Properties

Label 33.7.h.a.5.17
Level $33$
Weight $7$
Character 33.5
Analytic conductor $7.592$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,7,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.59178475946\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 5.17
Character \(\chi\) \(=\) 33.5
Dual form 33.7.h.a.20.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(9.48700 - 3.08251i) q^{2} +(-26.6534 + 4.31225i) q^{3} +(28.7242 - 20.8694i) q^{4} +(210.493 + 68.3933i) q^{5} +(-239.568 + 123.070i) q^{6} +(290.276 - 210.898i) q^{7} +(-167.074 + 229.958i) q^{8} +(691.809 - 229.872i) q^{9} +O(q^{10})\) \(q+(9.48700 - 3.08251i) q^{2} +(-26.6534 + 4.31225i) q^{3} +(28.7242 - 20.8694i) q^{4} +(210.493 + 68.3933i) q^{5} +(-239.568 + 123.070i) q^{6} +(290.276 - 210.898i) q^{7} +(-167.074 + 229.958i) q^{8} +(691.809 - 229.872i) q^{9} +2207.77 q^{10} +(979.624 - 901.054i) q^{11} +(-675.604 + 680.105i) q^{12} +(622.975 + 1917.32i) q^{13} +(2103.75 - 2895.57i) q^{14} +(-5905.28 - 915.217i) q^{15} +(-1578.37 + 4857.73i) q^{16} +(-3892.09 - 1264.62i) q^{17} +(5854.61 - 4313.31i) q^{18} +(-2591.87 - 1883.10i) q^{19} +(7473.56 - 2428.31i) q^{20} +(-6827.41 + 6872.89i) q^{21} +(6516.18 - 11568.0i) q^{22} +8032.42i q^{23} +(3461.46 - 6849.62i) q^{24} +(26988.7 + 19608.4i) q^{25} +(11820.3 + 16269.3i) q^{26} +(-17447.8 + 9110.13i) q^{27} +(3936.65 - 12115.8i) q^{28} +(-18470.0 - 25421.8i) q^{29} +(-58844.6 + 9520.44i) q^{30} +(-13111.2 - 40352.2i) q^{31} +32759.0i q^{32} +(-22224.8 + 28240.5i) q^{33} -40822.4 q^{34} +(75525.0 - 24539.6i) q^{35} +(15074.4 - 21040.5i) q^{36} +(-9972.40 + 7245.37i) q^{37} +(-30393.8 - 9875.53i) q^{38} +(-24872.4 - 48416.7i) q^{39} +(-50895.4 + 36977.7i) q^{40} +(-5178.43 + 7127.50i) q^{41} +(-43585.8 + 86248.7i) q^{42} -48965.3 q^{43} +(9334.50 - 46326.2i) q^{44} +(161343. - 1071.37i) q^{45} +(24760.0 + 76203.6i) q^{46} +(56788.8 - 78163.1i) q^{47} +(21121.3 - 136281. i) q^{48} +(3426.75 - 10546.4i) q^{49} +(316485. + 102832. i) q^{50} +(109191. + 16922.7i) q^{51} +(57907.7 + 42072.4i) q^{52} +(20323.0 - 6603.34i) q^{53} +(-137445. + 140211. i) q^{54} +(267830. - 122666. i) q^{55} +101987. i q^{56} +(77202.6 + 39014.3i) q^{57} +(-253588. - 184242. i) q^{58} +(-201717. - 277639. i) q^{59} +(-188724. + 96950.5i) q^{60} +(-109974. + 338464. i) q^{61} +(-248772. - 342406. i) q^{62} +(152336. - 212628. i) q^{63} +(-35.6075 - 109.589i) q^{64} +446189. i q^{65} +(-123794. + 336426. i) q^{66} -14649.5 q^{67} +(-138189. + 44900.3i) q^{68} +(-34637.8 - 214091. i) q^{69} +(640862. - 465614. i) q^{70} +(332066. + 107895. i) q^{71} +(-62722.4 + 197492. i) q^{72} +(-216710. + 157449. i) q^{73} +(-72274.2 + 99476.9i) q^{74} +(-803897. - 406250. i) q^{75} -113749. q^{76} +(94331.0 - 468155. i) q^{77} +(-385209. - 382660. i) q^{78} +(68408.7 + 210540. i) q^{79} +(-664471. + 914566. i) q^{80} +(425759. - 318055. i) q^{81} +(-27157.2 + 83581.2i) q^{82} +(142726. + 46374.5i) q^{83} +(-52679.0 + 339902. i) q^{84} +(-732765. - 532385. i) q^{85} +(-464534. + 150936. i) q^{86} +(601914. + 597930. i) q^{87} +(43534.6 + 375815. i) q^{88} -151502. i q^{89} +(1.52735e6 - 507505. i) q^{90} +(585193. + 425168. i) q^{91} +(167631. + 230725. i) q^{92} +(523467. + 1.01898e6i) q^{93} +(297817. - 916585. i) q^{94} +(-416778. - 573646. i) q^{95} +(-141265. - 873140. i) q^{96} +(83506.1 + 257005. i) q^{97} -110617. i q^{98} +(470585. - 848546. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24} + 68152 q^{25} + 65385 q^{27} - 37986 q^{28} + 20928 q^{30} + 96222 q^{31} - 67159 q^{33} - 186548 q^{34} - 107169 q^{36} - 112854 q^{37} - 257545 q^{39} + 246958 q^{40} - 130324 q^{42} + 40328 q^{43} + 505478 q^{45} - 30630 q^{46} + 647882 q^{48} - 327700 q^{49} + 88197 q^{51} - 132630 q^{52} - 1639642 q^{54} - 216226 q^{55} + 174477 q^{57} + 1571894 q^{58} + 772854 q^{60} + 559626 q^{61} + 1129495 q^{63} + 1406654 q^{64} + 34620 q^{66} - 3229336 q^{67} - 2492844 q^{69} - 2066360 q^{70} - 2672882 q^{72} + 1068798 q^{73} - 1207057 q^{75} + 913268 q^{76} + 6763180 q^{78} - 255558 q^{79} + 3363409 q^{81} - 3580072 q^{82} - 2958906 q^{84} - 2098978 q^{85} + 365046 q^{87} + 2251838 q^{88} - 813500 q^{90} + 7887166 q^{91} + 4000307 q^{93} + 11260802 q^{94} + 4588186 q^{96} + 3850038 q^{97} - 1274785 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.48700 3.08251i 1.18588 0.385314i 0.351329 0.936252i \(-0.385730\pi\)
0.834546 + 0.550938i \(0.185730\pi\)
\(3\) −26.6534 + 4.31225i −0.987164 + 0.159713i
\(4\) 28.7242 20.8694i 0.448816 0.326084i
\(5\) 210.493 + 68.3933i 1.68394 + 0.547146i 0.985670 0.168686i \(-0.0539524\pi\)
0.698272 + 0.715832i \(0.253952\pi\)
\(6\) −239.568 + 123.070i −1.10911 + 0.569768i
\(7\) 290.276 210.898i 0.846286 0.614863i −0.0778334 0.996966i \(-0.524800\pi\)
0.924120 + 0.382104i \(0.124800\pi\)
\(8\) −167.074 + 229.958i −0.326316 + 0.449136i
\(9\) 691.809 229.872i 0.948984 0.315325i
\(10\) 2207.77 2.20777
\(11\) 979.624 901.054i 0.736006 0.676975i
\(12\) −675.604 + 680.105i −0.390975 + 0.393580i
\(13\) 622.975 + 1917.32i 0.283557 + 0.872699i 0.986827 + 0.161776i \(0.0517223\pi\)
−0.703270 + 0.710922i \(0.748278\pi\)
\(14\) 2103.75 2895.57i 0.766674 1.05524i
\(15\) −5905.28 915.217i −1.74971 0.271175i
\(16\) −1578.37 + 4857.73i −0.385344 + 1.18597i
\(17\) −3892.09 1264.62i −0.792202 0.257402i −0.115161 0.993347i \(-0.536738\pi\)
−0.677042 + 0.735945i \(0.736738\pi\)
\(18\) 5854.61 4313.31i 1.00388 0.739593i
\(19\) −2591.87 1883.10i −0.377879 0.274545i 0.382592 0.923917i \(-0.375032\pi\)
−0.760470 + 0.649373i \(0.775032\pi\)
\(20\) 7473.56 2428.31i 0.934195 0.303538i
\(21\) −6827.41 + 6872.89i −0.737221 + 0.742133i
\(22\) 6516.18 11568.0i 0.611963 1.08640i
\(23\) 8032.42i 0.660181i 0.943949 + 0.330090i \(0.107079\pi\)
−0.943949 + 0.330090i \(0.892921\pi\)
\(24\) 3461.46 6849.62i 0.250395 0.495488i
\(25\) 26988.7 + 19608.4i 1.72728 + 1.25494i
\(26\) 11820.3 + 16269.3i 0.672526 + 0.925653i
\(27\) −17447.8 + 9110.13i −0.886440 + 0.462843i
\(28\) 3936.65 12115.8i 0.179330 0.551920i
\(29\) −18470.0 25421.8i −0.757309 1.04235i −0.997433 0.0716044i \(-0.977188\pi\)
0.240124 0.970742i \(-0.422812\pi\)
\(30\) −58844.6 + 9520.44i −2.17943 + 0.352609i
\(31\) −13111.2 40352.2i −0.440107 1.35451i −0.887762 0.460303i \(-0.847741\pi\)
0.447655 0.894206i \(-0.352259\pi\)
\(32\) 32759.0i 0.999726i
\(33\) −22224.8 + 28240.5i −0.618437 + 0.785835i
\(34\) −40822.4 −1.03863
\(35\) 75525.0 24539.6i 1.76152 0.572351i
\(36\) 15074.4 21040.5i 0.323096 0.450971i
\(37\) −9972.40 + 7245.37i −0.196877 + 0.143039i −0.681856 0.731486i \(-0.738827\pi\)
0.484980 + 0.874526i \(0.338827\pi\)
\(38\) −30393.8 9875.53i −0.553903 0.179974i
\(39\) −24872.4 48416.7i −0.419298 0.816209i
\(40\) −50895.4 + 36977.7i −0.795241 + 0.577776i
\(41\) −5178.43 + 7127.50i −0.0751358 + 0.103416i −0.844931 0.534876i \(-0.820358\pi\)
0.769795 + 0.638291i \(0.220358\pi\)
\(42\) −43585.8 + 86248.7i −0.588298 + 1.16414i
\(43\) −48965.3 −0.615861 −0.307931 0.951409i \(-0.599636\pi\)
−0.307931 + 0.951409i \(0.599636\pi\)
\(44\) 9334.50 46326.2i 0.109580 0.543837i
\(45\) 161343. 1071.37i 1.77056 0.0117571i
\(46\) 24760.0 + 76203.6i 0.254377 + 0.782892i
\(47\) 56788.8 78163.1i 0.546977 0.752849i −0.442621 0.896709i \(-0.645951\pi\)
0.989598 + 0.143859i \(0.0459513\pi\)
\(48\) 21121.3 136281.i 0.190984 1.23229i
\(49\) 3426.75 10546.4i 0.0291269 0.0896433i
\(50\) 316485. + 102832.i 2.53188 + 0.822657i
\(51\) 109191. + 16922.7i 0.823143 + 0.127573i
\(52\) 57907.7 + 42072.4i 0.411838 + 0.299218i
\(53\) 20323.0 6603.34i 0.136509 0.0443543i −0.239966 0.970781i \(-0.577136\pi\)
0.376474 + 0.926427i \(0.377136\pi\)
\(54\) −137445. + 140211.i −0.872868 + 0.890432i
\(55\) 267830. 122666.i 1.60980 0.737284i
\(56\) 101987.i 0.580737i
\(57\) 77202.6 + 39014.3i 0.416876 + 0.210669i
\(58\) −253588. 184242.i −1.29970 0.944291i
\(59\) −201717. 277639.i −0.982168 1.35184i −0.935653 0.352921i \(-0.885188\pi\)
−0.0465155 0.998918i \(-0.514812\pi\)
\(60\) −188724. + 96950.5i −0.873724 + 0.448845i
\(61\) −109974. + 338464.i −0.484506 + 1.49116i 0.348188 + 0.937425i \(0.386797\pi\)
−0.832694 + 0.553733i \(0.813203\pi\)
\(62\) −248772. 342406.i −1.04382 1.43670i
\(63\) 152336. 212628.i 0.609230 0.850350i
\(64\) −35.6075 109.589i −0.000135832 0.000418047i
\(65\) 446189.i 1.62472i
\(66\) −123794. + 336426.i −0.430595 + 1.17019i
\(67\) −14649.5 −0.0487079 −0.0243539 0.999703i \(-0.507753\pi\)
−0.0243539 + 0.999703i \(0.507753\pi\)
\(68\) −138189. + 44900.3i −0.439487 + 0.142798i
\(69\) −34637.8 214091.i −0.105439 0.651706i
\(70\) 640862. 465614.i 1.86840 1.35747i
\(71\) 332066. + 107895.i 0.927791 + 0.301457i 0.733659 0.679518i \(-0.237811\pi\)
0.194132 + 0.980975i \(0.437811\pi\)
\(72\) −62722.4 + 197492.i −0.168045 + 0.529119i
\(73\) −216710. + 157449.i −0.557071 + 0.404736i −0.830386 0.557189i \(-0.811880\pi\)
0.273315 + 0.961925i \(0.411880\pi\)
\(74\) −72274.2 + 99476.9i −0.178356 + 0.245486i
\(75\) −803897. 406250.i −1.90553 0.962962i
\(76\) −113749. −0.259122
\(77\) 94331.0 468155.i 0.206625 1.02546i
\(78\) −385209. 382660.i −0.811732 0.806360i
\(79\) 68408.7 + 210540.i 0.138749 + 0.427026i 0.996154 0.0876161i \(-0.0279249\pi\)
−0.857405 + 0.514642i \(0.827925\pi\)
\(80\) −664471. + 914566.i −1.29780 + 1.78626i
\(81\) 425759. 318055.i 0.801140 0.598477i
\(82\) −27157.2 + 83581.2i −0.0492542 + 0.151589i
\(83\) 142726. + 46374.5i 0.249614 + 0.0811044i 0.431151 0.902280i \(-0.358107\pi\)
−0.181538 + 0.983384i \(0.558107\pi\)
\(84\) −52679.0 + 339902.i −0.0888790 + 0.573477i
\(85\) −732765. 532385.i −1.19319 0.866900i
\(86\) −464534. + 150936.i −0.730334 + 0.237300i
\(87\) 601914. + 597930.i 0.914064 + 0.908015i
\(88\) 43534.6 + 375815.i 0.0638831 + 0.551475i
\(89\) 151502.i 0.214906i −0.994210 0.107453i \(-0.965731\pi\)
0.994210 0.107453i \(-0.0342694\pi\)
\(90\) 1.52735e6 507505.i 2.09514 0.696165i
\(91\) 585193. + 425168.i 0.776560 + 0.564204i
\(92\) 167631. + 230725.i 0.215274 + 0.296299i
\(93\) 523467. + 1.01898e6i 0.650790 + 1.26683i
\(94\) 297817. 916585.i 0.358563 1.10354i
\(95\) −416778. 573646.i −0.486110 0.669072i
\(96\) −141265. 873140.i −0.159669 0.986893i
\(97\) 83506.1 + 257005.i 0.0914962 + 0.281596i 0.986325 0.164814i \(-0.0527023\pi\)
−0.894829 + 0.446410i \(0.852702\pi\)
\(98\) 110617.i 0.117529i
\(99\) 470585. 848546.i 0.484990 0.874520i
\(100\) 1.18444e6 1.18444
\(101\) −1.04826e6 + 340599.i −1.01743 + 0.330582i −0.769808 0.638275i \(-0.779648\pi\)
−0.247620 + 0.968857i \(0.579648\pi\)
\(102\) 1.08806e6 176036.i 1.02530 0.165883i
\(103\) −416371. + 302511.i −0.381038 + 0.276840i −0.761773 0.647844i \(-0.775671\pi\)
0.380735 + 0.924684i \(0.375671\pi\)
\(104\) −544985. 177076.i −0.484490 0.157420i
\(105\) −1.90718e6 + 979746.i −1.64749 + 0.846341i
\(106\) 172449. 125292.i 0.144792 0.105197i
\(107\) −89809.9 + 123613.i −0.0733116 + 0.100905i −0.844098 0.536189i \(-0.819864\pi\)
0.770786 + 0.637094i \(0.219864\pi\)
\(108\) −311052. + 625806.i −0.246923 + 0.496785i
\(109\) −1.07819e6 −0.832561 −0.416281 0.909236i \(-0.636667\pi\)
−0.416281 + 0.909236i \(0.636667\pi\)
\(110\) 2.16278e6 1.98932e6i 1.62493 1.49460i
\(111\) 234555. 236117.i 0.171504 0.172647i
\(112\) 566321. + 1.74296e6i 0.403096 + 1.24060i
\(113\) 1.02661e6 1.41301e6i 0.711493 0.979286i −0.288271 0.957549i \(-0.593080\pi\)
0.999764 0.0217368i \(-0.00691957\pi\)
\(114\) 852683. + 132151.i 0.575537 + 0.0891983i
\(115\) −549363. + 1.69077e6i −0.361215 + 1.11171i
\(116\) −1.06107e6 344763.i −0.679784 0.220875i
\(117\) 871718. + 1.18321e6i 0.544275 + 0.738764i
\(118\) −2.76951e6 2.01217e6i −1.68561 1.22467i
\(119\) −1.39649e6 + 453746.i −0.828697 + 0.269260i
\(120\) 1.19708e6 1.20506e6i 0.692755 0.697370i
\(121\) 147765. 1.76539e6i 0.0834093 0.996515i
\(122\) 3.55001e6i 1.95501i
\(123\) 107287. 212303.i 0.0576545 0.114088i
\(124\) −1.21873e6 885462.i −0.639210 0.464413i
\(125\) 2.30716e6 + 3.17553e6i 1.18126 + 1.62587i
\(126\) 789785. 2.48678e6i 0.394818 1.24315i
\(127\) 695123. 2.13937e6i 0.339352 1.04442i −0.625186 0.780475i \(-0.714977\pi\)
0.964538 0.263942i \(-0.0850229\pi\)
\(128\) −1.23301e6 1.69710e6i −0.587946 0.809239i
\(129\) 1.30509e6 211150.i 0.607956 0.0983609i
\(130\) 1.37538e6 + 4.23300e6i 0.626028 + 1.92672i
\(131\) 21148.4i 0.00940727i 0.999989 + 0.00470363i \(0.00149722\pi\)
−0.999989 + 0.00470363i \(0.998503\pi\)
\(132\) −49026.4 + 1.27500e6i −0.0213161 + 0.554357i
\(133\) −1.14950e6 −0.488601
\(134\) −138980. + 45157.4i −0.0577615 + 0.0187678i
\(135\) −4.29571e6 + 724304.i −1.74596 + 0.294388i
\(136\) 941075. 683731.i 0.374117 0.271812i
\(137\) −1.37007e6 445162.i −0.532819 0.173123i 0.0302359 0.999543i \(-0.490374\pi\)
−0.563055 + 0.826419i \(0.690374\pi\)
\(138\) −988548. 1.92431e6i −0.376150 0.732215i
\(139\) −2.42382e6 + 1.76101e6i −0.902518 + 0.655718i −0.939111 0.343613i \(-0.888349\pi\)
0.0365937 + 0.999330i \(0.488349\pi\)
\(140\) 1.65727e6 2.28104e6i 0.603962 0.831282i
\(141\) −1.17656e6 + 2.32820e6i −0.419716 + 0.830545i
\(142\) 3.48290e6 1.21640
\(143\) 2.33789e6 + 1.31692e6i 0.799495 + 0.450350i
\(144\) 24724.9 + 3.72344e6i 0.00828032 + 1.24697i
\(145\) −2.14913e6 6.61433e6i −0.704949 2.16961i
\(146\) −1.57059e6 + 2.16173e6i −0.504666 + 0.694613i
\(147\) −45855.7 + 295876.i −0.0144358 + 0.0931445i
\(148\) −135243. + 416235.i −0.0417186 + 0.128397i
\(149\) 2.81436e6 + 914440.i 0.850786 + 0.276437i 0.701775 0.712398i \(-0.252391\pi\)
0.149011 + 0.988836i \(0.452391\pi\)
\(150\) −8.87884e6 1.37607e6i −2.63077 0.407724i
\(151\) 2.64356e6 + 1.92066e6i 0.767818 + 0.557852i 0.901298 0.433199i \(-0.142615\pi\)
−0.133481 + 0.991051i \(0.542615\pi\)
\(152\) 866068. 281403.i 0.246616 0.0801304i
\(153\) −2.98328e6 + 19810.0i −0.832952 + 0.00553108i
\(154\) −548176. 4.73216e6i −0.150092 1.29568i
\(155\) 9.39056e6i 2.52172i
\(156\) −1.72486e6 871661.i −0.454340 0.229601i
\(157\) 5.92609e6 + 4.30555e6i 1.53133 + 1.11258i 0.955493 + 0.295013i \(0.0953240\pi\)
0.575838 + 0.817564i \(0.304676\pi\)
\(158\) 1.29799e6 + 1.78653e6i 0.329078 + 0.452937i
\(159\) −513202. + 263639.i −0.127672 + 0.0655872i
\(160\) −2.24050e6 + 6.89554e6i −0.546996 + 1.68348i
\(161\) 1.69402e6 + 2.33162e6i 0.405921 + 0.558702i
\(162\) 3.05876e6 4.32980e6i 0.719450 1.01841i
\(163\) −572366. 1.76156e6i −0.132163 0.406757i 0.862975 0.505247i \(-0.168599\pi\)
−0.995138 + 0.0984903i \(0.968599\pi\)
\(164\) 312802.i 0.0709151i
\(165\) −6.60961e6 + 4.42441e6i −1.47138 + 0.984925i
\(166\) 1.49699e6 0.327261
\(167\) 579532. 188301.i 0.124431 0.0404300i −0.246140 0.969234i \(-0.579162\pi\)
0.370571 + 0.928804i \(0.379162\pi\)
\(168\) −439792. 2.71830e6i −0.0927512 0.573283i
\(169\) 616955. 448244.i 0.127818 0.0928656i
\(170\) −8.59283e6 2.79198e6i −1.74900 0.568284i
\(171\) −2.22595e6 706949.i −0.445171 0.141384i
\(172\) −1.40649e6 + 1.02187e6i −0.276408 + 0.200822i
\(173\) 2.09773e6 2.88728e6i 0.405147 0.557636i −0.556880 0.830593i \(-0.688002\pi\)
0.962026 + 0.272957i \(0.0880016\pi\)
\(174\) 7.55349e6 + 3.81716e6i 1.43384 + 0.724590i
\(175\) 1.19695e7 2.23339
\(176\) 2.83086e6 + 6.18094e6i 0.519255 + 1.13375i
\(177\) 6.57369e6 + 6.53018e6i 1.18547 + 1.17762i
\(178\) −467006. 1.43730e6i −0.0828061 0.254851i
\(179\) 5.82390e6 8.01592e6i 1.01544 1.39764i 0.100091 0.994978i \(-0.468087\pi\)
0.915351 0.402658i \(-0.131913\pi\)
\(180\) 4.61208e6 3.39789e6i 0.790822 0.582628i
\(181\) −445639. + 1.37154e6i −0.0751532 + 0.231298i −0.981575 0.191075i \(-0.938803\pi\)
0.906422 + 0.422373i \(0.138803\pi\)
\(182\) 6.86232e6 + 2.22970e6i 1.13830 + 0.369856i
\(183\) 1.47163e6 9.49547e6i 0.240130 1.54940i
\(184\) −1.84712e6 1.34201e6i −0.296511 0.215428i
\(185\) −2.59465e6 + 843054.i −0.409792 + 0.133150i
\(186\) 8.10717e6 + 8.05351e6i 1.25988 + 1.25155i
\(187\) −4.95227e6 + 2.26813e6i −0.757320 + 0.346852i
\(188\) 3.43032e6i 0.516251i
\(189\) −3.14337e6 + 6.32416e6i −0.465598 + 0.936737i
\(190\) −5.72225e6 4.15745e6i −0.834268 0.606131i
\(191\) 5.59238e6 + 7.69724e6i 0.802595 + 1.10468i 0.992424 + 0.122860i \(0.0392065\pi\)
−0.189829 + 0.981817i \(0.560794\pi\)
\(192\) 1421.63 + 2767.36i 0.000200856 + 0.000390987i
\(193\) −558015. + 1.71740e6i −0.0776201 + 0.238890i −0.982336 0.187125i \(-0.940083\pi\)
0.904716 + 0.426015i \(0.140083\pi\)
\(194\) 1.58445e6 + 2.18080e6i 0.217006 + 0.298683i
\(195\) −1.92408e6 1.18925e7i −0.259489 1.60387i
\(196\) −121667. 374452.i −0.0161586 0.0497311i
\(197\) 819617.i 0.107204i −0.998562 0.0536022i \(-0.982930\pi\)
0.998562 0.0536022i \(-0.0170703\pi\)
\(198\) 1.84879e6 9.50074e6i 0.238173 1.22394i
\(199\) 2.11410e6 0.268266 0.134133 0.990963i \(-0.457175\pi\)
0.134133 + 0.990963i \(0.457175\pi\)
\(200\) −9.01822e6 + 2.93020e6i −1.12728 + 0.366274i
\(201\) 390460. 63172.4i 0.0480827 0.00777928i
\(202\) −8.89491e6 + 6.46253e6i −1.07916 + 0.784059i
\(203\) −1.07228e7 3.48405e6i −1.28180 0.416482i
\(204\) 3.48958e6 1.79265e6i 0.411039 0.211157i
\(205\) −1.57750e6 + 1.14612e6i −0.183108 + 0.133036i
\(206\) −3.01761e6 + 4.15339e6i −0.345193 + 0.475117i
\(207\) 1.84643e6 + 5.55690e6i 0.208172 + 0.626501i
\(208\) −1.02971e7 −1.14426
\(209\) −4.23583e6 + 490681.i −0.463981 + 0.0537478i
\(210\) −1.50733e7 + 1.51738e7i −1.62761 + 1.63846i
\(211\) −1.96341e6 6.04276e6i −0.209008 0.643262i −0.999525 0.0308209i \(-0.990188\pi\)
0.790517 0.612441i \(-0.209812\pi\)
\(212\) 445954. 613804.i 0.0468040 0.0644202i
\(213\) −9.31598e6 1.44382e6i −0.964028 0.149408i
\(214\) −470989. + 1.44955e6i −0.0480584 + 0.147908i
\(215\) −1.03068e7 3.34889e6i −1.03707 0.336966i
\(216\) 820131. 5.53432e6i 0.0813808 0.549166i
\(217\) −1.23161e7 8.94815e6i −1.20529 0.875697i
\(218\) −1.02288e7 + 3.32354e6i −0.987314 + 0.320798i
\(219\) 5.09711e6 5.13106e6i 0.485279 0.488512i
\(220\) 5.13324e6 9.11291e6i 0.482085 0.855833i
\(221\) 8.25020e6i 0.764342i
\(222\) 1.49739e6 2.96306e6i 0.136859 0.270821i
\(223\) 4.99382e6 + 3.62822e6i 0.450317 + 0.327174i 0.789721 0.613466i \(-0.210225\pi\)
−0.339404 + 0.940641i \(0.610225\pi\)
\(224\) 6.90881e6 + 9.50916e6i 0.614694 + 0.846054i
\(225\) 2.31784e7 + 7.36134e6i 2.03487 + 0.646263i
\(226\) 5.38384e6 1.65698e7i 0.466409 1.43546i
\(227\) −2.37256e6 3.26554e6i −0.202833 0.279176i 0.695467 0.718558i \(-0.255197\pi\)
−0.898300 + 0.439382i \(0.855197\pi\)
\(228\) 3.03179e6 490512.i 0.255796 0.0413852i
\(229\) 5.51270e6 + 1.69664e7i 0.459048 + 1.41280i 0.866316 + 0.499496i \(0.166481\pi\)
−0.407268 + 0.913309i \(0.633519\pi\)
\(230\) 1.77337e7i 1.45753i
\(231\) −495443. + 1.28847e7i −0.0401937 + 1.04529i
\(232\) 8.93180e6 0.715278
\(233\) 2.04435e7 6.64248e6i 1.61617 0.525125i 0.645134 0.764069i \(-0.276801\pi\)
0.971033 + 0.238944i \(0.0768013\pi\)
\(234\) 1.19173e7 + 8.53807e6i 0.930098 + 0.666365i
\(235\) 1.72995e7 1.25688e7i 1.33300 0.968479i
\(236\) −1.15883e7 3.76527e6i −0.881625 0.286457i
\(237\) −2.73123e6 5.31662e6i −0.205170 0.399384i
\(238\) −1.18498e7 + 8.60937e6i −0.878981 + 0.638617i
\(239\) −1.51821e7 + 2.08963e7i −1.11208 + 1.53065i −0.293775 + 0.955875i \(0.594912\pi\)
−0.818309 + 0.574778i \(0.805088\pi\)
\(240\) 1.37666e7 2.72417e7i 0.995847 1.97061i
\(241\) −2.11925e7 −1.51402 −0.757009 0.653404i \(-0.773340\pi\)
−0.757009 + 0.653404i \(0.773340\pi\)
\(242\) −4.03999e6 1.72037e7i −0.285058 1.21388i
\(243\) −9.97639e6 + 1.03132e7i −0.695271 + 0.718747i
\(244\) 3.90463e6 + 1.20172e7i 0.268788 + 0.827245i
\(245\) 1.44261e6 1.98558e6i 0.0980960 0.135017i
\(246\) 363409. 2.34483e6i 0.0244113 0.157509i
\(247\) 1.99584e6 6.14257e6i 0.132445 0.407623i
\(248\) 1.14698e7 + 3.72678e6i 0.751973 + 0.244331i
\(249\) −4.00411e6 620568.i −0.259363 0.0401968i
\(250\) 3.16766e7 + 2.30144e7i 2.02730 + 1.47292i
\(251\) −1.68801e7 + 5.48468e6i −1.06747 + 0.346841i −0.789500 0.613750i \(-0.789660\pi\)
−0.277966 + 0.960591i \(0.589660\pi\)
\(252\) −61666.9 9.28671e6i −0.00385346 0.580310i
\(253\) 7.23764e6 + 7.86875e6i 0.446926 + 0.485897i
\(254\) 2.24389e7i 1.36931i
\(255\) 2.18265e7 + 1.10300e7i 1.31632 + 0.665205i
\(256\) −1.69229e7 1.22952e7i −1.00869 0.732854i
\(257\) 1.38182e6 + 1.90191e6i 0.0814050 + 0.112044i 0.847777 0.530352i \(-0.177940\pi\)
−0.766372 + 0.642396i \(0.777940\pi\)
\(258\) 1.17305e7 6.02615e6i 0.683060 0.350898i
\(259\) −1.36672e6 + 4.20632e6i −0.0786645 + 0.242104i
\(260\) 9.31168e6 + 1.28164e7i 0.529795 + 0.729200i
\(261\) −1.86215e7 1.33413e7i −1.04735 0.750371i
\(262\) 65190.2 + 200635.i 0.00362475 + 0.0111558i
\(263\) 2.24387e7i 1.23347i −0.787169 0.616737i \(-0.788454\pi\)
0.787169 0.616737i \(-0.211546\pi\)
\(264\) −2.78095e6 9.82901e6i −0.151141 0.534193i
\(265\) 4.72947e6 0.254141
\(266\) −1.09053e7 + 3.54335e6i −0.579419 + 0.188265i
\(267\) 653313. + 4.03804e6i 0.0343232 + 0.212147i
\(268\) −420796. + 305726.i −0.0218609 + 0.0158828i
\(269\) 1.98465e7 + 6.44853e6i 1.01960 + 0.331287i 0.770669 0.637236i \(-0.219922\pi\)
0.248927 + 0.968522i \(0.419922\pi\)
\(270\) −3.85207e7 + 2.01131e7i −1.95706 + 1.02185i
\(271\) 2.12585e7 1.54452e7i 1.06813 0.776042i 0.0925555 0.995708i \(-0.470496\pi\)
0.975575 + 0.219665i \(0.0704964\pi\)
\(272\) 1.22863e7 1.69107e7i 0.610541 0.840338i
\(273\) −1.74308e7 8.80868e6i −0.856703 0.432935i
\(274\) −1.43700e7 −0.698564
\(275\) 4.41070e7 5.10938e6i 2.12085 0.245680i
\(276\) −5.46289e6 5.42674e6i −0.259834 0.258114i
\(277\) 2.69340e6 + 8.28944e6i 0.126725 + 0.390019i 0.994211 0.107442i \(-0.0342659\pi\)
−0.867487 + 0.497461i \(0.834266\pi\)
\(278\) −1.75664e7 + 2.41781e7i −0.817616 + 1.12535i
\(279\) −1.83463e7 2.49021e7i −0.844765 1.14663i
\(280\) −6.97521e6 + 2.14675e7i −0.317748 + 0.977928i
\(281\) −5.58509e6 1.81470e6i −0.251716 0.0817875i 0.180441 0.983586i \(-0.442247\pi\)
−0.432157 + 0.901798i \(0.642247\pi\)
\(282\) −3.98529e6 + 2.57144e7i −0.177710 + 1.14664i
\(283\) 1.47329e7 + 1.07041e7i 0.650022 + 0.472268i 0.863279 0.504728i \(-0.168407\pi\)
−0.213257 + 0.976996i \(0.568407\pi\)
\(284\) 1.17900e7 3.83082e6i 0.514707 0.167239i
\(285\) 1.35823e7 + 1.34924e7i 0.586729 + 0.582846i
\(286\) 2.62390e7 + 5.28703e6i 1.12163 + 0.226003i
\(287\) 3.16107e6i 0.133717i
\(288\) 7.53039e6 + 2.26630e7i 0.315239 + 0.948723i
\(289\) −5.97860e6 4.34371e6i −0.247689 0.179956i
\(290\) −4.07775e7 5.61254e7i −1.67196 2.30126i
\(291\) −3.33399e6 6.48997e6i −0.135296 0.263369i
\(292\) −2.93896e6 + 9.04520e6i −0.118044 + 0.363304i
\(293\) 1.58541e7 + 2.18212e7i 0.630286 + 0.867514i 0.998051 0.0624047i \(-0.0198769\pi\)
−0.367765 + 0.929919i \(0.619877\pi\)
\(294\) 477008. + 2.94832e6i 0.0187709 + 0.116020i
\(295\) −2.34713e7 7.22371e7i −0.914262 2.81381i
\(296\) 3.50374e6i 0.135101i
\(297\) −8.88357e6 + 2.46459e7i −0.339093 + 0.940753i
\(298\) 2.95186e7 1.11544
\(299\) −1.54007e7 + 5.00399e6i −0.576139 + 0.187199i
\(300\) −3.15695e7 + 5.10761e6i −1.16924 + 0.189171i
\(301\) −1.42134e7 + 1.03267e7i −0.521195 + 0.378670i
\(302\) 3.09999e7 + 1.00725e7i 1.12548 + 0.365692i
\(303\) 2.64709e7 1.35985e7i 0.951570 0.488835i
\(304\) 1.32385e7 9.61835e6i 0.471215 0.342358i
\(305\) −4.62974e7 + 6.37229e7i −1.63176 + 2.24593i
\(306\) −2.82413e7 + 9.38395e6i −0.985646 + 0.327507i
\(307\) −3.56180e7 −1.23099 −0.615494 0.788141i \(-0.711044\pi\)
−0.615494 + 0.788141i \(0.711044\pi\)
\(308\) −7.06051e6 1.54160e7i −0.241648 0.527618i
\(309\) 9.79320e6 9.85844e6i 0.331932 0.334143i
\(310\) −2.89465e7 8.90883e7i −0.971654 2.99044i
\(311\) −3.92183e6 + 5.39793e6i −0.130379 + 0.179451i −0.869215 0.494433i \(-0.835376\pi\)
0.738837 + 0.673885i \(0.235376\pi\)
\(312\) 1.52893e7 + 2.36958e6i 0.503413 + 0.0780203i
\(313\) −1.60139e7 + 4.92856e7i −0.522231 + 1.60726i 0.247496 + 0.968889i \(0.420392\pi\)
−0.769727 + 0.638373i \(0.779608\pi\)
\(314\) 6.94927e7 + 2.25796e7i 2.24466 + 0.729334i
\(315\) 4.66079e7 3.43378e7i 1.49117 1.09860i
\(316\) 6.35883e6 + 4.61996e6i 0.201519 + 0.146412i
\(317\) 1.62935e7 5.29409e6i 0.511491 0.166193i −0.0418895 0.999122i \(-0.513338\pi\)
0.553380 + 0.832929i \(0.313338\pi\)
\(318\) −4.05608e6 + 4.08310e6i −0.126132 + 0.126972i
\(319\) −4.10001e7 8.26132e6i −1.26303 0.254494i
\(320\) 25502.9i 0.000778288i
\(321\) 1.86069e6 3.68198e6i 0.0562548 0.111318i
\(322\) 2.32584e7 + 1.68982e7i 0.696647 + 0.506144i
\(323\) 7.70638e6 + 1.06069e7i 0.228688 + 0.314762i
\(324\) 5.59196e6 1.80212e7i 0.164410 0.529845i
\(325\) −2.07823e7 + 6.39615e7i −0.605403 + 1.86324i
\(326\) −1.08601e7 1.49476e7i −0.313458 0.431438i
\(327\) 2.87375e7 4.64942e6i 0.821874 0.132971i
\(328\) −773842. 2.38164e6i −0.0219296 0.0674924i
\(329\) 3.46655e7i 0.973442i
\(330\) −4.90671e7 + 6.23486e7i −1.36536 + 1.73494i
\(331\) −3.65485e7 −1.00782 −0.503912 0.863755i \(-0.668107\pi\)
−0.503912 + 0.863755i \(0.668107\pi\)
\(332\) 5.06749e6 1.64653e6i 0.138477 0.0449940i
\(333\) −5.23349e6 + 7.30479e6i −0.141729 + 0.197822i
\(334\) 4.91758e6 3.57283e6i 0.131981 0.0958900i
\(335\) −3.08362e6 1.00193e6i −0.0820213 0.0266503i
\(336\) −2.26104e7 4.40136e7i −0.596062 1.16030i
\(337\) 1.38512e6 1.00635e6i 0.0361907 0.0262941i −0.569543 0.821962i \(-0.692880\pi\)
0.605734 + 0.795668i \(0.292880\pi\)
\(338\) 4.47134e6 6.15427e6i 0.115794 0.159377i
\(339\) −2.12694e7 + 4.20885e7i −0.545955 + 1.08035i
\(340\) −3.21586e7 −0.818203
\(341\) −4.92036e7 2.77160e7i −1.24089 0.698985i
\(342\) −2.32968e7 + 154698.i −0.582395 + 0.00386730i
\(343\) 1.18149e7 + 3.63625e7i 0.292784 + 0.901096i
\(344\) 8.18082e6 1.12599e7i 0.200966 0.276605i
\(345\) 7.35141e6 4.74337e7i 0.179025 1.15513i
\(346\) 1.10011e7 3.38580e7i 0.265588 0.817396i
\(347\) 9.60147e6 + 3.11971e6i 0.229800 + 0.0746664i 0.421653 0.906757i \(-0.361450\pi\)
−0.191854 + 0.981424i \(0.561450\pi\)
\(348\) 2.97679e7 + 4.61352e6i 0.706335 + 0.109470i
\(349\) −1.07772e7 7.83008e6i −0.253530 0.184200i 0.453760 0.891124i \(-0.350082\pi\)
−0.707290 + 0.706924i \(0.750082\pi\)
\(350\) 1.13555e8 3.68963e7i 2.64852 0.860555i
\(351\) −2.83366e7 2.77776e7i −0.655279 0.642353i
\(352\) 2.95176e7 + 3.20915e7i 0.676790 + 0.735804i
\(353\) 2.18364e7i 0.496428i 0.968705 + 0.248214i \(0.0798436\pi\)
−0.968705 + 0.248214i \(0.920156\pi\)
\(354\) 8.24940e7 + 4.16884e7i 1.85957 + 0.939734i
\(355\) 6.25183e7 + 4.54222e7i 1.39740 + 1.01527i
\(356\) −3.16174e6 4.35177e6i −0.0700772 0.0964530i
\(357\) 3.52644e7 1.81159e7i 0.775055 0.398157i
\(358\) 3.05422e7 9.39993e7i 0.665658 2.04869i
\(359\) −3.27183e6 4.50329e6i −0.0707144 0.0973300i 0.772195 0.635386i \(-0.219159\pi\)
−0.842909 + 0.538056i \(0.819159\pi\)
\(360\) −2.67098e7 + 3.72809e7i −0.572483 + 0.799060i
\(361\) −1.13663e7 3.49818e7i −0.241600 0.743567i
\(362\) 1.43854e7i 0.303248i
\(363\) 3.67435e6 + 4.76908e7i 0.0768176 + 0.997045i
\(364\) 2.56822e7 0.532510
\(365\) −5.63844e7 + 1.83204e7i −1.15953 + 0.376753i
\(366\) −1.53085e7 9.46198e7i −0.312241 1.92992i
\(367\) −6.76713e7 + 4.91661e7i −1.36901 + 0.994643i −0.371195 + 0.928555i \(0.621052\pi\)
−0.997814 + 0.0660880i \(0.978948\pi\)
\(368\) −3.90193e7 1.26781e7i −0.782953 0.254397i
\(369\) −1.94407e6 + 6.12125e6i −0.0386931 + 0.121832i
\(370\) −2.20167e7 + 1.59961e7i −0.434658 + 0.315798i
\(371\) 4.50665e6 6.20287e6i 0.0882535 0.121471i
\(372\) 3.63017e7 + 1.83451e7i 0.705178 + 0.356362i
\(373\) 1.00002e8 1.92700 0.963500 0.267709i \(-0.0862665\pi\)
0.963500 + 0.267709i \(0.0862665\pi\)
\(374\) −3.99906e7 + 3.67832e7i −0.764440 + 0.703129i
\(375\) −7.51873e7 7.46896e7i −1.42577 1.41634i
\(376\) 8.48627e6 + 2.61180e7i 0.159644 + 0.491334i
\(377\) 3.72353e7 5.12500e7i 0.694914 0.956467i
\(378\) −1.03269e7 + 6.96868e7i −0.191203 + 1.29025i
\(379\) −612065. + 1.88374e6i −0.0112429 + 0.0346022i −0.956521 0.291665i \(-0.905791\pi\)
0.945278 + 0.326267i \(0.105791\pi\)
\(380\) −2.39432e7 7.77963e6i −0.436347 0.141778i
\(381\) −9.30191e6 + 6.00190e7i −0.168189 + 1.08521i
\(382\) 7.67817e7 + 5.57852e7i 1.37742 + 1.00076i
\(383\) −2.36416e6 + 768163.i −0.0420805 + 0.0136728i −0.329982 0.943987i \(-0.607043\pi\)
0.287901 + 0.957660i \(0.407043\pi\)
\(384\) 4.01823e7 + 3.99164e7i 0.709645 + 0.704948i
\(385\) 5.18746e7 9.20917e7i 0.909019 1.61376i
\(386\) 1.80130e7i 0.313202i
\(387\) −3.38746e7 + 1.12558e7i −0.584442 + 0.194197i
\(388\) 7.76218e6 + 5.63956e6i 0.132889 + 0.0965495i
\(389\) 1.51202e7 + 2.08112e7i 0.256868 + 0.353548i 0.917902 0.396808i \(-0.129882\pi\)
−0.661034 + 0.750356i \(0.729882\pi\)
\(390\) −5.49124e7 1.06893e8i −0.925714 1.80200i
\(391\) 1.01579e7 3.12629e7i 0.169932 0.522997i
\(392\) 1.85272e6 + 2.55004e6i 0.0307575 + 0.0423340i
\(393\) −91197.1 563677.i −0.00150246 0.00928651i
\(394\) −2.52648e6 7.77571e6i −0.0413073 0.127131i
\(395\) 4.89959e7i 0.795003i
\(396\) −4.19141e6 3.41946e7i −0.0674954 0.550645i
\(397\) 7.15475e7 1.14347 0.571733 0.820440i \(-0.306271\pi\)
0.571733 + 0.820440i \(0.306271\pi\)
\(398\) 2.00564e7 6.51673e6i 0.318130 0.103367i
\(399\) 3.06381e7 4.95693e6i 0.482329 0.0780358i
\(400\) −1.37850e8 + 1.00154e8i −2.15391 + 1.56491i
\(401\) 6.79705e7 + 2.20850e7i 1.05411 + 0.342502i 0.784282 0.620405i \(-0.213032\pi\)
0.269832 + 0.962907i \(0.413032\pi\)
\(402\) 3.50957e6 1.80292e6i 0.0540226 0.0277522i
\(403\) 6.92001e7 5.02768e7i 1.05728 0.768161i
\(404\) −2.30023e7 + 3.16599e7i −0.348840 + 0.480137i
\(405\) 1.11372e8 3.78293e7i 1.67653 0.569461i
\(406\) −1.12467e8 −1.68053
\(407\) −3.24073e6 + 1.60834e7i −0.0480684 + 0.238558i
\(408\) −2.21345e7 + 2.22819e7i −0.325903 + 0.328074i
\(409\) −4.04057e7 1.24356e8i −0.590572 1.81759i −0.575636 0.817706i \(-0.695245\pi\)
−0.0149365 0.999888i \(-0.504755\pi\)
\(410\) −1.14328e7 + 1.57359e7i −0.165882 + 0.228318i
\(411\) 3.84366e7 + 5.95701e6i 0.553630 + 0.0858031i
\(412\) −5.64671e6 + 1.73788e7i −0.0807427 + 0.248501i
\(413\) −1.17107e8 3.80504e7i −1.66239 0.540144i
\(414\) 3.46463e7 + 4.70267e7i 0.488265 + 0.662740i
\(415\) 2.68711e7 + 1.95230e7i 0.375959 + 0.273150i
\(416\) −6.28095e7 + 2.04080e7i −0.872460 + 0.283479i
\(417\) 5.70091e7 5.73890e7i 0.786206 0.791444i
\(418\) −3.86728e7 + 1.77121e7i −0.529514 + 0.242517i
\(419\) 5.50702e7i 0.748642i 0.927299 + 0.374321i \(0.122124\pi\)
−0.927299 + 0.374321i \(0.877876\pi\)
\(420\) −3.43355e7 + 6.79440e7i −0.463443 + 0.917072i
\(421\) −9.95474e6 7.23254e6i −0.133409 0.0969270i 0.519080 0.854726i \(-0.326275\pi\)
−0.652488 + 0.757799i \(0.726275\pi\)
\(422\) −3.72537e7 5.12754e7i −0.495716 0.682294i
\(423\) 2.13195e7 6.71281e7i 0.281680 0.886918i
\(424\) −1.87696e6 + 5.77668e6i −0.0246239 + 0.0757845i
\(425\) −8.02452e7 1.10448e8i −1.04533 1.43877i
\(426\) −9.28312e7 + 1.50191e7i −1.20079 + 0.194275i
\(427\) 3.94587e7 + 1.21441e8i 0.506826 + 1.55985i
\(428\) 5.42495e6i 0.0691934i
\(429\) −6.79916e7 2.50188e7i −0.861159 0.316880i
\(430\) −1.08104e8 −1.35968
\(431\) −7.58300e7 + 2.46386e7i −0.947129 + 0.307741i −0.741548 0.670899i \(-0.765908\pi\)
−0.205580 + 0.978640i \(0.565908\pi\)
\(432\) −1.67154e7 9.91358e7i −0.207332 1.22964i
\(433\) 1.26363e7 9.18078e6i 0.155652 0.113088i −0.507233 0.861809i \(-0.669332\pi\)
0.662885 + 0.748721i \(0.269332\pi\)
\(434\) −1.44425e8 4.69266e7i −1.76675 0.574051i
\(435\) 8.58041e7 + 1.67027e8i 1.04241 + 2.02917i
\(436\) −3.09702e7 + 2.25011e7i −0.373666 + 0.271485i
\(437\) 1.51259e7 2.08190e7i 0.181249 0.249468i
\(438\) 3.25397e7 6.43903e7i 0.387249 0.766299i
\(439\) −1.20838e8 −1.42827 −0.714135 0.700008i \(-0.753180\pi\)
−0.714135 + 0.700008i \(0.753180\pi\)
\(440\) −1.65395e7 + 8.20838e7i −0.194162 + 0.963605i
\(441\) −53679.4 8.08384e6i −0.000625881 0.0942545i
\(442\) −2.54314e7 7.82697e7i −0.294512 0.906414i
\(443\) −5.59431e7 + 7.69991e7i −0.643481 + 0.885675i −0.998795 0.0490718i \(-0.984374\pi\)
0.355315 + 0.934747i \(0.384374\pi\)
\(444\) 1.80978e6 1.16773e7i 0.0206765 0.133411i
\(445\) 1.03617e7 3.18900e7i 0.117585 0.361888i
\(446\) 5.85604e7 + 1.90274e7i 0.660085 + 0.214474i
\(447\) −7.89555e7 1.22368e7i −0.884016 0.137007i
\(448\) −33448.0 24301.4i −0.000371994 0.000270270i
\(449\) 1.23122e8 4.00047e7i 1.36018 0.441949i 0.464077 0.885795i \(-0.346386\pi\)
0.896103 + 0.443846i \(0.146386\pi\)
\(450\) 2.42585e8 1.61085e6i 2.66212 0.0176773i
\(451\) 1.34935e6 + 1.16483e7i 0.0147094 + 0.126980i
\(452\) 6.20122e7i 0.671525i
\(453\) −7.87422e7 3.97924e7i −0.847058 0.428061i
\(454\) −3.25745e7 2.36668e7i −0.348105 0.252913i
\(455\) 9.41004e7 + 1.29518e8i 0.998981 + 1.37498i
\(456\) −2.18702e7 + 1.12350e7i −0.230652 + 0.118490i
\(457\) 1.83580e7 5.65002e7i 0.192343 0.591972i −0.807654 0.589657i \(-0.799263\pi\)
0.999997 0.00231534i \(-0.000736997\pi\)
\(458\) 1.04598e8 + 1.43967e8i 1.08875 + 1.49853i
\(459\) 7.94292e7 1.33927e7i 0.821377 0.138493i
\(460\) 1.95052e7 + 6.00308e7i 0.200390 + 0.616738i
\(461\) 1.77711e8i 1.81389i −0.421247 0.906946i \(-0.638408\pi\)
0.421247 0.906946i \(-0.361592\pi\)
\(462\) 3.50170e7 + 1.23764e8i 0.355102 + 1.25508i
\(463\) 1.42784e8 1.43858 0.719292 0.694708i \(-0.244466\pi\)
0.719292 + 0.694708i \(0.244466\pi\)
\(464\) 1.52645e8 4.95972e7i 1.52801 0.496482i
\(465\) 4.04944e7 + 2.50291e8i 0.402751 + 2.48935i
\(466\) 1.73471e8 1.26034e8i 1.71424 1.24546i
\(467\) 1.32992e8 + 4.32118e7i 1.30580 + 0.424279i 0.877594 0.479404i \(-0.159147\pi\)
0.428202 + 0.903683i \(0.359147\pi\)
\(468\) 4.97323e7 + 1.57947e7i 0.485178 + 0.154090i
\(469\) −4.25241e6 + 3.08956e6i −0.0412208 + 0.0299487i
\(470\) 1.25377e8 1.72566e8i 1.20760 1.66212i
\(471\) −1.76517e8 8.92030e7i −1.68937 0.853722i
\(472\) 9.75469e7 0.927657
\(473\) −4.79675e7 + 4.41203e7i −0.453277 + 0.416923i
\(474\) −4.22997e7 4.20198e7i −0.397194 0.394565i
\(475\) −3.30264e7 1.01645e8i −0.308163 0.948429i
\(476\) −3.06436e7 + 4.21772e7i −0.284131 + 0.391072i
\(477\) 1.25417e7 9.23994e6i 0.115558 0.0851362i
\(478\) −7.96192e7 + 2.45043e8i −0.729011 + 2.24366i
\(479\) −9.52590e7 3.09515e7i −0.866761 0.281628i −0.158311 0.987389i \(-0.550605\pi\)
−0.708449 + 0.705762i \(0.750605\pi\)
\(480\) 2.99816e7 1.93451e8i 0.271101 1.74923i
\(481\) −2.01042e7 1.46066e7i −0.180656 0.131254i
\(482\) −2.01053e8 + 6.53262e7i −1.79544 + 0.583373i
\(483\) −5.52060e7 5.48406e7i −0.489942 0.486699i
\(484\) −3.25981e7 5.37931e7i −0.287512 0.474450i
\(485\) 5.98090e7i 0.524254i
\(486\) −6.28553e7 + 1.28594e8i −0.547562 + 1.12024i
\(487\) 4.52944e7 + 3.29083e7i 0.392155 + 0.284917i 0.766338 0.642438i \(-0.222077\pi\)
−0.374183 + 0.927355i \(0.622077\pi\)
\(488\) −5.94587e7 8.18379e7i −0.511630 0.704199i
\(489\) 2.28518e7 + 4.44834e7i 0.195431 + 0.380427i
\(490\) 7.56546e6 2.32841e7i 0.0643054 0.197912i
\(491\) 1.20867e7 + 1.66359e7i 0.102109 + 0.140540i 0.857014 0.515294i \(-0.172317\pi\)
−0.754905 + 0.655834i \(0.772317\pi\)
\(492\) −1.34888e6 8.33725e6i −0.0113260 0.0700048i
\(493\) 3.97381e7 + 1.22301e8i 0.331640 + 1.02068i
\(494\) 6.44267e7i 0.534423i
\(495\) 1.57090e8 1.46428e8i 1.29519 1.20728i
\(496\) 2.16714e8 1.77600
\(497\) 1.19146e8 3.87128e7i 0.970531 0.315345i
\(498\) −3.98999e7 + 6.45539e6i −0.323061 + 0.0522679i
\(499\) −1.27645e8 + 9.27392e7i −1.02731 + 0.746383i −0.967768 0.251843i \(-0.918963\pi\)
−0.0595397 + 0.998226i \(0.518963\pi\)
\(500\) 1.32542e8 + 4.30657e7i 1.06034 + 0.344525i
\(501\) −1.46345e7 + 7.51796e6i −0.116376 + 0.0597843i
\(502\) −1.43235e8 + 1.04066e8i −1.13224 + 0.822620i
\(503\) 1.06285e8 1.46288e8i 0.835153 1.14949i −0.151789 0.988413i \(-0.548503\pi\)
0.986942 0.161076i \(-0.0514966\pi\)
\(504\) 2.34439e7 + 7.05554e7i 0.183121 + 0.551110i
\(505\) −2.43945e8 −1.89417
\(506\) 9.29190e7 + 5.23407e7i 0.717221 + 0.404006i
\(507\) −1.45110e7 + 1.46077e7i −0.111346 + 0.112088i
\(508\) −2.46804e7 7.59584e7i −0.188261 0.579408i
\(509\) 4.70944e7 6.48199e7i 0.357121 0.491536i −0.592222 0.805775i \(-0.701749\pi\)
0.949344 + 0.314239i \(0.101749\pi\)
\(510\) 2.41068e8 + 3.73614e7i 1.81731 + 0.281652i
\(511\) −2.97001e7 + 9.14074e7i −0.222584 + 0.685045i
\(512\) −7.07647e7 2.29928e7i −0.527238 0.171310i
\(513\) 6.23777e7 + 9.24376e6i 0.462038 + 0.0684694i
\(514\) 1.89720e7 + 1.37839e7i 0.139708 + 0.101504i
\(515\) −1.08333e8 + 3.51994e7i −0.793118 + 0.257700i
\(516\) 3.30811e7 3.33015e7i 0.240786 0.242390i
\(517\) −1.47975e7 1.27740e8i −0.107082 0.924392i
\(518\) 4.41182e7i 0.317416i
\(519\) −4.34611e7 + 8.60019e7i −0.310884 + 0.615185i
\(520\) −1.02605e8 7.45466e7i −0.729721 0.530173i
\(521\) −1.00653e8 1.38537e8i −0.711727 0.979608i −0.999758 0.0219873i \(-0.993001\pi\)
0.288031 0.957621i \(-0.406999\pi\)
\(522\) −2.17787e8 6.91678e7i −1.53116 0.486287i
\(523\) −2.13560e7 + 6.57270e7i −0.149285 + 0.459451i −0.997537 0.0701413i \(-0.977655\pi\)
0.848252 + 0.529592i \(0.177655\pi\)
\(524\) 441353. + 607471.i 0.00306756 + 0.00422213i
\(525\) −3.19029e8 + 5.16156e7i −2.20472 + 0.356700i
\(526\) −6.91675e7 2.12876e8i −0.475275 1.46275i
\(527\) 1.73635e8i 1.18633i
\(528\) −1.02106e8 1.52536e8i −0.693664 1.03626i
\(529\) 8.35161e7 0.564161
\(530\) 4.48685e7 1.45786e7i 0.301379 0.0979241i
\(531\) −2.03371e8 1.45704e8i −1.35833 0.973170i
\(532\) −3.30185e7 + 2.39893e7i −0.219292 + 0.159325i
\(533\) −1.68917e7 5.48846e6i −0.111556 0.0362467i
\(534\) 1.86453e7 + 3.62950e7i 0.122446 + 0.238354i
\(535\) −2.73586e7 + 1.98772e7i −0.178662 + 0.129806i
\(536\) 2.44756e6 3.36877e6i 0.0158942 0.0218765i
\(537\) −1.20660e8 + 2.38766e8i −0.779187 + 1.54187i
\(538\) 2.08162e8 1.33676
\(539\) −6.14599e6 1.34192e7i −0.0392487 0.0856962i
\(540\) −1.08275e8 + 1.10454e8i −0.687618 + 0.701454i
\(541\) 7.35254e7 + 2.26288e8i 0.464350 + 1.42912i 0.859798 + 0.510634i \(0.170589\pi\)
−0.395448 + 0.918488i \(0.629411\pi\)
\(542\) 1.54069e8 2.12058e8i 0.967650 1.33186i
\(543\) 5.96340e6 3.84778e7i 0.0372473 0.240332i
\(544\) 4.14276e7 1.27501e8i 0.257332 0.791985i
\(545\) −2.26951e8 7.37410e7i −1.40198 0.455533i
\(546\) −1.92519e8 2.98372e7i −1.18276 0.183307i
\(547\) 5.66815e7 + 4.11815e7i 0.346321 + 0.251617i 0.747324 0.664460i \(-0.231338\pi\)
−0.401003 + 0.916077i \(0.631338\pi\)
\(548\) −4.86443e7 + 1.58055e7i −0.295590 + 0.0960431i
\(549\) 1.72272e6 + 2.59433e8i 0.0104111 + 1.56786i
\(550\) 4.02693e8 1.84433e8i 2.42040 1.10854i
\(551\) 1.00671e8i 0.601796i
\(552\) 5.50190e7 + 2.78039e7i 0.327111 + 0.165306i
\(553\) 6.42599e7 + 4.66876e7i 0.379984 + 0.276074i
\(554\) 5.11046e7 + 7.03395e7i 0.300560 + 0.413685i
\(555\) 6.55209e7 3.36590e7i 0.383266 0.196890i
\(556\) −3.28712e7 + 1.01167e8i −0.191245 + 0.588593i
\(557\) 1.32458e8 + 1.82313e8i 0.766501 + 1.05500i 0.996645 + 0.0818411i \(0.0260800\pi\)
−0.230145 + 0.973156i \(0.573920\pi\)
\(558\) −2.50812e8 1.79694e8i −1.44360 1.03426i
\(559\) −3.05041e7 9.38820e7i −0.174632 0.537461i
\(560\) 4.05612e8i 2.30965i
\(561\) 1.22214e8 8.18089e7i 0.692202 0.463353i
\(562\) −5.85796e7 −0.330018
\(563\) 1.16364e8 3.78090e7i 0.652069 0.211870i 0.0357428 0.999361i \(-0.488620\pi\)
0.616326 + 0.787491i \(0.288620\pi\)
\(564\) 1.47924e7 + 9.14297e7i 0.0824519 + 0.509624i
\(565\) 3.12734e8 2.27215e8i 1.73392 1.25977i
\(566\) 1.72766e8 + 5.61351e7i 0.952816 + 0.309589i
\(567\) 5.65103e7 1.82115e8i 0.310012 0.999074i
\(568\) −8.02909e7 + 5.83348e7i −0.438149 + 0.318334i
\(569\) 2.38392e7 3.28118e7i 0.129406 0.178112i −0.739397 0.673269i \(-0.764890\pi\)
0.868803 + 0.495157i \(0.164890\pi\)
\(570\) 1.70445e8 + 8.61346e7i 0.920366 + 0.465107i
\(571\) −1.88098e8 −1.01036 −0.505180 0.863014i \(-0.668574\pi\)
−0.505180 + 0.863014i \(0.668574\pi\)
\(572\) 9.46372e7 1.09628e7i 0.505678 0.0585780i
\(573\) −1.82248e8 1.81042e8i −0.968723 0.962312i
\(574\) 9.74403e6 + 2.99890e7i 0.0515232 + 0.158572i
\(575\) −1.57503e8 + 2.16784e8i −0.828487 + 1.14031i
\(576\) −49825.0 67629.2i −0.000260723 0.000353889i
\(577\) 8.14976e7 2.50824e8i 0.424246 1.30569i −0.479469 0.877559i \(-0.659171\pi\)
0.903715 0.428135i \(-0.140829\pi\)
\(578\) −7.01085e7 2.27796e7i −0.363067 0.117968i
\(579\) 7.46719e6 4.81807e7i 0.0384699 0.248221i
\(580\) −1.99769e8 1.45140e8i −1.02387 0.743883i
\(581\) 5.12102e7 1.66392e7i 0.261113 0.0848407i
\(582\) −5.16350e7 5.12933e7i −0.261924 0.260191i
\(583\) 1.39589e7 2.47809e7i 0.0704444 0.125058i
\(584\) 7.61398e7i 0.382273i
\(585\) 1.02566e8 + 3.08678e8i 0.512316 + 1.54183i
\(586\) 2.17672e8 + 1.58148e8i 1.08171 + 0.785905i
\(587\) 1.70850e8 + 2.35154e8i 0.844695 + 1.16262i 0.985007 + 0.172516i \(0.0551896\pi\)
−0.140312 + 0.990107i \(0.544810\pi\)
\(588\) 4.85757e6 + 9.45577e6i 0.0238939 + 0.0465120i
\(589\) −4.20048e7 + 1.29277e8i −0.205567 + 0.632669i
\(590\) −4.45344e8 6.12963e8i −2.16840 2.98455i
\(591\) 3.53439e6 + 2.18456e7i 0.0171219 + 0.105828i
\(592\) −1.94559e7 5.98790e7i −0.0937747 0.288609i
\(593\) 2.09831e8i 1.00625i −0.864214 0.503125i \(-0.832184\pi\)
0.864214 0.503125i \(-0.167816\pi\)
\(594\) −8.30707e6 + 2.61200e8i −0.0396359 + 1.24627i
\(595\) −3.24983e8 −1.54280
\(596\) 9.99240e7 3.24673e7i 0.471988 0.153358i
\(597\) −5.63479e7 + 9.11651e6i −0.264822 + 0.0428455i
\(598\) −1.30682e8 + 9.49458e7i −0.611098 + 0.443989i
\(599\) −1.12408e8 3.65237e7i −0.523020 0.169939i 0.0355955 0.999366i \(-0.488667\pi\)
−0.558615 + 0.829427i \(0.688667\pi\)
\(600\) 2.27731e8 1.16988e8i 1.05431 0.541613i
\(601\) −2.07934e8 + 1.51073e8i −0.957861 + 0.695927i −0.952653 0.304060i \(-0.901658\pi\)
−0.00520787 + 0.999986i \(0.501658\pi\)
\(602\) −1.03011e8 + 1.41782e8i −0.472165 + 0.649879i
\(603\) −1.01347e7 + 3.36752e6i −0.0462230 + 0.0153588i
\(604\) 1.16017e8 0.526515
\(605\) 1.51844e8 3.61495e8i 0.685696 1.63244i
\(606\) 2.09212e8 2.10606e8i 0.940087 0.946351i
\(607\) −4.25583e7 1.30981e8i −0.190291 0.585656i 0.809708 0.586833i \(-0.199625\pi\)
−0.999999 + 0.00117699i \(0.999625\pi\)
\(608\) 6.16886e7 8.49071e7i 0.274470 0.377775i
\(609\) 3.00824e8 + 4.66225e7i 1.33186 + 0.206416i
\(610\) −2.42797e8 + 7.47251e8i −1.06968 + 3.29213i
\(611\) 1.85242e8 + 6.01886e7i 0.812110 + 0.263871i
\(612\) −8.52790e7 + 6.28282e7i −0.372038 + 0.274095i
\(613\) −1.81084e8 1.31565e8i −0.786138 0.571163i 0.120677 0.992692i \(-0.461494\pi\)
−0.906815 + 0.421529i \(0.861494\pi\)
\(614\) −3.37908e8 + 1.09793e8i −1.45980 + 0.474317i
\(615\) 3.71033e7 3.73505e7i 0.159510 0.160573i
\(616\) 9.18956e7 + 9.99087e7i 0.393145 + 0.427426i
\(617\) 1.10958e8i 0.472392i 0.971705 + 0.236196i \(0.0759007\pi\)
−0.971705 + 0.236196i \(0.924099\pi\)
\(618\) 6.25193e7 1.23715e8i 0.264880 0.524150i
\(619\) −9.60887e7 6.98125e7i −0.405135 0.294348i 0.366494 0.930420i \(-0.380558\pi\)
−0.771629 + 0.636072i \(0.780558\pi\)
\(620\) −1.95975e8 2.69736e8i −0.822291 1.13179i
\(621\) −7.31764e7 1.40148e8i −0.305560 0.585211i
\(622\) −2.05672e7 + 6.32993e7i −0.0854680 + 0.263044i
\(623\) −3.19514e7 4.39773e7i −0.132137 0.181872i
\(624\) 2.74453e8 4.44036e7i 1.12957 0.182753i
\(625\) 1.07381e8 + 3.30484e8i 0.439831 + 1.35366i
\(626\) 5.16935e8i 2.10724i
\(627\) 1.10783e8 3.13443e7i 0.449441 0.127162i
\(628\) 2.60076e8 1.05008
\(629\) 4.79761e7 1.55884e7i 0.192785 0.0626396i
\(630\) 3.36323e8 4.69432e8i 1.34504 1.87738i
\(631\) 3.07959e8 2.23745e8i 1.22576 0.890565i 0.229192 0.973381i \(-0.426392\pi\)
0.996565 + 0.0828165i \(0.0263915\pi\)
\(632\) −5.98447e7 1.94447e7i −0.237069 0.0770283i
\(633\) 7.83894e7 + 1.52593e8i 0.309063 + 0.601623i
\(634\) 1.38258e8 1.00450e8i 0.542527 0.394169i
\(635\) 2.92637e8 4.02780e8i 1.14290 1.57306i
\(636\) −9.23934e6 + 1.82830e7i −0.0359145 + 0.0710684i
\(637\) 2.23557e7 0.0864907
\(638\) −4.14433e8 + 4.80082e7i −1.59585 + 0.184864i
\(639\) 2.54529e8 1.69016e6i 0.975515 0.00647775i
\(640\) −1.43470e8 4.41556e8i −0.547296 1.68440i
\(641\) 2.29082e7 3.15305e7i 0.0869795 0.119717i −0.763310 0.646033i \(-0.776427\pi\)
0.850289 + 0.526316i \(0.176427\pi\)
\(642\) 6.30262e6 4.06666e7i 0.0238186 0.153685i
\(643\) −6.50247e7 + 2.00125e8i −0.244594 + 0.752782i 0.751109 + 0.660178i \(0.229519\pi\)
−0.995703 + 0.0926041i \(0.970481\pi\)
\(644\) 9.73188e7 + 3.16208e7i 0.364367 + 0.118390i
\(645\) 2.89154e8 + 4.48138e7i 1.07758 + 0.167006i
\(646\) 1.05806e8 + 7.68729e7i 0.392477 + 0.285151i
\(647\) −7.76723e6 + 2.52373e6i −0.0286783 + 0.00931814i −0.323321 0.946289i \(-0.604799\pi\)
0.294643 + 0.955607i \(0.404799\pi\)
\(648\) 2.00607e6 + 1.51045e8i 0.00737261 + 0.555114i
\(649\) −4.47775e8 9.02244e7i −1.63804 0.330058i
\(650\) 6.70864e8i 2.44284i
\(651\) 3.66852e8 + 1.85389e8i 1.32968 + 0.671955i
\(652\) −5.32034e7 3.86545e7i −0.191954 0.139463i
\(653\) −1.40189e8 1.92954e8i −0.503471 0.692969i 0.479330 0.877635i \(-0.340880\pi\)
−0.982801 + 0.184666i \(0.940880\pi\)
\(654\) 2.58300e8 1.32693e8i 0.923404 0.474366i
\(655\) −1.44641e6 + 4.45158e6i −0.00514715 + 0.0158413i
\(656\) −2.64500e7 3.64053e7i −0.0936944 0.128959i
\(657\) −1.13729e8 + 1.58740e8i −0.401028 + 0.559746i
\(658\) −1.06857e8 3.28872e8i −0.375081 1.15438i
\(659\) 5.69225e6i 0.0198897i −0.999951 0.00994483i \(-0.996834\pi\)
0.999951 0.00994483i \(-0.00316559\pi\)
\(660\) −9.75213e7 + 2.65026e8i −0.339209 + 0.921842i
\(661\) 3.28619e8 1.13786 0.568929 0.822387i \(-0.307358\pi\)
0.568929 + 0.822387i \(0.307358\pi\)
\(662\) −3.46735e8 + 1.12661e8i −1.19515 + 0.388329i
\(663\) 3.55769e7 + 2.19896e8i 0.122075 + 0.754531i
\(664\) −3.45100e7 + 2.50729e7i −0.117880 + 0.0856448i
\(665\) −2.41961e8 7.86181e7i −0.822775 0.267336i
\(666\) −2.71330e7 + 8.54328e7i −0.0918490 + 0.289203i
\(667\) 2.04198e8 1.48359e8i 0.688137 0.499961i
\(668\) 1.27169e7 1.75033e7i 0.0426630 0.0587205i
\(669\) −1.48748e8 7.51699e7i −0.496790 0.251053i
\(670\) −3.23428e7 −0.107536
\(671\) 1.97242e8 + 4.30660e8i 0.652877 + 1.42550i
\(672\) −2.25149e8 2.23659e8i −0.741930 0.737019i
\(673\) 3.62307e7 + 1.11507e8i 0.118859 + 0.365810i 0.992732 0.120344i \(-0.0383996\pi\)
−0.873873 + 0.486153i \(0.838400\pi\)
\(674\) 1.00385e7 1.38169e7i 0.0327862 0.0451263i
\(675\) −6.49529e8 9.62536e7i −2.11197 0.312972i
\(676\) 8.36698e6 2.57509e7i 0.0270850 0.0833590i
\(677\) 1.03770e8 + 3.37168e7i 0.334430 + 0.108663i 0.471418 0.881910i \(-0.343742\pi\)
−0.136988 + 0.990573i \(0.543742\pi\)
\(678\) −7.20448e7 + 4.64857e8i −0.231161 + 1.49152i
\(679\) 7.84418e7 + 5.69913e7i 0.250575 + 0.182053i
\(680\) 2.44852e8 7.95573e7i 0.778713 0.253019i
\(681\) 7.73186e7 + 7.68068e7i 0.244817 + 0.243197i
\(682\) −5.52229e8 1.11272e8i −1.74087 0.350777i
\(683\) 3.51234e8i 1.10239i −0.834377 0.551194i \(-0.814172\pi\)
0.834377 0.551194i \(-0.185828\pi\)
\(684\) −7.86922e7 + 2.61476e7i −0.245903 + 0.0817079i
\(685\) −2.57943e8 1.87407e8i −0.802513 0.583060i
\(686\) 2.24176e8 + 3.08551e8i 0.694410 + 0.955774i
\(687\) −2.20095e8 4.28439e8i −0.678798 1.32135i
\(688\) 7.72853e7 2.37860e8i 0.237319 0.730392i
\(689\) 2.53214e7 + 3.48520e7i 0.0774160 + 0.106554i
\(690\) −7.64722e7 4.72664e8i −0.232786 1.43882i
\(691\) 8.26635e7 + 2.54412e8i 0.250542 + 0.771088i 0.994675 + 0.103057i \(0.0328625\pi\)
−0.744134 + 0.668031i \(0.767138\pi\)
\(692\) 1.26713e8i 0.382388i
\(693\) −4.23568e7 3.45558e8i −0.127269 1.03830i
\(694\) 1.00706e8 0.301284
\(695\) −6.30637e8 + 2.04906e8i −1.87856 + 0.610381i
\(696\) −2.38063e8 + 3.85161e7i −0.706096 + 0.114239i
\(697\) 2.91685e7 2.11921e7i 0.0861421 0.0625859i
\(698\) −1.26379e8 4.10632e7i −0.371630 0.120750i
\(699\) −5.16244e8 + 2.65202e8i −1.51155 + 0.776507i
\(700\) 3.43816e8 2.49797e8i 1.00238 0.728270i
\(701\) −1.90393e8 + 2.62053e8i −0.552709 + 0.760738i −0.990377 0.138398i \(-0.955805\pi\)
0.437668 + 0.899137i \(0.355805\pi\)
\(702\) −3.54454e8 1.76179e8i −1.02459 0.509263i
\(703\) 3.94909e7 0.113666
\(704\) −133627. 75271.4i −0.000382981 0.000215731i
\(705\) −4.06890e8 + 4.09601e8i −1.16121 + 1.16894i
\(706\) 6.73108e7 + 2.07161e8i 0.191281 + 0.588701i
\(707\) −2.32452e8 + 3.19943e8i −0.657772 + 0.905346i
\(708\) 3.25105e8 + 5.03856e7i 0.916059 + 0.141973i
\(709\) 5.97151e7 1.83784e8i 0.167550 0.515667i −0.831665 0.555278i \(-0.812612\pi\)
0.999215 + 0.0396110i \(0.0126119\pi\)
\(710\) 7.33126e8 + 2.38207e8i 2.04835 + 0.665548i
\(711\) 9.57231e7 + 1.29928e8i 0.266323 + 0.361489i
\(712\) 3.48390e7 + 2.53120e7i 0.0965218 + 0.0701272i
\(713\) 3.24126e8 1.05315e8i 0.894221 0.290550i
\(714\) 2.78711e8 2.80568e8i 0.765703 0.770804i
\(715\) 4.02040e8 + 4.37097e8i 1.09990 + 1.19580i
\(716\) 3.51792e8i 0.958400i
\(717\) 3.14544e8 6.22428e8i 0.853344 1.68862i
\(718\) −4.49213e7 3.26373e7i −0.121361 0.0881739i
\(719\) −2.41129e8 3.31885e8i −0.648727 0.892897i 0.350316 0.936632i \(-0.386074\pi\)
−0.999043 + 0.0437349i \(0.986074\pi\)
\(720\) −2.49454e8 + 7.85449e8i −0.668333 + 2.10436i
\(721\) −5.70635e7 + 1.75623e8i −0.152248 + 0.468572i
\(722\) −2.15664e8 2.96835e8i −0.573014 0.788686i
\(723\) 5.64853e8 9.13873e7i 1.49458 0.241808i
\(724\) 1.58224e7 + 4.86964e7i 0.0416925 + 0.128316i
\(725\) 1.04827e9i 2.75080i
\(726\) 1.81866e8 + 4.41117e8i 0.475272 + 1.15277i
\(727\) −241246. −0.000627853 −0.000313926 1.00000i \(-0.500100\pi\)
−0.000313926 1.00000i \(0.500100\pi\)
\(728\) −1.95541e8 + 6.35352e7i −0.506809 + 0.164672i
\(729\) 2.21432e8 3.17904e8i 0.571553 0.820565i
\(730\) −4.78446e8 + 3.47611e8i −1.22988 + 0.893563i
\(731\) 1.90577e8 + 6.19223e7i 0.487886 + 0.158524i
\(732\) −1.55893e8 3.03462e8i −0.397459 0.773697i
\(733\) −2.61204e8 + 1.89776e8i −0.663235 + 0.481869i −0.867754 0.496994i \(-0.834437\pi\)
0.204519 + 0.978863i \(0.434437\pi\)
\(734\) −4.90442e8 + 6.75036e8i −1.24022 + 1.70702i
\(735\) −2.98882e7 + 5.91435e7i −0.0752727 + 0.148952i
\(736\) −2.63134e8 −0.660000
\(737\) −1.43510e7 + 1.32000e7i −0.0358493 + 0.0329740i
\(738\) 425413. + 6.40649e7i 0.00105838 + 0.159386i
\(739\) −1.45677e8 4.48346e8i −0.360958 1.11091i −0.952474 0.304620i \(-0.901470\pi\)
0.591516 0.806293i \(-0.298530\pi\)
\(740\) −5.69353e7 + 7.83648e7i −0.140503 + 0.193386i
\(741\) −2.67077e7 + 1.72327e8i −0.0656420 + 0.423544i
\(742\) 2.36342e7 7.27385e7i 0.0578533 0.178054i
\(743\) −3.53359e8 1.14813e8i −0.861488 0.279914i −0.155238 0.987877i \(-0.549614\pi\)
−0.706250 + 0.707963i \(0.749614\pi\)
\(744\) −3.21781e8 4.98705e7i −0.781343 0.121095i
\(745\) 5.29860e8 + 3.84966e8i 1.28142 + 0.931009i
\(746\) 9.48718e8 3.08257e8i 2.28518 0.742500i
\(747\) 1.09399e8 726448.i 0.262454 0.00174278i
\(748\) −9.49155e7 + 1.68501e8i −0.226795 + 0.402622i
\(749\) 5.48225e7i 0.130471i
\(750\) −9.43533e8 4.76815e8i −2.23652 1.13023i
\(751\) 4.23964e8 + 3.08028e8i 1.00094 + 0.727227i 0.962290 0.272026i \(-0.0876936\pi\)
0.0386522 + 0.999253i \(0.487694\pi\)
\(752\) 2.90061e8 + 3.99235e8i 0.682081 + 0.938804i
\(753\) 4.26261e8 2.18977e8i 0.998369 0.512877i
\(754\) 1.95273e8 6.00988e8i 0.455541 1.40201i
\(755\) 4.25090e8 + 5.85086e8i 0.987734 + 1.35950i
\(756\) 4.16902e7 + 2.47257e8i 0.0964870 + 0.572246i
\(757\) 3.68353e7 + 1.13367e8i 0.0849135 + 0.261337i 0.984494 0.175418i \(-0.0561277\pi\)
−0.899581 + 0.436755i \(0.856128\pi\)
\(758\) 1.97578e7i 0.0453660i
\(759\) −2.26840e8 1.78519e8i −0.518793 0.408280i
\(760\) 2.01547e8 0.459130
\(761\) 3.41670e8 1.11015e8i 0.775269 0.251900i 0.105450 0.994425i \(-0.466372\pi\)
0.669819 + 0.742524i \(0.266372\pi\)
\(762\) 9.67621e7 + 5.98074e8i 0.218696 + 1.35173i
\(763\) −3.12973e8 + 2.27388e8i −0.704585 + 0.511911i
\(764\) 3.21273e8 + 1.04388e8i 0.720434 + 0.234083i
\(765\) −6.29314e8 1.99867e8i −1.40567 0.446432i
\(766\) −2.00609e7 + 1.45751e7i −0.0446339 + 0.0324284i
\(767\) 4.06659e8 5.59718e8i 0.901247 1.24046i
\(768\) 5.04074e8 + 2.54734e8i 1.11278 + 0.562346i
\(769\) −3.60022e7 −0.0791682 −0.0395841 0.999216i \(-0.512603\pi\)
−0.0395841 + 0.999216i \(0.512603\pi\)
\(770\) 2.08261e8 1.03358e9i 0.456179 2.26397i
\(771\) −4.50316e7 4.47336e7i −0.0982550 0.0976047i
\(772\) 1.98124e7 + 6.09762e7i 0.0430611 + 0.132528i
\(773\) −1.82076e8 + 2.50607e8i −0.394199 + 0.542568i −0.959276 0.282470i \(-0.908846\pi\)
0.565078 + 0.825038i \(0.308846\pi\)
\(774\) −2.86672e8 + 2.11202e8i −0.618249 + 0.455487i
\(775\) 4.37388e8 1.34614e9i 0.939641 2.89192i
\(776\) −7.30521e7 2.37361e7i −0.156332 0.0507953i
\(777\) 1.82890e7 1.18006e8i 0.0389875 0.251560i
\(778\) 2.07596e8 + 1.50828e8i 0.440840 + 0.320289i
\(779\) 2.68436e7 8.72203e6i 0.0567844 0.0184504i
\(780\) −3.03456e8 3.01447e8i −0.639457 0.635225i
\(781\) 4.22519e8 1.93513e8i 0.886939 0.406217i
\(782\) 3.27903e8i 0.685686i
\(783\) 5.53857e8 + 2.75290e8i 1.15375 + 0.573463i
\(784\) 4.58231e7 + 3.32924e7i 0.0950902 + 0.0690871i
\(785\) 9.52928e8 + 1.31159e9i 1.96993 + 2.71138i
\(786\) −2.60273e6 5.06649e6i −0.00535996 0.0104337i
\(787\) −3.97401e7 + 1.22307e8i −0.0815276 + 0.250916i −0.983509 0.180858i \(-0.942112\pi\)
0.901982 + 0.431775i \(0.142112\pi\)
\(788\) −1.71049e7 2.35428e7i −0.0349576 0.0481150i
\(789\) 9.67611e7 + 5.98067e8i 0.197002 + 1.21764i
\(790\) 1.51031e8 + 4.64824e8i 0.306326 + 0.942774i
\(791\) 6.26673e8i 1.26623i
\(792\) 1.16507e8 + 2.49985e8i 0.234518 + 0.503197i
\(793\) −7.17455e8 −1.43872
\(794\) 6.78771e8 2.20546e8i 1.35601 0.440593i
\(795\) −1.26056e8 + 2.03946e7i −0.250879 + 0.0405896i
\(796\) 6.07257e7 4.41198e7i 0.120402 0.0874772i
\(797\) −5.18466e8 1.68460e8i −1.02411 0.332752i −0.251649 0.967819i \(-0.580973\pi\)
−0.772458 + 0.635066i \(0.780973\pi\)
\(798\) 2.75384e8 1.41469e8i 0.541913 0.278389i
\(799\) −3.19873e8 + 2.32402e8i −0.627101 + 0.455616i
\(800\) −6.42353e8 + 8.84123e8i −1.25460 + 1.72680i
\(801\) −3.48260e7 1.04810e8i −0.0677652 0.203942i
\(802\) 7.12914e8 1.38202
\(803\) −7.04243e7 + 3.49508e8i −0.136012 + 0.675011i
\(804\) 9.89729e6 9.96323e6i 0.0190436 0.0191704i
\(805\) 1.97112e8 + 6.06649e8i 0.377855 + 1.16292i
\(806\) 5.01522e8 6.90286e8i 0.957822 1.31833i
\(807\) −5.56786e8 8.62922e7i −1.05942 0.164192i
\(808\) 9.68131e7 2.97960e8i 0.183527 0.564838i
\(809\) −5.29990e8 1.72204e8i −1.00097 0.325236i −0.237719 0.971334i \(-0.576400\pi\)
−0.763254 + 0.646098i \(0.776400\pi\)
\(810\) 9.39976e8 7.02192e8i 1.76873 1.32130i
\(811\) −4.96630e8 3.60823e8i −0.931044 0.676443i 0.0152041 0.999884i \(-0.495160\pi\)
−0.946248 + 0.323441i \(0.895160\pi\)
\(812\) −3.80714e8 + 1.23701e8i −0.711100 + 0.231050i
\(813\) −5.00008e8 + 5.03339e8i −0.930476 + 0.936675i
\(814\) 1.88325e7 + 1.62573e8i 0.0349169 + 0.301422i
\(815\) 4.09942e8i 0.757267i
\(816\) −2.54549e8 + 5.03709e8i −0.468491 + 0.927062i
\(817\) 1.26912e8 + 9.22066e7i 0.232721 + 0.169081i
\(818\) −7.66658e8 1.05521e9i −1.40069 1.92788i
\(819\) 5.02576e8 + 1.59615e8i 0.914851 + 0.290551i
\(820\) −2.13936e7 + 6.58427e7i −0.0388009 + 0.119417i
\(821\) 4.40900e8 + 6.06847e8i 0.796729 + 1.09660i 0.993237 + 0.116101i \(0.0370397\pi\)
−0.196508 + 0.980502i \(0.562960\pi\)
\(822\) 3.83011e8 6.19671e7i 0.689597 0.111570i
\(823\) −2.29493e8 7.06307e8i −0.411690 1.26705i −0.915178 0.403049i \(-0.867950\pi\)
0.503489 0.864002i \(-0.332050\pi\)
\(824\) 1.46289e8i 0.261476i
\(825\) −1.15357e9 + 3.26383e8i −2.05439 + 0.581253i
\(826\) −1.22829e9 −2.17951
\(827\) −8.01263e8 + 2.60346e8i −1.41664 + 0.460293i −0.914532 0.404514i \(-0.867441\pi\)
−0.502105 + 0.864807i \(0.667441\pi\)
\(828\) 1.69006e8 + 1.21084e8i 0.297722 + 0.213302i
\(829\) −7.51251e8 + 5.45815e8i −1.31862 + 0.958037i −0.318676 + 0.947864i \(0.603238\pi\)
−0.999948 + 0.0101733i \(0.996762\pi\)
\(830\) 3.15106e8 + 1.02384e8i 0.551089 + 0.179060i
\(831\) −1.07534e8 2.09327e8i −0.187389 0.364773i
\(832\) 187934. 136542.i 0.000326313 0.000237081i
\(833\) −2.66744e7 + 3.67142e7i −0.0461487 + 0.0635183i
\(834\) 3.63944e8 7.20181e8i 0.627388 1.24149i
\(835\) 1.34866e8 0.231656
\(836\) −1.11431e8 + 1.02494e8i −0.190716 + 0.175419i
\(837\) 5.96376e8 + 5.84612e8i 1.01705 + 0.996992i
\(838\) 1.69755e8 + 5.22451e8i 0.288462 + 0.887796i
\(839\) 3.59699e7 4.95083e7i 0.0609050 0.0838286i −0.777478 0.628910i \(-0.783501\pi\)
0.838383 + 0.545082i \(0.183501\pi\)
\(840\) 9.33400e7 6.02261e8i 0.157482 1.01612i
\(841\) −1.21316e8 + 3.73371e8i −0.203952 + 0.627701i
\(842\) −1.16735e8 3.79295e7i −0.195553 0.0635391i
\(843\) 1.56687e8 + 2.42838e7i 0.261547 + 0.0405354i
\(844\) −1.82506e8 1.32598e8i −0.303563 0.220552i
\(845\) 1.60522e8 5.21566e7i 0.266050 0.0864449i
\(846\) −4.66525e6 7.02562e8i −0.00770484 1.16031i
\(847\) −3.29424e8 5.43613e8i −0.542132 0.894622i
\(848\) 1.09146e8i 0.178987i
\(849\) −4.38840e8 2.21768e8i −0.717105 0.362389i
\(850\) −1.10174e9 8.00464e8i −1.79401 1.30342i
\(851\) −5.81979e7 8.01025e7i −0.0944318 0.129974i
\(852\) −2.97725e8 + 1.52946e8i −0.481390 + 0.247297i
\(853\) 2.12931e8 6.55333e8i 0.343077 1.05588i −0.619529 0.784974i \(-0.712676\pi\)
0.962605 0.270907i \(-0.0873237\pi\)
\(854\) 7.48689e8 + 1.03048e9i 1.20207 + 1.65450i
\(855\) −4.20196e8 3.01048e8i −0.672285 0.481656i
\(856\) −1.34208e7 4.13049e7i −0.0213972 0.0658538i
\(857\) 8.27098e8i 1.31406i 0.753865 + 0.657029i \(0.228187\pi\)
−0.753865 + 0.657029i \(0.771813\pi\)
\(858\) −7.22157e8 2.77684e7i −1.14333 0.0439631i
\(859\) −1.63485e8 −0.257927 −0.128964 0.991649i \(-0.541165\pi\)
−0.128964 + 0.991649i \(0.541165\pi\)
\(860\) −3.65945e8 + 1.18903e8i −0.575334 + 0.186937i
\(861\) −1.36313e7 8.42532e7i −0.0213564 0.132001i
\(862\) −6.43450e8 + 4.67494e8i −1.00460 + 0.729884i
\(863\) 6.91705e7 + 2.24749e7i 0.107619 + 0.0349675i 0.362331 0.932049i \(-0.381981\pi\)
−0.254713 + 0.967017i \(0.581981\pi\)
\(864\) −2.98439e8 5.71573e8i −0.462716 0.886198i
\(865\) 6.39029e8 4.64281e8i 0.987352 0.717353i
\(866\) 9.15803e7 1.26049e8i 0.141009 0.194083i
\(867\) 1.78081e8 + 8.99934e7i 0.273250 + 0.138087i
\(868\) −5.40511e8 −0.826505
\(869\) 2.56723e8 + 1.44610e8i 0.391206 + 0.220364i
\(870\) 1.32889e9 + 1.32009e9i 2.01804 + 2.00469i
\(871\) −9.12629e6 2.80878e7i −0.0138115 0.0425073i
\(872\) 1.80138e8 2.47938e8i 0.271678 0.373933i
\(873\) 1.16849e8 + 1.58603e8i 0.175623 + 0.238379i
\(874\) 7.93244e7 2.44135e8i 0.118815 0.365676i
\(875\) 1.33942e9 + 4.35206e8i 1.99937 + 0.649636i
\(876\) 3.93283e7 2.53759e8i 0.0585050 0.377493i
\(877\) −1.71659e8 1.24717e8i −0.254488 0.184896i 0.453226 0.891396i \(-0.350273\pi\)
−0.707713 + 0.706500i \(0.750273\pi\)
\(878\) −1.14639e9 + 3.72485e8i −1.69375 + 0.550333i
\(879\) −5.16663e8 5.13244e8i −0.760748 0.755713i
\(880\) 1.73142e8 + 1.49466e9i 0.254070 + 2.19327i
\(881\) 1.33809e9i 1.95685i −0.206612 0.978423i \(-0.566244\pi\)
0.206612 0.978423i \(-0.433756\pi\)
\(882\) −2.54278e7 7.65259e7i −0.0370598 0.111533i
\(883\) 8.08417e8 + 5.87349e8i 1.17423 + 0.853128i 0.991509 0.130036i \(-0.0415094\pi\)
0.182721 + 0.983165i \(0.441509\pi\)
\(884\) −1.72176e8 2.36980e8i −0.249239 0.343049i
\(885\) 9.37094e8 + 1.82415e9i 1.35193 + 2.63167i
\(886\) −2.93382e8 + 9.02936e8i −0.421824 + 1.29824i
\(887\) 1.41796e8 + 1.95165e8i 0.203186 + 0.279661i 0.898434 0.439109i \(-0.144706\pi\)
−0.695248 + 0.718769i \(0.744706\pi\)
\(888\) 1.51090e7 + 9.33867e7i 0.0215773 + 0.133366i
\(889\) −2.49411e8 7.67607e8i −0.354985 1.09253i
\(890\) 3.34481e8i 0.474462i
\(891\) 1.30498e8 6.95206e8i 0.184489 0.982835i
\(892\) 2.19162e8 0.308796
\(893\) −2.94378e8 + 9.56493e7i −0.413382 + 0.134316i
\(894\) −7.86771e8 + 1.27291e8i −1.10112 + 0.178150i
\(895\) 1.77412e9 1.28898e9i 2.47466 1.79794i
\(896\) −7.15828e8 2.32587e8i −0.995142 0.323341i
\(897\) 3.88903e8 1.99785e8i 0.538845 0.276813i
\(898\) 1.04474e9 7.59050e8i 1.44271 1.04819i
\(899\) −7.83660e8 + 1.07862e9i −1.07857 + 1.48453i
\(900\) 8.19409e8 2.72271e8i 1.12402 0.373485i
\(901\) −8.74496e7 −0.119559
\(902\) 4.87074e7 + 1.06348e8i 0.0663705 + 0.144914i
\(903\) 3.34306e8 3.36533e8i 0.454026 0.457051i
\(904\) 1.53412e8 + 4.72154e8i 0.207661 + 0.639114i
\(905\) −1.87607e8 + 2.58220e8i −0.253107 + 0.348372i
\(906\) −8.69688e8 1.34787e8i −1.16944 0.181243i
\(907\) −7.84265e7 + 2.41372e8i −0.105109 + 0.323493i −0.989756 0.142769i \(-0.954399\pi\)
0.884647 + 0.466262i \(0.154399\pi\)
\(908\) −1.36300e8 4.42864e7i −0.182069 0.0591579i
\(909\) −6.46899e8 + 4.76595e8i −0.861281 + 0.634538i
\(910\) 1.29197e9 + 9.38672e8i 1.71447 + 1.24563i
\(911\) −1.05689e9 + 3.43403e8i −1.39789 + 0.454202i −0.908508 0.417868i \(-0.862777\pi\)
−0.489381 + 0.872070i \(0.662777\pi\)
\(912\) −3.11375e8 + 3.13450e8i −0.410487 + 0.413222i
\(913\) 1.81604e8 8.31742e7i 0.238623 0.109289i
\(914\) 5.92606e8i 0.776118i
\(915\) 9.59194e8 1.89808e9i 1.25211 2.47771i
\(916\) 5.12425e8 + 3.72298e8i 0.666720 + 0.484401i
\(917\) 4.46015e6 + 6.13887e6i 0.00578418 + 0.00796124i
\(918\) 7.12262e8 3.71898e8i 0.920687 0.480724i
\(919\) −2.69106e8 + 8.28223e8i −0.346718 + 1.06709i 0.613939 + 0.789353i \(0.289584\pi\)
−0.960657 + 0.277736i \(0.910416\pi\)
\(920\) −2.97020e8 4.08813e8i −0.381437 0.525003i
\(921\) 9.49340e8 1.53593e8i 1.21519 0.196605i
\(922\) −5.47796e8 1.68594e9i −0.698918 2.15105i
\(923\) 7.03893e8i 0.895162i
\(924\) 2.54664e8 + 3.80443e8i 0.322814 + 0.482251i
\(925\) −4.11212e8 −0.519566
\(926\) 1.35459e9 4.40132e8i 1.70598 0.554307i
\(927\) −2.18510e8 + 3.04992e8i −0.274304 + 0.382868i
\(928\) 8.32793e8 6.05060e8i 1.04206 0.757102i
\(929\) −9.30547e8 3.02353e8i −1.16062 0.377109i −0.335488 0.942045i \(-0.608901\pi\)
−0.825135 + 0.564935i \(0.808901\pi\)
\(930\) 1.15569e9 + 2.24968e9i 1.43679 + 2.79687i
\(931\) −2.87417e7 + 2.08821e7i −0.0356175 + 0.0258776i
\(932\) 4.48598e8 6.17442e8i 0.554127 0.762690i
\(933\) 8.12529e7 1.60785e8i 0.100045 0.197971i
\(934\) 1.39490e9 1.71199
\(935\) −1.19754e9 + 1.38724e8i −1.46506 + 0.169713i
\(936\) −4.17731e8 + 2.77387e6i −0.509411 + 0.00338266i
\(937\) 1.06900e8 + 3.29004e8i 0.129945 + 0.399929i 0.994770 0.102145i \(-0.0325705\pi\)
−0.864825 + 0.502074i \(0.832571\pi\)
\(938\) −3.08190e7 + 4.24187e7i −0.0373431 + 0.0513984i
\(939\) 2.14292e8 1.38268e9i 0.258827 1.67004i
\(940\) 2.34611e8 7.22057e8i 0.282465 0.869337i
\(941\) 5.74651e8 + 1.86715e8i 0.689660 + 0.224084i 0.632820 0.774299i \(-0.281897\pi\)
0.0568405 + 0.998383i \(0.481897\pi\)
\(942\) −1.94959e9 3.02152e8i −2.33233 0.361471i
\(943\) −5.72511e7 4.15954e7i −0.0682730 0.0496032i
\(944\) 1.66708e9 5.41667e8i 1.98171 0.643897i
\(945\) −1.09419e9 + 1.11620e9i −1.29657 + 1.32266i
\(946\) −3.19067e8 + 5.66430e8i −0.376884 + 0.669072i
\(947\) 4.87332e8i 0.573819i −0.957958 0.286909i \(-0.907372\pi\)
0.957958 0.286909i \(-0.0926278\pi\)
\(948\) −1.89407e8 9.57168e7i −0.222316 0.112347i
\(949\) −4.36885e8 3.17416e8i −0.511174 0.371390i
\(950\) −6.26644e8 8.62501e8i −0.730886 1.00598i
\(951\) −4.11449e8 + 2.11367e8i −0.478382 + 0.245752i
\(952\) 1.28974e8 3.96942e8i 0.149483 0.460061i
\(953\) −7.14274e8 9.83114e8i −0.825251 1.13586i −0.988788 0.149324i \(-0.952290\pi\)
0.163537 0.986537i \(-0.447710\pi\)
\(954\) 9.05009e7 1.26319e8i 0.104234 0.145487i
\(955\) 6.50715e8 + 2.00270e9i 0.747104 + 2.29935i
\(956\) 9.17071e8i 1.04961i
\(957\) 1.12842e9 + 4.33899e7i 1.28746 + 0.0495054i
\(958\) −9.99130e8 −1.13639
\(959\) −4.91581e8 + 1.59724e8i −0.557365 + 0.181099i
\(960\) 109975. + 679740.i 0.000124303 + 0.000768297i
\(961\) −7.38389e8 + 5.36471e8i −0.831984 + 0.604472i
\(962\) −2.35754e8 7.66011e7i −0.264810 0.0860419i
\(963\) −3.37162e7 + 1.06161e8i −0.0377537 + 0.118874i
\(964\) −6.08738e8 + 4.42274e8i −0.679515 + 0.493697i
\(965\) −2.34916e8 + 3.23335e8i −0.261416 + 0.359808i
\(966\) −6.92786e8 3.50100e8i −0.768542 0.388383i
\(967\) −4.28573e8 −0.473964 −0.236982 0.971514i \(-0.576158\pi\)
−0.236982 + 0.971514i \(0.576158\pi\)
\(968\) 3.81277e8 + 3.28930e8i 0.420353 + 0.362641i
\(969\) −2.51141e8 2.49479e8i −0.276024 0.274197i
\(970\) 1.84362e8 + 5.67408e8i 0.202002 + 0.621700i
\(971\) 1.27910e8 1.76053e8i 0.139716 0.192303i −0.733425 0.679771i \(-0.762079\pi\)
0.873141 + 0.487468i \(0.162079\pi\)
\(972\) −7.13331e7 + 5.04440e8i −0.0776770 + 0.549302i
\(973\) −3.32184e8 + 1.02236e9i −0.360612 + 1.10985i
\(974\) 5.31149e8 + 1.72581e8i 0.574830 + 0.186773i
\(975\) 2.78103e8 1.79441e9i 0.300048 1.93601i
\(976\) −1.47059e9 1.06844e9i −1.58176 1.14922i
\(977\) 9.60496e7 3.12084e7i 0.102994 0.0334648i −0.257067 0.966394i \(-0.582756\pi\)
0.360061 + 0.932929i \(0.382756\pi\)
\(978\) 3.53916e8 + 3.51573e8i 0.378341 + 0.375837i
\(979\) −1.36511e8 1.48415e8i −0.145486 0.158172i
\(980\) 8.71407e7i 0.0925855i
\(981\) −7.45902e8 + 2.47846e8i −0.790087 + 0.262528i
\(982\) 1.65946e8 + 1.20567e8i 0.175240 + 0.127319i
\(983\) −5.57610e8 7.67485e8i −0.587043 0.807996i 0.407402 0.913249i \(-0.366435\pi\)
−0.994445 + 0.105253i \(0.966435\pi\)
\(984\) 3.08958e7 + 6.01419e7i 0.0324275 + 0.0631236i
\(985\) 5.60563e7 1.72523e8i 0.0586564 0.180526i
\(986\) 7.53991e8 + 1.03778e9i 0.786567 + 1.08262i
\(987\) 1.49486e8 + 9.23955e8i 0.155471 + 0.960946i
\(988\) −7.08624e7 2.18092e8i −0.0734760 0.226136i
\(989\) 3.93310e8i 0.406580i
\(990\) 1.03894e9 1.87339e9i 1.07075 1.93074i
\(991\) 1.18110e9 1.21358 0.606788 0.794863i \(-0.292458\pi\)
0.606788 + 0.794863i \(0.292458\pi\)
\(992\) 1.32190e9 4.29511e8i 1.35414 0.439986i
\(993\) 9.74141e8 1.57606e8i 0.994888 0.160963i
\(994\) 1.01100e9 7.34537e8i 1.02942 0.747919i
\(995\) 4.45002e8 + 1.44590e8i 0.451744 + 0.146781i
\(996\) −1.27966e8 + 6.57379e7i −0.129514 + 0.0665331i
\(997\) 1.60802e8 1.16829e8i 0.162258 0.117887i −0.503694 0.863882i \(-0.668026\pi\)
0.665951 + 0.745995i \(0.268026\pi\)
\(998\) −9.25094e8 + 1.27328e9i −0.930667 + 1.28095i
\(999\) 1.07990e8 2.17266e8i 0.108315 0.217919i
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 33.7.h.a.5.17 yes 88
3.2 odd 2 inner 33.7.h.a.5.6 88
11.9 even 5 inner 33.7.h.a.20.6 yes 88
33.20 odd 10 inner 33.7.h.a.20.17 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.7.h.a.5.6 88 3.2 odd 2 inner
33.7.h.a.5.17 yes 88 1.1 even 1 trivial
33.7.h.a.20.6 yes 88 11.9 even 5 inner
33.7.h.a.20.17 yes 88 33.20 odd 10 inner