Properties

Label 75.3.h.a.14.14
Level $75$
Weight $3$
Character 75.14
Analytic conductor $2.044$
Analytic rank $0$
Dimension $72$
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] = [75,3,Mod(14,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.h (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 14.14
Character \(\chi\) \(=\) 75.14
Dual form 75.3.h.a.59.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.88806 - 1.37175i) q^{2} +(-2.67611 - 1.35589i) q^{3} +(0.446980 - 1.37566i) q^{4} +(0.465978 - 4.97824i) q^{5} +(-6.91259 + 1.11096i) q^{6} -12.5544i q^{7} +(1.84155 + 5.66769i) q^{8} +(5.32311 + 7.25703i) q^{9} +O(q^{10})\) \(q+(1.88806 - 1.37175i) q^{2} +(-2.67611 - 1.35589i) q^{3} +(0.446980 - 1.37566i) q^{4} +(0.465978 - 4.97824i) q^{5} +(-6.91259 + 1.11096i) q^{6} -12.5544i q^{7} +(1.84155 + 5.66769i) q^{8} +(5.32311 + 7.25703i) q^{9} +(-5.94912 - 10.0384i) q^{10} +(7.59880 + 10.4589i) q^{11} +(-3.06142 + 3.07537i) q^{12} +(-2.92256 + 4.02255i) q^{13} +(-17.2215 - 23.7033i) q^{14} +(-7.99696 + 12.6905i) q^{15} +(15.9325 + 11.5756i) q^{16} +(3.32914 + 10.2460i) q^{17} +(20.0052 + 6.39968i) q^{18} +(-1.29722 - 3.99244i) q^{19} +(-6.64010 - 2.86620i) q^{20} +(-17.0224 + 33.5969i) q^{21} +(28.6939 + 9.32322i) q^{22} +(17.6249 - 12.8053i) q^{23} +(2.75661 - 17.6643i) q^{24} +(-24.5657 - 4.63950i) q^{25} +11.6038i q^{26} +(-4.40547 - 26.6382i) q^{27} +(-17.2706 - 5.61156i) q^{28} +(26.0760 + 8.47261i) q^{29} +(2.30950 + 34.9302i) q^{30} +(-8.64023 - 26.5919i) q^{31} +22.1228 q^{32} +(-6.15414 - 38.2922i) q^{33} +(20.3406 + 14.7783i) q^{34} +(-62.4987 - 5.85006i) q^{35} +(12.3626 - 4.07906i) q^{36} +(-0.0202976 + 0.0279372i) q^{37} +(-7.92586 - 5.75848i) q^{38} +(13.2752 - 6.80212i) q^{39} +(29.0733 - 6.52663i) q^{40} +(-44.4000 + 61.1113i) q^{41} +(13.9474 + 86.7832i) q^{42} +43.3942i q^{43} +(17.7844 - 5.77849i) q^{44} +(38.6077 - 23.1181i) q^{45} +(15.7112 - 48.3541i) q^{46} +(-1.52001 + 4.67812i) q^{47} +(-26.9417 - 52.5803i) q^{48} -108.612 q^{49} +(-52.7457 + 24.9385i) q^{50} +(4.98338 - 31.9334i) q^{51} +(4.22736 + 5.81846i) q^{52} +(0.528642 - 1.62699i) q^{53} +(-44.8587 - 44.2511i) q^{54} +(55.6075 - 32.9550i) q^{55} +(71.1543 - 23.1194i) q^{56} +(-1.94181 + 12.4431i) q^{57} +(60.8553 - 19.7731i) q^{58} +(28.0481 - 38.6049i) q^{59} +(13.8834 + 16.6735i) q^{60} +(-5.28161 + 3.83732i) q^{61} +(-52.7907 - 38.3547i) q^{62} +(91.1074 - 66.8283i) q^{63} +(-21.9608 + 15.9555i) q^{64} +(18.6634 + 16.4236i) q^{65} +(-64.1467 - 63.8558i) q^{66} +(-3.93744 + 1.27935i) q^{67} +15.5831 q^{68} +(-64.5288 + 10.3708i) q^{69} +(-126.026 + 74.6874i) q^{70} +(-51.8456 - 16.8457i) q^{71} +(-31.3279 + 43.5339i) q^{72} +(21.0676 + 28.9970i) q^{73} +0.0805904i q^{74} +(59.4499 + 45.7243i) q^{75} -6.07208 q^{76} +(131.304 - 95.3981i) q^{77} +(15.7335 - 31.0531i) q^{78} +(5.27573 - 16.2370i) q^{79} +(65.0503 - 73.9216i) q^{80} +(-24.3290 + 77.2600i) q^{81} +176.287i q^{82} +(17.6925 + 54.4519i) q^{83} +(38.6093 + 38.4342i) q^{84} +(52.5585 - 11.7988i) q^{85} +(59.5261 + 81.9306i) q^{86} +(-58.2943 - 58.0299i) q^{87} +(-45.2840 + 62.3281i) q^{88} +(44.4639 + 61.1993i) q^{89} +(41.1811 - 96.6085i) q^{90} +(50.5006 + 36.6908i) q^{91} +(-9.73774 - 29.9697i) q^{92} +(-12.9335 + 82.8780i) q^{93} +(3.54736 + 10.9176i) q^{94} +(-20.4798 + 4.59749i) q^{95} +(-59.2029 - 29.9961i) q^{96} +(-28.4310 - 9.23778i) q^{97} +(-205.066 + 148.989i) q^{98} +(-35.4509 + 110.818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30} - 126 q^{31} + 20 q^{33} + 210 q^{34} - 213 q^{36} + 110 q^{37} - 191 q^{39} + 140 q^{40} - 175 q^{42} - 405 q^{45} - 210 q^{46} + 150 q^{48} - 224 q^{49} - 60 q^{51} - 320 q^{52} + 320 q^{54} - 10 q^{55} - 70 q^{58} + 1190 q^{60} + 294 q^{61} + 795 q^{63} + 362 q^{64} - 470 q^{66} - 260 q^{67} + 335 q^{69} + 1200 q^{70} + 215 q^{72} - 150 q^{73} + 200 q^{75} - 16 q^{76} - 1295 q^{78} - 346 q^{79} + 507 q^{81} - 456 q^{84} - 1450 q^{85} - 430 q^{87} - 1710 q^{88} - 820 q^{90} + 538 q^{91} - 560 q^{94} + 740 q^{96} - 150 q^{97} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.88806 1.37175i 0.944028 0.685876i −0.00535908 0.999986i \(-0.501706\pi\)
0.949387 + 0.314109i \(0.101706\pi\)
\(3\) −2.67611 1.35589i −0.892036 0.451964i
\(4\) 0.446980 1.37566i 0.111745 0.343916i
\(5\) 0.465978 4.97824i 0.0931956 0.995648i
\(6\) −6.91259 + 1.11096i −1.15210 + 0.185160i
\(7\) 12.5544i 1.79348i −0.442556 0.896741i \(-0.645928\pi\)
0.442556 0.896741i \(-0.354072\pi\)
\(8\) 1.84155 + 5.66769i 0.230193 + 0.708462i
\(9\) 5.32311 + 7.25703i 0.591457 + 0.806337i
\(10\) −5.94912 10.0384i −0.594912 1.00384i
\(11\) 7.59880 + 10.4589i 0.690800 + 0.950805i 1.00000 0.000192365i \(-6.12317e-5\pi\)
−0.309200 + 0.950997i \(0.600061\pi\)
\(12\) −3.06142 + 3.07537i −0.255118 + 0.256281i
\(13\) −2.92256 + 4.02255i −0.224812 + 0.309427i −0.906492 0.422223i \(-0.861250\pi\)
0.681680 + 0.731651i \(0.261250\pi\)
\(14\) −17.2215 23.7033i −1.23011 1.69310i
\(15\) −7.99696 + 12.6905i −0.533131 + 0.846033i
\(16\) 15.9325 + 11.5756i 0.995778 + 0.723475i
\(17\) 3.32914 + 10.2460i 0.195831 + 0.602707i 0.999966 + 0.00825983i \(0.00262922\pi\)
−0.804134 + 0.594448i \(0.797371\pi\)
\(18\) 20.0052 + 6.39968i 1.11140 + 0.355538i
\(19\) −1.29722 3.99244i −0.0682748 0.210128i 0.911098 0.412190i \(-0.135236\pi\)
−0.979373 + 0.202061i \(0.935236\pi\)
\(20\) −6.64010 2.86620i −0.332005 0.143310i
\(21\) −17.0224 + 33.5969i −0.810589 + 1.59985i
\(22\) 28.6939 + 9.32322i 1.30427 + 0.423783i
\(23\) 17.6249 12.8053i 0.766301 0.556751i −0.134535 0.990909i \(-0.542954\pi\)
0.900837 + 0.434158i \(0.142954\pi\)
\(24\) 2.75661 17.6643i 0.114859 0.736012i
\(25\) −24.5657 4.63950i −0.982629 0.185580i
\(26\) 11.6038i 0.446301i
\(27\) −4.40547 26.6382i −0.163166 0.986599i
\(28\) −17.2706 5.61156i −0.616807 0.200413i
\(29\) 26.0760 + 8.47261i 0.899172 + 0.292159i 0.721895 0.692002i \(-0.243271\pi\)
0.177277 + 0.984161i \(0.443271\pi\)
\(30\) 2.30950 + 34.9302i 0.0769834 + 1.16434i
\(31\) −8.64023 26.5919i −0.278717 0.857803i −0.988212 0.153092i \(-0.951077\pi\)
0.709495 0.704711i \(-0.248923\pi\)
\(32\) 22.1228 0.691336
\(33\) −6.15414 38.2922i −0.186489 1.16037i
\(34\) 20.3406 + 14.7783i 0.598253 + 0.434656i
\(35\) −62.4987 5.85006i −1.78568 0.167145i
\(36\) 12.3626 4.07906i 0.343404 0.113307i
\(37\) −0.0202976 + 0.0279372i −0.000548584 + 0.000755061i −0.809291 0.587408i \(-0.800149\pi\)
0.808743 + 0.588163i \(0.200149\pi\)
\(38\) −7.92586 5.75848i −0.208575 0.151539i
\(39\) 13.2752 6.80212i 0.340390 0.174413i
\(40\) 29.0733 6.52663i 0.726831 0.163166i
\(41\) −44.4000 + 61.1113i −1.08293 + 1.49052i −0.226668 + 0.973972i \(0.572783\pi\)
−0.856258 + 0.516548i \(0.827217\pi\)
\(42\) 13.9474 + 86.7832i 0.332081 + 2.06627i
\(43\) 43.3942i 1.00917i 0.863363 + 0.504583i \(0.168354\pi\)
−0.863363 + 0.504583i \(0.831646\pi\)
\(44\) 17.7844 5.77849i 0.404190 0.131329i
\(45\) 38.6077 23.1181i 0.857949 0.513736i
\(46\) 15.7112 48.3541i 0.341548 1.05118i
\(47\) −1.52001 + 4.67812i −0.0323407 + 0.0995346i −0.965924 0.258826i \(-0.916664\pi\)
0.933583 + 0.358361i \(0.116664\pi\)
\(48\) −26.9417 52.5803i −0.561285 1.09542i
\(49\) −108.612 −2.21658
\(50\) −52.7457 + 24.9385i −1.05491 + 0.498769i
\(51\) 4.98338 31.9334i 0.0977134 0.626146i
\(52\) 4.22736 + 5.81846i 0.0812953 + 0.111893i
\(53\) 0.528642 1.62699i 0.00997438 0.0306980i −0.945945 0.324326i \(-0.894863\pi\)
0.955920 + 0.293628i \(0.0948626\pi\)
\(54\) −44.8587 44.2511i −0.830717 0.819465i
\(55\) 55.6075 32.9550i 1.01105 0.599183i
\(56\) 71.1543 23.1194i 1.27061 0.412847i
\(57\) −1.94181 + 12.4431i −0.0340668 + 0.218300i
\(58\) 60.8553 19.7731i 1.04923 0.340915i
\(59\) 28.0481 38.6049i 0.475392 0.654321i −0.502219 0.864740i \(-0.667483\pi\)
0.977611 + 0.210420i \(0.0674830\pi\)
\(60\) 13.8834 + 16.6735i 0.231389 + 0.277892i
\(61\) −5.28161 + 3.83732i −0.0865838 + 0.0629068i −0.630235 0.776404i \(-0.717041\pi\)
0.543651 + 0.839311i \(0.317041\pi\)
\(62\) −52.7907 38.3547i −0.851463 0.618624i
\(63\) 91.1074 66.8283i 1.44615 1.06077i
\(64\) −21.9608 + 15.9555i −0.343138 + 0.249304i
\(65\) 18.6634 + 16.4236i 0.287129 + 0.252671i
\(66\) −64.1467 63.8558i −0.971920 0.967512i
\(67\) −3.93744 + 1.27935i −0.0587677 + 0.0190948i −0.338253 0.941055i \(-0.609836\pi\)
0.279486 + 0.960150i \(0.409836\pi\)
\(68\) 15.5831 0.229164
\(69\) −64.5288 + 10.3708i −0.935200 + 0.150301i
\(70\) −126.026 + 74.6874i −1.80037 + 1.06696i
\(71\) −51.8456 16.8457i −0.730220 0.237263i −0.0797717 0.996813i \(-0.525419\pi\)
−0.650449 + 0.759550i \(0.725419\pi\)
\(72\) −31.3279 + 43.5339i −0.435109 + 0.604638i
\(73\) 21.0676 + 28.9970i 0.288597 + 0.397220i 0.928558 0.371188i \(-0.121049\pi\)
−0.639961 + 0.768408i \(0.721049\pi\)
\(74\) 0.0805904i 0.00108906i
\(75\) 59.4499 + 45.7243i 0.792665 + 0.609657i
\(76\) −6.07208 −0.0798958
\(77\) 131.304 95.3981i 1.70525 1.23894i
\(78\) 15.7335 31.0531i 0.201712 0.398117i
\(79\) 5.27573 16.2370i 0.0667813 0.205532i −0.912097 0.409974i \(-0.865538\pi\)
0.978879 + 0.204442i \(0.0655379\pi\)
\(80\) 65.0503 73.9216i 0.813129 0.924020i
\(81\) −24.3290 + 77.2600i −0.300358 + 0.953827i
\(82\) 176.287i 2.14985i
\(83\) 17.6925 + 54.4519i 0.213162 + 0.656046i 0.999279 + 0.0379682i \(0.0120885\pi\)
−0.786117 + 0.618078i \(0.787911\pi\)
\(84\) 38.6093 + 38.4342i 0.459635 + 0.457550i
\(85\) 52.5585 11.7988i 0.618335 0.138810i
\(86\) 59.5261 + 81.9306i 0.692164 + 0.952682i
\(87\) −58.2943 58.0299i −0.670049 0.667010i
\(88\) −45.2840 + 62.3281i −0.514591 + 0.708274i
\(89\) 44.4639 + 61.1993i 0.499595 + 0.687633i 0.982121 0.188248i \(-0.0602809\pi\)
−0.482527 + 0.875881i \(0.660281\pi\)
\(90\) 41.1811 96.6085i 0.457568 1.07343i
\(91\) 50.5006 + 36.6908i 0.554952 + 0.403196i
\(92\) −9.73774 29.9697i −0.105845 0.325757i
\(93\) −12.9335 + 82.8780i −0.139070 + 0.891161i
\(94\) 3.54736 + 10.9176i 0.0377378 + 0.116145i
\(95\) −20.4798 + 4.59749i −0.215577 + 0.0483946i
\(96\) −59.2029 29.9961i −0.616697 0.312459i
\(97\) −28.4310 9.23778i −0.293103 0.0952349i 0.158775 0.987315i \(-0.449246\pi\)
−0.451878 + 0.892080i \(0.649246\pi\)
\(98\) −205.066 + 148.989i −2.09251 + 1.52030i
\(99\) −35.4509 + 110.818i −0.358090 + 1.11938i
\(100\) −17.3628 + 31.7204i −0.173628 + 0.317204i
\(101\) 26.0891i 0.258308i −0.991625 0.129154i \(-0.958774\pi\)
0.991625 0.129154i \(-0.0412261\pi\)
\(102\) −34.3959 67.1280i −0.337214 0.658118i
\(103\) −44.7560 14.5421i −0.434524 0.141185i 0.0835838 0.996501i \(-0.473363\pi\)
−0.518108 + 0.855315i \(0.673363\pi\)
\(104\) −28.1806 9.15644i −0.270967 0.0880427i
\(105\) 159.321 + 100.397i 1.51734 + 0.956160i
\(106\) −1.23373 3.79702i −0.0116389 0.0358209i
\(107\) −149.068 −1.39316 −0.696581 0.717478i \(-0.745296\pi\)
−0.696581 + 0.717478i \(0.745296\pi\)
\(108\) −38.6143 5.84629i −0.357540 0.0541323i
\(109\) 120.472 + 87.5279i 1.10525 + 0.803008i 0.981908 0.189357i \(-0.0606402\pi\)
0.123338 + 0.992365i \(0.460640\pi\)
\(110\) 59.7839 138.501i 0.543490 1.25910i
\(111\) 0.0921985 0.0472417i 0.000830617 0.000425601i
\(112\) 145.324 200.022i 1.29754 1.78591i
\(113\) −47.3048 34.3689i −0.418626 0.304150i 0.358458 0.933546i \(-0.383302\pi\)
−0.777085 + 0.629396i \(0.783302\pi\)
\(114\) 13.4026 + 26.1569i 0.117567 + 0.229447i
\(115\) −55.5348 93.7081i −0.482912 0.814853i
\(116\) 23.3109 32.0847i 0.200956 0.276592i
\(117\) −44.7489 + 0.203422i −0.382469 + 0.00173865i
\(118\) 111.363i 0.943757i
\(119\) 128.632 41.7952i 1.08094 0.351220i
\(120\) −86.6526 21.9542i −0.722105 0.182952i
\(121\) −14.2548 + 43.8716i −0.117808 + 0.362575i
\(122\) −4.70813 + 14.4901i −0.0385912 + 0.118772i
\(123\) 201.679 103.339i 1.63967 0.840154i
\(124\) −40.4435 −0.326157
\(125\) −34.5436 + 120.132i −0.276349 + 0.961057i
\(126\) 80.3440 251.152i 0.637651 1.99327i
\(127\) −78.3016 107.773i −0.616548 0.848605i 0.380548 0.924761i \(-0.375735\pi\)
−0.997096 + 0.0761557i \(0.975735\pi\)
\(128\) −46.9215 + 144.410i −0.366574 + 1.12820i
\(129\) 58.8378 116.128i 0.456107 0.900213i
\(130\) 57.7666 + 5.40713i 0.444359 + 0.0415933i
\(131\) 201.121 65.3482i 1.53528 0.498841i 0.585208 0.810883i \(-0.301013\pi\)
0.950068 + 0.312042i \(0.101013\pi\)
\(132\) −55.4279 8.64983i −0.419909 0.0655290i
\(133\) −50.1225 + 16.2858i −0.376861 + 0.122450i
\(134\) −5.67915 + 7.81668i −0.0423817 + 0.0583334i
\(135\) −134.664 + 9.51868i −0.997511 + 0.0705088i
\(136\) −51.9406 + 37.7370i −0.381916 + 0.277478i
\(137\) −155.247 112.794i −1.13319 0.823312i −0.147036 0.989131i \(-0.546973\pi\)
−0.986156 + 0.165819i \(0.946973\pi\)
\(138\) −107.608 + 108.098i −0.779767 + 0.783320i
\(139\) 82.6077 60.0180i 0.594300 0.431784i −0.249551 0.968362i \(-0.580283\pi\)
0.843851 + 0.536577i \(0.180283\pi\)
\(140\) −35.9834 + 83.3623i −0.257024 + 0.595445i
\(141\) 10.4108 10.4582i 0.0738352 0.0741716i
\(142\) −120.996 + 39.3138i −0.852081 + 0.276858i
\(143\) −64.2792 −0.449505
\(144\) 0.805710 + 177.240i 0.00559521 + 1.23084i
\(145\) 54.3295 125.865i 0.374686 0.868031i
\(146\) 79.5535 + 25.8485i 0.544887 + 0.177045i
\(147\) 290.658 + 147.266i 1.97727 + 1.00181i
\(148\) 0.0293596 + 0.0404101i 0.000198376 + 0.000273041i
\(149\) 114.565i 0.768892i 0.923148 + 0.384446i \(0.125607\pi\)
−0.923148 + 0.384446i \(0.874393\pi\)
\(150\) 174.967 + 4.77947i 1.16645 + 0.0318631i
\(151\) −163.992 −1.08604 −0.543019 0.839720i \(-0.682719\pi\)
−0.543019 + 0.839720i \(0.682719\pi\)
\(152\) 20.2390 14.7045i 0.133151 0.0967402i
\(153\) −56.6344 + 78.7004i −0.370159 + 0.514382i
\(154\) 117.047 360.234i 0.760046 2.33918i
\(155\) −136.407 + 30.6219i −0.880044 + 0.197560i
\(156\) −3.42366 21.3027i −0.0219466 0.136556i
\(157\) 73.2155i 0.466341i −0.972436 0.233170i \(-0.925090\pi\)
0.972436 0.233170i \(-0.0749100\pi\)
\(158\) −12.3123 37.8934i −0.0779260 0.239831i
\(159\) −3.62073 + 3.63723i −0.0227719 + 0.0228756i
\(160\) 10.3087 110.132i 0.0644295 0.688327i
\(161\) −160.762 221.270i −0.998522 1.37435i
\(162\) 60.0471 + 179.244i 0.370661 + 1.10645i
\(163\) 11.4612 15.7750i 0.0703141 0.0967790i −0.772412 0.635122i \(-0.780950\pi\)
0.842726 + 0.538343i \(0.180950\pi\)
\(164\) 64.2227 + 88.3950i 0.391602 + 0.538994i
\(165\) −193.495 + 12.7934i −1.17270 + 0.0775360i
\(166\) 108.099 + 78.5384i 0.651198 + 0.473123i
\(167\) 28.1359 + 86.5934i 0.168478 + 0.518523i 0.999276 0.0380519i \(-0.0121152\pi\)
−0.830797 + 0.556575i \(0.812115\pi\)
\(168\) −221.764 34.6075i −1.32002 0.205997i
\(169\) 44.5843 + 137.216i 0.263812 + 0.811931i
\(170\) 83.0483 94.3740i 0.488519 0.555141i
\(171\) 22.0680 30.6662i 0.129053 0.179334i
\(172\) 59.6958 + 19.3963i 0.347069 + 0.112769i
\(173\) 35.0251 25.4472i 0.202457 0.147094i −0.481937 0.876206i \(-0.660067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(174\) −189.665 29.5983i −1.09003 0.170105i
\(175\) −58.2460 + 308.407i −0.332834 + 1.76233i
\(176\) 254.596i 1.44657i
\(177\) −127.404 + 65.2807i −0.719796 + 0.368818i
\(178\) 167.901 + 54.5542i 0.943262 + 0.306485i
\(179\) 86.3556 + 28.0587i 0.482434 + 0.156752i 0.540129 0.841582i \(-0.318375\pi\)
−0.0576956 + 0.998334i \(0.518375\pi\)
\(180\) −14.5459 63.4445i −0.0808104 0.352470i
\(181\) −34.0023 104.648i −0.187858 0.578168i 0.812128 0.583480i \(-0.198309\pi\)
−0.999986 + 0.00531154i \(0.998309\pi\)
\(182\) 145.679 0.800433
\(183\) 19.3372 3.10778i 0.105668 0.0169824i
\(184\) 105.033 + 76.3112i 0.570834 + 0.414735i
\(185\) 0.129620 + 0.114064i 0.000700649 + 0.000616565i
\(186\) 89.2688 + 174.220i 0.479940 + 0.936666i
\(187\) −81.8642 + 112.676i −0.437777 + 0.602548i
\(188\) 5.75611 + 4.18206i 0.0306176 + 0.0222450i
\(189\) −334.425 + 55.3079i −1.76945 + 0.292634i
\(190\) −32.3603 + 36.7735i −0.170318 + 0.193545i
\(191\) −57.8437 + 79.6151i −0.302847 + 0.416833i −0.933134 0.359529i \(-0.882937\pi\)
0.630287 + 0.776362i \(0.282937\pi\)
\(192\) 80.4034 12.9221i 0.418768 0.0673024i
\(193\) 183.115i 0.948784i −0.880314 0.474392i \(-0.842668\pi\)
0.880314 0.474392i \(-0.157332\pi\)
\(194\) −66.3512 + 21.5588i −0.342017 + 0.111128i
\(195\) −27.6766 69.2569i −0.141931 0.355164i
\(196\) −48.5475 + 149.414i −0.247691 + 0.762316i
\(197\) 104.482 321.562i 0.530365 1.63229i −0.223092 0.974797i \(-0.571615\pi\)
0.753457 0.657497i \(-0.228385\pi\)
\(198\) 85.0820 + 257.861i 0.429707 + 1.30233i
\(199\) −12.6514 −0.0635749 −0.0317875 0.999495i \(-0.510120\pi\)
−0.0317875 + 0.999495i \(0.510120\pi\)
\(200\) −18.9436 147.775i −0.0947182 0.738874i
\(201\) 12.2717 + 1.91506i 0.0610531 + 0.00952767i
\(202\) −35.7878 49.2577i −0.177167 0.243850i
\(203\) 106.368 327.368i 0.523981 1.61265i
\(204\) −41.7022 21.1291i −0.204422 0.103574i
\(205\) 283.537 + 249.510i 1.38311 + 1.21712i
\(206\) −104.450 + 33.9378i −0.507038 + 0.164747i
\(207\) 186.748 + 59.7408i 0.902163 + 0.288603i
\(208\) −93.1270 + 30.2588i −0.447726 + 0.145475i
\(209\) 31.8990 43.9052i 0.152627 0.210073i
\(210\) 438.527 28.9943i 2.08822 0.138068i
\(211\) 293.037 212.904i 1.38880 1.00902i 0.392808 0.919621i \(-0.371504\pi\)
0.995995 0.0894038i \(-0.0284962\pi\)
\(212\) −2.00190 1.45447i −0.00944294 0.00686069i
\(213\) 115.904 + 115.378i 0.544149 + 0.541681i
\(214\) −281.449 + 204.485i −1.31518 + 0.955537i
\(215\) 216.027 + 20.2207i 1.00477 + 0.0940499i
\(216\) 142.864 74.0242i 0.661408 0.342705i
\(217\) −333.844 + 108.473i −1.53845 + 0.499874i
\(218\) 347.524 1.59415
\(219\) −17.0623 106.165i −0.0779099 0.484770i
\(220\) −20.4796 91.2275i −0.0930891 0.414671i
\(221\) −50.9448 16.5530i −0.230519 0.0749003i
\(222\) 0.109272 0.215669i 0.000492216 0.000971480i
\(223\) −134.126 184.609i −0.601462 0.827842i 0.394379 0.918948i \(-0.370960\pi\)
−0.995841 + 0.0911062i \(0.970960\pi\)
\(224\) 277.737i 1.23990i
\(225\) −97.0971 202.971i −0.431543 0.902093i
\(226\) −136.460 −0.603804
\(227\) −251.371 + 182.632i −1.10736 + 0.804545i −0.982246 0.187598i \(-0.939930\pi\)
−0.125115 + 0.992142i \(0.539930\pi\)
\(228\) 16.2496 + 8.23309i 0.0712700 + 0.0361101i
\(229\) 37.5038 115.425i 0.163772 0.504039i −0.835172 0.549989i \(-0.814632\pi\)
0.998944 + 0.0459508i \(0.0146317\pi\)
\(230\) −233.397 100.746i −1.01477 0.438026i
\(231\) −480.734 + 77.2613i −2.08110 + 0.334464i
\(232\) 163.393i 0.704282i
\(233\) 124.270 + 382.465i 0.533350 + 1.64148i 0.747188 + 0.664612i \(0.231403\pi\)
−0.213839 + 0.976869i \(0.568597\pi\)
\(234\) −84.2093 + 61.7685i −0.359869 + 0.263968i
\(235\) 22.5805 + 9.74690i 0.0960873 + 0.0414762i
\(236\) −40.5704 55.8404i −0.171909 0.236612i
\(237\) −36.1341 + 36.2987i −0.152464 + 0.153159i
\(238\) 185.532 255.363i 0.779548 1.07296i
\(239\) −115.387 158.817i −0.482792 0.664507i 0.496246 0.868182i \(-0.334711\pi\)
−0.979038 + 0.203675i \(0.934711\pi\)
\(240\) −274.311 + 109.621i −1.14296 + 0.456754i
\(241\) −291.933 212.102i −1.21134 0.880091i −0.215989 0.976396i \(-0.569298\pi\)
−0.995352 + 0.0963050i \(0.969298\pi\)
\(242\) 33.2672 + 102.386i 0.137468 + 0.423083i
\(243\) 169.863 173.769i 0.699025 0.715097i
\(244\) 2.91808 + 8.98093i 0.0119594 + 0.0368071i
\(245\) −50.6109 + 540.697i −0.206575 + 2.20693i
\(246\) 239.027 471.764i 0.971653 1.91774i
\(247\) 19.8510 + 6.44998i 0.0803684 + 0.0261133i
\(248\) 134.803 97.9403i 0.543562 0.394921i
\(249\) 26.4839 169.708i 0.106361 0.681559i
\(250\) 99.5713 + 274.202i 0.398285 + 1.09681i
\(251\) 337.441i 1.34439i 0.740376 + 0.672193i \(0.234647\pi\)
−0.740376 + 0.672193i \(0.765353\pi\)
\(252\) −51.2101 155.204i −0.203215 0.615889i
\(253\) 267.857 + 87.0319i 1.05872 + 0.344000i
\(254\) −295.676 96.0708i −1.16408 0.378231i
\(255\) −156.650 39.6887i −0.614314 0.155642i
\(256\) 75.9506 + 233.752i 0.296682 + 0.913094i
\(257\) 190.928 0.742911 0.371455 0.928451i \(-0.378859\pi\)
0.371455 + 0.928451i \(0.378859\pi\)
\(258\) −48.2091 299.966i −0.186857 1.16266i
\(259\) 0.350735 + 0.254824i 0.00135419 + 0.000983875i
\(260\) 30.9355 18.3335i 0.118983 0.0705135i
\(261\) 77.3195 + 234.335i 0.296243 + 0.897835i
\(262\) 290.086 399.270i 1.10720 1.52393i
\(263\) −221.916 161.231i −0.843787 0.613047i 0.0796388 0.996824i \(-0.474623\pi\)
−0.923426 + 0.383776i \(0.874623\pi\)
\(264\) 205.695 105.397i 0.779148 0.399229i
\(265\) −7.85322 3.38985i −0.0296348 0.0127919i
\(266\) −72.2940 + 99.5042i −0.271782 + 0.374076i
\(267\) −36.0105 224.064i −0.134871 0.839192i
\(268\) 5.98844i 0.0223449i
\(269\) −132.545 + 43.0665i −0.492733 + 0.160099i −0.544835 0.838543i \(-0.683408\pi\)
0.0521023 + 0.998642i \(0.483408\pi\)
\(270\) −241.196 + 202.698i −0.893318 + 0.750731i
\(271\) −108.618 + 334.292i −0.400805 + 1.23355i 0.523543 + 0.851999i \(0.324610\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(272\) −65.5626 + 201.781i −0.241039 + 0.741842i
\(273\) −85.3963 166.662i −0.312807 0.610484i
\(274\) −447.841 −1.63446
\(275\) −138.146 292.184i −0.502350 1.06249i
\(276\) −14.5764 + 93.4054i −0.0528131 + 0.338426i
\(277\) 234.264 + 322.437i 0.845719 + 1.16403i 0.984790 + 0.173750i \(0.0555884\pi\)
−0.139071 + 0.990282i \(0.544412\pi\)
\(278\) 73.6381 226.635i 0.264885 0.815233i
\(279\) 146.985 204.254i 0.526829 0.732093i
\(280\) −81.9377 364.996i −0.292635 1.30356i
\(281\) 167.897 54.5530i 0.597498 0.194139i 0.00537353 0.999986i \(-0.498290\pi\)
0.592124 + 0.805847i \(0.298290\pi\)
\(282\) 5.31004 34.0266i 0.0188299 0.120662i
\(283\) −306.568 + 99.6099i −1.08328 + 0.351979i −0.795646 0.605762i \(-0.792868\pi\)
−0.287633 + 0.957741i \(0.592868\pi\)
\(284\) −46.3480 + 63.7925i −0.163197 + 0.224621i
\(285\) 61.0398 + 15.4650i 0.214175 + 0.0542632i
\(286\) −121.363 + 88.1752i −0.424345 + 0.308305i
\(287\) 767.214 + 557.414i 2.67322 + 1.94221i
\(288\) 117.762 + 160.545i 0.408895 + 0.557450i
\(289\) 139.908 101.649i 0.484111 0.351727i
\(290\) −70.0779 312.166i −0.241648 1.07643i
\(291\) 63.5589 + 63.2706i 0.218416 + 0.217425i
\(292\) 49.3070 16.0208i 0.168860 0.0548658i
\(293\) −330.675 −1.12858 −0.564292 0.825575i \(-0.690851\pi\)
−0.564292 + 0.825575i \(0.690851\pi\)
\(294\) 750.792 120.664i 2.55371 0.410421i
\(295\) −179.115 157.619i −0.607169 0.534303i
\(296\) −0.195719 0.0635929i −0.000661212 0.000214841i
\(297\) 245.128 248.494i 0.825348 0.836681i
\(298\) 157.155 + 216.305i 0.527365 + 0.725855i
\(299\) 108.321i 0.362279i
\(300\) 89.4742 61.3452i 0.298247 0.204484i
\(301\) 544.787 1.80992
\(302\) −309.626 + 224.956i −1.02525 + 0.744888i
\(303\) −35.3740 + 69.8173i −0.116746 + 0.230420i
\(304\) 25.5470 78.6254i 0.0840360 0.258636i
\(305\) 16.6420 + 28.0812i 0.0545638 + 0.0920697i
\(306\) 1.02863 + 226.279i 0.00336154 + 0.739474i
\(307\) 169.985i 0.553697i 0.960914 + 0.276849i \(0.0892901\pi\)
−0.960914 + 0.276849i \(0.910710\pi\)
\(308\) −72.5454 223.272i −0.235537 0.724908i
\(309\) 100.054 + 99.6005i 0.323800 + 0.322332i
\(310\) −215.538 + 244.932i −0.695284 + 0.790104i
\(311\) −269.449 370.864i −0.866394 1.19249i −0.980007 0.198964i \(-0.936242\pi\)
0.113613 0.993525i \(-0.463758\pi\)
\(312\) 62.9992 + 62.7135i 0.201921 + 0.201005i
\(313\) −187.842 + 258.542i −0.600133 + 0.826012i −0.995720 0.0924161i \(-0.970541\pi\)
0.395587 + 0.918428i \(0.370541\pi\)
\(314\) −100.434 138.235i −0.319852 0.440239i
\(315\) −290.233 484.695i −0.921375 1.53871i
\(316\) −19.9785 14.5153i −0.0632232 0.0459343i
\(317\) −75.8505 233.444i −0.239276 0.736415i −0.996525 0.0832897i \(-0.973457\pi\)
0.757249 0.653126i \(-0.226543\pi\)
\(318\) −1.84676 + 11.8340i −0.00580743 + 0.0372139i
\(319\) 109.533 + 337.107i 0.343362 + 1.05676i
\(320\) 69.1969 + 116.761i 0.216240 + 0.364878i
\(321\) 398.923 + 202.121i 1.24275 + 0.629659i
\(322\) −607.055 197.244i −1.88526 0.612560i
\(323\) 36.5880 26.5827i 0.113276 0.0822995i
\(324\) 95.4092 + 68.0022i 0.294473 + 0.209883i
\(325\) 90.4574 85.2578i 0.278330 0.262332i
\(326\) 45.5060i 0.139589i
\(327\) −203.717 397.581i −0.622988 1.21584i
\(328\) −428.125 139.106i −1.30526 0.424104i
\(329\) 58.7309 + 19.0828i 0.178513 + 0.0580025i
\(330\) −347.780 + 289.582i −1.05388 + 0.877522i
\(331\) −46.4064 142.824i −0.140200 0.431493i 0.856162 0.516707i \(-0.172842\pi\)
−0.996363 + 0.0852145i \(0.972842\pi\)
\(332\) 82.8156 0.249445
\(333\) −0.310788 + 0.00141280i −0.000933297 + 4.24264e-6i
\(334\) 171.907 + 124.898i 0.514691 + 0.373945i
\(335\) 4.53416 + 20.1977i 0.0135348 + 0.0602915i
\(336\) −660.112 + 338.236i −1.96462 + 1.00665i
\(337\) 371.305 511.058i 1.10180 1.51649i 0.268816 0.963192i \(-0.413368\pi\)
0.832981 0.553301i \(-0.186632\pi\)
\(338\) 272.404 + 197.913i 0.805930 + 0.585542i
\(339\) 79.9922 + 156.115i 0.235965 + 0.460517i
\(340\) 7.26140 77.5766i 0.0213571 0.228167i
\(341\) 212.465 292.433i 0.623065 0.857575i
\(342\) −0.400814 88.1712i −0.00117197 0.257811i
\(343\) 748.394i 2.18191i
\(344\) −245.945 + 79.9123i −0.714956 + 0.232303i
\(345\) 21.5591 + 326.072i 0.0624902 + 0.945137i
\(346\) 31.2221 96.0916i 0.0902371 0.277721i
\(347\) −177.557 + 546.463i −0.511690 + 1.57482i 0.277534 + 0.960716i \(0.410483\pi\)
−0.789224 + 0.614105i \(0.789517\pi\)
\(348\) −105.886 + 54.2551i −0.304270 + 0.155905i
\(349\) 461.206 1.32151 0.660754 0.750603i \(-0.270237\pi\)
0.660754 + 0.750603i \(0.270237\pi\)
\(350\) 313.087 + 662.189i 0.894534 + 1.89197i
\(351\) 120.029 + 60.1303i 0.341962 + 0.171311i
\(352\) 168.106 + 231.379i 0.477575 + 0.657326i
\(353\) 54.2919 167.093i 0.153801 0.473352i −0.844236 0.535971i \(-0.819945\pi\)
0.998037 + 0.0626196i \(0.0199455\pi\)
\(354\) −150.997 + 298.020i −0.426544 + 0.841865i
\(355\) −108.021 + 250.250i −0.304284 + 0.704930i
\(356\) 104.064 33.8125i 0.292315 0.0949790i
\(357\) −400.904 62.5632i −1.12298 0.175247i
\(358\) 201.534 65.4823i 0.562944 0.182911i
\(359\) 271.386 373.531i 0.755950 1.04048i −0.241590 0.970379i \(-0.577669\pi\)
0.997540 0.0700981i \(-0.0223312\pi\)
\(360\) 202.124 + 176.243i 0.561456 + 0.489565i
\(361\) 277.798 201.832i 0.769525 0.559092i
\(362\) −207.750 150.939i −0.573895 0.416959i
\(363\) 97.6324 98.0773i 0.268960 0.270185i
\(364\) 73.0471 53.0718i 0.200679 0.145802i
\(365\) 154.171 91.3675i 0.422387 0.250322i
\(366\) 32.2465 32.3935i 0.0881053 0.0885067i
\(367\) 375.313 121.946i 1.02265 0.332279i 0.250770 0.968047i \(-0.419316\pi\)
0.771881 + 0.635768i \(0.219316\pi\)
\(368\) 429.037 1.16586
\(369\) −679.833 + 3.09042i −1.84236 + 0.00837513i
\(370\) 0.401198 + 0.0375533i 0.00108432 + 0.000101496i
\(371\) −20.4259 6.63677i −0.0550562 0.0178889i
\(372\) 108.231 + 54.8370i 0.290944 + 0.147411i
\(373\) −203.237 279.732i −0.544871 0.749951i 0.444434 0.895812i \(-0.353405\pi\)
−0.989305 + 0.145861i \(0.953405\pi\)
\(374\) 325.037i 0.869082i
\(375\) 255.329 274.649i 0.680877 0.732398i
\(376\) −29.3133 −0.0779610
\(377\) −110.290 + 80.1304i −0.292547 + 0.212548i
\(378\) −555.545 + 563.173i −1.46970 + 1.48988i
\(379\) −115.909 + 356.732i −0.305829 + 0.941245i 0.673537 + 0.739153i \(0.264774\pi\)
−0.979367 + 0.202092i \(0.935226\pi\)
\(380\) −2.82946 + 30.2283i −0.00744594 + 0.0795481i
\(381\) 63.4151 + 394.580i 0.166444 + 1.03564i
\(382\) 229.665i 0.601217i
\(383\) 39.2793 + 120.889i 0.102557 + 0.315638i 0.989149 0.146914i \(-0.0469340\pi\)
−0.886592 + 0.462552i \(0.846934\pi\)
\(384\) 321.371 322.835i 0.836903 0.840716i
\(385\) −413.730 698.118i −1.07462 1.81329i
\(386\) −251.189 345.732i −0.650748 0.895678i
\(387\) −314.913 + 230.992i −0.813728 + 0.596879i
\(388\) −25.4162 + 34.9824i −0.0655056 + 0.0901607i
\(389\) 157.269 + 216.462i 0.404291 + 0.556458i 0.961814 0.273703i \(-0.0882484\pi\)
−0.557524 + 0.830161i \(0.688248\pi\)
\(390\) −147.258 92.7954i −0.377585 0.237937i
\(391\) 189.879 + 137.955i 0.485624 + 0.352826i
\(392\) −200.014 615.581i −0.510240 1.57036i
\(393\) −626.827 97.8197i −1.59498 0.248905i
\(394\) −243.836 750.450i −0.618873 1.90470i
\(395\) −78.3734 33.8299i −0.198414 0.0856454i
\(396\) 136.603 + 98.3022i 0.344957 + 0.248238i
\(397\) −68.6142 22.2941i −0.172832 0.0561564i 0.221323 0.975201i \(-0.428963\pi\)
−0.394155 + 0.919044i \(0.628963\pi\)
\(398\) −23.8866 + 17.3546i −0.0600165 + 0.0436045i
\(399\) 156.215 + 24.3782i 0.391517 + 0.0610983i
\(400\) −337.687 358.282i −0.844218 0.895704i
\(401\) 255.533i 0.637239i −0.947883 0.318620i \(-0.896781\pi\)
0.947883 0.318620i \(-0.103219\pi\)
\(402\) 25.7966 13.2180i 0.0641706 0.0328805i
\(403\) 132.219 + 42.9605i 0.328086 + 0.106602i
\(404\) −35.8898 11.6613i −0.0888362 0.0288646i
\(405\) 373.282 + 157.117i 0.921683 + 0.387943i
\(406\) −248.238 763.999i −0.611425 1.88177i
\(407\) −0.446429 −0.00109688
\(408\) 190.166 30.5626i 0.466093 0.0749082i
\(409\) −577.930 419.891i −1.41303 1.02663i −0.992873 0.119178i \(-0.961974\pi\)
−0.420160 0.907450i \(-0.638026\pi\)
\(410\) 877.600 + 82.1460i 2.14049 + 0.200356i
\(411\) 262.522 + 512.347i 0.638741 + 1.24659i
\(412\) −40.0101 + 55.0691i −0.0971118 + 0.133663i
\(413\) −484.660 352.126i −1.17351 0.852606i
\(414\) 434.540 143.378i 1.04961 0.346323i
\(415\) 279.319 62.7040i 0.673057 0.151094i
\(416\) −64.6550 + 88.9900i −0.155421 + 0.213918i
\(417\) −302.445 + 48.6076i −0.725288 + 0.116565i
\(418\) 126.653i 0.302997i
\(419\) 4.75627 1.54540i 0.0113515 0.00368832i −0.303336 0.952884i \(-0.598100\pi\)
0.314687 + 0.949195i \(0.398100\pi\)
\(420\) 209.326 174.297i 0.498395 0.414993i
\(421\) −34.6754 + 106.720i −0.0823643 + 0.253491i −0.983755 0.179515i \(-0.942547\pi\)
0.901391 + 0.433006i \(0.142547\pi\)
\(422\) 261.219 803.950i 0.619003 1.90509i
\(423\) −42.0405 + 13.8714i −0.0993865 + 0.0327929i
\(424\) 10.1948 0.0240444
\(425\) −34.2462 267.147i −0.0805793 0.628580i
\(426\) 377.103 + 58.8489i 0.885217 + 0.138143i
\(427\) 48.1751 + 66.3073i 0.112822 + 0.155287i
\(428\) −66.6306 + 205.068i −0.155679 + 0.479131i
\(429\) 172.018 + 87.1557i 0.400975 + 0.203160i
\(430\) 435.608 258.157i 1.01304 0.600366i
\(431\) −418.838 + 136.089i −0.971783 + 0.315751i −0.751535 0.659693i \(-0.770686\pi\)
−0.220247 + 0.975444i \(0.570686\pi\)
\(432\) 238.163 475.407i 0.551303 1.10048i
\(433\) 701.374 227.890i 1.61980 0.526305i 0.647906 0.761720i \(-0.275645\pi\)
0.971895 + 0.235415i \(0.0756449\pi\)
\(434\) −481.519 + 662.754i −1.10949 + 1.52708i
\(435\) −316.050 + 263.162i −0.726553 + 0.604970i
\(436\) 174.257 126.605i 0.399673 0.290380i
\(437\) −73.9877 53.7552i −0.169308 0.123010i
\(438\) −177.846 177.039i −0.406041 0.404200i
\(439\) −150.664 + 109.464i −0.343199 + 0.249349i −0.746010 0.665934i \(-0.768033\pi\)
0.402811 + 0.915283i \(0.368033\pi\)
\(440\) 289.183 + 254.478i 0.657234 + 0.578360i
\(441\) −578.155 788.202i −1.31101 1.78731i
\(442\) −118.893 + 38.6307i −0.268989 + 0.0873998i
\(443\) 474.687 1.07153 0.535764 0.844368i \(-0.320024\pi\)
0.535764 + 0.844368i \(0.320024\pi\)
\(444\) −0.0237779 0.147950i −5.35537e−5 0.000333221i
\(445\) 325.384 192.834i 0.731200 0.433336i
\(446\) −506.475 164.564i −1.13559 0.368977i
\(447\) 155.338 306.588i 0.347511 0.685879i
\(448\) 200.311 + 275.704i 0.447122 + 0.615411i
\(449\) 211.075i 0.470100i 0.971983 + 0.235050i \(0.0755254\pi\)
−0.971983 + 0.235050i \(0.924475\pi\)
\(450\) −461.750 250.027i −1.02611 0.555615i
\(451\) −976.541 −2.16528
\(452\) −68.4244 + 49.7133i −0.151381 + 0.109985i
\(453\) 438.860 + 222.355i 0.968786 + 0.490850i
\(454\) −224.077 + 689.637i −0.493561 + 1.51902i
\(455\) 206.188 234.307i 0.453160 0.514961i
\(456\) −74.0995 + 11.9089i −0.162499 + 0.0261161i
\(457\) 353.601i 0.773743i −0.922134 0.386872i \(-0.873556\pi\)
0.922134 0.386872i \(-0.126444\pi\)
\(458\) −87.5251 269.374i −0.191103 0.588154i
\(459\) 258.269 133.821i 0.562677 0.291548i
\(460\) −153.734 + 34.5116i −0.334204 + 0.0750252i
\(461\) 175.509 + 241.567i 0.380713 + 0.524007i 0.955773 0.294104i \(-0.0950214\pi\)
−0.575060 + 0.818111i \(0.695021\pi\)
\(462\) −801.669 + 805.322i −1.73521 + 1.74312i
\(463\) 305.117 419.957i 0.659000 0.907035i −0.340448 0.940263i \(-0.610579\pi\)
0.999448 + 0.0332279i \(0.0105787\pi\)
\(464\) 317.379 + 436.835i 0.684007 + 0.941454i
\(465\) 406.560 + 103.006i 0.874322 + 0.221517i
\(466\) 759.277 + 551.647i 1.62935 + 1.18379i
\(467\) 131.808 + 405.664i 0.282244 + 0.868659i 0.987211 + 0.159419i \(0.0509619\pi\)
−0.704967 + 0.709240i \(0.749038\pi\)
\(468\) −19.7220 + 61.6503i −0.0421411 + 0.131732i
\(469\) 16.0615 + 49.4321i 0.0342462 + 0.105399i
\(470\) 56.0036 12.5722i 0.119157 0.0267494i
\(471\) −99.2724 + 195.933i −0.210769 + 0.415993i
\(472\) 270.453 + 87.8754i 0.572993 + 0.186177i
\(473\) −453.853 + 329.744i −0.959521 + 0.697133i
\(474\) −18.4303 + 118.101i −0.0388824 + 0.249158i
\(475\) 13.3443 + 104.096i 0.0280932 + 0.219149i
\(476\) 195.637i 0.411001i
\(477\) 14.6212 4.82429i 0.0306523 0.0101138i
\(478\) −435.715 141.573i −0.911539 0.296177i
\(479\) −280.502 91.1407i −0.585600 0.190273i 0.00120777 0.999999i \(-0.499616\pi\)
−0.586808 + 0.809726i \(0.699616\pi\)
\(480\) −176.915 + 280.749i −0.368573 + 0.584893i
\(481\) −0.0530582 0.163296i −0.000110308 0.000339493i
\(482\) −842.137 −1.74717
\(483\) 130.198 + 810.118i 0.269562 + 1.67726i
\(484\) 53.9810 + 39.2195i 0.111531 + 0.0810320i
\(485\) −59.2361 + 137.232i −0.122136 + 0.282952i
\(486\) 82.3436 561.095i 0.169431 1.15452i
\(487\) −389.881 + 536.625i −0.800576 + 1.10190i 0.192133 + 0.981369i \(0.438459\pi\)
−0.992710 + 0.120530i \(0.961541\pi\)
\(488\) −31.4751 22.8680i −0.0644981 0.0468606i
\(489\) −52.0606 + 26.6754i −0.106463 + 0.0545509i
\(490\) 646.147 + 1090.29i 1.31867 + 2.22509i
\(491\) 315.408 434.122i 0.642379 0.884158i −0.356361 0.934348i \(-0.615983\pi\)
0.998740 + 0.0501900i \(0.0159827\pi\)
\(492\) −52.0129 323.634i −0.105717 0.657792i
\(493\) 295.382i 0.599152i
\(494\) 46.3276 15.0527i 0.0937805 0.0304711i
\(495\) 535.161 + 228.122i 1.08113 + 0.460853i
\(496\) 170.157 523.690i 0.343059 1.05583i
\(497\) −211.487 + 650.889i −0.425527 + 1.30964i
\(498\) −182.795 356.748i −0.367057 0.716361i
\(499\) −791.222 −1.58562 −0.792808 0.609472i \(-0.791382\pi\)
−0.792808 + 0.609472i \(0.791382\pi\)
\(500\) 149.821 + 101.217i 0.299642 + 0.202434i
\(501\) 42.1166 269.882i 0.0840651 0.538688i
\(502\) 462.885 + 637.107i 0.922082 + 1.26914i
\(503\) −135.778 + 417.883i −0.269937 + 0.830781i 0.720578 + 0.693374i \(0.243877\pi\)
−0.990515 + 0.137407i \(0.956123\pi\)
\(504\) 546.541 + 393.302i 1.08441 + 0.780360i
\(505\) −129.878 12.1570i −0.257184 0.0240732i
\(506\) 625.115 203.112i 1.23540 0.401407i
\(507\) 66.7382 427.657i 0.131633 0.843505i
\(508\) −183.259 + 59.5443i −0.360745 + 0.117213i
\(509\) −311.605 + 428.888i −0.612191 + 0.842609i −0.996755 0.0804893i \(-0.974352\pi\)
0.384564 + 0.923098i \(0.374352\pi\)
\(510\) −350.207 + 139.951i −0.686681 + 0.274413i
\(511\) 364.040 264.490i 0.712406 0.517593i
\(512\) −27.3195 19.8488i −0.0533584 0.0387671i
\(513\) −100.636 + 52.1442i −0.196172 + 0.101646i
\(514\) 360.483 261.906i 0.701328 0.509545i
\(515\) −93.2493 + 216.030i −0.181067 + 0.419475i
\(516\) −133.453 132.848i −0.258630 0.257457i
\(517\) −60.4781 + 19.6505i −0.116979 + 0.0380088i
\(518\) 1.01176 0.00195321
\(519\) −128.235 + 20.6093i −0.247080 + 0.0397096i
\(520\) −58.7145 + 136.023i −0.112912 + 0.261583i
\(521\) 363.355 + 118.061i 0.697419 + 0.226605i 0.636206 0.771519i \(-0.280503\pi\)
0.0612134 + 0.998125i \(0.480503\pi\)
\(522\) 467.433 + 336.374i 0.895466 + 0.644395i
\(523\) 66.4150 + 91.4124i 0.126988 + 0.174785i 0.867777 0.496953i \(-0.165548\pi\)
−0.740789 + 0.671738i \(0.765548\pi\)
\(524\) 305.885i 0.583749i
\(525\) 574.040 746.356i 1.09341 1.42163i
\(526\) −640.159 −1.21703
\(527\) 243.697 177.056i 0.462422 0.335970i
\(528\) 345.205 681.326i 0.653797 1.29039i
\(529\) −16.8065 + 51.7251i −0.0317703 + 0.0977790i
\(530\) −19.4774 + 4.37246i −0.0367497 + 0.00824992i
\(531\) 429.460 1.95227i 0.808777 0.00367658i
\(532\) 76.2312i 0.143292i
\(533\) −116.062 357.202i −0.217753 0.670174i
\(534\) −375.351 373.648i −0.702904 0.699716i
\(535\) −69.4626 + 742.098i −0.129837 + 1.38710i
\(536\) −14.5019 19.9602i −0.0270559 0.0372392i
\(537\) −193.053 192.177i −0.359502 0.357871i
\(538\) −191.176 + 263.131i −0.355346 + 0.489091i
\(539\) −825.322 1135.96i −1.53121 2.10753i
\(540\) −47.0976 + 189.507i −0.0872179 + 0.350939i
\(541\) −53.3470 38.7589i −0.0986082 0.0716431i 0.537389 0.843335i \(-0.319411\pi\)
−0.635997 + 0.771692i \(0.719411\pi\)
\(542\) 253.489 + 780.160i 0.467692 + 1.43941i
\(543\) −50.8981 + 326.154i −0.0937350 + 0.600652i
\(544\) 73.6496 + 226.670i 0.135385 + 0.416673i
\(545\) 491.872 558.951i 0.902517 1.02560i
\(546\) −389.852 197.525i −0.714015 0.361767i
\(547\) −807.148 262.258i −1.47559 0.479448i −0.542798 0.839863i \(-0.682635\pi\)
−0.932792 + 0.360415i \(0.882635\pi\)
\(548\) −224.559 + 163.152i −0.409779 + 0.297722i
\(549\) −55.9622 17.9024i −0.101935 0.0326090i
\(550\) −661.632 362.157i −1.20297 0.658467i
\(551\) 115.098i 0.208889i
\(552\) −177.611 346.631i −0.321759 0.627955i
\(553\) −203.845 66.2334i −0.368617 0.119771i
\(554\) 884.607 + 287.426i 1.59676 + 0.518820i
\(555\) −0.192218 0.481000i −0.000346339 0.000866666i
\(556\) −45.6406 140.467i −0.0820874 0.252639i
\(557\) 309.269 0.555241 0.277621 0.960691i \(-0.410454\pi\)
0.277621 + 0.960691i \(0.410454\pi\)
\(558\) −2.66965 587.270i −0.00478431 1.05246i
\(559\) −174.555 126.822i −0.312264 0.226873i
\(560\) −928.039 816.665i −1.65721 1.45833i
\(561\) 371.855 190.535i 0.662843 0.339635i
\(562\) 242.165 333.312i 0.430899 0.593082i
\(563\) 426.536 + 309.897i 0.757614 + 0.550438i 0.898177 0.439633i \(-0.144892\pi\)
−0.140564 + 0.990072i \(0.544892\pi\)
\(564\) −9.73355 18.9963i −0.0172581 0.0336814i
\(565\) −193.140 + 219.479i −0.341840 + 0.388459i
\(566\) −442.177 + 608.604i −0.781231 + 1.07527i
\(567\) 969.950 + 305.435i 1.71067 + 0.538686i
\(568\) 324.867i 0.571949i
\(569\) 619.336 201.235i 1.08846 0.353663i 0.290811 0.956780i \(-0.406075\pi\)
0.797653 + 0.603117i \(0.206075\pi\)
\(570\) 136.461 54.5328i 0.239405 0.0956715i
\(571\) −179.914 + 553.718i −0.315086 + 0.969734i 0.660634 + 0.750708i \(0.270288\pi\)
−0.975719 + 0.219025i \(0.929712\pi\)
\(572\) −28.7315 + 88.4266i −0.0502300 + 0.154592i
\(573\) 262.746 134.629i 0.458544 0.234954i
\(574\) 2213.18 3.85571
\(575\) −492.379 + 232.800i −0.856312 + 0.404869i
\(576\) −232.689 74.4376i −0.403974 0.129232i
\(577\) 135.871 + 187.010i 0.235478 + 0.324107i 0.910359 0.413819i \(-0.135805\pi\)
−0.674881 + 0.737926i \(0.735805\pi\)
\(578\) 124.717 383.838i 0.215773 0.664080i
\(579\) −248.285 + 490.036i −0.428816 + 0.846349i
\(580\) −148.863 130.998i −0.256660 0.225859i
\(581\) 683.609 222.118i 1.17661 0.382303i
\(582\) 206.794 + 32.2714i 0.355317 + 0.0554491i
\(583\) 21.0335 6.83420i 0.0360781 0.0117225i
\(584\) −125.549 + 172.804i −0.214982 + 0.295897i
\(585\) −19.8393 + 222.865i −0.0339134 + 0.380967i
\(586\) −624.333 + 453.604i −1.06541 + 0.774069i
\(587\) −443.896 322.509i −0.756212 0.549420i 0.141534 0.989933i \(-0.454796\pi\)
−0.897746 + 0.440513i \(0.854796\pi\)
\(588\) 332.508 334.023i 0.565489 0.568066i
\(589\) −94.9581 + 68.9911i −0.161219 + 0.117133i
\(590\) −554.393 51.8929i −0.939650 0.0879540i
\(591\) −715.608 + 718.869i −1.21084 + 1.21636i
\(592\) −0.646781 + 0.210152i −0.00109254 + 0.000354986i
\(593\) −1005.47 −1.69557 −0.847783 0.530343i \(-0.822063\pi\)
−0.847783 + 0.530343i \(0.822063\pi\)
\(594\) 121.943 805.426i 0.205292 1.35594i
\(595\) −148.127 659.838i −0.248952 1.10897i
\(596\) 157.603 + 51.2082i 0.264434 + 0.0859199i
\(597\) 33.8565 + 17.1540i 0.0567111 + 0.0287336i
\(598\) 148.590 + 204.517i 0.248478 + 0.342001i
\(599\) 288.607i 0.481814i −0.970548 0.240907i \(-0.922555\pi\)
0.970548 0.240907i \(-0.0774449\pi\)
\(600\) −149.672 + 421.147i −0.249453 + 0.701912i
\(601\) 265.405 0.441605 0.220802 0.975319i \(-0.429132\pi\)
0.220802 + 0.975319i \(0.429132\pi\)
\(602\) 1028.59 747.312i 1.70862 1.24138i
\(603\) −30.2437 21.7640i −0.0501554 0.0360928i
\(604\) −73.3011 + 225.598i −0.121359 + 0.373506i
\(605\) 211.761 + 91.4068i 0.350018 + 0.151086i
\(606\) 28.9839 + 180.343i 0.0478282 + 0.297596i
\(607\) 357.546i 0.589038i −0.955646 0.294519i \(-0.904841\pi\)
0.955646 0.294519i \(-0.0951595\pi\)
\(608\) −28.6981 88.3237i −0.0472008 0.145269i
\(609\) −728.528 + 731.848i −1.19627 + 1.20172i
\(610\) 69.9415 + 30.1903i 0.114658 + 0.0494923i
\(611\) −14.3757 19.7864i −0.0235281 0.0323837i
\(612\) 82.9508 + 113.087i 0.135541 + 0.184783i
\(613\) −201.824 + 277.787i −0.329240 + 0.453160i −0.941260 0.337682i \(-0.890357\pi\)
0.612020 + 0.790842i \(0.290357\pi\)
\(614\) 233.178 + 320.941i 0.379768 + 0.522706i
\(615\) −420.468 1052.16i −0.683687 1.71083i
\(616\) 782.490 + 568.512i 1.27028 + 0.922910i
\(617\) 47.6139 + 146.541i 0.0771701 + 0.237505i 0.982198 0.187846i \(-0.0601506\pi\)
−0.905028 + 0.425351i \(0.860151\pi\)
\(618\) 325.535 + 50.8015i 0.526756 + 0.0822031i
\(619\) −321.394 989.150i −0.519216 1.59798i −0.775479 0.631374i \(-0.782491\pi\)
0.256263 0.966607i \(-0.417509\pi\)
\(620\) −18.8458 + 201.337i −0.0303964 + 0.324738i
\(621\) −418.755 413.083i −0.674323 0.665189i
\(622\) −1017.47 330.595i −1.63580 0.531504i
\(623\) 768.319 558.216i 1.23326 0.896014i
\(624\) 290.245 + 45.2944i 0.465137 + 0.0725871i
\(625\) 581.950 + 227.945i 0.931120 + 0.364713i
\(626\) 745.814i 1.19140i
\(627\) −144.896 + 74.2434i −0.231094 + 0.118411i
\(628\) −100.720 32.7259i −0.160382 0.0521113i
\(629\) −0.353819 0.114963i −0.000562511 0.000182771i
\(630\) −1212.86 517.003i −1.92517 0.820640i
\(631\) 271.623 + 835.969i 0.430464 + 1.32483i 0.897664 + 0.440681i \(0.145263\pi\)
−0.467200 + 0.884152i \(0.654737\pi\)
\(632\) 101.742 0.160984
\(633\) −1072.88 + 172.427i −1.69491 + 0.272397i
\(634\) −463.437 336.707i −0.730973 0.531083i
\(635\) −573.006 + 339.584i −0.902372 + 0.534778i
\(636\) 3.38521 + 6.60668i 0.00532265 + 0.0103879i
\(637\) 317.425 436.898i 0.498313 0.685869i
\(638\) 669.231 + 486.224i 1.04895 + 0.762107i
\(639\) −153.731 465.917i −0.240580 0.729134i
\(640\) 697.041 + 300.878i 1.08913 + 0.470122i
\(641\) −305.155 + 420.009i −0.476060 + 0.655241i −0.977742 0.209812i \(-0.932715\pi\)
0.501682 + 0.865052i \(0.332715\pi\)
\(642\) 1030.45 165.609i 1.60506 0.257957i
\(643\) 702.045i 1.09183i −0.837842 0.545914i \(-0.816183\pi\)
0.837842 0.545914i \(-0.183817\pi\)
\(644\) −376.250 + 122.251i −0.584240 + 0.189831i
\(645\) −550.693 347.022i −0.853788 0.538018i
\(646\) 32.6152 100.379i 0.0504880 0.155386i
\(647\) −95.5712 + 294.138i −0.147714 + 0.454618i −0.997350 0.0727520i \(-0.976822\pi\)
0.849636 + 0.527370i \(0.176822\pi\)
\(648\) −482.689 + 4.38856i −0.744890 + 0.00677247i
\(649\) 616.895 0.950532
\(650\) 53.8360 285.056i 0.0828246 0.438548i
\(651\) 1040.48 + 162.373i 1.59828 + 0.249420i
\(652\) −16.5781 22.8179i −0.0254266 0.0349967i
\(653\) 40.3685 124.241i 0.0618200 0.190263i −0.915377 0.402598i \(-0.868107\pi\)
0.977197 + 0.212336i \(0.0681071\pi\)
\(654\) −930.012 471.205i −1.42204 0.720497i
\(655\) −231.601 1031.68i −0.353589 1.57508i
\(656\) −1414.80 + 459.697i −2.15671 + 0.700757i
\(657\) −98.2873 + 307.243i −0.149600 + 0.467645i
\(658\) 137.064 44.5348i 0.208304 0.0676821i
\(659\) 543.472 748.024i 0.824691 1.13509i −0.164197 0.986428i \(-0.552503\pi\)
0.988888 0.148663i \(-0.0474968\pi\)
\(660\) −68.8891 + 271.903i −0.104377 + 0.411974i
\(661\) −723.767 + 525.847i −1.09496 + 0.795533i −0.980230 0.197864i \(-0.936600\pi\)
−0.114728 + 0.993397i \(0.536600\pi\)
\(662\) −283.537 206.002i −0.428304 0.311181i
\(663\) 113.890 + 113.373i 0.171779 + 0.171000i
\(664\) −276.035 + 200.551i −0.415715 + 0.302035i
\(665\) 57.7186 + 257.111i 0.0867949 + 0.386633i
\(666\) −0.584847 + 0.428991i −0.000878148 + 0.000644131i
\(667\) 568.082 184.581i 0.851697 0.276733i
\(668\) 131.700 0.197155
\(669\) 108.626 + 675.893i 0.162371 + 1.01030i
\(670\) 36.2669 + 31.9146i 0.0541298 + 0.0476337i
\(671\) −80.2679 26.0806i −0.119624 0.0388683i
\(672\) −376.582 + 743.255i −0.560390 + 1.10603i
\(673\) −157.836 217.242i −0.234526 0.322797i 0.675491 0.737368i \(-0.263932\pi\)
−0.910017 + 0.414571i \(0.863932\pi\)
\(674\) 1474.25i 2.18731i
\(675\) −15.3642 + 674.825i −0.0227618 + 0.999741i
\(676\) 208.692 0.308716
\(677\) 674.872 490.323i 0.996857 0.724259i 0.0354451 0.999372i \(-0.488715\pi\)
0.961412 + 0.275113i \(0.0887151\pi\)
\(678\) 365.181 + 185.025i 0.538615 + 0.272898i
\(679\) −115.975 + 356.933i −0.170802 + 0.525674i
\(680\) 163.661 + 276.157i 0.240678 + 0.406114i
\(681\) 920.325 147.910i 1.35143 0.217196i
\(682\) 843.580i 1.23692i
\(683\) 244.142 + 751.391i 0.357455 + 1.10013i 0.954572 + 0.297980i \(0.0963127\pi\)
−0.597117 + 0.802154i \(0.703687\pi\)
\(684\) −32.3224 44.0653i −0.0472549 0.0644230i
\(685\) −633.856 + 720.299i −0.925338 + 1.05153i
\(686\) 1026.61 + 1413.01i 1.49652 + 2.05978i
\(687\) −256.868 + 258.038i −0.373898 + 0.375602i
\(688\) −502.314 + 691.376i −0.730107 + 1.00491i
\(689\) 4.99968 + 6.88147i 0.00725643 + 0.00998762i
\(690\) 487.995 + 586.069i 0.707240 + 0.849375i
\(691\) −760.429 552.484i −1.10048 0.799543i −0.119339 0.992854i \(-0.538078\pi\)
−0.981138 + 0.193310i \(0.938078\pi\)
\(692\) −19.3513 59.5572i −0.0279643 0.0860653i
\(693\) 1391.25 + 445.064i 2.00758 + 0.642228i
\(694\) 414.375 + 1275.32i 0.597082 + 1.83763i
\(695\) −260.291 439.208i −0.374519 0.631954i
\(696\) 221.544 437.259i 0.318310 0.628245i
\(697\) −773.962 251.475i −1.11042 0.360797i
\(698\) 870.783 632.661i 1.24754 0.906390i
\(699\) 186.020 1192.02i 0.266124 1.70532i
\(700\) 398.230 + 217.979i 0.568900 + 0.311398i
\(701\) 959.479i 1.36873i −0.729140 0.684365i \(-0.760080\pi\)
0.729140 0.684365i \(-0.239920\pi\)
\(702\) 309.105 51.1203i 0.440320 0.0728210i
\(703\) 0.137868 + 0.0447961i 0.000196114 + 6.37213e-5i
\(704\) −333.752 108.443i −0.474079 0.154038i
\(705\) −47.2122 56.7005i −0.0669676 0.0804263i
\(706\) −126.704 389.956i −0.179468 0.552346i
\(707\) −327.532 −0.463271
\(708\) 32.8573 + 204.444i 0.0464086 + 0.288763i
\(709\) 394.579 + 286.678i 0.556529 + 0.404342i 0.830187 0.557485i \(-0.188234\pi\)
−0.273658 + 0.961827i \(0.588234\pi\)
\(710\) 139.332 + 620.664i 0.196243 + 0.874175i
\(711\) 145.916 48.1453i 0.205226 0.0677150i
\(712\) −264.977 + 364.709i −0.372158 + 0.512232i
\(713\) −492.799 358.040i −0.691163 0.502160i
\(714\) −842.750 + 431.818i −1.18032 + 0.604788i
\(715\) −29.9527 + 319.997i −0.0418919 + 0.447549i
\(716\) 77.1985 106.255i 0.107819 0.148400i
\(717\) 93.4502 + 581.465i 0.130335 + 0.810969i
\(718\) 1077.52i 1.50073i
\(719\) −9.24954 + 3.00536i −0.0128644 + 0.00417991i −0.315442 0.948945i \(-0.602153\pi\)
0.302578 + 0.953125i \(0.402153\pi\)
\(720\) 882.721 + 78.5792i 1.22600 + 0.109138i
\(721\) −182.567 + 561.883i −0.253213 + 0.779311i
\(722\) 247.635 762.141i 0.342984 1.05560i
\(723\) 493.658 + 963.438i 0.682790 + 1.33256i
\(724\) −159.159 −0.219834
\(725\) −601.267 329.115i −0.829334 0.453952i
\(726\) 49.7977 319.103i 0.0685919 0.439536i
\(727\) 542.782 + 747.076i 0.746606 + 1.02761i 0.998211 + 0.0597846i \(0.0190414\pi\)
−0.251606 + 0.967830i \(0.580959\pi\)
\(728\) −114.953 + 353.790i −0.157903 + 0.485975i
\(729\) −690.184 + 234.707i −0.946754 + 0.321958i
\(730\) 165.750 383.992i 0.227055 0.526016i
\(731\) −444.618 + 144.465i −0.608232 + 0.197627i
\(732\) 4.36808 27.9906i 0.00596732 0.0382385i
\(733\) −527.602 + 171.428i −0.719784 + 0.233872i −0.645929 0.763397i \(-0.723530\pi\)
−0.0738544 + 0.997269i \(0.523530\pi\)
\(734\) 541.331 745.078i 0.737508 1.01509i
\(735\) 868.568 1378.34i 1.18173 1.87530i
\(736\) 389.912 283.288i 0.529772 0.384902i
\(737\) −43.3004 31.4596i −0.0587522 0.0426860i
\(738\) −1279.32 + 938.397i −1.73350 + 1.27154i
\(739\) 1100.89 799.845i 1.48970 1.08233i 0.515440 0.856925i \(-0.327628\pi\)
0.974264 0.225408i \(-0.0723717\pi\)
\(740\) 0.214852 0.127329i 0.000290340 0.000172066i
\(741\) −44.3779 44.1767i −0.0598893 0.0596176i
\(742\) −47.6692 + 15.4887i −0.0642442 + 0.0208742i
\(743\) 124.104 0.167031 0.0835155 0.996506i \(-0.473385\pi\)
0.0835155 + 0.996506i \(0.473385\pi\)
\(744\) −493.545 + 79.3201i −0.663366 + 0.106613i
\(745\) 570.331 + 53.3847i 0.765545 + 0.0716573i
\(746\) −767.445 249.358i −1.02875 0.334260i
\(747\) −300.980 + 418.248i −0.402918 + 0.559904i
\(748\) 118.413 + 162.982i 0.158306 + 0.217890i
\(749\) 1871.46i 2.49861i
\(750\) 105.324 868.801i 0.140432 1.15840i
\(751\) 632.917 0.842766 0.421383 0.906883i \(-0.361545\pi\)
0.421383 + 0.906883i \(0.361545\pi\)
\(752\) −78.3697 + 56.9389i −0.104215 + 0.0757166i
\(753\) 457.534 903.028i 0.607614 1.19924i
\(754\) −98.3147 + 302.581i −0.130391 + 0.401302i
\(755\) −76.4166 + 816.390i −0.101214 + 1.08131i
\(756\) −73.3965 + 484.778i −0.0970853 + 0.641241i
\(757\) 1271.62i 1.67981i 0.542734 + 0.839904i \(0.317389\pi\)
−0.542734 + 0.839904i \(0.682611\pi\)
\(758\) 270.505 + 832.529i 0.356867 + 1.09832i
\(759\) −598.808 596.092i −0.788943 0.785365i
\(760\) −63.7716 107.607i −0.0839100 0.141588i
\(761\) 706.088 + 971.847i 0.927843 + 1.27707i 0.960695 + 0.277606i \(0.0895409\pi\)
−0.0328525 + 0.999460i \(0.510459\pi\)
\(762\) 660.998 + 658.000i 0.867451 + 0.863517i
\(763\) 1098.86 1512.45i 1.44018 1.98224i
\(764\) 83.6686 + 115.160i 0.109514 + 0.150733i
\(765\) 365.399 + 318.612i 0.477646 + 0.416486i
\(766\) 239.992 + 174.364i 0.313305 + 0.227629i
\(767\) 73.3182 + 225.650i 0.0955908 + 0.294198i
\(768\) 113.690 728.527i 0.148034 0.948602i
\(769\) −164.777 507.132i −0.214275 0.659469i −0.999204 0.0398846i \(-0.987301\pi\)
0.784930 0.619585i \(-0.212699\pi\)
\(770\) −1738.79 750.550i −2.25817 0.974740i
\(771\) −510.944 258.878i −0.662703 0.335769i
\(772\) −251.905 81.8489i −0.326302 0.106022i
\(773\) −816.217 + 593.017i −1.05591 + 0.767163i −0.973327 0.229422i \(-0.926316\pi\)
−0.0825815 + 0.996584i \(0.526316\pi\)
\(774\) −277.709 + 868.108i −0.358797 + 1.12159i
\(775\) 88.8804 + 693.335i 0.114684 + 0.894626i
\(776\) 178.150i 0.229575i
\(777\) −0.593090 1.15749i −0.000763308 0.00148970i
\(778\) 593.865 + 192.959i 0.763323 + 0.248019i
\(779\) 301.580 + 97.9892i 0.387137 + 0.125788i
\(780\) −107.645 + 7.11723i −0.138007 + 0.00912466i
\(781\) −217.778 670.253i −0.278846 0.858198i
\(782\) 547.742 0.700437
\(783\) 110.818 731.943i 0.141530 0.934793i
\(784\) −1730.46 1257.25i −2.20722 1.60364i
\(785\) −364.484 34.1168i −0.464311 0.0434609i
\(786\) −1317.67 + 675.163i −1.67642 + 0.858986i
\(787\) 527.782 726.430i 0.670625 0.923037i −0.329149 0.944278i \(-0.606762\pi\)
0.999774 + 0.0212413i \(0.00676184\pi\)
\(788\) −395.660 287.464i −0.502107 0.364802i
\(789\) 375.259 + 732.367i 0.475613 + 0.928222i
\(790\) −194.380 + 43.6361i −0.246050 + 0.0552356i
\(791\) −431.480 + 593.882i −0.545487 + 0.750799i
\(792\) −693.369 + 3.15196i −0.875466 + 0.00397974i
\(793\) 32.4604i 0.0409336i
\(794\) −160.129 + 52.0292i −0.201674 + 0.0655279i
\(795\) 16.4198 + 19.7197i 0.0206538 + 0.0248047i
\(796\) −5.65493 + 17.4041i −0.00710419 + 0.0218644i
\(797\) 24.0490 74.0152i 0.0301744 0.0928673i −0.934835 0.355082i \(-0.884453\pi\)
0.965010 + 0.262215i \(0.0844529\pi\)
\(798\) 328.384 168.261i 0.411508 0.210854i
\(799\) −52.9925 −0.0663235
\(800\) −543.462 102.639i −0.679327 0.128298i
\(801\) −207.439 + 648.447i −0.258975 + 0.809547i
\(802\) −350.528 482.460i −0.437067 0.601572i
\(803\) −143.187 + 440.685i −0.178316 + 0.548799i
\(804\) 8.11968 16.0257i 0.0100991 0.0199325i
\(805\) −1176.45 + 697.205i −1.46142 + 0.866093i
\(806\) 308.568 100.260i 0.382838 0.124392i
\(807\) 413.099 + 64.4663i 0.511894 + 0.0798839i
\(808\) 147.865 48.0443i 0.183001 0.0594607i
\(809\) 503.318 692.758i 0.622148 0.856314i −0.375359 0.926880i \(-0.622481\pi\)
0.997507 + 0.0705660i \(0.0224805\pi\)
\(810\) 920.302 215.405i 1.13618 0.265932i
\(811\) 859.986 624.817i 1.06040 0.770427i 0.0862396 0.996274i \(-0.472515\pi\)
0.974163 + 0.225847i \(0.0725149\pi\)
\(812\) −402.803 292.654i −0.496063 0.360411i
\(813\) 743.938 747.328i 0.915053 0.919222i
\(814\) −0.842883 + 0.612390i −0.00103548 + 0.000752322i
\(815\) −73.1910 64.4074i −0.0898049 0.0790274i
\(816\) 449.046 451.092i 0.550302 0.552809i
\(817\) 173.249 56.2919i 0.212055 0.0689007i
\(818\) −1667.15 −2.03808
\(819\) 2.55384 + 561.794i 0.00311824 + 0.685951i
\(820\) 469.978 278.526i 0.573144 0.339666i
\(821\) 711.389 + 231.144i 0.866491 + 0.281540i 0.708337 0.705874i \(-0.249446\pi\)
0.158154 + 0.987414i \(0.449446\pi\)
\(822\) 1198.47 + 607.224i 1.45799 + 0.738715i
\(823\) −458.192 630.647i −0.556733 0.766278i 0.434173 0.900829i \(-0.357041\pi\)
−0.990907 + 0.134552i \(0.957041\pi\)
\(824\) 280.443i 0.340343i
\(825\) −26.4758 + 969.227i −0.0320918 + 1.17482i
\(826\) −1398.10 −1.69261
\(827\) 551.236 400.497i 0.666549 0.484276i −0.202319 0.979320i \(-0.564848\pi\)
0.868868 + 0.495043i \(0.164848\pi\)
\(828\) 165.656 230.199i 0.200067 0.278018i
\(829\) 131.487 404.674i 0.158609 0.488147i −0.839900 0.542741i \(-0.817386\pi\)
0.998509 + 0.0545941i \(0.0173865\pi\)
\(830\) 441.355 501.545i 0.531753 0.604271i
\(831\) −189.726 1180.51i −0.228311 1.42059i
\(832\) 134.969i 0.162223i
\(833\) −361.585 1112.84i −0.434075 1.33595i
\(834\) −504.356 + 506.654i −0.604743 + 0.607499i
\(835\) 444.193 99.7166i 0.531968 0.119421i
\(836\) −46.1406 63.5070i −0.0551921 0.0759653i
\(837\) −670.295 + 347.310i −0.800830 + 0.414946i
\(838\) 6.86018 9.44223i 0.00818637 0.0112676i
\(839\) 795.202 + 1094.50i 0.947797 + 1.30453i 0.952499 + 0.304542i \(0.0985033\pi\)
−0.00470187 + 0.999989i \(0.501497\pi\)
\(840\) −275.622 + 1087.87i −0.328121 + 1.29508i
\(841\) −72.2106 52.4640i −0.0858627 0.0623829i
\(842\) 80.9242 + 249.059i 0.0961095 + 0.295795i
\(843\) −523.278 81.6603i −0.620733 0.0968687i
\(844\) −161.903 498.285i −0.191828 0.590385i
\(845\) 703.871 158.011i 0.832983 0.186996i
\(846\) −60.3467 + 83.8591i −0.0713318 + 0.0991242i
\(847\) 550.780 + 178.959i 0.650272 + 0.211286i
\(848\) 27.2560 19.8026i 0.0321415 0.0233522i
\(849\) 955.469 + 149.106i 1.12541 + 0.175626i
\(850\) −431.118 457.410i −0.507197 0.538130i
\(851\) 0.752308i 0.000884028i
\(852\) 210.528 107.873i 0.247099 0.126611i
\(853\) 1153.47 + 374.784i 1.35225 + 0.439372i 0.893448 0.449167i \(-0.148279\pi\)
0.458800 + 0.888539i \(0.348279\pi\)
\(854\) 181.915 + 59.1076i 0.213015 + 0.0692127i
\(855\) −142.380 124.149i −0.166527 0.145204i
\(856\) −274.516 844.873i −0.320696 0.987002i
\(857\) −549.363 −0.641031 −0.320515 0.947243i \(-0.603856\pi\)
−0.320515 + 0.947243i \(0.603856\pi\)
\(858\) 444.336 71.4115i 0.517874 0.0832302i
\(859\) 414.050 + 300.825i 0.482013 + 0.350203i 0.802105 0.597183i \(-0.203714\pi\)
−0.320091 + 0.947387i \(0.603714\pi\)
\(860\) 124.377 288.142i 0.144624 0.335049i
\(861\) −1297.35 2531.96i −1.50680 2.94072i
\(862\) −604.110 + 831.486i −0.700823 + 0.964601i
\(863\) 342.771 + 249.038i 0.397185 + 0.288572i 0.768394 0.639978i \(-0.221056\pi\)
−0.371208 + 0.928550i \(0.621056\pi\)
\(864\) −97.4611 589.310i −0.112802 0.682071i
\(865\) −110.362 186.221i −0.127586 0.215285i
\(866\) 1011.62 1392.38i 1.16816 1.60783i
\(867\) −512.234 + 82.3238i −0.590812 + 0.0949525i
\(868\) 507.743i 0.584957i
\(869\) 209.910 68.2038i 0.241553 0.0784854i
\(870\) −235.727 + 930.408i −0.270951 + 1.06943i
\(871\) 6.36113 19.5775i 0.00730325 0.0224771i
\(872\) −274.227 + 843.984i −0.314480 + 0.967871i
\(873\) −84.3024 255.498i −0.0965663 0.292667i
\(874\) −213.432 −0.244201
\(875\) 1508.18 + 433.674i 1.72364 + 0.495627i
\(876\) −153.673 23.9815i −0.175426 0.0273762i
\(877\) −65.6432 90.3501i −0.0748497 0.103022i 0.769951 0.638103i \(-0.220281\pi\)
−0.844800 + 0.535082i \(0.820281\pi\)
\(878\) −134.305 + 413.349i −0.152967 + 0.470784i
\(879\) 884.922 + 448.360i 1.00674 + 0.510079i
\(880\) 1267.44 + 118.636i 1.44027 + 0.134814i
\(881\) 264.217 85.8494i 0.299906 0.0974454i −0.155199 0.987883i \(-0.549602\pi\)
0.455105 + 0.890438i \(0.349602\pi\)
\(882\) −2172.81 695.084i −2.46350 0.788077i
\(883\) −998.750 + 324.514i −1.13109 + 0.367513i −0.813989 0.580880i \(-0.802709\pi\)
−0.317098 + 0.948393i \(0.602709\pi\)
\(884\) −45.5426 + 62.6840i −0.0515188 + 0.0709095i
\(885\) 265.616 + 664.667i 0.300131 + 0.751036i
\(886\) 896.236 651.153i 1.01155 0.734936i
\(887\) 527.586 + 383.313i 0.594798 + 0.432146i 0.844029 0.536298i \(-0.180178\pi\)
−0.249231 + 0.968444i \(0.580178\pi\)
\(888\) 0.437539 + 0.435555i 0.000492725 + 0.000490490i
\(889\) −1353.02 + 983.027i −1.52196 + 1.10577i
\(890\) 349.822 810.429i 0.393059 0.910594i
\(891\) −992.921 + 332.630i −1.11439 + 0.373322i
\(892\) −313.911 + 101.996i −0.351918 + 0.114345i
\(893\) 20.6489 0.0231231
\(894\) −127.277 791.940i −0.142368 0.885839i
\(895\) 179.923 416.824i 0.201031 0.465726i
\(896\) 1812.97 + 589.070i 2.02341 + 0.657444i
\(897\) 146.872 289.880i 0.163737 0.323166i
\(898\) 289.543 + 398.521i 0.322431 + 0.443788i
\(899\) 766.615i 0.852742i
\(900\) −322.620 + 42.8490i −0.358467 + 0.0476100i
\(901\) 18.4301 0.0204552
\(902\) −1843.76 + 1339.57i −2.04408 + 1.48511i
\(903\) −1457.91 738.672i −1.61452 0.818020i
\(904\) 107.679 331.401i 0.119114 0.366594i
\(905\) −536.809 + 120.508i −0.593160 + 0.133158i
\(906\) 1133.61 182.188i 1.25122 0.201091i
\(907\) 1.34888i 0.00148718i 1.00000 0.000743592i \(0.000236693\pi\)
−1.00000 0.000743592i \(0.999763\pi\)
\(908\) 138.882 + 427.435i 0.152954 + 0.470743i
\(909\) 189.329 138.875i 0.208283 0.152778i
\(910\) 67.8831 725.224i 0.0745968 0.796949i
\(911\) −460.782 634.213i −0.505798 0.696172i 0.477405 0.878683i \(-0.341577\pi\)
−0.983204 + 0.182511i \(0.941577\pi\)
\(912\) −174.974 + 175.771i −0.191857 + 0.192732i
\(913\) −435.062 + 598.812i −0.476519 + 0.655873i
\(914\) −485.052 667.617i −0.530692 0.730435i
\(915\) −6.46056 97.7132i −0.00706072 0.106790i
\(916\) −142.022 103.185i −0.155046 0.112648i
\(917\) −820.406 2524.95i −0.894663 2.75349i
\(918\) 304.057 606.942i 0.331217 0.661157i
\(919\) 10.8003 + 33.2399i 0.0117522 + 0.0361697i 0.956761 0.290876i \(-0.0939468\pi\)
−0.945008 + 0.327046i \(0.893947\pi\)
\(920\) 428.839 487.322i 0.466129 0.529698i
\(921\) 230.482 454.899i 0.250251 0.493918i
\(922\) 662.740 + 215.337i 0.718807 + 0.233555i
\(923\) 219.284 159.319i 0.237578 0.172610i
\(924\) −108.593 + 695.863i −0.117525 + 0.753098i
\(925\) 0.628240 0.592128i 0.000679179 0.000640139i
\(926\) 1211.45i 1.30826i
\(927\) −132.709 402.205i −0.143159 0.433878i
\(928\) 576.873 + 187.437i 0.621630 + 0.201980i
\(929\) −317.359 103.116i −0.341613 0.110997i 0.133186 0.991091i \(-0.457479\pi\)
−0.474799 + 0.880094i \(0.657479\pi\)
\(930\) 908.905 363.219i 0.977318 0.390558i
\(931\) 140.894 + 433.627i 0.151336 + 0.465765i
\(932\) 581.690 0.624131
\(933\) 218.222 + 1357.82i 0.233892 + 1.45532i
\(934\) 805.331 + 585.108i 0.862239 + 0.626453i
\(935\) 522.783 + 460.044i 0.559127 + 0.492026i
\(936\) −83.5600 253.248i −0.0892735 0.270564i
\(937\) −156.678 + 215.649i −0.167213 + 0.230148i −0.884397 0.466735i \(-0.845430\pi\)
0.717185 + 0.696883i \(0.245430\pi\)
\(938\) 98.1335 + 71.2981i 0.104620 + 0.0760108i
\(939\) 853.239 437.193i 0.908668 0.465594i
\(940\) 23.5015 26.7065i 0.0250016 0.0284112i
\(941\) −53.2570 + 73.3019i −0.0565961 + 0.0778979i −0.836377 0.548155i \(-0.815330\pi\)
0.779781 + 0.626053i \(0.215330\pi\)
\(942\) 81.3394 + 506.109i 0.0863476 + 0.537271i
\(943\) 1645.64i 1.74511i
\(944\) 893.751 290.397i 0.946770 0.307624i
\(945\) 119.501 + 1690.62i 0.126456 + 1.78902i
\(946\) −404.573 + 1245.15i −0.427667 + 1.31622i
\(947\) 406.796 1251.99i 0.429562 1.32206i −0.468995 0.883201i \(-0.655384\pi\)
0.898557 0.438856i \(-0.144616\pi\)
\(948\) 33.7836 + 65.9331i 0.0356367 + 0.0695497i
\(949\) −178.213 −0.187791
\(950\) 167.988 + 178.233i 0.176830 + 0.187614i
\(951\) −113.541 + 727.566i −0.119391 + 0.765053i
\(952\) 473.765 + 652.081i 0.497652 + 0.684959i
\(953\) −533.396 + 1641.62i −0.559702 + 1.72259i 0.123488 + 0.992346i \(0.460592\pi\)
−0.683190 + 0.730240i \(0.739408\pi\)
\(954\) 20.9878 29.1651i 0.0219998 0.0305714i
\(955\) 369.389 + 325.059i 0.386795 + 0.340376i
\(956\) −270.055 + 87.7461i −0.282484 + 0.0917846i
\(957\) 163.959 1050.65i 0.171326 1.09786i
\(958\) −654.627 + 212.701i −0.683326 + 0.222026i
\(959\) −1416.05 + 1949.03i −1.47660 + 2.03236i
\(960\) −26.8628 406.289i −0.0279821 0.423218i
\(961\) 144.991 105.342i 0.150875 0.109617i
\(962\) −0.324179 0.235530i −0.000336984 0.000244834i
\(963\) −793.507 1081.79i −0.823995 1.12336i
\(964\) −422.269 + 306.797i −0.438039 + 0.318254i
\(965\) −911.591 85.3277i −0.944654 0.0884225i
\(966\) 1357.10 + 1350.95i 1.40487 + 1.39850i
\(967\) −692.020 + 224.851i −0.715636 + 0.232524i −0.644130 0.764916i \(-0.722780\pi\)
−0.0715060 + 0.997440i \(0.522780\pi\)
\(968\) −274.902 −0.283989
\(969\) −133.957 + 21.5289i −0.138242 + 0.0222176i
\(970\) 76.4067 + 340.358i 0.0787698 + 0.350885i
\(971\) −1094.40 355.593i −1.12709 0.366213i −0.314619 0.949218i \(-0.601877\pi\)
−0.812468 + 0.583005i \(0.801877\pi\)
\(972\) −163.122 311.346i −0.167821 0.320315i
\(973\) −753.489 1037.09i −0.774397 1.06587i
\(974\) 1548.00i 1.58932i
\(975\) −357.674 + 105.509i −0.366845 + 0.108214i
\(976\) −128.568 −0.131730
\(977\) −214.381 + 155.757i −0.219428 + 0.159424i −0.692069 0.721831i \(-0.743301\pi\)
0.472641 + 0.881255i \(0.343301\pi\)
\(978\) −61.7012 + 121.779i −0.0630892 + 0.124518i
\(979\) −302.202 + 930.083i −0.308685 + 0.950034i
\(980\) 721.196 + 311.305i 0.735914 + 0.317658i
\(981\) 6.09231 + 1340.19i 0.00621030 + 1.36615i
\(982\) 1252.31i 1.27526i
\(983\) −500.620 1540.75i −0.509277 1.56739i −0.793459 0.608624i \(-0.791722\pi\)
0.284181 0.958771i \(-0.408278\pi\)
\(984\) 957.095 + 952.754i 0.972658 + 0.968246i
\(985\) −1552.13 669.976i −1.57576 0.680179i
\(986\) 405.191 + 557.697i 0.410944 + 0.565616i
\(987\) −131.296 130.700i −0.133025 0.132422i
\(988\) 17.7460 24.4253i 0.0179615 0.0247219i
\(989\) 555.674 + 764.819i 0.561854 + 0.773326i
\(990\) 1323.34 303.401i 1.33671 0.306466i
\(991\) −262.932 191.031i −0.265320 0.192766i 0.447169 0.894449i \(-0.352432\pi\)
−0.712489 + 0.701683i \(0.752432\pi\)
\(992\) −191.146 588.286i −0.192687 0.593030i
\(993\) −69.4657 + 445.135i −0.0699554 + 0.448273i
\(994\) 493.560 + 1519.02i 0.496540 + 1.52819i
\(995\) −5.89528 + 62.9818i −0.00592491 + 0.0632982i
\(996\) −221.624 112.289i −0.222514 0.112740i
\(997\) 779.958 + 253.424i 0.782305 + 0.254186i 0.672824 0.739803i \(-0.265081\pi\)
0.109481 + 0.993989i \(0.465081\pi\)
\(998\) −1493.87 + 1085.36i −1.49687 + 1.08754i
\(999\) 0.833618 + 0.417614i 0.000834452 + 0.000418032i
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 75.3.h.a.14.14 yes 72
3.2 odd 2 inner 75.3.h.a.14.5 72
5.2 odd 4 375.3.j.b.176.27 144
5.3 odd 4 375.3.j.b.176.10 144
5.4 even 2 375.3.h.a.74.5 72
15.2 even 4 375.3.j.b.176.9 144
15.8 even 4 375.3.j.b.176.28 144
15.14 odd 2 375.3.h.a.74.14 72
25.9 even 10 inner 75.3.h.a.59.5 yes 72
25.12 odd 20 375.3.j.b.326.9 144
25.13 odd 20 375.3.j.b.326.28 144
25.16 even 5 375.3.h.a.299.14 72
75.38 even 20 375.3.j.b.326.10 144
75.41 odd 10 375.3.h.a.299.5 72
75.59 odd 10 inner 75.3.h.a.59.14 yes 72
75.62 even 20 375.3.j.b.326.27 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.h.a.14.5 72 3.2 odd 2 inner
75.3.h.a.14.14 yes 72 1.1 even 1 trivial
75.3.h.a.59.5 yes 72 25.9 even 10 inner
75.3.h.a.59.14 yes 72 75.59 odd 10 inner
375.3.h.a.74.5 72 5.4 even 2
375.3.h.a.74.14 72 15.14 odd 2
375.3.h.a.299.5 72 75.41 odd 10
375.3.h.a.299.14 72 25.16 even 5
375.3.j.b.176.9 144 15.2 even 4
375.3.j.b.176.10 144 5.3 odd 4
375.3.j.b.176.27 144 5.2 odd 4
375.3.j.b.176.28 144 15.8 even 4
375.3.j.b.326.9 144 25.12 odd 20
375.3.j.b.326.10 144 75.38 even 20
375.3.j.b.326.27 144 75.62 even 20
375.3.j.b.326.28 144 25.13 odd 20