LMFDB - Embedded newform 1148.2.r.a.737.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			737.20
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48683 - 0.858424i) q^{3} +(1.14679 - 1.98629i) q^{5} +(2.58388 + 0.568830i) q^{7} +(-0.0262152 + 0.0454060i) q^{9} +O(q^{10})$	\(q+(1.48683 - 0.858424i) q^{3} +(1.14679 - 1.98629i) q^{5} +(2.58388 + 0.568830i) q^{7} +(-0.0262152 + 0.0454060i) q^{9} +(0.876249 - 0.505903i) q^{11} -5.49899i q^{13} -3.93772i q^{15} +(-3.76985 + 2.17652i) q^{17} +(-0.0236876 - 0.0136760i) q^{19} +(4.33010 - 1.37231i) q^{21} +(4.62858 - 8.01694i) q^{23} +(-0.130240 - 0.225582i) q^{25} +5.24056i q^{27} +3.46316i q^{29} +(-0.927599 - 1.60665i) q^{31} +(0.868559 - 1.50439i) q^{33} +(4.09302 - 4.48002i) q^{35} +(-1.06145 + 1.83848i) q^{37} +(-4.72047 - 8.17609i) q^{39} +(0.247452 + 6.39834i) q^{41} -8.16986 q^{43} +(0.0601264 + 0.104142i) q^{45} +(10.1569 + 5.86411i) q^{47} +(6.35287 + 2.93958i) q^{49} +(-3.73676 + 6.47226i) q^{51} +(-1.98638 + 1.14684i) q^{53} -2.32065i q^{55} -0.0469593 q^{57} +(-4.40841 - 7.63559i) q^{59} +(7.35245 - 12.7348i) q^{61} +(-0.0935651 + 0.102412i) q^{63} +(-10.9226 - 6.30617i) q^{65} +(-6.35625 + 3.66979i) q^{67} -15.8932i q^{69} +8.23771i q^{71} +(-5.17947 - 8.97111i) q^{73} +(-0.387291 - 0.223603i) q^{75} +(2.55190 - 0.808755i) q^{77} +(-11.5262 - 6.65466i) q^{79} +(4.41998 + 7.65563i) q^{81} +12.1779 q^{83} +9.98403i q^{85} +(2.97286 + 5.14915i) q^{87} +(-0.364394 - 0.210383i) q^{89} +(3.12799 - 14.2087i) q^{91} +(-2.75837 - 1.59255i) q^{93} +(-0.0543292 + 0.0313670i) q^{95} +9.28117i q^{97} +0.0530493i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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
$3$	1.48683	−	0.858424i	0.858424	−	0.495612i	−0.00505996	−	0.999987i	$-0.501611\pi$
$3$	1.48683	−	0.858424i	0.858424	−	0.495612i	0.863484	+	0.504376i	$0.168277\pi$
$4$		0			0
$5$	1.14679	−	1.98629i	0.512859	−	0.888297i	−0.487030	−	0.873385i	$-0.661920\pi$
$5$	1.14679	−	1.98629i	0.512859	−	0.888297i	0.999889	−	0.0149121i	$-0.00474685\pi$
$6$		0			0
$7$	2.58388	+	0.568830i	0.976615	+	0.214997i
$7$	2.58388	+	0.568830i	0.976615	+	0.214997i
$8$		0			0
$9$	−0.0262152	+	0.0454060i	−0.00873839	+	0.0151353i
$10$		0			0
$11$	0.876249	−	0.505903i	0.264199	−	0.152535i	−0.362049	−	0.932159i	$-0.617923\pi$
$11$	0.876249	−	0.505903i	0.264199	−	0.152535i	0.626249	+	0.779623i	$0.284590\pi$
$12$		0			0
$13$		−	5.49899i		−	1.52515i	−0.646903	−	0.762573i	$-0.723936\pi$
$13$		−	5.49899i		−	1.52515i	0.646903	−	0.762573i	$-0.276064\pi$
$14$		0			0
$15$		−	3.93772i		−	1.01671i
$16$		0			0
$17$	−3.76985	+	2.17652i	−0.914322	+	0.527884i	−0.881819	−	0.471588i	$-0.843681\pi$
$17$	−3.76985	+	2.17652i	−0.914322	+	0.527884i	−0.0325029	+	0.999472i	$0.510348\pi$
$18$		0			0
$19$	−0.0236876	−	0.0136760i	−0.00543430	−	0.00313749i	0.497280	−	0.867590i	$-0.334332\pi$
$19$	−0.0236876	−	0.0136760i	−0.00543430	−	0.00313749i	−0.502715	+	0.864452i	$0.667665\pi$
$20$		0			0
$21$	4.33010	−	1.37231i	0.944905	−	0.299462i
$22$		0			0
$23$	4.62858	−	8.01694i	0.965126	−	1.67165i	0.255851	−	0.966716i	$-0.417644\pi$
$23$	4.62858	−	8.01694i	0.965126	−	1.67165i	0.709275	−	0.704932i	$-0.249022\pi$
$24$		0			0
$25$	−0.130240	−	0.225582i	−0.0260480	−	0.0451165i
$26$		0			0
$27$			5.24056i			1.00855i
$28$		0			0
$29$			3.46316i			0.643093i	0.946894	+	0.321547i	$0.104203\pi$
$29$			3.46316i			0.643093i	−0.946894	+	0.321547i	$0.895797\pi$
$30$		0			0
$31$	−0.927599	−	1.60665i	−0.166602	−	0.288563i	0.770621	−	0.637294i	$-0.219946\pi$
$31$	−0.927599	−	1.60665i	−0.166602	−	0.288563i	−0.937223	+	0.348731i	$0.886613\pi$
$32$		0			0
$33$	0.868559	−	1.50439i	0.151197	−	0.261880i
$34$		0			0
$35$	4.09302	−	4.48002i	0.691847	−	0.757261i
$36$		0			0
$37$	−1.06145	+	1.83848i	−0.174501	+	0.302244i	−0.939988	−	0.341206i	$-0.889165\pi$
$37$	−1.06145	+	1.83848i	−0.174501	+	0.302244i	0.765488	+	0.643451i	$0.222498\pi$
$38$		0			0
$39$	−4.72047	−	8.17609i	−0.755880	−	1.30922i
$40$		0			0
$41$	0.247452	+	6.39834i	0.0386455	+	0.999253i
$41$	0.247452	+	6.39834i	0.0386455	+	0.999253i
$42$		0			0
$43$	−8.16986			−1.24589			−0.622946	−	0.782265i	$-0.714064\pi$
$43$	−8.16986			−1.24589			−0.622946	+	0.782265i	$0.714064\pi$
$44$		0			0
$45$	0.0601264	+	0.104142i	0.00896311	+	0.0155246i
$46$		0			0
$47$	10.1569	+	5.86411i	1.48154	+	0.855369i	0.999781	−	0.0209334i	$-0.00666380\pi$
$47$	10.1569	+	5.86411i	1.48154	+	0.855369i	0.481762	+	0.876302i	$0.339997\pi$
$48$		0			0
$49$	6.35287	+	2.93958i	0.907552	+	0.419939i
$50$		0			0
$51$	−3.73676	+	6.47226i	−0.523251	+	0.906297i
$52$		0			0
$53$	−1.98638	+	1.14684i	−0.272850	+	0.157530i	−0.630182	−	0.776447i	$-0.717020\pi$
$53$	−1.98638	+	1.14684i	−0.272850	+	0.157530i	0.357332	+	0.933977i	$0.383687\pi$
$54$		0			0
$55$		−	2.32065i		−	0.312917i
$56$		0			0
$57$	−0.0469593			−0.00621991
$58$		0			0
$59$	−4.40841	−	7.63559i	−0.573926	−	0.994069i	−0.996157	−	0.0875808i	$-0.972086\pi$
$59$	−4.40841	−	7.63559i	−0.573926	−	0.994069i	0.422232	−	0.906488i	$-0.361247\pi$
$60$		0			0
$61$	7.35245	−	12.7348i	0.941385	−	1.63053i	0.178552	−	0.983930i	$-0.442859\pi$
$61$	7.35245	−	12.7348i	0.941385	−	1.63053i	0.762833	−	0.646596i	$-0.223808\pi$
$62$		0			0
$63$	−0.0935651	+	0.102412i	−0.0117881	+	0.0129027i
$64$		0			0
$65$	−10.9226	−	6.30617i	−1.35478	−	0.782184i
$66$		0			0
$67$	−6.35625	+	3.66979i	−0.776540	+	0.448336i	−0.835203	−	0.549942i	$-0.814650\pi$
$67$	−6.35625	+	3.66979i	−0.776540	+	0.448336i	0.0586626	+	0.998278i	$0.481316\pi$
$68$		0			0
$69$		−	15.8932i		−	1.91331i
$70$		0			0
$71$			8.23771i			0.977637i	0.872386	+	0.488818i	$0.162572\pi$
$71$			8.23771i			0.977637i	−0.872386	+	0.488818i	$0.837428\pi$
$72$		0			0
$73$	−5.17947	−	8.97111i	−0.606211	−	1.04999i	−0.991859	−	0.127342i	$-0.959355\pi$
$73$	−5.17947	−	8.97111i	−0.606211	−	1.04999i	0.385648	−	0.922646i	$-0.373978\pi$
$74$		0			0
$75$	−0.387291	−	0.223603i	−0.0447205	−	0.0258194i
$76$		0			0
$77$	2.55190	−	0.808755i	0.290815	−	0.0921662i
$78$		0			0
$79$	−11.5262	−	6.65466i	−1.29680	−	0.748707i	−0.316949	−	0.948442i	$-0.602658\pi$
$79$	−11.5262	−	6.65466i	−1.29680	−	0.748707i	−0.979850	+	0.199735i	$0.935992\pi$
$80$		0			0
$81$	4.41998	+	7.65563i	0.491109	+	0.850626i
$82$		0			0
$83$	12.1779			1.33670			0.668348	−	0.743849i	$-0.267002\pi$
$83$	12.1779			1.33670			0.668348	+	0.743849i	$0.267002\pi$
$84$		0			0
$85$			9.98403i			1.08292i
$86$		0			0
$87$	2.97286	+	5.14915i	0.318724	+	0.552047i
$88$		0			0
$89$	−0.364394	−	0.210383i	−0.0386257	−	0.0223006i	0.480563	−	0.876960i	$-0.340432\pi$
$89$	−0.364394	−	0.210383i	−0.0386257	−	0.0223006i	−0.519189	+	0.854660i	$0.673766\pi$
$90$		0			0
$91$	3.12799	−	14.2087i	0.327902	−	1.48948i
$92$		0			0
$93$	−2.75837	−	1.59255i	−0.286030	−	0.165140i
$94$		0			0
$95$	−0.0543292	+	0.0313670i	−0.00557406	+	0.00321818i
$96$		0			0
$97$			9.28117i			0.942360i	0.882037	+	0.471180i	$0.156172\pi$
$97$			9.28117i			0.942360i	−0.882037	+	0.471180i	$0.843828\pi$
$98$		0			0
$99$			0.0530493i			0.00533166i
$100$		0			0
$101$	−1.37577	+	0.794299i	−0.136894	+	0.0790357i	−0.566883	−	0.823798i	$-0.691851\pi$
$101$	−1.37577	+	0.794299i	−0.136894	+	0.0790357i	0.429989	+	0.902834i	$0.358517\pi$
$102$		0			0
$103$	−8.76840	+	15.1873i	−0.863976	+	1.49645i	0.00408443	+	0.999992i	$0.498700\pi$
$103$	−8.76840	+	15.1873i	−0.863976	+	1.49645i	−0.868060	+	0.496459i	$0.834633\pi$
$104$		0			0
$105$	2.23989	−	10.1746i	0.218591	−	0.992938i
$106$		0			0
$107$	0.941777	−	1.63121i	0.0910450	−	0.157695i	−0.816906	−	0.576771i	$-0.804313\pi$
$107$	0.941777	−	1.63121i	0.0910450	−	0.157695i	0.907951	+	0.419076i	$0.137646\pi$
$108$		0			0
$109$	8.52823	−	4.92377i	0.816856	−	0.471612i	−0.0324751	−	0.999473i	$-0.510339\pi$
$109$	8.52823	−	4.92377i	0.816856	−	0.471612i	0.849331	+	0.527861i	$0.177006\pi$
$110$		0			0
$111$			3.64469i			0.345939i
$112$		0			0
$113$	6.77649			0.637478			0.318739	−	0.947842i	$-0.396741\pi$
$113$	6.77649			0.637478			0.318739	+	0.947842i	$0.396741\pi$
$114$		0			0
$115$	−10.6160	−	18.3874i	−0.989947	−	1.71464i
$116$		0			0
$117$	0.249687	+	0.144157i	0.0230836	+	0.0133273i
$118$		0			0
$119$	−10.9789	+	3.47947i	−1.00643	+	0.318962i
$120$		0			0
$121$	−4.98812	+	8.63969i	−0.453466	+	0.785426i
$122$		0			0
$123$	5.86041	+	9.30086i	0.528416	+	0.838630i
$124$		0			0
$125$	10.8704			0.972282
$126$		0			0
$127$	−0.228661			−0.0202904			−0.0101452	−	0.999949i	$-0.503229\pi$
$127$	−0.228661			−0.0202904			−0.0101452	+	0.999949i	$0.503229\pi$
$128$		0			0
$129$	−12.1472	+	7.01321i	−1.06950	+	0.617478i
$130$		0			0
$131$	−6.06690	+	10.5082i	−0.530068	+	0.918104i	0.469317	+	0.883030i	$0.344500\pi$
$131$	−6.06690	+	10.5082i	−0.530068	+	0.918104i	−0.999385	+	0.0350745i	$0.988833\pi$
$132$		0			0
$133$	−0.0534265	−	0.0488114i	−0.00463266	−	0.00423248i
$134$		0			0
$135$	10.4093	+	6.00981i	0.895889	+	0.517242i
$136$		0			0
$137$	8.78538	−	5.07224i	0.750586	−	0.433351i	−0.0753199	−	0.997159i	$-0.523998\pi$
$137$	8.78538	−	5.07224i	0.750586	−	0.433351i	0.825905	+	0.563809i	$0.190664\pi$
$138$		0			0
$139$	20.6427			1.75089			0.875447	−	0.483313i	$-0.160567\pi$
$139$	20.6427			1.75089			0.875447	+	0.483313i	$0.160567\pi$
$140$		0			0
$141$	20.1356			1.69572
$142$		0			0
$143$	−2.78195	−	4.81849i	−0.232639	−	0.402942i
$144$		0			0
$145$	6.87885	+	3.97151i	0.571258	+	0.329816i
$146$		0			0
$147$	11.9691	−	1.08279i	0.987192	−	0.0893072i
$148$		0			0
$149$	−5.52383	−	3.18919i	−0.452530	−	0.261268i	0.256368	−	0.966579i	$-0.417474\pi$
$149$	−5.52383	−	3.18919i	−0.452530	−	0.261268i	−0.708898	+	0.705311i	$0.750807\pi$
$150$		0			0
$151$	−7.92964	+	4.57818i	−0.645305	+	0.372567i	−0.786655	−	0.617393i	$-0.788189\pi$
$151$	−7.92964	+	4.57818i	−0.645305	+	0.372567i	0.141350	+	0.989960i	$0.454856\pi$
$152$		0			0
$153$		−	0.228231i		−	0.0184514i
$154$		0			0
$155$	−4.25504			−0.341773
$156$		0			0
$157$	2.19772	−	1.26886i	0.175397	−	0.101266i	−0.409731	−	0.912206i	$-0.634377\pi$
$157$	2.19772	−	1.26886i	0.175397	−	0.101266i	0.585128	+	0.810941i	$0.301044\pi$
$158$		0			0
$159$	−1.96895	+	3.41032i	−0.156148	+	0.270456i
$160$		0			0
$161$	16.5200	−	18.0819i	1.30196	−	1.42506i
$162$		0			0
$163$	−10.6290	+	18.4100i	−0.832530	+	1.44198i	0.0634965	+	0.997982i	$0.479775\pi$
$163$	−10.6290	+	18.4100i	−0.832530	+	1.44198i	−0.896026	+	0.444001i	$0.853559\pi$
$164$		0			0
$165$	−1.99210	−	3.45042i	−0.155085	−	0.268615i
$166$		0			0
$167$			20.6811i			1.60035i	0.599766	+	0.800175i	$0.295260\pi$
$167$			20.6811i			1.60035i	−0.599766	+	0.800175i	$0.704740\pi$
$168$		0			0
$169$	−17.2389			−1.32607
$170$		0			0
$171$	0.00124195		0.000717038i	9.49740e−5		5.48333e-5i
$172$		0			0
$173$	8.51697	−	14.7518i	0.647533	−	1.12156i	−0.336177	−	0.941799i	$-0.609134\pi$
$173$	8.51697	−	14.7518i	0.647533	−	1.12156i	0.983710	−	0.179762i	$-0.0575326\pi$
$174$		0			0
$175$	−0.208207	−	0.656962i	−0.0157389	−	0.0496617i
$176$		0			0
$177$	−13.1091	−	7.56857i	−0.985344	−	0.568889i
$178$		0			0
$179$	8.32902	−	4.80876i	0.622540	−	0.359424i	−0.155317	−	0.987865i	$-0.549640\pi$
$179$	8.32902	−	4.80876i	0.622540	−	0.359424i	0.777857	+	0.628441i	$0.216307\pi$
$180$		0			0
$181$			11.0178i			0.818944i	0.912323	+	0.409472i	$0.134287\pi$
$181$			11.0178i			0.818944i	−0.912323	+	0.409472i	$0.865713\pi$
$182$		0			0
$183$		−	25.2461i		−	1.86624i
$184$		0			0
$185$	2.43451	+	4.21669i	0.178989	+	0.310017i
$186$		0			0
$187$	−2.20222	+	3.81435i	−0.161042	+	0.278933i
$188$		0			0
$189$	−2.98099	+	13.5410i	−0.216835	+	0.984961i
$190$		0			0
$191$	−18.3580	−	10.5990i	−1.32834	−	0.766917i	−0.343296	−	0.939227i	$-0.611543\pi$
$191$	−18.3580	−	10.5990i	−1.32834	−	0.766917i	−0.985043	+	0.172311i	$0.944877\pi$
$192$		0			0
$193$	−5.79448	+	3.34544i	−0.417096	+	0.240810i	−0.693834	−	0.720135i	$-0.744080\pi$
$193$	−5.79448	+	3.34544i	−0.417096	+	0.240810i	0.276738	+	0.960945i	$0.410747\pi$
$194$		0			0
$195$	−21.6535			−1.55064
$196$		0			0
$197$	−15.8608			−1.13003			−0.565017	−	0.825080i	$-0.691130\pi$
$197$	−15.8608			−1.13003			−0.565017	+	0.825080i	$0.691130\pi$
$198$		0			0
$199$	−14.8162	+	8.55412i	−1.05029	+	0.606385i	−0.922731	−	0.385445i	$-0.874048\pi$
$199$	−14.8162	+	8.55412i	−1.05029	+	0.606385i	−0.127560	+	0.991831i	$0.540714\pi$
$200$		0			0
$201$	−6.30047	+	10.9127i	−0.444401	+	0.769725i
$202$		0			0
$203$	−1.96995	+	8.94839i	−0.138263	+	0.628054i
$204$		0			0
$205$	12.9928	+	6.84602i	0.907453	+	0.478147i
$206$		0			0
$207$	0.242678	+	0.420331i	0.0168673	+	0.0292150i
$208$		0			0
$209$	−0.0276750			−0.00191432
$210$		0			0
$211$		−	9.40556i		−	0.647506i	−0.946142	−	0.323753i	$-0.895055\pi$
$211$		−	9.40556i		−	0.647506i	0.946142	−	0.323753i	$-0.104945\pi$
$212$		0			0
$213$	7.07145	+	12.2481i	0.484528	+	0.839227i
$214$		0			0
$215$	−9.36909	+	16.2277i	−0.638966	+	1.10672i
$216$		0			0
$217$	−1.48290	−	4.67903i	−0.100665	−	0.317634i
$218$		0			0
$219$	−15.4020	−	8.89237i	−1.04077	−	0.600891i
$220$		0			0
$221$	11.9687	+	20.7303i	0.805100	+	1.39447i
$222$		0			0
$223$	−9.24919			−0.619371			−0.309686	−	0.950839i	$-0.600224\pi$
$223$	−9.24919			−0.619371			−0.309686	+	0.950839i	$0.600224\pi$
$224$		0			0
$225$	0.0136571			0.000910471
$226$		0			0
$227$	13.8955	−	8.02258i	0.922278	−	0.532477i	0.0379169	−	0.999281i	$-0.487928\pi$
$227$	13.8955	−	8.02258i	0.922278	−	0.532477i	0.884361	+	0.466803i	$0.154594\pi$
$228$		0			0
$229$	6.97763	+	4.02854i	0.461095	+	0.266213i	0.712505	−	0.701667i	$-0.247561\pi$
$229$	6.97763	+	4.02854i	0.461095	+	0.266213i	−0.251410	+	0.967881i	$0.580894\pi$
$230$		0			0
$231$	3.09999	−	3.39309i	0.203964	−	0.223249i
$232$		0			0
$233$	14.9946	+	8.65715i	0.982330	+	0.567149i	0.902973	−	0.429698i	$-0.141380\pi$
$233$	14.9946	+	8.65715i	0.982330	+	0.567149i	0.0793574	+	0.996846i	$0.474713\pi$
$234$		0			0
$235$	23.2957	−	13.4498i	1.51964	−	0.877367i
$236$		0			0
$237$	−22.8501			−1.48427
$238$		0			0
$239$			18.4320i			1.19227i	0.802884	+	0.596135i	$0.203298\pi$
$239$			18.4320i			1.19227i	−0.802884	+	0.596135i	$0.796702\pi$
$240$		0			0
$241$	−13.2748	−	22.9926i	−0.855104	−	1.48108i	−0.876549	−	0.481313i	$-0.840160\pi$
$241$	−13.2748	−	22.9926i	−0.855104	−	1.48108i	0.0214453	−	0.999770i	$-0.493173\pi$
$242$		0			0
$243$	−0.471819	−	0.272405i	−0.0302672	−	0.0174748i
$244$		0			0
$245$	13.1242	−	9.24759i	0.838477	−	0.590807i
$246$		0			0
$247$	−0.0752043	+	0.130258i	−0.00478513	+	0.00828810i
$248$		0			0
$249$	18.1065	−	10.4538i	1.14745	−	0.662482i
$250$		0			0
$251$	5.44527			0.343703			0.171851	−	0.985123i	$-0.445025\pi$
$251$	5.44527			0.343703			0.171851	+	0.985123i	$0.445025\pi$
$252$		0			0
$253$		−	9.36646i		−	0.588864i
$254$		0			0
$255$	8.57053	+	14.8446i	0.536708	+	0.929605i
$256$		0			0
$257$	5.69005	+	3.28515i	0.354935	+	0.204922i	0.666857	−	0.745186i	$-0.267639\pi$
$257$	5.69005	+	3.28515i	0.354935	+	0.204922i	−0.311921	+	0.950108i	$0.600973\pi$
$258$		0			0
$259$	−3.78843	+	4.14663i	−0.235402	+	0.257659i
$260$		0			0
$261$	−0.157248	−	0.0907873i	−0.00973342	−	0.00561960i
$262$		0			0
$263$	11.2079	−	6.47086i	0.691106	−	0.399010i	−0.112920	−	0.993604i	$-0.536020\pi$
$263$	11.2079	−	6.47086i	0.691106	−	0.399010i	0.804026	+	0.594594i	$0.202687\pi$
$264$		0			0
$265$			5.26071i			0.323163i
$266$		0			0
$267$	−0.722392			−0.0442097
$268$		0			0
$269$	13.5290	+	23.4329i	0.824876	+	1.42873i	0.902014	+	0.431706i	$0.142088\pi$
$269$	13.5290	+	23.4329i	0.824876	+	1.42873i	−0.0771385	+	0.997020i	$0.524578\pi$
$270$		0			0
$271$	3.20052	−	5.54346i	0.194418	−	0.336741i	−0.752292	−	0.658830i	$-0.771052\pi$
$271$	3.20052	−	5.54346i	0.194418	−	0.336741i	0.946709	+	0.322089i	$0.104385\pi$
$272$		0			0
$273$	−7.54631	−	23.8112i	−0.456724	−	1.44112i
$274$		0			0
$275$	−0.228246	−	0.131778i	−0.0137637	−	0.00794649i
$276$		0			0
$277$	5.02681	+	8.70669i	0.302032	+	0.523134i	0.976596	−	0.215082i	$-0.0690018\pi$
$277$	5.02681	+	8.70669i	0.302032	+	0.523134i	−0.674564	+	0.738216i	$0.735668\pi$
$278$		0			0
$279$	0.0972687			0.00582332
$280$		0			0
$281$			7.01572i			0.418523i	0.977860	+	0.209262i	$0.0671060\pi$
$281$			7.01572i			0.418523i	−0.977860	+	0.209262i	$0.932894\pi$
$282$		0			0
$283$	2.46189	+	4.26411i	0.146344	+	0.253475i	0.929874	−	0.367879i	$-0.119916\pi$
$283$	2.46189	+	4.26411i	0.146344	+	0.253475i	−0.783530	+	0.621354i	$0.786583\pi$
$284$		0			0
$285$	−0.0538523	+	0.0932750i	−0.00318994	+	0.00552513i
$286$		0			0
$287$	−3.00018	+	16.6733i	−0.177095	+	0.984194i
$288$		0			0
$289$	0.974496	−	1.68788i	0.0573233	−	0.0992868i
$290$		0			0
$291$	7.96718	+	13.7996i	0.467044	+	0.808945i
$292$		0			0
$293$			28.2933i			1.65291i	0.563003	+	0.826455i	$0.309646\pi$
$293$			28.2933i			1.65291i	−0.563003	+	0.826455i	$0.690354\pi$
$294$		0			0
$295$	−20.2220			−1.17737
$296$		0			0
$297$	2.65121	+	4.59204i	0.153839	+	0.266457i
$298$		0			0
$299$	−44.0851	−	25.4525i	−2.54951	−	1.47196i
$300$		0			0
$301$	−21.1099	−	4.64726i	−1.21676	−	0.267864i
$302$		0			0
$303$	−1.36369	+	2.36198i	−0.0783420	+	0.135692i
$304$		0			0
$305$	−16.8634	−	29.2082i	−0.965595	−	1.67246i
$306$		0			0
$307$	−31.2351			−1.78268			−0.891342	−	0.453331i	$-0.850235\pi$
$307$	−31.2351			−1.78268			−0.891342	+	0.453331i	$0.850235\pi$
$308$		0			0
$309$			30.1080i			1.71279i
$310$		0			0
$311$	−18.7231	+	10.8098i	−1.06169	+	0.612968i	−0.925900	−	0.377769i	$-0.876691\pi$
$311$	−18.7231	+	10.8098i	−1.06169	+	0.612968i	−0.135792	+	0.990737i	$0.543358\pi$
$312$		0			0
$313$	20.3229	+	11.7334i	1.14872	+	0.663213i	0.948575	−	0.316553i	$-0.102526\pi$
$313$	20.3229	+	11.7334i	1.14872	+	0.663213i	0.200144	+	0.979766i	$0.435859\pi$
$314$		0			0
$315$	0.0961203	+	0.303292i	0.00541577	+	0.0170886i
$316$		0			0
$317$	−8.48989	−	4.90164i	−0.476840	−	0.275304i	0.242259	−	0.970212i	$-0.422112\pi$
$317$	−8.48989	−	4.90164i	−0.476840	−	0.275304i	−0.719099	+	0.694908i	$0.755445\pi$
$318$		0			0
$319$	1.75202	+	3.03459i	0.0980945	+	0.169905i
$320$		0			0
$321$		−	3.23378i		−	0.180492i
$322$		0			0
$323$	0.119065			0.00662493
$324$		0			0
$325$	−1.24048	+	0.716189i	−0.0688092	+	0.0397270i
$326$		0			0
$327$	8.45338	−	14.6417i	0.467473	−	0.809686i
$328$		0			0
$329$	22.9086	+	20.9297i	1.26299	+	1.15389i
$330$		0			0
$331$	−19.8968	−	11.4874i	−1.09363	−	0.631406i	−0.159088	−	0.987264i	$-0.550855\pi$
$331$	−19.8968	−	11.4874i	−1.09363	−	0.631406i	−0.934540	+	0.355858i	$0.884189\pi$
$332$		0			0
$333$	−0.0556520	−	0.0963921i	−0.00304971	−	0.00528226i
$334$		0			0
$335$			16.8338i			0.919731i
$336$		0			0
$337$	4.18581			0.228016			0.114008	−	0.993480i	$-0.463631\pi$
$337$	4.18581			0.228016			0.114008	+	0.993480i	$0.463631\pi$
$338$		0			0
$339$	10.0755	−	5.81710i	0.547227	−	0.315942i
$340$		0			0
$341$	−1.62562	−	0.938550i	−0.0880321	−	0.0508254i
$342$		0			0
$343$	14.7429	+	11.2092i	0.796043	+	0.605240i
$344$		0			0
$345$	−31.5685	−	18.2261i	−1.69959	−	0.981258i
$346$		0			0
$347$	−7.77971	+	4.49162i	−0.417637	+	0.241123i	−0.694066	−	0.719912i	$-0.744182\pi$
$347$	−7.77971	+	4.49162i	−0.417637	+	0.241123i	0.276429	+	0.961034i	$0.410849\pi$
$348$		0			0
$349$	22.4024			1.19918			0.599588	−	0.800309i	$-0.295331\pi$
$349$	22.4024			1.19918			0.599588	+	0.800309i	$0.295331\pi$
$350$		0			0
$351$	28.8178			1.53818
$352$		0			0
$353$	12.6767	+	21.9567i	0.674712	+	1.16864i	0.976553	+	0.215277i	$0.0690655\pi$
$353$	12.6767	+	21.9567i	0.674712	+	1.16864i	−0.301841	+	0.953358i	$0.597601\pi$
$354$		0			0
$355$	16.3625	+	9.44690i	0.868432	+	0.501389i
$356$		0			0
$357$	−13.3369	+	14.5980i	−0.705866	+	0.772605i
$358$		0			0
$359$	−8.32664	+	14.4222i	−0.439463	+	0.761173i	−0.997648	−	0.0685440i	$-0.978165\pi$
$359$	−8.32664	+	14.4222i	−0.439463	+	0.761173i	0.558185	+	0.829717i	$0.311498\pi$
$360$		0			0
$361$	−9.49963	−	16.4538i	−0.499980	−	0.865991i
$362$		0			0
$363$			17.1277i			0.898972i
$364$		0			0
$365$	−23.7590			−1.24360
$366$		0			0
$367$	−6.83457	−	11.8378i	−0.356762	−	0.617929i	0.630656	−	0.776062i	$-0.282786\pi$
$367$	−6.83457	−	11.8378i	−0.356762	−	0.617929i	−0.987418	+	0.158133i	$0.949453\pi$
$368$		0			0
$369$	−0.297010	−	0.156498i	−0.0154617	−	0.00814695i
$370$		0			0
$371$	−5.78492	+	1.83338i	−0.300338	+	0.0951842i
$372$		0			0
$373$	10.3549	−	17.9352i	0.536157	−	0.928651i	−0.462949	−	0.886385i	$-0.653209\pi$
$373$	10.3549	−	17.9352i	0.536157	−	0.928651i	0.999106	−	0.0422664i	$-0.0134578\pi$
$374$		0			0
$375$	16.1625	−	9.33145i	0.834630	−	0.481874i
$376$		0			0
$377$	19.0439			0.980810
$378$		0			0
$379$	−2.44098			−0.125385			−0.0626923	−	0.998033i	$-0.519969\pi$
$379$	−2.44098			−0.125385			−0.0626923	+	0.998033i	$0.519969\pi$
$380$		0			0
$381$	−0.339981	+	0.196288i	−0.0174178	+	0.0100562i
$382$		0			0
$383$	−0.631121	−	0.364378i	−0.0322488	−	0.0186188i	0.483789	−	0.875185i	$-0.339260\pi$
$383$	−0.631121	−	0.364378i	−0.0322488	−	0.0186188i	−0.516038	+	0.856566i	$0.672594\pi$
$384$		0			0
$385$	1.32006	−	5.99628i	0.0672763	−	0.305599i
$386$		0			0
$387$	0.214174	−	0.370961i	0.0108871	−	0.0188570i
$388$		0			0
$389$	4.87641	+	8.44619i	0.247244	+	0.428239i	0.962760	−	0.270357i	$-0.0871418\pi$
$389$	4.87641	+	8.44619i	0.247244	+	0.428239i	−0.715516	+	0.698596i	$0.753808\pi$
$390$		0			0
$391$			40.2969i			2.03790i
$392$		0			0
$393$			20.8319i			1.05083i
$394$		0			0
$395$	−26.4362	+	15.2629i	−1.33015	+	0.767962i
$396$		0			0
$397$	8.84743	+	5.10806i	0.444040	+	0.256366i	0.705310	−	0.708899i	$-0.250808\pi$
$397$	8.84743	+	5.10806i	0.444040	+	0.256366i	−0.261270	+	0.965266i	$0.584141\pi$
$398$		0			0
$399$	−0.121337	−	0.0267119i	−0.00607446	−	0.00133727i
$400$		0			0
$401$	−6.43352	+	11.1432i	−0.321275	+	0.556464i	−0.980751	−	0.195261i	$-0.937445\pi$
$401$	−6.43352	+	11.1432i	−0.321275	+	0.556464i	0.659477	+	0.751725i	$0.270778\pi$
$402$		0			0
$403$	−8.83495	+	5.10086i	−0.440100	+	0.254092i
$404$		0			0
$405$	20.2751			1.00748
$406$		0			0
$407$			2.14796i			0.106470i
$408$		0			0
$409$	−1.20473	−	2.08665i	−0.0595700	−	0.103178i	0.834702	−	0.550701i	$-0.185640\pi$
$409$	−1.20473	−	2.08665i	−0.0595700	−	0.103178i	−0.894272	+	0.447523i	$0.852306\pi$
$410$		0			0
$411$	8.70827	−	15.0832i	0.429547	−	0.743998i
$412$		0			0
$413$	−7.04745	−	22.2371i	−0.346782	−	1.09421i
$414$		0			0
$415$	13.9654	−	24.1888i	0.685536	−	1.18738i
$416$		0			0
$417$	30.6923	−	17.7202i	1.50301	−	0.867764i
$418$		0			0
$419$	−24.1047			−1.17759			−0.588795	−	0.808283i	$-0.700397\pi$
$419$	−24.1047			−1.17759			−0.588795	+	0.808283i	$0.700397\pi$
$420$		0			0
$421$		−	20.3312i		−	0.990883i	−0.868641	−	0.495441i	$-0.835006\pi$
$421$		−	20.3312i		−	0.990883i	0.868641	−	0.495441i	$-0.164994\pi$
$422$		0			0
$423$	−0.532532	+	0.307457i	−0.0258926	+	0.0149491i
$424$		0			0
$425$	0.981970	+	0.566941i	0.0476326	+	0.0275007i
$426$		0			0
$427$	26.2418	−	28.7229i	1.26993	−	1.39000i
$428$		0			0
$429$	−8.27261	−	4.77619i	−0.399405	−	0.230597i
$430$		0			0
$431$	−4.12872	−	7.15115i	−0.198873	−	0.344459i	0.749290	−	0.662242i	$-0.230395\pi$
$431$	−4.12872	−	7.15115i	−0.198873	−	0.344459i	−0.948163	+	0.317783i	$0.897062\pi$
$432$		0			0
$433$	−14.4302			−0.693472			−0.346736	−	0.937963i	$-0.612710\pi$
$433$	−14.4302			−0.693472			−0.346736	+	0.937963i	$0.612710\pi$
$434$		0			0
$435$	13.6370			0.653842
$436$		0			0
$437$	−0.219280	+	0.126601i	−0.0104896	+	0.00605616i
$438$		0			0
$439$	−3.82678	−	2.20939i	−0.182642	−	0.105449i	0.405891	−	0.913921i	$-0.366961\pi$
$439$	−3.82678	−	2.20939i	−0.182642	−	0.105449i	−0.588533	+	0.808473i	$0.700294\pi$
$440$		0			0
$441$	−0.300016	+	0.211397i	−0.0142865	+	0.0100665i
$442$		0			0
$443$	−6.35249	+	11.0028i	−0.301816	+	0.522761i	−0.976547	−	0.215303i	$-0.930926\pi$
$443$	−6.35249	+	11.0028i	−0.301816	+	0.522761i	0.674731	+	0.738063i	$0.264259\pi$
$444$		0			0
$445$	−0.835765	+	0.482529i	−0.0396190	+	0.0228741i
$446$		0			0
$447$	−10.9507			−0.517950
$448$		0			0
$449$	−1.96485			−0.0927271			−0.0463636	−	0.998925i	$-0.514763\pi$
$449$	−1.96485			−0.0927271			−0.0463636	+	0.998925i	$0.514763\pi$
$450$		0			0
$451$	3.45377	+	5.48136i	0.162632	+	0.258107i
$452$		0			0
$453$	−7.86004	+	13.6140i	−0.369297	+	0.639641i
$454$		0			0
$455$	−24.6356	−	22.5075i	−1.15493	−	1.05517i
$456$		0			0
$457$	3.14173	+	1.81388i	0.146964	+	0.0848497i	0.571679	−	0.820477i	$-0.306292\pi$
$457$	3.14173	+	1.81388i	0.146964	+	0.0848497i	−0.424715	+	0.905327i	$0.639626\pi$
$458$		0			0
$459$	−11.4062	−	19.7561i	−0.532396	−	0.922136i
$460$		0			0
$461$	10.5514			0.491427			0.245713	−	0.969343i	$-0.420978\pi$
$461$	10.5514			0.491427			0.245713	+	0.969343i	$0.420978\pi$
$462$		0			0
$463$		−	15.4984i		−	0.720273i	−0.932900	−	0.360137i	$-0.882730\pi$
$463$		−	15.4984i		−	0.720273i	0.932900	−	0.360137i	$-0.117270\pi$
$464$		0			0
$465$	−6.32653	+	3.65263i	−0.293386	+	0.169386i
$466$		0			0
$467$	−10.4487	+	18.0976i	−0.483507	+	0.837459i	−0.999821	−	0.0189410i	$-0.993971\pi$
$467$	−10.4487	+	18.0976i	−0.483507	+	0.837459i	0.516314	+	0.856400i	$0.327304\pi$
$468$		0			0
$469$	−18.5113	+	5.86666i	−0.854771	+	0.270897i
$470$		0			0
$471$	2.17843	−	3.77316i	0.100377	−	0.173858i
$472$		0			0
$473$	−7.15883	+	4.13316i	−0.329164	+	0.190043i
$474$		0			0
$475$			0.00712467i			0.000326902i
$476$		0			0
$477$		−	0.120258i		−	0.00550624i
$478$		0			0
$479$	28.4879	−	16.4475i	1.30164	−	0.751504i	0.320958	−	0.947093i	$-0.395995\pi$
$479$	28.4879	−	16.4475i	1.30164	−	0.751504i	0.980686	+	0.195589i	$0.0626618\pi$
$480$		0			0
$481$	10.1098	+	5.83689i	0.460966	+	0.266139i
$482$		0			0
$483$	9.04050	−	41.0660i	0.411357	−	1.86857i
$484$		0			0
$485$	18.4351	+	10.6435i	0.837096	+	0.483297i
$486$		0			0
$487$	−13.3327	−	23.0929i	−0.604163	−	1.04644i	−0.992183	−	0.124790i	$-0.960174\pi$
$487$	−13.3327	−	23.0929i	−0.604163	−	1.04644i	0.388020	−	0.921651i	$-0.373159\pi$
$488$		0			0
$489$			36.4969i			1.65045i
$490$		0			0
$491$	21.3066			0.961554			0.480777	−	0.876843i	$-0.340355\pi$
$491$	21.3066			0.961554			0.480777	+	0.876843i	$0.340355\pi$
$492$		0			0
$493$	−7.53765	−	13.0556i	−0.339479	−	0.587994i
$494$		0			0
$495$	0.105371	+	0.0608362i	0.00473609	+	0.00273439i
$496$		0			0
$497$	−4.68586	+	21.2853i	−0.210189	+	0.954774i
$498$		0			0
$499$	−20.6019	−	11.8945i	−0.922266	−	0.532471i	−0.0379090	−	0.999281i	$-0.512070\pi$
$499$	−20.6019	−	11.8945i	−0.922266	−	0.532471i	−0.884357	+	0.466810i	$0.845403\pi$
$500$		0			0
$501$	17.7531	+	30.7494i	0.793152	+	1.37378i
$502$		0			0
$503$		−	26.3595i		−	1.17531i	−0.809111	−	0.587656i	$-0.800051\pi$
$503$		−	26.3595i		−	1.17531i	0.809111	−	0.587656i	$-0.199949\pi$
$504$		0			0
$505$			3.64356i			0.162137i
$506$		0			0
$507$	−25.6314	+	14.7983i	−1.13833	+	0.657214i
$508$		0			0
$509$	−20.9992	−	12.1239i	−0.930773	−	0.537382i	−0.0437171	−	0.999044i	$-0.513920\pi$
$509$	−20.9992	−	12.1239i	−0.930773	−	0.537382i	−0.887056	+	0.461662i	$0.847253\pi$
$510$		0			0
$511$	−8.28010	−	26.1265i	−0.366290	−	1.15577i
$512$		0			0
$513$	0.0716700	−	0.124136i	0.00316431	−	0.00548074i
$514$		0			0
$515$	20.1110	+	34.8332i	0.886195	+	1.53493i
$516$		0			0
$517$	11.8667			0.521896
$518$		0			0
$519$		−	29.2447i		−	1.28370i
$520$		0			0
$521$	12.5413	−	7.24075i	0.549446	−	0.317223i	−0.199452	−	0.979908i	$-0.563916\pi$
$521$	12.5413	−	7.24075i	0.549446	−	0.317223i	0.748899	+	0.662685i	$0.230583\pi$
$522$		0			0
$523$	14.4025	−	24.9458i	0.629776	−	1.09080i	−0.357821	−	0.933790i	$-0.616480\pi$
$523$	14.4025	−	24.9458i	0.629776	−	1.09080i	0.987596	−	0.157013i	$-0.0501866\pi$
$524$		0			0
$525$	−0.873521	−	0.798065i	−0.0381236	−	0.0348304i
$526$		0			0
$527$	6.99382	+	4.03788i	0.304655	+	0.175893i
$528$		0			0
$529$	−31.3476	−	54.2956i	−1.36294	−	2.36068i
$530$		0			0
$531$	0.462269			0.0200607
$532$		0			0
$533$	35.1844	−	1.36074i	1.52401	−	0.0589400i
$534$		0			0
$535$	−2.16003	−	3.74129i	−0.0933864	−	0.161750i
$536$		0			0
$537$	8.25592	−	14.2997i	0.356269	−	0.617076i
$538$		0			0
$539$	7.05383	−	0.638132i	0.303830	−	0.0274863i
$540$		0			0
$541$	11.0565	−	19.1505i	0.475358	−	0.823344i	−0.524244	−	0.851568i	$-0.675652\pi$
$541$	11.0565	−	19.1505i	0.475358	−	0.823344i	0.999602	+	0.0282240i	$0.00898518\pi$
$542$		0			0
$543$	9.45792	+	16.3816i	0.405878	+	0.703002i
$544$		0			0
$545$		−	22.5861i		−	0.967481i
$546$		0			0
$547$		−	26.1752i		−	1.11917i	−0.828772	−	0.559586i	$-0.810960\pi$
$547$		−	26.1752i		−	1.11917i	0.828772	−	0.559586i	$-0.189040\pi$
$548$		0			0
$549$	0.385491	+	0.667691i	0.0164524	+	0.0284963i
$550$		0			0
$551$	0.0473623	−	0.0820339i	0.00201770	−	0.00349476i
$552$		0			0
$553$	−25.9970	−	23.7513i	−1.10550	−	1.01001i
$554$		0			0
$555$	7.23942	+	4.17968i	0.307296	+	0.177418i
$556$		0			0
$557$	35.9931	−	20.7806i	1.52507	−	0.880502i	0.525516	−	0.850784i	$-0.323872\pi$
$557$	35.9931	−	20.7806i	1.52507	−	0.880502i	0.999558	−	0.0297187i	$-0.00946115\pi$
$558$		0			0
$559$			44.9260i			1.90017i
$560$		0			0
$561$			7.56175i			0.319257i
$562$		0			0
$563$	−8.57560	+	4.95112i	−0.361418	+	0.208665i	−0.669703	−	0.742629i	$-0.733578\pi$
$563$	−8.57560	+	4.95112i	−0.361418	+	0.208665i	0.308284	+	0.951294i	$0.400245\pi$
$564$		0			0
$565$	7.77119	−	13.4601i	0.326936	−	0.566270i
$566$		0			0
$567$	7.06595	+	22.2954i	0.296742	+	0.936321i
$568$		0			0
$569$	15.2764	−	26.4595i	0.640420	−	1.10924i	−0.344920	−	0.938632i	$-0.612094\pi$
$569$	15.2764	−	26.4595i	0.640420	−	1.10924i	0.985339	−	0.170607i	$-0.0545729\pi$
$570$		0			0
$571$	24.2741	−	14.0146i	1.01584	−	0.586495i	0.102943	−	0.994687i	$-0.467174\pi$
$571$	24.2741	−	14.0146i	1.01584	−	0.586495i	0.912896	+	0.408193i	$0.133841\pi$
$572$		0			0
$573$	−36.3938			−1.52037
$574$		0			0
$575$	−2.41131			−0.100559
$576$		0			0
$577$	5.97252	−	3.44823i	0.248639	−	0.143552i	−0.370502	−	0.928832i	$-0.620814\pi$
$577$	5.97252	−	3.44823i	0.248639	−	0.143552i	0.619141	+	0.785280i	$0.287481\pi$
$578$		0			0
$579$	−5.74362	+	9.94825i	−0.238697	+	0.413435i
$580$		0			0
$581$	31.4662	+	6.92714i	1.30544	+	0.287386i
$582$		0			0
$583$	−1.16038	+	2.00983i	−0.0480579	+	0.0832387i
$584$		0			0
$585$	0.572676	−	0.330634i	0.0236772	−	0.0136700i
$586$		0			0
$587$		−	9.20050i		−	0.379745i	−0.981809	−	0.189873i	$-0.939193\pi$
$587$		−	9.20050i		−	0.379745i	0.981809	−	0.189873i	$-0.0608075\pi$
$588$		0			0
$589$			0.0507435i			0.00209085i
$590$		0			0
$591$	−23.5823	+	13.6153i	−0.970048	+	0.560057i
$592$		0			0
$593$	−22.5149	−	12.9990i	−0.924578	−	0.533805i	−0.0394854	−	0.999220i	$-0.512572\pi$
$593$	−22.5149	−	12.9990i	−0.924578	−	0.533805i	−0.885093	+	0.465415i	$0.845905\pi$
$594$		0			0
$595$	−5.67921	+	25.7975i	−0.232825	+	1.05760i
$596$		0			0
$597$	−14.6861	+	25.4371i	−0.601063	+	1.04107i
$598$		0			0
$599$	−19.8871	−	34.4455i	−0.812565	−	1.40740i	−0.911063	−	0.412266i	$-0.864737\pi$
$599$	−19.8871	−	34.4455i	−0.812565	−	1.40740i	0.0984989	−	0.995137i	$-0.468596\pi$
$600$		0			0
$601$		−	19.2196i		−	0.783986i	−0.919968	−	0.391993i	$-0.871786\pi$
$601$		−	19.2196i		−	0.783986i	0.919968	−	0.391993i	$-0.128214\pi$
$602$		0			0
$603$		−	0.384816i		−	0.0156709i
$604$		0			0
$605$	11.4406	+	19.8158i	0.465128	+	0.805625i
$606$		0			0
$607$	−1.84464	+	3.19502i	−0.0748718	+	0.129682i	−0.901031	−	0.433756i	$-0.857188\pi$
$607$	−1.84464	+	3.19502i	−0.0748718	+	0.129682i	0.826159	+	0.563437i	$0.190521\pi$
$608$		0			0
$609$	4.75253	+	14.9958i	0.192582	+	0.607662i
$610$		0			0
$611$	32.2467	−	55.8529i	1.30456	−	2.25957i
$612$		0			0
$613$	2.49271	+	4.31750i	0.100680	+	0.174382i	0.911965	−	0.410268i	$-0.134565\pi$
$613$	2.49271	+	4.31750i	0.100680	+	0.174382i	−0.811285	+	0.584650i	$0.801232\pi$
$614$		0			0
$615$	25.1949	−	0.974396i	1.01596	−	0.0392915i
$616$		0			0
$617$	−6.67816			−0.268852			−0.134426	−	0.990924i	$-0.542919\pi$
$617$	−6.67816			−0.268852			−0.134426	+	0.990924i	$0.542919\pi$
$618$		0			0
$619$	−11.9535	−	20.7041i	−0.480454	−	0.832170i	0.519295	−	0.854595i	$-0.326195\pi$
$619$	−11.9535	−	20.7041i	−0.480454	−	0.832170i	−0.999749	+	0.0224251i	$0.992861\pi$
$620$		0			0
$621$	42.0133	+	24.2564i	1.68593	+	0.973375i
$622$		0			0
$623$	−0.821878	−	0.750883i	−0.0329279	−	0.0300835i
$624$		0			0
$625$	13.1173	−	22.7198i	0.524691	−	0.908792i
$626$		0			0
$627$	−0.0411481	+	0.0237569i	−0.00164330	+	0.000948757i
$628$		0			0
$629$		−	9.24105i		−	0.368465i
$630$		0			0
$631$	45.2373			1.80087			0.900435	−	0.434991i	$-0.143248\pi$
$631$	45.2373			1.80087			0.900435	+	0.434991i	$0.143248\pi$
$632$		0			0
$633$	−8.07397	−	13.9845i	−0.320911	−	0.555835i
$634$		0			0
$635$	−0.262226	+	0.454188i	−0.0104061	+	0.0180239i
$636$		0			0
$637$	16.1647	−	34.9343i	0.640468	−	1.38415i
$638$		0			0
$639$	−0.374042	−	0.215953i	−0.0147969	−	0.00854297i
$640$		0			0
$641$	−12.8816	+	7.43721i	−0.508794	+	0.293752i	−0.732338	−	0.680942i	$-0.761571\pi$
$641$	−12.8816	+	7.43721i	−0.508794	+	0.293752i	0.223544	+	0.974694i	$0.428237\pi$
$642$		0			0
$643$			7.47902i			0.294944i	0.989066	+	0.147472i	$0.0471136\pi$
$643$			7.47902i			0.294944i	−0.989066	+	0.147472i	$0.952886\pi$
$644$		0			0
$645$			32.1706i			1.26672i
$646$		0			0
$647$	1.41876	+	2.45737i	0.0557773	+	0.0966092i	0.892566	−	0.450917i	$-0.148903\pi$
$647$	1.41876	+	2.45737i	0.0557773	+	0.0966092i	−0.836789	+	0.547526i	$0.815570\pi$
$648$		0			0
$649$	−7.72573	−	4.46045i	−0.303261	−	0.175088i
$650$		0			0
$651$	−6.22142	−	5.68400i	−0.243837	−	0.222773i
$652$		0			0
$653$	−21.5235	−	12.4266i	−0.842280	−	0.486290i	0.0157587	−	0.999876i	$-0.494984\pi$
$653$	−21.5235	−	12.4266i	−0.842280	−	0.486290i	−0.858039	+	0.513585i	$0.828317\pi$
$654$		0			0
$655$	13.9149	+	24.1013i	0.543700	+	0.941715i
$656$		0			0
$657$	0.543123			0.0211892
$658$		0			0
$659$			17.3630i			0.676366i	0.941080	+	0.338183i	$0.109812\pi$
$659$			17.3630i			0.676366i	−0.941080	+	0.338183i	$0.890188\pi$
$660$		0			0
$661$	12.0085	+	20.7993i	0.467076	+	0.808999i	0.999293	−	0.0376093i	$-0.0119742\pi$
$661$	12.0085	+	20.7993i	0.467076	+	0.808999i	−0.532217	+	0.846608i	$0.678641\pi$
$662$		0			0
$663$	35.5909	+	20.5484i	1.38223	+	0.798034i
$664$		0			0
$665$	−0.158222	+	0.0501444i	−0.00613560	+	0.00194452i
$666$		0			0
$667$	27.7640	+	16.0295i	1.07503	+	0.620666i
$668$		0			0
$669$	−13.7520	+	7.93973i	−0.531683	+	0.306968i
$670$		0			0
$671$		−	14.8785i		−	0.574378i
$672$		0			0
$673$			45.8308i			1.76665i	0.468764	+	0.883323i	$0.344699\pi$
$673$			45.8308i			1.76665i	−0.468764	+	0.883323i	$0.655301\pi$
$674$		0			0
$675$	1.18218	−	0.682531i	0.0455021	−	0.0262706i
$676$		0			0
$677$	3.21947	−	5.57628i	0.123734	−	0.214314i	−0.797503	−	0.603315i	$-0.793846\pi$
$677$	3.21947	−	5.57628i	0.123734	−	0.214314i	0.921237	+	0.389001i	$0.127180\pi$
$678$		0			0
$679$	−5.27940	+	23.9814i	−0.202605	+	0.920322i
$680$		0			0
$681$	13.7736	−	23.8565i	0.527804	−	0.914183i
$682$		0			0
$683$	−23.1415	+	13.3608i	−0.885486	+	0.511236i	−0.872463	−	0.488680i	$-0.837479\pi$
$683$	−23.1415	+	13.3608i	−0.885486	+	0.511236i	−0.0130227	+	0.999915i	$0.504145\pi$
$684$		0			0
$685$		−	23.2671i		−	0.888991i
$686$		0			0
$687$	13.8328			0.527754
$688$		0			0
$689$	6.30645	+	10.9231i	0.240256	+	0.416136i
$690$		0			0
$691$	−16.8343	−	9.71927i	−0.640406	−	0.369738i	0.144365	−	0.989524i	$-0.453886\pi$
$691$	−16.8343	−	9.71927i	−0.640406	−	0.369738i	−0.784771	+	0.619786i	$0.787219\pi$
$692$		0			0
$693$	−0.0301760	+	0.137073i	−0.00114629	+	0.00520697i
$694$		0			0
$695$	23.6728	−	41.0025i	0.897962	−	1.55532i
$696$		0			0
$697$	−14.8590	−	23.5822i	−0.562824	−	0.893239i
$698$		0			0
$699$	29.7260			1.12434
$700$		0			0
$701$	3.47798			0.131362			0.0656808	−	0.997841i	$-0.479078\pi$
$701$	3.47798			0.131362			0.0656808	+	0.997841i	$0.479078\pi$
$702$		0			0
$703$	0.0502862	−	0.0290327i	0.00189658	−	0.00109499i
$704$		0			0
$705$	23.0912	−	39.9952i	0.869666	−	1.50631i
$706$		0			0
$707$	−4.00663	+	1.26980i	−0.150685	+	0.0477556i
$708$		0			0
$709$	−43.6247	−	25.1867i	−1.63836	−	0.945907i	−0.981398	−	0.191983i	$-0.938508\pi$
$709$	−43.6247	−	25.1867i	−1.63836	−	0.945907i	−0.656961	−	0.753924i	$-0.728159\pi$
$710$		0			0
$711$	0.604323	−	0.348906i	0.0226639	−	0.0130850i
$712$		0			0
$713$	−17.1739			−0.643167
$714$		0			0
$715$	−12.7612			−0.477243
$716$		0			0
$717$	15.8225	+	27.4054i	0.590903	+	1.02347i
$718$		0			0
$719$	34.2592	+	19.7796i	1.27765	+	0.737653i	0.976416	−	0.215896i	$-0.0692672\pi$
$719$	34.2592	+	19.7796i	1.27765	+	0.737653i	0.301237	+	0.953549i	$0.402601\pi$
$720$		0			0
$721$	−31.2955	+	34.2545i	−1.16550	+	1.27570i
$722$		0			0
$723$	−39.4748	−	22.7908i	−1.46808	−	0.847598i
$724$		0			0
$725$	0.781229	−	0.451043i	0.0290141	−	0.0167513i
$726$		0			0
$727$			4.91826i			0.182408i	0.995832	+	0.0912042i	$0.0290716\pi$
$727$			4.91826i			0.182408i	−0.995832	+	0.0912042i	$0.970928\pi$
$728$		0			0
$729$	−27.4552			−1.01686
$730$		0			0
$731$	30.7991	−	17.7819i	1.13915	−	0.657687i
$732$		0			0
$733$	−12.1875	+	21.1094i	−0.450156	+	0.779692i	−0.998395	−	0.0566289i	$-0.981965\pi$
$733$	−12.1875	+	21.1094i	−0.450156	+	0.779692i	0.548240	+	0.836321i	$0.315298\pi$
$734$		0			0
$735$	11.5752	−	25.0158i	0.426958	−	0.922722i
$736$		0			0
$737$	−3.71311	+	6.43130i	−0.136774	+	0.236900i
$738$		0			0
$739$	−8.07210	−	13.9813i	−0.296937	−	0.514310i	0.678497	−	0.734604i	$-0.262632\pi$
$739$	−8.07210	−	13.9813i	−0.296937	−	0.514310i	−0.975434	+	0.220294i	$0.929298\pi$
$740$		0			0
$741$			0.258229i			0.00948627i
$742$		0			0
$743$	32.5746			1.19504			0.597522	−	0.801852i	$-0.296152\pi$
$743$	32.5746			1.19504			0.597522	+	0.801852i	$0.296152\pi$
$744$		0			0
$745$	−12.6693	+	7.31463i	−0.464168	+	0.267987i
$746$		0			0
$747$	−0.319245	+	0.552949i	−0.0116806	+	0.0202313i
$748$		0			0
$749$	3.36132	−	3.67913i	0.122820	−	0.134432i
$750$		0			0
$751$	−2.13907	−	1.23499i	−0.0780558	−	0.0450656i	0.460464	−	0.887678i	$-0.347683\pi$
$751$	−2.13907	−	1.23499i	−0.0780558	−	0.0450656i	−0.538520	+	0.842613i	$0.681016\pi$
$752$		0			0
$753$	8.09622	−	4.67436i	0.295043	−	0.170343i
$754$		0			0
$755$			21.0008i			0.764297i
$756$		0			0
$757$		−	5.24953i		−	0.190797i	−0.995439	−	0.0953987i	$-0.969587\pi$
$757$		−	5.24953i		−	0.190797i	0.995439	−	0.0953987i	$-0.0304126\pi$
$758$		0			0
$759$	−8.04039	−	13.9264i	−0.291848	−	0.505495i
$760$		0			0
$761$	7.17769	−	12.4321i	0.260191	−	0.450664i	−0.706101	−	0.708111i	$-0.749548\pi$
$761$	7.17769	−	12.4321i	0.260191	−	0.450664i	0.966293	+	0.257446i	$0.0828811\pi$
$762$		0			0
$763$	24.8367	−	7.87133i	0.899149	−	0.284961i
$764$		0			0
$765$	−0.453335	−	0.261733i	−0.0163903	−	0.00946297i
$766$		0			0
$767$	−41.9880	+	24.2418i	−1.51610	+	0.875320i
$768$		0			0
$769$	−14.8461			−0.535365			−0.267682	−	0.963507i	$-0.586258\pi$
$769$	−14.8461			−0.535365			−0.267682	+	0.963507i	$0.586258\pi$
$770$		0			0
$771$	11.2802			0.406247
$772$		0			0
$773$	7.30467	−	4.21735i	0.262731	−	0.151688i	−0.362849	−	0.931848i	$-0.618196\pi$
$773$	7.30467	−	4.21735i	0.262731	−	0.151688i	0.625580	+	0.780160i	$0.284863\pi$
$774$		0			0
$775$	−0.241621	+	0.418500i	−0.00867929	+	0.0150330i
$776$		0			0
$777$	−2.07321	+	9.41744i	−0.0743759	+	0.337849i
$778$		0			0
$779$	0.0816423	−	0.154945i	0.00292514	−	0.00555149i
$780$		0			0
$781$	4.16748	+	7.21829i	0.149124	+	0.258291i
$782$		0			0
$783$	−18.1489			−0.648589
$784$		0			0
$785$		−	5.82043i		−	0.207740i
$786$		0			0
$787$	−11.6135	−	20.1152i	−0.413976	−	0.717028i	0.581344	−	0.813658i	$-0.302527\pi$
$787$	−11.6135	−	20.1152i	−0.413976	−	0.717028i	−0.995320	+	0.0966299i	$0.969194\pi$
$788$		0			0
$789$	11.1095	−	19.2422i	0.395508	−	0.685041i
$790$		0			0
$791$	17.5096	+	3.85467i	0.622571	+	0.137056i
$792$		0			0
$793$	−70.0286	−	40.4310i	−2.48679	−	1.43575i
$794$		0			0
$795$	4.51592	+	7.82181i	0.160163	+	0.277411i
$796$		0			0
$797$	−31.0982			−1.10156			−0.550778	−	0.834652i	$-0.685669\pi$
$797$	−31.0982			−1.10156			−0.550778	+	0.834652i	$0.685669\pi$
$798$		0			0
$799$	−51.0535			−1.80614
$800$		0			0
$801$	0.0191053	−	0.0110304i	0.000675053	−	0.000389742i
$802$		0			0
$803$	−9.07702	−	5.24062i	−0.320321	−	0.184937i
$804$		0			0
$805$	−16.9711	−	53.5496i	−0.598154	−	1.88738i
$806$		0			0
$807$	40.2307	+	23.2272i	1.41619	+	0.817636i
$808$		0			0
$809$	42.7653	−	24.6905i	1.50355	−	0.868073i	0.503555	−	0.863963i	$-0.332025\pi$
$809$	42.7653	−	24.6905i	1.50355	−	0.868073i	0.999992	−	0.00411023i	$-0.00130833\pi$
$810$		0			0
$811$	−1.14547			−0.0402230			−0.0201115	−	0.999798i	$-0.506402\pi$
$811$	−1.14547			−0.0402230			−0.0201115	+	0.999798i	$0.506402\pi$
$812$		0			0
$813$		−	10.9896i		−	0.385423i
$814$		0			0
$815$	24.3785	+	42.2247i	0.853940	+	1.47907i
$816$		0			0
$817$	0.193524	+	0.111731i	0.00677055	+	0.00390898i
$818$		0			0
$819$	0.563160	+	0.514513i	0.0196784	+	0.0179786i
$820$		0			0
$821$	−13.1621	+	22.7974i	−0.459361	+	0.795636i	−0.998927	−	0.0463067i	$-0.985255\pi$
$821$	−13.1621	+	22.7974i	−0.459361	+	0.795636i	0.539566	+	0.841943i	$0.318588\pi$
$822$		0			0
$823$	−41.1597	+	23.7635i	−1.43474	+	0.828345i	−0.997477	−	0.0709909i	$-0.977384\pi$
$823$	−41.1597	+	23.7635i	−1.43474	+	0.828345i	−0.437259	+	0.899336i	$0.644051\pi$
$824$		0			0
$825$	−0.452485			−0.0157535
$826$		0			0
$827$			18.2082i			0.633160i	0.948566	+	0.316580i	$0.102535\pi$
$827$			18.2082i			0.633160i	−0.948566	+	0.316580i	$0.897465\pi$
$828$		0			0
$829$	13.4581	+	23.3101i	0.467419	+	0.809594i	0.999307	−	0.0372211i	$-0.0118506\pi$
$829$	13.4581	+	23.3101i	0.467419	+	0.809594i	−0.531888	+	0.846815i	$0.678517\pi$
$830$		0			0
$831$	14.9481	+	8.63027i	0.518543	+	0.299381i
$832$		0			0
$833$	−30.3474	+	2.74540i	−1.05147	+	0.0951226i
$834$		0			0
$835$	41.0787	+	23.7168i	1.42159	+	0.820754i
$836$		0			0
$837$	8.41974	−	4.86114i	0.291029	−	0.168026i
$838$		0			0
$839$		−	34.5300i		−	1.19211i	−0.802944	−	0.596054i	$-0.796734\pi$
$839$		−	34.5300i		−	1.19211i	0.802944	−	0.596054i	$-0.203266\pi$
$840$		0			0
$841$	17.0065			0.586431
$842$		0			0
$843$	6.02247	+	10.4312i	0.207425	+	0.359270i
$844$		0			0
$845$	−19.7693	+	34.2415i	−0.680085	+	1.17794i
$846$		0			0
$847$	−17.8032	+	19.4865i	−0.611726	+	0.669564i
$848$		0			0
$849$	7.32083	+	4.22668i	0.251250	+	0.145059i
$850$		0			0
$851$	9.82599	+	17.0191i	0.336831	+	0.583408i
$852$		0			0
$853$	−25.5341			−0.874271			−0.437136	−	0.899396i	$-0.644007\pi$
$853$	−25.5341			−0.874271			−0.437136	+	0.899396i	$0.644007\pi$
$854$		0			0
$855$		−	0.00328916i		−	0.000112487i
$856$		0			0
$857$	−27.9384	−	48.3907i	−0.954358	−	1.65300i	−0.735831	−	0.677166i	$-0.763208\pi$
$857$	−27.9384	−	48.3907i	−0.954358	−	1.65300i	−0.218527	−	0.975831i	$-0.570125\pi$
$858$		0			0
$859$	5.44029	−	9.42285i	0.185620	−	0.321504i	−0.758165	−	0.652063i	$-0.773904\pi$
$859$	5.44029	−	9.42285i	0.185620	−	0.321504i	0.943785	+	0.330559i	$0.107237\pi$
$860$		0			0
$861$	9.85199	+	27.3659i	0.335755	+	0.932626i
$862$		0			0
$863$	−1.39835	+	2.42201i	−0.0476003	+	0.0824462i	−0.888844	−	0.458210i	$-0.848491\pi$
$863$	−1.39835	+	2.42201i	−0.0476003	+	0.0824462i	0.841244	+	0.540656i	$0.181824\pi$
$864$		0			0
$865$	−19.5343	−	33.8344i	−0.664186	−	1.15040i
$866$		0			0
$867$		−	3.34612i		−	0.113640i
$868$		0			0
$869$	−13.4664			−0.456818
$870$		0			0
$871$	20.1801	+	34.9530i	0.683777	+	1.18434i
$872$		0			0
$873$	−0.421421	−	0.243307i	−0.0142629	−	0.00823470i
$874$		0			0
$875$	28.0879	+	6.18343i	0.949544	+	0.209038i
$876$		0			0
$877$	−7.76745	+	13.4536i	−0.262288	+	0.454296i	−0.966850	−	0.255347i	$-0.917810\pi$
$877$	−7.76745	+	13.4536i	−0.262288	+	0.454296i	0.704561	+	0.709643i	$0.251144\pi$
$878$		0			0
$879$	24.2876	+	42.0674i	0.819201	+	1.41890i
$880$		0			0
$881$	−5.58885			−0.188293			−0.0941465	−	0.995558i	$-0.530012\pi$
$881$	−5.58885			−0.188293			−0.0941465	+	0.995558i	$0.530012\pi$
$882$		0			0
$883$			13.5523i			0.456070i	0.973653	+	0.228035i	$0.0732300\pi$
$883$			13.5523i			0.456070i	−0.973653	+	0.228035i	$0.926770\pi$
$884$		0			0
$885$	−30.0668	+	17.3591i	−1.01068	+	0.583519i
$886$		0			0
$887$	−1.04877	−	0.605507i	−0.0352142	−	0.0203309i	0.482290	−	0.876012i	$-0.339805\pi$
$887$	−1.04877	−	0.605507i	−0.0352142	−	0.0203309i	−0.517504	+	0.855681i	$0.673139\pi$
$888$		0			0
$889$	−0.590833	−	0.130069i	−0.0198159	−	0.00436238i
$890$		0			0
$891$	7.74601	+	4.47216i	0.259501	+	0.149823i
$892$		0			0
$893$	−0.160395	−	0.277813i	−0.00536743	−	0.00929666i
$894$		0			0
$895$		−	22.0585i		−	0.737334i
$896$		0			0
$897$	−87.3963			−2.91808
$898$		0			0
$899$	5.56409	−	3.21243i	0.185573	−	0.107140i
$900$		0			0
$901$	4.99223	−	8.64680i	0.166315	−	0.288067i
$902$		0			0
$903$	−35.3763	+	11.2116i	−1.17725	+	0.373098i
$904$		0			0
$905$	21.8845	+	12.6350i	0.727466	+	0.420003i
$906$		0			0
$907$	−5.99985	−	10.3921i	−0.199222	−	0.345062i	0.749054	−	0.662508i	$-0.230508\pi$
$907$	−5.99985	−	10.3921i	−0.199222	−	0.345062i	−0.948276	+	0.317446i	$0.897175\pi$
$908$		0			0
$909$		−	0.0832907i		−	0.00276258i
$910$		0			0
$911$	13.5560			0.449130			0.224565	−	0.974459i	$-0.427904\pi$
$911$	13.5560			0.449130			0.224565	+	0.974459i	$0.427904\pi$
$912$		0			0
$913$	10.6709	−	6.16083i	0.353154	−	0.203894i
$914$		0			0
$915$	−50.1461	−	28.9519i	−1.65778	−	0.957120i
$916$		0			0
$917$	−21.6535	+	23.7008i	−0.715062	+	0.782671i
$918$		0			0
$919$	−26.2218	−	15.1392i	−0.864978	−	0.499395i	0.000698268	−	1.00000i	$-0.499778\pi$
$919$	−26.2218	−	15.1392i	−0.864978	−	0.499395i	−0.865676	+	0.500605i	$0.833111\pi$
$920$		0			0
$921$	−46.4415	+	26.8130i	−1.53030	+	0.883519i
$922$		0			0
$923$	45.2991			1.49104
$924$		0			0
$925$	0.552972			0.0181816
$926$		0			0
$927$	−0.459730	−	0.796276i	−0.0150995	−	0.0261531i
$928$		0			0
$929$	18.8118	+	10.8610i	0.617197	+	0.356339i	0.775777	−	0.631007i	$-0.217358\pi$
$929$	18.8118	+	10.8610i	0.617197	+	0.356339i	−0.158580	+	0.987346i	$0.550692\pi$
$930$		0			0
$931$	−0.110282	−	0.156513i	−0.00361435	−	0.00512952i
$932$		0			0
$933$	−18.5588	+	32.1448i	−0.607588	+	1.05237i
$934$		0			0
$935$	5.05095	+	8.74850i	0.165184	+	0.286106i
$936$		0			0
$937$		−	37.0546i		−	1.21052i	−0.796027	−	0.605261i	$-0.793069\pi$
$937$		−	37.0546i		−	1.21052i	0.796027	−	0.605261i	$-0.206931\pi$
$938$		0			0
$939$	40.2891			1.31478
$940$		0			0
$941$	−21.6032	−	37.4179i	−0.704245	−	1.21979i	−0.966963	−	0.254916i	$-0.917952\pi$
$941$	−21.6032	−	37.4179i	−0.704245	−	1.21979i	0.262718	−	0.964873i	$-0.415381\pi$
$942$		0			0
$943$	52.4405	+	27.6314i	1.70770	+	0.899804i
$944$		0			0
$945$	23.4778	+	21.4497i	0.763733	+	0.697760i
$946$		0			0
$947$	−17.9431	+	31.0783i	−0.583072	+	1.00991i	0.412041	+	0.911165i	$0.364816\pi$
$947$	−17.9431	+	31.0783i	−0.583072	+	1.00991i	−0.995113	+	0.0987443i	$0.968517\pi$
$948$		0			0
$949$	−49.3320	+	28.4819i	−1.60138	+	0.924560i
$950$		0			0
$951$	−16.8307			−0.545774
$952$		0			0
$953$	8.40033			0.272113			0.136057	−	0.990701i	$-0.456557\pi$
$953$	8.40033			0.272113			0.136057	+	0.990701i	$0.456557\pi$
$954$		0			0
$955$	−42.1054	+	24.3096i	−1.36250	+	0.786640i
$956$		0			0
$957$	5.20994	+	3.00796i	0.168413	+	0.0972335i
$958$		0			0
$959$	25.5856	−	8.10867i	0.826202	−	0.261843i
$960$		0			0
$961$	13.7791	−	23.8661i	0.444488	−	0.769875i
$962$		0			0
$963$	0.0493777	+	0.0855246i	0.00159117	+	0.00275599i
$964$		0			0
$965$			15.3460i			0.494007i
$966$		0			0
$967$		−	56.5090i		−	1.81721i	−0.417660	−	0.908603i	$-0.637150\pi$
$967$		−	56.5090i		−	1.81721i	0.417660	−	0.908603i	$-0.362850\pi$
$968$		0			0
$969$	0.177029	−	0.102208i	0.00568700	−	0.00328339i
$970$		0			0
$971$	−18.9521	−	10.9420i	−0.608202	−	0.351146i	0.164059	−	0.986450i	$-0.447541\pi$
$971$	−18.9521	−	10.9420i	−0.608202	−	0.351146i	−0.772262	+	0.635305i	$0.780875\pi$
$972$		0			0
$973$	53.3384	+	11.7422i	1.70995	+	0.376438i
$974$		0			0
$975$	−1.22959	+	2.12971i	−0.0393783	+	0.0682053i
$976$		0			0
$977$	−18.2467	+	10.5347i	−0.583764	+	0.337036i	−0.762628	−	0.646838i	$-0.776091\pi$
$977$	−18.2467	+	10.5347i	−0.583764	+	0.337036i	0.178864	+	0.983874i	$0.442758\pi$
$978$		0			0
$979$	−0.425734			−0.0136065
$980$		0			0
$981$			0.516310i			0.0164845i
$982$		0			0
$983$	−10.6247	−	18.4024i	−0.338874	−	0.586947i	0.645347	−	0.763889i	$-0.276713\pi$
$983$	−10.6247	−	18.4024i	−0.338874	−	0.586947i	−0.984221	+	0.176942i	$0.943379\pi$
$984$		0			0
$985$	−18.1889	+	31.5041i	−0.579547	+	1.00381i
$986$		0			0
$987$	52.0279	+	11.4537i	1.65607	+	0.364576i
$988$		0			0
$989$	−37.8149	+	65.4973i	−1.20244	+	2.08269i
$990$		0			0
$991$	39.9587	−	23.0702i	1.26933	−	0.732848i	0.294469	−	0.955661i	$-0.404857\pi$
$991$	39.9587	−	23.0702i	1.26933	−	0.732848i	0.974861	+	0.222813i	$0.0715241\pi$
$992$		0			0
$993$	−39.4444			−1.25173
$994$		0			0
$995$			39.2390i			1.24396i
$996$		0			0
$997$	−20.5535	+	11.8665i	−0.650935	+	0.375817i	−0.788814	−	0.614632i	$-0.789305\pi$
$997$	−20.5535	+	11.8665i	−0.650935	+	0.375817i	0.137880	+	0.990449i	$0.455971\pi$
$998$		0			0
$999$	−9.63467	−	5.56258i	−0.304827	−	0.175992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.20	yes	56
7.4	even	3	inner	1148.2.r.a.81.9	✓	56
41.40	even	2	inner	1148.2.r.a.737.9	yes	56
287.81	even	6	inner	1148.2.r.a.81.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.9	✓	56	7.4	even	3	inner
1148.2.r.a.81.20	yes	56	287.81	even	6	inner
1148.2.r.a.737.9	yes	56	41.40	even	2	inner
1148.2.r.a.737.20	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48683 - 0.858424i) q^{3} +(1.14679 - 1.98629i) q^{5} +(2.58388 + 0.568830i) q^{7} +(-0.0262152 + 0.0454060i) q^{9} +O(q^{10})\)	\(q+(1.48683 - 0.858424i) q^{3} +(1.14679 - 1.98629i) q^{5} +(2.58388 + 0.568830i) q^{7} +(-0.0262152 + 0.0454060i) q^{9} +(0.876249 - 0.505903i) q^{11} -5.49899i q^{13} -3.93772i q^{15} +(-3.76985 + 2.17652i) q^{17} +(-0.0236876 - 0.0136760i) q^{19} +(4.33010 - 1.37231i) q^{21} +(4.62858 - 8.01694i) q^{23} +(-0.130240 - 0.225582i) q^{25} +5.24056i q^{27} +3.46316i q^{29} +(-0.927599 - 1.60665i) q^{31} +(0.868559 - 1.50439i) q^{33} +(4.09302 - 4.48002i) q^{35} +(-1.06145 + 1.83848i) q^{37} +(-4.72047 - 8.17609i) q^{39} +(0.247452 + 6.39834i) q^{41} -8.16986 q^{43} +(0.0601264 + 0.104142i) q^{45} +(10.1569 + 5.86411i) q^{47} +(6.35287 + 2.93958i) q^{49} +(-3.73676 + 6.47226i) q^{51} +(-1.98638 + 1.14684i) q^{53} -2.32065i q^{55} -0.0469593 q^{57} +(-4.40841 - 7.63559i) q^{59} +(7.35245 - 12.7348i) q^{61} +(-0.0935651 + 0.102412i) q^{63} +(-10.9226 - 6.30617i) q^{65} +(-6.35625 + 3.66979i) q^{67} -15.8932i q^{69} +8.23771i q^{71} +(-5.17947 - 8.97111i) q^{73} +(-0.387291 - 0.223603i) q^{75} +(2.55190 - 0.808755i) q^{77} +(-11.5262 - 6.65466i) q^{79} +(4.41998 + 7.65563i) q^{81} +12.1779 q^{83} +9.98403i q^{85} +(2.97286 + 5.14915i) q^{87} +(-0.364394 - 0.210383i) q^{89} +(3.12799 - 14.2087i) q^{91} +(-2.75837 - 1.59255i) q^{93} +(-0.0543292 + 0.0313670i) q^{95} +9.28117i q^{97} +0.0530493i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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