LMFDB - Embedded newform 1148.2.r.a.81.8

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			81.8
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59496 - 0.920850i) q^{3} +(1.70544 + 2.95391i) q^{5} +(2.57642 - 0.601730i) q^{7} +(0.195929 + 0.339358i) q^{9} +O(q^{10})$	\(q+(-1.59496 - 0.920850i) q^{3} +(1.70544 + 2.95391i) q^{5} +(2.57642 - 0.601730i) q^{7} +(0.195929 + 0.339358i) q^{9} +(4.43105 + 2.55827i) q^{11} -4.75965i q^{13} -6.28183i q^{15} +(-1.32577 - 0.765436i) q^{17} +(0.164258 - 0.0948345i) q^{19} +(-4.66338 - 1.41276i) q^{21} +(0.638818 + 1.10647i) q^{23} +(-3.31707 + 5.74533i) q^{25} +4.80342i q^{27} -6.12593i q^{29} +(-3.46240 + 5.99706i) q^{31} +(-4.71156 - 8.16066i) q^{33} +(6.17139 + 6.58430i) q^{35} +(5.21486 + 9.03241i) q^{37} +(-4.38293 + 7.59145i) q^{39} +(5.72483 - 2.86817i) q^{41} -0.258062 q^{43} +(-0.668290 + 1.15751i) q^{45} +(2.76284 - 1.59513i) q^{47} +(6.27584 - 3.10061i) q^{49} +(1.40970 + 2.44168i) q^{51} +(5.49774 + 3.17412i) q^{53} +17.4519i q^{55} -0.349313 q^{57} +(5.59384 - 9.68881i) q^{59} +(-6.82916 - 11.8285i) q^{61} +(0.708996 + 0.756433i) q^{63} +(14.0596 - 8.11731i) q^{65} +(-1.11534 - 0.643944i) q^{67} -2.35302i q^{69} +2.74600i q^{71} +(1.22045 - 2.11388i) q^{73} +(10.5812 - 6.10904i) q^{75} +(12.9556 + 3.92487i) q^{77} +(-6.75063 + 3.89748i) q^{79} +(5.01101 - 8.67932i) q^{81} +2.45819 q^{83} -5.22163i q^{85} +(-5.64106 + 9.77061i) q^{87} +(0.445657 - 0.257300i) q^{89} +(-2.86402 - 12.2628i) q^{91} +(11.0448 - 6.37671i) q^{93} +(0.560266 + 0.323469i) q^{95} +13.9101i q^{97} +2.00495i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	−1.59496	−	0.920850i	−0.920850	−	0.531653i	−0.0369437	−	0.999317i	$-0.511762\pi$
$3$	−1.59496	−	0.920850i	−0.920850	−	0.531653i	−0.883906	+	0.467664i	$0.845096\pi$
$4$		0			0
$5$	1.70544	+	2.95391i	0.762697	+	1.32103i	0.941456	+	0.337137i	$0.109459\pi$
$5$	1.70544	+	2.95391i	0.762697	+	1.32103i	−0.178758	+	0.983893i	$0.557208\pi$
$6$		0			0
$7$	2.57642	−	0.601730i	0.973794	−	0.227432i
$7$	2.57642	−	0.601730i	0.973794	−	0.227432i
$8$		0			0
$9$	0.195929	+	0.339358i	0.0653096	+	0.113119i
$10$		0			0
$11$	4.43105	+	2.55827i	1.33601	+	0.771346i	0.986213	−	0.165479i	$-0.0529171\pi$
$11$	4.43105	+	2.55827i	1.33601	+	0.771346i	0.349798	+	0.936825i	$0.386250\pi$
$12$		0			0
$13$		−	4.75965i		−	1.32009i	−0.751226	−	0.660045i	$-0.770537\pi$
$13$		−	4.75965i		−	1.32009i	0.751226	−	0.660045i	$-0.229463\pi$
$14$		0			0
$15$		−	6.28183i		−	1.62196i
$16$		0			0
$17$	−1.32577	−	0.765436i	−0.321547	−	0.185645i	0.330535	−	0.943794i	$-0.392771\pi$
$17$	−1.32577	−	0.765436i	−0.321547	−	0.185645i	−0.652082	+	0.758148i	$0.726104\pi$
$18$		0			0
$19$	0.164258	−	0.0948345i	0.0376834	−	0.0217565i	−0.481040	−	0.876699i	$-0.659741\pi$
$19$	0.164258	−	0.0948345i	0.0376834	−	0.0217565i	0.518723	+	0.854942i	$0.326407\pi$
$20$		0			0
$21$	−4.66338	−	1.41276i	−1.01763	−	0.308289i
$22$		0			0
$23$	0.638818	+	1.10647i	0.133203	+	0.230714i	0.924909	−	0.380187i	$-0.124140\pi$
$23$	0.638818	+	1.10647i	0.133203	+	0.230714i	−0.791707	+	0.610901i	$0.790807\pi$
$24$		0			0
$25$	−3.31707	+	5.74533i	−0.663414	+	1.14907i
$26$		0			0
$27$			4.80342i			0.924418i
$28$		0			0
$29$		−	6.12593i		−	1.13756i	−0.822491	−	0.568778i	$-0.807416\pi$
$29$		−	6.12593i		−	1.13756i	0.822491	−	0.568778i	$-0.192584\pi$
$30$		0			0
$31$	−3.46240	+	5.99706i	−0.621866	+	1.07710i	0.367272	+	0.930114i	$0.380292\pi$
$31$	−3.46240	+	5.99706i	−0.621866	+	1.07710i	−0.989138	+	0.146990i	$0.953041\pi$
$32$		0			0
$33$	−4.71156	−	8.16066i	−0.820177	−	1.42059i
$34$		0			0
$35$	6.17139	+	6.58430i	1.04315	+	1.11295i
$36$		0			0
$37$	5.21486	+	9.03241i	0.857318	+	1.48492i	0.874478	+	0.485066i	$0.161204\pi$
$37$	5.21486	+	9.03241i	0.857318	+	1.48492i	−0.0171594	+	0.999853i	$0.505462\pi$
$38$		0			0
$39$	−4.38293	+	7.59145i	−0.701830	+	1.21560i
$40$		0			0
$41$	5.72483	−	2.86817i	0.894068	−	0.447932i
$41$	5.72483	−	2.86817i	0.894068	−	0.447932i
$42$		0			0
$43$	−0.258062			−0.0393541			−0.0196771	−	0.999806i	$-0.506264\pi$
$43$	−0.258062			−0.0393541			−0.0196771	+	0.999806i	$0.506264\pi$
$44$		0			0
$45$	−0.668290	+	1.15751i	−0.0996228	+	0.172552i
$46$		0			0
$47$	2.76284	−	1.59513i	0.403002	−	0.232674i	−0.284776	−	0.958594i	$-0.591919\pi$
$47$	2.76284	−	1.59513i	0.403002	−	0.232674i	0.687779	+	0.725920i	$0.258586\pi$
$48$		0			0
$49$	6.27584	−	3.10061i	0.896549	−	0.442945i
$50$		0			0
$51$	1.40970	+	2.44168i	0.197398	+	0.341903i
$52$		0			0
$53$	5.49774	+	3.17412i	0.755173	+	0.435999i	0.827560	−	0.561377i	$-0.189728\pi$
$53$	5.49774	+	3.17412i	0.755173	+	0.435999i	−0.0723869	+	0.997377i	$0.523062\pi$
$54$		0			0
$55$			17.4519i			2.35321i
$56$		0			0
$57$	−0.349313			−0.0462677
$58$		0			0
$59$	5.59384	−	9.68881i	0.728256	−	1.26138i	−0.229364	−	0.973341i	$-0.573665\pi$
$59$	5.59384	−	9.68881i	0.728256	−	1.26138i	0.957620	−	0.288035i	$-0.0930021\pi$
$60$		0			0
$61$	−6.82916	−	11.8285i	−0.874384	−	1.51448i	−0.857417	−	0.514622i	$-0.827932\pi$
$61$	−6.82916	−	11.8285i	−0.874384	−	1.51448i	−0.0169675	−	0.999856i	$-0.505401\pi$
$62$		0			0
$63$	0.708996	+	0.756433i	0.0893251	+	0.0953016i
$64$		0			0
$65$	14.0596	−	8.11731i	1.74388	−	1.00683i
$66$		0			0
$67$	−1.11534	−	0.643944i	−0.136261	−	0.0786702i	0.430320	−	0.902676i	$-0.358401\pi$
$67$	−1.11534	−	0.643944i	−0.136261	−	0.0786702i	−0.566581	+	0.824006i	$0.691734\pi$
$68$		0			0
$69$		−	2.35302i		−	0.283271i
$70$		0			0
$71$			2.74600i			0.325891i	0.986635	+	0.162945i	$0.0520994\pi$
$71$			2.74600i			0.325891i	−0.986635	+	0.162945i	$0.947901\pi$
$72$		0			0
$73$	1.22045	−	2.11388i	0.142843	−	0.247411i	−0.785723	−	0.618578i	$-0.787709\pi$
$73$	1.22045	−	2.11388i	0.142843	−	0.247411i	0.928566	+	0.371167i	$0.121042\pi$
$74$		0			0
$75$	10.5812	−	6.10904i	1.22181	−	0.705412i
$76$		0			0
$77$	12.9556	+	3.92487i	1.47643	+	0.447280i
$78$		0			0
$79$	−6.75063	+	3.89748i	−0.759505	+	0.438501i	−0.829118	−	0.559074i	$-0.811157\pi$
$79$	−6.75063	+	3.89748i	−0.759505	+	0.438501i	0.0696128	+	0.997574i	$0.477824\pi$
$80$		0			0
$81$	5.01101	−	8.67932i	0.556779	−	0.964369i
$82$		0			0
$83$	2.45819			0.269821			0.134911	−	0.990858i	$-0.456925\pi$
$83$	2.45819			0.269821			0.134911	+	0.990858i	$0.456925\pi$
$84$		0			0
$85$		−	5.22163i		−	0.566365i
$86$		0			0
$87$	−5.64106	+	9.77061i	−0.604785	+	1.04752i
$88$		0			0
$89$	0.445657	−	0.257300i	0.0472396	−	0.0272738i	−0.476194	−	0.879340i	$-0.657984\pi$
$89$	0.445657	−	0.257300i	0.0472396	−	0.0272738i	0.523434	+	0.852066i	$0.324651\pi$
$90$		0			0
$91$	−2.86402	−	12.2628i	−0.300231	−	1.28550i
$92$		0			0
$93$	11.0448	−	6.37671i	1.14529	−	0.661234i
$94$		0			0
$95$	0.560266	+	0.323469i	0.0574820	+	0.0331873i
$96$		0			0
$97$			13.9101i			1.41236i	0.708031	+	0.706181i	$0.249583\pi$
$97$			13.9101i			1.41236i	−0.708031	+	0.706181i	$0.750417\pi$
$98$		0			0
$99$			2.00495i			0.201505i
$100$		0			0
$101$	−8.12995	−	4.69383i	−0.808960	−	0.467053i	0.0376345	−	0.999292i	$-0.488018\pi$
$101$	−8.12995	−	4.69383i	−0.808960	−	0.467053i	−0.846595	+	0.532238i	$0.821351\pi$
$102$		0			0
$103$	7.62327	+	13.2039i	0.751143	+	1.30102i	0.947269	+	0.320440i	$0.103831\pi$
$103$	7.62327	+	13.2039i	0.751143	+	1.30102i	−0.196126	+	0.980579i	$0.562836\pi$
$104$		0			0
$105$	−3.77996	−	16.1846i	−0.368886	−	1.57946i
$106$		0			0
$107$	9.85744	+	17.0736i	0.952955	+	1.65057i	0.738980	+	0.673727i	$0.235308\pi$
$107$	9.85744	+	17.0736i	0.952955	+	1.65057i	0.213975	+	0.976839i	$0.431359\pi$
$108$		0			0
$109$	5.91868	+	3.41715i	0.566907	+	0.327304i	0.755913	−	0.654672i	$-0.227193\pi$
$109$	5.91868	+	3.41715i	0.566907	+	0.327304i	−0.189006	+	0.981976i	$0.560527\pi$
$110$		0			0
$111$		−	19.2084i		−	1.82318i
$112$		0			0
$113$	−4.53474			−0.426592			−0.213296	−	0.976988i	$-0.568420\pi$
$113$	−4.53474			−0.426592			−0.213296	+	0.976988i	$0.568420\pi$
$114$		0			0
$115$	−2.17894	+	3.77403i	−0.203187	+	0.351930i
$116$		0			0
$117$	1.61523	−	0.932553i	0.149328	−	0.0862145i
$118$		0			0
$119$	−3.87633	−	1.17432i	−0.355343	−	0.107650i
$120$		0			0
$121$	7.58945	+	13.1453i	0.689950	+	1.19503i
$122$		0			0
$123$	−11.7720	−	0.697099i	−1.06145	−	0.0628553i
$124$		0			0
$125$	−5.57385			−0.498541
$126$		0			0
$127$	21.1994			1.88114			0.940572	−	0.339595i	$-0.110290\pi$
$127$	21.1994			1.88114			0.940572	+	0.339595i	$0.110290\pi$
$128$		0			0
$129$	0.411599	+	0.237637i	0.0362393	+	0.0209227i
$130$		0			0
$131$	4.56477	+	7.90641i	0.398825	+	0.690786i	0.993581	−	0.113120i	$-0.0360846\pi$
$131$	4.56477	+	7.90641i	0.398825	+	0.690786i	−0.594756	+	0.803906i	$0.702751\pi$
$132$		0			0
$133$	0.366133	−	0.343172i	0.0317477	−	0.0297568i
$134$		0			0
$135$	−14.1889	+	8.19195i	−1.22118	+	0.705051i
$136$		0			0
$137$	−16.2179	−	9.36341i	−1.38559	−	0.799970i	−0.392775	−	0.919635i	$-0.628485\pi$
$137$	−16.2179	−	9.36341i	−1.38559	−	0.799970i	−0.992814	+	0.119664i	$0.961818\pi$
$138$		0			0
$139$	−13.3534			−1.13262			−0.566310	−	0.824192i	$-0.691630\pi$
$139$	−13.3534			−1.13262			−0.566310	+	0.824192i	$0.691630\pi$
$140$		0			0
$141$	−5.87550			−0.494806
$142$		0			0
$143$	12.1765	−	21.0902i	1.01825	−	1.76365i
$144$		0			0
$145$	18.0955	−	10.4474i	1.50275	−	0.867611i
$146$		0			0
$147$	−12.8649	−	0.833761i	−1.06108	−	0.0687675i
$148$		0			0
$149$	15.3202	−	8.84515i	1.25508	−	0.724623i	0.282969	−	0.959129i	$-0.408681\pi$
$149$	15.3202	−	8.84515i	1.25508	−	0.724623i	0.972115	+	0.234507i	$0.0753474\pi$
$150$		0			0
$151$	16.0218	+	9.25017i	1.30383	+	0.752769i	0.981059	−	0.193708i	$-0.0620513\pi$
$151$	16.0218	+	9.25017i	1.30383	+	0.752769i	0.322774	+	0.946476i	$0.395385\pi$
$152$		0			0
$153$		−	0.599883i		−	0.0484977i
$154$		0			0
$155$	−23.6197			−1.89718
$156$		0			0
$157$	−13.3609	−	7.71393i	−1.06632	−	0.615638i	−0.139144	−	0.990272i	$-0.544435\pi$
$157$	−13.3609	−	7.71393i	−1.06632	−	0.615638i	−0.927173	+	0.374634i	$0.877768\pi$
$158$		0			0
$159$	−5.84578	−	10.1252i	−0.463601	−	0.802980i
$160$		0			0
$161$	2.31166	+	2.46632i	0.182184	+	0.194373i
$162$		0			0
$163$	−3.08825	−	5.34900i	−0.241890	−	0.418966i	0.719363	−	0.694635i	$-0.244434\pi$
$163$	−3.08825	−	5.34900i	−0.241890	−	0.418966i	−0.961253	+	0.275669i	$0.911101\pi$
$164$		0			0
$165$	16.0706	−	27.8351i	1.25109	−	2.16696i
$166$		0			0
$167$			3.63626i			0.281382i	0.990054	+	0.140691i	$0.0449324\pi$
$167$			3.63626i			0.281382i	−0.990054	+	0.140691i	$0.955068\pi$
$168$		0			0
$169$	−9.65429			−0.742638
$170$		0			0
$171$	0.0643658	+	0.0371616i	0.00492217	+	0.00284182i
$172$		0			0
$173$	0.101342	+	0.175530i	0.00770489	+	0.0133453i	0.869852	−	0.493313i	$-0.164214\pi$
$173$	0.101342	+	0.175530i	0.00770489	+	0.0133453i	−0.862147	+	0.506658i	$0.830881\pi$
$174$		0			0
$175$	−5.08901	+	16.7983i	−0.384693	+	1.26984i
$176$		0			0
$177$	−17.8439	+	10.3022i	−1.34123	+	0.774359i
$178$		0			0
$179$	−7.35919	−	4.24883i	−0.550052	−	0.317572i	0.199091	−	0.979981i	$-0.436201\pi$
$179$	−7.35919	−	4.24883i	−0.550052	−	0.317572i	−0.749143	+	0.662409i	$0.769534\pi$
$180$		0			0
$181$		−	1.61837i		−	0.120293i	−0.998190	−	0.0601463i	$-0.980843\pi$
$181$		−	1.61837i		−	0.120293i	0.998190	−	0.0601463i	$-0.0191567\pi$
$182$		0			0
$183$			25.1545i			1.85948i
$184$		0			0
$185$	−17.7873	+	30.8085i	−1.30775	+	2.26509i
$186$		0			0
$187$	−3.91638	−	6.78336i	−0.286394	−	0.496049i
$188$		0			0
$189$	2.89036	+	12.3756i	0.210243	+	0.900192i
$190$		0			0
$191$	−9.36245	+	5.40541i	−0.677443	+	0.391122i	−0.798891	−	0.601476i	$-0.794580\pi$
$191$	−9.36245	+	5.40541i	−0.677443	+	0.391122i	0.121448	+	0.992598i	$0.461246\pi$
$192$		0			0
$193$	3.87819	+	2.23908i	0.279158	+	0.161172i	0.633042	−	0.774117i	$-0.281806\pi$
$193$	3.87819	+	2.23908i	0.279158	+	0.161172i	−0.353884	+	0.935289i	$0.615139\pi$
$194$		0			0
$195$	−29.8993			−2.14113
$196$		0			0
$197$	−7.60990			−0.542183			−0.271092	−	0.962554i	$-0.587385\pi$
$197$	−7.60990			−0.542183			−0.271092	+	0.962554i	$0.587385\pi$
$198$		0			0
$199$	−19.6687	−	11.3557i	−1.39428	−	0.804987i	−0.400494	−	0.916300i	$-0.631161\pi$
$199$	−19.6687	−	11.3557i	−1.39428	−	0.804987i	−0.993785	+	0.111312i	$0.964495\pi$
$200$		0			0
$201$	1.18595	+	2.05413i	0.0836505	+	0.144887i
$202$		0			0
$203$	−3.68615	−	15.7829i	−0.258717	−	1.10775i
$204$		0			0
$205$	18.2357	+	12.0191i	1.27363	+	0.839454i
$206$		0			0
$207$	−0.250326	+	0.433577i	−0.0173988	+	0.0301357i
$208$		0			0
$209$	0.970447			0.0671272
$210$		0			0
$211$		−	14.4213i		−	0.992801i	−0.868094	−	0.496401i	$-0.834655\pi$
$211$		−	14.4213i		−	0.992801i	0.868094	−	0.496401i	$-0.165345\pi$
$212$		0			0
$213$	2.52866	−	4.37976i	0.173261	−	0.300096i
$214$		0			0
$215$	−0.440111	−	0.762294i	−0.0300153	−	0.0519880i
$216$		0			0
$217$	−5.31199	+	17.5344i	−0.360601	+	1.19031i
$218$		0			0
$219$	−3.89313	+	2.24770i	−0.263073	+	0.151885i
$220$		0			0
$221$	−3.64321	+	6.31022i	−0.245069	+	0.424471i
$222$		0			0
$223$	−1.76047			−0.117890			−0.0589449	−	0.998261i	$-0.518774\pi$
$223$	−1.76047			−0.117890			−0.0589449	+	0.998261i	$0.518774\pi$
$224$		0			0
$225$	−2.59964			−0.173309
$226$		0			0
$227$	−11.4360	−	6.60259i	−0.759035	−	0.438229i	0.0699142	−	0.997553i	$-0.477727\pi$
$227$	−11.4360	−	6.60259i	−0.759035	−	0.438229i	−0.828949	+	0.559324i	$0.811061\pi$
$228$		0			0
$229$	−12.5476	+	7.24434i	−0.829167	+	0.478720i	−0.853567	−	0.520983i	$-0.825566\pi$
$229$	−12.5476	+	7.24434i	−0.829167	+	0.478720i	0.0244005	+	0.999702i	$0.492232\pi$
$230$		0			0
$231$	−17.0494	−	18.1902i	−1.12177	−	1.19683i
$232$		0			0
$233$	−13.5717	+	7.83564i	−0.889114	+	0.513330i	−0.873653	−	0.486550i	$-0.838255\pi$
$233$	−13.5717	+	7.83564i	−0.889114	+	0.513330i	−0.0154613	+	0.999880i	$0.504922\pi$
$234$		0			0
$235$	9.42375	+	5.44080i	0.614737	+	0.354919i
$236$		0			0
$237$	14.3560			0.932520
$238$		0			0
$239$			9.32274i			0.603038i	0.953460	+	0.301519i	$0.0974936\pi$
$239$			9.32274i			0.603038i	−0.953460	+	0.301519i	$0.902506\pi$
$240$		0			0
$241$	2.44115	−	4.22819i	0.157248	−	0.272362i	−0.776627	−	0.629961i	$-0.783071\pi$
$241$	2.44115	−	4.22819i	0.157248	−	0.272362i	0.933875	+	0.357599i	$0.116404\pi$
$242$		0			0
$243$	−3.50507	+	2.02365i	−0.224850	+	0.129817i
$244$		0			0
$245$	19.8620	+	13.2504i	1.26894	+	0.846536i
$246$		0			0
$247$	−0.451379	−	0.781812i	−0.0287206	−	0.0497455i
$248$		0			0
$249$	−3.92071	−	2.26362i	−0.248465	−	0.143451i
$250$		0			0
$251$	−20.3751			−1.28607			−0.643033	−	0.765838i	$-0.722324\pi$
$251$	−20.3751			−1.28607			−0.643033	+	0.765838i	$0.722324\pi$
$252$		0			0
$253$			6.53707i			0.410982i
$254$		0			0
$255$	−4.80833	+	8.32828i	−0.301110	+	0.521537i
$256$		0			0
$257$	−23.1652	+	13.3745i	−1.44501	+	0.834276i	−0.998178	−	0.0603432i	$-0.980780\pi$
$257$	−23.1652	+	13.3745i	−1.44501	+	0.834276i	−0.446830	+	0.894619i	$0.647447\pi$
$258$		0			0
$259$	18.8707	+	20.1333i	1.17257	+	1.25102i
$260$		0			0
$261$	2.07889	−	1.20025i	0.128680	−	0.0742933i
$262$		0			0
$263$	1.97787	+	1.14192i	0.121961	+	0.0704140i	0.559739	−	0.828669i	$-0.310901\pi$
$263$	1.97787	+	1.14192i	0.121961	+	0.0704140i	−0.437779	+	0.899083i	$0.644235\pi$
$264$		0			0
$265$			21.6531i			1.33014i
$266$		0			0
$267$	−0.947740			−0.0580008
$268$		0			0
$269$	5.06183	−	8.76735i	0.308626	−	0.534555i	−0.669436	−	0.742869i	$-0.733464\pi$
$269$	5.06183	−	8.76735i	0.308626	−	0.534555i	0.978062	+	0.208314i	$0.0667977\pi$
$270$		0			0
$271$	−7.35252	−	12.7349i	−0.446634	−	0.773592i	0.551531	−	0.834155i	$-0.314044\pi$
$271$	−7.35252	−	12.7349i	−0.446634	−	0.773592i	−0.998164	+	0.0605623i	$0.980711\pi$
$272$		0			0
$273$	−6.72424	+	22.1961i	−0.406970	+	1.34337i
$274$		0			0
$275$	−29.3962	+	16.9719i	−1.77266	+	1.02344i
$276$		0			0
$277$	−9.66945	+	16.7480i	−0.580981	+	1.00629i	0.414382	+	0.910103i	$0.363998\pi$
$277$	−9.66945	+	16.7480i	−0.580981	+	1.00629i	−0.995363	+	0.0961860i	$0.969336\pi$
$278$		0			0
$279$	−2.71354			−0.162455
$280$		0			0
$281$		−	27.1645i		−	1.62050i	−0.586084	−	0.810250i	$-0.699331\pi$
$281$		−	27.1645i		−	1.62050i	0.586084	−	0.810250i	$-0.300669\pi$
$282$		0			0
$283$	10.1735	−	17.6211i	0.604754	−	1.04746i	−0.387336	−	0.921939i	$-0.626605\pi$
$283$	10.1735	−	17.6211i	0.604754	−	1.04746i	0.992090	−	0.125526i	$-0.0400620\pi$
$284$		0			0
$285$	−0.595734	−	1.03184i	−0.0352882	−	0.0611210i
$286$		0			0
$287$	13.0237	−	10.8344i	0.768763	−	0.639534i
$288$		0			0
$289$	−7.32822	−	12.6928i	−0.431072	−	0.746638i
$290$		0			0
$291$	12.8092	−	22.1861i	0.750886	−	1.30057i
$292$		0			0
$293$		−	30.9381i		−	1.80742i	−0.428141	−	0.903712i	$-0.640831\pi$
$293$		−	30.9381i		−	1.80742i	0.428141	−	0.903712i	$-0.359169\pi$
$294$		0			0
$295$	38.1599			2.22175
$296$		0			0
$297$	−12.2884	+	21.2842i	−0.713046	+	1.23503i
$298$		0			0
$299$	5.26639	−	3.04055i	0.304563	−	0.175840i
$300$		0			0
$301$	−0.664876	+	0.155284i	−0.0383228	+	0.00895041i
$302$		0			0
$303$	8.64462	+	14.9729i	0.496620	+	0.860172i
$304$		0			0
$305$	23.2935	−	40.3455i	1.33378	−	2.31018i
$306$		0			0
$307$	−28.7412			−1.64035			−0.820173	−	0.572115i	$-0.806123\pi$
$307$	−28.7412			−1.64035			−0.820173	+	0.572115i	$0.806123\pi$
$308$		0			0
$309$		−	28.0796i		−	1.59739i
$310$		0			0
$311$	10.0657	+	5.81145i	0.570775	+	0.329537i	0.757459	−	0.652883i	$-0.226441\pi$
$311$	10.0657	+	5.81145i	0.570775	+	0.329537i	−0.186684	+	0.982420i	$0.559774\pi$
$312$		0			0
$313$	−3.01385	+	1.74004i	−0.170353	+	0.0983531i	−0.582752	−	0.812650i	$-0.698024\pi$
$313$	−3.01385	+	1.74004i	−0.170353	+	0.0983531i	0.412399	+	0.911003i	$0.364691\pi$
$314$		0			0
$315$	−1.02528	+	3.38437i	−0.0577682	+	0.190687i
$316$		0			0
$317$	3.48485	−	2.01198i	0.195729	−	0.113004i	−0.398933	−	0.916980i	$-0.630619\pi$
$317$	3.48485	−	2.01198i	0.195729	−	0.113004i	0.594662	+	0.803976i	$0.297286\pi$
$318$		0			0
$319$	15.6718	−	27.1443i	0.877450	−	1.51979i
$320$		0			0
$321$		−	36.3089i		−	2.02656i
$322$		0			0
$323$	−0.290359			−0.0161560
$324$		0			0
$325$	27.3458	+	15.7881i	1.51687	+	0.875766i
$326$		0			0
$327$	−6.29337	−	10.9004i	−0.348024	−	0.602795i
$328$		0			0
$329$	6.15840	−	5.77220i	0.339524	−	0.318232i
$330$		0			0
$331$	6.03234	−	3.48277i	0.331567	−	0.191430i	−0.324969	−	0.945725i	$-0.605354\pi$
$331$	6.03234	−	3.48277i	0.331567	−	0.191430i	0.656537	+	0.754294i	$0.272021\pi$
$332$		0			0
$333$	−2.04348	+	3.53942i	−0.111982	+	0.193959i
$334$		0			0
$335$		−	4.39284i		−	0.240006i
$336$		0			0
$337$	10.7543			0.585826			0.292913	−	0.956139i	$-0.405375\pi$
$337$	10.7543			0.585826			0.292913	+	0.956139i	$0.405375\pi$
$338$		0			0
$339$	7.23272	+	4.17581i	0.392827	+	0.226799i
$340$		0			0
$341$	−30.6842	+	17.7155i	−1.66164	+	0.959348i
$342$		0			0
$343$	14.3035	−	11.7648i	0.772314	−	0.635241i
$344$		0			0
$345$	6.95062	−	4.01295i	0.374209	−	0.216050i
$346$		0			0
$347$	8.59574	+	4.96275i	0.461443	+	0.266414i	0.712651	−	0.701519i	$-0.247494\pi$
$347$	8.59574	+	4.96275i	0.461443	+	0.266414i	−0.251208	+	0.967933i	$0.580828\pi$
$348$		0			0
$349$	−30.3844			−1.62644			−0.813221	−	0.581955i	$-0.802288\pi$
$349$	−30.3844			−1.62644			−0.813221	+	0.581955i	$0.802288\pi$
$350$		0			0
$351$	22.8626			1.22031
$352$		0			0
$353$	14.7103	−	25.4790i	0.782952	−	1.35611i	−0.147263	−	0.989097i	$-0.547046\pi$
$353$	14.7103	−	25.4790i	0.782952	−	1.35611i	0.930215	−	0.367015i	$-0.119620\pi$
$354$		0			0
$355$	−8.11145	+	4.68315i	−0.430511	+	0.248556i
$356$		0			0
$357$	5.10121	+	5.44252i	0.269985	+	0.288049i
$358$		0			0
$359$	−6.06991	−	10.5134i	−0.320358	−	0.554876i	0.660204	−	0.751086i	$-0.270470\pi$
$359$	−6.06991	−	10.5134i	−0.320358	−	0.554876i	−0.980562	+	0.196210i	$0.937136\pi$
$360$		0			0
$361$	−9.48201	+	16.4233i	−0.499053	+	0.864386i
$362$		0			0
$363$		−	27.9550i		−	1.46726i
$364$		0			0
$365$	8.32562			0.435783
$366$		0			0
$367$	−7.19812	+	12.4675i	−0.375739	+	0.650799i	−0.990437	−	0.137963i	$-0.955944\pi$
$367$	−7.19812	+	12.4675i	−0.375739	+	0.650799i	0.614698	+	0.788762i	$0.289278\pi$
$368$		0			0
$369$	2.09499	+	1.38081i	0.109061	+	0.0718822i
$370$		0			0
$371$	16.0744	+	4.86971i	0.834543	+	0.252823i
$372$		0			0
$373$	−10.1621	−	17.6013i	−0.526173	−	0.911359i	−0.999535	−	0.0304908i	$-0.990293\pi$
$373$	−10.1621	−	17.6013i	−0.526173	−	0.911359i	0.473362	−	0.880868i	$-0.343040\pi$
$374$		0			0
$375$	8.89006	+	5.13268i	0.459081	+	0.265051i
$376$		0			0
$377$	−29.1573			−1.50168
$378$		0			0
$379$	−22.6087			−1.16133			−0.580667	−	0.814141i	$-0.697208\pi$
$379$	−22.6087			−1.16133			−0.580667	+	0.814141i	$0.697208\pi$
$380$		0			0
$381$	−33.8122	−	19.5215i	−1.73225	−	1.00012i
$382$		0			0
$383$	−20.4563	+	11.8105i	−1.04527	+	0.603487i	−0.921321	−	0.388802i	$-0.872889\pi$
$383$	−20.4563	+	11.8105i	−1.04527	+	0.603487i	−0.123948	+	0.992289i	$0.539556\pi$
$384$		0			0
$385$	10.5013	+	44.9634i	0.535197	+	2.29155i
$386$		0			0
$387$	−0.0505618	−	0.0875757i	−0.00257020	−	0.00445172i
$388$		0			0
$389$	14.7319	−	25.5164i	0.746937	−	1.29373i	−0.202347	−	0.979314i	$-0.564857\pi$
$389$	14.7319	−	25.5164i	0.746937	−	1.29373i	0.949284	−	0.314420i	$-0.101810\pi$
$390$		0			0
$391$		−	1.95590i		−	0.0989140i
$392$		0			0
$393$		−	16.8139i		−	0.848147i
$394$		0			0
$395$	−23.0256	−	13.2939i	−1.15854	−	0.668886i
$396$		0			0
$397$	12.3328	−	7.12036i	0.618967	−	0.357360i	−0.157500	−	0.987519i	$-0.550343\pi$
$397$	12.3328	−	7.12036i	0.618967	−	0.357360i	0.776467	+	0.630158i	$0.217010\pi$
$398$		0			0
$399$	−0.899976	+	0.210192i	−0.0450552	+	0.0105228i
$400$		0			0
$401$	14.0558	+	24.3454i	0.701914	+	1.21575i	0.967794	+	0.251745i	$0.0810044\pi$
$401$	14.0558	+	24.3454i	0.701914	+	1.21575i	−0.265879	+	0.964006i	$0.585662\pi$
$402$		0			0
$403$	28.5439	+	16.4798i	1.42187	+	0.820919i
$404$		0			0
$405$	34.1840			1.69861
$406$		0			0
$407$			53.3640i			2.64516i
$408$		0			0
$409$	−12.5848	+	21.7975i	−0.622279	+	1.07782i	0.366782	+	0.930307i	$0.380460\pi$
$409$	−12.5848	+	21.7975i	−0.622279	+	1.07782i	−0.989060	+	0.147511i	$0.952874\pi$
$410$		0			0
$411$	17.2446	+	29.8685i	0.850613	+	1.47331i
$412$		0			0
$413$	8.58201	−	28.3284i	0.422293	−	1.39395i
$414$		0			0
$415$	4.19230	+	7.26128i	0.205792	+	0.356442i
$416$		0			0
$417$	21.2981	+	12.2965i	1.04297	+	0.602161i
$418$		0			0
$419$	11.1264			0.543560			0.271780	−	0.962359i	$-0.412388\pi$
$419$	11.1264			0.543560			0.271780	+	0.962359i	$0.412388\pi$
$420$		0			0
$421$			1.95239i			0.0951537i	0.998868	+	0.0475769i	$0.0151499\pi$
$421$			1.95239i			0.0951537i	−0.998868	+	0.0475769i	$0.984850\pi$
$422$		0			0
$423$	1.08264	+	0.625063i	0.0526398	+	0.0303916i
$424$		0			0
$425$	8.79536	−	5.07801i	0.426638	−	0.246319i
$426$		0			0
$427$	−24.7123	−	26.3657i	−1.19591	−	1.27593i
$428$		0			0
$429$	−38.8419	+	22.4254i	−1.87530	+	1.08271i
$430$		0			0
$431$	0.546539	−	0.946633i	0.0263258	−	0.0455977i	−0.852562	−	0.522626i	$-0.824953\pi$
$431$	0.546539	−	0.946633i	0.0263258	−	0.0455977i	0.878888	+	0.477028i	$0.158286\pi$
$432$		0			0
$433$	−29.4234			−1.41400			−0.707000	−	0.707213i	$-0.749952\pi$
$433$	−29.4234			−1.41400			−0.707000	+	0.707213i	$0.749952\pi$
$434$		0			0
$435$	−38.4820			−1.84507
$436$		0			0
$437$	0.209862	+	0.121164i	0.0100391	+	0.00579606i
$438$		0			0
$439$	21.3205	−	12.3094i	1.01757	−	0.587496i	0.104174	−	0.994559i	$-0.466780\pi$
$439$	21.3205	−	12.3094i	1.01757	−	0.587496i	0.913400	+	0.407063i	$0.133447\pi$
$440$		0			0
$441$	2.28184	+	1.52226i	0.108659	+	0.0724887i
$442$		0			0
$443$	0.0496196	+	0.0859436i	0.00235750	+	0.00408330i	0.867202	−	0.497957i	$-0.165916\pi$
$443$	0.0496196	+	0.0859436i	0.00235750	+	0.00408330i	−0.864844	+	0.502040i	$0.832583\pi$
$444$		0			0
$445$	1.52009	+	0.877622i	0.0720590	+	0.0416033i
$446$		0			0
$447$	−32.5802			−1.54099
$448$		0			0
$449$	25.6492			1.21046			0.605229	−	0.796051i	$-0.293081\pi$
$449$	25.6492			1.21046			0.605229	+	0.796051i	$0.293081\pi$
$450$		0			0
$451$	32.7045	+	1.93665i	1.53999	+	0.0911933i
$452$		0			0
$453$	−17.0360	−	29.5073i	−0.800423	−	1.38637i
$454$		0			0
$455$	31.3390	−	29.3737i	1.46919	−	1.37706i
$456$		0			0
$457$	7.72041	−	4.45738i	0.361145	−	0.208507i	−0.308438	−	0.951245i	$-0.599806\pi$
$457$	7.72041	−	4.45738i	0.361145	−	0.208507i	0.669583	+	0.742737i	$0.266473\pi$
$458$		0			0
$459$	3.67671	−	6.36824i	0.171614	−	0.297244i
$460$		0			0
$461$	−0.610615			−0.0284392			−0.0142196	−	0.999899i	$-0.504526\pi$
$461$	−0.610615			−0.0284392			−0.0142196	+	0.999899i	$0.504526\pi$
$462$		0			0
$463$			24.3452i			1.13142i	0.824606	+	0.565708i	$0.191397\pi$
$463$			24.3452i			1.13142i	−0.824606	+	0.565708i	$0.808603\pi$
$464$		0			0
$465$	37.6725	+	21.7502i	1.74702	+	1.00864i
$466$		0			0
$467$	−0.658834	−	1.14113i	−0.0304872	−	0.0528053i	0.850379	−	0.526170i	$-0.176373\pi$
$467$	−0.658834	−	1.14113i	−0.0304872	−	0.0528053i	−0.880866	+	0.473365i	$0.843039\pi$
$468$		0			0
$469$	−3.26107	−	0.987932i	−0.150582	−	0.0456185i
$470$		0			0
$471$	14.2067	+	24.6068i	0.654612	+	1.13382i
$472$		0			0
$473$	−1.14349	−	0.660192i	−0.0525776	−	0.0303557i
$474$		0			0
$475$			1.25829i			0.0577343i
$476$		0			0
$477$			2.48761i			0.113900i
$478$		0			0
$479$	10.5766	+	6.10641i	0.483258	+	0.279009i	0.721773	−	0.692130i	$-0.243327\pi$
$479$	10.5766	+	6.10641i	0.483258	+	0.279009i	−0.238515	+	0.971139i	$0.576661\pi$
$480$		0			0
$481$	42.9911	−	24.8209i	1.96023	−	1.13174i
$482$		0			0
$483$	−1.41588	−	6.06237i	−0.0644249	−	0.275847i
$484$		0			0
$485$	−41.0894	+	23.7230i	−1.86577	+	1.07720i
$486$		0			0
$487$	9.07553	−	15.7193i	0.411252	−	0.712309i	−0.583775	−	0.811915i	$-0.698425\pi$
$487$	9.07553	−	15.7193i	0.411252	−	0.712309i	0.995027	+	0.0996066i	$0.0317584\pi$
$488$		0			0
$489$			11.3752i			0.514406i
$490$		0			0
$491$	−15.0993			−0.681423			−0.340711	−	0.940168i	$-0.610668\pi$
$491$	−15.0993			−0.681423			−0.340711	+	0.940168i	$0.610668\pi$
$492$		0			0
$493$	−4.68901	+	8.12160i	−0.211182	+	0.365778i
$494$		0			0
$495$	−5.92245	+	3.41933i	−0.266194	+	0.153687i
$496$		0			0
$497$	1.65235	+	7.07485i	0.0741181	+	0.317350i
$498$		0			0
$499$	−0.740745	+	0.427669i	−0.0331603	+	0.0191451i	−0.516489	−	0.856294i	$-0.672761\pi$
$499$	−0.740745	+	0.427669i	−0.0331603	+	0.0191451i	0.483328	+	0.875439i	$0.339428\pi$
$500$		0			0
$501$	3.34844	−	5.79968i	0.149597	−	0.259110i
$502$		0			0
$503$			5.99714i			0.267399i	0.991022	+	0.133700i	$0.0426857\pi$
$503$			5.99714i			0.267399i	−0.991022	+	0.133700i	$0.957314\pi$
$504$		0			0
$505$		−	32.0202i		−	1.42488i
$506$		0			0
$507$	15.3982	+	8.89015i	0.683858	+	0.394826i
$508$		0			0
$509$	−31.6136	+	18.2521i	−1.40125	+	0.809011i	−0.994521	−	0.104538i	$-0.966664\pi$
$509$	−31.6136	+	18.2521i	−1.40125	+	0.809011i	−0.406728	+	0.913549i	$0.633330\pi$
$510$		0			0
$511$	1.87240	−	6.18061i	0.0828301	−	0.273414i
$512$		0			0
$513$	0.455529	+	0.789000i	0.0201121	+	0.0348352i
$514$		0			0
$515$	−26.0021	+	45.0370i	−1.14579	+	1.98457i
$516$		0			0
$517$	16.3231			0.717887
$518$		0			0
$519$		−	0.373283i		−	0.0163853i
$520$		0			0
$521$	2.51297	+	1.45086i	0.110095	+	0.0635634i	0.554036	−	0.832492i	$-0.313087\pi$
$521$	2.51297	+	1.45086i	0.110095	+	0.0635634i	−0.443941	+	0.896056i	$0.646420\pi$
$522$		0			0
$523$	8.39878	+	14.5471i	0.367253	+	0.636101i	0.989135	−	0.147010i	$-0.0469650\pi$
$523$	8.39878	+	14.5471i	0.367253	+	0.636101i	−0.621882	+	0.783111i	$0.713632\pi$
$524$		0			0
$525$	23.5855	−	22.1064i	1.02936	−	0.964804i
$526$		0			0
$527$	9.18073	−	5.30050i	0.399919	−	0.230893i
$528$		0			0
$529$	10.6838	−	18.5049i	0.464514	−	0.804562i
$530$		0			0
$531$	4.38398			0.190248
$532$		0			0
$533$	−13.6515	−	27.2482i	−0.591311	−	1.18025i
$534$		0			0
$535$	−33.6226	+	58.2361i	−1.45363	+	2.51776i
$536$		0			0
$537$	7.82507	+	13.5534i	0.337677	+	0.584873i
$538$		0			0
$539$	35.7407	+	2.31632i	1.53946	+	0.0997710i
$540$		0			0
$541$	−2.11917	−	3.67050i	−0.0911101	−	0.157807i	0.816868	−	0.576824i	$-0.195708\pi$
$541$	−2.11917	−	3.67050i	−0.0911101	−	0.157807i	−0.907979	+	0.419017i	$0.862375\pi$
$542$		0			0
$543$	−1.49028	+	2.58124i	−0.0639539	+	0.110771i
$544$		0			0
$545$			23.3110i			0.998535i
$546$		0			0
$547$			35.9406i			1.53671i	0.640025	+	0.768354i	$0.278924\pi$
$547$			35.9406i			1.53671i	−0.640025	+	0.768354i	$0.721076\pi$
$548$		0			0
$549$	2.67606	−	4.63507i	0.114211	−	0.197820i
$550$		0			0
$551$	−0.580949	−	1.00623i	−0.0247493	−	0.0428670i
$552$		0			0
$553$	−15.0472	+	14.1036i	−0.639872	+	0.599745i
$554$		0			0
$555$	56.7400	−	32.7589i	2.40848	−	1.39054i
$556$		0			0
$557$	−29.6477	−	17.1171i	−1.25621	−	0.725276i	−0.283878	−	0.958860i	$-0.591621\pi$
$557$	−29.6477	−	17.1171i	−1.25621	−	0.725276i	−0.972336	+	0.233585i	$0.924954\pi$
$558$		0			0
$559$			1.22829i			0.0519510i
$560$		0			0
$561$			14.4256i			0.609048i
$562$		0			0
$563$	−32.4007	−	18.7066i	−1.36553	−	0.788387i	−0.375174	−	0.926955i	$-0.622417\pi$
$563$	−32.4007	−	18.7066i	−1.36553	−	0.788387i	−0.990353	+	0.138567i	$0.955750\pi$
$564$		0			0
$565$	−7.73373	−	13.3952i	−0.325361	−	0.563541i
$566$		0			0
$567$	7.68784	−	25.3768i	0.322859	−	1.06573i
$568$		0			0
$569$	−6.03775	−	10.4577i	−0.253116	−	0.438409i	0.711266	−	0.702923i	$-0.248122\pi$
$569$	−6.03775	−	10.4577i	−0.253116	−	0.438409i	−0.964382	+	0.264514i	$0.914789\pi$
$570$		0			0
$571$	−23.9092	−	13.8040i	−1.00057	−	0.577678i	−0.0921515	−	0.995745i	$-0.529374\pi$
$571$	−23.9092	−	13.8040i	−1.00057	−	0.577678i	−0.908416	+	0.418067i	$0.862708\pi$
$572$		0			0
$573$	19.9103			0.831765
$574$		0			0
$575$	−8.47602			−0.353474
$576$		0			0
$577$	29.2413	+	16.8825i	1.21733	+	0.702827i	0.964347	−	0.264643i	$-0.0852540\pi$
$577$	29.2413	+	16.8825i	1.21733	+	0.702827i	0.252986	+	0.967470i	$0.418587\pi$
$578$		0			0
$579$	−4.12371	−	7.14247i	−0.171375	−	0.296831i
$580$		0			0
$581$	6.33332	−	1.47917i	0.262750	−	0.0613661i
$582$		0			0
$583$	16.2405	+	28.1294i	0.672613	+	1.16500i
$584$		0			0
$585$	5.50936	+	3.18083i	0.227784	+	0.131511i
$586$		0			0
$587$		−	5.82279i		−	0.240332i	−0.992754	−	0.120166i	$-0.961657\pi$
$587$		−	5.82279i		−	0.240332i	0.992754	−	0.120166i	$-0.0383427\pi$
$588$		0			0
$589$			1.31342i			0.0541186i
$590$		0			0
$591$	12.1375	+	7.00758i	0.499269	+	0.288253i
$592$		0			0
$593$	22.3909	−	12.9274i	0.919485	−	0.530865i	0.0360146	−	0.999351i	$-0.488534\pi$
$593$	22.3909	−	12.9274i	0.919485	−	0.530865i	0.883471	+	0.468486i	$0.155200\pi$
$594$		0			0
$595$	−3.14201	−	13.4531i	−0.128810	−	0.551523i
$596$		0			0
$597$	20.9139	+	36.2239i	0.855948	+	1.48254i
$598$		0			0
$599$	6.49872	−	11.2561i	0.265530	−	0.459912i	−0.702172	−	0.712007i	$-0.747786\pi$
$599$	6.49872	−	11.2561i	0.265530	−	0.459912i	0.967702	+	0.252095i	$0.0811196\pi$
$600$		0			0
$601$			14.1758i			0.578242i	0.957293	+	0.289121i	$0.0933631\pi$
$601$			14.1758i			0.578242i	−0.957293	+	0.289121i	$0.906637\pi$
$602$		0			0
$603$		−	0.504668i		−	0.0205517i
$604$		0			0
$605$	−25.8867	+	44.8371i	−1.05245	+	1.82289i
$606$		0			0
$607$	−6.89131	−	11.9361i	−0.279710	−	0.484472i	0.691603	−	0.722278i	$-0.256905\pi$
$607$	−6.89131	−	11.9361i	−0.279710	−	0.484472i	−0.971313	+	0.237807i	$0.923572\pi$
$608$		0			0
$609$	−8.65446	+	28.5675i	−0.350697	+	1.15762i
$610$		0			0
$611$	−7.59226	−	13.1502i	−0.307150	−	0.531999i
$612$		0			0
$613$	5.61166	−	9.71967i	0.226653	−	0.392574i	−0.730161	−	0.683275i	$-0.760555\pi$
$613$	5.61166	−	9.71967i	0.226653	−	0.392574i	0.956814	+	0.290701i	$0.0938885\pi$
$614$		0			0
$615$	−18.0173	−	35.9624i	−0.726528	−	1.45014i
$616$		0			0
$617$	−41.6837			−1.67812			−0.839061	−	0.544037i	$-0.816895\pi$
$617$	−41.6837			−1.67812			−0.839061	+	0.544037i	$0.816895\pi$
$618$		0			0
$619$	−11.3423	+	19.6454i	−0.455884	+	0.789614i	−0.998739	−	0.0502126i	$-0.984010\pi$
$619$	−11.3423	+	19.6454i	−0.455884	+	0.789614i	0.542855	+	0.839827i	$0.317343\pi$
$620$		0			0
$621$	−5.31481	+	3.06851i	−0.213276	+	0.123135i
$622$		0			0
$623$	0.993374	−	0.931078i	0.0397987	−	0.0373029i
$624$		0			0
$625$	7.07946	+	12.2620i	0.283178	+	0.490479i
$626$		0			0
$627$	−1.54782	−	0.893636i	−0.0618141	−	0.0356884i
$628$		0			0
$629$		−	15.9666i		−	0.636629i
$630$		0			0
$631$	−39.8577			−1.58671			−0.793355	−	0.608760i	$-0.791667\pi$
$631$	−39.8577			−1.58671			−0.793355	+	0.608760i	$0.791667\pi$
$632$		0			0
$633$	−13.2798	+	23.0013i	−0.527826	+	0.914221i
$634$		0			0
$635$	36.1544	+	62.6212i	1.43474	+	2.48505i
$636$		0			0
$637$	−14.7578	−	29.8708i	−0.584727	−	1.18353i
$638$		0			0
$639$	−0.931879	+	0.538021i	−0.0368646	+	0.0212838i
$640$		0			0
$641$	−26.2953	−	15.1816i	−1.03860	−	0.599637i	−0.119164	−	0.992875i	$-0.538022\pi$
$641$	−26.2953	−	15.1816i	−1.03860	−	0.599637i	−0.919437	+	0.393238i	$0.871355\pi$
$642$		0			0
$643$		−	10.9876i		−	0.433311i	−0.976248	−	0.216655i	$-0.930485\pi$
$643$		−	10.9876i		−	0.433311i	0.976248	−	0.216655i	$-0.0695148\pi$
$644$		0			0
$645$			1.62110i			0.0638309i
$646$		0			0
$647$	3.76865	−	6.52750i	0.148161	−	0.256623i	−0.782387	−	0.622793i	$-0.785998\pi$
$647$	3.76865	−	6.52750i	0.148161	−	0.256623i	0.930548	+	0.366170i	$0.119331\pi$
$648$		0			0
$649$	49.5731	−	28.6211i	1.94592	−	1.12347i
$650$		0			0
$651$	24.6189	−	23.0750i	0.964891	−	0.904382i
$652$		0			0
$653$	8.60476	−	4.96796i	0.336730	−	0.194411i	−0.322095	−	0.946707i	$-0.604387\pi$
$653$	8.60476	−	4.96796i	0.336730	−	0.194411i	0.658825	+	0.752296i	$0.271054\pi$
$654$		0			0
$655$	−15.5699	+	26.9678i	−0.608366	+	1.05372i
$656$		0			0
$657$	0.956484			0.0373160
$658$		0			0
$659$		−	17.8545i		−	0.695512i	−0.937585	−	0.347756i	$-0.886944\pi$
$659$		−	17.8545i		−	0.695512i	0.937585	−	0.347756i	$-0.113056\pi$
$660$		0			0
$661$	3.51574	−	6.08944i	0.136746	−	0.236852i	−0.789517	−	0.613729i	$-0.789669\pi$
$661$	3.51574	−	6.08944i	0.136746	−	0.236852i	0.926263	+	0.376877i	$0.123002\pi$
$662$		0			0
$663$	11.6215	−	6.70970i	0.451343	−	0.260583i
$664$		0			0
$665$	1.63812	+	0.496264i	0.0635235	+	0.0192443i
$666$		0			0
$667$	6.77813	−	3.91336i	0.262450	−	0.151526i
$668$		0			0
$669$	2.80788	+	1.62113i	0.108559	+	0.0626765i
$670$		0			0
$671$		−	69.8832i		−	2.69781i
$672$		0			0
$673$			32.4238i			1.24984i	0.780687	+	0.624922i	$0.214869\pi$
$673$			32.4238i			1.24984i	−0.780687	+	0.624922i	$0.785131\pi$
$674$		0			0
$675$	−27.5972	−	15.9333i	−1.06222	−	0.613271i
$676$		0			0
$677$	2.42214	+	4.19527i	0.0930904	+	0.161237i	0.908810	−	0.417210i	$-0.136992\pi$
$677$	2.42214	+	4.19527i	0.0930904	+	0.161237i	−0.815720	+	0.578447i	$0.803659\pi$
$678$		0			0
$679$	8.37015	+	35.8383i	0.321217	+	1.37535i
$680$		0			0
$681$	12.1600	+	21.0617i	0.465971	+	0.807086i
$682$		0			0
$683$	4.48589	+	2.58993i	0.171648	+	0.0991009i	0.583363	−	0.812212i	$-0.301737\pi$
$683$	4.48589	+	2.58993i	0.171648	+	0.0991009i	−0.411715	+	0.911313i	$0.635070\pi$
$684$		0			0
$685$		−	63.8751i		−	2.44054i
$686$		0			0
$687$	26.6838			1.01805
$688$		0			0
$689$	15.1077	−	26.1673i	0.575559	−	0.996897i
$690$		0			0
$691$	−2.34043	+	1.35125i	−0.0890341	+	0.0514039i	−0.543856	−	0.839179i	$-0.683036\pi$
$691$	−2.34043	+	1.35125i	−0.0890341	+	0.0514039i	0.454822	+	0.890582i	$0.349703\pi$
$692$		0			0
$693$	1.20644	+	5.16559i	0.0458288	+	0.196224i
$694$		0			0
$695$	−22.7735	−	39.4448i	−0.863847	−	1.49623i
$696$		0			0
$697$	−9.78522	−	0.579448i	−0.370642	−	0.0219481i
$698$		0			0
$699$	28.8618			1.09165
$700$		0			0
$701$	13.3659			0.504821			0.252411	−	0.967620i	$-0.418777\pi$
$701$	13.3659			0.504821			0.252411	+	0.967620i	$0.418777\pi$
$702$		0			0
$703$	1.71317	+	0.989098i	0.0646133	+	0.0373045i
$704$		0			0
$705$	−10.0203	−	17.3557i	−0.377387	−	0.653654i
$706$		0			0
$707$	−23.7705	−	7.20123i	−0.893983	−	0.270830i
$708$		0			0
$709$	−7.19931	+	4.15653i	−0.270376	+	0.156102i	−0.629058	−	0.777358i	$-0.716559\pi$
$709$	−7.19931	+	4.15653i	−0.270376	+	0.156102i	0.358683	+	0.933460i	$0.383226\pi$
$710$		0			0
$711$	−2.64528	−	1.52726i	−0.0992059	−	0.0572766i
$712$		0			0
$713$	−8.84739			−0.331337
$714$		0			0
$715$	83.0650			3.10645
$716$		0			0
$717$	8.58484	−	14.8694i	0.320607	−	0.555307i
$718$		0			0
$719$	42.6965	−	24.6508i	1.59231	−	0.919321i	0.599401	−	0.800449i	$-0.295405\pi$
$719$	42.6965	−	24.6508i	1.59231	−	0.919321i	0.992910	−	0.118872i	$-0.0379279\pi$
$720$		0			0
$721$	27.5859	+	29.4316i	1.02735	+	1.09609i
$722$		0			0
$723$	−7.78706	+	4.49586i	−0.289604	+	0.167203i
$724$		0			0
$725$	35.1955	+	20.3201i	1.30713	+	0.754671i
$726$		0			0
$727$			34.4294i			1.27691i	0.769657	+	0.638457i	$0.220427\pi$
$727$			34.4294i			1.27691i	−0.769657	+	0.638457i	$0.779573\pi$
$728$		0			0
$729$	−22.6121			−0.837487
$730$		0			0
$731$	0.342132	+	0.197530i	0.0126542	+	0.00730592i
$732$		0			0
$733$	−19.9788	−	34.6043i	−0.737934	−	1.27814i	−0.953424	−	0.301633i	$-0.902468\pi$
$733$	−19.9788	−	34.6043i	−0.737934	−	1.27814i	0.215491	−	0.976506i	$-0.430865\pi$
$734$		0			0
$735$	−19.4775	−	39.4238i	−0.718438	−	1.45417i
$736$		0			0
$737$	−3.29476	−	5.70669i	−0.121364	−	0.210209i
$738$		0			0
$739$	−15.0104	+	25.9988i	−0.552168	+	0.956382i	0.445950	+	0.895058i	$0.352866\pi$
$739$	−15.0104	+	25.9988i	−0.552168	+	0.956382i	−0.998118	+	0.0613245i	$0.980468\pi$
$740$		0			0
$741$			1.66261i			0.0610775i
$742$		0			0
$743$	−34.7941			−1.27647			−0.638237	−	0.769840i	$-0.720336\pi$
$743$	−34.7941			−1.27647			−0.638237	+	0.769840i	$0.720336\pi$
$744$		0			0
$745$	52.2556	+	30.1698i	1.91450	+	1.10534i
$746$		0			0
$747$	0.481630	+	0.834208i	0.0176219	+	0.0305221i
$748$		0			0
$749$	35.6706	+	38.0572i	1.30337	+	1.39058i
$750$		0			0
$751$	−20.3205	+	11.7320i	−0.741504	+	0.428108i	−0.822616	−	0.568597i	$-0.807486\pi$
$751$	−20.3205	+	11.7320i	−0.741504	+	0.428108i	0.0811117	+	0.996705i	$0.474153\pi$
$752$		0			0
$753$	32.4975	+	18.7624i	1.18427	+	0.683741i
$754$		0			0
$755$			63.1026i			2.29654i
$756$		0			0
$757$			6.20722i			0.225605i	0.993617	+	0.112803i	$0.0359828\pi$
$757$			6.20722i			0.225605i	−0.993617	+	0.112803i	$0.964017\pi$
$758$		0			0
$759$	6.01966	−	10.4264i	0.218500	−	0.378453i
$760$		0			0
$761$	16.2682	+	28.1773i	0.589722	+	1.02143i	0.994269	+	0.106911i	$0.0340958\pi$
$761$	16.2682	+	28.1773i	0.589722	+	1.02143i	−0.404547	+	0.914517i	$0.632571\pi$
$762$		0			0
$763$	17.3052	+	5.24256i	0.626490	+	0.189793i
$764$		0			0
$765$	1.77200	−	1.02307i	0.0640669	−	0.0369891i
$766$		0			0
$767$	−46.1154	−	26.6247i	−1.66513	−	0.961363i
$768$		0			0
$769$	−0.156285			−0.00563579			−0.00281789	−	0.999996i	$-0.500897\pi$
$769$	−0.156285			−0.00563579			−0.00281789	+	0.999996i	$0.500897\pi$
$770$		0			0
$771$	49.2635			1.77418
$772$		0			0
$773$	13.8986	+	8.02434i	0.499896	+	0.288615i	0.728671	−	0.684864i	$-0.240138\pi$
$773$	13.8986	+	8.02434i	0.499896	+	0.288615i	−0.228774	+	0.973479i	$0.573472\pi$
$774$		0			0
$775$	−22.9701	−	39.7853i	−0.825109	−	1.42913i
$776$		0			0
$777$	−11.5583	−	49.4889i	−0.414651	−	1.77540i
$778$		0			0
$779$	0.668348	−	1.01403i	0.0239461	−	0.0363314i
$780$		0			0
$781$	−7.02501	+	12.1677i	−0.251374	+	0.435393i
$782$		0			0
$783$	29.4254			1.05158
$784$		0			0
$785$		−	52.6226i		−	1.87818i
$786$		0			0
$787$	11.2854	−	19.5468i	0.402280	−	0.696770i	−0.591720	−	0.806143i	$-0.701551\pi$
$787$	11.2854	−	19.5468i	0.402280	−	0.696770i	0.994001	+	0.109373i	$0.0348844\pi$
$788$		0			0
$789$	−2.10308	−	3.64264i	−0.0748716	−	0.129681i
$790$		0			0
$791$	−11.6834	+	2.72869i	−0.415413	+	0.0970209i
$792$		0			0
$793$	−56.2993	+	32.5044i	−1.99925	+	1.15427i
$794$		0			0
$795$	19.9393	−	34.5359i	0.707174	−	1.22486i
$796$		0			0
$797$	−9.90336			−0.350795			−0.175398	−	0.984498i	$-0.556121\pi$
$797$	−9.90336			−0.350795			−0.175398	+	0.984498i	$0.556121\pi$
$798$		0			0
$799$	−4.88388			−0.172779
$800$		0			0
$801$	0.174634	+	0.100825i	0.00617040	+	0.00356248i
$802$		0			0
$803$	10.8157	−	6.24446i	0.381679	−	0.220362i
$804$		0			0
$805$	−3.34290	+	11.0346i	−0.117822	+	0.388918i
$806$		0			0
$807$	−16.1468	+	9.32238i	−0.568395	+	0.328163i
$808$		0			0
$809$	14.0816	+	8.13004i	0.495084	+	0.285837i	0.726681	−	0.686975i	$-0.241062\pi$
$809$	14.0816	+	8.13004i	0.495084	+	0.285837i	−0.231597	+	0.972812i	$0.574395\pi$
$810$		0			0
$811$	54.9718			1.93032			0.965161	−	0.261658i	$-0.0842694\pi$
$811$	54.9718			1.93032			0.965161	+	0.261658i	$0.0842694\pi$
$812$		0			0
$813$			27.0823i			0.949816i
$814$		0			0
$815$	10.5337	−	18.2448i	0.368978	−	0.639088i
$816$		0			0
$817$	−0.0423888	+	0.0244732i	−0.00148300	+	0.000856209i
$818$		0			0
$819$	3.60036	−	3.37457i	0.125807	−	0.117917i
$820$		0			0
$821$	−13.2244	−	22.9054i	−0.461536	−	0.799404i	0.537501	−	0.843263i	$-0.319368\pi$
$821$	−13.2244	−	22.9054i	−0.461536	−	0.799404i	−0.999038	+	0.0438585i	$0.986035\pi$
$822$		0			0
$823$	−12.6556	−	7.30673i	−0.441147	−	0.254696i	0.262937	−	0.964813i	$-0.415309\pi$
$823$	−12.6556	−	7.30673i	−0.441147	−	0.254696i	−0.704084	+	0.710117i	$0.748642\pi$
$824$		0			0
$825$	62.5142			2.17647
$826$		0			0
$827$		−	6.17588i		−	0.214756i	−0.994218	−	0.107378i	$-0.965754\pi$
$827$		−	6.17588i		−	0.214756i	0.994218	−	0.107378i	$-0.0342455\pi$
$828$		0			0
$829$	13.7767	−	23.8620i	0.478486	−	0.828762i	−0.521210	−	0.853429i	$-0.674519\pi$
$829$	13.7767	−	23.8620i	0.478486	−	0.828762i	0.999696	+	0.0246664i	$0.00785235\pi$
$830$		0			0
$831$	30.8448	−	17.8082i	1.06999	−	0.617761i
$832$		0			0
$833$	−10.6937	−	0.693046i	−0.370514	−	0.0240126i
$834$		0			0
$835$	−10.7412	+	6.20142i	−0.371714	+	0.214609i
$836$		0			0
$837$	−28.8064	−	16.6314i	−0.995694	−	0.574864i
$838$		0			0
$839$		−	3.46029i		−	0.119463i	−0.998214	−	0.0597313i	$-0.980976\pi$
$839$		−	3.46029i		−	0.119463i	0.998214	−	0.0597313i	$-0.0190244\pi$
$840$		0			0
$841$	−8.52702			−0.294035
$842$		0			0
$843$	−25.0145	+	43.3263i	−0.861544	+	1.49224i
$844$		0			0
$845$	−16.4648	−	28.5179i	−0.566408	−	0.981047i
$846$		0			0
$847$	27.4635	+	29.3010i	0.943657	+	1.00679i
$848$		0			0
$849$	−32.4527	+	18.7366i	−1.11378	+	0.643039i
$850$		0			0
$851$	−6.66270	+	11.5401i	−0.228394	+	0.395591i
$852$		0			0
$853$	−4.14615			−0.141961			−0.0709807	−	0.997478i	$-0.522613\pi$
$853$	−4.14615			−0.141961			−0.0709807	+	0.997478i	$0.522613\pi$
$854$		0			0
$855$			0.253508i			0.00866978i
$856$		0			0
$857$	20.7915	−	36.0119i	0.710224	−	1.23014i	−0.254549	−	0.967060i	$-0.581927\pi$
$857$	20.7915	−	36.0119i	0.710224	−	1.23014i	0.964773	−	0.263084i	$-0.0847395\pi$
$858$		0			0
$859$	−10.3556	−	17.9365i	−0.353330	−	0.611986i	0.633501	−	0.773742i	$-0.281617\pi$
$859$	−10.3556	−	17.9365i	−0.353330	−	0.611986i	−0.986831	+	0.161756i	$0.948284\pi$
$860$		0			0
$861$	−30.7491	+	5.28755i	−1.04793	+	0.180199i
$862$		0			0
$863$	27.6980	+	47.9744i	0.942852	+	1.63307i	0.759995	+	0.649929i	$0.225201\pi$
$863$	27.6980	+	47.9744i	0.942852	+	1.63307i	0.182857	+	0.983139i	$0.441465\pi$
$864$		0			0
$865$	−0.345666	+	0.598711i	−0.0117530	+	0.0203568i
$866$		0			0
$867$			26.9927i			0.916722i
$868$		0			0
$869$	−39.8831			−1.35294
$870$		0			0
$871$	−3.06495	+	5.30865i	−0.103852	+	0.179877i
$872$		0			0
$873$	−4.72053	+	2.72540i	−0.159766	+	0.0922407i
$874$		0			0
$875$	−14.3606	+	3.35395i	−0.485476	+	0.113384i
$876$		0			0
$877$	24.1987	+	41.9134i	0.817132	+	1.41531i	0.907787	+	0.419432i	$0.137771\pi$
$877$	24.1987	+	41.9134i	0.817132	+	1.41531i	−0.0906551	+	0.995882i	$0.528896\pi$
$878$		0			0
$879$	−28.4894	+	49.3450i	−0.960922	+	1.66437i
$880$		0			0
$881$	5.85819			0.197367			0.0986837	−	0.995119i	$-0.468537\pi$
$881$	5.85819			0.197367			0.0986837	+	0.995119i	$0.468537\pi$
$882$		0			0
$883$			41.9837i			1.41286i	0.707782	+	0.706431i	$0.249696\pi$
$883$			41.9837i			1.41286i	−0.707782	+	0.706431i	$0.750304\pi$
$884$		0			0
$885$	−60.8634	−	35.1395i	−2.04590	−	1.18120i
$886$		0			0
$887$	−8.21981	+	4.74571i	−0.275994	+	0.159345i	−0.631608	−	0.775287i	$-0.717605\pi$
$887$	−8.21981	+	4.74571i	−0.275994	+	0.159345i	0.355614	+	0.934633i	$0.384272\pi$
$888$		0			0
$889$	54.6185	−	12.7563i	1.83185	−	0.427833i
$890$		0			0
$891$	44.4080	−	25.6390i	1.48773	−	0.858939i
$892$		0			0
$893$	0.302546	−	0.524026i	0.0101243	−	0.0175359i
$894$		0			0
$895$		−	28.9845i		−	0.968846i
$896$		0			0
$897$	−11.1996			−0.373943
$898$		0			0
$899$	36.7376	+	21.2104i	1.22527	+	0.707408i
$900$		0			0
$901$	−4.85918	−	8.41634i	−0.161883	−	0.280389i
$902$		0			0
$903$	1.20344	+	0.364580i	0.0400481	+	0.0121325i
$904$		0			0
$905$	4.78053	−	2.76004i	0.158910	−	0.0917468i
$906$		0			0
$907$	8.96077	−	15.5205i	0.297538	−	0.515350i	−0.678034	−	0.735030i	$-0.737168\pi$
$907$	8.96077	−	15.5205i	0.297538	−	0.515350i	0.975572	+	0.219680i	$0.0705013\pi$
$908$		0			0
$909$		−	3.67862i		−	0.122012i
$910$		0			0
$911$	28.2931			0.937393			0.468696	−	0.883359i	$-0.344724\pi$
$911$	28.2931			0.937393			0.468696	+	0.883359i	$0.344724\pi$
$912$		0			0
$913$	10.8924	+	6.28870i	0.360484	+	0.208126i
$914$		0			0
$915$	−74.3043	+	42.8996i	−2.45642	+	1.41822i
$916$		0			0
$917$	16.5183	+	17.6234i	0.545481	+	0.581977i
$918$		0			0
$919$	−17.4754	+	10.0894i	−0.576459	+	0.332819i	−0.759725	−	0.650244i	$-0.774666\pi$
$919$	−17.4754	+	10.0894i	−0.576459	+	0.332819i	0.183266	+	0.983063i	$0.441333\pi$
$920$		0			0
$921$	45.8410	+	26.4663i	1.51051	+	0.872095i
$922$		0			0
$923$	13.0700			0.430205
$924$		0			0
$925$	−69.1922			−2.27503
$926$		0			0
$927$	−2.98724	+	5.17404i	−0.0981137	+	0.169938i
$928$		0			0
$929$	−33.4259	+	19.2984i	−1.09667	+	0.633161i	−0.935344	−	0.353741i	$-0.884910\pi$
$929$	−33.4259	+	19.2984i	−1.09667	+	0.633161i	−0.161323	+	0.986902i	$0.551576\pi$
$930$		0			0
$931$	0.736813	−	1.10447i	0.0241481	−	0.0361974i
$932$		0			0
$933$	−10.7029	−	18.5380i	−0.350399	−	0.606908i
$934$		0			0
$935$	13.3583	−	23.1373i	0.436863	−	0.756670i
$936$		0			0
$937$			57.8589i			1.89017i	0.326830	+	0.945083i	$0.394020\pi$
$937$			57.8589i			1.89017i	−0.326830	+	0.945083i	$0.605980\pi$
$938$		0			0
$939$	6.40928			0.209159
$940$		0			0
$941$	6.35327	−	11.0042i	0.207111	−	0.358726i	−0.743693	−	0.668522i	$-0.766927\pi$
$941$	6.35327	−	11.0042i	0.207111	−	0.358726i	0.950803	+	0.309796i	$0.100261\pi$
$942$		0			0
$943$	6.83065	+	4.50209i	0.222437	+	0.146608i
$944$		0			0
$945$	−31.6271	+	29.6437i	−1.02883	+	0.964311i
$946$		0			0
$947$	−9.92878	−	17.1971i	−0.322642	−	0.558832i	0.658390	−	0.752677i	$-0.271238\pi$
$947$	−9.92878	−	17.1971i	−0.322642	−	0.558832i	−0.981032	+	0.193845i	$0.937904\pi$
$948$		0			0
$949$	−10.0613	−	5.80891i	−0.326605	−	0.188565i
$950$		0			0
$951$	−7.41093			−0.240316
$952$		0			0
$953$	−46.9206			−1.51991			−0.759954	−	0.649977i	$-0.774779\pi$
$953$	−46.9206			−1.51991			−0.759954	+	0.649977i	$0.774779\pi$
$954$		0			0
$955$	−31.9342	−	18.4372i	−1.03337	−	0.596615i
$956$		0			0
$957$	−49.9916	+	28.8627i	−1.61600	+	0.932998i
$958$		0			0
$959$	−47.4183	−	14.3653i	−1.53122	−	0.463878i
$960$		0			0
$961$	−8.47649	−	14.6817i	−0.273435	−	0.473604i
$962$		0			0
$963$	−3.86271	+	6.69041i	−0.124474	+	0.215596i
$964$		0			0
$965$			15.2745i			0.491702i
$966$		0			0
$967$		−	23.8051i		−	0.765522i	−0.923847	−	0.382761i	$-0.874973\pi$
$967$		−	23.8051i		−	0.765522i	0.923847	−	0.382761i	$-0.125027\pi$
$968$		0			0
$969$	0.463110	+	0.267377i	0.0148772	+	0.00858938i
$970$		0			0
$971$	10.5450	−	6.08817i	0.338406	−	0.195379i	−0.321161	−	0.947025i	$-0.604073\pi$
$971$	10.5450	−	6.08817i	0.338406	−	0.195379i	0.659567	+	0.751646i	$0.270740\pi$
$972$		0			0
$973$	−34.4039	+	8.03514i	−1.10294	+	0.257595i
$974$		0			0
$975$	−29.0769	−	50.3627i	−0.931207	−	1.61290i
$976$		0			0
$977$	0.927717	+	0.535618i	0.0296803	+	0.0171359i	0.514767	−	0.857330i	$-0.327879\pi$
$977$	0.927717	+	0.535618i	0.0296803	+	0.0171359i	−0.485086	+	0.874466i	$0.661212\pi$
$978$		0			0
$979$	2.63297			0.0841501
$980$		0			0
$981$			2.67807i			0.0855043i
$982$		0			0
$983$	−15.9128	+	27.5618i	−0.507540	+	0.879086i	0.492422	+	0.870357i	$0.336112\pi$
$983$	−15.9128	+	27.5618i	−0.507540	+	0.879086i	−0.999962	+	0.00872886i	$0.997221\pi$
$984$		0			0
$985$	−12.9783	−	22.4790i	−0.413521	−	0.716240i
$986$		0			0
$987$	−15.1377	+	3.53546i	−0.481839	+	0.112535i
$988$		0			0
$989$	−0.164855	−	0.285537i	−0.00524208	−	0.00907955i
$990$		0			0
$991$	−47.4378	−	27.3882i	−1.50691	−	0.870016i	−0.999968	−	0.00803788i	$-0.997441\pi$
$991$	−47.4378	−	27.3882i	−1.50691	−	0.870016i	−0.506945	−	0.861978i	$-0.669225\pi$
$992$		0			0
$993$	−12.8284			−0.407098
$994$		0			0
$995$		−	77.4663i		−	2.45585i
$996$		0			0
$997$	15.8562	+	9.15457i	0.502170	+	0.289928i	0.729609	−	0.683864i	$-0.239702\pi$
$997$	15.8562	+	9.15457i	0.502170	+	0.289928i	−0.227439	+	0.973792i	$0.573035\pi$
$998$		0			0
$999$	−43.3864	+	25.0492i	−1.37269	+	0.792520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.8	✓	56
7.2	even	3	inner	1148.2.r.a.737.21	yes	56
41.40	even	2	inner	1148.2.r.a.81.21	yes	56
287.163	even	6	inner	1148.2.r.a.737.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.8	✓	56	1.1	even	1	trivial
1148.2.r.a.81.21	yes	56	41.40	even	2	inner
1148.2.r.a.737.8	yes	56	287.163	even	6	inner
1148.2.r.a.737.21	yes	56	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.59496 - 0.920850i) q^{3} +(1.70544 + 2.95391i) q^{5} +(2.57642 - 0.601730i) q^{7} +(0.195929 + 0.339358i) q^{9} +O(q^{10})\)	\(q+(-1.59496 - 0.920850i) q^{3} +(1.70544 + 2.95391i) q^{5} +(2.57642 - 0.601730i) q^{7} +(0.195929 + 0.339358i) q^{9} +(4.43105 + 2.55827i) q^{11} -4.75965i q^{13} -6.28183i q^{15} +(-1.32577 - 0.765436i) q^{17} +(0.164258 - 0.0948345i) q^{19} +(-4.66338 - 1.41276i) q^{21} +(0.638818 + 1.10647i) q^{23} +(-3.31707 + 5.74533i) q^{25} +4.80342i q^{27} -6.12593i q^{29} +(-3.46240 + 5.99706i) q^{31} +(-4.71156 - 8.16066i) q^{33} +(6.17139 + 6.58430i) q^{35} +(5.21486 + 9.03241i) q^{37} +(-4.38293 + 7.59145i) q^{39} +(5.72483 - 2.86817i) q^{41} -0.258062 q^{43} +(-0.668290 + 1.15751i) q^{45} +(2.76284 - 1.59513i) q^{47} +(6.27584 - 3.10061i) q^{49} +(1.40970 + 2.44168i) q^{51} +(5.49774 + 3.17412i) q^{53} +17.4519i q^{55} -0.349313 q^{57} +(5.59384 - 9.68881i) q^{59} +(-6.82916 - 11.8285i) q^{61} +(0.708996 + 0.756433i) q^{63} +(14.0596 - 8.11731i) q^{65} +(-1.11534 - 0.643944i) q^{67} -2.35302i q^{69} +2.74600i q^{71} +(1.22045 - 2.11388i) q^{73} +(10.5812 - 6.10904i) q^{75} +(12.9556 + 3.92487i) q^{77} +(-6.75063 + 3.89748i) q^{79} +(5.01101 - 8.67932i) q^{81} +2.45819 q^{83} -5.22163i q^{85} +(-5.64106 + 9.77061i) q^{87} +(0.445657 - 0.257300i) q^{89} +(-2.86402 - 12.2628i) q^{91} +(11.0448 - 6.37671i) q^{93} +(0.560266 + 0.323469i) q^{95} +13.9101i q^{97} +2.00495i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 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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