Properties

Label 75.6.i.a.4.5
Level $75$
Weight $6$
Character 75.4
Analytic conductor $12.029$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,6,Mod(4,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 75.i (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.0287864860\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 4.5
Character \(\chi\) \(=\) 75.4
Dual form 75.6.i.a.19.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.50815 - 2.43955i) q^{2} +(-5.29007 + 7.28115i) q^{3} +(24.5324 + 17.8239i) q^{4} +(-44.0632 + 34.4011i) q^{5} +(57.4814 - 41.7627i) q^{6} +98.6919i q^{7} +(7.77820 + 10.7058i) q^{8} +(-25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(-7.50815 - 2.43955i) q^{2} +(-5.29007 + 7.28115i) q^{3} +(24.5324 + 17.8239i) q^{4} +(-44.0632 + 34.4011i) q^{5} +(57.4814 - 41.7627i) q^{6} +98.6919i q^{7} +(7.77820 + 10.7058i) q^{8} +(-25.0304 - 77.0356i) q^{9} +(414.756 - 150.794i) q^{10} +(-185.523 + 570.980i) q^{11} +(-259.557 + 84.3350i) q^{12} +(789.702 - 256.590i) q^{13} +(240.763 - 740.994i) q^{14} +(-17.3823 - 502.815i) q^{15} +(-332.141 - 1022.22i) q^{16} +(576.784 + 793.876i) q^{17} +639.458i q^{18} +(-1902.58 + 1382.30i) q^{19} +(-1694.14 + 58.5662i) q^{20} +(-718.591 - 522.087i) q^{21} +(2785.86 - 3834.41i) q^{22} +(-3969.32 - 1289.71i) q^{23} -119.098 q^{24} +(758.131 - 3031.64i) q^{25} -6555.17 q^{26} +(693.320 + 225.273i) q^{27} +(-1759.07 + 2421.15i) q^{28} +(-4839.10 - 3515.81i) q^{29} +(-1096.13 + 3817.62i) q^{30} +(-866.621 + 629.637i) q^{31} +8061.83i q^{32} +(-3175.96 - 4371.34i) q^{33} +(-2393.89 - 7367.63i) q^{34} +(-3395.11 - 4348.68i) q^{35} +(759.015 - 2336.01i) q^{36} +(6432.84 - 2090.16i) q^{37} +(17657.0 - 5737.12i) q^{38} +(-2309.31 + 7107.32i) q^{39} +(-711.022 - 204.152i) q^{40} +(4308.85 + 13261.3i) q^{41} +(4121.63 + 5672.94i) q^{42} -14449.3i q^{43} +(-14728.4 + 10700.8i) q^{44} +(3753.03 + 2533.36i) q^{45} +(26655.9 + 19366.7i) q^{46} +(7078.92 - 9743.30i) q^{47} +(9200.01 + 2989.27i) q^{48} +7066.92 q^{49} +(-13088.0 + 20912.6i) q^{50} -8831.56 q^{51} +(23946.7 + 7780.77i) q^{52} +(-503.508 + 693.020i) q^{53} +(-4655.99 - 3382.77i) q^{54} +(-11467.6 - 31541.4i) q^{55} +(-1056.57 + 767.645i) q^{56} -21165.4i q^{57} +(27755.7 + 38202.5i) q^{58} +(-11564.0 - 35590.2i) q^{59} +(8535.68 - 12645.1i) q^{60} +(-2135.37 + 6571.99i) q^{61} +(8042.75 - 2613.25i) q^{62} +(7602.78 - 2470.29i) q^{63} +(9038.71 - 27818.3i) q^{64} +(-25969.8 + 38472.8i) q^{65} +(13181.5 + 40568.6i) q^{66} +(35163.1 + 48397.8i) q^{67} +29756.2i q^{68} +(30388.5 - 22078.5i) q^{69} +(14882.2 + 40933.1i) q^{70} +(-22795.9 - 16562.2i) q^{71} +(630.034 - 867.167i) q^{72} +(-24680.5 - 8019.17i) q^{73} -53397.8 q^{74} +(18063.3 + 21557.7i) q^{75} -71312.8 q^{76} +(-56351.1 - 18309.6i) q^{77} +(34677.3 - 47729.2i) q^{78} +(-75285.8 - 54698.4i) q^{79} +(49800.8 + 33616.4i) q^{80} +(-5307.96 + 3856.46i) q^{81} -110079. i q^{82} +(31106.1 + 42813.8i) q^{83} +(-8323.18 - 25616.1i) q^{84} +(-52725.1 - 15138.7i) q^{85} +(-35249.7 + 108487. i) q^{86} +(51198.4 - 16635.4i) q^{87} +(-7555.81 + 2455.03i) q^{88} +(29496.4 - 90780.6i) q^{89} +(-21998.0 - 28176.6i) q^{90} +(25323.3 + 77937.1i) q^{91} +(-74389.4 - 102388. i) q^{92} -9640.82i q^{93} +(-76918.9 + 55884.8i) q^{94} +(36280.9 - 126359. i) q^{95} +(-58699.4 - 42647.6i) q^{96} +(-28840.6 + 39695.7i) q^{97} +(-53059.5 - 17240.1i) q^{98} +48629.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 352 q^{4} - 120 q^{5} + 72 q^{6} - 1230 q^{8} + 1944 q^{9} - 890 q^{10} + 474 q^{11} + 2748 q^{14} - 780 q^{16} + 1910 q^{17} - 5522 q^{19} - 19220 q^{20} + 1764 q^{21} + 6170 q^{22} + 21980 q^{23} + 13824 q^{24} + 11790 q^{25} - 11028 q^{26} - 9120 q^{28} - 24304 q^{29} - 22860 q^{30} + 1566 q^{31} - 3690 q^{33} + 24224 q^{34} + 10250 q^{35} - 28512 q^{36} + 16490 q^{37} + 68730 q^{38} - 12168 q^{39} - 106480 q^{40} + 26126 q^{41} - 43560 q^{42} - 10814 q^{44} + 9720 q^{45} + 22956 q^{46} + 66440 q^{47} - 123480 q^{49} + 329620 q^{50} - 83232 q^{51} + 251240 q^{52} - 91690 q^{53} - 5832 q^{54} - 123470 q^{55} + 116100 q^{56} - 483290 q^{58} - 97428 q^{59} + 119610 q^{60} + 91560 q^{61} - 138410 q^{62} + 47790 q^{63} + 127738 q^{64} - 235130 q^{65} + 118296 q^{66} + 163960 q^{67} - 73332 q^{69} + 209520 q^{70} + 155672 q^{71} - 99630 q^{72} + 18980 q^{73} + 100588 q^{74} - 464032 q^{76} + 119560 q^{77} - 112020 q^{79} - 66300 q^{80} - 157464 q^{81} + 148010 q^{83} - 61128 q^{84} + 346980 q^{85} - 295956 q^{86} - 371160 q^{87} - 189090 q^{88} - 494082 q^{89} - 144180 q^{90} - 79494 q^{91} + 599810 q^{92} + 234622 q^{94} + 605800 q^{95} + 210744 q^{96} + 372140 q^{97} + 891060 q^{98} + 25596 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.50815 2.43955i −1.32727 0.431255i −0.442282 0.896876i \(-0.645831\pi\)
−0.884984 + 0.465621i \(0.845831\pi\)
\(3\) −5.29007 + 7.28115i −0.339358 + 0.467086i
\(4\) 24.5324 + 17.8239i 0.766639 + 0.556996i
\(5\) −44.0632 + 34.4011i −0.788226 + 0.615385i
\(6\) 57.4814 41.7627i 0.651852 0.473598i
\(7\) 98.6919i 0.761266i 0.924726 + 0.380633i \(0.124294\pi\)
−0.924726 + 0.380633i \(0.875706\pi\)
\(8\) 7.77820 + 10.7058i 0.0429689 + 0.0591416i
\(9\) −25.0304 77.0356i −0.103006 0.317019i
\(10\) 414.756 150.794i 1.31157 0.476854i
\(11\) −185.523 + 570.980i −0.462291 + 1.42278i 0.400068 + 0.916486i \(0.368987\pi\)
−0.862358 + 0.506299i \(0.831013\pi\)
\(12\) −259.557 + 84.3350i −0.520330 + 0.169065i
\(13\) 789.702 256.590i 1.29600 0.421096i 0.421812 0.906684i \(-0.361394\pi\)
0.874188 + 0.485588i \(0.161394\pi\)
\(14\) 240.763 740.994i 0.328300 1.01040i
\(15\) −17.3823 502.815i −0.0199470 0.577006i
\(16\) −332.141 1022.22i −0.324356 0.998265i
\(17\) 576.784 + 793.876i 0.484051 + 0.666239i 0.979277 0.202525i \(-0.0649147\pi\)
−0.495226 + 0.868764i \(0.664915\pi\)
\(18\) 639.458i 0.465190i
\(19\) −1902.58 + 1382.30i −1.20909 + 0.878454i −0.995148 0.0983921i \(-0.968630\pi\)
−0.213941 + 0.976847i \(0.568630\pi\)
\(20\) −1694.14 + 58.5662i −0.947052 + 0.0327395i
\(21\) −718.591 522.087i −0.355577 0.258342i
\(22\) 2785.86 3834.41i 1.22717 1.68905i
\(23\) −3969.32 1289.71i −1.56457 0.508361i −0.606549 0.795046i \(-0.707447\pi\)
−0.958025 + 0.286685i \(0.907447\pi\)
\(24\) −119.098 −0.0422061
\(25\) 758.131 3031.64i 0.242602 0.970126i
\(26\) −6555.17 −1.90174
\(27\) 693.320 + 225.273i 0.183031 + 0.0594703i
\(28\) −1759.07 + 2421.15i −0.424022 + 0.583616i
\(29\) −4839.10 3515.81i −1.06849 0.776302i −0.0928484 0.995680i \(-0.529597\pi\)
−0.975640 + 0.219378i \(0.929597\pi\)
\(30\) −1096.13 + 3817.62i −0.222362 + 0.774443i
\(31\) −866.621 + 629.637i −0.161966 + 0.117676i −0.665816 0.746116i \(-0.731917\pi\)
0.503850 + 0.863791i \(0.331917\pi\)
\(32\) 8061.83i 1.39174i
\(33\) −3175.96 4371.34i −0.507681 0.698763i
\(34\) −2393.89 7367.63i −0.355146 1.09303i
\(35\) −3395.11 4348.68i −0.468472 0.600050i
\(36\) 759.015 2336.01i 0.0976100 0.300413i
\(37\) 6432.84 2090.16i 0.772500 0.251000i 0.103865 0.994591i \(-0.466879\pi\)
0.668635 + 0.743591i \(0.266879\pi\)
\(38\) 17657.0 5737.12i 1.98362 0.644518i
\(39\) −2309.31 + 7107.32i −0.243120 + 0.748246i
\(40\) −711.022 204.152i −0.0702641 0.0201746i
\(41\) 4308.85 + 13261.3i 0.400315 + 1.23204i 0.924745 + 0.380588i \(0.124278\pi\)
−0.524430 + 0.851454i \(0.675722\pi\)
\(42\) 4121.63 + 5672.94i 0.360534 + 0.496232i
\(43\) 14449.3i 1.19172i −0.803088 0.595861i \(-0.796811\pi\)
0.803088 0.595861i \(-0.203189\pi\)
\(44\) −14728.4 + 10700.8i −1.14689 + 0.833268i
\(45\) 3753.03 + 2533.36i 0.276281 + 0.186494i
\(46\) 26655.9 + 19366.7i 1.85737 + 1.34946i
\(47\) 7078.92 9743.30i 0.467436 0.643371i −0.508594 0.861007i \(-0.669835\pi\)
0.976030 + 0.217636i \(0.0698345\pi\)
\(48\) 9200.01 + 2989.27i 0.576349 + 0.187267i
\(49\) 7066.92 0.420475
\(50\) −13088.0 + 20912.6i −0.740369 + 1.18299i
\(51\) −8831.56 −0.475458
\(52\) 23946.7 + 7780.77i 1.22811 + 0.399038i
\(53\) −503.508 + 693.020i −0.0246216 + 0.0338888i −0.821150 0.570712i \(-0.806667\pi\)
0.796529 + 0.604601i \(0.206667\pi\)
\(54\) −4655.99 3382.77i −0.217284 0.157866i
\(55\) −11467.6 31541.4i −0.511171 1.40596i
\(56\) −1056.57 + 767.645i −0.0450225 + 0.0327107i
\(57\) 21165.4i 0.862859i
\(58\) 27755.7 + 38202.5i 1.08338 + 1.49115i
\(59\) −11564.0 35590.2i −0.432490 1.33107i −0.895637 0.444786i \(-0.853280\pi\)
0.463147 0.886282i \(-0.346720\pi\)
\(60\) 8535.68 12645.1i 0.306098 0.453465i
\(61\) −2135.37 + 6571.99i −0.0734765 + 0.226137i −0.981050 0.193757i \(-0.937933\pi\)
0.907573 + 0.419894i \(0.137933\pi\)
\(62\) 8042.75 2613.25i 0.265721 0.0863379i
\(63\) 7602.78 2470.29i 0.241336 0.0784147i
\(64\) 9038.71 27818.3i 0.275840 0.848947i
\(65\) −25969.8 + 38472.8i −0.762405 + 1.12946i
\(66\) 13181.5 + 40568.6i 0.372483 + 1.14638i
\(67\) 35163.1 + 48397.8i 0.956973 + 1.31716i 0.948359 + 0.317198i \(0.102742\pi\)
0.00861357 + 0.999963i \(0.497258\pi\)
\(68\) 29756.2i 0.780379i
\(69\) 30388.5 22078.5i 0.768399 0.558275i
\(70\) 14882.2 + 40933.1i 0.363012 + 0.998457i
\(71\) −22795.9 16562.2i −0.536675 0.389917i 0.286174 0.958178i \(-0.407616\pi\)
−0.822849 + 0.568261i \(0.807616\pi\)
\(72\) 630.034 867.167i 0.0143230 0.0197139i
\(73\) −24680.5 8019.17i −0.542058 0.176125i 0.0251742 0.999683i \(-0.491986\pi\)
−0.567233 + 0.823558i \(0.691986\pi\)
\(74\) −53397.8 −1.13356
\(75\) 18063.3 + 21557.7i 0.370804 + 0.442536i
\(76\) −71312.8 −1.41623
\(77\) −56351.1 18309.6i −1.08312 0.351926i
\(78\) 34677.3 47729.2i 0.645369 0.888275i
\(79\) −75285.8 54698.4i −1.35721 0.986067i −0.998617 0.0525715i \(-0.983258\pi\)
−0.358588 0.933496i \(-0.616742\pi\)
\(80\) 49800.8 + 33616.4i 0.869984 + 0.587255i
\(81\) −5307.96 + 3856.46i −0.0898908 + 0.0653095i
\(82\) 110079.i 1.80789i
\(83\) 31106.1 + 42813.8i 0.495621 + 0.682164i 0.981412 0.191911i \(-0.0614685\pi\)
−0.485791 + 0.874075i \(0.661468\pi\)
\(84\) −8323.18 25616.1i −0.128704 0.396109i
\(85\) −52725.1 15138.7i −0.791536 0.227269i
\(86\) −35249.7 + 108487.i −0.513936 + 1.58173i
\(87\) 51198.4 16635.4i 0.725200 0.235632i
\(88\) −7555.81 + 2455.03i −0.104010 + 0.0337948i
\(89\) 29496.4 90780.6i 0.394725 1.21484i −0.534451 0.845199i \(-0.679482\pi\)
0.929176 0.369638i \(-0.120518\pi\)
\(90\) −21998.0 28176.6i −0.286271 0.366675i
\(91\) 25323.3 + 77937.1i 0.320566 + 0.986600i
\(92\) −74389.4 102388.i −0.916308 1.26119i
\(93\) 9640.82i 0.115586i
\(94\) −76918.9 + 55884.8i −0.897869 + 0.652340i
\(95\) 36280.9 126359.i 0.412448 1.43648i
\(96\) −58699.4 42647.6i −0.650063 0.472299i
\(97\) −28840.6 + 39695.7i −0.311225 + 0.428365i −0.935763 0.352630i \(-0.885288\pi\)
0.624537 + 0.780995i \(0.285288\pi\)
\(98\) −53059.5 17240.1i −0.558082 0.181332i
\(99\) 48629.5 0.498668
\(100\) 72634.4 60860.8i 0.726344 0.608608i
\(101\) 20732.0 0.202227 0.101113 0.994875i \(-0.467760\pi\)
0.101113 + 0.994875i \(0.467760\pi\)
\(102\) 66308.7 + 21545.0i 0.631059 + 0.205044i
\(103\) −37632.7 + 51796.9i −0.349520 + 0.481073i −0.947192 0.320668i \(-0.896093\pi\)
0.597672 + 0.801741i \(0.296093\pi\)
\(104\) 8889.45 + 6458.56i 0.0805919 + 0.0585535i
\(105\) 49623.7 1715.49i 0.439255 0.0151850i
\(106\) 5471.07 3974.97i 0.0472942 0.0343613i
\(107\) 30255.2i 0.255470i −0.991808 0.127735i \(-0.959229\pi\)
0.991808 0.127735i \(-0.0407708\pi\)
\(108\) 12993.6 + 17884.2i 0.107194 + 0.147540i
\(109\) 6625.37 + 20390.8i 0.0534126 + 0.164387i 0.974204 0.225667i \(-0.0724562\pi\)
−0.920792 + 0.390054i \(0.872456\pi\)
\(110\) 9153.87 + 264793.i 0.0721312 + 2.08653i
\(111\) −18811.4 + 57895.5i −0.144915 + 0.446003i
\(112\) 100885. 32779.6i 0.759945 0.246921i
\(113\) 167740. 54502.0i 1.23578 0.401528i 0.382973 0.923760i \(-0.374900\pi\)
0.852804 + 0.522231i \(0.174900\pi\)
\(114\) −51634.1 + 158913.i −0.372112 + 1.14524i
\(115\) 219268. 79720.1i 1.54608 0.562112i
\(116\) −56049.6 172503.i −0.386748 1.19029i
\(117\) −39533.1 54412.6i −0.266991 0.367481i
\(118\) 295427.i 1.95320i
\(119\) −78349.1 + 56923.9i −0.507185 + 0.368491i
\(120\) 5247.82 4097.08i 0.0332679 0.0259730i
\(121\) −161306. 117196.i −1.00159 0.727694i
\(122\) 32065.3 44134.2i 0.195046 0.268457i
\(123\) −119351. 38779.6i −0.711320 0.231122i
\(124\) −32482.9 −0.189715
\(125\) 70886.1 + 159664.i 0.405776 + 0.913973i
\(126\) −63109.3 −0.354133
\(127\) −199755. 64904.3i −1.09898 0.357079i −0.297267 0.954794i \(-0.596075\pi\)
−0.801708 + 0.597715i \(0.796075\pi\)
\(128\) 15907.9 21895.3i 0.0858199 0.118121i
\(129\) 105207. + 76437.6i 0.556637 + 0.404420i
\(130\) 288842. 225505.i 1.49900 1.17030i
\(131\) −14580.0 + 10593.0i −0.0742298 + 0.0539311i −0.624281 0.781200i \(-0.714608\pi\)
0.550051 + 0.835131i \(0.314608\pi\)
\(132\) 163848.i 0.818475i
\(133\) −136422. 187769.i −0.668737 0.920438i
\(134\) −145941. 449160.i −0.702126 2.16092i
\(135\) −38299.6 + 13924.7i −0.180867 + 0.0657584i
\(136\) −4012.71 + 12349.8i −0.0186033 + 0.0572551i
\(137\) −209035. + 67919.6i −0.951519 + 0.309167i −0.743333 0.668922i \(-0.766756\pi\)
−0.208186 + 0.978089i \(0.566756\pi\)
\(138\) −282023. + 91634.9i −1.26063 + 0.409603i
\(139\) −69312.8 + 213323.i −0.304282 + 0.936485i 0.675662 + 0.737212i \(0.263858\pi\)
−0.979944 + 0.199273i \(0.936142\pi\)
\(140\) −5780.00 167198.i −0.0249234 0.720958i
\(141\) 33494.5 + 103085.i 0.141881 + 0.436666i
\(142\) 130751. + 179963.i 0.544157 + 0.748967i
\(143\) 498507.i 2.03860i
\(144\) −70434.0 + 51173.3i −0.283058 + 0.205654i
\(145\) 334174. 11552.4i 1.31994 0.0456300i
\(146\) 165742. + 120418.i 0.643501 + 0.467531i
\(147\) −37384.5 + 51455.3i −0.142691 + 0.196398i
\(148\) 195068. + 63381.4i 0.732034 + 0.237852i
\(149\) 215266. 0.794347 0.397174 0.917743i \(-0.369991\pi\)
0.397174 + 0.917743i \(0.369991\pi\)
\(150\) −83031.1 205925.i −0.301309 0.747274i
\(151\) −349615. −1.24781 −0.623905 0.781500i \(-0.714455\pi\)
−0.623905 + 0.781500i \(0.714455\pi\)
\(152\) −29597.2 9616.73i −0.103906 0.0337612i
\(153\) 46719.5 64303.9i 0.161350 0.222080i
\(154\) 378425. + 274942.i 1.28581 + 0.934199i
\(155\) 16525.9 57556.5i 0.0552505 0.192427i
\(156\) −183333. + 133199.i −0.603155 + 0.438218i
\(157\) 174487.i 0.564956i −0.959274 0.282478i \(-0.908844\pi\)
0.959274 0.282478i \(-0.0911565\pi\)
\(158\) 431818. + 594347.i 1.37613 + 1.89408i
\(159\) −2382.39 7332.24i −0.00747343 0.0230009i
\(160\) −277336. 355230.i −0.856457 1.09701i
\(161\) 127284. 391739.i 0.386998 1.19106i
\(162\) 49261.0 16005.9i 0.147474 0.0479172i
\(163\) 59450.9 19316.8i 0.175263 0.0569463i −0.220071 0.975484i \(-0.570629\pi\)
0.395334 + 0.918538i \(0.370629\pi\)
\(164\) −130660. + 402132.i −0.379345 + 1.16750i
\(165\) 290322. + 83358.6i 0.830176 + 0.238364i
\(166\) −129103. 397337.i −0.363635 1.11915i
\(167\) −4243.52 5840.70i −0.0117743 0.0162059i 0.803089 0.595859i \(-0.203188\pi\)
−0.814864 + 0.579653i \(0.803188\pi\)
\(168\) 11754.0i 0.0321300i
\(169\) 257408. 187018.i 0.693276 0.503694i
\(170\) 358937. + 242289.i 0.952568 + 0.643001i
\(171\) 154109. + 111967.i 0.403030 + 0.292818i
\(172\) 257542. 354476.i 0.663784 0.913620i
\(173\) −25839.7 8395.82i −0.0656405 0.0213279i 0.276013 0.961154i \(-0.410987\pi\)
−0.341653 + 0.939826i \(0.610987\pi\)
\(174\) −424988. −1.06415
\(175\) 299199. + 74821.4i 0.738524 + 0.184685i
\(176\) 645289. 1.57026
\(177\) 320312. + 104076.i 0.768492 + 0.249698i
\(178\) −442927. + 609637.i −1.04781 + 1.44219i
\(179\) −456112. 331385.i −1.06399 0.773036i −0.0891698 0.996016i \(-0.528421\pi\)
−0.974823 + 0.222980i \(0.928421\pi\)
\(180\) 46916.6 + 129043.i 0.107931 + 0.296861i
\(181\) 55058.2 40002.2i 0.124918 0.0907584i −0.523572 0.851982i \(-0.675401\pi\)
0.648490 + 0.761223i \(0.275401\pi\)
\(182\) 646942.i 1.44773i
\(183\) −36555.4 50314.2i −0.0806908 0.111061i
\(184\) −17066.8 52526.2i −0.0371627 0.114375i
\(185\) −211548. + 313396.i −0.454443 + 0.673230i
\(186\) −23519.2 + 72384.8i −0.0498472 + 0.153414i
\(187\) −560294. + 182050.i −1.17169 + 0.380704i
\(188\) 347326. 112853.i 0.716710 0.232873i
\(189\) −22232.6 + 68425.1i −0.0452727 + 0.139335i
\(190\) −580662. + 860217.i −1.16692 + 1.72872i
\(191\) −42517.3 130855.i −0.0843300 0.259541i 0.899996 0.435897i \(-0.143569\pi\)
−0.984326 + 0.176356i \(0.943569\pi\)
\(192\) 154734. + 212973.i 0.302923 + 0.416938i
\(193\) 306283.i 0.591874i 0.955207 + 0.295937i \(0.0956318\pi\)
−0.955207 + 0.295937i \(0.904368\pi\)
\(194\) 313379. 227683.i 0.597814 0.434337i
\(195\) −142744. 392614.i −0.268826 0.739399i
\(196\) 173369. + 125960.i 0.322352 + 0.234203i
\(197\) −164636. + 226603.i −0.302246 + 0.416006i −0.932943 0.360023i \(-0.882769\pi\)
0.630698 + 0.776029i \(0.282769\pi\)
\(198\) −365118. 118634.i −0.661865 0.215053i
\(199\) 351689. 0.629544 0.314772 0.949167i \(-0.398072\pi\)
0.314772 + 0.949167i \(0.398072\pi\)
\(200\) 38353.0 15464.3i 0.0677991 0.0273374i
\(201\) −538407. −0.939984
\(202\) −155659. 50576.8i −0.268409 0.0872113i
\(203\) 346982. 477580.i 0.590972 0.813403i
\(204\) −216660. 157413.i −0.364504 0.264828i
\(205\) −646064. 436105.i −1.07372 0.724780i
\(206\) 408913. 297093.i 0.671372 0.487780i
\(207\) 338060.i 0.548363i
\(208\) −524584. 722028.i −0.840731 1.15717i
\(209\) −436296. 1.34278e6i −0.690901 2.12637i
\(210\) −376768. 108179.i −0.589556 0.169276i
\(211\) −297350. + 915149.i −0.459792 + 1.41510i 0.405623 + 0.914040i \(0.367055\pi\)
−0.865415 + 0.501055i \(0.832945\pi\)
\(212\) −24704.6 + 8027.01i −0.0377518 + 0.0122663i
\(213\) 241184. 78365.4i 0.364250 0.118352i
\(214\) −73809.0 + 227161.i −0.110173 + 0.339077i
\(215\) 497071. + 636681.i 0.733368 + 0.939347i
\(216\) 2981.06 + 9174.75i 0.00434746 + 0.0133801i
\(217\) −62140.1 85528.4i −0.0895823 0.123299i
\(218\) 169260.i 0.241220i
\(219\) 188950. 137280.i 0.266218 0.193418i
\(220\) 280861. 978184.i 0.391232 1.36259i
\(221\) 659188. + 478928.i 0.907880 + 0.659614i
\(222\) 282478. 388797.i 0.384682 0.529469i
\(223\) −505073. 164108.i −0.680130 0.220987i −0.0514774 0.998674i \(-0.516393\pi\)
−0.628652 + 0.777687i \(0.716393\pi\)
\(224\) −795637. −1.05948
\(225\) −252521. + 17480.1i −0.332538 + 0.0230191i
\(226\) −1.39238e6 −1.81337
\(227\) −634773. 206250.i −0.817625 0.265662i −0.129801 0.991540i \(-0.541434\pi\)
−0.687824 + 0.725878i \(0.741434\pi\)
\(228\) 377250. 519240.i 0.480609 0.661501i
\(229\) 668799. + 485911.i 0.842765 + 0.612305i 0.923142 0.384460i \(-0.125612\pi\)
−0.0803765 + 0.996765i \(0.525612\pi\)
\(230\) −1.84078e6 + 63635.6i −2.29447 + 0.0793196i
\(231\) 431416. 313442.i 0.531944 0.386480i
\(232\) 79153.0i 0.0965489i
\(233\) −796112. 1.09575e6i −0.960692 1.32228i −0.946611 0.322379i \(-0.895518\pi\)
−0.0140814 0.999901i \(-0.504482\pi\)
\(234\) 164078. + 504981.i 0.195890 + 0.602886i
\(235\) 23260.1 + 672843.i 0.0274753 + 0.794775i
\(236\) 350663. 1.07923e6i 0.409835 1.26134i
\(237\) 796534. 258810.i 0.921157 0.299302i
\(238\) 727125. 236257.i 0.832084 0.270360i
\(239\) −817.164 + 2514.97i −0.000925368 + 0.00284799i −0.951518 0.307593i \(-0.900477\pi\)
0.950593 + 0.310441i \(0.100477\pi\)
\(240\) −508216. + 184774.i −0.569535 + 0.207068i
\(241\) 25330.5 + 77959.4i 0.0280932 + 0.0864621i 0.964120 0.265467i \(-0.0855260\pi\)
−0.936027 + 0.351929i \(0.885526\pi\)
\(242\) 925208. + 1.27344e6i 1.01555 + 1.39778i
\(243\) 59049.0i 0.0641500i
\(244\) −169524. + 123166.i −0.182287 + 0.132440i
\(245\) −311391. + 243110.i −0.331429 + 0.258754i
\(246\) 801504. + 582327.i 0.844438 + 0.613520i
\(247\) −1.14778e6 + 1.57979e6i −1.19707 + 1.64762i
\(248\) −13481.5 4380.41i −0.0139190 0.00452257i
\(249\) −476287. −0.486822
\(250\) −142715. 1.37172e6i −0.144418 1.38808i
\(251\) 127047. 0.127286 0.0636429 0.997973i \(-0.479728\pi\)
0.0636429 + 0.997973i \(0.479728\pi\)
\(252\) 230545. + 74908.6i 0.228694 + 0.0743071i
\(253\) 1.47280e6 2.02713e6i 1.44658 1.99104i
\(254\) 1.34145e6 + 974623.i 1.30464 + 0.947878i
\(255\) 389147. 303815.i 0.374768 0.292590i
\(256\) −930090. + 675750.i −0.887003 + 0.644446i
\(257\) 1.67789e6i 1.58464i 0.610107 + 0.792319i \(0.291127\pi\)
−0.610107 + 0.792319i \(0.708873\pi\)
\(258\) −603440. 830564.i −0.564397 0.776826i
\(259\) 206281. + 634869.i 0.191078 + 0.588077i
\(260\) −1.32284e6 + 480948.i −1.21359 + 0.441230i
\(261\) −149718. + 460785.i −0.136042 + 0.418694i
\(262\) 135311. 43965.1i 0.121781 0.0395690i
\(263\) 599681. 194848.i 0.534602 0.173703i −0.0292599 0.999572i \(-0.509315\pi\)
0.563862 + 0.825869i \(0.309315\pi\)
\(264\) 22095.3 68002.3i 0.0195115 0.0600501i
\(265\) −1654.44 47857.9i −0.00144723 0.0418638i
\(266\) 566207. + 1.74261e6i 0.490649 + 1.51006i
\(267\) 504950. + 695003.i 0.433481 + 0.596635i
\(268\) 1.81406e6i 1.54282i
\(269\) 368179. 267498.i 0.310226 0.225393i −0.421767 0.906704i \(-0.638590\pi\)
0.731994 + 0.681312i \(0.238590\pi\)
\(270\) 321529. 11115.2i 0.268417 0.00927916i
\(271\) 431488. + 313494.i 0.356899 + 0.259302i 0.751758 0.659440i \(-0.229206\pi\)
−0.394858 + 0.918742i \(0.629206\pi\)
\(272\) 619945. 853281.i 0.508079 0.699310i
\(273\) −701434. 227910.i −0.569614 0.185079i
\(274\) 1.73516e6 1.39625
\(275\) 1.59036e6 + 995316.i 1.26813 + 0.793650i
\(276\) 1.13903e6 0.900041
\(277\) 1.82895e6 + 594261.i 1.43219 + 0.465348i 0.919454 0.393197i \(-0.128631\pi\)
0.512739 + 0.858545i \(0.328631\pi\)
\(278\) 1.04082e6 1.43257e6i 0.807728 1.11174i
\(279\) 70196.3 + 51000.6i 0.0539888 + 0.0392252i
\(280\) 20148.1 70172.1i 0.0153582 0.0534896i
\(281\) −1.41984e6 + 1.03157e6i −1.07269 + 0.779354i −0.976394 0.215998i \(-0.930699\pi\)
−0.0962955 + 0.995353i \(0.530699\pi\)
\(282\) 855692.i 0.640759i
\(283\) 393623. + 541776.i 0.292156 + 0.402118i 0.929713 0.368285i \(-0.120055\pi\)
−0.637557 + 0.770403i \(0.720055\pi\)
\(284\) −264037. 812622.i −0.194254 0.597851i
\(285\) 728114. + 932617.i 0.530991 + 0.680128i
\(286\) 1.21613e6 3.74287e6i 0.879155 2.70576i
\(287\) −1.30878e6 + 425248.i −0.937911 + 0.304746i
\(288\) 621048. 201791.i 0.441208 0.143357i
\(289\) 141202. 434574.i 0.0994478 0.306069i
\(290\) −2.53721e6 728497.i −1.77158 0.508666i
\(291\) −136462. 419986.i −0.0944666 0.290738i
\(292\) −462539. 636631.i −0.317462 0.436949i
\(293\) 1.15530e6i 0.786187i 0.919499 + 0.393093i \(0.128595\pi\)
−0.919499 + 0.393093i \(0.871405\pi\)
\(294\) 406216. 295133.i 0.274087 0.199136i
\(295\) 1.73389e6 + 1.17040e6i 1.16002 + 0.783035i
\(296\) 72412.6 + 52610.8i 0.0480380 + 0.0349017i
\(297\) −257253. + 354079.i −0.169227 + 0.232921i
\(298\) −1.61625e6 525152.i −1.05431 0.342566i
\(299\) −3.46550e6 −2.24176
\(300\) 58895.9 + 850820.i 0.0377817 + 0.545801i
\(301\) 1.42603e6 0.907217
\(302\) 2.62497e6 + 852903.i 1.65618 + 0.538124i
\(303\) −109674. + 150953.i −0.0686273 + 0.0944573i
\(304\) 2.04495e6 + 1.48574e6i 1.26911 + 0.922059i
\(305\) −131992. 363042.i −0.0812455 0.223464i
\(306\) −507650. + 368829.i −0.309928 + 0.225176i
\(307\) 139944.i 0.0847438i 0.999102 + 0.0423719i \(0.0134914\pi\)
−0.999102 + 0.0423719i \(0.986509\pi\)
\(308\) −1.05608e6 1.45357e6i −0.634338 0.873092i
\(309\) −178062. 548019.i −0.106090 0.326512i
\(310\) −264491. + 391828.i −0.156317 + 0.231575i
\(311\) −227175. + 699174.i −0.133187 + 0.409906i −0.995304 0.0968033i \(-0.969138\pi\)
0.862117 + 0.506709i \(0.169138\pi\)
\(312\) −94051.6 + 30559.2i −0.0546990 + 0.0177728i
\(313\) −281464. + 91453.3i −0.162391 + 0.0527641i −0.389084 0.921202i \(-0.627209\pi\)
0.226693 + 0.973966i \(0.427209\pi\)
\(314\) −425670. + 1.31008e6i −0.243640 + 0.749848i
\(315\) −250022. + 370393.i −0.141972 + 0.210323i
\(316\) −872009. 2.68377e6i −0.491251 1.51192i
\(317\) −1.30504e6 1.79623e6i −0.729417 1.00396i −0.999158 0.0410235i \(-0.986938\pi\)
0.269741 0.962933i \(-0.413062\pi\)
\(318\) 60863.6i 0.0337512i
\(319\) 2.90522e6 2.11077e6i 1.59846 1.16135i
\(320\) 558705. + 1.53670e6i 0.305005 + 0.838910i
\(321\) 220293. + 160052.i 0.119327 + 0.0866959i
\(322\) −1.91133e6 + 2.63072e6i −1.02730 + 1.41395i
\(323\) −2.19475e6 713119.i −1.17052 0.380326i
\(324\) −198954. −0.105291
\(325\) −179191. 2.58862e6i −0.0941039 1.35944i
\(326\) −493490. −0.257179
\(327\) −183517. 59628.3i −0.0949090 0.0308378i
\(328\) −108457. + 149278.i −0.0556638 + 0.0766147i
\(329\) 961584. + 698632.i 0.489776 + 0.355843i
\(330\) −1.97643e6 1.33412e6i −0.999069 0.674390i
\(331\) 1.98796e6 1.44434e6i 0.997329 0.724602i 0.0358149 0.999358i \(-0.488597\pi\)
0.961514 + 0.274757i \(0.0885973\pi\)
\(332\) 1.60476e6i 0.799032i
\(333\) −322033. 443240.i −0.159144 0.219042i
\(334\) 17612.3 + 54205.2i 0.00863875 + 0.0265873i
\(335\) −3.21433e6 922915.i −1.56487 0.449314i
\(336\) −295016. + 907966.i −0.142560 + 0.438754i
\(337\) −1.36489e6 + 443480.i −0.654671 + 0.212716i −0.617473 0.786592i \(-0.711843\pi\)
−0.0371987 + 0.999308i \(0.511843\pi\)
\(338\) −2.38890e6 + 776201.i −1.13738 + 0.369558i
\(339\) −490518. + 1.50966e6i −0.231822 + 0.713476i
\(340\) −1.02365e6 1.31116e6i −0.480234 0.615116i
\(341\) −198732. 611635.i −0.0925513 0.284844i
\(342\) −883924. 1.21662e6i −0.408648 0.562456i
\(343\) 2.35616e6i 1.08136i
\(344\) 154691. 112389.i 0.0704803 0.0512070i
\(345\) −579489. + 2.01825e6i −0.262118 + 0.912908i
\(346\) 173526. + 126074.i 0.0779247 + 0.0566156i
\(347\) 2.34426e6 3.22660e6i 1.04516 1.43854i 0.152226 0.988346i \(-0.451356\pi\)
0.892932 0.450191i \(-0.148644\pi\)
\(348\) 1.55253e6 + 504447.i 0.687213 + 0.223289i
\(349\) −4.24080e6 −1.86374 −0.931868 0.362797i \(-0.881822\pi\)
−0.931868 + 0.362797i \(0.881822\pi\)
\(350\) −2.06390e6 1.29168e6i −0.900572 0.563618i
\(351\) 605319. 0.262251
\(352\) −4.60314e6 1.49565e6i −1.98015 0.643389i
\(353\) 1.18842e6 1.63572e6i 0.507615 0.698672i −0.475900 0.879500i \(-0.657878\pi\)
0.983515 + 0.180827i \(0.0578775\pi\)
\(354\) −2.15105e6 1.56283e6i −0.912311 0.662832i
\(355\) 1.57422e6 54420.5i 0.662970 0.0229188i
\(356\) 2.34168e6 1.70133e6i 0.979270 0.711482i
\(357\) 871603.i 0.361950i
\(358\) 2.61613e6 + 3.60079e6i 1.07883 + 1.48488i
\(359\) 1.47486e6 + 4.53914e6i 0.603968 + 1.85882i 0.503735 + 0.863858i \(0.331959\pi\)
0.100233 + 0.994964i \(0.468041\pi\)
\(360\) 2070.18 + 59884.0i 0.000841885 + 0.0243531i
\(361\) 943881. 2.90497e6i 0.381197 1.17320i
\(362\) −510973. + 166025.i −0.204940 + 0.0665890i
\(363\) 1.70664e6 554522.i 0.679792 0.220878i
\(364\) −767898. + 2.36335e6i −0.303774 + 0.934920i
\(365\) 1.36337e6 495684.i 0.535650 0.194748i
\(366\) 151720. + 466945.i 0.0592024 + 0.182206i
\(367\) 1.00271e6 + 1.38012e6i 0.388608 + 0.534872i 0.957839 0.287305i \(-0.0927592\pi\)
−0.569232 + 0.822177i \(0.692759\pi\)
\(368\) 4.48589e6i 1.72675i
\(369\) 913737. 663869.i 0.349346 0.253815i
\(370\) 2.35288e6 1.83694e6i 0.893501 0.697575i
\(371\) −68395.4 49692.2i −0.0257984 0.0187436i
\(372\) 171837. 236513.i 0.0643811 0.0886130i
\(373\) −1.67384e6 543865.i −0.622935 0.202404i −0.0194920 0.999810i \(-0.506205\pi\)
−0.603443 + 0.797406i \(0.706205\pi\)
\(374\) 4.65089e6 1.71932
\(375\) −1.53753e6 328503.i −0.564607 0.120632i
\(376\) 159371. 0.0581352
\(377\) −4.72357e6 1.53478e6i −1.71166 0.556151i
\(378\) 333852. 459508.i 0.120178 0.165411i
\(379\) 874177. + 635127.i 0.312609 + 0.227124i 0.733015 0.680212i \(-0.238112\pi\)
−0.420406 + 0.907336i \(0.638112\pi\)
\(380\) 3.14227e6 2.45324e6i 1.11631 0.871527i
\(381\) 1.52930e6 1.11110e6i 0.539733 0.392139i
\(382\) 1.08620e6i 0.380848i
\(383\) −2.66467e6 3.66760e6i −0.928210 1.27757i −0.960554 0.278095i \(-0.910297\pi\)
0.0323437 0.999477i \(-0.489703\pi\)
\(384\) 75269.5 + 231656.i 0.0260490 + 0.0801705i
\(385\) 3.11288e6 1.13176e6i 1.07031 0.389137i
\(386\) 747191. 2.29962e6i 0.255249 0.785574i
\(387\) −1.11311e6 + 361671.i −0.377798 + 0.122754i
\(388\) −1.41506e6 + 459781.i −0.477195 + 0.155050i
\(389\) 390129. 1.20069e6i 0.130718 0.402308i −0.864182 0.503180i \(-0.832163\pi\)
0.994899 + 0.100872i \(0.0321633\pi\)
\(390\) 113944. + 3.29604e6i 0.0379340 + 1.09731i
\(391\) −1.26557e6 3.89503e6i −0.418644 1.28845i
\(392\) 54967.9 + 75656.8i 0.0180673 + 0.0248675i
\(393\) 162197.i 0.0529737i
\(394\) 1.78892e6 1.29973e6i 0.580565 0.421805i
\(395\) 5.19902e6 179729.i 1.67660 0.0579598i
\(396\) 1.19300e6 + 866765.i 0.382298 + 0.277756i
\(397\) −1.28977e6 + 1.77522e6i −0.410712 + 0.565297i −0.963392 0.268097i \(-0.913605\pi\)
0.552680 + 0.833394i \(0.313605\pi\)
\(398\) −2.64054e6 857962.i −0.835573 0.271494i
\(399\) 2.08886e6 0.656865
\(400\) −3.35082e6 + 231952.i −1.04713 + 0.0724851i
\(401\) −5.53532e6 −1.71902 −0.859512 0.511115i \(-0.829232\pi\)
−0.859512 + 0.511115i \(0.829232\pi\)
\(402\) 4.04244e6 + 1.31347e6i 1.24761 + 0.405373i
\(403\) −522814. + 719592.i −0.160356 + 0.220711i
\(404\) 508608. + 369525.i 0.155035 + 0.112639i
\(405\) 101219. 352528.i 0.0306638 0.106796i
\(406\) −3.77027e6 + 2.73926e6i −1.13516 + 0.824744i
\(407\) 4.06079e6i 1.21514i
\(408\) −68693.6 94548.6i −0.0204299 0.0281193i
\(409\) −308363. 949043.i −0.0911493 0.280529i 0.895082 0.445902i \(-0.147117\pi\)
−0.986231 + 0.165373i \(0.947117\pi\)
\(410\) 3.78685e6 + 4.85045e6i 1.11255 + 1.42502i
\(411\) 611276. 1.88131e6i 0.178498 0.549360i
\(412\) −1.84644e6 + 599946.i −0.535911 + 0.174128i
\(413\) 3.51246e6 1.14127e6i 1.01330 0.329240i
\(414\) 824714. 2.53821e6i 0.236485 0.727825i
\(415\) −2.84347e6 816432.i −0.810455 0.232702i
\(416\) 2.06858e6 + 6.36644e6i 0.586056 + 1.80370i
\(417\) −1.18657e6 1.63317e6i −0.334158 0.459930i
\(418\) 1.11462e7i 3.12022i
\(419\) −3.23938e6 + 2.35355e6i −0.901419 + 0.654919i −0.938830 0.344381i \(-0.888089\pi\)
0.0374109 + 0.999300i \(0.488089\pi\)
\(420\) 1.24797e6 + 842402.i 0.345208 + 0.233022i
\(421\) −1.16240e6 844531.i −0.319631 0.232226i 0.416387 0.909188i \(-0.363296\pi\)
−0.736018 + 0.676962i \(0.763296\pi\)
\(422\) 4.46510e6 6.14568e6i 1.22053 1.67992i
\(423\) −927769. 301450.i −0.252109 0.0819153i
\(424\) −11335.7 −0.00306220
\(425\) 2.84403e6 1.14674e6i 0.763768 0.307960i
\(426\) −2.00202e6 −0.534496
\(427\) −648602. 210743.i −0.172151 0.0559351i
\(428\) 539264. 742234.i 0.142296 0.195854i
\(429\) −3.62971e6 2.63714e6i −0.952200 0.691814i
\(430\) −2.17887e6 5.99293e6i −0.568277 1.56303i
\(431\) −4.08029e6 + 2.96450e6i −1.05803 + 0.768703i −0.973723 0.227736i \(-0.926868\pi\)
−0.0843067 + 0.996440i \(0.526868\pi\)
\(432\) 783551.i 0.202003i
\(433\) 1.66389e6 + 2.29015e6i 0.426486 + 0.587007i 0.967142 0.254236i \(-0.0818241\pi\)
−0.540657 + 0.841243i \(0.681824\pi\)
\(434\) 257906. + 793754.i 0.0657261 + 0.202284i
\(435\) −1.68369e6 + 2.49429e6i −0.426618 + 0.632009i
\(436\) −200906. + 618326.i −0.0506148 + 0.155776i
\(437\) 9.33470e6 3.03303e6i 2.33828 0.759753i
\(438\) −1.75357e6 + 569769.i −0.436754 + 0.141910i
\(439\) 871251. 2.68144e6i 0.215766 0.664058i −0.783333 0.621603i \(-0.786482\pi\)
0.999098 0.0424556i \(-0.0135181\pi\)
\(440\) 248477. 368105.i 0.0611865 0.0906441i
\(441\) −176888. 544404.i −0.0433113 0.133298i
\(442\) −3.78092e6 5.20399e6i −0.920538 1.26701i
\(443\) 2.85447e6i 0.691061i −0.938408 0.345530i \(-0.887699\pi\)
0.938408 0.345530i \(-0.112301\pi\)
\(444\) −1.49341e6 + 1.08503e6i −0.359519 + 0.261206i
\(445\) 1.82325e6 + 5.01479e6i 0.436461 + 1.20047i
\(446\) 3.39181e6 + 2.46430e6i 0.807411 + 0.586619i
\(447\) −1.13877e6 + 1.56739e6i −0.269568 + 0.371029i
\(448\) 2.74544e6 + 892047.i 0.646274 + 0.209987i
\(449\) −2.95959e6 −0.692813 −0.346406 0.938085i \(-0.612598\pi\)
−0.346406 + 0.938085i \(0.612598\pi\)
\(450\) 1.93861e6 + 484793.i 0.451293 + 0.112856i
\(451\) −8.37131e6 −1.93799
\(452\) 5.08650e6 + 1.65270e6i 1.17104 + 0.380495i
\(453\) 1.84949e6 2.54560e6i 0.423454 0.582835i
\(454\) 4.26282e6 + 3.09712e6i 0.970638 + 0.705210i
\(455\) −3.79695e6 2.56301e6i −0.859817 0.580393i
\(456\) 226592. 164629.i 0.0510309 0.0370761i
\(457\) 3.60240e6i 0.806867i −0.915009 0.403433i \(-0.867817\pi\)
0.915009 0.403433i \(-0.132183\pi\)
\(458\) −3.83604e6 5.27986e6i −0.854515 1.17614i
\(459\) 221057. + 680344.i 0.0489748 + 0.150729i
\(460\) 6.80010e6 + 1.95248e6i 1.49838 + 0.430221i
\(461\) 1.51877e6 4.67429e6i 0.332843 1.02438i −0.634932 0.772568i \(-0.718972\pi\)
0.967775 0.251817i \(-0.0810280\pi\)
\(462\) −4.00379e6 + 1.30091e6i −0.872703 + 0.283558i
\(463\) −1.36410e6 + 443223.i −0.295729 + 0.0960881i −0.453124 0.891448i \(-0.649690\pi\)
0.157395 + 0.987536i \(0.449690\pi\)
\(464\) −1.98669e6 + 6.11439e6i −0.428385 + 1.31843i
\(465\) 331655. + 424806.i 0.0711302 + 0.0911083i
\(466\) 3.30419e6 + 1.01692e7i 0.704855 + 2.16932i
\(467\) 2.89974e6 + 3.99115e6i 0.615272 + 0.846849i 0.996998 0.0774265i \(-0.0246703\pi\)
−0.381726 + 0.924275i \(0.624670\pi\)
\(468\) 2.03951e6i 0.430438i
\(469\) −4.77647e6 + 3.47031e6i −1.00271 + 0.728511i
\(470\) 1.46679e6 5.10856e6i 0.306284 1.06673i
\(471\) 1.27047e6 + 923050.i 0.263883 + 0.191722i
\(472\) 291074. 400629.i 0.0601378 0.0827726i
\(473\) 8.25024e6 + 2.68067e6i 1.69556 + 0.550922i
\(474\) −6.61188e6 −1.35170
\(475\) 2.74825e6 + 6.81590e6i 0.558884 + 1.38608i
\(476\) −2.93670e6 −0.594076
\(477\) 65990.2 + 21441.5i 0.0132796 + 0.00431479i
\(478\) 12270.8 16889.3i 0.00245642 0.00338097i
\(479\) −6.44308e6 4.68117e6i −1.28308 0.932215i −0.283442 0.958989i \(-0.591476\pi\)
−0.999641 + 0.0267745i \(0.991476\pi\)
\(480\) 4.05361e6 140133.i 0.803043 0.0277611i
\(481\) 4.54371e6 3.30120e6i 0.895464 0.650593i
\(482\) 647126.i 0.126874i
\(483\) 2.17897e6 + 2.99910e6i 0.424995 + 0.584956i
\(484\) −1.86835e6 5.75020e6i −0.362532 1.11576i
\(485\) −94765.3 2.74127e6i −0.0182934 0.529172i
\(486\) −144053. + 443349.i −0.0276650 + 0.0851442i
\(487\) −1.57177e6 + 510698.i −0.300307 + 0.0975757i −0.455295 0.890341i \(-0.650466\pi\)
0.154988 + 0.987916i \(0.450466\pi\)
\(488\) −86967.5 + 28257.5i −0.0165313 + 0.00537135i
\(489\) −173851. + 535058.i −0.0328779 + 0.101188i
\(490\) 2.93105e6 1.06565e6i 0.551484 0.200505i
\(491\) 1.73234e6 + 5.33160e6i 0.324287 + 0.998053i 0.971761 + 0.235965i \(0.0758252\pi\)
−0.647474 + 0.762087i \(0.724175\pi\)
\(492\) −2.23678e6 3.07866e6i −0.416591 0.573389i
\(493\) 5.86951e6i 1.08764i
\(494\) 1.24717e7 9.06123e6i 2.29937 1.67059i
\(495\) −2.14277e6 + 1.67291e6i −0.393063 + 0.306873i
\(496\) 931470. + 676753.i 0.170006 + 0.123517i
\(497\) 1.63455e6 2.24977e6i 0.296830 0.408552i
\(498\) 3.57604e6 + 1.16192e6i 0.646143 + 0.209945i
\(499\) −5.40101e6 −0.971009 −0.485505 0.874234i \(-0.661364\pi\)
−0.485505 + 0.874234i \(0.661364\pi\)
\(500\) −1.10683e6 + 5.18042e6i −0.197995 + 0.926702i
\(501\) 64975.6 0.0115653
\(502\) −953888. 309937.i −0.168942 0.0548926i
\(503\) −2.17162e6 + 2.98898e6i −0.382704 + 0.526747i −0.956298 0.292392i \(-0.905549\pi\)
0.573594 + 0.819140i \(0.305549\pi\)
\(504\) 85582.4 + 62179.2i 0.0150075 + 0.0109036i
\(505\) −913520. + 713205.i −0.159400 + 0.124447i
\(506\) −1.60033e7 + 1.16270e7i −2.77864 + 2.01880i
\(507\) 2.86357e6i 0.494752i
\(508\) −3.74363e6 5.15267e6i −0.643626 0.885875i
\(509\) −1.14347e6 3.51924e6i −0.195628 0.602081i −0.999969 0.00791268i \(-0.997481\pi\)
0.804341 0.594168i \(-0.202519\pi\)
\(510\) −3.66295e6 + 1.33175e6i −0.623598 + 0.226724i
\(511\) 791426. 2.43576e6i 0.134078 0.412650i
\(512\) 7.80812e6 2.53701e6i 1.31635 0.427708i
\(513\) −1.63049e6 + 529779.i −0.273543 + 0.0888794i
\(514\) 4.09329e6 1.25978e7i 0.683383 2.10324i
\(515\) −123655. 3.57694e6i −0.0205443 0.594284i
\(516\) 1.21858e6 + 3.75040e6i 0.201479 + 0.620089i
\(517\) 4.24993e6 + 5.84952e6i 0.699286 + 0.962485i
\(518\) 5.26993e6i 0.862939i
\(519\) 197825. 143728.i 0.0322376 0.0234220i
\(520\) −613879. + 21221.7i −0.0995576 + 0.00344170i
\(521\) −608903. 442394.i −0.0982775 0.0714027i 0.537561 0.843225i \(-0.319346\pi\)
−0.635839 + 0.771822i \(0.719346\pi\)
\(522\) 2.24821e6 3.09440e6i 0.361128 0.497050i
\(523\) 8.09200e6 + 2.62925e6i 1.29361 + 0.420318i 0.873352 0.487089i \(-0.161941\pi\)
0.420253 + 0.907407i \(0.361941\pi\)
\(524\) −546490. −0.0869469
\(525\) −2.12757e6 + 1.78270e6i −0.336887 + 0.282280i
\(526\) −4.97783e6 −0.784470
\(527\) −999707. 324825.i −0.156800 0.0509474i
\(528\) −3.41362e6 + 4.69845e6i −0.532881 + 0.733448i
\(529\) 8.88501e6 + 6.45534e6i 1.38044 + 1.00295i
\(530\) −104330. + 363361.i −0.0161331 + 0.0561886i
\(531\) −2.45226e6 + 1.78167e6i −0.377425 + 0.274215i
\(532\) 7.03800e6i 1.07813i
\(533\) 6.80541e6 + 9.36684e6i 1.03762 + 1.42815i
\(534\) −2.09575e6 6.45004e6i −0.318043 0.978835i
\(535\) 1.04081e6 + 1.33314e6i 0.157213 + 0.201368i
\(536\) −244631. + 752895.i −0.0367789 + 0.113194i
\(537\) 4.82572e6 1.56797e6i 0.722149 0.234640i
\(538\) −3.41692e6 + 1.11022e6i −0.508955 + 0.165369i
\(539\) −1.31107e6 + 4.03507e6i −0.194381 + 0.598245i
\(540\) −1.18777e6 341039.i −0.175287 0.0503292i
\(541\) −1.68346e6 5.18117e6i −0.247292 0.761087i −0.995251 0.0973420i \(-0.968966\pi\)
0.747959 0.663745i \(-0.231034\pi\)
\(542\) −2.47489e6 3.40640e6i −0.361875 0.498078i
\(543\) 612502.i 0.0891472i
\(544\) −6.40009e6 + 4.64994e6i −0.927233 + 0.673674i
\(545\) −993401. 670564.i −0.143263 0.0967050i
\(546\) 4.71048e6 + 3.42236e6i 0.676213 + 0.491298i
\(547\) −3.27736e6 + 4.51090e6i −0.468334 + 0.644607i −0.976211 0.216823i \(-0.930431\pi\)
0.507877 + 0.861430i \(0.330431\pi\)
\(548\) −6.33873e6 2.05958e6i −0.901676 0.292972i
\(549\) 559726. 0.0792583
\(550\) −9.51252e6 1.13527e7i −1.34088 1.60027i
\(551\) 1.40667e7 1.97384
\(552\) 472736. + 153601.i 0.0660345 + 0.0214559i
\(553\) 5.39828e6 7.43010e6i 0.750659 1.03319i
\(554\) −1.22823e7 8.92360e6i −1.70022 1.23528i
\(555\) −1.16278e6 3.19820e6i −0.160238 0.440730i
\(556\) −5.50265e6 + 3.99791e6i −0.754893 + 0.548462i
\(557\) 3.74540e6i 0.511518i −0.966741 0.255759i \(-0.917675\pi\)
0.966741 0.255759i \(-0.0823253\pi\)
\(558\) −402626. 554168.i −0.0547415 0.0753452i
\(559\) −3.70754e6 1.14106e7i −0.501829 1.54447i
\(560\) −3.31767e6 + 4.91493e6i −0.447057 + 0.662289i
\(561\) 1.63845e6 5.04264e6i 0.219800 0.676474i
\(562\) 1.31770e7 4.28145e6i 1.75985 0.571808i
\(563\) 2.95235e6 959278.i 0.392552 0.127548i −0.106089 0.994357i \(-0.533833\pi\)
0.498641 + 0.866809i \(0.333833\pi\)
\(564\) −1.01568e6 + 3.12594e6i −0.134449 + 0.413792i
\(565\) −5.51623e6 + 8.17196e6i −0.726977 + 1.07697i
\(566\) −1.63370e6 5.02800e6i −0.214353 0.659711i
\(567\) −380601. 523852.i −0.0497179 0.0684308i
\(568\) 372872.i 0.0484941i
\(569\) −9.71653e6 + 7.05947e6i −1.25814 + 0.914096i −0.998665 0.0516529i \(-0.983551\pi\)
−0.259480 + 0.965749i \(0.583551\pi\)
\(570\) −3.19163e6 8.77850e6i −0.411458 1.13170i
\(571\) 9.06714e6 + 6.58766e6i 1.16380 + 0.845553i 0.990254 0.139272i \(-0.0444761\pi\)
0.173550 + 0.984825i \(0.444476\pi\)
\(572\) −8.88532e6 + 1.22296e7i −1.13549 + 1.56287i
\(573\) 1.17769e6 + 382656.i 0.149846 + 0.0486880i
\(574\) 1.08639e7 1.37628
\(575\) −6.91920e6 + 1.10558e7i −0.872743 + 1.39450i
\(576\) −2.36924e6 −0.297545
\(577\) −6.00994e6 1.95275e6i −0.751502 0.244178i −0.0918749 0.995771i \(-0.529286\pi\)
−0.659628 + 0.751593i \(0.729286\pi\)
\(578\) −2.12033e6 + 2.91838e6i −0.263988 + 0.363348i
\(579\) −2.23009e6 1.62026e6i −0.276456 0.200857i
\(580\) 8.40402e6 + 5.67287e6i 1.03733 + 0.700217i
\(581\) −4.22538e6 + 3.06991e6i −0.519308 + 0.377299i
\(582\) 3.48622e6i 0.426626i
\(583\) −302288. 416064.i −0.0368341 0.0506978i
\(584\) −106118. 326598.i −0.0128753 0.0396261i
\(585\) 3.61381e6 + 1.03761e6i 0.436591 + 0.125356i
\(586\) 2.81841e6 8.67417e6i 0.339047 1.04348i
\(587\) −4.98903e6 + 1.62104e6i −0.597615 + 0.194177i −0.592176 0.805808i \(-0.701731\pi\)
−0.00543833 + 0.999985i \(0.501731\pi\)
\(588\) −1.83426e6 + 595989.i −0.218786 + 0.0710877i
\(589\) 778464. 2.39587e6i 0.0924592 0.284560i
\(590\) −1.01630e7 1.30175e7i −1.20197 1.53956i
\(591\) −778990. 2.39749e6i −0.0917410 0.282350i
\(592\) −4.27321e6 5.88157e6i −0.501130 0.689746i
\(593\) 1.36939e7i 1.59916i 0.600560 + 0.799580i \(0.294945\pi\)
−0.600560 + 0.799580i \(0.705055\pi\)
\(594\) 2.79529e6 2.03090e6i 0.325058 0.236168i
\(595\) 1.49407e6 5.20354e6i 0.173012 0.602569i
\(596\) 5.28101e6 + 3.83688e6i 0.608978 + 0.442448i
\(597\) −1.86046e6 + 2.56070e6i −0.213641 + 0.294051i
\(598\) 2.60195e7 + 8.45426e6i 2.97541 + 0.966768i
\(599\) −5.28430e6 −0.601756 −0.300878 0.953663i \(-0.597280\pi\)
−0.300878 + 0.953663i \(0.597280\pi\)
\(600\) −90291.5 + 361061.i −0.0102393 + 0.0409452i
\(601\) −1.46172e7 −1.65074 −0.825369 0.564594i \(-0.809033\pi\)
−0.825369 + 0.564594i \(0.809033\pi\)
\(602\) −1.07068e7 3.47886e6i −1.20412 0.391242i
\(603\) 2.84821e6 3.92022e6i 0.318991 0.439053i
\(604\) −8.57692e6 6.23150e6i −0.956619 0.695025i
\(605\) 1.11393e7 385086.i 1.23729 0.0427729i
\(606\) 1.19171e6 865825.i 0.131822 0.0957742i
\(607\) 730831.i 0.0805092i 0.999189 + 0.0402546i \(0.0128169\pi\)
−0.999189 + 0.0402546i \(0.987183\pi\)
\(608\) −1.11439e7 1.53382e7i −1.22258 1.68274i
\(609\) 1.64177e6 + 5.05286e6i 0.179378 + 0.552070i
\(610\) 105361. + 3.04778e6i 0.0114645 + 0.331633i
\(611\) 3.09021e6 9.51068e6i 0.334876 1.03064i
\(612\) 2.29229e6 744810.i 0.247395 0.0803835i
\(613\) −1.01682e7 + 3.30385e6i −1.09293 + 0.355115i −0.799379 0.600827i \(-0.794838\pi\)
−0.293554 + 0.955943i \(0.594838\pi\)
\(614\) 341400. 1.05072e6i 0.0365462 0.112478i
\(615\) 6.59307e6 2.39706e6i 0.702910 0.255559i
\(616\) −242292. 745697.i −0.0257269 0.0791791i
\(617\) 4.00857e6 + 5.51733e6i 0.423913 + 0.583466i 0.966543 0.256506i \(-0.0825712\pi\)
−0.542630 + 0.839972i \(0.682571\pi\)
\(618\) 4.54900e6i 0.479120i
\(619\) −1.42870e7 + 1.03801e7i −1.49870 + 1.08887i −0.527808 + 0.849363i \(0.676986\pi\)
−0.970894 + 0.239508i \(0.923014\pi\)
\(620\) 1.43130e6 1.11745e6i 0.149538 0.116748i
\(621\) −2.46147e6 1.78836e6i −0.256133 0.186092i
\(622\) 3.41134e6 4.69530e6i 0.353548 0.486617i
\(623\) 8.95931e6 + 2.91106e6i 0.924814 + 0.300490i
\(624\) 8.03228e6 0.825805
\(625\) −8.61610e6 4.59677e6i −0.882289 0.470709i
\(626\) 2.33638e6 0.238291
\(627\) 1.20850e7 + 3.92667e6i 1.22766 + 0.398892i
\(628\) 3.11004e6 4.28060e6i 0.314678 0.433118i
\(629\) 5.36968e6 + 3.90130e6i 0.541156 + 0.393173i
\(630\) 2.78080e6 2.17103e6i 0.279137 0.217928i
\(631\) −2.71378e6 + 1.97168e6i −0.271333 + 0.197135i −0.715128 0.698993i \(-0.753632\pi\)
0.443796 + 0.896128i \(0.353632\pi\)
\(632\) 1.23145e6i 0.122637i
\(633\) −5.09034e6 7.00625e6i −0.504937 0.694987i
\(634\) 5.41645e6 + 1.66701e7i 0.535170 + 1.64708i
\(635\) 1.10346e7 4.01189e6i 1.08598 0.394835i
\(636\) 72243.1 222341.i 0.00708196 0.0217960i
\(637\) 5.58076e6 1.81330e6i 0.544935 0.177060i
\(638\) −2.69622e7 + 8.76054e6i −2.62243 + 0.852078i
\(639\) −705288. + 2.17065e6i −0.0683305 + 0.210300i
\(640\) 52270.6 + 1.51203e6i 0.00504438 + 0.145918i
\(641\) −1.47841e6 4.55008e6i −0.142118 0.437395i 0.854511 0.519434i \(-0.173857\pi\)
−0.996629 + 0.0820383i \(0.973857\pi\)
\(642\) −1.26354e6 1.73911e6i −0.120990 0.166529i
\(643\) 237872.i 0.0226890i −0.999936 0.0113445i \(-0.996389\pi\)
0.999936 0.0113445i \(-0.00361115\pi\)
\(644\) 1.01049e7 7.34163e6i 0.960101 0.697554i
\(645\) −7.26531e6 + 251161.i −0.687630 + 0.0237713i
\(646\) 1.47389e7 + 1.07084e7i 1.38958 + 1.00959i
\(647\) 9.51653e6 1.30984e7i 0.893754 1.23015i −0.0786641 0.996901i \(-0.525065\pi\)
0.972418 0.233245i \(-0.0749345\pi\)
\(648\) −82572.7 26829.5i −0.00772501 0.00251001i
\(649\) 2.24667e7 2.09376
\(650\) −4.96968e6 + 1.98729e7i −0.461365 + 1.84492i
\(651\) 951471. 0.0879920
\(652\) 1.80277e6 + 585757.i 0.166082 + 0.0539633i
\(653\) 1.95193e6 2.68661e6i 0.179136 0.246559i −0.710001 0.704200i \(-0.751306\pi\)
0.889137 + 0.457641i \(0.151306\pi\)
\(654\) 1.23241e6 + 895398.i 0.112671 + 0.0818600i
\(655\) 278031. 968327.i 0.0253215 0.0881899i
\(656\) 1.21248e7 8.80921e6i 1.10006 0.799240i
\(657\) 2.10200e6i 0.189985i
\(658\) −5.51538e6 7.59127e6i −0.496604 0.683517i
\(659\) 3.47657e6 + 1.06998e7i 0.311844 + 0.959758i 0.977034 + 0.213084i \(0.0683507\pi\)
−0.665190 + 0.746674i \(0.731649\pi\)
\(660\) 5.63654e6 + 7.21965e6i 0.503677 + 0.645144i
\(661\) −3.82049e6 + 1.17583e7i −0.340107 + 1.04674i 0.624045 + 0.781389i \(0.285488\pi\)
−0.964151 + 0.265353i \(0.914512\pi\)
\(662\) −1.84495e7 + 5.99459e6i −1.63621 + 0.531637i
\(663\) −6.97430e6 + 2.26609e6i −0.616193 + 0.200213i
\(664\) −216406. + 666029.i −0.0190480 + 0.0586236i
\(665\) 1.24706e7 + 3.58063e6i 1.09354 + 0.313982i
\(666\) 1.33657e6 + 4.11353e6i 0.116763 + 0.359359i
\(667\) 1.46735e7 + 2.01964e7i 1.27709 + 1.75776i
\(668\) 218923.i 0.0189823i
\(669\) 3.86676e6 2.80937e6i 0.334028 0.242685i
\(670\) 2.18822e7 + 1.47709e7i 1.88323 + 1.27122i
\(671\) −3.35631e6 2.43850e6i −0.287777 0.209082i
\(672\) 4.20897e6 5.79315e6i 0.359545 0.494871i
\(673\) −1.10290e7 3.58354e6i −0.938638 0.304982i −0.200548 0.979684i \(-0.564272\pi\)
−0.738090 + 0.674702i \(0.764272\pi\)
\(674\) 1.13297e7 0.960658
\(675\) 1.20858e6 1.93111e6i 0.102097 0.163135i
\(676\) 9.64825e6 0.812048
\(677\) 6.53659e6 + 2.12387e6i 0.548125 + 0.178097i 0.569971 0.821665i \(-0.306954\pi\)
−0.0218460 + 0.999761i \(0.506954\pi\)
\(678\) 7.36576e6 1.01381e7i 0.615380 0.846998i
\(679\) −3.91764e6 2.84633e6i −0.326100 0.236925i
\(680\) −248035. 682215.i −0.0205703 0.0565782i
\(681\) 4.85973e6 3.53080e6i 0.401555 0.291747i
\(682\) 5.07707e6i 0.417977i
\(683\) 9.12105e6 + 1.25540e7i 0.748157 + 1.02975i 0.998108 + 0.0614917i \(0.0195858\pi\)
−0.249950 + 0.968259i \(0.580414\pi\)
\(684\) 1.78499e6 + 5.49363e6i 0.145880 + 0.448972i
\(685\) 6.87424e6 1.01838e7i 0.559755 0.829244i
\(686\) 5.74797e6 1.76904e7i 0.466341 1.43525i
\(687\) −7.07598e6 + 2.29912e6i −0.571998 + 0.185853i
\(688\) −1.47704e7 + 4.79919e6i −1.18965 + 0.386542i
\(689\) −219800. + 676474.i −0.0176392 + 0.0542879i
\(690\) 9.27451e6 1.37396e7i 0.741597 1.09863i
\(691\) −5.57077e6 1.71451e7i −0.443834 1.36598i −0.883758 0.467945i \(-0.844995\pi\)
0.439924 0.898035i \(-0.355005\pi\)
\(692\) −484265. 666533.i −0.0384430 0.0529123i
\(693\) 4.79933e6i 0.379619i
\(694\) −2.54725e7 + 1.85069e7i −2.00758 + 1.45859i
\(695\) −4.28440e6 1.17841e7i −0.336456 0.925413i
\(696\) 576325. + 418725.i 0.0450967 + 0.0327647i
\(697\) −8.04252e6 + 1.10696e7i −0.627062 + 0.863076i
\(698\) 3.18406e7 + 1.03456e7i 2.47368 + 0.803746i
\(699\) 1.21898e7 0.943637
\(700\) 6.00647e6 + 7.16843e6i 0.463312 + 0.552941i
\(701\) −1.96020e7 −1.50663 −0.753315 0.657660i \(-0.771546\pi\)
−0.753315 + 0.657660i \(0.771546\pi\)
\(702\) −4.54483e6 1.47670e6i −0.348077 0.113097i
\(703\) −9.34974e6 + 1.28688e7i −0.713528 + 0.982087i
\(704\) 1.42068e7 + 1.03218e7i 1.08035 + 0.784920i
\(705\) −5.02212e6 3.39003e6i −0.380552 0.256880i
\(706\) −1.29133e7 + 9.38206e6i −0.975047 + 0.708413i
\(707\) 2.04608e6i 0.153948i
\(708\) 6.00300e6 + 8.26242e6i 0.450075 + 0.619475i
\(709\) 1.18777e6 + 3.65559e6i 0.0887397 + 0.273113i 0.985572 0.169259i \(-0.0541373\pi\)
−0.896832 + 0.442371i \(0.854137\pi\)
\(710\) −1.19522e7 3.43178e6i −0.889822 0.255490i
\(711\) −2.32929e6 + 7.16881e6i −0.172802 + 0.531830i
\(712\) 1.20131e6 390328.i 0.0888083 0.0288556i
\(713\) 4.25194e6 1.38154e6i 0.313230 0.101775i
\(714\) −2.12632e6 + 6.54413e6i −0.156093 + 0.480404i
\(715\) −1.71492e7 2.19658e7i −1.25452 1.60688i
\(716\) −5.28298e6 1.62593e7i −0.385120 1.18528i
\(717\) −13989.0 19254.3i −0.00101623 0.00139871i
\(718\) 3.76786e7i 2.72762i
\(719\) 1.55149e6 1.12722e6i 0.111925 0.0813183i −0.530415 0.847738i \(-0.677964\pi\)
0.642340 + 0.766420i \(0.277964\pi\)
\(720\) 1.34313e6 4.67786e6i 0.0965577 0.336292i
\(721\) −5.11194e6 3.71404e6i −0.366224 0.266078i
\(722\) −1.41736e7 + 1.95083e7i −1.01190 + 1.39276i
\(723\) −701635. 227975.i −0.0499189 0.0162196i
\(724\) 2.06371e6 0.146319
\(725\) −1.43274e7 + 1.20050e7i −1.01233 + 0.848236i
\(726\) −1.41665e7 −0.997520
\(727\) −1.84925e7 6.00858e6i −1.29766 0.421634i −0.422892 0.906180i \(-0.638985\pi\)
−0.874766 + 0.484546i \(0.838985\pi\)
\(728\) −637408. + 877316.i −0.0445747 + 0.0613519i
\(729\) 429945. + 312373.i 0.0299636 + 0.0217698i
\(730\) −1.14456e7 + 395674.i −0.794936 + 0.0274809i
\(731\) 1.14709e7 8.33412e6i 0.793972 0.576854i
\(732\) 1.88589e6i 0.130088i
\(733\) −1.35558e7 1.86579e7i −0.931890 1.28264i −0.959118 0.283007i \(-0.908668\pi\)
0.0272278 0.999629i \(-0.491332\pi\)
\(734\) −4.16166e6 1.28083e7i −0.285119 0.877507i
\(735\) −122839. 3.55335e6i −0.00838722 0.242616i
\(736\) 1.03974e7 3.19999e7i 0.707507 2.17748i
\(737\) −3.41577e7 + 1.10985e7i −2.31643 + 0.752655i
\(738\) −8.48002e6 + 2.75533e6i −0.573134 + 0.186222i
\(739\) 3.47175e6 1.06849e7i 0.233850 0.719716i −0.763422 0.645900i \(-0.776482\pi\)
0.997272 0.0738158i \(-0.0235177\pi\)
\(740\) −1.07757e7 + 3.91776e6i −0.723380 + 0.263002i
\(741\) −5.43083e6 1.67144e7i −0.363346 1.11827i
\(742\) 392297. + 539950.i 0.0261580 + 0.0360035i
\(743\) 1.82082e7i 1.21002i −0.796216 0.605012i \(-0.793168\pi\)
0.796216 0.605012i \(-0.206832\pi\)
\(744\) 103212. 74988.2i 0.00683596 0.00496662i
\(745\) −9.48532e6 + 7.40540e6i −0.626126 + 0.488830i
\(746\) 1.12407e7 + 8.16684e6i 0.739513 + 0.537288i
\(747\) 2.51959e6 3.46792e6i 0.165207 0.227388i
\(748\) −1.69902e7 5.52045e6i −1.11031 0.360762i
\(749\) 2.98594e6 0.194481
\(750\) 1.07426e7 + 6.21734e6i 0.697361 + 0.403600i
\(751\) 2.90578e7 1.88002 0.940011 0.341143i \(-0.110814\pi\)
0.940011 + 0.341143i \(0.110814\pi\)
\(752\) −1.23110e7 4.00010e6i −0.793871 0.257944i
\(753\) −672087. + 925048.i −0.0431954 + 0.0594534i
\(754\) 3.17211e7 + 2.30467e7i 2.03198 + 1.47632i
\(755\) 1.54052e7 1.20272e7i 0.983557 0.767884i
\(756\) −1.76502e6 + 1.28236e6i −0.112317 + 0.0816030i
\(757\) 2.65577e7i 1.68442i −0.539146 0.842212i \(-0.681253\pi\)
0.539146 0.842212i \(-0.318747\pi\)
\(758\) −5.01404e6 6.90123e6i −0.316967 0.436268i
\(759\) 6.96865e6 + 2.14473e7i 0.439081 + 1.35135i
\(760\) 1.63497e6 594433.i 0.102678 0.0373310i
\(761\) 109427. 336782.i 0.00684957 0.0210808i −0.947573 0.319538i \(-0.896472\pi\)
0.954423 + 0.298458i \(0.0964722\pi\)
\(762\) −1.41928e7 + 4.61151e6i −0.885481 + 0.287710i
\(763\) −2.01241e6 + 653870.i −0.125142 + 0.0406612i
\(764\) 1.28928e6 3.96801e6i 0.0799126 0.245946i
\(765\) 153512. + 4.44064e6i 0.00948396 + 0.274342i
\(766\) 1.10595e7 + 3.40375e7i 0.681023 + 2.09597i
\(767\) −1.82641e7 2.51384e7i −1.12101 1.54294i
\(768\) 1.03469e7i 0.633005i
\(769\) −5.65406e6 + 4.10791e6i −0.344782 + 0.250499i −0.746677 0.665187i \(-0.768352\pi\)
0.401895 + 0.915686i \(0.368352\pi\)
\(770\) −2.61329e7 + 903413.i −1.58841 + 0.0549110i
\(771\) −1.22170e7 8.87614e6i −0.740163 0.537760i
\(772\) −5.45914e6 + 7.51386e6i −0.329671 + 0.453753i
\(773\) 1.33563e7 + 4.33971e6i 0.803963 + 0.261223i 0.682039 0.731316i \(-0.261094\pi\)
0.121924 + 0.992539i \(0.461094\pi\)
\(774\) 9.23970e6 0.554377
\(775\) 1.25182e6 + 3.10463e6i 0.0748667 + 0.185676i
\(776\) −649301. −0.0387072
\(777\) −5.71382e6 1.85653e6i −0.339527 0.110319i
\(778\) −5.85830e6 + 8.06326e6i −0.346995 + 0.477597i
\(779\) −2.65290e7 1.92744e7i −1.56631 1.13799i
\(780\) 3.49604e6 1.21760e7i 0.205750 0.716587i
\(781\) 1.36858e7 9.94334e6i 0.802867 0.583317i
\(782\) 3.23319e7i 1.89066i
\(783\) −2.56303e6 3.52771e6i −0.149399 0.205631i
\(784\) −2.34721e6 7.22397e6i −0.136384 0.419745i
\(785\) 6.00256e6 + 7.68847e6i 0.347666 + 0.445314i
\(786\) −395686. + 1.21780e6i −0.0228452 + 0.0703102i
\(787\) 9.26317e6 3.00979e6i 0.533118 0.173220i −0.0300726 0.999548i \(-0.509574\pi\)
0.563190 + 0.826327i \(0.309574\pi\)
\(788\) −8.07787e6 + 2.62466e6i −0.463427 + 0.150577i
\(789\) −1.75363e6 + 5.39712e6i −0.100287 + 0.308653i
\(790\) −3.94735e7 1.13338e7i −2.25029 0.646113i
\(791\) 5.37890e6 + 1.65546e7i 0.305670 + 0.940754i
\(792\) 378250. + 520616.i 0.0214272 + 0.0294920i
\(793\) 5.73782e6i 0.324014i
\(794\) 1.40146e7 1.01822e7i 0.788912 0.573178i
\(795\) 357213. + 241125.i 0.0200452 + 0.0135308i
\(796\) 8.62779e6 + 6.26846e6i 0.482633 + 0.350653i
\(797\) 4.24234e6 5.83908e6i 0.236570 0.325611i −0.674181 0.738566i \(-0.735503\pi\)
0.910751 + 0.412955i \(0.135503\pi\)
\(798\) −1.56834e7 5.09586e6i −0.871835 0.283276i
\(799\) 1.18180e7 0.654902
\(800\) 2.44406e7 + 6.11192e6i 1.35016 + 0.337639i
\(801\) −7.73164e6 −0.425785
\(802\) 4.15601e7 + 1.35037e7i 2.28160 + 0.741338i
\(803\) 9.15756e6 1.26043e7i 0.501177 0.689811i
\(804\) −1.32084e7 9.59649e6i −0.720628 0.523567i
\(805\) 7.86772e6 + 2.16400e7i 0.427917 + 1.17697i
\(806\) 5.68085e6 4.12738e6i 0.308017 0.223788i
\(807\) 4.09585e6i 0.221391i
\(808\) 161258. + 221952.i 0.00868946 + 0.0119600i
\(809\) 7.24596e6 + 2.23008e7i 0.389246 + 1.19798i 0.933353 + 0.358961i \(0.116869\pi\)
−0.544106 + 0.839016i \(0.683131\pi\)
\(810\) −1.61998e6 + 2.39990e6i −0.0867554 + 0.128523i
\(811\) 218415. 672212.i 0.0116608 0.0358884i −0.945057 0.326906i \(-0.893994\pi\)
0.956718 + 0.291018i \(0.0939939\pi\)
\(812\) 1.70246e7 5.53164e6i 0.906125 0.294418i
\(813\) −4.56520e6 + 1.48332e6i −0.242233 + 0.0787063i
\(814\) 9.90649e6 3.04890e7i 0.524033 1.61281i
\(815\) −1.95508e6 + 2.89633e6i −0.103103 + 0.152741i
\(816\) 2.93332e6 + 9.02783e6i 0.154218 + 0.474633i
\(817\) 1.99733e7 + 2.74909e7i 1.04687 + 1.44090i
\(818\) 7.87782e6i 0.411645i
\(819\) 5.37008e6 3.90159e6i 0.279751 0.203251i
\(820\) −8.07644e6 2.22141e7i −0.419455 1.15370i
\(821\) 2.07459e7 + 1.50728e7i 1.07417 + 0.780432i 0.976658 0.214802i \(-0.0689106\pi\)
0.0975151 + 0.995234i \(0.468911\pi\)
\(822\) −9.17911e6 + 1.26340e7i −0.473828 + 0.652169i
\(823\) 7.78782e6 + 2.53042e6i 0.400790 + 0.130224i 0.502474 0.864592i \(-0.332423\pi\)
−0.101685 + 0.994817i \(0.532423\pi\)
\(824\) −847241. −0.0434699
\(825\) −1.56601e7 + 6.31434e6i −0.801052 + 0.322993i
\(826\) −2.91563e7 −1.48690
\(827\) −2.61163e7 8.48569e6i −1.32785 0.431443i −0.442663 0.896688i \(-0.645966\pi\)
−0.885182 + 0.465245i \(0.845966\pi\)
\(828\) −6.02554e6 + 8.29345e6i −0.305436 + 0.420397i
\(829\) −2.21236e7 1.60737e7i −1.11807 0.812325i −0.134154 0.990961i \(-0.542832\pi\)
−0.983915 + 0.178636i \(0.942832\pi\)
\(830\) 1.93575e7 + 1.30667e7i 0.975336 + 0.658370i
\(831\) −1.40022e7 + 1.01732e7i −0.703384 + 0.511038i
\(832\) 2.42874e7i 1.21639i
\(833\) 4.07609e6 + 5.61025e6i 0.203531 + 0.280137i
\(834\) 4.92474e6 + 1.51568e7i 0.245170 + 0.754557i
\(835\) 387910. + 111378.i 0.0192537 + 0.00552822i
\(836\) 1.32301e7 4.07182e7i 0.654710 2.01499i
\(837\) −742686. + 241313.i −0.0366431 + 0.0119061i
\(838\) 3.00634e7 9.76818e6i 1.47886 0.480511i
\(839\) 6.06134e6 1.86549e7i 0.297279 0.914929i −0.685168 0.728385i \(-0.740271\pi\)
0.982447 0.186544i \(-0.0597287\pi\)
\(840\) 404349. + 517917.i 0.0197723 + 0.0253257i
\(841\) 4.71767e6 + 1.45195e7i 0.230005 + 0.707883i
\(842\) 6.66718e6 + 9.17659e6i 0.324087 + 0.446068i
\(843\) 1.57952e7i 0.765518i
\(844\) −2.36062e7 + 1.71509e7i −1.14070 + 0.828765i
\(845\) −4.90861e6 + 1.70958e7i −0.236492 + 0.823657i
\(846\) 6.23043e6 + 4.52667e6i 0.299290 + 0.217447i
\(847\) 1.15663e7 1.59196e7i 0.553969 0.762473i
\(848\) 875657. + 284518.i 0.0418162 + 0.0135869i
\(849\) −6.02704e6 −0.286969
\(850\) −2.41509e7 + 1.67179e6i −1.14653 + 0.0793659i
\(851\) −2.82297e7 −1.33623
\(852\) 7.31360e6 + 2.37633e6i 0.345169 + 0.112152i
\(853\) 8.17011e6 1.12452e7i 0.384464 0.529169i −0.572296 0.820047i \(-0.693947\pi\)
0.956760 + 0.290878i \(0.0939473\pi\)
\(854\) 4.35568e6 + 3.16459e6i 0.204367 + 0.148482i
\(855\) −1.06423e7 + 367903.i −0.497875 + 0.0172115i
\(856\) 323905. 235331.i 0.0151089 0.0109773i
\(857\) 3.47918e6i 0.161817i 0.996722 + 0.0809085i \(0.0257822\pi\)
−0.996722 + 0.0809085i \(0.974218\pi\)
\(858\) 2.08190e7 + 2.86549e7i 0.965475 + 1.32886i
\(859\) 803944. + 2.47428e6i 0.0371743 + 0.114411i 0.967922 0.251252i \(-0.0808423\pi\)
−0.930747 + 0.365663i \(0.880842\pi\)
\(860\) 846239. + 2.44791e7i 0.0390164 + 1.12862i
\(861\) 3.82723e6 1.17790e7i 0.175945 0.541503i
\(862\) 3.78675e7 1.23039e7i 1.73579 0.563994i
\(863\) 2.06057e7 6.69520e6i 0.941805 0.306011i 0.202423 0.979298i \(-0.435118\pi\)
0.739381 + 0.673287i \(0.235118\pi\)
\(864\) −1.81612e6 + 5.58943e6i −0.0827674 + 0.254732i
\(865\) 1.42740e6 518966.i 0.0648645 0.0235830i
\(866\) −6.90581e6 2.12539e7i −0.312910 0.963039i
\(867\) 2.41723e6 + 3.32704e6i 0.109212 + 0.150318i
\(868\) 3.20580e6i 0.144423i
\(869\) 4.51989e7 3.28389e7i 2.03038 1.47516i
\(870\) 1.87263e7 1.46200e7i 0.838792 0.654863i
\(871\) 4.01867e7 + 2.91974e7i 1.79489 + 1.30406i
\(872\) −166766. + 229533.i −0.00742704 + 0.0102224i
\(873\) 3.77987e6 + 1.22815e6i 0.167858 + 0.0545403i
\(874\) −7.74856e7 −3.43117
\(875\) −1.57576e7 + 6.99588e6i −0.695776 + 0.308903i
\(876\) 7.08227e6 0.311826
\(877\) 9.99255e6 + 3.24678e6i 0.438710 + 0.142545i 0.520040 0.854142i \(-0.325917\pi\)
−0.0813305 + 0.996687i \(0.525917\pi\)
\(878\) −1.30830e7 + 1.80072e7i −0.572757 + 0.788332i
\(879\) −8.41191e6 6.11161e6i −0.367217 0.266799i
\(880\) −2.84335e7 + 2.21986e7i −1.23772 + 0.966317i
\(881\) 1.98575e7 1.44273e7i 0.861957 0.626248i −0.0664596 0.997789i \(-0.521170\pi\)
0.928417 + 0.371541i \(0.121170\pi\)
\(882\) 4.51900e6i 0.195601i
\(883\) −1.35294e7 1.86216e7i −0.583951 0.803740i 0.410170 0.912009i \(-0.365469\pi\)
−0.994122 + 0.108269i \(0.965469\pi\)
\(884\) 7.63514e6 + 2.34986e7i 0.328614 + 1.01137i
\(885\) −1.76943e7 + 6.43316e6i −0.759407 + 0.276100i
\(886\) −6.96362e6 + 2.14318e7i −0.298024 + 0.917222i
\(887\) 5.12240e6 1.66437e6i 0.218607 0.0710298i −0.197666 0.980269i \(-0.563336\pi\)
0.416273 + 0.909240i \(0.363336\pi\)
\(888\) −766135. + 248932.i −0.0326042 + 0.0105937i
\(889\) 6.40553e6 1.97142e7i 0.271832 0.836613i
\(890\) −1.45538e6 4.20997e7i −0.0615889 1.78158i
\(891\) −1.21721e6 3.74620e6i −0.0513656 0.158087i
\(892\) −9.46563e6 1.30283e7i −0.398325 0.548247i
\(893\) 2.83226e7i 1.18851i
\(894\) 1.23738e7 8.99009e6i 0.517797 0.376201i
\(895\) 3.14977e7 1.08887e6i 1.31438 0.0454380i
\(896\) 2.16089e6 + 1.56998e6i 0.0899214 + 0.0653317i
\(897\) 1.83327e7 2.52329e7i 0.760758 1.04709i
\(898\) 2.22211e7 + 7.22006e6i 0.919547 + 0.298779i
\(899\) 6.40735e6 0.264411
\(900\) −6.50651e6 4.07207e6i −0.267758 0.167575i
\(901\) −840588. −0.0344962
\(902\) 6.28531e7 + 2.04222e7i 2.57223 + 0.835769i
\(903\) −7.54377e6 + 1.03831e7i −0.307871 + 0.423748i
\(904\) 1.88820e6 + 1.37186e6i 0.0768470 + 0.0558326i
\(905\) −1.04992e6 + 3.65669e6i −0.0426125 + 0.148411i
\(906\) −2.00964e7 + 1.46009e7i −0.813387 + 0.590960i
\(907\) 3.80471e7i 1.53569i 0.640637 + 0.767844i \(0.278670\pi\)
−0.640637 + 0.767844i \(0.721330\pi\)
\(908\) −1.18964e7 1.63739e7i −0.478850 0.659081i
\(909\) −518931. 1.59710e6i −0.0208305 0.0641097i
\(910\) 2.22555e7 + 2.85063e7i 0.890910 + 1.14114i
\(911\) −1.08173e7 + 3.32924e7i −0.431842 + 1.32907i 0.464446 + 0.885601i \(0.346253\pi\)
−0.896288 + 0.443472i \(0.853747\pi\)
\(912\) −2.16358e7 + 7.02990e6i −0.861362 + 0.279874i
\(913\) −3.02167e7 + 9.81800e6i −1.19969 + 0.389804i
\(914\) −8.78823e6 + 2.70474e7i −0.347965 + 1.07093i
\(915\) 3.34161e6 + 959459.i 0.131948 + 0.0378856i
\(916\) 7.74646e6 + 2.38411e7i 0.305045 + 0.938833i
\(917\) −1.04544e6 1.43892e6i −0.0410559 0.0565086i
\(918\) 5.64741e6i 0.221178i
\(919\) −1.51147e7 + 1.09815e7i −0.590351 + 0.428915i −0.842441 0.538789i \(-0.818882\pi\)
0.252090 + 0.967704i \(0.418882\pi\)
\(920\) 2.55898e6 + 1.72736e6i 0.0996774 + 0.0672841i
\(921\) −1.01895e6 740313.i −0.0395827 0.0287585i
\(922\) −2.28063e7 + 3.13902e7i −0.883542 + 1.21609i
\(923\) −2.22517e7 7.23000e6i −0.859722 0.279341i
\(924\) 1.61704e7 0.623077
\(925\) −1.45967e6 2.10867e7i −0.0560920 0.810315i
\(926\) 1.13231e7 0.433949
\(927\) 4.93217e6 + 1.60256e6i 0.188512 + 0.0612512i
\(928\) 2.83439e7 3.90120e7i 1.08041 1.48706i
\(929\) −2.64374e7 1.92079e7i −1.00503 0.730198i −0.0418705 0.999123i \(-0.513332\pi\)
−0.963161 + 0.268925i \(0.913332\pi\)
\(930\) −1.45378e6 3.99859e6i −0.0551178 0.151600i
\(931\) −1.34454e7 + 9.76862e6i −0.508391 + 0.369368i
\(932\) 4.10713e7i 1.54881i
\(933\) −3.88902e6 5.35278e6i −0.146264 0.201314i
\(934\) −1.20351e7 3.70402e7i −0.451422 1.38933i
\(935\) 1.84256e7 2.72964e7i 0.689275 1.02112i
\(936\) 275033. 846464.i 0.0102611 0.0315805i
\(937\) −2.14896e7 + 6.98240e6i −0.799613 + 0.259810i −0.680192 0.733034i \(-0.738104\pi\)
−0.119420 + 0.992844i \(0.538104\pi\)
\(938\) 4.43284e7 1.44032e7i 1.64504 0.534505i
\(939\) 823080. 2.53318e6i 0.0304634 0.0937566i
\(940\) −1.14220e7 + 1.69211e7i −0.421623 + 0.624609i
\(941\) 8.11806e6 + 2.49848e7i 0.298867 + 0.919818i 0.981895 + 0.189426i \(0.0606627\pi\)
−0.683028 + 0.730392i \(0.739337\pi\)
\(942\) −7.28706e6 1.00298e7i −0.267562 0.368268i
\(943\) 5.81953e7i 2.13112i
\(944\) −3.25403e7 + 2.36419e7i −1.18848 + 0.863480i
\(945\) −1.37425e6 3.77985e6i −0.0500596 0.137688i
\(946\) −5.54045e7 4.02537e7i −2.01288 1.46244i
\(947\) 1.64951e7 2.27035e7i 0.597695 0.822657i −0.397800 0.917472i \(-0.630226\pi\)
0.995495 + 0.0948155i \(0.0302261\pi\)
\(948\) 2.41539e7 + 7.84809e6i 0.872905 + 0.283624i
\(949\) −2.15478e7 −0.776673
\(950\) −4.00655e6 5.78793e7i −0.144033 2.08072i
\(951\) 1.99824e7 0.716468
\(952\) −1.21883e6 396022.i −0.0435863 0.0141621i
\(953\) −1.24463e7 + 1.71309e7i −0.443924 + 0.611009i −0.971079 0.238760i \(-0.923259\pi\)
0.527154 + 0.849770i \(0.323259\pi\)
\(954\) −443157. 321972.i −0.0157647 0.0114538i
\(955\) 6.37499e6 + 4.30324e6i 0.226189 + 0.152682i
\(956\) −64873.6 + 47133.4i −0.00229574 + 0.00166795i
\(957\) 3.23195e7i 1.14073i
\(958\) 3.69557e7 + 5.08652e7i 1.30097 + 1.79063i
\(959\) −6.70311e6 2.06300e7i −0.235358 0.724359i
\(960\) −1.41446e7 4.06125e6i −0.495349 0.142227i
\(961\) −8.49230e6 + 2.61366e7i −0.296631 + 0.912938i
\(962\) −4.21683e7 + 1.37013e7i −1.46909 + 0.477337i
\(963\) −2.33073e6 + 757299.i −0.0809889 + 0.0263149i
\(964\) −768118. + 2.36402e6i −0.0266217 + 0.0819331i
\(965\) −1.05365e7 1.34958e7i −0.364230 0.466531i
\(966\) −9.04362e6 2.78334e7i −0.311817 0.959674i
\(967\) 1.23908e7 + 1.70545e7i 0.426123 + 0.586508i 0.967058 0.254557i \(-0.0819295\pi\)
−0.540935 + 0.841064i \(0.681930\pi\)
\(968\) 2.63848e6i 0.0905036i
\(969\) 1.68027e7 1.22079e7i 0.574871 0.417668i
\(970\) −5.97594e6 + 2.08130e7i −0.203928 + 0.710242i
\(971\) −1.88038e7 1.36618e7i −0.640026 0.465006i 0.219833 0.975537i \(-0.429449\pi\)
−0.859859 + 0.510531i \(0.829449\pi\)
\(972\) 1.05248e6 1.44862e6i 0.0357313 0.0491799i
\(973\) −2.10532e7 6.84061e6i −0.712914 0.231640i
\(974\) 1.30469e7 0.440668
\(975\) 1.97961e7 + 1.23893e7i 0.666911 + 0.417383i
\(976\) 7.42728e6 0.249578
\(977\) 4.31446e7 + 1.40185e7i 1.44607 + 0.469857i 0.923784 0.382913i \(-0.125079\pi\)
0.522286 + 0.852770i \(0.325079\pi\)
\(978\) 2.61060e6 3.59318e6i 0.0872756 0.120125i
\(979\) 4.63617e7 + 3.36837e7i 1.54597 + 1.12322i
\(980\) −1.19723e7 + 413882.i −0.398211 + 0.0137661i
\(981\) 1.40498e6 1.02078e6i 0.0466120 0.0338656i
\(982\) 4.42566e7i 1.46453i
\(983\) −3.99787e6 5.50260e6i −0.131961 0.181629i 0.737923 0.674885i \(-0.235807\pi\)
−0.869884 + 0.493256i \(0.835807\pi\)
\(984\) −513173. 1.57938e6i −0.0168957 0.0519996i
\(985\) −540967. 1.56485e7i −0.0177656 0.513904i
\(986\) −1.43190e7 + 4.40692e7i −0.469050 + 1.44359i
\(987\) −1.01737e7 + 3.30563e6i −0.332419 + 0.108009i
\(988\) −5.63159e7 + 1.82981e7i −1.83543 + 0.596368i
\(989\) −1.86354e7 + 5.73537e7i −0.605825 + 1.86454i
\(990\) 2.01694e7 7.33305e6i 0.654040 0.237792i
\(991\) 2.65254e6 + 8.16366e6i 0.0857980 + 0.264059i 0.984746 0.173995i \(-0.0556678\pi\)
−0.898949 + 0.438054i \(0.855668\pi\)
\(992\) −5.07603e6 6.98655e6i −0.163774 0.225415i
\(993\) 2.21153e7i 0.711738i
\(994\) −1.77609e7 + 1.29041e7i −0.570163 + 0.414248i
\(995\) −1.54965e7 + 1.20985e7i −0.496223 + 0.387412i
\(996\) −1.16845e7 8.48928e6i −0.373217 0.271158i
\(997\) 1.51817e7 2.08958e7i 0.483707 0.665765i −0.495505 0.868605i \(-0.665017\pi\)
0.979212 + 0.202840i \(0.0650171\pi\)
\(998\) 4.05516e7 + 1.31760e7i 1.28879 + 0.418753i
\(999\) 4.93087e6 0.156318
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 75.6.i.a.4.5 96
25.19 even 10 inner 75.6.i.a.19.5 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.6.i.a.4.5 96 1.1 even 1 trivial
75.6.i.a.19.5 yes 96 25.19 even 10 inner