LMFDB - Embedded newform 400.3.bg.f.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.f.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.60705 - 0.888069i) q^{3} +(-0.904406 - 4.91752i) q^{5} +(3.60781 - 3.60781i) q^{7} +(22.0908 + 7.17774i) q^{9} +O(q^{10})$	\(q+(-5.60705 - 0.888069i) q^{3} +(-0.904406 - 4.91752i) q^{5} +(3.60781 - 3.60781i) q^{7} +(22.0908 + 7.17774i) q^{9} +(-0.881114 - 2.71179i) q^{11} +(21.0390 - 10.7199i) q^{13} +(0.703948 + 28.3760i) q^{15} +(-11.7819 + 1.86607i) q^{17} +(-0.670318 + 0.922614i) q^{19} +(-23.4331 + 17.0252i) q^{21} +(14.1584 - 27.7875i) q^{23} +(-23.3641 + 8.89488i) q^{25} +(-71.9662 - 36.6686i) q^{27} +(-22.9319 - 31.5630i) q^{29} +(28.8267 + 20.9438i) q^{31} +(2.53219 + 15.9876i) q^{33} +(-21.0044 - 14.4786i) q^{35} +(-17.1799 - 33.7175i) q^{37} +(-127.487 + 41.4230i) q^{39} +(-15.8966 + 48.9249i) q^{41} +(-7.81270 - 7.81270i) q^{43} +(15.3176 - 115.124i) q^{45} +(6.62783 - 41.8465i) q^{47} +22.9674i q^{49} +67.7189 q^{51} +(-38.0300 - 6.02336i) q^{53} +(-12.5384 + 6.78546i) q^{55} +(4.57785 - 4.57785i) q^{57} +(4.45355 + 1.44705i) q^{59} +(1.23832 + 3.81117i) q^{61} +(105.595 - 53.8035i) q^{63} +(-71.7433 - 93.7648i) q^{65} +(-35.0328 + 5.54865i) q^{67} +(-104.064 + 143.232i) q^{69} +(3.51757 - 2.55566i) q^{71} +(8.42727 - 16.5395i) q^{73} +(138.903 - 29.1251i) q^{75} +(-12.9625 - 6.60473i) q^{77} +(-49.2221 - 67.7484i) q^{79} +(201.830 + 146.638i) q^{81} +(23.5721 + 148.828i) q^{83} +(19.8321 + 56.2501i) q^{85} +(100.550 + 197.340i) q^{87} +(-102.308 + 33.2420i) q^{89} +(37.2294 - 114.580i) q^{91} +(-143.033 - 143.033i) q^{93} +(5.14322 + 2.46189i) q^{95} +(13.1205 - 82.8397i) q^{97} -66.2301i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

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
$3$	−5.60705	−	0.888069i	−1.86902	−	0.296023i	−0.883869	−	0.467735i	$-0.845070\pi$
$3$	−5.60705	−	0.888069i	−1.86902	−	0.296023i	−0.985147	+	0.171712i	$0.945070\pi$
$4$		0			0
$5$	−0.904406	−	4.91752i	−0.180881	−	0.983505i
$5$	−0.904406	−	4.91752i	−0.180881	−	0.983505i
$6$		0			0
$7$	3.60781	−	3.60781i	0.515401	−	0.515401i	−0.400775	−	0.916176i	$-0.631259\pi$
$7$	3.60781	−	3.60781i	0.515401	−	0.515401i	0.916176	+	0.400775i	$0.131259\pi$
$8$		0			0
$9$	22.0908	+	7.17774i	2.45453	+	0.797527i
$10$		0			0
$11$	−0.881114	−	2.71179i	−0.0801013	−	0.246526i	0.902984	−	0.429674i	$-0.141371\pi$
$11$	−0.881114	−	2.71179i	−0.0801013	−	0.246526i	−0.983085	+	0.183147i	$0.941371\pi$
$12$		0			0
$13$	21.0390	−	10.7199i	1.61839	−	0.824609i	0.619161	−	0.785264i	$-0.287473\pi$
$13$	21.0390	−	10.7199i	1.61839	−	0.824609i	0.999226	−	0.0393455i	$-0.0125273\pi$
$14$		0			0
$15$	0.703948	+	28.3760i	0.0469298	+	1.89173i
$16$		0			0
$17$	−11.7819	+	1.86607i	−0.693053	+	0.109769i	−0.493017	−	0.870020i	$-0.664106\pi$
$17$	−11.7819	+	1.86607i	−0.693053	+	0.109769i	−0.200036	+	0.979789i	$0.564106\pi$
$18$		0			0
$19$	−0.670318	+	0.922614i	−0.0352799	+	0.0485586i	−0.826293	−	0.563241i	$-0.809554\pi$
$19$	−0.670318	+	0.922614i	−0.0352799	+	0.0485586i	0.791013	+	0.611800i	$0.209554\pi$
$20$		0			0
$21$	−23.4331	+	17.0252i	−1.11586	+	0.810722i
$22$		0			0
$23$	14.1584	−	27.7875i	0.615583	−	1.20815i	−0.347178	−	0.937799i	$-0.612860\pi$
$23$	14.1584	−	27.7875i	0.615583	−	1.20815i	0.962762	−	0.270351i	$-0.0871399\pi$
$24$		0			0
$25$	−23.3641	+	8.89488i	−0.934564	+	0.355795i
$26$		0			0
$27$	−71.9662	−	36.6686i	−2.66541	−	1.35810i
$28$		0			0
$29$	−22.9319	−	31.5630i	−0.790754	−	1.08838i	−0.994014	−	0.109254i	$-0.965154\pi$
$29$	−22.9319	−	31.5630i	−0.790754	−	1.08838i	0.203260	−	0.979125i	$-0.434846\pi$
$30$		0			0
$31$	28.8267	+	20.9438i	0.929894	+	0.675607i	0.945967	−	0.324264i	$-0.105116\pi$
$31$	28.8267	+	20.9438i	0.929894	+	0.675607i	−0.0160731	+	0.999871i	$0.505116\pi$
$32$		0			0
$33$	2.53219	+	15.9876i	0.0767331	+	0.484474i
$34$		0			0
$35$	−21.0044	−	14.4786i	−0.600126	−	0.413673i
$36$		0			0
$37$	−17.1799	−	33.7175i	−0.464323	−	0.911285i	−0.997852	−	0.0655032i	$-0.979135\pi$
$37$	−17.1799	−	33.7175i	−0.464323	−	0.911285i	0.533530	−	0.845781i	$-0.320865\pi$
$38$		0			0
$39$	−127.487	+	41.4230i	−3.26889	+	1.06213i
$40$		0			0
$41$	−15.8966	+	48.9249i	−0.387723	+	1.19329i	0.546762	+	0.837288i	$0.315860\pi$
$41$	−15.8966	+	48.9249i	−0.387723	+	1.19329i	−0.934485	+	0.356001i	$0.884140\pi$
$42$		0			0
$43$	−7.81270	−	7.81270i	−0.181691	−	0.181691i	0.610401	−	0.792092i	$-0.291008\pi$
$43$	−7.81270	−	7.81270i	−0.181691	−	0.181691i	−0.792092	+	0.610401i	$0.791008\pi$
$44$		0			0
$45$	15.3176	−	115.124i	0.340392	−	2.55830i
$46$		0			0
$47$	6.62783	−	41.8465i	0.141018	−	0.890350i	−0.811164	−	0.584818i	$-0.801166\pi$
$47$	6.62783	−	41.8465i	0.141018	−	0.890350i	0.952182	−	0.305532i	$-0.0988343\pi$
$48$		0			0
$49$			22.9674i			0.468723i
$50$		0			0
$51$	67.7189			1.32782
$52$		0			0
$53$	−38.0300	−	6.02336i	−0.717547	−	0.113648i	−0.213024	−	0.977047i	$-0.568331\pi$
$53$	−38.0300	−	6.02336i	−0.717547	−	0.113648i	−0.504522	+	0.863399i	$0.668331\pi$
$54$		0			0
$55$	−12.5384	+	6.78546i	−0.227971	+	0.123372i
$56$		0			0
$57$	4.57785	−	4.57785i	0.0803132	−	0.0803132i
$58$		0			0
$59$	4.45355	+	1.44705i	0.0754840	+	0.0245262i	0.346516	−	0.938044i	$-0.387365\pi$
$59$	4.45355	+	1.44705i	0.0754840	+	0.0245262i	−0.271032	+	0.962570i	$0.587365\pi$
$60$		0			0
$61$	1.23832	+	3.81117i	0.0203004	+	0.0624782i	0.960694	−	0.277611i	$-0.0895427\pi$
$61$	1.23832	+	3.81117i	0.0203004	+	0.0624782i	−0.940393	+	0.340089i	$0.889543\pi$
$62$		0			0
$63$	105.595	−	53.8035i	1.67612	−	0.854024i
$64$		0			0
$65$	−71.7433	−	93.7648i	−1.10374	−	1.44254i
$66$		0			0
$67$	−35.0328	+	5.54865i	−0.522878	+	0.0828157i	−0.412294	−	0.911051i	$-0.635272\pi$
$67$	−35.0328	+	5.54865i	−0.522878	+	0.0828157i	−0.110584	+	0.993867i	$0.535272\pi$
$68$		0			0
$69$	−104.064	+	143.232i	−1.50818	+	2.07583i
$70$		0			0
$71$	3.51757	−	2.55566i	0.0495432	−	0.0359952i	−0.562738	−	0.826635i	$-0.690252\pi$
$71$	3.51757	−	2.55566i	0.0495432	−	0.0359952i	0.612281	+	0.790640i	$0.290252\pi$
$72$		0			0
$73$	8.42727	−	16.5395i	0.115442	−	0.226568i	−0.826055	−	0.563590i	$-0.809420\pi$
$73$	8.42727	−	16.5395i	0.115442	−	0.226568i	0.941497	+	0.337022i	$0.109420\pi$
$74$		0			0
$75$	138.903	−	29.1251i	1.85204	−	0.388335i
$76$		0			0
$77$	−12.9625	−	6.60473i	−0.168344	−	0.0857757i
$78$		0			0
$79$	−49.2221	−	67.7484i	−0.623065	−	0.857575i	0.374507	−	0.927224i	$-0.377812\pi$
$79$	−49.2221	−	67.7484i	−0.623065	−	0.857575i	−0.997572	+	0.0696491i	$0.977812\pi$
$80$		0			0
$81$	201.830	+	146.638i	2.49172	+	1.81034i
$82$		0			0
$83$	23.5721	+	148.828i	0.284001	+	1.79311i	0.556389	+	0.830922i	$0.312186\pi$
$83$	23.5721	+	148.828i	0.284001	+	1.79311i	−0.272388	+	0.962187i	$0.587814\pi$
$84$		0			0
$85$	19.8321	+	56.2501i	0.233319	+	0.661766i
$86$		0			0
$87$	100.550	+	197.340i	1.15575	+	2.26828i
$88$		0			0
$89$	−102.308	+	33.2420i	−1.14953	+	0.373505i	−0.820967	−	0.570976i	$-0.806565\pi$
$89$	−102.308	+	33.2420i	−1.14953	+	0.373505i	−0.328564	+	0.944482i	$0.606565\pi$
$90$		0			0
$91$	37.2294	−	114.580i	0.409114	−	1.25912i
$92$		0			0
$93$	−143.033	−	143.033i	−1.53799	−	1.53799i
$94$		0			0
$95$	5.14322	+	2.46189i	0.0541391	+	0.0259146i
$96$		0			0
$97$	13.1205	−	82.8397i	0.135263	−	0.854018i	−0.822982	−	0.568068i	$-0.807691\pi$
$97$	13.1205	−	82.8397i	0.135263	−	0.854018i	0.958245	−	0.285950i	$-0.0923090\pi$
$98$		0			0
$99$		−	66.2301i		−	0.668990i
$100$		0			0
$101$	−22.5839			−0.223603			−0.111801	−	0.993731i	$-0.535662\pi$
$101$	−22.5839			−0.223603			−0.111801	+	0.993731i	$0.535662\pi$
$102$		0			0
$103$	55.9724	+	8.86515i	0.543421	+	0.0860694i	0.422109	−	0.906545i	$-0.361290\pi$
$103$	55.9724	+	8.86515i	0.543421	+	0.0860694i	0.121312	+	0.992614i	$0.461290\pi$
$104$		0			0
$105$	104.915	+	99.8354i	0.999188	+	0.950813i
$106$		0			0
$107$	−34.6629	+	34.6629i	−0.323952	+	0.323952i	−0.850281	−	0.526329i	$-0.823568\pi$
$107$	−34.6629	+	34.6629i	−0.323952	+	0.323952i	0.526329	+	0.850281i	$0.323568\pi$
$108$		0			0
$109$	144.123	+	46.8285i	1.32223	+	0.429619i	0.883261	−	0.468882i	$-0.155343\pi$
$109$	144.123	+	46.8285i	1.32223	+	0.429619i	0.438971	+	0.898501i	$0.355343\pi$
$110$		0			0
$111$	66.3852	+	204.313i	0.598065	+	1.84066i
$112$		0			0
$113$	53.3172	−	27.1665i	0.471834	−	0.240411i	−0.201871	−	0.979412i	$-0.564702\pi$
$113$	53.3172	−	27.1665i	0.471834	−	0.240411i	0.673704	+	0.739001i	$0.264702\pi$
$114$		0			0
$115$	−149.450	−	44.4932i	−1.29957	−	0.386898i
$116$		0			0
$117$	541.714	−	85.7991i	4.63003	−	0.733325i
$118$		0			0
$119$	−35.7744	+	49.2393i	−0.300625	+	0.413775i
$120$		0			0
$121$	91.3136	−	66.3432i	0.754658	−	0.548291i
$122$		0			0
$123$	132.582	−	260.207i	1.07790	−	2.11550i
$124$		0			0
$125$	64.8714	+	106.849i	0.518971	+	0.854792i
$126$		0			0
$127$	−91.5268	−	46.6352i	−0.720683	−	0.367207i	0.0548657	−	0.998494i	$-0.482527\pi$
$127$	−91.5268	−	46.6352i	−0.720683	−	0.367207i	−0.775549	+	0.631287i	$0.782527\pi$
$128$		0			0
$129$	36.8680	+	50.7444i	0.285798	+	0.393368i
$130$		0			0
$131$	−100.462	−	72.9901i	−0.766887	−	0.557176i	0.134128	−	0.990964i	$-0.457177\pi$
$131$	−100.462	−	72.9901i	−0.766887	−	0.557176i	−0.901015	+	0.433788i	$0.857177\pi$
$132$		0			0
$133$	0.910234	+	5.74699i	0.00684387	+	0.0432105i
$134$		0			0
$135$	−115.232	+	387.059i	−0.853571	+	2.86710i
$136$		0			0
$137$	−111.947	−	219.709i	−0.817132	−	1.60371i	−0.797049	−	0.603914i	$-0.793607\pi$
$137$	−111.947	−	219.709i	−0.817132	−	1.60371i	−0.0200833	−	0.999798i	$-0.506393\pi$
$138$		0			0
$139$	−47.8827	+	15.5580i	−0.344480	+	0.111928i	−0.476147	−	0.879366i	$-0.657967\pi$
$139$	−47.8827	+	15.5580i	−0.344480	+	0.111928i	0.131667	+	0.991294i	$0.457967\pi$
$140$		0			0
$141$	−74.3251	+	228.749i	−0.527128	+	1.62233i
$142$		0			0
$143$	−47.6080	−	47.6080i	−0.332923	−	0.332923i
$144$		0			0
$145$	−134.472	+	141.314i	−0.927394	+	0.974578i
$146$		0			0
$147$	20.3967	−	128.780i	0.138753	−	0.876051i
$148$		0			0
$149$		−	5.80459i		−	0.0389570i	−0.999810	−	0.0194785i	$-0.993799\pi$
$149$		−	5.80459i		−	0.0389570i	0.999810	−	0.0194785i	$-0.00620058\pi$
$150$		0			0
$151$	−28.1784			−0.186612			−0.0933059	−	0.995637i	$-0.529743\pi$
$151$	−28.1784			−0.186612			−0.0933059	+	0.995637i	$0.529743\pi$
$152$		0			0
$153$	−273.666	−	43.3444i	−1.78867	−	0.283297i
$154$		0			0
$155$	76.9207	−	160.698i	0.496263	−	1.03676i
$156$		0			0
$157$	−186.688	+	186.688i	−1.18910	+	1.18910i	−0.211778	+	0.977318i	$0.567925\pi$
$157$	−186.688	+	186.688i	−1.18910	+	1.18910i	−0.977318	+	0.211778i	$0.932075\pi$
$158$		0			0
$159$	207.887	+	67.5465i	1.30746	+	0.424821i
$160$		0			0
$161$	−49.1710	−	151.333i	−0.305410	−	0.939955i
$162$		0			0
$163$	−90.3109	+	46.0157i	−0.554054	+	0.282305i	−0.708517	−	0.705694i	$-0.750635\pi$
$163$	−90.3109	+	46.0157i	−0.554054	+	0.282305i	0.154462	+	0.987999i	$0.450635\pi$
$164$		0			0
$165$	76.3294	−	26.9114i	0.462603	−	0.163100i
$166$		0			0
$167$	−49.9612	+	7.91307i	−0.299169	+	0.0473837i	−0.304214	−	0.952604i	$-0.598394\pi$
$167$	−49.9612	+	7.91307i	−0.299169	+	0.0473837i	0.00504565	+	0.999987i	$0.498394\pi$
$168$		0			0
$169$	228.388	−	314.350i	1.35141	−	1.86006i
$170$		0			0
$171$	−21.4302	+	15.5699i	−0.125323	+	0.0910522i
$172$		0			0
$173$	82.8886	−	162.678i	0.479125	−	0.940335i	−0.517296	−	0.855806i	$-0.673061\pi$
$173$	82.8886	−	162.678i	0.479125	−	0.940335i	0.996421	−	0.0845288i	$-0.0269385\pi$
$174$		0			0
$175$	−52.2022	+	116.384i	−0.298298	+	0.665053i
$176$		0			0
$177$	−23.6862	−	12.0687i	−0.133820	−	0.0681849i
$178$		0			0
$179$	−156.233	−	215.036i	−0.872809	−	1.20132i	−0.978361	−	0.206905i	$-0.933661\pi$
$179$	−156.233	−	215.036i	−0.872809	−	1.20132i	0.105552	−	0.994414i	$-0.466339\pi$
$180$		0			0
$181$	16.6491	+	12.0963i	0.0919839	+	0.0668302i	0.632827	−	0.774294i	$-0.281895\pi$
$181$	16.6491	+	12.0963i	0.0919839	+	0.0668302i	−0.540843	+	0.841124i	$0.681895\pi$
$182$		0			0
$183$	−3.55876	−	22.4691i	−0.0194468	−	0.122782i
$184$		0			0
$185$	−150.269	+	114.977i	−0.812266	+	0.621498i
$186$		0			0
$187$	15.4416	+	30.3058i	0.0825753	+	0.162063i
$188$		0			0
$189$	−391.934	+	127.347i	−2.07372	+	0.673793i
$190$		0			0
$191$	65.7335	−	202.307i	0.344154	−	1.05920i	−0.617880	−	0.786272i	$-0.712008\pi$
$191$	65.7335	−	202.307i	0.344154	−	1.05920i	0.962035	−	0.272926i	$-0.0879916\pi$
$192$		0			0
$193$	179.125	+	179.125i	0.928109	+	0.928109i	0.997584	−	0.0694751i	$-0.0221324\pi$
$193$	179.125	+	179.125i	0.928109	+	0.928109i	−0.0694751	+	0.997584i	$0.522132\pi$
$194$		0			0
$195$	318.999	+	589.457i	1.63589	+	3.02285i
$196$		0			0
$197$	9.35053	−	59.0369i	0.0474646	−	0.299680i	−0.952524	−	0.304464i	$-0.901523\pi$
$197$	9.35053	−	59.0369i	0.0474646	−	0.299680i	0.999989	+	0.00478389i	$0.00152277\pi$
$198$		0			0
$199$		−	104.287i		−	0.524055i	−0.965060	−	0.262028i	$-0.915609\pi$
$199$		−	104.287i		−	0.524055i	0.965060	−	0.262028i	$-0.0843912\pi$
$200$		0			0
$201$	201.358			1.00178
$202$		0			0
$203$	−196.607	−	31.1395i	−0.968507	−	0.153396i
$204$		0			0
$205$	254.966	+	33.9242i	1.24374	+	0.165484i
$206$		0			0
$207$	512.222	−	512.222i	2.47450	−	2.47450i
$208$		0			0
$209$	3.09256	+	1.00483i	0.0147969	+	0.00480782i
$210$		0			0
$211$	45.9934	+	141.553i	0.217978	+	0.670868i	0.998929	+	0.0462753i	$0.0147351\pi$
$211$	45.9934	+	141.553i	0.217978	+	0.670868i	−0.780950	+	0.624593i	$0.785265\pi$
$212$		0			0
$213$	−21.9928	+	11.2059i	−0.103252	+	0.0526097i
$214$		0			0
$215$	−31.3533	+	45.4850i	−0.145829	+	0.211558i
$216$		0			0
$217$	179.563	−	28.4399i	0.827477	−	0.131059i
$218$		0			0
$219$	−61.9403	+	85.2535i	−0.282832	+	0.389285i
$220$		0			0
$221$	−227.876	+	165.561i	−1.03111	+	0.749147i
$222$		0			0
$223$	−170.790	+	335.194i	−0.765875	+	1.50311i	0.0956594	+	0.995414i	$0.469504\pi$
$223$	−170.790	+	335.194i	−0.765875	+	1.50311i	−0.861534	+	0.507700i	$0.830496\pi$
$224$		0			0
$225$	−579.977	+	28.7937i	−2.57768	+	0.127972i
$226$		0			0
$227$	226.994	+	115.659i	0.999973	+	0.509512i	0.875762	−	0.482744i	$-0.160360\pi$
$227$	226.994	+	115.659i	0.999973	+	0.509512i	0.124212	+	0.992256i	$0.460360\pi$
$228$		0			0
$229$	100.528	+	138.365i	0.438987	+	0.604214i	0.969987	−	0.243158i	$-0.0781834\pi$
$229$	100.528	+	138.365i	0.438987	+	0.604214i	−0.531000	+	0.847372i	$0.678183\pi$
$230$		0			0
$231$	66.8160	+	48.5446i	0.289247	+	0.210150i
$232$		0			0
$233$	−18.4276	−	116.347i	−0.0790883	−	0.499344i	−0.995155	−	0.0983181i	$-0.968654\pi$
$233$	−18.4276	−	116.347i	−0.0790883	−	0.499344i	0.916067	−	0.401026i	$-0.131346\pi$
$234$		0			0
$235$	−211.775	+	5.25370i	−0.901171	+	0.0223562i
$236$		0			0
$237$	215.825	+	423.581i	0.910656	+	1.78726i
$238$		0			0
$239$	−215.408	+	69.9902i	−0.901287	+	0.292846i	−0.722768	−	0.691091i	$-0.757131\pi$
$239$	−215.408	+	69.9902i	−0.901287	+	0.292846i	−0.178519	+	0.983936i	$0.557131\pi$
$240$		0			0
$241$	21.5879	−	66.4407i	0.0895763	−	0.275688i	−0.896226	−	0.443598i	$-0.853702\pi$
$241$	21.5879	−	66.4407i	0.0895763	−	0.275688i	0.985802	+	0.167910i	$0.0537019\pi$
$242$		0			0
$243$	−487.429	−	487.429i	−2.00588	−	2.00588i
$244$		0			0
$245$	112.943	−	20.7719i	0.460992	−	0.0847833i
$246$		0			0
$247$	−4.21250	+	26.5967i	−0.0170546	+	0.107679i
$248$		0			0
$249$		−	855.420i		−	3.43542i
$250$		0			0
$251$	422.980			1.68518			0.842589	−	0.538557i	$-0.181030\pi$
$251$	422.980			1.68518			0.842589	+	0.538557i	$0.181030\pi$
$252$		0			0
$253$	−87.8289	−	13.9107i	−0.347150	−	0.0549832i
$254$		0			0
$255$	−61.2454	−	333.009i	−0.240178	−	1.30592i
$256$		0			0
$257$	−76.5969	+	76.5969i	−0.298042	+	0.298042i	−0.840247	−	0.542204i	$-0.817590\pi$
$257$	−76.5969	+	76.5969i	−0.298042	+	0.298042i	0.542204	+	0.840247i	$0.317590\pi$
$258$		0			0
$259$	−183.628	−	59.6644i	−0.708990	−	0.230365i
$260$		0			0
$261$	−280.032	−	861.851i	−1.07292	−	3.30211i
$262$		0			0
$263$	−321.922	+	164.027i	−1.22404	+	0.623678i	−0.941964	−	0.335715i	$-0.891022\pi$
$263$	−321.922	+	164.027i	−1.22404	+	0.623678i	−0.282073	+	0.959393i	$0.591022\pi$
$264$		0			0
$265$	4.77455	+	192.461i	0.0180172	+	0.726268i
$266$		0			0
$267$	603.168	−	95.5325i	2.25906	−	0.357800i
$268$		0			0
$269$	4.51084	−	6.20864i	0.0167689	−	0.0230805i	−0.800550	−	0.599266i	$-0.795459\pi$
$269$	4.51084	−	6.20864i	0.0167689	−	0.0230805i	0.817319	+	0.576185i	$0.195459\pi$
$270$		0			0
$271$	373.379	−	271.276i	1.37778	−	1.00102i	0.380699	−	0.924699i	$-0.375684\pi$
$271$	373.379	−	271.276i	1.37778	−	1.00102i	0.997084	−	0.0763181i	$-0.0243165\pi$
$272$		0			0
$273$	−310.502	+	609.394i	−1.13737	+	2.23221i
$274$		0			0
$275$	44.7075	+	55.5211i	0.162573	+	0.201895i
$276$		0			0
$277$	134.744	+	68.6553i	0.486439	+	0.247853i	0.679968	−	0.733241i	$-0.261993\pi$
$277$	134.744	+	68.6553i	0.486439	+	0.247853i	−0.193529	+	0.981094i	$0.561993\pi$
$278$		0			0
$279$	486.476	+	669.577i	1.74364	+	2.39992i
$280$		0			0
$281$	113.237	+	82.2714i	0.402978	+	0.292781i	0.770753	−	0.637134i	$-0.219880\pi$
$281$	113.237	+	82.2714i	0.402978	+	0.292781i	−0.367775	+	0.929915i	$0.619880\pi$
$282$		0			0
$283$	−71.1130	−	448.990i	−0.251283	−	1.58654i	−0.714075	−	0.700069i	$-0.753153\pi$
$283$	−71.1130	−	448.990i	−0.251283	−	1.58654i	0.462793	−	0.886467i	$-0.346847\pi$
$284$		0			0
$285$	−26.6519	−	18.3715i	−0.0935156	−	0.0644613i
$286$		0			0
$287$	119.159	+	233.864i	0.415190	+	0.814856i
$288$		0			0
$289$	−139.524	+	45.3342i	−0.482783	+	0.156866i
$290$		0			0
$291$	−147.135	+	452.834i	−0.505618	+	1.55613i
$292$		0			0
$293$	−45.8619	−	45.8619i	−0.156525	−	0.156525i	0.624500	−	0.781025i	$-0.285303\pi$
$293$	−45.8619	−	45.8619i	−0.156525	−	0.156525i	−0.781025	+	0.624500i	$0.785303\pi$
$294$		0			0
$295$	3.08807	−	23.2092i	0.0104680	−	0.0786752i
$296$		0			0
$297$	−36.0271	+	227.466i	−0.121304	+	0.765880i
$298$		0			0
$299$		−	736.398i		−	2.46287i
$300$		0			0
$301$	−56.3735			−0.187287
$302$		0			0
$303$	126.629	+	20.0560i	0.417917	+	0.0661916i
$304$		0			0
$305$	17.6216	−	9.53633i	0.0577756	−	0.0312667i
$306$		0			0
$307$	−328.045	+	328.045i	−1.06855	+	1.06855i	−0.0710783	+	0.997471i	$0.522644\pi$
$307$	−328.045	+	328.045i	−1.06855	+	1.06855i	−0.997471	+	0.0710783i	$0.977356\pi$
$308$		0			0
$309$	−305.967	−	99.4146i	−0.990184	−	0.321730i
$310$		0			0
$311$	−88.0879	−	271.107i	−0.283241	−	0.871726i	−0.986920	−	0.161208i	$-0.948461\pi$
$311$	−88.0879	−	271.107i	−0.283241	−	0.871726i	0.703679	−	0.710518i	$-0.251539\pi$
$312$		0			0
$313$	143.583	−	73.1592i	0.458732	−	0.233736i	−0.209324	−	0.977846i	$-0.567126\pi$
$313$	143.583	−	73.1592i	0.458732	−	0.233736i	0.668056	+	0.744111i	$0.267126\pi$
$314$		0			0
$315$	−360.081	−	470.607i	−1.14311	−	1.49399i
$316$		0			0
$317$	−321.892	+	50.9826i	−1.01543	+	0.160828i	−0.641899	−	0.766789i	$-0.721853\pi$
$317$	−321.892	+	50.9826i	−1.01543	+	0.160828i	−0.373532	+	0.927617i	$0.621853\pi$
$318$		0			0
$319$	−65.3866	+	89.9970i	−0.204974	+	0.282122i
$320$		0			0
$321$	225.139	−	163.573i	0.701369	−	0.509574i
$322$		0			0
$323$	6.17596	−	12.1210i	0.0191206	−	0.0375263i
$324$		0			0
$325$	−396.206	+	437.601i	−1.21909	+	1.34646i
$326$		0			0
$327$	−766.519	−	390.561i	−2.34409	−	1.19438i
$328$		0			0
$329$	−127.062	−	174.886i	−0.386207	−	0.531568i
$330$		0			0
$331$	59.2894	+	43.0762i	0.179122	+	0.130140i	0.673733	−	0.738975i	$-0.264690\pi$
$331$	59.2894	+	43.0762i	0.179122	+	0.130140i	−0.494611	+	0.869114i	$0.664690\pi$
$332$		0			0
$333$	−137.503	−	868.161i	−0.412922	−	2.60709i
$334$		0			0
$335$	58.9696	+	167.257i	0.176029	+	0.499273i
$336$		0			0
$337$	−195.911	−	384.497i	−0.581339	−	1.14094i	−0.975108	−	0.221732i	$-0.928829\pi$
$337$	−195.911	−	384.497i	−0.581339	−	1.14094i	0.393769	−	0.919210i	$-0.371171\pi$
$338$		0			0
$339$	−323.078	+	104.974i	−0.953032	+	0.309659i
$340$		0			0
$341$	31.3956	−	96.6259i	0.0920693	−	0.283360i
$342$		0			0
$343$	259.645	+	259.645i	0.756982	+	0.756982i
$344$		0			0
$345$	798.463	+	382.198i	2.31439	+	1.10782i
$346$		0			0
$347$	13.0574	−	82.4412i	0.0376294	−	0.237583i	−0.961704	−	0.274090i	$-0.911623\pi$
$347$	13.0574	−	82.4412i	0.0376294	−	0.237583i	0.999333	+	0.0365075i	$0.0116233\pi$
$348$		0			0
$349$			61.3926i			0.175910i	0.996124	+	0.0879550i	$0.0280332\pi$
$349$			61.3926i			0.175910i	−0.996124	+	0.0879550i	$0.971967\pi$
$350$		0			0
$351$	−1907.18			−5.43357
$352$		0			0
$353$	530.943	+	84.0932i	1.50409	+	0.238224i	0.853455	−	0.521167i	$-0.174503\pi$
$353$	530.943	+	84.0932i	1.50409	+	0.238224i	0.650634	+	0.759391i	$0.274503\pi$
$354$		0			0
$355$	−15.7488	−	14.9864i	−0.0443629	−	0.0422151i
$356$		0			0
$357$	244.317	−	244.317i	0.684361	−	0.684361i
$358$		0			0
$359$	120.114	+	39.0273i	0.334579	+	0.108711i	0.471488	−	0.881872i	$-0.343717\pi$
$359$	120.114	+	39.0273i	0.334579	+	0.108711i	−0.136910	+	0.990584i	$0.543717\pi$
$360$		0			0
$361$	111.153	+	342.095i	0.307904	+	0.947630i
$362$		0			0
$363$	−570.917	+	290.897i	−1.57277	+	0.801369i
$364$		0			0
$365$	−88.9549	−	26.4829i	−0.243712	−	0.0725560i
$366$		0			0
$367$	413.727	−	65.5280i	1.12732	−	0.178550i	0.435202	−	0.900333i	$-0.356677\pi$
$367$	413.727	−	65.5280i	1.12732	−	0.178550i	0.692120	+	0.721782i	$0.256677\pi$
$368$		0			0
$369$	−702.340	+	966.688i	−1.90336	+	2.61975i
$370$		0			0
$371$	−158.936	+	115.474i	−0.428399	+	0.311250i
$372$		0			0
$373$	205.218	−	402.763i	0.550182	−	1.07979i	−0.433714	−	0.901051i	$-0.642797\pi$
$373$	205.218	−	402.763i	0.550182	−	1.07979i	0.983896	−	0.178742i	$-0.0572028\pi$
$374$		0			0
$375$	−268.848	−	656.717i	−0.716928	−	1.75125i
$376$		0			0
$377$	−820.817	−	418.227i	−2.17723	−	1.10936i
$378$		0			0
$379$	411.506	+	566.389i	1.08577	+	1.49443i	0.853010	+	0.521895i	$0.174775\pi$
$379$	411.506	+	566.389i	1.08577	+	1.49443i	0.232758	+	0.972535i	$0.425225\pi$
$380$		0			0
$381$	471.780	+	342.768i	1.23827	+	0.899654i
$382$		0			0
$383$	2.64601	+	16.7062i	0.00690863	+	0.0436194i	0.990902	−	0.134587i	$-0.0429707\pi$
$383$	2.64601	+	16.7062i	0.00690863	+	0.0436194i	−0.983993	+	0.178206i	$0.942971\pi$
$384$		0			0
$385$	−20.7555	+	69.7168i	−0.0539105	+	0.181083i
$386$		0			0
$387$	−116.511	−	228.667i	−0.301063	−	0.590870i
$388$		0			0
$389$	−75.7317	+	24.6067i	−0.194683	+	0.0632563i	−0.404736	−	0.914434i	$-0.632636\pi$
$389$	−75.7317	+	24.6067i	−0.194683	+	0.0632563i	0.210053	+	0.977690i	$0.432636\pi$
$390$		0			0
$391$	−114.960	+	353.810i	−0.294015	+	0.904884i
$392$		0			0
$393$	498.476	+	498.476i	1.26839	+	1.26839i
$394$		0			0
$395$	−288.638	+	303.323i	−0.730729	+	0.767907i
$396$		0			0
$397$	−15.5627	+	98.2590i	−0.0392007	+	0.247504i	−0.999505	−	0.0314498i	$-0.989988\pi$
$397$	−15.5627	+	98.2590i	−0.0392007	+	0.247504i	0.960305	+	0.278954i	$0.0899876\pi$
$398$		0			0
$399$		−	33.0320i		−	0.0827870i
$400$		0			0
$401$	481.359			1.20040			0.600199	−	0.799851i	$-0.295088\pi$
$401$	481.359			1.20040			0.600199	+	0.799851i	$0.295088\pi$
$402$		0			0
$403$	831.002	+	131.618i	2.06204	+	0.326595i
$404$		0			0
$405$	538.559	−	1125.12i	1.32978	−	2.77808i
$406$		0			0
$407$	−76.2974	+	76.2974i	−0.187463	+	0.187463i
$408$		0			0
$409$	476.944	+	154.968i	1.16612	+	0.378896i	0.827194	−	0.561917i	$-0.189936\pi$
$409$	476.944	+	154.968i	1.16612	+	0.378896i	0.338927	+	0.940813i	$0.389936\pi$
$410$		0			0
$411$	432.577	+	1331.33i	1.05250	+	3.23925i
$412$		0			0
$413$	21.2882	−	10.8469i	0.0515454	−	0.0262637i
$414$		0			0
$415$	710.547	−	250.517i	1.71216	−	0.603656i
$416$		0			0
$417$	282.297	−	44.7115i	0.676972	−	0.107222i
$418$		0			0
$419$	208.201	−	286.565i	0.496901	−	0.683925i	−0.484741	−	0.874658i	$-0.661086\pi$
$419$	208.201	−	286.565i	0.496901	−	0.683925i	0.981642	+	0.190732i	$0.0610863\pi$
$420$		0			0
$421$	−92.2847	+	67.0487i	−0.219203	+	0.159261i	−0.691968	−	0.721928i	$-0.743256\pi$
$421$	−92.2847	+	67.0487i	−0.219203	+	0.159261i	0.472765	+	0.881189i	$0.343256\pi$
$422$		0			0
$423$	446.777	−	876.850i	1.05621	−	2.07293i
$424$		0			0
$425$	258.675	−	148.398i	0.608647	−	0.349171i
$426$		0			0
$427$	18.2176	+	9.28233i	0.0426642	+	0.0217385i
$428$		0			0
$429$	224.661	+	309.219i	0.523685	+	0.720791i
$430$		0			0
$431$	121.831	+	88.5158i	0.282672	+	0.205373i	0.720082	−	0.693889i	$-0.244104\pi$
$431$	121.831	+	88.5158i	0.282672	+	0.205373i	−0.437410	+	0.899262i	$0.644104\pi$
$432$		0			0
$433$	−47.3574	−	299.003i	−0.109370	−	0.690538i	−0.980060	−	0.198704i	$-0.936327\pi$
$433$	−47.3574	−	299.003i	−0.109370	−	0.690538i	0.870689	−	0.491834i	$-0.163673\pi$
$434$		0			0
$435$	879.488	−	672.933i	2.02181	−	1.54697i
$436$		0			0
$437$	16.1465	+	31.6892i	0.0369484	+	0.0725153i
$438$		0			0
$439$	89.8304	−	29.1877i	0.204625	−	0.0664867i	−0.204911	−	0.978781i	$-0.565691\pi$
$439$	89.8304	−	29.1877i	0.204625	−	0.0664867i	0.409536	+	0.912294i	$0.365691\pi$
$440$		0			0
$441$	−164.854	+	507.369i	−0.373819	+	1.15050i
$442$		0			0
$443$	228.066	+	228.066i	0.514822	+	0.514822i	0.916000	−	0.401178i	$-0.131399\pi$
$443$	228.066	+	228.066i	0.514822	+	0.514822i	−0.401178	+	0.916000i	$0.631399\pi$
$444$		0			0
$445$	255.996	+	473.039i	0.575273	+	1.06301i
$446$		0			0
$447$	−5.15487	+	32.5466i	−0.0115322	+	0.0728112i
$448$		0			0
$449$		−	307.931i		−	0.685816i	−0.939369	−	0.342908i	$-0.888588\pi$
$449$		−	307.931i		−	0.685816i	0.939369	−	0.342908i	$-0.111412\pi$
$450$		0			0
$451$	146.681			0.325234
$452$		0			0
$453$	157.998	+	25.0244i	0.348780	+	0.0552414i
$454$		0			0
$455$	−597.121	−	79.4493i	−1.31235	−	0.174614i
$456$		0			0
$457$	−4.84146	+	4.84146i	−0.0105940	+	0.0105940i	−0.712384	−	0.701790i	$-0.752385\pi$
$457$	−4.84146	+	4.84146i	−0.0105940	+	0.0105940i	0.701790	+	0.712384i	$0.252385\pi$
$458$		0			0
$459$	916.325	+	297.732i	1.99635	+	0.648654i
$460$		0			0
$461$	0.492459	+	1.51563i	0.00106824	+	0.00328770i	0.951589	−	0.307373i	$-0.0994498\pi$
$461$	0.492459	+	1.51563i	0.00106824	+	0.00328770i	−0.950521	+	0.310660i	$0.899450\pi$
$462$		0			0
$463$	514.654	−	262.229i	1.11156	−	0.566369i	0.200938	−	0.979604i	$-0.435601\pi$
$463$	514.654	−	262.229i	1.11156	−	0.566369i	0.910625	+	0.413234i	$0.135601\pi$
$464$		0			0
$465$	−574.009	+	832.729i	−1.23443	+	1.79082i
$466$		0			0
$467$	278.647	−	44.1334i	0.596675	−	0.0945041i	0.149210	−	0.988805i	$-0.452327\pi$
$467$	278.647	−	44.1334i	0.596675	−	0.0945041i	0.447465	+	0.894301i	$0.352327\pi$
$468$		0			0
$469$	−106.373	+	146.410i	−0.226809	+	0.312175i
$470$		0			0
$471$	1212.56	−	880.977i	2.57444	−	1.87044i
$472$		0			0
$473$	−14.3025	+	28.0703i	−0.0302379	+	0.0593452i
$474$		0			0
$475$	7.45484	−	27.5184i	0.0156944	−	0.0579336i
$476$		0			0
$477$	−796.879	−	406.030i	−1.67061	−	0.851216i
$478$		0			0
$479$	−108.466	−	149.291i	−0.226443	−	0.311673i	0.680644	−	0.732614i	$-0.261700\pi$
$479$	−108.466	−	149.291i	−0.226443	−	0.311673i	−0.907088	+	0.420941i	$0.861700\pi$
$480$		0			0
$481$	−722.898	−	525.216i	−1.50291	−	1.09193i
$482$		0			0
$483$	141.310	+	892.197i	0.292568	+	1.84720i
$484$		0			0
$485$	−419.233	+	10.4003i	−0.864397	+	0.0214439i
$486$		0			0
$487$	−138.654	−	272.124i	−0.284711	−	0.558776i	0.703715	−	0.710482i	$-0.251523\pi$
$487$	−138.654	−	272.124i	−0.284711	−	0.558776i	−0.988426	+	0.151706i	$0.951523\pi$
$488$		0			0
$489$	547.243	−	177.810i	1.11911	−	0.363619i
$490$		0			0
$491$	94.1503	−	289.765i	0.191752	−	0.590152i	−0.808247	−	0.588843i	$-0.799583\pi$
$491$	94.1503	−	289.765i	0.191752	−	0.590152i	0.999999	−	0.00130868i	$-0.000416567\pi$
$492$		0			0
$493$	329.080	+	329.080i	0.667505	+	0.667505i
$494$		0			0
$495$	−325.688	+	59.8989i	−0.657955	+	0.121008i
$496$		0			0
$497$	3.47037	−	21.9110i	0.00698263	−	0.0440866i
$498$		0			0
$499$			194.528i			0.389836i	0.980820	+	0.194918i	$0.0624440\pi$
$499$			194.528i			0.389836i	−0.980820	+	0.194918i	$0.937556\pi$
$500$		0			0
$501$	287.162			0.573178
$502$		0			0
$503$	472.931	+	74.9049i	0.940220	+	0.148916i	0.607688	−	0.794176i	$-0.292097\pi$
$503$	472.931	+	74.9049i	0.940220	+	0.148916i	0.332532	+	0.943092i	$0.392097\pi$
$504$		0			0
$505$	20.4250	+	111.057i	0.0404456	+	0.219914i
$506$		0			0
$507$	−1559.75	+	1559.75i	−3.07643	+	3.07643i
$508$		0			0
$509$	0.377035	+	0.122506i	0.000740737	+	0.000240680i	0.309387	−	0.950936i	$-0.399876\pi$
$509$	0.377035	+	0.122506i	0.000740737	+	0.000240680i	−0.308647	+	0.951177i	$0.599876\pi$
$510$		0			0
$511$	−29.2672	−	90.0752i	−0.0572744	−	0.176272i
$512$		0			0
$513$	82.0712	−	41.8174i	0.159983	−	0.0815153i
$514$		0			0
$515$	−7.02716	−	283.263i	−0.0136450	−	0.550026i
$516$		0			0
$517$	−119.319	+	18.8982i	−0.230791	+	0.0365536i
$518$		0			0
$519$	−609.230	+	838.533i	−1.17385	+	1.61567i
$520$		0			0
$521$	124.355	−	90.3495i	0.238686	−	0.173416i	−0.462012	−	0.886874i	$-0.652872\pi$
$521$	124.355	−	90.3495i	0.238686	−	0.173416i	0.700698	+	0.713458i	$0.252872\pi$
$522$		0			0
$523$	−98.6677	+	193.646i	−0.188657	+	0.370261i	−0.965890	−	0.258952i	$-0.916623\pi$
$523$	−98.6677	+	193.646i	−0.188657	+	0.370261i	0.777233	+	0.629213i	$0.216623\pi$
$524$		0			0
$525$	396.057	−	606.213i	0.754395	−	1.15469i
$526$		0			0
$527$	−378.716	−	192.965i	−0.718626	−	0.366158i
$528$		0			0
$529$	−260.744	−	358.883i	−0.492899	−	0.678418i
$530$		0			0
$531$	87.9961	+	63.9329i	0.165718	+	0.120401i
$532$		0			0
$533$	190.021	+	1199.74i	0.356511	+	2.25092i
$534$		0			0
$535$	201.805	+	139.106i	0.377205	+	0.260012i
$536$		0			0
$537$	685.038	+	1344.46i	1.27568	+	2.50365i
$538$		0			0
$539$	62.2829	−	20.2369i	0.115553	−	0.0375453i
$540$		0			0
$541$	120.466	−	370.755i	0.222672	−	0.685314i	−0.775847	−	0.630921i	$-0.782677\pi$
$541$	120.466	−	370.755i	0.222672	−	0.685314i	0.998520	−	0.0543938i	$-0.0173226\pi$
$542$		0			0
$543$	−82.6099	−	82.6099i	−0.152136	−	0.152136i
$544$		0			0
$545$	99.9342	−	751.081i	0.183366	−	1.37813i
$546$		0			0
$547$	−49.6266	+	313.330i	−0.0907251	+	0.572816i	0.899888	+	0.436121i	$0.143648\pi$
$547$	−49.6266	+	313.330i	−0.0907251	+	0.572816i	−0.990613	+	0.136695i	$0.956352\pi$
$548$		0			0
$549$			93.0802i			0.169545i
$550$		0			0
$551$	44.4921			0.0807479
$552$		0			0
$553$	−422.007	−	66.8394i	−0.763124	−	0.120867i
$554$		0			0
$555$	944.674	−	511.233i	1.70212	−	0.921140i
$556$		0			0
$557$	−164.486	+	164.486i	−0.295307	+	0.295307i	−0.839172	−	0.543866i	$-0.816960\pi$
$557$	−164.486	+	164.486i	−0.295307	+	0.295307i	0.543866	+	0.839172i	$0.316960\pi$
$558$		0			0
$559$	−248.123	−	80.6201i	−0.443870	−	0.144222i
$560$		0			0
$561$	−59.6681	−	183.639i	−0.106360	−	0.327343i
$562$		0			0
$563$	−899.777	+	458.459i	−1.59818	+	0.814315i	−0.598267	+	0.801296i	$0.704144\pi$
$563$	−899.777	+	458.459i	−1.59818	+	0.814315i	−0.999915	+	0.0130183i	$0.995856\pi$
$564$		0			0
$565$	−181.812	−	237.619i	−0.321792	−	0.420565i
$566$		0			0
$567$	1257.20	−	199.121i	2.21729	−	0.351184i
$568$		0			0
$569$	10.0497	−	13.8322i	0.0176621	−	0.0243097i	−0.800095	−	0.599874i	$-0.795217\pi$
$569$	10.0497	−	13.8322i	0.0176621	−	0.0243097i	0.817757	+	0.575564i	$0.195217\pi$
$570$		0			0
$571$	597.683	−	434.242i	1.04673	−	0.760495i	0.0751430	−	0.997173i	$-0.476059\pi$
$571$	597.683	−	434.242i	1.04673	−	0.760495i	0.971588	+	0.236678i	$0.0760587\pi$
$572$		0			0
$573$	−548.233	+	1075.97i	−0.956777	+	1.87778i
$574$		0			0
$575$	−83.6325	+	775.166i	−0.145448	+	1.34812i
$576$		0			0
$577$	−230.489	−	117.440i	−0.399461	−	0.203536i	0.242707	−	0.970100i	$-0.421965\pi$
$577$	−230.489	−	117.440i	−0.399461	−	0.203536i	−0.642168	+	0.766564i	$0.721965\pi$
$578$		0			0
$579$	−845.287	−	1163.44i	−1.45991	−	2.00939i
$580$		0			0
$581$	621.987	+	451.900i	1.07054	+	0.777796i
$582$		0			0
$583$	17.1747	+	108.437i	0.0294591	+	0.185998i
$584$		0			0
$585$	−911.849	−	2586.30i	−1.55872	−	4.42102i
$586$		0			0
$587$	−376.054	−	738.047i	−0.640636	−	1.25732i	−0.951729	−	0.306940i	$-0.900695\pi$
$587$	−376.054	−	738.047i	−0.640636	−	1.25732i	0.311093	−	0.950380i	$-0.399305\pi$
$588$		0			0
$589$	−38.6461	+	12.5569i	−0.0656131	+	0.0213190i
$590$		0			0
$591$	−104.858	+	322.719i	−0.177424	+	0.546056i
$592$		0			0
$593$	−103.236	−	103.236i	−0.174092	−	0.174092i	0.614683	−	0.788774i	$-0.289284\pi$
$593$	−103.236	−	103.236i	−0.174092	−	0.174092i	−0.788774	+	0.614683i	$0.789284\pi$
$594$		0			0
$595$	274.490	+	131.389i	0.461328	+	0.220822i
$596$		0			0
$597$	−92.6141	+	584.742i	−0.155132	+	0.979468i
$598$		0			0
$599$		−	272.933i		−	0.455648i	−0.973702	−	0.227824i	$-0.926839\pi$
$599$		−	272.933i		−	0.455648i	0.973702	−	0.227824i	$-0.0731610\pi$
$600$		0			0
$601$	−389.161			−0.647522			−0.323761	−	0.946139i	$-0.604947\pi$
$601$	−389.161			−0.647522			−0.323761	+	0.946139i	$0.604947\pi$
$602$		0			0
$603$	−813.730	−	128.882i	−1.34947	−	0.213735i
$604$		0			0
$605$	−408.829	−	389.036i	−0.675750	−	0.643034i
$606$		0			0
$607$	800.589	−	800.589i	1.31893	−	1.31893i	0.404303	−	0.914625i	$-0.367514\pi$
$607$	800.589	−	800.589i	1.31893	−	1.31893i	0.914625	−	0.404303i	$-0.132486\pi$
$608$		0			0
$609$	1074.73	+	349.201i	1.76475	+	0.573401i
$610$		0			0
$611$	−309.148	−	951.459i	−0.505970	−	1.55722i
$612$		0			0
$613$	660.013	−	336.294i	1.07669	−	0.548603i	0.176593	−	0.984284i	$-0.443492\pi$
$613$	660.013	−	336.294i	1.07669	−	0.548603i	0.900101	+	0.435681i	$0.143492\pi$
$614$		0			0
$615$	−1399.48	−	416.642i	−2.27558	−	0.677467i
$616$		0			0
$617$	−478.466	+	75.7815i	−0.775471	+	0.122823i	−0.531612	−	0.846988i	$-0.678413\pi$
$617$	−478.466	+	75.7815i	−0.775471	+	0.122823i	−0.243859	+	0.969811i	$0.578413\pi$
$618$		0			0
$619$	−164.009	+	225.740i	−0.264959	+	0.364684i	−0.920680	−	0.390319i	$-0.872365\pi$
$619$	−164.009	+	225.740i	−0.264959	+	0.364684i	0.655721	+	0.755003i	$0.272365\pi$
$620$		0			0
$621$	−2037.86	+	1480.59i	−3.28157	+	2.38420i
$622$		0			0
$623$	−249.178	+	489.039i	−0.399965	+	0.784975i
$624$		0			0
$625$	466.762	−	415.642i	0.746819	−	0.665027i
$626$		0			0
$627$	−16.4478	−	8.38056i	−0.0262325	−	0.0133661i
$628$		0			0
$629$	265.332	+	365.198i	0.421831	+	0.580600i
$630$		0			0
$631$	−119.420	−	86.7635i	−0.189255	−	0.137502i	0.489123	−	0.872215i	$-0.337317\pi$
$631$	−119.420	−	86.7635i	−0.189255	−	0.137502i	−0.678378	+	0.734713i	$0.737317\pi$
$632$		0			0
$633$	−132.178	−	834.541i	−0.208813	−	1.31839i
$634$		0			0
$635$	−146.552	+	492.262i	−0.230791	+	0.775216i
$636$		0			0
$637$	246.209	+	483.213i	0.386514	+	0.758576i
$638$		0			0
$639$	96.0498	−	31.2085i	0.150313	−	0.0488395i
$640$		0			0
$641$	−203.571	+	626.527i	−0.317583	+	0.977421i	0.657095	+	0.753808i	$0.271785\pi$
$641$	−203.571	+	626.527i	−0.317583	+	0.977421i	−0.974678	+	0.223613i	$0.928215\pi$
$642$		0			0
$643$	314.726	+	314.726i	0.489465	+	0.489465i	0.908137	−	0.418672i	$-0.137504\pi$
$643$	314.726	+	314.726i	0.489465	+	0.489465i	−0.418672	+	0.908137i	$0.637504\pi$
$644$		0			0
$645$	216.193	−	227.193i	0.335183	−	0.352237i
$646$		0			0
$647$	−156.034	+	985.160i	−0.241165	+	1.52266i	0.508628	+	0.860987i	$0.330153\pi$
$647$	−156.034	+	985.160i	−0.241165	+	1.52266i	−0.749793	+	0.661672i	$0.769847\pi$
$648$		0			0
$649$		−	13.3521i		−	0.0205734i
$650$		0			0
$651$	−1032.07			−1.58536
$652$		0			0
$653$	181.014	+	28.6699i	0.277204	+	0.0439049i	0.293489	−	0.955963i	$-0.405184\pi$
$653$	181.014	+	28.6699i	0.277204	+	0.0439049i	−0.0162843	+	0.999867i	$0.505184\pi$
$654$		0			0
$655$	−268.072	+	560.038i	−0.409270	+	0.855020i
$656$		0			0
$657$	304.881	−	304.881i	0.464051	−	0.464051i
$658$		0			0
$659$	−104.192	−	33.8539i	−0.158105	−	0.0513716i	0.228895	−	0.973451i	$-0.426489\pi$
$659$	−104.192	−	33.8539i	−0.158105	−	0.0513716i	−0.387000	+	0.922080i	$0.626489\pi$
$660$		0			0
$661$	−344.449	−	1060.11i	−0.521103	−	1.60379i	−0.771895	−	0.635750i	$-0.780691\pi$
$661$	−344.449	−	1060.11i	−0.521103	−	1.60379i	0.250792	−	0.968041i	$-0.419309\pi$
$662$		0			0
$663$	1424.74	−	725.941i	2.14893	−	1.09493i
$664$		0			0
$665$	27.4378	−	9.67372i	0.0412598	−	0.0145469i
$666$		0			0
$667$	−1201.73	+	190.336i	−1.80170	+	0.285361i
$668$		0			0
$669$	1255.30	−	1727.78i	1.87639	−	2.58263i
$670$		0			0
$671$	9.24398	−	6.71615i	0.0137764	−	0.0100092i
$672$		0			0
$673$	−470.131	+	922.683i	−0.698559	+	1.37100i	0.219915	+	0.975519i	$0.429422\pi$
$673$	−470.131	+	922.683i	−0.698559	+	1.37100i	−0.918474	+	0.395481i	$0.870578\pi$
$674$		0			0
$675$	2007.59	+	216.598i	2.97420	+	0.320886i
$676$		0			0
$677$	−384.833	−	196.082i	−0.568439	−	0.289634i	0.146054	−	0.989277i	$-0.453343\pi$
$677$	−384.833	−	196.082i	−0.568439	−	0.289634i	−0.714493	+	0.699642i	$0.753343\pi$
$678$		0			0
$679$	−251.533	−	346.206i	−0.370447	−	0.509876i
$680$		0			0
$681$	−1170.05	−	850.093i	−1.71814	−	1.24830i
$682$		0			0
$683$	−113.277	−	715.203i	−0.165852	−	1.04715i	−0.920421	−	0.390928i	$-0.872154\pi$
$683$	−113.277	−	715.203i	−0.165852	−	1.04715i	0.754569	−	0.656221i	$-0.227846\pi$
$684$		0			0
$685$	−979.177	+	749.209i	−1.42946	+	1.09374i
$686$		0			0
$687$	−440.788	−	865.095i	−0.641613	−	1.25924i
$688$		0			0
$689$	−864.684	+	280.953i	−1.25498	+	0.407769i
$690$		0			0
$691$	−108.325	+	333.392i	−0.156766	+	0.482477i	−0.998336	−	0.0576722i	$-0.981632\pi$
$691$	−108.325	+	333.392i	−0.156766	+	0.482477i	0.841569	+	0.540149i	$0.181632\pi$
$692$		0			0
$693$	−238.945	−	238.945i	−0.344798	−	0.344798i
$694$		0			0
$695$	119.813	+	221.394i	0.172392	+	0.318552i
$696$		0			0
$697$	95.9956	−	606.092i	0.137727	−	0.869573i
$698$		0			0
$699$			668.729i			0.956694i
$700$		0			0
$701$	1060.87			1.51337			0.756683	−	0.653781i	$-0.226818\pi$
$701$	1060.87			1.51337			0.756683	+	0.653781i	$0.226818\pi$
$702$		0			0
$703$	42.6243	+	6.75102i	0.0606320	+	0.00960316i
$704$		0			0
$705$	1192.10	+	158.613i	1.69092	+	0.224984i
$706$		0			0
$707$	−81.4783	+	81.4783i	−0.115245	+	0.115245i
$708$		0			0
$709$	288.942	+	93.8829i	0.407534	+	0.132416i	0.505608	−	0.862763i	$-0.331268\pi$
$709$	288.942	+	93.8829i	0.407534	+	0.132416i	−0.0980738	+	0.995179i	$0.531268\pi$
$710$		0			0
$711$	−601.076	−	1849.92i	−0.845395	−	2.60186i
$712$		0			0
$713$	990.116	−	504.489i	1.38866	−	0.707559i
$714$		0			0
$715$	−191.056	+	277.170i	−0.267212	+	0.387651i
$716$		0			0
$717$	1269.96	−	201.141i	1.77121	−	0.280532i
$718$		0			0
$719$	376.006	−	517.527i	0.522956	−	0.719787i	−0.463080	−	0.886316i	$-0.653256\pi$
$719$	376.006	−	517.527i	0.522956	−	0.719787i	0.986037	+	0.166529i	$0.0532559\pi$
$720$		0			0
$721$	233.921	−	169.954i	0.324440	−	0.235719i
$722$		0			0
$723$	−180.048	+	353.365i	−0.249029	+	0.488748i
$724$		0			0
$725$	816.531	+	533.465i	1.12625	+	0.735814i
$726$		0			0
$727$	−793.518	−	404.318i	−1.09150	−	0.556145i	−0.186885	−	0.982382i	$-0.559839\pi$
$727$	−793.518	−	404.318i	−1.09150	−	0.556145i	−0.904612	+	0.426237i	$0.859839\pi$
$728$		0			0
$729$	980.429	+	1349.44i	1.34490	+	1.85109i
$730$		0			0
$731$	106.628	+	77.4695i	0.145865	+	0.105977i
$732$		0			0
$733$	139.834	+	882.880i	0.190770	+	1.20447i	0.878225	+	0.478247i	$0.158728\pi$
$733$	139.834	+	882.880i	0.190770	+	1.20447i	−0.687455	+	0.726227i	$0.741272\pi$
$734$		0			0
$735$	−651.724	+	16.1679i	−0.886699	+	0.0219971i
$736$		0			0
$737$	45.9147	+	90.1127i	0.0622995	+	0.122270i
$738$		0			0
$739$	676.181	−	219.704i	0.914994	−	0.297300i	0.186583	−	0.982439i	$-0.440259\pi$
$739$	676.181	−	219.704i	0.914994	−	0.297300i	0.728412	+	0.685140i	$0.240259\pi$
$740$		0			0
$741$	47.2393	−	145.388i	0.0637508	−	0.196205i
$742$		0			0
$743$	−558.124	−	558.124i	−0.751176	−	0.751176i	0.223523	−	0.974699i	$-0.428244\pi$
$743$	−558.124	−	558.124i	−0.751176	−	0.751176i	−0.974699	+	0.223523i	$0.928244\pi$
$744$		0			0
$745$	−28.5442	+	5.24970i	−0.0383144	+	0.00704658i
$746$		0			0
$747$	−547.524	+	3456.93i	−0.732963	+	4.62775i
$748$		0			0
$749$			250.114i			0.333930i
$750$		0			0
$751$	−1208.38			−1.60903			−0.804514	−	0.593933i	$-0.797574\pi$
$751$	−1208.38			−1.60903			−0.804514	+	0.593933i	$0.797574\pi$
$752$		0			0
$753$	−2371.67	−	375.635i	−3.14962	−	0.498852i
$754$		0			0
$755$	25.4847	+	138.568i	0.0337546	+	0.183534i
$756$		0			0
$757$	358.715	−	358.715i	0.473864	−	0.473864i	−0.429298	−	0.903163i	$-0.641239\pi$
$757$	358.715	−	358.715i	0.473864	−	0.473864i	0.903163	+	0.429298i	$0.141239\pi$
$758$		0			0
$759$	480.107	+	155.996i	0.632553	+	0.205529i
$760$		0			0
$761$	−34.4242	−	105.947i	−0.0452355	−	0.139221i	0.925888	−	0.377798i	$-0.123319\pi$
$761$	−34.4242	−	105.947i	−0.0452355	−	0.139221i	−0.971123	+	0.238578i	$0.923319\pi$
$762$		0			0
$763$	688.917	−	351.021i	0.902906	−	0.460053i
$764$		0			0
$765$	34.3579	+	1384.96i	0.0449123	+	1.81041i
$766$		0			0
$767$	109.211	−	17.2973i	0.142387	−	0.0225519i
$768$		0			0
$769$	426.548	−	587.092i	0.554678	−	0.763449i	−0.435960	−	0.899966i	$-0.643591\pi$
$769$	426.548	−	587.092i	0.554678	−	0.763449i	0.990638	+	0.136517i	$0.0435909\pi$
$770$		0			0
$771$	497.506	−	361.459i	0.645273	−	0.468819i
$772$		0			0
$773$	316.627	−	621.415i	0.409608	−	0.803901i	−0.590387	−	0.807120i	$-0.701025\pi$
$773$	316.627	−	621.415i	0.409608	−	0.803901i	0.999995	+	0.00321951i	$0.00102480\pi$
$774$		0			0
$775$	−859.803	−	232.924i	−1.10942	−	0.300546i
$776$		0			0
$777$	976.626	+	497.616i	1.25692	+	0.640432i
$778$		0			0
$779$	−34.4829	−	47.4617i	−0.0442656	−	0.0609264i
$780$		0			0
$781$	−10.0298	−	7.28707i	−0.0128422	−	0.00933044i
$782$		0			0
$783$	492.948	+	3112.35i	0.629563	+	3.97490i
$784$		0			0
$785$	1086.88	+	749.201i	1.38457	+	0.954396i
$786$		0			0
$787$	−133.431	−	261.873i	−0.169544	−	0.332749i	0.790564	−	0.612380i	$-0.209788\pi$
$787$	−133.431	−	261.873i	−0.169544	−	0.332749i	−0.960107	+	0.279631i	$0.909788\pi$
$788$		0			0
$789$	1950.70	−	633.820i	2.47237	−	0.803321i
$790$		0			0
$791$	94.3468	−	290.370i	0.119275	−	0.367092i
$792$		0			0
$793$	66.9086	+	66.9086i	0.0843740	+	0.0843740i
$794$		0			0
$795$	144.147	−	1083.38i	0.181318	−	1.36274i
$796$		0			0
$797$	−53.3751	+	336.997i	−0.0669701	+	0.422832i	0.931311	+	0.364225i	$0.118666\pi$
$797$	−53.3751	+	336.997i	−0.0669701	+	0.422832i	−0.998281	+	0.0586075i	$0.981334\pi$
$798$		0			0
$799$			505.399i			0.632539i
$800$		0			0
$801$	−2498.67			−3.11944
$802$		0			0
$803$	−52.2769	−	8.27985i	−0.0651020	−	0.0103111i
$804$		0			0
$805$	−699.712	+	378.666i	−0.869207	+	0.470392i
$806$		0			0
$807$	−30.8062	+	30.8062i	−0.0381737	+	0.0381737i
$808$		0			0
$809$	−728.516	−	236.709i	−0.900515	−	0.292595i	−0.178065	−	0.984019i	$-0.556984\pi$
$809$	−728.516	−	236.709i	−0.900515	−	0.292595i	−0.722449	+	0.691424i	$0.756984\pi$
$810$		0			0
$811$	21.6100	+	66.5086i	0.0266461	+	0.0820082i	0.963495	−	0.267726i	$-0.0862721\pi$
$811$	21.6100	+	66.5086i	0.0266461	+	0.0820082i	−0.936849	+	0.349734i	$0.886272\pi$
$812$		0			0
$813$	−2334.47	+	1189.47i	−2.87142	+	1.46306i
$814$		0			0
$815$	307.961	+	402.489i	0.377866	+	0.493852i
$816$		0			0
$817$	12.4451	−	1.97111i	0.0152327	−	0.00241262i
$818$		0			0
$819$	1644.85	−	2263.95i	2.00837	−	2.76428i
$820$		0			0
$821$	257.891	−	187.369i	0.314118	−	0.228220i	−0.419543	−	0.907735i	$-0.637810\pi$
$821$	257.891	−	187.369i	0.314118	−	0.228220i	0.733662	+	0.679515i	$0.237810\pi$
$822$		0			0
$823$	540.121	−	1060.05i	0.656283	−	1.28803i	−0.287601	−	0.957750i	$-0.592858\pi$
$823$	540.121	−	1060.05i	0.656283	−	1.28803i	0.943884	−	0.330277i	$-0.107142\pi$
$824$		0			0
$825$	−201.370	−	351.013i	−0.244085	−	0.425470i
$826$		0			0
$827$	535.642	+	272.923i	0.647693	+	0.330016i	0.746788	−	0.665062i	$-0.231595\pi$
$827$	535.642	+	272.923i	0.647693	+	0.330016i	−0.0990951	+	0.995078i	$0.531595\pi$
$828$		0			0
$829$	−695.307	−	957.008i	−0.838729	−	1.15441i	−0.986235	−	0.165351i	$-0.947124\pi$
$829$	−695.307	−	957.008i	−0.838729	−	1.15441i	0.147505	−	0.989061i	$-0.452876\pi$
$830$		0			0
$831$	−694.543	−	504.615i	−0.835792	−	0.607239i
$832$		0			0
$833$	−42.8589	−	270.600i	−0.0514512	−	0.324850i
$834$		0			0
$835$	84.0979	+	238.529i	0.100716	+	0.285663i
$836$		0			0
$837$	−1306.57	−	2564.28i	−1.56101	−	3.06366i
$838$		0			0
$839$	940.886	−	305.712i	1.12144	−	0.364377i	0.311121	−	0.950370i	$-0.399295\pi$
$839$	940.886	−	305.712i	1.12144	−	0.364377i	0.810316	+	0.585993i	$0.199295\pi$
$840$		0			0
$841$	−210.469	+	647.758i	−0.250261	+	0.770224i
$842$		0			0
$843$	−561.862	−	561.862i	−0.666503	−	0.666503i
$844$		0			0
$845$	−1752.38	−	838.806i	−2.07382	−	0.992669i
$846$		0			0
$847$	90.0884	−	568.796i	0.106362	−	0.671541i
$848$		0			0
$849$			2580.66i			3.03965i
$850$		0			0
$851$	−1180.17			−1.38680
$852$		0			0
$853$	−1232.08	−	195.143i	−1.44441	−	0.228772i	−0.615492	−	0.788143i	$-0.711043\pi$
$853$	−1232.08	−	195.143i	−1.44441	−	0.228772i	−0.828918	+	0.559371i	$0.811043\pi$
$854$		0			0
$855$	95.9470	+	91.3018i	0.112219	+	0.106786i
$856$		0			0
$857$	896.226	−	896.226i	1.04577	−	1.04577i	0.0468704	−	0.998901i	$-0.485075\pi$
$857$	896.226	−	896.226i	1.04577	−	1.04577i	0.998901	−	0.0468704i	$-0.0149248\pi$
$858$		0			0
$859$	−145.746	−	47.3557i	−0.169669	−	0.0551289i	0.222951	−	0.974830i	$-0.428431\pi$
$859$	−145.746	−	47.3557i	−0.169669	−	0.0551289i	−0.392620	+	0.919701i	$0.628431\pi$
$860$		0			0
$861$	−460.446	−	1417.11i	−0.534780	−	1.64588i
$862$		0			0
$863$	−1025.56	+	522.551i	−1.18837	+	0.605505i	−0.932487	−	0.361203i	$-0.882366\pi$
$863$	−1025.56	+	522.551i	−1.18837	+	0.605505i	−0.255883	+	0.966708i	$0.582366\pi$
$864$		0			0
$865$	−874.938	−	260.480i	−1.01149	−	0.301132i
$866$		0			0
$867$	822.579	−	130.284i	0.948765	−	0.150270i
$868$		0			0
$869$	−140.349	+	193.174i	−0.161507	+	0.222295i
$870$		0			0
$871$	−677.575	+	492.287i	−0.777928	+	0.565198i
$872$		0			0
$873$	884.445	−	1735.82i	1.01311	−	1.98834i
$874$		0			0
$875$	619.534	+	151.447i	0.708039	+	0.173082i
$876$		0			0
$877$	−665.904	−	339.295i	−0.759298	−	0.386881i	0.0310678	−	0.999517i	$-0.490109\pi$
$877$	−665.904	−	339.295i	−0.759298	−	0.386881i	−0.790365	+	0.612636i	$0.790109\pi$
$878$		0			0
$879$	216.421	+	297.878i	0.246213	+	0.338883i
$880$		0			0
$881$	577.102	+	419.289i	0.655054	+	0.475924i	0.864989	−	0.501791i	$-0.167325\pi$
$881$	577.102	+	419.289i	0.655054	+	0.475924i	−0.209935	+	0.977715i	$0.567325\pi$
$882$		0			0
$883$	0.190359	+	1.20188i	0.000215582	+	0.00136113i	0.987796	−	0.155754i	$-0.0497807\pi$
$883$	0.190359	+	1.20188i	0.000215582	+	0.00136113i	−0.987580	+	0.157115i	$0.949781\pi$
$884$		0			0
$885$	−37.9263	+	127.393i	−0.0428546	+	0.143946i
$886$		0			0
$887$	653.141	+	1281.86i	0.736348	+	1.44516i	0.889487	+	0.456960i	$0.151062\pi$
$887$	653.141	+	1281.86i	0.736348	+	1.44516i	−0.153139	+	0.988205i	$0.548938\pi$
$888$		0			0
$889$	−498.462	+	161.960i	−0.560700	+	0.182182i
$890$		0			0
$891$	219.816	−	676.524i	0.246707	−	0.759286i
$892$		0			0
$893$	34.1654	+	34.1654i	0.0382591	+	0.0382591i
$894$		0			0
$895$	−916.147	+	962.758i	−1.02363	+	1.07571i
$896$		0			0
$897$	−653.973	+	4129.02i	−0.729067	+	4.60315i
$898$		0			0
$899$		−	1390.14i		−	1.54632i
$900$		0			0
$901$	459.306			0.509773
$902$		0			0
$903$	316.089	+	50.0635i	0.350043	+	0.0554414i
$904$		0			0
$905$	44.4262	−	92.8122i	0.0490897	−	0.102555i
$906$		0			0
$907$	924.463	−	924.463i	1.01925	−	1.01925i	0.0194427	−	0.999811i	$-0.493811\pi$
$907$	924.463	−	924.463i	1.01925	−	1.01925i	0.999811	−	0.0194427i	$-0.00618920\pi$
$908$		0			0
$909$	−498.896	−	162.101i	−0.548841	−	0.178329i
$910$		0			0
$911$	−92.4877	−	284.648i	−0.101523	−	0.312456i	0.887375	−	0.461047i	$-0.152526\pi$
$911$	−92.4877	−	284.648i	−0.101523	−	0.312456i	−0.988899	+	0.148591i	$0.952526\pi$
$912$		0			0
$913$	382.821	−	195.057i	0.419300	−	0.213644i
$914$		0			0
$915$	−107.274	+	37.8215i	−0.117239	+	0.0413350i
$916$		0			0
$917$	−625.783	+	99.1142i	−0.682424	+	0.108085i
$918$		0			0
$919$	451.577	−	621.542i	0.491378	−	0.676324i	−0.489263	−	0.872136i	$-0.662734\pi$
$919$	451.577	−	621.542i	0.491378	−	0.676324i	0.980641	+	0.195812i	$0.0627342\pi$
$920$		0			0
$921$	2130.69	−	1548.04i	2.31345	−	1.68082i
$922$		0			0
$923$	46.6097	−	91.4767i	0.0504980	−	0.0991080i
$924$		0			0
$925$	701.307	+	634.966i	0.758170	+	0.686450i
$926$		0			0
$927$	1172.84	+	597.593i	1.26520	+	0.644653i
$928$		0			0
$929$	−843.119	−	1160.45i	−0.907556	−	1.24914i	−0.967994	−	0.250972i	$-0.919250\pi$
$929$	−843.119	−	1160.45i	−0.907556	−	1.24914i	0.0604386	−	0.998172i	$-0.480750\pi$
$930$		0			0
$931$	−21.1901	−	15.3955i	−0.0227606	−	0.0165365i
$932$		0			0
$933$	253.152	+	1598.34i	0.271331	+	1.71312i
$934$		0			0
$935$	135.064	−	103.343i	0.144454	−	0.110527i
$936$		0			0
$937$	−213.762	−	419.532i	−0.228135	−	0.447740i	0.748356	−	0.663297i	$-0.230843\pi$
$937$	−213.762	−	419.532i	−0.228135	−	0.447740i	−0.976491	+	0.215557i	$0.930843\pi$
$938$		0			0
$939$	−870.048	+	282.696i	−0.926568	+	0.301060i
$940$		0			0
$941$	23.2808	−	71.6510i	0.0247405	−	0.0761434i	−0.937924	−	0.346841i	$-0.887254\pi$
$941$	23.2808	−	71.6510i	0.0247405	−	0.0761434i	0.962664	+	0.270698i	$0.0872543\pi$
$942$		0			0
$943$	1134.43	+	1134.43i	1.20300	+	1.20300i
$944$		0			0
$945$	980.699	+	1812.17i	1.03778	+	1.91764i
$946$		0			0
$947$	29.4865	−	186.170i	0.0311367	−	0.196590i	−0.967217	−	0.253953i	$-0.918269\pi$
$947$	29.4865	−	186.170i	0.0311367	−	0.196590i	0.998353	+	0.0573631i	$0.0182693\pi$
$948$		0			0
$949$		−	438.314i		−	0.461869i
$950$		0			0
$951$	1850.14			1.94547
$952$		0			0
$953$	−456.234	−	72.2603i	−0.478734	−	0.0758240i	−0.0875961	−	0.996156i	$-0.527918\pi$
$953$	−456.234	−	72.2603i	−0.478734	−	0.0758240i	−0.391138	+	0.920332i	$0.627918\pi$
$954$		0			0
$955$	−1054.30	−	140.278i	−1.10398	−	0.146888i
$956$		0			0
$957$	446.550	−	446.550i	0.466614	−	0.466614i
$958$		0			0
$959$	−1196.55	−	388.783i	−1.24771	−	0.405404i
$960$		0			0
$961$	95.3697	+	293.518i	0.0992400	+	0.305429i
$962$		0			0
$963$	−1014.53	+	516.930i	−1.05351	+	0.536791i
$964$		0			0
$965$	718.850	−	1042.85i	0.744922	−	1.08068i
$966$		0			0
$967$	−1540.85	+	244.046i	−1.59343	+	0.252374i	−0.889173	−	0.457572i	$-0.848719\pi$
$967$	−1540.85	+	244.046i	−1.59343	+	0.252374i	−0.704256	+	0.709946i	$0.748719\pi$
$968$		0			0
$969$	−45.3932	+	62.4784i	−0.0468454	+	0.0644772i
$970$		0			0
$971$	775.545	−	563.467i	0.798708	−	0.580295i	−0.111827	−	0.993728i	$-0.535670\pi$
$971$	775.545	−	563.467i	0.798708	−	0.580295i	0.910535	+	0.413432i	$0.135670\pi$
$972$		0			0
$973$	−116.621	+	228.882i	−0.119857	+	0.235233i
$974$		0			0
$975$	2610.16	−	2101.79i	2.67709	−	2.15568i
$976$		0			0
$977$	1375.81	+	701.008i	1.40819	+	0.717511i	0.982309	−	0.187266i	$-0.0599626\pi$
$977$	1375.81	+	701.008i	1.40819	+	0.717511i	0.425886	+	0.904777i	$0.359963\pi$
$978$		0			0
$979$	180.290	+	248.149i	0.184158	+	0.253471i
$980$		0			0
$981$	2847.68	+	2068.96i	2.90283	+	2.10903i
$982$		0			0
$983$	18.9549	+	119.676i	0.0192827	+	0.121746i	0.995452	−	0.0952640i	$-0.0303695\pi$
$983$	18.9549	+	119.676i	0.0192827	+	0.121746i	−0.976169	+	0.217010i	$0.930370\pi$
$984$		0			0
$985$	−298.772	+	7.41191i	−0.303322	+	0.00752478i
$986$		0			0
$987$	557.132	+	1093.43i	0.564470	+	1.10784i
$988$		0			0
$989$	−327.711	+	106.480i	−0.331356	+	0.107664i
$990$		0			0
$991$	−82.9634	+	255.335i	−0.0837169	+	0.257654i	−0.984149	−	0.177342i	$-0.943250\pi$
$991$	−82.9634	+	255.335i	−0.0837169	+	0.257654i	0.900432	+	0.434996i	$0.143250\pi$
$992$		0			0
$993$	−294.184	−	294.184i	−0.296257	−	0.296257i
$994$		0			0
$995$	−512.834	+	94.3178i	−0.515411	+	0.0947918i
$996$		0			0
$997$	−12.8867	+	81.3634i	−0.0129255	+	0.0816082i	−0.993308	−	0.115497i	$-0.963154\pi$
$997$	−12.8867	+	81.3634i	−0.0129255	+	0.0816082i	0.980382	+	0.197105i	$0.0631540\pi$
$998$		0			0
$999$			3056.49i			3.05955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.33.1		64
4.3	odd	2		200.3.u.b.33.8	✓	64
25.22	odd	20	inner	400.3.bg.f.97.1		64
100.47	even	20		200.3.u.b.97.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.8	✓	64	4.3	odd	2
200.3.u.b.97.8	yes	64	100.47	even	20
400.3.bg.f.33.1		64	1.1	even	1	trivial
400.3.bg.f.97.1		64	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-5.60705 - 0.888069i) q^{3} +(-0.904406 - 4.91752i) q^{5} +(3.60781 - 3.60781i) q^{7} +(22.0908 + 7.17774i) q^{9} +O(q^{10})\)	\(q+(-5.60705 - 0.888069i) q^{3} +(-0.904406 - 4.91752i) q^{5} +(3.60781 - 3.60781i) q^{7} +(22.0908 + 7.17774i) q^{9} +(-0.881114 - 2.71179i) q^{11} +(21.0390 - 10.7199i) q^{13} +(0.703948 + 28.3760i) q^{15} +(-11.7819 + 1.86607i) q^{17} +(-0.670318 + 0.922614i) q^{19} +(-23.4331 + 17.0252i) q^{21} +(14.1584 - 27.7875i) q^{23} +(-23.3641 + 8.89488i) q^{25} +(-71.9662 - 36.6686i) q^{27} +(-22.9319 - 31.5630i) q^{29} +(28.8267 + 20.9438i) q^{31} +(2.53219 + 15.9876i) q^{33} +(-21.0044 - 14.4786i) q^{35} +(-17.1799 - 33.7175i) q^{37} +(-127.487 + 41.4230i) q^{39} +(-15.8966 + 48.9249i) q^{41} +(-7.81270 - 7.81270i) q^{43} +(15.3176 - 115.124i) q^{45} +(6.62783 - 41.8465i) q^{47} +22.9674i q^{49} +67.7189 q^{51} +(-38.0300 - 6.02336i) q^{53} +(-12.5384 + 6.78546i) q^{55} +(4.57785 - 4.57785i) q^{57} +(4.45355 + 1.44705i) q^{59} +(1.23832 + 3.81117i) q^{61} +(105.595 - 53.8035i) q^{63} +(-71.7433 - 93.7648i) q^{65} +(-35.0328 + 5.54865i) q^{67} +(-104.064 + 143.232i) q^{69} +(3.51757 - 2.55566i) q^{71} +(8.42727 - 16.5395i) q^{73} +(138.903 - 29.1251i) q^{75} +(-12.9625 - 6.60473i) q^{77} +(-49.2221 - 67.7484i) q^{79} +(201.830 + 146.638i) q^{81} +(23.5721 + 148.828i) q^{83} +(19.8321 + 56.2501i) q^{85} +(100.550 + 197.340i) q^{87} +(-102.308 + 33.2420i) q^{89} +(37.2294 - 114.580i) q^{91} +(-143.033 - 143.033i) q^{93} +(5.14322 + 2.46189i) q^{95} +(13.1205 - 82.8397i) q^{97} -66.2301i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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