Properties

Label 143.2.h.b.92.2
Level $143$
Weight $2$
Character 143.92
Analytic conductor $1.142$
Analytic rank $0$
Dimension $16$
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] = [143,2,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: 16.0.273503893564697265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 19 x^{12} - 16 x^{11} + 49 x^{10} - 32 x^{9} + 98 x^{8} - 110 x^{7} + 145 x^{6} - 40 x^{5} + 52 x^{4} + 24 x^{3} + 19 x^{2} + 6 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 92.2
Root \(0.538745 - 1.65809i\) of defining polynomial
Character \(\chi\) \(=\) 143.92
Dual form 143.2.h.b.14.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.446411 - 0.324336i) q^{2} +(-0.828765 + 2.55067i) q^{3} +(-0.523946 - 1.61254i) q^{4} +(2.94178 - 2.13733i) q^{5} +(1.19725 - 0.869850i) q^{6} +(1.17546 + 3.61770i) q^{7} +(-0.630137 + 1.93936i) q^{8} +(-3.39204 - 2.46446i) q^{9} +O(q^{10})\) \(q+(-0.446411 - 0.324336i) q^{2} +(-0.828765 + 2.55067i) q^{3} +(-0.523946 - 1.61254i) q^{4} +(2.94178 - 2.13733i) q^{5} +(1.19725 - 0.869850i) q^{6} +(1.17546 + 3.61770i) q^{7} +(-0.630137 + 1.93936i) q^{8} +(-3.39204 - 2.46446i) q^{9} -2.00645 q^{10} +(2.49918 + 2.18038i) q^{11} +4.54729 q^{12} +(0.809017 + 0.587785i) q^{13} +(0.648613 - 1.99622i) q^{14} +(3.01358 + 9.27486i) q^{15} +(-1.83311 + 1.33183i) q^{16} +(0.435860 - 0.316671i) q^{17} +(0.714929 + 2.20032i) q^{18} +(1.48561 - 4.57223i) q^{19} +(-4.98785 - 3.62389i) q^{20} -10.2018 q^{21} +(-0.408484 - 1.78392i) q^{22} -0.778209 q^{23} +(-4.42445 - 3.21455i) q^{24} +(2.54080 - 7.81979i) q^{25} +(-0.170514 - 0.524787i) q^{26} +(2.58804 - 1.88032i) q^{27} +(5.21780 - 3.79096i) q^{28} +(-0.506341 - 1.55836i) q^{29} +(1.66288 - 5.11781i) q^{30} +(-8.53404 - 6.20034i) q^{31} +5.32861 q^{32} +(-7.63269 + 4.56758i) q^{33} -0.297280 q^{34} +(11.1902 + 8.13012i) q^{35} +(-2.19680 + 6.76104i) q^{36} +(-1.99115 - 6.12812i) q^{37} +(-2.14613 + 1.55925i) q^{38} +(-2.16973 + 1.57640i) q^{39} +(2.29133 + 7.05198i) q^{40} +(-2.68832 + 8.27380i) q^{41} +(4.55417 + 3.30880i) q^{42} -1.03817 q^{43} +(2.20652 - 5.17243i) q^{44} -15.2460 q^{45} +(0.347401 + 0.252401i) q^{46} +(-0.269432 + 0.829226i) q^{47} +(-1.87785 - 5.77944i) q^{48} +(-6.04292 + 4.39044i) q^{49} +(-3.67048 + 2.66676i) q^{50} +(0.446499 + 1.37418i) q^{51} +(0.523946 - 1.61254i) q^{52} +(1.58391 + 1.15078i) q^{53} -1.76519 q^{54} +(12.0122 + 1.07263i) q^{55} -7.75674 q^{56} +(10.4310 + 7.57860i) q^{57} +(-0.279396 + 0.859892i) q^{58} +(-0.807023 - 2.48376i) q^{59} +(13.3771 - 9.71904i) q^{60} +(3.22805 - 2.34531i) q^{61} +(1.79869 + 5.53580i) q^{62} +(4.92847 - 15.1683i) q^{63} +(1.28747 + 0.935400i) q^{64} +3.63624 q^{65} +(4.88875 + 0.436541i) q^{66} -9.73566 q^{67} +(-0.739011 - 0.536923i) q^{68} +(0.644952 - 1.98496i) q^{69} +(-2.35851 - 7.25874i) q^{70} +(3.71171 - 2.69672i) q^{71} +(6.91694 - 5.02545i) q^{72} +(-1.25975 - 3.87711i) q^{73} +(-1.09870 + 3.38146i) q^{74} +(17.8400 + 12.9615i) q^{75} -8.15127 q^{76} +(-4.95028 + 11.6043i) q^{77} +1.47988 q^{78} +(-7.12323 - 5.17533i) q^{79} +(-2.54604 + 7.83590i) q^{80} +(-1.23572 - 3.80314i) q^{81} +(3.88359 - 2.82159i) q^{82} +(-6.04966 + 4.39534i) q^{83} +(5.34517 + 16.4507i) q^{84} +(0.605374 - 1.86315i) q^{85} +(0.463450 + 0.336716i) q^{86} +4.39450 q^{87} +(-5.80339 + 3.47288i) q^{88} +7.75356 q^{89} +(6.80597 + 4.94483i) q^{90} +(-1.17546 + 3.61770i) q^{91} +(0.407739 + 1.25489i) q^{92} +(22.8878 - 16.6289i) q^{93} +(0.389225 - 0.282789i) q^{94} +(-5.40201 - 16.6257i) q^{95} +(-4.41617 + 13.5916i) q^{96} +(-2.36312 - 1.71691i) q^{97} +4.12160 q^{98} +(-3.10386 - 13.5551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20} - 8 q^{21} + 2 q^{22} - 46 q^{23} + 3 q^{24} + 23 q^{25} + 3 q^{26} + 17 q^{27} - 9 q^{28} - 25 q^{29} + 22 q^{30} + 3 q^{31} + 24 q^{32} - 10 q^{33} + 4 q^{34} + 26 q^{35} - 2 q^{36} - 7 q^{37} + 5 q^{38} + 25 q^{40} - 3 q^{41} - 12 q^{42} - 16 q^{43} + 32 q^{44} - 46 q^{45} - 11 q^{46} + 13 q^{47} - 24 q^{48} + 19 q^{49} - 19 q^{50} - 23 q^{51} + 8 q^{52} - 14 q^{53} + 6 q^{54} - 5 q^{55} - 68 q^{56} + 23 q^{57} + 20 q^{58} + 16 q^{59} + 34 q^{60} - 13 q^{61} + 28 q^{62} + 18 q^{63} - 40 q^{64} + 10 q^{65} + 41 q^{66} - 62 q^{67} + 13 q^{68} + 4 q^{69} - 2 q^{70} + 54 q^{71} + 21 q^{72} - 42 q^{73} + 42 q^{74} + 51 q^{75} - 4 q^{76} + 14 q^{77} - 6 q^{78} - 15 q^{79} - 19 q^{80} + q^{81} - 7 q^{82} - 43 q^{83} - 35 q^{84} - 3 q^{85} - 32 q^{86} + 4 q^{87} + 41 q^{88} - 30 q^{89} + 26 q^{90} - 9 q^{91} + 3 q^{92} + 49 q^{93} + 4 q^{94} + 23 q^{95} + 23 q^{96} - 12 q^{97} + 24 q^{98} - 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.446411 0.324336i −0.315660 0.229340i 0.418661 0.908142i \(-0.362499\pi\)
−0.734321 + 0.678802i \(0.762499\pi\)
\(3\) −0.828765 + 2.55067i −0.478487 + 1.47263i 0.362709 + 0.931903i \(0.381852\pi\)
−0.841196 + 0.540730i \(0.818148\pi\)
\(4\) −0.523946 1.61254i −0.261973 0.806269i
\(5\) 2.94178 2.13733i 1.31560 0.955841i 0.315627 0.948883i \(-0.397785\pi\)
0.999976 0.00695775i \(-0.00221474\pi\)
\(6\) 1.19725 0.869850i 0.488773 0.355115i
\(7\) 1.17546 + 3.61770i 0.444283 + 1.36736i 0.883268 + 0.468868i \(0.155338\pi\)
−0.438985 + 0.898494i \(0.644662\pi\)
\(8\) −0.630137 + 1.93936i −0.222787 + 0.685668i
\(9\) −3.39204 2.46446i −1.13068 0.821487i
\(10\) −2.00645 −0.634496
\(11\) 2.49918 + 2.18038i 0.753532 + 0.657411i
\(12\) 4.54729 1.31269
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i
\(14\) 0.648613 1.99622i 0.173349 0.533513i
\(15\) 3.01358 + 9.27486i 0.778104 + 2.39476i
\(16\) −1.83311 + 1.33183i −0.458277 + 0.332958i
\(17\) 0.435860 0.316671i 0.105712 0.0768039i −0.533674 0.845690i \(-0.679189\pi\)
0.639385 + 0.768887i \(0.279189\pi\)
\(18\) 0.714929 + 2.20032i 0.168510 + 0.518621i
\(19\) 1.48561 4.57223i 0.340821 1.04894i −0.622962 0.782252i \(-0.714071\pi\)
0.963783 0.266688i \(-0.0859293\pi\)
\(20\) −4.98785 3.62389i −1.11532 0.810326i
\(21\) −10.2018 −2.22621
\(22\) −0.408484 1.78392i −0.0870891 0.380334i
\(23\) −0.778209 −0.162268 −0.0811339 0.996703i \(-0.525854\pi\)
−0.0811339 + 0.996703i \(0.525854\pi\)
\(24\) −4.42445 3.21455i −0.903137 0.656167i
\(25\) 2.54080 7.81979i 0.508161 1.56396i
\(26\) −0.170514 0.524787i −0.0334405 0.102919i
\(27\) 2.58804 1.88032i 0.498069 0.361869i
\(28\) 5.21780 3.79096i 0.986072 0.716423i
\(29\) −0.506341 1.55836i −0.0940252 0.289380i 0.892973 0.450110i \(-0.148615\pi\)
−0.986998 + 0.160730i \(0.948615\pi\)
\(30\) 1.66288 5.11781i 0.303598 0.934380i
\(31\) −8.53404 6.20034i −1.53276 1.11361i −0.954680 0.297634i \(-0.903802\pi\)
−0.578079 0.815981i \(-0.696198\pi\)
\(32\) 5.32861 0.941975
\(33\) −7.63269 + 4.56758i −1.32868 + 0.795114i
\(34\) −0.297280 −0.0509831
\(35\) 11.1902 + 8.13012i 1.89148 + 1.37424i
\(36\) −2.19680 + 6.76104i −0.366133 + 1.12684i
\(37\) −1.99115 6.12812i −0.327343 1.00746i −0.970372 0.241615i \(-0.922323\pi\)
0.643030 0.765841i \(-0.277677\pi\)
\(38\) −2.14613 + 1.55925i −0.348148 + 0.252944i
\(39\) −2.16973 + 1.57640i −0.347435 + 0.252427i
\(40\) 2.29133 + 7.05198i 0.362291 + 1.11502i
\(41\) −2.68832 + 8.27380i −0.419845 + 1.29215i 0.487999 + 0.872844i \(0.337727\pi\)
−0.907845 + 0.419307i \(0.862273\pi\)
\(42\) 4.55417 + 3.30880i 0.702724 + 0.510559i
\(43\) −1.03817 −0.158319 −0.0791597 0.996862i \(-0.525224\pi\)
−0.0791597 + 0.996862i \(0.525224\pi\)
\(44\) 2.20652 5.17243i 0.332645 0.779774i
\(45\) −15.2460 −2.27274
\(46\) 0.347401 + 0.252401i 0.0512214 + 0.0372145i
\(47\) −0.269432 + 0.829226i −0.0393007 + 0.120955i −0.968782 0.247914i \(-0.920255\pi\)
0.929481 + 0.368869i \(0.120255\pi\)
\(48\) −1.87785 5.77944i −0.271045 0.834190i
\(49\) −6.04292 + 4.39044i −0.863275 + 0.627206i
\(50\) −3.67048 + 2.66676i −0.519085 + 0.377137i
\(51\) 0.446499 + 1.37418i 0.0625223 + 0.192424i
\(52\) 0.523946 1.61254i 0.0726582 0.223619i
\(53\) 1.58391 + 1.15078i 0.217567 + 0.158071i 0.691231 0.722634i \(-0.257069\pi\)
−0.473664 + 0.880706i \(0.657069\pi\)
\(54\) −1.76519 −0.240212
\(55\) 12.0122 + 1.07263i 1.61973 + 0.144634i
\(56\) −7.75674 −1.03654
\(57\) 10.4310 + 7.57860i 1.38163 + 1.00381i
\(58\) −0.279396 + 0.859892i −0.0366865 + 0.112909i
\(59\) −0.807023 2.48376i −0.105065 0.323358i 0.884680 0.466198i \(-0.154377\pi\)
−0.989746 + 0.142840i \(0.954377\pi\)
\(60\) 13.3771 9.71904i 1.72698 1.25472i
\(61\) 3.22805 2.34531i 0.413309 0.300287i −0.361631 0.932321i \(-0.617780\pi\)
0.774940 + 0.632035i \(0.217780\pi\)
\(62\) 1.79869 + 5.53580i 0.228434 + 0.703047i
\(63\) 4.92847 15.1683i 0.620929 1.91102i
\(64\) 1.28747 + 0.935400i 0.160934 + 0.116925i
\(65\) 3.63624 0.451020
\(66\) 4.88875 + 0.436541i 0.601763 + 0.0537345i
\(67\) −9.73566 −1.18940 −0.594700 0.803948i \(-0.702729\pi\)
−0.594700 + 0.803948i \(0.702729\pi\)
\(68\) −0.739011 0.536923i −0.0896182 0.0651114i
\(69\) 0.644952 1.98496i 0.0776431 0.238961i
\(70\) −2.35851 7.25874i −0.281896 0.867586i
\(71\) 3.71171 2.69672i 0.440499 0.320041i −0.345334 0.938480i \(-0.612234\pi\)
0.785833 + 0.618439i \(0.212234\pi\)
\(72\) 6.91694 5.02545i 0.815169 0.592255i
\(73\) −1.25975 3.87711i −0.147442 0.453781i 0.849875 0.526985i \(-0.176678\pi\)
−0.997317 + 0.0732038i \(0.976678\pi\)
\(74\) −1.09870 + 3.38146i −0.127722 + 0.393087i
\(75\) 17.8400 + 12.9615i 2.05999 + 1.49667i
\(76\) −8.15127 −0.935014
\(77\) −4.95028 + 11.6043i −0.564137 + 1.32243i
\(78\) 1.47988 0.167563
\(79\) −7.12323 5.17533i −0.801426 0.582270i 0.109906 0.993942i \(-0.464945\pi\)
−0.911332 + 0.411672i \(0.864945\pi\)
\(80\) −2.54604 + 7.83590i −0.284656 + 0.876081i
\(81\) −1.23572 3.80314i −0.137302 0.422572i
\(82\) 3.88359 2.82159i 0.428871 0.311593i
\(83\) −6.04966 + 4.39534i −0.664037 + 0.482451i −0.868024 0.496523i \(-0.834610\pi\)
0.203987 + 0.978974i \(0.434610\pi\)
\(84\) 5.34517 + 16.4507i 0.583205 + 1.79492i
\(85\) 0.605374 1.86315i 0.0656620 0.202087i
\(86\) 0.463450 + 0.336716i 0.0499751 + 0.0363090i
\(87\) 4.39450 0.471140
\(88\) −5.80339 + 3.47288i −0.618643 + 0.370211i
\(89\) 7.75356 0.821876 0.410938 0.911663i \(-0.365201\pi\)
0.410938 + 0.911663i \(0.365201\pi\)
\(90\) 6.80597 + 4.94483i 0.717412 + 0.521230i
\(91\) −1.17546 + 3.61770i −0.123222 + 0.379238i
\(92\) 0.407739 + 1.25489i 0.0425097 + 0.130832i
\(93\) 22.8878 16.6289i 2.37335 1.72434i
\(94\) 0.389225 0.282789i 0.0401455 0.0291674i
\(95\) −5.40201 16.6257i −0.554235 1.70576i
\(96\) −4.41617 + 13.5916i −0.450723 + 1.38718i
\(97\) −2.36312 1.71691i −0.239939 0.174326i 0.461317 0.887235i \(-0.347377\pi\)
−0.701256 + 0.712910i \(0.747377\pi\)
\(98\) 4.12160 0.416345
\(99\) −3.10386 13.5551i −0.311950 1.36234i
\(100\) −13.9410 −1.39410
\(101\) 5.28841 + 3.84226i 0.526217 + 0.382319i 0.818941 0.573878i \(-0.194562\pi\)
−0.292724 + 0.956197i \(0.594562\pi\)
\(102\) 0.246375 0.758265i 0.0243948 0.0750794i
\(103\) 2.42799 + 7.47259i 0.239237 + 0.736296i 0.996531 + 0.0832217i \(0.0265210\pi\)
−0.757294 + 0.653074i \(0.773479\pi\)
\(104\) −1.64972 + 1.19859i −0.161768 + 0.117532i
\(105\) −30.0113 + 21.8045i −2.92880 + 2.12790i
\(106\) −0.333835 1.02744i −0.0324249 0.0997936i
\(107\) −2.78343 + 8.56651i −0.269084 + 0.828156i 0.721640 + 0.692268i \(0.243389\pi\)
−0.990724 + 0.135887i \(0.956611\pi\)
\(108\) −4.38809 3.18813i −0.422244 0.306778i
\(109\) −0.668803 −0.0640597 −0.0320298 0.999487i \(-0.510197\pi\)
−0.0320298 + 0.999487i \(0.510197\pi\)
\(110\) −5.01449 4.37484i −0.478113 0.417125i
\(111\) 17.2810 1.64024
\(112\) −6.97292 5.06612i −0.658879 0.478703i
\(113\) 1.23952 3.81485i 0.116604 0.358871i −0.875674 0.482903i \(-0.839582\pi\)
0.992278 + 0.124032i \(0.0395825\pi\)
\(114\) −2.19851 6.76633i −0.205910 0.633725i
\(115\) −2.28932 + 1.66329i −0.213480 + 0.155102i
\(116\) −2.24762 + 1.63299i −0.208686 + 0.151619i
\(117\) −1.29564 3.98758i −0.119782 0.368652i
\(118\) −0.445310 + 1.37052i −0.0409941 + 0.126167i
\(119\) 1.65796 + 1.20458i 0.151985 + 0.110423i
\(120\) −19.8863 −1.81536
\(121\) 1.49184 + 10.8984i 0.135622 + 0.990761i
\(122\) −2.20170 −0.199333
\(123\) −18.8758 13.7141i −1.70197 1.23656i
\(124\) −5.52692 + 17.0101i −0.496332 + 1.52755i
\(125\) −3.62067 11.1433i −0.323842 0.996684i
\(126\) −7.11974 + 5.17279i −0.634277 + 0.460829i
\(127\) 16.4372 11.9423i 1.45857 1.05971i 0.474833 0.880076i \(-0.342509\pi\)
0.983733 0.179634i \(-0.0574914\pi\)
\(128\) −3.56462 10.9708i −0.315071 0.969688i
\(129\) 0.860398 2.64803i 0.0757538 0.233146i
\(130\) −1.62325 1.17936i −0.142369 0.103437i
\(131\) 7.73078 0.675441 0.337721 0.941246i \(-0.390344\pi\)
0.337721 + 0.941246i \(0.390344\pi\)
\(132\) 11.3645 + 9.91484i 0.989154 + 0.862976i
\(133\) 18.2872 1.58570
\(134\) 4.34610 + 3.15763i 0.375446 + 0.272777i
\(135\) 3.59458 11.0630i 0.309372 0.952150i
\(136\) 0.339488 + 1.04484i 0.0291108 + 0.0895940i
\(137\) 10.2168 7.42294i 0.872880 0.634185i −0.0584781 0.998289i \(-0.518625\pi\)
0.931358 + 0.364104i \(0.118625\pi\)
\(138\) −0.931707 + 0.676925i −0.0793122 + 0.0576237i
\(139\) 0.474657 + 1.46084i 0.0402599 + 0.123907i 0.969166 0.246407i \(-0.0792500\pi\)
−0.928907 + 0.370314i \(0.879250\pi\)
\(140\) 7.24710 22.3043i 0.612492 1.88506i
\(141\) −1.89179 1.37447i −0.159317 0.115751i
\(142\) −2.53159 −0.212446
\(143\) 0.740284 + 3.23295i 0.0619057 + 0.270353i
\(144\) 9.50023 0.791686
\(145\) −4.82026 3.50213i −0.400301 0.290836i
\(146\) −0.695122 + 2.13936i −0.0575287 + 0.177055i
\(147\) −6.19043 19.0522i −0.510578 1.57140i
\(148\) −8.83858 + 6.42160i −0.726527 + 0.527852i
\(149\) 1.22517 0.890135i 0.100370 0.0729227i −0.536469 0.843920i \(-0.680242\pi\)
0.636838 + 0.770998i \(0.280242\pi\)
\(150\) −3.76008 11.5723i −0.307009 0.944876i
\(151\) −4.43215 + 13.6408i −0.360683 + 1.11007i 0.591957 + 0.805969i \(0.298355\pi\)
−0.952640 + 0.304099i \(0.901645\pi\)
\(152\) 7.93107 + 5.76226i 0.643295 + 0.467381i
\(153\) −2.25888 −0.182619
\(154\) 5.97354 3.57471i 0.481362 0.288058i
\(155\) −38.3574 −3.08094
\(156\) 3.67883 + 2.67283i 0.294543 + 0.213998i
\(157\) 3.00016 9.23354i 0.239439 0.736917i −0.757063 0.653342i \(-0.773366\pi\)
0.996502 0.0835746i \(-0.0266337\pi\)
\(158\) 1.50134 + 4.62064i 0.119440 + 0.367598i
\(159\) −4.24794 + 3.08631i −0.336884 + 0.244760i
\(160\) 15.6756 11.3890i 1.23926 0.900378i
\(161\) −0.914755 2.81533i −0.0720928 0.221879i
\(162\) −0.681861 + 2.09855i −0.0535720 + 0.164878i
\(163\) 1.64047 + 1.19187i 0.128492 + 0.0933548i 0.650175 0.759785i \(-0.274696\pi\)
−0.521683 + 0.853139i \(0.674696\pi\)
\(164\) 14.7504 1.15181
\(165\) −12.6913 + 29.7503i −0.988013 + 2.31606i
\(166\) 4.12620 0.320255
\(167\) −9.06208 6.58399i −0.701245 0.509484i 0.179092 0.983832i \(-0.442684\pi\)
−0.880337 + 0.474348i \(0.842684\pi\)
\(168\) 6.42851 19.7849i 0.495970 1.52644i
\(169\) 0.309017 + 0.951057i 0.0237705 + 0.0731582i
\(170\) −0.874532 + 0.635385i −0.0670735 + 0.0487318i
\(171\) −16.3073 + 11.8480i −1.24705 + 0.906036i
\(172\) 0.543944 + 1.67409i 0.0414754 + 0.127648i
\(173\) −5.44322 + 16.7525i −0.413840 + 1.27367i 0.499444 + 0.866346i \(0.333538\pi\)
−0.913284 + 0.407323i \(0.866462\pi\)
\(174\) −1.96175 1.42530i −0.148720 0.108051i
\(175\) 31.2763 2.36426
\(176\) −7.48518 0.668391i −0.564217 0.0503819i
\(177\) 7.00410 0.526460
\(178\) −3.46127 2.51476i −0.259433 0.188489i
\(179\) 2.06087 6.34272i 0.154037 0.474077i −0.844025 0.536304i \(-0.819820\pi\)
0.998062 + 0.0622266i \(0.0198201\pi\)
\(180\) 7.98807 + 24.5847i 0.595395 + 1.83244i
\(181\) −4.31149 + 3.13248i −0.320470 + 0.232835i −0.736376 0.676572i \(-0.763465\pi\)
0.415906 + 0.909408i \(0.363465\pi\)
\(182\) 1.69809 1.23373i 0.125871 0.0914505i
\(183\) 3.30684 + 10.1774i 0.244449 + 0.752336i
\(184\) 0.490378 1.50923i 0.0361512 0.111262i
\(185\) −18.9553 13.7718i −1.39362 1.01253i
\(186\) −15.6107 −1.14463
\(187\) 1.77976 + 0.158924i 0.130149 + 0.0116217i
\(188\) 1.47833 0.107818
\(189\) 9.84460 + 7.15252i 0.716089 + 0.520269i
\(190\) −2.98080 + 9.17395i −0.216250 + 0.665548i
\(191\) −4.28424 13.1855i −0.309996 0.954071i −0.977765 0.209702i \(-0.932751\pi\)
0.667769 0.744369i \(-0.267249\pi\)
\(192\) −3.45291 + 2.50869i −0.249192 + 0.181049i
\(193\) −13.2720 + 9.64270i −0.955342 + 0.694097i −0.952064 0.305898i \(-0.901043\pi\)
−0.00327793 + 0.999995i \(0.501043\pi\)
\(194\) 0.498067 + 1.53289i 0.0357591 + 0.110055i
\(195\) −3.01358 + 9.27486i −0.215807 + 0.664186i
\(196\) 10.2459 + 7.44410i 0.731851 + 0.531721i
\(197\) −23.3992 −1.66712 −0.833562 0.552425i \(-0.813702\pi\)
−0.833562 + 0.552425i \(0.813702\pi\)
\(198\) −3.01082 + 7.05783i −0.213969 + 0.501578i
\(199\) 16.2726 1.15353 0.576766 0.816909i \(-0.304314\pi\)
0.576766 + 0.816909i \(0.304314\pi\)
\(200\) 13.5644 + 9.85508i 0.959145 + 0.696859i
\(201\) 8.06857 24.8325i 0.569113 1.75155i
\(202\) −1.11462 3.43045i −0.0784244 0.241365i
\(203\) 5.04249 3.66358i 0.353913 0.257133i
\(204\) 1.98198 1.43999i 0.138766 0.100820i
\(205\) 9.77537 + 30.0855i 0.682742 + 2.10126i
\(206\) 1.33975 4.12333i 0.0933448 0.287286i
\(207\) 2.63972 + 1.91787i 0.183473 + 0.133301i
\(208\) −2.26585 −0.157108
\(209\) 13.6820 8.18764i 0.946405 0.566351i
\(210\) 20.4693 1.41252
\(211\) 6.50875 + 4.72889i 0.448081 + 0.325550i 0.788838 0.614602i \(-0.210683\pi\)
−0.340757 + 0.940152i \(0.610683\pi\)
\(212\) 1.02579 3.15706i 0.0704516 0.216828i
\(213\) 3.80231 + 11.7023i 0.260530 + 0.801829i
\(214\) 4.02098 2.92141i 0.274869 0.199704i
\(215\) −3.05406 + 2.21891i −0.208285 + 0.151328i
\(216\) 2.01581 + 6.20402i 0.137158 + 0.422130i
\(217\) 12.3995 38.1619i 0.841736 2.59060i
\(218\) 0.298561 + 0.216917i 0.0202211 + 0.0146915i
\(219\) 10.9333 0.738803
\(220\) −4.56409 19.9322i −0.307711 1.34383i
\(221\) 0.538752 0.0362404
\(222\) −7.71444 5.60487i −0.517759 0.376174i
\(223\) −2.59724 + 7.99350i −0.173924 + 0.535284i −0.999583 0.0288863i \(-0.990804\pi\)
0.825658 + 0.564170i \(0.190804\pi\)
\(224\) 6.26358 + 19.2773i 0.418503 + 1.28802i
\(225\) −27.8901 + 20.2633i −1.85934 + 1.35089i
\(226\) −1.79063 + 1.30097i −0.119111 + 0.0865391i
\(227\) 7.66315 + 23.5848i 0.508621 + 1.56538i 0.794596 + 0.607138i \(0.207683\pi\)
−0.285975 + 0.958237i \(0.592317\pi\)
\(228\) 6.75548 20.7912i 0.447393 1.37693i
\(229\) 5.29677 + 3.84833i 0.350021 + 0.254305i 0.748878 0.662708i \(-0.230593\pi\)
−0.398857 + 0.917013i \(0.630593\pi\)
\(230\) 1.56144 0.102958
\(231\) −25.4961 22.2438i −1.67752 1.46353i
\(232\) 3.34129 0.219366
\(233\) 4.83003 + 3.50922i 0.316426 + 0.229897i 0.734649 0.678447i \(-0.237347\pi\)
−0.418223 + 0.908344i \(0.637347\pi\)
\(234\) −0.714929 + 2.20032i −0.0467363 + 0.143840i
\(235\) 0.979718 + 3.01526i 0.0639097 + 0.196694i
\(236\) −3.58233 + 2.60271i −0.233190 + 0.169422i
\(237\) 19.1041 13.8799i 1.24094 0.901597i
\(238\) −0.349442 1.07547i −0.0226509 0.0697124i
\(239\) 6.25153 19.2402i 0.404378 1.24455i −0.517036 0.855964i \(-0.672965\pi\)
0.921414 0.388583i \(-0.127035\pi\)
\(240\) −17.8768 12.9882i −1.15394 0.838387i
\(241\) −18.1841 −1.17134 −0.585670 0.810549i \(-0.699169\pi\)
−0.585670 + 0.810549i \(0.699169\pi\)
\(242\) 2.86876 5.34901i 0.184411 0.343847i
\(243\) 20.3217 1.30364
\(244\) −5.47323 3.97653i −0.350388 0.254571i
\(245\) −8.39313 + 25.8314i −0.536217 + 1.65031i
\(246\) 3.97839 + 12.2442i 0.253653 + 0.780662i
\(247\) 3.88937 2.82579i 0.247474 0.179801i
\(248\) 17.4023 12.6435i 1.10505 0.802865i
\(249\) −6.19733 19.0734i −0.392740 1.20873i
\(250\) −1.99786 + 6.14878i −0.126356 + 0.388883i
\(251\) 22.6437 + 16.4516i 1.42926 + 1.03842i 0.990154 + 0.139981i \(0.0447043\pi\)
0.439105 + 0.898436i \(0.355296\pi\)
\(252\) −27.0417 −1.70347
\(253\) −1.94489 1.69679i −0.122274 0.106677i
\(254\) −11.2111 −0.703445
\(255\) 4.25057 + 3.08822i 0.266181 + 0.193392i
\(256\) −0.983397 + 3.02659i −0.0614623 + 0.189162i
\(257\) −7.03880 21.6632i −0.439068 1.35131i −0.888860 0.458179i \(-0.848502\pi\)
0.449792 0.893133i \(-0.351498\pi\)
\(258\) −1.24294 + 0.903052i −0.0773823 + 0.0562215i
\(259\) 19.8292 14.4067i 1.23213 0.895192i
\(260\) −1.90519 5.86357i −0.118155 0.363643i
\(261\) −2.12298 + 6.53387i −0.131409 + 0.404437i
\(262\) −3.45110 2.50737i −0.213210 0.154906i
\(263\) 17.4897 1.07846 0.539232 0.842157i \(-0.318715\pi\)
0.539232 + 0.842157i \(0.318715\pi\)
\(264\) −4.04856 17.6808i −0.249171 1.08818i
\(265\) 7.11909 0.437322
\(266\) −8.16361 5.93121i −0.500543 0.363666i
\(267\) −6.42587 + 19.7768i −0.393257 + 1.21032i
\(268\) 5.10096 + 15.6991i 0.311591 + 0.958977i
\(269\) −19.2665 + 13.9979i −1.17470 + 0.853469i −0.991564 0.129619i \(-0.958625\pi\)
−0.183135 + 0.983088i \(0.558625\pi\)
\(270\) −5.19279 + 3.77278i −0.316023 + 0.229604i
\(271\) −7.32646 22.5485i −0.445051 1.36973i −0.882428 0.470448i \(-0.844092\pi\)
0.437377 0.899278i \(-0.355908\pi\)
\(272\) −0.377226 + 1.16098i −0.0228727 + 0.0703950i
\(273\) −8.25340 5.99644i −0.499518 0.362921i
\(274\) −6.96842 −0.420977
\(275\) 23.4001 14.0032i 1.41108 0.844422i
\(276\) −3.53874 −0.213007
\(277\) −4.66664 3.39051i −0.280391 0.203716i 0.438697 0.898635i \(-0.355440\pi\)
−0.719088 + 0.694919i \(0.755440\pi\)
\(278\) 0.261913 0.806085i 0.0157085 0.0483458i
\(279\) 13.6673 + 42.0636i 0.818240 + 2.51828i
\(280\) −22.8186 + 16.5787i −1.36367 + 0.990765i
\(281\) −3.38815 + 2.46164i −0.202120 + 0.146849i −0.684241 0.729256i \(-0.739867\pi\)
0.482121 + 0.876105i \(0.339867\pi\)
\(282\) 0.398726 + 1.22715i 0.0237438 + 0.0730759i
\(283\) −9.50515 + 29.2538i −0.565022 + 1.73896i 0.102862 + 0.994696i \(0.467200\pi\)
−0.667885 + 0.744265i \(0.732800\pi\)
\(284\) −6.29329 4.57234i −0.373438 0.271319i
\(285\) 46.8837 2.77715
\(286\) 0.718093 1.68333i 0.0424617 0.0995371i
\(287\) −33.0922 −1.95337
\(288\) −18.0749 13.1322i −1.06507 0.773821i
\(289\) −5.16360 + 15.8919i −0.303741 + 0.934818i
\(290\) 1.01595 + 3.12677i 0.0596586 + 0.183610i
\(291\) 6.33775 4.60464i 0.371525 0.269929i
\(292\) −5.59195 + 4.06279i −0.327244 + 0.237757i
\(293\) 1.19469 + 3.67689i 0.0697947 + 0.214806i 0.979870 0.199637i \(-0.0639764\pi\)
−0.910075 + 0.414443i \(0.863976\pi\)
\(294\) −3.41584 + 10.5129i −0.199216 + 0.613123i
\(295\) −7.68269 5.58180i −0.447303 0.324985i
\(296\) 13.1393 0.763709
\(297\) 10.5678 + 0.943656i 0.613208 + 0.0547565i
\(298\) −0.835630 −0.0484068
\(299\) −0.629584 0.457420i −0.0364098 0.0264533i
\(300\) 11.5538 35.5588i 0.667057 2.05299i
\(301\) −1.22033 3.75579i −0.0703386 0.216480i
\(302\) 6.40275 4.65187i 0.368437 0.267685i
\(303\) −14.1832 + 10.3047i −0.814803 + 0.591989i
\(304\) 3.36616 + 10.3600i 0.193062 + 0.594185i
\(305\) 4.48349 13.7988i 0.256724 0.790116i
\(306\) 1.00839 + 0.732636i 0.0576456 + 0.0418820i
\(307\) −17.1098 −0.976510 −0.488255 0.872701i \(-0.662366\pi\)
−0.488255 + 0.872701i \(0.662366\pi\)
\(308\) 21.3060 + 1.90252i 1.21402 + 0.108406i
\(309\) −21.0724 −1.19877
\(310\) 17.1231 + 12.4407i 0.972530 + 0.706584i
\(311\) −2.98467 + 9.18587i −0.169245 + 0.520883i −0.999324 0.0367631i \(-0.988295\pi\)
0.830079 + 0.557646i \(0.188295\pi\)
\(312\) −1.68999 5.20125i −0.0956768 0.294463i
\(313\) 7.48184 5.43588i 0.422899 0.307254i −0.355904 0.934522i \(-0.615827\pi\)
0.778803 + 0.627269i \(0.215827\pi\)
\(314\) −4.33407 + 3.14889i −0.244586 + 0.177702i
\(315\) −17.9211 55.1554i −1.00974 3.10766i
\(316\) −4.61323 + 14.1981i −0.259515 + 0.798704i
\(317\) 23.5905 + 17.1395i 1.32497 + 0.962649i 0.999856 + 0.0169751i \(0.00540360\pi\)
0.325117 + 0.945674i \(0.394596\pi\)
\(318\) 2.89733 0.162474
\(319\) 2.13238 4.99864i 0.119390 0.279870i
\(320\) 5.78670 0.323486
\(321\) −19.5436 14.1992i −1.09082 0.792524i
\(322\) −0.504756 + 1.55348i −0.0281290 + 0.0865720i
\(323\) −0.800374 2.46330i −0.0445340 0.137062i
\(324\) −5.48527 + 3.98528i −0.304737 + 0.221405i
\(325\) 6.65191 4.83289i 0.368982 0.268081i
\(326\) −0.345757 1.06413i −0.0191497 0.0589367i
\(327\) 0.554280 1.70590i 0.0306517 0.0943364i
\(328\) −14.3519 10.4273i −0.792451 0.575749i
\(329\) −3.31660 −0.182850
\(330\) 15.3146 9.16463i 0.843042 0.504496i
\(331\) −36.3427 −1.99758 −0.998788 0.0492197i \(-0.984327\pi\)
−0.998788 + 0.0492197i \(0.984327\pi\)
\(332\) 10.2573 + 7.45240i 0.562945 + 0.409003i
\(333\) −8.34847 + 25.6939i −0.457493 + 1.40802i
\(334\) 1.90998 + 5.87832i 0.104510 + 0.321648i
\(335\) −28.6401 + 20.8083i −1.56478 + 1.13688i
\(336\) 18.7009 13.5870i 1.02022 0.741233i
\(337\) −3.70801 11.4121i −0.201988 0.621656i −0.999824 0.0187804i \(-0.994022\pi\)
0.797835 0.602875i \(-0.205978\pi\)
\(338\) 0.170514 0.524787i 0.00927472 0.0285447i
\(339\) 8.70317 + 6.32322i 0.472691 + 0.343430i
\(340\) −3.32158 −0.180138
\(341\) −7.80900 34.1033i −0.422881 1.84680i
\(342\) 11.1225 0.601435
\(343\) −1.44473 1.04966i −0.0780082 0.0566762i
\(344\) 0.654189 2.01339i 0.0352715 0.108555i
\(345\) −2.34520 7.21777i −0.126261 0.388592i
\(346\) 7.86336 5.71306i 0.422737 0.307136i
\(347\) −13.3213 + 9.67846i −0.715123 + 0.519567i −0.884822 0.465929i \(-0.845720\pi\)
0.169700 + 0.985496i \(0.445720\pi\)
\(348\) −2.30248 7.08631i −0.123426 0.379866i
\(349\) −7.96502 + 24.5138i −0.426358 + 1.31219i 0.475331 + 0.879807i \(0.342328\pi\)
−0.901688 + 0.432387i \(0.857672\pi\)
\(350\) −13.9621 10.1440i −0.746303 0.542221i
\(351\) 3.19900 0.170750
\(352\) 13.3172 + 11.6184i 0.709809 + 0.619264i
\(353\) 9.52734 0.507089 0.253545 0.967324i \(-0.418404\pi\)
0.253545 + 0.967324i \(0.418404\pi\)
\(354\) −3.12670 2.27168i −0.166182 0.120739i
\(355\) 5.15526 15.8663i 0.273613 0.842094i
\(356\) −4.06244 12.5029i −0.215309 0.662653i
\(357\) −4.44654 + 3.23060i −0.235336 + 0.170981i
\(358\) −2.97717 + 2.16304i −0.157348 + 0.114320i
\(359\) −9.80713 30.1832i −0.517601 1.59301i −0.778500 0.627645i \(-0.784019\pi\)
0.260899 0.965366i \(-0.415981\pi\)
\(360\) 9.60706 29.5675i 0.506337 1.55834i
\(361\) −3.32689 2.41713i −0.175100 0.127217i
\(362\) 2.94067 0.154558
\(363\) −29.0346 5.22697i −1.52392 0.274345i
\(364\) 6.44956 0.338049
\(365\) −11.9925 8.71309i −0.627719 0.456064i
\(366\) 1.82469 5.61583i 0.0953783 0.293544i
\(367\) −0.794330 2.44470i −0.0414637 0.127612i 0.928182 0.372127i \(-0.121371\pi\)
−0.969646 + 0.244515i \(0.921371\pi\)
\(368\) 1.42654 1.03644i 0.0743636 0.0540283i
\(369\) 29.5094 21.4398i 1.53620 1.11611i
\(370\) 3.99514 + 12.2958i 0.207698 + 0.639227i
\(371\) −2.30134 + 7.08280i −0.119480 + 0.367721i
\(372\) −38.8068 28.1948i −2.01204 1.46183i
\(373\) 36.0244 1.86527 0.932637 0.360816i \(-0.117502\pi\)
0.932637 + 0.360816i \(0.117502\pi\)
\(374\) −0.742958 0.648185i −0.0384174 0.0335169i
\(375\) 31.4235 1.62270
\(376\) −1.43839 1.04505i −0.0741794 0.0538945i
\(377\) 0.506341 1.55836i 0.0260779 0.0802595i
\(378\) −2.07491 6.38592i −0.106722 0.328456i
\(379\) −4.14022 + 3.00805i −0.212669 + 0.154513i −0.689020 0.724742i \(-0.741959\pi\)
0.476352 + 0.879255i \(0.341959\pi\)
\(380\) −23.9792 + 17.4219i −1.23011 + 0.893725i
\(381\) 16.8384 + 51.8233i 0.862659 + 2.65499i
\(382\) −2.36402 + 7.27569i −0.120954 + 0.372257i
\(383\) 30.4920 + 22.1537i 1.55807 + 1.13200i 0.937572 + 0.347790i \(0.113068\pi\)
0.620494 + 0.784211i \(0.286932\pi\)
\(384\) 30.9371 1.57875
\(385\) 10.2395 + 44.7175i 0.521851 + 2.27902i
\(386\) 9.05226 0.460748
\(387\) 3.52151 + 2.55853i 0.179009 + 0.130057i
\(388\) −1.53043 + 4.71019i −0.0776960 + 0.239124i
\(389\) −1.44540 4.44849i −0.0732848 0.225547i 0.907704 0.419610i \(-0.137833\pi\)
−0.980989 + 0.194063i \(0.937833\pi\)
\(390\) 4.35347 3.16298i 0.220446 0.160164i
\(391\) −0.339190 + 0.246436i −0.0171536 + 0.0124628i
\(392\) −4.70679 14.4860i −0.237729 0.731654i
\(393\) −6.40699 + 19.7187i −0.323190 + 0.994677i
\(394\) 10.4457 + 7.58921i 0.526244 + 0.382339i
\(395\) −32.0163 −1.61091
\(396\) −20.2319 + 12.1072i −1.01669 + 0.608411i
\(397\) −0.0408623 −0.00205082 −0.00102541 0.999999i \(-0.500326\pi\)
−0.00102541 + 0.999999i \(0.500326\pi\)
\(398\) −7.26425 5.27779i −0.364124 0.264552i
\(399\) −15.1558 + 46.6447i −0.758739 + 2.33516i
\(400\) 5.75707 + 17.7184i 0.287854 + 0.885922i
\(401\) 2.31147 1.67938i 0.115429 0.0838644i −0.528573 0.848888i \(-0.677273\pi\)
0.644002 + 0.765024i \(0.277273\pi\)
\(402\) −11.6560 + 8.46856i −0.581347 + 0.422374i
\(403\) −3.25971 10.0324i −0.162378 0.499748i
\(404\) 3.42495 10.5409i 0.170397 0.524430i
\(405\) −11.7638 8.54687i −0.584546 0.424698i
\(406\) −3.43925 −0.170687
\(407\) 8.38542 19.6568i 0.415650 0.974350i
\(408\) −2.94639 −0.145868
\(409\) 8.01847 + 5.82576i 0.396488 + 0.288065i 0.768109 0.640319i \(-0.221198\pi\)
−0.371621 + 0.928384i \(0.621198\pi\)
\(410\) 5.39399 16.6010i 0.266390 0.819865i
\(411\) 10.4662 + 32.2116i 0.516259 + 1.58888i
\(412\) 10.7777 7.83046i 0.530979 0.385779i
\(413\) 8.03688 5.83913i 0.395469 0.287325i
\(414\) −0.556364 1.71231i −0.0273438 0.0841555i
\(415\) −8.40249 + 25.8602i −0.412462 + 1.26943i
\(416\) 4.31094 + 3.13208i 0.211361 + 0.153563i
\(417\) −4.11952 −0.201734
\(418\) −8.76334 0.782524i −0.428629 0.0382745i
\(419\) 21.0584 1.02877 0.514386 0.857559i \(-0.328020\pi\)
0.514386 + 0.857559i \(0.328020\pi\)
\(420\) 50.8849 + 36.9700i 2.48293 + 1.80395i
\(421\) 10.3346 31.8065i 0.503676 1.55016i −0.299308 0.954156i \(-0.596756\pi\)
0.802985 0.596000i \(-0.203244\pi\)
\(422\) −1.37183 4.22205i −0.0667795 0.205526i
\(423\) 2.95752 2.14876i 0.143800 0.104476i
\(424\) −3.22985 + 2.34663i −0.156856 + 0.113962i
\(425\) −1.36886 4.21293i −0.0663996 0.204357i
\(426\) 2.09809 6.45726i 0.101653 0.312855i
\(427\) 12.2791 + 8.92128i 0.594227 + 0.431731i
\(428\) 15.2722 0.738209
\(429\) −8.85973 0.791131i −0.427752 0.0381962i
\(430\) 2.08304 0.100453
\(431\) 8.00132 + 5.81330i 0.385410 + 0.280017i 0.763572 0.645723i \(-0.223444\pi\)
−0.378162 + 0.925739i \(0.623444\pi\)
\(432\) −2.23989 + 6.89368i −0.107767 + 0.331672i
\(433\) 0.481627 + 1.48230i 0.0231455 + 0.0712346i 0.961962 0.273183i \(-0.0880764\pi\)
−0.938817 + 0.344418i \(0.888076\pi\)
\(434\) −17.9126 + 13.0142i −0.859831 + 0.624704i
\(435\) 12.9276 9.39249i 0.619833 0.450335i
\(436\) 0.350416 + 1.07847i 0.0167819 + 0.0516493i
\(437\) −1.15611 + 3.55815i −0.0553043 + 0.170209i
\(438\) −4.88073 3.54606i −0.233210 0.169437i
\(439\) −3.20249 −0.152847 −0.0764233 0.997075i \(-0.524350\pi\)
−0.0764233 + 0.997075i \(0.524350\pi\)
\(440\) −9.64959 + 22.6202i −0.460026 + 1.07837i
\(441\) 31.3179 1.49133
\(442\) −0.240505 0.174737i −0.0114396 0.00831139i
\(443\) −8.75126 + 26.9336i −0.415785 + 1.27965i 0.495762 + 0.868458i \(0.334889\pi\)
−0.911547 + 0.411196i \(0.865111\pi\)
\(444\) −9.05432 27.8663i −0.429699 1.32248i
\(445\) 22.8092 16.5719i 1.08126 0.785582i
\(446\) 3.75202 2.72600i 0.177663 0.129080i
\(447\) 1.25507 + 3.86271i 0.0593628 + 0.182700i
\(448\) −1.87063 + 5.75720i −0.0883789 + 0.272002i
\(449\) −7.59543 5.51840i −0.358450 0.260430i 0.393955 0.919130i \(-0.371107\pi\)
−0.752406 + 0.658700i \(0.771107\pi\)
\(450\) 19.0226 0.896732
\(451\) −24.7587 + 14.8162i −1.16584 + 0.697667i
\(452\) −6.80103 −0.319894
\(453\) −31.1199 22.6099i −1.46214 1.06231i
\(454\) 4.22848 13.0139i 0.198452 0.610774i
\(455\) 4.27426 + 13.1548i 0.200380 + 0.616707i
\(456\) −21.2706 + 15.4540i −0.996089 + 0.723701i
\(457\) 1.75791 1.27720i 0.0822317 0.0597448i −0.545910 0.837844i \(-0.683816\pi\)
0.628142 + 0.778099i \(0.283816\pi\)
\(458\) −1.11638 3.43587i −0.0521651 0.160548i
\(459\) 0.532581 1.63912i 0.0248587 0.0765074i
\(460\) 3.88159 + 2.82014i 0.180980 + 0.131490i
\(461\) 25.9078 1.20664 0.603322 0.797497i \(-0.293843\pi\)
0.603322 + 0.797497i \(0.293843\pi\)
\(462\) 4.16726 + 18.1992i 0.193878 + 0.846701i
\(463\) −4.34094 −0.201741 −0.100870 0.994900i \(-0.532163\pi\)
−0.100870 + 0.994900i \(0.532163\pi\)
\(464\) 3.00365 + 2.18228i 0.139441 + 0.101310i
\(465\) 31.7893 97.8373i 1.47419 4.53709i
\(466\) −1.01801 3.13311i −0.0471584 0.145139i
\(467\) 16.3681 11.8921i 0.757427 0.550303i −0.140693 0.990053i \(-0.544933\pi\)
0.898120 + 0.439751i \(0.144933\pi\)
\(468\) −5.75129 + 4.17855i −0.265853 + 0.193154i
\(469\) −11.4439 35.2207i −0.528430 1.62634i
\(470\) 0.540602 1.66380i 0.0249361 0.0767455i
\(471\) 21.0653 + 15.3049i 0.970639 + 0.705211i
\(472\) 5.32545 0.245124
\(473\) −2.59458 2.26361i −0.119299 0.104081i
\(474\) −13.0300 −0.598488
\(475\) −31.9792 23.2342i −1.46731 1.06606i
\(476\) 1.07375 3.30465i 0.0492151 0.151468i
\(477\) −2.53664 7.80696i −0.116145 0.357456i
\(478\) −9.03105 + 6.56144i −0.413071 + 0.300114i
\(479\) −16.7939 + 12.2015i −0.767332 + 0.557500i −0.901151 0.433506i \(-0.857276\pi\)
0.133818 + 0.991006i \(0.457276\pi\)
\(480\) 16.0582 + 49.4221i 0.732954 + 2.25580i
\(481\) 1.99115 6.12812i 0.0907885 0.279418i
\(482\) 8.11758 + 5.89776i 0.369745 + 0.268636i
\(483\) 7.93910 0.361241
\(484\) 16.7924 8.11581i 0.763291 0.368900i
\(485\) −10.6214 −0.482291
\(486\) −9.07182 6.59106i −0.411506 0.298977i
\(487\) −1.11657 + 3.43646i −0.0505968 + 0.155721i −0.973162 0.230119i \(-0.926088\pi\)
0.922566 + 0.385840i \(0.126088\pi\)
\(488\) 2.51430 + 7.73822i 0.113817 + 0.350293i
\(489\) −4.39965 + 3.19653i −0.198959 + 0.144552i
\(490\) 12.1248 8.80921i 0.547744 0.397960i
\(491\) −3.46536 10.6653i −0.156390 0.481318i 0.841909 0.539619i \(-0.181432\pi\)
−0.998299 + 0.0583011i \(0.981432\pi\)
\(492\) −12.2246 + 37.6234i −0.551127 + 1.69619i
\(493\) −0.714180 0.518882i −0.0321651 0.0233693i
\(494\) −2.65276 −0.119353
\(495\) −38.1025 33.2421i −1.71258 1.49412i
\(496\) 23.9016 1.07322
\(497\) 14.1189 + 10.2580i 0.633318 + 0.460133i
\(498\) −3.41965 + 10.5246i −0.153238 + 0.471618i
\(499\) −11.7773 36.2469i −0.527226 1.62263i −0.759872 0.650073i \(-0.774738\pi\)
0.232646 0.972562i \(-0.425262\pi\)
\(500\) −16.0719 + 11.6769i −0.718758 + 0.522208i
\(501\) 24.3039 17.6579i 1.08582 0.788895i
\(502\) −4.77254 14.6884i −0.213009 0.655573i
\(503\) −0.0248588 + 0.0765076i −0.00110840 + 0.00341131i −0.951609 0.307311i \(-0.900571\pi\)
0.950501 + 0.310722i \(0.100571\pi\)
\(504\) 26.3112 + 19.1162i 1.17199 + 0.851503i
\(505\) 23.7695 1.05773
\(506\) 0.317886 + 1.38826i 0.0141318 + 0.0617159i
\(507\) −2.68194 −0.119109
\(508\) −27.8697 20.2485i −1.23652 0.898382i
\(509\) −3.91614 + 12.0526i −0.173580 + 0.534224i −0.999566 0.0294670i \(-0.990619\pi\)
0.825986 + 0.563691i \(0.190619\pi\)
\(510\) −0.895879 2.75723i −0.0396702 0.122092i
\(511\) 12.5454 9.11479i 0.554977 0.403215i
\(512\) −17.2440 + 12.5285i −0.762083 + 0.553685i
\(513\) −4.75245 14.6265i −0.209826 0.645778i
\(514\) −3.88396 + 11.9536i −0.171314 + 0.527251i
\(515\) 23.1140 + 16.7933i 1.01852 + 0.740000i
\(516\) −4.72086 −0.207824
\(517\) −2.48139 + 1.48492i −0.109131 + 0.0653068i
\(518\) −13.5246 −0.594236
\(519\) −38.2191 27.7678i −1.67763 1.21887i
\(520\) −2.29133 + 7.05198i −0.100481 + 0.309250i
\(521\) 6.86751 + 21.1360i 0.300871 + 0.925986i 0.981186 + 0.193066i \(0.0618431\pi\)
−0.680315 + 0.732920i \(0.738157\pi\)
\(522\) 3.06690 2.22823i 0.134234 0.0975270i
\(523\) −23.2937 + 16.9239i −1.01856 + 0.740029i −0.965988 0.258588i \(-0.916743\pi\)
−0.0525746 + 0.998617i \(0.516743\pi\)
\(524\) −4.05051 12.4662i −0.176947 0.544587i
\(525\) −25.9207 + 79.7756i −1.13127 + 3.48169i
\(526\) −7.80761 5.67256i −0.340428 0.247335i
\(527\) −5.68311 −0.247560
\(528\) 7.90830 18.5383i 0.344165 0.806777i
\(529\) −22.3944 −0.973669
\(530\) −3.17804 2.30898i −0.138045 0.100296i
\(531\) −3.38368 + 10.4139i −0.146839 + 0.451925i
\(532\) −9.58150 29.4888i −0.415411 1.27850i
\(533\) −7.03812 + 5.11349i −0.304855 + 0.221490i
\(534\) 9.28291 6.74443i 0.401711 0.291860i
\(535\) 10.1212 + 31.1498i 0.437578 + 1.34673i
\(536\) 6.13480 18.8810i 0.264983 0.815534i
\(537\) 14.4702 + 10.5132i 0.624437 + 0.453680i
\(538\) 13.1408 0.566540
\(539\) −24.6752 2.20338i −1.06284 0.0949063i
\(540\) −19.7229 −0.848737
\(541\) 20.0344 + 14.5559i 0.861347 + 0.625805i 0.928251 0.371954i \(-0.121312\pi\)
−0.0669041 + 0.997759i \(0.521312\pi\)
\(542\) −4.04270 + 12.4421i −0.173649 + 0.534436i
\(543\) −4.41673 13.5933i −0.189540 0.583344i
\(544\) 2.32253 1.68742i 0.0995776 0.0723474i
\(545\) −1.96747 + 1.42945i −0.0842771 + 0.0612309i
\(546\) 1.73954 + 5.35375i 0.0744454 + 0.229119i
\(547\) 3.90127 12.0069i 0.166806 0.513376i −0.832359 0.554237i \(-0.813010\pi\)
0.999165 + 0.0408609i \(0.0130100\pi\)
\(548\) −17.3228 12.5858i −0.739994 0.537637i
\(549\) −16.7296 −0.714002
\(550\) −14.9878 1.33834i −0.639081 0.0570669i
\(551\) −7.87739 −0.335588
\(552\) 3.44315 + 2.50159i 0.146550 + 0.106475i
\(553\) 10.3497 31.8531i 0.440114 1.35453i
\(554\) 0.983571 + 3.02712i 0.0417879 + 0.128610i
\(555\) 50.8369 36.9352i 2.15791 1.56781i
\(556\) 2.10697 1.53081i 0.0893556 0.0649206i
\(557\) 13.3327 + 41.0339i 0.564926 + 1.73866i 0.668171 + 0.744008i \(0.267077\pi\)
−0.103245 + 0.994656i \(0.532923\pi\)
\(558\) 7.54154 23.2105i 0.319259 0.982577i
\(559\) −0.839897 0.610221i −0.0355239 0.0258096i
\(560\) −31.3407 −1.32439
\(561\) −1.88036 + 4.40787i −0.0793890 + 0.186101i
\(562\) 2.31091 0.0974797
\(563\) 9.63844 + 7.00273i 0.406212 + 0.295130i 0.772066 0.635542i \(-0.219223\pi\)
−0.365855 + 0.930672i \(0.619223\pi\)
\(564\) −1.22518 + 3.77073i −0.0515896 + 0.158776i
\(565\) −4.50719 13.8717i −0.189619 0.583586i
\(566\) 13.7313 9.97636i 0.577169 0.419338i
\(567\) 12.3061 8.94090i 0.516808 0.375483i
\(568\) 2.89102 + 8.89766i 0.121305 + 0.373337i
\(569\) 9.48744 29.1993i 0.397734 1.22410i −0.529078 0.848573i \(-0.677462\pi\)
0.926812 0.375526i \(-0.122538\pi\)
\(570\) −20.9294 15.2061i −0.876636 0.636913i
\(571\) −25.3360 −1.06028 −0.530138 0.847911i \(-0.677860\pi\)
−0.530138 + 0.847911i \(0.677860\pi\)
\(572\) 4.82539 2.88763i 0.201760 0.120738i
\(573\) 37.1826 1.55333
\(574\) 14.7727 + 10.7330i 0.616600 + 0.447986i
\(575\) −1.97728 + 6.08543i −0.0824581 + 0.253780i
\(576\) −2.06189 6.34583i −0.0859119 0.264410i
\(577\) 7.38018 5.36201i 0.307241 0.223224i −0.423471 0.905910i \(-0.639188\pi\)
0.730712 + 0.682686i \(0.239188\pi\)
\(578\) 7.45941 5.41958i 0.310270 0.225425i
\(579\) −13.5960 41.8442i −0.565030 1.73899i
\(580\) −3.12176 + 9.60778i −0.129624 + 0.398941i
\(581\) −23.0122 16.7193i −0.954705 0.693634i
\(582\) −4.32269 −0.179181
\(583\) 1.44934 + 6.32953i 0.0600256 + 0.262142i
\(584\) 8.31294 0.343992
\(585\) −12.3343 8.96137i −0.509959 0.370507i
\(586\) 0.659224 2.02888i 0.0272323 0.0838124i
\(587\) −4.82392 14.8465i −0.199104 0.612780i −0.999904 0.0138479i \(-0.995592\pi\)
0.800800 0.598932i \(-0.204408\pi\)
\(588\) −27.4789 + 19.9646i −1.13321 + 0.823327i
\(589\) −41.0276 + 29.8083i −1.69051 + 1.22823i
\(590\) 1.61925 + 4.98355i 0.0666636 + 0.205169i
\(591\) 19.3924 59.6838i 0.797698 2.45506i
\(592\) 11.8116 + 8.58164i 0.485454 + 0.352703i
\(593\) −13.7793 −0.565847 −0.282924 0.959142i \(-0.591304\pi\)
−0.282924 + 0.959142i \(0.591304\pi\)
\(594\) −4.41153 3.84879i −0.181007 0.157918i
\(595\) 7.45191 0.305498
\(596\) −2.07730 1.50925i −0.0850894 0.0618211i
\(597\) −13.4861 + 41.5061i −0.551951 + 1.69873i
\(598\) 0.132695 + 0.408394i 0.00542631 + 0.0167005i
\(599\) −14.6828 + 10.6677i −0.599924 + 0.435870i −0.845852 0.533418i \(-0.820907\pi\)
0.245928 + 0.969288i \(0.420907\pi\)
\(600\) −36.3788 + 26.4307i −1.48516 + 1.07903i
\(601\) −7.75926 23.8806i −0.316507 0.974108i −0.975130 0.221635i \(-0.928861\pi\)
0.658623 0.752473i \(-0.271139\pi\)
\(602\) −0.673370 + 2.07242i −0.0274445 + 0.0844655i
\(603\) 33.0238 + 23.9932i 1.34483 + 0.977077i
\(604\) 24.3184 0.989504
\(605\) 27.6820 + 28.8720i 1.12543 + 1.17381i
\(606\) 9.67371 0.392968
\(607\) −5.35137 3.88800i −0.217205 0.157809i 0.473862 0.880599i \(-0.342859\pi\)
−0.691068 + 0.722790i \(0.742859\pi\)
\(608\) 7.91622 24.3636i 0.321045 0.988075i
\(609\) 5.16557 + 15.8980i 0.209320 + 0.644219i
\(610\) −6.47692 + 4.70576i −0.262243 + 0.190531i
\(611\) −0.705382 + 0.512490i −0.0285367 + 0.0207331i
\(612\) 1.18353 + 3.64253i 0.0478413 + 0.147240i
\(613\) −6.81385 + 20.9709i −0.275209 + 0.847005i 0.713955 + 0.700191i \(0.246902\pi\)
−0.989164 + 0.146814i \(0.953098\pi\)
\(614\) 7.63801 + 5.54934i 0.308245 + 0.223953i
\(615\) −84.8398 −3.42107
\(616\) −19.3855 16.9127i −0.781065 0.681431i
\(617\) 12.3573 0.497484 0.248742 0.968570i \(-0.419983\pi\)
0.248742 + 0.968570i \(0.419983\pi\)
\(618\) 9.40693 + 6.83453i 0.378402 + 0.274925i
\(619\) 12.6875 39.0480i 0.509952 1.56947i −0.282331 0.959317i \(-0.591108\pi\)
0.792283 0.610154i \(-0.208892\pi\)
\(620\) 20.0972 + 61.8528i 0.807123 + 2.48407i
\(621\) −2.01404 + 1.46328i −0.0808206 + 0.0587196i
\(622\) 4.31170 3.13263i 0.172883 0.125607i
\(623\) 9.11401 + 28.0500i 0.365145 + 1.12380i
\(624\) 1.87785 5.77944i 0.0751743 0.231363i
\(625\) −1.20843 0.877979i −0.0483374 0.0351192i
\(626\) −5.10302 −0.203958
\(627\) 9.54484 + 41.6840i 0.381184 + 1.66470i
\(628\) −16.4614 −0.656880
\(629\) −2.80846 2.04046i −0.111981 0.0813586i
\(630\) −9.88874 + 30.4344i −0.393977 + 1.21254i
\(631\) 10.7360 + 33.0419i 0.427393 + 1.31538i 0.900685 + 0.434474i \(0.143066\pi\)
−0.473292 + 0.880906i \(0.656934\pi\)
\(632\) 14.5254 10.5534i 0.577791 0.419790i
\(633\) −17.4561 + 12.6826i −0.693817 + 0.504087i
\(634\) −4.97208 15.3025i −0.197467 0.607739i
\(635\) 22.8299 70.2633i 0.905978 2.78831i
\(636\) 7.20249 + 5.23291i 0.285597 + 0.207499i
\(637\) −7.46947 −0.295951
\(638\) −2.57316 + 1.53984i −0.101872 + 0.0609628i
\(639\) −19.2362 −0.760973
\(640\) −33.9344 24.6548i −1.34138 0.974567i
\(641\) 5.78848 17.8151i 0.228631 0.703655i −0.769271 0.638922i \(-0.779381\pi\)
0.997903 0.0647326i \(-0.0206195\pi\)
\(642\) 4.11913 + 12.6774i 0.162569 + 0.500336i
\(643\) 17.1099 12.4311i 0.674750 0.490234i −0.196862 0.980431i \(-0.563075\pi\)
0.871612 + 0.490197i \(0.163075\pi\)
\(644\) −4.06054 + 2.95016i −0.160008 + 0.116252i
\(645\) −3.12861 9.62887i −0.123189 0.379137i
\(646\) −0.441641 + 1.35923i −0.0173761 + 0.0534783i
\(647\) −14.7003 10.6804i −0.577928 0.419889i 0.260048 0.965596i \(-0.416261\pi\)
−0.837977 + 0.545706i \(0.816261\pi\)
\(648\) 8.15435 0.320333
\(649\) 3.39866 7.96700i 0.133409 0.312732i
\(650\) −4.53697 −0.177954
\(651\) 87.0622 + 63.2544i 3.41224 + 2.47914i
\(652\) 1.06242 3.26980i 0.0416077 0.128055i
\(653\) −1.68209 5.17695i −0.0658254 0.202590i 0.912734 0.408554i \(-0.133967\pi\)
−0.978559 + 0.205964i \(0.933967\pi\)
\(654\) −0.800721 + 0.581758i −0.0313107 + 0.0227485i
\(655\) 22.7422 16.5232i 0.888612 0.645614i
\(656\) −6.09133 18.7472i −0.237826 0.731954i
\(657\) −5.28187 + 16.2559i −0.206065 + 0.634204i
\(658\) 1.48056 + 1.07569i 0.0577184 + 0.0419349i
\(659\) 3.93194 0.153166 0.0765832 0.997063i \(-0.475599\pi\)
0.0765832 + 0.997063i \(0.475599\pi\)
\(660\) 54.6231 + 4.87758i 2.12620 + 0.189860i
\(661\) 38.3348 1.49105 0.745526 0.666477i \(-0.232198\pi\)
0.745526 + 0.666477i \(0.232198\pi\)
\(662\) 16.2238 + 11.7873i 0.630555 + 0.458125i
\(663\) −0.446499 + 1.37418i −0.0173406 + 0.0533688i
\(664\) −4.71204 14.5022i −0.182862 0.562793i
\(665\) 53.7969 39.0857i 2.08615 1.51568i
\(666\) 12.0603 8.76234i 0.467328 0.339534i
\(667\) 0.394039 + 1.21273i 0.0152573 + 0.0469570i
\(668\) −5.86890 + 18.0626i −0.227074 + 0.698863i
\(669\) −18.2363 13.2495i −0.705057 0.512254i
\(670\) 19.5341 0.754670
\(671\) 13.1812 + 1.17701i 0.508853 + 0.0454382i
\(672\) −54.3612 −2.09703
\(673\) 23.0134 + 16.7202i 0.887101 + 0.644516i 0.935120 0.354330i \(-0.115291\pi\)
−0.0480197 + 0.998846i \(0.515291\pi\)
\(674\) −2.04606 + 6.29712i −0.0788112 + 0.242556i
\(675\) −8.12803 25.0155i −0.312848 0.962847i
\(676\) 1.37171 0.996604i 0.0527580 0.0383309i
\(677\) 12.6075 9.15990i 0.484547 0.352044i −0.318537 0.947911i \(-0.603191\pi\)
0.803083 + 0.595867i \(0.203191\pi\)
\(678\) −1.83434 5.64551i −0.0704473 0.216814i
\(679\) 3.43350 10.5672i 0.131766 0.405533i
\(680\) 3.23185 + 2.34808i 0.123936 + 0.0900447i
\(681\) −66.5080 −2.54859
\(682\) −7.57491 + 17.7568i −0.290058 + 0.679944i
\(683\) −34.3475 −1.31427 −0.657135 0.753773i \(-0.728232\pi\)
−0.657135 + 0.753773i \(0.728232\pi\)
\(684\) 27.6494 + 20.0885i 1.05720 + 0.768103i
\(685\) 14.1903 43.6733i 0.542184 1.66867i
\(686\) 0.304501 + 0.937158i 0.0116259 + 0.0357808i
\(687\) −14.2056 + 10.3210i −0.541978 + 0.393770i
\(688\) 1.90308 1.38267i 0.0725542 0.0527137i
\(689\) 0.604999 + 1.86200i 0.0230486 + 0.0709364i
\(690\) −1.29407 + 3.98272i −0.0492642 + 0.151620i
\(691\) −19.4465 14.1287i −0.739779 0.537481i 0.152863 0.988247i \(-0.451151\pi\)
−0.892642 + 0.450767i \(0.851151\pi\)
\(692\) 29.8660 1.13534
\(693\) 45.3898 27.1623i 1.72422 1.03181i
\(694\) 9.08583 0.344893
\(695\) 4.51864 + 3.28298i 0.171402 + 0.124531i
\(696\) −2.76914 + 8.52254i −0.104964 + 0.323046i
\(697\) 1.44834 + 4.45753i 0.0548598 + 0.168841i
\(698\) 11.5064 8.35988i 0.435523 0.316426i
\(699\) −12.9539 + 9.41153i −0.489960 + 0.355977i
\(700\) −16.3871 50.4342i −0.619373 1.90623i
\(701\) 8.49859 26.1560i 0.320987 0.987898i −0.652232 0.758019i \(-0.726167\pi\)
0.973219 0.229878i \(-0.0738328\pi\)
\(702\) −1.42807 1.03755i −0.0538989 0.0391599i
\(703\) −30.9772 −1.16833
\(704\) 1.17809 + 5.14491i 0.0444008 + 0.193906i
\(705\) −8.50291 −0.320238
\(706\) −4.25311 3.09006i −0.160068 0.116296i
\(707\) −7.68380 + 23.6483i −0.288979 + 0.889386i
\(708\) −3.66977 11.2944i −0.137918 0.424469i
\(709\) 14.5489 10.5704i 0.546394 0.396978i −0.280060 0.959982i \(-0.590355\pi\)
0.826454 + 0.563004i \(0.190355\pi\)
\(710\) −7.44737 + 5.41083i −0.279495 + 0.203065i
\(711\) 11.4079 + 35.1098i 0.427829 + 1.31672i
\(712\) −4.88581 + 15.0370i −0.183103 + 0.563534i
\(713\) 6.64127 + 4.82516i 0.248717 + 0.180704i
\(714\) 3.03278 0.113499
\(715\) 9.08762 + 7.92839i 0.339858 + 0.296505i
\(716\) −11.3077 −0.422587
\(717\) 43.8945 + 31.8912i 1.63927 + 1.19100i
\(718\) −5.41151 + 16.6549i −0.201956 + 0.621556i
\(719\) 7.53309 + 23.1845i 0.280937 + 0.864635i 0.987587 + 0.157072i \(0.0502055\pi\)
−0.706650 + 0.707563i \(0.749795\pi\)
\(720\) 27.9476 20.3051i 1.04154 0.756726i
\(721\) −24.1796 + 17.5675i −0.900494 + 0.654247i
\(722\) 0.701198 + 2.15806i 0.0260959 + 0.0803149i
\(723\) 15.0703 46.3817i 0.560472 1.72496i
\(724\) 7.31023 + 5.31119i 0.271682 + 0.197389i
\(725\) −13.4725 −0.500358
\(726\) 11.2660 + 11.7503i 0.418122 + 0.436096i
\(727\) −7.34590 −0.272444 −0.136222 0.990678i \(-0.543496\pi\)
−0.136222 + 0.990678i \(0.543496\pi\)
\(728\) −6.27533 4.55930i −0.232579 0.168979i
\(729\) −13.1348 + 40.4246i −0.486472 + 1.49721i
\(730\) 2.52763 + 7.77924i 0.0935517 + 0.287922i
\(731\) −0.452496 + 0.328758i −0.0167362 + 0.0121596i
\(732\) 14.6789 10.6648i 0.542546 0.394183i
\(733\) 2.35444 + 7.24623i 0.0869633 + 0.267646i 0.985076 0.172120i \(-0.0550616\pi\)
−0.898113 + 0.439765i \(0.855062\pi\)
\(734\) −0.438307 + 1.34897i −0.0161782 + 0.0497914i
\(735\) −58.9316 42.8163i −2.17372 1.57930i
\(736\) −4.14677 −0.152852
\(737\) −24.3312 21.2275i −0.896252 0.781925i
\(738\) −20.1270 −0.740885
\(739\) −20.6501 15.0032i −0.759626 0.551900i 0.139170 0.990269i \(-0.455557\pi\)
−0.898796 + 0.438368i \(0.855557\pi\)
\(740\) −12.2761 + 37.7818i −0.451277 + 1.38889i
\(741\) 3.98430 + 12.2624i 0.146367 + 0.450471i
\(742\) 3.32455 2.41543i 0.122048 0.0886731i
\(743\) 42.0759 30.5699i 1.54362 1.12150i 0.595598 0.803282i \(-0.296915\pi\)
0.948017 0.318220i \(-0.103085\pi\)
\(744\) 17.8271 + 54.8662i 0.653574 + 2.01149i
\(745\) 1.70166 5.23716i 0.0623438 0.191875i
\(746\) −16.0817 11.6840i −0.588792 0.427783i
\(747\) 31.3528 1.14714
\(748\) −0.676225 2.95320i −0.0247253 0.107980i
\(749\) −34.2629 −1.25194
\(750\) −14.0278 10.1918i −0.512223 0.372152i
\(751\) −13.2363 + 40.7370i −0.482998 + 1.48652i 0.351861 + 0.936052i \(0.385549\pi\)
−0.834859 + 0.550464i \(0.814451\pi\)
\(752\) −0.610491 1.87890i −0.0222623 0.0685164i
\(753\) −60.7291 + 44.1222i −2.21309 + 1.60790i
\(754\) −0.731468 + 0.531443i −0.0266385 + 0.0193540i
\(755\) 16.1163 + 49.6010i 0.586534 + 1.80517i
\(756\) 6.37568 19.6223i 0.231881 0.713657i
\(757\) 1.47080 + 1.06860i 0.0534570 + 0.0388388i 0.614193 0.789156i \(-0.289482\pi\)
−0.560736 + 0.827995i \(0.689482\pi\)
\(758\) 2.82386 0.102567
\(759\) 5.93983 3.55453i 0.215602 0.129021i
\(760\) 35.6473 1.29306
\(761\) −14.7867 10.7432i −0.536017 0.389439i 0.286587 0.958054i \(-0.407479\pi\)
−0.822604 + 0.568615i \(0.807479\pi\)
\(762\) 9.29134 28.5958i 0.336590 1.03592i
\(763\) −0.786152 2.41953i −0.0284606 0.0875928i
\(764\) −19.0175 + 13.8170i −0.688028 + 0.499881i
\(765\) −6.64511 + 4.82796i −0.240255 + 0.174555i
\(766\) −6.42668 19.7793i −0.232205 0.714655i
\(767\) 0.807023 2.48376i 0.0291399 0.0896834i
\(768\) −6.90483 5.01665i −0.249157 0.181023i
\(769\) 39.1521 1.41186 0.705930 0.708282i \(-0.250529\pi\)
0.705930 + 0.708282i \(0.250529\pi\)
\(770\) 9.93251 23.2834i 0.357943 0.839075i
\(771\) 61.0893 2.20008
\(772\) 22.5031 + 16.3494i 0.809903 + 0.588429i
\(773\) −14.2613 + 43.8919i −0.512944 + 1.57868i 0.274047 + 0.961716i \(0.411638\pi\)
−0.786991 + 0.616964i \(0.788362\pi\)
\(774\) −0.742217 2.28431i −0.0266784 0.0821078i
\(775\) −70.1687 + 50.9805i −2.52053 + 1.83128i
\(776\) 4.81880 3.50106i 0.172985 0.125681i
\(777\) 20.3132 + 62.5176i 0.728732 + 2.24281i
\(778\) −0.797564 + 2.45465i −0.0285940 + 0.0880034i
\(779\) 33.8359 + 24.5832i 1.21230 + 0.880785i
\(780\) 16.5350 0.592049
\(781\) 15.1561 + 1.35337i 0.542329 + 0.0484274i
\(782\) 0.231346 0.00827292
\(783\) −4.24065 3.08101i −0.151549 0.110106i
\(784\) 5.23001 16.0963i 0.186786 0.574868i
\(785\) −10.9093 33.5753i −0.389369 1.19835i
\(786\) 9.25564 6.72462i 0.330138 0.239859i
\(787\) −36.3902 + 26.4390i −1.29717 + 0.942450i −0.999924 0.0123504i \(-0.996069\pi\)
−0.297247 + 0.954800i \(0.596069\pi\)
\(788\) 12.2599 + 37.7321i 0.436741 + 1.34415i
\(789\) −14.4949 + 44.6107i −0.516031 + 1.58818i
\(790\) 14.2924 + 10.3840i 0.508501 + 0.369448i
\(791\) 15.2580 0.542512
\(792\) 28.2441 + 2.52206i 1.00361 + 0.0896176i
\(793\) 3.99009 0.141692
\(794\) 0.0182414 + 0.0132531i 0.000647362 + 0.000470336i
\(795\) −5.90005 + 18.1585i −0.209253 + 0.644015i
\(796\) −8.52595 26.2402i −0.302194 0.930058i
\(797\) −8.43809 + 6.13063i −0.298892 + 0.217158i −0.727116 0.686515i \(-0.759140\pi\)
0.428223 + 0.903673i \(0.359140\pi\)
\(798\) 21.8943 15.9071i 0.775049 0.563106i
\(799\) 0.145157 + 0.446747i 0.00513529 + 0.0158048i
\(800\) 13.5390 41.6686i 0.478675 1.47321i
\(801\) −26.3004 19.1084i −0.929279 0.675160i
\(802\) −1.57655 −0.0556699
\(803\) 5.30525 12.4363i 0.187218 0.438869i
\(804\) −44.2709 −1.56131
\(805\) −8.70827 6.32693i −0.306926 0.222995i
\(806\) −1.79869 + 5.53580i −0.0633562 + 0.194990i
\(807\) −19.7368 60.7435i −0.694767 2.13827i
\(808\) −10.7840 + 7.83500i −0.379378 + 0.275634i
\(809\) −12.0771 + 8.77452i −0.424608 + 0.308496i −0.779489 0.626416i \(-0.784521\pi\)
0.354881 + 0.934911i \(0.384521\pi\)
\(810\) 2.47941 + 7.63083i 0.0871175 + 0.268120i
\(811\) 14.0585 43.2677i 0.493661 1.51933i −0.325371 0.945586i \(-0.605489\pi\)
0.819032 0.573747i \(-0.194511\pi\)
\(812\) −8.54966 6.21169i −0.300034 0.217988i
\(813\) 63.5859 2.23005
\(814\) −10.1187 + 6.05529i −0.354662 + 0.212238i
\(815\) 7.37333 0.258277
\(816\) −2.64866 1.92436i −0.0927217 0.0673662i
\(817\) −1.54231 + 4.74675i −0.0539586 + 0.166068i
\(818\) −1.69002 5.20136i −0.0590903 0.181861i
\(819\) 12.9029 9.37451i 0.450864 0.327572i
\(820\) 43.3923 31.5263i 1.51532 1.10095i
\(821\) −13.2173 40.6787i −0.461287 1.41970i −0.863592 0.504191i \(-0.831791\pi\)
0.402305 0.915506i \(-0.368209\pi\)
\(822\) 5.77518 17.7742i 0.201432 0.619945i
\(823\) −28.3417 20.5914i −0.987929 0.717772i −0.0284623 0.999595i \(-0.509061\pi\)
−0.959467 + 0.281823i \(0.909061\pi\)
\(824\) −16.0220 −0.558154
\(825\) 16.3244 + 71.2913i 0.568341 + 2.48205i
\(826\) −5.48159 −0.190729
\(827\) −16.9061 12.2830i −0.587883 0.427122i 0.253674 0.967290i \(-0.418361\pi\)
−0.841558 + 0.540167i \(0.818361\pi\)
\(828\) 1.70957 5.26150i 0.0594115 0.182850i
\(829\) 6.54346 + 20.1387i 0.227264 + 0.699446i 0.998054 + 0.0623567i \(0.0198616\pi\)
−0.770790 + 0.637089i \(0.780138\pi\)
\(830\) 12.1384 8.81903i 0.421329 0.306113i
\(831\) 12.5156 9.09315i 0.434163 0.315438i
\(832\) 0.491769 + 1.51351i 0.0170490 + 0.0524715i
\(833\) −1.24354 + 3.82723i −0.0430862 + 0.132606i
\(834\) 1.83900 + 1.33611i 0.0636792 + 0.0462657i
\(835\) −40.7307 −1.40955
\(836\) −20.3715 17.7729i −0.704564 0.614689i
\(837\) −33.7451 −1.16640
\(838\) −9.40071 6.83001i −0.324742 0.235939i
\(839\) −8.47164 + 26.0730i −0.292473 + 0.900141i 0.691585 + 0.722295i \(0.256913\pi\)
−0.984058 + 0.177846i \(0.943087\pi\)
\(840\) −23.3756 71.9426i −0.806534 2.48226i
\(841\) 21.2894 15.4677i 0.734117 0.533367i
\(842\) −14.9295 + 10.8469i −0.514504 + 0.373809i
\(843\) −3.47086 10.6822i −0.119543 0.367914i
\(844\) 4.21528 12.9733i 0.145096 0.446559i
\(845\) 2.94178 + 2.13733i 0.101200 + 0.0735262i
\(846\) −2.01719 −0.0693524
\(847\) −37.6734 + 18.2077i −1.29447 + 0.625622i
\(848\) −4.43612 −0.152337
\(849\) −66.7395 48.4891i −2.29049 1.66414i
\(850\) −0.755330 + 2.32467i −0.0259076 + 0.0797355i
\(851\) 1.54953 + 4.76896i 0.0531171 + 0.163478i
\(852\) 16.8782 12.2627i 0.578238 0.420115i
\(853\) 12.3449 8.96911i 0.422682 0.307096i −0.356034 0.934473i \(-0.615871\pi\)
0.778716 + 0.627377i \(0.215871\pi\)
\(854\) −2.58802 7.96511i −0.0885602 0.272560i
\(855\) −22.6495 + 69.7081i −0.774598 + 2.38397i
\(856\) −14.8596 10.7962i −0.507892 0.369005i
\(857\) −28.5193 −0.974201 −0.487100 0.873346i \(-0.661945\pi\)
−0.487100 + 0.873346i \(0.661945\pi\)
\(858\) 3.69849 + 3.22670i 0.126264 + 0.110158i
\(859\) 15.0825 0.514609 0.257305 0.966330i \(-0.417166\pi\)
0.257305 + 0.966330i \(0.417166\pi\)
\(860\) 5.17824 + 3.76221i 0.176576 + 0.128290i
\(861\) 27.4256 84.4073i 0.934662 2.87659i
\(862\) −1.68641 5.19024i −0.0574394 0.176780i
\(863\) 20.8735 15.1655i 0.710541 0.516238i −0.172807 0.984956i \(-0.555284\pi\)
0.883348 + 0.468718i \(0.155284\pi\)
\(864\) 13.7907 10.0195i 0.469169 0.340871i
\(865\) 19.7928 + 60.9161i 0.672976 + 2.07121i
\(866\) 0.265759 0.817921i 0.00903085 0.0277941i
\(867\) −36.2557 26.3413i −1.23131 0.894598i
\(868\) −68.0342 −2.30923
\(869\) −6.51805 28.4655i −0.221110 0.965625i
\(870\) −8.81736 −0.298937
\(871\) −7.87631 5.72248i −0.266879 0.193899i
\(872\) 0.421437 1.29705i 0.0142717 0.0439237i
\(873\) 3.78455 + 11.6476i 0.128088 + 0.394213i
\(874\) 1.67014 1.21342i 0.0564932 0.0410447i
\(875\) 36.0570 26.1970i 1.21895 0.885619i
\(876\) −5.72844 17.6303i −0.193546 0.595674i
\(877\) 5.55934 17.1099i 0.187726 0.577760i −0.812259 0.583297i \(-0.801762\pi\)
0.999985 + 0.00553674i \(0.00176241\pi\)
\(878\) 1.42963 + 1.03868i 0.0482476 + 0.0350539i
\(879\) −10.3687 −0.349726
\(880\) −23.4483 + 14.0320i −0.790442 + 0.473019i
\(881\) 23.6578 0.797052 0.398526 0.917157i \(-0.369522\pi\)
0.398526 + 0.917157i \(0.369522\pi\)
\(882\) −13.9807 10.1575i −0.470753 0.342022i
\(883\) 10.2829 31.6476i 0.346048 1.06503i −0.614973 0.788548i \(-0.710833\pi\)
0.961021 0.276477i \(-0.0891670\pi\)
\(884\) −0.282277 0.868759i −0.00949400 0.0292195i
\(885\) 20.6045 14.9700i 0.692613 0.503213i
\(886\) 12.6422 9.18509i 0.424723 0.308579i
\(887\) 14.1290 + 43.4845i 0.474405 + 1.46007i 0.846759 + 0.531977i \(0.178551\pi\)
−0.372354 + 0.928091i \(0.621449\pi\)
\(888\) −10.8894 + 33.5142i −0.365425 + 1.12466i
\(889\) 62.5251 + 45.4271i 2.09702 + 1.52358i
\(890\) −15.5571 −0.521477
\(891\) 5.20404 12.1991i 0.174342 0.408685i
\(892\) 14.2506 0.477147
\(893\) 3.39114 + 2.46381i 0.113480 + 0.0824481i
\(894\) 0.692541 2.13142i 0.0231620 0.0712854i
\(895\) −7.49383 23.0636i −0.250491 0.770932i
\(896\) 35.4989 25.7915i 1.18593 0.861632i
\(897\) 1.68851 1.22677i 0.0563776 0.0409607i
\(898\) 1.60086 + 4.92695i 0.0534215 + 0.164414i
\(899\) −5.34122 + 16.4386i −0.178140 + 0.548257i
\(900\) 47.2883 + 34.3570i 1.57628 + 1.14523i
\(901\) 1.05478 0.0351398
\(902\) 15.8580 + 1.41604i 0.528013 + 0.0471490i
\(903\) 10.5912 0.352452
\(904\) 6.61731 + 4.80776i 0.220088 + 0.159904i
\(905\) −5.98830 + 18.4301i −0.199058 + 0.612637i
\(906\) 6.55904 + 20.1866i 0.217909 + 0.670656i
\(907\) 21.9637 15.9576i 0.729294 0.529863i −0.160046 0.987109i \(-0.551164\pi\)
0.889340 + 0.457247i \(0.151164\pi\)
\(908\) 34.0163 24.7143i 1.12887 0.820171i
\(909\) −8.46942 26.0662i −0.280913 0.864561i
\(910\) 2.35851 7.25874i 0.0781838 0.240625i
\(911\) −0.776479 0.564145i −0.0257259 0.0186910i 0.574848 0.818260i \(-0.305061\pi\)
−0.600574 + 0.799569i \(0.705061\pi\)
\(912\) −29.2147 −0.967394
\(913\) −24.7027 2.20584i −0.817542 0.0730025i
\(914\) −1.19899 −0.0396592
\(915\) 31.4804 + 22.8719i 1.04071 + 0.756121i
\(916\) 3.43036 10.5576i 0.113342 0.348832i
\(917\) 9.08723 + 27.9676i 0.300087 + 0.923573i
\(918\) −0.769374 + 0.558983i −0.0253931 + 0.0184492i
\(919\) 30.5295 22.1810i 1.00708 0.731683i 0.0434816 0.999054i \(-0.486155\pi\)
0.963594 + 0.267371i \(0.0861550\pi\)
\(920\) −1.78313 5.48791i −0.0587881 0.180931i
\(921\) 14.1800 43.6416i 0.467248 1.43804i
\(922\) −11.5655 8.40283i −0.380889 0.276732i
\(923\) 4.58793 0.151013
\(924\) −22.5104 + 52.7679i −0.740537 + 1.73594i
\(925\) −52.9797 −1.74196
\(926\) 1.93784 + 1.40793i 0.0636815 + 0.0462673i
\(927\) 10.1801 31.3310i 0.334357 1.02905i
\(928\) −2.69810 8.30389i −0.0885694 0.272589i
\(929\) −44.4655 + 32.3061i −1.45887 + 1.05993i −0.475209 + 0.879873i \(0.657628\pi\)
−0.983656 + 0.180055i \(0.942372\pi\)
\(930\) −45.9232 + 33.3652i −1.50588 + 1.09409i
\(931\) 11.0967 + 34.1521i 0.363679 + 1.11929i
\(932\) 3.12809 9.62726i 0.102464 0.315351i
\(933\) −20.9566 15.2258i −0.686088 0.498472i
\(934\) −11.1640 −0.365296
\(935\) 5.57532 3.33640i 0.182333 0.109112i
\(936\) 8.54981 0.279459
\(937\) 20.5432 + 14.9255i 0.671117 + 0.487595i 0.870399 0.492347i \(-0.163861\pi\)
−0.199282 + 0.979942i \(0.563861\pi\)
\(938\) −6.31467 + 19.4346i −0.206181 + 0.634561i
\(939\) 7.66447 + 23.5888i 0.250120 + 0.769792i
\(940\) 4.34891 3.15967i 0.141846 0.103057i
\(941\) −32.2913 + 23.4610i −1.05267 + 0.764807i −0.972718 0.231992i \(-0.925476\pi\)
−0.0799487 + 0.996799i \(0.525476\pi\)
\(942\) −4.43987 13.6645i −0.144659 0.445214i
\(943\) 2.09208 6.43875i 0.0681274 0.209674i
\(944\) 4.78731 + 3.47819i 0.155814 + 0.113205i
\(945\) 44.2479 1.43938
\(946\) 0.424076 + 1.85201i 0.0137879 + 0.0602142i
\(947\) −54.4758 −1.77023 −0.885113 0.465377i \(-0.845919\pi\)
−0.885113 + 0.465377i \(0.845919\pi\)
\(948\) −32.3914 23.5337i −1.05202 0.764339i
\(949\) 1.25975 3.87711i 0.0408932 0.125856i
\(950\) 6.74014 + 20.7440i 0.218679 + 0.673025i
\(951\) −63.2682 + 45.9670i −2.05161 + 1.49058i
\(952\) −3.38085 + 2.45633i −0.109574 + 0.0796101i
\(953\) −8.79349 27.0636i −0.284849 0.876675i −0.986444 0.164099i \(-0.947528\pi\)
0.701595 0.712576i \(-0.252472\pi\)
\(954\) −1.39970 + 4.30783i −0.0453170 + 0.139471i
\(955\) −40.7850 29.6321i −1.31977 0.958871i
\(956\) −34.3011 −1.10938
\(957\) 10.9827 + 9.58171i 0.355019 + 0.309733i
\(958\) 11.4544 0.370073
\(959\) 38.8634 + 28.2359i 1.25497 + 0.911786i
\(960\) −4.79581 + 14.7600i −0.154784 + 0.476377i
\(961\) 24.8061 + 76.3452i 0.800196 + 2.46275i
\(962\) −2.87644 + 2.08986i −0.0927402 + 0.0673797i
\(963\) 30.5533 22.1983i 0.984568 0.715330i
\(964\) 9.52748 + 29.3226i 0.306859 + 0.944416i
\(965\) −18.4338 + 56.7333i −0.593404 + 1.82631i
\(966\) −3.54410 2.57494i −0.114029 0.0828473i
\(967\) −25.6387 −0.824484 −0.412242 0.911074i \(-0.635254\pi\)
−0.412242 + 0.911074i \(0.635254\pi\)
\(968\) −22.0760 3.97424i −0.709548 0.127737i
\(969\) 6.94639 0.223150
\(970\) 4.74149 + 3.44489i 0.152240 + 0.110609i
\(971\) −13.9701 + 42.9957i −0.448323 + 1.37980i 0.430475 + 0.902603i \(0.358346\pi\)
−0.878798 + 0.477194i \(0.841654\pi\)
\(972\) −10.6475 32.7695i −0.341518 1.05108i
\(973\) −4.72696 + 3.43433i −0.151539 + 0.110100i
\(974\) 1.61302 1.17193i 0.0516845 0.0375510i
\(975\) 6.81428 + 20.9722i 0.218232 + 0.671648i
\(976\) −2.79380 + 8.59843i −0.0894273 + 0.275229i
\(977\) −21.8127 15.8479i −0.697851 0.507018i 0.181381 0.983413i \(-0.441943\pi\)
−0.879232 + 0.476395i \(0.841943\pi\)
\(978\) 3.00080 0.0959551
\(979\) 19.3776 + 16.9057i 0.619310 + 0.540310i
\(980\) 46.0517 1.47107
\(981\) 2.26861 + 1.64824i 0.0724310 + 0.0526242i
\(982\) −1.91217 + 5.88504i −0.0610197 + 0.187799i
\(983\) −7.36552 22.6687i −0.234923 0.723020i −0.997132 0.0756880i \(-0.975885\pi\)
0.762208 0.647332i \(-0.224115\pi\)
\(984\) 38.4909 27.9653i 1.22705 0.891501i
\(985\) −68.8352 + 50.0117i −2.19327 + 1.59351i
\(986\) 0.150525 + 0.463269i 0.00479370 + 0.0147535i
\(987\) 2.74868 8.45956i 0.0874914 0.269271i
\(988\) −6.59451 4.79119i −0.209799 0.152428i
\(989\) 0.807913 0.0256901
\(990\) 6.22775 + 27.1977i 0.197931 + 0.864399i
\(991\) 26.4139 0.839066 0.419533 0.907740i \(-0.362194\pi\)
0.419533 + 0.907740i \(0.362194\pi\)
\(992\) −45.4746 33.0392i −1.44382 1.04900i
\(993\) 30.1195 92.6984i 0.955815 2.94170i
\(994\) −2.97579 9.15853i −0.0943862 0.290491i
\(995\) 47.8703 34.7798i 1.51759 1.10259i
\(996\) −27.5096 + 19.9869i −0.871674 + 0.633308i
\(997\) 17.9633 + 55.2853i 0.568903 + 1.75090i 0.656059 + 0.754710i \(0.272222\pi\)
−0.0871554 + 0.996195i \(0.527778\pi\)
\(998\) −6.49866 + 20.0008i −0.205712 + 0.633115i
\(999\) −16.6760 12.1158i −0.527606 0.383328i
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 143.2.h.b.92.2 yes 16
11.3 even 5 inner 143.2.h.b.14.2 16
11.5 even 5 1573.2.a.o.1.5 8
11.6 odd 10 1573.2.a.n.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.h.b.14.2 16 11.3 even 5 inner
143.2.h.b.92.2 yes 16 1.1 even 1 trivial
1573.2.a.n.1.4 8 11.6 odd 10
1573.2.a.o.1.5 8 11.5 even 5