LMFDB - Embedded newform 441.2.bb.f.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.f.352.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80148 + 1.67153i) q^{2} +(0.301863 - 4.02808i) q^{4} +(-1.44677 + 3.68631i) q^{5} +(-0.227334 + 2.63597i) q^{7} +(3.12479 + 3.91837i) q^{8} +O(q^{10})$	\(q+(-1.80148 + 1.67153i) q^{2} +(0.301863 - 4.02808i) q^{4} +(-1.44677 + 3.68631i) q^{5} +(-0.227334 + 2.63597i) q^{7} +(3.12479 + 3.91837i) q^{8} +(-3.55545 - 9.05915i) q^{10} +(1.06785 + 0.329389i) q^{11} +(1.36425 + 5.97717i) q^{13} +(-3.99657 - 5.12865i) q^{14} +(-4.19044 - 0.631607i) q^{16} +(1.60512 - 1.09435i) q^{17} +(-0.748418 - 1.29630i) q^{19} +(14.4120 + 6.94045i) q^{20} +(-2.47431 + 1.19156i) q^{22} +(0.555137 + 0.378486i) q^{23} +(-7.83046 - 7.26560i) q^{25} +(-12.4487 - 8.48739i) q^{26} +(10.5492 + 1.71142i) q^{28} +(-7.67124 - 3.69428i) q^{29} +(-3.00183 + 5.19933i) q^{31} +(0.322912 - 0.220158i) q^{32} +(-1.06235 + 4.65447i) q^{34} +(-9.38808 - 4.65166i) q^{35} +(-0.418449 - 5.58382i) q^{37} +(3.51507 + 1.08426i) q^{38} +(-18.9652 + 5.84998i) q^{40} +(3.55547 + 4.45842i) q^{41} +(5.70555 - 7.15454i) q^{43} +(1.64915 - 4.20196i) q^{44} +(-1.63272 + 0.246093i) q^{46} +(6.09084 - 5.65147i) q^{47} +(-6.89664 - 1.19849i) q^{49} +26.2512 q^{50} +(24.4883 - 3.69102i) q^{52} +(-0.551467 + 7.35882i) q^{53} +(-2.75917 + 3.45989i) q^{55} +(-11.0391 + 7.34607i) q^{56} +(19.9947 - 6.16756i) q^{58} +(-3.84718 - 9.80244i) q^{59} +(-0.00728034 - 0.0971493i) q^{61} +(-3.28309 - 14.3842i) q^{62} +(1.67227 - 7.32668i) q^{64} +(-24.0074 - 3.61854i) q^{65} +(-2.54112 + 4.40135i) q^{67} +(-3.92360 - 6.79588i) q^{68} +(24.6879 - 7.31260i) q^{70} +(7.01623 - 3.37884i) q^{71} +(1.90751 + 1.76991i) q^{73} +(10.0874 + 9.35971i) q^{74} +(-5.44751 + 2.62338i) q^{76} +(-1.11102 + 2.73994i) q^{77} +(7.93102 + 13.7369i) q^{79} +(8.39090 - 14.5335i) q^{80} +(-13.8575 - 2.08868i) q^{82} +(-1.32427 + 5.80199i) q^{83} +(1.71188 + 7.50023i) q^{85} +(1.68058 + 22.4258i) q^{86} +(2.04615 + 5.21352i) q^{88} +(3.40745 - 1.05106i) q^{89} +(-16.0658 + 2.23730i) q^{91} +(1.69214 - 2.12188i) q^{92} +(-1.52593 + 20.3621i) q^{94} +(5.86134 - 0.883455i) q^{95} +2.91041 q^{97} +(14.4275 - 9.36890i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.80148	+	1.67153i	−1.27384	+	1.18195i	−0.300199	+	0.953877i	$0.597053\pi$
$2$	−1.80148	+	1.67153i	−1.27384	+	1.18195i	−0.973643	+	0.228076i	$0.926757\pi$
$3$		0			0
$3$		0			0
$4$	0.301863	−	4.02808i	0.150931	−	2.01404i
$5$	−1.44677	+	3.68631i	−0.647015	+	1.64857i	0.109024	+	0.994039i	$0.465228\pi$
$5$	−1.44677	+	3.68631i	−0.647015	+	1.64857i	−0.756038	+	0.654527i	$0.772868\pi$
$6$		0			0
$7$	−0.227334	+	2.63597i	−0.0859243	+	0.996302i
$7$	−0.227334	+	2.63597i	−0.0859243	+	0.996302i
$8$	3.12479	+	3.91837i	1.10478	+	1.38535i
$9$		0			0
$10$	−3.55545	−	9.05915i	−1.12433	−	2.86475i
$11$	1.06785	+	0.329389i	0.321970	+	0.0993146i	0.451527	−	0.892257i	$-0.350879\pi$
$11$	1.06785	+	0.329389i	0.321970	+	0.0993146i	−0.129557	+	0.991572i	$0.541356\pi$
$12$		0			0
$13$	1.36425	+	5.97717i	0.378375	+	1.65777i	0.702447	+	0.711737i	$0.252091\pi$
$13$	1.36425	+	5.97717i	0.378375	+	1.65777i	−0.324072	+	0.946033i	$0.605052\pi$
$14$	−3.99657	−	5.12865i	−1.06813	−	1.37069i
$15$		0			0
$16$	−4.19044	−	0.631607i	−1.04761	−	0.157902i
$17$	1.60512	−	1.09435i	0.389298	−	0.265419i	−0.352816	−	0.935693i	$-0.614776\pi$
$17$	1.60512	−	1.09435i	0.389298	−	0.265419i	0.742114	+	0.670274i	$0.233823\pi$
$18$		0			0
$19$	−0.748418	−	1.29630i	−0.171699	−	0.297391i	0.767315	−	0.641270i	$-0.221592\pi$
$19$	−0.748418	−	1.29630i	−0.171699	−	0.297391i	−0.939014	+	0.343879i	$0.888259\pi$
$20$	14.4120	+	6.94045i	3.22262	+	1.55193i
$21$		0			0
$22$	−2.47431	+	1.19156i	−0.527524	+	0.254042i
$23$	0.555137	+	0.378486i	0.115754	+	0.0789197i	0.619813	−	0.784749i	$-0.287208\pi$
$23$	0.555137	+	0.378486i	0.115754	+	0.0789197i	−0.504059	+	0.863669i	$0.668161\pi$
$24$		0			0
$25$	−7.83046	−	7.26560i	−1.56609	−	1.45312i
$26$	−12.4487	−	8.48739i	−2.44139	−	1.66451i
$27$		0			0
$28$	10.5492	+	1.71142i	1.99362	+	0.323428i
$29$	−7.67124	−	3.69428i	−1.42451	−	0.686010i	−0.446545	−	0.894761i	$-0.647346\pi$
$29$	−7.67124	−	3.69428i	−1.42451	−	0.686010i	−0.977969	+	0.208751i	$0.933060\pi$
$30$		0			0
$31$	−3.00183	+	5.19933i	−0.539145	+	0.933826i	0.459805	+	0.888020i	$0.347919\pi$
$31$	−3.00183	+	5.19933i	−0.539145	+	0.933826i	−0.998950	+	0.0458067i	$0.985414\pi$
$32$	0.322912	−	0.220158i	0.0570834	−	0.0389188i
$33$		0			0
$34$	−1.06235	+	4.65447i	−0.182192	+	0.798234i
$35$	−9.38808	−	4.65166i	−1.58688	−	0.786274i
$36$		0			0
$37$	−0.418449	−	5.58382i	−0.0687926	−	0.917974i	−0.919691	−	0.392643i	$-0.871561\pi$
$37$	−0.418449	−	5.58382i	−0.0687926	−	0.917974i	0.850898	−	0.525331i	$-0.176058\pi$
$38$	3.51507	+	1.08426i	0.570220	+	0.175889i
$39$		0			0
$40$	−18.9652	+	5.84998i	−2.99865	+	0.924962i
$41$	3.55547	+	4.45842i	0.555271	+	0.696288i	0.977676	−	0.210120i	$-0.0673853\pi$
$41$	3.55547	+	4.45842i	0.555271	+	0.696288i	−0.422405	+	0.906407i	$0.638814\pi$
$42$		0			0
$43$	5.70555	−	7.15454i	0.870089	−	1.09106i	−0.125009	−	0.992156i	$-0.539896\pi$
$43$	5.70555	−	7.15454i	0.870089	−	1.09106i	0.995097	−	0.0989009i	$-0.0315327\pi$
$44$	1.64915	−	4.20196i	0.248619	−	0.633470i
$45$		0			0
$46$	−1.63272	+	0.246093i	−0.240732	+	0.0362845i
$47$	6.09084	−	5.65147i	0.888440	−	0.824352i	−0.0968402	−	0.995300i	$-0.530874\pi$
$47$	6.09084	−	5.65147i	0.888440	−	0.824352i	0.985280	+	0.170948i	$0.0546831\pi$
$48$		0			0
$49$	−6.89664	−	1.19849i	−0.985234	−	0.171213i
$50$	26.2512			3.71247
$51$		0			0
$52$	24.4883	−	3.69102i	3.39592	−	0.511852i
$53$	−0.551467	+	7.35882i	−0.0757498	+	1.01081i	0.821765	+	0.569827i	$0.192990\pi$
$53$	−0.551467	+	7.35882i	−0.0757498	+	1.01081i	−0.897515	+	0.440984i	$0.854629\pi$
$54$		0			0
$55$	−2.75917	+	3.45989i	−0.372046	+	0.466531i
$56$	−11.0391	+	7.34607i	−1.47516	+	0.981660i
$57$		0			0
$58$	19.9947	−	6.16756i	2.62544	−	0.809840i
$59$	−3.84718	−	9.80244i	−0.500860	−	1.27617i	−0.928201	−	0.372079i	$-0.878645\pi$
$59$	−3.84718	−	9.80244i	−0.500860	−	1.27617i	0.427342	−	0.904090i	$-0.359450\pi$
$60$		0			0
$61$	−0.00728034	−	0.0971493i	−0.000932152	−	0.0124387i	0.996718	−	0.0809480i	$-0.0257948\pi$
$61$	−0.00728034	−	0.0971493i	−0.000932152	−	0.0124387i	−0.997650	+	0.0685093i	$0.978176\pi$
$62$	−3.28309	−	14.3842i	−0.416953	−	1.82679i
$63$		0			0
$64$	1.67227	−	7.32668i	0.209033	−	0.915834i
$65$	−24.0074	−	3.61854i	−2.97776	−	0.448825i
$66$		0			0
$67$	−2.54112	+	4.40135i	−0.310447	+	0.537710i	−0.978459	−	0.206440i	$-0.933812\pi$
$67$	−2.54112	+	4.40135i	−0.310447	+	0.537710i	0.668012	+	0.744150i	$0.267145\pi$
$68$	−3.92360	−	6.79588i	−0.475807	−	0.824122i
$69$		0			0
$70$	24.6879	−	7.31260i	2.95077	−	0.874023i
$71$	7.01623	−	3.37884i	0.832673	−	0.400994i	0.0315561	−	0.999502i	$-0.489954\pi$
$71$	7.01623	−	3.37884i	0.832673	−	0.400994i	0.801117	+	0.598508i	$0.204239\pi$
$72$		0			0
$73$	1.90751	+	1.76991i	0.223257	+	0.207152i	0.783869	−	0.620927i	$-0.213244\pi$
$73$	1.90751	+	1.76991i	0.223257	+	0.207152i	−0.560612	+	0.828079i	$0.689434\pi$
$74$	10.0874	+	9.35971i	1.17263	+	1.08804i
$75$		0			0
$76$	−5.44751	+	2.62338i	−0.624872	+	0.300922i
$77$	−1.11102	+	2.73994i	−0.126612	+	0.312246i
$78$		0			0
$79$	7.93102	+	13.7369i	0.892310	+	1.54553i	0.837099	+	0.547051i	$0.184250\pi$
$79$	7.93102	+	13.7369i	0.892310	+	1.54553i	0.0552103	+	0.998475i	$0.482417\pi$
$80$	8.39090	−	14.5335i	0.938131	−	1.62489i
$81$		0			0
$82$	−13.8575	−	2.08868i	−1.53031	−	0.230657i
$83$	−1.32427	+	5.80199i	−0.145357	+	0.636851i	0.848782	+	0.528743i	$0.177336\pi$
$83$	−1.32427	+	5.80199i	−0.145357	+	0.636851i	−0.994139	+	0.108108i	$0.965521\pi$
$84$		0			0
$85$	1.71188	+	7.50023i	0.185679	+	0.813515i
$86$	1.68058	+	22.4258i	0.181222	+	2.41824i
$87$		0			0
$88$	2.04615	+	5.21352i	0.218121	+	0.555763i
$89$	3.40745	−	1.05106i	0.361189	−	0.111412i	−0.108849	−	0.994058i	$-0.534716\pi$
$89$	3.40745	−	1.05106i	0.361189	−	0.111412i	0.470038	+	0.882646i	$0.344240\pi$
$90$		0			0
$91$	−16.0658	+	2.23730i	−1.68415	+	0.234533i
$92$	1.69214	−	2.12188i	0.176418	−	0.221221i
$93$		0			0
$94$	−1.52593	+	20.3621i	−0.157387	+	2.10019i
$95$	5.86134	−	0.883455i	0.601361	−	0.0906406i
$96$		0			0
$97$	2.91041			0.295508			0.147754	−	0.989024i	$-0.452796\pi$
$97$	2.91041			0.295508			0.147754	+	0.989024i	$0.452796\pi$
$98$	14.4275	−	9.36890i	1.45740	−	0.946402i
$99$		0			0
$100$	−31.6301	+	29.3485i	−3.16301	+	2.93485i
$101$	−9.61047	+	1.44855i	−0.956278	+	0.144136i	−0.608599	−	0.793478i	$-0.708268\pi$
$101$	−9.61047	+	1.44855i	−0.956278	+	0.144136i	−0.347679	+	0.937614i	$0.613030\pi$
$102$		0			0
$103$	−4.10790	+	10.4668i	−0.404764	+	1.03132i	0.572615	+	0.819824i	$0.305929\pi$
$103$	−4.10790	+	10.4668i	−0.404764	+	1.03132i	−0.977379	+	0.211497i	$0.932166\pi$
$104$	−19.1577	+	24.0231i	−1.87857	+	2.35565i
$105$		0			0
$106$	−11.3070	−	14.1786i	−1.09824	−	1.37715i
$107$	−3.23638	+	0.998290i	−0.312872	+	0.0965083i	−0.447215	−	0.894427i	$-0.647584\pi$
$107$	−3.23638	+	0.998290i	−0.312872	+	0.0965083i	0.134342	+	0.990935i	$0.457108\pi$
$108$		0			0
$109$	−3.30415	−	1.01919i	−0.316480	−	0.0976211i	0.132446	−	0.991190i	$-0.457717\pi$
$109$	−3.30415	−	1.01919i	−0.316480	−	0.0976211i	−0.448926	+	0.893569i	$0.648193\pi$
$110$	−0.812718	−	10.8450i	−0.0774896	−	1.03403i
$111$		0			0
$112$	2.61753	−	10.9023i	0.247333	−	1.03017i
$113$	−1.87031	+	8.19437i	−0.175944	+	0.770861i	0.807532	+	0.589824i	$0.200803\pi$
$113$	−1.87031	+	8.19437i	−0.175944	+	0.770861i	−0.983476	+	0.181038i	$0.942054\pi$
$114$		0			0
$115$	−2.19837	+	1.49882i	−0.204999	+	0.139766i
$116$	−17.1965	+	29.7852i	−1.59665	+	2.76548i
$117$		0			0
$118$	23.3157	+	11.2283i	2.14639	+	1.03365i
$119$	2.51977	+	4.47982i	0.230987	+	0.410665i
$120$		0			0
$121$	−8.05681	−	5.49304i	−0.732437	−	0.499367i
$122$	0.175504	+	0.162844i	0.0158894	+	0.0147432i
$123$		0			0
$124$	20.0371	+	13.6611i	1.79939	+	1.22680i
$125$	20.2727	−	9.76282i	1.81325	−	0.873213i
$126$		0			0
$127$	−2.42284	−	1.16678i	−0.214992	−	0.103535i	0.323288	−	0.946300i	$-0.395212\pi$
$127$	−2.42284	−	1.16678i	−0.214992	−	0.103535i	−0.538280	+	0.842766i	$0.680926\pi$
$128$	9.62504	+	16.6711i	0.850742	+	1.47353i
$129$		0			0
$130$	49.2975	−	33.6105i	4.32368	−	2.94784i
$131$	8.44498	+	1.27288i	0.737841	+	0.111212i	0.507201	−	0.861828i	$-0.330680\pi$
$131$	8.44498	+	1.27288i	0.737841	+	0.111212i	0.230640	+	0.973039i	$0.425918\pi$
$132$		0			0
$133$	3.58714	−	1.67811i	0.311045	−	0.145511i
$134$	−2.77921	−	12.1765i	−0.240087	−	1.05189i
$135$		0			0
$136$	9.30373	+	2.86982i	0.797789	+	0.246085i
$137$	4.56962	+	11.6432i	0.390409	+	0.994746i	0.982063	+	0.188554i	$0.0603800\pi$
$137$	4.56962	+	11.6432i	0.390409	+	0.994746i	−0.591654	+	0.806192i	$0.701525\pi$
$138$		0			0
$139$	−0.555454	−	0.696517i	−0.0471130	−	0.0590778i	0.757717	−	0.652584i	$-0.226315\pi$
$139$	−0.555454	−	0.696517i	−0.0471130	−	0.0590778i	−0.804830	+	0.593506i	$0.797743\pi$
$140$	−21.5711	+	36.4117i	−1.82309	+	3.07735i
$141$		0			0
$142$	−6.99179	+	17.8148i	−0.586738	+	1.49498i
$143$	−0.511996	+	6.83211i	−0.0428153	+	0.571330i
$144$		0			0
$145$	24.7168	−	22.9338i	2.05261	−	1.90455i
$146$	−6.39480			−0.529237
$147$		0			0
$148$	−22.6184			−1.85922
$149$	11.3503	−	10.5315i	0.929852	−	0.862777i	−0.0609436	−	0.998141i	$-0.519411\pi$
$149$	11.3503	−	10.5315i	0.929852	−	0.862777i	0.990796	+	0.135364i	$0.0432205\pi$
$150$		0			0
$151$	−1.02647	+	13.6973i	−0.0835327	+	1.11467i	0.785153	+	0.619302i	$0.212585\pi$
$151$	−1.02647	+	13.6973i	−0.0835327	+	1.11467i	−0.868685	+	0.495364i	$0.835035\pi$
$152$	2.74072	−	6.98324i	0.222302	−	0.566416i
$153$		0			0
$154$	−2.57843	−	6.79307i	−0.207776	−	0.547401i
$155$	−14.8234	−	18.5879i	−1.19064	−	1.49302i
$156$		0			0
$157$	−3.70786	−	9.44746i	−0.295919	−	0.753990i	−0.999077	−	0.0429558i	$-0.986323\pi$
$157$	−3.70786	−	9.44746i	−0.295919	−	0.753990i	0.703158	−	0.711034i	$-0.251773\pi$
$158$	−37.2494	−	11.4899i	−2.96340	−	0.914088i
$159$		0			0
$160$	0.344390	+	1.50887i	0.0272264	+	0.119287i
$161$	−1.12388	+	1.37728i	−0.0885740	+	0.108545i
$162$		0			0
$163$	−9.04469	−	1.36327i	−0.708435	−	0.106779i	−0.215066	−	0.976600i	$-0.568997\pi$
$163$	−9.04469	−	1.36327i	−0.708435	−	0.106779i	−0.493369	+	0.869820i	$0.664235\pi$
$164$	19.0321	−	12.9759i	1.48616	−	1.01325i
$165$		0			0
$166$	−7.31258	−	12.6658i	−0.567566	−	0.983053i
$167$	15.7437	+	7.58177i	1.21828	+	0.586695i	0.928833	−	0.370498i	$-0.120813\pi$
$167$	15.7437	+	7.58177i	1.21828	+	0.586695i	0.289451	+	0.957193i	$0.406527\pi$
$168$		0			0
$169$	−22.1528	+	10.6682i	−1.70406	+	0.820633i
$170$	−15.6208	−	10.6501i	−1.19806	−	0.816825i
$171$		0			0
$172$	−27.0967	−	25.1421i	−2.06611	−	1.91707i
$173$	9.88737	+	6.74109i	0.751722	+	0.512516i	0.877520	−	0.479540i	$-0.159197\pi$
$173$	9.88737	+	6.74109i	0.751722	+	0.512516i	−0.125797	+	0.992056i	$0.540149\pi$
$174$		0			0
$175$	20.9320	−	18.9891i	1.58231	−	1.43544i
$176$	−4.26673	−	2.05475i	−0.321617	−	0.154883i
$177$		0			0
$178$	−4.38159	+	7.58913i	−0.328414	+	0.568829i
$179$	6.74670	−	4.59982i	0.504272	−	0.343807i	−0.284314	−	0.958731i	$-0.591766\pi$
$179$	6.74670	−	4.59982i	0.504272	−	0.343807i	0.788586	+	0.614924i	$0.210813\pi$
$180$		0			0
$181$	−0.492264	+	2.15675i	−0.0365897	+	0.160310i	−0.989922	−	0.141613i	$-0.954771\pi$
$181$	−0.492264	+	2.15675i	−0.0365897	+	0.160310i	0.953332	+	0.301923i	$0.0976284\pi$
$182$	25.2025	−	30.8849i	1.86813	−	2.28934i
$183$		0			0
$184$	0.251641	+	3.35792i	0.0185512	+	0.247549i
$185$	21.1891	+	6.53596i	1.55785	+	0.480533i
$186$		0			0
$187$	2.07450	−	0.639898i	0.151702	−	0.0467940i
$188$	−20.9260	−	26.2403i	−1.52618	−	1.91377i
$189$		0			0
$190$	−9.08239	+	11.3890i	−0.658906	+	0.826242i
$191$	−8.86560	+	22.5892i	−0.641492	+	1.63450i	0.124935	+	0.992165i	$0.460128\pi$
$191$	−8.86560	+	22.5892i	−0.641492	+	1.63450i	−0.766428	+	0.642331i	$0.777968\pi$
$192$		0			0
$193$	12.8085	−	1.93057i	0.921976	−	0.138966i	0.329133	−	0.944284i	$-0.393244\pi$
$193$	12.8085	−	1.93057i	0.921976	−	0.138966i	0.592843	+	0.805318i	$0.298005\pi$
$194$	−5.24306	+	4.86485i	−0.376430	+	0.349276i
$195$		0			0
$196$	−6.90945	+	27.4184i	−0.493532	+	1.95846i
$197$	−12.3748			−0.881665			−0.440832	−	0.897589i	$-0.645317\pi$
$197$	−12.3748			−0.881665			−0.440832	+	0.897589i	$0.645317\pi$
$198$		0			0
$199$	22.4878	−	3.38949i	1.59412	−	0.240274i	0.708850	−	0.705360i	$-0.249214\pi$
$199$	22.4878	−	3.38949i	1.59412	−	0.240274i	0.885266	+	0.465085i	$0.153976\pi$
$200$	4.00074	−	53.3861i	0.282895	−	3.77497i
$201$		0			0
$202$	14.8918	−	18.6738i	1.04779	−	1.31388i
$203$	11.4819	−	19.3813i	0.805873	−	1.36030i
$204$		0			0
$205$	−21.5790	+	6.65625i	−1.50715	+	0.464893i
$206$	−10.0952	−	25.7222i	−0.703368	−	1.79215i
$207$		0			0
$208$	−1.94158	−	25.9086i	−0.134625	−	1.79644i
$209$	−0.372214	−	1.63078i	−0.0257466	−	0.112803i
$210$		0			0
$211$	−0.904470	+	3.96274i	−0.0622663	+	0.272807i	−0.996472	−	0.0839290i	$-0.973253\pi$
$211$	−0.904470	+	3.96274i	−0.0622663	+	0.272807i	0.934205	+	0.356735i	$0.116110\pi$
$212$	29.4754	+	4.44270i	2.02438	+	0.305126i
$213$		0			0
$214$	4.16161	−	7.20811i	0.284482	−	0.492736i
$215$	18.1192	+	31.3834i	1.23572	+	2.14033i
$216$		0			0
$217$	−13.0228	−	9.09471i	−0.884047	−	0.617389i
$218$	7.65599	−	3.68693i	0.518529	−	0.249710i
$219$		0			0
$220$	13.1038	+	12.1585i	0.883458	+	0.819729i
$221$	8.73091	+	8.10110i	0.587304	+	0.544939i
$222$		0			0
$223$	3.91788	−	1.88675i	0.262360	−	0.126346i	−0.298080	−	0.954541i	$-0.596346\pi$
$223$	3.91788	−	1.88675i	0.262360	−	0.126346i	0.560440	+	0.828195i	$0.310632\pi$
$224$	0.506920	+	0.901235i	0.0338700	+	0.0602163i
$225$		0			0
$226$	−10.3278	−	17.8883i	−0.686997	−	1.18991i
$227$	−2.58110	+	4.47060i	−0.171314	+	0.296724i	−0.938879	−	0.344246i	$-0.888135\pi$
$227$	−2.58110	+	4.47060i	−0.171314	+	0.296724i	0.767566	+	0.640970i	$0.221468\pi$
$228$		0			0
$229$	−16.9009	−	2.54740i	−1.11684	−	0.168337i	−0.435420	−	0.900227i	$-0.643400\pi$
$229$	−16.9009	−	2.54740i	−1.11684	−	0.168337i	−0.681422	+	0.731890i	$0.738638\pi$
$230$	1.45500	−	6.37475i	0.0959396	−	0.420339i
$231$		0			0
$232$	−9.49552	−	41.6026i	−0.623411	−	2.73134i
$233$	−1.66511	−	22.2193i	−0.109085	−	1.45563i	−0.736230	−	0.676732i	$-0.763396\pi$
$233$	−1.66511	−	22.2193i	−0.109085	−	1.45563i	0.627145	−	0.778903i	$-0.284223\pi$
$234$		0			0
$235$	12.0210	+	30.6291i	0.784165	+	1.99802i
$236$	−40.6463	+	12.5377i	−2.64585	+	0.816136i
$237$		0			0
$238$	−12.0275	−	3.85844i	−0.779628	−	0.250106i
$239$	2.78115	−	3.48745i	0.179897	−	0.225584i	−0.683704	−	0.729760i	$-0.739632\pi$
$239$	2.78115	−	3.48745i	0.179897	−	0.225584i	0.863601	+	0.504175i	$0.168203\pi$
$240$		0			0
$241$	−0.830372	+	11.0805i	−0.0534889	+	0.713760i	0.904412	+	0.426661i	$0.140310\pi$
$241$	−0.830372	+	11.0805i	−0.0534889	+	0.713760i	−0.957901	+	0.287100i	$0.907309\pi$
$242$	23.6960	−	3.57160i	1.52324	−	0.229591i
$243$		0			0
$244$	−0.393523			−0.0251927
$245$	14.3958	−	23.6892i	0.919717	−	1.51345i
$246$		0			0
$247$	6.72717	−	6.24190i	0.428039	−	0.397163i
$248$	−29.7530	+	4.48454i	−1.88932	+	0.284768i
$249$		0			0
$250$	−20.2021	+	51.4741i	−1.27769	+	3.25551i
$251$	−3.85326	+	4.83183i	−0.243215	+	0.304982i	−0.888424	−	0.459024i	$-0.848199\pi$
$251$	−3.85326	+	4.83183i	−0.243215	+	0.304982i	0.645208	+	0.764007i	$0.276771\pi$
$252$		0			0
$253$	0.468136	+	0.587023i	0.0294314	+	0.0369058i
$254$	6.31501	−	1.94792i	0.396239	−	0.122224i
$255$		0			0
$256$	−30.8432	−	9.51386i	−1.92770	−	0.594616i
$257$	−0.696609	−	9.29560i	−0.0434533	−	0.579843i	−0.975855	−	0.218420i	$-0.929910\pi$
$257$	−0.696609	−	9.29560i	−0.0434533	−	0.579843i	0.932402	−	0.361424i	$-0.117709\pi$
$258$		0			0
$259$	14.8139	+	0.166375i	0.920490	+	0.0103381i
$260$	−21.8227	+	95.6115i	−1.35339	+	5.92957i
$261$		0			0
$262$	−17.3412	+	11.8230i	−1.07134	+	0.730427i
$263$	−0.780251	+	1.35143i	−0.0481123	+	0.0833330i	−0.889079	−	0.457754i	$-0.848654\pi$
$263$	−0.780251	+	1.35143i	−0.0481123	+	0.0833330i	0.840966	+	0.541087i	$0.181987\pi$
$264$		0			0
$265$	−26.3290	−	12.6794i	−1.61738	−	0.778888i
$266$	−3.65716	+	9.01912i	−0.224235	+	0.552998i
$267$		0			0
$268$	16.9619	+	11.5644i	1.03611	+	0.706409i
$269$	−2.94561	−	2.73313i	−0.179597	−	0.166642i	0.585252	−	0.810852i	$-0.300996\pi$
$269$	−2.94561	−	2.73313i	−0.179597	−	0.166642i	−0.764849	+	0.644210i	$0.777186\pi$
$270$		0			0
$271$	−6.01752	−	4.10268i	−0.365539	−	0.249220i	0.366596	−	0.930380i	$-0.380523\pi$
$271$	−6.01752	−	4.10268i	−0.365539	−	0.249220i	−0.732134	+	0.681160i	$0.761476\pi$
$272$	−7.41735	+	3.57201i	−0.449743	+	0.216585i
$273$		0			0
$274$	−27.6941	−	13.3368i	−1.67306	−	0.805704i
$275$	−5.96857	−	10.3379i	−0.359918	−	0.623397i
$276$		0			0
$277$	−5.34365	+	3.64324i	−0.321069	+	0.218901i	−0.713119	−	0.701043i	$-0.752718\pi$
$277$	−5.34365	+	3.64324i	−0.321069	+	0.218901i	0.392051	+	0.919944i	$0.371766\pi$
$278$	2.16489	+	0.326305i	0.129842	+	0.0195705i
$279$		0			0
$280$	−11.1089	−	51.3214i	−0.663884	−	3.06704i
$281$	−3.59513	−	15.7513i	−0.214468	−	0.939644i	−0.961489	−	0.274844i	$-0.911374\pi$
$281$	−3.59513	−	15.7513i	−0.214468	−	0.939644i	0.747021	−	0.664800i	$-0.231483\pi$
$282$		0			0
$283$	0.536915	+	0.165616i	0.0319163	+	0.00984487i	0.310672	−	0.950517i	$-0.399446\pi$
$283$	0.536915	+	0.165616i	0.0319163	+	0.00984487i	−0.278756	+	0.960362i	$0.589922\pi$
$284$	−11.4923	−	29.2818i	−0.681941	−	1.73756i
$285$		0			0
$286$	−10.4978	−	13.1638i	−0.620745	−	0.778390i
$287$	−12.5605	+	8.35855i	−0.741424	+	0.493389i
$288$		0			0
$289$	−4.83200	+	12.3117i	−0.284235	+	0.724219i
$290$	−6.19224	+	82.6297i	−0.363621	+	4.85219i
$291$		0			0
$292$	7.70512	−	7.14931i	0.450908	−	0.418382i
$293$	−9.62152			−0.562095			−0.281047	−	0.959694i	$-0.590682\pi$
$293$	−9.62152			−0.562095			−0.281047	+	0.959694i	$0.590682\pi$
$294$		0			0
$295$	41.7008			2.42791
$296$	20.5719	−	19.0879i	1.19572	−	1.10946i
$297$		0			0
$298$	−2.84357	+	37.9448i	−0.164724	+	2.19808i
$299$	−1.50493	+	3.83450i	−0.0870323	+	0.221755i
$300$		0			0
$301$	17.5620	+	16.6661i	1.01226	+	0.960619i
$302$	−21.0463	−	26.3912i	−1.21108	−	1.51864i
$303$		0			0
$304$	2.31745	+	5.90477i	0.132915	+	0.338662i
$305$	0.368655	+	0.113715i	0.0211091	+	0.00651131i
$306$		0			0
$307$	5.76446	+	25.2558i	0.328995	+	1.44142i	0.821049	+	0.570858i	$0.193389\pi$
$307$	5.76446	+	25.2558i	0.328995	+	1.44142i	−0.492054	+	0.870565i	$0.663754\pi$
$308$	10.7013	+	5.30235i	0.609765	+	0.302130i
$309$		0			0
$310$	57.7743	+	8.70808i	3.28136	+	0.494586i
$311$	−26.3564	+	17.9695i	−1.49453	+	1.01896i	−0.506932	+	0.861986i	$0.669220\pi$
$311$	−26.3564	+	17.9695i	−1.49453	+	1.01896i	−0.987603	+	0.156970i	$0.949827\pi$
$312$		0			0
$313$	−14.5255	−	25.1589i	−0.821028	−	1.42206i	−0.904917	−	0.425587i	$-0.860068\pi$
$313$	−14.5255	−	25.1589i	−0.821028	−	1.42206i	0.0838893	−	0.996475i	$-0.473266\pi$
$314$	22.4714	+	10.8217i	1.26813	+	0.610701i
$315$		0			0
$316$	57.7275	−	27.8001i	3.24742	−	1.56388i
$317$	2.67767	+	1.82561i	0.150393	+	0.102536i	0.636179	−	0.771542i	$-0.280514\pi$
$317$	2.67767	+	1.82561i	0.150393	+	0.102536i	−0.485786	+	0.874078i	$0.661466\pi$
$318$		0			0
$319$	−6.97491	−	6.47177i	−0.390520	−	0.362350i
$320$	24.5890	+	16.7645i	1.37457	+	0.937164i
$321$		0			0
$322$	−0.277520	−	4.35975i	−0.0154656	−	0.242959i
$323$	−2.61991	−	1.26168i	−0.145775	−	0.0702018i
$324$		0			0
$325$	32.7451	−	56.7161i	1.81637	−	3.14604i
$326$	18.5726	−	12.6626i	1.02864	−	0.701316i
$327$		0			0
$328$	−6.35961	+	27.8633i	−0.351151	+	1.53849i
$329$	13.5124	+	17.3400i	0.744964	+	0.955986i
$330$		0			0
$331$	−1.71636	−	22.9032i	−0.0943395	−	1.25887i	−0.820620	−	0.571474i	$-0.806372\pi$
$331$	−1.71636	−	22.9032i	−0.0943395	−	1.25887i	0.726280	−	0.687399i	$-0.241247\pi$
$332$	22.9711	+	7.08565i	1.26070	+	0.388876i
$333$		0			0
$334$	−41.0352	+	12.6577i	−2.24535	+	0.692598i
$335$	−12.5483	−	15.7351i	−0.685587	−	0.859699i
$336$		0			0
$337$	3.65854	−	4.58767i	0.199294	−	0.249906i	−0.672135	−	0.740429i	$-0.734623\pi$
$337$	3.65854	−	4.58767i	0.199294	−	0.249906i	0.871429	+	0.490522i	$0.163194\pi$
$338$	22.0756	−	56.2478i	1.20076	−	3.05948i
$339$		0			0
$340$	30.7283	−	4.63154i	1.66647	−	0.251180i
$341$	−4.91812	+	4.56335i	−0.266331	+	0.247119i
$342$		0			0
$343$	4.72703	−	17.9068i	0.255235	−	0.966879i
$344$	45.8628			2.47275
$345$		0			0
$346$	−29.0799	+	4.38309i	−1.56334	+	0.235636i
$347$	−0.722235	+	9.63755i	−0.0387716	+	0.517371i	0.943681	+	0.330857i	$0.107338\pi$
$347$	−0.722235	+	9.63755i	−0.0387716	+	0.517371i	−0.982452	+	0.186514i	$0.940281\pi$
$348$		0			0
$349$	8.54502	−	10.7151i	0.457404	−	0.573567i	−0.498632	−	0.866814i	$-0.666164\pi$
$349$	8.54502	−	10.7151i	0.457404	−	0.573567i	0.956037	+	0.293247i	$0.0947357\pi$
$350$	−5.96779	+	69.1972i	−0.318992	+	3.69874i
$351$		0			0
$352$	0.417341	−	0.128733i	0.0222443	−	0.00686147i
$353$	11.1668	+	28.4526i	0.594349	+	1.51438i	0.838646	+	0.544677i	$0.183348\pi$
$353$	11.1668	+	28.4526i	0.594349	+	1.51438i	−0.244297	+	0.969701i	$0.578557\pi$
$354$		0			0
$355$	2.30457	+	30.7524i	0.122314	+	1.63217i
$356$	−3.20516	−	14.0427i	−0.169873	−	0.744264i
$357$		0			0
$358$	−4.46532	+	19.5638i	−0.235999	+	1.03398i
$359$	3.96125	+	0.597062i	0.209067	+	0.0315117i	0.252740	−	0.967534i	$-0.418668\pi$
$359$	3.96125	+	0.597062i	0.209067	+	0.0315117i	−0.0436738	+	0.999046i	$0.513906\pi$
$360$		0			0
$361$	8.37974	−	14.5141i	0.441039	−	0.763902i
$362$	−2.71827	−	4.70819i	−0.142869	−	0.247457i
$363$		0			0
$364$	4.16237	+	65.3895i	0.218167	+	3.42734i
$365$	−9.28414	+	4.47101i	−0.485954	+	0.234023i
$366$		0			0
$367$	8.23426	+	7.64028i	0.429825	+	0.398819i	0.865198	−	0.501431i	$-0.167193\pi$
$367$	8.23426	+	7.64028i	0.429825	+	0.398819i	−0.435373	+	0.900250i	$0.643383\pi$
$368$	−2.08721	−	1.93665i	−0.108803	−	0.100955i
$369$		0			0
$370$	−49.0969	+	23.6438i	−2.55242	+	1.22918i
$371$	−19.2722	−	3.12656i	−1.00056	−	0.162323i
$372$		0			0
$373$	−7.77070	−	13.4592i	−0.402351	−	0.696893i	0.591658	−	0.806189i	$-0.298474\pi$
$373$	−7.77070	−	13.4592i	−0.402351	−	0.696893i	−0.994009	+	0.109296i	$0.965140\pi$
$374$	−2.66757	+	4.62036i	−0.137937	+	0.238913i
$375$		0			0
$376$	41.1771	+	6.20645i	2.12355	+	0.320073i
$377$	11.6158	−	50.8923i	0.598245	−	2.62108i
$378$		0			0
$379$	7.50971	+	32.9022i	0.385748	+	1.69007i	0.679082	+	0.734062i	$0.262378\pi$
$379$	7.50971	+	32.9022i	0.385748	+	1.69007i	−0.293334	+	0.956010i	$0.594765\pi$
$380$	−1.78930	−	23.8766i	−0.0917894	−	1.22484i
$381$		0			0
$382$	−21.7873	−	55.5132i	−1.11474	−	2.84030i
$383$	26.8145	−	8.27117i	1.37016	−	0.422637i	0.479590	−	0.877492i	$-0.340785\pi$
$383$	26.8145	−	8.27117i	1.37016	−	0.422637i	0.890565	+	0.454855i	$0.150309\pi$
$384$		0			0
$385$	−8.49289	−	8.05962i	−0.432838	−	0.410756i
$386$	−19.8473	+	24.8877i	−1.01020	+	1.26675i
$387$		0			0
$388$	0.878545	−	11.7234i	0.0446013	−	0.595164i
$389$	−25.4124	+	3.83030i	−1.28846	+	0.194204i	−0.757300	−	0.653067i	$-0.773482\pi$
$389$	−25.4124	+	3.83030i	−1.28846	+	0.194204i	−0.531160	+	0.847271i	$0.678244\pi$
$390$		0			0
$391$	1.30526			0.0660097
$392$	−16.8544	−	30.7686i	−0.851278	−	1.55405i
$393$		0			0
$394$	22.2929	−	20.6848i	1.12310	−	1.04209i
$395$	−62.1129	+	9.36201i	−3.12524	+	0.471054i
$396$		0			0
$397$	−6.39914	+	16.3047i	−0.321164	+	0.818311i	0.675551	+	0.737314i	$0.263906\pi$
$397$	−6.39914	+	16.3047i	−0.321164	+	0.818311i	−0.996714	+	0.0809979i	$0.974189\pi$
$398$	−34.8457	+	43.6952i	−1.74666	+	2.19024i
$399$		0			0
$400$	28.2241	+	35.3919i	1.41120	+	1.76959i
$401$	−16.3375	+	5.03944i	−0.815854	+	0.251658i	−0.674475	−	0.738298i	$-0.735630\pi$
$401$	−16.3375	+	5.03944i	−0.815854	+	0.251658i	−0.141379	+	0.989956i	$0.545154\pi$
$402$		0			0
$403$	−35.1725	−	10.8493i	−1.75207	−	0.540441i
$404$	2.93381	+	39.1490i	0.145962	+	1.94773i
$405$		0			0
$406$	11.7120	+	54.1075i	0.581256	+	2.68531i
$407$	1.39241	−	6.10053i	0.0690191	−	0.302392i
$408$		0			0
$409$	−3.84806	+	2.62356i	−0.190274	+	0.129727i	−0.654710	−	0.755880i	$-0.727209\pi$
$409$	−3.84806	+	2.62356i	−0.190274	+	0.129727i	0.464436	+	0.885607i	$0.346257\pi$
$410$	27.7482	−	48.0612i	1.37038	−	2.37357i
$411$		0			0
$412$	40.9209	+	19.7065i	2.01603	+	0.970868i
$413$	26.7135	−	7.91259i	1.31449	−	0.389353i
$414$		0			0
$415$	−19.4720	−	13.2758i	−0.955844	−	0.651683i
$416$	1.75645	+	1.62975i	0.0861173	+	0.0799051i
$417$		0			0
$418$	3.39644	+	2.31565i	0.166125	+	0.113262i
$419$	−6.16214	+	2.96753i	−0.301040	+	0.144973i	−0.578306	−	0.815820i	$-0.696286\pi$
$419$	−6.16214	+	2.96753i	−0.301040	+	0.144973i	0.277266	+	0.960793i	$0.410572\pi$
$420$		0			0
$421$	31.1198	+	14.9865i	1.51669	+	0.730398i	0.992618	−	0.121279i	$-0.0386996\pi$
$421$	31.1198	+	14.9865i	1.51669	+	0.730398i	0.524068	+	0.851677i	$0.324414\pi$
$422$	−4.99447	−	8.65067i	−0.243127	−	0.421108i
$423$		0			0
$424$	−30.5578	+	20.8339i	−1.48402	+	1.01178i
$425$	−20.5199	−	3.09288i	−0.995363	−	0.150027i
$426$		0			0
$427$	0.257737	+	0.00289466i	0.0124728	+	0.000140082i
$428$	3.04425	+	13.3377i	0.147149	+	0.644703i
$429$		0			0
$430$	−85.0998	−	26.2498i	−4.10388	−	1.26588i
$431$	4.61149	+	11.7499i	0.222128	+	0.565972i	0.997881	−	0.0650643i	$-0.0207253\pi$
$431$	4.61149	+	11.7499i	0.222128	+	0.565972i	−0.775754	+	0.631036i	$0.782630\pi$
$432$		0			0
$433$	10.3481	+	12.9762i	0.497300	+	0.623594i	0.965618	−	0.259966i	$-0.0837113\pi$
$433$	10.3481	+	12.9762i	0.497300	+	0.623594i	−0.468318	+	0.883560i	$0.655140\pi$
$434$	38.6625	−	5.38411i	1.85586	−	0.258445i
$435$		0			0
$436$	−5.10279	+	13.0017i	−0.244379	+	0.622668i
$437$	0.0751561	−	1.00289i	0.00359520	−	0.0479747i
$438$		0			0
$439$	21.7632	−	20.1933i	1.03870	−	0.963772i	0.0393284	−	0.999226i	$-0.487478\pi$
$439$	21.7632	−	20.1933i	1.03870	−	0.963772i	0.999371	+	0.0354539i	$0.0112877\pi$
$440$	−22.1789			−1.05734
$441$		0			0
$442$	−29.2699			−1.39223
$443$	−14.1257	+	13.1067i	−0.671131	+	0.622719i	−0.940289	−	0.340377i	$-0.889445\pi$
$443$	−14.1257	+	13.1067i	−0.671131	+	0.622719i	0.269158	+	0.963096i	$0.413255\pi$
$444$		0			0
$445$	−1.05527	+	14.0815i	−0.0500244	+	0.667529i
$446$	−3.90423	+	9.94781i	−0.184871	+	0.471043i
$447$		0			0
$448$	18.9327	+	6.07364i	0.894486	+	0.286953i
$449$	1.84997	+	2.31978i	0.0873053	+	0.109477i	0.823566	−	0.567221i	$-0.191982\pi$
$449$	1.84997	+	2.31978i	0.0873053	+	0.109477i	−0.736260	+	0.676698i	$0.763410\pi$
$450$		0			0
$451$	2.32817	+	5.93207i	0.109629	+	0.279330i
$452$	32.4430	+	10.0073i	1.52599	+	0.470705i
$453$		0			0
$454$	−2.82294	−	12.3681i	−0.132487	−	0.580465i
$455$	14.9961	−	62.4602i	0.703026	−	2.92818i
$456$		0			0
$457$	26.5800	+	4.00628i	1.24336	+	0.187406i	0.737581	−	0.675258i	$-0.235968\pi$
$457$	26.5800	+	4.00628i	1.24336	+	0.187406i	0.505777	+	0.862665i	$0.331206\pi$
$458$	34.7048	−	23.6613i	1.62165	−	1.10562i
$459$		0			0
$460$	5.37377	+	9.30764i	0.250553	+	0.433971i
$461$	4.47708	+	2.15605i	0.208518	+	0.100417i	0.535228	−	0.844708i	$-0.320226\pi$
$461$	4.47708	+	2.15605i	0.208518	+	0.100417i	−0.326710	+	0.945125i	$0.605940\pi$
$462$		0			0
$463$	−16.2488	+	7.82502i	−0.755147	+	0.363660i	−0.771519	−	0.636206i	$-0.780503\pi$
$463$	−16.2488	+	7.82502i	−0.755147	+	0.363660i	0.0163719	+	0.999866i	$0.494788\pi$
$464$	29.8126	+	20.3259i	1.38401	+	0.943604i
$465$		0			0
$466$	40.1400	+	37.2444i	1.85945	+	1.72532i
$467$	0.310155	+	0.211460i	0.0143523	+	0.00978521i	0.570475	−	0.821315i	$-0.306759\pi$
$467$	0.310155	+	0.211460i	0.0143523	+	0.00978521i	−0.556123	+	0.831100i	$0.687712\pi$
$468$		0			0
$469$	−11.0241	−	7.69888i	−0.509046	−	0.355501i
$470$	−72.8532	−	35.0842i	−3.36047	−	1.61832i
$471$		0			0
$472$	26.3879	−	45.7052i	1.21460	−	2.10375i
$473$	8.44932	−	5.76065i	0.388500	−	0.264875i
$474$		0			0
$475$	−3.55793	+	15.5883i	−0.163249	+	0.715241i
$476$	18.8057	−	8.79755i	0.861957	−	0.403235i
$477$		0			0
$478$	0.819193	+	10.9314i	0.0374690	+	0.499989i
$479$	3.18037	+	0.981013i	0.145315	+	0.0448236i	0.366559	−	0.930395i	$-0.380536\pi$
$479$	3.18037	+	0.981013i	0.145315	+	0.0448236i	−0.221245	+	0.975218i	$0.571012\pi$
$480$		0			0
$481$	32.8046	−	10.1189i	1.49576	−	0.461381i
$482$	−17.0256	−	21.3494i	−0.775494	−	0.972439i
$483$		0			0
$484$	−24.5584	+	30.7953i	−1.11629	+	1.39979i
$485$	−4.21070	+	10.7287i	−0.191198	+	0.487164i
$486$		0			0
$487$	−6.49963	+	0.979662i	−0.294527	+	0.0443927i	−0.294643	−	0.955607i	$-0.595201\pi$
$487$	−6.49963	+	0.979662i	−0.294527	+	0.0443927i	0.000116930		1.00000i	$0.499963\pi$
$488$	0.357917	−	0.332099i	0.0162022	−	0.0150334i
$489$		0			0
$490$	13.6634	+	66.7388i	0.617248	+	3.01495i
$491$	34.5060			1.55723			0.778617	−	0.627499i	$-0.215921\pi$
$491$	34.5060			1.55723			0.778617	+	0.627499i	$0.215921\pi$
$492$		0			0
$493$	−16.3561	+	2.46528i	−0.736641	+	0.111031i
$494$	−1.68535	+	22.4894i	−0.0758273	+	1.01184i
$495$		0			0
$496$	15.8629	−	19.8915i	0.712266	−	0.893154i
$497$	7.31147	+	19.2627i	0.327964	+	0.864049i
$498$		0			0
$499$	−14.3530	+	4.42732i	−0.642529	+	0.198194i	−0.598862	−	0.800852i	$-0.704380\pi$
$499$	−14.3530	+	4.42732i	−0.642529	+	0.198194i	−0.0436672	+	0.999046i	$0.513904\pi$
$500$	−33.2058	−	84.6070i	−1.48501	−	3.78374i
$501$		0			0
$502$	−1.13498	−	15.1453i	−0.0506568	−	0.675969i
$503$	4.77835	+	20.9353i	0.213056	+	0.933460i	0.962476	+	0.271365i	$0.0874751\pi$
$503$	4.77835	+	20.9353i	0.213056	+	0.933460i	−0.749420	+	0.662094i	$0.769668\pi$
$504$		0			0
$505$	8.56435	−	37.5229i	0.381108	−	1.66975i
$506$	−1.82457	−	0.275009i	−0.0811120	−	0.0122257i
$507$		0			0
$508$	−5.43123	+	9.40716i	−0.240972	+	0.417375i
$509$	−19.4711	−	33.7249i	−0.863042	−	1.49483i	−0.868979	−	0.494850i	$-0.835223\pi$
$509$	−19.4711	−	33.7249i	−0.863042	−	1.49483i	0.00593701	−	0.999982i	$-0.498110\pi$
$510$		0			0
$511$	−5.09906	+	4.62576i	−0.225569	+	0.204632i
$512$	36.7788	−	17.7117i	1.62541	−	0.782755i
$513$		0			0
$514$	16.7928	+	15.5815i	0.740700	+	0.687269i
$515$	−32.6405	−	30.2860i	−1.43831	−	1.33456i
$516$		0			0
$517$	8.36566	−	4.02869i	0.367921	−	0.177181i
$518$	−26.9651	+	24.4622i	−1.18478	+	1.07481i
$519$		0			0
$520$	−60.8395	−	105.377i	−2.66799	−	4.62109i
$521$	5.17606	−	8.96521i	0.226768	−	0.392773i	−0.730081	−	0.683361i	$-0.760518\pi$
$521$	5.17606	−	8.96521i	0.226768	−	0.392773i	0.956848	+	0.290588i	$0.0938509\pi$
$522$		0			0
$523$	10.4291	+	1.57193i	0.456033	+	0.0687358i	0.373042	−	0.927814i	$-0.378315\pi$
$523$	10.4291	+	1.57193i	0.456033	+	0.0687358i	0.0829906	+	0.996550i	$0.473553\pi$
$524$	7.67646	−	33.6328i	0.335348	−	1.46925i
$525$		0			0
$526$	−0.853357	−	3.73880i	−0.0372081	−	0.163020i
$527$	0.871592	+	11.6306i	0.0379672	+	0.506637i
$528$		0			0
$529$	−8.23792	−	20.9899i	−0.358170	−	0.912603i
$530$	68.6253	−	21.1681i	2.98089	−	0.919484i
$531$		0			0
$532$	−5.67674	−	14.9558i	−0.246118	−	0.648418i
$533$	−21.7982	+	27.3340i	−0.944184	+	1.18397i
$534$		0			0
$535$	1.00229	−	13.3746i	0.0433326	−	0.578233i
$536$	−25.1866	+	3.79626i	−1.08789	+	0.163974i
$537$		0			0
$538$	9.87499			0.425741
$539$	−6.96983	−	3.55149i	−0.300212	−	0.152974i
$540$		0			0
$541$	18.4105	−	17.0824i	0.791527	−	0.734430i	−0.176764	−	0.984253i	$-0.556563\pi$
$541$	18.4105	−	17.0824i	0.791527	−	0.734430i	0.968291	+	0.249823i	$0.0803726\pi$
$542$	17.6982	−	2.66758i	0.760204	−	0.114582i
$543$		0			0
$544$	0.277382	−	0.706759i	0.0118927	−	0.0303020i
$545$	8.53740	−	10.7056i	0.365702	−	0.458576i
$546$		0			0
$547$	−3.15355	−	3.95443i	−0.134836	−	0.169079i	0.709829	−	0.704374i	$-0.248772\pi$
$547$	−3.15355	−	3.95443i	−0.134836	−	0.169079i	−0.844666	+	0.535294i	$0.820201\pi$
$548$	48.2791	−	14.8921i	2.06238	−	0.636160i
$549$		0			0
$550$	28.0324	+	8.64685i	1.19531	+	0.368703i
$551$	0.952414	+	12.7091i	0.0405742	+	0.541425i
$552$		0			0
$553$	−38.0131	+	17.7830i	−1.61648	+	0.756211i
$554$	3.53671	−	15.4953i	0.150260	−	0.658333i
$555$		0			0
$556$	−2.97329	+	2.02716i	−0.126096	+	0.0859706i
$557$	−17.7341	+	30.7164i	−0.751418	+	1.30149i	0.195717	+	0.980660i	$0.437297\pi$
$557$	−17.7341	+	30.7164i	−0.751418	+	1.30149i	−0.947135	+	0.320834i	$0.896037\pi$
$558$		0			0
$559$	50.5477	+	24.3425i	2.13794	+	1.02958i
$560$	36.4022	+	25.4221i	1.53827	+	1.07428i
$561$		0			0
$562$	32.8054	+	22.3663i	1.38381	+	0.943467i
$563$	22.4577	+	20.8377i	0.946477	+	0.878202i	0.992685	−	0.120729i	$-0.0385233\pi$
$563$	22.4577	+	20.8377i	0.946477	+	0.878202i	−0.0462083	+	0.998932i	$0.514714\pi$
$564$		0			0
$565$	−27.5010	−	18.7499i	−1.15698	−	0.788814i
$566$	−1.24408	+	0.599116i	−0.0522925	+	0.0251827i
$567$		0			0
$568$	35.1638	+	16.9340i	1.47544	+	0.710534i
$569$	−11.9300	−	20.6633i	−0.500130	−	0.866250i	−1.00000		0.000150037i	$-0.999952\pi$
$569$	−11.9300	−	20.6633i	−0.500130	−	0.866250i	0.499870	−	0.866100i	$-0.333381\pi$
$570$		0			0
$571$	0.415921	−	0.283570i	0.0174058	−	0.0118670i	−0.554586	−	0.832126i	$-0.687123\pi$
$571$	0.415921	−	0.283570i	0.0174058	−	0.0118670i	0.571992	+	0.820259i	$0.306171\pi$
$572$	27.3657	+	4.12472i	1.14422	+	0.172463i
$573$		0			0
$574$	8.65599	−	36.0531i	0.361294	−	1.50483i
$575$	−1.59705	−	6.99712i	−0.0666015	−	0.291800i
$576$		0			0
$577$	24.4705	+	7.54814i	1.01872	+	0.314233i	0.758749	−	0.651384i	$-0.225811\pi$
$577$	24.4705	+	7.54814i	1.01872	+	0.314233i	0.259970	+	0.965617i	$0.416287\pi$
$578$	−11.8747	−	30.2562i	−0.493922	−	1.25849i
$579$		0			0
$580$	−84.9180	−	106.484i	−3.52603	−	4.42150i
$581$	−14.9928	−	4.80971i	−0.622006	−	0.199541i
$582$		0			0
$583$	−3.01280	+	7.67649i	−0.124777	+	0.317928i
$584$	−0.974582	+	13.0049i	−0.0403285	+	0.538146i
$585$		0			0
$586$	17.3330	−	16.0827i	0.716020	−	0.664370i
$587$	27.7971			1.14731			0.573654	−	0.819097i	$-0.305525\pi$
$587$	27.7971			1.14731			0.573654	+	0.819097i	$0.305525\pi$
$588$		0			0
$589$	8.98650			0.370282
$590$	−75.1233	+	69.7043i	−3.09278	+	2.86968i
$591$		0			0
$592$	−1.77329	+	23.6630i	−0.0728819	+	0.972541i
$593$	−13.8909	+	35.3935i	−0.570433	+	1.45344i	0.296509	+	0.955030i	$0.404177\pi$
$593$	−13.8909	+	35.3935i	−0.570433	+	1.45344i	−0.866942	+	0.498409i	$0.833918\pi$
$594$		0			0
$595$	−20.1595	+	2.80740i	−0.826460	+	0.115092i
$596$	−38.9956	−	48.8989i	−1.59732	−	2.00298i
$597$		0			0
$598$	−3.69838	−	9.42333i	−0.151238	−	0.385348i
$599$	−18.9362	−	5.84104i	−0.773711	−	0.238658i	−0.117335	−	0.993092i	$-0.537435\pi$
$599$	−18.9362	−	5.84104i	−0.773711	−	0.238658i	−0.656376	+	0.754434i	$0.727911\pi$
$600$		0			0
$601$	−0.903079	−	3.95665i	−0.0368374	−	0.161395i	0.953164	−	0.302455i	$-0.0978062\pi$
$601$	−0.903079	−	3.95665i	−0.0368374	−	0.161395i	−0.990001	+	0.141060i	$0.954949\pi$
$602$	−59.4957	−	0.668199i	−2.42486	−	0.0272338i
$603$		0			0
$604$	54.8637	+	8.26938i	2.23237	+	0.336476i
$605$	31.9054	−	21.7527i	1.29714	−	0.884374i
$606$		0			0
$607$	3.99990	+	6.92804i	0.162351	+	0.281200i	0.935711	−	0.352766i	$-0.114759\pi$
$607$	3.99990	+	6.92804i	0.162351	+	0.281200i	−0.773360	+	0.633967i	$0.781426\pi$
$608$	−0.527064	−	0.253821i	−0.0213753	−	0.0102938i
$609$		0			0
$610$	−0.854205	+	0.411364i	−0.0345858	+	0.0166556i
$611$	42.0892	+	28.6960i	1.70275	+	1.16091i
$612$		0			0
$613$	−4.73599	−	4.39436i	−0.191285	−	0.177486i	0.578716	−	0.815529i	$-0.303554\pi$
$613$	−4.73599	−	4.39436i	−0.191285	−	0.177486i	−0.770001	+	0.638043i	$0.779744\pi$
$614$	−52.6004	−	35.8624i	−2.12278	−	1.44729i
$615$		0			0
$616$	−14.2078	+	4.20838i	−0.572449	+	0.169561i
$617$	−19.0163	−	9.15775i	−0.765566	−	0.368677i	0.00999465	−	0.999950i	$-0.496819\pi$
$617$	−19.0163	−	9.15775i	−0.765566	−	0.368677i	−0.775561	+	0.631273i	$0.782533\pi$
$618$		0			0
$619$	−20.6150	+	35.7063i	−0.828589	+	1.43516i	0.0705567	+	0.997508i	$0.477522\pi$
$619$	−20.6150	+	35.7063i	−0.828589	+	1.43516i	−0.899145	+	0.437650i	$0.855811\pi$
$620$	−79.3481	+	54.0986i	−3.18669	+	2.17265i
$621$		0			0
$622$	17.4441	−	76.4274i	0.699443	−	3.06446i
$623$	1.99593	+	9.22086i	0.0799651	+	0.369426i
$624$		0			0
$625$	2.66750	+	35.5953i	0.106700	+	1.42381i
$626$	68.2213	+	21.0435i	2.72667	+	0.841066i
$627$		0			0
$628$	−39.1744	+	12.0837i	−1.56323	+	0.482192i
$629$	−6.78232	−	8.50476i	−0.270429	−	0.339107i
$630$		0			0
$631$	20.6208	−	25.8577i	0.820903	−	1.02938i	−0.178068	−	0.984018i	$-0.556985\pi$
$631$	20.6208	−	25.8577i	0.820903	−	1.02938i	0.998971	−	0.0453613i	$-0.0144439\pi$
$632$	−29.0435	+	74.0017i	−1.15529	+	2.94363i
$633$		0			0
$634$	−7.87535	+	1.18702i	−0.312770	+	0.0471425i
$635$	7.80638	−	7.24326i	0.309787	−	0.287440i
$636$		0			0
$637$	−2.24515	−	42.8574i	−0.0889562	−	1.69807i
$638$	23.3830			0.925741
$639$		0			0
$640$	−75.3799	+	11.3617i	−2.97965	+	0.449110i
$641$	−0.106904	+	1.42653i	−0.00422244	+	0.0563445i	−0.998917	−	0.0465280i	$-0.985184\pi$
$641$	−0.106904	+	1.42653i	−0.00422244	+	0.0563445i	0.994695	+	0.102873i	$0.0328034\pi$
$642$		0			0
$643$	−12.8744	+	16.1439i	−0.507715	+	0.636654i	−0.967950	−	0.251143i	$-0.919194\pi$
$643$	−12.8744	+	16.1439i	−0.507715	+	0.636654i	0.460235	+	0.887797i	$0.347765\pi$
$644$	5.20853	+	4.94281i	0.205245	+	0.194774i
$645$		0			0
$646$	6.82866	−	2.10636i	0.268670	−	0.0828737i
$647$	7.01977	+	17.8861i	0.275975	+	0.703174i	0.999911	+	0.0133069i	$0.00423583\pi$
$647$	7.01977	+	17.8861i	0.275975	+	0.703174i	−0.723936	+	0.689867i	$0.757669\pi$
$648$		0			0
$649$	−0.879401	−	11.7348i	−0.0345195	−	0.460631i
$650$	35.8131	+	156.908i	1.40471	+	6.15442i
$651$		0			0
$652$	−8.22160	+	36.0212i	−0.321983	+	1.41070i
$653$	23.4343	+	3.53215i	0.917054	+	0.138224i	0.590577	−	0.806981i	$-0.298900\pi$
$653$	23.4343	+	3.53215i	0.917054	+	0.138224i	0.326477	+	0.945205i	$0.394138\pi$
$654$		0			0
$655$	−16.9101	+	29.2892i	−0.660734	+	1.14442i
$656$	−12.0830	−	20.9284i	−0.471762	−	0.817116i
$657$		0			0
$658$	−53.3268	−	8.65129i	−2.07890	−	0.337262i
$659$	31.5912	−	15.2135i	1.23062	−	0.592635i	0.298369	−	0.954451i	$-0.403557\pi$
$659$	31.5912	−	15.2135i	1.23062	−	0.592635i	0.932250	+	0.361816i	$0.117843\pi$
$660$		0			0
$661$	10.9100	+	10.1230i	0.424352	+	0.393741i	0.863234	−	0.504804i	$-0.168435\pi$
$661$	10.9100	+	10.1230i	0.424352	+	0.393741i	−0.438883	+	0.898544i	$0.644626\pi$
$662$	41.3754	+	38.3908i	1.60810	+	1.49210i
$663$		0			0
$664$	−26.8724	+	12.9411i	−1.04285	+	0.502211i
$665$	0.996274	+	15.6511i	0.0386338	+	0.606925i
$666$		0			0
$667$	−2.86036	−	4.95428i	−0.110753	−	0.191831i
$668$	35.2924	−	61.1282i	1.36550	−	2.36512i
$669$		0			0
$670$	48.9073	+	7.37158i	1.88945	+	0.284789i
$671$	0.0242256	−	0.106139i	0.000935219	−	0.00409746i
$672$		0			0
$673$	−1.48260	−	6.49569i	−0.0571500	−	0.250390i	0.938281	−	0.345874i	$-0.112417\pi$
$673$	−1.48260	−	6.49569i	−0.0571500	−	0.250390i	−0.995431	+	0.0954834i	$0.969560\pi$
$674$	1.07763	+	14.3800i	0.0415088	+	0.553896i
$675$		0			0
$676$	36.2853	+	92.4535i	1.39559	+	3.55590i
$677$	−1.84582	+	0.569360i	−0.0709406	+	0.0218823i	−0.330022	−	0.943973i	$-0.607056\pi$
$677$	−1.84582	+	0.569360i	−0.0709406	+	0.0218823i	0.259082	+	0.965855i	$0.416580\pi$
$678$		0			0
$679$	−0.661637	+	7.67175i	−0.0253913	+	0.294415i
$680$	−24.0394	+	30.1444i	−0.921869	+	1.15599i
$681$		0			0
$682$	1.23213	−	16.4416i	0.0471806	−	0.629581i
$683$	4.80731	−	0.724586i	0.183947	−	0.0277255i	−0.0564228	−	0.998407i	$-0.517969\pi$
$683$	4.80731	−	0.724586i	0.183947	−	0.0277255i	0.240370	+	0.970681i	$0.422731\pi$
$684$		0			0
$685$	−49.5316			−1.89251
$686$	21.4162	+	40.1603i	0.817675	+	1.53333i
$687$		0			0
$688$	−28.4276	+	26.3770i	−1.08379	+	1.00561i
$689$	−44.7372	+	6.74305i	−1.70435	+	0.256890i
$690$		0			0
$691$	11.9553	−	30.4617i	0.454803	−	1.15882i	−0.501166	−	0.865351i	$-0.667096\pi$
$691$	11.9553	−	30.4617i	0.454803	−	1.15882i	0.955969	−	0.293468i	$-0.0948092\pi$
$692$	30.1383	−	37.7922i	1.14568	−	1.43664i
$693$		0			0
$694$	−14.8084	−	18.5691i	−0.562119	−	0.704875i
$695$	3.37119	−	1.03987i	0.127876	−	0.0394447i
$696$		0			0
$697$	10.5860	+	3.26536i	0.400974	+	0.123684i
$698$	2.51695	+	33.5864i	0.0952681	+	1.27126i
$699$		0			0
$700$	−70.1710	−	90.0479i	−2.65221	−	3.40349i
$701$	−0.803531	+	3.52050i	−0.0303490	+	0.132967i	−0.987833	−	0.155519i	$-0.950295\pi$
$701$	−0.803531	+	3.52050i	−0.0303490	+	0.132967i	0.957484	+	0.288487i	$0.0931521\pi$
$702$		0			0
$703$	−6.92512	+	4.72147i	−0.261186	+	0.178073i
$704$	4.19906	−	7.27299i	0.158258	−	0.274111i
$705$		0			0
$706$	−67.6763	−	32.5912i	−2.54703	−	1.22658i
$707$	−1.63353	−	25.6622i	−0.0614351	−	0.965126i
$708$		0			0
$709$	3.63182	+	2.47613i	0.136396	+	0.0929932i	0.629596	−	0.776923i	$-0.283221\pi$
$709$	3.63182	+	2.47613i	0.136396	+	0.0929932i	−0.493200	+	0.869916i	$0.664173\pi$
$710$	−55.5553	−	51.5477i	−2.08495	−	1.93455i
$711$		0			0
$712$	14.7660	+	10.0673i	0.553380	+	0.377288i
$713$	−3.63430	+	1.75019i	−0.136106	+	0.0655450i
$714$		0			0
$715$	−24.4445	−	11.7719i	−0.914174	−	0.440243i
$716$	−16.4919	−	28.5647i	−0.616329	−	1.06751i
$717$		0			0
$718$	−8.13413	+	5.54576i	−0.303563	+	0.206966i
$719$	−43.5650	−	6.56637i	−1.62470	−	0.244884i	−0.727371	−	0.686245i	$-0.759258\pi$
$719$	−43.5650	−	6.56637i	−1.62470	−	0.244884i	−0.897330	+	0.441360i	$0.854496\pi$
$720$		0			0
$721$	−26.6562	−	13.2077i	−0.992728	−	0.491882i
$722$	9.16489	+	40.1540i	0.341082	+	1.49438i
$723$		0			0
$724$	8.53896	+	2.63392i	0.317348	+	0.0978889i
$725$	33.2282	+	84.6641i	1.23406	+	3.14435i
$726$		0			0
$727$	−0.491911	−	0.616837i	−0.0182440	−	0.0228772i	0.772626	−	0.634862i	$-0.218943\pi$
$727$	−0.491911	−	0.616837i	−0.0182440	−	0.0228772i	−0.790870	+	0.611984i	$0.790371\pi$
$728$	−58.9688	−	55.9605i	−2.18553	−	2.07403i
$729$		0			0
$730$	9.25180	−	23.5732i	0.342424	−	0.872483i
$731$	1.32851	−	17.7278i	0.0491368	−	0.655685i
$732$		0			0
$733$	4.05085	−	3.75864i	0.149622	−	0.138829i	−0.601811	−	0.798639i	$-0.705554\pi$
$733$	4.05085	−	3.75864i	0.149622	−	0.138829i	0.751432	+	0.659810i	$0.229363\pi$
$734$	−27.6049			−1.01891
$735$		0			0
$736$	0.262587			0.00967909
$737$	−4.16330	+	3.86298i	−0.153357	+	0.142295i
$738$		0			0
$739$	1.19003	−	15.8799i	0.0437761	−	0.584151i	−0.931583	−	0.363528i	$-0.881572\pi$
$739$	1.19003	−	15.8799i	0.0437761	−	0.584151i	0.975359	−	0.220623i	$-0.0708089\pi$
$740$	32.7235	−	83.3782i	1.20294	−	3.06504i
$741$		0			0
$742$	39.9448	−	26.5817i	1.46642	−	0.975845i
$743$	−11.3675	−	14.2544i	−0.417032	−	0.522942i	0.528297	−	0.849060i	$-0.322831\pi$
$743$	−11.3675	−	14.2544i	−0.417032	−	0.522942i	−0.945329	+	0.326118i	$0.894259\pi$
$744$		0			0
$745$	22.4012	+	57.0774i	0.820717	+	2.09115i
$746$	36.4964	+	11.2576i	1.33623	+	0.412171i
$747$		0			0
$748$	−1.95134	−	8.54940i	−0.0713482	−	0.312597i
$749$	−1.89572	−	8.75792i	−0.0692681	−	0.320008i
$750$		0			0
$751$	−12.3741	−	1.86509i	−0.451536	−	0.0680581i	−0.0806625	−	0.996741i	$-0.525704\pi$
$751$	−12.3741	−	1.86509i	−0.451536	−	0.0680581i	−0.370874	+	0.928683i	$0.620942\pi$
$752$	−29.0928	+	19.8351i	−1.06090	+	0.723313i
$753$		0			0
$754$	64.1424	+	111.098i	2.33593	+	4.04594i
$755$	−49.0072	−	23.6006i	−1.78356	−	0.858915i
$756$		0			0
$757$	−32.2238	+	15.5182i	−1.17119	+	0.564018i	−0.915334	−	0.402696i	$-0.868073\pi$
$757$	−32.2238	+	15.5182i	−1.17119	+	0.564018i	−0.255861	+	0.966714i	$0.582359\pi$
$758$	−68.5257	−	46.7201i	−2.48897	−	1.69695i
$759$		0			0
$760$	21.7772	+	20.2063i	0.789941	+	0.732959i
$761$	29.6193	+	20.1941i	1.07370	+	0.732034i	0.965055	−	0.262047i	$-0.0843974\pi$
$761$	29.6193	+	20.1941i	1.07370	+	0.732034i	0.108642	+	0.994081i	$0.465350\pi$
$762$		0			0
$763$	3.43771	−	8.47792i	0.124453	−	0.306921i
$764$	88.3147	+	42.5301i	3.19511	+	1.53869i
$765$		0			0
$766$	−34.4803	+	59.7217i	−1.24582	+	2.15783i
$767$	53.3424	−	36.3682i	1.92608	−	1.31318i
$768$		0			0
$769$	−5.16477	+	22.6283i	−0.186246	+	0.815998i	0.792327	+	0.610097i	$0.208870\pi$
$769$	−5.16477	+	22.6283i	−0.186246	+	0.815998i	−0.978573	+	0.205901i	$0.933988\pi$
$770$	28.7717	+	0.323137i	1.03686	+	0.0116450i
$771$		0			0
$772$	−3.91008	−	52.1764i	−0.140727	−	1.87787i
$773$	−11.8039	−	3.64103i	−0.424558	−	0.130959i	0.0751110	−	0.997175i	$-0.476069\pi$
$773$	−11.8039	−	3.64103i	−0.424558	−	0.130959i	−0.499669	+	0.866216i	$0.666545\pi$
$774$		0			0
$775$	61.2820	−	18.9030i	2.20131	−	0.679015i
$776$	9.09444	+	11.4041i	0.326471	+	0.409382i
$777$		0			0
$778$	39.3776	−	49.3779i	1.41175	−	1.77028i
$779$	3.11846	−	7.94571i	0.111730	−	0.284685i
$780$		0			0
$781$	8.60526	−	1.29703i	0.307920	−	0.0464115i
$782$	−2.35140	+	2.18178i	−0.0840859	+	0.0780203i
$783$		0			0
$784$	28.1430	+	9.37817i	1.00511	+	0.334935i
$785$	40.1907			1.43447
$786$		0			0
$787$	33.1164	−	4.99149i	1.18047	−	0.177927i	0.470657	−	0.882316i	$-0.344017\pi$
$787$	33.1164	−	4.99149i	1.18047	−	0.177927i	0.709814	+	0.704389i	$0.248779\pi$
$788$	−3.73547	+	49.8464i	−0.133071	+	1.77571i
$789$		0			0
$790$	96.2465	−	120.689i	3.42430	−	4.29393i
$791$	−21.1749	−	6.79294i	−0.752892	−	0.241529i
$792$		0			0
$793$	0.570746	−	0.176052i	0.0202678	−	0.00625178i
$794$	−15.7260	−	40.0691i	−0.558094	−	1.42200i
$795$		0			0
$796$	−6.86489	−	91.6056i	−0.243320	−	3.24687i
$797$	2.61932	+	11.4760i	0.0927811	+	0.406501i	0.999897	−	0.0143812i	$-0.00457785\pi$
$797$	2.61932	+	11.4760i	0.0927811	+	0.406501i	−0.907115	+	0.420882i	$0.861721\pi$
$798$		0			0
$799$	3.59182	−	15.7368i	0.127069	−	0.556728i
$800$	−4.12813	−	0.622216i	−0.145951	−	0.0219986i
$801$		0			0
$802$	21.0081	−	36.3871i	0.741821	−	1.28487i
$803$	1.45395	+	2.51831i	0.0513087	+	0.0888693i
$804$		0			0
$805$	−3.45108	−	6.13556i	−0.121635	−	0.216250i
$806$	81.4977	−	39.2472i	2.87063	−	1.38242i
$807$		0			0
$808$	−35.7067	−	33.1309i	−1.25616	−	1.16554i
$809$	−24.4647	−	22.6999i	−0.860132	−	0.798086i	0.120751	−	0.992683i	$-0.461470\pi$
$809$	−24.4647	−	22.6999i	−0.860132	−	0.798086i	−0.980883	+	0.194597i	$0.937660\pi$
$810$		0			0
$811$	16.2286	−	7.81527i	0.569862	−	0.274431i	−0.126684	−	0.991943i	$-0.540433\pi$
$811$	16.2286	−	7.81527i	0.569862	−	0.274431i	0.696546	+	0.717512i	$0.254719\pi$
$812$	−74.6034	−	52.1005i	−2.61807	−	1.82837i
$813$		0			0
$814$	7.68885	+	13.3175i	0.269494	+	0.466777i
$815$	18.1110	−	31.3692i	0.634401	−	1.09881i
$816$		0			0
$817$	−13.5446	−	2.04151i	−0.473864	−	0.0714235i
$818$	2.54685	−	11.1585i	0.0890484	−	0.390146i
$819$		0			0
$820$	20.2980	+	88.9313i	0.708836	+	3.10561i
$821$	−0.696624	−	9.29581i	−0.0243124	−	0.324426i	−0.996078	−	0.0884782i	$-0.971800\pi$
$821$	−0.696624	−	9.29581i	−0.0243124	−	0.324426i	0.971766	−	0.235948i	$-0.0758194\pi$
$822$		0			0
$823$	2.34531	+	5.97575i	0.0817523	+	0.208301i	0.965905	−	0.258896i	$-0.0833588\pi$
$823$	2.34531	+	5.97575i	0.0817523	+	0.208301i	−0.884153	+	0.467198i	$0.845264\pi$
$824$	−53.8490	+	16.6102i	−1.87592	+	0.578644i
$825$		0			0
$826$	−34.8978	+	58.9069i	−1.21425	+	2.04963i
$827$	17.6323	−	22.1102i	0.613136	−	0.768848i	−0.374225	−	0.927338i	$-0.622091\pi$
$827$	17.6323	−	22.1102i	0.613136	−	0.768848i	0.987361	+	0.158490i	$0.0506625\pi$
$828$		0			0
$829$	0.432217	−	5.76754i	0.0150115	−	0.200315i	−0.984655	−	0.174510i	$-0.944166\pi$
$829$	0.432217	−	5.76754i	0.0150115	−	0.200315i	0.999667	−	0.0258053i	$-0.00821499\pi$
$830$	57.2695	−	8.63198i	1.98785	−	0.299621i
$831$		0			0
$832$	46.0742			1.59733
$833$	−12.3815	+	5.62362i	−0.428993	+	0.194847i
$834$		0			0
$835$	−50.7262	+	47.0670i	−1.75545	+	1.62882i
$836$	−6.68125	+	1.00704i	−0.231076	+	0.0348291i
$837$		0			0
$838$	6.14067	−	15.6462i	0.212126	−	0.540488i
$839$	−8.02425	+	10.0621i	−0.277028	+	0.347382i	−0.900808	−	0.434218i	$-0.857025\pi$
$839$	−8.02425	+	10.0621i	−0.277028	+	0.347382i	0.623780	+	0.781600i	$0.285596\pi$
$840$		0			0
$841$	27.1191	+	34.0063i	0.935141	+	1.17263i
$842$	−81.1123	+	25.0198i	−2.79531	+	0.862240i
$843$		0			0
$844$	15.6892	+	4.83948i	0.540045	+	0.166582i
$845$	−7.27638	−	97.0965i	−0.250315	−	3.34022i
$846$		0			0
$847$	16.3111	−	19.9887i	0.560455	−	0.686821i
$848$	6.95877	−	30.4884i	0.238965	−	1.04697i
$849$		0			0
$850$	42.1362	−	28.7280i	1.44526	−	0.985362i
$851$	1.88110	−	3.25816i	0.0644833	−	0.111688i
$852$		0			0
$853$	−0.0343360	−	0.0165354i	−0.00117564	−	0.000566160i	0.433296	−	0.901252i	$-0.357351\pi$
$853$	−0.0343360	−	0.0165354i	−0.00117564	−	0.000566160i	−0.434471	+	0.900686i	$0.643065\pi$
$854$	−0.469149	+	0.425602i	−0.0160539	+	0.0145638i
$855$		0			0
$856$	−14.0247	−	9.56186i	−0.479353	−	0.326818i
$857$	36.3154	+	33.6958i	1.24051	+	1.15103i	0.982774	+	0.184810i	$0.0591671\pi$
$857$	36.3154	+	33.6958i	1.24051	+	1.15103i	0.257736	+	0.966215i	$0.417023\pi$
$858$		0			0
$859$	−7.64209	−	5.21029i	−0.260745	−	0.177773i	0.425891	−	0.904775i	$-0.359961\pi$
$859$	−7.64209	−	5.21029i	−0.260745	−	0.177773i	−0.686635	+	0.727002i	$0.740913\pi$
$860$	131.884	−	63.5120i	4.49721	−	2.16574i
$861$		0			0
$862$	−27.9478	−	13.4590i	−0.951907	−	0.458414i
$863$	3.90482	+	6.76334i	0.132922	+	0.230227i	0.924802	−	0.380450i	$-0.124231\pi$
$863$	3.90482	+	6.76334i	0.132922	+	0.230227i	−0.791880	+	0.610677i	$0.790897\pi$
$864$		0			0
$865$	−39.1545	+	26.6951i	−1.33129	+	0.907659i
$866$	−40.3321	−	6.07908i	−1.37054	−	0.206576i
$867$		0			0
$868$	−40.5653	+	49.7116i	−1.37688	+	1.68732i
$869$	3.94437	+	17.2814i	0.133804	+	0.586232i
$870$		0			0
$871$	−29.7743	−	9.18416i	−1.00886	−	0.311193i
$872$	−6.33120	−	16.1316i	−0.214401	−	0.546286i
$873$		0			0
$874$	1.54097	+	1.93231i	0.0521241	+	0.0653615i
$875$	21.1258	+	55.6576i	0.714182	+	1.88157i
$876$		0			0
$877$	−10.8283	+	27.5901i	−0.365647	+	0.931653i	0.623112	+	0.782133i	$0.285868\pi$
$877$	−10.8283	+	27.5901i	−0.365647	+	0.931653i	−0.988759	+	0.149520i	$0.952227\pi$
$878$	−5.45229	+	72.7557i	−0.184006	+	2.45539i
$879$		0			0
$880$	13.7474	−	12.7557i	0.463425	−	0.429996i
$881$	20.2334			0.681679			0.340840	−	0.940121i	$-0.389289\pi$
$881$	20.2334			0.681679			0.340840	+	0.940121i	$0.389289\pi$
$882$		0			0
$883$	−25.6862			−0.864409			−0.432204	−	0.901776i	$-0.642264\pi$
$883$	−25.6862			−0.864409			−0.432204	+	0.901776i	$0.642264\pi$
$884$	35.2674	−	32.7233i	1.18617	−	1.10061i
$885$		0			0
$886$	3.53888	−	47.2231i	0.118891	−	1.58649i
$887$	11.3546	−	28.9310i	0.381250	−	0.971409i	−0.603489	−	0.797371i	$-0.706223\pi$
$887$	11.3546	−	28.9310i	0.381250	−	0.971409i	0.984739	−	0.174038i	$-0.0556814\pi$
$888$		0			0
$889$	3.62638	−	6.12127i	0.121625	−	0.205301i
$890$	−21.6367	−	27.1316i	−0.725265	−	0.909453i
$891$		0			0
$892$	−6.41731	−	16.3510i	−0.214867	−	0.547473i
$893$	−11.8845	−	3.66588i	−0.397699	−	0.122674i
$894$		0			0
$895$	7.19544	+	31.5253i	0.240517	+	1.05377i
$896$	−46.1325	+	21.5814i	−1.54118	+	0.720983i
$897$		0			0
$898$	−7.21028	−	1.08677i	−0.240610	−	0.0362661i
$899$	42.2355	−	28.7957i	1.40863	−	0.960390i
$900$		0			0
$901$	7.16796	+	12.4153i	0.238799	+	0.413613i
$902$	−14.1098	−	6.79493i	−0.469805	−	0.226246i
$903$		0			0
$904$	−37.9529	+	18.2771i	−1.26229	+	0.607889i
$905$	−7.23825	−	4.93496i	−0.240608	−	0.164044i
$906$		0			0
$907$	13.5497	+	12.5723i	0.449911	+	0.417456i	0.872310	−	0.488954i	$-0.162621\pi$
$907$	13.5497	+	12.5723i	0.449911	+	0.417456i	−0.422399	+	0.906410i	$0.638812\pi$
$908$	17.2288	+	11.7464i	0.571757	+	0.389818i
$909$		0			0
$910$	77.3891	+	137.588i	2.56542	+	4.56098i
$911$	51.7803	+	24.9361i	1.71556	+	0.826169i	0.990505	+	0.137476i	$0.0438991\pi$
$911$	51.7803	+	24.9361i	1.71556	+	0.826169i	0.725053	+	0.688693i	$0.241815\pi$
$912$		0			0
$913$	−3.32524	+	5.75948i	−0.110049	+	0.190611i
$914$	−54.5800	+	37.2120i	−1.80535	+	1.23086i
$915$		0			0
$916$	−15.3629	+	67.3091i	−0.507603	+	2.22396i
$917$	−5.27509	+	21.9713i	−0.174199	+	0.725557i
$918$		0			0
$919$	−3.60214	−	48.0672i	−0.118824	−	1.58559i	−0.664300	−	0.747466i	$-0.731270\pi$
$919$	−3.60214	−	48.0672i	−0.118824	−	1.58559i	0.545476	−	0.838126i	$-0.316349\pi$
$920$	−12.7424	−	3.93051i	−0.420104	−	0.129585i
$921$		0			0
$922$	−11.6693	+	3.59950i	−0.384308	+	0.118543i
$923$	29.7678	+	37.3276i	0.979818	+	1.22865i
$924$		0			0
$925$	−37.2932	+	46.7642i	−1.22619	+	1.53760i
$926$	16.1922	−	41.2571i	0.532110	−	1.35579i
$927$		0			0
$928$	−3.29046	+	0.495957i	−0.108015	+	0.0162806i
$929$	−24.3682	+	22.6104i	−0.799494	+	0.741822i	−0.969887	−	0.243554i	$-0.921687\pi$
$929$	−24.3682	+	22.6104i	−0.799494	+	0.741822i	0.170393	+	0.985376i	$0.445496\pi$
$930$		0			0
$931$	3.60797	+	9.83707i	0.118246	+	0.322397i
$932$	−90.0036			−2.94817
$933$		0			0
$934$	−0.912202	+	0.137492i	−0.0298482	+	0.00449889i
$935$	−0.642459	+	8.57303i	−0.0210107	+	0.280368i
$936$		0			0
$937$	−17.7946	+	22.3137i	−0.581325	+	0.728958i	−0.982338	−	0.187114i	$-0.940087\pi$
$937$	−17.7946	+	22.3137i	−0.581325	+	0.728958i	0.401014	+	0.916072i	$0.368658\pi$
$938$	32.7287	−	4.55777i	1.06863	−	0.148816i
$939$		0			0
$940$	127.005	−	39.1758i	4.14244	−	1.27777i
$941$	−2.09870	−	5.34741i	−0.0684157	−	0.174320i	0.892576	−	0.450896i	$-0.148896\pi$
$941$	−2.09870	−	5.34741i	−0.0684157	−	0.174320i	−0.960992	+	0.276576i	$0.910800\pi$
$942$		0			0
$943$	0.286324	+	3.82073i	0.00932399	+	0.124420i
$944$	9.93006	+	43.5064i	0.323196	+	1.41601i
$945$		0			0
$946$	−5.59220	+	24.5010i	−0.181818	+	0.796598i
$947$	−32.2758	−	4.86480i	−1.04882	−	0.158085i	−0.398056	−	0.917361i	$-0.630315\pi$
$947$	−32.2758	−	4.86480i	−1.04882	−	0.158085i	−0.650768	+	0.759276i	$0.725553\pi$
$948$		0			0
$949$	−7.97672	+	13.8161i	−0.258935	+	0.448489i
$950$	−19.6468	−	34.0293i	−0.637428	−	1.10406i
$951$		0			0
$952$	−9.67981	+	23.8719i	−0.313725	+	0.773693i
$953$	29.9482	−	14.4223i	0.970118	−	0.467184i	0.119423	−	0.992844i	$-0.461896\pi$
$953$	29.9482	−	14.4223i	0.970118	−	0.467184i	0.850695	+	0.525659i	$0.176181\pi$
$954$		0			0
$955$	−70.4442	−	65.3626i	−2.27952	−	2.11509i
$956$	−13.2082	−	12.2554i	−0.427183	−	0.396368i
$957$		0			0
$958$	−7.36918	+	3.54881i	−0.238087	+	0.114657i
$959$	−31.7299	+	9.39847i	−1.02461	+	0.303492i
$960$		0			0
$961$	−2.52199	−	4.36822i	−0.0813545	−	0.140910i
$962$	−42.1829	+	73.0629i	−1.36003	+	2.35564i
$963$		0			0
$964$	44.3826	+	6.68960i	1.42947	+	0.215458i
$965$	−11.4143	+	50.0092i	−0.367438	+	1.60985i
$966$		0			0
$967$	0.111684	+	0.489321i	0.00359152	+	0.0157355i	0.976692	−	0.214646i	$-0.0688598\pi$
$967$	0.111684	+	0.489321i	0.00359152	+	0.0157355i	−0.973100	+	0.230381i	$0.926003\pi$
$968$	−3.65212	−	48.7342i	−0.117384	−	1.56638i
$969$		0			0
$970$	−10.3478	−	26.3659i	−0.332249	−	0.846557i
$971$	25.6351	−	7.90738i	0.822670	−	0.253760i	0.145286	−	0.989390i	$-0.453590\pi$
$971$	25.6351	−	7.90738i	0.822670	−	0.253760i	0.677384	+	0.735630i	$0.263114\pi$
$972$		0			0
$973$	1.96227	−	1.30581i	0.0629074	−	0.0418625i
$974$	10.0715	−	12.6292i	0.322710	−	0.404666i
$975$		0			0
$976$	−0.0308524	+	0.411697i	−0.000987562	+	0.0131781i
$977$	−30.5448	+	4.60388i	−0.977213	+	0.147291i	−0.618183	−	0.786035i	$-0.712131\pi$
$977$	−30.5448	+	4.60388i	−0.977213	+	0.147291i	−0.359031	+	0.933326i	$0.616893\pi$
$978$		0			0
$979$	3.98486			0.127357
$980$	−91.0763	−	65.1384i	−2.90932	−	2.08077i
$981$		0			0
$982$	−62.1620	+	57.6779i	−1.98367	+	1.84058i
$983$	−7.16984	+	1.08068i	−0.228682	+	0.0344683i	−0.262384	−	0.964964i	$-0.584509\pi$
$983$	−7.16984	+	1.08068i	−0.228682	+	0.0344683i	0.0337013	+	0.999432i	$0.489271\pi$
$984$		0			0
$985$	17.9034	−	45.6171i	0.570450	−	1.45348i
$986$	25.3444	−	31.7809i	0.807131	−	1.01211i
$987$		0			0
$988$	−23.1122	−	28.9817i	−0.735296	−	0.922032i
$989$	5.87525	−	1.81228i	0.186822	−	0.0576270i
$990$		0			0
$991$	47.8894	+	14.7719i	1.52126	+	0.469246i	0.939046	−	0.343791i	$-0.111711\pi$
$991$	47.8894	+	14.7719i	1.52126	+	0.469246i	0.582212	+	0.813037i	$0.302187\pi$
$992$	0.175344	+	2.33980i	0.00556718	+	0.0742888i
$993$		0			0
$994$	−45.3697	−	22.4800i	−1.43904	−	0.713023i
$995$	−20.0399	+	87.8006i	−0.635308	+	2.78347i
$996$		0			0
$997$	40.0898	−	27.3328i	1.26966	−	0.865638i	0.274277	−	0.961651i	$-0.411561\pi$
$997$	40.0898	−	27.3328i	1.26966	−	0.865638i	0.995380	+	0.0960130i	$0.0306090\pi$
$998$	18.4563	−	31.9673i	0.584225	−	1.01191i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.109.1	✓	72
3.2	odd	2	inner	441.2.bb.f.109.6	yes	72
49.9	even	21	inner	441.2.bb.f.352.1	yes	72
147.107	odd	42	inner	441.2.bb.f.352.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.109.1	✓	72	1.1	even	1	trivial
441.2.bb.f.109.6	yes	72	3.2	odd	2	inner
441.2.bb.f.352.1	yes	72	49.9	even	21	inner
441.2.bb.f.352.6	yes	72	147.107	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80148 + 1.67153i) q^{2} +(0.301863 - 4.02808i) q^{4} +(-1.44677 + 3.68631i) q^{5} +(-0.227334 + 2.63597i) q^{7} +(3.12479 + 3.91837i) q^{8} +O(q^{10})\)	\(q+(-1.80148 + 1.67153i) q^{2} +(0.301863 - 4.02808i) q^{4} +(-1.44677 + 3.68631i) q^{5} +(-0.227334 + 2.63597i) q^{7} +(3.12479 + 3.91837i) q^{8} +(-3.55545 - 9.05915i) q^{10} +(1.06785 + 0.329389i) q^{11} +(1.36425 + 5.97717i) q^{13} +(-3.99657 - 5.12865i) q^{14} +(-4.19044 - 0.631607i) q^{16} +(1.60512 - 1.09435i) q^{17} +(-0.748418 - 1.29630i) q^{19} +(14.4120 + 6.94045i) q^{20} +(-2.47431 + 1.19156i) q^{22} +(0.555137 + 0.378486i) q^{23} +(-7.83046 - 7.26560i) q^{25} +(-12.4487 - 8.48739i) q^{26} +(10.5492 + 1.71142i) q^{28} +(-7.67124 - 3.69428i) q^{29} +(-3.00183 + 5.19933i) q^{31} +(0.322912 - 0.220158i) q^{32} +(-1.06235 + 4.65447i) q^{34} +(-9.38808 - 4.65166i) q^{35} +(-0.418449 - 5.58382i) q^{37} +(3.51507 + 1.08426i) q^{38} +(-18.9652 + 5.84998i) q^{40} +(3.55547 + 4.45842i) q^{41} +(5.70555 - 7.15454i) q^{43} +(1.64915 - 4.20196i) q^{44} +(-1.63272 + 0.246093i) q^{46} +(6.09084 - 5.65147i) q^{47} +(-6.89664 - 1.19849i) q^{49} +26.2512 q^{50} +(24.4883 - 3.69102i) q^{52} +(-0.551467 + 7.35882i) q^{53} +(-2.75917 + 3.45989i) q^{55} +(-11.0391 + 7.34607i) q^{56} +(19.9947 - 6.16756i) q^{58} +(-3.84718 - 9.80244i) q^{59} +(-0.00728034 - 0.0971493i) q^{61} +(-3.28309 - 14.3842i) q^{62} +(1.67227 - 7.32668i) q^{64} +(-24.0074 - 3.61854i) q^{65} +(-2.54112 + 4.40135i) q^{67} +(-3.92360 - 6.79588i) q^{68} +(24.6879 - 7.31260i) q^{70} +(7.01623 - 3.37884i) q^{71} +(1.90751 + 1.76991i) q^{73} +(10.0874 + 9.35971i) q^{74} +(-5.44751 + 2.62338i) q^{76} +(-1.11102 + 2.73994i) q^{77} +(7.93102 + 13.7369i) q^{79} +(8.39090 - 14.5335i) q^{80} +(-13.8575 - 2.08868i) q^{82} +(-1.32427 + 5.80199i) q^{83} +(1.71188 + 7.50023i) q^{85} +(1.68058 + 22.4258i) q^{86} +(2.04615 + 5.21352i) q^{88} +(3.40745 - 1.05106i) q^{89} +(-16.0658 + 2.23730i) q^{91} +(1.69214 - 2.12188i) q^{92} +(-1.52593 + 20.3621i) q^{94} +(5.86134 - 0.883455i) q^{95} +2.91041 q^{97} +(14.4275 - 9.36890i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

L-functions

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