Properties

Label 33.3.g.a.19.1
Level $33$
Weight $3$
Character 33.19
Analytic conductor $0.899$
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] = [33,3,Mod(7,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.g (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.899184872389\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + 1868 x^{7} - 1619 x^{6} - 16804 x^{5} + 32427 x^{4} + 43316 x^{3} + \cdots + 83521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.1
Root \(2.24350 + 2.23726i\) of defining polynomial
Character \(\chi\) \(=\) 33.19
Dual form 33.3.g.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.577539 - 0.794915i) q^{2} +(-0.535233 - 1.64728i) q^{3} +(0.937730 - 2.88604i) q^{4} +(-0.321645 - 0.233689i) q^{5} +(-1.00033 + 1.37683i) q^{6} +(6.87311 + 2.23321i) q^{7} +(-6.57364 + 2.13591i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})\) \(q+(-0.577539 - 0.794915i) q^{2} +(-0.535233 - 1.64728i) q^{3} +(0.937730 - 2.88604i) q^{4} +(-0.321645 - 0.233689i) q^{5} +(-1.00033 + 1.37683i) q^{6} +(6.87311 + 2.23321i) q^{7} +(-6.57364 + 2.13591i) q^{8} +(-2.42705 + 1.76336i) q^{9} +0.390645i q^{10} +(-0.495253 + 10.9888i) q^{11} -5.25601 q^{12} +(7.14728 + 9.83739i) q^{13} +(-2.19428 - 6.75330i) q^{14} +(-0.212796 + 0.654918i) q^{15} +(-4.32564 - 3.14276i) q^{16} +(12.2903 - 16.9162i) q^{17} +(2.80344 + 0.910891i) q^{18} +(-10.5689 + 3.43403i) q^{19} +(-0.976052 + 0.709143i) q^{20} -12.5172i q^{21} +(9.02122 - 5.95281i) q^{22} -5.92990 q^{23} +(7.03686 + 9.68541i) q^{24} +(-7.67658 - 23.6261i) q^{25} +(3.69205 - 11.3630i) q^{26} +(4.20378 + 3.05422i) q^{27} +(12.8902 - 17.7419i) q^{28} +(23.7332 + 7.71140i) q^{29} +(0.643502 - 0.209086i) q^{30} +(-48.2383 + 35.0472i) q^{31} +32.9013i q^{32} +(18.3668 - 5.06578i) q^{33} -20.5451 q^{34} +(-1.68883 - 2.32447i) q^{35} +(2.81319 + 8.65811i) q^{36} +(-1.84391 + 5.67498i) q^{37} +(8.83370 + 6.41806i) q^{38} +(12.3795 - 17.0389i) q^{39} +(2.61352 + 0.849184i) q^{40} +(-49.4926 + 16.0811i) q^{41} +(-9.95011 + 7.22918i) q^{42} +17.6439i q^{43} +(31.2498 + 11.7339i) q^{44} +1.19273 q^{45} +(3.42475 + 4.71376i) q^{46} +(-17.1074 - 52.6513i) q^{47} +(-2.86177 + 8.80763i) q^{48} +(2.61054 + 1.89667i) q^{49} +(-14.3472 + 19.7472i) q^{50} +(-34.4438 - 11.1915i) q^{51} +(35.0933 - 11.4025i) q^{52} +(76.5751 - 55.6350i) q^{53} -5.10558i q^{54} +(2.72727 - 3.41878i) q^{55} -49.9513 q^{56} +(11.3136 + 15.5719i) q^{57} +(-7.57698 - 23.3195i) q^{58} +(-7.75795 + 23.8765i) q^{59} +(1.69057 + 1.22827i) q^{60} +(19.6356 - 27.0261i) q^{61} +(55.7191 + 18.1042i) q^{62} +(-20.6193 + 6.69962i) q^{63} +(8.85121 - 6.43078i) q^{64} -4.83439i q^{65} +(-14.6344 - 11.6743i) q^{66} +94.6640 q^{67} +(-37.2957 - 51.3331i) q^{68} +(3.17388 + 9.76819i) q^{69} +(-0.872392 + 2.68495i) q^{70} +(-66.9252 - 48.6240i) q^{71} +(12.1882 - 16.7756i) q^{72} +(-44.2990 - 14.3936i) q^{73} +(5.57606 - 1.81177i) q^{74} +(-34.8100 + 25.2909i) q^{75} +33.7223i q^{76} +(-27.9443 + 74.4215i) q^{77} -20.6941 q^{78} +(35.4547 + 48.7992i) q^{79} +(0.656893 + 2.02171i) q^{80} +(2.78115 - 8.55951i) q^{81} +(41.3671 + 30.0549i) q^{82} +(-88.5635 + 121.897i) q^{83} +(-36.1251 - 11.7378i) q^{84} +(-7.90625 + 2.56890i) q^{85} +(14.0254 - 10.1900i) q^{86} -43.2227i q^{87} +(-20.2155 - 73.2946i) q^{88} +134.190 q^{89} +(-0.688847 - 0.948116i) q^{90} +(27.1551 + 83.5748i) q^{91} +(-5.56064 + 17.1139i) q^{92} +(83.5512 + 60.7035i) q^{93} +(-31.9731 + 44.0072i) q^{94} +(4.20192 + 1.36529i) q^{95} +(54.1976 - 17.6099i) q^{96} +(-30.4243 + 22.1046i) q^{97} -3.17056i q^{98} +(-18.1752 - 27.5438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9} - 10 q^{11} - 24 q^{12} + 30 q^{13} - 2 q^{14} - 24 q^{15} + 16 q^{16} - 10 q^{17} - 30 q^{18} + 42 q^{20} + 42 q^{22} + 132 q^{23} + 90 q^{24} - 2 q^{25} + 46 q^{26} - 50 q^{28} + 160 q^{29} + 180 q^{30} + 10 q^{31} + 12 q^{33} - 368 q^{34} - 320 q^{35} + 60 q^{36} - 126 q^{37} - 130 q^{38} + 30 q^{40} - 120 q^{41} - 204 q^{42} - 206 q^{44} - 12 q^{45} + 50 q^{46} - 150 q^{47} - 96 q^{48} + 210 q^{49} + 330 q^{50} - 60 q^{51} + 110 q^{52} + 342 q^{53} + 244 q^{55} + 524 q^{56} + 60 q^{57} + 150 q^{58} + 110 q^{59} + 36 q^{60} - 90 q^{61} + 40 q^{62} + 90 q^{63} - 168 q^{64} + 48 q^{66} + 36 q^{67} + 80 q^{68} + 210 q^{69} + 340 q^{70} - 236 q^{71} - 150 q^{72} - 350 q^{73} - 730 q^{74} - 408 q^{75} - 390 q^{77} - 312 q^{78} + 210 q^{79} - 806 q^{80} - 36 q^{81} + 114 q^{82} - 190 q^{83} - 180 q^{84} + 110 q^{85} + 736 q^{86} + 144 q^{88} + 76 q^{89} + 60 q^{90} + 306 q^{91} - 150 q^{92} + 144 q^{93} - 350 q^{94} + 430 q^{95} + 450 q^{96} - 354 q^{97} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.577539 0.794915i −0.288770 0.397457i 0.639844 0.768505i \(-0.278999\pi\)
−0.928614 + 0.371047i \(0.878999\pi\)
\(3\) −0.535233 1.64728i −0.178411 0.549093i
\(4\) 0.937730 2.88604i 0.234433 0.721509i
\(5\) −0.321645 0.233689i −0.0643291 0.0467378i 0.555156 0.831746i \(-0.312659\pi\)
−0.619485 + 0.785008i \(0.712659\pi\)
\(6\) −1.00033 + 1.37683i −0.166721 + 0.229472i
\(7\) 6.87311 + 2.23321i 0.981872 + 0.319030i 0.755599 0.655034i \(-0.227346\pi\)
0.226273 + 0.974064i \(0.427346\pi\)
\(8\) −6.57364 + 2.13591i −0.821705 + 0.266988i
\(9\) −2.42705 + 1.76336i −0.269672 + 0.195928i
\(10\) 0.390645i 0.0390645i
\(11\) −0.495253 + 10.9888i −0.0450230 + 0.998986i
\(12\) −5.25601 −0.438001
\(13\) 7.14728 + 9.83739i 0.549791 + 0.756722i 0.989984 0.141181i \(-0.0450899\pi\)
−0.440193 + 0.897903i \(0.645090\pi\)
\(14\) −2.19428 6.75330i −0.156734 0.482379i
\(15\) −0.212796 + 0.654918i −0.0141864 + 0.0436612i
\(16\) −4.32564 3.14276i −0.270352 0.196422i
\(17\) 12.2903 16.9162i 0.722960 0.995069i −0.276460 0.961025i \(-0.589161\pi\)
0.999420 0.0340440i \(-0.0108386\pi\)
\(18\) 2.80344 + 0.910891i 0.155746 + 0.0506051i
\(19\) −10.5689 + 3.43403i −0.556256 + 0.180739i −0.573636 0.819110i \(-0.694468\pi\)
0.0173798 + 0.999849i \(0.494468\pi\)
\(20\) −0.976052 + 0.709143i −0.0488026 + 0.0354572i
\(21\) 12.5172i 0.596057i
\(22\) 9.02122 5.95281i 0.410056 0.270582i
\(23\) −5.92990 −0.257822 −0.128911 0.991656i \(-0.541148\pi\)
−0.128911 + 0.991656i \(0.541148\pi\)
\(24\) 7.03686 + 9.68541i 0.293203 + 0.403559i
\(25\) −7.67658 23.6261i −0.307063 0.945043i
\(26\) 3.69205 11.3630i 0.142002 0.437037i
\(27\) 4.20378 + 3.05422i 0.155695 + 0.113119i
\(28\) 12.8902 17.7419i 0.460366 0.633639i
\(29\) 23.7332 + 7.71140i 0.818388 + 0.265910i 0.688146 0.725572i \(-0.258425\pi\)
0.130242 + 0.991482i \(0.458425\pi\)
\(30\) 0.643502 0.209086i 0.0214501 0.00696955i
\(31\) −48.2383 + 35.0472i −1.55607 + 1.13055i −0.616937 + 0.787012i \(0.711627\pi\)
−0.939137 + 0.343542i \(0.888373\pi\)
\(32\) 32.9013i 1.02817i
\(33\) 18.3668 5.06578i 0.556569 0.153508i
\(34\) −20.5451 −0.604267
\(35\) −1.68883 2.32447i −0.0482522 0.0664135i
\(36\) 2.81319 + 8.65811i 0.0781442 + 0.240503i
\(37\) −1.84391 + 5.67498i −0.0498355 + 0.153378i −0.972877 0.231322i \(-0.925695\pi\)
0.923042 + 0.384700i \(0.125695\pi\)
\(38\) 8.83370 + 6.41806i 0.232466 + 0.168896i
\(39\) 12.3795 17.0389i 0.317422 0.436894i
\(40\) 2.61352 + 0.849184i 0.0653380 + 0.0212296i
\(41\) −49.4926 + 16.0811i −1.20714 + 0.392223i −0.842382 0.538881i \(-0.818847\pi\)
−0.364755 + 0.931104i \(0.618847\pi\)
\(42\) −9.95011 + 7.22918i −0.236907 + 0.172123i
\(43\) 17.6439i 0.410323i 0.978728 + 0.205161i \(0.0657719\pi\)
−0.978728 + 0.205161i \(0.934228\pi\)
\(44\) 31.2498 + 11.7339i 0.710223 + 0.266679i
\(45\) 1.19273 0.0265050
\(46\) 3.42475 + 4.71376i 0.0744511 + 0.102473i
\(47\) −17.1074 52.6513i −0.363988 1.12024i −0.950612 0.310381i \(-0.899543\pi\)
0.586624 0.809860i \(-0.300457\pi\)
\(48\) −2.86177 + 8.80763i −0.0596203 + 0.183492i
\(49\) 2.61054 + 1.89667i 0.0532763 + 0.0387075i
\(50\) −14.3472 + 19.7472i −0.286944 + 0.394944i
\(51\) −34.4438 11.1915i −0.675369 0.219441i
\(52\) 35.0933 11.4025i 0.674871 0.219279i
\(53\) 76.5751 55.6350i 1.44481 1.04972i 0.457803 0.889054i \(-0.348636\pi\)
0.987009 0.160664i \(-0.0513636\pi\)
\(54\) 5.10558i 0.0945477i
\(55\) 2.72727 3.41878i 0.0495867 0.0621596i
\(56\) −49.9513 −0.891987
\(57\) 11.3136 + 15.5719i 0.198484 + 0.273190i
\(58\) −7.57698 23.3195i −0.130638 0.402061i
\(59\) −7.75795 + 23.8765i −0.131491 + 0.404687i −0.995028 0.0995988i \(-0.968244\pi\)
0.863537 + 0.504285i \(0.168244\pi\)
\(60\) 1.69057 + 1.22827i 0.0281762 + 0.0204712i
\(61\) 19.6356 27.0261i 0.321896 0.443052i −0.617149 0.786846i \(-0.711712\pi\)
0.939045 + 0.343795i \(0.111712\pi\)
\(62\) 55.7191 + 18.1042i 0.898694 + 0.292004i
\(63\) −20.6193 + 6.69962i −0.327291 + 0.106343i
\(64\) 8.85121 6.43078i 0.138300 0.100481i
\(65\) 4.83439i 0.0743753i
\(66\) −14.6344 11.6743i −0.221733 0.176884i
\(67\) 94.6640 1.41290 0.706448 0.707765i \(-0.250296\pi\)
0.706448 + 0.707765i \(0.250296\pi\)
\(68\) −37.2957 51.3331i −0.548466 0.754899i
\(69\) 3.17388 + 9.76819i 0.0459982 + 0.141568i
\(70\) −0.872392 + 2.68495i −0.0124627 + 0.0383564i
\(71\) −66.9252 48.6240i −0.942609 0.684845i 0.00643861 0.999979i \(-0.497951\pi\)
−0.949047 + 0.315134i \(0.897951\pi\)
\(72\) 12.1882 16.7756i 0.169281 0.232995i
\(73\) −44.2990 14.3936i −0.606836 0.197173i −0.0105491 0.999944i \(-0.503358\pi\)
−0.596287 + 0.802771i \(0.703358\pi\)
\(74\) 5.57606 1.81177i 0.0753522 0.0244834i
\(75\) −34.8100 + 25.2909i −0.464133 + 0.337212i
\(76\) 33.7223i 0.443715i
\(77\) −27.9443 + 74.4215i −0.362913 + 0.966513i
\(78\) −20.6941 −0.265309
\(79\) 35.4547 + 48.7992i 0.448794 + 0.617712i 0.972138 0.234410i \(-0.0753158\pi\)
−0.523344 + 0.852121i \(0.675316\pi\)
\(80\) 0.656893 + 2.02171i 0.00821116 + 0.0252713i
\(81\) 2.78115 8.55951i 0.0343352 0.105673i
\(82\) 41.3671 + 30.0549i 0.504476 + 0.366524i
\(83\) −88.5635 + 121.897i −1.06703 + 1.46864i −0.193982 + 0.981005i \(0.562140\pi\)
−0.873048 + 0.487635i \(0.837860\pi\)
\(84\) −36.1251 11.7378i −0.430061 0.139735i
\(85\) −7.90625 + 2.56890i −0.0930147 + 0.0302223i
\(86\) 14.0254 10.1900i 0.163086 0.118489i
\(87\) 43.2227i 0.496812i
\(88\) −20.2155 73.2946i −0.229722 0.832893i
\(89\) 134.190 1.50775 0.753874 0.657019i \(-0.228183\pi\)
0.753874 + 0.657019i \(0.228183\pi\)
\(90\) −0.688847 0.948116i −0.00765385 0.0105346i
\(91\) 27.1551 + 83.5748i 0.298408 + 0.918405i
\(92\) −5.56064 + 17.1139i −0.0604418 + 0.186021i
\(93\) 83.5512 + 60.7035i 0.898400 + 0.652726i
\(94\) −31.9731 + 44.0072i −0.340139 + 0.468161i
\(95\) 4.20192 + 1.36529i 0.0442308 + 0.0143715i
\(96\) 54.1976 17.6099i 0.564559 0.183436i
\(97\) −30.4243 + 22.1046i −0.313653 + 0.227882i −0.733462 0.679730i \(-0.762097\pi\)
0.419809 + 0.907612i \(0.362097\pi\)
\(98\) 3.17056i 0.0323526i
\(99\) −18.1752 27.5438i −0.183588 0.278220i
\(100\) −75.3843 −0.753843
\(101\) −47.4940 65.3699i −0.470238 0.647227i 0.506354 0.862325i \(-0.330993\pi\)
−0.976592 + 0.215098i \(0.930993\pi\)
\(102\) 10.9964 + 33.8434i 0.107808 + 0.331798i
\(103\) 30.7976 94.7853i 0.299006 0.920246i −0.682840 0.730568i \(-0.739256\pi\)
0.981846 0.189678i \(-0.0607444\pi\)
\(104\) −67.9954 49.4016i −0.653802 0.475015i
\(105\) −2.92513 + 4.02610i −0.0278584 + 0.0383438i
\(106\) −88.4502 28.7392i −0.834436 0.271125i
\(107\) 102.955 33.4522i 0.962199 0.312637i 0.214536 0.976716i \(-0.431176\pi\)
0.747663 + 0.664079i \(0.231176\pi\)
\(108\) 12.7566 9.26821i 0.118117 0.0858168i
\(109\) 175.446i 1.60960i −0.593546 0.804800i \(-0.702273\pi\)
0.593546 0.804800i \(-0.297727\pi\)
\(110\) −4.29274 0.193468i −0.0390249 0.00175880i
\(111\) 10.3352 0.0931099
\(112\) −22.7121 31.2606i −0.202787 0.279112i
\(113\) 30.4454 + 93.7013i 0.269428 + 0.829215i 0.990640 + 0.136500i \(0.0435855\pi\)
−0.721212 + 0.692715i \(0.756414\pi\)
\(114\) 5.84424 17.9867i 0.0512653 0.157778i
\(115\) 1.90732 + 1.38575i 0.0165854 + 0.0120500i
\(116\) 44.5108 61.2638i 0.383713 0.528136i
\(117\) −34.6936 11.2726i −0.296527 0.0963474i
\(118\) 23.4603 7.62272i 0.198816 0.0645993i
\(119\) 122.250 88.8199i 1.02731 0.746385i
\(120\) 4.75971i 0.0396642i
\(121\) −120.509 10.8845i −0.995946 0.0899546i
\(122\) −32.8238 −0.269048
\(123\) 52.9802 + 72.9209i 0.430733 + 0.592853i
\(124\) 55.9129 + 172.082i 0.450911 + 1.38776i
\(125\) −6.12346 + 18.8461i −0.0489877 + 0.150769i
\(126\) 17.2341 + 12.5213i 0.136779 + 0.0993754i
\(127\) −12.8526 + 17.6901i −0.101202 + 0.139292i −0.856614 0.515957i \(-0.827436\pi\)
0.755413 + 0.655249i \(0.227436\pi\)
\(128\) 114.940 + 37.3464i 0.897971 + 0.291768i
\(129\) 29.0644 9.44359i 0.225305 0.0732061i
\(130\) −3.84293 + 2.79205i −0.0295610 + 0.0214773i
\(131\) 16.3593i 0.124880i 0.998049 + 0.0624402i \(0.0198883\pi\)
−0.998049 + 0.0624402i \(0.980112\pi\)
\(132\) 2.60305 57.7575i 0.0197201 0.437557i
\(133\) −80.3099 −0.603834
\(134\) −54.6722 75.2499i −0.408002 0.561566i
\(135\) −0.638387 1.96475i −0.00472879 0.0145537i
\(136\) −44.6608 + 137.452i −0.328388 + 1.01068i
\(137\) −24.7472 17.9799i −0.180637 0.131240i 0.493793 0.869580i \(-0.335610\pi\)
−0.674429 + 0.738340i \(0.735610\pi\)
\(138\) 5.93184 8.16448i 0.0429843 0.0591629i
\(139\) −26.3884 8.57411i −0.189845 0.0616843i 0.212552 0.977150i \(-0.431823\pi\)
−0.402396 + 0.915466i \(0.631823\pi\)
\(140\) −8.29217 + 2.69429i −0.0592298 + 0.0192449i
\(141\) −77.5749 + 56.3615i −0.550177 + 0.399727i
\(142\) 81.2821i 0.572409i
\(143\) −111.641 + 73.6684i −0.780708 + 0.515164i
\(144\) 16.0403 0.111391
\(145\) −5.83162 8.02654i −0.0402181 0.0553554i
\(146\) 14.1427 + 43.5268i 0.0968680 + 0.298129i
\(147\) 1.72709 5.31544i 0.0117489 0.0361595i
\(148\) 14.6491 + 10.6432i 0.0989805 + 0.0719135i
\(149\) −116.856 + 160.838i −0.784265 + 1.07945i 0.210533 + 0.977587i \(0.432480\pi\)
−0.994799 + 0.101862i \(0.967520\pi\)
\(150\) 40.2083 + 13.0645i 0.268055 + 0.0870964i
\(151\) 124.120 40.3290i 0.821986 0.267079i 0.132320 0.991207i \(-0.457757\pi\)
0.689666 + 0.724128i \(0.257757\pi\)
\(152\) 62.1412 45.1482i 0.408824 0.297028i
\(153\) 62.7286i 0.409991i
\(154\) 75.2977 20.7680i 0.488946 0.134857i
\(155\) 23.7058 0.152940
\(156\) −37.5662 51.7054i −0.240809 0.331445i
\(157\) −21.8126 67.1324i −0.138934 0.427595i 0.857247 0.514905i \(-0.172173\pi\)
−0.996181 + 0.0873102i \(0.972173\pi\)
\(158\) 18.3147 56.3669i 0.115916 0.356753i
\(159\) −132.632 96.3627i −0.834163 0.606055i
\(160\) 7.68868 10.5826i 0.0480543 0.0661410i
\(161\) −40.7568 13.2427i −0.253148 0.0822527i
\(162\) −8.41031 + 2.73267i −0.0519155 + 0.0168684i
\(163\) 62.2214 45.2065i 0.381726 0.277340i −0.380330 0.924851i \(-0.624190\pi\)
0.762057 + 0.647510i \(0.224190\pi\)
\(164\) 157.917i 0.962910i
\(165\) −7.09140 2.66273i −0.0429782 0.0161377i
\(166\) 148.047 0.891848
\(167\) −59.8117 82.3237i −0.358154 0.492956i 0.591479 0.806320i \(-0.298544\pi\)
−0.949633 + 0.313364i \(0.898544\pi\)
\(168\) 26.7356 + 82.2836i 0.159140 + 0.489784i
\(169\) 6.53325 20.1073i 0.0386583 0.118978i
\(170\) 6.60823 + 4.80116i 0.0388719 + 0.0282421i
\(171\) 19.5958 26.9712i 0.114595 0.157727i
\(172\) 50.9209 + 16.5452i 0.296052 + 0.0961930i
\(173\) −118.789 + 38.5969i −0.686643 + 0.223104i −0.631501 0.775375i \(-0.717561\pi\)
−0.0551414 + 0.998479i \(0.517561\pi\)
\(174\) −34.3583 + 24.9628i −0.197462 + 0.143464i
\(175\) 179.528i 1.02587i
\(176\) 36.6776 45.9773i 0.208395 0.261235i
\(177\) 43.4836 0.245670
\(178\) −77.4997 106.669i −0.435392 0.599265i
\(179\) −31.8999 98.1779i −0.178212 0.548480i 0.821554 0.570131i \(-0.193108\pi\)
−0.999766 + 0.0216514i \(0.993108\pi\)
\(180\) 1.11846 3.44225i 0.00621364 0.0191236i
\(181\) 90.9834 + 66.1033i 0.502671 + 0.365212i 0.810036 0.586380i \(-0.199447\pi\)
−0.307365 + 0.951592i \(0.599447\pi\)
\(182\) 50.7517 69.8537i 0.278856 0.383812i
\(183\) −55.0292 17.8801i −0.300706 0.0977054i
\(184\) 38.9810 12.6657i 0.211853 0.0688353i
\(185\) 1.91927 1.39443i 0.0103744 0.00753746i
\(186\) 101.475i 0.545563i
\(187\) 179.802 + 143.434i 0.961511 + 0.767028i
\(188\) −167.996 −0.893595
\(189\) 22.0723 + 30.3799i 0.116785 + 0.160740i
\(190\) −1.34149 4.12868i −0.00706047 0.0217299i
\(191\) 59.0444 181.720i 0.309133 0.951414i −0.668969 0.743290i \(-0.733264\pi\)
0.978102 0.208124i \(-0.0667357\pi\)
\(192\) −15.3307 11.1384i −0.0798476 0.0580127i
\(193\) 32.0683 44.1382i 0.166157 0.228695i −0.717817 0.696232i \(-0.754858\pi\)
0.883974 + 0.467537i \(0.154858\pi\)
\(194\) 35.1425 + 11.4185i 0.181147 + 0.0588582i
\(195\) −7.96359 + 2.58753i −0.0408389 + 0.0132694i
\(196\) 7.92184 5.75555i 0.0404175 0.0293651i
\(197\) 75.2950i 0.382208i 0.981570 + 0.191104i \(0.0612068\pi\)
−0.981570 + 0.191104i \(0.938793\pi\)
\(198\) −11.3981 + 30.3554i −0.0575659 + 0.153310i
\(199\) −60.7193 −0.305122 −0.152561 0.988294i \(-0.548752\pi\)
−0.152561 + 0.988294i \(0.548752\pi\)
\(200\) 100.926 + 138.913i 0.504631 + 0.694565i
\(201\) −50.6673 155.938i −0.252076 0.775811i
\(202\) −24.5338 + 75.5074i −0.121455 + 0.373799i
\(203\) 145.900 + 106.003i 0.718719 + 0.522180i
\(204\) −64.5981 + 88.9116i −0.316657 + 0.435841i
\(205\) 19.6771 + 6.39346i 0.0959856 + 0.0311876i
\(206\) −93.1331 + 30.2608i −0.452102 + 0.146897i
\(207\) 14.3922 10.4565i 0.0695274 0.0505146i
\(208\) 65.0152i 0.312573i
\(209\) −32.5018 117.840i −0.155511 0.563830i
\(210\) 4.88979 0.0232847
\(211\) 240.517 + 331.043i 1.13989 + 1.56893i 0.767751 + 0.640748i \(0.221376\pi\)
0.372140 + 0.928177i \(0.378624\pi\)
\(212\) −88.7580 273.169i −0.418670 1.28853i
\(213\) −44.2767 + 136.270i −0.207872 + 0.639763i
\(214\) −86.0524 62.5207i −0.402114 0.292153i
\(215\) 4.12318 5.67507i 0.0191776 0.0263957i
\(216\) −34.1577 11.0985i −0.158137 0.0513819i
\(217\) −409.815 + 133.157i −1.88855 + 0.613626i
\(218\) −139.465 + 101.327i −0.639747 + 0.464804i
\(219\) 80.6768i 0.368387i
\(220\) −7.30927 11.0769i −0.0332240 0.0503495i
\(221\) 254.254 1.15047
\(222\) −5.96898 8.21560i −0.0268873 0.0370072i
\(223\) −45.5218 140.102i −0.204133 0.628258i −0.999748 0.0224549i \(-0.992852\pi\)
0.795614 0.605803i \(-0.207148\pi\)
\(224\) −73.4755 + 226.134i −0.328016 + 1.00953i
\(225\) 60.2926 + 43.8052i 0.267967 + 0.194690i
\(226\) 56.9011 78.3177i 0.251775 0.346539i
\(227\) −130.316 42.3421i −0.574078 0.186529i 0.00756813 0.999971i \(-0.497591\pi\)
−0.581646 + 0.813442i \(0.697591\pi\)
\(228\) 55.5501 18.0493i 0.243641 0.0791637i
\(229\) −69.3377 + 50.3768i −0.302785 + 0.219986i −0.728794 0.684733i \(-0.759919\pi\)
0.426010 + 0.904719i \(0.359919\pi\)
\(230\) 2.31649i 0.0100717i
\(231\) 137.550 + 6.19918i 0.595453 + 0.0268363i
\(232\) −172.485 −0.743469
\(233\) 127.215 + 175.096i 0.545986 + 0.751486i 0.989461 0.144801i \(-0.0462543\pi\)
−0.443474 + 0.896287i \(0.646254\pi\)
\(234\) 11.0762 + 34.0889i 0.0473340 + 0.145679i
\(235\) −6.80150 + 20.9329i −0.0289426 + 0.0890761i
\(236\) 61.6336 + 44.7794i 0.261159 + 0.189743i
\(237\) 61.4094 84.5227i 0.259111 0.356636i
\(238\) −141.208 45.8814i −0.593313 0.192779i
\(239\) 157.155 51.0629i 0.657554 0.213652i 0.0388122 0.999247i \(-0.487643\pi\)
0.618742 + 0.785594i \(0.287643\pi\)
\(240\) 2.97872 2.16417i 0.0124114 0.00901738i
\(241\) 233.818i 0.970199i 0.874459 + 0.485100i \(0.161217\pi\)
−0.874459 + 0.485100i \(0.838783\pi\)
\(242\) 60.9467 + 102.081i 0.251846 + 0.421822i
\(243\) −15.5885 −0.0641500
\(244\) −59.5855 82.0124i −0.244203 0.336116i
\(245\) −0.396437 1.22011i −0.00161811 0.00498004i
\(246\) 27.3678 84.2294i 0.111251 0.342396i
\(247\) −109.321 79.4261i −0.442594 0.321563i
\(248\) 242.244 333.420i 0.976790 1.34444i
\(249\) 248.201 + 80.6453i 0.996790 + 0.323877i
\(250\) 18.5176 6.01672i 0.0740703 0.0240669i
\(251\) −216.317 + 157.163i −0.861819 + 0.626148i −0.928379 0.371634i \(-0.878798\pi\)
0.0665602 + 0.997782i \(0.478798\pi\)
\(252\) 65.7905i 0.261074i
\(253\) 2.93680 65.1627i 0.0116079 0.257560i
\(254\) 21.4850 0.0845866
\(255\) 8.46338 + 11.6488i 0.0331897 + 0.0456817i
\(256\) −50.2188 154.558i −0.196167 0.603741i
\(257\) 15.3004 47.0899i 0.0595348 0.183229i −0.916866 0.399195i \(-0.869290\pi\)
0.976401 + 0.215965i \(0.0692898\pi\)
\(258\) −24.2927 17.6497i −0.0941577 0.0684096i
\(259\) −25.3468 + 34.8869i −0.0978642 + 0.134698i
\(260\) −13.9522 4.53336i −0.0536625 0.0174360i
\(261\) −71.1997 + 23.1342i −0.272796 + 0.0886368i
\(262\) 13.0043 9.44816i 0.0496347 0.0360617i
\(263\) 198.763i 0.755752i −0.925856 0.377876i \(-0.876655\pi\)
0.925856 0.377876i \(-0.123345\pi\)
\(264\) −109.917 + 72.5303i −0.416350 + 0.274736i
\(265\) −37.6313 −0.142005
\(266\) 46.3821 + 63.8395i 0.174369 + 0.239998i
\(267\) −71.8227 221.047i −0.268999 0.827893i
\(268\) 88.7693 273.204i 0.331229 1.01942i
\(269\) −8.71548 6.33217i −0.0323995 0.0235397i 0.571468 0.820625i \(-0.306374\pi\)
−0.603867 + 0.797085i \(0.706374\pi\)
\(270\) −1.19312 + 1.64219i −0.00441895 + 0.00608217i
\(271\) 277.924 + 90.3028i 1.02555 + 0.333221i 0.773029 0.634371i \(-0.218741\pi\)
0.252520 + 0.967592i \(0.418741\pi\)
\(272\) −106.327 + 34.5477i −0.390908 + 0.127014i
\(273\) 123.137 89.4640i 0.451050 0.327707i
\(274\) 30.0560i 0.109693i
\(275\) 263.425 72.6559i 0.957910 0.264203i
\(276\) 31.1676 0.112926
\(277\) −103.077 141.874i −0.372120 0.512179i 0.581356 0.813650i \(-0.302523\pi\)
−0.953476 + 0.301470i \(0.902523\pi\)
\(278\) 8.42466 + 25.9284i 0.0303045 + 0.0932677i
\(279\) 55.2762 170.123i 0.198123 0.609758i
\(280\) 16.0666 + 11.6731i 0.0573807 + 0.0416895i
\(281\) 133.651 183.955i 0.475626 0.654644i −0.502031 0.864850i \(-0.667414\pi\)
0.977657 + 0.210206i \(0.0674135\pi\)
\(282\) 89.6051 + 29.1145i 0.317749 + 0.103243i
\(283\) −225.825 + 73.3749i −0.797967 + 0.259275i −0.679493 0.733682i \(-0.737800\pi\)
−0.118474 + 0.992957i \(0.537800\pi\)
\(284\) −203.088 + 147.552i −0.715100 + 0.519551i
\(285\) 7.65249i 0.0268508i
\(286\) 123.037 + 46.1989i 0.430201 + 0.161535i
\(287\) −376.080 −1.31038
\(288\) −58.0167 79.8532i −0.201447 0.277268i
\(289\) −45.7992 140.955i −0.158475 0.487735i
\(290\) −3.01242 + 9.27128i −0.0103877 + 0.0319699i
\(291\) 52.6965 + 38.2862i 0.181088 + 0.131568i
\(292\) −83.0811 + 114.351i −0.284524 + 0.391614i
\(293\) 27.8981 + 9.06463i 0.0952152 + 0.0309373i 0.356237 0.934396i \(-0.384060\pi\)
−0.261022 + 0.965333i \(0.584060\pi\)
\(294\) −5.22279 + 1.69699i −0.0177646 + 0.00577207i
\(295\) 8.07499 5.86682i 0.0273728 0.0198875i
\(296\) 41.2437i 0.139337i
\(297\) −35.6443 + 44.6820i −0.120014 + 0.150445i
\(298\) 195.341 0.655507
\(299\) −42.3827 58.3347i −0.141748 0.195099i
\(300\) 40.3482 + 124.179i 0.134494 + 0.413930i
\(301\) −39.4025 + 121.268i −0.130905 + 0.402885i
\(302\) −103.742 75.3731i −0.343517 0.249580i
\(303\) −82.2621 + 113.224i −0.271492 + 0.373677i
\(304\) 56.5094 + 18.3610i 0.185886 + 0.0603981i
\(305\) −12.6314 + 4.10420i −0.0414145 + 0.0134564i
\(306\) 49.8639 36.2283i 0.162954 0.118393i
\(307\) 347.331i 1.13137i 0.824621 + 0.565686i \(0.191389\pi\)
−0.824621 + 0.565686i \(0.808611\pi\)
\(308\) 188.579 + 150.436i 0.612269 + 0.488427i
\(309\) −172.622 −0.558646
\(310\) −13.6910 18.8441i −0.0441646 0.0607873i
\(311\) 136.144 + 419.008i 0.437762 + 1.34729i 0.890230 + 0.455512i \(0.150544\pi\)
−0.452467 + 0.891781i \(0.649456\pi\)
\(312\) −44.9847 + 138.449i −0.144182 + 0.443746i
\(313\) 20.6012 + 14.9677i 0.0658186 + 0.0478200i 0.620208 0.784437i \(-0.287048\pi\)
−0.554389 + 0.832257i \(0.687048\pi\)
\(314\) −40.7669 + 56.1108i −0.129831 + 0.178697i
\(315\) 8.19774 + 2.66361i 0.0260246 + 0.00845589i
\(316\) 174.083 56.5631i 0.550896 0.178997i
\(317\) −73.9310 + 53.7140i −0.233221 + 0.169445i −0.698258 0.715846i \(-0.746041\pi\)
0.465037 + 0.885291i \(0.346041\pi\)
\(318\) 161.084i 0.506554i
\(319\) −96.4933 + 256.982i −0.302487 + 0.805586i
\(320\) −4.34975 −0.0135930
\(321\) −110.210 151.691i −0.343334 0.472558i
\(322\) 13.0119 + 40.0464i 0.0404095 + 0.124368i
\(323\) −71.8041 + 220.990i −0.222304 + 0.684180i
\(324\) −22.0951 16.0530i −0.0681947 0.0495464i
\(325\) 177.552 244.380i 0.546315 0.751938i
\(326\) −71.8706 23.3522i −0.220462 0.0716324i
\(327\) −289.009 + 93.9047i −0.883819 + 0.287170i
\(328\) 290.999 211.423i 0.887192 0.644583i
\(329\) 400.083i 1.21606i
\(330\) 1.97892 + 7.17489i 0.00599673 + 0.0217421i
\(331\) −318.761 −0.963024 −0.481512 0.876439i \(-0.659912\pi\)
−0.481512 + 0.876439i \(0.659912\pi\)
\(332\) 268.751 + 369.904i 0.809491 + 1.11417i
\(333\) −5.53174 17.0249i −0.0166118 0.0511260i
\(334\) −30.8967 + 95.0904i −0.0925052 + 0.284702i
\(335\) −30.4483 22.1220i −0.0908903 0.0660357i
\(336\) −39.3386 + 54.1449i −0.117079 + 0.161145i
\(337\) 587.526 + 190.899i 1.74340 + 0.566465i 0.995275 0.0970929i \(-0.0309544\pi\)
0.748125 + 0.663558i \(0.230954\pi\)
\(338\) −19.7568 + 6.41937i −0.0584520 + 0.0189922i
\(339\) 138.057 100.304i 0.407247 0.295882i
\(340\) 25.2267i 0.0741961i
\(341\) −361.238 547.441i −1.05935 1.60540i
\(342\) −32.7572 −0.0957812
\(343\) −194.436 267.618i −0.566869 0.780228i
\(344\) −37.6857 115.985i −0.109551 0.337165i
\(345\) 1.26186 3.88359i 0.00365755 0.0112568i
\(346\) 99.2867 + 72.1360i 0.286956 + 0.208486i
\(347\) −118.221 + 162.717i −0.340694 + 0.468925i −0.944644 0.328097i \(-0.893593\pi\)
0.603950 + 0.797022i \(0.293593\pi\)
\(348\) −124.742 40.5312i −0.358454 0.116469i
\(349\) 461.013 149.792i 1.32095 0.429204i 0.438131 0.898911i \(-0.355640\pi\)
0.882822 + 0.469707i \(0.155640\pi\)
\(350\) −142.709 + 103.684i −0.407741 + 0.296241i
\(351\) 63.1836i 0.180010i
\(352\) −361.548 16.2945i −1.02712 0.0462911i
\(353\) 108.957 0.308661 0.154330 0.988019i \(-0.450678\pi\)
0.154330 + 0.988019i \(0.450678\pi\)
\(354\) −25.1135 34.5657i −0.0709420 0.0976433i
\(355\) 10.1633 + 31.2794i 0.0286290 + 0.0881109i
\(356\) 125.834 387.276i 0.353465 1.08785i
\(357\) −211.743 153.841i −0.593118 0.430926i
\(358\) −59.6196 + 82.0593i −0.166535 + 0.229216i
\(359\) −407.539 132.418i −1.13521 0.368851i −0.319655 0.947534i \(-0.603567\pi\)
−0.815553 + 0.578683i \(0.803567\pi\)
\(360\) −7.84056 + 2.54755i −0.0217793 + 0.00707654i
\(361\) −192.147 + 139.603i −0.532262 + 0.386711i
\(362\) 110.501i 0.305252i
\(363\) 46.5708 + 204.338i 0.128294 + 0.562916i
\(364\) 266.664 0.732594
\(365\) 10.8849 + 14.9818i 0.0298218 + 0.0410462i
\(366\) 17.5684 + 54.0700i 0.0480011 + 0.147732i
\(367\) 132.239 406.991i 0.360325 1.10897i −0.592532 0.805547i \(-0.701871\pi\)
0.952857 0.303420i \(-0.0981285\pi\)
\(368\) 25.6506 + 18.6362i 0.0697027 + 0.0506419i
\(369\) 91.7643 126.303i 0.248684 0.342284i
\(370\) −2.21691 0.720316i −0.00599164 0.00194680i
\(371\) 650.553 211.377i 1.75351 0.569751i
\(372\) 253.541 184.208i 0.681562 0.495184i
\(373\) 104.312i 0.279656i −0.990176 0.139828i \(-0.955345\pi\)
0.990176 0.139828i \(-0.0446549\pi\)
\(374\) 10.1750 225.767i 0.0272059 0.603654i
\(375\) 34.3222 0.0915259
\(376\) 224.917 + 309.571i 0.598182 + 0.823327i
\(377\) 93.7682 + 288.589i 0.248722 + 0.765488i
\(378\) 11.4018 35.0912i 0.0301635 0.0928338i
\(379\) −181.753 132.051i −0.479558 0.348420i 0.321596 0.946877i \(-0.395781\pi\)
−0.801155 + 0.598457i \(0.795781\pi\)
\(380\) 7.88054 10.8466i 0.0207383 0.0285438i
\(381\) 36.0196 + 11.7035i 0.0945397 + 0.0307178i
\(382\) −178.552 + 58.0152i −0.467415 + 0.151872i
\(383\) −47.9484 + 34.8366i −0.125192 + 0.0909571i −0.648619 0.761113i \(-0.724653\pi\)
0.523427 + 0.852070i \(0.324653\pi\)
\(384\) 209.328i 0.545124i
\(385\) 26.3796 17.4071i 0.0685186 0.0452131i
\(386\) −53.6068 −0.138878
\(387\) −31.1124 42.8226i −0.0803939 0.110653i
\(388\) 35.2648 + 108.534i 0.0908886 + 0.279726i
\(389\) −127.369 + 392.001i −0.327426 + 1.00771i 0.642908 + 0.765944i \(0.277728\pi\)
−0.970334 + 0.241770i \(0.922272\pi\)
\(390\) 6.65615 + 4.83598i 0.0170671 + 0.0123999i
\(391\) −72.8804 + 100.311i −0.186395 + 0.256550i
\(392\) −21.2119 6.89215i −0.0541119 0.0175820i
\(393\) 26.9484 8.75606i 0.0685710 0.0222801i
\(394\) 59.8531 43.4858i 0.151911 0.110370i
\(395\) 23.9814i 0.0607125i
\(396\) −96.5359 + 26.6258i −0.243777 + 0.0672368i
\(397\) 619.925 1.56152 0.780762 0.624829i \(-0.214831\pi\)
0.780762 + 0.624829i \(0.214831\pi\)
\(398\) 35.0678 + 48.2666i 0.0881100 + 0.121273i
\(399\) 42.9845 + 132.293i 0.107731 + 0.331561i
\(400\) −41.0450 + 126.323i −0.102612 + 0.315809i
\(401\) 543.725 + 395.039i 1.35592 + 0.985135i 0.998693 + 0.0511186i \(0.0162786\pi\)
0.357230 + 0.934017i \(0.383721\pi\)
\(402\) −94.6951 + 130.337i −0.235560 + 0.324220i
\(403\) −689.546 224.047i −1.71103 0.555948i
\(404\) −233.197 + 75.7702i −0.577219 + 0.187550i
\(405\) −2.89481 + 2.10320i −0.00714768 + 0.00519309i
\(406\) 177.199i 0.436450i
\(407\) −61.4483 23.0730i −0.150979 0.0566905i
\(408\) 250.326 0.613543
\(409\) −361.103 497.016i −0.882893 1.21520i −0.975611 0.219505i \(-0.929556\pi\)
0.0927184 0.995692i \(-0.470444\pi\)
\(410\) −6.28202 19.3341i −0.0153220 0.0471562i
\(411\) −16.3724 + 50.3890i −0.0398354 + 0.122601i
\(412\) −244.674 177.766i −0.593869 0.431471i
\(413\) −106.642 + 146.781i −0.258214 + 0.355401i
\(414\) −16.6241 5.40149i −0.0401548 0.0130471i
\(415\) 56.9721 18.5113i 0.137282 0.0446056i
\(416\) −323.663 + 235.155i −0.778037 + 0.565277i
\(417\) 48.0582i 0.115247i
\(418\) −74.9020 + 93.8936i −0.179191 + 0.224626i
\(419\) −60.9488 −0.145462 −0.0727312 0.997352i \(-0.523172\pi\)
−0.0727312 + 0.997352i \(0.523172\pi\)
\(420\) 8.87649 + 12.2174i 0.0211345 + 0.0290891i
\(421\) 64.4635 + 198.398i 0.153120 + 0.471255i 0.997966 0.0637555i \(-0.0203078\pi\)
−0.844846 + 0.535010i \(0.820308\pi\)
\(422\) 124.243 382.381i 0.294415 0.906116i
\(423\) 134.364 + 97.6209i 0.317645 + 0.230782i
\(424\) −384.546 + 529.282i −0.906948 + 1.24831i
\(425\) −494.011 160.514i −1.16238 0.377680i
\(426\) 133.894 43.5049i 0.314306 0.102124i
\(427\) 195.313 141.903i 0.457407 0.332326i
\(428\) 328.502i 0.767528i
\(429\) 181.106 + 144.475i 0.422160 + 0.336770i
\(430\) −6.89250 −0.0160291
\(431\) 159.126 + 219.018i 0.369202 + 0.508163i 0.952684 0.303963i \(-0.0983100\pi\)
−0.583482 + 0.812126i \(0.698310\pi\)
\(432\) −8.58532 26.4229i −0.0198734 0.0611641i
\(433\) −193.847 + 596.600i −0.447684 + 1.37783i 0.431830 + 0.901955i \(0.357868\pi\)
−0.879514 + 0.475873i \(0.842132\pi\)
\(434\) 342.532 + 248.864i 0.789245 + 0.573420i
\(435\) −10.1007 + 13.9024i −0.0232199 + 0.0319595i
\(436\) −506.345 164.521i −1.16134 0.377343i
\(437\) 62.6723 20.3635i 0.143415 0.0465983i
\(438\) 64.1312 46.5940i 0.146418 0.106379i
\(439\) 495.244i 1.12812i 0.825734 + 0.564060i \(0.190761\pi\)
−0.825734 + 0.564060i \(0.809239\pi\)
\(440\) −10.6259 + 28.2990i −0.0241498 + 0.0643159i
\(441\) −9.68041 −0.0219510
\(442\) −146.841 202.110i −0.332220 0.457262i
\(443\) 229.292 + 705.688i 0.517589 + 1.59298i 0.778521 + 0.627618i \(0.215970\pi\)
−0.260932 + 0.965357i \(0.584030\pi\)
\(444\) 9.69163 29.8278i 0.0218280 0.0671796i
\(445\) −43.1614 31.3586i −0.0969920 0.0704688i
\(446\) −85.0782 + 117.100i −0.190758 + 0.262556i
\(447\) 327.490 + 106.408i 0.732639 + 0.238049i
\(448\) 75.1966 24.4329i 0.167850 0.0545376i
\(449\) 577.287 419.423i 1.28572 0.934128i 0.286007 0.958227i \(-0.407672\pi\)
0.999710 + 0.0240995i \(0.00767186\pi\)
\(450\) 73.2267i 0.162726i
\(451\) −152.202 551.831i −0.337476 1.22357i
\(452\) 298.975 0.661449
\(453\) −132.866 182.875i −0.293303 0.403697i
\(454\) 41.6040 + 128.044i 0.0916388 + 0.282035i
\(455\) 10.7962 33.2273i 0.0237279 0.0730270i
\(456\) −107.632 78.1990i −0.236034 0.171489i
\(457\) −166.058 + 228.559i −0.363364 + 0.500128i −0.951082 0.308938i \(-0.900027\pi\)
0.587718 + 0.809066i \(0.300027\pi\)
\(458\) 80.0905 + 26.0230i 0.174870 + 0.0568187i
\(459\) 103.332 33.5745i 0.225123 0.0731470i
\(460\) 5.78789 4.20515i 0.0125824 0.00914162i
\(461\) 198.186i 0.429905i −0.976624 0.214953i \(-0.931040\pi\)
0.976624 0.214953i \(-0.0689597\pi\)
\(462\) −74.5125 112.921i −0.161283 0.244417i
\(463\) −226.915 −0.490097 −0.245049 0.969511i \(-0.578804\pi\)
−0.245049 + 0.969511i \(0.578804\pi\)
\(464\) −78.4263 107.945i −0.169022 0.232639i
\(465\) −12.6881 39.0500i −0.0272863 0.0839785i
\(466\) 65.7150 202.250i 0.141019 0.434013i
\(467\) −121.076 87.9672i −0.259264 0.188367i 0.450558 0.892747i \(-0.351225\pi\)
−0.709823 + 0.704380i \(0.751225\pi\)
\(468\) −65.0666 + 89.5564i −0.139031 + 0.191360i
\(469\) 650.636 + 211.404i 1.38728 + 0.450756i
\(470\) 20.5680 6.68295i 0.0437617 0.0142190i
\(471\) −98.9109 + 71.8630i −0.210002 + 0.152575i
\(472\) 173.526i 0.367640i
\(473\) −193.886 8.73818i −0.409907 0.0184740i
\(474\) −102.655 −0.216571
\(475\) 162.266 + 223.339i 0.341612 + 0.470188i
\(476\) −141.700 436.107i −0.297689 0.916192i
\(477\) −87.7472 + 270.058i −0.183956 + 0.566160i
\(478\) −131.354 95.4344i −0.274799 0.199653i
\(479\) 191.483 263.554i 0.399755 0.550216i −0.560927 0.827865i \(-0.689555\pi\)
0.960683 + 0.277649i \(0.0895552\pi\)
\(480\) −21.5477 7.00126i −0.0448910 0.0145860i
\(481\) −69.0060 + 22.4214i −0.143464 + 0.0466142i
\(482\) 185.865 135.039i 0.385613 0.280164i
\(483\) 74.2257i 0.153676i
\(484\) −144.418 + 337.588i −0.298385 + 0.697496i
\(485\) 14.9514 0.0308277
\(486\) 9.00295 + 12.3915i 0.0185246 + 0.0254969i
\(487\) −94.8447 291.902i −0.194753 0.599388i −0.999979 0.00642054i \(-0.997956\pi\)
0.805226 0.592967i \(-0.202044\pi\)
\(488\) −71.3524 + 219.600i −0.146214 + 0.450000i
\(489\) −107.771 78.2999i −0.220390 0.160123i
\(490\) −0.740925 + 1.01980i −0.00151209 + 0.00208121i
\(491\) −583.829 189.698i −1.18906 0.386349i −0.353335 0.935497i \(-0.614953\pi\)
−0.835726 + 0.549147i \(0.814953\pi\)
\(492\) 260.134 84.5225i 0.528727 0.171794i
\(493\) 422.137 306.700i 0.856261 0.622110i
\(494\) 132.772i 0.268770i
\(495\) −0.590701 + 13.1067i −0.00119334 + 0.0264782i
\(496\) 318.806 0.642754
\(497\) −351.397 483.656i −0.707035 0.973151i
\(498\) −79.2395 243.874i −0.159115 0.489707i
\(499\) 126.532 389.425i 0.253571 0.780412i −0.740537 0.672016i \(-0.765429\pi\)
0.994108 0.108396i \(-0.0345714\pi\)
\(500\) 48.6483 + 35.3451i 0.0972966 + 0.0706901i
\(501\) −103.597 + 142.589i −0.206780 + 0.284609i
\(502\) 249.863 + 81.1853i 0.497734 + 0.161724i
\(503\) 673.153 218.721i 1.33828 0.434832i 0.449543 0.893259i \(-0.351587\pi\)
0.888732 + 0.458426i \(0.151587\pi\)
\(504\) 121.234 88.0819i 0.240544 0.174766i
\(505\) 32.1248i 0.0636134i
\(506\) −53.4949 + 35.2995i −0.105721 + 0.0697619i
\(507\) −36.6191 −0.0722270
\(508\) 39.0019 + 53.6816i 0.0767755 + 0.105672i
\(509\) 63.6414 + 195.868i 0.125032 + 0.384810i 0.993907 0.110222i \(-0.0351563\pi\)
−0.868875 + 0.495032i \(0.835156\pi\)
\(510\) 4.37190 13.4553i 0.00857236 0.0263830i
\(511\) −272.328 197.858i −0.532932 0.387197i
\(512\) 190.291 261.913i 0.371662 0.511549i
\(513\) −54.9174 17.8438i −0.107052 0.0347832i
\(514\) −46.2691 + 15.0337i −0.0900177 + 0.0292485i
\(515\) −32.0562 + 23.2902i −0.0622450 + 0.0452237i
\(516\) 92.7364i 0.179722i
\(517\) 587.050 161.915i 1.13549 0.313183i
\(518\) 42.3709 0.0817971
\(519\) 127.160 + 175.020i 0.245009 + 0.337226i
\(520\) 10.3258 + 31.7796i 0.0198573 + 0.0611146i
\(521\) −102.734 + 316.183i −0.197186 + 0.606877i 0.802758 + 0.596305i \(0.203365\pi\)
−0.999944 + 0.0105716i \(0.996635\pi\)
\(522\) 59.5104 + 43.2368i 0.114005 + 0.0828291i
\(523\) 183.858 253.058i 0.351544 0.483859i −0.596225 0.802818i \(-0.703333\pi\)
0.947769 + 0.318959i \(0.103333\pi\)
\(524\) 47.2137 + 15.3406i 0.0901024 + 0.0292760i
\(525\) −295.733 + 96.0893i −0.563300 + 0.183027i
\(526\) −157.999 + 114.793i −0.300379 + 0.218238i
\(527\) 1246.75i 2.36575i
\(528\) −95.3684 35.8096i −0.180622 0.0678212i
\(529\) −493.836 −0.933528
\(530\) 21.7336 + 29.9137i 0.0410067 + 0.0564409i
\(531\) −23.2738 71.6295i −0.0438302 0.134896i
\(532\) −75.3090 + 231.777i −0.141558 + 0.435671i
\(533\) −511.934 371.942i −0.960477 0.697827i
\(534\) −134.233 + 184.757i −0.251374 + 0.345986i
\(535\) −40.9325 13.2998i −0.0765094 0.0248594i
\(536\) −622.288 + 202.194i −1.16098 + 0.377227i
\(537\) −144.652 + 105.096i −0.269371 + 0.195710i
\(538\) 10.5851i 0.0196750i
\(539\) −22.1351 + 27.7475i −0.0410669 + 0.0514796i
\(540\) −6.26898 −0.0116092
\(541\) 35.8960 + 49.4065i 0.0663511 + 0.0913245i 0.840903 0.541186i \(-0.182025\pi\)
−0.774552 + 0.632510i \(0.782025\pi\)
\(542\) −88.7288 273.079i −0.163706 0.503836i
\(543\) 60.1932 185.256i 0.110853 0.341171i
\(544\) 556.565 + 404.368i 1.02310 + 0.743324i
\(545\) −40.9999 + 56.4315i −0.0752292 + 0.103544i
\(546\) −142.233 46.2142i −0.260499 0.0846413i
\(547\) 543.135 176.475i 0.992933 0.322624i 0.232895 0.972502i \(-0.425180\pi\)
0.760038 + 0.649878i \(0.225180\pi\)
\(548\) −75.0968 + 54.5610i −0.137038 + 0.0995639i
\(549\) 100.218i 0.182547i
\(550\) −209.894 167.439i −0.381625 0.304435i
\(551\) −277.315 −0.503294
\(552\) −41.7279 57.4335i −0.0755940 0.104046i
\(553\) 134.705 + 414.580i 0.243590 + 0.749692i
\(554\) −53.2463 + 163.875i −0.0961125 + 0.295804i
\(555\) −3.32427 2.41522i −0.00598967 0.00435175i
\(556\) −49.4904 + 68.1177i −0.0890115 + 0.122514i
\(557\) 669.660 + 217.586i 1.20226 + 0.390638i 0.840592 0.541668i \(-0.182207\pi\)
0.361669 + 0.932307i \(0.382207\pi\)
\(558\) −167.157 + 54.3127i −0.299565 + 0.0973345i
\(559\) −173.570 + 126.106i −0.310501 + 0.225592i
\(560\) 15.3624i 0.0274328i
\(561\) 140.040 372.955i 0.249625 0.664805i
\(562\) −223.417 −0.397539
\(563\) −296.842 408.568i −0.527251 0.725699i 0.459457 0.888200i \(-0.348044\pi\)
−0.986708 + 0.162501i \(0.948044\pi\)
\(564\) 89.9169 + 276.736i 0.159427 + 0.490666i
\(565\) 12.1044 37.2534i 0.0214236 0.0659351i
\(566\) 188.749 + 137.135i 0.333480 + 0.242287i
\(567\) 38.2303 52.6195i 0.0674256 0.0928034i
\(568\) 543.799 + 176.691i 0.957392 + 0.311076i
\(569\) −640.526 + 208.120i −1.12570 + 0.365764i −0.811942 0.583738i \(-0.801590\pi\)
−0.313763 + 0.949501i \(0.601590\pi\)
\(570\) −6.08307 + 4.41961i −0.0106721 + 0.00775371i
\(571\) 446.598i 0.782134i −0.920362 0.391067i \(-0.872106\pi\)
0.920362 0.391067i \(-0.127894\pi\)
\(572\) 107.920 + 391.282i 0.188672 + 0.684059i
\(573\) −330.946 −0.577567
\(574\) 217.201 + 298.952i 0.378399 + 0.520822i
\(575\) 45.5213 + 140.100i 0.0791675 + 0.243653i
\(576\) −10.1426 + 31.2157i −0.0176087 + 0.0541939i
\(577\) 466.552 + 338.970i 0.808583 + 0.587470i 0.913419 0.407020i \(-0.133432\pi\)
−0.104837 + 0.994489i \(0.533432\pi\)
\(578\) −85.5967 + 117.814i −0.148091 + 0.203830i
\(579\) −89.8718 29.2011i −0.155219 0.0504337i
\(580\) −28.6334 + 9.30354i −0.0493679 + 0.0160406i
\(581\) −880.928 + 640.031i −1.51623 + 1.10160i
\(582\) 64.0010i 0.109967i
\(583\) 573.441 + 869.025i 0.983603 + 1.49061i
\(584\) 321.949 0.551283
\(585\) 8.52476 + 11.7333i 0.0145722 + 0.0200570i
\(586\) −8.90662 27.4118i −0.0151990 0.0467777i
\(587\) 280.070 861.968i 0.477122 1.46843i −0.365953 0.930633i \(-0.619257\pi\)
0.843075 0.537796i \(-0.180743\pi\)
\(588\) −13.7210 9.96891i −0.0233351 0.0169539i
\(589\) 389.471 536.061i 0.661241 0.910121i
\(590\) −9.32725 3.03061i −0.0158089 0.00513662i
\(591\) 124.032 40.3004i 0.209868 0.0681901i
\(592\) 25.8112 18.7529i 0.0436000 0.0316772i
\(593\) 724.877i 1.22239i −0.791480 0.611195i \(-0.790689\pi\)
0.791480 0.611195i \(-0.209311\pi\)
\(594\) 56.1044 + 2.52855i 0.0944518 + 0.00425682i
\(595\) −60.0774 −0.100970
\(596\) 354.605 + 488.072i 0.594975 + 0.818912i
\(597\) 32.4990 + 100.022i 0.0544371 + 0.167540i
\(598\) −21.8935 + 67.3812i −0.0366112 + 0.112678i
\(599\) −322.233 234.116i −0.537951 0.390844i 0.285373 0.958417i \(-0.407883\pi\)
−0.823323 + 0.567572i \(0.807883\pi\)
\(600\) 174.809 240.604i 0.291349 0.401007i
\(601\) −937.236 304.526i −1.55946 0.506700i −0.602797 0.797894i \(-0.705947\pi\)
−0.956664 + 0.291195i \(0.905947\pi\)
\(602\) 119.154 38.7156i 0.197931 0.0643117i
\(603\) −229.754 + 166.926i −0.381019 + 0.276826i
\(604\) 396.032i 0.655682i
\(605\) 36.2177 + 31.6627i 0.0598640 + 0.0523350i
\(606\) 137.513 0.226919
\(607\) −105.195 144.789i −0.173304 0.238532i 0.713526 0.700629i \(-0.247097\pi\)
−0.886829 + 0.462097i \(0.847097\pi\)
\(608\) −112.984 347.730i −0.185829 0.571924i
\(609\) 96.5252 297.074i 0.158498 0.487806i
\(610\) 10.5576 + 7.67057i 0.0173076 + 0.0125747i
\(611\) 395.680 544.607i 0.647594 0.891336i
\(612\) 181.037 + 58.8225i 0.295812 + 0.0961153i
\(613\) −1008.97 + 327.833i −1.64595 + 0.534800i −0.977856 0.209280i \(-0.932888\pi\)
−0.668090 + 0.744080i \(0.732888\pi\)
\(614\) 276.099 200.597i 0.449672 0.326706i
\(615\) 35.8356i 0.0582692i
\(616\) 24.7385 548.907i 0.0401599 0.891082i
\(617\) 55.3570 0.0897196 0.0448598 0.998993i \(-0.485716\pi\)
0.0448598 + 0.998993i \(0.485716\pi\)
\(618\) 99.6958 + 137.220i 0.161320 + 0.222038i
\(619\) −232.546 715.704i −0.375681 1.15623i −0.943018 0.332741i \(-0.892027\pi\)
0.567338 0.823485i \(-0.307973\pi\)
\(620\) 22.2296 68.4157i 0.0358542 0.110348i
\(621\) −24.9280 18.1112i −0.0401416 0.0291646i
\(622\) 254.447 350.217i 0.409079 0.563049i
\(623\) 922.299 + 299.673i 1.48042 + 0.481016i
\(624\) −107.098 + 34.7983i −0.171632 + 0.0557665i
\(625\) −496.065 + 360.412i −0.793704 + 0.576660i
\(626\) 25.0206i 0.0399690i
\(627\) −176.720 + 116.612i −0.281850 + 0.185983i
\(628\) −214.201 −0.341084
\(629\) 73.3367 + 100.939i 0.116593 + 0.160476i
\(630\) −2.61718 8.05484i −0.00415425 0.0127855i
\(631\) −103.743 + 319.289i −0.164411 + 0.506005i −0.998992 0.0448799i \(-0.985709\pi\)
0.834582 + 0.550884i \(0.185709\pi\)
\(632\) −337.297 245.061i −0.533698 0.387754i
\(633\) 416.588 573.384i 0.658116 0.905819i
\(634\) 85.3961 + 27.7469i 0.134694 + 0.0437648i
\(635\) 8.26796 2.68642i 0.0130204 0.00423059i
\(636\) −402.479 + 292.418i −0.632829 + 0.459777i
\(637\) 39.2369i 0.0615964i
\(638\) 260.007 71.7132i 0.407535 0.112403i
\(639\) 248.172 0.388376
\(640\) −28.2426 38.8726i −0.0441290 0.0607384i
\(641\) −170.606 525.071i −0.266156 0.819144i −0.991425 0.130678i \(-0.958285\pi\)
0.725269 0.688466i \(-0.241715\pi\)
\(642\) −56.9309 + 175.215i −0.0886775 + 0.272921i
\(643\) 111.934 + 81.3249i 0.174081 + 0.126477i 0.671414 0.741082i \(-0.265687\pi\)
−0.497333 + 0.867560i \(0.665687\pi\)
\(644\) −76.4378 + 105.208i −0.118692 + 0.163366i
\(645\) −11.5553 3.75454i −0.0179152 0.00582099i
\(646\) 217.138 70.5525i 0.336127 0.109214i
\(647\) 819.415 595.340i 1.26648 0.920154i 0.267427 0.963578i \(-0.413827\pi\)
0.999057 + 0.0434241i \(0.0138267\pi\)
\(648\) 62.2074i 0.0959991i
\(649\) −258.533 97.0758i −0.398356 0.149578i
\(650\) −296.805 −0.456623
\(651\) 438.693 + 603.809i 0.673875 + 0.927510i
\(652\) −72.1207 221.965i −0.110615 0.340437i
\(653\) −2.38169 + 7.33010i −0.00364731 + 0.0112253i −0.952864 0.303399i \(-0.901879\pi\)
0.949216 + 0.314624i \(0.101879\pi\)
\(654\) 241.560 + 175.504i 0.369358 + 0.268354i
\(655\) 3.82300 5.26191i 0.00583664 0.00803345i
\(656\) 264.626 + 85.9822i 0.403393 + 0.131070i
\(657\) 132.897 43.1809i 0.202279 0.0657243i
\(658\) −318.032 + 231.063i −0.483331 + 0.351160i
\(659\) 736.073i 1.11695i 0.829520 + 0.558477i \(0.188614\pi\)
−0.829520 + 0.558477i \(0.811386\pi\)
\(660\) −14.3346 + 17.9691i −0.0217190 + 0.0272259i
\(661\) −471.170 −0.712813 −0.356407 0.934331i \(-0.615998\pi\)
−0.356407 + 0.934331i \(0.615998\pi\)
\(662\) 184.097 + 253.388i 0.278092 + 0.382761i
\(663\) −136.085 418.826i −0.205256 0.631714i
\(664\) 321.824 990.472i 0.484674 1.49167i
\(665\) 25.8313 + 18.7675i 0.0388441 + 0.0282219i
\(666\) −10.3386 + 14.2298i −0.0155234 + 0.0213661i
\(667\) −140.736 45.7278i −0.210998 0.0685574i
\(668\) −293.677 + 95.4213i −0.439635 + 0.142846i
\(669\) −206.422 + 149.974i −0.308552 + 0.224176i
\(670\) 36.9801i 0.0551941i
\(671\) 287.262 + 229.158i 0.428110 + 0.341517i
\(672\) 411.833 0.612846
\(673\) 676.225 + 930.745i 1.00479 + 1.38298i 0.922338 + 0.386384i \(0.126276\pi\)
0.0824545 + 0.996595i \(0.473724\pi\)
\(674\) −187.571 577.285i −0.278295 0.856505i
\(675\) 39.8887 122.765i 0.0590943 0.181874i
\(676\) −51.9039 37.7104i −0.0767809 0.0557846i
\(677\) −689.120 + 948.493i −1.01790 + 1.40102i −0.104239 + 0.994552i \(0.533241\pi\)
−0.913664 + 0.406471i \(0.866759\pi\)
\(678\) −159.466 51.8138i −0.235201 0.0764215i
\(679\) −258.474 + 83.9832i −0.380668 + 0.123687i
\(680\) 46.4860 33.7740i 0.0683617 0.0496677i
\(681\) 237.329i 0.348501i
\(682\) −226.539 + 603.322i −0.332169 + 0.884636i
\(683\) −329.083 −0.481820 −0.240910 0.970547i \(-0.577446\pi\)
−0.240910 + 0.970547i \(0.577446\pi\)
\(684\) −59.4645 81.8458i −0.0869364 0.119658i
\(685\) 3.75812 + 11.5663i 0.00548631 + 0.0168851i
\(686\) −100.439 + 309.120i −0.146413 + 0.450612i
\(687\) 120.096 + 87.2551i 0.174813 + 0.127009i
\(688\) 55.4505 76.3210i 0.0805966 0.110932i
\(689\) 1094.61 + 355.659i 1.58869 + 0.516197i
\(690\) −3.81590 + 1.23986i −0.00553029 + 0.00179690i
\(691\) −581.750 + 422.666i −0.841896 + 0.611674i −0.922900 0.385040i \(-0.874188\pi\)
0.0810034 + 0.996714i \(0.474188\pi\)
\(692\) 379.023i 0.547722i
\(693\) −63.4093 229.901i −0.0914998 0.331747i
\(694\) 197.623 0.284760
\(695\) 6.48403 + 8.92451i 0.00932955 + 0.0128410i
\(696\) 92.3195 + 284.130i 0.132643 + 0.408233i
\(697\) −336.249 + 1034.87i −0.482423 + 1.48475i
\(698\) −385.325 279.955i −0.552042 0.401082i
\(699\) 220.343 303.275i 0.315225 0.433870i
\(700\) −518.124 168.349i −0.740178 0.240498i
\(701\) 95.7601 31.1144i 0.136605 0.0443857i −0.239917 0.970794i \(-0.577120\pi\)
0.376522 + 0.926408i \(0.377120\pi\)
\(702\) 50.2256 36.4910i 0.0715464 0.0519815i
\(703\) 66.3102i 0.0943246i
\(704\) 66.2833 + 100.449i 0.0941524 + 0.142684i
\(705\) 38.1227 0.0540747
\(706\) −62.9271 86.6118i −0.0891319 0.122680i
\(707\) −180.447 555.358i −0.255229 0.785514i
\(708\) 40.7759 125.495i 0.0575930 0.177253i
\(709\) −222.948 161.981i −0.314454 0.228464i 0.419351 0.907824i \(-0.362258\pi\)
−0.733805 + 0.679360i \(0.762258\pi\)
\(710\) 18.9947 26.1440i 0.0267532 0.0368226i
\(711\) −172.101 55.9189i −0.242055 0.0786483i
\(712\) −882.114 + 286.616i −1.23892 + 0.402551i
\(713\) 286.048 207.826i 0.401190 0.291481i
\(714\) 257.167i 0.360178i
\(715\) 53.1244 + 2.39425i 0.0742999 + 0.00334860i
\(716\) −313.258 −0.437512
\(717\) −168.230 231.548i −0.234630 0.322940i
\(718\) 130.109 + 400.435i 0.181211 + 0.557710i
\(719\) 28.6486 88.1712i 0.0398450 0.122630i −0.929155 0.369689i \(-0.879464\pi\)
0.969000 + 0.247059i \(0.0794641\pi\)
\(720\) −5.15930 3.74845i −0.00716570 0.00520618i
\(721\) 423.350 582.692i 0.587171 0.808172i
\(722\) 221.945 + 72.1142i 0.307403 + 0.0998811i
\(723\) 385.163 125.147i 0.532729 0.173094i
\(724\) 276.095 200.594i 0.381346 0.277064i
\(725\) 619.921i 0.855063i
\(726\) 135.535 155.033i 0.186687 0.213544i
\(727\) 40.4150 0.0555915 0.0277958 0.999614i \(-0.491151\pi\)
0.0277958 + 0.999614i \(0.491151\pi\)
\(728\) −357.016 491.390i −0.490406 0.674987i
\(729\) 8.34346 + 25.6785i 0.0114451 + 0.0352243i
\(730\) 5.62280 17.3052i 0.00770247 0.0237058i
\(731\) 298.467 + 216.849i 0.408300 + 0.296647i
\(732\) −103.205 + 142.050i −0.140991 + 0.194057i
\(733\) 679.400 + 220.751i 0.926876 + 0.301160i 0.733285 0.679922i \(-0.237986\pi\)
0.193592 + 0.981082i \(0.437986\pi\)
\(734\) −399.897 + 129.934i −0.544818 + 0.177022i
\(735\) −1.79767 + 1.30609i −0.00244581 + 0.00177699i
\(736\) 195.102i 0.265084i
\(737\) −46.8826 + 1040.25i −0.0636128 + 1.41146i
\(738\) −153.397 −0.207856
\(739\) −30.3170 41.7277i −0.0410243 0.0564651i 0.788012 0.615660i \(-0.211110\pi\)
−0.829036 + 0.559195i \(0.811110\pi\)
\(740\) −2.22462 6.84667i −0.00300624 0.00925226i
\(741\) −72.3248 + 222.593i −0.0976044 + 0.300395i
\(742\) −543.747 395.055i −0.732813 0.532420i
\(743\) −528.170 + 726.964i −0.710862 + 0.978418i 0.288916 + 0.957354i \(0.406705\pi\)
−0.999778 + 0.0210631i \(0.993295\pi\)
\(744\) −678.893 220.586i −0.912490 0.296486i
\(745\) 75.1721 24.4249i 0.100902 0.0327851i
\(746\) −82.9189 + 60.2441i −0.111151 + 0.0807562i
\(747\) 452.019i 0.605113i
\(748\) 582.563 384.414i 0.778827 0.513922i
\(749\) 782.328 1.04450
\(750\) −19.8224 27.2832i −0.0264299 0.0363776i
\(751\) 105.701 + 325.316i 0.140748 + 0.433177i 0.996440 0.0843087i \(-0.0268682\pi\)
−0.855692 + 0.517485i \(0.826868\pi\)
\(752\) −91.4698 + 281.515i −0.121635 + 0.374355i
\(753\) 374.671 + 272.215i 0.497571 + 0.361507i
\(754\) 175.249 241.209i 0.232425 0.319906i
\(755\) −49.3470 16.0338i −0.0653603 0.0212369i
\(756\) 108.375 35.2133i 0.143354 0.0465784i
\(757\) 653.654 474.907i 0.863479 0.627354i −0.0653503 0.997862i \(-0.520816\pi\)
0.928829 + 0.370508i \(0.120816\pi\)
\(758\) 220.743i 0.291217i
\(759\) −108.913 + 30.0395i −0.143495 + 0.0395778i
\(760\) −30.5381 −0.0401817
\(761\) −459.858 632.941i −0.604282 0.831722i 0.391810 0.920046i \(-0.371849\pi\)
−0.996092 + 0.0883239i \(0.971849\pi\)
\(762\) −11.4995 35.3917i −0.0150912 0.0464459i
\(763\) 391.808 1205.86i 0.513510 1.58042i
\(764\) −469.083 340.809i −0.613983 0.446085i
\(765\) 14.6590 20.1764i 0.0191621 0.0263744i
\(766\) 55.3842 + 17.9954i 0.0723032 + 0.0234927i
\(767\) −290.331 + 94.3342i −0.378528 + 0.122991i
\(768\) −227.721 + 165.449i −0.296511 + 0.215428i
\(769\) 652.678i 0.848736i 0.905490 + 0.424368i \(0.139504\pi\)
−0.905490 + 0.424368i \(0.860496\pi\)
\(770\) −29.0724 10.9163i −0.0377564 0.0141770i
\(771\) −85.7595 −0.111232
\(772\) −97.3130 133.940i −0.126053 0.173497i
\(773\) −267.215 822.403i −0.345686 1.06391i −0.961216 0.275797i \(-0.911058\pi\)
0.615530 0.788113i \(-0.288942\pi\)
\(774\) −16.0717 + 49.4635i −0.0207644 + 0.0639063i
\(775\) 1198.33 + 870.640i 1.54624 + 1.12341i
\(776\) 152.785 210.291i 0.196888 0.270994i
\(777\) 71.0349 + 23.0806i 0.0914220 + 0.0297048i
\(778\) 385.167 125.148i 0.495074 0.160859i
\(779\) 467.858 339.919i 0.600588 0.436352i
\(780\) 25.4096i 0.0325764i
\(781\) 567.467 711.350i 0.726590 0.910819i
\(782\) 121.830 0.155793
\(783\) 76.2169 + 104.904i 0.0973396 + 0.133976i
\(784\) −5.33147 16.4086i −0.00680035 0.0209293i
\(785\) −8.67218 + 26.6902i −0.0110474 + 0.0340003i
\(786\) −22.5241 16.3647i −0.0286566 0.0208202i
\(787\) −256.642 + 353.238i −0.326102 + 0.448841i −0.940318 0.340297i \(-0.889472\pi\)
0.614216 + 0.789138i \(0.289472\pi\)
\(788\) 217.304 + 70.6063i 0.275766 + 0.0896020i
\(789\) −327.418 + 106.384i −0.414978 + 0.134835i
\(790\) −19.0632 + 13.8502i −0.0241306 + 0.0175319i
\(791\) 712.010i 0.900139i
\(792\) 178.309 + 142.242i 0.225137 + 0.179599i
\(793\) 406.208 0.512243
\(794\) −358.031 492.787i −0.450921 0.620639i
\(795\) 20.1415 + 61.9892i 0.0253353 + 0.0779739i
\(796\) −56.9383 + 175.238i −0.0715305 + 0.220148i
\(797\) −366.573 266.331i −0.459941 0.334167i 0.333567 0.942726i \(-0.391748\pi\)
−0.793508 + 0.608560i \(0.791748\pi\)
\(798\) 80.3362 110.573i 0.100672 0.138563i
\(799\) −1100.92 357.709i −1.37787 0.447696i
\(800\) 777.330 252.570i 0.971662 0.315712i
\(801\) −325.685 + 236.624i −0.406598 + 0.295411i
\(802\) 660.366i 0.823399i
\(803\) 180.109 479.667i 0.224295 0.597343i
\(804\) −497.555 −0.618850
\(805\) 10.0146 + 13.7839i 0.0124405 + 0.0171228i
\(806\) 220.142 + 677.526i 0.273129 + 0.840603i
\(807\) −5.76603 + 17.7460i −0.00714501 + 0.0219901i
\(808\) 451.833 + 328.276i 0.559199 + 0.406282i
\(809\) 67.7382 93.2336i 0.0837307 0.115245i −0.765097 0.643915i \(-0.777309\pi\)
0.848828 + 0.528670i \(0.177309\pi\)
\(810\) 3.34373 + 1.08644i 0.00412806 + 0.00134129i
\(811\) 31.6398 10.2804i 0.0390134 0.0126762i −0.289445 0.957195i \(-0.593471\pi\)
0.328459 + 0.944518i \(0.393471\pi\)
\(812\) 442.742 321.671i 0.545249 0.396146i
\(813\) 506.151i 0.622571i
\(814\) 17.1477 + 62.1717i 0.0210660 + 0.0763781i
\(815\) −30.5775 −0.0375184
\(816\) 113.819 + 156.659i 0.139485 + 0.191984i
\(817\) −60.5897 186.476i −0.0741612 0.228245i
\(818\) −186.534 + 574.093i −0.228037 + 0.701825i
\(819\) −213.279 154.956i −0.260414 0.189202i
\(820\) 36.9035 50.7934i 0.0450043 0.0619431i
\(821\) −680.061 220.965i −0.828332 0.269141i −0.135990 0.990710i \(-0.543421\pi\)
−0.692343 + 0.721569i \(0.743421\pi\)
\(822\) 49.5106 16.0870i 0.0602319 0.0195705i
\(823\) 127.047 92.3053i 0.154371 0.112157i −0.507918 0.861405i \(-0.669585\pi\)
0.662290 + 0.749248i \(0.269585\pi\)
\(824\) 688.866i 0.836002i
\(825\) −260.678 395.047i −0.315974 0.478845i
\(826\) 178.268 0.215821
\(827\) −502.151 691.151i −0.607195 0.835733i 0.389148 0.921175i \(-0.372770\pi\)
−0.996343 + 0.0854425i \(0.972770\pi\)
\(828\) −16.6819 51.3417i −0.0201473 0.0620069i
\(829\) −424.643 + 1306.92i −0.512235 + 1.57650i 0.276023 + 0.961151i \(0.410983\pi\)
−0.788258 + 0.615345i \(0.789017\pi\)
\(830\) −47.6186 34.5969i −0.0573718 0.0416830i
\(831\) −178.535 + 245.732i −0.214844 + 0.295707i
\(832\) 126.524 + 41.1102i 0.152072 + 0.0494113i
\(833\) 64.1688 20.8497i 0.0770333 0.0250296i
\(834\) 38.2022 27.7555i 0.0458060 0.0332800i
\(835\) 40.4564i 0.0484508i
\(836\) −370.570 16.7011i −0.443265 0.0199774i
\(837\) −309.825 −0.370161
\(838\) 35.2003 + 48.4491i 0.0420052 + 0.0578151i
\(839\) 201.645 + 620.599i 0.240339 + 0.739689i 0.996368 + 0.0851502i \(0.0271370\pi\)
−0.756029 + 0.654538i \(0.772863\pi\)
\(840\) 10.6294 32.7140i 0.0126541 0.0389452i
\(841\) −176.582 128.294i −0.209967 0.152550i
\(842\) 120.479 165.826i 0.143087 0.196943i
\(843\) −374.559 121.702i −0.444317 0.144367i
\(844\) 1180.94 383.712i 1.39922 0.454635i
\(845\) −6.80024 + 4.94066i −0.00804762 + 0.00584694i
\(846\) 163.188i 0.192893i
\(847\) −803.967 343.933i −0.949193 0.406060i
\(848\) −506.083 −0.596796
\(849\) 241.738 + 332.723i 0.284732 + 0.391900i
\(850\) 157.716 + 485.400i 0.185548 + 0.571058i
\(851\) 10.9342 33.6521i 0.0128487 0.0395441i
\(852\) 351.760 + 255.568i 0.412863 + 0.299963i
\(853\) −778.060 + 1070.91i −0.912145 + 1.25546i 0.0542838 + 0.998526i \(0.482712\pi\)
−0.966429 + 0.256934i \(0.917288\pi\)
\(854\) −225.602 73.3025i −0.264171 0.0858343i
\(855\) −12.6058 + 4.09586i −0.0147436 + 0.00479048i
\(856\) −605.340 + 439.806i −0.707173 + 0.513792i
\(857\) 38.8452i 0.0453269i 0.999743 + 0.0226634i \(0.00721462\pi\)
−0.999743 + 0.0226634i \(0.992785\pi\)
\(858\) 10.2488 227.404i 0.0119450 0.265040i
\(859\) 227.261 0.264564 0.132282 0.991212i \(-0.457770\pi\)
0.132282 + 0.991212i \(0.457770\pi\)
\(860\) −12.5120 17.2213i −0.0145489 0.0200248i
\(861\) 201.291 + 619.509i 0.233787 + 0.719523i
\(862\) 82.1993 252.983i 0.0953588 0.293484i
\(863\) −774.412 562.643i −0.897348 0.651962i 0.0404352 0.999182i \(-0.487126\pi\)
−0.937784 + 0.347220i \(0.887126\pi\)
\(864\) −100.488 + 138.310i −0.116306 + 0.160081i
\(865\) 47.2277 + 15.3452i 0.0545985 + 0.0177401i
\(866\) 586.200 190.468i 0.676906 0.219940i
\(867\) −207.679 + 150.888i −0.239538 + 0.174035i
\(868\) 1307.61i 1.50646i
\(869\) −553.806 + 365.438i −0.637291 + 0.420527i
\(870\) 16.8847 0.0194077
\(871\) 676.591 + 931.247i 0.776798 + 1.06917i
\(872\) 374.737 + 1153.32i 0.429744 + 1.32262i
\(873\) 34.8632 107.298i 0.0399349 0.122907i
\(874\) −52.3829 38.0584i −0.0599347 0.0435451i
\(875\) −84.1744 + 115.856i −0.0961993 + 0.132407i
\(876\) 232.836 + 75.6531i 0.265795 + 0.0863619i
\(877\) 1145.02 372.039i 1.30561 0.424218i 0.428079 0.903741i \(-0.359190\pi\)
0.877529 + 0.479523i \(0.159190\pi\)
\(878\) 393.677 286.023i 0.448379 0.325767i
\(879\) 50.8075i 0.0578015i
\(880\) −22.5416 + 6.21724i −0.0256154 + 0.00706504i
\(881\) 1170.77 1.32892 0.664458 0.747326i \(-0.268663\pi\)
0.664458 + 0.747326i \(0.268663\pi\)
\(882\) 5.59082 + 7.69510i 0.00633880 + 0.00872461i
\(883\) 112.550 + 346.392i 0.127463 + 0.392290i 0.994342 0.106229i \(-0.0338775\pi\)
−0.866879 + 0.498519i \(0.833878\pi\)
\(884\) 238.421 733.785i 0.269707 0.830074i
\(885\) −13.9863 10.1616i −0.0158037 0.0114821i
\(886\) 428.537 589.830i 0.483676 0.665723i
\(887\) −270.792 87.9858i −0.305290 0.0991948i 0.152366 0.988324i \(-0.451311\pi\)
−0.457656 + 0.889129i \(0.651311\pi\)
\(888\) −67.9399 + 22.0750i −0.0765089 + 0.0248592i
\(889\) −127.843 + 92.8833i −0.143805 + 0.104481i
\(890\) 52.4205i 0.0588995i
\(891\) 92.6817 + 34.8008i 0.104020 + 0.0390581i
\(892\) −447.025 −0.501150
\(893\) 361.613 + 497.717i 0.404941 + 0.557354i
\(894\) −104.553 321.781i −0.116950 0.359934i
\(895\) −12.6826 + 39.0331i −0.0141705 + 0.0436124i
\(896\) 706.594 + 513.371i 0.788610 + 0.572959i
\(897\) −73.4089 + 101.039i −0.0818383 + 0.112641i
\(898\) −666.812 216.660i −0.742552 0.241270i
\(899\) −1415.11 + 459.799i −1.57410 + 0.511456i
\(900\) 182.962 132.929i 0.203291 0.147699i
\(901\) 1979.13i 2.19659i
\(902\) −350.756 + 439.691i −0.388865 + 0.487463i
\(903\) 220.852 0.244576
\(904\) −400.274 550.931i −0.442781 0.609436i
\(905\) −13.8168 42.5237i −0.0152672 0.0469875i
\(906\) −68.6343 + 211.235i −0.0757552 + 0.233151i
\(907\) −612.207 444.795i −0.674981 0.490402i 0.196708 0.980462i \(-0.436975\pi\)
−0.871689 + 0.490060i \(0.836975\pi\)
\(908\) −244.402 + 336.390i −0.269165 + 0.370474i
\(909\) 230.541 + 74.9073i 0.253620 + 0.0824062i
\(910\) −32.6481 + 10.6080i −0.0358770 + 0.0116572i
\(911\) 533.420 387.552i 0.585532 0.425414i −0.255182 0.966893i \(-0.582135\pi\)
0.840714 + 0.541479i \(0.182135\pi\)
\(912\) 102.914i 0.112844i
\(913\) −1295.65 1033.58i −1.41911 1.13207i
\(914\) 277.589 0.303708
\(915\) 13.5215 + 18.6108i 0.0147776 + 0.0203396i
\(916\) 80.3692 + 247.351i 0.0877393 + 0.270034i
\(917\) −36.5338 + 112.439i −0.0398406 + 0.122617i
\(918\) −86.3669 62.7492i −0.0940816 0.0683542i
\(919\) −439.038 + 604.284i −0.477735 + 0.657545i −0.978068 0.208288i \(-0.933211\pi\)
0.500333 + 0.865833i \(0.333211\pi\)
\(920\) −15.4979 5.03557i −0.0168456 0.00547345i
\(921\) 572.151 185.903i 0.621228 0.201849i
\(922\) −157.541 + 114.460i −0.170869 + 0.124144i
\(923\) 1005.90i 1.08981i
\(924\) 146.875 391.160i 0.158956 0.423333i
\(925\) 148.233 0.160251
\(926\) 131.052 + 180.378i 0.141525 + 0.194793i
\(927\) 92.3928 + 284.356i 0.0996686 + 0.306749i
\(928\) −253.715 + 780.855i −0.273400 + 0.841439i
\(929\) 981.029 + 712.759i 1.05601 + 0.767233i 0.973345 0.229345i \(-0.0736584\pi\)
0.0826603 + 0.996578i \(0.473658\pi\)
\(930\) −23.7135 + 32.6389i −0.0254984 + 0.0350956i
\(931\) −34.1037 11.0810i −0.0366312 0.0119022i
\(932\) 624.627 202.954i 0.670201 0.217761i
\(933\) 617.354 448.534i 0.661687 0.480744i
\(934\) 147.050i 0.157441i
\(935\) −24.3136 88.1528i −0.0260039 0.0942811i
\(936\) 252.141 0.269381
\(937\) −935.658 1287.82i −0.998568 1.37441i −0.926200 0.377033i \(-0.876944\pi\)
−0.0723682 0.997378i \(-0.523056\pi\)
\(938\) −207.719 639.295i −0.221449 0.681551i
\(939\) 13.6294 41.9471i 0.0145149 0.0446721i
\(940\) 54.0351 + 39.2588i 0.0574841 + 0.0417647i
\(941\) 350.794 482.827i 0.372789 0.513100i −0.580867 0.813998i \(-0.697287\pi\)
0.953656 + 0.300898i \(0.0972865\pi\)
\(942\) 114.250 + 37.1220i 0.121284 + 0.0394077i
\(943\) 293.486 95.3594i 0.311226 0.101123i
\(944\) 108.596 78.8997i 0.115038 0.0835802i
\(945\) 14.9296i 0.0157985i
\(946\) 105.031 + 159.169i 0.111026 + 0.168255i
\(947\) −883.411 −0.932852 −0.466426 0.884560i \(-0.654459\pi\)
−0.466426 + 0.884560i \(0.654459\pi\)
\(948\) −186.350 256.489i −0.196572 0.270558i
\(949\) −175.022 538.662i −0.184428 0.567610i
\(950\) 83.8210 257.975i 0.0882326 0.271552i
\(951\) 128.052 + 93.0354i 0.134650 + 0.0978290i
\(952\) −613.917 + 844.985i −0.644871 + 0.887589i
\(953\) −269.023 87.4107i −0.282290 0.0917216i 0.164450 0.986385i \(-0.447415\pi\)
−0.446740 + 0.894664i \(0.647415\pi\)
\(954\) 265.351 86.2177i 0.278145 0.0903749i
\(955\) −61.4573 + 44.6514i −0.0643532 + 0.0467554i
\(956\) 501.440i 0.524518i
\(957\) 474.967 + 21.4061i 0.496308 + 0.0223680i
\(958\) −320.091 −0.334125
\(959\) −129.937 178.843i −0.135493 0.186489i
\(960\) 2.32813 + 7.16526i 0.00242514 + 0.00746381i
\(961\) 801.664 2467.27i 0.834198 2.56740i
\(962\) 57.6768 + 41.9046i 0.0599551 + 0.0435599i
\(963\) −190.890 + 262.737i −0.198224 + 0.272832i
\(964\) 674.808 + 219.258i 0.700008 + 0.227446i
\(965\) −20.6292 + 6.70284i −0.0213774 + 0.00694595i
\(966\) 59.0031 42.8683i 0.0610799 0.0443771i
\(967\) 335.731i 0.347188i −0.984817 0.173594i \(-0.944462\pi\)
0.984817 0.173594i \(-0.0555381\pi\)
\(968\) 815.434 185.846i 0.842391 0.191990i
\(969\) 402.464 0.415340
\(970\) −8.63505 11.8851i −0.00890211 0.0122527i
\(971\) 431.183 + 1327.04i 0.444061 + 1.36668i 0.883511 + 0.468411i \(0.155173\pi\)
−0.439450 + 0.898267i \(0.644827\pi\)
\(972\) −14.6178 + 44.9889i −0.0150389 + 0.0462848i
\(973\) −162.223 117.862i −0.166724 0.121132i
\(974\) −177.261 + 243.978i −0.181992 + 0.250491i
\(975\) −497.594 161.678i −0.510352 0.165824i
\(976\) −169.873 + 55.1952i −0.174051 + 0.0565524i
\(977\) 941.558 684.082i 0.963724 0.700187i 0.00971140 0.999953i \(-0.496909\pi\)
0.954013 + 0.299766i \(0.0969087\pi\)
\(978\) 130.890i 0.133834i
\(979\) −66.4577 + 1474.59i −0.0678833 + 1.50622i
\(980\) −3.89303 −0.00397248
\(981\) 309.374 + 425.817i 0.315366 + 0.434064i
\(982\) 186.391 + 573.652i 0.189807 + 0.584167i
\(983\) −126.632 + 389.732i −0.128821 + 0.396472i −0.994578 0.103994i \(-0.966838\pi\)
0.865756 + 0.500466i \(0.166838\pi\)
\(984\) −504.025 366.196i −0.512221 0.372150i
\(985\) 17.5956 24.2183i 0.0178636 0.0245871i
\(986\) −487.601 158.431i −0.494525 0.160681i
\(987\) −659.047 + 214.137i −0.667728 + 0.216958i
\(988\) −331.740 + 241.023i −0.335769 + 0.243951i
\(989\) 104.626i 0.105790i
\(990\) 10.7599 7.10007i 0.0108685 0.00717179i
\(991\) 1604.17 1.61874 0.809372 0.587297i \(-0.199808\pi\)
0.809372 + 0.587297i \(0.199808\pi\)
\(992\) −1153.10 1587.10i −1.16240 1.59990i
\(993\) 170.611 + 525.088i 0.171814 + 0.528790i
\(994\) −181.520 + 558.661i −0.182616 + 0.562033i
\(995\) 19.5301 + 14.1894i 0.0196282 + 0.0142607i
\(996\) 465.490 640.693i 0.467360 0.643266i
\(997\) 68.8415 + 22.3680i 0.0690487 + 0.0224353i 0.343338 0.939212i \(-0.388442\pi\)
−0.274289 + 0.961647i \(0.588442\pi\)
\(998\) −382.637 + 124.326i −0.383404 + 0.124576i
\(999\) −25.0840 + 18.2246i −0.0251092 + 0.0182429i
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 33.3.g.a.19.1 yes 16
3.2 odd 2 99.3.k.c.19.4 16
4.3 odd 2 528.3.bf.b.481.3 16
11.2 odd 10 363.3.c.e.241.7 16
11.3 even 5 363.3.g.g.94.1 16
11.4 even 5 363.3.g.f.40.4 16
11.5 even 5 363.3.g.a.112.4 16
11.6 odd 10 363.3.g.g.112.1 16
11.7 odd 10 inner 33.3.g.a.7.1 16
11.8 odd 10 363.3.g.a.94.4 16
11.9 even 5 363.3.c.e.241.10 16
11.10 odd 2 363.3.g.f.118.4 16
33.2 even 10 1089.3.c.m.604.10 16
33.20 odd 10 1089.3.c.m.604.7 16
33.29 even 10 99.3.k.c.73.4 16
44.7 even 10 528.3.bf.b.337.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.g.a.7.1 16 11.7 odd 10 inner
33.3.g.a.19.1 yes 16 1.1 even 1 trivial
99.3.k.c.19.4 16 3.2 odd 2
99.3.k.c.73.4 16 33.29 even 10
363.3.c.e.241.7 16 11.2 odd 10
363.3.c.e.241.10 16 11.9 even 5
363.3.g.a.94.4 16 11.8 odd 10
363.3.g.a.112.4 16 11.5 even 5
363.3.g.f.40.4 16 11.4 even 5
363.3.g.f.118.4 16 11.10 odd 2
363.3.g.g.94.1 16 11.3 even 5
363.3.g.g.112.1 16 11.6 odd 10
528.3.bf.b.337.3 16 44.7 even 10
528.3.bf.b.481.3 16 4.3 odd 2
1089.3.c.m.604.7 16 33.20 odd 10
1089.3.c.m.604.10 16 33.2 even 10