Properties

Label 105.3.t.b.86.13
Level $105$
Weight $3$
Character 105.86
Analytic conductor $2.861$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(11,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), 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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 86.13
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50527 + 0.869067i) q^{2} +(-1.33489 - 2.68664i) q^{3} +(-0.489445 - 0.847743i) q^{4} +(1.93649 + 1.11803i) q^{5} +(0.325501 - 5.20423i) q^{6} +(2.93407 - 6.35541i) q^{7} -8.65398i q^{8} +(-5.43612 + 7.17277i) q^{9} +O(q^{10})\) \(q+(1.50527 + 0.869067i) q^{2} +(-1.33489 - 2.68664i) q^{3} +(-0.489445 - 0.847743i) q^{4} +(1.93649 + 1.11803i) q^{5} +(0.325501 - 5.20423i) q^{6} +(2.93407 - 6.35541i) q^{7} -8.65398i q^{8} +(-5.43612 + 7.17277i) q^{9} +(1.94329 + 3.36588i) q^{10} +(11.0674 - 6.38976i) q^{11} +(-1.62423 + 2.44661i) q^{12} +0.690184 q^{13} +(9.93984 - 7.01669i) q^{14} +(0.418749 - 6.69512i) q^{15} +(5.56311 - 9.63559i) q^{16} +(-12.5056 + 7.22012i) q^{17} +(-14.4164 + 6.07260i) q^{18} +(-13.8399 + 23.9714i) q^{19} -2.18886i q^{20} +(-20.9914 + 0.600994i) q^{21} +22.2125 q^{22} +(37.3582 + 21.5687i) q^{23} +(-23.2502 + 11.5521i) q^{24} +(2.50000 + 4.33013i) q^{25} +(1.03891 + 0.599816i) q^{26} +(26.5273 + 5.03002i) q^{27} +(-6.82382 + 0.623284i) q^{28} +26.6616i q^{29} +(6.44884 - 9.71403i) q^{30} +(-8.94214 - 15.4882i) q^{31} +(-13.2303 + 7.63853i) q^{32} +(-31.9408 - 21.2045i) q^{33} -25.0991 q^{34} +(12.7874 - 9.02681i) q^{35} +(8.74134 + 1.09776i) q^{36} +(17.5794 - 30.4484i) q^{37} +(-41.6655 + 24.0556i) q^{38} +(-0.921322 - 1.85428i) q^{39} +(9.67544 - 16.7584i) q^{40} -15.0963i q^{41} +(-32.1200 - 17.3383i) q^{42} -23.1680 q^{43} +(-10.8337 - 6.25487i) q^{44} +(-18.5464 + 7.81225i) q^{45} +(37.4894 + 64.9335i) q^{46} +(38.1508 + 22.0264i) q^{47} +(-33.3136 - 2.08361i) q^{48} +(-31.7825 - 37.2944i) q^{49} +8.69067i q^{50} +(36.0916 + 23.9600i) q^{51} +(-0.337807 - 0.585099i) q^{52} +(78.5866 - 45.3720i) q^{53} +(35.5593 + 30.6256i) q^{54} +28.5759 q^{55} +(-54.9996 - 25.3914i) q^{56} +(82.8774 + 5.18359i) q^{57} +(-23.1707 + 40.1329i) q^{58} +(-21.3447 + 12.3233i) q^{59} +(-5.88070 + 2.92190i) q^{60} +(-33.0900 + 57.3136i) q^{61} -31.0853i q^{62} +(29.6359 + 55.5942i) q^{63} -71.0584 q^{64} +(1.33654 + 0.771649i) q^{65} +(-29.6514 - 59.6771i) q^{66} +(-13.6163 - 23.5841i) q^{67} +(12.2416 + 7.06770i) q^{68} +(8.07836 - 129.160i) q^{69} +(27.0933 - 2.47469i) q^{70} +76.5254i q^{71} +(62.0730 + 47.0440i) q^{72} +(24.7119 + 42.8023i) q^{73} +(52.9234 - 30.5554i) q^{74} +(8.29628 - 12.4969i) q^{75} +27.0954 q^{76} +(-8.13704 - 89.0858i) q^{77} +(0.224655 - 3.59188i) q^{78} +(18.5245 - 32.0854i) q^{79} +(21.5458 - 12.4395i) q^{80} +(-21.8973 - 77.9840i) q^{81} +(13.1197 - 22.7239i) q^{82} +20.0443i q^{83} +(10.7836 + 17.5012i) q^{84} -32.2894 q^{85} +(-34.8741 - 20.1346i) q^{86} +(71.6303 - 35.5904i) q^{87} +(-55.2968 - 95.7769i) q^{88} +(-62.7886 - 36.2510i) q^{89} +(-34.7067 - 4.35853i) q^{90} +(2.02505 - 4.38640i) q^{91} -42.2268i q^{92} +(-29.6746 + 44.6995i) q^{93} +(38.2848 + 66.3112i) q^{94} +(-53.6016 + 30.9469i) q^{95} +(38.1831 + 25.3485i) q^{96} +23.2629 q^{97} +(-15.4298 - 83.7592i) q^{98} +(-14.3313 + 114.119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9} + 20 q^{10} - 42 q^{12} - 100 q^{13} + 20 q^{15} - 12 q^{16} - 14 q^{18} + 50 q^{19} - 12 q^{21} + 256 q^{22} - 140 q^{24} + 90 q^{25} + 4 q^{27} - 48 q^{28} + 60 q^{30} - 82 q^{31} - 76 q^{33} - 64 q^{34} + 296 q^{36} - 26 q^{37} - 130 q^{39} - 60 q^{40} - 98 q^{42} - 204 q^{43} + 40 q^{45} + 28 q^{46} + 532 q^{48} - 382 q^{49} + 208 q^{51} + 200 q^{52} - 44 q^{54} - 160 q^{55} + 252 q^{57} + 264 q^{58} - 130 q^{60} - 324 q^{61} - 258 q^{63} - 24 q^{64} - 164 q^{66} - 142 q^{67} - 112 q^{69} + 200 q^{70} - 322 q^{72} + 386 q^{73} - 20 q^{75} - 424 q^{76} - 440 q^{78} + 334 q^{79} + 186 q^{81} - 68 q^{82} + 80 q^{84} - 200 q^{85} + 342 q^{87} + 180 q^{88} + 100 q^{90} + 46 q^{91} - 2 q^{93} + 324 q^{94} + 732 q^{96} + 1616 q^{97} + 384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50527 + 0.869067i 0.752634 + 0.434534i 0.826645 0.562724i \(-0.190247\pi\)
−0.0740107 + 0.997257i \(0.523580\pi\)
\(3\) −1.33489 2.68664i −0.444965 0.895548i
\(4\) −0.489445 0.847743i −0.122361 0.211936i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 0.325501 5.20423i 0.0542501 0.867372i
\(7\) 2.93407 6.35541i 0.419153 0.907916i
\(8\) 8.65398i 1.08175i
\(9\) −5.43612 + 7.17277i −0.604013 + 0.796975i
\(10\) 1.94329 + 3.36588i 0.194329 + 0.336588i
\(11\) 11.0674 6.38976i 1.00613 0.580887i 0.0960710 0.995374i \(-0.469372\pi\)
0.910055 + 0.414487i \(0.136039\pi\)
\(12\) −1.62423 + 2.44661i −0.135352 + 0.203884i
\(13\) 0.690184 0.0530911 0.0265455 0.999648i \(-0.491549\pi\)
0.0265455 + 0.999648i \(0.491549\pi\)
\(14\) 9.93984 7.01669i 0.709989 0.501192i
\(15\) 0.418749 6.69512i 0.0279166 0.446341i
\(16\) 5.56311 9.63559i 0.347694 0.602224i
\(17\) −12.5056 + 7.22012i −0.735625 + 0.424713i −0.820476 0.571681i \(-0.806292\pi\)
0.0848518 + 0.996394i \(0.472958\pi\)
\(18\) −14.4164 + 6.07260i −0.800913 + 0.337366i
\(19\) −13.8399 + 23.9714i −0.728415 + 1.26165i 0.229138 + 0.973394i \(0.426409\pi\)
−0.957553 + 0.288258i \(0.906924\pi\)
\(20\) 2.18886i 0.109443i
\(21\) −20.9914 + 0.600994i −0.999590 + 0.0286188i
\(22\) 22.2125 1.00966
\(23\) 37.3582 + 21.5687i 1.62427 + 0.937771i 0.985760 + 0.168156i \(0.0537811\pi\)
0.638507 + 0.769616i \(0.279552\pi\)
\(24\) −23.2502 + 11.5521i −0.968757 + 0.481339i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 1.03891 + 0.599816i 0.0399581 + 0.0230698i
\(27\) 26.5273 + 5.03002i 0.982493 + 0.186297i
\(28\) −6.82382 + 0.623284i −0.243708 + 0.0222601i
\(29\) 26.6616i 0.919366i 0.888083 + 0.459683i \(0.152037\pi\)
−0.888083 + 0.459683i \(0.847963\pi\)
\(30\) 6.44884 9.71403i 0.214961 0.323801i
\(31\) −8.94214 15.4882i −0.288456 0.499621i 0.684985 0.728557i \(-0.259809\pi\)
−0.973441 + 0.228936i \(0.926475\pi\)
\(32\) −13.2303 + 7.63853i −0.413447 + 0.238704i
\(33\) −31.9408 21.2045i −0.967903 0.642560i
\(34\) −25.0991 −0.738208
\(35\) 12.7874 9.02681i 0.365353 0.257909i
\(36\) 8.74134 + 1.09776i 0.242815 + 0.0304932i
\(37\) 17.5794 30.4484i 0.475119 0.822930i −0.524475 0.851426i \(-0.675738\pi\)
0.999594 + 0.0284956i \(0.00907164\pi\)
\(38\) −41.6655 + 24.0556i −1.09646 + 0.633041i
\(39\) −0.921322 1.85428i −0.0236236 0.0475456i
\(40\) 9.67544 16.7584i 0.241886 0.418959i
\(41\) 15.0963i 0.368202i −0.982907 0.184101i \(-0.941063\pi\)
0.982907 0.184101i \(-0.0589373\pi\)
\(42\) −32.1200 17.3383i −0.764762 0.412816i
\(43\) −23.1680 −0.538791 −0.269395 0.963030i \(-0.586824\pi\)
−0.269395 + 0.963030i \(0.586824\pi\)
\(44\) −10.8337 6.25487i −0.246222 0.142156i
\(45\) −18.5464 + 7.81225i −0.412142 + 0.173606i
\(46\) 37.4894 + 64.9335i 0.814986 + 1.41160i
\(47\) 38.1508 + 22.0264i 0.811719 + 0.468646i 0.847552 0.530712i \(-0.178075\pi\)
−0.0358338 + 0.999358i \(0.511409\pi\)
\(48\) −33.3136 2.08361i −0.694032 0.0434085i
\(49\) −31.7825 37.2944i −0.648622 0.761111i
\(50\) 8.69067i 0.173813i
\(51\) 36.0916 + 23.9600i 0.707678 + 0.469805i
\(52\) −0.337807 0.585099i −0.00649628 0.0112519i
\(53\) 78.5866 45.3720i 1.48277 0.856075i 0.482957 0.875644i \(-0.339563\pi\)
0.999809 + 0.0195689i \(0.00622937\pi\)
\(54\) 35.5593 + 30.6256i 0.658506 + 0.567140i
\(55\) 28.5759 0.519561
\(56\) −54.9996 25.3914i −0.982135 0.453417i
\(57\) 82.8774 + 5.18359i 1.45399 + 0.0909402i
\(58\) −23.1707 + 40.1329i −0.399495 + 0.691946i
\(59\) −21.3447 + 12.3233i −0.361774 + 0.208870i −0.669859 0.742489i \(-0.733645\pi\)
0.308085 + 0.951359i \(0.400312\pi\)
\(60\) −5.88070 + 2.92190i −0.0980116 + 0.0486983i
\(61\) −33.0900 + 57.3136i −0.542460 + 0.939568i 0.456302 + 0.889825i \(0.349174\pi\)
−0.998762 + 0.0497429i \(0.984160\pi\)
\(62\) 31.0853i 0.501375i
\(63\) 29.6359 + 55.5942i 0.470412 + 0.882447i
\(64\) −71.0584 −1.11029
\(65\) 1.33654 + 0.771649i 0.0205621 + 0.0118715i
\(66\) −29.6514 59.6771i −0.449263 0.904199i
\(67\) −13.6163 23.5841i −0.203228 0.352001i 0.746339 0.665566i \(-0.231810\pi\)
−0.949567 + 0.313565i \(0.898477\pi\)
\(68\) 12.2416 + 7.06770i 0.180024 + 0.103937i
\(69\) 8.07836 129.160i 0.117078 1.87188i
\(70\) 27.0933 2.47469i 0.387047 0.0353527i
\(71\) 76.5254i 1.07782i 0.842362 + 0.538912i \(0.181164\pi\)
−0.842362 + 0.538912i \(0.818836\pi\)
\(72\) 62.0730 + 47.0440i 0.862125 + 0.653389i
\(73\) 24.7119 + 42.8023i 0.338520 + 0.586333i 0.984155 0.177313i \(-0.0567405\pi\)
−0.645635 + 0.763646i \(0.723407\pi\)
\(74\) 52.9234 30.5554i 0.715182 0.412910i
\(75\) 8.29628 12.4969i 0.110617 0.166625i
\(76\) 27.0954 0.356519
\(77\) −8.13704 89.0858i −0.105676 1.15696i
\(78\) 0.224655 3.59188i 0.00288020 0.0460497i
\(79\) 18.5245 32.0854i 0.234487 0.406144i −0.724636 0.689132i \(-0.757992\pi\)
0.959124 + 0.282988i \(0.0913255\pi\)
\(80\) 21.5458 12.4395i 0.269323 0.155494i
\(81\) −21.8973 77.9840i −0.270337 0.962766i
\(82\) 13.1197 22.7239i 0.159996 0.277121i
\(83\) 20.0443i 0.241498i 0.992683 + 0.120749i \(0.0385296\pi\)
−0.992683 + 0.120749i \(0.961470\pi\)
\(84\) 10.7836 + 17.5012i 0.128376 + 0.208347i
\(85\) −32.2894 −0.379875
\(86\) −34.8741 20.1346i −0.405512 0.234123i
\(87\) 71.6303 35.5904i 0.823336 0.409085i
\(88\) −55.2968 95.7769i −0.628373 1.08837i
\(89\) −62.7886 36.2510i −0.705489 0.407315i 0.103899 0.994588i \(-0.466868\pi\)
−0.809389 + 0.587273i \(0.800201\pi\)
\(90\) −34.7067 4.35853i −0.385630 0.0484281i
\(91\) 2.02505 4.38640i 0.0222533 0.0482022i
\(92\) 42.2268i 0.458987i
\(93\) −29.6746 + 44.6995i −0.319082 + 0.480640i
\(94\) 38.2848 + 66.3112i 0.407285 + 0.705438i
\(95\) −53.6016 + 30.9469i −0.564228 + 0.325757i
\(96\) 38.1831 + 25.3485i 0.397740 + 0.264047i
\(97\) 23.2629 0.239823 0.119912 0.992785i \(-0.461739\pi\)
0.119912 + 0.992785i \(0.461739\pi\)
\(98\) −15.4298 83.7592i −0.157447 0.854686i
\(99\) −14.3313 + 114.119i −0.144761 + 1.15272i
\(100\) 2.44722 4.23872i 0.0244722 0.0423872i
\(101\) −124.801 + 72.0539i −1.23565 + 0.713405i −0.968203 0.250166i \(-0.919515\pi\)
−0.267451 + 0.963571i \(0.586181\pi\)
\(102\) 33.5046 + 67.4323i 0.328477 + 0.661101i
\(103\) 75.7306 131.169i 0.735249 1.27349i −0.219365 0.975643i \(-0.570399\pi\)
0.954614 0.297846i \(-0.0962681\pi\)
\(104\) 5.97284i 0.0574311i
\(105\) −41.3216 22.3053i −0.393539 0.212431i
\(106\) 157.725 1.48797
\(107\) −35.8969 20.7251i −0.335485 0.193692i 0.322789 0.946471i \(-0.395380\pi\)
−0.658274 + 0.752779i \(0.728713\pi\)
\(108\) −8.71949 24.9503i −0.0807360 0.231021i
\(109\) −1.31599 2.27937i −0.0120733 0.0209116i 0.859926 0.510419i \(-0.170510\pi\)
−0.871999 + 0.489508i \(0.837176\pi\)
\(110\) 43.0144 + 24.8343i 0.391040 + 0.225767i
\(111\) −105.271 6.58420i −0.948385 0.0593171i
\(112\) −44.9156 63.6273i −0.401032 0.568101i
\(113\) 140.014i 1.23907i 0.784971 + 0.619533i \(0.212678\pi\)
−0.784971 + 0.619533i \(0.787322\pi\)
\(114\) 120.248 + 79.8287i 1.05481 + 0.700252i
\(115\) 48.2292 + 83.5354i 0.419384 + 0.726395i
\(116\) 22.6022 13.0494i 0.194847 0.112495i
\(117\) −3.75192 + 4.95053i −0.0320677 + 0.0423122i
\(118\) −42.8393 −0.363045
\(119\) 9.19447 + 100.663i 0.0772645 + 0.845905i
\(120\) −57.9394 3.62384i −0.482829 0.0301987i
\(121\) 21.1580 36.6468i 0.174860 0.302866i
\(122\) −99.6188 + 57.5149i −0.816547 + 0.471434i
\(123\) −40.5583 + 20.1519i −0.329742 + 0.163837i
\(124\) −8.75337 + 15.1613i −0.0705917 + 0.122268i
\(125\) 11.1803i 0.0894427i
\(126\) −3.70500 + 109.440i −0.0294048 + 0.868570i
\(127\) −235.143 −1.85152 −0.925758 0.378117i \(-0.876572\pi\)
−0.925758 + 0.378117i \(0.876572\pi\)
\(128\) −54.0408 31.2004i −0.422193 0.243754i
\(129\) 30.9268 + 62.2442i 0.239743 + 0.482513i
\(130\) 1.34123 + 2.32308i 0.0103171 + 0.0178698i
\(131\) −67.6099 39.0346i −0.516106 0.297974i 0.219234 0.975672i \(-0.429644\pi\)
−0.735340 + 0.677698i \(0.762978\pi\)
\(132\) −2.34270 + 37.4560i −0.0177477 + 0.283758i
\(133\) 111.741 + 158.292i 0.840156 + 1.19016i
\(134\) 47.3338i 0.353238i
\(135\) 45.7462 + 39.3990i 0.338861 + 0.291845i
\(136\) 62.4828 + 108.223i 0.459432 + 0.795760i
\(137\) −123.931 + 71.5516i −0.904606 + 0.522274i −0.878692 0.477390i \(-0.841583\pi\)
−0.0259142 + 0.999664i \(0.508250\pi\)
\(138\) 124.409 187.400i 0.901514 1.35797i
\(139\) 119.427 0.859185 0.429593 0.903023i \(-0.358657\pi\)
0.429593 + 0.903023i \(0.358657\pi\)
\(140\) −13.9111 6.42228i −0.0993652 0.0458734i
\(141\) 8.24976 131.900i 0.0585089 0.935464i
\(142\) −66.5057 + 115.191i −0.468350 + 0.811206i
\(143\) 7.63853 4.41011i 0.0534163 0.0308399i
\(144\) 38.8722 + 92.2831i 0.269945 + 0.640855i
\(145\) −29.8086 + 51.6300i −0.205576 + 0.356069i
\(146\) 85.9054i 0.588393i
\(147\) −57.7707 + 135.172i −0.392998 + 0.919539i
\(148\) −34.4166 −0.232545
\(149\) −124.082 71.6388i −0.832765 0.480797i 0.0220332 0.999757i \(-0.492986\pi\)
−0.854799 + 0.518960i \(0.826319\pi\)
\(150\) 23.3487 11.6011i 0.155658 0.0773408i
\(151\) 1.71655 + 2.97316i 0.0113679 + 0.0196898i 0.871653 0.490123i \(-0.163048\pi\)
−0.860285 + 0.509813i \(0.829715\pi\)
\(152\) 207.448 + 119.770i 1.36479 + 0.787961i
\(153\) 16.1937 128.949i 0.105841 0.842806i
\(154\) 65.1731 141.170i 0.423202 0.916686i
\(155\) 39.9905i 0.258003i
\(156\) −1.12102 + 1.68861i −0.00718600 + 0.0108244i
\(157\) −121.784 210.937i −0.775697 1.34355i −0.934402 0.356221i \(-0.884065\pi\)
0.158705 0.987326i \(-0.449268\pi\)
\(158\) 55.7687 32.1981i 0.352966 0.203785i
\(159\) −226.803 150.567i −1.42643 0.946965i
\(160\) −34.1605 −0.213503
\(161\) 246.690 174.142i 1.53223 1.08163i
\(162\) 34.8121 136.417i 0.214889 0.842081i
\(163\) −4.62591 + 8.01232i −0.0283798 + 0.0491553i −0.879866 0.475221i \(-0.842368\pi\)
0.851487 + 0.524376i \(0.175701\pi\)
\(164\) −12.7978 + 7.38879i −0.0780351 + 0.0450536i
\(165\) −38.1458 76.7732i −0.231186 0.465292i
\(166\) −17.4199 + 30.1721i −0.104939 + 0.181760i
\(167\) 196.020i 1.17378i 0.809668 + 0.586888i \(0.199647\pi\)
−0.809668 + 0.586888i \(0.800353\pi\)
\(168\) 5.20099 + 181.659i 0.0309583 + 1.08130i
\(169\) −168.524 −0.997181
\(170\) −48.6042 28.0616i −0.285907 0.165068i
\(171\) −96.7060 229.582i −0.565532 1.34258i
\(172\) 11.3395 + 19.6405i 0.0659271 + 0.114189i
\(173\) −89.9489 51.9320i −0.519936 0.300185i 0.216972 0.976178i \(-0.430382\pi\)
−0.736909 + 0.675992i \(0.763715\pi\)
\(174\) 138.753 + 8.67837i 0.797432 + 0.0498757i
\(175\) 34.8549 3.18363i 0.199171 0.0181922i
\(176\) 142.188i 0.807885i
\(177\) 61.6013 + 40.8952i 0.348030 + 0.231046i
\(178\) −63.0091 109.135i −0.353984 0.613118i
\(179\) 243.418 140.537i 1.35988 0.785124i 0.370269 0.928925i \(-0.379266\pi\)
0.989607 + 0.143800i \(0.0459323\pi\)
\(180\) 15.7002 + 11.8989i 0.0872234 + 0.0661051i
\(181\) 53.4762 0.295448 0.147724 0.989029i \(-0.452805\pi\)
0.147724 + 0.989029i \(0.452805\pi\)
\(182\) 6.86032 4.84281i 0.0376940 0.0266088i
\(183\) 198.153 + 12.3936i 1.08280 + 0.0677243i
\(184\) 186.655 323.297i 1.01443 1.75705i
\(185\) 68.0847 39.3087i 0.368026 0.212480i
\(186\) −83.5151 + 41.4956i −0.449006 + 0.223094i
\(187\) −92.2697 + 159.816i −0.493421 + 0.854630i
\(188\) 43.1227i 0.229376i
\(189\) 109.801 153.834i 0.580957 0.813934i
\(190\) −107.580 −0.566209
\(191\) 91.5701 + 52.8680i 0.479424 + 0.276796i 0.720177 0.693791i \(-0.244061\pi\)
−0.240752 + 0.970587i \(0.577394\pi\)
\(192\) 94.8555 + 190.909i 0.494039 + 0.994316i
\(193\) 45.0633 + 78.0519i 0.233489 + 0.404414i 0.958832 0.283973i \(-0.0916525\pi\)
−0.725344 + 0.688387i \(0.758319\pi\)
\(194\) 35.0169 + 20.2170i 0.180499 + 0.104211i
\(195\) 0.289014 4.62086i 0.00148212 0.0236967i
\(196\) −16.0603 + 45.1969i −0.0819405 + 0.230597i
\(197\) 195.601i 0.992897i −0.868066 0.496448i \(-0.834637\pi\)
0.868066 0.496448i \(-0.165363\pi\)
\(198\) −120.750 + 159.325i −0.609848 + 0.804673i
\(199\) 116.030 + 200.970i 0.583067 + 1.00990i 0.995113 + 0.0987388i \(0.0314808\pi\)
−0.412046 + 0.911163i \(0.635186\pi\)
\(200\) 37.4728 21.6349i 0.187364 0.108175i
\(201\) −45.1858 + 68.0644i −0.224805 + 0.338629i
\(202\) −250.479 −1.23999
\(203\) 169.445 + 78.2270i 0.834707 + 0.385355i
\(204\) 2.64714 42.3235i 0.0129762 0.207468i
\(205\) 16.8781 29.2338i 0.0823324 0.142604i
\(206\) 227.990 131.630i 1.10675 0.638981i
\(207\) −357.791 + 150.711i −1.72846 + 0.728074i
\(208\) 3.83957 6.65033i 0.0184595 0.0319727i
\(209\) 353.734i 1.69251i
\(210\) −42.8153 69.4867i −0.203882 0.330889i
\(211\) 210.912 0.999585 0.499793 0.866145i \(-0.333410\pi\)
0.499793 + 0.866145i \(0.333410\pi\)
\(212\) −76.9276 44.4142i −0.362866 0.209501i
\(213\) 205.597 102.153i 0.965242 0.479593i
\(214\) −36.0230 62.3936i −0.168332 0.291559i
\(215\) −44.8647 25.9026i −0.208673 0.120477i
\(216\) 43.5297 229.567i 0.201526 1.06281i
\(217\) −124.671 + 11.3874i −0.574521 + 0.0524764i
\(218\) 4.57475i 0.0209851i
\(219\) 82.0069 123.529i 0.374461 0.564058i
\(220\) −13.9863 24.2250i −0.0635741 0.110114i
\(221\) −8.63117 + 4.98321i −0.0390551 + 0.0225485i
\(222\) −152.739 101.398i −0.688012 0.456749i
\(223\) −99.6553 −0.446885 −0.223442 0.974717i \(-0.571729\pi\)
−0.223442 + 0.974717i \(0.571729\pi\)
\(224\) 9.72729 + 106.496i 0.0434254 + 0.475429i
\(225\) −44.6493 5.60715i −0.198441 0.0249207i
\(226\) −121.682 + 210.759i −0.538415 + 0.932563i
\(227\) 266.629 153.939i 1.17458 0.678143i 0.219824 0.975539i \(-0.429452\pi\)
0.954754 + 0.297396i \(0.0961182\pi\)
\(228\) −36.1695 72.7958i −0.158638 0.319280i
\(229\) −27.9040 + 48.3312i −0.121852 + 0.211053i −0.920498 0.390748i \(-0.872217\pi\)
0.798646 + 0.601801i \(0.205550\pi\)
\(230\) 167.658i 0.728946i
\(231\) −228.480 + 140.781i −0.989090 + 0.609443i
\(232\) 230.729 0.994522
\(233\) −176.629 101.977i −0.758062 0.437668i 0.0705372 0.997509i \(-0.477529\pi\)
−0.828600 + 0.559842i \(0.810862\pi\)
\(234\) −9.94999 + 4.19121i −0.0425213 + 0.0179111i
\(235\) 49.2524 + 85.3077i 0.209585 + 0.363012i
\(236\) 20.8941 + 12.0632i 0.0885342 + 0.0511152i
\(237\) −110.930 6.93817i −0.468060 0.0292750i
\(238\) −73.6425 + 159.515i −0.309422 + 0.670231i
\(239\) 83.9724i 0.351349i 0.984448 + 0.175674i \(0.0562106\pi\)
−0.984448 + 0.175674i \(0.943789\pi\)
\(240\) −62.1819 41.2806i −0.259091 0.172002i
\(241\) −68.2986 118.297i −0.283397 0.490858i 0.688822 0.724930i \(-0.258128\pi\)
−0.972219 + 0.234072i \(0.924795\pi\)
\(242\) 63.6971 36.7755i 0.263211 0.151965i
\(243\) −180.285 + 162.931i −0.741913 + 0.670496i
\(244\) 64.7830 0.265504
\(245\) −19.8500 107.754i −0.0810205 0.439813i
\(246\) −78.5645 4.91385i −0.319368 0.0199750i
\(247\) −9.55206 + 16.5447i −0.0386723 + 0.0669824i
\(248\) −134.035 + 77.3851i −0.540463 + 0.312037i
\(249\) 53.8520 26.7571i 0.216273 0.107458i
\(250\) −9.71647 + 16.8294i −0.0388659 + 0.0673176i
\(251\) 130.419i 0.519597i 0.965663 + 0.259799i \(0.0836562\pi\)
−0.965663 + 0.259799i \(0.916344\pi\)
\(252\) 32.6244 52.3339i 0.129462 0.207674i
\(253\) 551.276 2.17896
\(254\) −353.953 204.355i −1.39351 0.804546i
\(255\) 43.1029 + 86.7500i 0.169031 + 0.340196i
\(256\) 87.8863 + 152.224i 0.343306 + 0.594623i
\(257\) 139.531 + 80.5581i 0.542921 + 0.313456i 0.746262 0.665652i \(-0.231847\pi\)
−0.203341 + 0.979108i \(0.565180\pi\)
\(258\) −7.54120 + 120.572i −0.0292295 + 0.467332i
\(259\) −141.933 201.062i −0.548004 0.776302i
\(260\) 1.51072i 0.00581045i
\(261\) −191.238 144.936i −0.732711 0.555309i
\(262\) −67.8474 117.515i −0.258959 0.448531i
\(263\) −237.621 + 137.191i −0.903503 + 0.521638i −0.878335 0.478046i \(-0.841345\pi\)
−0.0251677 + 0.999683i \(0.508012\pi\)
\(264\) −183.503 + 276.415i −0.695088 + 1.04703i
\(265\) 202.910 0.765697
\(266\) 30.6336 + 335.382i 0.115164 + 1.26083i
\(267\) −13.5775 + 217.082i −0.0508519 + 0.813040i
\(268\) −13.3288 + 23.0862i −0.0497344 + 0.0861426i
\(269\) 153.258 88.4834i 0.569732 0.328935i −0.187311 0.982301i \(-0.559977\pi\)
0.757042 + 0.653366i \(0.226644\pi\)
\(270\) 34.6199 + 99.0627i 0.128222 + 0.366899i
\(271\) 142.395 246.636i 0.525444 0.910096i −0.474117 0.880462i \(-0.657233\pi\)
0.999561 0.0296340i \(-0.00943416\pi\)
\(272\) 160.665i 0.590681i
\(273\) −14.4879 + 0.414797i −0.0530693 + 0.00151940i
\(274\) −248.733 −0.907783
\(275\) 55.3369 + 31.9488i 0.201225 + 0.116177i
\(276\) −113.448 + 56.3683i −0.411045 + 0.204233i
\(277\) −35.1794 60.9325i −0.127001 0.219973i 0.795512 0.605938i \(-0.207202\pi\)
−0.922514 + 0.385965i \(0.873869\pi\)
\(278\) 179.769 + 103.790i 0.646652 + 0.373345i
\(279\) 159.704 + 20.0560i 0.572416 + 0.0718852i
\(280\) −78.1178 110.662i −0.278992 0.395220i
\(281\) 410.358i 1.46035i 0.683261 + 0.730174i \(0.260561\pi\)
−0.683261 + 0.730174i \(0.739439\pi\)
\(282\) 127.048 191.376i 0.450526 0.678638i
\(283\) −209.909 363.573i −0.741727 1.28471i −0.951708 0.307004i \(-0.900674\pi\)
0.209981 0.977705i \(-0.432660\pi\)
\(284\) 64.8739 37.4550i 0.228429 0.131884i
\(285\) 154.696 + 102.698i 0.542793 + 0.360343i
\(286\) 15.3307 0.0536039
\(287\) −95.9430 44.2935i −0.334296 0.154333i
\(288\) 17.1321 136.422i 0.0594866 0.473687i
\(289\) −40.2397 + 69.6972i −0.139238 + 0.241167i
\(290\) −89.7398 + 51.8113i −0.309448 + 0.178660i
\(291\) −31.0535 62.4991i −0.106713 0.214773i
\(292\) 24.1903 41.8988i 0.0828434 0.143489i
\(293\) 22.0605i 0.0752917i 0.999291 + 0.0376458i \(0.0119859\pi\)
−0.999291 + 0.0376458i \(0.988014\pi\)
\(294\) −204.434 + 153.264i −0.695354 + 0.521306i
\(295\) −55.1117 −0.186819
\(296\) −263.500 152.132i −0.890203 0.513959i
\(297\) 325.729 113.834i 1.09673 0.383279i
\(298\) −124.518 215.671i −0.417845 0.723729i
\(299\) 25.7840 + 14.8864i 0.0862341 + 0.0497873i
\(300\) −14.6547 0.916584i −0.0488490 0.00305528i
\(301\) −67.9766 + 147.242i −0.225836 + 0.489177i
\(302\) 5.96720i 0.0197589i
\(303\) 360.179 + 239.112i 1.18871 + 0.789147i
\(304\) 153.986 + 266.711i 0.506531 + 0.877338i
\(305\) −128.157 + 73.9916i −0.420187 + 0.242595i
\(306\) 136.442 180.030i 0.445887 0.588333i
\(307\) 477.487 1.55533 0.777666 0.628678i \(-0.216404\pi\)
0.777666 + 0.628678i \(0.216404\pi\)
\(308\) −71.5392 + 50.5007i −0.232270 + 0.163963i
\(309\) −453.498 28.3642i −1.46763 0.0917934i
\(310\) 34.7544 60.1964i 0.112111 0.194182i
\(311\) 158.616 91.5767i 0.510018 0.294459i −0.222823 0.974859i \(-0.571527\pi\)
0.732841 + 0.680400i \(0.238194\pi\)
\(312\) −16.0469 + 7.97310i −0.0514323 + 0.0255548i
\(313\) 50.2014 86.9514i 0.160388 0.277800i −0.774620 0.632427i \(-0.782059\pi\)
0.935008 + 0.354627i \(0.115392\pi\)
\(314\) 423.356i 1.34827i
\(315\) −4.76639 + 140.792i −0.0151314 + 0.446958i
\(316\) −36.2669 −0.114769
\(317\) −264.854 152.913i −0.835501 0.482377i 0.0202312 0.999795i \(-0.493560\pi\)
−0.855733 + 0.517418i \(0.826893\pi\)
\(318\) −210.546 423.751i −0.662096 1.33255i
\(319\) 170.361 + 295.074i 0.534048 + 0.924998i
\(320\) −137.604 79.4458i −0.430013 0.248268i
\(321\) −7.76237 + 124.108i −0.0241819 + 0.386629i
\(322\) 522.675 47.7409i 1.62322 0.148264i
\(323\) 399.703i 1.23747i
\(324\) −55.3929 + 56.7321i −0.170966 + 0.175099i
\(325\) 1.72546 + 2.98858i 0.00530911 + 0.00919564i
\(326\) −13.9265 + 8.04046i −0.0427193 + 0.0246640i
\(327\) −4.36714 + 6.57832i −0.0133552 + 0.0201172i
\(328\) −130.643 −0.398301
\(329\) 251.924 177.837i 0.765725 0.540538i
\(330\) 9.30146 148.716i 0.0281863 0.450653i
\(331\) −91.0722 + 157.742i −0.275143 + 0.476561i −0.970171 0.242421i \(-0.922058\pi\)
0.695028 + 0.718982i \(0.255392\pi\)
\(332\) 16.9925 9.81060i 0.0511821 0.0295500i
\(333\) 122.836 + 291.614i 0.368876 + 0.875718i
\(334\) −170.355 + 295.063i −0.510045 + 0.883423i
\(335\) 60.8939i 0.181773i
\(336\) −110.987 + 205.608i −0.330317 + 0.611928i
\(337\) 127.130 0.377241 0.188621 0.982050i \(-0.439598\pi\)
0.188621 + 0.982050i \(0.439598\pi\)
\(338\) −253.673 146.458i −0.750513 0.433309i
\(339\) 376.169 186.904i 1.10964 0.551340i
\(340\) 15.8039 + 27.3731i 0.0464819 + 0.0805091i
\(341\) −197.932 114.276i −0.580447 0.335121i
\(342\) 53.9533 429.626i 0.157758 1.25622i
\(343\) −330.273 + 92.5661i −0.962896 + 0.269872i
\(344\) 200.495i 0.582836i
\(345\) 160.049 241.086i 0.463910 0.698799i
\(346\) −90.2649 156.343i −0.260881 0.451859i
\(347\) 304.200 175.630i 0.876658 0.506139i 0.00710329 0.999975i \(-0.497739\pi\)
0.869555 + 0.493836i \(0.164406\pi\)
\(348\) −65.2306 43.3045i −0.187444 0.124438i
\(349\) −542.999 −1.55587 −0.777936 0.628344i \(-0.783733\pi\)
−0.777936 + 0.628344i \(0.783733\pi\)
\(350\) 55.2328 + 25.4990i 0.157808 + 0.0728544i
\(351\) 18.3087 + 3.47164i 0.0521616 + 0.00989071i
\(352\) −97.6167 + 169.077i −0.277320 + 0.480333i
\(353\) −45.4717 + 26.2531i −0.128815 + 0.0743714i −0.563023 0.826441i \(-0.690362\pi\)
0.434208 + 0.900813i \(0.357028\pi\)
\(354\) 57.1859 + 115.094i 0.161542 + 0.325124i
\(355\) −85.5580 + 148.191i −0.241009 + 0.417439i
\(356\) 70.9714i 0.199358i
\(357\) 258.171 159.076i 0.723168 0.445592i
\(358\) 488.545 1.36465
\(359\) 366.445 + 211.567i 1.02074 + 0.589323i 0.914318 0.404998i \(-0.132728\pi\)
0.106420 + 0.994321i \(0.466061\pi\)
\(360\) 67.6070 + 160.500i 0.187797 + 0.445834i
\(361\) −202.585 350.887i −0.561177 0.971986i
\(362\) 80.4960 + 46.4744i 0.222365 + 0.128382i
\(363\) −126.701 7.92454i −0.349038 0.0218307i
\(364\) −4.70969 + 0.430180i −0.0129387 + 0.00118181i
\(365\) 110.515i 0.302781i
\(366\) 287.503 + 190.864i 0.785526 + 0.521486i
\(367\) −25.6698 44.4614i −0.0699449 0.121148i 0.828932 0.559350i \(-0.188949\pi\)
−0.898877 + 0.438201i \(0.855616\pi\)
\(368\) 415.655 239.979i 1.12950 0.652116i
\(369\) 108.282 + 82.0651i 0.293447 + 0.222399i
\(370\) 136.648 0.369318
\(371\) −57.7790 632.574i −0.155739 1.70505i
\(372\) 52.4178 + 3.27849i 0.140908 + 0.00881314i
\(373\) −236.881 + 410.290i −0.635070 + 1.09997i 0.351430 + 0.936214i \(0.385696\pi\)
−0.986500 + 0.163760i \(0.947638\pi\)
\(374\) −277.781 + 160.377i −0.742731 + 0.428816i
\(375\) 30.0376 14.9246i 0.0801003 0.0397988i
\(376\) 190.616 330.156i 0.506956 0.878074i
\(377\) 18.4014i 0.0488101i
\(378\) 298.972 136.136i 0.790930 0.360149i
\(379\) −359.932 −0.949689 −0.474845 0.880070i \(-0.657496\pi\)
−0.474845 + 0.880070i \(0.657496\pi\)
\(380\) 52.4701 + 30.2936i 0.138079 + 0.0797200i
\(381\) 313.890 + 631.744i 0.823859 + 1.65812i
\(382\) 91.8917 + 159.161i 0.240554 + 0.416652i
\(383\) −322.534 186.215i −0.842125 0.486201i 0.0158611 0.999874i \(-0.494951\pi\)
−0.857986 + 0.513673i \(0.828284\pi\)
\(384\) −11.6858 + 186.838i −0.0304318 + 0.486556i
\(385\) 83.8436 181.611i 0.217776 0.471718i
\(386\) 156.652i 0.405835i
\(387\) 125.944 166.179i 0.325437 0.429403i
\(388\) −11.3859 19.7209i −0.0293451 0.0508272i
\(389\) −550.051 + 317.572i −1.41401 + 0.816381i −0.995764 0.0919506i \(-0.970690\pi\)
−0.418250 + 0.908332i \(0.637356\pi\)
\(390\) 4.45088 6.70447i 0.0114125 0.0171909i
\(391\) −622.916 −1.59313
\(392\) −322.745 + 275.045i −0.823330 + 0.701645i
\(393\) −14.6200 + 233.751i −0.0372011 + 0.594786i
\(394\) 169.990 294.432i 0.431447 0.747288i
\(395\) 71.7451 41.4220i 0.181633 0.104866i
\(396\) 103.758 43.7058i 0.262016 0.110368i
\(397\) 380.530 659.097i 0.958514 1.66019i 0.232400 0.972620i \(-0.425342\pi\)
0.726114 0.687575i \(-0.241325\pi\)
\(398\) 403.353i 1.01345i
\(399\) 276.112 511.511i 0.692010 1.28198i
\(400\) 55.6311 0.139078
\(401\) −16.9155 9.76619i −0.0421834 0.0243546i 0.478760 0.877946i \(-0.341086\pi\)
−0.520943 + 0.853591i \(0.674420\pi\)
\(402\) −127.169 + 63.1857i −0.316341 + 0.157178i
\(403\) −6.17172 10.6897i −0.0153144 0.0265254i
\(404\) 122.166 + 70.5328i 0.302392 + 0.174586i
\(405\) 44.7849 175.497i 0.110580 0.433327i
\(406\) 187.076 + 265.012i 0.460779 + 0.652739i
\(407\) 449.313i 1.10396i
\(408\) 207.350 312.336i 0.508210 0.765529i
\(409\) 308.387 + 534.141i 0.754002 + 1.30597i 0.945869 + 0.324548i \(0.105212\pi\)
−0.191868 + 0.981421i \(0.561454\pi\)
\(410\) 50.8123 29.3365i 0.123932 0.0715524i
\(411\) 357.668 + 237.445i 0.870240 + 0.577724i
\(412\) −148.264 −0.359864
\(413\) 15.6932 + 171.812i 0.0379980 + 0.416009i
\(414\) −669.550 84.0834i −1.61727 0.203100i
\(415\) −22.4103 + 38.8157i −0.0540006 + 0.0935318i
\(416\) −9.13135 + 5.27199i −0.0219504 + 0.0126730i
\(417\) −159.422 320.857i −0.382307 0.769442i
\(418\) −307.419 + 532.465i −0.735451 + 1.27384i
\(419\) 476.423i 1.13705i −0.822667 0.568523i \(-0.807515\pi\)
0.822667 0.568523i \(-0.192485\pi\)
\(420\) 1.31549 + 45.9473i 0.00313213 + 0.109398i
\(421\) −168.350 −0.399881 −0.199941 0.979808i \(-0.564075\pi\)
−0.199941 + 0.979808i \(0.564075\pi\)
\(422\) 317.480 + 183.297i 0.752322 + 0.434353i
\(423\) −365.382 + 153.909i −0.863787 + 0.363851i
\(424\) −392.648 680.087i −0.926057 1.60398i
\(425\) −62.5281 36.1006i −0.147125 0.0849426i
\(426\) 398.256 + 24.9091i 0.934874 + 0.0584720i
\(427\) 267.163 + 378.463i 0.625675 + 0.886330i
\(428\) 40.5751i 0.0948016i
\(429\) −22.0450 14.6350i −0.0513870 0.0341142i
\(430\) −45.0222 77.9808i −0.104703 0.181351i
\(431\) −93.3104 + 53.8728i −0.216498 + 0.124995i −0.604327 0.796736i \(-0.706558\pi\)
0.387830 + 0.921731i \(0.373225\pi\)
\(432\) 196.042 227.624i 0.453800 0.526907i
\(433\) −49.6338 −0.114628 −0.0573139 0.998356i \(-0.518254\pi\)
−0.0573139 + 0.998356i \(0.518254\pi\)
\(434\) −197.560 91.2064i −0.455207 0.210153i
\(435\) 178.503 + 11.1645i 0.410351 + 0.0256656i
\(436\) −1.28821 + 2.23125i −0.00295462 + 0.00511754i
\(437\) −1034.07 + 597.018i −2.36628 + 1.36617i
\(438\) 230.797 114.675i 0.526934 0.261814i
\(439\) 67.1866 116.371i 0.153045 0.265081i −0.779301 0.626650i \(-0.784426\pi\)
0.932345 + 0.361569i \(0.117759\pi\)
\(440\) 247.295i 0.562034i
\(441\) 440.278 25.2314i 0.998362 0.0572141i
\(442\) −17.3230 −0.0391923
\(443\) 381.536 + 220.280i 0.861256 + 0.497246i 0.864433 0.502749i \(-0.167678\pi\)
−0.00317679 + 0.999995i \(0.501011\pi\)
\(444\) 45.9425 + 92.4651i 0.103474 + 0.208255i
\(445\) −81.0597 140.400i −0.182157 0.315504i
\(446\) −150.008 86.6071i −0.336341 0.194186i
\(447\) −26.8316 + 428.995i −0.0600260 + 0.959719i
\(448\) −208.490 + 451.605i −0.465380 + 1.00805i
\(449\) 206.559i 0.460042i −0.973186 0.230021i \(-0.926121\pi\)
0.973186 0.230021i \(-0.0738795\pi\)
\(450\) −62.3362 47.2435i −0.138525 0.104986i
\(451\) −96.4615 167.076i −0.213884 0.370457i
\(452\) 118.696 68.5293i 0.262602 0.151613i
\(453\) 5.69640 8.58062i 0.0125748 0.0189418i
\(454\) 535.132 1.17870
\(455\) 8.82563 6.23016i 0.0193970 0.0136927i
\(456\) 44.8587 717.219i 0.0983744 1.57285i
\(457\) −14.6514 + 25.3770i −0.0320600 + 0.0555295i −0.881610 0.471978i \(-0.843540\pi\)
0.849550 + 0.527508i \(0.176873\pi\)
\(458\) −84.0061 + 48.5009i −0.183419 + 0.105897i
\(459\) −368.058 + 128.627i −0.801869 + 0.280233i
\(460\) 47.2110 81.7719i 0.102633 0.177765i
\(461\) 41.0856i 0.0891228i 0.999007 + 0.0445614i \(0.0141890\pi\)
−0.999007 + 0.0445614i \(0.985811\pi\)
\(462\) −466.272 + 13.3496i −1.00925 + 0.0288952i
\(463\) 228.244 0.492968 0.246484 0.969147i \(-0.420725\pi\)
0.246484 + 0.969147i \(0.420725\pi\)
\(464\) 256.900 + 148.321i 0.553664 + 0.319658i
\(465\) −107.440 + 53.3830i −0.231054 + 0.114802i
\(466\) −177.249 307.004i −0.380362 0.658807i
\(467\) −508.155 293.383i −1.08813 0.628230i −0.155049 0.987907i \(-0.549553\pi\)
−0.933077 + 0.359677i \(0.882887\pi\)
\(468\) 6.03313 + 0.757653i 0.0128913 + 0.00161892i
\(469\) −189.838 + 17.3397i −0.404771 + 0.0369716i
\(470\) 171.215i 0.364287i
\(471\) −404.143 + 608.770i −0.858053 + 1.29251i
\(472\) 106.646 + 184.716i 0.225945 + 0.391348i
\(473\) −256.409 + 148.038i −0.542092 + 0.312977i
\(474\) −160.950 106.850i −0.339557 0.225421i
\(475\) −138.399 −0.291366
\(476\) 80.8359 57.0634i 0.169823 0.119881i
\(477\) −101.763 + 810.331i −0.213340 + 1.69881i
\(478\) −72.9776 + 126.401i −0.152673 + 0.264437i
\(479\) −629.208 + 363.273i −1.31359 + 0.758399i −0.982688 0.185267i \(-0.940685\pi\)
−0.330898 + 0.943666i \(0.607352\pi\)
\(480\) 45.6007 + 91.7772i 0.0950014 + 0.191202i
\(481\) 12.1330 21.0150i 0.0252246 0.0436902i
\(482\) 237.424i 0.492582i
\(483\) −797.163 430.306i −1.65044 0.890903i
\(484\) −41.4228 −0.0855842
\(485\) 45.0484 + 26.0087i 0.0928832 + 0.0536262i
\(486\) −412.975 + 88.5747i −0.849742 + 0.182252i
\(487\) 317.553 + 550.018i 0.652060 + 1.12940i 0.982622 + 0.185617i \(0.0594284\pi\)
−0.330562 + 0.943784i \(0.607238\pi\)
\(488\) 495.991 + 286.360i 1.01637 + 0.586804i
\(489\) 27.7014 + 1.73259i 0.0566490 + 0.00354313i
\(490\) 63.7660 179.450i 0.130135 0.366225i
\(491\) 68.0254i 0.138545i −0.997598 0.0692723i \(-0.977932\pi\)
0.997598 0.0692723i \(-0.0220677\pi\)
\(492\) 36.9347 + 24.5198i 0.0750705 + 0.0498369i
\(493\) −192.500 333.420i −0.390467 0.676308i
\(494\) −28.7568 + 16.6028i −0.0582122 + 0.0336088i
\(495\) −155.342 + 204.968i −0.313822 + 0.414077i
\(496\) −198.984 −0.401178
\(497\) 486.350 + 224.531i 0.978572 + 0.451773i
\(498\) 104.315 + 6.52445i 0.209469 + 0.0131013i
\(499\) 354.547 614.093i 0.710515 1.23065i −0.254149 0.967165i \(-0.581795\pi\)
0.964664 0.263483i \(-0.0848712\pi\)
\(500\) 9.47806 5.47216i 0.0189561 0.0109443i
\(501\) 526.637 261.666i 1.05117 0.522288i
\(502\) −113.343 + 196.315i −0.225782 + 0.391067i
\(503\) 96.8787i 0.192602i −0.995352 0.0963009i \(-0.969299\pi\)
0.995352 0.0963009i \(-0.0307011\pi\)
\(504\) 481.111 256.469i 0.954585 0.508867i
\(505\) −322.235 −0.638089
\(506\) 829.819 + 479.096i 1.63996 + 0.946830i
\(507\) 224.961 + 452.763i 0.443710 + 0.893024i
\(508\) 115.089 + 199.340i 0.226554 + 0.392402i
\(509\) 550.592 + 317.884i 1.08171 + 0.624527i 0.931358 0.364105i \(-0.118625\pi\)
0.150355 + 0.988632i \(0.451958\pi\)
\(510\) −10.5102 + 168.041i −0.0206083 + 0.329493i
\(511\) 344.533 31.4694i 0.674233 0.0615841i
\(512\) 555.120i 1.08422i
\(513\) −487.712 + 566.282i −0.950705 + 1.10386i
\(514\) 140.021 + 242.523i 0.272414 + 0.471835i
\(515\) 293.303 169.339i 0.569521 0.328813i
\(516\) 37.6301 56.6831i 0.0729266 0.109851i
\(517\) 562.972 1.08892
\(518\) −38.9108 426.002i −0.0751173 0.822397i
\(519\) −19.4506 + 310.985i −0.0374772 + 0.599200i
\(520\) 6.67783 11.5663i 0.0128420 0.0222430i
\(521\) −3.34581 + 1.93170i −0.00642190 + 0.00370769i −0.503208 0.864166i \(-0.667847\pi\)
0.496786 + 0.867873i \(0.334514\pi\)
\(522\) −161.905 384.365i −0.310163 0.736332i
\(523\) 414.213 717.439i 0.791995 1.37178i −0.132735 0.991152i \(-0.542376\pi\)
0.924730 0.380624i \(-0.124291\pi\)
\(524\) 76.4211i 0.145842i
\(525\) −55.0809 89.3929i −0.104916 0.170272i
\(526\) −476.912 −0.906676
\(527\) 223.654 + 129.127i 0.424391 + 0.245022i
\(528\) −382.008 + 189.806i −0.723500 + 0.359480i
\(529\) 665.921 + 1153.41i 1.25883 + 2.18036i
\(530\) 305.434 + 176.342i 0.576290 + 0.332721i
\(531\) 27.6395 220.092i 0.0520518 0.414485i
\(532\) 79.4999 172.203i 0.149436 0.323689i
\(533\) 10.4192i 0.0195482i
\(534\) −209.096 + 314.967i −0.391566 + 0.589825i
\(535\) −46.3427 80.2679i −0.0866218 0.150033i
\(536\) −204.096 + 117.835i −0.380776 + 0.219841i
\(537\) −702.510 466.374i −1.30821 0.868481i
\(538\) 307.592 0.571733
\(539\) −590.051 209.670i −1.09471 0.388998i
\(540\) 11.0100 58.0647i 0.0203890 0.107527i
\(541\) −13.9137 + 24.0992i −0.0257185 + 0.0445457i −0.878598 0.477562i \(-0.841521\pi\)
0.852880 + 0.522107i \(0.174854\pi\)
\(542\) 428.687 247.502i 0.790935 0.456646i
\(543\) −71.3850 143.671i −0.131464 0.264588i
\(544\) 110.302 191.049i 0.202761 0.351193i
\(545\) 5.88530i 0.0107987i
\(546\) −22.1687 11.9666i −0.0406020 0.0219168i
\(547\) −610.439 −1.11598 −0.557988 0.829849i \(-0.688426\pi\)
−0.557988 + 0.829849i \(0.688426\pi\)
\(548\) 121.315 + 70.0411i 0.221377 + 0.127812i
\(549\) −231.216 548.911i −0.421159 0.999837i
\(550\) 55.5313 + 96.1830i 0.100966 + 0.174878i
\(551\) −639.116 368.994i −1.15992 0.669680i
\(552\) −1117.75 69.9100i −2.02491 0.126649i
\(553\) −149.564 211.872i −0.270458 0.383131i
\(554\) 122.293i 0.220746i
\(555\) −196.495 130.446i −0.354044 0.235039i
\(556\) −58.4528 101.243i −0.105131 0.182092i
\(557\) 438.946 253.425i 0.788053 0.454983i −0.0512234 0.998687i \(-0.516312\pi\)
0.839277 + 0.543704i \(0.182979\pi\)
\(558\) 222.968 + 168.983i 0.399583 + 0.302837i
\(559\) −15.9902 −0.0286050
\(560\) −15.8411 173.431i −0.0282876 0.309698i
\(561\) 552.538 + 34.5587i 0.984917 + 0.0616020i
\(562\) −356.629 + 617.699i −0.634571 + 1.09911i
\(563\) 942.956 544.416i 1.67488 0.966990i 0.710032 0.704169i \(-0.248680\pi\)
0.964845 0.262821i \(-0.0846529\pi\)
\(564\) −115.855 + 57.5643i −0.205417 + 0.102064i
\(565\) −156.541 + 271.137i −0.277063 + 0.479888i
\(566\) 729.699i 1.28922i
\(567\) −559.869 89.6445i −0.987423 0.158103i
\(568\) 662.249 1.16593
\(569\) 39.3937 + 22.7440i 0.0692333 + 0.0399718i 0.534217 0.845347i \(-0.320607\pi\)
−0.464984 + 0.885319i \(0.653940\pi\)
\(570\) 143.608 + 289.029i 0.251943 + 0.507068i
\(571\) −225.847 391.179i −0.395529 0.685077i 0.597639 0.801765i \(-0.296105\pi\)
−0.993169 + 0.116688i \(0.962772\pi\)
\(572\) −7.47728 4.31701i −0.0130722 0.00754722i
\(573\) 19.8012 316.589i 0.0345571 0.552512i
\(574\) −105.926 150.055i −0.184540 0.261419i
\(575\) 215.687i 0.375109i
\(576\) 386.282 509.686i 0.670628 0.884871i
\(577\) −322.681 558.900i −0.559239 0.968630i −0.997560 0.0698117i \(-0.977760\pi\)
0.438321 0.898818i \(-0.355573\pi\)
\(578\) −121.143 + 69.9420i −0.209590 + 0.121007i
\(579\) 149.543 225.260i 0.258278 0.389050i
\(580\) 58.3586 0.100618
\(581\) 127.390 + 58.8115i 0.219260 + 0.101225i
\(582\) 7.57208 121.065i 0.0130104 0.208016i
\(583\) 579.832 1004.30i 0.994566 1.72264i
\(584\) 370.411 213.857i 0.634265 0.366193i
\(585\) −12.8004 + 5.39189i −0.0218811 + 0.00921690i
\(586\) −19.1720 + 33.2069i −0.0327168 + 0.0566671i
\(587\) 1139.56i 1.94133i −0.240439 0.970664i \(-0.577291\pi\)
0.240439 0.970664i \(-0.422709\pi\)
\(588\) 142.867 17.1847i 0.242971 0.0292256i
\(589\) 495.033 0.840463
\(590\) −82.9579 47.8957i −0.140607 0.0811792i
\(591\) −525.509 + 261.106i −0.889187 + 0.441804i
\(592\) −195.592 338.776i −0.330392 0.572256i
\(593\) 379.938 + 219.358i 0.640706 + 0.369912i 0.784886 0.619640i \(-0.212721\pi\)
−0.144181 + 0.989551i \(0.546055\pi\)
\(594\) 589.239 + 111.729i 0.991984 + 0.188097i
\(595\) −94.7393 + 205.212i −0.159226 + 0.344894i
\(596\) 140.253i 0.235324i
\(597\) 385.048 580.006i 0.644971 0.971535i
\(598\) 25.8746 + 44.8160i 0.0432685 + 0.0749432i
\(599\) 749.729 432.856i 1.25163 0.722631i 0.280200 0.959942i \(-0.409599\pi\)
0.971434 + 0.237310i \(0.0762658\pi\)
\(600\) −108.148 71.7958i −0.180246 0.119660i
\(601\) −85.8542 −0.142852 −0.0714261 0.997446i \(-0.522755\pi\)
−0.0714261 + 0.997446i \(0.522755\pi\)
\(602\) −230.286 + 162.563i −0.382535 + 0.270038i
\(603\) 243.183 + 30.5394i 0.403288 + 0.0506458i
\(604\) 1.68032 2.91039i 0.00278198 0.00481853i
\(605\) 81.9447 47.3108i 0.135446 0.0781997i
\(606\) 334.363 + 672.947i 0.551753 + 1.11047i
\(607\) −512.102 + 886.986i −0.843660 + 1.46126i 0.0431202 + 0.999070i \(0.486270\pi\)
−0.886780 + 0.462192i \(0.847063\pi\)
\(608\) 422.865i 0.695502i
\(609\) −16.0235 559.664i −0.0263111 0.918989i
\(610\) −257.215 −0.421663
\(611\) 26.3310 + 15.2022i 0.0430950 + 0.0248809i
\(612\) −117.242 + 49.3855i −0.191572 + 0.0806952i
\(613\) −164.682 285.238i −0.268650 0.465315i 0.699864 0.714276i \(-0.253244\pi\)
−0.968513 + 0.248961i \(0.919911\pi\)
\(614\) 718.746 + 414.968i 1.17060 + 0.675844i
\(615\) −101.071 6.32155i −0.164344 0.0102789i
\(616\) −770.946 + 70.4178i −1.25154 + 0.114315i
\(617\) 249.124i 0.403766i 0.979410 + 0.201883i \(0.0647061\pi\)
−0.979410 + 0.201883i \(0.935294\pi\)
\(618\) −657.985 436.816i −1.06470 0.706821i
\(619\) 286.676 + 496.537i 0.463128 + 0.802161i 0.999115 0.0420654i \(-0.0133938\pi\)
−0.535987 + 0.844226i \(0.680060\pi\)
\(620\) −33.9016 + 19.5731i −0.0546801 + 0.0315696i
\(621\) 882.521 + 760.073i 1.42113 + 1.22395i
\(622\) 318.345 0.511809
\(623\) −414.616 + 292.684i −0.665515 + 0.469798i
\(624\) −22.9925 1.43807i −0.0368469 0.00230460i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 151.133 87.2568i 0.241427 0.139388i
\(627\) 950.358 472.197i 1.51572 0.753106i
\(628\) −119.214 + 206.484i −0.189830 + 0.328796i
\(629\) 507.702i 0.807157i
\(630\) −129.532 + 207.787i −0.205606 + 0.329820i
\(631\) 919.331 1.45694 0.728471 0.685076i \(-0.240231\pi\)
0.728471 + 0.685076i \(0.240231\pi\)
\(632\) −277.666 160.311i −0.439345 0.253656i
\(633\) −281.546 566.647i −0.444780 0.895177i
\(634\) −265.784 460.352i −0.419218 0.726107i
\(635\) −455.352 262.897i −0.717089 0.414012i
\(636\) −16.6349 + 265.965i −0.0261555 + 0.418184i
\(637\) −21.9357 25.7400i −0.0344360 0.0404082i
\(638\) 592.221i 0.928247i
\(639\) −548.899 416.001i −0.858998 0.651019i
\(640\) −69.7663 120.839i −0.109010 0.188811i
\(641\) −534.570 + 308.634i −0.833962 + 0.481488i −0.855207 0.518286i \(-0.826570\pi\)
0.0212454 + 0.999774i \(0.493237\pi\)
\(642\) −119.543 + 180.070i −0.186203 + 0.280482i
\(643\) −787.857 −1.22528 −0.612642 0.790361i \(-0.709893\pi\)
−0.612642 + 0.790361i \(0.709893\pi\)
\(644\) −268.369 123.896i −0.416722 0.192386i
\(645\) −9.70158 + 155.113i −0.0150412 + 0.240485i
\(646\) 347.368 601.660i 0.537722 0.931362i
\(647\) −525.918 + 303.639i −0.812857 + 0.469303i −0.847947 0.530081i \(-0.822162\pi\)
0.0350901 + 0.999384i \(0.488828\pi\)
\(648\) −674.872 + 189.499i −1.04147 + 0.292436i
\(649\) −157.486 + 272.774i −0.242660 + 0.420300i
\(650\) 5.99816i 0.00922794i
\(651\) 197.016 + 319.746i 0.302637 + 0.491161i
\(652\) 9.05652 0.0138904
\(653\) 922.762 + 532.757i 1.41311 + 0.815861i 0.995680 0.0928474i \(-0.0295969\pi\)
0.417432 + 0.908708i \(0.362930\pi\)
\(654\) −12.2907 + 6.10680i −0.0187931 + 0.00933762i
\(655\) −87.2840 151.180i −0.133258 0.230810i
\(656\) −145.461 83.9822i −0.221740 0.128022i
\(657\) −441.348 55.4254i −0.671763 0.0843614i
\(658\) 533.765 48.7538i 0.811193 0.0740939i
\(659\) 894.888i 1.35795i −0.734162 0.678974i \(-0.762425\pi\)
0.734162 0.678974i \(-0.237575\pi\)
\(660\) −46.4137 + 69.9140i −0.0703238 + 0.105930i
\(661\) 241.970 + 419.105i 0.366067 + 0.634047i 0.988947 0.148271i \(-0.0473707\pi\)
−0.622880 + 0.782318i \(0.714037\pi\)
\(662\) −274.176 + 158.296i −0.414163 + 0.239117i
\(663\) 24.9098 + 16.5368i 0.0375714 + 0.0249424i
\(664\) 173.463 0.261240
\(665\) 39.4094 + 431.461i 0.0592622 + 0.648813i
\(666\) −68.5314 + 545.710i −0.102900 + 0.819385i
\(667\) −575.057 + 996.029i −0.862155 + 1.49330i
\(668\) 166.175 95.9412i 0.248765 0.143624i
\(669\) 133.029 + 267.738i 0.198848 + 0.400207i
\(670\) 52.9208 91.6616i 0.0789863 0.136808i
\(671\) 845.749i 1.26043i
\(672\) 273.132 168.295i 0.406447 0.250439i
\(673\) −466.753 −0.693540 −0.346770 0.937950i \(-0.612722\pi\)
−0.346770 + 0.937950i \(0.612722\pi\)
\(674\) 191.365 + 110.485i 0.283925 + 0.163924i
\(675\) 44.5377 + 127.442i 0.0659817 + 0.188803i
\(676\) 82.4830 + 142.865i 0.122016 + 0.211338i
\(677\) 958.597 + 553.446i 1.41595 + 0.817498i 0.995940 0.0900224i \(-0.0286939\pi\)
0.420008 + 0.907520i \(0.362027\pi\)
\(678\) 728.668 + 45.5748i 1.07473 + 0.0672194i
\(679\) 68.2549 147.845i 0.100523 0.217739i
\(680\) 279.431i 0.410929i
\(681\) −769.500 510.847i −1.12996 0.750142i
\(682\) −198.627 344.033i −0.291243 0.504447i
\(683\) −222.898 + 128.690i −0.326351 + 0.188419i −0.654220 0.756305i \(-0.727003\pi\)
0.327869 + 0.944723i \(0.393670\pi\)
\(684\) −147.294 + 194.349i −0.215342 + 0.284136i
\(685\) −319.988 −0.467136
\(686\) −577.596 147.693i −0.841977 0.215296i
\(687\) 167.098 + 10.4512i 0.243228 + 0.0152128i
\(688\) −128.886 + 223.237i −0.187335 + 0.324473i
\(689\) 54.2392 31.3150i 0.0787216 0.0454499i
\(690\) 450.436 223.805i 0.652806 0.324355i
\(691\) −237.797 + 411.877i −0.344135 + 0.596059i −0.985196 0.171431i \(-0.945161\pi\)
0.641061 + 0.767490i \(0.278494\pi\)
\(692\) 101.671i 0.146924i
\(693\) 683.226 + 425.916i 0.985896 + 0.614597i
\(694\) 610.538 0.879738
\(695\) 231.269 + 133.523i 0.332761 + 0.192120i
\(696\) −307.999 619.887i −0.442527 0.890642i
\(697\) 108.997 + 188.788i 0.156380 + 0.270858i
\(698\) −817.359 471.903i −1.17100 0.676078i
\(699\) −38.1943 + 610.666i −0.0546414 + 0.873628i
\(700\) −19.7584 27.9898i −0.0282264 0.0399854i
\(701\) 310.690i 0.443209i 0.975137 + 0.221605i \(0.0711294\pi\)
−0.975137 + 0.221605i \(0.928871\pi\)
\(702\) 24.5425 + 21.1373i 0.0349608 + 0.0301101i
\(703\) 486.594 + 842.805i 0.692168 + 1.19887i
\(704\) −786.431 + 454.046i −1.11709 + 0.644952i
\(705\) 163.445 246.201i 0.231836 0.349221i
\(706\) −91.2628 −0.129267
\(707\) 91.7571 + 1004.57i 0.129784 + 1.42090i
\(708\) 4.51815 72.2380i 0.00638157 0.102031i
\(709\) 134.556 233.058i 0.189783 0.328714i −0.755395 0.655270i \(-0.772555\pi\)
0.945178 + 0.326556i \(0.105888\pi\)
\(710\) −257.576 + 148.711i −0.362783 + 0.209453i
\(711\) 129.440 + 307.292i 0.182053 + 0.432197i
\(712\) −313.715 + 543.371i −0.440611 + 0.763161i
\(713\) 771.483i 1.08202i
\(714\) 526.865 15.0844i 0.737906 0.0211266i
\(715\) 19.7226 0.0275841
\(716\) −238.279 137.570i −0.332792 0.192137i
\(717\) 225.604 112.094i 0.314650 0.156338i
\(718\) 367.732 + 636.930i 0.512161 + 0.887090i
\(719\) −845.804 488.325i −1.17636 0.679173i −0.221192 0.975230i \(-0.570995\pi\)
−0.955170 + 0.296057i \(0.904328\pi\)
\(720\) −27.9000 + 222.166i −0.0387500 + 0.308564i
\(721\) −611.436 866.159i −0.848038 1.20133i
\(722\) 704.239i 0.975400i
\(723\) −226.650 + 341.408i −0.313485 + 0.472210i
\(724\) −26.1736 45.3340i −0.0361514 0.0626161i
\(725\) −115.448 + 66.6540i −0.159239 + 0.0919366i
\(726\) −183.832 122.040i −0.253211 0.168099i
\(727\) 214.232 0.294680 0.147340 0.989086i \(-0.452929\pi\)
0.147340 + 0.989086i \(0.452929\pi\)
\(728\) −37.9598 17.5247i −0.0521426 0.0240724i
\(729\) 678.398 + 266.866i 0.930587 + 0.366072i
\(730\) −96.0451 + 166.355i −0.131569 + 0.227884i
\(731\) 289.730 167.276i 0.396348 0.228832i
\(732\) −86.4784 174.049i −0.118140 0.237772i
\(733\) −29.1732 + 50.5295i −0.0397997 + 0.0689352i −0.885239 0.465136i \(-0.846005\pi\)
0.845439 + 0.534071i \(0.179339\pi\)
\(734\) 89.2351i 0.121574i
\(735\) −263.000 + 197.170i −0.357823 + 0.268259i
\(736\) −659.014 −0.895399
\(737\) −301.393 174.010i −0.408946 0.236105i
\(738\) 91.6735 + 217.634i 0.124219 + 0.294898i
\(739\) −444.978 770.724i −0.602135 1.04293i −0.992497 0.122267i \(-0.960984\pi\)
0.390363 0.920661i \(-0.372350\pi\)
\(740\) −66.6474 38.4789i −0.0900641 0.0519985i
\(741\) 57.2006 + 3.57763i 0.0771938 + 0.00482811i
\(742\) 462.777 1002.41i 0.623688 1.35095i
\(743\) 625.012i 0.841200i −0.907246 0.420600i \(-0.861820\pi\)
0.907246 0.420600i \(-0.138180\pi\)
\(744\) 386.829 + 256.803i 0.519931 + 0.345166i
\(745\) −160.189 277.456i −0.215019 0.372424i
\(746\) −713.140 + 411.731i −0.955951 + 0.551919i
\(747\) −143.773 108.963i −0.192468 0.145868i
\(748\) 180.644 0.241502
\(749\) −237.040 + 167.331i −0.316476 + 0.223405i
\(750\) 58.1851 + 3.63921i 0.0775801 + 0.00485228i
\(751\) 84.2527 145.930i 0.112187 0.194314i −0.804465 0.594001i \(-0.797548\pi\)
0.916652 + 0.399686i \(0.130881\pi\)
\(752\) 424.474 245.070i 0.564460 0.325891i
\(753\) 350.389 174.095i 0.465324 0.231202i
\(754\) −15.9921 + 27.6991i −0.0212096 + 0.0367362i
\(755\) 7.67666i 0.0101678i
\(756\) −184.153 17.7899i −0.243588 0.0235316i
\(757\) 226.565 0.299294 0.149647 0.988740i \(-0.452186\pi\)
0.149647 + 0.988740i \(0.452186\pi\)
\(758\) −541.795 312.805i −0.714769 0.412672i
\(759\) −735.895 1481.08i −0.969559 1.95136i
\(760\) 267.814 + 463.867i 0.352387 + 0.610352i
\(761\) 216.707 + 125.116i 0.284766 + 0.164410i 0.635579 0.772036i \(-0.280761\pi\)
−0.350813 + 0.936446i \(0.614095\pi\)
\(762\) −76.5390 + 1223.74i −0.100445 + 1.60595i
\(763\) −18.3475 + 1.67585i −0.0240466 + 0.00219640i
\(764\) 103.504i 0.135476i
\(765\) 175.529 231.604i 0.229449 0.302751i
\(766\) −323.667 560.607i −0.422541 0.731863i
\(767\) −14.7317 + 8.50537i −0.0192070 + 0.0110891i
\(768\) 291.652 439.322i 0.379755 0.572033i
\(769\) 55.8478 0.0726240 0.0363120 0.999341i \(-0.488439\pi\)
0.0363120 + 0.999341i \(0.488439\pi\)
\(770\) 284.040 200.508i 0.368883 0.260400i
\(771\) 30.1722 482.406i 0.0391339 0.625688i
\(772\) 44.1120 76.4042i 0.0571399 0.0989692i
\(773\) −1160.40 + 669.957i −1.50116 + 0.866697i −0.501165 + 0.865352i \(0.667095\pi\)
−0.999999 + 0.00134522i \(0.999572\pi\)
\(774\) 334.000 140.690i 0.431525 0.181770i
\(775\) 44.7107 77.4412i 0.0576912 0.0999241i
\(776\) 201.316i 0.259428i
\(777\) −350.717 + 649.720i −0.451373 + 0.836191i
\(778\) −1103.97 −1.41898
\(779\) 361.878 + 208.931i 0.464542 + 0.268204i
\(780\) −4.05876 + 2.01665i −0.00520354 + 0.00258545i
\(781\) 488.979 + 846.937i 0.626094 + 1.08443i
\(782\) −937.655 541.356i −1.19905 0.692271i
\(783\) −134.109 + 707.261i −0.171275 + 0.903271i
\(784\) −536.163 + 98.7697i −0.683882 + 0.125982i
\(785\) 544.637i 0.693805i
\(786\) −225.152 + 339.152i −0.286453 + 0.431491i
\(787\) −203.728 352.868i −0.258867 0.448371i 0.707072 0.707142i \(-0.250016\pi\)
−0.965939 + 0.258771i \(0.916682\pi\)
\(788\) −165.819 + 95.7357i −0.210430 + 0.121492i
\(789\) 685.782 + 455.269i 0.869178 + 0.577020i
\(790\) 143.994 0.182271
\(791\) 889.849 + 410.812i 1.12497 + 0.519358i
\(792\) 987.586 + 124.023i 1.24695 + 0.156595i
\(793\) −22.8382 + 39.5569i −0.0287998 + 0.0498826i
\(794\) 1145.60 661.412i 1.44282 0.833013i
\(795\) −270.863 545.146i −0.340708 0.685718i
\(796\) 113.581 196.728i 0.142690 0.247145i
\(797\) 551.602i 0.692098i −0.938216 0.346049i \(-0.887523\pi\)
0.938216 0.346049i \(-0.112477\pi\)
\(798\) 860.159 530.001i 1.07789 0.664162i
\(799\) −636.132 −0.796160
\(800\) −66.1516 38.1926i −0.0826895 0.0477408i
\(801\) 601.346 253.303i 0.750744 0.316234i
\(802\) −16.9749 29.4015i −0.0211658 0.0366602i
\(803\) 546.993 + 315.807i 0.681187 + 0.393284i
\(804\) 79.8170 + 4.99218i 0.0992749 + 0.00620919i
\(805\) 672.409 61.4175i 0.835291 0.0762950i
\(806\) 21.4546i 0.0266186i
\(807\) −442.306 293.633i −0.548087 0.363858i
\(808\) 623.553 + 1080.03i 0.771724 + 1.33667i
\(809\) −641.297 + 370.253i −0.792703 + 0.457668i −0.840913 0.541170i \(-0.817982\pi\)
0.0482100 + 0.998837i \(0.484648\pi\)
\(810\) 219.932 225.249i 0.271521 0.278086i
\(811\) 1613.59 1.98964 0.994818 0.101674i \(-0.0324200\pi\)
0.994818 + 0.101674i \(0.0324200\pi\)
\(812\) −16.6177 181.934i −0.0204652 0.224057i
\(813\) −852.706 53.3328i −1.04884 0.0656000i
\(814\) 390.483 676.336i 0.479709 0.830880i
\(815\) −17.9161 + 10.3439i −0.0219829 + 0.0126919i
\(816\) 431.650 214.471i 0.528983 0.262832i
\(817\) 320.643 555.369i 0.392463 0.679766i
\(818\) 1072.03i 1.31056i
\(819\) 20.4543 + 38.3702i 0.0249747 + 0.0468500i
\(820\) −33.0437 −0.0402972
\(821\) 33.3307 + 19.2435i 0.0405977 + 0.0234391i 0.520161 0.854068i \(-0.325872\pi\)
−0.479564 + 0.877507i \(0.659205\pi\)
\(822\) 332.032 + 668.256i 0.403931 + 0.812963i
\(823\) −327.466 567.187i −0.397893 0.689170i 0.595573 0.803301i \(-0.296925\pi\)
−0.993466 + 0.114131i \(0.963592\pi\)
\(824\) −1135.14 655.371i −1.37759 0.795353i
\(825\) 11.9661 191.319i 0.0145044 0.231902i
\(826\) −125.693 + 272.261i −0.152171 + 0.329614i
\(827\) 523.381i 0.632867i 0.948615 + 0.316433i \(0.102485\pi\)
−0.948615 + 0.316433i \(0.897515\pi\)
\(828\) 302.883 + 229.550i 0.365801 + 0.277234i
\(829\) 517.938 + 897.096i 0.624775 + 1.08214i 0.988584 + 0.150668i \(0.0481426\pi\)
−0.363810 + 0.931473i \(0.618524\pi\)
\(830\) −67.4669 + 38.9520i −0.0812854 + 0.0469302i
\(831\) −116.743 + 175.853i −0.140485 + 0.211616i
\(832\) −49.0434 −0.0589464
\(833\) 666.730 + 236.917i 0.800396 + 0.284414i
\(834\) 38.8735 621.525i 0.0466109 0.745233i
\(835\) −219.158 + 379.592i −0.262464 + 0.454601i
\(836\) 299.876 173.133i 0.358703 0.207097i
\(837\) −159.305 455.841i −0.190328 0.544613i
\(838\) 414.043 717.144i 0.494085 0.855780i
\(839\) 941.095i 1.12169i 0.827922 + 0.560843i \(0.189523\pi\)
−0.827922 + 0.560843i \(0.810477\pi\)
\(840\) −193.029 + 357.596i −0.229797 + 0.425710i
\(841\) 130.159 0.154766
\(842\) −253.412 146.307i −0.300964 0.173762i
\(843\) 1102.49 547.784i 1.30781 0.649804i
\(844\) −103.230 178.800i −0.122310 0.211848i
\(845\) −326.345 188.415i −0.386207 0.222977i
\(846\) −683.755 85.8673i −0.808221 0.101498i
\(847\) −170.826 241.992i −0.201684 0.285705i
\(848\) 1009.64i 1.19061i
\(849\) −696.584 + 1049.28i −0.820476 + 1.23590i
\(850\) −62.7477 108.682i −0.0738208 0.127861i
\(851\) 1313.47 758.331i 1.54344 0.891106i
\(852\) −187.228 124.295i −0.219751 0.145886i
\(853\) 39.6225 0.0464507 0.0232254 0.999730i \(-0.492606\pi\)
0.0232254 + 0.999730i \(0.492606\pi\)
\(854\) 73.2424 + 801.871i 0.0857640 + 0.938959i
\(855\) 69.4096 552.703i 0.0811808 0.646437i
\(856\) −179.354 + 310.651i −0.209526 + 0.362910i
\(857\) 424.897 245.314i 0.495796 0.286248i −0.231180 0.972911i \(-0.574259\pi\)
0.726976 + 0.686663i \(0.240925\pi\)
\(858\) −20.4649 41.1882i −0.0238518 0.0480049i
\(859\) 553.321 958.381i 0.644146 1.11569i −0.340352 0.940298i \(-0.610546\pi\)
0.984498 0.175395i \(-0.0561204\pi\)
\(860\) 50.7116i 0.0589670i
\(861\) 9.07277 + 316.892i 0.0105375 + 0.368051i
\(862\) −187.276 −0.217258
\(863\) −487.589 281.510i −0.564993 0.326199i 0.190154 0.981754i \(-0.439101\pi\)
−0.755147 + 0.655555i \(0.772435\pi\)
\(864\) −389.387 + 136.081i −0.450679 + 0.157501i
\(865\) −116.124 201.132i −0.134247 0.232522i
\(866\) −74.7122 43.1351i −0.0862728 0.0498096i
\(867\) 240.967 + 15.0714i 0.277932 + 0.0173834i
\(868\) 70.6731 + 100.115i 0.0814206 + 0.115340i
\(869\) 473.468i 0.544843i
\(870\) 258.992 + 171.936i 0.297692 + 0.197628i
\(871\) −9.39774 16.2774i −0.0107896 0.0186881i
\(872\) −19.7256 + 11.3886i −0.0226211 + 0.0130603i
\(873\) −126.460 + 166.859i −0.144856 + 0.191133i
\(874\) −2075.39 −2.37459
\(875\) 71.0556 + 32.8039i 0.0812064 + 0.0374902i
\(876\) −144.859 9.06023i −0.165364 0.0103427i
\(877\) 642.022 1112.01i 0.732066 1.26798i −0.223933 0.974605i \(-0.571890\pi\)
0.955999 0.293371i \(-0.0947770\pi\)
\(878\) 202.268 116.779i 0.230373 0.133006i
\(879\) 59.2686 29.4484i 0.0674273 0.0335021i
\(880\) 158.971 275.345i 0.180649 0.312892i
\(881\) 674.103i 0.765156i −0.923923 0.382578i \(-0.875036\pi\)
0.923923 0.382578i \(-0.124964\pi\)
\(882\) 684.664 + 344.651i 0.776263 + 0.390760i
\(883\) −1198.11 −1.35686 −0.678431 0.734664i \(-0.737340\pi\)
−0.678431 + 0.734664i \(0.737340\pi\)
\(884\) 8.44896 + 4.87801i 0.00955765 + 0.00551811i
\(885\) 73.5682 + 148.065i 0.0831280 + 0.167306i
\(886\) 382.876 + 663.161i 0.432140 + 0.748489i
\(887\) 207.517 + 119.810i 0.233954 + 0.135073i 0.612395 0.790552i \(-0.290206\pi\)
−0.378441 + 0.925626i \(0.623540\pi\)
\(888\) −56.9795 + 911.011i −0.0641661 + 1.02591i
\(889\) −689.925 + 1494.43i −0.776068 + 1.68102i
\(890\) 281.785i 0.316613i
\(891\) −740.645 723.161i −0.831251 0.811629i
\(892\) 48.7758 + 84.4821i 0.0546813 + 0.0947109i
\(893\) −1056.00 + 609.684i −1.18254 + 0.682737i
\(894\) −413.214 + 622.433i −0.462208 + 0.696234i
\(895\) 628.502 0.702237
\(896\) −356.851 + 251.907i −0.398271 + 0.281146i
\(897\) 5.57556 89.1442i 0.00621578 0.0993804i
\(898\) 179.513 310.926i 0.199904 0.346243i
\(899\) 412.941 238.412i 0.459334 0.265197i
\(900\) 17.0999 + 40.5955i 0.0189999 + 0.0451061i
\(901\) −655.182 + 1134.81i −0.727172 + 1.25950i
\(902\) 335.326i 0.371759i
\(903\) 486.329 13.9238i 0.538570 0.0154195i
\(904\) 1211.68 1.34036
\(905\) 103.556 + 59.7882i 0.114427 + 0.0660643i
\(906\) 16.0317 7.96558i 0.0176951 0.00879203i
\(907\) 577.816 + 1000.81i 0.637063 + 1.10342i 0.986074 + 0.166306i \(0.0531840\pi\)
−0.349012 + 0.937118i \(0.613483\pi\)
\(908\) −261.001 150.689i −0.287446 0.165957i
\(909\) 161.607 1286.86i 0.177785 1.41569i
\(910\) 18.6994 1.70799i 0.0205488 0.00187691i
\(911\) 1411.99i 1.54994i −0.631998 0.774970i \(-0.717765\pi\)
0.631998 0.774970i \(-0.282235\pi\)
\(912\) 511.003 769.735i 0.560310 0.844008i
\(913\) 128.079 + 221.839i 0.140283 + 0.242978i
\(914\) −44.1086 + 25.4661i −0.0482589 + 0.0278623i
\(915\) 369.865 + 245.542i 0.404224 + 0.268352i
\(916\) 54.6299 0.0596396
\(917\) −446.453 + 315.158i −0.486863 + 0.343684i
\(918\) −665.811 126.249i −0.725285 0.137526i
\(919\) −694.896 + 1203.60i −0.756144 + 1.30968i 0.188660 + 0.982043i \(0.439586\pi\)
−0.944804 + 0.327637i \(0.893748\pi\)
\(920\) 722.913 417.374i 0.785775 0.453668i
\(921\) −637.394 1282.84i −0.692068 1.39287i
\(922\) −35.7061 + 61.8448i −0.0387268 + 0.0670768i
\(923\) 52.8166i 0.0572228i
\(924\) 231.175 + 124.787i 0.250189 + 0.135051i
\(925\) 175.794 0.190048
\(926\) 343.569 + 198.360i 0.371025 + 0.214211i
\(927\) 529.167 + 1256.25i 0.570838 + 1.35518i
\(928\) −203.655 352.741i −0.219456 0.380109i
\(929\) 280.389 + 161.883i 0.301818 + 0.174255i 0.643259 0.765648i \(-0.277582\pi\)
−0.341441 + 0.939903i \(0.610915\pi\)
\(930\) −208.120 13.0169i −0.223785 0.0139967i
\(931\) 1333.86 245.719i 1.43272 0.263930i
\(932\) 199.647i 0.214214i
\(933\) −457.769 303.898i −0.490642 0.325722i
\(934\) −509.939 883.241i −0.545974 0.945654i
\(935\) −357.359 + 206.321i −0.382202 + 0.220664i
\(936\) 42.8418 + 32.4690i 0.0457711 + 0.0346891i
\(937\) 1523.58 1.62602 0.813009 0.582252i \(-0.197828\pi\)
0.813009 + 0.582252i \(0.197828\pi\)
\(938\) −300.826 138.881i −0.320710 0.148061i
\(939\) −300.621 18.8025i −0.320150 0.0200239i
\(940\) 48.2127 83.5068i 0.0512901 0.0888370i
\(941\) −32.4890 + 18.7575i −0.0345260 + 0.0199336i −0.517164 0.855887i \(-0.673012\pi\)
0.482638 + 0.875820i \(0.339679\pi\)
\(942\) −1137.41 + 565.135i −1.20744 + 0.599931i
\(943\) 325.608 563.969i 0.345289 0.598058i
\(944\) 274.224i 0.290492i
\(945\) 384.620 175.136i 0.407005 0.185329i
\(946\) −514.620 −0.543996
\(947\) 604.606 + 349.069i 0.638443 + 0.368605i 0.784015 0.620742i \(-0.213169\pi\)
−0.145571 + 0.989348i \(0.546502\pi\)
\(948\) 48.4124 + 97.4362i 0.0510680 + 0.102781i
\(949\) 17.0558 + 29.5415i 0.0179724 + 0.0311291i
\(950\) −208.327 120.278i −0.219292 0.126608i
\(951\) −57.2723 + 915.692i −0.0602232 + 0.962872i
\(952\) 871.132 79.5687i 0.915055 0.0835806i
\(953\) 439.544i 0.461221i −0.973046 0.230610i \(-0.925928\pi\)
0.973046 0.230610i \(-0.0740723\pi\)
\(954\) −857.412 + 1131.33i −0.898755 + 1.18588i
\(955\) 118.216 + 204.757i 0.123787 + 0.214405i
\(956\) 71.1870 41.0998i 0.0744634 0.0429915i
\(957\) 565.346 851.593i 0.590748 0.889857i
\(958\) −1262.84 −1.31820
\(959\) 91.1175 + 997.570i 0.0950130 + 1.04022i
\(960\) −29.7556 + 475.745i −0.0309955 + 0.495568i
\(961\) 320.576 555.254i 0.333586 0.577788i
\(962\) 36.5269 21.0888i 0.0379698 0.0219218i
\(963\) 343.796 144.816i 0.357005 0.150380i
\(964\) −66.8568 + 115.799i −0.0693535 + 0.120124i
\(965\) 201.529i 0.208839i
\(966\) −825.979 1340.51i −0.855051 1.38770i
\(967\) −868.372 −0.898006 −0.449003 0.893530i \(-0.648221\pi\)
−0.449003 + 0.893530i \(0.648221\pi\)
\(968\) −317.141 183.101i −0.327625 0.189154i
\(969\) −1073.86 + 533.561i −1.10821 + 0.550630i
\(970\) 45.2066 + 78.3001i 0.0466047 + 0.0807218i
\(971\) 472.253 + 272.655i 0.486357 + 0.280799i 0.723062 0.690783i \(-0.242734\pi\)
−0.236705 + 0.971582i \(0.576067\pi\)
\(972\) 226.363 + 73.0897i 0.232883 + 0.0751952i
\(973\) 350.406 759.006i 0.360130 0.780068i
\(974\) 1103.90i 1.13337i
\(975\) 5.72596 8.62514i 0.00587278 0.00884630i
\(976\) 368.167 + 637.684i 0.377220 + 0.653365i
\(977\) −370.680 + 214.012i −0.379407 + 0.219051i −0.677560 0.735467i \(-0.736963\pi\)
0.298153 + 0.954518i \(0.403629\pi\)
\(978\) 40.1922 + 26.6824i 0.0410964 + 0.0272826i
\(979\) −926.540 −0.946415
\(980\) −81.6324 + 69.5675i −0.0832984 + 0.0709872i
\(981\) 23.5033 + 2.95159i 0.0239585 + 0.00300875i
\(982\) 59.1186 102.396i 0.0602023 0.104273i
\(983\) −435.599 + 251.493i −0.443133 + 0.255843i −0.704926 0.709281i \(-0.749020\pi\)
0.261793 + 0.965124i \(0.415686\pi\)
\(984\) 174.394 + 350.991i 0.177230 + 0.356698i
\(985\) 218.688 378.779i 0.222018 0.384547i
\(986\) 669.182i 0.678683i
\(987\) −814.076 439.436i −0.824798 0.445224i
\(988\) 18.7008 0.0189280
\(989\) −865.514 499.705i −0.875141 0.505263i
\(990\) −411.962 + 173.530i −0.416123 + 0.175283i
\(991\) −649.616 1125.17i −0.655516 1.13539i −0.981764 0.190103i \(-0.939118\pi\)
0.326248 0.945284i \(-0.394215\pi\)
\(992\) 236.615 + 136.610i 0.238523 + 0.137711i
\(993\) 545.368 + 34.1102i 0.549212 + 0.0343507i
\(994\) 536.956 + 760.651i 0.540197 + 0.765242i
\(995\) 518.903i 0.521511i
\(996\) −49.0407 32.5566i −0.0492377 0.0326873i
\(997\) −804.600 1393.61i −0.807021 1.39780i −0.914918 0.403639i \(-0.867745\pi\)
0.107897 0.994162i \(-0.465588\pi\)
\(998\) 1067.38 616.250i 1.06952 0.617485i
\(999\) 619.491 719.290i 0.620111 0.720010i
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 105.3.t.b.86.13 yes 36
3.2 odd 2 inner 105.3.t.b.86.6 yes 36
7.4 even 3 inner 105.3.t.b.11.6 36
21.11 odd 6 inner 105.3.t.b.11.13 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.t.b.11.6 36 7.4 even 3 inner
105.3.t.b.11.13 yes 36 21.11 odd 6 inner
105.3.t.b.86.6 yes 36 3.2 odd 2 inner
105.3.t.b.86.13 yes 36 1.1 even 1 trivial