Properties

Label 43.9.f.a.22.11
Level $43$
Weight $9$
Character 43.22
Analytic conductor $17.517$
Analytic rank $0$
Dimension $174$
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] = [43,9,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), 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: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(174\)
Relative dimension: \(29\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 22.11
Character \(\chi\) \(=\) 43.22
Dual form 43.9.f.a.2.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.04009 + 10.4659i) q^{2} +(-24.0340 - 49.9071i) q^{3} +(75.4818 + 94.6511i) q^{4} +(11.0383 - 2.51943i) q^{5} +643.453 q^{6} +674.726i q^{7} +(-4270.24 + 974.653i) q^{8} +(2177.63 - 2730.67i) q^{9} +O(q^{10})\) \(q+(-5.04009 + 10.4659i) q^{2} +(-24.0340 - 49.9071i) q^{3} +(75.4818 + 94.6511i) q^{4} +(11.0383 - 2.51943i) q^{5} +643.453 q^{6} +674.726i q^{7} +(-4270.24 + 974.653i) q^{8} +(2177.63 - 2730.67i) q^{9} +(-29.2663 + 128.224i) q^{10} +(11361.9 - 14247.3i) q^{11} +(2909.63 - 6041.92i) q^{12} +(7866.45 + 34465.2i) q^{13} +(-7061.58 - 3400.68i) q^{14} +(-391.032 - 490.339i) q^{15} +(4425.37 - 19388.8i) q^{16} +(-28127.5 + 123235. i) q^{17} +(17603.3 + 36553.6i) q^{18} +(39450.9 - 31461.1i) q^{19} +(1071.66 + 854.621i) q^{20} +(33673.6 - 16216.3i) q^{21} +(91845.6 + 190719. i) q^{22} +(-113128. + 141859. i) q^{23} +(151273. + 189690. i) q^{24} +(-351825. + 169430. i) q^{25} +(-400355. - 91378.5i) q^{26} +(-542936. - 123922. i) q^{27} +(-63863.6 + 50929.5i) q^{28} +(-453185. + 941048. i) q^{29} +(7102.66 - 1621.14i) q^{30} +(1.19527e6 + 575614. i) q^{31} +(-696046. - 555078. i) q^{32} +(-984113. - 224617. i) q^{33} +(-1.14799e6 - 915493. i) q^{34} +(1699.92 + 7447.85i) q^{35} +422832. q^{36} +2.38635e6i q^{37} +(130431. + 571454. i) q^{38} +(1.53099e6 - 1.22093e6i) q^{39} +(-44680.7 + 21517.1i) q^{40} +(3.16692e6 + 1.52511e6i) q^{41} +434155. i q^{42} +(-326137. + 3.40321e6i) q^{43} +2.20614e6 q^{44} +(17157.7 - 35628.4i) q^{45} +(-914493. - 1.89896e6i) q^{46} +(-3.57668e6 - 4.48501e6i) q^{47} +(-1.07400e6 + 245133. i) q^{48} +5.30955e6 q^{49} -4.53610e6i q^{50} +(6.82630e6 - 1.55806e6i) q^{51} +(-2.66840e6 + 3.34606e6i) q^{52} +(1.78170e6 - 7.80614e6i) q^{53} +(4.03339e6 - 5.05771e6i) q^{54} +(89521.0 - 185892. i) q^{55} +(-657624. - 2.88124e6i) q^{56} +(-2.51829e6 - 1.21275e6i) q^{57} +(-7.56478e6 - 9.48593e6i) q^{58} +(-1.78551e6 + 7.82283e6i) q^{59} +(16895.3 - 74023.3i) q^{60} +(-8.28638e6 - 1.72069e7i) q^{61} +(-1.20486e7 + 9.60842e6i) q^{62} +(1.84245e6 + 1.46931e6i) q^{63} +(1.39045e7 - 6.69606e6i) q^{64} +(173665. + 360620. i) q^{65} +(7.31083e6 - 9.16749e6i) q^{66} +(6.68407e6 + 8.38155e6i) q^{67} +(-1.37874e7 + 6.63967e6i) q^{68} +(9.79866e6 + 2.23648e6i) q^{69} +(-86515.9 - 19746.7i) q^{70} +(-724001. + 577372. i) q^{71} +(-6.63756e6 + 1.37830e7i) q^{72} +(3.06823e7 - 7.00305e6i) q^{73} +(-2.49752e7 - 1.20274e7i) q^{74} +(1.69115e7 + 1.34865e7i) q^{75} +(5.95565e6 + 1.35934e6i) q^{76} +(9.61304e6 + 7.66614e6i) q^{77} +(5.06170e6 + 2.21767e7i) q^{78} -6.41156e7 q^{79} -225170. i q^{80} +(1.76521e6 + 7.73389e6i) q^{81} +(-3.19231e7 + 2.54578e7i) q^{82} +(6.76139e7 - 3.25612e7i) q^{83} +(4.07664e6 + 1.96320e6i) q^{84} +1.43117e6i q^{85} +(-3.39737e7 - 2.05658e7i) q^{86} +5.78568e7 q^{87} +(-3.46316e7 + 7.19133e7i) q^{88} +(7.71418e6 + 1.60187e7i) q^{89} +(286405. + 359141. i) q^{90} +(-2.32545e7 + 5.30770e6i) q^{91} -2.19662e7 q^{92} -7.34869e7i q^{93} +(6.49662e7 - 1.48281e7i) q^{94} +(356209. - 446672. i) q^{95} +(-1.09736e7 + 4.80783e7i) q^{96} +(-9.66526e7 + 1.21198e8i) q^{97} +(-2.67606e7 + 5.55689e7i) q^{98} +(-1.41627e7 - 6.20509e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9} - 24989 q^{10} - 14864 q^{11} - 1799 q^{12} + 133078 q^{13} - 243363 q^{14} - 7457 q^{15} - 558511 q^{16} + 55162 q^{17} - 45934 q^{18} + 619745 q^{19} + 1207493 q^{20} + 307272 q^{21} + 432761 q^{22} + 473962 q^{23} + 179363 q^{24} + 2991984 q^{25} + 112889 q^{26} - 7 q^{27} + 458745 q^{28} + 1369823 q^{29} + 4208148 q^{30} + 608540 q^{31} - 15074437 q^{32} - 10988257 q^{33} + 1542905 q^{34} - 4078926 q^{35} + 53343072 q^{36} - 15207265 q^{38} - 16862587 q^{39} - 537581 q^{40} - 852935 q^{41} + 2982351 q^{43} - 10366284 q^{44} + 52423812 q^{45} + 51003036 q^{46} + 5828578 q^{47} - 32078599 q^{48} - 145853506 q^{49} - 30015937 q^{51} + 71975797 q^{52} - 7800770 q^{53} + 43151245 q^{54} - 53485957 q^{55} + 25379079 q^{56} - 21662515 q^{57} - 191329035 q^{58} + 69716890 q^{59} - 106388277 q^{60} - 49131775 q^{61} + 67656953 q^{62} + 355075 q^{63} + 227160853 q^{64} - 87064999 q^{65} + 146686057 q^{66} - 31581292 q^{67} + 200919430 q^{68} - 30179079 q^{69} + 86518670 q^{70} - 60255454 q^{71} - 438784346 q^{72} - 50897868 q^{73} + 5087868 q^{74} + 206284834 q^{75} + 461519674 q^{76} + 256281375 q^{77} - 182130842 q^{78} - 236682026 q^{79} - 488977844 q^{81} - 226181851 q^{82} - 429023996 q^{83} - 513228846 q^{84} + 336855461 q^{86} + 255103986 q^{87} + 977894029 q^{88} - 258201748 q^{89} + 1399550866 q^{90} + 246776320 q^{91} + 363749100 q^{92} - 637129955 q^{94} + 60088655 q^{95} - 1169196874 q^{96} + 218930393 q^{97} - 330217825 q^{98} + 459482633 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.04009 + 10.4659i −0.315006 + 0.654116i −0.997013 0.0772290i \(-0.975393\pi\)
0.682008 + 0.731345i \(0.261107\pi\)
\(3\) −24.0340 49.9071i −0.296716 0.616136i 0.698306 0.715800i \(-0.253938\pi\)
−0.995021 + 0.0996633i \(0.968223\pi\)
\(4\) 75.4818 + 94.6511i 0.294851 + 0.369731i
\(5\) 11.0383 2.51943i 0.0176613 0.00403109i −0.213681 0.976903i \(-0.568545\pi\)
0.231342 + 0.972872i \(0.425688\pi\)
\(6\) 643.453 0.496492
\(7\) 674.726i 0.281019i 0.990079 + 0.140509i \(0.0448740\pi\)
−0.990079 + 0.140509i \(0.955126\pi\)
\(8\) −4270.24 + 974.653i −1.04254 + 0.237952i
\(9\) 2177.63 2730.67i 0.331906 0.416197i
\(10\) −29.2663 + 128.224i −0.00292663 + 0.0128224i
\(11\) 11361.9 14247.3i 0.776031 0.973112i −0.223968 0.974596i \(-0.571901\pi\)
0.999999 + 0.00148488i \(0.000472653\pi\)
\(12\) 2909.63 6041.92i 0.140318 0.291373i
\(13\) 7866.45 + 34465.2i 0.275426 + 1.20672i 0.903507 + 0.428574i \(0.140984\pi\)
−0.628080 + 0.778148i \(0.716159\pi\)
\(14\) −7061.58 3400.68i −0.183819 0.0885225i
\(15\) −391.032 490.339i −0.00772410 0.00968571i
\(16\) 4425.37 19388.8i 0.0675258 0.295850i
\(17\) −28127.5 + 123235.i −0.336772 + 1.47549i 0.468963 + 0.883218i \(0.344628\pi\)
−0.805735 + 0.592276i \(0.798230\pi\)
\(18\) 17603.3 + 36553.6i 0.167689 + 0.348209i
\(19\) 39450.9 31461.1i 0.302721 0.241412i −0.460333 0.887746i \(-0.652270\pi\)
0.763055 + 0.646334i \(0.223699\pi\)
\(20\) 1071.66 + 854.621i 0.00669788 + 0.00534138i
\(21\) 33673.6 16216.3i 0.173146 0.0833826i
\(22\) 91845.6 + 190719.i 0.392074 + 0.814150i
\(23\) −113128. + 141859.i −0.404259 + 0.506925i −0.941736 0.336353i \(-0.890806\pi\)
0.537476 + 0.843279i \(0.319378\pi\)
\(24\) 151273. + 189690.i 0.455949 + 0.571741i
\(25\) −351825. + 169430.i −0.900673 + 0.433741i
\(26\) −400355. 91378.5i −0.876097 0.199963i
\(27\) −542936. 123922.i −1.02163 0.233180i
\(28\) −63863.6 + 50929.5i −0.103901 + 0.0828585i
\(29\) −453185. + 941048.i −0.640742 + 1.33051i 0.287229 + 0.957862i \(0.407266\pi\)
−0.927971 + 0.372653i \(0.878448\pi\)
\(30\) 7102.66 1621.14i 0.00876871 0.00200140i
\(31\) 1.19527e6 + 575614.i 1.29426 + 0.623282i 0.949015 0.315231i \(-0.102082\pi\)
0.345243 + 0.938513i \(0.387796\pi\)
\(32\) −696046. 555078.i −0.663801 0.529364i
\(33\) −984113. 224617.i −0.829830 0.189403i
\(34\) −1.14799e6 915493.i −0.859059 0.685077i
\(35\) 1699.92 + 7447.85i 0.00113281 + 0.00496317i
\(36\) 422832. 0.251743
\(37\) 2.38635e6i 1.27329i 0.771156 + 0.636646i \(0.219679\pi\)
−0.771156 + 0.636646i \(0.780321\pi\)
\(38\) 130431. + 571454.i 0.0625526 + 0.274061i
\(39\) 1.53099e6 1.22093e6i 0.661782 0.527754i
\(40\) −44680.7 + 21517.1i −0.0174534 + 0.00840512i
\(41\) 3.16692e6 + 1.52511e6i 1.12073 + 0.539715i 0.900118 0.435646i \(-0.143480\pi\)
0.220613 + 0.975361i \(0.429194\pi\)
\(42\) 434155.i 0.139523i
\(43\) −326137. + 3.40321e6i −0.0953950 + 0.995439i
\(44\) 2.20614e6 0.588603
\(45\) 17157.7 35628.4i 0.00418418 0.00868854i
\(46\) −914493. 1.89896e6i −0.204244 0.424117i
\(47\) −3.57668e6 4.48501e6i −0.732973 0.919119i 0.266021 0.963967i \(-0.414291\pi\)
−0.998994 + 0.0448481i \(0.985720\pi\)
\(48\) −1.07400e6 + 245133.i −0.202320 + 0.0461782i
\(49\) 5.30955e6 0.921029
\(50\) 4.53610e6i 0.725776i
\(51\) 6.82630e6 1.55806e6i 1.00903 0.230305i
\(52\) −2.66840e6 + 3.34606e6i −0.364953 + 0.457636i
\(53\) 1.78170e6 7.80614e6i 0.225804 0.989311i −0.727217 0.686407i \(-0.759187\pi\)
0.953021 0.302904i \(-0.0979560\pi\)
\(54\) 4.03339e6 5.05771e6i 0.474346 0.594811i
\(55\) 89521.0 185892.i 0.00978305 0.0203147i
\(56\) −657624. 2.88124e6i −0.0668691 0.292973i
\(57\) −2.51829e6 1.21275e6i −0.238565 0.114887i
\(58\) −7.56478e6 9.48593e6i −0.668474 0.838239i
\(59\) −1.78551e6 + 7.82283e6i −0.147351 + 0.645589i 0.846264 + 0.532765i \(0.178847\pi\)
−0.993615 + 0.112824i \(0.964010\pi\)
\(60\) 16895.3 74023.3i 0.00130365 0.00571168i
\(61\) −8.28638e6 1.72069e7i −0.598475 1.24275i −0.951649 0.307188i \(-0.900612\pi\)
0.353174 0.935558i \(-0.385102\pi\)
\(62\) −1.20486e7 + 9.60842e6i −0.815397 + 0.650258i
\(63\) 1.84245e6 + 1.46931e6i 0.116959 + 0.0932717i
\(64\) 1.39045e7 6.69606e6i 0.828773 0.399116i
\(65\) 173665. + 360620.i 0.00972880 + 0.0202021i
\(66\) 7.31083e6 9.16749e6i 0.385293 0.483142i
\(67\) 6.68407e6 + 8.38155e6i 0.331697 + 0.415935i 0.919513 0.393060i \(-0.128583\pi\)
−0.587816 + 0.808995i \(0.700012\pi\)
\(68\) −1.37874e7 + 6.63967e6i −0.644833 + 0.310535i
\(69\) 9.79866e6 + 2.23648e6i 0.432285 + 0.0986663i
\(70\) −86515.9 19746.7i −0.00360333 0.000822436i
\(71\) −724001. + 577372.i −0.0284909 + 0.0227207i −0.637632 0.770341i \(-0.720086\pi\)
0.609141 + 0.793062i \(0.291514\pi\)
\(72\) −6.63756e6 + 1.37830e7i −0.246989 + 0.512879i
\(73\) 3.06823e7 7.00305e6i 1.08043 0.246601i 0.354979 0.934874i \(-0.384488\pi\)
0.725452 + 0.688273i \(0.241631\pi\)
\(74\) −2.49752e7 1.20274e7i −0.832881 0.401094i
\(75\) 1.69115e7 + 1.34865e7i 0.534488 + 0.426240i
\(76\) 5.95565e6 + 1.35934e6i 0.178515 + 0.0407449i
\(77\) 9.61304e6 + 7.66614e6i 0.273462 + 0.218079i
\(78\) 5.06170e6 + 2.21767e7i 0.136747 + 0.599128i
\(79\) −6.41156e7 −1.64610 −0.823049 0.567971i \(-0.807729\pi\)
−0.823049 + 0.567971i \(0.807729\pi\)
\(80\) 225170.i 0.00549731i
\(81\) 1.76521e6 + 7.73389e6i 0.0410069 + 0.179663i
\(82\) −3.19231e7 + 2.54578e7i −0.706073 + 0.563074i
\(83\) 6.76139e7 3.25612e7i 1.42470 0.686100i 0.446697 0.894685i \(-0.352600\pi\)
0.978004 + 0.208585i \(0.0668859\pi\)
\(84\) 4.07664e6 + 1.96320e6i 0.0818813 + 0.0394320i
\(85\) 1.43117e6i 0.0274168i
\(86\) −3.39737e7 2.05658e7i −0.621083 0.375968i
\(87\) 5.78568e7 1.00990
\(88\) −3.46316e7 + 7.19133e7i −0.577487 + 1.19916i
\(89\) 7.71418e6 + 1.60187e7i 0.122950 + 0.255309i 0.953355 0.301852i \(-0.0976049\pi\)
−0.830404 + 0.557161i \(0.811891\pi\)
\(90\) 286405. + 359141.i 0.00436527 + 0.00547388i
\(91\) −2.32545e7 + 5.30770e6i −0.339111 + 0.0774000i
\(92\) −2.19662e7 −0.306622
\(93\) 7.34869e7i 0.982377i
\(94\) 6.49662e7 1.48281e7i 0.832101 0.189922i
\(95\) 356209. 446672.i 0.00437331 0.00548396i
\(96\) −1.09736e7 + 4.80783e7i −0.129200 + 0.566063i
\(97\) −9.66526e7 + 1.21198e8i −1.09176 + 1.36902i −0.168115 + 0.985767i \(0.553768\pi\)
−0.923643 + 0.383254i \(0.874803\pi\)
\(98\) −2.67606e7 + 5.55689e7i −0.290129 + 0.602459i
\(99\) −1.41627e7 6.20509e7i −0.147437 0.645963i
\(100\) −4.25932e7 2.05118e7i −0.425932 0.205118i
\(101\) 3.67074e7 + 4.60296e7i 0.352751 + 0.442335i 0.926272 0.376855i \(-0.122995\pi\)
−0.573522 + 0.819190i \(0.694423\pi\)
\(102\) −1.80987e7 + 7.92958e7i −0.167204 + 0.732571i
\(103\) −2.78152e7 + 1.21866e8i −0.247134 + 1.08277i 0.687228 + 0.726442i \(0.258827\pi\)
−0.934362 + 0.356324i \(0.884030\pi\)
\(104\) −6.71832e7 1.39507e8i −0.574285 1.19251i
\(105\) 330845. 263840.i 0.00272187 0.00217062i
\(106\) 7.27180e7 + 5.79907e7i 0.575995 + 0.459340i
\(107\) 1.61315e8 7.76854e7i 1.23067 0.592658i 0.298404 0.954440i \(-0.403546\pi\)
0.932263 + 0.361782i \(0.117831\pi\)
\(108\) −2.92524e7 6.07433e7i −0.215014 0.446482i
\(109\) 2.90827e7 3.64686e7i 0.206029 0.258353i −0.668071 0.744097i \(-0.732880\pi\)
0.874101 + 0.485744i \(0.161451\pi\)
\(110\) 1.49433e6 + 1.87383e6i 0.0102065 + 0.0127985i
\(111\) 1.19096e8 5.73536e7i 0.784522 0.377806i
\(112\) 1.30821e7 + 2.98591e6i 0.0831394 + 0.0189760i
\(113\) −2.56644e8 5.85773e7i −1.57404 0.359265i −0.655692 0.755029i \(-0.727623\pi\)
−0.918353 + 0.395763i \(0.870480\pi\)
\(114\) 2.53848e7 2.02437e7i 0.150299 0.119859i
\(115\) −891347. + 1.85090e6i −0.00509631 + 0.0105826i
\(116\) −1.23278e8 + 2.81375e7i −0.680856 + 0.155401i
\(117\) 1.11243e8 + 5.35719e7i 0.593649 + 0.285886i
\(118\) −7.28735e7 5.81147e7i −0.375873 0.299749i
\(119\) −8.31496e7 1.89784e7i −0.414641 0.0946392i
\(120\) 2.14771e6 + 1.71274e6i 0.0103574 + 0.00825975i
\(121\) −2.61950e7 1.14768e8i −0.122202 0.535401i
\(122\) 2.21849e8 1.00142
\(123\) 1.94706e8i 0.850665i
\(124\) 3.57389e7 + 1.56582e8i 0.151166 + 0.662302i
\(125\) −6.91454e6 + 5.51416e6i −0.0283220 + 0.0225860i
\(126\) −2.46637e7 + 1.18774e7i −0.0978533 + 0.0471237i
\(127\) 7.34245e7 + 3.53594e7i 0.282245 + 0.135922i 0.569651 0.821887i \(-0.307079\pi\)
−0.287406 + 0.957809i \(0.592793\pi\)
\(128\) 4.86395e7i 0.181196i
\(129\) 1.77683e8 6.55161e7i 0.641632 0.236586i
\(130\) −4.64948e6 −0.0162791
\(131\) 1.97250e8 4.09593e8i 0.669779 1.39081i −0.237961 0.971275i \(-0.576479\pi\)
0.907739 0.419535i \(-0.137807\pi\)
\(132\) −5.30223e7 1.10102e8i −0.174648 0.362660i
\(133\) 2.12276e7 + 2.66186e7i 0.0678413 + 0.0850703i
\(134\) −1.21408e8 + 2.77107e7i −0.376556 + 0.0859465i
\(135\) −6.30532e6 −0.0189833
\(136\) 5.53656e8i 1.61839i
\(137\) 5.51852e8 1.25957e8i 1.56654 0.357552i 0.650774 0.759271i \(-0.274444\pi\)
0.915763 + 0.401720i \(0.131587\pi\)
\(138\) −7.27928e7 + 9.12793e7i −0.200712 + 0.251684i
\(139\) −1.83142e7 + 8.02399e7i −0.0490602 + 0.214947i −0.993516 0.113691i \(-0.963733\pi\)
0.944456 + 0.328638i \(0.106590\pi\)
\(140\) −576635. + 723077.i −0.00150103 + 0.00188223i
\(141\) −1.37872e8 + 2.86294e8i −0.348818 + 0.724329i
\(142\) −2.39366e6 1.04873e7i −0.00588720 0.0257935i
\(143\) 5.80414e8 + 2.79513e8i 1.38801 + 0.668433i
\(144\) −4.33076e7 5.43060e7i −0.100720 0.126298i
\(145\) −2.63150e6 + 1.15294e7i −0.00595295 + 0.0260816i
\(146\) −8.13489e7 + 3.56413e8i −0.179036 + 0.784408i
\(147\) −1.27609e8 2.64984e8i −0.273284 0.567479i
\(148\) −2.25871e8 + 1.80126e8i −0.470776 + 0.375431i
\(149\) −3.95385e8 3.15309e8i −0.802186 0.639722i 0.134097 0.990968i \(-0.457187\pi\)
−0.936283 + 0.351246i \(0.885758\pi\)
\(150\) −2.26383e8 + 1.09020e8i −0.447177 + 0.215349i
\(151\) 4.37758e7 + 9.09013e7i 0.0842027 + 0.174849i 0.938819 0.344412i \(-0.111922\pi\)
−0.854616 + 0.519261i \(0.826207\pi\)
\(152\) −1.37801e8 + 1.72797e8i −0.258154 + 0.323715i
\(153\) 2.75261e8 + 3.45167e8i 0.502319 + 0.629888i
\(154\) −1.28683e8 + 6.19706e7i −0.228791 + 0.110180i
\(155\) 1.46441e7 + 3.34241e6i 0.0253708 + 0.00579073i
\(156\) 2.31124e8 + 5.27526e7i 0.390254 + 0.0890729i
\(157\) −4.36843e8 + 3.48371e8i −0.718997 + 0.573381i −0.913166 0.407587i \(-0.866370\pi\)
0.194169 + 0.980968i \(0.437799\pi\)
\(158\) 3.23148e8 6.71025e8i 0.518530 1.07674i
\(159\) −4.32403e8 + 9.86931e7i −0.676550 + 0.154418i
\(160\) −9.08167e6 4.37350e6i −0.0138575 0.00667344i
\(161\) −9.57156e7 7.63306e7i −0.142455 0.113604i
\(162\) −8.98387e7 2.05051e7i −0.130438 0.0297716i
\(163\) 7.60352e8 + 6.06361e8i 1.07712 + 0.858975i 0.990534 0.137269i \(-0.0438326\pi\)
0.0865868 + 0.996244i \(0.472404\pi\)
\(164\) 9.46914e7 + 4.14870e8i 0.130899 + 0.573504i
\(165\) −1.14289e7 −0.0154194
\(166\) 8.71749e8i 1.14805i
\(167\) −2.21563e8 9.70732e8i −0.284860 1.24805i −0.891479 0.453061i \(-0.850332\pi\)
0.606619 0.794993i \(-0.292525\pi\)
\(168\) −1.27989e8 + 1.02068e8i −0.160670 + 0.128130i
\(169\) −3.91020e8 + 1.88305e8i −0.479349 + 0.230842i
\(170\) −1.49784e7 7.21324e6i −0.0179337 0.00863643i
\(171\) 1.76238e8i 0.206118i
\(172\) −3.46735e8 + 2.26011e8i −0.396172 + 0.258235i
\(173\) −1.41396e9 −1.57853 −0.789264 0.614055i \(-0.789537\pi\)
−0.789264 + 0.614055i \(0.789537\pi\)
\(174\) −2.91603e8 + 6.05521e8i −0.318123 + 0.660590i
\(175\) −1.14319e8 2.37386e8i −0.121889 0.253106i
\(176\) −2.25958e8 2.83343e8i −0.235493 0.295299i
\(177\) 4.33328e8 9.89042e7i 0.441492 0.100768i
\(178\) −2.06529e8 −0.205732
\(179\) 1.04127e9i 1.01427i 0.861867 + 0.507134i \(0.169295\pi\)
−0.861867 + 0.507134i \(0.830705\pi\)
\(180\) 4.66737e6 1.06530e6i 0.00444613 0.00101480i
\(181\) −5.73190e7 + 7.18757e7i −0.0534052 + 0.0669681i −0.807817 0.589434i \(-0.799351\pi\)
0.754412 + 0.656402i \(0.227922\pi\)
\(182\) 6.16554e7 2.70130e8i 0.0561935 0.246200i
\(183\) −6.59589e8 + 8.27098e8i −0.588124 + 0.737484i
\(184\) 3.44822e8 7.16030e8i 0.300832 0.624683i
\(185\) 6.01225e6 + 2.63414e7i 0.00513275 + 0.0224881i
\(186\) 7.69103e8 + 3.70381e8i 0.642589 + 0.309454i
\(187\) 1.43618e9 + 1.80092e9i 1.17447 + 1.47274i
\(188\) 1.54537e8 6.77073e8i 0.123709 0.542006i
\(189\) 8.36131e7 3.66333e8i 0.0655280 0.287097i
\(190\) 2.87948e6 + 5.97930e6i 0.00220953 + 0.00458813i
\(191\) −3.63053e8 + 2.89525e8i −0.272795 + 0.217547i −0.750326 0.661068i \(-0.770103\pi\)
0.477531 + 0.878615i \(0.341532\pi\)
\(192\) −6.68361e8 5.33000e8i −0.491820 0.392213i
\(193\) 1.20085e9 5.78300e8i 0.865487 0.416796i 0.0521841 0.998637i \(-0.483382\pi\)
0.813302 + 0.581841i \(0.197667\pi\)
\(194\) −7.81308e8 1.62240e9i −0.551589 1.14539i
\(195\) 1.38236e7 1.73342e7i 0.00956054 0.0119885i
\(196\) 4.00774e8 + 5.02555e8i 0.271566 + 0.340533i
\(197\) 3.62541e8 1.74591e8i 0.240709 0.115919i −0.309641 0.950854i \(-0.600209\pi\)
0.550350 + 0.834934i \(0.314494\pi\)
\(198\) 7.20797e8 + 1.64517e8i 0.468978 + 0.107041i
\(199\) −2.54109e8 5.79987e7i −0.162035 0.0369833i 0.140734 0.990047i \(-0.455054\pi\)
−0.302769 + 0.953064i \(0.597911\pi\)
\(200\) 1.33724e9 1.06641e9i 0.835776 0.666509i
\(201\) 2.57654e8 5.35024e8i 0.157853 0.327785i
\(202\) −6.66748e8 + 1.52181e8i −0.400457 + 0.0914017i
\(203\) −6.34949e8 3.05775e8i −0.373899 0.180061i
\(204\) 6.62733e8 + 5.28512e8i 0.382664 + 0.305165i
\(205\) 3.87999e7 + 8.85583e6i 0.0219693 + 0.00501434i
\(206\) −1.13524e9 9.05326e8i −0.630406 0.502732i
\(207\) 1.41016e8 + 6.17832e8i 0.0768046 + 0.336503i
\(208\) 7.03052e8 0.375607
\(209\) 9.19527e8i 0.481925i
\(210\) 1.09382e6 + 4.79235e6i 0.000562431 + 0.00246417i
\(211\) 2.10408e9 1.67795e9i 1.06153 0.846541i 0.0729635 0.997335i \(-0.476754\pi\)
0.988565 + 0.150794i \(0.0481829\pi\)
\(212\) 8.73346e8 4.20581e8i 0.432357 0.208212i
\(213\) 4.62156e7 + 2.22562e7i 0.0224528 + 0.0108127i
\(214\) 2.07984e9i 0.991689i
\(215\) 4.97414e6 + 3.83875e7i 0.00232790 + 0.0179653i
\(216\) 2.43924e9 1.12057
\(217\) −3.88381e8 + 8.06482e8i −0.175154 + 0.363711i
\(218\) 2.35095e8 + 4.88181e8i 0.104092 + 0.216150i
\(219\) −1.08692e9 1.36295e9i −0.472521 0.592523i
\(220\) 2.43521e7 5.55821e6i 0.0103955 0.00237271i
\(221\) −4.46857e9 −1.87327
\(222\) 1.53551e9i 0.632179i
\(223\) −1.17555e9 + 2.68311e8i −0.475358 + 0.108497i −0.453486 0.891263i \(-0.649820\pi\)
−0.0218719 + 0.999761i \(0.506963\pi\)
\(224\) 3.74526e8 4.69640e8i 0.148761 0.186541i
\(225\) −3.03490e8 + 1.32968e9i −0.118417 + 0.518819i
\(226\) 1.90657e9 2.39076e9i 0.730834 0.916437i
\(227\) 1.31836e9 2.73759e9i 0.496511 1.03102i −0.490660 0.871351i \(-0.663244\pi\)
0.987171 0.159665i \(-0.0510414\pi\)
\(228\) −7.52974e7 3.29899e8i −0.0278638 0.122079i
\(229\) −2.50331e9 1.20553e9i −0.910274 0.438365i −0.0806854 0.996740i \(-0.525711\pi\)
−0.829589 + 0.558375i \(0.811425\pi\)
\(230\) −1.48788e7 1.86574e7i −0.00531688 0.00666715i
\(231\) 1.51555e8 6.64006e8i 0.0532259 0.233198i
\(232\) 1.01801e9 4.46019e9i 0.351399 1.53958i
\(233\) −5.52291e7 1.14684e8i −0.0187389 0.0389117i 0.891389 0.453238i \(-0.149731\pi\)
−0.910128 + 0.414327i \(0.864017\pi\)
\(234\) −1.12135e9 + 8.94248e8i −0.374006 + 0.298260i
\(235\) −5.07802e7 4.04959e7i −0.0166503 0.0132782i
\(236\) −8.75214e8 + 4.21481e8i −0.282141 + 0.135872i
\(237\) 1.54095e9 + 3.19982e9i 0.488423 + 1.01422i
\(238\) 6.17706e8 7.74579e8i 0.192519 0.241412i
\(239\) −4.41643e8 5.53803e8i −0.135357 0.169732i 0.709533 0.704672i \(-0.248906\pi\)
−0.844890 + 0.534940i \(0.820334\pi\)
\(240\) −1.12376e7 + 5.41173e6i −0.00338709 + 0.00163114i
\(241\) −1.82765e9 4.17149e8i −0.541782 0.123658i −0.0571324 0.998367i \(-0.518196\pi\)
−0.484650 + 0.874708i \(0.661053\pi\)
\(242\) 1.33317e9 + 3.04287e8i 0.388708 + 0.0887201i
\(243\) −2.51311e9 + 2.00414e9i −0.720754 + 0.574782i
\(244\) 1.00318e9 2.08312e9i 0.283021 0.587699i
\(245\) 5.86086e7 1.33770e7i 0.0162666 0.00371275i
\(246\) 2.03776e9 + 9.81335e8i 0.556434 + 0.267964i
\(247\) 1.39465e9 + 1.11220e9i 0.374695 + 0.298809i
\(248\) −5.66513e9 1.29303e9i −1.49762 0.341823i
\(249\) −3.25006e9 2.59184e9i −0.845463 0.674234i
\(250\) −2.28605e7 1.00158e8i −0.00585229 0.0256406i
\(251\) 5.60453e8 0.141203 0.0706016 0.997505i \(-0.477508\pi\)
0.0706016 + 0.997505i \(0.477508\pi\)
\(252\) 2.85296e8i 0.0707446i
\(253\) 7.35755e8 + 3.22355e9i 0.179577 + 0.786779i
\(254\) −7.40132e8 + 5.90236e8i −0.177817 + 0.141805i
\(255\) 7.14256e7 3.43967e7i 0.0168925 0.00813498i
\(256\) 4.06861e9 + 1.95934e9i 0.947296 + 0.456194i
\(257\) 3.17588e8i 0.0728001i 0.999337 + 0.0364001i \(0.0115891\pi\)
−0.999337 + 0.0364001i \(0.988411\pi\)
\(258\) −2.09854e8 + 2.18981e9i −0.0473628 + 0.494228i
\(259\) −1.61013e9 −0.357819
\(260\) −2.10245e7 + 4.36578e7i −0.00460079 + 0.00955363i
\(261\) 1.58282e9 + 3.28675e9i 0.341090 + 0.708280i
\(262\) 3.29259e9 + 4.12878e9i 0.698767 + 0.876226i
\(263\) −5.62497e9 + 1.28386e9i −1.17570 + 0.268346i −0.765370 0.643590i \(-0.777444\pi\)
−0.410331 + 0.911936i \(0.634587\pi\)
\(264\) 4.42132e9 0.910198
\(265\) 9.06557e7i 0.0183828i
\(266\) −3.85575e8 + 8.80050e7i −0.0770162 + 0.0175785i
\(267\) 6.14042e8 7.69984e8i 0.120824 0.151508i
\(268\) −2.88798e8 + 1.26531e9i −0.0559829 + 0.245277i
\(269\) 3.80521e9 4.77158e9i 0.726724 0.911284i −0.271973 0.962305i \(-0.587676\pi\)
0.998698 + 0.0510213i \(0.0162476\pi\)
\(270\) 3.17794e7 6.59906e7i 0.00597986 0.0124173i
\(271\) 3.80577e8 + 1.66742e9i 0.0705611 + 0.309148i 0.997877 0.0651321i \(-0.0207469\pi\)
−0.927316 + 0.374280i \(0.877890\pi\)
\(272\) 2.26490e9 + 1.09072e9i 0.413784 + 0.199268i
\(273\) 8.23791e8 + 1.03300e9i 0.148309 + 0.185973i
\(274\) −1.46314e9 + 6.41044e9i −0.259588 + 1.13733i
\(275\) −1.58347e9 + 6.93762e9i −0.276871 + 1.21305i
\(276\) 5.27935e8 + 1.09627e9i 0.0909796 + 0.188921i
\(277\) 3.03731e9 2.42218e9i 0.515906 0.411421i −0.330624 0.943763i \(-0.607259\pi\)
0.846530 + 0.532341i \(0.178688\pi\)
\(278\) −7.47474e8 5.96090e8i −0.125146 0.0998005i
\(279\) 4.17468e9 2.01042e9i 0.688980 0.331795i
\(280\) −1.45181e7 3.01472e7i −0.00236200 0.00490474i
\(281\) 1.75622e9 2.20223e9i 0.281678 0.353213i −0.620785 0.783981i \(-0.713186\pi\)
0.902463 + 0.430768i \(0.141757\pi\)
\(282\) −2.30142e9 2.88589e9i −0.363915 0.456335i
\(283\) −7.20006e9 + 3.46737e9i −1.12251 + 0.540573i −0.900667 0.434509i \(-0.856922\pi\)
−0.221844 + 0.975082i \(0.571208\pi\)
\(284\) −1.09298e8 2.49465e7i −0.0168011 0.00383475i
\(285\) −3.08532e7 7.04204e6i −0.00467650 0.00106738i
\(286\) −5.85068e9 + 4.66576e9i −0.874465 + 0.697362i
\(287\) −1.02903e9 + 2.13680e9i −0.151670 + 0.314946i
\(288\) −3.03147e9 + 6.91913e8i −0.440639 + 0.100573i
\(289\) −8.11069e9 3.90590e9i −1.16270 0.559925i
\(290\) −1.07402e8 8.56500e7i −0.0151852 0.0121098i
\(291\) 8.37160e9 + 1.91076e9i 1.16745 + 0.266462i
\(292\) 2.97880e9 + 2.37552e9i 0.409742 + 0.326758i
\(293\) −1.83514e9 8.04025e9i −0.248999 1.09094i −0.932552 0.361035i \(-0.882423\pi\)
0.683553 0.729901i \(-0.260434\pi\)
\(294\) 3.41645e9 0.457283
\(295\) 9.08496e7i 0.0119960i
\(296\) −2.32587e9 1.01903e10i −0.302983 1.32746i
\(297\) −7.93432e9 + 6.32741e9i −1.01973 + 0.813205i
\(298\) 5.29275e9 2.54886e9i 0.671145 0.323207i
\(299\) −5.77910e9 2.78307e9i −0.723062 0.348208i
\(300\) 2.61868e9i 0.323294i
\(301\) −2.29623e9 2.20053e8i −0.279737 0.0268078i
\(302\) −1.17199e9 −0.140896
\(303\) 1.41498e9 2.93823e9i 0.167872 0.348590i
\(304\) −4.35408e8 9.04134e8i −0.0509803 0.105862i
\(305\) −1.34819e8 1.69058e8i −0.0155795 0.0195361i
\(306\) −4.99981e9 + 1.14117e9i −0.570253 + 0.130157i
\(307\) 9.46261e9 1.06526 0.532632 0.846347i \(-0.321203\pi\)
0.532632 + 0.846347i \(0.321203\pi\)
\(308\) 1.48854e9i 0.165408i
\(309\) 6.75049e9 1.54076e9i 0.740460 0.169005i
\(310\) −1.08789e8 + 1.36417e8i −0.0117798 + 0.0147714i
\(311\) 8.52209e8 3.73377e9i 0.0910971 0.399123i −0.908736 0.417371i \(-0.862952\pi\)
0.999833 + 0.0182480i \(0.00580884\pi\)
\(312\) −5.34772e9 + 6.70583e9i −0.564353 + 0.707676i
\(313\) 4.70244e9 9.76472e9i 0.489944 1.01738i −0.498655 0.866801i \(-0.666172\pi\)
0.988598 0.150578i \(-0.0481133\pi\)
\(314\) −1.44427e9 6.32776e9i −0.148570 0.650926i
\(315\) 2.40394e7 + 1.15768e7i 0.00244164 + 0.00117583i
\(316\) −4.83956e9 6.06862e9i −0.485353 0.608613i
\(317\) 1.35022e8 5.91569e8i 0.0133711 0.0585826i −0.967802 0.251712i \(-0.919007\pi\)
0.981173 + 0.193129i \(0.0618636\pi\)
\(318\) 1.14644e9 5.02289e9i 0.112110 0.491185i
\(319\) 8.25839e9 + 1.71487e10i 0.797504 + 1.65603i
\(320\) 1.36612e8 1.08945e8i 0.0130284 0.0103898i
\(321\) −7.75410e9 6.18368e9i −0.730316 0.582408i
\(322\) 1.28128e9 6.17032e8i 0.119185 0.0573964i
\(323\) 2.76744e9 + 5.74664e9i 0.254254 + 0.527964i
\(324\) −5.98781e8 + 7.50847e8i −0.0543360 + 0.0681352i
\(325\) −8.60706e9 1.07929e10i −0.771474 0.967398i
\(326\) −1.01783e10 + 4.90162e9i −0.901168 + 0.433980i
\(327\) −2.51901e9 5.74948e8i −0.220313 0.0502849i
\(328\) −1.50099e10 3.42592e9i −1.29683 0.295993i
\(329\) 3.02615e9 2.41327e9i 0.258290 0.205979i
\(330\) 5.76026e7 1.19613e8i 0.00485720 0.0100861i
\(331\) 1.81992e10 4.15386e9i 1.51615 0.346051i 0.618153 0.786058i \(-0.287881\pi\)
0.897994 + 0.440007i \(0.145024\pi\)
\(332\) 8.18557e9 + 3.94196e9i 0.673747 + 0.324459i
\(333\) 6.51634e9 + 5.19661e9i 0.529940 + 0.422613i
\(334\) 1.12762e10 + 2.57373e9i 0.906105 + 0.206812i
\(335\) 9.48977e7 + 7.56784e7i 0.00753488 + 0.00600887i
\(336\) −1.65398e8 7.24655e8i −0.0129769 0.0568557i
\(337\) 1.49717e10 1.16078 0.580392 0.814337i \(-0.302899\pi\)
0.580392 + 0.814337i \(0.302899\pi\)
\(338\) 5.04143e9i 0.386267i
\(339\) 3.24475e9 + 1.42162e10i 0.245687 + 1.07643i
\(340\) −1.35462e8 + 1.08027e8i −0.0101368 + 0.00808385i
\(341\) 2.17815e10 1.04894e10i 1.61091 0.775772i
\(342\) 1.84448e9 + 8.88256e8i 0.134825 + 0.0649282i
\(343\) 7.47215e9i 0.539845i
\(344\) −1.92427e9 1.48504e10i −0.137414 1.06048i
\(345\) 1.13796e8 0.00803247
\(346\) 7.12648e9 1.47983e10i 0.497245 1.03254i
\(347\) −6.05515e9 1.25736e10i −0.417645 0.867248i −0.998579 0.0532976i \(-0.983027\pi\)
0.580934 0.813951i \(-0.302687\pi\)
\(348\) 4.36713e9 + 5.47621e9i 0.297769 + 0.373390i
\(349\) −1.06492e10 + 2.43062e9i −0.717822 + 0.163838i −0.565804 0.824540i \(-0.691434\pi\)
−0.152018 + 0.988378i \(0.548577\pi\)
\(350\) 3.06062e9 0.203957
\(351\) 1.96872e10i 1.29705i
\(352\) −1.58168e10 + 3.61007e9i −1.03026 + 0.235150i
\(353\) −4.49689e9 + 5.63893e9i −0.289610 + 0.363160i −0.905258 0.424861i \(-0.860323\pi\)
0.615648 + 0.788021i \(0.288894\pi\)
\(354\) −1.14889e9 + 5.03363e9i −0.0731588 + 0.320530i
\(355\) −6.53713e6 + 8.19730e6i −0.000411598 + 0.000516128i
\(356\) −9.33905e8 + 1.93927e9i −0.0581437 + 0.120737i
\(357\) 1.05126e9 + 4.60588e9i 0.0647199 + 0.283557i
\(358\) −1.08978e10 5.24811e9i −0.663449 0.319500i
\(359\) 7.21817e9 + 9.05129e9i 0.434559 + 0.544920i 0.950100 0.311945i \(-0.100980\pi\)
−0.515541 + 0.856865i \(0.672409\pi\)
\(360\) −3.85422e7 + 1.68865e8i −0.00229471 + 0.0100538i
\(361\) −3.21262e9 + 1.40754e10i −0.189161 + 0.828767i
\(362\) −4.63348e8 9.62152e8i −0.0269819 0.0560285i
\(363\) −5.09816e9 + 4.06564e9i −0.293621 + 0.234155i
\(364\) −2.25767e9 1.80044e9i −0.128604 0.102559i
\(365\) 3.21039e8 1.54604e8i 0.0180878 0.00871062i
\(366\) −5.33190e9 1.10718e10i −0.297138 0.617013i
\(367\) 1.16276e10 1.45806e10i 0.640954 0.803731i −0.350168 0.936687i \(-0.613875\pi\)
0.991122 + 0.132956i \(0.0424469\pi\)
\(368\) 2.24983e9 + 2.82120e9i 0.122676 + 0.153831i
\(369\) 1.10609e10 5.32667e9i 0.596605 0.287310i
\(370\) −3.05988e8 6.98397e7i −0.0163266 0.00372645i
\(371\) 5.26700e9 + 1.20216e9i 0.278015 + 0.0634551i
\(372\) 6.95562e9 5.54692e9i 0.363215 0.289655i
\(373\) −6.16100e9 + 1.27934e10i −0.318285 + 0.660925i −0.997319 0.0731820i \(-0.976685\pi\)
0.679034 + 0.734107i \(0.262399\pi\)
\(374\) −2.60866e10 + 5.95411e9i −1.33331 + 0.304320i
\(375\) 4.41379e8 + 2.12557e8i 0.0223196 + 0.0107486i
\(376\) 1.96446e10 + 1.56660e10i 0.982859 + 0.783804i
\(377\) −3.59983e10 8.21639e9i −1.78204 0.406739i
\(378\) 3.41257e9 + 2.72143e9i 0.167153 + 0.133300i
\(379\) 6.06210e9 + 2.65598e10i 0.293810 + 1.28727i 0.879176 + 0.476496i \(0.158093\pi\)
−0.585366 + 0.810769i \(0.699049\pi\)
\(380\) 6.91653e7 0.00331706
\(381\) 4.51423e9i 0.214232i
\(382\) −1.20031e9 5.25890e9i −0.0563689 0.246968i
\(383\) 1.06925e10 8.52699e9i 0.496917 0.396278i −0.342710 0.939441i \(-0.611345\pi\)
0.839627 + 0.543163i \(0.182773\pi\)
\(384\) −2.42745e9 + 1.16900e9i −0.111642 + 0.0537637i
\(385\) 1.25426e8 + 6.04021e7i 0.00570881 + 0.00274922i
\(386\) 1.54826e10i 0.697422i
\(387\) 8.58283e9 + 8.30152e9i 0.382637 + 0.370095i
\(388\) −1.87671e10 −0.828075
\(389\) −2.97605e9 + 6.17983e9i −0.129970 + 0.269885i −0.955791 0.294047i \(-0.904998\pi\)
0.825821 + 0.563932i \(0.190712\pi\)
\(390\) 1.11745e8 + 2.32042e8i 0.00483027 + 0.0100302i
\(391\) −1.42999e10 1.79315e10i −0.611822 0.767200i
\(392\) −2.26730e10 + 5.17497e9i −0.960207 + 0.219161i
\(393\) −2.51823e10 −1.05566
\(394\) 4.67425e9i 0.193967i
\(395\) −7.07730e8 + 1.61535e8i −0.0290723 + 0.00663556i
\(396\) 4.80416e9 6.02423e9i 0.195361 0.244974i
\(397\) −1.61925e9 + 7.09438e9i −0.0651855 + 0.285596i −0.997006 0.0773229i \(-0.975363\pi\)
0.931821 + 0.362919i \(0.118220\pi\)
\(398\) 1.88774e9 2.36715e9i 0.0752332 0.0943394i
\(399\) 8.18271e8 1.69916e9i 0.0322853 0.0670412i
\(400\) 1.72809e9 + 7.57128e9i 0.0675037 + 0.295753i
\(401\) 3.90779e10 + 1.88189e10i 1.51131 + 0.727809i 0.991936 0.126738i \(-0.0404508\pi\)
0.519374 + 0.854547i \(0.326165\pi\)
\(402\) 4.30089e9 + 5.39314e9i 0.164685 + 0.206508i
\(403\) −1.04361e10 + 4.57234e10i −0.395655 + 1.73348i
\(404\) −1.58602e9 + 6.94879e9i −0.0595363 + 0.260846i
\(405\) 3.89700e7 + 8.09220e7i 0.00144847 + 0.00300778i
\(406\) 6.40040e9 5.10415e9i 0.235561 0.187854i
\(407\) 3.39992e10 + 2.71134e10i 1.23906 + 0.988114i
\(408\) −2.76313e10 + 1.33065e10i −0.997151 + 0.480203i
\(409\) 4.02390e8 + 8.35572e8i 0.0143799 + 0.0298601i 0.908035 0.418894i \(-0.137582\pi\)
−0.893655 + 0.448754i \(0.851868\pi\)
\(410\) −2.88239e8 + 3.61440e8i −0.0102004 + 0.0127909i
\(411\) −1.95493e10 2.45141e10i −0.685117 0.859109i
\(412\) −1.36343e10 + 6.56594e9i −0.473200 + 0.227881i
\(413\) −5.27827e9 1.20473e9i −0.181423 0.0414085i
\(414\) −7.17687e9 1.63807e9i −0.244306 0.0557612i
\(415\) 6.64310e8 5.29770e8i 0.0223964 0.0178605i
\(416\) 1.36555e10 2.83559e10i 0.455967 0.946824i
\(417\) 4.44470e9 1.01447e9i 0.146994 0.0335503i
\(418\) 9.62363e9 + 4.63450e9i 0.315235 + 0.151809i
\(419\) 2.56887e10 + 2.04861e10i 0.833464 + 0.664665i 0.944268 0.329177i \(-0.106771\pi\)
−0.110804 + 0.993842i \(0.535343\pi\)
\(420\) 4.99455e7 + 1.13997e7i 0.00160509 + 0.000366351i
\(421\) −4.37729e10 3.49077e10i −1.39340 1.11120i −0.979628 0.200822i \(-0.935639\pi\)
−0.413775 0.910379i \(-0.635790\pi\)
\(422\) 6.95640e9 + 3.04780e10i 0.219348 + 0.961028i
\(423\) −2.00358e10 −0.625812
\(424\) 3.50706e10i 1.08512i
\(425\) −1.09837e10 4.81228e10i −0.336661 1.47501i
\(426\) −4.65861e8 + 3.71512e8i −0.0141455 + 0.0112807i
\(427\) 1.16099e10 5.59104e9i 0.349235 0.168183i
\(428\) 1.95294e10 + 9.40485e9i 0.581987 + 0.280270i
\(429\) 3.56846e10i 1.05354i
\(430\) −4.26828e8 1.41418e8i −0.0124847 0.00413647i
\(431\) 8.14089e9 0.235919 0.117959 0.993018i \(-0.462365\pi\)
0.117959 + 0.993018i \(0.462365\pi\)
\(432\) −4.80539e9 + 9.97849e9i −0.137973 + 0.286504i
\(433\) −1.27302e10 2.64346e10i −0.362147 0.752006i 0.637686 0.770297i \(-0.279892\pi\)
−0.999833 + 0.0182907i \(0.994178\pi\)
\(434\) −6.48305e9 8.12949e9i −0.182734 0.229142i
\(435\) 6.38643e8 1.45766e8i 0.0178361 0.00407098i
\(436\) 5.64701e9 0.156269
\(437\) 9.15559e9i 0.251050i
\(438\) 1.97427e10 4.50613e9i 0.536425 0.122436i
\(439\) 3.38187e9 4.24074e9i 0.0910541 0.114178i −0.734217 0.678914i \(-0.762451\pi\)
0.825271 + 0.564736i \(0.191022\pi\)
\(440\) −2.01095e8 + 8.81056e8i −0.00536526 + 0.0235068i
\(441\) 1.15622e10 1.44986e10i 0.305695 0.383329i
\(442\) 2.25220e10 4.67674e10i 0.590090 1.22533i
\(443\) −6.11964e9 2.68119e10i −0.158895 0.696166i −0.990119 0.140228i \(-0.955216\pi\)
0.831224 0.555938i \(-0.187641\pi\)
\(444\) 1.44182e10 + 6.94342e9i 0.371003 + 0.178666i
\(445\) 1.25510e8 + 1.57384e8i 0.00320064 + 0.00401348i
\(446\) 3.11676e9 1.36554e10i 0.0787706 0.345116i
\(447\) −6.23347e9 + 2.73106e10i −0.156135 + 0.684072i
\(448\) 4.51800e9 + 9.38173e9i 0.112159 + 0.232901i
\(449\) −2.61058e10 + 2.08187e10i −0.642320 + 0.512233i −0.889617 0.456707i \(-0.849029\pi\)
0.247298 + 0.968940i \(0.420457\pi\)
\(450\) −1.23866e10 9.87796e9i −0.302065 0.240889i
\(451\) 5.77108e10 2.77920e10i 1.39492 0.671760i
\(452\) −1.38275e10 2.87131e10i −0.331276 0.687903i
\(453\) 3.48451e9 4.36944e9i 0.0827464 0.103761i
\(454\) 2.20066e10 + 2.75954e10i 0.518000 + 0.649552i
\(455\) −2.43319e8 + 1.17176e8i −0.00567716 + 0.00273397i
\(456\) 1.19357e10 + 2.72425e9i 0.276051 + 0.0630067i
\(457\) 1.03360e10 + 2.35913e9i 0.236968 + 0.0540863i 0.339355 0.940658i \(-0.389791\pi\)
−0.102388 + 0.994745i \(0.532648\pi\)
\(458\) 2.52338e10 2.01233e10i 0.573483 0.457338i
\(459\) 3.05429e10 6.34229e10i 0.688112 1.42888i
\(460\) −2.42470e8 + 5.53423e7i −0.00541536 + 0.00123602i
\(461\) −2.68975e10 1.29532e10i −0.595537 0.286795i 0.111734 0.993738i \(-0.464360\pi\)
−0.707271 + 0.706943i \(0.750074\pi\)
\(462\) 6.18554e9 + 4.93281e9i 0.135772 + 0.108274i
\(463\) −3.32407e10 7.58698e9i −0.723347 0.165099i −0.155031 0.987910i \(-0.549548\pi\)
−0.568316 + 0.822810i \(0.692405\pi\)
\(464\) 1.62403e10 + 1.29512e10i 0.350366 + 0.279408i
\(465\) −1.85145e8 8.11174e8i −0.00396005 0.0173501i
\(466\) 1.47863e9 0.0313557
\(467\) 4.55224e10i 0.957101i 0.878060 + 0.478550i \(0.158838\pi\)
−0.878060 + 0.478550i \(0.841162\pi\)
\(468\) 3.32619e9 + 1.45730e10i 0.0693368 + 0.303784i
\(469\) −5.65525e9 + 4.50991e9i −0.116885 + 0.0932130i
\(470\) 6.79761e8 3.27356e8i 0.0139304 0.00670855i
\(471\) 2.78853e10 + 1.34288e10i 0.566619 + 0.272869i
\(472\) 3.51456e10i 0.708114i
\(473\) 4.47811e10 + 4.33134e10i 0.894644 + 0.865321i
\(474\) −4.12554e10 −0.817274
\(475\) −8.54939e9 + 1.77530e10i −0.167942 + 0.348736i
\(476\) −4.47996e9 9.30273e9i −0.0872662 0.181210i
\(477\) −1.74361e10 2.18641e10i −0.336802 0.422337i
\(478\) 8.02195e9 1.83096e9i 0.153663 0.0350725i
\(479\) 7.95082e9 0.151032 0.0755162 0.997145i \(-0.475940\pi\)
0.0755162 + 0.997145i \(0.475940\pi\)
\(480\) 5.58352e8i 0.0105182i
\(481\) −8.22461e10 + 1.87721e10i −1.53651 + 0.350698i
\(482\) 1.35773e10 1.70254e10i 0.251551 0.315435i
\(483\) −1.50901e9 + 6.61141e9i −0.0277271 + 0.121480i
\(484\) 8.88566e9 1.11423e10i 0.161923 0.203045i
\(485\) −7.61533e8 + 1.58134e9i −0.0137633 + 0.0285797i
\(486\) −8.30873e9 3.64029e10i −0.148933 0.652516i
\(487\) −3.73753e10 1.79990e10i −0.664460 0.319987i 0.0710777 0.997471i \(-0.477356\pi\)
−0.735538 + 0.677484i \(0.763070\pi\)
\(488\) 5.21555e10 + 6.54010e10i 0.919647 + 1.15320i
\(489\) 1.19874e10 5.25202e10i 0.209647 0.918525i
\(490\) −1.55391e8 + 6.80810e8i −0.00269551 + 0.0118098i
\(491\) 2.03654e10 + 4.22892e10i 0.350402 + 0.727618i 0.999451 0.0331288i \(-0.0105472\pi\)
−0.649049 + 0.760747i \(0.724833\pi\)
\(492\) 1.84291e10 1.46967e10i 0.314517 0.250819i
\(493\) −1.03223e11 8.23174e10i −1.74738 1.39349i
\(494\) −1.86693e10 + 8.99064e9i −0.313487 + 0.150967i
\(495\) −3.12666e8 6.49257e8i −0.00520786 0.0108142i
\(496\) 1.64500e10 2.06277e10i 0.271794 0.340819i
\(497\) −3.89568e8 4.88502e8i −0.00638495 0.00800647i
\(498\) 4.35064e10 2.09516e10i 0.707353 0.340643i
\(499\) 5.74617e10 + 1.31153e10i 0.926780 + 0.211531i 0.659168 0.751996i \(-0.270909\pi\)
0.267611 + 0.963527i \(0.413766\pi\)
\(500\) −1.04384e9 2.38250e8i −0.0167015 0.00381201i
\(501\) −4.31213e10 + 3.43881e10i −0.684449 + 0.545830i
\(502\) −2.82473e9 + 5.86562e9i −0.0444798 + 0.0923632i
\(503\) 4.72720e10 1.07895e10i 0.738468 0.168550i 0.163289 0.986578i \(-0.447790\pi\)
0.575179 + 0.818028i \(0.304933\pi\)
\(504\) −9.29976e9 4.47853e9i −0.144128 0.0694086i
\(505\) 5.21157e8 + 4.15609e8i 0.00801314 + 0.00639027i
\(506\) −3.74455e10 8.54670e9i −0.571213 0.130376i
\(507\) 1.87955e10 + 1.49889e10i 0.284461 + 0.226850i
\(508\) 2.19541e9 + 9.61870e9i 0.0329655 + 0.144431i
\(509\) 1.63212e10 0.243154 0.121577 0.992582i \(-0.461205\pi\)
0.121577 + 0.992582i \(0.461205\pi\)
\(510\) 9.20893e8i 0.0136122i
\(511\) 4.72514e9 + 2.07022e10i 0.0692996 + 0.303621i
\(512\) −3.12772e10 + 2.49427e10i −0.455143 + 0.362964i
\(513\) −2.53180e10 + 1.21925e10i −0.365562 + 0.176045i
\(514\) −3.32384e9 1.60067e9i −0.0476197 0.0229325i
\(515\) 1.41528e9i 0.0201193i
\(516\) 1.96130e10 + 1.18726e10i 0.276659 + 0.167474i
\(517\) −1.04537e11 −1.46322
\(518\) 8.11522e9 1.68514e10i 0.112715 0.234055i
\(519\) 3.39830e10 + 7.05665e10i 0.468374 + 0.972588i
\(520\) −1.09307e9 1.37067e9i −0.0149498 0.0187464i
\(521\) −1.18096e11 + 2.69547e10i −1.60282 + 0.365834i −0.928127 0.372263i \(-0.878582\pi\)
−0.674695 + 0.738097i \(0.735725\pi\)
\(522\) −4.23762e10 −0.570743
\(523\) 6.05205e10i 0.808901i −0.914560 0.404451i \(-0.867463\pi\)
0.914560 0.404451i \(-0.132537\pi\)
\(524\) 5.36572e10 1.22469e10i 0.711710 0.162443i
\(525\) −9.09968e9 + 1.14106e10i −0.119781 + 0.150201i
\(526\) 1.49136e10 6.53409e10i 0.194823 0.853576i
\(527\) −1.04556e11 + 1.31109e11i −1.35552 + 1.69977i
\(528\) −8.71013e9 + 1.80868e10i −0.112070 + 0.232716i
\(529\) 1.01000e10 + 4.42511e10i 0.128973 + 0.565069i
\(530\) 9.48789e8 + 4.56913e8i 0.0120245 + 0.00579068i
\(531\) 1.74734e10 + 2.19109e10i 0.219785 + 0.275602i
\(532\) −9.17181e8 + 4.01843e9i −0.0114501 + 0.0501661i
\(533\) −2.76507e10 + 1.21146e11i −0.342608 + 1.50106i
\(534\) 4.96372e9 + 1.03073e10i 0.0610438 + 0.126759i
\(535\) 1.58493e9 1.26394e9i 0.0193462 0.0154281i
\(536\) −3.67116e10 2.92766e10i −0.444779 0.354700i
\(537\) 5.19669e10 2.50259e10i 0.624928 0.300949i
\(538\) 3.07601e10 + 6.38740e10i 0.367163 + 0.762422i
\(539\) 6.03263e10 7.56468e10i 0.714746 0.896263i
\(540\) −4.75937e8 5.96806e8i −0.00559725 0.00701872i
\(541\) 5.95592e10 2.86822e10i 0.695280 0.334829i −0.0526442 0.998613i \(-0.516765\pi\)
0.747924 + 0.663784i \(0.231051\pi\)
\(542\) −1.93691e10 4.42087e9i −0.224446 0.0512284i
\(543\) 4.96471e9 + 1.13316e9i 0.0571076 + 0.0130344i
\(544\) 8.79829e10 7.01641e10i 1.00462 0.801160i
\(545\) 2.29145e8 4.75825e8i 0.00259731 0.00539338i
\(546\) −1.49632e10 + 3.41526e9i −0.168366 + 0.0384284i
\(547\) 5.34401e10 + 2.57354e10i 0.596923 + 0.287463i 0.707847 0.706366i \(-0.249667\pi\)
−0.110924 + 0.993829i \(0.535381\pi\)
\(548\) 5.35767e10 + 4.27260e10i 0.594092 + 0.473773i
\(549\) −6.50309e10 1.48429e10i −0.715864 0.163391i
\(550\) −6.46273e10 5.15385e10i −0.706261 0.563224i
\(551\) 1.17278e10 + 5.13829e10i 0.127236 + 0.557458i
\(552\) −4.40224e10 −0.474152
\(553\) 4.32605e10i 0.462584i
\(554\) 1.00418e10 + 4.39961e10i 0.106604 + 0.467062i
\(555\) 1.17012e9 9.33142e8i 0.0123327 0.00983503i
\(556\) −8.97719e9 + 4.32318e9i −0.0939379 + 0.0452381i
\(557\) 1.39087e11 + 6.69807e10i 1.44499 + 0.695871i 0.981717 0.190345i \(-0.0609605\pi\)
0.463273 + 0.886215i \(0.346675\pi\)
\(558\) 5.38243e10i 0.555190i
\(559\) −1.19858e11 + 1.55308e10i −1.22749 + 0.159055i
\(560\) 1.51928e8 0.00154485
\(561\) 5.53613e10 1.14959e11i 0.558927 1.16062i
\(562\) 1.41967e10 + 2.94797e10i 0.142312 + 0.295514i
\(563\) 7.05288e10 + 8.84404e10i 0.701994 + 0.880272i 0.997171 0.0751704i \(-0.0239501\pi\)
−0.295177 + 0.955443i \(0.595379\pi\)
\(564\) −3.75049e10 + 8.56024e9i −0.370656 + 0.0845998i
\(565\) −2.98050e9 −0.0292480
\(566\) 9.28307e10i 0.904536i
\(567\) −5.21826e9 + 1.19103e9i −0.0504886 + 0.0115237i
\(568\) 2.52892e9 3.17116e9i 0.0242964 0.0304667i
\(569\) −2.40896e10 + 1.05543e11i −0.229816 + 1.00689i 0.719974 + 0.694001i \(0.244154\pi\)
−0.949790 + 0.312889i \(0.898703\pi\)
\(570\) 2.29204e8 2.87413e8i 0.00217131 0.00272274i
\(571\) −1.21562e10 + 2.52426e10i −0.114355 + 0.237460i −0.950289 0.311370i \(-0.899212\pi\)
0.835934 + 0.548830i \(0.184926\pi\)
\(572\) 1.73545e10 + 7.60350e10i 0.162117 + 0.710280i
\(573\) 2.31750e10 + 1.11605e10i 0.214981 + 0.103530i
\(574\) −1.71770e10 2.15393e10i −0.158234 0.198420i
\(575\) 1.57663e10 6.90768e10i 0.144231 0.631918i
\(576\) 1.19942e10 5.25501e10i 0.108964 0.477402i
\(577\) 2.38504e10 + 4.95258e10i 0.215175 + 0.446815i 0.980418 0.196926i \(-0.0630957\pi\)
−0.765244 + 0.643741i \(0.777381\pi\)
\(578\) 8.17573e10 6.51992e10i 0.732512 0.584159i
\(579\) −5.77225e10 4.60322e10i −0.513607 0.409588i
\(580\) −1.28990e9 + 6.21183e8i −0.0113984 + 0.00548918i
\(581\) 2.19699e10 + 4.56209e10i 0.192807 + 0.400368i
\(582\) −6.21914e10 + 7.79856e10i −0.542049 + 0.679708i
\(583\) −9.09732e10 1.14077e11i −0.787479 0.987468i
\(584\) −1.24195e11 + 5.98093e10i −1.06771 + 0.514183i
\(585\) 1.36291e9 + 3.11076e8i 0.0116371 + 0.00265609i
\(586\) 9.33974e10 + 2.13173e10i 0.792035 + 0.180777i
\(587\) −1.28999e11 + 1.02873e11i −1.08651 + 0.866463i −0.991641 0.129026i \(-0.958815\pi\)
−0.0948695 + 0.995490i \(0.530243\pi\)
\(588\) 1.54488e10 3.20798e10i 0.129237 0.268363i
\(589\) 6.52641e10 1.48961e10i 0.542267 0.123769i
\(590\) −9.50819e8 4.57890e8i −0.00784675 0.00377879i
\(591\) −1.74266e10 1.38972e10i −0.142844 0.113914i
\(592\) 4.62686e10 + 1.05605e10i 0.376703 + 0.0859801i
\(593\) −8.47394e10 6.75774e10i −0.685278 0.546491i 0.217787 0.975996i \(-0.430116\pi\)
−0.903064 + 0.429506i \(0.858688\pi\)
\(594\) −2.62320e10 1.14930e11i −0.210711 0.923183i
\(595\) −9.65649e8 −0.00770462
\(596\) 6.12237e10i 0.485215i
\(597\) 3.21270e9 + 1.40758e10i 0.0252914 + 0.110809i
\(598\) 5.82544e10 4.64563e10i 0.455537 0.363279i
\(599\) 1.35745e11 6.53713e10i 1.05443 0.507785i 0.175370 0.984503i \(-0.443888\pi\)
0.879057 + 0.476717i \(0.158173\pi\)
\(600\) −8.53608e10 4.11076e10i −0.658649 0.317188i
\(601\) 1.03542e11i 0.793628i −0.917899 0.396814i \(-0.870116\pi\)
0.917899 0.396814i \(-0.129884\pi\)
\(602\) 1.38763e10 2.29230e10i 0.105654 0.174536i
\(603\) 3.74427e10 0.283203
\(604\) −5.29964e9 + 1.10048e10i −0.0398198 + 0.0826866i
\(605\) −5.78299e8 1.20085e9i −0.00431649 0.00896329i
\(606\) 2.36195e10 + 2.96179e10i 0.175138 + 0.219616i
\(607\) 8.40041e9 1.91734e9i 0.0618793 0.0141236i −0.191469 0.981499i \(-0.561325\pi\)
0.253349 + 0.967375i \(0.418468\pi\)
\(608\) −4.49230e10 −0.328742
\(609\) 3.90374e10i 0.283800i
\(610\) 2.44884e9 5.58932e8i 0.0176865 0.00403682i
\(611\) 1.26441e11 1.58552e11i 0.907241 1.13764i
\(612\) −1.18932e10 + 5.21076e10i −0.0847801 + 0.371446i
\(613\) 7.41980e10 9.30413e10i 0.525473 0.658922i −0.446288 0.894889i \(-0.647254\pi\)
0.971761 + 0.235967i \(0.0758259\pi\)
\(614\) −4.76924e10 + 9.90344e10i −0.335565 + 0.696807i
\(615\) −4.90548e8 2.14923e9i −0.00342911 0.0150239i
\(616\) −4.85218e10 2.33668e10i −0.336987 0.162285i
\(617\) −1.52631e11 1.91393e11i −1.05318 1.32064i −0.945201 0.326490i \(-0.894134\pi\)
−0.107977 0.994153i \(-0.534437\pi\)
\(618\) −1.78978e10 + 7.84152e10i −0.122700 + 0.537584i
\(619\) −4.92106e10 + 2.15606e11i −0.335194 + 1.46858i 0.473732 + 0.880669i \(0.342907\pi\)
−0.808925 + 0.587911i \(0.799950\pi\)
\(620\) 7.88997e8 + 1.63837e9i 0.00533960 + 0.0110878i
\(621\) 7.90008e10 6.30010e10i 0.531209 0.423625i
\(622\) 3.47819e10 + 2.77377e10i 0.232376 + 0.185314i
\(623\) −1.08082e10 + 5.20496e9i −0.0717466 + 0.0345513i
\(624\) −1.68971e10 3.50872e10i −0.111449 0.231425i
\(625\) 9.50433e10 1.19181e11i 0.622876 0.781062i
\(626\) 7.84954e10 + 9.84302e10i 0.511148 + 0.640960i
\(627\) −4.58909e10 + 2.20999e10i −0.296931 + 0.142995i
\(628\) −6.59474e10 1.50521e10i −0.423994 0.0967738i
\(629\) −2.94082e11 6.71222e10i −1.87873 0.428809i
\(630\) −2.42322e8 + 1.93245e8i −0.00153826 + 0.00122672i
\(631\) 1.27001e11 2.63720e11i 0.801105 1.66351i 0.0542481 0.998527i \(-0.482724\pi\)
0.746857 0.664985i \(-0.231562\pi\)
\(632\) 2.73789e11 6.24905e10i 1.71612 0.391693i
\(633\) −1.34311e11 6.46806e10i −0.836557 0.402865i
\(634\) 5.51076e9 + 4.39468e9i 0.0341078 + 0.0272001i
\(635\) 8.99570e8 + 2.05321e8i 0.00553274 + 0.00126281i
\(636\) −4.19799e10 3.34779e10i −0.256574 0.204611i
\(637\) 4.17673e10 + 1.82994e11i 0.253676 + 1.11143i
\(638\) −2.21099e11 −1.33446
\(639\) 3.23431e9i 0.0193990i
\(640\) −1.22544e8 5.36899e8i −0.000730417 0.00320017i
\(641\) −4.31430e10 + 3.44054e10i −0.255551 + 0.203796i −0.742883 0.669422i \(-0.766542\pi\)
0.487331 + 0.873217i \(0.337970\pi\)
\(642\) 1.03799e11 4.99869e10i 0.611016 0.294250i
\(643\) 1.07158e11 + 5.16044e10i 0.626873 + 0.301886i 0.720218 0.693748i \(-0.244042\pi\)
−0.0933452 + 0.995634i \(0.529756\pi\)
\(644\) 1.48212e10i 0.0861666i
\(645\) 1.79626e9 1.17085e9i 0.0103784 0.00676490i
\(646\) −7.40917e10 −0.425441
\(647\) 2.33851e10 4.85596e10i 0.133451 0.277114i −0.823526 0.567279i \(-0.807996\pi\)
0.956976 + 0.290166i \(0.0937104\pi\)
\(648\) −1.50757e10 3.13051e10i −0.0855024 0.177548i
\(649\) 9.11677e10 + 1.14321e11i 0.513881 + 0.644386i
\(650\) 1.56337e11 3.56830e10i 0.875810 0.199898i
\(651\) 4.95835e10 0.276066
\(652\) 1.17737e11i 0.651514i
\(653\) 2.23496e11 5.10114e10i 1.22918 0.280553i 0.441855 0.897087i \(-0.354321\pi\)
0.787329 + 0.616534i \(0.211464\pi\)
\(654\) 1.87134e10 2.34658e10i 0.102292 0.128270i
\(655\) 1.14537e9 5.01819e9i 0.00622272 0.0272635i
\(656\) 4.35848e10 5.46536e10i 0.235353 0.295123i
\(657\) 4.76919e10 9.90333e10i 0.255967 0.531520i
\(658\) 1.00049e10 + 4.38344e10i 0.0533715 + 0.233836i
\(659\) 6.89964e10 + 3.32269e10i 0.365834 + 0.176177i 0.607765 0.794117i \(-0.292066\pi\)
−0.241930 + 0.970294i \(0.577781\pi\)
\(660\) −8.62672e8 1.08176e9i −0.00454642 0.00570104i
\(661\) 4.96246e10 2.17420e11i 0.259951 1.13892i −0.661352 0.750075i \(-0.730017\pi\)
0.921303 0.388845i \(-0.127126\pi\)
\(662\) −4.82522e10 + 2.11407e11i −0.251238 + 1.10074i
\(663\) 1.07398e11 + 2.23013e11i 0.555828 + 1.15419i
\(664\) −2.56992e11 + 2.04944e11i −1.32205 + 1.05430i
\(665\) 3.01381e8 + 2.40343e8i 0.00154109 + 0.00122898i
\(666\) −8.72299e10 + 4.20077e10i −0.443372 + 0.213517i
\(667\) −8.22276e10 1.70747e11i −0.415446 0.862682i
\(668\) 7.51569e10 9.42438e10i 0.377453 0.473311i
\(669\) 4.16437e10 + 5.22195e10i 0.207895 + 0.260692i
\(670\) −1.27033e9 + 6.11760e8i −0.00630403 + 0.00303586i
\(671\) −3.39300e11 7.74431e10i −1.67376 0.382026i
\(672\) −3.24397e10 7.40415e9i −0.159074 0.0363076i
\(673\) 2.26918e11 1.80961e11i 1.10614 0.882116i 0.112380 0.993665i \(-0.464153\pi\)
0.993759 + 0.111549i \(0.0355812\pi\)
\(674\) −7.54587e10 + 1.56692e11i −0.365653 + 0.759287i
\(675\) 2.12015e11 4.83910e10i 1.02129 0.233104i
\(676\) −4.73382e10 2.27969e10i −0.226686 0.109166i
\(677\) 2.47053e11 + 1.97018e11i 1.17608 + 0.937890i 0.998928 0.0462943i \(-0.0147412\pi\)
0.177149 + 0.984184i \(0.443313\pi\)
\(678\) −1.65138e11 3.76917e10i −0.781500 0.178372i
\(679\) −8.17757e10 6.52140e10i −0.384721 0.306804i
\(680\) −1.39490e9 6.11144e9i −0.00652389 0.0285830i
\(681\) −1.68310e11 −0.782569
\(682\) 2.80830e11i 1.29809i
\(683\) 7.10956e10 + 3.11490e11i 0.326708 + 1.43140i 0.825364 + 0.564601i \(0.190970\pi\)
−0.498656 + 0.866800i \(0.666173\pi\)
\(684\) 1.66811e10 1.33028e10i 0.0762081 0.0607739i
\(685\) 5.77420e9 2.78071e9i 0.0262258 0.0126297i
\(686\) −7.82024e10 3.76603e10i −0.353121 0.170054i
\(687\) 1.53906e11i 0.690923i
\(688\) 6.45410e10 + 2.13839e10i 0.288059 + 0.0954405i
\(689\) 2.83056e11 1.25602
\(690\) −5.73540e8 + 1.19097e9i −0.00253027 + 0.00525417i
\(691\) −3.68704e10 7.65622e10i −0.161721 0.335816i 0.804324 0.594191i \(-0.202528\pi\)
−0.966045 + 0.258374i \(0.916813\pi\)
\(692\) −1.06728e11 1.33833e11i −0.465430 0.583630i
\(693\) 4.18674e10 9.55595e9i 0.181528 0.0414325i
\(694\) 1.62113e11 0.698841
\(695\) 9.31856e8i 0.00399402i
\(696\) −2.47062e11 + 5.63903e10i −1.05286 + 0.240307i
\(697\) −2.77024e11 + 3.47377e11i −1.17378 + 1.47187i
\(698\) 2.82346e10 1.23704e11i 0.118949 0.521149i
\(699\) −4.39619e9 + 5.51264e9i −0.0184148 + 0.0230914i
\(700\) 1.38398e10 2.87387e10i 0.0576420 0.119695i
\(701\) 1.73855e10 + 7.61706e10i 0.0719969 + 0.315439i 0.998084 0.0618702i \(-0.0197065\pi\)
−0.926087 + 0.377309i \(0.876849\pi\)
\(702\) 2.06044e11 + 9.92253e10i 0.848419 + 0.408577i
\(703\) 7.50772e10 + 9.41439e10i 0.307388 + 0.385452i
\(704\) 6.25802e10 2.74182e11i 0.254769 1.11621i
\(705\) −8.00580e8 + 3.50757e9i −0.00324077 + 0.0141987i
\(706\) −3.63514e10 7.54845e10i −0.146320 0.303836i
\(707\) −3.10574e10 + 2.47674e10i −0.124304 + 0.0991295i
\(708\) 4.20697e10 + 3.35495e10i 0.167431 + 0.133522i
\(709\) −3.38270e11 + 1.62902e11i −1.33869 + 0.644677i −0.959779 0.280758i \(-0.909414\pi\)
−0.378907 + 0.925435i \(0.623700\pi\)
\(710\) −5.28440e7 1.09732e8i −0.000207952 0.000431816i
\(711\) −1.39620e11 + 1.75078e11i −0.546349 + 0.685100i
\(712\) −4.85540e10 6.08848e10i −0.188932 0.236913i
\(713\) −2.16875e11 + 1.04442e11i −0.839173 + 0.404125i
\(714\) −5.35029e10 1.22117e10i −0.205866 0.0469876i
\(715\) 7.11102e9 + 1.62304e9i 0.0272087 + 0.00621021i
\(716\) −9.85577e10 + 7.85972e10i −0.375006 + 0.299058i
\(717\) −1.70242e10 + 3.53512e10i −0.0644156 + 0.133760i
\(718\) −1.31110e11 + 2.99249e10i −0.493330 + 0.112599i
\(719\) −1.91084e10 9.20211e9i −0.0715004 0.0344328i 0.397792 0.917476i \(-0.369777\pi\)
−0.469292 + 0.883043i \(0.655491\pi\)
\(720\) −6.14864e8 4.90338e8i −0.00228796 0.00182459i
\(721\) −8.22263e10 1.87676e10i −0.304277 0.0694493i
\(722\) −1.31119e11 1.04564e11i −0.482523 0.384799i
\(723\) 2.31070e10 + 1.01238e11i 0.0845649 + 0.370503i
\(724\) −1.11297e10 −0.0405067
\(725\) 4.07868e11i 1.47628i
\(726\) −1.68553e10 7.38478e10i −0.0606722 0.265822i
\(727\) 4.77490e10 3.80785e10i 0.170933 0.136315i −0.534287 0.845303i \(-0.679420\pi\)
0.705220 + 0.708989i \(0.250848\pi\)
\(728\) 9.41292e10 4.53302e10i 0.335119 0.161385i
\(729\) 2.07314e11 + 9.98370e10i 0.734037 + 0.353493i
\(730\) 4.13916e9i 0.0145754i
\(731\) −4.10220e11 1.35915e11i −1.43664 0.475991i
\(732\) −1.28073e11 −0.446079
\(733\) 4.95604e10 1.02913e11i 0.171680 0.356497i −0.797321 0.603556i \(-0.793750\pi\)
0.969000 + 0.247059i \(0.0794642\pi\)
\(734\) 9.39940e10 + 1.95181e11i 0.323829 + 0.672438i
\(735\) −2.07620e9 2.60348e9i −0.00711411 0.00892082i
\(736\) 1.57485e11 3.59450e10i 0.536696 0.122497i
\(737\) 1.95358e11 0.662158
\(738\) 1.42609e11i 0.480753i
\(739\) −4.22585e11 + 9.64523e10i −1.41689 + 0.323396i −0.861316 0.508070i \(-0.830359\pi\)
−0.555575 + 0.831466i \(0.687502\pi\)
\(740\) −2.03943e9 + 2.55736e9i −0.00680113 + 0.00852835i
\(741\) 2.19875e10 9.63334e10i 0.0729294 0.319524i
\(742\) −3.91278e10 + 4.90647e10i −0.129083 + 0.161865i
\(743\) 2.87613e10 5.97234e10i 0.0943741 0.195970i −0.848438 0.529295i \(-0.822456\pi\)
0.942812 + 0.333325i \(0.108171\pi\)
\(744\) 7.16243e10 + 3.13806e11i 0.233759 + 1.02417i
\(745\) −5.15879e9 2.48434e9i −0.0167465 0.00806467i
\(746\) −1.02842e11 1.28960e11i −0.332060 0.416390i
\(747\) 5.83247e10 2.55537e11i 0.187314 0.820677i
\(748\) −6.20532e10 + 2.71873e11i −0.198225 + 0.868479i
\(749\) 5.24163e10 + 1.08844e11i 0.166548 + 0.345840i
\(750\) −4.44918e9 + 3.54811e9i −0.0140616 + 0.0112138i
\(751\) 1.55779e11 + 1.24230e11i 0.489723 + 0.390541i 0.836984 0.547228i \(-0.184317\pi\)
−0.347261 + 0.937769i \(0.612888\pi\)
\(752\) −1.02787e11 + 4.94997e10i −0.321416 + 0.154786i
\(753\) −1.34699e10 2.79706e10i −0.0418972 0.0870004i
\(754\) 2.67426e11 3.35342e11i 0.827407 1.03754i
\(755\) 7.12232e8 + 8.93110e8i 0.00219196 + 0.00274864i
\(756\) 4.09851e10 1.97374e10i 0.125470 0.0604230i
\(757\) 3.97262e11 + 9.06724e10i 1.20974 + 0.276116i 0.779387 0.626543i \(-0.215531\pi\)
0.430356 + 0.902659i \(0.358388\pi\)
\(758\) −3.08525e11 7.04187e10i −0.934573 0.213310i
\(759\) 1.43195e11 1.14194e11i 0.431480 0.344094i
\(760\) −1.08575e9 + 2.25457e9i −0.00325442 + 0.00675787i
\(761\) 2.43781e11 5.56415e10i 0.726878 0.165905i 0.156958 0.987605i \(-0.449831\pi\)
0.569920 + 0.821700i \(0.306974\pi\)
\(762\) 4.72452e10 + 2.27521e10i 0.140132 + 0.0674842i
\(763\) 2.46063e10 + 1.96229e10i 0.0726019 + 0.0578981i
\(764\) −5.48078e10 1.25095e10i −0.160868 0.0367170i
\(765\) 3.90805e9 + 3.11657e9i 0.0114108 + 0.00909978i
\(766\) 3.53510e10 + 1.54883e11i 0.102680 + 0.449872i
\(767\) −2.83661e11 −0.819631
\(768\) 2.50143e11i 0.719024i
\(769\) 2.56317e10 + 1.12300e11i 0.0732946 + 0.321125i 0.998263 0.0589201i \(-0.0187657\pi\)
−0.924968 + 0.380045i \(0.875909\pi\)
\(770\) −1.26432e9 + 1.00826e9i −0.00359662 + 0.00286821i
\(771\) 1.58499e10 7.63291e9i 0.0448548 0.0216009i
\(772\) 1.45379e11 + 7.00109e10i 0.409292 + 0.197105i
\(773\) 5.61852e10i 0.157364i −0.996900 0.0786818i \(-0.974929\pi\)
0.996900 0.0786818i \(-0.0250711\pi\)
\(774\) −1.30141e11 + 4.79862e10i −0.362618 + 0.133707i
\(775\) −5.18054e11 −1.43605
\(776\) 2.94603e11 6.11749e11i 0.812437 1.68704i
\(777\) 3.86979e10 + 8.03571e10i 0.106170 + 0.220465i
\(778\) −4.96777e10 6.22938e10i −0.135595 0.170030i
\(779\) 1.72919e11 3.94677e10i 0.469563 0.107175i
\(780\) 2.68413e9 0.00725147
\(781\) 1.68751e10i 0.0453568i
\(782\) 2.59741e11 5.92841e10i 0.694565 0.158530i
\(783\) 3.62666e11 4.54769e11i 0.964851 1.20989i
\(784\) 2.34967e10 1.02946e11i 0.0621932 0.272486i
\(785\) −3.94433e9 + 4.94603e9i −0.0103871 + 0.0130250i
\(786\) 1.26921e11 2.63554e11i 0.332540 0.690526i
\(787\) 1.36937e11 + 5.99961e11i 0.356963 + 1.56396i 0.760714 + 0.649087i \(0.224849\pi\)
−0.403752 + 0.914869i \(0.632294\pi\)
\(788\) 4.38904e10 + 2.11365e10i 0.113832 + 0.0548187i
\(789\) 1.99264e11 + 2.49869e11i 0.514187 + 0.644770i
\(790\) 1.87642e9 8.22115e9i 0.00481751 0.0211069i
\(791\) 3.95236e10 1.73164e11i 0.100960 0.442336i
\(792\) 1.20956e11 + 2.51168e11i 0.307417 + 0.638358i
\(793\) 5.27853e11 4.20949e11i 1.33481 1.06448i
\(794\) −6.60876e10 5.27031e10i −0.166279 0.132603i
\(795\) −4.52436e9 + 2.17882e9i −0.0113263 + 0.00545446i
\(796\) −1.36909e10 2.84295e10i −0.0341021 0.0708137i
\(797\) −3.16456e11 + 3.96823e11i −0.784296 + 0.983476i 0.215680 + 0.976464i \(0.430803\pi\)
−0.999975 + 0.00701142i \(0.997768\pi\)
\(798\) 1.36590e10 + 1.71278e10i 0.0336827 + 0.0422367i
\(799\) 6.53312e11 3.14618e11i 1.60300 0.771964i
\(800\) 3.38934e11 + 7.73594e10i 0.827475 + 0.188866i
\(801\) 6.05403e10 + 1.38179e10i 0.147067 + 0.0335670i
\(802\) −3.93912e11 + 3.14135e11i −0.952143 + 0.759308i
\(803\) 2.48834e11 5.16709e11i 0.598477 1.24275i
\(804\) 7.00888e10 1.59973e10i 0.167735 0.0382845i
\(805\) −1.24885e9 6.01415e8i −0.00297390 0.00143216i
\(806\) −4.25936e11 3.39672e11i −1.00926 0.804860i
\(807\) −3.29590e11 7.52268e10i −0.777106 0.177369i
\(808\) −2.01612e11 1.60780e11i −0.473011 0.377214i
\(809\) −4.83012e10 2.11621e11i −0.112762 0.494043i −0.999495 0.0317620i \(-0.989888\pi\)
0.886733 0.462281i \(-0.152969\pi\)
\(810\) −1.04333e9 −0.00242372
\(811\) 3.89159e11i 0.899588i 0.893132 + 0.449794i \(0.148503\pi\)
−0.893132 + 0.449794i \(0.851497\pi\)
\(812\) −1.89851e10 8.31791e10i −0.0436706 0.191333i
\(813\) 7.40691e10 5.90681e10i 0.169541 0.135204i
\(814\) −4.55124e11 + 2.19176e11i −1.03665 + 0.499224i
\(815\) 9.92071e9 + 4.77756e9i 0.0224860 + 0.0108287i
\(816\) 1.39249e11i 0.314073i
\(817\) 9.42022e10 + 1.44520e11i 0.211433 + 0.324370i
\(818\) −1.07731e10 −0.0240617
\(819\) −3.61463e10 + 7.50587e10i −0.0803394 + 0.166827i
\(820\) 2.09047e9 + 4.34091e9i 0.00462369 + 0.00960120i
\(821\) −7.85604e10 9.85117e10i −0.172914 0.216828i 0.687821 0.725880i \(-0.258567\pi\)
−0.860736 + 0.509052i \(0.829996\pi\)
\(822\) 3.55091e11 8.10473e10i 0.777773 0.177522i
\(823\) −4.79706e11 −1.04562 −0.522812 0.852448i \(-0.675117\pi\)
−0.522812 + 0.852448i \(0.675117\pi\)
\(824\) 5.47508e11i 1.18763i
\(825\) 3.84293e11 8.77123e10i 0.829558 0.189341i
\(826\) 3.92115e10 4.91696e10i 0.0842351 0.105627i
\(827\) 7.31893e10 3.20663e11i 0.156468 0.685532i −0.834452 0.551080i \(-0.814216\pi\)
0.990920 0.134451i \(-0.0429271\pi\)
\(828\) −4.78343e10 + 5.99824e10i −0.101770 + 0.127615i
\(829\) −3.05447e11 + 6.34268e11i −0.646723 + 1.34293i 0.277369 + 0.960763i \(0.410537\pi\)
−0.924092 + 0.382170i \(0.875177\pi\)
\(830\) 2.19631e9 + 9.62266e9i 0.00462787 + 0.0202760i
\(831\) −1.93882e11 9.33688e10i −0.406569 0.195793i
\(832\) 3.40160e11 + 4.26547e11i 0.709888 + 0.890172i
\(833\) −1.49344e11 + 6.54320e11i −0.310176 + 1.35897i
\(834\) −1.17844e10 + 5.16306e10i −0.0243580 + 0.106719i
\(835\) −4.89138e9 1.01571e10i −0.0100620 0.0208940i
\(836\) 8.70342e10 6.94075e10i 0.178182 0.142096i
\(837\) −5.77626e11 4.60642e11i −1.17692 0.938559i
\(838\) −3.43878e11 + 1.65603e11i −0.697314 + 0.335809i
\(839\) −3.56618e11 7.40524e11i −0.719706 1.49448i −0.863216 0.504835i \(-0.831553\pi\)
0.143510 0.989649i \(-0.454161\pi\)
\(840\) −1.15563e9 + 1.44912e9i −0.00232114 + 0.00291062i
\(841\) −3.68296e11 4.61829e11i −0.736230 0.923203i
\(842\) 5.85958e11 2.82183e11i 1.16578 0.561412i
\(843\) −1.52116e11 3.47194e10i −0.301206 0.0687483i
\(844\) 3.17639e11 + 7.24990e10i 0.625985 + 0.142877i
\(845\) −3.84179e9 + 3.06373e9i −0.00753541 + 0.00600929i
\(846\) 1.00982e11 2.09691e11i 0.197134 0.409354i
\(847\) 7.74369e10 1.76745e10i 0.150458 0.0343410i
\(848\) −1.43467e11 6.90902e10i −0.277440 0.133608i
\(849\) 3.46092e11 + 2.75999e11i 0.666133 + 0.531224i
\(850\) 5.59005e11 + 1.27589e11i 1.07088 + 0.244421i
\(851\) −3.38525e11 2.69964e11i −0.645464 0.514740i
\(852\) 1.38185e9 + 6.05430e9i 0.00262243 + 0.0114896i
\(853\) −2.19861e11 −0.415291 −0.207646 0.978204i \(-0.566580\pi\)
−0.207646 + 0.978204i \(0.566580\pi\)
\(854\) 1.49687e11i 0.281418i
\(855\) −4.44019e8 1.94538e9i −0.000830878 0.00364032i
\(856\) −6.13138e11 + 4.88961e11i −1.14199 + 0.910709i
\(857\) −1.29403e11 + 6.23174e10i −0.239896 + 0.115528i −0.549969 0.835185i \(-0.685361\pi\)
0.310074 + 0.950713i \(0.399646\pi\)
\(858\) 3.73470e11 + 1.79853e11i 0.689138 + 0.331871i
\(859\) 1.01778e12i 1.86931i −0.355561 0.934653i \(-0.615710\pi\)
0.355561 0.934653i \(-0.384290\pi\)
\(860\) −3.25796e9 + 3.36836e9i −0.00595596 + 0.00615779i
\(861\) 1.31373e11 0.239053
\(862\) −4.10308e10 + 8.52013e10i −0.0743158 + 0.154318i
\(863\) 2.26905e11 + 4.71173e11i 0.409073 + 0.849449i 0.999114 + 0.0420757i \(0.0133971\pi\)
−0.590042 + 0.807373i \(0.700889\pi\)
\(864\) 3.09122e11 + 3.87627e11i 0.554722 + 0.695599i
\(865\) −1.56077e10 + 3.56237e9i −0.0278789 + 0.00636318i
\(866\) 3.40822e11 0.605977
\(867\) 4.98655e11i 0.882519i
\(868\) −1.05650e11 + 2.41140e10i −0.186119 + 0.0424805i
\(869\) −7.28473e11 + 9.13476e11i −1.27742 + 1.60184i
\(870\) −1.69325e9 + 7.41862e9i −0.00295559 + 0.0129493i
\(871\) −2.36292e11 + 2.96301e11i −0.410560 + 0.514825i
\(872\) −8.86459e10 + 1.84075e11i −0.153318 + 0.318368i
\(873\) 1.20479e11 + 5.27852e11i 0.207421 + 0.908772i
\(874\) −9.58211e10 4.61450e10i −0.164216 0.0790822i
\(875\) −3.72055e9 4.66542e9i −0.00634709 0.00795900i
\(876\) 4.69626e10 2.05756e11i 0.0797509 0.349411i
\(877\) −1.74569e11 + 7.64838e11i −0.295100 + 1.29292i 0.582227 + 0.813026i \(0.302182\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(878\) 2.73380e10 + 5.67679e10i 0.0460032 + 0.0955267i
\(879\) −3.57160e11 + 2.84825e11i −0.598283 + 0.477115i
\(880\) −3.20807e9 2.55835e9i −0.00534950 0.00426608i
\(881\) 5.40485e9 2.60284e9i 0.00897181 0.00432059i −0.429392 0.903118i \(-0.641272\pi\)
0.438364 + 0.898797i \(0.355558\pi\)
\(882\) 9.34655e10 + 1.94083e11i 0.154446 + 0.320711i
\(883\) 3.80812e11 4.77524e11i 0.626424 0.785510i −0.362809 0.931864i \(-0.618182\pi\)
0.989232 + 0.146353i \(0.0467536\pi\)
\(884\) −3.37296e11 4.22955e11i −0.552334 0.692605i
\(885\) 4.53403e9 2.18348e9i 0.00739115 0.00355939i
\(886\) 3.11453e11 + 7.10871e10i 0.505426 + 0.115360i
\(887\) −7.45906e11 1.70248e11i −1.20501 0.275035i −0.427562 0.903986i \(-0.640628\pi\)
−0.777445 + 0.628951i \(0.783485\pi\)
\(888\) −4.52668e11 + 3.60990e11i −0.727994 + 0.580556i
\(889\) −2.38579e10 + 4.95414e10i −0.0381966 + 0.0793161i
\(890\) −2.27974e9 + 5.20336e8i −0.00363350 + 0.000829323i
\(891\) 1.30243e11 + 6.27219e10i 0.206655 + 0.0995196i
\(892\) −1.14128e11 9.10143e10i −0.180274 0.143764i
\(893\) −2.82206e11 6.44117e10i −0.443773 0.101288i
\(894\) −2.54412e11 2.02887e11i −0.398279 0.317617i
\(895\) 2.62342e9 + 1.14939e10i 0.00408860 + 0.0179133i
\(896\) 3.28183e10 0.0509195
\(897\) 3.55306e11i 0.548824i
\(898\) −8.63096e10 3.78147e11i −0.132725 0.581508i
\(899\) −1.08336e12 + 8.63951e11i −1.65857 + 1.32267i
\(900\) −1.48763e11 + 7.16406e10i −0.226739 + 0.109192i
\(901\) 9.11872e11 + 4.39135e11i 1.38368 + 0.666344i
\(902\) 7.44067e11i 1.12405i
\(903\) 4.42054e10 + 1.19887e11i 0.0664851 + 0.180311i
\(904\) 1.15302e12 1.72649
\(905\) −4.51620e8 + 9.37799e8i −0.000673254 + 0.00139803i
\(906\) 2.81677e10 + 5.84908e10i 0.0418060 + 0.0868110i
\(907\) 3.21973e11 + 4.03741e11i 0.475762 + 0.596587i 0.960572 0.278033i \(-0.0896824\pi\)
−0.484809 + 0.874620i \(0.661111\pi\)
\(908\) 3.58628e11 8.18545e10i 0.527595 0.120420i
\(909\) 2.05627e11 0.301179
\(910\) 3.13712e9i 0.00457474i
\(911\) 1.84451e11 4.20998e10i 0.267799 0.0611233i −0.0865130 0.996251i \(-0.527572\pi\)
0.354311 + 0.935127i \(0.384715\pi\)
\(912\) −3.46581e10 + 4.34599e10i −0.0500986 + 0.0628216i
\(913\) 3.04311e11 1.33327e12i 0.437960 1.91883i
\(914\) −7.67849e10 + 9.62852e10i −0.110025 + 0.137967i
\(915\) −5.19695e9 + 1.07916e10i −0.00741420 + 0.0153957i
\(916\) −7.48493e10 3.27936e11i −0.106318 0.465809i
\(917\) 2.76363e11 + 1.33090e11i 0.390843 + 0.188220i
\(918\) 5.09836e11 + 6.39315e11i 0.717894 + 0.900210i
\(919\) 5.29582e10 2.32025e11i 0.0742457 0.325292i −0.924142 0.382048i \(-0.875219\pi\)
0.998388 + 0.0567567i \(0.0180759\pi\)
\(920\) 2.00227e9 8.77254e9i 0.00279494 0.0122454i
\(921\) −2.27424e11 4.72251e11i −0.316081 0.656349i
\(922\) 2.71132e11 2.16220e11i 0.375195 0.299208i
\(923\) −2.55946e10 2.04110e10i −0.0352647 0.0281227i
\(924\) 7.42886e10 3.57755e10i 0.101914 0.0490792i
\(925\) −4.04321e11 8.39580e11i −0.552279 1.14682i
\(926\) 2.46941e11 3.09654e11i 0.335852 0.421146i
\(927\) 2.72205e11 + 3.41334e11i 0.368618 + 0.462233i
\(928\) 8.37793e11 4.03460e11i 1.12965 0.544012i
\(929\) −2.47489e11 5.64877e10i −0.332271 0.0758387i 0.0531307 0.998588i \(-0.483080\pi\)
−0.385402 + 0.922749i \(0.625937\pi\)
\(930\) 9.42277e9 + 2.15069e9i 0.0125964 + 0.00287505i
\(931\) 2.09467e11 1.67044e11i 0.278815 0.222347i
\(932\) 6.68622e9 1.38841e10i 0.00886170 0.0184015i
\(933\) −2.06824e11 + 4.72061e10i −0.272944 + 0.0622977i
\(934\) −4.76431e11 2.29437e11i −0.626055 0.301492i
\(935\) 2.03904e10 + 1.62608e10i 0.0266796 + 0.0212762i
\(936\) −5.27249e11 1.20341e11i −0.686929 0.156787i
\(937\) −6.36327e11 5.07454e11i −0.825510 0.658322i 0.116766 0.993159i \(-0.462747\pi\)
−0.942276 + 0.334837i \(0.891319\pi\)
\(938\) −1.86971e10 8.19174e10i −0.0241526 0.105819i
\(939\) −6.00347e11 −0.772218
\(940\) 7.86311e9i 0.0100712i
\(941\) −6.77705e10 2.96922e11i −0.0864335 0.378690i 0.913148 0.407629i \(-0.133644\pi\)
−0.999581 + 0.0289390i \(0.990787\pi\)
\(942\) −2.81088e11 + 2.24161e11i −0.356976 + 0.284679i
\(943\) −5.74618e11 + 2.76721e11i −0.726662 + 0.349942i
\(944\) 1.43774e11 + 6.92379e10i 0.181047 + 0.0871879i
\(945\) 4.25436e9i 0.00533467i
\(946\) −6.79012e11 + 2.50369e11i −0.847839 + 0.312620i
\(947\) −3.53081e11 −0.439010 −0.219505 0.975611i \(-0.570444\pi\)
−0.219505 + 0.975611i \(0.570444\pi\)
\(948\) −1.86553e11 + 3.87381e11i −0.230977 + 0.479629i
\(949\) 4.82723e11 + 1.00238e12i 0.595159 + 1.23586i
\(950\) −1.42710e11 1.78953e11i −0.175211 0.219708i
\(951\) −3.27686e10 + 7.47922e9i −0.0400623 + 0.00914395i
\(952\) 3.73566e11 0.454799
\(953\) 5.55268e10i 0.0673179i −0.999433 0.0336590i \(-0.989284\pi\)
0.999433 0.0336590i \(-0.0107160\pi\)
\(954\) 3.16706e11 7.22862e10i 0.382352 0.0872693i
\(955\) −3.27807e9 + 4.11057e9i −0.00394098 + 0.00494183i
\(956\) 1.90821e10 8.36041e10i 0.0228452 0.100091i
\(957\) 6.57361e11 8.24304e11i 0.783711 0.982742i
\(958\) −4.00729e10 + 8.32122e10i −0.0475760 + 0.0987927i
\(959\) 8.49862e10 + 3.72349e11i 0.100479 + 0.440226i
\(960\) −8.72045e9 4.19955e9i −0.0102672 0.00494445i
\(961\) 5.65581e11 + 7.09216e11i 0.663134 + 0.831543i
\(962\) 2.18061e11 9.55390e11i 0.254612 1.11553i
\(963\) 1.39153e11 6.09669e11i 0.161803 0.708906i
\(964\) −9.84705e10 2.04476e11i −0.114024 0.236774i
\(965\) 1.17984e10 9.40894e9i 0.0136055 0.0108500i
\(966\) −6.15885e10 4.91152e10i −0.0707280 0.0564037i
\(967\) −7.29400e10 + 3.51261e10i −0.0834180 + 0.0401720i −0.475128 0.879917i \(-0.657598\pi\)
0.391710 + 0.920089i \(0.371884\pi\)
\(968\) 2.23718e11 + 4.64555e11i 0.254800 + 0.529097i
\(969\) 2.20286e11 2.76229e11i 0.249857 0.313310i
\(970\) −1.27119e10 1.59402e10i −0.0143589 0.0180056i
\(971\) 3.95531e11 1.90478e11i 0.444942 0.214273i −0.197977 0.980207i \(-0.563437\pi\)
0.642919 + 0.765934i \(0.277723\pi\)
\(972\) −3.79389e11 8.65930e10i −0.425030 0.0970102i
\(973\) −5.41399e10 1.23571e10i −0.0604041 0.0137868i
\(974\) 3.76750e11 3.00448e11i 0.418617 0.333836i
\(975\) −3.31781e11 + 6.88950e11i −0.367141 + 0.762376i
\(976\) −3.70291e11 + 8.45165e10i −0.408079 + 0.0931413i
\(977\) 9.16917e11 + 4.41564e11i 1.00636 + 0.484636i 0.863091 0.505049i \(-0.168526\pi\)
0.143265 + 0.989684i \(0.454240\pi\)
\(978\) 4.89251e11 + 3.90165e11i 0.534782 + 0.426474i
\(979\) 3.15871e11 + 7.20954e10i 0.343857 + 0.0784832i
\(980\) 5.69003e9 + 4.53765e9i 0.00616894 + 0.00491956i
\(981\) −3.62520e10 1.58831e11i −0.0391432 0.171498i
\(982\) −5.45236e11 −0.586325
\(983\) 6.18007e9i 0.00661880i −0.999995 0.00330940i \(-0.998947\pi\)
0.999995 0.00330940i \(-0.00105342\pi\)
\(984\) 1.89771e11 + 8.31440e11i 0.202418 + 0.886851i
\(985\) 3.56198e9 2.84059e9i 0.00378396 0.00301761i
\(986\) 1.38177e12 6.65428e11i 1.46194 0.704033i
\(987\) −1.93170e11 9.30257e10i −0.203550 0.0980244i
\(988\) 2.15956e11i 0.226640i
\(989\) −4.45879e11 4.31265e11i −0.466049 0.450774i
\(990\) 8.37090e9 0.00871428
\(991\) 4.75138e11 9.86634e11i 0.492635 1.02297i −0.495390 0.868671i \(-0.664975\pi\)
0.988025 0.154296i \(-0.0493109\pi\)
\(992\) −5.12455e11 1.06412e12i −0.529187 1.09887i
\(993\) −6.44707e11 8.08437e11i −0.663079 0.831475i
\(994\) 7.07605e9 1.61506e9i 0.00724846 0.00165441i
\(995\) −2.95106e9 −0.00301083
\(996\) 5.03259e11i 0.511392i
\(997\) 2.66213e11 6.07614e10i 0.269432 0.0614961i −0.0856703 0.996324i \(-0.527303\pi\)
0.355102 + 0.934827i \(0.384446\pi\)
\(998\) −4.26875e11 + 5.35284e11i −0.430307 + 0.539588i
\(999\) 2.95721e11 1.29564e12i 0.296907 1.30083i
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 43.9.f.a.22.11 yes 174
43.2 odd 14 inner 43.9.f.a.2.11 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.9.f.a.2.11 174 43.2 odd 14 inner
43.9.f.a.22.11 yes 174 1.1 even 1 trivial