Properties

Label 49.6.g.a.11.1
Level $49$
Weight $6$
Character 49.11
Analytic conductor $7.859$
Analytic rank $0$
Dimension $264$
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] = [49,6,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, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(7.85880717084\)
Analytic rank: \(0\)
Dimension: \(264\)
Relative dimension: \(22\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 11.1
Character \(\chi\) \(=\) 49.11
Dual form 49.6.g.a.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.22587 + 7.63249i) q^{2} +(11.6068 - 1.74945i) q^{3} +(7.01864 - 93.6572i) q^{4} +(15.3540 - 39.1213i) q^{5} +(-82.1236 + 102.980i) q^{6} +(-87.9777 + 95.2204i) q^{7} +(433.218 + 543.238i) q^{8} +(-100.546 + 31.0144i) q^{9} +O(q^{10})\) \(q+(-8.22587 + 7.63249i) q^{2} +(11.6068 - 1.74945i) q^{3} +(7.01864 - 93.6572i) q^{4} +(15.3540 - 39.1213i) q^{5} +(-82.1236 + 102.980i) q^{6} +(-87.9777 + 95.2204i) q^{7} +(433.218 + 543.238i) q^{8} +(-100.546 + 31.0144i) q^{9} +(172.293 + 438.996i) q^{10} +(-193.918 - 59.8157i) q^{11} +(-82.3843 - 1099.34i) q^{12} +(232.081 + 1016.82i) q^{13} +(-3.07634 - 1454.76i) q^{14} +(109.770 - 480.935i) q^{15} +(-4737.98 - 714.136i) q^{16} +(-594.219 + 405.131i) q^{17} +(590.363 - 1022.54i) q^{18} +(524.518 + 908.491i) q^{19} +(-3556.23 - 1712.59i) q^{20} +(-854.559 + 1259.12i) q^{21} +(2051.68 - 988.039i) q^{22} +(1219.19 + 831.232i) q^{23} +(5978.65 + 5547.38i) q^{24} +(996.056 + 924.205i) q^{25} +(-9669.90 - 6592.83i) q^{26} +(-3682.61 + 1773.45i) q^{27} +(8300.59 + 8908.06i) q^{28} +(-4384.19 - 2111.31i) q^{29} +(2767.78 + 4793.93i) q^{30} +(-1057.40 + 1831.47i) q^{31} +(26053.7 - 17763.1i) q^{32} +(-2355.42 - 355.022i) q^{33} +(1795.80 - 7867.93i) q^{34} +(2374.34 + 4903.81i) q^{35} +(2199.02 + 9634.55i) q^{36} +(121.590 + 1622.51i) q^{37} +(-11248.7 - 3469.75i) q^{38} +(4472.60 + 11396.0i) q^{39} +(27903.8 - 8607.17i) q^{40} +(-1482.43 - 1858.91i) q^{41} +(-2580.73 - 16879.8i) q^{42} +(-4480.15 + 5617.93i) q^{43} +(-6963.21 + 17742.0i) q^{44} +(-330.461 + 4409.69i) q^{45} +(-16373.3 + 2467.88i) q^{46} +(-8752.99 + 8121.59i) q^{47} -56242.3 q^{48} +(-1326.86 - 16754.5i) q^{49} -15247.4 q^{50} +(-6188.24 + 5741.85i) q^{51} +(96861.0 - 14599.4i) q^{52} +(56.4366 - 753.094i) q^{53} +(16756.8 - 42695.7i) q^{54} +(-5317.48 + 6667.90i) q^{55} +(-89840.8 - 6541.62i) q^{56} +(7677.35 + 9627.09i) q^{57} +(52178.4 - 16094.9i) q^{58} +(-4512.45 - 11497.5i) q^{59} +(-44272.6 - 13656.3i) q^{60} +(-772.508 - 10308.4i) q^{61} +(-5280.65 - 23136.0i) q^{62} +(5892.61 - 12302.6i) q^{63} +(-44618.7 + 195487. i) q^{64} +(43342.5 + 6532.83i) q^{65} +(22085.0 - 15057.3i) q^{66} +(3478.95 - 6025.72i) q^{67} +(33772.9 + 58496.3i) q^{68} +(15605.2 + 7515.05i) q^{69} +(-56959.3 - 22216.0i) q^{70} +(51538.0 - 24819.4i) q^{71} +(-60406.6 - 41184.5i) q^{72} +(23873.3 + 22151.2i) q^{73} +(-13383.9 - 12418.5i) q^{74} +(13177.9 + 8984.55i) q^{75} +(88768.1 - 42748.5i) q^{76} +(22756.1 - 13202.5i) q^{77} +(-123771. - 59604.9i) q^{78} +(33902.2 + 58720.3i) q^{79} +(-100685. + 174391. i) q^{80} +(-18515.1 + 12623.4i) q^{81} +(26382.4 + 3976.51i) q^{82} +(19560.6 - 85700.6i) q^{83} +(111928. + 88872.9i) q^{84} +(6725.64 + 29467.0i) q^{85} +(-6025.67 - 80407.0i) q^{86} +(-54580.2 - 16835.8i) q^{87} +(-51514.4 - 131257. i) q^{88} +(-128358. + 39593.1i) q^{89} +(-30938.6 - 38795.8i) q^{90} +(-117240. - 67358.1i) q^{91} +(86407.9 - 108352. i) q^{92} +(-9069.00 + 23107.4i) q^{93} +(10013.0 - 133614. i) q^{94} +(43594.8 - 6570.85i) q^{95} +(271325. - 251753. i) q^{96} +13844.3 q^{97} +(138793. + 127693. i) q^{98} +21352.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17} - 1336 q^{18} + 9741 q^{19} + 8330 q^{20} + 1512 q^{21} + 842 q^{22} - 1553 q^{23} + 1756 q^{24} + 13144 q^{25} - 1946 q^{26} - 19849 q^{27} - 31584 q^{28} - 30356 q^{29} + 6129 q^{30} + 43903 q^{31} + 27725 q^{32} - 3412 q^{33} - 73182 q^{34} - 17360 q^{35} - 102868 q^{36} - 22105 q^{37} + 19116 q^{38} + 109165 q^{39} + 77354 q^{40} + 47446 q^{41} + 157738 q^{42} + 6674 q^{43} + 15154 q^{44} - 130923 q^{45} - 136952 q^{46} - 195163 q^{47} - 151484 q^{48} - 131194 q^{49} + 263000 q^{50} - 84276 q^{51} - 58758 q^{52} - 110577 q^{53} + 170313 q^{54} + 290245 q^{55} + 79688 q^{56} + 47310 q^{57} + 252156 q^{58} + 127308 q^{59} + 86254 q^{60} + 166863 q^{61} - 63578 q^{62} - 243033 q^{63} - 293812 q^{64} - 16702 q^{65} - 661788 q^{66} + 46195 q^{67} + 393869 q^{68} + 321394 q^{69} - 64330 q^{70} - 61793 q^{71} + 333944 q^{72} + 21699 q^{73} + 133514 q^{74} - 431136 q^{75} + 3087 q^{76} - 48993 q^{77} - 450576 q^{78} - 181 q^{79} + 264228 q^{80} + 142090 q^{81} - 512442 q^{82} + 102424 q^{83} + 344932 q^{84} - 205502 q^{85} + 611991 q^{86} + 1427200 q^{87} + 685993 q^{88} + 145800 q^{89} + 677844 q^{90} + 732956 q^{91} + 10018 q^{92} - 1233536 q^{93} - 601938 q^{94} - 945265 q^{95} - 2372958 q^{96} - 1932952 q^{97} - 672973 q^{98} + 1090736 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.22587 + 7.63249i −1.45414 + 1.34925i −0.640362 + 0.768074i \(0.721215\pi\)
−0.813780 + 0.581173i \(0.802594\pi\)
\(3\) 11.6068 1.74945i 0.744579 0.112227i 0.234214 0.972185i \(-0.424748\pi\)
0.510365 + 0.859958i \(0.329510\pi\)
\(4\) 7.01864 93.6572i 0.219332 2.92679i
\(5\) 15.3540 39.1213i 0.274660 0.699823i −0.725275 0.688459i \(-0.758287\pi\)
0.999935 0.0113638i \(-0.00361729\pi\)
\(6\) −82.1236 + 102.980i −0.931301 + 1.16781i
\(7\) −87.9777 + 95.2204i −0.678621 + 0.734489i
\(8\) 433.218 + 543.238i 2.39321 + 3.00099i
\(9\) −100.546 + 31.0144i −0.413770 + 0.127631i
\(10\) 172.293 + 438.996i 0.544839 + 1.38823i
\(11\) −193.918 59.8157i −0.483210 0.149051i 0.0435732 0.999050i \(-0.486126\pi\)
−0.526783 + 0.850000i \(0.676602\pi\)
\(12\) −82.3843 1099.34i −0.165155 2.20384i
\(13\) 232.081 + 1016.82i 0.380875 + 1.66872i 0.694746 + 0.719255i \(0.255517\pi\)
−0.313871 + 0.949466i \(0.601626\pi\)
\(14\) −3.07634 1454.76i −0.00419482 1.98368i
\(15\) 109.770 480.935i 0.125967 0.551898i
\(16\) −4737.98 714.136i −4.62693 0.697398i
\(17\) −594.219 + 405.131i −0.498682 + 0.339996i −0.786398 0.617720i \(-0.788057\pi\)
0.287716 + 0.957716i \(0.407104\pi\)
\(18\) 590.363 1022.54i 0.429475 0.743872i
\(19\) 524.518 + 908.491i 0.333331 + 0.577347i 0.983163 0.182732i \(-0.0584939\pi\)
−0.649832 + 0.760078i \(0.725161\pi\)
\(20\) −3556.23 1712.59i −1.98799 0.957366i
\(21\) −854.559 + 1259.12i −0.422857 + 0.623044i
\(22\) 2051.68 988.039i 0.903762 0.435229i
\(23\) 1219.19 + 831.232i 0.480566 + 0.327644i 0.779256 0.626706i \(-0.215597\pi\)
−0.298690 + 0.954350i \(0.596550\pi\)
\(24\) 5978.65 + 5547.38i 2.11873 + 1.96589i
\(25\) 996.056 + 924.205i 0.318738 + 0.295746i
\(26\) −9669.90 6592.83i −2.80536 1.91266i
\(27\) −3682.61 + 1773.45i −0.972180 + 0.468177i
\(28\) 8300.59 + 8908.06i 2.00085 + 2.14728i
\(29\) −4384.19 2111.31i −0.968043 0.466185i −0.118066 0.993006i \(-0.537670\pi\)
−0.849976 + 0.526821i \(0.823384\pi\)
\(30\) 2767.78 + 4793.93i 0.561472 + 0.972498i
\(31\) −1057.40 + 1831.47i −0.197622 + 0.342291i −0.947757 0.318994i \(-0.896655\pi\)
0.750135 + 0.661285i \(0.229989\pi\)
\(32\) 26053.7 17763.1i 4.49773 3.06650i
\(33\) −2355.42 355.022i −0.376515 0.0567506i
\(34\) 1795.80 7867.93i 0.266417 1.16725i
\(35\) 2374.34 + 4903.81i 0.327622 + 0.676649i
\(36\) 2199.02 + 9634.55i 0.282796 + 1.23901i
\(37\) 121.590 + 1622.51i 0.0146014 + 0.194842i 0.999734 + 0.0230482i \(0.00733713\pi\)
−0.985133 + 0.171793i \(0.945044\pi\)
\(38\) −11248.7 3469.75i −1.26369 0.389798i
\(39\) 4472.60 + 11396.0i 0.470867 + 1.19975i
\(40\) 27903.8 8607.17i 2.75748 0.850571i
\(41\) −1482.43 1858.91i −0.137726 0.172703i 0.708185 0.706027i \(-0.249514\pi\)
−0.845911 + 0.533324i \(0.820943\pi\)
\(42\) −2580.73 16879.8i −0.225746 1.47653i
\(43\) −4480.15 + 5617.93i −0.369506 + 0.463345i −0.931471 0.363815i \(-0.881474\pi\)
0.561965 + 0.827161i \(0.310045\pi\)
\(44\) −6963.21 + 17742.0i −0.542223 + 1.38156i
\(45\) −330.461 + 4409.69i −0.0243270 + 0.324621i
\(46\) −16373.3 + 2467.88i −1.14088 + 0.171960i
\(47\) −8752.99 + 8121.59i −0.577979 + 0.536286i −0.914077 0.405541i \(-0.867083\pi\)
0.336098 + 0.941827i \(0.390893\pi\)
\(48\) −56242.3 −3.52338
\(49\) −1326.86 16754.5i −0.0789469 0.996879i
\(50\) −15247.4 −0.862524
\(51\) −6188.24 + 5741.85i −0.333151 + 0.309119i
\(52\) 96861.0 14599.4i 4.96753 0.748734i
\(53\) 56.4366 753.094i 0.00275976 0.0368264i −0.995654 0.0931306i \(-0.970313\pi\)
0.998414 + 0.0563041i \(0.0179316\pi\)
\(54\) 16756.8 42695.7i 0.782002 1.99251i
\(55\) −5317.48 + 6667.90i −0.237028 + 0.297223i
\(56\) −89840.8 6541.62i −3.82828 0.278750i
\(57\) 7677.35 + 9627.09i 0.312985 + 0.392471i
\(58\) 52178.4 16094.9i 2.03667 0.628229i
\(59\) −4512.45 11497.5i −0.168765 0.430006i 0.821321 0.570466i \(-0.193237\pi\)
−0.990086 + 0.140459i \(0.955142\pi\)
\(60\) −44272.6 13656.3i −1.58766 0.489728i
\(61\) −772.508 10308.4i −0.0265814 0.354704i −0.994597 0.103813i \(-0.966896\pi\)
0.968015 0.250891i \(-0.0807235\pi\)
\(62\) −5280.65 23136.0i −0.174465 0.764381i
\(63\) 5892.61 12302.6i 0.187050 0.390523i
\(64\) −44618.7 + 195487.i −1.36166 + 5.96580i
\(65\) 43342.5 + 6532.83i 1.27242 + 0.191786i
\(66\) 22085.0 15057.3i 0.624077 0.425489i
\(67\) 3478.95 6025.72i 0.0946806 0.163992i −0.814795 0.579750i \(-0.803150\pi\)
0.909475 + 0.415758i \(0.136484\pi\)
\(68\) 33772.9 + 58496.3i 0.885718 + 1.53411i
\(69\) 15605.2 + 7515.05i 0.394590 + 0.190024i
\(70\) −56959.3 22216.0i −1.38938 0.541902i
\(71\) 51538.0 24819.4i 1.21334 0.584313i 0.285889 0.958263i \(-0.407711\pi\)
0.927449 + 0.373950i \(0.121997\pi\)
\(72\) −60406.6 41184.5i −1.37326 0.936273i
\(73\) 23873.3 + 22151.2i 0.524330 + 0.486507i 0.897352 0.441315i \(-0.145488\pi\)
−0.373022 + 0.927822i \(0.621678\pi\)
\(74\) −13383.9 12418.5i −0.284122 0.263627i
\(75\) 13177.9 + 8984.55i 0.270516 + 0.184435i
\(76\) 88768.1 42748.5i 1.76288 0.848959i
\(77\) 22756.1 13202.5i 0.437392 0.253763i
\(78\) −123771. 59604.9i −2.30346 1.10929i
\(79\) 33902.2 + 58720.3i 0.611167 + 1.05857i 0.991044 + 0.133535i \(0.0426328\pi\)
−0.379878 + 0.925037i \(0.624034\pi\)
\(80\) −100685. + 174391.i −1.75889 + 3.04649i
\(81\) −18515.1 + 12623.4i −0.313555 + 0.213778i
\(82\) 26382.4 + 3976.51i 0.433291 + 0.0653081i
\(83\) 19560.6 85700.6i 0.311664 1.36549i −0.540116 0.841591i \(-0.681620\pi\)
0.851780 0.523900i \(-0.175523\pi\)
\(84\) 111928. + 88872.9i 1.73077 + 1.37427i
\(85\) 6725.64 + 29467.0i 0.100969 + 0.442373i
\(86\) −6025.67 80407.0i −0.0878535 1.17232i
\(87\) −54580.2 16835.8i −0.773102 0.238471i
\(88\) −51514.4 131257.i −0.709124 1.80682i
\(89\) −128358. + 39593.1i −1.71770 + 0.529840i −0.988070 0.154003i \(-0.950783\pi\)
−0.729629 + 0.683843i \(0.760307\pi\)
\(90\) −30938.6 38795.8i −0.402619 0.504868i
\(91\) −117240. 67358.1i −1.48413 0.852681i
\(92\) 86407.9 108352.i 1.06435 1.33465i
\(93\) −9069.00 + 23107.4i −0.108731 + 0.277041i
\(94\) 10013.0 133614.i 0.116881 1.55967i
\(95\) 43594.8 6570.85i 0.495593 0.0746987i
\(96\) 271325. 251753.i 3.00477 2.78802i
\(97\) 13844.3 0.149397 0.0746984 0.997206i \(-0.476201\pi\)
0.0746984 + 0.997206i \(0.476201\pi\)
\(98\) 138793. + 127693.i 1.45984 + 1.34308i
\(99\) 21352.8 0.218961
\(100\) 93549.4 86801.2i 0.935494 0.868012i
\(101\) 57037.9 8597.09i 0.556366 0.0838586i 0.135160 0.990824i \(-0.456845\pi\)
0.421206 + 0.906965i \(0.361607\pi\)
\(102\) 7079.05 94463.4i 0.0673712 0.899007i
\(103\) −64168.0 + 163497.i −0.595971 + 1.51851i 0.240584 + 0.970628i \(0.422661\pi\)
−0.836556 + 0.547882i \(0.815434\pi\)
\(104\) −451830. + 566578.i −4.09630 + 5.13660i
\(105\) 36137.5 + 52763.9i 0.319879 + 0.467051i
\(106\) 5283.74 + 6625.60i 0.0456748 + 0.0572744i
\(107\) −66777.4 + 20598.1i −0.563858 + 0.173927i −0.563563 0.826073i \(-0.690570\pi\)
−0.000294579 1.00000i \(0.500094\pi\)
\(108\) 140250. + 357351.i 1.15703 + 2.94805i
\(109\) 49806.9 + 15363.4i 0.401535 + 0.123857i 0.488944 0.872315i \(-0.337382\pi\)
−0.0874085 + 0.996173i \(0.527859\pi\)
\(110\) −7151.86 95434.9i −0.0563556 0.752013i
\(111\) 4249.77 + 18619.4i 0.0327384 + 0.143436i
\(112\) 484837. 388325.i 3.65217 2.92516i
\(113\) −4939.02 + 21639.3i −0.0363869 + 0.159421i −0.989857 0.142065i \(-0.954626\pi\)
0.953470 + 0.301487i \(0.0974828\pi\)
\(114\) −136631. 20593.9i −0.984665 0.148414i
\(115\) 51238.3 34933.7i 0.361285 0.246320i
\(116\) −228511. + 395792.i −1.57675 + 2.73101i
\(117\) −54870.8 95039.0i −0.370575 0.641856i
\(118\) 124874. + 60136.0i 0.825593 + 0.397584i
\(119\) 13701.2 92224.3i 0.0886933 0.597005i
\(120\) 308817. 148718.i 1.95771 0.942781i
\(121\) −99040.4 67524.6i −0.614963 0.419275i
\(122\) 85033.3 + 78899.4i 0.517237 + 0.479926i
\(123\) −20458.4 18982.6i −0.121930 0.113134i
\(124\) 164109. + 111888.i 0.958469 + 0.653473i
\(125\) 169776. 81759.8i 0.971855 0.468021i
\(126\) 45427.8 + 146175.i 0.254915 + 0.820251i
\(127\) −242586. 116823.i −1.33462 0.642717i −0.375789 0.926705i \(-0.622628\pi\)
−0.958828 + 0.283988i \(0.908342\pi\)
\(128\) −620502. 1.07474e6i −3.34748 5.79801i
\(129\) −42172.0 + 73044.1i −0.223126 + 0.386466i
\(130\) −406391. + 277073.i −2.10905 + 1.43792i
\(131\) 236358. + 35625.3i 1.20335 + 0.181376i 0.719952 0.694023i \(-0.244164\pi\)
0.483400 + 0.875400i \(0.339402\pi\)
\(132\) −49782.1 + 218110.i −0.248679 + 1.08953i
\(133\) −132653. 29982.1i −0.650260 0.146972i
\(134\) 17373.8 + 76119.8i 0.0835861 + 0.366214i
\(135\) 12837.0 + 171298.i 0.0606220 + 0.808944i
\(136\) −477509. 147292.i −2.21378 0.682860i
\(137\) −80174.9 204282.i −0.364953 0.929885i −0.988922 0.148436i \(-0.952576\pi\)
0.623969 0.781449i \(-0.285519\pi\)
\(138\) −185725. + 57288.4i −0.830179 + 0.256076i
\(139\) 221658. + 277950.i 0.973075 + 1.22020i 0.975455 + 0.220201i \(0.0706713\pi\)
−0.00237910 + 0.999997i \(0.500757\pi\)
\(140\) 475942. 187956.i 2.05227 0.810468i
\(141\) −87386.2 + 109579.i −0.370165 + 0.464172i
\(142\) −234511. + 597525.i −0.975984 + 2.48677i
\(143\) 15816.8 211061.i 0.0646813 0.863112i
\(144\) 498534. 75142.0i 2.00350 0.301979i
\(145\) −149912. + 139098.i −0.592130 + 0.549416i
\(146\) −365447. −1.41887
\(147\) −44711.9 192146.i −0.170659 0.733395i
\(148\) 152813. 0.573463
\(149\) 51951.4 48203.9i 0.191704 0.177875i −0.578481 0.815696i \(-0.696354\pi\)
0.770185 + 0.637820i \(0.220164\pi\)
\(150\) −176974. + 26674.6i −0.642217 + 0.0967987i
\(151\) 17940.7 239403.i 0.0640321 0.854449i −0.869036 0.494749i \(-0.835260\pi\)
0.933068 0.359700i \(-0.117121\pi\)
\(152\) −266296. + 678512.i −0.934881 + 2.38204i
\(153\) 47181.5 59163.7i 0.162946 0.204328i
\(154\) −86420.9 + 282288.i −0.293641 + 0.959158i
\(155\) 55414.2 + 69487.2i 0.185264 + 0.232314i
\(156\) 1.09871e6 338907.i 3.61469 1.11498i
\(157\) −75516.1 192412.i −0.244506 0.622992i 0.754956 0.655775i \(-0.227658\pi\)
−0.999462 + 0.0327831i \(0.989563\pi\)
\(158\) −727056. 224267.i −2.31700 0.714699i
\(159\) −662.449 8839.77i −0.00207807 0.0277299i
\(160\) −294887. 1.29199e6i −0.910660 3.98986i
\(161\) −186412. + 42962.2i −0.566773 + 0.130624i
\(162\) 55955.0 245155.i 0.167514 0.733927i
\(163\) 554839. + 83628.5i 1.63568 + 0.246539i 0.901614 0.432541i \(-0.142383\pi\)
0.734064 + 0.679080i \(0.237621\pi\)
\(164\) −184505. + 125793.i −0.535672 + 0.365215i
\(165\) −50053.9 + 86695.9i −0.143129 + 0.247907i
\(166\) 493206. + 854258.i 1.38918 + 2.40613i
\(167\) 254476. + 122549.i 0.706083 + 0.340032i 0.752228 0.658903i \(-0.228979\pi\)
−0.0461446 + 0.998935i \(0.514693\pi\)
\(168\) −1.05421e6 + 81244.4i −2.88174 + 0.222085i
\(169\) −645528. + 310870.i −1.73859 + 0.837263i
\(170\) −280231. 191058.i −0.743692 0.507041i
\(171\) −80914.5 75077.7i −0.211610 0.196345i
\(172\) 494715. + 459028.i 1.27507 + 1.18309i
\(173\) −79110.4 53936.6i −0.200964 0.137015i 0.458657 0.888614i \(-0.348331\pi\)
−0.659621 + 0.751599i \(0.729283\pi\)
\(174\) 577468. 278094.i 1.44596 0.696336i
\(175\) −175634. + 13535.5i −0.433524 + 0.0334102i
\(176\) 876062. + 421889.i 2.13183 + 1.02664i
\(177\) −72489.6 125556.i −0.173917 0.301233i
\(178\) 753660. 1.30538e6i 1.78289 3.08806i
\(179\) 164316. 112029.i 0.383309 0.261335i −0.356301 0.934371i \(-0.615962\pi\)
0.739610 + 0.673036i \(0.235010\pi\)
\(180\) 410680. + 61900.0i 0.944761 + 0.142400i
\(181\) 56657.5 248233.i 0.128547 0.563200i −0.869100 0.494636i \(-0.835301\pi\)
0.997647 0.0685635i \(-0.0218416\pi\)
\(182\) 1.47851e6 340751.i 3.30861 0.762532i
\(183\) −27000.4 118296.i −0.0595994 0.261122i
\(184\) 76619.4 + 1.02242e6i 0.166838 + 2.22630i
\(185\) 65341.4 + 20155.2i 0.140365 + 0.0432969i
\(186\) −101767. 259298.i −0.215687 0.549562i
\(187\) 139463. 43018.6i 0.291645 0.0899605i
\(188\) 699211. + 876783.i 1.44282 + 1.80925i
\(189\) 155119. 506685.i 0.315871 1.03177i
\(190\) −308453. + 386788.i −0.619876 + 0.777300i
\(191\) −49637.7 + 126475.i −0.0984528 + 0.250854i −0.971611 0.236583i \(-0.923973\pi\)
0.873159 + 0.487436i \(0.162068\pi\)
\(192\) −175887. + 2.34705e6i −0.344334 + 4.59482i
\(193\) −184605. + 27824.7i −0.356738 + 0.0537696i −0.324967 0.945726i \(-0.605353\pi\)
−0.0317717 + 0.999495i \(0.510115\pi\)
\(194\) −113881. + 105666.i −0.217244 + 0.201573i
\(195\) 514498. 0.968940
\(196\) −1.57850e6 + 6676.02i −2.93497 + 0.0124130i
\(197\) −473930. −0.870060 −0.435030 0.900416i \(-0.643262\pi\)
−0.435030 + 0.900416i \(0.643262\pi\)
\(198\) −175646. + 162975.i −0.318401 + 0.295433i
\(199\) 719085. 108385.i 1.28721 0.194015i 0.530452 0.847715i \(-0.322022\pi\)
0.756754 + 0.653700i \(0.226784\pi\)
\(200\) −70554.0 + 941477.i −0.124723 + 1.66431i
\(201\) 29837.9 76025.7i 0.0520928 0.132730i
\(202\) −403569. + 506060.i −0.695889 + 0.872617i
\(203\) 586751. 231716.i 0.999341 0.394653i
\(204\) 494332. + 619873.i 0.831656 + 1.04286i
\(205\) −95484.2 + 29453.0i −0.158689 + 0.0489491i
\(206\) −720055. 1.83467e6i −1.18222 3.01224i
\(207\) −148365. 45764.6i −0.240661 0.0742342i
\(208\) −373453. 4.98339e6i −0.598519 7.98668i
\(209\) −47371.2 207547.i −0.0750152 0.328663i
\(210\) −699983. 158210.i −1.09532 0.247563i
\(211\) −133135. + 583303.i −0.205867 + 0.901961i 0.761417 + 0.648263i \(0.224504\pi\)
−0.967283 + 0.253698i \(0.918353\pi\)
\(212\) −70136.6 10571.4i −0.107178 0.0161545i
\(213\) 554773. 378238.i 0.837850 0.571236i
\(214\) 392087. 679115.i 0.585259 1.01370i
\(215\) 150992. + 261527.i 0.222771 + 0.385851i
\(216\) −2.55878e6 1.23224e6i −3.73163 1.79706i
\(217\) −81365.8 261815.i −0.117299 0.377437i
\(218\) −526966. + 253774.i −0.751003 + 0.361664i
\(219\) 315845. + 215340.i 0.445004 + 0.303399i
\(220\) 587176. + 544819.i 0.817921 + 0.758920i
\(221\) −549851. 510187.i −0.757294 0.702666i
\(222\) −177071. 120725.i −0.241137 0.164405i
\(223\) −67370.3 + 32443.8i −0.0907207 + 0.0436888i −0.478694 0.877982i \(-0.658890\pi\)
0.387973 + 0.921671i \(0.373175\pi\)
\(224\) −600731. + 4.04359e6i −0.799945 + 5.38453i
\(225\) −128813. 62033.2i −0.169631 0.0816899i
\(226\) −124534. 215699.i −0.162187 0.280916i
\(227\) −57058.1 + 98827.6i −0.0734942 + 0.127296i −0.900430 0.435000i \(-0.856748\pi\)
0.826936 + 0.562296i \(0.190082\pi\)
\(228\) 955531. 651470.i 1.21733 0.829960i
\(229\) −583925. 88012.5i −0.735814 0.110906i −0.229565 0.973293i \(-0.573730\pi\)
−0.506249 + 0.862387i \(0.668968\pi\)
\(230\) −154849. + 678436.i −0.193013 + 0.845647i
\(231\) 241029. 193050.i 0.297194 0.238034i
\(232\) −752363. 3.29632e6i −0.917714 4.02077i
\(233\) 70062.9 + 934925.i 0.0845471 + 1.12820i 0.864591 + 0.502477i \(0.167578\pi\)
−0.780043 + 0.625725i \(0.784803\pi\)
\(234\) 1.17674e6 + 362978.i 1.40489 + 0.433351i
\(235\) 183334. + 467127.i 0.216557 + 0.551779i
\(236\) −1.10850e6 + 341926.i −1.29555 + 0.399625i
\(237\) 496225. + 622246.i 0.573862 + 0.719600i
\(238\) 591197. + 863199.i 0.676534 + 0.987799i
\(239\) 253121. 317404.i 0.286638 0.359433i −0.617577 0.786511i \(-0.711885\pi\)
0.904215 + 0.427078i \(0.140457\pi\)
\(240\) −863543. + 2.20027e6i −0.967733 + 2.46574i
\(241\) −114058. + 1.52200e6i −0.126498 + 1.68800i 0.467861 + 0.883802i \(0.345025\pi\)
−0.594359 + 0.804200i \(0.702594\pi\)
\(242\) 1.33007e6 200476.i 1.45995 0.220052i
\(243\) 535276. 496664.i 0.581517 0.539569i
\(244\) −970878. −1.04397
\(245\) −675832. 205340.i −0.719322 0.218554i
\(246\) 313173. 0.329949
\(247\) −802037. + 744181.i −0.836473 + 0.776133i
\(248\) −1.45301e6 + 219006.i −1.50016 + 0.226113i
\(249\) 77107.9 1.02893e6i 0.0788134 1.05169i
\(250\) −772524. + 1.96836e6i −0.781740 + 1.99184i
\(251\) 449935. 564201.i 0.450781 0.565262i −0.503568 0.863956i \(-0.667980\pi\)
0.954349 + 0.298694i \(0.0965510\pi\)
\(252\) −1.11087e6 638233.i −1.10195 0.633109i
\(253\) −186702. 234117.i −0.183379 0.229949i
\(254\) 2.88713e6 890563.i 2.80791 0.866124i
\(255\) 129614. + 330252.i 0.124825 + 0.318050i
\(256\) 7.17572e6 + 2.21342e6i 6.84330 + 2.11088i
\(257\) 141095. + 1.88279e6i 0.133254 + 1.77815i 0.518246 + 0.855232i \(0.326585\pi\)
−0.384992 + 0.922920i \(0.625796\pi\)
\(258\) −210607. 922729.i −0.196981 0.863028i
\(259\) −165193. 131166.i −0.153018 0.121499i
\(260\) 916052. 4.01348e6i 0.840401 3.68204i
\(261\) 506295. + 76311.7i 0.460047 + 0.0693409i
\(262\) −2.21616e6 + 1.51095e6i −1.99457 + 1.35987i
\(263\) −338340. + 586022.i −0.301623 + 0.522426i −0.976504 0.215501i \(-0.930862\pi\)
0.674881 + 0.737927i \(0.264195\pi\)
\(264\) −827546. 1.43335e6i −0.730773 1.26574i
\(265\) −28595.5 13770.9i −0.0250140 0.0120461i
\(266\) 1.32002e6 765842.i 1.14387 0.663644i
\(267\) −1.42056e6 + 684106.i −1.21950 + 0.587280i
\(268\) −539934. 368121.i −0.459202 0.313079i
\(269\) −380261. 352831.i −0.320406 0.297294i 0.503528 0.863979i \(-0.332035\pi\)
−0.823934 + 0.566685i \(0.808226\pi\)
\(270\) −1.41303e6 1.31110e6i −1.17962 1.09453i
\(271\) 156246. + 106527.i 0.129237 + 0.0881120i 0.626213 0.779652i \(-0.284604\pi\)
−0.496976 + 0.867764i \(0.665556\pi\)
\(272\) 3.10471e6 1.49515e6i 2.54448 1.22536i
\(273\) −1.47862e6 576710.i −1.20074 0.468329i
\(274\) 2.21869e6 + 1.06847e6i 1.78534 + 0.859774i
\(275\) −137871. 238800.i −0.109936 0.190415i
\(276\) 813366. 1.40879e6i 0.642707 1.11320i
\(277\) −1.35523e6 + 923980.i −1.06124 + 0.723541i −0.962420 0.271564i \(-0.912459\pi\)
−0.0988194 + 0.995105i \(0.531507\pi\)
\(278\) −3.94478e6 594580.i −3.06134 0.461422i
\(279\) 49515.6 216942.i 0.0380830 0.166853i
\(280\) −1.63533e6 + 3.41425e6i −1.24655 + 2.60255i
\(281\) 182609. + 800062.i 0.137961 + 0.604446i 0.995882 + 0.0906640i \(0.0288989\pi\)
−0.857921 + 0.513782i \(0.828244\pi\)
\(282\) −117532. 1.56835e6i −0.0880102 1.17441i
\(283\) 1.58766e6 + 489728.i 1.17840 + 0.363487i 0.821254 0.570563i \(-0.193275\pi\)
0.357142 + 0.934050i \(0.383751\pi\)
\(284\) −1.96279e6 5.00110e6i −1.44404 3.67934i
\(285\) 494502. 152534.i 0.360625 0.111238i
\(286\) 1.48081e6 + 1.85688e6i 1.07049 + 1.34236i
\(287\) 307427. + 22384.8i 0.220312 + 0.0160416i
\(288\) −2.06868e6 + 2.59405e6i −1.46965 + 1.84288i
\(289\) −329768. + 840234.i −0.232254 + 0.591774i
\(290\) 171492. 2.28841e6i 0.119743 1.59786i
\(291\) 160688. 24219.9i 0.111238 0.0167664i
\(292\) 2.24217e6 2.08043e6i 1.53891 1.42790i
\(293\) −1.00835e6 −0.686187 −0.343094 0.939301i \(-0.611475\pi\)
−0.343094 + 0.939301i \(0.611475\pi\)
\(294\) 1.83435e6 + 1.23930e6i 1.23769 + 0.836199i
\(295\) −519082. −0.347281
\(296\) −828731. + 768950.i −0.549774 + 0.510116i
\(297\) 820205. 123626.i 0.539549 0.0813240i
\(298\) −59429.9 + 793037.i −0.0387672 + 0.517312i
\(299\) −562257. + 1.43261e6i −0.363711 + 0.926721i
\(300\) 933959. 1.17115e6i 0.599135 0.751291i
\(301\) −140789. 920853.i −0.0895676 0.585834i
\(302\) 1.67966e6 + 2.10623e6i 1.05975 + 1.32889i
\(303\) 646990. 199570.i 0.404847 0.124879i
\(304\) −1.83637e6 4.67899e6i −1.13966 2.90381i
\(305\) −415139. 128053.i −0.255531 0.0788209i
\(306\) 63457.8 + 846786.i 0.0387420 + 0.516975i
\(307\) −133665. 585626.i −0.0809418 0.354629i 0.918197 0.396124i \(-0.129645\pi\)
−0.999139 + 0.0414951i \(0.986788\pi\)
\(308\) −1.07679e6 2.22394e6i −0.646777 1.33581i
\(309\) −458757. + 2.00995e6i −0.273329 + 1.19753i
\(310\) −986190. 148644.i −0.582850 0.0878504i
\(311\) 2.04860e6 1.39671e6i 1.20104 0.818852i 0.213607 0.976920i \(-0.431479\pi\)
0.987428 + 0.158068i \(0.0505264\pi\)
\(312\) −4.25312e6 + 7.36663e6i −2.47355 + 4.28432i
\(313\) 107595. + 186359.i 0.0620769 + 0.107520i 0.895394 0.445276i \(-0.146894\pi\)
−0.833317 + 0.552796i \(0.813561\pi\)
\(314\) 2.08977e6 + 1.00638e6i 1.19612 + 0.576020i
\(315\) −390819. 419421.i −0.221922 0.238163i
\(316\) 5.73752e6 2.76304e6i 3.23226 1.55658i
\(317\) −764427. 521178.i −0.427256 0.291298i 0.330537 0.943793i \(-0.392770\pi\)
−0.757793 + 0.652495i \(0.773722\pi\)
\(318\) 72918.7 + 67658.6i 0.0404363 + 0.0375194i
\(319\) 723883. + 671665.i 0.398283 + 0.369552i
\(320\) 6.96264e6 + 4.74705e6i 3.80101 + 2.59149i
\(321\) −739038. + 355902.i −0.400317 + 0.192783i
\(322\) 1.20549e6 1.77619e6i 0.647924 0.954662i
\(323\) −679736. 327344.i −0.362522 0.174581i
\(324\) 1.05232e6 + 1.82267e6i 0.556910 + 0.964597i
\(325\) −708580. + 1.22730e6i −0.372118 + 0.644527i
\(326\) −5.20233e6 + 3.54689e6i −2.71115 + 1.84843i
\(327\) 604978. + 91185.8i 0.312875 + 0.0471583i
\(328\) 367615. 1.61063e6i 0.188672 0.826628i
\(329\) −3273.47 1.54798e6i −0.00166732 0.788453i
\(330\) −249969. 1.09518e6i −0.126357 0.553608i
\(331\) 143905. + 1.92028e6i 0.0721949 + 0.963374i 0.909249 + 0.416253i \(0.136657\pi\)
−0.837054 + 0.547121i \(0.815724\pi\)
\(332\) −7.88919e6 2.43349e6i −3.92814 1.21167i
\(333\) −62546.4 159366.i −0.0309095 0.0787561i
\(334\) −3.02864e6 + 934213.i −1.48553 + 0.458226i
\(335\) −182318. 228620.i −0.0887601 0.111302i
\(336\) 4.94806e6 5.35541e6i 2.39104 2.58788i
\(337\) 1.19825e6 1.50256e6i 0.574742 0.720704i −0.406464 0.913667i \(-0.633238\pi\)
0.981206 + 0.192963i \(0.0618097\pi\)
\(338\) 2.93732e6 7.48416e6i 1.39849 3.56329i
\(339\) −19469.6 + 259804.i −0.00920148 + 0.122785i
\(340\) 2.80700e6 423087.i 1.31688 0.198487i
\(341\) 314599. 291906.i 0.146512 0.135943i
\(342\) 1.23862e6 0.572629
\(343\) 1.71211e6 + 1.34768e6i 0.785771 + 0.618517i
\(344\) −4.99275e6 −2.27480
\(345\) 533600. 495108.i 0.241361 0.223951i
\(346\) 1.06242e6 160134.i 0.477097 0.0719108i
\(347\) −69184.9 + 923209.i −0.0308452 + 0.411601i 0.960314 + 0.278922i \(0.0899770\pi\)
−0.991159 + 0.132679i \(0.957642\pi\)
\(348\) −1.95987e6 + 4.99366e6i −0.867519 + 2.21040i
\(349\) 1.19003e6 1.49225e6i 0.522991 0.655809i −0.448250 0.893908i \(-0.647953\pi\)
0.971241 + 0.238099i \(0.0765241\pi\)
\(350\) 1.34143e6 1.45187e6i 0.585327 0.633514i
\(351\) −2.65794e6 3.33295e6i −1.15154 1.44398i
\(352\) −6.11478e6 + 1.88616e6i −2.63041 + 0.811375i
\(353\) 358517. + 913485.i 0.153134 + 0.390180i 0.986768 0.162138i \(-0.0518388\pi\)
−0.833634 + 0.552318i \(0.813744\pi\)
\(354\) 1.55459e6 + 479528.i 0.659338 + 0.203379i
\(355\) −179654. 2.39731e6i −0.0756598 1.00961i
\(356\) 2.80728e6 + 1.22995e7i 1.17398 + 5.14355i
\(357\) −2314.30 1.09440e6i −0.000961056 0.454471i
\(358\) −496585. + 2.17568e6i −0.204779 + 0.897196i
\(359\) 1.49673e6 + 225595.i 0.612924 + 0.0923835i 0.448166 0.893950i \(-0.352077\pi\)
0.164758 + 0.986334i \(0.447316\pi\)
\(360\) −2.53867e6 + 1.73084e6i −1.03241 + 0.703882i
\(361\) 687812. 1.19133e6i 0.277781 0.481130i
\(362\) 1.42858e6 + 2.47437e6i 0.572970 + 0.992414i
\(363\) −1.26768e6 610481.i −0.504942 0.243167i
\(364\) −7.13144e6 + 1.05076e7i −2.82113 + 4.15670i
\(365\) 1.23313e6 593845.i 0.484481 0.233314i
\(366\) 1.12500e6 + 767010.i 0.438984 + 0.299294i
\(367\) −1.64608e6 1.52733e6i −0.637947 0.591928i 0.293432 0.955980i \(-0.405203\pi\)
−0.931379 + 0.364052i \(0.881393\pi\)
\(368\) −5.18290e6 4.80903e6i −1.99505 1.85113i
\(369\) 206706. + 140930.i 0.0790291 + 0.0538811i
\(370\) −691324. + 332924.i −0.262529 + 0.126427i
\(371\) 66744.8 + 71629.4i 0.0251758 + 0.0270182i
\(372\) 2.10053e6 + 1.01156e6i 0.786993 + 0.378996i
\(373\) 2.17578e6 + 3.76856e6i 0.809735 + 1.40250i 0.913048 + 0.407853i \(0.133722\pi\)
−0.103313 + 0.994649i \(0.532944\pi\)
\(374\) −818864. + 1.41831e6i −0.302714 + 0.524316i
\(375\) 1.82753e6 1.24599e6i 0.671098 0.457547i
\(376\) −8.20390e6 1.23654e6i −2.99261 0.451064i
\(377\) 1.12933e6 4.94791e6i 0.409229 1.79295i
\(378\) 2.59128e6 + 5.35186e6i 0.932791 + 1.92653i
\(379\) −8023.12 35151.6i −0.00286910 0.0125703i 0.973473 0.228801i \(-0.0734807\pi\)
−0.976342 + 0.216231i \(0.930624\pi\)
\(380\) −309432. 4.12908e6i −0.109927 1.46688i
\(381\) −3.02003e6 931556.i −1.06586 0.328773i
\(382\) −557004. 1.41922e6i −0.195299 0.497614i
\(383\) 4.63827e6 1.43072e6i 1.61569 0.498376i 0.650412 0.759582i \(-0.274596\pi\)
0.965283 + 0.261206i \(0.0841203\pi\)
\(384\) −9.08227e6 1.13888e7i −3.14316 3.94140i
\(385\) −167102. 1.09296e6i −0.0574551 0.375796i
\(386\) 1.30616e6 1.63788e6i 0.446200 0.559517i
\(387\) 276225. 703810.i 0.0937531 0.238879i
\(388\) 97168.0 1.29662e6i 0.0327676 0.437253i
\(389\) 4.43227e6 668057.i 1.48509 0.223841i 0.644119 0.764925i \(-0.277224\pi\)
0.840968 + 0.541084i \(0.181986\pi\)
\(390\) −4.23219e6 + 3.92690e6i −1.40898 + 1.30734i
\(391\) −1.06123e6 −0.351047
\(392\) 8.52688e6 7.97916e6i 2.80269 2.62266i
\(393\) 2.80570e6 0.916346
\(394\) 3.89849e6 3.61727e6i 1.26519 1.17392i
\(395\) 2.81774e6 424707.i 0.908676 0.136961i
\(396\) 149868. 1.99985e6i 0.0480253 0.640854i
\(397\) 1.66172e6 4.23398e6i 0.529152 1.34826i −0.377356 0.926068i \(-0.623167\pi\)
0.906508 0.422189i \(-0.138738\pi\)
\(398\) −5.08786e6 + 6.37997e6i −1.61000 + 2.01888i
\(399\) −1.59213e6 115928.i −0.500664 0.0364551i
\(400\) −4.05929e6 5.09019e6i −1.26853 1.59068i
\(401\) −5.49437e6 + 1.69479e6i −1.70631 + 0.526326i −0.985916 0.167242i \(-0.946514\pi\)
−0.720391 + 0.693568i \(0.756038\pi\)
\(402\) 334823. + 853115.i 0.103336 + 0.263295i
\(403\) −2.10767e6 650130.i −0.646458 0.199406i
\(404\) −404850. 5.40235e6i −0.123407 1.64676i
\(405\) 209563. + 918154.i 0.0634858 + 0.278149i
\(406\) −3.05797e6 + 6.38444e6i −0.920699 + 1.92224i
\(407\) 73472.9 321906.i 0.0219857 0.0963258i
\(408\) −5.80004e6 874216.i −1.72497 0.259997i
\(409\) −3.77550e6 + 2.57409e6i −1.11600 + 0.760879i −0.973448 0.228907i \(-0.926485\pi\)
−0.142557 + 0.989787i \(0.545532\pi\)
\(410\) 560641. 971059.i 0.164712 0.285289i
\(411\) −1.28796e6 2.23081e6i −0.376095 0.651415i
\(412\) 1.48623e7 + 7.15732e6i 4.31364 + 2.07734i
\(413\) 1.49180e6 + 581849.i 0.430362 + 0.167855i
\(414\) 1.56973e6 755943.i 0.450116 0.216764i
\(415\) −3.05238e6 2.08108e6i −0.870000 0.593156i
\(416\) 2.41083e7 + 2.23693e7i 6.83021 + 6.33751i
\(417\) 3.05901e6 + 2.83834e6i 0.861471 + 0.799328i
\(418\) 1.97377e6 + 1.34569e6i 0.552530 + 0.376708i
\(419\) −3.05120e6 + 1.46938e6i −0.849055 + 0.408883i −0.807227 0.590242i \(-0.799032\pi\)
−0.0418280 + 0.999125i \(0.513318\pi\)
\(420\) 5.19536e6 3.01421e6i 1.43712 0.833777i
\(421\) −4.17672e6 2.01140e6i −1.14850 0.553088i −0.239916 0.970794i \(-0.577120\pi\)
−0.908582 + 0.417706i \(0.862834\pi\)
\(422\) −3.35690e6 5.81432e6i −0.917608 1.58934i
\(423\) 628194. 1.08806e6i 0.170704 0.295667i
\(424\) 433558. 295595.i 0.117120 0.0798514i
\(425\) −966300. 145646.i −0.259501 0.0391135i
\(426\) −1.67659e6 + 7.34563e6i −0.447614 + 1.96112i
\(427\) 1.04953e6 + 833350.i 0.278565 + 0.221186i
\(428\) 1.46047e6 + 6.39875e6i 0.385375 + 1.68844i
\(429\) −185657. 2.47742e6i −0.0487043 0.649914i
\(430\) −3.23814e6 998835.i −0.844549 0.260509i
\(431\) 785126. + 2.00047e6i 0.203585 + 0.518726i 0.995804 0.0915105i \(-0.0291695\pi\)
−0.792219 + 0.610237i \(0.791074\pi\)
\(432\) 1.87146e7 5.77270e6i 4.82472 1.48823i
\(433\) −981714. 1.23103e6i −0.251632 0.315536i 0.639932 0.768431i \(-0.278962\pi\)
−0.891564 + 0.452896i \(0.850391\pi\)
\(434\) 2.66760e6 + 1.53263e6i 0.679824 + 0.390582i
\(435\) −1.49666e6 + 1.87675e6i −0.379228 + 0.475536i
\(436\) 1.78847e6 4.55695e6i 0.450573 1.14804i
\(437\) −115678. + 1.54362e6i −0.0289767 + 0.386667i
\(438\) −4.24168e6 + 639331.i −1.05646 + 0.159236i
\(439\) −1.49087e6 + 1.38332e6i −0.369213 + 0.342580i −0.842858 0.538136i \(-0.819129\pi\)
0.473645 + 0.880716i \(0.342938\pi\)
\(440\) −5.92588e6 −1.45922
\(441\) 653043. + 1.64345e6i 0.159899 + 0.402403i
\(442\) 8.41700e6 2.04928
\(443\) −4.26719e6 + 3.95937e6i −1.03308 + 0.958555i −0.999164 0.0408703i \(-0.986987\pi\)
−0.0339116 + 0.999425i \(0.510796\pi\)
\(444\) 1.77367e6 267338.i 0.426988 0.0643581i
\(445\) −421868. + 5.62943e6i −0.100989 + 1.34761i
\(446\) 306552. 781082.i 0.0729738 0.185934i
\(447\) 518661. 650380.i 0.122776 0.153957i
\(448\) −1.46889e7 2.14471e7i −3.45776 5.04864i
\(449\) 3.31098e6 + 4.15184e6i 0.775071 + 0.971908i 0.999997 0.00246804i \(-0.000785601\pi\)
−0.224926 + 0.974376i \(0.572214\pi\)
\(450\) 1.53307e6 472889.i 0.356887 0.110085i
\(451\) 176278. + 449149.i 0.0408090 + 0.103980i
\(452\) 1.99201e6 + 614453.i 0.458611 + 0.141463i
\(453\) −210587. 2.81009e6i −0.0482155 0.643391i
\(454\) −284948. 1.24844e6i −0.0648822 0.284268i
\(455\) −4.43523e6 + 3.55235e6i −1.00436 + 0.804428i
\(456\) −1.90384e6 + 8.34125e6i −0.428763 + 1.87853i
\(457\) −1.29661e6 195432.i −0.290415 0.0437730i 0.00221918 0.999998i \(-0.499294\pi\)
−0.292634 + 0.956225i \(0.594532\pi\)
\(458\) 5.47504e6 3.73282e6i 1.21962 0.831521i
\(459\) 1.46980e6 2.54576e6i 0.325631 0.564009i
\(460\) −2.91217e6 5.04402e6i −0.641685 1.11143i
\(461\) −4.31793e6 2.07940e6i −0.946288 0.455708i −0.103905 0.994587i \(-0.533134\pi\)
−0.842383 + 0.538879i \(0.818848\pi\)
\(462\) −509225. + 3.42766e6i −0.110995 + 0.747123i
\(463\) 418109. 201351.i 0.0906435 0.0436516i −0.388013 0.921654i \(-0.626838\pi\)
0.478656 + 0.878002i \(0.341124\pi\)
\(464\) 1.92644e7 + 1.31343e7i 4.15395 + 2.83212i
\(465\) 764748. + 709582.i 0.164016 + 0.152184i
\(466\) −7.71214e6 7.15582e6i −1.64517 1.52649i
\(467\) 4.34088e6 + 2.95956e6i 0.921056 + 0.627965i 0.928229 0.372009i \(-0.121331\pi\)
−0.00717350 + 0.999974i \(0.502283\pi\)
\(468\) −9.28621e6 + 4.47200e6i −1.95985 + 0.943816i
\(469\) 267701. + 861395.i 0.0561977 + 0.180830i
\(470\) −5.07342e6 2.44323e6i −1.05939 0.510176i
\(471\) −1.21312e6 2.10118e6i −0.251971 0.436427i
\(472\) 4.29102e6 7.43227e6i 0.886555 1.53556i
\(473\) 1.20482e6 821432.i 0.247611 0.168818i
\(474\) −8.83117e6 1.33108e6i −1.80540 0.272120i
\(475\) −317183. + 1.38967e6i −0.0645024 + 0.282604i
\(476\) −8.54130e6 1.93050e6i −1.72785 0.390529i
\(477\) 17682.3 + 77471.1i 0.00355829 + 0.0155899i
\(478\) 340441. + 4.54287e6i 0.0681510 + 0.909412i
\(479\) −670826. 206923.i −0.133589 0.0412068i 0.227240 0.973839i \(-0.427030\pi\)
−0.360829 + 0.932632i \(0.617506\pi\)
\(480\) −5.68297e6 1.44800e7i −1.12583 2.86857i
\(481\) −1.62157e6 + 500188.i −0.319575 + 0.0985759i
\(482\) −1.06784e7 1.33903e7i −2.09358 2.62527i
\(483\) −2.08849e6 + 824774.i −0.407347 + 0.160867i
\(484\) −7.01929e6 + 8.80192e6i −1.36201 + 1.70791i
\(485\) 212565. 541607.i 0.0410334 0.104551i
\(486\) −612330. + 8.17098e6i −0.117597 + 1.56922i
\(487\) 6.42909e6 969029.i 1.22836 0.185146i 0.497375 0.867536i \(-0.334297\pi\)
0.730989 + 0.682390i \(0.239059\pi\)
\(488\) 5.26525e6 4.88543e6i 1.00085 0.928653i
\(489\) 6.58623e6 1.24556
\(490\) 7.12656e6 3.46918e6i 1.34088 0.652734i
\(491\) −1.44689e6 −0.270852 −0.135426 0.990787i \(-0.543240\pi\)
−0.135426 + 0.990787i \(0.543240\pi\)
\(492\) −1.92145e6 + 1.78284e6i −0.357863 + 0.332048i
\(493\) 3.46053e6 521591.i 0.641247 0.0966524i
\(494\) 917492. 1.22431e7i 0.169155 2.25722i
\(495\) 327851. 835351.i 0.0601400 0.153234i
\(496\) 6.31786e6 7.92235e6i 1.15310 1.44594i
\(497\) −2.17088e6 + 7.09103e6i −0.394226 + 1.28771i
\(498\) 7.21904e6 + 9.05239e6i 1.30439 + 1.63565i
\(499\) 929544. 286726.i 0.167116 0.0515485i −0.210068 0.977687i \(-0.567369\pi\)
0.377184 + 0.926138i \(0.376892\pi\)
\(500\) −6.46580e6 1.64746e7i −1.15664 2.94706i
\(501\) 3.16806e6 + 977216.i 0.563896 + 0.173939i
\(502\) 605150. + 8.07517e6i 0.107178 + 1.43019i
\(503\) 500496. + 2.19282e6i 0.0882025 + 0.386440i 0.999690 0.0248868i \(-0.00792252\pi\)
−0.911488 + 0.411327i \(0.865065\pi\)
\(504\) 9.23603e6 2.12862e6i 1.61960 0.373269i
\(505\) 539430. 2.36340e6i 0.0941254 0.412390i
\(506\) 3.32269e6 + 500815.i 0.576917 + 0.0869562i
\(507\) −6.94868e6 + 4.73753e6i −1.20056 + 0.818526i
\(508\) −1.26440e7 + 2.19000e7i −2.17382 + 3.76517i
\(509\) −2.98995e6 5.17874e6i −0.511528 0.885993i −0.999911 0.0133630i \(-0.995746\pi\)
0.488383 0.872630i \(-0.337587\pi\)
\(510\) −3.58684e6 1.72733e6i −0.610641 0.294069i
\(511\) −4.20956e6 + 324416.i −0.713155 + 0.0549604i
\(512\) −4.01410e7 + 1.93309e7i −6.76727 + 3.25894i
\(513\) −3.54276e6 2.41542e6i −0.594359 0.405227i
\(514\) −1.55310e7 1.44107e7i −2.59293 2.40589i
\(515\) 5.41099e6 + 5.02067e6i 0.898999 + 0.834149i
\(516\) 6.54512e6 + 4.46238e6i 1.08216 + 0.737807i
\(517\) 2.18316e6 1.05135e6i 0.359219 0.172991i
\(518\) 2.35998e6 181876.i 0.386442 0.0297817i
\(519\) −1.01258e6 487633.i −0.165010 0.0794648i
\(520\) 1.52278e7 + 2.63754e7i 2.46962 + 4.27751i
\(521\) −4.52940e6 + 7.84515e6i −0.731049 + 1.26621i 0.225386 + 0.974270i \(0.427636\pi\)
−0.956435 + 0.291945i \(0.905698\pi\)
\(522\) −4.74716e6 + 3.23656e6i −0.762532 + 0.519885i
\(523\) 1.10083e7 + 1.65924e6i 1.75982 + 0.265250i 0.947910 0.318538i \(-0.103192\pi\)
0.811906 + 0.583788i \(0.198430\pi\)
\(524\) 4.99548e6 2.18866e7i 0.794784 3.48217i
\(525\) −2.01487e6 + 464367.i −0.319043 + 0.0735297i
\(526\) −1.68967e6 7.40292e6i −0.266279 1.16664i
\(527\) −113659. 1.51668e6i −0.0178270 0.237885i
\(528\) 1.09064e7 + 3.36417e6i 1.70253 + 0.525162i
\(529\) −1.55598e6 3.96456e6i −0.241748 0.615965i
\(530\) 340329. 104977.i 0.0526270 0.0162333i
\(531\) 810299. + 1.01608e6i 0.124712 + 0.156384i
\(532\) −3.73908e6 + 1.22134e7i −0.572778 + 1.87094i
\(533\) 1.54612e6 1.93878e6i 0.235736 0.295604i
\(534\) 6.46391e6 1.64698e7i 0.980940 2.49939i
\(535\) −219474. + 2.92868e6i −0.0331512 + 0.442372i
\(536\) 4.78054e6 720550.i 0.718728 0.108331i
\(537\) 1.71120e6 1.58777e6i 0.256074 0.237602i
\(538\) 5.82095e6 0.867039
\(539\) −744883. + 3.32837e6i −0.110437 + 0.493469i
\(540\) 1.61334e7 2.38090
\(541\) 2.65625e6 2.46464e6i 0.390190 0.362043i −0.460547 0.887635i \(-0.652347\pi\)
0.850737 + 0.525592i \(0.176156\pi\)
\(542\) −2.09832e6 + 316271.i −0.306813 + 0.0462446i
\(543\) 223344. 2.98031e6i 0.0325068 0.433773i
\(544\) −8.28518e6 + 2.11103e7i −1.20034 + 3.05842i
\(545\) 1.36577e6 1.71262e6i 0.196964 0.246985i
\(546\) 1.65647e7 6.54161e6i 2.37794 0.939081i
\(547\) −733644. 919960.i −0.104838 0.131462i 0.726645 0.687013i \(-0.241079\pi\)
−0.831482 + 0.555551i \(0.812507\pi\)
\(548\) −1.96952e7 + 6.07517e6i −2.80162 + 0.864186i
\(549\) 397381. + 1.01251e6i 0.0562700 + 0.143374i
\(550\) 2.95675e6 + 912035.i 0.416780 + 0.128560i
\(551\) −381474. 5.09042e6i −0.0535286 0.714290i
\(552\) 2.67797e6 + 1.17330e7i 0.374075 + 1.63893i
\(553\) −8.57400e6 1.93789e6i −1.19226 0.269474i
\(554\) 4.09567e6 1.79443e7i 0.566958 2.48400i
\(555\) 793667. + 119626.i 0.109372 + 0.0164852i
\(556\) 2.75878e7 1.88090e7i 3.78469 2.58036i
\(557\) −801217. + 1.38775e6i −0.109424 + 0.189528i −0.915537 0.402234i \(-0.868234\pi\)
0.806113 + 0.591761i \(0.201567\pi\)
\(558\) 1.24850e6 + 2.16246e6i 0.169747 + 0.294011i
\(559\) −6.75215e6 3.25166e6i −0.913929 0.440125i
\(560\) −7.74758e6 2.49298e7i −1.04399 3.35929i
\(561\) 1.54346e6 743292.i 0.207056 0.0997132i
\(562\) −7.60858e6 5.18744e6i −1.01616 0.692807i
\(563\) 802603. + 744707.i 0.106716 + 0.0990181i 0.731727 0.681598i \(-0.238715\pi\)
−0.625010 + 0.780616i \(0.714905\pi\)
\(564\) 9.64951e6 + 8.95344e6i 1.27734 + 1.18520i
\(565\) 770722. + 525469.i 0.101573 + 0.0692510i
\(566\) −1.67977e7 + 8.08935e6i −2.20399 + 1.06138i
\(567\) 426912. 2.87359e6i 0.0557674 0.375377i
\(568\) 3.58100e7 + 1.72452e7i 4.65729 + 2.24283i
\(569\) 2.72840e6 + 4.72572e6i 0.353286 + 0.611910i 0.986823 0.161803i \(-0.0517309\pi\)
−0.633537 + 0.773712i \(0.718398\pi\)
\(570\) −2.90350e6 + 5.02900e6i −0.374312 + 0.648328i
\(571\) −2.20105e6 + 1.50065e6i −0.282513 + 0.192614i −0.696283 0.717767i \(-0.745164\pi\)
0.413770 + 0.910381i \(0.364212\pi\)
\(572\) −1.96563e7 2.96272e6i −2.51196 0.378617i
\(573\) −354875. + 1.55481e6i −0.0451532 + 0.197829i
\(574\) −2.69971e6 + 2.16230e6i −0.342009 + 0.273928i
\(575\) 446156. + 1.95474e6i 0.0562752 + 0.246558i
\(576\) −1.57668e6 2.10393e7i −0.198010 2.64226i
\(577\) 1.23627e7 + 3.81339e6i 1.54587 + 0.476839i 0.946248 0.323442i \(-0.104840\pi\)
0.599626 + 0.800281i \(0.295316\pi\)
\(578\) −3.70046e6 9.42861e6i −0.460718 1.17389i
\(579\) −2.09400e6 + 645913.i −0.259585 + 0.0800715i
\(580\) 1.19754e7 + 1.50166e7i 1.47815 + 1.85354i
\(581\) 6.43955e6 + 9.40231e6i 0.791435 + 1.15556i
\(582\) −1.13694e6 + 1.42568e6i −0.139133 + 0.174468i
\(583\) −55990.9 + 142662.i −0.00682254 + 0.0173835i
\(584\) −1.69102e6 + 2.25651e7i −0.205172 + 2.73782i
\(585\) −4.56053e6 + 687390.i −0.550968 + 0.0830450i
\(586\) 8.29456e6 7.69623e6i 0.997813 0.925836i
\(587\) −2.07367e6 −0.248396 −0.124198 0.992257i \(-0.539636\pi\)
−0.124198 + 0.992257i \(0.539636\pi\)
\(588\) −1.83097e7 + 2.83899e6i −2.18392 + 0.338626i
\(589\) −2.21850e6 −0.263494
\(590\) 4.26990e6 3.96189e6i 0.504996 0.468568i
\(591\) −5.50083e6 + 829117.i −0.647828 + 0.0976443i
\(592\) 582598. 7.77423e6i 0.0683227 0.911703i
\(593\) 3.52514e6 8.98191e6i 0.411661 1.04889i −0.563248 0.826288i \(-0.690448\pi\)
0.974908 0.222607i \(-0.0714565\pi\)
\(594\) −5.80332e6 + 7.27714e6i −0.674855 + 0.846242i
\(595\) −3.39756e6 1.95202e6i −0.393437 0.226043i
\(596\) −4.15001e6 5.20395e6i −0.478557 0.600091i
\(597\) 8.15669e6 2.51601e6i 0.936652 0.288919i
\(598\) −6.30931e6 1.60759e7i −0.721488 1.83832i
\(599\) 7.38282e6 + 2.27730e6i 0.840727 + 0.259330i 0.685066 0.728481i \(-0.259773\pi\)
0.155661 + 0.987811i \(0.450249\pi\)
\(600\) 828158. + 1.10510e7i 0.0939150 + 1.25321i
\(601\) −2.78219e6 1.21896e7i −0.314196 1.37658i −0.847561 0.530697i \(-0.821930\pi\)
0.533365 0.845885i \(-0.320927\pi\)
\(602\) 8.18651e6 + 6.50025e6i 0.920678 + 0.731036i
\(603\) −162911. + 713760.i −0.0182456 + 0.0799391i
\(604\) −2.22958e7 3.36056e6i −2.48675 0.374817i
\(605\) −4.16231e6 + 2.83782e6i −0.462324 + 0.315207i
\(606\) −3.79884e6 + 6.57978e6i −0.420213 + 0.727830i
\(607\) −3.78867e6 6.56217e6i −0.417364 0.722895i 0.578310 0.815817i \(-0.303713\pi\)
−0.995673 + 0.0929221i \(0.970379\pi\)
\(608\) 2.98032e7 + 1.43525e7i 3.26967 + 1.57459i
\(609\) 6.40495e6 3.71598e6i 0.699797 0.406004i
\(610\) 4.39224e6 2.11519e6i 0.477927 0.230158i
\(611\) −1.02896e7 7.01530e6i −1.11505 0.760227i
\(612\) −5.20996e6 4.83414e6i −0.562284 0.521723i
\(613\) 5.88683e6 + 5.46218e6i 0.632747 + 0.587103i 0.929939 0.367714i \(-0.119860\pi\)
−0.297192 + 0.954818i \(0.596050\pi\)
\(614\) 5.56930e6 + 3.79708e6i 0.596183 + 0.406471i
\(615\) −1.05674e6 + 508900.i −0.112663 + 0.0542557i
\(616\) 1.70304e7 + 6.64243e6i 1.80831 + 0.705302i
\(617\) 1.31396e7 + 6.32770e6i 1.38953 + 0.669164i 0.971009 0.239041i \(-0.0768330\pi\)
0.418525 + 0.908205i \(0.362547\pi\)
\(618\) −1.15672e7 2.00350e7i −1.21831 2.11017i
\(619\) 36007.2 62366.3i 0.00377714 0.00654219i −0.864131 0.503268i \(-0.832131\pi\)
0.867908 + 0.496725i \(0.165464\pi\)
\(620\) 6.89691e6 4.70223e6i 0.720569 0.491275i
\(621\) −5.96397e6 898924.i −0.620592 0.0935392i
\(622\) −6.19112e6 + 2.71251e7i −0.641642 + 2.81122i
\(623\) 7.52254e6 1.57056e7i 0.776505 1.62119i
\(624\) −1.30528e7 5.71880e7i −1.34197 5.87954i
\(625\) −274495. 3.66288e6i −0.0281083 0.375079i
\(626\) −2.30744e6 711752.i −0.235340 0.0725927i
\(627\) −912923. 2.32609e6i −0.0927396 0.236297i
\(628\) −1.85508e7 + 5.72216e6i −1.87699 + 0.578976i
\(629\) −729579. 914863.i −0.0735268 0.0921997i
\(630\) 6.41605e6 + 467175.i 0.644046 + 0.0468952i
\(631\) 6.48363e6 8.13022e6i 0.648254 0.812884i −0.343754 0.939060i \(-0.611699\pi\)
0.992008 + 0.126175i \(0.0402701\pi\)
\(632\) −1.72120e7 + 4.38556e7i −1.71411 + 4.36749i
\(633\) −524818. + 7.00321e6i −0.0520594 + 0.694685i
\(634\) 1.02660e7 1.54734e6i 1.01432 0.152885i
\(635\) −8.29494e6 + 7.69658e6i −0.816354 + 0.757466i
\(636\) −832557. −0.0816153
\(637\) 1.67283e7 5.23759e6i 1.63344 0.511426i
\(638\) −1.10810e7 −1.07778
\(639\) −4.41219e6 + 4.09392e6i −0.427467 + 0.396631i
\(640\) −5.15725e7 + 7.77330e6i −4.97700 + 0.750162i
\(641\) −1.13634e6 + 1.51633e7i −0.109235 + 1.45764i 0.625998 + 0.779824i \(0.284692\pi\)
−0.735233 + 0.677814i \(0.762927\pi\)
\(642\) 3.36281e6 8.56831e6i 0.322007 0.820460i
\(643\) −1.85831e6 + 2.33024e6i −0.177251 + 0.222266i −0.862518 0.506026i \(-0.831114\pi\)
0.685267 + 0.728292i \(0.259686\pi\)
\(644\) 2.71537e6 + 1.77604e7i 0.257996 + 1.68747i
\(645\) 2.21007e6 + 2.77134e6i 0.209174 + 0.262295i
\(646\) 8.08987e6 2.49539e6i 0.762711 0.235265i
\(647\) 3.33985e6 + 8.50979e6i 0.313665 + 0.799205i 0.997572 + 0.0696365i \(0.0221840\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(648\) −1.48786e7 4.58943e6i −1.39195 0.429360i
\(649\) 187311. + 2.49949e6i 0.0174563 + 0.232938i
\(650\) −3.53864e6 1.55038e7i −0.328514 1.43931i
\(651\) −1.40243e6 2.89649e6i −0.129697 0.267868i
\(652\) 1.17266e7 5.13777e7i 1.08032 4.73321i
\(653\) 7.59883e6 + 1.14534e6i 0.697371 + 0.105112i 0.488154 0.872758i \(-0.337670\pi\)
0.209217 + 0.977869i \(0.432909\pi\)
\(654\) −5.67245e6 + 3.86741e6i −0.518592 + 0.353570i
\(655\) 5.02275e6 8.69966e6i 0.457444 0.792317i
\(656\) 5.69622e6 + 9.86614e6i 0.516805 + 0.895133i
\(657\) −3.08737e6 1.48680e6i −0.279046 0.134381i
\(658\) 1.18419e7 + 1.27085e7i 1.06624 + 1.14427i
\(659\) −6.17734e6 + 2.97485e6i −0.554100 + 0.266840i −0.689911 0.723894i \(-0.742350\pi\)
0.135811 + 0.990735i \(0.456636\pi\)
\(660\) 7.76838e6 + 5.29639e6i 0.694178 + 0.473283i
\(661\) −3.57672e6 3.31871e6i −0.318406 0.295437i 0.504735 0.863274i \(-0.331590\pi\)
−0.823141 + 0.567837i \(0.807781\pi\)
\(662\) −1.58403e7 1.46976e7i −1.40481 1.30347i
\(663\) −7.27457e6 4.95972e6i −0.642723 0.438201i
\(664\) 5.50298e7 2.65009e7i 4.84370 2.33260i
\(665\) −3.20969e6 + 4.72920e6i −0.281455 + 0.414700i
\(666\) 1.73086e6 + 833536.i 0.151208 + 0.0728180i
\(667\) −3.59018e6 6.21838e6i −0.312465 0.541206i
\(668\) 1.32637e7 2.29734e7i 1.15007 1.99198i
\(669\) −725197. + 494431.i −0.0626456 + 0.0427111i
\(670\) 3.24466e6 + 489054.i 0.279243 + 0.0420891i
\(671\) −466801. + 2.04519e6i −0.0400245 + 0.175359i
\(672\) 101471. + 4.79843e7i 0.00866799 + 4.09898i
\(673\) −121448. 532099.i −0.0103360 0.0452850i 0.969497 0.245103i \(-0.0788219\pi\)
−0.979833 + 0.199818i \(0.935965\pi\)
\(674\) 1.61161e6 + 2.15055e7i 0.136651 + 1.82347i
\(675\) −5.30713e6 1.63703e6i −0.448332 0.138292i
\(676\) 2.45845e7 + 6.26402e7i 2.06916 + 5.27213i
\(677\) 1.46985e7 4.53388e6i 1.23254 0.380188i 0.391003 0.920389i \(-0.372128\pi\)
0.841536 + 0.540202i \(0.181652\pi\)
\(678\) −1.82280e6 2.28571e6i −0.152287 0.190962i
\(679\) −1.21799e6 + 1.31826e6i −0.101384 + 0.109730i
\(680\) −1.30939e7 + 1.64192e7i −1.08592 + 1.36170i
\(681\) −489371. + 1.24690e6i −0.0404362 + 0.103030i
\(682\) −359887. + 4.80235e6i −0.0296282 + 0.395360i
\(683\) −1.17154e7 + 1.76581e6i −0.960961 + 0.144842i −0.610745 0.791827i \(-0.709130\pi\)
−0.350216 + 0.936669i \(0.613892\pi\)
\(684\) −7.59948e6 + 7.05129e6i −0.621074 + 0.576273i
\(685\) −9.22279e6 −0.750993
\(686\) −2.43697e7 + 1.98181e6i −1.97715 + 0.160787i
\(687\) −6.93149e6 −0.560318
\(688\) 2.52388e7 2.34182e7i 2.03281 1.88618i
\(689\) 778855. 117394.i 0.0625041 0.00942098i
\(690\) −610413. + 8.14539e6i −0.0488091 + 0.651312i
\(691\) −3.57071e6 + 9.09802e6i −0.284485 + 0.724856i 0.715179 + 0.698941i \(0.246345\pi\)
−0.999664 + 0.0259150i \(0.991750\pi\)
\(692\) −5.60680e6 + 7.03070e6i −0.445092 + 0.558127i
\(693\) −1.87857e6 + 2.03323e6i −0.148592 + 0.160825i
\(694\) −6.47728e6 8.12225e6i −0.510498 0.640144i
\(695\) 1.42771e7 4.40391e6i 1.12119 0.345841i
\(696\) −1.44993e7 3.69436e7i −1.13455 2.89078i
\(697\) 1.63399e6 + 504020.i 0.127400 + 0.0392976i
\(698\) 1.60056e6 + 2.13579e7i 0.124346 + 1.65928i
\(699\) 2.44881e6 + 1.07289e7i 0.189567 + 0.830547i
\(700\) 34985.9 + 1.65444e7i 0.00269866 + 1.27616i
\(701\) −4.65306e6 + 2.03864e7i −0.357638 + 1.56692i 0.401420 + 0.915894i \(0.368517\pi\)
−0.759059 + 0.651022i \(0.774341\pi\)
\(702\) 4.73026e7 + 7.12972e6i 3.62278 + 0.546047i
\(703\) −1.41026e6 + 961496.i −0.107624 + 0.0733769i
\(704\) 2.03456e7 3.52396e7i 1.54717 2.67978i
\(705\) 2.94514e6 + 5.10113e6i 0.223169 + 0.386539i
\(706\) −9.92128e6 4.77784e6i −0.749128 0.360761i
\(707\) −4.19945e6 + 6.18753e6i −0.315968 + 0.465553i
\(708\) −1.22680e7 + 5.90794e6i −0.919792 + 0.442948i
\(709\) −3.30874e6 2.25586e6i −0.247199 0.168538i 0.433382 0.901210i \(-0.357320\pi\)
−0.680581 + 0.732673i \(0.738273\pi\)
\(710\) 1.97753e7 + 1.83488e7i 1.47223 + 1.36603i
\(711\) −5.22991e6 4.85264e6i −0.387989 0.360002i
\(712\) −7.71153e7 5.25763e7i −5.70086 3.88678i
\(713\) −2.81155e6 + 1.35397e6i −0.207120 + 0.0997438i
\(714\) 8.37204e6 + 8.98474e6i 0.614591 + 0.659568i
\(715\) −8.01411e6 3.85939e6i −0.586260 0.282328i
\(716\) −9.33905e6 1.61757e7i −0.680801 1.17918i
\(717\) 2.38266e6 4.12688e6i 0.173087 0.299795i
\(718\) −1.40337e7 + 9.56804e6i −1.01593 + 0.692647i
\(719\) 1.35730e6 + 204579.i 0.0979157 + 0.0147584i 0.197817 0.980239i \(-0.436615\pi\)
−0.0999016 + 0.994997i \(0.531853\pi\)
\(720\) 4.71483e6 2.06570e7i 0.338950 1.48503i
\(721\) −9.92294e6 2.04942e7i −0.710890 1.46823i
\(722\) 3.43493e6 + 1.50494e7i 0.245231 + 1.07443i
\(723\) 1.33881e6 + 1.78652e7i 0.0952518 + 1.27105i
\(724\) −2.28511e7 7.04864e6i −1.62017 0.499757i
\(725\) −2.41561e6 6.15488e6i −0.170680 0.434885i
\(726\) 1.50872e7 4.65379e6i 1.06235 0.327692i
\(727\) 7.45400e6 + 9.34702e6i 0.523062 + 0.655899i 0.971256 0.238037i \(-0.0765040\pi\)
−0.448194 + 0.893936i \(0.647933\pi\)
\(728\) −1.41988e7 9.28697e7i −0.992938 6.49450i
\(729\) 8.73910e6 1.09585e7i 0.609043 0.763716i
\(730\) −5.61106e6 + 1.42968e7i −0.389707 + 0.992957i
\(731\) 386188. 5.15332e6i 0.0267304 0.356693i
\(732\) −1.12688e7 + 1.69850e6i −0.777321 + 0.117162i
\(733\) 8.25636e6 7.66079e6i 0.567582 0.526639i −0.343343 0.939210i \(-0.611559\pi\)
0.910926 + 0.412571i \(0.135369\pi\)
\(734\) 2.51978e7 1.72632
\(735\) −8.20350e6 1.20102e6i −0.560120 0.0820032i
\(736\) 4.65297e7 3.16618
\(737\) −1.03506e6 + 960397.i −0.0701936 + 0.0651302i
\(738\) −2.77598e6 + 418412.i −0.187618 + 0.0282789i
\(739\) −404649. + 5.39966e6i −0.0272563 + 0.363710i 0.966853 + 0.255332i \(0.0821848\pi\)
−0.994110 + 0.108378i \(0.965434\pi\)
\(740\) 2.34628e6 5.97823e6i 0.157507 0.401322i
\(741\) −8.00720e6 + 1.00407e7i −0.535717 + 0.671767i
\(742\) −1.09574e6 79784.9i −0.0730633 0.00531999i
\(743\) −9.32589e6 1.16943e7i −0.619753 0.777145i 0.368557 0.929605i \(-0.379852\pi\)
−0.988310 + 0.152460i \(0.951280\pi\)
\(744\) −1.64817e7 + 5.08393e6i −1.09161 + 0.336718i
\(745\) −1.08814e6 2.77253e6i −0.0718278 0.183014i
\(746\) −4.66612e7 1.43931e7i −3.06979 0.946905i
\(747\) 691208. + 9.22353e6i 0.0453218 + 0.604777i
\(748\) −3.05016e6 1.33636e7i −0.199328 0.873314i
\(749\) 3.91356e6 8.17074e6i 0.254898 0.532178i
\(750\) −5.52302e6 + 2.41979e7i −0.358528 + 1.57081i
\(751\) −2.16814e7 3.26795e6i −1.40278 0.211434i −0.596328 0.802741i \(-0.703374\pi\)
−0.806447 + 0.591306i \(0.798612\pi\)
\(752\) 4.72714e7 3.22291e7i 3.04827 2.07828i
\(753\) 4.23528e6 7.33572e6i 0.272204 0.471472i
\(754\) 2.84752e7 + 4.93204e7i 1.82405 + 3.15936i
\(755\) −9.09027e6 4.37764e6i −0.580376 0.279494i
\(756\) −4.63659e7 1.80842e7i −2.95049 1.15079i
\(757\) 7.00919e6 3.37545e6i 0.444558 0.214088i −0.198193 0.980163i \(-0.563507\pi\)
0.642751 + 0.766075i \(0.277793\pi\)
\(758\) 334291. + 227916.i 0.0211326 + 0.0144079i
\(759\) −2.57660e6 2.39074e6i −0.162346 0.150635i
\(760\) 2.24556e7 + 2.08357e7i 1.41023 + 1.30850i
\(761\) 3.73048e6 + 2.54340e6i 0.233509 + 0.159204i 0.674422 0.738346i \(-0.264393\pi\)
−0.440913 + 0.897550i \(0.645345\pi\)
\(762\) 3.19525e7 1.53875e7i 1.99350 0.960021i
\(763\) −5.84481e6 + 3.39100e6i −0.363462 + 0.210871i
\(764\) 1.14969e7 + 5.53660e6i 0.712601 + 0.343171i
\(765\) −1.59014e6 2.75420e6i −0.0982384 0.170154i
\(766\) −2.72339e7 + 4.71705e7i −1.67702 + 2.90468i
\(767\) 1.06436e7 7.25669e6i 0.653282 0.445400i
\(768\) 8.71596e7 + 1.31372e7i 5.33227 + 0.803711i
\(769\) 5.39077e6 2.36185e7i 0.328727 1.44025i −0.492833 0.870124i \(-0.664039\pi\)
0.821560 0.570123i \(-0.193104\pi\)
\(770\) 9.71655e6 + 7.71513e6i 0.590589 + 0.468939i
\(771\) 4.93151e6 + 2.16064e7i 0.298775 + 1.30902i
\(772\) 1.31031e6 + 1.74849e7i 0.0791280 + 1.05589i
\(773\) −1.41419e7 4.36220e6i −0.851253 0.262577i −0.161725 0.986836i \(-0.551706\pi\)
−0.689528 + 0.724259i \(0.742182\pi\)
\(774\) 3.09963e6 + 7.89773e6i 0.185976 + 0.473860i
\(775\) −2.74589e6 + 846994.i −0.164221 + 0.0506554i
\(776\) 5.99759e6 + 7.52074e6i 0.357538 + 0.448339i
\(777\) −2.14684e6 1.23343e6i −0.127569 0.0732929i
\(778\) −3.13603e7 + 3.93246e7i −1.85751 + 2.32925i
\(779\) 911242. 2.32181e6i 0.0538010 0.137083i
\(780\) 3.61107e6 4.81864e7i 0.212520 2.83588i
\(781\) −1.14787e7 + 1.73014e6i −0.673389 + 0.101497i
\(782\) 8.72950e6 8.09979e6i 0.510472 0.473649i
\(783\) 1.98896e7 1.15937
\(784\) −5.67837e6 + 8.03302e7i −0.329939 + 4.66755i
\(785\) −8.68687e6 −0.503140
\(786\) −2.30793e7 + 2.14145e7i −1.33250 + 1.23638i
\(787\) 3.20066e7 4.82422e6i 1.84206 0.277646i 0.866790 0.498673i \(-0.166179\pi\)
0.975268 + 0.221027i \(0.0709410\pi\)
\(788\) −3.32635e6 + 4.43870e7i −0.190832 + 2.54648i
\(789\) −2.90184e6 + 7.39377e6i −0.165952 + 0.422838i
\(790\) −1.99368e7 + 2.50000e7i −1.13655 + 1.42519i
\(791\) −1.62598e6 2.37407e6i −0.0924002 0.134912i
\(792\) 9.25042e6 + 1.15997e7i 0.524021 + 0.657102i
\(793\) 1.03025e7 3.17789e6i 0.581778 0.179455i
\(794\) 1.86468e7 + 4.75112e7i 1.04967 + 2.67451i
\(795\) −355994. 109810.i −0.0199768 0.00616202i
\(796\) −5.10401e6 6.81082e7i −0.285515 3.80993i
\(797\) 3.80838e6 + 1.66856e7i 0.212371 + 0.930457i 0.962951 + 0.269677i \(0.0869171\pi\)
−0.750580 + 0.660780i \(0.770226\pi\)
\(798\) 1.39815e7 1.11983e7i 0.777223 0.622508i
\(799\) 1.91088e6 8.37211e6i 0.105893 0.463946i
\(800\) 4.23676e7 + 6.38590e6i 2.34050 + 0.352774i
\(801\) 1.16779e7 7.96188e6i 0.643109 0.438464i
\(802\) 3.22605e7 5.58769e7i 1.77107 3.06758i
\(803\) −3.30446e6 5.72350e6i −0.180847 0.313237i
\(804\) −6.91093e6 3.32813e6i −0.377048 0.181577i
\(805\) −1.18143e6 + 7.95232e6i −0.0642565 + 0.432518i
\(806\) 2.22995e7 1.07389e7i 1.20909 0.582266i
\(807\) −5.03089e6 3.43000e6i −0.271932 0.185400i
\(808\) 2.93801e7 + 2.72607e7i 1.58316 + 1.46896i
\(809\) −9.71657e6 9.01566e6i −0.521966 0.484313i 0.374623 0.927177i \(-0.377772\pi\)
−0.896589 + 0.442864i \(0.853963\pi\)
\(810\) −8.73164e6 5.95313e6i −0.467609 0.318811i
\(811\) 2.49898e7 1.20345e7i 1.33417 0.642502i 0.375447 0.926844i \(-0.377489\pi\)
0.958723 + 0.284342i \(0.0917750\pi\)
\(812\) −1.75837e7 5.65798e7i −0.935879 3.01142i
\(813\) 1.99988e6 + 963092.i 0.106115 + 0.0511024i
\(814\) 1.85256e6 + 3.20873e6i 0.0979969 + 0.169736i
\(815\) 1.17906e7 2.04220e7i 0.621789 1.07697i
\(816\) 3.34202e7 2.27855e7i 1.75705 1.19794i
\(817\) −7.45375e6 1.12347e6i −0.390679 0.0588853i
\(818\) 1.14100e7 4.99906e7i 0.596216 2.61219i
\(819\) 1.38771e7 + 3.13649e6i 0.722916 + 0.163393i
\(820\) 2.08831e6 + 9.14950e6i 0.108458 + 0.475185i
\(821\) 761139. + 1.01567e7i 0.0394100 + 0.525889i 0.981617 + 0.190859i \(0.0611274\pi\)
−0.942207 + 0.335030i \(0.891254\pi\)
\(822\) 2.76212e7 + 8.52001e6i 1.42581 + 0.439806i
\(823\) −1.00801e7 2.56838e7i −0.518761 1.32178i −0.914934 0.403605i \(-0.867757\pi\)
0.396173 0.918176i \(-0.370338\pi\)
\(824\) −1.16617e8 + 3.59715e7i −5.98332 + 1.84561i
\(825\) −2.01801e6 2.53051e6i −0.103226 0.129441i
\(826\) −1.67123e7 + 6.59990e6i −0.852286 + 0.336579i
\(827\) −1.71959e6 + 2.15630e6i −0.0874301 + 0.109634i −0.823622 0.567138i \(-0.808050\pi\)
0.736192 + 0.676772i \(0.236622\pi\)
\(828\) −5.32751e6 + 1.35743e7i −0.270053 + 0.688083i
\(829\) 1.66749e6 2.22511e7i 0.0842708 1.12452i −0.781443 0.623976i \(-0.785516\pi\)
0.865714 0.500539i \(-0.166865\pi\)
\(830\) 4.09923e7 6.17860e6i 2.06542 0.311311i
\(831\) −1.41135e7 + 1.30954e7i −0.708975 + 0.657833i
\(832\) −2.09130e8 −10.4739
\(833\) 7.57624e6 + 9.41831e6i 0.378304 + 0.470284i
\(834\) −4.68266e7 −2.33119
\(835\) 8.70151e6 8.07382e6i 0.431895 0.400740i
\(836\) −1.97707e7 + 2.97996e6i −0.978379 + 0.147467i
\(837\) 645969. 8.61985e6i 0.0318712 0.425291i
\(838\) 1.38837e7 3.53752e7i 0.682962 1.74016i
\(839\) −1.06590e6 + 1.33660e6i −0.0522772 + 0.0655535i −0.807283 0.590165i \(-0.799063\pi\)
0.755006 + 0.655718i \(0.227634\pi\)
\(840\) −1.30079e7 + 4.24895e7i −0.636078 + 2.07770i
\(841\) 1.97499e6 + 2.47655e6i 0.0962884 + 0.120742i
\(842\) 4.97092e7 1.53333e7i 2.41633 0.745339i
\(843\) 3.51918e6 + 8.96672e6i 0.170558 + 0.434575i
\(844\) 5.36961e7 + 1.65630e7i 2.59469 + 0.800357i
\(845\) 2.25021e6 + 3.00270e7i 0.108413 + 1.44667i
\(846\) 3.13719e6 + 1.37449e7i 0.150701 + 0.660263i
\(847\) 1.51431e7 3.49001e6i 0.725279 0.167155i
\(848\) −805207. + 3.52784e6i −0.0384519 + 0.168469i
\(849\) 1.92844e7 + 2.90666e6i 0.918201 + 0.138397i
\(850\) 9.06030e6 6.17721e6i 0.430126 0.293255i
\(851\) −1.20044e6 + 2.07922e6i −0.0568218 + 0.0984183i
\(852\) −3.15309e7 5.46132e7i −1.48812 2.57750i
\(853\) 27858.4 + 13415.9i 0.00131094 + 0.000631316i 0.434539 0.900653i \(-0.356911\pi\)
−0.433228 + 0.901284i \(0.642626\pi\)
\(854\) −1.49939e7 + 1.15552e6i −0.703508 + 0.0542169i
\(855\) −4.17950e6 + 2.01274e6i −0.195528 + 0.0941613i
\(856\) −4.01188e7 2.73525e7i −1.87139 1.27589i
\(857\) −2.06249e7 1.91371e7i −0.959266 0.890069i 0.0347399 0.999396i \(-0.488940\pi\)
−0.994006 + 0.109328i \(0.965130\pi\)
\(858\) 2.04360e7 + 1.89619e7i 0.947717 + 0.879353i
\(859\) 1.35383e7 + 9.23023e6i 0.626008 + 0.426805i 0.834338 0.551254i \(-0.185850\pi\)
−0.208330 + 0.978059i \(0.566803\pi\)
\(860\) 2.55536e7 1.23060e7i 1.17816 0.567374i
\(861\) 3.60742e6 278011.i 0.165840 0.0127807i
\(862\) −2.17269e7 1.04631e7i −0.995931 0.479615i
\(863\) −5.97128e6 1.03426e7i −0.272923 0.472717i 0.696686 0.717376i \(-0.254657\pi\)
−0.969609 + 0.244659i \(0.921324\pi\)
\(864\) −6.44436e7 + 1.11620e8i −2.93694 + 5.08693i
\(865\) −3.32473e6 + 2.26676e6i −0.151083 + 0.103007i
\(866\) 1.74713e7 + 2.63337e6i 0.791644 + 0.119321i
\(867\) −2.35761e6 + 1.03294e7i −0.106518 + 0.466688i
\(868\) −2.50919e7 + 5.78291e6i −1.13041 + 0.260524i
\(869\) −3.06184e6 1.34148e7i −0.137541 0.602607i
\(870\) −2.01297e6 2.68612e7i −0.0901650 1.20317i
\(871\) 6.93444e6 + 2.13899e6i 0.309718 + 0.0955352i
\(872\) 1.32313e7 + 3.37127e7i 0.589264 + 1.50142i
\(873\) −1.39199e6 + 429372.i −0.0618160 + 0.0190677i
\(874\) −1.08301e7 1.35805e7i −0.479573 0.601365i
\(875\) −7.15129e6 + 2.33592e7i −0.315765 + 1.03143i
\(876\) 2.23849e7 2.80698e7i 0.985588 1.23589i
\(877\) −1.54966e7 + 3.94847e7i −0.680358 + 1.73352i −0.000695876 1.00000i \(0.500222\pi\)
−0.679662 + 0.733525i \(0.737874\pi\)
\(878\) 1.70548e6 2.27580e7i 0.0746638 0.996319i
\(879\) −1.17038e7 + 1.76406e6i −0.510920 + 0.0770089i
\(880\) 2.99559e7 2.77950e7i 1.30399 1.20993i
\(881\) 1.07627e7 0.467177 0.233588 0.972336i \(-0.424953\pi\)
0.233588 + 0.972336i \(0.424953\pi\)
\(882\) −1.79155e7 8.53449e6i −0.775456 0.369408i
\(883\) 86612.0 0.00373832 0.00186916 0.999998i \(-0.499405\pi\)
0.00186916 + 0.999998i \(0.499405\pi\)
\(884\) −5.16419e7 + 4.79167e7i −2.22265 + 2.06232i
\(885\) −6.02490e6 + 908108.i −0.258578 + 0.0389744i
\(886\) 4.88146e6 6.51385e7i 0.208913 2.78775i
\(887\) −1.48497e6 + 3.78365e6i −0.0633738 + 0.161474i −0.959053 0.283227i \(-0.908595\pi\)
0.895679 + 0.444701i \(0.146690\pi\)
\(888\) −8.27371e6 + 1.03749e7i −0.352101 + 0.441521i
\(889\) 3.24661e7 1.28213e7i 1.37777 0.544099i
\(890\) −3.94964e7 4.95269e7i −1.67141 2.09588i
\(891\) 4.34548e6 1.34040e6i 0.183377 0.0565642i
\(892\) 2.56575e6 + 6.53742e6i 0.107970 + 0.275102i
\(893\) −1.19695e7 3.69210e6i −0.502281 0.154933i
\(894\) 697585. + 9.30862e6i 0.0291913 + 0.389531i
\(895\) −1.85981e6 8.14836e6i −0.0776088 0.340027i
\(896\) 1.56928e8 + 3.54688e7i 6.53025 + 1.47596i
\(897\) −4.01975e6 + 1.76117e7i −0.166808 + 0.730835i
\(898\) −5.89246e7 8.88146e6i −2.43841 0.367530i
\(899\) 8.50266e6 5.79701e6i 0.350877 0.239224i
\(900\) −6.71395e6 + 1.16289e7i −0.276294 + 0.478556i
\(901\) 271566. + 470367.i 0.0111446 + 0.0193030i
\(902\) −4.87816e6 2.34920e6i −0.199636 0.0961398i
\(903\) −3.24509e6 1.04419e7i −0.132437 0.426147i
\(904\) −1.38949e7 + 6.69144e6i −0.565503 + 0.272332i
\(905\) −8.84126e6 6.02787e6i −0.358833 0.244649i
\(906\) 2.31803e7 + 2.15081e7i 0.938205 + 0.870527i
\(907\) −429047. 398098.i −0.0173176 0.0160684i 0.671467 0.741035i \(-0.265665\pi\)
−0.688784 + 0.724967i \(0.741855\pi\)
\(908\) 8.85544e6 + 6.03754e6i 0.356448 + 0.243022i
\(909\) −5.46831e6 + 2.63340e6i −0.219505 + 0.105708i
\(910\) 9.37036e6 6.30730e7i 0.375105 2.52488i
\(911\) −2.36128e7 1.13713e7i −0.942653 0.453958i −0.101549 0.994831i \(-0.532380\pi\)
−0.841104 + 0.540873i \(0.818094\pi\)
\(912\) −2.95001e7 5.10956e7i −1.17445 2.03421i
\(913\) −8.91939e6 + 1.54488e7i −0.354126 + 0.613365i
\(914\) 1.21574e7 8.28876e6i 0.481365 0.328189i
\(915\) −5.04247e6 760030.i −0.199109 0.0300108i
\(916\) −1.23414e7 + 5.40710e7i −0.485987 + 2.12925i
\(917\) −2.41865e7 + 1.93719e7i −0.949839 + 0.760763i
\(918\) 7.34015e6 + 3.21593e7i 0.287474 + 1.25951i
\(919\) 2.92408e6 + 3.90192e7i 0.114209 + 1.52402i 0.700346 + 0.713804i \(0.253029\pi\)
−0.586137 + 0.810212i \(0.699352\pi\)
\(920\) 4.11746e7 + 1.27007e7i 1.60384 + 0.494718i
\(921\) −2.57595e6 6.56342e6i −0.100067 0.254965i
\(922\) 5.13897e7 1.58516e7i 1.99090 0.614111i
\(923\) 3.71978e7 + 4.66445e7i 1.43718 + 1.80217i
\(924\) −1.63888e7 2.39291e7i −0.631491 0.922032i
\(925\) −1.37842e6 + 1.72848e6i −0.0529696 + 0.0664218i
\(926\) −1.90250e6 + 4.84749e6i −0.0729117 + 0.185776i
\(927\) 1.38108e6 1.84292e7i 0.0527859 0.704379i
\(928\) −1.51728e8 + 2.28693e7i −5.78355 + 0.871731i
\(929\) 1.32583e7 1.23019e7i 0.504019 0.467662i −0.386706 0.922203i \(-0.626387\pi\)
0.890726 + 0.454541i \(0.150197\pi\)
\(930\) −1.17066e7 −0.443837
\(931\) 1.45254e7 9.99349e6i 0.549229 0.377871i
\(932\) 8.80542e7 3.32055
\(933\) 2.13343e7 1.97953e7i 0.802368 0.744488i
\(934\) −5.82964e7 + 8.78676e6i −2.18662 + 0.329581i
\(935\) 458366. 6.11647e6i 0.0171468 0.228808i
\(936\) 2.78578e7 7.09805e7i 1.03934 2.64819i
\(937\) 1.87538e6 2.35165e6i 0.0697814 0.0875032i −0.745716 0.666264i \(-0.767892\pi\)
0.815497 + 0.578761i \(0.196464\pi\)
\(938\) −8.77667e6 5.04250e6i −0.325704 0.187128i
\(939\) 1.57486e6 + 1.97481e6i 0.0582878 + 0.0730906i
\(940\) 4.50365e7 1.38919e7i 1.66244 0.512794i
\(941\) −3.79376e6 9.66634e6i −0.139668 0.355867i 0.843876 0.536538i \(-0.180268\pi\)
−0.983544 + 0.180671i \(0.942173\pi\)
\(942\) 2.60162e7 + 8.02493e6i 0.955248 + 0.294655i
\(943\) −262185. 3.49861e6i −0.00960127 0.128120i
\(944\) 1.31691e7 + 5.76976e7i 0.480979 + 2.10731i
\(945\) −1.74405e7 1.38481e7i −0.635299 0.504440i
\(946\) −3.64112e6 + 1.59528e7i −0.132284 + 0.579573i
\(947\) 3.12987e7 + 4.71752e6i 1.13410 + 0.170938i 0.689151 0.724618i \(-0.257984\pi\)
0.444949 + 0.895556i \(0.353222\pi\)
\(948\) 6.17606e7 4.21077e7i 2.23198 1.52174i
\(949\) −1.69831e7 + 2.94156e7i −0.612141 + 1.06026i
\(950\) −7.99754e6 1.38521e7i −0.287506 0.497975i
\(951\) −9.78435e6 4.71189e6i −0.350817 0.168945i
\(952\) 5.60353e7 3.25102e7i 2.00387 1.16259i
\(953\) 1.67925e7 8.08686e6i 0.598941 0.288435i −0.109744 0.993960i \(-0.535003\pi\)
0.708685 + 0.705525i \(0.249289\pi\)
\(954\) −736749. 502307.i −0.0262089 0.0178689i
\(955\) 4.18572e6 + 3.88378e6i 0.148512 + 0.137799i
\(956\) −2.79506e7 2.59344e7i −0.989115 0.917765i
\(957\) 9.57703e6 + 6.52951e6i 0.338027 + 0.230463i
\(958\) 7.09746e6 3.41796e6i 0.249856 0.120324i
\(959\) 2.65055e7 + 1.03380e7i 0.930655 + 0.362986i
\(960\) 8.91190e7 + 4.29174e7i 3.12099 + 1.50299i
\(961\) 1.20784e7 + 2.09204e7i 0.421891 + 0.730737i
\(962\) 9.52114e6 1.64911e7i 0.331704 0.574529i
\(963\) 6.07537e6 4.14212e6i 0.211109 0.143932i
\(964\) 1.41746e8 + 2.13648e7i 4.91268 + 0.740467i
\(965\) −1.74588e6 + 7.64920e6i −0.0603526 + 0.264422i
\(966\) 1.08846e7 2.27249e7i 0.375292 0.783536i
\(967\) 6.02874e6 + 2.64136e7i 0.207329 + 0.908369i 0.966335 + 0.257285i \(0.0828280\pi\)
−0.759006 + 0.651083i \(0.774315\pi\)
\(968\) −6.22414e6 8.30553e7i −0.213496 2.84891i
\(969\) −8.46226e6 2.61026e6i −0.289519 0.0893047i
\(970\) 2.38528e6 + 6.07758e6i 0.0813972 + 0.207397i
\(971\) −4.43316e7 + 1.36745e7i −1.50892 + 0.465439i −0.935351 0.353720i \(-0.884916\pi\)
−0.573566 + 0.819160i \(0.694440\pi\)
\(972\) −4.27592e7 5.36184e7i −1.45166 1.82032i
\(973\) −4.59675e7 3.34705e6i −1.55657 0.113339i
\(974\) −4.54887e7 + 5.70410e7i −1.53641 + 1.92659i
\(975\) −6.07728e6 + 1.54846e7i −0.204738 + 0.521663i
\(976\) −3.70147e6 + 4.93927e7i −0.124380 + 1.65973i
\(977\) −5.11273e7 + 7.70620e6i −1.71363 + 0.258288i −0.931215 0.364472i \(-0.881250\pi\)
−0.782413 + 0.622759i \(0.786012\pi\)
\(978\) −5.41774e7 + 5.02693e7i −1.81122 + 1.68057i
\(979\) 2.72591e7 0.908982
\(980\) −2.39750e7 + 6.18553e7i −0.797432 + 2.05737i
\(981\) −5.48439e6 −0.181951
\(982\) 1.19019e7 1.10434e7i 0.393857 0.365446i
\(983\) 2.16471e7 3.26277e6i 0.714521 0.107697i 0.218286 0.975885i \(-0.429953\pi\)
0.496235 + 0.868188i \(0.334715\pi\)
\(984\) 1.44914e6 1.93374e7i 0.0477113 0.636664i
\(985\) −7.27671e6 + 1.85408e7i −0.238971 + 0.608888i
\(986\) −2.44848e7 + 3.07030e7i −0.802056 + 1.00575i
\(987\) −2.74611e6 1.79614e7i −0.0897274 0.586878i
\(988\) 6.40687e7 + 8.03396e7i 2.08811 + 2.61841i
\(989\) −1.01320e7 + 3.12530e6i −0.329384 + 0.101602i
\(990\) 3.67895e6 + 9.37380e6i 0.119299 + 0.303968i
\(991\) −2.33057e7 7.18885e6i −0.753837 0.232528i −0.106062 0.994360i \(-0.533824\pi\)
−0.647775 + 0.761831i \(0.724300\pi\)
\(992\) 4.98343e6 + 6.64992e7i 0.160786 + 2.14554i
\(993\) 5.02972e6 + 2.20366e7i 0.161872 + 0.709205i
\(994\) −3.62648e7 7.48991e7i −1.16418 2.40442i
\(995\) 6.80067e6 2.97957e7i 0.217768 0.954104i
\(996\) −9.58258e7 1.44434e7i −3.06079 0.461340i
\(997\) −1.17590e7 + 8.01712e6i −0.374655 + 0.255435i −0.735978 0.677005i \(-0.763277\pi\)
0.361324 + 0.932441i \(0.382325\pi\)
\(998\) −5.45787e6 + 9.45331e6i −0.173459 + 0.300440i
\(999\) −3.32521e6 5.75943e6i −0.105416 0.182585i
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 49.6.g.a.11.1 yes 264
49.9 even 21 inner 49.6.g.a.9.1 264
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.6.g.a.9.1 264 49.9 even 21 inner
49.6.g.a.11.1 yes 264 1.1 even 1 trivial