Properties

Label 201.3.k.a.14.15
Level $201$
Weight $3$
Character 201.14
Analytic conductor $5.477$
Analytic rank $0$
Dimension $440$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(14,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.k (of order \(22\), degree \(10\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(44\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 14.15
Character \(\chi\) \(=\) 201.14
Dual form 201.3.k.a.158.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30691 + 0.596845i) q^{2} +(-1.63302 + 2.51659i) q^{3} +(-1.26766 + 1.46295i) q^{4} +(7.35419 - 1.05737i) q^{5} +(0.632194 - 4.26362i) q^{6} +(-4.35656 - 9.53954i) q^{7} +(2.40267 - 8.18273i) q^{8} +(-3.66648 - 8.21930i) q^{9} +O(q^{10})\) \(q+(-1.30691 + 0.596845i) q^{2} +(-1.63302 + 2.51659i) q^{3} +(-1.26766 + 1.46295i) q^{4} +(7.35419 - 1.05737i) q^{5} +(0.632194 - 4.26362i) q^{6} +(-4.35656 - 9.53954i) q^{7} +(2.40267 - 8.18273i) q^{8} +(-3.66648 - 8.21930i) q^{9} +(-8.98017 + 5.77121i) q^{10} +(14.8759 - 2.13883i) q^{11} +(-1.61155 - 5.57921i) q^{12} +(7.35659 - 2.16009i) q^{13} +(11.3873 + 9.86712i) q^{14} +(-9.34857 + 20.2342i) q^{15} +(0.641807 + 4.46386i) q^{16} +(-20.5847 + 17.8368i) q^{17} +(9.69741 + 8.55356i) q^{18} +(6.56461 - 14.3745i) q^{19} +(-7.77569 + 12.0992i) q^{20} +(31.1215 + 4.61458i) q^{21} +(-18.1649 + 11.6739i) q^{22} +(12.9814 - 20.1995i) q^{23} +(16.6690 + 19.4091i) q^{24} +(28.9788 - 8.50893i) q^{25} +(-8.32516 + 7.21379i) q^{26} +(26.6721 + 4.19525i) q^{27} +(19.4785 + 5.71941i) q^{28} -5.16179i q^{29} +(0.141037 - 32.0239i) q^{30} +(44.4005 + 13.0372i) q^{31} +(14.9397 + 23.2466i) q^{32} +(-18.9101 + 40.9293i) q^{33} +(16.2566 - 35.5969i) q^{34} +(-42.1259 - 65.5491i) q^{35} +(16.6723 + 5.05535i) q^{36} -42.7731 q^{37} +22.7042i q^{38} +(-6.57740 + 22.0410i) q^{39} +(9.01747 - 62.7179i) q^{40} +(12.0516 - 10.4428i) q^{41} +(-43.4272 + 12.5439i) q^{42} +(-26.3936 - 30.4599i) q^{43} +(-15.7285 + 24.4740i) q^{44} +(-35.6549 - 56.5695i) q^{45} +(-4.90957 + 34.1468i) q^{46} +(4.55899 - 7.09393i) q^{47} +(-12.2818 - 5.67442i) q^{48} +(-39.9351 + 46.0875i) q^{49} +(-32.7941 + 28.4162i) q^{50} +(-11.2726 - 80.9311i) q^{51} +(-6.16552 + 13.5006i) q^{52} +(64.8875 + 56.2254i) q^{53} +(-37.3619 + 10.4363i) q^{54} +(107.139 - 31.4587i) q^{55} +(-88.5269 + 12.7282i) q^{56} +(25.4546 + 39.9943i) q^{57} +(3.08079 + 6.74600i) q^{58} +(-10.3270 + 35.1705i) q^{59} +(-17.7509 - 39.3265i) q^{60} +(4.27952 - 29.7647i) q^{61} +(-65.8086 + 9.46185i) q^{62} +(-62.4351 + 70.7845i) q^{63} +(-48.5749 - 31.2172i) q^{64} +(51.8178 - 23.6644i) q^{65} +(0.285286 - 64.7773i) q^{66} +(13.3248 - 65.6616i) q^{67} -52.7253i q^{68} +(29.6350 + 65.6552i) q^{69} +(94.1774 + 60.5241i) q^{70} +(-79.0775 - 68.5210i) q^{71} +(-76.0656 + 10.2536i) q^{72} +(1.43235 - 9.96222i) q^{73} +(55.9006 - 25.5289i) q^{74} +(-25.9094 + 86.8230i) q^{75} +(12.7075 + 27.8256i) q^{76} +(-85.2113 - 132.591i) q^{77} +(-4.55901 - 32.7313i) q^{78} +(121.302 - 35.6175i) q^{79} +(9.43994 + 32.1495i) q^{80} +(-54.1138 + 60.2718i) q^{81} +(-9.51762 + 20.8407i) q^{82} +(75.5751 - 10.8661i) q^{83} +(-46.2023 + 39.6796i) q^{84} +(-132.524 + 152.941i) q^{85} +(52.6740 + 24.0554i) q^{86} +(12.9901 + 8.42932i) q^{87} +(18.2403 - 126.864i) q^{88} +(48.9382 + 76.1493i) q^{89} +(80.3609 + 52.6507i) q^{90} +(-52.6557 - 60.7680i) q^{91} +(13.0949 + 44.5972i) q^{92} +(-105.316 + 90.4481i) q^{93} +(-1.72421 + 11.9921i) q^{94} +(33.0782 - 112.654i) q^{95} +(-82.8992 - 0.365097i) q^{96} -11.6706 q^{97} +(24.6844 - 84.0673i) q^{98} +(-72.1219 - 114.427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30691 + 0.596845i −0.653455 + 0.298423i −0.714420 0.699717i \(-0.753309\pi\)
0.0609653 + 0.998140i \(0.480582\pi\)
\(3\) −1.63302 + 2.51659i −0.544341 + 0.838864i
\(4\) −1.26766 + 1.46295i −0.316914 + 0.365738i
\(5\) 7.35419 1.05737i 1.47084 0.211475i 0.640166 0.768237i \(-0.278866\pi\)
0.830672 + 0.556762i \(0.187956\pi\)
\(6\) 0.632194 4.26362i 0.105366 0.710603i
\(7\) −4.35656 9.53954i −0.622366 1.36279i −0.913786 0.406197i \(-0.866855\pi\)
0.291419 0.956595i \(-0.405873\pi\)
\(8\) 2.40267 8.18273i 0.300333 1.02284i
\(9\) −3.66648 8.21930i −0.407387 0.913256i
\(10\) −8.98017 + 5.77121i −0.898017 + 0.577121i
\(11\) 14.8759 2.13883i 1.35235 0.194439i 0.572245 0.820083i \(-0.306073\pi\)
0.780109 + 0.625644i \(0.215164\pi\)
\(12\) −1.61155 5.57921i −0.134296 0.464934i
\(13\) 7.35659 2.16009i 0.565892 0.166161i 0.0137417 0.999906i \(-0.495626\pi\)
0.552150 + 0.833745i \(0.313808\pi\)
\(14\) 11.3873 + 9.86712i 0.813376 + 0.704795i
\(15\) −9.34857 + 20.2342i −0.623238 + 1.34895i
\(16\) 0.641807 + 4.46386i 0.0401129 + 0.278991i
\(17\) −20.5847 + 17.8368i −1.21087 + 1.04922i −0.213480 + 0.976947i \(0.568480\pi\)
−0.997385 + 0.0722734i \(0.976975\pi\)
\(18\) 9.69741 + 8.55356i 0.538745 + 0.475198i
\(19\) 6.56461 14.3745i 0.345506 0.756552i −0.654494 0.756067i \(-0.727118\pi\)
1.00000 0.000484878i \(-0.000154341\pi\)
\(20\) −7.77569 + 12.0992i −0.388785 + 0.604961i
\(21\) 31.1215 + 4.61458i 1.48198 + 0.219742i
\(22\) −18.1649 + 11.6739i −0.825677 + 0.530630i
\(23\) 12.9814 20.1995i 0.564410 0.878239i −0.435347 0.900263i \(-0.643374\pi\)
0.999757 + 0.0220233i \(0.00701079\pi\)
\(24\) 16.6690 + 19.4091i 0.694541 + 0.808713i
\(25\) 28.9788 8.50893i 1.15915 0.340357i
\(26\) −8.32516 + 7.21379i −0.320198 + 0.277453i
\(27\) 26.6721 + 4.19525i 0.987855 + 0.155380i
\(28\) 19.4785 + 5.71941i 0.695662 + 0.204265i
\(29\) 5.16179i 0.177993i −0.996032 0.0889964i \(-0.971634\pi\)
0.996032 0.0889964i \(-0.0283660\pi\)
\(30\) 0.141037 32.0239i 0.00470123 1.06746i
\(31\) 44.4005 + 13.0372i 1.43228 + 0.420554i 0.903639 0.428295i \(-0.140885\pi\)
0.528636 + 0.848849i \(0.322704\pi\)
\(32\) 14.9397 + 23.2466i 0.466866 + 0.726457i
\(33\) −18.9101 + 40.9293i −0.573033 + 1.24028i
\(34\) 16.2566 35.5969i 0.478134 1.04697i
\(35\) −42.1259 65.5491i −1.20360 1.87283i
\(36\) 16.6723 + 5.05535i 0.463119 + 0.140427i
\(37\) −42.7731 −1.15603 −0.578015 0.816026i \(-0.696172\pi\)
−0.578015 + 0.816026i \(0.696172\pi\)
\(38\) 22.7042i 0.597479i
\(39\) −6.57740 + 22.0410i −0.168651 + 0.565154i
\(40\) 9.01747 62.7179i 0.225437 1.56795i
\(41\) 12.0516 10.4428i 0.293941 0.254702i −0.495388 0.868672i \(-0.664974\pi\)
0.789329 + 0.613970i \(0.210429\pi\)
\(42\) −43.4272 + 12.5439i −1.03398 + 0.298664i
\(43\) −26.3936 30.4599i −0.613806 0.708370i 0.360713 0.932677i \(-0.382533\pi\)
−0.974518 + 0.224307i \(0.927988\pi\)
\(44\) −15.7285 + 24.4740i −0.357466 + 0.556228i
\(45\) −35.6549 56.5695i −0.792330 1.25710i
\(46\) −4.90957 + 34.1468i −0.106730 + 0.742322i
\(47\) 4.55899 7.09393i 0.0969999 0.150935i −0.789362 0.613928i \(-0.789588\pi\)
0.886362 + 0.462994i \(0.153225\pi\)
\(48\) −12.2818 5.67442i −0.255871 0.118217i
\(49\) −39.9351 + 46.0875i −0.815002 + 0.940562i
\(50\) −32.7941 + 28.4162i −0.655882 + 0.568325i
\(51\) −11.2726 80.9311i −0.221031 1.58689i
\(52\) −6.16552 + 13.5006i −0.118568 + 0.259627i
\(53\) 64.8875 + 56.2254i 1.22429 + 1.06086i 0.996189 + 0.0872190i \(0.0277980\pi\)
0.228104 + 0.973637i \(0.426747\pi\)
\(54\) −37.3619 + 10.4363i −0.691887 + 0.193265i
\(55\) 107.139 31.4587i 1.94797 0.571977i
\(56\) −88.5269 + 12.7282i −1.58084 + 0.227290i
\(57\) 25.4546 + 39.9943i 0.446572 + 0.701654i
\(58\) 3.08079 + 6.74600i 0.0531171 + 0.116310i
\(59\) −10.3270 + 35.1705i −0.175034 + 0.596110i 0.824508 + 0.565850i \(0.191452\pi\)
−0.999542 + 0.0302603i \(0.990366\pi\)
\(60\) −17.7509 39.3265i −0.295849 0.655442i
\(61\) 4.27952 29.7647i 0.0701561 0.487946i −0.924205 0.381897i \(-0.875271\pi\)
0.994361 0.106049i \(-0.0338200\pi\)
\(62\) −65.8086 + 9.46185i −1.06143 + 0.152611i
\(63\) −62.4351 + 70.7845i −0.991034 + 1.12356i
\(64\) −48.5749 31.2172i −0.758983 0.487769i
\(65\) 51.8178 23.6644i 0.797196 0.364067i
\(66\) 0.285286 64.7773i 0.00432252 0.981474i
\(67\) 13.3248 65.6616i 0.198877 0.980024i
\(68\) 52.7253i 0.775372i
\(69\) 29.6350 + 65.6552i 0.429492 + 0.951525i
\(70\) 94.1774 + 60.5241i 1.34539 + 0.864630i
\(71\) −79.0775 68.5210i −1.11377 0.965085i −0.114170 0.993461i \(-0.536421\pi\)
−0.999597 + 0.0283765i \(0.990966\pi\)
\(72\) −76.0656 + 10.2536i −1.05647 + 0.142411i
\(73\) 1.43235 9.96222i 0.0196212 0.136469i −0.977656 0.210211i \(-0.932585\pi\)
0.997277 + 0.0737419i \(0.0234941\pi\)
\(74\) 55.9006 25.5289i 0.755413 0.344986i
\(75\) −25.9094 + 86.8230i −0.345459 + 1.15764i
\(76\) 12.7075 + 27.8256i 0.167204 + 0.366126i
\(77\) −85.2113 132.591i −1.10664 1.72196i
\(78\) −4.55901 32.7313i −0.0584489 0.419632i
\(79\) 121.302 35.6175i 1.53547 0.450854i 0.598749 0.800937i \(-0.295665\pi\)
0.936719 + 0.350083i \(0.113847\pi\)
\(80\) 9.43994 + 32.1495i 0.117999 + 0.401868i
\(81\) −54.1138 + 60.2718i −0.668072 + 0.744097i
\(82\) −9.51762 + 20.8407i −0.116069 + 0.254155i
\(83\) 75.5751 10.8661i 0.910543 0.130916i 0.328904 0.944363i \(-0.393321\pi\)
0.581639 + 0.813447i \(0.302412\pi\)
\(84\) −46.2023 + 39.6796i −0.550027 + 0.472376i
\(85\) −132.524 + 152.941i −1.55910 + 1.79930i
\(86\) 52.6740 + 24.0554i 0.612488 + 0.279714i
\(87\) 12.9901 + 8.42932i 0.149312 + 0.0968887i
\(88\) 18.2403 126.864i 0.207276 1.44164i
\(89\) 48.9382 + 76.1493i 0.549867 + 0.855610i 0.999289 0.0377095i \(-0.0120062\pi\)
−0.449421 + 0.893320i \(0.648370\pi\)
\(90\) 80.3609 + 52.6507i 0.892899 + 0.585008i
\(91\) −52.6557 60.7680i −0.578635 0.667780i
\(92\) 13.0949 + 44.5972i 0.142336 + 0.484753i
\(93\) −105.316 + 90.4481i −1.13243 + 0.972560i
\(94\) −1.72421 + 11.9921i −0.0183427 + 0.127576i
\(95\) 33.0782 112.654i 0.348191 1.18583i
\(96\) −82.8992 0.365097i −0.863533 0.00380309i
\(97\) −11.6706 −0.120316 −0.0601579 0.998189i \(-0.519160\pi\)
−0.0601579 + 0.998189i \(0.519160\pi\)
\(98\) 24.6844 84.0673i 0.251882 0.857830i
\(99\) −72.1219 114.427i −0.728504 1.15583i
\(100\) −24.2869 + 53.1809i −0.242869 + 0.531809i
\(101\) 51.7177 + 23.6187i 0.512056 + 0.233848i 0.654649 0.755933i \(-0.272817\pi\)
−0.142593 + 0.989781i \(0.545544\pi\)
\(102\) 63.0356 + 99.0417i 0.617996 + 0.970997i
\(103\) −71.1887 20.9029i −0.691152 0.202941i −0.0827510 0.996570i \(-0.526371\pi\)
−0.608401 + 0.793630i \(0.708189\pi\)
\(104\) 65.3870i 0.628721i
\(105\) 233.753 + 1.02947i 2.22622 + 0.00980450i
\(106\) −118.360 34.7536i −1.11660 0.327864i
\(107\) −149.569 21.5048i −1.39784 0.200980i −0.598149 0.801385i \(-0.704097\pi\)
−0.799696 + 0.600405i \(0.795006\pi\)
\(108\) −39.9485 + 33.7018i −0.369893 + 0.312054i
\(109\) 16.9234 4.96916i 0.155261 0.0455886i −0.203179 0.979142i \(-0.565127\pi\)
0.358439 + 0.933553i \(0.383309\pi\)
\(110\) −121.244 + 105.059i −1.10222 + 0.955081i
\(111\) 69.8494 107.643i 0.629274 0.969752i
\(112\) 39.7871 25.5696i 0.355242 0.228300i
\(113\) 80.5320 + 11.5788i 0.712672 + 0.102467i 0.489109 0.872223i \(-0.337322\pi\)
0.223563 + 0.974689i \(0.428231\pi\)
\(114\) −57.1372 37.0765i −0.501204 0.325232i
\(115\) 74.1095 162.277i 0.644431 1.41111i
\(116\) 7.55146 + 6.54338i 0.0650988 + 0.0564084i
\(117\) −44.7272 52.5461i −0.382284 0.449112i
\(118\) −7.49491 52.1283i −0.0635162 0.441765i
\(119\) 259.833 + 118.662i 2.18347 + 0.997158i
\(120\) 143.110 + 125.113i 1.19258 + 1.04261i
\(121\) 100.619 29.5444i 0.831562 0.244168i
\(122\) 12.1720 + 41.4540i 0.0997704 + 0.339787i
\(123\) 6.59968 + 47.3822i 0.0536559 + 0.385221i
\(124\) −75.3573 + 48.4292i −0.607720 + 0.390558i
\(125\) 35.1583 16.0562i 0.281266 0.128450i
\(126\) 39.3497 129.773i 0.312299 1.02994i
\(127\) 56.4953 + 123.707i 0.444845 + 0.974074i 0.990684 + 0.136184i \(0.0434837\pi\)
−0.545839 + 0.837890i \(0.683789\pi\)
\(128\) −27.2934 3.92420i −0.213230 0.0306578i
\(129\) 119.757 16.6804i 0.928345 0.129306i
\(130\) −53.5971 + 61.8544i −0.412286 + 0.475803i
\(131\) −29.9453 + 46.5958i −0.228590 + 0.355693i −0.936535 0.350575i \(-0.885986\pi\)
0.707945 + 0.706268i \(0.249623\pi\)
\(132\) −35.9062 79.5488i −0.272017 0.602643i
\(133\) −165.725 −1.24605
\(134\) 21.7756 + 93.7666i 0.162504 + 0.699751i
\(135\) 200.588 + 2.65036i 1.48583 + 0.0196323i
\(136\) 96.4951 + 211.295i 0.709523 + 1.55364i
\(137\) 4.39446 6.83792i 0.0320764 0.0499118i −0.824845 0.565359i \(-0.808738\pi\)
0.856921 + 0.515447i \(0.172374\pi\)
\(138\) −77.9162 68.1179i −0.564610 0.493608i
\(139\) 3.93456 + 27.3655i 0.0283062 + 0.196874i 0.999068 0.0431724i \(-0.0137465\pi\)
−0.970761 + 0.240046i \(0.922837\pi\)
\(140\) 149.296 + 21.4656i 1.06640 + 0.153326i
\(141\) 10.4076 + 23.0577i 0.0738128 + 0.163530i
\(142\) 144.244 + 42.3537i 1.01580 + 0.298266i
\(143\) 104.816 47.8678i 0.732978 0.334740i
\(144\) 34.3367 21.6419i 0.238449 0.150291i
\(145\) −5.45794 37.9608i −0.0376410 0.261799i
\(146\) 4.07395 + 13.8746i 0.0279038 + 0.0950316i
\(147\) −50.7687 175.762i −0.345366 1.19566i
\(148\) 54.2216 62.5750i 0.366362 0.422804i
\(149\) −102.252 46.6970i −0.686256 0.313403i 0.0415982 0.999134i \(-0.486755\pi\)
−0.727854 + 0.685732i \(0.759482\pi\)
\(150\) −17.9587 128.934i −0.119724 0.859558i
\(151\) 44.5848 + 51.4536i 0.295264 + 0.340752i 0.883926 0.467626i \(-0.154891\pi\)
−0.588663 + 0.808379i \(0.700345\pi\)
\(152\) −101.850 88.2535i −0.670065 0.580615i
\(153\) 222.079 + 103.794i 1.45150 + 0.678391i
\(154\) 190.500 + 122.427i 1.23701 + 0.794980i
\(155\) 340.315 + 48.9299i 2.19558 + 0.315677i
\(156\) −23.9071 37.5629i −0.153251 0.240788i
\(157\) −206.172 132.499i −1.31320 0.843942i −0.318616 0.947884i \(-0.603218\pi\)
−0.994583 + 0.103942i \(0.966854\pi\)
\(158\) −137.272 + 118.947i −0.868813 + 0.752831i
\(159\) −247.459 + 71.4783i −1.55635 + 0.449549i
\(160\) 134.450 + 155.163i 0.840311 + 0.969771i
\(161\) −249.249 35.8365i −1.54813 0.222587i
\(162\) 34.7489 111.067i 0.214499 0.685601i
\(163\) −60.1436 −0.368979 −0.184490 0.982834i \(-0.559063\pi\)
−0.184490 + 0.982834i \(0.559063\pi\)
\(164\) 30.8687i 0.188224i
\(165\) −95.7908 + 320.997i −0.580550 + 1.94544i
\(166\) −92.2844 + 59.3076i −0.555930 + 0.357275i
\(167\) −53.3708 24.3736i −0.319586 0.145950i 0.249162 0.968462i \(-0.419845\pi\)
−0.568748 + 0.822512i \(0.692572\pi\)
\(168\) 112.534 243.572i 0.669848 1.44983i
\(169\) −92.7184 + 59.5865i −0.548630 + 0.352583i
\(170\) 81.9147 278.976i 0.481851 1.64103i
\(171\) −142.217 1.25270i −0.831680 0.00732575i
\(172\) 78.0194 0.453601
\(173\) −51.6876 + 176.032i −0.298772 + 1.01753i 0.664117 + 0.747629i \(0.268808\pi\)
−0.962889 + 0.269897i \(0.913011\pi\)
\(174\) −22.0079 3.26325i −0.126482 0.0187543i
\(175\) −207.419 239.374i −1.18525 1.36785i
\(176\) 19.0949 + 65.0312i 0.108494 + 0.369496i
\(177\) −71.6456 83.4230i −0.404778 0.471316i
\(178\) −109.407 70.3117i −0.614647 0.395010i
\(179\) −31.7214 49.3595i −0.177214 0.275751i 0.741271 0.671206i \(-0.234223\pi\)
−0.918485 + 0.395455i \(0.870587\pi\)
\(180\) 127.957 + 19.5492i 0.710870 + 0.108607i
\(181\) 187.029 + 120.197i 1.03331 + 0.664069i 0.943324 0.331874i \(-0.107681\pi\)
0.0899880 + 0.995943i \(0.471317\pi\)
\(182\) 105.085 + 47.9909i 0.577392 + 0.263686i
\(183\) 67.9171 + 59.3762i 0.371132 + 0.324460i
\(184\) −134.097 154.756i −0.728788 0.841066i
\(185\) −314.562 + 45.2271i −1.70033 + 0.244471i
\(186\) 83.6553 181.065i 0.449760 0.973468i
\(187\) −268.066 + 309.365i −1.43351 + 1.65436i
\(188\) 4.59885 + 15.6623i 0.0244620 + 0.0833099i
\(189\) −76.1778 272.716i −0.403057 1.44294i
\(190\) 24.0068 + 166.971i 0.126352 + 0.878795i
\(191\) 99.1835 + 154.333i 0.519286 + 0.808024i 0.997533 0.0702011i \(-0.0223641\pi\)
−0.478247 + 0.878225i \(0.658728\pi\)
\(192\) 157.885 71.2649i 0.822317 0.371172i
\(193\) −248.622 73.0019i −1.28820 0.378248i −0.435279 0.900296i \(-0.643350\pi\)
−0.852916 + 0.522047i \(0.825168\pi\)
\(194\) 15.2525 6.96557i 0.0786209 0.0359050i
\(195\) −25.0659 + 169.049i −0.128543 + 0.866916i
\(196\) −16.8000 116.846i −0.0857141 0.596154i
\(197\) 7.51438 + 6.51125i 0.0381441 + 0.0330520i 0.673724 0.738983i \(-0.264694\pi\)
−0.635580 + 0.772035i \(0.719239\pi\)
\(198\) 162.552 + 106.501i 0.820971 + 0.537882i
\(199\) 164.003 + 359.117i 0.824136 + 1.80461i 0.527307 + 0.849675i \(0.323202\pi\)
0.296829 + 0.954931i \(0.404071\pi\)
\(200\) 257.569i 1.28785i
\(201\) 143.484 + 140.760i 0.713851 + 0.700298i
\(202\) −81.6870 −0.404391
\(203\) −49.2412 + 22.4877i −0.242567 + 0.110777i
\(204\) 132.688 + 86.1016i 0.650432 + 0.422066i
\(205\) 77.5878 89.5411i 0.378477 0.436786i
\(206\) 105.513 15.1705i 0.512199 0.0736431i
\(207\) −213.622 32.6372i −1.03199 0.157668i
\(208\) 14.3639 + 31.4525i 0.0690570 + 0.151214i
\(209\) 66.9098 227.874i 0.320143 1.09031i
\(210\) −306.108 + 138.169i −1.45766 + 0.657947i
\(211\) 314.195 201.921i 1.48907 0.956970i 0.492853 0.870113i \(-0.335954\pi\)
0.996221 0.0868569i \(-0.0276823\pi\)
\(212\) −164.510 + 23.6530i −0.775991 + 0.111571i
\(213\) 301.575 87.1095i 1.41584 0.408965i
\(214\) 208.309 61.1649i 0.973405 0.285817i
\(215\) −226.311 196.100i −1.05261 0.912093i
\(216\) 98.4127 208.171i 0.455614 0.963753i
\(217\) −69.0651 480.358i −0.318272 2.21363i
\(218\) −19.1515 + 16.5949i −0.0878511 + 0.0761234i
\(219\) 22.7318 + 19.8732i 0.103798 + 0.0907451i
\(220\) −89.7922 + 196.618i −0.408146 + 0.893716i
\(221\) −112.904 + 175.683i −0.510879 + 0.794944i
\(222\) −27.0409 + 182.368i −0.121806 + 0.821479i
\(223\) −279.023 + 179.317i −1.25123 + 0.804114i −0.987058 0.160363i \(-0.948734\pi\)
−0.264168 + 0.964477i \(0.585097\pi\)
\(224\) 156.677 243.793i 0.699449 1.08836i
\(225\) −176.188 206.987i −0.783056 0.919944i
\(226\) −112.159 + 32.9328i −0.496278 + 0.145720i
\(227\) −55.5963 + 48.1745i −0.244918 + 0.212222i −0.768666 0.639651i \(-0.779079\pi\)
0.523748 + 0.851873i \(0.324533\pi\)
\(228\) −90.7774 13.4601i −0.398146 0.0590357i
\(229\) −58.0946 17.0581i −0.253688 0.0744896i 0.152416 0.988316i \(-0.451295\pi\)
−0.406104 + 0.913827i \(0.633113\pi\)
\(230\) 256.314i 1.11441i
\(231\) 472.830 + 2.08239i 2.04688 + 0.00901469i
\(232\) −42.2375 12.4021i −0.182058 0.0534572i
\(233\) −16.8153 26.1651i −0.0721687 0.112297i 0.803293 0.595584i \(-0.203079\pi\)
−0.875462 + 0.483287i \(0.839443\pi\)
\(234\) 89.8164 + 41.9778i 0.383831 + 0.179392i
\(235\) 26.0268 56.9907i 0.110752 0.242514i
\(236\) −38.3617 59.6920i −0.162550 0.252932i
\(237\) −108.454 + 363.432i −0.457612 + 1.53347i
\(238\) −410.401 −1.72437
\(239\) 4.78144i 0.0200060i 0.999950 + 0.0100030i \(0.00318411\pi\)
−0.999950 + 0.0100030i \(0.996816\pi\)
\(240\) −96.3227 28.7443i −0.401345 0.119768i
\(241\) −16.3685 + 113.846i −0.0679192 + 0.472389i 0.927268 + 0.374398i \(0.122151\pi\)
−0.995187 + 0.0979907i \(0.968758\pi\)
\(242\) −113.866 + 98.6658i −0.470522 + 0.407710i
\(243\) −63.3106 234.608i −0.260538 0.965464i
\(244\) 38.1194 + 43.9921i 0.156227 + 0.180296i
\(245\) −244.959 + 381.163i −0.999831 + 1.55577i
\(246\) −36.9050 57.9853i −0.150021 0.235712i
\(247\) 17.2430 119.927i 0.0698095 0.485536i
\(248\) 213.359 331.993i 0.860320 1.33868i
\(249\) −96.0703 + 207.936i −0.385825 + 0.835085i
\(250\) −36.3656 + 41.9681i −0.145462 + 0.167872i
\(251\) −203.467 + 176.305i −0.810626 + 0.702411i −0.958031 0.286665i \(-0.907453\pi\)
0.147405 + 0.989076i \(0.452908\pi\)
\(252\) −24.4081 181.070i −0.0968575 0.718532i
\(253\) 149.907 328.251i 0.592518 1.29743i
\(254\) −147.668 127.955i −0.581371 0.503761i
\(255\) −168.475 583.264i −0.660687 2.28731i
\(256\) 259.621 76.2316i 1.01414 0.297780i
\(257\) −18.4676 + 2.65524i −0.0718583 + 0.0103317i −0.178150 0.984003i \(-0.557011\pi\)
0.106292 + 0.994335i \(0.466102\pi\)
\(258\) −146.555 + 93.2759i −0.568044 + 0.361535i
\(259\) 186.344 + 408.036i 0.719474 + 1.57543i
\(260\) −31.0672 + 105.805i −0.119489 + 0.406943i
\(261\) −42.4263 + 18.9256i −0.162553 + 0.0725119i
\(262\) 11.3253 78.7692i 0.0432263 0.300646i
\(263\) −237.337 + 34.1240i −0.902424 + 0.129749i −0.577880 0.816122i \(-0.696120\pi\)
−0.324544 + 0.945871i \(0.605211\pi\)
\(264\) 289.479 + 253.076i 1.09651 + 0.958620i
\(265\) 536.646 + 344.882i 2.02508 + 1.30144i
\(266\) 216.588 98.9123i 0.814240 0.371851i
\(267\) −271.554 1.19595i −1.01706 0.00447922i
\(268\) 79.1686 + 102.730i 0.295405 + 0.383320i
\(269\) 317.885i 1.18173i 0.806771 + 0.590864i \(0.201213\pi\)
−0.806771 + 0.590864i \(0.798787\pi\)
\(270\) −263.732 + 116.256i −0.976784 + 0.430578i
\(271\) 15.2431 + 9.79617i 0.0562478 + 0.0361482i 0.568462 0.822709i \(-0.307538\pi\)
−0.512215 + 0.858857i \(0.671175\pi\)
\(272\) −92.8322 80.4396i −0.341295 0.295734i
\(273\) 238.916 33.2777i 0.875151 0.121896i
\(274\) −1.66198 + 11.5594i −0.00606563 + 0.0421874i
\(275\) 412.886 188.559i 1.50140 0.685668i
\(276\) −133.617 39.8736i −0.484121 0.144470i
\(277\) 58.1091 + 127.241i 0.209780 + 0.459354i 0.985048 0.172278i \(-0.0551126\pi\)
−0.775268 + 0.631632i \(0.782385\pi\)
\(278\) −21.4751 33.4159i −0.0772485 0.120201i
\(279\) −55.6373 412.742i −0.199417 1.47936i
\(280\) −637.585 + 187.212i −2.27709 + 0.668614i
\(281\) −59.6691 203.214i −0.212346 0.723183i −0.994924 0.100630i \(-0.967914\pi\)
0.782578 0.622552i \(-0.213904\pi\)
\(282\) −27.3637 23.9226i −0.0970343 0.0848318i
\(283\) 110.493 241.946i 0.390435 0.854934i −0.607716 0.794154i \(-0.707914\pi\)
0.998151 0.0607793i \(-0.0193586\pi\)
\(284\) 200.486 28.8255i 0.705937 0.101498i
\(285\) 229.487 + 267.211i 0.805217 + 0.937581i
\(286\) −108.415 + 125.118i −0.379074 + 0.437474i
\(287\) −152.123 69.4721i −0.530045 0.242063i
\(288\) 136.295 208.027i 0.473246 0.722317i
\(289\) 64.4515 448.270i 0.223016 1.55111i
\(290\) 29.7898 + 46.3538i 0.102723 + 0.159841i
\(291\) 19.0584 29.3702i 0.0654928 0.100929i
\(292\) 12.7585 + 14.7241i 0.0436936 + 0.0504251i
\(293\) −21.7236 73.9836i −0.0741418 0.252504i 0.914080 0.405535i \(-0.132915\pi\)
−0.988221 + 0.153031i \(0.951097\pi\)
\(294\) 171.253 + 199.404i 0.582494 + 0.678246i
\(295\) −38.7583 + 269.570i −0.131384 + 0.913797i
\(296\) −102.769 + 350.001i −0.347194 + 1.18243i
\(297\) 405.744 + 5.36109i 1.36614 + 0.0180508i
\(298\) 161.505 0.541964
\(299\) 51.8664 176.641i 0.173466 0.590771i
\(300\) −94.1737 147.966i −0.313912 0.493220i
\(301\) −175.588 + 384.484i −0.583348 + 1.27735i
\(302\) −88.9782 40.6350i −0.294630 0.134553i
\(303\) −143.895 + 91.5825i −0.474900 + 0.302253i
\(304\) 68.3789 + 20.0779i 0.224931 + 0.0660456i
\(305\) 223.420i 0.732526i
\(306\) −352.186 3.10219i −1.15093 0.0101379i
\(307\) −84.0375 24.6756i −0.273738 0.0803767i 0.141983 0.989869i \(-0.454652\pi\)
−0.415720 + 0.909493i \(0.636470\pi\)
\(308\) 301.993 + 43.4201i 0.980498 + 0.140974i
\(309\) 168.857 145.018i 0.546462 0.469314i
\(310\) −473.965 + 139.169i −1.52892 + 0.448931i
\(311\) −388.101 + 336.291i −1.24791 + 1.08132i −0.254460 + 0.967083i \(0.581898\pi\)
−0.993453 + 0.114240i \(0.963557\pi\)
\(312\) 164.552 + 106.778i 0.527411 + 0.342238i
\(313\) −55.8794 + 35.9115i −0.178529 + 0.114733i −0.626853 0.779138i \(-0.715657\pi\)
0.448324 + 0.893871i \(0.352021\pi\)
\(314\) 348.530 + 50.1110i 1.10997 + 0.159589i
\(315\) −384.314 + 586.580i −1.22005 + 1.86216i
\(316\) −101.662 + 222.610i −0.321716 + 0.704461i
\(317\) 127.177 + 110.199i 0.401189 + 0.347632i 0.831966 0.554826i \(-0.187215\pi\)
−0.430778 + 0.902458i \(0.641761\pi\)
\(318\) 280.745 241.110i 0.882846 0.758209i
\(319\) −11.0402 76.7863i −0.0346088 0.240709i
\(320\) −390.237 178.215i −1.21949 0.556923i
\(321\) 298.369 341.287i 0.929498 1.06320i
\(322\) 347.134 101.928i 1.07806 0.316546i
\(323\) 121.264 + 412.986i 0.375429 + 1.27859i
\(324\) −19.5771 155.570i −0.0604232 0.480154i
\(325\) 194.805 125.193i 0.599400 0.385211i
\(326\) 78.6023 35.8964i 0.241111 0.110112i
\(327\) −15.1309 + 50.7041i −0.0462720 + 0.155058i
\(328\) −56.4944 123.705i −0.172239 0.377151i
\(329\) −87.5344 12.5856i −0.266062 0.0382540i
\(330\) −66.3957 476.686i −0.201199 1.44450i
\(331\) 308.060 355.520i 0.930695 1.07408i −0.0663911 0.997794i \(-0.521148\pi\)
0.997086 0.0762855i \(-0.0243061\pi\)
\(332\) −79.9067 + 124.337i −0.240683 + 0.374510i
\(333\) 156.827 + 351.565i 0.470951 + 1.05575i
\(334\) 84.2981 0.252390
\(335\) 28.5641 496.977i 0.0852661 1.48351i
\(336\) −0.624871 + 141.884i −0.00185974 + 0.422273i
\(337\) −22.7076 49.7227i −0.0673816 0.147545i 0.872945 0.487819i \(-0.162207\pi\)
−0.940326 + 0.340274i \(0.889480\pi\)
\(338\) 85.6106 133.213i 0.253286 0.394120i
\(339\) −160.649 + 183.758i −0.473892 + 0.542059i
\(340\) −55.7503 387.752i −0.163972 1.14045i
\(341\) 688.382 + 98.9744i 2.01871 + 0.290247i
\(342\) 186.613 83.2445i 0.545651 0.243405i
\(343\) 120.574 + 35.4037i 0.351528 + 0.103218i
\(344\) −312.660 + 142.787i −0.908896 + 0.415079i
\(345\) 287.363 + 451.506i 0.832937 + 1.30871i
\(346\) −37.5128 260.907i −0.108418 0.754067i
\(347\) 35.1578 + 119.736i 0.101319 + 0.345062i 0.994513 0.104610i \(-0.0333593\pi\)
−0.893194 + 0.449671i \(0.851541\pi\)
\(348\) −28.7987 + 8.31847i −0.0827549 + 0.0239037i
\(349\) 65.3653 75.4356i 0.187293 0.216148i −0.654336 0.756204i \(-0.727052\pi\)
0.841629 + 0.540056i \(0.181597\pi\)
\(350\) 413.948 + 189.044i 1.18271 + 0.540124i
\(351\) 205.278 26.7513i 0.584837 0.0762146i
\(352\) 271.962 + 313.861i 0.772620 + 0.891651i
\(353\) 419.783 + 363.744i 1.18919 + 1.03044i 0.998812 + 0.0487262i \(0.0155162\pi\)
0.190376 + 0.981711i \(0.439029\pi\)
\(354\) 143.425 + 66.2649i 0.405155 + 0.187189i
\(355\) −654.003 420.302i −1.84226 1.18395i
\(356\) −173.440 24.9369i −0.487190 0.0700473i
\(357\) −722.937 + 460.117i −2.02503 + 1.28884i
\(358\) 70.9170 + 45.5756i 0.198092 + 0.127306i
\(359\) 142.702 123.652i 0.397499 0.344435i −0.433060 0.901365i \(-0.642566\pi\)
0.830559 + 0.556930i \(0.188021\pi\)
\(360\) −548.559 + 155.837i −1.52378 + 0.432879i
\(361\) 72.8730 + 84.0999i 0.201864 + 0.232964i
\(362\) −316.169 45.4583i −0.873396 0.125575i
\(363\) −89.9617 + 301.464i −0.247828 + 0.830478i
\(364\) 155.650 0.427610
\(365\) 74.7786i 0.204873i
\(366\) −124.200 37.0633i −0.339344 0.101266i
\(367\) 47.8106 30.7260i 0.130274 0.0837221i −0.473881 0.880589i \(-0.657147\pi\)
0.604155 + 0.796867i \(0.293511\pi\)
\(368\) 98.4994 + 44.9832i 0.267661 + 0.122237i
\(369\) −130.019 60.7675i −0.352356 0.164682i
\(370\) 384.110 246.852i 1.03813 0.667169i
\(371\) 253.678 863.947i 0.683767 2.32870i
\(372\) 1.18351 268.730i 0.00318149 0.722392i
\(373\) 307.670 0.824852 0.412426 0.910991i \(-0.364682\pi\)
0.412426 + 0.910991i \(0.364682\pi\)
\(374\) 165.695 564.306i 0.443035 1.50884i
\(375\) −17.0072 + 114.699i −0.0453525 + 0.305865i
\(376\) −47.0940 54.3494i −0.125250 0.144546i
\(377\) −11.1499 37.9732i −0.0295754 0.100725i
\(378\) 262.327 + 310.949i 0.693987 + 0.822617i
\(379\) −548.160 352.281i −1.44633 0.929501i −0.999389 0.0349376i \(-0.988877\pi\)
−0.446942 0.894563i \(-0.647487\pi\)
\(380\) 122.876 + 191.198i 0.323357 + 0.503153i
\(381\) −403.579 59.8412i −1.05926 0.157064i
\(382\) −221.737 142.501i −0.580462 0.373040i
\(383\) −259.630 118.569i −0.677884 0.309579i 0.0465575 0.998916i \(-0.485175\pi\)
−0.724441 + 0.689336i \(0.757902\pi\)
\(384\) 54.4463 62.2781i 0.141787 0.162183i
\(385\) −766.858 885.002i −1.99184 2.29871i
\(386\) 368.497 52.9819i 0.954655 0.137259i
\(387\) −153.587 + 328.618i −0.396866 + 0.849142i
\(388\) 14.7943 17.0736i 0.0381298 0.0440041i
\(389\) 115.555 + 393.543i 0.297056 + 1.01168i 0.963852 + 0.266439i \(0.0858471\pi\)
−0.666796 + 0.745240i \(0.732335\pi\)
\(390\) −68.1371 235.892i −0.174710 0.604851i
\(391\) 93.0745 + 647.348i 0.238042 + 1.65562i
\(392\) 281.171 + 437.511i 0.717273 + 1.11610i
\(393\) −68.3613 151.452i −0.173947 0.385374i
\(394\) −13.7068 4.02469i −0.0347889 0.0102149i
\(395\) 854.416 390.199i 2.16308 0.987845i
\(396\) 258.828 + 39.5437i 0.653605 + 0.0998579i
\(397\) 8.24425 + 57.3400i 0.0207664 + 0.144433i 0.997567 0.0697189i \(-0.0222102\pi\)
−0.976800 + 0.214152i \(0.931301\pi\)
\(398\) −428.674 371.448i −1.07707 0.933287i
\(399\) 270.633 417.063i 0.678278 1.04527i
\(400\) 56.5815 + 123.896i 0.141454 + 0.309740i
\(401\) 506.500i 1.26309i 0.775338 + 0.631546i \(0.217579\pi\)
−0.775338 + 0.631546i \(0.782421\pi\)
\(402\) −271.532 98.3227i −0.675454 0.244584i
\(403\) 354.798 0.880392
\(404\) −100.113 + 45.7202i −0.247805 + 0.113169i
\(405\) −334.234 + 500.469i −0.825268 + 1.23573i
\(406\) 50.9321 58.7787i 0.125448 0.144775i
\(407\) −636.288 + 91.4844i −1.56336 + 0.224777i
\(408\) −689.322 102.210i −1.68951 0.250515i
\(409\) −318.315 697.013i −0.778276 1.70419i −0.707520 0.706694i \(-0.750186\pi\)
−0.0707567 0.997494i \(-0.522541\pi\)
\(410\) −47.9580 + 163.330i −0.116971 + 0.398366i
\(411\) 10.0320 + 22.2255i 0.0244088 + 0.0540767i
\(412\) 120.823 77.6480i 0.293259 0.188466i
\(413\) 380.501 54.7077i 0.921309 0.132464i
\(414\) 298.664 84.8455i 0.721410 0.204941i
\(415\) 544.304 159.822i 1.31158 0.385114i
\(416\) 160.120 + 138.745i 0.384904 + 0.333521i
\(417\) −75.2930 34.7867i −0.180559 0.0834214i
\(418\) 48.5604 + 337.745i 0.116173 + 0.808003i
\(419\) 208.097 180.317i 0.496652 0.430351i −0.370174 0.928962i \(-0.620702\pi\)
0.866826 + 0.498611i \(0.166156\pi\)
\(420\) −297.824 + 340.664i −0.709105 + 0.811106i
\(421\) −275.144 + 602.482i −0.653550 + 1.43107i 0.234863 + 0.972028i \(0.424536\pi\)
−0.888413 + 0.459045i \(0.848192\pi\)
\(422\) −290.108 + 451.417i −0.687461 + 1.06971i
\(423\) −75.0226 11.4620i −0.177359 0.0270969i
\(424\) 615.980 395.866i 1.45278 0.933647i
\(425\) −444.748 + 692.041i −1.04647 + 1.62833i
\(426\) −342.140 + 293.838i −0.803145 + 0.689760i
\(427\) −302.586 + 88.8472i −0.708632 + 0.208073i
\(428\) 221.063 191.552i 0.516502 0.447552i
\(429\) −50.7028 + 341.948i −0.118188 + 0.797081i
\(430\) 412.810 + 121.212i 0.960023 + 0.281888i
\(431\) 131.321i 0.304690i −0.988327 0.152345i \(-0.951318\pi\)
0.988327 0.152345i \(-0.0486824\pi\)
\(432\) −1.60872 + 121.753i −0.00372389 + 0.281836i
\(433\) 540.776 + 158.786i 1.24891 + 0.366712i 0.838354 0.545126i \(-0.183518\pi\)
0.410551 + 0.911838i \(0.365336\pi\)
\(434\) 376.961 + 586.563i 0.868575 + 1.35153i
\(435\) 104.445 + 48.2554i 0.240103 + 0.110932i
\(436\) −14.1834 + 31.0573i −0.0325308 + 0.0712324i
\(437\) −205.139 319.203i −0.469427 0.730442i
\(438\) −41.5696 12.4051i −0.0949078 0.0283220i
\(439\) 550.425 1.25382 0.626908 0.779094i \(-0.284320\pi\)
0.626908 + 0.779094i \(0.284320\pi\)
\(440\) 952.271i 2.16425i
\(441\) 525.229 + 159.259i 1.19099 + 0.361132i
\(442\) 42.7004 296.988i 0.0966072 0.671918i
\(443\) 251.521 217.944i 0.567768 0.491974i −0.323021 0.946392i \(-0.604698\pi\)
0.890788 + 0.454418i \(0.150153\pi\)
\(444\) 68.9309 + 238.640i 0.155250 + 0.537477i
\(445\) 440.419 + 508.271i 0.989706 + 1.14218i
\(446\) 257.633 400.885i 0.577653 0.898846i
\(447\) 284.497 181.070i 0.636459 0.405078i
\(448\) −86.1782 + 599.382i −0.192362 + 1.33791i
\(449\) −61.5180 + 95.7239i −0.137011 + 0.213193i −0.902978 0.429686i \(-0.858624\pi\)
0.765967 + 0.642880i \(0.222261\pi\)
\(450\) 353.801 + 165.357i 0.786224 + 0.367460i
\(451\) 156.943 181.122i 0.347989 0.401600i
\(452\) −119.026 + 103.137i −0.263332 + 0.228178i
\(453\) −202.296 + 28.1770i −0.446569 + 0.0622008i
\(454\) 43.9066 96.1421i 0.0967107 0.211767i
\(455\) −451.495 391.222i −0.992296 0.859830i
\(456\) 388.421 112.195i 0.851801 0.246042i
\(457\) 383.596 112.634i 0.839379 0.246464i 0.166338 0.986069i \(-0.446806\pi\)
0.673041 + 0.739605i \(0.264988\pi\)
\(458\) 86.1054 12.3801i 0.188003 0.0270308i
\(459\) −623.867 + 389.385i −1.35919 + 0.848334i
\(460\) 143.459 + 314.130i 0.311866 + 0.682892i
\(461\) 166.254 566.208i 0.360637 1.22822i −0.556904 0.830577i \(-0.688011\pi\)
0.917541 0.397640i \(-0.130171\pi\)
\(462\) −619.189 + 279.485i −1.34024 + 0.604946i
\(463\) −38.4045 + 267.109i −0.0829471 + 0.576910i 0.905385 + 0.424592i \(0.139583\pi\)
−0.988332 + 0.152317i \(0.951326\pi\)
\(464\) 23.0415 3.31287i 0.0496585 0.00713981i
\(465\) −678.879 + 776.531i −1.45995 + 1.66996i
\(466\) 37.5926 + 24.1593i 0.0806709 + 0.0518440i
\(467\) −321.219 + 146.696i −0.687834 + 0.314123i −0.728497 0.685050i \(-0.759781\pi\)
0.0406621 + 0.999173i \(0.487053\pi\)
\(468\) 133.571 + 1.17655i 0.285409 + 0.00251399i
\(469\) −684.432 + 158.947i −1.45934 + 0.338906i
\(470\) 90.0156i 0.191523i
\(471\) 670.130 302.478i 1.42278 0.642204i
\(472\) 262.978 + 169.006i 0.557157 + 0.358063i
\(473\) −457.778 396.667i −0.967817 0.838619i
\(474\) −75.1730 539.702i −0.158593 1.13861i
\(475\) 67.9227 472.413i 0.142995 0.994553i
\(476\) −502.975 + 229.701i −1.05667 + 0.482566i
\(477\) 224.224 739.479i 0.470072 1.55027i
\(478\) −2.85378 6.24890i −0.00597025 0.0130730i
\(479\) −133.310 207.434i −0.278309 0.433057i 0.673756 0.738954i \(-0.264680\pi\)
−0.952065 + 0.305897i \(0.901044\pi\)
\(480\) −610.043 + 84.9704i −1.27092 + 0.177022i
\(481\) −314.664 + 92.3938i −0.654188 + 0.192087i
\(482\) −46.5561 158.555i −0.0965894 0.328953i
\(483\) 497.214 568.735i 1.02943 1.17751i
\(484\) −84.3281 + 184.653i −0.174232 + 0.381514i
\(485\) −85.8281 + 12.3402i −0.176965 + 0.0254437i
\(486\) 222.766 + 268.824i 0.458366 + 0.553136i
\(487\) −628.630 + 725.478i −1.29082 + 1.48969i −0.517487 + 0.855691i \(0.673132\pi\)
−0.773335 + 0.633997i \(0.781413\pi\)
\(488\) −233.274 106.533i −0.478021 0.218305i
\(489\) 98.2158 151.357i 0.200850 0.309524i
\(490\) 92.6432 644.348i 0.189068 1.31500i
\(491\) 346.077 + 538.507i 0.704842 + 1.09675i 0.990378 + 0.138387i \(0.0441918\pi\)
−0.285537 + 0.958368i \(0.592172\pi\)
\(492\) −77.6841 50.4093i −0.157894 0.102458i
\(493\) 92.0696 + 106.254i 0.186754 + 0.215525i
\(494\) 49.0431 + 167.026i 0.0992776 + 0.338108i
\(495\) −651.391 765.262i −1.31594 1.54598i
\(496\) −29.6996 + 206.565i −0.0598782 + 0.416462i
\(497\) −309.153 + 1052.88i −0.622039 + 2.11847i
\(498\) 1.44936 329.093i 0.00291036 0.660829i
\(499\) −812.640 −1.62854 −0.814268 0.580489i \(-0.802861\pi\)
−0.814268 + 0.580489i \(0.802861\pi\)
\(500\) −21.0791 + 71.7887i −0.0421581 + 0.143577i
\(501\) 148.494 94.5100i 0.296396 0.188643i
\(502\) 160.686 351.853i 0.320092 0.700903i
\(503\) 372.699 + 170.206i 0.740953 + 0.338382i 0.749876 0.661578i \(-0.230113\pi\)
−0.00892323 + 0.999960i \(0.502840\pi\)
\(504\) 429.199 + 680.961i 0.851586 + 1.35111i
\(505\) 405.315 + 119.011i 0.802605 + 0.235666i
\(506\) 518.465i 1.02464i
\(507\) 1.45618 330.640i 0.00287214 0.652151i
\(508\) −252.595 74.1684i −0.497233 0.146001i
\(509\) 586.904 + 84.3841i 1.15305 + 0.165784i 0.692209 0.721697i \(-0.256638\pi\)
0.460844 + 0.887481i \(0.347547\pi\)
\(510\) 568.300 + 661.719i 1.11431 + 1.29749i
\(511\) −101.275 + 29.7371i −0.198190 + 0.0581939i
\(512\) −210.446 + 182.353i −0.411028 + 0.356158i
\(513\) 235.396 355.857i 0.458862 0.693679i
\(514\) 22.5507 14.4924i 0.0438729 0.0281954i
\(515\) −545.637 78.4508i −1.05949 0.152332i
\(516\) −127.407 + 196.343i −0.246914 + 0.380510i
\(517\) 52.6464 115.280i 0.101831 0.222978i
\(518\) −487.069 422.048i −0.940287 0.814764i
\(519\) −358.594 417.541i −0.690932 0.804510i
\(520\) −69.1384 480.868i −0.132958 0.924747i
\(521\) −548.352 250.424i −1.05250 0.480660i −0.187412 0.982281i \(-0.560010\pi\)
−0.865087 + 0.501621i \(0.832737\pi\)
\(522\) 44.1517 50.0560i 0.0845818 0.0958928i
\(523\) 518.071 152.119i 0.990575 0.290859i 0.253992 0.967206i \(-0.418256\pi\)
0.736583 + 0.676347i \(0.236438\pi\)
\(524\) −30.2071 102.876i −0.0576472 0.196328i
\(525\) 941.128 131.086i 1.79262 0.249688i
\(526\) 289.812 186.251i 0.550973 0.354089i
\(527\) −1146.51 + 523.595i −2.17555 + 0.993539i
\(528\) −194.839 58.1433i −0.369014 0.110120i
\(529\) −19.7478 43.2417i −0.0373305 0.0817423i
\(530\) −907.189 130.434i −1.71168 0.246102i
\(531\) 326.941 44.0713i 0.615707 0.0829969i
\(532\) 210.082 242.448i 0.394892 0.455729i
\(533\) 66.1013 102.856i 0.124018 0.192975i
\(534\) 355.610 160.513i 0.665937 0.300586i
\(535\) −1122.70 −2.09851
\(536\) −505.276 266.796i −0.942680 0.497754i
\(537\) 176.019 + 0.775208i 0.327783 + 0.00144359i
\(538\) −189.728 415.447i −0.352655 0.772206i
\(539\) −495.497 + 771.008i −0.919289 + 1.43044i
\(540\) −258.153 + 290.090i −0.478062 + 0.537204i
\(541\) −22.4769 156.330i −0.0415469 0.288965i −0.999993 0.00369214i \(-0.998825\pi\)
0.958446 0.285273i \(-0.0920843\pi\)
\(542\) −25.7682 3.70491i −0.0475428 0.00683562i
\(543\) −607.909 + 274.393i −1.11954 + 0.505329i
\(544\) −722.174 212.049i −1.32753 0.389797i
\(545\) 119.204 54.4385i 0.218722 0.0998872i
\(546\) −292.380 + 186.087i −0.535495 + 0.340819i
\(547\) −83.0189 577.409i −0.151771 1.05559i −0.913249 0.407402i \(-0.866435\pi\)
0.761478 0.648191i \(-0.224474\pi\)
\(548\) 4.43288 + 15.0970i 0.00808920 + 0.0275493i
\(549\) −260.336 + 73.9571i −0.474200 + 0.134712i
\(550\) −427.064 + 492.858i −0.776480 + 0.896105i
\(551\) −74.1981 33.8851i −0.134661 0.0614975i
\(552\) 608.442 84.7474i 1.10225 0.153528i
\(553\) −868.234 1002.00i −1.57004 1.81193i
\(554\) −151.887 131.611i −0.274164 0.237564i
\(555\) 399.868 865.480i 0.720482 1.55942i
\(556\) −45.0221 28.9339i −0.0809749 0.0520394i
\(557\) −203.384 29.2422i −0.365141 0.0524994i −0.0426977 0.999088i \(-0.513595\pi\)
−0.322444 + 0.946589i \(0.604504\pi\)
\(558\) 319.056 + 506.209i 0.571785 + 0.907185i
\(559\) −259.963 167.068i −0.465051 0.298870i
\(560\) 265.566 230.114i 0.474224 0.410918i
\(561\) −340.788 1179.81i −0.607465 2.10305i
\(562\) 199.270 + 229.969i 0.354572 + 0.409198i
\(563\) 122.350 + 17.5912i 0.217317 + 0.0312455i 0.250113 0.968217i \(-0.419532\pi\)
−0.0327962 + 0.999462i \(0.510441\pi\)
\(564\) −46.9256 14.0034i −0.0832013 0.0248287i
\(565\) 604.491 1.06990
\(566\) 382.149i 0.675175i
\(567\) 810.716 + 253.643i 1.42983 + 0.447342i
\(568\) −750.686 + 482.436i −1.32163 + 0.849360i
\(569\) −258.062 117.853i −0.453536 0.207123i 0.175531 0.984474i \(-0.443836\pi\)
−0.629067 + 0.777351i \(0.716563\pi\)
\(570\) −459.402 212.252i −0.805968 0.372372i
\(571\) −138.815 + 89.2109i −0.243108 + 0.156236i −0.656521 0.754307i \(-0.727973\pi\)
0.413413 + 0.910544i \(0.364337\pi\)
\(572\) −62.8421 + 214.020i −0.109864 + 0.374162i
\(573\) −550.361 2.42385i −0.960491 0.00423010i
\(574\) 240.275 0.418597
\(575\) 204.310 695.815i 0.355321 1.21011i
\(576\) −78.4846 + 513.709i −0.136258 + 0.891856i
\(577\) −212.966 245.776i −0.369093 0.425956i 0.540573 0.841297i \(-0.318208\pi\)
−0.909666 + 0.415342i \(0.863662\pi\)
\(578\) 183.316 + 624.316i 0.317155 + 1.08013i
\(579\) 589.721 506.466i 1.01852 0.874725i
\(580\) 62.4536 + 40.1365i 0.107679 + 0.0692009i
\(581\) −432.905 673.613i −0.745103 1.15940i
\(582\) −7.37810 + 49.7592i −0.0126772 + 0.0854968i
\(583\) 1085.52 + 697.619i 1.86195 + 1.19660i
\(584\) −78.0767 35.6564i −0.133693 0.0610555i
\(585\) −384.494 339.141i −0.657254 0.579728i
\(586\) 72.5475 + 83.7243i 0.123801 + 0.142874i
\(587\) 703.427 101.138i 1.19834 0.172296i 0.485893 0.874018i \(-0.338495\pi\)
0.712450 + 0.701723i \(0.247586\pi\)
\(588\) 321.489 + 148.534i 0.546750 + 0.252609i
\(589\) 478.875 552.651i 0.813030 0.938287i
\(590\) −110.238 375.436i −0.186844 0.636333i
\(591\) −28.6573 + 8.27763i −0.0484895 + 0.0140061i
\(592\) −27.4521 190.933i −0.0463717 0.322522i
\(593\) 492.474 + 766.304i 0.830478 + 1.29225i 0.953970 + 0.299904i \(0.0969545\pi\)
−0.123491 + 0.992346i \(0.539409\pi\)
\(594\) −533.470 + 235.160i −0.898098 + 0.395892i
\(595\) 2036.33 + 597.921i 3.42241 + 1.00491i
\(596\) 197.936 90.3944i 0.332107 0.151668i
\(597\) −1171.57 173.716i −1.96243 0.290982i
\(598\) 37.6425 + 261.809i 0.0629473 + 0.437808i
\(599\) 865.763 + 750.188i 1.44535 + 1.25240i 0.914287 + 0.405067i \(0.132752\pi\)
0.531061 + 0.847334i \(0.321793\pi\)
\(600\) 648.197 + 420.616i 1.08033 + 0.701027i
\(601\) 46.0323 + 100.797i 0.0765929 + 0.167715i 0.944055 0.329788i \(-0.106977\pi\)
−0.867462 + 0.497504i \(0.834250\pi\)
\(602\) 607.284i 1.00878i
\(603\) −588.548 + 131.227i −0.976033 + 0.217623i
\(604\) −131.792 −0.218199
\(605\) 708.731 323.667i 1.17146 0.534986i
\(606\) 133.397 205.573i 0.220126 0.339229i
\(607\) 397.625 458.884i 0.655066 0.755986i −0.326897 0.945060i \(-0.606003\pi\)
0.981963 + 0.189074i \(0.0605486\pi\)
\(608\) 432.232 62.1456i 0.710908 0.102213i
\(609\) 23.8195 160.643i 0.0391125 0.263781i
\(610\) 133.347 + 291.990i 0.218602 + 0.478672i
\(611\) 18.2151 62.0350i 0.0298120 0.101530i
\(612\) −433.365 + 193.316i −0.708113 + 0.315876i
\(613\) −496.552 + 319.114i −0.810035 + 0.520578i −0.878876 0.477050i \(-0.841706\pi\)
0.0688410 + 0.997628i \(0.478070\pi\)
\(614\) 124.557 17.9086i 0.202861 0.0291671i
\(615\) 98.6360 + 341.480i 0.160384 + 0.555251i
\(616\) −1289.69 + 378.688i −2.09366 + 0.614753i
\(617\) 616.248 + 533.982i 0.998781 + 0.865449i 0.990911 0.134520i \(-0.0429493\pi\)
0.00787051 + 0.999969i \(0.497495\pi\)
\(618\) −134.127 + 290.307i −0.217034 + 0.469752i
\(619\) 133.631 + 929.427i 0.215883 + 1.50150i 0.753017 + 0.658001i \(0.228598\pi\)
−0.537134 + 0.843497i \(0.680493\pi\)
\(620\) −502.984 + 435.839i −0.811265 + 0.702965i
\(621\) 430.984 484.302i 0.694016 0.779875i
\(622\) 306.499 671.139i 0.492763 1.07900i
\(623\) 513.228 798.598i 0.823800 1.28186i
\(624\) −102.610 15.2146i −0.164438 0.0243823i
\(625\) −393.609 + 252.957i −0.629774 + 0.404731i
\(626\) 51.5957 80.2845i 0.0824213 0.128250i
\(627\) 464.201 + 540.508i 0.740352 + 0.862054i
\(628\) 455.195 133.657i 0.724833 0.212830i
\(629\) 880.472 762.933i 1.39980 1.21293i
\(630\) 152.166 995.983i 0.241534 1.58093i
\(631\) −219.099 64.3333i −0.347225 0.101954i 0.103470 0.994633i \(-0.467006\pi\)
−0.450695 + 0.892678i \(0.648824\pi\)
\(632\) 1078.16i 1.70595i
\(633\) −4.93454 + 1120.44i −0.00779548 + 1.77005i
\(634\) −231.981 68.1156i −0.365900 0.107438i
\(635\) 546.282 + 850.031i 0.860286 + 1.33863i
\(636\) 209.124 452.631i 0.328811 0.711683i
\(637\) −194.233 + 425.311i −0.304918 + 0.667678i
\(638\) 60.2581 + 93.7634i 0.0944484 + 0.146965i
\(639\) −273.259 + 901.193i −0.427635 + 1.41032i
\(640\) −204.870 −0.320110
\(641\) 383.963i 0.599006i 0.954095 + 0.299503i \(0.0968208\pi\)
−0.954095 + 0.299503i \(0.903179\pi\)
\(642\) −186.245 + 624.112i −0.290102 + 0.972137i
\(643\) −153.632 + 1068.54i −0.238931 + 1.66180i 0.418449 + 0.908240i \(0.362574\pi\)
−0.657380 + 0.753559i \(0.728335\pi\)
\(644\) 368.388 319.210i 0.572032 0.495668i
\(645\) 863.075 249.298i 1.33810 0.386509i
\(646\) −404.969 467.359i −0.626887 0.723467i
\(647\) 36.6260 56.9912i 0.0566090 0.0880853i −0.811795 0.583942i \(-0.801510\pi\)
0.868404 + 0.495857i \(0.165146\pi\)
\(648\) 363.171 + 587.612i 0.560448 + 0.906808i
\(649\) −78.3995 + 545.280i −0.120800 + 0.840185i
\(650\) −179.871 + 279.885i −0.276725 + 0.430592i
\(651\) 1321.65 + 610.626i 2.03019 + 0.937982i
\(652\) 76.2414 87.9873i 0.116935 0.134950i
\(653\) −130.957 + 113.475i −0.200546 + 0.173774i −0.749344 0.662181i \(-0.769631\pi\)
0.548798 + 0.835955i \(0.315086\pi\)
\(654\) −10.4877 75.2965i −0.0160363 0.115132i
\(655\) −170.954 + 374.338i −0.260999 + 0.571508i
\(656\) 54.3499 + 47.0944i 0.0828504 + 0.0717903i
\(657\) −87.1342 + 24.7534i −0.132624 + 0.0376764i
\(658\) 121.911 35.7964i 0.185275 0.0544018i
\(659\) −923.909 + 132.838i −1.40199 + 0.201575i −0.801469 0.598037i \(-0.795948\pi\)
−0.600517 + 0.799612i \(0.705039\pi\)
\(660\) −348.174 547.051i −0.527536 0.828865i
\(661\) −200.280 438.552i −0.302995 0.663467i 0.695487 0.718539i \(-0.255189\pi\)
−0.998482 + 0.0550713i \(0.982461\pi\)
\(662\) −190.416 + 648.497i −0.287637 + 0.979603i
\(663\) −257.746 571.028i −0.388758 0.861278i
\(664\) 92.6677 644.518i 0.139560 0.970660i
\(665\) −1218.77 + 175.233i −1.83274 + 0.263509i
\(666\) −414.788 365.862i −0.622805 0.549343i
\(667\) −104.266 67.0075i −0.156320 0.100461i
\(668\) 103.313 47.1816i 0.154661 0.0706311i
\(669\) 4.38216 995.017i 0.00655031 1.48732i
\(670\) 259.288 + 666.553i 0.386997 + 0.994855i
\(671\) 451.930i 0.673517i
\(672\) 357.673 + 792.411i 0.532251 + 1.17918i
\(673\) 738.249 + 474.444i 1.09695 + 0.704969i 0.958412 0.285388i \(-0.0921224\pi\)
0.138541 + 0.990357i \(0.455759\pi\)
\(674\) 59.3535 + 51.4301i 0.0880616 + 0.0763058i
\(675\) 808.621 105.378i 1.19796 0.156115i
\(676\) 30.3628 211.178i 0.0449153 0.312393i
\(677\) 1041.98 475.859i 1.53912 0.702893i 0.548077 0.836428i \(-0.315360\pi\)
0.991044 + 0.133535i \(0.0426328\pi\)
\(678\) 100.279 336.038i 0.147904 0.495631i
\(679\) 50.8439 + 111.333i 0.0748805 + 0.163965i
\(680\) 933.061 + 1451.87i 1.37215 + 2.13510i
\(681\) −30.4456 218.583i −0.0447072 0.320974i
\(682\) −958.725 + 281.507i −1.40576 + 0.412767i
\(683\) −20.4895 69.7807i −0.0299992 0.102168i 0.943133 0.332417i \(-0.107864\pi\)
−0.973132 + 0.230249i \(0.926046\pi\)
\(684\) 182.115 206.469i 0.266250 0.301855i
\(685\) 25.0875 54.9339i 0.0366241 0.0801955i
\(686\) −178.710 + 25.6946i −0.260510 + 0.0374557i
\(687\) 137.798 118.344i 0.200579 0.172262i
\(688\) 119.029 137.367i 0.173007 0.199661i
\(689\) 598.803 + 273.464i 0.869090 + 0.396900i
\(690\) −645.037 418.566i −0.934836 0.606617i
\(691\) −67.3736 + 468.594i −0.0975017 + 0.678139i 0.881184 + 0.472774i \(0.156747\pi\)
−0.978685 + 0.205365i \(0.934162\pi\)
\(692\) −192.004 298.764i −0.277463 0.431740i
\(693\) −777.382 + 1186.52i −1.12176 + 1.71215i
\(694\) −117.412 135.501i −0.169182 0.195246i
\(695\) 57.8710 + 197.091i 0.0832677 + 0.283584i
\(696\) 100.186 86.0419i 0.143945 0.123623i
\(697\) −61.8135 + 429.923i −0.0886851 + 0.616819i
\(698\) −40.4031 + 137.600i −0.0578841 + 0.197135i
\(699\) 93.3068 + 0.410933i 0.133486 + 0.000587887i
\(700\) 613.130 0.875899
\(701\) 106.074 361.255i 0.151318 0.515343i −0.848588 0.529055i \(-0.822547\pi\)
0.999906 + 0.0137120i \(0.00436480\pi\)
\(702\) −252.313 + 157.481i −0.359420 + 0.224331i
\(703\) −280.789 + 614.841i −0.399415 + 0.874597i
\(704\) −789.364 360.490i −1.12126 0.512060i
\(705\) 100.920 + 158.566i 0.143149 + 0.224916i
\(706\) −765.718 224.835i −1.08459 0.318463i
\(707\) 596.259i 0.843365i
\(708\) 212.866 + 0.937484i 0.300658 + 0.00132413i
\(709\) −337.586 99.1243i −0.476144 0.139809i 0.0348501 0.999393i \(-0.488905\pi\)
−0.510995 + 0.859584i \(0.670723\pi\)
\(710\) 1105.58 + 158.958i 1.55715 + 0.223885i
\(711\) −737.502 866.426i −1.03727 1.21860i
\(712\) 740.691 217.487i 1.04030 0.305459i
\(713\) 839.727 727.627i 1.17774 1.02052i
\(714\) 670.194 1032.81i 0.938647 1.44652i
\(715\) 720.221 462.858i 1.00730 0.647354i
\(716\) 112.422 + 16.1639i 0.157014 + 0.0225753i
\(717\) −12.0329 7.80819i −0.0167823 0.0108901i
\(718\) −112.698 + 246.773i −0.156960 + 0.343695i
\(719\) −945.066 818.905i −1.31442 1.13895i −0.980537 0.196334i \(-0.937096\pi\)
−0.333881 0.942615i \(-0.608358\pi\)
\(720\) 229.635 195.465i 0.318937 0.271479i
\(721\) 110.734 + 770.172i 0.153584 + 1.06820i
\(722\) −145.433 66.4170i −0.201431 0.0919903i
\(723\) −259.773 227.105i −0.359299 0.314115i
\(724\) −412.931 + 121.247i −0.570346 + 0.167469i
\(725\) −43.9213 149.582i −0.0605812 0.206321i
\(726\) −62.3554 447.679i −0.0858890 0.616637i
\(727\) 254.589 163.615i 0.350191 0.225054i −0.353705 0.935357i \(-0.615078\pi\)
0.703896 + 0.710303i \(0.251442\pi\)
\(728\) −623.762 + 284.863i −0.856816 + 0.391295i
\(729\) 693.800 + 223.792i 0.951714 + 0.306985i
\(730\) 44.6313 + 97.7289i 0.0611387 + 0.133875i
\(731\) 1086.61 + 156.231i 1.48647 + 0.213722i
\(732\) −172.960 + 24.0909i −0.236284 + 0.0329111i
\(733\) 81.7077 94.2957i 0.111470 0.128644i −0.697272 0.716806i \(-0.745603\pi\)
0.808743 + 0.588163i \(0.200149\pi\)
\(734\) −44.1454 + 68.6916i −0.0601436 + 0.0935853i
\(735\) −559.209 1238.91i −0.760829 1.68559i
\(736\) 663.509 0.901507
\(737\) 57.7789 1005.27i 0.0783974 1.36401i
\(738\) 206.192 + 1.81622i 0.279393 + 0.00246100i
\(739\) 222.087 + 486.303i 0.300524 + 0.658055i 0.998301 0.0582593i \(-0.0185550\pi\)
−0.697778 + 0.716314i \(0.745828\pi\)
\(740\) 332.591 517.521i 0.449447 0.699353i
\(741\) 273.650 + 239.237i 0.369299 + 0.322858i
\(742\) 184.109 + 1280.51i 0.248125 + 1.72575i
\(743\) −451.168 64.8681i −0.607224 0.0873057i −0.168158 0.985760i \(-0.553782\pi\)
−0.439067 + 0.898454i \(0.644691\pi\)
\(744\) 487.072 + 1079.09i 0.654667 + 1.45039i
\(745\) −801.358 235.300i −1.07565 0.315839i
\(746\) −402.096 + 183.631i −0.539003 + 0.246154i
\(747\) −366.406 581.334i −0.490503 0.778225i
\(748\) −112.770 784.336i −0.150763 1.04858i
\(749\) 446.462 + 1520.51i 0.596078 + 2.03005i
\(750\) −46.2309 160.052i −0.0616412 0.213403i
\(751\) 39.8024 45.9344i 0.0529992 0.0611644i −0.728631 0.684907i \(-0.759843\pi\)
0.781630 + 0.623742i \(0.214388\pi\)
\(752\) 34.5923 + 15.7978i 0.0460004 + 0.0210077i
\(753\) −111.422 799.954i −0.147971 1.06236i
\(754\) 37.2361 + 42.9727i 0.0493847 + 0.0569930i
\(755\) 382.291 + 331.257i 0.506345 + 0.438751i
\(756\) 495.538 + 234.266i 0.655474 + 0.309876i
\(757\) −317.102 203.789i −0.418893 0.269206i 0.314170 0.949367i \(-0.398274\pi\)
−0.733063 + 0.680161i \(0.761910\pi\)
\(758\) 926.652 + 133.232i 1.22250 + 0.175768i
\(759\) 581.272 + 913.296i 0.765839 + 1.20329i
\(760\) −842.341 541.340i −1.10834 0.712289i
\(761\) −692.346 + 599.921i −0.909784 + 0.788332i −0.977841 0.209349i \(-0.932865\pi\)
0.0680571 + 0.997681i \(0.478320\pi\)
\(762\) 563.157 162.667i 0.739051 0.213474i
\(763\) −121.131 139.793i −0.158757 0.183215i
\(764\) −351.512 50.5398i −0.460094 0.0661515i
\(765\) 1742.96 + 528.499i 2.27838 + 0.690848i
\(766\) 410.080 0.535352
\(767\) 281.042i 0.366418i
\(768\) −232.123 + 777.848i −0.302243 + 1.01282i
\(769\) 259.987 167.083i 0.338084 0.217273i −0.360572 0.932732i \(-0.617418\pi\)
0.698656 + 0.715458i \(0.253782\pi\)
\(770\) 1530.42 + 698.921i 1.98756 + 0.907690i
\(771\) 23.4758 50.8114i 0.0304485 0.0659033i
\(772\) 421.965 271.180i 0.546587 0.351270i
\(773\) 45.8960 156.307i 0.0593739 0.202209i −0.924464 0.381269i \(-0.875487\pi\)
0.983838 + 0.179060i \(0.0573055\pi\)
\(774\) 4.59041 521.142i 0.00593077 0.673310i
\(775\) 1397.60 1.80336
\(776\) −28.0406 + 95.4976i −0.0361348 + 0.123064i
\(777\) −1331.16 197.380i −1.71321 0.254028i
\(778\) −385.904 445.357i −0.496021 0.572439i
\(779\) −70.9954 241.788i −0.0911366 0.310383i
\(780\) −215.535 250.966i −0.276327 0.321751i
\(781\) −1322.90 850.178i −1.69386 1.08858i
\(782\) −508.006 790.473i −0.649625 1.01084i
\(783\) 21.6550 137.676i 0.0276565 0.175831i
\(784\) −231.359 148.685i −0.295101 0.189650i
\(785\) −1656.33 756.421i −2.10998 0.963594i
\(786\) 179.736 + 157.133i 0.228671 + 0.199915i
\(787\) 631.503 + 728.793i 0.802418 + 0.926040i 0.998511 0.0545453i \(-0.0173709\pi\)
−0.196093 + 0.980585i \(0.562825\pi\)
\(788\) −19.0513 + 2.73916i −0.0241768 + 0.00347609i
\(789\) 301.701 653.007i 0.382384 0.827639i
\(790\) −883.756 + 1019.91i −1.11868 + 1.29102i
\(791\) −240.387 818.682i −0.303902 1.03500i
\(792\) −1109.61 + 315.223i −1.40103 + 0.398009i
\(793\) −32.8118 228.211i −0.0413768 0.287782i
\(794\) −44.9976 70.0176i −0.0566720 0.0881834i
\(795\) −1744.28 + 787.321i −2.19407 + 0.990341i
\(796\) −733.270 215.307i −0.921193 0.270487i
\(797\) 407.671 186.177i 0.511507 0.233597i −0.142904 0.989737i \(-0.545644\pi\)
0.654411 + 0.756139i \(0.272917\pi\)
\(798\) −104.770 + 706.589i −0.131291 + 0.885450i
\(799\) 32.6872 + 227.344i 0.0409101 + 0.284536i
\(800\) 630.738 + 546.538i 0.788423 + 0.683172i
\(801\) 446.463 681.438i 0.557382 0.850734i
\(802\) −302.302 661.950i −0.376935 0.825374i
\(803\) 151.260i 0.188369i
\(804\) −387.813 + 31.4751i −0.482355 + 0.0391482i
\(805\) −1870.91 −2.32412
\(806\) −463.689 + 211.760i −0.575296 + 0.262729i
\(807\) −799.987 519.113i −0.991310 0.643263i
\(808\) 317.525 366.444i 0.392977 0.453520i
\(809\) 331.538 47.6679i 0.409812 0.0589221i 0.0656739 0.997841i \(-0.479080\pi\)
0.344138 + 0.938919i \(0.388171\pi\)
\(810\) 138.110 853.553i 0.170507 1.05377i
\(811\) −84.9900 186.102i −0.104797 0.229472i 0.849969 0.526833i \(-0.176621\pi\)
−0.954765 + 0.297361i \(0.903894\pi\)
\(812\) 29.5224 100.544i 0.0363577 0.123823i
\(813\) −49.5454 + 22.3634i −0.0609414 + 0.0275073i
\(814\) 776.969 499.328i 0.954507 0.613425i
\(815\) −442.308 + 63.5942i −0.542709 + 0.0780297i
\(816\) 354.031 102.261i 0.433861 0.125320i
\(817\) −611.109 + 179.438i −0.747992 + 0.219630i
\(818\) 832.018 + 720.947i 1.01714 + 0.881354i
\(819\) −306.409 + 655.598i −0.374126 + 0.800486i
\(820\) 32.6398 + 227.015i 0.0398046 + 0.276847i
\(821\) −1190.84 + 1031.87i −1.45047 + 1.25684i −0.541039 + 0.840998i \(0.681969\pi\)
−0.909435 + 0.415845i \(0.863486\pi\)
\(822\) −26.3761 23.0592i −0.0320877 0.0280526i
\(823\) 403.255 883.006i 0.489982 1.07291i −0.489615 0.871939i \(-0.662863\pi\)
0.979597 0.200973i \(-0.0644102\pi\)
\(824\) −342.085 + 532.295i −0.415152 + 0.645989i
\(825\) −199.726 + 1346.99i −0.242092 + 1.63271i
\(826\) −464.628 + 298.598i −0.562503 + 0.361499i
\(827\) −535.446 + 833.170i −0.647455 + 1.00746i 0.350040 + 0.936735i \(0.386168\pi\)
−0.997496 + 0.0707256i \(0.977469\pi\)
\(828\) 318.546 271.146i 0.384717 0.327471i
\(829\) 435.773 127.954i 0.525660 0.154348i −0.00812626 0.999967i \(-0.502587\pi\)
0.533787 + 0.845619i \(0.320769\pi\)
\(830\) −615.967 + 533.739i −0.742129 + 0.643058i
\(831\) −415.108 61.5506i −0.499528 0.0740681i
\(832\) −424.778 124.726i −0.510550 0.149911i
\(833\) 1661.01i 1.99401i
\(834\) 119.163 + 0.524808i 0.142882 + 0.000629266i
\(835\) −418.271 122.816i −0.500924 0.147084i
\(836\) 248.550 + 386.751i 0.297309 + 0.462621i
\(837\) 1129.56 + 534.000i 1.34953 + 0.637993i
\(838\) −164.343 + 359.860i −0.196113 + 0.429427i
\(839\) −380.257 591.691i −0.453226 0.705233i 0.537173 0.843472i \(-0.319492\pi\)
−0.990399 + 0.138239i \(0.955856\pi\)
\(840\) 570.054 1910.26i 0.678636 2.27412i
\(841\) 814.356 0.968319
\(842\) 951.608i 1.13018i
\(843\) 608.849 + 181.690i 0.722240 + 0.215528i
\(844\) −102.890 + 715.617i −0.121908 + 0.847888i
\(845\) −618.864 + 536.248i −0.732383 + 0.634613i
\(846\) 104.889 29.7972i 0.123982 0.0352212i
\(847\) −720.193 831.147i −0.850287 0.981283i
\(848\) −209.337 + 325.735i −0.246860 + 0.384121i
\(849\) 428.443 + 673.170i 0.504644 + 0.792897i
\(850\) 168.203 1169.88i 0.197886 1.37633i
\(851\) −555.256 + 863.996i −0.652475 + 1.01527i
\(852\) −254.856 + 551.614i −0.299127 + 0.647435i
\(853\) −757.042 + 873.673i −0.887505 + 1.02424i 0.112029 + 0.993705i \(0.464265\pi\)
−0.999534 + 0.0305303i \(0.990280\pi\)
\(854\) 342.424 296.712i 0.400965 0.347438i
\(855\) −1047.22 + 141.164i −1.22482 + 0.165104i
\(856\) −535.333 + 1172.22i −0.625389 + 1.36941i
\(857\) 176.203 + 152.681i 0.205605 + 0.178158i 0.751576 0.659646i \(-0.229294\pi\)
−0.545971 + 0.837804i \(0.683839\pi\)
\(858\) −137.826 477.157i −0.160637 0.556126i
\(859\) 790.388 232.079i 0.920125 0.270173i 0.212828 0.977090i \(-0.431733\pi\)
0.707297 + 0.706916i \(0.249914\pi\)
\(860\) 573.770 82.4956i 0.667174 0.0959252i
\(861\) 423.253 269.382i 0.491583 0.312871i
\(862\) 78.3785 + 171.625i 0.0909263 + 0.199101i
\(863\) 81.8583 278.784i 0.0948532 0.323040i −0.898374 0.439232i \(-0.855251\pi\)
0.993227 + 0.116192i \(0.0370688\pi\)
\(864\) 300.948 + 682.712i 0.348319 + 0.790176i
\(865\) −193.989 + 1349.22i −0.224265 + 1.55980i
\(866\) −801.516 + 115.241i −0.925538 + 0.133072i
\(867\) 1022.86 + 894.233i 1.17977 + 1.03141i
\(868\) 790.292 + 507.890i 0.910474 + 0.585126i
\(869\) 1728.29 789.286i 1.98883 0.908269i
\(870\) −165.301 0.728003i −0.190001 0.000836785i
\(871\) −43.8101 511.829i −0.0502986 0.587633i
\(872\) 150.419i 0.172499i
\(873\) 42.7902 + 95.9245i 0.0490151 + 0.109879i
\(874\) 458.614 + 294.733i 0.524730 + 0.337223i
\(875\) −306.339 265.444i −0.350101 0.303364i
\(876\) −57.8896 + 8.06321i −0.0660840 + 0.00920458i
\(877\) −61.0104 + 424.337i −0.0695672 + 0.483850i 0.925018 + 0.379924i \(0.124050\pi\)
−0.994585 + 0.103927i \(0.966859\pi\)
\(878\) −719.355 + 328.519i −0.819311 + 0.374167i
\(879\) 221.662 + 66.1475i 0.252175 + 0.0752532i
\(880\) 209.190 + 458.062i 0.237716 + 0.520525i
\(881\) −284.181 442.194i −0.322566 0.501922i 0.641665 0.766985i \(-0.278244\pi\)
−0.964231 + 0.265062i \(0.914607\pi\)
\(882\) −781.480 + 105.343i −0.886031 + 0.119436i
\(883\) 678.642 199.267i 0.768564 0.225671i 0.126132 0.992013i \(-0.459744\pi\)
0.642432 + 0.766343i \(0.277926\pi\)
\(884\) −113.891 387.879i −0.128836 0.438777i
\(885\) −615.105 537.753i −0.695034 0.607630i
\(886\) −198.636 + 434.953i −0.224194 + 0.490917i
\(887\) −467.341 + 67.1935i −0.526878 + 0.0757537i −0.400621 0.916244i \(-0.631206\pi\)
−0.126257 + 0.991998i \(0.540296\pi\)
\(888\) −712.985 830.188i −0.802911 0.934896i
\(889\) 933.987 1077.88i 1.05060 1.21246i
\(890\) −878.947 401.402i −0.987581 0.451013i
\(891\) −676.080 + 1012.34i −0.758788 + 1.13618i
\(892\) 91.3726 635.511i 0.102436 0.712456i
\(893\) −72.0436 112.102i −0.0806760 0.125534i
\(894\) −263.741 + 406.443i −0.295013 + 0.454634i
\(895\) −285.477 329.457i −0.318968 0.368109i
\(896\) 81.4704 + 277.463i 0.0909268 + 0.309668i
\(897\) 359.834 + 418.984i 0.401152 + 0.467095i
\(898\) 23.2661 161.819i 0.0259088 0.180199i
\(899\) 67.2952 229.186i 0.0748556 0.254935i
\(900\) 526.158 + 4.63460i 0.584620 + 0.00514955i
\(901\) −2338.57 −2.59553
\(902\) −97.0084 + 330.380i −0.107548 + 0.366275i
\(903\) −680.851 1069.75i −0.753987 1.18467i
\(904\) 288.237 631.152i 0.318847 0.698176i
\(905\) 1502.54 + 686.188i 1.66027 + 0.758219i
\(906\) 247.565 157.564i 0.273250 0.173912i
\(907\) −1293.66 379.852i −1.42630 0.418801i −0.524672 0.851304i \(-0.675812\pi\)
−0.901632 + 0.432504i \(0.857630\pi\)
\(908\) 142.403i 0.156832i
\(909\) 4.50708 511.680i 0.00495828 0.562905i
\(910\) 823.562 + 241.820i 0.905013 + 0.265736i
\(911\) 1082.67 + 155.664i 1.18844 + 0.170872i 0.708035 0.706177i \(-0.249582\pi\)
0.480402 + 0.877048i \(0.340491\pi\)
\(912\) −162.192 + 139.294i −0.177842 + 0.152735i
\(913\) 1101.01 323.285i 1.20592 0.354091i
\(914\) −434.100 + 376.150i −0.474946 + 0.411543i
\(915\) 562.258 + 364.850i 0.614490 + 0.398744i
\(916\) 98.5991 63.3658i 0.107641 0.0691766i
\(917\) 574.961 + 82.6669i 0.627002 + 0.0901493i
\(918\) 582.934 881.243i 0.635005 0.959960i
\(919\) −297.430 + 651.280i −0.323645 + 0.708684i −0.999601 0.0282586i \(-0.991004\pi\)
0.675956 + 0.736942i \(0.263731\pi\)
\(920\) −1149.81 996.316i −1.24979 1.08295i
\(921\) 199.334 171.192i 0.216432 0.185877i
\(922\) 120.660 + 839.210i 0.130868 + 0.910206i
\(923\) −729.752 333.267i −0.790631 0.361069i
\(924\) −602.432 + 689.088i −0.651983 + 0.745767i
\(925\) −1239.51 + 363.953i −1.34001 + 0.393463i
\(926\) −109.232 372.009i −0.117961 0.401738i
\(927\) 89.2049 + 661.761i 0.0962296 + 0.713874i
\(928\) 119.994 77.1157i 0.129304 0.0830988i
\(929\) 643.658 293.949i 0.692850 0.316414i −0.0376846 0.999290i \(-0.511998\pi\)
0.730535 + 0.682876i \(0.239271\pi\)
\(930\) 423.764 1420.04i 0.455660 1.52693i
\(931\) 400.327 + 876.593i 0.429996 + 0.941561i
\(932\) 59.5944 + 8.56838i 0.0639425 + 0.00919354i
\(933\) −212.531 1525.86i −0.227794 1.63544i
\(934\) 332.249 383.436i 0.355727 0.410531i
\(935\) −1644.30 + 2558.57i −1.75860 + 2.73644i
\(936\) −537.435 + 239.740i −0.574183 + 0.256133i
\(937\) 1081.80 1.15454 0.577268 0.816555i \(-0.304119\pi\)
0.577268 + 0.816555i \(0.304119\pi\)
\(938\) 799.624 616.229i 0.852478 0.656961i
\(939\) 0.877606 199.270i 0.000934618 0.212215i
\(940\) 50.3817 + 110.321i 0.0535975 + 0.117362i
\(941\) −273.818 + 426.069i −0.290986 + 0.452783i −0.955712 0.294304i \(-0.904912\pi\)
0.664726 + 0.747088i \(0.268548\pi\)
\(942\) −695.266 + 795.276i −0.738074 + 0.844242i
\(943\) −54.4917 378.998i −0.0577855 0.401907i
\(944\) −163.624 23.5256i −0.173331 0.0249212i
\(945\) −848.589 1925.06i −0.897978 2.03710i
\(946\) 835.022 + 245.185i 0.882688 + 0.259180i
\(947\) −1020.05 + 465.841i −1.07714 + 0.491913i −0.873345 0.487101i \(-0.838054\pi\)
−0.203793 + 0.979014i \(0.565327\pi\)
\(948\) −394.201 619.369i −0.415824 0.653343i
\(949\) −10.9821 76.3820i −0.0115723 0.0804868i
\(950\) 193.189 + 657.940i 0.203356 + 0.692568i
\(951\) −485.009 + 140.094i −0.509999 + 0.147313i
\(952\) 1595.27 1841.04i 1.67570 1.93386i
\(953\) 64.9087 + 29.6428i 0.0681099 + 0.0311047i 0.449179 0.893442i \(-0.351717\pi\)
−0.381069 + 0.924547i \(0.624444\pi\)
\(954\) 148.314 + 1100.26i 0.155466 + 1.15331i
\(955\) 892.602 + 1030.12i 0.934662 + 1.07866i
\(956\) −6.99501 6.06121i −0.00731696 0.00634018i
\(957\) 211.269 + 97.6100i 0.220761 + 0.101996i
\(958\) 298.030 + 191.532i 0.311096 + 0.199929i
\(959\) −84.3754 12.1313i −0.0879827 0.0126500i
\(960\) 1085.76 691.039i 1.13100 0.719832i
\(961\) 992.994 + 638.159i 1.03329 + 0.664057i
\(962\) 356.093 308.556i 0.370159 0.320745i
\(963\) 371.639 + 1308.20i 0.385918 + 1.35847i
\(964\) −145.801 168.263i −0.151246 0.174547i
\(965\) −1905.60 273.984i −1.97472 0.283921i
\(966\) −310.367 + 1040.05i −0.321291 + 1.07665i
\(967\) −340.837 −0.352468 −0.176234 0.984348i \(-0.556392\pi\)
−0.176234 + 0.984348i \(0.556392\pi\)
\(968\) 894.323i 0.923887i
\(969\) −1237.34 369.244i −1.27693 0.381056i
\(970\) 104.804 67.3536i 0.108046 0.0694367i
\(971\) 713.624 + 325.901i 0.734937 + 0.335634i 0.747478 0.664287i \(-0.231265\pi\)
−0.0125409 + 0.999921i \(0.503992\pi\)
\(972\) 423.476 + 204.781i 0.435675 + 0.210680i
\(973\) 243.913 156.753i 0.250681 0.161103i
\(974\) 388.565 1323.33i 0.398937 1.35865i
\(975\) −3.05948 + 694.688i −0.00313793 + 0.712501i
\(976\) 135.612 0.138947
\(977\) 163.454 556.674i 0.167302 0.569779i −0.832572 0.553917i \(-0.813133\pi\)
0.999874 0.0158621i \(-0.00504927\pi\)
\(978\) −38.0224 + 256.430i −0.0388777 + 0.262198i
\(979\) 890.870 + 1028.12i 0.909980 + 1.05017i
\(980\) −247.100 841.546i −0.252143 0.858720i
\(981\) −102.892 120.879i −0.104885 0.123220i
\(982\) −773.697 497.225i −0.787879 0.506339i
\(983\) −855.602 1331.34i −0.870399 1.35437i −0.934329 0.356413i \(-0.884000\pi\)
0.0639296 0.997954i \(-0.479637\pi\)
\(984\) 403.573 + 59.8403i 0.410135 + 0.0608133i
\(985\) 62.1470 + 39.9395i 0.0630934 + 0.0405477i
\(986\) −183.744 83.9130i −0.186353 0.0851045i
\(987\) 174.618 199.736i 0.176918 0.202367i
\(988\) 153.590 + 177.252i 0.155455 + 0.179405i
\(989\) −957.902 + 137.726i −0.968556 + 0.139257i
\(990\) 1308.05 + 611.348i 1.32126 + 0.617523i
\(991\) 396.990 458.151i 0.400595 0.462311i −0.519233 0.854633i \(-0.673782\pi\)
0.919828 + 0.392321i \(0.128328\pi\)
\(992\) 360.260 + 1226.93i 0.363166 + 1.23683i
\(993\) 391.631 + 1355.83i 0.394392 + 1.36539i
\(994\) −224.371 1560.53i −0.225725 1.56995i
\(995\) 1585.83 + 2467.60i 1.59380 + 2.48000i
\(996\) −182.417 404.138i −0.183149 0.405761i
\(997\) 1453.88 + 426.898i 1.45826 + 0.428183i 0.912262 0.409607i \(-0.134334\pi\)
0.545994 + 0.837789i \(0.316152\pi\)
\(998\) 1062.05 485.020i 1.06417 0.485992i
\(999\) −1140.85 179.444i −1.14199 0.179624i
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 201.3.k.a.14.15 440
3.2 odd 2 inner 201.3.k.a.14.30 yes 440
67.24 even 11 inner 201.3.k.a.158.30 yes 440
201.158 odd 22 inner 201.3.k.a.158.15 yes 440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.k.a.14.15 440 1.1 even 1 trivial
201.3.k.a.14.30 yes 440 3.2 odd 2 inner
201.3.k.a.158.15 yes 440 201.158 odd 22 inner
201.3.k.a.158.30 yes 440 67.24 even 11 inner