi\)
\(558\) 3.04508 9.37181i 0.128909 0.396740i
\(559\) −16.0623 11.6699i −0.679363 0.493586i
\(560\) 0.809017 1.40126i 0.0341872 0.0592140i
\(561\) −22.0372 28.0864i −0.930411 1.18581i
\(562\) −3.56231 −0.150267
\(563\) 10.6180 + 7.71445i 0.447497 + 0.325125i 0.788607 0.614898i \(-0.210803\pi\)
−0.341110 + 0.940023i \(0.610803\pi\)
\(564\) 1.33826 + 1.48629i 0.0563510 + 0.0625841i
\(565\) −2.82024 + 3.13219i −0.118648 + 0.131772i
\(566\) −1.64778 15.6776i −0.0692613 0.658978i
\(567\) −42.5682 18.9526i −1.78770 0.795935i
\(568\) −4.23308 + 4.70131i −0.177616 + 0.197263i
\(569\) 6.96556 21.4378i 0.292011 0.898719i −0.692198 0.721708i \(-0.743357\pi\)
0.984209 0.177011i \(-0.0566427\pi\)
\(570\) −0.503010 + 3.29169i −0.0210688 + 0.137874i
\(571\) 1.03444 0.0432900 0.0216450 0.999766i \(-0.493110\pi\)
0.0216450 + 0.999766i \(0.493110\pi\)
\(572\) −5.43552 2.87572i −0.227271 0.120240i
\(573\) 0.291796 + 0.505406i 0.0121900 + 0.0211136i
\(574\) 38.4827 17.1336i 1.60624 0.715144i
\(575\) −4.74803 + 1.00922i −0.198006 + 0.0420876i
\(576\) −0.978148 0.207912i −0.0407562 0.00866299i
\(577\) −27.9615 + 20.3152i −1.16405 + 0.845733i −0.990285 0.139053i \(-0.955594\pi\)
−0.173767 + 0.984787i \(0.555594\pi\)
\(578\) −9.68034 + 7.03318i −0.402649 + 0.292542i
\(579\) −16.4650 3.49974i −0.684261 0.145444i
\(580\) −0.571506 0.634721i −0.0237305 0.0263554i
\(581\) −39.3156 28.5645i −1.63109 1.18505i
\(582\) −32.3607 −1.34139
\(583\) −21.5771 6.13888i −0.893634 0.254247i
\(584\) 5.61803 + 9.73072i 0.232476 + 0.402660i
\(585\) 0.646976 0.288052i 0.0267492 0.0119095i
\(586\) 18.0140 3.82899i 0.744150 0.158174i
\(587\) −13.2619 + 14.7289i −0.547379 + 0.607926i −0.951827 0.306635i \(-0.900797\pi\)
0.404448 + 0.914561i \(0.367464\pi\)
\(588\) −17.7082 + 12.8658i −0.730274 + 0.530575i
\(589\) −38.3770 19.2918i −1.58130 0.794903i
\(590\) −1.02786 3.16344i −0.0423165 0.130237i
\(591\) −50.0074 + 10.6294i −2.05703 + 0.437235i
\(592\) 0.353512 3.36344i 0.0145292 0.138237i
\(593\) 18.2361 31.5858i 0.748866 1.29707i −0.199501 0.979898i \(-0.563932\pi\)
0.948367 0.317176i \(-0.102734\pi\)
\(594\) 2.27668 13.0697i 0.0934134 0.536256i
\(595\) −4.35410 + 7.54153i −0.178501 + 0.309172i
\(596\) 7.35410 + 5.34307i 0.301236 + 0.218861i
\(597\) 12.8885 39.6669i 0.527493 1.62346i
\(598\) −1.81359 0.385489i −0.0741630 0.0157638i
\(599\) 1.46117 + 13.9021i 0.0597019 + 0.568026i 0.982957 + 0.183838i \(0.0588520\pi\)
−0.923255 + 0.384188i \(0.874481\pi\)
\(600\) 7.85410 5.70634i 0.320642 0.232960i
\(601\) 6.38197 + 19.6417i 0.260326 + 0.801201i 0.992733 + 0.120334i \(0.0383966\pi\)
−0.732408 + 0.680866i \(0.761603\pi\)
\(602\) −30.3522 33.7096i −1.23706 1.37390i
\(603\) −1.28844 + 12.2587i −0.0524694 + 0.499213i
\(604\) −3.88197 + 6.72376i −0.157955 + 0.273586i
\(605\) 0.999596 4.08099i 0.0406394 0.165916i
\(606\) −2.76393 4.78727i −0.112277 0.194470i
\(607\) −34.3713 24.9722i −1.39509 1.01359i −0.995285 0.0969907i \(-0.969078\pi\)
−0.399804 0.916601i \(-0.630922\pi\)
\(608\) −1.53993 + 4.07782i −0.0624523 + 0.165377i
\(609\) 5.85410 + 18.0171i 0.237220 + 0.730089i
\(610\) 2.49351 + 1.11018i 0.100959 + 0.0449500i
\(611\) −1.69381 0.754131i −0.0685241 0.0305089i
\(612\) 5.26436 + 1.11897i 0.212799 + 0.0452318i
\(613\) −8.08978 + 1.71954i −0.326743 + 0.0694514i −0.368363 0.929682i \(-0.620082\pi\)
0.0416197 + 0.999134i \(0.486748\pi\)
\(614\) 7.55549 3.36392i 0.304915 0.135757i
\(615\) −7.59675 −0.306330
\(616\) −10.7812 9.00854i −0.434385 0.362964i
\(617\) −1.56231 + 2.70599i −0.0628961 + 0.108939i −0.895759 0.444540i \(-0.853367\pi\)
0.832863 + 0.553480i \(0.186700\pi\)
\(618\) 16.3420 7.27593i 0.657372 0.292681i
\(619\) 11.7812 36.2587i 0.473525 1.45736i −0.374413 0.927262i \(-0.622156\pi\)
0.847937 0.530096i \(-0.177844\pi\)
\(620\) −1.16312 3.57971i −0.0467120 0.143765i
\(621\) −0.418114 3.97809i −0.0167783 0.159635i
\(622\) −14.2169 6.32976i −0.570045 0.253800i
\(623\) −60.9434 12.9539i −2.44165 0.518988i
\(624\) 3.62717 0.770979i 0.145203 0.0308639i
\(625\) −2.38668 + 22.7077i −0.0954672 + 0.908309i
\(626\) −5.05573 −0.202068
\(627\) 27.4083 + 9.20783i 1.09458 + 0.367725i
\(628\) 8.61803 0.343897
\(629\) −1.90259 + 18.1019i −0.0758612 + 0.721771i
\(630\) 1.58268 0.336408i 0.0630553 0.0134028i
\(631\) −34.8734 7.41257i −1.38829 0.295090i −0.547659 0.836702i \(-0.684481\pi\)
−0.840629 + 0.541612i \(0.817814\pi\)
\(632\) 3.38761 + 1.50826i 0.134752 + 0.0599955i
\(633\) −1.86266 17.7220i −0.0740342 0.704388i
\(634\) −0.399187 1.22857i −0.0158537 0.0487928i
\(635\) 0.0663712 0.204270i 0.00263386 0.00810619i
\(636\) 12.3583 5.50228i 0.490039 0.218180i
\(637\) 10.1459 17.5732i 0.401995 0.696276i
\(638\) −6.28115 + 3.94298i −0.248673 + 0.156104i
\(639\) −6.32624 −0.250262
\(640\) −0.348943 + 0.155360i −0.0137932 + 0.00614113i
\(641\) 15.4531 3.28467i 0.610362 0.129737i 0.107648 0.994189i \(-0.465668\pi\)
0.502714 + 0.864453i \(0.332335\pi\)
\(642\) −11.9142 2.53244i −0.470215 0.0999472i
\(643\) 12.4212 + 5.53030i 0.489846 + 0.218094i 0.636769 0.771054i \(-0.280270\pi\)
−0.146923 + 0.989148i \(0.546937\pi\)
\(644\) −3.86984 1.72296i −0.152493 0.0678943i
\(645\) 2.52786 + 7.77997i 0.0995345 + 0.306336i
\(646\) 8.28783 21.9467i 0.326080 0.863481i
\(647\) 8.54508 + 6.20837i 0.335942 + 0.244076i 0.742948 0.669349i \(-0.233427\pi\)
−0.407006 + 0.913426i \(0.633427\pi\)
\(648\) 5.50000 + 9.52628i 0.216060 + 0.374228i
\(649\) −28.5924 + 4.07871i −1.12235 + 0.160103i
\(650\) −4.50000 + 7.79423i −0.176505 + 0.305715i
\(651\) −8.72659 + 83.0280i −0.342022 + 3.25412i
\(652\) −3.30836 3.67431i −0.129566 0.143897i
\(653\) −1.50658 4.63677i −0.0589569 0.181451i 0.917241 0.398333i \(-0.130411\pi\)
−0.976198 + 0.216882i \(0.930411\pi\)
\(654\) −12.7984 + 9.29856i −0.500456 + 0.363603i
\(655\) 0.138630 + 1.31897i 0.00541671 + 0.0515365i
\(656\) −9.72697 2.06753i −0.379774 0.0807235i
\(657\) −3.47214 + 10.6861i −0.135461 + 0.416906i
\(658\) −3.42705 2.48990i −0.133600 0.0970663i
\(659\) −11.8369 + 20.5021i −0.461099 + 0.798648i −0.999016 0.0443504i \(-0.985878\pi\)
0.537917 + 0.842998i \(0.319212\pi\)
\(660\) 1.11540 + 2.27495i 0.0434168 + 0.0885524i
\(661\) 2.92705 5.06980i 0.113849 0.197192i −0.803470 0.595345i \(-0.797015\pi\)
0.917319 + 0.398153i \(0.130349\pi\)
\(662\) −1.25794 + 11.9685i −0.0488913 + 0.465170i
\(663\) −19.5213 + 4.14938i −0.758145 + 0.161149i
\(664\) 3.54508 + 10.9106i 0.137576 + 0.423415i
\(665\) −0.407432 7.04107i −0.0157995 0.273041i
\(666\) 2.73607 1.98787i 0.106020 0.0770284i
\(667\) −1.49622 + 1.66172i −0.0579339 + 0.0643421i
\(668\) −16.6285 + 3.53450i −0.643376 + 0.136754i
\(669\) 37.4045 16.6535i 1.44614 0.643863i
\(670\) 2.35410 + 4.07742i 0.0909469 + 0.157525i
\(671\) 13.2124 19.6758i 0.510058 0.759575i
\(672\) 8.47214 0.326820
\(673\) 32.2705 + 23.4459i 1.24394 + 0.903773i 0.997854 0.0654759i \(-0.0208566\pi\)
0.246083 + 0.969249i \(0.420857\pi\)
\(674\) 15.3900 + 17.0923i 0.592801 + 0.658372i
\(675\) −18.9921 4.03690i −0.731007 0.155380i
\(676\) 7.73607 5.62058i 0.297541 0.216176i
\(677\) −10.2361 + 7.43694i −0.393404 + 0.285825i −0.766849 0.641828i \(-0.778176\pi\)
0.373445 + 0.927652i \(0.378176\pi\)
\(678\) −21.5866 4.58838i −0.829029 0.176216i
\(679\) 67.0432 14.2505i 2.57288 0.546883i
\(680\) 1.87800 0.836140i 0.0720181 0.0320645i
\(681\) −7.00000 12.1244i −0.268241 0.464606i
\(682\) −32.3548 + 4.61542i −1.23893 + 0.176734i
\(683\) 14.7082 0.562794 0.281397 0.959591i \(-0.409202\pi\)
0.281397 + 0.959591i \(0.409202\pi\)
\(684\) −4.06082 + 1.58421i −0.155269 + 0.0605737i
\(685\) 1.30244 4.00850i 0.0497636 0.153157i
\(686\) 11.1800 12.4166i 0.426853 0.474069i
\(687\) 34.1816 + 15.2186i 1.30411 + 0.580627i
\(688\) 1.11931 + 10.6495i 0.0426734 + 0.406010i
\(689\) −8.39158 + 9.31979i −0.319694 + 0.355056i
\(690\) 0.511170 + 0.567712i 0.0194599 + 0.0216124i
\(691\) 18.9894 + 13.7966i 0.722389 + 0.524846i 0.887147 0.461488i \(-0.152684\pi\)
−0.164757 + 0.986334i \(0.552684\pi\)
\(692\) 21.1246 0.803037
\(693\) −0.519352 14.0398i −0.0197286 0.533330i
\(694\) −2.61803 + 4.53457i −0.0993792 + 0.172130i
\(695\) −3.21885 2.33863i −0.122098 0.0887093i
\(696\) 1.38197 4.25325i 0.0523833 0.161219i
\(697\) 52.3502 + 11.1274i 1.98291 + 0.421480i
\(698\) 15.7968 + 7.03321i 0.597919 + 0.266211i
\(699\) 2.12107 + 20.1806i 0.0802262 + 0.763302i
\(700\) −13.7589 + 15.2808i −0.520036 + 0.577559i
\(701\) −8.51791 + 1.81054i −0.321717 + 0.0683831i −0.365939 0.930639i \(-0.619252\pi\)
0.0442225 + 0.999022i \(0.485919\pi\)
\(702\) −6.00000 4.35926i −0.226455 0.164529i
\(703\) −6.76393 13.0983i −0.255107 0.494012i
\(704\) 0.809017 + 3.21644i 0.0304910 + 0.121224i
\(705\) 0.381966 + 0.661585i 0.0143857 + 0.0249167i
\(706\) −0.418114 + 3.97809i −0.0157359 + 0.149717i
\(707\) 7.83432 + 8.70089i 0.294640 + 0.327231i
\(708\) 11.6539 12.9429i 0.437979 0.486424i
\(709\) −5.12189 48.7316i −0.192357 1.83015i −0.485677 0.874138i \(-0.661427\pi\)
0.293320 0.956014i \(-0.405240\pi\)
\(710\) −1.95492 + 1.42033i −0.0733667 + 0.0533040i
\(711\) 1.14590 + 3.52671i 0.0429745 + 0.132262i
\(712\) 9.84171 + 10.9303i 0.368834 + 0.409631i
\(713\) −9.00217 + 4.00802i −0.337134 + 0.150102i
\(714\) −45.5967 −1.70642
\(715\) −1.80244 1.50609i −0.0674074 0.0563244i
\(716\) 0.854102 1.47935i 0.0319193 0.0552858i
\(717\) 5.29463 50.3750i 0.197731 1.88129i
\(718\) 15.5107 + 17.2263i 0.578853 + 0.642882i
\(719\) −6.55639 + 7.28161i −0.244512 + 0.271558i −0.852892 0.522088i \(-0.825153\pi\)
0.608379 + 0.793646i \(0.291820\pi\)
\(720\) −0.348943 0.155360i −0.0130043 0.00578991i
\(721\) −30.6525 + 22.2703i −1.14156 + 0.829390i
\(722\) 4.15231 + 18.5407i 0.154533 + 0.690014i
\(723\) −3.29180 + 10.1311i −0.122423 + 0.376780i
\(724\) −1.12514 + 10.7050i −0.0418154 + 0.397847i
\(725\) 5.42705 + 9.39993i 0.201556 + 0.349105i
\(726\) 21.1225 6.15143i 0.783929 0.228301i
\(727\) −15.7812 27.3338i −0.585291 1.01375i −0.994839 0.101465i \(-0.967647\pi\)
0.409549 0.912288i \(-0.365686\pi\)
\(728\) −7.17508 + 3.19455i −0.265926 + 0.118398i
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) 1.32624 + 4.08174i 0.0490863 + 0.151072i
\(731\) −6.02410 57.3155i −0.222809 2.11989i
\(732\) 1.49390 + 14.2135i 0.0552161 + 0.525346i
\(733\) −5.98278 18.4131i −0.220979 0.680103i −0.998675 0.0514628i \(-0.983612\pi\)
0.777696 0.628641i \(-0.216388\pi\)
\(734\) −8.40983 + 25.8828i −0.310412 + 0.955351i
\(735\) −7.63786 + 3.40059i −0.281727 + 0.125433i
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 38.3871 14.0617i 1.41401 0.517970i
\(738\) −4.97214 8.61199i −0.183027 0.317012i
\(739\) 1.65498 15.7461i 0.0608794 0.579229i −0.920979 0.389613i \(-0.872609\pi\)
0.981858 0.189616i \(-0.0607244\pi\)
\(740\) 0.399187 1.22857i 0.0146744 0.0451632i
\(741\) 11.3671 11.4915i 0.417581 0.422150i
\(742\) −23.1803 + 16.8415i −0.850977 + 0.618271i
\(743\) 42.8348 + 19.0713i 1.57146 + 0.699658i 0.993224 0.116214i \(-0.0370759\pi\)
0.578233 + 0.815872i \(0.303743\pi\)
\(744\) 13.1874 14.6460i 0.483472 0.536950i
\(745\) 2.32331 + 2.58030i 0.0851196 + 0.0945349i
\(746\) 1.60563 15.2765i 0.0587862 0.559314i
\(747\) −5.73607 + 9.93516i −0.209872 + 0.363509i
\(748\) −4.35410 17.3108i −0.159202 0.632945i
\(749\) 25.7984 0.942652
\(750\) 6.87705 3.06186i 0.251114 0.111803i
\(751\) −24.2928 26.9798i −0.886455 0.984508i 0.113504 0.993538i \(-0.463793\pi\)
−0.999959 + 0.00902930i \(0.997126\pi\)
\(752\) 0.309017 + 0.951057i 0.0112687 + 0.0346815i
\(753\) 33.7426 24.5155i 1.22965 0.893393i
\(754\) 0.433364 + 4.12319i 0.0157822 + 0.150158i
\(755\) −1.98435 + 2.20384i −0.0722177 + 0.0802059i
\(756\) −11.3379 12.5920i −0.412357 0.457968i
\(757\) −0.534293 + 5.08346i −0.0194192 + 0.184761i −0.999932 0.0116959i \(-0.996277\pi\)
0.980512 + 0.196457i \(0.0629437\pi\)
\(758\) 8.16312 + 14.1389i 0.296498 + 0.513549i
\(759\) 5.61803 3.52671i 0.203922 0.128012i
\(760\) −0.899187 + 1.40126i −0.0326169 + 0.0508290i
\(761\) 16.3713 + 11.8945i 0.593460 + 0.431174i 0.843552 0.537048i \(-0.180461\pi\)
−0.250092 + 0.968222i \(0.580461\pi\)
\(762\) 1.10004 0.233820i 0.0398501 0.00847040i
\(763\) 22.4203 24.9002i 0.811669 0.901449i
\(764\) 0.0305010 + 0.290198i 0.00110349 + 0.0104990i
\(765\) 1.87800 + 0.836140i 0.0678993 + 0.0302307i
\(766\) −24.6846 5.24687i −0.891891 0.189577i
\(767\) −4.98936 + 15.3557i −0.180155 + 0.554461i
\(768\) −1.61803 1.17557i −0.0583858 0.0424197i
\(769\) 4.13525 7.16247i 0.149121 0.258285i −0.781782 0.623552i \(-0.785689\pi\)
0.930903 + 0.365267i \(0.119022\pi\)
\(770\) −3.31263 4.22195i −0.119379 0.152148i
\(771\) 28.0000 1.00840
\(772\) −6.80902 4.94704i −0.245062 0.178048i
\(773\) −0.181006 0.201028i −0.00651035 0.00723047i 0.739881 0.672738i \(-0.234882\pi\)
−0.746391 + 0.665507i \(0.768215\pi\)
\(774\) −7.16519 + 7.95775i −0.257547 + 0.286035i
\(775\) 4.99989 + 47.5708i 0.179601 + 1.70879i
\(776\) −14.7815 6.58114i −0.530624 0.236249i
\(777\) −19.1722 + 21.2929i −0.687801 + 0.763880i
\(778\) −4.26393 + 13.1230i −0.152869 + 0.470484i
\(779\) −40.3819 + 15.7538i −1.44683 + 0.564438i
\(780\) 1.41641 0.0507155
\(781\) 9.23677 + 18.8392i 0.330518 + 0.674120i
\(782\) −2.69098 4.66092i −0.0962294 0.166674i
\(783\) −8.17100 + 3.63796i −0.292008 + 0.130010i
\(784\) −10.7051 + 2.27544i −0.382325 + 0.0812658i
\(785\) 3.21986 + 0.684403i 0.114922 + 0.0244274i
\(786\) −5.61803 + 4.08174i −0.200389 + 0.145591i
\(787\) 13.6074 9.88635i 0.485051 0.352410i −0.318227 0.948015i \(-0.603087\pi\)
0.803278 + 0.595604i \(0.203087\pi\)
\(788\) −25.0037 5.31470i −0.890720 0.189328i
\(789\) 22.4806 + 24.9672i 0.800331 + 0.888858i
\(790\) 1.14590 + 0.832544i 0.0407692 + 0.0296206i
\(791\) 46.7426 1.66198
\(792\) −1.84894 + 2.75344i −0.0656993 + 0.0978391i
\(793\) −6.62461 11.4742i −0.235247 0.407460i
\(794\) −0.964456 + 0.429403i −0.0342272 + 0.0152390i
\(795\) 5.05427 1.07432i 0.179256 0.0381021i
\(796\) 13.9541 15.4976i 0.494591 0.549299i
\(797\) −9.70820 + 7.05342i −0.343882 + 0.249845i −0.746298 0.665612i \(-0.768171\pi\)
0.402416 + 0.915457i \(0.368171\pi\)
\(798\) 30.8615 20.2813i 1.09249 0.717950i
\(799\) −1.66312 5.11855i −0.0588369 0.181081i
\(800\) 4.74803 1.00922i 0.167868 0.0356815i
\(801\) −1.53743 + 14.6276i −0.0543223 + 0.516842i
\(802\) −9.47214 + 16.4062i −0.334473 + 0.579324i
\(803\) 36.8923 5.26270i 1.30190 0.185717i
\(804\) −12.3262 + 21.3497i −0.434713 + 0.752945i
\(805\) −1.30902 0.951057i −0.0461368 0.0335203i
\(806\) −5.64590 + 17.3763i −0.198868 + 0.612054i
\(807\) 29.9826 + 6.37301i 1.05544 + 0.224341i
\(808\) −0.288910 2.74879i −0.0101638 0.0967021i
\(809\) −9.97214 + 7.24518i −0.350602 + 0.254727i −0.749121 0.662433i \(-0.769524\pi\)
0.398520 + 0.917160i \(0.369524\pi\)
\(810\) 1.29837 + 3.99598i 0.0456202 + 0.140405i
\(811\) −5.27847 5.86233i −0.185352 0.205854i 0.643306 0.765609i \(-0.277562\pi\)
−0.828659 + 0.559754i \(0.810895\pi\)
\(812\) −0.990108 + 9.42025i −0.0347460 + 0.330586i
\(813\) −2.61803 + 4.53457i −0.0918185 + 0.159034i
\(814\) −9.91464 5.24544i −0.347508 0.183852i
\(815\) −0.944272 1.63553i −0.0330764 0.0572900i
\(816\) 8.70820 + 6.32688i 0.304848 + 0.221485i
\(817\) 29.5711 + 36.1137i 1.03456 + 1.26346i
\(818\) −6.97214 21.4580i −0.243775 0.750262i
\(819\) −7.17508 3.19455i −0.250718 0.111627i
\(820\) −3.46999 1.54494i −0.121177 0.0539516i
\(821\) −43.8531 9.32127i −1.53048 0.325314i −0.635743 0.771900i \(-0.719306\pi\)
−0.894741 + 0.446586i \(0.852640\pi\)
\(822\) 21.5866 4.58838i 0.752920 0.160038i
\(823\) −12.7702 + 5.68566i −0.445141 + 0.198189i −0.617051 0.786923i \(-0.711673\pi\)
0.171910 + 0.985113i \(0.445006\pi\)
\(824\) 8.94427 0.311588
\(825\) −7.85410 31.2259i −0.273445 1.08715i
\(826\) −18.4443 + 31.9464i −0.641758 + 1.11156i
\(827\) −19.2159 + 8.55548i −0.668203 + 0.297503i −0.712661 0.701508i \(-0.752510\pi\)
0.0444585 + 0.999011i \(0.485844\pi\)
\(828\) −0.309017 + 0.951057i −0.0107391 + 0.0330515i
\(829\) −9.48936 29.2052i −0.329579 1.01434i −0.969331 0.245759i \(-0.920963\pi\)
0.639752 0.768581i \(-0.279037\pi\)
\(830\) 0.458040 + 4.35796i 0.0158988 + 0.151267i
\(831\) −22.6859 10.1004i −0.786965 0.350380i
\(832\) 1.81359 + 0.385489i 0.0628748 + 0.0133644i
\(833\) 57.6146 12.2464i 1.99623 0.424311i
\(834\) 2.17762 20.7187i 0.0754049 0.717430i
\(835\) −6.49342 −0.224714
\(836\) 10.6468 + 9.77987i 0.368227 + 0.338244i
\(837\) −39.4164 −1.36243
\(838\) 3.51764 33.4681i 0.121515 1.15614i
\(839\) −48.8866 + 10.3912i −1.68775 + 0.358743i −0.949010 0.315246i \(-0.897913\pi\)
−0.738742 + 0.673989i \(0.764580\pi\)
\(840\) 3.16535 + 0.672816i 0.109215 + 0.0232144i
\(841\) −21.9251 9.76168i −0.756038 0.336610i
\(842\) −0.264234 2.51402i −0.00910610 0.0866387i
\(843\) −2.20163 6.77591i −0.0758280 0.233375i
\(844\) 2.75329 8.47375i 0.0947721 0.291679i
\(845\) 3.33670 1.48560i 0.114786 0.0511060i
\(846\) −0.500000 + 0.866025i −0.0171904 + 0.0297746i
\(847\) −41.0517 + 22.0458i −1.41055 + 0.757503i
\(848\) 6.76393 0.232274
\(849\) 28.8021 12.8235i 0.988487 0.440103i
\(850\) −25.5537 + 5.43161i −0.876486 + 0.186303i
\(851\) −3.30806 0.703150i −0.113399 0.0241037i
\(852\) −11.5586 5.14623i −0.395992 0.176307i
\(853\) 26.2262 + 11.6767i 0.897970 + 0.399802i 0.803208 0.595698i \(-0.203125\pi\)
0.0947613 + 0.995500i \(0.469791\pi\)
\(854\) −9.35410 28.7890i −0.320091 0.985138i
\(855\) −1.64301 + 0.269399i −0.0561898 + 0.00921325i
\(856\) −4.92705 3.57971i −0.168403 0.122352i
\(857\) 20.2705 + 35.1096i 0.692427 + 1.19932i 0.971040 + 0.238916i \(0.0767921\pi\)
−0.278613 + 0.960404i \(0.589875\pi\)
\(858\) 2.11060 12.1163i 0.0720547 0.413643i
\(859\) 28.3885 49.1704i 0.968605 1.67767i 0.269003 0.963139i \(-0.413306\pi\)
0.699602 0.714533i \(-0.253361\pi\)
\(860\) −0.427539 + 4.06776i −0.0145790 + 0.138710i
\(861\) 56.3737 + 62.6094i 1.92121 + 2.13372i
\(862\) −6.63525 20.4212i −0.225998 0.695549i
\(863\) −37.1418 + 26.9851i −1.26432 + 0.918584i −0.998961 0.0455648i \(-0.985491\pi\)
−0.265361 + 0.964149i \(0.585491\pi\)
\(864\) 0.418114 + 3.97809i 0.0142245 + 0.135337i
\(865\) 7.89256 + 1.67762i 0.268355 + 0.0570406i
\(866\) −0.826238 + 2.54290i −0.0280767 + 0.0864112i
\(867\) −19.3607 14.0664i −0.657523 0.477719i
\(868\) −20.8713 + 36.1502i −0.708419 + 1.22702i
\(869\) 8.82927 8.56169i 0.299513 0.290435i
\(870\) 0.854102 1.47935i 0.0289568 0.0501546i
\(871\) 2.38890 22.7289i 0.0809449 0.770140i
\(872\) −7.73698 + 1.64455i −0.262007 + 0.0556914i
\(873\) −5.00000 15.3884i −0.169224 0.520819i
\(874\) 3.89452 + 1.95774i 0.131734 + 0.0662215i
\(875\) −12.8992 + 9.37181i −0.436072 + 0.316825i
\(876\) −15.0368 + 16.7001i −0.508046 + 0.564242i
\(877\) 53.1728 11.3022i 1.79552 0.381649i 0.815216 0.579158i \(-0.196618\pi\)
0.980301 + 0.197509i \(0.0632850\pi\)
\(878\) −32.7349 + 14.5745i −1.10475 + 0.491866i
\(879\) 18.4164 + 31.8982i 0.621170 + 1.07590i
\(880\) 0.0468299 + 1.26597i 0.00157864 + 0.0426759i
\(881\) 37.4164 1.26059 0.630295 0.776355i \(-0.282934\pi\)
0.630295 + 0.776355i \(0.282934\pi\)
\(882\) −8.85410 6.43288i −0.298133 0.216606i
\(883\) −1.81214 2.01259i −0.0609834 0.0677290i 0.711881 0.702300i \(-0.247843\pi\)
−0.772865 + 0.634571i \(0.781177\pi\)
\(884\) −9.76065 2.07469i −0.328286 0.0697794i
\(885\) 5.38197 3.91023i 0.180913 0.131441i
\(886\) −9.88197 + 7.17967i −0.331991 + 0.241206i
\(887\) 45.1167 + 9.58985i 1.51487 + 0.321996i 0.888991 0.457925i \(-0.151407\pi\)
0.625879 + 0.779920i \(0.284740\pi\)
\(888\) 6.61612 1.40630i 0.222023 0.0471924i
\(889\) −2.17603 + 0.968833i −0.0729818 + 0.0324936i
\(890\) 2.80902 + 4.86536i 0.0941585 + 0.163087i
\(891\) 36.1172 5.15213i 1.20997 0.172603i
\(892\) 20.4721 0.685458
\(893\) 3.40238 + 2.72467i 0.113856 + 0.0911777i
\(894\) −5.61803 + 17.2905i −0.187895 + 0.578282i
\(895\) 0.436592 0.484884i 0.0145936 0.0162079i
\(896\) 3.86984 + 1.72296i 0.129282 + 0.0575602i
\(897\) −0.387613 3.68789i −0.0129420 0.123135i
\(898\) 3.40599 3.78273i 0.113659 0.126231i
\(899\) 14.7439 + 16.3748i 0.491737 + 0.546130i
\(900\) 3.92705 + 2.85317i 0.130902 + 0.0951057i
\(901\) −36.4033 −1.21277
\(902\) −18.3864 + 27.3809i −0.612200 + 0.911685i
\(903\) 45.3607 78.5670i 1.50951 2.61455i
\(904\) −8.92705 6.48588i −0.296909 0.215717i
\(905\) −1.27051 + 3.91023i −0.0422332 + 0.129980i
\(906\) −15.1885 3.22842i −0.504606 0.107257i
\(907\) −0.380408 0.169368i −0.0126312 0.00562378i 0.400411 0.916336i \(-0.368867\pi\)
−0.413043 + 0.910712i \(0.635534\pi\)
\(908\) −0.731699 6.96165i −0.0242823 0.231031i
\(909\) 1.84943 2.05400i 0.0613418 0.0681269i
\(910\) −2.93444 + 0.623735i −0.0972758 + 0.0206766i
\(911\) −8.68034 6.30664i −0.287592 0.208948i 0.434630 0.900609i \(-0.356879\pi\)
−0.722222 + 0.691661i \(0.756879\pi\)
\(912\) −8.70820 0.408882i −0.288357 0.0135394i
\(913\) 37.9615 + 2.57565i 1.25634 + 0.0852417i
\(914\) −5.44427 9.42976i −0.180081 0.311909i
\(915\) −0.570619 + 5.42908i −0.0188641 + 0.179480i
\(916\) 12.5182 + 13.9029i 0.413614 + 0.459365i
\(917\) 9.84171 10.9303i 0.325002 0.360951i
\(918\) −2.25027 21.4099i −0.0742701 0.706633i
\(919\) −44.2705 + 32.1644i −1.46035 + 1.06101i −0.477078 + 0.878861i \(0.658304\pi\)
−0.983272 + 0.182145i \(0.941696\pi\)
\(920\) 0.118034 + 0.363271i 0.00389147 + 0.0119767i
\(921\) 11.0681 + 12.2924i 0.364706 + 0.405047i
\(922\) 3.33670 1.48560i 0.109888 0.0489255i
\(923\) 11.7295 0.386081
\(924\) 10.4721 26.0746i 0.344508 0.857790i
\(925\) −8.20820 + 14.2170i −0.269884 + 0.467453i
\(926\) −1.11931 + 10.6495i −0.0367829 + 0.349966i
\(927\) 5.98489 + 6.64689i 0.196569 + 0.218312i
\(928\) 1.49622 1.66172i 0.0491159 0.0545487i
\(929\) 24.4501 + 10.8859i 0.802181 + 0.357154i 0.766528 0.642210i \(-0.221982\pi\)
0.0356523 + 0.999364i \(0.488649\pi\)
\(930\) 6.09017 4.42477i 0.199705 0.145094i
\(931\) −33.5485 + 33.9155i −1.09951 + 1.11154i
\(932\) −3.13525 + 9.64932i −0.102699 + 0.316074i
\(933\) 3.25341 30.9541i 0.106512 1.01339i
\(934\) 9.18034 + 15.9008i 0.300390 + 0.520291i
\(935\) −0.252037 6.81342i −0.00824250 0.222823i
\(936\) 0.927051 + 1.60570i 0.0303016 + 0.0524839i
\(937\) −34.0483 + 15.1593i −1.11231 + 0.495232i −0.878833 0.477130i \(-0.841677\pi\)
−0.233477 + 0.972362i \(0.575010\pi\)
\(938\) 16.1353 49.6592i 0.526835 1.62143i
\(939\) −3.12461 9.61657i −0.101968 0.313825i
\(940\) 0.0399263 + 0.379874i 0.00130225 + 0.0123901i
\(941\) −1.09464 10.4148i −0.0356841 0.339512i −0.997769 0.0667614i \(-0.978733\pi\)
0.962085 0.272750i \(-0.0879333\pi\)
\(942\) 5.32624 + 16.3925i 0.173538 + 0.534096i
\(943\) −3.07295 + 9.45756i −0.100069 + 0.307981i
\(944\) 7.95534 3.54195i 0.258924 0.115281i
\(945\) −3.23607 5.60503i −0.105269 0.182332i
\(946\) 34.1595 + 9.71867i 1.11062 + 0.315981i
\(947\) −7.33688 12.7079i −0.238417 0.412950i 0.721844 0.692056i \(-0.243295\pi\)
−0.960260 + 0.279107i \(0.909962\pi\)
\(948\) −0.775226 + 7.37578i −0.0251782 + 0.239554i
\(949\) 6.43769 19.8132i 0.208976 0.643163i
\(950\) 14.8797 15.0425i 0.482762 0.488044i
\(951\) 2.09017 1.51860i 0.0677784 0.0492439i
\(952\) −20.8274 9.27293i −0.675018 0.300538i
\(953\) −29.8410 + 33.1418i −0.966646 + 1.07357i 0.0306090 + 0.999531i \(0.490255\pi\)
−0.997255 + 0.0740381i \(0.976411\pi\)
\(954\) 4.52595 + 5.02658i 0.146533 + 0.162742i
\(955\) −0.0116503 + 0.110846i −0.000376996 + 0.00358688i
\(956\) 12.6631 21.9332i 0.409555 0.709369i
\(957\) −11.3820 9.51057i −0.367927 0.307433i
\(958\) 31.8328 1.02847
\(959\) −42.7015 + 19.0119i −1.37890 + 0.613928i
\(960\) −0.511170 0.567712i −0.0164980 0.0183228i
\(961\) 20.4271 + 62.8680i 0.658937 + 2.02800i
\(962\) −5.07295 + 3.68571i −0.163558 + 0.118832i
\(963\) −0.636596 6.05681i −0.0205140 0.195178i
\(964\) −3.56395 + 3.95817i −0.114787 + 0.127484i
\(965\) −2.15111 2.38905i −0.0692466 0.0769062i
\(966\) 0.885579 8.42572i 0.0284930 0.271093i
\(967\) 12.0172 + 20.8144i 0.386448 + 0.669347i 0.991969 0.126482i \(-0.0403686\pi\)
−0.605521 + 0.795829i \(0.707035\pi\)
\(968\) 10.8992 + 1.48584i 0.350313 + 0.0477567i
\(969\) 46.8673 + 2.20059i 1.50559 + 0.0706931i
\(970\) −5.00000 3.63271i −0.160540 0.116639i
\(971\) −3.93341 + 0.836072i −0.126229 + 0.0268308i −0.270593 0.962694i \(-0.587220\pi\)
0.144364 + 0.989525i \(0.453886\pi\)
\(972\) −6.69131 + 7.43145i −0.214624 + 0.238364i
\(973\) 4.61228 + 43.8829i 0.147863 + 1.40682i
\(974\) 12.8405 + 5.71698i 0.411438 + 0.183184i
\(975\) −17.6067 3.74241i −0.563864 0.119853i
\(976\) −2.20820 + 6.79615i −0.0706829 + 0.217540i
\(977\) −17.1180 12.4370i −0.547654 0.397894i 0.279265 0.960214i \(-0.409909\pi\)
−0.826920 + 0.562320i \(0.809909\pi\)
\(978\) 4.94427 8.56373i 0.158100 0.273838i
\(979\) 45.8051 16.7790i 1.46394 0.536260i
\(980\) −4.18034 −0.133536
\(981\) −6.39919 4.64928i −0.204310 0.148440i
\(982\) 7.44382 + 8.26720i 0.237542 + 0.263817i
\(983\) −29.3299 + 32.5741i −0.935478 + 1.03895i 0.0636820 + 0.997970i \(0.479716\pi\)
−0.999160 + 0.0409832i \(0.986951\pi\)
\(984\) −2.07892 19.7796i −0.0662735 0.630550i
\(985\) −8.91980 3.97135i −0.284208 0.126538i
\(986\) −8.05261 + 8.94333i −0.256447 + 0.284814i
\(987\) 2.61803 8.05748i 0.0833329 0.256472i
\(988\) 7.52918 2.93728i 0.239535 0.0934474i
\(989\) 10.7082 0.340501
\(990\) −0.909465 + 0.881902i −0.0289047 + 0.0280287i
\(991\) −1.13525 1.96632i −0.0360626 0.0624622i 0.847431 0.530906i \(-0.178148\pi\)
−0.883493 + 0.468444i \(0.844815\pi\)
\(992\) 9.00217 4.00802i 0.285819 0.127255i
\(993\) −23.5429 + 5.00420i −0.747112 + 0.158804i
\(994\) 26.2128 + 5.57170i 0.831418 + 0.176723i
\(995\) 6.44427 4.68204i 0.204297 0.148431i
\(996\) −18.5623 + 13.4863i −0.588169 + 0.427330i
\(997\) 1.81359 + 0.385489i 0.0574368 + 0.0122086i 0.236540 0.971622i \(-0.423986\pi\)
−0.179104 + 0.983830i \(0.557320\pi\)
\(998\) 28.2099 + 31.3303i 0.892969 + 0.991743i
\(999\) −10.9443 7.95148i −0.346261 0.251574i
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 418.2.n.c.235.1 yes 8
11.3 even 5 inner 418.2.n.c.311.1 yes 8
19.11 even 3 inner 418.2.n.c.125.1 8
209.201 even 15 inner 418.2.n.c.201.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.n.c.125.1 8 19.11 even 3 inner
418.2.n.c.201.1 yes 8 209.201 even 15 inner
418.2.n.c.235.1 yes 8 1.1 even 1 trivial
418.2.n.c.311.1 yes 8 11.3 even 5 inner