Properties

Label 72.7.p.b.43.9
Level $72$
Weight $7$
Character 72.43
Analytic conductor $16.564$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,7,Mod(43,72)]
 
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, 4]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.43");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 72.p (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: \(16.5638940206\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.9
Character \(\chi\) \(=\) 72.43
Dual form 72.7.p.b.67.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.44575 + 2.92588i) q^{2} +(-21.4315 - 16.4223i) q^{3} +(46.8784 - 43.5708i) q^{4} +(-135.303 + 78.1175i) q^{5} +(207.623 + 59.5707i) q^{6} +(-19.7572 - 11.4068i) q^{7} +(-221.562 + 461.578i) q^{8} +(189.614 + 703.909i) q^{9} +O(q^{10})\) \(q+(-7.44575 + 2.92588i) q^{2} +(-21.4315 - 16.4223i) q^{3} +(46.8784 - 43.5708i) q^{4} +(-135.303 + 78.1175i) q^{5} +(207.623 + 59.5707i) q^{6} +(-19.7572 - 11.4068i) q^{7} +(-221.562 + 461.578i) q^{8} +(189.614 + 703.909i) q^{9} +(778.873 - 977.525i) q^{10} +(-823.638 + 1426.58i) q^{11} +(-1720.21 + 163.932i) q^{12} +(-648.782 + 374.574i) q^{13} +(180.482 + 27.1252i) q^{14} +(4182.62 + 547.826i) q^{15} +(299.173 - 4085.06i) q^{16} -4623.99 q^{17} +(-3471.38 - 4686.34i) q^{18} -3219.02 q^{19} +(-2939.17 + 9557.30i) q^{20} +(236.099 + 568.925i) q^{21} +(1958.59 - 13031.8i) q^{22} +(12177.5 - 7030.67i) q^{23} +(12328.6 - 6253.72i) q^{24} +(4392.19 - 7607.49i) q^{25} +(3734.71 - 4687.25i) q^{26} +(7496.11 - 18199.7i) q^{27} +(-1423.19 + 326.103i) q^{28} +(2284.39 + 1318.89i) q^{29} +(-32745.6 + 8158.88i) q^{30} +(39051.5 - 22546.4i) q^{31} +(9724.84 + 31291.7i) q^{32} +(41079.6 - 17047.7i) q^{33} +(34429.1 - 13529.3i) q^{34} +3564.29 q^{35} +(39558.7 + 24736.5i) q^{36} -48526.1i q^{37} +(23968.0 - 9418.46i) q^{38} +(20055.7 + 2626.83i) q^{39} +(-6079.20 - 79761.0i) q^{40} +(-24825.8 - 42999.6i) q^{41} +(-3422.54 - 3545.27i) q^{42} +(-64818.6 + 112269. i) q^{43} +(23546.5 + 102762. i) q^{44} +(-80643.1 - 80429.1i) q^{45} +(-70099.6 + 87978.5i) q^{46} +(-60674.6 - 35030.5i) q^{47} +(-73497.9 + 82635.6i) q^{48} +(-58564.3 - 101436. i) q^{49} +(-10444.5 + 69494.5i) q^{50} +(99098.8 + 75936.7i) q^{51} +(-14093.4 + 45827.4i) q^{52} -192622. i q^{53} +(-2563.99 + 157443. i) q^{54} -257362. i q^{55} +(9642.60 - 6592.18i) q^{56} +(68988.2 + 52863.7i) q^{57} +(-20867.9 - 3136.29i) q^{58} +(147514. + 255501. i) q^{59} +(219944. - 156559. i) q^{60} +(103879. + 59974.3i) q^{61} +(-224799. + 282135. i) q^{62} +(4283.12 - 16070.2i) q^{63} +(-163965. - 204536. i) q^{64} +(58521.6 - 101362. i) q^{65} +(-255989. + 247127. i) q^{66} +(-181212. - 313869. i) q^{67} +(-216765. + 201471. i) q^{68} +(-376441. - 49305.1i) q^{69} +(-26538.9 + 10428.7i) q^{70} +522397. i q^{71} +(-366920. - 68437.7i) q^{72} +509648. q^{73} +(141982. + 361313. i) q^{74} +(-219064. + 90909.6i) q^{75} +(-150902. + 140255. i) q^{76} +(32545.6 - 18790.2i) q^{77} +(-157016. + 39121.9i) q^{78} +(84902.3 + 49018.4i) q^{79} +(278635. + 576093. i) q^{80} +(-459534. + 266942. i) q^{81} +(310659. + 247527. i) q^{82} +(-17405.9 + 30147.9i) q^{83} +(35856.5 + 16383.3i) q^{84} +(625642. - 361214. i) q^{85} +(154137. - 1.02558e6i) q^{86} +(-27298.5 - 65780.8i) q^{87} +(-475992. - 696250. i) q^{88} +971603. q^{89} +(835774. + 362903. i) q^{90} +17090.8 q^{91} +(264529. - 860170. i) q^{92} +(-1.20719e6 - 158114. i) q^{93} +(554263. + 83301.6i) q^{94} +(435544. - 251461. i) q^{95} +(305465. - 830331. i) q^{96} +(29061.0 - 50335.1i) q^{97} +(732846. + 583917. i) q^{98} +(-1.16036e6 - 309265. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.44575 + 2.92588i −0.930719 + 0.365735i
\(3\) −21.4315 16.4223i −0.793758 0.608234i
\(4\) 46.8784 43.5708i 0.732475 0.680794i
\(5\) −135.303 + 78.1175i −1.08243 + 0.624940i −0.931550 0.363613i \(-0.881543\pi\)
−0.150877 + 0.988552i \(0.548210\pi\)
\(6\) 207.623 + 59.5707i 0.961218 + 0.275790i
\(7\) −19.7572 11.4068i −0.0576012 0.0332561i 0.470923 0.882174i \(-0.343921\pi\)
−0.528524 + 0.848918i \(0.677254\pi\)
\(8\) −221.562 + 461.578i −0.432738 + 0.901520i
\(9\) 189.614 + 703.909i 0.260102 + 0.965581i
\(10\) 778.873 977.525i 0.778873 0.977525i
\(11\) −823.638 + 1426.58i −0.618811 + 1.07181i 0.370892 + 0.928676i \(0.379052\pi\)
−0.989703 + 0.143137i \(0.954281\pi\)
\(12\) −1720.21 + 163.932i −0.995490 + 0.0948683i
\(13\) −648.782 + 374.574i −0.295304 + 0.170494i −0.640331 0.768099i \(-0.721203\pi\)
0.345028 + 0.938593i \(0.387870\pi\)
\(14\) 180.482 + 27.1252i 0.0657735 + 0.00988527i
\(15\) 4182.62 + 547.826i 1.23930 + 0.162319i
\(16\) 299.173 4085.06i 0.0730403 0.997329i
\(17\) −4623.99 −0.941174 −0.470587 0.882353i \(-0.655958\pi\)
−0.470587 + 0.882353i \(0.655958\pi\)
\(18\) −3471.38 4686.34i −0.595229 0.803556i
\(19\) −3219.02 −0.469313 −0.234656 0.972078i \(-0.575396\pi\)
−0.234656 + 0.972078i \(0.575396\pi\)
\(20\) −2939.17 + 9557.30i −0.367397 + 1.19466i
\(21\) 236.099 + 568.925i 0.0254939 + 0.0614323i
\(22\) 1958.59 13031.8i 0.183940 1.22388i
\(23\) 12177.5 7030.67i 1.00086 0.577848i 0.0923586 0.995726i \(-0.470559\pi\)
0.908503 + 0.417878i \(0.137226\pi\)
\(24\) 12328.6 6253.72i 0.891825 0.452382i
\(25\) 4392.19 7607.49i 0.281100 0.486879i
\(26\) 3734.71 4687.25i 0.212489 0.266685i
\(27\) 7496.11 18199.7i 0.380842 0.924640i
\(28\) −1423.19 + 326.103i −0.0648320 + 0.0148553i
\(29\) 2284.39 + 1318.89i 0.0936648 + 0.0540774i 0.546101 0.837720i \(-0.316112\pi\)
−0.452436 + 0.891797i \(0.649445\pi\)
\(30\) −32745.6 + 8158.88i −1.21280 + 0.302181i
\(31\) 39051.5 22546.4i 1.31085 0.756818i 0.328611 0.944465i \(-0.393420\pi\)
0.982236 + 0.187647i \(0.0600862\pi\)
\(32\) 9724.84 + 31291.7i 0.296778 + 0.954946i
\(33\) 41079.6 17047.7i 1.14310 0.474377i
\(34\) 34429.1 13529.3i 0.875969 0.344221i
\(35\) 3564.29 0.0831322
\(36\) 39558.7 + 24736.5i 0.847880 + 0.530189i
\(37\) 48526.1i 0.958010i −0.877812 0.479005i \(-0.840998\pi\)
0.877812 0.479005i \(-0.159002\pi\)
\(38\) 23968.0 9418.46i 0.436798 0.171644i
\(39\) 20055.7 + 2626.83i 0.338099 + 0.0442832i
\(40\) −6079.20 79761.0i −0.0949875 1.24627i
\(41\) −24825.8 42999.6i −0.360207 0.623897i 0.627788 0.778385i \(-0.283961\pi\)
−0.987995 + 0.154488i \(0.950627\pi\)
\(42\) −3422.54 3545.27i −0.0461956 0.0478522i
\(43\) −64818.6 + 112269.i −0.815257 + 1.41207i 0.0938864 + 0.995583i \(0.470071\pi\)
−0.909143 + 0.416483i \(0.863262\pi\)
\(44\) 23546.5 + 102762.i 0.276419 + 1.20636i
\(45\) −80643.1 80429.1i −0.884972 0.882624i
\(46\) −70099.6 + 87978.5i −0.720182 + 0.903864i
\(47\) −60674.6 35030.5i −0.584404 0.337406i 0.178478 0.983944i \(-0.442883\pi\)
−0.762882 + 0.646538i \(0.776216\pi\)
\(48\) −73497.9 + 82635.6i −0.664586 + 0.747212i
\(49\) −58564.3 101436.i −0.497788 0.862194i
\(50\) −10444.5 + 69494.5i −0.0835560 + 0.555956i
\(51\) 99098.8 + 75936.7i 0.747064 + 0.572455i
\(52\) −14093.4 + 45827.4i −0.100232 + 0.325923i
\(53\) 192622.i 1.29383i −0.762561 0.646916i \(-0.776058\pi\)
0.762561 0.646916i \(-0.223942\pi\)
\(54\) −2563.99 + 157443.i −0.0162830 + 0.999867i
\(55\) 257362.i 1.54688i
\(56\) 9642.60 6592.18i 0.0549073 0.0375375i
\(57\) 68988.2 + 52863.7i 0.372520 + 0.285452i
\(58\) −20867.9 3136.29i −0.106954 0.0160743i
\(59\) 147514. + 255501.i 0.718252 + 1.24405i 0.961692 + 0.274132i \(0.0883906\pi\)
−0.243440 + 0.969916i \(0.578276\pi\)
\(60\) 219944. 156559.i 1.01826 0.724809i
\(61\) 103879. + 59974.3i 0.457653 + 0.264226i 0.711057 0.703134i \(-0.248217\pi\)
−0.253404 + 0.967361i \(0.581550\pi\)
\(62\) −224799. + 282135.i −0.943235 + 1.18381i
\(63\) 4283.12 16070.2i 0.0171293 0.0642686i
\(64\) −163965. 204536.i −0.625475 0.780244i
\(65\) 58521.6 101362.i 0.213096 0.369094i
\(66\) −255989. + 247127.i −0.890408 + 0.859584i
\(67\) −181212. 313869.i −0.602509 1.04358i −0.992440 0.122732i \(-0.960834\pi\)
0.389931 0.920844i \(-0.372499\pi\)
\(68\) −216765. + 201471.i −0.689387 + 0.640745i
\(69\) −376441. 49305.1i −1.14591 0.150087i
\(70\) −26538.9 + 10428.7i −0.0773728 + 0.0304044i
\(71\) 522397.i 1.45957i 0.683676 + 0.729786i \(0.260380\pi\)
−0.683676 + 0.729786i \(0.739620\pi\)
\(72\) −366920. 68437.7i −0.983046 0.183357i
\(73\) 509648. 1.31009 0.655046 0.755589i \(-0.272649\pi\)
0.655046 + 0.755589i \(0.272649\pi\)
\(74\) 141982. + 361313.i 0.350378 + 0.891638i
\(75\) −219064. + 90909.6i −0.519262 + 0.215489i
\(76\) −150902. + 140255.i −0.343760 + 0.319505i
\(77\) 32545.6 18790.2i 0.0712886 0.0411585i
\(78\) −157016. + 39121.9i −0.330871 + 0.0824397i
\(79\) 84902.3 + 49018.4i 0.172202 + 0.0994209i 0.583624 0.812024i \(-0.301634\pi\)
−0.411422 + 0.911445i \(0.634968\pi\)
\(80\) 278635. + 576093.i 0.544210 + 1.12518i
\(81\) −459534. + 266942.i −0.864694 + 0.502299i
\(82\) 310659. + 247527.i 0.563432 + 0.448932i
\(83\) −17405.9 + 30147.9i −0.0304412 + 0.0527257i −0.880845 0.473405i \(-0.843025\pi\)
0.850403 + 0.526131i \(0.176358\pi\)
\(84\) 35856.5 + 16383.3i 0.0604964 + 0.0276416i
\(85\) 625642. 361214.i 1.01875 0.588177i
\(86\) 154137. 1.02558e6i 0.242332 1.61241i
\(87\) −27298.5 65780.8i −0.0414554 0.0998944i
\(88\) −475992. 696250.i −0.698477 1.02169i
\(89\) 971603. 1.37822 0.689110 0.724657i \(-0.258002\pi\)
0.689110 + 0.724657i \(0.258002\pi\)
\(90\) 835774. + 362903.i 1.14647 + 0.497809i
\(91\) 17090.8 0.0226798
\(92\) 264529. 860170.i 0.339712 1.10464i
\(93\) −1.20719e6 158114.i −1.50082 0.196572i
\(94\) 554263. + 83301.6i 0.667317 + 0.100293i
\(95\) 435544. 251461.i 0.507997 0.293292i
\(96\) 305465. 830331.i 0.345261 0.938507i
\(97\) 29061.0 50335.1i 0.0318416 0.0551513i −0.849665 0.527322i \(-0.823196\pi\)
0.881507 + 0.472171i \(0.156529\pi\)
\(98\) 732846. + 583917.i 0.778636 + 0.620402i
\(99\) −1.16036e6 309265.i −1.19588 0.318732i
\(100\) −125566. 547998.i −0.125566 0.547998i
\(101\) 43287.9 + 24992.3i 0.0420148 + 0.0242573i 0.520860 0.853642i \(-0.325611\pi\)
−0.478845 + 0.877899i \(0.658945\pi\)
\(102\) −960047. 275454.i −0.904674 0.259567i
\(103\) 1.64521e6 949863.i 1.50560 0.869259i 0.505622 0.862755i \(-0.331263\pi\)
0.999979 0.00650343i \(-0.00207012\pi\)
\(104\) −29149.8 382455.i −0.0259141 0.340001i
\(105\) −76388.0 58534.0i −0.0659868 0.0505639i
\(106\) 563589. + 1.43421e6i 0.473200 + 1.20419i
\(107\) 754822. 0.616160 0.308080 0.951360i \(-0.400314\pi\)
0.308080 + 0.951360i \(0.400314\pi\)
\(108\) −441569. 1.17978e6i −0.350532 0.936551i
\(109\) 236384.i 0.182532i 0.995827 + 0.0912660i \(0.0290914\pi\)
−0.995827 + 0.0912660i \(0.970909\pi\)
\(110\) 753011. + 1.91625e6i 0.565749 + 1.43971i
\(111\) −796911. + 1.03998e6i −0.582694 + 0.760427i
\(112\) −52508.4 + 77296.8i −0.0373745 + 0.0550184i
\(113\) −1.04811e6 1.81537e6i −0.726390 1.25814i −0.958399 0.285430i \(-0.907863\pi\)
0.232010 0.972713i \(-0.425470\pi\)
\(114\) −668342. 191759.i −0.451112 0.129432i
\(115\) −1.09844e6 + 1.90255e6i −0.722240 + 1.25096i
\(116\) 164554. 37705.0i 0.105423 0.0241560i
\(117\) −386684. 385658.i −0.241434 0.240794i
\(118\) −1.84592e6 1.47079e6i −1.12348 0.895169i
\(119\) 91357.2 + 52745.1i 0.0542128 + 0.0312998i
\(120\) −1.17957e6 + 1.80923e6i −0.682624 + 1.04701i
\(121\) −470978. 815758.i −0.265855 0.460474i
\(122\) −948932. 142617.i −0.522583 0.0785404i
\(123\) −174100. + 1.32924e6i −0.0935584 + 0.714313i
\(124\) 848308. 2.75844e6i 0.444926 1.44677i
\(125\) 1.06875e6i 0.547198i
\(126\) 15128.4 + 132186.i 0.00756279 + 0.0660808i
\(127\) 3.39068e6i 1.65530i 0.561248 + 0.827648i \(0.310321\pi\)
−0.561248 + 0.827648i \(0.689679\pi\)
\(128\) 1.81929e6 + 1.04319e6i 0.867504 + 0.497430i
\(129\) 3.23288e6 1.34162e6i 1.50598 0.624971i
\(130\) −139163. + 925947.i −0.0633422 + 0.421460i
\(131\) −747744. 1.29513e6i −0.332613 0.576103i 0.650410 0.759583i \(-0.274597\pi\)
−0.983023 + 0.183480i \(0.941264\pi\)
\(132\) 1.18296e6 2.58904e6i 0.514339 1.12568i
\(133\) 63598.8 + 36718.8i 0.0270330 + 0.0156075i
\(134\) 2.26761e6 + 1.80679e6i 0.942439 + 0.750918i
\(135\) 407465. + 3.04806e6i 0.165611 + 1.23886i
\(136\) 1.02450e6 2.13433e6i 0.407282 0.848487i
\(137\) 641312. 1.11079e6i 0.249407 0.431985i −0.713955 0.700192i \(-0.753098\pi\)
0.963361 + 0.268207i \(0.0864311\pi\)
\(138\) 2.94715e6 734309.i 1.12141 0.279410i
\(139\) 272285. + 471612.i 0.101386 + 0.175606i 0.912256 0.409620i \(-0.134339\pi\)
−0.810870 + 0.585227i \(0.801005\pi\)
\(140\) 167089. 155299.i 0.0608923 0.0565959i
\(141\) 725062. + 1.74717e6i 0.258653 + 0.623273i
\(142\) −1.52847e6 3.88964e6i −0.533817 1.35845i
\(143\) 1.23405e6i 0.422013i
\(144\) 2.93224e6 563995.i 0.982000 0.188881i
\(145\) −412114. −0.135180
\(146\) −3.79471e6 + 1.49117e6i −1.21933 + 0.479147i
\(147\) −410703. + 3.13569e6i −0.129293 + 0.987145i
\(148\) −2.11432e6 2.27483e6i −0.652207 0.701719i
\(149\) −4.37872e6 + 2.52806e6i −1.32370 + 0.764237i −0.984316 0.176412i \(-0.943551\pi\)
−0.339381 + 0.940649i \(0.610218\pi\)
\(150\) 1.36510e6 1.31784e6i 0.404475 0.390473i
\(151\) 3.85659e6 + 2.22660e6i 1.12014 + 0.646713i 0.941437 0.337189i \(-0.109476\pi\)
0.178704 + 0.983903i \(0.442810\pi\)
\(152\) 713212. 1.48583e6i 0.203090 0.423095i
\(153\) −876775. 3.25487e6i −0.244801 0.908780i
\(154\) −187348. + 235132.i −0.0512965 + 0.0643797i
\(155\) −3.52253e6 + 6.10120e6i −0.945932 + 1.63840i
\(156\) 1.05463e6 750702.i 0.277797 0.197740i
\(157\) 2.41739e6 1.39568e6i 0.624667 0.360652i −0.154017 0.988068i \(-0.549221\pi\)
0.778684 + 0.627417i \(0.215888\pi\)
\(158\) −775584. 116564.i −0.196633 0.0295525i
\(159\) −3.16330e6 + 4.12817e6i −0.786953 + 1.02699i
\(160\) −3.76023e6 3.47419e6i −0.918025 0.848192i
\(161\) −320791. −0.0768678
\(162\) 2.64053e6 3.33213e6i 0.621078 0.783748i
\(163\) 418159. 0.0965558 0.0482779 0.998834i \(-0.484627\pi\)
0.0482779 + 0.998834i \(0.484627\pi\)
\(164\) −3.03732e6 934072.i −0.688588 0.211762i
\(165\) −4.22648e6 + 5.51564e6i −0.940865 + 1.22785i
\(166\) 41390.7 275401.i 0.00904855 0.0602062i
\(167\) 6.73135e6 3.88635e6i 1.44528 0.834435i 0.447088 0.894490i \(-0.352461\pi\)
0.998195 + 0.0600552i \(0.0191277\pi\)
\(168\) −314914. 17074.0i −0.0664146 0.00360086i
\(169\) −2.13279e6 + 3.69411e6i −0.441864 + 0.765331i
\(170\) −3.60150e6 + 4.52007e6i −0.733056 + 0.920022i
\(171\) −610371. 2.26589e6i −0.122069 0.453159i
\(172\) 1.85306e6 + 8.08720e6i 0.364170 + 1.58933i
\(173\) −6.64127e6 3.83434e6i −1.28266 0.740546i −0.305329 0.952247i \(-0.598766\pi\)
−0.977335 + 0.211701i \(0.932100\pi\)
\(174\) 395725. + 409915.i 0.0751182 + 0.0778119i
\(175\) −173555. + 100202.i −0.0323834 + 0.0186966i
\(176\) 5.58126e6 + 3.79140e6i 1.02375 + 0.695444i
\(177\) 1.03449e6 7.89828e6i 0.186555 1.42434i
\(178\) −7.23431e6 + 2.84280e6i −1.28274 + 0.504064i
\(179\) 4.72783e6 0.824334 0.412167 0.911108i \(-0.364772\pi\)
0.412167 + 0.911108i \(0.364772\pi\)
\(180\) −7.28478e6 256707.i −1.24910 0.0440170i
\(181\) 2.86383e6i 0.482961i 0.970406 + 0.241480i \(0.0776329\pi\)
−0.970406 + 0.241480i \(0.922367\pi\)
\(182\) −127254. + 50005.8i −0.0211085 + 0.00829480i
\(183\) −1.24135e6 2.99127e6i −0.202554 0.488092i
\(184\) 547136. + 7.17859e6i 0.0878298 + 1.15235i
\(185\) 3.79073e6 + 6.56575e6i 0.598699 + 1.03698i
\(186\) 9.45108e6 2.35483e6i 1.46873 0.365948i
\(187\) 3.80849e6 6.59650e6i 0.582409 1.00876i
\(188\) −4.37063e6 + 1.00147e6i −0.657765 + 0.150717i
\(189\) −355703. + 274069.i −0.0526869 + 0.0405951i
\(190\) −2.50721e6 + 3.14667e6i −0.365535 + 0.458765i
\(191\) −1.05576e7 6.09541e6i −1.51518 0.874788i −0.999842 0.0178003i \(-0.994334\pi\)
−0.515336 0.856988i \(-0.672333\pi\)
\(192\) 155035. + 7.07619e6i 0.0219041 + 0.999760i
\(193\) 2.49686e6 + 4.32470e6i 0.347315 + 0.601567i 0.985771 0.168091i \(-0.0537603\pi\)
−0.638457 + 0.769658i \(0.720427\pi\)
\(194\) −69106.3 + 459812.i −0.00946482 + 0.0629760i
\(195\) −2.91881e6 + 1.21128e6i −0.393643 + 0.163358i
\(196\) −7.16506e6 2.20348e6i −0.951594 0.292645i
\(197\) 1.17618e7i 1.53842i −0.638994 0.769211i \(-0.720649\pi\)
0.638994 0.769211i \(-0.279351\pi\)
\(198\) 9.54461e6 1.09236e6i 1.22960 0.140724i
\(199\) 1.50727e6i 0.191263i 0.995417 + 0.0956315i \(0.0304870\pi\)
−0.995417 + 0.0956315i \(0.969513\pi\)
\(200\) 2.53831e6 + 3.71287e6i 0.317288 + 0.464108i
\(201\) −1.27082e6 + 9.70260e6i −0.156493 + 1.19481i
\(202\) −395435. 59431.0i −0.0479757 0.00721039i
\(203\) −30088.8 52115.3i −0.00359680 0.00622985i
\(204\) 7.95422e6 758022.i 0.936930 0.0892876i
\(205\) 6.71804e6 + 3.87866e6i 0.779796 + 0.450215i
\(206\) −9.47064e6 + 1.18861e7i −1.08337 + 1.35969i
\(207\) 7.25798e6 + 7.23872e6i 0.818285 + 0.816114i
\(208\) 1.33606e6 + 2.76238e6i 0.148469 + 0.306968i
\(209\) 2.65130e6 4.59219e6i 0.290416 0.503015i
\(210\) 740030. + 212327.i 0.0799082 + 0.0229270i
\(211\) −2.43614e6 4.21952e6i −0.259331 0.449175i 0.706732 0.707482i \(-0.250169\pi\)
−0.966063 + 0.258307i \(0.916835\pi\)
\(212\) −8.39268e6 9.02981e6i −0.880832 0.947700i
\(213\) 8.57897e6 1.11957e7i 0.887762 1.15855i
\(214\) −5.62022e6 + 2.20852e6i −0.573472 + 0.225351i
\(215\) 2.02539e7i 2.03795i
\(216\) 6.73973e6 + 7.49240e6i 0.668776 + 0.743464i
\(217\) −1.02873e6 −0.100675
\(218\) −691633. 1.76006e6i −0.0667584 0.169886i
\(219\) −1.09225e7 8.36960e6i −1.03989 0.796843i
\(220\) −1.12135e7 1.20647e7i −1.05311 1.13305i
\(221\) 2.99996e6 1.73203e6i 0.277932 0.160464i
\(222\) 2.89073e6 1.00751e7i 0.264210 0.920856i
\(223\) −1.08547e7 6.26696e6i −0.978821 0.565122i −0.0769068 0.997038i \(-0.524504\pi\)
−0.901914 + 0.431916i \(0.857838\pi\)
\(224\) 164803. 729166.i 0.0146630 0.0648758i
\(225\) 6.18780e6 + 1.64921e6i 0.543236 + 0.144787i
\(226\) 1.31155e7 + 1.04502e7i 1.13621 + 0.905312i
\(227\) 4.61321e6 7.99032e6i 0.394390 0.683104i −0.598633 0.801023i \(-0.704289\pi\)
0.993023 + 0.117920i \(0.0376225\pi\)
\(228\) 5.53737e6 527701.i 0.467196 0.0445229i
\(229\) 1.71451e7 9.89870e6i 1.42769 0.824274i 0.430747 0.902473i \(-0.358250\pi\)
0.996938 + 0.0781981i \(0.0249167\pi\)
\(230\) 2.61206e6 1.73798e7i 0.214684 1.42844i
\(231\) −1.00608e6 131773.i −0.0816199 0.0106903i
\(232\) −1.11491e6 + 762207.i −0.0892841 + 0.0610393i
\(233\) −2.27501e7 −1.79852 −0.899261 0.437412i \(-0.855895\pi\)
−0.899261 + 0.437412i \(0.855895\pi\)
\(234\) 4.00755e6 + 1.74012e6i 0.312774 + 0.135810i
\(235\) 1.09460e7 0.843433
\(236\) 1.80476e7 + 5.55021e6i 1.37304 + 0.422254i
\(237\) −1.01458e6 2.44483e6i −0.0762155 0.183655i
\(238\) −834549. 125426.i −0.0619043 0.00930376i
\(239\) 1.90062e6 1.09732e6i 0.139220 0.0803787i −0.428772 0.903413i \(-0.641054\pi\)
0.567992 + 0.823034i \(0.307720\pi\)
\(240\) 3.48923e6 1.69224e7i 0.252404 1.22413i
\(241\) −5.83380e6 + 1.01044e7i −0.416774 + 0.721874i −0.995613 0.0935683i \(-0.970173\pi\)
0.578839 + 0.815442i \(0.303506\pi\)
\(242\) 5.89360e6 + 4.69591e6i 0.415848 + 0.331340i
\(243\) 1.42323e7 + 1.82565e6i 0.991873 + 0.127233i
\(244\) 7.48279e6 1.71457e6i 0.515103 0.118028i
\(245\) 1.58479e7 + 9.14979e6i 1.07764 + 0.622175i
\(246\) −2.59290e6 1.04066e7i −0.174173 0.699042i
\(247\) 2.08844e6 1.20576e6i 0.138590 0.0800148i
\(248\) 1.75459e6 + 2.30207e7i 0.115032 + 1.50926i
\(249\) 868131. 360268.i 0.0562325 0.0233360i
\(250\) 3.12702e6 + 7.95761e6i 0.200130 + 0.509287i
\(251\) 2.30959e7 1.46054 0.730271 0.683158i \(-0.239394\pi\)
0.730271 + 0.683158i \(0.239394\pi\)
\(252\) −499405. 939964.i −0.0312069 0.0587367i
\(253\) 2.31629e7i 1.43032i
\(254\) −9.92073e6 2.52462e7i −0.605400 1.54061i
\(255\) −1.93404e7 2.53314e6i −1.16639 0.152770i
\(256\) −1.65982e7 2.44428e6i −0.989330 0.145690i
\(257\) −1.19227e7 2.06508e7i −0.702388 1.21657i −0.967626 0.252389i \(-0.918784\pi\)
0.265238 0.964183i \(-0.414549\pi\)
\(258\) −2.01458e7 + 1.94484e7i −1.17307 + 1.13246i
\(259\) −553529. + 958740.i −0.0318597 + 0.0551826i
\(260\) −1.67304e6 7.30154e6i −0.0951889 0.415427i
\(261\) −495227. + 1.85808e6i −0.0278537 + 0.104507i
\(262\) 9.35692e6 + 7.45541e6i 0.520270 + 0.414541i
\(263\) 1.51577e6 + 875129.i 0.0833231 + 0.0481066i 0.541083 0.840969i \(-0.318015\pi\)
−0.457760 + 0.889076i \(0.651348\pi\)
\(264\) −1.23284e6 + 2.27385e7i −0.0670029 + 1.23581i
\(265\) 1.50471e7 + 2.60624e7i 0.808567 + 1.40048i
\(266\) −580976. 87316.3i −0.0308683 0.00463928i
\(267\) −2.08229e7 1.59560e7i −1.09397 0.838281i
\(268\) −2.21705e7 6.81812e6i −1.15178 0.354210i
\(269\) 8.40041e6i 0.431562i −0.976442 0.215781i \(-0.930770\pi\)
0.976442 0.215781i \(-0.0692298\pi\)
\(270\) −1.19521e7 2.15029e7i −0.607232 1.09246i
\(271\) 7.27137e6i 0.365350i −0.983173 0.182675i \(-0.941524\pi\)
0.983173 0.182675i \(-0.0584755\pi\)
\(272\) −1.38337e6 + 1.88893e7i −0.0687436 + 0.938660i
\(273\) −366282. 280671.i −0.0180023 0.0137946i
\(274\) −1.52502e6 + 1.01470e7i −0.0741353 + 0.493273i
\(275\) 7.23514e6 + 1.25316e7i 0.347896 + 0.602573i
\(276\) −1.97952e7 + 1.40905e7i −0.941528 + 0.670192i
\(277\) 1.16896e7 + 6.74897e6i 0.549995 + 0.317540i 0.749120 0.662434i \(-0.230477\pi\)
−0.199125 + 0.979974i \(0.563810\pi\)
\(278\) −3.40725e6 2.71483e6i −0.158588 0.126360i
\(279\) 2.32753e7 + 2.32135e7i 1.07172 + 1.06888i
\(280\) −789713. + 1.64520e6i −0.0359745 + 0.0749453i
\(281\) −79871.6 + 138342.i −0.00359976 + 0.00623497i −0.867820 0.496879i \(-0.834479\pi\)
0.864220 + 0.503114i \(0.167813\pi\)
\(282\) −1.05107e7 1.08876e7i −0.468686 0.485493i
\(283\) −7.89522e6 1.36749e7i −0.348341 0.603345i 0.637614 0.770356i \(-0.279922\pi\)
−0.985955 + 0.167012i \(0.946588\pi\)
\(284\) 2.27612e7 + 2.44891e7i 0.993667 + 1.06910i
\(285\) −1.34639e7 1.76346e6i −0.581617 0.0761783i
\(286\) 3.61070e6 + 9.18846e6i 0.154345 + 0.392776i
\(287\) 1.13274e6i 0.0479163i
\(288\) −2.01825e7 + 1.27787e7i −0.844886 + 0.534947i
\(289\) −2.75629e6 −0.114191
\(290\) 3.06850e6 1.20580e6i 0.125815 0.0494403i
\(291\) −1.44944e6 + 601506.i −0.0588195 + 0.0244096i
\(292\) 2.38915e7 2.22058e7i 0.959610 0.891902i
\(293\) −3.76233e7 + 2.17218e7i −1.49573 + 0.863562i −0.999988 0.00490652i \(-0.998438\pi\)
−0.495745 + 0.868468i \(0.665105\pi\)
\(294\) −6.11667e6 2.45492e7i −0.240698 0.966042i
\(295\) −3.99183e7 2.30468e7i −1.55491 0.897728i
\(296\) 2.23986e7 + 1.07515e7i 0.863664 + 0.414568i
\(297\) 1.97893e7 + 2.56838e7i 0.755372 + 0.980369i
\(298\) 2.52061e7 3.16349e7i 0.952482 1.19541i
\(299\) −5.26702e6 + 9.12275e6i −0.197039 + 0.341281i
\(300\) −6.30835e6 + 1.38065e7i −0.233643 + 0.511351i
\(301\) 2.56127e6 1.47875e6i 0.0939196 0.0542245i
\(302\) −3.52300e7 5.29480e6i −1.27906 0.192233i
\(303\) −517291. 1.24651e6i −0.0185955 0.0448092i
\(304\) −963043. + 1.31499e7i −0.0342787 + 0.468059i
\(305\) −1.87402e7 −0.660502
\(306\) 1.60516e7 + 2.16696e7i 0.560214 + 0.756286i
\(307\) −7.64160e6 −0.264100 −0.132050 0.991243i \(-0.542156\pi\)
−0.132050 + 0.991243i \(0.542156\pi\)
\(308\) 706982. 2.29889e6i 0.0241967 0.0786804i
\(309\) −5.08582e7 6.66125e6i −1.72379 0.225777i
\(310\) 8.37649e6 5.57346e7i 0.281175 1.87085i
\(311\) −1.39857e7 + 8.07463e6i −0.464945 + 0.268436i −0.714121 0.700022i \(-0.753174\pi\)
0.249176 + 0.968458i \(0.419840\pi\)
\(312\) −5.65608e6 + 8.67527e6i −0.186231 + 0.285640i
\(313\) −1.87981e7 + 3.25592e7i −0.613028 + 1.06180i 0.377699 + 0.925928i \(0.376715\pi\)
−0.990727 + 0.135867i \(0.956618\pi\)
\(314\) −1.39157e7 + 1.74649e7i −0.449486 + 0.564128i
\(315\) 675841. + 2.50894e6i 0.0216229 + 0.0802709i
\(316\) 6.11586e6 1.40136e6i 0.193819 0.0444107i
\(317\) 2.49165e7 + 1.43856e7i 0.782185 + 0.451595i 0.837204 0.546891i \(-0.184189\pi\)
−0.0550191 + 0.998485i \(0.517522\pi\)
\(318\) 1.14746e7 3.99927e7i 0.356826 1.24365i
\(319\) −3.76302e6 + 2.17258e6i −0.115922 + 0.0669274i
\(320\) 3.81628e7 + 1.48660e7i 1.16464 + 0.453674i
\(321\) −1.61769e7 1.23959e7i −0.489082 0.374770i
\(322\) 2.38853e6 938597.i 0.0715424 0.0281133i
\(323\) 1.48847e7 0.441705
\(324\) −9.91133e6 + 3.25361e7i −0.291405 + 0.956600i
\(325\) 6.58080e6i 0.191703i
\(326\) −3.11351e6 + 1.22348e6i −0.0898663 + 0.0353139i
\(327\) 3.88198e6 5.06606e6i 0.111022 0.144886i
\(328\) 2.53481e7 1.93198e6i 0.718330 0.0547495i
\(329\) 799174. + 1.38421e6i 0.0224416 + 0.0388700i
\(330\) 1.53312e7 5.34343e7i 0.426614 1.48689i
\(331\) 3.27900e7 5.67940e7i 0.904186 1.56610i 0.0821803 0.996617i \(-0.473812\pi\)
0.822006 0.569479i \(-0.192855\pi\)
\(332\) 497606. + 2.17167e6i 0.0135979 + 0.0593444i
\(333\) 3.41579e7 9.20124e6i 0.925036 0.249180i
\(334\) −3.87490e7 + 4.86319e7i −1.03997 + 1.30522i
\(335\) 4.90374e7 + 2.83117e7i 1.30435 + 0.753064i
\(336\) 2.39473e6 794272.i 0.0631303 0.0209388i
\(337\) −2.25359e7 3.90333e7i −0.588823 1.01987i −0.994387 0.105805i \(-0.966258\pi\)
0.405563 0.914067i \(-0.367075\pi\)
\(338\) 5.07173e6 3.37457e7i 0.131343 0.873913i
\(339\) −7.35021e6 + 5.61184e7i −0.188669 + 1.44048i
\(340\) 1.35907e7 4.41929e7i 0.345784 1.12439i
\(341\) 7.42802e7i 1.87331i
\(342\) 1.11744e7 + 1.50854e7i 0.279348 + 0.377119i
\(343\) 5.35614e6i 0.132730i
\(344\) −3.74596e7 5.47934e7i −0.920212 1.34603i
\(345\) 5.47854e7 2.27355e7i 1.33416 0.553665i
\(346\) 6.06681e7 + 9.11796e6i 1.46464 + 0.220125i
\(347\) 2.34102e7 + 4.05477e7i 0.560296 + 0.970460i 0.997470 + 0.0710839i \(0.0226458\pi\)
−0.437175 + 0.899377i \(0.644021\pi\)
\(348\) −4.14583e6 1.89428e6i −0.0983725 0.0449477i
\(349\) 2.22437e6 + 1.28424e6i 0.0523275 + 0.0302113i 0.525936 0.850524i \(-0.323715\pi\)
−0.473608 + 0.880736i \(0.657049\pi\)
\(350\) 999067. 1.25388e6i 0.0233019 0.0292450i
\(351\) 1.95380e6 + 1.46155e7i 0.0451813 + 0.337981i
\(352\) −5.26499e7 1.18997e7i −1.20717 0.272841i
\(353\) 5.14841e6 8.91730e6i 0.117044 0.202726i −0.801551 0.597926i \(-0.795992\pi\)
0.918595 + 0.395200i \(0.129325\pi\)
\(354\) 1.54069e7 + 6.18355e7i 0.347300 + 1.39389i
\(355\) −4.08083e7 7.06821e7i −0.912145 1.57988i
\(356\) 4.55472e7 4.23335e7i 1.00951 0.938283i
\(357\) −1.09172e6 2.63070e6i −0.0239942 0.0578185i
\(358\) −3.52023e7 + 1.38331e7i −0.767223 + 0.301488i
\(359\) 2.25511e7i 0.487398i 0.969851 + 0.243699i \(0.0783610\pi\)
−0.969851 + 0.243699i \(0.921639\pi\)
\(360\) 5.49917e7 1.94030e7i 1.17866 0.415874i
\(361\) −3.66838e7 −0.779746
\(362\) −8.37924e6 2.13234e7i −0.176636 0.449501i
\(363\) −3.30290e6 + 2.52174e7i −0.0690519 + 0.527207i
\(364\) 801192. 744661.i 0.0166124 0.0154403i
\(365\) −6.89571e7 + 3.98124e7i −1.41808 + 0.818729i
\(366\) 1.79949e7 + 1.86402e7i 0.367033 + 0.380195i
\(367\) −1.19225e7 6.88347e6i −0.241196 0.139254i 0.374530 0.927215i \(-0.377804\pi\)
−0.615726 + 0.787960i \(0.711137\pi\)
\(368\) −2.50775e7 5.18491e7i −0.503201 1.04039i
\(369\) 2.55604e7 2.56284e7i 0.508732 0.510086i
\(370\) −4.74355e7 3.77957e7i −0.936479 0.746168i
\(371\) −2.19721e6 + 3.80567e6i −0.0430278 + 0.0745263i
\(372\) −6.34805e7 + 4.51862e7i −1.23314 + 0.877763i
\(373\) 7.38379e7 4.26303e7i 1.42283 0.821471i 0.426289 0.904587i \(-0.359821\pi\)
0.996540 + 0.0831165i \(0.0264874\pi\)
\(374\) −9.05650e6 + 6.02591e7i −0.173119 + 1.15188i
\(375\) −1.75513e7 + 2.29048e7i −0.332824 + 0.434342i
\(376\) 2.96125e7 2.02446e7i 0.557072 0.380843i
\(377\) −1.97609e6 −0.0368794
\(378\) 1.84659e6 3.08139e6i 0.0341896 0.0570521i
\(379\) 4.22114e7 0.775376 0.387688 0.921791i \(-0.373274\pi\)
0.387688 + 0.921791i \(0.373274\pi\)
\(380\) 9.46124e6 3.07651e7i 0.172424 0.560670i
\(381\) 5.56828e7 7.26672e7i 1.00681 1.31390i
\(382\) 9.64435e7 + 1.44947e7i 1.73015 + 0.260028i
\(383\) 2.91516e7 1.68307e7i 0.518879 0.299575i −0.217597 0.976039i \(-0.569822\pi\)
0.736476 + 0.676464i \(0.236489\pi\)
\(384\) −2.18584e7 5.22339e7i −0.386034 0.922485i
\(385\) −2.93569e6 + 5.08476e6i −0.0514432 + 0.0891022i
\(386\) −3.12446e7 2.48951e7i −0.543266 0.432864i
\(387\) −9.13178e7 2.43386e7i −1.57551 0.419915i
\(388\) −830807. 3.62584e6i −0.0142235 0.0620746i
\(389\) 6.07252e7 + 3.50597e7i 1.03162 + 0.595606i 0.917449 0.397855i \(-0.130245\pi\)
0.114172 + 0.993461i \(0.463578\pi\)
\(390\) 1.81887e7 1.75590e7i 0.306625 0.296010i
\(391\) −5.63086e7 + 3.25098e7i −0.941985 + 0.543856i
\(392\) 5.97964e7 4.55754e6i 0.992697 0.0756611i
\(393\) −5.24382e6 + 4.00362e7i −0.0863913 + 0.659592i
\(394\) 3.44137e7 + 8.75756e7i 0.562656 + 1.43184i
\(395\) −1.53168e7 −0.248528
\(396\) −6.78707e7 + 3.60598e7i −1.09294 + 0.580681i
\(397\) 3.68007e7i 0.588145i −0.955783 0.294072i \(-0.904989\pi\)
0.955783 0.294072i \(-0.0950107\pi\)
\(398\) −4.41008e6 1.12227e7i −0.0699516 0.178012i
\(399\) −760007. 1.83138e6i −0.0119646 0.0288310i
\(400\) −2.97630e7 2.02183e7i −0.465047 0.315911i
\(401\) −2.99266e7 5.18344e7i −0.464114 0.803869i 0.535047 0.844822i \(-0.320294\pi\)
−0.999161 + 0.0409531i \(0.986961\pi\)
\(402\) −1.89265e7 7.59614e7i −0.291335 1.16927i
\(403\) −1.68906e7 + 2.92553e7i −0.258065 + 0.446982i
\(404\) 3.11820e6 714489.i 0.0472890 0.0108356i
\(405\) 4.13237e7 7.20159e7i 0.622062 1.08408i
\(406\) 376517. + 300002.i 0.00562609 + 0.00448276i
\(407\) 6.92264e7 + 3.99679e7i 1.02681 + 0.592827i
\(408\) −5.70072e7 + 2.89171e7i −0.839362 + 0.425770i
\(409\) 4.11363e7 + 7.12502e7i 0.601251 + 1.04140i 0.992632 + 0.121168i \(0.0386640\pi\)
−0.391381 + 0.920229i \(0.628003\pi\)
\(410\) −6.13694e7 9.22336e6i −0.890430 0.133825i
\(411\) −3.19859e7 + 1.32739e7i −0.460716 + 0.191194i
\(412\) 3.57386e7 1.16211e8i 0.511029 1.66171i
\(413\) 6.73066e6i 0.0955450i
\(414\) −7.52207e7 3.26617e7i −1.06008 0.460297i
\(415\) 5.43881e6i 0.0760957i
\(416\) −1.80304e7 1.66588e7i −0.250452 0.231400i
\(417\) 1.90950e6 1.45789e7i 0.0263336 0.201056i
\(418\) −6.30473e6 + 4.19497e7i −0.0863252 + 0.574381i
\(419\) 1.72597e7 + 2.98947e7i 0.234634 + 0.406399i 0.959166 0.282843i \(-0.0912774\pi\)
−0.724532 + 0.689241i \(0.757944\pi\)
\(420\) −6.13132e6 + 584304.i −0.0827573 + 0.00788662i
\(421\) −1.04662e8 6.04264e7i −1.40262 0.809805i −0.407963 0.912999i \(-0.633761\pi\)
−0.994661 + 0.103193i \(0.967094\pi\)
\(422\) 3.04847e7 + 2.42896e7i 0.405644 + 0.323209i
\(423\) 1.31535e7 4.93516e7i 0.173788 0.652049i
\(424\) 8.89100e7 + 4.26777e7i 1.16641 + 0.559891i
\(425\) −2.03094e7 + 3.51770e7i −0.264564 + 0.458238i
\(426\) −3.11195e7 + 1.08462e8i −0.402535 + 1.40297i
\(427\) −1.36824e6 2.36985e6i −0.0175743 0.0304395i
\(428\) 3.53849e7 3.28882e7i 0.451322 0.419478i
\(429\) −2.02660e7 + 2.64476e7i −0.256683 + 0.334976i
\(430\) 5.92605e7 + 1.50805e8i 0.745349 + 1.89676i
\(431\) 1.39715e8i 1.74506i −0.488561 0.872530i \(-0.662478\pi\)
0.488561 0.872530i \(-0.337522\pi\)
\(432\) −7.21042e7 3.60669e7i −0.894354 0.447361i
\(433\) 5.85609e7 0.721347 0.360673 0.932692i \(-0.382547\pi\)
0.360673 + 0.932692i \(0.382547\pi\)
\(434\) 7.65968e6 3.00995e6i 0.0937004 0.0368205i
\(435\) 8.83221e6 + 6.76788e6i 0.107300 + 0.0822214i
\(436\) 1.02994e7 + 1.10813e7i 0.124267 + 0.133700i
\(437\) −3.91995e7 + 2.26318e7i −0.469717 + 0.271191i
\(438\) 1.05815e8 + 3.03601e7i 1.25928 + 0.361310i
\(439\) −4.39948e7 2.54004e7i −0.520005 0.300225i 0.216932 0.976187i \(-0.430395\pi\)
−0.736937 + 0.675962i \(0.763728\pi\)
\(440\) 1.18793e8 + 5.70217e7i 1.39454 + 0.669394i
\(441\) 6.02973e7 6.04577e7i 0.703043 0.704913i
\(442\) −1.72692e7 + 2.16738e7i −0.199989 + 0.250997i
\(443\) 1.63472e7 2.83141e7i 0.188032 0.325681i −0.756562 0.653922i \(-0.773122\pi\)
0.944594 + 0.328241i \(0.106456\pi\)
\(444\) 7.95500e6 + 8.34749e7i 0.0908848 + 0.953689i
\(445\) −1.31461e8 + 7.58992e7i −1.49182 + 0.861305i
\(446\) 9.91578e7 + 1.49027e7i 1.11769 + 0.167981i
\(447\) 1.35359e8 + 1.77289e7i 1.51553 + 0.198499i
\(448\) 906370. + 5.91139e6i 0.0100803 + 0.0657439i
\(449\) 3.79985e7 0.419785 0.209893 0.977724i \(-0.432689\pi\)
0.209893 + 0.977724i \(0.432689\pi\)
\(450\) −5.08982e7 + 5.82517e6i −0.558554 + 0.0639251i
\(451\) 8.17899e7 0.891600
\(452\) −1.28231e8 3.94350e7i −1.38860 0.427038i
\(453\) −4.60863e7 1.11053e8i −0.495767 1.19464i
\(454\) −1.09701e7 + 7.29917e7i −0.117231 + 0.780020i
\(455\) −2.31245e6 + 1.33509e6i −0.0245492 + 0.0141735i
\(456\) −3.96859e7 + 2.01308e7i −0.418545 + 0.212308i
\(457\) −8.28266e6 + 1.43460e7i −0.0867804 + 0.150308i −0.906148 0.422960i \(-0.860991\pi\)
0.819368 + 0.573268i \(0.194325\pi\)
\(458\) −9.86954e7 + 1.23868e8i −1.02731 + 1.28932i
\(459\) −3.46619e7 + 8.41552e7i −0.358438 + 0.870248i
\(460\) 3.14026e7 + 1.37048e8i 0.322620 + 1.40799i
\(461\) −1.24507e8 7.18842e7i −1.27084 0.733720i −0.295695 0.955282i \(-0.595551\pi\)
−0.975146 + 0.221562i \(0.928884\pi\)
\(462\) 7.87656e6 1.96252e6i 0.0798750 0.0199016i
\(463\) −6.38937e7 + 3.68890e7i −0.643747 + 0.371667i −0.786056 0.618155i \(-0.787880\pi\)
0.142310 + 0.989822i \(0.454547\pi\)
\(464\) 6.07118e6 8.93729e6i 0.0607742 0.0894648i
\(465\) 1.75689e8 7.29095e7i 1.74737 0.725146i
\(466\) 1.69392e8 6.65642e7i 1.67392 0.657783i
\(467\) −4.75986e7 −0.467352 −0.233676 0.972315i \(-0.575075\pi\)
−0.233676 + 0.972315i \(0.575075\pi\)
\(468\) −3.49306e7 1.23091e6i −0.340776 0.0120085i
\(469\) 8.26825e6i 0.0801484i
\(470\) −8.15010e7 + 3.20266e7i −0.784999 + 0.308473i
\(471\) −7.47286e7 9.78772e6i −0.715195 0.0936739i
\(472\) −1.50617e8 + 1.14797e7i −1.43235 + 0.109170i
\(473\) −1.06774e8 1.84938e8i −1.00898 1.74761i
\(474\) 1.47076e7 + 1.52350e7i 0.138104 + 0.143057i
\(475\) −1.41385e7 + 2.44886e7i −0.131924 + 0.228499i
\(476\) 6.58083e6 1.50790e6i 0.0610182 0.0139814i
\(477\) 1.35588e8 3.65239e7i 1.24930 0.336528i
\(478\) −1.09409e7 + 1.37314e7i −0.100177 + 0.125728i
\(479\) 1.24626e8 + 7.19528e7i 1.13397 + 0.654698i 0.944931 0.327271i \(-0.106129\pi\)
0.189040 + 0.981969i \(0.439462\pi\)
\(480\) 2.35329e7 + 1.36209e8i 0.212790 + 1.23163i
\(481\) 1.81766e7 + 3.14828e7i 0.163335 + 0.282904i
\(482\) 1.38726e7 9.23042e7i 0.123885 0.824290i
\(483\) 6.87502e6 + 5.26814e6i 0.0610144 + 0.0467537i
\(484\) −5.76219e7 1.77206e7i −0.508220 0.156294i
\(485\) 9.08069e6i 0.0795964i
\(486\) −1.11312e8 + 2.80487e7i −0.969688 + 0.244345i
\(487\) 4.13467e7i 0.357976i −0.983851 0.178988i \(-0.942718\pi\)
0.983851 0.178988i \(-0.0572823\pi\)
\(488\) −5.06984e7 + 3.46600e7i −0.436249 + 0.298242i
\(489\) −8.96175e6 6.86714e6i −0.0766419 0.0587286i
\(490\) −1.44771e8 2.17580e7i −1.23053 0.184940i
\(491\) −2.88978e6 5.00524e6i −0.0244129 0.0422845i 0.853561 0.520993i \(-0.174438\pi\)
−0.877974 + 0.478709i \(0.841105\pi\)
\(492\) 4.97546e7 + 6.98984e7i 0.417770 + 0.586911i
\(493\) −1.05630e7 6.09855e6i −0.0881549 0.0508962i
\(494\) −1.20221e7 + 1.50883e7i −0.0997238 + 0.125158i
\(495\) 1.81159e8 4.87995e7i 1.49364 0.402346i
\(496\) −8.04201e7 1.66273e8i −0.659052 1.36262i
\(497\) 5.95890e6 1.03211e7i 0.0485397 0.0840731i
\(498\) −5.40979e6 + 5.22251e6i −0.0438018 + 0.0422855i
\(499\) 2.48913e7 + 4.31130e7i 0.200330 + 0.346981i 0.948635 0.316374i \(-0.102465\pi\)
−0.748305 + 0.663355i \(0.769132\pi\)
\(500\) −4.65661e7 5.01011e7i −0.372529 0.400809i
\(501\) −2.08086e8 2.72544e7i −1.65474 0.216732i
\(502\) −1.71966e8 + 6.75759e7i −1.35935 + 0.534172i
\(503\) 6.69958e7i 0.526434i −0.964737 0.263217i \(-0.915216\pi\)
0.964737 0.263217i \(-0.0847835\pi\)
\(504\) 6.46867e6 + 5.53754e6i 0.0505270 + 0.0432539i
\(505\) −7.80934e6 −0.0606373
\(506\) −6.77720e7 1.72465e8i −0.523117 1.33122i
\(507\) 1.06375e8 4.41446e7i 0.816233 0.338730i
\(508\) 1.47735e8 + 1.58950e8i 1.12691 + 1.21246i
\(509\) 4.82651e7 2.78658e7i 0.365999 0.211309i −0.305710 0.952125i \(-0.598894\pi\)
0.671709 + 0.740815i \(0.265561\pi\)
\(510\) 1.51415e8 3.77266e7i 1.14146 0.284405i
\(511\) −1.00692e7 5.81347e6i −0.0754629 0.0435685i
\(512\) 1.30738e8 3.03649e7i 0.974072 0.226236i
\(513\) −2.41301e7 + 5.85851e7i −0.178734 + 0.433945i
\(514\) 1.49196e8 + 1.18876e8i 1.09867 + 0.875398i
\(515\) −1.48402e8 + 2.57039e8i −1.08647 + 1.88182i
\(516\) 9.30969e7 2.03752e8i 0.677620 1.48304i
\(517\) 9.99477e7 5.77049e7i 0.723272 0.417581i
\(518\) 1.31628e6 8.75810e6i 0.00947018 0.0630116i
\(519\) 7.93633e7 + 1.91241e8i 0.567698 + 1.36797i
\(520\) 3.38205e7 + 4.94704e7i 0.240530 + 0.351832i
\(521\) 6.25931e7 0.442602 0.221301 0.975206i \(-0.428970\pi\)
0.221301 + 0.975206i \(0.428970\pi\)
\(522\) −1.74919e6 1.52838e7i −0.0122978 0.107453i
\(523\) −1.22952e8 −0.859470 −0.429735 0.902955i \(-0.641393\pi\)
−0.429735 + 0.902955i \(0.641393\pi\)
\(524\) −9.14829e7 2.81339e7i −0.635838 0.195540i
\(525\) 5.36508e6 + 702701.i 0.0370765 + 0.00485616i
\(526\) −1.38465e7 2.08103e6i −0.0951446 0.0142995i
\(527\) −1.80574e8 + 1.04254e8i −1.23374 + 0.712298i
\(528\) −5.73509e7 1.72913e8i −0.389618 1.17469i
\(529\) 2.48428e7 4.30290e7i 0.167816 0.290666i
\(530\) −1.88293e8 1.50028e8i −1.26475 1.00773i
\(531\) −1.51879e8 + 1.52283e8i −1.01441 + 1.01711i
\(532\) 4.58128e6 1.04973e6i 0.0304265 0.00697177i
\(533\) 3.22131e7 + 1.85982e7i 0.212741 + 0.122826i
\(534\) 2.01727e8 + 5.78790e7i 1.32477 + 0.380099i
\(535\) −1.02130e8 + 5.89648e7i −0.666949 + 0.385063i
\(536\) 1.85025e8 1.41022e7i 1.20153 0.0915782i
\(537\) −1.01324e8 7.76420e7i −0.654321 0.501388i
\(538\) 2.45786e7 + 6.25473e7i 0.157838 + 0.401663i
\(539\) 1.92943e8 1.23215
\(540\) 1.51908e8 + 1.25135e8i 0.964713 + 0.794687i
\(541\) 1.66457e8i 1.05126i 0.850713 + 0.525631i \(0.176171\pi\)
−0.850713 + 0.525631i \(0.823829\pi\)
\(542\) 2.12752e7 + 5.41408e7i 0.133621 + 0.340038i
\(543\) 4.70308e7 6.13761e7i 0.293753 0.383354i
\(544\) −4.49675e7 1.44692e8i −0.279320 0.898771i
\(545\) −1.84657e7 3.19836e7i −0.114072 0.197578i
\(546\) 3.54845e6 + 1.01811e6i 0.0218002 + 0.00625486i
\(547\) −5.22941e6 + 9.05760e6i −0.0319515 + 0.0553416i −0.881559 0.472074i \(-0.843506\pi\)
0.849607 + 0.527415i \(0.176839\pi\)
\(548\) −1.83341e7 8.00143e7i −0.111408 0.486213i
\(549\) −2.25196e7 + 8.44930e7i −0.136095 + 0.510627i
\(550\) −9.05372e7 7.21382e7i −0.544175 0.433588i
\(551\) −7.35349e6 4.24554e6i −0.0439581 0.0253792i
\(552\) 1.06163e8 1.62833e8i 0.631185 0.968110i
\(553\) −1.11829e6 1.93693e6i −0.00661270 0.0114535i
\(554\) −1.06784e8 1.60489e7i −0.628026 0.0943876i
\(555\) 2.65839e7 2.02966e8i 0.155503 1.18726i
\(556\) 3.33128e7 + 1.02447e7i 0.193815 + 0.0596041i
\(557\) 2.65077e8i 1.53393i −0.641687 0.766967i \(-0.721765\pi\)
0.641687 0.766967i \(-0.278235\pi\)
\(558\) −2.41222e8 1.04741e8i −1.38840 0.602859i
\(559\) 9.71176e7i 0.555984i
\(560\) 1.06634e6 1.45604e7i 0.00607200 0.0829102i
\(561\) −1.89951e8 + 7.88283e7i −1.07586 + 0.446472i
\(562\) 189933. 1.26375e6i 0.00107002 0.00711956i
\(563\) 6.59761e7 + 1.14274e8i 0.369710 + 0.640357i 0.989520 0.144395i \(-0.0461236\pi\)
−0.619810 + 0.784752i \(0.712790\pi\)
\(564\) 1.10115e8 + 5.03131e7i 0.613777 + 0.280443i
\(565\) 2.83625e8 + 1.63751e8i 1.57253 + 0.907900i
\(566\) 9.87970e7 + 7.87196e7i 0.544872 + 0.434144i
\(567\) 1.21241e7 32211.4i 0.0665120 0.000176710i
\(568\) −2.41127e8 1.15743e8i −1.31583 0.631613i
\(569\) −5.97768e7 + 1.03536e8i −0.324486 + 0.562026i −0.981408 0.191932i \(-0.938525\pi\)
0.656922 + 0.753958i \(0.271858\pi\)
\(570\) 1.05409e8 2.62636e7i 0.569183 0.141817i
\(571\) −8.52868e7 1.47721e8i −0.458114 0.793477i 0.540747 0.841185i \(-0.318142\pi\)
−0.998861 + 0.0477084i \(0.984808\pi\)
\(572\) −5.37687e7 5.78505e7i −0.287304 0.309114i
\(573\) 1.26163e8 + 3.04013e8i 0.670607 + 1.61595i
\(574\) −3.31425e6 8.43408e6i −0.0175247 0.0445966i
\(575\) 1.23520e8i 0.649732i
\(576\) 1.12885e8 1.54199e8i 0.590702 0.806890i
\(577\) −1.19871e8 −0.624004 −0.312002 0.950081i \(-0.601000\pi\)
−0.312002 + 0.950081i \(0.601000\pi\)
\(578\) 2.05226e7 8.06457e6i 0.106280 0.0417636i
\(579\) 1.75101e7 1.33689e8i 0.0902099 0.688747i
\(580\) −1.93193e7 + 1.79562e7i −0.0990163 + 0.0920300i
\(581\) 687784. 397092.i 0.00350690 0.00202471i
\(582\) 9.03223e6 8.71955e6i 0.0458169 0.0442308i
\(583\) 2.74791e8 + 1.58651e8i 1.38675 + 0.800638i
\(584\) −1.12919e8 + 2.35242e8i −0.566927 + 1.18107i
\(585\) 8.24464e7 + 2.19741e7i 0.411817 + 0.109760i
\(586\) 2.16578e8 2.71817e8i 1.07627 1.35078i
\(587\) 8.49561e7 1.47148e8i 0.420030 0.727514i −0.575912 0.817512i \(-0.695353\pi\)
0.995942 + 0.0899983i \(0.0286862\pi\)
\(588\) 1.17371e8 + 1.64891e8i 0.577338 + 0.811081i
\(589\) −1.25707e8 + 7.25771e7i −0.615197 + 0.355184i
\(590\) 3.64654e8 + 5.48047e7i 1.77552 + 0.266847i
\(591\) −1.93156e8 + 2.52073e8i −0.935722 + 1.22113i
\(592\) −1.98232e8 1.45177e7i −0.955451 0.0699733i
\(593\) −9.20313e7 −0.441338 −0.220669 0.975349i \(-0.570824\pi\)
−0.220669 + 0.975349i \(0.570824\pi\)
\(594\) −2.22494e8 1.33334e8i −1.06159 0.636182i
\(595\) −1.64813e7 −0.0782419
\(596\) −9.51182e7 + 3.09296e8i −0.449288 + 1.46095i
\(597\) 2.47528e7 3.23029e7i 0.116333 0.151816i
\(598\) 1.25248e7 8.33364e7i 0.0585691 0.389701i
\(599\) −1.58965e8 + 9.17783e7i −0.739639 + 0.427031i −0.821938 0.569577i \(-0.807107\pi\)
0.0822988 + 0.996608i \(0.473774\pi\)
\(600\) 6.57430e6 1.21257e8i 0.0304366 0.561375i
\(601\) 2.11505e8 3.66338e8i 0.974311 1.68756i 0.292119 0.956382i \(-0.405640\pi\)
0.682191 0.731174i \(-0.261027\pi\)
\(602\) −1.47439e7 + 1.85044e7i −0.0675809 + 0.0848175i
\(603\) 1.86575e8 1.87071e8i 0.850944 0.853208i
\(604\) 2.77806e8 6.36550e7i 1.26075 0.288883i
\(605\) 1.27450e8 + 7.35833e7i 0.575538 + 0.332287i
\(606\) 7.49876e6 + 7.76766e6i 0.0336955 + 0.0349038i
\(607\) 6.63284e7 3.82947e7i 0.296574 0.171227i −0.344329 0.938849i \(-0.611893\pi\)
0.640903 + 0.767622i \(0.278560\pi\)
\(608\) −3.13044e7 1.00728e8i −0.139282 0.448168i
\(609\) −211008. + 1.61104e6i −0.000934217 + 0.00713269i
\(610\) 1.39535e8 5.48316e7i 0.614742 0.241569i
\(611\) 5.24861e7 0.230102
\(612\) −1.82919e8 1.14381e8i −0.798003 0.499000i
\(613\) 2.20650e8i 0.957903i −0.877841 0.478952i \(-0.841017\pi\)
0.877841 0.478952i \(-0.158983\pi\)
\(614\) 5.68975e7 2.23584e7i 0.245803 0.0965909i
\(615\) −8.02807e7 1.93451e8i −0.345132 0.831660i
\(616\) 1.46228e6 + 1.91855e7i 0.00625587 + 0.0820789i
\(617\) 1.70768e8 + 2.95780e8i 0.727030 + 1.25925i 0.958133 + 0.286323i \(0.0924332\pi\)
−0.231103 + 0.972929i \(0.574233\pi\)
\(618\) 3.98168e8 9.92071e7i 1.68694 0.420318i
\(619\) 9.43277e7 1.63380e8i 0.397711 0.688855i −0.595732 0.803183i \(-0.703138\pi\)
0.993443 + 0.114328i \(0.0364714\pi\)
\(620\) 1.00704e8 + 4.39494e8i 0.422542 + 1.84407i
\(621\) −3.66724e7 2.74329e8i −0.153131 1.14551i
\(622\) 8.05084e7 1.01042e8i 0.334557 0.419886i
\(623\) −1.91962e7 1.10829e7i −0.0793872 0.0458342i
\(624\) 1.67309e7 8.11429e7i 0.0688598 0.333962i
\(625\) 1.52116e8 + 2.63472e8i 0.623066 + 1.07918i
\(626\) 4.47013e7 2.97429e8i 0.182221 1.21244i
\(627\) −1.32236e8 + 5.48768e7i −0.536471 + 0.222631i
\(628\) 5.25126e7 1.70755e8i 0.212024 0.689438i
\(629\) 2.24384e8i 0.901654i
\(630\) −1.23730e7 1.67035e7i −0.0494827 0.0668014i
\(631\) 2.39627e8i 0.953779i −0.878963 0.476889i \(-0.841764\pi\)
0.878963 0.476889i \(-0.158236\pi\)
\(632\) −4.14369e7 + 2.83284e7i −0.164148 + 0.112220i
\(633\) −1.70843e7 + 1.30437e8i −0.0673575 + 0.514270i
\(634\) −2.27613e8 3.42085e7i −0.893158 0.134235i
\(635\) −2.64871e8 4.58771e8i −1.03446 1.79174i
\(636\) 3.15770e7 + 3.31349e8i 0.122744 + 1.28800i
\(637\) 7.59909e7 + 4.38733e7i 0.293997 + 0.169739i
\(638\) 2.16618e7 2.71866e7i 0.0834127 0.104687i
\(639\) −3.67720e8 + 9.90539e7i −1.40933 + 0.379637i
\(640\) −3.27647e8 + 971564.i −1.24987 + 0.00370622i
\(641\) −9.33434e7 + 1.61675e8i −0.354413 + 0.613861i −0.987017 0.160614i \(-0.948653\pi\)
0.632605 + 0.774475i \(0.281986\pi\)
\(642\) 1.56719e8 + 4.49653e7i 0.592264 + 0.169931i
\(643\) 9.32479e7 + 1.61510e8i 0.350757 + 0.607529i 0.986382 0.164469i \(-0.0525911\pi\)
−0.635625 + 0.771998i \(0.719258\pi\)
\(644\) −1.50382e7 + 1.39771e7i −0.0563038 + 0.0523311i
\(645\) −3.32616e8 + 4.34070e8i −1.23955 + 1.61764i
\(646\) −1.10828e8 + 4.35509e7i −0.411103 + 0.161547i
\(647\) 1.79540e8i 0.662901i −0.943473 0.331451i \(-0.892462\pi\)
0.943473 0.331451i \(-0.107538\pi\)
\(648\) −2.13994e7 2.71255e8i −0.0786462 0.996903i
\(649\) −4.85992e8 −1.77785
\(650\) −1.92547e7 4.89990e7i −0.0701125 0.178422i
\(651\) 2.20472e7 + 1.68942e7i 0.0799117 + 0.0612341i
\(652\) 1.96026e7 1.82195e7i 0.0707248 0.0657346i
\(653\) −1.10320e8 + 6.36932e7i −0.396200 + 0.228746i −0.684843 0.728691i \(-0.740129\pi\)
0.288643 + 0.957437i \(0.406796\pi\)
\(654\) −1.40816e7 + 4.90788e7i −0.0503405 + 0.175453i
\(655\) 2.02345e8 + 1.16824e8i 0.720059 + 0.415726i
\(656\) −1.83083e8 + 8.85506e7i −0.648540 + 0.313675i
\(657\) 9.66365e7 + 3.58746e8i 0.340757 + 1.26500i
\(658\) −1.00005e7 7.96819e6i −0.0351029 0.0279693i
\(659\) 1.25191e8 2.16836e8i 0.437437 0.757663i −0.560054 0.828456i \(-0.689220\pi\)
0.997491 + 0.0707933i \(0.0225531\pi\)
\(660\) 4.21900e7 + 4.42716e8i 0.146750 + 1.53990i
\(661\) 1.29316e8 7.46604e7i 0.447761 0.258515i −0.259123 0.965844i \(-0.583433\pi\)
0.706884 + 0.707329i \(0.250100\pi\)
\(662\) −7.79738e7 + 5.18814e8i −0.268766 + 1.78829i
\(663\) −9.27374e7 1.21465e7i −0.318211 0.0416782i
\(664\) −1.00591e7 1.47138e7i −0.0343602 0.0502598i
\(665\) −1.14735e7 −0.0390150
\(666\) −2.27410e8 + 1.68452e8i −0.769815 + 0.570235i
\(667\) 3.70908e7 0.124994
\(668\) 1.46224e8 4.75476e8i 0.490557 1.59514i
\(669\) 1.29714e8 + 3.12570e8i 0.433219 + 1.04392i
\(670\) −4.47957e8 6.73246e7i −1.48940 0.223846i
\(671\) −1.71117e8 + 9.87943e7i −0.566402 + 0.327012i
\(672\) −1.55066e7 + 1.29206e7i −0.0510985 + 0.0425771i
\(673\) −2.27813e8 + 3.94584e8i −0.747367 + 1.29448i 0.201714 + 0.979444i \(0.435349\pi\)
−0.949081 + 0.315032i \(0.897985\pi\)
\(674\) 2.82004e8 + 2.24695e8i 0.921032 + 0.733861i
\(675\) −1.05530e8 1.36963e8i −0.343134 0.445340i
\(676\) 6.09731e7 + 2.66101e8i 0.197378 + 0.861404i
\(677\) 2.45001e8 + 1.41451e8i 0.789591 + 0.455870i 0.839818 0.542867i \(-0.182661\pi\)
−0.0502277 + 0.998738i \(0.515995\pi\)
\(678\) −1.09468e8 4.39349e8i −0.351235 1.40968i
\(679\) −1.14833e6 + 662988.i −0.00366823 + 0.00211786i
\(680\) 2.81102e7 + 3.68814e8i 0.0893998 + 1.17295i
\(681\) −2.30088e8 + 9.54845e7i −0.728537 + 0.302337i
\(682\) −2.17335e8 5.53072e8i −0.685136 1.74353i
\(683\) −6.53397e7 −0.205076 −0.102538 0.994729i \(-0.532696\pi\)
−0.102538 + 0.994729i \(0.532696\pi\)
\(684\) −1.27340e8 7.96271e7i −0.397921 0.248824i
\(685\) 2.00391e8i 0.623456i
\(686\) −1.56714e7 3.98805e7i −0.0485441 0.123534i
\(687\) −5.30003e8 6.94181e7i −1.63459 0.214093i
\(688\) 4.39234e8 + 2.98376e8i 1.34875 + 0.916217i
\(689\) 7.21512e7 + 1.24970e8i 0.220590 + 0.382073i
\(690\) −3.41397e8 + 3.29578e8i −1.03923 + 1.00326i
\(691\) −2.65636e8 + 4.60095e8i −0.805105 + 1.39448i 0.111115 + 0.993808i \(0.464558\pi\)
−0.916220 + 0.400675i \(0.868775\pi\)
\(692\) −4.78397e8 + 1.09618e8i −1.44368 + 0.330797i
\(693\) 1.93977e7 + 1.93462e7i 0.0582842 + 0.0581295i
\(694\) −2.92945e8 2.33413e8i −0.876409 0.698306i
\(695\) −7.36823e7 4.25405e7i −0.219487 0.126721i
\(696\) 3.64113e7 + 1.97414e6i 0.107996 + 0.00585532i
\(697\) 1.14794e8 + 1.98830e8i 0.339018 + 0.587196i
\(698\) −2.03196e7 3.05388e6i −0.0597515 0.00898021i
\(699\) 4.87568e8 + 3.73610e8i 1.42759 + 1.09392i
\(700\) −3.77010e6 + 1.22592e7i −0.0109915 + 0.0357412i
\(701\) 6.29860e8i 1.82848i −0.405175 0.914239i \(-0.632789\pi\)
0.405175 0.914239i \(-0.367211\pi\)
\(702\) −5.73107e7 1.03107e8i −0.165663 0.298041i
\(703\) 1.56206e8i 0.449606i
\(704\) 4.26835e8 6.54450e7i 1.22333 0.187568i
\(705\) −2.34588e8 1.79758e8i −0.669482 0.513005i
\(706\) −1.22428e7 + 8.14596e7i −0.0347909 + 0.231488i
\(707\) −570166. 987556.i −0.00161340 0.00279450i
\(708\) −2.95639e8 4.15333e8i −0.833033 1.17030i
\(709\) −4.16592e7 2.40519e7i −0.116889 0.0674856i 0.440416 0.897794i \(-0.354831\pi\)
−0.557304 + 0.830308i \(0.688164\pi\)
\(710\) 5.10656e8 + 4.06881e8i 1.42677 + 1.13682i
\(711\) −1.84058e7 + 6.90581e7i −0.0512089 + 0.192135i
\(712\) −2.15270e8 + 4.48470e8i −0.596409 + 1.24249i
\(713\) 3.17032e8 5.49116e8i 0.874651 1.51494i
\(714\) 1.58258e7 + 1.63933e7i 0.0434782 + 0.0450373i
\(715\) 9.64013e7 + 1.66972e8i 0.263733 + 0.456799i
\(716\) 2.21633e8 2.05995e8i 0.603804 0.561201i
\(717\) −5.87537e7 7.69537e6i −0.159396 0.0208772i
\(718\) −6.59818e7 1.67910e8i −0.178259 0.453631i
\(719\) 1.85854e7i 0.0500018i 0.999687 + 0.0250009i \(0.00795887\pi\)
−0.999687 + 0.0250009i \(0.992041\pi\)
\(720\) −3.52684e8 + 3.05369e8i −0.944905 + 0.818141i
\(721\) −4.33397e7 −0.115633
\(722\) 2.73139e8 1.07333e8i 0.725724 0.285181i
\(723\) 2.90965e8 1.20748e8i 0.769886 0.319496i
\(724\) 1.24779e8 + 1.34252e8i 0.328797 + 0.353757i
\(725\) 2.00669e7 1.15856e7i 0.0526583 0.0304023i
\(726\) −4.91907e7 1.97427e8i −0.128550 0.515936i
\(727\) 4.39676e8 + 2.53847e8i 1.14427 + 0.660645i 0.947485 0.319801i \(-0.103616\pi\)
0.196787 + 0.980446i \(0.436949\pi\)
\(728\) −3.78668e6 + 7.88876e6i −0.00981442 + 0.0204463i
\(729\) −2.75037e8 2.72854e8i −0.709919 0.704283i
\(730\) 3.96951e8 4.98194e8i 1.02040 1.28065i
\(731\) 2.99721e8 5.19131e8i 0.767299 1.32900i
\(732\) −1.88524e8 8.61392e7i −0.480656 0.219618i
\(733\) 4.70054e8 2.71386e8i 1.19354 0.689089i 0.234430 0.972133i \(-0.424678\pi\)
0.959107 + 0.283044i \(0.0913443\pi\)
\(734\) 1.08912e8 + 1.63687e7i 0.275416 + 0.0413929i
\(735\) −1.89383e8 4.56353e8i −0.476956 1.14931i
\(736\) 3.38426e8 + 3.12682e8i 0.848848 + 0.784277i
\(737\) 5.97014e8 1.49136
\(738\) −1.15331e8 + 2.65610e8i −0.286930 + 0.660808i
\(739\) 4.13700e8 1.02507 0.512533 0.858668i \(-0.328707\pi\)
0.512533 + 0.858668i \(0.328707\pi\)
\(740\) 4.63778e8 + 1.42626e8i 1.14450 + 0.351969i
\(741\) −6.45597e7 8.45582e6i −0.158674 0.0207827i
\(742\) 5.22490e6 3.47649e7i 0.0127899 0.0850998i
\(743\) 3.75774e8 2.16953e8i 0.916137 0.528932i 0.0337366 0.999431i \(-0.489259\pi\)
0.882401 + 0.470499i \(0.155926\pi\)
\(744\) 3.40450e8 5.22182e8i 0.826675 1.26795i
\(745\) 3.94971e8 6.84110e8i 0.955205 1.65446i
\(746\) −4.25047e8 + 5.33456e8i −1.02381 + 1.28494i
\(747\) −2.45217e7 6.53568e6i −0.0588287 0.0156794i
\(748\) −1.08879e8 4.75173e8i −0.260159 1.13539i
\(749\) −1.49132e7 8.61014e6i −0.0354916 0.0204911i
\(750\) 6.36659e7 2.21896e8i 0.150912 0.525976i
\(751\) 1.50102e8 8.66614e7i 0.354378 0.204600i −0.312234 0.950005i \(-0.601077\pi\)
0.666612 + 0.745405i \(0.267744\pi\)
\(752\) −1.61254e8 + 2.37379e8i −0.379190 + 0.558199i
\(753\) −4.94979e8 3.79289e8i −1.15932 0.888351i
\(754\) 1.47135e7 5.78182e6i 0.0343243 0.0134881i
\(755\) −6.95747e8 −1.61663
\(756\) −4.73343e6 + 2.83462e7i −0.0109549 + 0.0656038i
\(757\) 4.26553e8i 0.983299i −0.870793 0.491649i \(-0.836394\pi\)
0.870793 0.491649i \(-0.163606\pi\)
\(758\) −3.14296e8 + 1.23506e8i −0.721658 + 0.283583i
\(759\) 3.80389e8 4.96415e8i 0.869967 1.13532i
\(760\) 1.95690e7 + 2.56752e8i 0.0445788 + 0.584888i
\(761\) 1.63469e8 + 2.83137e8i 0.370921 + 0.642454i 0.989708 0.143105i \(-0.0457087\pi\)
−0.618786 + 0.785559i \(0.712375\pi\)
\(762\) −2.01985e8 + 7.03983e8i −0.456514 + 1.59110i
\(763\) 2.69640e6 4.67030e6i 0.00607030 0.0105141i
\(764\) −7.60504e8 + 1.74258e8i −1.70538 + 0.390762i
\(765\) 3.72893e8 + 3.71903e8i 0.832913 + 0.830703i
\(766\) −1.67811e8 + 2.10611e8i −0.373365 + 0.468592i
\(767\) −1.91409e8 1.10510e8i −0.424204 0.244915i
\(768\) 3.15583e8 + 3.24966e8i 0.696674 + 0.717387i
\(769\) −2.29008e8 3.96653e8i −0.503583 0.872232i −0.999991 0.00414260i \(-0.998681\pi\)
0.496408 0.868089i \(-0.334652\pi\)
\(770\) 6.98099e6 4.64493e7i 0.0152913 0.101744i
\(771\) −8.36125e7 + 6.38376e8i −0.182435 + 1.39288i
\(772\) 3.05480e8 + 9.39446e7i 0.663942 + 0.204183i
\(773\) 4.77166e8i 1.03307i −0.856265 0.516537i \(-0.827221\pi\)
0.856265 0.516537i \(-0.172779\pi\)
\(774\) 7.51141e8 8.59663e7i 1.61994 0.185398i
\(775\) 3.96111e8i 0.850966i
\(776\) 1.67948e7 + 2.45663e7i 0.0359409 + 0.0525719i
\(777\) 2.76077e7 1.14570e7i 0.0588528 0.0244234i
\(778\) −5.54725e8 8.33711e7i −1.17798 0.177042i
\(779\) 7.99147e7 + 1.38416e8i 0.169050 + 0.292803i
\(780\) −8.40527e7 + 1.83958e8i −0.177120 + 0.387645i
\(781\) −7.45242e8 4.30266e8i −1.56439 0.903200i
\(782\) 3.24140e8 4.06812e8i 0.677816 0.850694i
\(783\) 4.11275e7 3.16886e7i 0.0856736 0.0660113i
\(784\) −4.31894e8 + 2.08892e8i −0.896250 + 0.433484i
\(785\) −2.18055e8 + 3.77681e8i −0.450771 + 0.780759i
\(786\) −7.80972e7 3.13443e8i −0.160830 0.645491i
\(787\) −2.38365e8 4.12860e8i −0.489010 0.846991i 0.510910 0.859634i \(-0.329309\pi\)
−0.999920 + 0.0126435i \(0.995975\pi\)
\(788\) −5.12472e8 5.51375e8i −1.04735 1.12686i
\(789\) −1.81134e7 4.36477e7i −0.0368782 0.0888649i
\(790\) 1.14045e8 4.48151e7i 0.231310 0.0908956i
\(791\) 4.78223e7i 0.0966275i
\(792\) 3.99841e8 4.67074e8i 0.804845 0.940178i
\(793\) −8.98594e7 −0.180195
\(794\) 1.07674e8 + 2.74009e8i 0.215105 + 0.547398i
\(795\) 1.05523e8 8.05664e8i 0.210013 1.60344i
\(796\) 6.56728e7 + 7.06583e7i 0.130211 + 0.140095i
\(797\) −8.03779e7 + 4.64062e7i −0.158767 + 0.0916644i −0.577279 0.816547i \(-0.695885\pi\)
0.418511 + 0.908212i \(0.362552\pi\)
\(798\) 1.10172e7 + 1.14123e7i 0.0216802 + 0.0224576i
\(799\) 2.80559e8 + 1.61981e8i 0.550026 + 0.317558i
\(800\) 2.80764e8 + 6.34573e7i 0.548368 + 0.123940i
\(801\) 1.84230e8 + 6.83919e8i 0.358478 + 1.33078i
\(802\) 3.74488e8 + 2.98385e8i 0.725963 + 0.578433i
\(803\) −4.19765e8 + 7.27055e8i −0.810699 + 1.40417i
\(804\) 3.63176e8 + 5.10213e8i 0.698794 + 0.981711i
\(805\) 4.34041e7 2.50594e7i 0.0832039 0.0480378i
\(806\) 4.01654e7 2.67248e8i 0.0767090 0.510398i
\(807\) −1.37954e8 + 1.80033e8i −0.262491 + 0.342556i
\(808\) −2.11268e7 + 1.44434e7i −0.0400498 + 0.0273801i
\(809\) 2.18461e7 0.0412599 0.0206300 0.999787i \(-0.493433\pi\)
0.0206300 + 0.999787i \(0.493433\pi\)
\(810\) −9.69757e7 + 6.57120e8i −0.182477 + 1.23649i
\(811\) 5.65020e8 1.05926 0.529628 0.848230i \(-0.322331\pi\)
0.529628 + 0.848230i \(0.322331\pi\)
\(812\) −3.68122e6 1.13209e6i −0.00687581 0.00211453i
\(813\) −1.19413e8 + 1.55836e8i −0.222218 + 0.289999i
\(814\) −6.32384e8 9.50426e7i −1.17249 0.176216i
\(815\) −5.65783e7 + 3.26655e7i −0.104515 + 0.0603416i
\(816\) 3.39854e8 3.82106e8i 0.625491 0.703257i
\(817\) 2.08652e8 3.61396e8i 0.382610 0.662701i
\(818\) −5.14761e8 4.10151e8i −0.940471 0.749349i
\(819\) 3.24067e6 + 1.20304e7i 0.00589906 + 0.0218992i
\(820\) 4.83927e8 1.10885e8i 0.877685 0.201108i
\(821\) 2.54980e8 + 1.47213e8i 0.460763 + 0.266021i 0.712365 0.701809i \(-0.247624\pi\)
−0.251602 + 0.967831i \(0.580957\pi\)
\(822\) 1.99321e8 1.92421e8i 0.358871 0.346448i
\(823\) 3.97631e8 2.29572e8i 0.713314 0.411832i −0.0989729 0.995090i \(-0.531556\pi\)
0.812287 + 0.583258i \(0.198222\pi\)
\(824\) 7.39195e7 + 9.69846e8i 0.132123 + 1.73349i
\(825\) 5.07390e7 3.87389e8i 0.0903608 0.689899i
\(826\) 1.96931e7 + 5.01148e7i 0.0349442 + 0.0889255i
\(827\) 3.42111e8 0.604854 0.302427 0.953173i \(-0.402203\pi\)
0.302427 + 0.953173i \(0.402203\pi\)
\(828\) 6.55639e8 + 2.31040e7i 1.15498 + 0.0407001i
\(829\) 6.65950e8i 1.16890i 0.811429 + 0.584451i \(0.198690\pi\)
−0.811429 + 0.584451i \(0.801310\pi\)
\(830\) 1.59133e7 + 4.04961e7i 0.0278309 + 0.0708237i
\(831\) −1.39690e8 3.36610e8i −0.243424 0.586575i
\(832\) 1.82991e8 + 7.12826e7i 0.317732 + 0.123769i
\(833\) 2.70801e8 + 4.69040e8i 0.468505 + 0.811475i
\(834\) 2.84385e7 + 1.14138e8i 0.0490239 + 0.196757i
\(835\) −6.07184e8 + 1.05167e9i −1.04294 + 1.80643i
\(836\) −7.57965e7 3.30794e8i −0.129727 0.566160i
\(837\) −1.17603e8 8.79734e8i −0.200559 1.50029i
\(838\) −2.15980e8 1.72089e8i −0.367013 0.292429i
\(839\) −2.00532e8 1.15777e8i −0.339545 0.196037i 0.320526 0.947240i \(-0.396140\pi\)
−0.660071 + 0.751203i \(0.729474\pi\)
\(840\) 4.39427e7 2.22901e7i 0.0741394 0.0376075i
\(841\) −2.93933e8 5.09106e8i −0.494151 0.855895i
\(842\) 9.56085e8 + 1.43692e8i 1.60162 + 0.240712i
\(843\) 3.98366e6 1.65319e6i 0.00664966 0.00275955i
\(844\) −2.98050e8 9.16598e7i −0.495749 0.152458i
\(845\) 6.66434e8i 1.10455i
\(846\) 4.64595e7 + 4.05946e8i 0.0767296 + 0.670435i
\(847\) 2.14895e7i 0.0353652i
\(848\) −7.86872e8 5.76272e7i −1.29038 0.0945018i
\(849\) −5.53680e7 + 4.22731e8i −0.0904765 + 0.690782i
\(850\) 4.82953e7 3.21342e8i 0.0786408 0.523252i
\(851\) −3.41171e8 5.90925e8i −0.553584 0.958835i
\(852\) −8.56378e7 8.98630e8i −0.138467 1.45299i
\(853\) −5.44012e8 3.14086e8i −0.876520 0.506059i −0.00701033 0.999975i \(-0.502231\pi\)
−0.869509 + 0.493917i \(0.835565\pi\)
\(854\) 1.71214e7 + 1.36420e7i 0.0274895 + 0.0219031i
\(855\) 2.59591e8 + 2.58902e8i 0.415328 + 0.414226i
\(856\) −1.67240e8 + 3.48409e8i −0.266636 + 0.555480i
\(857\) −2.65340e8 + 4.59583e8i −0.421561 + 0.730165i −0.996092 0.0883174i \(-0.971851\pi\)
0.574531 + 0.818483i \(0.305184\pi\)
\(858\) 7.35134e7 2.56218e8i 0.116387 0.405647i
\(859\) −8.48459e7 1.46957e8i −0.133860 0.231853i 0.791301 0.611426i \(-0.209404\pi\)
−0.925161 + 0.379574i \(0.876071\pi\)
\(860\) −8.82477e8 9.49470e8i −1.38742 1.49275i
\(861\) 1.86022e7 2.42762e7i 0.0291443 0.0380339i
\(862\) 4.08789e8 + 1.04028e9i 0.638230 + 1.62416i
\(863\) 7.14971e8i 1.11239i 0.831053 + 0.556193i \(0.187739\pi\)
−0.831053 + 0.556193i \(0.812261\pi\)
\(864\) 6.42397e8 + 5.75768e7i 0.996007 + 0.0892701i
\(865\) 1.19812e9 1.85119
\(866\) −4.36030e8 + 1.71342e8i −0.671371 + 0.263822i
\(867\) 5.90713e7 + 4.52647e7i 0.0906398 + 0.0694548i
\(868\) −4.82253e7 + 4.48226e7i −0.0737421 + 0.0685391i
\(869\) −1.39858e8 + 8.07468e7i −0.213121 + 0.123046i
\(870\) −8.55645e7 2.45499e7i −0.129938 0.0372814i
\(871\) 2.35135e8 + 1.35755e8i 0.355846 + 0.205448i
\(872\) −1.09110e8 5.23738e7i −0.164556 0.0789886i
\(873\) 4.09417e7 + 1.09120e7i 0.0615351 + 0.0164007i
\(874\) 2.25652e8 2.83204e8i 0.337990 0.424195i
\(875\) −1.21910e7 + 2.11154e7i −0.0181977 + 0.0315193i
\(876\) −8.76700e8 + 8.35478e7i −1.30418 + 0.124286i
\(877\) −8.63012e8 + 4.98260e8i −1.27944 + 0.738682i −0.976744 0.214407i \(-0.931218\pi\)
−0.302691 + 0.953089i \(0.597885\pi\)
\(878\) 4.01893e8 + 6.04015e7i 0.593781 + 0.0892409i
\(879\) 1.16304e9 + 1.52332e8i 1.71250 + 0.224297i
\(880\) −1.05134e9 7.69958e7i −1.54275 0.112985i
\(881\) −2.52131e8 −0.368722 −0.184361 0.982859i \(-0.559022\pi\)
−0.184361 + 0.982859i \(0.559022\pi\)
\(882\) −2.72066e8 + 6.26575e8i −0.396524 + 0.913204i
\(883\) −1.24812e9 −1.81290 −0.906448 0.422318i \(-0.861217\pi\)
−0.906448 + 0.422318i \(0.861217\pi\)
\(884\) 6.51676e7 2.11905e8i 0.0943354 0.306750i
\(885\) 4.77024e8 + 1.14948e9i 0.688193 + 1.65833i
\(886\) −3.88732e7 + 2.58650e8i −0.0558919 + 0.371887i
\(887\) −7.45420e8 + 4.30369e8i −1.06815 + 0.616694i −0.927674 0.373391i \(-0.878195\pi\)
−0.140471 + 0.990085i \(0.544862\pi\)
\(888\) −3.03469e8 5.98258e8i −0.433386 0.854377i
\(889\) 3.86769e7 6.69904e7i 0.0550487 0.0953471i
\(890\) 7.56755e8 9.49766e8i 1.07346 1.34725i
\(891\) −2.32585e6 8.75427e8i −0.00328812 1.23762i
\(892\) −7.81908e8 + 1.79162e8i −1.10169 + 0.252437i
\(893\) 1.95312e8 + 1.12764e8i 0.274268 + 0.158349i
\(894\) −1.05972e9 + 2.64040e8i −1.48313 + 0.369536i
\(895\) −6.39692e8 + 3.69327e8i −0.892282 + 0.515159i
\(896\) −2.40446e7 4.13628e7i −0.0334267 0.0575024i
\(897\) 2.62697e8 1.09017e8i 0.363980 0.151049i
\(898\) −2.82927e8 + 1.11179e8i −0.390702 + 0.153530i
\(899\) 1.18945e8 0.163707
\(900\) 3.61932e8 1.92295e8i 0.496477 0.263779i
\(901\) 8.90681e8i 1.21772i
\(902\) −6.08988e8 + 2.39308e8i −0.829829 + 0.326090i
\(903\) −7.91763e7 1.03703e7i −0.107531 0.0140840i
\(904\) 1.07016e9 8.15649e7i 1.44858 0.110407i
\(905\) −2.23715e8 3.87486e8i −0.301821 0.522770i
\(906\) 6.68077e8 + 6.92034e8i 0.898342 + 0.930556i
\(907\) −4.77802e8 + 8.27577e8i −0.640363 + 1.10914i 0.344989 + 0.938607i \(0.387883\pi\)
−0.985352 + 0.170534i \(0.945451\pi\)
\(908\) −1.31884e8 5.75575e8i −0.176172 0.768855i
\(909\) −9.38428e6 + 3.52096e7i −0.0124942 + 0.0468781i
\(910\) 1.33116e7 1.67067e7i 0.0176647 0.0221701i
\(911\) −1.96400e8 1.13391e8i −0.259768 0.149977i 0.364461 0.931219i \(-0.381253\pi\)
−0.624229 + 0.781242i \(0.714587\pi\)
\(912\) 2.36591e8 2.66005e8i 0.311899 0.350676i
\(913\) −2.86723e7 4.96618e7i −0.0376747 0.0652545i
\(914\) 1.96960e7 1.31051e8i 0.0257952 0.171633i
\(915\) 4.01629e8 + 3.07757e8i 0.524278 + 0.401740i
\(916\) 3.72439e8 1.21106e9i 0.484583 1.57572i
\(917\) 3.41176e7i 0.0442456i
\(918\) 1.18559e7 7.28015e8i 0.0153252 0.941050i
\(919\) 7.40854e8i 0.954522i 0.878762 + 0.477261i \(0.158370\pi\)
−0.878762 + 0.477261i \(0.841630\pi\)
\(920\) −6.34803e8 9.28547e8i −0.815221 1.19245i
\(921\) 1.63771e8 + 1.25493e8i 0.209632 + 0.160635i
\(922\) 1.13737e9 + 1.70939e8i 1.45114 + 0.218096i
\(923\) −1.95676e8 3.38922e8i −0.248848 0.431017i
\(924\) −5.29048e7 + 3.76583e7i −0.0670624 + 0.0477359i
\(925\) −3.69162e8 2.13136e8i −0.466435 0.269296i
\(926\) 3.67803e8 4.61612e8i 0.463215 0.581359i
\(927\) 9.80572e8 + 9.77970e8i 1.23095 + 1.22768i
\(928\) −1.90551e7 + 8.43084e7i −0.0238433 + 0.105494i
\(929\) 6.99467e8 1.21151e9i 0.872409 1.51106i 0.0129115 0.999917i \(-0.495890\pi\)
0.859497 0.511140i \(-0.170777\pi\)
\(930\) −1.09481e9 + 1.05691e9i −1.36110 + 1.31398i
\(931\) 1.88519e8 + 3.26525e8i 0.233618 + 0.404639i
\(932\) −1.06649e9 + 9.91240e8i −1.31737 + 1.22442i
\(933\) 4.32337e8 + 5.66262e7i 0.532326 + 0.0697224i
\(934\) 3.54407e8 1.39268e8i 0.434973 0.170927i
\(935\) 1.19004e9i 1.45588i
\(936\) 2.63686e8 9.30378e7i 0.321558 0.113457i
\(937\) −6.68910e8 −0.813110 −0.406555 0.913626i \(-0.633270\pi\)
−0.406555 + 0.913626i \(0.633270\pi\)
\(938\) −2.41919e7 6.15633e7i −0.0293131 0.0745956i
\(939\) 9.37568e8 3.89083e8i 1.13242 0.469944i
\(940\) 5.13130e8 4.76925e8i 0.617794 0.574204i
\(941\) 8.08150e8 4.66586e8i 0.969891 0.559967i 0.0706881 0.997498i \(-0.477480\pi\)
0.899203 + 0.437532i \(0.144147\pi\)
\(942\) 5.85048e8 1.45770e8i 0.699905 0.174388i
\(943\) −6.04632e8 3.49085e8i −0.721035 0.416290i
\(944\) 1.08787e9 5.26163e8i 1.29319 0.625467i
\(945\) 2.67183e7 6.48691e7i 0.0316602 0.0768674i
\(946\) 1.33612e9 + 1.06460e9i 1.57824 + 1.25751i
\(947\) −5.72400e8 + 9.91427e8i −0.673985 + 1.16738i 0.302780 + 0.953060i \(0.402085\pi\)
−0.976765 + 0.214315i \(0.931248\pi\)
\(948\) −1.54085e8 7.04035e7i −0.180857 0.0826360i
\(949\) −3.30650e8 + 1.90901e8i −0.386875 + 0.223362i
\(950\) 3.36210e7 2.23704e8i 0.0392139 0.260917i
\(951\) −2.97753e8 7.17490e8i −0.346190 0.834208i
\(952\) −4.45873e7 + 3.04822e7i −0.0516773 + 0.0353293i
\(953\) −3.60885e8 −0.416956 −0.208478 0.978027i \(-0.566851\pi\)
−0.208478 + 0.978027i \(0.566851\pi\)
\(954\) −9.02691e8 + 6.68663e8i −1.03967 + 0.770126i
\(955\) 1.90463e9 2.18676
\(956\) 4.12868e7 1.34252e8i 0.0472539 0.153656i
\(957\) 1.16326e8 + 1.52360e7i 0.132721 + 0.0173834i
\(958\) −1.13846e9 1.71102e8i −1.29485 0.194607i
\(959\) −2.53411e7 + 1.46307e7i −0.0287322 + 0.0165886i
\(960\) −5.73751e8 9.45322e8i −0.648500 1.06848i
\(961\) 5.72925e8 9.92336e8i 0.645547 1.11812i
\(962\) −2.27454e8 1.81231e8i −0.255486 0.203567i
\(963\) 1.43125e8 + 5.31326e8i 0.160264 + 0.594952i
\(964\) 1.66779e8 + 7.27864e8i 0.186170 + 0.812492i
\(965\) −6.75669e8 3.90098e8i −0.751886 0.434102i
\(966\) −6.66036e7 1.91097e7i −0.0738867 0.0211994i
\(967\) −1.42337e9 + 8.21786e8i −1.57413 + 0.908823i −0.578473 + 0.815702i \(0.696351\pi\)
−0.995655 + 0.0931211i \(0.970316\pi\)
\(968\) 4.80887e8 3.66521e7i 0.530172 0.0404085i
\(969\) −3.19001e8 2.44441e8i −0.350607 0.268660i
\(970\) −2.65690e7 6.76125e7i −0.0291112 0.0740819i
\(971\) −1.11625e9 −1.21928 −0.609638 0.792680i \(-0.708685\pi\)
−0.609638 + 0.792680i \(0.708685\pi\)
\(972\) 7.46733e8 5.34528e8i 0.813142 0.582066i
\(973\) 1.24237e7i 0.0134869i
\(974\) 1.20976e8 + 3.07857e8i 0.130924 + 0.333175i
\(975\) 1.08072e8 1.41036e8i 0.116600 0.152166i
\(976\) 2.76076e8 4.06407e8i 0.296948 0.437132i
\(977\) 1.73356e8 + 3.00262e8i 0.185890 + 0.321971i 0.943876 0.330300i \(-0.107150\pi\)
−0.757986 + 0.652271i \(0.773817\pi\)
\(978\) 8.68194e7 + 2.49100e7i 0.0928112 + 0.0266291i
\(979\) −8.00249e8 + 1.38607e9i −0.852858 + 1.47719i
\(980\) 1.14159e9 2.61578e8i 1.21292 0.277922i
\(981\) −1.66393e8 + 4.48218e7i −0.176249 + 0.0474769i
\(982\) 3.61613e7 + 2.88127e7i 0.0381865 + 0.0304263i
\(983\) 9.13956e8 + 5.27673e8i 0.962198 + 0.555525i 0.896849 0.442337i \(-0.145850\pi\)
0.0653494 + 0.997862i \(0.479184\pi\)
\(984\) −5.74975e8 3.74870e8i −0.603481 0.393455i
\(985\) 9.18804e8 + 1.59141e9i 0.961422 + 1.66523i
\(986\) 9.64931e7 + 1.45022e7i 0.100662 + 0.0151287i
\(987\) 5.60449e6 4.27899e7i 0.00582887 0.0445031i
\(988\) 4.53668e7 1.47519e8i 0.0470400 0.152960i
\(989\) 1.82287e9i 1.88438i
\(990\) −1.20609e9 + 8.93400e8i −1.24300 + 0.920748i
\(991\) 4.13365e8i 0.424729i −0.977190 0.212365i \(-0.931884\pi\)
0.977190 0.212365i \(-0.0681165\pi\)
\(992\) 1.08528e9 + 1.00273e9i 1.11175 + 1.02718i
\(993\) −1.63543e9 + 6.78689e8i −1.67026 + 0.693144i
\(994\) −1.41701e7 + 9.42835e7i −0.0144283 + 0.0960011i
\(995\) −1.17744e8 2.03938e8i −0.119528 0.207028i
\(996\) 2.49995e7 5.47139e7i 0.0253019 0.0553758i
\(997\) −1.36759e9 7.89576e8i −1.37997 0.796725i −0.387814 0.921738i \(-0.626770\pi\)
−0.992155 + 0.125012i \(0.960103\pi\)
\(998\) −3.11478e8 2.48179e8i −0.313354 0.249675i
\(999\) −8.83160e8 3.63757e8i −0.885814 0.364850i
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 72.7.p.b.43.9 136
8.3 odd 2 inner 72.7.p.b.43.38 yes 136
9.4 even 3 inner 72.7.p.b.67.38 yes 136
72.67 odd 6 inner 72.7.p.b.67.9 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.7.p.b.43.9 136 1.1 even 1 trivial
72.7.p.b.43.38 yes 136 8.3 odd 2 inner
72.7.p.b.67.9 yes 136 72.67 odd 6 inner
72.7.p.b.67.38 yes 136 9.4 even 3 inner