Properties

Label 43.7.h.a.12.20
Level $43$
Weight $7$
Character 43.12
Analytic conductor $9.892$
Analytic rank $0$
Dimension $252$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,7,Mod(3,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(252\)
Relative dimension: \(21\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 12.20
Character \(\chi\) \(=\) 43.12
Dual form 43.7.h.a.18.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.34296 + 13.1713i) q^{2} +(10.7567 + 15.7772i) q^{3} +(-93.3463 + 117.053i) q^{4} +(-134.366 + 144.812i) q^{5} +(-139.577 + 241.754i) q^{6} +(570.233 - 329.224i) q^{7} +(-1221.67 - 278.837i) q^{8} +(133.120 - 339.185i) q^{9} +O(q^{10})\) \(q+(6.34296 + 13.1713i) q^{2} +(10.7567 + 15.7772i) q^{3} +(-93.3463 + 117.053i) q^{4} +(-134.366 + 144.812i) q^{5} +(-139.577 + 241.754i) q^{6} +(570.233 - 329.224i) q^{7} +(-1221.67 - 278.837i) q^{8} +(133.120 - 339.185i) q^{9} +(-2759.64 - 851.237i) q^{10} +(745.090 + 934.314i) q^{11} +(-2850.86 - 213.643i) q^{12} +(815.676 - 251.603i) q^{13} +(7953.27 + 5422.45i) q^{14} +(-3730.07 - 562.218i) q^{15} +(-1944.17 - 8517.98i) q^{16} +(-4602.80 + 4270.77i) q^{17} +(5311.88 - 398.070i) q^{18} +(-1274.80 + 500.323i) q^{19} +(-4408.06 - 29245.6i) q^{20} +(11328.1 + 5455.32i) q^{21} +(-7580.04 + 15740.1i) q^{22} +(-9950.59 + 1499.81i) q^{23} +(-8741.84 - 22273.8i) q^{24} +(-1748.67 - 23334.4i) q^{25} +(8487.73 + 9147.60i) q^{26} +(20354.7 - 4645.83i) q^{27} +(-14692.6 + 97479.2i) q^{28} +(15643.3 - 22944.5i) q^{29} +(-16254.6 - 52696.0i) q^{30} +(-2036.95 + 27181.2i) q^{31} +(37160.1 - 29634.2i) q^{32} +(-6726.14 + 21805.6i) q^{33} +(-85446.9 - 33535.4i) q^{34} +(-28944.3 + 126813. i) q^{35} +(27276.2 + 47243.7i) q^{36} +(15416.6 + 8900.75i) q^{37} +(-14675.9 - 13617.3i) q^{38} +(12743.6 + 10162.7i) q^{39} +(204529. - 139446. i) q^{40} +(8652.63 - 4166.88i) q^{41} +183808. i q^{42} +(63023.4 - 48470.8i) q^{43} -178915. q^{44} +(31231.3 + 64852.4i) q^{45} +(-82870.6 - 121549. i) q^{46} +(-62817.8 + 78771.0i) q^{47} +(113477. - 122299. i) q^{48} +(157953. - 273582. i) q^{49} +(296253. - 171041. i) q^{50} +(-116892. - 26679.8i) q^{51} +(-46689.6 + 118963. i) q^{52} +(145066. + 44747.0i) q^{53} +(190301. + 238630. i) q^{54} +(-235415. - 17641.9i) q^{55} +(-788434. + 243200. i) q^{56} +(-21606.4 - 14731.0i) q^{57} +(401432. + 60506.2i) q^{58} +(50111.9 + 219554. i) q^{59} +(413998. - 384134. i) q^{60} +(177268. - 13284.4i) q^{61} +(-370932. + 145580. i) q^{62} +(-35758.3 - 237241. i) q^{63} +(122231. + 58863.3i) q^{64} +(-73164.1 + 151927. i) q^{65} +(-329871. + 49720.1i) q^{66} +(20337.2 + 51818.3i) q^{67} +(-70250.7 - 937430. i) q^{68} +(-130699. - 140860. i) q^{69} +(-1.85389e6 + 423138. i) q^{70} +(12118.0 - 80397.9i) q^{71} +(-257206. + 377251. i) q^{72} +(-155599. - 504441. i) q^{73} +(-19447.8 + 259513. i) q^{74} +(349342. - 278591. i) q^{75} +(60434.0 - 195922. i) q^{76} +(732474. + 287475. i) q^{77} +(-53023.4 + 232311. i) q^{78} +(110504. + 191398. i) q^{79} +(1.49474e6 + 862987. i) q^{80} +(97529.7 + 90494.3i) q^{81} +(109766. + 87535.8i) q^{82} +(553695. - 377503. i) q^{83} +(-1.69599e6 + 816748. i) q^{84} -1.24039e6i q^{85} +(1.03818e6 + 522651. i) q^{86} +530270. q^{87} +(-649730. - 1.34918e6i) q^{88} +(-50358.2 - 73861.9i) q^{89} +(-656091. + 822712. i) q^{90} +(382292. - 412013. i) q^{91} +(753295. - 1.30474e6i) q^{92} +(-450755. + 260243. i) q^{93} +(-1.43597e6 - 327750. i) q^{94} +(98837.4 - 251834. i) q^{95} +(867266. + 267516. i) q^{96} +(657462. + 824431. i) q^{97} +(4.60532e6 + 345121. i) q^{98} +(416092. - 128347. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + 967 q^{10} + 4090 q^{11} - 484 q^{12} + 1527 q^{13} + 7812 q^{14} - 8923 q^{15} - 13760 q^{16} - 3655 q^{17} + 5596 q^{18} + 38605 q^{19} + 26085 q^{20} + 24873 q^{21} - 25214 q^{22} + 27991 q^{23} - 20480 q^{24} - 24146 q^{25} - 34923 q^{26} - 14 q^{27} - 77634 q^{28} - 112735 q^{29} + 375072 q^{30} + 290647 q^{31} - 344064 q^{32} - 152174 q^{33} - 198311 q^{34} - 182471 q^{35} - 930891 q^{36} + 282762 q^{37} + 487342 q^{38} + 857290 q^{39} + 745459 q^{40} + 27674 q^{41} + 148802 q^{43} - 1255832 q^{44} - 191310 q^{45} - 1344785 q^{46} + 69166 q^{47} - 871241 q^{48} + 1786604 q^{49} + 837705 q^{50} - 182756 q^{51} + 2906416 q^{52} + 7779 q^{53} + 487154 q^{54} - 529592 q^{55} - 2464007 q^{56} - 767855 q^{57} - 1523780 q^{58} + 1531338 q^{59} - 1858647 q^{60} + 646957 q^{61} - 448559 q^{62} - 2007847 q^{63} + 3937366 q^{64} - 1473542 q^{65} + 1513319 q^{66} - 575523 q^{67} + 2717157 q^{68} + 967041 q^{69} + 4624473 q^{70} - 2149319 q^{71} - 9986371 q^{72} - 514565 q^{73} - 882972 q^{74} - 6655138 q^{75} + 1152658 q^{76} - 341803 q^{77} + 6322388 q^{78} - 2476742 q^{79} + 10750038 q^{80} + 4308941 q^{81} + 5079172 q^{82} + 2318609 q^{83} + 5578407 q^{84} + 585292 q^{86} - 1990710 q^{87} - 2864890 q^{88} - 4561993 q^{89} - 17681545 q^{90} - 4648506 q^{91} - 1991714 q^{92} - 8868294 q^{93} - 10200218 q^{94} + 10091737 q^{95} + 6250318 q^{96} - 1676750 q^{97} + 7512700 q^{98} + 18452884 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{13}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.34296 + 13.1713i 0.792870 + 1.64641i 0.762601 + 0.646869i \(0.223922\pi\)
0.0302685 + 0.999542i \(0.490364\pi\)
\(3\) 10.7567 + 15.7772i 0.398397 + 0.584341i 0.972055 0.234754i \(-0.0754284\pi\)
−0.573658 + 0.819095i \(0.694476\pi\)
\(4\) −93.3463 + 117.053i −1.45854 + 1.82895i
\(5\) −134.366 + 144.812i −1.07493 + 1.15850i −0.0882033 + 0.996102i \(0.528113\pi\)
−0.986726 + 0.162396i \(0.948078\pi\)
\(6\) −139.577 + 241.754i −0.646189 + 1.11923i
\(7\) 570.233 329.224i 1.66249 0.959838i 0.690966 0.722888i \(-0.257186\pi\)
0.971522 0.236950i \(-0.0761478\pi\)
\(8\) −1221.67 278.837i −2.38607 0.544604i
\(9\) 133.120 339.185i 0.182607 0.465274i
\(10\) −2759.64 851.237i −2.75964 0.851237i
\(11\) 745.090 + 934.314i 0.559797 + 0.701964i 0.978520 0.206150i \(-0.0660936\pi\)
−0.418723 + 0.908114i \(0.637522\pi\)
\(12\) −2850.86 213.643i −1.64981 0.123636i
\(13\) 815.676 251.603i 0.371268 0.114521i −0.103506 0.994629i \(-0.533006\pi\)
0.474774 + 0.880108i \(0.342530\pi\)
\(14\) 7953.27 + 5422.45i 2.89842 + 1.97611i
\(15\) −3730.07 562.218i −1.10521 0.166583i
\(16\) −1944.17 8517.98i −0.474651 2.07958i
\(17\) −4602.80 + 4270.77i −0.936861 + 0.869280i −0.991616 0.129220i \(-0.958753\pi\)
0.0547550 + 0.998500i \(0.482562\pi\)
\(18\) 5311.88 398.070i 0.910816 0.0682562i
\(19\) −1274.80 + 500.323i −0.185858 + 0.0729441i −0.456445 0.889752i \(-0.650878\pi\)
0.270587 + 0.962696i \(0.412782\pi\)
\(20\) −4408.06 29245.6i −0.551008 3.65570i
\(21\) 11328.1 + 5455.32i 1.22320 + 0.589063i
\(22\) −7580.04 + 15740.1i −0.711874 + 1.47822i
\(23\) −9950.59 + 1499.81i −0.817835 + 0.123269i −0.544618 0.838684i \(-0.683326\pi\)
−0.273216 + 0.961953i \(0.588087\pi\)
\(24\) −8741.84 22273.8i −0.632367 1.61124i
\(25\) −1748.67 23334.4i −0.111915 1.49340i
\(26\) 8487.73 + 9147.60i 0.482916 + 0.520460i
\(27\) 20354.7 4645.83i 1.03413 0.236033i
\(28\) −14692.6 + 97479.2i −0.669307 + 4.44056i
\(29\) 15643.3 22944.5i 0.641406 0.940770i −0.358567 0.933504i \(-0.616735\pi\)
0.999974 0.00726651i \(-0.00231302\pi\)
\(30\) −16254.6 52696.0i −0.602021 1.95170i
\(31\) −2036.95 + 27181.2i −0.0683747 + 0.912397i 0.852547 + 0.522650i \(0.175057\pi\)
−0.920922 + 0.389747i \(0.872562\pi\)
\(32\) 37160.1 29634.2i 1.13404 0.904364i
\(33\) −6726.14 + 21805.6i −0.187165 + 0.606773i
\(34\) −85446.9 33535.4i −2.17400 0.853232i
\(35\) −28944.3 + 126813.i −0.675086 + 2.95775i
\(36\) 27276.2 + 47243.7i 0.584623 + 1.01260i
\(37\) 15416.6 + 8900.75i 0.304356 + 0.175720i 0.644398 0.764690i \(-0.277108\pi\)
−0.340042 + 0.940410i \(0.610441\pi\)
\(38\) −14675.9 13617.3i −0.267457 0.248164i
\(39\) 12743.6 + 10162.7i 0.214831 + 0.171322i
\(40\) 204529. 139446.i 3.19577 2.17884i
\(41\) 8652.63 4166.88i 0.125544 0.0604589i −0.370057 0.929009i \(-0.620662\pi\)
0.495601 + 0.868550i \(0.334948\pi\)
\(42\) 183808.i 2.48094i
\(43\) 63023.4 48470.8i 0.792677 0.609642i
\(44\) −178915. −2.10034
\(45\) 31231.3 + 64852.4i 0.342730 + 0.711686i
\(46\) −82870.6 121549.i −0.851387 1.24876i
\(47\) −62817.8 + 78771.0i −0.605047 + 0.758705i −0.986155 0.165825i \(-0.946971\pi\)
0.381108 + 0.924531i \(0.375543\pi\)
\(48\) 113477. 122299.i 1.02609 1.10586i
\(49\) 157953. 273582.i 1.34258 2.32541i
\(50\) 296253. 171041.i 2.37002 1.36833i
\(51\) −116892. 26679.8i −0.881199 0.201128i
\(52\) −46689.6 + 118963.i −0.332055 + 0.846063i
\(53\) 145066. + 44747.0i 0.974404 + 0.300564i 0.740768 0.671761i \(-0.234462\pi\)
0.233635 + 0.972324i \(0.424938\pi\)
\(54\) 190301. + 238630.i 1.20854 + 1.51546i
\(55\) −235415. 17641.9i −1.41497 0.106037i
\(56\) −788434. + 243200.i −4.48953 + 1.38484i
\(57\) −21606.4 14731.0i −0.116670 0.0795440i
\(58\) 401432. + 60506.2i 2.05745 + 0.310110i
\(59\) 50111.9 + 219554.i 0.243997 + 1.06902i 0.937341 + 0.348414i \(0.113280\pi\)
−0.693344 + 0.720607i \(0.743863\pi\)
\(60\) 413998. 384134.i 1.91666 1.77840i
\(61\) 177268. 13284.4i 0.780981 0.0585264i 0.321728 0.946832i \(-0.395736\pi\)
0.459253 + 0.888306i \(0.348117\pi\)
\(62\) −370932. + 145580.i −1.55639 + 0.610839i
\(63\) −35758.3 237241.i −0.143006 0.948785i
\(64\) 122231. + 58863.3i 0.466274 + 0.224546i
\(65\) −73164.1 + 151927.i −0.266414 + 0.553215i
\(66\) −329871. + 49720.1i −1.14739 + 0.172942i
\(67\) 20337.2 + 51818.3i 0.0676187 + 0.172290i 0.960689 0.277628i \(-0.0895484\pi\)
−0.893070 + 0.449918i \(0.851453\pi\)
\(68\) −70250.7 937430.i −0.223421 2.98135i
\(69\) −130699. 140860.i −0.397854 0.428785i
\(70\) −1.85389e6 + 423138.i −5.40492 + 1.23364i
\(71\) 12118.0 80397.9i 0.0338577 0.224631i −0.965503 0.260393i \(-0.916148\pi\)
0.999360 + 0.0357623i \(0.0113859\pi\)
\(72\) −257206. + 377251.i −0.689101 + 1.01073i
\(73\) −155599. 504441.i −0.399981 1.29671i −0.901957 0.431825i \(-0.857870\pi\)
0.501977 0.864881i \(-0.332606\pi\)
\(74\) −19447.8 + 259513.i −0.0479927 + 0.640418i
\(75\) 349342. 278591.i 0.828070 0.660364i
\(76\) 60434.0 195922.i 0.137670 0.446317i
\(77\) 732474. + 287475.i 1.60443 + 0.629691i
\(78\) −53023.4 + 232311.i −0.111734 + 0.489537i
\(79\) 110504. + 191398.i 0.224127 + 0.388200i 0.956057 0.293180i \(-0.0947135\pi\)
−0.731930 + 0.681380i \(0.761380\pi\)
\(80\) 1.49474e6 + 862987.i 2.91941 + 1.68552i
\(81\) 97529.7 + 90494.3i 0.183519 + 0.170281i
\(82\) 109766. + 87535.8i 0.199080 + 0.158761i
\(83\) 553695. 377503.i 0.968360 0.660216i 0.0277173 0.999616i \(-0.491176\pi\)
0.940642 + 0.339399i \(0.110224\pi\)
\(84\) −1.69599e6 + 816748.i −2.86145 + 1.37800i
\(85\) 1.24039e6i 2.01977i
\(86\) 1.03818e6 + 522651.i 1.63221 + 0.821706i
\(87\) 530270. 0.805265
\(88\) −649730. 1.34918e6i −0.953421 1.97980i
\(89\) −50358.2 73861.9i −0.0714332 0.104773i 0.788860 0.614573i \(-0.210672\pi\)
−0.860293 + 0.509800i \(0.829719\pi\)
\(90\) −656091. + 822712.i −0.899987 + 1.12855i
\(91\) 382292. 412013.i 0.507307 0.546747i
\(92\) 753295. 1.30474e6i 0.967390 1.67557i
\(93\) −450755. + 260243.i −0.560391 + 0.323542i
\(94\) −1.43597e6 327750.i −1.72886 0.394602i
\(95\) 98837.4 251834.i 0.115279 0.293726i
\(96\) 867266. + 267516.i 0.980254 + 0.302368i
\(97\) 657462. + 824431.i 0.720370 + 0.903315i 0.998359 0.0572692i \(-0.0182393\pi\)
−0.277989 + 0.960584i \(0.589668\pi\)
\(98\) 4.60532e6 + 345121.i 4.89307 + 0.366685i
\(99\) 416092. 128347.i 0.428828 0.132276i
\(100\) 2.89459e6 + 1.97350e6i 2.89459 + 1.97350i
\(101\) −1.80910e6 272678.i −1.75589 0.264659i −0.809372 0.587296i \(-0.800192\pi\)
−0.946523 + 0.322638i \(0.895430\pi\)
\(102\) −390033. 1.70885e6i −0.367537 1.61028i
\(103\) 619467. 574781.i 0.566900 0.526006i −0.343818 0.939036i \(-0.611720\pi\)
0.910717 + 0.413030i \(0.135530\pi\)
\(104\) −1.06664e6 + 79933.6i −0.948238 + 0.0710606i
\(105\) −2.31211e6 + 907435.i −1.99729 + 0.783877i
\(106\) 330773. + 2.19454e6i 0.277724 + 1.84258i
\(107\) −558457. 268939.i −0.455867 0.219534i 0.191836 0.981427i \(-0.438556\pi\)
−0.647703 + 0.761893i \(0.724270\pi\)
\(108\) −1.35623e6 + 2.81625e6i −1.07662 + 2.23563i
\(109\) −631478. + 95180.0i −0.487617 + 0.0734964i −0.388249 0.921554i \(-0.626920\pi\)
−0.0993677 + 0.995051i \(0.531682\pi\)
\(110\) −1.26086e6 3.21262e6i −0.947303 2.41369i
\(111\) 25402.5 + 338973.i 0.0185741 + 0.247854i
\(112\) −3.91296e6 4.21716e6i −2.78516 3.00169i
\(113\) −289747. + 66132.9i −0.200809 + 0.0458334i −0.321742 0.946827i \(-0.604269\pi\)
0.120933 + 0.992661i \(0.461411\pi\)
\(114\) 56977.7 378022.i 0.0384583 0.255154i
\(115\) 1.11983e6 1.64249e6i 0.736308 1.07996i
\(116\) 1.22547e6 + 3.97286e6i 0.785104 + 2.54525i
\(117\) 23243.2 310158.i 0.0145123 0.193654i
\(118\) −2.57396e6 + 2.05266e6i −1.56659 + 1.24931i
\(119\) −1.21863e6 + 3.95069e6i −0.723152 + 2.34440i
\(120\) 4.40013e6 + 1.72693e6i 2.54637 + 0.999378i
\(121\) 76426.8 334848.i 0.0431410 0.189013i
\(122\) 1.29937e6 + 2.25058e6i 0.715574 + 1.23941i
\(123\) 158816. + 91692.3i 0.0853450 + 0.0492740i
\(124\) −2.99149e6 2.77570e6i −1.56900 1.45582i
\(125\) 1.20081e6 + 957617.i 0.614817 + 0.490300i
\(126\) 2.89795e6 1.97579e6i 1.44870 0.987710i
\(127\) 502892. 242180.i 0.245507 0.118230i −0.307084 0.951682i \(-0.599353\pi\)
0.552591 + 0.833452i \(0.313639\pi\)
\(128\) 1.05859e6i 0.504773i
\(129\) 1.44266e6 + 472947.i 0.672039 + 0.220314i
\(130\) −2.46515e6 −1.12205
\(131\) −616396. 1.27996e6i −0.274186 0.569354i 0.717719 0.696333i \(-0.245186\pi\)
−0.991905 + 0.126979i \(0.959472\pi\)
\(132\) −1.92454e6 2.82278e6i −0.836769 1.22731i
\(133\) −562216. + 704997.i −0.238973 + 0.299663i
\(134\) −553516. + 596548.i −0.230047 + 0.247931i
\(135\) −2.06221e6 + 3.57186e6i −0.838170 + 1.45175i
\(136\) 6.81393e6 3.93402e6i 2.70882 1.56394i
\(137\) 505538. + 115386.i 0.196604 + 0.0448736i 0.319689 0.947523i \(-0.396422\pi\)
−0.123085 + 0.992396i \(0.539279\pi\)
\(138\) 1.02629e6 2.61493e6i 0.390509 0.995001i
\(139\) 1.17226e6 + 361594.i 0.436494 + 0.134641i 0.505212 0.862995i \(-0.331414\pi\)
−0.0687172 + 0.997636i \(0.521891\pi\)
\(140\) −1.21420e7 1.52256e7i −4.42492 5.54868i
\(141\) −1.91850e6 143772.i −0.684392 0.0512881i
\(142\) 1.13581e6 350350.i 0.396680 0.122359i
\(143\) 842828. + 574631.i 0.288225 + 0.196508i
\(144\) −3.14798e6 474481.i −1.05425 0.158903i
\(145\) 1.22071e6 + 5.34829e6i 0.400414 + 1.75433i
\(146\) 5.65717e6 5.24909e6i 1.81778 1.68665i
\(147\) 6.01542e6 450793.i 1.89371 0.141914i
\(148\) −2.48093e6 + 973695.i −0.765297 + 0.300357i
\(149\) −443972. 2.94556e6i −0.134214 0.890449i −0.950035 0.312145i \(-0.898953\pi\)
0.815821 0.578305i \(-0.196285\pi\)
\(150\) 5.88526e6 + 2.83419e6i 1.74378 + 0.839761i
\(151\) −170129. + 353276.i −0.0494136 + 0.102608i −0.924214 0.381876i \(-0.875278\pi\)
0.874800 + 0.484484i \(0.160993\pi\)
\(152\) 1.69689e6 255765.i 0.483196 0.0728301i
\(153\) 835856. + 2.12973e6i 0.233376 + 0.594633i
\(154\) 859638. + 1.14711e7i 0.235371 + 3.14081i
\(155\) −3.66248e6 3.94721e6i −0.983512 1.05997i
\(156\) −2.37913e6 + 543022.i −0.626679 + 0.143035i
\(157\) −475690. + 3.15600e6i −0.122921 + 0.815526i 0.839381 + 0.543543i \(0.182918\pi\)
−0.962302 + 0.271983i \(0.912321\pi\)
\(158\) −1.82004e6 + 2.66950e6i −0.461433 + 0.676798i
\(159\) 854454. + 2.77007e6i 0.212568 + 0.689128i
\(160\) −701665. + 9.36308e6i −0.171305 + 2.28591i
\(161\) −5.18039e6 + 4.13122e6i −1.24132 + 0.989921i
\(162\) −573300. + 1.85859e6i −0.134846 + 0.437159i
\(163\) −6.31115e6 2.47694e6i −1.45729 0.571944i −0.501281 0.865285i \(-0.667138\pi\)
−0.956008 + 0.293341i \(0.905233\pi\)
\(164\) −319946. + 1.40178e6i −0.0725346 + 0.317795i
\(165\) −2.25395e6 3.90396e6i −0.501757 0.869068i
\(166\) 8.48427e6 + 4.89840e6i 1.85477 + 1.07085i
\(167\) 251780. + 233618.i 0.0540595 + 0.0501599i 0.706740 0.707473i \(-0.250165\pi\)
−0.652680 + 0.757633i \(0.726356\pi\)
\(168\) −1.23180e7 9.82326e6i −2.59784 2.07170i
\(169\) −3.38607e6 + 2.30859e6i −0.701514 + 0.478284i
\(170\) 1.63375e7 7.86773e6i 3.32536 1.60141i
\(171\) 498997.i 0.0997952i
\(172\) −209371. + 1.19016e7i −0.0411463 + 2.33895i
\(173\) 6.83701e6 1.32047 0.660234 0.751060i \(-0.270457\pi\)
0.660234 + 0.751060i \(0.270457\pi\)
\(174\) 3.36348e6 + 6.98433e6i 0.638470 + 1.32580i
\(175\) −8.67941e6 1.27304e7i −1.61948 2.37534i
\(176\) 6.50988e6 8.16313e6i 1.19408 1.49733i
\(177\) −2.92492e6 + 3.15231e6i −0.527465 + 0.568472i
\(178\) 653437. 1.13179e6i 0.115863 0.200680i
\(179\) −4.15666e6 + 2.39985e6i −0.724745 + 0.418432i −0.816497 0.577350i \(-0.804087\pi\)
0.0917515 + 0.995782i \(0.470753\pi\)
\(180\) −1.05065e7 2.39803e6i −1.80152 0.411185i
\(181\) 3.04741e6 7.76467e6i 0.513919 1.30944i −0.404754 0.914426i \(-0.632643\pi\)
0.918673 0.395019i \(-0.129262\pi\)
\(182\) 7.85160e6 + 2.42190e6i 1.30240 + 0.401737i
\(183\) 2.11641e6 + 2.65389e6i 0.345340 + 0.433042i
\(184\) 1.25745e7 + 942328.i 2.01854 + 0.151269i
\(185\) −3.36040e6 + 1.03655e6i −0.530733 + 0.163709i
\(186\) −6.28686e6 4.28631e6i −0.977001 0.666108i
\(187\) −7.41974e6 1.11835e6i −1.13466 0.171022i
\(188\) −3.35654e6 1.47060e7i −0.505148 2.21320i
\(189\) 1.00774e7 9.35048e6i 1.49267 1.38500i
\(190\) 3.94389e6 295554.i 0.574995 0.0430900i
\(191\) 1.02549e7 4.02475e6i 1.47174 0.577615i 0.512119 0.858914i \(-0.328861\pi\)
0.959620 + 0.281299i \(0.0907654\pi\)
\(192\) 386105. + 2.56164e6i 0.0545509 + 0.361922i
\(193\) 1.54269e6 + 742922.i 0.214589 + 0.103341i 0.538091 0.842887i \(-0.319146\pi\)
−0.323502 + 0.946228i \(0.604860\pi\)
\(194\) −6.68857e6 + 1.38890e7i −0.916068 + 1.90224i
\(195\) −3.18399e6 + 479909.i −0.429405 + 0.0647224i
\(196\) 1.72792e7 + 4.40267e7i 2.29486 + 5.84720i
\(197\) −204222. 2.72516e6i −0.0267119 0.356445i −0.994504 0.104696i \(-0.966613\pi\)
0.967792 0.251749i \(-0.0810059\pi\)
\(198\) 4.32975e6 + 4.66636e6i 0.557786 + 0.601150i
\(199\) 5.35953e6 1.22328e6i 0.680092 0.155226i 0.131499 0.991316i \(-0.458021\pi\)
0.548593 + 0.836090i \(0.315164\pi\)
\(200\) −4.37021e6 + 2.89944e7i −0.546276 + 3.62431i
\(201\) −598787. + 878259.i −0.0737368 + 0.108152i
\(202\) −7.88352e6 2.55578e7i −0.956459 3.10076i
\(203\) 1.36644e6 1.82338e7i 0.163343 2.17967i
\(204\) 1.40344e7 1.11920e7i 1.65311 1.31831i
\(205\) −559204. + 1.81289e6i −0.0649096 + 0.210432i
\(206\) 1.14999e7 + 4.51336e6i 1.31550 + 0.516295i
\(207\) −815912. + 3.57475e6i −0.0919883 + 0.403027i
\(208\) −3.72896e6 6.45875e6i −0.414379 0.717726i
\(209\) −1.41730e6 818280.i −0.155247 0.0896320i
\(210\) −2.66177e7 2.46976e7i −2.87417 2.66684i
\(211\) 6.34488e6 + 5.05987e6i 0.675424 + 0.538632i 0.900036 0.435816i \(-0.143540\pi\)
−0.224612 + 0.974448i \(0.572112\pi\)
\(212\) −1.87792e7 + 1.28034e7i −1.97092 + 1.34375i
\(213\) 1.39880e6 673629.i 0.144750 0.0697079i
\(214\) 9.06146e6i 0.924606i
\(215\) −1.44905e6 + 1.56394e7i −0.145803 + 1.57364i
\(216\) −2.61621e7 −2.59604
\(217\) 7.78718e6 + 1.61702e7i 0.762081 + 1.58248i
\(218\) −5.25908e6 7.71366e6i −0.507622 0.744545i
\(219\) 6.28493e6 7.88105e6i 0.598368 0.750329i
\(220\) 2.40402e7 2.59091e7i 2.25772 2.43324i
\(221\) −2.67985e6 + 4.64164e6i −0.248276 + 0.430026i
\(222\) −4.30359e6 + 2.48468e6i −0.393343 + 0.227097i
\(223\) −1.72566e7 3.93872e6i −1.55612 0.355173i −0.643973 0.765048i \(-0.722715\pi\)
−0.912142 + 0.409875i \(0.865572\pi\)
\(224\) 1.14336e7 2.91324e7i 1.01728 2.59199i
\(225\) −8.14746e6 2.51316e6i −0.715278 0.220634i
\(226\) −2.70891e6 3.39686e6i −0.234676 0.294275i
\(227\) 1.02721e7 + 769786.i 0.878174 + 0.0658101i 0.506183 0.862426i \(-0.331056\pi\)
0.371991 + 0.928236i \(0.378675\pi\)
\(228\) 3.74118e6 1.15400e6i 0.315649 0.0973648i
\(229\) −1.37728e7 9.39010e6i −1.14687 0.781923i −0.167876 0.985808i \(-0.553691\pi\)
−0.978995 + 0.203885i \(0.934643\pi\)
\(230\) 2.87368e7 + 4.33137e6i 2.36186 + 0.355993i
\(231\) 3.34347e6 + 1.46487e7i 0.271245 + 1.18840i
\(232\) −2.55086e7 + 2.36685e7i −2.04278 + 1.89543i
\(233\) 5.93619e6 444856.i 0.469289 0.0351683i 0.162012 0.986789i \(-0.448202\pi\)
0.307276 + 0.951620i \(0.400582\pi\)
\(234\) 4.23261e6 1.66118e6i 0.330340 0.129649i
\(235\) −2.96643e6 1.96809e7i −0.228576 1.51650i
\(236\) −3.03772e7 1.46289e7i −2.31106 1.11295i
\(237\) −1.83107e6 + 3.80225e6i −0.137550 + 0.285625i
\(238\) −5.97654e7 + 9.00818e6i −4.43321 + 0.668199i
\(239\) −6.65185e6 1.69486e7i −0.487246 1.24148i −0.937313 0.348488i \(-0.886695\pi\)
0.450067 0.892995i \(-0.351400\pi\)
\(240\) 2.46295e6 + 3.28657e7i 0.178164 + 2.37744i
\(241\) 1.40379e7 + 1.51292e7i 1.00288 + 1.08085i 0.996725 + 0.0808691i \(0.0257696\pi\)
0.00615769 + 0.999981i \(0.498040\pi\)
\(242\) 4.89515e6 1.11729e6i 0.345398 0.0788348i
\(243\) 1.88980e6 1.25380e7i 0.131704 0.873797i
\(244\) −1.49923e7 + 2.19897e7i −1.03205 + 1.51373i
\(245\) 1.83946e7 + 5.96337e7i 1.25081 + 4.05502i
\(246\) −200344. + 2.67341e6i −0.0134577 + 0.179581i
\(247\) −913944. + 728846.i −0.0606497 + 0.0483665i
\(248\) 1.00676e7 3.26384e7i 0.660041 2.13980i
\(249\) 1.19119e7 + 4.67507e6i 0.771583 + 0.302824i
\(250\) −4.99634e6 + 2.18904e7i −0.319766 + 1.40098i
\(251\) −6.19701e6 1.07335e7i −0.391887 0.678768i 0.600811 0.799391i \(-0.294844\pi\)
−0.992698 + 0.120622i \(0.961511\pi\)
\(252\) 3.11076e7 + 1.79600e7i 1.94386 + 1.12229i
\(253\) −8.81539e6 8.17948e6i −0.544352 0.505085i
\(254\) 6.37965e6 + 5.08760e6i 0.389310 + 0.310464i
\(255\) 1.95699e7 1.33425e7i 1.18023 0.804669i
\(256\) 2.17657e7 1.04818e7i 1.29734 0.624765i
\(257\) 6.71552e6i 0.395622i −0.980240 0.197811i \(-0.936617\pi\)
0.980240 0.197811i \(-0.0633832\pi\)
\(258\) 2.92141e6 + 2.20016e7i 0.170111 + 1.28113i
\(259\) 1.17214e7 0.674651
\(260\) −1.09538e7 2.27459e7i −0.623226 1.29414i
\(261\) −5.69997e6 8.36033e6i −0.320591 0.470221i
\(262\) 1.29489e7 1.62375e7i 0.719996 0.902847i
\(263\) 8.26110e6 8.90335e6i 0.454120 0.489425i −0.463940 0.885867i \(-0.653565\pi\)
0.918060 + 0.396442i \(0.129755\pi\)
\(264\) 1.42973e7 2.47637e7i 0.777038 1.34587i
\(265\) −2.59719e7 + 1.49949e7i −1.39562 + 0.805760i
\(266\) −1.28518e7 2.93335e6i −0.682842 0.155854i
\(267\) 623646. 1.58902e6i 0.0327646 0.0834828i
\(268\) −7.96387e6 2.45653e6i −0.413733 0.127620i
\(269\) 1.34526e6 + 1.68690e6i 0.0691113 + 0.0866628i 0.815185 0.579200i \(-0.196635\pi\)
−0.746074 + 0.665863i \(0.768064\pi\)
\(270\) −6.01265e7 4.50586e6i −3.05474 0.228921i
\(271\) −1.37671e7 + 4.24658e6i −0.691726 + 0.213369i −0.620634 0.784101i \(-0.713125\pi\)
−0.0710922 + 0.997470i \(0.522648\pi\)
\(272\) 4.53270e7 + 3.09034e7i 2.25242 + 1.53568i
\(273\) 1.06126e7 + 1.59959e6i 0.521596 + 0.0786180i
\(274\) 1.68683e6 + 7.39048e6i 0.0820010 + 0.359270i
\(275\) 2.04987e7 1.90201e7i 0.985665 0.914563i
\(276\) 2.86882e7 2.14988e6i 1.36451 0.102256i
\(277\) −2.56998e7 + 1.00864e7i −1.20918 + 0.474568i −0.882385 0.470528i \(-0.844064\pi\)
−0.326794 + 0.945096i \(0.605968\pi\)
\(278\) 2.67293e6 + 1.77337e7i 0.124409 + 0.825402i
\(279\) 8.94830e6 + 4.30927e6i 0.412029 + 0.198423i
\(280\) 7.07205e7 1.46853e8i 3.22160 6.68972i
\(281\) −2.60681e6 + 392914.i −0.117487 + 0.0177084i −0.207523 0.978230i \(-0.566540\pi\)
0.0900354 + 0.995939i \(0.471302\pi\)
\(282\) −1.02753e7 2.61811e7i −0.458192 1.16745i
\(283\) 3.08374e6 + 4.11496e7i 0.136056 + 1.81554i 0.480783 + 0.876840i \(0.340353\pi\)
−0.344726 + 0.938703i \(0.612028\pi\)
\(284\) 8.27961e6 + 8.92329e6i 0.361455 + 0.389556i
\(285\) 5.03640e6 1.14953e6i 0.217563 0.0496574i
\(286\) −2.22260e6 + 1.47460e7i −0.0950087 + 0.630341i
\(287\) 3.56217e6 5.22475e6i 0.150685 0.221014i
\(288\) −5.10471e6 1.65491e7i −0.213695 0.692781i
\(289\) 1.14245e6 1.52449e7i 0.0473308 0.631585i
\(290\) −6.27010e7 + 5.00024e7i −2.57087 + 2.05020i
\(291\) −5.93509e6 + 1.92411e7i −0.240851 + 0.780820i
\(292\) 7.35707e7 + 2.88744e7i 2.95499 + 1.15975i
\(293\) −3.32458e6 + 1.45659e7i −0.132170 + 0.579076i 0.864856 + 0.502020i \(0.167409\pi\)
−0.997027 + 0.0770569i \(0.975448\pi\)
\(294\) 4.40931e7 + 7.63715e7i 1.73512 + 3.00531i
\(295\) −3.85275e7 2.22439e7i −1.50074 0.866451i
\(296\) −1.63520e7 1.51724e7i −0.630516 0.585033i
\(297\) 1.95068e7 + 1.55561e7i 0.744588 + 0.593789i
\(298\) 3.59807e7 2.45312e7i 1.35963 0.926981i
\(299\) −7.73910e6 + 3.72696e6i −0.289519 + 0.139425i
\(300\) 6.68968e7i 2.47766i
\(301\) 1.99803e7 4.83885e7i 0.732659 1.77436i
\(302\) −5.73221e6 −0.208114
\(303\) −1.51579e7 3.14757e7i −0.544892 1.13148i
\(304\) 6.74018e6 + 9.88603e6i 0.239911 + 0.351885i
\(305\) −2.18950e7 + 2.74555e7i −0.771696 + 0.967676i
\(306\) −2.27494e7 + 2.45180e7i −0.793974 + 0.855700i
\(307\) −7.70408e6 + 1.33439e7i −0.266260 + 0.461176i −0.967893 0.251363i \(-0.919121\pi\)
0.701633 + 0.712539i \(0.252455\pi\)
\(308\) −1.02023e8 + 5.89033e7i −3.49179 + 2.01598i
\(309\) 1.57319e7 + 3.59070e6i 0.533218 + 0.121704i
\(310\) 2.87589e7 7.32765e7i 0.965356 2.45969i
\(311\) 4.28883e7 + 1.32293e7i 1.42580 + 0.439801i 0.909176 0.416413i \(-0.136713\pi\)
0.516623 + 0.856213i \(0.327189\pi\)
\(312\) −1.27347e7 1.59688e7i −0.419299 0.525784i
\(313\) 1.43288e7 + 1.07380e6i 0.467280 + 0.0350178i 0.306290 0.951938i \(-0.400912\pi\)
0.160990 + 0.986956i \(0.448531\pi\)
\(314\) −4.45858e7 + 1.37529e7i −1.44015 + 0.444228i
\(315\) 3.91601e7 + 2.66989e7i 1.25289 + 0.854204i
\(316\) −3.27187e7 4.93155e6i −1.03690 0.156287i
\(317\) −1.03178e7 4.52054e7i −0.323900 1.41910i −0.830549 0.556946i \(-0.811973\pi\)
0.506649 0.862153i \(-0.330884\pi\)
\(318\) −3.10657e7 + 2.88247e7i −0.966049 + 0.896363i
\(319\) 3.30930e7 2.47997e6i 1.01944 0.0763968i
\(320\) −2.49478e7 + 9.79130e6i −0.761347 + 0.298807i
\(321\) −1.76406e6 1.17038e7i −0.0533334 0.353844i
\(322\) −8.72724e7 4.20282e7i −2.61402 1.25885i
\(323\) 3.73089e6 7.74728e6i 0.110715 0.229901i
\(324\) −1.96966e7 + 2.96879e6i −0.579105 + 0.0872860i
\(325\) −7.29735e6 1.85934e7i −0.212577 0.541636i
\(326\) −7.40682e6 9.88371e7i −0.213786 2.85277i
\(327\) −8.29431e6 8.93914e6i −0.237212 0.255654i
\(328\) −1.17325e7 + 2.67787e6i −0.332483 + 0.0758870i
\(329\) −9.88746e6 + 6.55990e7i −0.277650 + 1.84208i
\(330\) 3.71235e7 5.44501e7i 1.03302 1.51516i
\(331\) 3.75668e6 + 1.21788e7i 0.103590 + 0.335832i 0.992499 0.122253i \(-0.0390118\pi\)
−0.888909 + 0.458085i \(0.848536\pi\)
\(332\) −7.49771e6 + 1.00050e8i −0.204887 + 2.73403i
\(333\) 5.07125e6 4.04419e6i 0.137335 0.109521i
\(334\) −1.48002e6 + 4.79810e6i −0.0397216 + 0.128774i
\(335\) −1.02366e7 4.01755e6i −0.272282 0.106863i
\(336\) 2.44445e7 1.07098e8i 0.644412 2.82335i
\(337\) −2.45950e7 4.25998e7i −0.642624 1.11306i −0.984845 0.173438i \(-0.944512\pi\)
0.342221 0.939620i \(-0.388821\pi\)
\(338\) −5.18848e7 2.99557e7i −1.34366 0.775763i
\(339\) −4.16012e6 3.86003e6i −0.106784 0.0990813i
\(340\) 1.45191e8 + 1.15786e8i 3.69404 + 2.94590i
\(341\) −2.69135e7 + 1.83493e7i −0.678746 + 0.462761i
\(342\) −6.57243e6 + 3.16512e6i −0.164304 + 0.0791246i
\(343\) 1.30542e8i 3.23495i
\(344\) −9.05089e7 + 4.16418e7i −2.22339 + 1.02295i
\(345\) 3.79597e7 0.924411
\(346\) 4.33668e7 + 9.00522e7i 1.04696 + 2.17403i
\(347\) 3.03983e7 + 4.45861e7i 0.727546 + 1.06711i 0.994635 + 0.103443i \(0.0329858\pi\)
−0.267089 + 0.963672i \(0.586062\pi\)
\(348\) −4.94987e7 + 6.20694e7i −1.17451 + 1.47279i
\(349\) −2.57185e7 + 2.77180e7i −0.605020 + 0.652057i −0.959070 0.283170i \(-0.908614\pi\)
0.354050 + 0.935227i \(0.384804\pi\)
\(350\) 1.12622e8 1.95067e8i 2.62675 4.54967i
\(351\) 1.54340e7 8.91080e6i 0.356908 0.206061i
\(352\) 5.53753e7 + 1.26391e7i 1.26966 + 0.289792i
\(353\) 6.38686e6 1.62734e7i 0.145199 0.369961i −0.839710 0.543035i \(-0.817275\pi\)
0.984909 + 0.173075i \(0.0553702\pi\)
\(354\) −6.00726e7 1.85299e7i −1.35415 0.417700i
\(355\) 1.00143e7 + 1.25576e7i 0.223840 + 0.280686i
\(356\) 1.33465e7 + 1.00018e6i 0.295813 + 0.0221681i
\(357\) −7.54393e7 + 2.32699e7i −1.65803 + 0.511435i
\(358\) −5.79746e7 3.95264e7i −1.26354 0.861466i
\(359\) −8.91908e7 1.34434e7i −1.92769 0.290552i −0.930551 0.366163i \(-0.880671\pi\)
−0.997137 + 0.0756112i \(0.975909\pi\)
\(360\) −2.00709e7 8.79364e7i −0.430189 1.88478i
\(361\) −3.31123e7 + 3.07237e7i −0.703829 + 0.653058i
\(362\) 1.21600e8 9.11268e6i 2.56336 0.192097i
\(363\) 6.10507e6 2.39606e6i 0.127635 0.0500931i
\(364\) 1.25416e7 + 8.32081e7i 0.260045 + 1.72529i
\(365\) 9.39565e7 + 4.52471e7i 1.93218 + 0.930490i
\(366\) −2.15309e7 + 4.47094e7i −0.439156 + 0.911917i
\(367\) −5.57281e7 + 8.39967e6i −1.12740 + 0.169928i −0.686151 0.727459i \(-0.740701\pi\)
−0.441245 + 0.897387i \(0.645463\pi\)
\(368\) 3.21210e7 + 8.18430e7i 0.644534 + 1.64225i
\(369\) −261505. 3.48954e6i −0.00520475 0.0694526i
\(370\) −3.49675e7 3.76860e7i −0.690335 0.744004i
\(371\) 9.74534e7 2.22431e7i 1.90843 0.435586i
\(372\) 1.16141e7 7.70548e7i 0.225610 1.49682i
\(373\) 1.60250e7 2.35044e7i 0.308796 0.452921i −0.640200 0.768208i \(-0.721149\pi\)
0.948996 + 0.315287i \(0.102101\pi\)
\(374\) −3.23330e7 1.04821e8i −0.618062 2.00371i
\(375\) −2.19171e6 + 2.92463e7i −0.0415613 + 0.554597i
\(376\) 9.87066e7 7.87159e7i 1.85688 1.48081i
\(377\) 6.98695e6 2.26511e7i 0.130396 0.422733i
\(378\) 1.87079e8 + 7.34229e7i 3.46377 + 1.35943i
\(379\) 1.02129e7 4.47458e7i 0.187600 0.821929i −0.790277 0.612750i \(-0.790063\pi\)
0.977877 0.209180i \(-0.0670794\pi\)
\(380\) 2.02517e7 + 3.50769e7i 0.369071 + 0.639250i
\(381\) 9.23040e6 + 5.32917e6i 0.166896 + 0.0963574i
\(382\) 1.18057e8 + 1.09541e8i 2.11789 + 1.96511i
\(383\) −1.67415e7 1.33509e7i −0.297987 0.237637i 0.463070 0.886322i \(-0.346748\pi\)
−0.761057 + 0.648685i \(0.775319\pi\)
\(384\) 1.67015e7 1.13869e7i 0.294960 0.201100i
\(385\) −1.40050e8 + 6.74443e7i −2.45414 + 1.18185i
\(386\) 2.50316e7i 0.435237i
\(387\) −8.05086e6 2.78290e7i −0.138902 0.480137i
\(388\) −1.57873e8 −2.70280
\(389\) −3.45638e7 7.17726e7i −0.587183 1.21930i −0.956972 0.290182i \(-0.906284\pi\)
0.369789 0.929116i \(-0.379430\pi\)
\(390\) −2.65169e7 3.88932e7i −0.447022 0.655661i
\(391\) 3.93952e7 4.94000e7i 0.659042 0.826413i
\(392\) −2.69250e8 + 2.90183e8i −4.46990 + 4.81741i
\(393\) 1.35638e7 2.34932e7i 0.223462 0.387047i
\(394\) 3.45984e7 1.99754e7i 0.565676 0.326593i
\(395\) −4.25647e7 9.71511e6i −0.690650 0.157636i
\(396\) −2.38172e7 + 6.06854e7i −0.383536 + 0.977233i
\(397\) −5.76758e7 1.77906e7i −0.921769 0.284328i −0.202679 0.979245i \(-0.564965\pi\)
−0.719090 + 0.694917i \(0.755441\pi\)
\(398\) 5.01074e7 + 6.28327e7i 0.794790 + 0.996636i
\(399\) −1.71705e7 1.28675e6i −0.270311 0.0202570i
\(400\) −1.95362e8 + 6.02613e7i −3.05254 + 0.941583i
\(401\) −7.20639e7 4.91323e7i −1.11760 0.761964i −0.143849 0.989600i \(-0.545948\pi\)
−0.973746 + 0.227636i \(0.926900\pi\)
\(402\) −1.53659e7 2.31604e6i −0.236526 0.0356506i
\(403\) 5.17738e6 + 2.26836e7i 0.0791033 + 0.346574i
\(404\) 2.00791e8 1.86306e8i 3.04508 2.82542i
\(405\) −2.62094e7 + 1.96412e6i −0.394541 + 0.0295667i
\(406\) 2.48830e8 9.76587e7i 3.71813 1.45926i
\(407\) 3.17063e6 + 2.10358e7i 0.0470286 + 0.312015i
\(408\) 1.35363e8 + 6.51876e7i 1.99306 + 0.959808i
\(409\) −1.82499e7 + 3.78963e7i −0.266741 + 0.553894i −0.990718 0.135930i \(-0.956598\pi\)
0.723977 + 0.689824i \(0.242312\pi\)
\(410\) −2.74252e7 + 4.13368e6i −0.397922 + 0.0599770i
\(411\) 3.61747e6 + 9.21716e6i 0.0521050 + 0.132761i
\(412\) 9.45467e6 + 1.26164e8i 0.135193 + 1.80403i
\(413\) 1.00858e8 + 1.08699e8i 1.43173 + 1.54304i
\(414\) −5.22593e7 + 1.19278e7i −0.736483 + 0.168097i
\(415\) −1.97308e7 + 1.30906e8i −0.276059 + 1.83153i
\(416\) 2.28546e7 3.35215e7i 0.317463 0.465633i
\(417\) 6.90471e6 + 2.23845e7i 0.0952220 + 0.308702i
\(418\) 1.78791e6 2.38580e7i 0.0244803 0.326667i
\(419\) −7.00364e6 + 5.58522e6i −0.0952098 + 0.0759273i −0.669938 0.742417i \(-0.733679\pi\)
0.574728 + 0.818344i \(0.305108\pi\)
\(420\) 1.09609e8 3.55344e8i 1.47944 4.79624i
\(421\) −3.14723e7 1.23520e7i −0.421776 0.165535i 0.144954 0.989438i \(-0.453697\pi\)
−0.566730 + 0.823903i \(0.691792\pi\)
\(422\) −2.63997e7 + 1.15665e8i −0.351287 + 1.53909i
\(423\) 1.83556e7 + 3.17929e7i 0.242520 + 0.420057i
\(424\) −1.64745e8 9.51158e7i −2.16130 1.24783i
\(425\) 1.07705e8 + 9.99354e7i 1.40303 + 1.30183i
\(426\) 1.77451e7 + 1.41513e7i 0.229536 + 0.183049i
\(427\) 9.67104e7 6.59361e7i 1.24219 0.846914i
\(428\) 8.36099e7 4.02644e7i 1.06641 0.513558i
\(429\) 1.94786e7i 0.246710i
\(430\) −2.15182e8 + 8.01142e7i −2.70645 + 1.00764i
\(431\) −1.40018e8 −1.74884 −0.874421 0.485168i \(-0.838759\pi\)
−0.874421 + 0.485168i \(0.838759\pi\)
\(432\) −7.91462e7 1.64349e8i −0.981700 2.03852i
\(433\) 4.61420e7 + 6.76779e7i 0.568372 + 0.833648i 0.997578 0.0695583i \(-0.0221590\pi\)
−0.429206 + 0.903207i \(0.641207\pi\)
\(434\) −1.63589e8 + 2.05134e8i −2.00118 + 2.50940i
\(435\) −7.12503e7 + 7.67895e7i −0.865603 + 0.932898i
\(436\) 4.78051e7 8.28009e7i 0.576786 0.999023i
\(437\) 1.19347e7 6.89048e6i 0.143010 0.0825667i
\(438\) 1.43669e8 + 3.27914e7i 1.70978 + 0.390246i
\(439\) 2.30659e7 5.87709e7i 0.272632 0.694654i −0.727333 0.686284i \(-0.759241\pi\)
0.999965 0.00836956i \(-0.00266415\pi\)
\(440\) 2.82679e8 + 8.71950e7i 3.31845 + 1.02361i
\(441\) −7.17682e7 8.99945e7i −0.836790 1.04930i
\(442\) −7.81346e7 5.85538e6i −0.904850 0.0678091i
\(443\) 5.87929e7 1.81352e7i 0.676260 0.208598i 0.0624447 0.998048i \(-0.480110\pi\)
0.613815 + 0.789450i \(0.289634\pi\)
\(444\) −4.20489e7 2.86685e7i −0.480403 0.327533i
\(445\) 1.74626e7 + 2.63206e6i 0.198165 + 0.0298686i
\(446\) −5.75802e7 2.52275e8i −0.649036 2.84361i
\(447\) 4.16971e7 3.86892e7i 0.466856 0.433179i
\(448\) 8.90794e7 6.67558e6i 0.990702 0.0742429i
\(449\) 6.99008e7 2.74341e7i 0.772224 0.303076i 0.0536810 0.998558i \(-0.482905\pi\)
0.718543 + 0.695483i \(0.244809\pi\)
\(450\) −1.85775e7 1.23253e8i −0.203868 1.35258i
\(451\) 1.03402e7 + 4.97956e6i 0.112719 + 0.0542827i
\(452\) 1.93058e7 4.00889e7i 0.209061 0.434119i
\(453\) −7.40373e6 + 1.11593e6i −0.0796445 + 0.0120045i
\(454\) 5.50163e7 + 1.40179e8i 0.587927 + 1.49801i
\(455\) 8.29740e6 + 1.10721e8i 0.0880862 + 1.17543i
\(456\) 2.22883e7 + 2.40210e7i 0.235061 + 0.253336i
\(457\) 9.90547e7 2.26086e7i 1.03783 0.236878i 0.330533 0.943794i \(-0.392771\pi\)
0.707297 + 0.706916i \(0.249914\pi\)
\(458\) 3.63198e7 2.40966e8i 0.378048 2.50818i
\(459\) −7.38474e7 + 1.08314e8i −0.763655 + 1.12008i
\(460\) 8.77257e7 + 2.84400e8i 0.901267 + 2.92184i
\(461\) −1.95551e6 + 2.60945e7i −0.0199599 + 0.266346i 0.978291 + 0.207234i \(0.0664460\pi\)
−0.998251 + 0.0591123i \(0.981173\pi\)
\(462\) −1.71735e8 + 1.36954e8i −1.74153 + 1.38883i
\(463\) 2.63702e7 8.54900e7i 0.265687 0.861336i −0.720177 0.693790i \(-0.755940\pi\)
0.985864 0.167546i \(-0.0535842\pi\)
\(464\) −2.25853e8 8.86410e7i −2.26086 0.887320i
\(465\) 2.28797e7 1.00243e8i 0.227558 0.996997i
\(466\) 4.35123e7 + 7.53656e7i 0.429986 + 0.744758i
\(467\) −8.65404e7 4.99641e7i −0.849705 0.490578i 0.0108460 0.999941i \(-0.496548\pi\)
−0.860551 + 0.509363i \(0.829881\pi\)
\(468\) 3.41352e7 + 3.16728e7i 0.333016 + 0.308993i
\(469\) 2.86568e7 + 2.28530e7i 0.277785 + 0.221526i
\(470\) 2.40407e8 1.63907e8i 2.31555 1.57872i
\(471\) −5.49097e7 + 2.64431e7i −0.525517 + 0.253076i
\(472\) 2.82195e8i 2.68363i
\(473\) 9.22450e7 + 2.27685e7i 0.871685 + 0.215155i
\(474\) −6.16949e7 −0.579314
\(475\) 1.39040e7 + 2.88719e7i 0.129735 + 0.269398i
\(476\) −3.48684e8 5.11426e8i −3.23304 4.74200i
\(477\) 3.44888e7 4.32476e7i 0.317777 0.398480i
\(478\) 1.81043e8 1.95118e8i 1.65767 1.78654i
\(479\) −2.27734e7 + 3.94446e7i −0.207215 + 0.358907i −0.950836 0.309694i \(-0.899773\pi\)
0.743621 + 0.668601i \(0.233107\pi\)
\(480\) −1.55271e8 + 8.96457e7i −1.40400 + 0.810598i
\(481\) 1.48144e7 + 3.38128e6i 0.133121 + 0.0303841i
\(482\) −1.10230e8 + 2.80861e8i −0.984368 + 2.50813i
\(483\) −1.20903e8 3.72937e7i −1.07299 0.330974i
\(484\) 3.20606e7 + 4.02028e7i 0.282772 + 0.354585i
\(485\) −2.07728e8 1.55671e7i −1.82084 0.136453i
\(486\) 1.77129e8 5.46371e7i 1.54305 0.475969i
\(487\) 1.43430e8 + 9.77890e7i 1.24181 + 0.846648i 0.992556 0.121791i \(-0.0388638\pi\)
0.249249 + 0.968439i \(0.419816\pi\)
\(488\) −2.20266e8 3.31998e7i −1.89534 0.285677i
\(489\) −2.88080e7 1.26216e8i −0.246369 1.07941i
\(490\) −6.68777e8 + 6.20534e8i −5.68451 + 5.27445i
\(491\) 6.83585e7 5.12276e6i 0.577495 0.0432773i 0.217219 0.976123i \(-0.430302\pi\)
0.360276 + 0.932846i \(0.382682\pi\)
\(492\) −2.55577e7 + 1.00307e7i −0.214598 + 0.0842236i
\(493\) 2.59878e7 + 1.72417e8i 0.216884 + 1.43893i
\(494\) −1.53969e7 7.41478e6i −0.127718 0.0615060i
\(495\) −3.73224e7 + 7.75007e7i −0.307718 + 0.638984i
\(496\) 2.35489e8 3.54943e7i 1.92986 0.290880i
\(497\) −1.95588e7 4.98351e7i −0.159321 0.405944i
\(498\) 1.39799e7 + 1.86549e8i 0.113192 + 1.51044i
\(499\) −3.15581e7 3.40115e7i −0.253986 0.273731i 0.593169 0.805078i \(-0.297877\pi\)
−0.847155 + 0.531347i \(0.821686\pi\)
\(500\) −2.24183e8 + 5.11683e7i −1.79346 + 0.409347i
\(501\) −977509. + 6.48535e6i −0.00777334 + 0.0515727i
\(502\) 1.02067e8 1.49705e8i 0.806816 1.18338i
\(503\) −510030. 1.65348e6i −0.00400767 0.0129925i 0.953547 0.301245i \(-0.0974021\pi\)
−0.957555 + 0.288252i \(0.906926\pi\)
\(504\) −2.24669e7 + 2.99800e8i −0.175490 + 2.34174i
\(505\) 2.82569e8 2.25341e8i 2.19407 1.74971i
\(506\) 5.18187e7 1.67992e8i 0.399977 1.29669i
\(507\) −7.28461e7 2.85900e7i −0.558962 0.219376i
\(508\) −1.85953e7 + 8.14715e7i −0.141845 + 0.621462i
\(509\) 9.88336e7 + 1.71185e8i 0.749465 + 1.29811i 0.948080 + 0.318033i \(0.103022\pi\)
−0.198615 + 0.980078i \(0.563644\pi\)
\(510\) 2.99869e8 + 1.73129e8i 2.26059 + 1.30515i
\(511\) −2.54802e8 2.36422e8i −1.90959 1.77184i
\(512\) 2.23149e8 + 1.77956e8i 1.66259 + 1.32587i
\(513\) −2.36239e7 + 1.61065e7i −0.174984 + 0.119302i
\(514\) 8.84521e7 4.25963e7i 0.651356 0.313677i
\(515\) 1.66937e8i 1.22217i
\(516\) −1.90027e8 + 1.24719e8i −1.38314 + 0.907787i
\(517\) −1.20402e8 −0.871287
\(518\) 7.43482e7 + 1.54386e8i 0.534910 + 1.11075i
\(519\) 7.35438e7 + 1.07869e8i 0.526070 + 0.771603i
\(520\) 1.31745e8 1.65203e8i 0.936965 1.17492i
\(521\) −9.84645e7 + 1.06119e8i −0.696252 + 0.750381i −0.977886 0.209141i \(-0.932933\pi\)
0.281634 + 0.959522i \(0.409124\pi\)
\(522\) 7.39616e7 1.28105e8i 0.519990 0.900648i
\(523\) −1.42603e8 + 8.23318e7i −0.996835 + 0.575523i −0.907310 0.420462i \(-0.861868\pi\)
−0.0895245 + 0.995985i \(0.528535\pi\)
\(524\) 2.07361e8 + 4.73288e7i 1.44123 + 0.328951i
\(525\) 1.07488e8 2.73874e8i 0.742814 1.89266i
\(526\) 1.69668e8 + 5.23358e7i 1.16585 + 0.359618i
\(527\) −1.06709e8 1.33809e8i −0.729071 0.914226i
\(528\) 1.98816e8 + 1.48992e7i 1.35067 + 0.101219i
\(529\) −4.46942e7 + 1.37863e7i −0.301915 + 0.0931283i
\(530\) −3.62241e8 2.46972e8i −2.43315 1.65890i
\(531\) 8.11404e7 + 1.22299e7i 0.541943 + 0.0816848i
\(532\) −3.00409e7 1.31618e8i −0.199516 0.874137i
\(533\) 6.00934e6 5.57585e6i 0.0396867 0.0368239i
\(534\) 2.48853e7 1.86489e6i 0.163425 0.0122470i
\(535\) 1.13983e8 4.47351e7i 0.744355 0.292138i
\(536\) −1.03964e7 6.89754e7i −0.0675130 0.447919i
\(537\) −8.25749e7 3.97660e7i −0.533243 0.256796i
\(538\) −1.36857e7 + 2.84187e7i −0.0878864 + 0.182498i
\(539\) 3.73301e8 5.62660e7i 2.38393 0.359319i
\(540\) −2.25595e8 5.74807e8i −1.43268 3.65040i
\(541\) −1.83254e6 2.44535e7i −0.0115734 0.154436i −0.999996 0.00271253i \(-0.999137\pi\)
0.988423 0.151724i \(-0.0484825\pi\)
\(542\) −1.43257e8 1.54394e8i −0.899742 0.969691i
\(543\) 1.55285e8 3.54428e7i 0.969907 0.221375i
\(544\) −4.44796e7 + 2.95103e8i −0.276289 + 1.83306i
\(545\) 7.10661e7 1.04235e8i 0.439008 0.643907i
\(546\) 4.62467e7 + 1.49928e8i 0.284120 + 0.921096i
\(547\) −122116. + 1.62953e6i −0.000746124 + 0.00995634i −0.997564 0.0697510i \(-0.977780\pi\)
0.996818 + 0.0797073i \(0.0253986\pi\)
\(548\) −6.06964e7 + 4.84037e7i −0.368825 + 0.294129i
\(549\) 1.90921e7 6.18949e7i 0.115381 0.374057i
\(550\) 3.80541e8 + 1.49351e8i 2.28725 + 0.897680i
\(551\) −8.46243e6 + 3.70763e7i −0.0505872 + 0.221637i
\(552\) 1.20393e8 + 2.08527e8i 0.715788 + 1.23978i
\(553\) 1.26026e8 + 7.27609e7i 0.745218 + 0.430252i
\(554\) −2.95864e8 2.74522e8i −1.74006 1.61454i
\(555\) −5.25007e7 4.18679e7i −0.307105 0.244908i
\(556\) −1.51751e8 + 1.03462e8i −0.882894 + 0.601947i
\(557\) −2.59888e8 + 1.25156e8i −1.50391 + 0.724243i −0.990958 0.134176i \(-0.957161\pi\)
−0.512949 + 0.858419i \(0.671447\pi\)
\(558\) 1.45194e8i 0.835692i
\(559\) 3.92113e7 5.53933e7i 0.224479 0.317119i
\(560\) 1.13647e9 6.47131
\(561\) −6.21677e7 1.29093e8i −0.352108 0.731160i
\(562\) −2.17101e7 3.18429e7i −0.122307 0.179392i
\(563\) 5.31618e7 6.66627e7i 0.297902 0.373558i −0.610242 0.792215i \(-0.708928\pi\)
0.908144 + 0.418657i \(0.137499\pi\)
\(564\) 1.95914e8 2.11145e8i 1.09201 1.17691i
\(565\) 2.93554e7 5.08450e7i 0.162758 0.281905i
\(566\) −5.22433e8 + 3.01627e8i −2.88125 + 1.66349i
\(567\) 8.54076e7 + 1.94937e7i 0.468541 + 0.106941i
\(568\) −3.72221e7 + 9.48403e7i −0.203121 + 0.517545i
\(569\) 1.84322e8 + 5.68558e7i 1.00055 + 0.308630i 0.751409 0.659837i \(-0.229375\pi\)
0.249144 + 0.968466i \(0.419851\pi\)
\(570\) 4.70864e7 + 5.90445e7i 0.254256 + 0.318827i
\(571\) 1.03215e8 + 7.73492e6i 0.554416 + 0.0415477i 0.348993 0.937125i \(-0.386524\pi\)
0.205423 + 0.978673i \(0.434143\pi\)
\(572\) −1.45937e8 + 4.50156e7i −0.779789 + 0.240533i
\(573\) 1.73808e8 + 1.18500e8i 0.923861 + 0.629878i
\(574\) 9.14114e7 + 1.37781e7i 0.483353 + 0.0728538i
\(575\) 5.23975e7 + 2.29569e8i 0.275618 + 1.20756i
\(576\) 3.62370e7 3.36230e7i 0.189620 0.175942i
\(577\) −2.32519e7 + 1.74249e6i −0.121041 + 0.00907075i −0.135113 0.990830i \(-0.543140\pi\)
0.0140720 + 0.999901i \(0.495521\pi\)
\(578\) 2.08042e8 8.16504e7i 1.07738 0.422839i
\(579\) 4.87308e6 + 3.23308e7i 0.0251055 + 0.166564i
\(580\) −7.39981e8 3.56356e8i −3.79259 1.82642i
\(581\) 1.91452e8 3.97555e8i 0.976185 2.02707i
\(582\) −2.91076e8 + 4.38726e7i −1.47651 + 0.222549i
\(583\) 6.62797e7 + 1.68878e8i 0.334484 + 0.852251i
\(584\) 4.94335e7 + 6.59645e8i 0.248189 + 3.31186i
\(585\) 4.17916e7 + 4.50407e7i 0.208748 + 0.224977i
\(586\) −2.12940e8 + 4.86022e7i −1.05819 + 0.241525i
\(587\) −3.35647e6 + 2.22687e7i −0.0165947 + 0.110098i −0.995595 0.0937619i \(-0.970111\pi\)
0.979000 + 0.203860i \(0.0653488\pi\)
\(588\) −5.08751e8 + 7.46200e8i −2.50249 + 3.67049i
\(589\) −1.10027e7 3.56698e7i −0.0538459 0.174564i
\(590\) 4.86020e7 6.48549e8i 0.236645 3.15781i
\(591\) 4.07986e7 3.25358e7i 0.197644 0.157616i
\(592\) 4.58439e7 1.48622e8i 0.220962 0.716340i
\(593\) −8.42996e7 3.30852e7i −0.404261 0.158661i 0.154494 0.987994i \(-0.450625\pi\)
−0.558755 + 0.829333i \(0.688721\pi\)
\(594\) −8.11637e7 + 3.55601e8i −0.387260 + 1.69670i
\(595\) −4.08366e8 7.07311e8i −1.93865 3.35784i
\(596\) 3.86229e8 + 2.22989e8i 1.82434 + 1.05328i
\(597\) 7.69509e7 + 7.14000e7i 0.361652 + 0.335564i
\(598\) −9.81776e7 7.82940e7i −0.459102 0.366121i
\(599\) −2.23609e8 + 1.52454e8i −1.04042 + 0.709347i −0.957859 0.287239i \(-0.907263\pi\)
−0.0825619 + 0.996586i \(0.526310\pi\)
\(600\) −5.04461e8 + 2.42935e8i −2.33547 + 1.12470i
\(601\) 2.42174e8i 1.11559i 0.829979 + 0.557795i \(0.188352\pi\)
−0.829979 + 0.557795i \(0.811648\pi\)
\(602\) 7.64072e8 4.37602e7i 3.50223 0.200581i
\(603\) 2.02833e7 0.0925095
\(604\) −2.54710e7 5.28910e7i −0.115594 0.240033i
\(605\) 3.82209e7 + 5.60598e7i 0.172598 + 0.253154i
\(606\) 3.18429e8 3.99298e8i 1.43085 1.79423i
\(607\) 85324.9 91958.4i 0.000381514 0.000411174i −0.732861 0.680378i \(-0.761815\pi\)
0.733243 + 0.679967i \(0.238006\pi\)
\(608\) −3.25452e7 + 5.63699e7i −0.144802 + 0.250805i
\(609\) 3.02377e8 1.74578e8i 1.33874 0.772924i
\(610\) −5.00504e8 1.14237e8i −2.20505 0.503288i
\(611\) −3.14200e7 + 8.00568e7i −0.137747 + 0.350974i
\(612\) −3.27314e8 1.00963e8i −1.42794 0.440461i
\(613\) −2.14183e8 2.68577e8i −0.929831 1.16597i −0.985865 0.167543i \(-0.946417\pi\)
0.0560335 0.998429i \(-0.482155\pi\)
\(614\) −2.24623e8 1.68331e7i −0.970394 0.0727210i
\(615\) −3.46176e7 + 1.06781e7i −0.148824 + 0.0459060i
\(616\) −8.14680e8 5.55439e8i −3.48534 2.37626i
\(617\) −2.58494e8 3.89617e7i −1.10051 0.165875i −0.426421 0.904525i \(-0.640226\pi\)
−0.674090 + 0.738649i \(0.735464\pi\)
\(618\) 5.24925e7 + 2.29985e8i 0.222398 + 0.974391i
\(619\) 3.05791e8 2.83733e8i 1.28930 1.19629i 0.320834 0.947135i \(-0.396037\pi\)
0.968463 0.249158i \(-0.0801538\pi\)
\(620\) 8.03910e8 6.02447e7i 3.37312 0.252781i
\(621\) −1.95574e8 + 7.67571e7i −0.816650 + 0.320511i
\(622\) 9.77920e7 + 6.48808e8i 0.406380 + 2.69615i
\(623\) −5.30331e7 2.55394e7i −0.219322 0.105620i
\(624\) 6.17897e7 1.28308e8i 0.254309 0.528079i
\(625\) 6.15155e7 9.27198e6i 0.251968 0.0379780i
\(626\) 7.67438e7 + 1.95540e8i 0.312839 + 0.797100i
\(627\) −2.33535e6 3.11631e7i −0.00947435 0.126426i
\(628\) −3.25014e8 3.50282e8i −1.31227 1.41429i
\(629\) −1.08972e8 + 2.48722e7i −0.437889 + 0.0999454i
\(630\) −1.03268e8 + 6.85139e8i −0.412995 + 2.74004i
\(631\) −2.41994e8 + 3.54940e8i −0.963201 + 1.41276i −0.0529977 + 0.998595i \(0.516878\pi\)
−0.910203 + 0.414162i \(0.864075\pi\)
\(632\) −8.16296e7 2.64637e8i −0.323367 1.04833i
\(633\) −1.15806e7 + 1.54532e8i −0.0456583 + 0.609267i
\(634\) 5.29968e8 4.22635e8i 2.07961 1.65843i
\(635\) −3.25010e7 + 1.05366e8i −0.126933 + 0.411508i
\(636\) −4.04004e8 1.58560e8i −1.57042 0.616343i
\(637\) 6.00043e7 2.62896e8i 0.232147 1.01710i
\(638\) 2.42572e8 + 4.20146e8i 0.934067 + 1.61785i
\(639\) −2.56566e7 1.48128e7i −0.0983323 0.0567722i
\(640\) 1.53296e8 + 1.42238e8i 0.584779 + 0.542596i
\(641\) −1.76398e8 1.40673e8i −0.669762 0.534117i 0.228519 0.973539i \(-0.426612\pi\)
−0.898281 + 0.439422i \(0.855183\pi\)
\(642\) 1.42965e8 9.74716e7i 0.540286 0.368361i
\(643\) 1.32612e8 6.38626e7i 0.498827 0.240223i −0.167514 0.985870i \(-0.553574\pi\)
0.666341 + 0.745647i \(0.267860\pi\)
\(644\) 9.92012e8i 3.71415i
\(645\) −2.62333e8 + 1.45367e8i −0.977628 + 0.541733i
\(646\) 1.25707e8 0.466295
\(647\) 4.18740e7 + 8.69524e7i 0.154608 + 0.321047i 0.963858 0.266418i \(-0.0858402\pi\)
−0.809249 + 0.587465i \(0.800126\pi\)
\(648\) −9.39155e7 1.37749e8i −0.345153 0.506247i
\(649\) −1.67795e8 + 2.10408e8i −0.613825 + 0.769712i
\(650\) 1.98612e8 2.14052e8i 0.723210 0.779435i
\(651\) −1.71357e8 + 2.96799e8i −0.621096 + 1.07577i
\(652\) 8.79055e8 5.07523e8i 3.17156 1.83110i
\(653\) −1.53851e8 3.51154e7i −0.552535 0.126112i −0.0628675 0.998022i \(-0.520025\pi\)
−0.489667 + 0.871909i \(0.662882\pi\)
\(654\) 6.51295e7 1.65947e8i 0.232833 0.593249i
\(655\) 2.68177e8 + 8.27215e7i 0.954326 + 0.294371i
\(656\) −5.23156e7 6.56017e7i −0.185319 0.232383i
\(657\) −1.91812e8 1.43743e7i −0.676363 0.0506864i
\(658\) −9.26739e8 + 2.85861e8i −3.25297 + 1.00341i
\(659\) 4.70991e8 + 3.21116e8i 1.64572 + 1.12203i 0.873749 + 0.486377i \(0.161682\pi\)
0.771972 + 0.635657i \(0.219271\pi\)
\(660\) 6.67367e8 + 1.00589e8i 2.32131 + 0.349881i
\(661\) 8.16064e7 + 3.57541e8i 0.282566 + 1.23800i 0.894491 + 0.447087i \(0.147538\pi\)
−0.611924 + 0.790916i \(0.709604\pi\)
\(662\) −1.36583e8 + 1.26730e8i −0.470784 + 0.436824i
\(663\) −1.02059e8 + 7.64824e6i −0.350194 + 0.0262434i
\(664\) −7.81693e8 + 3.06792e8i −2.67013 + 1.04795i
\(665\) −2.65494e7 1.76144e8i −0.0902795 0.598966i
\(666\) 8.54339e7 + 4.11428e7i 0.289206 + 0.139274i
\(667\) −1.21247e8 + 2.51773e8i −0.408597 + 0.848460i
\(668\) −5.08483e7 + 7.66415e6i −0.170587 + 0.0257119i
\(669\) −1.23483e8 3.14629e8i −0.412409 1.05080i
\(670\) −1.20137e7 1.60312e8i −0.0399441 0.533017i
\(671\) 1.44492e8 + 1.55726e8i 0.478274 + 0.515457i
\(672\) 5.82617e8 1.32979e8i 1.91989 0.438201i
\(673\) −6.60601e7 + 4.38280e8i −0.216717 + 1.43783i 0.570575 + 0.821246i \(0.306720\pi\)
−0.787292 + 0.616580i \(0.788518\pi\)
\(674\) 4.05089e8 5.94156e8i 1.32303 1.94053i
\(675\) −1.44002e8 4.66842e8i −0.468227 1.51795i
\(676\) 4.58516e7 6.11847e8i 0.148427 1.98063i
\(677\) −6.53874e7 + 5.21447e7i −0.210731 + 0.168052i −0.723167 0.690673i \(-0.757314\pi\)
0.512436 + 0.858725i \(0.328743\pi\)
\(678\) 2.44541e7 7.92782e7i 0.0784625 0.254369i
\(679\) 6.46329e8 + 2.53666e8i 2.06464 + 0.810312i
\(680\) −3.45866e8 + 1.51534e9i −1.09997 + 4.81929i
\(681\) 9.83488e7 + 1.70345e8i 0.311407 + 0.539372i
\(682\) −4.12395e8 2.38096e8i −1.30005 0.750585i
\(683\) 1.12458e8 + 1.04346e8i 0.352962 + 0.327501i 0.836648 0.547741i \(-0.184512\pi\)
−0.483686 + 0.875242i \(0.660702\pi\)
\(684\) −5.84089e7 4.65795e7i −0.182520 0.145555i
\(685\) −8.46365e7 + 5.77042e7i −0.263321 + 0.179529i
\(686\) 1.71940e9 8.28021e8i 5.32605 2.56489i
\(687\) 3.18302e8i 0.981679i
\(688\) −5.35401e8 4.42596e8i −1.64405 1.35907i
\(689\) 1.29586e8 0.396186
\(690\) 2.40776e8 + 4.99978e8i 0.732937 + 1.52196i
\(691\) −3.39236e6 4.97567e6i −0.0102818 0.0150806i 0.821063 0.570837i \(-0.193381\pi\)
−0.831345 + 0.555756i \(0.812429\pi\)
\(692\) −6.38209e8 + 8.00289e8i −1.92595 + 2.41506i
\(693\) 1.95014e8 2.10175e8i 0.585958 0.631513i
\(694\) −3.94441e8 + 6.83192e8i −1.18006 + 2.04392i
\(695\) −2.09875e8 + 1.21171e8i −0.625182 + 0.360949i
\(696\) −6.47812e8 1.47859e8i −1.92142 0.438551i
\(697\) −2.20305e7 + 5.61327e7i −0.0650617 + 0.165775i
\(698\) −5.28213e8 1.62932e8i −1.55326 0.479116i
\(699\) 7.08725e7 + 8.88713e7i 0.207514 + 0.260214i
\(700\) 2.30031e9 + 1.72385e8i 6.70645 + 0.502579i
\(701\) 5.70152e8 1.75869e8i 1.65515 0.510545i 0.680209 0.733019i \(-0.261889\pi\)
0.974939 + 0.222473i \(0.0714130\pi\)
\(702\) 2.15264e8 + 1.46764e8i 0.622242 + 0.424237i
\(703\) −2.41063e7 3.63344e6i −0.0693849 0.0104581i
\(704\) 3.60763e7 + 1.58061e8i 0.103396 + 0.453008i
\(705\) 2.78601e8 2.58504e8i 0.795090 0.737735i
\(706\) 2.54854e8 1.90986e7i 0.724231 0.0542736i
\(707\) −1.12138e9 + 4.40110e8i −3.17318 + 1.24538i
\(708\) −9.59559e7 6.36626e8i −0.270378 1.79384i
\(709\) 2.03454e8 + 9.79783e7i 0.570857 + 0.274910i 0.696964 0.717106i \(-0.254534\pi\)
−0.126106 + 0.992017i \(0.540248\pi\)
\(710\) −1.01879e8 + 2.11554e8i −0.284649 + 0.591080i
\(711\) 7.96295e7 1.20022e7i 0.221547 0.0333928i
\(712\) 4.09254e7 + 1.04276e8i 0.113384 + 0.288899i
\(713\) −2.04978e7 2.73524e8i −0.0565508 0.754618i
\(714\) −7.85003e8 8.46032e8i −2.15664 2.32430i
\(715\) −1.96461e8 + 4.48410e7i −0.537475 + 0.122675i
\(716\) 1.07100e8 7.10565e8i 0.291778 1.93582i
\(717\) 1.95850e8 2.87259e8i 0.531332 0.779321i
\(718\) −3.88667e8 1.26003e9i −1.05004 3.40414i
\(719\) −1.39653e7 + 1.86353e8i −0.0375718 + 0.501361i 0.946395 + 0.323011i \(0.104695\pi\)
−0.983967 + 0.178350i \(0.942924\pi\)
\(720\) 4.91692e8 3.92111e8i 1.31733 1.05054i
\(721\) 1.64009e8 5.31703e8i 0.437583 1.41861i
\(722\) −6.14700e8 2.41252e8i −1.63325 0.641002i
\(723\) −8.76955e7 + 3.84219e8i −0.232040 + 1.01663i
\(724\) 6.24410e8 + 1.08151e9i 1.64534 + 2.84980i
\(725\) −5.62750e8 3.24904e8i −1.47673 0.852592i
\(726\) 7.02834e7 + 6.52135e7i 0.183672 + 0.170423i
\(727\) −2.26513e8 1.80638e8i −0.589508 0.470117i 0.282729 0.959200i \(-0.408760\pi\)
−0.872237 + 0.489083i \(0.837332\pi\)
\(728\) −5.81917e8 + 3.96744e8i −1.50823 + 1.02829i
\(729\) 3.05529e8 1.47135e8i 0.788623 0.379781i
\(730\) 1.52453e9i 3.91892i
\(731\) −8.30762e7 + 4.92260e8i −0.212679 + 1.26021i
\(732\) −5.08204e8 −1.29570
\(733\) 2.20560e8 + 4.57997e8i 0.560034 + 1.16292i 0.968238 + 0.250032i \(0.0804412\pi\)
−0.408203 + 0.912891i \(0.633845\pi\)
\(734\) −4.64116e8 6.80733e8i −1.17365 1.72143i
\(735\) −7.42988e8 + 9.31678e8i −1.87120 + 2.34641i
\(736\) −3.25320e8 + 3.50611e8i −0.815975 + 0.879412i
\(737\) −3.32615e7 + 5.76107e7i −0.0830883 + 0.143913i
\(738\) 4.43030e7 2.55783e7i 0.110221 0.0636360i
\(739\) −2.56617e8 5.85711e7i −0.635846 0.145128i −0.107566 0.994198i \(-0.534306\pi\)
−0.528280 + 0.849070i \(0.677163\pi\)
\(740\) 1.92351e8 4.90101e8i 0.474677 1.20946i
\(741\) −2.13302e7 6.57949e6i −0.0524252 0.0161710i
\(742\) 9.11113e8 + 1.14250e9i 2.23029 + 2.79669i
\(743\) −3.38428e8 2.53617e7i −0.825087 0.0618318i −0.344508 0.938783i \(-0.611954\pi\)
−0.480579 + 0.876951i \(0.659573\pi\)
\(744\) 6.23237e8 1.92243e8i 1.51333 0.466801i
\(745\) 4.86208e8 + 3.31491e8i 1.17585 + 0.801684i
\(746\) 4.11229e8 + 6.19828e7i 0.990529 + 0.149298i
\(747\) −5.43353e7 2.38058e8i −0.130353 0.571113i
\(748\) 8.23511e8 7.64107e8i 1.96773 1.82578i
\(749\) −4.06992e8 + 3.04998e7i −0.968590 + 0.0725858i
\(750\) −3.99113e8 + 1.56640e8i −0.946047 + 0.371296i
\(751\) 7.32654e7 + 4.86084e8i 0.172973 + 1.14760i 0.891805 + 0.452419i \(0.149439\pi\)
−0.718832 + 0.695184i \(0.755323\pi\)
\(752\) 7.93098e8 + 3.81936e8i 1.86498 + 0.898126i
\(753\) 1.02686e8 2.13229e8i 0.240506 0.499415i
\(754\) 3.42662e8 5.16480e7i 0.799378 0.120487i
\(755\) −2.82991e7 7.21050e7i −0.0657555 0.167542i
\(756\) 1.53808e8 + 2.05242e9i 0.355969 + 4.75008i
\(757\) −3.20188e8 3.45080e8i −0.738103 0.795485i 0.246713 0.969089i \(-0.420649\pi\)
−0.984816 + 0.173603i \(0.944459\pi\)
\(758\) 6.54140e8 1.49303e8i 1.50198 0.342816i
\(759\) 3.42248e7 2.27067e8i 0.0782736 0.519312i
\(760\) −1.90967e8 + 2.80097e8i −0.435028 + 0.638069i
\(761\) 1.14347e8 + 3.70702e8i 0.259459 + 0.841146i 0.987773 + 0.155902i \(0.0498283\pi\)
−0.728313 + 0.685244i \(0.759695\pi\)
\(762\) −1.16440e7 + 1.55379e8i −0.0263172 + 0.351178i
\(763\) −3.28754e8 + 2.62173e8i −0.740113 + 0.590220i
\(764\) −4.86149e8 + 1.57606e9i −1.09016 + 3.53421i
\(765\) −4.20721e8 1.65121e8i −0.939745 0.368823i
\(766\) 6.96578e7 3.05191e8i 0.154983 0.679024i
\(767\) 9.61155e7 + 1.66477e8i 0.213014 + 0.368950i
\(768\) 3.99502e8 + 2.30652e8i 0.881932 + 0.509184i
\(769\) 4.92637e7 + 4.57100e7i 0.108330 + 0.100515i 0.732478 0.680790i \(-0.238364\pi\)
−0.624149 + 0.781306i \(0.714554\pi\)
\(770\) −1.77666e9 1.41684e9i −3.89163 3.10347i
\(771\) 1.05952e8 7.22370e7i 0.231178 0.157615i
\(772\) −2.30966e8 + 1.11227e8i −0.501990 + 0.241746i
\(773\) 6.51427e8i 1.41035i −0.709033 0.705175i \(-0.750868\pi\)
0.709033 0.705175i \(-0.249132\pi\)
\(774\) 3.15478e8 2.82558e8i 0.680371 0.609376i
\(775\) 6.37820e8 1.37023
\(776\) −5.73316e8 1.19050e9i −1.22690 2.54768i
\(777\) 1.26084e8 + 1.84931e8i 0.268779 + 0.394226i
\(778\) 7.26100e8 9.10500e8i 1.54190 1.93349i
\(779\) −8.94560e6 + 9.64107e6i −0.0189233 + 0.0203945i
\(780\) 2.41039e8 4.17492e8i 0.507929 0.879759i
\(781\) 8.41459e7 4.85816e7i 0.176636 0.101981i
\(782\) 9.00544e8 + 2.05543e8i 1.88315 + 0.429817i
\(783\) 2.11818e8 5.39704e8i 0.441243 1.12427i
\(784\) −2.63745e9 8.13547e8i −5.47314 1.68824i
\(785\) −3.93111e8 4.92945e8i −0.812654 1.01904i
\(786\) 3.95470e8 + 2.96364e7i 0.814415 + 0.0610320i
\(787\) −9.56767e7 + 2.95124e7i −0.196283 + 0.0605452i −0.391338 0.920247i \(-0.627988\pi\)
0.195055 + 0.980792i \(0.437511\pi\)
\(788\) 3.38050e8 + 2.30479e8i 0.690879 + 0.471034i
\(789\) 2.29332e8 + 3.45663e7i 0.466911 + 0.0703756i
\(790\) −1.42025e8 6.22254e8i −0.288061 1.26208i
\(791\) −1.43451e8 + 1.33103e8i −0.289850 + 0.268942i
\(792\) −5.44113e8 + 4.07756e7i −1.09525 + 0.0820777i
\(793\) 1.41251e8 5.54368e7i 0.283251 0.111168i
\(794\) −1.31510e8 8.72509e8i −0.262722 1.74304i
\(795\) −5.15950e8 2.48469e8i −1.02685 0.494504i
\(796\) −3.57105e8 + 7.41535e8i −0.708037 + 1.47025i
\(797\) −5.96104e8 + 8.98482e7i −1.17746 + 0.177474i −0.708478 0.705733i \(-0.750618\pi\)
−0.468984 + 0.883207i \(0.655380\pi\)
\(798\) −9.19636e7 2.34319e8i −0.180970 0.461105i
\(799\) −4.72755e7 6.30848e8i −0.0926821 1.23676i
\(800\) −7.56478e8 8.15289e8i −1.47750 1.59236i
\(801\) −3.17565e7 + 7.24822e6i −0.0617925 + 0.0141037i
\(802\) 1.90038e8 1.26082e9i 0.368398 2.44416i
\(803\) 3.55370e8 5.21233e8i 0.686333 1.00666i
\(804\) −4.69080e7 1.52072e8i −0.0902565 0.292604i
\(805\) 9.78172e7 1.30528e9i 0.187511 2.50216i
\(806\) −2.65932e8 + 2.12074e8i −0.507885 + 0.405025i
\(807\) −1.21440e7 + 3.93700e7i −0.0231069 + 0.0749108i
\(808\) 2.13408e9 + 8.37565e8i 4.04554 + 1.58776i
\(809\) −7.93642e6 + 3.47717e7i −0.0149892 + 0.0656720i −0.981869 0.189559i \(-0.939294\pi\)
0.966880 + 0.255231i \(0.0821514\pi\)
\(810\) −1.92115e8 3.32753e8i −0.361498 0.626133i
\(811\) 3.18226e8 + 1.83728e8i 0.596587 + 0.344439i 0.767698 0.640812i \(-0.221402\pi\)
−0.171111 + 0.985252i \(0.554736\pi\)
\(812\) 2.00677e9 + 1.86201e9i 3.74825 + 3.47787i
\(813\) −2.15088e8 1.71527e8i −0.400262 0.319198i
\(814\) −2.56957e8 + 1.75190e8i −0.476417 + 0.324815i
\(815\) 1.20670e9 5.81114e8i 2.22908 1.07347i
\(816\) 1.04755e9i 1.92799i
\(817\) −5.60913e7 + 9.33228e7i −0.102856 + 0.171128i
\(818\) −6.14901e8 −1.12343
\(819\) −8.88576e7 1.84515e8i −0.161750 0.335876i
\(820\) −1.60004e8 2.34683e8i −0.290195 0.425638i
\(821\) 5.98956e8 7.51067e8i 1.08234 1.35722i 0.152906 0.988241i \(-0.451137\pi\)
0.929439 0.368976i \(-0.120292\pi\)
\(822\) −9.84564e7 + 1.06111e8i −0.177267 + 0.191049i
\(823\) −4.31146e7 + 7.46767e7i −0.0773437 + 0.133963i −0.902103 0.431521i \(-0.857977\pi\)
0.824759 + 0.565484i \(0.191311\pi\)
\(824\) −9.17051e8 + 5.29460e8i −1.63912 + 0.946349i
\(825\) 5.20583e8 + 1.18820e8i 0.927103 + 0.211605i
\(826\) −7.91969e8 + 2.01790e9i −1.40530 + 3.58064i
\(827\) 8.06387e8 + 2.48738e8i 1.42570 + 0.439769i 0.909142 0.416485i \(-0.136738\pi\)
0.516554 + 0.856255i \(0.327214\pi\)
\(828\) −3.42271e8 4.29194e8i −0.602947 0.756071i
\(829\) 7.38565e8 + 5.53478e7i 1.29636 + 0.0971487i 0.704970 0.709237i \(-0.250961\pi\)
0.591389 + 0.806386i \(0.298580\pi\)
\(830\) −1.84935e9 + 5.70448e8i −3.23433 + 0.997658i
\(831\) −4.35582e8 2.96974e8i −0.759043 0.517507i
\(832\) 1.14511e8 + 1.72598e7i 0.198828 + 0.0299685i
\(833\) 4.41383e8 + 1.93382e9i 0.763625 + 3.34566i
\(834\) −2.51037e8 + 2.32928e8i −0.432752 + 0.401535i
\(835\) −6.76614e7 + 5.07052e6i −0.116220 + 0.00870950i
\(836\) 2.28082e8 8.95155e7i 0.390366 0.153207i
\(837\) 8.48179e7 + 5.62730e8i 0.144647 + 0.959673i
\(838\) −1.17988e8 5.68201e7i −0.200496 0.0965540i
\(839\) −5.03922e8 + 1.04641e9i −0.853252 + 1.77180i −0.262526 + 0.964925i \(0.584556\pi\)
−0.590726 + 0.806872i \(0.701159\pi\)
\(840\) 3.07765e9 4.63881e8i 5.19255 0.782652i
\(841\) −6.44228e7 1.64147e8i −0.108306 0.275959i
\(842\) −3.69362e7 4.92879e8i −0.0618750 0.825665i
\(843\) −3.42399e7 3.69018e7i −0.0571543 0.0615977i
\(844\) −1.18454e9 + 2.70364e8i −1.97026 + 0.449699i
\(845\) 1.20662e8 8.00541e8i 0.199987 1.32682i
\(846\) −3.02324e8 + 4.43428e8i −0.499300 + 0.732339i
\(847\) −6.66589e7 2.16103e8i −0.109700 0.355640i
\(848\) 9.91202e7 1.32267e9i 0.162545 2.16902i
\(849\) −6.16055e8 + 4.91288e8i −1.00669 + 0.802810i
\(850\) −6.33111e8 + 2.05250e9i −1.03092 + 3.34215i
\(851\) −1.66753e8 6.54458e7i −0.270574 0.106192i
\(852\) −5.17233e7 + 2.26615e8i −0.0836310 + 0.366411i
\(853\) −1.46538e8 2.53812e8i −0.236105 0.408945i 0.723489 0.690336i \(-0.242537\pi\)
−0.959593 + 0.281391i \(0.909204\pi\)
\(854\) 1.48189e9 + 8.55571e8i 2.37927 + 1.37367i
\(855\) −7.22609e7 6.70483e7i −0.115613 0.107273i
\(856\) 6.07257e8 + 4.84272e8i 0.968170 + 0.772089i
\(857\) −4.37458e8 + 2.98254e8i −0.695015 + 0.473853i −0.858580 0.512679i \(-0.828653\pi\)
0.163565 + 0.986533i \(0.447701\pi\)
\(858\) −2.56559e8 + 1.23552e8i −0.406186 + 0.195609i
\(859\) 5.51576e8i 0.870214i −0.900379 0.435107i \(-0.856710\pi\)
0.900379 0.435107i \(-0.143290\pi\)
\(860\) −1.69537e9 1.62949e9i −2.66544 2.56187i
\(861\) 1.20749e8 0.189180
\(862\) −8.88125e8 1.84421e9i −1.38660 2.87931i
\(863\) −6.53439e8 9.58418e8i −1.01665 1.49116i −0.864395 0.502814i \(-0.832298\pi\)
−0.152258 0.988341i \(-0.548654\pi\)
\(864\) 6.18709e8 7.75836e8i 0.959279 1.20290i
\(865\) −9.18662e8 + 9.90082e8i −1.41941 + 1.52976i
\(866\) −5.98728e8 + 1.03703e9i −0.921883 + 1.59675i
\(867\) 2.52811e8 1.45961e8i 0.387918 0.223964i
\(868\) −2.61967e9 5.97924e8i −4.00579 0.914295i
\(869\) −9.64904e7 + 2.45854e8i −0.147036 + 0.374643i
\(870\) −1.46335e9 4.51385e8i −2.22224 0.685472i
\(871\) 2.96262e7 + 3.71501e7i 0.0448354 + 0.0562219i
\(872\) 7.97995e8 + 5.98014e7i 1.20351 + 0.0901908i
\(873\) 3.67156e8 1.13253e8i 0.551833 0.170218i
\(874\) 1.66457e8 + 1.13489e8i 0.249327 + 0.169988i
\(875\) 1.00001e9 + 1.50728e8i 1.49273 + 0.224993i
\(876\) 3.35823e8 + 1.47133e9i 0.499571 + 2.18877i
\(877\) −4.88267e8 + 4.53046e8i −0.723867 + 0.671651i −0.953420 0.301646i \(-0.902464\pi\)
0.229553 + 0.973296i \(0.426274\pi\)
\(878\) 9.20393e8 6.89740e7i 1.35985 0.101906i
\(879\) −2.65572e8 + 1.04229e8i −0.391035 + 0.153470i
\(880\) 3.07414e8 + 2.03956e9i 0.451103 + 2.99287i
\(881\) −3.85980e8 1.85878e8i −0.564464 0.271832i 0.129814 0.991538i \(-0.458562\pi\)
−0.694278 + 0.719707i \(0.744276\pi\)
\(882\) 7.30121e8 1.51611e9i 1.06412 2.20966i
\(883\) 6.62532e8 9.98607e7i 0.962332 0.145048i 0.350959 0.936391i \(-0.385856\pi\)
0.611373 + 0.791343i \(0.290618\pi\)
\(884\) −2.93162e8 7.46964e8i −0.424376 1.08129i
\(885\) −6.34834e7 8.47128e8i −0.0915863 1.22213i
\(886\) 6.11785e8 + 6.59347e8i 0.879625 + 0.948010i
\(887\) 6.21619e8 1.41881e8i 0.890745 0.203307i 0.247428 0.968906i \(-0.420415\pi\)
0.643317 + 0.765600i \(0.277558\pi\)
\(888\) 6.34849e7 4.21195e8i 0.0906633 0.601512i
\(889\) 2.07034e8 3.03664e8i 0.294671 0.432203i
\(890\) 7.60967e7 + 2.46699e8i 0.107943 + 0.349943i
\(891\) −1.18817e7 + 1.58550e8i −0.0167975 + 0.224147i
\(892\) 2.07188e9 1.65227e9i 2.91924 2.32802i
\(893\) 4.06693e7 1.31847e8i 0.0571101 0.185146i
\(894\) 7.74069e8 + 3.03800e8i 1.08335 + 0.425182i
\(895\) 2.10987e8 9.24394e8i 0.294297 1.28940i
\(896\) −3.48512e8 6.03641e8i −0.484501 0.839180i
\(897\) −1.42048e8 8.20117e7i −0.196815 0.113631i
\(898\) 8.04720e8 + 7.46671e8i 1.11126 + 1.03110i
\(899\) 5.91794e8 + 4.71940e8i 0.814500 + 0.649542i
\(900\) 1.05471e9 7.19088e8i 1.44679 0.986403i
\(901\) −8.58815e8 + 4.13584e8i −1.17415 + 0.565443i
\(902\) 1.67778e8i 0.228621i
\(903\) 9.78357e8 2.05268e8i 1.32872 0.278778i
\(904\) 3.72414e8 0.504105
\(905\) 7.14951e8 + 1.48461e9i 0.964563 + 2.00293i
\(906\) −6.16598e7 9.04383e7i −0.0829121 0.121610i
\(907\) −9.87358e6 + 1.23811e7i −0.0132328 + 0.0165935i −0.788404 0.615158i \(-0.789092\pi\)
0.775171 + 0.631751i \(0.217664\pi\)
\(908\) −1.04897e9 + 1.13052e9i −1.40121 + 1.51015i
\(909\) −3.33316e8 + 5.77320e8i −0.443777 + 0.768644i
\(910\) −1.40571e9 + 8.11587e8i −1.86540 + 1.07699i
\(911\) 1.77735e8 + 4.05668e7i 0.235081 + 0.0536557i 0.338438 0.940989i \(-0.390101\pi\)
−0.103357 + 0.994644i \(0.532958\pi\)
\(912\) −8.34717e7 + 2.12682e8i −0.110041 + 0.280380i
\(913\) 7.65260e8 + 2.36051e8i 1.00553 + 0.310166i
\(914\) 9.26084e8 + 1.16127e9i 1.21286 + 1.52088i
\(915\) −6.68690e8 5.01114e7i −0.872895 0.0654144i
\(916\) 2.38477e9 7.35605e8i 3.10285 0.957102i
\(917\) −7.72883e8 5.26943e8i −1.00232 0.683369i
\(918\) −1.89505e9 2.85633e8i −2.44958 0.369215i
\(919\) −7.52724e7 3.29790e8i −0.0969816 0.424904i 0.903007 0.429625i \(-0.141354\pi\)
−0.999989 + 0.00472116i \(0.998497\pi\)
\(920\) −1.82605e9 + 1.69432e9i −2.34503 + 2.17587i
\(921\) −2.93400e8 + 2.19873e7i −0.375561 + 0.0281444i
\(922\) −3.56102e8 + 1.39760e8i −0.454340 + 0.178315i
\(923\) −1.03439e7 6.86276e7i −0.0131547 0.0872757i
\(924\) −2.02677e9 9.76040e8i −2.56914 1.23723i
\(925\) 1.80735e8 3.75301e8i 0.228359 0.474192i
\(926\) 1.29328e9 1.94930e8i 1.62877 0.245497i
\(927\) −1.12493e8 2.86629e8i −0.141217 0.359816i
\(928\) −9.86351e7 1.31619e9i −0.123421 1.64693i
\(929\) −9.36436e7 1.00924e8i −0.116797 0.125877i 0.671947 0.740600i \(-0.265458\pi\)
−0.788743 + 0.614723i \(0.789268\pi\)
\(930\) 1.46545e9 3.34480e8i 1.82189 0.415835i
\(931\) −6.44791e7 + 4.27791e8i −0.0799043 + 0.530130i
\(932\) −5.02050e8 + 7.36372e8i −0.620154 + 0.909598i
\(933\) 2.52616e8 + 8.18963e8i 0.311040 + 1.00837i
\(934\) 1.09170e8 1.45677e9i 0.133987 1.78793i
\(935\) 1.15891e9 9.24202e8i 1.41780 1.13066i
\(936\) −1.14879e8 + 3.72429e8i −0.140092 + 0.454167i
\(937\) −1.47294e8 5.78085e7i −0.179046 0.0702705i 0.274124 0.961694i \(-0.411612\pi\)
−0.453171 + 0.891424i \(0.649707\pi\)
\(938\) −1.19235e8 + 5.22403e8i −0.144476 + 0.632990i
\(939\) 1.37190e8 + 2.37619e8i 0.165701 + 0.287002i
\(940\) 2.58061e9 + 1.48992e9i 3.10698 + 1.79382i
\(941\) −8.15193e8 7.56389e8i −0.978344 0.907771i 0.0174078 0.999848i \(-0.494459\pi\)
−0.995752 + 0.0920779i \(0.970649\pi\)
\(942\) −6.96580e8 5.55504e8i −0.833332 0.664560i
\(943\) −7.98492e7 + 5.44403e7i −0.0952216 + 0.0649210i
\(944\) 1.77273e9 8.53703e8i 2.10730 1.01482i
\(945\) 2.71572e9i 3.21803i
\(946\) 2.85216e8 + 1.35941e9i 0.336899 + 1.60574i
\(947\) 7.61542e8 0.896693 0.448346 0.893860i \(-0.352013\pi\)
0.448346 + 0.893860i \(0.352013\pi\)
\(948\) −2.74140e8 5.69257e8i −0.321771 0.668165i
\(949\) −2.53837e8 3.72311e8i −0.297000 0.435619i
\(950\) −2.92088e8 + 3.66266e8i −0.340677 + 0.427195i
\(951\) 6.02229e8 6.49049e8i 0.700197 0.754633i
\(952\) 2.59035e9 4.48662e9i 3.00226 5.20006i
\(953\) 9.13074e8 5.27164e8i 1.05494 0.609069i 0.130911 0.991394i \(-0.458210\pi\)
0.924028 + 0.382325i \(0.124876\pi\)
\(954\) 7.88387e8 + 1.79944e8i 0.908017 + 0.207249i
\(955\) −7.95077e8 + 2.02582e9i −0.912849 + 2.32590i
\(956\) 2.60481e9 + 8.03476e8i 2.98127 + 0.919601i
\(957\) 3.95099e8 + 4.95438e8i 0.450785 + 0.565267i
\(958\) −6.63987e8 4.97590e7i −0.755202 0.0565946i
\(959\) 3.26263e8 1.00639e8i 0.369923 0.114106i
\(960\) −4.22836e8 2.88285e8i −0.477924 0.325843i
\(961\) 1.42922e8 + 2.15420e7i 0.161038 + 0.0242725i
\(962\) 4.94311e7 + 2.16572e8i 0.0555232 + 0.243263i
\(963\) −1.65562e8 + 1.53619e8i −0.185388 + 0.172015i
\(964\) −3.08130e9 + 2.30911e8i −3.43956 + 0.257759i
\(965\) −3.14870e8 + 1.23577e8i −0.350388 + 0.137517i
\(966\) −2.75678e8 1.82900e9i −0.305823 2.02900i
\(967\) −6.46525e8 3.11350e8i −0.714999 0.344326i 0.0407653 0.999169i \(-0.487020\pi\)
−0.755765 + 0.654843i \(0.772735\pi\)
\(968\) −1.86736e8 + 3.87761e8i −0.205874 + 0.427502i
\(969\) 1.62363e8 2.44722e7i 0.178449 0.0268969i
\(970\) −1.11257e9 2.83479e9i −1.21903 3.10603i
\(971\) −3.63162e7 4.84606e8i −0.0396682 0.529335i −0.981274 0.192618i \(-0.938302\pi\)
0.941606 0.336718i \(-0.109317\pi\)
\(972\) 1.29120e9 + 1.39159e9i 1.40603 + 1.51534i
\(973\) 7.87506e8 1.79743e8i 0.854900 0.195125i
\(974\) −3.78236e8 + 2.50943e9i −0.409341 + 2.71580i
\(975\) 2.14856e8 3.15135e8i 0.231810 0.340003i
\(976\) −4.57795e8 1.48414e9i −0.492404 1.59634i
\(977\) −1.07450e8 + 1.43382e9i −0.115218 + 1.53748i 0.577571 + 0.816340i \(0.304001\pi\)
−0.692789 + 0.721140i \(0.743618\pi\)
\(978\) 1.47970e9 1.18002e9i 1.58182 1.26146i
\(979\) 3.14888e7 1.02084e8i 0.0335589 0.108795i
\(980\) −8.69734e9 3.41346e9i −9.24077 3.62674i
\(981\) −5.17789e7 + 2.26858e8i −0.0548461 + 0.240297i
\(982\) 5.01068e8 + 8.67876e8i 0.529130 + 0.916481i
\(983\) −1.34023e9 7.73784e8i −1.41098 0.814628i −0.415496 0.909595i \(-0.636392\pi\)
−0.995480 + 0.0949671i \(0.969725\pi\)
\(984\) −1.68452e8 1.56301e8i −0.176804 0.164050i
\(985\) 4.22076e8 + 3.36595e8i 0.441654 + 0.352208i
\(986\) −2.10612e9 + 1.43593e9i −2.19711 + 1.49797i
\(987\) −1.14133e9 + 5.49634e8i −1.18702 + 0.571639i
\(988\) 1.75015e8i 0.181469i
\(989\) −5.54423e8 + 5.76836e8i −0.573129 + 0.596298i
\(990\) −1.25752e9 −1.29601
\(991\) −5.74966e8 1.19393e9i −0.590774 1.22675i −0.955321 0.295570i \(-0.904491\pi\)
0.364547 0.931185i \(-0.381224\pi\)
\(992\) 7.29801e8 + 1.07042e9i 0.747600 + 1.09653i
\(993\) −1.51739e8 + 1.90274e8i −0.154970 + 0.194327i
\(994\) 5.32331e8 5.73717e8i 0.542030 0.584169i
\(995\) −5.42994e8 + 9.40492e8i −0.551221 + 0.954742i
\(996\) −1.65916e9 + 9.57917e8i −1.67923 + 0.969505i
\(997\) 5.03404e8 + 1.14899e8i 0.507962 + 0.115939i 0.468818 0.883295i \(-0.344680\pi\)
0.0391436 + 0.999234i \(0.487537\pi\)
\(998\) 2.47804e8 6.31395e8i 0.249297 0.635198i
\(999\) 3.55151e8 + 1.09550e8i 0.356219 + 0.109879i
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 43.7.h.a.12.20 252
43.18 odd 42 inner 43.7.h.a.18.20 yes 252
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.h.a.12.20 252 1.1 even 1 trivial
43.7.h.a.18.20 yes 252 43.18 odd 42 inner