LMFDB - Embedded newform 1148.2.r.a.81.18

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			81.18
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900937 + 0.520156i) q^{3} +(-0.292521 - 0.506661i) q^{5} +(2.31637 + 1.27845i) q^{7} +(-0.958875 - 1.66082i) q^{9} +O(q^{10})$	\(q+(0.900937 + 0.520156i) q^{3} +(-0.292521 - 0.506661i) q^{5} +(2.31637 + 1.27845i) q^{7} +(-0.958875 - 1.66082i) q^{9} +(-3.20234 - 1.84887i) q^{11} -5.26808i q^{13} -0.608626i q^{15} +(6.11543 + 3.53075i) q^{17} +(1.31072 - 0.756747i) q^{19} +(1.42191 + 2.35668i) q^{21} +(-0.874295 - 1.51432i) q^{23} +(2.32886 - 4.03371i) q^{25} -5.11600i q^{27} -5.75036i q^{29} +(-0.171926 + 0.297785i) q^{31} +(-1.92340 - 3.33143i) q^{33} +(-0.0298462 - 1.54759i) q^{35} +(5.45853 + 9.45446i) q^{37} +(2.74022 - 4.74620i) q^{39} +(5.85299 - 2.59664i) q^{41} -6.68054 q^{43} +(-0.560982 + 0.971650i) q^{45} +(3.16800 - 1.82904i) q^{47} +(3.73114 + 5.92272i) q^{49} +(3.67308 + 6.36196i) q^{51} +(-5.70126 - 3.29163i) q^{53} +2.16333i q^{55} +1.57451 q^{57} +(-4.32530 + 7.49164i) q^{59} +(4.89099 + 8.47144i) q^{61} +(-0.0978348 - 5.07295i) q^{63} +(-2.66913 + 1.54102i) q^{65} +(5.77152 + 3.33219i) q^{67} -1.81908i q^{69} +0.578775i q^{71} +(1.30933 - 2.26783i) q^{73} +(4.19632 - 2.42274i) q^{75} +(-5.05411 - 8.37670i) q^{77} +(6.98613 - 4.03344i) q^{79} +(-0.215510 + 0.373274i) q^{81} -12.5509 q^{83} -4.13127i q^{85} +(2.99108 - 5.18071i) q^{87} +(5.86660 - 3.38708i) q^{89} +(6.73497 - 12.2028i) q^{91} +(-0.309790 + 0.178857i) q^{93} +(-0.766829 - 0.442729i) q^{95} -13.7925i q^{97} +7.09135i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.900937	+	0.520156i	0.520156	+	0.300312i	0.736999	−	0.675894i	$-0.236242\pi$
$3$	0.900937	+	0.520156i	0.520156	+	0.300312i	−0.216842	+	0.976207i	$0.569576\pi$
$4$		0			0
$5$	−0.292521	−	0.506661i	−0.130819	−	0.226586i	0.793173	−	0.608996i	$-0.208427\pi$
$5$	−0.292521	−	0.506661i	−0.130819	−	0.226586i	−0.923993	+	0.382410i	$0.875094\pi$
$6$		0			0
$7$	2.31637	+	1.27845i	0.875505	+	0.483208i
$7$	2.31637	+	1.27845i	0.875505	+	0.483208i
$8$		0			0
$9$	−0.958875	−	1.66082i	−0.319625	−	0.553607i
$10$		0			0
$11$	−3.20234	−	1.84887i	−0.965541	−	0.557456i	−0.0676673	−	0.997708i	$-0.521556\pi$
$11$	−3.20234	−	1.84887i	−0.965541	−	0.557456i	−0.897874	+	0.440252i	$0.854889\pi$
$12$		0			0
$13$		−	5.26808i		−	1.46110i	−0.682858	−	0.730551i	$-0.739263\pi$
$13$		−	5.26808i		−	1.46110i	0.682858	−	0.730551i	$-0.260737\pi$
$14$		0			0
$15$		−	0.608626i		−	0.157147i
$16$		0			0
$17$	6.11543	+	3.53075i	1.48321	+	0.856332i	0.999818	−	0.0190716i	$-0.00607104\pi$
$17$	6.11543	+	3.53075i	1.48321	+	0.856332i	0.483393	+	0.875404i	$0.339404\pi$
$18$		0			0
$19$	1.31072	−	0.756747i	0.300701	−	0.173610i	−0.342057	−	0.939679i	$-0.611124\pi$
$19$	1.31072	−	0.756747i	0.300701	−	0.173610i	0.642758	+	0.766070i	$0.277790\pi$
$20$		0			0
$21$	1.42191	+	2.35668i	0.310286	+	0.514269i
$22$		0			0
$23$	−0.874295	−	1.51432i	−0.182303	−	0.315758i	0.760361	−	0.649500i	$-0.225022\pi$
$23$	−0.874295	−	1.51432i	−0.182303	−	0.315758i	−0.942664	+	0.333742i	$0.891689\pi$
$24$		0			0
$25$	2.32886	−	4.03371i	0.465773	−	0.806742i
$26$		0			0
$27$		−	5.11600i		−	0.984574i
$28$		0			0
$29$		−	5.75036i		−	1.06781i	−0.845543	−	0.533907i	$-0.820723\pi$
$29$		−	5.75036i		−	1.06781i	0.845543	−	0.533907i	$-0.179277\pi$
$30$		0			0
$31$	−0.171926	+	0.297785i	−0.0308789	+	0.0534838i	−0.881052	−	0.473020i	$-0.843164\pi$
$31$	−0.171926	+	0.297785i	−0.0308789	+	0.0534838i	0.850173	+	0.526503i	$0.176497\pi$
$32$		0			0
$33$	−1.92340	−	3.33143i	−0.334821	−	0.579928i
$34$		0			0
$35$	−0.0298462	−	1.54759i	−0.00504492	−	0.261590i
$36$		0			0
$37$	5.45853	+	9.45446i	0.897377	+	1.55430i	0.830835	+	0.556520i	$0.187864\pi$
$37$	5.45853	+	9.45446i	0.897377	+	1.55430i	0.0665428	+	0.997784i	$0.478803\pi$
$38$		0			0
$39$	2.74022	−	4.74620i	0.438787	−	0.760001i
$40$		0			0
$41$	5.85299	−	2.59664i	0.914083	−	0.405527i
$41$	5.85299	−	2.59664i	0.914083	−	0.405527i
$42$		0			0
$43$	−6.68054			−1.01877			−0.509386	−	0.860538i	$-0.670128\pi$
$43$	−6.68054			−1.01877			−0.509386	+	0.860538i	$0.670128\pi$
$44$		0			0
$45$	−0.560982	+	0.971650i	−0.0836263	+	0.144845i
$46$		0			0
$47$	3.16800	−	1.82904i	0.462100	−	0.266793i	−0.250827	−	0.968032i	$-0.580702\pi$
$47$	3.16800	−	1.82904i	0.462100	−	0.266793i	0.712927	+	0.701238i	$0.247369\pi$
$48$		0			0
$49$	3.73114	+	5.92272i	0.533019	+	0.846103i
$50$		0			0
$51$	3.67308	+	6.36196i	0.514334	+	0.890853i
$52$		0			0
$53$	−5.70126	−	3.29163i	−0.783129	−	0.452140i	0.0544092	−	0.998519i	$-0.482672\pi$
$53$	−5.70126	−	3.29163i	−0.783129	−	0.452140i	−0.837538	+	0.546379i	$0.816006\pi$
$54$		0			0
$55$			2.16333i			0.291704i
$56$		0			0
$57$	1.57451			0.208549
$58$		0			0
$59$	−4.32530	+	7.49164i	−0.563106	+	0.975329i	0.434117	+	0.900857i	$0.357061\pi$
$59$	−4.32530	+	7.49164i	−0.563106	+	0.975329i	−0.997223	+	0.0744722i	$0.976273\pi$
$60$		0			0
$61$	4.89099	+	8.47144i	0.626227	+	1.08466i	0.988302	+	0.152508i	$0.0487349\pi$
$61$	4.89099	+	8.47144i	0.626227	+	1.08466i	−0.362075	+	0.932149i	$0.617932\pi$
$62$		0			0
$63$	−0.0978348	−	5.07295i	−0.0123260	−	0.639131i
$64$		0			0
$65$	−2.66913	+	1.54102i	−0.331065	+	0.191140i
$66$		0			0
$67$	5.77152	+	3.33219i	0.705103	+	0.407092i	0.809245	−	0.587471i	$-0.199876\pi$
$67$	5.77152	+	3.33219i	0.705103	+	0.407092i	−0.104142	+	0.994562i	$0.533210\pi$
$68$		0			0
$69$		−	1.81908i		−	0.218991i
$70$		0			0
$71$			0.578775i			0.0686879i	0.999410	+	0.0343440i	$0.0109342\pi$
$71$			0.578775i			0.0686879i	−0.999410	+	0.0343440i	$0.989066\pi$
$72$		0			0
$73$	1.30933	−	2.26783i	0.153246	−	0.265430i	−0.779173	−	0.626809i	$-0.784361\pi$
$73$	1.30933	−	2.26783i	0.153246	−	0.265430i	0.932419	+	0.361379i	$0.117694\pi$
$74$		0			0
$75$	4.19632	−	2.42274i	0.484549	−	0.279754i
$76$		0			0
$77$	−5.05411	−	8.37670i	−0.575970	−	0.954613i
$78$		0			0
$79$	6.98613	−	4.03344i	0.786001	−	0.453798i	−0.0525521	−	0.998618i	$-0.516736\pi$
$79$	6.98613	−	4.03344i	0.786001	−	0.453798i	0.838553	+	0.544821i	$0.183402\pi$
$80$		0			0
$81$	−0.215510	+	0.373274i	−0.0239455	+	0.0414749i
$82$		0			0
$83$	−12.5509			−1.37764			−0.688818	−	0.724934i	$-0.741870\pi$
$83$	−12.5509			−1.37764			−0.688818	+	0.724934i	$0.741870\pi$
$84$		0			0
$85$		−	4.13127i		−	0.448099i
$86$		0			0
$87$	2.99108	−	5.18071i	0.320678	−	0.555430i
$88$		0			0
$89$	5.86660	−	3.38708i	0.621858	−	0.359030i	−0.155734	−	0.987799i	$-0.549774\pi$
$89$	5.86660	−	3.38708i	0.621858	−	0.359030i	0.777592	+	0.628769i	$0.216441\pi$
$90$		0			0
$91$	6.73497	−	12.2028i	0.706017	−	1.27920i
$92$		0			0
$93$	−0.309790	+	0.178857i	−0.0321237	+	0.0185466i
$94$		0			0
$95$	−0.766829	−	0.442729i	−0.0786750	−	0.0454230i
$96$		0			0
$97$		−	13.7925i		−	1.40042i	−0.713937	−	0.700210i	$-0.753090\pi$
$97$		−	13.7925i		−	1.40042i	0.713937	−	0.700210i	$-0.246910\pi$
$98$		0			0
$99$			7.09135i			0.712707i
$100$		0			0
$101$	−7.25226	−	4.18710i	−0.721627	−	0.416632i	0.0937241	−	0.995598i	$-0.470123\pi$
$101$	−7.25226	−	4.18710i	−0.721627	−	0.416632i	−0.815351	+	0.578967i	$0.803456\pi$
$102$		0			0
$103$	−3.43768	−	5.95424i	−0.338725	−	0.586689i	0.645468	−	0.763787i	$-0.276662\pi$
$103$	−3.43768	−	5.95424i	−0.338725	−	0.586689i	−0.984193	+	0.177098i	$0.943329\pi$
$104$		0			0
$105$	0.778098	−	1.40980i	0.0759345	−	0.137583i
$106$		0			0
$107$	−2.90236	−	5.02704i	−0.280582	−	0.485982i	0.690946	−	0.722906i	$-0.257194\pi$
$107$	−2.90236	−	5.02704i	−0.280582	−	0.485982i	−0.971528	+	0.236924i	$0.923861\pi$
$108$		0			0
$109$	7.86552	+	4.54116i	0.753380	+	0.434964i	0.826914	−	0.562329i	$-0.190094\pi$
$109$	7.86552	+	4.54116i	0.753380	+	0.434964i	−0.0735340	+	0.997293i	$0.523428\pi$
$110$		0			0
$111$			11.3572i			1.07797i
$112$		0			0
$113$	3.42377			0.322081			0.161041	−	0.986948i	$-0.448515\pi$
$113$	3.42377			0.322081			0.161041	+	0.986948i	$0.448515\pi$
$114$		0			0
$115$	−0.511499	+	0.885943i	−0.0476976	+	0.0826146i
$116$		0			0
$117$	−8.74933	+	5.05143i	−0.808876	+	0.467005i
$118$		0			0
$119$	9.65173	+	15.9968i	0.884772	+	1.46642i
$120$		0			0
$121$	1.33665	+	2.31514i	0.121513	+	0.210467i
$122$		0			0
$123$	6.62383	+	0.705059i	0.597251	+	0.0635730i
$124$		0			0
$125$	−5.65017			−0.505367
$126$		0			0
$127$	7.31448			0.649055			0.324527	−	0.945876i	$-0.394795\pi$
$127$	7.31448			0.649055			0.324527	+	0.945876i	$0.394795\pi$
$128$		0			0
$129$	−6.01874	−	3.47492i	−0.529921	−	0.305950i
$130$		0			0
$131$	9.56165	+	16.5613i	0.835406	+	1.44696i	0.893700	+	0.448665i	$0.148100\pi$
$131$	9.56165	+	16.5613i	0.835406	+	1.44696i	−0.0582943	+	0.998299i	$0.518566\pi$
$132$		0			0
$133$	4.00359	−	0.0772115i	0.347155	−	0.00669509i
$134$		0			0
$135$	−2.59208	+	1.49654i	−0.223090	+	0.128801i
$136$		0			0
$137$	1.23653	+	0.713909i	0.105644	+	0.0609933i	0.551891	−	0.833916i	$-0.313906\pi$
$137$	1.23653	+	0.713909i	0.105644	+	0.0609933i	−0.446247	+	0.894910i	$0.647240\pi$
$138$		0			0
$139$	−12.3168			−1.04470			−0.522348	−	0.852732i	$-0.674944\pi$
$139$	−12.3168			−1.04470			−0.522348	+	0.852732i	$0.674944\pi$
$140$		0			0
$141$	3.80555			0.320485
$142$		0			0
$143$	−9.74000	+	16.8702i	−0.814499	+	1.41075i
$144$		0			0
$145$	−2.91348	+	1.68210i	−0.241952	+	0.139691i
$146$		0			0
$147$	0.280778	+	7.27677i	0.0231582	+	0.600178i
$148$		0			0
$149$	−14.3161	+	8.26542i	−1.17282	+	0.677129i	−0.954343	−	0.298712i	$-0.903443\pi$
$149$	−14.3161	+	8.26542i	−1.17282	+	0.677129i	−0.218479	+	0.975842i	$0.570110\pi$
$150$		0			0
$151$	2.00794	+	1.15929i	0.163404	+	0.0943414i	0.579472	−	0.814992i	$-0.303259\pi$
$151$	2.00794	+	1.15929i	0.163404	+	0.0943414i	−0.416068	+	0.909334i	$0.636592\pi$
$152$		0			0
$153$		−	13.5422i		−	1.09482i
$154$		0			0
$155$	0.201168			0.0161582
$156$		0			0
$157$	−3.76182	−	2.17189i	−0.300226	−	0.173335i	0.342319	−	0.939584i	$-0.388788\pi$
$157$	−3.76182	−	2.17189i	−0.300226	−	0.173335i	−0.642544	+	0.766249i	$0.722121\pi$
$158$		0			0
$159$	−3.42432	−	5.93109i	−0.271566	−	0.470366i
$160$		0			0
$161$	−0.0892051	−	4.62548i	−0.00703034	−	0.364539i
$162$		0			0
$163$	9.99921	+	17.3191i	0.783199	+	1.35654i	0.930069	+	0.367385i	$0.119747\pi$
$163$	9.99921	+	17.3191i	0.783199	+	1.35654i	−0.146870	+	0.989156i	$0.546920\pi$
$164$		0			0
$165$	−1.12527	+	1.94903i	−0.0876023	+	0.151732i
$166$		0			0
$167$			10.1008i			0.781626i	0.920470	+	0.390813i	$0.127806\pi$
$167$			10.1008i			0.781626i	−0.920470	+	0.390813i	$0.872194\pi$
$168$		0			0
$169$	−14.7526			−1.13482
$170$		0			0
$171$	−2.51364	−	1.45125i	−0.192223	−	0.110980i
$172$		0			0
$173$	−11.8888	−	20.5921i	−0.903891	−	1.56559i	−0.822399	−	0.568912i	$-0.807365\pi$
$173$	−11.8888	−	20.5921i	−0.903891	−	1.56559i	−0.0814928	−	0.996674i	$-0.525969\pi$
$174$		0			0
$175$	10.5514	−	6.36623i	0.797611	−	0.481242i
$176$		0			0
$177$	−7.79365	+	4.49966i	−0.585806	+	0.338215i
$178$		0			0
$179$	−1.44227	−	0.832694i	−0.107800	−	0.0622385i	0.445131	−	0.895466i	$-0.353157\pi$
$179$	−1.44227	−	0.832694i	−0.107800	−	0.0622385i	−0.552931	+	0.833227i	$0.686491\pi$
$180$		0			0
$181$			3.05454i			0.227042i	0.993536	+	0.113521i	$0.0362129\pi$
$181$			3.05454i			0.227042i	−0.993536	+	0.113521i	$0.963787\pi$
$182$		0			0
$183$			10.1763i			0.752254i
$184$		0			0
$185$	3.19347	−	5.53125i	0.234789	−	0.406666i
$186$		0			0
$187$	−13.0558	−	22.6133i	−0.954734	−	1.65365i
$188$		0			0
$189$	6.54054	−	11.8505i	0.475754	−	0.862000i
$190$		0			0
$191$	−23.6233	+	13.6389i	−1.70932	+	0.986876i	−0.773920	+	0.633283i	$0.781707\pi$
$191$	−23.6233	+	13.6389i	−1.70932	+	0.986876i	−0.935399	+	0.353593i	$0.884960\pi$
$192$		0			0
$193$	16.3992	+	9.46809i	1.18044	+	0.681528i	0.956116	−	0.292987i	$-0.0946492\pi$
$193$	16.3992	+	9.46809i	1.18044	+	0.681528i	0.224324	+	0.974515i	$0.427983\pi$
$194$		0			0
$195$	−3.20629			−0.229607
$196$		0			0
$197$	−8.61440			−0.613750			−0.306875	−	0.951750i	$-0.599283\pi$
$197$	−8.61440			−0.613750			−0.306875	+	0.951750i	$0.599283\pi$
$198$		0			0
$199$	16.9211	+	9.76942i	1.19951	+	0.692536i	0.960445	−	0.278469i	$-0.0898269\pi$
$199$	16.9211	+	9.76942i	1.19951	+	0.692536i	0.239061	+	0.971004i	$0.423160\pi$
$200$		0			0
$201$	3.46652	+	6.00418i	0.244509	+	0.423502i
$202$		0			0
$203$	7.35154	−	13.3200i	0.515977	−	0.934877i
$204$		0			0
$205$	−3.02774	−	2.20591i	−0.211466	−	0.154067i
$206$		0			0
$207$	−1.67668	+	2.90410i	−0.116537	+	0.201849i
$208$		0			0
$209$	−5.59651			−0.387119
$210$		0			0
$211$			0.936344i			0.0644606i	0.999480	+	0.0322303i	$0.0102610\pi$
$211$			0.936344i			0.0644606i	−0.999480	+	0.0322303i	$0.989739\pi$
$212$		0			0
$213$	−0.301053	+	0.521439i	−0.0206278	+	0.0357284i
$214$		0			0
$215$	1.95420	+	3.38477i	0.133275	+	0.230839i
$216$		0			0
$217$	−0.778949	+	0.469982i	−0.0528785	+	0.0319044i
$218$		0			0
$219$	2.35925	−	1.36212i	0.159424	−	0.0920432i
$220$		0			0
$221$	18.6003	−	32.2166i	1.25119	−	2.16712i
$222$		0			0
$223$	−18.5956			−1.24526			−0.622628	−	0.782518i	$-0.713935\pi$
$223$	−18.5956			−1.24526			−0.622628	+	0.782518i	$0.713935\pi$
$224$		0			0
$225$	−8.93236			−0.595490
$226$		0			0
$227$	9.12475	+	5.26818i	0.605631	+	0.349661i	0.771254	−	0.636528i	$-0.219630\pi$
$227$	9.12475	+	5.26818i	0.605631	+	0.349661i	−0.165623	+	0.986189i	$0.552963\pi$
$228$		0			0
$229$	5.83362	−	3.36804i	0.385496	−	0.222567i	−0.294711	−	0.955587i	$-0.595223\pi$
$229$	5.83362	−	3.36804i	0.385496	−	0.222567i	0.680207	+	0.733020i	$0.261890\pi$
$230$		0			0
$231$	−0.196246	−	10.1758i	−0.0129121	−	0.669518i
$232$		0			0
$233$	6.97709	−	4.02822i	0.457084	−	0.263898i	−0.253733	−	0.967274i	$-0.581659\pi$
$233$	6.97709	−	4.02822i	0.457084	−	0.263898i	0.710817	+	0.703376i	$0.248325\pi$
$234$		0			0
$235$	−1.85341	−	1.07007i	−0.120903	−	0.0698035i
$236$		0			0
$237$	8.39208			0.545124
$238$		0			0
$239$			8.32187i			0.538297i	0.963099	+	0.269148i	$0.0867422\pi$
$239$			8.32187i			0.538297i	−0.963099	+	0.269148i	$0.913258\pi$
$240$		0			0
$241$	−2.96507	+	5.13565i	−0.190997	+	0.330816i	−0.945581	−	0.325387i	$-0.894505\pi$
$241$	−2.96507	+	5.13565i	−0.190997	+	0.330816i	0.754584	+	0.656203i	$0.227839\pi$
$242$		0			0
$243$	−13.6801	+	7.89819i	−0.877577	+	0.506669i
$244$		0			0
$245$	1.90938	−	3.62294i	0.121986	−	0.231461i
$246$		0			0
$247$	−3.98660	−	6.90500i	−0.253662	−	0.439355i
$248$		0			0
$249$	−11.3075	−	6.52841i	−0.716586	−	0.413721i
$250$		0			0
$251$	−2.32172			−0.146545			−0.0732727	−	0.997312i	$-0.523344\pi$
$251$	−2.32172			−0.146545			−0.0732727	+	0.997312i	$0.523344\pi$
$252$		0			0
$253$			6.46584i			0.406504i
$254$		0			0
$255$	2.14891	−	3.72201i	0.134570	−	0.233082i
$256$		0			0
$257$	−7.45940	+	4.30669i	−0.465305	+	0.268644i	−0.714272	−	0.699868i	$-0.753242\pi$
$257$	−7.45940	+	4.30669i	−0.465305	+	0.268644i	0.248967	+	0.968512i	$0.419909\pi$
$258$		0			0
$259$	0.556939	+	28.8785i	0.0346065	+	1.79442i
$260$		0			0
$261$	−9.55031	+	5.51388i	−0.591150	+	0.341300i
$262$		0			0
$263$	−19.2714	−	11.1264i	−1.18833	−	0.686081i	−0.230401	−	0.973096i	$-0.574004\pi$
$263$	−19.2714	−	11.1264i	−1.18833	−	0.686081i	−0.957926	+	0.287015i	$0.907337\pi$
$264$		0			0
$265$			3.85148i			0.236594i
$266$		0			0
$267$	7.04724			0.431284
$268$		0			0
$269$	−3.10793	+	5.38310i	−0.189494	+	0.328213i	−0.945082	−	0.326834i	$-0.894018\pi$
$269$	−3.10793	+	5.38310i	−0.189494	+	0.328213i	0.755588	+	0.655048i	$0.227351\pi$
$270$		0			0
$271$	−3.63733	−	6.30003i	−0.220952	−	0.382700i	0.734145	−	0.678992i	$-0.237583\pi$
$271$	−3.63733	−	6.30003i	−0.220952	−	0.382700i	−0.955097	+	0.296292i	$0.904250\pi$
$272$		0			0
$273$	12.4151	−	7.49073i	0.751399	−	0.453360i
$274$		0			0
$275$	−14.9156	+	8.61153i	−0.899445	+	0.519295i
$276$		0			0
$277$	−2.27160	+	3.93452i	−0.136487	+	0.236403i	−0.926165	−	0.377120i	$-0.876915\pi$
$277$	−2.27160	+	3.93452i	−0.136487	+	0.236403i	0.789677	+	0.613522i	$0.210248\pi$
$278$		0			0
$279$	0.659424			0.0394787
$280$		0			0
$281$			8.41305i			0.501880i	0.968003	+	0.250940i	$0.0807398\pi$
$281$			8.41305i			0.501880i	−0.968003	+	0.250940i	$0.919260\pi$
$282$		0			0
$283$	−10.3453	+	17.9186i	−0.614965	+	1.06515i	0.375426	+	0.926853i	$0.377497\pi$
$283$	−10.3453	+	17.9186i	−0.614965	+	1.06515i	−0.990391	+	0.138298i	$0.955837\pi$
$284$		0			0
$285$	−0.460576	−	0.797741i	−0.0272822	−	0.0472541i
$286$		0			0
$287$	16.8774	+	1.46797i	0.996239	+	0.0866515i
$288$		0			0
$289$	16.4324	+	28.4617i	0.966609	+	1.67422i
$290$		0			0
$291$	7.17427	−	12.4262i	0.420563	−	0.728437i
$292$		0			0
$293$		−	0.574132i		−	0.0335411i	−0.999859	−	0.0167706i	$-0.994662\pi$
$293$		−	0.574132i		−	0.0335411i	0.999859	−	0.0167706i	$-0.00533849\pi$
$294$		0			0
$295$	5.06097			0.294661
$296$		0			0
$297$	−9.45882	+	16.3832i	−0.548856	+	0.950647i
$298$		0			0
$299$	−7.97758	+	4.60586i	−0.461355	+	0.266363i
$300$		0			0
$301$	−15.4746	−	8.54073i	−0.891941	−	0.492279i
$302$		0			0
$303$	−4.35589	−	7.54462i	−0.250239	−	0.433427i
$304$		0			0
$305$	2.86143	−	4.95615i	0.163845	−	0.283788i
$306$		0			0
$307$	−5.74527			−0.327900			−0.163950	−	0.986469i	$-0.552424\pi$
$307$	−5.74527			−0.327900			−0.163950	+	0.986469i	$0.552424\pi$
$308$		0			0
$309$		−	7.15253i		−	0.406893i
$310$		0			0
$311$	7.92886	+	4.57773i	0.449604	+	0.259579i	0.707663	−	0.706550i	$-0.249749\pi$
$311$	7.92886	+	4.57773i	0.449604	+	0.259579i	−0.258059	+	0.966129i	$0.583083\pi$
$312$		0			0
$313$	−4.03179	+	2.32776i	−0.227890	+	0.131573i	−0.609598	−	0.792710i	$-0.708669\pi$
$313$	−4.03179	+	2.32776i	−0.227890	+	0.131573i	0.381708	+	0.924283i	$0.375336\pi$
$314$		0			0
$315$	−2.54165	+	1.53351i	−0.143206	+	0.0864036i
$316$		0			0
$317$	−13.0258	+	7.52048i	−0.731605	+	0.422392i	−0.819009	−	0.573781i	$-0.805476\pi$
$317$	−13.0258	+	7.52048i	−0.731605	+	0.422392i	0.0874044	+	0.996173i	$0.472143\pi$
$318$		0			0
$319$	−10.6317	+	18.4146i	−0.595259	+	1.03102i
$320$		0			0
$321$		−	6.03873i		−	0.337049i
$322$		0			0
$323$	10.6875			0.594670
$324$		0			0
$325$	−21.2499	−	12.2686i	−1.17873	−	0.680541i
$326$		0			0
$327$	4.72422	+	8.18259i	0.261250	+	0.452498i
$328$		0			0
$329$	9.67659	−	0.186619i	0.533488	−	0.0102886i
$330$		0			0
$331$	21.6856	−	12.5202i	1.19195	−	0.688173i	0.233202	−	0.972428i	$-0.425080\pi$
$331$	21.6856	−	12.5202i	1.19195	−	0.688173i	0.958748	+	0.284256i	$0.0917465\pi$
$332$		0			0
$333$	10.4681	−	18.1313i	0.573649	−	0.993589i
$334$		0			0
$335$		−	3.89894i		−	0.213022i
$336$		0			0
$337$	−24.4017			−1.32924			−0.664622	−	0.747180i	$-0.731407\pi$
$337$	−24.4017			−1.32924			−0.664622	+	0.747180i	$0.731407\pi$
$338$		0			0
$339$	3.08460	+	1.78090i	0.167533	+	0.0967250i
$340$		0			0
$341$	1.10113	−	0.635740i	0.0596297	−	0.0344272i
$342$		0			0
$343$	1.07079	+	18.4893i	0.0578174	+	0.998327i
$344$		0			0
$345$	−0.921657	+	0.532119i	−0.0496203	+	0.0286483i
$346$		0			0
$347$	24.6563	+	14.2354i	1.32362	+	0.764194i	0.984305	−	0.176478i	$-0.0564705\pi$
$347$	24.6563	+	14.2354i	1.32362	+	0.764194i	0.339318	+	0.940672i	$0.389804\pi$
$348$		0			0
$349$	−20.7122			−1.10870			−0.554349	−	0.832284i	$-0.687033\pi$
$349$	−20.7122			−1.10870			−0.554349	+	0.832284i	$0.687033\pi$
$350$		0			0
$351$	−26.9515			−1.43856
$352$		0			0
$353$	5.20828	−	9.02101i	0.277209	−	0.480140i	−0.693481	−	0.720475i	$-0.743924\pi$
$353$	5.20828	−	9.02101i	0.277209	−	0.480140i	0.970690	+	0.240335i	$0.0772573\pi$
$354$		0			0
$355$	0.293243	−	0.169304i	0.0155637	−	0.00898571i
$356$		0			0
$357$	0.374767	+	19.4325i	0.0198348	+	1.02848i
$358$		0			0
$359$	−0.194552	−	0.336974i	−0.0102681	−	0.0177848i	0.860846	−	0.508866i	$-0.169935\pi$
$359$	−0.194552	−	0.336974i	−0.0102681	−	0.0177848i	−0.871114	+	0.491081i	$0.836602\pi$
$360$		0			0
$361$	−8.35467	+	14.4707i	−0.439719	+	0.761616i
$362$		0			0
$363$			2.78106i			0.145968i
$364$		0			0
$365$	−1.53203			−0.0801901
$366$		0			0
$367$	−13.5896	+	23.5378i	−0.709370	+	1.22867i	0.255721	+	0.966751i	$0.417687\pi$
$367$	−13.5896	+	23.5378i	−0.709370	+	1.22867i	−0.965091	+	0.261915i	$0.915646\pi$
$368$		0			0
$369$	−9.92484	−	7.23091i	−0.516666	−	0.376426i
$370$		0			0
$371$	−8.99806	−	14.9134i	−0.467156	−	0.774265i
$372$		0			0
$373$	11.2112	+	19.4183i	0.580491	+	1.00544i	0.995421	+	0.0955871i	$0.0304728\pi$
$373$	11.2112	+	19.4183i	0.580491	+	1.00544i	−0.414930	+	0.909853i	$0.636194\pi$
$374$		0			0
$375$	−5.09045	−	2.93897i	−0.262870	−	0.151768i
$376$		0			0
$377$	−30.2933			−1.56019
$378$		0			0
$379$	32.0751			1.64759			0.823793	−	0.566890i	$-0.191854\pi$
$379$	32.0751			1.64759			0.823793	+	0.566890i	$0.191854\pi$
$380$		0			0
$381$	6.58988	+	3.80467i	0.337610	+	0.194919i
$382$		0			0
$383$	−15.0836	+	8.70853i	−0.770737	+	0.444985i	−0.833137	−	0.553066i	$-0.813458\pi$
$383$	−15.0836	+	8.70853i	−0.770737	+	0.444985i	0.0624006	+	0.998051i	$0.480124\pi$
$384$		0			0
$385$	−2.76571	+	5.01108i	−0.140954	+	0.255388i
$386$		0			0
$387$	6.40580	+	11.0952i	0.325625	+	0.563999i
$388$		0			0
$389$	1.13827	−	1.97154i	0.0577124	−	0.0999609i	−0.835726	−	0.549147i	$-0.814953\pi$
$389$	1.13827	−	1.97154i	0.0577124	−	0.0999609i	0.893438	+	0.449186i	$0.148286\pi$
$390$		0			0
$391$		−	12.3477i		−	0.624448i
$392$		0			0
$393$			19.8942i			1.00353i
$394$		0			0
$395$	−4.08718	−	2.35973i	−0.205648	−	0.118731i
$396$		0			0
$397$	16.1801	−	9.34156i	0.812054	−	0.468840i	−0.0356146	−	0.999366i	$-0.511339\pi$
$397$	16.1801	−	9.34156i	0.812054	−	0.468840i	0.847669	+	0.530526i	$0.178006\pi$
$398$		0			0
$399$	3.64714	+	2.01293i	0.182585	+	0.100772i
$400$		0			0
$401$	19.5182	+	33.8065i	0.974693	+	1.68822i	0.680945	+	0.732334i	$0.261569\pi$
$401$	19.5182	+	33.8065i	0.974693	+	1.68822i	0.293748	+	0.955883i	$0.405097\pi$
$402$		0			0
$403$	1.56876	+	0.905722i	0.0781453	+	0.0451172i
$404$		0			0
$405$	0.252164			0.0125301
$406$		0			0
$407$		−	40.3685i		−	2.00099i
$408$		0			0
$409$	13.3868	−	23.1865i	0.661932	−	1.14650i	−0.318175	−	0.948032i	$-0.603070\pi$
$409$	13.3868	−	23.1865i	0.661932	−	1.14650i	0.980107	−	0.198468i	$-0.0635967\pi$
$410$		0			0
$411$	0.742688	+	1.28637i	0.0366341	+	0.0634521i
$412$		0			0
$413$	−19.5967	+	11.8237i	−0.964290	+	0.581808i
$414$		0			0
$415$	3.67139	+	6.35904i	0.180222	+	0.312153i
$416$		0			0
$417$	−11.0966	−	6.40665i	−0.543405	−	0.313735i
$418$		0			0
$419$	22.1830			1.08371			0.541856	−	0.840471i	$-0.317722\pi$
$419$	22.1830			1.08371			0.541856	+	0.840471i	$0.317722\pi$
$420$		0			0
$421$		−	32.2304i		−	1.57081i	−0.618981	−	0.785406i	$-0.712454\pi$
$421$		−	32.2304i		−	1.57081i	0.618981	−	0.785406i	$-0.287546\pi$
$422$		0			0
$423$	−6.07543	−	3.50765i	−0.295397	−	0.170548i
$424$		0			0
$425$	28.4840	−	16.4453i	1.38168	−	0.797712i
$426$		0			0
$427$	0.499031	+	25.8759i	0.0241498	+	1.25222i
$428$		0			0
$429$	−17.5502	+	10.1326i	−0.847334	+	0.489208i
$430$		0			0
$431$	11.1879	−	19.3781i	0.538904	−	0.933409i	−0.460059	−	0.887888i	$-0.652172\pi$
$431$	11.1879	−	19.3781i	0.538904	−	0.933409i	0.998963	−	0.0455210i	$-0.0144948\pi$
$432$		0			0
$433$	36.1125			1.73546			0.867729	−	0.497038i	$-0.165579\pi$
$433$	36.1125			1.73546			0.867729	+	0.497038i	$0.165579\pi$
$434$		0			0
$435$	−3.49982			−0.167803
$436$		0			0
$437$	−2.29192	−	1.32324i	−0.109637	−	0.0632992i
$438$		0			0
$439$	−4.80962	+	2.77684i	−0.229551	+	0.132531i	−0.610365	−	0.792120i	$-0.708977\pi$
$439$	−4.80962	+	2.77684i	−0.229551	+	0.132531i	0.380814	+	0.924652i	$0.375644\pi$
$440$		0			0
$441$	6.25888	−	11.8759i	0.298042	−	0.565519i
$442$		0			0
$443$	17.1112	+	29.6374i	0.812977	+	1.40812i	0.910772	+	0.412911i	$0.135488\pi$
$443$	17.1112	+	29.6374i	0.812977	+	1.40812i	−0.0977946	+	0.995207i	$0.531179\pi$
$444$		0			0
$445$	−3.43220	−	1.98158i	−0.162702	−	0.0939361i
$446$		0			0
$447$	−17.1972			−0.813401
$448$		0			0
$449$	−5.79859			−0.273652			−0.136826	−	0.990595i	$-0.543690\pi$
$449$	−5.79859			−0.273652			−0.136826	+	0.990595i	$0.543690\pi$
$450$		0			0
$451$	−23.5441	−	2.50610i	−1.10865	−	0.118008i
$452$		0			0
$453$	1.20602	+	2.08889i	0.0566638	+	0.0981445i
$454$		0			0
$455$	−8.15281	+	0.157232i	−0.382210	+	0.00737114i
$456$		0			0
$457$	27.2389	−	15.7264i	1.27418	−	0.735650i	0.298411	−	0.954438i	$-0.403543\pi$
$457$	27.2389	−	15.7264i	1.27418	−	0.735650i	0.975773	+	0.218787i	$0.0702101\pi$
$458$		0			0
$459$	18.0633	−	31.2865i	0.843122	−	1.46033i
$460$		0			0
$461$	−22.0603			−1.02745			−0.513726	−	0.857955i	$-0.671735\pi$
$461$	−22.0603			−1.02745			−0.513726	+	0.857955i	$0.671735\pi$
$462$		0			0
$463$			18.2913i			0.850070i	0.905177	+	0.425035i	$0.139738\pi$
$463$			18.2913i			0.850070i	−0.905177	+	0.425035i	$0.860262\pi$
$464$		0			0
$465$	0.181240	+	0.104639i	0.00840480	+	0.00485252i
$466$		0			0
$467$	−16.7429	−	28.9995i	−0.774768	−	1.34194i	−0.934925	−	0.354846i	$-0.884533\pi$
$467$	−16.7429	−	28.9995i	−0.774768	−	1.34194i	0.160157	−	0.987092i	$-0.448800\pi$
$468$		0			0
$469$	9.10894	+	15.0972i	0.420612	+	0.697123i
$470$		0			0
$471$	−2.25944	−	3.91347i	−0.104110	−	0.180323i
$472$		0			0
$473$	21.3933	+	12.3515i	0.983667	+	0.567920i
$474$		0			0
$475$		−	7.04944i		−	0.323451i
$476$		0			0
$477$			12.6250i			0.578061i
$478$		0			0
$479$	−1.69684	−	0.979671i	−0.0775306	−	0.0447623i	0.460734	−	0.887539i	$-0.347586\pi$
$479$	−1.69684	−	0.979671i	−0.0775306	−	0.0447623i	−0.538264	+	0.842776i	$0.680920\pi$
$480$		0			0
$481$	49.8068	−	28.7560i	2.27100	−	1.31116i
$482$		0			0
$483$	2.32560	−	4.21366i	0.105819	−	0.191728i
$484$		0			0
$485$	−6.98814	+	4.03460i	−0.317315	+	0.183202i
$486$		0			0
$487$	−7.91828	+	13.7149i	−0.358811	+	0.621480i	−0.987763	−	0.155965i	$-0.950151\pi$
$487$	−7.91828	+	13.7149i	−0.358811	+	0.621480i	0.628951	+	0.777445i	$0.283485\pi$
$488$		0			0
$489$			20.8046i			0.940817i
$490$		0			0
$491$	−6.42402			−0.289912			−0.144956	−	0.989438i	$-0.546304\pi$
$491$	−6.42402			−0.289912			−0.144956	+	0.989438i	$0.546304\pi$
$492$		0			0
$493$	20.3031	−	35.1659i	0.914404	−	1.58379i
$494$		0			0
$495$	3.59291	−	2.07437i	0.161489	−	0.0932359i
$496$		0			0
$497$	−0.739934	+	1.34066i	−0.0331906	+	0.0601366i
$498$		0			0
$499$	36.7146	−	21.1972i	1.64357	−	0.948917i	0.664023	−	0.747712i	$-0.268848\pi$
$499$	36.7146	−	21.1972i	1.64357	−	0.948917i	0.979549	−	0.201205i	$-0.0644856\pi$
$500$		0			0
$501$	−5.25401	+	9.10021i	−0.234732	+	0.406567i
$502$		0			0
$503$		−	32.2174i		−	1.43650i	−0.695783	−	0.718252i	$-0.744942\pi$
$503$		−	32.2174i		−	1.43650i	0.695783	−	0.718252i	$-0.255058\pi$
$504$		0			0
$505$			4.89925i			0.218014i
$506$		0			0
$507$	−13.2912	−	7.67368i	−0.590283	−	0.340800i
$508$		0			0
$509$	9.01038	−	5.20215i	0.399378	−	0.230581i	−0.286837	−	0.957979i	$-0.592604\pi$
$509$	9.01038	−	5.20215i	0.399378	−	0.230581i	0.686216	+	0.727398i	$0.259271\pi$
$510$		0			0
$511$	5.93221	−	3.57922i	0.262425	−	0.158335i
$512$		0			0
$513$	−3.87152	−	6.70566i	−0.170932	−	0.296062i
$514$		0			0
$515$	−2.01119	+	3.48348i	−0.0886236	+	0.153501i
$516$		0			0
$517$	−13.5267			−0.594902
$518$		0			0
$519$		−	24.7362i		−	1.08580i
$520$		0			0
$521$	−30.8054	−	17.7855i	−1.34961	−	0.779196i	−0.361414	−	0.932405i	$-0.617706\pi$
$521$	−30.8054	−	17.7855i	−1.34961	−	0.779196i	−0.988194	+	0.153209i	$0.951039\pi$
$522$		0			0
$523$	2.77765	+	4.81103i	0.121458	+	0.210372i	0.920343	−	0.391112i	$-0.127910\pi$
$523$	2.77765	+	4.81103i	0.121458	+	0.210372i	−0.798885	+	0.601484i	$0.794576\pi$
$524$		0			0
$525$	12.8176	−	0.247195i	0.559405	−	0.0107885i
$526$		0			0
$527$	−2.10281	+	1.21406i	−0.0915999	+	0.0528852i
$528$		0			0
$529$	9.97122	−	17.2707i	0.433531	−	0.750898i
$530$		0			0
$531$	16.5897			0.719932
$532$		0			0
$533$	−13.6793	−	30.8340i	−0.592516	−	1.33557i
$534$		0			0
$535$	−1.69800	+	2.94103i	−0.0734111	+	0.127152i
$536$		0			0
$537$	−0.866262	−	1.50041i	−0.0373820	−	0.0647475i
$538$		0			0
$539$	−0.998013	−	25.8649i	−0.0429875	−	1.11408i
$540$		0			0
$541$	−16.2603	−	28.1638i	−0.699087	−	1.21085i	−0.968783	−	0.247909i	$-0.920257\pi$
$541$	−16.2603	−	28.1638i	−0.699087	−	1.21085i	0.269696	−	0.962945i	$-0.413077\pi$
$542$		0			0
$543$	−1.58884	+	2.75194i	−0.0681835	+	0.118097i
$544$		0			0
$545$		−	5.31354i		−	0.227607i
$546$		0			0
$547$			14.1614i			0.605498i	0.953070	+	0.302749i	$0.0979044\pi$
$547$			14.1614i			0.605498i	−0.953070	+	0.302749i	$0.902096\pi$
$548$		0			0
$549$	9.37969	−	16.2461i	0.400316	−	0.693367i
$550$		0			0
$551$	−4.35157	−	7.53714i	−0.185383	−	0.321093i
$552$		0			0
$553$	21.3390	−	0.411535i	0.907426	−	0.0175003i
$554$		0			0
$555$	5.75423	−	3.32221i	0.244253	−	0.141020i
$556$		0			0
$557$	−13.5490	−	7.82251i	−0.574089	−	0.331451i	0.184692	−	0.982797i	$-0.440871\pi$
$557$	−13.5490	−	7.82251i	−0.574089	−	0.331451i	−0.758781	+	0.651346i	$0.774205\pi$
$558$		0			0
$559$			35.1936i			1.48853i
$560$		0			0
$561$		−	27.1642i		−	1.14687i
$562$		0			0
$563$	5.19721	+	3.00061i	0.219036	+	0.126461i	0.605504	−	0.795842i	$-0.292972\pi$
$563$	5.19721	+	3.00061i	0.219036	+	0.126461i	−0.386468	+	0.922303i	$0.626305\pi$
$564$		0			0
$565$	−1.00153	−	1.73469i	−0.0421345	−	0.0729791i
$566$		0			0
$567$	−0.976411	+	0.589122i	−0.0410054	+	0.0247408i
$568$		0			0
$569$	20.6124	+	35.7018i	0.864119	+	1.49670i	0.867920	+	0.496705i	$0.165457\pi$
$569$	20.6124	+	35.7018i	0.864119	+	1.49670i	−0.00380101	+	0.999993i	$0.501210\pi$
$570$		0			0
$571$	28.0634	+	16.2024i	1.17442	+	0.678050i	0.954717	−	0.297517i	$-0.0961585\pi$
$571$	28.0634	+	16.2024i	1.17442	+	0.678050i	0.219701	+	0.975567i	$0.429492\pi$
$572$		0			0
$573$	−28.3774			−1.18548
$574$		0			0
$575$	−8.14446			−0.339647
$576$		0			0
$577$	23.8069	+	13.7449i	0.991094	+	0.572209i	0.905601	−	0.424130i	$-0.139420\pi$
$577$	23.8069	+	13.7449i	0.991094	+	0.572209i	0.0854930	+	0.996339i	$0.472753\pi$
$578$		0			0
$579$	9.84976	+	17.0603i	0.409342	+	0.709002i
$580$		0			0
$581$	−29.0724	−	16.0456i	−1.20613	−	0.665685i
$582$		0			0
$583$	12.1716	+	21.0818i	0.504096	+	0.873119i
$584$		0			0
$585$	5.11873	+	2.95530i	0.211633	+	0.122187i
$586$		0			0
$587$		−	19.7733i		−	0.816131i	−0.912953	−	0.408065i	$-0.866204\pi$
$587$		−	19.7733i		−	0.816131i	0.912953	−	0.408065i	$-0.133796\pi$
$588$		0			0
$589$			0.520420i			0.0214435i
$590$		0			0
$591$	−7.76103	−	4.48083i	−0.319246	−	0.184317i
$592$		0			0
$593$	−8.04327	+	4.64378i	−0.330297	+	0.190697i	−0.655973	−	0.754784i	$-0.727742\pi$
$593$	−8.04327	+	4.64378i	−0.330297	+	0.190697i	0.325676	+	0.945482i	$0.394408\pi$
$594$		0			0
$595$	5.28162	−	9.56955i	0.216525	−	0.392313i
$596$		0			0
$597$	10.1632	+	17.6033i	0.415954	+	0.720453i
$598$		0			0
$599$	−4.34701	+	7.52925i	−0.177614	+	0.307637i	−0.941063	−	0.338232i	$-0.890171\pi$
$599$	−4.34701	+	7.52925i	−0.177614	+	0.307637i	0.763449	+	0.645868i	$0.223505\pi$
$600$		0			0
$601$		−	9.12212i		−	0.372099i	−0.982540	−	0.186050i	$-0.940432\pi$
$601$		−	9.12212i		−	0.372099i	0.982540	−	0.186050i	$-0.0595685\pi$
$602$		0			0
$603$		−	12.7806i		−	0.520467i
$604$		0			0
$605$	0.781995	−	1.35446i	0.0317926	−	0.0550664i
$606$		0			0
$607$	11.3288	+	19.6220i	0.459821	+	0.796434i	0.998951	−	0.0457886i	$-0.0145801\pi$
$607$	11.3288	+	19.6220i	0.459821	+	0.796434i	−0.539130	+	0.842223i	$0.681247\pi$
$608$		0			0
$609$	13.5517	−	8.17649i	0.549144	−	0.331328i
$610$		0			0
$611$	−9.63555	−	16.6893i	−0.389812	−	0.675175i
$612$		0			0
$613$	−14.5566	+	25.2129i	−0.587937	+	1.01834i	0.406565	+	0.913622i	$0.366727\pi$
$613$	−14.5566	+	25.2129i	−0.587937	+	1.01834i	−0.994502	+	0.104716i	$0.966607\pi$
$614$		0			0
$615$	−1.58038	−	3.56228i	−0.0637272	−	0.143645i
$616$		0			0
$617$	26.3830			1.06214			0.531070	−	0.847328i	$-0.321790\pi$
$617$	26.3830			1.06214			0.531070	+	0.847328i	$0.321790\pi$
$618$		0			0
$619$	1.18786	−	2.05743i	0.0477440	−	0.0826950i	−0.841166	−	0.540777i	$-0.818130\pi$
$619$	1.18786	−	2.05743i	0.0477440	−	0.0826950i	0.888910	+	0.458082i	$0.151464\pi$
$620$		0			0
$621$	−7.74727	+	4.47289i	−0.310887	+	0.179491i
$622$		0			0
$623$	17.9194	−	0.345587i	0.717926	−	0.0138456i
$624$		0			0
$625$	−9.99152	−	17.3058i	−0.399661	−	0.692233i
$626$		0			0
$627$	−5.04210	−	2.91106i	−0.201362	−	0.116257i
$628$		0			0
$629$			77.0908i			3.07381i
$630$		0			0
$631$	11.2459			0.447692			0.223846	−	0.974625i	$-0.428139\pi$
$631$	11.2459			0.447692			0.223846	+	0.974625i	$0.428139\pi$
$632$		0			0
$633$	−0.487045	+	0.843587i	−0.0193583	+	0.0335296i
$634$		0			0
$635$	−2.13964	−	3.70596i	−0.0849089	−	0.147067i
$636$		0			0
$637$	31.2014	−	19.6559i	1.23624	−	0.778796i
$638$		0			0
$639$	0.961241	−	0.554973i	0.0380261	−	0.0219544i
$640$		0			0
$641$	17.2431	+	9.95529i	0.681060	+	0.393210i	0.800254	−	0.599661i	$-0.204698\pi$
$641$	17.2431	+	9.95529i	0.681060	+	0.393210i	−0.119194	+	0.992871i	$0.538031\pi$
$642$		0			0
$643$		−	28.5171i		−	1.12460i	−0.826932	−	0.562302i	$-0.809916\pi$
$643$		−	28.5171i		−	1.12460i	0.826932	−	0.562302i	$-0.190084\pi$
$644$		0			0
$645$			4.06595i			0.160097i
$646$		0			0
$647$	−12.4912	+	21.6353i	−0.491078	+	0.850572i	−0.999947	−	0.0102720i	$-0.996730\pi$
$647$	−12.4912	+	21.6353i	−0.491078	+	0.850572i	0.508869	+	0.860844i	$0.330064\pi$
$648$		0			0
$649$	27.7022	−	15.9939i	1.08741	−	0.627814i
$650$		0			0
$651$	−0.946247	+	0.0182489i	−0.0370864	+	0.000715233i
$652$		0			0
$653$	22.6188	−	13.0590i	0.885141	−	0.511037i	0.0127912	−	0.999918i	$-0.495928\pi$
$653$	22.6188	−	13.0590i	0.885141	−	0.511037i	0.872350	+	0.488882i	$0.162595\pi$
$654$		0			0
$655$	5.59397	−	9.68904i	0.218574	−	0.378582i
$656$		0			0
$657$	−5.02195			−0.195925
$658$		0			0
$659$			14.3637i			0.559530i	0.960069	+	0.279765i	$0.0902565\pi$
$659$			14.3637i			0.559530i	−0.960069	+	0.279765i	$0.909744\pi$
$660$		0			0
$661$	5.48560	−	9.50134i	0.213365	−	0.369559i	−0.739400	−	0.673266i	$-0.764891\pi$
$661$	5.48560	−	9.50134i	0.213365	−	0.369559i	0.952766	+	0.303707i	$0.0982243\pi$
$662$		0			0
$663$	33.5153	−	19.3501i	1.30163	−	0.751494i
$664$		0			0
$665$	−1.21025	−	2.00588i	−0.0469316	−	0.0777845i
$666$		0			0
$667$	−8.70790	+	5.02751i	−0.337171	+	0.194666i
$668$		0			0
$669$	−16.7535	−	9.67263i	−0.647727	−	0.373966i
$670$		0			0
$671$		−	36.1712i		−	1.39637i
$672$		0			0
$673$			29.2345i			1.12691i	0.826148	+	0.563454i	$0.190528\pi$
$673$			29.2345i			1.12691i	−0.826148	+	0.563454i	$0.809472\pi$
$674$		0			0
$675$	−20.6364	−	11.9145i	−0.794297	−	0.458588i
$676$		0			0
$677$	−0.00843068	−	0.0146024i	−0.000324017	−	0.000561215i	0.865863	−	0.500281i	$-0.166770\pi$
$677$	−0.00843068	−	0.0146024i	−0.000324017	−	0.000561215i	−0.866187	+	0.499719i	$0.833436\pi$
$678$		0			0
$679$	17.6331	−	31.9486i	0.676694	−	1.22607i
$680$		0			0
$681$	5.48055	+	9.49259i	0.210015	+	0.363757i
$682$		0			0
$683$	27.5896	+	15.9289i	1.05569	+	0.609502i	0.924236	−	0.381821i	$-0.124703\pi$
$683$	27.5896	+	15.9289i	1.05569	+	0.609502i	0.131452	+	0.991323i	$0.458036\pi$
$684$		0			0
$685$		−	0.835333i		−	0.0319164i
$686$		0			0
$687$	7.00763			0.267358
$688$		0			0
$689$	−17.3405	+	30.0347i	−0.660622	+	1.14423i
$690$		0			0
$691$	−23.9978	+	13.8551i	−0.912918	+	0.527073i	−0.881369	−	0.472429i	$-0.843377\pi$
$691$	−23.9978	+	13.8551i	−0.912918	+	0.527073i	−0.0315489	+	0.999502i	$0.510044\pi$
$692$		0			0
$693$	−9.06593	+	16.4262i	−0.344386	+	0.623979i
$694$		0			0
$695$	3.60292	+	6.24044i	0.136667	+	0.236713i
$696$		0			0
$697$	44.9616	+	4.78584i	1.70304	+	0.181277i
$698$		0			0
$699$	8.38122			0.317007
$700$		0			0
$701$	−3.43510			−0.129742			−0.0648710	−	0.997894i	$-0.520664\pi$
$701$	−3.43510			−0.129742			−0.0648710	+	0.997894i	$0.520664\pi$
$702$		0			0
$703$	14.3093	+	8.26146i	0.539684	+	0.311587i
$704$		0			0
$705$	−1.11320	−	1.92813i	−0.0419257	−	0.0726174i
$706$		0			0
$707$	−11.4459	−	18.9705i	−0.430469	−	0.713460i
$708$		0			0
$709$	−32.6236	+	18.8352i	−1.22520	+	0.707372i	−0.966023	−	0.258457i	$-0.916786\pi$
$709$	−32.6236	+	18.8352i	−1.22520	+	0.707372i	−0.259181	+	0.965829i	$0.583453\pi$
$710$		0			0
$711$	−13.3976	−	7.73513i	−0.502451	−	0.290090i
$712$		0			0
$713$	0.601258			0.0225173
$714$		0			0
$715$	11.3966			0.426209
$716$		0			0
$717$	−4.32867	+	7.49748i	−0.161657	+	0.279998i
$718$		0			0
$719$	−11.3528	+	6.55453i	−0.423387	+	0.244443i	−0.696525	−	0.717532i	$-0.745272\pi$
$719$	−11.3528	+	6.55453i	−0.423387	+	0.244443i	0.273138	+	0.961975i	$0.411938\pi$
$720$		0			0
$721$	−0.350750	−	18.1871i	−0.0130626	−	0.677324i
$722$		0			0
$723$	−5.34268	+	3.08460i	−0.198696	+	0.114717i
$724$		0			0
$725$	−23.1953	−	13.3918i	−0.861451	−	0.497359i
$726$		0			0
$727$		−	37.5578i		−	1.39294i	−0.717586	−	0.696470i	$-0.754753\pi$
$727$		−	37.5578i		−	1.39294i	0.717586	−	0.696470i	$-0.245247\pi$
$728$		0			0
$729$	−15.1401			−0.560745
$730$		0			0
$731$	−40.8544	−	23.5873i	−1.51105	−	0.872407i
$732$		0			0
$733$	8.71153	+	15.0888i	0.321768	+	0.557318i	0.980853	−	0.194750i	$-0.0623897\pi$
$733$	8.71153	+	15.0888i	0.321768	+	0.557318i	−0.659085	+	0.752068i	$0.729056\pi$
$734$		0			0
$735$	3.60472	−	2.27087i	0.132962	−	0.0837622i
$736$		0			0
$737$	−12.3216	−	21.3416i	−0.453871	−	0.786128i
$738$		0			0
$739$	13.8677	−	24.0195i	0.510131	−	0.883572i	−0.489800	−	0.871835i	$-0.662930\pi$
$739$	13.8677	−	24.0195i	0.510131	−	0.883572i	0.999931	−	0.0117377i	$-0.00373630\pi$
$740$		0			0
$741$		−	8.29462i		−	0.304711i
$742$		0			0
$743$	18.1178			0.664676			0.332338	−	0.943160i	$-0.392163\pi$
$743$	18.1178			0.664676			0.332338	+	0.943160i	$0.392163\pi$
$744$		0			0
$745$	8.37553	+	4.83562i	0.306856	+	0.177163i
$746$		0			0
$747$	12.0347	+	20.8447i	0.440327	+	0.762669i
$748$		0			0
$749$	−0.296130	−	15.3550i	−0.0108204	−	0.561060i
$750$		0			0
$751$	−24.2287	+	13.9884i	−0.884118	+	0.510446i	−0.872014	−	0.489481i	$-0.837186\pi$
$751$	−24.2287	+	13.9884i	−0.884118	+	0.510446i	−0.0121037	+	0.999927i	$0.503853\pi$
$752$		0			0
$753$	−2.09172	−	1.20766i	−0.0762265	−	0.0440094i
$754$		0			0
$755$		−	1.35646i		−	0.0493667i
$756$		0			0
$757$		−	8.89388i		−	0.323254i	−0.986852	−	0.161627i	$-0.948326\pi$
$757$		−	8.89388i		−	0.323254i	0.986852	−	0.161627i	$-0.0516741\pi$
$758$		0			0
$759$	−3.36324	+	5.82531i	−0.122078	+	0.211445i
$760$		0			0
$761$	1.17287	+	2.03146i	0.0425163	+	0.0736405i	0.886500	−	0.462728i	$-0.153129\pi$
$761$	1.17287	+	2.03146i	0.0425163	+	0.0736405i	−0.843984	+	0.536368i	$0.819796\pi$
$762$		0			0
$763$	12.4138	+	20.5747i	0.449410	+	0.744853i
$764$		0			0
$765$	−6.86130	+	3.96137i	−0.248071	+	0.143224i
$766$		0			0
$767$	39.4666	+	22.7860i	1.42505	+	0.822756i
$768$		0			0
$769$	−33.5978			−1.21157			−0.605783	−	0.795630i	$-0.707140\pi$
$769$	−33.5978			−1.21157			−0.605783	+	0.795630i	$0.707140\pi$
$770$		0			0
$771$	−8.96060			−0.322708
$772$		0			0
$773$	19.9753	+	11.5328i	0.718463	+	0.414805i	0.814187	−	0.580603i	$-0.197183\pi$
$773$	19.9753	+	11.5328i	0.718463	+	0.414805i	−0.0957237	+	0.995408i	$0.530517\pi$
$774$		0			0
$775$	0.800786	+	1.38700i	0.0287651	+	0.0498226i
$776$		0			0
$777$	−14.5195	+	26.3074i	−0.520886	+	0.943772i
$778$		0			0
$779$	5.70666	−	7.83271i	0.204462	−	0.280636i
$780$		0			0
$781$	1.07008	−	1.85343i	0.0382905	−	0.0663210i
$782$		0			0
$783$	−29.4188			−1.05134
$784$		0			0
$785$			2.54129i			0.0907025i
$786$		0			0
$787$	3.16267	−	5.47791i	0.112737	−	0.195266i	−0.804136	−	0.594446i	$-0.797372\pi$
$787$	3.16267	−	5.47791i	0.112737	−	0.195266i	0.916873	+	0.399179i	$0.130705\pi$
$788$		0			0
$789$	−11.5749	−	20.0483i	−0.412077	−	0.713738i
$790$		0			0
$791$	7.93072	+	4.37712i	0.281984	+	0.155632i
$792$		0			0
$793$	44.6282	−	25.7661i	1.58479	−	0.914981i
$794$		0			0
$795$	−2.00337	+	3.46994i	−0.0710522	+	0.123066i
$796$		0			0
$797$	46.0158			1.62996			0.814982	−	0.579487i	$-0.196747\pi$
$797$	46.0158			1.62996			0.814982	+	0.579487i	$0.196747\pi$
$798$		0			0
$799$	25.8316			0.913855
$800$		0			0
$801$	−11.2507	−	6.49558i	−0.397523	−	0.229510i
$802$		0			0
$803$	−8.38586	+	4.84158i	−0.295930	+	0.170856i
$804$		0			0
$805$	−2.31745	+	1.39825i	−0.0816795	+	0.0492817i
$806$		0			0
$807$	−5.60010	+	3.23322i	−0.197133	+	0.113815i
$808$		0			0
$809$	−11.0256	−	6.36564i	−0.387640	−	0.223804i	0.293497	−	0.955960i	$-0.405181\pi$
$809$	−11.0256	−	6.36564i	−0.387640	−	0.223804i	−0.681137	+	0.732156i	$0.738514\pi$
$810$		0			0
$811$	−28.4308			−0.998342			−0.499171	−	0.866504i	$-0.666362\pi$
$811$	−28.4308			−0.998342			−0.499171	+	0.866504i	$0.666362\pi$
$812$		0			0
$813$		−	7.56791i		−	0.265418i
$814$		0			0
$815$	5.84996	−	10.1324i	0.204915	−	0.354923i
$816$		0			0
$817$	−8.75635	+	5.05548i	−0.306346	+	0.176869i
$818$		0			0
$819$	−26.7247	+	0.515402i	−0.933836	+	0.0180096i
$820$		0			0
$821$	15.1866	+	26.3039i	0.530014	+	0.918012i	0.999387	+	0.0350117i	$0.0111468\pi$
$821$	15.1866	+	26.3039i	0.530014	+	0.918012i	−0.469372	+	0.883000i	$0.655520\pi$
$822$		0			0
$823$	−34.8687	−	20.1314i	−1.21545	−	0.701738i	−0.251505	−	0.967856i	$-0.580926\pi$
$823$	−34.8687	−	20.1314i	−1.21545	−	0.701738i	−0.963941	+	0.266118i	$0.914259\pi$
$824$		0			0
$825$	−17.9174			−0.623803
$826$		0			0
$827$		−	24.0056i		−	0.834756i	−0.908733	−	0.417378i	$-0.862949\pi$
$827$		−	24.0056i		−	0.834756i	0.908733	−	0.417378i	$-0.137051\pi$
$828$		0			0
$829$	−26.1467	+	45.2874i	−0.908112	+	1.57290i	−0.0914267	+	0.995812i	$0.529143\pi$
$829$	−26.1467	+	45.2874i	−0.908112	+	1.57290i	−0.816685	+	0.577084i	$0.804191\pi$
$830$		0			0
$831$	−4.09313	+	2.36317i	−0.141989	+	0.0819775i
$832$		0			0
$833$	1.90588	+	49.3937i	0.0660349	+	1.71139i
$834$		0			0
$835$	5.11770	−	2.95470i	0.177105	−	0.102252i
$836$		0			0
$837$	1.52347	+	0.879575i	0.0526588	+	0.0304026i
$838$		0			0
$839$		−	12.2679i		−	0.423536i	−0.977320	−	0.211768i	$-0.932078\pi$
$839$		−	12.2679i		−	0.423536i	0.977320	−	0.211768i	$-0.0679221\pi$
$840$		0			0
$841$	−4.06661			−0.140228
$842$		0			0
$843$	−4.37610	+	7.57962i	−0.150721	+	0.261056i
$844$		0			0
$845$	4.31546	+	7.47459i	0.148456	+	0.257134i
$846$		0			0
$847$	0.136379	+	7.07156i	0.00468605	+	0.242982i
$848$		0			0
$849$	−18.6409	+	10.7624i	−0.639756	+	0.369363i
$850$		0			0
$851$	9.54474	−	16.5320i	0.327189	−	0.566709i
$852$		0			0
$853$	44.2232			1.51418			0.757088	−	0.653313i	$-0.226622\pi$
$853$	44.2232			1.51418			0.757088	+	0.653313i	$0.226622\pi$
$854$		0			0
$855$			1.69809i			0.0580734i
$856$		0			0
$857$	10.5558	−	18.2832i	0.360579	−	0.624542i	−0.627477	−	0.778635i	$-0.715912\pi$
$857$	10.5558	−	18.2832i	0.360579	−	0.624542i	0.988056	+	0.154093i	$0.0492457\pi$
$858$		0			0
$859$	3.85048	+	6.66923i	0.131377	+	0.227551i	0.924207	−	0.381891i	$-0.124727\pi$
$859$	3.85048	+	6.66923i	0.131377	+	0.227551i	−0.792831	+	0.609442i	$0.791394\pi$
$860$		0			0
$861$	14.4419	+	10.1014i	0.492177	+	0.344255i
$862$		0			0
$863$	−21.2174	−	36.7495i	−0.722247	−	1.25097i	−0.960097	−	0.279667i	$-0.909776\pi$
$863$	−21.2174	−	36.7495i	−0.722247	−	1.25097i	0.237850	−	0.971302i	$-0.423557\pi$
$864$		0			0
$865$	−6.95547	+	12.0472i	−0.236493	+	0.409618i
$866$		0			0
$867$			34.1896i			1.16114i
$868$		0			0
$869$	−29.8293			−1.01189
$870$		0			0
$871$	17.5542	−	30.4048i	0.594802	−	1.03023i
$872$		0			0
$873$	−22.9069	+	13.2253i	−0.775282	+	0.447609i
$874$		0			0
$875$	−13.0879	−	7.22346i	−0.442451	−	0.244198i
$876$		0			0
$877$	−8.73195	−	15.1242i	−0.294857	−	0.510707i	0.680095	−	0.733124i	$-0.261939\pi$
$877$	−8.73195	−	15.1242i	−0.294857	−	0.510707i	−0.974952	+	0.222417i	$0.928605\pi$
$878$		0			0
$879$	0.298638	−	0.517256i	0.0100728	−	0.0174466i
$880$		0			0
$881$	36.2007			1.21963			0.609816	−	0.792543i	$-0.291244\pi$
$881$	36.2007			1.21963			0.609816	+	0.792543i	$0.291244\pi$
$882$		0			0
$883$		−	39.5032i		−	1.32939i	−0.747115	−	0.664695i	$-0.768561\pi$
$883$		−	39.5032i		−	1.32939i	0.747115	−	0.664695i	$-0.231439\pi$
$884$		0			0
$885$	4.55961	+	2.63249i	0.153270	+	0.0884903i
$886$		0			0
$887$	−47.5877	+	27.4748i	−1.59784	+	0.922513i	−0.605937	+	0.795512i	$0.707202\pi$
$887$	−47.5877	+	27.4748i	−1.59784	+	0.922513i	−0.991903	+	0.127001i	$0.959465\pi$
$888$		0			0
$889$	16.9430	+	9.35118i	0.568251	+	0.313629i
$890$		0			0
$891$	1.38027	−	0.796899i	0.0462408	−	0.0266971i
$892$		0			0
$893$	2.76825	−	4.79475i	0.0926359	−	0.160450i
$894$		0			0
$895$			0.974322i			0.0325680i
$896$		0			0
$897$	−9.58305			−0.319969
$898$		0			0
$899$	1.71237	+	0.988639i	0.0571108	+	0.0329729i
$900$		0			0
$901$	−23.2438	−	40.2594i	−0.774363	−	1.34124i
$902$		0			0
$903$	−9.49912	−	15.7439i	−0.316111	−	0.523923i
$904$		0			0
$905$	1.54761	−	0.893516i	0.0514445	−	0.0297015i
$906$		0			0
$907$	−23.2387	+	40.2506i	−0.771628	+	1.33650i	0.165042	+	0.986286i	$0.447224\pi$
$907$	−23.2387	+	40.2506i	−0.771628	+	1.33650i	−0.936670	+	0.350212i	$0.886109\pi$
$908$		0			0
$909$			16.0596i			0.532664i
$910$		0			0
$911$	52.0452			1.72433			0.862167	−	0.506625i	$-0.169107\pi$
$911$	52.0452			1.72433			0.862167	+	0.506625i	$0.169107\pi$
$912$		0			0
$913$	40.1921	+	23.2049i	1.33017	+	0.767971i
$914$		0			0
$915$	5.15594	−	2.97678i	0.170450	−	0.0984094i
$916$		0			0
$917$	0.975583	+	50.5861i	0.0322166	+	1.67050i
$918$		0			0
$919$	23.2435	−	13.4196i	0.766731	−	0.442672i	−0.0649762	−	0.997887i	$-0.520697\pi$
$919$	23.2435	−	13.4196i	0.766731	−	0.442672i	0.831707	+	0.555214i	$0.187364\pi$
$920$		0			0
$921$	−5.17612	−	2.98844i	−0.170559	−	0.0984723i
$922$		0			0
$923$	3.04903			0.100360
$924$		0			0
$925$	50.8487			1.67190
$926$		0			0
$927$	−6.59262	+	11.4188i	−0.216530	+	0.375041i
$928$		0			0
$929$	−39.0869	+	22.5668i	−1.28240	+	0.740394i	−0.977287	−	0.211922i	$-0.932028\pi$
$929$	−39.0869	+	22.5668i	−1.28240	+	0.740394i	−0.305113	+	0.952316i	$0.598694\pi$
$930$		0			0
$931$	9.37250	+	4.93953i	0.307171	+	0.161887i
$932$		0			0
$933$	4.76227	+	8.24849i	0.155910	+	0.270043i
$934$		0			0
$935$	−7.63819	+	13.2297i	−0.249795	+	0.432658i
$936$		0			0
$937$			28.4963i			0.930933i	0.885066	+	0.465466i	$0.154113\pi$
$937$			28.4963i			0.930933i	−0.885066	+	0.465466i	$0.845887\pi$
$938$		0			0
$939$	−4.84319			−0.158051
$940$		0			0
$941$	6.54446	−	11.3353i	0.213343	−	0.369522i	−0.739415	−	0.673249i	$-0.764898\pi$
$941$	6.54446	−	11.3353i	0.213343	−	0.369522i	0.952759	+	0.303728i	$0.0982314\pi$
$942$		0			0
$943$	−9.04939	−	6.59309i	−0.294689	−	0.214700i
$944$		0			0
$945$	−7.91745	+	0.152693i	−0.257555	+	0.00496710i
$946$		0			0
$947$	−10.7983	−	18.7031i	−0.350896	−	0.607770i	0.635510	−	0.772092i	$-0.280790\pi$
$947$	−10.7983	−	18.7031i	−0.350896	−	0.607770i	−0.986407	+	0.164322i	$0.947456\pi$
$948$		0			0
$949$	−11.9471	−	6.89767i	−0.387820	−	0.223908i
$950$		0			0
$951$	−15.6473			−0.507398
$952$		0			0
$953$	−42.7433			−1.38459			−0.692295	−	0.721614i	$-0.743400\pi$
$953$	−42.7433			−1.38459			−0.692295	+	0.721614i	$0.743400\pi$
$954$		0			0
$955$	13.8206	+	7.97933i	0.447224	+	0.258205i
$956$		0			0
$957$	−19.1569	+	11.0603i	−0.619255	+	0.357527i
$958$		0			0
$959$	1.95156	+	3.23451i	0.0630190	+	0.104448i
$960$		0			0
$961$	15.4409	+	26.7444i	0.498093	+	0.862722i
$962$		0			0
$963$	−5.56601	+	9.64061i	−0.179362	+	0.310664i
$964$		0			0
$965$		−	11.0785i		−	0.356628i
$966$		0			0
$967$			36.6835i			1.17966i	0.807526	+	0.589831i	$0.200806\pi$
$967$			36.6835i			1.17966i	−0.807526	+	0.589831i	$0.799194\pi$
$968$		0			0
$969$	9.62879	+	5.55919i	0.309321	+	0.178587i
$970$		0			0
$971$	42.2893	−	24.4157i	1.35713	−	0.783539i	0.367893	−	0.929868i	$-0.380079\pi$
$971$	42.2893	−	24.4157i	1.35713	−	0.783539i	0.989236	+	0.146330i	$0.0467460\pi$
$972$		0			0
$973$	−28.5302	−	15.7464i	−0.914637	−	0.504806i
$974$		0			0
$975$	−12.7632	−	22.1065i	−0.408750	−	0.707975i
$976$		0			0
$977$	49.6851	+	28.6857i	1.58957	+	0.917736i	0.993378	+	0.114891i	$0.0366519\pi$
$977$	49.6851	+	28.6857i	1.58957	+	0.917736i	0.596188	+	0.802845i	$0.296681\pi$
$978$		0			0
$979$	−25.0491			−0.800573
$980$		0			0
$981$		−	17.4176i		−	0.556102i
$982$		0			0
$983$	8.20981	−	14.2198i	0.261852	−	0.453541i	−0.704882	−	0.709325i	$-0.749000\pi$
$983$	8.20981	−	14.2198i	0.261852	−	0.453541i	0.966734	+	0.255783i	$0.0823334\pi$
$984$		0			0
$985$	2.51989	+	4.36458i	0.0802904	+	0.139067i
$986$		0			0
$987$	8.81507	+	4.86521i	0.280587	+	0.154861i
$988$		0			0
$989$	5.84076	+	10.1165i	0.185725	+	0.321686i
$990$		0			0
$991$	−40.9544	−	23.6451i	−1.30096	−	0.751110i	−0.320391	−	0.947285i	$-0.603814\pi$
$991$	−40.9544	−	23.6451i	−1.30096	−	0.751110i	−0.980569	+	0.196175i	$0.937148\pi$
$992$		0			0
$993$	26.0498			0.826667
$994$		0			0
$995$		−	11.4310i		−	0.362388i
$996$		0			0
$997$	12.9347	+	7.46785i	0.409646	+	0.236509i	0.690638	−	0.723201i	$-0.257330\pi$
$997$	12.9347	+	7.46785i	0.409646	+	0.236509i	−0.280992	+	0.959710i	$0.590663\pi$
$998$		0			0
$999$	48.3690	−	27.9258i	1.53033	−	0.883534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.18	yes	56
7.2	even	3	inner	1148.2.r.a.737.11	yes	56
41.40	even	2	inner	1148.2.r.a.81.11	✓	56
287.163	even	6	inner	1148.2.r.a.737.18	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.11	✓	56	41.40	even	2	inner
1148.2.r.a.81.18	yes	56	1.1	even	1	trivial
1148.2.r.a.737.11	yes	56	7.2	even	3	inner
1148.2.r.a.737.18	yes	56	287.163	even	6	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)

\(f(q)\)	\(=\)	\(q+(0.900937 + 0.520156i) q^{3} +(-0.292521 - 0.506661i) q^{5} +(2.31637 + 1.27845i) q^{7} +(-0.958875 - 1.66082i) q^{9} +O(q^{10})\)	\(q+(0.900937 + 0.520156i) q^{3} +(-0.292521 - 0.506661i) q^{5} +(2.31637 + 1.27845i) q^{7} +(-0.958875 - 1.66082i) q^{9} +(-3.20234 - 1.84887i) q^{11} -5.26808i q^{13} -0.608626i q^{15} +(6.11543 + 3.53075i) q^{17} +(1.31072 - 0.756747i) q^{19} +(1.42191 + 2.35668i) q^{21} +(-0.874295 - 1.51432i) q^{23} +(2.32886 - 4.03371i) q^{25} -5.11600i q^{27} -5.75036i q^{29} +(-0.171926 + 0.297785i) q^{31} +(-1.92340 - 3.33143i) q^{33} +(-0.0298462 - 1.54759i) q^{35} +(5.45853 + 9.45446i) q^{37} +(2.74022 - 4.74620i) q^{39} +(5.85299 - 2.59664i) q^{41} -6.68054 q^{43} +(-0.560982 + 0.971650i) q^{45} +(3.16800 - 1.82904i) q^{47} +(3.73114 + 5.92272i) q^{49} +(3.67308 + 6.36196i) q^{51} +(-5.70126 - 3.29163i) q^{53} +2.16333i q^{55} +1.57451 q^{57} +(-4.32530 + 7.49164i) q^{59} +(4.89099 + 8.47144i) q^{61} +(-0.0978348 - 5.07295i) q^{63} +(-2.66913 + 1.54102i) q^{65} +(5.77152 + 3.33219i) q^{67} -1.81908i q^{69} +0.578775i q^{71} +(1.30933 - 2.26783i) q^{73} +(4.19632 - 2.42274i) q^{75} +(-5.05411 - 8.37670i) q^{77} +(6.98613 - 4.03344i) q^{79} +(-0.215510 + 0.373274i) q^{81} -12.5509 q^{83} -4.13127i q^{85} +(2.99108 - 5.18071i) q^{87} +(5.86660 - 3.38708i) q^{89} +(6.73497 - 12.2028i) q^{91} +(-0.309790 + 0.178857i) q^{93} +(-0.766829 - 0.442729i) q^{95} -13.7925i q^{97} +7.09135i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 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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