Properties

Label 32.8.g.a.13.4
Level $32$
Weight $8$
Character 32.13
Analytic conductor $9.996$
Analytic rank $0$
Dimension $108$
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] = [32,8,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), 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: \(9.99632081549\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(27\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 13.4
Character \(\chi\) \(=\) 32.13
Dual form 32.8.g.a.5.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.3072 - 4.66502i) q^{2} +(9.79359 - 23.6438i) q^{3} +(84.4752 + 96.1662i) q^{4} +(215.611 - 89.3089i) q^{5} +(-211.243 + 198.013i) q^{6} +(-1104.78 + 1104.78i) q^{7} +(-422.082 - 1385.28i) q^{8} +(1083.33 + 1083.33i) q^{9} +O(q^{10})\) \(q+(-10.3072 - 4.66502i) q^{2} +(9.79359 - 23.6438i) q^{3} +(84.4752 + 96.1662i) q^{4} +(215.611 - 89.3089i) q^{5} +(-211.243 + 198.013i) q^{6} +(-1104.78 + 1104.78i) q^{7} +(-422.082 - 1385.28i) q^{8} +(1083.33 + 1083.33i) q^{9} +(-2638.96 - 85.3073i) q^{10} +(334.276 + 807.013i) q^{11} +(3101.05 - 1055.50i) q^{12} +(8883.52 + 3679.67i) q^{13} +(16541.0 - 6233.33i) q^{14} -5972.51i q^{15} +(-2111.89 + 16247.3i) q^{16} -28083.3i q^{17} +(-6112.28 - 16219.8i) q^{18} +(50934.0 + 21097.6i) q^{19} +(26802.3 + 13190.1i) q^{20} +(15301.5 + 36941.0i) q^{21} +(319.298 - 9877.42i) q^{22} +(32277.1 + 32277.1i) q^{23} +(-36887.0 - 3587.23i) q^{24} +(-16730.8 + 16730.8i) q^{25} +(-74398.1 - 79368.8i) q^{26} +(87932.7 - 36422.9i) q^{27} +(-199569. - 12916.1i) q^{28} +(29095.0 - 70241.5i) q^{29} +(-27861.9 + 61559.7i) q^{30} -191917. q^{31} +(97561.7 - 157612. i) q^{32} +22354.6 q^{33} +(-131009. + 289459. i) q^{34} +(-139536. + 336869. i) q^{35} +(-12665.3 + 195694. i) q^{36} +(100671. - 41699.2i) q^{37} +(-426565. - 455064. i) q^{38} +(174003. - 174003. i) q^{39} +(-214723. - 260985. i) q^{40} +(531029. + 531029. i) q^{41} +(14615.9 - 452139. i) q^{42} +(-18772.2 - 45320.0i) q^{43} +(-49369.4 + 100319. i) q^{44} +(330328. + 136826. i) q^{45} +(-182112. - 483258. i) q^{46} +839218. i q^{47} +(363466. + 209053. i) q^{48} -1.61754e6i q^{49} +(250497. - 94397.6i) q^{50} +(-663996. - 275036. i) q^{51} +(396576. + 1.16514e6i) q^{52} +(36572.2 + 88293.2i) q^{53} +(-1.07625e6 - 34790.9i) q^{54} +(144147. + 144147. i) q^{55} +(1.99674e6 + 1.06412e6i) q^{56} +(997654. - 997654. i) q^{57} +(-627565. + 588262. i) q^{58} +(-892154. + 369542. i) q^{59} +(574354. - 504529. i) q^{60} +(-423062. + 1.02136e6i) q^{61} +(1.97812e6 + 895298. i) q^{62} -2.39368e6 q^{63} +(-1.74085e6 + 1.16940e6i) q^{64} +2.24401e6 q^{65} +(-230413. - 104285. i) q^{66} +(280122. - 676273. i) q^{67} +(2.70067e6 - 2.37234e6i) q^{68} +(1.07926e6 - 447045. i) q^{69} +(3.00972e6 - 2.82123e6i) q^{70} +(-704985. + 704985. i) q^{71} +(1.04346e6 - 1.95796e6i) q^{72} +(-4.04776e6 - 4.04776e6i) q^{73} +(-1.23216e6 - 39830.9i) q^{74} +(231726. + 559435. i) q^{75} +(2.27379e6 + 6.68036e6i) q^{76} +(-1.26087e6 - 522271. i) q^{77} +(-2.60520e6 + 981749. i) q^{78} +4.52587e6i q^{79} +(995683. + 3.69171e6i) q^{80} +914833. i q^{81} +(-2.99614e6 - 7.95067e6i) q^{82} +(-4.39869e6 - 1.82200e6i) q^{83} +(-2.25988e6 + 4.59208e6i) q^{84} +(-2.50809e6 - 6.05506e6i) q^{85} +(-17931.1 + 554694. i) q^{86} +(-1.37583e6 - 1.37583e6i) q^{87} +(976847. - 803691. i) q^{88} +(1.02984e6 - 1.02984e6i) q^{89} +(-2.76644e6 - 2.95128e6i) q^{90} +(-1.38796e7 + 5.74911e6i) q^{91} +(-377354. + 5.83058e6i) q^{92} +(-1.87956e6 + 4.53766e6i) q^{93} +(3.91497e6 - 8.64996e6i) q^{94} +1.28661e7 q^{95} +(-2.77106e6 - 3.85031e6i) q^{96} +6.28752e6 q^{97} +(-7.54585e6 + 1.66722e7i) q^{98} +(-512129. + 1.23639e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.3072 4.66502i −0.911033 0.412333i
\(3\) 9.79359 23.6438i 0.209420 0.505584i −0.783913 0.620871i \(-0.786779\pi\)
0.993332 + 0.115288i \(0.0367790\pi\)
\(4\) 84.4752 + 96.1662i 0.659962 + 0.751299i
\(5\) 215.611 89.3089i 0.771392 0.319521i 0.0379561 0.999279i \(-0.487915\pi\)
0.733436 + 0.679758i \(0.237915\pi\)
\(6\) −211.243 + 198.013i −0.399257 + 0.374253i
\(7\) −1104.78 + 1104.78i −1.21740 + 1.21740i −0.248860 + 0.968540i \(0.580056\pi\)
−0.968540 + 0.248860i \(0.919944\pi\)
\(8\) −422.082 1385.28i −0.291462 0.956582i
\(9\) 1083.33 + 1083.33i 0.495348 + 0.495348i
\(10\) −2638.96 85.3073i −0.834513 0.0269765i
\(11\) 334.276 + 807.013i 0.0757235 + 0.182813i 0.957208 0.289400i \(-0.0934556\pi\)
−0.881485 + 0.472212i \(0.843456\pi\)
\(12\) 3101.05 1055.50i 0.518053 0.176329i
\(13\) 8883.52 + 3679.67i 1.12146 + 0.464523i 0.864869 0.501997i \(-0.167401\pi\)
0.256589 + 0.966521i \(0.417401\pi\)
\(14\) 16541.0 6233.33i 1.61107 0.607117i
\(15\) 5972.51i 0.456917i
\(16\) −2111.89 + 16247.3i −0.128900 + 0.991658i
\(17\) 28083.3i 1.38636i −0.720763 0.693181i \(-0.756208\pi\)
0.720763 0.693181i \(-0.243792\pi\)
\(18\) −6112.28 16219.8i −0.247030 0.655528i
\(19\) 50934.0 + 21097.6i 1.70361 + 0.705659i 0.999988 0.00491379i \(-0.00156412\pi\)
0.703624 + 0.710573i \(0.251564\pi\)
\(20\) 26802.3 + 13190.1i 0.749146 + 0.368674i
\(21\) 15301.5 + 36941.0i 0.360550 + 0.870445i
\(22\) 319.298 9877.42i 0.00639318 0.197772i
\(23\) 32277.1 + 32277.1i 0.553155 + 0.553155i 0.927350 0.374195i \(-0.122081\pi\)
−0.374195 + 0.927350i \(0.622081\pi\)
\(24\) −36887.0 3587.23i −0.544670 0.0529688i
\(25\) −16730.8 + 16730.8i −0.214154 + 0.214154i
\(26\) −74398.1 79368.8i −0.830147 0.885611i
\(27\) 87932.7 36422.9i 0.859760 0.356124i
\(28\) −199569. 12916.1i −1.71807 0.111193i
\(29\) 29095.0 70241.5i 0.221526 0.534811i −0.773571 0.633709i \(-0.781532\pi\)
0.995098 + 0.0988976i \(0.0315316\pi\)
\(30\) −27861.9 + 61559.7i −0.188402 + 0.416267i
\(31\) −191917. −1.15704 −0.578520 0.815668i \(-0.696369\pi\)
−0.578520 + 0.815668i \(0.696369\pi\)
\(32\) 97561.7 157612.i 0.526325 0.850283i
\(33\) 22354.6 0.108285
\(34\) −131009. + 289459.i −0.571644 + 1.26302i
\(35\) −139536. + 336869.i −0.550108 + 1.32808i
\(36\) −12665.3 + 195694.i −0.0452434 + 0.699066i
\(37\) 100671. 41699.2i 0.326737 0.135339i −0.213285 0.976990i \(-0.568416\pi\)
0.540021 + 0.841651i \(0.318416\pi\)
\(38\) −426565. 455064.i −1.26108 1.34533i
\(39\) 174003. 174003.i 0.469711 0.469711i
\(40\) −214723. 260985.i −0.530480 0.644772i
\(41\) 531029. + 531029.i 1.20330 + 1.20330i 0.973156 + 0.230148i \(0.0739209\pi\)
0.230148 + 0.973156i \(0.426079\pi\)
\(42\) 14615.9 452139.i 0.0304405 0.941671i
\(43\) −18772.2 45320.0i −0.0360060 0.0869262i 0.904854 0.425723i \(-0.139980\pi\)
−0.940860 + 0.338797i \(0.889980\pi\)
\(44\) −49369.4 + 100319.i −0.0873723 + 0.177540i
\(45\) 330328. + 136826.i 0.540382 + 0.223834i
\(46\) −182112. 483258.i −0.275858 0.732027i
\(47\) 839218.i 1.17905i 0.807750 + 0.589525i \(0.200685\pi\)
−0.807750 + 0.589525i \(0.799315\pi\)
\(48\) 363466. + 209053.i 0.474372 + 0.272842i
\(49\) 1.61754e6i 1.96412i
\(50\) 250497. 94397.6i 0.283405 0.106799i
\(51\) −663996. 275036.i −0.700922 0.290332i
\(52\) 396576. + 1.16514e6i 0.391124 + 1.14912i
\(53\) 36572.2 + 88293.2i 0.0337432 + 0.0814632i 0.939853 0.341580i \(-0.110962\pi\)
−0.906110 + 0.423043i \(0.860962\pi\)
\(54\) −1.07625e6 34790.9i −0.930111 0.0300668i
\(55\) 144147. + 144147.i 0.116825 + 0.116825i
\(56\) 1.99674e6 + 1.06412e6i 1.51937 + 0.809717i
\(57\) 997654. 997654.i 0.713539 0.713539i
\(58\) −627565. + 588262.i −0.422338 + 0.395888i
\(59\) −892154. + 369542.i −0.565533 + 0.234251i −0.647085 0.762418i \(-0.724012\pi\)
0.0815523 + 0.996669i \(0.474012\pi\)
\(60\) 574354. 504529.i 0.343281 0.301548i
\(61\) −423062. + 1.02136e6i −0.238644 + 0.576136i −0.997143 0.0755372i \(-0.975933\pi\)
0.758499 + 0.651674i \(0.225933\pi\)
\(62\) 1.97812e6 + 895298.i 1.05410 + 0.477086i
\(63\) −2.39368e6 −1.20607
\(64\) −1.74085e6 + 1.16940e6i −0.830100 + 0.557614i
\(65\) 2.24401e6 1.01351
\(66\) −230413. 104285.i −0.0986513 0.0446496i
\(67\) 280122. 676273.i 0.113785 0.274701i −0.856720 0.515781i \(-0.827502\pi\)
0.970505 + 0.241080i \(0.0775017\pi\)
\(68\) 2.70067e6 2.37234e6i 1.04157 0.914947i
\(69\) 1.07926e6 447045.i 0.395508 0.163825i
\(70\) 3.00972e6 2.82123e6i 1.04878 0.983095i
\(71\) −704985. + 704985.i −0.233763 + 0.233763i −0.814261 0.580498i \(-0.802858\pi\)
0.580498 + 0.814261i \(0.302858\pi\)
\(72\) 1.04346e6 1.95796e6i 0.329467 0.618217i
\(73\) −4.04776e6 4.04776e6i −1.21783 1.21783i −0.968392 0.249434i \(-0.919755\pi\)
−0.249434 0.968392i \(-0.580245\pi\)
\(74\) −1.23216e6 39830.9i −0.353473 0.0114264i
\(75\) 231726. + 559435.i 0.0634248 + 0.153121i
\(76\) 2.27379e6 + 6.68036e6i 0.594159 + 1.74563i
\(77\) −1.26087e6 522271.i −0.314742 0.130370i
\(78\) −2.60520e6 + 981749.i −0.621600 + 0.234245i
\(79\) 4.52587e6i 1.03278i 0.856354 + 0.516389i \(0.172724\pi\)
−0.856354 + 0.516389i \(0.827276\pi\)
\(80\) 995683. + 3.69171e6i 0.217423 + 0.806143i
\(81\) 914833.i 0.191269i
\(82\) −2.99614e6 7.95067e6i −0.600087 1.59241i
\(83\) −4.39869e6 1.82200e6i −0.844404 0.349764i −0.0818155 0.996647i \(-0.526072\pi\)
−0.762589 + 0.646884i \(0.776072\pi\)
\(84\) −2.25988e6 + 4.59208e6i −0.416015 + 0.845341i
\(85\) −2.50809e6 6.05506e6i −0.442972 1.06943i
\(86\) −17931.1 + 554694.i −0.00303992 + 0.0940391i
\(87\) −1.37583e6 1.37583e6i −0.224000 0.224000i
\(88\) 976847. 803691.i 0.152805 0.125719i
\(89\) 1.02984e6 1.02984e6i 0.154848 0.154848i −0.625431 0.780279i \(-0.715077\pi\)
0.780279 + 0.625431i \(0.215077\pi\)
\(90\) −2.76644e6 2.95128e6i −0.400012 0.426738i
\(91\) −1.38796e7 + 5.74911e6i −1.93077 + 0.799752i
\(92\) −377354. + 5.83058e6i −0.0505233 + 0.780646i
\(93\) −1.87956e6 + 4.53766e6i −0.242307 + 0.584980i
\(94\) 3.91497e6 8.64996e6i 0.486162 1.07415i
\(95\) 1.28661e7 1.53963
\(96\) −2.77106e6 3.85031e6i −0.319666 0.444168i
\(97\) 6.28752e6 0.699485 0.349743 0.936846i \(-0.386269\pi\)
0.349743 + 0.936846i \(0.386269\pi\)
\(98\) −7.54585e6 + 1.66722e7i −0.809873 + 1.78938i
\(99\) −512129. + 1.23639e6i −0.0530465 + 0.128065i
\(100\) −3.02228e6 195601.i −0.302228 0.0195601i
\(101\) 3.71275e6 1.53787e6i 0.358568 0.148524i −0.196125 0.980579i \(-0.562836\pi\)
0.554693 + 0.832055i \(0.312836\pi\)
\(102\) 5.56087e6 + 5.93240e6i 0.518850 + 0.553515i
\(103\) 4.33067e6 4.33067e6i 0.390504 0.390504i −0.484363 0.874867i \(-0.660949\pi\)
0.874867 + 0.484363i \(0.160949\pi\)
\(104\) 1.34781e6 1.38593e7i 0.117493 1.20816i
\(105\) 6.59832e6 + 6.59832e6i 0.556251 + 0.556251i
\(106\) 34933.6 1.08066e6i 0.00284887 0.0881291i
\(107\) −5.64463e6 1.36273e7i −0.445443 1.07540i −0.974010 0.226504i \(-0.927270\pi\)
0.528567 0.848892i \(-0.322730\pi\)
\(108\) 1.09308e7 + 5.37932e6i 0.834964 + 0.410908i
\(109\) 1.08053e7 + 4.47569e6i 0.799177 + 0.331030i 0.744627 0.667481i \(-0.232628\pi\)
0.0545499 + 0.998511i \(0.482628\pi\)
\(110\) −813297. 2.15819e6i −0.0582606 0.154602i
\(111\) 2.78863e6i 0.193535i
\(112\) −1.56166e7 2.02829e7i −1.05032 1.36417i
\(113\) 4.88853e6i 0.318716i −0.987221 0.159358i \(-0.949058\pi\)
0.987221 0.159358i \(-0.0509424\pi\)
\(114\) −1.49371e7 + 5.62890e6i −0.944274 + 0.355842i
\(115\) 9.84192e6 + 4.07666e6i 0.603444 + 0.249955i
\(116\) 9.21266e6 3.13571e6i 0.548002 0.186523i
\(117\) 5.63747e6 + 1.36100e7i 0.325412 + 0.785614i
\(118\) 1.09195e7 + 352985.i 0.611809 + 0.0197774i
\(119\) 3.10259e7 + 3.10259e7i 1.68776 + 1.68776i
\(120\) −8.27360e6 + 2.52089e6i −0.437079 + 0.133174i
\(121\) 1.32400e7 1.32400e7i 0.679420 0.679420i
\(122\) 9.12524e6 8.55375e6i 0.454972 0.426479i
\(123\) 1.77562e7 7.35488e6i 0.860366 0.356375i
\(124\) −1.62122e7 1.84560e7i −0.763602 0.869282i
\(125\) −9.09039e6 + 2.19461e7i −0.416291 + 1.00502i
\(126\) 2.46720e7 + 1.11666e7i 1.09877 + 0.497305i
\(127\) −6.97029e6 −0.301952 −0.150976 0.988537i \(-0.548242\pi\)
−0.150976 + 0.988537i \(0.548242\pi\)
\(128\) 2.33985e7 3.93214e6i 0.986172 0.165727i
\(129\) −1.25539e6 −0.0514888
\(130\) −2.31294e7 1.04683e7i −0.923341 0.417904i
\(131\) 5.67516e6 1.37011e7i 0.220561 0.532481i −0.774406 0.632690i \(-0.781951\pi\)
0.994966 + 0.100208i \(0.0319509\pi\)
\(132\) 1.88841e6 + 2.14976e6i 0.0714641 + 0.0813544i
\(133\) −7.95792e7 + 3.29628e7i −2.93304 + 1.21491i
\(134\) −6.04209e6 + 5.66369e6i −0.216930 + 0.203344i
\(135\) 1.57063e7 1.57063e7i 0.549423 0.549423i
\(136\) −3.89032e7 + 1.18534e7i −1.32617 + 0.404072i
\(137\) −1.75333e7 1.75333e7i −0.582561 0.582561i 0.353046 0.935606i \(-0.385146\pi\)
−0.935606 + 0.353046i \(0.885146\pi\)
\(138\) −1.32096e7 427015.i −0.427871 0.0138314i
\(139\) −9.98305e6 2.41012e7i −0.315291 0.761179i −0.999492 0.0318856i \(-0.989849\pi\)
0.684201 0.729294i \(-0.260151\pi\)
\(140\) −4.41828e7 + 1.50385e7i −1.36083 + 0.463186i
\(141\) 1.98423e7 + 8.21895e6i 0.596109 + 0.246916i
\(142\) 1.05552e7 3.97763e6i 0.309354 0.116578i
\(143\) 8.39914e6i 0.240192i
\(144\) −1.98890e7 + 1.53133e7i −0.555066 + 0.427366i
\(145\) 1.77433e7i 0.483332i
\(146\) 2.28381e7 + 6.06039e7i 0.607329 + 1.61163i
\(147\) −3.82448e7 1.58415e7i −0.993028 0.411326i
\(148\) 1.25143e7 + 6.15859e6i 0.317314 + 0.156158i
\(149\) 1.68840e6 + 4.07615e6i 0.0418141 + 0.100948i 0.943407 0.331638i \(-0.107601\pi\)
−0.901593 + 0.432586i \(0.857601\pi\)
\(150\) 221343. 6.84719e6i 0.00535483 0.165651i
\(151\) 1.21078e7 + 1.21078e7i 0.286184 + 0.286184i 0.835569 0.549385i \(-0.185138\pi\)
−0.549385 + 0.835569i \(0.685138\pi\)
\(152\) 7.72770e6 7.94628e7i 0.178483 1.83532i
\(153\) 3.04234e7 3.04234e7i 0.686733 0.686733i
\(154\) 1.05596e7 + 1.12651e7i 0.232984 + 0.248550i
\(155\) −4.13794e7 + 1.71399e7i −0.892531 + 0.369699i
\(156\) 3.14321e7 + 2.03428e6i 0.662885 + 0.0429017i
\(157\) −1.30296e7 + 3.14562e7i −0.268709 + 0.648721i −0.999423 0.0339626i \(-0.989187\pi\)
0.730714 + 0.682684i \(0.239187\pi\)
\(158\) 2.11133e7 4.66489e7i 0.425849 0.940895i
\(159\) 2.44576e6 0.0482530
\(160\) 6.95922e6 4.26959e7i 0.134320 0.824074i
\(161\) −7.13182e7 −1.34682
\(162\) 4.26771e6 9.42933e6i 0.0788665 0.174252i
\(163\) 2.52574e7 6.09767e7i 0.456806 1.10283i −0.512878 0.858462i \(-0.671421\pi\)
0.969683 0.244365i \(-0.0785795\pi\)
\(164\) −6.20830e6 + 9.59259e7i −0.109906 + 1.69818i
\(165\) 4.81990e6 1.99647e6i 0.0835303 0.0345994i
\(166\) 3.68384e7 + 3.92996e7i 0.625061 + 0.666822i
\(167\) 3.94088e7 3.94088e7i 0.654765 0.654765i −0.299372 0.954137i \(-0.596777\pi\)
0.954137 + 0.299372i \(0.0967770\pi\)
\(168\) 4.47151e7 3.67889e7i 0.727565 0.598597i
\(169\) 2.10070e7 + 2.10070e7i 0.334780 + 0.334780i
\(170\) −2.39571e6 + 7.41108e7i −0.0373993 + 1.15694i
\(171\) 3.23227e7 + 7.80338e7i 0.494334 + 1.19343i
\(172\) 2.77248e6 5.63367e6i 0.0415449 0.0844193i
\(173\) −8.25058e7 3.41750e7i −1.21150 0.501819i −0.316802 0.948492i \(-0.602609\pi\)
−0.894698 + 0.446672i \(0.852609\pi\)
\(174\) 7.76264e6 + 2.05992e7i 0.111709 + 0.296434i
\(175\) 3.69678e7i 0.521423i
\(176\) −1.38178e7 + 3.72676e6i −0.191048 + 0.0515273i
\(177\) 2.47131e7i 0.334981i
\(178\) −1.54190e7 + 5.81052e6i −0.204921 + 0.0772227i
\(179\) −7.08217e7 2.93353e7i −0.922955 0.382301i −0.129954 0.991520i \(-0.541483\pi\)
−0.793002 + 0.609219i \(0.791483\pi\)
\(180\) 1.47464e7 + 4.33248e7i 0.188466 + 0.553710i
\(181\) −2.49431e7 6.02179e7i −0.312662 0.754833i −0.999605 0.0281211i \(-0.991048\pi\)
0.686943 0.726712i \(-0.258952\pi\)
\(182\) 1.69879e8 + 5.49151e6i 2.08876 + 0.0675215i
\(183\) 2.00056e7 + 2.00056e7i 0.241309 + 0.241309i
\(184\) 3.10892e7 5.83364e7i 0.367915 0.690362i
\(185\) 1.79816e7 1.79816e7i 0.208799 0.208799i
\(186\) 4.05412e7 3.80022e7i 0.461956 0.433025i
\(187\) 2.26636e7 9.38757e6i 0.253445 0.104980i
\(188\) −8.07044e7 + 7.08931e7i −0.885819 + 0.778129i
\(189\) −5.69070e7 + 1.37386e8i −0.613125 + 1.48022i
\(190\) −1.32613e8 6.00207e7i −1.40265 0.634839i
\(191\) 2.69419e6 0.0279777 0.0139888 0.999902i \(-0.495547\pi\)
0.0139888 + 0.999902i \(0.495547\pi\)
\(192\) 1.06000e7 + 5.26129e7i 0.108082 + 0.536460i
\(193\) −6.31485e6 −0.0632285 −0.0316142 0.999500i \(-0.510065\pi\)
−0.0316142 + 0.999500i \(0.510065\pi\)
\(194\) −6.48065e7 2.93314e7i −0.637254 0.288421i
\(195\) 2.19769e7 5.30569e7i 0.212249 0.512414i
\(196\) 1.55553e8 1.36642e8i 1.47564 1.29625i
\(197\) 1.70721e8 7.07149e7i 1.59094 0.658990i 0.600845 0.799365i \(-0.294831\pi\)
0.990098 + 0.140375i \(0.0448308\pi\)
\(198\) 1.10464e7 1.03546e7i 0.101133 0.0947990i
\(199\) −5.26695e7 + 5.26695e7i −0.473776 + 0.473776i −0.903134 0.429358i \(-0.858740\pi\)
0.429358 + 0.903134i \(0.358740\pi\)
\(200\) 3.02386e7 + 1.61151e7i 0.267274 + 0.142439i
\(201\) −1.32463e7 1.32463e7i −0.115056 0.115056i
\(202\) −4.54422e7 1.46897e6i −0.387908 0.0125396i
\(203\) 4.54579e7 + 1.09745e8i 0.381393 + 0.920765i
\(204\) −2.96420e7 8.70877e7i −0.244457 0.718210i
\(205\) 1.61921e8 + 6.70700e7i 1.31270 + 0.543738i
\(206\) −6.48396e7 + 2.44343e7i −0.516779 + 0.194744i
\(207\) 6.99333e7i 0.548009i
\(208\) −7.85459e7 + 1.36562e8i −0.605204 + 1.05223i
\(209\) 4.81569e7i 0.364877i
\(210\) −3.72286e7 9.87912e7i −0.277402 0.736124i
\(211\) −8.74301e7 3.62147e7i −0.640726 0.265397i 0.0385768 0.999256i \(-0.487718\pi\)
−0.679303 + 0.733858i \(0.737718\pi\)
\(212\) −5.40138e6 + 1.09756e7i −0.0389340 + 0.0791139i
\(213\) 9.76421e6 + 2.35729e7i 0.0692322 + 0.167141i
\(214\) −5.39172e6 + 1.66792e8i −0.0376079 + 1.16339i
\(215\) −8.09497e6 8.09497e6i −0.0555495 0.0555495i
\(216\) −8.75707e7 1.06438e8i −0.591249 0.718634i
\(217\) 2.12027e8 2.12027e8i 1.40858 1.40858i
\(218\) −9.04924e7 9.65384e7i −0.591582 0.631106i
\(219\) −1.35347e8 + 5.60624e7i −0.870750 + 0.360676i
\(220\) −1.68523e6 + 2.60389e7i −0.0106704 + 0.164871i
\(221\) 1.03337e8 2.49478e8i 0.643998 1.55475i
\(222\) −1.30090e7 + 2.87428e7i −0.0798011 + 0.176317i
\(223\) −2.34440e8 −1.41568 −0.707838 0.706375i \(-0.750329\pi\)
−0.707838 + 0.706375i \(0.750329\pi\)
\(224\) 6.63421e7 + 2.81911e8i 0.394386 + 1.67588i
\(225\) −3.62499e7 −0.212162
\(226\) −2.28051e7 + 5.03869e7i −0.131417 + 0.290361i
\(227\) 5.24600e7 1.26650e8i 0.297672 0.718643i −0.702305 0.711876i \(-0.747846\pi\)
0.999977 0.00676743i \(-0.00215416\pi\)
\(228\) 1.80218e8 + 1.16636e7i 1.00699 + 0.0651722i
\(229\) −1.90723e8 + 7.89999e7i −1.04949 + 0.434713i −0.839709 0.543036i \(-0.817275\pi\)
−0.209780 + 0.977749i \(0.567275\pi\)
\(230\) −8.24246e7 8.79315e7i −0.446693 0.476537i
\(231\) −2.46970e7 + 2.46970e7i −0.131826 + 0.131826i
\(232\) −1.09585e8 1.06570e7i −0.576158 0.0560309i
\(233\) 1.26375e8 + 1.26375e8i 0.654510 + 0.654510i 0.954076 0.299566i \(-0.0968419\pi\)
−0.299566 + 0.954076i \(0.596842\pi\)
\(234\) 5.38487e6 1.66580e8i 0.0274739 0.849898i
\(235\) 7.49496e7 + 1.80944e8i 0.376731 + 0.909510i
\(236\) −1.10902e8 5.45780e7i −0.549223 0.270287i
\(237\) 1.07009e8 + 4.43245e7i 0.522156 + 0.216284i
\(238\) −1.75052e8 4.64525e8i −0.841684 2.23352i
\(239\) 6.95503e7i 0.329539i −0.986332 0.164769i \(-0.947312\pi\)
0.986332 0.164769i \(-0.0526880\pi\)
\(240\) 9.70373e7 + 1.26133e7i 0.453106 + 0.0588965i
\(241\) 1.25350e8i 0.576851i 0.957502 + 0.288425i \(0.0931317\pi\)
−0.957502 + 0.288425i \(0.906868\pi\)
\(242\) −1.98231e8 + 7.47018e7i −0.899122 + 0.338827i
\(243\) 2.13939e8 + 8.86164e7i 0.956462 + 0.396179i
\(244\) −1.33959e8 + 4.55955e7i −0.590346 + 0.200936i
\(245\) −1.44461e8 3.48759e8i −0.627579 1.51511i
\(246\) −2.17327e8 7.02533e6i −0.930767 0.0300881i
\(247\) 3.74841e8 + 3.74841e8i 1.58273 + 1.58273i
\(248\) 8.10048e7 + 2.65859e8i 0.337233 + 1.10680i
\(249\) −8.61580e7 + 8.61580e7i −0.353670 + 0.353670i
\(250\) 1.96075e8 1.83796e8i 0.793657 0.743952i
\(251\) −2.27338e8 + 9.41665e7i −0.907432 + 0.375871i −0.787073 0.616860i \(-0.788405\pi\)
−0.120359 + 0.992730i \(0.538405\pi\)
\(252\) −2.02206e8 2.30191e8i −0.795963 0.906122i
\(253\) −1.52586e7 + 3.68375e7i −0.0592369 + 0.143011i
\(254\) 7.18439e7 + 3.25166e7i 0.275088 + 0.124505i
\(255\) −1.67728e8 −0.633453
\(256\) −2.59515e8 6.86252e7i −0.966770 0.255649i
\(257\) −2.83743e8 −1.04270 −0.521351 0.853343i \(-0.674572\pi\)
−0.521351 + 0.853343i \(0.674572\pi\)
\(258\) 1.29395e7 + 5.85640e6i 0.0469080 + 0.0212306i
\(259\) −6.51508e7 + 1.57288e8i −0.233008 + 0.562530i
\(260\) 1.89563e8 + 2.15798e8i 0.668878 + 0.761448i
\(261\) 1.07614e8 4.45751e7i 0.374651 0.155185i
\(262\) −1.22410e8 + 1.14744e8i −0.420498 + 0.394163i
\(263\) 2.99377e8 2.99377e8i 1.01478 1.01478i 0.0148956 0.999889i \(-0.495258\pi\)
0.999889 0.0148956i \(-0.00474158\pi\)
\(264\) −9.43548e6 3.09674e7i −0.0315610 0.103584i
\(265\) 1.57707e7 + 1.57707e7i 0.0520585 + 0.0520585i
\(266\) 9.74007e8 + 3.14858e7i 3.17305 + 0.102572i
\(267\) −1.42636e7 3.44353e7i −0.0458605 0.110717i
\(268\) 8.86980e7 3.01901e7i 0.281476 0.0958059i
\(269\) 5.09689e8 + 2.11120e8i 1.59651 + 0.661297i 0.990917 0.134475i \(-0.0429347\pi\)
0.605596 + 0.795772i \(0.292935\pi\)
\(270\) −2.35158e8 + 8.86174e7i −0.727088 + 0.273997i
\(271\) 2.27139e8i 0.693264i −0.938001 0.346632i \(-0.887325\pi\)
0.938001 0.346632i \(-0.112675\pi\)
\(272\) 4.56278e8 + 5.93089e7i 1.37480 + 0.178702i
\(273\) 3.84470e8i 1.14365i
\(274\) 9.89252e7 + 2.62511e8i 0.290523 + 0.770941i
\(275\) −1.90947e7 7.90928e6i −0.0553667 0.0229336i
\(276\) 1.34161e8 + 6.60244e7i 0.384101 + 0.189026i
\(277\) −2.20470e8 5.32262e8i −0.623262 1.50469i −0.847852 0.530233i \(-0.822104\pi\)
0.224590 0.974453i \(-0.427896\pi\)
\(278\) −9.53575e6 + 2.94986e8i −0.0266194 + 0.823464i
\(279\) −2.07909e8 2.07909e8i −0.573138 0.573138i
\(280\) 5.25554e8 + 5.11097e7i 1.43075 + 0.139140i
\(281\) 3.45297e8 3.45297e8i 0.928370 0.928370i −0.0692309 0.997601i \(-0.522055\pi\)
0.997601 + 0.0692309i \(0.0220545\pi\)
\(282\) −1.66176e8 1.77279e8i −0.441263 0.470744i
\(283\) 5.00871e8 2.07468e8i 1.31363 0.544124i 0.387690 0.921790i \(-0.373273\pi\)
0.925942 + 0.377666i \(0.123273\pi\)
\(284\) −1.27350e8 8.24204e6i −0.329901 0.0213511i
\(285\) 1.26006e8 3.04204e8i 0.322428 0.778410i
\(286\) 3.91822e7 8.65713e7i 0.0990392 0.218823i
\(287\) −1.17334e9 −2.92980
\(288\) 2.76436e8 6.50538e7i 0.681901 0.160472i
\(289\) −3.78333e8 −0.922002
\(290\) −8.27727e7 + 1.82883e8i −0.199294 + 0.440331i
\(291\) 6.15774e7 1.48661e8i 0.146486 0.353648i
\(292\) 4.73227e7 7.31194e8i 0.111232 1.71867i
\(293\) −5.42312e7 + 2.24633e7i −0.125954 + 0.0521719i −0.444770 0.895645i \(-0.646715\pi\)
0.318816 + 0.947817i \(0.396715\pi\)
\(294\) 3.20294e8 + 3.41694e8i 0.735078 + 0.784190i
\(295\) −1.59355e8 + 1.59355e8i −0.361400 + 0.361400i
\(296\) −1.00256e8 1.21857e8i −0.224694 0.273105i
\(297\) 5.87875e7 + 5.87875e7i 0.130208 + 0.130208i
\(298\) 1.61275e6 4.98899e7i 0.00353028 0.109208i
\(299\) 1.67965e8 + 4.05503e8i 0.363387 + 0.877294i
\(300\) −3.42237e7 + 6.95425e7i −0.0731817 + 0.148705i
\(301\) 7.08079e7 + 2.93296e7i 0.149658 + 0.0619902i
\(302\) −6.83138e7 1.81280e8i −0.142720 0.378726i
\(303\) 1.02845e8i 0.212390i
\(304\) −4.50346e8 + 7.82986e8i −0.919367 + 1.59844i
\(305\) 2.58000e8i 0.520679i
\(306\) −4.55505e8 + 1.71653e8i −0.908799 + 0.342473i
\(307\) 6.85858e8 + 2.84092e8i 1.35285 + 0.560369i 0.937084 0.349103i \(-0.113514\pi\)
0.415766 + 0.909472i \(0.363514\pi\)
\(308\) −5.62877e7 1.65372e8i −0.109771 0.322504i
\(309\) −5.99808e7 1.44806e8i −0.115653 0.279211i
\(310\) 5.06463e8 + 1.63719e7i 0.965565 + 0.0312129i
\(311\) −6.69612e8 6.69612e8i −1.26230 1.26230i −0.949976 0.312322i \(-0.898893\pi\)
−0.312322 0.949976i \(-0.601107\pi\)
\(312\) −3.14486e8 1.67599e8i −0.586220 0.312414i
\(313\) −6.59919e8 + 6.59919e8i −1.21643 + 1.21643i −0.247551 + 0.968875i \(0.579626\pi\)
−0.968875 + 0.247551i \(0.920374\pi\)
\(314\) 2.81042e8 2.63441e8i 0.512292 0.480209i
\(315\) −5.16103e8 + 2.13777e8i −0.930356 + 0.385366i
\(316\) −4.35236e8 + 3.82324e8i −0.775925 + 0.681595i
\(317\) −3.79771e8 + 9.16850e8i −0.669599 + 1.61656i 0.112683 + 0.993631i \(0.464056\pi\)
−0.782282 + 0.622925i \(0.785944\pi\)
\(318\) −2.52089e7 1.14095e7i −0.0439600 0.0198963i
\(319\) 6.64115e7 0.114545
\(320\) −2.70907e8 + 4.07609e8i −0.462163 + 0.695374i
\(321\) −3.77484e8 −0.636987
\(322\) 7.35089e8 + 3.32701e8i 1.22700 + 0.555340i
\(323\) 5.92489e8 1.43040e9i 0.978299 2.36182i
\(324\) −8.79760e7 + 7.72806e7i −0.143700 + 0.126230i
\(325\) −2.10192e8 + 8.70645e7i −0.339645 + 0.140686i
\(326\) −5.44789e8 + 5.10671e8i −0.870898 + 0.816355i
\(327\) 2.11645e8 2.11645e8i 0.334726 0.334726i
\(328\) 5.11486e8 9.59762e8i 0.800342 1.50178i
\(329\) −9.27152e8 9.27152e8i −1.43537 1.43537i
\(330\) −5.89930e7 1.90701e6i −0.0903653 0.00292116i
\(331\) 3.09994e8 + 7.48393e8i 0.469846 + 1.13431i 0.964230 + 0.265066i \(0.0853937\pi\)
−0.494384 + 0.869244i \(0.664606\pi\)
\(332\) −1.96366e8 5.76919e8i −0.294498 0.865231i
\(333\) 1.54233e8 + 6.38856e7i 0.228888 + 0.0948087i
\(334\) −5.90036e8 + 2.22350e8i −0.866494 + 0.326531i
\(335\) 1.70829e8i 0.248259i
\(336\) −6.32507e8 + 1.70592e8i −0.909658 + 0.245342i
\(337\) 1.46998e8i 0.209222i 0.994513 + 0.104611i \(0.0333598\pi\)
−0.994513 + 0.104611i \(0.966640\pi\)
\(338\) −1.18524e8 3.14520e8i −0.166955 0.443037i
\(339\) −1.15584e8 4.78763e7i −0.161138 0.0667454i
\(340\) 3.70421e8 7.52696e8i 0.511116 1.03859i
\(341\) −6.41533e7 1.54880e8i −0.0876151 0.211521i
\(342\) 3.08744e7 9.55093e8i 0.0417357 1.29108i
\(343\) 8.77192e8 + 8.77192e8i 1.17372 + 1.17372i
\(344\) −5.48575e7 + 4.51335e7i −0.0726577 + 0.0597784i
\(345\) 1.92775e8 1.92775e8i 0.252746 0.252746i
\(346\) 6.90974e8 + 7.37139e8i 0.896799 + 0.956716i
\(347\) −1.54508e8 + 6.39992e7i −0.198517 + 0.0822283i −0.479727 0.877418i \(-0.659264\pi\)
0.281210 + 0.959646i \(0.409264\pi\)
\(348\) 1.60850e7 2.48532e8i 0.0204594 0.316123i
\(349\) −1.86122e8 + 4.49339e8i −0.234374 + 0.565828i −0.996683 0.0813849i \(-0.974066\pi\)
0.762309 + 0.647213i \(0.224066\pi\)
\(350\) −1.72455e8 + 3.81033e8i −0.215000 + 0.475033i
\(351\) 9.15176e8 1.12961
\(352\) 1.59807e8 + 2.60478e7i 0.195298 + 0.0318325i
\(353\) 3.83647e8 0.464217 0.232108 0.972690i \(-0.425438\pi\)
0.232108 + 0.972690i \(0.425438\pi\)
\(354\) 1.15287e8 2.54722e8i 0.138124 0.305179i
\(355\) −8.90410e7 + 2.14964e8i −0.105631 + 0.255015i
\(356\) 1.86032e8 + 1.20400e7i 0.218531 + 0.0141433i
\(357\) 1.03743e9 4.29716e8i 1.20675 0.499853i
\(358\) 5.93121e8 + 6.32748e8i 0.683207 + 0.728854i
\(359\) 5.13698e8 5.13698e8i 0.585973 0.585973i −0.350566 0.936538i \(-0.614011\pi\)
0.936538 + 0.350566i \(0.114011\pi\)
\(360\) 5.01172e7 5.15348e8i 0.0566146 0.582159i
\(361\) 1.51711e9 + 1.51711e9i 1.69723 + 1.69723i
\(362\) −2.38255e7 + 7.37036e8i −0.0263974 + 0.816599i
\(363\) −1.83377e8 4.42710e8i −0.201220 0.485788i
\(364\) −1.72535e9 8.49090e8i −1.87509 0.922781i
\(365\) −1.23424e9 5.11240e8i −1.32854 0.550300i
\(366\) −1.12874e8 2.99527e8i −0.120340 0.319340i
\(367\) 1.00157e8i 0.105767i −0.998601 0.0528834i \(-0.983159\pi\)
0.998601 0.0528834i \(-0.0168412\pi\)
\(368\) −5.92582e8 + 4.56250e8i −0.619842 + 0.477239i
\(369\) 1.15056e9i 1.19211i
\(370\) −2.69224e8 + 1.01455e8i −0.276317 + 0.104128i
\(371\) −1.37949e8 5.71403e7i −0.140252 0.0580944i
\(372\) −5.95145e8 + 2.02569e8i −0.599408 + 0.204020i
\(373\) −2.21469e8 5.34673e8i −0.220969 0.533467i 0.774053 0.633121i \(-0.218226\pi\)
−0.995022 + 0.0996538i \(0.968226\pi\)
\(374\) −2.77390e8 8.96695e6i −0.274183 0.00886327i
\(375\) 4.29863e8 + 4.29863e8i 0.420940 + 0.420940i
\(376\) 1.16255e9 3.54219e8i 1.12786 0.343648i
\(377\) 5.16931e8 5.16931e8i 0.496865 0.496865i
\(378\) 1.22746e9 1.15058e9i 1.16892 1.09571i
\(379\) 1.02900e9 4.26228e8i 0.970912 0.402165i 0.159861 0.987140i \(-0.448896\pi\)
0.811052 + 0.584975i \(0.198896\pi\)
\(380\) 1.08687e9 + 1.23729e9i 1.01609 + 1.15672i
\(381\) −6.82642e7 + 1.64804e8i −0.0632347 + 0.152662i
\(382\) −2.77695e7 1.25685e7i −0.0254886 0.0115361i
\(383\) −1.94613e8 −0.177001 −0.0885004 0.996076i \(-0.528207\pi\)
−0.0885004 + 0.996076i \(0.528207\pi\)
\(384\) 1.36184e8 5.91739e8i 0.122735 0.533299i
\(385\) −3.18501e8 −0.284445
\(386\) 6.50882e7 + 2.94589e7i 0.0576032 + 0.0260712i
\(387\) 2.87600e7 6.94328e7i 0.0252232 0.0608943i
\(388\) 5.31140e8 + 6.04648e8i 0.461634 + 0.525522i
\(389\) −2.25776e8 + 9.35196e7i −0.194471 + 0.0805525i −0.477794 0.878472i \(-0.658563\pi\)
0.283323 + 0.959025i \(0.408563\pi\)
\(390\) −4.74031e8 + 4.44344e8i −0.404651 + 0.379309i
\(391\) 9.06447e8 9.06447e8i 0.766874 0.766874i
\(392\) −2.24074e9 + 6.82734e8i −1.87884 + 0.572467i
\(393\) −2.68365e8 2.68365e8i −0.223024 0.223024i
\(394\) −2.08953e9 6.75464e7i −1.72113 0.0556372i
\(395\) 4.04200e8 + 9.75826e8i 0.329995 + 0.796677i
\(396\) −1.62161e8 + 5.51947e7i −0.131224 + 0.0446646i
\(397\) 1.96265e9 + 8.12955e8i 1.57426 + 0.652078i 0.987490 0.157679i \(-0.0504010\pi\)
0.586766 + 0.809757i \(0.300401\pi\)
\(398\) 7.88577e8 2.97169e8i 0.626980 0.236272i
\(399\) 2.20438e9i 1.73732i
\(400\) −2.36497e8 3.07165e8i −0.184763 0.239972i
\(401\) 1.26185e9i 0.977239i −0.872497 0.488620i \(-0.837501\pi\)
0.872497 0.488620i \(-0.162499\pi\)
\(402\) 7.47374e7 + 1.98326e8i 0.0573782 + 0.152261i
\(403\) −1.70490e9 7.06193e8i −1.29757 0.537472i
\(404\) 4.61527e8 + 2.27130e8i 0.348227 + 0.171372i
\(405\) 8.17027e7 + 1.97248e8i 0.0611144 + 0.147543i
\(406\) 4.34211e7 1.34322e9i 0.0322003 0.996108i
\(407\) 6.73037e7 + 6.73037e7i 0.0494833 + 0.0494833i
\(408\) −1.00741e8 + 1.03591e9i −0.0734340 + 0.755111i
\(409\) −2.31797e8 + 2.31797e8i −0.167524 + 0.167524i −0.785890 0.618366i \(-0.787795\pi\)
0.618366 + 0.785890i \(0.287795\pi\)
\(410\) −1.35607e9 1.44667e9i −0.971712 1.03663i
\(411\) −5.86267e8 + 2.42840e8i −0.416533 + 0.172534i
\(412\) 7.82299e8 + 5.06302e7i 0.551103 + 0.0356672i
\(413\) 5.77372e8 1.39390e9i 0.403302 0.973657i
\(414\) 3.26240e8 7.20814e8i 0.225962 0.499254i
\(415\) −1.11113e9 −0.763124
\(416\) 1.44665e9 1.04115e9i 0.985229 0.709067i
\(417\) −6.67614e8 −0.450868
\(418\) 2.24653e8 4.96360e8i 0.150451 0.332415i
\(419\) −5.11329e8 + 1.23446e9i −0.339587 + 0.819835i 0.658168 + 0.752871i \(0.271331\pi\)
−0.997755 + 0.0669646i \(0.978669\pi\)
\(420\) −7.71414e7 + 1.19193e9i −0.0508060 + 0.785015i
\(421\) −2.50581e9 + 1.03794e9i −1.63667 + 0.677932i −0.995956 0.0898460i \(-0.971363\pi\)
−0.640716 + 0.767778i \(0.721363\pi\)
\(422\) 7.32213e8 + 7.81134e8i 0.474290 + 0.505978i
\(423\) −9.09148e8 + 9.09148e8i −0.584041 + 0.584041i
\(424\) 1.06874e8 8.79297e7i 0.0680915 0.0560216i
\(425\) 4.69856e8 + 4.69856e8i 0.296896 + 0.296896i
\(426\) 9.32671e6 2.88520e8i 0.00584514 0.180818i
\(427\) −6.60991e8 1.59577e9i −0.410864 0.991913i
\(428\) 8.33659e8 1.69400e9i 0.513967 1.04438i
\(429\) 1.98588e8 + 8.22577e7i 0.121437 + 0.0503009i
\(430\) 4.56729e7 + 1.21199e8i 0.0277025 + 0.0735124i
\(431\) 2.21100e9i 1.33021i −0.746751 0.665103i \(-0.768388\pi\)
0.746751 0.665103i \(-0.231612\pi\)
\(432\) 4.06070e8 + 1.50559e9i 0.242330 + 0.898491i
\(433\) 2.90608e9i 1.72028i −0.510054 0.860142i \(-0.670375\pi\)
0.510054 0.860142i \(-0.329625\pi\)
\(434\) −3.17450e9 + 1.19628e9i −1.86407 + 0.702458i
\(435\) −4.19518e8 1.73770e8i −0.244365 0.101219i
\(436\) 4.82367e8 + 1.41719e9i 0.278724 + 0.818887i
\(437\) 9.63035e8 + 2.32497e9i 0.552023 + 1.33270i
\(438\) 1.65657e9 + 5.35505e7i 0.942000 + 0.0304512i
\(439\) 6.82634e7 + 6.82634e7i 0.0385090 + 0.0385090i 0.726099 0.687590i \(-0.241331\pi\)
−0.687590 + 0.726099i \(0.741331\pi\)
\(440\) 1.38842e8 2.60525e8i 0.0777027 0.145803i
\(441\) 1.75232e9 1.75232e9i 0.972925 0.972925i
\(442\) −2.22894e9 + 2.08934e9i −1.22778 + 1.15089i
\(443\) −1.27243e9 + 5.27057e8i −0.695376 + 0.288034i −0.702238 0.711942i \(-0.747816\pi\)
0.00686186 + 0.999976i \(0.497816\pi\)
\(444\) 2.68172e8 2.35570e8i 0.145403 0.127726i
\(445\) 1.30071e8 3.14019e8i 0.0699714 0.168926i
\(446\) 2.41641e9 + 1.09367e9i 1.28973 + 0.583731i
\(447\) 1.12911e8 0.0597944
\(448\) 6.31320e8 3.21519e9i 0.331724 1.68940i
\(449\) 1.09074e9 0.568666 0.284333 0.958726i \(-0.408228\pi\)
0.284333 + 0.958726i \(0.408228\pi\)
\(450\) 3.73633e8 + 1.69106e8i 0.193287 + 0.0874815i
\(451\) −2.51037e8 + 6.06058e8i −0.128861 + 0.311097i
\(452\) 4.70112e8 4.12960e8i 0.239451 0.210341i
\(453\) 4.04853e8 1.67696e8i 0.204623 0.0847574i
\(454\) −1.13154e9 + 1.06067e9i −0.567510 + 0.531968i
\(455\) −2.47914e9 + 2.47914e9i −1.23385 + 1.23385i
\(456\) −1.80312e9 9.60938e8i −0.890529 0.474590i
\(457\) −1.55142e9 1.55142e9i −0.760364 0.760364i 0.216024 0.976388i \(-0.430691\pi\)
−0.976388 + 0.216024i \(0.930691\pi\)
\(458\) 2.33435e9 + 7.54602e7i 1.13537 + 0.0367019i
\(459\) −1.02288e9 2.46944e9i −0.493717 1.19194i
\(460\) 4.39361e8 + 1.29084e9i 0.210460 + 0.618328i
\(461\) −2.04800e9 8.48308e8i −0.973590 0.403274i −0.161542 0.986866i \(-0.551647\pi\)
−0.812047 + 0.583592i \(0.801647\pi\)
\(462\) 3.69767e8 1.39344e8i 0.174454 0.0657417i
\(463\) 4.42035e8i 0.206978i −0.994631 0.103489i \(-0.966999\pi\)
0.994631 0.103489i \(-0.0330006\pi\)
\(464\) 1.07979e9 + 6.21058e8i 0.501795 + 0.288615i
\(465\) 1.14623e9i 0.528672i
\(466\) −7.13027e8 1.89211e9i −0.326404 0.866156i
\(467\) 1.51207e7 + 6.26320e6i 0.00687010 + 0.00284569i 0.386116 0.922450i \(-0.373816\pi\)
−0.379246 + 0.925296i \(0.623816\pi\)
\(468\) −8.32601e8 + 1.69184e9i −0.375471 + 0.762957i
\(469\) 4.37661e8 + 1.05661e9i 0.195899 + 0.472943i
\(470\) 7.15914e7 2.21466e9i 0.0318067 0.983933i
\(471\) 6.16139e8 + 6.16139e8i 0.271710 + 0.271710i
\(472\) 8.88482e8 + 1.07991e9i 0.388912 + 0.472704i
\(473\) 3.02988e7 3.02988e7i 0.0131647 0.0131647i
\(474\) −8.96182e8 9.56058e8i −0.386520 0.412344i
\(475\) −1.20515e9 + 4.99189e8i −0.515956 + 0.213716i
\(476\) −3.62726e8 + 5.60456e9i −0.154154 + 2.38187i
\(477\) −5.60307e7 + 1.35270e8i −0.0236381 + 0.0570673i
\(478\) −3.24453e8 + 7.16866e8i −0.135880 + 0.300221i
\(479\) 2.17560e9 0.904491 0.452246 0.891893i \(-0.350623\pi\)
0.452246 + 0.891893i \(0.350623\pi\)
\(480\) −9.41338e8 5.82688e8i −0.388509 0.240487i
\(481\) 1.04775e9 0.429290
\(482\) 5.84759e8 1.29200e9i 0.237855 0.525530i
\(483\) −6.98461e8 + 1.68623e9i −0.282051 + 0.680931i
\(484\) 2.39169e9 + 1.54790e8i 0.958839 + 0.0620559i
\(485\) 1.35566e9 5.61532e8i 0.539578 0.223500i
\(486\) −1.79171e9 1.91141e9i −0.708010 0.755314i
\(487\) −2.79123e8 + 2.79123e8i −0.109508 + 0.109508i −0.759738 0.650230i \(-0.774673\pi\)
0.650230 + 0.759738i \(0.274673\pi\)
\(488\) 1.59344e9 + 1.54961e8i 0.620678 + 0.0603605i
\(489\) −1.19436e9 1.19436e9i −0.461907 0.461907i
\(490\) −1.37988e8 + 4.26862e9i −0.0529852 + 1.63909i
\(491\) −1.07017e8 2.58361e8i −0.0408006 0.0985013i 0.902166 0.431390i \(-0.141977\pi\)
−0.942966 + 0.332889i \(0.891977\pi\)
\(492\) 2.20725e9 + 1.08625e9i 0.835553 + 0.411198i
\(493\) −1.97261e9 8.17083e8i −0.741443 0.307116i
\(494\) −2.11491e9 5.61219e9i −0.789309 2.09454i
\(495\) 3.12316e8i 0.115738i
\(496\) 4.05309e8 3.11814e9i 0.149142 1.14739i
\(497\) 1.55771e9i 0.569166i
\(498\) 1.28997e9 4.86115e8i 0.468034 0.176375i
\(499\) 2.66046e8 + 1.10200e8i 0.0958528 + 0.0397035i 0.430095 0.902784i \(-0.358480\pi\)
−0.334242 + 0.942487i \(0.608480\pi\)
\(500\) −2.87839e9 + 9.79715e8i −1.02980 + 0.350514i
\(501\) −5.45821e8 1.31773e9i −0.193918 0.468159i
\(502\) 2.78250e9 + 8.99473e7i 0.981685 + 0.0317340i
\(503\) −6.24632e8 6.24632e8i −0.218845 0.218845i 0.589167 0.808011i \(-0.299456\pi\)
−0.808011 + 0.589167i \(0.799456\pi\)
\(504\) 1.01033e9 + 3.31591e9i 0.351524 + 1.15371i
\(505\) 6.63164e8 6.63164e8i 0.229140 0.229140i
\(506\) 3.29120e8 3.08508e8i 0.112935 0.105862i
\(507\) 7.02419e8 2.90951e8i 0.239369 0.0991500i
\(508\) −5.88817e8 6.70307e8i −0.199277 0.226856i
\(509\) −9.48631e6 + 2.29020e7i −0.00318849 + 0.00769769i −0.925466 0.378831i \(-0.876326\pi\)
0.922277 + 0.386529i \(0.126326\pi\)
\(510\) 1.72880e9 + 7.82454e8i 0.577097 + 0.261194i
\(511\) 8.94379e9 2.96516
\(512\) 2.35473e9 + 1.91797e9i 0.775347 + 0.631536i
\(513\) 5.24720e9 1.71600
\(514\) 2.92459e9 + 1.32367e9i 0.949935 + 0.429941i
\(515\) 5.46972e8 1.32051e9i 0.176457 0.426006i
\(516\) −1.06049e8 1.20726e8i −0.0339807 0.0386835i
\(517\) −6.77260e8 + 2.80530e8i −0.215545 + 0.0892818i
\(518\) 1.40527e9 1.31726e9i 0.444228 0.416407i
\(519\) −1.61606e9 + 1.61606e9i −0.507423 + 0.507423i
\(520\) −9.47155e8 3.10858e9i −0.295399 0.969505i
\(521\) 2.63756e9 + 2.63756e9i 0.817089 + 0.817089i 0.985685 0.168596i \(-0.0539232\pi\)
−0.168596 + 0.985685i \(0.553923\pi\)
\(522\) −1.31714e9 4.25779e7i −0.405307 0.0131020i
\(523\) 1.44182e8 + 3.48085e8i 0.0440711 + 0.106397i 0.944382 0.328850i \(-0.106661\pi\)
−0.900311 + 0.435247i \(0.856661\pi\)
\(524\) 1.79699e9 6.11640e8i 0.545614 0.185710i
\(525\) −8.74059e8 3.62047e8i −0.263623 0.109196i
\(526\) −4.48233e9 + 1.68913e9i −1.34293 + 0.506073i
\(527\) 5.38967e9i 1.60408i
\(528\) −4.72105e7 + 3.63203e8i −0.0139579 + 0.107382i
\(529\) 1.32120e9i 0.388039i
\(530\) −8.89807e7 2.36122e8i −0.0259615 0.0688924i
\(531\) −1.36683e9 5.66160e8i −0.396172 0.164100i
\(532\) −9.89237e9 4.86829e9i −2.84846 1.40180i
\(533\) 2.76339e9 + 6.67142e9i 0.790492 + 1.90842i
\(534\) −1.36245e7 + 4.21470e8i −0.00387191 + 0.119777i
\(535\) −2.43409e9 2.43409e9i −0.687223 0.687223i
\(536\) −1.05506e9 1.02604e8i −0.295938 0.0287798i
\(537\) −1.38720e9 + 1.38720e9i −0.386570 + 0.386570i
\(538\) −4.26857e9 4.55376e9i −1.18180 1.26076i
\(539\) 1.30538e9 5.40704e8i 0.359066 0.148730i
\(540\) 2.83721e9 + 1.83624e8i 0.775379 + 0.0501824i
\(541\) −1.61636e9 + 3.90224e9i −0.438883 + 1.05956i 0.537453 + 0.843294i \(0.319387\pi\)
−0.976335 + 0.216262i \(0.930613\pi\)
\(542\) −1.05961e9 + 2.34116e9i −0.285856 + 0.631587i
\(543\) −1.66806e9 −0.447109
\(544\) −4.42626e9 2.73985e9i −1.17880 0.729678i
\(545\) 2.72945e9 0.722250
\(546\) 1.79356e9 3.96280e9i 0.471566 1.04190i
\(547\) −4.83771e8 + 1.16793e9i −0.126382 + 0.305112i −0.974388 0.224874i \(-0.927803\pi\)
0.848006 + 0.529986i \(0.177803\pi\)
\(548\) 2.04983e8 3.16724e9i 0.0532090 0.822145i
\(549\) −1.56478e9 + 6.48155e8i −0.403600 + 0.167177i
\(550\) 1.59915e8 + 1.70599e8i 0.0409845 + 0.0437228i
\(551\) 2.96385e9 2.96385e9i 0.754789 0.754789i
\(552\) −1.07482e9 1.30639e9i −0.271987 0.330587i
\(553\) −5.00009e9 5.00009e9i −1.25730 1.25730i
\(554\) −2.10592e8 + 6.51461e9i −0.0526207 + 1.62781i
\(555\) −2.49049e8 6.01258e8i −0.0618386 0.149292i
\(556\) 1.47440e9 2.99599e9i 0.363793 0.739227i
\(557\) 2.63711e9 + 1.09233e9i 0.646600 + 0.267830i 0.681788 0.731550i \(-0.261203\pi\)
−0.0351876 + 0.999381i \(0.511203\pi\)
\(558\) 1.17305e9 + 3.11285e9i 0.285824 + 0.758471i
\(559\) 4.71677e8i 0.114210i
\(560\) −5.17854e9 2.97852e9i −1.24609 0.716707i
\(561\) 6.27792e8i 0.150122i
\(562\) −5.16985e9 + 1.94822e9i −1.22857 + 0.462978i
\(563\) −5.33627e8 2.21036e8i −0.126026 0.0522015i 0.318780 0.947829i \(-0.396727\pi\)
−0.444805 + 0.895627i \(0.646727\pi\)
\(564\) 8.85797e8 + 2.60246e9i 0.207901 + 0.610811i
\(565\) −4.36589e8 1.05402e9i −0.101837 0.245855i
\(566\) −6.13040e9 1.98172e8i −1.42112 0.0459393i
\(567\) −1.01069e9 1.01069e9i −0.232850 0.232850i
\(568\) 1.27416e9 + 6.79040e8i 0.291747 + 0.155481i
\(569\) −5.33677e9 + 5.33677e9i −1.21447 + 1.21447i −0.244926 + 0.969542i \(0.578764\pi\)
−0.969542 + 0.244926i \(0.921236\pi\)
\(570\) −2.71788e9 + 2.54766e9i −0.614707 + 0.576209i
\(571\) 6.36527e9 2.63658e9i 1.43084 0.592672i 0.473279 0.880913i \(-0.343070\pi\)
0.957558 + 0.288241i \(0.0930703\pi\)
\(572\) −8.07714e8 + 7.09519e8i −0.180456 + 0.158518i
\(573\) 2.63858e7 6.37010e7i 0.00585908 0.0141451i
\(574\) 1.20938e10 + 5.47367e9i 2.66915 + 1.20806i
\(575\) −1.08004e9 −0.236921
\(576\) −3.15275e9 6.19060e8i −0.687402 0.134975i
\(577\) −6.45903e9 −1.39975 −0.699877 0.714263i \(-0.746762\pi\)
−0.699877 + 0.714263i \(0.746762\pi\)
\(578\) 3.89954e9 + 1.76493e9i 0.839974 + 0.380172i
\(579\) −6.18451e7 + 1.49307e8i −0.0132413 + 0.0319673i
\(580\) 1.70630e9 1.49886e9i 0.363127 0.318981i
\(581\) 6.87250e9 2.84668e9i 1.45378 0.602175i
\(582\) −1.32819e9 + 1.24501e9i −0.279275 + 0.261784i
\(583\) −5.90286e7 + 5.90286e7i −0.0123374 + 0.0123374i
\(584\) −3.89880e9 + 7.31577e9i −0.810001 + 1.51990i
\(585\) 2.43100e9 + 2.43100e9i 0.502040 + 0.502040i
\(586\) 6.63761e8 + 2.14568e7i 0.136261 + 0.00440477i
\(587\) −1.92973e9 4.65878e9i −0.393789 0.950690i −0.989107 0.147200i \(-0.952974\pi\)
0.595318 0.803490i \(-0.297026\pi\)
\(588\) −1.70732e9 5.01607e9i −0.346333 1.01752i
\(589\) −9.77513e9 4.04899e9i −1.97115 0.816475i
\(590\) 2.38589e9 8.99101e8i 0.478264 0.180230i
\(591\) 4.72904e9i 0.942361i
\(592\) 4.64895e8 + 1.72370e9i 0.0920935 + 0.341456i
\(593\) 3.60623e8i 0.0710170i 0.999369 + 0.0355085i \(0.0113051\pi\)
−0.999369 + 0.0355085i \(0.988695\pi\)
\(594\) −3.31687e8 8.80177e8i −0.0649346 0.172313i
\(595\) 9.46040e9 + 3.91863e9i 1.84120 + 0.762649i
\(596\) −2.49360e8 + 5.06700e8i −0.0482465 + 0.0980368i
\(597\) 7.29484e8 + 1.76113e9i 0.140316 + 0.338752i
\(598\) 1.60439e8 4.96315e9i 0.0306800 0.949080i
\(599\) −1.05984e9 1.05984e9i −0.201486 0.201486i 0.599150 0.800636i \(-0.295505\pi\)
−0.800636 + 0.599150i \(0.795505\pi\)
\(600\) 6.77166e8 5.57132e8i 0.127987 0.105300i
\(601\) −5.71591e9 + 5.71591e9i −1.07405 + 1.07405i −0.0770212 + 0.997029i \(0.524541\pi\)
−0.997029 + 0.0770212i \(0.975459\pi\)
\(602\) −5.93005e8 6.32625e8i −0.110782 0.118184i
\(603\) 1.03609e9 4.29162e8i 0.192436 0.0797096i
\(604\) −1.41553e8 + 2.18717e9i −0.0261390 + 0.403880i
\(605\) 1.67223e9 4.03713e9i 0.307010 0.741189i
\(606\) −4.79774e8 + 1.06004e9i −0.0875754 + 0.193494i
\(607\) 3.60067e8 0.0653466 0.0326733 0.999466i \(-0.489598\pi\)
0.0326733 + 0.999466i \(0.489598\pi\)
\(608\) 8.29444e9 5.96949e9i 1.49666 1.07715i
\(609\) 3.03999e9 0.545395
\(610\) 1.20357e9 2.65925e9i 0.214693 0.474356i
\(611\) −3.08805e9 + 7.45521e9i −0.547696 + 1.32226i
\(612\) 5.49573e9 + 3.55682e8i 0.969159 + 0.0627238i
\(613\) −3.65011e9 + 1.51193e9i −0.640021 + 0.265105i −0.679004 0.734134i \(-0.737588\pi\)
0.0389830 + 0.999240i \(0.487588\pi\)
\(614\) −5.74395e9 6.12772e9i −1.00143 1.06834i
\(615\) 3.17158e9 3.17158e9i 0.549810 0.549810i
\(616\) −1.91300e8 + 1.96710e9i −0.0329747 + 0.339074i
\(617\) 4.88626e9 + 4.88626e9i 0.837487 + 0.837487i 0.988528 0.151040i \(-0.0482623\pi\)
−0.151040 + 0.988528i \(0.548262\pi\)
\(618\) −5.72933e7 + 1.77235e9i −0.00976437 + 0.302058i
\(619\) −2.51267e8 6.06611e8i −0.0425812 0.102800i 0.901158 0.433491i \(-0.142718\pi\)
−0.943739 + 0.330691i \(0.892718\pi\)
\(620\) −5.14382e9 2.53141e9i −0.866791 0.426571i
\(621\) 4.01384e9 + 1.66258e9i 0.672572 + 0.278589i
\(622\) 3.77805e9 + 1.00256e10i 0.629508 + 1.67048i
\(623\) 2.27550e9i 0.377024i
\(624\) 2.45961e9 + 3.19456e9i 0.405247 + 0.526338i
\(625\) 3.69516e9i 0.605416i
\(626\) 9.88043e9 3.72336e9i 1.60978 0.606631i
\(627\) 1.13861e9 + 4.71628e8i 0.184476 + 0.0764123i
\(628\) −4.12571e9 + 1.40426e9i −0.664721 + 0.226251i
\(629\) −1.17105e9 2.82717e9i −0.187629 0.452976i
\(630\) 6.31683e9 + 2.04198e8i 1.00648 + 0.0325357i
\(631\) −1.31736e9 1.31736e9i −0.208737 0.208737i 0.594993 0.803731i \(-0.297155\pi\)
−0.803731 + 0.594993i \(0.797155\pi\)
\(632\) 6.26959e9 1.91029e9i 0.987938 0.301015i
\(633\) −1.71251e9 + 1.71251e9i −0.268361 + 0.268361i
\(634\) 8.19149e9 7.67847e9i 1.27659 1.19664i
\(635\) −1.50287e9 + 6.22509e8i −0.232924 + 0.0964801i
\(636\) 2.06606e8 + 2.35200e8i 0.0318451 + 0.0362524i
\(637\) 5.95202e9 1.43694e10i 0.912381 2.20268i
\(638\) −6.84515e8 3.09811e8i −0.104354 0.0472307i
\(639\) −1.52746e9 −0.231588
\(640\) 4.69379e9 2.93750e9i 0.707772 0.442943i
\(641\) 2.59445e9 0.389084 0.194542 0.980894i \(-0.437678\pi\)
0.194542 + 0.980894i \(0.437678\pi\)
\(642\) 3.89078e9 + 1.76097e9i 0.580316 + 0.262651i
\(643\) −5.48985e8 + 1.32537e9i −0.0814370 + 0.196606i −0.959353 0.282208i \(-0.908933\pi\)
0.877916 + 0.478814i \(0.158933\pi\)
\(644\) −6.02462e9 6.85841e9i −0.888851 1.01187i
\(645\) −2.70675e8 + 1.12117e8i −0.0397181 + 0.0164518i
\(646\) −1.27797e10 + 1.19793e10i −1.86512 + 1.74831i
\(647\) 5.51378e8 5.51378e8i 0.0800358 0.0800358i −0.665956 0.745991i \(-0.731976\pi\)
0.745991 + 0.665956i \(0.231976\pi\)
\(648\) 1.26730e9 3.86134e8i 0.182964 0.0557475i
\(649\) −5.96451e8 5.96451e8i −0.0856482 0.0856482i
\(650\) 2.57264e9 + 8.31635e7i 0.367437 + 0.0118778i
\(651\) −2.93662e9 7.08962e9i −0.417171 1.00714i
\(652\) 7.99752e9 2.72211e9i 1.13003 0.384626i
\(653\) −1.34674e9 5.57838e8i −0.189272 0.0783992i 0.286034 0.958219i \(-0.407663\pi\)
−0.475307 + 0.879820i \(0.657663\pi\)
\(654\) −3.16878e9 + 1.19413e9i −0.442966 + 0.166928i
\(655\) 3.46094e9i 0.481226i
\(656\) −9.74928e9 + 7.50633e9i −1.34837 + 1.03816i
\(657\) 8.77011e9i 1.20650i
\(658\) 5.23112e9 + 1.38815e10i 0.715821 + 1.89953i
\(659\) −6.84507e9 2.83532e9i −0.931707 0.385925i −0.135381 0.990794i \(-0.543226\pi\)
−0.796326 + 0.604868i \(0.793226\pi\)
\(660\) 5.99154e8 + 2.94859e8i 0.0811213 + 0.0399219i
\(661\) −1.12243e8 2.70979e8i −0.0151166 0.0364947i 0.916141 0.400856i \(-0.131287\pi\)
−0.931258 + 0.364361i \(0.881287\pi\)
\(662\) 2.96105e8 9.15993e9i 0.0396682 1.22713i
\(663\) −4.88658e9 4.88658e9i −0.651190 0.651190i
\(664\) −6.67369e8 + 6.86245e9i −0.0884662 + 0.909685i
\(665\) −1.42143e10 + 1.42143e10i −1.87434 + 1.87434i
\(666\) −1.29168e9 1.37798e9i −0.169432 0.180752i
\(667\) 3.20629e9 1.32809e9i 0.418372 0.173295i
\(668\) 7.11886e9 + 4.60731e8i 0.924044 + 0.0598040i
\(669\) −2.29600e9 + 5.54304e9i −0.296470 + 0.715743i
\(670\) −7.96921e8 + 1.76076e9i −0.102366 + 0.226172i
\(671\) −9.65672e8 −0.123396
\(672\) 7.31517e9 + 1.19234e9i 0.929891 + 0.151568i
\(673\) −5.35245e9 −0.676862 −0.338431 0.940991i \(-0.609896\pi\)
−0.338431 + 0.940991i \(0.609896\pi\)
\(674\) 6.85750e8 1.51514e9i 0.0862693 0.190608i
\(675\) −8.61800e8 + 2.08057e9i −0.107856 + 0.260387i
\(676\) −2.45594e8 + 3.79473e9i −0.0305777 + 0.472463i
\(677\) −1.02357e9 + 4.23978e8i −0.126782 + 0.0525150i −0.445173 0.895445i \(-0.646858\pi\)
0.318390 + 0.947960i \(0.396858\pi\)
\(678\) 9.67994e8 + 1.03267e9i 0.119280 + 0.127250i
\(679\) −6.94634e9 + 6.94634e9i −0.851553 + 0.851553i
\(680\) −7.32933e9 + 6.03013e9i −0.893888 + 0.735437i
\(681\) −2.48071e9 2.48071e9i −0.300996 0.300996i
\(682\) −6.12788e7 + 1.89565e9i −0.00739716 + 0.228830i
\(683\) 3.77606e9 + 9.11621e9i 0.453488 + 1.09482i 0.970987 + 0.239134i \(0.0768634\pi\)
−0.517498 + 0.855684i \(0.673137\pi\)
\(684\) −4.77376e9 + 9.70027e9i −0.570379 + 1.15901i
\(685\) −5.34624e9 2.21448e9i −0.635523 0.263242i
\(686\) −4.94924e9 1.31335e10i −0.585335 1.55326i
\(687\) 5.28310e9i 0.621642i
\(688\) 7.75974e8 2.09287e8i 0.0908422 0.0245009i
\(689\) 9.18928e8i 0.107032i
\(690\) −2.88627e9 + 1.08767e9i −0.334476 + 0.126044i
\(691\) 1.11217e10 + 4.60675e9i 1.28232 + 0.531155i 0.916688 0.399604i \(-0.130852\pi\)
0.365634 + 0.930759i \(0.380852\pi\)
\(692\) −3.68321e9 1.08212e10i −0.422527 1.24138i
\(693\) −8.00149e8 1.93173e9i −0.0913281 0.220486i
\(694\) 1.89109e9 + 6.11316e7i 0.214761 + 0.00694237i
\(695\) −4.30490e9 4.30490e9i −0.486426 0.486426i
\(696\) −1.32520e9 + 2.48663e9i −0.148987 + 0.279562i
\(697\) 1.49131e10 1.49131e10i 1.66821 1.66821i
\(698\) 4.01456e9 3.76314e9i 0.446832 0.418848i
\(699\) 4.22566e9 1.75032e9i 0.467977 0.193842i
\(700\) 3.55505e9 3.12286e9i 0.391744 0.344119i
\(701\) 1.10530e9 2.66842e9i 0.121190 0.292578i −0.851629 0.524145i \(-0.824385\pi\)
0.972819 + 0.231567i \(0.0743852\pi\)
\(702\) −9.43286e9 4.26931e9i −1.02911 0.465777i
\(703\) 6.00733e9 0.652135
\(704\) −1.52565e9 1.01398e9i −0.164797 0.109528i
\(705\) 5.01224e9 0.538729
\(706\) −3.95431e9 1.78972e9i −0.422917 0.191412i
\(707\) −2.40277e9 + 5.80079e9i −0.255708 + 0.617333i
\(708\) −2.37656e9 + 2.08764e9i −0.251671 + 0.221075i
\(709\) 9.19053e9 3.80684e9i 0.968453 0.401146i 0.158317 0.987388i \(-0.449393\pi\)
0.810136 + 0.586242i \(0.199393\pi\)
\(710\) 1.92057e9 1.80029e9i 0.201384 0.188772i
\(711\) −4.90300e9 + 4.90300e9i −0.511585 + 0.511585i
\(712\) −1.86130e9 9.91943e8i −0.193257 0.102993i
\(713\) −6.19453e9 6.19453e9i −0.640022 0.640022i
\(714\) −1.26975e10 4.10462e8i −1.30550 0.0422016i
\(715\) 7.50118e8 + 1.81094e9i 0.0767465 + 0.185282i
\(716\) −3.16161e9 9.28876e9i −0.321894 0.945719i
\(717\) −1.64443e9 6.81147e8i −0.166609 0.0690118i
\(718\) −7.69118e9 + 2.89836e9i −0.775457 + 0.292224i
\(719\) 8.42750e9i 0.845567i −0.906231 0.422783i \(-0.861053\pi\)
0.906231 0.422783i \(-0.138947\pi\)
\(720\) −2.92068e9 + 5.07798e9i −0.291621 + 0.507022i
\(721\) 9.56889e9i 0.950798i
\(722\) −8.55973e9 2.27144e10i −0.846408 2.24606i
\(723\) 2.96374e9 + 1.22762e9i 0.291646 + 0.120804i
\(724\) 3.68386e9 7.48560e9i 0.360760 0.733064i
\(725\) 6.88415e8 + 1.66198e9i 0.0670914 + 0.161973i
\(726\) −1.75160e8 + 5.41854e9i −0.0169886 + 0.525538i
\(727\) −1.75922e9 1.75922e9i −0.169805 0.169805i 0.617089 0.786893i \(-0.288312\pi\)
−0.786893 + 0.617089i \(0.788312\pi\)
\(728\) 1.38224e10 + 1.68005e10i 1.32778 + 1.61385i
\(729\) 2.77572e9 2.77572e9i 0.265356 0.265356i
\(730\) 1.03366e10 + 1.10272e10i 0.983439 + 1.04914i
\(731\) −1.27274e9 + 5.27185e8i −0.120511 + 0.0499174i
\(732\) −2.33887e8 + 3.61384e9i −0.0220403 + 0.340549i
\(733\) −4.52370e9 + 1.09212e10i −0.424258 + 1.02425i 0.556820 + 0.830633i \(0.312021\pi\)
−0.981078 + 0.193615i \(0.937979\pi\)
\(734\) −4.67234e8 + 1.03233e9i −0.0436112 + 0.0963570i
\(735\) −9.66077e9 −0.897442
\(736\) 8.23626e9 1.93824e9i 0.761478 0.179199i
\(737\) 6.39399e8 0.0588350
\(738\) 5.36737e9 1.18590e10i 0.491546 1.08605i
\(739\) 6.55112e9 1.58158e10i 0.597118 1.44157i −0.279387 0.960178i \(-0.590131\pi\)
0.876505 0.481392i \(-0.159869\pi\)
\(740\) 3.24822e9 + 2.10224e8i 0.294669 + 0.0190709i
\(741\) 1.25337e10 5.19164e9i 1.13166 0.468749i
\(742\) 1.15530e9 + 1.23249e9i 0.103820 + 0.110757i
\(743\) −1.32616e10 + 1.32616e10i −1.18614 + 1.18614i −0.208013 + 0.978126i \(0.566700\pi\)
−0.978126 + 0.208013i \(0.933300\pi\)
\(744\) 7.07925e9 + 6.88452e8i 0.630205 + 0.0612870i
\(745\) 7.28072e8 + 7.28072e8i 0.0645101 + 0.0645101i
\(746\) −2.11546e8 + 6.54412e9i −0.0186560 + 0.577119i
\(747\) −2.79140e9 6.73904e9i −0.245019 0.591529i
\(748\) 2.81728e9 + 1.38646e9i 0.246135 + 0.121130i
\(749\) 2.12913e10 + 8.81915e9i 1.85147 + 0.766903i
\(750\) −2.42535e9 6.43598e9i −0.209923 0.557058i
\(751\) 7.70277e9i 0.663601i 0.943350 + 0.331801i \(0.107656\pi\)
−0.943350 + 0.331801i \(0.892344\pi\)
\(752\) −1.36350e10 1.77234e9i −1.16921 0.151979i
\(753\) 6.29736e9i 0.537497i
\(754\) −7.73959e9 + 2.91660e9i −0.657534 + 0.247786i
\(755\) 3.69190e9 + 1.52924e9i 0.312202 + 0.129318i
\(756\) −1.80191e10 + 6.13314e9i −1.51672 + 0.516246i
\(757\) 3.75960e9 + 9.07647e9i 0.314997 + 0.760469i 0.999505 + 0.0314639i \(0.0100169\pi\)
−0.684508 + 0.729005i \(0.739983\pi\)
\(758\) −1.25945e10 4.07130e8i −1.05036 0.0339540i
\(759\) 7.21542e8 + 7.21542e8i 0.0598984 + 0.0598984i
\(760\) −5.43056e9 1.78232e10i −0.448742 1.47278i
\(761\) 1.33785e10 1.33785e10i 1.10042 1.10042i 0.106064 0.994359i \(-0.466175\pi\)
0.994359 0.106064i \(-0.0338248\pi\)
\(762\) 1.47243e9 1.38021e9i 0.120557 0.113006i
\(763\) −1.68821e10 + 6.99280e9i −1.37591 + 0.569922i
\(764\) 2.27592e8 + 2.59090e8i 0.0184642 + 0.0210196i
\(765\) 3.84253e9 9.27669e9i 0.310315 0.749166i
\(766\) 2.00590e9 + 9.07871e8i 0.161254 + 0.0729833i
\(767\) −9.28526e9 −0.743037
\(768\) −4.16415e9 + 5.46384e9i −0.331712 + 0.435245i
\(769\) 1.22117e10 0.968352 0.484176 0.874971i \(-0.339119\pi\)
0.484176 + 0.874971i \(0.339119\pi\)
\(770\) 3.28285e9 + 1.48582e9i 0.259139 + 0.117286i
\(771\) −2.77887e9 + 6.70878e9i −0.218362 + 0.527173i
\(772\) −5.33448e8 6.07276e8i −0.0417284 0.0475035i
\(773\) 1.46718e8 6.07727e7i 0.0114250 0.00473239i −0.376964 0.926228i \(-0.623032\pi\)
0.388389 + 0.921496i \(0.373032\pi\)
\(774\) −6.20340e8 + 5.81489e8i −0.0480880 + 0.0450763i
\(775\) 3.21093e9 3.21093e9i 0.247785 0.247785i
\(776\) −2.65385e9 8.70998e9i −0.203873 0.669115i
\(777\) 3.08082e9 + 3.08082e9i 0.235610 + 0.235610i
\(778\) 2.76338e9 + 8.93293e7i 0.210384 + 0.00680089i
\(779\) 1.58440e10 + 3.82509e10i 1.20084 + 2.89908i
\(780\) 6.95879e9 2.36856e9i 0.525052 0.178712i
\(781\) −8.04592e8 3.33273e8i −0.0604362 0.0250335i
\(782\) −1.35715e10 + 5.11430e9i −1.01485 + 0.382440i
\(783\) 7.23624e9i 0.538700i
\(784\) 2.62807e10 + 3.41607e9i 1.94774 + 0.253175i
\(785\) 7.94596e9i 0.586277i
\(786\) 1.51415e9 + 4.01801e9i 0.111222 + 0.295143i
\(787\) −8.34857e9 3.45809e9i −0.610521 0.252886i 0.0559301 0.998435i \(-0.482188\pi\)
−0.666451 + 0.745549i \(0.732188\pi\)
\(788\) 2.12221e10 + 1.04439e10i 1.54506 + 0.760365i
\(789\) −4.14644e9 1.00104e10i −0.300543 0.725574i
\(790\) 3.86090e8 1.19436e10i 0.0278608 0.861867i
\(791\) 5.40076e9 + 5.40076e9i 0.388005 + 0.388005i
\(792\) 1.92890e9 + 1.87585e8i 0.137966 + 0.0134171i
\(793\) −7.51656e9 + 7.51656e9i −0.535258 + 0.535258i
\(794\) −1.64369e10 1.75350e10i −1.16533 1.24318i
\(795\) 5.27332e8 2.18428e8i 0.0372220 0.0154178i
\(796\) −9.51429e9 6.15763e8i −0.668622 0.0432731i
\(797\) 1.08593e10 2.62168e10i 0.759800 1.83432i 0.268678 0.963230i \(-0.413413\pi\)
0.491123 0.871090i \(-0.336587\pi\)
\(798\) 1.02835e10 2.27209e10i 0.716357 1.58276i
\(799\) 2.35680e10 1.63459
\(800\) 1.00469e9 + 4.26926e9i 0.0693770 + 0.294807i
\(801\) 2.23131e9 0.153408
\(802\) −5.88654e9 + 1.30060e10i −0.402948 + 0.890297i
\(803\) 1.91353e9 4.61967e9i 0.130416 0.314852i
\(804\) 1.54863e8 2.39283e9i 0.0105088 0.162374i
\(805\) −1.53770e10 + 6.36935e9i −1.03893 + 0.430338i
\(806\) 1.42783e10 + 1.52322e10i 0.960513 + 1.02469i
\(807\) 9.98337e9 9.98337e9i 0.668682 0.668682i
\(808\) −3.69747e9 4.49409e9i −0.246584 0.299711i
\(809\) 2.45438e9 + 2.45438e9i 0.162975 + 0.162975i 0.783883 0.620908i \(-0.213236\pi\)
−0.620908 + 0.783883i \(0.713236\pi\)
\(810\) 7.80419e7 2.41421e9i 0.00515977 0.159616i
\(811\) −2.81790e9 6.80302e9i −0.185504 0.447846i 0.803581 0.595196i \(-0.202926\pi\)
−0.989084 + 0.147350i \(0.952926\pi\)
\(812\) −6.71371e9 + 1.36422e10i −0.440064 + 0.894210i
\(813\) −5.37043e9 2.22450e9i −0.350503 0.145183i
\(814\) −3.79737e8 1.00768e9i −0.0246773 0.0654845i
\(815\) 1.54029e10i 0.996671i
\(816\) 5.87089e9 1.02073e10i 0.378258 0.657651i
\(817\) 2.70438e9i 0.173496i
\(818\) 3.47051e9 1.30783e9i 0.221696 0.0835442i
\(819\) −2.12643e10 8.80795e9i −1.35256 0.560249i
\(820\) 7.22846e9 + 2.12371e10i 0.457823 + 1.34508i
\(821\) −3.18874e9 7.69830e9i −0.201103 0.485505i 0.790866 0.611990i \(-0.209631\pi\)
−0.991969 + 0.126484i \(0.959631\pi\)
\(822\) 7.17560e9 + 2.31959e8i 0.450616 + 0.0145667i
\(823\) 1.12529e10 + 1.12529e10i 0.703664 + 0.703664i 0.965195 0.261531i \(-0.0842273\pi\)
−0.261531 + 0.965195i \(0.584227\pi\)
\(824\) −7.82709e9 4.17129e9i −0.487366 0.259732i
\(825\) −3.74011e8 + 3.74011e8i −0.0231897 + 0.0231897i
\(826\) −1.24536e10 + 1.16737e10i −0.768893 + 0.720739i
\(827\) 1.53316e10 6.35055e9i 0.942579 0.390429i 0.142142 0.989846i \(-0.454601\pi\)
0.800437 + 0.599417i \(0.204601\pi\)
\(828\) −6.72522e9 + 5.90763e9i −0.411719 + 0.361665i
\(829\) −5.28314e9 + 1.27546e10i −0.322071 + 0.777547i 0.677063 + 0.735925i \(0.263252\pi\)
−0.999133 + 0.0416219i \(0.986748\pi\)
\(830\) 1.14526e10 + 5.18343e9i 0.695231 + 0.314661i
\(831\) −1.47439e10 −0.891268
\(832\) −1.97679e10 + 3.98266e9i −1.18995 + 0.239741i
\(833\) −4.54258e10 −2.72299
\(834\) 6.88121e9 + 3.11443e9i 0.410756 + 0.185908i
\(835\) 4.97740e9 1.20165e10i 0.295869 0.714292i
\(836\) −4.63106e9 + 4.06806e9i −0.274131 + 0.240805i
\(837\) −1.68758e10 + 6.99018e9i −0.994776 + 0.412050i
\(838\) 1.10291e10 1.03384e10i 0.647420 0.606874i
\(839\) 1.80748e10 1.80748e10i 1.05659 1.05659i 0.0582924 0.998300i \(-0.481434\pi\)
0.998300 0.0582924i \(-0.0185656\pi\)
\(840\) 6.35549e9 1.19255e10i 0.369974 0.694226i
\(841\) 8.11016e9 + 8.11016e9i 0.470157 + 0.470157i
\(842\) 3.06699e10 + 9.91436e8i 1.77060 + 0.0572364i
\(843\) −4.78244e9 1.15458e10i −0.274950 0.663787i
\(844\) −3.90304e9 1.14671e10i −0.223462 0.656529i
\(845\) 6.40544e9 + 2.65322e9i 0.365217 + 0.151278i
\(846\) 1.36119e10 5.12954e9i 0.772900 0.291261i
\(847\) 2.92546e10i 1.65425i
\(848\) −1.51176e9 + 4.07735e8i −0.0851331 + 0.0229611i
\(849\) 1.38744e10i 0.778101i
\(850\) −2.65100e9 7.03478e9i −0.148062 0.392902i
\(851\) 4.59529e9 + 1.90343e9i 0.255599 + 0.105873i
\(852\) −1.44208e9 + 2.93031e9i −0.0798825 + 0.162321i
\(853\) −3.35058e9 8.08901e9i −0.184841 0.446245i 0.804112 0.594478i \(-0.202641\pi\)
−0.988952 + 0.148233i \(0.952641\pi\)
\(854\) −6.31374e8 + 1.95314e10i −0.0346884 + 1.07308i
\(855\) 1.39382e10 + 1.39382e10i 0.762651 + 0.762651i
\(856\) −1.64952e10 + 1.35712e10i −0.898874 + 0.739540i
\(857\) 1.09220e10 1.09220e10i 0.592748 0.592748i −0.345625 0.938373i \(-0.612333\pi\)
0.938373 + 0.345625i \(0.112333\pi\)
\(858\) −1.66314e9 1.77426e9i −0.0898925 0.0958984i
\(859\) −1.38229e10 + 5.72565e9i −0.744088 + 0.308211i −0.722327 0.691552i \(-0.756927\pi\)
−0.0217614 + 0.999763i \(0.506927\pi\)
\(860\) 9.46388e7 1.46229e9i 0.00507370 0.0783949i
\(861\) −1.14912e10 + 2.77423e10i −0.613558 + 1.48126i
\(862\) −1.03144e10 + 2.27892e10i −0.548489 + 1.21186i
\(863\) −1.43038e10 −0.757552 −0.378776 0.925488i \(-0.623655\pi\)
−0.378776 + 0.925488i \(0.623655\pi\)
\(864\) 2.83818e9 1.74127e10i 0.149707 0.918476i
\(865\) −2.08413e10 −1.09488
\(866\) −1.35569e10 + 2.99535e10i −0.709331 + 1.56724i
\(867\) −3.70524e9 + 8.94523e9i −0.193085 + 0.466149i
\(868\) 3.83008e10 + 2.47882e9i 1.98787 + 0.128655i
\(869\) −3.65244e9 + 1.51289e9i −0.188805 + 0.0782056i
\(870\) 3.51340e9 + 3.74814e9i 0.180888 + 0.192974i
\(871\) 4.97693e9 4.97693e9i 0.255210 0.255210i
\(872\) 1.63937e9 1.68574e10i 0.0837278 0.860961i
\(873\) 6.81145e9 + 6.81145e9i 0.346489 + 0.346489i
\(874\) 9.19885e8 2.84564e10i 0.0466062 1.44175i
\(875\) −1.42028e10 3.42886e10i −0.716713 1.73030i
\(876\) −1.68247e10 8.27990e9i −0.845637 0.416160i
\(877\) −1.89585e10 7.85286e9i −0.949084 0.393124i −0.146198 0.989255i \(-0.546704\pi\)
−0.802887 + 0.596132i \(0.796704\pi\)
\(878\) −3.85152e8 1.02205e9i −0.0192044 0.0509615i
\(879\) 1.50223e9i 0.0746062i
\(880\) −2.64642e9 + 2.03758e9i −0.130909 + 0.100792i
\(881\) 2.56384e10i 1.26321i −0.775291 0.631605i \(-0.782397\pi\)
0.775291 0.631605i \(-0.217603\pi\)
\(882\) −2.62361e10 + 9.88686e9i −1.28754 + 0.485197i
\(883\) −3.32299e10 1.37643e10i −1.62430 0.672807i −0.629724 0.776819i \(-0.716832\pi\)
−0.994576 + 0.104012i \(0.966832\pi\)
\(884\) 3.27208e10 1.11372e10i 1.59309 0.542240i
\(885\) 2.20710e9 + 5.32840e9i 0.107034 + 0.258402i
\(886\) 1.55738e10 + 5.03441e8i 0.752277 + 0.0243182i
\(887\) −7.22220e7 7.22220e7i −0.00347485 0.00347485i 0.705367 0.708842i \(-0.250782\pi\)
−0.708842 + 0.705367i \(0.750782\pi\)
\(888\) −3.86303e9 + 1.17703e9i −0.185133 + 0.0564082i
\(889\) 7.70065e9 7.70065e9i 0.367596 0.367596i
\(890\) −2.80557e9 + 2.62986e9i −0.133400 + 0.125046i
\(891\) −7.38282e8 + 3.05806e8i −0.0349664 + 0.0144835i
\(892\) −1.98043e10 2.25452e10i −0.934293 1.06360i
\(893\) −1.77055e10 + 4.27448e10i −0.832007 + 2.00864i
\(894\) −1.16379e9 5.26733e8i −0.0544747 0.0246552i
\(895\) −1.78898e10 −0.834114
\(896\) −2.15060e10 + 3.01943e10i −0.998809 + 1.40232i
\(897\) 1.12326e10 0.519646
\(898\) −1.12424e10 5.08830e9i −0.518073 0.234480i
\(899\) −5.58383e9 + 1.34806e10i −0.256315 + 0.618798i
\(900\) −3.06222e9 3.48602e9i −0.140019 0.159397i
\(901\) 2.47956e9 1.02707e9i 0.112938 0.0467803i
\(902\) 5.41476e9 5.07564e9i 0.245672 0.230286i
\(903\) 1.38693e9 1.38693e9i 0.0626825 0.0626825i
\(904\) −6.77198e9 + 2.06336e9i −0.304878 + 0.0928936i
\(905\) −1.07560e10 1.07560e10i −0.482370 0.482370i
\(906\) −4.95519e9 1.60182e8i −0.221366 0.00715590i
\(907\) 7.29680e9 + 1.76160e10i 0.324718 + 0.783939i 0.998967 + 0.0454351i \(0.0144674\pi\)
−0.674249 + 0.738504i \(0.735533\pi\)
\(908\) 1.66110e10 5.65387e9i 0.736368 0.250637i
\(909\) 5.68815e9 + 2.35611e9i 0.251187 + 0.104045i
\(910\) 3.71181e10 1.39876e10i 1.63283 0.615318i
\(911\) 3.45790e10i 1.51530i −0.652662 0.757649i \(-0.726348\pi\)
0.652662 0.757649i \(-0.273652\pi\)
\(912\) 1.41023e10 + 1.83161e10i 0.615612 + 0.799562i
\(913\) 4.15885e9i 0.180853i
\(914\) 8.75331e9 + 2.32281e10i 0.379193 + 1.00624i
\(915\) 6.10010e9 + 2.52674e9i 0.263247 + 0.109040i
\(916\) −2.37085e10 1.16675e10i −1.01922 0.501586i
\(917\) 8.86685e9 + 2.14065e10i 0.379732 + 0.916753i
\(918\) −9.77044e8 + 3.02246e10i −0.0416836 + 1.28947i
\(919\) 2.04191e10 + 2.04191e10i 0.867824 + 0.867824i 0.992231 0.124407i \(-0.0397028\pi\)
−0.124407 + 0.992231i \(0.539703\pi\)
\(920\) 1.49321e9 1.53545e10i 0.0632215 0.650097i
\(921\) 1.34340e10 1.34340e10i 0.566627 0.566627i
\(922\) 1.71517e10 + 1.82976e10i 0.720689 + 0.768839i
\(923\) −8.85687e9 + 3.66863e9i −0.370744 + 0.153567i
\(924\) −4.46129e9 2.88734e8i −0.186041 0.0120405i
\(925\) −9.86644e8 + 2.38197e9i −0.0409887 + 0.0989555i
\(926\) −2.06210e9 + 4.55613e9i −0.0853438 + 0.188564i
\(927\) 9.38307e9 0.386871
\(928\) −8.23233e9 1.14386e10i −0.338146 0.469845i
\(929\) 8.92640e9 0.365276 0.182638 0.983180i \(-0.441536\pi\)
0.182638 + 0.983180i \(0.441536\pi\)
\(930\) 5.34718e9 1.18144e10i 0.217989 0.481637i
\(931\) 3.41262e10 8.23878e10i 1.38600 3.34610i
\(932\) −1.47746e9 + 2.28286e10i −0.0597806 + 0.923684i
\(933\) −2.23901e10 + 9.27428e9i −0.902547 + 0.373847i
\(934\) −1.26634e8 1.35094e8i −0.00508551 0.00542529i
\(935\) 4.04812e9 4.04812e9i 0.161962 0.161962i
\(936\) 1.64742e10 1.35540e10i 0.656659 0.540260i
\(937\) 1.41226e10 + 1.41226e10i 0.560824 + 0.560824i 0.929541 0.368718i \(-0.120203\pi\)
−0.368718 + 0.929541i \(0.620203\pi\)
\(938\) 4.18051e8 1.29323e10i 0.0165394 0.511642i
\(939\) 9.14003e9 + 2.20660e10i 0.360262 + 0.869748i
\(940\) −1.10694e10 + 2.24929e10i −0.434685 + 0.883280i
\(941\) 1.88075e10 + 7.79032e9i 0.735813 + 0.304784i 0.718938 0.695074i \(-0.244628\pi\)
0.0168748 + 0.999858i \(0.494628\pi\)
\(942\) −3.47634e9 9.22494e9i −0.135502 0.359572i
\(943\) 3.42802e10i 1.33123i
\(944\) −4.11994e9 1.52756e10i −0.159400 0.591010i
\(945\) 3.47041e10i 1.33773i
\(946\) −4.53639e8 + 1.70950e8i −0.0174217 + 0.00656523i
\(947\) 1.74498e10 + 7.22794e9i 0.667675 + 0.276560i 0.690664 0.723175i \(-0.257318\pi\)
−0.0229889 + 0.999736i \(0.507318\pi\)
\(948\) 4.77707e9 + 1.40350e10i 0.182109 + 0.535034i
\(949\) −2.10639e10 5.08528e10i −0.800033 1.93145i
\(950\) 1.47504e10 + 4.76822e8i 0.558175 + 0.0180436i
\(951\) 1.79585e10 + 1.79585e10i 0.677077 + 0.677077i
\(952\) 2.98841e10 5.60750e10i 1.12256 2.10640i
\(953\) −1.32324e10 + 1.32324e10i −0.495236 + 0.495236i −0.909951 0.414715i \(-0.863881\pi\)
0.414715 + 0.909951i \(0.363881\pi\)
\(954\) 1.20856e9 1.13287e9i 0.0450658 0.0422435i
\(955\) 5.80897e8 2.40615e8i 0.0215818 0.00893947i
\(956\) 6.68839e9 5.87527e9i 0.247582 0.217483i
\(957\) 6.50407e8 1.57022e9i 0.0239880 0.0579121i
\(958\) −2.24242e10 1.01492e10i −0.824021 0.372952i
\(959\) 3.87409e10 1.41842
\(960\) 6.98427e9 + 1.03972e10i 0.254784 + 0.379287i
\(961\) 9.31964e9 0.338741
\(962\) −1.07993e10 4.88778e9i −0.391097 0.177010i
\(963\) 8.64789e9 2.08779e10i 0.312046 0.753345i
\(964\) −1.20544e10 + 1.05889e10i −0.433387 + 0.380700i
\(965\) −1.36155e9 + 5.63973e8i −0.0487740 + 0.0202028i
\(966\) 1.50655e10 1.41220e10i 0.537728 0.504052i
\(967\) 2.86986e10 2.86986e10i 1.02063 1.02063i 0.0208468 0.999783i \(-0.493364\pi\)
0.999783 0.0208468i \(-0.00663623\pi\)
\(968\) −2.39294e10 1.27527e10i −0.847947 0.451897i
\(969\) −2.80174e10 2.80174e10i −0.989224 0.989224i
\(970\) −1.65925e10 5.36372e8i −0.583730 0.0188697i
\(971\) −1.28933e9 3.11271e9i −0.0451956 0.109112i 0.899670 0.436572i \(-0.143807\pi\)
−0.944865 + 0.327460i \(0.893807\pi\)
\(972\) 9.55062e9 + 2.80596e10i 0.333580 + 0.980052i
\(973\) 3.76556e10 + 1.55975e10i 1.31049 + 0.542824i
\(974\) 4.17908e9 1.57485e9i 0.144919 0.0546114i
\(975\) 5.82242e9i 0.201181i
\(976\) −1.57009e10 9.03063e9i −0.540569 0.310916i
\(977\) 3.90751e10i 1.34051i 0.742132 + 0.670254i \(0.233815\pi\)
−0.742132 + 0.670254i \(0.766185\pi\)
\(978\) 6.73875e9 + 1.78822e10i 0.230353 + 0.611272i
\(979\) 1.17535e9 + 4.86845e8i 0.0400338 + 0.0165826i
\(980\) 2.13355e10 4.33537e10i 0.724121 1.47141i
\(981\) 6.85700e9 + 1.65543e10i 0.231896 + 0.559846i
\(982\) −1.02222e8 + 3.16220e9i −0.00344471 + 0.106561i
\(983\) −2.80283e10 2.80283e10i −0.941150 0.941150i 0.0572117 0.998362i \(-0.481779\pi\)
−0.998362 + 0.0572117i \(0.981779\pi\)
\(984\) −1.76831e10 2.14930e10i −0.591666 0.719141i
\(985\) 3.04938e10 3.04938e10i 1.01668 1.01668i
\(986\) 1.65203e10 + 1.76241e10i 0.548845 + 0.585514i
\(987\) −3.10016e10 + 1.28413e10i −1.02630 + 0.425106i
\(988\) −4.38230e9 + 6.77119e10i −0.144561 + 2.23365i
\(989\) 8.56888e8 2.06871e9i 0.0281668 0.0680006i
\(990\) 1.45696e9 3.21910e9i 0.0477227 0.105441i
\(991\) −2.22017e10 −0.724649 −0.362324 0.932052i \(-0.618017\pi\)
−0.362324 + 0.932052i \(0.618017\pi\)
\(992\) −1.87238e10 + 3.02484e10i −0.608979 + 0.983811i
\(993\) 2.07308e10 0.671883
\(994\) −7.26675e9 + 1.60556e10i −0.234686 + 0.518529i
\(995\) −6.65225e9 + 1.60600e10i −0.214086 + 0.516849i
\(996\) −1.55637e10 1.00728e9i −0.499120 0.0323029i
\(997\) −1.21721e10 + 5.04184e9i −0.388984 + 0.161122i −0.568599 0.822615i \(-0.692515\pi\)
0.179616 + 0.983737i \(0.442515\pi\)
\(998\) −2.22809e9 2.37696e9i −0.0709540 0.0756945i
\(999\) 7.33345e9 7.33345e9i 0.232718 0.232718i
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 32.8.g.a.13.4 yes 108
32.5 even 8 inner 32.8.g.a.5.4 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.8.g.a.5.4 108 32.5 even 8 inner
32.8.g.a.13.4 yes 108 1.1 even 1 trivial