Properties

Label 605.2.m.g.112.4
Level $605$
Weight $2$
Character 605.112
Analytic conductor $4.831$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(112,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.112");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.m (of order \(20\), degree \(8\), not 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(20\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 112.4
Character \(\chi\) \(=\) 605.112
Dual form 605.2.m.g.578.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.890440 - 1.74759i) q^{2} +(0.459138 - 2.89888i) q^{3} +(-1.08561 + 1.49421i) q^{4} +(0.260122 - 2.22089i) q^{5} +(-5.47488 + 1.77890i) q^{6} +(-2.07637 + 0.328864i) q^{7} +(-0.296505 - 0.0469618i) q^{8} +(-5.33954 - 1.73492i) q^{9} +O(q^{10})\) \(q+(-0.890440 - 1.74759i) q^{2} +(0.459138 - 2.89888i) q^{3} +(-1.08561 + 1.49421i) q^{4} +(0.260122 - 2.22089i) q^{5} +(-5.47488 + 1.77890i) q^{6} +(-2.07637 + 0.328864i) q^{7} +(-0.296505 - 0.0469618i) q^{8} +(-5.33954 - 1.73492i) q^{9} +(-4.11281 + 1.52298i) q^{10} +(3.83309 + 3.83309i) q^{12} +(2.16733 - 1.10431i) q^{13} +(2.42360 + 3.33580i) q^{14} +(-6.31865 - 1.77376i) q^{15} +(1.32342 + 4.07308i) q^{16} +(4.47771 + 2.28151i) q^{17} +(1.72261 + 10.8761i) q^{18} +(0.336219 - 0.244277i) q^{19} +(3.03608 + 2.79968i) q^{20} +6.17014i q^{21} +(4.64435 - 4.64435i) q^{23} +(-0.272273 + 0.837971i) q^{24} +(-4.86467 - 1.15540i) q^{25} +(-3.85976 - 2.80428i) q^{26} +(-3.48350 + 6.83676i) q^{27} +(1.76273 - 3.45954i) q^{28} +(-6.62623 - 4.81424i) q^{29} +(2.52659 + 12.6218i) q^{30} +(-0.438612 + 1.34991i) q^{31} +(5.51508 - 5.51508i) q^{32} -9.85672i q^{34} +(0.190261 + 4.69692i) q^{35} +(8.38896 - 6.09494i) q^{36} +(-0.0954369 - 0.602565i) q^{37} +(-0.726278 - 0.370057i) q^{38} +(-2.20616 - 6.78986i) q^{39} +(-0.181424 + 0.646288i) q^{40} +(-0.193687 - 0.266587i) q^{41} +(10.7829 - 5.49414i) q^{42} +(-3.73558 - 3.73558i) q^{43} +(-5.24199 + 11.4072i) q^{45} +(-12.2519 - 3.98089i) q^{46} +(9.03617 + 1.43119i) q^{47} +(12.4150 - 1.96634i) q^{48} +(-2.45424 + 0.797432i) q^{49} +(2.31253 + 9.53026i) q^{50} +(8.66970 - 11.9328i) q^{51} +(-0.702797 + 4.43729i) q^{52} +(1.47679 + 2.89837i) q^{53} +15.0497 q^{54} +0.631097 q^{56} +(-0.553760 - 1.08682i) q^{57} +(-2.51304 + 15.8667i) q^{58} +(1.78995 - 2.46366i) q^{59} +(9.50993 - 7.51578i) q^{60} +(-1.36399 + 0.443187i) q^{61} +(2.74964 - 0.435500i) q^{62} +(11.6574 + 1.84635i) q^{63} +(-6.40277 - 2.08039i) q^{64} +(-1.88878 - 5.10065i) q^{65} +(-4.17367 - 4.17367i) q^{67} +(-8.27007 + 4.21381i) q^{68} +(-11.3310 - 15.5958i) q^{69} +(8.03886 - 4.51482i) q^{70} +(2.34719 + 7.22390i) q^{71} +(1.50172 + 0.765166i) q^{72} +(1.22162 + 7.71298i) q^{73} +(-0.968054 + 0.703332i) q^{74} +(-5.58293 + 13.5716i) q^{75} +0.767569i q^{76} +(-9.90142 + 9.90142i) q^{78} +(1.11121 - 3.41995i) q^{79} +(9.39010 - 1.87967i) q^{80} +(4.59331 + 3.33723i) q^{81} +(-0.293418 + 0.575865i) q^{82} +(1.14399 - 2.24521i) q^{83} +(-9.21947 - 6.69834i) q^{84} +(6.23172 - 9.35101i) q^{85} +(-3.20194 + 9.85455i) q^{86} +(-16.9983 + 16.9983i) q^{87} +7.76892i q^{89} +(24.6028 - 0.996599i) q^{90} +(-4.13701 + 3.00571i) q^{91} +(1.89769 + 11.9816i) q^{92} +(3.71184 + 1.89128i) q^{93} +(-5.54504 - 17.0659i) q^{94} +(-0.455054 - 0.810245i) q^{95} +(-13.4554 - 18.5197i) q^{96} +(12.2277 - 6.23033i) q^{97} +(3.57894 + 3.57894i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 8 q^{3} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 8 q^{3} + 4 q^{5} - 128 q^{12} - 32 q^{15} + 24 q^{16} - 32 q^{20} - 96 q^{23} + 52 q^{25} + 8 q^{26} - 32 q^{27} - 16 q^{31} + 40 q^{36} - 36 q^{37} - 32 q^{38} - 32 q^{42} + 256 q^{45} - 32 q^{47} + 16 q^{48} + 68 q^{53} + 320 q^{56} - 132 q^{58} + 64 q^{60} - 352 q^{67} + 8 q^{70} + 16 q^{75} - 992 q^{78} + 164 q^{80} + 40 q^{81} - 100 q^{82} + 80 q^{86} + 96 q^{91} + 56 q^{92} - 24 q^{93} + 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.890440 1.74759i −0.629636 1.23573i −0.956796 0.290761i \(-0.906091\pi\)
0.327160 0.944969i \(-0.393909\pi\)
\(3\) 0.459138 2.89888i 0.265083 1.67367i −0.392087 0.919928i \(-0.628247\pi\)
0.657170 0.753742i \(-0.271753\pi\)
\(4\) −1.08561 + 1.49421i −0.542803 + 0.747104i
\(5\) 0.260122 2.22089i 0.116330 0.993211i
\(6\) −5.47488 + 1.77890i −2.23511 + 0.726232i
\(7\) −2.07637 + 0.328864i −0.784793 + 0.124299i −0.535956 0.844246i \(-0.680049\pi\)
−0.248838 + 0.968545i \(0.580049\pi\)
\(8\) −0.296505 0.0469618i −0.104830 0.0166035i
\(9\) −5.33954 1.73492i −1.77985 0.578307i
\(10\) −4.11281 + 1.52298i −1.30059 + 0.481608i
\(11\) 0 0
\(12\) 3.83309 + 3.83309i 1.10652 + 1.10652i
\(13\) 2.16733 1.10431i 0.601109 0.306280i −0.126827 0.991925i \(-0.540479\pi\)
0.727937 + 0.685644i \(0.240479\pi\)
\(14\) 2.42360 + 3.33580i 0.647734 + 0.891530i
\(15\) −6.31865 1.77376i −1.63147 0.457982i
\(16\) 1.32342 + 4.07308i 0.330856 + 1.01827i
\(17\) 4.47771 + 2.28151i 1.08600 + 0.553346i 0.902945 0.429756i \(-0.141400\pi\)
0.183058 + 0.983102i \(0.441400\pi\)
\(18\) 1.72261 + 10.8761i 0.406024 + 2.56353i
\(19\) 0.336219 0.244277i 0.0771339 0.0560410i −0.548550 0.836118i \(-0.684820\pi\)
0.625684 + 0.780077i \(0.284820\pi\)
\(20\) 3.03608 + 2.79968i 0.678887 + 0.626028i
\(21\) 6.17014i 1.34643i
\(22\) 0 0
\(23\) 4.64435 4.64435i 0.968413 0.968413i −0.0311028 0.999516i \(-0.509902\pi\)
0.999516 + 0.0311028i \(0.00990191\pi\)
\(24\) −0.272273 + 0.837971i −0.0555775 + 0.171050i
\(25\) −4.86467 1.15540i −0.972935 0.231081i
\(26\) −3.85976 2.80428i −0.756960 0.549964i
\(27\) −3.48350 + 6.83676i −0.670401 + 1.31574i
\(28\) 1.76273 3.45954i 0.333124 0.653792i
\(29\) −6.62623 4.81424i −1.23046 0.893981i −0.233535 0.972348i \(-0.575029\pi\)
−0.996925 + 0.0783668i \(0.975029\pi\)
\(30\) 2.52659 + 12.6218i 0.461290 + 2.30442i
\(31\) −0.438612 + 1.34991i −0.0787771 + 0.242451i −0.982687 0.185271i \(-0.940684\pi\)
0.903910 + 0.427722i \(0.140684\pi\)
\(32\) 5.51508 5.51508i 0.974938 0.974938i
\(33\) 0 0
\(34\) 9.85672i 1.69041i
\(35\) 0.190261 + 4.69692i 0.0321600 + 0.793925i
\(36\) 8.38896 6.09494i 1.39816 1.01582i
\(37\) −0.0954369 0.602565i −0.0156897 0.0990610i 0.978601 0.205768i \(-0.0659693\pi\)
−0.994290 + 0.106707i \(0.965969\pi\)
\(38\) −0.726278 0.370057i −0.117818 0.0600312i
\(39\) −2.20616 6.78986i −0.353268 1.08725i
\(40\) −0.181424 + 0.646288i −0.0286857 + 0.102187i
\(41\) −0.193687 0.266587i −0.0302489 0.0416340i 0.793625 0.608408i \(-0.208191\pi\)
−0.823874 + 0.566774i \(0.808191\pi\)
\(42\) 10.7829 5.49414i 1.66383 0.847764i
\(43\) −3.73558 3.73558i −0.569670 0.569670i 0.362366 0.932036i \(-0.381969\pi\)
−0.932036 + 0.362366i \(0.881969\pi\)
\(44\) 0 0
\(45\) −5.24199 + 11.4072i −0.781430 + 1.70049i
\(46\) −12.2519 3.98089i −1.80645 0.586950i
\(47\) 9.03617 + 1.43119i 1.31806 + 0.208760i 0.775549 0.631288i \(-0.217473\pi\)
0.542512 + 0.840048i \(0.317473\pi\)
\(48\) 12.4150 1.96634i 1.79195 0.283817i
\(49\) −2.45424 + 0.797432i −0.350606 + 0.113919i
\(50\) 2.31253 + 9.53026i 0.327041 + 1.34778i
\(51\) 8.66970 11.9328i 1.21400 1.67093i
\(52\) −0.702797 + 4.43729i −0.0974605 + 0.615341i
\(53\) 1.47679 + 2.89837i 0.202853 + 0.398122i 0.969912 0.243455i \(-0.0782807\pi\)
−0.767059 + 0.641577i \(0.778281\pi\)
\(54\) 15.0497 2.04800
\(55\) 0 0
\(56\) 0.631097 0.0843339
\(57\) −0.553760 1.08682i −0.0733473 0.143952i
\(58\) −2.51304 + 15.8667i −0.329978 + 2.08340i
\(59\) 1.78995 2.46366i 0.233032 0.320741i −0.676447 0.736492i \(-0.736481\pi\)
0.909479 + 0.415750i \(0.136481\pi\)
\(60\) 9.50993 7.51578i 1.22773 0.970284i
\(61\) −1.36399 + 0.443187i −0.174641 + 0.0567443i −0.395032 0.918667i \(-0.629267\pi\)
0.220391 + 0.975412i \(0.429267\pi\)
\(62\) 2.74964 0.435500i 0.349205 0.0553086i
\(63\) 11.6574 + 1.84635i 1.46869 + 0.232618i
\(64\) −6.40277 2.08039i −0.800347 0.260048i
\(65\) −1.88878 5.10065i −0.234274 0.632658i
\(66\) 0 0
\(67\) −4.17367 4.17367i −0.509895 0.509895i 0.404599 0.914494i \(-0.367411\pi\)
−0.914494 + 0.404599i \(0.867411\pi\)
\(68\) −8.27007 + 4.21381i −1.00289 + 0.510999i
\(69\) −11.3310 15.5958i −1.36409 1.87751i
\(70\) 8.03886 4.51482i 0.960828 0.539625i
\(71\) 2.34719 + 7.22390i 0.278560 + 0.857320i 0.988255 + 0.152811i \(0.0488326\pi\)
−0.709695 + 0.704509i \(0.751167\pi\)
\(72\) 1.50172 + 0.765166i 0.176980 + 0.0901757i
\(73\) 1.22162 + 7.71298i 0.142979 + 0.902736i 0.950008 + 0.312224i \(0.101074\pi\)
−0.807029 + 0.590512i \(0.798926\pi\)
\(74\) −0.968054 + 0.703332i −0.112534 + 0.0817607i
\(75\) −5.58293 + 13.5716i −0.644662 + 1.56712i
\(76\) 0.767569i 0.0880462i
\(77\) 0 0
\(78\) −9.90142 + 9.90142i −1.12112 + 1.12112i
\(79\) 1.11121 3.41995i 0.125021 0.384774i −0.868884 0.495016i \(-0.835162\pi\)
0.993905 + 0.110241i \(0.0351623\pi\)
\(80\) 9.39010 1.87967i 1.04984 0.210154i
\(81\) 4.59331 + 3.33723i 0.510368 + 0.370804i
\(82\) −0.293418 + 0.575865i −0.0324026 + 0.0635937i
\(83\) 1.14399 2.24521i 0.125569 0.246444i −0.819660 0.572850i \(-0.805838\pi\)
0.945230 + 0.326406i \(0.105838\pi\)
\(84\) −9.21947 6.69834i −1.00593 0.730849i
\(85\) 6.23172 9.35101i 0.675924 1.01426i
\(86\) −3.20194 + 9.85455i −0.345274 + 1.06264i
\(87\) −16.9983 + 16.9983i −1.82240 + 1.82240i
\(88\) 0 0
\(89\) 7.76892i 0.823504i 0.911296 + 0.411752i \(0.135083\pi\)
−0.911296 + 0.411752i \(0.864917\pi\)
\(90\) 24.6028 0.996599i 2.59336 0.105051i
\(91\) −4.13701 + 3.00571i −0.433676 + 0.315084i
\(92\) 1.89769 + 11.9816i 0.197848 + 1.24916i
\(93\) 3.71184 + 1.89128i 0.384900 + 0.196116i
\(94\) −5.54504 17.0659i −0.571927 1.76021i
\(95\) −0.455054 0.810245i −0.0466875 0.0831294i
\(96\) −13.4554 18.5197i −1.37328 1.89016i
\(97\) 12.2277 6.23033i 1.24154 0.632594i 0.295094 0.955468i \(-0.404649\pi\)
0.946442 + 0.322874i \(0.104649\pi\)
\(98\) 3.57894 + 3.57894i 0.361527 + 0.361527i
\(99\) 0 0
\(100\) 7.00753 6.01452i 0.700753 0.601452i
\(101\) 9.38878 + 3.05060i 0.934219 + 0.303546i 0.736287 0.676670i \(-0.236577\pi\)
0.197932 + 0.980216i \(0.436577\pi\)
\(102\) −28.5735 4.52559i −2.82920 0.448101i
\(103\) −7.15211 + 1.13278i −0.704718 + 0.111616i −0.498500 0.866890i \(-0.666116\pi\)
−0.206218 + 0.978506i \(0.566116\pi\)
\(104\) −0.694484 + 0.225652i −0.0680998 + 0.0221270i
\(105\) 13.7032 + 1.60499i 1.33729 + 0.156631i
\(106\) 3.75016 5.16165i 0.364248 0.501344i
\(107\) 2.52009 15.9112i 0.243626 1.53819i −0.497878 0.867247i \(-0.665887\pi\)
0.741505 0.670948i \(-0.234113\pi\)
\(108\) −6.43383 12.6271i −0.619096 1.21504i
\(109\) −7.94953 −0.761427 −0.380714 0.924693i \(-0.624322\pi\)
−0.380714 + 0.924693i \(0.624322\pi\)
\(110\) 0 0
\(111\) −1.79058 −0.169955
\(112\) −4.08740 8.02198i −0.386223 0.758006i
\(113\) −3.01632 + 19.0443i −0.283751 + 1.79154i 0.274210 + 0.961670i \(0.411584\pi\)
−0.557962 + 0.829867i \(0.688416\pi\)
\(114\) −1.40621 + 1.93549i −0.131704 + 0.181275i
\(115\) −9.10647 11.5227i −0.849183 1.07449i
\(116\) 14.3869 4.67460i 1.33579 0.434026i
\(117\) −13.4884 + 2.13636i −1.24701 + 0.197506i
\(118\) −5.89931 0.934358i −0.543075 0.0860147i
\(119\) −10.0477 3.26469i −0.921069 0.299273i
\(120\) 1.79021 + 0.822662i 0.163423 + 0.0750985i
\(121\) 0 0
\(122\) 1.98906 + 1.98906i 0.180081 + 0.180081i
\(123\) −0.861735 + 0.439076i −0.0777000 + 0.0395901i
\(124\) −1.54089 2.12085i −0.138376 0.190458i
\(125\) −3.83143 + 10.5033i −0.342694 + 0.939447i
\(126\) −7.15355 22.0164i −0.637289 1.96137i
\(127\) −18.4577 9.40466i −1.63786 0.834529i −0.997807 0.0661944i \(-0.978914\pi\)
−0.640048 0.768335i \(-0.721086\pi\)
\(128\) −0.374594 2.36509i −0.0331097 0.209047i
\(129\) −12.5441 + 9.11385i −1.10445 + 0.802430i
\(130\) −7.23199 + 7.84262i −0.634287 + 0.687844i
\(131\) 6.00178i 0.524378i −0.965017 0.262189i \(-0.915556\pi\)
0.965017 0.262189i \(-0.0844444\pi\)
\(132\) 0 0
\(133\) −0.617780 + 0.617780i −0.0535683 + 0.0535683i
\(134\) −3.57745 + 11.0103i −0.309044 + 0.951141i
\(135\) 14.2775 + 9.51486i 1.22881 + 0.818909i
\(136\) −1.22052 0.886758i −0.104659 0.0760389i
\(137\) 4.10738 8.06118i 0.350917 0.688713i −0.646315 0.763071i \(-0.723691\pi\)
0.997232 + 0.0743579i \(0.0236907\pi\)
\(138\) −17.1654 + 33.6891i −1.46122 + 2.86780i
\(139\) 10.5906 + 7.69449i 0.898279 + 0.652638i 0.938023 0.346572i \(-0.112654\pi\)
−0.0397440 + 0.999210i \(0.512654\pi\)
\(140\) −7.22473 4.81472i −0.610601 0.406918i
\(141\) 8.29769 25.5377i 0.698792 2.15066i
\(142\) 10.5344 10.5344i 0.884024 0.884024i
\(143\) 0 0
\(144\) 24.0444i 2.00370i
\(145\) −12.4155 + 13.4638i −1.03105 + 1.11811i
\(146\) 12.3913 9.00283i 1.02551 0.745079i
\(147\) 1.18483 + 7.48069i 0.0977227 + 0.616997i
\(148\) 1.00396 + 0.511545i 0.0825253 + 0.0420488i
\(149\) 4.20301 + 12.9355i 0.344324 + 1.05972i 0.961945 + 0.273244i \(0.0880967\pi\)
−0.617621 + 0.786476i \(0.711903\pi\)
\(150\) 28.6889 2.32805i 2.34243 0.190085i
\(151\) 4.88099 + 6.71810i 0.397209 + 0.546711i 0.960041 0.279860i \(-0.0902881\pi\)
−0.562832 + 0.826571i \(0.690288\pi\)
\(152\) −0.111162 + 0.0566400i −0.00901644 + 0.00459411i
\(153\) −19.9506 19.9506i −1.61291 1.61291i
\(154\) 0 0
\(155\) 2.88390 + 1.32525i 0.231641 + 0.106447i
\(156\) 12.5405 + 4.07465i 1.00404 + 0.326233i
\(157\) 3.41496 + 0.540877i 0.272544 + 0.0431667i 0.291210 0.956659i \(-0.405942\pi\)
−0.0186665 + 0.999826i \(0.505942\pi\)
\(158\) −6.96612 + 1.10333i −0.554195 + 0.0877759i
\(159\) 9.08009 2.95030i 0.720098 0.233974i
\(160\) −10.8138 13.6830i −0.854904 1.08173i
\(161\) −8.11601 + 11.1707i −0.639632 + 0.880377i
\(162\) 1.74204 10.9988i 0.136868 0.864148i
\(163\) −6.38941 12.5399i −0.500457 0.982202i −0.993675 0.112296i \(-0.964179\pi\)
0.493218 0.869906i \(-0.335821\pi\)
\(164\) 0.608605 0.0475241
\(165\) 0 0
\(166\) −4.94236 −0.383601
\(167\) −3.47332 6.81678i −0.268774 0.527499i 0.716688 0.697394i \(-0.245657\pi\)
−0.985462 + 0.169895i \(0.945657\pi\)
\(168\) 0.289761 1.82948i 0.0223555 0.141147i
\(169\) −4.16339 + 5.73041i −0.320261 + 0.440801i
\(170\) −21.8907 2.56395i −1.67894 0.196646i
\(171\) −2.21905 + 0.721014i −0.169695 + 0.0551373i
\(172\) 9.63709 1.52637i 0.734821 0.116384i
\(173\) −19.9312 3.15679i −1.51534 0.240006i −0.657316 0.753615i \(-0.728308\pi\)
−0.858024 + 0.513609i \(0.828308\pi\)
\(174\) 44.8419 + 14.5700i 3.39945 + 1.10455i
\(175\) 10.4808 + 0.799226i 0.792276 + 0.0604158i
\(176\) 0 0
\(177\) −6.32002 6.32002i −0.475042 0.475042i
\(178\) 13.5769 6.91776i 1.01763 0.518508i
\(179\) −8.30815 11.4352i −0.620981 0.854706i 0.376443 0.926440i \(-0.377147\pi\)
−0.997424 + 0.0717332i \(0.977147\pi\)
\(180\) −11.3540 20.2164i −0.846278 1.50684i
\(181\) −0.783815 2.41233i −0.0582605 0.179307i 0.917691 0.397295i \(-0.130051\pi\)
−0.975952 + 0.217987i \(0.930051\pi\)
\(182\) 8.93650 + 4.55337i 0.662417 + 0.337518i
\(183\) 0.658488 + 4.15753i 0.0486769 + 0.307334i
\(184\) −1.59518 + 1.15896i −0.117598 + 0.0854400i
\(185\) −1.36305 + 0.0552140i −0.100214 + 0.00405941i
\(186\) 8.17084i 0.599115i
\(187\) 0 0
\(188\) −11.9482 + 11.9482i −0.871413 + 0.871413i
\(189\) 4.98467 15.3412i 0.362581 1.11591i
\(190\) −1.01078 + 1.51672i −0.0733294 + 0.110035i
\(191\) −7.67146 5.57364i −0.555087 0.403295i 0.274570 0.961567i \(-0.411464\pi\)
−0.829658 + 0.558272i \(0.811464\pi\)
\(192\) −8.97055 + 17.6057i −0.647394 + 1.27058i
\(193\) 5.21892 10.2427i 0.375666 0.737287i −0.623336 0.781954i \(-0.714223\pi\)
0.999002 + 0.0446678i \(0.0142229\pi\)
\(194\) −21.7761 15.8212i −1.56343 1.13590i
\(195\) −15.6534 + 3.13344i −1.12096 + 0.224390i
\(196\) 1.47281 4.53285i 0.105201 0.323775i
\(197\) 19.0770 19.0770i 1.35918 1.35918i 0.484247 0.874932i \(-0.339094\pi\)
0.874932 0.484247i \(-0.160906\pi\)
\(198\) 0 0
\(199\) 3.29236i 0.233389i 0.993168 + 0.116694i \(0.0372298\pi\)
−0.993168 + 0.116694i \(0.962770\pi\)
\(200\) 1.38814 + 0.571036i 0.0981563 + 0.0403784i
\(201\) −14.0153 + 10.1827i −0.988560 + 0.718231i
\(202\) −3.02896 19.1241i −0.213117 1.34557i
\(203\) 15.3417 + 7.81700i 1.07678 + 0.548646i
\(204\) 8.41823 + 25.9087i 0.589394 + 1.81397i
\(205\) −0.642443 + 0.360812i −0.0448702 + 0.0252002i
\(206\) 8.34816 + 11.4903i 0.581644 + 0.800564i
\(207\) −32.8562 + 16.7411i −2.28367 + 1.16359i
\(208\) 7.36624 + 7.36624i 0.510757 + 0.510757i
\(209\) 0 0
\(210\) −9.39700 25.3766i −0.648454 1.75115i
\(211\) 19.9161 + 6.47112i 1.37108 + 0.445490i 0.899726 0.436455i \(-0.143766\pi\)
0.471352 + 0.881945i \(0.343766\pi\)
\(212\) −5.93399 0.939851i −0.407548 0.0645492i
\(213\) 22.0189 3.48745i 1.50871 0.238956i
\(214\) −30.0502 + 9.76390i −2.05419 + 0.667447i
\(215\) −9.26800 + 7.32458i −0.632072 + 0.499532i
\(216\) 1.35394 1.86354i 0.0921241 0.126798i
\(217\) 0.466783 2.94715i 0.0316873 0.200066i
\(218\) 7.07858 + 13.8925i 0.479422 + 0.940919i
\(219\) 22.9199 1.54878
\(220\) 0 0
\(221\) 12.2242 0.822286
\(222\) 1.59441 + 3.12920i 0.107010 + 0.210018i
\(223\) 4.18639 26.4318i 0.280342 1.77001i −0.298346 0.954458i \(-0.596435\pi\)
0.578688 0.815549i \(-0.303565\pi\)
\(224\) −9.63762 + 13.2651i −0.643941 + 0.886308i
\(225\) 23.9706 + 14.6091i 1.59804 + 0.973943i
\(226\) 35.9674 11.6865i 2.39252 0.777376i
\(227\) 6.04730 0.957798i 0.401373 0.0635713i 0.0475154 0.998871i \(-0.484870\pi\)
0.353858 + 0.935299i \(0.384870\pi\)
\(228\) 2.22509 + 0.352420i 0.147360 + 0.0233396i
\(229\) 1.55740 + 0.506029i 0.102916 + 0.0334393i 0.360022 0.932944i \(-0.382769\pi\)
−0.257107 + 0.966383i \(0.582769\pi\)
\(230\) −12.0281 + 26.1746i −0.793109 + 1.72590i
\(231\) 0 0
\(232\) 1.73862 + 1.73862i 0.114146 + 0.114146i
\(233\) −19.1872 + 9.77638i −1.25700 + 0.640472i −0.950300 0.311336i \(-0.899224\pi\)
−0.306697 + 0.951807i \(0.599224\pi\)
\(234\) 15.7441 + 21.6699i 1.02922 + 1.41661i
\(235\) 5.52902 19.6960i 0.360673 1.28483i
\(236\) 1.73804 + 5.34913i 0.113137 + 0.348199i
\(237\) −9.40383 4.79149i −0.610845 0.311241i
\(238\) 3.24153 + 20.4662i 0.210117 + 1.32663i
\(239\) 19.8856 14.4477i 1.28629 0.934546i 0.286569 0.958060i \(-0.407485\pi\)
0.999724 + 0.0235135i \(0.00748525\pi\)
\(240\) −1.13761 28.0838i −0.0734322 1.81280i
\(241\) 19.3936i 1.24925i 0.780923 + 0.624627i \(0.214749\pi\)
−0.780923 + 0.624627i \(0.785251\pi\)
\(242\) 0 0
\(243\) −4.49385 + 4.49385i −0.288280 + 0.288280i
\(244\) 0.818542 2.51921i 0.0524018 0.161276i
\(245\) 1.13260 + 5.65803i 0.0723593 + 0.361478i
\(246\) 1.53465 + 1.11499i 0.0978454 + 0.0710889i
\(247\) 0.458939 0.900719i 0.0292016 0.0573114i
\(248\) 0.193445 0.379657i 0.0122838 0.0241082i
\(249\) −5.98335 4.34716i −0.379179 0.275490i
\(250\) 21.7672 2.65684i 1.37668 0.168033i
\(251\) 2.34668 7.22234i 0.148121 0.455870i −0.849278 0.527946i \(-0.822962\pi\)
0.997399 + 0.0720759i \(0.0229624\pi\)
\(252\) −15.4142 + 15.4142i −0.971001 + 0.971001i
\(253\) 0 0
\(254\) 40.6307i 2.54940i
\(255\) −24.2462 22.3584i −1.51836 1.40014i
\(256\) −14.6927 + 10.6749i −0.918294 + 0.667179i
\(257\) 3.18557 + 20.1129i 0.198710 + 1.25461i 0.862257 + 0.506472i \(0.169051\pi\)
−0.663546 + 0.748135i \(0.730949\pi\)
\(258\) 27.0970 + 13.8066i 1.68699 + 0.859563i
\(259\) 0.396324 + 1.21976i 0.0246264 + 0.0757922i
\(260\) 9.67190 + 2.71507i 0.599826 + 0.168382i
\(261\) 27.0287 + 37.2018i 1.67303 + 2.30273i
\(262\) −10.4886 + 5.34423i −0.647990 + 0.330167i
\(263\) −4.23725 4.23725i −0.261280 0.261280i 0.564294 0.825574i \(-0.309148\pi\)
−0.825574 + 0.564294i \(0.809148\pi\)
\(264\) 0 0
\(265\) 6.82110 2.52586i 0.419017 0.155162i
\(266\) 1.62972 + 0.529528i 0.0999245 + 0.0324674i
\(267\) 22.5212 + 3.56701i 1.37827 + 0.218297i
\(268\) 10.7673 1.70537i 0.657717 0.104172i
\(269\) 16.4380 5.34104i 1.00224 0.325649i 0.238483 0.971147i \(-0.423350\pi\)
0.763762 + 0.645498i \(0.223350\pi\)
\(270\) 3.91476 33.4236i 0.238245 2.03410i
\(271\) 10.8999 15.0024i 0.662122 0.911333i −0.337427 0.941352i \(-0.609557\pi\)
0.999549 + 0.0300184i \(0.00955660\pi\)
\(272\) −3.36685 + 21.2574i −0.204145 + 1.28892i
\(273\) 6.81375 + 13.3727i 0.412387 + 0.809354i
\(274\) −17.7450 −1.07201
\(275\) 0 0
\(276\) 35.6044 2.14313
\(277\) 4.91280 + 9.64191i 0.295181 + 0.579326i 0.990199 0.139667i \(-0.0446032\pi\)
−0.695017 + 0.718993i \(0.744603\pi\)
\(278\) 4.01653 25.3594i 0.240896 1.52096i
\(279\) 4.68397 6.44693i 0.280422 0.385968i
\(280\) 0.164162 1.40160i 0.00981058 0.0837613i
\(281\) −16.6298 + 5.40335i −0.992051 + 0.322337i −0.759685 0.650291i \(-0.774647\pi\)
−0.232366 + 0.972628i \(0.574647\pi\)
\(282\) −52.0179 + 8.23883i −3.09762 + 0.490615i
\(283\) −10.7431 1.70154i −0.638610 0.101146i −0.171271 0.985224i \(-0.554787\pi\)
−0.467339 + 0.884078i \(0.654787\pi\)
\(284\) −13.3421 4.33512i −0.791710 0.257242i
\(285\) −2.55774 + 0.947133i −0.151507 + 0.0561033i
\(286\) 0 0
\(287\) 0.489837 + 0.489837i 0.0289142 + 0.0289142i
\(288\) −39.0162 + 19.8797i −2.29905 + 1.17143i
\(289\) 4.85224 + 6.67853i 0.285426 + 0.392855i
\(290\) 34.5844 + 9.70845i 2.03087 + 0.570100i
\(291\) −12.4468 38.3073i −0.729643 2.24561i
\(292\) −12.8510 6.54791i −0.752048 0.383187i
\(293\) 0.134841 + 0.851352i 0.00787749 + 0.0497365i 0.991314 0.131517i \(-0.0419847\pi\)
−0.983436 + 0.181253i \(0.941985\pi\)
\(294\) 12.0181 8.73169i 0.700912 0.509243i
\(295\) −5.00590 4.61614i −0.291455 0.268762i
\(296\) 0.183145i 0.0106451i
\(297\) 0 0
\(298\) 18.8634 18.8634i 1.09273 1.09273i
\(299\) 4.93704 15.1946i 0.285516 0.878728i
\(300\) −14.2180 23.0755i −0.820874 1.33226i
\(301\) 8.98493 + 6.52793i 0.517883 + 0.376264i
\(302\) 7.39424 14.5120i 0.425491 0.835072i
\(303\) 13.1541 25.8163i 0.755682 1.48311i
\(304\) 1.43992 + 1.04616i 0.0825851 + 0.0600016i
\(305\) 0.629465 + 3.14455i 0.0360430 + 0.180056i
\(306\) −17.1006 + 52.6303i −0.977578 + 3.00868i
\(307\) 4.61342 4.61342i 0.263302 0.263302i −0.563092 0.826394i \(-0.690388\pi\)
0.826394 + 0.563092i \(0.190388\pi\)
\(308\) 0 0
\(309\) 21.2532i 1.20905i
\(310\) −0.251954 6.21992i −0.0143100 0.353268i
\(311\) −4.46098 + 3.24109i −0.252959 + 0.183786i −0.707037 0.707176i \(-0.749969\pi\)
0.454078 + 0.890962i \(0.349969\pi\)
\(312\) 0.335273 + 2.11683i 0.0189811 + 0.119842i
\(313\) −14.2348 7.25301i −0.804600 0.409964i 0.00277974 0.999996i \(-0.499115\pi\)
−0.807380 + 0.590032i \(0.799115\pi\)
\(314\) −2.09559 6.44956i −0.118261 0.363970i
\(315\) 7.13288 25.4095i 0.401892 1.43166i
\(316\) 3.90378 + 5.37310i 0.219605 + 0.302260i
\(317\) 9.04885 4.61062i 0.508234 0.258958i −0.181018 0.983480i \(-0.557939\pi\)
0.689252 + 0.724522i \(0.257939\pi\)
\(318\) −13.2412 13.2412i −0.742528 0.742528i
\(319\) 0 0
\(320\) −6.28581 + 13.6787i −0.351387 + 0.764661i
\(321\) −44.9676 14.6109i −2.50985 0.815499i
\(322\) 26.7487 + 4.23657i 1.49064 + 0.236095i
\(323\) 2.06281 0.326717i 0.114778 0.0181790i
\(324\) −9.97304 + 3.24044i −0.554058 + 0.180024i
\(325\) −11.8193 + 2.86796i −0.655616 + 0.159086i
\(326\) −16.2252 + 22.3321i −0.898631 + 1.23686i
\(327\) −3.64993 + 23.0448i −0.201842 + 1.27438i
\(328\) 0.0449098 + 0.0881404i 0.00247973 + 0.00486674i
\(329\) −19.2331 −1.06035
\(330\) 0 0
\(331\) −32.1615 −1.76775 −0.883877 0.467719i \(-0.845076\pi\)
−0.883877 + 0.467719i \(0.845076\pi\)
\(332\) 2.11289 + 4.14678i 0.115960 + 0.227584i
\(333\) −0.535813 + 3.38299i −0.0293624 + 0.185387i
\(334\) −8.82013 + 12.1399i −0.482616 + 0.664264i
\(335\) −10.3549 + 8.18358i −0.565749 + 0.447117i
\(336\) −25.1315 + 8.16571i −1.37103 + 0.445476i
\(337\) 5.84909 0.926404i 0.318620 0.0504645i 0.00492392 0.999988i \(-0.498433\pi\)
0.313696 + 0.949523i \(0.398433\pi\)
\(338\) 13.7216 + 2.17329i 0.746359 + 0.118212i
\(339\) 53.8222 + 17.4879i 2.92322 + 0.949813i
\(340\) 7.20716 + 19.4630i 0.390863 + 1.05553i
\(341\) 0 0
\(342\) 3.23597 + 3.23597i 0.174981 + 0.174981i
\(343\) 17.9455 9.14369i 0.968966 0.493713i
\(344\) 0.932187 + 1.28305i 0.0502602 + 0.0691772i
\(345\) −37.5840 + 21.1081i −2.02345 + 1.13642i
\(346\) 12.2308 + 37.6424i 0.657530 + 2.02367i
\(347\) −0.195485 0.0996045i −0.0104942 0.00534705i 0.448736 0.893665i \(-0.351875\pi\)
−0.459230 + 0.888318i \(0.651875\pi\)
\(348\) −6.94553 43.8523i −0.372319 2.35073i
\(349\) 17.3755 12.6240i 0.930089 0.675749i −0.0159259 0.999873i \(-0.505070\pi\)
0.946015 + 0.324124i \(0.105070\pi\)
\(350\) −7.93583 19.0278i −0.424188 1.01708i
\(351\) 18.6644i 0.996231i
\(352\) 0 0
\(353\) 17.5847 17.5847i 0.935941 0.935941i −0.0621273 0.998068i \(-0.519788\pi\)
0.998068 + 0.0621273i \(0.0197885\pi\)
\(354\) −5.41719 + 16.6724i −0.287920 + 0.886128i
\(355\) 16.6540 3.33374i 0.883904 0.176937i
\(356\) −11.6084 8.43399i −0.615243 0.447000i
\(357\) −14.0772 + 27.6281i −0.745045 + 1.46223i
\(358\) −12.5861 + 24.7016i −0.665195 + 1.30552i
\(359\) 9.61923 + 6.98878i 0.507683 + 0.368854i 0.811944 0.583735i \(-0.198409\pi\)
−0.304261 + 0.952589i \(0.598409\pi\)
\(360\) 2.08998 3.13612i 0.110152 0.165288i
\(361\) −5.81795 + 17.9058i −0.306208 + 0.942411i
\(362\) −3.51782 + 3.51782i −0.184893 + 0.184893i
\(363\) 0 0
\(364\) 9.44457i 0.495030i
\(365\) 17.4474 0.706753i 0.913240 0.0369931i
\(366\) 6.67930 4.85280i 0.349133 0.253660i
\(367\) −0.712169 4.49646i −0.0371749 0.234713i 0.962104 0.272683i \(-0.0879110\pi\)
−0.999279 + 0.0379697i \(0.987911\pi\)
\(368\) 25.0632 + 12.7704i 1.30651 + 0.665701i
\(369\) 0.571692 + 1.75949i 0.0297611 + 0.0915952i
\(370\) 1.31021 + 2.33289i 0.0681145 + 0.121281i
\(371\) −4.01954 5.53242i −0.208684 0.287229i
\(372\) −6.85556 + 3.49308i −0.355444 + 0.181108i
\(373\) 25.4846 + 25.4846i 1.31954 + 1.31954i 0.914138 + 0.405402i \(0.132869\pi\)
0.405402 + 0.914138i \(0.367131\pi\)
\(374\) 0 0
\(375\) 28.6888 + 15.9293i 1.48148 + 0.822588i
\(376\) −2.61206 0.848709i −0.134707 0.0437688i
\(377\) −19.6776 3.11663i −1.01345 0.160515i
\(378\) −31.2487 + 4.94930i −1.60726 + 0.254565i
\(379\) 6.76838 2.19918i 0.347668 0.112964i −0.129977 0.991517i \(-0.541490\pi\)
0.477645 + 0.878553i \(0.341490\pi\)
\(380\) 1.70468 + 0.199662i 0.0874485 + 0.0102424i
\(381\) −35.7376 + 49.1886i −1.83089 + 2.52001i
\(382\) −2.90945 + 18.3695i −0.148860 + 0.939867i
\(383\) 4.07786 + 8.00325i 0.208369 + 0.408947i 0.971412 0.237401i \(-0.0762955\pi\)
−0.763043 + 0.646348i \(0.776296\pi\)
\(384\) −7.02811 −0.358652
\(385\) 0 0
\(386\) −22.5472 −1.14762
\(387\) 13.4653 + 26.4272i 0.684481 + 1.34337i
\(388\) −3.96506 + 25.0344i −0.201296 + 1.27093i
\(389\) 19.1790 26.3976i 0.972413 1.33841i 0.0315952 0.999501i \(-0.489941\pi\)
0.940818 0.338912i \(-0.110059\pi\)
\(390\) 19.4144 + 24.5655i 0.983084 + 1.24392i
\(391\) 31.3921 10.1999i 1.58757 0.515832i
\(392\) 0.765144 0.121187i 0.0386456 0.00612086i
\(393\) −17.3985 2.75564i −0.877636 0.139004i
\(394\) −50.3256 16.3518i −2.53537 0.823790i
\(395\) −7.30627 3.35747i −0.367618 0.168933i
\(396\) 0 0
\(397\) −14.3673 14.3673i −0.721076 0.721076i 0.247748 0.968824i \(-0.420309\pi\)
−0.968824 + 0.247748i \(0.920309\pi\)
\(398\) 5.75368 2.93165i 0.288406 0.146950i
\(399\) 1.50722 + 2.07452i 0.0754556 + 0.103856i
\(400\) −1.73197 21.3433i −0.0865985 1.06716i
\(401\) 0.814264 + 2.50605i 0.0406624 + 0.125146i 0.969327 0.245774i \(-0.0790423\pi\)
−0.928665 + 0.370920i \(0.879042\pi\)
\(402\) 30.2749 + 15.4258i 1.50997 + 0.769370i
\(403\) 0.540101 + 3.41006i 0.0269043 + 0.169867i
\(404\) −14.7507 + 10.7170i −0.733877 + 0.533193i
\(405\) 8.60644 9.33313i 0.427657 0.463767i
\(406\) 33.7716i 1.67605i
\(407\) 0 0
\(408\) −3.13099 + 3.13099i −0.155007 + 0.155007i
\(409\) 5.33152 16.4087i 0.263626 0.811359i −0.728380 0.685173i \(-0.759726\pi\)
0.992007 0.126186i \(-0.0402735\pi\)
\(410\) 1.20261 + 0.801443i 0.0593925 + 0.0395805i
\(411\) −21.4826 15.6080i −1.05966 0.769885i
\(412\) 6.07176 11.9165i 0.299134 0.587084i
\(413\) −2.90639 + 5.70412i −0.143014 + 0.280681i
\(414\) 58.5130 + 42.5122i 2.87576 + 2.08936i
\(415\) −4.68878 3.12471i −0.230163 0.153386i
\(416\) 5.86264 18.0434i 0.287440 0.884649i
\(417\) 27.1679 27.1679i 1.33042 1.33042i
\(418\) 0 0
\(419\) 24.0620i 1.17551i −0.809041 0.587753i \(-0.800013\pi\)
0.809041 0.587753i \(-0.199987\pi\)
\(420\) −17.2744 + 18.7330i −0.842906 + 0.914077i
\(421\) 16.7203 12.1480i 0.814897 0.592057i −0.100349 0.994952i \(-0.531996\pi\)
0.915246 + 0.402895i \(0.131996\pi\)
\(422\) −6.42521 40.5672i −0.312774 1.97478i
\(423\) −45.7660 23.3189i −2.22522 1.13381i
\(424\) −0.301764 0.928734i −0.0146550 0.0451033i
\(425\) −19.1465 16.2723i −0.928742 0.789324i
\(426\) −25.7012 35.3746i −1.24523 1.71391i
\(427\) 2.68640 1.36879i 0.130004 0.0662403i
\(428\) 21.0388 + 21.0388i 1.01695 + 1.01695i
\(429\) 0 0
\(430\) 21.0529 + 9.67453i 1.01526 + 0.466547i
\(431\) 32.6102 + 10.5957i 1.57078 + 0.510377i 0.959660 0.281163i \(-0.0907201\pi\)
0.611118 + 0.791540i \(0.290720\pi\)
\(432\) −32.4568 5.14065i −1.56158 0.247330i
\(433\) −3.16433 + 0.501180i −0.152068 + 0.0240852i −0.232004 0.972715i \(-0.574528\pi\)
0.0799363 + 0.996800i \(0.474528\pi\)
\(434\) −5.56605 + 1.80852i −0.267179 + 0.0868116i
\(435\) 33.3296 + 42.1728i 1.59803 + 2.02203i
\(436\) 8.63006 11.8783i 0.413305 0.568865i
\(437\) 0.427008 2.69602i 0.0204266 0.128968i
\(438\) −20.4088 40.0545i −0.975170 1.91388i
\(439\) −12.3536 −0.589607 −0.294803 0.955558i \(-0.595254\pi\)
−0.294803 + 0.955558i \(0.595254\pi\)
\(440\) 0 0
\(441\) 14.4880 0.689905
\(442\) −10.8849 21.3628i −0.517741 1.01612i
\(443\) −0.397358 + 2.50882i −0.0188791 + 0.119198i −0.995328 0.0965505i \(-0.969219\pi\)
0.976449 + 0.215748i \(0.0692191\pi\)
\(444\) 1.94387 2.67550i 0.0922518 0.126974i
\(445\) 17.2539 + 2.02087i 0.817913 + 0.0957984i
\(446\) −49.9197 + 16.2199i −2.36376 + 0.768034i
\(447\) 39.4284 6.24484i 1.86490 0.295371i
\(448\) 13.9787 + 2.21401i 0.660430 + 0.104602i
\(449\) 24.4859 + 7.95595i 1.15556 + 0.375464i 0.823235 0.567700i \(-0.192167\pi\)
0.332325 + 0.943165i \(0.392167\pi\)
\(450\) 4.18640 54.8992i 0.197349 2.58797i
\(451\) 0 0
\(452\) −25.1816 25.1816i −1.18444 1.18444i
\(453\) 21.7160 11.0649i 1.02031 0.519873i
\(454\) −7.05859 9.71531i −0.331276 0.455962i
\(455\) 5.59922 + 9.96968i 0.262495 + 0.467386i
\(456\) 0.113154 + 0.348251i 0.00529891 + 0.0163084i
\(457\) −9.78007 4.98320i −0.457492 0.233104i 0.210028 0.977695i \(-0.432644\pi\)
−0.667521 + 0.744591i \(0.732644\pi\)
\(458\) −0.502439 3.17227i −0.0234774 0.148231i
\(459\) −31.1962 + 22.6654i −1.45611 + 1.05793i
\(460\) 27.1033 1.09789i 1.26370 0.0511893i
\(461\) 4.12125i 0.191946i −0.995384 0.0959728i \(-0.969404\pi\)
0.995384 0.0959728i \(-0.0305962\pi\)
\(462\) 0 0
\(463\) 7.07687 7.07687i 0.328890 0.328890i −0.523274 0.852164i \(-0.675290\pi\)
0.852164 + 0.523274i \(0.175290\pi\)
\(464\) 10.8395 33.3604i 0.503209 1.54872i
\(465\) 5.16585 7.75162i 0.239560 0.359473i
\(466\) 34.1701 + 24.8261i 1.58290 + 1.15004i
\(467\) 3.32943 6.53438i 0.154068 0.302375i −0.801052 0.598595i \(-0.795726\pi\)
0.955120 + 0.296220i \(0.0957260\pi\)
\(468\) 11.4510 22.4738i 0.529321 1.03885i
\(469\) 10.0386 + 7.29350i 0.463542 + 0.336783i
\(470\) −39.3438 + 7.87569i −1.81479 + 0.363279i
\(471\) 3.13588 9.65124i 0.144494 0.444706i
\(472\) −0.646428 + 0.646428i −0.0297543 + 0.0297543i
\(473\) 0 0
\(474\) 20.7005i 0.950808i
\(475\) −1.91783 + 0.799860i −0.0879962 + 0.0367001i
\(476\) 15.7859 11.4691i 0.723547 0.525688i
\(477\) −2.85695 18.0381i −0.130811 0.825907i
\(478\) −42.9556 21.8870i −1.96474 1.00109i
\(479\) −1.66414 5.12171i −0.0760367 0.234017i 0.905813 0.423678i \(-0.139261\pi\)
−0.981850 + 0.189661i \(0.939261\pi\)
\(480\) −44.6303 + 25.0655i −2.03709 + 1.14408i
\(481\) −0.872262 1.20057i −0.0397717 0.0547411i
\(482\) 33.8921 17.2689i 1.54374 0.786576i
\(483\) 28.6563 + 28.6563i 1.30391 + 1.30391i
\(484\) 0 0
\(485\) −10.6562 28.7770i −0.483871 1.30670i
\(486\) 11.8549 + 3.85189i 0.537749 + 0.174725i
\(487\) 13.7792 + 2.18242i 0.624397 + 0.0988948i 0.460612 0.887601i \(-0.347630\pi\)
0.163785 + 0.986496i \(0.447630\pi\)
\(488\) 0.425243 0.0673518i 0.0192498 0.00304887i
\(489\) −39.2854 + 12.7646i −1.77655 + 0.577235i
\(490\) 8.87938 7.01745i 0.401129 0.317016i
\(491\) 19.1750 26.3921i 0.865354 1.19106i −0.114912 0.993376i \(-0.536659\pi\)
0.980266 0.197682i \(-0.0633414\pi\)
\(492\) 0.279434 1.76427i 0.0125978 0.0795396i
\(493\) −18.6866 36.6745i −0.841602 1.65174i
\(494\) −1.98274 −0.0892078
\(495\) 0 0
\(496\) −6.07876 −0.272944
\(497\) −7.24931 14.2276i −0.325176 0.638194i
\(498\) −2.26922 + 14.3273i −0.101686 + 0.642022i
\(499\) −22.8865 + 31.5006i −1.02454 + 1.41016i −0.115572 + 0.993299i \(0.536870\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(500\) −11.5348 17.1274i −0.515850 0.765962i
\(501\) −21.3558 + 6.93891i −0.954106 + 0.310008i
\(502\) −14.7112 + 2.33003i −0.656595 + 0.103994i
\(503\) 41.3883 + 6.55527i 1.84542 + 0.292285i 0.978512 0.206191i \(-0.0661068\pi\)
0.866903 + 0.498476i \(0.166107\pi\)
\(504\) −3.36977 1.09490i −0.150101 0.0487709i
\(505\) 9.21727 20.0579i 0.410163 0.892564i
\(506\) 0 0
\(507\) 14.7002 + 14.7002i 0.652859 + 0.652859i
\(508\) 34.0903 17.3699i 1.51251 0.770664i
\(509\) −10.7098 14.7407i −0.474702 0.653372i 0.502774 0.864418i \(-0.332313\pi\)
−0.977476 + 0.211046i \(0.932313\pi\)
\(510\) −17.4834 + 62.2812i −0.774179 + 2.75786i
\(511\) −5.07305 15.6132i −0.224419 0.690689i
\(512\) 27.4711 + 13.9972i 1.21406 + 0.618595i
\(513\) 0.498846 + 3.14959i 0.0220246 + 0.139058i
\(514\) 32.3124 23.4764i 1.42524 1.03550i
\(515\) 0.655359 + 16.1787i 0.0288786 + 0.712918i
\(516\) 28.6376i 1.26070i
\(517\) 0 0
\(518\) 1.77873 1.77873i 0.0781531 0.0781531i
\(519\) −18.3023 + 56.3288i −0.803383 + 2.47256i
\(520\) 0.320496 + 1.60107i 0.0140547 + 0.0702115i
\(521\) −14.0506 10.2083i −0.615566 0.447235i 0.235804 0.971801i \(-0.424228\pi\)
−0.851370 + 0.524566i \(0.824228\pi\)
\(522\) 40.9459 80.3609i 1.79215 3.51730i
\(523\) −7.95808 + 15.6186i −0.347982 + 0.682954i −0.996965 0.0778493i \(-0.975195\pi\)
0.648983 + 0.760803i \(0.275195\pi\)
\(524\) 8.96791 + 6.51557i 0.391765 + 0.284634i
\(525\) 7.12900 30.0157i 0.311135 1.30999i
\(526\) −3.63195 + 11.1780i −0.158360 + 0.487383i
\(527\) −5.04380 + 5.04380i −0.219711 + 0.219711i
\(528\) 0 0
\(529\) 20.1399i 0.875649i
\(530\) −10.4879 9.67134i −0.455567 0.420096i
\(531\) −13.8318 + 10.0494i −0.600248 + 0.436106i
\(532\) −0.252426 1.59376i −0.0109441 0.0690981i
\(533\) −0.714179 0.363893i −0.0309345 0.0157619i
\(534\) −13.8201 42.5339i −0.598055 1.84062i
\(535\) −34.6815 9.73569i −1.49941 0.420911i
\(536\) 1.04151 + 1.43352i 0.0449864 + 0.0619185i
\(537\) −36.9639 + 18.8340i −1.59511 + 0.812748i
\(538\) −23.9710 23.9710i −1.03346 1.03346i
\(539\) 0 0
\(540\) −29.7170 + 11.0042i −1.27881 + 0.473546i
\(541\) −0.118543 0.0385168i −0.00509654 0.00165597i 0.306468 0.951881i \(-0.400853\pi\)
−0.311564 + 0.950225i \(0.600853\pi\)
\(542\) −35.9238 5.68977i −1.54306 0.244396i
\(543\) −7.35295 + 1.16459i −0.315545 + 0.0499775i
\(544\) 37.2776 12.1122i 1.59826 0.519307i
\(545\) −2.06785 + 17.6550i −0.0885770 + 0.756258i
\(546\) 17.3028 23.8152i 0.740490 1.01920i
\(547\) −0.329513 + 2.08046i −0.0140890 + 0.0889542i −0.993731 0.111799i \(-0.964339\pi\)
0.979642 + 0.200753i \(0.0643388\pi\)
\(548\) 7.58609 + 14.8885i 0.324062 + 0.636007i
\(549\) 8.05197 0.343650
\(550\) 0 0
\(551\) −3.40387 −0.145010
\(552\) 2.62730 + 5.15636i 0.111825 + 0.219469i
\(553\) −1.18258 + 7.46651i −0.0502884 + 0.317508i
\(554\) 12.4755 17.1711i 0.530034 0.729529i
\(555\) −0.465770 + 3.97668i −0.0197709 + 0.168801i
\(556\) −22.9943 + 7.47131i −0.975177 + 0.316854i
\(557\) 30.1946 4.78236i 1.27939 0.202635i 0.520503 0.853860i \(-0.325744\pi\)
0.758885 + 0.651225i \(0.225744\pi\)
\(558\) −15.4374 2.44504i −0.653516 0.103507i
\(559\) −12.2215 3.97099i −0.516913 0.167955i
\(560\) −18.8791 + 6.99096i −0.797789 + 0.295422i
\(561\) 0 0
\(562\) 24.2507 + 24.2507i 1.02295 + 1.02295i
\(563\) −22.4594 + 11.4436i −0.946550 + 0.482291i −0.857926 0.513774i \(-0.828247\pi\)
−0.0886241 + 0.996065i \(0.528247\pi\)
\(564\) 29.1506 + 40.1223i 1.22746 + 1.68945i
\(565\) 41.5106 + 11.6527i 1.74636 + 0.490235i
\(566\) 6.59249 + 20.2896i 0.277103 + 0.852835i
\(567\) −10.6349 5.41875i −0.446624 0.227566i
\(568\) −0.356706 2.25215i −0.0149670 0.0944981i
\(569\) −12.6331 + 9.17847i −0.529606 + 0.384781i −0.820210 0.572062i \(-0.806144\pi\)
0.290604 + 0.956843i \(0.406144\pi\)
\(570\) 3.93271 + 3.62650i 0.164723 + 0.151898i
\(571\) 13.3555i 0.558911i 0.960159 + 0.279455i \(0.0901539\pi\)
−0.960159 + 0.279455i \(0.909846\pi\)
\(572\) 0 0
\(573\) −19.6796 + 19.6796i −0.822126 + 0.822126i
\(574\) 0.419862 1.29220i 0.0175247 0.0539355i
\(575\) −27.9593 + 17.2271i −1.16598 + 0.718421i
\(576\) 30.5785 + 22.2166i 1.27411 + 0.925692i
\(577\) −15.8403 + 31.0884i −0.659442 + 1.29423i 0.282763 + 0.959190i \(0.408749\pi\)
−0.942205 + 0.335038i \(0.891251\pi\)
\(578\) 7.35069 14.4265i 0.305748 0.600065i
\(579\) −27.2962 19.8319i −1.13439 0.824184i
\(580\) −6.63939 33.1677i −0.275686 1.37722i
\(581\) −1.63698 + 5.03810i −0.0679133 + 0.209016i
\(582\) −55.8621 + 55.8621i −2.31556 + 2.31556i
\(583\) 0 0
\(584\) 2.34431i 0.0970081i
\(585\) 1.23597 + 30.5120i 0.0511009 + 1.26152i
\(586\) 1.36774 0.993724i 0.0565010 0.0410503i
\(587\) −2.33252 14.7270i −0.0962734 0.607847i −0.987902 0.155079i \(-0.950437\pi\)
0.891629 0.452768i \(-0.149563\pi\)
\(588\) −12.4640 6.35071i −0.514005 0.261899i
\(589\) 0.182282 + 0.561008i 0.00751082 + 0.0231159i
\(590\) −3.60965 + 12.8586i −0.148607 + 0.529382i
\(591\) −46.5429 64.0608i −1.91452 2.63511i
\(592\) 2.32799 1.18617i 0.0956798 0.0487513i
\(593\) 0.611093 + 0.611093i 0.0250946 + 0.0250946i 0.719543 0.694448i \(-0.244351\pi\)
−0.694448 + 0.719543i \(0.744351\pi\)
\(594\) 0 0
\(595\) −9.86412 + 21.4655i −0.404390 + 0.880000i
\(596\) −23.8912 7.76272i −0.978622 0.317973i
\(597\) 9.54415 + 1.51164i 0.390616 + 0.0618675i
\(598\) −30.9501 + 4.90201i −1.26564 + 0.200458i
\(599\) 5.39887 1.75420i 0.220592 0.0716747i −0.196636 0.980477i \(-0.563002\pi\)
0.417228 + 0.908802i \(0.363002\pi\)
\(600\) 2.29271 3.76187i 0.0935997 0.153578i
\(601\) 3.91920 5.39431i 0.159867 0.220039i −0.721568 0.692344i \(-0.756578\pi\)
0.881435 + 0.472305i \(0.156578\pi\)
\(602\) 3.40759 21.5147i 0.138883 0.876873i
\(603\) 15.0445 + 29.5264i 0.612658 + 1.20241i
\(604\) −15.3371 −0.624056
\(605\) 0 0
\(606\) −56.8292 −2.30853
\(607\) 14.9530 + 29.3470i 0.606925 + 1.19116i 0.966168 + 0.257913i \(0.0830349\pi\)
−0.359243 + 0.933244i \(0.616965\pi\)
\(608\) 0.507065 3.20148i 0.0205642 0.129837i
\(609\) 29.7045 40.8848i 1.20369 1.65673i
\(610\) 4.93488 3.90008i 0.199807 0.157910i
\(611\) 21.1648 6.87688i 0.856238 0.278209i
\(612\) 51.4690 8.15188i 2.08051 0.329520i
\(613\) −16.5680 2.62411i −0.669173 0.105987i −0.187402 0.982283i \(-0.560007\pi\)
−0.481772 + 0.876297i \(0.660007\pi\)
\(614\) −12.1703 3.95438i −0.491154 0.159586i
\(615\) 0.750981 + 2.02803i 0.0302825 + 0.0817780i
\(616\) 0 0
\(617\) 0.420747 + 0.420747i 0.0169386 + 0.0169386i 0.715525 0.698587i \(-0.246187\pi\)
−0.698587 + 0.715525i \(0.746187\pi\)
\(618\) 37.1419 18.9247i 1.49406 0.761264i
\(619\) 3.59245 + 4.94459i 0.144393 + 0.198740i 0.875088 0.483965i \(-0.160804\pi\)
−0.730695 + 0.682704i \(0.760804\pi\)
\(620\) −5.11098 + 2.87045i −0.205262 + 0.115280i
\(621\) 15.5737 + 47.9309i 0.624951 + 1.92340i
\(622\) 9.63633 + 4.90995i 0.386382 + 0.196871i
\(623\) −2.55492 16.1311i −0.102361 0.646281i
\(624\) 24.7360 17.9717i 0.990231 0.719445i
\(625\) 22.3301 + 11.2413i 0.893203 + 0.449653i
\(626\) 31.3350i 1.25240i
\(627\) 0 0
\(628\) −4.51549 + 4.51549i −0.180188 + 0.180188i
\(629\) 0.947416 2.91585i 0.0377760 0.116262i
\(630\) −50.7567 + 10.1603i −2.02219 + 0.404795i
\(631\) 25.0603 + 18.2074i 0.997636 + 0.724825i 0.961580 0.274524i \(-0.0885204\pi\)
0.0360563 + 0.999350i \(0.488520\pi\)
\(632\) −0.490086 + 0.961848i −0.0194946 + 0.0382602i
\(633\) 27.9032 54.7631i 1.10905 2.17664i
\(634\) −16.1149 11.7082i −0.640005 0.464991i
\(635\) −25.6879 + 38.5461i −1.01940 + 1.52965i
\(636\) −5.44903 + 16.7704i −0.216068 + 0.664990i
\(637\) −4.43854 + 4.43854i −0.175862 + 0.175862i
\(638\) 0 0
\(639\) 42.6445i 1.68699i
\(640\) −5.35004 + 0.216717i −0.211479 + 0.00856650i
\(641\) −13.8769 + 10.0822i −0.548106 + 0.398222i −0.827087 0.562074i \(-0.810003\pi\)
0.278981 + 0.960297i \(0.410003\pi\)
\(642\) 14.5072 + 91.5950i 0.572554 + 3.61496i
\(643\) 32.0312 + 16.3207i 1.26319 + 0.643626i 0.951818 0.306663i \(-0.0992126\pi\)
0.311369 + 0.950289i \(0.399213\pi\)
\(644\) −7.88061 24.2540i −0.310540 0.955743i
\(645\) 16.9778 + 30.2298i 0.668501 + 1.19030i
\(646\) −2.40777 3.31401i −0.0947325 0.130388i
\(647\) −1.57506 + 0.802534i −0.0619220 + 0.0315509i −0.484677 0.874693i \(-0.661063\pi\)
0.422755 + 0.906244i \(0.361063\pi\)
\(648\) −1.20522 1.20522i −0.0473453 0.0473453i
\(649\) 0 0
\(650\) 15.5364 + 18.1015i 0.609387 + 0.709998i
\(651\) −8.32913 2.70630i −0.326444 0.106068i
\(652\) 25.6736 + 4.06630i 1.00546 + 0.159249i
\(653\) 27.8781 4.41546i 1.09095 0.172790i 0.415064 0.909792i \(-0.363759\pi\)
0.675891 + 0.737002i \(0.263759\pi\)
\(654\) 43.5228 14.1414i 1.70187 0.552972i
\(655\) −13.3293 1.56120i −0.520818 0.0610010i
\(656\) 0.829502 1.14171i 0.0323866 0.0445763i
\(657\) 6.85855 43.3032i 0.267577 1.68942i
\(658\) 17.1259 + 33.6115i 0.667637 + 1.31031i
\(659\) −26.3172 −1.02517 −0.512586 0.858636i \(-0.671312\pi\)
−0.512586 + 0.858636i \(0.671312\pi\)
\(660\) 0 0
\(661\) −31.2578 −1.21579 −0.607893 0.794019i \(-0.707985\pi\)
−0.607893 + 0.794019i \(0.707985\pi\)
\(662\) 28.6379 + 56.2050i 1.11304 + 2.18447i
\(663\) 5.61257 35.4364i 0.217974 1.37624i
\(664\) −0.444638 + 0.611992i −0.0172553 + 0.0237499i
\(665\) 1.21132 + 1.53272i 0.0469730 + 0.0594362i
\(666\) 6.38918 2.07597i 0.247576 0.0804423i
\(667\) −53.1335 + 8.41552i −2.05734 + 0.325850i
\(668\) 13.9564 + 2.21047i 0.539988 + 0.0855256i
\(669\) −74.7006 24.2717i −2.88809 0.938399i
\(670\) 23.5219 + 10.8091i 0.908732 + 0.417593i
\(671\) 0 0
\(672\) 34.0288 + 34.0288i 1.31269 + 1.31269i
\(673\) −20.0257 + 10.2036i −0.771933 + 0.393320i −0.795151 0.606411i \(-0.792609\pi\)
0.0232184 + 0.999730i \(0.492609\pi\)
\(674\) −6.82723 9.39688i −0.262975 0.361954i
\(675\) 24.8453 29.2338i 0.956297 1.12521i
\(676\) −4.04263 12.4419i −0.155486 0.478536i
\(677\) 2.59702 + 1.32325i 0.0998115 + 0.0508565i 0.503184 0.864180i \(-0.332162\pi\)
−0.403372 + 0.915036i \(0.632162\pi\)
\(678\) −17.3638 109.631i −0.666854 4.21035i
\(679\) −23.3403 + 16.9577i −0.895718 + 0.650777i
\(680\) −2.28687 + 2.47997i −0.0876976 + 0.0951024i
\(681\) 17.9702i 0.688618i
\(682\) 0 0
\(683\) 13.6345 13.6345i 0.521710 0.521710i −0.396378 0.918087i \(-0.629733\pi\)
0.918087 + 0.396378i \(0.129733\pi\)
\(684\) 1.33167 4.09847i 0.0509178 0.156709i
\(685\) −16.8345 11.2189i −0.643215 0.428652i
\(686\) −31.9588 23.2194i −1.22019 0.886521i
\(687\) 2.18198 4.28237i 0.0832476 0.163383i
\(688\) 10.2715 20.1590i 0.391599 0.768556i
\(689\) 6.40140 + 4.65089i 0.243874 + 0.177185i
\(690\) 70.3545 + 46.8858i 2.67835 + 1.78491i
\(691\) 5.36693 16.5177i 0.204168 0.628363i −0.795579 0.605850i \(-0.792833\pi\)
0.999747 0.0225132i \(-0.00716677\pi\)
\(692\) 26.3543 26.3543i 1.00184 1.00184i
\(693\) 0 0
\(694\) 0.430318i 0.0163347i
\(695\) 19.8434 21.5189i 0.752704 0.816259i
\(696\) 5.83833 4.24180i 0.221301 0.160785i
\(697\) −0.259053 1.63560i −0.00981235 0.0619527i
\(698\) −37.5334 19.1242i −1.42066 0.723863i
\(699\) 19.5310 + 60.1102i 0.738730 + 2.27358i
\(700\) −12.5722 + 14.7929i −0.475186 + 0.559118i
\(701\) 18.9667 + 26.1054i 0.716363 + 0.985989i 0.999637 + 0.0269497i \(0.00857939\pi\)
−0.283274 + 0.959039i \(0.591421\pi\)
\(702\) 32.6176 16.6195i 1.23107 0.627263i
\(703\) −0.179281 0.179281i −0.00676169 0.00676169i
\(704\) 0 0
\(705\) −54.5579 25.0712i −2.05477 0.944234i
\(706\) −46.3890 15.0727i −1.74587 0.567269i
\(707\) −20.4978 3.24653i −0.770899 0.122098i
\(708\) 16.3045 2.58238i 0.612760 0.0970517i
\(709\) 1.87031 0.607701i 0.0702410 0.0228227i −0.273686 0.961819i \(-0.588243\pi\)
0.343927 + 0.938996i \(0.388243\pi\)
\(710\) −20.6554 26.1359i −0.775184 0.980861i
\(711\) −11.8667 + 16.3331i −0.445035 + 0.612539i
\(712\) 0.364842 2.30352i 0.0136730 0.0863282i
\(713\) 4.23238 + 8.30652i 0.158504 + 0.311081i
\(714\) 60.8174 2.27603
\(715\) 0 0
\(716\) 26.1059 0.975625
\(717\) −32.7520 64.2795i −1.22315 2.40056i
\(718\) 3.64815 23.0335i 0.136148 0.859604i
\(719\) 0.795714 1.09521i 0.0296751 0.0408443i −0.793922 0.608020i \(-0.791964\pi\)
0.823597 + 0.567176i \(0.191964\pi\)
\(720\) −53.3999 6.25448i −1.99010 0.233091i
\(721\) 14.4779 4.70415i 0.539185 0.175192i
\(722\) 36.4725 5.77668i 1.35737 0.214986i
\(723\) 56.2199 + 8.90435i 2.09084 + 0.331156i
\(724\) 4.45544 + 1.44766i 0.165585 + 0.0538019i
\(725\) 26.6720 + 31.0757i 0.990575 + 1.15412i
\(726\) 0 0
\(727\) 17.8003 + 17.8003i 0.660177 + 0.660177i 0.955422 0.295245i \(-0.0954012\pi\)
−0.295245 + 0.955422i \(0.595401\pi\)
\(728\) 1.36780 0.696927i 0.0506939 0.0258298i
\(729\) 20.9755 + 28.8703i 0.776872 + 1.06927i
\(730\) −16.7710 29.8616i −0.620722 1.10523i
\(731\) −8.20408 25.2496i −0.303439 0.933888i
\(732\) −6.92708 3.52952i −0.256032 0.130455i
\(733\) 5.30013 + 33.4637i 0.195765 + 1.23601i 0.868336 + 0.495977i \(0.165190\pi\)
−0.672571 + 0.740033i \(0.734810\pi\)
\(734\) −7.22381 + 5.24840i −0.266636 + 0.193722i
\(735\) 16.9220 0.685468i 0.624176 0.0252839i
\(736\) 51.2279i 1.88829i
\(737\) 0 0
\(738\) 2.56580 2.56580i 0.0944483 0.0944483i
\(739\) −10.7474 + 33.0772i −0.395351 + 1.21676i 0.533337 + 0.845903i \(0.320938\pi\)
−0.928688 + 0.370862i \(0.879062\pi\)
\(740\) 1.39724 2.09663i 0.0513635 0.0770735i
\(741\) −2.40036 1.74396i −0.0881795 0.0640661i
\(742\) −6.08923 + 11.9508i −0.223543 + 0.438727i
\(743\) 3.92415 7.70158i 0.143963 0.282544i −0.807754 0.589520i \(-0.799317\pi\)
0.951717 + 0.306976i \(0.0993171\pi\)
\(744\) −1.01176 0.735088i −0.0370930 0.0269496i
\(745\) 29.8217 5.96959i 1.09258 0.218709i
\(746\) 21.8440 67.2290i 0.799766 2.46143i
\(747\) −10.0037 + 10.0037i −0.366014 + 0.366014i
\(748\) 0 0
\(749\) 33.8663i 1.23745i
\(750\) 2.29227 64.3203i 0.0837019 2.34864i
\(751\) −39.7842 + 28.9049i −1.45175 + 1.05475i −0.466326 + 0.884613i \(0.654423\pi\)
−0.985420 + 0.170142i \(0.945577\pi\)
\(752\) 6.12934 + 38.6991i 0.223514 + 1.41121i
\(753\) −19.8593 10.1188i −0.723711 0.368749i
\(754\) 12.0752 + 37.1636i 0.439752 + 1.35342i
\(755\) 16.1898 9.09259i 0.589207 0.330913i
\(756\) 17.5116 + 24.1027i 0.636891 + 0.876605i
\(757\) 8.85952 4.51415i 0.322005 0.164070i −0.285515 0.958374i \(-0.592165\pi\)
0.607520 + 0.794305i \(0.292165\pi\)
\(758\) −9.87010 9.87010i −0.358498 0.358498i
\(759\) 0 0
\(760\) 0.0968751 + 0.261612i 0.00351403 + 0.00948966i
\(761\) −31.3316 10.1803i −1.13577 0.369034i −0.320004 0.947416i \(-0.603684\pi\)
−0.815766 + 0.578383i \(0.803684\pi\)
\(762\) 117.784 + 18.6551i 4.26685 + 0.675803i
\(763\) 16.5062 2.61432i 0.597563 0.0946447i
\(764\) 16.6564 5.41198i 0.602606 0.195799i
\(765\) −49.4977 + 39.1185i −1.78959 + 1.41433i
\(766\) 10.3553 14.2528i 0.374152 0.514975i
\(767\) 1.15878 7.31623i 0.0418410 0.264174i
\(768\) 24.1992 + 47.4936i 0.873214 + 1.71378i
\(769\) 48.3159 1.74232 0.871159 0.491002i \(-0.163369\pi\)
0.871159 + 0.491002i \(0.163369\pi\)
\(770\) 0 0
\(771\) 59.7675 2.15247
\(772\) 9.63905 + 18.9177i 0.346917 + 0.680863i
\(773\) 0.171355 1.08189i 0.00616320 0.0389129i −0.984415 0.175861i \(-0.943729\pi\)
0.990578 + 0.136948i \(0.0437292\pi\)
\(774\) 34.1937 47.0636i 1.22907 1.69167i
\(775\) 3.69339 6.06009i 0.132671 0.217685i
\(776\) −3.91816 + 1.27309i −0.140654 + 0.0457012i
\(777\) 3.71791 0.588859i 0.133379 0.0211252i
\(778\) −63.2099 10.0115i −2.26618 0.358928i
\(779\) −0.130242 0.0423183i −0.00466642 0.00151621i
\(780\) 12.3114 26.7911i 0.440819 0.959275i
\(781\) 0 0
\(782\) −45.7781 45.7781i −1.63702 1.63702i
\(783\) 55.9963 28.5315i 2.00114 1.01963i
\(784\) −6.49601 8.94099i −0.232000 0.319321i
\(785\) 2.08953 7.44355i 0.0745787 0.265672i
\(786\) 10.6766 + 32.8590i 0.380820 + 1.17204i
\(787\) 45.9412 + 23.4082i 1.63763 + 0.834412i 0.997828 + 0.0658696i \(0.0209821\pi\)
0.639798 + 0.768543i \(0.279018\pi\)
\(788\) 7.79490 + 49.2150i 0.277682 + 1.75321i
\(789\) −14.2288 + 10.3378i −0.506557 + 0.368036i
\(790\) 0.638317 + 15.7580i 0.0227103 + 0.560643i
\(791\) 40.5349i 1.44126i
\(792\) 0 0
\(793\) −2.46680 + 2.46680i −0.0875987 + 0.0875987i
\(794\) −12.3149 + 37.9014i −0.437040 + 1.34507i
\(795\) −4.19035 20.9333i −0.148616 0.742427i
\(796\) −4.91946 3.57420i −0.174366 0.126684i
\(797\) 0.966918 1.89768i 0.0342500 0.0672194i −0.873247 0.487277i \(-0.837990\pi\)
0.907497 + 0.420058i \(0.137990\pi\)
\(798\) 2.28330 4.48124i 0.0808281 0.158634i
\(799\) 37.1961 + 27.0245i 1.31590 + 0.956059i
\(800\) −33.2012 + 20.4569i −1.17384 + 0.723261i
\(801\) 13.4785 41.4825i 0.476238 1.46571i
\(802\) 3.65448 3.65448i 0.129044 0.129044i
\(803\) 0 0
\(804\) 31.9961i 1.12842i
\(805\) 22.6978 + 20.9305i 0.799992 + 0.737703i
\(806\) 5.47845 3.98033i 0.192970 0.140201i
\(807\) −7.93573 50.1042i −0.279351 1.76375i
\(808\) −2.64056 1.34543i −0.0928945 0.0473321i
\(809\) −4.56323 14.0442i −0.160435 0.493767i 0.838236 0.545307i \(-0.183587\pi\)
−0.998671 + 0.0515402i \(0.983587\pi\)
\(810\) −23.9740 6.72991i −0.842359 0.236465i
\(811\) 23.9177 + 32.9199i 0.839865 + 1.15598i 0.986006 + 0.166711i \(0.0533148\pi\)
−0.146141 + 0.989264i \(0.546685\pi\)
\(812\) −28.3353 + 14.4375i −0.994373 + 0.506659i
\(813\) −38.4857 38.4857i −1.34975 1.34975i
\(814\) 0 0
\(815\) −29.5118 + 10.9282i −1.03375 + 0.382799i
\(816\) 60.0770 + 19.5202i 2.10311 + 0.683343i
\(817\) −2.16849 0.343455i −0.0758657 0.0120160i
\(818\) −33.4231 + 5.29369i −1.16861 + 0.185090i
\(819\) 27.3044 8.87173i 0.954092 0.310003i
\(820\) 0.158312 1.35164i 0.00552848 0.0472014i
\(821\) 2.48495 3.42025i 0.0867255 0.119367i −0.763450 0.645867i \(-0.776496\pi\)
0.850175 + 0.526500i \(0.176496\pi\)
\(822\) −8.14739 + 51.4406i −0.284173 + 1.79420i
\(823\) −8.06872 15.8357i −0.281258 0.552000i 0.706553 0.707660i \(-0.250249\pi\)
−0.987811 + 0.155661i \(0.950249\pi\)
\(824\) 2.17383 0.0757291
\(825\) 0 0
\(826\) 12.5564 0.436893
\(827\) −9.04943 17.7605i −0.314680 0.617594i 0.678446 0.734651i \(-0.262654\pi\)
−0.993125 + 0.117057i \(0.962654\pi\)
\(828\) 10.6542 67.2683i 0.370261 2.33773i
\(829\) −17.0873 + 23.5187i −0.593466 + 0.816837i −0.995091 0.0989681i \(-0.968446\pi\)
0.401624 + 0.915805i \(0.368446\pi\)
\(830\) −1.28562 + 10.9764i −0.0446244 + 0.380997i
\(831\) 30.2064 9.81465i 1.04785 0.340467i
\(832\) −16.1743 + 2.56176i −0.560744 + 0.0888131i
\(833\) −12.8087 2.02870i −0.443796 0.0702904i
\(834\) −71.6698 23.2869i −2.48172 0.806360i
\(835\) −16.0428 + 5.94066i −0.555184 + 0.205585i
\(836\) 0 0
\(837\) −7.70110 7.70110i −0.266189 0.266189i
\(838\) −42.0504 + 21.4258i −1.45261 + 0.740141i
\(839\) 20.6522 + 28.4253i 0.712992 + 0.981349i 0.999728 + 0.0233391i \(0.00742975\pi\)
−0.286736 + 0.958010i \(0.592570\pi\)
\(840\) −3.98769 1.11941i −0.137588 0.0386234i
\(841\) 11.7685 + 36.2198i 0.405812 + 1.24896i
\(842\) −36.1181 18.4031i −1.24471 0.634212i
\(843\) 8.02831 + 50.6887i 0.276510 + 1.74581i
\(844\) −31.2902 + 22.7336i −1.07705 + 0.782524i
\(845\) 11.6436 + 10.7370i 0.400552 + 0.369365i
\(846\) 100.744i 3.46365i
\(847\) 0 0
\(848\) −9.85087 + 9.85087i −0.338280 + 0.338280i
\(849\) −9.86511 + 30.3617i −0.338570 + 1.04201i
\(850\) −11.3885 + 47.9497i −0.390622 + 1.64466i
\(851\) −3.24176 2.35528i −0.111126 0.0807379i
\(852\) −18.6929 + 36.6869i −0.640408 + 1.25687i
\(853\) −18.3228 + 35.9605i −0.627361 + 1.23127i 0.330438 + 0.943828i \(0.392803\pi\)
−0.957799 + 0.287438i \(0.907197\pi\)
\(854\) −4.78415 3.47589i −0.163710 0.118943i
\(855\) 1.02407 + 5.11582i 0.0350223 + 0.174957i
\(856\) −1.49444 + 4.59940i −0.0510788 + 0.157204i
\(857\) −27.5489 + 27.5489i −0.941052 + 0.941052i −0.998357 0.0573050i \(-0.981749\pi\)
0.0573050 + 0.998357i \(0.481749\pi\)
\(858\) 0 0
\(859\) 39.9841i 1.36424i 0.731240 + 0.682120i \(0.238942\pi\)
−0.731240 + 0.682120i \(0.761058\pi\)
\(860\) −0.883062 21.7999i −0.0301122 0.743371i
\(861\) 1.64488 1.19508i 0.0560574 0.0407281i
\(862\) −10.5205 66.4240i −0.358330 2.26241i
\(863\) 5.99932 + 3.05681i 0.204219 + 0.104055i 0.553109 0.833109i \(-0.313441\pi\)
−0.348890 + 0.937164i \(0.613441\pi\)
\(864\) 18.4935 + 56.9171i 0.629161 + 1.93636i
\(865\) −12.1954 + 43.4438i −0.414657 + 1.47713i
\(866\) 3.69350 + 5.08367i 0.125510 + 0.172750i
\(867\) 21.5881 10.9997i 0.733171 0.373569i
\(868\) 3.89692 + 3.89692i 0.132270 + 0.132270i
\(869\) 0 0
\(870\) 44.0227 95.7987i 1.49251 3.24788i
\(871\) −13.6547 4.43670i −0.462673 0.150332i
\(872\) 2.35708 + 0.373324i 0.0798206 + 0.0126423i
\(873\) −76.0994 + 12.0530i −2.57558 + 0.407931i
\(874\) −5.09176 + 1.65441i −0.172231 + 0.0559614i
\(875\) 4.50129 23.0688i 0.152171 0.779868i
\(876\) −24.8820 + 34.2471i −0.840684 + 1.15710i
\(877\) 6.83998 43.1859i 0.230970 1.45828i −0.550758 0.834665i \(-0.685661\pi\)
0.781728 0.623620i \(-0.214339\pi\)
\(878\) 11.0002 + 21.5890i 0.371238 + 0.728595i
\(879\) 2.52988 0.0853307
\(880\) 0 0
\(881\) 57.5099 1.93756 0.968779 0.247928i \(-0.0797496\pi\)
0.968779 + 0.247928i \(0.0797496\pi\)
\(882\) −12.9007 25.3190i −0.434389 0.852537i
\(883\) 3.13240 19.7772i 0.105414 0.665555i −0.877233 0.480066i \(-0.840613\pi\)
0.982646 0.185490i \(-0.0593871\pi\)
\(884\) −13.2706 + 18.2654i −0.446339 + 0.614333i
\(885\) −15.6800 + 12.3921i −0.527079 + 0.416555i
\(886\) 4.73821 1.53954i 0.159183 0.0517218i
\(887\) 27.6952 4.38649i 0.929914 0.147284i 0.326940 0.945045i \(-0.393982\pi\)
0.602974 + 0.797761i \(0.293982\pi\)
\(888\) 0.530916 + 0.0840889i 0.0178164 + 0.00282184i
\(889\) 41.4178 + 13.4575i 1.38911 + 0.451349i
\(890\) −11.8319 31.9521i −0.396607 1.07104i
\(891\) 0 0
\(892\) 34.9499 + 34.9499i 1.17021 + 1.17021i
\(893\) 3.38774 1.72614i 0.113366 0.0577630i
\(894\) −46.0220 63.3438i −1.53921 2.11853i
\(895\) −27.5574 + 15.4769i −0.921142 + 0.517336i
\(896\) 1.55559 + 4.78761i 0.0519686 + 0.159943i
\(897\) −41.7807 21.2883i −1.39502 0.710796i
\(898\) −7.89950 49.8755i −0.263610 1.66437i
\(899\) 9.40513 6.83323i 0.313679 0.227901i
\(900\) −47.8517 + 19.9572i −1.59506 + 0.665241i
\(901\) 16.3474i 0.544610i
\(902\) 0 0
\(903\) 23.0490 23.0490i 0.767023 0.767023i
\(904\) 1.78871 5.50507i 0.0594915 0.183096i
\(905\) −5.56141 + 1.11326i −0.184867 + 0.0370061i
\(906\) −38.6736 28.0980i −1.28485 0.933495i
\(907\) −25.1656 + 49.3903i −0.835610 + 1.63998i −0.0692198 + 0.997601i \(0.522051\pi\)
−0.766390 + 0.642375i \(0.777949\pi\)
\(908\) −5.13383 + 10.0757i −0.170372 + 0.334374i
\(909\) −44.8392 32.5776i −1.48722 1.08053i
\(910\) 12.4371 18.6625i 0.412286 0.618656i
\(911\) −1.27192 + 3.91455i −0.0421404 + 0.129695i −0.969913 0.243450i \(-0.921721\pi\)
0.927773 + 0.373145i \(0.121721\pi\)
\(912\) 3.69382 3.69382i 0.122315 0.122315i
\(913\) 0 0
\(914\) 21.5288i 0.712108i
\(915\) 9.40469 0.380961i 0.310910 0.0125942i
\(916\) −2.44683 + 1.77773i −0.0808456 + 0.0587377i
\(917\) 1.97377 + 12.4619i 0.0651797 + 0.411528i
\(918\) 67.3881 + 34.3359i 2.22414 + 1.13325i
\(919\) −4.21427 12.9702i −0.139016 0.427848i 0.857177 0.515022i \(-0.172216\pi\)
−0.996193 + 0.0871745i \(0.972216\pi\)
\(920\) 2.15899 + 3.84418i 0.0711797 + 0.126739i
\(921\) −11.2556 15.4919i −0.370883 0.510477i
\(922\) −7.20224 + 3.66972i −0.237193 + 0.120856i
\(923\) 13.0646 + 13.0646i 0.430025 + 0.430025i
\(924\) 0 0
\(925\) −0.231937 + 3.04155i −0.00762603 + 0.100006i
\(926\) −18.6690 6.06592i −0.613501 0.199339i
\(927\) 40.1543 + 6.35981i 1.31884 + 0.208884i
\(928\) −63.0951 + 9.99328i −2.07120 + 0.328046i
\(929\) −35.5942 + 11.5653i −1.16781 + 0.379444i −0.827824 0.560988i \(-0.810421\pi\)
−0.339983 + 0.940431i \(0.610421\pi\)
\(930\) −18.1465 2.12542i −0.595047 0.0696952i
\(931\) −0.630368 + 0.867627i −0.0206595 + 0.0284353i
\(932\) 6.22181 39.2830i 0.203802 1.28676i
\(933\) 7.34734 + 14.4200i 0.240541 + 0.472088i
\(934\) −14.3841 −0.470661
\(935\) 0 0
\(936\) 4.09971 0.134003
\(937\) −9.78959 19.2132i −0.319812 0.627667i 0.674001 0.738730i \(-0.264574\pi\)
−0.993813 + 0.111064i \(0.964574\pi\)
\(938\) 3.80722 24.0378i 0.124310 0.784863i
\(939\) −27.5614 + 37.9350i −0.899431 + 1.23796i
\(940\) 23.4276 + 29.6436i 0.764125 + 0.966868i
\(941\) 12.1926 3.96162i 0.397467 0.129145i −0.103461 0.994633i \(-0.532992\pi\)
0.500929 + 0.865488i \(0.332992\pi\)
\(942\) −19.6587 + 3.11363i −0.640515 + 0.101448i
\(943\) −2.13768 0.338575i −0.0696123 0.0110255i
\(944\) 12.4035 + 4.03016i 0.403701 + 0.131170i
\(945\) −32.7745 15.0610i −1.06615 0.489934i
\(946\) 0 0
\(947\) −2.58080 2.58080i −0.0838646 0.0838646i 0.663930 0.747795i \(-0.268887\pi\)
−0.747795 + 0.663930i \(0.768887\pi\)
\(948\) 17.3683 8.84961i 0.564097 0.287422i
\(949\) 11.1652 + 15.3675i 0.362437 + 0.498851i
\(950\) 3.10554 + 2.63935i 0.100757 + 0.0856319i
\(951\) −9.21097 28.3484i −0.298686 0.919261i
\(952\) 2.82587 + 1.43985i 0.0915869 + 0.0466659i
\(953\) −4.66265 29.4388i −0.151038 0.953617i −0.940494 0.339810i \(-0.889637\pi\)
0.789456 0.613807i \(-0.210363\pi\)
\(954\) −28.9792 + 21.0546i −0.938235 + 0.681668i
\(955\) −14.3739 + 15.5876i −0.465130 + 0.504403i
\(956\) 45.3978i 1.46827i
\(957\) 0 0
\(958\) −7.46881 + 7.46881i −0.241306 + 0.241306i
\(959\) −5.87739 + 18.0887i −0.189791 + 0.584116i
\(960\) 36.7668 + 24.5022i 1.18664 + 0.790805i
\(961\) 23.4497 + 17.0372i 0.756440 + 0.549586i
\(962\) −1.32140 + 2.59338i −0.0426035 + 0.0836141i
\(963\) −41.0608 + 80.5863i −1.32317 + 2.59686i
\(964\) −28.9781 21.0539i −0.933323 0.678099i
\(965\) −21.3903 14.2550i −0.688580 0.458884i
\(966\) 24.5626 75.5960i 0.790290 2.43226i
\(967\) −12.1066 + 12.1066i −0.389321 + 0.389321i −0.874445 0.485124i \(-0.838774\pi\)
0.485124 + 0.874445i \(0.338774\pi\)
\(968\) 0 0
\(969\) 6.12984i 0.196919i
\(970\) −40.8016 + 44.2467i −1.31006 + 1.42068i
\(971\) 38.0484 27.6438i 1.22103 0.887131i 0.224846 0.974394i \(-0.427812\pi\)
0.996185 + 0.0872629i \(0.0278120\pi\)
\(972\) −1.83620 11.5933i −0.0588960 0.371855i
\(973\) −24.5203 12.4937i −0.786086 0.400531i
\(974\) −8.45562 26.0237i −0.270936 0.833854i
\(975\) 2.88721 + 35.5795i 0.0924648 + 1.13946i
\(976\) −3.61027 4.96912i −0.115562 0.159058i
\(977\) −52.5140 + 26.7572i −1.68007 + 0.856039i −0.688687 + 0.725059i \(0.741813\pi\)
−0.991385 + 0.130981i \(0.958187\pi\)
\(978\) 57.2885 + 57.2885i 1.83188 + 1.83188i
\(979\) 0 0
\(980\) −9.68383 4.45004i −0.309339 0.142151i
\(981\) 42.4468 + 13.7918i 1.35522 + 0.440339i
\(982\) −63.1966 10.0094i −2.01668 0.319411i
\(983\) 6.20601 0.982936i 0.197941 0.0313508i −0.0566766 0.998393i \(-0.518050\pi\)
0.254618 + 0.967042i \(0.418050\pi\)
\(984\) 0.276128 0.0897195i 0.00880265 0.00286015i
\(985\) −37.4054 47.3301i −1.19184 1.50806i
\(986\) −47.4526 + 65.3129i −1.51120 + 2.07999i
\(987\) −8.83063 + 55.7544i −0.281082 + 1.77468i
\(988\) 0.847635 + 1.66358i 0.0269668 + 0.0529254i
\(989\) −34.6986 −1.10335
\(990\) 0 0
\(991\) −18.0262 −0.572622 −0.286311 0.958137i \(-0.592429\pi\)
−0.286311 + 0.958137i \(0.592429\pi\)
\(992\) 5.02588 + 9.86384i 0.159572 + 0.313177i
\(993\) −14.7665 + 93.2323i −0.468602 + 2.95864i
\(994\) −18.4088 + 25.3376i −0.583893 + 0.803660i
\(995\) 7.31195 + 0.856415i 0.231804 + 0.0271502i
\(996\) 12.9911 4.22107i 0.411639 0.133750i
\(997\) 37.0811 5.87307i 1.17437 0.186002i 0.461397 0.887194i \(-0.347348\pi\)
0.712972 + 0.701192i \(0.247348\pi\)
\(998\) 75.4291 + 11.9468i 2.38767 + 0.378169i
\(999\) 4.45205 + 1.44656i 0.140857 + 0.0457671i
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 605.2.m.g.112.4 160
5.3 odd 4 inner 605.2.m.g.233.4 160
11.2 odd 10 inner 605.2.m.g.602.17 160
11.3 even 5 inner 605.2.m.g.282.4 160
11.4 even 5 605.2.e.c.362.17 yes 40
11.5 even 5 inner 605.2.m.g.457.17 160
11.6 odd 10 inner 605.2.m.g.457.4 160
11.7 odd 10 605.2.e.c.362.4 40
11.8 odd 10 inner 605.2.m.g.282.17 160
11.9 even 5 inner 605.2.m.g.602.4 160
11.10 odd 2 inner 605.2.m.g.112.17 160
55.3 odd 20 inner 605.2.m.g.403.17 160
55.8 even 20 inner 605.2.m.g.403.4 160
55.13 even 20 inner 605.2.m.g.118.4 160
55.18 even 20 605.2.e.c.483.17 yes 40
55.28 even 20 inner 605.2.m.g.578.4 160
55.38 odd 20 inner 605.2.m.g.578.17 160
55.43 even 4 inner 605.2.m.g.233.17 160
55.48 odd 20 605.2.e.c.483.4 yes 40
55.53 odd 20 inner 605.2.m.g.118.17 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.e.c.362.4 40 11.7 odd 10
605.2.e.c.362.17 yes 40 11.4 even 5
605.2.e.c.483.4 yes 40 55.48 odd 20
605.2.e.c.483.17 yes 40 55.18 even 20
605.2.m.g.112.4 160 1.1 even 1 trivial
605.2.m.g.112.17 160 11.10 odd 2 inner
605.2.m.g.118.4 160 55.13 even 20 inner
605.2.m.g.118.17 160 55.53 odd 20 inner
605.2.m.g.233.4 160 5.3 odd 4 inner
605.2.m.g.233.17 160 55.43 even 4 inner
605.2.m.g.282.4 160 11.3 even 5 inner
605.2.m.g.282.17 160 11.8 odd 10 inner
605.2.m.g.403.4 160 55.8 even 20 inner
605.2.m.g.403.17 160 55.3 odd 20 inner
605.2.m.g.457.4 160 11.6 odd 10 inner
605.2.m.g.457.17 160 11.5 even 5 inner
605.2.m.g.578.4 160 55.28 even 20 inner
605.2.m.g.578.17 160 55.38 odd 20 inner
605.2.m.g.602.4 160 11.9 even 5 inner
605.2.m.g.602.17 160 11.2 odd 10 inner