Properties

Label 33.6.e.b.31.1
Level $33$
Weight $6$
Character 33.31
Analytic conductor $5.293$
Analytic rank $0$
Dimension $20$
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] = [33,6,Mod(4,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\), 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: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} - 1581925 x^{13} + 89291182 x^{12} - 100741271 x^{11} + 2277268901 x^{10} + \cdots + 25599187870096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 31.1
Root \(-2.34585 - 7.21978i\) of defining polynomial
Character \(\chi\) \(=\) 33.31
Dual form 33.6.e.b.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.65487 + 8.17084i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-33.8257 - 24.5758i) q^{4} +(-21.1802 - 65.1858i) q^{5} +(23.8938 + 73.5376i) q^{6} +(-196.384 - 142.681i) q^{7} +(68.1911 - 49.5438i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(-2.65487 + 8.17084i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-33.8257 - 24.5758i) q^{4} +(-21.1802 - 65.1858i) q^{5} +(23.8938 + 73.5376i) q^{6} +(-196.384 - 142.681i) q^{7} +(68.1911 - 49.5438i) q^{8} +(25.0304 - 77.0356i) q^{9} +588.853 q^{10} +(375.536 - 141.505i) q^{11} -376.298 q^{12} +(-286.400 + 881.450i) q^{13} +(1687.20 - 1225.82i) q^{14} +(-499.053 - 362.583i) q^{15} +(-189.673 - 583.755i) q^{16} +(-344.664 - 1060.77i) q^{17} +(562.993 + 409.038i) q^{18} +(-1005.28 + 730.379i) q^{19} +(-885.562 + 2725.48i) q^{20} -2184.69 q^{21} +(159.215 + 3444.12i) q^{22} +40.4597 q^{23} +(234.420 - 721.471i) q^{24} +(-1272.41 + 924.461i) q^{25} +(-6441.83 - 4680.26i) q^{26} +(-225.273 - 693.320i) q^{27} +(3136.32 + 9652.59i) q^{28} +(439.264 + 319.144i) q^{29} +(4287.53 - 3115.07i) q^{30} +(1934.42 - 5953.52i) q^{31} +7970.57 q^{32} +(1985.77 - 3016.93i) q^{33} +9582.38 q^{34} +(-5141.34 + 15823.4i) q^{35} +(-2739.89 + 1990.64i) q^{36} +(-7458.44 - 5418.87i) q^{37} +(-3298.92 - 10153.0i) q^{38} +(2577.60 + 7933.05i) q^{39} +(-4673.85 - 3395.75i) q^{40} +(6960.86 - 5057.36i) q^{41} +(5800.06 - 17850.8i) q^{42} -2237.97 q^{43} +(-16180.4 - 4442.61i) q^{44} -5551.77 q^{45} +(-107.415 + 330.589i) q^{46} +(550.006 - 399.603i) q^{47} +(-4469.14 - 3247.02i) q^{48} +(13015.0 + 40056.0i) q^{49} +(-4175.54 - 12851.0i) q^{50} +(-8121.07 - 5900.30i) q^{51} +(31350.1 - 22777.2i) q^{52} +(1606.89 - 4945.49i) q^{53} +6263.08 q^{54} +(-17178.0 - 21482.5i) q^{55} -20460.6 q^{56} +(-3455.85 + 10636.0i) q^{57} +(-3773.86 + 2741.87i) q^{58} +(9705.90 + 7051.75i) q^{59} +(7970.06 + 24529.3i) q^{60} +(-741.370 - 2281.70i) q^{61} +(43509.6 + 31611.6i) q^{62} +(-15907.1 + 11557.2i) q^{63} +(-15091.2 + 46446.1i) q^{64} +63524.0 q^{65} +(19378.9 + 24234.9i) q^{66} -9776.60 q^{67} +(-14410.7 + 44351.6i) q^{68} +(294.593 - 214.034i) q^{69} +(-115641. - 84018.2i) q^{70} +(2358.37 + 7258.31i) q^{71} +(-2109.78 - 6493.24i) q^{72} +(-22924.7 - 16655.8i) q^{73} +(64077.9 - 46555.3i) q^{74} +(-4374.16 + 13462.3i) q^{75} +51954.0 q^{76} +(-93939.2 - 25792.7i) q^{77} -71662.8 q^{78} +(21854.2 - 67260.5i) q^{79} +(-34035.2 + 24728.0i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(22842.7 + 70302.7i) q^{82} +(7348.06 + 22615.0i) q^{83} +(73898.8 + 53690.6i) q^{84} +(-61846.8 + 44934.4i) q^{85} +(5941.52 - 18286.1i) q^{86} +4886.64 q^{87} +(18597.6 - 28254.8i) q^{88} +15462.4 q^{89} +(14739.2 - 45362.6i) q^{90} +(182010. - 132238. i) q^{91} +(-1368.58 - 994.330i) q^{92} +(-17409.7 - 53581.7i) q^{93} +(1804.90 + 5554.90i) q^{94} +(68902.3 + 50060.5i) q^{95} +(58034.9 - 42164.8i) q^{96} +(17830.1 - 54875.5i) q^{97} -361844. q^{98} +(-1501.10 - 32471.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65487 + 8.17084i −0.469319 + 1.44441i 0.384151 + 0.923270i \(0.374494\pi\)
−0.853469 + 0.521143i \(0.825506\pi\)
\(3\) 7.28115 5.29007i 0.467086 0.339358i
\(4\) −33.8257 24.5758i −1.05705 0.767995i
\(5\) −21.1802 65.1858i −0.378882 1.16608i −0.940822 0.338901i \(-0.889945\pi\)
0.561940 0.827178i \(-0.310055\pi\)
\(6\) 23.8938 + 73.5376i 0.270961 + 0.833933i
\(7\) −196.384 142.681i −1.51482 1.10058i −0.963983 0.265964i \(-0.914310\pi\)
−0.550834 0.834615i \(-0.685690\pi\)
\(8\) 68.1911 49.5438i 0.376706 0.273693i
\(9\) 25.0304 77.0356i 0.103006 0.317019i
\(10\) 588.853 1.86212
\(11\) 375.536 141.505i 0.935772 0.352606i
\(12\) −376.298 −0.754361
\(13\) −286.400 + 881.450i −0.470019 + 1.44657i 0.382541 + 0.923939i \(0.375049\pi\)
−0.852559 + 0.522630i \(0.824951\pi\)
\(14\) 1687.20 1225.82i 2.30062 1.67150i
\(15\) −499.053 362.583i −0.572689 0.416083i
\(16\) −189.673 583.755i −0.185228 0.570073i
\(17\) −344.664 1060.77i −0.289250 0.890220i −0.985093 0.172025i \(-0.944969\pi\)
0.695843 0.718194i \(-0.255031\pi\)
\(18\) 562.993 + 409.038i 0.409564 + 0.297566i
\(19\) −1005.28 + 730.379i −0.638856 + 0.464156i −0.859457 0.511208i \(-0.829198\pi\)
0.220601 + 0.975364i \(0.429198\pi\)
\(20\) −885.562 + 2725.48i −0.495044 + 1.52359i
\(21\) −2184.69 −1.08104
\(22\) 159.215 + 3444.12i 0.0701338 + 1.51713i
\(23\) 40.4597 0.0159479 0.00797393 0.999968i \(-0.497462\pi\)
0.00797393 + 0.999968i \(0.497462\pi\)
\(24\) 234.420 721.471i 0.0830744 0.255677i
\(25\) −1272.41 + 924.461i −0.407172 + 0.295828i
\(26\) −6441.83 4680.26i −1.86886 1.35780i
\(27\) −225.273 693.320i −0.0594703 0.183031i
\(28\) 3136.32 + 9652.59i 0.756005 + 2.32674i
\(29\) 439.264 + 319.144i 0.0969907 + 0.0704679i 0.635224 0.772328i \(-0.280908\pi\)
−0.538233 + 0.842796i \(0.680908\pi\)
\(30\) 4287.53 3115.07i 0.869769 0.631924i
\(31\) 1934.42 5953.52i 0.361531 1.11268i −0.590594 0.806969i \(-0.701106\pi\)
0.952125 0.305709i \(-0.0988936\pi\)
\(32\) 7970.57 1.37599
\(33\) 1985.77 3016.93i 0.317427 0.482259i
\(34\) 9582.38 1.42160
\(35\) −5141.34 + 15823.4i −0.709425 + 2.18339i
\(36\) −2739.89 + 1990.64i −0.352352 + 0.255998i
\(37\) −7458.44 5418.87i −0.895661 0.650736i 0.0416872 0.999131i \(-0.486727\pi\)
−0.937348 + 0.348395i \(0.886727\pi\)
\(38\) −3298.92 10153.0i −0.370607 1.14061i
\(39\) 2577.60 + 7933.05i 0.271365 + 0.835177i
\(40\) −4673.85 3395.75i −0.461875 0.335572i
\(41\) 6960.86 5057.36i 0.646701 0.469856i −0.215445 0.976516i \(-0.569120\pi\)
0.862146 + 0.506660i \(0.169120\pi\)
\(42\) 5800.06 17850.8i 0.507352 1.56147i
\(43\) −2237.97 −0.184580 −0.0922899 0.995732i \(-0.529419\pi\)
−0.0922899 + 0.995732i \(0.529419\pi\)
\(44\) −16180.4 4442.61i −1.25996 0.345945i
\(45\) −5551.77 −0.408696
\(46\) −107.415 + 330.589i −0.00748463 + 0.0230353i
\(47\) 550.006 399.603i 0.0363181 0.0263866i −0.569478 0.822006i \(-0.692855\pi\)
0.605796 + 0.795620i \(0.292855\pi\)
\(48\) −4469.14 3247.02i −0.279976 0.203415i
\(49\) 13015.0 + 40056.0i 0.774379 + 2.38329i
\(50\) −4175.54 12851.0i −0.236204 0.726962i
\(51\) −8121.07 5900.30i −0.437208 0.317650i
\(52\) 31350.1 22777.2i 1.60779 1.16813i
\(53\) 1606.89 4945.49i 0.0785770 0.241835i −0.904050 0.427427i \(-0.859420\pi\)
0.982627 + 0.185592i \(0.0594202\pi\)
\(54\) 6263.08 0.292283
\(55\) −17178.0 21482.5i −0.765714 0.957588i
\(56\) −20460.6 −0.871862
\(57\) −3455.85 + 10636.0i −0.140886 + 0.433602i
\(58\) −3773.86 + 2741.87i −0.147304 + 0.107023i
\(59\) 9705.90 + 7051.75i 0.362999 + 0.263734i 0.754302 0.656528i \(-0.227975\pi\)
−0.391303 + 0.920262i \(0.627975\pi\)
\(60\) 7970.06 + 24529.3i 0.285814 + 0.879644i
\(61\) −741.370 2281.70i −0.0255100 0.0785117i 0.937491 0.348010i \(-0.113142\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(62\) 43509.6 + 31611.6i 1.43749 + 1.04440i
\(63\) −15907.1 + 11557.2i −0.504939 + 0.366860i
\(64\) −15091.2 + 46446.1i −0.460548 + 1.41742i
\(65\) 63524.0 1.86490
\(66\) 19378.9 + 24234.9i 0.547607 + 0.684828i
\(67\) −9776.60 −0.266073 −0.133037 0.991111i \(-0.542473\pi\)
−0.133037 + 0.991111i \(0.542473\pi\)
\(68\) −14410.7 + 44351.6i −0.377931 + 1.16315i
\(69\) 294.593 214.034i 0.00744903 0.00541204i
\(70\) −115641. 84018.2i −2.82077 2.04941i
\(71\) 2358.37 + 7258.31i 0.0555221 + 0.170879i 0.974972 0.222328i \(-0.0713655\pi\)
−0.919450 + 0.393207i \(0.871366\pi\)
\(72\) −2109.78 6493.24i −0.0479630 0.147615i
\(73\) −22924.7 16655.8i −0.503497 0.365812i 0.306854 0.951756i \(-0.400724\pi\)
−0.810351 + 0.585945i \(0.800724\pi\)
\(74\) 64077.9 46555.3i 1.36028 0.988302i
\(75\) −4374.16 + 13462.3i −0.0897928 + 0.276354i
\(76\) 51954.0 1.03178
\(77\) −93939.2 25792.7i −1.80559 0.495757i
\(78\) −71662.8 −1.33370
\(79\) 21854.2 67260.5i 0.393974 1.21253i −0.535783 0.844356i \(-0.679983\pi\)
0.929757 0.368173i \(-0.120017\pi\)
\(80\) −34035.2 + 24728.0i −0.594571 + 0.431981i
\(81\) −5307.96 3856.46i −0.0898908 0.0653095i
\(82\) 22842.7 + 70302.7i 0.375157 + 1.15462i
\(83\) 7348.06 + 22615.0i 0.117079 + 0.360331i 0.992375 0.123256i \(-0.0393337\pi\)
−0.875296 + 0.483587i \(0.839334\pi\)
\(84\) 73898.8 + 53690.6i 1.14272 + 0.830234i
\(85\) −61846.8 + 44934.4i −0.928475 + 0.674577i
\(86\) 5941.52 18286.1i 0.0866267 0.266610i
\(87\) 4886.64 0.0692169
\(88\) 18597.6 28254.8i 0.256005 0.388943i
\(89\) 15462.4 0.206919 0.103460 0.994634i \(-0.467009\pi\)
0.103460 + 0.994634i \(0.467009\pi\)
\(90\) 14739.2 45362.6i 0.191809 0.590326i
\(91\) 182010. 132238.i 2.30406 1.67399i
\(92\) −1368.58 994.330i −0.0168578 0.0122479i
\(93\) −17409.7 53581.7i −0.208730 0.642405i
\(94\) 1804.90 + 5554.90i 0.0210685 + 0.0648421i
\(95\) 68902.3 + 50060.5i 0.783294 + 0.569096i
\(96\) 58034.9 42164.8i 0.642705 0.466952i
\(97\) 17830.1 54875.5i 0.192409 0.592174i −0.807588 0.589747i \(-0.799228\pi\)
0.999997 0.00242673i \(-0.000772452\pi\)
\(98\) −361844. −3.80589
\(99\) −1501.10 32471.6i −0.0153929 0.332978i
\(100\) 65759.7 0.657597
\(101\) 11568.0 35602.5i 0.112838 0.347278i −0.878652 0.477462i \(-0.841557\pi\)
0.991490 + 0.130184i \(0.0415568\pi\)
\(102\) 69770.8 50691.5i 0.664008 0.482430i
\(103\) 54570.6 + 39647.8i 0.506834 + 0.368236i 0.811621 0.584184i \(-0.198585\pi\)
−0.304787 + 0.952420i \(0.598585\pi\)
\(104\) 24140.4 + 74296.4i 0.218857 + 0.673573i
\(105\) 46272.1 + 142411.i 0.409587 + 1.26058i
\(106\) 36142.7 + 26259.2i 0.312432 + 0.226995i
\(107\) 160498. 116608.i 1.35522 0.984624i 0.356486 0.934301i \(-0.383975\pi\)
0.998733 0.0503235i \(-0.0160252\pi\)
\(108\) −9418.89 + 28988.4i −0.0777034 + 0.239147i
\(109\) −234029. −1.88670 −0.943350 0.331799i \(-0.892344\pi\)
−0.943350 + 0.331799i \(0.892344\pi\)
\(110\) 221136. 83325.6i 1.74252 0.656593i
\(111\) −82972.2 −0.639183
\(112\) −46042.0 + 141703.i −0.346824 + 1.06741i
\(113\) −158064. + 114841.i −1.16450 + 0.846056i −0.990340 0.138662i \(-0.955720\pi\)
−0.174157 + 0.984718i \(0.555720\pi\)
\(114\) −77730.2 56474.3i −0.560180 0.406995i
\(115\) −856.942 2637.40i −0.00604236 0.0185965i
\(116\) −7015.19 21590.5i −0.0484055 0.148977i
\(117\) 60734.3 + 44126.0i 0.410175 + 0.298010i
\(118\) −83386.6 + 60583.9i −0.551304 + 0.400546i
\(119\) −83664.9 + 257494.i −0.541596 + 1.66686i
\(120\) −51994.7 −0.329615
\(121\) 121004. 106280.i 0.751338 0.659917i
\(122\) 20611.7 0.125376
\(123\) 23929.3 73646.9i 0.142616 0.438926i
\(124\) −211746. + 153842.i −1.23669 + 0.898508i
\(125\) −86070.7 62534.1i −0.492698 0.357966i
\(126\) −52200.6 160657.i −0.292920 0.901515i
\(127\) −40135.3 123524.i −0.220809 0.679581i −0.998690 0.0511692i \(-0.983705\pi\)
0.777881 0.628412i \(-0.216295\pi\)
\(128\) −133092. 96696.8i −0.718003 0.521660i
\(129\) −16295.0 + 11839.0i −0.0862146 + 0.0626386i
\(130\) −168648. + 519044.i −0.875230 + 2.69368i
\(131\) 133081. 0.677544 0.338772 0.940868i \(-0.389988\pi\)
0.338772 + 0.940868i \(0.389988\pi\)
\(132\) −141314. + 53248.0i −0.705910 + 0.265992i
\(133\) 301632. 1.47859
\(134\) 25955.6 79883.0i 0.124873 0.384320i
\(135\) −40423.3 + 29369.3i −0.190896 + 0.138694i
\(136\) −76057.3 55258.9i −0.352609 0.256186i
\(137\) −75443.0 232190.i −0.343414 1.05692i −0.962427 0.271539i \(-0.912467\pi\)
0.619014 0.785380i \(-0.287533\pi\)
\(138\) 966.735 + 2975.30i 0.00432125 + 0.0132994i
\(139\) 291358. + 211684.i 1.27906 + 0.929288i 0.999524 0.0308487i \(-0.00982102\pi\)
0.279531 + 0.960137i \(0.409821\pi\)
\(140\) 562784. 408886.i 2.42673 1.76312i
\(141\) 1890.75 5819.14i 0.00800916 0.0246497i
\(142\) −65567.6 −0.272878
\(143\) 17175.7 + 371543.i 0.0702384 + 1.51939i
\(144\) −49717.5 −0.199803
\(145\) 11500.0 35393.3i 0.0454231 0.139798i
\(146\) 196954. 143095.i 0.764684 0.555575i
\(147\) 306663. + 222804.i 1.17049 + 0.850412i
\(148\) 119114. + 366595.i 0.447000 + 1.37573i
\(149\) −102713. 316118.i −0.379017 1.16650i −0.940728 0.339162i \(-0.889857\pi\)
0.561711 0.827334i \(-0.310143\pi\)
\(150\) −98385.4 71481.1i −0.357028 0.259396i
\(151\) −181918. + 132171.i −0.649282 + 0.471731i −0.863026 0.505159i \(-0.831434\pi\)
0.213745 + 0.976890i \(0.431434\pi\)
\(152\) −32365.5 + 99610.7i −0.113625 + 0.349701i
\(153\) −90343.8 −0.312011
\(154\) 460144. 699086.i 1.56348 2.37536i
\(155\) −429056. −1.43445
\(156\) 107772. 331688.i 0.354564 1.09123i
\(157\) 29287.5 21278.6i 0.0948272 0.0688960i −0.539361 0.842074i \(-0.681334\pi\)
0.634189 + 0.773178i \(0.281334\pi\)
\(158\) 491554. + 357135.i 1.56649 + 1.13812i
\(159\) −14462.0 44509.4i −0.0453665 0.139624i
\(160\) −168818. 519568.i −0.521337 1.60451i
\(161\) −7945.61 5772.83i −0.0241581 0.0175519i
\(162\) 45602.4 33132.1i 0.136521 0.0991885i
\(163\) −80652.1 + 248222.i −0.237764 + 0.731763i 0.758979 + 0.651116i \(0.225699\pi\)
−0.996743 + 0.0806473i \(0.974301\pi\)
\(164\) −359745. −1.04445
\(165\) −238720. 65544.7i −0.682619 0.187425i
\(166\) −204292. −0.575414
\(167\) 82298.7 253289.i 0.228350 0.702790i −0.769584 0.638546i \(-0.779536\pi\)
0.997934 0.0642445i \(-0.0204638\pi\)
\(168\) −148977. + 108238.i −0.407235 + 0.295873i
\(169\) −394546. 286654.i −1.06263 0.772043i
\(170\) −202956. 624635.i −0.538617 1.65769i
\(171\) 31102.6 + 95724.0i 0.0813404 + 0.250340i
\(172\) 75701.2 + 55000.1i 0.195111 + 0.141756i
\(173\) −597169. + 433869.i −1.51699 + 1.10216i −0.554032 + 0.832495i \(0.686912\pi\)
−0.962955 + 0.269661i \(0.913088\pi\)
\(174\) −12973.4 + 39927.9i −0.0324848 + 0.0999778i
\(175\) 381784. 0.942372
\(176\) −153833. 192381.i −0.374342 0.468146i
\(177\) 107974. 0.259052
\(178\) −41050.6 + 126341.i −0.0971112 + 0.298877i
\(179\) 391868. 284709.i 0.914128 0.664153i −0.0279275 0.999610i \(-0.508891\pi\)
0.942055 + 0.335457i \(0.108891\pi\)
\(180\) 187793. + 136440.i 0.432014 + 0.313877i
\(181\) 39532.8 + 121669.i 0.0896934 + 0.276048i 0.985834 0.167721i \(-0.0536409\pi\)
−0.896141 + 0.443769i \(0.853641\pi\)
\(182\) 597285. + 1.83825e6i 1.33660 + 4.11365i
\(183\) −17468.4 12691.5i −0.0385590 0.0280147i
\(184\) 2758.99 2004.52i 0.00600766 0.00436482i
\(185\) −195263. + 600957.i −0.419459 + 1.29096i
\(186\) 484028. 1.02586
\(187\) −279537. 349584.i −0.584569 0.731051i
\(188\) −28424.9 −0.0586550
\(189\) −54683.6 + 168299.i −0.111353 + 0.342710i
\(190\) −591962. + 430086.i −1.18962 + 0.864313i
\(191\) −524014. 380719.i −1.03934 0.755128i −0.0691873 0.997604i \(-0.522041\pi\)
−0.970158 + 0.242475i \(0.922041\pi\)
\(192\) 135821. + 418015.i 0.265898 + 0.818349i
\(193\) −142540. 438693.i −0.275450 0.847749i −0.989100 0.147246i \(-0.952959\pi\)
0.713650 0.700503i \(-0.247041\pi\)
\(194\) 401042. + 291374.i 0.765043 + 0.555836i
\(195\) 462528. 336046.i 0.871067 0.632867i
\(196\) 544169. 1.67478e6i 1.01180 3.11399i
\(197\) −144289. −0.264891 −0.132446 0.991190i \(-0.542283\pi\)
−0.132446 + 0.991190i \(0.542283\pi\)
\(198\) 269305. + 73942.4i 0.488182 + 0.134039i
\(199\) 634482. 1.13576 0.567880 0.823111i \(-0.307764\pi\)
0.567880 + 0.823111i \(0.307764\pi\)
\(200\) −40965.9 + 126080.i −0.0724182 + 0.222880i
\(201\) −71184.9 + 51718.9i −0.124279 + 0.0902940i
\(202\) 260191. + 189040.i 0.448657 + 0.325968i
\(203\) −40728.4 125349.i −0.0693677 0.213492i
\(204\) 129696. + 399164.i 0.218199 + 0.671547i
\(205\) −477100. 346634.i −0.792912 0.576084i
\(206\) −468834. + 340628.i −0.769752 + 0.559258i
\(207\) 1012.72 3116.83i 0.00164272 0.00505577i
\(208\) 568873. 0.911711
\(209\) −274167. + 416536.i −0.434159 + 0.659609i
\(210\) −1.28646e6 −2.01302
\(211\) −27561.8 + 84826.6i −0.0426189 + 0.131167i −0.970102 0.242698i \(-0.921968\pi\)
0.927483 + 0.373865i \(0.121968\pi\)
\(212\) −175894. + 127794.i −0.268788 + 0.195286i
\(213\) 55568.6 + 40372.9i 0.0839229 + 0.0609735i
\(214\) 526689. + 1.62098e6i 0.786176 + 2.41960i
\(215\) 47400.6 + 145884.i 0.0699339 + 0.215235i
\(216\) −49711.3 36117.4i −0.0724972 0.0526723i
\(217\) −1.22934e6 + 893169.i −1.77224 + 1.28761i
\(218\) 621315. 1.91221e6i 0.885463 2.72518i
\(219\) −255028. −0.359317
\(220\) 53108.0 + 1.14883e6i 0.0739781 + 1.60029i
\(221\) 1.03372e6 1.42372
\(222\) 220280. 677953.i 0.299980 0.923245i
\(223\) 607155. 441124.i 0.817594 0.594017i −0.0984284 0.995144i \(-0.531382\pi\)
0.916022 + 0.401127i \(0.131382\pi\)
\(224\) −1.56529e6 1.13725e6i −2.08437 1.51438i
\(225\) 39367.5 + 121161.i 0.0518419 + 0.159553i
\(226\) −518704. 1.59641e6i −0.675536 2.07908i
\(227\) 676504. + 491509.i 0.871376 + 0.633092i 0.930956 0.365132i \(-0.118976\pi\)
−0.0595796 + 0.998224i \(0.518976\pi\)
\(228\) 378285. 274840.i 0.481928 0.350141i
\(229\) −57656.6 + 177449.i −0.0726541 + 0.223606i −0.980789 0.195071i \(-0.937506\pi\)
0.908135 + 0.418677i \(0.137506\pi\)
\(230\) 23824.8 0.0296968
\(231\) −820430. + 309144.i −1.01161 + 0.381181i
\(232\) 45765.5 0.0558236
\(233\) −399106. + 1.22832e6i −0.481613 + 1.48225i 0.355215 + 0.934785i \(0.384408\pi\)
−0.836827 + 0.547467i \(0.815592\pi\)
\(234\) −521788. + 379101.i −0.622952 + 0.452601i
\(235\) −37697.6 27388.9i −0.0445292 0.0323523i
\(236\) −155007. 477061.i −0.181163 0.557563i
\(237\) −196688. 605344.i −0.227461 0.700054i
\(238\) −1.88182e6 1.36722e6i −2.15346 1.56458i
\(239\) 1.21302e6 881313.i 1.37364 0.998011i 0.376202 0.926538i \(-0.377230\pi\)
0.997443 0.0714733i \(-0.0227701\pi\)
\(240\) −117003. + 360097.i −0.131120 + 0.403545i
\(241\) 441931. 0.490130 0.245065 0.969507i \(-0.421191\pi\)
0.245065 + 0.969507i \(0.421191\pi\)
\(242\) 547151. + 1.27086e6i 0.600577 + 1.39495i
\(243\) −59049.0 −0.0641500
\(244\) −30997.4 + 95400.1i −0.0333312 + 0.102583i
\(245\) 2.33542e6 1.69678e6i 2.48571 1.80597i
\(246\) 538228. + 391045.i 0.567059 + 0.411992i
\(247\) −355879. 1.09528e6i −0.371159 1.14231i
\(248\) −163050. 501816.i −0.168341 0.518102i
\(249\) 173137. + 125792.i 0.176967 + 0.128574i
\(250\) 739462. 537251.i 0.748283 0.543659i
\(251\) 196781. 605630.i 0.197151 0.606769i −0.802794 0.596257i \(-0.796654\pi\)
0.999945 0.0105118i \(-0.00334608\pi\)
\(252\) 822096. 0.815494
\(253\) 15194.1 5725.24i 0.0149236 0.00562331i
\(254\) 1.11585e6 1.08523
\(255\) −212611. + 654348.i −0.204755 + 0.630171i
\(256\) −120866. + 87814.0i −0.115266 + 0.0837459i
\(257\) 1.14461e6 + 831609.i 1.08100 + 0.785392i 0.977857 0.209275i \(-0.0671103\pi\)
0.103142 + 0.994667i \(0.467110\pi\)
\(258\) −53473.7 164575.i −0.0500139 0.153927i
\(259\) 691544. + 2.12835e6i 0.640576 + 1.97149i
\(260\) −2.14875e6 1.56116e6i −1.97130 1.43223i
\(261\) 35580.3 25850.6i 0.0323302 0.0234893i
\(262\) −353312. + 1.08738e6i −0.317984 + 0.978654i
\(263\) −213952. −0.190734 −0.0953668 0.995442i \(-0.530402\pi\)
−0.0953668 + 0.995442i \(0.530402\pi\)
\(264\) −14058.4 304110.i −0.0124144 0.268547i
\(265\) −356410. −0.311770
\(266\) −800792. + 2.46458e6i −0.693930 + 2.13570i
\(267\) 112584. 81797.0i 0.0966492 0.0702198i
\(268\) 330701. + 240268.i 0.281254 + 0.204343i
\(269\) −307552. 946546.i −0.259142 0.797556i −0.992985 0.118238i \(-0.962276\pi\)
0.733844 0.679318i \(-0.237724\pi\)
\(270\) −132653. 408264.i −0.110741 0.340825i
\(271\) 1.09169e6 + 793157.i 0.902974 + 0.656049i 0.939228 0.343294i \(-0.111543\pi\)
−0.0362544 + 0.999343i \(0.511543\pi\)
\(272\) −553854. + 402398.i −0.453913 + 0.329787i
\(273\) 625696. 1.92570e6i 0.508109 1.56380i
\(274\) 2.09748e6 1.68780
\(275\) −347021. + 527221.i −0.276709 + 0.420398i
\(276\) −15224.9 −0.0120304
\(277\) −563446. + 1.73411e6i −0.441218 + 1.35793i 0.445361 + 0.895351i \(0.353075\pi\)
−0.886579 + 0.462577i \(0.846925\pi\)
\(278\) −2.50315e6 + 1.81864e6i −1.94256 + 1.41135i
\(279\) −410214. 298038.i −0.315500 0.229224i
\(280\) 433358. + 1.33374e6i 0.330333 + 1.01666i
\(281\) −499967. 1.53874e6i −0.377725 1.16252i −0.941622 0.336672i \(-0.890699\pi\)
0.563897 0.825845i \(-0.309301\pi\)
\(282\) 42527.5 + 30898.1i 0.0318455 + 0.0231371i
\(283\) 9505.69 6906.29i 0.00705533 0.00512600i −0.584252 0.811572i \(-0.698612\pi\)
0.591307 + 0.806446i \(0.298612\pi\)
\(284\) 98605.5 303477.i 0.0725447 0.223269i
\(285\) 766511. 0.558993
\(286\) −3.08142e6 846058.i −2.22759 0.611624i
\(287\) −2.08859e6 −1.49675
\(288\) 199506. 614017.i 0.141734 0.436214i
\(289\) 142257. 103356.i 0.100191 0.0727932i
\(290\) 258662. + 187929.i 0.180608 + 0.131219i
\(291\) −160471. 493879.i −0.111087 0.341892i
\(292\) 366116. + 1.12679e6i 0.251282 + 0.773366i
\(293\) −182591. 132660.i −0.124254 0.0902756i 0.523923 0.851766i \(-0.324468\pi\)
−0.648176 + 0.761490i \(0.724468\pi\)
\(294\) −2.63464e6 + 1.91418e6i −1.77768 + 1.29156i
\(295\) 254101. 782044.i 0.170001 0.523210i
\(296\) −777070. −0.515503
\(297\) −182706. 228490.i −0.120188 0.150306i
\(298\) 2.85564e6 1.86278
\(299\) −11587.7 + 35663.2i −0.00749580 + 0.0230697i
\(300\) 478806. 347873.i 0.307154 0.223161i
\(301\) 439501. + 319317.i 0.279604 + 0.203145i
\(302\) −596981. 1.83732e6i −0.376655 1.15922i
\(303\) −104112. 320423.i −0.0651468 0.200501i
\(304\) 617037. + 448304.i 0.382937 + 0.278220i
\(305\) −133032. + 96653.6i −0.0818856 + 0.0594934i
\(306\) 239851. 738184.i 0.146432 0.450673i
\(307\) −2.72970e6 −1.65298 −0.826492 0.562949i \(-0.809667\pi\)
−0.826492 + 0.562949i \(0.809667\pi\)
\(308\) 2.54369e6 + 3.18109e6i 1.52787 + 1.91073i
\(309\) 607076. 0.361699
\(310\) 1.13909e6 3.50575e6i 0.673213 2.07194i
\(311\) −829760. + 602856.i −0.486465 + 0.353437i −0.803823 0.594868i \(-0.797204\pi\)
0.317358 + 0.948306i \(0.397204\pi\)
\(312\) 568803. + 413259.i 0.330807 + 0.240346i
\(313\) 369434. + 1.13700e6i 0.213145 + 0.655994i 0.999280 + 0.0379390i \(0.0120793\pi\)
−0.786135 + 0.618055i \(0.787921\pi\)
\(314\) 96109.6 + 295795.i 0.0550102 + 0.169304i
\(315\) 1.09028e6 + 792133.i 0.619100 + 0.449802i
\(316\) −2.39222e6 + 1.73805e6i −1.34767 + 0.979139i
\(317\) 146042. 449472.i 0.0816264 0.251220i −0.901912 0.431920i \(-0.857836\pi\)
0.983538 + 0.180700i \(0.0578363\pi\)
\(318\) 402074. 0.222966
\(319\) 210120. + 57692.1i 0.115609 + 0.0317424i
\(320\) 3.34726e6 1.82732
\(321\) 551742. 1.69809e6i 0.298864 0.919809i
\(322\) 68263.4 49596.2i 0.0366900 0.0266569i
\(323\) 1.12124e6 + 814632.i 0.597990 + 0.434465i
\(324\) 84770.0 + 260895.i 0.0448621 + 0.138071i
\(325\) −450447. 1.38633e6i −0.236557 0.728046i
\(326\) −1.81406e6 1.31799e6i −0.945381 0.686860i
\(327\) −1.70400e6 + 1.23803e6i −0.881252 + 0.640267i
\(328\) 224108. 689735.i 0.115020 0.353995i
\(329\) −165028. −0.0840558
\(330\) 1.16932e6 1.77653e6i 0.591085 0.898023i
\(331\) −2.42829e6 −1.21823 −0.609116 0.793081i \(-0.708476\pi\)
−0.609116 + 0.793081i \(0.708476\pi\)
\(332\) 307229. 945554.i 0.152974 0.470805i
\(333\) −604133. + 438929.i −0.298554 + 0.216912i
\(334\) 1.85109e6 + 1.34490e6i 0.907951 + 0.659665i
\(335\) 207070. + 637295.i 0.100810 + 0.310262i
\(336\) 414378. + 1.27532e6i 0.200239 + 0.616272i
\(337\) 421009. + 305881.i 0.201937 + 0.146716i 0.684158 0.729334i \(-0.260170\pi\)
−0.482221 + 0.876050i \(0.660170\pi\)
\(338\) 3.38967e6 2.46274e6i 1.61386 1.17254i
\(339\) −543377. + 1.67234e6i −0.256804 + 0.790362i
\(340\) 3.19632e6 1.49952
\(341\) −116009. 2.50949e6i −0.0540263 1.16869i
\(342\) −864719. −0.399769
\(343\) 1.89858e6 5.84323e6i 0.871352 2.68174i
\(344\) −152610. + 110878.i −0.0695324 + 0.0505182i
\(345\) −20191.5 14670.0i −0.00913317 0.00663563i
\(346\) −1.95967e6 6.03124e6i −0.880019 2.70842i
\(347\) −127858. 393507.i −0.0570039 0.175440i 0.918501 0.395420i \(-0.129401\pi\)
−0.975504 + 0.219980i \(0.929401\pi\)
\(348\) −165294. 120093.i −0.0731660 0.0531582i
\(349\) −3.07807e6 + 2.23635e6i −1.35274 + 0.982825i −0.353873 + 0.935293i \(0.615136\pi\)
−0.998870 + 0.0475318i \(0.984864\pi\)
\(350\) −1.01359e6 + 3.11949e6i −0.442273 + 1.36118i
\(351\) 675645. 0.292719
\(352\) 2.99324e6 1.12787e6i 1.28761 0.485181i
\(353\) 1.74031e6 0.743343 0.371671 0.928364i \(-0.378785\pi\)
0.371671 + 0.928364i \(0.378785\pi\)
\(354\) −286657. + 882241.i −0.121578 + 0.374179i
\(355\) 423188. 307464.i 0.178223 0.129486i
\(356\) −523027. 380001.i −0.218725 0.158913i
\(357\) 752984. + 2.31745e6i 0.312691 + 0.962363i
\(358\) 1.28595e6 + 3.95775e6i 0.530294 + 1.63208i
\(359\) −571532. 415243.i −0.234048 0.170046i 0.464580 0.885531i \(-0.346205\pi\)
−0.698627 + 0.715486i \(0.746205\pi\)
\(360\) −378582. + 275056.i −0.153958 + 0.111857i
\(361\) −288022. + 886440.i −0.116321 + 0.357999i
\(362\) −1.09909e6 −0.440822
\(363\) 318817. 1.41396e6i 0.126991 0.563211i
\(364\) −9.40651e6 −3.72113
\(365\) −600171. + 1.84714e6i −0.235800 + 0.725716i
\(366\) 150077. 109037.i 0.0585613 0.0425473i
\(367\) 1.72998e6 + 1.25690e6i 0.670464 + 0.487121i 0.870181 0.492733i \(-0.164002\pi\)
−0.199716 + 0.979854i \(0.564002\pi\)
\(368\) −7674.12 23618.5i −0.00295399 0.00909145i
\(369\) −215364. 662822.i −0.0823393 0.253414i
\(370\) −4.39192e6 3.19092e6i −1.66782 1.21175i
\(371\) −1.02119e6 + 741940.i −0.385188 + 0.279856i
\(372\) −727918. + 2.24030e6i −0.272725 + 0.839361i
\(373\) −1.11222e6 −0.413923 −0.206961 0.978349i \(-0.566357\pi\)
−0.206961 + 0.978349i \(0.566357\pi\)
\(374\) 3.59853e6 1.35595e6i 1.33029 0.501263i
\(375\) −957504. −0.351611
\(376\) 17707.7 54498.7i 0.00645941 0.0198800i
\(377\) −407114. + 295786.i −0.147524 + 0.107183i
\(378\) −1.22997e6 893622.i −0.442755 0.321680i
\(379\) 57461.2 + 176847.i 0.0205483 + 0.0632412i 0.960805 0.277226i \(-0.0894149\pi\)
−0.940257 + 0.340467i \(0.889415\pi\)
\(380\) −1.10039e6 3.38666e6i −0.390921 1.20313i
\(381\) −945681. 687077.i −0.333758 0.242490i
\(382\) 4.50198e6 3.27088e6i 1.57850 1.14685i
\(383\) −340027. + 1.04649e6i −0.118445 + 0.364536i −0.992650 0.121021i \(-0.961383\pi\)
0.874205 + 0.485557i \(0.161383\pi\)
\(384\) −1.48059e6 −0.512399
\(385\) 308331. + 6.66979e6i 0.106015 + 2.29330i
\(386\) 3.96291e6 1.35377
\(387\) −56017.3 + 172404.i −0.0190128 + 0.0585153i
\(388\) −1.95173e6 + 1.41801e6i −0.658173 + 0.478191i
\(389\) 1.67883e6 + 1.21974e6i 0.562513 + 0.408690i 0.832378 0.554208i \(-0.186979\pi\)
−0.269865 + 0.962898i \(0.586979\pi\)
\(390\) 1.51783e6 + 4.67140e6i 0.505314 + 1.55520i
\(391\) −13945.0 42918.2i −0.00461292 0.0141971i
\(392\) 2.87203e6 + 2.08665e6i 0.944005 + 0.685860i
\(393\) 968983. 704007.i 0.316472 0.229930i
\(394\) 383068. 1.17896e6i 0.124318 0.382612i
\(395\) −4.84730e6 −1.56317
\(396\) −747240. + 1.13527e6i −0.239454 + 0.363797i
\(397\) −322459. −0.102683 −0.0513415 0.998681i \(-0.516350\pi\)
−0.0513415 + 0.998681i \(0.516350\pi\)
\(398\) −1.68446e6 + 5.18425e6i −0.533033 + 1.64051i
\(399\) 2.19623e6 1.59565e6i 0.690629 0.501771i
\(400\) 781001. + 567431.i 0.244063 + 0.177322i
\(401\) 614225. + 1.89039e6i 0.190751 + 0.587071i 1.00000 0.000394646i \(-0.000125620\pi\)
−0.809249 + 0.587466i \(0.800126\pi\)
\(402\) −233600. 718947.i −0.0720955 0.221887i
\(403\) 4.69371e6 + 3.41018e6i 1.43964 + 1.04596i
\(404\) −1.26626e6 + 919990.i −0.385983 + 0.280433i
\(405\) −138963. + 427684.i −0.0420980 + 0.129564i
\(406\) 1.13234e6 0.340926
\(407\) −3.56771e6 979577.i −1.06759 0.293125i
\(408\) −846108. −0.251638
\(409\) 1.47525e6 4.54035e6i 0.436071 1.34209i −0.455914 0.890024i \(-0.650688\pi\)
0.891985 0.452065i \(-0.149312\pi\)
\(410\) 4.09893e6 2.97804e6i 1.20423 0.874926i
\(411\) −1.77761e6 1.29151e6i −0.519078 0.377132i
\(412\) −871511. 2.68224e6i −0.252947 0.778492i
\(413\) −899928. 2.76969e6i −0.259617 0.799018i
\(414\) 22778.5 + 16549.6i 0.00653167 + 0.00474554i
\(415\) 1.31854e6 957978.i 0.375815 0.273046i
\(416\) −2.28277e6 + 7.02565e6i −0.646740 + 1.99046i
\(417\) 3.24124e6 0.912790
\(418\) −2.67557e6 3.34602e6i −0.748989 0.936673i
\(419\) 5.83487e6 1.62366 0.811831 0.583892i \(-0.198471\pi\)
0.811831 + 0.583892i \(0.198471\pi\)
\(420\) 1.93468e6 5.95433e6i 0.535162 1.64706i
\(421\) −23921.2 + 17379.8i −0.00657776 + 0.00477902i −0.591069 0.806621i \(-0.701294\pi\)
0.584492 + 0.811400i \(0.301294\pi\)
\(422\) −619931. 450406.i −0.169458 0.123119i
\(423\) −17016.8 52372.2i −0.00462409 0.0142315i
\(424\) −135443. 416850.i −0.0365882 0.112607i
\(425\) 1.41919e6 + 1.03110e6i 0.381126 + 0.276904i
\(426\) −477408. + 346857.i −0.127458 + 0.0926033i
\(427\) −179963. + 553869.i −0.0477654 + 0.147007i
\(428\) −8.29471e6 −2.18873
\(429\) 2.09055e6 + 2.61440e6i 0.548424 + 0.685850i
\(430\) −1.31784e6 −0.343709
\(431\) −1.48857e6 + 4.58134e6i −0.385989 + 1.18795i 0.549771 + 0.835315i \(0.314715\pi\)
−0.935760 + 0.352637i \(0.885285\pi\)
\(432\) −362001. + 263009.i −0.0933254 + 0.0678049i
\(433\) 2.78818e6 + 2.02573e6i 0.714662 + 0.519233i 0.884674 0.466209i \(-0.154381\pi\)
−0.170012 + 0.985442i \(0.554381\pi\)
\(434\) −4.03420e6 1.24160e7i −1.02810 3.16415i
\(435\) −103500. 318539.i −0.0262250 0.0807123i
\(436\) 7.91620e6 + 5.75145e6i 1.99435 + 1.44898i
\(437\) −40673.3 + 29550.9i −0.0101884 + 0.00740230i
\(438\) 677066. 2.08380e6i 0.168634 0.519003i
\(439\) −5.75405e6 −1.42499 −0.712495 0.701677i \(-0.752435\pi\)
−0.712495 + 0.701677i \(0.752435\pi\)
\(440\) −2.23571e6 613854.i −0.550534 0.151159i
\(441\) 3.41151e6 0.835314
\(442\) −2.74440e6 + 8.44639e6i −0.668177 + 2.05644i
\(443\) −3.85328e6 + 2.79957e6i −0.932871 + 0.677770i −0.946694 0.322134i \(-0.895600\pi\)
0.0138233 + 0.999904i \(0.495600\pi\)
\(444\) 2.80660e6 + 2.03911e6i 0.675651 + 0.490889i
\(445\) −327496. 1.00793e6i −0.0783981 0.241284i
\(446\) 1.99244e6 + 6.13209e6i 0.474294 + 1.45973i
\(447\) −2.42015e6 1.75834e6i −0.572893 0.416231i
\(448\) 9.59065e6 6.96801e6i 2.25763 1.64026i
\(449\) 2.16639e6 6.66745e6i 0.507131 1.56079i −0.290028 0.957018i \(-0.593665\pi\)
0.797159 0.603770i \(-0.206335\pi\)
\(450\) −1.09450e6 −0.254791
\(451\) 1.89841e6 2.88422e6i 0.439491 0.667708i
\(452\) 8.16895e6 1.88070
\(453\) −625378. + 1.92472e6i −0.143185 + 0.440678i
\(454\) −5.81207e6 + 4.22272e6i −1.32340 + 0.961506i
\(455\) −1.24751e7 9.06367e6i −2.82497 2.05246i
\(456\) 291289. + 896496.i 0.0656013 + 0.201900i
\(457\) −2.13691e6 6.57673e6i −0.478625 1.47306i −0.841005 0.541027i \(-0.818036\pi\)
0.362380 0.932031i \(-0.381964\pi\)
\(458\) −1.29683e6 942205.i −0.288882 0.209885i
\(459\) −657807. + 477925.i −0.145736 + 0.105883i
\(460\) −35829.5 + 110272.i −0.00789490 + 0.0242980i
\(461\) 4.06231e6 0.890267 0.445134 0.895464i \(-0.353156\pi\)
0.445134 + 0.895464i \(0.353156\pi\)
\(462\) −347835. 7.52434e6i −0.0758174 1.64007i
\(463\) −6.39084e6 −1.38550 −0.692748 0.721179i \(-0.743600\pi\)
−0.692748 + 0.721179i \(0.743600\pi\)
\(464\) 102985. 316955.i 0.0222064 0.0683444i
\(465\) −3.12402e6 + 2.26974e6i −0.670011 + 0.486792i
\(466\) −8.97684e6 6.52205e6i −1.91495 1.39130i
\(467\) 2.09813e6 + 6.45739e6i 0.445185 + 1.37014i 0.882280 + 0.470724i \(0.156007\pi\)
−0.437095 + 0.899415i \(0.643993\pi\)
\(468\) −969948. 2.98519e6i −0.204707 0.630025i
\(469\) 1.91996e6 + 1.39494e6i 0.403052 + 0.292834i
\(470\) 323873. 235307.i 0.0676285 0.0491350i
\(471\) 100681. 309865.i 0.0209121 0.0643607i
\(472\) 1.01123e6 0.208926
\(473\) −840440. + 316684.i −0.172725 + 0.0650839i
\(474\) 5.46835e6 1.11792
\(475\) 603923. 1.85868e6i 0.122814 0.377983i
\(476\) 9.15816e6 6.65379e6i 1.85264 1.34602i
\(477\) −340758. 247575.i −0.0685724 0.0498208i
\(478\) 3.98065e6 + 1.22512e7i 0.796864 + 2.45250i
\(479\) 72621.9 + 223507.i 0.0144620 + 0.0445095i 0.958027 0.286678i \(-0.0925509\pi\)
−0.943565 + 0.331187i \(0.892551\pi\)
\(480\) −3.97774e6 2.89000e6i −0.788012 0.572524i
\(481\) 6.91256e6 5.02227e6i 1.36231 0.989777i
\(482\) −1.17327e6 + 3.61094e6i −0.230027 + 0.707951i
\(483\) −88391.9 −0.0172403
\(484\) −6.70497e6 + 621243.i −1.30102 + 0.120545i
\(485\) −3.95475e6 −0.763421
\(486\) 156767. 482480.i 0.0301068 0.0926592i
\(487\) 7.10321e6 5.16078e6i 1.35716 0.986037i 0.358543 0.933513i \(-0.383273\pi\)
0.998620 0.0525237i \(-0.0167265\pi\)
\(488\) −163599. 118862.i −0.0310979 0.0225940i
\(489\) 725869. + 2.23399e6i 0.137273 + 0.422484i
\(490\) 7.66392e6 + 2.35871e7i 1.44198 + 4.43797i
\(491\) 3.08650e6 + 2.24247e6i 0.577780 + 0.419782i 0.837923 0.545789i \(-0.183770\pi\)
−0.260143 + 0.965570i \(0.583770\pi\)
\(492\) −2.61936e6 + 1.90308e6i −0.487846 + 0.354441i
\(493\) 187138. 575953.i 0.0346773 0.106726i
\(494\) 9.89420e6 1.82416
\(495\) −2.08489e6 + 785603.i −0.382446 + 0.144109i
\(496\) −3.84230e6 −0.701274
\(497\) 572478. 1.76191e6i 0.103960 0.319957i
\(498\) −1.48748e6 + 1.08072e6i −0.268768 + 0.195271i
\(499\) 5.35146e6 + 3.88806e6i 0.962101 + 0.699007i 0.953638 0.300957i \(-0.0973061\pi\)
0.00846312 + 0.999964i \(0.497306\pi\)
\(500\) 1.37458e6 + 4.23052e6i 0.245892 + 0.756779i
\(501\) −740688. 2.27960e6i −0.131838 0.405756i
\(502\) 4.42608e6 + 3.21573e6i 0.783899 + 0.569536i
\(503\) 7.90542e6 5.74362e6i 1.39317 1.01220i 0.397664 0.917531i \(-0.369821\pi\)
0.995509 0.0946680i \(-0.0301790\pi\)
\(504\) −512136. + 1.57619e6i −0.0898067 + 0.276397i
\(505\) −2.56579e6 −0.447706
\(506\) 6441.78 + 139348.i 0.00111848 + 0.0241949i
\(507\) −4.38917e6 −0.758337
\(508\) −1.67809e6 + 5.16464e6i −0.288508 + 0.887935i
\(509\) 7.34117e6 5.33367e6i 1.25595 0.912498i 0.257395 0.966306i \(-0.417136\pi\)
0.998551 + 0.0538080i \(0.0171359\pi\)
\(510\) −4.78212e6 3.47441e6i −0.814132 0.591502i
\(511\) 2.12557e6 + 6.54184e6i 0.360100 + 1.10828i
\(512\) −2.02340e6 6.22739e6i −0.341120 1.04986i
\(513\) 732849. + 532446.i 0.122948 + 0.0893269i
\(514\) −9.83373e6 + 7.14463e6i −1.64176 + 1.19281i
\(515\) 1.42866e6 4.39697e6i 0.237362 0.730526i
\(516\) 842146. 0.139240
\(517\) 150001. 227894.i 0.0246814 0.0374978i
\(518\) −1.92264e7 −3.14828
\(519\) −2.05288e6 + 6.31813e6i −0.334538 + 1.02960i
\(520\) 4.33177e6 3.14722e6i 0.702518 0.510409i
\(521\) −705377. 512487.i −0.113848 0.0827158i 0.529404 0.848370i \(-0.322416\pi\)
−0.643253 + 0.765654i \(0.722416\pi\)
\(522\) 116760. + 359351.i 0.0187551 + 0.0577222i
\(523\) −2.12948e6 6.55385e6i −0.340423 1.04771i −0.963989 0.265943i \(-0.914317\pi\)
0.623566 0.781771i \(-0.285683\pi\)
\(524\) −4.50156e6 3.27058e6i −0.716201 0.520351i
\(525\) 2.77983e6 2.01966e6i 0.440169 0.319801i
\(526\) 568014. 1.74817e6i 0.0895148 0.275498i
\(527\) −6.98202e6 −1.09510
\(528\) −2.13779e6 586969.i −0.333719 0.0916285i
\(529\) −6.43471e6 −0.999746
\(530\) 946220. 2.91217e6i 0.146320 0.450325i
\(531\) 786178. 571192.i 0.121000 0.0879114i
\(532\) −1.02029e7 7.41285e6i −1.56295 1.13555i
\(533\) 2.46422e6 + 7.58408e6i 0.375717 + 1.15634i
\(534\) 369455. + 1.13707e6i 0.0560672 + 0.172557i
\(535\) −1.10006e7 7.99239e6i −1.66162 1.20724i
\(536\) −666677. + 484369.i −0.100231 + 0.0728224i
\(537\) 1.34712e6 4.14601e6i 0.201591 0.620433i
\(538\) 8.55058e6 1.27362
\(539\) 1.05557e7 + 1.32008e7i 1.56501 + 1.95717i
\(540\) 2.08912e6 0.308304
\(541\) −599827. + 1.84608e6i −0.0881116 + 0.271180i −0.985397 0.170271i \(-0.945536\pi\)
0.897286 + 0.441450i \(0.145536\pi\)
\(542\) −9.37904e6 + 6.81427e6i −1.37139 + 0.996372i
\(543\) 931483. + 676762.i 0.135574 + 0.0985000i
\(544\) −2.74717e6 8.45491e6i −0.398004 1.22493i
\(545\) 4.95676e6 + 1.52553e7i 0.714837 + 2.20004i
\(546\) 1.40734e7 + 1.02249e7i 2.02031 + 1.46784i
\(547\) 1.13528e6 824829.i 0.162231 0.117868i −0.503708 0.863874i \(-0.668031\pi\)
0.665939 + 0.746006i \(0.268031\pi\)
\(548\) −3.15434e6 + 9.70807e6i −0.448701 + 1.38096i
\(549\) −194329. −0.0275174
\(550\) −3.38654e6 4.23515e6i −0.477364 0.596983i
\(551\) −674679. −0.0946712
\(552\) 9484.56 29190.5i 0.00132486 0.00407750i
\(553\) −1.38886e7 + 1.00907e7i −1.93128 + 1.40316i
\(554\) −1.26732e7 9.20765e6i −1.75434 1.27460i
\(555\) 1.75736e6 + 5.40861e6i 0.242175 + 0.745338i
\(556\) −4.65308e6 1.43207e7i −0.638343 1.96462i
\(557\) 1.02381e6 + 743840.i 0.139824 + 0.101588i 0.655498 0.755197i \(-0.272459\pi\)
−0.515675 + 0.856784i \(0.672459\pi\)
\(558\) 3.52428e6 2.56054e6i 0.479165 0.348134i
\(559\) 640957. 1.97266e6i 0.0867559 0.267007i
\(560\) 1.02122e7 1.37609
\(561\) −3.88468e6 1.06661e6i −0.521132 0.143086i
\(562\) 1.39001e7 1.85643
\(563\) 3.66510e6 1.12800e7i 0.487321 1.49982i −0.341270 0.939965i \(-0.610857\pi\)
0.828591 0.559854i \(-0.189143\pi\)
\(564\) −206966. + 150370.i −0.0273969 + 0.0199050i
\(565\) 1.08338e7 + 7.87122e6i 1.42778 + 1.03734i
\(566\) 31193.8 + 96004.7i 0.00409287 + 0.0125965i
\(567\) 492153. + 1.51469e6i 0.0642898 + 0.197864i
\(568\) 520424. + 378110.i 0.0676840 + 0.0491753i
\(569\) 374585. 272152.i 0.0485031 0.0352396i −0.563270 0.826273i \(-0.690457\pi\)
0.611773 + 0.791034i \(0.290457\pi\)
\(570\) −2.03499e6 + 6.26304e6i −0.262346 + 0.807417i
\(571\) 1.08452e7 1.39203 0.696013 0.718029i \(-0.254956\pi\)
0.696013 + 0.718029i \(0.254956\pi\)
\(572\) 8.55001e6 1.29898e7i 1.09264 1.66002i
\(573\) −5.82945e6 −0.741722
\(574\) 5.54493e6 1.70655e7i 0.702451 2.16192i
\(575\) −51481.3 + 37403.4i −0.00649352 + 0.00471782i
\(576\) 3.20026e6 + 2.32513e6i 0.401910 + 0.292005i
\(577\) −3.87978e6 1.19407e7i −0.485140 1.49311i −0.831778 0.555109i \(-0.812677\pi\)
0.346637 0.937999i \(-0.387323\pi\)
\(578\) 466831. + 1.43676e6i 0.0581219 + 0.178881i
\(579\) −3.35857e6 2.44014e6i −0.416349 0.302496i
\(580\) −1.25881e6 + 914582.i −0.155379 + 0.112889i
\(581\) 1.78369e6 5.48964e6i 0.219220 0.674689i
\(582\) 4.46144e6 0.545968
\(583\) −96366.5 2.08459e6i −0.0117423 0.254009i
\(584\) −2.38845e6 −0.289791
\(585\) 1.59003e6 4.89361e6i 0.192095 0.591207i
\(586\) 1.56870e6 1.13972e6i 0.188710 0.137106i
\(587\) −1.48615e6 1.07975e6i −0.178019 0.129339i 0.495207 0.868775i \(-0.335092\pi\)
−0.673227 + 0.739436i \(0.735092\pi\)
\(588\) −4.89752e6 1.50730e7i −0.584161 1.79786i
\(589\) 2.40369e6 + 7.39781e6i 0.285490 + 0.878648i
\(590\) 5.71535e6 + 4.15244e6i 0.675947 + 0.491104i
\(591\) −1.05059e6 + 763298.i −0.123727 + 0.0898929i
\(592\) −1.74862e6 + 5.38171e6i −0.205065 + 0.631126i
\(593\) −8.32530e6 −0.972217 −0.486108 0.873899i \(-0.661584\pi\)
−0.486108 + 0.873899i \(0.661584\pi\)
\(594\) 2.35201e6 886256.i 0.273510 0.103061i
\(595\) 1.85570e7 2.14889
\(596\) −4.29452e6 + 1.32172e7i −0.495221 + 1.52413i
\(597\) 4.61976e6 3.35645e6i 0.530498 0.385429i
\(598\) −260634. 189362.i −0.0298043 0.0216541i
\(599\) 3.98687e6 + 1.22703e7i 0.454010 + 1.39730i 0.872294 + 0.488982i \(0.162632\pi\)
−0.418284 + 0.908316i \(0.637368\pi\)
\(600\) 368693. + 1.13472e6i 0.0418107 + 0.128680i
\(601\) −9.94943e6 7.22868e6i −1.12360 0.816343i −0.138849 0.990314i \(-0.544340\pi\)
−0.984751 + 0.173970i \(0.944340\pi\)
\(602\) −3.77590e6 + 2.74335e6i −0.424648 + 0.308525i
\(603\) −244712. + 753146.i −0.0274070 + 0.0843502i
\(604\) 9.40173e6 1.04861
\(605\) −9.49085e6 5.63669e6i −1.05418 0.626089i
\(606\) 2.89453e6 0.320181
\(607\) −1.07598e6 + 3.31153e6i −0.118531 + 0.364802i −0.992667 0.120880i \(-0.961428\pi\)
0.874136 + 0.485681i \(0.161428\pi\)
\(608\) −8.01265e6 + 5.82153e6i −0.879058 + 0.638673i
\(609\) −959655. 697230.i −0.104851 0.0761786i
\(610\) −436558. 1.34359e6i −0.0475026 0.146198i
\(611\) 194708. + 599249.i 0.0210999 + 0.0649388i
\(612\) 3.05595e6 + 2.22027e6i 0.329812 + 0.239623i
\(613\) 3.16775e6 2.30151e6i 0.340487 0.247378i −0.404381 0.914591i \(-0.632513\pi\)
0.744867 + 0.667213i \(0.232513\pi\)
\(614\) 7.24698e6 2.23039e7i 0.775776 2.38759i
\(615\) −5.30756e6 −0.565857
\(616\) −7.68368e6 + 2.89527e6i −0.815864 + 0.307424i
\(617\) −170678. −0.0180495 −0.00902475 0.999959i \(-0.502873\pi\)
−0.00902475 + 0.999959i \(0.502873\pi\)
\(618\) −1.61171e6 + 4.96032e6i −0.169752 + 0.522443i
\(619\) 1.25470e7 9.11590e6i 1.31617 0.956253i 0.316198 0.948693i \(-0.397594\pi\)
0.999971 0.00755984i \(-0.00240640\pi\)
\(620\) 1.45131e7 + 1.05444e7i 1.51629 + 1.10165i
\(621\) −9114.48 28051.5i −0.000948425 0.00291895i
\(622\) −2.72294e6 8.38033e6i −0.282203 0.868531i
\(623\) −3.03656e6 2.20619e6i −0.313445 0.227731i
\(624\) 4.14205e6 3.00938e6i 0.425847 0.309396i
\(625\) −3.77215e6 + 1.16095e7i −0.386268 + 1.18881i
\(626\) −1.02711e7 −1.04756
\(627\) 207250. + 4.48322e6i 0.0210536 + 0.455430i
\(628\) −1.51361e6 −0.153149
\(629\) −3.17750e6 + 9.77934e6i −0.320228 + 0.985560i
\(630\) −9.36693e6 + 6.80547e6i −0.940255 + 0.683136i
\(631\) −5.15852e6 3.74788e6i −0.515765 0.374725i 0.299241 0.954178i \(-0.403266\pi\)
−0.815006 + 0.579452i \(0.803266\pi\)
\(632\) −1.84207e6 5.66931e6i −0.183448 0.564595i
\(633\) 248056. + 763439.i 0.0246060 + 0.0757295i
\(634\) 3.28484e6 + 2.38658e6i 0.324557 + 0.235805i
\(635\) −7.20193e6 + 5.23251e6i −0.708785 + 0.514962i
\(636\) −604669. + 1.86098e6i −0.0592754 + 0.182431i
\(637\) −3.90349e7 −3.81157
\(638\) −1.02923e6 + 1.56369e6i −0.100106 + 0.152089i
\(639\) 618179. 0.0598911
\(640\) −3.48436e6 + 1.07237e7i −0.336258 + 1.03490i
\(641\) −2.57941e6 + 1.87405e6i −0.247956 + 0.180151i −0.704821 0.709386i \(-0.748972\pi\)
0.456864 + 0.889536i \(0.348972\pi\)
\(642\) 1.24100e7 + 9.01639e6i 1.18832 + 0.863367i
\(643\) −330137. 1.01606e6i −0.0314896 0.0969150i 0.934076 0.357073i \(-0.116225\pi\)
−0.965566 + 0.260158i \(0.916225\pi\)
\(644\) 126894. + 390540.i 0.0120567 + 0.0371066i
\(645\) 1.11687e6 + 811452.i 0.105707 + 0.0768004i
\(646\) −9.63298e6 + 6.99877e6i −0.908195 + 0.659843i
\(647\) −2.25968e6 + 6.95458e6i −0.212220 + 0.653146i 0.787119 + 0.616801i \(0.211572\pi\)
−0.999339 + 0.0363451i \(0.988428\pi\)
\(648\) −553019. −0.0517372
\(649\) 4.64277e6 + 1.27475e6i 0.432679 + 0.118800i
\(650\) 1.25234e7 1.16262
\(651\) −4.22610e6 + 1.30066e7i −0.390830 + 1.20285i
\(652\) 8.82837e6 6.41419e6i 0.813320 0.590912i
\(653\) 1.34877e7 + 9.79938e6i 1.23781 + 0.899322i 0.997451 0.0713612i \(-0.0227343\pi\)
0.240361 + 0.970684i \(0.422734\pi\)
\(654\) −5.59184e6 1.72099e7i −0.511223 1.57338i
\(655\) −2.81867e6 8.67499e6i −0.256709 0.790070i
\(656\) −4.27255e6 3.10419e6i −0.387639 0.281636i
\(657\) −1.85690e6 + 1.34912e6i −0.167832 + 0.121937i
\(658\) 438127. 1.34842e6i 0.0394489 0.121411i
\(659\) −7.46758e6 −0.669833 −0.334916 0.942248i \(-0.608708\pi\)
−0.334916 + 0.942248i \(0.608708\pi\)
\(660\) 6.46406e6 + 8.08384e6i 0.577624 + 0.722367i
\(661\) 1.67759e7 1.49342 0.746711 0.665149i \(-0.231632\pi\)
0.746711 + 0.665149i \(0.231632\pi\)
\(662\) 6.44678e6 1.98411e7i 0.571739 1.75963i
\(663\) 7.52670e6 5.46847e6i 0.664999 0.483150i
\(664\) 1.62150e6 + 1.17809e6i 0.142724 + 0.103695i
\(665\) −6.38860e6 1.96621e7i −0.560211 1.72415i
\(666\) −1.98252e6 6.10157e6i −0.173194 0.533036i
\(667\) 17772.5 + 12912.4i 0.00154680 + 0.00112381i
\(668\) −9.00862e6 + 6.54514e6i −0.781119 + 0.567516i
\(669\) 2.08721e6 6.42379e6i 0.180303 0.554914i
\(670\) −5.75698e6 −0.495459
\(671\) −601283. 751955.i −0.0515553 0.0644741i
\(672\) −1.74132e7 −1.48750
\(673\) −235056. + 723428.i −0.0200048 + 0.0615684i −0.960561 0.278071i \(-0.910305\pi\)
0.940556 + 0.339639i \(0.110305\pi\)
\(674\) −3.61703e6 + 2.62792e6i −0.306692 + 0.222825i
\(675\) 927588. + 673932.i 0.0783602 + 0.0569320i
\(676\) 6.30104e6 + 1.93926e7i 0.530329 + 1.63218i
\(677\) −4.10496e6 1.26338e7i −0.344221 1.05940i −0.962000 0.273050i \(-0.911967\pi\)
0.617779 0.786352i \(-0.288033\pi\)
\(678\) −1.22219e7 8.87970e6i −1.02109 0.741863i
\(679\) −1.13312e7 + 8.23262e6i −0.943198 + 0.685273i
\(680\) −1.99119e6 + 6.12825e6i −0.165135 + 0.508235i
\(681\) 7.52585e6 0.621853
\(682\) 2.08126e7 + 5.71448e6i 1.71343 + 0.470452i
\(683\) 8.02422e6 0.658189 0.329095 0.944297i \(-0.393256\pi\)
0.329095 + 0.944297i \(0.393256\pi\)
\(684\) 1.30043e6 4.00231e6i 0.106279 0.327092i
\(685\) −1.35376e7 + 9.83563e6i −1.10234 + 0.800895i
\(686\) 4.27036e7 + 3.10260e7i 3.46461 + 2.51718i
\(687\) 518909. + 1.59704e6i 0.0419469 + 0.129099i
\(688\) 424484. + 1.30643e6i 0.0341893 + 0.105224i
\(689\) 3.89899e6 + 2.83278e6i 0.312899 + 0.227334i
\(690\) 173472. 126035.i 0.0138710 0.0100778i
\(691\) −6.07806e6 + 1.87063e7i −0.484250 + 1.49037i 0.348813 + 0.937192i \(0.386585\pi\)
−0.833064 + 0.553177i \(0.813415\pi\)
\(692\) 3.08624e7 2.44999
\(693\) −4.33829e6 + 6.59106e6i −0.343151 + 0.521341i
\(694\) 3.55473e6 0.280161
\(695\) 7.62777e6 2.34759e7i 0.599012 1.84357i
\(696\) 333225. 242102.i 0.0260744 0.0189442i
\(697\) −7.76384e6 5.64076e6i −0.605333 0.439800i
\(698\) −1.01010e7 3.10876e7i −0.784739 2.41518i
\(699\) 3.59195e6 + 1.10549e7i 0.278059 + 0.855778i
\(700\) −1.29141e7 9.38266e6i −0.996139 0.723737i
\(701\) 1.43283e7 1.04101e7i 1.10128 0.800128i 0.120013 0.992772i \(-0.461706\pi\)
0.981269 + 0.192644i \(0.0617062\pi\)
\(702\) −1.79375e6 + 5.52059e6i −0.137378 + 0.422807i
\(703\) 1.14556e7 0.874241
\(704\) 905037. + 1.95777e7i 0.0688232 + 1.48878i
\(705\) −419372. −0.0317780
\(706\) −4.62028e6 + 1.42198e7i −0.348865 + 1.07369i
\(707\) −7.35157e6 + 5.34123e6i −0.553135 + 0.401876i
\(708\) −3.65231e6 2.65356e6i −0.273832 0.198951i
\(709\) 4.19391e6 + 1.29075e7i 0.313331 + 0.964333i 0.976436 + 0.215807i \(0.0692382\pi\)
−0.663105 + 0.748526i \(0.730762\pi\)
\(710\) 1.38873e6 + 4.27408e6i 0.103389 + 0.318197i
\(711\) −4.63443e6 3.36711e6i −0.343813 0.249795i
\(712\) 1.05440e6 766065.i 0.0779479 0.0566325i
\(713\) 78265.8 240877.i 0.00576565 0.0177448i
\(714\) −2.09345e7 −1.53680
\(715\) 2.38556e7 8.98895e6i 1.74512 0.657573i
\(716\) −2.02522e7 −1.47635
\(717\) 4.17000e6 1.28339e7i 0.302927 0.932314i
\(718\) 4.91022e6 3.56749e6i 0.355459 0.258256i
\(719\) −1.62962e7 1.18399e7i −1.17561 0.854134i −0.183944 0.982937i \(-0.558887\pi\)
−0.991670 + 0.128803i \(0.958887\pi\)
\(720\) 1.05302e6 + 3.24087e6i 0.0757019 + 0.232987i
\(721\) −5.05977e6 1.55724e7i −0.362487 1.11562i
\(722\) −6.47830e6 4.70676e6i −0.462507 0.336031i
\(723\) 3.21777e6 2.33784e6i 0.228933 0.166330i
\(724\) 1.65290e6 5.08711e6i 0.117193 0.360682i
\(725\) −853960. −0.0603382
\(726\) 1.07068e7 + 6.35888e6i 0.753910 + 0.447754i
\(727\) 1.04332e7 0.732119 0.366059 0.930592i \(-0.380707\pi\)
0.366059 + 0.930592i \(0.380707\pi\)
\(728\) 5.85991e6 1.80350e7i 0.409791 1.26121i
\(729\) −429945. + 312373.i −0.0299636 + 0.0217698i
\(730\) −1.34993e7 9.80780e6i −0.937570 0.681184i
\(731\) 771349. + 2.37397e6i 0.0533897 + 0.164317i
\(732\) 278976. + 858601.i 0.0192438 + 0.0592262i
\(733\) 4.34866e6 + 3.15948e6i 0.298948 + 0.217198i 0.727140 0.686490i \(-0.240849\pi\)
−0.428192 + 0.903688i \(0.640849\pi\)
\(734\) −1.48628e7 + 1.07985e7i −1.01827 + 0.739813i
\(735\) 8.02847e6 2.47091e7i 0.548169 1.68709i
\(736\) 322486. 0.0219441
\(737\) −3.67147e6 + 1.38344e6i −0.248984 + 0.0938189i
\(738\) 5.98757e6 0.404678
\(739\) 5.86573e6 1.80529e7i 0.395104 1.21600i −0.533777 0.845625i \(-0.679228\pi\)
0.928881 0.370379i \(-0.120772\pi\)
\(740\) 2.13739e7 1.55291e7i 1.43484 1.04248i
\(741\) −8.38534e6 6.09231e6i −0.561016 0.407602i
\(742\) −3.35114e6 1.03138e7i −0.223451 0.687713i
\(743\) −3.05019e6 9.38752e6i −0.202700 0.623848i −0.999800 0.0199999i \(-0.993633\pi\)
0.797100 0.603848i \(-0.206367\pi\)
\(744\) −3.84183e6 2.79125e6i −0.254452 0.184870i
\(745\) −1.84309e7 + 1.33908e7i −1.21662 + 0.883929i
\(746\) 2.95280e6 9.08778e6i 0.194262 0.597876i
\(747\) 1.92608e6 0.126291
\(748\) 864224. + 1.86948e7i 0.0564771 + 1.22171i
\(749\) −4.81569e7 −3.13656
\(750\) 2.54204e6 7.82361e6i 0.165017 0.507872i
\(751\) −1.65255e7 + 1.20065e7i −1.06919 + 0.776812i −0.975766 0.218814i \(-0.929781\pi\)
−0.0934235 + 0.995626i \(0.529781\pi\)
\(752\) −337592. 245275.i −0.0217694 0.0158164i
\(753\) −1.77103e6 5.45067e6i −0.113825 0.350318i
\(754\) −1.33598e6 4.11174e6i −0.0855801 0.263389i
\(755\) 1.24687e7 + 9.05906e6i 0.796077 + 0.578383i
\(756\) 5.98580e6 4.34894e6i 0.380906 0.276745i
\(757\) 5.70523e6 1.75589e7i 0.361854 1.11367i −0.590074 0.807349i \(-0.700901\pi\)
0.951928 0.306323i \(-0.0990987\pi\)
\(758\) −1.59754e6 −0.100990
\(759\) 80343.4 122064.i 0.00506228 0.00769100i
\(760\) 7.17871e6 0.450830
\(761\) −5.24183e6 + 1.61327e7i −0.328111 + 1.00982i 0.641905 + 0.766784i \(0.278144\pi\)
−0.970017 + 0.243039i \(0.921856\pi\)
\(762\) 8.12465e6 5.90291e6i 0.506894 0.368280i
\(763\) 4.59594e7 + 3.33915e7i 2.85801 + 2.07646i
\(764\) 8.36869e6 + 2.57562e7i 0.518709 + 1.59642i
\(765\) 1.91349e6 + 5.88913e6i 0.118215 + 0.363829i
\(766\) −7.64801e6 5.55660e6i −0.470952 0.342167i
\(767\) −8.99553e6 + 6.53564e6i −0.552126 + 0.401143i
\(768\) −415499. + 1.27877e6i −0.0254195 + 0.0782331i
\(769\) 1.54762e7 0.943729 0.471865 0.881671i \(-0.343581\pi\)
0.471865 + 0.881671i \(0.343581\pi\)
\(770\) −5.53164e7 1.51881e7i −3.36223 0.923158i
\(771\) 1.27334e7 0.771449
\(772\) −5.95973e6 + 1.83422e7i −0.359901 + 1.10766i
\(773\) 1.30579e7 9.48713e6i 0.786005 0.571066i −0.120770 0.992680i \(-0.538536\pi\)
0.906775 + 0.421615i \(0.138536\pi\)
\(774\) −1.25996e6 915417.i −0.0755972 0.0549246i
\(775\) 3.04243e6 + 9.36362e6i 0.181956 + 0.560002i
\(776\) −1.50288e6 4.62539e6i −0.0895922 0.275737i
\(777\) 1.62944e7 + 1.18386e7i 0.968245 + 0.703471i
\(778\) −1.44234e7 + 1.04792e7i −0.854315 + 0.620696i
\(779\) −3.30383e6 + 1.01681e7i −0.195062 + 0.600340i
\(780\) −2.39040e7 −1.40680
\(781\) 1.91274e6 + 2.39204e6i 0.112209 + 0.140327i
\(782\) 387700. 0.0226714
\(783\) 122314. 376445.i 0.00712973 0.0219430i
\(784\) 2.09143e7 1.51951e7i 1.21521 0.882905i
\(785\) −2.00738e6 1.45844e6i −0.116266 0.0844725i
\(786\) 3.17981e6 + 9.78645e6i 0.183588 + 0.565026i
\(787\) 1.80144e6 + 5.54427e6i 0.103677 + 0.319086i 0.989418 0.145095i \(-0.0463487\pi\)
−0.885740 + 0.464181i \(0.846349\pi\)
\(788\) 4.88068e6 + 3.54602e6i 0.280004 + 0.203435i
\(789\) −1.55782e6 + 1.13182e6i −0.0890890 + 0.0647270i
\(790\) 1.28689e7 3.96065e7i 0.733627 2.25787i
\(791\) 4.74268e7 2.69515
\(792\) −1.71112e6 2.13990e6i −0.0969323 0.121222i
\(793\) 2.22354e6 0.125563
\(794\) 856087. 2.63476e6i 0.0481911 0.148317i
\(795\) −2.59507e6 + 1.88543e6i −0.145624 + 0.105802i
\(796\) −2.14618e7 1.55929e7i −1.20056 0.872258i
\(797\) 7.94845e6 + 2.44628e7i 0.443238 + 1.36415i 0.884405 + 0.466721i \(0.154565\pi\)
−0.441167 + 0.897425i \(0.645435\pi\)
\(798\) 7.20713e6 + 2.21813e7i 0.400641 + 1.23304i
\(799\) −613452. 445699.i −0.0339949 0.0246987i
\(800\) −1.01418e7 + 7.36848e6i −0.560263 + 0.407055i
\(801\) 387029. 1.19115e6i 0.0213139 0.0655974i
\(802\) −1.70768e7 −0.937497
\(803\) −1.09659e7 3.01089e6i −0.600145 0.164780i
\(804\) 3.67892e6 0.200715
\(805\) −208017. + 640210.i −0.0113138 + 0.0348203i
\(806\) −4.03252e7 + 2.92980e7i −2.18645 + 1.58855i
\(807\) −7.24662e6 5.26498e6i −0.391698 0.284586i
\(808\) −975051. 3.00090e6i −0.0525411 0.161705i
\(809\) −1.70971e6 5.26195e6i −0.0918442 0.282667i 0.894574 0.446919i \(-0.147479\pi\)
−0.986418 + 0.164252i \(0.947479\pi\)
\(810\) −3.12561e6 2.27089e6i −0.167387 0.121614i
\(811\) −2.77912e7 + 2.01915e7i −1.48373 + 1.07800i −0.507403 + 0.861709i \(0.669395\pi\)
−0.976330 + 0.216287i \(0.930605\pi\)
\(812\) −1.70289e6 + 5.24096e6i −0.0906352 + 0.278947i
\(813\) 1.21446e7 0.644402
\(814\) 1.74758e7 2.65505e7i 0.924432 1.40447i
\(815\) 1.78887e7 0.943378
\(816\) −1.90398e6 + 5.85985e6i −0.100101 + 0.308078i
\(817\) 2.24979e6 1.63457e6i 0.117920 0.0856738i
\(818\) 3.31819e7 + 2.41081e7i 1.73388 + 1.25973i
\(819\) −5.63127e6 1.73313e7i −0.293357 0.902860i
\(820\) 7.61946e6 + 2.34503e7i 0.395722 + 1.21791i
\(821\) −1.57948e7 1.14756e7i −0.817815 0.594178i 0.0982706 0.995160i \(-0.468669\pi\)
−0.916086 + 0.400982i \(0.868669\pi\)
\(822\) 1.52720e7 1.10958e7i 0.788348 0.572768i
\(823\) 7.59001e6 2.33597e7i 0.390610 1.20217i −0.541719 0.840560i \(-0.682226\pi\)
0.932328 0.361613i \(-0.117774\pi\)
\(824\) 5.68553e6 0.291711
\(825\) 262323. + 5.67454e6i 0.0134184 + 0.290266i
\(826\) 2.50199e7 1.27596
\(827\) −200938. + 618424.i −0.0102164 + 0.0314429i −0.956035 0.293253i \(-0.905262\pi\)
0.945818 + 0.324696i \(0.105262\pi\)
\(828\) −110855. + 80540.8i −0.00561926 + 0.00408263i
\(829\) −3.71773e6 2.70109e6i −0.187885 0.136506i 0.489867 0.871797i \(-0.337045\pi\)
−0.677751 + 0.735291i \(0.737045\pi\)
\(830\) 4.32693e6 + 1.33169e7i 0.218014 + 0.670978i
\(831\) 5.07101e6 + 1.56070e7i 0.254737 + 0.784000i
\(832\) −3.66177e7 2.66043e7i −1.83393 1.33243i
\(833\) 3.80043e7 2.76117e7i 1.89767 1.37874i
\(834\) −8.60506e6 + 2.64836e7i −0.428389 + 1.31845i
\(835\) −1.82540e7 −0.906027
\(836\) 1.95106e7 7.35175e6i 0.965507 0.363810i
\(837\) −4.56347e6 −0.225155
\(838\) −1.54908e7 + 4.76757e7i −0.762015 + 2.34524i
\(839\) 2.28259e6 1.65840e6i 0.111950 0.0813363i −0.530402 0.847746i \(-0.677959\pi\)
0.642352 + 0.766410i \(0.277959\pi\)
\(840\) 1.02109e7 + 7.41866e6i 0.499306 + 0.362767i
\(841\) −6.24719e6 1.92269e7i −0.304576 0.937387i
\(842\) −78499.7 241597.i −0.00381582 0.0117439i
\(843\) −1.17804e7 8.55894e6i −0.570939 0.414812i
\(844\) 3.01698e6 2.19197e6i 0.145786 0.105920i
\(845\) −1.03293e7 + 3.17902e7i −0.497654 + 1.53162i
\(846\) 473102. 0.0227263
\(847\) −3.89273e7 + 3.60678e6i −1.86443 + 0.172747i
\(848\) −3.19174e6 −0.152418
\(849\) 32677.6 100571.i 0.00155590 0.00478857i
\(850\) −1.21927e7 + 8.85854e6i −0.578834 + 0.420547i
\(851\) −301766. 219246.i −0.0142839 0.0103778i
\(852\) −887450. 2.73129e6i −0.0418837 0.128905i
\(853\) −4.69315e6 1.44440e7i −0.220847 0.679698i −0.998687 0.0512351i \(-0.983684\pi\)
0.777839 0.628463i \(-0.216316\pi\)
\(854\) −4.04779e6 2.94089e6i −0.189921 0.137986i
\(855\) 5.58109e6 4.05490e6i 0.261098 0.189699i
\(856\) 5.16730e6 1.59033e7i 0.241035 0.741828i
\(857\) 3.25712e7 1.51489 0.757446 0.652898i \(-0.226447\pi\)
0.757446 + 0.652898i \(0.226447\pi\)
\(858\) −2.69120e7 + 1.01406e7i −1.24804 + 0.470270i
\(859\) −2.43268e7 −1.12487 −0.562434 0.826842i \(-0.690135\pi\)
−0.562434 + 0.826842i \(0.690135\pi\)
\(860\) 1.98186e6 6.09955e6i 0.0913751 0.281224i
\(861\) −1.52073e7 + 1.10488e7i −0.699110 + 0.507933i
\(862\) −3.34814e7 2.43257e7i −1.53474 1.11506i
\(863\) −1.12886e7 3.47428e7i −0.515958 1.58795i −0.781533 0.623864i \(-0.785562\pi\)
0.265575 0.964090i \(-0.414438\pi\)
\(864\) −1.79556e6 5.52616e6i −0.0818304 0.251848i
\(865\) 4.09302e7 + 2.97375e7i 1.85996 + 1.35134i
\(866\) −2.39542e7 + 1.74037e7i −1.08539 + 0.788583i
\(867\) 489037. 1.50510e6i 0.0220950 0.0680014i
\(868\) 6.35338e7 2.86224
\(869\) −1.31062e6 2.83512e7i −0.0588745 1.27357i
\(870\) 2.87751e6 0.128890
\(871\) 2.80002e6 8.61758e6i 0.125059 0.384893i
\(872\) −1.59587e7 + 1.15947e7i −0.710732 + 0.516377i
\(873\) −3.78107e6 2.74711e6i −0.167911 0.121994i
\(874\) −133473. 410789.i −0.00591038 0.0181903i
\(875\) 7.98046e6 + 2.45613e7i 0.352377 + 1.08451i
\(876\) 8.62653e6 + 6.26754e6i 0.379818 + 0.275954i
\(877\) 2.16298e7 1.57150e7i 0.949629 0.689946i −0.00108992 0.999999i \(-0.500347\pi\)
0.950719 + 0.310053i \(0.100347\pi\)
\(878\) 1.52762e7 4.70154e7i 0.668774 2.05828i
\(879\) −2.03125e6 −0.0886729
\(880\) −9.28232e6 + 1.41024e7i −0.404064 + 0.613885i
\(881\) −2.08247e7 −0.903938 −0.451969 0.892034i \(-0.649278\pi\)
−0.451969 + 0.892034i \(0.649278\pi\)
\(882\) −9.05710e6 + 2.78749e7i −0.392029 + 1.20654i
\(883\) 1.05586e7 7.67125e6i 0.455726 0.331104i −0.336127 0.941817i \(-0.609117\pi\)
0.791852 + 0.610713i \(0.209117\pi\)
\(884\) −3.49665e7 2.54046e7i −1.50495 1.09341i
\(885\) −2.28691e6 7.03839e6i −0.0981503 0.302075i
\(886\) −1.26449e7 3.89170e7i −0.541167 1.66554i
\(887\) 2.96154e6 + 2.15169e6i 0.126389 + 0.0918269i 0.649184 0.760632i \(-0.275111\pi\)
−0.522795 + 0.852459i \(0.675111\pi\)
\(888\) −5.65797e6 + 4.11075e6i −0.240784 + 0.174940i
\(889\) −9.74259e6 + 2.99846e7i −0.413447 + 1.27246i
\(890\) 9.10507e6 0.385308
\(891\) −2.53904e6 697138.i −0.107146 0.0294188i
\(892\) −3.13785e7 −1.32044
\(893\) −261049. + 803426.i −0.0109545 + 0.0337145i
\(894\) 2.07923e7 1.51065e7i 0.870080 0.632150i
\(895\) −2.68588e7 1.95140e7i −1.12080 0.814310i
\(896\) 1.23402e7 + 3.79793e7i 0.513515 + 1.58044i
\(897\) 104289. + 320968.i 0.00432770 + 0.0133193i
\(898\) 4.87272e7 + 3.54024e7i 2.01642 + 1.46501i
\(899\) 2.74975e6 1.99781e6i 0.113473 0.0824431i
\(900\) 1.64599e6 5.06584e6i 0.0677362 0.208471i
\(901\) −5.79984e6 −0.238015
\(902\) 1.85264e7 + 2.31689e7i 0.758186 + 0.948174i
\(903\) 4.88928e6 0.199538
\(904\) −5.08896e6 + 1.56622e7i −0.207113 + 0.637430i
\(905\) 7.09380e6 5.15395e6i 0.287911 0.209179i
\(906\) −1.40663e7 1.02197e7i −0.569322 0.413637i
\(907\) −1.93406e6 5.95244e6i −0.0780644 0.240257i 0.904407 0.426671i \(-0.140314\pi\)
−0.982471 + 0.186413i \(0.940314\pi\)
\(908\) −1.08040e7 3.32513e7i −0.434881 1.33843i
\(909\) −2.45311e6 1.78229e6i −0.0984708 0.0715432i
\(910\) 1.07177e8 7.78690e7i 4.29042 3.11717i
\(911\) 8.16194e6 2.51199e7i 0.325835 1.00282i −0.645228 0.763990i \(-0.723237\pi\)
0.971062 0.238826i \(-0.0767626\pi\)
\(912\) 6.86430e6 0.273281
\(913\) 5.95959e6 + 7.45296e6i 0.236614 + 0.295905i
\(914\) 5.94106e7 2.35233
\(915\) −457324. + 1.40750e6i −0.0180581 + 0.0555771i
\(916\) 6.31123e6 4.58538e6i 0.248528 0.180566i
\(917\) −2.61349e7 1.89881e7i −1.02636 0.745691i
\(918\) −2.15866e6 6.64366e6i −0.0845428 0.260196i
\(919\) 5.86700e6 + 1.80568e7i 0.229154 + 0.705263i 0.997843 + 0.0656411i \(0.0209092\pi\)
−0.768689 + 0.639622i \(0.779091\pi\)
\(920\) −189102. 137391.i −0.00736592 0.00535166i
\(921\) −1.98753e7 + 1.44403e7i −0.772086 + 0.560953i
\(922\) −1.07849e7 + 3.31924e7i −0.417819 + 1.28591i
\(923\) −7.07327e6 −0.273285
\(924\) 3.53492e7 + 9.70573e6i 1.36207 + 0.373980i
\(925\) 1.44997e7 0.557193
\(926\) 1.69668e7 5.22185e7i 0.650239 2.00123i
\(927\) 4.42022e6 3.21148e6i 0.168945 0.122745i
\(928\) 3.50118e6 + 2.54376e6i 0.133458 + 0.0969629i
\(929\) 1.49422e7 + 4.59873e7i 0.568035 + 1.74823i 0.658757 + 0.752356i \(0.271083\pi\)
−0.0907221 + 0.995876i \(0.528917\pi\)
\(930\) −1.02518e7 3.15517e7i −0.388680 1.19623i
\(931\) −4.23398e7 3.07616e7i −1.60094 1.16315i
\(932\) 4.36871e7 3.17405e7i 1.64745 1.19694i
\(933\) −2.85246e6 + 8.77897e6i −0.107279 + 0.330171i
\(934\) −5.83326e7 −2.18798
\(935\) −1.68673e7 + 2.56261e7i −0.630981 + 0.958636i
\(936\) 6.32771e6 0.236079
\(937\) −1.15084e7 + 3.54191e7i −0.428218 + 1.31792i 0.471661 + 0.881780i \(0.343655\pi\)
−0.899879 + 0.436139i \(0.856345\pi\)
\(938\) −1.64950e7 + 1.19843e7i −0.612134 + 0.444741i
\(939\) 8.70472e6 + 6.32435e6i 0.322174 + 0.234073i
\(940\) 602045. + 1.85290e6i 0.0222233 + 0.0683964i
\(941\) 7.56279e6 + 2.32759e7i 0.278425 + 0.856903i 0.988293 + 0.152569i \(0.0487545\pi\)
−0.709868 + 0.704335i \(0.751245\pi\)
\(942\) 2.26456e6 + 1.64530e6i 0.0831491 + 0.0604114i
\(943\) 281634. 204619.i 0.0103135 0.00749320i
\(944\) 2.27554e6 7.00339e6i 0.0831103 0.255787i
\(945\) 1.21289e7 0.441817
\(946\) −356319. 7.70786e6i −0.0129453 0.280031i
\(947\) −1.62114e6 −0.0587417 −0.0293708 0.999569i \(-0.509350\pi\)
−0.0293708 + 0.999569i \(0.509350\pi\)
\(948\) −8.22372e6 + 2.53100e7i −0.297199 + 0.914684i
\(949\) 2.12469e7 1.54368e7i 0.765825 0.556404i
\(950\) 1.35837e7 + 9.86912e6i 0.488324 + 0.354788i
\(951\) −1.31438e6 4.04525e6i −0.0471270 0.145042i
\(952\) 7.05202e6 + 2.17039e7i 0.252186 + 0.776149i
\(953\) −1.80644e7 1.31246e7i −0.644305 0.468115i 0.217021 0.976167i \(-0.430366\pi\)
−0.861327 + 0.508052i \(0.830366\pi\)
\(954\) 2.92756e6 2.12700e6i 0.104144 0.0756651i
\(955\) −1.37187e7 + 4.22220e7i −0.486750 + 1.49806i
\(956\) −6.26904e7 −2.21848
\(957\) 1.83511e6 691483.i 0.0647712 0.0244063i
\(958\) −2.01904e6 −0.0710774
\(959\) −1.83133e7 + 5.63626e7i −0.643014 + 1.97899i
\(960\) 2.43719e7 1.77072e7i 0.853516 0.620115i
\(961\) −8.54098e6 6.20538e6i −0.298331 0.216751i
\(962\) 2.26842e7 + 6.98149e7i 0.790290 + 2.43226i
\(963\) −4.96568e6 1.52828e7i −0.172549 0.531052i
\(964\) −1.49486e7 1.08608e7i −0.518095 0.376418i
\(965\) −2.55775e7 + 1.85832e7i −0.884179 + 0.642394i
\(966\) 234669. 722236.i 0.00809119 0.0249021i
\(967\) 1.23920e7 0.426164 0.213082 0.977034i \(-0.431650\pi\)
0.213082 + 0.977034i \(0.431650\pi\)
\(968\) 2.98586e6 1.32424e7i 0.102419 0.454231i
\(969\) 1.24734e7 0.426752
\(970\) 1.04993e7 3.23136e7i 0.358288 1.10270i
\(971\) 3.05313e7 2.21823e7i 1.03920 0.755020i 0.0690677 0.997612i \(-0.477998\pi\)
0.970128 + 0.242592i \(0.0779976\pi\)
\(972\) 1.99738e6 + 1.45118e6i 0.0678101 + 0.0492669i
\(973\) −2.70146e7 8.31424e7i −0.914779 2.81540i
\(974\) 2.33099e7 + 7.17403e7i 0.787303 + 2.42307i
\(975\) −1.06136e7 7.71121e6i −0.357561 0.259783i
\(976\) −1.19134e6 + 865557.i −0.0400323 + 0.0290851i
\(977\) 2.67265e6 8.22557e6i 0.0895789 0.275695i −0.896224 0.443602i \(-0.853701\pi\)
0.985803 + 0.167906i \(0.0537006\pi\)
\(978\) −2.01807e7 −0.674666
\(979\) 5.80668e6 2.18800e6i 0.193629 0.0729610i
\(980\) −1.20697e8 −4.01451
\(981\) −5.85783e6 + 1.80285e7i −0.194341 + 0.598120i
\(982\) −2.65171e7 + 1.92658e7i −0.877501 + 0.637542i
\(983\) −1.56170e7 1.13464e7i −0.515481 0.374519i 0.299418 0.954122i \(-0.403208\pi\)
−0.814899 + 0.579603i \(0.803208\pi\)
\(984\) −2.01698e6 6.20761e6i −0.0664068 0.204379i
\(985\) 3.05606e6 + 9.40558e6i 0.100362 + 0.308884i
\(986\) 4.20919e6 + 3.05816e6i 0.137882 + 0.100177i
\(987\) −1.20159e6 + 873009.i −0.0392613 + 0.0285250i
\(988\) −1.48796e7 + 4.57949e7i −0.484954 + 1.49253i
\(989\) −90547.7 −0.00294365
\(990\) −883925. 1.91210e7i −0.0286634 0.620044i
\(991\) −2.59473e7 −0.839283 −0.419642 0.907690i \(-0.637844\pi\)
−0.419642 + 0.907690i \(0.637844\pi\)
\(992\) 1.54184e7 4.74529e7i 0.497462 1.53103i
\(993\) −1.76807e7 + 1.28458e7i −0.569019 + 0.413417i
\(994\) 1.28764e7 + 9.35526e6i 0.413360 + 0.300324i
\(995\) −1.34384e7 4.13592e7i −0.430319 1.32439i
\(996\) −2.76506e6 8.50999e6i −0.0883195 0.271819i
\(997\) 3.97731e7 + 2.88968e7i 1.26722 + 0.920687i 0.999088 0.0426955i \(-0.0135945\pi\)
0.268129 + 0.963383i \(0.413595\pi\)
\(998\) −4.59761e7 + 3.34036e7i −1.46119 + 1.06161i
\(999\) −2.07683e6 + 6.39181e6i −0.0658395 + 0.202633i
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 33.6.e.b.31.1 yes 20
3.2 odd 2 99.6.f.b.64.5 20
11.4 even 5 363.6.a.r.1.2 10
11.5 even 5 inner 33.6.e.b.16.1 20
11.7 odd 10 363.6.a.t.1.9 10
33.5 odd 10 99.6.f.b.82.5 20
33.26 odd 10 1089.6.a.bk.1.9 10
33.29 even 10 1089.6.a.bi.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.e.b.16.1 20 11.5 even 5 inner
33.6.e.b.31.1 yes 20 1.1 even 1 trivial
99.6.f.b.64.5 20 3.2 odd 2
99.6.f.b.82.5 20 33.5 odd 10
363.6.a.r.1.2 10 11.4 even 5
363.6.a.t.1.9 10 11.7 odd 10
1089.6.a.bi.1.2 10 33.29 even 10
1089.6.a.bk.1.9 10 33.26 odd 10