Properties

Label 72.8.l.b.11.35
Level $72$
Weight $8$
Character 72.11
Analytic conductor $22.492$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,8,Mod(11,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\), degree \(2\), 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: \(22.4917218349\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(80\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.35
Character \(\chi\) \(=\) 72.11
Dual form 72.8.l.b.59.35

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.29566 - 10.8231i) q^{2} +(44.4541 - 14.5199i) q^{3} +(-106.277 + 71.3383i) q^{4} +(211.100 + 365.636i) q^{5} +(-303.656 - 433.277i) q^{6} +(-1251.64 - 722.637i) q^{7} +(1122.35 + 915.138i) q^{8} +(1765.34 - 1290.94i) q^{9} +O(q^{10})\) \(q+(-3.29566 - 10.8231i) q^{2} +(44.4541 - 14.5199i) q^{3} +(-106.277 + 71.3383i) q^{4} +(211.100 + 365.636i) q^{5} +(-303.656 - 433.277i) q^{6} +(-1251.64 - 722.637i) q^{7} +(1122.35 + 915.138i) q^{8} +(1765.34 - 1290.94i) q^{9} +(3261.59 - 3489.77i) q^{10} +(1108.65 + 640.081i) q^{11} +(-3688.64 + 4714.42i) q^{12} +(-9420.66 + 5439.02i) q^{13} +(-3696.15 + 15928.2i) q^{14} +(14693.3 + 13188.9i) q^{15} +(6205.70 - 15163.3i) q^{16} +36042.7i q^{17} +(-19789.9 - 14851.9i) q^{18} -6546.42 q^{19} +(-48519.0 - 23799.3i) q^{20} +(-66133.4 - 13950.4i) q^{21} +(3273.89 - 14108.5i) q^{22} +(36171.2 + 62650.3i) q^{23} +(63181.0 + 24385.2i) q^{24} +(-50064.2 + 86713.7i) q^{25} +(89914.2 + 84035.2i) q^{26} +(59732.4 - 83020.5i) q^{27} +(184573. - 12490.3i) q^{28} +(-57572.1 + 99717.9i) q^{29} +(94320.0 - 202493. i) q^{30} +(-29420.0 + 16985.6i) q^{31} +(-184565. - 17191.7i) q^{32} +(58578.2 + 12356.7i) q^{33} +(390093. - 118785. i) q^{34} -610195. i q^{35} +(-95522.1 + 263134. i) q^{36} +310900. i q^{37} +(21574.8 + 70852.3i) q^{38} +(-339813. + 378575. i) q^{39} +(-97678.9 + 603559. i) q^{40} +(551241. - 318259. i) q^{41} +(66967.1 + 761741. i) q^{42} +(-83929.4 + 145370. i) q^{43} +(-163487. + 11063.3i) q^{44} +(844680. + 372955. i) q^{45} +(558860. - 597957. i) q^{46} +(-35601.9 + 61664.3i) q^{47} +(55699.4 - 764177. i) q^{48} +(632636. + 1.09576e6i) q^{49} +(1.10350e6 + 256069. i) q^{50} +(523338. + 1.60225e6i) q^{51} +(613192. - 1.25010e6i) q^{52} +31114.2 q^{53} +(-1.09539e6 - 372880. i) q^{54} +540485. i q^{55} +(-743473. - 1.95648e6i) q^{56} +(-291016. + 95053.6i) q^{57} +(1.26899e6 + 294470. i) q^{58} +(267644. - 154524. i) q^{59} +(-2.50244e6 - 353484. i) q^{60} +(-1.05466e6 - 608911. i) q^{61} +(280795. + 262435. i) q^{62} +(-3.14246e6 + 340099. i) q^{63} +(422197. + 2.05421e6i) q^{64} +(-3.97741e6 - 2.29636e6i) q^{65} +(-59316.7 - 674719. i) q^{66} +(-1.62901e6 - 2.82152e6i) q^{67} +(-2.57123e6 - 3.83052e6i) q^{68} +(2.51764e6 + 2.25986e6i) q^{69} +(-6.60418e6 + 2.01100e6i) q^{70} +790644. q^{71} +(3.16273e6 + 166639. i) q^{72} -394829. q^{73} +(3.36489e6 - 1.02462e6i) q^{74} +(-966483. + 4.58171e6i) q^{75} +(695735. - 467010. i) q^{76} +(-925093. - 1.60231e6i) q^{77} +(5.21724e6 + 2.43017e6i) q^{78} +(1.88453e6 + 1.08803e6i) q^{79} +(6.85427e6 - 931940. i) q^{80} +(1.44990e6 - 4.55791e6i) q^{81} +(-5.26124e6 - 4.91724e6i) q^{82} +(-6.17252e6 - 3.56370e6i) q^{83} +(8.02367e6 - 3.23523e6i) q^{84} +(-1.31785e7 + 7.60863e6i) q^{85} +(1.84995e6 + 429283. i) q^{86} +(-1.11142e6 + 5.26882e6i) q^{87} +(658537. + 1.73297e6i) q^{88} +6.66492e6i q^{89} +(1.25274e6 - 1.03712e7i) q^{90} +1.57218e7 q^{91} +(-8.31354e6 - 4.07791e6i) q^{92} +(-1.06121e6 + 1.18226e6i) q^{93} +(784728. + 182097. i) q^{94} +(-1.38195e6 - 2.39361e6i) q^{95} +(-8.45430e6 + 1.91563e6i) q^{96} +(-5.22623e6 + 9.05209e6i) q^{97} +(9.77450e6 - 1.04583e7i) q^{98} +(2.78346e6 - 301246. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 3 q^{2} - 90 q^{3} - 257 q^{4} - 459 q^{6} + 3018 q^{9} + 252 q^{10} - 26448 q^{11} - 27234 q^{12} - 43488 q^{14} + 32767 q^{16} + 21762 q^{18} - 119452 q^{19} + 130806 q^{20} - 6049 q^{22} - 83379 q^{24} - 1312502 q^{25} - 94428 q^{27} - 32772 q^{28} + 735060 q^{30} + 308907 q^{32} - 1249812 q^{33} - 188203 q^{34} - 1410345 q^{36} + 353415 q^{38} - 477876 q^{40} - 1612476 q^{41} - 39360 q^{42} + 220508 q^{43} + 1082496 q^{46} - 3515619 q^{48} + 9882514 q^{49} - 136947 q^{50} - 2358786 q^{51} + 1089018 q^{52} - 8083005 q^{54} - 1285266 q^{56} - 2070294 q^{57} + 1295022 q^{58} - 8748744 q^{59} - 3070044 q^{60} + 16058050 q^{64} - 6 q^{65} - 19546374 q^{66} + 3851300 q^{67} + 10545975 q^{68} + 979920 q^{70} + 12593427 q^{72} - 9731236 q^{73} + 13246572 q^{74} + 8347746 q^{75} - 4009903 q^{76} - 9123732 q^{78} - 6855198 q^{81} + 21020522 q^{82} - 14348826 q^{83} + 44644836 q^{84} + 80099985 q^{86} + 10463891 q^{88} + 7437678 q^{90} - 3294180 q^{91} - 57890184 q^{92} - 1609122 q^{94} + 69780834 q^{96} + 9938888 q^{97} - 16049670 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.29566 10.8231i −0.291298 0.956632i
\(3\) 44.4541 14.5199i 0.950578 0.310485i
\(4\) −106.277 + 71.3383i −0.830291 + 0.557330i
\(5\) 211.100 + 365.636i 0.755255 + 1.30814i 0.945247 + 0.326355i \(0.105821\pi\)
−0.189992 + 0.981786i \(0.560846\pi\)
\(6\) −303.656 433.277i −0.573922 0.818910i
\(7\) −1251.64 722.637i −1.37923 0.796300i −0.387166 0.922010i \(-0.626546\pi\)
−0.992067 + 0.125710i \(0.959879\pi\)
\(8\) 1122.35 + 915.138i 0.775022 + 0.631934i
\(9\) 1765.34 1290.94i 0.807198 0.590280i
\(10\) 3261.59 3489.77i 1.03141 1.10356i
\(11\) 1108.65 + 640.081i 0.251143 + 0.144998i 0.620288 0.784374i \(-0.287016\pi\)
−0.369144 + 0.929372i \(0.620349\pi\)
\(12\) −3688.64 + 4714.42i −0.616214 + 0.787579i
\(13\) −9420.66 + 5439.02i −1.18927 + 0.686624i −0.958140 0.286299i \(-0.907575\pi\)
−0.231128 + 0.972923i \(0.574242\pi\)
\(14\) −3696.15 + 15928.2i −0.359999 + 1.55138i
\(15\) 14693.3 + 13188.9i 1.12409 + 1.00899i
\(16\) 6205.70 15163.3i 0.378766 0.925493i
\(17\) 36042.7i 1.77929i 0.456654 + 0.889645i \(0.349048\pi\)
−0.456654 + 0.889645i \(0.650952\pi\)
\(18\) −19789.9 14851.9i −0.799817 0.600244i
\(19\) −6546.42 −0.218961 −0.109480 0.993989i \(-0.534919\pi\)
−0.109480 + 0.993989i \(0.534919\pi\)
\(20\) −48519.0 23799.3i −1.35615 0.665211i
\(21\) −66133.4 13950.4i −1.55831 0.328715i
\(22\) 3273.89 14108.5i 0.0655519 0.282489i
\(23\) 36171.2 + 62650.3i 0.619891 + 1.07368i 0.989505 + 0.144498i \(0.0461566\pi\)
−0.369614 + 0.929185i \(0.620510\pi\)
\(24\) 63181.0 + 24385.2i 0.932925 + 0.360070i
\(25\) −50064.2 + 86713.7i −0.640822 + 1.10994i
\(26\) 89914.2 + 84035.2i 1.00328 + 0.937680i
\(27\) 59732.4 83020.5i 0.584032 0.811731i
\(28\) 184573. 12490.3i 1.58897 0.107527i
\(29\) −57572.1 + 99717.9i −0.438348 + 0.759242i −0.997562 0.0697818i \(-0.977770\pi\)
0.559214 + 0.829023i \(0.311103\pi\)
\(30\) 94320.0 202493.i 0.637793 1.36926i
\(31\) −29420.0 + 16985.6i −0.177369 + 0.102404i −0.586056 0.810271i \(-0.699320\pi\)
0.408687 + 0.912675i \(0.365987\pi\)
\(32\) −184565. 17191.7i −0.995690 0.0927455i
\(33\) 58578.2 + 12356.7i 0.283751 + 0.0598554i
\(34\) 390093. 118785.i 1.70213 0.518303i
\(35\) 610195.i 2.40564i
\(36\) −95522.1 + 263134.i −0.341228 + 0.939980i
\(37\) 310900.i 1.00905i 0.863396 + 0.504527i \(0.168333\pi\)
−0.863396 + 0.504527i \(0.831667\pi\)
\(38\) 21574.8 + 70852.3i 0.0637828 + 0.209465i
\(39\) −339813. + 378575.i −0.917306 + 1.02194i
\(40\) −97678.9 + 603559.i −0.241319 + 1.49111i
\(41\) 551241. 318259.i 1.24910 0.721169i 0.278172 0.960531i \(-0.410272\pi\)
0.970930 + 0.239362i \(0.0769382\pi\)
\(42\) 66967.1 + 761741.i 0.139473 + 1.58648i
\(43\) −83929.4 + 145370.i −0.160981 + 0.278827i −0.935221 0.354065i \(-0.884799\pi\)
0.774240 + 0.632892i \(0.218132\pi\)
\(44\) −163487. + 11063.3i −0.289333 + 0.0195795i
\(45\) 844680. + 372955.i 1.38181 + 0.610116i
\(46\) 558860. 597957.i 0.846547 0.905770i
\(47\) −35601.9 + 61664.3i −0.0500185 + 0.0866346i −0.889951 0.456057i \(-0.849261\pi\)
0.839932 + 0.542691i \(0.182595\pi\)
\(48\) 55699.4 764177.i 0.0726952 0.997354i
\(49\) 632636. + 1.09576e6i 0.768189 + 1.33054i
\(50\) 1.10350e6 + 256069.i 1.24847 + 0.289709i
\(51\) 523338. + 1.60225e6i 0.552442 + 1.69135i
\(52\) 613192. 1.25010e6i 0.604762 1.23291i
\(53\) 31114.2 0.0287073 0.0143537 0.999897i \(-0.495431\pi\)
0.0143537 + 0.999897i \(0.495431\pi\)
\(54\) −1.09539e6 372880.i −0.946655 0.322248i
\(55\) 540485.i 0.438041i
\(56\) −743473. 1.95648e6i −0.565727 1.48873i
\(57\) −291016. + 95053.6i −0.208139 + 0.0679840i
\(58\) 1.26899e6 + 294470.i 0.854005 + 0.198173i
\(59\) 267644. 154524.i 0.169658 0.0979522i −0.412766 0.910837i \(-0.635437\pi\)
0.582425 + 0.812885i \(0.302104\pi\)
\(60\) −2.50244e6 353484.i −1.49566 0.211271i
\(61\) −1.05466e6 608911.i −0.594922 0.343478i 0.172120 0.985076i \(-0.444938\pi\)
−0.767041 + 0.641598i \(0.778272\pi\)
\(62\) 280795. + 262435.i 0.149630 + 0.139846i
\(63\) −3.14246e6 + 340099.i −1.58335 + 0.171362i
\(64\) 422197. + 2.05421e6i 0.201319 + 0.979526i
\(65\) −3.97741e6 2.29636e6i −1.79640 1.03715i
\(66\) −59316.7 674719.i −0.0253965 0.288881i
\(67\) −1.62901e6 2.82152e6i −0.661700 1.14610i −0.980169 0.198165i \(-0.936502\pi\)
0.318468 0.947934i \(-0.396832\pi\)
\(68\) −2.57123e6 3.83052e6i −0.991652 1.47733i
\(69\) 2.51764e6 + 2.25986e6i 0.922617 + 0.828153i
\(70\) −6.60418e6 + 2.01100e6i −2.30131 + 0.700758i
\(71\) 790644. 0.262166 0.131083 0.991371i \(-0.458155\pi\)
0.131083 + 0.991371i \(0.458155\pi\)
\(72\) 3.16273e6 + 166639.i 0.998615 + 0.0526155i
\(73\) −394829. −0.118790 −0.0593949 0.998235i \(-0.518917\pi\)
−0.0593949 + 0.998235i \(0.518917\pi\)
\(74\) 3.36489e6 1.02462e6i 0.965294 0.293935i
\(75\) −966483. + 4.58171e6i −0.264533 + 1.25405i
\(76\) 695735. 467010.i 0.181801 0.122033i
\(77\) −925093. 1.60231e6i −0.230923 0.399971i
\(78\) 5.21724e6 + 2.43017e6i 1.24483 + 0.579835i
\(79\) 1.88453e6 + 1.08803e6i 0.430039 + 0.248283i 0.699363 0.714766i \(-0.253467\pi\)
−0.269324 + 0.963050i \(0.586800\pi\)
\(80\) 6.85427e6 931940.i 1.49674 0.203504i
\(81\) 1.44990e6 4.55791e6i 0.303138 0.952947i
\(82\) −5.26124e6 4.91724e6i −1.05376 0.984856i
\(83\) −6.17252e6 3.56370e6i −1.18492 0.684114i −0.227772 0.973714i \(-0.573144\pi\)
−0.957147 + 0.289601i \(0.906477\pi\)
\(84\) 8.02367e6 3.23523e6i 1.47705 0.595563i
\(85\) −1.31785e7 + 7.60863e6i −2.32756 + 1.34382i
\(86\) 1.84995e6 + 429283.i 0.313629 + 0.0727778i
\(87\) −1.11142e6 + 5.26882e6i −0.180951 + 0.857819i
\(88\) 658537. + 1.73297e6i 0.103013 + 0.271082i
\(89\) 6.66492e6i 1.00214i 0.865406 + 0.501072i \(0.167061\pi\)
−0.865406 + 0.501072i \(0.832939\pi\)
\(90\) 1.25274e6 1.03712e7i 0.181138 1.49961i
\(91\) 1.57218e7 2.18704
\(92\) −8.31354e6 4.07791e6i −1.11309 0.545985i
\(93\) −1.06121e6 + 1.18226e6i −0.136808 + 0.152413i
\(94\) 784728. + 182097.i 0.0974478 + 0.0226128i
\(95\) −1.38195e6 2.39361e6i −0.165371 0.286431i
\(96\) −8.45430e6 + 1.91563e6i −0.975277 + 0.220985i
\(97\) −5.22623e6 + 9.05209e6i −0.581416 + 1.00704i 0.413895 + 0.910324i \(0.364168\pi\)
−0.995312 + 0.0967183i \(0.969165\pi\)
\(98\) 9.77450e6 1.04583e7i 1.04907 1.12246i
\(99\) 2.78346e6 301246.i 0.288312 0.0312031i
\(100\) −865324. 1.27872e7i −0.0865324 1.27872i
\(101\) −7.74059e6 + 1.34071e7i −0.747565 + 1.29482i 0.201422 + 0.979505i \(0.435444\pi\)
−0.948987 + 0.315316i \(0.897889\pi\)
\(102\) 1.56165e7 1.09446e7i 1.45708 1.02117i
\(103\) 1.02783e7 5.93420e6i 0.926814 0.535096i 0.0410115 0.999159i \(-0.486942\pi\)
0.885803 + 0.464062i \(0.153609\pi\)
\(104\) −1.55508e7 2.51671e6i −1.35561 0.219390i
\(105\) −8.86000e6 2.71257e7i −0.746915 2.28675i
\(106\) −102542. 336751.i −0.00836239 0.0274624i
\(107\) 2.12721e7i 1.67868i 0.543609 + 0.839339i \(0.317058\pi\)
−0.543609 + 0.839339i \(0.682942\pi\)
\(108\) −425656. + 1.30844e7i −0.0325144 + 0.999471i
\(109\) 1.76727e7i 1.30710i −0.756882 0.653551i \(-0.773278\pi\)
0.756882 0.653551i \(-0.226722\pi\)
\(110\) 5.84971e6 1.78126e6i 0.419044 0.127600i
\(111\) 4.51425e6 + 1.38208e7i 0.313296 + 0.959185i
\(112\) −1.87249e7 + 1.44945e7i −1.25938 + 0.974858i
\(113\) 1.86655e7 1.07765e7i 1.21693 0.702593i 0.252668 0.967553i \(-0.418692\pi\)
0.964259 + 0.264960i \(0.0853587\pi\)
\(114\) 1.98786e6 + 2.83641e6i 0.125666 + 0.179309i
\(115\) −1.52715e7 + 2.64510e7i −0.936352 + 1.62181i
\(116\) −995093. 1.47048e7i −0.0591917 0.874696i
\(117\) −9.60923e6 + 2.17633e7i −0.554674 + 1.25624i
\(118\) −2.55449e6 2.38746e6i −0.143125 0.133767i
\(119\) 2.60458e7 4.51127e7i 1.41685 2.45405i
\(120\) 4.42140e6 + 2.82490e7i 0.233575 + 1.49234i
\(121\) −8.92418e6 1.54571e7i −0.457951 0.793195i
\(122\) −3.11446e6 + 1.34215e7i −0.155283 + 0.669176i
\(123\) 1.98838e7 2.21519e7i 0.963457 1.07336i
\(124\) 1.91495e6 3.90396e6i 0.0901948 0.183878i
\(125\) −9.28984e6 −0.425425
\(126\) 1.40374e7 + 3.28902e7i 0.625158 + 1.46477i
\(127\) 1.07680e7i 0.466470i 0.972420 + 0.233235i \(0.0749312\pi\)
−0.972420 + 0.233235i \(0.925069\pi\)
\(128\) 2.08415e7 1.13395e7i 0.878402 0.477922i
\(129\) −1.62025e6 + 7.68095e6i −0.0664534 + 0.315029i
\(130\) −1.17454e7 + 5.06158e7i −0.468886 + 2.02062i
\(131\) 4.45365e6 2.57131e6i 0.173088 0.0999322i −0.410953 0.911656i \(-0.634804\pi\)
0.584041 + 0.811724i \(0.301471\pi\)
\(132\) −7.10703e6 + 2.86563e6i −0.268955 + 0.108446i
\(133\) 8.19378e6 + 4.73068e6i 0.301998 + 0.174359i
\(134\) −2.51689e7 + 2.69296e7i −0.903643 + 0.966860i
\(135\) 4.29648e7 + 4.31469e6i 1.50295 + 0.150932i
\(136\) −3.29841e7 + 4.04526e7i −1.12439 + 1.37899i
\(137\) −1.77964e7 1.02747e7i −0.591303 0.341389i 0.174310 0.984691i \(-0.444231\pi\)
−0.765612 + 0.643302i \(0.777564\pi\)
\(138\) 1.61614e7 3.46963e7i 0.523481 1.12384i
\(139\) 5.13760e6 + 8.89859e6i 0.162259 + 0.281041i 0.935678 0.352854i \(-0.114789\pi\)
−0.773420 + 0.633894i \(0.781455\pi\)
\(140\) 4.35303e7 + 6.48499e7i 1.34074 + 1.99738i
\(141\) −687290. + 3.25817e6i −0.0206478 + 0.0978830i
\(142\) −2.60569e6 8.55718e6i −0.0763685 0.250797i
\(143\) −1.39257e7 −0.398235
\(144\) −8.61973e6 3.47796e7i −0.240561 0.970634i
\(145\) −4.86140e7 −1.32426
\(146\) 1.30122e6 + 4.27326e6i 0.0346032 + 0.113638i
\(147\) 4.40337e7 + 3.95252e7i 1.14334 + 1.02627i
\(148\) −2.21791e7 3.30416e7i −0.562376 0.837808i
\(149\) −1.32771e7 2.29966e7i −0.328815 0.569524i 0.653462 0.756959i \(-0.273316\pi\)
−0.982277 + 0.187435i \(0.939983\pi\)
\(150\) 5.27734e7 4.63948e6i 1.27672 0.112240i
\(151\) −3.41288e7 1.97043e7i −0.806682 0.465738i 0.0391205 0.999235i \(-0.487544\pi\)
−0.845802 + 0.533497i \(0.820878\pi\)
\(152\) −7.34739e6 5.99088e6i −0.169699 0.138369i
\(153\) 4.65291e7 + 6.36278e7i 1.05028 + 1.43624i
\(154\) −1.42931e7 + 1.52930e7i −0.315358 + 0.337419i
\(155\) −1.24211e7 7.17135e6i −0.267917 0.154682i
\(156\) 9.10756e6 6.44756e7i 0.192073 1.35975i
\(157\) 2.82576e7 1.63146e7i 0.582757 0.336455i −0.179472 0.983763i \(-0.557439\pi\)
0.762228 + 0.647308i \(0.224105\pi\)
\(158\) 5.56508e6 2.39821e7i 0.112246 0.483713i
\(159\) 1.38315e6 451776.i 0.0272886 0.00891320i
\(160\) −3.26758e7 7.11128e7i −0.630676 1.37255i
\(161\) 1.04555e8i 1.97448i
\(162\) −5.41090e7 671013.i −0.999923 0.0124002i
\(163\) 4.99451e7 0.903309 0.451654 0.892193i \(-0.350834\pi\)
0.451654 + 0.892193i \(0.350834\pi\)
\(164\) −3.58803e7 + 7.31483e7i −0.635189 + 1.29494i
\(165\) 7.84782e6 + 2.40268e7i 0.136005 + 0.416392i
\(166\) −1.82277e7 + 7.85503e7i −0.309280 + 1.33281i
\(167\) −2.16874e7 3.75637e7i −0.360329 0.624109i 0.627685 0.778467i \(-0.284002\pi\)
−0.988015 + 0.154358i \(0.950669\pi\)
\(168\) −6.14584e7 7.61785e7i −0.999997 1.23951i
\(169\) 2.77917e7 4.81366e7i 0.442906 0.767135i
\(170\) 1.25781e8 + 1.17557e8i 1.96355 + 1.83517i
\(171\) −1.15567e7 + 8.45106e6i −0.176745 + 0.129248i
\(172\) −1.45066e6 2.14369e7i −0.0217378 0.321227i
\(173\) 4.27529e7 7.40502e7i 0.627775 1.08734i −0.360222 0.932867i \(-0.617299\pi\)
0.987997 0.154472i \(-0.0493677\pi\)
\(174\) 6.06876e7 5.33524e6i 0.873328 0.0767771i
\(175\) 1.25325e8 7.23564e7i 1.76768 1.02057i
\(176\) 1.65857e7 1.28387e7i 0.229319 0.177511i
\(177\) 9.65419e6 1.07554e7i 0.130861 0.145788i
\(178\) 7.21348e7 2.19653e7i 0.958683 0.291922i
\(179\) 4.63883e7i 0.604537i 0.953223 + 0.302269i \(0.0977440\pi\)
−0.953223 + 0.302269i \(0.902256\pi\)
\(180\) −1.16376e8 + 2.06214e7i −1.48734 + 0.263551i
\(181\) 1.92853e7i 0.241741i −0.992668 0.120871i \(-0.961431\pi\)
0.992668 0.120871i \(-0.0385686\pi\)
\(182\) −5.18136e7 1.70157e8i −0.637079 2.09219i
\(183\) −5.57255e7 1.17549e7i −0.672164 0.141789i
\(184\) −1.67369e7 + 1.03417e8i −0.198067 + 1.22386i
\(185\) −1.13676e8 + 6.56310e7i −1.31998 + 0.762093i
\(186\) 1.62930e7 + 7.58922e6i 0.185655 + 0.0864772i
\(187\) −2.30703e7 + 3.99589e7i −0.257993 + 0.446856i
\(188\) −615354. 9.09329e6i −0.00675417 0.0998087i
\(189\) −1.34757e8 + 6.07472e7i −1.45190 + 0.654500i
\(190\) −2.13517e7 + 2.28455e7i −0.225837 + 0.241636i
\(191\) −1.51053e7 + 2.61631e7i −0.156860 + 0.271689i −0.933735 0.357966i \(-0.883470\pi\)
0.776875 + 0.629655i \(0.216804\pi\)
\(192\) 4.85955e7 + 8.51881e7i 0.495498 + 0.868609i
\(193\) 3.30681e7 + 5.72756e7i 0.331099 + 0.573481i 0.982728 0.185057i \(-0.0592471\pi\)
−0.651628 + 0.758538i \(0.725914\pi\)
\(194\) 1.15195e8 + 2.67311e7i 1.13274 + 0.262852i
\(195\) −2.10155e8 4.43309e7i −2.02964 0.428140i
\(196\) −1.45404e8 7.13230e7i −1.37937 0.676602i
\(197\) −1.40451e8 −1.30886 −0.654430 0.756123i \(-0.727091\pi\)
−0.654430 + 0.756123i \(0.727091\pi\)
\(198\) −1.24337e7 2.91328e7i −0.113834 0.266719i
\(199\) 2.02091e8i 1.81786i −0.416943 0.908932i \(-0.636899\pi\)
0.416943 0.908932i \(-0.363101\pi\)
\(200\) −1.35545e8 + 5.15077e7i −1.19806 + 0.455268i
\(201\) −1.13385e8 1.01775e8i −0.984844 0.884009i
\(202\) 1.70616e8 + 3.95916e7i 1.45643 + 0.337966i
\(203\) 1.44120e8 8.32075e7i 1.20917 0.698114i
\(204\) −1.69921e8 1.32949e8i −1.40133 1.09642i
\(205\) 2.32734e8 + 1.34369e8i 1.88678 + 1.08933i
\(206\) −9.81001e7 9.16859e7i −0.781870 0.730748i
\(207\) 1.44733e8 + 6.39044e7i 1.13415 + 0.500765i
\(208\) 2.40115e7 + 1.76601e8i 0.185011 + 1.36073i
\(209\) −7.25771e6 4.19024e6i −0.0549905 0.0317488i
\(210\) −2.64384e8 + 1.85289e8i −1.97000 + 1.38065i
\(211\) 8.13034e6 + 1.40822e7i 0.0595827 + 0.103200i 0.894278 0.447512i \(-0.147690\pi\)
−0.834695 + 0.550712i \(0.814356\pi\)
\(212\) −3.30673e6 + 2.21963e6i −0.0238354 + 0.0159995i
\(213\) 3.51474e7 1.14801e7i 0.249209 0.0813986i
\(214\) 2.30229e8 7.01057e7i 1.60588 0.488995i
\(215\) −7.08701e7 −0.486327
\(216\) 1.43016e8 3.85148e7i 0.965598 0.260040i
\(217\) 4.90978e7 0.326177
\(218\) −1.91272e8 + 5.82431e7i −1.25042 + 0.380756i
\(219\) −1.75518e7 + 5.73289e6i −0.112919 + 0.0368824i
\(220\) −3.85573e7 5.74413e7i −0.244133 0.363701i
\(221\) −1.96037e8 3.39546e8i −1.22170 2.11605i
\(222\) 1.34706e8 9.44066e7i 0.826325 0.579118i
\(223\) 1.75402e8 + 1.01268e8i 1.05917 + 0.611514i 0.925203 0.379472i \(-0.123894\pi\)
0.133969 + 0.990985i \(0.457228\pi\)
\(224\) 2.18586e8 + 1.54891e8i 1.29943 + 0.920786i
\(225\) 2.35620e7 + 2.17709e8i 0.137903 + 1.27420i
\(226\) −1.78150e8 1.66502e8i −1.02661 0.959488i
\(227\) 1.47107e8 + 8.49321e7i 0.834722 + 0.481927i 0.855467 0.517858i \(-0.173270\pi\)
−0.0207448 + 0.999785i \(0.506604\pi\)
\(228\) 2.41474e7 3.08626e7i 0.134927 0.172449i
\(229\) −1.32305e7 + 7.63863e6i −0.0728034 + 0.0420331i −0.535960 0.844243i \(-0.680050\pi\)
0.463156 + 0.886277i \(0.346717\pi\)
\(230\) 3.36611e8 + 7.81108e7i 1.82423 + 0.423315i
\(231\) −6.43896e7 5.77969e7i −0.343696 0.308505i
\(232\) −1.55872e8 + 5.92321e7i −0.819520 + 0.311422i
\(233\) 3.79428e7i 0.196509i 0.995161 + 0.0982547i \(0.0313260\pi\)
−0.995161 + 0.0982547i \(0.968674\pi\)
\(234\) 2.67214e8 + 3.22769e7i 1.36334 + 0.164678i
\(235\) −3.00623e7 −0.151107
\(236\) −1.74209e7 + 3.55156e7i −0.0862739 + 0.175884i
\(237\) 9.95733e7 + 2.10043e7i 0.485874 + 0.102492i
\(238\) −5.74095e8 1.33219e8i −2.76035 0.640542i
\(239\) 1.24355e8 + 2.15390e8i 0.589213 + 1.02055i 0.994336 + 0.106284i \(0.0338954\pi\)
−0.405123 + 0.914262i \(0.632771\pi\)
\(240\) 2.91169e8 1.40952e8i 1.35958 0.658162i
\(241\) 1.20758e8 2.09158e8i 0.555718 0.962532i −0.442129 0.896951i \(-0.645777\pi\)
0.997847 0.0655806i \(-0.0208899\pi\)
\(242\) −1.37882e8 + 1.47528e8i −0.625396 + 0.669147i
\(243\) −1.72657e6 2.23671e8i −0.00771904 0.999970i
\(244\) 1.55525e8 1.05246e7i 0.685389 0.0463811i
\(245\) −2.67099e8 + 4.62630e8i −1.16036 + 2.00980i
\(246\) −3.05282e8 1.42199e8i −1.30746 0.609008i
\(247\) 6.16716e7 3.56061e7i 0.260403 0.150344i
\(248\) −4.85638e7 7.85948e6i −0.202177 0.0327200i
\(249\) −3.26139e8 6.87968e7i −1.33877 0.282404i
\(250\) 3.06162e7 + 1.00544e8i 0.123925 + 0.406975i
\(251\) 4.10195e8i 1.63732i 0.574280 + 0.818659i \(0.305282\pi\)
−0.574280 + 0.818659i \(0.694718\pi\)
\(252\) 3.09710e8 2.60323e8i 1.21914 1.02473i
\(253\) 9.26100e7i 0.359531i
\(254\) 1.16543e8 3.54878e7i 0.446240 0.135882i
\(255\) −4.75364e8 + 5.29587e8i −1.79529 + 2.00008i
\(256\) −1.91414e8 1.88197e8i −0.713073 0.701090i
\(257\) 1.98047e8 1.14342e8i 0.727784 0.420186i −0.0898271 0.995957i \(-0.528631\pi\)
0.817611 + 0.575771i \(0.195298\pi\)
\(258\) 8.84711e7 7.77778e6i 0.320725 0.0281960i
\(259\) 2.24668e8 3.89136e8i 0.803510 1.39172i
\(260\) 5.86526e8 3.96909e7i 2.06957 0.140050i
\(261\) 2.70956e7 + 2.50359e8i 0.0943314 + 0.871607i
\(262\) −4.25072e7 3.97279e7i −0.146018 0.136471i
\(263\) 5.01016e7 8.67785e7i 0.169827 0.294149i −0.768532 0.639811i \(-0.779012\pi\)
0.938359 + 0.345663i \(0.112346\pi\)
\(264\) 5.44373e7 + 6.74757e7i 0.182089 + 0.225701i
\(265\) 6.56822e6 + 1.13765e7i 0.0216814 + 0.0375532i
\(266\) 2.41965e7 1.04273e8i 0.0788256 0.339691i
\(267\) 9.67742e7 + 2.96283e8i 0.311150 + 0.952616i
\(268\) 3.74409e8 + 1.83653e8i 1.18816 + 0.582810i
\(269\) −1.17716e8 −0.368724 −0.184362 0.982858i \(-0.559022\pi\)
−0.184362 + 0.982858i \(0.559022\pi\)
\(270\) −9.48993e7 4.79231e8i −0.293420 1.48174i
\(271\) 6.42585e7i 0.196127i 0.995180 + 0.0980637i \(0.0312649\pi\)
−0.995180 + 0.0980637i \(0.968735\pi\)
\(272\) 5.46526e8 + 2.23670e8i 1.64672 + 0.673934i
\(273\) 6.98897e8 2.28279e8i 2.07895 0.679042i
\(274\) −5.25534e7 + 2.26473e8i −0.154338 + 0.665105i
\(275\) −1.11008e8 + 6.40903e7i −0.321876 + 0.185835i
\(276\) −4.28782e8 6.05681e7i −1.22760 0.173405i
\(277\) 4.00609e8 + 2.31292e8i 1.13251 + 0.653855i 0.944565 0.328325i \(-0.106484\pi\)
0.187945 + 0.982180i \(0.439817\pi\)
\(278\) 7.93781e7 8.49313e7i 0.221587 0.237089i
\(279\) −3.00089e7 + 6.79650e7i −0.0827246 + 0.187357i
\(280\) 5.58413e8 6.84854e8i 1.52021 1.86443i
\(281\) 3.00950e8 + 1.73754e8i 0.809138 + 0.467156i 0.846657 0.532140i \(-0.178612\pi\)
−0.0375182 + 0.999296i \(0.511945\pi\)
\(282\) 3.75285e7 3.29925e6i 0.0996527 0.00876079i
\(283\) −1.47111e6 2.54803e6i −0.00385826 0.00668271i 0.864090 0.503338i \(-0.167895\pi\)
−0.867948 + 0.496655i \(0.834561\pi\)
\(284\) −8.40274e7 + 5.64032e7i −0.217674 + 0.146113i
\(285\) −9.61885e7 8.63400e7i −0.246131 0.220930i
\(286\) 4.58943e7 + 1.50718e8i 0.116005 + 0.380965i
\(287\) −9.19943e8 −2.29707
\(288\) −3.48014e8 + 2.07914e8i −0.858465 + 0.512872i
\(289\) −8.88740e8 −2.16587
\(290\) 1.60215e8 + 5.26152e8i 0.385754 + 1.26683i
\(291\) −1.00892e8 + 4.78288e8i −0.240010 + 1.13779i
\(292\) 4.19613e7 2.81664e7i 0.0986301 0.0662051i
\(293\) 7.36473e6 + 1.27561e7i 0.0171049 + 0.0296265i 0.874451 0.485114i \(-0.161222\pi\)
−0.857346 + 0.514740i \(0.827888\pi\)
\(294\) 2.82663e8 6.06840e8i 0.648714 1.39270i
\(295\) 1.12999e8 + 6.52402e7i 0.256271 + 0.147958i
\(296\) −2.84516e8 + 3.48939e8i −0.637655 + 0.782039i
\(297\) 1.19362e8 5.38073e7i 0.264375 0.119177i
\(298\) −2.05137e8 + 2.19488e8i −0.449042 + 0.480456i
\(299\) −6.81513e8 3.93472e8i −1.47443 0.851264i
\(300\) −2.24136e8 5.55879e8i −0.479279 1.18866i
\(301\) 2.10099e8 1.21301e8i 0.444060 0.256378i
\(302\) −1.00784e8 + 4.34317e8i −0.210555 + 0.907366i
\(303\) −1.49431e8 + 7.08394e8i −0.308597 + 1.46294i
\(304\) −4.06251e7 + 9.92651e7i −0.0829349 + 0.202647i
\(305\) 5.14165e8i 1.03765i
\(306\) 5.35303e8 7.13283e8i 1.06801 1.42310i
\(307\) −1.20135e8 −0.236966 −0.118483 0.992956i \(-0.537803\pi\)
−0.118483 + 0.992956i \(0.537803\pi\)
\(308\) 2.12622e8 + 1.04294e8i 0.414649 + 0.203392i
\(309\) 3.70751e8 4.13041e8i 0.714870 0.796413i
\(310\) −3.66801e7 + 1.58069e8i −0.0699301 + 0.301357i
\(311\) 1.99189e7 + 3.45006e7i 0.0375495 + 0.0650377i 0.884189 0.467129i \(-0.154711\pi\)
−0.846640 + 0.532166i \(0.821378\pi\)
\(312\) −7.27838e8 + 1.13918e8i −1.35673 + 0.212349i
\(313\) −4.66910e8 + 8.08712e8i −0.860653 + 1.49069i 0.0106465 + 0.999943i \(0.496611\pi\)
−0.871300 + 0.490751i \(0.836722\pi\)
\(314\) −2.69701e8 2.52067e8i −0.491619 0.459475i
\(315\) −7.87728e8 1.07720e9i −1.42000 1.94183i
\(316\) −2.77901e8 + 1.88059e7i −0.495433 + 0.0335265i
\(317\) 1.20941e8 2.09475e8i 0.213238 0.369339i −0.739488 0.673170i \(-0.764932\pi\)
0.952726 + 0.303831i \(0.0982657\pi\)
\(318\) −9.44801e6 1.34811e7i −0.0164758 0.0235087i
\(319\) −1.27655e8 + 7.37017e7i −0.220176 + 0.127119i
\(320\) −6.61970e8 + 5.88016e8i −1.12931 + 1.00315i
\(321\) 3.08870e8 + 9.45633e8i 0.521204 + 1.59571i
\(322\) −1.13160e9 + 3.44576e8i −1.88885 + 0.575162i
\(323\) 2.35951e8i 0.389594i
\(324\) 1.71062e8 + 5.87836e8i 0.279413 + 0.960171i
\(325\) 1.08920e9i 1.76001i
\(326\) −1.64602e8 5.40559e8i −0.263132 0.864134i
\(327\) −2.56606e8 7.85624e8i −0.405835 1.24250i
\(328\) 9.09937e8 + 1.47263e8i 1.42381 + 0.230428i
\(329\) 8.91218e7 5.14545e7i 0.137974 0.0796595i
\(330\) 2.34180e8 1.64122e8i 0.358716 0.251401i
\(331\) 4.45987e8 7.72472e8i 0.675965 1.17081i −0.300221 0.953870i \(-0.597060\pi\)
0.976186 0.216936i \(-0.0696062\pi\)
\(332\) 9.10226e8 6.15961e7i 1.36511 0.0923782i
\(333\) 4.01354e8 + 5.48845e8i 0.595625 + 0.814507i
\(334\) −3.35080e8 + 3.58521e8i −0.492080 + 0.526505i
\(335\) 6.87768e8 1.19125e9i 0.999506 1.73119i
\(336\) −6.21938e8 + 9.16226e8i −0.894457 + 1.31770i
\(337\) 6.41948e8 + 1.11189e9i 0.913683 + 1.58254i 0.808819 + 0.588058i \(0.200107\pi\)
0.104864 + 0.994487i \(0.466559\pi\)
\(338\) −6.12577e8 1.42149e8i −0.862884 0.200233i
\(339\) 6.73283e8 7.50083e8i 0.938640 1.04571i
\(340\) 8.57792e8 1.74876e9i 1.18360 2.41298i
\(341\) −4.34888e7 −0.0593932
\(342\) 1.29553e8 + 9.72267e7i 0.175128 + 0.131430i
\(343\) 6.38420e8i 0.854235i
\(344\) −2.27232e8 + 8.63493e7i −0.300964 + 0.114368i
\(345\) −2.94814e8 + 1.39760e9i −0.386529 + 1.83238i
\(346\) −9.42349e8 2.18673e8i −1.22305 0.283811i
\(347\) −5.92629e8 + 3.42155e8i −0.761430 + 0.439612i −0.829809 0.558048i \(-0.811551\pi\)
0.0683789 + 0.997659i \(0.478217\pi\)
\(348\) −2.57749e8 6.39242e8i −0.327846 0.813089i
\(349\) 677300. + 391039.i 0.000852888 + 0.000492415i 0.500426 0.865779i \(-0.333177\pi\)
−0.499573 + 0.866272i \(0.666510\pi\)
\(350\) −1.19615e9 1.11794e9i −1.49124 1.39373i
\(351\) −1.11169e8 + 1.10699e9i −0.137217 + 1.36638i
\(352\) −1.93614e8 1.37196e8i −0.236613 0.167665i
\(353\) 1.04175e9 + 6.01457e8i 1.26053 + 0.727768i 0.973177 0.230056i \(-0.0738910\pi\)
0.287354 + 0.957824i \(0.407224\pi\)
\(354\) −1.48223e8 6.90417e7i −0.177585 0.0827180i
\(355\) 1.66905e8 + 2.89088e8i 0.198002 + 0.342950i
\(356\) −4.75464e8 7.08329e8i −0.558525 0.832070i
\(357\) 5.02811e8 2.38363e9i 0.584879 2.77268i
\(358\) 5.02064e8 1.52880e8i 0.578320 0.176101i
\(359\) 1.34070e9 1.52933 0.764667 0.644425i \(-0.222903\pi\)
0.764667 + 0.644425i \(0.222903\pi\)
\(360\) 6.06723e8 + 1.19159e9i 0.685381 + 1.34607i
\(361\) −8.51016e8 −0.952056
\(362\) −2.08726e8 + 6.35577e7i −0.231257 + 0.0704187i
\(363\) −6.21153e8 5.57555e8i −0.681594 0.611807i
\(364\) −1.67086e9 + 1.12156e9i −1.81588 + 1.21890i
\(365\) −8.33485e7 1.44364e8i −0.0897166 0.155394i
\(366\) 5.64281e7 + 6.41861e8i 0.0601605 + 0.684317i
\(367\) −3.79883e8 2.19326e8i −0.401161 0.231611i 0.285824 0.958282i \(-0.407733\pi\)
−0.686985 + 0.726672i \(0.741066\pi\)
\(368\) 1.17445e9 1.59684e8i 1.22848 0.167030i
\(369\) 5.62275e8 1.27346e9i 0.582581 1.31945i
\(370\) 1.08497e9 + 1.01403e9i 1.11355 + 1.04074i
\(371\) −3.89439e7 2.24843e7i −0.0395941 0.0228597i
\(372\) 2.84422e7 2.01352e8i 0.0286459 0.202794i
\(373\) −1.15503e8 + 6.66859e7i −0.115243 + 0.0665354i −0.556513 0.830839i \(-0.687861\pi\)
0.441271 + 0.897374i \(0.354528\pi\)
\(374\) 5.08509e8 + 1.18000e8i 0.502630 + 0.116636i
\(375\) −4.12972e8 + 1.34888e8i −0.404400 + 0.132088i
\(376\) −9.63892e7 + 3.66284e7i −0.0935128 + 0.0355354i
\(377\) 1.25254e9i 1.20392i
\(378\) 1.10158e9 + 1.25828e9i 1.04905 + 1.19828i
\(379\) 7.55421e8 0.712774 0.356387 0.934338i \(-0.384008\pi\)
0.356387 + 0.934338i \(0.384008\pi\)
\(380\) 3.17626e8 + 1.55800e8i 0.296943 + 0.145655i
\(381\) 1.56351e8 + 4.78684e8i 0.144832 + 0.443416i
\(382\) 3.32947e8 + 7.72605e7i 0.305600 + 0.0709146i
\(383\) 1.02085e8 + 1.76816e8i 0.0928467 + 0.160815i 0.908708 0.417433i \(-0.137070\pi\)
−0.815861 + 0.578248i \(0.803737\pi\)
\(384\) 7.61841e8 8.06703e8i 0.686602 0.727033i
\(385\) 3.90575e8 6.76495e8i 0.348812 0.604160i
\(386\) 5.10916e8 5.46659e8i 0.452162 0.483794i
\(387\) 3.95003e7 + 3.64976e8i 0.0346427 + 0.320093i
\(388\) −9.03316e7 1.33486e9i −0.0785107 1.16018i
\(389\) 4.30524e8 7.45689e8i 0.370829 0.642294i −0.618865 0.785498i \(-0.712407\pi\)
0.989693 + 0.143204i \(0.0457404\pi\)
\(390\) 2.12805e8 + 2.42062e9i 0.181658 + 2.06634i
\(391\) −2.25809e9 + 1.30371e9i −1.91039 + 1.10297i
\(392\) −2.92729e8 + 1.80878e9i −0.245451 + 1.51664i
\(393\) 1.60648e8 1.78972e8i 0.133506 0.148734i
\(394\) 4.62879e8 + 1.52011e9i 0.381268 + 1.25210i
\(395\) 9.18736e8i 0.750069i
\(396\) −2.74328e8 + 2.30583e8i −0.221992 + 0.186592i
\(397\) 2.15255e9i 1.72658i 0.504709 + 0.863289i \(0.331600\pi\)
−0.504709 + 0.863289i \(0.668400\pi\)
\(398\) −2.18724e9 + 6.66024e8i −1.73903 + 0.529541i
\(399\) 4.32937e8 + 9.13252e7i 0.341208 + 0.0719757i
\(400\) 1.00418e9 + 1.29726e9i 0.784516 + 1.01348i
\(401\) −5.09278e8 + 2.94032e8i −0.394412 + 0.227714i −0.684070 0.729417i \(-0.739792\pi\)
0.289658 + 0.957130i \(0.406458\pi\)
\(402\) −7.27844e8 + 1.56258e9i −0.558788 + 1.19964i
\(403\) 1.84771e8 3.20032e8i 0.140626 0.243571i
\(404\) −1.33791e8 1.97707e9i −0.100946 1.49172i
\(405\) 1.97261e9 4.32041e8i 1.47554 0.323171i
\(406\) −1.37553e9 1.28559e9i −1.02007 0.953371i
\(407\) −1.99001e8 + 3.44680e8i −0.146310 + 0.253417i
\(408\) −8.78909e8 + 2.27721e9i −0.640668 + 1.65994i
\(409\) −3.54883e8 6.14675e8i −0.256480 0.444236i 0.708816 0.705393i \(-0.249229\pi\)
−0.965296 + 0.261157i \(0.915896\pi\)
\(410\) 6.87272e8 2.96173e9i 0.492476 2.12228i
\(411\) −9.40312e8 1.98353e8i −0.668076 0.140926i
\(412\) −6.69018e8 + 1.36391e9i −0.471300 + 0.960827i
\(413\) −4.46659e8 −0.311998
\(414\) 2.14651e8 1.77706e9i 0.148673 1.23084i
\(415\) 3.00920e9i 2.06672i
\(416\) 1.83223e9 8.41895e8i 1.24782 0.573365i
\(417\) 3.57595e8 + 3.20981e8i 0.241499 + 0.216772i
\(418\) −2.14323e7 + 9.23602e7i −0.0143533 + 0.0618540i
\(419\) −1.88791e8 + 1.08999e8i −0.125381 + 0.0723889i −0.561379 0.827559i \(-0.689729\pi\)
0.435998 + 0.899948i \(0.356396\pi\)
\(420\) 2.87672e9 + 2.25079e9i 1.89463 + 1.48239i
\(421\) 9.14209e8 + 5.27819e8i 0.597115 + 0.344745i 0.767906 0.640563i \(-0.221299\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(422\) 1.25617e8 1.34405e8i 0.0813684 0.0870608i
\(423\) 1.67556e7 + 1.54819e8i 0.0107639 + 0.0994562i
\(424\) 3.49211e7 + 2.84738e7i 0.0222488 + 0.0181411i
\(425\) −3.12540e9 1.80445e9i −1.97490 1.14021i
\(426\) −2.40084e8 3.42568e8i −0.150463 0.214691i
\(427\) 8.80042e8 + 1.52428e9i 0.547024 + 0.947473i
\(428\) −1.51752e9 2.26074e9i −0.935578 1.39379i
\(429\) −6.19054e8 + 2.02200e8i −0.378554 + 0.123646i
\(430\) 2.33564e8 + 7.67031e8i 0.141666 + 0.465236i
\(431\) 1.26185e9 0.759168 0.379584 0.925157i \(-0.376067\pi\)
0.379584 + 0.925157i \(0.376067\pi\)
\(432\) −8.88180e8 1.42094e9i −0.530039 0.847973i
\(433\) 2.43441e9 1.44107 0.720536 0.693418i \(-0.243896\pi\)
0.720536 + 0.693418i \(0.243896\pi\)
\(434\) −1.61810e8 5.31388e8i −0.0950146 0.312031i
\(435\) −2.16109e9 + 7.05872e8i −1.25881 + 0.411163i
\(436\) 1.26074e9 + 1.87820e9i 0.728488 + 1.08527i
\(437\) −2.36792e8 4.10135e8i −0.135732 0.235094i
\(438\) 1.19892e8 + 1.71070e8i 0.0681760 + 0.0972782i
\(439\) −1.77175e9 1.02292e9i −0.999483 0.577052i −0.0913879 0.995815i \(-0.529130\pi\)
−0.908095 + 0.418763i \(0.862464\pi\)
\(440\) −4.94619e8 + 6.06615e8i −0.276813 + 0.339491i
\(441\) 2.53138e9 + 1.11769e9i 1.40547 + 0.620564i
\(442\) −3.02886e9 + 3.24075e9i −1.66840 + 1.78512i
\(443\) 2.01481e9 + 1.16325e9i 1.10108 + 0.635711i 0.936505 0.350653i \(-0.114040\pi\)
0.164578 + 0.986364i \(0.447374\pi\)
\(444\) −1.46571e9 1.14680e9i −0.794709 0.621793i
\(445\) −2.43694e9 + 1.40697e9i −1.31094 + 0.756874i
\(446\) 5.17967e8 2.23213e9i 0.276459 1.19137i
\(447\) −9.24132e8 8.29513e8i −0.489393 0.439285i
\(448\) 9.56011e8 2.87624e9i 0.502331 1.51130i
\(449\) 1.48267e9i 0.773005i −0.922288 0.386503i \(-0.873683\pi\)
0.922288 0.386503i \(-0.126317\pi\)
\(450\) 2.27863e9 9.72510e8i 1.17877 0.503095i
\(451\) 8.14847e8 0.418271
\(452\) −1.21494e9 + 2.47686e9i −0.618827 + 1.26159i
\(453\) −1.80327e9 3.80389e8i −0.911419 0.192258i
\(454\) 4.34411e8 1.87205e9i 0.217874 0.938906i
\(455\) 3.31887e9 + 5.74845e9i 1.65177 + 2.86095i
\(456\) −4.13609e8 1.59636e8i −0.204274 0.0788412i
\(457\) −1.56683e9 + 2.71383e9i −0.767919 + 1.33007i 0.170771 + 0.985311i \(0.445374\pi\)
−0.938689 + 0.344764i \(0.887959\pi\)
\(458\) 1.26277e8 + 1.18020e8i 0.0614177 + 0.0574020i
\(459\) 2.99228e9 + 2.15292e9i 1.44430 + 1.03916i
\(460\) −2.63957e8 3.90058e9i −0.126439 1.86843i
\(461\) 9.14182e8 1.58341e9i 0.434590 0.752731i −0.562673 0.826680i \(-0.690227\pi\)
0.997262 + 0.0739488i \(0.0235601\pi\)
\(462\) −4.13333e8 + 8.87372e8i −0.195008 + 0.418657i
\(463\) 2.12196e9 1.22512e9i 0.993583 0.573646i 0.0872399 0.996187i \(-0.472195\pi\)
0.906343 + 0.422542i \(0.138862\pi\)
\(464\) 1.15477e9 + 1.49180e9i 0.536641 + 0.693263i
\(465\) −6.56299e8 1.38442e8i −0.302703 0.0638532i
\(466\) 4.10657e8 1.25047e8i 0.187987 0.0572428i
\(467\) 1.71972e9i 0.781356i 0.920527 + 0.390678i \(0.127759\pi\)
−0.920527 + 0.390678i \(0.872241\pi\)
\(468\) −5.31313e8 2.99845e9i −0.239602 1.35218i
\(469\) 4.70872e9i 2.10765i
\(470\) 9.90751e7 + 3.25366e8i 0.0440172 + 0.144554i
\(471\) 1.01928e9 1.13555e9i 0.449492 0.500764i
\(472\) 4.41801e8 + 7.15004e7i 0.193388 + 0.0312976i
\(473\) −1.86097e8 + 1.07443e8i −0.0808585 + 0.0466837i
\(474\) −1.00829e8 1.14691e9i −0.0434870 0.494658i
\(475\) 3.27741e8 5.67664e8i 0.140315 0.243032i
\(476\) 4.50183e8 + 6.65251e9i 0.191322 + 2.82723i
\(477\) 5.49272e7 4.01667e7i 0.0231725 0.0169454i
\(478\) 1.92134e9 2.05576e9i 0.804651 0.860943i
\(479\) 3.30830e8 5.73015e8i 0.137541 0.238227i −0.789025 0.614362i \(-0.789414\pi\)
0.926565 + 0.376134i \(0.122747\pi\)
\(480\) −2.48513e9 2.68681e9i −1.02566 1.10890i
\(481\) −1.69099e9 2.92888e9i −0.692841 1.20004i
\(482\) −2.66171e9 6.17651e8i −1.08267 0.251234i
\(483\) −1.51813e9 4.64788e9i −0.613046 1.87690i
\(484\) 2.05112e9 + 1.00611e9i 0.822305 + 0.403352i
\(485\) −4.41303e9 −1.75647
\(486\) −2.41511e9 + 7.55830e8i −0.954355 + 0.298674i
\(487\) 5.97696e8i 0.234492i −0.993103 0.117246i \(-0.962593\pi\)
0.993103 0.117246i \(-0.0374067\pi\)
\(488\) −6.26467e8 1.64858e9i −0.244022 0.642154i
\(489\) 2.22027e9 7.25200e8i 0.858666 0.280464i
\(490\) 5.88734e9 + 1.36616e9i 2.26065 + 0.524585i
\(491\) −5.01380e8 + 2.89472e8i −0.191153 + 0.110362i −0.592522 0.805554i \(-0.701868\pi\)
0.401369 + 0.915916i \(0.368534\pi\)
\(492\) −5.32920e8 + 3.77272e9i −0.201736 + 1.42816i
\(493\) −3.59410e9 2.07506e9i −1.35091 0.779948i
\(494\) −5.88616e8 5.50130e8i −0.219679 0.205315i
\(495\) 6.97736e8 + 9.54142e8i 0.258567 + 0.353586i
\(496\) 7.49862e7 + 5.51511e8i 0.0275928 + 0.202940i
\(497\) −9.89604e8 5.71348e8i −0.361588 0.208763i
\(498\) 3.30250e8 + 3.75655e9i 0.119823 + 1.36297i
\(499\) −1.24903e9 2.16338e9i −0.450008 0.779437i 0.548378 0.836231i \(-0.315246\pi\)
−0.998386 + 0.0567936i \(0.981912\pi\)
\(500\) 9.87298e8 6.62721e8i 0.353226 0.237102i
\(501\) −1.50952e9 1.35496e9i −0.536298 0.481388i
\(502\) 4.43957e9 1.35187e9i 1.56631 0.476947i
\(503\) 4.80118e9 1.68213 0.841067 0.540931i \(-0.181928\pi\)
0.841067 + 0.540931i \(0.181928\pi\)
\(504\) −3.83819e9 2.49408e9i −1.33542 0.867766i
\(505\) −6.53616e9 −2.25841
\(506\) 1.00232e9 3.05211e8i 0.343939 0.104731i
\(507\) 5.36515e8 2.54340e9i 0.182833 0.866738i
\(508\) −7.68174e8 1.14440e9i −0.259978 0.387306i
\(509\) 1.68682e9 + 2.92165e9i 0.566964 + 0.982010i 0.996864 + 0.0791337i \(0.0252154\pi\)
−0.429900 + 0.902876i \(0.641451\pi\)
\(510\) 7.29839e9 + 3.39955e9i 2.43630 + 1.13482i
\(511\) 4.94185e8 + 2.85318e8i 0.163839 + 0.0945924i
\(512\) −1.40604e9 + 2.69192e9i −0.462969 + 0.886375i
\(513\) −3.91033e8 + 5.43487e8i −0.127880 + 0.177737i
\(514\) −1.89023e9 1.76664e9i −0.613966 0.573822i
\(515\) 4.33952e9 + 2.50542e9i 1.39996 + 0.808269i
\(516\) −3.75750e8 9.31896e8i −0.120400 0.298602i
\(517\) −7.89403e7 + 4.55762e7i −0.0251236 + 0.0145051i
\(518\) −4.95207e9 1.14913e9i −1.56543 0.363258i
\(519\) 8.25339e8 3.91261e9i 0.259147 1.22852i
\(520\) −2.36257e9 6.21720e9i −0.736840 1.93902i
\(521\) 1.43096e9i 0.443297i −0.975127 0.221648i \(-0.928856\pi\)
0.975127 0.221648i \(-0.0711437\pi\)
\(522\) 2.62035e9 1.11835e9i 0.806329 0.344138i
\(523\) −2.90587e9 −0.888220 −0.444110 0.895972i \(-0.646480\pi\)
−0.444110 + 0.895972i \(0.646480\pi\)
\(524\) −2.89888e8 + 5.90987e8i −0.0880179 + 0.179440i
\(525\) 4.52061e9 5.03626e9i 1.36345 1.51897i
\(526\) −1.10433e9 2.56260e8i −0.330862 0.0767769i
\(527\) −6.12209e8 1.06038e9i −0.182206 0.315590i
\(528\) 5.50886e8 8.11555e8i 0.162871 0.239938i
\(529\) −9.14298e8 + 1.58361e9i −0.268530 + 0.465107i
\(530\) 1.01482e8 1.08581e8i 0.0296089 0.0316803i
\(531\) 2.73001e8 6.18301e8i 0.0791285 0.179213i
\(532\) −1.20829e9 + 8.17665e7i −0.347921 + 0.0235442i
\(533\) −3.46204e9 + 5.99642e9i −0.990345 + 1.71533i
\(534\) 2.88776e9 2.02384e9i 0.820665 0.575152i
\(535\) −7.77786e9 + 4.49055e9i −2.19595 + 1.26783i
\(536\) 7.53764e8 4.65751e9i 0.211426 1.30640i
\(537\) 6.73556e8 + 2.06215e9i 0.187700 + 0.574660i
\(538\) 3.87951e8 + 1.27404e9i 0.107409 + 0.352733i
\(539\) 1.61975e9i 0.445542i
\(540\) −4.87399e9 + 2.60648e9i −1.33201 + 0.712323i
\(541\) 1.24100e9i 0.336963i 0.985705 + 0.168482i \(0.0538864\pi\)
−0.985705 + 0.168482i \(0.946114\pi\)
\(542\) 6.95474e8 2.11774e8i 0.187622 0.0571315i
\(543\) −2.80021e8 8.57310e8i −0.0750570 0.229794i
\(544\) 6.19635e8 6.65222e9i 0.165021 1.77162i
\(545\) 6.46177e9 3.73071e9i 1.70987 0.987196i
\(546\) −4.77400e9 6.81187e9i −1.25519 1.79099i
\(547\) −7.53277e8 + 1.30471e9i −0.196788 + 0.340847i −0.947485 0.319799i \(-0.896384\pi\)
0.750697 + 0.660647i \(0.229718\pi\)
\(548\) 2.62433e9 1.77592e8i 0.681220 0.0460989i
\(549\) −2.64791e9 + 2.86576e8i −0.682968 + 0.0739156i
\(550\) 1.05950e9 + 9.90222e8i 0.271538 + 0.253783i
\(551\) 3.76891e8 6.52795e8i 0.0959811 0.166244i
\(552\) 7.57590e8 + 4.84035e9i 0.191711 + 1.22487i
\(553\) −1.57250e9 2.72366e9i −0.395416 0.684880i
\(554\) 1.18301e9 5.09808e9i 0.295601 1.27386i
\(555\) −4.10042e9 + 4.56814e9i −1.01813 + 1.13426i
\(556\) −1.18082e9 5.79210e8i −0.291355 0.142914i
\(557\) −2.20530e9 −0.540723 −0.270362 0.962759i \(-0.587143\pi\)
−0.270362 + 0.962759i \(0.587143\pi\)
\(558\) 8.34488e8 + 1.00798e8i 0.203330 + 0.0245602i
\(559\) 1.82598e9i 0.442134i
\(560\) −9.25256e9 3.78669e9i −2.22640 0.911175i
\(561\) −4.45369e8 + 2.11132e9i −0.106500 + 0.504875i
\(562\) 8.88717e8 3.82984e9i 0.211196 0.910130i
\(563\) −5.50688e9 + 3.17940e9i −1.30055 + 0.750872i −0.980498 0.196529i \(-0.937033\pi\)
−0.320050 + 0.947401i \(0.603700\pi\)
\(564\) −1.59389e8 3.95300e8i −0.0374095 0.0927790i
\(565\) 7.88058e9 + 4.54985e9i 1.83818 + 1.06127i
\(566\) −2.27292e7 + 2.43193e7i −0.00526899 + 0.00563760i
\(567\) −5.10847e9 + 4.65713e9i −1.17693 + 1.07295i
\(568\) 8.87381e8 + 7.23548e8i 0.203185 + 0.165672i
\(569\) 2.21102e9 + 1.27653e9i 0.503153 + 0.290496i 0.730015 0.683431i \(-0.239513\pi\)
−0.226861 + 0.973927i \(0.572846\pi\)
\(570\) −6.17458e8 + 1.32560e9i −0.139652 + 0.299813i
\(571\) 2.46696e9 + 4.27290e9i 0.554544 + 0.960498i 0.997939 + 0.0641714i \(0.0204404\pi\)
−0.443395 + 0.896326i \(0.646226\pi\)
\(572\) 1.47998e9 9.93433e8i 0.330651 0.221949i
\(573\) −2.91605e8 + 1.38239e9i −0.0647522 + 0.306964i
\(574\) 3.03182e9 + 9.95660e9i 0.669132 + 2.19745i
\(575\) −7.24352e9 −1.58896
\(576\) 3.39720e9 + 3.08136e9i 0.740699 + 0.671837i
\(577\) −2.56379e8 −0.0555606 −0.0277803 0.999614i \(-0.508844\pi\)
−0.0277803 + 0.999614i \(0.508844\pi\)
\(578\) 2.92899e9 + 9.61889e9i 0.630914 + 2.07194i
\(579\) 2.30165e9 + 2.06599e9i 0.492793 + 0.442337i
\(580\) 5.16656e9 3.46804e9i 1.09952 0.738050i
\(581\) 5.15053e9 + 8.92097e9i 1.08952 + 1.88710i
\(582\) 5.50904e9 4.84317e8i 1.15837 0.101836i
\(583\) 3.44949e7 + 1.99156e7i 0.00720965 + 0.00416250i
\(584\) −4.43137e8 3.61323e8i −0.0920647 0.0750673i
\(585\) −9.98596e9 + 1.08075e9i −2.06226 + 0.223193i
\(586\) 1.13788e8 1.21749e8i 0.0233591 0.0249932i
\(587\) −1.86136e9 1.07466e9i −0.379837 0.219299i 0.297910 0.954594i \(-0.403710\pi\)
−0.677747 + 0.735295i \(0.737044\pi\)
\(588\) −7.49943e9 1.05934e9i −1.52127 0.214889i
\(589\) 1.92596e8 1.11195e8i 0.0388367 0.0224224i
\(590\) 3.33691e8 1.43801e9i 0.0668902 0.288257i
\(591\) −6.24363e9 + 2.03934e9i −1.24417 + 0.406381i
\(592\) 4.71426e9 + 1.92935e9i 0.933872 + 0.382195i
\(593\) 3.14866e9i 0.620062i 0.950726 + 0.310031i \(0.100339\pi\)
−0.950726 + 0.310031i \(0.899661\pi\)
\(594\) −9.75738e8 1.11454e9i −0.191021 0.218193i
\(595\) 2.19931e10 4.28033
\(596\) 3.05159e9 + 1.49685e9i 0.590425 + 0.289612i
\(597\) −2.93435e9 8.98379e9i −0.564420 1.72802i
\(598\) −2.01253e9 + 8.67281e9i −0.384848 + 1.65846i
\(599\) 1.66479e9 + 2.88349e9i 0.316493 + 0.548182i 0.979754 0.200206i \(-0.0641612\pi\)
−0.663261 + 0.748389i \(0.730828\pi\)
\(600\) −5.27763e9 + 4.25783e9i −0.997493 + 0.804746i
\(601\) 3.29834e9 5.71289e9i 0.619776 1.07348i −0.369750 0.929131i \(-0.620557\pi\)
0.989526 0.144353i \(-0.0461100\pi\)
\(602\) −2.00526e9 1.87415e9i −0.374614 0.350120i
\(603\) −6.51819e9 2.87800e9i −1.21064 0.534540i
\(604\) 5.03279e9 3.40575e8i 0.929350 0.0628902i
\(605\) 3.76779e9 6.52601e9i 0.691741 1.19813i
\(606\) 8.15946e9 7.17324e8i 1.48939 0.130937i
\(607\) 8.56929e9 4.94748e9i 1.55519 0.897891i 0.557488 0.830185i \(-0.311765\pi\)
0.997705 0.0677058i \(-0.0215679\pi\)
\(608\) 1.20824e9 + 1.12544e8i 0.218017 + 0.0203076i
\(609\) 5.19855e9 5.79153e9i 0.932656 1.03904i
\(610\) −5.56484e9 + 1.69451e9i −0.992654 + 0.302267i
\(611\) 7.74558e8i 0.137376i
\(612\) −9.48408e9 3.44288e9i −1.67250 0.607144i
\(613\) 9.62891e8i 0.168836i 0.996430 + 0.0844181i \(0.0269031\pi\)
−0.996430 + 0.0844181i \(0.973097\pi\)
\(614\) 3.95926e8 + 1.30023e9i 0.0690279 + 0.226690i
\(615\) 1.22970e10 + 2.59398e9i 2.13176 + 0.449680i
\(616\) 4.28053e8 2.64494e9i 0.0737844 0.455915i
\(617\) 3.25993e9 1.88212e9i 0.558741 0.322589i −0.193899 0.981021i \(-0.562113\pi\)
0.752640 + 0.658432i \(0.228780\pi\)
\(618\) −5.69223e9 2.65141e9i −0.970114 0.451874i
\(619\) 5.08172e9 8.80181e9i 0.861180 1.49161i −0.00961106 0.999954i \(-0.503059\pi\)
0.870791 0.491653i \(-0.163607\pi\)
\(620\) 1.83168e9 1.23952e8i 0.308658 0.0208873i
\(621\) 7.36185e9 + 7.39305e8i 1.23358 + 0.123881i
\(622\) 3.07756e8 3.29286e8i 0.0512790 0.0548664i
\(623\) 4.81631e9 8.34210e9i 0.798007 1.38219i
\(624\) 3.63165e9 + 7.50200e9i 0.598353 + 1.23604i
\(625\) 1.95018e9 + 3.37781e9i 0.319517 + 0.553420i
\(626\) 1.02915e10 + 2.38816e9i 1.67675 + 0.389092i
\(627\) −3.83477e8 8.08921e7i −0.0621303 0.0131060i
\(628\) −1.83929e9 + 3.74972e9i −0.296341 + 0.604143i
\(629\) −1.12057e10 −1.79540
\(630\) −9.06256e9 + 1.20757e10i −1.44397 + 1.92407i
\(631\) 6.13308e9i 0.971798i 0.874015 + 0.485899i \(0.161508\pi\)
−0.874015 + 0.485899i \(0.838492\pi\)
\(632\) 1.11940e9 + 2.94576e9i 0.176391 + 0.464181i
\(633\) 5.65900e8 + 5.07959e8i 0.0886802 + 0.0796004i
\(634\) −2.66574e9 6.18587e8i −0.415437 0.0964026i
\(635\) −3.93719e9 + 2.27314e9i −0.610209 + 0.352304i
\(636\) −1.14769e8 + 1.46685e8i −0.0176899 + 0.0226093i
\(637\) −1.19197e10 6.88185e9i −1.82716 1.05491i
\(638\) 1.21839e9 + 1.13872e9i 0.185743 + 0.173598i
\(639\) 1.39576e9 1.02068e9i 0.211620 0.154752i
\(640\) 8.54576e9 + 5.22664e9i 1.28861 + 0.788120i
\(641\) −6.84831e9 3.95388e9i −1.02702 0.592952i −0.110893 0.993832i \(-0.535371\pi\)
−0.916131 + 0.400880i \(0.868704\pi\)
\(642\) 9.21672e9 6.45940e9i 1.37469 0.963429i
\(643\) −6.01896e9 1.04251e10i −0.892859 1.54648i −0.836432 0.548070i \(-0.815363\pi\)
−0.0564268 0.998407i \(-0.517971\pi\)
\(644\) 7.45874e9 + 1.11118e10i 1.10044 + 1.63939i
\(645\) −3.15047e9 + 1.02903e9i −0.462292 + 0.150997i
\(646\) −2.55371e9 + 7.77614e8i −0.372699 + 0.113488i
\(647\) 9.09378e9 1.32002 0.660009 0.751258i \(-0.270553\pi\)
0.660009 + 0.751258i \(0.270553\pi\)
\(648\) 5.79842e9 3.78873e9i 0.837138 0.546992i
\(649\) 3.95632e8 0.0568113
\(650\) −1.17885e10 + 3.58964e9i −1.68369 + 0.512689i
\(651\) 2.18260e9 7.12897e8i 0.310056 0.101273i
\(652\) −5.30803e9 + 3.56300e9i −0.750009 + 0.503441i
\(653\) 7.15261e8 + 1.23887e9i 0.100524 + 0.174112i 0.911901 0.410411i \(-0.134615\pi\)
−0.811377 + 0.584523i \(0.801282\pi\)
\(654\) −7.65716e9 + 5.36641e9i −1.07040 + 0.750174i
\(655\) 1.88033e9 + 1.08561e9i 0.261451 + 0.150949i
\(656\) −1.40501e9 1.03336e10i −0.194320 1.42919i
\(657\) −6.97009e8 + 5.09702e8i −0.0958869 + 0.0701193i
\(658\) −8.50610e8 7.94994e8i −0.116397 0.108786i
\(659\) −2.47663e9 1.42989e9i −0.337103 0.194627i 0.321887 0.946778i \(-0.395683\pi\)
−0.658990 + 0.752151i \(0.729016\pi\)
\(660\) −2.54808e9 1.99365e9i −0.344992 0.269927i
\(661\) 4.70021e9 2.71367e9i 0.633012 0.365470i −0.148906 0.988851i \(-0.547575\pi\)
0.781918 + 0.623382i \(0.214242\pi\)
\(662\) −9.83033e9 2.28114e9i −1.31694 0.305596i
\(663\) −1.36449e10 1.22478e10i −1.81833 1.63215i
\(664\) −3.66646e9 9.64843e9i −0.486024 1.27899i
\(665\) 3.99460e9i 0.526741i
\(666\) 4.61745e9 6.15268e9i 0.605679 0.807058i
\(667\) −8.32981e9 −1.08691
\(668\) 4.98460e9 + 2.44502e9i 0.647013 + 0.317369i
\(669\) 9.26774e9 + 1.95497e9i 1.19669 + 0.252434i
\(670\) −1.51596e10 3.51780e9i −1.94727 0.451866i
\(671\) −7.79505e8 1.35014e9i −0.0996070 0.172524i
\(672\) 1.19661e10 + 3.71170e9i 1.52110 + 0.471824i
\(673\) −2.49940e9 + 4.32909e9i −0.316070 + 0.547450i −0.979664 0.200643i \(-0.935697\pi\)
0.663594 + 0.748093i \(0.269030\pi\)
\(674\) 9.91838e9 1.06122e10i 1.24776 1.33505i
\(675\) 4.20856e9 + 9.33597e9i 0.526708 + 1.16841i
\(676\) 4.80359e8 + 7.09843e9i 0.0598071 + 0.883790i
\(677\) 4.51637e9 7.82258e9i 0.559409 0.968924i −0.438137 0.898908i \(-0.644362\pi\)
0.997546 0.0700161i \(-0.0223051\pi\)
\(678\) −1.03371e10 4.81497e9i −1.27378 0.593321i
\(679\) 1.30828e10 7.55333e9i 1.60382 0.925964i
\(680\) −2.17539e10 3.52062e9i −2.65312 0.429376i
\(681\) 7.77271e9 + 1.63960e9i 0.943099 + 0.198941i
\(682\) 1.43324e8 + 4.70681e8i 0.0173011 + 0.0568175i
\(683\) 7.67901e9i 0.922217i 0.887344 + 0.461108i \(0.152548\pi\)
−0.887344 + 0.461108i \(0.847452\pi\)
\(684\) 6.25327e8 1.72259e9i 0.0747156 0.205819i
\(685\) 8.67601e9i 1.03134i
\(686\) −6.90966e9 + 2.10402e9i −0.817188 + 0.248837i
\(687\) −4.77238e8 + 5.31675e8i −0.0561547 + 0.0625601i
\(688\) 1.68344e9 + 2.17477e9i 0.197078 + 0.254597i
\(689\) −2.93116e8 + 1.69231e8i −0.0341407 + 0.0197112i
\(690\) 1.60979e10 1.41522e9i 1.86551 0.164003i
\(691\) −6.73421e9 + 1.16640e10i −0.776450 + 1.34485i 0.157525 + 0.987515i \(0.449648\pi\)
−0.933976 + 0.357336i \(0.883685\pi\)
\(692\) 7.38953e8 + 1.09198e10i 0.0847707 + 1.25269i
\(693\) −3.70159e9 1.63438e9i −0.422496 0.186546i
\(694\) 5.65627e9 + 5.28644e9i 0.642350 + 0.600351i
\(695\) −2.16910e9 + 3.75699e9i −0.245094 + 0.424515i
\(696\) −6.06910e9 + 4.89636e9i −0.682326 + 0.550480i
\(697\) 1.14709e10 + 1.98682e10i 1.28317 + 2.22251i
\(698\) 2.00009e6 8.61919e6i 0.000222616 0.000959340i
\(699\) 5.50927e8 + 1.68671e9i 0.0610132 + 0.186798i
\(700\) −8.15741e9 + 1.66303e10i −0.898896 + 1.83256i
\(701\) −7.38841e9 −0.810098 −0.405049 0.914295i \(-0.632746\pi\)
−0.405049 + 0.914295i \(0.632746\pi\)
\(702\) 1.23474e10 2.44509e9i 1.34709 0.266757i
\(703\) 2.03528e9i 0.220943i
\(704\) −8.46794e8 + 2.54765e9i −0.0914689 + 0.275192i
\(705\) −1.33639e9 + 4.36503e8i −0.143639 + 0.0469164i
\(706\) 3.07634e9 1.32572e10i 0.329016 1.41786i
\(707\) 1.93769e10 1.11873e10i 2.06213 1.19057i
\(708\) −2.58748e8 + 1.83177e9i −0.0274007 + 0.193979i
\(709\) 1.20228e10 + 6.94139e9i 1.26691 + 0.731450i 0.974402 0.224814i \(-0.0721773\pi\)
0.292507 + 0.956263i \(0.405511\pi\)
\(710\) 2.57876e9 2.75916e9i 0.270400 0.289316i
\(711\) 4.73143e9 5.12068e8i 0.493683 0.0534299i
\(712\) −6.09932e9 + 7.48039e9i −0.633288 + 0.776683i
\(713\) −2.12831e9 1.22878e9i −0.219898 0.126958i
\(714\) −2.74552e10 + 2.41368e9i −2.82281 + 0.248162i
\(715\) −2.93971e9 5.09173e9i −0.300769 0.520948i
\(716\) −3.30926e9 4.93002e9i −0.336927 0.501942i
\(717\) 8.65557e9 + 7.76934e9i 0.876957 + 0.787168i
\(718\) −4.41851e9 1.45105e10i −0.445492 1.46301i
\(719\) −9.40961e9 −0.944106 −0.472053 0.881570i \(-0.656487\pi\)
−0.472053 + 0.881570i \(0.656487\pi\)
\(720\) 1.08971e10 1.04937e10i 1.08804 1.04776i
\(721\) −1.71531e10 −1.70439
\(722\) 2.80466e9 + 9.21060e9i 0.277332 + 0.910768i
\(723\) 2.33121e9 1.10513e10i 0.229402 1.08750i
\(724\) 1.37578e9 + 2.04958e9i 0.134730 + 0.200716i
\(725\) −5.76460e9 9.98459e9i −0.561806 0.973077i
\(726\) −3.98734e9 + 8.56029e9i −0.386727 + 0.830253i
\(727\) −1.33679e10 7.71797e9i −1.29031 0.744959i −0.311599 0.950214i \(-0.600865\pi\)
−0.978709 + 0.205254i \(0.934198\pi\)
\(728\) 1.76453e10 + 1.43876e10i 1.69500 + 1.38206i
\(729\) −3.32444e9 9.91802e9i −0.317813 0.948153i
\(730\) −1.28777e9 + 1.37786e9i −0.122520 + 0.131092i
\(731\) −5.23953e9 3.02504e9i −0.496114 0.286432i
\(732\) 6.76093e9 2.72608e9i 0.637115 0.256892i
\(733\) −6.34787e9 + 3.66494e9i −0.595338 + 0.343719i −0.767205 0.641401i \(-0.778353\pi\)
0.171867 + 0.985120i \(0.445020\pi\)
\(734\) −1.12181e9 + 4.83432e9i −0.104709 + 0.451231i
\(735\) −5.15632e9 + 2.44441e10i −0.478999 + 2.27074i
\(736\) −5.59887e9 1.21849e10i −0.517640 1.12655i
\(737\) 4.17079e9i 0.383780i
\(738\) −1.56358e10 1.88865e9i −1.43193 0.172963i
\(739\) −1.42877e10 −1.30229 −0.651145 0.758954i \(-0.725711\pi\)
−0.651145 + 0.758954i \(0.725711\pi\)
\(740\) 7.39920e9 1.50846e10i 0.671233 1.36843i
\(741\) 2.22456e9 2.47831e9i 0.200854 0.223765i
\(742\) −1.15003e8 + 4.95592e8i −0.0103346 + 0.0445360i
\(743\) −5.12568e9 8.87793e9i −0.458448 0.794056i 0.540431 0.841388i \(-0.318261\pi\)
−0.998879 + 0.0473326i \(0.984928\pi\)
\(744\) −2.27298e9 + 3.55757e8i −0.202344 + 0.0316700i
\(745\) 5.60560e9 9.70919e9i 0.496679 0.860273i
\(746\) 1.10240e9 + 1.03033e9i 0.0972199 + 0.0908633i
\(747\) −1.54971e10 + 1.67721e9i −1.36028 + 0.147219i
\(748\) −3.98753e8 5.89252e9i −0.0348376 0.514808i
\(749\) 1.53720e10 2.66251e10i 1.33673 2.31529i
\(750\) 2.82091e9 + 4.02507e9i 0.244161 + 0.348385i
\(751\) −6.81429e9 + 3.93423e9i −0.587057 + 0.338938i −0.763933 0.645295i \(-0.776734\pi\)
0.176876 + 0.984233i \(0.443401\pi\)
\(752\) 7.14098e8 + 9.22512e8i 0.0612344 + 0.0791060i
\(753\) 5.95601e9 + 1.82349e10i 0.508362 + 1.55640i
\(754\) −1.35564e10 + 4.12796e9i −1.15171 + 0.350700i
\(755\) 1.66383e10i 1.40700i
\(756\) 9.98803e9 1.60694e10i 0.840724 1.35261i
\(757\) 1.44178e8i 0.0120799i 0.999982 + 0.00603995i \(0.00192259\pi\)
−0.999982 + 0.00603995i \(0.998077\pi\)
\(758\) −2.48961e9 8.17597e9i −0.207630 0.681863i
\(759\) 1.34469e9 + 4.11690e9i 0.111629 + 0.341762i
\(760\) 6.39447e8 3.95115e9i 0.0528393 0.326494i
\(761\) −1.79888e9 + 1.03858e9i −0.147964 + 0.0854270i −0.572154 0.820146i \(-0.693892\pi\)
0.424190 + 0.905573i \(0.360559\pi\)
\(762\) 4.66555e9 3.26978e9i 0.381997 0.267717i
\(763\) −1.27709e10 + 2.21199e10i −1.04085 + 1.80280i
\(764\) −2.61084e8 3.85813e9i −0.0211813 0.313004i
\(765\) −1.34423e10 + 3.04446e10i −1.08557 + 2.45864i
\(766\) 1.57726e9 1.68760e9i 0.126795 0.135665i
\(767\) −1.68092e9 + 2.91144e9i −0.134513 + 0.232983i
\(768\) −1.12418e10 5.58684e9i −0.895509 0.445043i
\(769\) −3.40743e9 5.90183e9i −0.270199 0.467999i 0.698713 0.715402i \(-0.253756\pi\)
−0.968913 + 0.247403i \(0.920423\pi\)
\(770\) −8.60895e9 1.99771e9i −0.679568 0.157694i
\(771\) 7.14376e9 7.95863e9i 0.561354 0.625386i
\(772\) −7.60033e9 3.72807e9i −0.594527 0.291624i
\(773\) 4.91311e9 0.382585 0.191293 0.981533i \(-0.438732\pi\)
0.191293 + 0.981533i \(0.438732\pi\)
\(774\) 3.81998e9 1.63035e9i 0.296120 0.126383i
\(775\) 3.40149e9i 0.262490i
\(776\) −1.41496e10 + 5.37692e9i −1.08700 + 0.413064i
\(777\) 4.33718e9 2.05609e10i 0.331691 1.57242i
\(778\) −9.48949e9 2.20204e9i −0.722461 0.167648i
\(779\) −3.60865e9 + 2.08346e9i −0.273504 + 0.157908i
\(780\) 2.54972e10 1.02808e10i 1.92381 0.775700i
\(781\) 8.76550e8 + 5.06076e8i 0.0658412 + 0.0380134i
\(782\) 2.15520e10 + 2.01429e10i 1.61163 + 1.50625i
\(783\) 4.83970e9 + 1.07361e10i 0.360290 + 0.799242i
\(784\) 2.05412e10 2.79289e9i 1.52237 0.206989i
\(785\) 1.19304e10 + 6.88802e9i 0.880260 + 0.508218i
\(786\) −2.46647e9 1.14887e9i −0.181174 0.0843900i
\(787\) 1.64787e9 + 2.85420e9i 0.120507 + 0.208724i 0.919968 0.391994i \(-0.128215\pi\)
−0.799461 + 0.600718i \(0.794881\pi\)
\(788\) 1.49267e10 1.00195e10i 1.08673 0.729467i
\(789\) 9.67205e8 4.58514e9i 0.0701050 0.332340i
\(790\) 9.94354e9 3.02784e9i 0.717540 0.218494i
\(791\) −3.11500e10 −2.23790
\(792\) 3.39971e9 + 2.20915e9i 0.243166 + 0.158011i
\(793\) 1.32475e10 0.943362
\(794\) 2.32972e10 7.09407e9i 1.65170 0.502949i
\(795\) 4.57170e8 + 4.10362e8i 0.0322696 + 0.0289656i
\(796\) 1.44168e10 + 2.14777e10i 1.01315 + 1.50936i
\(797\) −2.29482e8 3.97475e8i −0.0160563 0.0278103i 0.857886 0.513841i \(-0.171778\pi\)
−0.873942 + 0.486030i \(0.838444\pi\)
\(798\) −4.38395e8 4.98668e9i −0.0305390 0.347377i
\(799\) −2.22255e9 1.28319e9i −0.154148 0.0889974i
\(800\) 1.07308e10 1.51436e10i 0.741001 1.04572i
\(801\) 8.60403e9 + 1.17659e10i 0.591545 + 0.808928i
\(802\) 4.86073e9 + 4.54292e9i 0.332730 + 0.310974i
\(803\) −4.37729e8 2.52723e8i −0.0298332 0.0172242i
\(804\) 1.93107e10 + 2.72775e9i 1.31039 + 0.185101i
\(805\) 3.82290e10 2.20715e10i 2.58290 1.49124i
\(806\) −4.07267e9 9.45066e8i −0.273972 0.0635754i
\(807\) −5.23295e9 + 1.70923e9i −0.350501 + 0.114483i
\(808\) −2.09570e10 + 7.96377e9i −1.39762 + 0.531103i
\(809\) 1.27052e10i 0.843648i 0.906678 + 0.421824i \(0.138610\pi\)
−0.906678 + 0.421824i \(0.861390\pi\)
\(810\) −1.11771e10 1.99259e10i −0.738976 1.31741i
\(811\) 1.28555e9 0.0846281 0.0423141 0.999104i \(-0.486527\pi\)
0.0423141 + 0.999104i \(0.486527\pi\)
\(812\) −9.38075e9 + 1.91243e10i −0.614882 + 1.25354i
\(813\) 9.33030e8 + 2.85656e9i 0.0608946 + 0.186434i
\(814\) 4.38633e9 + 1.01785e9i 0.285047 + 0.0661454i
\(815\) 1.05434e10 + 1.82617e10i 0.682229 + 1.18165i
\(816\) 2.75430e10 + 2.00756e9i 1.77458 + 0.129346i
\(817\) 5.49437e8 9.51653e8i 0.0352485 0.0610522i
\(818\) −5.48309e9 + 5.86668e9i −0.350259 + 0.374762i
\(819\) 2.77543e10 2.02959e10i 1.76537 1.29096i
\(820\) −3.43200e10 + 2.32248e9i −2.17370 + 0.147097i
\(821\) −1.16104e10 + 2.01099e10i −0.732229 + 1.26826i 0.223699 + 0.974658i \(0.428187\pi\)
−0.955928 + 0.293600i \(0.905147\pi\)
\(822\) 9.52167e8 + 1.08308e10i 0.0597945 + 0.680154i
\(823\) −8.69944e9 + 5.02263e9i −0.543991 + 0.314074i −0.746695 0.665167i \(-0.768361\pi\)
0.202704 + 0.979240i \(0.435027\pi\)
\(824\) 1.69665e10 + 2.74583e9i 1.05645 + 0.170974i
\(825\) −4.00416e9 + 4.46090e9i −0.248269 + 0.276588i
\(826\) 1.47204e9 + 4.83422e9i 0.0908843 + 0.298467i
\(827\) 2.01241e10i 1.23722i −0.785698 0.618611i \(-0.787696\pi\)
0.785698 0.618611i \(-0.212304\pi\)
\(828\) −1.99406e10 + 3.53339e9i −1.22077 + 0.216315i
\(829\) 1.60240e10i 0.976857i 0.872604 + 0.488429i \(0.162430\pi\)
−0.872604 + 0.488429i \(0.837570\pi\)
\(830\) −3.25687e10 + 9.91729e9i −1.97709 + 0.602032i
\(831\) 2.11671e10 + 4.46506e9i 1.27955 + 0.269913i
\(832\) −1.51503e10 1.70557e10i −0.911988 1.02669i
\(833\) −3.94941e10 + 2.28019e10i −2.36742 + 1.36683i
\(834\) 2.29549e9 4.92811e9i 0.137023 0.294171i
\(835\) 9.15643e9 1.58594e10i 0.544282 0.942723i
\(836\) 1.07025e9 7.24253e7i 0.0633527 0.00428715i
\(837\) −3.47171e8 + 3.45705e9i −0.0204646 + 0.203783i
\(838\) 1.80189e9 + 1.68408e9i 0.105773 + 0.0988570i
\(839\) 2.58730e9 4.48134e9i 0.151245 0.261963i −0.780441 0.625230i \(-0.785005\pi\)
0.931685 + 0.363266i \(0.118339\pi\)
\(840\) 1.48797e10 3.85527e10i 0.866199 2.24428i
\(841\) 1.99584e9 + 3.45689e9i 0.115701 + 0.200401i
\(842\) 2.69969e9 1.16340e10i 0.155855 0.671643i
\(843\) 1.59014e10 + 3.35429e9i 0.914194 + 0.192843i
\(844\) −1.86867e9 9.16609e8i −0.106988 0.0524790i
\(845\) 2.34673e10 1.33803
\(846\) 1.62039e9 6.91576e8i 0.0920076 0.0392685i
\(847\) 2.57958e10i 1.45867i
\(848\) 1.93085e8 4.71793e8i 0.0108734 0.0265684i
\(849\) −1.02394e8 9.19103e7i −0.00574246 0.00515451i
\(850\) −9.22941e9 + 3.97732e10i −0.515475 + 2.22139i
\(851\) −1.94780e10 + 1.12456e10i −1.08340 + 0.625503i
\(852\) −2.91640e9 + 3.72743e9i −0.161550 + 0.206476i
\(853\) −2.09162e10 1.20760e10i −1.15388 0.666194i −0.204051 0.978960i \(-0.565411\pi\)
−0.949830 + 0.312767i \(0.898744\pi\)
\(854\) 1.35970e10 1.45483e10i 0.747036 0.799297i
\(855\) −5.52963e9 2.44152e9i −0.302562 0.133592i
\(856\) −1.94669e10 + 2.38748e10i −1.06081 + 1.30101i
\(857\) 1.72007e10 + 9.93085e9i 0.933500 + 0.538956i 0.887917 0.460004i \(-0.152152\pi\)
0.0455832 + 0.998961i \(0.485485\pi\)
\(858\) 4.22861e9 + 6.03367e9i 0.228556 + 0.326119i
\(859\) −7.22479e9 1.25137e10i −0.388910 0.673612i 0.603393 0.797444i \(-0.293815\pi\)
−0.992303 + 0.123832i \(0.960482\pi\)
\(860\) 7.53188e9 5.05575e9i 0.403793 0.271045i
\(861\) −4.08953e10 + 1.33575e10i −2.18355 + 0.713206i
\(862\) −4.15864e9 1.36571e10i −0.221144 0.726245i
\(863\) −2.94148e10 −1.55786 −0.778930 0.627111i \(-0.784237\pi\)
−0.778930 + 0.627111i \(0.784237\pi\)
\(864\) −1.24518e10 + 1.42958e10i −0.656799 + 0.754066i
\(865\) 3.61006e10 1.89652
\(866\) −8.02298e9 2.63477e10i −0.419781 1.37858i
\(867\) −3.95082e10 + 1.29045e10i −2.05883 + 0.672470i
\(868\) −5.21798e9 + 3.50255e9i −0.270822 + 0.181788i
\(869\) 1.39286e9 + 2.41250e9i 0.0720009 + 0.124709i
\(870\) 1.47619e10 + 2.10633e10i 0.760021 + 1.08445i
\(871\) 3.06927e10 + 1.77204e10i 1.57388 + 0.908679i
\(872\) 1.61729e10 1.98350e10i 0.826002 1.01303i
\(873\) 2.45965e9 + 2.27268e10i 0.125119 + 1.15608i
\(874\) −3.65853e9 + 3.91448e9i −0.185360 + 0.198328i
\(875\) 1.16276e10 + 6.71318e9i 0.586760 + 0.338766i
\(876\) 1.45638e9 1.86139e9i 0.0731999 0.0935563i
\(877\) 1.08616e10 6.27097e9i 0.543747 0.313932i −0.202849 0.979210i \(-0.565020\pi\)
0.746596 + 0.665278i \(0.231687\pi\)
\(878\) −5.23203e9 + 2.25469e10i −0.260879 + 1.12423i
\(879\) 5.12610e8 + 4.60125e8i 0.0254581 + 0.0228515i
\(880\) 8.19553e9 + 3.35409e9i 0.405404 + 0.165915i
\(881\) 2.15802e10i 1.06326i −0.846977 0.531630i \(-0.821580\pi\)
0.846977 0.531630i \(-0.178420\pi\)
\(882\) 3.75426e9 3.10808e10i 0.184240 1.52529i
\(883\) 3.23716e10 1.58235 0.791174 0.611591i \(-0.209470\pi\)
0.791174 + 0.611591i \(0.209470\pi\)
\(884\) 4.50570e10 + 2.21011e10i 2.19371 + 1.07605i
\(885\) 5.97057e9 + 1.25945e9i 0.289544 + 0.0610774i
\(886\) 5.94979e9 2.56400e10i 0.287398 1.23851i
\(887\) −6.89367e9 1.19402e10i −0.331679 0.574485i 0.651162 0.758939i \(-0.274282\pi\)
−0.982841 + 0.184454i \(0.940948\pi\)
\(888\) −7.58135e9 + 1.96429e10i −0.363330 + 0.941372i
\(889\) 7.78139e9 1.34778e10i 0.371450 0.643371i
\(890\) 2.32590e10 + 2.17382e10i 1.10593 + 1.03362i
\(891\) 4.52487e9 4.12509e9i 0.214306 0.195372i
\(892\) −2.58655e10 + 1.75035e9i −1.22024 + 0.0825748i
\(893\) 2.33065e8 4.03680e8i 0.0109521 0.0189696i
\(894\) −5.93224e9 + 1.27357e10i −0.277675 + 0.596132i
\(895\) −1.69613e10 + 9.79259e9i −0.790820 + 0.456580i
\(896\) −3.42804e10 8.67852e8i −1.59209 0.0403058i
\(897\) −3.60093e10 7.59592e9i −1.66587 0.351404i
\(898\) −1.60470e10 + 4.88638e9i −0.739482 + 0.225175i
\(899\) 3.91160e9i 0.179554i
\(900\) −1.80351e10 2.14567e10i −0.824651 0.981101i
\(901\) 1.12144e9i 0.0510787i
\(902\) −2.68546e9 8.81914e9i −0.121842 0.400132i
\(903\) 7.57851e9 8.44296e9i 0.342513 0.381582i
\(904\) 3.08112e10 + 4.98644e9i 1.38714 + 0.224492i
\(905\) 7.05140e9 4.07113e9i 0.316232 0.182576i
\(906\) 1.82601e9 + 2.07706e10i 0.0815744 + 0.927897i
\(907\) −2.01816e10 + 3.49556e10i −0.898111 + 1.55557i −0.0682055 + 0.997671i \(0.521727\pi\)
−0.829906 + 0.557903i \(0.811606\pi\)
\(908\) −2.16930e10 + 1.46799e9i −0.961654 + 0.0650763i
\(909\) 3.64300e9 + 3.36608e10i 0.160874 + 1.48645i
\(910\) 5.12779e10 5.48652e10i 2.25572 2.41353i
\(911\) 1.40597e10 2.43520e10i 0.616113 1.06714i −0.374075 0.927398i \(-0.622040\pi\)
0.990188 0.139741i \(-0.0446269\pi\)
\(912\) −3.64631e8 + 5.00262e9i −0.0159174 + 0.218381i
\(913\) −4.56212e9 7.90182e9i −0.198390 0.343621i
\(914\) 3.45357e10 + 8.01404e9i 1.49609 + 0.347168i
\(915\) −7.46564e9 2.28568e10i −0.322176 0.986372i
\(916\) 8.61173e8 1.75565e9i 0.0370217 0.0754752i
\(917\) −7.43250e9 −0.318304
\(918\) 1.34396e10 3.94810e10i 0.573373 1.68437i
\(919\) 2.37663e10i 1.01008i −0.863095 0.505041i \(-0.831477\pi\)
0.863095 0.505041i \(-0.168523\pi\)
\(920\) −4.13463e10 + 1.57118e10i −1.75057 + 0.665226i
\(921\) −5.34052e9 + 1.74436e9i −0.225255 + 0.0735745i
\(922\) −2.01502e10 4.67586e9i −0.846682 0.196473i
\(923\) −7.44839e9 + 4.30033e9i −0.311786 + 0.180010i
\(924\) 1.09663e10 + 1.54905e9i 0.457307 + 0.0645973i
\(925\) −2.69593e10 1.55649e10i −1.11998 0.646623i
\(926\) −2.02528e10 1.89286e10i −0.838197 0.783392i
\(927\) 1.04841e10 2.37447e10i 0.432266 0.979009i
\(928\) 1.23401e10 1.74147e10i 0.506875 0.715314i
\(929\) 5.92378e9 + 3.42009e9i 0.242406 + 0.139953i 0.616282 0.787525i \(-0.288638\pi\)
−0.373876 + 0.927479i \(0.621971\pi\)
\(930\) 6.64573e8 + 7.55942e9i 0.0270927 + 0.308175i
\(931\) −4.14150e9 7.17329e9i −0.168203 0.291336i
\(932\) −2.70677e9 4.03245e9i −0.109521 0.163160i
\(933\) 1.38643e9 + 1.24447e9i 0.0558870 + 0.0501649i
\(934\) 1.86126e10 5.66762e9i 0.747470 0.227607i
\(935\) −1.94806e10 −0.779401
\(936\) −3.07013e10 + 1.56323e10i −1.22375 + 0.623099i
\(937\) 6.50383e9 0.258274 0.129137 0.991627i \(-0.458779\pi\)
0.129137 + 0.991627i \(0.458779\pi\)
\(938\) 5.09628e10 1.55184e10i 2.01625 0.613954i
\(939\) −9.01364e9 + 4.27301e10i −0.355280 + 1.68424i
\(940\) 3.19494e9 2.14459e9i 0.125463 0.0842165i
\(941\) 9.55473e8 + 1.65493e9i 0.0373813 + 0.0647464i 0.884111 0.467277i \(-0.154765\pi\)
−0.846729 + 0.532024i \(0.821432\pi\)
\(942\) −1.56493e10 7.28938e9i −0.609983 0.284127i
\(943\) 3.98781e10 + 2.30236e10i 1.54861 + 0.894093i
\(944\) −6.82175e8 5.01728e9i −0.0263933 0.194118i
\(945\) −5.06587e10 3.64484e10i −1.95273 1.40497i
\(946\) 1.77618e9 + 1.66004e9i 0.0682131 + 0.0637530i
\(947\) 8.98857e9 + 5.18955e9i 0.343927 + 0.198566i 0.662007 0.749498i \(-0.269705\pi\)
−0.318080 + 0.948064i \(0.603038\pi\)
\(948\) −1.20808e10 + 4.87110e9i −0.460538 + 0.185694i
\(949\) 3.71955e9 2.14748e9i 0.141273 0.0815639i
\(950\) −7.22399e9 1.67633e9i −0.273366 0.0634348i
\(951\) 2.33474e9 1.10681e10i 0.0880252 0.417293i
\(952\) 7.05169e10 2.67968e10i 2.64889 1.00659i
\(953\) 1.32327e10i 0.495248i −0.968856 0.247624i \(-0.920350\pi\)
0.968856 0.247624i \(-0.0796498\pi\)
\(954\) −6.15748e8 4.62105e8i −0.0229606 0.0172314i
\(955\) −1.27549e10 −0.473877
\(956\) −2.85817e10 1.40197e10i −1.05800 0.518964i
\(957\) −4.60465e9 + 5.12989e9i −0.169826 + 0.189198i
\(958\) −7.29208e9 1.69213e9i −0.267961 0.0621806i
\(959\) 1.48498e10 + 2.57206e10i 0.543696 + 0.941709i
\(960\) −2.08893e10 + 3.57515e10i −0.762036 + 1.30420i
\(961\) −1.31793e10 + 2.28272e10i −0.479027 + 0.829699i
\(962\) −2.61265e10 + 2.79543e10i −0.946170 + 1.01236i
\(963\) 2.74611e10 + 3.75526e10i 0.990890 + 1.35503i
\(964\) 2.08721e9 + 3.08434e10i 0.0750405 + 1.10890i
\(965\) −1.39614e10 + 2.41818e10i −0.500129 + 0.866249i
\(966\) −4.53011e10 + 3.17486e10i −1.61692 + 1.13320i
\(967\) 8.76214e9 5.05882e9i 0.311614 0.179911i −0.336034 0.941850i \(-0.609086\pi\)
0.647649 + 0.761939i \(0.275752\pi\)
\(968\) 4.12934e9 2.55152e10i 0.146324 0.904139i
\(969\) −3.42599e9 1.04890e10i −0.120963 0.370340i
\(970\) 1.45439e10 + 4.77625e10i 0.511657 + 1.68030i
\(971\) 1.07669e10i 0.377419i −0.982033 0.188709i \(-0.939570\pi\)
0.982033 0.188709i \(-0.0604304\pi\)
\(972\) 1.61398e10 + 2.36479e10i 0.563723 + 0.825964i
\(973\) 1.48505e10i 0.516827i
\(974\) −6.46890e9 + 1.96980e9i −0.224323 + 0.0683072i
\(975\) −1.58151e10 4.84195e10i −0.546458 1.67303i
\(976\) −1.57780e10 + 1.22134e10i −0.543222 + 0.420498i
\(977\) 2.24873e10 1.29831e10i 0.771449 0.445396i −0.0619425 0.998080i \(-0.519730\pi\)
0.833391 + 0.552684i \(0.186396\pi\)
\(978\) −1.51661e10 2.16401e10i −0.518428 0.739729i
\(979\) −4.26609e9 + 7.38908e9i −0.145308 + 0.251681i
\(980\) −4.61662e9 6.82214e10i −0.156687 2.31542i
\(981\) −2.28144e10 3.11983e10i −0.771557 1.05509i
\(982\) 4.78535e9 + 4.47246e9i 0.161259 + 0.150715i
\(983\) 9.76384e9 1.69115e10i 0.327856 0.567864i −0.654230 0.756296i \(-0.727007\pi\)
0.982086 + 0.188432i \(0.0603405\pi\)
\(984\) 4.25887e10 6.66580e9i 1.42499 0.223033i
\(985\) −2.96493e10 5.13540e10i −0.988523 1.71217i
\(986\) −1.06135e10 + 4.57379e10i −0.352606 + 1.51952i
\(987\) 3.21472e9 3.58141e9i 0.106422 0.118562i
\(988\) −4.01421e9 + 8.18367e9i −0.132419 + 0.269960i
\(989\) −1.21433e10 −0.399163
\(990\) 8.02723e9 1.06962e10i 0.262932 0.350352i
\(991\) 2.57177e10i 0.839410i −0.907661 0.419705i \(-0.862134\pi\)
0.907661 0.419705i \(-0.137866\pi\)
\(992\) 5.72191e9 2.62917e9i 0.186102 0.0855123i
\(993\) 8.60972e9 4.08153e10i 0.279040 1.32282i
\(994\) −2.92234e9 + 1.25935e10i −0.0943795 + 0.406719i
\(995\) 7.38919e10 4.26615e10i 2.37802 1.37295i
\(996\) 3.95690e10 1.59546e10i 1.26896 0.511657i
\(997\) −2.48407e10 1.43418e10i −0.793837 0.458322i 0.0474744 0.998872i \(-0.484883\pi\)
−0.841312 + 0.540550i \(0.818216\pi\)
\(998\) −1.92980e10 + 2.06481e10i −0.614548 + 0.657541i
\(999\) 2.58110e10 + 1.85708e10i 0.819080 + 0.589320i
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 72.8.l.b.11.35 yes 160
8.3 odd 2 inner 72.8.l.b.11.7 160
9.5 odd 6 inner 72.8.l.b.59.7 yes 160
72.59 even 6 inner 72.8.l.b.59.35 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.8.l.b.11.7 160 8.3 odd 2 inner
72.8.l.b.11.35 yes 160 1.1 even 1 trivial
72.8.l.b.59.7 yes 160 9.5 odd 6 inner
72.8.l.b.59.35 yes 160 72.59 even 6 inner