Properties

Label 224.3.w.a.99.3
Level $224$
Weight $3$
Character 224.99
Analytic conductor $6.104$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,3,Mod(43,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 5, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 99.3
Character \(\chi\) \(=\) 224.99
Dual form 224.3.w.a.43.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.99185 + 0.180328i) q^{2} +(0.825363 - 1.99260i) q^{3} +(3.93496 - 0.718374i) q^{4} +(0.360772 + 0.870982i) q^{5} +(-1.28468 + 4.11781i) q^{6} +(1.87083 + 1.87083i) q^{7} +(-7.70833 + 2.14048i) q^{8} +(3.07472 + 3.07472i) q^{9} +O(q^{10})\) \(q+(-1.99185 + 0.180328i) q^{2} +(0.825363 - 1.99260i) q^{3} +(3.93496 - 0.718374i) q^{4} +(0.360772 + 0.870982i) q^{5} +(-1.28468 + 4.11781i) q^{6} +(1.87083 + 1.87083i) q^{7} +(-7.70833 + 2.14048i) q^{8} +(3.07472 + 3.07472i) q^{9} +(-0.875668 - 1.66981i) q^{10} +(5.69947 + 13.7597i) q^{11} +(1.81634 - 8.43374i) q^{12} +(2.01655 - 4.86839i) q^{13} +(-4.06378 - 3.38905i) q^{14} +2.03329 q^{15} +(14.9679 - 5.65355i) q^{16} +19.7416i q^{17} +(-6.67884 - 5.56993i) q^{18} +(-23.8235 - 9.86802i) q^{19} +(2.04532 + 3.16811i) q^{20} +(5.27193 - 2.18371i) q^{21} +(-13.8338 - 26.3796i) q^{22} +(18.8473 - 18.8473i) q^{23} +(-2.09705 + 17.1263i) q^{24} +(17.0492 - 17.0492i) q^{25} +(-3.13877 + 10.0608i) q^{26} +(26.5979 - 11.0172i) q^{27} +(8.70560 + 6.01769i) q^{28} +(45.5859 + 18.8823i) q^{29} +(-4.05002 + 0.366659i) q^{30} +37.3014i q^{31} +(-28.7943 + 13.9602i) q^{32} +32.1218 q^{33} +(-3.55997 - 39.3224i) q^{34} +(-0.954514 + 2.30440i) q^{35} +(14.3077 + 9.89010i) q^{36} +(19.3858 + 46.8015i) q^{37} +(49.2324 + 15.3596i) q^{38} +(-8.03638 - 8.03638i) q^{39} +(-4.64527 - 5.94159i) q^{40} +(-16.8279 - 16.8279i) q^{41} +(-10.1071 + 5.30030i) q^{42} +(-31.7055 - 76.5439i) q^{43} +(32.3118 + 50.0497i) q^{44} +(-1.56875 + 3.78730i) q^{45} +(-34.1423 + 40.9397i) q^{46} +83.8956 q^{47} +(1.08866 - 34.4913i) q^{48} +7.00000i q^{49} +(-30.8851 + 37.0340i) q^{50} +(39.3372 + 16.2940i) q^{51} +(4.43774 - 20.6056i) q^{52} +(-25.3103 + 10.4839i) q^{53} +(-50.9924 + 26.7410i) q^{54} +(-9.92827 + 9.92827i) q^{55} +(-18.4254 - 10.4165i) q^{56} +(-39.3261 + 39.3261i) q^{57} +(-94.2055 - 29.3904i) q^{58} +(-37.1064 + 15.3700i) q^{59} +(8.00092 - 1.46066i) q^{60} +(-47.4525 - 19.6555i) q^{61} +(-6.72648 - 74.2989i) q^{62} +11.5045i q^{63} +(54.8367 - 32.9990i) q^{64} +4.96779 q^{65} +(-63.9820 + 5.79246i) q^{66} +(31.7213 - 76.5820i) q^{67} +(14.1819 + 77.6826i) q^{68} +(-21.9993 - 53.1110i) q^{69} +(1.48570 - 4.76216i) q^{70} +(-22.6464 - 22.6464i) q^{71} +(-30.2823 - 17.1196i) q^{72} +(37.4417 + 37.4417i) q^{73} +(-47.0533 - 89.7260i) q^{74} +(-19.9005 - 48.0441i) q^{75} +(-100.834 - 21.7161i) q^{76} +(-15.0794 + 36.4048i) q^{77} +(17.4565 + 14.5581i) q^{78} -11.5269 q^{79} +(10.3241 + 10.9971i) q^{80} -22.9575i q^{81} +(36.5533 + 30.4842i) q^{82} +(-147.866 - 61.2479i) q^{83} +(19.1762 - 12.3800i) q^{84} +(-17.1946 + 7.12224i) q^{85} +(76.9558 + 146.747i) q^{86} +(75.2499 - 75.2499i) q^{87} +(-73.3858 - 93.8650i) q^{88} +(-103.987 + 103.987i) q^{89} +(2.44176 - 7.82663i) q^{90} +(12.8805 - 5.33530i) q^{91} +(60.6239 - 87.7027i) q^{92} +(74.3269 + 30.7872i) q^{93} +(-167.108 + 15.1287i) q^{94} -24.3100i q^{95} +(4.05129 + 68.8979i) q^{96} -82.5634 q^{97} +(-1.26230 - 13.9430i) q^{98} +(-24.7830 + 59.8315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99185 + 0.180328i −0.995927 + 0.0901639i
\(3\) 0.825363 1.99260i 0.275121 0.664201i −0.724566 0.689205i \(-0.757960\pi\)
0.999687 + 0.0250040i \(0.00795985\pi\)
\(4\) 3.93496 0.718374i 0.983741 0.179593i
\(5\) 0.360772 + 0.870982i 0.0721545 + 0.174196i 0.955842 0.293881i \(-0.0949469\pi\)
−0.883688 + 0.468077i \(0.844947\pi\)
\(6\) −1.28468 + 4.11781i −0.214114 + 0.686302i
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −7.70833 + 2.14048i −0.963541 + 0.267560i
\(9\) 3.07472 + 3.07472i 0.341635 + 0.341635i
\(10\) −0.875668 1.66981i −0.0875668 0.166981i
\(11\) 5.69947 + 13.7597i 0.518133 + 1.25088i 0.939048 + 0.343785i \(0.111709\pi\)
−0.420915 + 0.907100i \(0.638291\pi\)
\(12\) 1.81634 8.43374i 0.151362 0.702812i
\(13\) 2.01655 4.86839i 0.155119 0.374491i −0.827146 0.561987i \(-0.810037\pi\)
0.982265 + 0.187496i \(0.0600371\pi\)
\(14\) −4.06378 3.38905i −0.290270 0.242075i
\(15\) 2.03329 0.135553
\(16\) 14.9679 5.65355i 0.935492 0.353347i
\(17\) 19.7416i 1.16127i 0.814163 + 0.580636i \(0.197196\pi\)
−0.814163 + 0.580636i \(0.802804\pi\)
\(18\) −6.67884 5.56993i −0.371047 0.309441i
\(19\) −23.8235 9.86802i −1.25387 0.519370i −0.345847 0.938291i \(-0.612408\pi\)
−0.908023 + 0.418921i \(0.862408\pi\)
\(20\) 2.04532 + 3.16811i 0.102266 + 0.158406i
\(21\) 5.27193 2.18371i 0.251044 0.103986i
\(22\) −13.8338 26.3796i −0.628808 1.19907i
\(23\) 18.8473 18.8473i 0.819447 0.819447i −0.166581 0.986028i \(-0.553273\pi\)
0.986028 + 0.166581i \(0.0532728\pi\)
\(24\) −2.09705 + 17.1263i −0.0873770 + 0.713597i
\(25\) 17.0492 17.0492i 0.681969 0.681969i
\(26\) −3.13877 + 10.0608i −0.120722 + 0.386952i
\(27\) 26.5979 11.0172i 0.985107 0.408045i
\(28\) 8.70560 + 6.01769i 0.310914 + 0.214917i
\(29\) 45.5859 + 18.8823i 1.57193 + 0.651114i 0.987109 0.160049i \(-0.0511652\pi\)
0.584820 + 0.811163i \(0.301165\pi\)
\(30\) −4.05002 + 0.366659i −0.135001 + 0.0122220i
\(31\) 37.3014i 1.20327i 0.798771 + 0.601636i \(0.205484\pi\)
−0.798771 + 0.601636i \(0.794516\pi\)
\(32\) −28.7943 + 13.9602i −0.899823 + 0.436255i
\(33\) 32.1218 0.973389
\(34\) −3.55997 39.3224i −0.104705 1.15654i
\(35\) −0.954514 + 2.30440i −0.0272718 + 0.0658400i
\(36\) 14.3077 + 9.89010i 0.397436 + 0.274725i
\(37\) 19.3858 + 46.8015i 0.523941 + 1.26491i 0.935437 + 0.353494i \(0.115007\pi\)
−0.411496 + 0.911412i \(0.634993\pi\)
\(38\) 49.2324 + 15.3596i 1.29559 + 0.404200i
\(39\) −8.03638 8.03638i −0.206061 0.206061i
\(40\) −4.64527 5.94159i −0.116132 0.148540i
\(41\) −16.8279 16.8279i −0.410437 0.410437i 0.471454 0.881891i \(-0.343729\pi\)
−0.881891 + 0.471454i \(0.843729\pi\)
\(42\) −10.1071 + 5.30030i −0.240646 + 0.126198i
\(43\) −31.7055 76.5439i −0.737338 1.78009i −0.616403 0.787431i \(-0.711411\pi\)
−0.120935 0.992660i \(-0.538589\pi\)
\(44\) 32.3118 + 50.0497i 0.734360 + 1.13749i
\(45\) −1.56875 + 3.78730i −0.0348611 + 0.0841621i
\(46\) −34.1423 + 40.9397i −0.742224 + 0.889993i
\(47\) 83.8956 1.78501 0.892506 0.451035i \(-0.148945\pi\)
0.892506 + 0.451035i \(0.148945\pi\)
\(48\) 1.08866 34.4913i 0.0226804 0.718568i
\(49\) 7.00000i 0.142857i
\(50\) −30.8851 + 37.0340i −0.617702 + 0.740680i
\(51\) 39.3372 + 16.2940i 0.771319 + 0.319491i
\(52\) 4.43774 20.6056i 0.0853411 0.396261i
\(53\) −25.3103 + 10.4839i −0.477553 + 0.197809i −0.608458 0.793586i \(-0.708212\pi\)
0.130905 + 0.991395i \(0.458212\pi\)
\(54\) −50.9924 + 26.7410i −0.944303 + 0.495204i
\(55\) −9.92827 + 9.92827i −0.180514 + 0.180514i
\(56\) −18.4254 10.4165i −0.329026 0.186009i
\(57\) −39.3261 + 39.3261i −0.689932 + 0.689932i
\(58\) −94.2055 29.3904i −1.62423 0.506731i
\(59\) −37.1064 + 15.3700i −0.628922 + 0.260508i −0.674295 0.738462i \(-0.735552\pi\)
0.0453732 + 0.998970i \(0.485552\pi\)
\(60\) 8.00092 1.46066i 0.133349 0.0243444i
\(61\) −47.4525 19.6555i −0.777909 0.322221i −0.0418379 0.999124i \(-0.513321\pi\)
−0.736071 + 0.676904i \(0.763321\pi\)
\(62\) −6.72648 74.2989i −0.108492 1.19837i
\(63\) 11.5045i 0.182612i
\(64\) 54.8367 32.9990i 0.856823 0.515610i
\(65\) 4.96779 0.0764276
\(66\) −63.9820 + 5.79246i −0.969424 + 0.0877646i
\(67\) 31.7213 76.5820i 0.473452 1.14301i −0.489175 0.872186i \(-0.662702\pi\)
0.962627 0.270829i \(-0.0872979\pi\)
\(68\) 14.1819 + 77.6826i 0.208557 + 1.14239i
\(69\) −21.9993 53.1110i −0.318830 0.769725i
\(70\) 1.48570 4.76216i 0.0212244 0.0680308i
\(71\) −22.6464 22.6464i −0.318963 0.318963i 0.529406 0.848369i \(-0.322415\pi\)
−0.848369 + 0.529406i \(0.822415\pi\)
\(72\) −30.2823 17.1196i −0.420587 0.237772i
\(73\) 37.4417 + 37.4417i 0.512899 + 0.512899i 0.915414 0.402514i \(-0.131864\pi\)
−0.402514 + 0.915414i \(0.631864\pi\)
\(74\) −47.0533 89.7260i −0.635856 1.21251i
\(75\) −19.9005 48.0441i −0.265340 0.640588i
\(76\) −100.834 21.7161i −1.32676 0.285739i
\(77\) −15.0794 + 36.4048i −0.195836 + 0.472790i
\(78\) 17.4565 + 14.5581i 0.223801 + 0.186642i
\(79\) −11.5269 −0.145910 −0.0729549 0.997335i \(-0.523243\pi\)
−0.0729549 + 0.997335i \(0.523243\pi\)
\(80\) 10.3241 + 10.9971i 0.129052 + 0.137464i
\(81\) 22.9575i 0.283426i
\(82\) 36.5533 + 30.4842i 0.445772 + 0.371759i
\(83\) −147.866 61.2479i −1.78151 0.737927i −0.992308 0.123796i \(-0.960493\pi\)
−0.789204 0.614131i \(-0.789507\pi\)
\(84\) 19.1762 12.3800i 0.228288 0.147381i
\(85\) −17.1946 + 7.12224i −0.202289 + 0.0837910i
\(86\) 76.9558 + 146.747i 0.894835 + 1.70636i
\(87\) 75.2499 75.2499i 0.864942 0.864942i
\(88\) −73.3858 93.8650i −0.833930 1.06665i
\(89\) −103.987 + 103.987i −1.16839 + 1.16839i −0.185806 + 0.982586i \(0.559490\pi\)
−0.982586 + 0.185806i \(0.940510\pi\)
\(90\) 2.44176 7.82663i 0.0271307 0.0869625i
\(91\) 12.8805 5.33530i 0.141544 0.0586296i
\(92\) 60.6239 87.7027i 0.658956 0.953290i
\(93\) 74.3269 + 30.7872i 0.799214 + 0.331045i
\(94\) −167.108 + 15.1287i −1.77774 + 0.160944i
\(95\) 24.3100i 0.255894i
\(96\) 4.05129 + 68.8979i 0.0422009 + 0.717687i
\(97\) −82.5634 −0.851169 −0.425584 0.904919i \(-0.639931\pi\)
−0.425584 + 0.904919i \(0.639931\pi\)
\(98\) −1.26230 13.9430i −0.0128806 0.142275i
\(99\) −24.7830 + 59.8315i −0.250334 + 0.604359i
\(100\) 54.8403 79.3358i 0.548403 0.793358i
\(101\) 44.0037 + 106.234i 0.435680 + 1.05183i 0.977425 + 0.211282i \(0.0677639\pi\)
−0.541745 + 0.840543i \(0.682236\pi\)
\(102\) −81.2923 25.3617i −0.796983 0.248644i
\(103\) −11.9420 11.9420i −0.115942 0.115942i 0.646756 0.762697i \(-0.276125\pi\)
−0.762697 + 0.646756i \(0.776125\pi\)
\(104\) −5.12357 + 41.8435i −0.0492651 + 0.402342i
\(105\) 3.80394 + 3.80394i 0.0362280 + 0.0362280i
\(106\) 48.5239 25.4465i 0.457772 0.240061i
\(107\) 21.5408 + 52.0041i 0.201316 + 0.486020i 0.992005 0.126198i \(-0.0402775\pi\)
−0.790689 + 0.612218i \(0.790278\pi\)
\(108\) 96.7472 62.4595i 0.895808 0.578329i
\(109\) 34.1859 82.5321i 0.313632 0.757175i −0.685932 0.727665i \(-0.740605\pi\)
0.999564 0.0295097i \(-0.00939461\pi\)
\(110\) 17.9853 21.5660i 0.163503 0.196055i
\(111\) 109.257 0.984299
\(112\) 38.5792 + 17.4255i 0.344457 + 0.155585i
\(113\) 54.0821i 0.478603i 0.970945 + 0.239301i \(0.0769184\pi\)
−0.970945 + 0.239301i \(0.923082\pi\)
\(114\) 71.2403 85.4235i 0.624915 0.749329i
\(115\) 23.2152 + 9.61605i 0.201871 + 0.0836179i
\(116\) 192.944 + 41.5535i 1.66331 + 0.358220i
\(117\) 21.1692 8.76859i 0.180934 0.0749452i
\(118\) 71.1389 37.3060i 0.602872 0.316153i
\(119\) −36.9332 + 36.9332i −0.310363 + 0.310363i
\(120\) −15.6733 + 4.35221i −0.130611 + 0.0362685i
\(121\) −71.2864 + 71.2864i −0.589144 + 0.589144i
\(122\) 98.0628 + 30.5938i 0.803794 + 0.250769i
\(123\) −47.4205 + 19.6422i −0.385533 + 0.159693i
\(124\) 26.7963 + 146.780i 0.216100 + 1.18371i
\(125\) 42.7750 + 17.7180i 0.342200 + 0.141744i
\(126\) −2.07459 22.9154i −0.0164650 0.181868i
\(127\) 48.1308i 0.378983i 0.981882 + 0.189491i \(0.0606839\pi\)
−0.981882 + 0.189491i \(0.939316\pi\)
\(128\) −103.276 + 75.6178i −0.806844 + 0.590764i
\(129\) −178.690 −1.38520
\(130\) −9.89512 + 0.895832i −0.0761163 + 0.00689101i
\(131\) 59.6654 144.045i 0.455461 1.09958i −0.514755 0.857337i \(-0.672117\pi\)
0.970216 0.242242i \(-0.0778829\pi\)
\(132\) 126.398 23.0755i 0.957562 0.174814i
\(133\) −26.1083 63.0311i −0.196303 0.473918i
\(134\) −49.3743 + 158.260i −0.368465 + 1.18105i
\(135\) 19.1916 + 19.1916i 0.142160 + 0.142160i
\(136\) −42.2565 152.175i −0.310710 1.11893i
\(137\) 40.9566 + 40.9566i 0.298953 + 0.298953i 0.840604 0.541650i \(-0.182200\pi\)
−0.541650 + 0.840604i \(0.682200\pi\)
\(138\) 53.3968 + 101.822i 0.386933 + 0.737842i
\(139\) −22.0683 53.2776i −0.158765 0.383292i 0.824401 0.566006i \(-0.191512\pi\)
−0.983166 + 0.182713i \(0.941512\pi\)
\(140\) −2.10056 + 9.75343i −0.0150040 + 0.0696674i
\(141\) 69.2444 167.171i 0.491095 1.18561i
\(142\) 49.1921 + 41.0245i 0.346423 + 0.288905i
\(143\) 78.4810 0.548818
\(144\) 63.4050 + 28.6389i 0.440313 + 0.198881i
\(145\) 46.5167i 0.320805i
\(146\) −81.3301 67.8265i −0.557055 0.464565i
\(147\) 13.9482 + 5.77754i 0.0948859 + 0.0393030i
\(148\) 109.903 + 170.236i 0.742591 + 1.15024i
\(149\) −76.6801 + 31.7619i −0.514632 + 0.213167i −0.624857 0.780739i \(-0.714843\pi\)
0.110225 + 0.993907i \(0.464843\pi\)
\(150\) 48.3026 + 92.1083i 0.322018 + 0.614055i
\(151\) −42.2155 + 42.2155i −0.279573 + 0.279573i −0.832938 0.553366i \(-0.813343\pi\)
0.553366 + 0.832938i \(0.313343\pi\)
\(152\) 204.762 + 25.0722i 1.34712 + 0.164949i
\(153\) −60.6999 + 60.6999i −0.396732 + 0.396732i
\(154\) 23.4711 75.2323i 0.152410 0.488522i
\(155\) −32.4888 + 13.4573i −0.209605 + 0.0868214i
\(156\) −37.3960 25.8497i −0.239718 0.165703i
\(157\) −11.7705 4.87549i −0.0749712 0.0310541i 0.344883 0.938646i \(-0.387919\pi\)
−0.419854 + 0.907592i \(0.637919\pi\)
\(158\) 22.9598 2.07862i 0.145315 0.0131558i
\(159\) 59.0864i 0.371613i
\(160\) −22.5473 20.0429i −0.140920 0.125268i
\(161\) 70.5200 0.438013
\(162\) 4.13987 + 45.7279i 0.0255548 + 0.282271i
\(163\) 65.3939 157.875i 0.401189 0.968557i −0.586188 0.810175i \(-0.699372\pi\)
0.987378 0.158382i \(-0.0506278\pi\)
\(164\) −78.3060 54.1285i −0.477476 0.330052i
\(165\) 11.5887 + 27.9775i 0.0702344 + 0.169561i
\(166\) 305.571 + 95.3326i 1.84079 + 0.574293i
\(167\) −113.503 113.503i −0.679657 0.679657i 0.280265 0.959923i \(-0.409578\pi\)
−0.959923 + 0.280265i \(0.909578\pi\)
\(168\) −35.9636 + 28.1172i −0.214069 + 0.167364i
\(169\) 99.8663 + 99.8663i 0.590925 + 0.590925i
\(170\) 32.9648 17.2871i 0.193911 0.101689i
\(171\) −42.9092 103.592i −0.250931 0.605801i
\(172\) −179.747 278.421i −1.04504 1.61873i
\(173\) 110.682 267.210i 0.639781 1.54457i −0.187189 0.982324i \(-0.559938\pi\)
0.826971 0.562245i \(-0.190062\pi\)
\(174\) −136.317 + 163.457i −0.783432 + 0.939405i
\(175\) 63.7923 0.364528
\(176\) 163.100 + 173.732i 0.926706 + 0.987113i
\(177\) 86.6241i 0.489402i
\(178\) 188.375 225.879i 1.05829 1.26898i
\(179\) −138.016 57.1680i −0.771038 0.319375i −0.0377454 0.999287i \(-0.512018\pi\)
−0.733293 + 0.679913i \(0.762018\pi\)
\(180\) −3.45228 + 16.0298i −0.0191793 + 0.0890545i
\(181\) −57.9483 + 24.0030i −0.320156 + 0.132613i −0.536974 0.843599i \(-0.680432\pi\)
0.216817 + 0.976212i \(0.430432\pi\)
\(182\) −24.6941 + 12.9498i −0.135682 + 0.0711530i
\(183\) −78.3311 + 78.3311i −0.428039 + 0.428039i
\(184\) −104.939 + 185.623i −0.570320 + 1.00882i
\(185\) −33.7694 + 33.7694i −0.182537 + 0.182537i
\(186\) −153.600 47.9204i −0.825807 0.257637i
\(187\) −271.640 + 112.517i −1.45262 + 0.601694i
\(188\) 330.126 60.2684i 1.75599 0.320577i
\(189\) 70.3714 + 29.1488i 0.372335 + 0.154226i
\(190\) 4.38376 + 48.4219i 0.0230724 + 0.254852i
\(191\) 323.983i 1.69625i 0.529799 + 0.848123i \(0.322267\pi\)
−0.529799 + 0.848123i \(0.677733\pi\)
\(192\) −20.4938 136.504i −0.106739 0.710958i
\(193\) 196.427 1.01776 0.508879 0.860838i \(-0.330060\pi\)
0.508879 + 0.860838i \(0.330060\pi\)
\(194\) 164.454 14.8885i 0.847702 0.0767447i
\(195\) 4.10023 9.89884i 0.0210268 0.0507633i
\(196\) 5.02862 + 27.5447i 0.0256562 + 0.140534i
\(197\) −59.0619 142.588i −0.299807 0.723797i −0.999952 0.00979705i \(-0.996881\pi\)
0.700145 0.714000i \(-0.253119\pi\)
\(198\) 38.5749 123.645i 0.194823 0.624468i
\(199\) −86.8897 86.8897i −0.436632 0.436632i 0.454245 0.890877i \(-0.349909\pi\)
−0.890877 + 0.454245i \(0.849909\pi\)
\(200\) −94.9275 + 167.914i −0.474637 + 0.839572i
\(201\) −126.416 126.416i −0.628935 0.628935i
\(202\) −106.806 203.668i −0.528742 1.00826i
\(203\) 49.9579 + 120.609i 0.246098 + 0.594133i
\(204\) 166.496 + 35.8575i 0.816156 + 0.175772i
\(205\) 8.58577 20.7279i 0.0418818 0.101112i
\(206\) 25.9402 + 21.6332i 0.125923 + 0.105016i
\(207\) 115.900 0.559904
\(208\) 2.65984 84.2701i 0.0127877 0.405145i
\(209\) 384.048i 1.83755i
\(210\) −8.26284 6.89093i −0.0393469 0.0328140i
\(211\) −188.416 78.0443i −0.892965 0.369878i −0.111454 0.993770i \(-0.535551\pi\)
−0.781511 + 0.623891i \(0.785551\pi\)
\(212\) −92.0638 + 59.4359i −0.434263 + 0.280358i
\(213\) −63.8168 + 26.4338i −0.299609 + 0.124102i
\(214\) −52.2839 99.7002i −0.244317 0.465889i
\(215\) 55.2299 55.2299i 0.256883 0.256883i
\(216\) −181.443 + 141.856i −0.840015 + 0.656743i
\(217\) −69.7845 + 69.7845i −0.321588 + 0.321588i
\(218\) −53.2105 + 170.557i −0.244085 + 0.782369i
\(219\) 105.509 43.7034i 0.481778 0.199559i
\(220\) −31.9352 + 46.1996i −0.145160 + 0.209998i
\(221\) 96.1099 + 39.8100i 0.434886 + 0.180136i
\(222\) −217.624 + 19.7021i −0.980290 + 0.0887483i
\(223\) 53.3854i 0.239396i 0.992810 + 0.119698i \(0.0381927\pi\)
−0.992810 + 0.119698i \(0.961807\pi\)
\(224\) −79.9864 27.7522i −0.357082 0.123894i
\(225\) 104.843 0.465969
\(226\) −9.75252 107.724i −0.0431527 0.476654i
\(227\) 18.0211 43.5068i 0.0793882 0.191660i −0.879202 0.476449i \(-0.841924\pi\)
0.958590 + 0.284789i \(0.0919236\pi\)
\(228\) −126.496 + 182.998i −0.554807 + 0.802621i
\(229\) −135.242 326.504i −0.590578 1.42578i −0.882946 0.469475i \(-0.844443\pi\)
0.292368 0.956306i \(-0.405557\pi\)
\(230\) −47.9753 14.9674i −0.208588 0.0650758i
\(231\) 60.0944 + 60.0944i 0.260149 + 0.260149i
\(232\) −391.809 47.9754i −1.68883 0.206790i
\(233\) −46.1172 46.1172i −0.197928 0.197928i 0.601183 0.799111i \(-0.294696\pi\)
−0.799111 + 0.601183i \(0.794696\pi\)
\(234\) −40.5848 + 21.2831i −0.173439 + 0.0909536i
\(235\) 30.2672 + 73.0715i 0.128797 + 0.310943i
\(236\) −134.971 + 87.1365i −0.571911 + 0.369222i
\(237\) −9.51386 + 22.9685i −0.0401429 + 0.0969134i
\(238\) 66.9055 80.2256i 0.281115 0.337083i
\(239\) −210.976 −0.882743 −0.441371 0.897325i \(-0.645508\pi\)
−0.441371 + 0.897325i \(0.645508\pi\)
\(240\) 30.4340 11.4953i 0.126808 0.0478971i
\(241\) 4.45793i 0.0184976i 0.999957 + 0.00924882i \(0.00294403\pi\)
−0.999957 + 0.00924882i \(0.997056\pi\)
\(242\) 129.137 154.847i 0.533625 0.639864i
\(243\) 193.636 + 80.2066i 0.796855 + 0.330068i
\(244\) −200.844 43.2549i −0.823130 0.177274i
\(245\) −6.09687 + 2.52541i −0.0248852 + 0.0103078i
\(246\) 90.9128 47.6757i 0.369564 0.193804i
\(247\) −96.0827 + 96.0827i −0.388999 + 0.388999i
\(248\) −79.8429 287.532i −0.321947 1.15940i
\(249\) −244.086 + 244.086i −0.980263 + 0.980263i
\(250\) −88.3966 27.5781i −0.353586 0.110312i
\(251\) −43.0877 + 17.8475i −0.171664 + 0.0711056i −0.466860 0.884331i \(-0.654615\pi\)
0.295196 + 0.955437i \(0.404615\pi\)
\(252\) 8.26456 + 45.2699i 0.0327959 + 0.179643i
\(253\) 366.753 + 151.914i 1.44962 + 0.600451i
\(254\) −8.67933 95.8696i −0.0341706 0.377439i
\(255\) 40.1405i 0.157414i
\(256\) 192.075 169.243i 0.750292 0.661106i
\(257\) −390.515 −1.51951 −0.759757 0.650207i \(-0.774682\pi\)
−0.759757 + 0.650207i \(0.774682\pi\)
\(258\) 355.925 32.2228i 1.37955 0.124895i
\(259\) −51.2901 + 123.825i −0.198031 + 0.478089i
\(260\) 19.5481 3.56873i 0.0751849 0.0137259i
\(261\) 82.1061 + 198.222i 0.314583 + 0.759470i
\(262\) −92.8694 + 297.676i −0.354463 + 1.13617i
\(263\) 135.194 + 135.194i 0.514044 + 0.514044i 0.915763 0.401719i \(-0.131587\pi\)
−0.401719 + 0.915763i \(0.631587\pi\)
\(264\) −247.606 + 68.7561i −0.937900 + 0.260440i
\(265\) −18.2625 18.2625i −0.0689152 0.0689152i
\(266\) 63.3703 + 120.841i 0.238234 + 0.454288i
\(267\) 121.378 + 293.032i 0.454598 + 1.09750i
\(268\) 69.8077 324.135i 0.260476 1.20946i
\(269\) 70.1917 169.458i 0.260936 0.629954i −0.738061 0.674734i \(-0.764259\pi\)
0.998997 + 0.0447794i \(0.0142585\pi\)
\(270\) −41.6876 34.7660i −0.154398 0.128763i
\(271\) 4.76275 0.0175747 0.00878737 0.999961i \(-0.497203\pi\)
0.00878737 + 0.999961i \(0.497203\pi\)
\(272\) 111.610 + 295.490i 0.410332 + 1.08636i
\(273\) 30.0694i 0.110144i
\(274\) −88.9652 74.1940i −0.324691 0.270781i
\(275\) 331.764 + 137.421i 1.20642 + 0.499714i
\(276\) −124.720 193.186i −0.451884 0.699950i
\(277\) 377.813 156.495i 1.36395 0.564965i 0.423807 0.905753i \(-0.360694\pi\)
0.940140 + 0.340787i \(0.110694\pi\)
\(278\) 53.5643 + 102.142i 0.192677 + 0.367416i
\(279\) −114.691 + 114.691i −0.411080 + 0.411080i
\(280\) 2.42519 19.8062i 0.00866139 0.0707364i
\(281\) 67.0196 67.0196i 0.238504 0.238504i −0.577727 0.816230i \(-0.696060\pi\)
0.816230 + 0.577727i \(0.196060\pi\)
\(282\) −107.779 + 345.466i −0.382195 + 1.22506i
\(283\) −80.8989 + 33.5094i −0.285862 + 0.118408i −0.521007 0.853552i \(-0.674443\pi\)
0.235145 + 0.971960i \(0.424443\pi\)
\(284\) −105.381 72.8442i −0.371061 0.256494i
\(285\) −48.4401 20.0646i −0.169965 0.0704019i
\(286\) −156.323 + 14.1523i −0.546583 + 0.0494836i
\(287\) 62.9643i 0.219388i
\(288\) −131.458 45.6109i −0.456451 0.158371i
\(289\) −100.732 −0.348554
\(290\) −8.38827 92.6546i −0.0289251 0.319498i
\(291\) −68.1448 + 164.516i −0.234174 + 0.565347i
\(292\) 174.229 + 120.434i 0.596674 + 0.412447i
\(293\) −97.2004 234.663i −0.331742 0.800896i −0.998454 0.0555808i \(-0.982299\pi\)
0.666712 0.745315i \(-0.267701\pi\)
\(294\) −28.8247 8.99277i −0.0980431 0.0305877i
\(295\) −26.7739 26.7739i −0.0907591 0.0907591i
\(296\) −249.610 319.267i −0.843277 1.07860i
\(297\) 303.188 + 303.188i 1.02083 + 1.02083i
\(298\) 147.008 77.0927i 0.493316 0.258700i
\(299\) −53.7493 129.762i −0.179764 0.433988i
\(300\) −112.822 174.756i −0.376072 0.582520i
\(301\) 83.8849 202.516i 0.278688 0.672811i
\(302\) 76.4745 91.6997i 0.253227 0.303642i
\(303\) 248.002 0.818488
\(304\) −412.377 13.0160i −1.35650 0.0428157i
\(305\) 48.4214i 0.158759i
\(306\) 109.959 131.851i 0.359345 0.430887i
\(307\) 33.4486 + 13.8549i 0.108953 + 0.0451298i 0.436494 0.899707i \(-0.356220\pi\)
−0.327541 + 0.944837i \(0.606220\pi\)
\(308\) −33.1845 + 154.084i −0.107742 + 0.500274i
\(309\) −33.6521 + 13.9392i −0.108907 + 0.0451106i
\(310\) 62.2863 32.6637i 0.200924 0.105367i
\(311\) 331.934 331.934i 1.06731 1.06731i 0.0697470 0.997565i \(-0.477781\pi\)
0.997565 0.0697470i \(-0.0222192\pi\)
\(312\) 79.1487 + 44.7454i 0.253682 + 0.143415i
\(313\) 261.126 261.126i 0.834269 0.834269i −0.153829 0.988098i \(-0.549160\pi\)
0.988098 + 0.153829i \(0.0491604\pi\)
\(314\) 24.3243 + 7.58872i 0.0774658 + 0.0241679i
\(315\) −10.0202 + 4.15052i −0.0318103 + 0.0131763i
\(316\) −45.3578 + 8.28060i −0.143537 + 0.0262044i
\(317\) −89.3605 37.0143i −0.281894 0.116764i 0.237257 0.971447i \(-0.423752\pi\)
−0.519151 + 0.854683i \(0.673752\pi\)
\(318\) −10.6549 117.691i −0.0335061 0.370099i
\(319\) 734.870i 2.30367i
\(320\) 48.5251 + 35.8566i 0.151641 + 0.112052i
\(321\) 121.403 0.378201
\(322\) −140.466 + 12.7167i −0.436229 + 0.0394929i
\(323\) 194.811 470.315i 0.603130 1.45608i
\(324\) −16.4920 90.3369i −0.0509014 0.278817i
\(325\) −48.6216 117.383i −0.149605 0.361178i
\(326\) −101.786 + 326.256i −0.312226 + 1.00078i
\(327\) −136.238 136.238i −0.416630 0.416630i
\(328\) 165.735 + 93.6954i 0.505290 + 0.285657i
\(329\) 156.954 + 156.954i 0.477065 + 0.477065i
\(330\) −28.1281 53.6374i −0.0852366 0.162538i
\(331\) 33.3563 + 80.5292i 0.100774 + 0.243291i 0.966223 0.257706i \(-0.0829668\pi\)
−0.865449 + 0.500997i \(0.832967\pi\)
\(332\) −625.844 134.786i −1.88507 0.405981i
\(333\) −84.2955 + 203.507i −0.253140 + 0.611133i
\(334\) 246.549 + 205.613i 0.738170 + 0.615608i
\(335\) 78.1457 0.233271
\(336\) 66.5640 62.4906i 0.198107 0.185984i
\(337\) 601.688i 1.78542i −0.450627 0.892712i \(-0.648800\pi\)
0.450627 0.892712i \(-0.351200\pi\)
\(338\) −216.928 180.910i −0.641798 0.535238i
\(339\) 107.764 + 44.6374i 0.317889 + 0.131674i
\(340\) −62.5437 + 40.3779i −0.183952 + 0.118759i
\(341\) −513.257 + 212.598i −1.50515 + 0.623455i
\(342\) 104.149 + 198.602i 0.304530 + 0.580708i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 408.237 + 522.161i 1.18674 + 1.51791i
\(345\) 38.3220 38.3220i 0.111078 0.111078i
\(346\) −172.277 + 552.203i −0.497911 + 1.59596i
\(347\) −510.732 + 211.552i −1.47185 + 0.609661i −0.967280 0.253710i \(-0.918349\pi\)
−0.504570 + 0.863371i \(0.668349\pi\)
\(348\) 242.048 350.163i 0.695541 1.00622i
\(349\) 396.990 + 164.439i 1.13751 + 0.471171i 0.870326 0.492475i \(-0.163908\pi\)
0.267181 + 0.963646i \(0.413908\pi\)
\(350\) −127.065 + 11.5035i −0.363043 + 0.0328672i
\(351\) 151.706i 0.432210i
\(352\) −356.201 316.637i −1.01193 0.899536i
\(353\) −163.628 −0.463535 −0.231767 0.972771i \(-0.574451\pi\)
−0.231767 + 0.972771i \(0.574451\pi\)
\(354\) −15.6207 172.543i −0.0441264 0.487408i
\(355\) 11.5544 27.8948i 0.0325476 0.0785769i
\(356\) −334.483 + 483.886i −0.939560 + 1.35923i
\(357\) 43.1099 + 104.077i 0.120756 + 0.291531i
\(358\) 285.216 + 88.9823i 0.796694 + 0.248554i
\(359\) −229.746 229.746i −0.639961 0.639961i 0.310585 0.950546i \(-0.399475\pi\)
−0.950546 + 0.310585i \(0.899475\pi\)
\(360\) 3.98581 32.5516i 0.0110717 0.0904211i
\(361\) 214.916 + 214.916i 0.595336 + 0.595336i
\(362\) 111.096 58.2601i 0.306896 0.160940i
\(363\) 83.2084 + 200.883i 0.229224 + 0.553396i
\(364\) 46.8517 30.2472i 0.128714 0.0830968i
\(365\) −19.1031 + 46.1189i −0.0523372 + 0.126353i
\(366\) 141.899 170.149i 0.387702 0.464889i
\(367\) 604.291 1.64657 0.823285 0.567628i \(-0.192139\pi\)
0.823285 + 0.567628i \(0.192139\pi\)
\(368\) 175.550 388.658i 0.477037 1.05613i
\(369\) 103.482i 0.280440i
\(370\) 61.1741 73.3533i 0.165336 0.198252i
\(371\) −66.9647 27.7377i −0.180498 0.0747647i
\(372\) 314.590 + 67.7521i 0.845673 + 0.182129i
\(373\) 66.6128 27.5919i 0.178587 0.0739730i −0.291599 0.956541i \(-0.594187\pi\)
0.470185 + 0.882568i \(0.344187\pi\)
\(374\) 520.776 273.101i 1.39245 0.730217i
\(375\) 70.6098 70.6098i 0.188293 0.188293i
\(376\) −646.695 + 179.577i −1.71993 + 0.477598i
\(377\) 183.853 183.853i 0.487673 0.487673i
\(378\) −145.426 45.3702i −0.384724 0.120027i
\(379\) −241.151 + 99.8880i −0.636283 + 0.263557i −0.677420 0.735597i \(-0.736902\pi\)
0.0411373 + 0.999154i \(0.486902\pi\)
\(380\) −17.4636 95.6588i −0.0459569 0.251734i
\(381\) 95.9057 + 39.7254i 0.251721 + 0.104266i
\(382\) −58.4232 645.327i −0.152940 1.68934i
\(383\) 621.449i 1.62258i −0.584643 0.811291i \(-0.698765\pi\)
0.584643 0.811291i \(-0.301235\pi\)
\(384\) 65.4361 + 268.200i 0.170407 + 0.698439i
\(385\) −37.1482 −0.0964888
\(386\) −391.255 + 35.4213i −1.01361 + 0.0917651i
\(387\) 137.865 332.836i 0.356241 0.860042i
\(388\) −324.884 + 59.3113i −0.837329 + 0.152864i
\(389\) −26.5507 64.0991i −0.0682538 0.164779i 0.886072 0.463548i \(-0.153424\pi\)
−0.954325 + 0.298769i \(0.903424\pi\)
\(390\) −6.38203 + 20.4564i −0.0163642 + 0.0524524i
\(391\) 372.076 + 372.076i 0.951601 + 0.951601i
\(392\) −14.9834 53.9583i −0.0382228 0.137649i
\(393\) −237.779 237.779i −0.605035 0.605035i
\(394\) 143.355 + 273.364i 0.363846 + 0.693818i
\(395\) −4.15858 10.0397i −0.0105280 0.0254169i
\(396\) −54.5389 + 253.238i −0.137725 + 0.639491i
\(397\) −98.1441 + 236.941i −0.247214 + 0.596828i −0.997965 0.0637568i \(-0.979692\pi\)
0.750751 + 0.660585i \(0.229692\pi\)
\(398\) 188.740 + 157.403i 0.474222 + 0.395485i
\(399\) −147.145 −0.368784
\(400\) 158.802 351.579i 0.397005 0.878948i
\(401\) 25.0122i 0.0623745i −0.999514 0.0311873i \(-0.990071\pi\)
0.999514 0.0311873i \(-0.00992883\pi\)
\(402\) 274.598 + 229.006i 0.683081 + 0.569666i
\(403\) 181.598 + 75.2202i 0.450615 + 0.186651i
\(404\) 249.469 + 386.417i 0.617497 + 0.956478i
\(405\) 19.9955 8.28243i 0.0493717 0.0204504i
\(406\) −121.258 231.227i −0.298665 0.569524i
\(407\) −533.488 + 533.488i −1.31078 + 1.31078i
\(408\) −338.101 41.3991i −0.828680 0.101468i
\(409\) −410.030 + 410.030i −1.00252 + 1.00252i −0.00252225 + 0.999997i \(0.500803\pi\)
−0.999997 + 0.00252225i \(0.999197\pi\)
\(410\) −13.3638 + 42.8351i −0.0325946 + 0.104476i
\(411\) 115.414 47.8062i 0.280814 0.116317i
\(412\) −55.5701 38.4125i −0.134879 0.0932342i
\(413\) −98.1743 40.6651i −0.237710 0.0984627i
\(414\) −230.856 + 20.9000i −0.557623 + 0.0504831i
\(415\) 150.885i 0.363578i
\(416\) 9.89823 + 168.333i 0.0237938 + 0.404648i
\(417\) −124.376 −0.298263
\(418\) 69.2545 + 764.967i 0.165681 + 1.83006i
\(419\) −39.3223 + 94.9324i −0.0938479 + 0.226569i −0.963832 0.266511i \(-0.914129\pi\)
0.869984 + 0.493080i \(0.164129\pi\)
\(420\) 17.7010 + 12.2357i 0.0421452 + 0.0291326i
\(421\) −150.378 363.044i −0.357192 0.862338i −0.995693 0.0927168i \(-0.970445\pi\)
0.638500 0.769622i \(-0.279555\pi\)
\(422\) 389.370 + 121.476i 0.922678 + 0.287859i
\(423\) 257.955 + 257.955i 0.609823 + 0.609823i
\(424\) 172.660 134.989i 0.407216 0.318371i
\(425\) 336.579 + 336.579i 0.791951 + 0.791951i
\(426\) 122.347 64.1602i 0.287200 0.150611i
\(427\) −52.0035 125.547i −0.121788 0.294022i
\(428\) 122.121 + 189.160i 0.285329 + 0.441962i
\(429\) 64.7753 156.381i 0.150991 0.364526i
\(430\) −100.050 + 119.969i −0.232675 + 0.278998i
\(431\) 344.315 0.798876 0.399438 0.916760i \(-0.369205\pi\)
0.399438 + 0.916760i \(0.369205\pi\)
\(432\) 335.828 315.277i 0.777379 0.729807i
\(433\) 836.447i 1.93175i −0.259011 0.965874i \(-0.583397\pi\)
0.259011 0.965874i \(-0.416603\pi\)
\(434\) 126.416 151.585i 0.291282 0.349273i
\(435\) 92.6894 + 38.3932i 0.213079 + 0.0882603i
\(436\) 75.2314 349.319i 0.172549 0.801190i
\(437\) −634.994 + 263.023i −1.45307 + 0.601883i
\(438\) −202.278 + 106.077i −0.461823 + 0.242185i
\(439\) −269.081 + 269.081i −0.612942 + 0.612942i −0.943711 0.330770i \(-0.892692\pi\)
0.330770 + 0.943711i \(0.392692\pi\)
\(440\) 55.2791 97.7816i 0.125634 0.222231i
\(441\) −21.5230 + 21.5230i −0.0488050 + 0.0488050i
\(442\) −198.616 61.9645i −0.449357 0.140191i
\(443\) −0.0904257 + 0.0374556i −0.000204121 + 8.45498e-5i −0.382785 0.923837i \(-0.625035\pi\)
0.382581 + 0.923922i \(0.375035\pi\)
\(444\) 429.923 78.4875i 0.968296 0.176774i
\(445\) −128.086 53.0551i −0.287834 0.119225i
\(446\) −9.62688 106.336i −0.0215849 0.238421i
\(447\) 179.008i 0.400466i
\(448\) 164.326 + 40.8545i 0.366798 + 0.0911931i
\(449\) 336.165 0.748698 0.374349 0.927288i \(-0.377866\pi\)
0.374349 + 0.927288i \(0.377866\pi\)
\(450\) −208.832 + 18.9061i −0.464071 + 0.0420136i
\(451\) 135.638 327.458i 0.300748 0.726071i
\(452\) 38.8512 + 212.811i 0.0859539 + 0.470821i
\(453\) 49.2756 + 118.962i 0.108776 + 0.262609i
\(454\) −28.0499 + 89.9090i −0.0617840 + 0.198037i
\(455\) 9.29389 + 9.29389i 0.0204261 + 0.0204261i
\(456\) 218.962 387.315i 0.480180 0.849376i
\(457\) 423.550 + 423.550i 0.926805 + 0.926805i 0.997498 0.0706935i \(-0.0225212\pi\)
−0.0706935 + 0.997498i \(0.522521\pi\)
\(458\) 328.261 + 625.960i 0.716726 + 1.36672i
\(459\) 217.498 + 525.086i 0.473851 + 1.14398i
\(460\) 98.2589 + 21.1616i 0.213606 + 0.0460035i
\(461\) −129.970 + 313.776i −0.281931 + 0.680641i −0.999881 0.0154537i \(-0.995081\pi\)
0.717950 + 0.696095i \(0.245081\pi\)
\(462\) −130.536 108.863i −0.282546 0.235633i
\(463\) −15.0541 −0.0325143 −0.0162572 0.999868i \(-0.505175\pi\)
−0.0162572 + 0.999868i \(0.505175\pi\)
\(464\) 789.077 + 24.9059i 1.70060 + 0.0536765i
\(465\) 75.8446i 0.163107i
\(466\) 100.175 + 83.5424i 0.214968 + 0.179276i
\(467\) 128.179 + 53.0936i 0.274474 + 0.113691i 0.515675 0.856784i \(-0.327541\pi\)
−0.241201 + 0.970475i \(0.577541\pi\)
\(468\) 77.0011 49.7115i 0.164532 0.106221i
\(469\) 202.617 83.9267i 0.432019 0.178948i
\(470\) −73.4647 140.090i −0.156308 0.298063i
\(471\) −19.4298 + 19.4298i −0.0412523 + 0.0412523i
\(472\) 253.129 197.902i 0.536291 0.419284i
\(473\) 872.519 872.519i 1.84465 1.84465i
\(474\) 14.8084 47.4655i 0.0312413 0.100138i
\(475\) −574.414 + 237.930i −1.20929 + 0.500906i
\(476\) −118.799 + 171.863i −0.249578 + 0.361056i
\(477\) −110.057 45.5871i −0.230727 0.0955704i
\(478\) 420.232 38.0448i 0.879147 0.0795916i
\(479\) 134.284i 0.280342i −0.990127 0.140171i \(-0.955235\pi\)
0.990127 0.140171i \(-0.0447652\pi\)
\(480\) −58.5472 + 28.3851i −0.121973 + 0.0591356i
\(481\) 266.940 0.554970
\(482\) −0.803889 8.87955i −0.00166782 0.0184223i
\(483\) 58.2047 140.518i 0.120507 0.290929i
\(484\) −229.299 + 331.720i −0.473759 + 0.685371i
\(485\) −29.7866 71.9112i −0.0614156 0.148270i
\(486\) −400.158 124.842i −0.823370 0.256876i
\(487\) −618.569 618.569i −1.27016 1.27016i −0.946003 0.324158i \(-0.894919\pi\)
−0.324158 0.946003i \(-0.605081\pi\)
\(488\) 407.851 + 49.9397i 0.835761 + 0.102336i
\(489\) −260.608 260.608i −0.532941 0.532941i
\(490\) 11.6887 6.12968i 0.0238544 0.0125095i
\(491\) −19.8666 47.9621i −0.0404614 0.0976825i 0.902357 0.430990i \(-0.141835\pi\)
−0.942818 + 0.333307i \(0.891835\pi\)
\(492\) −172.488 + 111.357i −0.350585 + 0.226336i
\(493\) −372.768 + 899.941i −0.756121 + 1.82544i
\(494\) 174.056 208.709i 0.352341 0.422488i
\(495\) −61.0532 −0.123340
\(496\) 210.885 + 558.323i 0.425172 + 1.12565i
\(497\) 84.7351i 0.170493i
\(498\) 442.167 530.198i 0.887886 1.06466i
\(499\) 328.968 + 136.263i 0.659255 + 0.273072i 0.687125 0.726539i \(-0.258872\pi\)
−0.0278702 + 0.999612i \(0.508872\pi\)
\(500\) 181.046 + 38.9912i 0.362092 + 0.0779824i
\(501\) −319.847 + 132.485i −0.638417 + 0.264441i
\(502\) 82.6060 43.3195i 0.164554 0.0862939i
\(503\) 474.652 474.652i 0.943641 0.943641i −0.0548531 0.998494i \(-0.517469\pi\)
0.998494 + 0.0548531i \(0.0174690\pi\)
\(504\) −24.6252 88.6808i −0.0488596 0.175954i
\(505\) −76.6528 + 76.6528i −0.151788 + 0.151788i
\(506\) −757.912 236.455i −1.49785 0.467302i
\(507\) 281.420 116.568i 0.555069 0.229917i
\(508\) 34.5759 + 189.393i 0.0680628 + 0.372821i
\(509\) −278.699 115.441i −0.547542 0.226799i 0.0917249 0.995784i \(-0.470762\pi\)
−0.639267 + 0.768985i \(0.720762\pi\)
\(510\) −7.23844 79.9539i −0.0141930 0.156772i
\(511\) 140.094i 0.274156i
\(512\) −352.066 + 371.744i −0.687628 + 0.726063i
\(513\) −742.373 −1.44712
\(514\) 777.849 70.4208i 1.51333 0.137005i
\(515\) 6.09291 14.7096i 0.0118309 0.0285623i
\(516\) −703.140 + 128.366i −1.36267 + 0.248772i
\(517\) 478.160 + 1154.38i 0.924875 + 2.23285i
\(518\) 79.8332 255.891i 0.154118 0.493997i
\(519\) −441.091 441.091i −0.849887 0.849887i
\(520\) −38.2934 + 10.6335i −0.0736411 + 0.0204490i
\(521\) −151.306 151.306i −0.290415 0.290415i 0.546829 0.837244i \(-0.315835\pi\)
−0.837244 + 0.546829i \(0.815835\pi\)
\(522\) −199.288 380.022i −0.381778 0.728012i
\(523\) −76.0879 183.693i −0.145484 0.351229i 0.834293 0.551321i \(-0.185876\pi\)
−0.979777 + 0.200092i \(0.935876\pi\)
\(524\) 131.303 609.674i 0.250578 1.16350i
\(525\) 52.6519 127.113i 0.100289 0.242120i
\(526\) −293.665 244.907i −0.558298 0.465602i
\(527\) −736.391 −1.39733
\(528\) 480.796 181.602i 0.910598 0.343944i
\(529\) 181.439i 0.342986i
\(530\) 39.6695 + 33.0830i 0.0748481 + 0.0624208i
\(531\) −161.350 66.8333i −0.303860 0.125863i
\(532\) −148.015 229.270i −0.278224 0.430958i
\(533\) −115.859 + 47.9905i −0.217372 + 0.0900384i
\(534\) −294.608 561.789i −0.551701 1.05204i
\(535\) −37.5233 + 37.5233i −0.0701370 + 0.0701370i
\(536\) −80.5961 + 658.218i −0.150366 + 1.22802i
\(537\) −227.826 + 227.826i −0.424258 + 0.424258i
\(538\) −109.254 + 350.192i −0.203074 + 0.650915i
\(539\) −96.3181 + 39.8963i −0.178698 + 0.0740191i
\(540\) 89.3048 + 61.7314i 0.165379 + 0.114317i
\(541\) −91.6470 37.9614i −0.169403 0.0701690i 0.296370 0.955073i \(-0.404224\pi\)
−0.465773 + 0.884904i \(0.654224\pi\)
\(542\) −9.48671 + 0.858858i −0.0175032 + 0.00158461i
\(543\) 135.279i 0.249133i
\(544\) −275.597 568.447i −0.506611 1.04494i
\(545\) 84.2173 0.154527
\(546\) 5.42235 + 59.8938i 0.00993104 + 0.109696i
\(547\) −195.499 + 471.977i −0.357403 + 0.862847i 0.638261 + 0.769820i \(0.279654\pi\)
−0.995664 + 0.0930265i \(0.970346\pi\)
\(548\) 190.585 + 131.741i 0.347783 + 0.240403i
\(549\) −85.4679 206.338i −0.155679 0.375843i
\(550\) −685.607 213.897i −1.24656 0.388903i
\(551\) −899.686 899.686i −1.63282 1.63282i
\(552\) 283.261 + 362.308i 0.513154 + 0.656355i
\(553\) −21.5648 21.5648i −0.0389960 0.0389960i
\(554\) −724.328 + 379.846i −1.30745 + 0.685643i
\(555\) 39.4170 + 95.1610i 0.0710216 + 0.171461i
\(556\) −125.111 193.792i −0.225020 0.348547i
\(557\) −128.159 + 309.403i −0.230088 + 0.555481i −0.996187 0.0872413i \(-0.972195\pi\)
0.766100 + 0.642722i \(0.222195\pi\)
\(558\) 207.766 249.130i 0.372341 0.446470i
\(559\) −436.581 −0.781004
\(560\) −1.25901 + 39.8884i −0.00224823 + 0.0712293i
\(561\) 634.137i 1.13037i
\(562\) −121.408 + 145.579i −0.216028 + 0.259037i
\(563\) −305.681 126.617i −0.542949 0.224897i 0.0943148 0.995542i \(-0.469934\pi\)
−0.637264 + 0.770645i \(0.719934\pi\)
\(564\) 152.383 707.554i 0.270183 1.25453i
\(565\) −47.1046 + 19.5113i −0.0833709 + 0.0345334i
\(566\) 155.096 81.3342i 0.274022 0.143700i
\(567\) 42.9495 42.9495i 0.0757487 0.0757487i
\(568\) 223.040 + 126.092i 0.392676 + 0.221993i
\(569\) −496.100 + 496.100i −0.871880 + 0.871880i −0.992677 0.120797i \(-0.961455\pi\)
0.120797 + 0.992677i \(0.461455\pi\)
\(570\) 100.104 + 31.2305i 0.175621 + 0.0547904i
\(571\) −483.761 + 200.381i −0.847218 + 0.350929i −0.763695 0.645577i \(-0.776617\pi\)
−0.0835225 + 0.996506i \(0.526617\pi\)
\(572\) 308.820 56.3787i 0.539895 0.0985641i
\(573\) 645.570 + 267.404i 1.12665 + 0.466673i
\(574\) 11.3542 + 125.416i 0.0197809 + 0.218494i
\(575\) 642.662i 1.11767i
\(576\) 270.070 + 67.1446i 0.468872 + 0.116571i
\(577\) 760.250 1.31759 0.658795 0.752322i \(-0.271066\pi\)
0.658795 + 0.752322i \(0.271066\pi\)
\(578\) 200.643 18.1648i 0.347134 0.0314270i
\(579\) 162.124 391.402i 0.280007 0.675996i
\(580\) 33.4164 + 183.042i 0.0576145 + 0.315589i
\(581\) −162.047 391.215i −0.278910 0.673348i
\(582\) 106.068 339.980i 0.182247 0.584159i
\(583\) −288.510 288.510i −0.494872 0.494872i
\(584\) −368.756 208.470i −0.631431 0.356968i
\(585\) 15.2746 + 15.2746i 0.0261104 + 0.0261104i
\(586\) 235.925 + 449.886i 0.402603 + 0.767723i
\(587\) −180.706 436.264i −0.307847 0.743210i −0.999774 0.0212420i \(-0.993238\pi\)
0.691927 0.721968i \(-0.256762\pi\)
\(588\) 59.0362 + 12.7144i 0.100402 + 0.0216231i
\(589\) 368.091 888.651i 0.624942 1.50874i
\(590\) 58.1578 + 48.5017i 0.0985726 + 0.0822062i
\(591\) −332.869 −0.563230
\(592\) 554.759 + 590.921i 0.937093 + 0.998177i
\(593\) 534.025i 0.900547i 0.892891 + 0.450274i \(0.148674\pi\)
−0.892891 + 0.450274i \(0.851326\pi\)
\(594\) −658.579 549.232i −1.10872 0.924633i
\(595\) −45.4926 18.8437i −0.0764582 0.0316700i
\(596\) −278.917 + 180.067i −0.467981 + 0.302126i
\(597\) −244.852 + 101.421i −0.410138 + 0.169885i
\(598\) 130.461 + 248.775i 0.218161 + 0.416012i
\(599\) 373.320 373.320i 0.623239 0.623239i −0.323119 0.946358i \(-0.604731\pi\)
0.946358 + 0.323119i \(0.104731\pi\)
\(600\) 256.237 + 327.743i 0.427062 + 0.546239i
\(601\) 68.9545 68.9545i 0.114733 0.114733i −0.647409 0.762142i \(-0.724148\pi\)
0.762142 + 0.647409i \(0.224148\pi\)
\(602\) −130.567 + 418.509i −0.216889 + 0.695198i
\(603\) 333.002 137.934i 0.552242 0.228746i
\(604\) −135.790 + 196.443i −0.224818 + 0.325237i
\(605\) −87.8073 36.3710i −0.145136 0.0601173i
\(606\) −493.984 + 44.7217i −0.815155 + 0.0737981i
\(607\) 620.715i 1.02259i 0.859404 + 0.511297i \(0.170835\pi\)
−0.859404 + 0.511297i \(0.829165\pi\)
\(608\) 823.742 48.4371i 1.35484 0.0796663i
\(609\) 281.559 0.462331
\(610\) 8.73173 + 96.4483i 0.0143143 + 0.158112i
\(611\) 169.180 408.436i 0.276890 0.668472i
\(612\) −195.247 + 282.457i −0.319031 + 0.461531i
\(613\) 189.467 + 457.413i 0.309081 + 0.746187i 0.999735 + 0.0230022i \(0.00732248\pi\)
−0.690655 + 0.723185i \(0.742678\pi\)
\(614\) −69.1231 21.5651i −0.112578 0.0351224i
\(615\) −34.2161 34.2161i −0.0556359 0.0556359i
\(616\) 38.3130 312.898i 0.0621965 0.507951i
\(617\) −223.382 223.382i −0.362046 0.362046i 0.502520 0.864566i \(-0.332406\pi\)
−0.864566 + 0.502520i \(0.832406\pi\)
\(618\) 64.5165 33.8332i 0.104396 0.0547463i
\(619\) 374.604 + 904.373i 0.605176 + 1.46102i 0.868190 + 0.496231i \(0.165283\pi\)
−0.263015 + 0.964792i \(0.584717\pi\)
\(620\) −118.175 + 76.2932i −0.190605 + 0.123054i
\(621\) 293.653 708.942i 0.472872 1.14161i
\(622\) −601.307 + 721.021i −0.966731 + 1.15920i
\(623\) −389.083 −0.624532
\(624\) −165.722 74.8535i −0.265579 0.119957i
\(625\) 559.132i 0.894612i
\(626\) −473.037 + 567.213i −0.755650 + 0.906092i
\(627\) −765.255 316.979i −1.22050 0.505549i
\(628\) −49.8188 10.7293i −0.0793293 0.0170848i
\(629\) −923.938 + 382.708i −1.46890 + 0.608438i
\(630\) 19.2104 10.0742i 0.0304927 0.0159907i
\(631\) 120.246 120.246i 0.190564 0.190564i −0.605376 0.795940i \(-0.706977\pi\)
0.795940 + 0.605376i \(0.206977\pi\)
\(632\) 88.8529 24.6730i 0.140590 0.0390396i
\(633\) −311.023 + 311.023i −0.491347 + 0.491347i
\(634\) 184.668 + 57.6129i 0.291274 + 0.0908721i
\(635\) −41.9211 + 17.3643i −0.0660174 + 0.0273453i
\(636\) 42.4461 + 232.503i 0.0667392 + 0.365570i
\(637\) 34.0787 + 14.1159i 0.0534988 + 0.0221599i
\(638\) −132.517 1463.75i −0.207708 2.29428i
\(639\) 139.263i 0.217938i
\(640\) −103.121 62.6707i −0.161126 0.0979230i
\(641\) −278.072 −0.433810 −0.216905 0.976193i \(-0.569596\pi\)
−0.216905 + 0.976193i \(0.569596\pi\)
\(642\) −241.816 + 21.8923i −0.376661 + 0.0341001i
\(643\) −334.195 + 806.819i −0.519744 + 1.25477i 0.418317 + 0.908301i \(0.362620\pi\)
−0.938061 + 0.346471i \(0.887380\pi\)
\(644\) 277.494 50.6597i 0.430891 0.0786642i
\(645\) −64.4665 155.636i −0.0999481 0.241296i
\(646\) −303.224 + 971.929i −0.469387 + 1.50453i
\(647\) 409.640 + 409.640i 0.633137 + 0.633137i 0.948854 0.315716i \(-0.102245\pi\)
−0.315716 + 0.948854i \(0.602245\pi\)
\(648\) 49.1400 + 176.964i 0.0758333 + 0.273092i
\(649\) −422.973 422.973i −0.651731 0.651731i
\(650\) 118.014 + 225.042i 0.181561 + 0.346218i
\(651\) 81.4553 + 196.651i 0.125123 + 0.302075i
\(652\) 143.909 668.209i 0.220720 1.02486i
\(653\) −457.695 + 1104.97i −0.700911 + 1.69215i 0.0206388 + 0.999787i \(0.493430\pi\)
−0.721550 + 0.692362i \(0.756570\pi\)
\(654\) 295.934 + 246.799i 0.452498 + 0.377368i
\(655\) 146.986 0.224406
\(656\) −347.016 156.741i −0.528988 0.238934i
\(657\) 230.245i 0.350449i
\(658\) −340.933 284.327i −0.518136 0.432108i
\(659\) 820.050 + 339.676i 1.24439 + 0.515441i 0.905083 0.425236i \(-0.139809\pi\)
0.339303 + 0.940677i \(0.389809\pi\)
\(660\) 65.6993 + 101.766i 0.0995444 + 0.154190i
\(661\) −449.364 + 186.133i −0.679825 + 0.281593i −0.695754 0.718281i \(-0.744929\pi\)
0.0159290 + 0.999873i \(0.494929\pi\)
\(662\) −80.9625 154.387i −0.122300 0.233213i
\(663\) 158.651 158.651i 0.239293 0.239293i
\(664\) 1270.90 + 155.616i 1.91400 + 0.234361i
\(665\) 45.4798 45.4798i 0.0683906 0.0683906i
\(666\) 131.206 420.558i 0.197006 0.631468i
\(667\) 1215.05 503.291i 1.82167 0.754558i
\(668\) −528.167 365.092i −0.790669 0.546545i
\(669\) 106.376 + 44.0624i 0.159007 + 0.0658630i
\(670\) −155.655 + 14.0918i −0.232321 + 0.0210326i
\(671\) 764.959i 1.14003i
\(672\) −121.317 + 136.475i −0.180531 + 0.203088i
\(673\) −460.650 −0.684473 −0.342236 0.939614i \(-0.611184\pi\)
−0.342236 + 0.939614i \(0.611184\pi\)
\(674\) 108.501 + 1198.47i 0.160981 + 1.77815i
\(675\) 265.638 641.308i 0.393538 0.950086i
\(676\) 464.712 + 321.229i 0.687443 + 0.475191i
\(677\) 20.9880 + 50.6694i 0.0310014 + 0.0748441i 0.938622 0.344947i \(-0.112103\pi\)
−0.907621 + 0.419791i \(0.862103\pi\)
\(678\) −222.700 69.4783i −0.328466 0.102475i
\(679\) −154.462 154.462i −0.227484 0.227484i
\(680\) 117.297 91.7052i 0.172495 0.134861i
\(681\) −71.8179 71.8179i −0.105459 0.105459i
\(682\) 983.996 516.019i 1.44281 0.756626i
\(683\) −29.0552 70.1454i −0.0425405 0.102702i 0.901181 0.433443i \(-0.142701\pi\)
−0.943722 + 0.330741i \(0.892701\pi\)
\(684\) −243.264 376.806i −0.355649 0.550885i
\(685\) −20.8965 + 50.4485i −0.0305058 + 0.0736474i
\(686\) 23.7234 28.4465i 0.0345822 0.0414671i
\(687\) −762.217 −1.10949
\(688\) −907.309 966.451i −1.31876 1.40473i
\(689\) 144.362i 0.209523i
\(690\) −69.4212 + 83.2423i −0.100610 + 0.120641i
\(691\) 822.850 + 340.836i 1.19081 + 0.493250i 0.888019 0.459807i \(-0.152081\pi\)
0.302792 + 0.953057i \(0.402081\pi\)
\(692\) 243.573 1130.97i 0.351985 1.63436i
\(693\) −158.299 + 65.5697i −0.228426 + 0.0946172i
\(694\) 979.155 513.480i 1.41089 0.739885i
\(695\) 38.4422 38.4422i 0.0553125 0.0553125i
\(696\) −418.980 + 741.122i −0.601983 + 1.06483i
\(697\) 332.211 332.211i 0.476629 0.476629i
\(698\) −820.399 255.949i −1.17536 0.366690i
\(699\) −129.957 + 53.8298i −0.185918 + 0.0770097i
\(700\) 251.020 45.8267i 0.358601 0.0654668i
\(701\) −305.289 126.455i −0.435505 0.180392i 0.154150 0.988048i \(-0.450736\pi\)
−0.589655 + 0.807655i \(0.700736\pi\)
\(702\) 27.3567 + 302.175i 0.0389697 + 0.430449i
\(703\) 1306.28i 1.85815i
\(704\) 766.598 + 566.461i 1.08892 + 0.804633i
\(705\) 170.584 0.241963
\(706\) 325.923 29.5067i 0.461647 0.0417941i
\(707\) −116.423 + 281.070i −0.164672 + 0.397553i
\(708\) 62.2285 + 340.863i 0.0878933 + 0.481445i
\(709\) −81.1217 195.845i −0.114417 0.276227i 0.856289 0.516497i \(-0.172764\pi\)
−0.970706 + 0.240270i \(0.922764\pi\)
\(710\) −17.9845 + 57.6459i −0.0253302 + 0.0811915i
\(711\) −35.4419 35.4419i −0.0498479 0.0498479i
\(712\) 578.984 1024.15i 0.813179 1.43841i
\(713\) 703.030 + 703.030i 0.986016 + 0.986016i
\(714\) −104.637 199.531i −0.146550 0.279456i
\(715\) 28.3138 + 68.3555i 0.0395997 + 0.0956021i
\(716\) −584.155 125.807i −0.815860 0.175708i
\(717\) −174.131 + 420.391i −0.242861 + 0.586319i
\(718\) 499.050 + 416.191i 0.695055 + 0.579653i
\(719\) 1240.79 1.72571 0.862855 0.505451i \(-0.168674\pi\)
0.862855 + 0.505451i \(0.168674\pi\)
\(720\) −2.06919 + 65.5568i −0.00287387 + 0.0910511i
\(721\) 44.6828i 0.0619734i
\(722\) −466.838 389.327i −0.646589 0.539234i
\(723\) 8.88289 + 3.67941i 0.0122862 + 0.00508909i
\(724\) −210.781 + 136.079i −0.291135 + 0.187955i
\(725\) 1099.13 455.276i 1.51605 0.627967i
\(726\) −201.964 385.124i −0.278187 0.530474i
\(727\) −814.186 + 814.186i −1.11993 + 1.11993i −0.128174 + 0.991752i \(0.540912\pi\)
−0.991752 + 0.128174i \(0.959088\pi\)
\(728\) −87.8674 + 68.6967i −0.120697 + 0.0943637i
\(729\) 465.740 465.740i 0.638876 0.638876i
\(730\) 29.7340 95.3070i 0.0407315 0.130557i
\(731\) 1511.10 625.919i 2.06717 0.856250i
\(732\) −251.959 + 364.501i −0.344206 + 0.497952i
\(733\) 302.729 + 125.394i 0.413000 + 0.171070i 0.579502 0.814971i \(-0.303247\pi\)
−0.166502 + 0.986041i \(0.553247\pi\)
\(734\) −1203.66 + 108.971i −1.63986 + 0.148461i
\(735\) 14.2330i 0.0193647i
\(736\) −279.584 + 805.806i −0.379869 + 1.09484i
\(737\) 1234.54 1.67509
\(738\) 18.6607 + 206.121i 0.0252855 + 0.279297i
\(739\) 212.589 513.236i 0.287671 0.694500i −0.712301 0.701874i \(-0.752347\pi\)
0.999973 + 0.00737358i \(0.00234710\pi\)
\(740\) −108.622 + 157.140i −0.146787 + 0.212352i
\(741\) 112.152 + 270.758i 0.151352 + 0.365395i
\(742\) 138.386 + 43.1738i 0.186504 + 0.0581858i
\(743\) 308.665 + 308.665i 0.415431 + 0.415431i 0.883625 0.468195i \(-0.155095\pi\)
−0.468195 + 0.883625i \(0.655095\pi\)
\(744\) −638.836 78.2228i −0.858650 0.105138i
\(745\) −55.3282 55.3282i −0.0742660 0.0742660i
\(746\) −127.707 + 66.9712i −0.171190 + 0.0897738i
\(747\) −266.325 642.964i −0.356526 0.860729i
\(748\) −988.063 + 637.888i −1.32094 + 0.852792i
\(749\) −56.9916 + 137.590i −0.0760903 + 0.183698i
\(750\) −127.912 + 153.377i −0.170549 + 0.204503i
\(751\) −616.146 −0.820434 −0.410217 0.911988i \(-0.634547\pi\)
−0.410217 + 0.911988i \(0.634547\pi\)
\(752\) 1255.74 474.308i 1.66987 0.630728i
\(753\) 100.587i 0.133582i
\(754\) −333.054 + 399.362i −0.441716 + 0.529658i
\(755\) −51.9991 21.5387i −0.0688730 0.0285281i
\(756\) 297.849 + 64.1464i 0.393980 + 0.0848498i
\(757\) −164.876 + 68.2937i −0.217801 + 0.0902163i −0.488916 0.872331i \(-0.662608\pi\)
0.271115 + 0.962547i \(0.412608\pi\)
\(758\) 462.325 242.449i 0.609928 0.319853i
\(759\) 605.409 605.409i 0.797640 0.797640i
\(760\) 52.0350 + 187.389i 0.0684670 + 0.246565i
\(761\) 178.882 178.882i 0.235062 0.235062i −0.579740 0.814802i \(-0.696846\pi\)
0.814802 + 0.579740i \(0.196846\pi\)
\(762\) −198.194 61.8328i −0.260097 0.0811454i
\(763\) 218.359 90.4474i 0.286185 0.118542i
\(764\) 232.741 + 1274.86i 0.304635 + 1.66867i
\(765\) −74.7674 30.9697i −0.0977351 0.0404832i
\(766\) 112.065 + 1237.84i 0.146298 + 1.61597i
\(767\) 211.643i 0.275936i
\(768\) −178.703 522.416i −0.232686 0.680229i
\(769\) 615.128 0.799906 0.399953 0.916536i \(-0.369026\pi\)
0.399953 + 0.916536i \(0.369026\pi\)
\(770\) 73.9937 6.69885i 0.0960957 0.00869981i
\(771\) −322.317 + 778.142i −0.418051 + 1.00926i
\(772\) 772.935 141.108i 1.00121 0.182783i
\(773\) 354.467 + 855.758i 0.458560 + 1.10706i 0.968981 + 0.247136i \(0.0794896\pi\)
−0.510421 + 0.859925i \(0.670510\pi\)
\(774\) −214.588 + 687.822i −0.277245 + 0.888659i
\(775\) 635.960 + 635.960i 0.820593 + 0.820593i
\(776\) 636.426 176.725i 0.820136 0.227739i
\(777\) 204.402 + 204.402i 0.263065 + 0.263065i
\(778\) 64.4440 + 122.888i 0.0828329 + 0.157954i
\(779\) 234.842 + 566.959i 0.301466 + 0.727803i
\(780\) 9.02321 41.8971i 0.0115682 0.0537142i
\(781\) 182.536 440.681i 0.233721 0.564252i
\(782\) −808.216 674.025i −1.03352 0.861925i
\(783\) 1420.52 1.81420
\(784\) 39.5748 + 104.775i 0.0504781 + 0.133642i
\(785\) 12.0108i 0.0153004i
\(786\) 516.499 + 430.743i 0.657123 + 0.548019i
\(787\) −441.647 182.936i −0.561178 0.232448i 0.0840185 0.996464i \(-0.473225\pi\)
−0.645197 + 0.764017i \(0.723225\pi\)
\(788\) −334.838 518.650i −0.424921 0.658186i
\(789\) 380.971 157.803i 0.482853 0.200004i
\(790\) 10.0937 + 19.2477i 0.0127769 + 0.0243642i
\(791\) −101.178 + 101.178i −0.127912 + 0.127912i
\(792\) 62.9676 514.249i 0.0795046 0.649304i
\(793\) −191.381 + 191.381i −0.241338 + 0.241338i
\(794\) 152.762 489.650i 0.192395 0.616687i
\(795\) −51.4632 + 21.3167i −0.0647335 + 0.0268135i
\(796\) −404.327 279.489i −0.507949 0.351116i
\(797\) −614.208 254.413i −0.770650 0.319214i −0.0375142 0.999296i \(-0.511944\pi\)
−0.733136 + 0.680082i \(0.761944\pi\)
\(798\) 293.091 26.5343i 0.367282 0.0332510i
\(799\) 1656.24i 2.07289i
\(800\) −252.911 + 728.931i −0.316139 + 0.911164i
\(801\) −639.461 −0.798328
\(802\) 4.51040 + 49.8206i 0.00562394 + 0.0621205i
\(803\) −301.790 + 728.585i −0.375828 + 0.907329i
\(804\) −588.256 406.628i −0.731662 0.505757i
\(805\) 25.4417 + 61.4217i 0.0316046 + 0.0763002i
\(806\) −375.280 117.081i −0.465608 0.145261i
\(807\) −279.728 279.728i −0.346627 0.346627i
\(808\) −566.587 724.700i −0.701222 0.896906i
\(809\) −610.914 610.914i −0.755147 0.755147i 0.220288 0.975435i \(-0.429300\pi\)
−0.975435 + 0.220288i \(0.929300\pi\)
\(810\) −38.3347 + 20.1031i −0.0473267 + 0.0248187i
\(811\) −210.821 508.968i −0.259952 0.627580i 0.738983 0.673725i \(-0.235307\pi\)
−0.998935 + 0.0461444i \(0.985307\pi\)
\(812\) 283.225 + 438.704i 0.348799 + 0.540276i
\(813\) 3.93100 9.49028i 0.00483518 0.0116732i
\(814\) 966.427 1158.83i 1.18726 1.42363i
\(815\) 161.098 0.197667
\(816\) 680.914 + 21.4919i 0.834454 + 0.0263381i
\(817\) 2136.42i 2.61495i
\(818\) 742.781 890.660i 0.908045 1.08883i
\(819\) 56.0085 + 23.1995i 0.0683865 + 0.0283266i
\(820\) 18.8943 87.7312i 0.0230419 0.106989i
\(821\) 926.220 383.653i 1.12816 0.467299i 0.261005 0.965337i \(-0.415946\pi\)
0.867155 + 0.498038i \(0.165946\pi\)
\(822\) −221.268 + 116.035i −0.269182 + 0.141162i
\(823\) 242.079 242.079i 0.294142 0.294142i −0.544572 0.838714i \(-0.683308\pi\)
0.838714 + 0.544572i \(0.183308\pi\)
\(824\) 117.614 + 66.4912i 0.142736 + 0.0806932i
\(825\) 547.652 547.652i 0.663821 0.663821i
\(826\) 202.882 + 63.2954i 0.245620 + 0.0766288i
\(827\) 242.507 100.450i 0.293237 0.121463i −0.231215 0.972903i \(-0.574270\pi\)
0.524452 + 0.851440i \(0.324270\pi\)
\(828\) 456.062 83.2595i 0.550800 0.100555i
\(829\) −94.1207 38.9861i −0.113535 0.0470279i 0.325193 0.945648i \(-0.394571\pi\)
−0.438728 + 0.898620i \(0.644571\pi\)
\(830\) 27.2087 + 300.540i 0.0327816 + 0.362097i
\(831\) 881.998i 1.06137i
\(832\) −50.0710 333.511i −0.0601815 0.400854i
\(833\) −138.191 −0.165896
\(834\) 247.738 22.4284i 0.297048 0.0268925i
\(835\) 57.9102 139.808i 0.0693535 0.167434i
\(836\) −275.890 1511.21i −0.330012 1.80767i
\(837\) 410.957 + 992.138i 0.490988 + 1.18535i
\(838\) 61.2053 196.182i 0.0730373 0.234108i
\(839\) 428.770 + 428.770i 0.511049 + 0.511049i 0.914848 0.403799i \(-0.132310\pi\)
−0.403799 + 0.914848i \(0.632310\pi\)
\(840\) −37.4642 21.1798i −0.0446003 0.0252140i
\(841\) 1126.86 + 1126.86i 1.33990 + 1.33990i
\(842\) 364.998 + 696.014i 0.433489 + 0.826620i
\(843\) −78.2279 188.859i −0.0927971 0.224032i
\(844\) −797.474 171.749i −0.944874 0.203494i
\(845\) −50.9527 + 123.011i −0.0602991 + 0.145575i
\(846\) −560.326 467.293i −0.662323 0.552355i
\(847\) −266.729 −0.314911
\(848\) −319.570 + 300.014i −0.376852 + 0.353790i
\(849\) 188.857i 0.222446i
\(850\) −731.112 609.722i −0.860131 0.717320i
\(851\) 1247.45 + 516.711i 1.46586 + 0.607181i
\(852\) −232.127 + 149.860i −0.272450 + 0.175892i
\(853\) 371.009 153.677i 0.434946 0.180161i −0.154457 0.987999i \(-0.549363\pi\)
0.589403 + 0.807839i \(0.299363\pi\)
\(854\) 126.223 + 240.694i 0.147802 + 0.281844i
\(855\) 74.7462 74.7462i 0.0874225 0.0874225i
\(856\) −277.357 354.757i −0.324016 0.414436i
\(857\) −1060.01 + 1060.01i −1.23688 + 1.23688i −0.275614 + 0.961268i \(0.588881\pi\)
−0.961268 + 0.275614i \(0.911119\pi\)
\(858\) −100.823 + 323.170i −0.117509 + 0.376655i
\(859\) −274.108 + 113.539i −0.319101 + 0.132176i −0.536484 0.843910i \(-0.680248\pi\)
0.217383 + 0.976086i \(0.430248\pi\)
\(860\) 177.652 257.003i 0.206572 0.298841i
\(861\) −125.463 51.9685i −0.145718 0.0603583i
\(862\) −685.826 + 62.0897i −0.795622 + 0.0720298i
\(863\) 130.540i 0.151262i −0.997136 0.0756312i \(-0.975903\pi\)
0.997136 0.0756312i \(-0.0240972\pi\)
\(864\) −612.066 + 688.544i −0.708410 + 0.796926i
\(865\) 272.666 0.315221
\(866\) 150.835 + 1666.08i 0.174174 + 1.92388i
\(867\) −83.1405 + 200.719i −0.0958945 + 0.231510i
\(868\) −224.468 + 324.731i −0.258604 + 0.374114i
\(869\) −65.6970 158.607i −0.0756007 0.182516i
\(870\) −191.547 59.7592i −0.220169 0.0686887i
\(871\) −308.863 308.863i −0.354607 0.354607i
\(872\) −86.8581 + 709.359i −0.0996079 + 0.813485i
\(873\) −253.859 253.859i −0.290789 0.290789i
\(874\) 1217.38 638.410i 1.39289 0.730447i
\(875\) 46.8774 + 113.172i 0.0535741 + 0.129339i
\(876\) 383.780 247.766i 0.438105 0.282838i
\(877\) 206.520 498.583i 0.235485 0.568510i −0.761321 0.648375i \(-0.775449\pi\)
0.996806 + 0.0798650i \(0.0254489\pi\)
\(878\) 487.448 584.494i 0.555180 0.665710i
\(879\) −547.815 −0.623225
\(880\) −92.4751 + 204.735i −0.105085 + 0.232653i
\(881\) 755.009i 0.856991i −0.903544 0.428495i \(-0.859044\pi\)
0.903544 0.428495i \(-0.140956\pi\)
\(882\) 38.9895 46.7519i 0.0442058 0.0530067i
\(883\) 961.253 + 398.164i 1.08862 + 0.450922i 0.853526 0.521050i \(-0.174460\pi\)
0.235096 + 0.971972i \(0.424460\pi\)
\(884\) 406.787 + 87.6082i 0.460167 + 0.0991043i
\(885\) −75.4480 + 31.2516i −0.0852520 + 0.0353125i
\(886\) 0.173361 0.0909123i 0.000195667 0.000102610i
\(887\) −723.981 + 723.981i −0.816214 + 0.816214i −0.985557 0.169344i \(-0.945835\pi\)
0.169344 + 0.985557i \(0.445835\pi\)
\(888\) −842.191 + 233.863i −0.948413 + 0.263359i
\(889\) −90.0445 + 90.0445i −0.101287 + 0.101287i
\(890\) 264.697 + 82.5805i 0.297412 + 0.0927870i
\(891\) 315.889 130.845i 0.354533 0.146852i
\(892\) 38.3507 + 210.070i 0.0429940 + 0.235504i
\(893\) −1998.69 827.884i −2.23817 0.927081i
\(894\) −32.2802 356.558i −0.0361076 0.398835i
\(895\) 140.834i 0.157356i
\(896\) −334.680 51.7437i −0.373527 0.0577497i
\(897\) −302.928 −0.337712
\(898\) −669.592 + 60.6200i −0.745648 + 0.0675055i
\(899\) −704.337 + 1700.42i −0.783467 + 1.89146i
\(900\) 412.553 75.3165i 0.458393 0.0836850i
\(901\) −206.969 499.667i −0.229710 0.554569i
\(902\) −211.120 + 676.708i −0.234058 + 0.750230i
\(903\) −334.299 334.299i −0.370209 0.370209i
\(904\) −115.762 416.883i −0.128055 0.461154i
\(905\) −41.8123 41.8123i −0.0462015 0.0462015i
\(906\) −119.602 228.069i −0.132011 0.251732i
\(907\) −89.4720 216.005i −0.0986461 0.238153i 0.866851 0.498568i \(-0.166141\pi\)
−0.965497 + 0.260415i \(0.916141\pi\)
\(908\) 39.6583 184.144i 0.0436765 0.202801i
\(909\) −191.342 + 461.939i −0.210497 + 0.508184i
\(910\) −20.1880 16.8361i −0.0221846 0.0185012i
\(911\) −203.292 −0.223152 −0.111576 0.993756i \(-0.535590\pi\)
−0.111576 + 0.993756i \(0.535590\pi\)
\(912\) −366.296 + 810.961i −0.401641 + 0.889211i
\(913\) 2383.67i 2.61081i
\(914\) −920.027 767.271i −1.00659 0.839465i
\(915\) −96.4846 39.9652i −0.105448 0.0436779i
\(916\) −766.725 1187.63i −0.837036 1.29654i
\(917\) 381.107 157.860i 0.415602 0.172148i
\(918\) −527.911 1006.67i −0.575066 1.09659i
\(919\) 492.142 492.142i 0.535519 0.535519i −0.386690 0.922210i \(-0.626382\pi\)
0.922210 + 0.386690i \(0.126382\pi\)
\(920\) −199.533 24.4320i −0.216884 0.0265566i
\(921\) 55.2145 55.2145i 0.0599505 0.0599505i
\(922\) 202.299 648.432i 0.219413 0.703289i
\(923\) −155.919 + 64.5838i −0.168926 + 0.0699716i
\(924\) 279.640 + 193.299i 0.302640 + 0.209198i
\(925\) 1128.44 + 467.416i 1.21994 + 0.505315i
\(926\) 29.9857 2.71468i 0.0323819 0.00293162i
\(927\) 73.4365i 0.0792195i
\(928\) −1576.22 + 92.6837i −1.69851 + 0.0998747i
\(929\) 905.540 0.974747 0.487373 0.873194i \(-0.337955\pi\)
0.487373 + 0.873194i \(0.337955\pi\)
\(930\) −13.6769 151.071i −0.0147063 0.162442i
\(931\) 69.0762 166.765i 0.0741957 0.179124i
\(932\) −214.599 148.340i −0.230256 0.159163i
\(933\) −387.447 935.379i −0.415270 1.00255i
\(934\) −264.889 82.6403i −0.283607 0.0884800i
\(935\) −196.000 196.000i −0.209626 0.209626i
\(936\) −144.410 + 112.903i −0.154285 + 0.120623i
\(937\) −1264.02 1264.02i −1.34901 1.34901i −0.886744 0.462262i \(-0.847038\pi\)
−0.462262 0.886744i \(-0.652962\pi\)
\(938\) −388.449 + 203.707i −0.414125 + 0.217172i
\(939\) −304.797 735.845i −0.324597 0.783647i
\(940\) 171.593 + 265.791i 0.182546 + 0.282756i
\(941\) −6.43069 + 15.5250i −0.00683389 + 0.0164985i −0.927260 0.374419i \(-0.877842\pi\)
0.920426 + 0.390917i \(0.127842\pi\)
\(942\) 35.1977 42.2051i 0.0373648 0.0448038i
\(943\) −634.321 −0.672663
\(944\) −468.509 + 439.839i −0.496302 + 0.465931i
\(945\) 71.8083i 0.0759876i
\(946\) −1580.59 + 1895.27i −1.67082 + 2.00346i
\(947\) −1063.74 440.616i −1.12327 0.465275i −0.257784 0.966202i \(-0.582992\pi\)
−0.865489 + 0.500927i \(0.832992\pi\)
\(948\) −20.9367 + 97.2146i −0.0220852 + 0.102547i
\(949\) 257.784 106.777i 0.271637 0.112516i
\(950\) 1101.24 577.505i 1.15920 0.607900i
\(951\) −147.510 + 147.510i −0.155110 + 0.155110i
\(952\) 205.639 363.748i 0.216007 0.382088i
\(953\) 31.8270 31.8270i 0.0333967 0.0333967i −0.690211 0.723608i \(-0.742482\pi\)
0.723608 + 0.690211i \(0.242482\pi\)
\(954\) 227.438 + 70.9564i 0.238405 + 0.0743778i
\(955\) −282.183 + 116.884i −0.295480 + 0.122392i
\(956\) −830.181 + 151.559i −0.868390 + 0.158535i
\(957\) 1464.30 + 606.534i 1.53010 + 0.633787i
\(958\) 24.2151 + 267.474i 0.0252767 + 0.279200i
\(959\) 153.246i 0.159797i
\(960\) 111.499 67.0966i 0.116145 0.0698923i
\(961\) −430.395 −0.447861
\(962\) −531.706 + 48.1368i −0.552709 + 0.0500383i
\(963\) −93.6660 + 226.130i −0.0972648 + 0.234818i
\(964\) 3.20246 + 17.5418i 0.00332205 + 0.0181969i
\(965\) 70.8656 + 171.085i 0.0734358 + 0.177290i
\(966\) −90.5958 + 290.388i −0.0937844 + 0.300609i
\(967\) 427.458 + 427.458i 0.442046 + 0.442046i 0.892699 0.450653i \(-0.148809\pi\)
−0.450653 + 0.892699i \(0.648809\pi\)
\(968\) 396.912 702.086i 0.410033 0.725296i
\(969\) −776.362 776.362i −0.801199 0.801199i
\(970\) 72.2981 + 137.865i 0.0745341 + 0.142129i
\(971\) 487.038 + 1175.81i 0.501584 + 1.21093i 0.948621 + 0.316415i \(0.102479\pi\)
−0.447037 + 0.894515i \(0.647521\pi\)
\(972\) 819.568 + 176.507i 0.843177 + 0.181592i
\(973\) 58.3873 140.959i 0.0600075 0.144871i
\(974\) 1343.64 + 1120.55i 1.37951 + 1.15047i
\(975\) −274.028 −0.281054
\(976\) −821.386 25.9257i −0.841584 0.0265632i
\(977\) 1111.86i 1.13803i −0.822327 0.569015i \(-0.807325\pi\)
0.822327 0.569015i \(-0.192675\pi\)
\(978\) 566.088 + 472.098i 0.578822 + 0.482718i
\(979\) −2023.50 838.162i −2.06691 0.856141i
\(980\) −22.1768 + 14.3172i −0.0226294 + 0.0146094i
\(981\) 358.875 148.651i 0.365825 0.151530i
\(982\) 48.2202 + 91.9510i 0.0491041 + 0.0936365i
\(983\) −162.181 + 162.181i −0.164986 + 0.164986i −0.784771 0.619786i \(-0.787220\pi\)
0.619786 + 0.784771i \(0.287220\pi\)
\(984\) 323.489 252.911i 0.328749 0.257024i
\(985\) 102.884 102.884i 0.104450 0.104450i
\(986\) 580.214 1859.77i 0.588453 1.88618i
\(987\) 442.292 183.203i 0.448118 0.185616i
\(988\) −309.059 + 447.105i −0.312812 + 0.452536i
\(989\) −2040.21 845.081i −2.06290 0.854481i
\(990\) 121.609 11.0096i 0.122837 0.0111208i
\(991\) 856.333i 0.864110i 0.901847 + 0.432055i \(0.142211\pi\)
−0.901847 + 0.432055i \(0.857789\pi\)
\(992\) −520.734 1074.07i −0.524933 1.08273i
\(993\) 187.994 0.189319
\(994\) 15.2801 + 168.780i 0.0153723 + 0.169799i
\(995\) 44.3319 107.027i 0.0445547 0.107565i
\(996\) −785.123 + 1135.81i −0.788276 + 1.14037i
\(997\) −660.978 1595.74i −0.662967 1.60054i −0.793131 0.609051i \(-0.791551\pi\)
0.130165 0.991492i \(-0.458449\pi\)
\(998\) −679.828 212.094i −0.681191 0.212519i
\(999\) 1031.24 + 1031.24i 1.03228 + 1.03228i
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 224.3.w.a.99.3 yes 192
32.11 odd 8 inner 224.3.w.a.43.3 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.3.w.a.43.3 192 32.11 odd 8 inner
224.3.w.a.99.3 yes 192 1.1 even 1 trivial