LMFDB - Embedded newform 99.8.f.c.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(37,99)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	99.91
Dual form			99.8.f.c.37.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.43584 - 6.12900i) q^{2} +(-5.95538 + 18.3288i) q^{4} +(186.461 + 135.472i) q^{5} +(-43.6776 + 134.426i) q^{7} +(474.540 + 1460.49i) q^{8} +O(q^{10})$	\(q+(8.43584 - 6.12900i) q^{2} +(-5.95538 + 18.3288i) q^{4} +(186.461 + 135.472i) q^{5} +(-43.6776 + 134.426i) q^{7} +(474.540 + 1460.49i) q^{8} +2403.26 q^{10} +(-4405.31 + 283.647i) q^{11} +(-2402.15 + 1745.26i) q^{13} +(455.438 + 1401.69i) q^{14} +(10958.8 + 7962.01i) q^{16} +(-32135.9 - 23348.1i) q^{17} +(11338.9 + 34897.4i) q^{19} +(-3593.47 + 2610.81i) q^{20} +(-35424.0 + 29392.9i) q^{22} -26232.0 q^{23} +(-7726.90 - 23780.9i) q^{25} +(-9567.43 + 29445.5i) q^{26} +(-2203.74 - 1601.11i) q^{28} +(-62224.8 + 191508. i) q^{29} +(34405.6 - 24997.1i) q^{31} -55317.1 q^{32} -414194. q^{34} +(-26355.1 + 19148.1i) q^{35} +(-93379.6 + 287393. i) q^{37} +(309539. + 224893. i) q^{38} +(-109371. + 336610. i) q^{40} +(166492. + 512408. i) q^{41} +282374. q^{43} +(21036.4 - 82433.0i) q^{44} +(-221289. + 160776. i) q^{46} +(-225672. - 694546. i) q^{47} +(650098. + 472324. i) q^{49} +(-210936. - 153254. i) q^{50} +(-17682.8 - 54422.1i) q^{52} +(367870. - 267273. i) q^{53} +(-859843. - 543905. i) q^{55} -217054. q^{56} +(648835. + 1.99691e6i) q^{58} +(-367511. + 1.13108e6i) q^{59} +(353988. + 257188. i) q^{61} +(137033. - 421743. i) q^{62} +(-1.86937e6 + 1.35818e6i) q^{64} -684340. q^{65} +2.93699e6 q^{67} +(619324. - 449965. i) q^{68} +(-104969. + 323060. i) q^{70} +(-639020. - 464275. i) q^{71} +(-22813.8 + 70213.6i) q^{73} +(973695. + 2.99672e6i) q^{74} -707154. q^{76} +(154284. - 604576. i) q^{77} +(-4.91172e6 + 3.56858e6i) q^{79} +(964753. + 2.96920e6i) q^{80} +(4.54505e6 + 3.30217e6i) q^{82} +(-1.60269e6 - 1.16442e6i) q^{83} +(-2.82908e6 - 8.70702e6i) q^{85} +(2.38206e6 - 1.73067e6i) q^{86} +(-2.50476e6 - 6.29928e6i) q^{88} -7.69913e6 q^{89} +(-129688. - 399140. i) q^{91} +(156221. - 480800. i) q^{92} +(-6.16060e6 - 4.47594e6i) q^{94} +(-2.61336e6 + 8.04309e6i) q^{95} +(655646. - 476355. i) q^{97} +8.37899e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8}+O(q^{10}) $ 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8} - 1352 q^{10} + 18851 q^{11} + 14635 q^{13} - 62912 q^{14} - 36148 q^{16} + 10338 q^{17} + 90342 q^{19} + 289719 q^{20} - 202339 q^{22} - 138508 q^{23} - 174068 q^{25} - 466130 q^{26} - 640233 q^{28} + 487290 q^{29} - 388352 q^{31} - 2726322 q^{32} - 1543708 q^{34} - 742659 q^{35} + 670209 q^{37} - 2282072 q^{38} + 4641741 q^{40} + 2721357 q^{41} - 199784 q^{43} + 5887437 q^{44} + 3389447 q^{46} - 2112053 q^{47} + 3927748 q^{49} + 3663090 q^{50} - 4343053 q^{52} + 1743854 q^{53} - 8387710 q^{55} + 6307818 q^{56} + 546605 q^{58} + 218820 q^{59} - 743157 q^{61} - 3996183 q^{62} - 21725666 q^{64} - 4895794 q^{65} - 3235686 q^{67} - 961671 q^{68} + 31155916 q^{70} - 9848757 q^{71} - 6667768 q^{73} + 31115192 q^{74} - 6535748 q^{76} - 8320585 q^{77} - 10121851 q^{79} - 44592526 q^{80} + 24927115 q^{82} - 13288897 q^{83} - 28050005 q^{85} - 20937351 q^{86} + 39687014 q^{88} + 40241460 q^{89} + 8733043 q^{91} - 11607651 q^{92} - 7877385 q^{94} - 14371097 q^{95} + 30518151 q^{97} + 16954218 q^{98}+O(q^{100}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8 - 1352 * q^10 + 18851 * q^11 + 14635 * q^13 - 62912 * q^14 - 36148 * q^16 + 10338 * q^17 + 90342 * q^19 + 289719 * q^20 - 202339 * q^22 - 138508 * q^23 - 174068 * q^25 - 466130 * q^26 - 640233 * q^28 + 487290 * q^29 - 388352 * q^31 - 2726322 * q^32 - 1543708 * q^34 - 742659 * q^35 + 670209 * q^37 - 2282072 * q^38 + 4641741 * q^40 + 2721357 * q^41 - 199784 * q^43 + 5887437 * q^44 + 3389447 * q^46 - 2112053 * q^47 + 3927748 * q^49 + 3663090 * q^50 - 4343053 * q^52 + 1743854 * q^53 - 8387710 * q^55 + 6307818 * q^56 + 546605 * q^58 + 218820 * q^59 - 743157 * q^61 - 3996183 * q^62 - 21725666 * q^64 - 4895794 * q^65 - 3235686 * q^67 - 961671 * q^68 + 31155916 * q^70 - 9848757 * q^71 - 6667768 * q^73 + 31115192 * q^74 - 6535748 * q^76 - 8320585 * q^77 - 10121851 * q^79 - 44592526 * q^80 + 24927115 * q^82 - 13288897 * q^83 - 28050005 * q^85 - 20937351 * q^86 + 39687014 * q^88 + 40241460 * q^89 + 8733043 * q^91 - 11607651 * q^92 - 7877385 * q^94 - 14371097 * q^95 + 30518151 * q^97 + 16954218 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	8.43584	−	6.12900i	0.745630	−	0.541732i	−0.148839	−	0.988861i	$-0.547554\pi$
$2$	8.43584	−	6.12900i	0.745630	−	0.541732i	0.894469	+	0.447130i	$0.147554\pi$
$3$		0			0
$3$		0			0
$4$	−5.95538	+	18.3288i	−0.0465264	+	0.143193i
$5$	186.461	+	135.472i	0.667103	+	0.484678i	0.869054	−	0.494717i	$-0.164728\pi$
$5$	186.461	+	135.472i	0.667103	+	0.484678i	−0.201951	+	0.979396i	$0.564728\pi$
$6$		0			0
$7$	−43.6776	+	134.426i	−0.0481300	+	0.148129i	−0.972233	−	0.234014i	$-0.924814\pi$
$7$	−43.6776	+	134.426i	−0.0481300	+	0.148129i	0.924103	+	0.382143i	$0.124814\pi$
$8$	474.540	+	1460.49i	0.327686	+	1.00851i
$9$		0			0
$10$	2403.26			0.759977
$11$	−4405.31	+	283.647i	−0.997934	+	0.0642545i
$11$	−4405.31	+	283.647i	−0.997934	+	0.0642545i
$12$		0			0
$13$	−2402.15	+	1745.26i	−0.303248	+	0.220323i	−0.728994	−	0.684520i	$-0.760012\pi$
$13$	−2402.15	+	1745.26i	−0.303248	+	0.220323i	0.425746	+	0.904843i	$0.360012\pi$
$14$	455.438	+	1401.69i	0.0443590	+	0.136523i
$15$		0			0
$16$	10958.8	+	7962.01i	0.668870	+	0.485962i
$17$	−32135.9	−	23348.1i	−1.58643	−	1.15261i	−0.908826	−	0.417176i	$-0.863020\pi$
$17$	−32135.9	−	23348.1i	−1.58643	−	1.15261i	−0.677601	−	0.735430i	$-0.736980\pi$
$18$		0			0
$19$	11338.9	+	34897.4i	0.379255	+	1.16723i	0.940563	+	0.339620i	$0.110299\pi$
$19$	11338.9	+	34897.4i	0.379255	+	1.16723i	−0.561307	+	0.827607i	$0.689701\pi$
$20$	−3593.47	+	2610.81i	−0.100441	+	0.0729744i
$21$		0			0
$22$	−35424.0	+	29392.9i	−0.709280	+	0.588523i
$23$	−26232.0			−0.449556			−0.224778	−	0.974410i	$-0.572166\pi$
$23$	−26232.0			−0.449556			−0.224778	+	0.974410i	$0.572166\pi$
$24$		0			0
$25$	−7726.90	−	23780.9i	−0.0989043	−	0.304396i
$26$	−9567.43	+	29445.5i	−0.106755	+	0.328558i
$27$		0			0
$28$	−2203.74	−	1601.11i	−0.0189718	−	0.0137838i
$29$	−62224.8	+	191508.i	−0.473773	+	1.45812i	0.373832	+	0.927497i	$0.378044\pi$
$29$	−62224.8	+	191508.i	−0.473773	+	1.45812i	−0.847605	+	0.530628i	$0.821956\pi$
$30$		0			0
$31$	34405.6	−	24997.1i	0.207426	−	0.150704i	−0.479222	−	0.877694i	$-0.659081\pi$
$31$	34405.6	−	24997.1i	0.207426	−	0.150704i	0.686648	+	0.726990i	$0.259081\pi$
$32$	−55317.1			−0.298425
$33$		0			0
$34$	−414194.			−1.80729
$35$	−26355.1	+	19148.1i	−0.103902	+	0.0754896i
$36$		0			0
$37$	−93379.6	+	287393.i	−0.303072	+	0.932760i	0.677317	+	0.735691i	$0.263142\pi$
$37$	−93379.6	+	287393.i	−0.303072	+	0.932760i	−0.980390	+	0.197069i	$0.936858\pi$
$38$	309539.	+	224893.i	0.915109	+	0.664865i
$39$		0			0
$40$	−109371.	+	336610.i	−0.270205	+	0.831605i
$41$	166492.	+	512408.i	0.377267	+	1.16111i	0.941936	+	0.335791i	$0.109004\pi$
$41$	166492.	+	512408.i	0.377267	+	1.16111i	−0.564669	+	0.825317i	$0.690996\pi$
$42$		0			0
$43$	282374.			0.541607			0.270804	−	0.962635i	$-0.412711\pi$
$43$	282374.			0.541607			0.270804	+	0.962635i	$0.412711\pi$
$44$	21036.4	−	82433.0i	0.0372294	−	0.145887i
$45$		0			0
$46$	−221289.	+	160776.i	−0.335202	+	0.243539i
$47$	−225672.	−	694546.i	−0.317055	−	0.975795i	−0.974900	−	0.222642i	$-0.928532\pi$
$47$	−225672.	−	694546.i	−0.317055	−	0.975795i	0.657845	−	0.753153i	$-0.271468\pi$
$48$		0			0
$49$	650098.	+	472324.i	0.789391	+	0.573526i
$50$	−210936.	−	153254.i	−0.238647	−	0.173387i
$51$		0			0
$52$	−17682.8	−	54422.1i	−0.0174397	−	0.0536740i
$53$	367870.	−	267273.i	0.339413	−	0.246598i	−0.405001	−	0.914316i	$-0.632729\pi$
$53$	367870.	−	267273.i	0.339413	−	0.246598i	0.744414	+	0.667718i	$0.232729\pi$
$54$		0			0
$55$	−859843.	−	543905.i	−0.696867	−	0.440812i
$56$	−217054.			−0.165162
$57$		0			0
$58$	648835.	+	1.99691e6i	0.436653	+	1.34388i
$59$	−367511.	+	1.13108e6i	−0.232964	+	0.716989i	0.764421	+	0.644717i	$0.223025\pi$
$59$	−367511.	+	1.13108e6i	−0.232964	+	0.716989i	−0.997385	+	0.0722719i	$0.976975\pi$
$60$		0			0
$61$	353988.	+	257188.i	0.199680	+	0.145076i	0.683132	−	0.730295i	$-0.260617\pi$
$61$	353988.	+	257188.i	0.199680	+	0.145076i	−0.483452	+	0.875371i	$0.660617\pi$
$62$	137033.	−	421743.i	0.0730219	−	0.224738i
$63$		0			0
$64$	−1.86937e6	+	1.35818e6i	−0.891384	+	0.647628i
$65$	−684340.			−0.309083
$66$		0			0
$67$	2.93699e6			1.19300			0.596500	−	0.802613i	$-0.296557\pi$
$67$	2.93699e6			1.19300			0.596500	+	0.802613i	$0.296557\pi$
$68$	619324.	−	449965.i	0.238856	−	0.173539i
$69$		0			0
$70$	−104969.	+	323060.i	−0.0365777	+	0.112575i
$71$	−639020.	−	464275.i	−0.211890	−	0.153947i	0.476779	−	0.879023i	$-0.341804\pi$
$71$	−639020.	−	464275.i	−0.211890	−	0.153947i	−0.688668	+	0.725076i	$0.741804\pi$
$72$		0			0
$73$	−22813.8	+	70213.6i	−0.00686385	+	0.0211247i	−0.954430	−	0.298436i	$-0.903535\pi$
$73$	−22813.8	+	70213.6i	−0.00686385	+	0.0211247i	0.947566	+	0.319560i	$0.103535\pi$
$74$	973695.	+	2.99672e6i	0.279326	+	0.859678i
$75$		0			0
$76$	−707154.			−0.184785
$77$	154284.	−	604576.i	0.0385126	−	0.150915i
$78$		0			0
$79$	−4.91172e6	+	3.56858e6i	−1.12083	+	0.814329i	−0.984334	−	0.176312i	$-0.943583\pi$
$79$	−4.91172e6	+	3.56858e6i	−1.12083	+	0.814329i	−0.136494	+	0.990641i	$0.543583\pi$
$80$	964753.	+	2.96920e6i	0.210669	+	0.648373i
$81$		0			0
$82$	4.54505e6	+	3.30217e6i	0.910311	+	0.661380i
$83$	−1.60269e6	−	1.16442e6i	−0.307663	−	0.223530i	0.423230	−	0.906022i	$-0.360896\pi$
$83$	−1.60269e6	−	1.16442e6i	−0.307663	−	0.223530i	−0.730893	+	0.682492i	$0.760896\pi$
$84$		0			0
$85$	−2.82908e6	−	8.70702e6i	−0.499666	−	1.53781i
$86$	2.38206e6	−	1.73067e6i	0.403838	−	0.293406i
$87$		0			0
$88$	−2.50476e6	−	6.29928e6i	−0.391811	−	0.985375i
$89$	−7.69913e6			−1.15765			−0.578824	−	0.815452i	$-0.696488\pi$
$89$	−7.69913e6			−1.15765			−0.578824	+	0.815452i	$0.696488\pi$
$90$		0			0
$91$	−129688.	−	399140.i	−0.0180408	−	0.0555239i
$92$	156221.	−	480800.i	0.0209162	−	0.0643735i
$93$		0			0
$94$	−6.16060e6	−	4.47594e6i	−0.765025	−	0.555823i
$95$	−2.61336e6	+	8.04309e6i	−0.312728	+	0.962477i
$96$		0			0
$97$	655646.	−	476355.i	0.0729404	−	0.0529943i	−0.550717	−	0.834692i	$-0.685646\pi$
$97$	655646.	−	476355.i	0.0729404	−	0.0529943i	0.623658	+	0.781697i	$0.285646\pi$
$98$	8.37899e6			0.899291
$99$		0			0
$100$	481892.			0.0481892
$101$	8.80352e6	−	6.39613e6i	0.850221	−	0.617721i	−0.0749863	−	0.997185i	$-0.523891\pi$
$101$	8.80352e6	−	6.39613e6i	0.850221	−	0.617721i	0.925207	+	0.379463i	$0.123891\pi$
$102$		0			0
$103$	1.49685e6	−	4.60682e6i	0.134973	−	0.415404i	−0.860613	−	0.509260i	$-0.829919\pi$
$103$	1.49685e6	−	4.60682e6i	0.134973	−	0.415404i	0.995586	+	0.0938556i	$0.0299192\pi$
$104$	−3.68885e6	−	2.68010e6i	−0.321569	−	0.233633i
$105$		0			0
$106$	1.46518e6	−	4.50935e6i	0.119487	−	0.367742i
$107$	2.32748e6	+	7.16325e6i	0.183672	+	0.565284i	0.999923	−	0.0124131i	$-0.00395132\pi$
$107$	2.32748e6	+	7.16325e6i	0.183672	+	0.565284i	−0.816251	+	0.577698i	$0.803951\pi$
$108$		0			0
$109$	2.61616e7			1.93496			0.967478	−	0.252955i	$-0.0814024\pi$
$109$	2.61616e7			1.93496			0.967478	+	0.252955i	$0.0814024\pi$
$110$	−1.05871e7	+	681677.i	−0.758407	+	0.0488320i
$111$		0			0
$112$	−1.54895e6	+	1.12538e6i	−0.104178	+	0.0756895i
$113$	−8.84107e6	−	2.72100e7i	−0.576408	−	1.77400i	−0.631333	−	0.775512i	$-0.717492\pi$
$113$	−8.84107e6	−	2.72100e7i	−0.576408	−	1.77400i	0.0549245	−	0.998491i	$-0.482508\pi$
$114$		0			0
$115$	−4.89124e6	−	3.55369e6i	−0.299900	−	0.217890i
$116$	−3.13954e6	−	2.28101e6i	−0.186751	−	0.135683i
$117$		0			0
$118$	3.83214e6	+	1.17941e7i	0.214711	+	0.660813i
$119$	4.54221e6	−	3.30011e6i	0.247089	−	0.179521i
$120$		0			0
$121$	1.93263e7	−	2.49910e6i	0.991743	−	0.128243i
$122$	4.56249e6			0.227480
$123$		0			0
$124$	253268.	+	779479.i	0.0119290	+	0.0367137i
$125$	7.34508e6	−	2.26058e7i	0.336365	−	1.03523i
$126$		0			0
$127$	−4.72257e6	−	3.43114e6i	−0.204581	−	0.148637i	0.480778	−	0.876843i	$-0.340354\pi$
$127$	−4.72257e6	−	3.43114e6i	−0.204581	−	0.148637i	−0.685358	+	0.728206i	$0.740354\pi$
$128$	−5.25741e6	+	1.61807e7i	−0.221583	+	0.681964i
$129$		0			0
$130$	−5.77299e6	+	4.19432e6i	−0.230462	+	0.167440i
$131$	1.00146e7			0.389212			0.194606	−	0.980882i	$-0.437657\pi$
$131$	1.00146e7			0.389212			0.194606	+	0.980882i	$0.437657\pi$
$132$		0			0
$133$	−5.18637e6			−0.191154
$134$	2.47760e7	−	1.80008e7i	0.889537	−	0.646286i
$135$		0			0
$136$	1.88498e7	−	5.80137e7i	0.642570	−	1.97763i
$137$	−8.17048e6	−	5.93620e6i	−0.271472	−	0.197236i	0.443717	−	0.896167i	$-0.353660\pi$
$137$	−8.17048e6	−	5.93620e6i	−0.271472	−	0.197236i	−0.715189	+	0.698931i	$0.753660\pi$
$138$		0			0
$139$	1.03085e7	−	3.17262e7i	0.325568	−	1.00200i	−0.645615	−	0.763663i	$-0.723399\pi$
$139$	1.03085e7	−	3.17262e7i	0.325568	−	1.00200i	0.971183	−	0.238334i	$-0.0766012\pi$
$140$	−194006.	−	597090.i	−0.00597541	−	0.0183904i
$141$		0			0
$142$	−8.23621e6			−0.241389
$143$	1.00872e7	−	8.36978e6i	0.288465	−	0.239352i
$144$		0			0
$145$	−3.75465e7	+	2.72791e7i	−1.02278	+	0.743091i
$146$	237886.	+	732137.i	0.00632606	+	0.0194696i
$147$		0			0
$148$	−4.71145e6	−	3.42307e6i	−0.119464	−	0.0867959i
$149$	6.04337e7	+	4.39077e7i	1.49667	+	1.08740i	0.971682	+	0.236291i	$0.0759318\pi$
$149$	6.04337e7	+	4.39077e7i	1.49667	+	1.08740i	0.524992	+	0.851107i	$0.324068\pi$
$150$		0			0
$151$	7.17614e6	+	2.20859e7i	0.169618	+	0.522030i	0.999347	−	0.0361364i	$-0.0115051\pi$
$151$	7.17614e6	+	2.20859e7i	0.169618	+	0.522030i	−0.829729	+	0.558166i	$0.811505\pi$
$152$	−4.55864e7	+	3.31205e7i	−1.05289	+	0.764969i
$153$		0			0
$154$	−2.40393e6	−	6.04571e6i	−0.0530395	−	0.133390i
$155$	9.80170e6			0.211417
$156$		0			0
$157$	1.39882e7	+	4.30512e7i	0.288478	+	0.887844i	0.985335	+	0.170634i	$0.0545814\pi$
$157$	1.39882e7	+	4.30512e7i	0.288478	+	0.887844i	−0.696857	+	0.717211i	$0.745419\pi$
$158$	−1.95627e7	+	6.02079e7i	−0.394575	+	1.21438i
$159$		0			0
$160$	−1.03145e7	−	7.49391e6i	−0.199080	−	0.144640i
$161$	1.14575e6	−	3.52626e6i	0.0216371	−	0.0665922i
$162$		0			0
$163$	−5.19349e7	+	3.77329e7i	−0.939296	+	0.682439i	−0.948251	−	0.317521i	$-0.897150\pi$
$163$	−5.19349e7	+	3.77329e7i	−0.939296	+	0.682439i	0.00895476	+	0.999960i	$0.497150\pi$
$164$	−1.03833e7			−0.183816
$165$		0			0
$166$	−2.06567e7			−0.350496
$167$	1.37758e7	−	1.00087e7i	0.228881	−	0.166292i	−0.467434	−	0.884028i	$-0.654822\pi$
$167$	1.37758e7	−	1.00087e7i	0.228881	−	0.166292i	0.696315	+	0.717736i	$0.254822\pi$
$168$		0			0
$169$	−1.66660e7	+	5.12926e7i	−0.265600	+	0.817432i
$170$	−7.72310e7	−	5.61116e7i	−1.20565	−	0.875955i
$171$		0			0
$172$	−1.68164e6	+	5.17556e6i	−0.0251990	+	0.0775546i
$173$	5.33746e6	+	1.64270e7i	0.0783743	+	0.241211i	0.982566	−	0.185917i	$-0.0595254\pi$
$173$	5.33746e6	+	1.64270e7i	0.0783743	+	0.241211i	−0.904191	+	0.427128i	$0.859525\pi$
$174$		0			0
$175$	3.53427e6			0.0498501
$176$	−5.05351e7	−	3.19666e7i	−0.698713	−	0.441980i
$177$		0			0
$178$	−6.49486e7	+	4.71879e7i	−0.863177	+	0.627135i
$179$	2.01741e7	+	6.20894e7i	0.262911	+	0.809156i	0.992167	+	0.124916i	$0.0398660\pi$
$179$	2.01741e7	+	6.20894e7i	0.262911	+	0.809156i	−0.729257	+	0.684240i	$0.760134\pi$
$180$		0			0
$181$	5.73904e7	+	4.16966e7i	0.719390	+	0.522668i	0.886189	−	0.463323i	$-0.153343\pi$
$181$	5.73904e7	+	4.16966e7i	0.719390	+	0.522668i	−0.166799	+	0.985991i	$0.553343\pi$
$182$	−3.54036e6	−	2.57222e6i	−0.0435308	−	0.0316270i
$183$		0			0
$184$	−1.24481e7	−	3.83114e7i	−0.147313	−	0.453384i
$185$	−5.63453e7	+	4.09372e7i	−0.654269	+	0.475354i
$186$		0			0
$187$	1.48191e8	+	9.37404e7i	1.65721	+	1.04829i
$188$	1.40741e7			0.154479
$189$		0			0
$190$	2.72502e7	+	8.38675e7i	0.288225	+	0.887067i
$191$	−4.18386e7	+	1.28766e8i	−0.434470	+	1.33716i	0.459158	+	0.888355i	$0.348151\pi$
$191$	−4.18386e7	+	1.28766e8i	−0.434470	+	1.33716i	−0.893628	+	0.448808i	$0.851849\pi$
$192$		0			0
$193$	−6.49350e7	−	4.71780e7i	−0.650172	−	0.472377i	0.213158	−	0.977018i	$-0.431625\pi$
$193$	−6.49350e7	−	4.71780e7i	−0.650172	−	0.472377i	−0.863330	+	0.504640i	$0.831625\pi$
$194$	2.61135e6	−	8.03690e6i	0.0256779	−	0.0790283i
$195$		0			0
$196$	−1.25287e7	+	9.10262e6i	−0.118853	+	0.0863516i
$197$	−3.99173e7			−0.371989			−0.185994	−	0.982551i	$-0.559551\pi$
$197$	−3.99173e7			−0.371989			−0.185994	+	0.982551i	$0.559551\pi$
$198$		0			0
$199$	−1.48186e8			−1.33297			−0.666486	−	0.745517i	$-0.732203\pi$
$199$	−1.48186e8			−1.33297			−0.666486	+	0.745517i	$0.732203\pi$
$200$	3.10650e7	−	2.25700e7i	0.274578	−	0.199493i
$201$		0			0
$202$	3.50632e7	−	1.07913e8i	0.299311	−	0.921183i
$203$	−2.30258e7	−	1.67292e7i	−0.193188	−	0.140359i
$204$		0			0
$205$	−3.83727e7	+	1.18099e8i	−0.311088	+	0.957432i
$206$	−1.56080e7	−	4.80366e7i	−0.124398	−	0.382857i
$207$		0			0
$208$	−4.02204e7			−0.309902
$209$	−5.98497e7	−	1.50518e8i	−0.453471	−	1.14045i
$210$		0			0
$211$	2.01389e8	−	1.46318e8i	1.47587	−	1.07228i	0.497009	−	0.867745i	$-0.334432\pi$
$211$	2.01389e8	−	1.46318e8i	1.47587	−	1.07228i	0.978859	−	0.204535i	$-0.0655684\pi$
$212$	2.70798e6	+	8.33431e6i	0.0195196	+	0.0600751i
$213$		0			0
$214$	6.35378e7	+	4.61629e7i	0.443184	+	0.321992i
$215$	5.26516e7	+	3.82536e7i	0.361307	+	0.262505i
$216$		0			0
$217$	1.85751e6	+	5.71681e6i	0.0123402	+	0.0379791i
$218$	2.20695e8	−	1.60344e8i	1.44276	−	1.04823i
$219$		0			0
$220$	1.50898e7	−	1.25207e7i	0.0955442	−	0.0792774i
$221$	1.17944e8			0.735026
$222$		0			0
$223$	6.98917e7	+	2.15104e8i	0.422045	+	1.29892i	0.905796	+	0.423715i	$0.139274\pi$
$223$	6.98917e7	+	2.15104e8i	0.422045	+	1.29892i	−0.483751	+	0.875206i	$0.660726\pi$
$224$	2.41612e6	−	7.43605e6i	0.0143632	−	0.0442053i
$225$		0			0
$226$	−2.41352e8	−	1.75352e8i	−1.39082	−	1.01049i
$227$	−6.45858e7	+	1.98775e8i	−0.366477	+	1.12790i	0.582575	+	0.812777i	$0.302045\pi$
$227$	−6.45858e7	+	1.98775e8i	−0.366477	+	1.12790i	−0.949051	+	0.315122i	$0.897955\pi$
$228$		0			0
$229$	1.67995e8	−	1.22056e8i	0.924426	−	0.671635i	−0.0201957	−	0.999796i	$-0.506429\pi$
$229$	1.67995e8	−	1.22056e8i	0.924426	−	0.671635i	0.944622	+	0.328161i	$0.106429\pi$
$230$	−6.30423e7			−0.341652
$231$		0			0
$232$	−3.09223e8			−1.62579
$233$	2.41077e8	−	1.75153e8i	1.24856	−	0.907135i	0.250427	−	0.968136i	$-0.419429\pi$
$233$	2.41077e8	−	1.75153e8i	1.24856	−	0.907135i	0.998138	+	0.0610005i	$0.0194291\pi$
$234$		0			0
$235$	5.20124e7	−	1.60078e8i	0.261439	−	0.804625i
$236$	−1.85427e7	−	1.34721e7i	−0.0918292	−	0.0667178i
$237$		0			0
$238$	1.80910e7	−	5.56784e7i	0.0869849	−	0.267712i
$239$	5.88607e7	+	1.81155e8i	0.278890	+	0.858334i	0.988164	+	0.153402i	$0.0490228\pi$
$239$	5.88607e7	+	1.81155e8i	0.278890	+	0.858334i	−0.709274	+	0.704933i	$0.750977\pi$
$240$		0			0
$241$	2.77387e8			1.27652			0.638258	−	0.769822i	$-0.279655\pi$
$241$	2.77387e8			1.27652			0.638258	+	0.769822i	$0.279655\pi$
$242$	1.47716e8	−	1.39533e8i	0.669999	−	0.632881i
$243$		0			0
$244$	−6.82207e6	+	4.95652e6i	−0.0300643	+	0.0218430i
$245$	5.72313e7	+	1.76140e8i	0.248629	+	0.765202i
$246$		0			0
$247$	−8.81428e7	−	6.40395e7i	−0.372175	−	0.270401i
$248$	5.28348e7	+	3.83867e7i	0.219958	+	0.159809i
$249$		0			0
$250$	−7.65891e7	−	2.35717e8i	−0.310011	−	0.954116i
$251$	−2.43754e8	+	1.77097e8i	−0.972956	+	0.706894i	−0.956123	−	0.292964i	$-0.905358\pi$
$251$	−2.43754e8	+	1.77097e8i	−0.972956	+	0.706894i	−0.0168327	+	0.999858i	$0.505358\pi$
$252$		0			0
$253$	1.15560e8	−	7.44062e6i	0.448627	−	0.0288860i
$254$	−6.08683e7			−0.233063
$255$		0			0
$256$	−3.65760e7	−	1.12569e8i	−0.136256	−	0.419354i
$257$	8.22642e7	−	2.53183e8i	0.302305	−	0.930398i	−0.678364	−	0.734726i	$-0.737311\pi$
$257$	8.22642e7	−	2.53183e8i	0.302305	−	0.930398i	0.980669	−	0.195673i	$-0.0626891\pi$
$258$		0			0
$259$	−3.45544e7	−	2.51053e7i	−0.123582	−	0.0897875i
$260$	4.07550e6	−	1.25431e7i	0.0143805	−	0.0442587i
$261$		0			0
$262$	8.44819e7	−	6.13797e7i	0.290208	−	0.210848i
$263$	2.12685e8			0.720928			0.360464	−	0.932773i	$-0.382618\pi$
$263$	2.12685e8			0.720928			0.360464	+	0.932773i	$0.382618\pi$
$264$		0			0
$265$	1.04801e8			0.345944
$266$	−4.37514e7	+	3.17872e7i	−0.142530	+	0.103554i
$267$		0			0
$268$	−1.74909e7	+	5.38314e7i	−0.0555060	+	0.170830i
$269$	−4.09560e8	−	2.97562e8i	−1.28287	−	0.932063i	−0.283239	−	0.959050i	$-0.591409\pi$
$269$	−4.09560e8	−	2.97562e8i	−1.28287	−	0.932063i	−0.999636	+	0.0269868i	$0.991409\pi$
$270$		0			0
$271$	7.52920e7	−	2.31725e8i	0.229803	−	0.707262i	−0.767965	−	0.640492i	$-0.778731\pi$
$271$	7.52920e7	−	2.31725e8i	0.229803	−	0.707262i	0.997768	−	0.0667700i	$-0.0212694\pi$
$272$	−1.66272e8	−	5.11733e8i	−0.500989	−	1.54189i
$273$		0			0
$274$	−1.05308e8			−0.309267
$275$	4.07847e7	+	1.02571e8i	0.118259	+	0.297412i
$276$		0			0
$277$	5.61142e7	−	4.07694e7i	0.158633	−	0.115254i	−0.505637	−	0.862746i	$-0.668742\pi$
$277$	5.61142e7	−	4.07694e7i	0.158633	−	0.115254i	0.664270	+	0.747493i	$0.268742\pi$
$278$	−1.07489e8	−	3.30818e8i	−0.300060	−	0.923490i
$279$		0			0
$280$	−4.04720e7	−	2.94047e7i	−0.110180	−	0.0800503i
$281$	−1.36128e8	−	9.89028e7i	−0.365995	−	0.265911i	0.389553	−	0.921004i	$-0.372629\pi$
$281$	−1.36128e8	−	9.89028e7i	−0.365995	−	0.265911i	−0.755548	+	0.655093i	$0.772629\pi$
$282$		0			0
$283$	−5.24688e7	−	1.61482e8i	−0.137609	−	0.423518i	0.858377	−	0.513019i	$-0.171473\pi$
$283$	−5.24688e7	−	1.61482e8i	−0.137609	−	0.423518i	−0.995987	+	0.0895005i	$0.971473\pi$
$284$	1.23152e7	−	8.94751e6i	0.0319027	−	0.0231786i
$285$		0			0
$286$	3.37953e7	−	1.32430e8i	0.0854231	−	0.334739i
$287$	−7.61529e7			−0.190152
$288$		0			0
$289$	3.60782e8	+	1.11037e9i	0.879230	+	2.70599i
$290$	−1.49542e8	+	4.60244e8i	−0.360057	+	1.10814i
$291$		0			0
$292$	−1.15106e6	−	836297.i	−0.00270558	−	0.00196572i
$293$	−1.18547e8	+	3.64849e8i	−0.275330	+	0.847378i	0.713802	+	0.700347i	$0.246972\pi$
$293$	−1.18547e8	+	3.64849e8i	−0.275330	+	0.847378i	−0.989132	+	0.147030i	$0.953028\pi$
$294$		0			0
$295$	−2.21756e8	+	1.61115e8i	−0.502920	+	0.365393i
$296$	−4.64046e8			−1.04002
$297$		0			0
$298$	7.78919e8			1.70504
$299$	6.30131e7	−	4.57817e7i	0.136327	−	0.0990473i
$300$		0			0
$301$	−1.23334e7	+	3.79583e7i	−0.0260675	+	0.0802276i
$302$	1.95901e8	+	1.42330e8i	0.409272	+	0.297354i
$303$		0			0
$304$	−1.53594e8	+	4.72712e8i	−0.313556	+	0.965027i
$305$	3.11633e7	+	9.59108e7i	0.0628918	+	0.193561i
$306$		0			0
$307$	−3.53815e8			−0.697898			−0.348949	−	0.937142i	$-0.613461\pi$
$307$	−3.53815e8			−0.697898			−0.348949	+	0.937142i	$0.613461\pi$
$308$	1.01623e7	+	6.42831e6i	0.0198182	+	0.0125363i
$309$		0			0
$310$	8.26855e7	−	6.00746e7i	0.157639	−	0.114531i
$311$	2.49106e8	+	7.66668e8i	0.469593	+	1.44526i	0.853112	+	0.521727i	$0.174712\pi$
$311$	2.49106e8	+	7.66668e8i	0.469593	+	1.44526i	−0.383519	+	0.923533i	$0.625288\pi$
$312$		0			0
$313$	−6.95962e8	−	5.05646e8i	−1.28286	−	0.932055i	−0.283228	−	0.959053i	$-0.591405\pi$
$313$	−6.95962e8	−	5.05646e8i	−1.28286	−	0.932055i	−0.999635	+	0.0269981i	$0.991405\pi$
$314$	3.81863e8	+	2.77440e8i	0.696071	+	0.505725i
$315$		0			0
$316$	−3.61564e7	−	1.11278e8i	−0.0644586	−	0.198383i
$317$	4.81665e8	−	3.49950e8i	0.849255	−	0.617020i	−0.0756856	−	0.997132i	$-0.524115\pi$
$317$	4.81665e8	−	3.49950e8i	0.849255	−	0.617020i	0.924941	+	0.380112i	$0.124115\pi$
$318$		0			0
$319$	2.19799e8	−	8.61302e8i	0.379103	−	1.48555i
$320$	−5.32558e8			−0.908536
$321$		0			0
$322$	−1.19470e7	−	3.67692e7i	−0.0199418	−	0.0613746i
$323$	4.50405e8	−	1.38620e9i	0.743693	−	2.28885i
$324$		0			0
$325$	6.00652e7	+	4.36399e7i	0.0970579	+	0.0705167i
$326$	−2.06850e8	+	6.36618e8i	−0.330669	+	1.01769i
$327$		0			0
$328$	−6.69358e8	+	4.86317e8i	−1.04737	+	0.760959i
$329$	1.03222e8			0.159803
$330$		0			0
$331$	−5.78342e8			−0.876571			−0.438285	−	0.898836i	$-0.644414\pi$
$331$	−5.78342e8			−0.876571			−0.438285	+	0.898836i	$0.644414\pi$
$332$	3.08870e7	−	2.24407e7i	0.0463225	−	0.0336553i
$333$		0			0
$334$	5.48672e7	−	1.68864e8i	0.0805749	−	0.247984i
$335$	5.47634e8	+	3.97879e8i	0.795854	+	0.578222i
$336$		0			0
$337$	−1.39277e8	+	4.28650e8i	−0.198232	+	0.610096i	0.801691	+	0.597738i	$0.203934\pi$
$337$	−1.39277e8	+	4.28650e8i	−0.198232	+	0.610096i	−0.999924	+	0.0123580i	$0.996066\pi$
$338$	1.73781e8	+	5.34842e8i	0.244790	+	0.753385i
$339$		0			0
$340$	1.76437e8			0.243452
$341$	−1.44477e8	+	1.19879e8i	−0.197314	+	0.163720i
$342$		0			0
$343$	−1.86059e8	+	1.35180e8i	−0.248955	+	0.180876i
$344$	1.33998e8	+	4.12402e8i	0.177477	+	0.546219i
$345$		0			0
$346$	1.45707e8	+	1.05862e8i	0.189110	+	0.137396i
$347$	−9.98274e7	−	7.25288e7i	−0.128262	−	0.0931875i	0.521805	−	0.853065i	$-0.325259\pi$
$347$	−9.98274e7	−	7.25288e7i	−0.128262	−	0.0931875i	−0.650066	+	0.759877i	$0.725259\pi$
$348$		0			0
$349$	1.39224e8	+	4.28489e8i	0.175318	+	0.539573i	0.999648	−	0.0265364i	$-0.00844780\pi$
$349$	1.39224e8	+	4.28489e8i	0.175318	+	0.539573i	−0.824330	+	0.566110i	$0.808448\pi$
$350$	2.98145e7	−	2.16615e7i	0.0371697	−	0.0270054i
$351$		0			0
$352$	2.43689e8	−	1.56905e7i	0.297808	−	0.0191751i
$353$	−1.33385e9			−1.61397			−0.806984	−	0.590573i	$-0.798902\pi$
$353$	−1.33385e9			−1.61397			−0.806984	+	0.590573i	$0.798902\pi$
$354$		0			0
$355$	−5.62560e7	−	1.73138e8i	−0.0667375	−	0.205397i
$356$	4.58512e7	−	1.41116e8i	0.0538612	−	0.165768i
$357$		0			0
$358$	5.50731e8	+	4.00130e8i	0.634380	+	0.460904i
$359$	3.75671e8	−	1.15620e9i	0.428526	−	1.31887i	−0.471051	−	0.882106i	$-0.656125\pi$
$359$	3.75671e8	−	1.15620e9i	0.428526	−	1.31887i	0.899577	−	0.436762i	$-0.143875\pi$
$360$		0			0
$361$	−3.66102e8	+	2.65989e8i	−0.409569	+	0.297569i
$362$	7.39695e8			0.819545
$363$		0			0
$364$	8.08808e6			0.00879004
$365$	−1.37658e7	+	1.00015e7i	−0.0148176	+	0.0107656i
$366$		0			0
$367$	−2.27165e8	+	6.99143e8i	−0.239889	+	0.738303i	0.756546	+	0.653940i	$0.226885\pi$
$367$	−2.27165e8	+	6.99143e8i	−0.239889	+	0.738303i	−0.996435	+	0.0843623i	$0.973115\pi$
$368$	−2.87470e8	−	2.08859e8i	−0.300694	−	0.218467i
$369$		0			0
$370$	−2.24415e8	+	6.90680e8i	−0.230328	+	0.708877i
$371$	1.98607e7	+	6.11251e7i	0.0201923	+	0.0621456i
$372$		0			0
$373$	6.91646e8			0.690086			0.345043	−	0.938587i	$-0.387864\pi$
$373$	6.91646e8			0.690086			0.345043	+	0.938587i	$0.387864\pi$
$374$	1.82465e9	−	1.17485e8i	1.80356	−	0.116127i
$375$		0			0
$376$	9.07284e8	−	6.59181e8i	0.880209	−	0.639510i
$377$	−1.84759e8	−	5.68630e8i	−0.177587	−	0.546556i
$378$		0			0
$379$	−6.52577e8	−	4.74125e8i	−0.615736	−	0.447358i	0.235694	−	0.971827i	$-0.424264\pi$
$379$	−6.52577e8	−	4.74125e8i	−0.615736	−	0.447358i	−0.851429	+	0.524469i	$0.824264\pi$
$380$	−1.31856e8	−	9.57993e7i	−0.123270	−	0.0895612i
$381$		0			0
$382$	4.36262e8	+	1.34268e9i	0.400429	+	1.23239i
$383$	−9.79254e8	+	7.11470e8i	−0.890635	+	0.647084i	−0.936043	−	0.351884i	$-0.885541\pi$
$383$	−9.79254e8	+	7.11470e8i	−0.890635	+	0.647084i	0.0454086	+	0.998968i	$0.485541\pi$
$384$		0			0
$385$	1.10671e8	−	9.18287e7i	0.0988372	−	0.0820098i
$386$	−8.36935e8			−0.740689
$387$		0			0
$388$	4.82637e6	+	1.48541e7i	0.00419479	+	0.0129102i
$389$	1.68456e8	−	5.18454e8i	0.145098	−	0.446567i	−0.851925	−	0.523663i	$-0.824565\pi$
$389$	1.68456e8	−	5.18454e8i	0.145098	−	0.446567i	0.997024	+	0.0770965i	$0.0245649\pi$
$390$		0			0
$391$	8.42990e8	+	6.12468e8i	0.713187	+	0.518161i
$392$	−3.81324e8	+	1.17359e9i	−0.319737	+	0.984050i
$393$		0			0
$394$	−3.36736e8	+	2.44653e8i	−0.277366	+	0.201518i
$395$	−1.39929e9			−1.14240
$396$		0			0
$397$	−1.00331e9			−0.804764			−0.402382	−	0.915472i	$-0.631818\pi$
$397$	−1.00331e9			−0.804764			−0.402382	+	0.915472i	$0.631818\pi$
$398$	−1.25007e9	+	9.08231e8i	−0.993905	+	0.722114i
$399$		0			0
$400$	1.04667e8	−	3.22131e8i	0.0817709	−	0.251665i
$401$	7.81192e8	+	5.67569e8i	0.604996	+	0.439555i	0.847649	−	0.530558i	$-0.178018\pi$
$401$	7.81192e8	+	5.67569e8i	0.604996	+	0.439555i	−0.242653	+	0.970113i	$0.578018\pi$
$402$		0			0
$403$	−3.90208e7	+	1.20094e8i	−0.0296981	+	0.0914012i
$404$	6.48049e7	+	1.99449e8i	0.0488960	+	0.150486i
$405$		0			0
$406$	−2.96776e8			−0.220083
$407$	3.29848e8	−	1.29254e9i	0.242512	−	0.950307i
$408$		0			0
$409$	5.66070e8	−	4.11274e8i	0.409109	−	0.297235i	−0.364132	−	0.931347i	$-0.618634\pi$
$409$	5.66070e8	−	4.11274e8i	0.409109	−	0.297235i	0.773241	+	0.634112i	$0.218634\pi$
$410$	4.00123e8	+	1.23145e9i	0.286714	+	0.882416i
$411$		0			0
$412$	7.55230e7	+	5.48707e7i	0.0532034	+	0.0386545i
$413$	−1.35995e8	−	9.88060e7i	−0.0949942	−	0.0690174i
$414$		0			0
$415$	−1.41092e8	−	4.34238e8i	−0.0969025	−	0.298235i
$416$	1.32880e8	−	9.65429e7i	0.0904967	−	0.0657497i
$417$		0			0
$418$	−1.42740e9	−	9.02923e8i	−0.955938	−	0.604692i
$419$	−3.89971e8			−0.258990			−0.129495	−	0.991580i	$-0.541336\pi$
$419$	−3.89971e8			−0.258990			−0.129495	+	0.991580i	$0.541336\pi$
$420$		0			0
$421$	−5.74199e8	−	1.76720e9i	−0.375038	−	1.15425i	−0.943453	−	0.331506i	$-0.892443\pi$
$421$	−5.74199e8	−	1.76720e9i	−0.375038	−	1.15425i	0.568415	−	0.822742i	$-0.307557\pi$
$422$	8.02106e8	−	2.46863e9i	0.519563	−	1.59905i
$423$		0			0
$424$	5.64918e8	+	4.10437e8i	0.359919	+	0.261496i
$425$	−3.06930e8	+	9.44632e8i	−0.193944	+	0.596900i
$426$		0			0
$427$	−5.00340e7	+	3.63518e7i	−0.0311005	+	0.0225959i
$428$	−1.45155e8			−0.0894906
$429$		0			0
$430$	6.78617e8			0.411609
$431$	−1.65743e9	+	1.20419e9i	−0.997159	+	0.724478i	−0.961477	−	0.274885i	$-0.911360\pi$
$431$	−1.65743e9	+	1.20419e9i	−0.997159	+	0.724478i	−0.0356817	+	0.999363i	$0.511360\pi$
$432$		0			0
$433$	1.72649e8	−	5.31358e8i	0.102201	−	0.314543i	−0.886862	−	0.462034i	$-0.847120\pi$
$433$	1.72649e8	−	5.31358e8i	0.102201	−	0.314543i	0.989063	+	0.147491i	$0.0471198\pi$
$434$	5.07080e7	+	3.68415e7i	0.0297757	+	0.0216333i
$435$		0			0
$436$	−1.55802e8	+	4.79509e8i	−0.0900265	+	0.277073i
$437$	−2.97441e8	−	9.15428e8i	−0.170496	−	0.524734i
$438$		0			0
$439$	7.30903e8			0.412319			0.206160	−	0.978518i	$-0.433903\pi$
$439$	7.30903e8			0.412319			0.206160	+	0.978518i	$0.433903\pi$
$440$	3.86335e8	−	1.51389e9i	0.216212	−	0.847249i
$441$		0			0
$442$	9.94956e8	−	7.22878e8i	0.548057	−	0.398187i
$443$	3.12361e8	+	9.61349e8i	0.170704	+	0.525373i	0.999411	−	0.0343093i	$-0.0109231\pi$
$443$	3.12361e8	+	9.61349e8i	0.170704	+	0.525373i	−0.828707	+	0.559682i	$0.810923\pi$
$444$		0			0
$445$	−1.43559e9	−	1.04301e9i	−0.772270	−	0.561087i
$446$	1.90797e9	+	1.38622e9i	1.01836	+	0.739879i
$447$		0			0
$448$	−1.00924e8	−	3.10613e8i	−0.0530302	−	0.163210i
$449$	2.01099e9	−	1.46107e9i	1.04845	−	0.761742i	0.0765310	−	0.997067i	$-0.475616\pi$
$449$	2.01099e9	−	1.46107e9i	1.04845	−	0.761742i	0.971917	+	0.235325i	$0.0756156\pi$
$450$		0			0
$451$	−8.78789e8	−	2.21009e9i	−0.451094	−	1.13447i
$452$	5.51378e8			0.280844
$453$		0			0
$454$	6.73453e8	+	2.07268e9i	0.337763	+	1.03953i
$455$	2.98903e7	−	9.19930e7i	0.0148762	−	0.0457841i
$456$		0			0
$457$	−2.96445e8	−	2.15380e8i	−0.145290	−	0.105560i	0.512766	−	0.858529i	$-0.328621\pi$
$457$	−2.96445e8	−	2.15380e8i	−0.145290	−	0.105560i	−0.658056	+	0.752969i	$0.728621\pi$
$458$	6.69101e8	−	2.05928e9i	0.325434	−	1.00158i
$459$		0			0
$460$	9.42639e7	−	6.84868e7i	0.0451537	−	0.0328061i
$461$	−2.23618e8			−0.106305			−0.0531525	−	0.998586i	$-0.516927\pi$
$461$	−2.23618e8			−0.106305			−0.0531525	+	0.998586i	$0.516927\pi$
$462$		0			0
$463$	−1.54863e9			−0.725126			−0.362563	−	0.931959i	$-0.618098\pi$
$463$	−1.54863e9			−0.725126			−0.362563	+	0.931959i	$0.618098\pi$
$464$	−2.20670e9	+	1.60326e9i	−1.02549	+	0.745059i
$465$		0			0
$466$	9.60179e8	−	2.95513e9i	0.439543	−	1.35277i
$467$	7.09042e7	+	5.15149e7i	0.0322154	+	0.0234058i	0.603776	−	0.797154i	$-0.293662\pi$
$467$	7.09042e7	+	5.15149e7i	0.0322154	+	0.0234058i	−0.571561	+	0.820560i	$0.693662\pi$
$468$		0			0
$469$	−1.28281e8	+	3.94807e8i	−0.0574191	+	0.176718i
$470$	−5.42348e8	−	1.66918e9i	−0.240955	−	0.741582i
$471$		0			0
$472$	−1.82633e9			−0.799433
$473$	−1.24394e9	+	8.00944e7i	−0.540488	+	0.0348007i
$474$		0			0
$475$	7.42279e8	−	5.39297e8i	0.317790	−	0.230888i
$476$	3.34364e7	+	1.02907e8i	0.0142100	+	0.0437340i
$477$		0			0
$478$	1.60683e9	+	1.16743e9i	0.672936	+	0.488916i
$479$	2.99377e9	+	2.17510e9i	1.24464	+	0.904284i	0.997898	−	0.0647971i	$-0.0206400\pi$
$479$	2.99377e9	+	2.17510e9i	1.24464	+	0.904284i	0.246742	+	0.969081i	$0.420640\pi$
$480$		0			0
$481$	−2.77264e8	−	8.53332e8i	−0.113602	−	0.349631i
$482$	2.33999e9	−	1.70010e9i	0.951809	−	0.691530i
$483$		0			0
$484$	−6.92897e7	+	3.69110e8i	−0.0277786	+	0.147978i
$485$	1.86785e8			0.0743439
$486$		0			0
$487$	−9.56746e8	−	2.94456e9i	−0.375358	−	1.15523i	−0.943237	−	0.332120i	$-0.892236\pi$
$487$	−9.56746e8	−	2.94456e9i	−0.375358	−	1.15523i	0.567880	−	0.823112i	$-0.307764\pi$
$488$	−2.07637e8	+	6.39041e8i	−0.0808789	+	0.248920i
$489$		0			0
$490$	1.56235e9	+	1.13512e9i	0.599920	+	0.435867i
$491$	−2.67322e8	+	8.22734e8i	−0.101918	+	0.313671i	−0.988995	−	0.147951i	$-0.952732\pi$
$491$	−2.67322e8	+	8.22734e8i	−0.101918	+	0.313671i	0.887077	+	0.461622i	$0.152732\pi$
$492$		0			0
$493$	6.47101e9	−	4.70147e9i	2.43225	−	1.76713i
$494$	−1.13606e9			−0.423990
$495$		0			0
$496$	5.76070e8			0.211977
$497$	9.03214e7	−	6.56224e7i	0.0330022	−	0.0239775i
$498$		0			0
$499$	−1.46692e9	+	4.51472e9i	−0.528512	+	1.62659i	0.228751	+	0.973485i	$0.426536\pi$
$499$	−1.46692e9	+	4.51472e9i	−0.528512	+	1.62659i	−0.757264	+	0.653109i	$0.773464\pi$
$500$	3.70594e8	+	2.69252e8i	0.132588	+	0.0963307i
$501$		0			0
$502$	−9.70838e8	+	2.98793e9i	−0.342518	+	1.05416i
$503$	−1.29785e9	−	3.99437e9i	−0.454712	−	1.39946i	−0.871473	−	0.490444i	$-0.836835\pi$
$503$	−1.29785e9	−	3.99437e9i	−0.454712	−	1.39946i	0.416760	−	0.909016i	$-0.363165\pi$
$504$		0			0
$505$	2.50801e9			0.866581
$506$	9.29241e8	−	7.71034e8i	0.318861	−	0.264574i
$507$		0			0
$508$	9.10133e7	−	6.61250e7i	0.0308022	−	0.0223791i
$509$	1.49432e9	+	4.59904e9i	0.502263	+	1.54581i	0.805324	+	0.592834i	$0.201991\pi$
$509$	1.49432e9	+	4.59904e9i	0.502263	+	1.54581i	−0.303062	+	0.952971i	$0.598009\pi$
$510$		0			0
$511$	−8.44208e6	−	6.13353e6i	−0.00279883	−	0.00203347i
$512$	−2.76029e9	−	2.00547e9i	−0.908887	−	0.660345i
$513$		0			0
$514$	−8.57791e8	−	2.64001e9i	−0.278619	−	0.857501i
$515$	9.03197e8	−	6.56211e8i	0.291378	−	0.211699i
$516$		0			0
$517$	1.19116e9	+	2.99568e9i	0.379099	+	0.953407i
$518$	−4.45366e8			−0.140787
$519$		0			0
$520$	−3.24747e8	−	9.99469e8i	−0.101282	−	0.311715i
$521$	1.84993e9	−	5.69349e9i	0.573090	−	1.76379i	−0.0695027	−	0.997582i	$-0.522141\pi$
$521$	1.84993e9	−	5.69349e9i	0.573090	−	1.76379i	0.642593	−	0.766208i	$-0.277859\pi$
$522$		0			0
$523$	1.68254e9	+	1.22244e9i	0.514291	+	0.373654i	0.814449	−	0.580235i	$-0.197039\pi$
$523$	1.68254e9	+	1.22244e9i	0.514291	+	0.373654i	−0.300158	+	0.953890i	$0.597039\pi$
$524$	−5.96410e7	+	1.83556e8i	−0.0181086	+	0.0557326i
$525$		0			0
$526$	1.79418e9	−	1.30355e9i	0.537546	−	0.390550i
$527$	−1.68929e9			−0.502768
$528$		0			0
$529$	−2.71671e9			−0.797900
$530$	8.84087e8	−	6.42327e8i	0.257946	−	0.187409i
$531$		0			0
$532$	3.08868e7	−	9.50597e7i	0.00889369	−	0.0273720i
$533$	−1.29422e9	−	9.40310e8i	−0.370224	−	0.268983i
$534$		0			0
$535$	−5.36434e8	+	1.65097e9i	−0.151453	+	0.466125i
$536$	1.39372e9	+	4.28943e9i	0.390930	+	1.20316i
$537$		0			0
$538$	−5.27874e9			−1.46148
$539$	−2.99785e9	−	1.89633e9i	−0.824612	−	0.521619i
$540$		0			0
$541$	−4.95621e9	+	3.60089e9i	−1.34573	+	0.977732i	−0.346521	+	0.938042i	$0.612637\pi$
$541$	−4.95621e9	+	3.60089e9i	−1.34573	+	0.977732i	−0.999212	+	0.0396902i	$0.987363\pi$
$542$	−7.85090e8	−	2.41626e9i	−0.211798	−	0.651847i
$543$		0			0
$544$	1.77767e9	+	1.29155e9i	0.473429	+	0.343966i
$545$	4.87811e9	+	3.54415e9i	1.29081	+	0.937831i
$546$		0			0
$547$	2.31601e9	+	7.12793e9i	0.605040	+	1.86212i	0.496515	+	0.868028i	$0.334613\pi$
$547$	2.31601e9	+	7.12793e9i	0.605040	+	1.86212i	0.108525	+	0.994094i	$0.465387\pi$
$548$	1.57461e8	−	1.14402e8i	0.0408736	−	0.0296964i
$549$		0			0
$550$	9.72708e8	+	6.15300e8i	0.249295	+	0.157695i
$551$	−7.38870e9			−1.88164
$552$		0			0
$553$	−2.65177e8	−	8.16129e8i	−0.0666802	−	0.205221i
$554$	2.23495e8	−	6.87848e8i	0.0558450	−	0.171873i
$555$		0			0
$556$	5.20111e8	+	3.77883e8i	0.128332	+	0.0932386i
$557$	−2.15763e9	+	6.64050e9i	−0.529034	+	1.62820i	0.227163	+	0.973857i	$0.427055\pi$
$557$	−2.15763e9	+	6.64050e9i	−0.529034	+	1.62820i	−0.756198	+	0.654343i	$0.772945\pi$
$558$		0			0
$559$	−6.78303e8	+	4.92816e8i	−0.164241	+	0.119328i
$560$	−4.41276e8			−0.106182
$561$		0			0
$562$	−1.75453e9			−0.416949
$563$	−9.65564e8	+	7.01524e8i	−0.228035	+	0.165677i	−0.695936	−	0.718104i	$-0.745010\pi$
$563$	−9.65564e8	+	7.01524e8i	−0.228035	+	0.165677i	0.467901	+	0.883781i	$0.345010\pi$
$564$		0			0
$565$	2.03767e9	−	6.27132e9i	0.475297	−	1.46281i
$566$	−1.43234e9	−	1.04066e9i	−0.332039	−	0.241241i
$567$		0			0
$568$	3.74826e8	−	1.15360e9i	0.0858244	−	0.264140i
$569$	7.43163e8	+	2.28722e9i	0.169119	+	0.520494i	0.999316	−	0.0369757i	$-0.0117724\pi$
$569$	7.43163e8	+	2.28722e9i	0.169119	+	0.520494i	−0.830198	+	0.557469i	$0.811772\pi$
$570$		0			0
$571$	−8.35462e9			−1.87802			−0.939010	−	0.343890i	$-0.888255\pi$
$571$	−8.35462e9			−1.87802			−0.939010	+	0.343890i	$0.888255\pi$
$572$	9.33349e7	+	2.34730e8i	0.0208525	+	0.0524425i
$573$		0			0
$574$	−6.42414e8	+	4.66741e8i	−0.141783	+	0.103011i
$575$	2.02692e8	+	6.23821e8i	0.0444630	+	0.136843i
$576$		0			0
$577$	−1.82636e9	−	1.32693e9i	−0.395796	−	0.287563i	0.372030	−	0.928221i	$-0.378662\pi$
$577$	−1.82636e9	−	1.32693e9i	−0.395796	−	0.287563i	−0.767827	+	0.640658i	$0.778662\pi$
$578$	9.84898e9	+	7.15570e9i	2.12150	+	1.54136i
$579$		0			0
$580$	−2.76389e8	−	8.50637e8i	−0.0588197	−	0.181028i
$581$	2.26530e8	−	1.64583e8i	0.0479191	−	0.0348153i
$582$		0			0
$583$	−1.54477e9	+	1.28176e9i	−0.322867	+	0.267897i
$584$	−1.13372e8			−0.0235538
$585$		0			0
$586$	1.23612e9	+	3.80438e9i	0.253757	+	0.780985i
$587$	−8.89786e8	+	2.73848e9i	−0.181573	+	0.558826i	−0.999873	−	0.0159670i	$-0.994917\pi$
$587$	−8.89786e8	+	2.73848e9i	−0.181573	+	0.558826i	0.818299	+	0.574793i	$0.194917\pi$
$588$		0			0
$589$	1.26245e9	+	9.17227e8i	0.254573	+	0.184958i
$590$	−8.83225e8	+	2.71829e9i	−0.177047	+	0.544896i
$591$		0			0
$592$	−3.31155e9	+	2.40598e9i	−0.656002	+	0.476613i
$593$	−5.80926e9			−1.14401			−0.572004	−	0.820251i	$-0.693834\pi$
$593$	−5.80926e9			−1.14401			−0.572004	+	0.820251i	$0.693834\pi$
$594$		0			0
$595$	1.29402e9			0.251843
$596$	−1.16468e9	+	8.46189e8i	−0.225343	+	0.163721i
$597$		0			0
$598$	2.50973e8	−	7.72414e8i	0.0479924	−	0.147705i
$599$	4.89703e9	+	3.55790e9i	0.930977	+	0.676394i	0.946232	−	0.323489i	$-0.104856\pi$
$599$	4.89703e9	+	3.55790e9i	0.930977	+	0.676394i	−0.0152547	+	0.999884i	$0.504856\pi$
$600$		0			0
$601$	1.86016e9	−	5.72500e9i	0.349535	−	1.07576i	−0.609576	−	0.792728i	$-0.708660\pi$
$601$	1.86016e9	−	5.72500e9i	0.349535	−	1.07576i	0.959111	−	0.283030i	$-0.0913397\pi$
$602$	1.28604e8	+	3.95801e8i	0.0240251	+	0.0739417i
$603$		0			0
$604$	−4.47544e8			−0.0826430
$605$	3.94215e9	+	2.15218e9i	0.723751	+	0.395125i
$606$		0			0
$607$	−7.74364e9	+	5.62609e9i	−1.40535	+	1.02105i	−0.411373	+	0.911467i	$0.634951\pi$
$607$	−7.74364e9	+	5.62609e9i	−1.40535	+	1.02105i	−0.993978	+	0.109581i	$0.965049\pi$
$608$	−6.27233e8	−	1.93042e9i	−0.113179	−	0.348330i
$609$		0			0
$610$	8.50726e8	+	6.18089e8i	0.151752	+	0.110254i
$611$	1.75426e9	+	1.27455e9i	0.311136	+	0.226054i
$612$		0			0
$613$	5.66277e8	+	1.74282e9i	0.0992926	+	0.305591i	0.988349	−	0.152207i	$-0.0486381\pi$
$613$	5.66277e8	+	1.74282e9i	0.0992926	+	0.305591i	−0.889056	+	0.457799i	$0.848638\pi$
$614$	−2.98473e9	+	2.16853e9i	−0.520374	+	0.378074i
$615$		0			0
$616$	9.56188e8	−	6.15666e7i	0.164820	−	0.0106124i
$617$	−1.92297e9			−0.329590			−0.164795	−	0.986328i	$-0.552696\pi$
$617$	−1.92297e9			−0.329590			−0.164795	+	0.986328i	$0.552696\pi$
$618$		0			0
$619$	2.08801e9	+	6.42623e9i	0.353847	+	1.08903i	0.956675	+	0.291157i	$0.0940402\pi$
$619$	2.08801e9	+	6.42623e9i	0.353847	+	1.08903i	−0.602829	+	0.797871i	$0.705960\pi$
$620$	−5.83728e7	+	1.79653e8i	−0.00983648	+	0.0302736i
$621$		0			0
$622$	6.80032e9	+	4.94072e9i	1.13309	+	0.823235i
$623$	3.36279e8	−	1.03496e9i	0.0557176	−	0.171481i
$624$		0			0
$625$	2.85161e9	−	2.07181e9i	0.467207	−	0.339446i
$626$	−8.97013e9			−1.46146
$627$		0			0
$628$	−8.72381e8			−0.140555
$629$	9.71093e9	−	7.05540e9i	1.55591	−	1.13043i
$630$		0			0
$631$	−1.32115e9	+	4.06609e9i	−0.209339	+	0.644279i	0.790168	+	0.612890i	$0.209993\pi$
$631$	−1.32115e9	+	4.06609e9i	−0.209339	+	0.644279i	−0.999507	+	0.0313891i	$0.990007\pi$
$632$	−7.54266e9	−	5.48007e9i	−1.18854	−	0.863527i
$633$		0			0
$634$	1.91841e9	−	5.90425e9i	0.298971	−	0.920137i
$635$	−4.15750e8	−	1.27955e9i	−0.0644354	−	0.198312i
$636$		0			0
$637$	−2.38596e9			−0.365742
$638$	−3.42473e9	−	8.61295e9i	−0.522101	−	1.31305i
$639$		0			0
$640$	−3.17232e9	+	2.30483e9i	−0.478352	+	0.347543i
$641$	−3.79401e9	−	1.16768e10i	−0.568977	−	1.75113i	−0.655827	−	0.754911i	$-0.727680\pi$
$641$	−3.79401e9	−	1.16768e10i	−0.568977	−	1.75113i	0.0868498	−	0.996221i	$-0.472320\pi$
$642$		0			0
$643$	7.44868e9	+	5.41178e9i	1.10495	+	0.802790i	0.981860	−	0.189606i	$-0.0607211\pi$
$643$	7.44868e9	+	5.41178e9i	1.10495	+	0.802790i	0.123085	+	0.992396i	$0.460721\pi$
$644$	5.78086e7	+	4.20004e7i	0.00852887	+	0.00619659i
$645$		0			0
$646$	−4.69649e9	−	1.44543e10i	−0.685424	−	2.10952i
$647$	7.74654e9	−	5.62819e9i	1.12446	−	0.816965i	0.139578	−	0.990211i	$-0.455426\pi$
$647$	7.74654e9	−	5.62819e9i	1.12446	−	0.816965i	0.984879	+	0.173246i	$0.0554255\pi$
$648$		0			0
$649$	1.29817e9	−	5.08701e9i	0.186413	−	0.730477i
$650$	7.74169e8			0.110570
$651$		0			0
$652$	−3.82306e8	−	1.17662e9i	−0.0540187	−	0.166253i
$653$	1.77872e9	−	5.47435e9i	0.249984	−	0.769372i	−0.744793	−	0.667296i	$-0.767452\pi$
$653$	1.77872e9	−	5.47435e9i	0.249984	−	0.769372i	0.994777	−	0.102076i	$-0.0325484\pi$
$654$		0			0
$655$	1.86734e9	+	1.35670e9i	0.259644	+	0.188643i
$656$	−2.25526e9	+	6.94097e9i	−0.311912	+	0.959968i
$657$		0			0
$658$	8.70762e8	−	6.32646e8i	0.119154	−	0.0865705i
$659$	−3.26282e8			−0.0444114			−0.0222057	−	0.999753i	$-0.507069\pi$
$659$	−3.26282e8			−0.0444114			−0.0222057	+	0.999753i	$0.507069\pi$
$660$		0			0
$661$	7.99556e9			1.07682			0.538411	−	0.842682i	$-0.319025\pi$
$661$	7.99556e9			1.07682			0.538411	+	0.842682i	$0.319025\pi$
$662$	−4.87880e9	+	3.54466e9i	−0.653598	+	0.474866i
$663$		0			0
$664$	9.40079e8	−	2.89327e9i	0.124617	−	0.383531i
$665$	−9.67055e8	−	7.02606e8i	−0.127519	−	0.0926480i
$666$		0			0
$667$	1.63228e9	−	5.02364e9i	0.212988	−	0.655508i
$668$	1.01407e8	+	3.12099e8i	0.0131629	+	0.0405112i
$669$		0			0
$670$	7.05835e9			0.906653
$671$	−1.63238e9	−	1.03258e9i	−0.208589	−	0.131946i
$672$		0			0
$673$	−2.96463e9	+	2.15393e9i	−0.374902	+	0.272382i	−0.759241	−	0.650810i	$-0.774430\pi$
$673$	−2.96463e9	+	2.15393e9i	−0.374902	+	0.272382i	0.384339	+	0.923192i	$0.374430\pi$
$674$	1.45228e9	+	4.46965e9i	0.182701	+	0.562295i
$675$		0			0
$676$	−8.40878e8	−	6.10934e8i	−0.104694	−	0.0760643i
$677$	1.29185e10	+	9.38586e9i	1.60012	+	1.16256i	0.887281	+	0.461230i	$0.152592\pi$
$677$	1.29185e10	+	9.38586e9i	1.60012	+	1.16256i	0.712841	+	0.701326i	$0.247408\pi$
$678$		0			0
$679$	3.53973e7	+	1.08942e8i	0.00433937	+	0.0133552i
$680$	1.13740e10	−	8.26367e9i	1.38717	−	1.00784i
$681$		0			0
$682$	−4.84045e8	+	1.89678e9i	−0.0584306	+	0.228966i
$683$	−5.87207e9			−0.705210			−0.352605	−	0.935772i	$-0.614704\pi$
$683$	−5.87207e9			−0.705210			−0.352605	+	0.935772i	$0.614704\pi$
$684$		0			0
$685$	−7.19287e8	−	2.21374e9i	−0.0855037	−	0.263153i
$686$	−7.41047e8	+	2.28071e9i	−0.0876418	+	0.269734i
$687$		0			0
$688$	3.09446e9	+	2.24826e9i	0.362265	+	0.263201i
$689$	−4.17216e8	+	1.28406e9i	−0.0485952	+	0.149561i
$690$		0			0
$691$	4.09960e9	−	2.97853e9i	0.472681	−	0.343423i	−0.325804	−	0.945437i	$-0.605635\pi$
$691$	4.09960e9	−	2.97853e9i	0.472681	−	0.343423i	0.798485	+	0.602015i	$0.205635\pi$
$692$	−3.32874e8			−0.0381863
$693$		0			0
$694$	−1.28666e9			−0.146118
$695$	6.22013e9	−	4.51919e9i	0.702834	−	0.510639i
$696$		0			0
$697$	6.61342e9	−	2.03540e10i	0.739795	−	2.27685i
$698$	3.80068e9	+	2.76136e9i	0.423027	+	0.307347i
$699$		0			0
$700$	−2.10479e7	+	6.47787e7i	−0.00231935	+	0.00713821i
$701$	1.35114e9	+	4.15839e9i	0.148145	+	0.455945i	0.997402	−	0.0720354i	$-0.0229495\pi$
$701$	1.35114e9	+	4.15839e9i	0.148145	+	0.455945i	−0.849257	+	0.527980i	$0.822949\pi$
$702$		0			0
$703$	−1.10881e10			−1.20369
$704$	7.84989e9	−	6.51342e9i	0.847929	−	0.703566i
$705$		0			0
$706$	−1.12521e10	+	8.17515e9i	−1.20342	+	0.874338i
$707$	4.75289e8	+	1.46279e9i	0.0505813	+	0.155673i
$708$		0			0
$709$	7.06166e9	+	5.13059e9i	0.744123	+	0.540637i	0.894000	−	0.448068i	$-0.147888\pi$
$709$	7.06166e9	+	5.13059e9i	0.744123	+	0.540637i	−0.149877	+	0.988705i	$0.547888\pi$
$710$	−1.53573e9	−	1.11577e9i	−0.161031	−	0.116996i
$711$		0			0
$712$	−3.65355e9	−	1.12445e10i	−0.379345	−	1.16751i
$713$	−9.02527e8	+	6.55724e8i	−0.0932495	+	0.0677498i
$714$		0			0
$715$	3.01473e9	−	1.94111e8i	0.308444	−	0.0198600i
$716$	−1.25817e9			−0.128098
$717$		0			0
$718$	−3.91722e9	−	1.20560e10i	−0.394951	−	1.21553i
$719$	7.20995e8	−	2.21899e9i	0.0723404	−	0.222641i	−0.908349	−	0.418213i	$-0.862656\pi$
$719$	7.20995e8	−	2.21899e9i	0.0723404	−	0.222641i	0.980689	+	0.195572i	$0.0626564\pi$
$720$		0			0
$721$	5.53897e8	+	4.02430e8i	0.0550371	+	0.0399868i
$722$	−1.45814e9	+	4.48768e9i	−0.144184	+	0.443753i
$723$		0			0
$724$	−1.10603e9	+	8.03577e8i	−0.108313	+	0.0786942i
$725$	5.03505e9			0.490706
$726$		0			0
$727$	−7.21858e9			−0.696757			−0.348378	−	0.937354i	$-0.613268\pi$
$727$	−7.21858e9			−0.696757			−0.348378	+	0.937354i	$0.613268\pi$
$728$	5.21395e8	−	3.78816e8i	0.0500850	−	0.0363889i
$729$		0			0
$730$	−5.48275e7	+	1.68742e8i	−0.00521637	+	0.0160543i
$731$	−9.07434e9	−	6.59289e9i	−0.859220	−	0.624260i
$732$		0			0
$733$	−3.51840e8	+	1.08285e9i	−0.0329975	+	0.101556i	−0.966199	−	0.257798i	$-0.917003\pi$
$733$	−3.51840e8	+	1.08285e9i	−0.0329975	+	0.101556i	0.933201	+	0.359354i	$0.117003\pi$
$734$	2.36871e9	+	7.29015e9i	0.221094	+	0.680456i
$735$		0			0
$736$	1.45108e9			0.134159
$737$	−1.29383e10	+	8.33068e8i	−1.19054	+	0.0766557i
$738$		0			0
$739$	8.15627e9	−	5.92588e9i	0.743423	−	0.540128i	−0.150358	−	0.988632i	$-0.548043\pi$
$739$	8.15627e9	−	5.92588e9i	0.743423	−	0.540128i	0.893781	+	0.448503i	$0.148043\pi$
$740$	−4.14772e8	−	1.27654e9i	−0.0376269	−	0.115804i
$741$		0			0
$742$	5.42177e8	+	3.93915e8i	0.0487223	+	0.0353988i
$743$	2.16787e9	+	1.57505e9i	0.193897	+	0.140875i	0.680498	−	0.732750i	$-0.261763\pi$
$743$	2.16787e9	+	1.57505e9i	0.193897	+	0.140875i	−0.486601	+	0.873624i	$0.661763\pi$
$744$		0			0
$745$	5.32027e9	+	1.63741e10i	0.471397	+	1.45081i
$746$	5.83462e9	−	4.23910e9i	0.514549	−	0.373842i
$747$		0			0
$748$	−2.60068e9	+	2.15790e9i	−0.227212	+	0.188528i
$749$	−1.06459e9			−0.0925751
$750$		0			0
$751$	−3.44583e9	−	1.06052e10i	−0.296862	−	0.913646i	−0.982590	−	0.185788i	$-0.940516\pi$
$751$	−3.44583e9	−	1.06052e10i	−0.296862	−	0.913646i	0.685728	−	0.727858i	$-0.259484\pi$
$752$	3.05690e9	−	9.40817e9i	0.262131	−	0.806757i
$753$		0			0
$754$	−5.04373e9	−	3.66448e9i	−0.428501	−	0.311324i
$755$	−1.65394e9	+	5.09032e9i	−0.139864	+	0.430458i
$756$		0			0
$757$	1.08050e10	−	7.85030e9i	0.905294	−	0.657735i	−0.0345262	−	0.999404i	$-0.510992\pi$
$757$	1.08050e10	−	7.85030e9i	0.905294	−	0.657735i	0.939820	+	0.341669i	$0.110992\pi$
$758$	−8.41094e9			−0.701459
$759$		0			0
$760$	−1.29870e10			−1.07315
$761$	−5.18453e9	+	3.76678e9i	−0.426445	+	0.309831i	−0.780226	−	0.625498i	$-0.784896\pi$
$761$	−5.18453e9	+	3.76678e9i	−0.426445	+	0.309831i	0.353781	+	0.935328i	$0.384896\pi$
$762$		0			0
$763$	−1.14267e9	+	3.51679e9i	−0.0931294	+	0.286623i
$764$	−2.11096e9	−	1.53370e9i	−0.171259	−	0.124427i
$765$		0			0
$766$	−3.90024e9	+	1.20037e10i	−0.313538	+	0.964971i
$767$	−1.09122e9	−	3.35843e9i	−0.0873231	−	0.268753i
$768$		0			0
$769$	1.07084e10			0.849148			0.424574	−	0.905393i	$-0.360424\pi$
$769$	1.07084e10			0.849148			0.424574	+	0.905393i	$0.360424\pi$
$770$	3.70784e8	−	1.45295e9i	0.0292687	−	0.114692i
$771$		0			0
$772$	1.25143e9	−	9.09215e8i	0.0978915	−	0.0711223i
$773$	−2.20219e9	−	6.77765e9i	−0.171485	−	0.527778i	0.827970	−	0.560772i	$-0.189496\pi$
$773$	−2.20219e9	−	6.77765e9i	−0.171485	−	0.527778i	−0.999456	+	0.0329945i	$0.989496\pi$
$774$		0			0
$775$	−8.60304e8	−	6.25047e8i	−0.0663889	−	0.0482344i
$776$	1.00684e9	+	7.31512e8i	0.0773471	+	0.0561960i
$777$		0			0
$778$	−1.75654e9	−	5.40606e9i	−0.133730	−	0.411578i
$779$	−1.59939e10	+	1.16203e10i	−1.21220	+	0.880713i
$780$		0			0
$781$	2.94677e9	+	1.86402e9i	0.221344	+	0.140014i
$782$	1.08651e10			0.812478
$783$		0			0
$784$	3.36362e9	+	1.03522e10i	0.249288	+	0.767229i
$785$	−3.22397e9	+	9.92237e9i	−0.237874	+	0.732102i
$786$		0			0
$787$	−1.13247e10	−	8.22785e9i	−0.828159	−	0.601693i	0.0908786	−	0.995862i	$-0.471032\pi$
$787$	−1.13247e10	−	8.22785e9i	−0.828159	−	0.601693i	−0.919038	+	0.394169i	$0.871032\pi$
$788$	2.37723e8	−	7.31635e8i	0.0173073	−	0.0532664i
$789$		0			0
$790$	−1.18041e10	+	8.57621e9i	−0.851804	+	0.618872i
$791$	4.04389e9			0.290523
$792$		0			0
$793$	−1.29919e9			−0.0925161
$794$	−8.46377e9	+	6.14929e9i	−0.600056	+	0.435966i
$795$		0			0
$796$	8.82503e8	−	2.71607e9i	0.0620184	−	0.190873i
$797$	4.11909e9	+	2.99270e9i	0.288202	+	0.209391i	0.722487	−	0.691384i	$-0.242999\pi$
$797$	4.11909e9	+	2.99270e9i	0.288202	+	0.209391i	−0.434285	+	0.900776i	$0.642999\pi$
$798$		0			0
$799$	−8.96418e9	+	2.75889e10i	−0.621723	+	1.91347i
$800$	4.27430e8	+	1.31549e9i	0.0295155	+	0.0908393i
$801$		0			0
$802$	1.00686e10			0.689224
$803$	8.05858e7	−	3.15784e8i	0.00549230	−	0.0215221i
$804$		0			0
$805$	6.91346e8	−	5.02292e8i	0.0467100	−	0.0339368i
$806$	4.06880e8	+	1.25225e9i	0.0273712	+	0.0842399i
$807$		0			0
$808$	1.35191e10	+	9.82219e9i	0.901587	+	0.655041i
$809$	1.29726e10	+	9.42512e9i	0.861402	+	0.625845i	0.928266	−	0.371917i	$-0.121299\pi$
$809$	1.29726e10	+	9.42512e9i	0.861402	+	0.625845i	−0.0668639	+	0.997762i	$0.521299\pi$
$810$		0			0
$811$	6.88809e9	+	2.11994e10i	0.453446	+	1.39556i	0.872950	+	0.487810i	$0.162204\pi$
$811$	6.88809e9	+	2.11994e10i	0.453446	+	1.39556i	−0.419503	+	0.907754i	$0.637796\pi$
$812$	4.43754e8	−	3.22406e8i	0.0290868	−	0.0211328i
$813$		0			0
$814$	−5.13943e9	−	1.29253e10i	−0.333987	−	0.839953i
$815$	−1.47956e10			−0.957370
$816$		0			0
$817$	3.20179e9	+	9.85410e9i	0.205407	+	0.632179i
$818$	2.25458e9	−	6.93888e9i	0.144022	−	0.443254i
$819$		0			0
$820$	−1.93609e9	−	1.40665e9i	−0.122624	−	0.0890917i
$821$	−1.73643e9	+	5.34418e9i	−0.109511	+	0.337039i	−0.990763	−	0.135608i	$-0.956701\pi$
$821$	−1.73643e9	+	5.34418e9i	−0.109511	+	0.337039i	0.881252	+	0.472647i	$0.156701\pi$
$822$		0			0
$823$	9.20017e9	−	6.68432e9i	0.575303	−	0.417982i	−0.261725	−	0.965143i	$-0.584291\pi$
$823$	9.20017e9	−	6.68432e9i	0.575303	−	0.417982i	0.837028	+	0.547161i	$0.184291\pi$
$824$	7.43851e9			0.463170
$825$		0			0
$826$	−1.75281e9			−0.108219
$827$	−1.67392e10	+	1.21618e10i	−1.02912	+	0.747700i	−0.968132	−	0.250439i	$-0.919425\pi$
$827$	−1.67392e10	+	1.21618e10i	−1.02912	+	0.747700i	−0.0609879	+	0.998139i	$0.519425\pi$
$828$		0			0
$829$	6.34679e8	−	1.95334e9i	0.0386913	−	0.119080i	−0.929845	−	0.367951i	$-0.880060\pi$
$829$	6.34679e8	−	1.95334e9i	0.0386913	−	0.119080i	0.968537	+	0.248871i	$0.0800595\pi$
$830$	−3.85167e9	−	2.79840e9i	−0.233817	−	0.169878i
$831$		0			0
$832$	2.12013e9	−	6.52508e9i	0.127623	−	0.392784i
$833$	−9.86363e9	−	3.03571e10i	−0.591261	−	1.81971i
$834$		0			0
$835$	3.92455e9			0.233285
$836$	3.11523e9	−	2.00582e8i	0.184403	−	0.0118733i
$837$		0			0
$838$	−3.28973e9	+	2.39013e9i	−0.193111	+	0.140303i
$839$	1.96613e9	+	6.05112e9i	0.114933	+	0.353728i	0.991933	−	0.126763i	$-0.0404587\pi$
$839$	1.96613e9	+	6.05112e9i	0.114933	+	0.353728i	−0.877000	+	0.480490i	$0.840459\pi$
$840$		0			0
$841$	−1.88481e10	−	1.36939e10i	−1.09265	−	0.793856i
$842$	−1.56750e10	−	1.13886e10i	−0.904933	−	0.657472i
$843$		0			0
$844$	1.48248e9	+	4.56259e9i	0.0848768	+	0.261224i
$845$	−1.00563e10	+	7.30630e9i	−0.573374	+	0.416580i
$846$		0			0
$847$	−5.08181e8	+	2.70710e9i	−0.0287360	+	0.153078i
$848$	6.15943e9			0.346861
$849$		0			0
$850$	3.20044e9	+	9.84993e9i	0.178749	+	0.550132i
$851$	2.44953e9	−	7.53889e9i	0.136248	−	0.419328i
$852$		0			0
$853$	1.73484e10	+	1.26043e10i	0.957056	+	0.695342i	0.952465	−	0.304648i	$-0.0985387\pi$
$853$	1.73484e10	+	1.26043e10i	0.957056	+	0.695342i	0.00459087	+	0.999989i	$0.498539\pi$
$854$	−1.99279e8	+	6.13317e8i	−0.0109486	+	0.0336963i
$855$		0			0
$856$	−9.35734e9	+	6.79851e9i	−0.509911	+	0.370472i
$857$	1.33479e10			0.724405			0.362203	−	0.932099i	$-0.382025\pi$
$857$	1.33479e10			0.724405			0.362203	+	0.932099i	$0.382025\pi$
$858$		0			0
$859$	−6.06986e8			−0.0326740			−0.0163370	−	0.999867i	$-0.505200\pi$
$859$	−6.06986e8			−0.0326740			−0.0163370	+	0.999867i	$0.505200\pi$
$860$	−1.01470e9	+	7.37224e8i	−0.0543994	+	0.0395235i
$861$		0			0
$862$	−6.60131e9	+	2.03167e10i	−0.351039	+	1.08039i
$863$	2.53367e10	+	1.84082e10i	1.34187	+	0.974928i	0.999373	+	0.0354109i	$0.0112740\pi$
$863$	2.53367e10	+	1.84082e10i	1.34187	+	0.974928i	0.342501	+	0.939517i	$0.388726\pi$
$864$		0			0
$865$	−1.23017e9	+	3.78607e9i	−0.0646262	+	0.198899i
$866$	−1.80026e9	−	5.54062e9i	−0.0941937	−	0.289898i
$867$		0			0
$868$	−1.15844e8			−0.00601251
$869$	2.06254e10	−	1.71139e10i	1.06619	−	0.884665i
$870$		0			0
$871$	−7.05508e9	+	5.12582e9i	−0.361775	+	0.262845i
$872$	1.24147e10	+	3.82086e10i	0.634059	+	1.95143i
$873$		0			0
$874$	−8.11982e9	−	5.89939e9i	−0.411392	−	0.298894i
$875$	2.71799e9	+	1.97474e9i	0.137158	+	0.0996508i
$876$		0			0
$877$	1.81611e9	+	5.58941e9i	0.0909167	+	0.279813i	0.986168	−	0.165749i	$-0.0530040\pi$
$877$	1.81611e9	+	5.58941e9i	0.0909167	+	0.279813i	−0.895251	+	0.445562i	$0.853004\pi$
$878$	6.16578e9	−	4.47970e9i	0.307438	−	0.223367i
$879$		0			0
$880$	−5.09224e9	−	1.28066e10i	−0.251895	−	0.633497i
$881$	1.75602e10			0.865196			0.432598	−	0.901587i	$-0.357597\pi$
$881$	1.75602e10			0.865196			0.432598	+	0.901587i	$0.357597\pi$
$882$		0			0
$883$	−3.04366e9	−	9.36743e9i	−0.148776	−	0.457887i	0.848701	−	0.528873i	$-0.177385\pi$
$883$	−3.04366e9	−	9.36743e9i	−0.148776	−	0.457887i	−0.997477	+	0.0709865i	$0.977385\pi$
$884$	−7.02401e8	+	2.16177e9i	−0.0341981	+	0.105251i
$885$		0			0
$886$	8.52713e9	+	6.19532e9i	0.411893	+	0.299258i
$887$	3.58145e9	−	1.10226e10i	0.172316	−	0.530335i	−0.827184	−	0.561930i	$-0.810059\pi$
$887$	3.58145e9	−	1.10226e10i	0.172316	−	0.530335i	0.999501	+	0.0315955i	$0.0100588\pi$
$888$		0			0
$889$	6.67505e8	−	4.84971e8i	0.0318639	−	0.0231504i
$890$	−1.85030e10			−0.879786
$891$		0			0
$892$	−4.35883e9			−0.205633
$893$	2.16790e10	−	1.57507e10i	1.01873	−	0.740151i
$894$		0			0
$895$	−4.64969e9	+	1.43103e10i	−0.216792	+	0.667217i
$896$	−1.94547e9	−	1.41346e9i	−0.0903537	−	0.0656458i
$897$		0			0
$898$	8.00948e9	−	2.46506e10i	0.369094	−	1.13595i
$899$	2.64627e9	+	8.14440e9i	0.121472	+	0.373852i
$900$		0			0
$901$	−1.80622e10			−0.822684
$902$	−2.09590e10	−	1.32579e10i	−0.950927	−	0.601521i
$903$		0			0
$904$	3.55444e10	−	2.58245e10i	1.60023	−	1.16263i
$905$	5.05236e9	+	1.55496e10i	0.226581	+	0.697346i
$906$		0			0
$907$	−2.51450e10	−	1.82689e10i	−1.11899	−	0.812994i	−0.134935	−	0.990854i	$-0.543083\pi$
$907$	−2.51450e10	−	1.82689e10i	−1.11899	−	0.812994i	−0.984056	+	0.177860i	$0.943083\pi$
$908$	−3.25866e9	−	2.36755e9i	−0.144457	−	0.104954i
$909$		0			0
$910$	−3.11675e8	−	9.59236e8i	−0.0137106	−	0.0421969i
$911$	−5.19903e8	+	3.77732e8i	−0.0227828	+	0.0165527i	−0.599118	−	0.800660i	$-0.704482\pi$
$911$	−5.19903e8	+	3.77732e8i	−0.0227828	+	0.0165527i	0.576336	+	0.817213i	$0.304482\pi$
$912$		0			0
$913$	7.39061e9	+	4.67503e9i	0.321390	+	0.203300i
$914$	−3.82082e9			−0.165518
$915$		0			0
$916$	1.23665e9	+	3.80603e9i	0.0531635	+	0.163621i
$917$	−4.37416e8	+	1.34623e9i	−0.0187328	+	0.0576535i
$918$		0			0
$919$	−3.07354e10	−	2.23306e10i	−1.30627	−	0.949063i	−0.306278	−	0.951942i	$-0.599084\pi$
$919$	−3.07354e10	−	2.23306e10i	−1.30627	−	0.949063i	−0.999996	+	0.00287896i	$0.999084\pi$
$920$	2.86903e9	−	8.82995e9i	0.121472	−	0.373853i
$921$		0			0
$922$	−1.88641e9	+	1.37056e9i	−0.0792643	+	0.0575889i
$923$	2.34530e9			0.0981732
$924$		0			0
$925$	7.55601e9			0.313904
$926$	−1.30640e10	+	9.49153e9i	−0.540675	+	0.392824i
$927$		0			0
$928$	3.44210e9	−	1.05937e10i	0.141386	−	0.435140i
$929$	1.48211e10	+	1.07682e10i	0.606494	+	0.440644i	0.848178	−	0.529711i	$-0.177700\pi$
$929$	1.48211e10	+	1.07682e10i	0.606494	+	0.440644i	−0.241684	+	0.970355i	$0.577700\pi$
$930$		0			0
$931$	−9.11151e9	+	2.80423e10i	−0.370055	+	1.13891i
$932$	1.77463e9	+	5.46176e9i	0.0718046	+	0.220992i
$933$		0			0
$934$	9.13871e8			0.0367004
$935$	1.49327e10	+	3.75546e10i	0.597445	+	1.50253i
$936$		0			0
$937$	3.93000e10	−	2.85531e10i	1.56064	−	1.13387i	0.625163	−	0.780495i	$-0.285033\pi$
$937$	3.93000e10	−	2.85531e10i	1.56064	−	1.13387i	0.935480	−	0.353379i	$-0.114967\pi$
$938$	1.33762e9	+	4.11676e9i	0.0529203	+	0.162872i
$939$		0			0
$940$	2.62428e9	+	1.90665e9i	0.103053	+	0.0748726i
$941$	−3.29163e10	−	2.39151e10i	−1.28780	−	0.935640i	−0.288040	−	0.957618i	$-0.593004\pi$
$941$	−3.29163e10	−	2.39151e10i	−1.28780	−	0.935640i	−0.999758	+	0.0219781i	$0.993004\pi$
$942$		0			0
$943$	−4.36740e9	−	1.34415e10i	−0.169603	−	0.521983i
$944$	−1.30332e10	+	9.46915e9i	−0.504252	+	0.366361i
$945$		0			0
$946$	−1.00028e10	+	8.29978e9i	−0.384151	+	0.318748i
$947$	−2.40022e10			−0.918387			−0.459193	−	0.888336i	$-0.651861\pi$
$947$	−2.40022e10			−0.918387			−0.459193	+	0.888336i	$0.651861\pi$
$948$		0			0
$949$	−6.77391e7	−	2.08480e8i	−0.00257281	−	0.00791830i
$950$	2.95640e9	−	9.09885e9i	0.111874	−	0.344314i
$951$		0			0
$952$	6.97523e9	+	5.06780e9i	0.262017	+	0.190366i
$953$	2.10956e9	−	6.49257e9i	0.0789528	−	0.242992i	−0.903788	−	0.427981i	$-0.859225\pi$
$953$	2.10956e9	−	6.49257e9i	0.0789528	−	0.242992i	0.982741	+	0.184989i	$0.0592250\pi$
$954$		0			0
$955$	−2.52454e10	+	1.83419e10i	−0.937930	+	0.681446i
$956$	−3.67088e9			−0.135884
$957$		0			0
$958$	3.85861e10			1.41792
$959$	1.15485e9	−	8.39044e8i	0.0422823	−	0.0307199i
$960$		0			0
$961$	−7.94298e9	+	2.44460e10i	−0.288703	+	0.888537i
$962$	−7.56903e9	−	5.49922e9i	−0.274112	−	0.199154i
$963$		0			0
$964$	−1.65194e9	+	5.08416e9i	−0.0593917	+	0.182789i
$965$	−5.71654e9	−	1.75937e10i	−0.204780	−	0.630248i
$966$		0			0
$967$	−1.67010e10			−0.593950			−0.296975	−	0.954885i	$-0.595978\pi$
$967$	−1.67010e10			−0.593950			−0.296975	+	0.954885i	$0.595978\pi$
$968$	1.28210e10	+	2.70398e10i	0.454316	+	0.958164i
$969$		0			0
$970$	1.57569e9	−	1.14480e9i	0.0554331	−	0.0402745i
$971$	−7.08873e9	−	2.18169e10i	−0.248485	−	0.764760i	−0.995044	−	0.0994394i	$-0.968295\pi$
$971$	−7.08873e9	−	2.18169e10i	−0.248485	−	0.764760i	0.746558	−	0.665320i	$-0.231705\pi$
$972$		0			0
$973$	3.81457e9	+	2.77145e9i	0.132755	+	0.0964522i
$974$	−2.61182e10	−	1.89760e10i	−0.905704	−	0.658032i
$975$		0			0
$976$	1.83154e9	+	5.63692e9i	0.0630584	+	0.194074i
$977$	−5.87442e9	+	4.26801e9i	−0.201527	+	0.146418i	−0.683972	−	0.729508i	$-0.739749\pi$
$977$	−5.87442e9	+	4.26801e9i	−0.201527	+	0.146418i	0.482445	+	0.875926i	$0.339749\pi$
$978$		0			0
$979$	3.39170e10	−	2.18383e9i	1.15526	−	0.0743841i
$980$	−3.56926e9			−0.121140
$981$		0			0
$982$	2.78744e9	+	8.57887e9i	0.0939325	+	0.289095i
$983$	−1.72005e9	+	5.29376e9i	−0.0577568	+	0.177757i	−0.975773	−	0.218786i	$-0.929790\pi$
$983$	−1.72005e9	+	5.29376e9i	−0.0577568	+	0.177757i	0.918016	+	0.396543i	$0.129790\pi$
$984$		0			0
$985$	−7.44302e9	−	5.40767e9i	−0.248155	−	0.180295i
$986$	2.57732e10	−	7.93217e10i	0.856246	−	2.63525i
$987$		0			0
$988$	1.69869e9	−	1.23417e9i	0.0560356	−	0.0407123i
$989$	−7.40722e9			−0.243483
$990$		0			0
$991$	−1.26520e10			−0.412955			−0.206478	−	0.978451i	$-0.566200\pi$
$991$	−1.26520e10			−0.412955			−0.206478	+	0.978451i	$0.566200\pi$
$992$	−1.90322e9	+	1.38277e9i	−0.0619010	+	0.0449737i
$993$		0			0
$994$	3.59738e8	−	1.10716e9i	0.0116181	−	0.0357567i
$995$	−2.76309e10	−	2.00750e10i	−0.889230	−	0.646063i
$996$		0			0
$997$	5.87619e9	−	1.80851e10i	0.187786	−	0.577945i	−0.812199	−	0.583380i	$-0.801730\pi$
$997$	5.87619e9	−	1.80851e10i	0.187786	−	0.577945i	0.999985	+	0.00543464i	$0.00172991\pi$
$998$	1.52960e10	+	4.70762e10i	0.487103	+	1.49915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.c.91.5		28
3.2	odd	2		33.8.e.a.25.3	yes	28
11.4	even	5	inner	99.8.f.c.37.5		28
33.2	even	10		363.8.a.p.1.5		14
33.20	odd	10		363.8.a.q.1.10		14
33.26	odd	10		33.8.e.a.4.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.a.4.3	✓	28	33.26	odd	10
33.8.e.a.25.3	yes	28	3.2	odd	2
99.8.f.c.37.5		28	11.4	even	5	inner
99.8.f.c.91.5		28	1.1	even	1	trivial
363.8.a.p.1.5		14	33.2	even	10
363.8.a.q.1.10		14	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(8.43584 - 6.12900i) q^{2} +(-5.95538 + 18.3288i) q^{4} +(186.461 + 135.472i) q^{5} +(-43.6776 + 134.426i) q^{7} +(474.540 + 1460.49i) q^{8} +O(q^{10})\)	\(q+(8.43584 - 6.12900i) q^{2} +(-5.95538 + 18.3288i) q^{4} +(186.461 + 135.472i) q^{5} +(-43.6776 + 134.426i) q^{7} +(474.540 + 1460.49i) q^{8} +2403.26 q^{10} +(-4405.31 + 283.647i) q^{11} +(-2402.15 + 1745.26i) q^{13} +(455.438 + 1401.69i) q^{14} +(10958.8 + 7962.01i) q^{16} +(-32135.9 - 23348.1i) q^{17} +(11338.9 + 34897.4i) q^{19} +(-3593.47 + 2610.81i) q^{20} +(-35424.0 + 29392.9i) q^{22} -26232.0 q^{23} +(-7726.90 - 23780.9i) q^{25} +(-9567.43 + 29445.5i) q^{26} +(-2203.74 - 1601.11i) q^{28} +(-62224.8 + 191508. i) q^{29} +(34405.6 - 24997.1i) q^{31} -55317.1 q^{32} -414194. q^{34} +(-26355.1 + 19148.1i) q^{35} +(-93379.6 + 287393. i) q^{37} +(309539. + 224893. i) q^{38} +(-109371. + 336610. i) q^{40} +(166492. + 512408. i) q^{41} +282374. q^{43} +(21036.4 - 82433.0i) q^{44} +(-221289. + 160776. i) q^{46} +(-225672. - 694546. i) q^{47} +(650098. + 472324. i) q^{49} +(-210936. - 153254. i) q^{50} +(-17682.8 - 54422.1i) q^{52} +(367870. - 267273. i) q^{53} +(-859843. - 543905. i) q^{55} -217054. q^{56} +(648835. + 1.99691e6i) q^{58} +(-367511. + 1.13108e6i) q^{59} +(353988. + 257188. i) q^{61} +(137033. - 421743. i) q^{62} +(-1.86937e6 + 1.35818e6i) q^{64} -684340. q^{65} +2.93699e6 q^{67} +(619324. - 449965. i) q^{68} +(-104969. + 323060. i) q^{70} +(-639020. - 464275. i) q^{71} +(-22813.8 + 70213.6i) q^{73} +(973695. + 2.99672e6i) q^{74} -707154. q^{76} +(154284. - 604576. i) q^{77} +(-4.91172e6 + 3.56858e6i) q^{79} +(964753. + 2.96920e6i) q^{80} +(4.54505e6 + 3.30217e6i) q^{82} +(-1.60269e6 - 1.16442e6i) q^{83} +(-2.82908e6 - 8.70702e6i) q^{85} +(2.38206e6 - 1.73067e6i) q^{86} +(-2.50476e6 - 6.29928e6i) q^{88} -7.69913e6 q^{89} +(-129688. - 399140. i) q^{91} +(156221. - 480800. i) q^{92} +(-6.16060e6 - 4.47594e6i) q^{94} +(-2.61336e6 + 8.04309e6i) q^{95} +(655646. - 476355. i) q^{97} +8.37899e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8}+O(q^{10}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8} - 1352 q^{10} + 18851 q^{11} + 14635 q^{13} - 62912 q^{14} - 36148 q^{16} + 10338 q^{17} + 90342 q^{19} + 289719 q^{20} - 202339 q^{22} - 138508 q^{23} - 174068 q^{25} - 466130 q^{26} - 640233 q^{28} + 487290 q^{29} - 388352 q^{31} - 2726322 q^{32} - 1543708 q^{34} - 742659 q^{35} + 670209 q^{37} - 2282072 q^{38} + 4641741 q^{40} + 2721357 q^{41} - 199784 q^{43} + 5887437 q^{44} + 3389447 q^{46} - 2112053 q^{47} + 3927748 q^{49} + 3663090 q^{50} - 4343053 q^{52} + 1743854 q^{53} - 8387710 q^{55} + 6307818 q^{56} + 546605 q^{58} + 218820 q^{59} - 743157 q^{61} - 3996183 q^{62} - 21725666 q^{64} - 4895794 q^{65} - 3235686 q^{67} - 961671 q^{68} + 31155916 q^{70} - 9848757 q^{71} - 6667768 q^{73} + 31115192 q^{74} - 6535748 q^{76} - 8320585 q^{77} - 10121851 q^{79} - 44592526 q^{80} + 24927115 q^{82} - 13288897 q^{83} - 28050005 q^{85} - 20937351 q^{86} + 39687014 q^{88} + 40241460 q^{89} + 8733043 q^{91} - 11607651 q^{92} - 7877385 q^{94} - 14371097 q^{95} + 30518151 q^{97} + 16954218 q^{98}+O(q^{100}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8 - 1352 * q^10 + 18851 * q^11 + 14635 * q^13 - 62912 * q^14 - 36148 * q^16 + 10338 * q^17 + 90342 * q^19 + 289719 * q^20 - 202339 * q^22 - 138508 * q^23 - 174068 * q^25 - 466130 * q^26 - 640233 * q^28 + 487290 * q^29 - 388352 * q^31 - 2726322 * q^32 - 1543708 * q^34 - 742659 * q^35 + 670209 * q^37 - 2282072 * q^38 + 4641741 * q^40 + 2721357 * q^41 - 199784 * q^43 + 5887437 * q^44 + 3389447 * q^46 - 2112053 * q^47 + 3927748 * q^49 + 3663090 * q^50 - 4343053 * q^52 + 1743854 * q^53 - 8387710 * q^55 + 6307818 * q^56 + 546605 * q^58 + 218820 * q^59 - 743157 * q^61 - 3996183 * q^62 - 21725666 * q^64 - 4895794 * q^65 - 3235686 * q^67 - 961671 * q^68 + 31155916 * q^70 - 9848757 * q^71 - 6667768 * q^73 + 31115192 * q^74 - 6535748 * q^76 - 8320585 * q^77 - 10121851 * q^79 - 44592526 * q^80 + 24927115 * q^82 - 13288897 * q^83 - 28050005 * q^85 - 20937351 * q^86 + 39687014 * q^88 + 40241460 * q^89 + 8733043 * q^91 - 11607651 * q^92 - 7877385 * q^94 - 14371097 * q^95 + 30518151 * q^97 + 16954218 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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