Properties

Label 43.8.e.a.4.3
Level $43$
Weight $8$
Character 43.4
Analytic conductor $13.433$
Analytic rank $0$
Dimension $144$
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] = [43,8,Mod(4,43)]
 
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([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.e (of order \(7\), 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: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 4.3
Character \(\chi\) \(=\) 43.4
Dual form 43.8.e.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.9550 + 13.7371i) q^{2} +(47.1173 + 59.0832i) q^{3} +(-40.2142 - 176.190i) q^{4} +(310.040 + 149.307i) q^{5} -1327.80 q^{6} +256.844 q^{7} +(834.593 + 401.919i) q^{8} +(-784.134 + 3435.52i) q^{9} +O(q^{10})\) \(q+(-10.9550 + 13.7371i) q^{2} +(47.1173 + 59.0832i) q^{3} +(-40.2142 - 176.190i) q^{4} +(310.040 + 149.307i) q^{5} -1327.80 q^{6} +256.844 q^{7} +(834.593 + 401.919i) q^{8} +(-784.134 + 3435.52i) q^{9} +(-5447.55 + 2623.40i) q^{10} +(-1402.96 + 6146.75i) q^{11} +(8515.08 - 10677.6i) q^{12} +(3460.82 + 1666.64i) q^{13} +(-2813.73 + 3528.31i) q^{14} +(5786.69 + 25353.1i) q^{15} +(6177.27 - 2974.82i) q^{16} +(-13989.7 + 6737.08i) q^{17} +(-38604.0 - 48407.8i) q^{18} +(-9139.84 - 40044.2i) q^{19} +(13838.4 - 60630.2i) q^{20} +(12101.8 + 15175.2i) q^{21} +(-69069.4 - 86610.3i) q^{22} +(-4929.18 + 21596.2i) q^{23} +(15577.1 + 68247.8i) q^{24} +(25122.1 + 31502.1i) q^{25} +(-60808.1 + 29283.6i) q^{26} +(-91022.5 + 43834.1i) q^{27} +(-10328.8 - 45253.4i) q^{28} +(14207.6 - 17815.8i) q^{29} +(-411673. - 198251. i) q^{30} +(129578. - 162486. i) q^{31} +(-53190.9 + 233044. i) q^{32} +(-429273. + 206727. i) q^{33} +(60708.9 - 265983. i) q^{34} +(79632.1 + 38348.8i) q^{35} +636836. q^{36} +446988. q^{37} +(650220. + 313129. i) q^{38} +(64593.8 + 283004. i) q^{39} +(198748. + 249222. i) q^{40} +(494591. - 620197. i) q^{41} -341039. q^{42} +(-500870. + 144732. i) q^{43} +1.13941e6 q^{44} +(-756061. + 948071. i) q^{45} +(-242670. - 304299. i) q^{46} +(213276. + 934423. i) q^{47} +(466818. + 224808. i) q^{48} -757574. q^{49} -707960. q^{50} +(-1.05720e6 - 509123. i) q^{51} +(154471. - 676783. i) q^{52} +(-1.00629e6 + 484602. i) q^{53} +(394996. - 1.73059e6i) q^{54} +(-1.35273e6 + 1.69627e6i) q^{55} +(214361. + 103231. i) q^{56} +(1.93530e6 - 2.42679e6i) q^{57} +(89093.3 + 390343. i) q^{58} +(693387. - 333918. i) q^{59} +(4.23426e6 - 2.03911e6i) q^{60} +(386221. + 484306. i) q^{61} +(812563. + 3.56007e6i) q^{62} +(-201400. + 882393. i) q^{63} +(-2.07148e6 - 2.59755e6i) q^{64} +(824150. + 1.03345e6i) q^{65} +(1.86285e6 - 8.16168e6i) q^{66} +(211568. + 926941. i) q^{67} +(1.74959e6 + 2.19391e6i) q^{68} +(-1.50822e6 + 726321. i) q^{69} +(-1.39917e6 + 673806. i) q^{70} +(-900478. - 3.94525e6i) q^{71} +(-2.03523e6 + 2.55210e6i) q^{72} +(-3.86179e6 - 1.85974e6i) q^{73} +(-4.89676e6 + 6.14034e6i) q^{74} +(-677560. + 2.96858e6i) q^{75} +(-6.68783e6 + 3.22069e6i) q^{76} +(-360342. + 1.57876e6i) q^{77} +(-4.59529e6 - 2.21297e6i) q^{78} +7.66490e6 q^{79} +2.35937e6 q^{80} +(64896.6 + 31252.6i) q^{81} +(3.10149e6 + 1.35885e7i) q^{82} +(-3.43996e6 - 4.31357e6i) q^{83} +(2.18705e6 - 2.74247e6i) q^{84} -5.34326e6 q^{85} +(3.49883e6 - 8.46606e6i) q^{86} +1.72204e6 q^{87} +(-3.64139e6 + 4.56616e6i) q^{88} +(6.88405e6 + 8.63233e6i) q^{89} +(-4.74113e6 - 2.07722e7i) q^{90} +(888891. + 428068. i) q^{91} +4.00324e6 q^{92} +1.57056e7 q^{93} +(-1.51727e7 - 7.30680e6i) q^{94} +(3.14519e6 - 1.37800e7i) q^{95} +(-1.62752e7 + 7.83773e6i) q^{96} +(-3.38203e6 + 1.48177e7i) q^{97} +(8.29922e6 - 1.04069e7i) q^{98} +(-2.00172e7 - 9.63976e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + q^{2} - 33 q^{3} - 1531 q^{4} - 253 q^{5} + 484 q^{6} + 3440 q^{7} - 6339 q^{8} - 7461 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + q^{2} - 33 q^{3} - 1531 q^{4} - 253 q^{5} + 484 q^{6} + 3440 q^{7} - 6339 q^{8} - 7461 q^{9} - 3341 q^{10} - 2960 q^{11} + 13689 q^{12} + 21868 q^{13} + 39897 q^{14} - 29921 q^{15} - 190983 q^{16} - 47792 q^{17} - 8652 q^{18} - 57870 q^{19} - 29763 q^{20} - 5368 q^{21} - 158945 q^{22} - 4594 q^{23} + 615935 q^{24} - 395817 q^{25} - 393069 q^{26} - 12195 q^{27} - 310163 q^{28} - 351549 q^{29} + 446684 q^{30} - 1062532 q^{31} - 18837 q^{32} + 864286 q^{33} - 60405 q^{34} + 12628 q^{35} + 3122128 q^{36} - 699954 q^{37} - 3468417 q^{38} - 353795 q^{39} - 128577 q^{40} + 2170261 q^{41} + 395298 q^{42} - 817514 q^{43} + 7454824 q^{44} - 4456426 q^{45} + 4453814 q^{46} - 748674 q^{47} - 12117143 q^{48} + 10546384 q^{49} + 3042978 q^{50} + 1049484 q^{51} - 718239 q^{52} + 4445244 q^{53} + 6955665 q^{54} - 4115285 q^{55} - 3152781 q^{56} - 9217501 q^{57} + 9825959 q^{58} + 4995358 q^{59} - 2930621 q^{60} - 7764277 q^{61} + 4452543 q^{62} - 16888467 q^{63} + 9029845 q^{64} - 5616137 q^{65} + 11011393 q^{66} - 9868514 q^{67} + 19838976 q^{68} - 21931867 q^{69} + 5753942 q^{70} + 14147202 q^{71} + 7754068 q^{72} + 14623156 q^{73} - 12810086 q^{74} - 8522837 q^{75} - 49153968 q^{76} - 39877497 q^{77} - 24880828 q^{78} - 4675142 q^{79} + 26108098 q^{80} - 10465710 q^{81} - 20492413 q^{82} - 11604907 q^{83} + 63335734 q^{84} + 72214364 q^{85} - 23830431 q^{86} + 86376126 q^{87} - 35967739 q^{88} + 41753866 q^{89} - 47033632 q^{90} + 1637756 q^{91} - 33725352 q^{92} - 79434044 q^{93} - 92694615 q^{94} - 8060431 q^{95} - 98386924 q^{96} + 45598073 q^{97} - 13251727 q^{98} + 111493864 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9550 + 13.7371i −0.968294 + 1.21420i 0.00848722 + 0.999964i \(0.497298\pi\)
−0.976781 + 0.214238i \(0.931273\pi\)
\(3\) 47.1173 + 59.0832i 1.00753 + 1.26340i 0.964433 + 0.264326i \(0.0851494\pi\)
0.0430918 + 0.999071i \(0.486279\pi\)
\(4\) −40.2142 176.190i −0.314173 1.37648i
\(5\) 310.040 + 149.307i 1.10923 + 0.534179i 0.896550 0.442942i \(-0.146065\pi\)
0.212683 + 0.977121i \(0.431780\pi\)
\(6\) −1327.80 −2.50960
\(7\) 256.844 0.283026 0.141513 0.989936i \(-0.454803\pi\)
0.141513 + 0.989936i \(0.454803\pi\)
\(8\) 834.593 + 401.919i 0.576315 + 0.277539i
\(9\) −784.134 + 3435.52i −0.358543 + 1.57088i
\(10\) −5447.55 + 2623.40i −1.72267 + 0.829592i
\(11\) −1402.96 + 6146.75i −0.317812 + 1.39242i 0.523570 + 0.851983i \(0.324600\pi\)
−0.841382 + 0.540441i \(0.818257\pi\)
\(12\) 8515.08 10677.6i 1.42251 1.78377i
\(13\) 3460.82 + 1666.64i 0.436895 + 0.210397i 0.639385 0.768887i \(-0.279189\pi\)
−0.202490 + 0.979284i \(0.564903\pi\)
\(14\) −2813.73 + 3528.31i −0.274053 + 0.343651i
\(15\) 5786.69 + 25353.1i 0.442701 + 1.93960i
\(16\) 6177.27 2974.82i 0.377031 0.181568i
\(17\) −13989.7 + 6737.08i −0.690616 + 0.332583i −0.746060 0.665879i \(-0.768057\pi\)
0.0554439 + 0.998462i \(0.482343\pi\)
\(18\) −38604.0 48407.8i −1.56019 1.95642i
\(19\) −9139.84 40044.2i −0.305704 1.33938i −0.861373 0.507972i \(-0.830395\pi\)
0.555670 0.831403i \(-0.312462\pi\)
\(20\) 13838.4 60630.2i 0.386796 1.69466i
\(21\) 12101.8 + 15175.2i 0.285156 + 0.357575i
\(22\) −69069.4 86610.3i −1.38295 1.73416i
\(23\) −4929.18 + 21596.2i −0.0844748 + 0.370108i −0.999441 0.0334213i \(-0.989360\pi\)
0.914967 + 0.403530i \(0.132217\pi\)
\(24\) 15577.1 + 68247.8i 0.230010 + 1.00774i
\(25\) 25122.1 + 31502.1i 0.321562 + 0.403226i
\(26\) −60808.1 + 29283.6i −0.678508 + 0.326752i
\(27\) −91022.5 + 43834.1i −0.889971 + 0.428587i
\(28\) −10328.8 45253.4i −0.0889193 0.389581i
\(29\) 14207.6 17815.8i 0.108175 0.135647i −0.724796 0.688963i \(-0.758066\pi\)
0.832972 + 0.553316i \(0.186638\pi\)
\(30\) −411673. 198251.i −2.78373 1.34058i
\(31\) 129578. 162486.i 0.781208 0.979603i −0.218785 0.975773i \(-0.570209\pi\)
0.999993 0.00383034i \(-0.00121924\pi\)
\(32\) −53190.9 + 233044.i −0.286954 + 1.25723i
\(33\) −429273. + 206727.i −2.07939 + 1.00138i
\(34\) 60708.9 265983.i 0.264896 1.16059i
\(35\) 79632.1 + 38348.8i 0.313942 + 0.151187i
\(36\) 636836. 2.27493
\(37\) 446988. 1.45074 0.725371 0.688358i \(-0.241668\pi\)
0.725371 + 0.688358i \(0.241668\pi\)
\(38\) 650220. + 313129.i 1.92228 + 0.925723i
\(39\) 64593.8 + 283004.i 0.174367 + 0.763952i
\(40\) 198748. + 249222.i 0.491012 + 0.615710i
\(41\) 494591. 620197.i 1.12073 1.40536i 0.217577 0.976043i \(-0.430185\pi\)
0.903156 0.429312i \(-0.141244\pi\)
\(42\) −341039. −0.710283
\(43\) −500870. + 144732.i −0.960696 + 0.277604i
\(44\) 1.13941e6 2.01649
\(45\) −756061. + 948071.i −1.23684 + 1.55095i
\(46\) −242670. 304299.i −0.367590 0.460943i
\(47\) 213276. + 934423.i 0.299640 + 1.31281i 0.870666 + 0.491875i \(0.163688\pi\)
−0.571026 + 0.820932i \(0.693455\pi\)
\(48\) 466818. + 224808.i 0.609261 + 0.293405i
\(49\) −757574. −0.919896
\(50\) −707960. −0.800965
\(51\) −1.05720e6 509123.i −1.11600 0.537436i
\(52\) 154471. 676783.i 0.152348 0.667479i
\(53\) −1.00629e6 + 484602.i −0.928445 + 0.447115i −0.836079 0.548610i \(-0.815157\pi\)
−0.0923660 + 0.995725i \(0.529443\pi\)
\(54\) 394996. 1.73059e6i 0.341362 1.49560i
\(55\) −1.35273e6 + 1.69627e6i −1.09633 + 1.37475i
\(56\) 214361. + 103231.i 0.163112 + 0.0785508i
\(57\) 1.93530e6 2.42679e6i 1.38416 1.73568i
\(58\) 89093.3 + 390343.i 0.0599580 + 0.262693i
\(59\) 693387. 333918.i 0.439535 0.211669i −0.201010 0.979589i \(-0.564422\pi\)
0.640546 + 0.767920i \(0.278708\pi\)
\(60\) 4.23426e6 2.03911e6i 2.53074 1.21874i
\(61\) 386221. + 484306.i 0.217862 + 0.273190i 0.878738 0.477305i \(-0.158386\pi\)
−0.660876 + 0.750495i \(0.729815\pi\)
\(62\) 812563. + 3.56007e6i 0.432998 + 1.89709i
\(63\) −201400. + 882393.i −0.101477 + 0.444601i
\(64\) −2.07148e6 2.59755e6i −0.987759 1.23861i
\(65\) 824150. + 1.03345e6i 0.372228 + 0.466760i
\(66\) 1.86285e6 8.16168e6i 0.797580 3.49443i
\(67\) 211568. + 926941.i 0.0859387 + 0.376522i 0.999548 0.0300718i \(-0.00957359\pi\)
−0.913609 + 0.406594i \(0.866716\pi\)
\(68\) 1.74959e6 + 2.19391e6i 0.674768 + 0.846132i
\(69\) −1.50822e6 + 726321.i −0.552704 + 0.266168i
\(70\) −1.39917e6 + 673806.i −0.487560 + 0.234796i
\(71\) −900478. 3.94525e6i −0.298586 1.30819i −0.872235 0.489088i \(-0.837330\pi\)
0.573649 0.819101i \(-0.305527\pi\)
\(72\) −2.03523e6 + 2.55210e6i −0.642614 + 0.805812i
\(73\) −3.86179e6 1.85974e6i −1.16187 0.559529i −0.249294 0.968428i \(-0.580198\pi\)
−0.912580 + 0.408899i \(0.865913\pi\)
\(74\) −4.89676e6 + 6.14034e6i −1.40475 + 1.76149i
\(75\) −677560. + 2.96858e6i −0.185453 + 0.812521i
\(76\) −6.68783e6 + 3.22069e6i −1.74758 + 0.841592i
\(77\) −360342. + 1.57876e6i −0.0899491 + 0.394093i
\(78\) −4.59529e6 2.21297e6i −1.09643 0.528013i
\(79\) 7.66490e6 1.74909 0.874544 0.484947i \(-0.161161\pi\)
0.874544 + 0.484947i \(0.161161\pi\)
\(80\) 2.35937e6 0.515205
\(81\) 64896.6 + 31252.6i 0.0135683 + 0.00653414i
\(82\) 3.10149e6 + 1.35885e7i 0.621186 + 2.72159i
\(83\) −3.43996e6 4.31357e6i −0.660359 0.828064i 0.333023 0.942919i \(-0.391931\pi\)
−0.993382 + 0.114855i \(0.963360\pi\)
\(84\) 2.18705e6 2.74247e6i 0.402607 0.504853i
\(85\) −5.34326e6 −0.943714
\(86\) 3.49883e6 8.46606e6i 0.593169 1.43528i
\(87\) 1.72204e6 0.280366
\(88\) −3.64139e6 + 4.56616e6i −0.569611 + 0.714269i
\(89\) 6.88405e6 + 8.63233e6i 1.03509 + 1.29796i 0.953531 + 0.301296i \(0.0974193\pi\)
0.0815615 + 0.996668i \(0.474009\pi\)
\(90\) −4.74113e6 2.07722e7i −0.685540 3.00355i
\(91\) 888891. + 428068.i 0.123653 + 0.0595480i
\(92\) 4.00324e6 0.535988
\(93\) 1.57056e7 2.02471
\(94\) −1.51727e7 7.30680e6i −1.88415 0.907360i
\(95\) 3.14519e6 1.37800e7i 0.376369 1.64898i
\(96\) −1.62752e7 + 7.83773e6i −1.87749 + 0.904151i
\(97\) −3.38203e6 + 1.48177e7i −0.376250 + 1.64846i 0.332576 + 0.943077i \(0.392082\pi\)
−0.708826 + 0.705383i \(0.750775\pi\)
\(98\) 8.29922e6 1.04069e7i 0.890730 1.11694i
\(99\) −2.00172e7 9.63976e6i −2.07338 0.998488i
\(100\) 4.54008e6 5.69308e6i 0.454008 0.569308i
\(101\) 2.48552e6 + 1.08898e7i 0.240045 + 1.05171i 0.940975 + 0.338476i \(0.109911\pi\)
−0.700930 + 0.713230i \(0.747231\pi\)
\(102\) 1.85756e7 8.94552e6i 1.73317 0.834651i
\(103\) 2.33049e6 1.12230e6i 0.210144 0.101200i −0.325851 0.945421i \(-0.605651\pi\)
0.535995 + 0.844221i \(0.319937\pi\)
\(104\) 2.21852e6 + 2.78193e6i 0.193396 + 0.242510i
\(105\) 1.48628e6 + 6.51181e6i 0.125296 + 0.548958i
\(106\) 4.36682e6 1.91323e7i 0.356119 1.56026i
\(107\) −493183. 618432.i −0.0389193 0.0488033i 0.761991 0.647588i \(-0.224222\pi\)
−0.800910 + 0.598784i \(0.795651\pi\)
\(108\) 1.13835e7 + 1.42745e7i 0.869548 + 1.09038i
\(109\) −3.39331e6 + 1.48671e7i −0.250975 + 1.09959i 0.679626 + 0.733559i \(0.262142\pi\)
−0.930601 + 0.366036i \(0.880715\pi\)
\(110\) −8.48272e6 3.71652e7i −0.607660 2.66233i
\(111\) 2.10609e7 + 2.64095e7i 1.46166 + 1.83286i
\(112\) 1.58660e6 764065.i 0.106710 0.0513887i
\(113\) 2.04499e7 9.84814e6i 1.33326 0.642066i 0.374753 0.927124i \(-0.377727\pi\)
0.958510 + 0.285059i \(0.0920131\pi\)
\(114\) 1.21359e7 + 5.31709e7i 0.767194 + 3.36130i
\(115\) −4.75271e6 + 5.95971e6i −0.291406 + 0.365412i
\(116\) −3.71030e6 1.78679e6i −0.220702 0.106284i
\(117\) −8.43952e6 + 1.05828e7i −0.487155 + 0.610873i
\(118\) −3.00898e6 + 1.31832e7i −0.168590 + 0.738643i
\(119\) −3.59317e6 + 1.73038e6i −0.195463 + 0.0941299i
\(120\) −5.36037e6 + 2.34853e7i −0.283179 + 1.24069i
\(121\) −1.82570e7 8.79209e6i −0.936870 0.451173i
\(122\) −1.08840e7 −0.542663
\(123\) 5.99470e7 2.90469
\(124\) −3.38393e7 1.62961e7i −1.59384 0.767554i
\(125\) −2.89696e6 1.26924e7i −0.132665 0.581245i
\(126\) −9.91521e6 1.24333e7i −0.441576 0.553718i
\(127\) 6.59493e6 8.26978e6i 0.285691 0.358246i −0.618190 0.786029i \(-0.712134\pi\)
0.903881 + 0.427783i \(0.140705\pi\)
\(128\) 2.77792e7 1.17081
\(129\) −3.21509e7 2.27736e7i −1.31865 0.934047i
\(130\) −2.32252e7 −0.927168
\(131\) −2.34077e6 + 2.93524e6i −0.0909724 + 0.114076i −0.825234 0.564790i \(-0.808957\pi\)
0.734262 + 0.678866i \(0.237528\pi\)
\(132\) 5.36861e7 + 6.73202e7i 2.03167 + 2.54763i
\(133\) −2.34752e6 1.02851e7i −0.0865223 0.379079i
\(134\) −1.50512e7 7.24830e6i −0.540388 0.260237i
\(135\) −3.47654e7 −1.21613
\(136\) −1.43835e7 −0.490317
\(137\) 7.67328e6 + 3.69525e6i 0.254952 + 0.122779i 0.556995 0.830516i \(-0.311954\pi\)
−0.302043 + 0.953294i \(0.597669\pi\)
\(138\) 6.54499e6 2.86755e7i 0.211998 0.928824i
\(139\) 2.21033e7 1.06444e7i 0.698081 0.336178i −0.0509612 0.998701i \(-0.516228\pi\)
0.749042 + 0.662523i \(0.230514\pi\)
\(140\) 3.55433e6 1.55725e7i 0.109474 0.479635i
\(141\) −4.51597e7 + 5.66285e7i −1.35670 + 1.70125i
\(142\) 6.40612e7 + 3.08502e7i 1.87753 + 0.904168i
\(143\) −1.50998e7 + 1.89346e7i −0.431813 + 0.541476i
\(144\) 5.37622e6 + 2.35548e7i 0.150041 + 0.657370i
\(145\) 7.06495e6 3.40230e6i 0.192451 0.0926798i
\(146\) 6.78534e7 3.26765e7i 1.80442 0.868961i
\(147\) −3.56948e7 4.47599e7i −0.926819 1.16219i
\(148\) −1.79753e7 7.87548e7i −0.455784 1.99692i
\(149\) −6.95222e6 + 3.04597e7i −0.172176 + 0.754350i 0.812925 + 0.582369i \(0.197874\pi\)
−0.985100 + 0.171981i \(0.944983\pi\)
\(150\) −3.33572e7 4.18286e7i −0.806993 1.01194i
\(151\) −3.02441e7 3.79250e7i −0.714862 0.896408i 0.283173 0.959069i \(-0.408613\pi\)
−0.998035 + 0.0626605i \(0.980041\pi\)
\(152\) 8.46649e6 3.70941e7i 0.195547 0.856747i
\(153\) −1.21755e7 5.33446e7i −0.274833 1.20412i
\(154\) −1.77401e7 2.22454e7i −0.391411 0.490814i
\(155\) 6.44349e7 3.10302e7i 1.38982 0.669304i
\(156\) 4.72648e7 2.27615e7i 0.996785 0.480027i
\(157\) 4.75302e6 + 2.08243e7i 0.0980213 + 0.429459i 0.999997 0.00232679i \(-0.000740640\pi\)
−0.901976 + 0.431786i \(0.857883\pi\)
\(158\) −8.39689e7 + 1.05294e8i −1.69363 + 2.12375i
\(159\) −7.60453e7 3.66215e7i −1.50032 0.722514i
\(160\) −5.12866e7 + 6.43113e7i −0.989883 + 1.24127i
\(161\) −1.26603e6 + 5.54685e6i −0.0239086 + 0.104750i
\(162\) −1.14026e6 + 549122.i −0.0210718 + 0.0101477i
\(163\) −3.44106e6 + 1.50763e7i −0.0622351 + 0.272670i −0.996466 0.0839995i \(-0.973231\pi\)
0.934231 + 0.356669i \(0.116088\pi\)
\(164\) −1.29162e8 6.22011e7i −2.28655 1.10114i
\(165\) −1.63958e8 −2.84144
\(166\) 9.69409e7 1.64486
\(167\) 2.53111e7 + 1.21892e7i 0.420536 + 0.202519i 0.632170 0.774829i \(-0.282164\pi\)
−0.211634 + 0.977349i \(0.567879\pi\)
\(168\) 4.00089e6 + 1.75291e7i 0.0650990 + 0.285217i
\(169\) −2.99235e7 3.75229e7i −0.476880 0.597988i
\(170\) 5.85354e7 7.34011e7i 0.913792 1.14586i
\(171\) 1.44739e8 2.21361
\(172\) 4.56424e7 + 8.24280e7i 0.683942 + 1.23516i
\(173\) 4.80780e7 0.705969 0.352984 0.935629i \(-0.385167\pi\)
0.352984 + 0.935629i \(0.385167\pi\)
\(174\) −1.88649e7 + 2.36558e7i −0.271476 + 0.340421i
\(175\) 6.45246e6 + 8.09113e6i 0.0910106 + 0.114124i
\(176\) 9.61903e6 + 4.21437e7i 0.132995 + 0.582691i
\(177\) 5.23995e7 + 2.52343e7i 0.710265 + 0.342046i
\(178\) −1.93998e8 −2.57827
\(179\) −5.17000e6 −0.0673759 −0.0336880 0.999432i \(-0.510725\pi\)
−0.0336880 + 0.999432i \(0.510725\pi\)
\(180\) 1.97445e8 + 9.50844e7i 2.52343 + 1.21522i
\(181\) −8.12507e6 + 3.55982e7i −0.101848 + 0.446225i 0.898131 + 0.439728i \(0.144925\pi\)
−0.999979 + 0.00649675i \(0.997932\pi\)
\(182\) −1.56182e7 + 7.52134e6i −0.192036 + 0.0924795i
\(183\) −1.04167e7 + 4.56384e7i −0.125646 + 0.550492i
\(184\) −1.27938e7 + 1.60429e7i −0.151403 + 0.189854i
\(185\) 1.38584e8 + 6.67387e7i 1.60921 + 0.774956i
\(186\) −1.72055e8 + 2.15750e8i −1.96052 + 2.45841i
\(187\) −2.17842e7 9.54430e7i −0.243611 1.06733i
\(188\) 1.56059e8 7.51540e7i 1.71292 0.824897i
\(189\) −2.33786e7 + 1.12586e7i −0.251885 + 0.121302i
\(190\) 1.54842e8 + 1.94165e8i 1.63776 + 2.05369i
\(191\) −7.37905e6 3.23297e7i −0.0766273 0.335726i 0.922054 0.387061i \(-0.126510\pi\)
−0.998682 + 0.0513347i \(0.983652\pi\)
\(192\) 5.58693e7 2.44779e8i 0.569664 2.49586i
\(193\) −4.96717e7 6.22863e7i −0.497346 0.623652i 0.468283 0.883579i \(-0.344873\pi\)
−0.965628 + 0.259927i \(0.916301\pi\)
\(194\) −1.66502e8 2.08787e8i −1.63724 2.05304i
\(195\) −2.22279e7 + 9.73869e7i −0.214673 + 0.940545i
\(196\) 3.04652e7 + 1.33477e8i 0.289007 + 1.26622i
\(197\) 2.28873e7 + 2.86998e7i 0.213287 + 0.267453i 0.876953 0.480575i \(-0.159572\pi\)
−0.663667 + 0.748028i \(0.731001\pi\)
\(198\) 3.51711e8 1.69375e8i 3.22001 1.55068i
\(199\) −7.85962e7 + 3.78499e7i −0.706994 + 0.340470i −0.752590 0.658490i \(-0.771196\pi\)
0.0455958 + 0.998960i \(0.485481\pi\)
\(200\) 8.30542e6 + 3.63884e7i 0.0734102 + 0.321631i
\(201\) −4.47981e7 + 5.61751e7i −0.389111 + 0.487930i
\(202\) −1.76823e8 8.51536e7i −1.50942 0.726898i
\(203\) 3.64914e6 4.57588e6i 0.0306164 0.0383918i
\(204\) −4.71876e7 + 2.06743e8i −0.389155 + 1.70500i
\(205\) 2.45943e8 1.18440e8i 1.99387 0.960195i
\(206\) −1.01132e7 + 4.43090e7i −0.0806038 + 0.353148i
\(207\) −7.03288e7 3.38686e7i −0.551108 0.265400i
\(208\) 2.63364e7 0.202924
\(209\) 2.58965e8 1.96213
\(210\) −1.05736e8 5.09197e7i −0.787870 0.379418i
\(211\) 1.82677e6 + 8.00360e6i 0.0133874 + 0.0586539i 0.981180 0.193093i \(-0.0618520\pi\)
−0.967793 + 0.251747i \(0.918995\pi\)
\(212\) 1.25849e8 + 1.57809e8i 0.907139 + 1.13752i
\(213\) 1.90670e8 2.39093e8i 1.35193 1.69527i
\(214\) 1.38983e7 0.0969424
\(215\) −1.76900e8 2.99109e7i −1.21393 0.205256i
\(216\) −9.35845e7 −0.631853
\(217\) 3.32815e7 4.17337e7i 0.221102 0.277254i
\(218\) −1.67057e8 2.09483e8i −1.09211 1.36947i
\(219\) −7.20777e7 3.15793e8i −0.463710 2.03165i
\(220\) 3.53264e8 + 1.70123e8i 2.23676 + 1.07717i
\(221\) −5.96440e7 −0.371701
\(222\) −5.93513e8 −3.64078
\(223\) 2.14054e8 + 1.03083e8i 1.29257 + 0.622471i 0.948591 0.316504i \(-0.102509\pi\)
0.343984 + 0.938976i \(0.388224\pi\)
\(224\) −1.36618e7 + 5.98561e7i −0.0812155 + 0.355828i
\(225\) −1.27925e8 + 6.16054e7i −0.748714 + 0.360562i
\(226\) −8.87431e7 + 3.88809e8i −0.511393 + 2.24056i
\(227\) 3.73396e7 4.68223e7i 0.211875 0.265682i −0.664526 0.747265i \(-0.731367\pi\)
0.876401 + 0.481583i \(0.159938\pi\)
\(228\) −5.05401e8 2.43388e8i −2.82400 1.35997i
\(229\) 1.31020e8 1.64294e8i 0.720963 0.904060i −0.277429 0.960746i \(-0.589482\pi\)
0.998392 + 0.0566867i \(0.0180536\pi\)
\(230\) −2.98034e7 1.30577e8i −0.161517 0.707653i
\(231\) −1.10257e8 + 5.30967e7i −0.588521 + 0.283417i
\(232\) 1.90181e7 9.15861e6i 0.0999903 0.0481528i
\(233\) −8.99594e7 1.12806e8i −0.465909 0.584231i 0.492255 0.870451i \(-0.336173\pi\)
−0.958164 + 0.286220i \(0.907601\pi\)
\(234\) −5.29227e7 2.31870e8i −0.270014 1.18301i
\(235\) −7.33922e7 + 3.21552e8i −0.368903 + 1.61627i
\(236\) −8.67169e7 1.08740e8i −0.429449 0.538512i
\(237\) 3.61149e8 + 4.52867e8i 1.76225 + 2.20979i
\(238\) 1.55927e7 6.83162e7i 0.0749726 0.328477i
\(239\) 2.31598e7 + 1.01470e8i 0.109734 + 0.480776i 0.999694 + 0.0247377i \(0.00787504\pi\)
−0.889960 + 0.456039i \(0.849268\pi\)
\(240\) 1.11167e8 + 1.39399e8i 0.519082 + 0.650909i
\(241\) 2.04775e8 9.86146e7i 0.942363 0.453818i 0.101361 0.994850i \(-0.467680\pi\)
0.841002 + 0.541032i \(0.181966\pi\)
\(242\) 3.20783e8 1.54481e8i 1.45498 0.700682i
\(243\) 5.03766e7 + 2.20714e8i 0.225220 + 0.986752i
\(244\) 6.97982e7 8.75241e7i 0.307595 0.385712i
\(245\) −2.34878e8 1.13111e8i −1.02038 0.491389i
\(246\) −6.56719e8 + 8.23500e8i −2.81259 + 3.52688i
\(247\) 3.51081e7 1.53819e8i 0.148241 0.649486i
\(248\) 1.73451e8 8.35298e7i 0.722099 0.347745i
\(249\) 9.27782e7 4.06488e8i 0.380845 1.66859i
\(250\) 2.06094e8 + 9.92494e7i 0.834208 + 0.401733i
\(251\) −2.78225e8 −1.11055 −0.555275 0.831667i \(-0.687387\pi\)
−0.555275 + 0.831667i \(0.687387\pi\)
\(252\) 1.63568e8 0.643867
\(253\) −1.25831e8 6.05969e7i −0.488501 0.235250i
\(254\) 4.13556e7 + 1.81191e8i 0.158349 + 0.693774i
\(255\) −2.51760e8 3.15697e8i −0.950815 1.19228i
\(256\) −3.91717e7 + 4.91198e7i −0.145926 + 0.182985i
\(257\) 1.95245e8 0.717486 0.358743 0.933436i \(-0.383205\pi\)
0.358743 + 0.933436i \(0.383205\pi\)
\(258\) 6.65058e8 1.92176e8i 2.41096 0.696675i
\(259\) 1.14806e8 0.410598
\(260\) 1.48941e8 1.86766e8i 0.525542 0.659009i
\(261\) 5.00657e7 + 6.27804e7i 0.174300 + 0.218566i
\(262\) −1.46786e7 6.43110e7i −0.0504231 0.220918i
\(263\) −3.80514e8 1.83246e8i −1.28981 0.621139i −0.341916 0.939731i \(-0.611076\pi\)
−0.947892 + 0.318592i \(0.896790\pi\)
\(264\) −4.41356e8 −1.47630
\(265\) −3.84344e8 −1.26870
\(266\) 1.67005e8 + 8.04255e7i 0.544057 + 0.262004i
\(267\) −1.85668e8 + 8.13464e8i −0.596963 + 2.61546i
\(268\) 1.54809e8 7.45523e7i 0.491276 0.236586i
\(269\) 4.12149e7 1.80574e8i 0.129098 0.565617i −0.868459 0.495762i \(-0.834889\pi\)
0.997557 0.0698558i \(-0.0222539\pi\)
\(270\) 3.80855e8 4.77577e8i 1.17757 1.47662i
\(271\) −2.79382e8 1.34543e8i −0.852719 0.410648i −0.0441332 0.999026i \(-0.514053\pi\)
−0.808586 + 0.588378i \(0.799767\pi\)
\(272\) −6.63765e7 + 8.32335e7i −0.199997 + 0.250788i
\(273\) 1.65906e7 + 7.26880e7i 0.0493505 + 0.216219i
\(274\) −1.34823e8 + 6.49273e7i −0.395947 + 0.190678i
\(275\) −2.28880e8 + 1.10223e8i −0.663658 + 0.319601i
\(276\) 1.88622e8 + 2.36525e8i 0.540021 + 0.677165i
\(277\) 1.25167e8 + 5.48391e8i 0.353842 + 1.55028i 0.768224 + 0.640181i \(0.221140\pi\)
−0.414382 + 0.910103i \(0.636002\pi\)
\(278\) −9.59183e7 + 4.20245e8i −0.267759 + 1.17313i
\(279\) 4.56617e8 + 5.72579e8i 1.25874 + 1.57841i
\(280\) 5.10473e7 + 6.40113e7i 0.138970 + 0.174262i
\(281\) 1.11100e8 4.86762e8i 0.298705 1.30871i −0.573352 0.819309i \(-0.694357\pi\)
0.872057 0.489404i \(-0.162786\pi\)
\(282\) −2.83189e8 1.24073e9i −0.751976 3.29462i
\(283\) −3.88386e8 4.87020e8i −1.01862 1.27731i −0.960289 0.279008i \(-0.909995\pi\)
−0.0583279 0.998297i \(-0.518577\pi\)
\(284\) −6.58901e8 + 3.17310e8i −1.70689 + 0.821996i
\(285\) 9.62358e8 4.63447e8i 2.46252 1.18589i
\(286\) −9.46882e7 4.14856e8i −0.239340 1.04862i
\(287\) 1.27033e8 1.59294e8i 0.317197 0.397753i
\(288\) −7.58919e8 3.65476e8i −1.87207 0.901540i
\(289\) −1.05519e8 + 1.32316e8i −0.257151 + 0.322457i
\(290\) −3.06587e7 + 1.34324e8i −0.0738177 + 0.323416i
\(291\) −1.03483e9 + 4.98346e8i −2.46174 + 1.18551i
\(292\) −1.72369e8 + 7.55196e8i −0.405152 + 1.77509i
\(293\) 2.65478e8 + 1.27848e8i 0.616584 + 0.296931i 0.715984 0.698116i \(-0.245978\pi\)
−0.0994004 + 0.995048i \(0.531692\pi\)
\(294\) 1.00591e9 2.30857
\(295\) 2.64834e8 0.600617
\(296\) 3.73053e8 + 1.79653e8i 0.836084 + 0.402637i
\(297\) −1.41737e8 6.20990e8i −0.313932 1.37543i
\(298\) −3.42267e8 4.29189e8i −0.749217 0.939489i
\(299\) −5.30520e7 + 6.65252e7i −0.114777 + 0.143925i
\(300\) 5.50281e8 1.17669
\(301\) −1.28646e8 + 3.71737e7i −0.271902 + 0.0785692i
\(302\) 8.52305e8 1.78062
\(303\) −5.26293e8 + 6.59950e8i −1.08687 + 1.36289i
\(304\) −1.75584e8 2.20175e8i −0.358448 0.449480i
\(305\) 4.74336e7 + 2.07820e8i 0.0957274 + 0.419409i
\(306\) 8.66185e8 + 4.17132e8i 1.72817 + 0.832241i
\(307\) 4.59149e8 0.905669 0.452834 0.891595i \(-0.350413\pi\)
0.452834 + 0.891595i \(0.350413\pi\)
\(308\) 2.92652e8 0.570721
\(309\) 1.76116e8 + 8.48128e7i 0.339581 + 0.163533i
\(310\) −2.79618e8 + 1.22509e9i −0.533088 + 2.33561i
\(311\) 1.35720e8 6.53592e7i 0.255848 0.123210i −0.301564 0.953446i \(-0.597509\pi\)
0.557412 + 0.830236i \(0.311794\pi\)
\(312\) −5.98350e7 + 2.62154e8i −0.111536 + 0.488671i
\(313\) 3.82874e8 4.80109e8i 0.705751 0.884983i −0.291688 0.956514i \(-0.594217\pi\)
0.997438 + 0.0715304i \(0.0227883\pi\)
\(314\) −3.38136e8 1.62838e8i −0.616364 0.296825i
\(315\) −1.94190e8 + 2.43507e8i −0.350058 + 0.438959i
\(316\) −3.08237e8 1.35048e9i −0.549516 2.40759i
\(317\) −7.70715e7 + 3.71157e7i −0.135890 + 0.0654410i −0.500593 0.865683i \(-0.666885\pi\)
0.364703 + 0.931124i \(0.381170\pi\)
\(318\) 1.33615e9 6.43456e8i 2.33002 1.12208i
\(319\) 8.95765e7 + 1.12325e8i 0.154499 + 0.193736i
\(320\) −2.54408e8 1.11463e9i −0.434016 1.90155i
\(321\) 1.33015e7 5.82777e7i 0.0224457 0.0983411i
\(322\) −6.23285e7 7.81574e7i −0.104038 0.130459i
\(323\) 3.97645e8 + 4.98631e8i 0.656578 + 0.823323i
\(324\) 2.89662e6 1.26909e7i 0.00473134 0.0207293i
\(325\) 3.44402e7 + 1.50892e8i 0.0556511 + 0.243823i
\(326\) −1.69408e8 2.12431e8i −0.270814 0.339591i
\(327\) −1.03828e9 + 5.00008e8i −1.64209 + 0.790788i
\(328\) 6.62051e8 3.18827e8i 1.03594 0.498880i
\(329\) 5.47787e7 + 2.40001e8i 0.0848059 + 0.371559i
\(330\) 1.79616e9 2.25231e9i 2.75135 3.45008i
\(331\) −5.00593e8 2.41073e8i −0.758729 0.365384i 0.0141820 0.999899i \(-0.495486\pi\)
−0.772911 + 0.634515i \(0.781200\pi\)
\(332\) −6.21672e8 + 7.79553e8i −0.932349 + 1.16913i
\(333\) −3.50499e8 + 1.53564e9i −0.520154 + 2.27894i
\(334\) −4.44727e8 + 2.14169e8i −0.653102 + 0.314517i
\(335\) −7.28046e7 + 3.18978e8i −0.105804 + 0.463557i
\(336\) 1.19900e8 + 5.77406e7i 0.172437 + 0.0830413i
\(337\) −8.18028e8 −1.16430 −0.582148 0.813083i \(-0.697788\pi\)
−0.582148 + 0.813083i \(0.697788\pi\)
\(338\) 8.43269e8 1.18784
\(339\) 1.54540e9 + 7.44227e8i 2.15448 + 1.03754i
\(340\) 2.14875e8 + 9.41428e8i 0.296489 + 1.29901i
\(341\) 8.16969e8 + 1.02445e9i 1.11575 + 1.39910i
\(342\) −1.58562e9 + 1.98831e9i −2.14342 + 2.68777i
\(343\) −4.06101e8 −0.543381
\(344\) −4.76194e8 8.05168e7i −0.630709 0.106643i
\(345\) −5.76054e8 −0.755260
\(346\) −5.26695e8 + 6.60454e8i −0.683585 + 0.857189i
\(347\) 9.80384e7 + 1.22936e8i 0.125963 + 0.157953i 0.840814 0.541324i \(-0.182077\pi\)
−0.714851 + 0.699277i \(0.753505\pi\)
\(348\) −6.92502e7 3.03405e8i −0.0880834 0.385918i
\(349\) 4.42605e8 + 2.13147e8i 0.557349 + 0.268405i 0.691282 0.722585i \(-0.257046\pi\)
−0.133933 + 0.990990i \(0.542761\pi\)
\(350\) −1.81836e8 −0.226694
\(351\) −3.88068e8 −0.478997
\(352\) −1.35784e9 6.53902e8i −1.65940 0.799123i
\(353\) −2.40205e8 + 1.05241e9i −0.290650 + 1.27342i 0.592974 + 0.805222i \(0.297954\pi\)
−0.883624 + 0.468198i \(0.844903\pi\)
\(354\) −9.20683e8 + 4.43377e8i −1.10306 + 0.531205i
\(355\) 3.09871e8 1.35763e9i 0.367606 1.61059i
\(356\) 1.24409e9 1.56004e9i 1.46143 1.83257i
\(357\) −2.71537e8 1.30765e8i −0.315857 0.152109i
\(358\) 5.66373e7 7.10210e7i 0.0652397 0.0818080i
\(359\) −3.19291e8 1.39891e9i −0.364214 1.59573i −0.742374 0.669985i \(-0.766300\pi\)
0.378161 0.925740i \(-0.376557\pi\)
\(360\) −1.01205e9 + 4.87378e8i −1.14326 + 0.550563i
\(361\) −7.14654e8 + 3.44159e8i −0.799504 + 0.385021i
\(362\) −4.00008e8 5.01594e8i −0.443188 0.555741i
\(363\) −3.40754e8 1.49294e9i −0.373910 1.63821i
\(364\) 3.96751e7 1.73828e8i 0.0431184 0.188914i
\(365\) −9.19637e8 1.15319e9i −0.989900 1.24130i
\(366\) −5.12826e8 6.43063e8i −0.546747 0.685599i
\(367\) 3.11506e8 1.36479e9i 0.328954 1.44124i −0.492175 0.870496i \(-0.663798\pi\)
0.821129 0.570743i \(-0.193345\pi\)
\(368\) 3.37957e7 + 1.48069e8i 0.0353504 + 0.154880i
\(369\) 1.74287e9 + 2.18549e9i 1.80581 + 2.26442i
\(370\) −2.43499e9 + 1.17263e9i −2.49914 + 1.20352i
\(371\) −2.58459e8 + 1.24467e8i −0.262774 + 0.126545i
\(372\) −6.31587e8 2.76716e9i −0.636111 2.78698i
\(373\) 1.00368e9 1.25857e9i 1.00141 1.25573i 0.0348261 0.999393i \(-0.488912\pi\)
0.966587 0.256339i \(-0.0825163\pi\)
\(374\) 1.54976e9 + 7.46325e8i 1.53184 + 0.737696i
\(375\) 6.13412e8 7.69194e8i 0.600679 0.753228i
\(376\) −1.97563e8 + 8.65582e8i −0.191668 + 0.839751i
\(377\) 7.88624e7 3.79781e7i 0.0758010 0.0365039i
\(378\) 1.01453e8 4.44493e8i 0.0966144 0.423295i
\(379\) −3.51497e8 1.69272e8i −0.331653 0.159716i 0.260645 0.965435i \(-0.416065\pi\)
−0.592298 + 0.805719i \(0.701779\pi\)
\(380\) −2.55437e9 −2.38804
\(381\) 7.99340e8 0.740448
\(382\) 5.24955e8 + 2.52805e8i 0.481837 + 0.232041i
\(383\) −2.75910e8 1.20884e9i −0.250941 1.09944i −0.930635 0.365948i \(-0.880745\pi\)
0.679694 0.733495i \(-0.262112\pi\)
\(384\) 1.30888e9 + 1.64129e9i 1.17962 + 1.47919i
\(385\) −3.47441e8 + 4.35677e8i −0.310290 + 0.389092i
\(386\) 1.39979e9 1.23882
\(387\) −1.04480e8 1.83424e9i −0.0916316 1.60867i
\(388\) 2.74672e9 2.38728
\(389\) 7.48557e8 9.38661e8i 0.644765 0.808510i −0.346825 0.937930i \(-0.612740\pi\)
0.991590 + 0.129420i \(0.0413116\pi\)
\(390\) −1.09431e9 1.37222e9i −0.934145 1.17138i
\(391\) −7.65373e7 3.35332e8i −0.0647522 0.283698i
\(392\) −6.32266e8 3.04483e8i −0.530150 0.255307i
\(393\) −2.83714e8 −0.235780
\(394\) −6.44984e8 −0.531266
\(395\) 2.37643e9 + 1.14443e9i 1.94015 + 0.934325i
\(396\) −8.93453e8 + 3.91447e9i −0.723000 + 3.16767i
\(397\) 1.45602e9 7.01185e8i 1.16789 0.562426i 0.253530 0.967328i \(-0.418408\pi\)
0.914360 + 0.404901i \(0.132694\pi\)
\(398\) 3.41072e8 1.49433e9i 0.271178 1.18811i
\(399\) 4.97071e8 6.23307e8i 0.391754 0.491243i
\(400\) 2.48899e8 + 1.19863e8i 0.194452 + 0.0936432i
\(401\) −1.20124e9 + 1.50630e9i −0.930299 + 1.16656i 0.0554709 + 0.998460i \(0.482334\pi\)
−0.985770 + 0.168098i \(0.946237\pi\)
\(402\) −2.80921e8 1.23080e9i −0.215672 0.944920i
\(403\) 7.19253e8 3.46374e8i 0.547412 0.263620i
\(404\) 1.81872e9 8.75847e8i 1.37224 0.660836i
\(405\) 1.54543e7 + 1.93791e7i 0.0115600 + 0.0144958i
\(406\) 2.28831e7 + 1.00258e8i 0.0169697 + 0.0743491i
\(407\) −6.27105e8 + 2.74753e9i −0.461063 + 2.02005i
\(408\) −6.77709e8 8.49821e8i −0.494007 0.619465i
\(409\) −1.11619e9 1.39966e9i −0.806688 1.01156i −0.999540 0.0303274i \(-0.990345\pi\)
0.192852 0.981228i \(-0.438226\pi\)
\(410\) −1.06728e9 + 4.67606e9i −0.764777 + 3.35071i
\(411\) 1.43216e8 + 6.27472e8i 0.101753 + 0.445808i
\(412\) −2.91457e8 3.65475e8i −0.205321 0.257465i
\(413\) 1.78093e8 8.57649e7i 0.124400 0.0599080i
\(414\) 1.23571e9 5.95086e8i 0.855884 0.412172i
\(415\) −4.22477e8 1.85099e9i −0.290158 1.27127i
\(416\) −5.72485e8 + 7.17874e8i −0.389886 + 0.488902i
\(417\) 1.67035e9 + 8.04400e8i 1.12806 + 0.543245i
\(418\) −2.83696e9 + 3.55743e9i −1.89992 + 2.38243i
\(419\) −2.47000e8 + 1.08218e9i −0.164039 + 0.718702i 0.824265 + 0.566205i \(0.191589\pi\)
−0.988304 + 0.152498i \(0.951268\pi\)
\(420\) 1.08755e9 5.23734e8i 0.716267 0.344936i
\(421\) −3.25572e8 + 1.42642e9i −0.212647 + 0.931667i 0.750113 + 0.661310i \(0.229999\pi\)
−0.962760 + 0.270357i \(0.912858\pi\)
\(422\) −1.29959e8 6.25849e7i −0.0841807 0.0405393i
\(423\) −3.37746e9 −2.16970
\(424\) −1.03461e9 −0.659168
\(425\) −5.63681e8 2.71455e8i −0.356182 0.171528i
\(426\) 1.19566e9 + 5.23852e9i 0.749331 + 3.28303i
\(427\) 9.91987e7 + 1.24391e8i 0.0616607 + 0.0773201i
\(428\) −8.91285e7 + 1.11764e8i −0.0549495 + 0.0689044i
\(429\) −1.83018e9 −1.11916
\(430\) 2.34882e9 2.10242e9i 1.42466 1.27520i
\(431\) −1.79610e9 −1.08059 −0.540294 0.841476i \(-0.681687\pi\)
−0.540294 + 0.841476i \(0.681687\pi\)
\(432\) −4.31872e8 + 5.41551e8i −0.257728 + 0.323181i
\(433\) −1.37232e9 1.72083e9i −0.812359 1.01867i −0.999341 0.0363022i \(-0.988442\pi\)
0.186982 0.982363i \(-0.440129\pi\)
\(434\) 2.08702e8 + 9.14384e8i 0.122550 + 0.536926i
\(435\) 5.33900e8 + 2.57113e8i 0.310991 + 0.149765i
\(436\) 2.75588e9 1.59242
\(437\) 9.09854e8 0.521539
\(438\) 5.12770e9 + 2.46937e9i 2.91584 + 1.40419i
\(439\) 5.29887e8 2.32159e9i 0.298922 1.30966i −0.572814 0.819686i \(-0.694148\pi\)
0.871735 0.489977i \(-0.162995\pi\)
\(440\) −1.81074e9 + 8.72007e8i −1.01338 + 0.488018i
\(441\) 5.94040e8 2.60266e9i 0.329823 1.44505i
\(442\) 6.53400e8 8.19338e8i 0.359916 0.451321i
\(443\) 2.44610e9 + 1.17798e9i 1.33679 + 0.643762i 0.959336 0.282268i \(-0.0910867\pi\)
0.377450 + 0.926030i \(0.376801\pi\)
\(444\) 3.80614e9 4.77275e9i 2.06369 2.58778i
\(445\) 8.45461e8 + 3.70421e9i 0.454814 + 1.99267i
\(446\) −3.76102e9 + 1.81121e9i −2.00740 + 0.966712i
\(447\) −2.12722e9 + 1.02442e9i −1.12652 + 0.542501i
\(448\) −5.32048e8 6.67167e8i −0.279562 0.350560i
\(449\) −5.75429e8 2.52112e9i −0.300006 1.31441i −0.870117 0.492844i \(-0.835957\pi\)
0.570112 0.821567i \(-0.306900\pi\)
\(450\) 5.55135e8 2.43221e9i 0.287181 1.25822i
\(451\) 3.11831e9 + 3.91024e9i 1.60067 + 2.00717i
\(452\) −2.55752e9 3.20702e9i −1.30267 1.63349i
\(453\) 8.15706e8 3.57384e9i 0.412278 1.80631i
\(454\) 2.34150e8 + 1.02588e9i 0.117435 + 0.514517i
\(455\) 2.11678e8 + 2.65436e8i 0.105351 + 0.132105i
\(456\) 2.59056e9 1.24755e9i 1.27943 0.616141i
\(457\) 1.92142e9 9.25307e8i 0.941706 0.453502i 0.100935 0.994893i \(-0.467817\pi\)
0.840771 + 0.541391i \(0.182102\pi\)
\(458\) 8.21603e8 + 3.59968e9i 0.399607 + 1.75079i
\(459\) 9.78063e8 1.22645e9i 0.472087 0.591979i
\(460\) 1.24117e9 + 5.97714e8i 0.594535 + 0.286313i
\(461\) 4.72622e8 5.92649e8i 0.224678 0.281737i −0.656697 0.754155i \(-0.728047\pi\)
0.881375 + 0.472417i \(0.156618\pi\)
\(462\) 4.78463e8 2.09628e9i 0.225736 0.989015i
\(463\) −7.70801e8 + 3.71198e8i −0.360918 + 0.173809i −0.605550 0.795807i \(-0.707047\pi\)
0.244632 + 0.969616i \(0.421333\pi\)
\(464\) 3.47656e7 1.52318e8i 0.0161561 0.0707844i
\(465\) 4.86936e9 + 2.34496e9i 2.24588 + 1.08156i
\(466\) 2.53513e9 1.16051
\(467\) −2.15456e9 −0.978926 −0.489463 0.872024i \(-0.662807\pi\)
−0.489463 + 0.872024i \(0.662807\pi\)
\(468\) 2.20397e9 + 1.06138e9i 0.993907 + 0.478640i
\(469\) 5.43401e7 + 2.38080e8i 0.0243229 + 0.106566i
\(470\) −3.61319e9 4.53080e9i −1.60527 2.01295i
\(471\) −1.00642e9 + 1.26201e9i −0.443819 + 0.556531i
\(472\) 7.12904e8 0.312057
\(473\) −1.86934e8 3.28178e9i −0.0812220 1.42592i
\(474\) −1.01775e10 −4.38951
\(475\) 1.03186e9 1.29392e9i 0.441769 0.553960i
\(476\) 4.49372e8 + 5.63495e8i 0.190977 + 0.239478i
\(477\) −8.75794e8 3.83711e9i −0.369477 1.61879i
\(478\) −1.64762e9 7.93450e8i −0.690015 0.332294i
\(479\) −2.45987e9 −1.02268 −0.511338 0.859379i \(-0.670850\pi\)
−0.511338 + 0.859379i \(0.670850\pi\)
\(480\) −6.21620e9 −2.56555
\(481\) 1.54694e9 + 7.44969e8i 0.633822 + 0.305232i
\(482\) −8.88632e8 + 3.89335e9i −0.361457 + 1.58365i
\(483\) −3.87378e8 + 1.86551e8i −0.156430 + 0.0753327i
\(484\) −8.14887e8 + 3.57025e9i −0.326692 + 1.43133i
\(485\) −3.26095e9 + 4.08911e9i −1.29792 + 1.62754i
\(486\) −3.58385e9 1.72589e9i −1.41620 0.682004i
\(487\) −3.74027e8 + 4.69015e8i −0.146741 + 0.184007i −0.849770 0.527154i \(-0.823259\pi\)
0.703029 + 0.711161i \(0.251830\pi\)
\(488\) 1.27686e8 + 5.59428e8i 0.0497362 + 0.217909i
\(489\) −1.05289e9 + 5.07044e8i −0.407194 + 0.196094i
\(490\) 4.12692e9 1.98742e9i 1.58467 0.763138i
\(491\) 9.41078e8 + 1.18007e9i 0.358790 + 0.449908i 0.928165 0.372170i \(-0.121386\pi\)
−0.569375 + 0.822078i \(0.692815\pi\)
\(492\) −2.41072e9 1.05620e10i −0.912575 3.99825i
\(493\) −7.87337e7 + 3.44955e8i −0.0295935 + 0.129658i
\(494\) 1.72842e9 + 2.16737e9i 0.645066 + 0.808887i
\(495\) −4.76684e9 5.97742e9i −1.76649 2.21511i
\(496\) 3.17074e8 1.38919e9i 0.116674 0.511183i
\(497\) −2.31283e8 1.01332e9i −0.0845076 0.370252i
\(498\) 4.56759e9 + 5.72758e9i 1.65724 + 2.07811i
\(499\) 2.82058e8 1.35832e8i 0.101622 0.0489385i −0.382382 0.924004i \(-0.624896\pi\)
0.484004 + 0.875066i \(0.339182\pi\)
\(500\) −2.11977e9 + 1.02083e9i −0.758393 + 0.365223i
\(501\) 4.72414e8 + 2.06978e9i 0.167838 + 0.735347i
\(502\) 3.04795e9 3.82201e9i 1.07534 1.34843i
\(503\) −1.52440e9 7.34113e8i −0.534086 0.257202i 0.147344 0.989085i \(-0.452928\pi\)
−0.681430 + 0.731883i \(0.738642\pi\)
\(504\) −5.22738e8 + 6.55492e8i −0.181877 + 0.228066i
\(505\) −8.55315e8 + 3.74738e9i −0.295533 + 1.29481i
\(506\) 2.21090e9 1.06472e9i 0.758653 0.365348i
\(507\) 8.07058e8 3.53595e9i 0.275028 1.20498i
\(508\) −1.72226e9 8.29397e8i −0.582875 0.280698i
\(509\) 1.88174e9 0.632481 0.316240 0.948679i \(-0.397579\pi\)
0.316240 + 0.948679i \(0.397579\pi\)
\(510\) 7.09480e9 2.36834
\(511\) −9.91879e8 4.77664e8i −0.328841 0.158361i
\(512\) 5.45588e8 + 2.39038e9i 0.179647 + 0.787084i
\(513\) 2.58724e9 + 3.24429e9i 0.846107 + 1.06098i
\(514\) −2.13891e9 + 2.68210e9i −0.694737 + 0.871173i
\(515\) 8.90113e8 0.287157
\(516\) −2.71956e9 + 6.58048e9i −0.871415 + 2.10855i
\(517\) −6.04288e9 −1.92321
\(518\) −1.25770e9 + 1.57711e9i −0.397580 + 0.498550i
\(519\) 2.26531e9 + 2.84061e9i 0.711281 + 0.891918i
\(520\) 2.72466e8 + 1.19375e9i 0.0849769 + 0.372308i
\(521\) 1.20539e9 + 5.80486e8i 0.373419 + 0.179829i 0.611174 0.791496i \(-0.290697\pi\)
−0.237756 + 0.971325i \(0.576412\pi\)
\(522\) −1.41089e9 −0.434157
\(523\) −4.18576e9 −1.27943 −0.639717 0.768610i \(-0.720949\pi\)
−0.639717 + 0.768610i \(0.720949\pi\)
\(524\) 6.11291e8 + 2.94382e8i 0.185604 + 0.0893824i
\(525\) −1.74027e8 + 7.62464e8i −0.0524880 + 0.229965i
\(526\) 6.68580e9 3.21971e9i 2.00310 0.964643i
\(527\) −7.18079e8 + 3.14611e9i −0.213715 + 0.936347i
\(528\) −2.03676e9 + 2.55402e9i −0.602174 + 0.755102i
\(529\) 2.62554e9 + 1.26440e9i 0.771125 + 0.371354i
\(530\) 4.21049e9 5.27978e9i 1.22848 1.54046i
\(531\) 6.03471e8 + 2.64398e9i 0.174914 + 0.766350i
\(532\) −1.71773e9 + 8.27216e8i −0.494612 + 0.238193i
\(533\) 2.74533e9 1.32208e9i 0.785326 0.378193i
\(534\) −9.14067e9 1.14620e10i −2.59767 3.25737i
\(535\) −6.05701e7 2.65375e8i −0.0171009 0.0749241i
\(536\) −1.95982e8 + 8.58652e8i −0.0549716 + 0.240846i
\(537\) −2.43596e8 3.05460e8i −0.0678830 0.0851225i
\(538\) 2.02906e9 + 2.54436e9i 0.561769 + 0.704436i
\(539\) 1.06284e9 4.65662e9i 0.292354 1.28088i
\(540\) 1.39806e9 + 6.12531e9i 0.382075 + 1.67398i
\(541\) −1.80760e9 2.26666e9i −0.490809 0.615455i 0.473320 0.880891i \(-0.343056\pi\)
−0.964129 + 0.265436i \(0.914484\pi\)
\(542\) 4.90887e9 2.36399e9i 1.32429 0.637746i
\(543\) −2.48609e9 + 1.19724e9i −0.666373 + 0.320908i
\(544\) −8.25915e8 3.61857e9i −0.219958 0.963697i
\(545\) −3.27183e9 + 4.10274e9i −0.865770 + 1.08564i
\(546\) −1.18027e9 5.68390e8i −0.310319 0.149442i
\(547\) 2.22663e9 2.79210e9i 0.581691 0.729417i −0.400710 0.916205i \(-0.631236\pi\)
0.982400 + 0.186788i \(0.0598078\pi\)
\(548\) 3.42492e8 1.50055e9i 0.0889033 0.389511i
\(549\) −1.96669e9 + 9.47108e8i −0.507262 + 0.244285i
\(550\) 9.93237e8 4.35165e9i 0.254556 1.11528i
\(551\) −8.43274e8 4.06099e8i −0.214752 0.103419i
\(552\) −1.55067e9 −0.392404
\(553\) 1.96869e9 0.495038
\(554\) −8.90452e9 4.28819e9i −2.22498 1.07149i
\(555\) 2.58658e9 + 1.13326e10i 0.642245 + 2.81386i
\(556\) −2.76430e9 3.46632e9i −0.682061 0.855278i
\(557\) 9.35809e8 1.17347e9i 0.229453 0.287725i −0.653755 0.756706i \(-0.726807\pi\)
0.883208 + 0.468981i \(0.155379\pi\)
\(558\) −1.28678e10 −3.13535
\(559\) −1.97464e9 3.33880e8i −0.478130 0.0808442i
\(560\) 6.05990e8 0.145817
\(561\) 4.61266e9 5.78410e9i 1.10302 1.38314i
\(562\) 5.46961e9 + 6.85867e9i 1.29981 + 1.62991i
\(563\) 2.88886e8 + 1.26569e9i 0.0682256 + 0.298916i 0.997517 0.0704327i \(-0.0224380\pi\)
−0.929291 + 0.369349i \(0.879581\pi\)
\(564\) 1.17934e10 + 5.67941e9i 2.76798 + 1.33299i
\(565\) 7.81068e9 1.82188
\(566\) 1.09450e10 2.53723
\(567\) 1.66683e7 + 8.02705e6i 0.00384018 + 0.00184933i
\(568\) 8.34138e8 3.65460e9i 0.190994 0.836798i
\(569\) −1.06655e9 + 5.13622e8i −0.242710 + 0.116883i −0.551285 0.834317i \(-0.685862\pi\)
0.308575 + 0.951200i \(0.400148\pi\)
\(570\) −4.17619e9 + 1.82971e10i −0.944536 + 4.13828i
\(571\) 1.50827e8 1.89131e8i 0.0339041 0.0425145i −0.764590 0.644517i \(-0.777059\pi\)
0.798495 + 0.602002i \(0.205630\pi\)
\(572\) 3.94330e9 + 1.89899e9i 0.880996 + 0.424265i
\(573\) 1.56246e9 1.95927e9i 0.346951 0.435063i
\(574\) 7.96600e8 + 3.49013e9i 0.175812 + 0.770283i
\(575\) −8.04154e8 + 3.87260e8i −0.176401 + 0.0849504i
\(576\) 1.05483e10 5.07977e9i 2.29986 1.10756i
\(577\) 3.77662e9 + 4.73573e9i 0.818441 + 1.02629i 0.999086 + 0.0427446i \(0.0136102\pi\)
−0.180645 + 0.983548i \(0.557818\pi\)
\(578\) −6.61690e8 2.89905e9i −0.142530 0.624466i
\(579\) 1.33968e9 5.86953e9i 0.286831 1.25669i
\(580\) −8.83562e8 1.10795e9i −0.188035 0.235789i
\(581\) −8.83535e8 1.10792e9i −0.186899 0.234364i
\(582\) 4.49068e9 1.96749e10i 0.944238 4.13698i
\(583\) −1.56695e9 6.86527e9i −0.327503 1.43489i
\(584\) −2.47556e9 3.10425e9i −0.514314 0.644929i
\(585\) −4.19668e9 + 2.02102e9i −0.866684 + 0.417373i
\(586\) −4.66457e9 + 2.24634e9i −0.957569 + 0.461141i
\(587\) −7.12958e7 3.12368e8i −0.0145489 0.0637430i 0.967132 0.254273i \(-0.0818363\pi\)
−0.981681 + 0.190530i \(0.938979\pi\)
\(588\) −6.45080e9 + 8.08905e9i −1.30856 + 1.64088i
\(589\) −7.69096e9 3.70377e9i −1.55088 0.746862i
\(590\) −2.90126e9 + 3.63807e9i −0.581574 + 0.729270i
\(591\) −6.17288e8 + 2.70452e9i −0.123008 + 0.538931i
\(592\) 2.76117e9 1.32971e9i 0.546974 0.263409i
\(593\) −7.18415e8 + 3.14758e9i −0.141476 + 0.619849i 0.853616 + 0.520902i \(0.174404\pi\)
−0.995093 + 0.0989465i \(0.968453\pi\)
\(594\) 1.00834e10 + 4.85589e9i 1.97402 + 0.950640i
\(595\) −1.37239e9 −0.267096
\(596\) 5.64626e9 1.09244
\(597\) −5.93954e9 2.86033e9i −1.14246 0.550182i
\(598\) −3.32680e8 1.45757e9i −0.0636169 0.278724i
\(599\) −4.67526e9 5.86260e9i −0.888817 1.11454i −0.992779 0.119960i \(-0.961723\pi\)
0.103962 0.994581i \(-0.466848\pi\)
\(600\) −1.75862e9 + 2.20523e9i −0.332385 + 0.416798i
\(601\) 6.67072e9 1.25346 0.626732 0.779235i \(-0.284392\pi\)
0.626732 + 0.779235i \(0.284392\pi\)
\(602\) 8.98655e8 2.17446e9i 0.167882 0.406223i
\(603\) −3.35042e9 −0.622284
\(604\) −5.46575e9 + 6.85383e9i −1.00930 + 1.26562i
\(605\) −4.34767e9 5.45180e9i −0.798201 1.00091i
\(606\) −3.30029e9 1.44595e10i −0.602417 2.63936i
\(607\) −2.42378e9 1.16723e9i −0.439878 0.211834i 0.200818 0.979629i \(-0.435640\pi\)
−0.640696 + 0.767794i \(0.721354\pi\)
\(608\) 9.81824e9 1.77162
\(609\) 4.42295e8 0.0793509
\(610\) −3.37449e9 1.62507e9i −0.601940 0.289879i
\(611\) −8.19239e8 + 3.58932e9i −0.145300 + 0.636602i
\(612\) −8.90914e9 + 4.29041e9i −1.57111 + 0.756605i
\(613\) 6.95880e8 3.04885e9i 0.122018 0.534594i −0.876561 0.481291i \(-0.840168\pi\)
0.998578 0.0533029i \(-0.0169749\pi\)
\(614\) −5.02998e9 + 6.30739e9i −0.876954 + 1.09967i
\(615\) 1.85860e10 + 8.95054e9i 3.22198 + 1.55162i
\(616\) −9.35272e8 + 1.17279e9i −0.161215 + 0.202157i
\(617\) 1.01274e9 + 4.43710e9i 0.173580 + 0.760503i 0.984506 + 0.175354i \(0.0561068\pi\)
−0.810926 + 0.585149i \(0.801036\pi\)
\(618\) −3.09443e9 + 1.49020e9i −0.527377 + 0.253971i
\(619\) −3.64811e9 + 1.75684e9i −0.618232 + 0.297725i −0.716663 0.697419i \(-0.754332\pi\)
0.0984319 + 0.995144i \(0.468617\pi\)
\(620\) −8.05840e9 1.01049e10i −1.35793 1.70279i
\(621\) −4.97982e8 2.18180e9i −0.0834437 0.365591i
\(622\) −5.88962e8 + 2.58041e9i −0.0981343 + 0.429954i
\(623\) 1.76813e9 + 2.21716e9i 0.292958 + 0.367358i
\(624\) 1.24090e9 + 1.55604e9i 0.204451 + 0.256374i
\(625\) 1.69736e9 7.43663e9i 0.278096 1.21842i
\(626\) 2.40094e9 + 1.05192e10i 0.391175 + 1.71385i
\(627\) 1.22017e10 + 1.53005e10i 1.97690 + 2.47895i
\(628\) 3.47789e9 1.67487e9i 0.560348 0.269849i
\(629\) −6.25323e9 + 3.01140e9i −1.00191 + 0.482493i
\(630\) −1.21773e9 5.33523e9i −0.194026 0.850083i
\(631\) −1.80948e9 + 2.26902e9i −0.286716 + 0.359530i −0.904242 0.427020i \(-0.859563\pi\)
0.617527 + 0.786550i \(0.288135\pi\)
\(632\) 6.39707e9 + 3.08067e9i 1.00802 + 0.485439i
\(633\) −3.86806e8 + 4.85040e8i −0.0606151 + 0.0760089i
\(634\) 3.34455e8 1.46534e9i 0.0521225 0.228364i
\(635\) 3.27943e9 1.57929e9i 0.508266 0.244768i
\(636\) −3.39423e9 + 1.48711e10i −0.523169 + 2.29215i
\(637\) −2.62182e9 1.26260e9i −0.401898 0.193544i
\(638\) −2.52434e9 −0.384836
\(639\) 1.42601e10 2.16206
\(640\) 8.61267e9 + 4.14764e9i 1.29870 + 0.625420i
\(641\) −2.90022e9 1.27067e10i −0.434939 1.90559i −0.424023 0.905652i \(-0.639382\pi\)
−0.0109163 0.999940i \(-0.503475\pi\)
\(642\) 6.54851e8 + 8.21157e8i 0.0976719 + 0.122477i
\(643\) −7.64149e9 + 9.58212e9i −1.13355 + 1.42142i −0.240968 + 0.970533i \(0.577465\pi\)
−0.892580 + 0.450890i \(0.851107\pi\)
\(644\) 1.02821e9 0.151699
\(645\) −6.56780e9 1.18611e10i −0.963742 1.74047i
\(646\) −1.12060e10 −1.63544
\(647\) −1.13724e9 + 1.42605e9i −0.165077 + 0.207000i −0.857489 0.514502i \(-0.827977\pi\)
0.692412 + 0.721502i \(0.256548\pi\)
\(648\) 4.16013e7 + 5.21663e7i 0.00600612 + 0.00753144i
\(649\) 1.07972e9 + 4.73055e9i 0.155044 + 0.679290i
\(650\) −2.45012e9 1.17992e9i −0.349938 0.168521i
\(651\) 4.03389e9 0.573048
\(652\) 2.79466e9 0.394878
\(653\) 8.72606e9 + 4.20225e9i 1.22637 + 0.590589i 0.931079 0.364818i \(-0.118869\pi\)
0.295292 + 0.955407i \(0.404583\pi\)
\(654\) 4.50565e9 1.97406e10i 0.629848 2.75954i
\(655\) −1.16399e9 + 5.60546e8i −0.161847 + 0.0779412i
\(656\) 1.21025e9 5.30244e9i 0.167383 0.733352i
\(657\) 9.41733e9 1.18090e10i 1.29553 1.62455i
\(658\) −3.89703e9 1.87671e9i −0.533265 0.256807i
\(659\) −1.42671e9 + 1.78904e9i −0.194194 + 0.243512i −0.869390 0.494127i \(-0.835488\pi\)
0.675196 + 0.737639i \(0.264059\pi\)
\(660\) 6.59343e9 + 2.88877e10i 0.892704 + 3.91119i
\(661\) −4.59589e9 + 2.21326e9i −0.618962 + 0.298076i −0.716964 0.697110i \(-0.754469\pi\)
0.0980023 + 0.995186i \(0.468755\pi\)
\(662\) 8.79564e9 4.23576e9i 1.17832 0.567450i
\(663\) −2.81027e9 3.52396e9i −0.374498 0.469606i
\(664\) −1.13726e9 4.98266e9i −0.150755 0.660501i
\(665\) 8.07824e8 3.53931e9i 0.106522 0.466705i
\(666\) −1.72555e10 2.16377e10i −2.26344 2.83826i
\(667\) 3.14720e8 + 3.94647e8i 0.0410662 + 0.0514954i
\(668\) 1.12974e9 4.94973e9i 0.146643 0.642487i
\(669\) 3.99517e9 + 1.75040e10i 0.515874 + 2.26019i
\(670\) −3.58427e9 4.49453e9i −0.460403 0.577327i
\(671\) −3.51876e9 + 1.69455e9i −0.449636 + 0.216533i
\(672\) −4.18020e9 + 2.01308e9i −0.531379 + 0.255899i
\(673\) 2.54583e9 + 1.11540e10i 0.321941 + 1.41052i 0.834094 + 0.551622i \(0.185991\pi\)
−0.512153 + 0.858894i \(0.671152\pi\)
\(674\) 8.96149e9 1.12374e10i 1.12738 1.41369i
\(675\) −3.66754e9 1.76619e9i −0.458999 0.221042i
\(676\) −5.40780e9 + 6.78117e9i −0.673298 + 0.844289i
\(677\) 3.41048e8 1.49423e9i 0.0422430 0.185079i −0.949405 0.314056i \(-0.898312\pi\)
0.991648 + 0.128977i \(0.0411693\pi\)
\(678\) −2.71534e10 + 1.30764e10i −3.34596 + 1.61133i
\(679\) −8.68656e8 + 3.80583e9i −0.106489 + 0.466558i
\(680\) −4.45945e9 2.14756e9i −0.543876 0.261917i
\(681\) 4.52575e9 0.549131
\(682\) −2.30229e10 −2.77916
\(683\) −8.15773e9 3.92856e9i −0.979708 0.471803i −0.125704 0.992068i \(-0.540119\pi\)
−0.854005 + 0.520265i \(0.825833\pi\)
\(684\) −5.82058e9 2.55016e10i −0.695456 3.04699i
\(685\) 1.82729e9 + 2.29135e9i 0.217216 + 0.272380i
\(686\) 4.44884e9 5.57866e9i 0.526153 0.659775i
\(687\) 1.58803e10 1.86857
\(688\) −2.66346e9 + 2.38405e9i −0.311808 + 0.279097i
\(689\) −4.29023e9 −0.499705
\(690\) 6.31067e9 7.91333e9i 0.731314 0.917038i
\(691\) −6.73989e8 8.45156e8i −0.0777105 0.0974459i 0.741457 0.671001i \(-0.234135\pi\)
−0.819167 + 0.573555i \(0.805564\pi\)
\(692\) −1.93342e9 8.47086e9i −0.221796 0.971753i
\(693\) −5.14130e9 2.47592e9i −0.586822 0.282599i
\(694\) −2.76280e9 −0.313756
\(695\) 8.44220e9 0.953913
\(696\) 1.43720e9 + 6.92119e8i 0.161579 + 0.0778123i
\(697\) −2.74085e9 + 1.20085e10i −0.306599 + 1.34330i
\(698\) −7.77677e9 + 3.74510e9i −0.865576 + 0.416840i
\(699\) 2.42627e9 1.06302e10i 0.268701 1.17725i
\(700\) 1.16609e9 1.46223e9i 0.128496 0.161129i
\(701\) −7.71945e9 3.71749e9i −0.846395 0.407603i −0.0401570 0.999193i \(-0.512786\pi\)
−0.806238 + 0.591591i \(0.798500\pi\)
\(702\) 4.25128e9 5.33094e9i 0.463810 0.581600i
\(703\) −4.08540e9 1.78993e10i −0.443497 1.94309i
\(704\) 1.88727e10 9.08862e9i 2.03859 0.981734i
\(705\) −2.24564e10 + 1.08144e10i −2.41367 + 1.16236i
\(706\) −1.18256e10 1.48288e10i −1.26475 1.58595i
\(707\) 6.38393e8 + 2.79698e9i 0.0679391 + 0.297661i
\(708\) 2.33882e9 1.02470e10i 0.247674 1.08513i
\(709\) −9.07992e8 1.13859e9i −0.0956798 0.119979i 0.731687 0.681641i \(-0.238733\pi\)
−0.827367 + 0.561662i \(0.810162\pi\)
\(710\) 1.52554e10 + 1.91296e10i 1.59963 + 2.00587i
\(711\) −6.01031e9 + 2.63329e10i −0.627123 + 2.74761i
\(712\) 2.27589e9 + 9.97131e9i 0.236304 + 1.03531i
\(713\) 2.87036e9 + 3.59932e9i 0.296567 + 0.371883i
\(714\) 4.77103e9 2.29761e9i 0.490533 0.236228i
\(715\) −7.50862e9 + 3.61596e9i −0.768226 + 0.369958i
\(716\) 2.07907e8 + 9.10901e8i 0.0211677 + 0.0927418i
\(717\) −4.90392e9 + 6.14933e9i −0.496852 + 0.623032i
\(718\) 2.27148e10 + 1.09389e10i 2.29020 + 1.10290i
\(719\) −8.98965e8 + 1.12727e9i −0.0901969 + 0.113103i −0.824882 0.565305i \(-0.808759\pi\)
0.734685 + 0.678408i \(0.237330\pi\)
\(720\) −1.85006e9 + 8.10564e9i −0.184723 + 0.809326i
\(721\) 5.98572e8 2.88257e8i 0.0594762 0.0286422i
\(722\) 3.10127e9 1.35876e10i 0.306662 1.34357i
\(723\) 1.54749e10 + 7.45234e9i 1.52281 + 0.733345i
\(724\) 6.59879e9 0.646218
\(725\) 9.18157e8 0.0894817
\(726\) 2.42417e10 + 1.16742e10i 2.35117 + 1.13226i
\(727\) −4.18579e9 1.83391e10i −0.404024 1.77014i −0.610830 0.791762i \(-0.709164\pi\)
0.206806 0.978382i \(-0.433693\pi\)
\(728\) 5.69814e8 + 7.14524e8i 0.0547360 + 0.0686368i
\(729\) −1.05687e10 + 1.32527e10i −1.01036 + 1.26695i
\(730\) 2.59161e10 2.46570
\(731\) 6.03195e9 5.39916e9i 0.571146 0.511229i
\(732\) 8.45991e9 0.797218
\(733\) −1.39619e9 + 1.75077e9i −0.130942 + 0.164197i −0.842980 0.537945i \(-0.819201\pi\)
0.712038 + 0.702141i \(0.247772\pi\)
\(734\) 1.53358e10 + 1.92305e10i 1.43143 + 1.79496i
\(735\) −4.38384e9 1.92069e10i −0.407239 1.78423i
\(736\) −4.77068e9 2.29744e9i −0.441070 0.212408i
\(737\) −5.99450e9 −0.551590
\(738\) −4.91155e10 −4.49802
\(739\) −3.47411e9 1.67304e9i −0.316656 0.152494i 0.268804 0.963195i \(-0.413372\pi\)
−0.585460 + 0.810701i \(0.699086\pi\)
\(740\) 6.18562e9 2.71010e10i 0.561142 2.45852i
\(741\) 1.07423e10 5.17322e9i 0.969914 0.467086i
\(742\) 1.12159e9 4.91402e9i 0.100791 0.441595i
\(743\) −3.01425e9 + 3.77975e9i −0.269599 + 0.338067i −0.898140 0.439710i \(-0.855081\pi\)
0.628541 + 0.777777i \(0.283653\pi\)
\(744\) 1.31078e10 + 6.31237e9i 1.16687 + 0.561936i
\(745\) −6.70332e9 + 8.40570e9i −0.593941 + 0.744778i
\(746\) 6.29388e9 + 2.75753e10i 0.555051 + 2.43184i
\(747\) 1.75167e10 8.43562e9i 1.53756 0.740448i
\(748\) −1.59400e10 + 7.67632e9i −1.39262 + 0.670652i
\(749\) −1.26671e8 1.58841e8i −0.0110152 0.0138126i
\(750\) 3.84659e9 + 1.68530e10i 0.332937 + 1.45869i
\(751\) −6.54880e8 + 2.86922e9i −0.0564186 + 0.247186i −0.995271 0.0971327i \(-0.969033\pi\)
0.938853 + 0.344319i \(0.111890\pi\)
\(752\) 4.09720e9 + 5.13773e9i 0.351338 + 0.440563i
\(753\) −1.31092e10 1.64384e10i −1.11891 1.40307i
\(754\) −3.42227e8 + 1.49939e9i −0.0290746 + 0.127384i
\(755\) −3.71442e9 1.62739e10i −0.314106 1.37619i
\(756\) 2.92379e9 + 3.66632e9i 0.246105 + 0.308606i
\(757\) 2.59289e9 1.24867e9i 0.217244 0.104619i −0.322097 0.946707i \(-0.604388\pi\)
0.539341 + 0.842087i \(0.318673\pi\)
\(758\) 6.17596e9 2.97419e9i 0.515065 0.248042i
\(759\) −2.34855e9 1.02897e10i −0.194963 0.854190i
\(760\) 8.16338e9 1.02366e10i 0.674563 0.845875i
\(761\) 2.53503e6 + 1.22081e6i 0.000208515 + 0.000100416i 0.433988 0.900919i \(-0.357106\pi\)
−0.433779 + 0.901019i \(0.642820\pi\)
\(762\) −8.75677e9 + 1.09806e10i −0.716971 + 0.899053i
\(763\) −8.71553e8 + 3.81852e9i −0.0710327 + 0.311214i
\(764\) −5.39942e9 + 2.60022e9i −0.438047 + 0.210952i
\(765\) 4.18983e9 1.83569e10i 0.338362 1.48246i
\(766\) 1.96286e10 + 9.45262e9i 1.57793 + 0.759892i
\(767\) 2.95621e9 0.236565
\(768\) −4.74782e9 −0.378207
\(769\) 1.24865e10 + 6.01320e9i 0.990147 + 0.476830i 0.857584 0.514345i \(-0.171965\pi\)
0.132564 + 0.991174i \(0.457679\pi\)
\(770\) −2.17874e9 9.54568e9i −0.171984 0.753511i
\(771\) 9.19940e9 + 1.15357e10i 0.722885 + 0.906469i
\(772\) −8.97670e9 + 1.12564e10i −0.702193 + 0.880522i
\(773\) −4.46274e9 −0.347515 −0.173757 0.984788i \(-0.555591\pi\)
−0.173757 + 0.984788i \(0.555591\pi\)
\(774\) 2.63417e10 + 1.86588e10i 2.04198 + 1.44641i
\(775\) 8.37392e9 0.646209
\(776\) −8.77812e9 + 1.10074e10i −0.674350 + 0.845608i
\(777\) 5.40937e9 + 6.78314e9i 0.413688 + 0.518749i
\(778\) 4.69407e9 + 2.05661e10i 0.357372 + 1.56575i
\(779\) −2.93558e10 1.41370e10i −2.22491 1.07146i
\(780\) 1.80524e10 1.36209
\(781\) 2.55138e10 1.91645
\(782\) 5.44496e9 + 2.62216e9i 0.407166 + 0.196081i
\(783\) −5.12273e8 + 2.24441e9i −0.0381360 + 0.167085i
\(784\) −4.67974e9 + 2.25364e9i −0.346829 + 0.167024i
\(785\) −1.63560e9 + 7.16604e9i −0.120680 + 0.528732i
\(786\) 3.10809e9 3.89742e9i 0.228304 0.286285i
\(787\) 2.05696e10 + 9.90581e9i 1.50423 + 0.724400i 0.991001 0.133852i \(-0.0427345\pi\)
0.513230 + 0.858251i \(0.328449\pi\)
\(788\) 4.13622e9 5.18666e9i 0.301135 0.377612i
\(789\) −7.10203e9 3.11160e10i −0.514769 2.25535i
\(790\) −4.17549e10 + 2.01081e10i −3.01309 + 1.45103i
\(791\) 5.25244e9 2.52944e9i 0.377349 0.181722i
\(792\) −1.28318e10 1.60905e10i −0.917802 1.15089i
\(793\) 5.29476e8 + 2.31979e9i 0.0377042 + 0.165193i
\(794\) −6.31848e9 + 2.76831e10i −0.447962 + 1.96265i
\(795\) −1.81092e10 2.27083e10i −1.27825 1.60287i
\(796\) 9.82945e9 + 1.23257e10i 0.690770 + 0.866198i
\(797\) −3.15616e8 + 1.38280e9i −0.0220828 + 0.0967512i −0.984768 0.173871i \(-0.944372\pi\)
0.962686 + 0.270622i \(0.0872295\pi\)
\(798\) 3.11704e9 + 1.36566e10i 0.217136 + 0.951336i
\(799\) −9.27894e9 1.16354e10i −0.643554 0.806991i
\(800\) −8.67764e9 + 4.17893e9i −0.599220 + 0.288569i
\(801\) −3.50545e10 + 1.68814e10i −2.41007 + 1.16063i
\(802\) −7.53273e9 3.30031e10i −0.515635 2.25914i
\(803\) 1.68493e10 2.11283e10i 1.14836 1.43999i
\(804\) 1.16990e10 + 5.63394e9i 0.793875 + 0.382310i
\(805\) −1.22071e9 + 1.53072e9i −0.0824757 + 0.103421i
\(806\) −3.12123e9 + 1.36750e10i −0.209968 + 0.919930i
\(807\) 1.26108e10 6.07306e9i 0.844669 0.406771i
\(808\) −2.30241e9 + 1.00875e10i −0.153548 + 0.672736i
\(809\) −2.27657e9 1.09634e9i −0.151169 0.0727990i 0.356770 0.934192i \(-0.383878\pi\)
−0.507939 + 0.861393i \(0.669592\pi\)
\(810\) −4.35515e8 −0.0287943
\(811\) 5.66022e9 0.372615 0.186308 0.982491i \(-0.440348\pi\)
0.186308 + 0.982491i \(0.440348\pi\)
\(812\) −9.52970e8 4.58926e8i −0.0624645 0.0300813i
\(813\) −5.21448e9 2.28461e10i −0.340325 1.49106i
\(814\) −3.08732e10 3.87138e10i −2.00630 2.51582i
\(815\) −3.31787e9 + 4.16047e9i −0.214688 + 0.269210i
\(816\) −8.04519e9 −0.518347
\(817\) 1.03736e10 + 1.87341e10i 0.665504 + 1.20187i
\(818\) 3.14551e10 2.00934
\(819\) −2.16764e9 + 2.71814e9i −0.137878 + 0.172893i
\(820\) −3.07583e10 3.85697e10i −1.94811 2.44285i
\(821\) −4.66458e9 2.04369e10i −0.294179 1.28888i −0.878650 0.477467i \(-0.841555\pi\)
0.584471 0.811415i \(-0.301302\pi\)
\(822\) −1.01886e10 4.90657e9i −0.639828 0.308125i
\(823\) 2.20571e10 1.37927 0.689635 0.724158i \(-0.257771\pi\)
0.689635 + 0.724158i \(0.257771\pi\)
\(824\) 2.39608e9 0.149196
\(825\) −1.72966e10 8.32959e9i −1.07243 0.516457i
\(826\) −7.72841e8 + 3.38604e9i −0.0477156 + 0.209056i
\(827\) −1.88420e10 + 9.07384e9i −1.15840 + 0.557855i −0.911546 0.411198i \(-0.865111\pi\)
−0.246853 + 0.969053i \(0.579396\pi\)
\(828\) −3.13908e9 + 1.37532e10i −0.192175 + 0.841972i
\(829\) −1.64769e10 + 2.06613e10i −1.00446 + 1.25956i −0.0389389 + 0.999242i \(0.512398\pi\)
−0.965524 + 0.260315i \(0.916174\pi\)
\(830\) 3.00556e10 + 1.44740e10i 1.82453 + 0.878649i
\(831\) −2.65032e10 + 3.32340e10i −1.60212 + 2.00899i
\(832\) −2.83982e9 1.24421e10i −0.170946 0.748964i
\(833\) 1.05982e10 5.10384e9i 0.635295 0.305942i
\(834\) −2.93489e10 + 1.41337e10i −1.75190 + 0.843672i
\(835\) 6.02752e9 + 7.55827e9i 0.358291 + 0.449283i
\(836\) −1.04141e10 4.56269e10i −0.616450 2.70084i
\(837\) −4.67211e9 + 2.04698e10i −0.275406 + 1.20663i
\(838\) −1.21601e10 1.52483e10i −0.713812 0.895092i
\(839\) 1.02479e10 + 1.28505e10i 0.599058 + 0.751195i 0.985231 0.171231i \(-0.0547745\pi\)
−0.386173 + 0.922427i \(0.626203\pi\)
\(840\) −1.37678e9 + 6.03208e9i −0.0801471 + 0.351147i
\(841\) 3.72291e9 + 1.63111e10i 0.215823 + 0.945581i
\(842\) −1.60283e10 2.00989e10i −0.925328 1.16032i
\(843\) 3.39942e10 1.63707e10i 1.95438 0.941178i
\(844\) 1.33669e9 6.43717e8i 0.0765301 0.0368550i
\(845\) −3.67504e9 1.61014e10i −0.209538 0.918048i
\(846\) 3.70001e10 4.63966e10i 2.10090 2.63445i
\(847\) −4.68920e9 2.25820e9i −0.265159 0.127694i
\(848\) −4.77450e9 + 5.98704e9i −0.268870 + 0.337152i
\(849\) 1.04750e10 4.58942e10i 0.587461 2.57383i
\(850\) 9.90414e9 4.76958e9i 0.553160 0.266388i
\(851\) −2.20329e9 + 9.65323e9i −0.122551 + 0.536932i
\(852\) −4.97933e10 2.39792e10i −2.75824 1.32830i
\(853\) 9.17601e9 0.506212 0.253106 0.967439i \(-0.418548\pi\)
0.253106 + 0.967439i \(0.418548\pi\)
\(854\) −2.79550e9 −0.153588
\(855\) 4.48751e10 + 2.16107e10i 2.45541 + 1.18246i
\(856\) −1.63048e8 7.14359e8i −0.00888498 0.0389277i
\(857\) −6.33271e9 7.94097e9i −0.343682 0.430963i 0.579710 0.814823i \(-0.303166\pi\)
−0.923391 + 0.383860i \(0.874595\pi\)
\(858\) 2.00496e10 2.51414e10i 1.08368 1.35889i
\(859\) 2.25949e10 1.21628 0.608141 0.793829i \(-0.291916\pi\)
0.608141 + 0.793829i \(0.291916\pi\)
\(860\) 1.84387e9 + 3.23707e10i 0.0988521 + 1.73543i
\(861\) 1.53971e10 0.822104
\(862\) 1.96763e10 2.46733e10i 1.04633 1.31205i
\(863\) −4.03542e9 5.06026e9i −0.213723 0.268000i 0.663401 0.748264i \(-0.269112\pi\)
−0.877124 + 0.480264i \(0.840541\pi\)
\(864\) −5.37373e9 2.35439e10i −0.283451 1.24188i
\(865\) 1.49061e10 + 7.17841e9i 0.783084 + 0.377113i
\(866\) 3.86731e10 2.02347
\(867\) −1.27894e10 −0.666476
\(868\) −8.69143e9 4.18557e9i −0.451099 0.217238i
\(869\) −1.07535e10 + 4.71142e10i −0.555880 + 2.43547i
\(870\) −9.38087e9 + 4.51759e9i −0.482976 + 0.232589i
\(871\) −8.12680e8 + 3.56058e9i −0.0416731 + 0.182582i
\(872\) −8.80739e9 + 1.10441e10i −0.449821 + 0.564057i
\(873\) −4.82543e10 2.32381e10i −2.45463 1.18209i
\(874\) −9.96744e9 + 1.24988e10i −0.505003 + 0.633253i
\(875\) −7.44068e8 3.25998e9i −0.0375478 0.164508i
\(876\) −5.27409e10 + 2.53987e10i −2.65084 + 1.27658i
\(877\) −1.79666e10 + 8.65228e9i −0.899432 + 0.433143i −0.825684 0.564133i \(-0.809210\pi\)
−0.0737481 + 0.997277i \(0.523496\pi\)
\(878\) 2.60871e10 + 3.27121e10i 1.30075 + 1.63109i
\(879\) 4.95497e9 + 2.17091e10i 0.246082 + 1.07816i
\(880\) −3.31009e9 + 1.45024e10i −0.163738 + 0.717384i
\(881\) 1.05704e10 + 1.32548e10i 0.520804 + 0.653067i 0.970779 0.239974i \(-0.0771388\pi\)
−0.449976 + 0.893041i \(0.648567\pi\)
\(882\) 2.92453e10 + 3.66725e10i 1.43521 + 1.79970i
\(883\) 5.69528e9 2.49527e10i 0.278390 1.21970i −0.621440 0.783462i \(-0.713452\pi\)
0.899829 0.436242i \(-0.143691\pi\)
\(884\) 2.39853e9 + 1.05087e10i 0.116779 + 0.511640i
\(885\) 1.24783e10 + 1.56473e10i 0.605136 + 0.758817i
\(886\) −4.29791e10 + 2.06977e10i −2.07606 + 0.999777i
\(887\) 2.33041e10 1.12226e10i 1.12124 0.539961i 0.220965 0.975282i \(-0.429079\pi\)
0.900276 + 0.435321i \(0.143365\pi\)
\(888\) 6.96279e9 + 3.05060e10i 0.333686 + 1.46197i
\(889\) 1.69387e9 2.12405e9i 0.0808582 0.101393i
\(890\) −6.01472e10 2.89654e10i −2.85990 1.37725i
\(891\) −2.83149e8 + 3.55058e8i −0.0134104 + 0.0168162i
\(892\) 9.55415e9 4.18595e10i 0.450728 1.97477i
\(893\) 3.54689e10 1.70809e10i 1.66674 0.802660i
\(894\) 9.23118e9 4.04445e10i 0.432092 1.89312i
\(895\) −1.60291e9 7.71920e8i −0.0747357 0.0359908i
\(896\) 7.13494e9 0.331369
\(897\) −6.43019e9 −0.297475
\(898\) 4.09368e10 + 1.97141e10i 1.88646 + 0.908469i
\(899\) −1.05382e9 4.61707e9i −0.0483734 0.211938i
\(900\) 1.59986e10 + 2.00616e10i 0.731533 + 0.917313i
\(901\) 1.08128e10 1.35589e10i 0.492496 0.617570i
\(902\) −8.78765e10 −3.98703
\(903\) −8.25778e9 5.84929e9i −0.373213 0.264360i
\(904\) 2.10255e10 0.946578
\(905\) −7.83418e9 + 9.82375e9i −0.351337 + 0.440562i
\(906\) 4.01583e10 + 5.03569e10i 1.79402 + 2.24963i
\(907\) 1.03488e9 + 4.53409e9i 0.0460535 + 0.201774i 0.992721 0.120440i \(-0.0384304\pi\)
−0.946667 + 0.322213i \(0.895573\pi\)
\(908\) −9.75120e9 4.69593e9i −0.432272 0.208171i
\(909\) −3.93610e10 −1.73817
\(910\) −5.96527e9 −0.262413
\(911\) −3.59860e10 1.73300e10i −1.57696 0.759422i −0.578538 0.815655i \(-0.696377\pi\)
−0.998418 + 0.0562334i \(0.982091\pi\)
\(912\) 4.73561e9 2.07481e10i 0.206726 0.905724i
\(913\) 3.13406e10 1.50928e10i 1.36289 0.656331i
\(914\) −8.33808e9 + 3.65315e10i −0.361206 + 1.58254i
\(915\) −1.00437e10 + 1.25944e10i −0.433432 + 0.543507i
\(916\) −3.42157e10 1.64774e10i −1.47093 0.708362i
\(917\) −6.01214e8 + 7.53899e8i −0.0257476 + 0.0322865i
\(918\) 6.13326e9 + 2.68716e10i 0.261663 + 1.14642i
\(919\) 2.58259e10 1.24371e10i 1.09762 0.528586i 0.204710 0.978823i \(-0.434375\pi\)
0.892909 + 0.450237i \(0.148660\pi\)
\(920\) −6.36190e9 + 3.06373e9i −0.269358 + 0.129716i
\(921\) 2.16339e10 + 2.71280e10i 0.912484 + 1.14422i
\(922\) 2.96373e9 + 1.29849e10i 0.124532 + 0.545609i
\(923\) 3.45893e9 1.51546e10i 0.144789 0.634363i
\(924\) 1.37890e10 + 1.72908e10i 0.575016 + 0.721047i
\(925\) 1.12293e10 + 1.40811e10i 0.466504 + 0.584977i
\(926\) 3.34492e9 1.46551e10i 0.138436 0.606526i
\(927\) 2.02828e9 + 8.88646e9i 0.0836273 + 0.366395i
\(928\) 3.39615e9 + 4.25864e9i 0.139498 + 0.174925i
\(929\) −3.04160e10 + 1.46476e10i −1.24465 + 0.599392i −0.936072 0.351808i \(-0.885567\pi\)
−0.308577 + 0.951199i \(0.599853\pi\)
\(930\) −8.55569e10 + 4.12020e10i −3.48791 + 1.67969i
\(931\) 6.92410e9 + 3.03365e10i 0.281216 + 1.23209i
\(932\) −1.62575e10 + 2.03863e10i −0.657808 + 0.824865i
\(933\) 1.02564e10 + 4.93921e9i 0.413436 + 0.199100i
\(934\) 2.36032e10 2.95975e10i 0.947888 1.18861i
\(935\) 7.49636e9 3.28437e10i 0.299923 1.31405i
\(936\) −1.12970e10 + 5.44035e9i −0.450295 + 0.216851i
\(937\) 9.83650e8 4.30965e9i 0.0390618 0.171141i −0.951634 0.307233i \(-0.900597\pi\)
0.990696 + 0.136092i \(0.0434542\pi\)
\(938\) −3.86583e9 1.86168e9i −0.152944 0.0736540i
\(939\) 4.64064e10 1.82915
\(940\) 5.96056e10 2.34067
\(941\) −2.23697e10 1.07727e10i −0.875176 0.421463i −0.0583159 0.998298i \(-0.518573\pi\)
−0.816860 + 0.576836i \(0.804287\pi\)
\(942\) −6.31107e9 2.76506e10i −0.245994 1.07777i
\(943\) 1.09559e10 + 1.37383e10i 0.425460 + 0.533510i
\(944\) 3.28990e9 4.12540e9i 0.127286 0.159612i
\(945\) −8.92930e9 −0.344196
\(946\) 4.71301e10 + 3.33840e10i 1.81000 + 1.28209i
\(947\) −5.37228e9 −0.205558 −0.102779 0.994704i \(-0.532773\pi\)
−0.102779 + 0.994704i \(0.532773\pi\)
\(948\) 6.52672e10 8.18424e10i 2.48809 3.11996i
\(949\) −1.02654e10 1.28724e10i −0.389893 0.488910i
\(950\) 6.47064e9 + 2.83497e10i 0.244858 + 1.07279i
\(951\) −5.82431e9 2.80484e9i −0.219590 0.105749i
\(952\) −3.69431e9 −0.138773
\(953\) 5.87364e9 0.219828 0.109914 0.993941i \(-0.464943\pi\)
0.109914 + 0.993941i \(0.464943\pi\)
\(954\) 6.23051e10 + 3.00046e10i 2.32330 + 1.11884i
\(955\) 2.53927e9 1.11253e10i 0.0943402 0.413331i
\(956\) 1.69465e10 8.16103e9i 0.627305 0.302094i
\(957\) −2.41594e9 + 1.05849e10i −0.0891035 + 0.390388i
\(958\) 2.69479e10 3.37916e10i 0.990252 1.24174i
\(959\) 1.97084e9 + 9.49106e8i 0.0721582 + 0.0347496i
\(960\) 5.38691e10 6.75498e10i 1.96513 2.46419i
\(961\) −3.48905e9 1.52865e10i −0.126817 0.555620i
\(962\) −2.71805e10 + 1.30895e10i −0.984340 + 0.474033i
\(963\) 2.51136e9 1.20941e9i 0.0906184 0.0436395i
\(964\) −2.56098e10 3.21136e10i −0.920738 1.15457i
\(965\) −6.10040e9 2.67276e10i −0.218531 0.957447i
\(966\) 1.68104e9 7.36513e9i 0.0600011 0.262882i
\(967\) 3.35611e8 + 4.20843e8i 0.0119356 + 0.0149668i 0.787763 0.615978i \(-0.211239\pi\)
−0.775828 + 0.630945i \(0.782668\pi\)
\(968\) −1.17034e10 1.46756e10i −0.414714 0.520035i
\(969\) −1.07248e10 + 4.69882e10i −0.378664 + 1.65904i
\(970\) −2.04489e10 8.95923e10i −0.719396 3.15188i
\(971\) −1.97732e10 2.47949e10i −0.693123 0.869149i 0.303366 0.952874i \(-0.401890\pi\)
−0.996489 + 0.0837253i \(0.973318\pi\)
\(972\) 3.68617e10 1.77517e10i 1.28749 0.620022i
\(973\) 5.67711e9 2.73395e9i 0.197575 0.0951472i
\(974\) −2.34545e9 1.02761e10i −0.0813337 0.356346i
\(975\) −7.29247e9 + 9.14447e9i −0.251976 + 0.315968i
\(976\) 3.82651e9 + 1.84275e9i 0.131743 + 0.0634443i
\(977\) −2.74549e9 + 3.44273e9i −0.0941865 + 0.118106i −0.826691 0.562656i \(-0.809780\pi\)
0.732505 + 0.680762i \(0.238351\pi\)
\(978\) 4.56905e9 2.00183e10i 0.156185 0.684292i
\(979\) −6.27188e10 + 3.02038e10i −2.13628 + 1.02878i
\(980\) −1.04836e10 + 4.59318e10i −0.355812 + 1.55892i
\(981\) −4.84152e10 2.33156e10i −1.63735 0.788504i
\(982\) −2.65203e10 −0.893694
\(983\) 2.40417e9 0.0807285 0.0403643 0.999185i \(-0.487148\pi\)
0.0403643 + 0.999185i \(0.487148\pi\)
\(984\) 5.00313e10 + 2.40938e10i 1.67401 + 0.806163i
\(985\) 2.81090e9 + 1.23154e10i 0.0937170 + 0.410601i
\(986\) −3.87616e9 4.86055e9i −0.128775 0.161479i
\(987\) −1.15990e10 + 1.45447e10i −0.383982 + 0.481499i
\(988\) −2.85131e10 −0.940579
\(989\) −6.56777e8 1.15303e10i −0.0215889 0.379012i
\(990\) 1.34333e11 4.40008
\(991\) 1.93073e10 2.42106e10i 0.630178 0.790218i −0.359558 0.933123i \(-0.617073\pi\)
0.989737 + 0.142904i \(0.0456441\pi\)
\(992\) 3.09741e10 + 3.88403e10i 1.00741 + 1.26326i
\(993\) −9.34322e9 4.09353e10i −0.302813 1.32671i
\(994\) 1.64538e10 + 7.92371e9i 0.531389 + 0.255904i
\(995\) −3.00193e10 −0.966094
\(996\) −7.53500e10 −2.41644
\(997\) 3.27630e10 + 1.57778e10i 1.04701 + 0.504213i 0.876630 0.481165i \(-0.159786\pi\)
0.170380 + 0.985378i \(0.445501\pi\)
\(998\) −1.22400e9 + 5.36271e9i −0.0389786 + 0.170776i
\(999\) −4.06860e10 + 1.95934e10i −1.29112 + 0.621770i
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 43.8.e.a.4.3 144
43.11 even 7 inner 43.8.e.a.11.3 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.8.e.a.4.3 144 1.1 even 1 trivial
43.8.e.a.11.3 yes 144 43.11 even 7 inner