LMFDB - Embedded newform 400.3.bg.f.17.2

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			17.2
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.f.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.583470 + 3.68389i) q^{3} +(3.77915 + 3.27383i) q^{5} +(-8.52562 - 8.52562i) q^{7} +(-4.67107 - 1.51772i) q^{9} +O(q^{10})$	\(q+(-0.583470 + 3.68389i) q^{3} +(3.77915 + 3.27383i) q^{5} +(-8.52562 - 8.52562i) q^{7} +(-4.67107 - 1.51772i) q^{9} +(-5.80693 - 17.8719i) q^{11} +(-8.80916 - 17.2889i) q^{13} +(-14.2655 + 12.0118i) q^{15} +(-1.13625 - 7.17401i) q^{17} +(-3.29808 + 4.53941i) q^{19} +(36.3819 - 26.4330i) q^{21} +(5.92922 + 3.02109i) q^{23} +(3.56402 + 24.7447i) q^{25} +(-6.92312 + 13.5874i) q^{27} +(-19.8602 - 27.3352i) q^{29} +(22.2062 + 16.1337i) q^{31} +(69.2262 - 10.9644i) q^{33} +(-4.30817 - 60.1311i) q^{35} +(-17.8588 + 9.09952i) q^{37} +(68.8304 - 22.3644i) q^{39} +(-5.10925 + 15.7247i) q^{41} +(9.37391 - 9.37391i) q^{43} +(-12.6839 - 21.0280i) q^{45} +(-86.2478 - 13.6603i) q^{47} +96.3723i q^{49} +27.0912 q^{51} +(7.94833 - 50.1838i) q^{53} +(36.5643 - 86.5516i) q^{55} +(-14.7983 - 14.7983i) q^{57} +(51.4451 + 16.7155i) q^{59} +(-25.0529 - 77.1050i) q^{61} +(26.8842 + 52.7633i) q^{63} +(23.3100 - 94.1773i) q^{65} +(-2.97145 - 18.7610i) q^{67} +(-14.5889 + 20.0799i) q^{69} +(82.3537 - 59.8335i) q^{71} +(-32.8437 - 16.7347i) q^{73} +(-93.2360 - 1.30833i) q^{75} +(-102.861 + 201.877i) q^{77} +(38.8166 + 53.4265i) q^{79} +(-81.7760 - 59.4137i) q^{81} +(-144.339 + 22.8610i) q^{83} +(19.1924 - 30.8316i) q^{85} +(112.288 - 57.2134i) q^{87} +(-14.0411 + 4.56222i) q^{89} +(-72.2954 + 222.503i) q^{91} +(-72.3915 + 72.3915i) q^{93} +(-27.3252 + 6.35779i) q^{95} +(-70.7123 - 11.1997i) q^{97} +92.2942i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

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
$3$	−0.583470	+	3.68389i	−0.194490	+	1.22796i	0.676419	+	0.736517i	$0.263531\pi$
$3$	−0.583470	+	3.68389i	−0.194490	+	1.22796i	−0.870909	+	0.491445i	$0.836469\pi$
$4$		0			0
$5$	3.77915	+	3.27383i	0.755831	+	0.654767i
$5$	3.77915	+	3.27383i	0.755831	+	0.654767i
$6$		0			0
$7$	−8.52562	−	8.52562i	−1.21795	−	1.21795i	−0.968350	−	0.249595i	$-0.919702\pi$
$7$	−8.52562	−	8.52562i	−1.21795	−	1.21795i	−0.249595	−	0.968350i	$-0.580298\pi$
$8$		0			0
$9$	−4.67107	−	1.51772i	−0.519008	−	0.168636i
$10$		0			0
$11$	−5.80693	−	17.8719i	−0.527903	−	1.62472i	−0.758503	−	0.651670i	$-0.774069\pi$
$11$	−5.80693	−	17.8719i	−0.527903	−	1.62472i	0.230600	−	0.973049i	$-0.425931\pi$
$12$		0			0
$13$	−8.80916	−	17.2889i	−0.677628	−	1.32992i	−0.931875	−	0.362780i	$-0.881828\pi$
$13$	−8.80916	−	17.2889i	−0.677628	−	1.32992i	0.254247	−	0.967139i	$-0.418172\pi$
$14$		0			0
$15$	−14.2655	+	12.0118i	−0.951030	+	0.800786i
$16$		0			0
$17$	−1.13625	−	7.17401i	−0.0668383	−	0.422000i	−0.998306	−	0.0581771i	$-0.981471\pi$
$17$	−1.13625	−	7.17401i	−0.0668383	−	0.422000i	0.931468	−	0.363823i	$-0.118529\pi$
$18$		0			0
$19$	−3.29808	+	4.53941i	−0.173583	+	0.238916i	−0.886940	−	0.461884i	$-0.847174\pi$
$19$	−3.29808	+	4.53941i	−0.173583	+	0.238916i	0.713357	+	0.700800i	$0.247174\pi$
$20$		0			0
$21$	36.3819	−	26.4330i	1.73247	−	1.25871i
$22$		0			0
$23$	5.92922	+	3.02109i	0.257792	+	0.131352i	0.578111	−	0.815958i	$-0.303790\pi$
$23$	5.92922	+	3.02109i	0.257792	+	0.131352i	−0.320319	+	0.947310i	$0.603790\pi$
$24$		0			0
$25$	3.56402	+	24.7447i	0.142561	+	0.989786i
$26$		0			0
$27$	−6.92312	+	13.5874i	−0.256412	+	0.503237i
$28$		0			0
$29$	−19.8602	−	27.3352i	−0.684834	−	0.942594i	0.315145	−	0.949044i	$-0.397947\pi$
$29$	−19.8602	−	27.3352i	−0.684834	−	0.942594i	−0.999979	+	0.00644987i	$0.997947\pi$
$30$		0			0
$31$	22.2062	+	16.1337i	0.716328	+	0.520443i	0.885209	−	0.465194i	$-0.154015\pi$
$31$	22.2062	+	16.1337i	0.716328	+	0.520443i	−0.168881	+	0.985636i	$0.554015\pi$
$32$		0			0
$33$	69.2262	−	10.9644i	2.09776	−	0.332253i
$34$		0			0
$35$	−4.30817	−	60.1311i	−0.123091	−	1.71803i
$36$		0			0
$37$	−17.8588	+	9.09952i	−0.482671	+	0.245933i	−0.678355	−	0.734734i	$-0.737307\pi$
$37$	−17.8588	+	9.09952i	−0.482671	+	0.245933i	0.195685	+	0.980667i	$0.437307\pi$
$38$		0			0
$39$	68.8304	−	22.3644i	1.76488	−	0.573445i
$40$		0			0
$41$	−5.10925	+	15.7247i	−0.124616	+	0.383528i	−0.993831	−	0.110906i	$-0.964625\pi$
$41$	−5.10925	+	15.7247i	−0.124616	+	0.383528i	0.869215	+	0.494434i	$0.164625\pi$
$42$		0			0
$43$	9.37391	−	9.37391i	0.217998	−	0.217998i	−0.589656	−	0.807654i	$-0.700737\pi$
$43$	9.37391	−	9.37391i	0.217998	−	0.217998i	0.807654	+	0.589656i	$0.200737\pi$
$44$		0			0
$45$	−12.6839	−	21.0280i	−0.281865	−	0.467289i
$46$		0			0
$47$	−86.2478	−	13.6603i	−1.83506	−	0.290645i	−0.859623	−	0.510928i	$-0.829302\pi$
$47$	−86.2478	−	13.6603i	−1.83506	−	0.290645i	−0.975436	+	0.220284i	$0.929302\pi$
$48$		0			0
$49$			96.3723i			1.96678i
$50$		0			0
$51$	27.0912			0.531200
$52$		0			0
$53$	7.94833	−	50.1838i	0.149969	−	0.946864i	−0.791843	−	0.610724i	$-0.790878\pi$
$53$	7.94833	−	50.1838i	0.149969	−	0.946864i	0.941812	−	0.336140i	$-0.109122\pi$
$54$		0			0
$55$	36.5643	−	86.5516i	0.664806	−	1.57367i
$56$		0			0
$57$	−14.7983	−	14.7983i	−0.259620	−	0.259620i
$58$		0			0
$59$	51.4451	+	16.7155i	0.871950	+	0.283314i	0.710611	−	0.703585i	$-0.248419\pi$
$59$	51.4451	+	16.7155i	0.871950	+	0.283314i	0.161339	+	0.986899i	$0.448419\pi$
$60$		0			0
$61$	−25.0529	−	77.1050i	−0.410704	−	1.26402i	−0.916037	−	0.401093i	$-0.868631\pi$
$61$	−25.0529	−	77.1050i	−0.410704	−	1.26402i	0.505334	−	0.862924i	$-0.331369\pi$
$62$		0			0
$63$	26.8842	+	52.7633i	0.426734	+	0.837513i
$64$		0			0
$65$	23.3100	−	94.1773i	0.358615	−	1.44888i
$66$		0			0
$67$	−2.97145	−	18.7610i	−0.0443501	−	0.280015i	0.955540	−	0.294862i	$-0.0952738\pi$
$67$	−2.97145	−	18.7610i	−0.0443501	−	0.280015i	−0.999890	+	0.0148472i	$0.995274\pi$
$68$		0			0
$69$	−14.5889	+	20.0799i	−0.211433	+	0.291013i
$70$		0			0
$71$	82.3537	−	59.8335i	1.15991	−	0.842725i	0.170144	−	0.985419i	$-0.445577\pi$
$71$	82.3537	−	59.8335i	1.15991	−	0.842725i	0.989767	+	0.142694i	$0.0455766\pi$
$72$		0			0
$73$	−32.8437	−	16.7347i	−0.449913	−	0.229242i	0.214326	−	0.976762i	$-0.431244\pi$
$73$	−32.8437	−	16.7347i	−0.449913	−	0.229242i	−0.664240	+	0.747520i	$0.731244\pi$
$74$		0			0
$75$	−93.2360	−	1.30833i	−1.24315	−	0.0174444i
$76$		0			0
$77$	−102.861	+	201.877i	−1.33586	+	2.62178i
$78$		0			0
$79$	38.8166	+	53.4265i	0.491349	+	0.676284i	0.980636	−	0.195839i	$-0.0627429\pi$
$79$	38.8166	+	53.4265i	0.491349	+	0.676284i	−0.489287	+	0.872123i	$0.662743\pi$
$80$		0			0
$81$	−81.7760	−	59.4137i	−1.00958	−	0.733503i
$82$		0			0
$83$	−144.339	+	22.8610i	−1.73902	+	0.275434i	−0.943711	−	0.330772i	$-0.892691\pi$
$83$	−144.339	+	22.8610i	−1.73902	+	0.275434i	−0.795308	+	0.606205i	$0.792691\pi$
$84$		0			0
$85$	19.1924	−	30.8316i	0.225793	−	0.362724i
$86$		0			0
$87$	112.288	−	57.2134i	1.29066	−	0.657626i
$88$		0			0
$89$	−14.0411	+	4.56222i	−0.157765	+	0.0512608i	−0.386835	−	0.922149i	$-0.626432\pi$
$89$	−14.0411	+	4.56222i	−0.157765	+	0.0512608i	0.229070	+	0.973410i	$0.426432\pi$
$90$		0			0
$91$	−72.2954	+	222.503i	−0.794455	+	2.44508i
$92$		0			0
$93$	−72.3915	+	72.3915i	−0.778403	+	0.778403i
$94$		0			0
$95$	−27.3252	+	6.35779i	−0.287634	+	0.0669241i
$96$		0			0
$97$	−70.7123	−	11.1997i	−0.728993	−	0.115461i	−0.219104	−	0.975702i	$-0.570313\pi$
$97$	−70.7123	−	11.1997i	−0.728993	−	0.115461i	−0.509889	+	0.860240i	$0.670313\pi$
$98$		0			0
$99$			92.2942i			0.932265i
$100$		0			0
$101$	63.7698			0.631384			0.315692	−	0.948862i	$-0.397763\pi$
$101$	63.7698			0.631384			0.315692	+	0.948862i	$0.397763\pi$
$102$		0			0
$103$	6.02655	−	38.0502i	0.0585102	−	0.369419i	−0.941008	−	0.338384i	$-0.890120\pi$
$103$	6.02655	−	38.0502i	0.0585102	−	0.369419i	0.999518	−	0.0310350i	$-0.00988032\pi$
$104$		0			0
$105$	224.030	+	19.2139i	2.13362	+	0.182990i
$106$		0			0
$107$	9.97815	+	9.97815i	0.0932538	+	0.0932538i	0.752195	−	0.658941i	$-0.228995\pi$
$107$	9.97815	+	9.97815i	0.0932538	+	0.0932538i	−0.658941	+	0.752195i	$0.728995\pi$
$108$		0			0
$109$	112.793	+	36.6485i	1.03479	+	0.336225i	0.776684	−	0.629891i	$-0.216900\pi$
$109$	112.793	+	36.6485i	1.03479	+	0.336225i	0.258110	+	0.966116i	$0.416900\pi$
$110$		0			0
$111$	−23.1015	−	71.0991i	−0.208122	−	0.640533i
$112$		0			0
$113$	35.3419	+	69.3624i	0.312760	+	0.613826i	0.992859	−	0.119294i	$-0.0380631\pi$
$113$	35.3419	+	69.3624i	0.312760	+	0.613826i	−0.680099	+	0.733120i	$0.738063\pi$
$114$		0			0
$115$	12.5169	+	30.8285i	0.108843	+	0.268074i
$116$		0			0
$117$	14.9084	+	94.1278i	0.127422	+	0.804511i
$118$		0			0
$119$	−51.4756	+	70.8501i	−0.432568	+	0.595379i
$120$		0			0
$121$	−187.793	+	136.440i	−1.55201	+	1.12760i
$122$		0			0
$123$	−54.9467	−	27.9968i	−0.446721	−	0.227616i
$124$		0			0
$125$	−67.5409	+	105.182i	−0.540327	+	0.841455i
$126$		0			0
$127$	69.4344	−	136.273i	0.546728	−	1.07301i	−0.438010	−	0.898970i	$-0.644317\pi$
$127$	69.4344	−	136.273i	0.546728	−	1.07301i	0.984738	−	0.174044i	$-0.0556833\pi$
$128$		0			0
$129$	29.0630	+	40.0018i	0.225295	+	0.310092i
$130$		0			0
$131$	−49.5707	−	36.0152i	−0.378402	−	0.274925i	0.382284	−	0.924045i	$-0.375137\pi$
$131$	−49.5707	−	36.0152i	−0.378402	−	0.274925i	−0.760686	+	0.649120i	$0.775137\pi$
$132$		0			0
$133$	66.8194	−	10.5832i	0.502402	−	0.0795726i
$134$		0			0
$135$	−70.6464	+	28.6837i	−0.523307	+	0.212472i
$136$		0			0
$137$	152.854	−	77.8832i	1.11573	−	0.568491i	0.203869	−	0.978998i	$-0.434648\pi$
$137$	152.854	−	77.8832i	1.11573	−	0.568491i	0.911857	+	0.410507i	$0.134648\pi$
$138$		0			0
$139$	78.7456	−	25.5860i	0.566515	−	0.184072i	−0.0117356	−	0.999931i	$-0.503736\pi$
$139$	78.7456	−	25.5860i	0.566515	−	0.184072i	0.578250	+	0.815859i	$0.303736\pi$
$140$		0			0
$141$	100.646	−	309.757i	0.713802	−	2.19686i
$142$		0			0
$143$	−257.832	+	257.832i	−1.80302	+	1.80302i
$144$		0			0
$145$	14.4362	−	168.323i	0.0995601	−	1.16085i
$146$		0			0
$147$	−355.025	−	56.2304i	−2.41513	−	0.382520i
$148$		0			0
$149$			24.1881i			0.162337i	0.996700	+	0.0811683i	$0.0258651\pi$
$149$			24.1881i			0.162337i	−0.996700	+	0.0811683i	$0.974135\pi$
$150$		0			0
$151$	141.989			0.940326			0.470163	−	0.882580i	$-0.344195\pi$
$151$	141.989			0.940326			0.470163	+	0.882580i	$0.344195\pi$
$152$		0			0
$153$	−5.58065	+	35.2348i	−0.0364748	+	0.230293i
$154$		0			0
$155$	31.1014	+	133.671i	0.200654	+	0.862395i
$156$		0			0
$157$	−154.553	−	154.553i	−0.984414	−	0.984414i	0.0154665	−	0.999880i	$-0.495077\pi$
$157$	−154.553	−	154.553i	−0.984414	−	0.984414i	−0.999880	+	0.0154665i	$0.995077\pi$
$158$		0			0
$159$	180.234	+	58.5615i	1.13355	+	0.368311i
$160$		0			0
$161$	−24.7936	−	76.3069i	−0.153998	−	0.473956i
$162$		0			0
$163$	44.6073	+	87.5468i	0.273665	+	0.537097i	0.986405	−	0.164331i	$-0.0525464\pi$
$163$	44.6073	+	87.5468i	0.273665	+	0.537097i	−0.712741	+	0.701428i	$0.752546\pi$
$164$		0			0
$165$	297.512	+	185.199i	1.80310	+	1.12242i
$166$		0			0
$167$	27.7118	+	174.965i	0.165939	+	1.04770i	0.920293	+	0.391229i	$0.127950\pi$
$167$	27.7118	+	174.965i	0.165939	+	1.04770i	−0.754354	+	0.656467i	$0.772050\pi$
$168$		0			0
$169$	−121.971	+	167.878i	−0.721721	+	0.993363i
$170$		0			0
$171$	22.2951	−	16.1984i	0.130381	−	0.0947272i
$172$		0			0
$173$	137.157	+	69.8852i	0.792818	+	0.403961i	0.802994	−	0.595987i	$-0.203239\pi$
$173$	137.157	+	69.8852i	0.792818	+	0.403961i	−0.0101759	+	0.999948i	$0.503239\pi$
$174$		0			0
$175$	180.578	−	241.349i	1.03187	−	1.37914i
$176$		0			0
$177$	−91.5947	+	179.765i	−0.517484	+	1.01562i
$178$		0			0
$179$	−128.012	−	176.193i	−0.715148	−	0.984317i	−0.999671	−	0.0256478i	$-0.991835\pi$
$179$	−128.012	−	176.193i	−0.715148	−	0.984317i	0.284523	−	0.958669i	$-0.408165\pi$
$180$		0			0
$181$	−94.8798	−	68.9342i	−0.524198	−	0.380852i	0.293985	−	0.955810i	$-0.405018\pi$
$181$	−94.8798	−	68.9342i	−0.524198	−	0.380852i	−0.818183	+	0.574958i	$0.805018\pi$
$182$		0			0
$183$	298.664	−	47.3037i	1.63204	−	0.258490i
$184$		0			0
$185$	−97.2815	−	24.0783i	−0.525846	−	0.130153i
$186$		0			0
$187$	−121.615	+	61.9659i	−0.650348	+	0.331369i
$188$		0			0
$189$	174.865	−	56.8170i	0.925210	−	0.300619i
$190$		0			0
$191$	−23.6565	+	72.8073i	−0.123856	+	0.381190i	−0.993691	−	0.112153i	$-0.964225\pi$
$191$	−23.6565	+	72.8073i	−0.123856	+	0.381190i	0.869835	+	0.493343i	$0.164225\pi$
$192$		0			0
$193$	−113.325	+	113.325i	−0.587174	+	0.587174i	−0.936865	−	0.349691i	$-0.886287\pi$
$193$	−113.325	+	113.325i	−0.587174	+	0.587174i	0.349691	+	0.936865i	$0.386287\pi$
$194$		0			0
$195$	333.338	+	140.821i	1.70943	+	0.722159i
$196$		0			0
$197$	5.13411	+	0.813163i	0.0260615	+	0.00412773i	0.169452	−	0.985539i	$-0.445800\pi$
$197$	5.13411	+	0.813163i	0.0260615	+	0.00412773i	−0.143390	+	0.989666i	$0.545800\pi$
$198$		0			0
$199$		−	60.8485i		−	0.305772i	−0.988244	−	0.152886i	$-0.951143\pi$
$199$		−	60.8485i		−	0.305772i	0.988244	−	0.152886i	$-0.0488567\pi$
$200$		0			0
$201$	70.8472			0.352474
$202$		0			0
$203$	−63.7292	+	402.370i	−0.313937	+	1.98212i
$204$		0			0
$205$	−70.7886	+	42.6991i	−0.345310	+	0.208288i
$206$		0			0
$207$	−23.1106	−	23.1106i	−0.111646	−	0.111646i
$208$		0			0
$209$	100.280	+	32.5828i	0.479807	+	0.155899i
$210$		0			0
$211$	−92.5591	−	284.868i	−0.438669	−	1.35008i	−0.889280	−	0.457364i	$-0.848794\pi$
$211$	−92.5591	−	284.868i	−0.438669	−	1.35008i	0.450611	−	0.892720i	$-0.351206\pi$
$212$		0			0
$213$	172.369	+	338.293i	0.809243	+	1.58823i
$214$		0			0
$215$	66.1141	−	4.73683i	0.307507	−	0.0220318i
$216$		0			0
$217$	−51.7713	−	326.871i	−0.238578	−	1.50632i
$218$		0			0
$219$	80.8120	−	111.228i	0.369005	−	0.507891i
$220$		0			0
$221$	−114.022	+	82.8416i	−0.515935	+	0.374849i
$222$		0			0
$223$	220.845	+	112.526i	0.990336	+	0.504601i	0.872596	−	0.488443i	$-0.162435\pi$
$223$	220.845	+	112.526i	0.990336	+	0.504601i	0.117740	+	0.993044i	$0.462435\pi$
$224$		0			0
$225$	20.9077	−	120.993i	0.0929233	−	0.537748i
$226$		0			0
$227$	−60.1633	+	118.077i	−0.265037	+	0.520164i	−0.984721	−	0.174137i	$-0.944286\pi$
$227$	−60.1633	+	118.077i	−0.265037	+	0.520164i	0.719685	+	0.694301i	$0.244286\pi$
$228$		0			0
$229$	−242.617	−	333.934i	−1.05946	−	1.45823i	−0.880306	−	0.474406i	$-0.842663\pi$
$229$	−242.617	−	333.934i	−1.05946	−	1.45823i	−0.179157	−	0.983821i	$-0.557337\pi$
$230$		0			0
$231$	−683.674	−	496.718i	−2.95963	−	2.15030i
$232$		0			0
$233$	−247.796	+	39.2470i	−1.06350	+	0.168442i	−0.663579	−	0.748106i	$-0.730963\pi$
$233$	−247.796	+	39.2470i	−1.06350	+	0.168442i	−0.399924	+	0.916549i	$0.630963\pi$
$234$		0			0
$235$	−281.222	−	333.985i	−1.19669	−	1.42121i
$236$		0			0
$237$	−219.465	+	111.823i	−0.926014	+	0.471828i
$238$		0			0
$239$	83.2985	−	27.0653i	0.348529	−	0.113244i	−0.129521	−	0.991577i	$-0.541344\pi$
$239$	83.2985	−	27.0653i	0.348529	−	0.113244i	0.478050	+	0.878333i	$0.341344\pi$
$240$		0			0
$241$	9.42832	−	29.0174i	0.0391217	−	0.120404i	−0.929588	−	0.368599i	$-0.879837\pi$
$241$	9.42832	−	29.0174i	0.0391217	−	0.120404i	0.968710	+	0.248195i	$0.0798374\pi$
$242$		0			0
$243$	169.540	−	169.540i	0.697696	−	0.697696i
$244$		0			0
$245$	−315.507	+	364.206i	−1.28778	+	1.48655i
$246$		0			0
$247$	107.535	+	17.0319i	0.435364	+	0.0689549i
$248$		0			0
$249$		−	545.066i		−	2.18902i
$250$		0			0
$251$	−49.9803			−0.199125			−0.0995624	−	0.995031i	$-0.531744\pi$
$251$	−49.9803			−0.199125			−0.0995624	+	0.995031i	$0.531744\pi$
$252$		0			0
$253$	19.5620	−	123.510i	0.0773202	−	0.488181i
$254$		0			0
$255$	102.382	+	88.6921i	0.401497	+	0.347812i
$256$		0			0
$257$	126.662	+	126.662i	0.492850	+	0.492850i	0.909203	−	0.416353i	$-0.136692\pi$
$257$	126.662	+	126.662i	0.492850	+	0.492850i	−0.416353	+	0.909203i	$0.636692\pi$
$258$		0			0
$259$	229.836	+	74.6784i	0.887399	+	0.288334i
$260$		0			0
$261$	51.2811	+	157.827i	0.196479	+	0.604701i
$262$		0			0
$263$	−107.831	−	211.630i	−0.410004	−	0.804677i	0.589993	−	0.807409i	$-0.299131\pi$
$263$	−107.831	−	211.630i	−0.410004	−	0.804677i	−0.999996	+	0.00273129i	$0.999131\pi$
$264$		0			0
$265$	194.331	−	163.631i	0.733326	−	0.617475i
$266$		0			0
$267$	−8.61414	−	54.3876i	−0.0322627	−	0.203699i
$268$		0			0
$269$	−57.5661	+	79.2329i	−0.214000	+	0.294546i	−0.902499	−	0.430691i	$-0.858270\pi$
$269$	−57.5661	+	79.2329i	−0.214000	+	0.294546i	0.688499	+	0.725237i	$0.258270\pi$
$270$		0			0
$271$	147.592	−	107.232i	0.544618	−	0.395688i	−0.281179	−	0.959655i	$-0.590725\pi$
$271$	147.592	−	107.232i	0.544618	−	0.395688i	0.825797	+	0.563967i	$0.190725\pi$
$272$		0			0
$273$	−777.492	−	396.152i	−2.84795	−	1.45111i
$274$		0			0
$275$	421.538	−	207.386i	1.53287	−	0.754132i
$276$		0			0
$277$	180.143	−	353.551i	0.650336	−	1.27636i	−0.296621	−	0.954995i	$-0.595860\pi$
$277$	180.143	−	353.551i	0.650336	−	1.27636i	0.946957	−	0.321361i	$-0.104140\pi$
$278$		0			0
$279$	−79.2401	−	109.065i	−0.284015	−	0.390913i
$280$		0			0
$281$	126.315	+	91.7733i	0.449520	+	0.326595i	0.789406	−	0.613871i	$-0.210389\pi$
$281$	126.315	+	91.7733i	0.449520	+	0.326595i	−0.339886	+	0.940467i	$0.610389\pi$
$282$		0			0
$283$	−329.488	+	52.1857i	−1.16427	+	0.184402i	−0.708509	−	0.705702i	$-0.750632\pi$
$283$	−329.488	+	52.1857i	−1.16427	+	0.184402i	−0.455758	+	0.890104i	$0.650632\pi$
$284$		0			0
$285$	−7.47791	−	104.373i	−0.0262383	−	0.366220i
$286$		0			0
$287$	177.622	−	90.5029i	0.618892	−	0.315341i
$288$		0			0
$289$	224.680	−	73.0030i	0.777440	−	0.252605i
$290$		0			0
$291$	82.5170	−	253.961i	0.283564	−	0.872719i
$292$		0			0
$293$	−216.944	+	216.944i	−0.740423	+	0.740423i	−0.972659	−	0.232236i	$-0.925396\pi$
$293$	−216.944	+	216.944i	−0.740423	+	0.740423i	0.232236	+	0.972659i	$0.425396\pi$
$294$		0			0
$295$	139.695	+	231.593i	0.473542	+	0.785061i
$296$		0			0
$297$	283.035	+	44.8283i	0.952978	+	0.150937i
$298$		0			0
$299$		−	129.123i		−	0.431850i
$300$		0			0
$301$	−159.837			−0.531019
$302$		0			0
$303$	−37.2078	+	234.921i	−0.122798	+	0.775315i
$304$		0			0
$305$	157.750	−	373.411i	0.517214	−	1.22430i
$306$		0			0
$307$	−22.7849	−	22.7849i	−0.0742181	−	0.0742181i	0.669023	−	0.743241i	$-0.266713\pi$
$307$	−22.7849	−	22.7849i	−0.0742181	−	0.0742181i	−0.743241	+	0.669023i	$0.766713\pi$
$308$		0			0
$309$	136.656	+	44.4023i	0.442253	+	0.143697i
$310$		0			0
$311$	15.3975	+	47.3886i	0.0495096	+	0.152375i	0.972755	−	0.231836i	$-0.0744734\pi$
$311$	15.3975	+	47.3886i	0.0495096	+	0.152375i	−0.923245	+	0.384211i	$0.874473\pi$
$312$		0			0
$313$	185.482	+	364.028i	0.592593	+	1.16303i	0.971377	+	0.237544i	$0.0763424\pi$
$313$	185.482	+	364.028i	0.592593	+	1.16303i	−0.378784	+	0.925485i	$0.623658\pi$
$314$		0			0
$315$	−71.1386	+	287.415i	−0.225837	+	0.912429i
$316$		0			0
$317$	−84.2808	−	532.128i	−0.265870	−	1.67864i	−0.653581	−	0.756856i	$-0.726734\pi$
$317$	−84.2808	−	532.128i	−0.265870	−	1.67864i	0.387711	−	0.921781i	$-0.373266\pi$
$318$		0			0
$319$	−373.205	+	513.673i	−1.16992	+	1.61026i
$320$		0			0
$321$	−42.5803	+	30.9364i	−0.132649	+	0.0963751i
$322$		0			0
$323$	36.3132	+	18.5025i	0.112425	+	0.0572833i
$324$		0			0
$325$	396.413	−	279.598i	1.21973	−	0.860301i
$326$		0			0
$327$	−200.820	+	394.132i	−0.614129	+	1.20530i
$328$		0			0
$329$	618.853	+	851.778i	1.88101	+	2.58899i
$330$		0			0
$331$	166.615	+	121.053i	0.503370	+	0.365720i	0.810303	−	0.586011i	$-0.199303\pi$
$331$	166.615	+	121.053i	0.503370	+	0.365720i	−0.306933	+	0.951731i	$0.599303\pi$
$332$		0			0
$333$	97.2303	−	15.3998i	0.291983	−	0.0462456i
$334$		0			0
$335$	50.1909	−	80.6289i	0.149824	−	0.240683i
$336$		0			0
$337$	464.237	−	236.540i	1.37756	−	0.701900i	0.400783	−	0.916173i	$-0.368738\pi$
$337$	464.237	−	236.540i	1.37756	−	0.701900i	0.976774	+	0.214273i	$0.0687381\pi$
$338$		0			0
$339$	−276.144	+	89.7246i	−0.814584	+	0.264674i
$340$		0			0
$341$	159.391	−	490.554i	0.467421	−	1.43857i
$342$		0			0
$343$	403.878	−	403.878i	1.17749	−	1.17749i
$344$		0			0
$345$	−120.872	+	28.1233i	−0.350353	+	0.0815170i
$346$		0			0
$347$	254.756	+	40.3494i	0.734168	+	0.116281i	0.512313	−	0.858799i	$-0.328789\pi$
$347$	254.756	+	40.3494i	0.734168	+	0.116281i	0.221855	+	0.975080i	$0.428789\pi$
$348$		0			0
$349$			375.867i			1.07698i	0.842631	+	0.538491i	$0.181006\pi$
$349$			375.867i			1.07698i	−0.842631	+	0.538491i	$0.818994\pi$
$350$		0			0
$351$	295.899			0.843016
$352$		0			0
$353$	−4.56720	+	28.8361i	−0.0129382	+	0.0816888i	−0.993313	−	0.115456i	$-0.963167\pi$
$353$	−4.56720	+	28.8361i	−0.0129382	+	0.0816888i	0.980374	+	0.197145i	$0.0631670\pi$
$354$		0			0
$355$	507.112	+	43.4924i	1.42848	+	0.122514i
$356$		0			0
$357$	−230.969	−	230.969i	−0.646972	−	0.646972i
$358$		0			0
$359$	−273.200	−	88.7681i	−0.761003	−	0.247265i	−0.0972940	−	0.995256i	$-0.531019\pi$
$359$	−273.200	−	88.7681i	−0.761003	−	0.247265i	−0.663709	+	0.747991i	$0.731019\pi$
$360$		0			0
$361$	101.826	+	313.389i	0.282067	+	0.868113i
$362$		0			0
$363$	−393.057	−	771.418i	−1.08280	−	2.12512i
$364$		0			0
$365$	−69.3347	−	170.768i	−0.189958	−	0.467857i
$366$		0			0
$367$	−79.7054	−	503.240i	−0.217181	−	1.37123i	−0.819549	−	0.573009i	$-0.805776\pi$
$367$	−79.7054	−	503.240i	−0.217181	−	1.37123i	0.602368	−	0.798218i	$-0.294224\pi$
$368$		0			0
$369$	47.7313	−	65.6965i	0.129353	−	0.178039i
$370$		0			0
$371$	−495.612	+	360.084i	−1.33588	+	0.970576i
$372$		0			0
$373$	608.589	+	310.092i	1.63161	+	0.831345i	0.998351	+	0.0574016i	$0.0182815\pi$
$373$	608.589	+	310.092i	1.63161	+	0.831345i	0.633255	+	0.773943i	$0.281718\pi$
$374$		0			0
$375$	−348.070	−	310.184i	−0.928186	−	0.827156i
$376$		0			0
$377$	−297.646	+	584.162i	−0.789511	+	1.54950i
$378$		0			0
$379$	41.6448	+	57.3192i	0.109881	+	0.151238i	0.860416	−	0.509593i	$-0.170204\pi$
$379$	41.6448	+	57.3192i	0.109881	+	0.151238i	−0.750535	+	0.660831i	$0.770204\pi$
$380$		0			0
$381$	461.500	+	335.300i	1.21129	+	0.880051i
$382$		0			0
$383$	−403.771	+	63.9511i	−1.05423	+	0.166974i	−0.659411	−	0.751783i	$-0.729194\pi$
$383$	−403.771	+	63.9511i	−1.05423	+	0.166974i	−0.394823	+	0.918757i	$0.629194\pi$
$384$		0			0
$385$	−1049.64	+	426.172i	−2.72634	+	1.10694i
$386$		0			0
$387$	−58.0132	+	29.5592i	−0.149905	+	0.0763804i
$388$		0			0
$389$	329.861	−	107.178i	0.847972	−	0.275523i	0.147376	−	0.989081i	$-0.452917\pi$
$389$	329.861	−	107.178i	0.847972	−	0.275523i	0.700597	+	0.713558i	$0.252917\pi$
$390$		0			0
$391$	14.9362	−	45.9690i	0.0382001	−	0.117568i
$392$		0			0
$393$	161.599	−	161.599i	0.411193	−	0.411193i
$394$		0			0
$395$	−28.2155	+	328.986i	−0.0714316	+	0.832876i
$396$		0			0
$397$	−297.997	−	47.1981i	−0.750623	−	0.118887i	−0.230611	−	0.973046i	$-0.574072\pi$
$397$	−297.997	−	47.1981i	−0.750623	−	0.118887i	−0.520012	+	0.854159i	$0.674072\pi$
$398$		0			0
$399$			252.330i			0.632406i
$400$		0			0
$401$	−334.639			−0.834512			−0.417256	−	0.908789i	$-0.637008\pi$
$401$	−334.639			−0.834512			−0.417256	+	0.908789i	$0.637008\pi$
$402$		0			0
$403$	83.3175	−	526.046i	0.206743	−	1.30532i
$404$		0			0
$405$	−114.533	−	492.255i	−0.282799	−	1.21544i
$406$		0			0
$407$	266.331	+	266.331i	0.654375	+	0.654375i
$408$		0			0
$409$	564.343	+	183.366i	1.37981	+	0.448328i	0.902607	−	0.430465i	$-0.141650\pi$
$409$	564.343	+	183.366i	1.37981	+	0.448328i	0.477204	+	0.878793i	$0.341650\pi$
$410$		0			0
$411$	197.727	+	608.541i	0.481088	+	1.48064i
$412$		0			0
$413$	−296.091	−	581.111i	−0.716927	−	1.40705i
$414$		0			0
$415$	−620.321	−	386.145i	−1.49475	−	0.930471i
$416$		0			0
$417$	48.3102	+	305.018i	0.115852	+	0.731459i
$418$		0			0
$419$	−108.478	+	149.307i	−0.258898	+	0.356342i	−0.918603	−	0.395183i	$-0.870681\pi$
$419$	−108.478	+	149.307i	−0.258898	+	0.356342i	0.659705	+	0.751525i	$0.270681\pi$
$420$		0			0
$421$	−280.660	+	203.912i	−0.666652	+	0.484351i	−0.868903	−	0.494983i	$-0.835174\pi$
$421$	−280.660	+	203.912i	−0.666652	+	0.484351i	0.202251	+	0.979334i	$0.435174\pi$
$422$		0			0
$423$	382.137	+	194.708i	0.903397	+	0.460304i
$424$		0			0
$425$	173.469	−	53.6844i	0.408162	−	0.126316i
$426$		0			0
$427$	−443.776	+	870.960i	−1.03929	+	2.03972i
$428$		0			0
$429$	−799.387	−	1100.26i	−1.86337	−	2.56471i
$430$		0			0
$431$	−341.167	−	247.872i	−0.791570	−	0.575110i	0.116859	−	0.993149i	$-0.462718\pi$
$431$	−341.167	−	247.872i	−0.791570	−	0.575110i	−0.908429	+	0.418039i	$0.862718\pi$
$432$		0			0
$433$	298.857	−	47.3343i	0.690200	−	0.109317i	0.198525	−	0.980096i	$-0.436385\pi$
$433$	298.857	−	47.3343i	0.690200	−	0.109317i	0.491675	+	0.870779i	$0.336385\pi$
$434$		0			0
$435$	611.660	+	151.393i	1.40611	+	0.348030i
$436$		0			0
$437$	−33.2690	+	16.9514i	−0.0761304	+	0.0387904i
$438$		0			0
$439$	−290.343	+	94.3381i	−0.661373	+	0.214893i	−0.620422	−	0.784268i	$-0.713039\pi$
$439$	−290.343	+	94.3381i	−0.661373	+	0.214893i	−0.0409510	+	0.999161i	$0.513039\pi$
$440$		0			0
$441$	146.266	−	450.162i	0.331670	−	1.02078i
$442$		0			0
$443$	458.793	−	458.793i	1.03565	−	1.03565i	0.0363105	−	0.999341i	$-0.488439\pi$
$443$	458.793	−	458.793i	1.03565	−	1.03565i	0.999341	−	0.0363105i	$-0.0115605\pi$
$444$		0			0
$445$	−67.9993	−	28.7268i	−0.152807	−	0.0645545i
$446$		0			0
$447$	−89.1064	−	14.1131i	−0.199343	−	0.0315728i
$448$		0			0
$449$			434.116i			0.966850i	0.875386	+	0.483425i	$0.160607\pi$
$449$			434.116i			0.966850i	−0.875386	+	0.483425i	$0.839393\pi$
$450$		0			0
$451$	310.699			0.688910
$452$		0			0
$453$	−82.8464	+	523.072i	−0.182884	+	1.15468i
$454$		0			0
$455$	−1001.65	+	604.188i	−2.20143	+	1.32789i
$456$		0			0
$457$	38.1192	+	38.1192i	0.0834118	+	0.0834118i	0.747582	−	0.664170i	$-0.231215\pi$
$457$	38.1192	+	38.1192i	0.0834118	+	0.0834118i	−0.664170	+	0.747582i	$0.731215\pi$
$458$		0			0
$459$	105.342	+	34.2278i	0.229504	+	0.0745704i
$460$		0			0
$461$	277.885	+	855.243i	0.602788	+	1.85519i	0.511334	+	0.859382i	$0.329152\pi$
$461$	277.885	+	855.243i	0.602788	+	1.85519i	0.0914546	+	0.995809i	$0.470848\pi$
$462$		0			0
$463$	396.540	+	778.254i	0.856458	+	1.68089i	0.724104	+	0.689691i	$0.242253\pi$
$463$	396.540	+	778.254i	0.856458	+	1.68089i	0.132354	+	0.991203i	$0.457747\pi$
$464$		0			0
$465$	−510.576	+	36.5809i	−1.09801	+	0.0786685i
$466$		0			0
$467$	16.1224	+	101.793i	0.0345233	+	0.217971i	0.998919	−	0.0464936i	$-0.0148047\pi$
$467$	16.1224	+	101.793i	0.0345233	+	0.217971i	−0.964395	+	0.264465i	$0.914805\pi$
$468$		0			0
$469$	−134.616	+	185.283i	−0.287027	+	0.395059i
$470$		0			0
$471$	659.533	−	479.179i	1.40028	−	1.01736i
$472$		0			0
$473$	−221.963	−	113.096i	−0.469267	−	0.239103i
$474$		0			0
$475$	−124.081	−	65.4312i	−0.261222	−	0.137750i
$476$		0			0
$477$	−113.292	+	222.349i	−0.237510	+	0.466140i
$478$		0			0
$479$	−159.753	−	219.881i	−0.333514	−	0.459043i	0.609019	−	0.793156i	$-0.291563\pi$
$479$	−159.753	−	219.881i	−0.333514	−	0.459043i	−0.942533	+	0.334113i	$0.891563\pi$
$480$		0			0
$481$	314.642	+	228.601i	0.654142	+	0.475262i
$482$		0			0
$483$	295.572	−	46.8141i	0.611951	−	0.0969235i
$484$		0			0
$485$	−230.567	−	273.826i	−0.475395	−	0.564589i
$486$		0			0
$487$	415.493	−	211.704i	0.853169	−	0.434711i	0.0280072	−	0.999608i	$-0.491084\pi$
$487$	415.493	−	211.704i	0.853169	−	0.434711i	0.825162	+	0.564896i	$0.191084\pi$
$488$		0			0
$489$	−348.539	+	113.247i	−0.712760	+	0.231590i
$490$		0			0
$491$	−43.3682	+	133.474i	−0.0883263	+	0.271840i	−0.985457	−	0.169925i	$-0.945648\pi$
$491$	−43.3682	+	133.474i	−0.0883263	+	0.271840i	0.897131	+	0.441765i	$0.145648\pi$
$492$		0			0
$493$	−173.537	+	173.537i	−0.352002	+	0.352002i
$494$		0			0
$495$	−302.156	+	348.794i	−0.610416	+	0.704635i
$496$		0			0
$497$	−1212.23	−	191.999i	−2.43910	−	0.386316i
$498$		0			0
$499$		−	229.932i		−	0.460785i	−0.973098	−	0.230392i	$-0.925999\pi$
$499$		−	229.932i		−	0.460785i	0.973098	−	0.230392i	$-0.0740010\pi$
$500$		0			0
$501$	−660.721			−1.31881
$502$		0			0
$503$	−65.9361	+	416.304i	−0.131086	+	0.827642i	0.831274	+	0.555863i	$0.187612\pi$
$503$	−65.9361	+	416.304i	−0.131086	+	0.827642i	−0.962360	+	0.271779i	$0.912388\pi$
$504$		0			0
$505$	240.996	+	208.772i	0.477219	+	0.413409i
$506$		0			0
$507$	−547.278	−	547.278i	−1.07944	−	1.07944i
$508$		0			0
$509$	−245.566	−	79.7891i	−0.482447	−	0.156757i	0.0576882	−	0.998335i	$-0.481627\pi$
$509$	−245.566	−	79.7891i	−0.482447	−	0.156757i	−0.540136	+	0.841578i	$0.681627\pi$
$510$		0			0
$511$	137.339	+	422.686i	0.268765	+	0.827175i
$512$		0			0
$513$	−38.8458	−	76.2391i	−0.0757228	−	0.148614i
$514$		0			0
$515$	147.345	−	124.068i	0.286107	−	0.240908i
$516$		0			0
$517$	256.699	+	1620.74i	0.496517	+	3.13489i
$518$		0			0
$519$	−337.477	+	464.497i	−0.650244	+	0.894984i
$520$		0			0
$521$	−199.459	+	144.915i	−0.382838	+	0.278148i	−0.762514	−	0.646971i	$-0.776035\pi$
$521$	−199.459	+	144.915i	−0.382838	+	0.278148i	0.379676	+	0.925119i	$0.376035\pi$
$522$		0			0
$523$	−27.9831	−	14.2581i	−0.0535049	−	0.0272621i	0.427033	−	0.904236i	$-0.359559\pi$
$523$	−27.9831	−	14.2581i	−0.0535049	−	0.0272621i	−0.480538	+	0.876974i	$0.659559\pi$
$524$		0			0
$525$	783.740	+	806.049i	1.49284	+	1.53533i
$526$		0			0
$527$	90.5117	−	177.639i	0.171749	−	0.337076i
$528$		0			0
$529$	−284.910	−	392.145i	−0.538582	−	0.741294i
$530$		0			0
$531$	−214.934	−	156.159i	−0.404772	−	0.294084i
$532$		0			0
$533$	316.871	−	50.1874i	0.594505	−	0.0941603i
$534$		0			0
$535$	5.04216	+	70.3758i	0.00942460	+	0.131544i
$536$		0			0
$537$	723.765	−	368.777i	1.34779	−	0.686735i
$538$		0			0
$539$	1722.36	−	559.628i	3.19547	−	1.03827i
$540$		0			0
$541$	282.118	−	868.269i	0.521474	−	1.60493i	−0.249710	−	0.968321i	$-0.580335\pi$
$541$	282.118	−	868.269i	0.521474	−	1.60493i	0.771184	−	0.636612i	$-0.219665\pi$
$542$		0			0
$543$	309.305	−	309.305i	0.569623	−	0.569623i
$544$		0			0
$545$	306.279	+	507.764i	0.561980	+	0.931678i
$546$		0			0
$547$	44.5607	+	7.05772i	0.0814638	+	0.0129026i	0.197033	−	0.980397i	$-0.436869\pi$
$547$	44.5607	+	7.05772i	0.0814638	+	0.0129026i	−0.115569	+	0.993299i	$0.536869\pi$
$548$		0			0
$549$			398.186i			0.725294i
$550$		0			0
$551$	189.586			0.344077
$552$		0			0
$553$	124.558	−	786.429i	0.225241	−	1.42211i
$554$		0			0
$555$	145.463	−	344.325i	0.262095	−	0.620406i
$556$		0			0
$557$	−15.3560	−	15.3560i	−0.0275690	−	0.0275690i	0.693188	−	0.720757i	$-0.256206\pi$
$557$	−15.3560	−	15.3560i	−0.0275690	−	0.0275690i	−0.720757	+	0.693188i	$0.756206\pi$
$558$		0			0
$559$	−244.641	−	79.4888i	−0.437641	−	0.142198i
$560$		0			0
$561$	−157.317	−	484.171i	−0.280422	−	0.863050i
$562$		0			0
$563$	−139.447	−	273.680i	−0.247685	−	0.486110i	0.733372	−	0.679828i	$-0.237945\pi$
$563$	−139.447	−	273.680i	−0.247685	−	0.486110i	−0.981057	+	0.193718i	$0.937945\pi$
$564$		0			0
$565$	−93.5184	+	377.835i	−0.165519	+	0.668734i
$566$		0			0
$567$	190.652	+	1203.73i	0.336247	+	2.12298i
$568$		0			0
$569$	−13.7972	+	18.9902i	−0.0242481	+	0.0333747i	−0.820969	−	0.570973i	$-0.806566\pi$
$569$	−13.7972	+	18.9902i	−0.0242481	+	0.0333747i	0.796721	+	0.604348i	$0.206566\pi$
$570$		0			0
$571$	305.166	−	221.716i	0.534441	−	0.388294i	−0.287576	−	0.957758i	$-0.592849\pi$
$571$	305.166	−	221.716i	0.534441	−	0.388294i	0.822016	+	0.569464i	$0.192849\pi$
$572$		0			0
$573$	−254.411	−	129.629i	−0.443998	−	0.226228i
$574$		0			0
$575$	−53.6239	+	157.484i	−0.0932590	+	0.273885i
$576$		0			0
$577$	404.703	−	794.275i	0.701392	−	1.37656i	−0.215134	−	0.976584i	$-0.569019\pi$
$577$	404.703	−	794.275i	0.701392	−	1.37656i	0.916526	−	0.399975i	$-0.130981\pi$
$578$		0			0
$579$	−351.353	−	483.596i	−0.606828	−	0.835227i
$580$		0			0
$581$	1425.48	+	1035.67i	2.45349	+	1.78257i
$582$		0			0
$583$	−943.035	+	149.362i	−1.61756	+	0.256196i
$584$		0			0
$585$	−251.818	+	404.531i	−0.430458	+	0.691506i
$586$		0			0
$587$	958.708	−	488.486i	1.63323	−	0.832174i	0.635015	−	0.772500i	$-0.280994\pi$
$587$	958.708	−	488.486i	1.63323	−	0.832174i	0.998218	−	0.0596738i	$-0.0190061\pi$
$588$		0			0
$589$	−146.475	+	47.5927i	−0.248685	+	0.0808026i
$590$		0			0
$591$	−5.99120	+	18.4390i	−0.0101374	+	0.0311997i
$592$		0			0
$593$	279.857	−	279.857i	0.471934	−	0.471934i	−0.430606	−	0.902540i	$-0.641700\pi$
$593$	279.857	−	279.857i	0.471934	−	0.471934i	0.902540	+	0.430606i	$0.141700\pi$
$594$		0			0
$595$	−426.486	+	99.2308i	−0.716783	+	0.166775i
$596$		0			0
$597$	224.159	+	35.5033i	0.375476	+	0.0594695i
$598$		0			0
$599$			386.711i			0.645594i	0.946468	+	0.322797i	$0.104623\pi$
$599$			386.711i			0.645594i	−0.946468	+	0.322797i	$0.895377\pi$
$600$		0			0
$601$	733.180			1.21993			0.609967	−	0.792427i	$-0.291183\pi$
$601$	733.180			1.21993			0.609967	+	0.792427i	$0.291183\pi$
$602$		0			0
$603$	−14.5942	+	92.1439i	−0.0242026	+	0.152809i
$604$		0			0
$605$	−1156.38	−	99.1770i	−1.91137	−	0.163929i
$606$		0			0
$607$	−658.642	−	658.642i	−1.08508	−	1.08508i	−0.996027	−	0.0890502i	$-0.971617\pi$
$607$	−658.642	−	658.642i	−1.08508	−	1.08508i	−0.0890502	−	0.996027i	$-0.528383\pi$
$608$		0			0
$609$	−1445.10	−	469.542i	−2.37291	−	0.771005i
$610$		0			0
$611$	523.598	+	1611.47i	0.856953	+	2.63743i
$612$		0			0
$613$	−310.566	−	609.520i	−0.506632	−	0.994322i	−0.992724	−	0.120414i	$-0.961578\pi$
$613$	−310.566	−	609.520i	−0.506632	−	0.994322i	0.486091	−	0.873908i	$-0.338422\pi$
$614$		0			0
$615$	−115.995	−	285.691i	−0.188611	−	0.464538i
$616$		0			0
$617$	25.8421	+	163.160i	0.0418834	+	0.264442i	0.999740	−	0.0228056i	$-0.00725989\pi$
$617$	25.8421	+	163.160i	0.0418834	+	0.264442i	−0.957856	+	0.287247i	$0.907260\pi$
$618$		0			0
$619$	361.153	−	497.084i	0.583446	−	0.803044i	−0.410622	−	0.911806i	$-0.634688\pi$
$619$	361.153	−	497.084i	0.583446	−	0.803044i	0.994068	+	0.108762i	$0.0346885\pi$
$620$		0			0
$621$	−82.0974	+	59.6473i	−0.132202	+	0.0960504i
$622$		0			0
$623$	158.604	+	80.8130i	0.254582	+	0.129716i
$624$		0			0
$625$	−599.596	+	176.381i	−0.959353	+	0.282209i
$626$		0			0
$627$	−178.542	+	350.408i	−0.284755	+	0.558864i
$628$		0			0
$629$	85.5721	+	117.780i	0.136045	+	0.187249i
$630$		0			0
$631$	−608.710	−	442.254i	−0.964675	−	0.700878i	−0.0104434	−	0.999945i	$-0.503324\pi$
$631$	−608.710	−	442.254i	−0.964675	−	0.700878i	−0.954232	+	0.299068i	$0.903324\pi$
$632$		0			0
$633$	1103.43	−	174.765i	1.74317	−	0.276091i
$634$		0			0
$635$	708.538	−	287.679i	1.11581	−	0.453038i
$636$		0			0
$637$	1666.18	−	848.959i	2.61566	−	1.33275i
$638$		0			0
$639$	−475.490	+	154.496i	−0.744117	+	0.241778i
$640$		0			0
$641$	−84.2290	+	259.230i	−0.131403	+	0.404415i	−0.995013	−	0.0997441i	$-0.968198\pi$
$641$	−84.2290	+	259.230i	−0.131403	+	0.404415i	0.863611	+	0.504159i	$0.168198\pi$
$642$		0			0
$643$	−226.633	+	226.633i	−0.352462	+	0.352462i	−0.861025	−	0.508563i	$-0.830177\pi$
$643$	−226.633	+	226.633i	−0.352462	+	0.352462i	0.508563	+	0.861025i	$0.330177\pi$
$644$		0			0
$645$	−21.1257	+	246.321i	−0.0327530	+	0.381892i
$646$		0			0
$647$	63.5747	+	10.0692i	0.0982607	+	0.0155630i	0.205371	−	0.978684i	$-0.434160\pi$
$647$	63.5747	+	10.0692i	0.0982607	+	0.0155630i	−0.107110	+	0.994247i	$0.534160\pi$
$648$		0			0
$649$		−	1016.49i		−	1.56624i
$650$		0			0
$651$	1234.36			1.89610
$652$		0			0
$653$	168.107	−	1061.39i	0.257438	−	1.62540i	−0.432570	−	0.901600i	$-0.642393\pi$
$653$	168.107	−	1061.39i	0.257438	−	1.62540i	0.690009	−	0.723801i	$-0.257607\pi$
$654$		0			0
$655$	−69.4274	−	298.393i	−0.105996	−	0.455562i
$656$		0			0
$657$	128.017	+	128.017i	0.194850	+	0.194850i
$658$		0			0
$659$	−744.023	−	241.748i	−1.12902	−	0.366840i	−0.315815	−	0.948821i	$-0.602278\pi$
$659$	−744.023	−	241.748i	−1.12902	−	0.366840i	−0.813203	+	0.581981i	$0.802278\pi$
$660$		0			0
$661$	−170.560	−	524.930i	−0.258034	−	0.794146i	−0.993217	−	0.116277i	$-0.962904\pi$
$661$	−170.560	−	524.930i	−0.258034	−	0.794146i	0.735183	−	0.677868i	$-0.237096\pi$
$662$		0			0
$663$	−238.651	−	468.378i	−0.359956	−	0.706453i
$664$		0			0
$665$	287.168	+	178.760i	0.431832	+	0.268813i
$666$		0			0
$667$	−35.1734	−	222.076i	−0.0527337	−	0.332948i
$668$		0			0
$669$	−543.390	+	747.912i	−0.812242	+	1.11795i
$670$		0			0
$671$	−1232.53	+	895.487i	−1.83686	+	1.33456i
$672$		0			0
$673$	254.702	+	129.777i	0.378458	+	0.192834i	0.632863	−	0.774264i	$-0.281880\pi$
$673$	254.702	+	129.777i	0.378458	+	0.192834i	−0.254405	+	0.967098i	$0.581880\pi$
$674$		0			0
$675$	−360.889	−	122.884i	−0.534651	−	0.182051i
$676$		0			0
$677$	59.4926	−	116.761i	0.0878768	−	0.172468i	−0.842885	−	0.538093i	$-0.819145\pi$
$677$	59.4926	−	116.761i	0.0878768	−	0.172468i	0.930762	+	0.365625i	$0.119145\pi$
$678$		0			0
$679$	507.381	+	698.351i	0.747248	+	1.02850i
$680$		0			0
$681$	−399.879	−	290.529i	−0.587194	−	0.426622i
$682$		0			0
$683$	−340.153	+	53.8749i	−0.498027	+	0.0788797i	−0.400395	−	0.916343i	$-0.631127\pi$
$683$	−340.153	+	53.8749i	−0.498027	+	0.0788797i	−0.0976325	+	0.995223i	$0.531127\pi$
$684$		0			0
$685$	832.638	+	206.087i	1.21553	+	0.300858i
$686$		0			0
$687$	1371.73	−	698.933i	1.99670	−	1.01737i
$688$		0			0
$689$	−937.643	+	304.659i	−1.36088	+	0.442175i
$690$		0			0
$691$	−317.959	+	978.578i	−0.460144	+	1.41618i	0.404845	+	0.914385i	$0.367326\pi$
$691$	−317.959	+	978.578i	−0.460144	+	1.41618i	−0.864989	+	0.501792i	$0.832674\pi$
$692$		0			0
$693$	786.865	−	786.865i	1.13545	−	1.13545i
$694$		0			0
$695$	381.356	+	161.107i	0.548714	+	0.231808i
$696$		0			0
$697$	118.614	+	18.7866i	0.170178	+	0.0269536i
$698$		0			0
$699$		−	935.752i		−	1.33870i
$700$		0			0
$701$	−1007.26			−1.43689			−0.718443	−	0.695585i	$-0.755145\pi$
$701$	−1007.26			−1.43689			−0.718443	+	0.695585i	$0.755145\pi$
$702$		0			0
$703$	17.5932	−	111.079i	0.0250260	−	0.158008i
$704$		0			0
$705$	1394.45	−	841.120i	1.97794	−	1.19308i
$706$		0			0
$707$	−543.677	−	543.677i	−0.768991	−	0.768991i
$708$		0			0
$709$	545.856	+	177.359i	0.769895	+	0.250154i	0.667520	−	0.744592i	$-0.267356\pi$
$709$	545.856	+	177.359i	0.769895	+	0.250154i	0.102375	+	0.994746i	$0.467356\pi$
$710$		0			0
$711$	−100.229	−	308.472i	−0.140968	−	0.433856i
$712$		0			0
$713$	82.9239	+	162.747i	0.116303	+	0.228257i
$714$		0			0
$715$	−1818.49	+	130.288i	−2.54334	+	0.182221i
$716$		0			0
$717$	51.1034	+	322.654i	0.0712739	+	0.450006i
$718$		0			0
$719$	577.055	−	794.248i	0.802580	−	1.10466i	−0.189846	−	0.981814i	$-0.560799\pi$
$719$	577.055	−	794.248i	0.802580	−	1.10466i	0.992426	−	0.122843i	$-0.0392012\pi$
$720$		0			0
$721$	−375.781	+	273.021i	−0.521195	+	0.378670i
$722$		0			0
$723$	101.396	+	51.6636i	0.140243	+	0.0714573i
$724$		0			0
$725$	605.618	−	588.857i	0.835336	−	0.812216i
$726$		0			0
$727$	228.678	−	448.805i	0.314550	−	0.617338i	−0.678558	−	0.734547i	$-0.737395\pi$
$727$	228.678	−	448.805i	0.314550	−	0.617338i	0.993107	+	0.117209i	$0.0373947\pi$
$728$		0			0
$729$	−9.07850	−	12.4955i	−0.0124534	−	0.0171406i
$730$		0			0
$731$	−77.8996	−	56.5974i	−0.106566	−	0.0774246i
$732$		0			0
$733$	−1315.57	+	208.366i	−1.79477	+	0.284264i	−0.962734	−	0.270450i	$-0.912827\pi$
$733$	−1315.57	+	208.366i	−1.79477	+	0.284264i	−0.832041	+	0.554715i	$0.812827\pi$
$734$		0			0
$735$	−1157.60	−	1374.80i	−1.57497	−	1.87047i
$736$		0			0
$737$	−318.040	+	162.050i	−0.431533	+	0.219877i
$738$		0			0
$739$	−627.341	+	203.835i	−0.848905	+	0.275826i	−0.700987	−	0.713174i	$-0.747257\pi$
$739$	−627.341	+	203.835i	−0.848905	+	0.275826i	−0.147918	+	0.989000i	$0.547257\pi$
$740$		0			0
$741$	−125.487	+	386.209i	−0.169348	+	0.521200i
$742$		0			0
$743$	−439.194	+	439.194i	−0.591110	+	0.591110i	−0.937931	−	0.346822i	$-0.887261\pi$
$743$	−439.194	+	439.194i	−0.591110	+	0.591110i	0.346822	+	0.937931i	$0.387261\pi$
$744$		0			0
$745$	−79.1880	+	91.4107i	−0.106293	+	0.122699i
$746$		0			0
$747$	708.912	+	112.281i	0.949013	+	0.150309i
$748$		0			0
$749$		−	170.140i		−	0.227156i
$750$		0			0
$751$	−177.871			−0.236846			−0.118423	−	0.992963i	$-0.537784\pi$
$751$	−177.871			−0.236846			−0.118423	+	0.992963i	$0.537784\pi$
$752$		0			0
$753$	29.1620	−	184.122i	0.0387278	−	0.244518i
$754$		0			0
$755$	536.599	+	464.849i	0.710727	+	0.615694i
$756$		0			0
$757$	10.0764	+	10.0764i	0.0133110	+	0.0133110i	0.713731	−	0.700420i	$-0.247004\pi$
$757$	10.0764	+	10.0764i	0.0133110	+	0.0133110i	−0.700420	+	0.713731i	$0.747004\pi$
$758$		0			0
$759$	443.582	+	144.128i	0.584429	+	0.189893i
$760$		0			0
$761$	55.3326	+	170.296i	0.0727104	+	0.223780i	0.980807	−	0.194981i	$-0.0624646\pi$
$761$	55.3326	+	170.296i	0.0727104	+	0.223780i	−0.908097	+	0.418761i	$0.862465\pi$
$762$		0			0
$763$	−649.175	−	1274.08i	−0.850819	−	1.66983i
$764$		0			0
$765$	−136.443	+	114.888i	−0.178357	+	0.150180i
$766$		0			0
$767$	−164.194	−	1036.68i	−0.214073	−	1.35160i
$768$		0			0
$769$	720.647	−	991.885i	0.937122	−	1.28984i	−0.0198936	−	0.999802i	$-0.506333\pi$
$769$	720.647	−	991.885i	0.937122	−	1.28984i	0.957016	−	0.290036i	$-0.0936673\pi$
$770$		0			0
$771$	−540.514	+	392.706i	−0.701056	+	0.509347i
$772$		0			0
$773$	−446.333	−	227.418i	−0.577404	−	0.294202i	0.140796	−	0.990039i	$-0.455034\pi$
$773$	−446.333	−	227.418i	−0.577404	−	0.294202i	−0.718200	+	0.695837i	$0.755034\pi$
$774$		0			0
$775$	−320.080	+	606.985i	−0.413007	+	0.783206i
$776$		0			0
$777$	−409.209	+	803.119i	−0.526653	+	1.03361i
$778$		0			0
$779$	−54.5300	−	75.0541i	−0.0700000	−	0.0963467i
$780$		0			0
$781$	−1547.56	−	1124.37i	−1.98151	−	1.43965i
$782$		0			0
$783$	508.909	−	80.6032i	0.649947	−	0.102942i
$784$		0			0
$785$	−78.0988	−	1090.06i	−0.0994889	−	1.38861i
$786$		0			0
$787$	326.278	−	166.247i	0.414585	−	0.211242i	−0.234241	−	0.972179i	$-0.575260\pi$
$787$	326.278	−	166.247i	0.414585	−	0.211242i	0.648826	+	0.760937i	$0.275260\pi$
$788$		0			0
$789$	842.537	−	273.757i	1.06785	−	0.346967i
$790$		0			0
$791$	290.046	−	892.669i	0.366682	−	1.12853i
$792$		0			0
$793$	−1112.37	+	1112.37i	−1.40274	+	1.40274i
$794$		0			0
$795$	489.411	+	811.369i	0.615611	+	1.02059i
$796$		0			0
$797$	1337.59	+	211.854i	1.67828	+	0.265814i	0.921649	−	0.388025i	$-0.126842\pi$
$797$	1337.59	+	211.854i	1.67828	+	0.265814i	0.756634	+	0.653839i	$0.226842\pi$
$798$		0			0
$799$			634.264i			0.793822i
$800$		0			0
$801$	72.5109			0.0905255
$802$		0			0
$803$	−108.360	+	684.156i	−0.134944	+	0.852000i
$804$		0			0
$805$	156.117	−	369.546i	0.193935	−	0.459063i
$806$		0			0
$807$	−258.297	−	258.297i	−0.320071	−	0.320071i
$808$		0			0
$809$	−751.366	−	244.134i	−0.928759	−	0.301772i	−0.194704	−	0.980862i	$-0.562375\pi$
$809$	−751.366	−	244.134i	−0.928759	−	0.301772i	−0.734055	+	0.679090i	$0.762375\pi$
$810$		0			0
$811$	−288.496	−	887.900i	−0.355729	−	1.09482i	−0.955586	−	0.294714i	$-0.904776\pi$
$811$	−288.496	−	887.900i	−0.355729	−	1.09482i	0.599857	−	0.800108i	$-0.295224\pi$
$812$		0			0
$813$	308.914	+	606.277i	0.379968	+	0.745728i
$814$		0			0
$815$	−118.036	+	476.890i	−0.144829	+	0.585141i
$816$		0			0
$817$	11.6362	+	73.4679i	0.0142426	+	0.0899240i
$818$		0			0
$819$	675.394	−	929.601i	0.824657	−	1.13504i
$820$		0			0
$821$	187.513	−	136.236i	0.228396	−	0.165939i	−0.467702	−	0.883886i	$-0.654918\pi$
$821$	187.513	−	136.236i	0.228396	−	0.165939i	0.696098	+	0.717947i	$0.254918\pi$
$822$		0			0
$823$	352.172	+	179.441i	0.427913	+	0.218033i	0.654664	−	0.755920i	$-0.272810\pi$
$823$	352.172	+	179.441i	0.427913	+	0.218033i	−0.226751	+	0.973953i	$0.572810\pi$
$824$		0			0
$825$	518.033	+	1673.90i	0.627918	+	2.02897i
$826$		0			0
$827$	131.419	−	257.924i	0.158911	−	0.311880i	−0.797799	−	0.602923i	$-0.794002\pi$
$827$	131.419	−	257.924i	0.158911	−	0.311880i	0.956710	+	0.291044i	$0.0940025\pi$
$828$		0			0
$829$	418.491	+	576.004i	0.504815	+	0.694818i	0.983034	−	0.183423i	$-0.0587177\pi$
$829$	418.491	+	576.004i	0.504815	+	0.694818i	−0.478220	+	0.878240i	$0.658718\pi$
$830$		0			0
$831$	1197.33	+	869.913i	1.44083	+	1.04683i
$832$		0			0
$833$	691.376	−	109.503i	0.829983	−	0.131456i
$834$		0			0
$835$	−468.080	+	751.945i	−0.560575	+	0.900533i
$836$		0			0
$837$	−372.951	+	190.028i	−0.445581	+	0.227035i
$838$		0			0
$839$	−919.265	+	298.687i	−1.09567	+	0.356004i	−0.800434	−	0.599421i	$-0.795398\pi$
$839$	−919.265	+	298.687i	−1.09567	+	0.356004i	−0.295234	+	0.955425i	$0.595398\pi$
$840$		0			0
$841$	−92.9034	+	285.927i	−0.110468	+	0.339985i
$842$		0			0
$843$	−411.783	+	411.783i	−0.488474	+	0.488474i
$844$		0			0
$845$	−1010.55	+	235.126i	−1.19592	+	0.278256i
$846$		0			0
$847$	2764.29	+	437.820i	3.26362	+	0.516907i
$848$		0			0
$849$		−	1244.24i		−	1.46554i
$850$		0			0
$851$	−133.379			−0.156732
$852$		0			0
$853$	68.6106	−	433.190i	0.0804345	−	0.507843i	−0.914273	−	0.405098i	$-0.867237\pi$
$853$	68.6106	−	433.190i	0.0804345	−	0.507843i	0.994708	−	0.102745i	$-0.0327626\pi$
$854$		0			0
$855$	137.287	+	11.7744i	0.160570	+	0.0137713i
$856$		0			0
$857$	−571.470	−	571.470i	−0.666826	−	0.666826i	0.290154	−	0.956980i	$-0.406294\pi$
$857$	−571.470	−	571.470i	−0.666826	−	0.666826i	−0.956980	+	0.290154i	$0.906294\pi$
$858$		0			0
$859$	1458.01	+	473.738i	1.69734	+	0.551499i	0.988146	−	0.153516i	$-0.0490596\pi$
$859$	1458.01	+	473.738i	1.69734	+	0.551499i	0.709193	+	0.705015i	$0.249060\pi$
$860$		0			0
$861$	229.765	+	707.145i	0.266859	+	0.821306i
$862$		0			0
$863$	410.261	+	805.183i	0.475390	+	0.933005i	0.996818	+	0.0797096i	$0.0253993\pi$
$863$	410.261	+	805.183i	0.475390	+	0.933005i	−0.521429	+	0.853295i	$0.674601\pi$
$864$		0			0
$865$	289.547	+	713.138i	0.334736	+	0.824437i
$866$		0			0
$867$	137.840	+	870.291i	0.158986	+	1.00380i
$868$		0			0
$869$	729.427	−	1003.97i	0.839387	−	1.15532i
$870$		0			0
$871$	−298.182	+	216.642i	−0.342345	+	0.248728i
$872$		0			0
$873$	313.304	+	159.636i	0.358882	+	0.182860i
$874$		0			0
$875$	1472.57	−	320.912i	1.68294	−	0.366757i
$876$		0			0
$877$	−65.4034	+	128.361i	−0.0745763	+	0.146364i	−0.925284	−	0.379275i	$-0.876174\pi$
$877$	−65.4034	+	128.361i	−0.0745763	+	0.146364i	0.850708	+	0.525639i	$0.176174\pi$
$878$		0			0
$879$	−672.617	−	925.777i	−0.765206	−	1.05322i
$880$		0			0
$881$	−572.312	−	415.809i	−0.649616	−	0.471974i	0.213524	−	0.976938i	$-0.431506\pi$
$881$	−572.312	−	415.809i	−0.649616	−	0.471974i	−0.863140	+	0.504964i	$0.831506\pi$
$882$		0			0
$883$	1368.56	−	216.758i	1.54989	−	0.245479i	0.677958	−	0.735101i	$-0.262865\pi$
$883$	1368.56	−	216.758i	1.54989	−	0.245479i	0.871935	+	0.489622i	$0.162865\pi$
$884$		0			0
$885$	−934.671	+	379.493i	−1.05612	+	0.428805i
$886$		0			0
$887$	1123.27	−	572.337i	1.26637	−	0.645250i	0.313780	−	0.949496i	$-0.398404\pi$
$887$	1123.27	−	572.337i	1.26637	−	0.645250i	0.952594	+	0.304246i	$0.0984044\pi$
$888$		0			0
$889$	−1753.78	+	569.838i	−1.97276	+	0.640987i
$890$		0			0
$891$	−586.969	+	1806.50i	−0.658775	+	2.02750i
$892$		0			0
$893$	346.462	−	346.462i	0.387975	−	0.387975i
$894$		0			0
$895$	93.0505	−	1084.95i	0.103967	−	1.21223i
$896$		0			0
$897$	475.675	+	75.3396i	0.530296	+	0.0839906i
$898$		0			0
$899$		−	927.430i		−	1.03162i
$900$		0			0
$901$	−369.050			−0.409601
$902$		0			0
$903$	93.2600	−	588.821i	0.103278	−	0.652071i
$904$		0			0
$905$	−132.886	−	571.134i	−0.146836	−	0.631087i
$906$		0			0
$907$	−76.3152	−	76.3152i	−0.0841402	−	0.0841402i	0.663784	−	0.747924i	$-0.268949\pi$
$907$	−76.3152	−	76.3152i	−0.0841402	−	0.0841402i	−0.747924	+	0.663784i	$0.768949\pi$
$908$		0			0
$909$	−297.873	−	96.7848i	−0.327693	−	0.106474i
$910$		0			0
$911$	−138.739	−	426.995i	−0.152293	−	0.468711i	0.845583	−	0.533844i	$-0.179253\pi$
$911$	−138.739	−	426.995i	−0.152293	−	0.468711i	−0.997877	+	0.0651328i	$0.979253\pi$
$912$		0			0
$913$	1246.73	+	2446.85i	1.36554	+	2.68001i
$914$		0			0
$915$	1283.56	+	799.008i	1.40280	+	0.873232i
$916$		0			0
$917$	115.569	+	729.672i	0.126029	+	0.795717i
$918$		0			0
$919$	144.067	−	198.291i	0.156765	−	0.215768i	−0.723409	−	0.690420i	$-0.757426\pi$
$919$	144.067	−	198.291i	0.156765	−	0.215768i	0.880174	+	0.474652i	$0.157426\pi$
$920$		0			0
$921$	97.2315	−	70.6428i	0.105572	−	0.0767023i
$922$		0			0
$923$	−1759.92	−	896.726i	−1.90674	−	0.971534i
$924$		0			0
$925$	−288.814	−	409.479i	−0.312231	−	0.442680i
$926$		0			0
$927$	−85.9001	+	168.588i	−0.0926646	+	0.181864i
$928$		0			0
$929$	−186.786	−	257.088i	−0.201061	−	0.276737i	0.696566	−	0.717493i	$-0.254710\pi$
$929$	−186.786	−	257.088i	−0.201061	−	0.276737i	−0.897627	+	0.440756i	$0.854710\pi$
$930$		0			0
$931$	−437.474	−	317.843i	−0.469897	−	0.341400i
$932$		0			0
$933$	−183.558	+	29.0728i	−0.196740	+	0.0311605i
$934$		0			0
$935$	−662.468	−	163.969i	−0.708522	−	0.175367i
$936$		0			0
$937$	132.930	−	67.7313i	0.141868	−	0.0722853i	−0.381616	−	0.924321i	$-0.624632\pi$
$937$	132.930	−	67.7313i	0.141868	−	0.0722853i	0.523483	+	0.852036i	$0.324632\pi$
$938$		0			0
$939$	−1449.26	+	470.894i	−1.54341	+	0.501484i
$940$		0			0
$941$	300.192	−	923.895i	0.319014	−	0.981823i	−0.655057	−	0.755579i	$-0.727355\pi$
$941$	300.192	−	923.895i	0.319014	−	0.981823i	0.974071	−	0.226244i	$-0.0726445\pi$
$942$		0			0
$943$	−77.7995	+	77.7995i	−0.0825021	+	0.0825021i
$944$		0			0
$945$	846.850	+	357.758i	0.896138	+	0.378580i
$946$		0			0
$947$	−1742.02	−	275.909i	−1.83952	−	0.291351i	−0.862746	−	0.505637i	$-0.831257\pi$
$947$	−1742.02	−	275.909i	−1.83952	−	0.291351i	−0.976771	+	0.214287i	$0.931257\pi$
$948$		0			0
$949$			715.251i			0.753690i
$950$		0			0
$951$	2009.47			2.11301
$952$		0			0
$953$	107.551	−	679.049i	0.112855	−	0.712538i	−0.864768	−	0.502172i	$-0.832534\pi$
$953$	107.551	−	679.049i	0.112855	−	0.712538i	0.977623	−	0.210366i	$-0.0674656\pi$
$954$		0			0
$955$	−327.761	+	197.703i	−0.343205	+	0.207018i
$956$		0			0
$957$	−1674.56	−	1674.56i	−1.74980	−	1.74980i
$958$		0			0
$959$	−1967.18	−	639.176i	−2.05128	−	0.666503i
$960$		0			0
$961$	−64.1485	−	197.429i	−0.0667518	−	0.205441i
$962$		0			0
$963$	−31.4646	−	61.7527i	−0.0326735	−	0.0641254i
$964$		0			0
$965$	−799.277	+	57.2652i	−0.828266	+	0.0593422i
$966$		0			0
$967$	141.030	+	890.427i	0.145843	+	0.920814i	0.946737	+	0.322008i	$0.104358\pi$
$967$	141.030	+	890.427i	0.145843	+	0.920814i	−0.800894	+	0.598806i	$0.795642\pi$
$968$		0			0
$969$	−89.3488	+	122.978i	−0.0922072	+	0.126912i
$970$		0			0
$971$	1279.47	−	929.592i	1.31769	−	0.957356i	0.317729	−	0.948182i	$-0.397080\pi$
$971$	1279.47	−	929.592i	1.31769	−	0.957356i	0.999958	−	0.00917399i	$-0.00292021\pi$
$972$		0			0
$973$	−889.491	−	453.218i	−0.914174	−	0.465795i
$974$		0			0
$975$	798.711	+	1623.48i	0.819191	+	1.66511i
$976$		0			0
$977$	−627.618	+	1231.77i	−0.642394	+	1.26077i	0.308492	+	0.951227i	$0.400176\pi$
$977$	−627.618	+	1231.77i	−0.642394	+	1.26077i	−0.950886	+	0.309541i	$0.899824\pi$
$978$		0			0
$979$	163.071	+	224.448i	0.166569	+	0.229262i
$980$		0			0
$981$	−471.240	−	342.376i	−0.480367	−	0.349007i
$982$		0			0
$983$	245.644	−	38.9061i	0.249892	−	0.0395790i	−0.0302318	−	0.999543i	$-0.509625\pi$
$983$	245.644	−	38.9061i	0.249892	−	0.0395790i	0.280124	+	0.959964i	$0.409625\pi$
$984$		0			0
$985$	16.7404	+	19.8813i	0.0169954	+	0.0201841i
$986$		0			0
$987$	−3498.94	+	1782.80i	−3.54502	+	1.80628i
$988$		0			0
$989$	83.8994	−	27.2606i	0.0848326	−	0.0275638i
$990$		0			0
$991$	393.525	−	1211.15i	0.397099	−	1.22215i	−0.530215	−	0.847863i	$-0.677889\pi$
$991$	393.525	−	1211.15i	0.397099	−	1.22215i	0.927315	−	0.374283i	$-0.122111\pi$
$992$		0			0
$993$	−543.161	+	543.161i	−0.546990	+	0.546990i
$994$		0			0
$995$	199.208	−	229.956i	0.200209	−	0.231112i
$996$		0			0
$997$	1537.28	+	243.481i	1.54190	+	0.244214i	0.868736	−	0.495276i	$-0.164933\pi$
$997$	1537.28	+	243.481i	1.54190	+	0.244214i	0.673168	+	0.739489i	$0.264933\pi$
$998$		0			0
$999$		−	305.652i		−	0.305958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.17.2		64
4.3	odd	2		200.3.u.b.17.7	✓	64
25.3	odd	20	inner	400.3.bg.f.353.2		64
100.3	even	20		200.3.u.b.153.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.17.7	✓	64	4.3	odd	2
200.3.u.b.153.7	yes	64	100.3	even	20
400.3.bg.f.17.2		64	1.1	even	1	trivial
400.3.bg.f.353.2		64	25.3	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)

\(f(q)\)	\(=\)	\(q+(-0.583470 + 3.68389i) q^{3} +(3.77915 + 3.27383i) q^{5} +(-8.52562 - 8.52562i) q^{7} +(-4.67107 - 1.51772i) q^{9} +O(q^{10})\)	\(q+(-0.583470 + 3.68389i) q^{3} +(3.77915 + 3.27383i) q^{5} +(-8.52562 - 8.52562i) q^{7} +(-4.67107 - 1.51772i) q^{9} +(-5.80693 - 17.8719i) q^{11} +(-8.80916 - 17.2889i) q^{13} +(-14.2655 + 12.0118i) q^{15} +(-1.13625 - 7.17401i) q^{17} +(-3.29808 + 4.53941i) q^{19} +(36.3819 - 26.4330i) q^{21} +(5.92922 + 3.02109i) q^{23} +(3.56402 + 24.7447i) q^{25} +(-6.92312 + 13.5874i) q^{27} +(-19.8602 - 27.3352i) q^{29} +(22.2062 + 16.1337i) q^{31} +(69.2262 - 10.9644i) q^{33} +(-4.30817 - 60.1311i) q^{35} +(-17.8588 + 9.09952i) q^{37} +(68.8304 - 22.3644i) q^{39} +(-5.10925 + 15.7247i) q^{41} +(9.37391 - 9.37391i) q^{43} +(-12.6839 - 21.0280i) q^{45} +(-86.2478 - 13.6603i) q^{47} +96.3723i q^{49} +27.0912 q^{51} +(7.94833 - 50.1838i) q^{53} +(36.5643 - 86.5516i) q^{55} +(-14.7983 - 14.7983i) q^{57} +(51.4451 + 16.7155i) q^{59} +(-25.0529 - 77.1050i) q^{61} +(26.8842 + 52.7633i) q^{63} +(23.3100 - 94.1773i) q^{65} +(-2.97145 - 18.7610i) q^{67} +(-14.5889 + 20.0799i) q^{69} +(82.3537 - 59.8335i) q^{71} +(-32.8437 - 16.7347i) q^{73} +(-93.2360 - 1.30833i) q^{75} +(-102.861 + 201.877i) q^{77} +(38.8166 + 53.4265i) q^{79} +(-81.7760 - 59.4137i) q^{81} +(-144.339 + 22.8610i) q^{83} +(19.1924 - 30.8316i) q^{85} +(112.288 - 57.2134i) q^{87} +(-14.0411 + 4.56222i) q^{89} +(-72.2954 + 222.503i) q^{91} +(-72.3915 + 72.3915i) q^{93} +(-27.3252 + 6.35779i) q^{95} +(-70.7123 - 11.1997i) q^{97} +92.2942i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 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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