LMFDB - Embedded newform 400.2.u.e.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			241.2
Root			$-0.983224 - 0.644389i$ of defining polynomial
Character	$\chi$	$=$	400.241
Dual form			400.2.u.e.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 + 0.587785i) q^{3} +(2.09089 + 0.792578i) q^{5} +0.833366 q^{7} +(2.11803 - 1.53884i) q^{9} +O(q^{10})$	\(q+(0.190983 + 0.587785i) q^{3} +(2.09089 + 0.792578i) q^{5} +0.833366 q^{7} +(2.11803 - 1.53884i) q^{9} +(-1.45608 - 1.05790i) q^{11} +(0.892334 - 0.648319i) q^{13} +(-0.0665412 + 1.38036i) q^{15} +(-0.642383 + 1.97705i) q^{17} +(-1.28187 + 3.94520i) q^{19} +(0.159159 + 0.489840i) q^{21} +(2.07411 + 1.50693i) q^{23} +(3.74364 + 3.31439i) q^{25} +(2.80902 + 2.04087i) q^{27} +(-0.740748 - 2.27979i) q^{29} +(2.74075 - 8.43516i) q^{31} +(0.343734 - 1.05790i) q^{33} +(1.74248 + 0.660507i) q^{35} +(-8.69331 + 6.31606i) q^{37} +(0.551493 + 0.400683i) q^{39} +(-1.51037 + 1.09735i) q^{41} +11.0324 q^{43} +(5.64823 - 1.53884i) q^{45} +(-0.628402 - 1.93402i) q^{47} -6.30550 q^{49} -1.28477 q^{51} +(-2.08052 - 6.40319i) q^{53} +(-2.20603 - 3.36602i) q^{55} -2.56375 q^{57} +(-10.8178 + 7.85956i) q^{59} +(-0.601258 - 0.436839i) q^{61} +(1.76510 - 1.28242i) q^{63} +(2.37962 - 0.648319i) q^{65} +(-1.37160 + 4.22134i) q^{67} +(-0.489632 + 1.50693i) q^{69} +(-3.32523 - 10.2340i) q^{71} +(-3.01794 - 2.19266i) q^{73} +(-1.23318 + 2.83345i) q^{75} +(-1.21345 - 0.881621i) q^{77} +(-3.96818 - 12.2128i) q^{79} +(1.76393 - 5.42882i) q^{81} +(-2.49532 + 7.67980i) q^{83} +(-2.91012 + 3.62466i) q^{85} +(1.19856 - 0.870802i) q^{87} +(-8.54813 - 6.21058i) q^{89} +(0.743641 - 0.540287i) q^{91} +5.48150 q^{93} +(-5.80713 + 7.23299i) q^{95} +(3.03299 + 9.33458i) q^{97} -4.71197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	0.990930	−	0.134380i	$-0.0429043\pi$
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	−0.880666	+	0.473738i	$0.842904\pi$
$4$		0			0
$5$	2.09089	+	0.792578i	0.935074	+	0.354452i
$5$	2.09089	+	0.792578i	0.935074	+	0.354452i
$6$		0			0
$7$	0.833366			0.314983			0.157491	−	0.987520i	$-0.449659\pi$
$7$	0.833366			0.314983			0.157491	+	0.987520i	$0.449659\pi$
$8$		0			0
$9$	2.11803	−	1.53884i	0.706011	−	0.512947i
$10$		0			0
$11$	−1.45608	−	1.05790i	−0.439025	−	0.318970i	0.346223	−	0.938152i	$-0.387464\pi$
$11$	−1.45608	−	1.05790i	−0.439025	−	0.318970i	−0.785247	+	0.619182i	$0.787464\pi$
$12$		0			0
$13$	0.892334	−	0.648319i	0.247489	−	0.179811i	−0.457124	−	0.889403i	$-0.651121\pi$
$13$	0.892334	−	0.648319i	0.247489	−	0.179811i	0.704613	+	0.709592i	$0.251121\pi$
$14$		0			0
$15$	−0.0665412	+	1.38036i	−0.0171809	+	0.356408i
$16$		0			0
$17$	−0.642383	+	1.97705i	−0.155801	+	0.479505i	−0.998241	−	0.0592843i	$-0.981118\pi$
$17$	−0.642383	+	1.97705i	−0.155801	+	0.479505i	0.842440	+	0.538789i	$0.181118\pi$
$18$		0			0
$19$	−1.28187	+	3.94520i	−0.294082	+	0.905091i	0.689447	+	0.724337i	$0.257854\pi$
$19$	−1.28187	+	3.94520i	−0.294082	+	0.905091i	−0.983528	+	0.180754i	$0.942146\pi$
$20$		0			0
$21$	0.159159	+	0.489840i	0.0347313	+	0.106892i
$22$		0			0
$23$	2.07411	+	1.50693i	0.432483	+	0.314217i	0.782641	−	0.622474i	$-0.213872\pi$
$23$	2.07411	+	1.50693i	0.432483	+	0.314217i	−0.350158	+	0.936691i	$0.613872\pi$
$24$		0			0
$25$	3.74364	+	3.31439i	0.748728	+	0.662877i
$26$		0			0
$27$	2.80902	+	2.04087i	0.540596	+	0.392766i
$28$		0			0
$29$	−0.740748	−	2.27979i	−0.137553	−	0.423346i	0.858425	−	0.512939i	$-0.171443\pi$
$29$	−0.740748	−	2.27979i	−0.137553	−	0.423346i	−0.995978	+	0.0895931i	$0.971443\pi$
$30$		0			0
$31$	2.74075	−	8.43516i	0.492253	−	1.51500i	−0.328942	−	0.944350i	$-0.606692\pi$
$31$	2.74075	−	8.43516i	0.492253	−	1.51500i	0.821195	−	0.570648i	$-0.193308\pi$
$32$		0			0
$33$	0.343734	−	1.05790i	0.0598364	−	0.184157i
$34$		0			0
$35$	1.74248	+	0.660507i	0.294532	+	0.111646i
$36$		0			0
$37$	−8.69331	+	6.31606i	−1.42917	+	1.03835i	−0.439002	+	0.898486i	$0.644668\pi$
$37$	−8.69331	+	6.31606i	−1.42917	+	1.03835i	−0.990170	+	0.139868i	$0.955332\pi$
$38$		0			0
$39$	0.551493	+	0.400683i	0.0883095	+	0.0641606i
$40$		0			0
$41$	−1.51037	+	1.09735i	−0.235880	+	0.171377i	−0.699446	−	0.714686i	$-0.746570\pi$
$41$	−1.51037	+	1.09735i	−0.235880	+	0.171377i	0.463566	+	0.886062i	$0.346570\pi$
$42$		0			0
$43$	11.0324			1.68243			0.841215	−	0.540701i	$-0.181841\pi$
$43$	11.0324			1.68243			0.841215	+	0.540701i	$0.181841\pi$
$44$		0			0
$45$	5.64823	−	1.53884i	0.841988	−	0.229397i
$46$		0			0
$47$	−0.628402	−	1.93402i	−0.0916619	−	0.282106i	0.894707	−	0.446653i	$-0.147384\pi$
$47$	−0.628402	−	1.93402i	−0.0916619	−	0.282106i	−0.986369	+	0.164546i	$0.947384\pi$
$48$		0			0
$49$	−6.30550			−0.900786
$50$		0			0
$51$	−1.28477			−0.179903
$52$		0			0
$53$	−2.08052	−	6.40319i	−0.285782	−	0.879545i	−0.986163	−	0.165777i	$-0.946987\pi$
$53$	−2.08052	−	6.40319i	−0.285782	−	0.879545i	0.700382	−	0.713769i	$-0.253013\pi$
$54$		0			0
$55$	−2.20603	−	3.36602i	−0.297461	−	0.453874i
$56$		0			0
$57$	−2.56375			−0.339576
$58$		0			0
$59$	−10.8178	+	7.85956i	−1.40835	+	1.02323i	−0.414792	+	0.909916i	$0.636146\pi$
$59$	−10.8178	+	7.85956i	−1.40835	+	1.02323i	−0.993560	+	0.113311i	$0.963854\pi$
$60$		0			0
$61$	−0.601258	−	0.436839i	−0.0769832	−	0.0559316i	0.548628	−	0.836067i	$-0.315150\pi$
$61$	−0.601258	−	0.436839i	−0.0769832	−	0.0559316i	−0.625611	+	0.780135i	$0.715150\pi$
$62$		0			0
$63$	1.76510	−	1.28242i	0.222381	−	0.161569i
$64$		0			0
$65$	2.37962	−	0.648319i	0.295155	−	0.0804140i
$66$		0			0
$67$	−1.37160	+	4.22134i	−0.167567	+	0.515719i	−0.999216	−	0.0395825i	$-0.987397\pi$
$67$	−1.37160	+	4.22134i	−0.167567	+	0.515719i	0.831649	+	0.555302i	$0.187397\pi$
$68$		0			0
$69$	−0.489632	+	1.50693i	−0.0589447	+	0.181413i
$70$		0			0
$71$	−3.32523	−	10.2340i	−0.394632	−	1.21455i	−0.929248	−	0.369458i	$-0.879544\pi$
$71$	−3.32523	−	10.2340i	−0.394632	−	1.21455i	0.534615	−	0.845095i	$-0.320456\pi$
$72$		0			0
$73$	−3.01794	−	2.19266i	−0.353223	−	0.256632i	0.396997	−	0.917820i	$-0.370052\pi$
$73$	−3.01794	−	2.19266i	−0.353223	−	0.256632i	−0.750220	+	0.661188i	$0.770052\pi$
$74$		0			0
$75$	−1.23318	+	2.83345i	−0.142395	+	0.327178i
$76$		0			0
$77$	−1.21345	−	0.881621i	−0.138285	−	0.100470i
$78$		0			0
$79$	−3.96818	−	12.2128i	−0.446455	−	1.37405i	−0.880881	−	0.473339i	$-0.843049\pi$
$79$	−3.96818	−	12.2128i	−0.446455	−	1.37405i	0.434426	−	0.900708i	$-0.356951\pi$
$80$		0			0
$81$	1.76393	−	5.42882i	0.195992	−	0.603203i
$82$		0			0
$83$	−2.49532	+	7.67980i	−0.273897	+	0.842968i	0.715612	+	0.698498i	$0.246148\pi$
$83$	−2.49532	+	7.67980i	−0.273897	+	0.842968i	−0.989509	+	0.144470i	$0.953852\pi$
$84$		0			0
$85$	−2.91012	+	3.62466i	−0.315647	+	0.393149i
$86$		0			0
$87$	1.19856	−	0.870802i	0.128499	−	0.0933597i
$88$		0			0
$89$	−8.54813	−	6.21058i	−0.906100	−	0.658321i	0.0339252	−	0.999424i	$-0.489199\pi$
$89$	−8.54813	−	6.21058i	−0.906100	−	0.658321i	−0.940026	+	0.341104i	$0.889199\pi$
$90$		0			0
$91$	0.743641	−	0.540287i	0.0779547	−	0.0566374i
$92$		0			0
$93$	5.48150			0.568405
$94$		0			0
$95$	−5.80713	+	7.23299i	−0.595799	+	0.742089i
$96$		0			0
$97$	3.03299	+	9.33458i	0.307953	+	0.947783i	0.978559	+	0.205969i	$0.0660345\pi$
$97$	3.03299	+	9.33458i	0.307953	+	0.947783i	−0.670605	+	0.741814i	$0.733966\pi$
$98$		0			0
$99$	−4.71197			−0.473571
$100$		0			0
$101$	−4.87628			−0.485208			−0.242604	−	0.970125i	$-0.578002\pi$
$101$	−4.87628			−0.485208			−0.242604	+	0.970125i	$0.578002\pi$
$102$		0			0
$103$	−3.87845	−	11.9366i	−0.382155	−	1.17615i	−0.938523	−	0.345216i	$-0.887806\pi$
$103$	−3.87845	−	11.9366i	−0.382155	−	1.17615i	0.556368	−	0.830936i	$-0.312194\pi$
$104$		0			0
$105$	−0.0554531	+	1.15035i	−0.00541167	+	0.112262i
$106$		0			0
$107$	−15.1540			−1.46499			−0.732497	−	0.680770i	$-0.761645\pi$
$107$	−15.1540			−1.46499			−0.732497	+	0.680770i	$0.761645\pi$
$108$		0			0
$109$	10.6005	−	7.70174i	1.01535	−	0.737693i	0.0500235	−	0.998748i	$-0.484070\pi$
$109$	10.6005	−	7.70174i	1.01535	−	0.737693i	0.965324	+	0.261055i	$0.0840704\pi$
$110$		0			0
$111$	−5.37276	−	3.90354i	−0.509960	−	0.370508i
$112$		0			0
$113$	7.25589	−	5.27172i	0.682577	−	0.495921i	−0.191635	−	0.981466i	$-0.561379\pi$
$113$	7.25589	−	5.27172i	0.682577	−	0.495921i	0.874212	+	0.485545i	$0.161379\pi$
$114$		0			0
$115$	3.14238	+	4.79473i	0.293029	+	0.447110i
$116$		0			0
$117$	0.892334	−	2.74632i	0.0824963	−	0.253898i
$118$		0			0
$119$	−0.535340	+	1.64761i	−0.0490745	+	0.151036i
$120$		0			0
$121$	−2.39818	−	7.38084i	−0.218016	−	0.670985i
$122$		0			0
$123$	−0.933459	−	0.678198i	−0.0841671	−	0.0611510i
$124$		0			0
$125$	5.20063	+	9.89714i	0.465159	+	0.885227i
$126$		0			0
$127$	10.2785	+	7.46778i	0.912071	+	0.662658i	0.941538	−	0.336908i	$-0.109381\pi$
$127$	10.2785	+	7.46778i	0.912071	+	0.662658i	−0.0294670	+	0.999566i	$0.509381\pi$
$128$		0			0
$129$	2.10701	+	6.48470i	0.185512	+	0.570946i
$130$		0			0
$131$	−2.04046	+	6.27990i	−0.178276	+	0.548678i	−0.999768	−	0.0215426i	$-0.993142\pi$
$131$	−2.04046	+	6.27990i	−0.178276	+	0.548678i	0.821492	+	0.570220i	$0.193142\pi$
$132$		0			0
$133$	−1.06827	+	3.28779i	−0.0926307	+	0.285088i
$134$		0			0
$135$	4.25580	+	6.49360i	0.366281	+	0.558880i
$136$		0			0
$137$	0.548854	−	0.398766i	0.0468918	−	0.0340689i	−0.564092	−	0.825712i	$-0.690774\pi$
$137$	0.548854	−	0.398766i	0.0468918	−	0.0340689i	0.610984	+	0.791643i	$0.290774\pi$
$138$		0			0
$139$	1.85573	+	1.34827i	0.157401	+	0.114359i	0.663698	−	0.748001i	$-0.268986\pi$
$139$	1.85573	+	1.34827i	0.157401	+	0.114359i	−0.506297	+	0.862359i	$0.668986\pi$
$140$		0			0
$141$	1.01678	−	0.738731i	0.0856280	−	0.0622124i
$142$		0			0
$143$	−1.98517			−0.166008
$144$		0			0
$145$	0.258087	−	5.35389i	0.0214330	−	0.444616i
$146$		0			0
$147$	−1.20424	−	3.70628i	−0.0993243	−	0.305689i
$148$		0			0
$149$	−23.5046			−1.92557			−0.962784	−	0.270271i	$-0.912887\pi$
$149$	−23.5046			−1.92557			−0.962784	+	0.270271i	$0.912887\pi$
$150$		0			0
$151$	0.497767			0.0405077			0.0202539	−	0.999795i	$-0.493553\pi$
$151$	0.497767			0.0405077			0.0202539	+	0.999795i	$0.493553\pi$
$152$		0			0
$153$	1.68178	+	5.17599i	0.135964	+	0.418454i
$154$		0			0
$155$	12.4161	−	15.4647i	0.997287	−	1.24216i
$156$		0			0
$157$	7.32045			0.584236			0.292118	−	0.956382i	$-0.405640\pi$
$157$	7.32045			0.584236			0.292118	+	0.956382i	$0.405640\pi$
$158$		0			0
$159$	3.36635	−	2.44580i	0.266969	−	0.193965i
$160$		0			0
$161$	1.72850	+	1.25583i	0.136225	+	0.0989729i
$162$		0			0
$163$	14.2778	−	10.3734i	1.11832	−	0.812509i	0.134369	−	0.990931i	$-0.457099\pi$
$163$	14.2778	−	10.3734i	1.11832	−	0.812509i	0.983954	+	0.178422i	$0.0570992\pi$
$164$		0			0
$165$	1.55718	−	1.93952i	0.121226	−	0.150992i
$166$		0			0
$167$	−6.11524	+	18.8208i	−0.473211	+	1.45639i	0.375143	+	0.926967i	$0.377593\pi$
$167$	−6.11524	+	18.8208i	−0.473211	+	1.45639i	−0.848355	+	0.529428i	$0.822407\pi$
$168$		0			0
$169$	−3.64128	+	11.2067i	−0.280098	+	0.862054i
$170$		0			0
$171$	3.35599	+	10.3287i	0.256639	+	0.789853i
$172$		0			0
$173$	2.58169	+	1.87571i	0.196282	+	0.142607i	0.681585	−	0.731739i	$-0.261291\pi$
$173$	2.58169	+	1.87571i	0.196282	+	0.142607i	−0.485303	+	0.874346i	$0.661291\pi$
$174$		0			0
$175$	3.11982	+	2.76210i	0.235836	+	0.208795i
$176$		0			0
$177$	−6.68574	−	4.85747i	−0.502531	−	0.365110i
$178$		0			0
$179$	−5.10054	−	15.6978i	−0.381232	−	1.17331i	−0.939177	−	0.343434i	$-0.888410\pi$
$179$	−5.10054	−	15.6978i	−0.381232	−	1.17331i	0.557945	−	0.829878i	$-0.311590\pi$
$180$		0			0
$181$	3.29585	−	10.1436i	0.244979	−	0.753967i	−0.750661	−	0.660687i	$-0.770265\pi$
$181$	3.29585	−	10.1436i	0.244979	−	0.753967i	0.995640	−	0.0932799i	$-0.0297351\pi$
$182$		0			0
$183$	0.141938	−	0.436839i	0.0104923	−	0.0322921i
$184$		0			0
$185$	−23.1827	+	6.31606i	−1.70443	+	0.464366i
$186$		0			0
$187$	3.02689	−	2.19916i	0.221348	−	0.160819i
$188$		0			0
$189$	2.34094	+	1.70079i	0.170278	+	0.123714i
$190$		0			0
$191$	0.398022	−	0.289180i	0.0287999	−	0.0209243i	−0.573292	−	0.819351i	$-0.694334\pi$
$191$	0.398022	−	0.289180i	0.0287999	−	0.0209243i	0.602092	+	0.798427i	$0.294334\pi$
$192$		0			0
$193$	16.6968			1.20186			0.600932	−	0.799300i	$-0.294796\pi$
$193$	16.6968			1.20186			0.600932	+	0.799300i	$0.294796\pi$
$194$		0			0
$195$	0.835538	+	1.27489i	0.0598341	+	0.0912964i
$196$		0			0
$197$	3.32005	+	10.2180i	0.236543	+	0.728006i	0.996913	+	0.0785151i	$0.0250179\pi$
$197$	3.32005	+	10.2180i	0.236543	+	0.728006i	−0.760370	+	0.649491i	$0.774982\pi$
$198$		0			0
$199$	12.8786			0.912940			0.456470	−	0.889739i	$-0.349114\pi$
$199$	12.8786			0.912940			0.456470	+	0.889739i	$0.349114\pi$
$200$		0			0
$201$	−2.74320			−0.193490
$202$		0			0
$203$	−0.617314	−	1.89990i	−0.0433270	−	0.133347i
$204$		0			0
$205$	−4.02775	+	1.09735i	−0.281310	+	0.0766420i
$206$		0			0
$207$	6.71197			0.466514
$208$		0			0
$209$	6.04015	−	4.38843i	0.417806	−	0.303554i
$210$		0			0
$211$	21.4185	+	15.5615i	1.47451	+	1.07130i	0.979274	+	0.202540i	$0.0649197\pi$
$211$	21.4185	+	15.5615i	1.47451	+	1.07130i	0.495240	+	0.868756i	$0.335080\pi$
$212$		0			0
$213$	5.38034	−	3.90904i	0.368655	−	0.267843i
$214$		0			0
$215$	23.0676	+	8.74406i	1.57320	+	0.596340i
$216$		0			0
$217$	2.28405	−	7.02957i	0.155051	−	0.477198i
$218$		0			0
$219$	0.712439	−	2.19266i	0.0481422	−	0.148166i
$220$		0			0
$221$	0.708539	+	2.18066i	0.0476615	+	0.146687i
$222$		0			0
$223$	−16.4494	−	11.9512i	−1.10153	−	0.800309i	−0.120222	−	0.992747i	$-0.538361\pi$
$223$	−16.4494	−	11.9512i	−1.10153	−	0.800309i	−0.981309	+	0.192438i	$0.938361\pi$
$224$		0			0
$225$	13.0295	+	1.25911i	0.868632	+	0.0839408i
$226$		0			0
$227$	−12.5859	−	9.14419i	−0.835356	−	0.606921i	0.0857138	−	0.996320i	$-0.472683\pi$
$227$	−12.5859	−	9.14419i	−0.835356	−	0.606921i	−0.921069	+	0.389398i	$0.872683\pi$
$228$		0			0
$229$	6.37276	+	19.6133i	0.421124	+	1.29609i	0.906657	+	0.421868i	$0.138626\pi$
$229$	6.37276	+	19.6133i	0.421124	+	1.29609i	−0.485533	+	0.874218i	$0.661374\pi$
$230$		0			0
$231$	0.286456	−	0.881621i	0.0188474	−	0.0580064i
$232$		0			0
$233$	−6.73211	+	20.7193i	−0.441035	+	1.35737i	0.445739	+	0.895163i	$0.352941\pi$
$233$	−6.73211	+	20.7193i	−0.441035	+	1.35737i	−0.886774	+	0.462203i	$0.847059\pi$
$234$		0			0
$235$	0.218944	−	4.54189i	0.0142823	−	0.296280i
$236$		0			0
$237$	6.42064	−	4.66487i	0.417066	−	0.303016i
$238$		0			0
$239$	19.2533	+	13.9883i	1.24539	+	0.904830i	0.997945	−	0.0640715i	$-0.0204086\pi$
$239$	19.2533	+	13.9883i	1.24539	+	0.904830i	0.247446	+	0.968902i	$0.420409\pi$
$240$		0			0
$241$	9.80377	−	7.12286i	0.631517	−	0.458824i	−0.225409	−	0.974264i	$-0.572372\pi$
$241$	9.80377	−	7.12286i	0.631517	−	0.458824i	0.856925	+	0.515441i	$0.172372\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$		0			0
$245$	−13.1841	−	4.99760i	−0.842302	−	0.319285i
$246$		0			0
$247$	1.41389	+	4.35150i	0.0899635	+	0.276879i
$248$		0			0
$249$	−4.99064			−0.316269
$250$		0			0
$251$	−7.11071			−0.448824			−0.224412	−	0.974494i	$-0.572046\pi$
$251$	−7.11071			−0.448824			−0.224412	+	0.974494i	$0.572046\pi$
$252$		0			0
$253$	−1.42589	−	4.38843i	−0.0896447	−	0.275898i
$254$		0			0
$255$	−2.68630	−	1.01828i	−0.168223	−	0.0637670i
$256$		0			0
$257$	25.6564			1.60040			0.800202	−	0.599730i	$-0.204725\pi$
$257$	25.6564			1.60040			0.800202	+	0.599730i	$0.204725\pi$
$258$		0			0
$259$	−7.24471	+	5.26359i	−0.450164	+	0.327063i
$260$		0			0
$261$	−5.07716	−	3.68878i	−0.314269	−	0.228329i
$262$		0			0
$263$	−20.1357	+	14.6294i	−1.24162	+	0.902089i	−0.997705	−	0.0677085i	$-0.978431\pi$
$263$	−20.1357	+	14.6294i	−1.24162	+	0.902089i	−0.243913	+	0.969797i	$0.578431\pi$
$264$		0			0
$265$	0.724883	−	15.0373i	0.0445292	−	0.923736i
$266$		0			0
$267$	2.01794	−	6.21058i	0.123496	−	0.380082i
$268$		0			0
$269$	0.748944	−	2.30501i	0.0456639	−	0.140539i	−0.925625	−	0.378442i	$-0.876460\pi$
$269$	0.748944	−	2.30501i	0.0456639	−	0.140539i	0.971289	+	0.237903i	$0.0764600\pi$
$270$		0			0
$271$	2.44851	+	7.53573i	0.148736	+	0.457763i	0.997473	−	0.0710533i	$-0.0226360\pi$
$271$	2.44851	+	7.53573i	0.148736	+	0.457763i	−0.848736	+	0.528816i	$0.822636\pi$
$272$		0			0
$273$	0.459595	+	0.333915i	0.0278160	+	0.0202095i
$274$		0			0
$275$	−1.94474	−	8.78642i	−0.117272	−	0.529841i
$276$		0			0
$277$	−6.36259	−	4.62269i	−0.382291	−	0.277750i	0.379998	−	0.924987i	$-0.375925\pi$
$277$	−6.36259	−	4.62269i	−0.382291	−	0.277750i	−0.762289	+	0.647237i	$0.775925\pi$
$278$		0			0
$279$	−7.17537	−	22.0835i	−0.429578	−	1.32211i
$280$		0			0
$281$	−3.84952	+	11.8476i	−0.229643	+	0.706769i	0.768144	+	0.640277i	$0.221181\pi$
$281$	−3.84952	+	11.8476i	−0.229643	+	0.706769i	−0.997787	+	0.0664914i	$0.978819\pi$
$282$		0			0
$283$	−4.28071	+	13.1747i	−0.254462	+	0.783153i	0.739474	+	0.673186i	$0.235074\pi$
$283$	−4.28071	+	13.1747i	−0.254462	+	0.783153i	−0.993935	+	0.109967i	$0.964926\pi$
$284$		0			0
$285$	−5.36051	−	2.03197i	−0.317529	−	0.120363i
$286$		0			0
$287$	−1.25869	+	0.914491i	−0.0742981	+	0.0539807i
$288$		0			0
$289$	10.2572	+	7.45230i	0.603366	+	0.438371i
$290$		0			0
$291$	−4.90748	+	3.56549i	−0.287682	+	0.209013i
$292$		0			0
$293$	9.26026			0.540990			0.270495	−	0.962721i	$-0.412813\pi$
$293$	9.26026			0.540990			0.270495	+	0.962721i	$0.412813\pi$
$294$		0			0
$295$	−28.8480	+	7.85956i	−1.67960	+	0.457601i
$296$		0			0
$297$	−1.93111	−	5.94334i	−0.112054	−	0.344868i
$298$		0			0
$299$	2.82777			0.163534
$300$		0			0
$301$	9.19405			0.529936
$302$		0			0
$303$	−0.931286	−	2.86620i	−0.0535010	−	0.164659i
$304$		0			0
$305$	−0.910935	−	1.38993i	−0.0521600	−	0.0795870i
$306$		0			0
$307$	−22.6968			−1.29538			−0.647688	−	0.761906i	$-0.724264\pi$
$307$	−22.6968			−1.29538			−0.647688	+	0.761906i	$0.724264\pi$
$308$		0			0
$309$	6.27546	−	4.55939i	0.356999	−	0.259375i
$310$		0			0
$311$	−8.39548	−	6.09967i	−0.476064	−	0.345881i	0.323736	−	0.946148i	$-0.395061\pi$
$311$	−8.39548	−	6.09967i	−0.476064	−	0.345881i	−0.799800	+	0.600267i	$0.795061\pi$
$312$		0			0
$313$	−13.7311	+	9.97621i	−0.776126	+	0.563889i	−0.903814	−	0.427926i	$-0.859245\pi$
$313$	−13.7311	+	9.97621i	−0.776126	+	0.563889i	0.127688	+	0.991814i	$0.459245\pi$
$314$		0			0
$315$	4.70704	−	1.28242i	0.265212	−	0.0722561i
$316$		0			0
$317$	5.99658	−	18.4556i	0.336802	−	1.03657i	−0.629026	−	0.777384i	$-0.716546\pi$
$317$	5.99658	−	18.4556i	0.336802	−	1.03657i	0.965828	−	0.259185i	$-0.0834538\pi$
$318$		0			0
$319$	−1.33321	+	4.10319i	−0.0746454	+	0.229735i
$320$		0			0
$321$	−2.89416	−	8.90731i	−0.161536	−	0.497157i
$322$		0			0
$323$	−6.97641	−	5.06865i	−0.388178	−	0.282028i
$324$		0			0
$325$	5.48936	+	0.530468i	0.304495	+	0.0294250i
$326$		0			0
$327$	6.55149	+	4.75994i	0.362298	+	0.263225i
$328$		0			0
$329$	−0.523689	−	1.61175i	−0.0288719	−	0.0888586i
$330$		0			0
$331$	−2.56085	+	7.88150i	−0.140757	+	0.433206i	−0.996441	−	0.0842928i	$-0.973137\pi$
$331$	−2.56085	+	7.88150i	−0.140757	+	0.433206i	0.855684	+	0.517499i	$0.173137\pi$
$332$		0			0
$333$	−8.69331	+	26.7553i	−0.476391	+	1.46618i
$334$		0			0
$335$	−6.21360	+	7.73927i	−0.339485	+	0.422841i
$336$		0			0
$337$	−6.66048	+	4.83912i	−0.362819	+	0.263604i	−0.754227	−	0.656614i	$-0.771988\pi$
$337$	−6.66048	+	4.83912i	−0.362819	+	0.263604i	0.391408	+	0.920217i	$0.371988\pi$
$338$		0			0
$339$	4.48439	+	3.25810i	0.243559	+	0.176956i
$340$		0			0
$341$	−12.9143	+	9.38281i	−0.699350	+	0.508108i
$342$		0			0
$343$	−11.0883			−0.598715
$344$		0			0
$345$	−2.21813	+	2.76276i	−0.119420	+	0.148742i
$346$		0			0
$347$	−6.16394	−	18.9706i	−0.330897	−	1.01840i	−0.968708	−	0.248204i	$-0.920160\pi$
$347$	−6.16394	−	18.9706i	−0.330897	−	1.01840i	0.637810	−	0.770193i	$-0.279840\pi$
$348$		0			0
$349$	4.67641			0.250322			0.125161	−	0.992136i	$-0.460055\pi$
$349$	4.67641			0.250322			0.125161	+	0.992136i	$0.460055\pi$
$350$		0			0
$351$	3.82972			0.204415
$352$		0			0
$353$	−7.67782	−	23.6299i	−0.408649	−	1.25769i	−0.917810	−	0.397021i	$-0.870044\pi$
$353$	−7.67782	−	23.6299i	−0.408649	−	1.25769i	0.509160	−	0.860672i	$-0.329956\pi$
$354$		0			0
$355$	1.15856	−	24.0337i	0.0614898	−	1.27558i
$356$		0			0
$357$	−1.07068			−0.0566664
$358$		0			0
$359$	15.2461	−	11.0770i	0.804660	−	0.584620i	−0.107618	−	0.994192i	$-0.534322\pi$
$359$	15.2461	−	11.0770i	0.804660	−	0.584620i	0.912277	+	0.409573i	$0.134322\pi$
$360$		0			0
$361$	1.44993	+	1.05343i	0.0763119	+	0.0554438i
$362$		0			0
$363$	3.88034	−	2.81923i	0.203665	−	0.147971i
$364$		0			0
$365$	−4.57233	−	6.97657i	−0.239326	−	0.365170i
$366$		0			0
$367$	−3.00893	+	9.26053i	−0.157065	+	0.483396i	−0.998364	−	0.0571736i	$-0.981791\pi$
$367$	−3.00893	+	9.26053i	−0.157065	+	0.483396i	0.841299	+	0.540569i	$0.181791\pi$
$368$		0			0
$369$	−1.51037	+	4.64844i	−0.0786266	+	0.241988i
$370$		0			0
$371$	−1.73384	−	5.33620i	−0.0900162	−	0.277042i
$372$		0			0
$373$	−23.5821	−	17.1334i	−1.22104	−	0.887135i	−0.224851	−	0.974393i	$-0.572189\pi$
$373$	−23.5821	−	17.1334i	−1.22104	−	0.887135i	−0.996186	+	0.0872583i	$0.972189\pi$
$374$		0			0
$375$	−4.82416	+	4.94704i	−0.249119	+	0.255464i
$376$		0			0
$377$	−2.13902	−	1.55409i	−0.110165	−	0.0800398i
$378$		0			0
$379$	−1.87942	−	5.78426i	−0.0965394	−	0.297118i	0.891112	−	0.453783i	$-0.149926\pi$
$379$	−1.87942	−	5.78426i	−0.0965394	−	0.297118i	−0.987652	+	0.156665i	$0.949926\pi$
$380$		0			0
$381$	−2.42643	+	7.46778i	−0.124310	+	0.382586i
$382$		0			0
$383$	−9.76498	+	30.0535i	−0.498967	+	1.53566i	0.311715	+	0.950176i	$0.399097\pi$
$383$	−9.76498	+	30.0535i	−0.498967	+	1.53566i	−0.810682	+	0.585487i	$0.800903\pi$
$384$		0			0
$385$	−1.83843	−	2.80512i	−0.0936951	−	0.142962i
$386$		0			0
$387$	23.3671	−	16.9772i	1.18781	−	0.862997i
$388$		0			0
$389$	−4.83362	−	3.51183i	−0.245074	−	0.178057i	0.458467	−	0.888712i	$-0.348399\pi$
$389$	−4.83362	−	3.51183i	−0.245074	−	0.178057i	−0.703541	+	0.710655i	$0.748399\pi$
$390$		0			0
$391$	−4.31166	+	3.13260i	−0.218050	+	0.158422i
$392$		0			0
$393$	−4.08093			−0.205856
$394$		0			0
$395$	1.38257	−	28.6807i	0.0695645	−	1.44308i
$396$		0			0
$397$	−0.501105	−	1.54224i	−0.0251497	−	0.0774029i	0.937694	−	0.347462i	$-0.112957\pi$
$397$	−0.501105	−	1.54224i	−0.0251497	−	0.0774029i	−0.962844	+	0.270060i	$0.912957\pi$
$398$		0			0
$399$	−2.13654			−0.106961
$400$		0			0
$401$	−5.63644			−0.281470			−0.140735	−	0.990047i	$-0.544947\pi$
$401$	−5.63644			−0.281470			−0.140735	+	0.990047i	$0.544947\pi$
$402$		0			0
$403$	−3.02301	−	9.30386i	−0.150587	−	0.463458i
$404$		0			0
$405$	7.99095	−	9.95302i	0.397074	−	0.494570i
$406$		0			0
$407$	19.3399			0.958645
$408$		0			0
$409$	26.8187	−	19.4849i	1.32610	−	0.963468i	0.326265	−	0.945278i	$-0.394210\pi$
$409$	26.8187	−	19.4849i	1.32610	−	0.963468i	0.999835	−	0.0181896i	$-0.00579024\pi$
$410$		0			0
$411$	0.339211	+	0.246451i	0.0167320	+	0.0121565i
$412$		0			0
$413$	−9.01515	+	6.54989i	−0.443606	+	0.322299i
$414$		0			0
$415$	−11.3043	+	14.0799i	−0.554905	+	0.691155i
$416$		0			0
$417$	−0.438079	+	1.34827i	−0.0214528	+	0.0660250i
$418$		0			0
$419$	−7.32237	+	22.5360i	−0.357721	+	1.10095i	0.596693	+	0.802469i	$0.296481\pi$
$419$	−7.32237	+	22.5360i	−0.357721	+	1.10095i	−0.954415	+	0.298484i	$0.903519\pi$
$420$		0			0
$421$	3.01571	+	9.28140i	0.146977	+	0.452348i	0.997260	−	0.0739778i	$-0.0235694\pi$
$421$	3.01571	+	9.28140i	0.146977	+	0.452348i	−0.850283	+	0.526325i	$0.823569\pi$
$422$		0			0
$423$	−4.30713	−	3.12931i	−0.209420	−	0.152152i
$424$		0			0
$425$	−8.95756	+	5.27226i	−0.434505	+	0.255742i
$426$		0			0
$427$	−0.501068	−	0.364047i	−0.0242484	−	0.0176175i
$428$		0			0
$429$	−0.379133	−	1.16685i	−0.0183047	−	0.0563362i
$430$		0			0
$431$	4.37321	−	13.4593i	0.210650	−	0.648314i	−0.788784	−	0.614671i	$-0.789289\pi$
$431$	4.37321	−	13.4593i	0.210650	−	0.648314i	0.999434	−	0.0336434i	$-0.0107111\pi$
$432$		0			0
$433$	−0.156266	+	0.480938i	−0.00750967	+	0.0231124i	−0.954741	−	0.297438i	$-0.903868\pi$
$433$	−0.156266	+	0.480938i	−0.00750967	+	0.0231124i	0.947231	+	0.320550i	$0.103868\pi$
$434$		0			0
$435$	3.19623	−	0.870802i	0.153247	−	0.0417517i
$436$		0			0
$437$	−8.60390	+	6.25110i	−0.411580	+	0.299031i
$438$		0			0
$439$	29.9702	+	21.7746i	1.43040	+	1.03925i	0.989942	+	0.141472i	$0.0451837\pi$
$439$	29.9702	+	21.7746i	1.43040	+	1.03925i	0.440457	+	0.897774i	$0.354816\pi$
$440$		0			0
$441$	−13.3553	+	9.70317i	−0.635965	+	0.462056i
$442$		0			0
$443$	20.7271			0.984775			0.492388	−	0.870376i	$-0.336124\pi$
$443$	20.7271			0.984775			0.492388	+	0.870376i	$0.336124\pi$
$444$		0			0
$445$	−12.9508	−	19.7607i	−0.613929	−	0.936747i
$446$		0			0
$447$	−4.48897	−	13.8156i	−0.212321	−	0.653457i
$448$		0			0
$449$	−6.56029			−0.309599			−0.154800	−	0.987946i	$-0.549473\pi$
$449$	−6.56029			−0.309599			−0.154800	+	0.987946i	$0.549473\pi$
$450$		0			0
$451$	3.36010			0.158221
$452$		0			0
$453$	0.0950651	+	0.292580i	0.00446655	+	0.0137466i
$454$		0			0
$455$	1.98309	−	0.540287i	0.0929687	−	0.0253290i
$456$		0			0
$457$	−28.9369			−1.35361			−0.676805	−	0.736163i	$-0.736636\pi$
$457$	−28.9369			−1.35361			−0.676805	+	0.736163i	$0.736636\pi$
$458$		0			0
$459$	−5.83937	+	4.24255i	−0.272558	+	0.198025i
$460$		0			0
$461$	27.5079	+	19.9856i	1.28117	+	0.930824i	0.999588	−	0.0287136i	$-0.00914107\pi$
$461$	27.5079	+	19.9856i	1.28117	+	0.930824i	0.281581	+	0.959537i	$0.409141\pi$
$462$		0			0
$463$	−2.13334	+	1.54996i	−0.0991445	+	0.0720327i	−0.636253	−	0.771480i	$-0.719517\pi$
$463$	−2.13334	+	1.54996i	−0.0991445	+	0.0720327i	0.537108	+	0.843513i	$0.319517\pi$
$464$		0			0
$465$	11.4612	+	4.34451i	0.531501	+	0.201472i
$466$		0			0
$467$	11.9619	−	36.8148i	0.553529	−	1.70359i	−0.146267	−	0.989245i	$-0.546726\pi$
$467$	11.9619	−	36.8148i	0.553529	−	1.70359i	0.699796	−	0.714342i	$-0.253274\pi$
$468$		0			0
$469$	−1.14304	+	3.51792i	−0.0527808	+	0.162443i
$470$		0			0
$471$	1.39808	+	4.30285i	0.0644202	+	0.198265i
$472$		0			0
$473$	−16.0641	−	11.6712i	−0.738628	−	0.536645i
$474$		0			0
$475$	−17.8748	+	10.5208i	−0.820151	+	0.482727i
$476$		0			0
$477$	−14.2601	−	10.3606i	−0.652925	−	0.474378i
$478$		0			0
$479$	2.49231	+	7.67054i	0.113877	+	0.350476i	0.991711	−	0.128488i	$-0.0410124\pi$
$479$	2.49231	+	7.67054i	0.113877	+	0.350476i	−0.877835	+	0.478964i	$0.841012\pi$
$480$		0			0
$481$	−3.66252	+	11.2721i	−0.166996	+	0.513962i
$482$		0			0
$483$	−0.408042	+	1.25583i	−0.0185666	+	0.0571420i
$484$		0			0
$485$	−1.05674	+	21.9215i	−0.0479839	+	0.995402i
$486$		0			0
$487$	6.04666	−	4.39316i	0.274000	−	0.199073i	−0.442296	−	0.896869i	$-0.645836\pi$
$487$	6.04666	−	4.39316i	0.274000	−	0.199073i	0.716296	+	0.697796i	$0.245836\pi$
$488$		0			0
$489$	8.82416	+	6.41113i	0.399042	+	0.289921i
$490$		0			0
$491$	5.51407	−	4.00621i	0.248847	−	0.180798i	−0.456369	−	0.889791i	$-0.650850\pi$
$491$	5.51407	−	4.00621i	0.248847	−	0.180798i	0.705216	+	0.708993i	$0.250850\pi$
$492$		0			0
$493$	4.98310			0.224428
$494$		0			0
$495$	−9.85222	−	3.73461i	−0.442824	−	0.167858i
$496$		0			0
$497$	−2.77113	−	8.52867i	−0.124302	−	0.382563i
$498$		0			0
$499$	−19.5176			−0.873727			−0.436863	−	0.899528i	$-0.643911\pi$
$499$	−19.5176			−0.873727			−0.436863	+	0.899528i	$0.643911\pi$
$500$		0			0
$501$	−12.2305			−0.546417
$502$		0			0
$503$	4.30626	+	13.2533i	0.192007	+	0.590935i	0.999998	+	0.00174190i	$0.000554465\pi$
$503$	4.30626	+	13.2533i	0.192007	+	0.590935i	−0.807992	+	0.589194i	$0.799446\pi$
$504$		0			0
$505$	−10.1958	−	3.86483i	−0.453705	−	0.171983i
$506$		0			0
$507$	−7.28256			−0.323430
$508$		0			0
$509$	18.8189	−	13.6727i	0.834134	−	0.606034i	−0.0865919	−	0.996244i	$-0.527598\pi$
$509$	18.8189	−	13.6727i	0.834134	−	0.606034i	0.920726	+	0.390210i	$0.127598\pi$
$510$		0			0
$511$	−2.51505	−	1.82729i	−0.111259	−	0.0808345i
$512$		0			0
$513$	−11.6524	+	8.46599i	−0.514468	+	0.373783i
$514$		0			0
$515$	1.35131	−	28.0322i	0.0595457	−	1.23525i
$516$		0			0
$517$	−1.13101	+	3.48088i	−0.0497416	+	0.153089i
$518$		0			0
$519$	−0.609454	+	1.87571i	−0.0267520	+	0.0823343i
$520$		0			0
$521$	13.4660	+	41.4440i	0.589955	+	1.81570i	0.578386	+	0.815763i	$0.303683\pi$
$521$	13.4660	+	41.4440i	0.589955	+	1.81570i	0.0115690	+	0.999933i	$0.496317\pi$
$522$		0			0
$523$	6.31766	+	4.59005i	0.276252	+	0.200709i	0.717281	−	0.696784i	$-0.245386\pi$
$523$	6.31766	+	4.59005i	0.276252	+	0.200709i	−0.441029	+	0.897493i	$0.645386\pi$
$524$		0			0
$525$	−1.02769	+	2.36130i	−0.0448519	+	0.103056i
$526$		0			0
$527$	14.9161	+	10.8372i	0.649756	+	0.472076i
$528$		0			0
$529$	−5.07629	−	15.6232i	−0.220708	−	0.679270i
$530$		0			0
$531$	−10.8178	+	33.2936i	−0.469451	+	1.44482i
$532$		0			0
$533$	−0.636323	+	1.95840i	−0.0275622	+	0.0848277i
$534$		0			0
$535$	−31.6854	−	12.0107i	−1.36988	−	0.519269i
$536$		0			0
$537$	8.25284	−	5.99604i	0.356137	−	0.258748i
$538$		0			0
$539$	9.18131	+	6.67061i	0.395467	+	0.287324i
$540$		0			0
$541$	20.8579	−	15.1541i	0.896749	−	0.651526i	−0.0408799	−	0.999164i	$-0.513016\pi$
$541$	20.8579	−	15.1541i	0.896749	−	0.651526i	0.937629	+	0.347638i	$0.113016\pi$
$542$		0			0
$543$	6.59171			0.282877
$544$		0			0
$545$	28.2688	−	7.70174i	1.21090	−	0.329906i
$546$		0			0
$547$	7.40053	+	22.7765i	0.316424	+	0.973852i	0.975164	+	0.221482i	$0.0710895\pi$
$547$	7.40053	+	22.7765i	0.316424	+	0.973852i	−0.658741	+	0.752370i	$0.728911\pi$
$548$		0			0
$549$	−1.94571			−0.0830410
$550$		0			0
$551$	9.94376			0.423619
$552$		0			0
$553$	−3.30694	−	10.1777i	−0.140625	−	0.432801i
$554$		0			0
$555$	−8.14000	−	12.4202i	−0.345524	−	0.527208i
$556$		0			0
$557$	22.4185			0.949904			0.474952	−	0.880012i	$-0.342465\pi$
$557$	22.4185			0.949904			0.474952	+	0.880012i	$0.342465\pi$
$558$		0			0
$559$	9.84461	−	7.15253i	0.416383	−	0.302520i
$560$		0			0
$561$	1.87072	+	1.35916i	0.0789819	+	0.0573837i
$562$		0			0
$563$	−8.17248	+	5.93765i	−0.344429	+	0.250242i	−0.746528	−	0.665354i	$-0.768281\pi$
$563$	−8.17248	+	5.93765i	−0.344429	+	0.250242i	0.402099	+	0.915596i	$0.368281\pi$
$564$		0			0
$565$	19.3495	−	5.27172i	0.814040	−	0.221783i
$566$		0			0
$567$	1.47000	−	4.52420i	0.0617342	−	0.189998i
$568$		0			0
$569$	3.48538	−	10.7269i	0.146115	−	0.449695i	−0.851038	−	0.525104i	$-0.824026\pi$
$569$	3.48538	−	10.7269i	0.146115	−	0.449695i	0.997153	+	0.0754091i	$0.0240263\pi$
$570$		0			0
$571$	−1.62957	−	5.01529i	−0.0681953	−	0.209883i	0.911151	−	0.412072i	$-0.135195\pi$
$571$	−1.62957	−	5.01529i	−0.0681953	−	0.209883i	−0.979347	+	0.202188i	$0.935195\pi$
$572$		0			0
$573$	0.245991	+	0.178723i	0.0102764	+	0.00746626i
$574$		0			0
$575$	2.77018	+	12.5158i	0.115525	+	0.521946i
$576$		0			0
$577$	13.8012	+	10.0272i	0.574553	+	0.417437i	0.836756	−	0.547576i	$-0.184449\pi$
$577$	13.8012	+	10.0272i	0.574553	+	0.417437i	−0.262203	+	0.965013i	$0.584449\pi$
$578$		0			0
$579$	3.18881	+	9.81415i	0.132522	+	0.407862i
$580$		0			0
$581$	−2.07951	+	6.40009i	−0.0862728	+	0.265520i
$582$		0			0
$583$	−3.74455	+	11.5245i	−0.155083	+	0.477298i
$584$		0			0
$585$	4.04245	−	5.03501i	0.167135	−	0.208172i
$586$		0			0
$587$	−1.82680	+	1.32725i	−0.0754001	+	0.0547814i	−0.624847	−	0.780747i	$-0.714839\pi$
$587$	−1.82680	+	1.32725i	−0.0754001	+	0.0547814i	0.549447	+	0.835529i	$0.314839\pi$
$588$		0			0
$589$	29.7651	+	21.6256i	1.22645	+	0.891067i
$590$		0			0
$591$	−5.37195	+	3.90295i	−0.220972	+	0.160546i
$592$		0			0
$593$	27.9744			1.14877			0.574385	−	0.818585i	$-0.305241\pi$
$593$	27.9744			1.14877			0.574385	+	0.818585i	$0.305241\pi$
$594$		0			0
$595$	−2.42519	+	3.02066i	−0.0994232	+	0.123835i
$596$		0			0
$597$	2.45960	+	7.56986i	0.100665	+	0.309814i
$598$		0			0
$599$	5.13906			0.209976			0.104988	−	0.994473i	$-0.466520\pi$
$599$	5.13906			0.209976			0.104988	+	0.994473i	$0.466520\pi$
$600$		0			0
$601$	37.9217			1.54686			0.773429	−	0.633882i	$-0.218540\pi$
$601$	37.9217			1.54686			0.773429	+	0.633882i	$0.218540\pi$
$602$		0			0
$603$	3.59089	+	11.0516i	0.146232	+	0.450057i
$604$		0			0
$605$	0.835559	−	17.3333i	0.0339703	−	0.704697i
$606$		0			0
$607$	39.0728			1.58592			0.792959	−	0.609275i	$-0.208539\pi$
$607$	39.0728			1.58592			0.792959	+	0.609275i	$0.208539\pi$
$608$		0			0
$609$	0.998835	−	0.725696i	0.0404748	−	0.0294067i
$610$		0			0
$611$	−1.81461	−	1.31839i	−0.0734112	−	0.0533363i
$612$		0			0
$613$	1.53761	−	1.11714i	0.0621035	−	0.0451208i	−0.556300	−	0.830981i	$-0.687780\pi$
$613$	1.53761	−	1.11714i	0.0621035	−	0.0451208i	0.618404	+	0.785860i	$0.287780\pi$
$614$		0			0
$615$	−1.41424	−	2.15788i	−0.0570275	−	0.0870139i
$616$		0			0
$617$	4.39305	−	13.5204i	0.176858	−	0.544312i	−0.822856	−	0.568250i	$-0.807621\pi$
$617$	4.39305	−	13.5204i	0.176858	−	0.544312i	0.999713	+	0.0239383i	$0.00762053\pi$
$618$		0			0
$619$	−6.80529	+	20.9445i	−0.273528	+	0.841831i	0.716078	+	0.698021i	$0.245936\pi$
$619$	−6.80529	+	20.9445i	−0.273528	+	0.841831i	−0.989605	+	0.143811i	$0.954064\pi$
$620$		0			0
$621$	2.75077	+	8.46599i	0.110385	+	0.339729i
$622$		0			0
$623$	−7.12372	−	5.17569i	−0.285406	−	0.207360i
$624$		0			0
$625$	3.02969	+	24.8157i	0.121188	+	0.992630i
$626$		0			0
$627$	3.73302	+	2.71220i	0.149082	+	0.108315i
$628$		0			0
$629$	−6.90274	−	21.2444i	−0.275230	−	0.847072i
$630$		0			0
$631$	9.56547	−	29.4395i	0.380795	−	1.17197i	−0.558689	−	0.829377i	$-0.688696\pi$
$631$	9.56547	−	29.4395i	0.380795	−	1.17197i	0.939485	−	0.342591i	$-0.111304\pi$
$632$		0			0
$633$	−5.05623	+	15.5615i	−0.200967	+	0.618514i
$634$		0			0
$635$	15.5724	+	23.7608i	0.617974	+	0.942920i
$636$		0			0
$637$	−5.62661	+	4.08797i	−0.222935	+	0.161971i
$638$		0			0
$639$	−22.7915	−	16.5590i	−0.901616	−	0.655063i
$640$		0			0
$641$	−16.2639	+	11.8164i	−0.642385	+	0.466720i	−0.860669	−	0.509166i	$-0.829954\pi$
$641$	−16.2639	+	11.8164i	−0.642385	+	0.466720i	0.218284	+	0.975885i	$0.429954\pi$
$642$		0			0
$643$	17.9165			0.706558			0.353279	−	0.935518i	$-0.385067\pi$
$643$	17.9165			0.706558			0.353279	+	0.935518i	$0.385067\pi$
$644$		0			0
$645$	−0.734110	+	15.2288i	−0.0289056	+	0.599632i
$646$		0			0
$647$	−7.64211	−	23.5200i	−0.300442	−	0.924666i	−0.981339	−	0.192287i	$-0.938410\pi$
$647$	−7.64211	−	23.5200i	−0.300442	−	0.924666i	0.680897	−	0.732380i	$-0.261590\pi$
$648$		0			0
$649$	24.0662			0.944680
$650$		0			0
$651$	4.56809			0.179038
$652$		0			0
$653$	−0.918758	−	2.82765i	−0.0359538	−	0.110654i	0.931469	−	0.363821i	$-0.118528\pi$
$653$	−0.918758	−	2.82765i	−0.0359538	−	0.110654i	−0.967423	+	0.253166i	$0.918528\pi$
$654$		0			0
$655$	−9.24370	+	11.5134i	−0.361181	+	0.449864i
$656$		0			0
$657$	−9.76626			−0.381018
$658$		0			0
$659$	15.3181	−	11.1293i	0.596709	−	0.433534i	−0.248001	−	0.968760i	$-0.579773\pi$
$659$	15.3181	−	11.1293i	0.596709	−	0.433534i	0.844709	+	0.535226i	$0.179773\pi$
$660$		0			0
$661$	−31.7914	−	23.0978i	−1.23654	−	0.898401i	−0.239179	−	0.970975i	$-0.576878\pi$
$661$	−31.7914	−	23.0978i	−1.23654	−	0.898401i	−0.997363	+	0.0725749i	$0.976878\pi$
$662$		0			0
$663$	−1.14644	+	0.832937i	−0.0445240	+	0.0323486i
$664$		0			0
$665$	−4.83946	+	6.02773i	−0.187666	+	0.233745i
$666$		0			0
$667$	1.89909	−	5.84480i	0.0735331	−	0.226311i
$668$		0			0
$669$	3.88317	−	11.9512i	0.150132	−	0.462059i
$670$		0			0
$671$	0.413345	+	1.27215i	0.0159570	+	0.0491107i
$672$		0			0
$673$	−19.9660	−	14.5061i	−0.769632	−	0.559170i	0.132217	−	0.991221i	$-0.457790\pi$
$673$	−19.9660	−	14.5061i	−0.769632	−	0.559170i	−0.901850	+	0.432050i	$0.857790\pi$
$674$		0			0
$675$	3.75172	+	16.9505i	0.144404	+	0.652423i
$676$		0			0
$677$	35.2934	+	25.6421i	1.35643	+	0.985508i	0.998663	+	0.0516988i	$0.0164636\pi$
$677$	35.2934	+	25.6421i	1.35643	+	0.985508i	0.357772	+	0.933809i	$0.383536\pi$
$678$		0			0
$679$	2.52759	+	7.77912i	0.0970000	+	0.298535i
$680$		0			0
$681$	2.97113	−	9.14419i	0.113854	−	0.350406i
$682$		0			0
$683$	−6.81741	+	20.9818i	−0.260861	+	0.802847i	0.731757	+	0.681565i	$0.238700\pi$
$683$	−6.81741	+	20.9818i	−0.260861	+	0.802847i	−0.992618	+	0.121282i	$0.961300\pi$
$684$		0			0
$685$	1.46365	−	0.398766i	0.0559231	−	0.0152361i
$686$		0			0
$687$	−10.3113	+	7.49163i	−0.393402	+	0.285824i
$688$		0			0
$689$	−6.00783	−	4.36494i	−0.228880	−	0.166291i
$690$		0			0
$691$	14.7311	−	10.7028i	0.560397	−	0.407152i	−0.271207	−	0.962521i	$-0.587423\pi$
$691$	14.7311	−	10.7028i	0.560397	−	0.407152i	0.831604	+	0.555369i	$0.187423\pi$
$692$		0			0
$693$	−3.92680			−0.149167
$694$		0			0
$695$	2.81152	+	4.28989i	0.106647	+	0.162725i
$696$		0			0
$697$	−1.19928	−	3.69099i	−0.0454258	−	0.139806i
$698$		0			0
$699$	−13.4642			−0.509263
$700$		0			0
$701$	1.95162			0.0737115			0.0368558	−	0.999321i	$-0.488266\pi$
$701$	1.95162			0.0737115			0.0368558	+	0.999321i	$0.488266\pi$
$702$		0			0
$703$	−13.7744	−	42.3932i	−0.519511	−	1.59889i
$704$		0			0
$705$	2.71147	−	0.738731i	0.102120	−	0.0278222i
$706$		0			0
$707$	−4.06372			−0.152832
$708$		0			0
$709$	−27.8786	+	20.2550i	−1.04700	+	0.760692i	−0.971640	−	0.236465i	$-0.924011\pi$
$709$	−27.8786	+	20.2550i	−1.04700	+	0.760692i	−0.0753622	+	0.997156i	$0.524011\pi$
$710$		0			0
$711$	−27.1983	−	19.7607i	−1.02002	−	0.741084i
$712$		0			0
$713$	18.3958	−	13.3654i	0.688929	−	0.500536i
$714$		0			0
$715$	−4.15077	−	1.57340i	−0.155230	−	0.0588419i
$716$		0			0
$717$	−4.54508	+	13.9883i	−0.169739	+	0.522404i
$718$		0			0
$719$	5.09724	−	15.6877i	0.190095	−	0.585052i	−0.809904	−	0.586562i	$-0.800481\pi$
$719$	5.09724	−	15.6877i	0.190095	−	0.585052i	0.999999	+	0.00151058i	$0.000480833\pi$
$720$		0			0
$721$	−3.23217	−	9.94759i	−0.120372	−	0.370468i
$722$		0			0
$723$	6.05907	+	4.40217i	0.225339	+	0.163718i
$724$		0			0
$725$	4.78300	−	10.9898i	0.177636	−	0.408152i
$726$		0			0
$727$	−6.01184	−	4.36786i	−0.222967	−	0.161995i	0.470694	−	0.882296i	$-0.344003\pi$
$727$	−6.01184	−	4.36786i	−0.222967	−	0.161995i	−0.693661	+	0.720301i	$0.744003\pi$
$728$		0			0
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$		0			0
$731$	−7.08704	+	21.8117i	−0.262124	+	0.806734i
$732$		0			0
$733$	−1.21919	+	3.75230i	−0.0450320	+	0.138594i	−0.971045	−	0.238898i	$-0.923214\pi$
$733$	−1.21919	+	3.75230i	−0.0450320	+	0.138594i	0.926013	+	0.377493i	$0.123214\pi$
$734$		0			0
$735$	0.419575	−	8.70388i	0.0154763	−	0.321048i
$736$		0			0
$737$	6.46293	−	4.69560i	0.238065	−	0.172964i
$738$		0			0
$739$	−8.04823	−	5.84738i	−0.296059	−	0.215099i	0.429833	−	0.902909i	$-0.358573\pi$
$739$	−8.04823	−	5.84738i	−0.296059	−	0.215099i	−0.725892	+	0.687809i	$0.758573\pi$
$740$		0			0
$741$	−2.28772	+	1.66212i	−0.0840414	+	0.0610597i
$742$		0			0
$743$	29.7044			1.08975			0.544875	−	0.838517i	$-0.316577\pi$
$743$	29.7044			1.08975			0.544875	+	0.838517i	$0.316577\pi$
$744$		0			0
$745$	−49.1455	−	18.6292i	−1.80055	−	0.682521i
$746$		0			0
$747$	6.53283	+	20.1060i	0.239024	+	0.735640i
$748$		0			0
$749$	−12.6288			−0.461448
$750$		0			0
$751$	3.82521			0.139584			0.0697919	−	0.997562i	$-0.477766\pi$
$751$	3.82521			0.139584			0.0697919	+	0.997562i	$0.477766\pi$
$752$		0			0
$753$	−1.35803	−	4.17957i	−0.0494892	−	0.152312i
$754$		0			0
$755$	1.04078	+	0.394519i	0.0378777	+	0.0143580i
$756$		0			0
$757$	−19.8075			−0.719917			−0.359959	−	0.932968i	$-0.617209\pi$
$757$	−19.8075			−0.719917			−0.359959	+	0.932968i	$0.617209\pi$
$758$		0			0
$759$	2.30713	−	1.67623i	0.0837436	−	0.0608433i
$760$		0			0
$761$	−2.24147	−	1.62852i	−0.0812532	−	0.0590339i	0.546417	−	0.837513i	$-0.315991\pi$
$761$	−2.24147	−	1.62852i	−0.0812532	−	0.0590339i	−0.627670	+	0.778479i	$0.715991\pi$
$762$		0			0
$763$	8.83412	−	6.41837i	0.319817	−	0.232360i
$764$		0			0
$765$	−0.585956	+	12.1554i	−0.0211853	+	0.439478i
$766$		0			0
$767$	−4.55755	+	14.0267i	−0.164564	+	0.506475i
$768$		0			0
$769$	−15.1222	+	46.5413i	−0.545320	+	1.67832i	0.174908	+	0.984585i	$0.444037\pi$
$769$	−15.1222	+	46.5413i	−0.545320	+	1.67832i	−0.720228	+	0.693738i	$0.755963\pi$
$770$		0			0
$771$	4.89994	+	15.0805i	0.176467	+	0.543110i
$772$		0			0
$773$	8.69890	+	6.32012i	0.312878	+	0.227319i	0.733130	−	0.680088i	$-0.238059\pi$
$773$	8.69890	+	6.32012i	0.312878	+	0.227319i	−0.420253	+	0.907407i	$0.638059\pi$
$774$		0			0
$775$	38.2177	−	22.4943i	1.37282	−	0.808019i
$776$		0			0
$777$	−4.47748	−	3.25308i	−0.160629	−	0.116703i
$778$		0			0
$779$	−2.39315	−	7.36536i	−0.0857435	−	0.263891i
$780$		0			0
$781$	−5.98479	+	18.4193i	−0.214153	+	0.659095i
$782$		0			0
$783$	2.57198	−	7.91574i	0.0919150	−	0.282885i
$784$		0			0
$785$	15.3063	+	5.80203i	0.546304	+	0.207083i
$786$		0			0
$787$	−19.3427	+	14.0533i	−0.689492	+	0.500945i	−0.876493	−	0.481415i	$-0.840123\pi$
$787$	−19.3427	+	14.0533i	−0.689492	+	0.500945i	0.187001	+	0.982360i	$0.440123\pi$
$788$		0			0
$789$	−12.4445	−	9.04148i	−0.443037	−	0.321885i
$790$		0			0
$791$	6.04681	−	4.39327i	0.215000	−	0.156207i
$792$		0			0
$793$	−0.819734			−0.0291096
$794$		0			0
$795$	8.97716	−	2.44580i	0.318387	−	0.0867436i
$796$		0			0
$797$	−12.9085	−	39.7284i	−0.457244	−	1.40725i	−0.868480	−	0.495724i	$-0.834903\pi$
$797$	−12.9085	−	39.7284i	−0.457244	−	1.40725i	0.411236	−	0.911529i	$-0.365097\pi$
$798$		0			0
$799$	4.22734			0.149552
$800$		0			0
$801$	−27.6623			−0.977401
$802$		0			0
$803$	2.07474	+	6.38538i	0.0732159	+	0.225335i
$804$		0			0
$805$	2.61875	+	3.99576i	0.0922989	+	0.140832i
$806$		0			0
$807$	1.49789			0.0527281
$808$		0			0
$809$	−21.8310	+	15.8612i	−0.767538	+	0.557649i	−0.901213	−	0.433376i	$-0.857322\pi$
$809$	−21.8310	+	15.8612i	−0.767538	+	0.557649i	0.133675	+	0.991025i	$0.457322\pi$
$810$		0			0
$811$	30.8555	+	22.4178i	1.08348	+	0.787196i	0.978287	−	0.207256i	$-0.0664533\pi$
$811$	30.8555	+	22.4178i	1.08348	+	0.787196i	0.105195	+	0.994452i	$0.466453\pi$
$812$		0			0
$813$	−3.96177	+	2.87839i	−0.138945	+	0.100950i
$814$		0			0
$815$	38.0750	−	10.3734i	1.33371	−	0.363365i
$816$		0			0
$817$	−14.1422	+	43.5251i	−0.494772	+	1.52275i
$818$		0			0
$819$	0.743641	−	2.28869i	0.0259849	−	0.0799733i
$820$		0			0
$821$	−14.3480	−	44.1587i	−0.500750	−	1.54115i	−0.807800	−	0.589457i	$-0.799342\pi$
$821$	−14.3480	−	44.1587i	−0.500750	−	1.54115i	0.307049	−	0.951694i	$-0.400658\pi$
$822$		0			0
$823$	−34.2286	−	24.8685i	−1.19313	−	0.866862i	−0.199541	−	0.979889i	$-0.563945\pi$
$823$	−34.2286	−	24.8685i	−1.19313	−	0.866862i	−0.993592	+	0.113028i	$0.963945\pi$
$824$		0			0
$825$	4.79312	−	2.82115i	0.166875	−	0.0982197i
$826$		0			0
$827$	−14.6821	−	10.6671i	−0.510546	−	0.370933i	0.302485	−	0.953154i	$-0.402184\pi$
$827$	−14.6821	−	10.6671i	−0.510546	−	0.370933i	−0.813030	+	0.582221i	$0.802184\pi$
$828$		0			0
$829$	−3.34078	−	10.2819i	−0.116030	−	0.357104i	0.876130	−	0.482074i	$-0.160116\pi$
$829$	−3.34078	−	10.2819i	−0.116030	−	0.357104i	−0.992160	+	0.124970i	$0.960116\pi$
$830$		0			0
$831$	1.50200	−	4.62269i	0.0521039	−	0.160359i
$832$		0			0
$833$	4.05055	−	12.4663i	0.140343	−	0.431932i
$834$		0			0
$835$	−27.7032	+	34.5054i	−0.958709	+	1.19411i
$836$		0			0
$837$	24.9139	−	18.1010i	0.861149	−	0.625662i
$838$		0			0
$839$	−24.0000	−	17.4370i	−0.828571	−	0.601992i	0.0905835	−	0.995889i	$-0.471127\pi$
$839$	−24.0000	−	17.4370i	−0.828571	−	0.601992i	−0.919155	+	0.393897i	$0.871127\pi$
$840$		0			0
$841$	18.8128	−	13.6683i	0.648716	−	0.471320i
$842$		0			0
$843$	−7.69904			−0.265169
$844$		0			0
$845$	−16.4957	+	20.5460i	−0.567469	+	0.706803i
$846$		0			0
$847$	−1.99856	−	6.15094i	−0.0686713	−	0.211349i
$848$		0			0
$849$	−8.56142			−0.293827
$850$		0			0
$851$	−27.5488			−0.944361
$852$		0			0
$853$	3.00414	+	9.24579i	0.102860	+	0.316570i	0.989222	−	0.146422i	$-0.0467758\pi$
$853$	3.00414	+	9.24579i	0.102860	+	0.316570i	−0.886362	+	0.462992i	$0.846776\pi$
$854$		0			0
$855$	−1.16927	+	24.2560i	−0.0399883	+	0.829537i
$856$		0			0
$857$	−1.25560			−0.0428905			−0.0214452	−	0.999770i	$-0.506827\pi$
$857$	−1.25560			−0.0428905			−0.0214452	+	0.999770i	$0.506827\pi$
$858$		0			0
$859$	22.5900	−	16.4126i	0.770761	−	0.559991i	−0.131431	−	0.991325i	$-0.541957\pi$
$859$	22.5900	−	16.4126i	0.770761	−	0.559991i	0.902192	+	0.431334i	$0.141957\pi$
$860$		0			0
$861$	−0.777913	−	0.565187i	−0.0265112	−	0.0192615i
$862$		0			0
$863$	15.8484	−	11.5145i	0.539484	−	0.391958i	−0.284409	−	0.958703i	$-0.591797\pi$
$863$	15.8484	−	11.5145i	0.539484	−	0.391958i	0.823894	+	0.566745i	$0.191797\pi$
$864$		0			0
$865$	3.91138	+	5.96808i	0.132991	+	0.202921i
$866$		0			0
$867$	−2.42140	+	7.45230i	−0.0822351	+	0.253093i
$868$		0			0
$869$	−7.14198	+	21.9807i	−0.242275	+	0.745646i
$870$		0			0
$871$	1.51285	+	4.65608i	0.0512611	+	0.157765i
$872$		0			0
$873$	20.7884	+	15.1037i	0.703581	+	0.511182i
$874$		0			0
$875$	4.33403	+	8.24794i	0.146517	+	0.278831i
$876$		0			0
$877$	−24.5200	−	17.8148i	−0.827980	−	0.601563i	0.0910069	−	0.995850i	$-0.470991\pi$
$877$	−24.5200	−	17.8148i	−0.827980	−	0.601563i	−0.918987	+	0.394287i	$0.870991\pi$
$878$		0			0
$879$	1.76855	+	5.44304i	0.0596518	+	0.183589i
$880$		0			0
$881$	6.74593	−	20.7618i	0.227276	−	0.699484i	−0.770776	−	0.637106i	$-0.780131\pi$
$881$	6.74593	−	20.7618i	0.227276	−	0.699484i	0.998053	−	0.0623785i	$-0.0198686\pi$
$882$		0			0
$883$	7.88167	−	24.2573i	0.265239	−	0.816323i	−0.726399	−	0.687273i	$-0.758807\pi$
$883$	7.88167	−	24.2573i	0.265239	−	0.816323i	0.991638	−	0.129049i	$-0.0411925\pi$
$884$		0			0
$885$	−10.1292	−	15.4554i	−0.340490	−	0.519528i
$886$		0			0
$887$	−34.0788	+	24.7597i	−1.14425	+	0.831349i	−0.987706	−	0.156322i	$-0.950036\pi$
$887$	−34.0788	+	24.7597i	−1.14425	+	0.831349i	−0.156547	+	0.987671i	$0.550036\pi$
$888$		0			0
$889$	8.56576	+	6.22339i	0.287286	+	0.208726i
$890$		0			0
$891$	−8.31160	+	6.03873i	−0.278449	+	0.202305i
$892$		0			0
$893$	8.43564			0.282288
$894$		0			0
$895$	1.77710	−	36.8650i	0.0594019	−	1.23226i
$896$		0			0
$897$	0.540057	+	1.66212i	0.0180320	+	0.0554967i
$898$		0			0
$899$	−21.2606			−0.709080
$900$		0			0
$901$	13.9959			0.466272
$902$		0			0
$903$	1.75591	+	5.40412i	0.0584329	+	0.179838i
$904$		0			0
$905$	14.9309	−	18.5969i	0.496318	−	0.618182i
$906$		0			0
$907$	−48.7145			−1.61754			−0.808769	−	0.588126i	$-0.799866\pi$
$907$	−48.7145			−1.61754			−0.808769	+	0.588126i	$0.799866\pi$
$908$		0			0
$909$	−10.3281	+	7.50382i	−0.342562	+	0.248886i
$910$		0			0
$911$	−14.7336	−	10.7046i	−0.488147	−	0.354659i	0.316324	−	0.948651i	$-0.397551\pi$
$911$	−14.7336	−	10.7046i	−0.488147	−	0.354659i	−0.804471	+	0.593992i	$0.797551\pi$
$912$		0			0
$913$	11.7579	−	8.54260i	0.389129	−	0.282719i
$914$		0			0
$915$	0.643006	−	0.800887i	0.0212571	−	0.0264765i
$916$		0			0
$917$	−1.70045	+	5.23346i	−0.0561539	+	0.172824i
$918$		0			0
$919$	3.09130	−	9.51404i	0.101973	−	0.313839i	−0.887035	−	0.461701i	$-0.847239\pi$
$919$	3.09130	−	9.51404i	0.101973	−	0.313839i	0.989008	+	0.147862i	$0.0472392\pi$
$920$		0			0
$921$	−4.33471	−	13.3409i	−0.142833	−	0.439596i
$922$		0			0
$923$	−9.60211	−	6.97634i	−0.316057	−	0.229629i
$924$		0			0
$925$	−53.4785	−	5.16793i	−1.75836	−	0.169920i
$926$		0			0
$927$	−26.5833	−	19.3139i	−0.873110	−	0.634352i
$928$		0			0
$929$	−14.5855	−	44.8895i	−0.478534	−	1.47278i	−0.841131	−	0.540831i	$-0.818110\pi$
$929$	−14.5855	−	44.8895i	−0.478534	−	1.47278i	0.362597	−	0.931946i	$-0.381890\pi$
$930$		0			0
$931$	8.08285	−	24.8765i	0.264905	−	0.815293i
$932$		0			0
$933$	1.98190	−	6.09967i	0.0648846	−	0.199694i
$934$		0			0
$935$	8.07190	−	2.19916i	0.263979	−	0.0719204i
$936$		0			0
$937$	−1.30953	+	0.951426i	−0.0427803	+	0.0310817i	−0.608970	−	0.793193i	$-0.708417\pi$
$937$	−1.30953	+	0.951426i	−0.0427803	+	0.0310817i	0.566190	+	0.824275i	$0.308417\pi$
$938$		0			0
$939$	−8.48627	−	6.16564i	−0.276939	−	0.201208i
$940$		0			0
$941$	11.2661	−	8.18530i	0.367265	−	0.266833i	−0.388811	−	0.921317i	$-0.627114\pi$
$941$	11.2661	−	8.18530i	0.367265	−	0.266833i	0.756076	+	0.654484i	$0.227114\pi$
$942$		0			0
$943$	−4.78630			−0.155863
$944$		0			0
$945$	3.54663	+	5.41154i	0.115372	+	0.176038i
$946$		0			0
$947$	13.1131	+	40.3580i	0.426119	+	1.31146i	0.901919	+	0.431905i	$0.142158\pi$
$947$	13.1131	+	40.3580i	0.426119	+	1.31146i	−0.475801	+	0.879553i	$0.657842\pi$
$948$		0			0
$949$	−4.11456			−0.133564
$950$		0			0
$951$	11.9932			0.388905
$952$		0			0
$953$	16.4010	+	50.4771i	0.531281	+	1.63511i	0.751550	+	0.659676i	$0.229306\pi$
$953$	16.4010	+	50.4771i	0.531281	+	1.63511i	−0.220270	+	0.975439i	$0.570694\pi$
$954$		0			0
$955$	1.06142	−	0.289180i	0.0343467	−	0.00935764i
$956$		0			0
$957$	−2.66642			−0.0861930
$958$		0			0
$959$	0.457396	−	0.332318i	0.0147701	−	0.0107311i
$960$		0			0
$961$	−38.5606	−	28.0159i	−1.24389	−	0.903740i
$962$		0			0
$963$	−32.0967	+	23.3196i	−1.03430	+	0.751464i
$964$		0			0
$965$	34.9112	+	13.2335i	1.12383	+	0.426003i
$966$		0			0
$967$	−8.32828	+	25.6318i	−0.267819	+	0.824263i	0.723211	+	0.690627i	$0.242665\pi$
$967$	−8.32828	+	25.6318i	−0.267819	+	0.824263i	−0.991030	+	0.133636i	$0.957335\pi$
$968$		0			0
$969$	1.64691	−	5.06865i	0.0529062	−	0.162829i
$970$		0			0
$971$	−8.41468	−	25.8977i	−0.270040	−	0.831097i	−0.990489	−	0.137590i	$-0.956064\pi$
$971$	−8.41468	−	25.8977i	−0.270040	−	0.831097i	0.720449	−	0.693508i	$-0.243936\pi$
$972$		0			0
$973$	1.54650	+	1.12360i	0.0495786	+	0.0360210i
$974$		0			0
$975$	0.736573	+	3.32787i	0.0235892	+	0.106577i
$976$		0			0
$977$	20.8970	+	15.1826i	0.668554	+	0.485733i	0.869541	−	0.493861i	$-0.164415\pi$
$977$	20.8970	+	15.1826i	0.668554	+	0.485733i	−0.200987	+	0.979594i	$0.564415\pi$
$978$		0			0
$979$	5.87657	+	18.0862i	0.187816	+	0.578038i
$980$		0			0
$981$	10.6005	−	32.6251i	0.338449	−	1.04164i
$982$		0			0
$983$	4.09840	−	12.6136i	0.130719	−	0.402311i	−0.864181	−	0.503181i	$-0.832163\pi$
$983$	4.09840	−	12.6136i	0.130719	−	0.402311i	0.994900	+	0.100870i	$0.0321628\pi$
$984$		0			0
$985$	−1.15675	+	23.9962i	−0.0368571	+	0.764583i
$986$		0			0
$987$	0.847346	−	0.615633i	0.0269713	−	0.0195958i
$988$		0			0
$989$	22.8825	+	16.6251i	0.727621	+	0.528648i
$990$		0			0
$991$	−19.3656	+	14.0700i	−0.615170	+	0.446947i	−0.851231	−	0.524791i	$-0.824143\pi$
$991$	−19.3656	+	14.0700i	−0.615170	+	0.446947i	0.236061	+	0.971738i	$0.424143\pi$
$992$		0			0
$993$	−5.12171			−0.162532
$994$		0			0
$995$	26.9277	+	10.2073i	0.853667	+	0.323593i
$996$		0			0
$997$	15.1968	+	46.7710i	0.481288	+	1.48125i	0.837286	+	0.546765i	$0.184141\pi$
$997$	15.1968	+	46.7710i	0.481288	+	1.48125i	−0.355999	+	0.934487i	$0.615859\pi$
$998$		0			0
$999$	−37.3099			−1.18043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.e.241.2		8
4.3	odd	2		200.2.m.b.41.2	✓	8
20.3	even	4		1000.2.q.b.49.4		16
20.7	even	4		1000.2.q.b.49.1		16
20.19	odd	2		1000.2.m.b.201.2		8
25.6	even	5		10000.2.a.q.1.4		4
25.11	even	5	inner	400.2.u.e.161.2		8
25.19	even	10		10000.2.a.z.1.1		4
100.11	odd	10		200.2.m.b.161.2	yes	8
100.19	odd	10		5000.2.a.f.1.4		4
100.23	even	20		1000.2.q.b.449.2		16
100.27	even	20		1000.2.q.b.449.3		16
100.31	odd	10		5000.2.a.i.1.1		4
100.39	odd	10		1000.2.m.b.801.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.b.41.2	✓	8	4.3	odd	2
200.2.m.b.161.2	yes	8	100.11	odd	10
400.2.u.e.161.2		8	25.11	even	5	inner
400.2.u.e.241.2		8	1.1	even	1	trivial
1000.2.m.b.201.2		8	20.19	odd	2
1000.2.m.b.801.2		8	100.39	odd	10
1000.2.q.b.49.1		16	20.7	even	4
1000.2.q.b.49.4		16	20.3	even	4
1000.2.q.b.449.2		16	100.23	even	20
1000.2.q.b.449.3		16	100.27	even	20
5000.2.a.f.1.4		4	100.19	odd	10
5000.2.a.i.1.1		4	100.31	odd	10
10000.2.a.q.1.4		4	25.6	even	5
10000.2.a.z.1.1		4	25.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.587785i) q^{3} +(2.09089 + 0.792578i) q^{5} +0.833366 q^{7} +(2.11803 - 1.53884i) q^{9} +O(q^{10})\)	\(q+(0.190983 + 0.587785i) q^{3} +(2.09089 + 0.792578i) q^{5} +0.833366 q^{7} +(2.11803 - 1.53884i) q^{9} +(-1.45608 - 1.05790i) q^{11} +(0.892334 - 0.648319i) q^{13} +(-0.0665412 + 1.38036i) q^{15} +(-0.642383 + 1.97705i) q^{17} +(-1.28187 + 3.94520i) q^{19} +(0.159159 + 0.489840i) q^{21} +(2.07411 + 1.50693i) q^{23} +(3.74364 + 3.31439i) q^{25} +(2.80902 + 2.04087i) q^{27} +(-0.740748 - 2.27979i) q^{29} +(2.74075 - 8.43516i) q^{31} +(0.343734 - 1.05790i) q^{33} +(1.74248 + 0.660507i) q^{35} +(-8.69331 + 6.31606i) q^{37} +(0.551493 + 0.400683i) q^{39} +(-1.51037 + 1.09735i) q^{41} +11.0324 q^{43} +(5.64823 - 1.53884i) q^{45} +(-0.628402 - 1.93402i) q^{47} -6.30550 q^{49} -1.28477 q^{51} +(-2.08052 - 6.40319i) q^{53} +(-2.20603 - 3.36602i) q^{55} -2.56375 q^{57} +(-10.8178 + 7.85956i) q^{59} +(-0.601258 - 0.436839i) q^{61} +(1.76510 - 1.28242i) q^{63} +(2.37962 - 0.648319i) q^{65} +(-1.37160 + 4.22134i) q^{67} +(-0.489632 + 1.50693i) q^{69} +(-3.32523 - 10.2340i) q^{71} +(-3.01794 - 2.19266i) q^{73} +(-1.23318 + 2.83345i) q^{75} +(-1.21345 - 0.881621i) q^{77} +(-3.96818 - 12.2128i) q^{79} +(1.76393 - 5.42882i) q^{81} +(-2.49532 + 7.67980i) q^{83} +(-2.91012 + 3.62466i) q^{85} +(1.19856 - 0.870802i) q^{87} +(-8.54813 - 6.21058i) q^{89} +(0.743641 - 0.540287i) q^{91} +5.48150 q^{93} +(-5.80713 + 7.23299i) q^{95} +(3.03299 + 9.33458i) q^{97} -4.71197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

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Database

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