Properties

Label 69.7.h.a.2.7
Level $69$
Weight $7$
Character 69.2
Analytic conductor $15.874$
Analytic rank $0$
Dimension $460$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,7,Mod(2,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 2]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.h (of order \(22\), degree \(10\), 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: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(460\)
Relative dimension: \(46\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 69.2
Dual form 69.7.h.a.35.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.67610 + 10.3882i) q^{2} +(-9.18523 - 25.3896i) q^{3} +(-36.7581 - 80.4889i) q^{4} +(-23.3451 + 79.5062i) q^{5} +(325.074 + 74.0853i) q^{6} +(-342.298 + 395.033i) q^{7} +(299.277 + 43.0296i) q^{8} +(-560.263 + 466.419i) q^{9} +O(q^{10})\) \(q+(-6.67610 + 10.3882i) q^{2} +(-9.18523 - 25.3896i) q^{3} +(-36.7581 - 80.4889i) q^{4} +(-23.3451 + 79.5062i) q^{5} +(325.074 + 74.0853i) q^{6} +(-342.298 + 395.033i) q^{7} +(299.277 + 43.0296i) q^{8} +(-560.263 + 466.419i) q^{9} +(-670.073 - 773.306i) q^{10} +(614.241 + 955.778i) q^{11} +(-1705.95 + 1672.58i) q^{12} +(29.3919 + 33.9200i) q^{13} +(-1818.47 - 6193.15i) q^{14} +(2233.06 - 137.560i) q^{15} +(1263.51 - 1458.16i) q^{16} +(-4299.54 - 1963.53i) q^{17} +(-1104.88 - 8933.99i) q^{18} +(-4401.47 - 9637.88i) q^{19} +(7257.49 - 1043.47i) q^{20} +(13173.8 + 5062.34i) q^{21} -14029.6 q^{22} +(10639.3 + 5902.67i) q^{23} +(-1656.43 - 7993.76i) q^{24} +(7368.34 + 4735.34i) q^{25} +(-548.591 + 78.8755i) q^{26} +(16988.3 + 9940.69i) q^{27} +(44378.0 + 13030.6i) q^{28} +(-13247.7 - 6050.00i) q^{29} +(-13479.1 + 24115.9i) q^{30} +(3294.14 - 22911.2i) q^{31} +(12164.1 + 41427.3i) q^{32} +(18624.9 - 24374.4i) q^{33} +(49101.7 - 31555.7i) q^{34} +(-23416.6 - 36437.0i) q^{35} +(58135.7 + 27950.3i) q^{36} +(-3170.65 + 930.986i) q^{37} +(129505. + 18620.0i) q^{38} +(591.244 - 1057.81i) q^{39} +(-10407.8 + 22789.9i) q^{40} +(1713.22 - 5834.68i) q^{41} +(-140538. + 103056. i) q^{42} +(-12423.4 - 86406.6i) q^{43} +(54351.2 - 84572.2i) q^{44} +(-24003.8 - 55433.0i) q^{45} +(-132347. + 71116.3i) q^{46} -151215. i q^{47} +(-48627.8 - 18686.3i) q^{48} +(-22140.0 - 153987. i) q^{49} +(-98383.5 + 44930.2i) q^{50} +(-10361.0 + 127199. i) q^{51} +(1649.80 - 3612.55i) q^{52} +(160700. + 139247. i) q^{53} +(-216682. + 110113. i) q^{54} +(-90329.9 + 26523.2i) q^{55} +(-119440. + 103495. i) q^{56} +(-204273. + 200278. i) q^{57} +(151291. - 97229.1i) q^{58} +(-95631.0 + 82864.7i) q^{59} +(-93155.1 - 174680. i) q^{60} +(56273.0 - 391387. i) q^{61} +(216015. + 187178. i) q^{62} +(7526.18 - 380977. i) q^{63} +(-393083. - 115419. i) q^{64} +(-3383.01 + 1544.97i) q^{65} +(128865. + 356205. i) q^{66} +(39446.9 + 25351.0i) q^{67} +418241. i q^{68} +(52142.2 - 324344. i) q^{69} +534846. q^{70} +(-158806. + 247107. i) q^{71} +(-187744. + 115481. i) q^{72} +(158348. + 346734. i) q^{73} +(11496.3 - 39152.7i) q^{74} +(52548.6 - 230574. i) q^{75} +(-613953. + 708540. i) q^{76} +(-587818. - 84515.4i) q^{77} +(7041.55 + 13204.0i) q^{78} +(255238. + 294561. i) q^{79} +(86436.4 + 134498. i) q^{80} +(96348.3 - 522634. i) q^{81} +(49174.2 + 56750.1i) q^{82} +(182604. + 621890. i) q^{83} +(-76781.8 - 1.24643e6i) q^{84} +(256486. - 296001. i) q^{85} +(980550. + 447802. i) q^{86} +(-31924.3 + 391923. i) q^{87} +(142702. + 312473. i) q^{88} +(-508647. + 73132.4i) q^{89} +(736101. + 120720. i) q^{90} -23460.3 q^{91} +(84020.5 - 1.07332e6i) q^{92} +(-611964. + 126808. i) q^{93} +(1.57085e6 + 1.00952e6i) q^{94} +(869025. - 124947. i) q^{95} +(940091. - 689362. i) q^{96} +(-957606. - 281178. i) q^{97} +(1.74746e6 + 798037. i) q^{98} +(-789929. - 248993. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{11}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.67610 + 10.3882i −0.834512 + 1.29853i 0.117688 + 0.993051i \(0.462452\pi\)
−0.952200 + 0.305476i \(0.901185\pi\)
\(3\) −9.18523 25.3896i −0.340194 0.940355i
\(4\) −36.7581 80.4889i −0.574345 1.25764i
\(5\) −23.3451 + 79.5062i −0.186761 + 0.636050i 0.811875 + 0.583832i \(0.198447\pi\)
−0.998636 + 0.0522181i \(0.983371\pi\)
\(6\) 325.074 + 74.0853i 1.50497 + 0.342987i
\(7\) −342.298 + 395.033i −0.997954 + 1.15170i −0.00953478 + 0.999955i \(0.503035\pi\)
−0.988420 + 0.151746i \(0.951510\pi\)
\(8\) 299.277 + 43.0296i 0.584526 + 0.0840421i
\(9\) −560.263 + 466.419i −0.768536 + 0.639806i
\(10\) −670.073 773.306i −0.670073 0.773306i
\(11\) 614.241 + 955.778i 0.461488 + 0.718090i 0.991529 0.129882i \(-0.0414598\pi\)
−0.530041 + 0.847972i \(0.677823\pi\)
\(12\) −1705.95 + 1672.58i −0.987240 + 0.967929i
\(13\) 29.3919 + 33.9200i 0.0133782 + 0.0154392i 0.762399 0.647107i \(-0.224021\pi\)
−0.749021 + 0.662546i \(0.769476\pi\)
\(14\) −1818.47 6193.15i −0.662708 2.25698i
\(15\) 2233.06 137.560i 0.661648 0.0407584i
\(16\) 1263.51 1458.16i 0.308473 0.355997i
\(17\) −4299.54 1963.53i −0.875134 0.399661i −0.0733729 0.997305i \(-0.523376\pi\)
−0.801762 + 0.597644i \(0.796104\pi\)
\(18\) −1104.88 8933.99i −0.189452 1.53189i
\(19\) −4401.47 9637.88i −0.641708 1.40514i −0.898628 0.438711i \(-0.855435\pi\)
0.256920 0.966433i \(-0.417292\pi\)
\(20\) 7257.49 1043.47i 0.907187 0.130434i
\(21\) 13173.8 + 5062.34i 1.42251 + 0.546630i
\(22\) −14029.6 −1.31758
\(23\) 10639.3 + 5902.67i 0.874438 + 0.485138i
\(24\) −1656.43 7993.76i −0.119823 0.578252i
\(25\) 7368.34 + 4735.34i 0.471574 + 0.303062i
\(26\) −548.591 + 78.8755i −0.0312125 + 0.00448768i
\(27\) 16988.3 + 9940.69i 0.863096 + 0.505039i
\(28\) 44378.0 + 13030.6i 2.02159 + 0.593594i
\(29\) −13247.7 6050.00i −0.543182 0.248063i 0.124876 0.992172i \(-0.460147\pi\)
−0.668058 + 0.744110i \(0.732874\pi\)
\(30\) −13479.1 + 24115.9i −0.499227 + 0.893181i
\(31\) 3294.14 22911.2i 0.110575 0.769065i −0.856788 0.515669i \(-0.827543\pi\)
0.967363 0.253396i \(-0.0815476\pi\)
\(32\) 12164.1 + 41427.3i 0.371220 + 1.26426i
\(33\) 18624.9 24374.4i 0.518264 0.678253i
\(34\) 49101.7 31555.7i 1.24928 0.802863i
\(35\) −23416.6 36437.0i −0.546160 0.849842i
\(36\) 58135.7 + 27950.3i 1.24605 + 0.599072i
\(37\) −3170.65 + 930.986i −0.0625955 + 0.0183797i −0.312880 0.949793i \(-0.601294\pi\)
0.250285 + 0.968172i \(0.419476\pi\)
\(38\) 129505. + 18620.0i 2.36013 + 0.339335i
\(39\) 591.244 1057.81i 0.00996720 0.0178326i
\(40\) −10407.8 + 22789.9i −0.162622 + 0.356092i
\(41\) 1713.22 5834.68i 0.0248577 0.0846574i −0.946130 0.323787i \(-0.895044\pi\)
0.970988 + 0.239130i \(0.0768621\pi\)
\(42\) −140538. + 103056.i −1.89691 + 1.39099i
\(43\) −12423.4 86406.6i −0.156255 1.08678i −0.905457 0.424438i \(-0.860472\pi\)
0.749201 0.662342i \(-0.230437\pi\)
\(44\) 54351.2 84572.2i 0.638045 0.992817i
\(45\) −24003.8 55433.0i −0.263416 0.608318i
\(46\) −132347. + 71116.3i −1.35969 + 0.730627i
\(47\) 151215.i 1.45646i −0.685330 0.728232i \(-0.740342\pi\)
0.685330 0.728232i \(-0.259658\pi\)
\(48\) −48627.8 18686.3i −0.439704 0.168966i
\(49\) −22140.0 153987.i −0.188187 1.30887i
\(50\) −98383.5 + 44930.2i −0.787068 + 0.359442i
\(51\) −10361.0 + 127199.i −0.0781076 + 0.958899i
\(52\) 1649.80 3612.55i 0.0117333 0.0256924i
\(53\) 160700. + 139247.i 1.07941 + 0.935317i 0.998115 0.0613723i \(-0.0195477\pi\)
0.0812990 + 0.996690i \(0.474093\pi\)
\(54\) −216682. + 110113.i −1.37607 + 0.699292i
\(55\) −90329.9 + 26523.2i −0.542929 + 0.159418i
\(56\) −119440. + 103495.i −0.680121 + 0.589328i
\(57\) −204273. + 200278.i −1.10303 + 1.08145i
\(58\) 151291. 97229.1i 0.775408 0.498324i
\(59\) −95631.0 + 82864.7i −0.465632 + 0.403472i −0.855829 0.517259i \(-0.826952\pi\)
0.390197 + 0.920731i \(0.372407\pi\)
\(60\) −93155.1 174680.i −0.431273 0.808705i
\(61\) 56273.0 391387.i 0.247919 1.72432i −0.362281 0.932069i \(-0.618002\pi\)
0.610200 0.792247i \(-0.291089\pi\)
\(62\) 216015. + 187178.i 0.906376 + 0.785379i
\(63\) 7526.18 380977.i 0.0300991 1.52362i
\(64\) −393083. 115419.i −1.49949 0.440290i
\(65\) −3383.01 + 1544.97i −0.0123187 + 0.00562574i
\(66\) 128865. + 356205.i 0.448231 + 1.23899i
\(67\) 39446.9 + 25351.0i 0.131156 + 0.0842889i 0.604574 0.796549i \(-0.293343\pi\)
−0.473418 + 0.880838i \(0.656980\pi\)
\(68\) 418241.i 1.33015i
\(69\) 52142.2 324344.i 0.158724 0.987323i
\(70\) 534846. 1.55932
\(71\) −158806. + 247107.i −0.443703 + 0.690416i −0.989015 0.147818i \(-0.952775\pi\)
0.545311 + 0.838234i \(0.316411\pi\)
\(72\) −187744. + 115481.i −0.503000 + 0.309394i
\(73\) 158348. + 346734.i 0.407046 + 0.891307i 0.996507 + 0.0835101i \(0.0266131\pi\)
−0.589461 + 0.807797i \(0.700660\pi\)
\(74\) 11496.3 39152.7i 0.0283702 0.0966199i
\(75\) 52548.6 230574.i 0.124560 0.546547i
\(76\) −613953. + 708540.i −1.39860 + 1.61407i
\(77\) −587818. 84515.4i −1.28757 0.185125i
\(78\) 7041.55 + 13204.0i 0.0148383 + 0.0278242i
\(79\) 255238. + 294561.i 0.517684 + 0.597439i 0.953049 0.302815i \(-0.0979264\pi\)
−0.435366 + 0.900254i \(0.643381\pi\)
\(80\) 86436.4 + 134498.i 0.168821 + 0.262691i
\(81\) 96348.3 522634.i 0.181296 0.983429i
\(82\) 49174.2 + 56750.1i 0.0891859 + 0.102926i
\(83\) 182604. + 621890.i 0.319356 + 1.08763i 0.950180 + 0.311701i \(0.100899\pi\)
−0.630825 + 0.775925i \(0.717283\pi\)
\(84\) −76781.8 1.24643e6i −0.129545 2.10295i
\(85\) 256486. 296001.i 0.417645 0.481988i
\(86\) 980550. + 447802.i 1.54161 + 0.704030i
\(87\) −31924.3 + 391923.i −0.0484801 + 0.595173i
\(88\) 142702. + 312473.i 0.209402 + 0.458526i
\(89\) −508647. + 73132.4i −0.721517 + 0.103739i −0.493284 0.869868i \(-0.664204\pi\)
−0.228233 + 0.973607i \(0.573295\pi\)
\(90\) 736101. + 120720.i 1.00974 + 0.165597i
\(91\) −23460.3 −0.0311322
\(92\) 84020.5 1.07332e6i 0.107900 1.37836i
\(93\) −611964. + 126808.i −0.760812 + 0.157652i
\(94\) 1.57085e6 + 1.00952e6i 1.89126 + 1.21544i
\(95\) 869025. 124947.i 1.01359 0.145732i
\(96\) 940091. 689362.i 1.06257 0.779172i
\(97\) −957606. 281178.i −1.04923 0.308082i −0.288725 0.957412i \(-0.593231\pi\)
−0.760507 + 0.649330i \(0.775050\pi\)
\(98\) 1.74746e6 + 798037.i 1.85664 + 0.847901i
\(99\) −789929. 248993.i −0.814109 0.256615i
\(100\) 110297. 767132.i 0.110297 0.767132i
\(101\) −524579. 1.78655e6i −0.509152 1.73401i −0.665584 0.746323i \(-0.731818\pi\)
0.156433 0.987689i \(-0.450001\pi\)
\(102\) −1.25220e6 956825.i −1.17997 0.901638i
\(103\) −381167. + 244961.i −0.348822 + 0.224174i −0.703305 0.710888i \(-0.748293\pi\)
0.354483 + 0.935062i \(0.384657\pi\)
\(104\) 7336.75 + 11416.2i 0.00652234 + 0.0101490i
\(105\) −710033. + 929220.i −0.613353 + 0.802695i
\(106\) −2.51938e6 + 739756.i −2.11532 + 0.621113i
\(107\) −1.22148e6 175623.i −0.997095 0.143361i −0.375603 0.926781i \(-0.622564\pi\)
−0.621492 + 0.783420i \(0.713473\pi\)
\(108\) 175657. 1.73277e6i 0.139442 1.37553i
\(109\) −411489. + 901036.i −0.317745 + 0.695765i −0.999354 0.0359523i \(-0.988554\pi\)
0.681608 + 0.731717i \(0.261281\pi\)
\(110\) 327522. 1.11544e6i 0.246072 0.838045i
\(111\) 52760.5 + 71950.2i 0.0385780 + 0.0526093i
\(112\) 143527. + 998254.i 0.102160 + 0.710538i
\(113\) 690644. 1.07466e6i 0.478651 0.744795i −0.515014 0.857182i \(-0.672213\pi\)
0.993665 + 0.112387i \(0.0358495\pi\)
\(114\) −716779. 3.45911e6i −0.483805 2.33480i
\(115\) −717675. + 708091.i −0.471883 + 0.465581i
\(116\) 1.28868e6i 0.825600i
\(117\) −32288.1 5295.22i −0.0201597 0.00330618i
\(118\) −222374. 1.54665e6i −0.135344 0.941337i
\(119\) 2.24738e6 1.02635e6i 1.33363 0.609050i
\(120\) 674223. + 54919.2i 0.390176 + 0.0317819i
\(121\) 199714. 437312.i 0.112733 0.246851i
\(122\) 3.69013e6 + 3.19751e6i 2.03218 + 1.76089i
\(123\) −163876. + 10095.0i −0.0880645 + 0.00542490i
\(124\) −1.96519e6 + 577031.i −1.03072 + 0.302645i
\(125\) −1.52700e6 + 1.32315e6i −0.781822 + 0.677453i
\(126\) 3.90742e6 + 2.62162e6i 1.95334 + 1.31056i
\(127\) 2.90716e6 1.86832e6i 1.41925 0.912095i 0.419257 0.907868i \(-0.362291\pi\)
0.999991 0.00422722i \(-0.00134557\pi\)
\(128\) 1.73491e6 1.50331e6i 0.827272 0.716835i
\(129\) −2.07972e6 + 1.10909e6i −0.968803 + 0.516652i
\(130\) 6535.84 45457.8i 0.00297489 0.0206908i
\(131\) −27041.9 23431.9i −0.0120288 0.0104230i 0.648826 0.760937i \(-0.275260\pi\)
−0.660854 + 0.750514i \(0.729806\pi\)
\(132\) −2.64648e6 603141.i −1.15066 0.262239i
\(133\) 5.31390e6 + 1.56030e6i 2.25870 + 0.663214i
\(134\) −526703. + 240537.i −0.218903 + 0.0999695i
\(135\) −1.18694e6 + 1.11861e6i −0.482423 + 0.454651i
\(136\) −1.20226e6 772647.i −0.477950 0.307160i
\(137\) 1.63549e6i 0.636043i 0.948084 + 0.318021i \(0.103018\pi\)
−0.948084 + 0.318021i \(0.896982\pi\)
\(138\) 3.02125e6 + 2.70702e6i 1.14961 + 1.03004i
\(139\) 784633. 0.292161 0.146080 0.989273i \(-0.453334\pi\)
0.146080 + 0.989273i \(0.453334\pi\)
\(140\) −2.07202e6 + 3.22413e6i −0.755110 + 1.17497i
\(141\) −3.83928e6 + 1.38894e6i −1.36959 + 0.495480i
\(142\) −1.50680e6 3.29943e6i −0.526247 1.15232i
\(143\) −14366.3 + 48927.2i −0.00491289 + 0.0167318i
\(144\) −27781.0 + 1.40628e6i −0.00930379 + 0.470960i
\(145\) 790282. 912034.i 0.259226 0.299162i
\(146\) −4.65909e6 669876.i −1.49707 0.215246i
\(147\) −3.70631e6 + 1.97653e6i −1.16678 + 0.622231i
\(148\) 191481. + 220981.i 0.0590664 + 0.0681663i
\(149\) −3.27945e6 5.10293e6i −0.991386 1.54263i −0.831525 0.555487i \(-0.812532\pi\)
−0.159860 0.987140i \(-0.551104\pi\)
\(150\) 2.04444e6 + 2.08522e6i 0.605759 + 0.617844i
\(151\) 3.16752e6 + 3.65551e6i 0.920001 + 1.06174i 0.997900 + 0.0647768i \(0.0206335\pi\)
−0.0778985 + 0.996961i \(0.524821\pi\)
\(152\) −902546. 3.07379e6i −0.257003 0.875273i
\(153\) 3.32470e6 905289.i 0.928278 0.252763i
\(154\) 4.80229e6 5.54214e6i 1.31488 1.51745i
\(155\) 1.74468e6 + 796770.i 0.468513 + 0.213963i
\(156\) −106875. 8705.56i −0.0281516 0.00229310i
\(157\) −298743. 654156.i −0.0771968 0.169037i 0.867099 0.498137i \(-0.165982\pi\)
−0.944295 + 0.329099i \(0.893255\pi\)
\(158\) −4.76395e6 + 684953.i −1.20780 + 0.173656i
\(159\) 2.05937e6 5.35912e6i 0.512321 1.33322i
\(160\) −3.57770e6 −0.873462
\(161\) −5.97356e6 + 2.18240e6i −1.43138 + 0.522945i
\(162\) 4.78600e6 + 4.49004e6i 1.12571 + 1.05610i
\(163\) 923514. + 593507.i 0.213246 + 0.137045i 0.642904 0.765947i \(-0.277729\pi\)
−0.429658 + 0.902992i \(0.641366\pi\)
\(164\) −532601. + 76576.5i −0.120745 + 0.0173606i
\(165\) 1.50312e6 + 2.04982e6i 0.334611 + 0.456313i
\(166\) −7.67941e6 2.25488e6i −1.67882 0.492945i
\(167\) 844538. + 385688.i 0.181330 + 0.0828107i 0.504011 0.863697i \(-0.331857\pi\)
−0.322681 + 0.946508i \(0.604584\pi\)
\(168\) 3.72479e6 + 2.08191e6i 0.785551 + 0.439070i
\(169\) 686640. 4.77569e6i 0.142255 0.989408i
\(170\) 1.36259e6 + 4.64056e6i 0.277344 + 0.944548i
\(171\) 6.96127e6 + 3.34682e6i 1.39220 + 0.669336i
\(172\) −6.49812e6 + 4.17609e6i −1.27703 + 0.820700i
\(173\) −4.31654e6 6.71667e6i −0.833676 1.29723i −0.952570 0.304319i \(-0.901571\pi\)
0.118894 0.992907i \(-0.462065\pi\)
\(174\) −3.85825e6 2.94816e6i −0.732391 0.559632i
\(175\) −4.39279e6 + 1.28984e6i −0.819646 + 0.240670i
\(176\) 2.16978e6 + 311967.i 0.397995 + 0.0572230i
\(177\) 2.98229e6 + 1.66690e6i 0.537812 + 0.300601i
\(178\) 2.63606e6 5.77217e6i 0.467408 1.02348i
\(179\) −323189. + 1.10068e6i −0.0563505 + 0.191912i −0.982858 0.184364i \(-0.940977\pi\)
0.926508 + 0.376276i \(0.122796\pi\)
\(180\) −3.57941e6 + 3.96965e6i −0.613754 + 0.680667i
\(181\) −741081. 5.15433e6i −0.124977 0.869233i −0.951789 0.306755i \(-0.900757\pi\)
0.826812 0.562479i \(-0.190152\pi\)
\(182\) 156623. 243711.i 0.0259802 0.0404260i
\(183\) −1.04540e7 + 2.16623e6i −1.70581 + 0.353470i
\(184\) 2.93010e6 + 2.22434e6i 0.470359 + 0.357065i
\(185\) 273820.i 0.0432465i
\(186\) 2.76822e6 7.20380e6i 0.430192 1.11950i
\(187\) −764251. 5.31548e6i −0.116872 0.812864i
\(188\) −1.21711e7 + 5.55835e6i −1.83171 + 0.836513i
\(189\) −9.74198e6 + 3.30827e6i −1.44298 + 0.490023i
\(190\) −4.50372e6 + 9.86177e6i −0.656615 + 1.43779i
\(191\) 6.74367e6 + 5.84342e6i 0.967823 + 0.838624i 0.986923 0.161194i \(-0.0515344\pi\)
−0.0190993 + 0.999818i \(0.506080\pi\)
\(192\) 680102. + 1.10404e7i 0.0960882 + 1.55984i
\(193\) −443866. + 130331.i −0.0617419 + 0.0181291i −0.312458 0.949932i \(-0.601152\pi\)
0.250716 + 0.968061i \(0.419334\pi\)
\(194\) 9.31401e6 8.07064e6i 1.27565 1.10536i
\(195\) 70299.9 + 71702.4i 0.00948093 + 0.00967007i
\(196\) −1.15804e7 + 7.44229e6i −1.53800 + 0.988412i
\(197\) −5.88079e6 + 5.09574e6i −0.769196 + 0.666512i −0.948320 0.317314i \(-0.897219\pi\)
0.179124 + 0.983826i \(0.442674\pi\)
\(198\) 7.86024e6 6.54365e6i 1.01261 0.842993i
\(199\) 668096. 4.64671e6i 0.0847773 0.589639i −0.902507 0.430675i \(-0.858275\pi\)
0.987284 0.158964i \(-0.0508155\pi\)
\(200\) 2.00142e6 + 1.73424e6i 0.250177 + 0.216780i
\(201\) 281322. 1.23440e6i 0.0346430 0.152008i
\(202\) 2.20612e7 + 6.47776e6i 2.67655 + 0.785907i
\(203\) 6.92461e6 3.16236e6i 0.827765 0.378027i
\(204\) 1.06190e7 3.84164e6i 1.25081 0.452508i
\(205\) 423898. + 272423.i 0.0492039 + 0.0316214i
\(206\) 5.59503e6i 0.640031i
\(207\) −8.71391e6 + 1.65531e6i −0.982431 + 0.186624i
\(208\) 86597.7 0.00962314
\(209\) 6.50811e6 1.01268e7i 0.712879 1.10926i
\(210\) −4.91269e6 1.35795e7i −0.530471 1.46631i
\(211\) −4.28419e6 9.38107e6i −0.456059 0.998630i −0.988368 0.152080i \(-0.951403\pi\)
0.532309 0.846550i \(-0.321324\pi\)
\(212\) 5.30085e6 1.80530e7i 0.556337 1.89471i
\(213\) 7.73263e6 + 1.76229e6i 0.800181 + 0.182364i
\(214\) 9.97916e6 1.15166e7i 1.01825 1.17512i
\(215\) 7.15989e6 + 1.02944e6i 0.720429 + 0.103582i
\(216\) 4.65647e6 + 3.70602e6i 0.462057 + 0.367745i
\(217\) 7.92312e6 + 9.14377e6i 0.775384 + 0.894841i
\(218\) −6.61301e6 1.02900e7i −0.638307 0.993225i
\(219\) 7.34896e6 7.20522e6i 0.699671 0.685985i
\(220\) 5.45518e6 + 6.29561e6i 0.512319 + 0.591248i
\(221\) −59768.3 203552.i −0.00553725 0.0188581i
\(222\) −1.09967e6 + 67741.0i −0.100508 + 0.00619146i
\(223\) −3.44243e6 + 3.97278e6i −0.310421 + 0.358245i −0.889426 0.457079i \(-0.848896\pi\)
0.579005 + 0.815324i \(0.303441\pi\)
\(224\) −2.05289e7 9.37524e6i −1.82651 0.834139i
\(225\) −6.33686e6 + 783693.i −0.556322 + 0.0688015i
\(226\) 6.55302e6 + 1.43491e7i 0.567696 + 1.24308i
\(227\) −1.13107e7 + 1.62623e6i −0.966968 + 0.139029i −0.607666 0.794192i \(-0.707894\pi\)
−0.359302 + 0.933221i \(0.616985\pi\)
\(228\) 2.36288e7 + 9.07992e6i 1.99360 + 0.766086i
\(229\) −4.79291e6 −0.399110 −0.199555 0.979887i \(-0.563950\pi\)
−0.199555 + 0.979887i \(0.563950\pi\)
\(230\) −2.56453e6 1.21826e7i −0.210777 1.00129i
\(231\) 3.25343e6 + 1.57008e7i 0.263940 + 1.27375i
\(232\) −3.70439e6 2.38067e6i −0.296656 0.190649i
\(233\) 9.05998e6 1.30263e6i 0.716241 0.102980i 0.225447 0.974255i \(-0.427616\pi\)
0.490794 + 0.871275i \(0.336707\pi\)
\(234\) 270566. 300064.i 0.0211167 0.0234189i
\(235\) 1.20225e7 + 3.53012e6i 0.926384 + 0.272011i
\(236\) 1.01849e7 + 4.65129e6i 0.774856 + 0.353865i
\(237\) 5.13435e6 9.18601e6i 0.385692 0.690052i
\(238\) −4.34186e6 + 3.01983e7i −0.322066 + 2.24002i
\(239\) 2.33182e6 + 7.94145e6i 0.170805 + 0.581709i 0.999750 + 0.0223782i \(0.00712379\pi\)
−0.828944 + 0.559331i \(0.811058\pi\)
\(240\) 2.62090e6 3.42998e6i 0.189591 0.248118i
\(241\) 1.78460e7 1.14689e7i 1.27494 0.819354i 0.284684 0.958621i \(-0.408111\pi\)
0.990255 + 0.139268i \(0.0444749\pi\)
\(242\) 3.20958e6 + 4.99421e6i 0.226466 + 0.352388i
\(243\) −1.41545e7 + 2.35427e6i −0.986448 + 0.164073i
\(244\) −3.35708e7 + 9.85728e6i −2.31096 + 0.678559i
\(245\) 1.27598e7 + 1.83458e6i 0.867651 + 0.124749i
\(246\) 989185. 1.76978e6i 0.0664465 0.118881i
\(247\) 197550. 432573.i 0.0131095 0.0287058i
\(248\) 1.97172e6 6.71506e6i 0.129268 0.440246i
\(249\) 1.41123e7 1.03484e7i 0.914112 0.670312i
\(250\) −3.55078e6 2.46962e7i −0.227250 1.58056i
\(251\) −5.99078e6 + 9.32183e6i −0.378846 + 0.589495i −0.977351 0.211623i \(-0.932125\pi\)
0.598506 + 0.801118i \(0.295761\pi\)
\(252\) −3.09411e7 + 1.33982e7i −1.93345 + 0.837230i
\(253\) 893440. + 1.37945e7i 0.0551701 + 0.851811i
\(254\) 4.26733e7i 2.60408i
\(255\) −9.87123e6 3.79325e6i −0.595320 0.228765i
\(256\) 302858. + 2.10642e6i 0.0180517 + 0.125553i
\(257\) 2.36273e7 1.07902e7i 1.39192 0.635669i 0.428471 0.903555i \(-0.359052\pi\)
0.963451 + 0.267886i \(0.0863250\pi\)
\(258\) 2.36294e6 2.90089e7i 0.137592 1.68917i
\(259\) 717537. 1.57119e6i 0.0412995 0.0904333i
\(260\) 248706. + 215505.i 0.0141503 + 0.0122613i
\(261\) 1.02440e7 2.78936e6i 0.576167 0.156886i
\(262\) 423950. 124483.i 0.0235728 0.00692159i
\(263\) 1.56377e7 1.35501e7i 0.859618 0.744863i −0.108835 0.994060i \(-0.534712\pi\)
0.968453 + 0.249197i \(0.0801665\pi\)
\(264\) 6.62281e6 6.49327e6i 0.359941 0.352900i
\(265\) −1.48226e7 + 9.52590e6i −0.796501 + 0.511880i
\(266\) −5.16849e7 + 4.47852e7i −2.74611 + 2.37952i
\(267\) 6.52885e6 + 1.22426e7i 0.343007 + 0.643191i
\(268\) 590482. 4.10689e6i 0.0306763 0.213358i
\(269\) −2.71921e7 2.35621e7i −1.39697 1.21048i −0.948538 0.316662i \(-0.897438\pi\)
−0.448430 0.893818i \(-0.648017\pi\)
\(270\) −3.69623e6 1.97982e7i −0.187788 1.00585i
\(271\) −1.51456e7 4.44716e6i −0.760991 0.223447i −0.121862 0.992547i \(-0.538887\pi\)
−0.639128 + 0.769100i \(0.720705\pi\)
\(272\) −8.29564e6 + 3.78849e6i −0.412233 + 0.188261i
\(273\) 215489. + 595648.i 0.0105910 + 0.0292753i
\(274\) −1.69898e7 1.09187e7i −0.825918 0.530785i
\(275\) 9.95114e6i 0.478492i
\(276\) −2.80228e7 + 7.72540e6i −1.33286 + 0.367446i
\(277\) −4.58119e6 −0.215546 −0.107773 0.994176i \(-0.534372\pi\)
−0.107773 + 0.994176i \(0.534372\pi\)
\(278\) −5.23828e6 + 8.15093e6i −0.243812 + 0.379378i
\(279\) 8.84064e6 + 1.43728e7i 0.407072 + 0.661801i
\(280\) −5.44019e6 1.19124e7i −0.247822 0.542655i
\(281\) 5.02907e6 1.71274e7i 0.226657 0.771922i −0.765114 0.643895i \(-0.777317\pi\)
0.991771 0.128027i \(-0.0408644\pi\)
\(282\) 1.12028e7 4.91559e7i 0.499549 2.19194i
\(283\) −2.40800e7 + 2.77898e7i −1.06242 + 1.22610i −0.0892514 + 0.996009i \(0.528447\pi\)
−0.973169 + 0.230090i \(0.926098\pi\)
\(284\) 2.57268e7 + 3.69896e6i 1.12313 + 0.161482i
\(285\) −1.11545e7 2.09165e7i −0.481856 0.903556i
\(286\) −412355. 475883.i −0.0176268 0.0203424i
\(287\) 1.71846e6 + 2.67398e6i 0.0726932 + 0.113113i
\(288\) −2.61376e7 1.75366e7i −1.09418 0.734121i
\(289\) −1.17620e6 1.35741e6i −0.0487290 0.0562363i
\(290\) 4.19840e6 + 1.42984e7i 0.172143 + 0.586266i
\(291\) 1.65683e6 + 2.68959e7i 0.0672354 + 1.09146i
\(292\) 2.20877e7 2.54905e7i 0.887158 1.02384i
\(293\) −3.11319e7 1.42175e7i −1.23767 0.565223i −0.314365 0.949302i \(-0.601792\pi\)
−0.923300 + 0.384079i \(0.874519\pi\)
\(294\) 4.21104e6 5.16974e7i 0.165709 2.03435i
\(295\) −4.35574e6 9.53775e6i −0.169667 0.371518i
\(296\) −988962. + 142191.i −0.0381333 + 0.00548274i
\(297\) 933840. + 2.23430e7i 0.0356454 + 0.852851i
\(298\) 7.49042e7 2.83046
\(299\) 112490. + 534375.i 0.00420822 + 0.0199909i
\(300\) −2.04903e7 + 4.24589e6i −0.758899 + 0.157255i
\(301\) 3.83860e7 + 2.46692e7i 1.40758 + 0.904598i
\(302\) −5.91209e7 + 8.50030e6i −2.14645 + 0.308612i
\(303\) −4.05415e7 + 2.97288e7i −1.45738 + 1.06868i
\(304\) −1.96149e7 5.75945e6i −0.698177 0.205003i
\(305\) 2.98040e7 + 1.36110e7i 1.05045 + 0.479724i
\(306\) −1.27917e7 + 4.05815e7i −0.446440 + 1.41633i
\(307\) 2.80765e6 1.95276e7i 0.0970349 0.674892i −0.882007 0.471235i \(-0.843808\pi\)
0.979042 0.203657i \(-0.0652827\pi\)
\(308\) 1.48045e7 + 5.04195e7i 0.506689 + 1.72562i
\(309\) 9.72058e6 + 7.42766e6i 0.329471 + 0.251754i
\(310\) −1.99247e7 + 1.28048e7i −0.668816 + 0.429822i
\(311\) −66001.1 102700.i −0.00219417 0.00341419i 0.840155 0.542347i \(-0.182464\pi\)
−0.842349 + 0.538933i \(0.818828\pi\)
\(312\) 222463. 291138.i 0.00732477 0.00958593i
\(313\) −2.68383e7 + 7.88043e6i −0.875229 + 0.256991i −0.688338 0.725390i \(-0.741659\pi\)
−0.186891 + 0.982381i \(0.559841\pi\)
\(314\) 8.78995e6 + 1.26380e6i 0.283921 + 0.0408217i
\(315\) 3.01143e7 + 9.49234e6i 0.963478 + 0.303698i
\(316\) 1.43268e7 3.13713e7i 0.454034 0.994195i
\(317\) 1.43122e7 4.87428e7i 0.449291 1.53014i −0.354398 0.935095i \(-0.615314\pi\)
0.803689 0.595049i \(-0.202868\pi\)
\(318\) 4.19232e7 + 5.71711e7i 1.30369 + 1.77785i
\(319\) −2.35480e6 1.63780e7i −0.0725407 0.504532i
\(320\) 1.83531e7 2.85580e7i 0.560093 0.871522i
\(321\) 6.76062e6 + 3.26261e7i 0.204396 + 0.986394i
\(322\) 1.72089e7 7.66245e7i 0.515448 2.29509i
\(323\) 5.00808e7i 1.48616i
\(324\) −4.56078e7 + 1.14561e7i −1.34093 + 0.336822i
\(325\) 55946.3 + 389115.i 0.00162975 + 0.0113352i
\(326\) −1.23309e7 + 5.63135e6i −0.355913 + 0.162540i
\(327\) 2.66566e7 + 2.17132e6i 0.762361 + 0.0620985i
\(328\) 763790. 1.67247e6i 0.0216447 0.0473953i
\(329\) 5.97348e7 + 5.17605e7i 1.67741 + 1.45349i
\(330\) −3.13289e7 + 1.92990e6i −0.871772 + 0.0537024i
\(331\) 3.45232e7 1.01369e7i 0.951977 0.279526i 0.231367 0.972866i \(-0.425680\pi\)
0.720610 + 0.693341i \(0.243862\pi\)
\(332\) 4.33431e7 3.75570e7i 1.18442 1.02631i
\(333\) 1.34217e6 2.00045e6i 0.0363475 0.0541744i
\(334\) −9.64482e6 + 6.19835e6i −0.258854 + 0.166355i
\(335\) −2.93646e6 + 2.54445e6i −0.0781068 + 0.0676800i
\(336\) 2.40269e7 1.28133e7i 0.633404 0.337787i
\(337\) −9.18567e6 + 6.38877e7i −0.240005 + 1.66927i 0.412095 + 0.911141i \(0.364797\pi\)
−0.652100 + 0.758133i \(0.726112\pi\)
\(338\) 4.50267e7 + 3.90159e7i 1.16606 + 1.01040i
\(339\) −3.36290e7 7.66414e6i −0.863206 0.196727i
\(340\) −3.32527e7 9.76389e6i −0.846040 0.248420i
\(341\) 2.39214e7 1.09246e7i 0.603287 0.275512i
\(342\) −8.12416e7 + 4.99714e7i −2.03095 + 1.24923i
\(343\) 1.66751e7 + 1.07164e7i 0.413224 + 0.265563i
\(344\) 2.63941e7i 0.648383i
\(345\) 2.45701e7 + 1.17175e7i 0.598343 + 0.285350i
\(346\) 9.85918e7 2.38019
\(347\) 3.75684e7 5.84576e7i 0.899155 1.39911i −0.0176797 0.999844i \(-0.505628\pi\)
0.916834 0.399268i \(-0.130736\pi\)
\(348\) 3.27190e7 1.18368e7i 0.776358 0.280864i
\(349\) −3.11053e7 6.81111e7i −0.731742 1.60229i −0.796679 0.604402i \(-0.793412\pi\)
0.0649371 0.997889i \(-0.479315\pi\)
\(350\) 1.59276e7 5.42443e7i 0.371488 1.26517i
\(351\) 162130. + 868420.i 0.00374924 + 0.0200821i
\(352\) −3.21235e7 + 3.70726e7i −0.736539 + 0.850011i
\(353\) −5.45521e7 7.84340e6i −1.24019 0.178312i −0.509167 0.860668i \(-0.670046\pi\)
−0.731020 + 0.682356i \(0.760955\pi\)
\(354\) −3.72262e7 + 1.98523e7i −0.839149 + 0.447509i
\(355\) −1.59392e7 1.83948e7i −0.356272 0.411160i
\(356\) 2.45832e7 + 3.82523e7i 0.544865 + 0.847827i
\(357\) −4.67013e7 4.76330e7i −1.02642 1.04689i
\(358\) −9.27647e6 1.07056e7i −0.202178 0.233326i
\(359\) −1.00806e7 3.43313e7i −0.217872 0.742005i −0.993800 0.111183i \(-0.964536\pi\)
0.775928 0.630822i \(-0.217282\pi\)
\(360\) −4.79852e6 1.76227e7i −0.102849 0.377716i
\(361\) −4.27073e7 + 4.92869e7i −0.907780 + 1.04763i
\(362\) 5.84918e7 + 2.67123e7i 1.23302 + 0.563100i
\(363\) −1.29376e7 1.05384e6i −0.270479 0.0220320i
\(364\) 862356. + 1.88830e6i 0.0178806 + 0.0391531i
\(365\) −3.12642e7 + 4.49511e6i −0.642936 + 0.0924403i
\(366\) 4.72889e7 1.23061e8i 0.964530 2.51001i
\(367\) −5.61215e6 −0.113535 −0.0567677 0.998387i \(-0.518079\pi\)
−0.0567677 + 0.998387i \(0.518079\pi\)
\(368\) 2.20499e7 8.05575e6i 0.442448 0.161645i
\(369\) 1.76155e6 + 4.06803e6i 0.0350603 + 0.0809664i
\(370\) 2.84450e6 + 1.82805e6i 0.0561567 + 0.0360897i
\(371\) −1.10015e8 + 1.58177e7i −2.15441 + 0.309758i
\(372\) 3.27013e7 + 4.45951e7i 0.635237 + 0.866281i
\(373\) 9.38296e7 + 2.75508e7i 1.80806 + 0.530895i 0.998428 0.0560413i \(-0.0178479\pi\)
0.809633 + 0.586936i \(0.199666\pi\)
\(374\) 6.03206e7 + 2.75475e7i 1.15306 + 0.526583i
\(375\) 4.76201e7 + 2.66164e7i 0.903017 + 0.504725i
\(376\) 6.50669e6 4.52551e7i 0.122404 0.851341i
\(377\) −184157. 627182.i −0.00343688 0.0117049i
\(378\) 3.06713e7 1.23288e8i 0.567881 2.28268i
\(379\) −2.20803e7 + 1.41902e7i −0.405591 + 0.260657i −0.727492 0.686116i \(-0.759314\pi\)
0.321902 + 0.946773i \(0.395678\pi\)
\(380\) −4.20005e7 6.53541e7i −0.765427 1.19103i
\(381\) −7.41389e7 5.66507e7i −1.34051 1.02431i
\(382\) −1.05724e8 + 3.10434e7i −1.89664 + 0.556902i
\(383\) 4.01857e7 + 5.77783e6i 0.715279 + 0.102842i 0.490340 0.871531i \(-0.336873\pi\)
0.224939 + 0.974373i \(0.427782\pi\)
\(384\) −5.41041e7 3.02405e7i −0.955512 0.534066i
\(385\) 2.04422e7 4.47622e7i 0.358216 0.784384i
\(386\) 1.60939e6 5.48107e6i 0.0279833 0.0953024i
\(387\) 4.72620e7 + 4.26159e7i 0.815417 + 0.735257i
\(388\) 1.25680e7 + 8.74122e7i 0.215164 + 1.49650i
\(389\) 2.08669e7 3.24696e7i 0.354495 0.551604i −0.617511 0.786562i \(-0.711859\pi\)
0.972006 + 0.234958i \(0.0754953\pi\)
\(390\) −1.21419e6 + 251598.i −0.0204688 + 0.00424144i
\(391\) −3.41539e7 4.62693e7i −0.571360 0.774039i
\(392\) 4.70375e7i 0.780882i
\(393\) −346541. + 901810.i −0.00570922 + 0.0148572i
\(394\) −1.36748e7 9.51105e7i −0.223580 1.55503i
\(395\) −2.93780e7 + 1.34165e7i −0.476684 + 0.217694i
\(396\) 8.99505e6 + 7.27331e7i 0.144850 + 1.17124i
\(397\) 5.14069e6 1.12565e7i 0.0821580 0.179901i −0.864095 0.503329i \(-0.832108\pi\)
0.946253 + 0.323428i \(0.104836\pi\)
\(398\) 4.38107e7 + 3.79622e7i 0.694914 + 0.602147i
\(399\) −9.19398e6 1.49250e8i −0.144739 2.34960i
\(400\) 1.62148e7 4.76111e6i 0.253357 0.0743923i
\(401\) −4.12862e7 + 3.57747e7i −0.640282 + 0.554808i −0.913344 0.407189i \(-0.866509\pi\)
0.273062 + 0.961997i \(0.411964\pi\)
\(402\) 1.09450e7 + 1.11634e7i 0.168476 + 0.171837i
\(403\) 873970. 561667.i 0.0133531 0.00858150i
\(404\) −1.24515e8 + 1.07893e8i −1.88833 + 1.63625i
\(405\) 3.93034e7 + 1.98613e7i 0.591651 + 0.298980i
\(406\) −1.33781e7 + 9.30465e7i −0.199901 + 1.39034i
\(407\) −2.83736e6 2.45859e6i −0.0420854 0.0364672i
\(408\) −8.57414e6 + 3.76219e7i −0.126244 + 0.553937i
\(409\) −1.12138e8 3.29266e7i −1.63901 0.481257i −0.672975 0.739665i \(-0.734984\pi\)
−0.966036 + 0.258408i \(0.916802\pi\)
\(410\) −5.65997e6 + 2.58482e6i −0.0821225 + 0.0375041i
\(411\) 4.15244e7 1.50224e7i 0.598106 0.216378i
\(412\) 3.37277e7 + 2.16754e7i 0.482275 + 0.309939i
\(413\) 6.61419e7i 0.938915i
\(414\) 4.09792e7 1.01573e8i 0.577514 1.43145i
\(415\) −5.37071e7 −0.751428
\(416\) −1.04769e6 + 1.63023e6i −0.0145530 + 0.0226449i
\(417\) −7.20703e6 1.99215e7i −0.0993913 0.274735i
\(418\) 6.17507e7 + 1.35215e8i 0.845499 + 1.85138i
\(419\) −2.24914e7 + 7.65987e7i −0.305756 + 1.04131i 0.653066 + 0.757301i \(0.273482\pi\)
−0.958822 + 0.284008i \(0.908336\pi\)
\(420\) 1.00891e8 + 2.29934e7i 1.36178 + 0.310353i
\(421\) −2.77670e7 + 3.20448e7i −0.372119 + 0.429449i −0.910664 0.413149i \(-0.864429\pi\)
0.538544 + 0.842597i \(0.318974\pi\)
\(422\) 1.26054e8 + 1.81238e7i 1.67733 + 0.241164i
\(423\) 7.05293e7 + 8.47199e7i 0.931855 + 1.11935i
\(424\) 4.21021e7 + 4.85884e7i 0.552339 + 0.637433i
\(425\) −2.23824e7 3.48277e7i −0.291568 0.453689i
\(426\) −6.99308e7 + 6.85630e7i −0.904565 + 0.886872i
\(427\) 1.35349e8 + 1.56201e8i 1.73848 + 2.00632i
\(428\) 3.07637e7 + 1.04772e8i 0.392380 + 1.33632i
\(429\) 1.37420e6 84652.6i 0.0174051 0.00107218i
\(430\) −5.84942e7 + 6.75059e7i −0.735711 + 0.849055i
\(431\) −9.96976e7 4.55304e7i −1.24524 0.568682i −0.319767 0.947496i \(-0.603605\pi\)
−0.925473 + 0.378814i \(0.876332\pi\)
\(432\) 3.59600e7 1.22116e7i 0.446035 0.151469i
\(433\) 3.73141e6 + 8.17066e6i 0.0459631 + 0.100645i 0.931221 0.364456i \(-0.118745\pi\)
−0.885257 + 0.465101i \(0.846018\pi\)
\(434\) −1.47883e8 + 2.12624e7i −1.80904 + 0.260101i
\(435\) −3.04151e7 1.16877e7i −0.369506 0.141991i
\(436\) 8.76489e7 1.05752
\(437\) 1.00608e7 1.28521e8i 0.120555 1.54003i
\(438\) 2.57869e7 + 1.24445e8i 0.306886 + 1.48100i
\(439\) −1.21382e8 7.80076e7i −1.43470 0.922026i −0.999767 0.0215633i \(-0.993136\pi\)
−0.434933 0.900463i \(-0.643228\pi\)
\(440\) −2.81749e7 + 4.05095e6i −0.330754 + 0.0475552i
\(441\) 8.42266e7 + 7.59467e7i 0.982050 + 0.885509i
\(442\) 2.51356e6 + 738048.i 0.0291087 + 0.00854708i
\(443\) 4.05050e7 + 1.84980e7i 0.465905 + 0.212772i 0.634514 0.772911i \(-0.281200\pi\)
−0.168609 + 0.985683i \(0.553928\pi\)
\(444\) 3.85182e6 6.89138e6i 0.0440065 0.0787331i
\(445\) 6.05996e6 4.21479e7i 0.0687685 0.478295i
\(446\) −1.82880e7 6.22833e7i −0.206140 0.702049i
\(447\) −9.94388e7 + 1.30136e8i −1.11335 + 1.45705i
\(448\) 1.80146e8 1.15773e8i 2.00351 1.28758i
\(449\) −2.11205e7 3.28642e7i −0.233327 0.363064i 0.704770 0.709436i \(-0.251050\pi\)
−0.938097 + 0.346371i \(0.887414\pi\)
\(450\) 3.41643e7 7.10606e7i 0.374917 0.779815i
\(451\) 6.62898e6 1.94644e6i 0.0722632 0.0212184i
\(452\) −1.11885e8 1.60867e7i −1.21159 0.174201i
\(453\) 6.37176e7 1.13999e8i 0.685432 1.22632i
\(454\) 5.86177e7 1.28355e8i 0.626414 1.37165i
\(455\) 547685. 1.86524e6i 0.00581428 0.0198016i
\(456\) −6.97522e7 + 5.11488e7i −0.735637 + 0.539437i
\(457\) −1.88782e7 1.31301e8i −0.197794 1.37568i −0.810669 0.585505i \(-0.800896\pi\)
0.612875 0.790180i \(-0.290013\pi\)
\(458\) 3.19979e7 4.97897e7i 0.333062 0.518255i
\(459\) −5.35231e7 7.60975e7i −0.553481 0.786923i
\(460\) 8.33738e7 + 3.17369e7i 0.856557 + 0.326055i
\(461\) 6.59057e7i 0.672698i 0.941737 + 0.336349i \(0.109192\pi\)
−0.941737 + 0.336349i \(0.890808\pi\)
\(462\) −1.84823e8 7.10224e7i −1.87426 0.720227i
\(463\) 1.69387e7 + 1.17811e8i 0.170662 + 1.18698i 0.877490 + 0.479594i \(0.159216\pi\)
−0.706828 + 0.707385i \(0.749875\pi\)
\(464\) −2.55604e7 + 1.16730e7i −0.255867 + 0.116850i
\(465\) 4.20435e6 5.16153e7i 0.0418158 0.513357i
\(466\) −4.69533e7 + 1.02813e8i −0.463990 + 1.01600i
\(467\) 7.96509e7 + 6.90179e7i 0.782060 + 0.677659i 0.951420 0.307896i \(-0.0996248\pi\)
−0.169361 + 0.985554i \(0.554170\pi\)
\(468\) 760642. + 2.79348e6i 0.00742066 + 0.0272526i
\(469\) −2.35171e7 + 6.90524e6i −0.227963 + 0.0669361i
\(470\) −1.16935e8 + 1.01325e8i −1.12629 + 0.975938i
\(471\) −1.38647e7 + 1.35935e7i −0.132693 + 0.130098i
\(472\) −3.21858e7 + 2.06846e7i −0.306082 + 0.196707i
\(473\) 7.49546e7 6.49485e7i 0.708296 0.613742i
\(474\) 6.11487e7 + 1.14663e8i 0.574186 + 1.07669i
\(475\) 1.32071e7 9.18577e7i 0.123233 0.857106i
\(476\) −1.65219e8 1.43163e8i −1.53193 1.32743i
\(477\) −1.54982e8 3.06166e6i −1.42799 0.0282099i
\(478\) −9.80649e7 2.87944e7i −0.897904 0.263648i
\(479\) 3.37216e7 1.54001e7i 0.306832 0.140126i −0.256048 0.966664i \(-0.582420\pi\)
0.562880 + 0.826538i \(0.309693\pi\)
\(480\) 3.28620e7 + 9.08364e7i 0.297146 + 0.821365i
\(481\) −124770. 80185.0i −0.00112118 0.000720540i
\(482\) 2.61955e8i 2.33930i
\(483\) 1.10279e8 + 1.31620e8i 0.978701 + 1.16811i
\(484\) −4.25399e7 −0.375198
\(485\) 4.47109e7 6.95715e7i 0.391912 0.609826i
\(486\) 7.00398e7 1.62757e8i 0.610149 1.41785i
\(487\) −2.09622e7 4.59007e7i −0.181488 0.397404i 0.796920 0.604085i \(-0.206461\pi\)
−0.978408 + 0.206681i \(0.933734\pi\)
\(488\) 3.36824e7 1.14712e8i 0.289830 0.987071i
\(489\) 6.58620e6 2.88991e7i 0.0563259 0.247149i
\(490\) −1.04244e8 + 1.20304e8i −0.886056 + 1.02256i
\(491\) −4.15522e7 5.97430e6i −0.351034 0.0504711i −0.0354574 0.999371i \(-0.511289\pi\)
−0.315577 + 0.948900i \(0.602198\pi\)
\(492\) 6.83631e6 + 1.28192e7i 0.0574019 + 0.107638i
\(493\) 4.50794e7 + 5.20244e7i 0.376216 + 0.434177i
\(494\) 3.17480e6 + 4.94009e6i 0.0263352 + 0.0409783i
\(495\) 3.82375e7 5.69915e7i 0.315264 0.469888i
\(496\) −2.92462e7 3.37519e7i −0.239676 0.276600i
\(497\) −4.32565e7 1.47318e8i −0.352357 1.20002i
\(498\) 1.32867e7 + 2.15689e8i 0.107580 + 1.74638i
\(499\) −9.59198e7 + 1.10697e8i −0.771981 + 0.890913i −0.996503 0.0835557i \(-0.973372\pi\)
0.224522 + 0.974469i \(0.427918\pi\)
\(500\) 1.62628e8 + 7.42699e7i 1.30103 + 0.594159i
\(501\) 2.03517e6 2.49851e7i 0.0161841 0.198686i
\(502\) −5.68421e7 1.24467e8i −0.449324 0.983882i
\(503\) −5.59985e7 + 8.05137e6i −0.440020 + 0.0632653i −0.358765 0.933428i \(-0.616802\pi\)
−0.0812553 + 0.996693i \(0.525893\pi\)
\(504\) 1.86457e7 1.13694e8i 0.145642 0.888066i
\(505\) 1.54289e8 1.19801
\(506\) −1.49264e8 8.28119e7i −1.15214 0.639206i
\(507\) −1.27560e8 + 2.64323e7i −0.978790 + 0.202820i
\(508\) −2.57241e8 1.65319e8i −1.96222 1.26104i
\(509\) 2.05418e8 2.95347e7i 1.55771 0.223965i 0.691027 0.722829i \(-0.257158\pi\)
0.866680 + 0.498864i \(0.166249\pi\)
\(510\) 1.05306e8 7.72203e7i 0.793860 0.582132i
\(511\) −1.91174e8 5.61336e7i −1.43273 0.420688i
\(512\) 1.09739e8 + 5.01161e7i 0.817619 + 0.373394i
\(513\) 2.10335e7 2.07485e8i 0.155797 1.53686i
\(514\) −4.56470e7 + 3.17482e8i −0.336142 + 2.33792i
\(515\) −1.05776e7 3.60239e7i −0.0774397 0.263735i
\(516\) 1.65716e8 + 1.26626e8i 1.20619 + 0.921668i
\(517\) 1.44528e8 9.28822e7i 1.04587 0.672142i
\(518\) 1.15315e7 + 1.79433e7i 0.0829651 + 0.129096i
\(519\) −1.30885e8 + 1.71289e8i −0.936242 + 1.22526i
\(520\) −1.07894e6 + 316804.i −0.00767337 + 0.00225310i
\(521\) −1.19489e8 1.71800e7i −0.844921 0.121481i −0.293759 0.955879i \(-0.594906\pi\)
−0.551162 + 0.834398i \(0.685815\pi\)
\(522\) −3.94135e7 + 1.25039e8i −0.277098 + 0.879091i
\(523\) 4.00577e7 8.77142e7i 0.280015 0.613147i −0.716405 0.697684i \(-0.754214\pi\)
0.996420 + 0.0845369i \(0.0269411\pi\)
\(524\) −892003. + 3.03788e6i −0.00619973 + 0.0211143i
\(525\) 7.30973e7 + 9.96836e7i 0.505153 + 0.688884i
\(526\) 3.63629e7 + 2.52910e8i 0.249863 + 1.73783i
\(527\) −5.91502e7 + 9.20395e7i −0.404133 + 0.628843i
\(528\) −1.20092e7 5.79553e7i −0.0815854 0.393723i
\(529\) 7.83528e7 + 1.25600e8i 0.529282 + 0.848446i
\(530\) 2.17576e8i 1.46145i
\(531\) 1.49289e7 9.10301e7i 0.0997110 0.607997i
\(532\) −6.97417e7 4.85064e8i −0.463188 3.22154i
\(533\) 248267. 113380.i 0.00163960 0.000748779i
\(534\) −1.70766e8 1.39098e7i −1.12144 0.0913477i
\(535\) 4.24788e7 9.30157e7i 0.277403 0.607428i
\(536\) 1.07147e7 + 9.28435e6i 0.0695803 + 0.0602917i
\(537\) 3.09144e7 1.90437e6i 0.199636 0.0122978i
\(538\) 4.26306e8 1.25175e8i 2.73763 0.803840i
\(539\) 1.33578e8 1.15746e8i 0.853039 0.739162i
\(540\) 1.33666e8 + 5.44177e7i 0.848864 + 0.345588i
\(541\) 2.75422e7 1.77003e7i 0.173943 0.111786i −0.450772 0.892639i \(-0.648851\pi\)
0.624715 + 0.780853i \(0.285215\pi\)
\(542\) 1.47312e8 1.27646e8i 0.925208 0.801697i
\(543\) −1.24059e8 + 6.61595e7i −0.774872 + 0.413231i
\(544\) 2.90436e7 2.02003e8i 0.180407 1.25476i
\(545\) −6.20317e7 5.37508e7i −0.383199 0.332044i
\(546\) −7.62634e6 1.73806e6i −0.0468531 0.0106780i
\(547\) 9.31739e7 + 2.73583e7i 0.569288 + 0.167158i 0.553694 0.832720i \(-0.313218\pi\)
0.0155945 + 0.999878i \(0.495036\pi\)
\(548\) 1.31639e8 6.01175e7i 0.799913 0.365308i
\(549\) 1.51023e8 + 2.45526e8i 0.912693 + 1.48382i
\(550\) −1.03375e8 6.64348e7i −0.621334 0.399307i
\(551\) 1.54308e8i 0.922432i
\(552\) 2.95614e7 9.48252e7i 0.175755 0.563776i
\(553\) −2.03729e8 −1.20470
\(554\) 3.05845e7 4.75904e7i 0.179875 0.279892i
\(555\) −6.95219e6 + 2.51510e6i −0.0406670 + 0.0147122i
\(556\) −2.88416e7 6.31542e7i −0.167801 0.367433i
\(557\) −4.40814e7 + 1.50128e8i −0.255088 + 0.868750i 0.727994 + 0.685584i \(0.240453\pi\)
−0.983082 + 0.183166i \(0.941365\pi\)
\(558\) −2.08328e8 4.11551e6i −1.19907 0.0236876i
\(559\) 2.56577e6 2.96105e6i 0.0146887 0.0169516i
\(560\) −8.27181e7 1.18931e7i −0.471017 0.0677220i
\(561\) −1.27938e8 + 6.82280e7i −0.724622 + 0.386433i
\(562\) 1.44349e8 + 1.66587e8i 0.813213 + 0.938497i
\(563\) 5.26862e7 + 8.19813e7i 0.295237 + 0.459398i 0.956906 0.290398i \(-0.0937877\pi\)
−0.661668 + 0.749797i \(0.730151\pi\)
\(564\) 2.52919e8 + 2.57964e8i 1.40975 + 1.43788i
\(565\) 6.93192e7 + 7.99987e7i 0.384334 + 0.443545i
\(566\) −1.27926e8 4.35675e8i −0.705519 2.40278i
\(567\) 1.73478e8 + 2.16958e8i 0.951690 + 1.19022i
\(568\) −5.81600e7 + 6.71202e7i −0.317380 + 0.366276i
\(569\) 9.81704e7 + 4.48329e7i 0.532898 + 0.243366i 0.663643 0.748050i \(-0.269010\pi\)
−0.130745 + 0.991416i \(0.541737\pi\)
\(570\) 2.91754e8 + 2.37650e7i 1.57541 + 0.128325i
\(571\) 3.12206e7 + 6.83636e7i 0.167700 + 0.367212i 0.974759 0.223259i \(-0.0716695\pi\)
−0.807059 + 0.590470i \(0.798942\pi\)
\(572\) 4.46617e6 642139.i 0.0238642 0.00343116i
\(573\) 8.64200e7 2.24892e8i 0.459357 1.19539i
\(574\) −3.92504e7 −0.207543
\(575\) 5.04426e7 + 9.38736e7i 0.265335 + 0.493787i
\(576\) 2.74064e8 1.18676e8i 1.43411 0.621005i
\(577\) 2.64484e8 + 1.69974e8i 1.37680 + 0.884818i 0.999154 0.0411308i \(-0.0130960\pi\)
0.377650 + 0.925949i \(0.376732\pi\)
\(578\) 2.19534e7 3.15643e6i 0.113689 0.0163460i
\(579\) 7.38606e6 + 1.00725e7i 0.0380520 + 0.0518919i
\(580\) −1.02458e8 3.00843e7i −0.525123 0.154190i
\(581\) −3.08172e8 1.40738e8i −1.57132 0.717599i
\(582\) −2.90462e8 1.62348e8i −1.47340 0.823529i
\(583\) −3.43810e7 + 2.39125e8i −0.173505 + 1.20675i
\(584\) 3.24701e7 + 1.10583e8i 0.163022 + 0.555201i
\(585\) 1.17477e6 2.44349e6i 0.00586795 0.0122051i
\(586\) 3.55534e8 2.28488e8i 1.76680 1.13546i
\(587\) 1.21478e8 + 1.89024e8i 0.600599 + 0.934551i 0.999843 + 0.0177062i \(0.00563635\pi\)
−0.399244 + 0.916845i \(0.630727\pi\)
\(588\) 2.95326e8 + 2.25663e8i 1.45268 + 1.11001i
\(589\) −2.35315e8 + 6.90947e7i −1.15160 + 0.338142i
\(590\) 1.28160e8 + 1.84266e7i 0.624015 + 0.0897198i
\(591\) 1.83395e8 + 1.02505e8i 0.888434 + 0.496574i
\(592\) −2.64860e6 + 5.79963e6i −0.0127659 + 0.0279534i
\(593\) −6.93963e7 + 2.36342e8i −0.332791 + 1.13338i 0.607870 + 0.794037i \(0.292024\pi\)
−0.940661 + 0.339347i \(0.889794\pi\)
\(594\) −2.38339e8 1.39463e8i −1.13720 0.665428i
\(595\) 2.91354e7 + 2.02641e8i 0.138315 + 0.962004i
\(596\) −2.90183e8 + 4.51534e8i −1.37067 + 2.13281i
\(597\) −1.24115e8 + 2.57184e7i −0.583311 + 0.120871i
\(598\) −6.30219e6 2.39898e6i −0.0294705 0.0112182i
\(599\) 2.92550e7i 0.136119i 0.997681 + 0.0680597i \(0.0216808\pi\)
−0.997681 + 0.0680597i \(0.978319\pi\)
\(600\) 2.56481e7 6.67445e7i 0.118741 0.309002i
\(601\) −4.38092e7 3.04700e8i −0.201810 1.40362i −0.798910 0.601450i \(-0.794590\pi\)
0.597101 0.802166i \(-0.296319\pi\)
\(602\) −5.12537e8 + 2.34068e8i −2.34929 + 1.07288i
\(603\) −3.39248e7 + 4.19555e6i −0.154727 + 0.0191354i
\(604\) 1.77796e8 3.89320e8i 0.806886 1.76683i
\(605\) 3.01067e7 + 2.60876e7i 0.135956 + 0.117806i
\(606\) −3.81698e7 6.19626e8i −0.171515 2.78427i
\(607\) 1.62978e7 4.78546e6i 0.0728722 0.0213972i −0.245093 0.969500i \(-0.578819\pi\)
0.317965 + 0.948102i \(0.397000\pi\)
\(608\) 3.45731e8 2.99578e8i 1.53825 1.33290i
\(609\) −1.43895e8 1.46766e8i −0.637081 0.649790i
\(610\) −3.40369e8 + 2.18742e8i −1.49955 + 0.963701i
\(611\) 5.12920e6 4.44448e6i 0.0224867 0.0194848i
\(612\) −1.95075e8 2.34325e8i −0.851036 1.02227i
\(613\) 6.20632e7 4.31659e8i 0.269434 1.87396i −0.184374 0.982856i \(-0.559026\pi\)
0.453808 0.891100i \(-0.350065\pi\)
\(614\) 1.84113e8 + 1.59535e8i 0.795389 + 0.689208i
\(615\) 3.02310e6 1.32649e7i 0.0129965 0.0570266i
\(616\) −1.72284e8 5.05871e7i −0.737059 0.216420i
\(617\) −2.62965e8 + 1.20092e8i −1.11955 + 0.511280i −0.887215 0.461357i \(-0.847363\pi\)
−0.232332 + 0.972637i \(0.574636\pi\)
\(618\) −1.42056e8 + 5.13917e7i −0.601857 + 0.217735i
\(619\) −1.89482e7 1.21772e7i −0.0798905 0.0513425i 0.500086 0.865976i \(-0.333302\pi\)
−0.579976 + 0.814633i \(0.696938\pi\)
\(620\) 1.69715e8i 0.712109i
\(621\) 1.22067e8 + 2.06038e8i 0.509710 + 0.860346i
\(622\) 1.50749e6 0.00626447
\(623\) 1.45219e8 2.25966e8i 0.600565 0.934498i
\(624\) −795420. 2.19868e6i −0.00327373 0.00904917i
\(625\) −1.26989e7 2.78066e7i −0.0520145 0.113896i
\(626\) 9.73114e7 3.31412e8i 0.396681 1.35097i
\(627\) −3.16894e8 7.22211e7i −1.28562 0.292996i
\(628\) −4.16711e7 + 4.80910e7i −0.168250 + 0.194171i
\(629\) 1.54603e7 + 2.22286e6i 0.0621251 + 0.00893224i
\(630\) −2.99655e8 + 2.49462e8i −1.19839 + 0.997662i
\(631\) 2.34047e8 + 2.70104e8i 0.931567 + 1.07509i 0.997013 + 0.0772296i \(0.0246074\pi\)
−0.0654463 + 0.997856i \(0.520847\pi\)
\(632\) 6.37122e7 + 9.91381e7i 0.252389 + 0.392726i
\(633\) −1.98830e8 + 1.94941e8i −0.783919 + 0.768586i
\(634\) 4.10801e8 + 4.74089e8i 1.61199 + 1.86034i
\(635\) 8.06750e7 + 2.74754e8i 0.315078 + 1.07306i
\(636\) −5.07048e8 + 3.12349e7i −1.97096 + 0.121414i
\(637\) 4.57251e6 5.27695e6i 0.0176903 0.0204157i
\(638\) 1.85859e8 + 8.48789e7i 0.715684 + 0.326842i
\(639\) −2.62822e7 2.12515e8i −0.100730 0.814494i
\(640\) 7.90209e7 + 1.73032e8i 0.301441 + 0.660063i
\(641\) 2.15263e8 3.09502e7i 0.817328 0.117514i 0.279045 0.960278i \(-0.409982\pi\)
0.538283 + 0.842764i \(0.319073\pi\)
\(642\) −3.84062e8 1.47584e8i −1.45143 0.557745i
\(643\) −1.17248e8 −0.441036 −0.220518 0.975383i \(-0.570775\pi\)
−0.220518 + 0.975383i \(0.570775\pi\)
\(644\) 3.95235e8 + 4.00585e8i 1.47978 + 1.49981i
\(645\) −3.96283e7 1.91242e8i −0.147682 0.712697i
\(646\) −5.20250e8 3.34345e8i −1.92981 1.24021i
\(647\) 3.68327e7 5.29574e6i 0.135994 0.0195530i −0.0739815 0.997260i \(-0.523571\pi\)
0.209976 + 0.977707i \(0.432661\pi\)
\(648\) 5.13236e7 1.52267e8i 0.188622 0.559603i
\(649\) −1.37941e8 4.05031e7i −0.504613 0.148168i
\(650\) −4.41571e6 2.01659e6i −0.0160790 0.00734305i
\(651\) 1.59381e8 2.85152e8i 0.577688 1.03356i
\(652\) 1.38241e7 9.61488e7i 0.0498763 0.346897i
\(653\) −1.05189e8 3.58242e8i −0.377774 1.28658i −0.900790 0.434256i \(-0.857011\pi\)
0.523016 0.852323i \(-0.324807\pi\)
\(654\) −2.00518e8 + 2.62418e8i −0.716836 + 0.938124i
\(655\) 2.49428e6 1.60298e6i 0.00887609 0.00570431i
\(656\) −6.34325e6 9.87030e6i −0.0224699 0.0349638i
\(657\) −2.50440e8 1.20406e8i −0.883094 0.424571i
\(658\) −9.36494e8 + 2.74979e8i −3.28721 + 0.965212i
\(659\) 3.24060e8 + 4.65928e7i 1.13232 + 0.162803i 0.682896 0.730516i \(-0.260720\pi\)
0.449424 + 0.893319i \(0.351629\pi\)
\(660\) 1.09736e8 1.96331e8i 0.381696 0.682901i
\(661\) 3.57205e7 7.82169e7i 0.123684 0.270830i −0.837654 0.546201i \(-0.816073\pi\)
0.961338 + 0.275371i \(0.0888008\pi\)
\(662\) −1.25176e8 + 4.26309e8i −0.431465 + 1.46944i
\(663\) −4.61912e6 + 3.38717e6i −0.0158496 + 0.0116224i
\(664\) 2.78894e7 + 1.93975e8i 0.0952653 + 0.662585i
\(665\) −2.48108e8 + 3.86063e8i −0.843675 + 1.31278i
\(666\) 1.18206e7 + 2.72979e7i 0.0400145 + 0.0924073i
\(667\) −1.05234e8 1.42564e8i −0.354634 0.480434i
\(668\) 8.21531e7i 0.275610i
\(669\) 1.32487e8 + 5.09111e7i 0.442480 + 0.170033i
\(670\) −6.82825e6 4.74915e7i −0.0227031 0.157904i
\(671\) 4.08644e8 1.86622e8i 1.35263 0.617724i
\(672\) −4.94707e7 + 6.07335e8i −0.163020 + 2.00134i
\(673\) −1.45399e8 + 3.18379e8i −0.476997 + 1.04448i 0.506281 + 0.862369i \(0.331020\pi\)
−0.983278 + 0.182110i \(0.941707\pi\)
\(674\) −6.02355e8 5.21943e8i −1.96731 1.70468i
\(675\) 7.81032e7 + 1.53692e8i 0.253955 + 0.499735i
\(676\) −4.09629e8 + 1.20278e8i −1.32602 + 0.389355i
\(677\) −2.89489e8 + 2.50844e8i −0.932968 + 0.808421i −0.981709 0.190390i \(-0.939025\pi\)
0.0487405 + 0.998811i \(0.484479\pi\)
\(678\) 3.04127e8 2.98178e8i 0.975811 0.956725i
\(679\) 4.38862e8 2.82039e8i 1.40190 0.900949i
\(680\) 8.94973e7 7.75498e7i 0.284632 0.246635i
\(681\) 1.45181e8 + 2.72237e8i 0.459693 + 0.861997i
\(682\) −4.62153e7 + 3.21434e8i −0.145691 + 1.01330i
\(683\) −1.67923e8 1.45506e8i −0.527044 0.456687i 0.350238 0.936661i \(-0.386101\pi\)
−0.877283 + 0.479974i \(0.840646\pi\)
\(684\) 1.34991e7 6.83328e8i 0.0421829 2.13531i
\(685\) −1.30032e8 3.81808e7i −0.404555 0.118788i
\(686\) −2.22649e8 + 1.01680e8i −0.689681 + 0.314967i
\(687\) 4.40240e7 + 1.21690e8i 0.135775 + 0.375305i
\(688\) −1.41692e8 9.10600e7i −0.435091 0.279616i
\(689\) 9.54368e6i 0.0291782i
\(690\) −2.85757e8 + 1.77013e8i −0.869859 + 0.538837i
\(691\) 4.93649e8 1.49618 0.748090 0.663598i \(-0.230971\pi\)
0.748090 + 0.663598i \(0.230971\pi\)
\(692\) −3.81950e8 + 5.94325e8i −1.15262 + 1.79352i
\(693\) 3.68752e8 2.26818e8i 1.10799 0.681520i
\(694\) 3.56459e8 + 7.80537e8i 1.06643 + 2.33515i
\(695\) −1.83174e7 + 6.23832e7i −0.0545643 + 0.185829i
\(696\) −2.64185e7 + 1.15920e8i −0.0783575 + 0.343820i
\(697\) −1.88226e7 + 2.17224e7i −0.0555880 + 0.0641520i
\(698\) 9.15214e8 + 1.31588e8i 2.69127 + 0.386946i
\(699\) −1.16291e8 2.18064e8i −0.340499 0.638488i
\(700\) 2.65288e8 + 3.06159e8i 0.773435 + 0.892591i
\(701\) 1.52040e7 + 2.36580e7i 0.0441372 + 0.0686789i 0.862621 0.505851i \(-0.168821\pi\)
−0.818484 + 0.574530i \(0.805185\pi\)
\(702\) −1.01037e7 4.11341e6i −0.0292059 0.0118902i
\(703\) 2.29283e7 + 2.64606e7i 0.0659941 + 0.0761613i
\(704\) −1.31132e8 4.46595e8i −0.375830 1.27996i
\(705\) −2.08010e7 3.37671e8i −0.0593632 0.963667i
\(706\) 4.45674e8 5.14335e8i 1.26649 1.46161i
\(707\) 8.85311e8 + 4.04308e8i 2.50517 + 1.14407i
\(708\) 2.45436e7 3.01314e8i 0.0691575 0.849022i
\(709\) 1.25671e8 + 2.75181e8i 0.352612 + 0.772112i 0.999951 + 0.00990990i \(0.00315447\pi\)
−0.647339 + 0.762202i \(0.724118\pi\)
\(710\) 2.97501e8 4.27742e7i 0.831216 0.119511i
\(711\) −2.80389e8 4.59836e7i −0.780104 0.127936i
\(712\) −1.55373e8 −0.430464
\(713\) 1.70285e8 2.24315e8i 0.469794 0.618856i
\(714\) 8.06603e8 1.67140e8i 2.21598 0.459184i
\(715\) −3.55463e6 2.28442e6i −0.00972471 0.00624969i
\(716\) 1.00473e8 1.44458e7i 0.273721 0.0393551i
\(717\) 1.80212e8 1.32148e8i 0.488907 0.358512i
\(718\) 4.23939e8 + 1.24480e8i 1.14533 + 0.336299i
\(719\) −4.29149e8 1.95986e8i −1.15457 0.527275i −0.256249 0.966611i \(-0.582487\pi\)
−0.898323 + 0.439335i \(0.855214\pi\)
\(720\) −1.11159e8 3.50385e7i −0.297816 0.0938746i
\(721\) 3.37050e7 2.34424e8i 0.0899268 0.625455i
\(722\) −2.26884e8 7.72696e8i −0.602827 2.05304i
\(723\) −4.55111e8 3.47758e8i −1.20421 0.920157i
\(724\) −3.87626e8 + 2.49112e8i −1.02140 + 0.656416i
\(725\) −6.89644e7 1.07311e8i −0.180972 0.281598i
\(726\) 9.73202e7 1.27363e8i 0.254327 0.332838i
\(727\) 1.14007e8 3.34756e7i 0.296708 0.0871214i −0.129990 0.991515i \(-0.541495\pi\)
0.426699 + 0.904394i \(0.359676\pi\)
\(728\) −7.02114e6 1.00949e6i −0.0181976 0.00261642i
\(729\) 1.89786e8 + 3.37751e8i 0.489871 + 0.871795i
\(730\) 1.62026e8 3.54788e8i 0.416502 0.912012i
\(731\) −1.16247e8 + 3.95902e8i −0.297599 + 1.01353i
\(732\) 5.58628e8 + 7.61808e8i 1.42426 + 1.94228i
\(733\) 5.75171e7 + 4.00040e8i 0.146045 + 1.01576i 0.922612 + 0.385728i \(0.126050\pi\)
−0.776568 + 0.630034i \(0.783041\pi\)
\(734\) 3.74673e7 5.83002e7i 0.0947466 0.147429i
\(735\) −7.06224e7 3.40817e8i −0.177861 0.858340i
\(736\) −1.15114e8 + 5.12557e8i −0.288732 + 1.28561i
\(737\) 5.32741e7i 0.133080i
\(738\) −5.40198e7 8.85920e6i −0.134395 0.0220407i
\(739\) −1.81363e7 1.26141e8i −0.0449383 0.312552i −0.999876 0.0157463i \(-0.994988\pi\)
0.954938 0.296806i \(-0.0959215\pi\)
\(740\) −2.20395e7 + 1.00651e7i −0.0543885 + 0.0248384i
\(741\) −1.27974e7 1.04242e6i −0.0314534 0.00256205i
\(742\) 5.70150e8 1.24846e9i 1.39565 3.05606i
\(743\) −5.87297e7 5.08896e7i −0.143183 0.124069i 0.580324 0.814385i \(-0.302926\pi\)
−0.723507 + 0.690317i \(0.757471\pi\)
\(744\) −1.88603e8 + 1.16182e7i −0.457963 + 0.0282112i
\(745\) 4.82274e8 1.41608e8i 1.16634 0.342468i
\(746\) −9.12619e8 + 7.90789e8i −2.19823 + 1.90478i
\(747\) −3.92367e8 2.63253e8i −0.941306 0.631554i
\(748\) −3.99745e8 + 2.56901e8i −0.955165 + 0.613847i
\(749\) 4.87489e8 4.22412e8i 1.16016 1.00529i
\(750\) −5.94413e8 + 3.16994e8i −1.40898 + 0.751392i
\(751\) 1.11286e7 7.74008e7i 0.0262736 0.182737i −0.972459 0.233076i \(-0.925121\pi\)
0.998732 + 0.0503389i \(0.0160301\pi\)
\(752\) −2.20496e8 1.91061e8i −0.518497 0.449280i
\(753\) 2.91704e8 + 6.64802e7i 0.683216 + 0.155707i
\(754\) 7.74475e6 + 2.27406e6i 0.0180673 + 0.00530504i
\(755\) −3.64582e8 + 1.66499e8i −0.847139 + 0.386875i
\(756\) 6.24376e8 + 6.62516e8i 1.44504 + 1.53331i
\(757\) 1.21867e8 + 7.83191e7i 0.280930 + 0.180543i 0.673516 0.739172i \(-0.264783\pi\)
−0.392586 + 0.919715i \(0.628420\pi\)
\(758\) 3.24110e8i 0.744192i
\(759\) 3.42029e8 1.49389e8i 0.782236 0.341660i
\(760\) 2.65456e8 0.604716
\(761\) 6.76253e7 1.05227e8i 0.153446 0.238767i −0.756017 0.654553i \(-0.772857\pi\)
0.909463 + 0.415786i \(0.136493\pi\)
\(762\) 1.08346e9 3.91964e8i 2.44876 0.885893i
\(763\) −2.15087e8 4.70975e8i −0.484218 1.06029i
\(764\) 2.22447e8 7.57584e8i 0.498822 1.69883i
\(765\) −5.63941e6 + 2.85468e8i −0.0125965 + 0.637637i
\(766\) −3.28305e8 + 3.78884e8i −0.730451 + 0.842986i
\(767\) −5.62155e6 808256.i −0.0124586 0.00179128i
\(768\) 5.06994e7 2.70374e7i 0.111923 0.0596872i
\(769\) −1.02350e8 1.18119e8i −0.225066 0.259740i 0.631974 0.774989i \(-0.282245\pi\)
−0.857040 + 0.515249i \(0.827699\pi\)
\(770\) 3.28525e8 + 5.11194e8i 0.719608 + 1.11973i
\(771\) −4.90982e8 5.00777e8i −1.07128 1.09265i
\(772\) 2.68058e7 + 3.09356e7i 0.0582609 + 0.0672367i
\(773\) −1.69797e7 5.78275e7i −0.0367613 0.125198i 0.939068 0.343731i \(-0.111691\pi\)
−0.975829 + 0.218534i \(0.929873\pi\)
\(774\) −7.58229e8 + 2.06460e8i −1.63523 + 0.445259i
\(775\) 1.32765e8 1.53219e8i 0.285219 0.329160i
\(776\) −2.74491e8 1.25356e8i −0.587411 0.268262i
\(777\) −4.64825e7 3.78626e6i −0.0990893 0.00807137i
\(778\) 1.97991e8 + 4.33540e8i 0.420443 + 0.920641i
\(779\) −6.37746e7 + 9.16940e6i −0.134907 + 0.0193967i
\(780\) 3.18716e6 8.29400e6i 0.00671614 0.0174775i
\(781\) −3.33725e8 −0.700545
\(782\) 7.08670e8 4.58992e7i 1.48192 0.0959808i
\(783\) −1.64914e8 2.34470e8i −0.343537 0.488430i
\(784\) −2.52512e8 1.62280e8i −0.524004 0.336757i
\(785\) 5.89837e7 8.48058e6i 0.121934 0.0175314i
\(786\) −7.05465e6 9.62051e6i −0.0145281 0.0198121i
\(787\) −5.59739e8 1.64354e8i −1.14832 0.337176i −0.348434 0.937333i \(-0.613286\pi\)
−0.799882 + 0.600157i \(0.795105\pi\)
\(788\) 6.26317e8 + 2.86029e8i 1.28002 + 0.584564i
\(789\) −4.87668e8 2.72574e8i −0.992873 0.554949i
\(790\) 5.67571e7 3.94754e8i 0.115117 0.800656i
\(791\) 1.88121e8 + 6.40683e8i 0.380110 + 1.29453i
\(792\) −2.25694e8 1.08508e8i −0.454301 0.218418i
\(793\) 1.49298e7 9.59482e6i 0.0299389 0.0192405i
\(794\) 8.26155e7 + 1.28552e8i 0.165044 + 0.256814i
\(795\) 3.78008e8 + 2.88842e8i 0.752314 + 0.574856i
\(796\) −3.98567e8 + 1.17030e8i −0.790245 + 0.232037i
\(797\) 2.05125e8 + 2.94925e7i 0.405176 + 0.0582556i 0.341890 0.939740i \(-0.388933\pi\)
0.0632860 + 0.997995i \(0.479842\pi\)
\(798\) 1.61182e9 + 9.00895e8i 3.17181 + 1.77282i
\(799\) −2.96915e8 + 6.50152e8i −0.582091 + 1.27460i
\(800\) −1.06543e8 + 3.62852e8i −0.208091 + 0.708694i
\(801\) 2.50866e8 2.78216e8i 0.488140 0.541358i
\(802\) −9.60043e7 6.67725e8i −0.186109 1.29442i
\(803\) −2.34137e8 + 3.64324e8i −0.452192 + 0.703624i
\(804\) −1.09696e8 + 2.27307e7i −0.211068 + 0.0437365i
\(805\) −3.40605e7 5.25884e8i −0.0652924 1.00810i
\(806\) 1.28287e7i 0.0245007i
\(807\) −3.48467e8 + 9.06821e8i −0.663041 + 1.72544i
\(808\) −8.01200e7 5.57247e8i −0.151882 1.05636i
\(809\) −4.85146e8 + 2.21559e8i −0.916277 + 0.418450i −0.817018 0.576612i \(-0.804374\pi\)
−0.0992590 + 0.995062i \(0.531647\pi\)
\(810\) −4.68716e8 + 2.75696e8i −0.881973 + 0.518772i
\(811\) 3.35632e8 7.34931e8i 0.629217 1.37779i −0.279404 0.960174i \(-0.590137\pi\)
0.908622 0.417620i \(-0.137136\pi\)
\(812\) −5.09070e8 4.41112e8i −0.950845 0.823912i
\(813\) 2.62046e7 + 4.25389e8i 0.0487647 + 0.791617i
\(814\) 4.44828e7 1.30613e7i 0.0824743 0.0242166i
\(815\) −6.87470e7 + 5.95697e7i −0.126993 + 0.110040i
\(816\) 1.72386e8 + 1.75825e8i 0.317271 + 0.323601i
\(817\) −7.78096e8 + 5.00052e8i −1.42681 + 0.916957i
\(818\) 1.09069e9 9.45089e8i 1.99270 1.72668i
\(819\) 1.31440e7 1.09423e7i 0.0239262 0.0199186i
\(820\) 6.34534e6 4.41328e7i 0.0115084 0.0800424i
\(821\) −7.92178e8 6.86426e8i −1.43151 1.24041i −0.925967 0.377604i \(-0.876748\pi\)
−0.505539 0.862804i \(-0.668706\pi\)
\(822\) −1.21166e8 + 5.31655e8i −0.218155 + 0.957227i
\(823\) −6.30839e8 1.85231e8i −1.13167 0.332288i −0.338305 0.941037i \(-0.609853\pi\)
−0.793363 + 0.608749i \(0.791672\pi\)
\(824\) −1.24615e8 + 5.69099e7i −0.222736 + 0.101720i
\(825\) 2.52655e8 9.14035e7i 0.449952 0.162780i
\(826\) 6.87096e8 + 4.41570e8i 1.21921 + 0.783536i
\(827\) 8.68686e8i 1.53584i −0.640545 0.767920i \(-0.721292\pi\)
0.640545 0.767920i \(-0.278708\pi\)
\(828\) 4.53541e8 + 6.40528e8i 0.798960 + 1.12836i
\(829\) 7.54901e8 1.32503 0.662516 0.749048i \(-0.269489\pi\)
0.662516 + 0.749048i \(0.269489\pi\)
\(830\) 3.58554e8 5.57920e8i 0.627076 0.975749i
\(831\) 4.20793e7 + 1.16315e8i 0.0733273 + 0.202690i
\(832\) −7.63840e6 1.67258e7i −0.0132627 0.0290413i
\(833\) −2.07167e8 + 7.05545e8i −0.358414 + 1.22065i
\(834\) 2.55064e8 + 5.81297e7i 0.439694 + 0.100207i
\(835\) −5.03804e7 + 5.81421e7i −0.0865371 + 0.0998692i
\(836\) −1.05432e9 1.51589e8i −1.80449 0.259446i
\(837\) 2.83715e8 3.56477e8i 0.483845 0.607933i
\(838\) −6.45569e8 7.45026e8i −1.09701 1.26602i
\(839\) 2.54251e7 + 3.95622e7i 0.0430503 + 0.0669875i 0.862112 0.506718i \(-0.169142\pi\)
−0.819061 + 0.573706i \(0.805505\pi\)
\(840\) −2.52480e8 + 2.47542e8i −0.425981 + 0.417649i
\(841\) −2.50628e8 2.89241e8i −0.421349 0.486263i
\(842\) −1.47513e8 5.02383e8i −0.247112 0.841587i
\(843\) −4.81052e8 + 2.96334e7i −0.802988 + 0.0494652i
\(844\) −5.97593e8 + 6.89660e8i −0.993982 + 1.14712i
\(845\) 3.63667e8 + 1.66081e8i 0.602745 + 0.275265i
\(846\) −1.35095e9 + 1.67075e8i −2.23114 + 0.275930i
\(847\) 1.04391e8 + 2.28585e8i 0.171796 + 0.376181i
\(848\) 4.06091e8 5.83870e7i 0.665941 0.0957478i
\(849\) 9.26751e8 + 3.56125e8i 1.51440 + 0.581942i
\(850\) 5.11225e8 0.832445
\(851\) −3.92287e7 8.81028e6i −0.0636525 0.0142956i
\(852\) −1.42392e8 6.87169e8i −0.230232 1.11108i
\(853\) −7.50005e7 4.81999e7i −0.120842 0.0776603i 0.478824 0.877911i \(-0.341063\pi\)
−0.599665 + 0.800251i \(0.704700\pi\)
\(854\) −2.52625e9 + 3.63220e8i −4.05604 + 0.583171i
\(855\) −4.28605e8 + 4.75333e8i −0.685739 + 0.760500i
\(856\) −3.58005e8 1.05120e8i −0.570779 0.167596i
\(857\) 1.07932e8 + 4.92911e7i 0.171478 + 0.0783115i 0.499305 0.866426i \(-0.333589\pi\)
−0.327826 + 0.944738i \(0.606316\pi\)
\(858\) −8.29490e6 + 1.48406e7i −0.0131326 + 0.0234958i
\(859\) −1.42249e7 + 9.89362e7i −0.0224424 + 0.156090i −0.997961 0.0638266i \(-0.979670\pi\)
0.975519 + 0.219917i \(0.0705786\pi\)
\(860\) −1.80326e8 6.14132e8i −0.283506 0.965532i
\(861\) 5.21067e7 6.81921e7i 0.0816365 0.106838i
\(862\) 1.13857e9 7.31715e8i 1.77762 1.14240i
\(863\) −4.60046e8 7.15845e8i −0.715762 1.11375i −0.988436 0.151641i \(-0.951544\pi\)
0.272674 0.962107i \(-0.412092\pi\)
\(864\) −2.05167e8 + 8.24700e8i −0.318102 + 1.27866i
\(865\) 6.34787e8 1.86390e8i 0.980799 0.287989i
\(866\) −1.09790e8 1.57854e7i −0.169047 0.0243053i
\(867\) −2.36603e7 + 4.23313e7i −0.0363048 + 0.0649538i
\(868\) 4.44734e8 9.73831e8i 0.680050 1.48910i
\(869\) −1.24757e8 + 4.24882e8i −0.190110 + 0.647455i
\(870\) 3.24468e8 2.37930e8i 0.492736 0.361320i
\(871\) 299512. + 2.08315e6i 0.000453273 + 0.00315258i
\(872\) −1.61920e8 + 2.51953e8i −0.244204 + 0.379988i
\(873\) 6.67658e8 2.89111e8i 1.00349 0.434533i
\(874\) 1.26793e9 + 9.62529e8i 1.89916 + 1.44172i
\(875\) 1.05613e9i 1.57649i
\(876\) −8.50074e8 3.26660e8i −1.26457 0.485942i
\(877\) −2.91259e7 2.02575e8i −0.0431798 0.300322i −0.999955 0.00949350i \(-0.996978\pi\)
0.956775 0.290829i \(-0.0939310\pi\)
\(878\) 1.62072e9 7.40157e8i 2.39455 1.09355i
\(879\) −7.50220e7 + 9.21018e8i −0.110464 + 1.35613i
\(880\) −7.54571e7 + 1.65228e8i −0.110727 + 0.242458i
\(881\) 6.46796e8 + 5.60452e8i 0.945887 + 0.819616i 0.983727 0.179668i \(-0.0575023\pi\)
−0.0378402 + 0.999284i \(0.512048\pi\)
\(882\) −1.35126e9 + 3.67936e8i −1.96939 + 0.536249i
\(883\) 1.61071e8 4.72946e7i 0.233956 0.0686957i −0.162653 0.986683i \(-0.552005\pi\)
0.396609 + 0.917988i \(0.370187\pi\)
\(884\) −1.41867e7 + 1.22929e7i −0.0205365 + 0.0177949i
\(885\) −2.02151e8 + 1.98197e8i −0.291639 + 0.285935i
\(886\) −4.62576e8 + 2.97280e8i −0.665093 + 0.427429i
\(887\) −3.57781e8 + 3.10019e8i −0.512681 + 0.444240i −0.872380 0.488828i \(-0.837425\pi\)
0.359700 + 0.933068i \(0.382879\pi\)
\(888\) 1.26940e7 + 2.38033e7i 0.0181284 + 0.0339937i
\(889\) −2.57068e8 + 1.78795e9i −0.365884 + 2.54478i
\(890\) 3.97385e8 + 3.44336e8i 0.563691 + 0.488441i
\(891\) 5.58703e8 2.28936e8i 0.789856 0.323654i
\(892\) 4.46302e8 + 1.31046e8i 0.628831 + 0.184641i
\(893\) −1.45739e9 + 6.65567e8i −2.04654 + 0.934625i
\(894\) −6.88013e8 1.90179e9i −0.962906 2.66164i
\(895\) −7.99662e7 5.13911e7i −0.111542 0.0716835i
\(896\) 1.19993e9i 1.66814i
\(897\) 1.25343e7 7.76442e6i 0.0173670 0.0107580i
\(898\) 4.82402e8 0.666163
\(899\) −1.82253e8 + 2.83591e8i −0.250839 + 0.390313i
\(900\) 2.96009e8 + 4.81240e8i 0.406048 + 0.660137i
\(901\) −4.17518e8 9.14238e8i −0.570823 1.24993i
\(902\) −2.40356e7 + 8.18579e7i −0.0327519 + 0.111543i
\(903\) 2.73756e8 1.20120e9i 0.371793 1.63137i
\(904\) 2.52936e8 2.91904e8i 0.342378 0.395125i
\(905\) 4.27102e8 + 6.14080e7i 0.576217 + 0.0828475i
\(906\) 7.58858e8 + 1.42298e9i 1.02041 + 1.91343i
\(907\) 6.54351e8 + 7.55162e8i 0.876979 + 1.01209i 0.999807 + 0.0196594i \(0.00625819\pi\)
−0.122828 + 0.992428i \(0.539196\pi\)
\(908\) 5.46653e8 + 8.50609e8i 0.730221 + 1.13625i
\(909\) 1.12718e9 + 7.56266e8i 1.50073 + 1.00689i
\(910\) 1.57201e7 + 1.81420e7i 0.0208609 + 0.0240747i
\(911\) −1.78929e8 6.09377e8i −0.236661 0.805992i −0.989089 0.147318i \(-0.952936\pi\)
0.752429 0.658674i \(-0.228882\pi\)
\(912\) 3.39372e7 + 5.50916e8i 0.0447395 + 0.726275i
\(913\) −4.82227e8 + 5.56519e8i −0.633634 + 0.731253i
\(914\) 1.49001e9 + 6.80466e8i 1.95142 + 0.891185i
\(915\) 7.18219e7 8.81733e8i 0.0937549 1.15100i
\(916\) 1.76178e8 + 3.85776e8i 0.229227 + 0.501936i
\(917\) 1.85128e7 2.66174e6i 0.0240084 0.00345189i
\(918\) 1.14784e9 4.79747e7i 1.48373 0.0620132i
\(919\) 6.10511e8 0.786587 0.393294 0.919413i \(-0.371336\pi\)
0.393294 + 0.919413i \(0.371336\pi\)
\(920\) −2.45253e8 + 1.81034e8i −0.314956 + 0.232486i
\(921\) −5.21588e8 + 1.08081e8i −0.667649 + 0.138347i
\(922\) −6.84642e8 4.39993e8i −0.873515 0.561374i
\(923\) −1.30495e7 + 1.87623e6i −0.0165954 + 0.00238606i
\(924\) 1.14415e9 8.38994e8i 1.45033 1.06351i
\(925\) −2.77710e7 8.15429e6i −0.0350886 0.0103029i
\(926\) −1.33693e9 6.10556e8i −1.68374 0.768940i
\(927\) 9.92994e7 3.15026e8i 0.124654 0.395465i
\(928\) 8.94887e7 6.22407e8i 0.111976 0.778809i
\(929\) 2.11094e8 + 7.18921e8i 0.263287 + 0.896673i 0.979948 + 0.199252i \(0.0638512\pi\)
−0.716661 + 0.697421i \(0.754331\pi\)
\(930\) 5.08122e8 + 3.88265e8i 0.631712 + 0.482702i
\(931\) −1.38666e9 + 8.91152e8i −1.71839 + 1.10434i
\(932\) −4.37874e8 6.81346e8i −0.540881 0.841627i
\(933\) −2.00127e6 + 2.61906e6i −0.00246411 + 0.00322478i
\(934\) −1.24873e9 + 3.66660e8i −1.53260 + 0.450011i
\(935\) 4.40456e8 + 6.33280e7i 0.538849 + 0.0774748i
\(936\) −9.43524e6 2.97408e6i −0.0115060 0.00362681i
\(937\) −2.10796e8 + 4.61578e8i −0.256237 + 0.561082i −0.993409 0.114624i \(-0.963434\pi\)
0.737171 + 0.675706i \(0.236161\pi\)
\(938\) 8.52693e7 2.90401e8i 0.103320 0.351875i
\(939\) 4.46597e8 + 6.09030e8i 0.539410 + 0.735600i
\(940\) −1.57788e8 1.09744e9i −0.189972 1.32129i
\(941\) −5.23668e8 + 8.14844e8i −0.628474 + 0.977925i 0.370324 + 0.928903i \(0.379247\pi\)
−0.998798 + 0.0490220i \(0.984390\pi\)
\(942\) −4.86503e7 2.34782e8i −0.0582013 0.280874i
\(943\) 5.26676e7 5.19642e7i 0.0628070 0.0619682i
\(944\) 2.44146e8i 0.290224i
\(945\) −3.56006e7 8.51780e8i −0.0421854 1.00933i
\(946\) 1.74295e8 + 1.21225e9i 0.205878 + 1.43192i
\(947\) −1.47138e9 + 6.71955e8i −1.73250 + 0.791207i −0.739493 + 0.673165i \(0.764935\pi\)
−0.993009 + 0.118042i \(0.962338\pi\)
\(948\) −9.28101e8 7.55989e7i −1.08936 0.0887340i
\(949\) −7.10707e6 + 1.55623e7i −0.00831557 + 0.0182086i
\(950\) 8.66064e8 + 7.50449e8i 1.01013 + 0.875287i
\(951\) −1.36902e9 + 8.43335e7i −1.59172 + 0.0980525i
\(952\) 7.16754e8 2.10458e8i 0.830729 0.243924i
\(953\) −6.87170e8 + 5.95436e8i −0.793936 + 0.687950i −0.954215 0.299122i \(-0.903306\pi\)
0.160279 + 0.987072i \(0.448761\pi\)
\(954\) 1.06648e9 1.58954e9i 1.22831 1.83074i
\(955\) −6.22021e8 + 3.99748e8i −0.714158 + 0.458962i
\(956\) 5.53486e8 4.79598e8i 0.633480 0.548913i
\(957\) −3.94201e8 + 2.10223e8i −0.449761 + 0.239853i
\(958\) −6.51487e7 + 4.53119e8i −0.0740985 + 0.515366i
\(959\) −6.46073e8 5.59826e8i −0.732531 0.634742i
\(960\) −8.93655e8 2.03667e8i −1.01008 0.230200i
\(961\) 3.37480e8 + 9.90932e7i 0.380258 + 0.111654i
\(962\) 1.66596e6 760817.i 0.00187128 0.000854585i
\(963\) 7.66266e8 4.71328e8i 0.858027 0.527770i
\(964\) −1.57910e9 1.01483e9i −1.76271 1.13282i
\(965\) 3.83327e7i 0.0426567i
\(966\) −2.10353e9 + 2.66887e8i −2.33355 + 0.296071i
\(967\) 1.13479e8 0.125498 0.0627490 0.998029i \(-0.480013\pi\)
0.0627490 + 0.998029i \(0.480013\pi\)
\(968\) 7.85871e7 1.22284e8i 0.0866414 0.134817i
\(969\) 1.27153e9 4.60004e8i 1.39751 0.505581i
\(970\) 4.24229e8 + 9.28932e8i 0.464820 + 1.01781i
\(971\) 5.04683e8 1.71879e9i 0.551266 1.87744i 0.0770575 0.997027i \(-0.475448\pi\)
0.474208 0.880413i \(-0.342734\pi\)
\(972\) 7.09783e8 + 1.05274e9i 0.772906 + 1.14636i
\(973\) −2.68578e8 + 3.09956e8i −0.291563 + 0.336482i
\(974\) 6.16772e8 + 8.86784e7i 0.667494 + 0.0959712i
\(975\) 9.36559e6 4.99456e6i 0.0101046 0.00538869i
\(976\) −4.99605e8 5.76575e8i −0.537375 0.620164i
\(977\) −5.52554e8 8.59791e8i −0.592504 0.921954i −0.999962 0.00873004i \(-0.997221\pi\)
0.407458 0.913224i \(-0.366415\pi\)
\(978\) 2.56240e8 + 2.61352e8i 0.273924 + 0.279389i
\(979\) −3.82330e8 4.41233e8i −0.407465 0.470240i
\(980\) −3.21362e8 1.09446e9i −0.341441 1.16284i
\(981\) −1.89718e8 6.96743e8i −0.200956 0.738016i
\(982\) 3.39468e8 3.91767e8i 0.358480 0.413708i
\(983\) −4.44442e7 2.02970e7i −0.0467901 0.0213683i 0.391883 0.920015i \(-0.371824\pi\)
−0.438673 + 0.898647i \(0.644551\pi\)
\(984\) −4.94788e7 4.03032e6i −0.0519319 0.00423013i
\(985\) −2.67855e8 5.86520e8i −0.280279 0.613726i
\(986\) −8.41395e8 + 1.20974e8i −0.877747 + 0.126201i
\(987\) 7.65500e8 1.99207e9i 0.796148 2.07183i
\(988\) −4.20789e7 −0.0436308
\(989\) 3.77854e8 9.92636e8i 0.390603 1.02613i
\(990\) 3.36762e8 + 7.77701e8i 0.347071 + 0.801506i
\(991\) −1.93273e8 1.24209e8i −0.198587 0.127624i 0.437568 0.899185i \(-0.355840\pi\)
−0.636155 + 0.771561i \(0.719476\pi\)
\(992\) 9.89220e8 1.42228e8i 1.01335 0.145697i
\(993\) −5.74475e8 7.83419e8i −0.586710 0.800104i
\(994\) 1.81916e9 + 5.34153e8i 1.85230 + 0.543884i
\(995\) 3.53846e8 + 1.61596e8i 0.359207 + 0.164044i
\(996\) −1.35168e9 7.55495e8i −1.36803 0.764634i
\(997\) 9.75738e7 6.78641e8i 0.0984573 0.684786i −0.879487 0.475922i \(-0.842114\pi\)
0.977945 0.208864i \(-0.0669765\pi\)
\(998\) −5.09577e8 1.73546e9i −0.512647 1.74591i
\(999\) −6.31187e7 1.57025e7i −0.0633084 0.0157497i
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 69.7.h.a.2.7 460
3.2 odd 2 inner 69.7.h.a.2.40 yes 460
23.12 even 11 inner 69.7.h.a.35.40 yes 460
69.35 odd 22 inner 69.7.h.a.35.7 yes 460
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.7.h.a.2.7 460 1.1 even 1 trivial
69.7.h.a.2.40 yes 460 3.2 odd 2 inner
69.7.h.a.35.7 yes 460 69.35 odd 22 inner
69.7.h.a.35.40 yes 460 23.12 even 11 inner