LMFDB - Embedded newform 968.2.i.t.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	968.9
Dual form			968.2.i.t.753.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46489 + 1.79085i) q^{3} +(0.550606 + 1.69459i) q^{5} +(0.285629 + 0.207522i) q^{7} +(1.94151 - 5.97534i) q^{9} +O(q^{10})$	\(q+(-2.46489 + 1.79085i) q^{3} +(0.550606 + 1.69459i) q^{5} +(0.285629 + 0.207522i) q^{7} +(1.94151 - 5.97534i) q^{9} +(1.71437 - 5.27629i) q^{13} +(-4.39194 - 3.19093i) q^{15} +(-1.17822 - 3.62619i) q^{17} +(3.73607 - 2.71441i) q^{19} -1.07569 q^{21} -7.00209 q^{23} +(1.47661 - 1.07282i) q^{25} +(3.09082 + 9.51255i) q^{27} +(1.71437 + 1.24556i) q^{29} +(1.06743 - 3.28521i) q^{31} +(-0.194395 + 0.598287i) q^{35} +(1.40809 + 1.02304i) q^{37} +(5.22330 + 16.0757i) q^{39} +(-1.19992 + 0.871790i) q^{41} +3.92979 q^{43} +11.1948 q^{45} +(0.979348 - 0.711538i) q^{47} +(-2.12460 - 6.53885i) q^{49} +(9.39814 + 6.82815i) q^{51} +(2.44939 - 7.53846i) q^{53} +(-4.34790 + 13.3815i) q^{57} +(2.50000 + 1.81636i) q^{59} +(2.35027 + 7.23339i) q^{61} +(1.79456 - 1.30383i) q^{63} +9.88510 q^{65} +1.17352 q^{67} +(17.2594 - 12.5397i) q^{69} +(-0.732238 - 2.25360i) q^{71} +(3.15861 + 2.29487i) q^{73} +(-1.71843 + 5.28878i) q^{75} +(-1.26985 + 3.90820i) q^{79} +(-9.40531 - 6.83335i) q^{81} +(-0.252890 - 0.778314i) q^{83} +(5.49617 - 3.99320i) q^{85} -6.45636 q^{87} -1.92979 q^{89} +(1.58462 - 1.15129i) q^{91} +(3.25221 + 10.0093i) q^{93} +(6.65692 + 4.83654i) q^{95} +(-2.92874 + 9.01374i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	$ 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) $ 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−2.46489	+	1.79085i	−1.42311	+	1.03395i	−0.431858	+	0.901942i	$0.642142\pi$
$3$	−2.46489	+	1.79085i	−1.42311	+	1.03395i	−0.991249	+	0.132006i	$0.957858\pi$
$4$		0			0
$5$	0.550606	+	1.69459i	0.246239	+	0.757844i	0.995430	+	0.0954911i	$0.0304422\pi$
$5$	0.550606	+	1.69459i	0.246239	+	0.757844i	−0.749192	+	0.662353i	$0.769558\pi$
$6$		0			0
$7$	0.285629	+	0.207522i	0.107958	+	0.0784358i	0.640454	−	0.767996i	$-0.278746\pi$
$7$	0.285629	+	0.207522i	0.107958	+	0.0784358i	−0.532497	+	0.846432i	$0.678746\pi$
$8$		0			0
$9$	1.94151	−	5.97534i	0.647169	−	1.99178i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	1.71437	−	5.27629i	0.475481	−	1.46338i	−0.369827	−	0.929101i	$-0.620583\pi$
$13$	1.71437	−	5.27629i	0.475481	−	1.46338i	0.845308	−	0.534279i	$-0.179417\pi$
$14$		0			0
$15$	−4.39194	−	3.19093i	−1.13400	−	0.823896i
$16$		0			0
$17$	−1.17822	−	3.62619i	−0.285760	−	0.879479i	−0.986170	−	0.165738i	$-0.946999\pi$
$17$	−1.17822	−	3.62619i	−0.285760	−	0.879479i	0.700410	−	0.713741i	$-0.253001\pi$
$18$		0			0
$19$	3.73607	−	2.71441i	0.857113	−	0.622729i	−0.0699852	−	0.997548i	$-0.522295\pi$
$19$	3.73607	−	2.71441i	0.857113	−	0.622729i	0.927098	+	0.374819i	$0.122295\pi$
$20$		0			0
$21$	−1.07569			−0.234734
$22$		0			0
$23$	−7.00209			−1.46004			−0.730018	−	0.683428i	$-0.760489\pi$
$23$	−7.00209			−1.46004			−0.730018	+	0.683428i	$0.760489\pi$
$24$		0			0
$25$	1.47661	−	1.07282i	0.295322	−	0.214564i
$26$		0			0
$27$	3.09082	+	9.51255i	0.594828	+	1.83069i
$28$		0			0
$29$	1.71437	+	1.24556i	0.318351	+	0.231295i	0.735471	−	0.677556i	$-0.236961\pi$
$29$	1.71437	+	1.24556i	0.318351	+	0.231295i	−0.417121	+	0.908851i	$0.636961\pi$
$30$		0			0
$31$	1.06743	−	3.28521i	0.191716	−	0.590040i	−0.808284	−	0.588793i	$-0.799603\pi$
$31$	1.06743	−	3.28521i	0.191716	−	0.590040i	0.999999	−	0.00124679i	$-0.000396866\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.194395	+	0.598287i	−0.0328588	+	0.101129i
$36$		0			0
$37$	1.40809	+	1.02304i	0.231489	+	0.168186i	0.697483	−	0.716601i	$-0.254303\pi$
$37$	1.40809	+	1.02304i	0.231489	+	0.168186i	−0.465994	+	0.884788i	$0.654303\pi$
$38$		0			0
$39$	5.22330	+	16.0757i	0.836398	+	2.57417i
$40$		0			0
$41$	−1.19992	+	0.871790i	−0.187395	+	0.136151i	−0.677528	−	0.735497i	$-0.736949\pi$
$41$	−1.19992	+	0.871790i	−0.187395	+	0.136151i	0.490132	+	0.871648i	$0.336949\pi$
$42$		0			0
$43$	3.92979			0.599287			0.299643	−	0.954051i	$-0.403132\pi$
$43$	3.92979			0.599287			0.299643	+	0.954051i	$0.403132\pi$
$44$		0			0
$45$	11.1948			1.66882
$46$		0			0
$47$	0.979348	−	0.711538i	0.142853	−	0.103788i	−0.514064	−	0.857752i	$-0.671860\pi$
$47$	0.979348	−	0.711538i	0.142853	−	0.103788i	0.656916	+	0.753964i	$0.271860\pi$
$48$		0			0
$49$	−2.12460	−	6.53885i	−0.303514	−	0.934121i
$50$		0			0
$51$	9.39814	+	6.82815i	1.31600	+	0.956132i
$52$		0			0
$53$	2.44939	−	7.53846i	0.336450	−	1.03549i	−0.629553	−	0.776957i	$-0.716762\pi$
$53$	2.44939	−	7.53846i	0.336450	−	1.03549i	0.966003	−	0.258530i	$-0.0832380\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.34790	+	13.3815i	−0.575894	+	1.77242i
$58$		0			0
$59$	2.50000	+	1.81636i	0.325472	+	0.236469i	0.738507	−	0.674246i	$-0.235531\pi$
$59$	2.50000	+	1.81636i	0.325472	+	0.236469i	−0.413035	+	0.910715i	$0.635531\pi$
$60$		0			0
$61$	2.35027	+	7.23339i	0.300921	+	0.926141i	0.981168	+	0.193157i	$0.0618728\pi$
$61$	2.35027	+	7.23339i	0.300921	+	0.926141i	−0.680246	+	0.732984i	$0.738127\pi$
$62$		0			0
$63$	1.79456	−	1.30383i	0.226094	−	0.164267i
$64$		0			0
$65$	9.88510			1.22610
$66$		0			0
$67$	1.17352			0.143368			0.0716839	−	0.997427i	$-0.477163\pi$
$67$	1.17352			0.143368			0.0716839	+	0.997427i	$0.477163\pi$
$68$		0			0
$69$	17.2594	−	12.5397i	2.07779	−	1.50960i
$70$		0			0
$71$	−0.732238	−	2.25360i	−0.0869006	−	0.267453i	0.898158	−	0.439673i	$-0.144906\pi$
$71$	−0.732238	−	2.25360i	−0.0869006	−	0.267453i	−0.985058	+	0.172221i	$0.944906\pi$
$72$		0			0
$73$	3.15861	+	2.29487i	0.369688	+	0.268594i	0.757081	−	0.653321i	$-0.226625\pi$
$73$	3.15861	+	2.29487i	0.369688	+	0.268594i	−0.387394	+	0.921914i	$0.626625\pi$
$74$		0			0
$75$	−1.71843	+	5.28878i	−0.198427	+	0.610696i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.26985	+	3.90820i	−0.142870	+	0.439707i	−0.996731	−	0.0807933i	$-0.974255\pi$
$79$	−1.26985	+	3.90820i	−0.142870	+	0.439707i	0.853861	+	0.520501i	$0.174255\pi$
$80$		0			0
$81$	−9.40531	−	6.83335i	−1.04503	−	0.759262i
$82$		0			0
$83$	−0.252890	−	0.778314i	−0.0277583	−	0.0854311i	0.936218	−	0.351421i	$-0.114301\pi$
$83$	−0.252890	−	0.778314i	−0.0277583	−	0.0854311i	−0.963976	+	0.265990i	$0.914301\pi$
$84$		0			0
$85$	5.49617	−	3.99320i	0.596143	−	0.433123i
$86$		0			0
$87$	−6.45636			−0.692194
$88$		0			0
$89$	−1.92979			−0.204557			−0.102279	−	0.994756i	$-0.532613\pi$
$89$	−1.92979			−0.204557			−0.102279	+	0.994756i	$0.532613\pi$
$90$		0			0
$91$	1.58462	−	1.15129i	0.166113	−	0.120688i
$92$		0			0
$93$	3.25221	+	10.0093i	0.337239	+	1.03791i
$94$		0			0
$95$	6.65692	+	4.83654i	0.682986	+	0.496218i
$96$		0			0
$97$	−2.92874	+	9.01374i	−0.297369	+	0.915207i	0.685047	+	0.728499i	$0.259782\pi$
$97$	−2.92874	+	9.01374i	−0.297369	+	0.915207i	−0.982416	+	0.186708i	$0.940218\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.45148	−	13.7003i	0.442939	−	1.36323i	−0.441789	−	0.897119i	$-0.645656\pi$
$101$	4.45148	−	13.7003i	0.442939	−	1.36323i	0.884728	−	0.466108i	$-0.154344\pi$
$102$		0			0
$103$	−6.49279	−	4.71729i	−0.639753	−	0.464808i	0.220012	−	0.975497i	$-0.429390\pi$
$103$	−6.49279	−	4.71729i	−0.639753	−	0.464808i	−0.859765	+	0.510689i	$0.829390\pi$
$104$		0			0
$105$	−0.592279	−	1.82285i	−0.0578005	−	0.177892i
$106$		0			0
$107$	3.70096	−	2.68891i	0.357785	−	0.259946i	−0.394342	−	0.918964i	$-0.629028\pi$
$107$	3.70096	−	2.68891i	0.357785	−	0.259946i	0.752128	+	0.659017i	$0.229028\pi$
$108$		0			0
$109$	20.6592			1.97880			0.989398	−	0.145228i	$-0.0463917\pi$
$109$	20.6592			1.97880			0.989398	+	0.145228i	$0.0463917\pi$
$110$		0			0
$111$	−5.30290			−0.503329
$112$		0			0
$113$	−7.12351	+	5.17553i	−0.670123	+	0.486873i	−0.870066	−	0.492935i	$-0.835924\pi$
$113$	−7.12351	+	5.17553i	−0.670123	+	0.486873i	0.199943	+	0.979807i	$0.435924\pi$
$114$		0			0
$115$	−3.85539	−	11.8657i	−0.359517	−	1.10648i
$116$		0			0
$117$	−28.1992	−	20.4879i	−2.60701	−	1.89411i
$118$		0			0
$119$	0.415978	−	1.28025i	0.0381327	−	0.117360i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	1.39642	−	4.29774i	0.125911	−	0.387514i
$124$		0			0
$125$	9.83855	+	7.14813i	0.879987	+	0.639348i
$126$		0			0
$127$	−5.49826	−	16.9219i	−0.487892	−	1.50158i	−0.827749	−	0.561099i	$-0.810379\pi$
$127$	−5.49826	−	16.9219i	−0.487892	−	1.50158i	0.339857	−	0.940477i	$-0.389621\pi$
$128$		0			0
$129$	−9.68651	+	7.03766i	−0.852849	+	0.619631i
$130$		0			0
$131$	−18.3585			−1.60399			−0.801996	−	0.597329i	$-0.796229\pi$
$131$	−18.3585			−1.60399			−0.801996	+	0.597329i	$0.796229\pi$
$132$		0			0
$133$	1.63043			0.141376
$134$		0			0
$135$	−14.4181	+	10.4753i	−1.24091	+	0.901574i
$136$		0			0
$137$	−4.16481	−	12.8180i	−0.355824	−	1.09511i	−0.955530	−	0.294893i	$-0.904716\pi$
$137$	−4.16481	−	12.8180i	−0.355824	−	1.09511i	0.599707	−	0.800220i	$-0.295284\pi$
$138$		0			0
$139$	11.5450	+	8.38796i	0.979237	+	0.711457i	0.957538	−	0.288307i	$-0.0930924\pi$
$139$	11.5450	+	8.38796i	0.979237	+	0.711457i	0.0216992	+	0.999765i	$0.493092\pi$
$140$		0			0
$141$	−1.13973	+	3.50773i	−0.0959827	+	0.295404i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−1.16678	+	3.59097i	−0.0968956	+	0.298214i
$146$		0			0
$147$	16.9470	+	12.3127i	1.39777	+	1.01554i
$148$		0			0
$149$	3.15286	+	9.70352i	0.258293	+	0.794943i	0.993163	+	0.116735i	$0.0372430\pi$
$149$	3.15286	+	9.70352i	0.258293	+	0.794943i	−0.734870	+	0.678208i	$0.762757\pi$
$150$		0			0
$151$	3.55061	−	2.57967i	0.288944	−	0.209930i	−0.433865	−	0.900978i	$-0.642851\pi$
$151$	3.55061	−	2.57967i	0.288944	−	0.209930i	0.722809	+	0.691048i	$0.242851\pi$
$152$		0			0
$153$	−23.9552			−1.93666
$154$		0			0
$155$	6.15481			0.494366
$156$		0			0
$157$	−17.9449	+	13.0377i	−1.43216	+	1.04052i	−0.442546	+	0.896746i	$0.645925\pi$
$157$	−17.9449	+	13.0377i	−1.43216	+	1.04052i	−0.989610	+	0.143777i	$0.954075\pi$
$158$		0			0
$159$	7.46275	+	22.9680i	0.591835	+	1.82148i
$160$		0			0
$161$	−2.00000	−	1.45309i	−0.157622	−	0.114519i
$162$		0			0
$163$	6.09696	−	18.7645i	0.477551	−	1.46975i	−0.364935	−	0.931033i	$-0.618909\pi$
$163$	6.09696	−	18.7645i	0.477551	−	1.46975i	0.842486	−	0.538718i	$-0.181091\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.305586	−	0.940497i	0.0236470	−	0.0727779i	−0.938537	−	0.345180i	$-0.887818\pi$
$167$	0.305586	−	0.940497i	0.0236470	−	0.0727779i	0.962184	+	0.272402i	$0.0878180\pi$
$168$		0			0
$169$	−14.3830	−	10.4498i	−1.10638	−	0.803833i
$170$		0			0
$171$	−8.96594	−	27.5943i	−0.685642	−	2.11019i
$172$		0			0
$173$	−14.1576	+	10.2861i	−1.07638	+	0.782037i	−0.977049	−	0.213017i	$-0.931671\pi$
$173$	−14.1576	+	10.2861i	−1.07638	+	0.782037i	−0.0993337	+	0.995054i	$0.531671\pi$
$174$		0			0
$175$	0.644397			0.0487118
$176$		0			0
$177$	−9.41506			−0.707679
$178$		0			0
$179$	2.30733	−	1.67637i	0.172458	−	0.125298i	−0.498208	−	0.867057i	$-0.666008\pi$
$179$	2.30733	−	1.67637i	0.172458	−	0.125298i	0.670666	+	0.741760i	$0.266008\pi$
$180$		0			0
$181$	−0.649728	−	1.99966i	−0.0482939	−	0.148633i	0.924002	−	0.382389i	$-0.124898\pi$
$181$	−0.649728	−	1.99966i	−0.0482939	−	0.148633i	−0.972295	+	0.233755i	$0.924898\pi$
$182$		0			0
$183$	−18.7471	−	13.6206i	−1.38582	−	1.00686i
$184$		0			0
$185$	−0.958327	+	2.94943i	−0.0704576	+	0.216846i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.09123	+	3.35847i	−0.0793756	+	0.244293i
$190$		0			0
$191$	13.8513	+	10.0636i	1.00225	+	0.728174i	0.962569	−	0.271038i	$-0.0873669\pi$
$191$	13.8513	+	10.0636i	1.00225	+	0.728174i	0.0396775	+	0.999213i	$0.487367\pi$
$192$		0			0
$193$	−6.22015	−	19.1437i	−0.447736	−	1.37799i	−0.879455	−	0.475982i	$-0.842093\pi$
$193$	−6.22015	−	19.1437i	−0.447736	−	1.37799i	0.431719	−	0.902008i	$-0.357907\pi$
$194$		0			0
$195$	−24.3657	+	17.7027i	−1.74487	+	1.26772i
$196$		0			0
$197$	−12.5589			−0.894786			−0.447393	−	0.894337i	$-0.647648\pi$
$197$	−12.5589			−0.894786			−0.447393	+	0.894337i	$0.647648\pi$
$198$		0			0
$199$	−3.32962			−0.236031			−0.118015	−	0.993012i	$-0.537653\pi$
$199$	−3.32962			−0.236031			−0.118015	+	0.993012i	$0.537653\pi$
$200$		0			0
$201$	−2.89259	+	2.10159i	−0.204028	+	0.148235i
$202$		0			0
$203$	0.231193	+	0.711538i	0.0162265	+	0.0499402i
$204$		0			0
$205$	−2.13801	−	1.55335i	−0.149325	−	0.108491i
$206$		0			0
$207$	−13.5946	+	41.8399i	−0.944890	+	2.90807i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	7.44556	−	22.9151i	0.512574	−	1.57754i	−0.275080	−	0.961421i	$-0.588704\pi$
$211$	7.44556	−	22.9151i	0.512574	−	1.57754i	0.787654	−	0.616118i	$-0.211296\pi$
$212$		0			0
$213$	5.84074	+	4.24355i	0.400201	+	0.290763i
$214$		0			0
$215$	2.16376	+	6.65938i	0.147568	+	0.454166i
$216$		0			0
$217$	0.986639	−	0.716835i	0.0669774	−	0.0486620i
$218$		0			0
$219$	−11.8954			−0.803817
$220$		0			0
$221$	−21.1527			−1.42289
$222$		0			0
$223$	−0.428145	+	0.311066i	−0.0286707	+	0.0208305i	−0.602028	−	0.798475i	$-0.705641\pi$
$223$	−0.428145	+	0.311066i	−0.0286707	+	0.0208305i	0.573358	+	0.819305i	$0.305641\pi$
$224$		0			0
$225$	−3.54362	−	10.9061i	−0.236241	−	0.727076i
$226$		0			0
$227$	−10.2584	−	7.45314i	−0.680871	−	0.494682i	0.192775	−	0.981243i	$-0.438251\pi$
$227$	−10.2584	−	7.45314i	−0.680871	−	0.494682i	−0.873647	+	0.486561i	$0.838251\pi$
$228$		0			0
$229$	−1.88580	+	5.80388i	−0.124617	+	0.383531i	−0.993831	−	0.110904i	$-0.964625\pi$
$229$	−1.88580	+	5.80388i	−0.124617	+	0.383531i	0.869214	+	0.494436i	$0.164625\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.769711	−	2.36893i	0.0504255	−	0.155194i	−0.922673	−	0.385584i	$-0.874000\pi$
$233$	0.769711	−	2.36893i	0.0504255	−	0.155194i	0.973098	+	0.230390i	$0.0740002\pi$
$234$		0			0
$235$	1.74500	+	1.26782i	0.113831	+	0.0827033i
$236$		0			0
$237$	−3.86896	−	11.9074i	−0.251316	−	0.773470i
$238$		0			0
$239$	18.0962	−	13.1477i	1.17055	−	0.850453i	0.179474	−	0.983763i	$-0.442560\pi$
$239$	18.0962	−	13.1477i	1.17055	−	0.850453i	0.991074	+	0.133310i	$0.0425604\pi$
$240$		0			0
$241$	24.1025			1.55258			0.776288	−	0.630378i	$-0.217100\pi$
$241$	24.1025			1.55258			0.776288	+	0.630378i	$0.217100\pi$
$242$		0			0
$243$	5.41432			0.347329
$244$		0			0
$245$	9.91086	−	7.20066i	0.633181	−	0.460033i
$246$		0			0
$247$	−7.91702	−	24.3661i	−0.503748	−	1.55038i
$248$		0			0
$249$	2.01719	+	1.46557i	0.127834	+	0.0928770i
$250$		0			0
$251$	−2.14182	+	6.59185i	−0.135191	+	0.416074i	−0.995620	−	0.0934965i	$-0.970196\pi$
$251$	−2.14182	+	6.59185i	−0.135191	+	0.416074i	0.860429	+	0.509570i	$0.170196\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−6.39625	+	19.6856i	−0.400549	+	1.23276i
$256$		0			0
$257$	11.8544	+	8.61274i	0.739459	+	0.537248i	0.892541	−	0.450965i	$-0.148920\pi$
$257$	11.8544	+	8.61274i	0.739459	+	0.537248i	−0.153083	+	0.988213i	$0.548920\pi$
$258$		0			0
$259$	0.189889	+	0.584418i	0.0117991	+	0.0363140i
$260$		0			0
$261$	10.7711	−	7.82568i	0.666716	−	0.484397i
$262$		0			0
$263$	22.9868			1.41742			0.708712	−	0.705497i	$-0.249276\pi$
$263$	22.9868			1.41742			0.708712	+	0.705497i	$0.249276\pi$
$264$		0			0
$265$	14.1233			0.867585
$266$		0			0
$267$	4.75672	−	3.45596i	0.291107	−	0.211501i
$268$		0			0
$269$	−1.71437	−	5.27629i	−0.104527	−	0.321701i	0.885092	−	0.465416i	$-0.154095\pi$
$269$	−1.71437	−	5.27629i	−0.104527	−	0.321701i	−0.989619	+	0.143715i	$0.954095\pi$
$270$		0			0
$271$	−10.9504	−	7.95596i	−0.665192	−	0.483290i	0.203220	−	0.979133i	$-0.434859\pi$
$271$	−10.9504	−	7.95596i	−0.665192	−	0.483290i	−0.868412	+	0.495843i	$0.834859\pi$
$272$		0			0
$273$	−1.84412	+	5.67563i	−0.111611	+	0.343505i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.914705	−	2.81517i	0.0549593	−	0.169147i	−0.919809	−	0.392366i	$-0.871657\pi$
$277$	0.914705	−	2.81517i	0.0549593	−	0.169147i	0.974768	+	0.223219i	$0.0716565\pi$
$278$		0			0
$279$	−17.5578	−	12.7565i	−1.05116	−	0.763711i
$280$		0			0
$281$	2.76971	+	8.52430i	0.165227	+	0.508517i	0.999053	−	0.0435108i	$-0.0138543\pi$
$281$	2.76971	+	8.52430i	0.165227	+	0.508517i	−0.833826	+	0.552028i	$0.813854\pi$
$282$		0			0
$283$	14.5952	−	10.6040i	0.867594	−	0.630344i	−0.0623461	−	0.998055i	$-0.519858\pi$
$283$	14.5952	−	10.6040i	0.867594	−	0.630344i	0.929940	+	0.367710i	$0.119858\pi$
$284$		0			0
$285$	−25.0701			−1.48503
$286$		0			0
$287$	−0.523646			−0.0309099
$288$		0			0
$289$	1.99226	−	1.44746i	0.117192	−	0.0851448i
$290$		0			0
$291$	−8.92322	−	27.4628i	−0.523088	−	1.60990i
$292$		0			0
$293$	22.3612	+	16.2464i	1.30636	+	0.949123i	0.999996	−	0.00279235i	$-0.000888833\pi$
$293$	22.3612	+	16.2464i	1.30636	+	0.949123i	0.306360	+	0.951916i	$0.400889\pi$
$294$		0			0
$295$	−1.70147	+	5.23658i	−0.0990632	+	0.304885i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.0042	+	36.9451i	−0.694220	+	2.13659i
$300$		0			0
$301$	1.12246	+	0.815516i	0.0646976	+	0.0470055i
$302$		0			0
$303$	13.5627	+	41.7416i	0.779155	+	2.39799i
$304$		0			0
$305$	−10.9636	+	7.96550i	−0.627772	+	0.456103i
$306$		0			0
$307$	−0.662166			−0.0377918			−0.0188959	−	0.999821i	$-0.506015\pi$
$307$	−0.662166			−0.0377918			−0.0188959	+	0.999821i	$0.506015\pi$
$308$		0			0
$309$	24.4520			1.39102
$310$		0			0
$311$	10.5739	−	7.68242i	0.599593	−	0.435630i	−0.246141	−	0.969234i	$-0.579163\pi$
$311$	10.5739	−	7.68242i	0.599593	−	0.435630i	0.845735	+	0.533604i	$0.179163\pi$
$312$		0			0
$313$	6.12249	+	18.8431i	0.346064	+	1.06507i	0.961012	+	0.276507i	$0.0891769\pi$
$313$	6.12249	+	18.8431i	0.346064	+	1.06507i	−0.614948	+	0.788567i	$0.710823\pi$
$314$		0			0
$315$	3.19755	+	2.32316i	0.180161	+	0.130895i
$316$		0			0
$317$	−6.09972	+	18.7730i	−0.342594	+	1.05440i	0.620265	+	0.784393i	$0.287025\pi$
$317$	−6.09972	+	18.7730i	−0.342594	+	1.05440i	−0.962859	+	0.270004i	$0.912975\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−4.30705	+	13.2557i	−0.240396	+	0.739863i
$322$		0			0
$323$	−14.2449	−	10.3495i	−0.792606	−	0.575862i
$324$		0			0
$325$	−3.12906	−	9.63025i	−0.173569	−	0.534190i
$326$		0			0
$327$	−50.9228	+	36.9976i	−2.81604	+	2.04597i
$328$		0			0
$329$	0.427390			0.0235628
$330$		0			0
$331$	21.0860			1.15899			0.579494	−	0.814976i	$-0.303250\pi$
$331$	21.0860			1.15899			0.579494	+	0.814976i	$0.303250\pi$
$332$		0			0
$333$	8.84681	−	6.42758i	0.484802	−	0.352229i
$334$		0			0
$335$	0.646145	+	1.98863i	0.0353027	+	0.108650i
$336$		0			0
$337$	−1.12142	−	0.814756i	−0.0610874	−	0.0443826i	0.556822	−	0.830632i	$-0.312020\pi$
$337$	−1.12142	−	0.814756i	−0.0610874	−	0.0443826i	−0.617910	+	0.786249i	$0.712020\pi$
$338$		0			0
$339$	8.29009	−	25.5143i	0.450256	−	1.38574i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.51381	−	4.65902i	0.0817380	−	0.251564i
$344$		0			0
$345$	30.7528	+	22.3432i	1.65567	+	1.20292i
$346$		0			0
$347$	−5.90722	−	18.1805i	−0.317116	−	0.975983i	−0.974875	−	0.222754i	$-0.928495\pi$
$347$	−5.90722	−	18.1805i	−0.317116	−	0.975983i	0.657759	−	0.753229i	$-0.271505\pi$
$348$		0			0
$349$	16.7599	−	12.1767i	0.897134	−	0.651806i	−0.0405939	−	0.999176i	$-0.512925\pi$
$349$	16.7599	−	12.1767i	0.897134	−	0.651806i	0.937728	+	0.347369i	$0.112925\pi$
$350$		0			0
$351$	55.4898			2.96183
$352$		0			0
$353$	5.09091			0.270962			0.135481	−	0.990780i	$-0.456742\pi$
$353$	5.09091			0.270962			0.135481	+	0.990780i	$0.456742\pi$
$354$		0			0
$355$	3.41575	−	2.48169i	0.181289	−	0.131714i
$356$		0			0
$357$	1.26739	+	3.90064i	0.0670776	+	0.206444i
$358$		0			0
$359$	−3.33668	−	2.42424i	−0.176103	−	0.127947i	0.496242	−	0.868184i	$-0.334713\pi$
$359$	−3.33668	−	2.42424i	−0.176103	−	0.127947i	−0.672345	+	0.740238i	$0.734713\pi$
$360$		0			0
$361$	0.718847	−	2.21238i	0.0378341	−	0.116441i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.14971	+	6.61613i	−0.112521	+	0.346304i
$366$		0			0
$367$	−29.5306	−	21.4552i	−1.54149	−	1.11995i	−0.949396	−	0.314083i	$-0.898303\pi$
$367$	−29.5306	−	21.4552i	−1.54149	−	1.11995i	−0.592090	−	0.805872i	$-0.701697\pi$
$368$		0			0
$369$	2.87960	+	8.86249i	0.149906	+	0.461363i
$370$		0			0
$371$	2.26401	−	1.64490i	0.117542	−	0.0853990i
$372$		0			0
$373$	5.01741			0.259792			0.129896	−	0.991528i	$-0.458536\pi$
$373$	5.01741			0.259792			0.129896	+	0.991528i	$0.458536\pi$
$374$		0			0
$375$	−37.0522			−1.91337
$376$		0			0
$377$	9.51102	−	6.91016i	0.489843	−	0.355892i
$378$		0			0
$379$	6.25707	+	19.2573i	0.321404	+	0.989180i	0.973038	+	0.230646i	$0.0740840\pi$
$379$	6.25707	+	19.2573i	0.321404	+	0.989180i	−0.651634	+	0.758534i	$0.725916\pi$
$380$		0			0
$381$	43.8572	+	31.8641i	2.24687	+	1.63245i
$382$		0			0
$383$	−2.90575	+	8.94299i	−0.148477	+	0.456965i	−0.997442	−	0.0714842i	$-0.977226\pi$
$383$	−2.90575	+	8.94299i	−0.148477	+	0.456965i	0.848965	+	0.528450i	$0.177226\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.62970	−	23.4818i	0.387840	−	1.19365i
$388$		0			0
$389$	−5.47273	−	3.97617i	−0.277479	−	0.201600i	0.440338	−	0.897832i	$-0.354859\pi$
$389$	−5.47273	−	3.97617i	−0.277479	−	0.201600i	−0.717817	+	0.696232i	$0.754859\pi$
$390$		0			0
$391$	8.25000	+	25.3909i	0.417220	+	1.28407i
$392$		0			0
$393$	45.2518	−	32.8774i	2.28265	−	1.65844i
$394$		0			0
$395$	−7.32200			−0.368410
$396$		0			0
$397$	−5.18919			−0.260438			−0.130219	−	0.991485i	$-0.541568\pi$
$397$	−5.18919			−0.260438			−0.130219	+	0.991485i	$0.541568\pi$
$398$		0			0
$399$	−4.01883	+	2.91985i	−0.201193	+	0.146175i
$400$		0			0
$401$	1.81987	+	5.60098i	0.0908799	+	0.279700i	0.986158	−	0.165808i	$-0.0530232\pi$
$401$	1.81987	+	5.60098i	0.0908799	+	0.279700i	−0.895278	+	0.445508i	$0.853023\pi$
$402$		0			0
$403$	−15.5037	−	11.2641i	−0.772296	−	0.561106i
$404$		0			0
$405$	6.40112	−	19.7006i	0.318074	−	0.978932i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	10.6731	−	32.8483i	0.527749	−	1.62425i	−0.231065	−	0.972938i	$-0.574221\pi$
$409$	10.6731	−	32.8483i	0.527749	−	1.62425i	0.758814	−	0.651307i	$-0.225779\pi$
$410$		0			0
$411$	33.2209	+	24.1364i	1.63866	+	1.19056i
$412$		0			0
$413$	0.337139	+	1.03761i	0.0165895	+	0.0510574i
$414$		0			0
$415$	1.17968	−	0.857089i	0.0579083	−	0.0420729i
$416$		0			0
$417$	−43.4789			−2.12917
$418$		0			0
$419$	−7.32141			−0.357674			−0.178837	−	0.983879i	$-0.557233\pi$
$419$	−7.32141			−0.357674			−0.178837	+	0.983879i	$0.557233\pi$
$420$		0			0
$421$	−26.5994	+	19.3256i	−1.29637	+	0.941871i	−0.999913	−	0.0131740i	$-0.995806\pi$
$421$	−26.5994	+	19.3256i	−1.29637	+	0.941871i	−0.296461	+	0.955045i	$0.595806\pi$
$422$		0			0
$423$	−2.35027	−	7.23339i	−0.114274	−	0.351700i
$424$		0			0
$425$	−5.63002	−	4.09045i	−0.273096	−	0.198416i
$426$		0			0
$427$	−0.829780	+	2.55380i	−0.0401558	+	0.123587i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.61187	−	4.96082i	0.0776409	−	0.238954i	−0.904702	−	0.426046i	$-0.859906\pi$
$431$	1.61187	−	4.96082i	0.0776409	−	0.238954i	0.982342	+	0.187092i	$0.0599062\pi$
$432$		0			0
$433$	−8.92198	−	6.48220i	−0.428763	−	0.311514i	0.352391	−	0.935853i	$-0.385369\pi$
$433$	−8.92198	−	6.48220i	−0.428763	−	0.311514i	−0.781154	+	0.624338i	$0.785369\pi$
$434$		0			0
$435$	−3.55491	−	10.9409i	−0.170445	−	0.524576i
$436$		0			0
$437$	−26.1603	+	19.0066i	−1.25142	+	0.909207i
$438$		0			0
$439$	−22.5808			−1.07772			−0.538862	−	0.842394i	$-0.681145\pi$
$439$	−22.5808			−1.07772			−0.538862	+	0.842394i	$0.681145\pi$
$440$		0			0
$441$	−43.1968			−2.05699
$442$		0			0
$443$	28.5729	−	20.7594i	1.35754	−	0.986311i	0.358944	−	0.933359i	$-0.383137\pi$
$443$	28.5729	−	20.7594i	1.35754	−	0.986311i	0.998597	−	0.0529520i	$-0.0168630\pi$
$444$		0			0
$445$	−1.06255	−	3.27020i	−0.0503698	−	0.155022i
$446$		0			0
$447$	−25.1490	−	18.2718i	−1.18951	−	0.864228i
$448$		0			0
$449$	11.4521	−	35.2460i	0.540459	−	1.66336i	−0.191091	−	0.981572i	$-0.561203\pi$
$449$	11.4521	−	35.2460i	0.540459	−	1.66336i	0.731550	−	0.681788i	$-0.238797\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−4.13207	+	12.7172i	−0.194142	+	0.597506i
$454$		0			0
$455$	2.82347	+	2.05137i	0.132366	+	0.0961698i
$456$		0			0
$457$	−0.109082	−	0.335720i	−0.00510264	−	0.0157043i	0.948473	−	0.316859i	$-0.102628\pi$
$457$	−0.109082	−	0.335720i	−0.00510264	−	0.0157043i	−0.953575	+	0.301154i	$0.902628\pi$
$458$		0			0
$459$	30.8526	−	22.4158i	1.44008	−	1.04628i
$460$		0			0
$461$	−12.2449			−0.570303			−0.285151	−	0.958482i	$-0.592044\pi$
$461$	−12.2449			−0.570303			−0.285151	+	0.958482i	$0.592044\pi$
$462$		0			0
$463$	20.9578			0.973992			0.486996	−	0.873404i	$-0.338093\pi$
$463$	20.9578			0.973992			0.486996	+	0.873404i	$0.338093\pi$
$464$		0			0
$465$	−15.1710	+	11.0223i	−0.703536	+	0.511149i
$466$		0			0
$467$	9.13973	+	28.1292i	0.422936	+	1.30166i	0.904957	+	0.425504i	$0.139903\pi$
$467$	9.13973	+	28.1292i	0.422936	+	1.30166i	−0.482020	+	0.876160i	$0.660097\pi$
$468$		0			0
$469$	0.335190	+	0.243530i	0.0154776	+	0.0112452i
$470$		0			0
$471$	20.8836	−	64.2731i	0.962266	−	2.96155i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	2.60464	−	8.01627i	0.119509	−	0.367812i
$476$		0			0
$477$	−40.2893	−	29.2719i	−1.84472	−	1.34027i
$478$		0			0
$479$	1.80036	+	5.54094i	0.0822606	+	0.253172i	0.983725	−	0.179682i	$-0.0575067\pi$
$479$	1.80036	+	5.54094i	0.0822606	+	0.253172i	−0.901464	+	0.432854i	$0.857507\pi$
$480$		0			0
$481$	7.81183	−	5.67563i	0.356189	−	0.258786i
$482$		0			0
$483$	7.53204			0.342720
$484$		0			0
$485$	−16.8872			−0.766808
$486$		0			0
$487$	−25.0405	+	18.1930i	−1.13469	+	0.824403i	−0.986371	−	0.164536i	$-0.947387\pi$
$487$	−25.0405	+	18.1930i	−1.13469	+	0.824403i	−0.148323	+	0.988939i	$0.547387\pi$
$488$		0			0
$489$	18.5761	+	57.1713i	0.840040	+	2.58538i
$490$		0			0
$491$	8.65080	+	6.28518i	0.390405	+	0.283646i	0.765622	−	0.643291i	$-0.222432\pi$
$491$	8.65080	+	6.28518i	0.390405	+	0.283646i	−0.375216	+	0.926937i	$0.622432\pi$
$492$		0			0
$493$	2.49674	−	7.68418i	0.112448	−	0.346078i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.258522	−	0.795648i	0.0115963	−	0.0356897i
$498$		0			0
$499$	−20.7754	−	15.0942i	−0.930033	−	0.675708i	0.0159682	−	0.999873i	$-0.494917\pi$
$499$	−20.7754	−	15.0942i	−0.930033	−	0.675708i	−0.946001	+	0.324164i	$0.894917\pi$
$500$		0			0
$501$	0.931052	+	2.86548i	0.0415963	+	0.128020i
$502$		0			0
$503$	−13.9614	+	10.1435i	−0.622507	+	0.452278i	−0.853796	−	0.520607i	$-0.825706\pi$
$503$	−13.9614	+	10.1435i	−0.622507	+	0.452278i	0.231289	+	0.972885i	$0.425706\pi$
$504$		0			0
$505$	25.6674			1.14218
$506$		0			0
$507$	54.1666			2.40562
$508$		0			0
$509$	−28.2532	+	20.5272i	−1.25230	+	0.909851i	−0.998353	−	0.0573662i	$-0.981730\pi$
$509$	−28.2532	+	20.5272i	−1.25230	+	0.909851i	−0.253950	+	0.967217i	$0.581730\pi$
$510$		0			0
$511$	0.425957	+	1.31096i	0.0188432	+	0.0579935i
$512$		0			0
$513$	37.3685	+	27.1498i	1.64986	+	1.19869i
$514$		0			0
$515$	4.41890	−	13.6000i	0.194720	−	0.599287i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	16.4761	−	50.7083i	0.723221	−	2.22585i
$520$		0			0
$521$	6.44775	+	4.68457i	0.282481	+	0.205235i	0.719999	−	0.693975i	$-0.244142\pi$
$521$	6.44775	+	4.68457i	0.282481	+	0.205235i	−0.437518	+	0.899210i	$0.644142\pi$
$522$		0			0
$523$	−7.05650	−	21.7177i	−0.308559	−	0.949647i	−0.978325	−	0.207075i	$-0.933606\pi$
$523$	−7.05650	−	21.7177i	−0.308559	−	0.949647i	0.669766	−	0.742572i	$-0.266394\pi$
$524$		0			0
$525$	−1.58837	+	1.15402i	−0.0693221	+	0.0503655i
$526$		0			0
$527$	−13.1704			−0.573713
$528$		0			0
$529$	26.0293			1.13171
$530$		0			0
$531$	15.7071	−	11.4119i	0.681631	−	0.495234i
$532$		0			0
$533$	2.54272	+	7.82568i	0.110137	+	0.338968i
$534$		0			0
$535$	6.59437	+	4.79109i	0.285099	+	0.207137i
$536$		0			0
$537$	−2.68518	+	8.26415i	−0.115874	+	0.356624i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−12.3476	+	38.0021i	−0.530866	+	1.63384i	0.221550	+	0.975149i	$0.428888\pi$
$541$	−12.3476	+	38.0021i	−0.530866	+	1.63384i	−0.752416	+	0.658688i	$0.771112\pi$
$542$		0			0
$543$	5.18260	+	3.76538i	0.222407	+	0.161588i
$544$		0			0
$545$	11.3751	+	35.0090i	0.487256	+	1.49962i
$546$		0			0
$547$	−13.4608	+	9.77983i	−0.575542	+	0.418156i	−0.837114	−	0.547028i	$-0.815759\pi$
$547$	−13.4608	+	9.77983i	−0.575542	+	0.418156i	0.261572	+	0.965184i	$0.415759\pi$
$548$		0			0
$549$	47.7850			2.03942
$550$		0			0
$551$	9.78598			0.416897
$552$		0			0
$553$	−1.17374	+	0.852775i	−0.0499126	+	0.0362637i
$554$		0			0
$555$	−2.91981	−	8.98625i	−0.123939	−	0.381445i
$556$		0			0
$557$	−15.9862	−	11.6146i	−0.677356	−	0.492128i	0.195124	−	0.980779i	$-0.437489\pi$
$557$	−15.9862	−	11.6146i	−0.677356	−	0.492128i	−0.872479	+	0.488651i	$0.837489\pi$
$558$		0			0
$559$	6.73711	−	20.7347i	0.284950	−	0.876984i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.49871	+	23.0787i	−0.316033	+	0.972649i	0.659294	+	0.751885i	$0.270855\pi$
$563$	−7.49871	+	23.0787i	−0.316033	+	0.972649i	−0.975327	+	0.220764i	$0.929145\pi$
$564$		0			0
$565$	−12.6927	−	9.22175i	−0.533984	−	0.387962i
$566$		0			0
$567$	−1.26836	−	3.90361i	−0.0532661	−	0.163936i
$568$		0			0
$569$	−23.0176	+	16.7233i	−0.964949	+	0.701076i	−0.954295	−	0.298867i	$-0.903391\pi$
$569$	−23.0176	+	16.7233i	−0.964949	+	0.701076i	−0.0106540	+	0.999943i	$0.503391\pi$
$570$		0			0
$571$	26.9485			1.12776			0.563879	−	0.825858i	$-0.309308\pi$
$571$	26.9485			1.12776			0.563879	+	0.825858i	$0.309308\pi$
$572$		0			0
$573$	−52.1644			−2.17920
$574$		0			0
$575$	−10.3394	+	7.51199i	−0.431182	+	0.313272i
$576$		0			0
$577$	3.36149	+	10.3456i	0.139940	+	0.430692i	0.996326	−	0.0856449i	$-0.0272951\pi$
$577$	3.36149	+	10.3456i	0.139940	+	0.430692i	−0.856385	+	0.516337i	$0.827295\pi$
$578$		0			0
$579$	49.6154	+	36.0477i	2.06195	+	1.49809i
$580$		0			0
$581$	0.0892844	−	0.274789i	0.00370414	−	0.0114002i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	19.1920	−	59.0668i	0.793491	−	2.44211i
$586$		0			0
$587$	21.8840	+	15.8996i	0.903248	+	0.656248i	0.939298	−	0.343102i	$-0.111478\pi$
$587$	21.8840	+	15.8996i	0.903248	+	0.656248i	−0.0360505	+	0.999350i	$0.511478\pi$
$588$		0			0
$589$	−4.92942	−	15.1712i	−0.203113	−	0.625118i
$590$		0			0
$591$	30.9564	−	22.4911i	1.27338	−	0.925162i
$592$		0			0
$593$	−6.72088			−0.275993			−0.137997	−	0.990433i	$-0.544066\pi$
$593$	−6.72088			−0.275993			−0.137997	+	0.990433i	$0.544066\pi$
$594$		0			0
$595$	2.39854			0.0983306
$596$		0			0
$597$	8.20716	−	5.96285i	0.335897	−	0.244043i
$598$		0			0
$599$	8.66286	+	26.6615i	0.353955	+	1.08936i	0.956613	+	0.291362i	$0.0941083\pi$
$599$	8.66286	+	26.6615i	0.353955	+	1.08936i	−0.602658	+	0.798000i	$0.705892\pi$
$600$		0			0
$601$	−13.8544	−	10.0658i	−0.565134	−	0.410594i	0.268201	−	0.963363i	$-0.413571\pi$
$601$	−13.8544	−	10.0658i	−0.565134	−	0.410594i	−0.833334	+	0.552769i	$0.813571\pi$
$602$		0			0
$603$	2.27839	−	7.01215i	0.0927831	−	0.285557i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.5897	+	35.6695i	−0.470412	+	1.44778i	0.381634	+	0.924314i	$0.375362\pi$
$607$	−11.5897	+	35.6695i	−0.470412	+	1.44778i	−0.852046	+	0.523467i	$0.824638\pi$
$608$		0			0
$609$	−1.84412	−	1.33983i	−0.0747277	−	0.0542928i
$610$		0			0
$611$	−2.07532	−	6.38717i	−0.0839583	−	0.258397i
$612$		0			0
$613$	21.5362	−	15.6470i	0.869838	−	0.631974i	−0.0607053	−	0.998156i	$-0.519335\pi$
$613$	21.5362	−	15.6470i	0.869838	−	0.631974i	0.930544	+	0.366181i	$0.119335\pi$
$614$		0			0
$615$	8.05179			0.324680
$616$		0			0
$617$	13.8616			0.558047			0.279024	−	0.960284i	$-0.409989\pi$
$617$	13.8616			0.558047			0.279024	+	0.960284i	$0.409989\pi$
$618$		0			0
$619$	−6.64461	+	4.82759i	−0.267069	+	0.194037i	−0.713258	−	0.700902i	$-0.752781\pi$
$619$	−6.64461	+	4.82759i	−0.267069	+	0.194037i	0.446188	+	0.894939i	$0.352781\pi$
$620$		0			0
$621$	−21.6422	−	66.6078i	−0.868470	−	2.67288i
$622$		0			0
$623$	−0.551203	−	0.400473i	−0.0220835	−	0.0160446i
$624$		0			0
$625$	−3.87591	+	11.9288i	−0.155036	+	0.477153i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.05069	−	6.31136i	0.0817662	−	0.251650i
$630$		0			0
$631$	−31.9269	−	23.1963i	−1.27099	−	0.923428i	−0.271748	−	0.962368i	$-0.587602\pi$
$631$	−31.9269	−	23.1963i	−1.27099	−	0.923428i	−0.999242	+	0.0389400i	$0.987602\pi$
$632$		0			0
$633$	22.6850	+	69.8171i	0.901646	+	2.77498i
$634$		0			0
$635$	25.6483	−	18.6346i	1.01782	−	0.739492i
$636$		0			0
$637$	−38.1432			−1.51129
$638$		0			0
$639$	−14.8876			−0.588946
$640$		0			0
$641$	29.2398	−	21.2440i	1.15490	−	0.839087i	0.165779	−	0.986163i	$-0.446986\pi$
$641$	29.2398	−	21.2440i	1.15490	−	0.839087i	0.989125	+	0.147076i	$0.0469863\pi$
$642$		0			0
$643$	−7.41192	−	22.8115i	−0.292298	−	0.899600i	−0.984116	−	0.177528i	$-0.943190\pi$
$643$	−7.41192	−	22.8115i	−0.292298	−	0.899600i	0.691818	−	0.722072i	$-0.256810\pi$
$644$		0			0
$645$	−17.2594	−	12.5397i	−0.679588	−	0.493750i
$646$		0			0
$647$	−12.8458	+	39.5353i	−0.505020	+	1.55429i	0.295717	+	0.955276i	$0.404441\pi$
$647$	−12.8458	+	39.5353i	−0.505020	+	1.55429i	−0.800737	+	0.599016i	$0.795559\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−1.14822	+	3.53385i	−0.0450021	+	0.138502i
$652$		0			0
$653$	−24.3111	−	17.6630i	−0.951365	−	0.691207i	−0.000235856	−	1.00000i	$-0.500075\pi$
$653$	−24.3111	−	17.6630i	−0.951365	−	0.691207i	−0.951129	+	0.308793i	$0.900075\pi$
$654$		0			0
$655$	−10.1083	−	31.1102i	−0.394965	−	1.21558i
$656$		0			0
$657$	19.8451	−	14.4183i	0.774230	−	0.562511i
$658$		0			0
$659$	−25.2450			−0.983405			−0.491702	−	0.870763i	$-0.663625\pi$
$659$	−25.2450			−0.983405			−0.491702	+	0.870763i	$0.663625\pi$
$660$		0			0
$661$	9.51852			0.370227			0.185114	−	0.982717i	$-0.440735\pi$
$661$	9.51852			0.370227			0.185114	+	0.982717i	$0.440735\pi$
$662$		0			0
$663$	52.1392	−	37.8814i	2.02492	−	1.47119i
$664$		0			0
$665$	0.897724	+	2.76291i	0.0348122	+	0.107141i
$666$		0			0
$667$	−12.0042	−	8.72155i	−0.464804	−	0.337700i
$668$		0			0
$669$	0.498260	−	1.53349i	0.0192638	−	0.0592880i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−3.48952	+	10.7396i	−0.134511	+	0.413982i	−0.995514	−	0.0946182i	$-0.969837\pi$
$673$	−3.48952	+	10.7396i	−0.134511	+	0.413982i	0.861003	+	0.508600i	$0.169837\pi$
$674$		0			0
$675$	14.7692	+	10.7305i	0.568467	+	0.413015i
$676$		0			0
$677$	10.9649	+	33.7464i	0.421414	+	1.29698i	0.906387	+	0.422449i	$0.138830\pi$
$677$	10.9649	+	33.7464i	0.421414	+	1.29698i	−0.484973	+	0.874529i	$0.661170\pi$
$678$		0			0
$679$	−2.70708	+	1.96681i	−0.103888	+	0.0754792i
$680$		0			0
$681$	38.6332			1.48043
$682$		0			0
$683$	24.8947			0.952569			0.476284	−	0.879291i	$-0.341983\pi$
$683$	24.8947			0.952569			0.476284	+	0.879291i	$0.341983\pi$
$684$		0			0
$685$	19.4280	−	14.1153i	0.742308	−	0.539318i
$686$		0			0
$687$	−5.74560	−	17.6831i	−0.219208	−	0.674654i
$688$		0			0
$689$	−35.5759	−	25.8474i	−1.35534	−	0.984709i
$690$		0			0
$691$	−0.196086	+	0.603492i	−0.00745947	+	0.0229579i	−0.954717	−	0.297516i	$-0.903842\pi$
$691$	−0.196086	+	0.603492i	−0.00745947	+	0.0229579i	0.947258	+	0.320473i	$0.103842\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.85740	+	24.1826i	−0.298048	+	0.917298i
$696$		0			0
$697$	4.57504	+	3.32396i	0.173292	+	0.125904i
$698$		0			0
$699$	2.34514	+	7.21759i	0.0887013	+	0.272994i
$700$		0			0
$701$	14.1272	−	10.2640i	0.533578	−	0.387667i	−0.288116	−	0.957595i	$-0.593029\pi$
$701$	14.1272	−	10.2640i	0.533578	−	0.387667i	0.821695	+	0.569928i	$0.193029\pi$
$702$		0			0
$703$	8.03767			0.303146
$704$		0			0
$705$	−6.57171			−0.247505
$706$		0			0
$707$	4.11457	−	2.98941i	0.154744	−	0.112428i
$708$		0			0
$709$	10.0755	+	31.0093i	0.378395	+	1.16458i	0.941159	+	0.337963i	$0.109738\pi$
$709$	10.0755	+	31.0093i	0.378395	+	1.16458i	−0.562764	+	0.826617i	$0.690262\pi$
$710$		0			0
$711$	20.8874	+	15.1756i	0.783339	+	0.569129i
$712$		0			0
$713$	−7.47423	+	23.0033i	−0.279912	+	0.861480i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−21.0598	+	64.8153i	−0.786491	+	2.42057i
$718$		0			0
$719$	28.3034	+	20.5636i	1.05554	+	0.766894i	0.973258	−	0.229715i	$-0.0737796\pi$
$719$	28.3034	+	20.5636i	1.05554	+	0.766894i	0.0822808	+	0.996609i	$0.473780\pi$
$720$		0			0
$721$	−0.875590	−	2.69479i	−0.0326087	−	0.100359i
$722$		0			0
$723$	−59.4100	+	43.1639i	−2.20948	+	1.60528i
$724$		0			0
$725$	3.86773			0.143644
$726$		0			0
$727$	−16.2644			−0.603214			−0.301607	−	0.953432i	$-0.597523\pi$
$727$	−16.2644			−0.603214			−0.301607	+	0.953432i	$0.597523\pi$
$728$		0			0
$729$	14.8702	−	10.8038i	0.550748	−	0.400142i
$730$		0			0
$731$	−4.63015	−	14.2501i	−0.171252	−	0.527061i
$732$		0			0
$733$	36.4713	+	26.4980i	1.34710	+	0.978725i	0.999150	+	0.0412120i	$0.0131219\pi$
$733$	36.4713	+	26.4980i	1.34710	+	0.978725i	0.347949	+	0.937513i	$0.386878\pi$
$734$		0			0
$735$	−11.5339	+	35.4977i	−0.425435	+	1.30935i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	4.52654	−	13.9313i	0.166512	−	0.512470i	−0.832633	−	0.553825i	$-0.813168\pi$
$739$	4.52654	−	13.9313i	0.166512	−	0.512470i	0.999145	+	0.0413554i	$0.0131676\pi$
$740$		0			0
$741$	63.1506	+	45.8816i	2.31990	+	1.68550i
$742$		0			0
$743$	−1.30823	−	4.02632i	−0.0479943	−	0.147711i	0.924187	−	0.381939i	$-0.124744\pi$
$743$	−1.30823	−	4.02632i	−0.0479943	−	0.147711i	−0.972182	+	0.234228i	$0.924744\pi$
$744$		0			0
$745$	−14.7075	+	10.6856i	−0.538841	+	0.391491i
$746$		0			0
$747$	−5.14168			−0.188124
$748$		0			0
$749$	1.61511			0.0590148
$750$		0			0
$751$	18.4769	−	13.4243i	0.674232	−	0.489858i	−0.197207	−	0.980362i	$-0.563187\pi$
$751$	18.4769	−	13.4243i	0.674232	−	0.489858i	0.871439	+	0.490504i	$0.163187\pi$
$752$		0			0
$753$	−6.52565	−	20.0839i	−0.237808	−	0.731897i
$754$		0			0
$755$	6.32647	+	4.59645i	0.230244	+	0.167282i
$756$		0			0
$757$	−9.57868	+	29.4801i	−0.348143	+	1.07147i	0.611737	+	0.791062i	$0.290471\pi$
$757$	−9.57868	+	29.4801i	−0.348143	+	1.07147i	−0.959880	+	0.280413i	$0.909529\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.93483	−	27.4986i	0.323887	−	0.996823i	−0.648053	−	0.761595i	$-0.724416\pi$
$761$	8.93483	−	27.4986i	0.323887	−	0.996823i	0.971940	−	0.235228i	$-0.0755836\pi$
$762$		0			0
$763$	5.90088	+	4.28724i	0.213626	+	0.155208i
$764$		0			0
$765$	−13.1899	−	40.5943i	−0.476881	−	1.46769i
$766$		0			0
$767$	13.8696	−	10.0768i	0.500801	−	0.363853i
$768$		0			0
$769$	−5.37741			−0.193914			−0.0969571	−	0.995289i	$-0.530911\pi$
$769$	−5.37741			−0.193914			−0.0969571	+	0.995289i	$0.530911\pi$
$770$		0			0
$771$	−44.6440			−1.60782
$772$		0			0
$773$	−36.0818	+	26.2150i	−1.29777	+	0.942887i	−0.999931	−	0.0117283i	$-0.996267\pi$
$773$	−36.0818	+	26.2150i	−1.29777	+	0.942887i	−0.297841	+	0.954615i	$0.596267\pi$
$774$		0			0
$775$	−1.94826	−	5.99613i	−0.0699836	−	0.215387i
$776$		0			0
$777$	−1.51466	−	1.10047i	−0.0543382	−	0.0394790i
$778$		0			0
$779$	−2.11657	+	6.51414i	−0.0758340	+	0.233393i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−6.54968	+	20.1579i	−0.234067	+	0.720383i
$784$		0			0
$785$	−31.9741	−	23.2306i	−1.14121	−	0.829135i
$786$		0			0
$787$	12.8638	+	39.5908i	0.458546	+	1.41126i	0.866921	+	0.498445i	$0.166095\pi$
$787$	12.8638	+	39.5908i	0.458546	+	1.41126i	−0.408376	+	0.912814i	$0.633905\pi$
$788$		0			0
$789$	−56.6599	+	41.1659i	−2.01715	+	1.46554i
$790$		0			0
$791$	−3.10871			−0.110533
$792$		0			0
$793$	42.1947			1.49838
$794$		0			0
$795$	−34.8123	+	25.2926i	−1.23467	+	0.897037i
$796$		0			0
$797$	−1.55827	−	4.79585i	−0.0551966	−	0.169878i	0.919658	−	0.392721i	$-0.128466\pi$
$797$	−1.55827	−	4.79585i	−0.0551966	−	0.169878i	−0.974854	+	0.222843i	$0.928466\pi$
$798$		0			0
$799$	−3.73406	−	2.71295i	−0.132101	−	0.0959773i
$800$		0			0
$801$	−3.74669	+	11.5311i	−0.132383	+	0.407433i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	1.36117	−	4.18926i	0.0479751	−	0.147652i
$806$		0			0
$807$	13.6748	+	9.93532i	0.481375	+	0.349740i
$808$		0			0
$809$	−8.65503	−	26.6374i	−0.304295	−	0.936523i	−0.979939	−	0.199295i	$-0.936135\pi$
$809$	−8.65503	−	26.6374i	−0.304295	−	0.936523i	0.675645	−	0.737227i	$-0.263865\pi$
$810$		0			0
$811$	−27.0203	+	19.6314i	−0.948810	+	0.689351i	−0.950525	−	0.310648i	$-0.899454\pi$
$811$	−27.0203	+	19.6314i	−0.948810	+	0.689351i	0.00171492	+	0.999999i	$0.499454\pi$
$812$		0			0
$813$	41.2396			1.44634
$814$		0			0
$815$	35.1552			1.23143
$816$		0			0
$817$	14.6820	−	10.6671i	0.513656	−	0.373193i
$818$		0			0
$819$	−3.80282	−	11.7039i	−0.132881	−	0.408967i
$820$		0			0
$821$	24.5560	+	17.8410i	0.857010	+	0.622654i	0.927070	−	0.374889i	$-0.122319\pi$
$821$	24.5560	+	17.8410i	0.857010	+	0.622654i	−0.0700601	+	0.997543i	$0.522319\pi$
$822$		0			0
$823$	2.08868	−	6.42829i	0.0728067	−	0.224076i	−0.908031	−	0.418903i	$-0.862415\pi$
$823$	2.08868	−	6.42829i	0.0728067	−	0.224076i	0.980838	+	0.194827i	$0.0624146\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.1454	−	31.2243i	0.352789	−	1.08577i	−0.604491	−	0.796612i	$-0.706623\pi$
$827$	10.1454	−	31.2243i	0.352789	−	1.08577i	0.957280	−	0.289162i	$-0.0933765\pi$
$828$		0			0
$829$	−12.5016	−	9.08297i	−0.434200	−	0.315465i	0.349126	−	0.937076i	$-0.386478\pi$
$829$	−12.5016	−	9.08297i	−0.434200	−	0.315465i	−0.783326	+	0.621611i	$0.786478\pi$
$830$		0			0
$831$	2.78690	+	8.57720i	0.0966766	+	0.297540i
$832$		0			0
$833$	−21.2078	+	15.4084i	−0.734808	+	0.533869i
$834$		0			0
$835$	1.76202			0.0609771
$836$		0			0
$837$	34.5499			1.19422
$838$		0			0
$839$	−22.6185	+	16.4333i	−0.780878	+	0.567341i	−0.905243	−	0.424895i	$-0.860311\pi$
$839$	−22.6185	+	16.4333i	−0.780878	+	0.567341i	0.124364	+	0.992237i	$0.460311\pi$
$840$		0			0
$841$	−7.57385	−	23.3099i	−0.261167	−	0.803790i
$842$		0			0
$843$	−22.0928	−	16.0513i	−0.760916	−	0.552838i
$844$		0			0
$845$	9.78885	−	30.1270i	0.336747	−	1.03640i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−16.9854	+	52.2756i	−0.582937	+	1.79409i
$850$		0			0
$851$	−9.85957	−	7.16340i	−0.337982	−	0.245558i
$852$		0			0
$853$	−4.35055	−	13.3896i	−0.148960	−	0.458452i	0.848539	−	0.529133i	$-0.177483\pi$
$853$	−4.35055	−	13.3896i	−0.148960	−	0.458452i	−0.997499	+	0.0706810i	$0.977483\pi$
$854$		0			0
$855$	41.8244	−	30.3872i	1.43036	−	1.03922i
$856$		0			0
$857$	−26.4776			−0.904457			−0.452228	−	0.891902i	$-0.649371\pi$
$857$	−26.4776			−0.904457			−0.452228	+	0.891902i	$0.649371\pi$
$858$		0			0
$859$	−47.5614			−1.62277			−0.811387	−	0.584510i	$-0.801287\pi$
$859$	−47.5614			−1.62277			−0.811387	+	0.584510i	$0.801287\pi$
$860$		0			0
$861$	1.29073	−	0.937772i	0.0439880	−	0.0319592i
$862$		0			0
$863$	13.4165	+	41.2919i	0.456705	+	1.40559i	0.869122	+	0.494597i	$0.164684\pi$
$863$	13.4165	+	41.2919i	0.456705	+	1.40559i	−0.412418	+	0.910995i	$0.635316\pi$
$864$		0			0
$865$	−25.2260	−	18.3278i	−0.857709	−	0.623162i
$866$		0			0
$867$	−2.31852	+	7.13568i	−0.0787412	+	0.242340i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	2.01184	−	6.19181i	0.0681686	−	0.209801i
$872$		0			0
$873$	48.1740	+	35.0005i	1.63044	+	1.18459i
$874$		0			0
$875$	1.32679	+	4.08342i	0.0448535	+	0.138045i
$876$		0			0
$877$	10.6262	−	7.72038i	0.358821	−	0.260699i	−0.393739	−	0.919222i	$-0.628819\pi$
$877$	10.6262	−	7.72038i	0.358821	−	0.260699i	0.752560	+	0.658523i	$0.228819\pi$
$878$		0			0
$879$	−84.2128			−2.84043
$880$		0			0
$881$	−36.3388			−1.22429			−0.612143	−	0.790747i	$-0.709692\pi$
$881$	−36.3388			−1.22429			−0.612143	+	0.790747i	$0.709692\pi$
$882$		0			0
$883$	−27.2130	+	19.7714i	−0.915789	+	0.665359i	−0.942472	−	0.334284i	$-0.891505\pi$
$883$	−27.2130	+	19.7714i	−0.915789	+	0.665359i	0.0266835	+	0.999644i	$0.491505\pi$
$884$		0			0
$885$	−5.18399	−	15.9547i	−0.174258	−	0.536310i
$886$		0			0
$887$	−28.3267	−	20.5806i	−0.951119	−	0.691028i	−4.75429e−5	−	1.00000i	$-0.500015\pi$
$887$	−28.3267	−	20.5806i	−0.951119	−	0.691028i	−0.951071	+	0.308972i	$0.900015\pi$
$888$		0			0
$889$	1.94120	−	5.97439i	0.0651057	−	0.200375i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.72750	−	5.31671i	0.0578087	−	0.177917i
$894$		0			0
$895$	4.11119	+	2.98695i	0.137422	+	0.0998429i
$896$		0			0
$897$	−36.5740	−	112.563i	−1.22117	−	3.75838i
$898$		0			0
$899$	5.92190	−	4.30251i	0.197506	−	0.143497i
$900$		0			0
$901$	−30.2218			−1.00683
$902$		0			0
$903$	−4.22721			−0.140673
$904$		0			0
$905$	3.03086	−	2.20205i	0.100749	−	0.0731985i
$906$		0			0
$907$	16.0199	+	49.3043i	0.531933	+	1.63712i	0.750184	+	0.661229i	$0.229965\pi$
$907$	16.0199	+	49.3043i	0.531933	+	1.63712i	−0.218251	+	0.975893i	$0.570035\pi$
$908$		0			0
$909$	−73.2211	−	53.1983i	−2.42859	−	1.76447i
$910$		0			0
$911$	−9.15631	+	28.1802i	−0.303362	+	0.933652i	0.676921	+	0.736055i	$0.263314\pi$
$911$	−9.15631	+	28.1802i	−0.303362	+	0.933652i	−0.980283	+	0.197597i	$0.936686\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	12.7590	−	39.2682i	0.421800	−	1.29817i
$916$		0			0
$917$	−5.24373	−	3.80979i	−0.173163	−	0.125810i
$918$		0			0
$919$	9.30344	+	28.6330i	0.306892	+	0.944517i	0.978964	+	0.204031i	$0.0654044\pi$
$919$	9.30344	+	28.6330i	0.306892	+	0.944517i	−0.672072	+	0.740485i	$0.734596\pi$
$920$		0			0
$921$	1.63217	−	1.18584i	0.0537818	−	0.0390748i
$922$		0			0
$923$	−13.1460			−0.432704
$924$		0			0
$925$	3.17674			0.104451
$926$		0			0
$927$	−40.7932	+	29.6380i	−1.33982	+	0.973439i
$928$		0			0
$929$	−15.7823	−	48.5729i	−0.517800	−	1.59362i	−0.778129	−	0.628105i	$-0.783831\pi$
$929$	−15.7823	−	48.5729i	−0.517800	−	1.59362i	0.260329	−	0.965520i	$-0.416169\pi$
$930$		0			0
$931$	−25.6868	−	18.6625i	−0.841850	−	0.611640i
$932$		0			0
$933$	−12.3056	+	37.8727i	−0.402867	+	1.23990i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.58070	−	7.94257i	0.0843077	−	0.259472i	−0.900012	−	0.435865i	$-0.856443\pi$
$937$	2.58070	−	7.94257i	0.0843077	−	0.259472i	0.984320	+	0.176392i	$0.0564427\pi$
$938$		0			0
$939$	−48.8364	−	35.4817i	−1.59372	−	1.15790i
$940$		0			0
$941$	−16.4996	−	50.7804i	−0.537870	−	1.65539i	−0.737365	−	0.675495i	$-0.763930\pi$
$941$	−16.4996	−	50.7804i	−0.537870	−	1.65539i	0.199495	−	0.979899i	$-0.436070\pi$
$942$		0			0
$943$	8.40192	−	6.10435i	0.273604	−	0.198785i
$944$		0			0
$945$	−6.29208			−0.204681
$946$		0			0
$947$	−19.2532			−0.625646			−0.312823	−	0.949811i	$-0.601275\pi$
$947$	−19.2532			−0.625646			−0.312823	+	0.949811i	$0.601275\pi$
$948$		0			0
$949$	17.5234	−	12.7315i	0.568834	−	0.413282i
$950$		0			0
$951$	−18.5845	−	57.1971i	−0.602643	−	1.85474i
$952$		0			0
$953$	−29.6500	−	21.5420i	−0.960457	−	0.697813i	−0.00719991	−	0.999974i	$-0.502292\pi$
$953$	−29.6500	−	21.5420i	−0.960457	−	0.697813i	−0.953257	+	0.302161i	$0.902292\pi$
$954$		0			0
$955$	−9.42702	+	29.0134i	−0.305051	+	0.938851i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.47041	−	4.52547i	0.0474822	−	0.146135i
$960$		0			0
$961$	15.4264	+	11.2079i	0.497624	+	0.361545i
$962$		0			0
$963$	−8.88169	−	27.3350i	−0.286208	−	0.880859i
$964$		0			0
$965$	29.0158	−	21.0812i	0.934052	−	0.678629i
$966$		0			0
$967$	45.6501			1.46801			0.734004	−	0.679146i	$-0.237649\pi$
$967$	45.6501			1.46801			0.734004	+	0.679146i	$0.237649\pi$
$968$		0			0
$969$	53.6465			1.72337
$970$		0			0
$971$	−37.3633	+	27.1460i	−1.19905	+	0.871158i	−0.994191	−	0.107635i	$-0.965672\pi$
$971$	−37.3633	+	27.1460i	−1.19905	+	0.871158i	−0.204855	+	0.978792i	$0.565672\pi$
$972$		0			0
$973$	1.55691	+	4.79169i	0.0499124	+	0.153614i
$974$		0			0
$975$	24.9591	+	18.1339i	0.799332	+	0.580749i
$976$		0			0
$977$	16.4846	−	50.7343i	0.527388	−	1.62313i	−0.232156	−	0.972679i	$-0.574578\pi$
$977$	16.4846	−	50.7343i	0.527388	−	1.62313i	0.759544	−	0.650456i	$-0.225422\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	40.1100	−	123.446i	1.28061	−	3.94133i
$982$		0			0
$983$	−9.77756	−	7.10382i	−0.311856	−	0.226577i	0.420837	−	0.907136i	$-0.361737\pi$
$983$	−9.77756	−	7.10382i	−0.311856	−	0.226577i	−0.732692	+	0.680560i	$0.761737\pi$
$984$		0			0
$985$	−6.91502	−	21.2822i	−0.220331	−	0.678109i
$986$		0			0
$987$	−1.05347	+	0.765391i	−0.0335323	+	0.0243627i
$988$		0			0
$989$	−27.5167			−0.874981
$990$		0			0
$991$	−36.0620			−1.14555			−0.572774	−	0.819714i	$-0.694133\pi$
$991$	−36.0620			−1.14555			−0.572774	+	0.819714i	$0.694133\pi$
$992$		0			0
$993$	−51.9746	+	37.7618i	−1.64936	+	1.19833i
$994$		0			0
$995$	−1.83331	−	5.64235i	−0.0581198	−	0.178874i
$996$		0			0
$997$	−7.54175	−	5.47940i	−0.238850	−	0.173534i	0.461921	−	0.886921i	$-0.347160\pi$
$997$	−7.54175	−	5.47940i	−0.238850	−	0.173534i	−0.700771	+	0.713387i	$0.747160\pi$
$998$		0			0
$999$	−5.37955	+	16.5566i	−0.170201	+	0.523826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.t.9.1		8
11.2	odd	10		88.2.i.b.25.2	✓	8
11.3	even	5		968.2.i.p.81.2		8
11.4	even	5		968.2.a.m.1.4		4
11.5	even	5	inner	968.2.i.t.753.1		8
11.6	odd	10		968.2.i.s.753.1		8
11.7	odd	10		968.2.a.n.1.4		4
11.8	odd	10		88.2.i.b.81.2	yes	8
11.9	even	5		968.2.i.p.729.2		8
11.10	odd	2		968.2.i.s.9.1		8
33.2	even	10		792.2.r.g.289.2		8
33.8	even	10		792.2.r.g.433.2		8
33.26	odd	10		8712.2.a.cd.1.2		4
33.29	even	10		8712.2.a.ce.1.2		4
44.7	even	10		1936.2.a.bb.1.1		4
44.15	odd	10		1936.2.a.bc.1.1		4
44.19	even	10		176.2.m.d.81.1		8
44.35	even	10		176.2.m.d.113.1		8
88.13	odd	10		704.2.m.l.641.1		8
88.19	even	10		704.2.m.i.257.2		8
88.29	odd	10		7744.2.a.di.1.1		4
88.35	even	10		704.2.m.i.641.2		8
88.37	even	10		7744.2.a.dh.1.1		4
88.51	even	10		7744.2.a.dr.1.4		4
88.59	odd	10		7744.2.a.ds.1.4		4
88.85	odd	10		704.2.m.l.257.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.25.2	✓	8	11.2	odd	10
88.2.i.b.81.2	yes	8	11.8	odd	10
176.2.m.d.81.1		8	44.19	even	10
176.2.m.d.113.1		8	44.35	even	10
704.2.m.i.257.2		8	88.19	even	10
704.2.m.i.641.2		8	88.35	even	10
704.2.m.l.257.1		8	88.85	odd	10
704.2.m.l.641.1		8	88.13	odd	10
792.2.r.g.289.2		8	33.2	even	10
792.2.r.g.433.2		8	33.8	even	10
968.2.a.m.1.4		4	11.4	even	5
968.2.a.n.1.4		4	11.7	odd	10
968.2.i.p.81.2		8	11.3	even	5
968.2.i.p.729.2		8	11.9	even	5
968.2.i.s.9.1		8	11.10	odd	2
968.2.i.s.753.1		8	11.6	odd	10
968.2.i.t.9.1		8	1.1	even	1	trivial
968.2.i.t.753.1		8	11.5	even	5	inner
1936.2.a.bb.1.1		4	44.7	even	10
1936.2.a.bc.1.1		4	44.15	odd	10
7744.2.a.dh.1.1		4	88.37	even	10
7744.2.a.di.1.1		4	88.29	odd	10
7744.2.a.dr.1.4		4	88.51	even	10
7744.2.a.ds.1.4		4	88.59	odd	10
8712.2.a.cd.1.2		4	33.26	odd	10
8712.2.a.ce.1.2		4	33.29	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.46489 + 1.79085i) q^{3} +(0.550606 + 1.69459i) q^{5} +(0.285629 + 0.207522i) q^{7} +(1.94151 - 5.97534i) q^{9} +O(q^{10})\)	\(q+(-2.46489 + 1.79085i) q^{3} +(0.550606 + 1.69459i) q^{5} +(0.285629 + 0.207522i) q^{7} +(1.94151 - 5.97534i) q^{9} +(1.71437 - 5.27629i) q^{13} +(-4.39194 - 3.19093i) q^{15} +(-1.17822 - 3.62619i) q^{17} +(3.73607 - 2.71441i) q^{19} -1.07569 q^{21} -7.00209 q^{23} +(1.47661 - 1.07282i) q^{25} +(3.09082 + 9.51255i) q^{27} +(1.71437 + 1.24556i) q^{29} +(1.06743 - 3.28521i) q^{31} +(-0.194395 + 0.598287i) q^{35} +(1.40809 + 1.02304i) q^{37} +(5.22330 + 16.0757i) q^{39} +(-1.19992 + 0.871790i) q^{41} +3.92979 q^{43} +11.1948 q^{45} +(0.979348 - 0.711538i) q^{47} +(-2.12460 - 6.53885i) q^{49} +(9.39814 + 6.82815i) q^{51} +(2.44939 - 7.53846i) q^{53} +(-4.34790 + 13.3815i) q^{57} +(2.50000 + 1.81636i) q^{59} +(2.35027 + 7.23339i) q^{61} +(1.79456 - 1.30383i) q^{63} +9.88510 q^{65} +1.17352 q^{67} +(17.2594 - 12.5397i) q^{69} +(-0.732238 - 2.25360i) q^{71} +(3.15861 + 2.29487i) q^{73} +(-1.71843 + 5.28878i) q^{75} +(-1.26985 + 3.90820i) q^{79} +(-9.40531 - 6.83335i) q^{81} +(-0.252890 - 0.778314i) q^{83} +(5.49617 - 3.99320i) q^{85} -6.45636 q^{87} -1.92979 q^{89} +(1.58462 - 1.15129i) q^{91} +(3.25221 + 10.0093i) q^{93} +(6.65692 + 4.83654i) q^{95} +(-2.92874 + 9.01374i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9}+O(q^{10}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9	\( 8 q - q^{3} + 2 q^{5} + 8 q^{7} + 7 q^{9} + 8 q^{13} - 3 q^{15} - 11 q^{17} + 12 q^{19} + 2 q^{21} - 4 q^{23} + 22 q^{25} + 8 q^{27} + 8 q^{29} + 2 q^{31} + 29 q^{35} - 14 q^{37} + 21 q^{39} + q^{41} - 6 q^{43} + 44 q^{45} - 6 q^{47} - 2 q^{49} + 52 q^{51} + 22 q^{53} + q^{57} + 20 q^{59} - 26 q^{61} + 5 q^{63} + 10 q^{65} - 10 q^{67} + 42 q^{69} + 30 q^{71} - 13 q^{73} - q^{75} + 6 q^{79} - 6 q^{81} + 20 q^{83} + 26 q^{85} + 6 q^{87} + 22 q^{89} - 13 q^{91} + 15 q^{93} + 13 q^{95} - 12 q^{97}+O(q^{100}) \) 8 * q - q^3 + 2 * q^5 + 8 * q^7 + 7 * q^9 + 8 * q^13 - 3 * q^15 - 11 * q^17 + 12 * q^19 + 2 * q^21 - 4 * q^23 + 22 * q^25 + 8 * q^27 + 8 * q^29 + 2 * q^31 + 29 * q^35 - 14 * q^37 + 21 * q^39 + q^41 - 6 * q^43 + 44 * q^45 - 6 * q^47 - 2 * q^49 + 52 * q^51 + 22 * q^53 + q^57 + 20 * q^59 - 26 * q^61 + 5 * q^63 + 10 * q^65 - 10 * q^67 + 42 * q^69 + 30 * q^71 - 13 * q^73 - q^75 + 6 * q^79 - 6 * q^81 + 20 * q^83 + 26 * q^85 + 6 * q^87 + 22 * q^89 - 13 * q^91 + 15 * q^93 + 13 * q^95 - 12 * q^97

Introduction

L-functions

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Database

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