Properties

Label 91.8.f.a.22.10
Level $91$
Weight $8$
Character 91.22
Analytic conductor $28.427$
Analytic rank $0$
Dimension $48$
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] = [91,8,Mod(22,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.22");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), 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: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.10
Character \(\chi\) \(=\) 91.22
Dual form 91.8.f.a.29.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96989 + 3.41195i) q^{2} +(18.4244 - 31.9119i) q^{3} +(56.2391 + 97.4089i) q^{4} +280.776 q^{5} +(72.5879 + 125.726i) q^{6} +(171.500 + 297.047i) q^{7} -947.431 q^{8} +(414.587 + 718.085i) q^{9} +O(q^{10})\) \(q+(-1.96989 + 3.41195i) q^{2} +(18.4244 - 31.9119i) q^{3} +(56.2391 + 97.4089i) q^{4} +280.776 q^{5} +(72.5879 + 125.726i) q^{6} +(171.500 + 297.047i) q^{7} -947.431 q^{8} +(414.587 + 718.085i) q^{9} +(-553.099 + 957.995i) q^{10} +(-2744.58 + 4753.75i) q^{11} +4144.67 q^{12} +(2582.39 + 7488.64i) q^{13} -1351.34 q^{14} +(5173.12 - 8960.11i) q^{15} +(-5332.26 + 9235.75i) q^{16} +(-334.086 - 578.655i) q^{17} -3266.76 q^{18} +(-28893.7 - 50045.4i) q^{19} +(15790.6 + 27350.1i) q^{20} +12639.1 q^{21} +(-10813.0 - 18728.7i) q^{22} +(-5782.31 + 10015.2i) q^{23} +(-17455.8 + 30234.3i) q^{24} +710.316 q^{25} +(-30637.9 - 5940.83i) q^{26} +111142. q^{27} +(-19290.0 + 33411.3i) q^{28} +(-36931.8 + 63967.8i) q^{29} +(20381.0 + 35300.9i) q^{30} +128091. q^{31} +(-81643.5 - 141411. i) q^{32} +(101134. + 175169. i) q^{33} +2632.45 q^{34} +(48153.1 + 83403.7i) q^{35} +(-46631.9 + 80768.9i) q^{36} +(-231827. + 401536. i) q^{37} +227670. q^{38} +(286556. + 55564.4i) q^{39} -266016. q^{40} +(87215.7 - 151062. i) q^{41} +(-24897.7 + 43124.0i) q^{42} +(279297. + 483756. i) q^{43} -617410. q^{44} +(116406. + 201621. i) q^{45} +(-22781.0 - 39457.9i) q^{46} +444019. q^{47} +(196487. + 340326. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-1399.25 + 2423.56i) q^{50} -24621.3 q^{51} +(-584230. + 672702. i) q^{52} -375418. q^{53} +(-218938. + 379211. i) q^{54} +(-770612. + 1.33474e6i) q^{55} +(-162484. - 281431. i) q^{56} -2.12939e6 q^{57} +(-145503. - 252019. i) q^{58} +(472989. + 819241. i) q^{59} +1.16373e6 q^{60} +(9755.99 + 16897.9i) q^{61} +(-252326. + 437041. i) q^{62} +(-142203. + 246303. i) q^{63} -721744. q^{64} +(725073. + 2.10263e6i) q^{65} -796892. q^{66} +(92054.6 - 159443. i) q^{67} +(37577.4 - 65086.0i) q^{68} +(213071. + 369049. i) q^{69} -379426. q^{70} +(-261524. - 452972. i) q^{71} +(-392792. - 680336. i) q^{72} +4.25363e6 q^{73} +(-913346. - 1.58196e6i) q^{74} +(13087.1 - 22667.6i) q^{75} +(3.24991e6 - 5.62901e6i) q^{76} -1.88278e6 q^{77} +(-754067. + 868258. i) q^{78} +5.64637e6 q^{79} +(-1.49717e6 + 2.59318e6i) q^{80} +(1.14102e6 - 1.97630e6i) q^{81} +(343611. + 595152. i) q^{82} +4.99552e6 q^{83} +(710811. + 1.23116e6i) q^{84} +(-93803.5 - 162472. i) q^{85} -2.20074e6 q^{86} +(1.36089e6 + 2.35713e6i) q^{87} +(2.60030e6 - 4.50385e6i) q^{88} +(4.48978e6 - 7.77652e6i) q^{89} -917229. q^{90} +(-1.78160e6 + 2.05139e6i) q^{91} -1.30077e6 q^{92} +(2.36000e6 - 4.08764e6i) q^{93} +(-874669. + 1.51497e6i) q^{94} +(-8.11267e6 - 1.40516e7i) q^{95} -6.01692e6 q^{96} +(-402495. - 697142. i) q^{97} +(-231756. - 401413. i) q^{98} -4.55146e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96989 + 3.41195i −0.174115 + 0.301577i −0.939855 0.341574i \(-0.889040\pi\)
0.765739 + 0.643151i \(0.222373\pi\)
\(3\) 18.4244 31.9119i 0.393974 0.682383i −0.598995 0.800752i \(-0.704433\pi\)
0.992970 + 0.118369i \(0.0377666\pi\)
\(4\) 56.2391 + 97.4089i 0.439368 + 0.761007i
\(5\) 280.776 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(6\) 72.5879 + 125.726i 0.137194 + 0.237627i
\(7\) 171.500 + 297.047i 0.188982 + 0.327327i
\(8\) −947.431 −0.654233
\(9\) 414.587 + 718.085i 0.189569 + 0.328342i
\(10\) −553.099 + 957.995i −0.174905 + 0.302945i
\(11\) −2744.58 + 4753.75i −0.621729 + 1.07687i 0.367435 + 0.930049i \(0.380236\pi\)
−0.989164 + 0.146817i \(0.953097\pi\)
\(12\) 4144.67 0.692398
\(13\) 2582.39 + 7488.64i 0.326002 + 0.945369i
\(14\) −1351.34 −0.131619
\(15\) 5173.12 8960.11i 0.395761 0.685478i
\(16\) −5332.26 + 9235.75i −0.325456 + 0.563706i
\(17\) −334.086 578.655i −0.0164925 0.0285659i 0.857661 0.514215i \(-0.171917\pi\)
−0.874154 + 0.485649i \(0.838583\pi\)
\(18\) −3266.76 −0.132027
\(19\) −28893.7 50045.4i −0.966420 1.67389i −0.705751 0.708460i \(-0.749390\pi\)
−0.260669 0.965428i \(-0.583943\pi\)
\(20\) 15790.6 + 27350.1i 0.441361 + 0.764459i
\(21\) 12639.1 0.297817
\(22\) −10813.0 18728.7i −0.216505 0.374998i
\(23\) −5782.31 + 10015.2i −0.0990954 + 0.171638i −0.911310 0.411720i \(-0.864928\pi\)
0.812215 + 0.583358i \(0.198262\pi\)
\(24\) −17455.8 + 30234.3i −0.257751 + 0.446438i
\(25\) 710.316 0.00909205
\(26\) −30637.9 5940.83i −0.341863 0.0662888i
\(27\) 111142. 1.08669
\(28\) −19290.0 + 33411.3i −0.166065 + 0.287634i
\(29\) −36931.8 + 63967.8i −0.281195 + 0.487044i −0.971679 0.236303i \(-0.924064\pi\)
0.690484 + 0.723347i \(0.257397\pi\)
\(30\) 20381.0 + 35300.9i 0.137816 + 0.238705i
\(31\) 128091. 0.772242 0.386121 0.922448i \(-0.373815\pi\)
0.386121 + 0.922448i \(0.373815\pi\)
\(32\) −81643.5 141411.i −0.440450 0.762882i
\(33\) 101134. + 175169.i 0.489890 + 0.848515i
\(34\) 2632.45 0.0114864
\(35\) 48153.1 + 83403.7i 0.189839 + 0.328812i
\(36\) −46631.9 + 80768.9i −0.166581 + 0.288526i
\(37\) −231827. + 401536.i −0.752415 + 1.30322i 0.194235 + 0.980955i \(0.437778\pi\)
−0.946649 + 0.322266i \(0.895556\pi\)
\(38\) 227670. 0.673074
\(39\) 286556. + 55564.4i 0.773540 + 0.149993i
\(40\) −266016. −0.657201
\(41\) 87215.7 151062.i 0.197629 0.342304i −0.750130 0.661290i \(-0.770009\pi\)
0.947759 + 0.318986i \(0.103342\pi\)
\(42\) −24897.7 + 43124.0i −0.0518544 + 0.0898145i
\(43\) 279297. + 483756.i 0.535706 + 0.927870i 0.999129 + 0.0417327i \(0.0132878\pi\)
−0.463423 + 0.886137i \(0.653379\pi\)
\(44\) −617410. −1.09267
\(45\) 116406. + 201621.i 0.190428 + 0.329832i
\(46\) −22781.0 39457.9i −0.0345081 0.0597697i
\(47\) 444019. 0.623820 0.311910 0.950112i \(-0.399031\pi\)
0.311910 + 0.950112i \(0.399031\pi\)
\(48\) 196487. + 340326.i 0.256442 + 0.444171i
\(49\) −58824.5 + 101887.i −0.0714286 + 0.123718i
\(50\) −1399.25 + 2423.56i −0.00158307 + 0.00274195i
\(51\) −24621.3 −0.0259905
\(52\) −584230. + 672702.i −0.576198 + 0.663454i
\(53\) −375418. −0.346377 −0.173189 0.984889i \(-0.555407\pi\)
−0.173189 + 0.984889i \(0.555407\pi\)
\(54\) −218938. + 379211.i −0.189209 + 0.327720i
\(55\) −770612. + 1.33474e6i −0.624549 + 1.08175i
\(56\) −162484. 281431.i −0.123638 0.214148i
\(57\) −2.12939e6 −1.52298
\(58\) −145503. 252019.i −0.0979207 0.169604i
\(59\) 472989. + 819241.i 0.299826 + 0.519313i 0.976096 0.217340i \(-0.0697381\pi\)
−0.676270 + 0.736654i \(0.736405\pi\)
\(60\) 1.16373e6 0.695539
\(61\) 9755.99 + 16897.9i 0.00550322 + 0.00953185i 0.868764 0.495227i \(-0.164915\pi\)
−0.863261 + 0.504758i \(0.831582\pi\)
\(62\) −252326. + 437041.i −0.134459 + 0.232890i
\(63\) −142203. + 246303.i −0.0716502 + 0.124102i
\(64\) −721744. −0.344155
\(65\) 725073. + 2.10263e6i 0.327480 + 0.949657i
\(66\) −796892. −0.341190
\(67\) 92054.6 159443.i 0.0373924 0.0647656i −0.846724 0.532033i \(-0.821428\pi\)
0.884116 + 0.467268i \(0.154762\pi\)
\(68\) 37577.4 65086.0i 0.0144926 0.0251019i
\(69\) 213071. + 369049.i 0.0780821 + 0.135242i
\(70\) −379426. −0.132216
\(71\) −261524. 452972.i −0.0867175 0.150199i 0.819404 0.573216i \(-0.194304\pi\)
−0.906122 + 0.423017i \(0.860971\pi\)
\(72\) −392792. 680336.i −0.124022 0.214813i
\(73\) 4.25363e6 1.27976 0.639882 0.768473i \(-0.278983\pi\)
0.639882 + 0.768473i \(0.278983\pi\)
\(74\) −913346. 1.58196e6i −0.262014 0.453821i
\(75\) 13087.1 22667.6i 0.00358203 0.00620426i
\(76\) 3.24991e6 5.62901e6i 0.849227 1.47091i
\(77\) −1.88278e6 −0.469983
\(78\) −754067. + 868258.i −0.179920 + 0.207166i
\(79\) 5.64637e6 1.28847 0.644235 0.764828i \(-0.277176\pi\)
0.644235 + 0.764828i \(0.277176\pi\)
\(80\) −1.49717e6 + 2.59318e6i −0.326932 + 0.566262i
\(81\) 1.14102e6 1.97630e6i 0.238559 0.413196i
\(82\) 343611. + 595152.i 0.0688206 + 0.119201i
\(83\) 4.99552e6 0.958975 0.479488 0.877549i \(-0.340823\pi\)
0.479488 + 0.877549i \(0.340823\pi\)
\(84\) 710811. + 1.23116e6i 0.130851 + 0.226641i
\(85\) −93803.5 162472.i −0.0165673 0.0286955i
\(86\) −2.20074e6 −0.373099
\(87\) 1.36089e6 + 2.35713e6i 0.221567 + 0.383765i
\(88\) 2.60030e6 4.50385e6i 0.406756 0.704522i
\(89\) 4.48978e6 7.77652e6i 0.675087 1.16929i −0.301356 0.953512i \(-0.597439\pi\)
0.976443 0.215774i \(-0.0692273\pi\)
\(90\) −917229. −0.132626
\(91\) −1.78160e6 + 2.05139e6i −0.247836 + 0.285367i
\(92\) −1.30077e6 −0.174157
\(93\) 2.36000e6 4.08764e6i 0.304243 0.526965i
\(94\) −874669. + 1.51497e6i −0.108617 + 0.188129i
\(95\) −8.11267e6 1.40516e7i −0.970803 1.68148i
\(96\) −6.01692e6 −0.694104
\(97\) −402495. 697142.i −0.0447775 0.0775568i 0.842768 0.538277i \(-0.180925\pi\)
−0.887545 + 0.460720i \(0.847591\pi\)
\(98\) −231756. 401413.i −0.0248736 0.0430824i
\(99\) −4.55146e6 −0.471441
\(100\) 39947.5 + 69191.2i 0.00399475 + 0.00691912i
\(101\) 3.38642e6 5.86545e6i 0.327051 0.566469i −0.654874 0.755738i \(-0.727278\pi\)
0.981925 + 0.189269i \(0.0606117\pi\)
\(102\) 48501.3 84006.7i 0.00452535 0.00783814i
\(103\) −5.52012e6 −0.497758 −0.248879 0.968535i \(-0.580062\pi\)
−0.248879 + 0.968535i \(0.580062\pi\)
\(104\) −2.44664e6 7.09497e6i −0.213281 0.618492i
\(105\) 3.54876e6 0.299167
\(106\) 739532. 1.28091e6i 0.0603096 0.104459i
\(107\) −2.88794e6 + 5.00206e6i −0.227900 + 0.394735i −0.957186 0.289475i \(-0.906519\pi\)
0.729285 + 0.684210i \(0.239853\pi\)
\(108\) 6.25053e6 + 1.08262e7i 0.477456 + 0.826978i
\(109\) −5.75194e6 −0.425424 −0.212712 0.977115i \(-0.568230\pi\)
−0.212712 + 0.977115i \(0.568230\pi\)
\(110\) −3.03604e6 5.25858e6i −0.217487 0.376699i
\(111\) 8.54251e6 + 1.47961e7i 0.592864 + 1.02687i
\(112\) −3.65793e6 −0.246021
\(113\) −7.30131e6 1.26462e7i −0.476021 0.824493i 0.523601 0.851963i \(-0.324588\pi\)
−0.999623 + 0.0274705i \(0.991255\pi\)
\(114\) 4.19467e6 7.26538e6i 0.265174 0.459295i
\(115\) −1.62353e6 + 2.81204e6i −0.0995449 + 0.172417i
\(116\) −8.30804e6 −0.494192
\(117\) −4.30686e6 + 4.95907e6i −0.248605 + 0.286253i
\(118\) −3.72695e6 −0.208817
\(119\) 114592. 198479.i 0.00623359 0.0107969i
\(120\) −4.90118e6 + 8.48909e6i −0.258920 + 0.448463i
\(121\) −5.32182e6 9.21766e6i −0.273093 0.473012i
\(122\) −76872.9 −0.00383278
\(123\) −3.21379e6 5.56644e6i −0.155722 0.269718i
\(124\) 7.20373e6 + 1.24772e7i 0.339298 + 0.587682i
\(125\) −2.17362e7 −0.995402
\(126\) −560249. 970380.i −0.0249508 0.0432161i
\(127\) 1.43189e7 2.48011e7i 0.620295 1.07438i −0.369136 0.929375i \(-0.620346\pi\)
0.989431 0.145007i \(-0.0463203\pi\)
\(128\) 1.18721e7 2.05631e7i 0.500373 0.866671i
\(129\) 2.05835e7 0.844217
\(130\) −8.60240e6 1.66804e6i −0.343414 0.0665895i
\(131\) 4.82640e7 1.87574 0.937872 0.346982i \(-0.112793\pi\)
0.937872 + 0.346982i \(0.112793\pi\)
\(132\) −1.13754e7 + 1.97027e7i −0.430484 + 0.745620i
\(133\) 9.91055e6 1.71656e7i 0.365272 0.632670i
\(134\) 362675. + 628171.i 0.0130212 + 0.0225534i
\(135\) 3.12061e7 1.09162
\(136\) 316524. + 548235.i 0.0107900 + 0.0186888i
\(137\) 3.91274e6 + 6.77707e6i 0.130005 + 0.225175i 0.923678 0.383169i \(-0.125167\pi\)
−0.793673 + 0.608344i \(0.791834\pi\)
\(138\) −1.67890e6 −0.0543812
\(139\) 1.42338e6 + 2.46536e6i 0.0449540 + 0.0778626i 0.887627 0.460563i \(-0.152353\pi\)
−0.842673 + 0.538426i \(0.819019\pi\)
\(140\) −5.41617e6 + 9.38109e6i −0.166819 + 0.288938i
\(141\) 8.18076e6 1.41695e7i 0.245769 0.425684i
\(142\) 2.06069e6 0.0603954
\(143\) −4.26867e7 8.27714e6i −1.22072 0.236703i
\(144\) −8.84274e6 −0.246785
\(145\) −1.03696e7 + 1.79606e7i −0.282470 + 0.489253i
\(146\) −8.37919e6 + 1.45132e7i −0.222827 + 0.385947i
\(147\) 2.16761e6 + 3.75440e6i 0.0562820 + 0.0974833i
\(148\) −5.21509e7 −1.32235
\(149\) 3.33982e7 + 5.78474e7i 0.827126 + 1.43262i 0.900284 + 0.435303i \(0.143359\pi\)
−0.0731581 + 0.997320i \(0.523308\pi\)
\(150\) 51560.4 + 89305.2i 0.00124737 + 0.00216052i
\(151\) 3.99796e6 0.0944972 0.0472486 0.998883i \(-0.484955\pi\)
0.0472486 + 0.998883i \(0.484955\pi\)
\(152\) 2.73748e7 + 4.74146e7i 0.632264 + 1.09511i
\(153\) 277015. 479805.i 0.00625294 0.0108304i
\(154\) 3.70887e6 6.42395e6i 0.0818312 0.141736i
\(155\) 3.59650e7 0.775745
\(156\) 1.07032e7 + 3.10380e7i 0.225723 + 0.654572i
\(157\) −3.46001e7 −0.713557 −0.356779 0.934189i \(-0.616125\pi\)
−0.356779 + 0.934189i \(0.616125\pi\)
\(158\) −1.11227e7 + 1.92651e7i −0.224342 + 0.388572i
\(159\) −6.91683e6 + 1.19803e7i −0.136464 + 0.236362i
\(160\) −2.29236e7 3.97048e7i −0.442448 0.766343i
\(161\) −3.96666e6 −0.0749091
\(162\) 4.49537e6 + 7.78620e6i 0.0830735 + 0.143888i
\(163\) 4.52211e6 + 7.83252e6i 0.0817870 + 0.141659i 0.904018 0.427495i \(-0.140604\pi\)
−0.822231 + 0.569154i \(0.807271\pi\)
\(164\) 1.96197e7 0.347328
\(165\) 2.83961e7 + 4.91834e7i 0.492112 + 0.852363i
\(166\) −9.84063e6 + 1.70445e7i −0.166972 + 0.289205i
\(167\) 2.99457e7 5.18675e7i 0.497539 0.861762i −0.502457 0.864602i \(-0.667571\pi\)
0.999996 + 0.00283982i \(0.000903945\pi\)
\(168\) −1.19747e7 −0.194842
\(169\) −4.94111e7 + 3.86772e7i −0.787446 + 0.616384i
\(170\) 739131. 0.0115385
\(171\) 2.39579e7 4.14963e7i 0.366406 0.634633i
\(172\) −3.14148e7 + 5.44120e7i −0.470744 + 0.815352i
\(173\) −4.49122e7 7.77903e7i −0.659483 1.14226i −0.980750 0.195269i \(-0.937442\pi\)
0.321267 0.946989i \(-0.395891\pi\)
\(174\) −1.07232e7 −0.154313
\(175\) 121819. + 210997.i 0.00171824 + 0.00297607i
\(176\) −2.92696e7 5.06965e7i −0.404690 0.700944i
\(177\) 3.48581e7 0.472494
\(178\) 1.76887e7 + 3.06378e7i 0.235086 + 0.407181i
\(179\) −2.52132e7 + 4.36705e7i −0.328581 + 0.569119i −0.982231 0.187678i \(-0.939904\pi\)
0.653650 + 0.756797i \(0.273237\pi\)
\(180\) −1.30931e7 + 2.26780e7i −0.167336 + 0.289835i
\(181\) −1.08576e7 −0.136100 −0.0680502 0.997682i \(-0.521678\pi\)
−0.0680502 + 0.997682i \(0.521678\pi\)
\(182\) −3.48970e6 1.01197e7i −0.0429080 0.124428i
\(183\) 718991. 0.00867250
\(184\) 5.47834e6 9.48876e6i 0.0648315 0.112292i
\(185\) −6.50914e7 + 1.12742e8i −0.755828 + 1.30913i
\(186\) 9.29787e6 + 1.61044e7i 0.105947 + 0.183505i
\(187\) 3.66770e6 0.0410156
\(188\) 2.49712e7 + 4.32514e7i 0.274086 + 0.474731i
\(189\) 1.90609e7 + 3.30144e7i 0.205365 + 0.355702i
\(190\) 6.39243e7 0.676127
\(191\) −2.47691e7 4.29013e7i −0.257213 0.445506i 0.708281 0.705931i \(-0.249471\pi\)
−0.965494 + 0.260424i \(0.916138\pi\)
\(192\) −1.32977e7 + 2.30322e7i −0.135588 + 0.234845i
\(193\) −3.43319e7 + 5.94645e7i −0.343753 + 0.595398i −0.985126 0.171831i \(-0.945032\pi\)
0.641373 + 0.767229i \(0.278365\pi\)
\(194\) 3.17148e6 0.0311858
\(195\) 8.04581e7 + 1.56012e7i 0.777049 + 0.150673i
\(196\) −1.32329e7 −0.125534
\(197\) 9.30989e7 1.61252e8i 0.867586 1.50270i 0.00313046 0.999995i \(-0.499004\pi\)
0.864456 0.502709i \(-0.167663\pi\)
\(198\) 8.96587e6 1.55294e7i 0.0820851 0.142176i
\(199\) −2.89774e7 5.01902e7i −0.260659 0.451475i 0.705758 0.708453i \(-0.250607\pi\)
−0.966417 + 0.256978i \(0.917273\pi\)
\(200\) −672976. −0.00594832
\(201\) −3.39209e6 5.87527e6i −0.0294633 0.0510319i
\(202\) 1.33417e7 + 2.31086e7i 0.113889 + 0.197262i
\(203\) −2.53352e7 −0.212563
\(204\) −1.38468e6 2.39833e6i −0.0114194 0.0197790i
\(205\) 2.44881e7 4.24147e7i 0.198526 0.343857i
\(206\) 1.08740e7 1.88344e7i 0.0866672 0.150112i
\(207\) −9.58907e6 −0.0751415
\(208\) −8.29332e7 1.60811e7i −0.639009 0.123907i
\(209\) 3.17204e8 2.40340
\(210\) −6.99067e6 + 1.21082e7i −0.0520896 + 0.0902219i
\(211\) −1.27779e8 + 2.21319e8i −0.936418 + 1.62192i −0.164332 + 0.986405i \(0.552547\pi\)
−0.772086 + 0.635518i \(0.780787\pi\)
\(212\) −2.11132e7 3.65691e7i −0.152187 0.263596i
\(213\) −1.92736e7 −0.136658
\(214\) −1.13779e7 1.97070e7i −0.0793619 0.137459i
\(215\) 7.84199e7 + 1.35827e8i 0.538136 + 0.932079i
\(216\) −1.05299e8 −0.710948
\(217\) 2.19676e7 + 3.80491e7i 0.145940 + 0.252776i
\(218\) 1.13307e7 1.96253e7i 0.0740728 0.128298i
\(219\) 7.83705e7 1.35742e8i 0.504194 0.873290i
\(220\) −1.73354e8 −1.09763
\(221\) 3.47060e6 3.99617e6i 0.0216287 0.0249041i
\(222\) −6.73112e7 −0.412907
\(223\) 1.49351e8 2.58683e8i 0.901862 1.56207i 0.0767865 0.997048i \(-0.475534\pi\)
0.825075 0.565023i \(-0.191133\pi\)
\(224\) 2.80037e7 4.85039e7i 0.166475 0.288342i
\(225\) 294488. + 510068.i 0.00172357 + 0.00298531i
\(226\) 5.75311e7 0.331530
\(227\) −1.32419e8 2.29356e8i −0.751380 1.30143i −0.947154 0.320780i \(-0.896055\pi\)
0.195773 0.980649i \(-0.437278\pi\)
\(228\) −1.19755e8 2.07422e8i −0.669147 1.15900i
\(229\) −3.18543e8 −1.75285 −0.876423 0.481541i \(-0.840077\pi\)
−0.876423 + 0.481541i \(0.840077\pi\)
\(230\) −6.39637e6 1.10788e7i −0.0346646 0.0600408i
\(231\) −3.46890e7 + 6.00831e7i −0.185161 + 0.320708i
\(232\) 3.49903e7 6.06050e7i 0.183967 0.318640i
\(233\) −4.37163e7 −0.226411 −0.113206 0.993572i \(-0.536112\pi\)
−0.113206 + 0.993572i \(0.536112\pi\)
\(234\) −8.43605e6 2.44636e7i −0.0430411 0.124814i
\(235\) 1.24670e8 0.626649
\(236\) −5.32009e7 + 9.21467e7i −0.263467 + 0.456339i
\(237\) 1.04031e8 1.80186e8i 0.507624 0.879230i
\(238\) 451466. + 781962.i 0.00217073 + 0.00375981i
\(239\) 2.06885e8 0.980248 0.490124 0.871653i \(-0.336952\pi\)
0.490124 + 0.871653i \(0.336952\pi\)
\(240\) 5.51689e7 + 9.55553e7i 0.257605 + 0.446186i
\(241\) −1.39251e8 2.41190e8i −0.640824 1.10994i −0.985249 0.171126i \(-0.945259\pi\)
0.344425 0.938814i \(-0.388074\pi\)
\(242\) 4.19336e7 0.190199
\(243\) 7.94888e7 + 1.37679e8i 0.355372 + 0.615523i
\(244\) −1.09733e6 + 1.90064e6i −0.00483587 + 0.00837598i
\(245\) −1.65165e7 + 2.86075e7i −0.0717526 + 0.124279i
\(246\) 2.53232e7 0.108454
\(247\) 3.00157e8 3.45611e8i 1.26739 1.45931i
\(248\) −1.21358e8 −0.505226
\(249\) 9.20392e7 1.59417e8i 0.377812 0.654389i
\(250\) 4.28179e7 7.41629e7i 0.173315 0.300190i
\(251\) 1.21821e8 + 2.11000e8i 0.486255 + 0.842218i 0.999875 0.0157993i \(-0.00502927\pi\)
−0.513620 + 0.858018i \(0.671696\pi\)
\(252\) −3.19895e7 −0.125923
\(253\) −3.17400e7 5.49752e7i −0.123221 0.213425i
\(254\) 5.64135e7 + 9.77111e7i 0.216006 + 0.374133i
\(255\) −6.91308e6 −0.0261084
\(256\) 581959. + 1.00798e6i 0.00216796 + 0.00375503i
\(257\) −1.19110e7 + 2.06304e7i −0.0437705 + 0.0758127i −0.887081 0.461614i \(-0.847270\pi\)
0.843310 + 0.537427i \(0.180604\pi\)
\(258\) −4.05472e7 + 7.02297e7i −0.146991 + 0.254596i
\(259\) −1.59033e8 −0.568772
\(260\) −1.64038e8 + 1.88879e8i −0.578812 + 0.666464i
\(261\) −6.12457e7 −0.213223
\(262\) −9.50747e7 + 1.64674e8i −0.326596 + 0.565681i
\(263\) 1.64147e7 2.84311e7i 0.0556401 0.0963715i −0.836864 0.547411i \(-0.815613\pi\)
0.892504 + 0.451040i \(0.148947\pi\)
\(264\) −9.58176e7 1.65961e8i −0.320503 0.555127i
\(265\) −1.05408e8 −0.347949
\(266\) 3.90454e7 + 6.76286e7i 0.127199 + 0.220315i
\(267\) −1.65442e8 2.86555e8i −0.531934 0.921336i
\(268\) 2.07082e7 0.0657161
\(269\) 5.76212e7 + 9.98029e7i 0.180489 + 0.312615i 0.942047 0.335481i \(-0.108899\pi\)
−0.761558 + 0.648096i \(0.775565\pi\)
\(270\) −6.14725e7 + 1.06474e8i −0.190067 + 0.329207i
\(271\) 2.62969e8 4.55476e8i 0.802625 1.39019i −0.115258 0.993336i \(-0.536770\pi\)
0.917883 0.396851i \(-0.129897\pi\)
\(272\) 7.12575e6 0.0214704
\(273\) 3.26391e7 + 9.46498e7i 0.0970887 + 0.281547i
\(274\) −3.08307e7 −0.0905433
\(275\) −1.94952e6 + 3.37666e6i −0.00565279 + 0.00979092i
\(276\) −2.39658e7 + 4.15099e7i −0.0686135 + 0.118842i
\(277\) 2.26865e8 + 3.92943e8i 0.641341 + 1.11084i 0.985134 + 0.171790i \(0.0549551\pi\)
−0.343792 + 0.939046i \(0.611712\pi\)
\(278\) −1.12156e7 −0.0313087
\(279\) 5.31049e7 + 9.19804e7i 0.146393 + 0.253560i
\(280\) −4.56218e7 7.90192e7i −0.124199 0.215119i
\(281\) 6.20358e8 1.66790 0.833950 0.551839i \(-0.186074\pi\)
0.833950 + 0.551839i \(0.186074\pi\)
\(282\) 3.22304e7 + 5.58247e7i 0.0855843 + 0.148236i
\(283\) −2.40931e8 + 4.17305e8i −0.631888 + 1.09446i 0.355277 + 0.934761i \(0.384387\pi\)
−0.987165 + 0.159702i \(0.948947\pi\)
\(284\) 2.94157e7 5.09495e7i 0.0762017 0.131985i
\(285\) −5.97883e8 −1.52989
\(286\) 1.12329e8 1.29340e8i 0.283930 0.326927i
\(287\) 5.98300e7 0.149394
\(288\) 6.76966e7 1.17254e8i 0.166991 0.289237i
\(289\) 2.04946e8 3.54977e8i 0.499456 0.865083i
\(290\) −4.08538e7 7.07609e7i −0.0983649 0.170373i
\(291\) −2.96628e7 −0.0705647
\(292\) 2.39220e8 + 4.14342e8i 0.562287 + 0.973910i
\(293\) 1.11806e8 + 1.93654e8i 0.259674 + 0.449769i 0.966155 0.257964i \(-0.0830515\pi\)
−0.706480 + 0.707733i \(0.749718\pi\)
\(294\) −1.70798e7 −0.0391983
\(295\) 1.32804e8 + 2.30023e8i 0.301186 + 0.521669i
\(296\) 2.19640e8 3.80427e8i 0.492255 0.852610i
\(297\) −3.05038e8 + 5.28341e8i −0.675626 + 1.17022i
\(298\) −2.63163e8 −0.576061
\(299\) −8.99328e7 1.74384e7i −0.194567 0.0377274i
\(300\) 2.94403e6 0.00629532
\(301\) −9.57988e7 + 1.65928e8i −0.202478 + 0.350702i
\(302\) −7.87554e6 + 1.36408e7i −0.0164534 + 0.0284982i
\(303\) −1.24785e8 2.16134e8i −0.257700 0.446349i
\(304\) 6.16276e8 1.25811
\(305\) 2.73925e6 + 4.74452e6i 0.00552818 + 0.00957509i
\(306\) 1.09138e6 + 1.89033e6i 0.00217746 + 0.00377148i
\(307\) −3.75385e8 −0.740445 −0.370223 0.928943i \(-0.620719\pi\)
−0.370223 + 0.928943i \(0.620719\pi\)
\(308\) −1.05886e8 1.83400e8i −0.206495 0.357660i
\(309\) −1.01705e8 + 1.76157e8i −0.196104 + 0.339661i
\(310\) −7.08471e7 + 1.22711e8i −0.135069 + 0.233946i
\(311\) −3.96905e8 −0.748213 −0.374106 0.927386i \(-0.622050\pi\)
−0.374106 + 0.927386i \(0.622050\pi\)
\(312\) −2.71492e8 5.26435e7i −0.506076 0.0981304i
\(313\) −3.69321e8 −0.680768 −0.340384 0.940287i \(-0.610557\pi\)
−0.340384 + 0.940287i \(0.610557\pi\)
\(314\) 6.81585e7 1.18054e8i 0.124241 0.215192i
\(315\) −3.99273e7 + 6.91561e7i −0.0719752 + 0.124665i
\(316\) 3.17546e8 + 5.50006e8i 0.566112 + 0.980535i
\(317\) 9.82340e8 1.73203 0.866013 0.500021i \(-0.166674\pi\)
0.866013 + 0.500021i \(0.166674\pi\)
\(318\) −2.72508e7 4.71998e7i −0.0475209 0.0823086i
\(319\) −2.02724e8 3.51129e8i −0.349654 0.605618i
\(320\) −2.02649e8 −0.345716
\(321\) 1.06417e8 + 1.84319e8i 0.179574 + 0.311031i
\(322\) 7.81389e6 1.35341e7i 0.0130428 0.0225908i
\(323\) −1.93060e7 + 3.34390e7i −0.0318774 + 0.0552134i
\(324\) 2.56680e8 0.419260
\(325\) 1.83431e6 + 5.31931e6i 0.00296402 + 0.00859534i
\(326\) −3.56322e7 −0.0569615
\(327\) −1.05976e8 + 1.83555e8i −0.167606 + 0.290302i
\(328\) −8.26309e7 + 1.43121e8i −0.129296 + 0.223947i
\(329\) 7.61493e7 + 1.31894e8i 0.117891 + 0.204193i
\(330\) −2.23748e8 −0.342737
\(331\) −1.36664e7 2.36709e7i −0.0207137 0.0358771i 0.855483 0.517831i \(-0.173261\pi\)
−0.876196 + 0.481954i \(0.839927\pi\)
\(332\) 2.80943e8 + 4.86608e8i 0.421343 + 0.729787i
\(333\) −3.84449e8 −0.570537
\(334\) 1.17979e8 + 2.04346e8i 0.173258 + 0.300092i
\(335\) 2.58467e7 4.47679e7i 0.0375620 0.0650593i
\(336\) −6.73951e7 + 1.16732e8i −0.0969261 + 0.167881i
\(337\) 1.12817e8 0.160573 0.0802863 0.996772i \(-0.474417\pi\)
0.0802863 + 0.996772i \(0.474417\pi\)
\(338\) −3.46302e7 2.44778e8i −0.0487806 0.344797i
\(339\) −5.38088e8 −0.750160
\(340\) 1.05508e7 1.82746e7i 0.0145583 0.0252157i
\(341\) −3.51556e8 + 6.08913e8i −0.480125 + 0.831601i
\(342\) 9.43889e7 + 1.63486e8i 0.127594 + 0.220999i
\(343\) −4.03536e7 −0.0539949
\(344\) −2.64615e8 4.58326e8i −0.350477 0.607044i
\(345\) 5.98251e7 + 1.03620e8i 0.0784363 + 0.135856i
\(346\) 3.53889e8 0.459304
\(347\) −6.38996e8 1.10677e9i −0.821004 1.42202i −0.904936 0.425548i \(-0.860081\pi\)
0.0839321 0.996471i \(-0.473252\pi\)
\(348\) −1.53070e8 + 2.65125e8i −0.194699 + 0.337228i
\(349\) 3.89347e7 6.74368e7i 0.0490284 0.0849197i −0.840470 0.541859i \(-0.817721\pi\)
0.889498 + 0.456939i \(0.151054\pi\)
\(350\) −959882. −0.00119669
\(351\) 2.87012e8 + 8.32303e8i 0.354262 + 1.02732i
\(352\) 8.96308e8 1.09536
\(353\) −5.36799e8 + 9.29764e8i −0.649532 + 1.12502i 0.333703 + 0.942678i \(0.391702\pi\)
−0.983235 + 0.182344i \(0.941632\pi\)
\(354\) −6.86665e7 + 1.18934e8i −0.0822685 + 0.142493i
\(355\) −7.34296e7 1.27184e8i −0.0871108 0.150880i
\(356\) 1.01000e9 1.18645
\(357\) −4.22255e6 7.31368e6i −0.00491175 0.00850740i
\(358\) −9.93345e7 1.72052e8i −0.114422 0.198185i
\(359\) 1.52679e9 1.74160 0.870800 0.491637i \(-0.163601\pi\)
0.870800 + 0.491637i \(0.163601\pi\)
\(360\) −1.10287e8 1.91022e8i −0.124585 0.215787i
\(361\) −1.22276e9 + 2.11788e9i −1.36794 + 2.36933i
\(362\) 2.13883e7 3.70456e7i 0.0236972 0.0410447i
\(363\) −3.92204e8 −0.430367
\(364\) −3.00019e8 5.81751e7i −0.326058 0.0632240i
\(365\) 1.19432e9 1.28557
\(366\) −1.41633e6 + 2.45316e6i −0.00151002 + 0.00261542i
\(367\) −8.46471e8 + 1.46613e9i −0.893883 + 1.54825i −0.0587030 + 0.998275i \(0.518696\pi\)
−0.835180 + 0.549976i \(0.814637\pi\)
\(368\) −6.16656e7 1.06808e8i −0.0645023 0.111721i
\(369\) 1.44634e8 0.149857
\(370\) −2.56446e8 4.44177e8i −0.263202 0.455880i
\(371\) −6.43842e7 1.11517e8i −0.0654592 0.113379i
\(372\) 5.30896e8 0.534699
\(373\) 4.25820e7 + 7.37542e7i 0.0424859 + 0.0735878i 0.886486 0.462755i \(-0.153139\pi\)
−0.844000 + 0.536342i \(0.819806\pi\)
\(374\) −7.22497e6 + 1.25140e7i −0.00714144 + 0.0123693i
\(375\) −4.00476e8 + 6.93644e8i −0.392163 + 0.679246i
\(376\) −4.20677e8 −0.408124
\(377\) −5.74404e8 1.11379e8i −0.552106 0.107056i
\(378\) −1.50191e8 −0.143029
\(379\) 3.54081e8 6.13286e8i 0.334091 0.578663i −0.649219 0.760602i \(-0.724904\pi\)
0.983310 + 0.181939i \(0.0582373\pi\)
\(380\) 9.12498e8 1.58049e9i 0.853079 1.47758i
\(381\) −5.27635e8 9.13890e8i −0.488760 0.846558i
\(382\) 1.95170e8 0.179139
\(383\) −3.66754e8 6.35237e8i −0.333564 0.577750i 0.649644 0.760239i \(-0.274918\pi\)
−0.983208 + 0.182489i \(0.941585\pi\)
\(384\) −4.37473e8 7.57725e8i −0.394268 0.682892i
\(385\) −5.28640e8 −0.472115
\(386\) −1.35260e8 2.34277e8i −0.119705 0.207336i
\(387\) −2.31585e8 + 4.01118e8i −0.203106 + 0.351790i
\(388\) 4.52719e7 7.84132e7i 0.0393475 0.0681519i
\(389\) 1.07338e9 0.924552 0.462276 0.886736i \(-0.347033\pi\)
0.462276 + 0.886736i \(0.347033\pi\)
\(390\) −2.11724e8 + 2.43786e8i −0.180736 + 0.208105i
\(391\) 7.72716e6 0.00653734
\(392\) 5.57322e7 9.65309e7i 0.0467310 0.0809404i
\(393\) 8.89232e8 1.54020e9i 0.738995 1.27998i
\(394\) 3.66789e8 + 6.35298e8i 0.302120 + 0.523288i
\(395\) 1.58537e9 1.29431
\(396\) −2.55970e8 4.43353e8i −0.207136 0.358770i
\(397\) −7.94743e8 1.37654e9i −0.637471 1.10413i −0.985986 0.166828i \(-0.946647\pi\)
0.348515 0.937303i \(-0.386686\pi\)
\(398\) 2.28329e8 0.181539
\(399\) −3.65191e8 6.32529e8i −0.287816 0.498512i
\(400\) −3.78760e6 + 6.56031e6i −0.00295906 + 0.00512524i
\(401\) 8.98908e8 1.55695e9i 0.696162 1.20579i −0.273626 0.961836i \(-0.588223\pi\)
0.969788 0.243951i \(-0.0784437\pi\)
\(402\) 2.67282e7 0.0205200
\(403\) 3.30781e8 + 9.59229e8i 0.251752 + 0.730054i
\(404\) 7.61796e8 0.574783
\(405\) 3.20371e8 5.54899e8i 0.239641 0.415070i
\(406\) 4.99076e7 8.64425e7i 0.0370105 0.0641042i
\(407\) −1.27253e9 2.20409e9i −0.935596 1.62050i
\(408\) 2.33270e7 0.0170039
\(409\) −5.97600e8 1.03507e9i −0.431895 0.748065i 0.565141 0.824994i \(-0.308822\pi\)
−0.997037 + 0.0769294i \(0.975488\pi\)
\(410\) 9.64778e7 + 1.67104e8i 0.0691328 + 0.119741i
\(411\) 2.88359e8 0.204874
\(412\) −3.10446e8 5.37708e8i −0.218699 0.378797i
\(413\) −1.62235e8 + 2.81000e8i −0.113323 + 0.196282i
\(414\) 1.88894e7 3.27174e7i 0.0130833 0.0226609i
\(415\) 1.40262e9 0.963325
\(416\) 8.48140e8 9.76577e8i 0.577618 0.665089i
\(417\) 1.04899e8 0.0708429
\(418\) −6.24857e8 + 1.08228e9i −0.418470 + 0.724811i
\(419\) 9.01534e8 1.56150e9i 0.598733 1.03704i −0.394276 0.918992i \(-0.629004\pi\)
0.993008 0.118044i \(-0.0376622\pi\)
\(420\) 1.99579e8 + 3.45681e8i 0.131444 + 0.227668i
\(421\) −2.04956e9 −1.33867 −0.669336 0.742960i \(-0.733421\pi\)
−0.669336 + 0.742960i \(0.733421\pi\)
\(422\) −5.03420e8 8.71949e8i −0.326089 0.564803i
\(423\) 1.84084e8 + 3.18843e8i 0.118257 + 0.204826i
\(424\) 3.55683e8 0.226612
\(425\) −237307. 411028.i −0.000149951 0.000259723i
\(426\) 3.79669e7 6.57606e7i 0.0237942 0.0412128i
\(427\) −3.34630e6 + 5.79597e6i −0.00208002 + 0.00360270i
\(428\) −6.49661e8 −0.400528
\(429\) −1.05061e9 + 1.20971e9i −0.642455 + 0.739744i
\(430\) −6.17915e8 −0.374791
\(431\) −8.79544e8 + 1.52342e9i −0.529160 + 0.916533i 0.470261 + 0.882527i \(0.344160\pi\)
−0.999422 + 0.0340053i \(0.989174\pi\)
\(432\) −5.92639e8 + 1.02648e9i −0.353669 + 0.612573i
\(433\) −2.11370e8 3.66103e8i −0.125122 0.216718i 0.796658 0.604430i \(-0.206599\pi\)
−0.921781 + 0.387712i \(0.873266\pi\)
\(434\) −1.73095e8 −0.101642
\(435\) 3.82105e8 + 6.61826e8i 0.222572 + 0.385506i
\(436\) −3.23484e8 5.60290e8i −0.186917 0.323750i
\(437\) 6.68289e8 0.383071
\(438\) 3.08762e8 + 5.34792e8i 0.175576 + 0.304107i
\(439\) −4.27906e8 + 7.41155e8i −0.241392 + 0.418103i −0.961111 0.276162i \(-0.910937\pi\)
0.719719 + 0.694265i \(0.244271\pi\)
\(440\) 7.30102e8 1.26457e9i 0.408601 0.707717i
\(441\) −9.75514e7 −0.0541625
\(442\) 6.79802e6 + 1.97135e7i 0.00374459 + 0.0108589i
\(443\) 3.12257e8 0.170647 0.0853235 0.996353i \(-0.472808\pi\)
0.0853235 + 0.996353i \(0.472808\pi\)
\(444\) −9.60846e8 + 1.66423e9i −0.520971 + 0.902348i
\(445\) 1.26062e9 2.18346e9i 0.678149 1.17459i
\(446\) 5.88409e8 + 1.01915e9i 0.314056 + 0.543961i
\(447\) 2.46136e9 1.30346
\(448\) −1.23779e8 2.14392e8i −0.0650391 0.112651i
\(449\) 8.92791e8 + 1.54636e9i 0.465466 + 0.806211i 0.999222 0.0394277i \(-0.0125535\pi\)
−0.533757 + 0.845638i \(0.679220\pi\)
\(450\) −2.32043e6 −0.00120040
\(451\) 4.78741e8 + 8.29203e8i 0.245744 + 0.425641i
\(452\) 8.21238e8 1.42243e9i 0.418297 0.724511i
\(453\) 7.36598e7 1.27583e8i 0.0372295 0.0644833i
\(454\) 1.04340e9 0.523307
\(455\) −5.00230e8 + 5.75982e8i −0.248960 + 0.286661i
\(456\) 2.01745e9 0.996383
\(457\) −1.80721e9 + 3.13018e9i −0.885732 + 1.53413i −0.0408595 + 0.999165i \(0.513010\pi\)
−0.844872 + 0.534968i \(0.820324\pi\)
\(458\) 6.27495e8 1.08685e9i 0.305198 0.528618i
\(459\) −3.71311e7 6.43129e7i −0.0179223 0.0310423i
\(460\) −3.65224e8 −0.174947
\(461\) −9.05855e8 1.56899e9i −0.430631 0.745875i 0.566297 0.824201i \(-0.308376\pi\)
−0.996928 + 0.0783266i \(0.975042\pi\)
\(462\) −1.36667e8 2.36714e8i −0.0644788 0.111681i
\(463\) −2.78556e9 −1.30430 −0.652152 0.758088i \(-0.726134\pi\)
−0.652152 + 0.758088i \(0.726134\pi\)
\(464\) −3.93860e8 6.82186e8i −0.183033 0.317022i
\(465\) 6.62631e8 1.14771e9i 0.305623 0.529355i
\(466\) 8.61163e7 1.49158e8i 0.0394216 0.0682803i
\(467\) 1.56540e9 0.711242 0.355621 0.934630i \(-0.384269\pi\)
0.355621 + 0.934630i \(0.384269\pi\)
\(468\) −7.25271e8 1.40633e8i −0.327069 0.0634202i
\(469\) 6.31494e7 0.0282660
\(470\) −2.45586e8 + 4.25368e8i −0.109109 + 0.188983i
\(471\) −6.37485e8 + 1.10416e9i −0.281123 + 0.486920i
\(472\) −4.48124e8 7.76174e8i −0.196156 0.339752i
\(473\) −3.06621e9 −1.33226
\(474\) 4.09858e8 + 7.09895e8i 0.176770 + 0.306175i
\(475\) −2.05237e7 3.55481e7i −0.00878674 0.0152191i
\(476\) 2.57781e7 0.0109554
\(477\) −1.55643e8 2.69582e8i −0.0656623 0.113730i
\(478\) −4.07540e8 + 7.05881e8i −0.170676 + 0.295620i
\(479\) −4.94955e8 + 8.57288e8i −0.205775 + 0.356412i −0.950379 0.311094i \(-0.899305\pi\)
0.744605 + 0.667506i \(0.232638\pi\)
\(480\) −1.68941e9 −0.697253
\(481\) −3.60562e9 6.99146e8i −1.47731 0.286458i
\(482\) 1.09724e9 0.446309
\(483\) −7.30832e7 + 1.26584e8i −0.0295123 + 0.0511167i
\(484\) 5.98588e8 1.03679e9i 0.239977 0.415652i
\(485\) −1.13011e8 1.95741e8i −0.0449806 0.0779086i
\(486\) −6.26337e8 −0.247503
\(487\) −2.27359e8 3.93798e8i −0.0891993 0.154498i 0.817974 0.575256i \(-0.195097\pi\)
−0.907173 + 0.420758i \(0.861764\pi\)
\(488\) −9.24312e6 1.60096e7i −0.00360039 0.00623606i
\(489\) 3.33267e8 0.128888
\(490\) −6.50715e7 1.12707e8i −0.0249864 0.0432778i
\(491\) −2.29862e9 + 3.98133e9i −0.876360 + 1.51790i −0.0210522 + 0.999778i \(0.506702\pi\)
−0.855307 + 0.518121i \(0.826632\pi\)
\(492\) 3.61481e8 6.26103e8i 0.136838 0.237011i
\(493\) 4.93536e7 0.0185505
\(494\) 5.87932e8 + 1.70494e9i 0.219423 + 0.636304i
\(495\) −1.27794e9 −0.473579
\(496\) −6.83016e8 + 1.18302e9i −0.251330 + 0.435317i
\(497\) 8.97026e7 1.55369e8i 0.0327761 0.0567699i
\(498\) 3.62614e8 + 6.28066e8i 0.131566 + 0.227878i
\(499\) 5.11523e9 1.84295 0.921475 0.388437i \(-0.126985\pi\)
0.921475 + 0.388437i \(0.126985\pi\)
\(500\) −1.22242e9 2.11730e9i −0.437348 0.757508i
\(501\) −1.10346e9 1.91125e9i −0.392035 0.679024i
\(502\) −9.59896e8 −0.338658
\(503\) 2.16429e9 + 3.74865e9i 0.758275 + 1.31337i 0.943730 + 0.330718i \(0.107291\pi\)
−0.185454 + 0.982653i \(0.559376\pi\)
\(504\) 1.34728e8 2.33355e8i 0.0468760 0.0811915i
\(505\) 9.50826e8 1.64688e9i 0.328535 0.569039i
\(506\) 2.50097e8 0.0858187
\(507\) 3.23896e8 + 2.28940e9i 0.110377 + 0.780179i
\(508\) 3.22114e9 1.09015
\(509\) 1.75460e9 3.03906e9i 0.589748 1.02147i −0.404517 0.914530i \(-0.632560\pi\)
0.994265 0.106943i \(-0.0341062\pi\)
\(510\) 1.36180e7 2.35871e7i 0.00454588 0.00787369i
\(511\) 7.29498e8 + 1.26353e9i 0.241853 + 0.418901i
\(512\) 3.03468e9 0.999236
\(513\) −3.21131e9 5.56215e9i −1.05020 1.81900i
\(514\) −4.69266e7 8.12793e7i −0.0152422 0.0264003i
\(515\) −1.54992e9 −0.500015
\(516\) 1.15759e9 + 2.00501e9i 0.370922 + 0.642455i
\(517\) −1.21864e9 + 2.11075e9i −0.387847 + 0.671770i
\(518\) 3.13278e8 5.42613e8i 0.0990320 0.171528i
\(519\) −3.30992e9 −1.03928
\(520\) −6.86957e8 1.99210e9i −0.214249 0.621297i
\(521\) −1.24518e9 −0.385745 −0.192873 0.981224i \(-0.561780\pi\)
−0.192873 + 0.981224i \(0.561780\pi\)
\(522\) 1.20647e8 2.08967e8i 0.0371254 0.0643031i
\(523\) −6.47259e8 + 1.12108e9i −0.197844 + 0.342675i −0.947829 0.318779i \(-0.896727\pi\)
0.749985 + 0.661454i \(0.230060\pi\)
\(524\) 2.71432e9 + 4.70134e9i 0.824141 + 1.42745i
\(525\) 8.97776e6 0.00270776
\(526\) 6.46703e7 + 1.12012e8i 0.0193756 + 0.0335595i
\(527\) −4.27935e7 7.41206e7i −0.0127362 0.0220598i
\(528\) −2.15709e9 −0.637750
\(529\) 1.63554e9 + 2.83284e9i 0.480360 + 0.832008i
\(530\) 2.07643e8 3.59649e8i 0.0605832 0.104933i
\(531\) −3.92190e8 + 6.79292e8i −0.113675 + 0.196891i
\(532\) 2.22944e9 0.641956
\(533\) 1.35648e9 + 2.63027e8i 0.388031 + 0.0752410i
\(534\) 1.30361e9 0.370471
\(535\) −8.10865e8 + 1.40446e9i −0.228934 + 0.396526i
\(536\) −8.72154e7 + 1.51061e8i −0.0244634 + 0.0423718i
\(537\) 9.29074e8 + 1.60920e9i 0.258905 + 0.448436i
\(538\) −4.54030e8 −0.125703
\(539\) −3.22897e8 5.59274e8i −0.0888184 0.153838i
\(540\) 1.75500e9 + 3.03975e9i 0.479622 + 0.830729i
\(541\) −1.41291e9 −0.383641 −0.191820 0.981430i \(-0.561439\pi\)
−0.191820 + 0.981430i \(0.561439\pi\)
\(542\) 1.03604e9 + 1.79448e9i 0.279499 + 0.484106i
\(543\) −2.00044e8 + 3.46487e8i −0.0536200 + 0.0928726i
\(544\) −5.45520e7 + 9.44868e7i −0.0145283 + 0.0251637i
\(545\) −1.61501e9 −0.427353
\(546\) −3.87236e8 7.50867e7i −0.101813 0.0197419i
\(547\) 6.49585e9 1.69700 0.848498 0.529199i \(-0.177508\pi\)
0.848498 + 0.529199i \(0.177508\pi\)
\(548\) −4.40098e8 + 7.62272e8i −0.114240 + 0.197869i
\(549\) −8.08940e6 + 1.40113e7i −0.00208647 + 0.00361388i
\(550\) −7.68067e6 1.33033e7i −0.00196847 0.00340950i
\(551\) 4.26839e9 1.08701
\(552\) −2.01870e8 3.49648e8i −0.0510839 0.0884799i
\(553\) 9.68352e8 + 1.67723e9i 0.243498 + 0.421751i
\(554\) −1.78760e9 −0.446669
\(555\) 2.39853e9 + 4.15438e9i 0.595553 + 1.03153i
\(556\) −1.60099e8 + 2.77299e8i −0.0395027 + 0.0684206i
\(557\) 1.39415e9 2.41475e9i 0.341836 0.592077i −0.642938 0.765918i \(-0.722285\pi\)
0.984774 + 0.173841i \(0.0556179\pi\)
\(558\) −4.18443e8 −0.101957
\(559\) −2.90143e9 + 3.34080e9i −0.702539 + 0.808927i
\(560\) −1.02706e9 −0.247137
\(561\) 6.75751e7 1.17043e8i 0.0161591 0.0279883i
\(562\) −1.22204e9 + 2.11663e9i −0.290407 + 0.503000i
\(563\) 5.98612e8 + 1.03683e9i 0.141373 + 0.244865i 0.928014 0.372546i \(-0.121515\pi\)
−0.786641 + 0.617411i \(0.788182\pi\)
\(564\) 1.84031e9 0.431932
\(565\) −2.05003e9 3.55076e9i −0.478180 0.828232i
\(566\) −9.49216e8 1.64409e9i −0.220043 0.381126i
\(567\) 7.82739e8 0.180334
\(568\) 2.47776e8 + 4.29160e8i 0.0567335 + 0.0982652i
\(569\) −7.42629e8 + 1.28627e9i −0.168997 + 0.292711i −0.938067 0.346453i \(-0.887386\pi\)
0.769070 + 0.639164i \(0.220719\pi\)
\(570\) 1.17776e9 2.03995e9i 0.266377 0.461378i
\(571\) 4.58955e9 1.03168 0.515838 0.856686i \(-0.327481\pi\)
0.515838 + 0.856686i \(0.327481\pi\)
\(572\) −1.59439e9 4.62356e9i −0.356212 1.03298i
\(573\) −1.82542e9 −0.405342
\(574\) −1.17859e8 + 2.04137e8i −0.0260117 + 0.0450537i
\(575\) −4.10727e6 + 7.11400e6i −0.000900981 + 0.00156054i
\(576\) −2.99226e8 5.18274e8i −0.0652409 0.113001i
\(577\) −3.02370e9 −0.655275 −0.327638 0.944803i \(-0.606253\pi\)
−0.327638 + 0.944803i \(0.606253\pi\)
\(578\) 8.07443e8 + 1.39853e9i 0.173926 + 0.301249i
\(579\) 1.26508e9 + 2.19119e9i 0.270860 + 0.469143i
\(580\) −2.33270e9 −0.496433
\(581\) 8.56732e8 + 1.48390e9i 0.181229 + 0.313898i
\(582\) 5.84325e7 1.01208e8i 0.0122864 0.0212807i
\(583\) 1.03036e9 1.78464e9i 0.215353 0.373002i
\(584\) −4.03003e9 −0.837265
\(585\) −1.20926e9 + 1.39239e9i −0.249733 + 0.287551i
\(586\) −8.80983e8 −0.180853
\(587\) 3.79474e9 6.57268e9i 0.774370 1.34125i −0.160778 0.986991i \(-0.551400\pi\)
0.935148 0.354257i \(-0.115266\pi\)
\(588\) −2.43808e8 + 4.22288e8i −0.0494570 + 0.0856621i
\(589\) −3.70103e9 6.41038e9i −0.746310 1.29265i
\(590\) −1.04644e9 −0.209764
\(591\) −3.43057e9 5.94193e9i −0.683613 1.18405i
\(592\) −2.47232e9 4.28219e9i −0.489755 0.848281i
\(593\) 9.40608e9 1.85232 0.926162 0.377125i \(-0.123087\pi\)
0.926162 + 0.377125i \(0.123087\pi\)
\(594\) −1.20178e9 2.08155e9i −0.235274 0.407506i
\(595\) 3.21746e7 5.57281e7i 0.00626187 0.0108459i
\(596\) −3.75657e9 + 6.50657e9i −0.726825 + 1.25890i
\(597\) −2.13556e9 −0.410772
\(598\) 2.36657e8 2.72495e8i 0.0452548 0.0521079i
\(599\) −5.18983e9 −0.986642 −0.493321 0.869847i \(-0.664217\pi\)
−0.493321 + 0.869847i \(0.664217\pi\)
\(600\) −1.23991e7 + 2.14759e7i −0.00234349 + 0.00405904i
\(601\) −1.08356e9 + 1.87679e9i −0.203607 + 0.352658i −0.949688 0.313197i \(-0.898600\pi\)
0.746081 + 0.665855i \(0.231933\pi\)
\(602\) −3.77426e8 6.53722e8i −0.0705090 0.122125i
\(603\) 1.52658e8 0.0283537
\(604\) 2.24842e8 + 3.89437e8i 0.0415190 + 0.0719131i
\(605\) −1.49424e9 2.58810e9i −0.274332 0.475157i
\(606\) 9.83252e8 0.179478
\(607\) 7.94678e8 + 1.37642e9i 0.144222 + 0.249799i 0.929082 0.369873i \(-0.120599\pi\)
−0.784861 + 0.619672i \(0.787265\pi\)
\(608\) −4.71797e9 + 8.17177e9i −0.851320 + 1.47453i
\(609\) −4.66785e8 + 8.08495e8i −0.0837445 + 0.145050i
\(610\) −2.15841e7 −0.00385016
\(611\) 1.14663e9 + 3.32510e9i 0.203366 + 0.589740i
\(612\) 6.23164e7 0.0109894
\(613\) −1.07371e9 + 1.85971e9i −0.188267 + 0.326088i −0.944672 0.328015i \(-0.893620\pi\)
0.756406 + 0.654103i \(0.226954\pi\)
\(614\) 7.39468e8 1.28080e9i 0.128923 0.223301i
\(615\) −9.02355e8 1.56292e9i −0.156428 0.270941i
\(616\) 1.78380e9 0.307478
\(617\) −4.50821e9 7.80846e9i −0.772692 1.33834i −0.936082 0.351781i \(-0.885576\pi\)
0.163390 0.986562i \(-0.447757\pi\)
\(618\) −4.00694e8 6.94022e8i −0.0682893 0.118281i
\(619\) 4.83807e9 0.819889 0.409944 0.912110i \(-0.365548\pi\)
0.409944 + 0.912110i \(0.365548\pi\)
\(620\) 2.02264e9 + 3.50331e9i 0.340837 + 0.590347i
\(621\) −6.42658e8 + 1.11312e9i −0.107686 + 0.186518i
\(622\) 7.81859e8 1.35422e9i 0.130275 0.225643i
\(623\) 3.07999e9 0.510318
\(624\) −2.04117e9 + 2.35027e9i −0.336305 + 0.387233i
\(625\) −6.15850e9 −1.00901
\(626\) 7.27522e8 1.26011e9i 0.118532 0.205304i
\(627\) 5.84428e9 1.01226e10i 0.946879 1.64004i
\(628\) −1.94588e9 3.37036e9i −0.313514 0.543022i
\(629\) 3.09801e8 0.0496369
\(630\) −1.57305e8 2.72460e8i −0.0250640 0.0434121i
\(631\) −5.78468e9 1.00194e10i −0.916594 1.58759i −0.804551 0.593884i \(-0.797594\pi\)
−0.112043 0.993703i \(-0.535739\pi\)
\(632\) −5.34954e9 −0.842960
\(633\) 4.70848e9 + 8.15532e9i 0.737849 + 1.27799i
\(634\) −1.93510e9 + 3.35170e9i −0.301572 + 0.522339i
\(635\) 4.02042e9 6.96357e9i 0.623108 1.07926i
\(636\) −1.55599e9 −0.239831
\(637\) −9.14903e8 1.77404e8i −0.140245 0.0271941i
\(638\) 1.59738e9 0.243520
\(639\) 2.16848e8 3.75592e8i 0.0328778 0.0569461i
\(640\) 3.33341e9 5.77364e9i 0.502642 0.870602i
\(641\) −2.28098e9 3.95077e9i −0.342073 0.592487i 0.642745 0.766080i \(-0.277796\pi\)
−0.984817 + 0.173593i \(0.944462\pi\)
\(642\) −8.38519e8 −0.125066
\(643\) 3.52332e9 + 6.10256e9i 0.522653 + 0.905261i 0.999653 + 0.0263575i \(0.00839083\pi\)
−0.477000 + 0.878903i \(0.658276\pi\)
\(644\) −2.23081e8 3.86388e8i −0.0329126 0.0570064i
\(645\) 5.77935e9 0.848047
\(646\) −7.60614e7 1.31742e8i −0.0111007 0.0192270i
\(647\) −1.50407e8 + 2.60513e8i −0.0218325 + 0.0378151i −0.876735 0.480973i \(-0.840283\pi\)
0.854903 + 0.518788i \(0.173617\pi\)
\(648\) −1.08104e9 + 1.87241e9i −0.156073 + 0.270327i
\(649\) −5.19262e9 −0.745641
\(650\) −2.17626e7 4.21987e6i −0.00310824 0.000602701i
\(651\) 1.61896e9 0.229986
\(652\) −5.08638e8 + 8.80987e8i −0.0718691 + 0.124481i
\(653\) 2.57398e9 4.45826e9i 0.361750 0.626570i −0.626499 0.779423i \(-0.715513\pi\)
0.988249 + 0.152852i \(0.0488459\pi\)
\(654\) −4.17521e8 7.23168e8i −0.0583655 0.101092i
\(655\) 1.35514e10 1.88425
\(656\) 9.30115e8 + 1.61101e9i 0.128639 + 0.222810i
\(657\) 1.76350e9 + 3.05447e9i 0.242603 + 0.420201i
\(658\) −6.00023e8 −0.0821064
\(659\) 5.95848e9 + 1.03204e10i 0.811029 + 1.40474i 0.912144 + 0.409869i \(0.134426\pi\)
−0.101115 + 0.994875i \(0.532241\pi\)
\(660\) −3.19393e9 + 5.53206e9i −0.432436 + 0.749002i
\(661\) 2.18225e9 3.77977e9i 0.293900 0.509050i −0.680828 0.732443i \(-0.738380\pi\)
0.974728 + 0.223393i \(0.0717134\pi\)
\(662\) 1.07685e8 0.0144263
\(663\) −6.35818e7 1.84380e8i −0.00847296 0.0245707i
\(664\) −4.73291e9 −0.627394
\(665\) 2.78265e9 4.81969e9i 0.366929 0.635540i
\(666\) 7.57322e8 1.31172e9i 0.0993392 0.172061i
\(667\) −4.27102e8 7.39762e8i −0.0557303 0.0965277i
\(668\) 6.73647e9 0.874410
\(669\) −5.50338e9 9.53213e9i −0.710621 1.23083i
\(670\) 1.01830e8 + 1.76376e8i 0.0130802 + 0.0226557i
\(671\) −1.07104e8 −0.0136860
\(672\) −1.03190e9 1.78731e9i −0.131173 0.227199i
\(673\) 3.86230e9 6.68970e9i 0.488420 0.845968i −0.511492 0.859288i \(-0.670907\pi\)
0.999911 + 0.0133205i \(0.00424018\pi\)
\(674\) −2.22238e8 + 3.84928e8i −0.0279582 + 0.0484250i
\(675\) 7.89460e7 0.00988023
\(676\) −6.54633e9 2.63791e9i −0.815051 0.328433i
\(677\) 8.87356e9 1.09910 0.549550 0.835461i \(-0.314799\pi\)
0.549550 + 0.835461i \(0.314799\pi\)
\(678\) 1.05997e9 1.83593e9i 0.130614 0.226231i
\(679\) 1.38056e8 2.39120e8i 0.0169243 0.0293137i
\(680\) 8.88724e7 + 1.53932e8i 0.0108389 + 0.0187735i
\(681\) −9.75894e9 −1.18410
\(682\) −1.38505e9 2.39898e9i −0.167194 0.289589i
\(683\) 1.19534e9 + 2.07040e9i 0.143556 + 0.248646i 0.928833 0.370498i \(-0.120813\pi\)
−0.785277 + 0.619144i \(0.787480\pi\)
\(684\) 5.38948e9 0.643947
\(685\) 1.09860e9 + 1.90284e9i 0.130594 + 0.226196i
\(686\) 7.94922e7 1.37685e8i 0.00940135 0.0162836i
\(687\) −5.86895e9 + 1.01653e10i −0.690576 + 1.19611i
\(688\) −5.95714e9 −0.697394
\(689\) −9.69475e8 2.81137e9i −0.112920 0.327455i
\(690\) −4.71396e8 −0.0546278
\(691\) 2.78751e9 4.82811e9i 0.321398 0.556678i −0.659379 0.751811i \(-0.729181\pi\)
0.980777 + 0.195133i \(0.0625140\pi\)
\(692\) 5.05164e9 8.74971e9i 0.579511 1.00374i
\(693\) −7.80575e8 1.35200e9i −0.0890940 0.154315i
\(694\) 5.03501e9 0.571797
\(695\) 3.99651e8 + 6.92215e8i 0.0451579 + 0.0782158i
\(696\) −1.28935e9 2.23322e9i −0.144957 0.251072i
\(697\) −1.16550e8 −0.0130376
\(698\) 1.53394e8 + 2.65686e8i 0.0170732 + 0.0295716i
\(699\) −8.05444e8 + 1.39507e9i −0.0892001 + 0.154499i
\(700\) −1.37020e7 + 2.37326e7i −0.00150987 + 0.00261518i
\(701\) −1.34671e10 −1.47660 −0.738298 0.674474i \(-0.764370\pi\)
−0.738298 + 0.674474i \(0.764370\pi\)
\(702\) −3.40516e9 6.60276e8i −0.371499 0.0720353i
\(703\) 2.67933e10 2.90859
\(704\) 1.98088e9 3.43099e9i 0.213971 0.370608i
\(705\) 2.29696e9 3.97846e9i 0.246884 0.427615i
\(706\) −2.11487e9 3.66307e9i −0.226187 0.391767i
\(707\) 2.32308e9 0.247227
\(708\) 1.96038e9 + 3.39549e9i 0.207599 + 0.359572i
\(709\) 7.26425e9 + 1.25820e10i 0.765471 + 1.32584i 0.939997 + 0.341183i \(0.110827\pi\)
−0.174526 + 0.984653i \(0.555839\pi\)
\(710\) 5.78593e8 0.0606693
\(711\) 2.34091e9 + 4.05457e9i 0.244253 + 0.423059i
\(712\) −4.25376e9 + 7.36772e9i −0.441665 + 0.764985i
\(713\) −7.40663e8 + 1.28287e9i −0.0765257 + 0.132546i
\(714\) 3.32719e7 0.00342085
\(715\) −1.19854e10 2.32402e9i −1.22626 0.237777i
\(716\) −5.67187e9 −0.577471
\(717\) 3.81172e9 6.60209e9i 0.386192 0.668905i
\(718\) −3.00761e9 + 5.20933e9i −0.303239 + 0.525226i
\(719\) 3.71154e9 + 6.42857e9i 0.372394 + 0.645006i 0.989933 0.141534i \(-0.0452036\pi\)
−0.617539 + 0.786540i \(0.711870\pi\)
\(720\) −2.48283e9 −0.247904
\(721\) −9.46700e8 1.63973e9i −0.0940673 0.162929i
\(722\) −4.81740e9 8.34398e9i −0.476357 0.825075i
\(723\) −1.02624e10 −1.00987
\(724\) −6.10622e8 1.05763e9i −0.0597981 0.103573i
\(725\) −2.62333e7 + 4.54373e7i −0.00255664 + 0.00442823i
\(726\) 7.72599e8 1.33818e9i 0.0749335 0.129789i
\(727\) −4.98321e9 −0.480993 −0.240497 0.970650i \(-0.577310\pi\)
−0.240497 + 0.970650i \(0.577310\pi\)
\(728\) 1.68794e9 1.94355e9i 0.162143 0.186697i
\(729\) 1.08489e10 1.03715
\(730\) −2.35268e9 + 4.07496e9i −0.223837 + 0.387698i
\(731\) 1.86619e8 3.23233e8i 0.0176703 0.0306059i
\(732\) 4.04354e7 + 7.00361e7i 0.00381042 + 0.00659984i
\(733\) 4.35668e9 0.408594 0.204297 0.978909i \(-0.434509\pi\)
0.204297 + 0.978909i \(0.434509\pi\)
\(734\) −3.33491e9 5.77623e9i −0.311278 0.539149i
\(735\) 6.08612e8 + 1.05415e9i 0.0565373 + 0.0979255i
\(736\) 1.88835e9 0.174586
\(737\) 5.05302e8 + 8.75208e8i 0.0464959 + 0.0805332i
\(738\) −2.84913e8 + 4.93484e8i −0.0260925 + 0.0451935i
\(739\) −1.21235e9 + 2.09986e9i −0.110503 + 0.191396i −0.915973 0.401240i \(-0.868579\pi\)
0.805470 + 0.592636i \(0.201913\pi\)
\(740\) −1.46427e10 −1.32834
\(741\) −5.49892e9 1.59463e10i −0.496494 1.43978i
\(742\) 5.07319e8 0.0455898
\(743\) −4.75742e9 + 8.24010e9i −0.425511 + 0.737007i −0.996468 0.0839732i \(-0.973239\pi\)
0.570957 + 0.820980i \(0.306572\pi\)
\(744\) −2.23593e9 + 3.87275e9i −0.199046 + 0.344758i
\(745\) 9.37743e9 + 1.62422e10i 0.830877 + 1.43912i
\(746\) −3.35528e8 −0.0295898
\(747\) 2.07108e9 + 3.58721e9i 0.181792 + 0.314872i
\(748\) 2.06268e8 + 3.57267e8i 0.0180209 + 0.0312131i
\(749\) −1.98113e9 −0.172277
\(750\) −1.57779e9 2.73281e9i −0.136563 0.236534i
\(751\) −8.97311e9 + 1.55419e10i −0.773042 + 1.33895i 0.162847 + 0.986651i \(0.447932\pi\)
−0.935888 + 0.352296i \(0.885401\pi\)
\(752\) −2.36763e9 + 4.10085e9i −0.203026 + 0.351651i
\(753\) 8.97789e9 0.766288
\(754\) 1.51153e9 1.74043e9i 0.128416 0.147862i
\(755\) 1.12253e9 0.0949258
\(756\) −2.14393e9 + 3.71340e9i −0.180461 + 0.312568i
\(757\) −7.42568e9 + 1.28617e10i −0.622158 + 1.07761i 0.366925 + 0.930250i \(0.380410\pi\)
−0.989083 + 0.147358i \(0.952923\pi\)
\(758\) 1.39500e9 + 2.41621e9i 0.116341 + 0.201508i
\(759\) −2.33915e9 −0.194184
\(760\) 7.68620e9 + 1.33129e10i 0.635132 + 1.10008i
\(761\) 4.63085e9 + 8.02087e9i 0.380903 + 0.659743i 0.991192 0.132436i \(-0.0422798\pi\)
−0.610289 + 0.792179i \(0.708946\pi\)
\(762\) 4.15753e9 0.340403
\(763\) −9.86458e8 1.70859e9i −0.0803975 0.139253i
\(764\) 2.78598e9 4.82546e9i 0.226022 0.391482i
\(765\) 7.77794e7 1.34718e8i 0.00628130 0.0108795i
\(766\) 2.88986e9 0.232315
\(767\) −4.91356e9 + 5.65764e9i −0.393199 + 0.452743i
\(768\) 4.28888e7 0.00341649
\(769\) −6.71164e9 + 1.16249e10i −0.532214 + 0.921822i 0.467078 + 0.884216i \(0.345307\pi\)
−0.999293 + 0.0376062i \(0.988027\pi\)
\(770\) 1.04136e9 1.80369e9i 0.0822024 0.142379i
\(771\) 4.38904e8 + 7.60204e8i 0.0344889 + 0.0597365i
\(772\) −7.72317e9 −0.604136
\(773\) −2.14709e9 3.71887e9i −0.167195 0.289589i 0.770238 0.637757i \(-0.220137\pi\)
−0.937432 + 0.348167i \(0.886804\pi\)
\(774\) −9.12396e8 1.58032e9i −0.0707278 0.122504i
\(775\) 9.09853e7 0.00702126
\(776\) 3.81336e8 + 6.60494e8i 0.0292949 + 0.0507403i
\(777\) −2.93008e9 + 5.07505e9i −0.224082 + 0.388121i
\(778\) −2.11445e9 + 3.66233e9i −0.160979 + 0.278823i
\(779\) −1.00800e10 −0.763972
\(780\) 3.00519e9 + 8.71473e9i 0.226747 + 0.657541i
\(781\) 2.87109e9 0.215659
\(782\) −1.52217e7 + 2.63647e7i −0.00113825 + 0.00197151i
\(783\) −4.10468e9 + 7.10951e9i −0.305571 + 0.529265i
\(784\) −6.27336e8 1.08658e9i −0.0464937 0.0805294i
\(785\) −9.71489e9 −0.716794
\(786\) 3.50338e9 + 6.06803e9i 0.257341 + 0.445727i
\(787\) −9.54567e9 1.65336e10i −0.698063 1.20908i −0.969137 0.246523i \(-0.920712\pi\)
0.271074 0.962559i \(-0.412621\pi\)
\(788\) 2.09432e10 1.52476
\(789\) −6.04861e8 1.04765e9i −0.0438415 0.0759358i
\(790\) −3.12300e9 + 5.40919e9i −0.225360 + 0.390335i
\(791\) 2.50435e9 4.33766e9i 0.179919 0.311629i
\(792\) 4.31219e9 0.308432
\(793\) −1.01348e8 + 1.16696e8i −0.00721706 + 0.00830997i
\(794\) 6.26223e9 0.443974
\(795\) −1.94208e9 + 3.36379e9i −0.137083 + 0.237434i
\(796\) 3.25932e9 5.64531e9i 0.229050 0.396727i
\(797\) −9.02091e9 1.56247e10i −0.631170 1.09322i −0.987313 0.158787i \(-0.949242\pi\)
0.356143 0.934431i \(-0.384092\pi\)
\(798\) 2.87754e9 0.200453
\(799\) −1.48341e8 2.56934e8i −0.0102884 0.0178200i
\(800\) −5.79928e7 1.00446e8i −0.00400460 0.00693616i
\(801\) 7.44561e9 0.511901
\(802\) 3.54150e9 + 6.13406e9i 0.242425 + 0.419892i
\(803\) −1.16744e10 + 2.02207e10i −0.795667 + 1.37814i
\(804\) 3.81536e8 6.60840e8i 0.0258904 0.0448436i
\(805\) −1.11374e9 −0.0752489
\(806\) −3.92445e9 7.60968e8i −0.264001 0.0511910i
\(807\) 4.24654e9 0.284431
\(808\) −3.20840e9 + 5.55711e9i −0.213968 + 0.370603i
\(809\) −9.22144e8 + 1.59720e9i −0.0612320 + 0.106057i −0.895016 0.446033i \(-0.852836\pi\)
0.833784 + 0.552090i \(0.186170\pi\)
\(810\) 1.26219e9 + 2.18618e9i 0.0834503 + 0.144540i
\(811\) 1.66773e10 1.09788 0.548938 0.835863i \(-0.315032\pi\)
0.548938 + 0.835863i \(0.315032\pi\)
\(812\) −1.42483e9 2.46788e9i −0.0933935 0.161762i
\(813\) −9.69008e9 1.67837e10i −0.632427 1.09540i
\(814\) 1.00270e10 0.651606
\(815\) 1.26970e9 + 2.19918e9i 0.0821579 + 0.142302i
\(816\) 1.31287e8 2.27396e8i 0.00845877 0.0146510i
\(817\) 1.61399e10 2.79550e10i 1.03543 1.79342i
\(818\) 4.70882e9 0.300799
\(819\) −2.21170e9 4.28859e8i −0.140680 0.0272785i
\(820\) 5.50875e9 0.348903
\(821\) −4.80894e9 + 8.32932e9i −0.303283 + 0.525301i −0.976878 0.213800i \(-0.931416\pi\)
0.673595 + 0.739101i \(0.264749\pi\)
\(822\) −5.68035e8 + 9.83866e8i −0.0356717 + 0.0617852i
\(823\) −7.15180e9 1.23873e10i −0.447214 0.774598i 0.550989 0.834512i \(-0.314251\pi\)
−0.998204 + 0.0599144i \(0.980917\pi\)
\(824\) 5.22993e9 0.325650
\(825\) 7.18372e7 + 1.24426e8i 0.00445411 + 0.00771474i
\(826\) −6.39171e8 1.10708e9i −0.0394627 0.0683514i
\(827\) 8.29655e9 0.510068 0.255034 0.966932i \(-0.417913\pi\)
0.255034 + 0.966932i \(0.417913\pi\)
\(828\) −5.39280e8 9.34061e8i −0.0330148 0.0571833i
\(829\) 4.99519e9 8.65192e9i 0.304517 0.527438i −0.672637 0.739973i \(-0.734838\pi\)
0.977154 + 0.212534i \(0.0681718\pi\)
\(830\) −2.76301e9 + 4.78568e9i −0.167730 + 0.290516i
\(831\) 1.67194e10 1.01069
\(832\) −1.86382e9 5.40489e9i −0.112195 0.325353i
\(833\) 7.86099e7 0.00471215
\(834\) −2.06640e8 + 3.57911e8i −0.0123348 + 0.0213646i
\(835\) 8.40804e9 1.45632e10i 0.499795 0.865671i
\(836\) 1.78393e10 + 3.08985e10i 1.05598 + 1.82901i
\(837\) 1.42363e10 0.839187
\(838\) 3.55185e9 + 6.15198e9i 0.208497 + 0.361128i
\(839\) 1.57890e10 + 2.73474e10i 0.922971 + 1.59863i 0.794792 + 0.606881i \(0.207580\pi\)
0.128179 + 0.991751i \(0.459087\pi\)
\(840\) −3.36221e9 −0.195725
\(841\) 5.89702e9 + 1.02139e10i 0.341859 + 0.592117i
\(842\) 4.03742e9 6.99301e9i 0.233083 0.403712i
\(843\) 1.14297e10 1.97968e10i 0.657110 1.13815i
\(844\) −2.87446e10 −1.64573
\(845\) −1.38735e10 + 1.08596e10i −0.791017 + 0.619180i
\(846\) −1.45050e9 −0.0823612
\(847\) 1.82538e9 3.16166e9i 0.103220 0.178782i
\(848\) 2.00183e9 3.46727e9i 0.112730 0.195255i
\(849\) 8.87800e9 + 1.53771e10i 0.497896 + 0.862380i
\(850\) 1.86988e6 0.000104435
\(851\) −2.68099e9 4.64360e9i −0.149122 0.258286i
\(852\) −1.08393e9 1.87742e9i −0.0600430 0.103998i
\(853\) −1.80520e10 −0.995873 −0.497937 0.867213i \(-0.665909\pi\)
−0.497937 + 0.867213i \(0.665909\pi\)
\(854\) −1.31837e7 2.28348e7i −0.000724327 0.00125457i
\(855\) 6.72681e9 1.16512e10i 0.368068 0.637512i
\(856\) 2.73613e9 4.73911e9i 0.149100 0.258249i
\(857\) −2.79607e10 −1.51745 −0.758727 0.651409i \(-0.774178\pi\)
−0.758727 + 0.651409i \(0.774178\pi\)
\(858\) −2.05789e9 5.96764e9i −0.111228 0.322550i
\(859\) −2.33350e10 −1.25612 −0.628061 0.778164i \(-0.716151\pi\)
−0.628061 + 0.778164i \(0.716151\pi\)
\(860\) −8.82053e9 + 1.52776e10i −0.472879 + 0.819050i
\(861\) 1.10233e9 1.90929e9i 0.0588573 0.101944i
\(862\) −3.46521e9 6.00192e9i −0.184270 0.319165i
\(863\) −2.58108e10 −1.36699 −0.683494 0.729956i \(-0.739540\pi\)
−0.683494 + 0.729956i \(0.739540\pi\)
\(864\) −9.07403e9 1.57167e10i −0.478633 0.829016i
\(865\) −1.26103e10 2.18417e10i −0.662474 1.14744i
\(866\) 1.66550e9 0.0871429
\(867\) −7.55200e9 1.30804e10i −0.393546 0.681641i
\(868\) −2.47088e9 + 4.27969e9i −0.128243 + 0.222123i
\(869\) −1.54969e10 + 2.68414e10i −0.801079 + 1.38751i
\(870\) −3.01082e9 −0.155013
\(871\) 1.43173e9 + 2.77620e8i 0.0734174 + 0.0142360i
\(872\) 5.44957e9 0.278326
\(873\) 3.33738e8 5.78051e8i 0.0169768 0.0294047i
\(874\) −1.31646e9 + 2.28017e9i −0.0666986 + 0.115525i
\(875\) −3.72776e9 6.45667e9i −0.188113 0.325822i
\(876\) 1.76299e10 0.886107
\(877\) −1.34986e10 2.33803e10i −0.675758 1.17045i −0.976247 0.216662i \(-0.930483\pi\)
0.300489 0.953785i \(-0.402850\pi\)
\(878\) −1.68586e9 2.91999e9i −0.0840601 0.145596i
\(879\) 8.23982e9 0.409220
\(880\) −8.21821e9 1.42344e10i −0.406526 0.704123i
\(881\) −1.19710e10 + 2.07344e10i −0.589814 + 1.02159i 0.404443 + 0.914563i \(0.367465\pi\)
−0.994256 + 0.107024i \(0.965868\pi\)
\(882\) 1.92166e8 3.32840e8i 0.00943052 0.0163341i
\(883\) 2.54074e10 1.24193 0.620966 0.783838i \(-0.286741\pi\)
0.620966 + 0.783838i \(0.286741\pi\)
\(884\) 5.84445e8 + 1.13327e8i 0.0284552 + 0.00551758i
\(885\) 9.78731e9 0.474638
\(886\) −6.15111e8 + 1.06540e9i −0.0297123 + 0.0514631i
\(887\) 9.39533e9 1.62732e10i 0.452043 0.782961i −0.546470 0.837479i \(-0.684029\pi\)
0.998513 + 0.0545176i \(0.0173621\pi\)
\(888\) −8.09344e9 1.40183e10i −0.387871 0.671813i
\(889\) 9.82280e9 0.468899
\(890\) 4.96658e9 + 8.60237e9i 0.236152 + 0.409028i
\(891\) 6.26323e9 + 1.08482e10i 0.296638 + 0.513792i
\(892\) 3.35974e10 1.58500
\(893\) −1.28294e10 2.22211e10i −0.602872 1.04420i
\(894\) −4.84862e9 + 8.39805e9i −0.226953 + 0.393095i
\(895\) −7.07927e9 + 1.22617e10i −0.330071 + 0.571700i
\(896\) 8.14428e9 0.378246
\(897\) −2.21345e9 + 2.54864e9i −0.102399 + 0.117906i
\(898\) −7.03481e9 −0.324179
\(899\) −4.73064e9 + 8.19371e9i −0.217151 + 0.376116i
\(900\) −3.31234e7 + 5.73714e7i −0.00151456 + 0.00262329i
\(901\) 1.25422e8 + 2.17237e8i 0.00571264 + 0.00989459i
\(902\) −3.77227e9 −0.171151
\(903\) 3.53006e9 + 6.11425e9i 0.159542 + 0.276335i
\(904\) 6.91749e9 + 1.19814e10i 0.311429 + 0.539411i
\(905\) −3.04856e9 −0.136718
\(906\) 2.90204e8 + 5.02647e8i 0.0129644 + 0.0224551i
\(907\) 1.76282e10 3.05329e10i 0.784481 1.35876i −0.144828 0.989457i \(-0.546263\pi\)
0.929309 0.369304i \(-0.120404\pi\)
\(908\) 1.48942e10 2.57976e10i 0.660265 1.14361i
\(909\) 5.61585e9 0.247995
\(910\) −9.79824e8 2.84138e9i −0.0431026 0.124993i
\(911\) 7.79922e9 0.341772 0.170886 0.985291i \(-0.445337\pi\)
0.170886 + 0.985291i \(0.445337\pi\)
\(912\) 1.13545e10 1.96665e10i 0.495662 0.858511i
\(913\) −1.37106e10 + 2.37474e10i −0.596223 + 1.03269i
\(914\) −7.12002e9 1.23322e10i −0.308439 0.534232i
\(915\) 2.01876e8 0.00871184
\(916\) −1.79146e10 3.10289e10i −0.770144 1.33393i
\(917\) 8.27727e9 + 1.43367e10i 0.354482 + 0.613981i
\(918\) 2.92576e8 0.0124822
\(919\) −5.42237e9 9.39182e9i −0.230454 0.399159i 0.727488 0.686121i \(-0.240688\pi\)
−0.957942 + 0.286962i \(0.907355\pi\)
\(920\) 1.53819e9 2.66422e9i 0.0651256 0.112801i
\(921\) −6.91623e9 + 1.19793e10i −0.291716 + 0.505268i
\(922\) 7.13774e9 0.299918
\(923\) 2.71679e9 3.12821e9i 0.113724 0.130945i
\(924\) −7.80351e9 −0.325415
\(925\) −1.64670e8 + 2.85217e8i −0.00684099 + 0.0118489i
\(926\) 5.48725e9 9.50419e9i 0.227099 0.393348i
\(927\) −2.28857e9 3.96391e9i −0.0943592 0.163435i
\(928\) 1.20610e10 0.495410
\(929\) −1.60193e10 2.77462e10i −0.655524 1.13540i −0.981762 0.190113i \(-0.939114\pi\)
0.326238 0.945288i \(-0.394219\pi\)
\(930\) 2.61062e9 + 4.52173e9i 0.106427 + 0.184338i
\(931\) 6.79864e9 0.276120
\(932\) −2.45856e9 4.25836e9i −0.0994777 0.172300i
\(933\) −7.31271e9 + 1.26660e10i −0.294776 + 0.510568i
\(934\) −3.08367e9 + 5.34108e9i −0.123838 + 0.214494i
\(935\) 1.02980e9 0.0412016
\(936\) 4.08045e9 4.69837e9i 0.162646 0.187276i
\(937\) 2.05762e10 0.817104 0.408552 0.912735i \(-0.366034\pi\)
0.408552 + 0.912735i \(0.366034\pi\)
\(938\) −1.24397e8 + 2.15463e8i −0.00492155 + 0.00852437i
\(939\) −6.80450e9 + 1.17857e10i −0.268205 + 0.464545i
\(940\) 7.01132e9 + 1.21440e10i 0.275329 + 0.476884i
\(941\) −4.98415e10 −1.94997 −0.974984 0.222274i \(-0.928652\pi\)
−0.974984 + 0.222274i \(0.928652\pi\)
\(942\) −2.51155e9 4.35013e9i −0.0978957 0.169560i
\(943\) 1.00862e9 + 1.74697e9i 0.0391683 + 0.0678415i
\(944\) −1.00884e10 −0.390320
\(945\) 5.35184e9 + 9.26966e9i 0.206296 + 0.357316i
\(946\) 6.04009e9 1.04617e10i 0.231966 0.401777i
\(947\) 1.73630e10 3.00735e10i 0.664353 1.15069i −0.315107 0.949056i \(-0.602040\pi\)
0.979460 0.201637i \(-0.0646262\pi\)
\(948\) 2.34023e10 0.892134
\(949\) 1.09845e10 + 3.18540e10i 0.417206 + 1.20985i
\(950\) 1.61718e8 0.00611963
\(951\) 1.80990e10 3.13484e10i 0.682374 1.18191i
\(952\) −1.08568e8 + 1.88045e8i −0.00407823 + 0.00706369i
\(953\) −2.52633e10 4.37573e10i −0.945507 1.63767i −0.754733 0.656032i \(-0.772234\pi\)
−0.190774 0.981634i \(-0.561100\pi\)
\(954\) 1.22640e9 0.0457313
\(955\) −6.95457e9 1.20457e10i −0.258380 0.447527i
\(956\) 1.16350e10 + 2.01524e10i 0.430689 + 0.745976i
\(957\) −1.49403e10 −0.551019
\(958\) −1.95002e9 3.37753e9i −0.0716570 0.124114i
\(959\) −1.34207e9 + 2.32453e9i −0.0491372 + 0.0851081i
\(960\) −3.73367e9 + 6.46691e9i −0.136203 + 0.235911i
\(961\) −1.11053e10 −0.403642
\(962\) 9.48814e9 1.09250e10i 0.343612 0.395646i
\(963\) −4.78921e9 −0.172811
\(964\) 1.56627e10 2.71286e10i 0.563115 0.975344i
\(965\) −9.63957e9 + 1.66962e10i −0.345312 + 0.598098i
\(966\) −2.87932e8 4.98712e8i −0.0102771 0.0178004i
\(967\) 3.53932e10 1.25871 0.629357 0.777117i \(-0.283319\pi\)
0.629357 + 0.777117i \(0.283319\pi\)
\(968\) 5.04206e9 + 8.73310e9i 0.178667 + 0.309460i
\(969\) 7.11401e8 + 1.23218e9i 0.0251178 + 0.0435053i
\(970\) 8.90477e8 0.0313272
\(971\) 1.80844e10 + 3.13231e10i 0.633924 + 1.09799i 0.986742 + 0.162296i \(0.0518901\pi\)
−0.352818 + 0.935692i \(0.614777\pi\)
\(972\) −8.94075e9 + 1.54858e10i −0.312278 + 0.540882i
\(973\) −4.88218e8 + 8.45619e8i −0.0169910 + 0.0294293i
\(974\) 1.79149e9 0.0621239
\(975\) 2.03545e8 + 3.94683e7i 0.00703307 + 0.00136374i
\(976\) −2.08086e8 −0.00716421
\(977\) −1.85678e10 + 3.21604e10i −0.636986 + 1.10329i 0.349104 + 0.937084i \(0.386486\pi\)
−0.986091 + 0.166209i \(0.946847\pi\)
\(978\) −6.56500e8 + 1.13709e9i −0.0224413 + 0.0388696i
\(979\) 2.46451e10 + 4.26865e10i 0.839442 + 1.45396i
\(980\) −3.71550e9 −0.126103
\(981\) −2.38468e9 4.13038e9i −0.0806470 0.139685i
\(982\) −9.05607e9 1.56856e10i −0.305175 0.528579i
\(983\) −4.98784e10 −1.67485 −0.837424 0.546554i \(-0.815939\pi\)
−0.837424 + 0.546554i \(0.815939\pi\)
\(984\) 3.04484e9 + 5.27382e9i 0.101878 + 0.176458i
\(985\) 2.61400e10 4.52757e10i 0.871522 1.50952i
\(986\) −9.72213e7 + 1.68392e8i −0.00322992 + 0.00559439i
\(987\) 5.61200e9 0.185784
\(988\) 5.05462e10 + 9.80113e9i 1.66740 + 0.323316i
\(989\) −6.45992e9 −0.212344
\(990\) 2.51740e9 4.36027e9i 0.0824574 0.142820i
\(991\) 2.16751e10 3.75424e10i 0.707464 1.22536i −0.258332 0.966056i \(-0.583173\pi\)
0.965795 0.259306i \(-0.0834940\pi\)
\(992\) −1.04578e10 1.81135e10i −0.340134 0.589130i
\(993\) −1.00718e9 −0.0326426
\(994\) 3.53409e8 + 6.12122e8i 0.0114137 + 0.0197690i
\(995\) −8.13615e9 1.40922e10i −0.261841 0.453523i
\(996\) 2.07048e10 0.663993
\(997\) −1.30797e10 2.26548e10i −0.417990 0.723980i 0.577747 0.816216i \(-0.303932\pi\)
−0.995737 + 0.0922355i \(0.970599\pi\)
\(998\) −1.00765e10 + 1.74529e10i −0.320886 + 0.555791i
\(999\) −2.57657e10 + 4.46275e10i −0.817641 + 1.41620i
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 91.8.f.a.22.10 48
13.3 even 3 inner 91.8.f.a.29.10 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.f.a.22.10 48 1.1 even 1 trivial
91.8.f.a.29.10 yes 48 13.3 even 3 inner