Properties

Label 76.8.f.a.27.14
Level $76$
Weight $8$
Character 76.27
Analytic conductor $23.741$
Analytic rank $0$
Dimension $136$
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] = [76,8,Mod(27,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.27");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 76.f (of order \(6\), degree \(2\), 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: \(23.7412619368\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 27.14
Character \(\chi\) \(=\) 76.27
Dual form 76.8.f.a.31.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.71169 - 7.21848i) q^{2} +(-6.98587 + 12.0999i) q^{3} +(23.7871 + 125.770i) q^{4} +(-138.667 + 240.178i) q^{5} +(148.201 - 54.9831i) q^{6} +1057.42i q^{7} +(700.644 - 1267.38i) q^{8} +(995.895 + 1724.94i) q^{9} +O(q^{10})\) \(q+(-8.71169 - 7.21848i) q^{2} +(-6.98587 + 12.0999i) q^{3} +(23.7871 + 125.770i) q^{4} +(-138.667 + 240.178i) q^{5} +(148.201 - 54.9831i) q^{6} +1057.42i q^{7} +(700.644 - 1267.38i) q^{8} +(995.895 + 1724.94i) q^{9} +(2941.74 - 1091.39i) q^{10} +3569.75i q^{11} +(-1687.98 - 590.793i) q^{12} +(-2480.66 + 1432.21i) q^{13} +(7632.96 - 9211.91i) q^{14} +(-1937.42 - 3355.70i) q^{15} +(-15252.3 + 5983.43i) q^{16} +(1358.05 - 2352.20i) q^{17} +(3775.52 - 22216.0i) q^{18} +(26696.1 - 13460.8i) q^{19} +(-33505.7 - 11727.0i) q^{20} +(-12794.6 - 7386.99i) q^{21} +(25768.2 - 31098.6i) q^{22} +(3376.21 - 1949.26i) q^{23} +(10440.5 + 17331.4i) q^{24} +(605.519 + 1048.79i) q^{25} +(31949.1 + 5429.61i) q^{26} -58384.9 q^{27} +(-132992. + 25153.0i) q^{28} +(28090.1 - 16217.8i) q^{29} +(-7344.90 + 43219.0i) q^{30} -194793. q^{31} +(176065. + 57972.9i) q^{32} +(-43193.6 - 24937.8i) q^{33} +(-28810.2 + 10688.7i) q^{34} +(-253969. - 146629. i) q^{35} +(-193257. + 166285. i) q^{36} +576988. i q^{37} +(-329734. - 75438.9i) q^{38} -40020.8i q^{39} +(207240. + 344023. i) q^{40} +(223725. + 129168. i) q^{41} +(58140.1 + 156711. i) q^{42} +(-555247. - 320572. i) q^{43} +(-448969. + 84914.2i) q^{44} -552391. q^{45} +(-43483.2 - 7389.79i) q^{46} +(-795845. + 459481. i) q^{47} +(34152.0 - 226351. i) q^{48} -294592. q^{49} +(2295.57 - 13507.7i) q^{50} +(18974.2 + 32864.4i) q^{51} +(-239137. - 277925. i) q^{52} +(1.15364e6 - 666052. i) q^{53} +(508632. + 421450. i) q^{54} +(-857376. - 495007. i) q^{55} +(1.34015e6 + 740874. i) q^{56} +(-23621.5 + 417054. i) q^{57} +(-361781. - 61483.2i) q^{58} +(182488. - 316079. i) q^{59} +(375962. - 323492. i) q^{60} +(-273227. - 473244. i) q^{61} +(1.69697e6 + 1.40611e6i) q^{62} +(-1.82399e6 + 1.05308e6i) q^{63} +(-1.11535e6 - 1.77596e6i) q^{64} -794398. i q^{65} +(196276. + 529043. i) q^{66} +(-917891. - 1.58983e6i) q^{67} +(328141. + 114850. i) q^{68} +54469.0i q^{69} +(1.15406e6 + 3.11065e6i) q^{70} +(1.42151e6 - 2.46213e6i) q^{71} +(2.88392e6 - 53607.1i) q^{72} +(46991.7 - 81392.1i) q^{73} +(4.16498e6 - 5.02654e6i) q^{74} -16920.3 q^{75} +(2.32799e6 + 3.03738e6i) q^{76} -3.77473e6 q^{77} +(-288889. + 348649. i) q^{78} +(2.06459e6 - 3.57597e6i) q^{79} +(677905. - 4.49298e6i) q^{80} +(-1.77015e6 + 3.06600e6i) q^{81} +(-1.01663e6 - 2.74022e6i) q^{82} -6.21446e6i q^{83} +(624716. - 1.78490e6i) q^{84} +(376632. + 652345. i) q^{85} +(2.52310e6 + 6.80077e6i) q^{86} +453183. i q^{87} +(4.52423e6 + 2.50113e6i) q^{88} +(858851. - 495858. i) q^{89} +(4.81226e6 + 3.98742e6i) q^{90} +(-1.51444e6 - 2.62309e6i) q^{91} +(325469. + 378260. i) q^{92} +(1.36080e6 - 2.35697e6i) q^{93} +(1.02499e7 + 1.74193e6i) q^{94} +(-468879. + 8.27837e6i) q^{95} +(-1.93143e6 + 1.72537e6i) q^{96} +(8.59906e6 + 4.96467e6i) q^{97} +(2.56639e6 + 2.12651e6i) q^{98} +(-6.15762e6 + 3.55510e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.71169 7.21848i −0.770012 0.638029i
\(3\) −6.98587 + 12.0999i −0.149381 + 0.258736i −0.930999 0.365022i \(-0.881061\pi\)
0.781618 + 0.623758i \(0.214395\pi\)
\(4\) 23.7871 + 125.770i 0.185837 + 0.982581i
\(5\) −138.667 + 240.178i −0.496110 + 0.859287i −0.999990 0.00448651i \(-0.998572\pi\)
0.503880 + 0.863773i \(0.331905\pi\)
\(6\) 148.201 54.9831i 0.280106 0.103920i
\(7\) 1057.42i 1.16521i 0.812756 + 0.582605i \(0.197966\pi\)
−0.812756 + 0.582605i \(0.802034\pi\)
\(8\) 700.644 1267.38i 0.483819 0.875168i
\(9\) 995.895 + 1724.94i 0.455371 + 0.788725i
\(10\) 2941.74 1091.39i 0.930261 0.345129i
\(11\) 3569.75i 0.808656i 0.914614 + 0.404328i \(0.132495\pi\)
−0.914614 + 0.404328i \(0.867505\pi\)
\(12\) −1687.98 590.793i −0.281989 0.0986963i
\(13\) −2480.66 + 1432.21i −0.313159 + 0.180802i −0.648339 0.761352i \(-0.724536\pi\)
0.335180 + 0.942154i \(0.391203\pi\)
\(14\) 7632.96 9211.91i 0.743438 0.897225i
\(15\) −1937.42 3355.70i −0.148219 0.256723i
\(16\) −15252.3 + 5983.43i −0.930929 + 0.365200i
\(17\) 1358.05 2352.20i 0.0670414 0.116119i −0.830556 0.556935i \(-0.811977\pi\)
0.897598 + 0.440816i \(0.145311\pi\)
\(18\) 3775.52 22216.0i 0.152589 0.897867i
\(19\) 26696.1 13460.8i 0.892914 0.450228i
\(20\) −33505.7 11727.0i −0.936514 0.327780i
\(21\) −12794.6 7386.99i −0.301481 0.174060i
\(22\) 25768.2 31098.6i 0.515946 0.622675i
\(23\) 3376.21 1949.26i 0.0578605 0.0334058i −0.470791 0.882245i \(-0.656031\pi\)
0.528651 + 0.848839i \(0.322698\pi\)
\(24\) 10440.5 + 17331.4i 0.154164 + 0.255915i
\(25\) 605.519 + 1048.79i 0.00775065 + 0.0134245i
\(26\) 31949.1 + 5429.61i 0.356493 + 0.0605846i
\(27\) −58384.9 −0.570857
\(28\) −132992. + 25153.0i −1.14491 + 0.216539i
\(29\) 28090.1 16217.8i 0.213875 0.123481i −0.389236 0.921138i \(-0.627261\pi\)
0.603111 + 0.797657i \(0.293928\pi\)
\(30\) −7344.90 + 43219.0i −0.0496662 + 0.292247i
\(31\) −194793. −1.17438 −0.587188 0.809451i \(-0.699765\pi\)
−0.587188 + 0.809451i \(0.699765\pi\)
\(32\) 176065. + 57972.9i 0.949835 + 0.312752i
\(33\) −43193.6 24937.8i −0.209228 0.120798i
\(34\) −28810.2 + 10688.7i −0.125710 + 0.0466387i
\(35\) −253969. 146629.i −1.00125 0.578071i
\(36\) −193257. + 166285.i −0.690361 + 0.594013i
\(37\) 576988.i 1.87267i 0.351109 + 0.936335i \(0.385805\pi\)
−0.351109 + 0.936335i \(0.614195\pi\)
\(38\) −329734. 75438.9i −0.974813 0.223025i
\(39\) 40020.8i 0.108034i
\(40\) 207240. + 344023.i 0.511994 + 0.849918i
\(41\) 223725. + 129168.i 0.506957 + 0.292692i 0.731582 0.681754i \(-0.238782\pi\)
−0.224625 + 0.974445i \(0.572116\pi\)
\(42\) 58140.1 + 156711.i 0.121089 + 0.326382i
\(43\) −555247. 320572.i −1.06499 0.614874i −0.138184 0.990407i \(-0.544127\pi\)
−0.926809 + 0.375532i \(0.877460\pi\)
\(44\) −448969. + 84914.2i −0.794570 + 0.150278i
\(45\) −552391. −0.903655
\(46\) −43483.2 7389.79i −0.0658672 0.0111939i
\(47\) −795845. + 459481.i −1.11811 + 0.645543i −0.940919 0.338633i \(-0.890036\pi\)
−0.177195 + 0.984176i \(0.556702\pi\)
\(48\) 34152.0 226351.i 0.0445731 0.295419i
\(49\) −294592. −0.357713
\(50\) 2295.57 13507.7i 0.00259714 0.0152822i
\(51\) 18974.2 + 32864.4i 0.0200294 + 0.0346920i
\(52\) −239137. 277925.i −0.235849 0.274104i
\(53\) 1.15364e6 666052.i 1.06440 0.614529i 0.137751 0.990467i \(-0.456013\pi\)
0.926645 + 0.375938i \(0.122679\pi\)
\(54\) 508632. + 421450.i 0.439567 + 0.364224i
\(55\) −857376. 495007.i −0.694868 0.401182i
\(56\) 1.34015e6 + 740874.i 1.01975 + 0.563750i
\(57\) −23621.5 + 417054.i −0.0168945 + 0.298284i
\(58\) −361781. 61483.2i −0.243471 0.0413769i
\(59\) 182488. 316079.i 0.115679 0.200361i −0.802372 0.596824i \(-0.796429\pi\)
0.918051 + 0.396463i \(0.129762\pi\)
\(60\) 375962. 323492.i 0.224706 0.193346i
\(61\) −273227. 473244.i −0.154124 0.266950i 0.778616 0.627501i \(-0.215922\pi\)
−0.932740 + 0.360551i \(0.882589\pi\)
\(62\) 1.69697e6 + 1.40611e6i 0.904283 + 0.749286i
\(63\) −1.82399e6 + 1.05308e6i −0.919030 + 0.530602i
\(64\) −1.11535e6 1.77596e6i −0.531839 0.846845i
\(65\) 794398.i 0.358791i
\(66\) 196276. + 529043.i 0.0840356 + 0.226510i
\(67\) −917891. 1.58983e6i −0.372846 0.645788i 0.617156 0.786841i \(-0.288285\pi\)
−0.990002 + 0.141053i \(0.954951\pi\)
\(68\) 328141. + 114850.i 0.126555 + 0.0442943i
\(69\) 54469.0i 0.0199608i
\(70\) 1.15406e6 + 3.11065e6i 0.402147 + 1.08395i
\(71\) 1.42151e6 2.46213e6i 0.471353 0.816407i −0.528110 0.849176i \(-0.677099\pi\)
0.999463 + 0.0327686i \(0.0104324\pi\)
\(72\) 2.88392e6 53607.1i 0.910584 0.0169262i
\(73\) 46991.7 81392.1i 0.0141381 0.0244879i −0.858870 0.512194i \(-0.828833\pi\)
0.873008 + 0.487706i \(0.162166\pi\)
\(74\) 4.16498e6 5.02654e6i 1.19482 1.44198i
\(75\) −16920.3 −0.00463120
\(76\) 2.32799e6 + 3.03738e6i 0.608321 + 0.793691i
\(77\) −3.77473e6 −0.942254
\(78\) −288889. + 348649.i −0.0689288 + 0.0831874i
\(79\) 2.06459e6 3.57597e6i 0.471127 0.816016i −0.528327 0.849041i \(-0.677181\pi\)
0.999455 + 0.0330247i \(0.0105140\pi\)
\(80\) 677905. 4.49298e6i 0.148032 0.981114i
\(81\) −1.77015e6 + 3.06600e6i −0.370095 + 0.641024i
\(82\) −1.01663e6 2.74022e6i −0.203617 0.548829i
\(83\) 6.21446e6i 1.19297i −0.802624 0.596485i \(-0.796563\pi\)
0.802624 0.596485i \(-0.203437\pi\)
\(84\) 624716. 1.78490e6i 0.115002 0.328577i
\(85\) 376632. + 652345.i 0.0665198 + 0.115216i
\(86\) 2.52310e6 + 6.80077e6i 0.427750 + 1.15296i
\(87\) 453183.i 0.0737830i
\(88\) 4.52423e6 + 2.50113e6i 0.707710 + 0.391243i
\(89\) 858851. 495858.i 0.129138 0.0745577i −0.434040 0.900894i \(-0.642912\pi\)
0.563177 + 0.826336i \(0.309579\pi\)
\(90\) 4.81226e6 + 3.98742e6i 0.695825 + 0.576558i
\(91\) −1.51444e6 2.62309e6i −0.210673 0.364896i
\(92\) 325469. + 378260.i 0.0435765 + 0.0506446i
\(93\) 1.36080e6 2.35697e6i 0.175430 0.303853i
\(94\) 1.02499e7 + 1.74193e6i 1.27284 + 0.216313i
\(95\) −468879. + 8.27837e6i −0.0561084 + 0.990631i
\(96\) −1.93143e6 + 1.72537e6i −0.222808 + 0.199037i
\(97\) 8.59906e6 + 4.96467e6i 0.956643 + 0.552318i 0.895138 0.445789i \(-0.147077\pi\)
0.0615049 + 0.998107i \(0.480410\pi\)
\(98\) 2.56639e6 + 2.12651e6i 0.275443 + 0.228231i
\(99\) −6.15762e6 + 3.55510e6i −0.637807 + 0.368238i
\(100\) −117503. + 101104.i −0.0117503 + 0.0101104i
\(101\) −2.28665e6 3.96060e6i −0.220839 0.382504i 0.734224 0.678907i \(-0.237546\pi\)
−0.955063 + 0.296403i \(0.904213\pi\)
\(102\) 71932.9 423269.i 0.00671161 0.0394926i
\(103\) −2.13976e7 −1.92945 −0.964727 0.263254i \(-0.915204\pi\)
−0.964727 + 0.263254i \(0.915204\pi\)
\(104\) 77092.9 + 4.14740e6i 0.00672044 + 0.361542i
\(105\) 3.54838e6 2.04866e6i 0.299136 0.172706i
\(106\) −1.48580e7 2.52506e6i −1.21168 0.205921i
\(107\) 1.23080e7 0.971281 0.485641 0.874159i \(-0.338586\pi\)
0.485641 + 0.874159i \(0.338586\pi\)
\(108\) −1.38881e6 7.34309e6i −0.106086 0.560913i
\(109\) −5.43146e6 3.13586e6i −0.401720 0.231933i 0.285506 0.958377i \(-0.407838\pi\)
−0.687226 + 0.726444i \(0.741172\pi\)
\(110\) 3.89601e6 + 1.05013e7i 0.279091 + 0.752261i
\(111\) −6.98149e6 4.03076e6i −0.484526 0.279741i
\(112\) −6.32699e6 1.61281e7i −0.425534 1.08473i
\(113\) 1.47960e7i 0.964648i 0.875993 + 0.482324i \(0.160207\pi\)
−0.875993 + 0.482324i \(0.839793\pi\)
\(114\) 3.21628e6 3.46273e6i 0.203323 0.218903i
\(115\) 1.08119e6i 0.0662917i
\(116\) 2.70791e6 + 3.14713e6i 0.161076 + 0.187202i
\(117\) −4.94095e6 2.85266e6i −0.285207 0.164664i
\(118\) −3.87139e6 + 1.43630e6i −0.216910 + 0.0804742i
\(119\) 2.48726e6 + 1.43602e6i 0.135303 + 0.0781173i
\(120\) −5.61039e6 + 104287.i −0.296386 + 0.00550931i
\(121\) 6.74402e6 0.346075
\(122\) −1.03583e6 + 6.09504e6i −0.0516449 + 0.303890i
\(123\) −3.12582e6 + 1.80470e6i −0.151460 + 0.0874452i
\(124\) −4.63356e6 2.44992e7i −0.218242 1.15392i
\(125\) −2.20026e7 −1.00760
\(126\) 2.34916e7 + 3.99231e6i 1.04620 + 0.177798i
\(127\) −7.45497e6 1.29124e7i −0.322948 0.559363i 0.658147 0.752890i \(-0.271341\pi\)
−0.981095 + 0.193527i \(0.938007\pi\)
\(128\) −3.10319e6 + 2.35228e7i −0.130790 + 0.991410i
\(129\) 7.75777e6 4.47895e6i 0.318180 0.183701i
\(130\) −5.73435e6 + 6.92055e6i −0.228919 + 0.276273i
\(131\) 2.46184e7 + 1.42134e7i 0.956775 + 0.552394i 0.895179 0.445707i \(-0.147048\pi\)
0.0615957 + 0.998101i \(0.480381\pi\)
\(132\) 2.10899e6 6.02567e6i 0.0798114 0.228032i
\(133\) 1.42337e7 + 2.82289e7i 0.524609 + 1.04043i
\(134\) −3.47980e6 + 2.04759e7i −0.124936 + 0.735151i
\(135\) 8.09605e6 1.40228e7i 0.283208 0.490530i
\(136\) −2.02963e6 3.36922e6i −0.0691879 0.114853i
\(137\) −1.88041e7 3.25696e7i −0.624783 1.08216i −0.988583 0.150679i \(-0.951854\pi\)
0.363799 0.931477i \(-0.381479\pi\)
\(138\) 393183. 474517.i 0.0127356 0.0153700i
\(139\) −2.73538e6 + 1.57927e6i −0.0863904 + 0.0498775i −0.542573 0.840009i \(-0.682550\pi\)
0.456182 + 0.889886i \(0.349216\pi\)
\(140\) 1.24004e7 3.54296e7i 0.381933 1.09124i
\(141\) 1.28395e7i 0.385728i
\(142\) −3.01566e7 + 1.11882e7i −0.883839 + 0.327906i
\(143\) −5.11263e6 8.85533e6i −0.146207 0.253238i
\(144\) −2.55108e7 2.03505e7i −0.711960 0.567946i
\(145\) 8.99551e6i 0.245040i
\(146\) −996904. + 369854.i −0.0265105 + 0.00983547i
\(147\) 2.05798e6 3.56452e6i 0.0534356 0.0925531i
\(148\) −7.25680e7 + 1.37249e7i −1.84005 + 0.348011i
\(149\) 1.11123e7 1.92471e7i 0.275202 0.476664i −0.694984 0.719025i \(-0.744589\pi\)
0.970186 + 0.242361i \(0.0779219\pi\)
\(150\) 147405. + 122139.i 0.00356608 + 0.00295484i
\(151\) −4.39960e7 −1.03990 −0.519952 0.854195i \(-0.674050\pi\)
−0.519952 + 0.854195i \(0.674050\pi\)
\(152\) 1.64454e6 4.32652e7i 0.0379833 0.999278i
\(153\) 5.40988e6 0.122115
\(154\) 3.28842e7 + 2.72478e7i 0.725547 + 0.601186i
\(155\) 2.70113e7 4.67849e7i 0.582619 1.00913i
\(156\) 5.03343e6 951981.i 0.106152 0.0200767i
\(157\) 2.03542e6 3.52545e6i 0.0419764 0.0727053i −0.844274 0.535912i \(-0.819968\pi\)
0.886250 + 0.463207i \(0.153301\pi\)
\(158\) −4.37991e7 + 1.62496e7i −0.883416 + 0.327749i
\(159\) 1.86118e7i 0.367196i
\(160\) −3.83382e7 + 3.42480e7i −0.739966 + 0.661021i
\(161\) 2.06118e6 + 3.57007e6i 0.0389247 + 0.0674196i
\(162\) 3.75529e7 1.39322e7i 0.693970 0.257464i
\(163\) 9.97018e7i 1.80321i 0.432560 + 0.901605i \(0.357610\pi\)
−0.432560 + 0.901605i \(0.642390\pi\)
\(164\) −1.09237e7 + 3.12105e7i −0.193382 + 0.552519i
\(165\) 1.19790e7 6.91610e6i 0.207600 0.119858i
\(166\) −4.48589e7 + 5.41384e7i −0.761150 + 0.918602i
\(167\) 4.43200e7 + 7.67645e7i 0.736364 + 1.27542i 0.954122 + 0.299417i \(0.0967921\pi\)
−0.217759 + 0.976003i \(0.569875\pi\)
\(168\) −1.83266e7 + 1.10400e7i −0.298194 + 0.179633i
\(169\) −2.72718e7 + 4.72362e7i −0.434621 + 0.752786i
\(170\) 1.42784e6 8.40174e6i 0.0222899 0.131159i
\(171\) 4.98055e7 + 3.26436e7i 0.761712 + 0.499243i
\(172\) 2.71107e7 7.74591e7i 0.406248 1.16071i
\(173\) 1.14685e8 + 6.62135e7i 1.68402 + 0.972267i 0.958945 + 0.283592i \(0.0915260\pi\)
0.725070 + 0.688675i \(0.241807\pi\)
\(174\) 3.27129e6 3.94799e6i 0.0470757 0.0568138i
\(175\) −1.10901e6 + 640288.i −0.0156424 + 0.00903113i
\(176\) −2.13594e7 5.44471e7i −0.295321 0.752802i
\(177\) 2.54968e6 + 4.41617e6i 0.0345604 + 0.0598604i
\(178\) −1.10614e7 1.87984e6i −0.147008 0.0249833i
\(179\) 9.47297e7 1.23453 0.617263 0.786757i \(-0.288241\pi\)
0.617263 + 0.786757i \(0.288241\pi\)
\(180\) −1.31398e7 6.94743e7i −0.167933 0.887914i
\(181\) −1.14741e7 + 6.62460e6i −0.143829 + 0.0830395i −0.570187 0.821515i \(-0.693129\pi\)
0.426359 + 0.904554i \(0.359796\pi\)
\(182\) −5.74137e6 + 3.37835e7i −0.0705937 + 0.415389i
\(183\) 7.63492e6 0.0920928
\(184\) −104925. 5.64468e6i −0.00124170 0.0668000i
\(185\) −1.38580e8 8.00092e7i −1.60916 0.929049i
\(186\) −2.88686e7 + 1.07103e7i −0.328950 + 0.122041i
\(187\) 8.39679e6 + 4.84789e6i 0.0939004 + 0.0542134i
\(188\) −7.67200e7 8.91639e7i −0.842085 0.978671i
\(189\) 6.17373e7i 0.665168i
\(190\) 6.38419e7 6.87340e7i 0.675256 0.726999i
\(191\) 4.25968e7i 0.442344i 0.975235 + 0.221172i \(0.0709882\pi\)
−0.975235 + 0.221172i \(0.929012\pi\)
\(192\) 2.92806e7 1.08893e6i 0.298556 0.0111031i
\(193\) −7.44295e7 4.29719e7i −0.745237 0.430263i 0.0787334 0.996896i \(-0.474912\pi\)
−0.823970 + 0.566633i \(0.808246\pi\)
\(194\) −3.90750e7 1.05323e8i −0.384232 1.03566i
\(195\) 9.61212e6 + 5.54956e6i 0.0928321 + 0.0535966i
\(196\) −7.00750e6 3.70509e7i −0.0664763 0.351482i
\(197\) 1.36073e8 1.26806 0.634028 0.773310i \(-0.281400\pi\)
0.634028 + 0.773310i \(0.281400\pi\)
\(198\) 7.93057e7 + 1.34777e7i 0.726066 + 0.123392i
\(199\) 8.60175e7 4.96623e7i 0.773751 0.446725i −0.0604600 0.998171i \(-0.519257\pi\)
0.834211 + 0.551445i \(0.185923\pi\)
\(200\) 1.75347e6 32593.9i 0.0154986 0.000288092i
\(201\) 2.56491e7 0.222785
\(202\) −8.66888e6 + 5.10097e7i −0.0740003 + 0.435434i
\(203\) 1.71491e7 + 2.97030e7i 0.143881 + 0.249210i
\(204\) −3.68202e6 + 3.16815e6i −0.0303655 + 0.0261276i
\(205\) −6.20464e7 + 3.58225e7i −0.503012 + 0.290414i
\(206\) 1.86409e8 + 1.54458e8i 1.48570 + 1.23105i
\(207\) 6.72471e6 + 3.88251e6i 0.0526959 + 0.0304240i
\(208\) 2.92663e7 3.66873e7i 0.225500 0.282680i
\(209\) 4.80516e7 + 9.52984e7i 0.364079 + 0.722060i
\(210\) −4.57006e7 7.76663e6i −0.340529 0.0578716i
\(211\) 6.77482e7 1.17343e8i 0.496489 0.859944i −0.503503 0.863993i \(-0.667956\pi\)
0.999992 + 0.00404978i \(0.00128909\pi\)
\(212\) 1.11211e8 + 1.29250e8i 0.801628 + 0.931652i
\(213\) 1.98610e7 + 3.44002e7i 0.140823 + 0.243912i
\(214\) −1.07224e8 8.88452e7i −0.747898 0.619706i
\(215\) 1.53989e8 8.89055e7i 1.05671 0.610090i
\(216\) −4.09071e7 + 7.39959e7i −0.276191 + 0.499596i
\(217\) 2.05978e8i 1.36839i
\(218\) 2.46811e7 + 6.65255e7i 0.161349 + 0.434901i
\(219\) 656556. + 1.13719e6i 0.00422394 + 0.00731607i
\(220\) 4.18626e7 1.19607e8i 0.265062 0.757318i
\(221\) 7.78001e6i 0.0484850i
\(222\) 3.17246e7 + 8.55105e7i 0.194608 + 0.524546i
\(223\) −1.57773e7 + 2.73272e7i −0.0952723 + 0.165016i −0.909722 0.415217i \(-0.863706\pi\)
0.814450 + 0.580234i \(0.197039\pi\)
\(224\) −6.13016e7 + 1.86174e8i −0.364422 + 1.10676i
\(225\) −1.20607e6 + 2.08897e6i −0.00705883 + 0.0122263i
\(226\) 1.06804e8 1.28898e8i 0.615474 0.742791i
\(227\) −1.17388e8 −0.666089 −0.333045 0.942911i \(-0.608076\pi\)
−0.333045 + 0.942911i \(0.608076\pi\)
\(228\) −5.30149e7 + 6.94963e6i −0.296228 + 0.0388320i
\(229\) −1.19473e8 −0.657422 −0.328711 0.944431i \(-0.606614\pi\)
−0.328711 + 0.944431i \(0.606614\pi\)
\(230\) 7.80454e6 9.41899e6i 0.0422961 0.0510454i
\(231\) 2.63697e7 4.56737e7i 0.140755 0.243795i
\(232\) −872975. 4.69638e7i −0.00458980 0.246919i
\(233\) 1.21693e8 2.10779e8i 0.630263 1.09165i −0.357235 0.934015i \(-0.616280\pi\)
0.987498 0.157633i \(-0.0503862\pi\)
\(234\) 2.24522e7 + 6.05176e7i 0.114552 + 0.308764i
\(235\) 2.54859e8i 1.28104i
\(236\) 4.40942e7 + 1.54330e7i 0.218368 + 0.0764290i
\(237\) 2.88458e7 + 4.99624e7i 0.140755 + 0.243795i
\(238\) −1.13024e7 3.04645e7i −0.0543439 0.146479i
\(239\) 3.42898e8i 1.62470i 0.583172 + 0.812349i \(0.301811\pi\)
−0.583172 + 0.812349i \(0.698189\pi\)
\(240\) 4.96287e7 + 3.95899e7i 0.231736 + 0.184861i
\(241\) −6.33832e7 + 3.65943e7i −0.291685 + 0.168404i −0.638702 0.769455i \(-0.720528\pi\)
0.347016 + 0.937859i \(0.387195\pi\)
\(242\) −5.87519e7 4.86816e7i −0.266482 0.220806i
\(243\) −8.85760e7 1.53418e8i −0.395999 0.685891i
\(244\) 5.30207e7 4.56210e7i 0.233658 0.201048i
\(245\) 4.08501e7 7.07545e7i 0.177465 0.307378i
\(246\) 4.02584e7 + 6.84174e6i 0.172418 + 0.0293018i
\(247\) −4.69451e7 + 7.16258e7i −0.198222 + 0.302434i
\(248\) −1.36480e8 + 2.46876e8i −0.568185 + 1.02778i
\(249\) 7.51941e7 + 4.34134e7i 0.308664 + 0.178207i
\(250\) 1.91679e8 + 1.58825e8i 0.775864 + 0.642878i
\(251\) −2.45481e8 + 1.41729e8i −0.979852 + 0.565718i −0.902225 0.431265i \(-0.858067\pi\)
−0.0776263 + 0.996983i \(0.524734\pi\)
\(252\) −1.75833e8 2.04354e8i −0.692149 0.804415i
\(253\) 6.95837e6 + 1.20522e7i 0.0270138 + 0.0467893i
\(254\) −2.82624e7 + 1.66302e8i −0.108216 + 0.636766i
\(255\) −1.05244e7 −0.0397472
\(256\) 1.96833e8 1.82523e8i 0.733258 0.679950i
\(257\) −4.60299e8 + 2.65754e8i −1.69151 + 0.976593i −0.738208 + 0.674573i \(0.764328\pi\)
−0.953302 + 0.302020i \(0.902339\pi\)
\(258\) −9.99145e7 1.69801e7i −0.362209 0.0615560i
\(259\) −6.10118e8 −2.18205
\(260\) 9.99117e7 1.88965e7i 0.352541 0.0666767i
\(261\) 5.59497e7 + 3.23026e7i 0.194785 + 0.112459i
\(262\) −1.11868e8 3.01530e8i −0.384284 1.03580i
\(263\) −2.63534e8 1.52151e8i −0.893287 0.515739i −0.0182707 0.999833i \(-0.505816\pi\)
−0.875016 + 0.484094i \(0.839149\pi\)
\(264\) −6.18690e7 + 3.72701e7i −0.206947 + 0.124666i
\(265\) 3.69437e8i 1.21949i
\(266\) 7.97705e7 3.48667e8i 0.259870 1.13586i
\(267\) 1.38560e7i 0.0445500i
\(268\) 1.78120e8 1.53261e8i 0.565250 0.486362i
\(269\) 3.39735e8 + 1.96146e8i 1.06416 + 0.614393i 0.926580 0.376098i \(-0.122734\pi\)
0.137580 + 0.990491i \(0.456068\pi\)
\(270\) −1.71753e8 + 6.37209e7i −0.531046 + 0.197019i
\(271\) −1.77235e8 1.02327e8i −0.540951 0.312318i 0.204513 0.978864i \(-0.434439\pi\)
−0.745464 + 0.666546i \(0.767772\pi\)
\(272\) −6.63912e6 + 4.40024e7i −0.0200041 + 0.132582i
\(273\) 4.23188e7 0.125882
\(274\) −7.12877e7 + 4.19473e8i −0.209357 + 1.23190i
\(275\) −3.74392e6 + 2.16156e6i −0.0108558 + 0.00626761i
\(276\) −6.85058e6 + 1.29566e6i −0.0196131 + 0.00370945i
\(277\) −5.32536e8 −1.50546 −0.752730 0.658329i \(-0.771264\pi\)
−0.752730 + 0.658329i \(0.771264\pi\)
\(278\) 3.52297e7 + 5.98714e6i 0.0983450 + 0.0167133i
\(279\) −1.93993e8 3.36006e8i −0.534776 0.926259i
\(280\) −3.63776e8 + 2.19140e8i −0.990333 + 0.596580i
\(281\) 2.58279e8 1.49117e8i 0.694412 0.400919i −0.110851 0.993837i \(-0.535358\pi\)
0.805263 + 0.592918i \(0.202024\pi\)
\(282\) −9.26816e7 + 1.11854e8i −0.246106 + 0.297015i
\(283\) −2.32123e8 1.34016e8i −0.608787 0.351483i 0.163703 0.986510i \(-0.447656\pi\)
−0.772491 + 0.635026i \(0.780989\pi\)
\(284\) 3.43477e8 + 1.20217e8i 0.889781 + 0.311424i
\(285\) −9.68917e7 6.35049e7i −0.247930 0.162499i
\(286\) −1.93824e7 + 1.14050e8i −0.0489921 + 0.288281i
\(287\) −1.36584e8 + 2.36571e8i −0.341047 + 0.590711i
\(288\) 7.53425e7 + 3.61437e8i 0.185852 + 0.891576i
\(289\) 2.01481e8 + 3.48975e8i 0.491011 + 0.850456i
\(290\) 6.49339e7 7.83661e7i 0.156343 0.188684i
\(291\) −1.20144e8 + 6.93650e7i −0.285809 + 0.165012i
\(292\) 1.13545e7 + 3.97408e6i 0.0266888 + 0.00934107i
\(293\) 4.65498e7i 0.108114i −0.998538 0.0540569i \(-0.982785\pi\)
0.998538 0.0540569i \(-0.0172152\pi\)
\(294\) −4.36589e7 + 1.61976e7i −0.100198 + 0.0371735i
\(295\) 5.06102e7 + 8.76594e7i 0.114779 + 0.198802i
\(296\) 7.31263e8 + 4.04263e8i 1.63890 + 0.906032i
\(297\) 2.08420e8i 0.461627i
\(298\) −2.35741e8 + 8.74606e7i −0.516034 + 0.191450i
\(299\) −5.58348e6 + 9.67087e6i −0.0120797 + 0.0209226i
\(300\) −402486. 2.12807e6i −0.000860649 0.00455053i
\(301\) 3.38979e8 5.87129e8i 0.716457 1.24094i
\(302\) 3.83279e8 + 3.17584e8i 0.800739 + 0.663490i
\(303\) 6.38970e7 0.131957
\(304\) −3.26636e8 + 3.65042e8i −0.666817 + 0.745222i
\(305\) 1.51550e8 0.305849
\(306\) −4.71292e7 3.90511e7i −0.0940298 0.0779128i
\(307\) 2.39812e8 4.15367e8i 0.473028 0.819309i −0.526495 0.850178i \(-0.676494\pi\)
0.999523 + 0.0308691i \(0.00982750\pi\)
\(308\) −8.97899e7 4.74748e8i −0.175106 0.925840i
\(309\) 1.49481e8 2.58908e8i 0.288224 0.499219i
\(310\) −5.73030e8 + 2.12596e8i −1.09248 + 0.405311i
\(311\) 2.02843e8i 0.382384i −0.981553 0.191192i \(-0.938765\pi\)
0.981553 0.191192i \(-0.0612353\pi\)
\(312\) −5.07216e7 2.80404e7i −0.0945478 0.0522688i
\(313\) 3.16069e8 + 5.47448e8i 0.582609 + 1.00911i 0.995169 + 0.0981775i \(0.0313013\pi\)
−0.412560 + 0.910930i \(0.635365\pi\)
\(314\) −4.31803e7 + 1.60200e7i −0.0787104 + 0.0292017i
\(315\) 5.84108e8i 1.05295i
\(316\) 4.98861e8 + 1.74602e8i 0.889354 + 0.311274i
\(317\) −7.70000e8 + 4.44560e8i −1.35764 + 0.783832i −0.989305 0.145863i \(-0.953404\pi\)
−0.368332 + 0.929694i \(0.620071\pi\)
\(318\) 1.34349e8 1.62140e8i 0.234282 0.282746i
\(319\) 5.78937e7 + 1.00275e8i 0.0998537 + 0.172952i
\(320\) 5.81209e8 2.16148e7i 0.991534 0.0368745i
\(321\) −8.59822e7 + 1.48926e8i −0.145091 + 0.251305i
\(322\) 7.81410e6 4.59799e7i 0.0130432 0.0767490i
\(323\) 4.59200e6 8.10749e7i 0.00758217 0.133868i
\(324\) −4.27718e8 1.49702e8i −0.698635 0.244522i
\(325\) −3.00417e6 1.73446e6i −0.00485437 0.00280267i
\(326\) 7.19695e8 8.68571e8i 1.15050 1.38849i
\(327\) 7.58869e7 4.38133e7i 0.120019 0.0692930i
\(328\) 3.20456e8 1.93044e8i 0.501429 0.302063i
\(329\) −4.85864e8 8.41541e8i −0.752193 1.30284i
\(330\) −1.54281e8 2.62195e7i −0.236328 0.0401629i
\(331\) 8.07975e8 1.22462 0.612308 0.790619i \(-0.290241\pi\)
0.612308 + 0.790619i \(0.290241\pi\)
\(332\) 7.81594e8 1.47824e8i 1.17219 0.221698i
\(333\) −9.95271e8 + 5.74620e8i −1.47702 + 0.852758i
\(334\) 1.68021e8 9.88672e8i 0.246746 1.45191i
\(335\) 5.09124e8 0.739890
\(336\) 2.39348e8 + 3.61130e7i 0.344225 + 0.0519369i
\(337\) −2.44796e7 1.41333e7i −0.0348417 0.0201159i 0.482478 0.875908i \(-0.339737\pi\)
−0.517320 + 0.855792i \(0.673070\pi\)
\(338\) 5.78557e8 2.14646e8i 0.814963 0.302353i
\(339\) −1.79029e8 1.03363e8i −0.249589 0.144100i
\(340\) −7.30867e7 + 6.28865e7i −0.100847 + 0.0867723i
\(341\) 6.95362e8i 0.949666i
\(342\) −1.98253e8 6.43901e8i −0.267996 0.870418i
\(343\) 5.59323e8i 0.748399i
\(344\) −7.95317e8 + 4.79102e8i −1.05338 + 0.634561i
\(345\) −1.30823e7 7.55304e6i −0.0171520 0.00990273i
\(346\) −5.21141e8 1.40468e9i −0.676377 1.82311i
\(347\) 2.67827e8 + 1.54630e8i 0.344113 + 0.198674i 0.662089 0.749425i \(-0.269670\pi\)
−0.317976 + 0.948099i \(0.603003\pi\)
\(348\) −5.69969e7 + 1.07799e7i −0.0724977 + 0.0137116i
\(349\) 8.97764e8 1.13051 0.565254 0.824917i \(-0.308778\pi\)
0.565254 + 0.824917i \(0.308778\pi\)
\(350\) 1.42833e7 + 2.42738e6i 0.0178069 + 0.00302622i
\(351\) 1.44833e8 8.36193e7i 0.178769 0.103212i
\(352\) −2.06949e8 + 6.28509e8i −0.252909 + 0.768090i
\(353\) 5.22979e8 0.632810 0.316405 0.948624i \(-0.397524\pi\)
0.316405 + 0.948624i \(0.397524\pi\)
\(354\) 9.66603e6 5.68771e7i 0.0115808 0.0681438i
\(355\) 3.94233e8 + 6.82832e8i 0.467686 + 0.810055i
\(356\) 8.27938e7 + 9.62229e7i 0.0972575 + 0.113033i
\(357\) −3.47514e7 + 2.00637e7i −0.0404235 + 0.0233385i
\(358\) −8.25256e8 6.83804e8i −0.950600 0.787664i
\(359\) 8.01172e8 + 4.62557e8i 0.913892 + 0.527636i 0.881681 0.471845i \(-0.156412\pi\)
0.0322107 + 0.999481i \(0.489745\pi\)
\(360\) −3.87029e8 + 7.00088e8i −0.437205 + 0.790850i
\(361\) 5.31487e8 7.18699e8i 0.594590 0.804029i
\(362\) 1.47779e8 + 2.51144e7i 0.163731 + 0.0278255i
\(363\) −4.71128e7 + 8.16018e7i −0.0516971 + 0.0895420i
\(364\) 2.93883e8 2.52868e8i 0.319389 0.274814i
\(365\) 1.30324e7 + 2.25728e7i 0.0140281 + 0.0242974i
\(366\) −6.65130e7 5.51125e7i −0.0709125 0.0587579i
\(367\) −1.03908e9 + 5.99916e8i −1.09729 + 0.633518i −0.935507 0.353309i \(-0.885057\pi\)
−0.161779 + 0.986827i \(0.551723\pi\)
\(368\) −3.98319e7 + 4.99321e7i −0.0416643 + 0.0522291i
\(369\) 5.14550e8i 0.533132i
\(370\) 6.29721e8 + 1.69735e9i 0.646312 + 1.74207i
\(371\) 7.04296e8 + 1.21988e9i 0.716055 + 1.24024i
\(372\) 3.28806e8 + 1.15082e8i 0.331161 + 0.115907i
\(373\) 1.03623e9i 1.03390i −0.856017 0.516948i \(-0.827068\pi\)
0.856017 0.516948i \(-0.172932\pi\)
\(374\) −3.81559e7 1.02845e8i −0.0377147 0.101656i
\(375\) 1.53707e8 2.66228e8i 0.150516 0.260702i
\(376\) 2.47330e7 + 1.33057e9i 0.0239949 + 1.29086i
\(377\) −4.64546e7 + 8.04618e7i −0.0446513 + 0.0773384i
\(378\) −4.45650e8 + 5.37837e8i −0.424397 + 0.512188i
\(379\) 1.20980e9 1.14150 0.570752 0.821122i \(-0.306652\pi\)
0.570752 + 0.821122i \(0.306652\pi\)
\(380\) −1.05233e9 + 1.37948e8i −0.983802 + 0.128965i
\(381\) 2.08318e8 0.192969
\(382\) 3.07484e8 3.71090e8i 0.282229 0.340610i
\(383\) −2.15562e8 + 3.73364e8i −0.196054 + 0.339576i −0.947246 0.320509i \(-0.896146\pi\)
0.751191 + 0.660084i \(0.229480\pi\)
\(384\) −2.62944e8 2.01875e8i −0.236976 0.181938i
\(385\) 5.23429e8 9.06606e8i 0.467461 0.809666i
\(386\) 3.38215e8 + 9.11625e8i 0.299321 + 0.806790i
\(387\) 1.27703e9i 1.11998i
\(388\) −4.19861e8 + 1.19960e9i −0.364917 + 1.04262i
\(389\) 6.15720e8 + 1.06646e9i 0.530347 + 0.918588i 0.999373 + 0.0354035i \(0.0112716\pi\)
−0.469026 + 0.883184i \(0.655395\pi\)
\(390\) −4.36784e7 1.17731e8i −0.0372856 0.100500i
\(391\) 1.05887e7i 0.00895828i
\(392\) −2.06404e8 + 3.73360e8i −0.173068 + 0.313059i
\(393\) −3.43961e8 + 1.98586e8i −0.285848 + 0.165035i
\(394\) −1.18542e9 9.82236e8i −0.976419 0.809057i
\(395\) 5.72579e8 + 9.91736e8i 0.467461 + 0.809667i
\(396\) −5.93598e8 6.89880e8i −0.480352 0.558265i
\(397\) −4.29262e8 + 7.43503e8i −0.344315 + 0.596370i −0.985229 0.171242i \(-0.945222\pi\)
0.640914 + 0.767612i \(0.278555\pi\)
\(398\) −1.10784e9 1.88274e8i −0.880822 0.149692i
\(399\) −4.41001e8 2.49779e7i −0.347564 0.0196857i
\(400\) −1.55110e7 1.23734e7i −0.0121179 0.00966674i
\(401\) 3.24613e8 + 1.87415e8i 0.251397 + 0.145144i 0.620404 0.784283i \(-0.286969\pi\)
−0.369007 + 0.929427i \(0.620302\pi\)
\(402\) −2.23447e8 1.85147e8i −0.171547 0.142143i
\(403\) 4.83214e8 2.78984e8i 0.367766 0.212330i
\(404\) 4.43733e8 3.81804e8i 0.334801 0.288075i
\(405\) −4.90923e8 8.50304e8i −0.367216 0.636036i
\(406\) 6.50135e7 3.82554e8i 0.0482128 0.283695i
\(407\) −2.05971e9 −1.51435
\(408\) 5.49458e7 1.02135e6i 0.0400520 0.000744496i
\(409\) −1.42214e9 + 8.21071e8i −1.02780 + 0.593403i −0.916355 0.400368i \(-0.868882\pi\)
−0.111449 + 0.993770i \(0.535549\pi\)
\(410\) 7.99114e8 + 1.35806e8i 0.572618 + 0.0973141i
\(411\) 5.25450e8 0.373324
\(412\) −5.08987e8 2.69118e9i −0.358564 1.89584i
\(413\) 3.34228e8 + 1.92967e8i 0.233463 + 0.134790i
\(414\) −3.05577e7 8.23654e7i −0.0211651 0.0570484i
\(415\) 1.49258e9 + 8.61739e8i 1.02510 + 0.591844i
\(416\) −5.19786e8 + 1.08351e8i −0.353995 + 0.0737913i
\(417\) 4.41303e7i 0.0298031i
\(418\) 2.69298e8 1.17707e9i 0.180350 0.788288i
\(419\) 1.87415e9i 1.24467i −0.782751 0.622335i \(-0.786184\pi\)
0.782751 0.622335i \(-0.213816\pi\)
\(420\) 3.42067e8 + 3.97550e8i 0.225288 + 0.261830i
\(421\) 6.74147e8 + 3.89219e8i 0.440319 + 0.254218i 0.703733 0.710465i \(-0.251515\pi\)
−0.263414 + 0.964683i \(0.584849\pi\)
\(422\) −1.43724e9 + 5.33220e8i −0.930972 + 0.345393i
\(423\) −1.58516e9 9.15190e8i −1.01831 0.587923i
\(424\) −3.58523e7 1.92876e9i −0.0228421 1.22885i
\(425\) 3.28929e6 0.00207846
\(426\) 7.52946e7 4.43050e8i 0.0471878 0.277664i
\(427\) 5.00417e8 2.88916e8i 0.311053 0.179586i
\(428\) 2.92773e8 + 1.54798e9i 0.180500 + 0.954362i
\(429\) 1.42865e8 0.0873622
\(430\) −1.98327e9 3.37048e8i −1.20293 0.204433i
\(431\) 9.26500e8 + 1.60475e9i 0.557410 + 0.965463i 0.997712 + 0.0676129i \(0.0215383\pi\)
−0.440301 + 0.897850i \(0.645128\pi\)
\(432\) 8.90507e8 3.49342e8i 0.531428 0.208477i
\(433\) −1.43233e9 + 8.26958e8i −0.847884 + 0.489526i −0.859936 0.510401i \(-0.829497\pi\)
0.0120524 + 0.999927i \(0.496164\pi\)
\(434\) −1.48684e9 + 1.79441e9i −0.873075 + 1.05368i
\(435\) −1.08845e8 6.28414e7i −0.0634007 0.0366044i
\(436\) 2.65199e8 7.57710e8i 0.153239 0.437825i
\(437\) 6.38931e7 9.74839e7i 0.0366242 0.0558789i
\(438\) 2.48906e6 1.46462e7i 0.00141539 0.00832846i
\(439\) −6.34530e7 + 1.09904e8i −0.0357953 + 0.0619993i −0.883368 0.468680i \(-0.844730\pi\)
0.847573 + 0.530679i \(0.178063\pi\)
\(440\) −1.22808e9 + 7.39798e8i −0.687292 + 0.414027i
\(441\) −2.93383e8 5.08154e8i −0.162892 0.282137i
\(442\) 5.61598e7 6.77770e7i 0.0309348 0.0373340i
\(443\) 5.83458e8 3.36859e8i 0.318857 0.184092i −0.332026 0.943270i \(-0.607732\pi\)
0.650883 + 0.759178i \(0.274399\pi\)
\(444\) 3.40881e8 9.73944e8i 0.184826 0.528073i
\(445\) 2.75036e8i 0.147955i
\(446\) 3.34708e8 1.24177e8i 0.178646 0.0662781i
\(447\) 1.55258e8 + 2.68915e8i 0.0822200 + 0.142409i
\(448\) 1.87794e9 1.17939e9i 0.986752 0.619704i
\(449\) 1.18770e9i 0.619218i −0.950864 0.309609i \(-0.899802\pi\)
0.950864 0.309609i \(-0.100198\pi\)
\(450\) 2.55861e7 9.49250e6i 0.0132361 0.00491062i
\(451\) −4.61097e8 + 7.98643e8i −0.236687 + 0.409954i
\(452\) −1.86089e9 + 3.51954e8i −0.947845 + 0.179267i
\(453\) 3.07350e8 5.32345e8i 0.155342 0.269060i
\(454\) 1.02265e9 + 8.47361e8i 0.512897 + 0.424984i
\(455\) 8.40012e8 0.418067
\(456\) 5.12015e8 + 3.22144e8i 0.252875 + 0.159101i
\(457\) 3.18100e8 0.155904 0.0779520 0.996957i \(-0.475162\pi\)
0.0779520 + 0.996957i \(0.475162\pi\)
\(458\) 1.04081e9 + 8.62410e8i 0.506223 + 0.419454i
\(459\) −7.92894e7 + 1.37333e8i −0.0382711 + 0.0662875i
\(460\) −1.35981e8 + 2.57184e7i −0.0651369 + 0.0123195i
\(461\) −9.37783e8 + 1.62429e9i −0.445809 + 0.772164i −0.998108 0.0614821i \(-0.980417\pi\)
0.552299 + 0.833646i \(0.313751\pi\)
\(462\) −5.59420e8 + 2.07546e8i −0.263931 + 0.0979191i
\(463\) 3.43315e9i 1.60753i 0.594947 + 0.803765i \(0.297173\pi\)
−0.594947 + 0.803765i \(0.702827\pi\)
\(464\) −3.31402e8 + 4.15436e8i −0.154008 + 0.193059i
\(465\) 3.77395e8 + 6.53667e8i 0.174065 + 0.301489i
\(466\) −2.58166e9 + 9.57803e8i −1.18181 + 0.438455i
\(467\) 3.67666e9i 1.67049i −0.549875 0.835247i \(-0.685325\pi\)
0.549875 0.835247i \(-0.314675\pi\)
\(468\) 2.41249e8 6.89281e8i 0.108794 0.310839i
\(469\) 1.68112e9 9.70596e8i 0.752478 0.434444i
\(470\) −1.83970e9 + 2.22025e9i −0.817341 + 0.986416i
\(471\) 2.84383e7 + 4.92566e7i 0.0125410 + 0.0217216i
\(472\) −2.72733e8 4.52741e8i −0.119382 0.198177i
\(473\) 1.14436e9 1.98210e9i 0.497222 0.861214i
\(474\) 1.09357e8 6.43480e8i 0.0471652 0.277531i
\(475\) 3.02825e7 + 1.98478e7i 0.0129648 + 0.00849738i
\(476\) −1.21444e8 + 3.46983e8i −0.0516122 + 0.147463i
\(477\) 2.29780e9 + 1.32664e9i 0.969389 + 0.559677i
\(478\) 2.47520e9 2.98722e9i 1.03660 1.25104i
\(479\) −3.49501e9 + 2.01785e9i −1.45303 + 0.838907i −0.998652 0.0519015i \(-0.983472\pi\)
−0.454378 + 0.890809i \(0.650138\pi\)
\(480\) −1.46571e8 7.03139e8i −0.0604929 0.290200i
\(481\) −8.26367e8 1.43131e9i −0.338583 0.586443i
\(482\) 8.16330e8 + 1.38732e8i 0.332048 + 0.0564302i
\(483\) −5.75965e7 −0.0232585
\(484\) 1.60421e8 + 8.48198e8i 0.0643136 + 0.340047i
\(485\) −2.38481e9 + 1.37687e9i −0.949200 + 0.548021i
\(486\) −3.35799e8 + 1.97592e9i −0.132694 + 0.780803i
\(487\) −4.08612e9 −1.60310 −0.801549 0.597929i \(-0.795991\pi\)
−0.801549 + 0.597929i \(0.795991\pi\)
\(488\) −7.91214e8 + 1.47073e7i −0.308194 + 0.00572879i
\(489\) −1.20638e9 6.96503e8i −0.466555 0.269366i
\(490\) −8.66613e8 + 3.21516e8i −0.332766 + 0.123457i
\(491\) 1.63188e9 + 9.42169e8i 0.622163 + 0.359206i 0.777711 0.628622i \(-0.216381\pi\)
−0.155548 + 0.987828i \(0.549714\pi\)
\(492\) −3.01331e8 3.50207e8i −0.114069 0.132571i
\(493\) 8.80983e7i 0.0331134i
\(494\) 9.26001e8 2.85110e8i 0.345595 0.106406i
\(495\) 1.97190e9i 0.730746i
\(496\) 2.97105e9 1.16553e9i 1.09326 0.428882i
\(497\) 2.60350e9 + 1.50313e9i 0.951286 + 0.549225i
\(498\) −3.41690e8 9.20991e8i −0.123974 0.334159i
\(499\) −1.73810e9 1.00349e9i −0.626213 0.361544i 0.153071 0.988215i \(-0.451084\pi\)
−0.779284 + 0.626671i \(0.784417\pi\)
\(500\) −5.23378e8 2.76727e9i −0.187249 0.990048i
\(501\) −1.23846e9 −0.439995
\(502\) 3.16162e9 + 5.37305e8i 1.11544 + 0.189565i
\(503\) 6.26421e8 3.61664e8i 0.219472 0.126712i −0.386234 0.922401i \(-0.626224\pi\)
0.605706 + 0.795689i \(0.292891\pi\)
\(504\) 5.66851e7 + 3.04951e9i 0.0197225 + 1.06102i
\(505\) 1.26833e9 0.438241
\(506\) 2.63797e7 1.55224e8i 0.00905198 0.0532639i
\(507\) −3.81035e8 6.59971e8i −0.129848 0.224904i
\(508\) 1.44666e9 1.24476e9i 0.489603 0.421273i
\(509\) 1.81599e8 1.04846e8i 0.0610380 0.0352403i −0.469170 0.883108i \(-0.655447\pi\)
0.530208 + 0.847867i \(0.322114\pi\)
\(510\) 9.16853e7 + 7.59701e7i 0.0306058 + 0.0253599i
\(511\) 8.60655e7 + 4.96900e7i 0.0285336 + 0.0164739i
\(512\) −3.03228e9 + 1.69250e8i −0.998446 + 0.0557294i
\(513\) −1.55865e9 + 7.85906e8i −0.509727 + 0.257016i
\(514\) 5.92832e9 + 1.00749e9i 1.92558 + 0.327244i
\(515\) 2.96713e9 5.13923e9i 0.957220 1.65795i
\(516\) 7.47854e8 + 8.69155e8i 0.239631 + 0.278499i
\(517\) −1.64023e9 2.84097e9i −0.522022 0.904169i
\(518\) 5.31516e9 + 4.40413e9i 1.68021 + 1.39221i
\(519\) −1.60235e9 + 9.25118e8i −0.503120 + 0.290477i
\(520\) −1.00680e9 5.56591e8i −0.314003 0.173590i
\(521\) 2.36897e8i 0.0733883i 0.999327 + 0.0366942i \(0.0116827\pi\)
−0.999327 + 0.0366942i \(0.988317\pi\)
\(522\) −2.54241e8 6.85281e8i −0.0782346 0.210874i
\(523\) −4.93614e8 8.54964e8i −0.150880 0.261332i 0.780671 0.624942i \(-0.214877\pi\)
−0.931551 + 0.363610i \(0.881544\pi\)
\(524\) −1.20203e9 + 3.43436e9i −0.364968 + 1.04276i
\(525\) 1.78919e7i 0.00539632i
\(526\) 1.19752e9 + 3.22781e9i 0.358785 + 0.967069i
\(527\) −2.64537e8 + 4.58192e8i −0.0787318 + 0.136367i
\(528\) 8.08017e8 + 1.21914e8i 0.238892 + 0.0360443i
\(529\) −1.69481e9 + 2.93550e9i −0.497768 + 0.862160i
\(530\) 2.66677e9 3.21842e9i 0.778074 0.939026i
\(531\) 7.26957e8 0.210707
\(532\) −3.21178e9 + 2.46166e9i −0.924816 + 0.708822i
\(533\) −7.39979e8 −0.211677
\(534\) 1.00019e8 1.20709e8i 0.0284242 0.0343041i
\(535\) −1.70671e9 + 2.95612e9i −0.481862 + 0.834609i
\(536\) −2.65804e9 + 4.94083e7i −0.745563 + 0.0138587i
\(537\) −6.61769e8 + 1.14622e9i −0.184415 + 0.319416i
\(538\) −1.54379e9 4.16113e9i −0.427415 1.15206i
\(539\) 1.05162e9i 0.289267i
\(540\) 1.95623e9 + 6.84682e8i 0.534616 + 0.187116i
\(541\) −1.27272e7 2.20441e7i −0.00345574 0.00598552i 0.864292 0.502990i \(-0.167767\pi\)
−0.867748 + 0.497004i \(0.834433\pi\)
\(542\) 8.05376e8 + 2.17081e9i 0.217271 + 0.585631i
\(543\) 1.85114e8i 0.0496181i
\(544\) 3.75468e8 3.35411e8i 0.0999947 0.0893266i
\(545\) 1.50633e9 8.69678e8i 0.398595 0.230129i
\(546\) −3.68668e8 3.05477e8i −0.0969307 0.0803164i
\(547\) −2.05459e9 3.55866e9i −0.536747 0.929674i −0.999077 0.0429653i \(-0.986320\pi\)
0.462329 0.886708i \(-0.347014\pi\)
\(548\) 3.64899e9 3.13973e9i 0.947198 0.815005i
\(549\) 5.44212e8 9.42602e8i 0.140367 0.243123i
\(550\) 4.82191e7 + 8.19463e6i 0.0123580 + 0.00210020i
\(551\) 5.31591e8 8.11067e8i 0.135378 0.206551i
\(552\) 6.90328e7 + 3.81634e7i 0.0174690 + 0.00965739i
\(553\) 3.78130e9 + 2.18313e9i 0.950829 + 0.548962i
\(554\) 4.63929e9 + 3.84410e9i 1.15922 + 0.960528i
\(555\) 1.93620e9 1.11787e9i 0.480756 0.277565i
\(556\) −2.63692e8 3.06463e8i −0.0650632 0.0756165i
\(557\) −9.88546e8 1.71221e9i −0.242384 0.419821i 0.719009 0.695001i \(-0.244596\pi\)
−0.961393 + 0.275180i \(0.911263\pi\)
\(558\) −7.35444e8 + 4.32752e9i −0.179197 + 1.05443i
\(559\) 1.83650e9 0.444683
\(560\) 4.75096e9 + 7.16830e8i 1.14320 + 0.172488i
\(561\) −1.17318e8 + 6.77334e7i −0.0280539 + 0.0161969i
\(562\) −3.32645e9 5.65316e8i −0.790503 0.134343i
\(563\) 2.76487e9 0.652974 0.326487 0.945202i \(-0.394135\pi\)
0.326487 + 0.945202i \(0.394135\pi\)
\(564\) 1.61483e9 3.05415e8i 0.379009 0.0716825i
\(565\) −3.55367e9 2.05171e9i −0.828910 0.478571i
\(566\) 1.05479e9 + 2.84308e9i 0.244517 + 0.659071i
\(567\) −3.24204e9 1.87179e9i −0.746927 0.431238i
\(568\) −2.12448e9 3.52667e9i −0.486445 0.807506i
\(569\) 2.23529e9i 0.508675i −0.967115 0.254338i \(-0.918143\pi\)
0.967115 0.254338i \(-0.0818574\pi\)
\(570\) 3.85681e8 + 1.25265e9i 0.0872302 + 0.283313i
\(571\) 2.76685e9i 0.621955i 0.950417 + 0.310978i \(0.100656\pi\)
−0.950417 + 0.310978i \(0.899344\pi\)
\(572\) 9.92123e8 8.53660e8i 0.221656 0.190721i
\(573\) −5.15416e8 2.97576e8i −0.114450 0.0660779i
\(574\) 2.89756e9 1.07500e9i 0.639501 0.237256i
\(575\) 4.08872e6 + 2.36063e6i 0.000896913 + 0.000517833i
\(576\) 1.95266e9 3.69258e9i 0.425744 0.805103i
\(577\) 1.93597e9 0.419550 0.209775 0.977750i \(-0.432727\pi\)
0.209775 + 0.977750i \(0.432727\pi\)
\(578\) 7.63830e8 4.49455e9i 0.164532 0.968141i
\(579\) 1.03991e9 6.00391e8i 0.222649 0.128546i
\(580\) −1.13137e9 + 2.13977e8i −0.240772 + 0.0455376i
\(581\) 6.57128e9 1.39006
\(582\) 1.54737e9 + 2.62968e8i 0.325359 + 0.0552934i
\(583\) 2.37764e9 + 4.11820e9i 0.496943 + 0.860730i
\(584\) −7.02301e7 1.16583e8i −0.0145908 0.0242209i
\(585\) 1.37029e9 7.91138e8i 0.282987 0.163383i
\(586\) −3.36019e8 + 4.05527e8i −0.0689798 + 0.0832489i
\(587\) −7.14967e9 4.12786e9i −1.45899 0.842349i −0.460030 0.887904i \(-0.652161\pi\)
−0.998962 + 0.0455545i \(0.985495\pi\)
\(588\) 4.97265e8 + 1.74043e8i 0.100871 + 0.0353049i
\(589\) −5.20020e9 + 2.62206e9i −1.04862 + 0.528736i
\(590\) 1.91867e8 1.12899e9i 0.0384608 0.226312i
\(591\) −9.50584e8 + 1.64646e9i −0.189424 + 0.328092i
\(592\) −3.45237e9 8.80043e9i −0.683898 1.74332i
\(593\) −4.26582e9 7.38861e9i −0.840061 1.45503i −0.889842 0.456268i \(-0.849186\pi\)
0.0497811 0.998760i \(-0.484148\pi\)
\(594\) −1.50447e9 + 1.81569e9i −0.294532 + 0.355459i
\(595\) −6.89802e8 + 3.98258e8i −0.134250 + 0.0775094i
\(596\) 2.68504e9 + 9.39764e8i 0.519503 + 0.181826i
\(597\) 1.38774e9i 0.266929i
\(598\) 1.18450e8 4.39454e7i 0.0226508 0.00840348i
\(599\) 1.69974e8 + 2.94404e8i 0.0323139 + 0.0559694i 0.881730 0.471754i \(-0.156379\pi\)
−0.849416 + 0.527724i \(0.823046\pi\)
\(600\) −1.18551e7 + 2.14444e7i −0.00224066 + 0.00405308i
\(601\) 7.90667e9i 1.48571i 0.669454 + 0.742854i \(0.266528\pi\)
−0.669454 + 0.742854i \(0.733472\pi\)
\(602\) −7.19126e9 + 2.66797e9i −1.34344 + 0.498418i
\(603\) 1.82825e9 3.16662e9i 0.339566 0.588146i
\(604\) −1.04654e9 5.53338e9i −0.193253 1.02179i
\(605\) −9.35173e8 + 1.61977e9i −0.171691 + 0.297378i
\(606\) −5.56651e8 4.61239e8i −0.101608 0.0841922i
\(607\) −2.04911e9 −0.371881 −0.185941 0.982561i \(-0.559533\pi\)
−0.185941 + 0.982561i \(0.559533\pi\)
\(608\) 5.48060e9 8.22321e8i 0.988930 0.148381i
\(609\) −4.79204e8 −0.0859726
\(610\) −1.32026e9 1.09396e9i −0.235508 0.195141i
\(611\) 1.31614e9 2.27963e9i 0.233431 0.404315i
\(612\) 1.28686e8 + 6.80403e8i 0.0226934 + 0.119988i
\(613\) −3.93752e8 + 6.81999e8i −0.0690417 + 0.119584i −0.898480 0.439015i \(-0.855327\pi\)
0.829438 + 0.558599i \(0.188661\pi\)
\(614\) −5.08749e9 + 1.88747e9i −0.886981 + 0.329072i
\(615\) 1.00101e9i 0.173530i
\(616\) −2.64474e9 + 4.78401e9i −0.455880 + 0.824631i
\(617\) 1.54693e9 + 2.67935e9i 0.265138 + 0.459232i 0.967600 0.252489i \(-0.0812493\pi\)
−0.702462 + 0.711721i \(0.747916\pi\)
\(618\) −3.17115e9 + 1.17650e9i −0.540452 + 0.200509i
\(619\) 5.23564e9i 0.887264i 0.896209 + 0.443632i \(0.146310\pi\)
−0.896209 + 0.443632i \(0.853690\pi\)
\(620\) 6.52668e9 + 2.28434e9i 1.09982 + 0.384937i
\(621\) −1.97120e8 + 1.13807e8i −0.0330301 + 0.0190699i
\(622\) −1.46422e9 + 1.76711e9i −0.243972 + 0.294440i
\(623\) 5.24330e8 + 9.08166e8i 0.0868753 + 0.150472i
\(624\) 2.39462e8 + 6.10411e8i 0.0394539 + 0.100572i
\(625\) 3.00372e9 5.20259e9i 0.492129 0.852393i
\(626\) 1.19824e9 7.05074e9i 0.195225 1.14875i
\(627\) −1.48878e9 8.43231e7i −0.241209 0.0136619i
\(628\) 4.91814e8 + 1.72135e8i 0.0792396 + 0.0277339i
\(629\) 1.35719e9 + 7.83576e8i 0.217453 + 0.125546i
\(630\) −4.21637e9 + 5.08857e9i −0.671811 + 0.810782i
\(631\) −6.66216e9 + 3.84640e9i −1.05563 + 0.609469i −0.924221 0.381858i \(-0.875284\pi\)
−0.131411 + 0.991328i \(0.541951\pi\)
\(632\) −3.08557e9 5.12209e9i −0.486211 0.807119i
\(633\) 9.46560e8 + 1.63949e9i 0.148332 + 0.256919i
\(634\) 9.91705e9 + 1.68536e9i 1.54550 + 0.262652i
\(635\) 4.13503e9 0.640871
\(636\) −2.34081e9 + 4.42721e8i −0.360800 + 0.0682387i
\(637\) 7.30781e8 4.21917e8i 0.112021 0.0646753i
\(638\) 2.19480e8 1.29147e9i 0.0334597 0.196884i
\(639\) 5.66271e9 0.858561
\(640\) −5.21934e9 4.00714e9i −0.787020 0.604234i
\(641\) −2.70817e9 1.56357e9i −0.406138 0.234484i 0.282991 0.959123i \(-0.408673\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(642\) 1.82407e9 6.76733e8i 0.272062 0.100936i
\(643\) 1.77146e9 + 1.02275e9i 0.262781 + 0.151717i 0.625602 0.780142i \(-0.284853\pi\)
−0.362822 + 0.931859i \(0.618187\pi\)
\(644\) −3.99979e8 + 3.44157e8i −0.0590115 + 0.0507757i
\(645\) 2.48433e9i 0.364544i
\(646\) −6.25242e8 + 6.73152e8i −0.0912502 + 0.0982425i
\(647\) 1.23744e9i 0.179622i −0.995959 0.0898110i \(-0.971374\pi\)
0.995959 0.0898110i \(-0.0286263\pi\)
\(648\) 2.64553e9 + 4.39163e9i 0.381945 + 0.634035i
\(649\) 1.12832e9 + 6.51439e8i 0.162023 + 0.0935442i
\(650\) 1.36513e7 + 3.67956e7i 0.00194974 + 0.00525532i
\(651\) 2.49230e9 + 1.43893e9i 0.354052 + 0.204412i
\(652\) −1.25395e10 + 2.37162e9i −1.77180 + 0.335103i
\(653\) −5.37149e9 −0.754916 −0.377458 0.926027i \(-0.623202\pi\)
−0.377458 + 0.926027i \(0.623202\pi\)
\(654\) −9.77369e8 1.66100e8i −0.136627 0.0232192i
\(655\) −6.82750e9 + 3.94186e9i −0.949330 + 0.548096i
\(656\) −4.18519e9 6.31466e8i −0.578832 0.0873347i
\(657\) 1.87195e8 0.0257523
\(658\) −1.84195e9 + 1.08384e10i −0.252050 + 1.48312i
\(659\) −2.59930e9 4.50213e9i −0.353800 0.612800i 0.633112 0.774060i \(-0.281777\pi\)
−0.986912 + 0.161261i \(0.948444\pi\)
\(660\) 1.15479e9 + 1.34209e9i 0.156350 + 0.181710i
\(661\) 8.15932e9 4.71079e9i 1.09888 0.634437i 0.162951 0.986634i \(-0.447899\pi\)
0.935926 + 0.352197i \(0.114565\pi\)
\(662\) −7.03883e9 5.83235e9i −0.942969 0.781341i
\(663\) −9.41371e7 5.43501e7i −0.0125448 0.00724274i
\(664\) −7.87607e9 4.35412e9i −1.04405 0.577181i
\(665\) −8.75370e9 4.95801e8i −1.15429 0.0653780i
\(666\) 1.28184e10 + 2.17843e9i 1.68141 + 0.285748i
\(667\) 6.32255e7 1.09510e8i 0.00824996 0.0142894i
\(668\) −8.60045e9 + 7.40015e9i −1.11636 + 0.960557i
\(669\) −2.20437e8 3.81808e8i −0.0284638 0.0493007i
\(670\) −4.43533e9 3.67510e9i −0.569724 0.472071i
\(671\) 1.68936e9 9.75354e8i 0.215871 0.124633i
\(672\) −1.82444e9 2.04233e9i −0.231920 0.259617i
\(673\) 1.28640e10i 1.62676i 0.581734 + 0.813379i \(0.302374\pi\)
−0.581734 + 0.813379i \(0.697626\pi\)
\(674\) 1.11238e8 + 2.99831e8i 0.0139940 + 0.0377195i
\(675\) −3.53532e7 6.12336e7i −0.00442452 0.00766349i
\(676\) −6.58963e9 2.30637e9i −0.820441 0.287155i
\(677\) 9.36328e9i 1.15976i 0.814703 + 0.579879i \(0.196900\pi\)
−0.814703 + 0.579879i \(0.803100\pi\)
\(678\) 8.13528e8 + 2.19278e9i 0.100246 + 0.270204i
\(679\) −5.24974e9 + 9.09281e9i −0.643566 + 1.11469i
\(680\) 1.09065e9 2.02733e7i 0.133017 0.00247254i
\(681\) 8.20055e8 1.42038e9i 0.0995012 0.172341i
\(682\) −5.01946e9 + 6.05778e9i −0.605915 + 0.731254i
\(683\) −5.72858e9 −0.687978 −0.343989 0.938974i \(-0.611778\pi\)
−0.343989 + 0.938974i \(0.611778\pi\)
\(684\) −2.92087e9 + 7.04055e9i −0.348992 + 0.841222i
\(685\) 1.04300e10 1.23984
\(686\) 4.03746e9 4.87265e9i 0.477501 0.576276i
\(687\) 8.34620e8 1.44560e9i 0.0982064 0.170099i
\(688\) 1.03869e10 + 1.56719e9i 1.21599 + 0.183469i
\(689\) −1.90785e9 + 3.30449e9i −0.222217 + 0.384890i
\(690\) 5.94471e7 + 1.60234e8i 0.00688904 + 0.0185687i
\(691\) 9.69474e9i 1.11780i −0.829236 0.558899i \(-0.811224\pi\)
0.829236 0.558899i \(-0.188776\pi\)
\(692\) −5.59966e9 + 1.59990e10i −0.642378 + 1.83536i
\(693\) −3.75923e9 6.51118e9i −0.429075 0.743179i
\(694\) −1.21703e9 3.28039e9i −0.138211 0.372535i
\(695\) 8.75970e8i 0.0989789i
\(696\) 5.74354e8 + 3.17520e8i 0.0645725 + 0.0356976i
\(697\) 6.07657e8 3.50831e8i 0.0679742 0.0392449i
\(698\) −7.82105e9 6.48049e9i −0.870504 0.721297i
\(699\) 1.70027e9 + 2.94495e9i 0.188299 + 0.326143i
\(700\) −1.06909e8 1.24250e8i −0.0117807 0.0136916i
\(701\) 5.98965e9 1.03744e10i 0.656732 1.13749i −0.324725 0.945809i \(-0.605272\pi\)
0.981457 0.191684i \(-0.0613950\pi\)
\(702\) −1.86534e9 3.17007e8i −0.203507 0.0345851i
\(703\) 7.76670e9 + 1.54033e10i 0.843127 + 1.67213i
\(704\) 6.33975e9 3.98152e9i 0.684807 0.430075i
\(705\) 3.08376e9 + 1.78041e9i 0.331451 + 0.191363i
\(706\) −4.55604e9 3.77512e9i −0.487271 0.403751i
\(707\) 4.18801e9 2.41795e9i 0.445697 0.257323i
\(708\) −4.94774e8 + 4.25722e8i −0.0523950 + 0.0450827i
\(709\) −6.59222e9 1.14181e10i −0.694656 1.20318i −0.970297 0.241918i \(-0.922223\pi\)
0.275641 0.961261i \(-0.411110\pi\)
\(710\) 1.49457e9 8.79438e9i 0.156715 0.922149i
\(711\) 8.22444e9 0.858150
\(712\) −2.66911e7 1.43591e9i −0.00277131 0.149090i
\(713\) −6.57662e8 + 3.79701e8i −0.0679500 + 0.0392309i
\(714\) 4.47573e8 + 7.60632e7i 0.0460172 + 0.00782043i
\(715\) 2.83581e9 0.290139
\(716\) 2.25335e9 + 1.19142e10i 0.229421 + 1.21302i
\(717\) −4.14903e9 2.39544e9i −0.420367 0.242699i
\(718\) −3.64060e9 9.81289e9i −0.367061 0.989376i
\(719\) −3.44067e9 1.98647e9i −0.345217 0.199311i 0.317360 0.948305i \(-0.397204\pi\)
−0.662577 + 0.748994i \(0.730537\pi\)
\(720\) 8.42525e9 3.30519e9i 0.841239 0.330014i
\(721\) 2.26262e10i 2.24822i
\(722\) −9.81807e9 + 2.42455e9i −0.970836 + 0.239746i
\(723\) 1.02257e9i 0.100626i
\(724\) −1.10611e9 1.28553e9i −0.108322 0.125891i
\(725\) 3.40183e7 + 1.96404e7i 0.00331535 + 0.00191412i
\(726\) 9.99474e8 3.70807e8i 0.0969378 0.0359642i
\(727\) 1.35288e10 + 7.81087e9i 1.30584 + 0.753926i 0.981399 0.191980i \(-0.0614909\pi\)
0.324440 + 0.945906i \(0.394824\pi\)
\(728\) −4.38554e9 + 8.15195e7i −0.421272 + 0.00783072i
\(729\) −5.26753e9 −0.503571
\(730\) 4.94068e7 2.90721e8i 0.00470064 0.0276596i
\(731\) −1.50810e9 + 8.70703e8i −0.142797 + 0.0824441i
\(732\) 1.81613e8 + 9.60246e8i 0.0171142 + 0.0904886i
\(733\) 1.56429e10 1.46708 0.733538 0.679648i \(-0.237867\pi\)
0.733538 + 0.679648i \(0.237867\pi\)
\(734\) 1.33827e10 + 2.27433e9i 1.24913 + 0.212284i
\(735\) 5.70747e8 + 9.88563e8i 0.0530198 + 0.0918329i
\(736\) 7.07437e8 1.47467e8i 0.0654056 0.0136340i
\(737\) 5.67532e9 3.27665e9i 0.522221 0.301504i
\(738\) 3.71427e9 4.48260e9i 0.340154 0.410518i
\(739\) 1.66473e10 + 9.61134e9i 1.51736 + 0.876049i 0.999792 + 0.0204077i \(0.00649642\pi\)
0.517569 + 0.855641i \(0.326837\pi\)
\(740\) 6.76636e9 1.93324e10i 0.613824 1.75378i
\(741\) −5.38711e8 1.06840e9i −0.0486398 0.0964649i
\(742\) 2.67004e9 1.57111e10i 0.239941 1.41187i
\(743\) −7.27660e8 + 1.26034e9i −0.0650830 + 0.112727i −0.896731 0.442576i \(-0.854065\pi\)
0.831648 + 0.555303i \(0.187398\pi\)
\(744\) −2.03374e9 3.37604e9i −0.181046 0.300540i
\(745\) 3.08181e9 + 5.33786e9i 0.273061 + 0.472955i
\(746\) −7.48003e9 + 9.02735e9i −0.659656 + 0.796112i
\(747\) 1.07196e10 6.18895e9i 0.940926 0.543244i
\(748\) −4.09985e8 + 1.17138e9i −0.0358189 + 0.102340i
\(749\) 1.30147e10i 1.13175i
\(750\) −3.26081e9 + 1.20977e9i −0.282235 + 0.104710i
\(751\) 8.19552e9 + 1.41951e10i 0.706052 + 1.22292i 0.966310 + 0.257379i \(0.0828590\pi\)
−0.260258 + 0.965539i \(0.583808\pi\)
\(752\) 9.38922e9 1.17700e10i 0.805132 1.00929i
\(753\) 3.96039e9i 0.338030i
\(754\) 9.85510e8 3.65626e8i 0.0837262 0.0310626i
\(755\) 6.10078e9 1.05669e10i 0.515906 0.893576i
\(756\) 7.76473e9 1.46855e9i 0.653582 0.123613i
\(757\) −1.14355e10 + 1.98069e10i −0.958121 + 1.65951i −0.231064 + 0.972939i \(0.574221\pi\)
−0.727058 + 0.686576i \(0.759113\pi\)
\(758\) −1.05394e10 8.73294e9i −0.878972 0.728313i
\(759\) −1.94441e8 −0.0161414
\(760\) 1.01633e10 + 6.39444e9i 0.839823 + 0.528390i
\(761\) −9.08358e9 −0.747155 −0.373577 0.927599i \(-0.621869\pi\)
−0.373577 + 0.927599i \(0.621869\pi\)
\(762\) −1.81480e9 1.50374e9i −0.148589 0.123120i
\(763\) 3.31591e9 5.74333e9i 0.270251 0.468088i
\(764\) −5.35741e9 + 1.01326e9i −0.434639 + 0.0822039i
\(765\) −7.50172e8 + 1.29934e9i −0.0605823 + 0.104932i
\(766\) 4.57303e9 1.69660e9i 0.367624 0.136389i
\(767\) 1.04544e9i 0.0836599i
\(768\) 8.33456e8 + 3.65673e9i 0.0663924 + 0.291292i
\(769\) −1.18131e9 2.04610e9i −0.0936749 0.162250i 0.815380 0.578926i \(-0.196528\pi\)
−0.909055 + 0.416677i \(0.863195\pi\)
\(770\) −1.11043e10 + 4.11971e9i −0.876542 + 0.325199i
\(771\) 7.42609e9i 0.583539i
\(772\) 3.63412e9 1.03832e10i 0.284275 0.812214i
\(773\) −1.84651e10 + 1.06608e10i −1.43788 + 0.830163i −0.997703 0.0677460i \(-0.978419\pi\)
−0.440182 + 0.897909i \(0.645086\pi\)
\(774\) −9.21818e9 + 1.11251e10i −0.714582 + 0.862400i
\(775\) −1.17951e8 2.04297e8i −0.00910217 0.0157654i
\(776\) 1.23170e10 7.41980e9i 0.946213 0.570002i
\(777\) 4.26221e9 7.38236e9i 0.325957 0.564575i
\(778\) 2.33425e9 1.37352e10i 0.177712 1.04570i
\(779\) 7.71127e9 + 4.36759e8i 0.584446 + 0.0331025i
\(780\) −4.69325e8 + 1.34093e9i −0.0354114 + 0.101175i
\(781\) 8.78920e9 + 5.07445e9i 0.660193 + 0.381163i
\(782\) −7.64344e7 + 9.22456e7i −0.00571565 + 0.00689798i
\(783\) −1.64004e9 + 9.46878e8i −0.122092 + 0.0704901i
\(784\) 4.49322e9 1.76267e9i 0.333005 0.130637i
\(785\) 5.64490e8 + 9.77726e8i 0.0416498 + 0.0721395i
\(786\) 4.42997e9 + 7.52856e8i 0.325403 + 0.0553010i
\(787\) 8.22701e9 0.601631 0.300816 0.953682i \(-0.402741\pi\)
0.300816 + 0.953682i \(0.402741\pi\)
\(788\) 3.23678e9 + 1.71139e10i 0.235652 + 1.24597i
\(789\) 3.68202e9 2.12582e9i 0.266880 0.154084i
\(790\) 2.17069e9 1.27728e10i 0.156640 0.921707i
\(791\) −1.56455e10 −1.12402
\(792\) 1.91364e8 + 1.02949e10i 0.0136874 + 0.736349i
\(793\) 1.35557e9 + 7.82636e8i 0.0965305 + 0.0557319i
\(794\) 9.10656e9 3.37855e9i 0.645628 0.239530i
\(795\) −4.47014e9 2.58084e9i −0.315527 0.182170i
\(796\) 8.29215e9 + 9.63713e9i 0.582735 + 0.677255i
\(797\) 1.99775e10i 1.39778i −0.715231 0.698888i \(-0.753679\pi\)
0.715231 0.698888i \(-0.246321\pi\)
\(798\) 3.66156e9 + 3.40095e9i 0.255068 + 0.236914i
\(799\) 2.49598e9i 0.173112i
\(800\) 4.58094e7 + 2.19759e8i 0.00316329 + 0.0151751i
\(801\) 1.71065e9 + 9.87645e8i 0.117611 + 0.0679027i
\(802\) −1.47507e9 3.97591e9i −0.100972 0.272161i
\(803\) 2.90550e8 + 1.67749e8i 0.0198023 + 0.0114329i
\(804\) 6.10118e8 + 3.22589e9i 0.0414016 + 0.218904i
\(805\) −1.14327e9 −0.0772437
\(806\) −6.22345e9 1.05765e9i −0.418657 0.0711490i
\(807\) −4.74668e9 + 2.74050e9i −0.317931 + 0.183557i
\(808\) −6.62171e9 + 1.23086e8i −0.441601 + 0.00820860i
\(809\) 1.47748e10 0.981075 0.490538 0.871420i \(-0.336800\pi\)
0.490538 + 0.871420i \(0.336800\pi\)
\(810\) −1.86113e9 + 1.09513e10i −0.123049 + 0.724050i
\(811\) 4.20637e9 + 7.28565e9i 0.276907 + 0.479618i 0.970615 0.240639i \(-0.0773571\pi\)
−0.693707 + 0.720257i \(0.744024\pi\)
\(812\) −3.32783e9 + 2.86339e9i −0.218130 + 0.187687i
\(813\) 2.47629e9 1.42968e9i 0.161616 0.0933089i
\(814\) 1.79435e10 + 1.48679e10i 1.16606 + 0.966197i
\(815\) −2.39462e10 1.38253e10i −1.54947 0.894590i
\(816\) −4.86043e8 3.87727e8i −0.0313155 0.0249811i
\(817\) −1.91381e10 1.08396e9i −1.22778 0.0695403i
\(818\) 1.83161e10 + 3.11275e9i 1.17003 + 0.198842i
\(819\) 3.01645e9 5.22465e9i 0.191868 0.332325i
\(820\) −5.98132e9 6.95148e9i −0.378834 0.440280i
\(821\) 1.39516e10 + 2.41648e10i 0.879878 + 1.52399i 0.851474 + 0.524397i \(0.175709\pi\)
0.0284038 + 0.999597i \(0.490958\pi\)
\(822\) −4.57756e9 3.79295e9i −0.287464 0.238191i
\(823\) −1.52618e10 + 8.81138e9i −0.954344 + 0.550991i −0.894428 0.447212i \(-0.852417\pi\)
−0.0599165 + 0.998203i \(0.519083\pi\)
\(824\) −1.49921e10 + 2.71188e10i −0.933505 + 1.68860i
\(825\) 6.04014e7i 0.00374505i
\(826\) −1.51877e9 4.09368e9i −0.0937693 0.252746i
\(827\) −1.26750e10 2.19538e10i −0.779254 1.34971i −0.932372 0.361499i \(-0.882265\pi\)
0.153119 0.988208i \(-0.451068\pi\)
\(828\) −3.28343e8 + 9.38122e8i −0.0201012 + 0.0574319i
\(829\) 2.22344e10i 1.35545i −0.735314 0.677726i \(-0.762966\pi\)
0.735314 0.677726i \(-0.237034\pi\)
\(830\) −6.78241e9 1.82813e10i −0.411729 1.10977i
\(831\) 3.72022e9 6.44361e9i 0.224887 0.389516i
\(832\) 5.31034e9 + 2.80814e9i 0.319662 + 0.169039i
\(833\) −4.00069e8 + 6.92940e8i −0.0239816 + 0.0415373i
\(834\) −3.18554e8 + 3.84450e8i −0.0190152 + 0.0229487i
\(835\) −2.45829e10 −1.46127
\(836\) −1.08427e10 + 8.31034e9i −0.641823 + 0.491923i
\(837\) 1.13730e10 0.670401
\(838\) −1.35285e10 + 1.63270e10i −0.794136 + 0.958411i
\(839\) 2.05500e9 3.55937e9i 0.120128 0.208068i −0.799690 0.600413i \(-0.795003\pi\)
0.919818 + 0.392345i \(0.128336\pi\)
\(840\) −1.10275e8 5.93253e9i −0.00641950 0.345352i
\(841\) −8.09890e9 + 1.40277e10i −0.469505 + 0.813206i
\(842\) −3.06339e9 8.25707e9i −0.176852 0.476687i
\(843\) 4.16686e9i 0.239559i
\(844\) 1.63698e10 + 5.72945e9i 0.937230 + 0.328031i
\(845\) −7.56340e9 1.31002e10i −0.431239 0.746928i
\(846\) 7.20311e9 + 1.94153e10i 0.409000 + 1.10242i
\(847\) 7.13126e9i 0.403250i
\(848\) −1.36104e10 + 1.70615e10i −0.766451 + 0.960800i
\(849\) 3.24316e9 1.87244e9i 0.181883 0.105010i
\(850\) −2.86553e7 2.37437e7i −0.00160044 0.00132612i
\(851\) 1.12470e9 + 1.94803e9i 0.0625580 + 0.108354i
\(852\) −3.85409e9 + 3.31621e9i −0.213493 + 0.183697i
\(853\) 8.50582e9 1.47325e10i 0.469239 0.812746i −0.530142 0.847909i \(-0.677862\pi\)
0.999382 + 0.0351624i \(0.0111948\pi\)
\(854\) −6.44501e9 1.09530e9i −0.354096 0.0601771i
\(855\) −1.47467e10 + 7.43560e9i −0.806886 + 0.406850i
\(856\) 8.62354e9 1.55989e10i 0.469924 0.850035i
\(857\) 7.82162e8 + 4.51581e8i 0.0424486 + 0.0245077i 0.521074 0.853511i \(-0.325532\pi\)
−0.478626 + 0.878019i \(0.658865\pi\)
\(858\) −1.24459e9 1.03126e9i −0.0672700 0.0557397i
\(859\) 1.22074e10 7.04796e9i 0.657125 0.379392i −0.134055 0.990974i \(-0.542800\pi\)
0.791181 + 0.611582i \(0.209467\pi\)
\(860\) 1.48446e10 + 1.72524e10i 0.795838 + 0.924922i
\(861\) −1.90832e9 3.30531e9i −0.101892 0.176482i
\(862\) 3.51244e9 2.06680e10i 0.186781 1.09906i
\(863\) −1.54117e10 −0.816229 −0.408115 0.912931i \(-0.633814\pi\)
−0.408115 + 0.912931i \(0.633814\pi\)
\(864\) −1.02795e10 3.38474e9i −0.542220 0.178537i
\(865\) −3.18061e10 + 1.83632e10i −1.67091 + 0.964702i
\(866\) 1.84474e10 + 3.13506e9i 0.965213 + 0.164034i
\(867\) −5.63007e9 −0.293391
\(868\) 2.59059e10 4.89962e9i 1.34456 0.254298i
\(869\) 1.27653e10 + 7.37006e9i 0.659876 + 0.380980i
\(870\) 4.94601e8 + 1.33315e9i 0.0254646 + 0.0686374i
\(871\) 4.55394e9 + 2.62922e9i 0.233520 + 0.134823i
\(872\) −7.77984e9 + 4.68660e9i −0.397341 + 0.239359i
\(873\) 1.97772e10i 1.00604i
\(874\) −1.26030e9 + 3.88039e8i −0.0638535 + 0.0196601i
\(875\) 2.32659e10i 1.17406i
\(876\) −1.27407e8 + 1.09626e8i −0.00640367 + 0.00550995i
\(877\) 8.32634e9 + 4.80721e9i 0.416827 + 0.240655i 0.693719 0.720246i \(-0.255971\pi\)
−0.276892 + 0.960901i \(0.589304\pi\)
\(878\) 1.34612e9 4.99414e8i 0.0671202 0.0249018i
\(879\) 5.63246e8 + 3.25191e8i 0.0279729 + 0.0161502i
\(880\) 1.60388e10 + 2.41996e9i 0.793384 + 0.119707i
\(881\) −1.92413e10 −0.948021 −0.474010 0.880519i \(-0.657194\pi\)
−0.474010 + 0.880519i \(0.657194\pi\)
\(882\) −1.11224e9 + 6.54466e9i −0.0545830 + 0.321179i
\(883\) 5.03497e9 2.90694e9i 0.246113 0.142093i −0.371870 0.928285i \(-0.621283\pi\)
0.617983 + 0.786191i \(0.287950\pi\)
\(884\) −9.78494e8 + 1.85064e8i −0.0476404 + 0.00901030i
\(885\) −1.41422e9 −0.0685830
\(886\) −7.51452e9 1.27706e9i −0.362980 0.0616870i
\(887\) −2.03629e10 3.52695e10i −0.979730 1.69694i −0.663350 0.748309i \(-0.730866\pi\)
−0.316380 0.948633i \(-0.602467\pi\)
\(888\) −1.00000e10 + 6.02406e9i −0.479244 + 0.288698i
\(889\) 1.36538e10 7.88303e9i 0.651775 0.376302i
\(890\) 1.98534e9 2.39603e9i 0.0943997 0.113927i
\(891\) −1.09449e10 6.31901e9i −0.518368 0.299280i
\(892\) −3.81224e9 1.33429e9i −0.179847 0.0629466i
\(893\) −1.50609e10 + 2.29790e10i −0.707738 + 1.07982i
\(894\) 5.88595e8 3.46343e9i 0.0275509 0.162116i
\(895\) −1.31359e10 + 2.27520e10i −0.612460 + 1.06081i
\(896\) −2.48734e10 3.28137e9i −1.15520 0.152397i
\(897\) −7.80109e7 1.35119e8i −0.00360896 0.00625089i
\(898\) −8.57337e9 + 1.03469e10i −0.395079 + 0.476805i
\(899\) −5.47176e9 + 3.15912e9i −0.251170 + 0.145013i
\(900\) −2.91419e8 1.01997e8i −0.0133251 0.00466378i
\(901\) 3.61811e9i 0.164796i
\(902\) 9.78192e9 3.62911e9i 0.443814 0.164656i
\(903\) 4.73613e9 + 8.20321e9i 0.214050 + 0.370746i
\(904\) 1.87521e10 + 1.03667e10i 0.844230 + 0.466715i
\(905\) 3.67445e9i 0.164787i
\(906\) −6.52026e9 + 2.41903e9i −0.291284 + 0.108067i
\(907\) −6.41186e9 + 1.11057e10i −0.285337 + 0.494219i −0.972691 0.232104i \(-0.925439\pi\)
0.687354 + 0.726323i \(0.258772\pi\)
\(908\) −2.79232e9 1.47639e10i −0.123784 0.654486i
\(909\) 4.55453e9 7.88868e9i 0.201127 0.348362i
\(910\) −7.31793e9 6.06361e9i −0.321916 0.266739i
\(911\) −1.57590e10 −0.690579 −0.345289 0.938496i \(-0.612219\pi\)
−0.345289 + 0.938496i \(0.612219\pi\)
\(912\) −2.13513e9 6.50239e9i −0.0932057 0.283851i
\(913\) 2.21841e10 0.964703
\(914\) −2.77119e9 2.29620e9i −0.120048 0.0994713i
\(915\) −1.05871e9 + 1.83374e9i −0.0456881 + 0.0791341i
\(916\) −2.84191e9 1.50261e10i −0.122173 0.645970i
\(917\) −1.50295e10 + 2.60319e10i −0.643655 + 1.11484i
\(918\) 1.68208e9 6.24056e8i 0.0717625 0.0266241i
\(919\) 2.07622e10i 0.882407i 0.897407 + 0.441204i \(0.145448\pi\)
−0.897407 + 0.441204i \(0.854552\pi\)
\(920\) 1.37028e9 + 7.57529e8i 0.0580164 + 0.0320732i
\(921\) 3.35059e9 + 5.80340e9i 0.141323 + 0.244779i
\(922\) 1.98946e10 7.38092e9i 0.835942 0.310136i
\(923\) 8.14360e9i 0.340887i
\(924\) 6.37166e9 + 2.23008e9i 0.265705 + 0.0929970i
\(925\) −6.05140e8 + 3.49378e8i −0.0251397 + 0.0145144i
\(926\) 2.47821e10 2.99085e10i 1.02565 1.23782i
\(927\) −2.13097e10 3.69096e10i −0.878616 1.52181i
\(928\) 5.88589e9 1.22693e9i 0.241765 0.0503966i
\(929\) 2.07241e10 3.58952e10i 0.848049 1.46886i −0.0348982 0.999391i \(-0.511111\pi\)
0.882947 0.469473i \(-0.155556\pi\)
\(930\) 1.43073e9 8.41876e9i 0.0583268 0.343208i
\(931\) −7.86444e9 + 3.96543e9i −0.319407 + 0.161052i
\(932\) 2.94045e10 + 1.02916e10i 1.18976 + 0.416415i
\(933\) 2.45438e9 + 1.41704e9i 0.0989364 + 0.0571209i
\(934\) −2.65399e10 + 3.20300e10i −1.06582 + 1.28630i
\(935\) −2.32871e9 + 1.34448e9i −0.0931698 + 0.0537916i
\(936\) −7.07724e9 + 4.26336e9i −0.282097 + 0.169936i
\(937\) −1.50990e10 2.61522e10i −0.599596 1.03853i −0.992881 0.119114i \(-0.961995\pi\)
0.393285 0.919417i \(-0.371339\pi\)
\(938\) −2.16516e10 3.67961e9i −0.856605 0.145577i
\(939\) −8.83207e9 −0.348123
\(940\) 3.20537e10 6.06237e9i 1.25873 0.238065i
\(941\) −3.02003e10 + 1.74361e10i −1.18154 + 0.682160i −0.956369 0.292160i \(-0.905626\pi\)
−0.225167 + 0.974320i \(0.572293\pi\)
\(942\) 1.07812e8 6.34390e8i 0.00420232 0.0247274i
\(943\) 1.00712e9 0.0391104
\(944\) −8.92137e8 + 5.91285e9i −0.0345167 + 0.228768i
\(945\) 1.48280e10 + 8.56092e9i 0.571571 + 0.329996i
\(946\) −2.42771e10 + 9.00685e9i −0.932346 + 0.345903i
\(947\) 2.21996e10 + 1.28170e10i 0.849416 + 0.490411i 0.860454 0.509528i \(-0.170180\pi\)
−0.0110374 + 0.999939i \(0.503513\pi\)
\(948\) −5.59763e9 + 4.81641e9i −0.213391 + 0.183609i
\(949\) 2.69208e8i 0.0102248i
\(950\) −1.20541e8 3.91502e8i −0.00456143 0.0148150i
\(951\) 1.24225e10i 0.468359i
\(952\) 3.56267e9 2.14617e9i 0.133828 0.0806184i
\(953\) −1.26157e10 7.28368e9i −0.472157 0.272600i 0.244985 0.969527i \(-0.421217\pi\)
−0.717142 + 0.696927i \(0.754550\pi\)
\(954\) −1.04414e10 2.81439e10i −0.389351 1.04946i
\(955\) −1.02308e10 5.90676e9i −0.380101 0.219451i
\(956\) −4.31264e10 + 8.15657e9i −1.59640 + 0.301929i
\(957\) −1.61775e9 −0.0596650
\(958\) 4.50133e10 + 7.64982e9i 1.65410 + 0.281107i
\(959\) 3.44397e10 1.98838e10i 1.26094 0.728004i
\(960\) −3.79871e9 + 7.18355e9i −0.138576 + 0.262054i
\(961\) 1.04316e10 0.379158
\(962\) −3.13282e9 + 1.84342e10i −0.113455 + 0.667594i
\(963\) 1.22575e10 + 2.12306e10i 0.442293 + 0.766074i
\(964\) −6.11018e9 7.10125e9i −0.219677 0.255308i
\(965\) 2.06418e10 1.19175e10i 0.739438 0.426915i
\(966\) 5.01763e8 + 4.15759e8i 0.0179093 + 0.0148396i
\(967\) 9.71662e9 + 5.60989e9i 0.345559 + 0.199509i 0.662728 0.748861i \(-0.269399\pi\)
−0.317168 + 0.948369i \(0.602732\pi\)
\(968\) 4.72516e9 8.54724e9i 0.167438 0.302874i
\(969\) 9.48917e8 + 6.21941e8i 0.0335039 + 0.0219592i
\(970\) 3.07146e10 + 5.21982e9i 1.08055 + 0.183635i
\(971\) 2.46620e10 4.27158e10i 0.864492 1.49734i −0.00305936 0.999995i \(-0.500974\pi\)
0.867551 0.497348i \(-0.165693\pi\)
\(972\) 1.71885e10 1.47896e10i 0.600352 0.516565i
\(973\) −1.66995e9 2.89244e9i −0.0581178 0.100663i
\(974\) 3.55971e10 + 2.94956e10i 1.23441 + 1.02282i
\(975\) 4.19735e7 2.42334e7i 0.00145030 0.000837333i
\(976\) 6.99898e9 + 5.58324e9i 0.240968 + 0.192226i
\(977\) 2.39217e10i 0.820656i −0.911938 0.410328i \(-0.865414\pi\)
0.911938 0.410328i \(-0.134586\pi\)
\(978\) 5.48191e9 + 1.47759e10i 0.187390 + 0.505090i
\(979\) 1.77009e9 + 3.06589e9i 0.0602915 + 0.104428i
\(980\) 9.87052e9 + 3.45469e9i 0.335003 + 0.117251i
\(981\) 1.24919e10i 0.422463i
\(982\) −7.41545e9 1.99876e10i −0.249889 0.673551i
\(983\) −6.47446e8 + 1.12141e9i −0.0217403 + 0.0376554i −0.876691 0.481054i \(-0.840254\pi\)
0.854951 + 0.518710i \(0.173587\pi\)
\(984\) 9.71432e7 + 5.22605e9i 0.00325035 + 0.174860i
\(985\) −1.88687e10 + 3.26816e10i −0.629095 + 1.08962i
\(986\) −6.35936e8 + 7.67485e8i −0.0211273 + 0.0254977i
\(987\) 1.35767e10 0.449454
\(988\) −1.01251e10 4.20053e9i −0.334002 0.138565i
\(989\) −2.49951e9 −0.0821614
\(990\) −1.42341e10 + 1.71786e10i −0.466237 + 0.562683i
\(991\) −1.27325e10 + 2.20534e10i −0.415581 + 0.719808i −0.995489 0.0948739i \(-0.969755\pi\)
0.579908 + 0.814682i \(0.303089\pi\)
\(992\) −3.42962e10 1.12927e10i −1.11546 0.367288i
\(993\) −5.64440e9 + 9.77639e9i −0.182935 + 0.316852i
\(994\) −1.18306e10 3.18882e10i −0.382080 1.02986i
\(995\) 2.75460e10i 0.886499i
\(996\) −3.67146e9 + 1.04899e10i −0.117742 + 0.336405i
\(997\) −1.75107e9 3.03294e9i −0.0559590 0.0969238i 0.836689 0.547678i \(-0.184488\pi\)
−0.892648 + 0.450755i \(0.851155\pi\)
\(998\) 7.89809e9 + 2.12885e10i 0.251516 + 0.677936i
\(999\) 3.36874e10i 1.06903i
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 76.8.f.a.27.14 yes 136
4.3 odd 2 inner 76.8.f.a.27.9 136
19.12 odd 6 inner 76.8.f.a.31.9 yes 136
76.31 even 6 inner 76.8.f.a.31.14 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.8.f.a.27.9 136 4.3 odd 2 inner
76.8.f.a.27.14 yes 136 1.1 even 1 trivial
76.8.f.a.31.9 yes 136 19.12 odd 6 inner
76.8.f.a.31.14 yes 136 76.31 even 6 inner