Properties

Label 43.7.h.a.12.19
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 12.19
Character \(\chi\) \(=\) 43.12
Dual form 43.7.h.a.18.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.69868 + 11.8334i) q^{2} +(18.7853 + 27.5530i) q^{3} +(-67.6517 + 84.8326i) q^{4} +(55.6001 - 59.9226i) q^{5} +(-218.995 + 379.310i) q^{6} +(-321.699 + 185.733i) q^{7} +(-569.878 - 130.071i) q^{8} +(-139.945 + 356.575i) q^{9} +O(q^{10})\) \(q+(5.69868 + 11.8334i) q^{2} +(18.7853 + 27.5530i) q^{3} +(-67.6517 + 84.8326i) q^{4} +(55.6001 - 59.9226i) q^{5} +(-218.995 + 379.310i) q^{6} +(-321.699 + 185.733i) q^{7} +(-569.878 - 130.071i) q^{8} +(-139.945 + 356.575i) q^{9} +(1025.94 + 316.460i) q^{10} +(427.578 + 536.166i) q^{11} +(-3608.25 - 270.401i) q^{12} +(-378.250 + 116.675i) q^{13} +(-4031.12 - 2748.37i) q^{14} +(2695.51 + 406.283i) q^{15} +(-163.110 - 714.634i) q^{16} +(4401.16 - 4083.68i) q^{17} +(-5017.00 + 375.973i) q^{18} +(8551.60 - 3356.25i) q^{19} +(1321.95 + 8770.57i) q^{20} +(-11160.7 - 5374.72i) q^{21} +(-3908.05 + 8115.15i) q^{22} +(-15092.0 + 2274.75i) q^{23} +(-7121.49 - 18145.3i) q^{24} +(668.305 + 8917.91i) q^{25} +(-3536.19 - 3811.10i) q^{26} +(11247.2 - 2567.10i) q^{27} +(6007.29 - 39855.8i) q^{28} +(-6396.77 + 9382.33i) q^{29} +(10553.1 + 34212.4i) q^{30} +(1200.31 - 16017.0i) q^{31} +(-21721.4 + 17322.2i) q^{32} +(-6740.78 + 21853.1i) q^{33} +(73404.7 + 28809.2i) q^{34} +(-6756.88 + 29603.8i) q^{35} +(-20781.6 - 35994.8i) q^{36} +(53456.2 + 30863.0i) q^{37} +(88448.8 + 82068.5i) q^{38} +(-10320.3 - 8230.14i) q^{39} +(-39479.4 + 26916.6i) q^{40} +(-11274.6 + 5429.56i) q^{41} -162698. i q^{42} +(78204.9 - 14330.3i) q^{43} -74410.7 q^{44} +(13585.9 + 28211.5i) q^{45} +(-112923. - 165627. i) q^{46} +(46407.1 - 58192.6i) q^{47} +(16626.2 - 17918.8i) q^{48} +(10169.1 - 17613.4i) q^{49} +(-101721. + 58728.6i) q^{50} +(195195. + 44551.9i) q^{51} +(15691.5 - 39981.2i) q^{52} +(-71071.6 - 21922.7i) q^{53} +(94471.7 + 118464. i) q^{54} +(55901.8 + 4189.26i) q^{55} +(207488. - 64001.5i) q^{56} +(253119. + 172574. i) q^{57} +(-147478. - 22228.8i) q^{58} +(-27267.5 - 119467. i) q^{59} +(-216822. + 201181. i) q^{60} +(-344915. + 25847.8i) q^{61} +(196377. - 77072.1i) q^{62} +(-21207.5 - 140702. i) q^{63} +(-371031. - 178679. i) q^{64} +(-14039.3 + 29152.8i) q^{65} +(-297010. + 44767.1i) q^{66} +(54576.6 + 139059. i) q^{67} +(48683.0 + 649630. i) q^{68} +(-346184. - 373098. i) q^{69} +(-388820. + 88745.7i) q^{70} +(68323.1 - 453294. i) q^{71} +(126132. - 185001. i) q^{72} +(-163446. - 529879. i) q^{73} +(-60584.8 + 808448. i) q^{74} +(-233161. + 185939. i) q^{75} +(-293811. + 952511. i) q^{76} +(-237135. - 93068.7i) q^{77} +(38578.9 - 169025. i) q^{78} +(201616. + 349209. i) q^{79} +(-51891.7 - 29959.7i) q^{80} +(486715. + 451605. i) q^{81} +(-128501. - 102476. i) q^{82} +(778628. - 530859. i) q^{83} +(1.21099e6 - 583184. i) q^{84} -490782. i q^{85} +(615241. + 843768. i) q^{86} -378676. q^{87} +(-173928. - 361165. i) q^{88} +(-370040. - 542749. i) q^{89} +(-256416. + 321536. i) q^{90} +(100012. - 107788. i) q^{91} +(828027. - 1.43418e6i) q^{92} +(463865. - 267813. i) q^{93} +(953077. + 217534. i) q^{94} +(274354. - 699042. i) q^{95} +(-885321. - 273085. i) q^{96} +(-873604. - 1.09546e6i) q^{97} +(266378. + 19962.3i) q^{98} +(-251021. + 77429.6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.69868 + 11.8334i 0.712335 + 1.47918i 0.870709 + 0.491799i \(0.163661\pi\)
−0.158374 + 0.987379i \(0.550625\pi\)
\(3\) 18.7853 + 27.5530i 0.695752 + 1.02048i 0.997742 + 0.0671693i \(0.0213968\pi\)
−0.301990 + 0.953311i \(0.597651\pi\)
\(4\) −67.6517 + 84.8326i −1.05706 + 1.32551i
\(5\) 55.6001 59.9226i 0.444800 0.479381i −0.470358 0.882476i \(-0.655875\pi\)
0.915158 + 0.403095i \(0.132066\pi\)
\(6\) −218.995 + 379.310i −1.01386 + 1.75607i
\(7\) −321.699 + 185.733i −0.937899 + 0.541496i −0.889301 0.457322i \(-0.848809\pi\)
−0.0485978 + 0.998818i \(0.515475\pi\)
\(8\) −569.878 130.071i −1.11304 0.254045i
\(9\) −139.945 + 356.575i −0.191969 + 0.489129i
\(10\) 1025.94 + 316.460i 1.02594 + 0.316460i
\(11\) 427.578 + 536.166i 0.321246 + 0.402829i 0.916065 0.401030i \(-0.131348\pi\)
−0.594819 + 0.803860i \(0.702776\pi\)
\(12\) −3608.25 270.401i −2.08811 0.156482i
\(13\) −378.250 + 116.675i −0.172167 + 0.0531064i −0.379640 0.925134i \(-0.623952\pi\)
0.207473 + 0.978241i \(0.433476\pi\)
\(14\) −4031.12 2748.37i −1.46907 1.00159i
\(15\) 2695.51 + 406.283i 0.798670 + 0.120380i
\(16\) −163.110 714.634i −0.0398219 0.174471i
\(17\) 4401.16 4083.68i 0.895819 0.831199i −0.0905254 0.995894i \(-0.528855\pi\)
0.986344 + 0.164696i \(0.0526642\pi\)
\(18\) −5017.00 + 375.973i −0.860255 + 0.0644672i
\(19\) 8551.60 3356.25i 1.24677 0.489321i 0.352064 0.935976i \(-0.385480\pi\)
0.894706 + 0.446655i \(0.147385\pi\)
\(20\) 1321.95 + 8770.57i 0.165244 + 1.09632i
\(21\) −11160.7 5374.72i −1.20513 0.580361i
\(22\) −3908.05 + 8115.15i −0.367022 + 0.762129i
\(23\) −15092.0 + 2274.75i −1.24040 + 0.186961i −0.736284 0.676673i \(-0.763421\pi\)
−0.504120 + 0.863633i \(0.668183\pi\)
\(24\) −7121.49 18145.3i −0.515154 1.31259i
\(25\) 668.305 + 8917.91i 0.0427715 + 0.570746i
\(26\) −3536.19 3811.10i −0.201194 0.216836i
\(27\) 11247.2 2567.10i 0.571416 0.130422i
\(28\) 6007.29 39855.8i 0.273656 1.81559i
\(29\) −6396.77 + 9382.33i −0.262281 + 0.384695i −0.934678 0.355495i \(-0.884312\pi\)
0.672397 + 0.740190i \(0.265265\pi\)
\(30\) 10553.1 + 34212.4i 0.390857 + 1.26713i
\(31\) 1200.31 16017.0i 0.0402910 0.537646i −0.940141 0.340787i \(-0.889307\pi\)
0.980432 0.196860i \(-0.0630744\pi\)
\(32\) −21721.4 + 17322.2i −0.662884 + 0.528632i
\(33\) −6740.78 + 21853.1i −0.187572 + 0.608094i
\(34\) 73404.7 + 28809.2i 1.86761 + 0.732985i
\(35\) −6756.88 + 29603.8i −0.157595 + 0.690468i
\(36\) −20781.6 35994.8i −0.445422 0.771494i
\(37\) 53456.2 + 30863.0i 1.05534 + 0.609302i 0.924140 0.382054i \(-0.124783\pi\)
0.131201 + 0.991356i \(0.458117\pi\)
\(38\) 88448.8 + 82068.5i 1.61191 + 1.49564i
\(39\) −10320.3 8230.14i −0.173979 0.138744i
\(40\) −39479.4 + 26916.6i −0.616866 + 0.420572i
\(41\) −11274.6 + 5429.56i −0.163587 + 0.0787794i −0.513886 0.857859i \(-0.671794\pi\)
0.350298 + 0.936638i \(0.386080\pi\)
\(42\) 162698.i 2.19602i
\(43\) 78204.9 14330.3i 0.983623 0.180240i
\(44\) −74410.7 −0.873529
\(45\) 13585.9 + 28211.5i 0.149091 + 0.309591i
\(46\) −112923. 165627.i −1.16013 1.70160i
\(47\) 46407.1 58192.6i 0.446982 0.560498i −0.506386 0.862307i \(-0.669019\pi\)
0.953369 + 0.301809i \(0.0975904\pi\)
\(48\) 16626.2 17918.8i 0.150338 0.162026i
\(49\) 10169.1 17613.4i 0.0864361 0.149712i
\(50\) −101721. + 58728.6i −0.813768 + 0.469829i
\(51\) 195195. + 44551.9i 1.47149 + 0.335858i
\(52\) 15691.5 39981.2i 0.111597 0.284345i
\(53\) −71071.6 21922.7i −0.477385 0.147254i 0.0467189 0.998908i \(-0.485123\pi\)
−0.524104 + 0.851654i \(0.675600\pi\)
\(54\) 94471.7 + 118464.i 0.599957 + 0.752323i
\(55\) 55901.8 + 4189.26i 0.335999 + 0.0251796i
\(56\) 207488. 64001.5i 1.18149 0.364440i
\(57\) 253119. + 172574.i 1.36679 + 0.931858i
\(58\) −147478. 22228.8i −0.755865 0.113928i
\(59\) −27267.5 119467.i −0.132767 0.581690i −0.996918 0.0784565i \(-0.975001\pi\)
0.864151 0.503233i \(-0.167856\pi\)
\(60\) −216822. + 201181.i −1.00381 + 0.931395i
\(61\) −344915. + 25847.8i −1.51958 + 0.113876i −0.808188 0.588924i \(-0.799552\pi\)
−0.711387 + 0.702800i \(0.751933\pi\)
\(62\) 196377. 77072.1i 0.823976 0.323387i
\(63\) −21207.5 140702.i −0.0848139 0.562703i
\(64\) −371031. 178679.i −1.41537 0.681607i
\(65\) −14039.3 + 29152.8i −0.0511216 + 0.106155i
\(66\) −297010. + 44767.1i −1.03309 + 0.155714i
\(67\) 54576.6 + 139059.i 0.181461 + 0.462354i 0.992442 0.122719i \(-0.0391613\pi\)
−0.810981 + 0.585073i \(0.801066\pi\)
\(68\) 48683.0 + 649630.i 0.154828 + 2.06604i
\(69\) −346184. 373098.i −1.05380 1.13573i
\(70\) −388820. + 88745.7i −1.13359 + 0.258734i
\(71\) 68323.1 453294.i 0.190894 1.26650i −0.664014 0.747720i \(-0.731149\pi\)
0.854908 0.518779i \(-0.173613\pi\)
\(72\) 126132. 185001.i 0.337930 0.495652i
\(73\) −163446. 529879.i −0.420151 1.36210i −0.880368 0.474290i \(-0.842705\pi\)
0.460217 0.887806i \(-0.347772\pi\)
\(74\) −60584.8 + 808448.i −0.149509 + 1.99507i
\(75\) −233161. + 185939.i −0.552677 + 0.440745i
\(76\) −293811. + 952511.i −0.669309 + 2.16985i
\(77\) −237135. 93068.7i −0.519426 0.203860i
\(78\) 38578.9 169025.i 0.0812954 0.356178i
\(79\) 201616. + 349209.i 0.408925 + 0.708279i 0.994770 0.102144i \(-0.0325704\pi\)
−0.585844 + 0.810424i \(0.699237\pi\)
\(80\) −51891.7 29959.7i −0.101351 0.0585150i
\(81\) 486715. + 451605.i 0.915840 + 0.849775i
\(82\) −128501. 102476.i −0.233058 0.185857i
\(83\) 778628. 530859.i 1.36174 0.928421i 0.361751 0.932275i \(-0.382179\pi\)
0.999993 + 0.00385322i \(0.00122652\pi\)
\(84\) 1.21099e6 583184.i 2.04317 0.983938i
\(85\) 490782.i 0.799156i
\(86\) 615241. + 843768.i 0.967275 + 1.32656i
\(87\) −378676. −0.575056
\(88\) −173928. 361165.i −0.255224 0.529977i
\(89\) −370040. 542749.i −0.524902 0.769890i 0.468636 0.883392i \(-0.344746\pi\)
−0.993538 + 0.113502i \(0.963793\pi\)
\(90\) −256416. + 321536.i −0.351737 + 0.441065i
\(91\) 100012. 107788.i 0.132718 0.143036i
\(92\) 828027. 1.43418e6i 1.06336 1.84180i
\(93\) 463865. 267813.i 0.576690 0.332952i
\(94\) 953077. + 217534.i 1.14748 + 0.261904i
\(95\) 274354. 699042.i 0.319993 0.815328i
\(96\) −885321. 273085.i −1.00066 0.308663i
\(97\) −873604. 1.09546e6i −0.957193 1.20028i −0.979687 0.200535i \(-0.935732\pi\)
0.0224938 0.999747i \(-0.492839\pi\)
\(98\) 266378. + 19962.3i 0.283022 + 0.0212096i
\(99\) −251021. + 77429.6i −0.258704 + 0.0797998i
\(100\) −801741. 546618.i −0.801741 0.546618i
\(101\) 1.85293e6 + 279285.i 1.79844 + 0.271071i 0.961217 0.275792i \(-0.0889402\pi\)
0.837222 + 0.546863i \(0.184178\pi\)
\(102\) 585150. + 2.56371e6i 0.551400 + 2.41584i
\(103\) 796919. 739433.i 0.729294 0.676686i −0.225403 0.974266i \(-0.572370\pi\)
0.954697 + 0.297580i \(0.0961794\pi\)
\(104\) 230732. 17291.0i 0.205120 0.0153716i
\(105\) −942604. + 369945.i −0.814257 + 0.319572i
\(106\) −145594. 965952.i −0.122243 0.811032i
\(107\) 1.08407e6 + 522060.i 0.884923 + 0.426156i 0.820420 0.571761i \(-0.193740\pi\)
0.0645029 + 0.997918i \(0.479454\pi\)
\(108\) −543118. + 1.12780e6i −0.431145 + 0.895282i
\(109\) −1.55332e6 + 234126.i −1.19945 + 0.180788i −0.718226 0.695810i \(-0.755045\pi\)
−0.481223 + 0.876598i \(0.659807\pi\)
\(110\) 268993. + 685383.i 0.202099 + 0.514939i
\(111\) 153825. + 2.05265e6i 0.112475 + 1.50088i
\(112\) 185204. + 199602.i 0.131824 + 0.142073i
\(113\) −258211. + 58935.0i −0.178953 + 0.0408449i −0.311058 0.950391i \(-0.600683\pi\)
0.132105 + 0.991236i \(0.457826\pi\)
\(114\) −599694. + 3.97871e6i −0.404776 + 2.68551i
\(115\) −702807. + 1.03083e6i −0.462107 + 0.677786i
\(116\) −363175. 1.17739e6i −0.232671 0.754301i
\(117\) 11331.1 151202.i 0.00707478 0.0944064i
\(118\) 1.25831e6 1.00347e6i 0.765848 0.610744i
\(119\) −657375. + 2.13116e6i −0.390097 + 1.26466i
\(120\) −1.48327e6 582139.i −0.858372 0.336886i
\(121\) 289559. 1.26864e6i 0.163448 0.716114i
\(122\) −2.27143e6 3.93423e6i −1.25089 2.16661i
\(123\) −361397. 208653.i −0.194209 0.112127i
\(124\) 1.27756e6 + 1.18541e6i 0.670066 + 0.621730i
\(125\) 1.57014e6 + 1.25214e6i 0.803910 + 0.641097i
\(126\) 1.54414e6 1.05277e6i 0.771923 0.526288i
\(127\) −886510. + 426921.i −0.432786 + 0.208419i −0.637576 0.770387i \(-0.720063\pi\)
0.204791 + 0.978806i \(0.434349\pi\)
\(128\) 3.63072e6i 1.73126i
\(129\) 1.86395e6 + 1.88558e6i 0.868288 + 0.878366i
\(130\) −424983. −0.193438
\(131\) −1.01916e6 2.11631e6i −0.453345 0.941381i −0.994914 0.100725i \(-0.967884\pi\)
0.541569 0.840656i \(-0.317830\pi\)
\(132\) −1.39783e6 2.05024e6i −0.607760 0.891420i
\(133\) −2.12767e6 + 2.66802e6i −0.904379 + 1.13405i
\(134\) −1.33453e6 + 1.43828e6i −0.554643 + 0.597763i
\(135\) 471517. 816692.i 0.191644 0.331938i
\(136\) −3.03929e6 + 1.75474e6i −1.20825 + 0.697582i
\(137\) −3.89289e6 888526.i −1.51394 0.345548i −0.616741 0.787166i \(-0.711548\pi\)
−0.897203 + 0.441618i \(0.854405\pi\)
\(138\) 2.44223e6 6.22271e6i 0.929287 2.36778i
\(139\) 2.31554e6 + 714251.i 0.862201 + 0.265954i 0.694155 0.719825i \(-0.255778\pi\)
0.168046 + 0.985779i \(0.446254\pi\)
\(140\) −2.05426e6 2.57596e6i −0.748635 0.938759i
\(141\) 2.47515e6 + 185487.i 0.882966 + 0.0661692i
\(142\) 5.75337e6 1.77468e6i 2.00936 0.619805i
\(143\) −224288. 152917.i −0.0767006 0.0522936i
\(144\) 277647. + 41848.5i 0.0929834 + 0.0140150i
\(145\) 206553. + 904969.i 0.0677529 + 0.296845i
\(146\) 5.33886e6 4.95374e6i 1.71550 1.59175i
\(147\) 676332. 50684.1i 0.212916 0.0159558i
\(148\) −6.23459e6 + 2.44690e6i −1.92319 + 0.754798i
\(149\) 684877. + 4.54386e6i 0.207040 + 1.37362i 0.814912 + 0.579584i \(0.196785\pi\)
−0.607873 + 0.794035i \(0.707977\pi\)
\(150\) −3.52901e6 1.69948e6i −1.04563 0.503550i
\(151\) −598776. + 1.24337e6i −0.173914 + 0.361135i −0.969646 0.244513i \(-0.921372\pi\)
0.795732 + 0.605648i \(0.207086\pi\)
\(152\) −5.30992e6 + 800341.i −1.51202 + 0.227900i
\(153\) 840215. + 2.14083e6i 0.234594 + 0.597735i
\(154\) −250036. 3.33649e6i −0.0684604 0.913541i
\(155\) −893045. 962473.i −0.239816 0.258460i
\(156\) 1.39637e6 318712.i 0.367812 0.0839508i
\(157\) −601656. + 3.99173e6i −0.155471 + 1.03148i 0.765945 + 0.642906i \(0.222271\pi\)
−0.921416 + 0.388577i \(0.872967\pi\)
\(158\) −2.98340e6 + 4.37584e6i −0.756380 + 1.10941i
\(159\) −731067. 2.37006e6i −0.181872 0.589614i
\(160\) −169717. + 2.26472e6i −0.0414349 + 0.552910i
\(161\) 4.43259e6 3.53487e6i 1.06214 0.847024i
\(162\) −2.57041e6 + 8.33306e6i −0.604585 + 1.96002i
\(163\) 4.07868e6 + 1.60076e6i 0.941796 + 0.369628i 0.786045 0.618169i \(-0.212125\pi\)
0.155751 + 0.987796i \(0.450220\pi\)
\(164\) 302142. 1.32377e6i 0.0684983 0.300111i
\(165\) 934706. + 1.61896e6i 0.208076 + 0.360399i
\(166\) 1.07190e7 + 6.18864e6i 2.34332 + 1.35292i
\(167\) −5.33728e6 4.95228e6i −1.14596 1.06330i −0.997227 0.0744220i \(-0.976289\pi\)
−0.148737 0.988877i \(-0.547521\pi\)
\(168\) 5.66115e6 + 4.51462e6i 1.19393 + 0.952123i
\(169\) −3.85864e6 + 2.63077e6i −0.799418 + 0.545034i
\(170\) 5.80763e6 2.79681e6i 1.18209 0.569267i
\(171\) 3.51897e6i 0.703765i
\(172\) −4.07502e6 + 7.60380e6i −0.800837 + 1.49433i
\(173\) −7.79690e6 −1.50586 −0.752929 0.658102i \(-0.771360\pi\)
−0.752929 + 0.658102i \(0.771360\pi\)
\(174\) −2.15795e6 4.48104e6i −0.409633 0.850611i
\(175\) −1.87134e6 2.74476e6i −0.349172 0.512142i
\(176\) 313420. 393016.i 0.0574895 0.0720895i
\(177\) 2.77944e6 2.99552e6i 0.501230 0.540198i
\(178\) 4.31384e6 7.47179e6i 0.764899 1.32484i
\(179\) −856874. + 494716.i −0.149402 + 0.0862576i −0.572838 0.819669i \(-0.694157\pi\)
0.423435 + 0.905926i \(0.360824\pi\)
\(180\) −3.31236e6 756025.i −0.567963 0.129634i
\(181\) 2.44797e6 6.23733e6i 0.412829 1.05187i −0.561646 0.827378i \(-0.689832\pi\)
0.974475 0.224495i \(-0.0720731\pi\)
\(182\) 1.84544e6 + 569242.i 0.306115 + 0.0944241i
\(183\) −7.19151e6 9.01787e6i −1.17346 1.47147i
\(184\) 8.89648e6 + 666699.i 1.42812 + 0.107023i
\(185\) 4.82156e6 1.48725e6i 0.761504 0.234893i
\(186\) 5.81256e6 + 3.96293e6i 0.903293 + 0.615854i
\(187\) 4.07137e6 + 613660.i 0.622609 + 0.0938432i
\(188\) 1.79711e6 + 7.87366e6i 0.270459 + 1.18496i
\(189\) −3.14142e6 + 2.91481e6i −0.465308 + 0.431742i
\(190\) 9.83552e6 737070.i 1.43396 0.107460i
\(191\) 159113. 62447.3i 0.0228353 0.00896218i −0.353896 0.935285i \(-0.615143\pi\)
0.376731 + 0.926323i \(0.377048\pi\)
\(192\) −2.04679e6 1.35796e7i −0.289181 1.91859i
\(193\) −7.24735e6 3.49014e6i −1.00811 0.485479i −0.144426 0.989516i \(-0.546133\pi\)
−0.863682 + 0.504036i \(0.831848\pi\)
\(194\) 7.98472e6 1.65804e7i 1.09359 2.27086i
\(195\) −1.06698e6 + 160821.i −0.143897 + 0.0216890i
\(196\) 806235. + 2.05425e6i 0.107076 + 0.272826i
\(197\) 683179. + 9.11639e6i 0.0893585 + 1.19241i 0.844027 + 0.536300i \(0.180179\pi\)
−0.754669 + 0.656106i \(0.772202\pi\)
\(198\) −2.34674e6 2.52919e6i −0.302322 0.325826i
\(199\) −8.60714e6 + 1.96452e6i −1.09219 + 0.249286i −0.730432 0.682985i \(-0.760681\pi\)
−0.361761 + 0.932271i \(0.617824\pi\)
\(200\) 779109. 5.16905e6i 0.0973886 0.646131i
\(201\) −2.80625e6 + 4.11601e6i −0.345572 + 0.506861i
\(202\) 7.25438e6 + 2.35181e7i 0.880128 + 2.85331i
\(203\) 315225. 4.20638e6i 0.0376818 0.502829i
\(204\) −1.69847e7 + 1.35449e7i −2.00063 + 1.59545i
\(205\) −301515. + 977487.i −0.0349983 + 0.113462i
\(206\) 1.32914e7 + 5.21650e6i 1.52044 + 0.596729i
\(207\) 1.30093e6 5.69977e6i 0.146671 0.642608i
\(208\) 145076. + 251279.i 0.0161215 + 0.0279233i
\(209\) 5.45598e6 + 3.15001e6i 0.597632 + 0.345043i
\(210\) −9.74931e6 9.04604e6i −1.05273 0.976788i
\(211\) −5.93645e6 4.73416e6i −0.631945 0.503959i 0.254331 0.967117i \(-0.418145\pi\)
−0.886276 + 0.463158i \(0.846716\pi\)
\(212\) 6.66788e6 4.54608e6i 0.699810 0.477123i
\(213\) 1.37731e7 6.63276e6i 1.42525 0.686365i
\(214\) 1.58033e7i 1.61253i
\(215\) 3.48949e6 5.48301e6i 0.351112 0.551701i
\(216\) −6.74343e6 −0.669144
\(217\) 2.58875e6 + 5.37560e6i 0.253345 + 0.526075i
\(218\) −1.16224e7 1.70469e7i −1.12183 1.64542i
\(219\) 1.15294e7 1.44574e7i 1.09767 1.37644i
\(220\) −4.13724e6 + 4.45889e6i −0.388546 + 0.418753i
\(221\) −1.18828e6 + 2.05816e6i −0.110088 + 0.190678i
\(222\) −2.34133e7 + 1.35177e7i −2.13995 + 1.23550i
\(223\) −1.68604e7 3.84827e6i −1.52038 0.347017i −0.620870 0.783914i \(-0.713220\pi\)
−0.899512 + 0.436897i \(0.856077\pi\)
\(224\) 3.77044e6 9.60693e6i 0.335466 0.854753i
\(225\) −3.27343e6 1.00972e6i −0.287379 0.0886447i
\(226\) −2.16886e6 2.71967e6i −0.187891 0.235608i
\(227\) −840739. 63004.7i −0.0718760 0.00538636i 0.0387436 0.999249i \(-0.487664\pi\)
−0.110620 + 0.993863i \(0.535284\pi\)
\(228\) −3.17638e7 + 9.79784e6i −2.67996 + 0.826658i
\(229\) 1.49148e7 + 1.01688e7i 1.24197 + 0.846762i 0.992574 0.121640i \(-0.0388152\pi\)
0.249397 + 0.968401i \(0.419768\pi\)
\(230\) −1.62033e7 2.44226e6i −1.33174 0.200728i
\(231\) −1.89034e6 8.28211e6i −0.153357 0.671900i
\(232\) 4.86575e6 4.51475e6i 0.389660 0.361551i
\(233\) −2.95037e6 + 221100.i −0.233243 + 0.0174792i −0.190839 0.981621i \(-0.561121\pi\)
−0.0424044 + 0.999101i \(0.513502\pi\)
\(234\) 1.85382e6 727569.i 0.144683 0.0567841i
\(235\) −906818. 6.01634e6i −0.0698742 0.463585i
\(236\) 1.19794e7 + 5.76897e6i 0.911378 + 0.438896i
\(237\) −5.83434e6 + 1.21151e7i −0.438275 + 0.910087i
\(238\) −2.89651e7 + 4.36578e6i −2.14854 + 0.323841i
\(239\) 6.69678e6 + 1.70631e7i 0.490537 + 1.24987i 0.935184 + 0.354163i \(0.115234\pi\)
−0.444647 + 0.895706i \(0.646671\pi\)
\(240\) −149323. 1.99257e6i −0.0108017 0.144139i
\(241\) 6.70172e6 + 7.22274e6i 0.478779 + 0.516001i 0.925539 0.378653i \(-0.123613\pi\)
−0.446760 + 0.894654i \(0.647422\pi\)
\(242\) 1.66625e7 3.80310e6i 1.17569 0.268344i
\(243\) −2.04653e6 + 1.35779e7i −0.142626 + 0.946265i
\(244\) 2.11414e7 3.10087e7i 1.45534 2.13459i
\(245\) −490039. 1.58867e6i −0.0333221 0.108028i
\(246\) 409591. 5.46561e6i 0.0275134 0.367141i
\(247\) −2.84305e6 + 2.26726e6i −0.188666 + 0.150456i
\(248\) −2.76738e6 + 8.97163e6i −0.181432 + 0.588188i
\(249\) 2.92535e7 + 1.14812e7i 1.89487 + 0.743682i
\(250\) −5.86943e6 + 2.57157e7i −0.375644 + 1.64580i
\(251\) 7.40908e6 + 1.28329e7i 0.468536 + 0.811529i 0.999353 0.0359578i \(-0.0114482\pi\)
−0.530817 + 0.847486i \(0.678115\pi\)
\(252\) 1.33709e7 + 7.71967e6i 0.835522 + 0.482389i
\(253\) −7.67265e6 7.11918e6i −0.473788 0.439611i
\(254\) −1.01039e7 8.05757e6i −0.616576 0.491703i
\(255\) 1.35225e7 9.21948e6i 0.815523 0.556014i
\(256\) 1.92178e7 9.25482e6i 1.14547 0.551630i
\(257\) 242668.i 0.0142959i −0.999974 0.00714796i \(-0.997725\pi\)
0.999974 0.00714796i \(-0.00227529\pi\)
\(258\) −1.16908e7 + 3.28022e7i −0.680748 + 1.91004i
\(259\) −2.29291e7 −1.31974
\(260\) −1.52333e6 3.16323e6i −0.0866711 0.179974i
\(261\) −2.45031e6 3.59394e6i −0.137816 0.202139i
\(262\) 1.92353e7 2.41203e7i 1.06954 1.34116i
\(263\) 6.46320e6 6.96568e6i 0.355288 0.382909i −0.529965 0.848020i \(-0.677795\pi\)
0.885253 + 0.465110i \(0.153985\pi\)
\(264\) 6.68387e6 1.15768e7i 0.363259 0.629183i
\(265\) −5.26525e6 + 3.03990e6i −0.282932 + 0.163351i
\(266\) −4.36968e7 9.97350e6i −2.32169 0.529911i
\(267\) 8.00303e6 2.03914e7i 0.420456 1.07130i
\(268\) −1.54889e7 4.77770e6i −0.804669 0.248207i
\(269\) 52175.7 + 65426.3i 0.00268048 + 0.00336121i 0.783170 0.621808i \(-0.213601\pi\)
−0.780489 + 0.625169i \(0.785030\pi\)
\(270\) 1.23513e7 + 925601.i 0.627510 + 0.0470254i
\(271\) −2.32312e7 + 7.16589e6i −1.16725 + 0.360050i −0.817018 0.576613i \(-0.804374\pi\)
−0.350234 + 0.936662i \(0.613898\pi\)
\(272\) −3.63621e6 2.47913e6i −0.180693 0.123195i
\(273\) 4.84864e6 + 730814.i 0.238304 + 0.0359186i
\(274\) −1.16700e7 5.11296e7i −0.567308 2.48554i
\(275\) −4.49572e6 + 4.17142e6i −0.216173 + 0.200579i
\(276\) 5.50708e7 4.12698e6i 2.61935 0.196293i
\(277\) 1.12186e7 4.40297e6i 0.527836 0.207160i −0.0864320 0.996258i \(-0.527547\pi\)
0.614268 + 0.789097i \(0.289451\pi\)
\(278\) 4.74351e6 + 3.14711e7i 0.220783 + 1.46480i
\(279\) 5.54329e6 + 2.66951e6i 0.255244 + 0.122919i
\(280\) 7.70120e6 1.59917e7i 0.350820 0.728485i
\(281\) −3.83391e6 + 577870.i −0.172792 + 0.0260442i −0.234868 0.972027i \(-0.575466\pi\)
0.0620763 + 0.998071i \(0.480228\pi\)
\(282\) 1.19101e7 + 3.03465e7i 0.531092 + 1.35320i
\(283\) −1.54651e6 2.06368e7i −0.0682329 0.910505i −0.921337 0.388764i \(-0.872902\pi\)
0.853104 0.521740i \(-0.174717\pi\)
\(284\) 3.38319e7 + 3.64622e7i 1.47697 + 1.59180i
\(285\) 2.44145e7 5.57245e6i 1.05466 0.240720i
\(286\) 531388. 3.52553e6i 0.0227150 0.150704i
\(287\) 2.61858e6 3.84075e6i 0.110769 0.162469i
\(288\) −3.13686e6 1.01695e7i −0.131316 0.425716i
\(289\) 889965. 1.18758e7i 0.0368706 0.492003i
\(290\) −9.53181e6 + 7.60136e6i −0.390824 + 0.311672i
\(291\) 1.37724e7 4.46490e7i 0.558896 1.81189i
\(292\) 5.60084e7 + 2.19817e7i 2.24960 + 0.882902i
\(293\) −2.00127e6 + 8.76812e6i −0.0795614 + 0.348581i −0.999003 0.0446457i \(-0.985784\pi\)
0.919442 + 0.393227i \(0.128641\pi\)
\(294\) 4.45397e6 + 7.71450e6i 0.175269 + 0.303575i
\(295\) −8.67484e6 5.00842e6i −0.337906 0.195090i
\(296\) −2.64491e7 2.45412e7i −1.01985 0.946283i
\(297\) 6.18544e6 + 4.93272e6i 0.236103 + 0.188286i
\(298\) −4.98666e7 + 3.39984e7i −1.88435 + 1.28473i
\(299\) 5.44314e6 2.62128e6i 0.203627 0.0980618i
\(300\) 3.23587e7i 1.19847i
\(301\) −2.24968e7 + 1.91353e7i −0.824939 + 0.701674i
\(302\) −1.81256e7 −0.658069
\(303\) 2.71128e7 + 5.63003e7i 0.974645 + 2.02387i
\(304\) −3.79335e6 5.56382e6i −0.135021 0.198040i
\(305\) −1.76284e7 + 2.21053e7i −0.621318 + 0.779108i
\(306\) −2.05453e7 + 2.21426e7i −0.717047 + 0.772793i
\(307\) 1.33112e7 2.30556e7i 0.460045 0.796822i −0.538917 0.842359i \(-0.681167\pi\)
0.998963 + 0.0455369i \(0.0144999\pi\)
\(308\) 2.39379e7 1.38205e7i 0.819282 0.473013i
\(309\) 3.53439e7 + 8.06703e6i 1.19795 + 0.273425i
\(310\) 6.30018e6 1.60526e7i 0.211479 0.538841i
\(311\) 1.20789e7 + 3.72586e6i 0.401558 + 0.123864i 0.488954 0.872309i \(-0.337379\pi\)
−0.0873965 + 0.996174i \(0.527855\pi\)
\(312\) 4.81080e6 + 6.03255e6i 0.158399 + 0.198626i
\(313\) −2.80490e7 2.10198e6i −0.914711 0.0685481i −0.390949 0.920412i \(-0.627853\pi\)
−0.523763 + 0.851864i \(0.675472\pi\)
\(314\) −5.06644e7 + 1.56279e7i −1.63649 + 0.504791i
\(315\) −9.61039e6 6.55225e6i −0.307475 0.209633i
\(316\) −4.32640e7 6.52100e6i −1.37109 0.206658i
\(317\) −1.78060e6 7.80130e6i −0.0558969 0.244900i 0.939259 0.343209i \(-0.111514\pi\)
−0.995156 + 0.0983087i \(0.968657\pi\)
\(318\) 2.38798e7 2.21572e7i 0.742591 0.689024i
\(319\) −7.76560e6 + 581951.i −0.239223 + 0.0179273i
\(320\) −3.13363e7 + 1.22986e7i −0.956308 + 0.375323i
\(321\) 5.98025e6 + 3.96764e7i 0.180802 + 1.19955i
\(322\) 6.70895e7 + 3.23086e7i 2.00950 + 0.967722i
\(323\) 2.39311e7 4.96934e7i 0.710157 1.47466i
\(324\) −7.12380e7 + 1.07374e7i −2.09448 + 0.315692i
\(325\) −1.29328e6 3.29522e6i −0.0376741 0.0959920i
\(326\) 4.30056e6 + 5.73870e7i 0.124129 + 1.65638i
\(327\) −3.56305e7 3.84005e7i −1.01901 1.09823i
\(328\) 7.13137e6 1.62769e6i 0.202093 0.0461264i
\(329\) −4.12082e6 + 2.73399e7i −0.115717 + 0.767730i
\(330\) −1.38312e7 + 2.02867e7i −0.384874 + 0.564507i
\(331\) −2.97768e6 9.65340e6i −0.0821096 0.266193i 0.905203 0.424978i \(-0.139718\pi\)
−0.987313 + 0.158786i \(0.949242\pi\)
\(332\) −7.64134e6 + 1.01967e8i −0.208812 + 2.78640i
\(333\) −1.84859e7 + 1.47420e7i −0.500619 + 0.399231i
\(334\) 2.81869e7 9.13798e7i 0.756499 2.45251i
\(335\) 1.13672e7 + 4.46131e6i 0.302357 + 0.118667i
\(336\) −2.02052e6 + 8.85250e6i −0.0532655 + 0.233372i
\(337\) −8.63415e6 1.49548e7i −0.225595 0.390743i 0.730903 0.682482i \(-0.239099\pi\)
−0.956498 + 0.291739i \(0.905766\pi\)
\(338\) −5.31202e7 3.06690e7i −1.37566 0.794235i
\(339\) −6.47440e6 6.00737e6i −0.166188 0.154200i
\(340\) 4.16343e7 + 3.32022e7i 1.05929 + 0.844755i
\(341\) 9.10101e6 6.20496e6i 0.229523 0.156486i
\(342\) −4.16415e7 + 2.00535e7i −1.04099 + 0.501317i
\(343\) 3.61477e7i 0.895773i
\(344\) −4.64312e7 2.00565e6i −1.14060 0.0492698i
\(345\) −4.16048e7 −1.01318
\(346\) −4.44320e7 9.22641e7i −1.07267 2.22743i
\(347\) 3.26987e7 + 4.79602e7i 0.782603 + 1.14787i 0.985667 + 0.168703i \(0.0539578\pi\)
−0.203063 + 0.979166i \(0.565090\pi\)
\(348\) 2.56181e7 3.21241e7i 0.607868 0.762243i
\(349\) −1.81117e7 + 1.95197e7i −0.426071 + 0.459196i −0.909204 0.416352i \(-0.863308\pi\)
0.483132 + 0.875547i \(0.339499\pi\)
\(350\) 2.18157e7 3.77859e7i 0.508821 0.881304i
\(351\) −3.95473e6 + 2.28327e6i −0.0914526 + 0.0528002i
\(352\) −1.85752e7 4.23966e6i −0.425897 0.0972082i
\(353\) 2.18950e7 5.57876e7i 0.497762 1.26828i −0.432584 0.901594i \(-0.642398\pi\)
0.930346 0.366683i \(-0.119507\pi\)
\(354\) 5.12864e7 + 1.58198e7i 1.15609 + 0.356607i
\(355\) −2.33638e7 2.92973e7i −0.522226 0.654850i
\(356\) 7.10766e7 + 5.32646e6i 1.57535 + 0.118056i
\(357\) −7.10687e7 + 2.19218e7i −1.56197 + 0.481805i
\(358\) −1.07372e7 7.32053e6i −0.234015 0.159549i
\(359\) −5.28142e7 7.96046e6i −1.14148 0.172050i −0.449029 0.893517i \(-0.648230\pi\)
−0.692448 + 0.721467i \(0.743468\pi\)
\(360\) −4.07283e6 1.78442e7i −0.0872948 0.382464i
\(361\) 2.73783e7 2.54033e7i 0.581949 0.539969i
\(362\) 8.77592e7 6.57664e6i 1.84998 0.138637i
\(363\) 4.03942e7 1.58536e7i 0.844499 0.331442i
\(364\) 2.37790e6 + 1.57763e7i 0.0493048 + 0.327116i
\(365\) −4.08393e7 1.96672e7i −0.839847 0.404449i
\(366\) 6.57302e7 1.36490e8i 1.34067 2.78393i
\(367\) 1.37072e7 2.06603e6i 0.277301 0.0417963i −0.00891956 0.999960i \(-0.502839\pi\)
0.286220 + 0.958164i \(0.407601\pi\)
\(368\) 4.08728e6 + 1.04142e7i 0.0820145 + 0.208970i
\(369\) −358217. 4.78008e6i −0.00712963 0.0951384i
\(370\) 4.50758e7 + 4.85802e7i 0.889894 + 0.959078i
\(371\) 2.69355e7 6.14785e6i 0.527476 0.120393i
\(372\) −8.66204e6 + 5.74689e7i −0.168264 + 1.11636i
\(373\) 8.83087e6 1.29525e7i 0.170168 0.249590i −0.731676 0.681653i \(-0.761262\pi\)
0.901844 + 0.432062i \(0.142214\pi\)
\(374\) 1.59397e7 + 5.16753e7i 0.304695 + 0.987798i
\(375\) −5.00475e6 + 6.67838e7i −0.0949050 + 1.26642i
\(376\) −3.40155e7 + 2.71265e7i −0.639902 + 0.510305i
\(377\) 1.32490e6 4.29521e6i 0.0247262 0.0801605i
\(378\) −5.23941e7 2.05632e7i −0.970079 0.380728i
\(379\) −1.74255e7 + 7.63463e7i −0.320087 + 1.40239i 0.517309 + 0.855799i \(0.326934\pi\)
−0.837396 + 0.546596i \(0.815923\pi\)
\(380\) 4.07410e7 + 7.05655e7i 0.742474 + 1.28600i
\(381\) −2.84163e7 1.64062e7i −0.513798 0.296642i
\(382\) 1.64570e6 + 1.52699e6i 0.0295230 + 0.0273934i
\(383\) 6.10474e7 + 4.86837e7i 1.08660 + 0.866538i 0.991652 0.128944i \(-0.0411589\pi\)
0.0949519 + 0.995482i \(0.469730\pi\)
\(384\) 1.00037e8 6.82041e7i 1.76672 1.20453i
\(385\) −1.87617e7 + 9.03514e6i −0.328768 + 0.158326i
\(386\) 1.05650e8i 1.83700i
\(387\) −5.83458e6 + 2.98913e7i −0.100665 + 0.515718i
\(388\) 1.52032e8 2.60279
\(389\) 7.79776e6 + 1.61922e7i 0.132471 + 0.275079i 0.956644 0.291259i \(-0.0940740\pi\)
−0.824173 + 0.566338i \(0.808360\pi\)
\(390\) −7.98344e6 1.17096e7i −0.134585 0.197400i
\(391\) −5.71329e7 + 7.16424e7i −0.955776 + 1.19851i
\(392\) −8.08615e6 + 8.71480e6i −0.134241 + 0.144677i
\(393\) 3.91654e7 6.78364e7i 0.645245 1.11760i
\(394\) −1.03985e8 + 6.00357e7i −1.70013 + 0.981570i
\(395\) 3.21354e7 + 7.33469e6i 0.521426 + 0.119012i
\(396\) 1.04134e7 2.65330e7i 0.167690 0.427268i
\(397\) 1.70885e6 + 527111.i 0.0273107 + 0.00842424i 0.308380 0.951263i \(-0.400213\pi\)
−0.281070 + 0.959687i \(0.590689\pi\)
\(398\) −7.22964e7 9.06568e7i −1.14675 1.43797i
\(399\) −1.13481e8 8.50422e6i −1.78650 0.133880i
\(400\) 6.26403e6 1.93220e6i 0.0978755 0.0301906i
\(401\) 8.21655e6 + 5.60195e6i 0.127426 + 0.0868772i 0.625356 0.780340i \(-0.284954\pi\)
−0.497930 + 0.867217i \(0.665906\pi\)
\(402\) −6.46984e7 9.75172e6i −0.995900 0.150108i
\(403\) 1.41476e6 + 6.19849e6i 0.0216157 + 0.0947045i
\(404\) −1.49047e8 + 1.38295e8i −2.26036 + 2.09731i
\(405\) 5.41228e7 4.05594e6i 0.814732 0.0610557i
\(406\) 5.15723e7 2.02406e7i 0.770616 0.302445i
\(407\) 6.30903e6 + 4.18577e7i 0.0935793 + 0.620858i
\(408\) −1.05442e8 5.07783e7i −1.55251 0.747649i
\(409\) −4.37332e7 + 9.08129e7i −0.639206 + 1.32733i 0.289738 + 0.957106i \(0.406432\pi\)
−0.928944 + 0.370220i \(0.879282\pi\)
\(410\) −1.32853e7 + 2.00243e6i −0.192761 + 0.0290540i
\(411\) −4.86475e7 1.23952e8i −0.700705 1.78537i
\(412\) 8.81505e6 + 1.17629e8i 0.126047 + 1.68198i
\(413\) 3.09609e7 + 3.33679e7i 0.439505 + 0.473673i
\(414\) 7.48614e7 1.70866e7i 1.05501 0.240799i
\(415\) 1.14813e7 7.61732e7i 0.160637 1.06576i
\(416\) 6.19505e6 9.08647e6i 0.0860527 0.126216i
\(417\) 2.38184e7 + 7.72175e7i 0.328477 + 1.06490i
\(418\) −6.18356e6 + 8.25139e7i −0.0846662 + 1.12979i
\(419\) 3.19524e7 2.54812e7i 0.434371 0.346399i −0.381765 0.924260i \(-0.624684\pi\)
0.816136 + 0.577860i \(0.196112\pi\)
\(420\) 3.23854e7 1.04991e8i 0.437121 1.41711i
\(421\) 9.25515e7 + 3.63238e7i 1.24033 + 0.486794i 0.892621 0.450809i \(-0.148864\pi\)
0.347709 + 0.937602i \(0.386960\pi\)
\(422\) 2.21914e7 9.72270e7i 0.295289 1.29375i
\(423\) 1.42556e7 + 2.46914e7i 0.188349 + 0.326230i
\(424\) 3.76507e7 + 2.17376e7i 0.493941 + 0.285177i
\(425\) 3.93592e7 + 3.65200e7i 0.512719 + 0.475734i
\(426\) 1.56977e8 + 1.25185e8i 2.03051 + 1.61928i
\(427\) 1.06158e8 7.23773e7i 1.36354 0.929649i
\(428\) −1.17627e8 + 5.66461e7i −1.50029 + 0.722502i
\(429\) 9.05241e6i 0.114655i
\(430\) 8.47682e7 + 1.00467e7i 1.06617 + 0.126362i
\(431\) −2.93301e7 −0.366338 −0.183169 0.983081i \(-0.558636\pi\)
−0.183169 + 0.983081i \(0.558636\pi\)
\(432\) −3.66907e6 7.61890e6i −0.0455098 0.0945020i
\(433\) −1.55527e7 2.28116e7i −0.191577 0.280991i 0.718418 0.695612i \(-0.244867\pi\)
−0.909994 + 0.414621i \(0.863914\pi\)
\(434\) −4.88593e7 + 6.12677e7i −0.597693 + 0.749484i
\(435\) −2.10544e7 + 2.26913e7i −0.255785 + 0.275671i
\(436\) 8.52234e7 1.47611e8i 1.02825 1.78098i
\(437\) −1.21426e8 + 7.01054e7i −1.45502 + 0.840053i
\(438\) 2.36782e8 + 5.40440e7i 2.81791 + 0.643169i
\(439\) −1.17467e7 + 2.99300e7i −0.138842 + 0.353764i −0.983335 0.181803i \(-0.941807\pi\)
0.844493 + 0.535567i \(0.179902\pi\)
\(440\) −3.13123e7 9.65857e6i −0.367584 0.113385i
\(441\) 4.85738e6 + 6.09097e6i 0.0566352 + 0.0710183i
\(442\) −3.11266e7 2.33262e6i −0.360467 0.0270133i
\(443\) 6.65570e7 2.05301e7i 0.765566 0.236146i 0.112710 0.993628i \(-0.464047\pi\)
0.652856 + 0.757482i \(0.273571\pi\)
\(444\) −1.84538e8 1.25816e8i −2.10832 1.43743i
\(445\) −5.30971e7 8.00311e6i −0.602547 0.0908194i
\(446\) −5.05436e7 2.21446e8i −0.569720 2.49611i
\(447\) −1.12331e8 + 1.04228e8i −1.25770 + 1.16698i
\(448\) 1.52547e8 1.14318e7i 1.69656 0.127140i
\(449\) 1.35292e8 5.30981e7i 1.49463 0.586597i 0.529483 0.848321i \(-0.322386\pi\)
0.965143 + 0.261723i \(0.0842908\pi\)
\(450\) −6.70578e6 4.44899e7i −0.0735888 0.488230i
\(451\) −7.73191e6 3.72349e6i −0.0842863 0.0405902i
\(452\) 1.24688e7 2.58918e7i 0.135024 0.280380i
\(453\) −4.55068e7 + 6.85904e6i −0.489532 + 0.0737851i
\(454\) −4.04554e6 1.03079e7i −0.0432324 0.110154i
\(455\) −898227. 1.19860e7i −0.00953569 0.127245i
\(456\) −1.21800e8 1.31269e8i −1.28456 1.38442i
\(457\) −1.75718e8 + 4.01065e7i −1.84106 + 0.420210i −0.993820 0.111002i \(-0.964594\pi\)
−0.847239 + 0.531212i \(0.821737\pi\)
\(458\) −3.53364e7 + 2.34442e8i −0.367812 + 2.44028i
\(459\) 3.90175e7 5.72281e7i 0.403479 0.591795i
\(460\) −3.99017e7 1.29358e8i −0.409938 1.32899i
\(461\) 4.47356e6 5.96955e7i 0.0456615 0.609311i −0.926696 0.375813i \(-0.877364\pi\)
0.972357 0.233498i \(-0.0750173\pi\)
\(462\) 8.72333e7 6.95662e7i 0.884619 0.705460i
\(463\) 4.93802e7 1.60087e8i 0.497519 1.61292i −0.263827 0.964570i \(-0.584985\pi\)
0.761346 0.648346i \(-0.224539\pi\)
\(464\) 7.74831e6 + 3.04099e6i 0.0775627 + 0.0304411i
\(465\) 9.74289e6 4.26864e7i 0.0969011 0.424552i
\(466\) −1.94296e7 3.36531e7i −0.192002 0.332558i
\(467\) −1.48352e7 8.56511e6i −0.145661 0.0840974i 0.425398 0.905006i \(-0.360134\pi\)
−0.571059 + 0.820909i \(0.693467\pi\)
\(468\) 1.20603e7 + 1.11904e7i 0.117658 + 0.109171i
\(469\) −4.33851e7 3.45985e7i −0.420554 0.335381i
\(470\) 6.60263e7 4.50160e7i 0.635951 0.433584i
\(471\) −1.21286e8 + 5.84084e7i −1.16078 + 0.559001i
\(472\) 7.16282e7i 0.681174i
\(473\) 4.11221e7 + 3.58035e7i 0.388590 + 0.338331i
\(474\) −1.76611e8 −1.65838
\(475\) 3.56458e7 + 7.40194e7i 0.332604 + 0.690660i
\(476\) −1.36319e8 1.99943e8i −1.26397 1.85390i
\(477\) 1.77632e7 2.22744e7i 0.163669 0.205235i
\(478\) −1.63752e8 + 1.76483e8i −1.49935 + 1.61592i
\(479\) 5.49964e7 9.52566e7i 0.500412 0.866739i −0.499588 0.866263i \(-0.666515\pi\)
1.00000 0.000475894i \(-0.000151482\pi\)
\(480\) −6.55879e7 + 3.78672e7i −0.593062 + 0.342404i
\(481\) −2.38207e7 5.43693e6i −0.214052 0.0488561i
\(482\) −4.72788e7 + 1.20464e8i −0.422207 + 1.07577i
\(483\) 1.80664e8 + 5.57274e7i 1.60335 + 0.494569i
\(484\) 8.80328e7 + 1.10390e8i 0.776441 + 0.973626i
\(485\) −1.14216e8 8.55927e6i −1.00115 0.0750260i
\(486\) −1.72335e8 + 5.31584e7i −1.50129 + 0.463087i
\(487\) −1.70589e7 1.16305e7i −0.147694 0.100696i 0.487219 0.873280i \(-0.338012\pi\)
−0.634913 + 0.772584i \(0.718964\pi\)
\(488\) 1.99921e8 + 3.01333e7i 1.72028 + 0.259291i
\(489\) 3.25134e7 + 1.42451e8i 0.278058 + 1.21825i
\(490\) 1.60068e7 1.48522e7i 0.136056 0.126241i
\(491\) −2.00094e8 + 1.49950e7i −1.69040 + 0.126678i −0.884859 0.465860i \(-0.845745\pi\)
−0.805543 + 0.592538i \(0.798126\pi\)
\(492\) 4.21497e7 1.65425e7i 0.353915 0.138901i
\(493\) 1.01612e7 + 6.74155e7i 0.0848020 + 0.562625i
\(494\) −4.30311e7 2.07227e7i −0.356945 0.171896i
\(495\) −9.31698e6 + 1.93469e7i −0.0768174 + 0.159513i
\(496\) −1.16421e7 + 1.75476e6i −0.0954082 + 0.0143805i
\(497\) 6.22122e7 + 1.58514e8i 0.506765 + 1.29122i
\(498\) 3.08449e7 + 4.11597e8i 0.249744 + 3.33260i
\(499\) 1.37386e8 + 1.48067e8i 1.10571 + 1.19167i 0.979873 + 0.199622i \(0.0639714\pi\)
0.125838 + 0.992051i \(0.459838\pi\)
\(500\) −2.12445e8 + 4.84892e7i −1.69956 + 0.387913i
\(501\) 3.61874e7 2.40088e8i 0.287769 1.90923i
\(502\) −1.09635e8 + 1.60805e8i −0.866641 + 1.27113i
\(503\) 4.74589e7 + 1.53858e8i 0.372918 + 1.20897i 0.926538 + 0.376202i \(0.122770\pi\)
−0.553619 + 0.832770i \(0.686754\pi\)
\(504\) −6.21562e6 + 8.29416e7i −0.0485504 + 0.647860i
\(505\) 1.19759e8 9.55044e7i 0.929893 0.741565i
\(506\) 4.05203e7 1.31364e8i 0.312767 1.01397i
\(507\) −1.44971e8 5.68970e7i −1.11239 0.436582i
\(508\) 2.37572e7 1.04087e8i 0.181219 0.793972i
\(509\) 3.56482e7 + 6.17445e7i 0.270324 + 0.468215i 0.968945 0.247277i \(-0.0795359\pi\)
−0.698621 + 0.715492i \(0.746203\pi\)
\(510\) 1.86158e8 + 1.07479e8i 1.40337 + 0.810236i
\(511\) 1.50997e8 + 1.40104e8i 1.13163 + 1.05000i
\(512\) 3.73615e7 + 2.97948e7i 0.278365 + 0.221988i
\(513\) 8.75656e7 5.97012e7i 0.648607 0.442212i
\(514\) 2.87159e6 1.38288e6i 0.0211462 0.0101835i
\(515\) 8.88660e7i 0.650600i
\(516\) −2.86058e8 + 3.05607e7i −2.08211 + 0.222440i
\(517\) 5.10435e7 0.369376
\(518\) −1.30666e8 2.71330e8i −0.940095 1.95213i
\(519\) −1.46467e8 2.14828e8i −1.04770 1.53670i
\(520\) 1.17926e7 1.47875e7i 0.0838687 0.105168i
\(521\) 5.13177e7 5.53073e7i 0.362872 0.391083i −0.525054 0.851069i \(-0.675955\pi\)
0.887926 + 0.459986i \(0.152145\pi\)
\(522\) 2.85651e7 4.94762e7i 0.200828 0.347844i
\(523\) −1.84185e8 + 1.06339e8i −1.28750 + 0.743340i −0.978208 0.207626i \(-0.933426\pi\)
−0.309295 + 0.950966i \(0.600093\pi\)
\(524\) 2.48480e8 + 5.67140e7i 1.72702 + 0.394181i
\(525\) 4.04725e7 1.03122e8i 0.279693 0.712647i
\(526\) 1.19260e8 + 3.67867e7i 0.819475 + 0.252775i
\(527\) −6.01256e7 7.53952e7i −0.410798 0.515124i
\(528\) 1.67164e7 + 1.25272e6i 0.113564 + 0.00851047i
\(529\) 8.11349e7 2.50268e7i 0.548076 0.169059i
\(530\) −6.59774e7 4.49826e7i −0.443167 0.302146i
\(531\) 4.64148e7 + 6.99591e6i 0.310008 + 0.0467262i
\(532\) −8.23942e7 3.60992e8i −0.547219 2.39753i
\(533\) 3.63112e6 3.36919e6i 0.0239806 0.0222507i
\(534\) 2.86907e8 2.15007e7i 1.88416 0.141198i
\(535\) 9.15575e7 3.59337e7i 0.597905 0.234661i
\(536\) −1.30145e7 8.63455e7i −0.0845148 0.560719i
\(537\) −2.97275e7 1.43160e7i −0.191971 0.0924485i
\(538\) −476885. + 990261.i −0.00306243 + 0.00635921i
\(539\) 1.37918e7 2.07878e6i 0.0880755 0.0132752i
\(540\) 3.73831e7 + 9.52506e7i 0.237407 + 0.604904i
\(541\) −6.63534e6 8.85425e7i −0.0419056 0.559191i −0.978158 0.207863i \(-0.933349\pi\)
0.936252 0.351328i \(-0.114270\pi\)
\(542\) −2.17184e8 2.34069e8i −1.36405 1.47010i
\(543\) 2.17843e8 4.97212e7i 1.36064 0.310558i
\(544\) −2.48609e7 + 1.64941e8i −0.154426 + 1.02455i
\(545\) −7.23353e7 + 1.06096e8i −0.446849 + 0.655407i
\(546\) 1.89828e7 + 6.15407e7i 0.116622 + 0.378080i
\(547\) 2.00956e7 2.68157e8i 0.122783 1.63843i −0.507206 0.861825i \(-0.669322\pi\)
0.629989 0.776604i \(-0.283059\pi\)
\(548\) 3.38737e8 2.70133e8i 2.05836 1.64148i
\(549\) 3.90525e7 1.26605e8i 0.236011 0.765129i
\(550\) −7.49819e7 2.94282e7i −0.450680 0.176879i
\(551\) −2.32131e7 + 1.01703e8i −0.138764 + 0.607966i
\(552\) 1.48753e8 + 2.57649e8i 0.884402 + 1.53183i
\(553\) −1.29719e8 7.48936e7i −0.767061 0.442863i
\(554\) 1.16033e8 + 1.07663e8i 0.682423 + 0.633196i
\(555\) 1.31553e8 + 1.04910e8i 0.769521 + 0.613673i
\(556\) −2.17242e8 + 1.48113e8i −1.26392 + 0.861727i
\(557\) 2.72393e8 1.31178e8i 1.57627 0.759092i 0.577898 0.816109i \(-0.303873\pi\)
0.998373 + 0.0570171i \(0.0181590\pi\)
\(558\) 8.08088e7i 0.465110i
\(559\) −2.79090e7 + 1.45450e7i −0.159775 + 0.0832679i
\(560\) 2.22580e7 0.126743
\(561\) 5.95737e7 + 1.23706e8i 0.337416 + 0.700652i
\(562\) −2.86864e7 4.20753e7i −0.161610 0.237038i
\(563\) 526901. 660713.i 0.00295260 0.00370244i −0.780353 0.625339i \(-0.784961\pi\)
0.783306 + 0.621637i \(0.213532\pi\)
\(564\) −1.83184e8 + 1.97425e8i −1.02106 + 1.10044i
\(565\) −1.08250e7 + 1.87495e7i −0.0600182 + 0.103955i
\(566\) 2.35391e8 1.35903e8i 1.29819 0.749513i
\(567\) −2.40454e8 5.48820e7i −1.31912 0.301079i
\(568\) −9.78962e7 + 2.49435e8i −0.534221 + 1.36117i
\(569\) −9.08240e7 2.80155e7i −0.493019 0.152076i 0.0382688 0.999267i \(-0.487816\pi\)
−0.531288 + 0.847191i \(0.678292\pi\)
\(570\) 2.05072e8 + 2.57152e8i 1.10734 + 1.38856i
\(571\) −1.48086e8 1.10975e7i −0.795435 0.0596096i −0.329188 0.944264i \(-0.606775\pi\)
−0.466247 + 0.884655i \(0.654394\pi\)
\(572\) 2.81459e7 8.68185e6i 0.150393 0.0463900i
\(573\) 4.70960e6 + 3.21095e6i 0.0250334 + 0.0170675i
\(574\) 6.03717e7 + 9.09957e6i 0.319226 + 0.0481155i
\(575\) −3.03721e7 1.33069e8i −0.159761 0.699959i
\(576\) 1.15637e8 1.07295e8i 0.605101 0.561452i
\(577\) 1.30710e8 9.79535e6i 0.680426 0.0509909i 0.269967 0.962870i \(-0.412987\pi\)
0.410460 + 0.911879i \(0.365368\pi\)
\(578\) 1.45603e8 5.71448e7i 0.754025 0.295933i
\(579\) −3.99799e7 2.65249e8i −0.205971 1.36653i
\(580\) −9.07446e7 4.37003e7i −0.465090 0.223975i
\(581\) −1.51886e8 + 3.15394e8i −0.774442 + 1.60814i
\(582\) 6.06835e8 9.14657e7i 3.07824 0.463970i
\(583\) −1.86345e7 4.74798e7i −0.0940397 0.239609i
\(584\) 2.42224e7 + 3.23226e8i 0.121613 + 1.62281i
\(585\) −8.43044e6 9.08585e6i −0.0421097 0.0453835i
\(586\) −1.15162e8 + 2.62849e7i −0.572288 + 0.130621i
\(587\) −5.01977e7 + 3.33040e8i −0.248182 + 1.64658i 0.423616 + 0.905842i \(0.360761\pi\)
−0.671797 + 0.740735i \(0.734477\pi\)
\(588\) −4.14554e7 + 6.08039e7i −0.203915 + 0.299088i
\(589\) −4.34926e7 1.41000e8i −0.212848 0.690037i
\(590\) 9.83167e6 1.31195e8i 0.0478709 0.638792i
\(591\) −2.38350e8 + 1.90078e8i −1.15466 + 0.920808i
\(592\) 1.33364e7 4.32357e7i 0.0642798 0.208390i
\(593\) 1.02774e8 + 4.03357e7i 0.492853 + 0.193431i 0.598734 0.800948i \(-0.295671\pi\)
−0.105880 + 0.994379i \(0.533766\pi\)
\(594\) −2.31222e7 + 1.01305e8i −0.110324 + 0.483361i
\(595\) 9.11544e7 + 1.57884e8i 0.432740 + 0.749527i
\(596\) −4.31801e8 2.49300e8i −2.03960 1.17756i
\(597\) −2.15816e8 2.00248e8i −1.01429 0.941121i
\(598\) 6.20374e7 + 4.94732e7i 0.290102 + 0.231348i
\(599\) 1.96063e8 1.33674e8i 0.912254 0.621965i −0.0135743 0.999908i \(-0.504321\pi\)
0.925829 + 0.377943i \(0.123369\pi\)
\(600\) 1.57058e8 7.56353e7i 0.727122 0.350164i
\(601\) 3.26037e8i 1.50191i −0.660353 0.750955i \(-0.729593\pi\)
0.660353 0.750955i \(-0.270407\pi\)
\(602\) −3.54638e8 1.57169e8i −1.62553 0.720406i
\(603\) −5.72226e7 −0.260985
\(604\) −6.49702e7 1.34912e8i −0.294852 0.612265i
\(605\) −5.99207e7 8.78875e7i −0.270589 0.396882i
\(606\) −5.11718e8 + 6.41674e8i −2.29939 + 2.88335i
\(607\) −1.91601e8 + 2.06497e8i −0.856708 + 0.923312i −0.997774 0.0666886i \(-0.978757\pi\)
0.141066 + 0.990000i \(0.454947\pi\)
\(608\) −1.27615e8 + 2.21035e8i −0.567793 + 0.983446i
\(609\) 1.21820e8 7.03328e7i 0.539345 0.311391i
\(610\) −3.62041e8 8.26334e7i −1.59503 0.364054i
\(611\) −1.07639e7 + 2.74259e7i −0.0471894 + 0.120237i
\(612\) −2.38455e8 7.35535e7i −1.04028 0.320885i
\(613\) −1.12902e8 1.41575e8i −0.490140 0.614617i 0.473833 0.880615i \(-0.342870\pi\)
−0.963974 + 0.265998i \(0.914299\pi\)
\(614\) 3.48683e8 + 2.61302e7i 1.50635 + 0.112885i
\(615\) −3.25967e7 + 1.00548e7i −0.140136 + 0.0432261i
\(616\) 1.23033e8 + 8.38822e7i 0.526354 + 0.358862i
\(617\) −8.96062e7 1.35060e7i −0.381490 0.0575003i −0.0445017 0.999009i \(-0.514170\pi\)
−0.336988 + 0.941509i \(0.609408\pi\)
\(618\) 1.05953e8 + 4.64212e8i 0.448899 + 1.96676i
\(619\) 4.98387e7 4.62436e7i 0.210133 0.194975i −0.568084 0.822971i \(-0.692315\pi\)
0.778217 + 0.627996i \(0.216124\pi\)
\(620\) 1.42065e8 1.06463e7i 0.596091 0.0446708i
\(621\) −1.63903e8 + 6.43272e7i −0.684403 + 0.268609i
\(622\) 2.47443e7 + 1.64168e8i 0.102826 + 0.682208i
\(623\) 2.19848e8 + 1.05873e8i 0.909198 + 0.437846i
\(624\) −4.19819e6 + 8.71764e6i −0.0172786 + 0.0358794i
\(625\) 2.41590e7 3.64138e6i 0.0989552 0.0149151i
\(626\) −1.34968e8 3.43894e8i −0.550186 1.40185i
\(627\) 1.57000e7 + 2.09502e8i 0.0636939 + 0.849937i
\(628\) −2.97925e8 3.21087e8i −1.20290 1.29642i
\(629\) 3.61304e8 8.24652e7i 1.45185 0.331374i
\(630\) 2.27691e7 1.51063e8i 0.0910592 0.604138i
\(631\) 1.30519e8 1.91436e8i 0.519501 0.761968i −0.473408 0.880843i \(-0.656977\pi\)
0.992909 + 0.118875i \(0.0379289\pi\)
\(632\) −6.94746e7 2.25231e8i −0.275217 0.892231i
\(633\) 1.89222e7 2.52499e8i 0.0746038 0.995518i
\(634\) 8.21691e7 6.55277e7i 0.322434 0.257133i
\(635\) −2.37078e7 + 7.68589e7i −0.0925913 + 0.300174i
\(636\) 2.50516e8 + 9.83204e7i 0.973788 + 0.382184i
\(637\) −1.79143e6 + 7.84876e6i −0.00693076 + 0.0303657i
\(638\) −5.11402e7 8.85773e7i −0.196925 0.341083i
\(639\) 1.52072e8 + 8.77986e7i 0.582835 + 0.336500i
\(640\) −2.17562e8 2.01868e8i −0.829933 0.770066i
\(641\) −1.07495e8 8.57244e7i −0.408145 0.325485i 0.397803 0.917471i \(-0.369773\pi\)
−0.805948 + 0.591986i \(0.798344\pi\)
\(642\) −4.35428e8 + 2.96870e8i −1.64555 + 1.12192i
\(643\) −1.51164e8 + 7.27968e7i −0.568612 + 0.273829i −0.696021 0.718021i \(-0.745048\pi\)
0.127409 + 0.991850i \(0.459334\pi\)
\(644\) 6.15168e8i 2.30322i
\(645\) 2.16624e8 6.85421e6i 0.807287 0.0255434i
\(646\) 7.24419e8 2.68715
\(647\) 1.59124e8 + 3.30425e8i 0.587520 + 1.22000i 0.956818 + 0.290688i \(0.0938840\pi\)
−0.369298 + 0.929311i \(0.620402\pi\)
\(648\) −2.18627e8 3.20667e8i −0.803488 1.17850i
\(649\) 5.23950e7 6.57013e7i 0.191671 0.240348i
\(650\) 3.16238e7 3.40824e7i 0.115153 0.124105i
\(651\) −9.94833e7 + 1.72310e8i −0.360585 + 0.624551i
\(652\) −4.11727e8 + 2.37711e8i −1.48548 + 0.857641i
\(653\) −2.94257e8 6.71623e7i −1.05679 0.241205i −0.341390 0.939922i \(-0.610898\pi\)
−0.715398 + 0.698717i \(0.753755\pi\)
\(654\) 2.51363e8 6.40463e8i 0.898604 2.28960i
\(655\) −1.83480e8 5.65961e7i −0.652928 0.201402i
\(656\) 5.71915e6 + 7.17158e6i 0.0202591 + 0.0254041i
\(657\) 2.11815e8 + 1.58733e7i 0.746896 + 0.0559721i
\(658\) −3.47007e8 + 1.07038e8i −1.21804 + 0.375715i
\(659\) 1.90222e8 + 1.29691e8i 0.664669 + 0.453163i 0.848077 0.529873i \(-0.177761\pi\)
−0.183408 + 0.983037i \(0.558713\pi\)
\(660\) −2.00575e8 3.02318e7i −0.697661 0.105156i
\(661\) 4.09368e7 + 1.79356e8i 0.141745 + 0.621028i 0.995029 + 0.0995810i \(0.0317502\pi\)
−0.853284 + 0.521447i \(0.825393\pi\)
\(662\) 9.72640e7 9.02478e7i 0.335257 0.311073i
\(663\) −7.90304e7 + 5.92251e6i −0.271178 + 0.0203220i
\(664\) −5.12772e8 + 2.01248e8i −1.75154 + 0.687429i
\(665\) 4.15759e7 + 2.75838e8i 0.141376 + 0.937970i
\(666\) −2.79794e8 1.34742e8i −0.947142 0.456120i
\(667\) 7.51975e7 1.56149e8i 0.253411 0.526214i
\(668\) 7.81191e8 1.17746e8i 2.62076 0.395017i
\(669\) −2.10696e8 5.36844e8i −0.703684 1.79296i
\(670\) 1.19856e7 + 1.59937e8i 0.0398507 + 0.531771i
\(671\) −1.61337e8 1.73880e8i −0.534030 0.575547i
\(672\) 3.35528e8 7.65821e7i 1.10566 0.252359i
\(673\) −9.14071e6 + 6.06446e7i −0.0299871 + 0.198951i −0.998808 0.0488104i \(-0.984457\pi\)
0.968821 + 0.247762i \(0.0796951\pi\)
\(674\) 1.27763e8 1.87394e8i 0.417279 0.612035i
\(675\) 3.04097e7 + 9.85858e7i 0.0988782 + 0.320555i
\(676\) 3.78681e7 5.05315e8i 0.122584 1.63577i
\(677\) 9.89146e7 7.88818e7i 0.318782 0.254220i −0.451004 0.892522i \(-0.648934\pi\)
0.769787 + 0.638301i \(0.220363\pi\)
\(678\) 3.41922e7 1.10848e8i 0.109708 0.355665i
\(679\) 4.84502e8 + 1.90153e8i 1.54770 + 0.607427i
\(680\) −6.38364e7 + 2.79686e8i −0.203021 + 0.889495i
\(681\) −1.40576e7 2.43484e7i −0.0445112 0.0770956i
\(682\) 1.25290e8 + 7.23360e7i 0.394968 + 0.228035i
\(683\) 2.32650e8 + 2.15868e8i 0.730198 + 0.677525i 0.954908 0.296901i \(-0.0959531\pi\)
−0.224710 + 0.974426i \(0.572144\pi\)
\(684\) −2.98524e8 2.38065e8i −0.932848 0.743921i
\(685\) −2.69687e8 + 1.83870e8i −0.839052 + 0.572056i
\(686\) 4.27751e8 2.05994e8i 1.32501 0.638090i
\(687\) 6.01971e8i 1.85654i
\(688\) −2.29970e7 5.35504e7i −0.0706163 0.164436i
\(689\) 2.94407e7 0.0900099
\(690\) −2.37093e8 4.92328e8i −0.721723 1.49867i
\(691\) 2.65260e8 + 3.89065e8i 0.803966 + 1.17920i 0.980811 + 0.194962i \(0.0624585\pi\)
−0.176845 + 0.984239i \(0.556589\pi\)
\(692\) 5.27474e8 6.61432e8i 1.59178 1.99603i
\(693\) 6.63719e7 7.15319e7i 0.199427 0.214932i
\(694\) −3.81194e8 + 6.60247e8i −1.14043 + 1.97528i
\(695\) 1.71544e8 9.90410e7i 0.511001 0.295026i
\(696\) 2.15799e8 + 4.92548e7i 0.640063 + 0.146090i
\(697\) −2.74487e7 + 6.99382e7i −0.0810632 + 0.206546i
\(698\) −3.34198e8 1.03086e8i −0.982738 0.303134i
\(699\) −6.15156e7 7.71381e7i −0.180117 0.225859i
\(700\) 3.59445e8 + 2.69367e7i 1.04794 + 0.0785325i
\(701\) −3.81533e8 + 1.17687e8i −1.10759 + 0.341646i −0.794002 0.607915i \(-0.792006\pi\)
−0.313585 + 0.949560i \(0.601530\pi\)
\(702\) −4.95556e7 3.37865e7i −0.143246 0.0976633i
\(703\) 5.60720e8 + 8.45149e7i 1.61391 + 0.243258i
\(704\) −6.28431e7 2.75334e8i −0.180111 0.789117i
\(705\) 1.48733e8 1.38004e8i 0.424464 0.393845i
\(706\) 7.84932e8 5.88225e7i 2.23058 0.167159i
\(707\) −6.47960e8 + 2.54306e8i −1.83354 + 0.719611i
\(708\) 6.60841e7 + 4.38439e8i 0.186207 + 1.23541i
\(709\) −5.20347e8 2.50586e8i −1.46000 0.703101i −0.475705 0.879605i \(-0.657807\pi\)
−0.984300 + 0.176504i \(0.943521\pi\)
\(710\) 2.13544e8 4.43430e8i 0.596641 1.23894i
\(711\) −1.52734e8 + 2.30210e7i −0.424940 + 0.0640495i
\(712\) 1.40282e8 + 3.57432e8i 0.388652 + 0.990269i
\(713\) 1.83197e7 + 2.44459e8i 0.0505417 + 0.674432i
\(714\) −6.64408e8 7.16061e8i −1.82532 1.96723i
\(715\) −2.16336e7 + 4.93774e6i −0.0591850 + 0.0135086i
\(716\) 1.60009e7 1.06159e8i 0.0435919 0.289214i
\(717\) −3.44338e8 + 5.05052e8i −0.934174 + 1.37018i
\(718\) −2.06772e8 6.70337e8i −0.558621 1.81101i
\(719\) 5.20167e6 6.94115e7i 0.0139945 0.186743i −0.985826 0.167773i \(-0.946342\pi\)
0.999820 0.0189697i \(-0.00603862\pi\)
\(720\) 1.79449e7 1.43105e7i 0.0480776 0.0383406i
\(721\) −1.19031e8 + 3.85889e8i −0.317581 + 1.02957i
\(722\) 4.56629e8 + 1.79214e8i 1.21325 + 0.476167i
\(723\) −7.31141e7 + 3.20334e8i −0.193458 + 0.847594i
\(724\) 3.63519e8 + 6.29634e8i 0.957882 + 1.65910i
\(725\) −8.79458e7 5.07755e7i −0.230782 0.133242i
\(726\) 4.17796e8 + 3.87658e8i 1.09183 + 1.01307i
\(727\) −5.25813e8 4.19322e8i −1.36845 1.09130i −0.985895 0.167367i \(-0.946473\pi\)
−0.382553 0.923933i \(-0.624955\pi\)
\(728\) −7.10149e7 + 4.84172e7i −0.184058 + 0.125489i
\(729\) 2.35359e7 1.13343e7i 0.0607504 0.0292558i
\(730\) 5.95346e8i 1.53039i
\(731\) 2.85672e8 3.82434e8i 0.731333 0.979048i
\(732\) 1.25153e9 3.19086
\(733\) −6.49518e6 1.34874e7i −0.0164922 0.0342465i 0.892560 0.450929i \(-0.148907\pi\)
−0.909052 + 0.416682i \(0.863193\pi\)
\(734\) 1.02561e8 + 1.50430e8i 0.259355 + 0.380404i
\(735\) 3.45670e7 4.33456e7i 0.0870562 0.109165i
\(736\) 2.88415e8 3.10838e8i 0.723410 0.779651i
\(737\) −5.12229e7 + 8.87207e7i −0.127956 + 0.221627i
\(738\) 5.45233e7 3.14791e7i 0.135648 0.0783164i
\(739\) 3.32705e8 + 7.59378e7i 0.824378 + 0.188159i 0.613844 0.789427i \(-0.289622\pi\)
0.210534 + 0.977586i \(0.432480\pi\)
\(740\) −2.00019e8 + 5.09641e8i −0.493602 + 1.25768i
\(741\) −1.15877e8 3.57434e7i −0.284802 0.0878499i
\(742\) 2.26247e8 + 2.83704e8i 0.553822 + 0.694471i
\(743\) −3.43384e7 2.57331e6i −0.0837169 0.00627372i 0.0328058 0.999462i \(-0.489556\pi\)
−0.116523 + 0.993188i \(0.537175\pi\)
\(744\) −2.99181e8 + 9.22851e7i −0.726466 + 0.224085i
\(745\) 3.10359e8 + 2.11599e8i 0.750578 + 0.511735i
\(746\) 2.03597e8 + 3.06873e7i 0.490405 + 0.0739166i
\(747\) 8.03258e7 + 3.51930e8i 0.192705 + 0.844296i
\(748\) −3.27493e8 + 3.03870e8i −0.782524 + 0.726076i
\(749\) −4.45708e8 + 3.34012e7i −1.06073 + 0.0794908i
\(750\) −8.18802e8 + 3.21356e8i −1.94086 + 0.761733i
\(751\) −2.11795e7 1.40517e8i −0.0500030 0.331748i −0.999821 0.0189438i \(-0.993970\pi\)
0.949818 0.312804i \(-0.101268\pi\)
\(752\) −4.91559e7 2.36722e7i −0.115590 0.0556654i
\(753\) −2.14403e8 + 4.45212e8i −0.502164 + 1.04275i
\(754\) 5.83772e7 8.79895e6i 0.136185 0.0205266i
\(755\) 4.12141e7 + 1.05012e8i 0.0957645 + 0.244004i
\(756\) −3.47485e7 4.63687e8i −0.0804212 1.07315i
\(757\) 1.27165e8 + 1.37051e8i 0.293143 + 0.315933i 0.862401 0.506226i \(-0.168960\pi\)
−0.569258 + 0.822159i \(0.692769\pi\)
\(758\) −1.00274e9 + 2.28869e8i −2.30240 + 0.525508i
\(759\) 5.20215e7 3.45140e8i 0.118976 0.789351i
\(760\) −2.47273e8 + 3.62683e8i −0.563295 + 0.826203i
\(761\) −1.42224e8 4.61080e8i −0.322716 1.04622i −0.961030 0.276443i \(-0.910844\pi\)
0.638315 0.769775i \(-0.279632\pi\)
\(762\) 3.22057e7 4.29756e8i 0.0727894 0.971308i
\(763\) 4.56217e8 3.63821e8i 1.02707 0.819058i
\(764\) −5.46672e6 + 1.77227e7i −0.0122588 + 0.0397419i
\(765\) 1.75000e8 + 6.86826e7i 0.390890 + 0.153413i
\(766\) −2.28205e8 + 9.99833e8i −0.507738 + 2.22455i
\(767\) 2.42527e7 + 4.20069e7i 0.0537494 + 0.0930968i
\(768\) 6.16010e8 + 3.55654e8i 1.35989 + 0.785134i
\(769\) −3.61252e8 3.35193e8i −0.794386 0.737082i 0.174482 0.984660i \(-0.444175\pi\)
−0.968868 + 0.247578i \(0.920365\pi\)
\(770\) −2.13833e8 1.70526e8i −0.468385 0.373525i
\(771\) 6.68621e6 4.55858e6i 0.0145887 0.00994642i
\(772\) 7.86373e8 3.78697e8i 1.70914 0.823077i
\(773\) 8.22721e7i 0.178120i −0.996026 0.0890602i \(-0.971614\pi\)
0.996026 0.0890602i \(-0.0283864\pi\)
\(774\) −3.86967e8 + 1.01298e8i −0.834546 + 0.218463i
\(775\) 1.43641e8 0.308583
\(776\) 3.55360e8 + 7.37912e8i 0.760471 + 1.57914i
\(777\) −4.30730e8 6.31765e8i −0.918210 1.34677i
\(778\) −1.47173e8 + 1.84549e8i −0.312527 + 0.391897i
\(779\) −7.81928e7 + 8.42718e7i −0.165407 + 0.178267i
\(780\) 5.85401e7 1.01395e8i 0.123359 0.213664i
\(781\) 2.72254e8 1.57186e8i 0.571507 0.329960i
\(782\) −1.17336e9 2.67811e8i −2.45364 0.560026i
\(783\) −4.78603e7 + 1.21946e8i −0.0996988 + 0.254028i
\(784\) −1.42458e7 4.39426e6i −0.0295624 0.00911880i
\(785\) 2.05743e8 + 2.57993e8i 0.425319 + 0.533334i
\(786\) 1.02593e9 + 7.68827e7i 2.11276 + 0.158329i
\(787\) −1.80758e8 + 5.57564e7i −0.370828 + 0.114385i −0.474567 0.880219i \(-0.657395\pi\)
0.103739 + 0.994605i \(0.466919\pi\)
\(788\) −8.19586e8 5.58784e8i −1.67500 1.14200i
\(789\) 3.13338e8 + 4.72281e7i 0.637944 + 0.0961546i
\(790\) 9.63347e7 + 4.22070e8i 0.195390 + 0.856058i
\(791\) 7.21201e7 6.69177e7i 0.145723 0.135211i
\(792\) 1.53123e8 1.14749e7i 0.308222 0.0230980i
\(793\) 1.27448e8 5.00198e7i 0.255573 0.100305i
\(794\) 3.50067e6 + 2.32254e7i 0.00699342 + 0.0463983i
\(795\) −1.82668e8 8.79680e7i −0.363546 0.175075i
\(796\) 4.15632e8 8.63069e8i 0.824081 1.71122i
\(797\) −6.37957e8 + 9.61566e7i −1.26013 + 0.189935i −0.744935 0.667137i \(-0.767520\pi\)
−0.515198 + 0.857071i \(0.672282\pi\)
\(798\) −5.46057e8 1.39133e9i −1.07456 2.73793i
\(799\) −3.33951e7 4.45626e8i −0.0654700 0.873636i
\(800\) −1.68994e8 1.82133e8i −0.330067 0.355728i
\(801\) 2.45316e8 5.59917e7i 0.477340 0.108950i
\(802\) −1.94668e7 + 1.29154e8i −0.0377373 + 0.250371i
\(803\) 2.14217e8 3.14199e8i 0.413721 0.606817i
\(804\) −1.59324e8 5.16517e8i −0.306559 0.993840i
\(805\) 3.46335e7 4.62151e8i 0.0663908 0.885924i
\(806\) −6.52871e7 + 5.20647e7i −0.124687 + 0.0994348i
\(807\) −822552. + 2.66665e6i −0.00156510 + 0.00507394i
\(808\) −1.01962e9 4.00171e8i −1.93288 0.758598i
\(809\) −2.10659e8 + 9.22957e8i −0.397864 + 1.74315i 0.237918 + 0.971285i \(0.423535\pi\)
−0.635781 + 0.771869i \(0.719322\pi\)
\(810\) 3.56424e8 + 6.17344e8i 0.670674 + 1.16164i
\(811\) 1.83575e8 + 1.05987e8i 0.344152 + 0.198696i 0.662107 0.749410i \(-0.269663\pi\)
−0.317954 + 0.948106i \(0.602996\pi\)
\(812\) 3.35513e8 + 3.11310e8i 0.626673 + 0.581468i
\(813\) −6.33848e8 5.05477e8i −1.17954 0.940653i
\(814\) −4.59367e8 + 3.13191e8i −0.851700 + 0.580679i
\(815\) 3.22697e8 1.55403e8i 0.596104 0.287068i
\(816\) 1.46759e8i 0.270107i
\(817\) 6.20680e8 3.85023e8i 1.13816 0.706025i
\(818\) −1.32385e9 −2.41868
\(819\) 2.44381e7 + 5.07463e7i 0.0444853 + 0.0923746i
\(820\) −6.25247e7 9.17070e7i −0.113399 0.166326i
\(821\) 3.56493e8 4.47028e8i 0.644202 0.807803i −0.347320 0.937747i \(-0.612908\pi\)
0.991521 + 0.129943i \(0.0414796\pi\)
\(822\) 1.18955e9 1.28203e9i 2.14174 2.30825i
\(823\) 1.32341e8 2.29221e8i 0.237408 0.411202i −0.722562 0.691306i \(-0.757036\pi\)
0.959970 + 0.280104i \(0.0903689\pi\)
\(824\) −5.50326e8 + 3.17731e8i −0.983644 + 0.567907i
\(825\) −1.99389e8 4.55092e7i −0.355090 0.0810470i
\(826\) −2.18421e8 + 5.56527e8i −0.387573 + 0.987520i
\(827\) −9.21746e8 2.84321e8i −1.62965 0.502681i −0.660849 0.750518i \(-0.729804\pi\)
−0.968802 + 0.247838i \(0.920280\pi\)
\(828\) 3.95516e8 + 4.95961e8i 0.696743 + 0.873688i
\(829\) 1.02370e9 + 7.67155e7i 1.79683 + 0.134654i 0.930846 0.365411i \(-0.119071\pi\)
0.865988 + 0.500065i \(0.166690\pi\)
\(830\) 9.66818e8 2.98224e8i 1.69087 0.521565i
\(831\) 3.32060e8 + 2.26394e8i 0.578646 + 0.394514i
\(832\) 1.61190e8 + 2.42955e7i 0.279878 + 0.0421847i
\(833\) −2.71717e7 1.19047e8i −0.0470091 0.205960i
\(834\) −7.78014e8 + 7.21892e8i −1.34119 + 1.24444i
\(835\) −5.93506e8 + 4.44772e7i −1.01945 + 0.0763972i
\(836\) −6.36331e8 + 2.49741e8i −1.08909 + 0.427437i
\(837\) −2.76172e7 1.83228e8i −0.0470980 0.312475i
\(838\) 4.83616e8 + 2.32897e8i 0.821804 + 0.395760i
\(839\) −1.33026e8 + 2.76232e8i −0.225243 + 0.467722i −0.982710 0.185152i \(-0.940722\pi\)
0.757467 + 0.652873i \(0.226437\pi\)
\(840\) 5.85288e8 8.82180e7i 0.987488 0.148840i
\(841\) 1.70204e8 + 4.33672e8i 0.286142 + 0.729077i
\(842\) 9.75863e7 + 1.30220e9i 0.163476 + 2.18143i
\(843\) −8.79433e7 9.47803e7i −0.146798 0.158211i
\(844\) 8.03222e8 1.83330e8i 1.33601 0.304935i
\(845\) −5.68976e7 + 3.77491e8i −0.0943026 + 0.625657i
\(846\) −2.10946e8 + 3.09400e8i −0.348385 + 0.510987i
\(847\) 1.42478e8 + 4.61901e8i 0.234475 + 0.760149i
\(848\) −4.07417e6 + 5.43660e7i −0.00668115 + 0.0891538i
\(849\) 5.39552e8 4.30279e8i 0.881679 0.703116i
\(850\) −2.07861e8 + 6.73870e8i −0.338467 + 1.09728i
\(851\) −8.76967e8 3.44184e8i −1.42297 0.558473i
\(852\) −3.69098e8 + 1.61712e9i −0.596792 + 2.61471i
\(853\) −4.18091e8 7.24155e8i −0.673633 1.16677i −0.976866 0.213851i \(-0.931399\pi\)
0.303233 0.952916i \(-0.401934\pi\)
\(854\) 1.46143e9 + 8.43759e8i 2.34642 + 1.35470i
\(855\) 2.10866e8 + 1.95655e8i 0.337372 + 0.313035i
\(856\) −5.49882e8 4.38516e8i −0.876695 0.699141i
\(857\) 4.07967e8 2.78147e8i 0.648161 0.441909i −0.194098 0.980982i \(-0.562178\pi\)
0.842259 + 0.539074i \(0.181226\pi\)
\(858\) 1.07121e8 5.15868e7i 0.169595 0.0816726i
\(859\) 1.89540e8i 0.299035i 0.988759 + 0.149517i \(0.0477720\pi\)
−0.988759 + 0.149517i \(0.952228\pi\)
\(860\) 2.29068e8 + 6.66957e8i 0.360138 + 1.04858i
\(861\) 1.55015e8 0.242864
\(862\) −1.67143e8 3.47076e8i −0.260955 0.541879i
\(863\) −2.56814e8 3.76676e8i −0.399563 0.586052i 0.572751 0.819730i \(-0.305876\pi\)
−0.972314 + 0.233678i \(0.924924\pi\)
\(864\) −1.99837e8 + 2.50587e8i −0.309837 + 0.388524i
\(865\) −4.33508e8 + 4.67211e8i −0.669806 + 0.721879i
\(866\) 1.81310e8 3.14038e8i 0.279169 0.483536i
\(867\) 3.43931e8 1.98569e8i 0.527733 0.304687i
\(868\) −6.31160e8 1.44058e8i −0.965118 0.220282i
\(869\) −1.01027e8 + 2.57414e8i −0.153950 + 0.392259i
\(870\) −3.88498e8 1.19836e8i −0.589972 0.181982i
\(871\) −3.68683e7 4.62313e7i −0.0557954 0.0699652i
\(872\) 9.15657e8 + 6.86190e7i 1.38097 + 0.103489i
\(873\) 5.12872e8 1.58200e8i 0.770843 0.237774i
\(874\) −1.52155e9 1.03738e9i −2.27905 1.55383i
\(875\) −7.37676e8 1.11187e8i −1.10114 0.165970i
\(876\) 4.46474e8 + 1.95613e9i 0.664177 + 2.90995i
\(877\) −2.20896e8 + 2.04962e8i −0.327484 + 0.303861i −0.826729 0.562600i \(-0.809801\pi\)
0.499245 + 0.866461i \(0.333611\pi\)
\(878\) −4.21115e8 + 3.15582e7i −0.622182 + 0.0466261i
\(879\) −2.79182e8 + 1.09571e8i −0.411075 + 0.161335i
\(880\) −6.12438e6 4.06326e7i −0.00898699 0.0596248i
\(881\) −4.83164e8 2.32679e8i −0.706589 0.340275i 0.0458401 0.998949i \(-0.485404\pi\)
−0.752429 + 0.658674i \(0.771118\pi\)
\(882\) −4.43964e7 + 9.21900e7i −0.0647056 + 0.134362i
\(883\) −4.21875e7 + 6.35874e6i −0.0612776 + 0.00923611i −0.179610 0.983738i \(-0.557483\pi\)
0.118332 + 0.992974i \(0.462245\pi\)
\(884\) −9.42097e7 2.40042e8i −0.136376 0.347481i
\(885\) −2.49626e7 3.33102e8i −0.0360130 0.480560i
\(886\) 6.22229e8 + 6.70603e8i 0.894641 + 0.964194i
\(887\) 7.86590e8 1.79534e8i 1.12714 0.257262i 0.381994 0.924165i \(-0.375238\pi\)
0.745145 + 0.666903i \(0.232380\pi\)
\(888\) 1.79328e8 1.18977e9i 0.256100 1.69912i
\(889\) 2.05896e8 3.01995e8i 0.293051 0.429827i
\(890\) −2.07879e8 6.73928e8i −0.294877 0.955969i
\(891\) −3.40268e7 + 4.54056e8i −0.0481048 + 0.641914i
\(892\) 1.46709e9 1.16997e9i 2.06711 1.64846i
\(893\) 2.01545e8 6.53394e8i 0.283021 0.917531i
\(894\) −1.87352e9 7.35301e8i −2.62207 1.02909i
\(895\) −1.79975e7 + 7.88524e7i −0.0251041 + 0.109988i
\(896\) 6.74345e8 + 1.16800e9i 0.937471 + 1.62375i
\(897\) 1.74475e8 + 1.00733e8i 0.241744 + 0.139571i
\(898\) 1.39932e9 + 1.29838e9i 1.93236 + 1.79296i
\(899\) 1.42599e8 + 1.13719e8i 0.196263 + 0.156514i
\(900\) 3.07110e8 2.09384e8i 0.421276 0.287221i
\(901\) −4.02323e8 + 1.93748e8i −0.550048 + 0.264889i
\(902\) 1.12714e8i 0.153588i
\(903\) −9.49844e8 2.60393e8i −1.29000 0.353643i
\(904\) 1.54815e8 0.209559
\(905\) −2.37650e8 4.93485e8i −0.320621 0.665776i
\(906\) −3.40494e8 4.99414e8i −0.457852 0.671546i
\(907\) 4.60051e8 5.76886e8i 0.616573 0.773158i −0.371285 0.928519i \(-0.621083\pi\)
0.987858 + 0.155361i \(0.0496541\pi\)
\(908\) 6.22223e7 6.70597e7i 0.0831168 0.0895786i
\(909\) −3.58895e8 + 6.21625e8i −0.477833 + 0.827631i
\(910\) 1.36717e8 7.89335e7i 0.181425 0.104746i
\(911\) 1.22437e9 + 2.79454e8i 1.61941 + 0.369620i 0.933645 0.358200i \(-0.116610\pi\)
0.685768 + 0.727821i \(0.259467\pi\)
\(912\) 8.20406e7 2.09036e8i 0.108154 0.275573i
\(913\) 6.17553e8 + 1.90490e8i 0.811450 + 0.250299i
\(914\) −1.47596e9 1.85079e9i −1.93302 2.42393i
\(915\) −9.40223e8 7.04599e7i −1.22735 0.0919770i
\(916\) −1.87166e9 + 5.77329e8i −2.43523 + 0.751168i
\(917\) 7.20932e8 + 4.91523e8i 0.934946 + 0.637435i
\(918\) 8.99553e8 + 1.35586e8i 1.16278 + 0.175261i
\(919\) 1.68118e8 + 7.36572e8i 0.216604 + 0.949005i 0.959966 + 0.280116i \(0.0903729\pi\)
−0.743362 + 0.668889i \(0.766770\pi\)
\(920\) 5.34595e8 4.96032e8i 0.686533 0.637010i
\(921\) 8.85304e8 6.63444e7i 1.13322 0.0849230i
\(922\) 7.31896e8 2.87248e8i 0.933806 0.366492i
\(923\) 2.70447e7 + 1.79430e8i 0.0343936 + 0.228187i
\(924\) 8.30477e8 + 3.99937e8i 1.05272 + 0.506962i
\(925\) −2.39508e8 + 4.97343e8i −0.302618 + 0.628393i
\(926\) 2.17577e9 3.27945e8i 2.74019 0.413017i
\(927\) 1.52138e8 + 3.87641e8i 0.190985 + 0.486621i
\(928\) −2.35763e7 3.14603e8i −0.0295006 0.393658i
\(929\) 8.38883e8 + 9.04100e8i 1.04629 + 1.12764i 0.991627 + 0.129133i \(0.0412194\pi\)
0.0546675 + 0.998505i \(0.482590\pi\)
\(930\) 5.60648e8 1.27964e8i 0.697014 0.159089i
\(931\) 2.78471e7 1.84753e8i 0.0345088 0.228951i
\(932\) 1.80841e8 2.65246e8i 0.223383 0.327643i
\(933\) 1.24248e8 + 4.02802e8i 0.152984 + 0.495960i
\(934\) 1.68136e7 2.24361e8i 0.0206357 0.275364i
\(935\) 2.63140e8 2.09847e8i 0.321923 0.256725i
\(936\) −2.61244e7 + 8.46931e7i −0.0318580 + 0.103281i
\(937\) −1.04376e9 4.09644e8i −1.26876 0.497953i −0.367015 0.930215i \(-0.619620\pi\)
−0.901748 + 0.432263i \(0.857715\pi\)
\(938\) 1.62181e8 7.10560e8i 0.196513 0.860979i
\(939\) −4.68993e8 8.12319e8i −0.566460 0.981138i
\(940\) 5.71730e8 + 3.30088e8i 0.688347 + 0.397417i
\(941\) 7.98855e8 + 7.41229e8i 0.958736 + 0.889577i 0.993953 0.109802i \(-0.0350218\pi\)
−0.0352171 + 0.999380i \(0.511212\pi\)
\(942\) −1.38234e9 1.10238e9i −1.65372 1.31880i
\(943\) 1.57805e8 1.07590e8i 0.188186 0.128303i
\(944\) −8.09274e7 + 3.89726e7i −0.0962010 + 0.0463280i
\(945\) 3.50305e8i 0.415099i
\(946\) −1.89336e8 + 6.90648e8i −0.223645 + 0.815799i
\(947\) 2.94075e8 0.346264 0.173132 0.984899i \(-0.444611\pi\)
0.173132 + 0.984899i \(0.444611\pi\)
\(948\) −6.33054e8 1.31455e9i −0.743047 1.54295i
\(949\) 1.23647e8 + 1.81357e8i 0.144672 + 0.212195i
\(950\) −6.72769e8 + 8.43625e8i −0.784684 + 0.983963i
\(951\) 1.81500e8 1.95611e8i 0.211026 0.227432i
\(952\) 6.51825e8 1.12899e9i 0.755475 1.30852i
\(953\) 8.59696e8 4.96346e8i 0.993268 0.573463i 0.0870182 0.996207i \(-0.472266\pi\)
0.906249 + 0.422743i \(0.138933\pi\)
\(954\) 3.64809e8 + 8.32653e7i 0.420166 + 0.0959001i
\(955\) 5.10470e6 1.30066e7i 0.00586084 0.0149332i
\(956\) −1.90056e9 5.86244e8i −2.17524 0.670972i
\(957\) −1.61914e8 2.03033e8i −0.184734 0.231650i
\(958\) 1.44062e9 + 1.07959e8i 1.63852 + 0.122790i
\(959\) 1.41737e9 4.37200e8i 1.60704 0.495706i
\(960\) −9.27524e8 6.32375e8i −1.04836 0.714762i
\(961\) 6.22487e8 + 9.38248e7i 0.701390 + 0.105718i
\(962\) −7.14092e7 3.12864e8i −0.0802101 0.351424i
\(963\) −3.37864e8 + 3.13492e8i −0.378323 + 0.351032i
\(964\) −1.06611e9 + 7.98937e7i −1.19006 + 0.0891829i
\(965\) −6.12091e8 + 2.40228e8i −0.681136 + 0.267326i
\(966\) 3.70099e8 + 2.45544e9i 0.410569 + 2.72395i
\(967\) −1.18026e9 5.68384e8i −1.30527 0.628583i −0.353508 0.935432i \(-0.615011\pi\)
−0.951758 + 0.306849i \(0.900725\pi\)
\(968\) −3.30026e8 + 6.85306e8i −0.363850 + 0.755542i
\(969\) 1.81875e9 2.74133e8i 1.99895 0.301294i
\(970\) −5.49592e8 1.40034e9i −0.602179 1.53433i
\(971\) 4.12266e7 + 5.50131e8i 0.0450318 + 0.600908i 0.973380 + 0.229197i \(0.0736099\pi\)
−0.928348 + 0.371712i \(0.878771\pi\)
\(972\) −1.01339e9 1.09218e9i −1.10352 1.18931i
\(973\) −8.77569e8 + 2.00299e8i −0.952670 + 0.217441i
\(974\) 4.04161e7 2.68143e8i 0.0437399 0.290195i
\(975\) 6.64986e7 9.75355e7i 0.0717461 0.105232i
\(976\) 7.47309e7 + 2.42272e8i 0.0803805 + 0.260587i
\(977\) −1.03891e8 + 1.38633e9i −0.111403 + 1.48657i 0.609088 + 0.793102i \(0.291535\pi\)
−0.720491 + 0.693464i \(0.756084\pi\)
\(978\) −1.50040e9 + 1.19653e9i −1.60394 + 1.27910i
\(979\) 1.32782e8 4.30470e8i 0.141512 0.458770i
\(980\) 1.67923e8 + 6.59049e7i 0.178415 + 0.0700228i
\(981\) 1.33897e8 5.86640e8i 0.141828 0.621390i
\(982\) −1.31771e9 2.28235e9i −1.39151 2.41017i
\(983\) 7.54498e8 + 4.35609e8i 0.794323 + 0.458603i 0.841482 0.540285i \(-0.181683\pi\)
−0.0471590 + 0.998887i \(0.515017\pi\)
\(984\) 1.78813e8 + 1.65914e8i 0.187678 + 0.174140i
\(985\) 5.84263e8 + 4.65934e8i 0.611364 + 0.487546i
\(986\) −7.39851e8 + 5.04422e8i −0.771815 + 0.526215i
\(987\) −8.30705e8 + 4.00046e8i −0.863963 + 0.416063i
\(988\) 3.94567e8i 0.409120i
\(989\) −1.14767e9 + 3.94170e8i −1.18639 + 0.407469i
\(990\) −2.82035e8 −0.290668
\(991\) −5.95395e8 1.23635e9i −0.611764 1.27034i −0.944868 0.327451i \(-0.893810\pi\)
0.333104 0.942890i \(-0.391904\pi\)
\(992\) 2.51378e8 + 3.68704e8i 0.257509 + 0.377696i
\(993\) 2.10043e8 2.63386e8i 0.214517 0.268995i
\(994\) −1.52124e9 + 1.63951e9i −1.54895 + 1.66937i
\(995\) −3.60838e8 + 6.24990e8i −0.366305 + 0.634459i
\(996\) −2.95303e9 + 1.70493e9i −2.98875 + 1.72555i
\(997\) 8.52324e7 + 1.94537e7i 0.0860041 + 0.0196299i 0.265306 0.964164i \(-0.414527\pi\)
−0.179302 + 0.983794i \(0.557384\pi\)
\(998\) −9.69222e8 + 2.46954e9i −0.975061 + 2.48441i
\(999\) 6.80460e8 + 2.09894e8i 0.682506 + 0.210525i
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.12.19 252
43.18 odd 42 inner 43.7.h.a.18.19 yes 252
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.h.a.12.19 252 1.1 even 1 trivial
43.7.h.a.18.19 yes 252 43.18 odd 42 inner