LMFDB - Embedded newform 400.3.bg.e.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.e.97.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.98022 - 0.630404i) q^{3} +(4.90048 - 0.992634i) q^{5} +(-1.90476 + 1.90476i) q^{7} +(6.88520 + 2.23714i) q^{9} +(1.35489 + 4.16991i) q^{11} +(-3.42985 + 1.74760i) q^{13} +(-20.1307 + 0.861615i) q^{15} +(-12.2313 + 1.93724i) q^{17} +(3.72375 - 5.12531i) q^{19} +(8.78215 - 6.38060i) q^{21} +(5.73201 - 11.2497i) q^{23} +(23.0294 - 9.72876i) q^{25} +(6.32116 + 3.22079i) q^{27} +(31.4788 + 43.3269i) q^{29} +(35.0244 + 25.4467i) q^{31} +(-2.76401 - 17.4513i) q^{33} +(-7.44352 + 11.2250i) q^{35} +(21.5720 + 42.3375i) q^{37} +(14.7533 - 4.79362i) q^{39} +(19.4646 - 59.9060i) q^{41} +(7.89405 + 7.89405i) q^{43} +(35.9614 + 4.12856i) q^{45} +(-0.830960 + 5.24648i) q^{47} +41.7437i q^{49} +49.9043 q^{51} +(-21.9849 - 3.48206i) q^{53} +(10.7788 + 19.0896i) q^{55} +(-18.0524 + 18.0524i) q^{57} +(86.6293 + 28.1476i) q^{59} +(4.43163 + 13.6392i) q^{61} +(-17.3759 + 8.85347i) q^{63} +(-15.0732 + 11.9687i) q^{65} +(11.7527 - 1.86144i) q^{67} +(-29.9065 + 41.1628i) q^{69} +(103.606 - 75.2742i) q^{71} +(30.5598 - 59.9770i) q^{73} +(-97.7949 + 24.2048i) q^{75} +(-10.5234 - 5.36196i) q^{77} +(25.8374 + 35.5621i) q^{79} +(-75.8413 - 55.1019i) q^{81} +(9.74229 + 61.5104i) q^{83} +(-58.0160 + 21.6346i) q^{85} +(-97.9791 - 192.295i) q^{87} +(-146.062 + 47.4585i) q^{89} +(3.20430 - 9.86183i) q^{91} +(-123.363 - 123.363i) q^{93} +(13.1606 - 28.8128i) q^{95} +(-2.23641 + 14.1201i) q^{97} +31.7417i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) $ 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−3.98022	−	0.630404i	−1.32674	−	0.210135i	−0.547470	−	0.836825i	$-0.684409\pi$
$3$	−3.98022	−	0.630404i	−1.32674	−	0.210135i	−0.779268	+	0.626690i	$0.784409\pi$
$4$		0			0
$5$	4.90048	−	0.992634i	0.980095	−	0.198527i
$5$	4.90048	−	0.992634i	0.980095	−	0.198527i
$6$		0			0
$7$	−1.90476	+	1.90476i	−0.272109	+	0.272109i	−0.829949	−	0.557840i	$-0.811630\pi$
$7$	−1.90476	+	1.90476i	−0.272109	+	0.272109i	0.557840	+	0.829949i	$0.311630\pi$
$8$		0			0
$9$	6.88520	+	2.23714i	0.765022	+	0.248571i
$10$		0			0
$11$	1.35489	+	4.16991i	0.123171	+	0.379082i	0.993563	−	0.113277i	$-0.0361347\pi$
$11$	1.35489	+	4.16991i	0.123171	+	0.379082i	−0.870392	+	0.492359i	$0.836135\pi$
$12$		0			0
$13$	−3.42985	+	1.74760i	−0.263835	+	0.134431i	−0.580905	−	0.813972i	$-0.697301\pi$
$13$	−3.42985	+	1.74760i	−0.263835	+	0.134431i	0.317070	+	0.948402i	$0.397301\pi$
$14$		0			0
$15$	−20.1307	+	0.861615i	−1.34205	+	0.0574410i
$16$		0			0
$17$	−12.2313	+	1.93724i	−0.719485	+	0.113955i	−0.505432	−	0.862867i	$-0.668667\pi$
$17$	−12.2313	+	1.93724i	−0.719485	+	0.113955i	−0.214054	+	0.976822i	$0.568667\pi$
$18$		0			0
$19$	3.72375	−	5.12531i	0.195987	−	0.269753i	−0.699701	−	0.714436i	$-0.746684\pi$
$19$	3.72375	−	5.12531i	0.195987	−	0.269753i	0.895688	+	0.444683i	$0.146684\pi$
$20$		0			0
$21$	8.78215	−	6.38060i	0.418198	−	0.303838i
$22$		0			0
$23$	5.73201	−	11.2497i	0.249218	−	0.489118i	−0.732178	−	0.681113i	$-0.761496\pi$
$23$	5.73201	−	11.2497i	0.249218	−	0.489118i	0.981396	+	0.191996i	$0.0614960\pi$
$24$		0			0
$25$	23.0294	−	9.72876i	0.921174	−	0.389150i
$26$		0			0
$27$	6.32116	+	3.22079i	0.234117	+	0.119289i
$28$		0			0
$29$	31.4788	+	43.3269i	1.08548	+	1.49403i	0.853345	+	0.521347i	$0.174570\pi$
$29$	31.4788	+	43.3269i	1.08548	+	1.49403i	0.232132	+	0.972684i	$0.425430\pi$
$30$		0			0
$31$	35.0244	+	25.4467i	1.12982	+	0.820863i	0.985669	−	0.168693i	$-0.0539545\pi$
$31$	35.0244	+	25.4467i	1.12982	+	0.820863i	0.144152	+	0.989556i	$0.453955\pi$
$32$		0			0
$33$	−2.76401	−	17.4513i	−0.0837578	−	0.528826i
$34$		0			0
$35$	−7.44352	+	11.2250i	−0.212672	+	0.320714i
$36$		0			0
$37$	21.5720	+	42.3375i	0.583028	+	1.14426i	0.974567	+	0.224095i	$0.0719426\pi$
$37$	21.5720	+	42.3375i	0.583028	+	1.14426i	−0.391539	+	0.920161i	$0.628057\pi$
$38$		0			0
$39$	14.7533	−	4.79362i	0.378289	−	0.122913i
$40$		0			0
$41$	19.4646	−	59.9060i	0.474748	−	1.46112i	−0.371550	−	0.928413i	$-0.621174\pi$
$41$	19.4646	−	59.9060i	0.474748	−	1.46112i	0.846298	−	0.532710i	$-0.178826\pi$
$42$		0			0
$43$	7.89405	+	7.89405i	0.183583	+	0.183583i	0.792915	−	0.609332i	$-0.208562\pi$
$43$	7.89405	+	7.89405i	0.183583	+	0.183583i	−0.609332	+	0.792915i	$0.708562\pi$
$44$		0			0
$45$	35.9614	+	4.12856i	0.799143	+	0.0917457i
$46$		0			0
$47$	−0.830960	+	5.24648i	−0.0176800	+	0.111627i	−0.994950	−	0.100371i	$-0.967997\pi$
$47$	−0.830960	+	5.24648i	−0.0176800	+	0.111627i	0.977270	+	0.211998i	$0.0679971\pi$
$48$		0			0
$49$			41.7437i			0.851913i
$50$		0			0
$51$	49.9043			0.978515
$52$		0			0
$53$	−21.9849	−	3.48206i	−0.414809	−	0.0656993i	−0.0544581	−	0.998516i	$-0.517343\pi$
$53$	−21.9849	−	3.48206i	−0.414809	−	0.0656993i	−0.360351	+	0.932817i	$0.617343\pi$
$54$		0			0
$55$	10.7788	+	19.0896i	0.195978	+	0.347084i
$56$		0			0
$57$	−18.0524	+	18.0524i	−0.316708	+	0.316708i
$58$		0			0
$59$	86.6293	+	28.1476i	1.46829	+	0.477077i	0.930592	−	0.366058i	$-0.119293\pi$
$59$	86.6293	+	28.1476i	1.46829	+	0.477077i	0.537701	+	0.843135i	$0.319293\pi$
$60$		0			0
$61$	4.43163	+	13.6392i	0.0726497	+	0.223593i	0.980788	−	0.195078i	$-0.0624961\pi$
$61$	4.43163	+	13.6392i	0.0726497	+	0.223593i	−0.908138	+	0.418671i	$0.862496\pi$
$62$		0			0
$63$	−17.3759	+	8.85347i	−0.275808	+	0.140531i
$64$		0			0
$65$	−15.0732	+	11.9687i	−0.231895	+	0.184133i
$66$		0			0
$67$	11.7527	−	1.86144i	0.175413	−	0.0277827i	−0.0681100	−	0.997678i	$-0.521697\pi$
$67$	11.7527	−	1.86144i	0.175413	−	0.0277827i	0.243523	+	0.969895i	$0.421697\pi$
$68$		0			0
$69$	−29.9065	+	41.1628i	−0.433428	+	0.596562i
$70$		0			0
$71$	103.606	−	75.2742i	1.45924	−	1.06020i	0.475680	−	0.879619i	$-0.342202\pi$
$71$	103.606	−	75.2742i	1.45924	−	1.06020i	0.983560	−	0.180581i	$-0.0577979\pi$
$72$		0			0
$73$	30.5598	−	59.9770i	0.418627	−	0.821602i	−0.581341	−	0.813660i	$-0.697472\pi$
$73$	30.5598	−	59.9770i	0.418627	−	0.821602i	0.999968	−	0.00794232i	$-0.00252814\pi$
$74$		0			0
$75$	−97.7949	+	24.2048i	−1.30393	+	0.322730i
$76$		0			0
$77$	−10.5234	−	5.36196i	−0.136668	−	0.0696358i
$78$		0			0
$79$	25.8374	+	35.5621i	0.327056	+	0.450153i	0.940605	−	0.339503i	$-0.110259\pi$
$79$	25.8374	+	35.5621i	0.327056	+	0.450153i	−0.613549	+	0.789656i	$0.710259\pi$
$80$		0			0
$81$	−75.8413	−	55.1019i	−0.936312	−	0.680271i
$82$		0			0
$83$	9.74229	+	61.5104i	0.117377	+	0.741089i	0.974235	+	0.225536i	$0.0724134\pi$
$83$	9.74229	+	61.5104i	0.117377	+	0.741089i	−0.856858	+	0.515553i	$0.827587\pi$
$84$		0			0
$85$	−58.0160	+	21.6346i	−0.682541	+	0.254524i
$86$		0			0
$87$	−97.9791	−	192.295i	−1.12620	−	2.21029i
$88$		0			0
$89$	−146.062	+	47.4585i	−1.64115	+	0.533242i	−0.976795	−	0.214176i	$-0.931293\pi$
$89$	−146.062	+	47.4585i	−1.64115	+	0.533242i	−0.664354	+	0.747418i	$0.731293\pi$
$90$		0			0
$91$	3.20430	−	9.86183i	0.0352121	−	0.108372i
$92$		0			0
$93$	−123.363	−	123.363i	−1.32649	−	1.32649i
$94$		0			0
$95$	13.1606	−	28.8128i	0.138533	−	0.303292i
$96$		0			0
$97$	−2.23641	+	14.1201i	−0.0230558	+	0.145568i	−0.996531	−	0.0832250i	$-0.973478\pi$
$97$	−2.23641	+	14.1201i	−0.0230558	+	0.145568i	0.973475	+	0.228793i	$0.0734780\pi$
$98$		0			0
$99$			31.7417i			0.320623i
$100$		0			0
$101$	−32.6157			−0.322927			−0.161464	−	0.986879i	$-0.551621\pi$
$101$	−32.6157			−0.322927			−0.161464	+	0.986879i	$0.551621\pi$
$102$		0			0
$103$	−148.877	−	23.5798i	−1.44541	−	0.228930i	−0.616076	−	0.787687i	$-0.711278\pi$
$103$	−148.877	−	23.5798i	−1.44541	−	0.228930i	−0.829331	+	0.558757i	$0.811278\pi$
$104$		0			0
$105$	36.7031	−	39.9855i	0.349553	−	0.380814i
$106$		0			0
$107$	−137.314	+	137.314i	−1.28331	+	1.28331i	−0.344542	+	0.938771i	$0.611966\pi$
$107$	−137.314	+	137.314i	−1.28331	+	1.28331i	−0.938771	+	0.344542i	$0.888034\pi$
$108$		0			0
$109$	81.7551	+	26.5639i	0.750047	+	0.243705i	0.659001	−	0.752142i	$-0.270979\pi$
$109$	81.7551	+	26.5639i	0.750047	+	0.243705i	0.0910456	+	0.995847i	$0.470979\pi$
$110$		0			0
$111$	−59.1716	−	182.111i	−0.533077	−	1.64064i
$112$		0			0
$113$	63.4934	−	32.3515i	0.561889	−	0.286297i	−0.149887	−	0.988703i	$-0.547891\pi$
$113$	63.4934	−	32.3515i	0.561889	−	0.286297i	0.711776	+	0.702407i	$0.247891\pi$
$114$		0			0
$115$	16.9228	−	60.8187i	0.147154	−	0.528858i
$116$		0			0
$117$	−27.5249	+	4.35951i	−0.235255	+	0.0372608i
$118$		0			0
$119$	19.6077	−	26.9876i	0.164770	−	0.226787i
$120$		0			0
$121$	82.3386	−	59.8225i	0.680485	−	0.494401i
$122$		0			0
$123$	−115.239	+	226.168i	−0.936899	+	1.83877i
$124$		0			0
$125$	103.198	−	70.5353i	0.825582	−	0.564282i
$126$		0			0
$127$	−218.894	−	111.532i	−1.72358	−	0.878206i	−0.977096	−	0.212797i	$-0.931743\pi$
$127$	−218.894	−	111.532i	−1.72358	−	0.878206i	−0.746480	−	0.665408i	$-0.768257\pi$
$128$		0			0
$129$	−26.4436	−	36.3965i	−0.204989	−	0.282143i
$130$		0			0
$131$	98.8177	+	71.7952i	0.754333	+	0.548055i	0.897167	−	0.441692i	$-0.145621\pi$
$131$	98.8177	+	71.7952i	0.754333	+	0.548055i	−0.142834	+	0.989747i	$0.545621\pi$
$132$		0			0
$133$	2.66963	+	16.8554i	0.0200724	+	0.126732i
$134$		0			0
$135$	34.1738	+	9.50882i	0.253139	+	0.0704357i
$136$		0			0
$137$	74.9433	+	147.084i	0.547031	+	1.07361i	0.984665	+	0.174456i	$0.0558166\pi$
$137$	74.9433	+	147.084i	0.547031	+	1.07361i	−0.437634	+	0.899153i	$0.644183\pi$
$138$		0			0
$139$	−135.906	+	44.1586i	−0.977743	+	0.317688i	−0.753938	−	0.656946i	$-0.771848\pi$
$139$	−135.906	+	44.1586i	−0.977743	+	0.317688i	−0.223805	+	0.974634i	$0.571848\pi$
$140$		0			0
$141$	6.61480	−	20.3583i	0.0469135	−	0.144385i
$142$		0			0
$143$	−11.9344	−	11.9344i	−0.0834572	−	0.0834572i
$144$		0			0
$145$	197.269	+	181.076i	1.36048	+	1.24880i
$146$		0			0
$147$	26.3154	−	166.149i	0.179017	−	1.13027i
$148$		0			0
$149$			0.295715i			0.00198467i	1.00000		0.000992333i	$0.000315869\pi$
$149$			0.295715i			0.00198467i	−1.00000		0.000992333i	$0.999684\pi$
$150$		0			0
$151$	−59.1891			−0.391981			−0.195990	−	0.980606i	$-0.562792\pi$
$151$	−59.1891			−0.391981			−0.195990	+	0.980606i	$0.562792\pi$
$152$		0			0
$153$	−88.5485	−	14.0247i	−0.578748	−	0.0916647i
$154$		0			0
$155$	196.896	+	89.9348i	1.27030	+	0.580224i
$156$		0			0
$157$	149.239	−	149.239i	0.950565	−	0.950565i	−0.0482693	−	0.998834i	$-0.515371\pi$
$157$	149.239	−	149.239i	0.950565	−	0.950565i	0.998834	+	0.0482693i	$0.0153706\pi$
$158$		0			0
$159$	85.3095	+	27.7187i	0.536538	+	0.174332i
$160$		0			0
$161$	10.5099	+	32.3462i	0.0652789	+	0.200908i
$162$		0			0
$163$	−14.3536	+	7.31350i	−0.0880586	+	0.0448681i	−0.497465	−	0.867484i	$-0.665736\pi$
$163$	−14.3536	+	7.31350i	−0.0880586	+	0.0448681i	0.409407	+	0.912352i	$0.365736\pi$
$164$		0			0
$165$	−30.8677	−	82.7758i	−0.187077	−	0.501672i
$166$		0			0
$167$	181.483	−	28.7441i	1.08673	−	0.172121i	0.412729	−	0.910854i	$-0.364576\pi$
$167$	181.483	−	28.7441i	1.08673	−	0.172121i	0.673998	+	0.738734i	$0.264576\pi$
$168$		0			0
$169$	−90.6259	+	124.736i	−0.536248	+	0.738082i
$170$		0			0
$171$	37.1048	−	26.9582i	0.216987	−	0.157650i
$172$		0			0
$173$	−56.9476	+	111.766i	−0.329177	+	0.646046i	−0.994979	−	0.100083i	$-0.968089\pi$
$173$	−56.9476	+	111.766i	−0.329177	+	0.646046i	0.665803	+	0.746128i	$0.268089\pi$
$174$		0			0
$175$	−25.3345	+	62.3965i	−0.144769	+	0.356551i
$176$		0			0
$177$	−327.059	−	166.645i	−1.84779	−	0.941497i
$178$		0			0
$179$	26.9978	+	37.1593i	0.150826	+	0.207594i	0.877744	−	0.479131i	$-0.159048\pi$
$179$	26.9978	+	37.1593i	0.150826	+	0.207594i	−0.726918	+	0.686724i	$0.759048\pi$
$180$		0			0
$181$	−102.885	−	74.7500i	−0.568423	−	0.412984i	0.266109	−	0.963943i	$-0.414262\pi$
$181$	−102.885	−	74.7500i	−0.568423	−	0.412984i	−0.834532	+	0.550959i	$0.814262\pi$
$182$		0			0
$183$	−9.04067	−	57.0805i	−0.0494025	−	0.311915i
$184$		0			0
$185$	147.739	+	186.061i	0.798588	+	1.00573i
$186$		0			0
$187$	−24.6501	−	48.3785i	−0.131818	−	0.258708i
$188$		0			0
$189$	−18.1752	+	5.90547i	−0.0961649	+	0.0312459i
$190$		0			0
$191$	−73.0756	+	224.904i	−0.382595	+	1.17751i	0.555615	+	0.831439i	$0.312483\pi$
$191$	−73.0756	+	224.904i	−0.382595	+	1.17751i	−0.938210	+	0.346066i	$0.887517\pi$
$192$		0			0
$193$	95.2843	+	95.2843i	0.493701	+	0.493701i	0.909470	−	0.415769i	$-0.136488\pi$
$193$	95.2843	+	95.2843i	0.493701	+	0.493701i	−0.415769	+	0.909470i	$0.636488\pi$
$194$		0			0
$195$	67.5397	−	38.1356i	0.346357	−	0.195567i
$196$		0			0
$197$	48.7930	−	308.067i	0.247680	−	1.56379i	−0.479623	−	0.877475i	$-0.659227\pi$
$197$	48.7930	−	308.067i	0.247680	−	1.56379i	0.727303	−	0.686316i	$-0.240773\pi$
$198$		0			0
$199$		−	282.147i		−	1.41782i	−0.705297	−	0.708912i	$-0.749186\pi$
$199$		−	282.147i		−	1.41782i	0.705297	−	0.708912i	$-0.250814\pi$
$200$		0			0
$201$	−47.9516			−0.238565
$202$		0			0
$203$	−142.487	−	22.5678i	−0.701908	−	0.111171i
$204$		0			0
$205$	35.9213	−	312.889i	0.175226	−	1.52629i
$206$		0			0
$207$	64.6332	−	64.6332i	0.312238	−	0.312238i
$208$		0			0
$209$	26.4173	+	8.58351i	0.126399	+	0.0410694i
$210$		0			0
$211$	−58.3239	−	179.503i	−0.276417	−	0.850723i	−0.988841	−	0.148974i	$-0.952403\pi$
$211$	−58.3239	−	179.503i	−0.276417	−	0.850723i	0.712424	−	0.701749i	$-0.247597\pi$
$212$		0			0
$213$	−459.828	+	234.294i	−2.15881	+	1.09997i
$214$		0			0
$215$	46.5205	+	30.8487i	0.216375	+	0.143482i
$216$		0			0
$217$	−115.183	+	18.2433i	−0.530799	+	0.0840703i
$218$		0			0
$219$	−159.444	+	219.456i	−0.728056	+	1.00208i
$220$		0			0
$221$	38.5659	−	28.0198i	0.174506	−	0.126786i
$222$		0			0
$223$	−0.131698	+	0.258473i	−0.000590576	+	0.00115907i	−0.891302	−	0.453411i	$-0.850207\pi$
$223$	−0.131698	+	0.258473i	−0.000590576	+	0.00115907i	0.890711	+	0.454570i	$0.150207\pi$
$224$		0			0
$225$	180.326	−	15.4646i	0.801450	−	0.0687316i
$226$		0			0
$227$	24.2509	+	12.3564i	0.106832	+	0.0544336i	0.506590	−	0.862187i	$-0.330906\pi$
$227$	24.2509	+	12.3564i	0.106832	+	0.0544336i	−0.399758	+	0.916621i	$0.630906\pi$
$228$		0			0
$229$	139.988	+	192.677i	0.611301	+	0.841384i	0.996684	−	0.0813728i	$-0.0259305\pi$
$229$	139.988	+	192.677i	0.611301	+	0.841384i	−0.385382	+	0.922757i	$0.625930\pi$
$230$		0			0
$231$	38.5053	+	27.9758i	0.166690	+	0.121107i
$232$		0			0
$233$	49.7015	+	313.803i	0.213311	+	1.34679i	0.829197	+	0.558957i	$0.188798\pi$
$233$	49.7015	+	313.803i	0.213311	+	1.34679i	−0.615885	+	0.787836i	$0.711202\pi$
$234$		0			0
$235$	1.13573	+	26.5351i	0.00483288	+	0.112915i
$236$		0			0
$237$	−80.4199	−	157.833i	−0.339324	−	0.665962i
$238$		0			0
$239$	−205.642	+	66.8170i	−0.860426	+	0.279569i	−0.705806	−	0.708405i	$-0.749415\pi$
$239$	−205.642	+	66.8170i	−0.860426	+	0.279569i	−0.154619	+	0.987974i	$0.549415\pi$
$240$		0			0
$241$	87.4914	−	269.271i	0.363035	−	1.11731i	−0.588168	−	0.808739i	$-0.700151\pi$
$241$	87.4914	−	269.271i	0.363035	−	1.11731i	0.951203	−	0.308567i	$-0.0998495\pi$
$242$		0			0
$243$	221.980	+	221.980i	0.913497	+	0.913497i
$244$		0			0
$245$	41.4362	+	204.564i	0.169128	+	0.834956i
$246$		0			0
$247$	−3.81496	+	24.0867i	−0.0154452	+	0.0975169i
$248$		0			0
$249$		−	250.966i		−	1.00790i
$250$		0			0
$251$	194.015			0.772967			0.386483	−	0.922296i	$-0.373690\pi$
$251$	194.015			0.772967			0.386483	+	0.922296i	$0.373690\pi$
$252$		0			0
$253$	54.6764	+	8.65990i	0.216112	+	0.0342288i
$254$		0			0
$255$	244.555	−	49.5367i	0.959038	−	0.194261i
$256$		0			0
$257$	−4.30308	+	4.30308i	−0.0167435	+	0.0167435i	−0.715429	−	0.698685i	$-0.753769\pi$
$257$	−4.30308	+	4.30308i	−0.0167435	+	0.0167435i	0.698685	+	0.715429i	$0.253769\pi$
$258$		0			0
$259$	−121.733	−	39.5533i	−0.470010	−	0.152716i
$260$		0			0
$261$	119.810	+	368.737i	0.459042	+	1.41278i
$262$		0			0
$263$	225.189	−	114.739i	0.856232	−	0.436272i	0.0299650	−	0.999551i	$-0.490460\pi$
$263$	225.189	−	114.739i	0.856232	−	0.436272i	0.826267	+	0.563279i	$0.190460\pi$
$264$		0			0
$265$	−111.193	+	4.75916i	−0.419596	+	0.0179591i
$266$		0			0
$267$	611.277	−	96.8168i	2.28943	−	0.362610i
$268$		0			0
$269$	−59.1153	+	81.3652i	−0.219759	+	0.302473i	−0.904635	−	0.426187i	$-0.859857\pi$
$269$	−59.1153	+	81.3652i	−0.219759	+	0.302473i	0.684876	+	0.728660i	$0.259857\pi$
$270$		0			0
$271$	−279.416	+	203.008i	−1.03106	+	0.749106i	−0.968520	−	0.248937i	$-0.919919\pi$
$271$	−279.416	+	203.008i	−1.03106	+	0.749106i	−0.0625356	+	0.998043i	$0.519919\pi$
$272$		0			0
$273$	−18.9708	+	37.2322i	−0.0694900	+	0.136382i
$274$		0			0
$275$	71.7702	+	82.8489i	0.260982	+	0.301269i
$276$		0			0
$277$	−270.424	−	137.788i	−0.976259	−	0.497429i	−0.108329	−	0.994115i	$-0.534550\pi$
$277$	−270.424	−	137.788i	−0.976259	−	0.497429i	−0.867930	+	0.496686i	$0.834550\pi$
$278$		0			0
$279$	184.222	+	253.560i	0.660296	+	0.908819i
$280$		0			0
$281$	−103.491	−	75.1905i	−0.368295	−	0.267582i	0.388209	−	0.921572i	$-0.373094\pi$
$281$	−103.491	−	75.1905i	−0.368295	−	0.267582i	−0.756504	+	0.653990i	$0.773094\pi$
$282$		0			0
$283$	−36.3165	−	229.294i	−0.128327	−	0.810225i	−0.964948	−	0.262442i	$-0.915472\pi$
$283$	−36.3165	−	229.294i	−0.128327	−	0.810225i	0.836621	−	0.547783i	$-0.184528\pi$
$284$		0			0
$285$	−70.5458	+	106.385i	−0.247529	+	0.373279i
$286$		0			0
$287$	77.0313	+	151.182i	0.268402	+	0.526768i
$288$		0			0
$289$	−129.005	+	41.9162i	−0.446383	+	0.145039i
$290$		0			0
$291$	17.8028	−	54.7913i	0.0611779	−	0.188286i
$292$		0			0
$293$	67.7573	+	67.7573i	0.231254	+	0.231254i	0.813216	−	0.581962i	$-0.197715\pi$
$293$	67.7573	+	67.7573i	0.231254	+	0.231254i	−0.581962	+	0.813216i	$0.697715\pi$
$294$		0			0
$295$	452.465	+	51.9454i	1.53378	+	0.176086i
$296$		0			0
$297$	−4.86596	+	30.7224i	−0.0163837	+	0.103443i
$298$		0			0
$299$			48.6021i			0.162549i
$300$		0			0
$301$	−30.0726			−0.0999091
$302$		0			0
$303$	129.817	+	20.5611i	0.428440	+	0.0678583i
$304$		0			0
$305$	35.2558	+	62.4394i	0.115593	+	0.204719i
$306$		0			0
$307$	−91.8763	+	91.8763i	−0.299271	+	0.299271i	−0.840728	−	0.541457i	$-0.817873\pi$
$307$	−91.8763	+	91.8763i	−0.299271	+	0.299271i	0.541457	+	0.840728i	$0.317873\pi$
$308$		0			0
$309$	577.697	+	187.705i	1.86957	+	0.607460i
$310$		0			0
$311$	−155.784	−	479.455i	−0.500915	−	1.54166i	−0.807532	−	0.589824i	$-0.799197\pi$
$311$	−155.784	−	479.455i	−0.500915	−	1.54166i	0.306617	−	0.951833i	$-0.400803\pi$
$312$		0			0
$313$	−13.1210	+	6.68546i	−0.0419200	+	0.0213593i	−0.474825	−	0.880080i	$-0.657489\pi$
$313$	−13.1210	+	6.68546i	−0.0419200	+	0.0213593i	0.432905	+	0.901440i	$0.357489\pi$
$314$		0			0
$315$	−76.3620	+	60.6341i	−0.242419	+	0.192489i
$316$		0			0
$317$	527.454	−	83.5405i	1.66389	−	0.263535i	0.747631	−	0.664115i	$-0.231191\pi$
$317$	527.454	−	83.5405i	1.66389	−	0.263535i	0.916262	+	0.400580i	$0.131191\pi$
$318$		0			0
$319$	−138.019	+	189.967i	−0.432661	+	0.595507i
$320$		0			0
$321$	633.105	−	459.978i	1.97229	−	1.43295i
$322$		0			0
$323$	−35.6172	+	69.9027i	−0.110270	+	0.216417i
$324$		0			0
$325$	−61.9854	+	73.6143i	−0.190724	+	0.226506i
$326$		0			0
$327$	−308.657	−	157.269i	−0.943906	−	0.480944i
$328$		0			0
$329$	−8.41052	−	11.5761i	−0.0255639	−	0.0351857i
$330$		0			0
$331$	−83.2871	−	60.5116i	−0.251623	−	0.182815i	0.454823	−	0.890582i	$-0.349703\pi$
$331$	−83.2871	−	60.5116i	−0.251623	−	0.182815i	−0.706446	+	0.707767i	$0.749703\pi$
$332$		0			0
$333$	53.8130	+	339.762i	0.161601	+	1.02031i
$334$		0			0
$335$	55.7459	−	20.7880i	0.166406	−	0.0620538i
$336$		0			0
$337$	−45.6552	−	89.6034i	−0.135475	−	0.265885i	0.813295	−	0.581851i	$-0.197671\pi$
$337$	−45.6552	−	89.6034i	−0.135475	−	0.265885i	−0.948771	+	0.315966i	$0.897671\pi$
$338$		0			0
$339$	−273.112	+	88.7395i	−0.805640	+	0.261768i
$340$		0			0
$341$	−58.6565	+	180.526i	−0.172013	+	0.529402i
$342$		0			0
$343$	−172.845	−	172.845i	−0.503923	−	0.503923i
$344$		0			0
$345$	−105.697	+	231.403i	−0.306367	+	0.670734i
$346$		0			0
$347$	−84.1859	+	531.529i	−0.242611	+	1.53178i	0.502343	+	0.864668i	$0.332471\pi$
$347$	−84.1859	+	531.529i	−0.242611	+	1.53178i	−0.744954	+	0.667116i	$0.767529\pi$
$348$		0			0
$349$		−	449.602i		−	1.28826i	−0.764917	−	0.644129i	$-0.777220\pi$
$349$		−	449.602i		−	1.28826i	0.764917	−	0.644129i	$-0.222780\pi$
$350$		0			0
$351$	−27.3093			−0.0778043
$352$		0			0
$353$	488.374	+	77.3508i	1.38350	+	0.219124i	0.803407	−	0.595430i	$-0.203018\pi$
$353$	488.374	+	77.3508i	1.38350	+	0.219124i	0.580088	+	0.814554i	$0.303018\pi$
$354$		0			0
$355$	432.999	−	471.722i	1.21972	−	1.32880i
$356$		0			0
$357$	−95.0559	+	95.0559i	−0.266263	+	0.266263i
$358$		0			0
$359$	574.700	+	186.731i	1.60083	+	0.520143i	0.967314	−	0.253583i	$-0.0816089\pi$
$359$	574.700	+	186.731i	1.60083	+	0.520143i	0.633521	+	0.773725i	$0.281609\pi$
$360$		0			0
$361$	99.1527	+	305.161i	0.274661	+	0.845320i
$362$		0			0
$363$	−365.438	+	186.200i	−1.00672	+	0.512947i
$364$		0			0
$365$	90.2224	−	324.250i	0.247185	−	0.888357i
$366$		0			0
$367$	−426.894	+	67.6133i	−1.16320	+	0.184233i	−0.708036	−	0.706176i	$-0.750419\pi$
$367$	−426.894	+	67.6133i	−1.16320	+	0.184233i	−0.455162	+	0.890409i	$0.650419\pi$
$368$		0			0
$369$	268.036	−	368.920i	0.726385	−	0.999783i
$370$		0			0
$371$	48.5086	−	35.2435i	0.130751	−	0.0949960i
$372$		0			0
$373$	150.832	−	296.025i	0.404376	−	0.793633i	−0.595577	−	0.803298i	$-0.703077\pi$
$373$	150.832	−	296.025i	0.404376	−	0.793633i	0.999953	+	0.00966547i	$0.00307666\pi$
$374$		0			0
$375$	−455.215	+	215.689i	−1.21391	+	0.575172i
$376$		0			0
$377$	−183.686	−	93.5926i	−0.487230	−	0.248256i
$378$		0			0
$379$	−84.8455	−	116.780i	−0.223867	−	0.308126i	0.682279	−	0.731092i	$-0.260989\pi$
$379$	−84.8455	−	116.780i	−0.223867	−	0.308126i	−0.906146	+	0.422966i	$0.860989\pi$
$380$		0			0
$381$	800.936	+	581.914i	2.10219	+	1.52733i
$382$		0			0
$383$	−79.6409	−	502.833i	−0.207940	−	1.31288i	−0.841950	−	0.539556i	$-0.818592\pi$
$383$	−79.6409	−	502.833i	−0.207940	−	1.31288i	0.634010	−	0.773325i	$-0.281408\pi$
$384$		0			0
$385$	−56.8923	−	15.8302i	−0.147772	−	0.0411175i
$386$		0			0
$387$	36.6921	+	72.0122i	0.0948115	+	0.186078i
$388$		0			0
$389$	−138.328	+	44.9454i	−0.355598	+	0.115541i	−0.481368	−	0.876519i	$-0.659860\pi$
$389$	−138.328	+	44.9454i	−0.355598	+	0.115541i	0.125770	+	0.992059i	$0.459860\pi$
$390$		0			0
$391$	−48.3163	+	148.702i	−0.123571	+	0.380313i
$392$		0			0
$393$	−348.056	−	348.056i	−0.885638	−	0.885638i
$394$		0			0
$395$	161.916	+	148.624i	0.409913	+	0.376264i
$396$		0			0
$397$	−50.9495	+	321.682i	−0.128336	+	0.810283i	0.836603	+	0.547810i	$0.184538\pi$
$397$	−50.9495	+	321.682i	−0.128336	+	0.810283i	−0.964939	+	0.262473i	$0.915462\pi$
$398$		0			0
$399$		−	68.7710i		−	0.172358i
$400$		0			0
$401$	−537.616			−1.34069			−0.670344	−	0.742050i	$-0.733853\pi$
$401$	−537.616			−1.34069			−0.670344	+	0.742050i	$0.733853\pi$
$402$		0			0
$403$	−164.599	−	26.0700i	−0.408435	−	0.0646898i
$404$		0			0
$405$	−426.355	−	194.743i	−1.05273	−	0.480847i
$406$		0			0
$407$	−147.316	+	147.316i	−0.361955	+	0.361955i
$408$		0			0
$409$	−251.808	−	81.8174i	−0.615667	−	0.200042i	−0.0154517	−	0.999881i	$-0.504919\pi$
$409$	−251.808	−	81.8174i	−0.615667	−	0.200042i	−0.600216	+	0.799838i	$0.704919\pi$
$410$		0			0
$411$	−205.568	−	632.672i	−0.500165	−	1.53935i
$412$		0			0
$413$	−218.623	+	111.394i	−0.529353	+	0.269719i
$414$		0			0
$415$	108.799	+	291.760i	0.262167	+	0.703035i
$416$		0			0
$417$	568.774	−	90.0850i	1.36397	−	0.216031i
$418$		0			0
$419$	−179.039	+	246.426i	−0.427300	+	0.588128i	−0.967331	−	0.253517i	$-0.918413\pi$
$419$	−179.039	+	246.426i	−0.427300	+	0.588128i	0.540031	+	0.841645i	$0.318413\pi$
$420$		0			0
$421$	26.2368	−	19.0622i	0.0623202	−	0.0452783i	−0.556189	−	0.831056i	$-0.687737\pi$
$421$	26.2368	−	19.0622i	0.0623202	−	0.0452783i	0.618509	+	0.785778i	$0.287737\pi$
$422$		0			0
$423$	−17.4584	+	34.2641i	−0.0412728	+	0.0810025i
$424$		0			0
$425$	−262.831	+	163.608i	−0.618426	+	0.384961i
$426$		0			0
$427$	−34.4206	−	17.5382i	−0.0806103	−	0.0410730i
$428$		0			0
$429$	39.9779	+	55.0249i	0.0931887	+	0.128263i
$430$		0			0
$431$	183.875	+	133.593i	0.426624	+	0.309961i	0.780298	−	0.625408i	$-0.215068\pi$
$431$	183.875	+	133.593i	0.426624	+	0.309961i	−0.353673	+	0.935369i	$0.615068\pi$
$432$		0			0
$433$	−97.5652	−	616.002i	−0.225324	−	1.42264i	−0.797902	−	0.602788i	$-0.794057\pi$
$433$	−97.5652	−	616.002i	−0.225324	−	1.42264i	0.572578	−	0.819850i	$-0.305943\pi$
$434$		0			0
$435$	−671.023	−	845.079i	−1.54258	−	1.94271i
$436$		0			0
$437$	−36.3136	−	71.2694i	−0.0830975	−	0.163088i
$438$		0			0
$439$	153.926	−	50.0134i	0.350628	−	0.113926i	−0.128408	−	0.991721i	$-0.540987\pi$
$439$	153.926	−	50.0134i	0.350628	−	0.113926i	0.479035	+	0.877796i	$0.340987\pi$
$440$		0			0
$441$	−93.3865	+	287.414i	−0.211761	+	0.651733i
$442$		0			0
$443$	−50.7120	−	50.7120i	−0.114474	−	0.114474i	0.647549	−	0.762023i	$-0.275794\pi$
$443$	−50.7120	−	50.7120i	−0.114474	−	0.114474i	−0.762023	+	0.647549i	$0.775794\pi$
$444$		0			0
$445$	−668.666	+	377.556i	−1.50262	+	0.848440i
$446$		0			0
$447$	0.186420	−	1.17701i	0.000417047	−	0.00263313i
$448$		0			0
$449$		−	210.806i		−	0.469501i	−0.972056	−	0.234750i	$-0.924573\pi$
$449$		−	210.806i		−	0.469501i	0.972056	−	0.234750i	$-0.0754273\pi$
$450$		0			0
$451$	276.175			0.612361
$452$		0			0
$453$	235.585	+	37.3131i	0.520056	+	0.0823688i
$454$		0			0
$455$	5.91343	−	51.5084i	0.0129965	−	0.113205i
$456$		0			0
$457$	−536.190	+	536.190i	−1.17328	+	1.17328i	−0.191860	+	0.981422i	$0.561452\pi$
$457$	−536.190	+	536.190i	−1.17328	+	1.17328i	−0.981422	+	0.191860i	$0.938548\pi$
$458$		0			0
$459$	−83.5551	−	27.1487i	−0.182037	−	0.0591475i
$460$		0			0
$461$	−129.370	−	398.159i	−0.280628	−	0.863685i	−0.987675	−	0.156518i	$-0.949973\pi$
$461$	−129.370	−	398.159i	−0.280628	−	0.863685i	0.707047	−	0.707167i	$-0.250027\pi$
$462$		0			0
$463$	609.985	−	310.803i	1.31746	−	0.671280i	0.353030	−	0.935612i	$-0.385151\pi$
$463$	609.985	−	310.803i	1.31746	−	0.671280i	0.964432	+	0.264332i	$0.0851513\pi$
$464$		0			0
$465$	−726.993	−	482.084i	−1.56342	−	1.03674i
$466$		0			0
$467$	45.8978	−	7.26949i	0.0982822	−	0.0155664i	−0.107100	−	0.994248i	$-0.534156\pi$
$467$	45.8978	−	7.26949i	0.0982822	−	0.0155664i	0.205382	+	0.978682i	$0.434156\pi$
$468$		0			0
$469$	−18.8405	+	25.9317i	−0.0401716	+	0.0552914i
$470$		0			0
$471$	−688.083	+	499.922i	−1.46090	+	1.06140i
$472$		0			0
$473$	−22.2219	+	43.6130i	−0.0469808	+	0.0922051i
$474$		0			0
$475$	35.8928	−	154.260i	0.0755637	−	0.324758i
$476$		0			0
$477$	−143.581	−	73.1579i	−0.301007	−	0.153371i
$478$		0			0
$479$	138.309	+	190.366i	0.288745	+	0.397423i	0.928606	−	0.371068i	$-0.121008\pi$
$479$	138.309	+	190.366i	0.288745	+	0.397423i	−0.639861	+	0.768490i	$0.721008\pi$
$480$		0			0
$481$	−147.978	−	107.512i	−0.307646	−	0.223518i
$482$		0			0
$483$	−21.4405	−	135.370i	−0.0443904	−	0.280270i
$484$		0			0
$485$	3.05665	+	71.4153i	0.00630236	+	0.147248i
$486$		0			0
$487$	319.262	+	626.586i	0.655568	+	1.28662i	0.944259	+	0.329203i	$0.106780\pi$
$487$	319.262	+	626.586i	0.655568	+	1.28662i	−0.288691	+	0.957422i	$0.593220\pi$
$488$		0			0
$489$	61.7407	−	20.0608i	0.126259	−	0.0410241i
$490$		0			0
$491$	194.692	−	599.202i	0.396522	−	1.22037i	−0.531247	−	0.847217i	$-0.678277\pi$
$491$	194.692	−	599.202i	0.396522	−	1.22037i	0.927770	−	0.373153i	$-0.121723\pi$
$492$		0			0
$493$	−468.960	−	468.960i	−0.951238	−	0.951238i
$494$		0			0
$495$	31.5079	+	155.550i	0.0636523	+	0.314242i
$496$		0			0
$497$	−53.9655	+	340.725i	−0.108582	+	0.685563i
$498$		0			0
$499$		−	309.730i		−	0.620702i	−0.950622	−	0.310351i	$-0.899553\pi$
$499$		−	309.730i		−	0.620702i	0.950622	−	0.310351i	$-0.100447\pi$
$500$		0			0
$501$	−740.463			−1.47797
$502$		0			0
$503$	−344.198	−	54.5155i	−0.684289	−	0.108381i	−0.195396	−	0.980724i	$-0.562599\pi$
$503$	−344.198	−	54.5155i	−0.684289	−	0.108381i	−0.488893	+	0.872344i	$0.662599\pi$
$504$		0			0
$505$	−159.832	+	32.3754i	−0.316500	+	0.0641097i
$506$		0			0
$507$	439.345	−	439.345i	0.866558	−	0.866558i
$508$		0			0
$509$	−277.283	−	90.0948i	−0.544761	−	0.177004i	0.0236920	−	0.999719i	$-0.492458\pi$
$509$	−277.283	−	90.0948i	−0.544761	−	0.177004i	−0.568453	+	0.822716i	$0.692458\pi$
$510$		0			0
$511$	56.0328	+	172.451i	0.109653	+	0.337478i
$512$		0			0
$513$	40.0460	−	20.4044i	0.0780623	−	0.0397747i
$514$		0			0
$515$	−752.974	+	32.2280i	−1.46209	+	0.0625787i
$516$		0			0
$517$	−23.0032	+	3.64334i	−0.0444936	+	0.00704709i
$518$		0			0
$519$	297.121	−	408.952i	0.572488	−	0.787962i
$520$		0			0
$521$	582.433	−	423.162i	1.11791	−	0.812211i	0.134022	−	0.990978i	$-0.457211\pi$
$521$	582.433	−	423.162i	1.11791	−	0.812211i	0.983891	+	0.178767i	$0.0572108\pi$
$522$		0			0
$523$	53.4143	−	104.832i	0.102131	−	0.200443i	−0.834287	−	0.551331i	$-0.814120\pi$
$523$	53.4143	−	104.832i	0.102131	−	0.200443i	0.936417	+	0.350888i	$0.114120\pi$
$524$		0			0
$525$	140.172	−	232.381i	0.266994	−	0.442630i
$526$		0			0
$527$	−477.689	−	243.395i	−0.906431	−	0.461850i
$528$		0			0
$529$	217.239	+	299.003i	0.410659	+	0.565223i
$530$		0			0
$531$	533.490	+	387.603i	1.00469	+	0.729950i
$532$		0			0
$533$	37.9308	+	239.485i	0.0711646	+	0.449316i
$534$		0			0
$535$	−536.604	+	809.210i	−1.00300	+	1.51254i
$536$		0			0
$537$	−84.0317	−	164.921i	−0.156484	−	0.307116i
$538$		0			0
$539$	−174.068	+	56.5580i	−0.322945	+	0.104931i
$540$		0			0
$541$	32.3179	−	99.4644i	0.0597374	−	0.183853i	−0.916735	−	0.399497i	$-0.869185\pi$
$541$	32.3179	−	99.4644i	0.0597374	−	0.183853i	0.976472	+	0.215644i	$0.0691850\pi$
$542$		0			0
$543$	362.380	+	362.380i	0.667367	+	0.667367i
$544$		0			0
$545$	427.007	+	49.0227i	0.783500	+	0.0899498i
$546$		0			0
$547$	−29.1700	+	184.172i	−0.0533272	+	0.336695i	0.946572	+	0.322493i	$0.104521\pi$
$547$	−29.1700	+	184.172i	−0.0533272	+	0.336695i	−0.999899	+	0.0142020i	$0.995479\pi$
$548$		0			0
$549$			103.823i			0.189112i
$550$		0			0
$551$	339.283			0.615759
$552$		0			0
$553$	−116.952	−	18.5233i	−0.211486	−	0.0334961i
$554$		0			0
$555$	−470.739	−	833.697i	−0.848178	−	1.50216i
$556$		0			0
$557$	−28.7119	+	28.7119i	−0.0515473	+	0.0515473i	−0.732411	−	0.680863i	$-0.761605\pi$
$557$	−28.7119	+	28.7119i	−0.0515473	+	0.0515473i	0.680863	+	0.732411i	$0.261605\pi$
$558$		0			0
$559$	−40.8711	−	13.2798i	−0.0731146	−	0.0237564i
$560$		0			0
$561$	67.6146	+	208.096i	0.120525	+	0.370938i
$562$		0			0
$563$	577.802	−	294.405i	1.02629	−	0.522922i	0.142005	−	0.989866i	$-0.454645\pi$
$563$	577.802	−	294.405i	1.02629	−	0.522922i	0.884287	+	0.466944i	$0.154645\pi$
$564$		0			0
$565$	279.035	−	221.564i	0.493867	−	0.392148i
$566$		0			0
$567$	249.416	−	39.5036i	0.439887	−	0.0696713i
$568$		0			0
$569$	−358.283	+	493.134i	−0.629672	+	0.866669i	−0.998012	−	0.0630223i	$-0.979926\pi$
$569$	−358.283	+	493.134i	−0.629672	+	0.866669i	0.368340	+	0.929691i	$0.379926\pi$
$570$		0			0
$571$	−116.835	+	84.8857i	−0.204615	+	0.148661i	−0.685374	−	0.728191i	$-0.740361\pi$
$571$	−116.835	+	84.8857i	−0.204615	+	0.148661i	0.480759	+	0.876853i	$0.340361\pi$
$572$		0			0
$573$	432.637	−	849.097i	0.755038	−	1.48185i
$574$		0			0
$575$	22.5589	−	314.839i	0.0392328	−	0.547546i
$576$		0			0
$577$	234.087	+	119.274i	0.405697	+	0.206713i	0.644917	−	0.764252i	$-0.276892\pi$
$577$	234.087	+	119.274i	0.405697	+	0.206713i	−0.239220	+	0.970965i	$0.576892\pi$
$578$		0			0
$579$	−319.184	−	439.320i	−0.551268	−	0.758756i
$580$		0			0
$581$	−135.720	−	98.6060i	−0.233596	−	0.169718i
$582$		0			0
$583$	−15.2671	−	96.3928i	−0.0261872	−	0.165339i
$584$		0			0
$585$	−130.558	+	48.6858i	−0.223175	+	0.0832235i
$586$		0			0
$587$	402.231	+	789.423i	0.685232	+	1.34484i	0.927203	+	0.374560i	$0.122206\pi$
$587$	402.231	+	789.423i	0.685232	+	1.34484i	−0.241970	+	0.970284i	$0.577794\pi$
$588$		0			0
$589$	260.845	−	84.7536i	0.442860	−	0.143894i
$590$		0			0
$591$	−388.413	+	1195.41i	−0.657214	+	2.02270i
$592$		0			0
$593$	398.483	+	398.483i	0.671977	+	0.671977i	0.958172	−	0.286194i	$-0.0923902\pi$
$593$	398.483	+	398.483i	0.671977	+	0.671977i	−0.286194	+	0.958172i	$0.592390\pi$
$594$		0			0
$595$	69.2981	−	151.716i	0.116467	−	0.254984i
$596$		0			0
$597$	−177.867	+	1123.01i	−0.297934	+	1.88108i
$598$		0			0
$599$			59.5862i			0.0994762i	0.998762	+	0.0497381i	$0.0158387\pi$
$599$			59.5862i			0.0994762i	−0.998762	+	0.0497381i	$0.984161\pi$
$600$		0			0
$601$	−751.926			−1.25113			−0.625563	−	0.780174i	$-0.715131\pi$
$601$	−751.926			−1.25113			−0.625563	+	0.780174i	$0.715131\pi$
$602$		0			0
$603$	85.0837	+	13.4759i	0.141101	+	0.0223482i
$604$		0			0
$605$	344.117	−	374.891i	0.568788	−	0.619655i
$606$		0			0
$607$	423.232	−	423.232i	0.697252	−	0.697252i	−0.266565	−	0.963817i	$-0.585889\pi$
$607$	423.232	−	423.232i	0.697252	−	0.697252i	0.963817	+	0.266565i	$0.0858887\pi$
$608$		0			0
$609$	552.904	+	179.649i	0.907888	+	0.294991i
$610$		0			0
$611$	−6.31866	−	19.4468i	−0.0103415	−	0.0318279i
$612$		0			0
$613$	−59.2693	+	30.1992i	−0.0966873	+	0.0492647i	−0.501665	−	0.865062i	$-0.667279\pi$
$613$	−59.2693	+	30.1992i	−0.0966873	+	0.0492647i	0.404978	+	0.914326i	$0.367279\pi$
$614$		0			0
$615$	−340.221	+	1222.72i	−0.553206	+	1.98817i
$616$		0			0
$617$	975.986	−	154.581i	1.58183	−	0.250536i	0.697213	−	0.716864i	$-0.254423\pi$
$617$	975.986	−	154.581i	1.58183	−	0.250536i	0.884612	+	0.466328i	$0.154423\pi$
$618$		0			0
$619$	618.932	−	851.887i	0.999890	−	1.37623i	0.0744971	−	0.997221i	$-0.476265\pi$
$619$	618.932	−	851.887i	0.999890	−	1.37623i	0.925393	−	0.379009i	$-0.123735\pi$
$620$		0			0
$621$	72.4659	−	52.6495i	0.116692	−	0.0847819i
$622$		0			0
$623$	187.817	−	368.612i	0.301472	−	0.591672i
$624$		0			0
$625$	435.703	−	448.094i	0.697124	−	0.716951i
$626$		0			0
$627$	−99.7355	−	50.8178i	−0.159068	−	0.0810491i
$628$		0			0
$629$	−345.871	−	476.050i	−0.549874	−	0.756837i
$630$		0			0
$631$	71.6367	+	52.0471i	0.113529	+	0.0824836i	0.643101	−	0.765781i	$-0.277648\pi$
$631$	71.6367	+	52.0471i	0.113529	+	0.0824836i	−0.529572	+	0.848265i	$0.677648\pi$
$632$		0			0
$633$	118.983	+	751.227i	0.187966	+	1.18677i
$634$		0			0
$635$	−1183.40	−	329.279i	−1.86362	−	0.518550i
$636$		0			0
$637$	−72.9513	−	143.175i	−0.114523	−	0.224764i
$638$		0			0
$639$	881.747	−	286.497i	1.37989	−	0.448352i
$640$		0			0
$641$	−347.724	+	1070.18i	−0.542471	+	1.66955i	0.184457	+	0.982841i	$0.440947\pi$
$641$	−347.724	+	1070.18i	−0.542471	+	1.66955i	−0.726928	+	0.686713i	$0.759053\pi$
$642$		0			0
$643$	711.872	+	711.872i	1.10711	+	1.10711i	0.993529	+	0.113582i	$0.0362326\pi$
$643$	711.872	+	711.872i	1.10711	+	1.10711i	0.113582	+	0.993529i	$0.463767\pi$
$644$		0			0
$645$	−165.715	−	152.111i	−0.256922	−	0.235831i
$646$		0			0
$647$	−58.6375	+	370.223i	−0.0906298	+	0.572214i	0.900027	+	0.435834i	$0.143547\pi$
$647$	−58.6375	+	370.223i	−0.0906298	+	0.572214i	−0.990657	+	0.136380i	$0.956453\pi$
$648$		0			0
$649$			399.373i			0.615367i
$650$		0			0
$651$	469.955			0.721898
$652$		0			0
$653$	1058.77	+	167.693i	1.62139	+	0.256804i	0.900054	−	0.435778i	$-0.143527\pi$
$653$	1058.77	+	167.693i	1.62139	+	0.256804i	0.721340	+	0.692582i	$0.243527\pi$
$654$		0			0
$655$	555.520	+	253.741i	0.848122	+	0.387391i
$656$		0			0
$657$	344.587	−	344.587i	0.524485	−	0.524485i
$658$		0			0
$659$	−519.831	−	168.903i	−0.788818	−	0.256302i	−0.113217	−	0.993570i	$-0.536116\pi$
$659$	−519.831	−	168.903i	−0.788818	−	0.256302i	−0.675600	+	0.737268i	$0.736116\pi$
$660$		0			0
$661$	−233.630	−	719.039i	−0.353449	−	1.08780i	−0.956903	−	0.290407i	$-0.906209\pi$
$661$	−233.630	−	719.039i	−0.353449	−	1.08780i	0.603454	−	0.797398i	$-0.293791\pi$
$662$		0			0
$663$	−171.164	+	87.2126i	−0.258167	+	0.131542i
$664$		0			0
$665$	29.8137	+	79.9494i	0.0448326	+	0.120225i
$666$		0			0
$667$	667.852	−	105.777i	1.00128	−	0.158587i
$668$		0			0
$669$	0.687130	−	0.945754i	0.00102710	−	0.00141368i
$670$		0			0
$671$	−50.8697	+	36.9590i	−0.0758118	+	0.0550805i
$672$		0			0
$673$	165.950	−	325.695i	0.246582	−	0.483945i	−0.734230	−	0.678901i	$-0.762457\pi$
$673$	165.950	−	325.695i	0.246582	−	0.483945i	0.980812	+	0.194956i	$0.0624565\pi$
$674$		0			0
$675$	176.906	+	12.6757i	0.262084	+	0.0187789i
$676$		0			0
$677$	364.907	+	185.930i	0.539006	+	0.274637i	0.702228	−	0.711952i	$-0.252189\pi$
$677$	364.907	+	185.930i	0.539006	+	0.274637i	−0.163222	+	0.986589i	$0.552189\pi$
$678$		0			0
$679$	−22.6357	−	31.1554i	−0.0333368	−	0.0458842i
$680$		0			0
$681$	−88.7341	−	64.4691i	−0.130300	−	0.0946683i
$682$		0			0
$683$	88.5297	+	558.955i	0.129619	+	0.818382i	0.963748	+	0.266813i	$0.0859706\pi$
$683$	88.5297	+	558.955i	0.129619	+	0.818382i	−0.834129	+	0.551569i	$0.814029\pi$
$684$		0			0
$685$	513.259	+	646.393i	0.749283	+	0.943639i
$686$		0			0
$687$	−435.718	−	855.145i	−0.634233	−	1.24475i
$688$		0			0
$689$	81.4902	−	26.4778i	0.118273	−	0.0384293i
$690$		0			0
$691$	−317.322	+	976.618i	−0.459222	+	1.41334i	0.406884	+	0.913480i	$0.366615\pi$
$691$	−317.322	+	976.618i	−0.459222	+	1.41334i	−0.866106	+	0.499860i	$0.833385\pi$
$692$		0			0
$693$	−60.4605	−	60.4605i	−0.0872446	−	0.0872446i
$694$		0			0
$695$	−622.173	+	351.304i	−0.895212	+	0.505473i
$696$		0			0
$697$	−122.025	+	770.433i	−0.175071	+	1.10536i
$698$		0			0
$699$		−	1280.33i		−	1.83167i
$700$		0			0
$701$	−639.169			−0.911796			−0.455898	−	0.890032i	$-0.650682\pi$
$701$	−639.169			−0.911796			−0.455898	+	0.890032i	$0.650682\pi$
$702$		0			0
$703$	297.322	+	47.0911i	0.422932	+	0.0669859i
$704$		0			0
$705$	12.2074	−	106.331i	0.0173154	−	0.150825i
$706$		0			0
$707$	62.1252	−	62.1252i	0.0878716	−	0.0878716i
$708$		0			0
$709$	−485.757	−	157.832i	−0.685130	−	0.222612i	−0.0542902	−	0.998525i	$-0.517290\pi$
$709$	−485.757	−	157.832i	−0.685130	−	0.222612i	−0.630840	+	0.775913i	$0.717290\pi$
$710$		0			0
$711$	98.3383	+	302.654i	0.138310	+	0.425674i
$712$		0			0
$713$	487.029	−	248.154i	0.683070	−	0.348042i
$714$		0			0
$715$	−70.3306	−	46.6377i	−0.0983645	−	0.0652275i
$716$		0			0
$717$	860.620	−	136.309i	1.20031	−	0.190110i
$718$		0			0
$719$	−4.62242	+	6.36221i	−0.00642895	+	0.00884869i	−0.812219	−	0.583352i	$-0.801741\pi$
$719$	−4.62242	+	6.36221i	−0.00642895	+	0.00884869i	0.805790	+	0.592201i	$0.201741\pi$
$720$		0			0
$721$	328.489	−	238.662i	0.455603	−	0.331015i
$722$		0			0
$723$	−517.984	+	1016.60i	−0.716437	+	1.40609i
$724$		0			0
$725$	1146.45	+	691.541i	1.58132	+	0.953849i
$726$		0			0
$727$	−620.365	−	316.092i	−0.853321	−	0.434789i	−0.0281045	−	0.999605i	$-0.508947\pi$
$727$	−620.365	−	316.092i	−0.853321	−	0.434789i	−0.825217	+	0.564816i	$0.808947\pi$
$728$		0			0
$729$	−247.673	−	340.893i	−0.339743	−	0.467617i
$730$		0			0
$731$	−111.847	−	81.2615i	−0.153005	−	0.111165i
$732$		0			0
$733$	−75.7308	−	478.146i	−0.103316	−	0.652313i	−0.983940	−	0.178498i	$-0.942876\pi$
$733$	−75.7308	−	478.146i	−0.103316	−	0.652313i	0.880624	−	0.473816i	$-0.157124\pi$
$734$		0			0
$735$	−35.9670	−	840.332i	−0.0489347	−	1.14331i
$736$		0			0
$737$	23.6855	+	46.4855i	0.0321378	+	0.0630739i
$738$		0			0
$739$	−995.645	+	323.505i	−1.34729	+	0.437760i	−0.891779	−	0.452472i	$-0.850542\pi$
$739$	−995.645	+	323.505i	−1.34729	+	0.437760i	−0.455508	+	0.890232i	$0.650542\pi$
$740$		0			0
$741$	30.3687	−	93.4652i	0.0409834	−	0.126134i
$742$		0			0
$743$	−232.950	−	232.950i	−0.313526	−	0.313526i	0.532748	−	0.846274i	$-0.321159\pi$
$743$	−232.950	−	232.950i	−0.313526	−	0.313526i	−0.846274	+	0.532748i	$0.821159\pi$
$744$		0			0
$745$	0.293537	+	1.44915i	0.000394009	+	0.00194516i
$746$		0			0
$747$	−70.5296	+	445.306i	−0.0944171	+	0.596126i
$748$		0			0
$749$		−	523.104i		−	0.698403i
$750$		0			0
$751$	−746.137			−0.993525			−0.496763	−	0.867886i	$-0.665478\pi$
$751$	−746.137			−0.993525			−0.496763	+	0.867886i	$0.665478\pi$
$752$		0			0
$753$	−772.220	−	122.308i	−1.02552	−	0.162427i
$754$		0			0
$755$	−290.055	+	58.7531i	−0.384179	+	0.0778187i
$756$		0			0
$757$	−384.700	+	384.700i	−0.508191	+	0.508191i	−0.913971	−	0.405780i	$-0.867000\pi$
$757$	−384.700	+	384.700i	−0.508191	+	0.508191i	0.405780	+	0.913971i	$0.367000\pi$
$758$		0			0
$759$	−212.165	−	68.9365i	−0.279532	−	0.0908255i
$760$		0			0
$761$	346.102	+	1065.19i	0.454799	+	1.39973i	0.871371	+	0.490625i	$0.163232\pi$
$761$	346.102	+	1065.19i	0.454799	+	1.39973i	−0.416572	+	0.909103i	$0.636768\pi$
$762$		0			0
$763$	−206.322	+	105.126i	−0.270409	+	0.137780i
$764$		0			0
$765$	−447.851	+	19.1685i	−0.585427	+	0.0250568i
$766$		0			0
$767$	−346.317	+	54.8512i	−0.451521	+	0.0715139i
$768$		0			0
$769$	600.078	−	825.937i	0.780336	−	1.07404i	−0.214909	−	0.976634i	$-0.568946\pi$
$769$	600.078	−	825.937i	0.780336	−	1.07404i	0.995245	−	0.0974058i	$-0.0310545\pi$
$770$		0			0
$771$	19.8399	−	14.4145i	0.0257326	−	0.0186958i
$772$		0			0
$773$	37.0343	−	72.6839i	0.0479098	−	0.0940283i	−0.865810	−	0.500372i	$-0.833197\pi$
$773$	37.0343	−	72.6839i	0.0479098	−	0.0940283i	0.913720	+	0.406344i	$0.133197\pi$
$774$		0			0
$775$	1054.16	+	245.278i	1.36020	+	0.316488i
$776$		0			0
$777$	459.587	+	234.172i	0.591490	+	0.301379i
$778$		0			0
$779$	−234.555	−	322.838i	−0.301098	−	0.414426i
$780$		0			0
$781$	454.261	+	330.040i	0.581640	+	0.422586i
$782$		0			0
$783$	59.4358	+	375.263i	0.0759078	+	0.479263i
$784$		0			0
$785$	583.202	−	879.480i	0.742932	−	1.12036i
$786$		0			0
$787$	−350.282	−	687.466i	−0.445085	−	0.873528i	−0.999157	−	0.0410592i	$-0.986927\pi$
$787$	−350.282	−	687.466i	−0.445085	−	0.873528i	0.554072	−	0.832469i	$-0.313073\pi$
$788$		0			0
$789$	−968.633	+	314.728i	−1.22767	+	0.398895i
$790$		0			0
$791$	−59.3180	+	182.562i	−0.0749912	+	0.230799i
$792$		0			0
$793$	−39.0356	−	39.0356i	−0.0492253	−	0.0492253i
$794$		0			0
$795$	445.572	+	51.1540i	0.560468	+	0.0643446i
$796$		0			0
$797$	−71.3343	+	450.387i	−0.0895035	+	0.565103i	0.901659	+	0.432448i	$0.142350\pi$
$797$	−71.3343	+	450.387i	−0.0895035	+	0.565103i	−0.991162	+	0.132655i	$0.957650\pi$
$798$		0			0
$799$		−	65.7807i		−	0.0823288i
$800$		0			0
$801$	−1111.84			−1.38806
$802$		0			0
$803$	291.503	+	46.1696i	0.363018	+	0.0574964i
$804$		0			0
$805$	83.6115	+	148.079i	0.103865	+	0.183949i
$806$		0			0
$807$	286.585	−	286.585i	0.355123	−	0.355123i
$808$		0			0
$809$	−997.324	−	324.050i	−1.23279	−	0.400557i	−0.381063	−	0.924549i	$-0.624442\pi$
$809$	−997.324	−	324.050i	−1.23279	−	0.400557i	−0.851723	+	0.523992i	$0.824442\pi$
$810$		0			0
$811$	−228.352	−	702.796i	−0.281569	−	0.866580i	−0.987406	−	0.158206i	$-0.949429\pi$
$811$	−228.352	−	702.796i	−0.281569	−	0.866580i	0.705837	−	0.708374i	$-0.250571\pi$
$812$		0			0
$813$	1240.11	−	631.869i	1.52535	−	0.777207i
$814$		0			0
$815$	−63.0796	+	50.0875i	−0.0773983	+	0.0614570i
$816$		0			0
$817$	69.8549	−	11.0639i	0.0855018	−	0.0135421i
$818$		0			0
$819$	44.1245	−	60.7322i	0.0538761	−	0.0741541i
$820$		0			0
$821$	−712.713	+	517.816i	−0.868103	+	0.630714i	−0.930077	−	0.367364i	$-0.880260\pi$
$821$	−712.713	+	517.816i	−0.868103	+	0.630714i	0.0619743	+	0.998078i	$0.480260\pi$
$822$		0			0
$823$	−137.871	+	270.588i	−0.167523	+	0.328782i	−0.959472	−	0.281806i	$-0.909067\pi$
$823$	−137.871	+	270.588i	−0.167523	+	0.328782i	0.791949	+	0.610588i	$0.209067\pi$
$824$		0			0
$825$	−233.432	−	375.001i	−0.282948	−	0.454547i
$826$		0			0
$827$	1046.14	+	533.033i	1.26498	+	0.644538i	0.952254	−	0.305306i	$-0.0987588\pi$
$827$	1046.14	+	533.033i	1.26498	+	0.644538i	0.312723	+	0.949844i	$0.398759\pi$
$828$		0			0
$829$	−640.752	−	881.920i	−0.772922	−	1.06384i	−0.996028	−	0.0890416i	$-0.971620\pi$
$829$	−640.752	−	881.920i	−0.772922	−	1.06384i	0.223106	−	0.974794i	$-0.428380\pi$
$830$		0			0
$831$	989.483	+	718.901i	1.19071	+	0.865104i
$832$		0			0
$833$	−80.8676	−	510.578i	−0.0970800	−	0.612939i
$834$		0			0
$835$	860.822	−	321.006i	1.03092	−	0.384439i
$836$		0			0
$837$	139.436	+	273.659i	0.166591	+	0.326953i
$838$		0			0
$839$	1560.33	−	506.981i	1.85975	−	0.604269i	0.865017	−	0.501742i	$-0.167307\pi$
$839$	1560.33	−	506.981i	1.85975	−	0.604269i	0.994730	−	0.102527i	$-0.0326928\pi$
$840$		0			0
$841$	−626.420	+	1927.92i	−0.744851	+	2.29242i
$842$		0			0
$843$	364.516	+	364.516i	0.432403	+	0.432403i
$844$		0			0
$845$	−320.293	+	701.224i	−0.379045	+	0.829850i
$846$		0			0
$847$	−42.8879	+	270.784i	−0.0506351	+	0.319697i
$848$		0			0
$849$			935.532i			1.10192i
$850$		0			0
$851$	599.935			0.704977
$852$		0			0
$853$	530.862	+	84.0803i	0.622347	+	0.0985701i	0.459642	−	0.888105i	$-0.347978\pi$
$853$	530.862	+	84.0803i	0.622347	+	0.0985701i	0.162706	+	0.986675i	$0.447978\pi$
$854$		0			0
$855$	155.072	−	168.940i	0.181370	−	0.197590i
$856$		0			0
$857$	989.462	−	989.462i	1.15456	−	1.15456i	0.168938	−	0.985627i	$-0.445966\pi$
$857$	989.462	−	989.462i	1.15456	−	1.15456i	0.985627	−	0.168938i	$-0.0540337\pi$
$858$		0			0
$859$	677.961	+	220.283i	0.789244	+	0.256441i	0.675782	−	0.737101i	$-0.263806\pi$
$859$	677.961	+	220.283i	0.789244	+	0.256441i	0.113462	+	0.993542i	$0.463806\pi$
$860$		0			0
$861$	−211.295	−	650.300i	−0.245407	−	0.755284i
$862$		0			0
$863$	1441.38	−	734.422i	1.67020	−	0.851011i	0.676821	−	0.736147i	$-0.263357\pi$
$863$	1441.38	−	734.422i	1.67020	−	0.851011i	0.993381	−	0.114863i	$-0.0366430\pi$
$864$		0			0
$865$	−168.128	+	604.234i	−0.194367	+	0.698537i
$866$		0			0
$867$	539.891	−	85.5103i	0.622711	−	0.0986278i
$868$		0			0
$869$	−113.284	+	155.922i	−0.130361	+	0.179427i
$870$		0			0
$871$	−37.0569	+	26.9234i	−0.0425452	+	0.0309109i
$872$		0			0
$873$	−46.9868	+	92.2168i	−0.0538222	+	0.105632i
$874$		0			0
$875$	−62.2143	+	330.921i	−0.0711021	+	0.378195i
$876$		0			0
$877$	237.415	+	120.969i	0.270712	+	0.137935i	0.584077	−	0.811698i	$-0.301456\pi$
$877$	237.415	+	120.969i	0.270712	+	0.137935i	−0.313365	+	0.949633i	$0.601456\pi$
$878$		0			0
$879$	−226.974	−	312.403i	−0.258219	−	0.355408i
$880$		0			0
$881$	−492.452	−	357.787i	−0.558969	−	0.406115i	0.272112	−	0.962265i	$-0.412278\pi$
$881$	−492.452	−	357.787i	−0.558969	−	0.406115i	−0.831082	+	0.556151i	$0.812278\pi$
$882$		0			0
$883$	121.885	+	769.549i	0.138035	+	0.871517i	0.955382	+	0.295372i	$0.0954435\pi$
$883$	121.885	+	769.549i	0.138035	+	0.871517i	−0.817348	+	0.576145i	$0.804556\pi$
$884$		0			0
$885$	−1768.16	−	491.990i	−1.99792	−	0.555921i
$886$		0			0
$887$	−407.291	−	799.353i	−0.459178	−	0.901188i	−0.998262	−	0.0589355i	$-0.981229\pi$
$887$	−407.291	−	799.353i	−0.459178	−	0.901188i	0.539084	−	0.842252i	$-0.318771\pi$
$888$		0			0
$889$	629.384	−	204.499i	0.707969	−	0.230033i
$890$		0			0
$891$	127.014	−	390.908i	0.142552	−	0.438729i
$892$		0			0
$893$	23.7955	+	23.7955i	0.0266467	+	0.0266467i
$894$		0			0
$895$	169.188	+	155.299i	0.189036	+	0.173519i
$896$		0			0
$897$	30.6390	−	193.447i	0.0341572	−	0.215660i
$898$		0			0
$899$			2318.53i			2.57902i
$900$		0			0
$901$	275.648			0.305936
$902$		0			0
$903$	119.696	+	18.9579i	0.132553	+	0.0209944i
$904$		0			0
$905$	−578.383	−	264.184i	−0.639097	−	0.291916i
$906$		0			0
$907$	−7.35179	+	7.35179i	−0.00810561	+	0.00810561i	−0.711148	−	0.703042i	$-0.751824\pi$
$907$	−7.35179	+	7.35179i	−0.00810561	+	0.00810561i	0.703042	+	0.711148i	$0.251824\pi$
$908$		0			0
$909$	−224.565	−	72.9657i	−0.247047	−	0.0802703i
$910$		0			0
$911$	−267.350	−	822.820i	−0.293469	−	0.903205i	−0.983731	−	0.179646i	$-0.942505\pi$
$911$	−267.350	−	822.820i	−0.293469	−	0.903205i	0.690262	−	0.723559i	$-0.257495\pi$
$912$		0			0
$913$	−243.293	+	123.964i	−0.266476	+	0.135776i
$914$		0			0
$915$	−100.964	−	270.748i	−0.110343	−	0.295899i
$916$		0			0
$917$	−324.977	+	51.4714i	−0.354392	+	0.0561302i
$918$		0			0
$919$	550.990	−	758.373i	0.599554	−	0.825215i	−0.396113	−	0.918202i	$-0.629641\pi$
$919$	550.990	−	758.373i	0.599554	−	0.825215i	0.995667	+	0.0929863i	$0.0296413\pi$
$920$		0			0
$921$	423.607	−	307.768i	0.459942	−	0.334168i
$922$		0			0
$923$	−223.805	+	439.241i	−0.242475	+	0.475884i
$924$		0			0
$925$	908.681	+	765.136i	0.982358	+	0.827174i
$926$		0			0
$927$	−972.296	−	495.410i	−1.04886	−	0.534422i
$928$		0			0
$929$	−283.057	−	389.594i	−0.304690	−	0.419369i	0.629026	−	0.777384i	$-0.283454\pi$
$929$	−283.057	−	389.594i	−0.304690	−	0.419369i	−0.933716	+	0.358015i	$0.883454\pi$
$930$		0			0
$931$	213.949	+	155.443i	0.229806	+	0.166964i
$932$		0			0
$933$	317.805	+	2006.54i	0.340627	+	2.15064i
$934$		0			0
$935$	−168.819	−	212.609i	−0.180555	−	0.227389i
$936$		0			0
$937$	−384.979	−	755.563i	−0.410863	−	0.806364i	0.589135	−	0.808034i	$-0.299468\pi$
$937$	−384.979	−	755.563i	−0.410863	−	0.806364i	−0.999999	+	0.00167001i	$0.999468\pi$
$938$		0			0
$939$	56.4388	−	18.3381i	0.0601052	−	0.0195294i
$940$		0			0
$941$	265.744	−	817.877i	0.282406	−	0.869157i	−0.704758	−	0.709448i	$-0.748944\pi$
$941$	265.744	−	817.877i	0.282406	−	0.869157i	0.987164	−	0.159709i	$-0.0510556\pi$
$942$		0			0
$943$	−562.353	−	562.353i	−0.596345	−	0.596345i
$944$		0			0
$945$	−83.2050	+	46.9809i	−0.0880477	+	0.0497152i
$946$		0			0
$947$	−102.488	+	647.082i	−0.108224	+	0.683297i	0.872605	+	0.488426i	$0.162429\pi$
$947$	−102.488	+	647.082i	−0.108224	+	0.683297i	−0.980829	+	0.194871i	$0.937571\pi$
$948$		0			0
$949$			259.118i			0.273044i
$950$		0			0
$951$	−2152.04			−2.26293
$952$		0			0
$953$	−992.284	−	157.162i	−1.04122	−	0.164913i	−0.387672	−	0.921797i	$-0.626721\pi$
$953$	−992.284	−	157.162i	−1.04122	−	0.164913i	−0.653549	+	0.756884i	$0.726721\pi$
$954$		0			0
$955$	−134.858	+	1174.67i	−0.141213	+	1.23002i
$956$		0			0
$957$	669.101	−	669.101i	0.699165	−	0.699165i
$958$		0			0
$959$	−422.911	−	137.412i	−0.440991	−	0.143287i
$960$		0			0
$961$	282.209	+	868.551i	0.293662	+	0.903800i
$962$		0			0
$963$	−1252.63	+	638.246i	−1.30076	+	0.662769i
$964$		0			0
$965$	561.521	+	372.356i	0.581887	+	0.385861i
$966$		0			0
$967$	1013.63	−	160.543i	1.04822	−	0.166022i	0.391518	−	0.920171i	$-0.371950\pi$
$967$	1013.63	−	160.543i	1.04822	−	0.166022i	0.656704	+	0.754149i	$0.271950\pi$
$968$		0			0
$969$	185.831	−	255.775i	0.191776	−	0.263957i
$970$		0			0
$971$	1143.48	−	830.785i	1.17763	−	0.855597i	0.185726	−	0.982602i	$-0.440536\pi$
$971$	1143.48	−	830.785i	1.17763	−	0.855597i	0.991902	+	0.127005i	$0.0405363\pi$
$972$		0			0
$973$	174.758	−	342.981i	0.179607	−	0.352499i
$974$		0			0
$975$	293.122	−	253.925i	0.300638	−	0.260436i
$976$		0			0
$977$	−1422.95	−	725.029i	−1.45645	−	0.742098i	−0.466633	−	0.884451i	$-0.654533\pi$
$977$	−1422.95	−	725.029i	−1.45645	−	0.742098i	−0.989816	+	0.142353i	$0.954533\pi$
$978$		0			0
$979$	−395.795	−	544.765i	−0.404285	−	0.556451i
$980$		0			0
$981$	503.474	+	365.795i	0.513225	+	0.372880i
$982$		0			0
$983$	−112.928	−	712.999i	−0.114881	−	0.725330i	−0.976137	−	0.217158i	$-0.930321\pi$
$983$	−112.928	−	712.999i	−0.114881	−	0.725330i	0.861256	−	0.508172i	$-0.169679\pi$
$984$		0			0
$985$	−66.6886	−	1558.11i	−0.0677041	−	1.58184i
$986$		0			0
$987$	26.1781	+	51.3774i	0.0265229	+	0.0520541i
$988$		0			0
$989$	134.055	−	43.5570i	0.135546	−	0.0440414i
$990$		0			0
$991$	−308.589	+	949.741i	−0.311392	+	0.958366i	0.665822	+	0.746110i	$0.268081\pi$
$991$	−308.589	+	949.741i	−0.311392	+	0.958366i	−0.977214	+	0.212256i	$0.931919\pi$
$992$		0			0
$993$	293.354	+	293.354i	0.295422	+	0.295422i
$994$		0			0
$995$	−280.069	−	1382.66i	−0.281476	−	1.38960i
$996$		0			0
$997$	−233.259	+	1472.74i	−0.233961	+	1.47717i	0.538779	+	0.842447i	$0.318886\pi$
$997$	−233.259	+	1472.74i	−0.233961	+	1.47717i	−0.772740	+	0.634723i	$0.781114\pi$
$998$		0			0
$999$			337.101i			0.337438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.e.33.2		56
4.3	odd	2		200.3.u.a.33.6	✓	56
25.22	odd	20	inner	400.3.bg.e.97.2		56
100.47	even	20		200.3.u.a.97.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.33.6	✓	56	4.3	odd	2
200.3.u.a.97.6	yes	56	100.47	even	20
400.3.bg.e.33.2		56	1.1	even	1	trivial
400.3.bg.e.97.2		56	25.22	odd	20	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.98022 - 0.630404i) q^{3} +(4.90048 - 0.992634i) q^{5} +(-1.90476 + 1.90476i) q^{7} +(6.88520 + 2.23714i) q^{9} +(1.35489 + 4.16991i) q^{11} +(-3.42985 + 1.74760i) q^{13} +(-20.1307 + 0.861615i) q^{15} +(-12.2313 + 1.93724i) q^{17} +(3.72375 - 5.12531i) q^{19} +(8.78215 - 6.38060i) q^{21} +(5.73201 - 11.2497i) q^{23} +(23.0294 - 9.72876i) q^{25} +(6.32116 + 3.22079i) q^{27} +(31.4788 + 43.3269i) q^{29} +(35.0244 + 25.4467i) q^{31} +(-2.76401 - 17.4513i) q^{33} +(-7.44352 + 11.2250i) q^{35} +(21.5720 + 42.3375i) q^{37} +(14.7533 - 4.79362i) q^{39} +(19.4646 - 59.9060i) q^{41} +(7.89405 + 7.89405i) q^{43} +(35.9614 + 4.12856i) q^{45} +(-0.830960 + 5.24648i) q^{47} +41.7437i q^{49} +49.9043 q^{51} +(-21.9849 - 3.48206i) q^{53} +(10.7788 + 19.0896i) q^{55} +(-18.0524 + 18.0524i) q^{57} +(86.6293 + 28.1476i) q^{59} +(4.43163 + 13.6392i) q^{61} +(-17.3759 + 8.85347i) q^{63} +(-15.0732 + 11.9687i) q^{65} +(11.7527 - 1.86144i) q^{67} +(-29.9065 + 41.1628i) q^{69} +(103.606 - 75.2742i) q^{71} +(30.5598 - 59.9770i) q^{73} +(-97.7949 + 24.2048i) q^{75} +(-10.5234 - 5.36196i) q^{77} +(25.8374 + 35.5621i) q^{79} +(-75.8413 - 55.1019i) q^{81} +(9.74229 + 61.5104i) q^{83} +(-58.0160 + 21.6346i) q^{85} +(-97.9791 - 192.295i) q^{87} +(-146.062 + 47.4585i) q^{89} +(3.20430 - 9.86183i) q^{91} +(-123.363 - 123.363i) q^{93} +(13.1606 - 28.8128i) q^{95} +(-2.23641 + 14.1201i) q^{97} +31.7417i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) \) 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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