Properties

Label 38.8.e.b.5.4
Level $38$
Weight $8$
Character 38.5
Analytic conductor $11.871$
Analytic rank $0$
Dimension $36$
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] = [38,8,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), 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: \(11.8706309684\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 38.5
Dual form 38.8.e.b.23.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(-0.665685 + 3.77529i) q^{3} +(49.0268 - 41.1384i) q^{4} +(10.1638 + 8.52843i) q^{5} +(5.32548 + 30.2023i) q^{6} +(-800.791 - 1387.01i) q^{7} +(256.000 - 443.405i) q^{8} +(2041.30 + 742.972i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(-0.665685 + 3.77529i) q^{3} +(49.0268 - 41.1384i) q^{4} +(10.1638 + 8.52843i) q^{5} +(5.32548 + 30.2023i) q^{6} +(-800.791 - 1387.01i) q^{7} +(256.000 - 443.405i) q^{8} +(2041.30 + 742.972i) q^{9} +(99.7418 + 36.3031i) q^{10} +(706.965 - 1224.50i) q^{11} +(122.673 + 212.476i) q^{12} +(-1782.69 - 10110.1i) q^{13} +(-9815.07 - 8235.82i) q^{14} +(-38.9631 + 32.6940i) q^{15} +(711.263 - 4033.77i) q^{16} +(19157.1 - 6972.61i) q^{17} +17378.4 q^{18} +(-27146.5 - 12527.6i) q^{19} +849.144 q^{20} +(5769.44 - 2099.90i) q^{21} +(1964.21 - 11139.6i) q^{22} +(-40776.7 + 34215.7i) q^{23} +(1503.57 + 1261.64i) q^{24} +(-13535.7 - 76764.7i) q^{25} +(-41064.4 - 71125.6i) q^{26} +(-8355.75 + 14472.6i) q^{27} +(-96319.7 - 35057.5i) q^{28} +(230577. + 83923.2i) q^{29} +(-203.451 + 352.388i) q^{30} +(40177.3 + 69589.1i) q^{31} +(-5690.10 - 32270.2i) q^{32} +(4152.22 + 3484.13i) q^{33} +(124936. - 104834. i) q^{34} +(3689.96 - 20926.8i) q^{35} +(130643. - 47550.2i) q^{36} -302101. q^{37} +(-238352. - 19900.0i) q^{38} +39355.4 q^{39} +(6383.48 - 2323.40i) q^{40} +(-137434. + 779428. i) q^{41} +(37626.3 - 31572.2i) q^{42} +(543716. + 456232. i) q^{43} +(-15713.7 - 89116.8i) q^{44} +(14410.9 + 24960.5i) q^{45} +(-212921. + 368789. i) q^{46} +(542065. + 197295. i) q^{47} +(14755.2 + 5370.44i) q^{48} +(-870762. + 1.50820e6i) q^{49} +(-311796. - 540046. i) q^{50} +(13571.0 + 76965.0i) q^{51} +(-503315. - 422331. i) q^{52} +(1.06840e6 - 896498. i) q^{53} +(-23215.4 + 131661. i) q^{54} +(17628.5 - 6416.25i) q^{55} -820010. q^{56} +(65366.4 - 94146.2i) q^{57} +1.96300e6 q^{58} +(-1.93477e6 + 704199. i) q^{59} +(-565.262 + 3205.76i) q^{60} +(1.31323e6 - 1.10193e6i) q^{61} +(492442. + 413208. i) q^{62} +(-604144. - 3.42627e6i) q^{63} +(-131072. - 227023. i) q^{64} +(68104.7 - 117961. i) q^{65} +(40747.6 + 14830.9i) q^{66} +(-448240. - 163146. i) q^{67} +(652369. - 1.12994e6i) q^{68} +(-102030. - 176720. i) q^{69} +(-29519.6 - 167414. i) q^{70} +(-481494. - 404022. i) q^{71} +(852010. - 714921. i) q^{72} +(830493. - 4.70996e6i) q^{73} +(-2.27106e6 + 826598. i) q^{74} +298819. q^{75} +(-1.84627e6 + 502571. i) q^{76} -2.26453e6 q^{77} +(295856. - 107683. i) q^{78} +(770818. - 4.37153e6i) q^{79} +(41630.9 - 34932.4i) q^{80} +(3.59027e6 + 3.01259e6i) q^{81} +(1.09947e6 + 6.23542e6i) q^{82} +(-291149. - 504286. i) q^{83} +(196471. - 340297. i) q^{84} +(254174. + 92511.7i) q^{85} +(5.33573e6 + 1.94205e6i) q^{86} +(-470326. + 814628. i) q^{87} +(-361966. - 626944. i) q^{88} +(-272892. - 1.54764e6i) q^{89} +(176631. + 148211. i) q^{90} +(-1.25953e7 + 1.05687e7i) q^{91} +(-591572. + 3.35497e6i) q^{92} +(-289464. + 105356. i) q^{93} +4.61483e6 q^{94} +(-169070. - 358845. i) q^{95} +125617. q^{96} +(-1.54608e6 + 562727. i) q^{97} +(-2.41930e6 + 1.37205e7i) q^{98} +(2.35290e6 - 1.97431e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 84 q^{3} + 672 q^{6} - 2988 q^{7} + 9216 q^{8} + 1428 q^{9} + 1800 q^{11} - 38334 q^{13} + 20832 q^{14} + 111228 q^{15} - 86574 q^{17} - 285888 q^{18} - 160152 q^{19} + 48384 q^{20} - 71442 q^{21} + 129984 q^{22} + 142920 q^{23} + 43008 q^{24} - 514068 q^{25} - 77856 q^{26} + 159492 q^{27} + 204288 q^{28} - 626034 q^{29} + 82656 q^{31} + 1576494 q^{33} + 85632 q^{34} + 581760 q^{35} + 91392 q^{36} + 1090848 q^{37} - 398496 q^{38} - 282624 q^{39} + 450780 q^{41} - 898128 q^{42} + 3066264 q^{43} - 1039872 q^{44} - 1208484 q^{45} + 166080 q^{46} - 1923516 q^{47} + 688128 q^{48} - 3667500 q^{49} + 4263456 q^{50} + 5070996 q^{51} + 440448 q^{52} - 4486374 q^{53} + 1382688 q^{54} - 5711508 q^{55} - 3059712 q^{56} - 5167644 q^{57} + 1718304 q^{58} - 5420364 q^{59} - 3484416 q^{60} + 20074776 q^{61} + 5592864 q^{62} - 4282596 q^{63} - 4718592 q^{64} + 10490790 q^{65} - 6939360 q^{66} + 5235372 q^{67} - 171648 q^{68} - 11912298 q^{69} - 4654080 q^{70} + 10980792 q^{71} + 1462272 q^{72} - 11218440 q^{73} - 443088 q^{74} - 8817984 q^{75} + 470016 q^{76} + 44477160 q^{77} - 11046144 q^{78} - 30314100 q^{79} - 40768188 q^{81} - 3606240 q^{82} + 4370208 q^{83} + 14171520 q^{84} - 20507004 q^{85} + 35895744 q^{86} + 14888064 q^{87} - 921600 q^{88} + 9695220 q^{89} + 34283424 q^{90} - 24159408 q^{91} - 3868416 q^{92} + 4014432 q^{93} - 46331520 q^{94} - 16025892 q^{95} - 47992770 q^{97} - 32609808 q^{98} + 62837148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 2.73616i 0.664463 0.241845i
\(3\) −0.665685 + 3.77529i −0.0142346 + 0.0807282i −0.991097 0.133138i \(-0.957495\pi\)
0.976863 + 0.213866i \(0.0686057\pi\)
\(4\) 49.0268 41.1384i 0.383022 0.321394i
\(5\) 10.1638 + 8.52843i 0.0363631 + 0.0305122i 0.660788 0.750573i \(-0.270222\pi\)
−0.624425 + 0.781085i \(0.714667\pi\)
\(6\) 5.32548 + 30.2023i 0.0100654 + 0.0570835i
\(7\) −800.791 1387.01i −0.882422 1.52840i −0.848640 0.528970i \(-0.822578\pi\)
−0.0337813 0.999429i \(-0.510755\pi\)
\(8\) 256.000 443.405i 0.176777 0.306186i
\(9\) 2041.30 + 742.972i 0.933378 + 0.339722i
\(10\) 99.7418 + 36.3031i 0.0315411 + 0.0114800i
\(11\) 706.965 1224.50i 0.160149 0.277386i −0.774773 0.632239i \(-0.782136\pi\)
0.934922 + 0.354853i \(0.115469\pi\)
\(12\) 122.673 + 212.476i 0.0204934 + 0.0354956i
\(13\) −1782.69 10110.1i −0.225047 1.27631i −0.862595 0.505896i \(-0.831162\pi\)
0.637547 0.770411i \(-0.279949\pi\)
\(14\) −9815.07 8235.82i −0.955972 0.802156i
\(15\) −38.9631 + 32.6940i −0.00298081 + 0.00250120i
\(16\) 711.263 4033.77i 0.0434120 0.246202i
\(17\) 19157.1 6972.61i 0.945711 0.344211i 0.177292 0.984158i \(-0.443266\pi\)
0.768418 + 0.639948i \(0.221044\pi\)
\(18\) 17378.4 0.702355
\(19\) −27146.5 12527.6i −0.907978 0.419017i
\(20\) 849.144 0.0237343
\(21\) 5769.44 2099.90i 0.135946 0.0494803i
\(22\) 1964.21 11139.6i 0.0393286 0.223044i
\(23\) −40776.7 + 34215.7i −0.698818 + 0.586378i −0.921437 0.388527i \(-0.872984\pi\)
0.222619 + 0.974906i \(0.428539\pi\)
\(24\) 1503.57 + 1261.64i 0.0222015 + 0.0186293i
\(25\) −13535.7 76764.7i −0.173257 0.982589i
\(26\) −41064.4 71125.6i −0.458204 0.793632i
\(27\) −8355.75 + 14472.6i −0.0816982 + 0.141505i
\(28\) −96319.7 35057.5i −0.829205 0.301806i
\(29\) 230577. + 83923.2i 1.75559 + 0.638983i 0.999873 0.0159146i \(-0.00506599\pi\)
0.755718 + 0.654898i \(0.227288\pi\)
\(30\) −203.451 + 352.388i −0.00137574 + 0.00238285i
\(31\) 40177.3 + 69589.1i 0.242223 + 0.419542i 0.961347 0.275339i \(-0.0887902\pi\)
−0.719124 + 0.694881i \(0.755457\pi\)
\(32\) −5690.10 32270.2i −0.0306970 0.174091i
\(33\) 4152.22 + 3484.13i 0.0201132 + 0.0168770i
\(34\) 124936. 104834.i 0.545144 0.457430i
\(35\) 3689.96 20926.8i 0.0145473 0.0825019i
\(36\) 130643. 47550.2i 0.466689 0.169861i
\(37\) −302101. −0.980497 −0.490249 0.871583i \(-0.663094\pi\)
−0.490249 + 0.871583i \(0.663094\pi\)
\(38\) −238352. 19900.0i −0.704655 0.0588316i
\(39\) 39355.4 0.106237
\(40\) 6383.48 2323.40i 0.0157706 0.00574002i
\(41\) −137434. + 779428.i −0.311423 + 1.76617i 0.280187 + 0.959945i \(0.409604\pi\)
−0.591610 + 0.806224i \(0.701508\pi\)
\(42\) 37626.3 31572.2i 0.0783645 0.0657556i
\(43\) 543716. + 456232.i 1.04288 + 0.875077i 0.992327 0.123645i \(-0.0394583\pi\)
0.0505494 + 0.998722i \(0.483903\pi\)
\(44\) −15713.7 89116.8i −0.0278096 0.157716i
\(45\) 14410.9 + 24960.5i 0.0235748 + 0.0408328i
\(46\) −212921. + 368789.i −0.322526 + 0.558632i
\(47\) 542065. + 197295.i 0.761568 + 0.277188i 0.693465 0.720490i \(-0.256083\pi\)
0.0681029 + 0.997678i \(0.478305\pi\)
\(48\) 14755.2 + 5370.44i 0.0192575 + 0.00700916i
\(49\) −870762. + 1.50820e6i −1.05734 + 1.83136i
\(50\) −311796. 540046.i −0.352757 0.610993i
\(51\) 13571.0 + 76965.0i 0.0143257 + 0.0812452i
\(52\) −503315. 422331.i −0.496395 0.416525i
\(53\) 1.06840e6 896498.i 0.985758 0.827149i 0.000809612 1.00000i \(-0.499742\pi\)
0.984948 + 0.172851i \(0.0552978\pi\)
\(54\) −23215.4 + 131661.i −0.0200631 + 0.113783i
\(55\) 17628.5 6416.25i 0.0142872 0.00520010i
\(56\) −820010. −0.623966
\(57\) 65366.4 94146.2i 0.0467512 0.0673350i
\(58\) 1.96300e6 1.32106
\(59\) −1.93477e6 + 704199.i −1.22644 + 0.446389i −0.872378 0.488832i \(-0.837423\pi\)
−0.354065 + 0.935221i \(0.615201\pi\)
\(60\) −565.262 + 3205.76i −0.000337848 + 0.00191603i
\(61\) 1.31323e6 1.10193e6i 0.740774 0.621583i −0.192272 0.981342i \(-0.561585\pi\)
0.933045 + 0.359759i \(0.117141\pi\)
\(62\) 492442. + 413208.i 0.262412 + 0.220190i
\(63\) −604144. 3.42627e6i −0.304403 1.72635i
\(64\) −131072. 227023.i −0.0625000 0.108253i
\(65\) 68104.7 117961.i 0.0307596 0.0532771i
\(66\) 40747.6 + 14830.9i 0.0174461 + 0.00634987i
\(67\) −448240. 163146.i −0.182075 0.0662697i 0.249374 0.968407i \(-0.419775\pi\)
−0.431449 + 0.902138i \(0.641997\pi\)
\(68\) 652369. 1.12994e6i 0.251601 0.435786i
\(69\) −102030. 176720.i −0.0373899 0.0647612i
\(70\) −29519.6 167414.i −0.0102865 0.0583377i
\(71\) −481494. 404022.i −0.159657 0.133968i 0.559460 0.828858i \(-0.311009\pi\)
−0.719116 + 0.694890i \(0.755453\pi\)
\(72\) 852010. 714921.i 0.269018 0.225733i
\(73\) 830493. 4.70996e6i 0.249865 1.41706i −0.559051 0.829133i \(-0.688835\pi\)
0.808917 0.587923i \(-0.200054\pi\)
\(74\) −2.27106e6 + 826598.i −0.651504 + 0.237128i
\(75\) 298819. 0.0817889
\(76\) −1.84627e6 + 502571.i −0.482445 + 0.131326i
\(77\) −2.26453e6 −0.565275
\(78\) 295856. 107683.i 0.0705909 0.0256930i
\(79\) 770818. 4.37153e6i 0.175896 0.997558i −0.761208 0.648508i \(-0.775393\pi\)
0.937104 0.349050i \(-0.113496\pi\)
\(80\) 41630.9 34932.4i 0.00909077 0.00762806i
\(81\) 3.59027e6 + 3.01259e6i 0.750636 + 0.629859i
\(82\) 1.09947e6 + 6.23542e6i 0.220210 + 1.24887i
\(83\) −291149. 504286.i −0.0558911 0.0968062i 0.836726 0.547622i \(-0.184467\pi\)
−0.892617 + 0.450815i \(0.851133\pi\)
\(84\) 196471. 340297.i 0.0361676 0.0626442i
\(85\) 254174. + 92511.7i 0.0448916 + 0.0163392i
\(86\) 5.33573e6 + 1.94205e6i 0.904585 + 0.329242i
\(87\) −470326. + 814628.i −0.0765740 + 0.132630i
\(88\) −361966. 626944.i −0.0566212 0.0980707i
\(89\) −272892. 1.54764e6i −0.0410322 0.232705i 0.957394 0.288785i \(-0.0932511\pi\)
−0.998426 + 0.0560793i \(0.982140\pi\)
\(90\) 176631. + 148211.i 0.0255398 + 0.0214304i
\(91\) −1.25953e7 + 1.05687e7i −1.75212 + 1.47020i
\(92\) −591572. + 3.35497e6i −0.0792046 + 0.449192i
\(93\) −289464. + 105356.i −0.0373168 + 0.0135822i
\(94\) 4.61483e6 0.573070
\(95\) −169070. 358845.i −0.0202317 0.0429412i
\(96\) 125617. 0.0144910
\(97\) −1.54608e6 + 562727.i −0.172001 + 0.0626032i −0.426585 0.904447i \(-0.640284\pi\)
0.254584 + 0.967051i \(0.418061\pi\)
\(98\) −2.41930e6 + 1.37205e7i −0.259656 + 1.47258i
\(99\) 2.35290e6 1.97431e6i 0.243713 0.204500i
\(100\) −3.82159e6 3.20670e6i −0.382159 0.320670i
\(101\) 1.50044e6 + 8.50944e6i 0.144909 + 0.821819i 0.967440 + 0.253099i \(0.0814500\pi\)
−0.822531 + 0.568720i \(0.807439\pi\)
\(102\) 312609. + 541455.i 0.0291677 + 0.0505199i
\(103\) 5.94229e6 1.02923e7i 0.535825 0.928077i −0.463297 0.886203i \(-0.653334\pi\)
0.999123 0.0418741i \(-0.0133328\pi\)
\(104\) −4.93925e6 1.79774e6i −0.430571 0.156715i
\(105\) 76548.2 + 27861.3i 0.00645316 + 0.00234876i
\(106\) 5.57881e6 9.66279e6i 0.454958 0.788010i
\(107\) 3.16764e6 + 5.48651e6i 0.249973 + 0.432965i 0.963518 0.267644i \(-0.0862451\pi\)
−0.713545 + 0.700609i \(0.752912\pi\)
\(108\) 185723. + 1.05329e6i 0.0141867 + 0.0804570i
\(109\) 1.60055e7 + 1.34302e7i 1.18380 + 0.993325i 0.999946 + 0.0103711i \(0.00330128\pi\)
0.183852 + 0.982954i \(0.441143\pi\)
\(110\) 114967. 96468.9i 0.00823568 0.00691055i
\(111\) 201104. 1.14052e6i 0.0139570 0.0791538i
\(112\) −6.16446e6 + 2.24368e6i −0.414603 + 0.150903i
\(113\) −8.70637e6 −0.567627 −0.283813 0.958880i \(-0.591600\pi\)
−0.283813 + 0.958880i \(0.591600\pi\)
\(114\) 233796. 886601.i 0.0147798 0.0560481i
\(115\) −706251. −0.0433029
\(116\) 1.47569e7 5.37109e6i 0.877796 0.319491i
\(117\) 3.87254e6 2.19623e7i 0.223535 1.26773i
\(118\) −1.26179e7 + 1.05877e7i −0.706969 + 0.593218i
\(119\) −2.50119e7 2.09875e7i −1.36061 1.14168i
\(120\) 4522.10 + 25646.1i 0.000238894 + 0.00135484i
\(121\) 8.74399e6 + 1.51450e7i 0.448705 + 0.777179i
\(122\) 6.85719e6 1.18770e7i 0.341890 0.592171i
\(123\) −2.85107e6 1.03771e6i −0.138147 0.0502813i
\(124\) 4.83255e6 + 1.75891e6i 0.227615 + 0.0828451i
\(125\) 1.03539e6 1.79334e6i 0.0474151 0.0821254i
\(126\) −1.39165e7 2.41041e7i −0.619774 1.07348i
\(127\) 2.26510e6 + 1.28460e7i 0.0981236 + 0.556487i 0.993745 + 0.111670i \(0.0356200\pi\)
−0.895622 + 0.444817i \(0.853269\pi\)
\(128\) −1.60651e6 1.34802e6i −0.0677094 0.0568149i
\(129\) −2.08435e6 + 1.74898e6i −0.0854883 + 0.0717332i
\(130\) 189220. 1.07312e6i 0.00755380 0.0428397i
\(131\) 794513. 289179.i 0.0308782 0.0112387i −0.326535 0.945185i \(-0.605881\pi\)
0.357413 + 0.933946i \(0.383659\pi\)
\(132\) 346902. 0.0131280
\(133\) 4.36266e6 + 4.76845e7i 0.160794 + 1.75750i
\(134\) −3.81606e6 −0.137009
\(135\) −208355. + 75834.8i −0.00728844 + 0.00265278i
\(136\) 1.81252e6 1.02793e7i 0.0617871 0.350412i
\(137\) 2.75792e7 2.31417e7i 0.916345 0.768905i −0.0569706 0.998376i \(-0.518144\pi\)
0.973315 + 0.229471i \(0.0736997\pi\)
\(138\) −1.25055e6 1.04933e6i −0.0405064 0.0339889i
\(139\) −3.98768e6 2.26152e7i −0.125941 0.714248i −0.980744 0.195296i \(-0.937433\pi\)
0.854803 0.518952i \(-0.173678\pi\)
\(140\) −679987. 1.17777e6i −0.0209437 0.0362755i
\(141\) −1.10569e6 + 1.91511e6i −0.0332175 + 0.0575344i
\(142\) −4.72512e6 1.71980e6i −0.138485 0.0504045i
\(143\) −1.36402e7 4.96461e6i −0.390071 0.141974i
\(144\) 4.44888e6 7.70568e6i 0.124160 0.215051i
\(145\) 1.62780e6 + 2.81944e6i 0.0443419 + 0.0768024i
\(146\) −6.64394e6 3.76797e7i −0.176681 1.00201i
\(147\) −5.11425e6 4.29136e6i −0.132792 0.111426i
\(148\) −1.48111e7 + 1.24280e7i −0.375552 + 0.315126i
\(149\) 3.82310e6 2.16819e7i 0.0946813 0.536964i −0.900163 0.435553i \(-0.856553\pi\)
0.994845 0.101412i \(-0.0323359\pi\)
\(150\) 2.24639e6 817618.i 0.0543457 0.0197802i
\(151\) −3.03990e7 −0.718522 −0.359261 0.933237i \(-0.616971\pi\)
−0.359261 + 0.933237i \(0.616971\pi\)
\(152\) −1.25043e7 + 8.82980e6i −0.288807 + 0.203938i
\(153\) 4.42858e7 0.999641
\(154\) −1.70237e7 + 6.19611e6i −0.375605 + 0.136709i
\(155\) −185132. + 1.04994e6i −0.00399321 + 0.0226466i
\(156\) 1.92947e6 1.61902e6i 0.0406913 0.0341441i
\(157\) 4.95435e6 + 4.15719e6i 0.102173 + 0.0857336i 0.692443 0.721472i \(-0.256534\pi\)
−0.590270 + 0.807206i \(0.700979\pi\)
\(158\) −6.16654e6 3.49722e7i −0.124378 0.705380i
\(159\) 2.67332e6 + 4.63032e6i 0.0527424 + 0.0913526i
\(160\) 217381. 376515.i 0.00419567 0.00726712i
\(161\) 8.01111e7 + 2.91581e7i 1.51287 + 0.550640i
\(162\) 3.52329e7 + 1.28237e7i 0.651098 + 0.236980i
\(163\) −4.07576e7 + 7.05943e7i −0.737144 + 1.27677i 0.216632 + 0.976253i \(0.430493\pi\)
−0.953776 + 0.300517i \(0.902841\pi\)
\(164\) 2.53265e7 + 4.38667e7i 0.448354 + 0.776572i
\(165\) 12488.2 + 70823.9i 0.000216424 + 0.00122740i
\(166\) −3.56854e6 2.99436e6i −0.0605497 0.0508072i
\(167\) 2.96768e7 2.49018e7i 0.493070 0.413735i −0.362055 0.932157i \(-0.617925\pi\)
0.855125 + 0.518422i \(0.173480\pi\)
\(168\) 545868. 3.09577e6i 0.00888189 0.0503717i
\(169\) −4.00726e7 + 1.45852e7i −0.638621 + 0.232439i
\(170\) 2.16389e6 0.0337803
\(171\) −4.61063e7 4.57417e7i −0.705138 0.699562i
\(172\) 4.54253e7 0.680689
\(173\) −1.63860e7 + 5.96400e6i −0.240608 + 0.0875742i −0.459510 0.888173i \(-0.651975\pi\)
0.218902 + 0.975747i \(0.429753\pi\)
\(174\) −1.30674e6 + 7.41089e6i −0.0188047 + 0.106647i
\(175\) −9.56343e7 + 8.02467e7i −1.34890 + 1.13186i
\(176\) −4.43652e6 3.72268e6i −0.0613406 0.0514708i
\(177\) −1.37061e6 7.77309e6i −0.0185783 0.105363i
\(178\) −6.28608e6 1.08878e7i −0.0835429 0.144701i
\(179\) 1.79346e7 3.10637e7i 0.233726 0.404825i −0.725176 0.688564i \(-0.758241\pi\)
0.958902 + 0.283739i \(0.0915748\pi\)
\(180\) 1.73336e6 + 630890.i 0.0221531 + 0.00806306i
\(181\) 5.22198e7 + 1.90065e7i 0.654577 + 0.238246i 0.647893 0.761731i \(-0.275650\pi\)
0.00668354 + 0.999978i \(0.497873\pi\)
\(182\) −6.57680e7 + 1.13914e8i −0.808658 + 1.40064i
\(183\) 3.28590e6 + 5.69135e6i 0.0396347 + 0.0686493i
\(184\) 4.73258e6 + 2.68398e7i 0.0560061 + 0.317626i
\(185\) −3.07049e6 2.57645e6i −0.0356539 0.0299172i
\(186\) −1.88779e6 + 1.58404e6i −0.0215109 + 0.0180498i
\(187\) 5.00544e6 2.83872e7i 0.0559753 0.317452i
\(188\) 3.46921e7 1.26269e7i 0.380784 0.138594i
\(189\) 2.67649e7 0.288369
\(190\) −2.25284e6 2.23503e6i −0.0238283 0.0236399i
\(191\) 1.31699e8 1.36762 0.683810 0.729661i \(-0.260322\pi\)
0.683810 + 0.729661i \(0.260322\pi\)
\(192\) 944331. 343708.i 0.00962875 0.00350458i
\(193\) −2.67112e7 + 1.51487e8i −0.267450 + 1.51679i 0.494515 + 0.869169i \(0.335346\pi\)
−0.761966 + 0.647617i \(0.775766\pi\)
\(194\) −1.00830e7 + 8.46064e6i −0.0991479 + 0.0831950i
\(195\) 399999. + 335639.i 0.00386312 + 0.00324154i
\(196\) 1.93544e7 + 1.09764e8i 0.183605 + 1.04127i
\(197\) 2.32782e6 + 4.03190e6i 0.0216929 + 0.0375732i 0.876668 0.481096i \(-0.159761\pi\)
−0.854975 + 0.518669i \(0.826428\pi\)
\(198\) 1.22860e7 2.12799e7i 0.112481 0.194823i
\(199\) −8.91994e7 3.24659e7i −0.802372 0.292040i −0.0919031 0.995768i \(-0.529295\pi\)
−0.710469 + 0.703728i \(0.751517\pi\)
\(200\) −3.75030e7 1.36500e7i −0.331483 0.120650i
\(201\) 914310. 1.58363e6i 0.00794159 0.0137552i
\(202\) 3.45628e7 + 5.98646e7i 0.295039 + 0.511023i
\(203\) −6.82417e7 3.87018e8i −0.572551 3.24710i
\(204\) 3.83156e6 + 3.21506e6i 0.0315988 + 0.0265145i
\(205\) −8.04414e6 + 6.74984e6i −0.0652141 + 0.0547211i
\(206\) 1.65099e7 9.36322e7i 0.131586 0.746259i
\(207\) −1.08659e8 + 3.95485e7i −0.851467 + 0.309909i
\(208\) −4.20500e7 −0.323999
\(209\) −3.45317e7 + 2.43842e7i −0.261641 + 0.184755i
\(210\) 651687. 0.00485592
\(211\) −2.38998e6 + 869880.i −0.0175148 + 0.00637486i −0.350763 0.936464i \(-0.614078\pi\)
0.333248 + 0.942839i \(0.391855\pi\)
\(212\) 1.55000e7 8.79049e7i 0.111727 0.633633i
\(213\) 1.84582e6 1.54883e6i 0.0130876 0.0109818i
\(214\) 3.88248e7 + 3.25779e7i 0.270808 + 0.227235i
\(215\) 1.63527e6 + 9.27409e6i 0.0112216 + 0.0636409i
\(216\) 4.27815e6 + 7.40997e6i 0.0288847 + 0.0500297i
\(217\) 6.43473e7 1.11453e8i 0.427485 0.740426i
\(218\) 1.57070e8 + 5.71687e7i 1.02682 + 0.373732i
\(219\) 1.72286e7 + 6.27070e6i 0.110840 + 0.0403424i
\(220\) 600316. 1.03978e6i 0.00380102 0.00658356i
\(221\) −1.04645e8 1.81251e8i −0.652148 1.12955i
\(222\) −1.60883e6 9.12415e6i −0.00986906 0.0559702i
\(223\) −6.09763e7 5.11652e7i −0.368209 0.308964i 0.439844 0.898074i \(-0.355034\pi\)
−0.808053 + 0.589110i \(0.799478\pi\)
\(224\) −4.02025e7 + 3.37339e7i −0.238993 + 0.200539i
\(225\) 2.94036e7 1.66756e8i 0.172093 0.975986i
\(226\) −6.54505e7 + 2.38220e7i −0.377167 + 0.137278i
\(227\) 2.17906e8 1.23646 0.618228 0.785998i \(-0.287851\pi\)
0.618228 + 0.785998i \(0.287851\pi\)
\(228\) −668313. 7.30476e6i −0.00373429 0.0408163i
\(229\) 2.41348e8 1.32806 0.664031 0.747705i \(-0.268844\pi\)
0.664031 + 0.747705i \(0.268844\pi\)
\(230\) −5.30927e6 + 1.93242e6i −0.0287732 + 0.0104726i
\(231\) 1.50746e6 8.54924e6i 0.00804645 0.0456337i
\(232\) 9.62397e7 8.07547e7i 0.505995 0.424581i
\(233\) −1.66078e8 1.39356e8i −0.860132 0.721737i 0.101864 0.994798i \(-0.467519\pi\)
−0.961996 + 0.273062i \(0.911964\pi\)
\(234\) −3.09804e7 1.75698e8i −0.158063 0.896421i
\(235\) 3.82681e6 + 6.62823e6i 0.0192353 + 0.0333165i
\(236\) −6.58861e7 + 1.14118e8i −0.326288 + 0.565148i
\(237\) 1.59906e7 + 5.82012e6i 0.0780273 + 0.0283996i
\(238\) −2.45453e8 8.93377e7i −1.18018 0.429552i
\(239\) 3.41656e7 5.91765e7i 0.161881 0.280386i −0.773662 0.633598i \(-0.781577\pi\)
0.935543 + 0.353212i \(0.114911\pi\)
\(240\) 104167. + 180422.i 0.000486397 + 0.000842464i
\(241\) 4.12786e7 + 2.34103e8i 0.189962 + 1.07733i 0.919413 + 0.393293i \(0.128664\pi\)
−0.729452 + 0.684032i \(0.760225\pi\)
\(242\) 1.07173e8 + 8.99284e7i 0.486104 + 0.407890i
\(243\) −4.17608e7 + 3.50415e7i −0.186701 + 0.156661i
\(244\) 1.90518e7 1.08048e8i 0.0839599 0.476160i
\(245\) −2.17128e7 + 7.90283e6i −0.0943269 + 0.0343322i
\(246\) −2.42724e7 −0.103954
\(247\) −7.82625e7 + 2.96787e8i −0.330457 + 1.25316i
\(248\) 4.11416e7 0.171277
\(249\) 2.09764e6 763477.i 0.00861058 0.00313400i
\(250\) 2.87668e6 1.63145e7i 0.0116440 0.0660364i
\(251\) −2.63663e8 + 2.21239e8i −1.05242 + 0.883088i −0.993346 0.115166i \(-0.963260\pi\)
−0.0590768 + 0.998253i \(0.518816\pi\)
\(252\) −1.70570e8 1.43126e8i −0.671432 0.563398i
\(253\) 1.30694e7 + 7.41203e7i 0.0507381 + 0.287750i
\(254\) 5.21767e7 + 9.03726e7i 0.199783 + 0.346034i
\(255\) −518458. + 897996.i −0.00195805 + 0.00339144i
\(256\) −1.57654e7 5.73815e6i −0.0587308 0.0213763i
\(257\) −9.08372e7 3.30620e7i −0.333809 0.121496i 0.169678 0.985500i \(-0.445727\pi\)
−0.503486 + 0.864003i \(0.667950\pi\)
\(258\) −1.08837e7 + 1.88511e7i −0.0394555 + 0.0683390i
\(259\) 2.41920e8 + 4.19018e8i 0.865212 + 1.49859i
\(260\) −1.51376e6 8.58496e6i −0.00534134 0.0302923i
\(261\) 4.08324e8 + 3.42625e8i 1.42155 + 1.19283i
\(262\) 5.18154e6 4.34783e6i 0.0177994 0.0149354i
\(263\) −2.14396e7 + 1.21590e8i −0.0726727 + 0.412147i 0.926669 + 0.375877i \(0.122659\pi\)
−0.999342 + 0.0362697i \(0.988452\pi\)
\(264\) 2.60785e6 949179.i 0.00872306 0.00317493i
\(265\) 1.85048e7 0.0610833
\(266\) 1.63269e8 + 3.46533e8i 0.531885 + 1.12891i
\(267\) 6.02446e6 0.0193700
\(268\) −2.86874e7 + 1.04414e7i −0.0910373 + 0.0331349i
\(269\) 1.03641e6 5.87776e6i 0.00324637 0.0184111i −0.983142 0.182846i \(-0.941469\pi\)
0.986388 + 0.164435i \(0.0525801\pi\)
\(270\) −1.35882e6 + 1.14018e6i −0.00420134 + 0.00352534i
\(271\) −2.34341e8 1.96635e8i −0.715246 0.600163i 0.210820 0.977525i \(-0.432387\pi\)
−0.926066 + 0.377362i \(0.876831\pi\)
\(272\) −1.45002e7 8.22347e7i −0.0436901 0.247779i
\(273\) −3.15154e7 5.45863e7i −0.0937463 0.162373i
\(274\) 1.44008e8 2.49429e8i 0.422922 0.732522i
\(275\) −1.03568e8 3.76956e7i −0.300303 0.109301i
\(276\) −1.22722e7 4.46671e6i −0.0351350 0.0127881i
\(277\) −8.35975e7 + 1.44795e8i −0.236327 + 0.409331i −0.959658 0.281171i \(-0.909277\pi\)
0.723330 + 0.690502i \(0.242610\pi\)
\(278\) −9.18564e7 1.59100e8i −0.256421 0.444133i
\(279\) 3.03111e7 + 1.71903e8i 0.0835578 + 0.473880i
\(280\) −8.33441e6 6.99340e6i −0.0226893 0.0190386i
\(281\) −5.32198e8 + 4.46567e8i −1.43087 + 1.20064i −0.485677 + 0.874138i \(0.661427\pi\)
−0.945195 + 0.326506i \(0.894129\pi\)
\(282\) −3.07202e6 + 1.74223e7i −0.00815741 + 0.0462630i
\(283\) 389772. 141865.i 0.00102225 0.000372069i −0.341509 0.939879i \(-0.610938\pi\)
0.342531 + 0.939506i \(0.388716\pi\)
\(284\) −4.02269e7 −0.104208
\(285\) 1.46729e6 399408.i 0.00375456 0.00102202i
\(286\) −1.16124e8 −0.293523
\(287\) 1.19113e9 4.33536e8i 2.97422 1.08253i
\(288\) 1.23606e7 7.01006e7i 0.0304907 0.172921i
\(289\) 4.03904e6 3.38916e6i 0.00984319 0.00825942i
\(290\) 1.99515e7 + 1.67413e7i 0.0480378 + 0.0403085i
\(291\) −1.09525e6 6.21149e6i −0.00260549 0.0147764i
\(292\) −1.53044e8 2.65080e8i −0.359729 0.623069i
\(293\) −8.44729e7 + 1.46311e8i −0.196192 + 0.339814i −0.947291 0.320376i \(-0.896191\pi\)
0.751099 + 0.660190i \(0.229524\pi\)
\(294\) −5.01884e7 1.82671e7i −0.115183 0.0419231i
\(295\) −2.56703e7 9.34323e6i −0.0582176 0.0211895i
\(296\) −7.73379e7 + 1.33953e8i −0.173329 + 0.300215i
\(297\) 1.18145e7 + 2.04632e7i 0.0261677 + 0.0453239i
\(298\) −3.05848e7 1.73455e8i −0.0669498 0.379691i
\(299\) 4.18617e8 + 3.51262e8i 0.905666 + 0.759944i
\(300\) 1.46502e7 1.22930e7i 0.0313270 0.0262864i
\(301\) 1.97396e8 1.11949e9i 0.417210 2.36612i
\(302\) −2.28526e8 + 8.31766e7i −0.477431 + 0.173771i
\(303\) −3.31244e7 −0.0684067
\(304\) −6.98419e7 + 1.00592e8i −0.142580 + 0.205356i
\(305\) 2.27451e7 0.0459027
\(306\) 3.32920e8 1.21173e8i 0.664225 0.241758i
\(307\) −8.52929e7 + 4.83720e8i −0.168240 + 0.954135i 0.777421 + 0.628980i \(0.216527\pi\)
−0.945661 + 0.325155i \(0.894584\pi\)
\(308\) −1.11023e8 + 9.31590e7i −0.216513 + 0.181676i
\(309\) 3.49009e7 + 2.92853e7i 0.0672948 + 0.0564670i
\(310\) 1.48106e6 + 8.39951e6i 0.00282362 + 0.0160136i
\(311\) −3.32210e8 5.75405e8i −0.626256 1.08471i −0.988297 0.152544i \(-0.951253\pi\)
0.362041 0.932162i \(-0.382080\pi\)
\(312\) 1.00750e7 1.74504e7i 0.0187803 0.0325285i
\(313\) −5.41374e8 1.97044e8i −0.997912 0.363210i −0.209133 0.977887i \(-0.567064\pi\)
−0.788779 + 0.614677i \(0.789286\pi\)
\(314\) 4.86192e7 + 1.76960e7i 0.0886246 + 0.0322567i
\(315\) 2.30803e7 3.99763e7i 0.0416059 0.0720635i
\(316\) −1.42047e8 2.46032e8i −0.253237 0.438619i
\(317\) −1.31916e7 7.48131e7i −0.0232589 0.131908i 0.970967 0.239212i \(-0.0768892\pi\)
−0.994226 + 0.107304i \(0.965778\pi\)
\(318\) 3.27661e7 + 2.74940e7i 0.0571385 + 0.0479449i
\(319\) 2.65774e8 2.23011e8i 0.458401 0.384644i
\(320\) 603965. 3.42525e6i 0.00103035 0.00584343i
\(321\) −2.28218e7 + 8.30645e6i −0.0385108 + 0.0140168i
\(322\) 6.82020e8 1.13842
\(323\) −6.07397e8 5.07116e7i −1.00291 0.0837333i
\(324\) 2.99953e8 0.489943
\(325\) −7.51972e8 + 2.73695e8i −1.21509 + 0.442258i
\(326\) −1.13240e8 + 6.42215e8i −0.181025 + 1.02664i
\(327\) −6.13577e7 + 5.14852e7i −0.0970402 + 0.0814264i
\(328\) 3.10419e8 + 2.60472e8i 0.485724 + 0.407571i
\(329\) −1.60430e8 9.09842e8i −0.248370 1.40858i
\(330\) 287666. + 498252.i 0.000440645 + 0.000763220i
\(331\) 3.03296e8 5.25323e8i 0.459693 0.796212i −0.539251 0.842145i \(-0.681293\pi\)
0.998945 + 0.0459330i \(0.0146261\pi\)
\(332\) −3.50197e7 1.27461e7i −0.0525205 0.0191159i
\(333\) −6.16679e8 2.24453e8i −0.915175 0.333096i
\(334\) 1.54961e8 2.68400e8i 0.227567 0.394158i
\(335\) −3.16444e6 5.48097e6i −0.00459875 0.00796527i
\(336\) −4.36695e6 2.47662e7i −0.00628045 0.0356182i
\(337\) 2.25304e8 + 1.89053e8i 0.320675 + 0.269078i 0.788887 0.614538i \(-0.210657\pi\)
−0.468213 + 0.883616i \(0.655102\pi\)
\(338\) −2.61340e8 + 2.19290e8i −0.368126 + 0.308895i
\(339\) 5.79570e6 3.28690e7i 0.00807992 0.0458235i
\(340\) 1.62671e7 5.92075e6i 0.0224458 0.00816960i
\(341\) 1.13616e8 0.155167
\(342\) −4.71763e8 2.17711e8i −0.637723 0.294299i
\(343\) 1.47022e9 1.96722
\(344\) 3.41487e8 1.24291e8i 0.452293 0.164621i
\(345\) 470141. 2.66630e6i 0.000616398 0.00349576i
\(346\) −1.06864e8 + 8.96692e7i −0.138696 + 0.116380i
\(347\) 1.09660e9 + 9.20157e8i 1.40895 + 1.18225i 0.956959 + 0.290225i \(0.0937300\pi\)
0.451990 + 0.892023i \(0.350714\pi\)
\(348\) 1.04539e7 + 5.92871e7i 0.0132969 + 0.0754107i
\(349\) −7.14339e8 1.23727e9i −0.899530 1.55803i −0.828096 0.560586i \(-0.810576\pi\)
−0.0714334 0.997445i \(-0.522757\pi\)
\(350\) −4.99367e8 + 8.64929e8i −0.622560 + 1.07831i
\(351\) 1.61216e8 + 5.86777e7i 0.198990 + 0.0724266i
\(352\) −4.35375e7 1.58464e7i −0.0532065 0.0193656i
\(353\) −1.11508e8 + 1.93137e8i −0.134925 + 0.233698i −0.925569 0.378579i \(-0.876413\pi\)
0.790644 + 0.612277i \(0.209746\pi\)
\(354\) −3.15720e7 5.46843e7i −0.0378260 0.0655166i
\(355\) −1.44813e6 8.21278e6i −0.00171795 0.00974296i
\(356\) −7.70466e7 6.46498e7i −0.0905063 0.0759438i
\(357\) 9.58838e7 8.04561e7i 0.111534 0.0935880i
\(358\) 4.98291e7 2.82595e8i 0.0573974 0.325517i
\(359\) −1.08104e9 + 3.93468e8i −1.23314 + 0.448827i −0.874672 0.484715i \(-0.838923\pi\)
−0.358469 + 0.933542i \(0.616701\pi\)
\(360\) 1.47568e7 0.0166699
\(361\) 5.79988e8 + 6.80162e8i 0.648849 + 0.760917i
\(362\) 4.44570e8 0.492561
\(363\) −6.29975e7 + 2.29292e7i −0.0691274 + 0.0251603i
\(364\) −1.82728e8 + 1.03630e9i −0.198587 + 1.12624i
\(365\) 4.86095e7 4.07882e7i 0.0523234 0.0439046i
\(366\) 4.02743e7 + 3.37942e7i 0.0429383 + 0.0360295i
\(367\) −1.85775e8 1.05358e9i −0.196180 1.11259i −0.910728 0.413007i \(-0.864479\pi\)
0.714548 0.699587i \(-0.246633\pi\)
\(368\) 1.09015e8 + 1.88820e8i 0.114030 + 0.197506i
\(369\) −8.59637e8 + 1.48893e9i −0.890682 + 1.54271i
\(370\) −3.01321e7 1.09672e7i −0.0309260 0.0112561i
\(371\) −2.09902e9 7.63981e8i −2.13407 0.776737i
\(372\) −9.85733e6 + 1.70734e7i −0.00992794 + 0.0171957i
\(373\) 1.94363e8 + 3.36647e8i 0.193925 + 0.335887i 0.946547 0.322564i \(-0.104545\pi\)
−0.752623 + 0.658452i \(0.771212\pi\)
\(374\) −4.00435e7 2.27098e8i −0.0395805 0.224472i
\(375\) 6.08113e6 + 5.10267e6i 0.00595491 + 0.00499676i
\(376\) 2.26250e8 1.89847e8i 0.219499 0.184181i
\(377\) 4.37428e8 2.48078e9i 0.420447 2.38448i
\(378\) 2.01206e8 7.32330e7i 0.191611 0.0697405i
\(379\) 1.50989e9 1.42465 0.712323 0.701852i \(-0.247643\pi\)
0.712323 + 0.701852i \(0.247643\pi\)
\(380\) −2.30513e7 1.06378e7i −0.0215502 0.00994508i
\(381\) −5.00052e7 −0.0463209
\(382\) 9.90051e8 3.60349e8i 0.908732 0.330752i
\(383\) −2.31239e8 + 1.31142e9i −0.210313 + 1.19274i 0.678545 + 0.734558i \(0.262611\pi\)
−0.888858 + 0.458183i \(0.848500\pi\)
\(384\) 6.15860e6 5.16768e6i 0.00555038 0.00465732i
\(385\) −2.30162e7 1.93129e7i −0.0205551 0.0172478i
\(386\) 2.13690e8 + 1.21189e9i 0.189116 + 1.07253i
\(387\) 7.70919e8 + 1.33527e9i 0.676115 + 1.17107i
\(388\) −5.26497e7 + 9.11919e7i −0.0457599 + 0.0792584i
\(389\) 1.14723e9 + 4.17556e8i 0.988155 + 0.359659i 0.785006 0.619489i \(-0.212660\pi\)
0.203149 + 0.979148i \(0.434882\pi\)
\(390\) 3.92538e6 + 1.42872e6i 0.00335085 + 0.00121961i
\(391\) −5.42589e8 + 9.39792e8i −0.459042 + 0.795084i
\(392\) 4.45830e8 + 7.72200e8i 0.373825 + 0.647484i
\(393\) 562839. + 3.19202e6i 0.000467746 + 0.00265272i
\(394\) 2.85314e7 + 2.39407e7i 0.0235010 + 0.0197197i
\(395\) 4.51167e7 3.78574e7i 0.0368339 0.0309073i
\(396\) 3.41349e7 1.93589e8i 0.0276227 0.156656i
\(397\) 7.86452e7 2.86245e7i 0.0630820 0.0229600i −0.310286 0.950643i \(-0.600425\pi\)
0.373368 + 0.927683i \(0.378203\pi\)
\(398\) −7.59392e8 −0.603775
\(399\) −1.82927e8 1.52725e7i −0.144169 0.0120367i
\(400\) −3.19279e8 −0.249437
\(401\) −1.08704e9 + 3.95649e8i −0.841857 + 0.306411i −0.726716 0.686938i \(-0.758954\pi\)
−0.115141 + 0.993349i \(0.536732\pi\)
\(402\) 2.54029e6 1.44067e7i 0.00195026 0.0110605i
\(403\) 6.31932e8 5.30254e8i 0.480953 0.403568i
\(404\) 4.23627e8 + 3.55465e8i 0.319631 + 0.268202i
\(405\) 1.07980e7 + 6.12387e7i 0.00807704 + 0.0458072i
\(406\) −1.57195e9 2.72270e9i −1.16573 2.01911i
\(407\) −2.13575e8 + 3.69923e8i −0.157026 + 0.271976i
\(408\) 3.76009e7 + 1.36856e7i 0.0274086 + 0.00997592i
\(409\) −2.01757e9 7.34337e8i −1.45814 0.530718i −0.513284 0.858219i \(-0.671571\pi\)
−0.944851 + 0.327501i \(0.893794\pi\)
\(410\) −4.20035e7 + 7.27523e7i −0.0300983 + 0.0521318i
\(411\) 6.90074e7 + 1.19524e8i 0.0490285 + 0.0849199i
\(412\) −1.32079e8 7.49057e8i −0.0930451 0.527685i
\(413\) 2.52608e9 + 2.11963e9i 1.76450 + 1.48059i
\(414\) −7.08634e8 + 5.94615e8i −0.490819 + 0.411846i
\(415\) 1.34158e6 7.60850e6i 0.000921403 0.00522553i
\(416\) −3.16112e8 + 1.15055e8i −0.215285 + 0.0783575i
\(417\) 8.80335e7 0.0594527
\(418\) −1.92874e8 + 2.77794e8i −0.129169 + 0.186040i
\(419\) 1.25489e9 0.833403 0.416701 0.909043i \(-0.363186\pi\)
0.416701 + 0.909043i \(0.363186\pi\)
\(420\) 4.89909e6 1.78312e6i 0.00322658 0.00117438i
\(421\) −2.64620e7 + 1.50074e8i −0.0172837 + 0.0980205i −0.992229 0.124423i \(-0.960292\pi\)
0.974946 + 0.222443i \(0.0714032\pi\)
\(422\) −1.55866e7 + 1.30787e7i −0.0100962 + 0.00847172i
\(423\) 9.59931e8 + 8.05478e8i 0.616664 + 0.517443i
\(424\) −1.24000e8 7.03239e8i −0.0790026 0.448046i
\(425\) −7.94555e8 1.37621e9i −0.502068 0.869608i
\(426\) 9.63819e6 1.66938e7i 0.00604035 0.0104622i
\(427\) −2.58001e9 9.39046e8i −1.60370 0.583700i
\(428\) 3.81006e8 + 1.38675e8i 0.234897 + 0.0854956i
\(429\) 2.78229e7 4.81906e7i 0.0170138 0.0294688i
\(430\) 3.76686e7 + 6.52440e7i 0.0228476 + 0.0395732i
\(431\) 2.88808e8 + 1.63791e9i 0.173755 + 0.985415i 0.939571 + 0.342355i \(0.111225\pi\)
−0.765815 + 0.643060i \(0.777664\pi\)
\(432\) 5.24360e7 + 4.39990e7i 0.0312922 + 0.0262573i
\(433\) −2.86251e8 + 2.40193e8i −0.169449 + 0.142185i −0.723569 0.690252i \(-0.757500\pi\)
0.554119 + 0.832437i \(0.313055\pi\)
\(434\) 1.78781e8 1.01392e9i 0.104980 0.595371i
\(435\) −1.17278e7 + 4.26857e6i −0.00683131 + 0.00248639i
\(436\) 1.33720e9 0.772670
\(437\) 1.53558e9 4.17999e8i 0.880214 0.239602i
\(438\) 1.46674e8 0.0834055
\(439\) 3.13184e9 1.13990e9i 1.76675 0.643043i 0.766747 0.641950i \(-0.221874\pi\)
0.999999 0.00109326i \(-0.000347997\pi\)
\(440\) 1.66790e6 9.45913e6i 0.000933438 0.00529379i
\(441\) −2.89804e9 + 2.43174e9i −1.60905 + 1.35015i
\(442\) −1.28261e9 1.07623e9i −0.706505 0.592828i
\(443\) −5.86332e8 3.32525e9i −0.320428 1.81724i −0.540027 0.841648i \(-0.681586\pi\)
0.219599 0.975590i \(-0.429525\pi\)
\(444\) −3.70596e7 6.41891e7i −0.0200937 0.0348034i
\(445\) 1.04254e7 1.80573e7i 0.00560830 0.00971386i
\(446\) −5.98388e8 2.17796e8i −0.319383 0.116246i
\(447\) 7.93104e7 + 2.88666e7i 0.0420004 + 0.0152869i
\(448\) −2.09923e8 + 3.63597e8i −0.110303 + 0.191050i
\(449\) −2.39316e8 4.14508e8i −0.124770 0.216108i 0.796873 0.604147i \(-0.206486\pi\)
−0.921643 + 0.388039i \(0.873153\pi\)
\(450\) −2.35229e8 1.33405e9i −0.121688 0.690126i
\(451\) 8.57248e8 + 7.19317e8i 0.440036 + 0.369234i
\(452\) −4.26846e8 + 3.58166e8i −0.217414 + 0.182432i
\(453\) 2.02362e7 1.14765e8i 0.0102278 0.0580050i
\(454\) 1.63812e9 5.96226e8i 0.821580 0.299031i
\(455\) −2.18151e8 −0.108572
\(456\) −2.50111e7 5.30852e7i −0.0123525 0.0262178i
\(457\) 1.03079e9 0.505200 0.252600 0.967571i \(-0.418714\pi\)
0.252600 + 0.967571i \(0.418714\pi\)
\(458\) 1.81434e9 6.60366e8i 0.882449 0.321185i
\(459\) −5.91602e7 + 3.35514e8i −0.0285552 + 0.161945i
\(460\) −3.46253e7 + 2.90540e7i −0.0165860 + 0.0139173i
\(461\) −2.87366e9 2.41129e9i −1.36610 1.14629i −0.974045 0.226354i \(-0.927320\pi\)
−0.392056 0.919941i \(-0.628236\pi\)
\(462\) −1.20597e7 6.83939e7i −0.00568970 0.0322679i
\(463\) −1.55464e9 2.69271e9i −0.727939 1.26083i −0.957753 0.287593i \(-0.907145\pi\)
0.229813 0.973235i \(-0.426188\pi\)
\(464\) 5.02528e8 8.70404e8i 0.233533 0.404490i
\(465\) −3.84058e6 1.39786e6i −0.00177138 0.000644729i
\(466\) −1.62979e9 5.93196e8i −0.746074 0.271549i
\(467\) 1.84255e9 3.19140e9i 0.837165 1.45001i −0.0550905 0.998481i \(-0.517545\pi\)
0.892255 0.451531i \(-0.149122\pi\)
\(468\) −7.13635e8 1.23605e9i −0.321822 0.557412i
\(469\) 1.32661e8 + 7.52361e8i 0.0593799 + 0.336760i
\(470\) 4.69041e7 + 3.93572e7i 0.0208386 + 0.0174857i
\(471\) −1.89926e7 + 1.59367e7i −0.00837552 + 0.00702789i
\(472\) −1.83056e8 + 1.03816e9i −0.0801285 + 0.454431i
\(473\) 9.43045e8 3.43240e8i 0.409749 0.149137i
\(474\) 1.36135e8 0.0587146
\(475\) −5.94235e8 + 2.25346e9i −0.254408 + 0.964767i
\(476\) −2.08965e9 −0.888073
\(477\) 2.84700e9 1.03622e9i 1.20109 0.437159i
\(478\) 9.49246e7 5.38344e8i 0.0397540 0.225456i
\(479\) −1.62680e9 + 1.36505e9i −0.676333 + 0.567510i −0.914932 0.403608i \(-0.867756\pi\)
0.238600 + 0.971118i \(0.423312\pi\)
\(480\) 1.27674e6 + 1.07132e6i 0.000526938 + 0.000442153i
\(481\) 5.38553e8 + 3.05428e9i 0.220658 + 1.25142i
\(482\) 9.50857e8 + 1.64693e9i 0.386768 + 0.669902i
\(483\) −1.63409e8 + 2.83032e8i −0.0659873 + 0.114293i
\(484\) 1.05173e9 + 3.82799e8i 0.421644 + 0.153466i
\(485\) −2.05132e7 7.46619e6i −0.00816464 0.00297169i
\(486\) −2.18060e8 + 3.77690e8i −0.0861684 + 0.149248i
\(487\) 2.09314e9 + 3.62543e9i 0.821197 + 1.42235i 0.904791 + 0.425855i \(0.140027\pi\)
−0.0835945 + 0.996500i \(0.526640\pi\)
\(488\) −1.52414e8 8.64385e8i −0.0593686 0.336696i
\(489\) −2.39382e8 2.00865e8i −0.0925785 0.0776826i
\(490\) −1.41604e8 + 1.18820e8i −0.0543737 + 0.0456249i
\(491\) −1.41986e8 + 8.05242e8i −0.0541328 + 0.307002i −0.999838 0.0180247i \(-0.994262\pi\)
0.945705 + 0.325027i \(0.105373\pi\)
\(492\) −1.82469e8 + 6.64132e7i −0.0690734 + 0.0251407i
\(493\) 5.00235e9 1.88023
\(494\) 2.23716e8 + 2.44525e9i 0.0834936 + 0.912596i
\(495\) 4.07521e7 0.0151019
\(496\) 3.09283e8 1.12570e8i 0.113807 0.0414225i
\(497\) −1.74806e8 + 9.91375e8i −0.0638718 + 0.362235i
\(498\) 1.36801e7 1.14789e7i 0.00496347 0.00416485i
\(499\) −2.00470e9 1.68214e9i −0.722267 0.606054i 0.205744 0.978606i \(-0.434038\pi\)
−0.928011 + 0.372552i \(0.878483\pi\)
\(500\) −2.30135e7 1.30516e8i −0.00823355 0.0466948i
\(501\) 7.42559e7 + 1.28615e8i 0.0263815 + 0.0456941i
\(502\) −1.37675e9 + 2.38460e9i −0.485726 + 0.841302i
\(503\) −3.33380e9 1.21341e9i −1.16802 0.425126i −0.316067 0.948737i \(-0.602362\pi\)
−0.851958 + 0.523611i \(0.824585\pi\)
\(504\) −1.67389e9 6.09245e8i −0.582397 0.211975i
\(505\) −5.73220e7 + 9.92845e7i −0.0198062 + 0.0343053i
\(506\) 3.01055e8 + 5.21443e8i 0.103304 + 0.178929i
\(507\) −2.83877e7 1.60994e8i −0.00967391 0.0548635i
\(508\) 6.39514e8 + 5.36616e8i 0.216435 + 0.181610i
\(509\) −8.33506e8 + 6.99395e8i −0.280154 + 0.235077i −0.772027 0.635590i \(-0.780757\pi\)
0.491873 + 0.870667i \(0.336312\pi\)
\(510\) −1.44047e6 + 8.16930e6i −0.000480848 + 0.00272703i
\(511\) −7.19782e9 + 2.61979e9i −2.38631 + 0.868547i
\(512\) −1.34218e8 −0.0441942
\(513\) 4.08136e8 2.88202e8i 0.133473 0.0942509i
\(514\) −7.73335e8 −0.251187
\(515\) 1.48174e8 5.39308e7i 0.0478020 0.0173985i
\(516\) −3.02390e7 + 1.71494e8i −0.00968931 + 0.0549508i
\(517\) 6.24809e8 5.24277e8i 0.198852 0.166857i
\(518\) 2.96514e9 + 2.48805e9i 0.937328 + 0.786512i
\(519\) −1.16079e7 6.58318e7i −0.00364476 0.0206705i
\(520\) −3.48696e7 6.03959e7i −0.0108752 0.0188363i
\(521\) −4.33767e8 + 7.51306e8i −0.134377 + 0.232748i −0.925359 0.379091i \(-0.876237\pi\)
0.790982 + 0.611839i \(0.209570\pi\)
\(522\) 4.00707e9 + 1.45845e9i 1.23305 + 0.448793i
\(523\) −5.87621e7 2.13877e7i −0.0179615 0.00653743i 0.333024 0.942918i \(-0.391931\pi\)
−0.350985 + 0.936381i \(0.614153\pi\)
\(524\) 2.70561e7 4.68625e7i 0.00821496 0.0142287i
\(525\) −2.39292e8 4.14466e8i −0.0721723 0.125006i
\(526\) 1.71517e8 + 9.72719e8i 0.0513873 + 0.291432i
\(527\) 1.25490e9 + 1.05298e9i 0.373483 + 0.313390i
\(528\) 1.70075e7 1.42710e7i 0.00502831 0.00421925i
\(529\) −9.92186e7 + 5.62697e8i −0.0291406 + 0.165264i
\(530\) 1.39110e8 5.06320e7i 0.0405876 0.0147727i
\(531\) −4.47264e9 −1.29638
\(532\) 2.17555e9 + 2.15835e9i 0.626438 + 0.621485i
\(533\) 8.12512e9 2.32426
\(534\) 4.52891e7 1.64839e7i 0.0128706 0.00468452i
\(535\) −1.45961e7 + 8.27787e7i −0.00412097 + 0.0233712i
\(536\) −1.87089e8 + 1.56987e8i −0.0524774 + 0.0440338i
\(537\) 1.05336e8 + 8.83870e7i 0.0293538 + 0.0246308i
\(538\) −8.29126e6 4.70221e7i −0.00229553 0.0130186i
\(539\) 1.23120e9 + 2.13250e9i 0.338662 + 0.586580i
\(540\) −7.09524e6 + 1.22893e7i −0.00193905 + 0.00335853i
\(541\) 2.05869e8 + 7.49302e7i 0.0558986 + 0.0203454i 0.369818 0.929104i \(-0.379420\pi\)
−0.313920 + 0.949450i \(0.601642\pi\)
\(542\) −2.29969e9 8.37020e8i −0.620401 0.225807i
\(543\) −1.06517e8 + 1.84493e8i −0.0285508 + 0.0494515i
\(544\) −3.34013e8 5.78528e8i −0.0889544 0.154074i
\(545\) 4.81380e7 + 2.73004e8i 0.0127380 + 0.0722407i
\(546\) −3.86276e8 3.24124e8i −0.101560 0.0852190i
\(547\) 1.66309e9 1.39550e9i 0.434470 0.364564i −0.399165 0.916879i \(-0.630700\pi\)
0.833635 + 0.552315i \(0.186255\pi\)
\(548\) 4.00108e8 2.26912e9i 0.103859 0.589015i
\(549\) 3.49939e9 1.27367e9i 0.902587 0.328515i
\(550\) −8.81716e8 −0.225974
\(551\) −5.20799e9 5.16681e9i −1.32629 1.31581i
\(552\) −1.04478e8 −0.0264386
\(553\) −6.68062e9 + 2.43155e9i −1.67988 + 0.611427i
\(554\) −2.32265e8 + 1.31724e9i −0.0580362 + 0.329140i
\(555\) 1.17708e7 9.87688e6i 0.00292268 0.00245242i
\(556\) −1.12586e9 9.44707e8i −0.277793 0.233096i
\(557\) −4.65771e8 2.64152e9i −0.114203 0.647680i −0.987141 0.159849i \(-0.948899\pi\)
0.872938 0.487831i \(-0.162212\pi\)
\(558\) 6.98219e8 + 1.20935e9i 0.170126 + 0.294668i
\(559\) 3.64329e9 6.31036e9i 0.882170 1.52796i
\(560\) −8.17893e7 2.97689e7i −0.0196806 0.00716316i
\(561\) 1.03838e8 + 3.77939e7i 0.0248305 + 0.00903758i
\(562\) −2.77894e9 + 4.81326e9i −0.660392 + 1.14383i
\(563\) −2.71161e8 4.69665e8i −0.0640395 0.110920i 0.832228 0.554434i \(-0.187065\pi\)
−0.896268 + 0.443514i \(0.853732\pi\)
\(564\) 2.45762e7 + 1.39378e8i 0.00576816 + 0.0327128i
\(565\) −8.84897e7 7.42517e7i −0.0206406 0.0173196i
\(566\) 2.54196e6 2.13296e6i 0.000589266 0.000494453i
\(567\) 1.30345e9 7.39220e9i 0.300298 1.70307i
\(568\) −3.02408e8 + 1.10067e8i −0.0692426 + 0.0252023i
\(569\) 8.27657e8 0.188347 0.0941733 0.995556i \(-0.469979\pi\)
0.0941733 + 0.995556i \(0.469979\pi\)
\(570\) 9.93756e6 7.01731e6i 0.00224759 0.00158712i
\(571\) −2.65557e9 −0.596942 −0.298471 0.954419i \(-0.596477\pi\)
−0.298471 + 0.954419i \(0.596477\pi\)
\(572\) −8.72970e8 + 3.17735e8i −0.195035 + 0.0709871i
\(573\) −8.76699e7 + 4.97201e8i −0.0194675 + 0.110405i
\(574\) 7.76815e9 6.51825e9i 1.71446 1.43860i
\(575\) 3.17850e9 + 2.66708e9i 0.697244 + 0.585057i
\(576\) −9.88851e7 5.60805e8i −0.0215602 0.122274i
\(577\) −9.92315e8 1.71874e9i −0.215047 0.372473i 0.738240 0.674538i \(-0.235657\pi\)
−0.953287 + 0.302065i \(0.902324\pi\)
\(578\) 2.10904e7 3.65296e7i 0.00454294 0.00786860i
\(579\) −5.54125e8 2.01685e8i −0.118640 0.0431816i
\(580\) 1.95793e8 + 7.12629e7i 0.0416677 + 0.0151658i
\(581\) −4.66300e8 + 8.07655e8i −0.0986391 + 0.170848i
\(582\) −2.52292e7 4.36983e7i −0.00530486 0.00918828i
\(583\) −3.42437e8 1.94205e9i −0.0715715 0.405902i
\(584\) −1.87581e9 1.57399e9i −0.389713 0.327008i
\(585\) 2.26664e8 1.90193e8i 0.0468097 0.0392780i
\(586\) −2.34697e8 + 1.33103e9i −0.0481799 + 0.273242i
\(587\) 2.13147e9 7.75790e8i 0.434956 0.158311i −0.115257 0.993336i \(-0.536769\pi\)
0.550212 + 0.835025i \(0.314547\pi\)
\(588\) −4.27275e8 −0.0866737
\(589\) −2.18883e8 2.39243e9i −0.0441376 0.482431i
\(590\) −2.18542e8 −0.0438080
\(591\) −1.67712e7 + 6.10421e6i −0.00334201 + 0.00121639i
\(592\) −2.14873e8 + 1.21861e9i −0.0425654 + 0.241400i
\(593\) −4.30163e9 + 3.60950e9i −0.847114 + 0.710813i −0.959152 0.282891i \(-0.908707\pi\)
0.112038 + 0.993704i \(0.464262\pi\)
\(594\) 1.44806e8 + 1.21507e8i 0.0283488 + 0.0237875i
\(595\) −7.52254e7 4.26625e8i −0.0146405 0.0830303i
\(596\) −7.04524e8 1.22027e9i −0.136312 0.236099i
\(597\) 1.81947e8 3.15141e8i 0.0349973 0.0606170i
\(598\) 4.10808e9 + 1.49522e9i 0.785570 + 0.285924i
\(599\) 2.58896e9 + 9.42305e8i 0.492189 + 0.179142i 0.576177 0.817325i \(-0.304544\pi\)
−0.0839886 + 0.996467i \(0.526766\pi\)
\(600\) 7.64978e7 1.32498e8i 0.0144584 0.0250426i
\(601\) −5.54828e8 9.60991e8i −0.104255 0.180575i 0.809178 0.587563i \(-0.199913\pi\)
−0.913434 + 0.406988i \(0.866579\pi\)
\(602\) −1.57917e9 8.95590e9i −0.295012 1.67310i
\(603\) −7.93779e8 6.66060e8i −0.147431 0.123709i
\(604\) −1.49037e9 + 1.25057e9i −0.275210 + 0.230928i
\(605\) −4.02913e7 + 2.28503e8i −0.00739720 + 0.0419516i
\(606\) −2.49014e8 + 9.06337e7i −0.0454537 + 0.0165438i
\(607\) 2.52657e9 0.458533 0.229266 0.973364i \(-0.426367\pi\)
0.229266 + 0.973364i \(0.426367\pi\)
\(608\) −2.49803e8 + 9.47304e8i −0.0450750 + 0.170933i
\(609\) 1.50653e9 0.270282
\(610\) 1.70987e8 6.22342e7i 0.0305006 0.0111013i
\(611\) 1.02835e9 5.83206e9i 0.182388 1.03438i
\(612\) 2.17119e9 1.82185e9i 0.382885 0.321279i
\(613\) 3.69007e9 + 3.09633e9i 0.647027 + 0.542920i 0.906167 0.422919i \(-0.138995\pi\)
−0.259140 + 0.965840i \(0.583439\pi\)
\(614\) 6.82343e8 + 3.86976e9i 0.118963 + 0.674675i
\(615\) −2.01277e7 3.48622e7i −0.00348924 0.00604355i
\(616\) −5.79719e8 + 1.00410e9i −0.0999275 + 0.173080i
\(617\) −8.13101e8 2.95944e8i −0.139363 0.0507238i 0.271397 0.962467i \(-0.412514\pi\)
−0.410760 + 0.911744i \(0.634737\pi\)
\(618\) 3.42498e8 + 1.24659e8i 0.0583711 + 0.0212454i
\(619\) −4.62428e9 + 8.00949e9i −0.783659 + 1.35734i 0.146138 + 0.989264i \(0.453316\pi\)
−0.929797 + 0.368073i \(0.880018\pi\)
\(620\) 3.41163e7 + 5.90912e7i 0.00574899 + 0.00995754i
\(621\) −1.54470e8 8.76041e8i −0.0258835 0.146793i
\(622\) −4.07180e9 3.41665e9i −0.678454 0.569291i
\(623\) −1.92807e9 + 1.61784e9i −0.319459 + 0.268058i
\(624\) 2.79920e7 1.58751e8i 0.00461199 0.0261559i
\(625\) −5.69669e9 + 2.07342e9i −0.933345 + 0.339710i
\(626\) −4.60894e9 −0.750916
\(627\) −6.90702e7 1.46599e8i −0.0111906 0.0237517i
\(628\) 4.13916e8 0.0666889
\(629\) −5.78738e9 + 2.10643e9i −0.927267 + 0.337498i
\(630\) 6.41256e7 3.63675e8i 0.0102174 0.0579457i
\(631\) −2.41772e9 + 2.02870e9i −0.383091 + 0.321452i −0.813915 0.580984i \(-0.802668\pi\)
0.430823 + 0.902436i \(0.358223\pi\)
\(632\) −1.74103e9 1.46090e9i −0.274344 0.230202i
\(633\) −1.69308e6 9.60191e6i −0.000265316 0.00150468i
\(634\) −3.03869e8 5.26316e8i −0.0473559 0.0820228i
\(635\) −8.65342e7 + 1.49882e8i −0.0134116 + 0.0232295i
\(636\) 3.21548e8 + 1.17034e8i 0.0495617 + 0.0180390i
\(637\) 1.68004e10 + 6.11486e9i 2.57533 + 0.937343i
\(638\) 1.38777e9 2.40369e9i 0.211566 0.366443i
\(639\) −6.82696e8 1.18246e9i −0.103508 0.179281i
\(640\) −4.83172e6 2.74020e7i −0.000728571 0.00413193i
\(641\) 1.23456e9 + 1.03592e9i 0.185143 + 0.155354i 0.730649 0.682754i \(-0.239218\pi\)
−0.545505 + 0.838107i \(0.683662\pi\)
\(642\) −1.48836e8 + 1.24888e8i −0.0221991 + 0.0186273i
\(643\) −1.05890e9 + 6.00531e9i −0.157078 + 0.890834i 0.799783 + 0.600289i \(0.204948\pi\)
−0.956861 + 0.290545i \(0.906163\pi\)
\(644\) 5.12711e9 1.86612e9i 0.756436 0.275320i
\(645\) −3.61009e7 −0.00529736
\(646\) −4.70489e9 + 1.28071e9i −0.686650 + 0.186912i
\(647\) 9.37758e8 0.136121 0.0680606 0.997681i \(-0.478319\pi\)
0.0680606 + 0.997681i \(0.478319\pi\)
\(648\) 2.25491e9 8.20720e8i 0.325549 0.118490i
\(649\) −5.05524e8 + 2.86697e9i −0.0725915 + 0.411687i
\(650\) −4.90411e9 + 4.11503e9i −0.700427 + 0.587728i
\(651\) 3.77931e8 + 3.17122e8i 0.0536882 + 0.0450498i
\(652\) 9.05918e8 + 5.13772e9i 0.128004 + 0.725945i
\(653\) 5.91389e9 + 1.02432e10i 0.831146 + 1.43959i 0.897130 + 0.441767i \(0.145648\pi\)
−0.0659838 + 0.997821i \(0.521019\pi\)
\(654\) −3.20387e8 + 5.54927e8i −0.0447871 + 0.0775735i
\(655\) 1.05415e7 + 3.83679e6i 0.00146574 + 0.000533487i
\(656\) 3.04628e9 + 1.10876e9i 0.421315 + 0.153346i
\(657\) 5.19465e9 8.99740e9i 0.714624 1.23776i
\(658\) −3.69551e9 6.40082e9i −0.505690 0.875880i
\(659\) 1.83036e9 + 1.03805e10i 0.249137 + 1.41292i 0.810686 + 0.585481i \(0.199094\pi\)
−0.561550 + 0.827443i \(0.689795\pi\)
\(660\) 3.52584e6 + 2.95853e6i 0.000477373 + 0.000400564i
\(661\) 6.14858e9 5.15927e9i 0.828076 0.694838i −0.126773 0.991932i \(-0.540462\pi\)
0.954848 + 0.297094i \(0.0960174\pi\)
\(662\) 8.42667e8 4.77900e9i 0.112889 0.640228i
\(663\) 7.53934e8 2.74410e8i 0.100470 0.0365681i
\(664\) −2.98137e8 −0.0395210
\(665\) −3.62332e8 + 5.21861e8i −0.0477784 + 0.0688144i
\(666\) −5.25005e9 −0.688658
\(667\) −1.22737e10 + 4.46725e9i −1.60152 + 0.582907i
\(668\) 4.30539e8 2.44171e9i 0.0558850 0.316940i
\(669\) 2.33754e8 1.96143e8i 0.0301834 0.0253269i
\(670\) −3.87856e7 3.25450e7i −0.00498206 0.00418044i
\(671\) −4.20905e8 2.38707e9i −0.0537843 0.305026i
\(672\) −1.00593e8 1.74232e8i −0.0127872 0.0221481i
\(673\) 2.44847e9 4.24088e9i 0.309629 0.536294i −0.668652 0.743576i \(-0.733128\pi\)
0.978281 + 0.207282i \(0.0664617\pi\)
\(674\) 2.21101e9 + 8.04742e8i 0.278151 + 0.101239i
\(675\) 1.22409e9 + 4.45531e8i 0.153196 + 0.0557589i
\(676\) −1.36462e9 + 2.36359e9i −0.169902 + 0.294278i
\(677\) 3.79960e8 + 6.58110e8i 0.0470628 + 0.0815151i 0.888597 0.458688i \(-0.151681\pi\)
−0.841534 + 0.540204i \(0.818347\pi\)
\(678\) −4.63656e7 2.62952e8i −0.00571336 0.0324021i
\(679\) 2.01859e9 + 1.69380e9i 0.247460 + 0.207643i
\(680\) 1.06089e8 8.90190e7i 0.0129386 0.0108568i
\(681\) −1.45057e8 + 8.22658e8i −0.0176004 + 0.0998170i
\(682\) 8.54112e8 3.10871e8i 0.103103 0.0375263i
\(683\) −5.38849e9 −0.647134 −0.323567 0.946205i \(-0.604882\pi\)
−0.323567 + 0.946205i \(0.604882\pi\)
\(684\) −4.14219e9 3.45831e8i −0.494918 0.0413207i
\(685\) 4.77671e8 0.0567821
\(686\) 1.10525e10 4.02277e9i 1.30715 0.475763i
\(687\) −1.60661e8 + 9.11156e8i −0.0189044 + 0.107212i
\(688\) 2.22706e9 1.86873e9i 0.260719 0.218769i
\(689\) −1.09683e10 9.20354e9i −1.27754 1.07198i
\(690\) −3.76113e6 2.13304e7i −0.000435859 0.00247188i
\(691\) 2.12238e9 + 3.67607e9i 0.244709 + 0.423848i 0.962050 0.272874i \(-0.0879743\pi\)
−0.717341 + 0.696722i \(0.754641\pi\)
\(692\) −5.58002e8 + 9.66488e8i −0.0640125 + 0.110873i
\(693\) −4.62258e9 1.68248e9i −0.527616 0.192036i
\(694\) 1.07614e10 + 3.91684e9i 1.22211 + 0.444813i
\(695\) 1.52342e8 2.63865e8i 0.0172137 0.0298150i
\(696\) 2.40807e8 + 4.17090e8i 0.0270730 + 0.0468918i
\(697\) 2.80181e9 + 1.58898e10i 0.313418 + 1.77748i
\(698\) −8.75545e9 7.34669e9i −0.974506 0.817708i
\(699\) 6.36663e8 5.34223e8i 0.0705081 0.0591633i
\(700\) −1.38743e9 + 7.86849e9i −0.152886 + 0.867058i
\(701\) −8.69424e9 + 3.16444e9i −0.953276 + 0.346964i −0.771395 0.636357i \(-0.780441\pi\)
−0.181881 + 0.983321i \(0.558218\pi\)
\(702\) 1.37250e9 0.149738
\(703\) 8.20098e9 + 3.78462e9i 0.890270 + 0.410845i
\(704\) −3.70653e8 −0.0400372
\(705\) −2.75709e7 + 1.00350e7i −0.00296339 + 0.00107859i
\(706\) −3.09810e8 + 1.75702e9i −0.0331344 + 0.187914i
\(707\) 1.06011e10 8.89542e9i 1.12820 0.946670i
\(708\) −3.86969e8 3.24705e8i −0.0409788 0.0343853i
\(709\) −2.55004e8 1.44620e9i −0.0268711 0.152394i 0.968420 0.249324i \(-0.0802085\pi\)
−0.995291 + 0.0969309i \(0.969097\pi\)
\(710\) −3.33579e7 5.77775e7i −0.00349779 0.00605836i
\(711\) 4.82139e9 8.35089e9i 0.503070 0.871343i
\(712\) −7.56094e8 2.75196e8i −0.0785047 0.0285734i
\(713\) −4.01934e9 1.46292e9i −0.415280 0.151150i
\(714\) 5.00670e8 8.67186e8i 0.0514763 0.0891596i
\(715\) −9.62953e7 1.66788e8i −0.00985222 0.0170645i
\(716\) −3.98633e8 2.26076e9i −0.0405861 0.230175i
\(717\) 2.00665e8 + 1.68378e8i 0.0203308 + 0.0170595i
\(718\) −7.05020e9 + 5.91582e9i −0.710830 + 0.596457i
\(719\) −1.82268e9 + 1.03369e10i −0.182877 + 1.03715i 0.745776 + 0.666196i \(0.232079\pi\)
−0.928653 + 0.370949i \(0.879032\pi\)
\(720\) 1.10935e8 4.03770e7i 0.0110765 0.00403153i
\(721\) −1.90341e10 −1.89130
\(722\) 6.22112e9 + 3.52621e9i 0.615160 + 0.348680i
\(723\) −9.11284e8 −0.0896746
\(724\) 3.34207e9 1.21641e9i 0.327288 0.119123i
\(725\) 3.32132e9 1.88362e10i 0.323689 1.83573i
\(726\) −4.10849e8 + 3.44743e8i −0.0398477 + 0.0334362i
\(727\) −9.89699e9 8.30456e9i −0.955285 0.801579i 0.0248947 0.999690i \(-0.492075\pi\)
−0.980180 + 0.198111i \(0.936519\pi\)
\(728\) 1.46182e9 + 8.29042e9i 0.140422 + 0.796373i
\(729\) 5.02049e9 + 8.69574e9i 0.479954 + 0.831304i
\(730\) 2.53821e8 4.39630e8i 0.0241489 0.0418271i
\(731\) 1.35971e10 + 4.94896e9i 1.28747 + 0.468601i
\(732\) 3.95230e8 + 1.43852e8i 0.0372444 + 0.0135559i
\(733\) 4.83479e9 8.37409e9i 0.453433 0.785369i −0.545163 0.838330i \(-0.683532\pi\)
0.998597 + 0.0529605i \(0.0168657\pi\)
\(734\) −4.27933e9 7.41202e9i −0.399429 0.691832i
\(735\) −1.53815e7 8.72330e7i −0.00142887 0.00810355i
\(736\) 1.33617e9 + 1.12118e9i 0.123535 + 0.103658i
\(737\) −5.16663e8 + 4.33532e8i −0.0475413 + 0.0398919i
\(738\) −2.38839e9 + 1.35452e10i −0.218730 + 1.24048i
\(739\) 1.07326e10 3.90634e9i 0.978247 0.356053i 0.197089 0.980386i \(-0.436851\pi\)
0.781158 + 0.624333i \(0.214629\pi\)
\(740\) −2.56528e8 −0.0232714
\(741\) −1.06836e9 4.93030e8i −0.0964613 0.0445153i
\(742\) −1.78699e10 −1.60586
\(743\) −6.03223e9 + 2.19555e9i −0.539532 + 0.196373i −0.597389 0.801951i \(-0.703795\pi\)
0.0578577 + 0.998325i \(0.481573\pi\)
\(744\) −2.73873e7 + 1.55321e8i −0.00243806 + 0.0138269i
\(745\) 2.23770e8 1.87765e8i 0.0198269 0.0166367i
\(746\) 2.38225e9 + 1.99895e9i 0.210088 + 0.176285i
\(747\) −2.19653e8 1.24571e9i −0.0192803 0.109344i
\(748\) −9.22405e8 1.59765e9i −0.0805872 0.139581i
\(749\) 5.07323e9 8.78710e9i 0.441162 0.764116i
\(750\) 5.96769e7 + 2.17206e7i 0.00516526 + 0.00188000i
\(751\) −1.10602e10 4.02557e9i −0.952843 0.346807i −0.181618 0.983369i \(-0.558133\pi\)
−0.771225 + 0.636563i \(0.780356\pi\)
\(752\) 1.18140e9 2.04624e9i 0.101305 0.175466i
\(753\) −6.59725e8 1.14268e9i −0.0563093 0.0975306i
\(754\) −3.49942e9 1.98462e10i −0.297301 1.68608i
\(755\) −3.08969e8 2.59256e8i −0.0261277 0.0219237i
\(756\) 1.31220e9 1.10106e9i 0.110452 0.0926800i
\(757\) 3.52456e8 1.99888e9i 0.0295304 0.167475i −0.966476 0.256757i \(-0.917346\pi\)
0.996006 + 0.0892818i \(0.0284572\pi\)
\(758\) 1.13506e10 4.13129e9i 0.946624 0.344543i
\(759\) −2.88526e8 −0.0239518
\(760\) −2.02395e8 1.68980e7i −0.0167245 0.00139633i
\(761\) −1.69690e10 −1.39575 −0.697877 0.716217i \(-0.745872\pi\)
−0.697877 + 0.716217i \(0.745872\pi\)
\(762\) −3.75916e8 + 1.36822e8i −0.0307785 + 0.0112025i
\(763\) 5.81080e9 3.29547e10i 0.473588 2.68585i
\(764\) 6.45678e9 5.41788e9i 0.523828 0.439544i
\(765\) 4.50111e8 + 3.77688e8i 0.0363500 + 0.0305013i
\(766\) 1.84991e9 + 1.04914e10i 0.148713 + 0.843396i
\(767\) 1.05686e10 + 1.83054e10i 0.845737 + 1.46486i
\(768\) 3.21579e7 5.56992e7i 0.00256168 0.00443695i
\(769\) −2.16072e10 7.86437e9i −1.71339 0.623622i −0.716154 0.697942i \(-0.754099\pi\)
−0.997234 + 0.0743196i \(0.976322\pi\)
\(770\) −2.25868e8 8.22093e7i −0.0178294 0.00648938i
\(771\) 1.85288e8 3.20927e8i 0.0145598 0.0252183i
\(772\) 4.92236e9 + 8.52578e9i 0.385046 + 0.666920i
\(773\) −4.41204e8 2.50219e9i −0.0343567 0.194846i 0.962799 0.270220i \(-0.0870963\pi\)
−0.997155 + 0.0753732i \(0.975985\pi\)
\(774\) 9.44893e9 + 7.92860e9i 0.732469 + 0.614615i
\(775\) 4.79817e9 4.02614e9i 0.370271 0.310694i
\(776\) −1.46280e8 + 8.29597e8i −0.0112375 + 0.0637311i
\(777\) −1.74295e9 + 6.34384e8i −0.133295 + 0.0485153i
\(778\) 9.76681e9 0.743574
\(779\) 1.34952e10 1.94370e10i 1.02282 1.47315i
\(780\) 3.34184e7 0.00252147
\(781\) −8.35124e8 + 3.03960e8i −0.0627296 + 0.0228317i
\(782\) −1.50751e9 + 8.54954e9i −0.112730 + 0.639321i
\(783\) −3.14123e9 + 2.63581e9i −0.233848 + 0.196222i
\(784\) 5.46441e9 + 4.58519e9i 0.404983 + 0.339821i
\(785\) 1.49006e7 + 8.45056e7i 0.00109941 + 0.00623507i
\(786\) 1.29650e7 + 2.24561e7i 0.000952346 + 0.00164951i
\(787\) −3.33136e9 + 5.77008e9i −0.243618 + 0.421959i −0.961742 0.273956i \(-0.911668\pi\)
0.718124 + 0.695915i \(0.245001\pi\)
\(788\) 2.79992e8 + 1.01909e8i 0.0203847 + 0.00741941i
\(789\) −4.44765e8 1.61881e8i −0.0322375 0.0117335i
\(790\) 2.35583e8 4.08041e8i 0.0170000 0.0294448i
\(791\) 6.97199e9 + 1.20758e10i 0.500886 + 0.867560i
\(792\) −2.73079e8 1.54871e9i −0.0195322 0.110773i
\(793\) −1.34817e10 1.13125e10i −0.960040 0.805569i
\(794\) 5.12898e8 4.30372e8i 0.0363629 0.0305121i
\(795\) −1.23183e7 + 6.98607e7i −0.000869495 + 0.00493115i
\(796\) −5.70876e9 + 2.07782e9i −0.401186 + 0.146020i
\(797\) 8.51927e9 0.596071 0.298036 0.954555i \(-0.403669\pi\)
0.298036 + 0.954555i \(0.403669\pi\)
\(798\) −1.41695e9 + 3.85705e8i −0.0987060 + 0.0268686i
\(799\) 1.17600e10 0.815634
\(800\) −2.40019e9 + 8.73599e8i −0.165741 + 0.0603250i
\(801\) 5.92803e8 3.36195e9i 0.0407565 0.231142i
\(802\) −7.08928e9 + 5.94861e9i −0.485279 + 0.407198i
\(803\) −5.18022e9 4.34672e9i −0.353056 0.296249i
\(804\) −2.03223e7 1.15254e8i −0.00137904 0.00782094i
\(805\) 5.65560e8 + 9.79578e8i 0.0382114 + 0.0661841i
\(806\) 3.29971e9 5.71527e9i 0.221975 0.384472i
\(807\) 2.15003e7 + 7.82547e6i 0.00144008 + 0.000524147i
\(808\) 4.15724e9 + 1.51311e9i 0.277246 + 0.100909i
\(809\) −4.39338e9 + 7.60956e9i −0.291728 + 0.505289i −0.974219 0.225606i \(-0.927564\pi\)
0.682490 + 0.730895i \(0.260897\pi\)
\(810\) 2.48734e8 + 4.30819e8i 0.0164451 + 0.0284838i
\(811\) 3.74491e9 + 2.12384e10i 0.246529 + 1.39814i 0.816915 + 0.576759i \(0.195683\pi\)
−0.570386 + 0.821377i \(0.693206\pi\)
\(812\) −1.92670e10 1.61669e10i −1.26290 1.05970i
\(813\) 8.98352e8 7.53807e8i 0.0586313 0.0491975i
\(814\) −5.93391e8 + 3.36529e9i −0.0385616 + 0.218694i
\(815\) −1.01631e9 + 3.69907e8i −0.0657619 + 0.0239354i
\(816\) 3.20112e8 0.0206246
\(817\) −9.04445e9 1.91966e10i −0.580236 1.23153i
\(818\) −1.71765e10 −1.09723
\(819\) −3.35630e10 + 1.22159e10i −2.13485 + 0.777022i
\(820\) −1.16701e8 + 6.61847e8i −0.00739142 + 0.0419188i
\(821\) 7.25893e9 6.09097e9i 0.457796 0.384136i −0.384523 0.923115i \(-0.625634\pi\)
0.842319 + 0.538979i \(0.181190\pi\)
\(822\) 8.45803e8 + 7.09713e8i 0.0531151 + 0.0445689i
\(823\) 2.70904e8 + 1.53637e9i 0.0169401 + 0.0960720i 0.992106 0.125405i \(-0.0400232\pi\)
−0.975165 + 0.221478i \(0.928912\pi\)
\(824\) −3.04245e9 5.26968e9i −0.189443 0.328125i
\(825\) 2.11255e8 3.65904e8i 0.0130984 0.0226871i
\(826\) 2.47896e10 + 9.02266e9i 1.53052 + 0.557063i
\(827\) 2.79016e10 + 1.01553e10i 1.71538 + 0.624346i 0.997423 0.0717451i \(-0.0228568\pi\)
0.717953 + 0.696091i \(0.245079\pi\)
\(828\) −3.70023e9 + 6.40898e9i −0.226528 + 0.392358i
\(829\) 2.96170e9 + 5.12981e9i 0.180551 + 0.312724i 0.942068 0.335421i \(-0.108879\pi\)
−0.761517 + 0.648145i \(0.775545\pi\)
\(830\) −1.07327e7 6.08680e7i −0.000651530 0.00369501i
\(831\) −4.90993e8 4.11992e8i −0.0296805 0.0249049i
\(832\) −2.06158e9 + 1.72987e9i −0.124099 + 0.104131i
\(833\) −6.16515e9 + 3.49643e10i −0.369561 + 2.09588i
\(834\) 6.61795e8 2.40874e8i 0.0395041 0.0143783i
\(835\) 5.14001e8 0.0305535
\(836\) −6.89853e8 + 2.61606e9i −0.0408352 + 0.154855i
\(837\) −1.34285e9 −0.0791566
\(838\) 9.43365e9 3.43357e9i 0.553765 0.201554i
\(839\) −4.35125e9 + 2.46771e10i −0.254359 + 1.44254i 0.543354 + 0.839503i \(0.317154\pi\)
−0.797713 + 0.603037i \(0.793957\pi\)
\(840\) 3.19502e7 2.68094e7i 0.00185993 0.00156066i
\(841\) 3.29086e10 + 2.76136e10i 1.90776 + 1.60080i
\(842\) 2.11696e8 + 1.20059e9i 0.0122214 + 0.0693110i
\(843\) −1.33164e9 2.30647e9i −0.0765581 0.132602i
\(844\) −8.13875e7 + 1.40967e8i −0.00465971 + 0.00807086i
\(845\) −5.31678e8 1.93515e8i −0.0303145 0.0110336i
\(846\) 9.42024e9 + 3.42869e9i 0.534891 + 0.194684i
\(847\) 1.40042e10 2.42560e10i 0.791894 1.37160i
\(848\) −2.85635e9 4.94735e9i −0.160852 0.278604i
\(849\) 276117. + 1.56594e6i 1.54852e−5 + 8.78209e-5i
\(850\) −9.73863e9 8.17168e9i −0.543916 0.456400i
\(851\) 1.23187e10 1.03366e10i 0.685189 0.574942i
\(852\) 2.67785e7 1.51868e8i 0.00148336 0.00841256i
\(853\) 8.62288e9 3.13847e9i 0.475698 0.173140i −0.0930340 0.995663i \(-0.529657\pi\)
0.568732 + 0.822523i \(0.307434\pi\)
\(854\) −2.19647e10 −1.20677
\(855\) −7.85098e7 8.58123e8i −0.00429578 0.0469535i
\(856\) 3.24366e9 0.176757
\(857\) −1.40480e10 + 5.11304e9i −0.762396 + 0.277490i −0.693812 0.720156i \(-0.744070\pi\)
−0.0685839 + 0.997645i \(0.521848\pi\)
\(858\) 7.73023e7 4.38403e8i 0.00417818 0.0236956i
\(859\) −1.71720e10 + 1.44090e10i −0.924368 + 0.775637i −0.974798 0.223091i \(-0.928385\pi\)
0.0504297 + 0.998728i \(0.483941\pi\)
\(860\) 4.61693e8 + 3.87407e8i 0.0247519 + 0.0207693i
\(861\) 8.43806e8 + 4.78546e9i 0.0450538 + 0.255513i
\(862\) 6.65271e9 + 1.15228e10i 0.353772 + 0.612750i
\(863\) −1.76423e10 + 3.05574e10i −0.934369 + 1.61837i −0.158612 + 0.987341i \(0.550702\pi\)
−0.775756 + 0.631033i \(0.782631\pi\)
\(864\) 5.14578e8 + 1.87291e8i 0.0271427 + 0.00987914i
\(865\) −2.17407e8 7.91296e7i −0.0114213 0.00415703i
\(866\) −1.49470e9 + 2.58889e9i −0.0782062 + 0.135457i
\(867\) 1.01063e7 + 1.75047e7i 0.000526655 + 0.000912193i
\(868\) −1.43025e9 8.11132e9i −0.0742320 0.420991i
\(869\) −4.80799e9 4.03438e9i −0.248539 0.208549i
\(870\) −7.64847e7 + 6.41783e7i −0.00393783 + 0.00330423i
\(871\) −8.50356e8 + 4.82261e9i −0.0436051 + 0.247297i
\(872\) 1.00525e10 3.65880e9i 0.513410 0.186866i
\(873\) −3.57410e9 −0.181809
\(874\) 1.04001e10 7.34393e9i 0.526923 0.372082i
\(875\) −3.31651e9 −0.167361
\(876\) 1.10263e9 4.01325e8i 0.0554199 0.0201712i
\(877\) −9.08867e8 + 5.15444e9i −0.0454990 + 0.258037i −0.999069 0.0431328i \(-0.986266\pi\)
0.953570 + 0.301170i \(0.0973773\pi\)
\(878\) 2.04248e10 1.71385e10i 1.01842 0.854557i
\(879\) −4.96135e8 4.16307e8i −0.0246399 0.0206753i
\(880\) −1.33432e7 7.56730e7i −0.000660040 0.00374328i
\(881\) −1.05074e10 1.81994e10i −0.517703 0.896688i −0.999789 0.0205641i \(-0.993454\pi\)
0.482085 0.876124i \(-0.339880\pi\)
\(882\) −1.51325e10 + 2.62102e10i −0.742626 + 1.28627i
\(883\) −4.48137e8 1.63108e8i −0.0219052 0.00797286i 0.331044 0.943615i \(-0.392599\pi\)
−0.352950 + 0.935642i \(0.614821\pi\)
\(884\) −1.25868e10 4.58122e9i −0.612819 0.223048i
\(885\) 5.23617e7 9.06931e7i 0.00253929 0.00439818i
\(886\) −1.35062e10 2.33934e10i −0.652402 1.12999i
\(887\) −1.23956e9 7.02990e9i −0.0596397 0.338233i 0.940358 0.340185i \(-0.110490\pi\)
−0.999998 + 0.00195191i \(0.999379\pi\)
\(888\) −4.54229e8 3.81143e8i −0.0217685 0.0182660i
\(889\) 1.60037e10 1.34287e10i 0.763947 0.641028i
\(890\) 2.89655e7 1.64272e8i 0.00137726 0.00781084i
\(891\) 6.22712e9 2.26649e9i 0.294927 0.107345i
\(892\) −5.09433e9 −0.240331
\(893\) −1.22435e10 1.21467e10i −0.575341 0.570791i
\(894\) 6.75203e8 0.0316048
\(895\) 4.47208e8 1.62771e8i 0.0208511 0.00758919i
\(896\) −5.83243e8 + 3.30774e9i −0.0270877 + 0.153622i
\(897\) −1.60478e9 + 1.34657e9i −0.0742407 + 0.0622953i
\(898\) −2.93323e9 2.46127e9i −0.135170 0.113421i
\(899\) 3.42383e9 + 1.94175e10i 0.157164 + 0.891321i
\(900\) −5.41852e9 9.38516e9i −0.247761 0.429134i
\(901\) 1.42166e10 2.46239e10i 0.647528 1.12155i
\(902\) 8.41256e9 + 3.06192e9i 0.381685 + 0.138922i
\(903\) 4.09498e9 + 1.49045e9i 0.185074 + 0.0673613i
\(904\) −2.22883e9 + 3.86045e9i −0.100343 + 0.173799i
\(905\) 3.68656e8 + 6.38531e8i 0.0165330 + 0.0286360i
\(906\) −1.61889e8 9.18119e8i −0.00723218 0.0410157i
\(907\) −1.11428e10 9.34993e9i −0.495872 0.416086i 0.360253 0.932854i \(-0.382690\pi\)
−0.856125 + 0.516769i \(0.827135\pi\)
\(908\) 1.06833e10 8.96431e9i 0.473590 0.397390i
\(909\) −3.25942e9 + 1.84851e10i −0.143935 + 0.816297i
\(910\) −1.63996e9 + 5.96895e8i −0.0721419 + 0.0262575i
\(911\) 2.52003e10 1.10431 0.552156 0.833741i \(-0.313805\pi\)
0.552156 + 0.833741i \(0.313805\pi\)
\(912\) −3.33271e8 3.30636e8i −0.0145484 0.0144334i
\(913\) −8.23331e8 −0.0358036
\(914\) 7.74900e9 2.82041e9i 0.335687 0.122180i
\(915\) −1.51411e7 + 8.58692e7i −0.000653405 + 0.00370564i
\(916\) 1.18325e10 9.92865e9i 0.508678 0.426831i
\(917\) −1.03733e9 8.70426e8i −0.0444248 0.0372769i
\(918\) 4.73281e8 + 2.68411e9i 0.0201916 + 0.114512i
\(919\) 1.30478e9 + 2.25995e9i 0.0554542 + 0.0960494i 0.892420 0.451206i \(-0.149006\pi\)
−0.836966 + 0.547255i \(0.815673\pi\)
\(920\) −1.80800e8 + 3.13155e8i −0.00765494 + 0.0132587i
\(921\) −1.76940e9 6.44010e8i −0.0746308 0.0271634i
\(922\) −2.82006e10 1.02642e10i −1.18495 0.431286i
\(923\) −3.22636e9 + 5.58822e9i −0.135054 + 0.233920i
\(924\) −2.77796e8 4.81157e8i −0.0115844 0.0200648i
\(925\) 4.08915e9 + 2.31907e10i 0.169878 + 0.963426i
\(926\) −1.90547e10 1.59888e10i −0.788614 0.661725i
\(927\) 1.97769e10 1.65948e10i 0.815416 0.684215i
\(928\) 1.39621e9 7.91830e9i 0.0573499 0.325248i
\(929\) −1.51497e9 + 5.51405e8i −0.0619940 + 0.0225640i −0.372831 0.927899i \(-0.621613\pi\)
0.310837 + 0.950463i \(0.399391\pi\)
\(930\) −3.26965e7 −0.00133294
\(931\) 4.25323e10 3.00338e10i 1.72741 1.21979i
\(932\) −1.38751e10 −0.561411
\(933\) 2.39347e9 8.71150e8i 0.0964809 0.0351162i
\(934\) 5.11930e9 2.90330e10i 0.205587 1.16594i
\(935\) 2.92973e8 2.45833e8i 0.0117216 0.00983559i
\(936\) −8.74682e9 7.33945e9i −0.348646 0.292549i
\(937\) −8.00877e9 4.54200e10i −0.318037 1.80368i −0.554662 0.832076i \(-0.687152\pi\)
0.236625 0.971601i \(-0.423959\pi\)
\(938\) 3.05587e9 + 5.29292e9i 0.120900 + 0.209404i
\(939\) 1.10428e9 1.91267e9i 0.0435262 0.0753895i
\(940\) 4.60291e8 + 1.67532e8i 0.0180753 + 0.00657887i
\(941\) 3.07632e10 + 1.11969e10i 1.20356 + 0.438061i 0.864466 0.502691i \(-0.167657\pi\)
0.339096 + 0.940752i \(0.389879\pi\)
\(942\) −9.91724e7 + 1.71772e8i −0.00386556 + 0.00669535i
\(943\) −2.10645e10 3.64849e10i −0.818015 1.41684i
\(944\) 1.46445e9 + 8.30530e9i 0.0566594 + 0.321331i
\(945\) 2.72032e8 + 2.28262e8i 0.0104860 + 0.00879878i
\(946\) 6.15022e9 5.16064e9i 0.236195 0.198191i
\(947\) 4.85988e8 2.75617e9i 0.0185952 0.105458i −0.974098 0.226128i \(-0.927393\pi\)
0.992693 + 0.120670i \(0.0385042\pi\)
\(948\) 1.02340e9 3.72487e8i 0.0390137 0.0141998i
\(949\) −4.90988e10 −1.86483
\(950\) 1.69864e9 + 1.85664e10i 0.0642791 + 0.702579i
\(951\) 2.91222e8 0.0109798
\(952\) −1.57090e10 + 5.71761e9i −0.590092 + 0.214776i
\(953\) −1.22803e9 + 6.96452e9i −0.0459605 + 0.260655i −0.999126 0.0417935i \(-0.986693\pi\)
0.953166 + 0.302448i \(0.0978040\pi\)
\(954\) 1.85672e10 1.55797e10i 0.692352 0.580952i
\(955\) 1.33856e9 + 1.12318e9i 0.0497308 + 0.0417291i
\(956\) −7.59397e8 4.30675e9i −0.0281104 0.159422i
\(957\) 6.65008e8 + 1.15183e9i 0.0245265 + 0.0424811i
\(958\) −8.49456e9 + 1.47130e10i −0.312149 + 0.540657i
\(959\) −5.41829e10 1.97210e10i −1.98380 0.722043i
\(960\) 1.25293e7 + 4.56028e6i 0.000457063 + 0.000166357i
\(961\) 1.05279e10 1.82348e10i 0.382656 0.662780i
\(962\) 1.24056e10 + 2.14871e10i 0.449268 + 0.778155i
\(963\) 2.38977e9 + 1.35531e10i 0.0862312 + 0.489041i
\(964\) 1.16544e10 + 9.77918e9i 0.419005 + 0.351587i
\(965\) −1.56343e9 + 1.31188e9i −0.0560058 + 0.0469945i
\(966\) −4.54010e8 + 2.57482e9i −0.0162049 + 0.0919024i
\(967\) 1.93795e10 7.05355e9i 0.689206 0.250851i 0.0264110 0.999651i \(-0.491592\pi\)
0.662795 + 0.748801i \(0.269370\pi\)
\(968\) 8.95384e9 0.317282
\(969\) 5.95786e8 2.25934e9i 0.0210357 0.0797716i
\(970\) −1.74637e8 −0.00614379
\(971\) −2.30256e10 + 8.38063e9i −0.807130 + 0.293771i −0.712438 0.701735i \(-0.752409\pi\)
−0.0946923 + 0.995507i \(0.530187\pi\)
\(972\) −6.05850e8 + 3.43595e9i −0.0211609 + 0.120009i
\(973\) −2.81743e10 + 2.36410e10i −0.980523 + 0.822757i
\(974\) 2.56550e10 + 2.15271e10i 0.889644 + 0.746500i
\(975\) −5.32702e8 3.02110e9i −0.0184064 0.104388i
\(976\) −3.51088e9 6.08102e9i −0.120876 0.209364i
\(977\) −1.08011e10 + 1.87080e10i −0.370540 + 0.641794i −0.989649 0.143511i \(-0.954161\pi\)
0.619109 + 0.785305i \(0.287494\pi\)
\(978\) −2.34916e9 8.55025e8i −0.0803021 0.0292276i
\(979\) −2.08802e9 7.59976e8i −0.0711204 0.0258857i
\(980\) −7.39403e8 + 1.28068e9i −0.0250951 + 0.0434661i
\(981\) 2.26938e10 + 3.93068e10i 0.767478 + 1.32931i
\(982\) 1.13589e9 + 6.44194e9i 0.0382776 + 0.217083i
\(983\) 4.05252e10 + 3.40047e10i 1.36078 + 1.14183i 0.975740 + 0.218931i \(0.0702570\pi\)
0.385041 + 0.922900i \(0.374187\pi\)
\(984\) −1.19000e9 + 9.98528e8i −0.0398166 + 0.0334101i
\(985\) −1.07263e7 + 6.08320e7i −0.000357622 + 0.00202818i
\(986\) 3.76054e10 1.36872e10i 1.24934 0.454723i
\(987\) 3.54171e9 0.117247
\(988\) 8.37239e9 + 1.77701e10i 0.276185 + 0.586194i
\(989\) −3.77812e10 −1.24191
\(990\) 3.06356e8 1.11504e8i 0.0100347 0.00365232i
\(991\) 4.45967e9 2.52920e10i 0.145561 0.825517i −0.821354 0.570418i \(-0.806781\pi\)
0.966915 0.255098i \(-0.0821078\pi\)
\(992\) 2.01704e9 1.69250e9i 0.0656030 0.0550475i
\(993\) 1.78135e9 + 1.49473e9i 0.0577332 + 0.0484439i
\(994\) 1.39845e9 + 7.93100e9i 0.0451642 + 0.256139i
\(995\) −6.29720e8 1.09071e9i −0.0202659 0.0351016i
\(996\) 7.14323e7 1.23724e8i 0.00229080 0.00396778i
\(997\) 2.98184e10 + 1.08530e10i 0.952909 + 0.346830i 0.771251 0.636531i \(-0.219631\pi\)
0.181658 + 0.983362i \(0.441854\pi\)
\(998\) −1.96730e10 7.16040e9i −0.626491 0.228024i
\(999\) 2.52428e9 4.37219e9i 0.0801049 0.138746i
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 38.8.e.b.5.4 36
19.4 even 9 inner 38.8.e.b.23.4 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.8.e.b.5.4 36 1.1 even 1 trivial
38.8.e.b.23.4 yes 36 19.4 even 9 inner