Properties

Label 49.4.g.a.4.1
Level $49$
Weight $4$
Character 49.4
Analytic conductor $2.891$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,4,Mod(2,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\), degree \(12\), 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: \(2.89109359028\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(13\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 4.1
Character \(\chi\) \(=\) 49.4
Dual form 49.4.g.a.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.51874 - 3.08083i) q^{2} +(0.164357 + 0.152501i) q^{3} +(8.00480 + 20.3959i) q^{4} +(12.0019 - 3.70210i) q^{5} +(-0.272857 - 1.19547i) q^{6} +(1.40336 + 18.4670i) q^{7} +(16.9288 - 74.1698i) q^{8} +(-2.01396 - 26.8744i) q^{9} +O(q^{10})\) \(q+(-4.51874 - 3.08083i) q^{2} +(0.164357 + 0.152501i) q^{3} +(8.00480 + 20.3959i) q^{4} +(12.0019 - 3.70210i) q^{5} +(-0.272857 - 1.19547i) q^{6} +(1.40336 + 18.4670i) q^{7} +(16.9288 - 74.1698i) q^{8} +(-2.01396 - 26.8744i) q^{9} +(-65.6390 - 20.2470i) q^{10} +(-0.844018 + 11.2626i) q^{11} +(-1.79475 + 4.57294i) q^{12} +(63.9190 - 30.7818i) q^{13} +(50.5522 - 87.7711i) q^{14} +(2.53717 + 1.22183i) q^{15} +(-176.509 + 163.776i) q^{16} +(73.2187 - 11.0359i) q^{17} +(-73.6947 + 127.643i) q^{18} +(-5.88057 - 10.1855i) q^{19} +(171.581 + 215.155i) q^{20} +(-2.58558 + 3.24919i) q^{21} +(38.5121 - 48.2926i) q^{22} +(66.1985 + 9.97782i) q^{23} +(14.0933 - 9.60865i) q^{24} +(27.0603 - 18.4494i) q^{25} +(-383.667 - 57.8284i) q^{26} +(7.54174 - 9.45704i) q^{27} +(-365.418 + 176.448i) q^{28} +(-50.8342 - 63.7440i) q^{29} +(-7.70054 - 13.3377i) q^{30} +(44.1759 - 76.5148i) q^{31} +(700.342 - 105.560i) q^{32} +(-1.85628 + 1.72238i) q^{33} +(-364.856 - 175.705i) q^{34} +(85.2097 + 216.444i) q^{35} +(532.006 - 256.201i) q^{36} +(-13.6144 + 34.6888i) q^{37} +(-4.80681 + 64.1424i) q^{38} +(15.1998 + 4.68850i) q^{39} +(-71.4063 - 952.850i) q^{40} +(-63.6555 + 278.893i) q^{41} +(21.6938 - 6.71653i) q^{42} +(87.2375 + 382.212i) q^{43} +(-236.468 + 72.9407i) q^{44} +(-123.663 - 315.088i) q^{45} +(-268.394 - 249.033i) q^{46} +(-1.60383 - 1.09347i) q^{47} -53.9863 q^{48} +(-339.061 + 51.8317i) q^{49} -179.118 q^{50} +(13.7170 + 9.35207i) q^{51} +(1139.48 + 1057.28i) q^{52} +(-137.328 - 349.907i) q^{53} +(-63.2146 + 19.4991i) q^{54} +(31.5655 + 138.298i) q^{55} +(1393.45 + 208.537i) q^{56} +(0.586777 - 2.57084i) q^{57} +(33.3222 + 444.654i) q^{58} +(-794.747 - 245.147i) q^{59} +(-4.61091 + 61.5283i) q^{60} +(-254.354 + 648.083i) q^{61} +(-435.348 + 209.653i) q^{62} +(493.463 - 74.9062i) q^{63} +(-1754.35 - 844.850i) q^{64} +(653.193 - 606.074i) q^{65} +(13.6944 - 2.06410i) q^{66} +(-54.8328 + 94.9732i) q^{67} +(811.189 + 1405.02i) q^{68} +(9.35854 + 11.7352i) q^{69} +(281.786 - 1240.57i) q^{70} +(301.823 - 378.475i) q^{71} +(-2027.36 - 305.575i) q^{72} +(343.798 - 234.398i) q^{73} +(168.390 - 114.806i) q^{74} +(7.26110 + 1.09443i) q^{75} +(160.669 - 201.472i) q^{76} +(-209.172 + 0.219038i) q^{77} +(-54.2393 - 68.0139i) q^{78} +(-3.40309 - 5.89432i) q^{79} +(-1512.12 + 2619.08i) q^{80} +(-716.834 + 108.045i) q^{81} +(1146.86 - 1064.13i) q^{82} +(-320.565 - 154.376i) q^{83} +(-86.9673 - 26.7261i) q^{84} +(837.908 - 403.515i) q^{85} +(783.326 - 1995.88i) q^{86} +(1.36608 - 18.2290i) q^{87} +(821.059 + 253.263i) q^{88} +(20.4228 + 272.523i) q^{89} +(-411.930 + 1804.78i) q^{90} +(658.149 + 1137.19i) q^{91} +(326.399 + 1430.05i) q^{92} +(18.9292 - 5.83888i) q^{93} +(3.87849 + 9.88223i) q^{94} +(-108.286 - 100.474i) q^{95} +(131.204 + 89.4532i) q^{96} +313.386 q^{97} +(1691.81 + 810.374i) q^{98} +304.376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9} + 85 q^{11} - 427 q^{12} + 14 q^{13} - 203 q^{14} + 230 q^{15} + 127 q^{16} + 189 q^{17} - 16 q^{18} - 490 q^{19} - 406 q^{20} + 231 q^{21} + 590 q^{22} - 377 q^{23} - 812 q^{24} + 142 q^{25} + 490 q^{26} + 14 q^{27} - 280 q^{28} + 172 q^{29} - 39 q^{30} - 1162 q^{31} - 1099 q^{32} - 49 q^{33} + 882 q^{34} + 847 q^{35} + 812 q^{36} - 377 q^{37} - 1596 q^{38} - 770 q^{39} - 1694 q^{40} - 938 q^{41} - 3290 q^{42} - 10 q^{43} + 4354 q^{44} + 1176 q^{45} + 3408 q^{46} + 1379 q^{47} + 9604 q^{48} + 2576 q^{49} - 6184 q^{50} + 2271 q^{51} + 6874 q^{52} + 1905 q^{53} + 1617 q^{54} - 1834 q^{55} + 1736 q^{56} + 2673 q^{57} - 4716 q^{58} + 63 q^{59} - 10850 q^{60} - 2625 q^{61} - 4298 q^{62} - 1806 q^{63} - 2756 q^{64} - 196 q^{65} + 2100 q^{66} - 202 q^{67} - 5635 q^{68} - 3248 q^{69} + 6650 q^{70} + 2608 q^{71} - 6424 q^{72} - 2471 q^{73} + 2582 q^{74} + 3612 q^{75} - 4529 q^{76} - 1281 q^{77} + 5040 q^{78} - 608 q^{79} - 12348 q^{80} - 17375 q^{81} - 3234 q^{82} - 9842 q^{83} - 11564 q^{84} - 512 q^{85} - 2301 q^{86} + 2254 q^{87} + 4033 q^{88} + 4977 q^{89} + 18312 q^{90} - 8932 q^{91} + 7714 q^{92} + 14164 q^{93} + 2506 q^{94} + 11504 q^{95} + 12642 q^{96} + 11116 q^{97} + 29771 q^{98} - 10804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.51874 3.08083i −1.59762 1.08924i −0.942755 0.333487i \(-0.891775\pi\)
−0.654861 0.755749i \(-0.727273\pi\)
\(3\) 0.164357 + 0.152501i 0.0316305 + 0.0293488i 0.695830 0.718207i \(-0.255037\pi\)
−0.664199 + 0.747556i \(0.731227\pi\)
\(4\) 8.00480 + 20.3959i 1.00060 + 2.54949i
\(5\) 12.0019 3.70210i 1.07348 0.331126i 0.292878 0.956150i \(-0.405387\pi\)
0.780605 + 0.625024i \(0.214911\pi\)
\(6\) −0.272857 1.19547i −0.0185656 0.0813411i
\(7\) 1.40336 + 18.4670i 0.0757743 + 0.997125i
\(8\) 16.9288 74.1698i 0.748153 3.27787i
\(9\) −2.01396 26.8744i −0.0745910 0.995347i
\(10\) −65.6390 20.2470i −2.07569 0.640265i
\(11\) −0.844018 + 11.2626i −0.0231346 + 0.308710i 0.973618 + 0.228185i \(0.0732789\pi\)
−0.996753 + 0.0805257i \(0.974340\pi\)
\(12\) −1.79475 + 4.57294i −0.0431749 + 0.110008i
\(13\) 63.9190 30.7818i 1.36369 0.656717i 0.398232 0.917285i \(-0.369624\pi\)
0.965456 + 0.260567i \(0.0839096\pi\)
\(14\) 50.5522 87.7711i 0.965046 1.67556i
\(15\) 2.53717 + 1.22183i 0.0436729 + 0.0210318i
\(16\) −176.509 + 163.776i −2.75795 + 2.55900i
\(17\) 73.2187 11.0359i 1.04460 0.157448i 0.395743 0.918361i \(-0.370487\pi\)
0.648853 + 0.760914i \(0.275249\pi\)
\(18\) −73.6947 + 127.643i −0.965000 + 1.67143i
\(19\) −5.88057 10.1855i −0.0710051 0.122984i 0.828337 0.560230i \(-0.189287\pi\)
−0.899342 + 0.437246i \(0.855954\pi\)
\(20\) 171.581 + 215.155i 1.91833 + 2.40551i
\(21\) −2.58558 + 3.24919i −0.0268676 + 0.0337634i
\(22\) 38.5121 48.2926i 0.373219 0.468001i
\(23\) 66.1985 + 9.97782i 0.600145 + 0.0904574i 0.442087 0.896972i \(-0.354238\pi\)
0.158059 + 0.987430i \(0.449476\pi\)
\(24\) 14.0933 9.60865i 0.119866 0.0817232i
\(25\) 27.0603 18.4494i 0.216483 0.147595i
\(26\) −383.667 57.8284i −2.89397 0.436196i
\(27\) 7.54174 9.45704i 0.0537558 0.0674077i
\(28\) −365.418 + 176.448i −2.46634 + 1.19091i
\(29\) −50.8342 63.7440i −0.325506 0.408171i 0.591972 0.805959i \(-0.298350\pi\)
−0.917478 + 0.397787i \(0.869778\pi\)
\(30\) −7.70054 13.3377i −0.0468640 0.0811708i
\(31\) 44.1759 76.5148i 0.255943 0.443305i −0.709209 0.704999i \(-0.750948\pi\)
0.965151 + 0.261693i \(0.0842809\pi\)
\(32\) 700.342 105.560i 3.86888 0.583140i
\(33\) −1.85628 + 1.72238i −0.00979203 + 0.00908567i
\(34\) −364.856 175.705i −1.84036 0.886272i
\(35\) 85.2097 + 216.444i 0.411516 + 1.04531i
\(36\) 532.006 256.201i 2.46299 1.18611i
\(37\) −13.6144 + 34.6888i −0.0604915 + 0.154130i −0.957924 0.287022i \(-0.907335\pi\)
0.897432 + 0.441152i \(0.145430\pi\)
\(38\) −4.80681 + 64.1424i −0.0205202 + 0.273823i
\(39\) 15.1998 + 4.68850i 0.0624079 + 0.0192503i
\(40\) −71.4063 952.850i −0.282258 3.76647i
\(41\) −63.6555 + 278.893i −0.242471 + 1.06234i 0.696288 + 0.717762i \(0.254834\pi\)
−0.938759 + 0.344574i \(0.888024\pi\)
\(42\) 21.6938 6.71653i 0.0797005 0.0246758i
\(43\) 87.2375 + 382.212i 0.309386 + 1.35551i 0.855502 + 0.517799i \(0.173248\pi\)
−0.546116 + 0.837709i \(0.683894\pi\)
\(44\) −236.468 + 72.9407i −0.810201 + 0.249914i
\(45\) −123.663 315.088i −0.409657 1.04379i
\(46\) −268.394 249.033i −0.860272 0.798216i
\(47\) −1.60383 1.09347i −0.00497750 0.00339360i 0.560829 0.827932i \(-0.310483\pi\)
−0.565806 + 0.824538i \(0.691435\pi\)
\(48\) −53.9863 −0.162339
\(49\) −339.061 + 51.8317i −0.988517 + 0.151113i
\(50\) −179.118 −0.506622
\(51\) 13.7170 + 9.35207i 0.0376620 + 0.0256775i
\(52\) 1139.48 + 1057.28i 3.03880 + 2.81959i
\(53\) −137.328 349.907i −0.355915 0.906857i −0.990933 0.134359i \(-0.957102\pi\)
0.635018 0.772498i \(-0.280993\pi\)
\(54\) −63.2146 + 19.4991i −0.159304 + 0.0491388i
\(55\) 31.5655 + 138.298i 0.0773872 + 0.339056i
\(56\) 1393.45 + 208.537i 3.32514 + 0.497624i
\(57\) 0.586777 2.57084i 0.00136352 0.00597396i
\(58\) 33.3222 + 444.654i 0.0754383 + 1.00665i
\(59\) −794.747 245.147i −1.75368 0.540940i −0.759681 0.650296i \(-0.774645\pi\)
−0.994003 + 0.109357i \(0.965121\pi\)
\(60\) −4.61091 + 61.5283i −0.00992110 + 0.132388i
\(61\) −254.354 + 648.083i −0.533880 + 1.36030i 0.368607 + 0.929585i \(0.379835\pi\)
−0.902487 + 0.430718i \(0.858260\pi\)
\(62\) −435.348 + 209.653i −0.891762 + 0.429450i
\(63\) 493.463 74.9062i 0.986833 0.149798i
\(64\) −1754.35 844.850i −3.42646 1.65010i
\(65\) 653.193 606.074i 1.24644 1.15653i
\(66\) 13.6944 2.06410i 0.0255403 0.00384959i
\(67\) −54.8328 + 94.9732i −0.0999835 + 0.173177i −0.911678 0.410906i \(-0.865212\pi\)
0.811694 + 0.584083i \(0.198546\pi\)
\(68\) 811.189 + 1405.02i 1.44663 + 2.50564i
\(69\) 9.35854 + 11.7352i 0.0163281 + 0.0204747i
\(70\) 281.786 1240.57i 0.481140 2.11824i
\(71\) 301.823 378.475i 0.504505 0.632629i −0.462734 0.886497i \(-0.653131\pi\)
0.967239 + 0.253868i \(0.0817029\pi\)
\(72\) −2027.36 305.575i −3.31843 0.500172i
\(73\) 343.798 234.398i 0.551213 0.375811i −0.255450 0.966822i \(-0.582224\pi\)
0.806663 + 0.591012i \(0.201271\pi\)
\(74\) 168.390 114.806i 0.264526 0.180351i
\(75\) 7.26110 + 1.09443i 0.0111792 + 0.00168499i
\(76\) 160.669 201.472i 0.242500 0.304085i
\(77\) −209.172 + 0.219038i −0.309576 + 0.000324179i
\(78\) −54.2393 68.0139i −0.0787358 0.0987315i
\(79\) −3.40309 5.89432i −0.00484655 0.00839446i 0.863592 0.504191i \(-0.168209\pi\)
−0.868439 + 0.495797i \(0.834876\pi\)
\(80\) −1512.12 + 2619.08i −2.11326 + 3.66027i
\(81\) −716.834 + 108.045i −0.983311 + 0.148210i
\(82\) 1146.86 1064.13i 1.54451 1.43310i
\(83\) −320.565 154.376i −0.423935 0.204156i 0.209737 0.977758i \(-0.432739\pi\)
−0.633673 + 0.773601i \(0.718453\pi\)
\(84\) −86.9673 26.7261i −0.112963 0.0347150i
\(85\) 837.908 403.515i 1.06922 0.514910i
\(86\) 783.326 1995.88i 0.982189 2.50258i
\(87\) 1.36608 18.2290i 0.00168343 0.0224638i
\(88\) 821.059 + 253.263i 0.994604 + 0.306795i
\(89\) 20.4228 + 272.523i 0.0243237 + 0.324578i 0.996071 + 0.0885551i \(0.0282249\pi\)
−0.971748 + 0.236023i \(0.924156\pi\)
\(90\) −411.930 + 1804.78i −0.482458 + 2.11379i
\(91\) 658.149 + 1137.19i 0.758162 + 1.31000i
\(92\) 326.399 + 1430.05i 0.369886 + 1.62058i
\(93\) 18.9292 5.83888i 0.0211061 0.00651036i
\(94\) 3.87849 + 9.88223i 0.00425570 + 0.0108433i
\(95\) −108.286 100.474i −0.116946 0.108510i
\(96\) 131.204 + 89.4532i 0.139489 + 0.0951019i
\(97\) 313.386 0.328036 0.164018 0.986457i \(-0.447555\pi\)
0.164018 + 0.986457i \(0.447555\pi\)
\(98\) 1691.81 + 810.374i 1.74387 + 0.835308i
\(99\) 304.376 0.308999
\(100\) 592.905 + 404.236i 0.592905 + 0.404236i
\(101\) −599.433 556.193i −0.590553 0.547953i 0.327276 0.944929i \(-0.393869\pi\)
−0.917829 + 0.396976i \(0.870060\pi\)
\(102\) −33.1713 84.5192i −0.0322005 0.0820456i
\(103\) −1621.57 + 500.188i −1.55124 + 0.478495i −0.947787 0.318903i \(-0.896686\pi\)
−0.603454 + 0.797398i \(0.706209\pi\)
\(104\) −1201.01 5261.95i −1.13239 4.96132i
\(105\) −19.0031 + 48.5686i −0.0176620 + 0.0451410i
\(106\) −457.451 + 2004.22i −0.419165 + 1.83648i
\(107\) −6.27471 83.7302i −0.00566915 0.0756496i 0.993652 0.112501i \(-0.0358862\pi\)
−0.999321 + 0.0368515i \(0.988267\pi\)
\(108\) 253.255 + 78.1188i 0.225643 + 0.0696017i
\(109\) 101.052 1348.44i 0.0887981 1.18493i −0.757724 0.652575i \(-0.773689\pi\)
0.846522 0.532354i \(-0.178692\pi\)
\(110\) 283.434 722.179i 0.245677 0.625974i
\(111\) −7.52768 + 3.62514i −0.00643690 + 0.00309985i
\(112\) −3272.16 3029.75i −2.76062 2.55611i
\(113\) −1395.35 671.967i −1.16163 0.559410i −0.249120 0.968473i \(-0.580141\pi\)
−0.912506 + 0.409063i \(0.865856\pi\)
\(114\) −10.5718 + 9.80920i −0.00868544 + 0.00805891i
\(115\) 831.447 125.320i 0.674199 0.101619i
\(116\) 893.200 1547.07i 0.714927 1.23829i
\(117\) −955.971 1655.79i −0.755380 1.30836i
\(118\) 2836.00 + 3556.23i 2.21250 + 2.77439i
\(119\) 306.553 + 1336.64i 0.236148 + 1.02966i
\(120\) 133.574 167.497i 0.101613 0.127419i
\(121\) 1190.00 + 179.364i 0.894064 + 0.134758i
\(122\) 3145.99 2144.90i 2.33463 1.59172i
\(123\) −52.9936 + 36.1304i −0.0388477 + 0.0264859i
\(124\) 1914.21 + 288.521i 1.38630 + 0.208951i
\(125\) −722.398 + 905.858i −0.516906 + 0.648179i
\(126\) −2460.60 1181.79i −1.73975 0.835575i
\(127\) 937.998 + 1176.21i 0.655385 + 0.821827i 0.992832 0.119518i \(-0.0381348\pi\)
−0.337447 + 0.941345i \(0.609563\pi\)
\(128\) 2491.60 + 4315.58i 1.72054 + 2.98006i
\(129\) −43.9496 + 76.1230i −0.0299965 + 0.0519555i
\(130\) −4818.82 + 726.320i −3.25106 + 0.490019i
\(131\) −1575.43 + 1461.79i −1.05073 + 0.974938i −0.999718 0.0237595i \(-0.992436\pi\)
−0.0510159 + 0.998698i \(0.516246\pi\)
\(132\) −49.9886 24.0732i −0.0329617 0.0158735i
\(133\) 179.842 122.890i 0.117250 0.0801200i
\(134\) 540.371 260.229i 0.348365 0.167764i
\(135\) 55.5043 141.423i 0.0353856 0.0901610i
\(136\) 420.969 5617.44i 0.265425 3.54185i
\(137\) −430.018 132.643i −0.268167 0.0827186i 0.157755 0.987478i \(-0.449574\pi\)
−0.425923 + 0.904760i \(0.640050\pi\)
\(138\) −6.13460 81.8606i −0.00378414 0.0504959i
\(139\) −10.4123 + 45.6191i −0.00635364 + 0.0278371i −0.978005 0.208580i \(-0.933116\pi\)
0.971652 + 0.236417i \(0.0759731\pi\)
\(140\) −3732.48 + 3470.52i −2.25323 + 2.09509i
\(141\) −0.0968448 0.424305i −5.78426e−5 0.000253425i
\(142\) −2529.88 + 780.363i −1.49509 + 0.461174i
\(143\) 292.735 + 745.877i 0.171187 + 0.436177i
\(144\) 4756.86 + 4413.72i 2.75281 + 2.55424i
\(145\) −846.093 576.857i −0.484581 0.330382i
\(146\) −2275.67 −1.28997
\(147\) −63.6314 43.1882i −0.0357022 0.0242320i
\(148\) −816.490 −0.453480
\(149\) 1500.61 + 1023.10i 0.825065 + 0.562520i 0.900613 0.434623i \(-0.143118\pi\)
−0.0755479 + 0.997142i \(0.524071\pi\)
\(150\) −29.4392 27.3156i −0.0160247 0.0148687i
\(151\) 887.065 + 2260.21i 0.478069 + 1.21810i 0.943012 + 0.332758i \(0.107979\pi\)
−0.464944 + 0.885340i \(0.653925\pi\)
\(152\) −855.004 + 263.734i −0.456250 + 0.140734i
\(153\) −444.043 1945.48i −0.234632 1.02799i
\(154\) 945.867 + 643.432i 0.494936 + 0.336683i
\(155\) 246.929 1081.87i 0.127960 0.560630i
\(156\) 26.0448 + 347.543i 0.0133670 + 0.178370i
\(157\) −2365.57 729.683i −1.20251 0.370924i −0.372158 0.928170i \(-0.621382\pi\)
−0.830348 + 0.557246i \(0.811858\pi\)
\(158\) −2.78170 + 37.1192i −0.00140063 + 0.0186902i
\(159\) 30.7902 78.4522i 0.0153574 0.0391300i
\(160\) 8014.64 3859.65i 3.96008 1.90708i
\(161\) −91.3602 + 1236.49i −0.0447217 + 0.605274i
\(162\) 3572.05 + 1720.21i 1.73239 + 0.834275i
\(163\) 1149.26 1066.36i 0.552254 0.512416i −0.353947 0.935266i \(-0.615161\pi\)
0.906200 + 0.422849i \(0.138970\pi\)
\(164\) −6197.83 + 934.172i −2.95103 + 0.444796i
\(165\) −15.9025 + 27.5439i −0.00750307 + 0.0129957i
\(166\) 972.946 + 1685.19i 0.454911 + 0.787929i
\(167\) 322.477 + 404.374i 0.149425 + 0.187373i 0.850911 0.525311i \(-0.176051\pi\)
−0.701485 + 0.712684i \(0.747479\pi\)
\(168\) 197.221 + 246.777i 0.0905710 + 0.113329i
\(169\) 1768.31 2217.39i 0.804876 1.00928i
\(170\) −5029.45 758.067i −2.26906 0.342006i
\(171\) −261.884 + 178.550i −0.117116 + 0.0798482i
\(172\) −7097.25 + 4838.82i −3.14628 + 2.14510i
\(173\) 1280.78 + 193.047i 0.562866 + 0.0848385i 0.424311 0.905516i \(-0.360516\pi\)
0.138555 + 0.990355i \(0.455754\pi\)
\(174\) −62.3333 + 78.1635i −0.0271579 + 0.0340549i
\(175\) 378.681 + 473.832i 0.163575 + 0.204676i
\(176\) −1695.57 2126.18i −0.726185 0.910608i
\(177\) −93.2370 161.491i −0.0395939 0.0685786i
\(178\) 747.312 1294.38i 0.314682 0.545045i
\(179\) 3367.08 507.506i 1.40596 0.211915i 0.598164 0.801373i \(-0.295897\pi\)
0.807799 + 0.589459i \(0.200659\pi\)
\(180\) 5436.60 5044.43i 2.25123 2.08883i
\(181\) 1993.16 + 959.855i 0.818510 + 0.394174i 0.795793 0.605568i \(-0.207054\pi\)
0.0227167 + 0.999742i \(0.492768\pi\)
\(182\) 529.496 7166.33i 0.215653 2.91870i
\(183\) −140.638 + 67.7276i −0.0568101 + 0.0273583i
\(184\) 1860.71 4741.02i 0.745508 1.89952i
\(185\) −34.9768 + 466.734i −0.0139003 + 0.185486i
\(186\) −103.525 31.9331i −0.0408107 0.0125884i
\(187\) 62.4959 + 833.950i 0.0244393 + 0.326120i
\(188\) 9.46402 41.4646i 0.00367146 0.0160857i
\(189\) 185.227 + 126.002i 0.0712872 + 0.0484935i
\(190\) 179.771 + 787.627i 0.0686418 + 0.300739i
\(191\) −1937.96 + 597.782i −0.734168 + 0.226461i −0.639223 0.769022i \(-0.720744\pi\)
−0.0949451 + 0.995483i \(0.530268\pi\)
\(192\) −159.499 406.396i −0.0599522 0.152756i
\(193\) −1109.76 1029.71i −0.413897 0.384041i 0.445557 0.895254i \(-0.353006\pi\)
−0.859454 + 0.511213i \(0.829196\pi\)
\(194\) −1416.11 965.486i −0.524075 0.357309i
\(195\) 199.783 0.0733681
\(196\) −3771.27 6500.56i −1.37437 2.36901i
\(197\) 203.732 0.0736817 0.0368409 0.999321i \(-0.488271\pi\)
0.0368409 + 0.999321i \(0.488271\pi\)
\(198\) −1375.40 937.729i −0.493662 0.336573i
\(199\) −2414.29 2240.13i −0.860021 0.797983i 0.120844 0.992671i \(-0.461440\pi\)
−0.980865 + 0.194689i \(0.937630\pi\)
\(200\) −910.291 2319.38i −0.321837 0.820026i
\(201\) −23.4956 + 7.24744i −0.00824504 + 0.00254326i
\(202\) 995.150 + 4360.04i 0.346626 + 1.51867i
\(203\) 1105.82 1028.21i 0.382333 0.355499i
\(204\) −80.9424 + 354.632i −0.0277799 + 0.121712i
\(205\) 268.502 + 3582.91i 0.0914779 + 1.22069i
\(206\) 8868.44 + 2735.55i 2.99948 + 0.925218i
\(207\) 134.827 1799.14i 0.0452711 0.604100i
\(208\) −6240.93 + 15901.6i −2.08044 + 5.30087i
\(209\) 119.678 57.6340i 0.0396092 0.0190748i
\(210\) 235.501 160.924i 0.0773863 0.0528799i
\(211\) −2269.59 1092.98i −0.740498 0.356605i 0.0253055 0.999680i \(-0.491944\pi\)
−0.765803 + 0.643075i \(0.777658\pi\)
\(212\) 6037.38 5601.87i 1.95589 1.81480i
\(213\) 107.324 16.1765i 0.0345246 0.00520375i
\(214\) −229.604 + 397.687i −0.0733432 + 0.127034i
\(215\) 2462.00 + 4264.32i 0.780964 + 1.35267i
\(216\) −573.754 719.465i −0.180736 0.226636i
\(217\) 1475.00 + 708.418i 0.461425 + 0.221616i
\(218\) −4610.94 + 5781.93i −1.43253 + 1.79634i
\(219\) 92.2514 + 13.9047i 0.0284647 + 0.00429036i
\(220\) −2568.03 + 1750.85i −0.786984 + 0.536557i
\(221\) 4340.36 2959.21i 1.32110 0.900714i
\(222\) 45.1841 + 6.81040i 0.0136602 + 0.00205894i
\(223\) 1400.33 1755.96i 0.420507 0.527299i −0.525783 0.850619i \(-0.676227\pi\)
0.946290 + 0.323320i \(0.104799\pi\)
\(224\) 2932.20 + 12785.1i 0.874625 + 3.81357i
\(225\) −550.315 690.073i −0.163056 0.204466i
\(226\) 4235.03 + 7335.28i 1.24650 + 2.15901i
\(227\) 1736.58 3007.85i 0.507757 0.879462i −0.492202 0.870481i \(-0.663808\pi\)
0.999960 0.00898079i \(-0.00285871\pi\)
\(228\) 57.1316 8.61121i 0.0165949 0.00250128i
\(229\) 443.444 411.456i 0.127963 0.118733i −0.613595 0.789621i \(-0.710277\pi\)
0.741559 + 0.670888i \(0.234087\pi\)
\(230\) −4143.18 1995.25i −1.18780 0.572013i
\(231\) −34.4122 31.8628i −0.00980153 0.00907541i
\(232\) −5588.44 + 2691.25i −1.58146 + 0.761592i
\(233\) 288.910 736.129i 0.0812322 0.206976i −0.884487 0.466564i \(-0.845492\pi\)
0.965719 + 0.259588i \(0.0835868\pi\)
\(234\) −781.415 + 10427.3i −0.218302 + 2.91304i
\(235\) −23.2971 7.18622i −0.00646697 0.00199480i
\(236\) −1361.80 18171.9i −0.375617 5.01226i
\(237\) 0.339568 1.48774i 9.30688e−5 0.000407761i
\(238\) 2732.73 6984.38i 0.744271 1.90223i
\(239\) −352.294 1543.50i −0.0953473 0.417744i 0.904617 0.426226i \(-0.140157\pi\)
−0.999964 + 0.00848210i \(0.997300\pi\)
\(240\) −647.939 + 199.863i −0.174268 + 0.0537545i
\(241\) 1495.34 + 3810.08i 0.399683 + 1.01838i 0.979106 + 0.203349i \(0.0651826\pi\)
−0.579423 + 0.815027i \(0.696722\pi\)
\(242\) −4824.71 4476.68i −1.28159 1.18914i
\(243\) −404.137 275.536i −0.106689 0.0727392i
\(244\) −15254.3 −4.00228
\(245\) −3877.49 + 1877.32i −1.01112 + 0.489540i
\(246\) 350.776 0.0909132
\(247\) −689.407 470.029i −0.177595 0.121082i
\(248\) −4927.25 4571.82i −1.26161 1.17061i
\(249\) −29.1446 74.2592i −0.00741753 0.0188995i
\(250\) 6055.12 1867.76i 1.53184 0.472509i
\(251\) −464.919 2036.94i −0.116914 0.512234i −0.999142 0.0414117i \(-0.986814\pi\)
0.882228 0.470822i \(-0.156043\pi\)
\(252\) 5477.85 + 9465.02i 1.36933 + 2.36603i
\(253\) −168.249 + 737.148i −0.0418092 + 0.183178i
\(254\) −614.865 8204.81i −0.151890 2.02683i
\(255\) 199.252 + 61.4611i 0.0489320 + 0.0150935i
\(256\) 872.544 11643.3i 0.213024 2.84260i
\(257\) 725.427 1848.36i 0.176074 0.448628i −0.815406 0.578889i \(-0.803486\pi\)
0.991480 + 0.130261i \(0.0415816\pi\)
\(258\) 433.118 208.579i 0.104515 0.0503316i
\(259\) −659.705 202.736i −0.158270 0.0486385i
\(260\) 17590.1 + 8470.95i 4.19574 + 2.02056i
\(261\) −1610.70 + 1494.51i −0.381992 + 0.354437i
\(262\) 11622.5 1751.81i 2.74061 0.413080i
\(263\) −3035.71 + 5258.01i −0.711749 + 1.23279i 0.252451 + 0.967610i \(0.418763\pi\)
−0.964200 + 0.265176i \(0.914570\pi\)
\(264\) 96.3237 + 166.838i 0.0224557 + 0.0388945i
\(265\) −2943.59 3691.15i −0.682352 0.855642i
\(266\) −1191.26 + 1.24746i −0.274591 + 0.000287543i
\(267\) −38.2034 + 47.9056i −0.00875659 + 0.0109804i
\(268\) −2375.99 358.123i −0.541555 0.0816263i
\(269\) −5718.10 + 3898.53i −1.29605 + 0.883635i −0.997494 0.0707554i \(-0.977459\pi\)
−0.298561 + 0.954391i \(0.596507\pi\)
\(270\) −686.508 + 468.053i −0.154739 + 0.105499i
\(271\) −4142.01 624.308i −0.928448 0.139941i −0.332627 0.943058i \(-0.607935\pi\)
−0.595821 + 0.803117i \(0.703173\pi\)
\(272\) −11116.3 + 13939.4i −2.47803 + 3.10735i
\(273\) −65.2519 + 287.274i −0.0144660 + 0.0636872i
\(274\) 1534.49 + 1924.19i 0.338328 + 0.424250i
\(275\) 184.950 + 320.342i 0.0405559 + 0.0702449i
\(276\) −164.438 + 284.814i −0.0358623 + 0.0621152i
\(277\) 5414.98 816.177i 1.17456 0.177037i 0.467374 0.884060i \(-0.345200\pi\)
0.707191 + 0.707023i \(0.249962\pi\)
\(278\) 187.595 174.063i 0.0404719 0.0375524i
\(279\) −2145.26 1033.10i −0.460334 0.221685i
\(280\) 17496.1 2655.85i 3.73426 0.566848i
\(281\) −7520.86 + 3621.86i −1.59664 + 0.768903i −0.999449 0.0331926i \(-0.989433\pi\)
−0.597195 + 0.802096i \(0.703718\pi\)
\(282\) −0.869592 + 2.21568i −0.000183629 + 0.000467880i
\(283\) −77.5167 + 1034.39i −0.0162823 + 0.217272i 0.983128 + 0.182921i \(0.0585554\pi\)
−0.999410 + 0.0343507i \(0.989064\pi\)
\(284\) 10135.4 + 3126.35i 2.11769 + 0.653220i
\(285\) −2.47505 33.0273i −0.000514419 0.00686445i
\(286\) 975.122 4272.29i 0.201609 0.883307i
\(287\) −5239.65 784.140i −1.07765 0.161276i
\(288\) −4247.30 18608.7i −0.869010 3.80738i
\(289\) 544.456 167.942i 0.110819 0.0341833i
\(290\) 2046.08 + 5213.33i 0.414311 + 1.05565i
\(291\) 51.5070 + 47.7915i 0.0103759 + 0.00962745i
\(292\) 7532.79 + 5135.77i 1.50967 + 1.02927i
\(293\) 4425.30 0.882352 0.441176 0.897421i \(-0.354561\pi\)
0.441176 + 0.897421i \(0.354561\pi\)
\(294\) 154.478 + 391.193i 0.0306441 + 0.0776015i
\(295\) −10446.0 −2.06167
\(296\) 2342.39 + 1597.01i 0.459961 + 0.313596i
\(297\) 100.146 + 92.9217i 0.0195658 + 0.0181544i
\(298\) −3628.88 9246.23i −0.705420 1.79738i
\(299\) 4538.48 1399.93i 0.877816 0.270770i
\(300\) 35.8017 + 156.857i 0.00689003 + 0.0301872i
\(301\) −6935.90 + 2147.40i −1.32817 + 0.411209i
\(302\) 2954.88 12946.2i 0.563027 2.46678i
\(303\) −13.7011 182.828i −0.00259771 0.0346640i
\(304\) 2706.10 + 834.723i 0.510545 + 0.157482i
\(305\) −653.464 + 8719.87i −0.122679 + 1.63704i
\(306\) −3987.17 + 10159.1i −0.744873 + 1.89791i
\(307\) 8959.71 4314.77i 1.66566 0.802140i 0.667306 0.744783i \(-0.267447\pi\)
0.998354 0.0573561i \(-0.0182670\pi\)
\(308\) −1678.85 4264.49i −0.310588 0.788935i
\(309\) −342.795 165.081i −0.0631097 0.0303920i
\(310\) −4448.85 + 4127.93i −0.815090 + 0.756293i
\(311\) −3546.68 + 534.576i −0.646669 + 0.0974696i −0.464184 0.885739i \(-0.653652\pi\)
−0.182485 + 0.983209i \(0.558414\pi\)
\(312\) 605.058 1047.99i 0.109791 0.190163i
\(313\) −101.350 175.543i −0.0183024 0.0317006i 0.856729 0.515767i \(-0.172493\pi\)
−0.875032 + 0.484066i \(0.839159\pi\)
\(314\) 8441.39 + 10585.2i 1.51712 + 1.90241i
\(315\) 5645.19 2725.86i 1.00975 0.487572i
\(316\) 92.9789 116.592i 0.0165521 0.0207557i
\(317\) −339.018 51.0987i −0.0600666 0.00905359i 0.118940 0.992901i \(-0.462050\pi\)
−0.179007 + 0.983848i \(0.557288\pi\)
\(318\) −380.831 + 259.646i −0.0671570 + 0.0457868i
\(319\) 760.831 518.725i 0.133537 0.0910440i
\(320\) −24183.2 3645.04i −4.22464 0.636762i
\(321\) 11.7376 14.7185i 0.00204091 0.00255921i
\(322\) 4222.25 5305.92i 0.730735 0.918283i
\(323\) −542.974 680.868i −0.0935352 0.117289i
\(324\) −7941.80 13755.6i −1.36176 2.35864i
\(325\) 1161.76 2012.23i 0.198286 0.343442i
\(326\) −8478.50 + 1277.93i −1.44043 + 0.217110i
\(327\) 222.247 206.215i 0.0375849 0.0348737i
\(328\) 19607.8 + 9442.63i 3.30080 + 1.58958i
\(329\) 17.9424 31.1525i 0.00300668 0.00522034i
\(330\) 156.717 75.4710i 0.0261424 0.0125895i
\(331\) −2086.21 + 5315.58i −0.346431 + 0.882691i 0.646382 + 0.763014i \(0.276281\pi\)
−0.992813 + 0.119677i \(0.961814\pi\)
\(332\) 582.579 7773.97i 0.0963047 1.28510i
\(333\) 959.659 + 296.016i 0.157925 + 0.0487134i
\(334\) −211.386 2820.75i −0.0346304 0.462110i
\(335\) −306.498 + 1342.86i −0.0499874 + 0.219009i
\(336\) −75.7622 996.966i −0.0123011 0.161872i
\(337\) 336.269 + 1473.29i 0.0543553 + 0.238146i 0.994807 0.101782i \(-0.0324544\pi\)
−0.940451 + 0.339928i \(0.889597\pi\)
\(338\) −14822.0 + 4571.97i −2.38523 + 0.735746i
\(339\) −126.860 323.235i −0.0203248 0.0517867i
\(340\) 14937.3 + 13859.8i 2.38262 + 2.21075i
\(341\) 824.473 + 562.116i 0.130932 + 0.0892678i
\(342\) 1733.47 0.274080
\(343\) −1433.00 6188.71i −0.225583 0.974224i
\(344\) 29825.4 4.67465
\(345\) 155.765 + 106.199i 0.0243076 + 0.0165726i
\(346\) −5192.77 4818.19i −0.806835 0.748634i
\(347\) 154.828 + 394.494i 0.0239527 + 0.0610304i 0.942350 0.334629i \(-0.108611\pi\)
−0.918397 + 0.395660i \(0.870516\pi\)
\(348\) 382.732 118.057i 0.0589558 0.0181854i
\(349\) −1923.24 8426.25i −0.294981 1.29240i −0.877499 0.479579i \(-0.840789\pi\)
0.582517 0.812818i \(-0.302068\pi\)
\(350\) −251.367 3307.77i −0.0383889 0.505166i
\(351\) 190.956 836.632i 0.0290384 0.127225i
\(352\) 597.778 + 7976.79i 0.0905161 + 1.20785i
\(353\) 11640.2 + 3590.51i 1.75508 + 0.541370i 0.994202 0.107526i \(-0.0342929\pi\)
0.760877 + 0.648896i \(0.224769\pi\)
\(354\) −76.2124 + 1016.98i −0.0114425 + 0.152689i
\(355\) 2221.31 5659.80i 0.332098 0.846171i
\(356\) −5394.88 + 2598.04i −0.803169 + 0.386786i
\(357\) −153.455 + 266.436i −0.0227499 + 0.0394994i
\(358\) −16778.5 8080.10i −2.47701 1.19287i
\(359\) −3552.84 + 3296.56i −0.522317 + 0.484639i −0.896702 0.442634i \(-0.854044\pi\)
0.374385 + 0.927273i \(0.377854\pi\)
\(360\) −25463.5 + 3838.00i −3.72789 + 0.561890i
\(361\) 3360.34 5820.28i 0.489917 0.848560i
\(362\) −6049.42 10477.9i −0.878317 1.52129i
\(363\) 168.231 + 210.955i 0.0243247 + 0.0305022i
\(364\) −17925.8 + 22526.6i −2.58122 + 3.24372i
\(365\) 3258.47 4085.99i 0.467277 0.585947i
\(366\) 844.163 + 127.237i 0.120560 + 0.0181716i
\(367\) −7916.65 + 5397.48i −1.12601 + 0.767701i −0.975302 0.220878i \(-0.929108\pi\)
−0.150708 + 0.988578i \(0.548155\pi\)
\(368\) −13318.7 + 9080.56i −1.88665 + 1.28630i
\(369\) 7623.28 + 1149.02i 1.07548 + 0.162102i
\(370\) 1595.98 2001.29i 0.224245 0.281195i
\(371\) 6269.01 3027.09i 0.877280 0.423608i
\(372\) 270.613 + 339.338i 0.0377168 + 0.0472954i
\(373\) 1885.91 + 3266.49i 0.261792 + 0.453438i 0.966718 0.255843i \(-0.0823531\pi\)
−0.704926 + 0.709281i \(0.749020\pi\)
\(374\) 2286.85 3960.94i 0.316177 0.547635i
\(375\) −256.875 + 38.7177i −0.0353732 + 0.00533166i
\(376\) −108.253 + 100.445i −0.0148477 + 0.0137767i
\(377\) −5211.42 2509.69i −0.711941 0.342853i
\(378\) −448.804 1140.02i −0.0610687 0.155123i
\(379\) 11776.7 5671.34i 1.59611 0.768646i 0.596683 0.802477i \(-0.296485\pi\)
0.999428 + 0.0338307i \(0.0107707\pi\)
\(380\) 1182.46 3012.86i 0.159629 0.406728i
\(381\) −25.2070 + 336.364i −0.00338948 + 0.0452295i
\(382\) 10598.8 + 3269.30i 1.41959 + 0.437885i
\(383\) 410.988 + 5484.26i 0.0548316 + 0.731677i 0.955089 + 0.296319i \(0.0957592\pi\)
−0.900257 + 0.435358i \(0.856622\pi\)
\(384\) −248.618 + 1089.27i −0.0330396 + 0.144756i
\(385\) −2509.65 + 777.003i −0.332217 + 0.102856i
\(386\) 1842.37 + 8071.95i 0.242938 + 1.06438i
\(387\) 10096.0 3114.21i 1.32612 0.409055i
\(388\) 2508.59 + 6391.78i 0.328233 + 0.836324i
\(389\) 7586.59 + 7039.32i 0.988831 + 0.917501i 0.996594 0.0824688i \(-0.0262805\pi\)
−0.00776264 + 0.999970i \(0.502471\pi\)
\(390\) −902.769 615.497i −0.117214 0.0799152i
\(391\) 4957.08 0.641152
\(392\) −1895.54 + 26025.5i −0.244233 + 3.35329i
\(393\) −481.856 −0.0618484
\(394\) −920.612 627.663i −0.117715 0.0802568i
\(395\) −62.6649 58.1445i −0.00798231 0.00740650i
\(396\) 2436.47 + 6208.03i 0.309185 + 0.787790i
\(397\) −7808.43 + 2408.58i −0.987138 + 0.304492i −0.745961 0.665989i \(-0.768010\pi\)
−0.241177 + 0.970481i \(0.577533\pi\)
\(398\) 4008.08 + 17560.6i 0.504791 + 2.21164i
\(399\) 48.2992 + 7.22821i 0.00606011 + 0.000906925i
\(400\) −1754.81 + 7688.31i −0.219351 + 0.961039i
\(401\) 425.359 + 5676.02i 0.0529711 + 0.706850i 0.958959 + 0.283546i \(0.0915108\pi\)
−0.905988 + 0.423304i \(0.860870\pi\)
\(402\) 128.499 + 39.6366i 0.0159426 + 0.00491765i
\(403\) 468.415 6250.56i 0.0578993 0.772612i
\(404\) 6545.71 16678.2i 0.806092 2.05389i
\(405\) −8203.38 + 3950.54i −1.00649 + 0.484701i
\(406\) −8164.67 + 1239.37i −0.998043 + 0.151500i
\(407\) −379.197 182.611i −0.0461820 0.0222401i
\(408\) 925.853 859.066i 0.112344 0.104240i
\(409\) 8364.33 1260.72i 1.01122 0.152417i 0.377525 0.925999i \(-0.376775\pi\)
0.633696 + 0.773582i \(0.281537\pi\)
\(410\) 9825.02 17017.4i 1.18347 2.04983i
\(411\) −50.4482 87.3788i −0.00605456 0.0104868i
\(412\) −23182.1 29069.5i −2.77209 3.47609i
\(413\) 3411.82 15020.6i 0.406500 1.78963i
\(414\) −6152.08 + 7714.46i −0.730334 + 0.915809i
\(415\) −4418.91 666.044i −0.522689 0.0787827i
\(416\) 41515.8 28305.0i 4.89298 3.33598i
\(417\) −8.66827 + 5.90993i −0.00101795 + 0.000694030i
\(418\) −718.356 108.275i −0.0840572 0.0126696i
\(419\) 2885.94 3618.85i 0.336485 0.421939i −0.584587 0.811331i \(-0.698743\pi\)
0.921072 + 0.389392i \(0.127315\pi\)
\(420\) −1142.72 + 1.19662i −0.132759 + 0.000139021i
\(421\) 6257.69 + 7846.89i 0.724421 + 0.908395i 0.998579 0.0532899i \(-0.0169707\pi\)
−0.274159 + 0.961685i \(0.588399\pi\)
\(422\) 6888.42 + 11931.1i 0.794604 + 1.37629i
\(423\) −26.1563 + 45.3041i −0.00300654 + 0.00520747i
\(424\) −28277.3 + 4262.12i −3.23884 + 0.488176i
\(425\) 1777.72 1649.48i 0.202898 0.188262i
\(426\) −534.808 257.550i −0.0608252 0.0292919i
\(427\) −12325.1 3787.66i −1.39685 0.429269i
\(428\) 1657.53 798.223i 0.187195 0.0901485i
\(429\) −65.6338 + 167.232i −0.00738655 + 0.0188206i
\(430\) 2012.45 26854.3i 0.225696 3.01170i
\(431\) −11351.7 3501.52i −1.26865 0.391328i −0.413882 0.910331i \(-0.635827\pi\)
−0.854773 + 0.519003i \(0.826304\pi\)
\(432\) 217.655 + 2904.40i 0.0242406 + 0.323468i
\(433\) −1568.40 + 6871.59i −0.174070 + 0.762650i 0.810225 + 0.586119i \(0.199345\pi\)
−0.984295 + 0.176531i \(0.943512\pi\)
\(434\) −4482.61 7745.36i −0.495788 0.856657i
\(435\) −51.0900 223.840i −0.00563122 0.0246720i
\(436\) 28311.6 8732.97i 3.10981 0.959250i
\(437\) −287.657 732.937i −0.0314885 0.0802314i
\(438\) −374.022 347.042i −0.0408024 0.0378591i
\(439\) −1650.15 1125.05i −0.179401 0.122314i 0.470290 0.882512i \(-0.344149\pi\)
−0.649691 + 0.760198i \(0.725102\pi\)
\(440\) 10791.9 1.16928
\(441\) 2075.80 + 9007.67i 0.224144 + 0.972645i
\(442\) −28729.8 −3.09171
\(443\) −6904.35 4707.31i −0.740487 0.504856i 0.133353 0.991069i \(-0.457426\pi\)
−0.873840 + 0.486213i \(0.838378\pi\)
\(444\) −134.196 124.515i −0.0143438 0.0133091i
\(445\) 1254.02 + 3195.19i 0.133587 + 0.340375i
\(446\) −11737.5 + 3620.55i −1.24616 + 0.384390i
\(447\) 90.6120 + 396.997i 0.00958792 + 0.0420074i
\(448\) 13139.9 33583.2i 1.38572 3.54165i
\(449\) −2002.70 + 8774.39i −0.210497 + 0.922247i 0.753733 + 0.657181i \(0.228251\pi\)
−0.964230 + 0.265067i \(0.914606\pi\)
\(450\) 360.736 + 4813.68i 0.0377894 + 0.504265i
\(451\) −3087.34 952.319i −0.322344 0.0994301i
\(452\) 2535.84 33838.5i 0.263885 3.52130i
\(453\) −198.888 + 506.758i −0.0206282 + 0.0525598i
\(454\) −17113.8 + 8241.58i −1.76914 + 0.851974i
\(455\) 12109.0 + 11212.0i 1.24765 + 1.15522i
\(456\) −180.745 87.0423i −0.0185618 0.00893888i
\(457\) −2281.77 + 2117.17i −0.233559 + 0.216711i −0.788266 0.615334i \(-0.789021\pi\)
0.554707 + 0.832046i \(0.312830\pi\)
\(458\) −3271.43 + 493.089i −0.333764 + 0.0503068i
\(459\) 447.829 775.662i 0.0455400 0.0788776i
\(460\) 9211.59 + 15954.9i 0.933680 + 1.61718i
\(461\) 5310.03 + 6658.56i 0.536470 + 0.672712i 0.974015 0.226485i \(-0.0727233\pi\)
−0.437545 + 0.899197i \(0.644152\pi\)
\(462\) 57.3358 + 249.998i 0.00577382 + 0.0251752i
\(463\) 9029.14 11322.2i 0.906307 1.13647i −0.0838459 0.996479i \(-0.526720\pi\)
0.990152 0.139994i \(-0.0447082\pi\)
\(464\) 19412.4 + 2925.95i 1.94224 + 0.292745i
\(465\) 205.570 140.155i 0.0205012 0.0139775i
\(466\) −3573.39 + 2436.30i −0.355224 + 0.242187i
\(467\) 4255.26 + 641.378i 0.421649 + 0.0635533i 0.356440 0.934318i \(-0.383990\pi\)
0.0652091 + 0.997872i \(0.479229\pi\)
\(468\) 26119.0 32752.2i 2.57981 3.23498i
\(469\) −1830.82 879.317i −0.180255 0.0865737i
\(470\) 83.1343 + 104.247i 0.00815893 + 0.0102310i
\(471\) −277.521 480.680i −0.0271496 0.0470245i
\(472\) −31636.6 + 54796.2i −3.08515 + 5.34364i
\(473\) −4378.35 + 659.930i −0.425617 + 0.0641514i
\(474\) −6.11790 + 5.67658i −0.000592836 + 0.000550072i
\(475\) −347.046 167.129i −0.0335233 0.0161440i
\(476\) −24808.2 + 16952.0i −2.38882 + 1.63234i
\(477\) −9126.95 + 4395.31i −0.876089 + 0.421902i
\(478\) −3163.33 + 8060.04i −0.302693 + 0.771250i
\(479\) −569.650 + 7601.45i −0.0543381 + 0.725092i 0.901796 + 0.432162i \(0.142249\pi\)
−0.956134 + 0.292930i \(0.905370\pi\)
\(480\) 1905.86 + 587.880i 0.181230 + 0.0559019i
\(481\) 197.567 + 2636.35i 0.0187282 + 0.249911i
\(482\) 4981.10 21823.6i 0.470712 2.06232i
\(483\) −203.581 + 189.293i −0.0191786 + 0.0178326i
\(484\) 5867.43 + 25706.9i 0.551036 + 2.41425i
\(485\) 3761.22 1160.18i 0.352141 0.108621i
\(486\) 977.311 + 2490.15i 0.0912176 + 0.232419i
\(487\) 909.984 + 844.342i 0.0846721 + 0.0785642i 0.721374 0.692546i \(-0.243511\pi\)
−0.636701 + 0.771110i \(0.719702\pi\)
\(488\) 43762.3 + 29836.6i 4.05948 + 2.76770i
\(489\) 351.510 0.0325068
\(490\) 23305.1 + 3462.77i 2.14860 + 0.319249i
\(491\) −1205.27 −0.110780 −0.0553902 0.998465i \(-0.517640\pi\)
−0.0553902 + 0.998465i \(0.517640\pi\)
\(492\) −1161.12 791.636i −0.106397 0.0725400i
\(493\) −4425.49 4106.25i −0.404288 0.375124i
\(494\) 1667.17 + 4247.88i 0.151841 + 0.386885i
\(495\) 3653.09 1126.83i 0.331706 0.102318i
\(496\) 4733.88 + 20740.5i 0.428543 + 1.87757i
\(497\) 7412.86 + 5042.64i 0.669039 + 0.455117i
\(498\) −97.0828 + 425.348i −0.00873571 + 0.0382737i
\(499\) −1547.97 20656.2i −0.138871 1.85311i −0.438102 0.898925i \(-0.644349\pi\)
0.299231 0.954181i \(-0.403270\pi\)
\(500\) −24258.4 7482.74i −2.16974 0.669277i
\(501\) −8.66598 + 115.639i −0.000772789 + 0.0103122i
\(502\) −4174.62 + 10636.8i −0.371160 + 0.945700i
\(503\) −13239.7 + 6375.88i −1.17361 + 0.565182i −0.916044 0.401078i \(-0.868636\pi\)
−0.257569 + 0.966260i \(0.582921\pi\)
\(504\) 2797.95 37868.1i 0.247283 3.34679i
\(505\) −9253.42 4456.21i −0.815389 0.392671i
\(506\) 3031.30 2812.63i 0.266320 0.247108i
\(507\) 628.789 94.7746i 0.0550798 0.00830195i
\(508\) −16481.4 + 28546.7i −1.43946 + 2.49322i
\(509\) −10695.8 18525.7i −0.931402 1.61324i −0.780927 0.624622i \(-0.785253\pi\)
−0.150475 0.988614i \(-0.548080\pi\)
\(510\) −711.017 891.588i −0.0617341 0.0774121i
\(511\) 4811.10 + 6019.98i 0.416498 + 0.521151i
\(512\) −14957.9 + 18756.7i −1.29112 + 1.61901i
\(513\) −140.674 21.2032i −0.0121070 0.00182484i
\(514\) −8972.48 + 6117.34i −0.769960 + 0.524950i
\(515\) −17610.2 + 12006.4i −1.50679 + 1.02731i
\(516\) −1904.41 287.043i −0.162474 0.0244891i
\(517\) 13.6690 17.1404i 0.00116279 0.00145810i
\(518\) 2356.44 + 2948.54i 0.199877 + 0.250100i
\(519\) 181.065 + 227.048i 0.0153138 + 0.0192029i
\(520\) −33894.6 58707.2i −2.85842 4.95093i
\(521\) 4607.37 7980.19i 0.387433 0.671053i −0.604671 0.796475i \(-0.706695\pi\)
0.992103 + 0.125423i \(0.0400287\pi\)
\(522\) 11882.7 1791.03i 0.996343 0.150175i
\(523\) −3871.50 + 3592.23i −0.323688 + 0.300339i −0.825232 0.564793i \(-0.808956\pi\)
0.501544 + 0.865132i \(0.332765\pi\)
\(524\) −42425.5 20431.0i −3.53696 1.70331i
\(525\) −10.0210 + 135.627i −0.000833052 + 0.0112747i
\(526\) 29916.6 14407.1i 2.47990 1.19425i
\(527\) 2390.09 6089.84i 0.197559 0.503373i
\(528\) 45.5654 608.028i 0.00375564 0.0501156i
\(529\) −7343.77 2265.25i −0.603581 0.186180i
\(530\) 1929.55 + 25748.0i 0.158140 + 2.11023i
\(531\) −4987.59 + 21852.1i −0.407614 + 1.78587i
\(532\) 3946.07 + 2684.33i 0.321586 + 0.218761i
\(533\) 4516.02 + 19786.0i 0.366999 + 1.60793i
\(534\) 320.220 98.7748i 0.0259499 0.00800450i
\(535\) −385.286 981.693i −0.0311353 0.0793314i
\(536\) 6115.89 + 5674.72i 0.492847 + 0.457296i
\(537\) 630.797 + 430.070i 0.0506907 + 0.0345603i
\(538\) 37849.3 3.03309
\(539\) −297.588 3862.47i −0.0237811 0.308661i
\(540\) 3328.75 0.265271
\(541\) −4832.46 3294.72i −0.384036 0.261832i 0.355878 0.934532i \(-0.384182\pi\)
−0.739915 + 0.672701i \(0.765134\pi\)
\(542\) 16793.3 + 15581.9i 1.33087 + 1.23487i
\(543\) 181.210 + 461.717i 0.0143213 + 0.0364902i
\(544\) 50113.2 15457.9i 3.94960 1.21829i
\(545\) −3779.25 16558.0i −0.297037 1.30140i
\(546\) 1179.90 1097.09i 0.0924815 0.0859907i
\(547\) 2927.04 12824.2i 0.228795 1.00242i −0.721828 0.692072i \(-0.756698\pi\)
0.950624 0.310346i \(-0.100445\pi\)
\(548\) −736.835 9832.38i −0.0574380 0.766457i
\(549\) 17929.1 + 5530.39i 1.39380 + 0.429929i
\(550\) 151.179 2017.34i 0.0117205 0.156399i
\(551\) −350.328 + 892.620i −0.0270861 + 0.0690144i
\(552\) 1028.83 495.458i 0.0793295 0.0382031i
\(553\) 104.075 71.1167i 0.00800309 0.00546870i
\(554\) −26983.4 12994.5i −2.06934 0.996541i
\(555\) −76.9259 + 71.3768i −0.00588346 + 0.00545906i
\(556\) −1013.79 + 152.804i −0.0773279 + 0.0116553i
\(557\) 5269.86 9127.66i 0.400881 0.694347i −0.592951 0.805238i \(-0.702037\pi\)
0.993833 + 0.110892i \(0.0353706\pi\)
\(558\) 6511.05 + 11277.5i 0.493969 + 0.855580i
\(559\) 17341.3 + 21745.3i 1.31209 + 1.64531i
\(560\) −50488.6 24248.9i −3.80988 1.82983i
\(561\) −116.906 + 146.596i −0.00879820 + 0.0110326i
\(562\) 45143.1 + 6804.23i 3.38834 + 0.510710i
\(563\) −11483.3 + 7829.21i −0.859619 + 0.586078i −0.910910 0.412606i \(-0.864619\pi\)
0.0512912 + 0.998684i \(0.483666\pi\)
\(564\) 7.87885 5.37171i 0.000588226 0.000401046i
\(565\) −19234.6 2899.15i −1.43222 0.215873i
\(566\) 3537.05 4435.32i 0.262673 0.329382i
\(567\) −3001.25 13086.2i −0.222294 0.969254i
\(568\) −22961.9 28793.3i −1.69623 2.12701i
\(569\) −3337.48 5780.69i −0.245896 0.425904i 0.716487 0.697600i \(-0.245749\pi\)
−0.962383 + 0.271696i \(0.912415\pi\)
\(570\) −90.5671 + 156.867i −0.00665516 + 0.0115271i
\(571\) 7494.08 1129.55i 0.549243 0.0827850i 0.131442 0.991324i \(-0.458039\pi\)
0.417800 + 0.908539i \(0.362801\pi\)
\(572\) −12869.5 + 11941.2i −0.940739 + 0.872878i
\(573\) −409.679 197.291i −0.0298684 0.0143839i
\(574\) 21260.8 + 19685.8i 1.54601 + 1.43148i
\(575\) 1975.44 951.321i 0.143272 0.0689962i
\(576\) −19171.6 + 48848.5i −1.38684 + 3.53360i
\(577\) 1296.36 17298.7i 0.0935322 1.24810i −0.731037 0.682338i \(-0.760963\pi\)
0.824569 0.565762i \(-0.191418\pi\)
\(578\) −2977.65 918.485i −0.214280 0.0660968i
\(579\) −25.3654 338.478i −0.00182064 0.0242948i
\(580\) 4992.70 21874.5i 0.357432 1.56601i
\(581\) 2401.00 6136.53i 0.171446 0.438186i
\(582\) −85.5095 374.642i −0.00609018 0.0266828i
\(583\) 4056.78 1251.35i 0.288190 0.0888948i
\(584\) −11565.1 29467.5i −0.819468 2.08797i
\(585\) −17603.4 16333.5i −1.24412 1.15437i
\(586\) −19996.8 13633.6i −1.40966 0.961089i
\(587\) −52.8058 −0.00371300 −0.00185650 0.999998i \(-0.500591\pi\)
−0.00185650 + 0.999998i \(0.500591\pi\)
\(588\) 371.506 1643.53i 0.0260555 0.115269i
\(589\) −1039.12 −0.0726929
\(590\) 47202.9 + 32182.4i 3.29375 + 2.24564i
\(591\) 33.4847 + 31.0693i 0.00233059 + 0.00216247i
\(592\) −3278.15 8352.58i −0.227586 0.579880i
\(593\) 9964.24 3073.56i 0.690021 0.212843i 0.0701375 0.997537i \(-0.477656\pi\)
0.619883 + 0.784694i \(0.287180\pi\)
\(594\) −166.257 728.421i −0.0114842 0.0503156i
\(595\) 8627.60 + 14907.4i 0.594449 + 1.02713i
\(596\) −8854.93 + 38796.0i −0.608577 + 2.66635i
\(597\) −55.1826 736.361i −0.00378304 0.0504811i
\(598\) −24821.2 7656.31i −1.69735 0.523562i
\(599\) 111.855 1492.61i 0.00762987 0.101813i −0.992089 0.125539i \(-0.959934\pi\)
0.999719 + 0.0237259i \(0.00755290\pi\)
\(600\) 204.095 520.026i 0.0138869 0.0353833i
\(601\) −13914.4 + 6700.82i −0.944393 + 0.454796i −0.841717 0.539919i \(-0.818455\pi\)
−0.102676 + 0.994715i \(0.532740\pi\)
\(602\) 37957.3 + 11664.8i 2.56981 + 0.789734i
\(603\) 2662.78 + 1282.33i 0.179829 + 0.0866009i
\(604\) −38998.2 + 36185.0i −2.62717 + 2.43766i
\(605\) 14946.3 2252.79i 1.00438 0.151387i
\(606\) −501.349 + 868.363i −0.0336071 + 0.0582093i
\(607\) 5014.93 + 8686.11i 0.335337 + 0.580821i 0.983550 0.180638i \(-0.0578164\pi\)
−0.648212 + 0.761460i \(0.724483\pi\)
\(608\) −5193.58 6512.55i −0.346427 0.434406i
\(609\) 338.552 0.354522i 0.0225268 2.35894e-5i
\(610\) 29817.2 37389.6i 1.97912 2.48174i
\(611\) −136.174 20.5249i −0.00901639 0.00135900i
\(612\) 36125.4 24629.9i 2.38608 1.62680i
\(613\) 8101.55 5523.55i 0.533799 0.363938i −0.266220 0.963912i \(-0.585775\pi\)
0.800019 + 0.599974i \(0.204823\pi\)
\(614\) −53779.6 8105.98i −3.53480 0.532786i
\(615\) −502.266 + 629.821i −0.0329322 + 0.0412957i
\(616\) −3524.77 + 15517.9i −0.230547 + 1.01499i
\(617\) 17079.6 + 21417.2i 1.11443 + 1.39745i 0.907994 + 0.418984i \(0.137614\pi\)
0.206432 + 0.978461i \(0.433815\pi\)
\(618\) 1040.41 + 1802.05i 0.0677210 + 0.117296i
\(619\) 13516.8 23411.7i 0.877681 1.52019i 0.0238015 0.999717i \(-0.492423\pi\)
0.853879 0.520471i \(-0.174244\pi\)
\(620\) 24042.3 3623.79i 1.55736 0.234734i
\(621\) 593.612 550.792i 0.0383588 0.0355918i
\(622\) 17673.5 + 8511.10i 1.13930 + 0.548656i
\(623\) −5004.03 + 759.597i −0.321802 + 0.0488485i
\(624\) −3450.75 + 1661.79i −0.221379 + 0.106611i
\(625\) −6812.24 + 17357.3i −0.435984 + 1.11087i
\(626\) −82.8440 + 1105.48i −0.00528932 + 0.0705810i
\(627\) 28.4592 + 8.77849i 0.00181268 + 0.000559137i
\(628\) −4053.41 54089.0i −0.257561 3.43692i
\(629\) −614.002 + 2690.12i −0.0389219 + 0.170528i
\(630\) −33907.0 5074.36i −2.14427 0.320900i
\(631\) 4252.08 + 18629.6i 0.268261 + 1.17533i 0.912035 + 0.410112i \(0.134511\pi\)
−0.643774 + 0.765216i \(0.722632\pi\)
\(632\) −494.790 + 152.623i −0.0311419 + 0.00960601i
\(633\) −206.343 525.752i −0.0129564 0.0330123i
\(634\) 1374.51 + 1275.36i 0.0861019 + 0.0798909i
\(635\) 15612.2 + 10644.2i 0.975673 + 0.665202i
\(636\) 1846.57 0.115128
\(637\) −20077.0 + 13749.9i −1.24879 + 0.855247i
\(638\) −5036.10 −0.312509
\(639\) −10779.1 7349.08i −0.667317 0.454969i
\(640\) 45880.7 + 42571.0i 2.83374 + 2.62932i
\(641\) −9765.99 24883.3i −0.601768 1.53328i −0.828888 0.559414i \(-0.811026\pi\)
0.227120 0.973867i \(-0.427069\pi\)
\(642\) −98.3845 + 30.3476i −0.00604817 + 0.00186561i
\(643\) 3080.22 + 13495.3i 0.188915 + 0.827689i 0.977190 + 0.212366i \(0.0681170\pi\)
−0.788276 + 0.615322i \(0.789026\pi\)
\(644\) −25950.7 + 8034.49i −1.58789 + 0.491620i
\(645\) −245.664 + 1076.33i −0.0149969 + 0.0657059i
\(646\) 355.924 + 4749.47i 0.0216775 + 0.289266i
\(647\) −16494.0 5087.72i −1.00223 0.309148i −0.250144 0.968209i \(-0.580478\pi\)
−0.752090 + 0.659060i \(0.770954\pi\)
\(648\) −4121.42 + 54996.5i −0.249853 + 3.33405i
\(649\) 3431.78 8744.04i 0.207564 0.528865i
\(650\) −11449.0 + 5513.57i −0.690875 + 0.332708i
\(651\) 134.391 + 341.371i 0.00809094 + 0.0205521i
\(652\) 30949.0 + 14904.3i 1.85898 + 0.895240i
\(653\) 16301.2 15125.3i 0.976901 0.906432i −0.0187283 0.999825i \(-0.505962\pi\)
0.995629 + 0.0933929i \(0.0297713\pi\)
\(654\) −1639.59 + 247.128i −0.0980320 + 0.0147760i
\(655\) −13496.5 + 23376.6i −0.805118 + 1.39450i
\(656\) −34440.2 59652.3i −2.04980 3.55035i
\(657\) −6991.69 8767.30i −0.415178 0.520616i
\(658\) −177.052 + 85.4925i −0.0104897 + 0.00506511i
\(659\) 9166.17 11494.0i 0.541826 0.679428i −0.433256 0.901271i \(-0.642636\pi\)
0.975083 + 0.221842i \(0.0712070\pi\)
\(660\) −689.080 103.862i −0.0406400 0.00612549i
\(661\) −3446.78 + 2349.98i −0.202820 + 0.138281i −0.660471 0.750851i \(-0.729643\pi\)
0.457651 + 0.889132i \(0.348691\pi\)
\(662\) 25803.4 17592.5i 1.51492 1.03286i
\(663\) 1164.65 + 175.542i 0.0682220 + 0.0102828i
\(664\) −16876.8 + 21162.9i −0.986367 + 1.23687i
\(665\) 1703.50 2140.71i 0.0993366 0.124832i
\(666\) −3424.48 4294.16i −0.199243 0.249843i
\(667\) −2729.12 4726.97i −0.158429 0.274407i
\(668\) −5666.20 + 9814.14i −0.328191 + 0.568444i
\(669\) 497.939 75.0522i 0.0287764 0.00433735i
\(670\) 5522.09 5123.75i 0.318413 0.295444i
\(671\) −7084.44 3411.69i −0.407588 0.196284i
\(672\) −1467.81 + 2548.48i −0.0842588 + 0.146294i
\(673\) 20967.1 10097.2i 1.20092 0.578334i 0.276984 0.960875i \(-0.410665\pi\)
0.923938 + 0.382541i \(0.124951\pi\)
\(674\) 3019.44 7693.40i 0.172558 0.439672i
\(675\) 29.6050 395.051i 0.00168814 0.0225267i
\(676\) 59380.8 + 18316.5i 3.37852 + 1.04213i
\(677\) −74.3673 992.362i −0.00422181 0.0563361i 0.994695 0.102868i \(-0.0328020\pi\)
−0.998917 + 0.0465322i \(0.985183\pi\)
\(678\) −422.581 + 1851.45i −0.0239368 + 0.104874i
\(679\) 439.793 + 5787.30i 0.0248567 + 0.327093i
\(680\) −15743.9 68978.4i −0.887868 3.89000i
\(681\) 744.118 229.530i 0.0418717 0.0129157i
\(682\) −1993.80 5080.12i −0.111945 0.285231i
\(683\) −8042.67 7462.51i −0.450577 0.418075i 0.421966 0.906612i \(-0.361340\pi\)
−0.872543 + 0.488537i \(0.837531\pi\)
\(684\) −5738.02 3912.11i −0.320758 0.218689i
\(685\) −5652.09 −0.315263
\(686\) −12591.0 + 32380.0i −0.700766 + 1.80215i
\(687\) 135.630 0.00753220
\(688\) −77995.4 53176.4i −4.32202 2.94670i
\(689\) −19548.6 18138.5i −1.08091 1.00293i
\(690\) −376.683 959.772i −0.0207827 0.0529535i
\(691\) 2188.50 675.062i 0.120484 0.0371643i −0.233927 0.972254i \(-0.575158\pi\)
0.354411 + 0.935090i \(0.384681\pi\)
\(692\) 6315.03 + 27668.0i 0.346910 + 1.51991i
\(693\) 427.149 + 5620.92i 0.0234142 + 0.308111i
\(694\) 515.742 2259.61i 0.0282094 0.123593i
\(695\) 43.9194 + 586.063i 0.00239706 + 0.0319865i
\(696\) −1328.92 409.916i −0.0723741 0.0223245i
\(697\) −1582.93 + 21122.7i −0.0860224 + 1.14789i
\(698\) −17269.2 + 44001.2i −0.936459 + 2.38606i
\(699\) 159.745 76.9289i 0.00864391 0.00416269i
\(700\) −6632.97 + 11516.5i −0.358147 + 0.621831i
\(701\) −5862.28 2823.13i −0.315857 0.152108i 0.269238 0.963074i \(-0.413228\pi\)
−0.585094 + 0.810965i \(0.698943\pi\)
\(702\) −3440.40 + 3192.22i −0.184971 + 0.171628i
\(703\) 433.382 65.3218i 0.0232508 0.00350449i
\(704\) 10995.9 19045.5i 0.588672 1.01961i
\(705\) −2.73314 4.73393i −0.000146008 0.000252894i
\(706\) −41537.1 52085.9i −2.21426 2.77660i
\(707\) 9429.99 11850.3i 0.501629 0.630375i
\(708\) 2547.41 3194.36i 0.135223 0.169564i
\(709\) 15413.0 + 2323.13i 0.816425 + 0.123056i 0.543962 0.839110i \(-0.316924\pi\)
0.272463 + 0.962166i \(0.412162\pi\)
\(710\) −27474.3 + 18731.7i −1.45224 + 0.990124i
\(711\) −151.552 + 103.327i −0.00799390 + 0.00545015i
\(712\) 20558.7 + 3098.73i 1.08212 + 0.163104i
\(713\) 3687.83 4624.39i 0.193703 0.242896i
\(714\) 1514.27 731.186i 0.0793697 0.0383249i
\(715\) 6274.68 + 7868.21i 0.328196 + 0.411544i
\(716\) 37303.9 + 64612.2i 1.94708 + 3.37244i
\(717\) 177.483 307.410i 0.00924439 0.0160118i
\(718\) 26210.5 3950.59i 1.36235 0.205341i
\(719\) −17159.3 + 15921.5i −0.890033 + 0.825830i −0.985513 0.169602i \(-0.945752\pi\)
0.0954799 + 0.995431i \(0.469561\pi\)
\(720\) 73431.4 + 35362.7i 3.80087 + 1.83040i
\(721\) −11512.6 29243.6i −0.594663 1.51052i
\(722\) −33115.7 + 15947.7i −1.70698 + 0.822039i
\(723\) −335.269 + 854.253i −0.0172459 + 0.0439419i
\(724\) −3622.26 + 48335.7i −0.185940 + 2.48119i
\(725\) −2551.63 787.073i −0.130711 0.0403189i
\(726\) −110.277 1471.54i −0.00563741 0.0752260i
\(727\) −5767.42 + 25268.7i −0.294225 + 1.28909i 0.584358 + 0.811496i \(0.301346\pi\)
−0.878583 + 0.477589i \(0.841511\pi\)
\(728\) 95487.1 29563.4i 4.86125 1.50507i
\(729\) 4331.03 + 18975.5i 0.220039 + 0.964054i
\(730\) −27312.4 + 8424.76i −1.38476 + 0.427143i
\(731\) 10605.5 + 27022.4i 0.536605 + 1.36725i
\(732\) −2507.15 2326.29i −0.126594 0.117462i
\(733\) −13592.6 9267.27i −0.684930 0.466977i 0.170187 0.985412i \(-0.445563\pi\)
−0.855117 + 0.518434i \(0.826515\pi\)
\(734\) 52402.0 2.63514
\(735\) −923.584 282.771i −0.0463495 0.0141907i
\(736\) 47414.8 2.37464
\(737\) −1023.37 697.721i −0.0511483 0.0348723i
\(738\) −30907.7 28678.1i −1.54164 1.43043i
\(739\) 4261.08 + 10857.1i 0.212106 + 0.540438i 0.996844 0.0793908i \(-0.0252975\pi\)
−0.784737 + 0.619828i \(0.787202\pi\)
\(740\) −9799.44 + 3022.73i −0.486803 + 0.150159i
\(741\) −41.6288 182.388i −0.00206379 0.00904207i
\(742\) −37654.0 5635.10i −1.86297 0.278802i
\(743\) 3692.90 16179.6i 0.182341 0.798888i −0.798171 0.602430i \(-0.794199\pi\)
0.980512 0.196457i \(-0.0629438\pi\)
\(744\) −112.621 1502.82i −0.00554956 0.0740537i
\(745\) 21797.8 + 6723.72i 1.07196 + 0.330655i
\(746\) 1541.55 20570.6i 0.0756571 1.00957i
\(747\) −3503.16 + 8925.90i −0.171585 + 0.437191i
\(748\) −16508.9 + 7950.26i −0.806985 + 0.388624i
\(749\) 1537.44 233.379i 0.0750025 0.0113852i
\(750\) 1280.03 + 616.432i 0.0623203 + 0.0300119i
\(751\) 4357.52 4043.19i 0.211729 0.196456i −0.567178 0.823595i \(-0.691965\pi\)
0.778907 + 0.627140i \(0.215774\pi\)
\(752\) 462.174 69.6615i 0.0224119 0.00337805i
\(753\) 234.223 405.686i 0.0113354 0.0196335i
\(754\) 15817.2 + 27396.1i 0.763961 + 1.32322i
\(755\) 19014.0 + 23842.8i 0.916542 + 1.14931i
\(756\) −1087.21 + 4786.49i −0.0523037 + 0.230269i
\(757\) −2187.25 + 2742.73i −0.105016 + 0.131686i −0.831562 0.555432i \(-0.812553\pi\)
0.726546 + 0.687118i \(0.241124\pi\)
\(758\) −70688.0 10654.5i −3.38721 0.510540i
\(759\) −140.069 + 95.4971i −0.00669850 + 0.00456696i
\(760\) −9285.30 + 6330.61i −0.443175 + 0.302152i
\(761\) 16724.2 + 2520.77i 0.796652 + 0.120076i 0.534741 0.845016i \(-0.320409\pi\)
0.261911 + 0.965092i \(0.415647\pi\)
\(762\) 1150.18 1442.28i 0.0546807 0.0685674i
\(763\) 25043.5 26.2248i 1.18825 0.00124430i
\(764\) −27705.3 34741.4i −1.31197 1.64516i
\(765\) −12531.7 21705.6i −0.592268 1.02584i
\(766\) 15038.9 26048.1i 0.709369 1.22866i
\(767\) −58345.5 + 8794.17i −2.74672 + 0.414001i
\(768\) 1919.02 1780.59i 0.0901649 0.0836608i
\(769\) −5847.03 2815.78i −0.274186 0.132041i 0.291738 0.956498i \(-0.405766\pi\)
−0.565925 + 0.824457i \(0.691481\pi\)
\(770\) 13734.3 + 4220.71i 0.642790 + 0.197537i
\(771\) 401.105 193.162i 0.0187360 0.00902277i
\(772\) 12118.4 30877.1i 0.564961 1.43950i
\(773\) −1394.53 + 18608.7i −0.0648871 + 0.865858i 0.865882 + 0.500249i \(0.166758\pi\)
−0.930769 + 0.365609i \(0.880861\pi\)
\(774\) −55215.7 17031.8i −2.56419 0.790949i
\(775\) −216.241 2885.54i −0.0100227 0.133744i
\(776\) 5305.23 23243.7i 0.245421 1.07526i
\(777\) −77.5096 133.926i −0.00357869 0.00618351i
\(778\) −12594.9 55181.8i −0.580397 2.54288i
\(779\) 3214.98 991.691i 0.147867 0.0456111i
\(780\) 1599.23 + 4074.76i 0.0734122 + 0.187051i
\(781\) 4007.88 + 3718.77i 0.183628 + 0.170381i
\(782\) −22399.8 15271.9i −1.02431 0.698366i
\(783\) −986.208 −0.0450117
\(784\) 51358.4 64678.8i 2.33958 2.94638i
\(785\) −31092.7 −1.41369
\(786\) 2177.38 + 1484.52i 0.0988101 + 0.0673676i
\(787\) −18719.5 17369.2i −0.847877 0.786715i 0.130953 0.991389i \(-0.458196\pi\)
−0.978830 + 0.204673i \(0.934387\pi\)
\(788\) 1630.83 + 4155.30i 0.0737260 + 0.187851i
\(789\) −1300.79 + 401.240i −0.0586937 + 0.0181046i
\(790\) 104.033 + 455.799i 0.00468523 + 0.0205274i
\(791\) 10451.0 26711.0i 0.469780 1.20068i
\(792\) 5152.71 22575.5i 0.231179 1.01286i
\(793\) 3691.10 + 49254.3i 0.165290 + 2.20564i
\(794\) 42704.7 + 13172.7i 1.90873 + 0.588766i
\(795\) 79.1036 1055.56i 0.00352895 0.0470906i
\(796\) 26363.6 67173.3i 1.17391 2.99108i
\(797\) 8938.42 4304.51i 0.397258 0.191310i −0.224579 0.974456i \(-0.572101\pi\)
0.621838 + 0.783146i \(0.286386\pi\)
\(798\) −195.983 181.464i −0.00869387 0.00804981i
\(799\) −129.498 62.3628i −0.00573379 0.00276125i
\(800\) 17004.0 15777.4i 0.751476 0.697268i
\(801\) 7282.77 1097.70i 0.321253 0.0484211i
\(802\) 15564.7 26958.9i 0.685299 1.18697i
\(803\) 2349.76 + 4069.91i 0.103264 + 0.178859i
\(804\) −335.896 421.200i −0.0147340 0.0184759i
\(805\) 3481.11 + 15178.5i 0.152414 + 0.664560i
\(806\) −21373.5 + 26801.6i −0.934058 + 1.17127i
\(807\) −1534.34 231.264i −0.0669284 0.0100878i
\(808\) −51400.3 + 35044.2i −2.23794 + 1.52580i
\(809\) 22167.2 15113.4i 0.963360 0.656808i 0.0239898 0.999712i \(-0.492363\pi\)
0.939370 + 0.342904i \(0.111411\pi\)
\(810\) 49239.8 + 7421.71i 2.13594 + 0.321941i
\(811\) 23228.1 29127.1i 1.00573 1.26115i 0.0406571 0.999173i \(-0.487055\pi\)
0.965075 0.261975i \(-0.0843737\pi\)
\(812\) 29823.2 + 14323.6i 1.28890 + 0.619041i
\(813\) −585.560 734.270i −0.0252601 0.0316752i
\(814\) 1150.90 + 1993.41i 0.0495564 + 0.0858342i
\(815\) 9845.59 17053.1i 0.423161 0.732936i
\(816\) −3952.81 + 595.790i −0.169578 + 0.0255598i
\(817\) 3380.00 3136.18i 0.144738 0.134298i
\(818\) −41680.3 20072.2i −1.78156 0.857954i
\(819\) 29235.9 19977.6i 1.24736 0.852349i
\(820\) −70927.3 + 34156.8i −3.02060 + 1.45464i
\(821\) 9367.76 23868.7i 0.398218 1.01464i −0.581372 0.813638i \(-0.697484\pi\)
0.979590 0.201005i \(-0.0644209\pi\)
\(822\) −41.2366 + 550.264i −0.00174975 + 0.0233487i
\(823\) 43646.7 + 13463.2i 1.84864 + 0.570229i 0.999087 + 0.0427225i \(0.0136031\pi\)
0.849551 + 0.527507i \(0.176873\pi\)
\(824\) 9647.65 + 128739.i 0.407878 + 5.44276i
\(825\) −18.4547 + 80.8553i −0.000778800 + 0.00341215i
\(826\) −61693.1 + 57363.2i −2.59876 + 2.41637i
\(827\) 3228.22 + 14143.8i 0.135739 + 0.594712i 0.996344 + 0.0854377i \(0.0272289\pi\)
−0.860604 + 0.509274i \(0.829914\pi\)
\(828\) 37774.3 11651.8i 1.58544 0.489045i
\(829\) 14012.3 + 35702.7i 0.587052 + 1.49578i 0.847767 + 0.530369i \(0.177947\pi\)
−0.260715 + 0.965416i \(0.583958\pi\)
\(830\) 17915.9 + 16623.6i 0.749243 + 0.695196i
\(831\) 1014.46 + 691.644i 0.0423479 + 0.0288723i
\(832\) −138142. −5.75627
\(833\) −24253.6 + 7536.91i −1.00881 + 0.313492i
\(834\) 57.3771 0.00238226
\(835\) 5367.37 + 3659.41i 0.222450 + 0.151664i
\(836\) 2133.50 + 1979.60i 0.0882639 + 0.0818970i
\(837\) −390.441 994.828i −0.0161238 0.0410828i
\(838\) −24189.8 + 7461.58i −0.997165 + 0.307585i
\(839\) −6193.79 27136.8i −0.254867 1.11665i −0.926658 0.375905i \(-0.877332\pi\)
0.671791 0.740741i \(-0.265525\pi\)
\(840\) 3280.62 + 2231.66i 0.134753 + 0.0916662i
\(841\) 3947.87 17296.8i 0.161871 0.709204i
\(842\) −4101.96 54736.9i −0.167890 2.24033i
\(843\) −1788.44 551.661i −0.0730690 0.0225388i
\(844\) 4124.63 55039.4i 0.168218 2.24471i
\(845\) 13014.1 33159.4i 0.529822 1.34996i
\(846\) 257.768 124.134i 0.0104755 0.00504471i
\(847\) −1642.31 + 22227.4i −0.0666240 + 0.901705i
\(848\) 81546.0 + 39270.5i 3.30224 + 1.59028i
\(849\) −170.485 + 158.187i −0.00689169 + 0.00639455i
\(850\) −13114.8 + 1976.74i −0.529216 + 0.0797665i
\(851\) −1247.37 + 2160.51i −0.0502459 + 0.0870284i
\(852\) 1189.05 + 2059.49i 0.0478123 + 0.0828133i
\(853\) −2598.67 3258.62i −0.104310 0.130801i 0.726936 0.686705i \(-0.240944\pi\)
−0.831246 + 0.555904i \(0.812372\pi\)
\(854\) 44024.8 + 55087.0i 1.76405 + 2.20730i
\(855\) −2482.10 + 3112.46i −0.0992820 + 0.124496i
\(856\) −6316.48 952.056i −0.252211 0.0380147i
\(857\) 4629.18 3156.12i 0.184515 0.125800i −0.467540 0.883972i \(-0.654859\pi\)
0.652055 + 0.758172i \(0.273907\pi\)
\(858\) 811.795 553.472i 0.0323010 0.0220224i
\(859\) −6842.71 1031.37i −0.271793 0.0409662i 0.0117316 0.999931i \(-0.496266\pi\)
−0.283524 + 0.958965i \(0.591504\pi\)
\(860\) −67266.7 + 84349.8i −2.66718 + 3.34454i
\(861\) −741.590 927.930i −0.0293535 0.0367291i
\(862\) 40507.6 + 50794.9i 1.60057 + 2.00706i
\(863\) −13026.2 22562.1i −0.513810 0.889945i −0.999872 0.0160204i \(-0.994900\pi\)
0.486062 0.873924i \(-0.338433\pi\)
\(864\) 4283.51 7419.26i 0.168667 0.292139i
\(865\) 16086.5 2424.65i 0.632320 0.0953069i
\(866\) 28257.3 26219.0i 1.10880 1.02882i
\(867\) 115.096 + 55.4274i 0.00450851 + 0.00217118i
\(868\) −2641.79 + 35754.6i −0.103304 + 1.39815i
\(869\) 69.2578 33.3528i 0.00270358 0.00130198i
\(870\) −458.750 + 1168.87i −0.0178771 + 0.0455501i
\(871\) −581.415 + 7758.44i −0.0226182 + 0.301820i
\(872\) −98302.9 30322.4i −3.81761 1.17758i
\(873\) −631.145 8422.04i −0.0244685 0.326510i
\(874\) −958.205 + 4198.17i −0.0370844 + 0.162477i
\(875\) −17742.3 12069.3i −0.685484 0.466304i
\(876\) 454.856 + 1992.85i 0.0175436 + 0.0768634i
\(877\) −15733.4 + 4853.12i −0.605793 + 0.186862i −0.582452 0.812865i \(-0.697907\pi\)
−0.0233412 + 0.999728i \(0.507430\pi\)
\(878\) 3990.50 + 10167.6i 0.153386 + 0.390821i
\(879\) 727.329 + 674.862i 0.0279092 + 0.0258959i
\(880\) −28221.4 19241.0i −1.08107 0.737063i
\(881\) −41813.5 −1.59902 −0.799508 0.600655i \(-0.794907\pi\)
−0.799508 + 0.600655i \(0.794907\pi\)
\(882\) 18371.1 47098.5i 0.701344 1.79806i
\(883\) −24103.7 −0.918634 −0.459317 0.888272i \(-0.651906\pi\)
−0.459317 + 0.888272i \(0.651906\pi\)
\(884\) 95099.4 + 64837.7i 3.61826 + 2.46689i
\(885\) −1716.88 1593.03i −0.0652115 0.0605074i
\(886\) 16696.6 + 42542.2i 0.633107 + 1.61313i
\(887\) 22560.1 6958.86i 0.853994 0.263422i 0.163306 0.986575i \(-0.447784\pi\)
0.690688 + 0.723153i \(0.257308\pi\)
\(888\) 141.441 + 619.696i 0.00534512 + 0.0234185i
\(889\) −20404.8 + 18972.7i −0.769803 + 0.715774i
\(890\) 4177.24 18301.7i 0.157327 0.689296i
\(891\) −611.854 8164.63i −0.0230055 0.306987i
\(892\) 47023.8 + 14504.9i 1.76510 + 0.544462i
\(893\) −1.70607 + 22.7660i −6.39323e−5 + 0.000853118i
\(894\) 813.626 2073.09i 0.0304382 0.0775552i
\(895\) 38532.5 18556.3i 1.43911 0.693037i
\(896\) −76199.3 + 52068.8i −2.84112 + 1.94140i
\(897\) 959.420 + 462.032i 0.0357125 + 0.0171982i
\(898\) 36082.0 33479.2i 1.34084 1.24412i
\(899\) −7123.01 + 1073.62i −0.264255 + 0.0398301i
\(900\) 9669.50 16748.1i 0.358130 0.620299i
\(901\) −13916.6 24104.2i −0.514570 0.891261i
\(902\) 11017.0 + 13814.9i 0.406680 + 0.509960i
\(903\) −1467.44 704.790i −0.0540790 0.0259734i
\(904\) −73461.2 + 92117.5i −2.70275 + 3.38914i
\(905\) 27475.2 + 4141.22i 1.00918 + 0.152109i
\(906\) 2459.96 1677.17i 0.0902059 0.0615013i
\(907\) −21197.4 + 14452.1i −0.776018 + 0.529080i −0.885350 0.464925i \(-0.846081\pi\)
0.109332 + 0.994005i \(0.465129\pi\)
\(908\) 75248.8 + 11341.9i 2.75024 + 0.414532i
\(909\) −13740.1 + 17229.5i −0.501353 + 0.628677i
\(910\) −20175.5 87969.8i −0.734957 3.20458i
\(911\) 4533.40 + 5684.70i 0.164872 + 0.206743i 0.857403 0.514645i \(-0.172076\pi\)
−0.692532 + 0.721387i \(0.743505\pi\)
\(912\) 317.471 + 549.875i 0.0115269 + 0.0199651i
\(913\) 2009.25 3480.11i 0.0728328 0.126150i
\(914\) 16833.4 2537.22i 0.609188 0.0918204i
\(915\) −1437.19 + 1333.52i −0.0519257 + 0.0481800i
\(916\) 11941.7 + 5750.82i 0.430748 + 0.207437i
\(917\) −29205.7 27042.1i −1.05175 0.973837i
\(918\) −4413.30 + 2125.33i −0.158672 + 0.0764123i
\(919\) −15519.6 + 39543.3i −0.557067 + 1.41938i 0.323848 + 0.946109i \(0.395023\pi\)
−0.880915 + 0.473275i \(0.843072\pi\)
\(920\) 4780.38 63789.8i 0.171309 2.28596i
\(921\) 2130.59 + 657.201i 0.0762274 + 0.0235130i
\(922\) −3480.76 46447.6i −0.124331 1.65908i
\(923\) 7642.13 33482.4i 0.272529 1.19403i
\(924\) 374.409 956.923i 0.0133302 0.0340698i
\(925\) 271.580 + 1189.87i 0.00965349 + 0.0422947i
\(926\) −75682.0 + 23344.8i −2.68582 + 0.828465i
\(927\) 16708.0 + 42571.3i 0.591977 + 1.50833i
\(928\) −42330.1 39276.6i −1.49736 1.38935i
\(929\) 20607.3 + 14049.8i 0.727774 + 0.496188i 0.869633 0.493699i \(-0.164356\pi\)
−0.141859 + 0.989887i \(0.545308\pi\)
\(930\) −1360.71 −0.0479779
\(931\) 2521.80 + 3148.69i 0.0887742 + 0.110842i
\(932\) 17326.7 0.608964
\(933\) −664.444 453.011i −0.0233150 0.0158959i
\(934\) −17252.5 16007.9i −0.604408 0.560809i
\(935\) 3837.43 + 9777.62i 0.134222 + 0.341992i
\(936\) −138993. + 42873.7i −4.85377 + 1.49719i
\(937\) −4240.25 18577.8i −0.147837 0.647715i −0.993484 0.113973i \(-0.963642\pi\)
0.845647 0.533742i \(-0.179215\pi\)
\(938\) 5563.99 + 9613.85i 0.193679 + 0.334652i
\(939\) 10.1129 44.3077i 0.000351463 0.00153986i
\(940\) −39.9196 532.691i −0.00138514 0.0184835i
\(941\) 22045.6 + 6800.16i 0.763725 + 0.235578i 0.652060 0.758168i \(-0.273905\pi\)
0.111666 + 0.993746i \(0.464381\pi\)
\(942\) −226.847 + 3027.06i −0.00784614 + 0.104700i
\(943\) −6996.65 + 17827.2i −0.241614 + 0.615623i
\(944\) 180429. 86890.0i 6.22083 2.99579i
\(945\) 2689.55 + 826.532i 0.0925831 + 0.0284520i
\(946\) 21817.8 + 10506.9i 0.749848 + 0.361108i
\(947\) −15561.4 + 14438.8i −0.533977 + 0.495458i −0.900443 0.434973i \(-0.856758\pi\)
0.366467 + 0.930431i \(0.380567\pi\)
\(948\) 33.0621 4.98330i 0.00113271 0.000170728i
\(949\) 14760.1 25565.2i 0.504881 0.874479i
\(950\) 1053.32 + 1824.40i 0.0359727 + 0.0623066i
\(951\) −47.9272 60.0988i −0.00163422 0.00204925i
\(952\) 104328. 109.249i 3.55178 0.00371932i
\(953\) 13781.7 17281.7i 0.468450 0.587418i −0.490341 0.871531i \(-0.663128\pi\)
0.958791 + 0.284113i \(0.0916990\pi\)
\(954\) 54783.5 + 8257.29i 1.85921 + 0.280230i
\(955\) −21046.2 + 14349.0i −0.713129 + 0.486203i
\(956\) 28661.1 19540.8i 0.969629 0.661082i
\(957\) 204.154 + 30.7712i 0.00689587 + 0.00103939i
\(958\) 25992.8 32594.0i 0.876608 1.09923i
\(959\) 1846.05 8127.29i 0.0621606 0.273664i
\(960\) −3418.81 4287.05i −0.114939 0.144129i
\(961\) 10992.5 + 19039.5i 0.368987 + 0.639104i
\(962\) 7229.37 12521.6i 0.242291 0.419661i
\(963\) −2237.56 + 337.258i −0.0748748 + 0.0112856i
\(964\) −65740.0 + 60997.8i −2.19641 + 2.03797i
\(965\) −17131.3 8250.00i −0.571478 0.275209i
\(966\) 1503.11 228.168i 0.0500640 0.00759956i
\(967\) −10100.0 + 4863.91i −0.335879 + 0.161751i −0.594219 0.804303i \(-0.702539\pi\)
0.258340 + 0.966054i \(0.416824\pi\)
\(968\) 33448.6 85225.6i 1.11062 2.82981i
\(969\) 14.5914 194.709i 0.000483740 0.00645507i
\(970\) −20570.3 6345.10i −0.680900 0.210030i
\(971\) 2561.07 + 34175.2i 0.0846435 + 1.12949i 0.864197 + 0.503153i \(0.167827\pi\)
−0.779554 + 0.626335i \(0.784554\pi\)
\(972\) 2384.77 10448.3i 0.0786948 0.344785i
\(973\) −857.061 128.263i −0.0282385 0.00422604i
\(974\) −1510.71 6618.86i −0.0496985 0.217743i
\(975\) 497.811 153.554i 0.0163515 0.00504377i
\(976\) −61244.8 156049.i −2.00861 5.11784i
\(977\) 15756.3 + 14619.7i 0.515954 + 0.478735i 0.894639 0.446790i \(-0.147433\pi\)
−0.378685 + 0.925526i \(0.623623\pi\)
\(978\) −1588.38 1082.94i −0.0519334 0.0354076i
\(979\) −3086.57 −0.100763
\(980\) −69328.1 64057.4i −2.25980 2.08800i
\(981\) −36442.0 −1.18604
\(982\) 5446.31 + 3713.23i 0.176985 + 0.120666i
\(983\) −32165.9 29845.6i −1.04368 0.968389i −0.0441447 0.999025i \(-0.514056\pi\)
−0.999531 + 0.0306360i \(0.990247\pi\)
\(984\) 1782.67 + 4542.17i 0.0577535 + 0.147153i
\(985\) 2445.17 754.235i 0.0790961 0.0243979i
\(986\) 7346.98 + 32189.2i 0.237298 + 1.03967i
\(987\) 7.69973 2.38389i 0.000248313 7.68793e-5i
\(988\) 4068.11 17823.6i 0.130996 0.573930i
\(989\) 1961.35 + 26172.3i 0.0630608 + 0.841488i
\(990\) −19978.9 6162.69i −0.641386 0.197841i
\(991\) 1876.62 25041.8i 0.0601542 0.802702i −0.882793 0.469761i \(-0.844340\pi\)
0.942948 0.332941i \(-0.108041\pi\)
\(992\) 22861.3 58249.7i 0.731702 1.86435i
\(993\) −1153.51 + 555.502i −0.0368637 + 0.0177526i
\(994\) −17961.3 45624.1i −0.573137 1.45584i
\(995\) −37269.2 17947.9i −1.18745 0.571846i
\(996\) 1281.29 1188.86i 0.0407622 0.0378218i
\(997\) 5520.88 832.139i 0.175374 0.0264334i −0.0607680 0.998152i \(-0.519355\pi\)
0.236142 + 0.971719i \(0.424117\pi\)
\(998\) −56643.4 + 98109.2i −1.79661 + 3.11182i
\(999\) 225.378 + 390.365i 0.00713777 + 0.0123630i
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 49.4.g.a.4.1 156
49.24 odd 42 2401.4.a.f.1.1 78
49.25 even 21 2401.4.a.g.1.1 78
49.37 even 21 inner 49.4.g.a.37.1 yes 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.g.a.4.1 156 1.1 even 1 trivial
49.4.g.a.37.1 yes 156 49.37 even 21 inner
2401.4.a.f.1.1 78 49.24 odd 42
2401.4.a.g.1.1 78 49.25 even 21