LMFDB - Embedded newform 864.2.bn.a.35.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.195262 - 1.40067i) q^{2} +(-1.92375 + 0.546996i) q^{4} +(-0.729399 - 0.559687i) q^{5} +(1.92647 - 0.516196i) q^{7} +(1.14179 + 2.58772i) q^{8} +(-0.641512 + 1.13093i) q^{10} +(0.262162 - 1.99132i) q^{11} +(0.110163 - 0.0145032i) q^{13} +(-1.09919 - 2.59755i) q^{14} +(3.40159 - 2.10456i) q^{16} +4.23415 q^{17} +(-3.65777 - 1.51510i) q^{19} +(1.70932 + 0.677718i) q^{20} +(-2.84037 + 0.0216274i) q^{22} +(-0.0835920 + 0.311970i) q^{23} +(-1.07532 - 4.01316i) q^{25} +(-0.0418248 - 0.151470i) q^{26} +(-3.42368 + 2.04680i) q^{28} +(-0.0770779 - 0.100450i) q^{29} +(8.31926 - 4.80313i) q^{31} +(-3.61200 - 4.35356i) q^{32} +(-0.826771 - 5.93065i) q^{34} +(-1.69407 - 0.701707i) q^{35} +(-3.10495 - 7.49601i) q^{37} +(-1.40793 + 5.41917i) q^{38} +(0.615491 - 2.52653i) q^{40} +(-0.591162 - 0.158401i) q^{41} +(-2.62459 - 0.345533i) q^{43} +(0.584909 + 3.97419i) q^{44} +(0.453288 + 0.0561688i) q^{46} +(-7.70189 - 4.44669i) q^{47} +(-2.61736 + 1.51113i) q^{49} +(-5.41114 + 2.28979i) q^{50} +(-0.203992 + 0.0881591i) q^{52} +(-0.936389 - 2.26064i) q^{53} +(-1.30574 + 1.30574i) q^{55} +(3.53540 + 4.39577i) q^{56} +(-0.125647 + 0.127575i) q^{58} +(-1.87698 + 2.44612i) q^{59} +(-3.86495 + 2.96568i) q^{61} +(-8.35203 - 10.7147i) q^{62} +(-5.39261 + 5.90930i) q^{64} +(-0.0884699 - 0.0510781i) q^{65} +(10.5722 - 1.39186i) q^{67} +(-8.14544 + 2.31606i) q^{68} +(-0.652071 + 2.50985i) q^{70} +(1.10615 - 1.10615i) q^{71} +(-5.15157 - 5.15157i) q^{73} +(-9.89315 + 5.81269i) q^{74} +(7.86537 + 0.913878i) q^{76} +(-0.522863 - 3.97154i) q^{77} +(8.82426 - 15.2841i) q^{79} +(-3.65901 - 0.368763i) q^{80} +(-0.106436 + 0.858952i) q^{82} +(-5.47758 - 7.13853i) q^{83} +(-3.08839 - 2.36980i) q^{85} +(0.0285052 + 3.74364i) q^{86} +(5.45231 - 1.59527i) q^{88} +(12.1468 + 12.1468i) q^{89} +(0.204739 - 0.0848055i) q^{91} +(-0.00983634 - 0.645875i) q^{92} +(-4.72445 + 11.6561i) q^{94} +(1.81999 + 3.15232i) q^{95} +(-5.14292 + 8.90780i) q^{97} +(2.62766 + 3.37098i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.195262	−	1.40067i	−0.138071	−	0.990422i
$2$	−0.195262	−	1.40067i	−0.138071	−	0.990422i
$3$		0			0
$3$		0			0
$4$	−1.92375	+	0.546996i	−0.961873	+	0.273498i
$5$	−0.729399	−	0.559687i	−0.326197	−	0.250300i	0.432660	−	0.901557i	$-0.357575\pi$
$5$	−0.729399	−	0.559687i	−0.326197	−	0.250300i	−0.758857	+	0.651258i	$0.774242\pi$
$6$		0			0
$7$	1.92647	−	0.516196i	0.728137	−	0.195104i	0.124337	−	0.992240i	$-0.460320\pi$
$7$	1.92647	−	0.516196i	0.728137	−	0.195104i	0.603799	+	0.797136i	$0.293653\pi$
$8$	1.14179	+	2.58772i	0.403685	+	0.914898i
$9$		0			0
$10$	−0.641512	+	1.13093i	−0.202864	+	0.357632i
$11$	0.262162	−	1.99132i	0.0790448	−	0.600405i	−0.905380	−	0.424601i	$-0.860414\pi$
$11$	0.262162	−	1.99132i	0.0790448	−	0.600405i	0.984425	−	0.175804i	$-0.0562523\pi$
$12$		0			0
$13$	0.110163	−	0.0145032i	0.0305537	−	0.00402247i	−0.115234	−	0.993338i	$-0.536762\pi$
$13$	0.110163	−	0.0145032i	0.0305537	−	0.00402247i	0.145788	+	0.989316i	$0.453428\pi$
$14$	−1.09919	−	2.59755i	−0.293770	−	0.694225i
$15$		0			0
$16$	3.40159	−	2.10456i	0.850398	−	0.526140i
$17$	4.23415			1.02693			0.513467	−	0.858110i	$-0.328361\pi$
$17$	4.23415			1.02693			0.513467	+	0.858110i	$0.328361\pi$
$18$		0			0
$19$	−3.65777	−	1.51510i	−0.839150	−	0.347587i	−0.0786318	−	0.996904i	$-0.525055\pi$
$19$	−3.65777	−	1.51510i	−0.839150	−	0.347587i	−0.760518	+	0.649316i	$0.775055\pi$
$20$	1.70932	+	0.677718i	0.382216	+	0.151542i
$21$		0			0
$22$	−2.84037	+	0.0216274i	−0.605568	+	0.00461098i
$23$	−0.0835920	+	0.311970i	−0.0174301	+	0.0650502i	−0.974093	−	0.226147i	$-0.927387\pi$
$23$	−0.0835920	+	0.311970i	−0.0174301	+	0.0650502i	0.956663	+	0.291197i	$0.0940536\pi$
$24$		0			0
$25$	−1.07532	−	4.01316i	−0.215065	−	0.802632i
$26$	−0.0418248	−	0.151470i	−0.00820253	−	0.0297056i
$27$		0			0
$28$	−3.42368	+	2.04680i	−0.647014	+	0.386809i
$29$	−0.0770779	−	0.100450i	−0.0143130	−	0.0186531i	0.786142	−	0.618046i	$-0.212075\pi$
$29$	−0.0770779	−	0.100450i	−0.0143130	−	0.0186531i	−0.800455	+	0.599393i	$0.795409\pi$
$30$		0			0
$31$	8.31926	−	4.80313i	1.49418	−	0.862667i	0.494206	−	0.869345i	$-0.335459\pi$
$31$	8.31926	−	4.80313i	1.49418	−	0.862667i	0.999978	+	0.00667771i	$0.00212560\pi$
$32$	−3.61200	−	4.35356i	−0.638517	−	0.769608i
$33$		0			0
$34$	−0.826771	−	5.93065i	−0.141790	−	1.01710i
$35$	−1.69407	−	0.701707i	−0.286350	−	0.118610i
$36$		0			0
$37$	−3.10495	−	7.49601i	−0.510450	−	1.23234i	−0.943622	−	0.331025i	$-0.892606\pi$
$37$	−3.10495	−	7.49601i	−0.510450	−	1.23234i	0.433172	−	0.901312i	$-0.357394\pi$
$38$	−1.40793	+	5.41917i	−0.228396	+	0.879105i
$39$		0			0
$40$	0.615491	−	2.52653i	0.0973177	−	0.399479i
$41$	−0.591162	−	0.158401i	−0.0923240	−	0.0247381i	0.212361	−	0.977191i	$-0.431885\pi$
$41$	−0.591162	−	0.158401i	−0.0923240	−	0.0247381i	−0.304685	+	0.952453i	$0.598551\pi$
$42$		0			0
$43$	−2.62459	−	0.345533i	−0.400246	−	0.0526933i	−0.0722833	−	0.997384i	$-0.523029\pi$
$43$	−2.62459	−	0.345533i	−0.400246	−	0.0526933i	−0.327962	+	0.944691i	$0.606362\pi$
$44$	0.584909	+	3.97419i	0.0881784	+	0.599131i
$45$		0			0
$46$	0.453288	+	0.0561688i	0.0668337	+	0.00828163i
$47$	−7.70189	−	4.44669i	−1.12344	−	0.648616i	−0.181160	−	0.983454i	$-0.557985\pi$
$47$	−7.70189	−	4.44669i	−1.12344	−	0.648616i	−0.942276	+	0.334837i	$0.891319\pi$
$48$		0			0
$49$	−2.61736	+	1.51113i	−0.373908	+	0.215876i
$50$	−5.41114	+	2.28979i	−0.765250	+	0.323825i
$51$		0			0
$52$	−0.203992	+	0.0881591i	−0.0282886	+	0.0122255i
$53$	−0.936389	−	2.26064i	−0.128623	−	0.310523i	0.846428	−	0.532502i	$-0.178748\pi$
$53$	−0.936389	−	2.26064i	−0.128623	−	0.310523i	−0.975051	+	0.221979i	$0.928748\pi$
$54$		0			0
$55$	−1.30574	+	1.30574i	−0.176065	+	0.176065i
$56$	3.53540	+	4.39577i	0.472438	+	0.587410i
$57$		0			0
$58$	−0.125647	+	0.127575i	−0.0164982	+	0.0167514i
$59$	−1.87698	+	2.44612i	−0.244361	+	0.318458i	−0.899391	−	0.437145i	$-0.855990\pi$
$59$	−1.87698	+	2.44612i	−0.244361	+	0.318458i	0.655029	+	0.755603i	$0.272656\pi$
$60$		0			0
$61$	−3.86495	+	2.96568i	−0.494856	+	0.379716i	−0.825826	−	0.563925i	$-0.809291\pi$
$61$	−3.86495	+	2.96568i	−0.494856	+	0.379716i	0.330970	+	0.943641i	$0.392624\pi$
$62$	−8.35203	−	10.7147i	−1.06071	−	1.36076i
$63$		0			0
$64$	−5.39261	+	5.90930i	−0.674076	+	0.738662i
$65$	−0.0884699	−	0.0510781i	−0.0109733	−	0.00633546i
$66$		0			0
$67$	10.5722	−	1.39186i	1.29160	−	0.170043i	0.546763	−	0.837287i	$-0.315860\pi$
$67$	10.5722	−	1.39186i	1.29160	−	0.170043i	0.744839	+	0.667244i	$0.232526\pi$
$68$	−8.14544	+	2.31606i	−0.987779	+	0.280864i
$69$		0			0
$70$	−0.652071	+	2.50985i	−0.0779374	+	0.299984i
$71$	1.10615	−	1.10615i	0.131276	−	0.131276i	−0.638416	−	0.769692i	$-0.720410\pi$
$71$	1.10615	−	1.10615i	0.131276	−	0.131276i	0.769692	+	0.638416i	$0.220410\pi$
$72$		0			0
$73$	−5.15157	−	5.15157i	−0.602946	−	0.602946i	0.338147	−	0.941093i	$-0.390200\pi$
$73$	−5.15157	−	5.15157i	−0.602946	−	0.602946i	−0.941093	+	0.338147i	$0.890200\pi$
$74$	−9.89315	+	5.81269i	−1.15005	+	0.675712i
$75$		0			0
$76$	7.86537	+	0.913878i	0.902220	+	0.104829i
$77$	−0.522863	−	3.97154i	−0.0595857	−	0.452599i
$78$		0			0
$79$	8.82426	−	15.2841i	0.992806	−	1.71959i	0.392712	−	0.919661i	$-0.371537\pi$
$79$	8.82426	−	15.2841i	0.992806	−	1.71959i	0.600094	−	0.799930i	$-0.295130\pi$
$80$	−3.65901	−	0.368763i	−0.409090	−	0.0412290i
$81$		0			0
$82$	−0.106436	+	0.858952i	−0.0117539	+	0.0948554i
$83$	−5.47758	−	7.13853i	−0.601243	−	0.783555i	0.389248	−	0.921133i	$-0.372735\pi$
$83$	−5.47758	−	7.13853i	−0.601243	−	0.783555i	−0.990491	+	0.137578i	$0.956068\pi$
$84$		0			0
$85$	−3.08839	−	2.36980i	−0.334983	−	0.257041i
$86$	0.0285052	+	3.74364i	0.00307380	+	0.403688i
$87$		0			0
$88$	5.45231	−	1.59527i	0.581218	−	0.170057i
$89$	12.1468	+	12.1468i	1.28756	+	1.28756i	0.936264	+	0.351298i	$0.114259\pi$
$89$	12.1468	+	12.1468i	1.28756	+	1.28756i	0.351298	+	0.936264i	$0.385741\pi$
$90$		0			0
$91$	0.204739	−	0.0848055i	0.0214624	−	0.00889004i
$92$	−0.00983634	−	0.645875i	−0.00102551	−	0.0673371i
$93$		0			0
$94$	−4.72445	+	11.6561i	−0.487290	+	1.20223i
$95$	1.81999	+	3.15232i	0.186727	+	0.323421i
$96$		0			0
$97$	−5.14292	+	8.90780i	−0.522184	+	0.904450i	0.477483	+	0.878641i	$0.341549\pi$
$97$	−5.14292	+	8.90780i	−0.522184	+	0.904450i	−0.999667	+	0.0258086i	$0.991784\pi$
$98$	2.62766	+	3.37098i	0.265434	+	0.340520i
$99$		0			0
$100$	4.26383	+	7.13210i	0.426383	+	0.713210i
$101$	−0.508954	+	3.86589i	−0.0506428	+	0.384670i	0.947289	+	0.320382i	$0.103811\pi$
$101$	−0.508954	+	3.86589i	−0.0506428	+	0.384670i	−0.997931	+	0.0642885i	$0.979522\pi$
$102$		0			0
$103$	3.04298	−	11.3565i	0.299833	−	1.11899i	−0.637469	−	0.770476i	$-0.720019\pi$
$103$	3.04298	−	11.3565i	0.299833	−	1.11899i	0.937302	−	0.348517i	$-0.113315\pi$
$104$	0.163314	+	0.268511i	0.0160142	+	0.0263297i
$105$		0			0
$106$	−2.98357	+	1.75299i	−0.289790	+	0.170265i
$107$	16.2878	−	6.74663i	1.57460	−	0.652221i	0.587055	−	0.809547i	$-0.300287\pi$
$107$	16.2878	−	6.74663i	1.57460	−	0.652221i	0.987547	+	0.157326i	$0.0502872\pi$
$108$		0			0
$109$	−5.97592	+	14.4272i	−0.572389	+	1.38187i	0.327126	+	0.944981i	$0.393920\pi$
$109$	−5.97592	+	14.4272i	−0.572389	+	1.38187i	−0.899515	+	0.436890i	$0.856080\pi$
$110$	2.08386	+	1.57394i	0.198689	+	0.150069i
$111$		0			0
$112$	5.46669	−	5.81026i	0.516554	−	0.549018i
$113$	6.51148	+	11.2782i	0.612549	+	1.06097i	0.990809	+	0.135266i	$0.0431890\pi$
$113$	6.51148	+	11.2782i	0.612549	+	1.06097i	−0.378261	+	0.925699i	$0.623478\pi$
$114$		0			0
$115$	0.235577	−	0.180765i	0.0219677	−	0.0168564i
$116$	0.203224	+	0.151079i	0.0188689	+	0.0140273i
$117$		0			0
$118$	3.79271	+	2.15139i	0.349147	+	0.198051i
$119$	8.15697	−	2.18565i	0.747748	−	0.200358i
$120$		0			0
$121$	6.72857	+	1.80291i	0.611688	+	0.163901i
$122$	4.90861	+	4.83442i	0.444405	+	0.437688i
$123$		0			0
$124$	−13.3768	+	13.7906i	−1.20128	+	1.23843i
$125$	−3.22095	+	7.77605i	−0.288090	+	0.695511i
$126$		0			0
$127$			7.79985i			0.692125i	0.938212	+	0.346062i	$0.112481\pi$
$127$			7.79985i			0.692125i	−0.938212	+	0.346062i	$0.887519\pi$
$128$	9.32994	+	6.39940i	0.824658	+	0.565632i
$129$		0			0
$130$	−0.0542687	+	0.133891i	−0.00475968	+	0.0117430i
$131$	−2.50627	−	19.0370i	−0.218974	−	1.66327i	−0.649251	−	0.760574i	$-0.724918\pi$
$131$	−2.50627	−	19.0370i	−0.218974	−	1.66327i	0.430277	−	0.902697i	$-0.358416\pi$
$132$		0			0
$133$	−7.82867	−	1.03066i	−0.678832	−	0.0893699i
$134$	−4.01389	−	14.5364i	−0.346747	−	1.25575i
$135$		0			0
$136$	4.83454	+	10.9568i	0.414558	+	0.939539i
$137$	1.01413	+	3.78480i	0.0866432	+	0.323357i	0.995620	−	0.0934892i	$-0.0298020\pi$
$137$	1.01413	+	3.78480i	0.0866432	+	0.323357i	−0.908977	+	0.416846i	$0.863135\pi$
$138$		0			0
$139$	−6.92686	+	9.02726i	−0.587529	+	0.765682i	−0.988633	−	0.150350i	$-0.951960\pi$
$139$	−6.92686	+	9.02726i	−0.587529	+	0.765682i	0.401104	+	0.916032i	$0.368627\pi$
$140$	3.64279	+	0.423256i	0.307872	+	0.0357717i
$141$		0			0
$142$	−1.76534	−	1.33336i	−0.148144	−	0.111893i
$143$		−	0.223171i		−	0.0186625i
$144$		0			0
$145$			0.116407i			0.00966711i
$146$	−6.20974	+	8.22155i	−0.513922	+	0.680421i
$147$		0			0
$148$	10.0734	+	12.7220i	0.828030	+	1.04574i
$149$	13.0959	−	17.0669i	1.07286	−	1.39817i	0.161346	−	0.986898i	$-0.448417\pi$
$149$	13.0959	−	17.0669i	1.07286	−	1.39817i	0.911511	−	0.411276i	$-0.134917\pi$
$150$		0			0
$151$	−0.570547	−	2.12931i	−0.0464305	−	0.173281i	0.938817	−	0.344416i	$-0.111923\pi$
$151$	−0.570547	−	2.12931i	−0.0464305	−	0.173281i	−0.985248	+	0.171135i	$0.945256\pi$
$152$	−0.255771	−	11.1952i	−0.0207458	−	0.908053i
$153$		0			0
$154$	−5.46071	+	1.50785i	−0.440037	+	0.121506i
$155$	−8.75631	−	1.15279i	−0.703323	−	0.0925943i
$156$		0			0
$157$	−0.334717	−	2.54243i	−0.0267133	−	0.202908i	0.972884	−	0.231295i	$-0.0742962\pi$
$157$	−0.334717	−	2.54243i	−0.0267133	−	0.202908i	−0.999597	+	0.0283871i	$0.990963\pi$
$158$	−23.1309	−	9.37546i	−1.84020	−	0.745871i
$159$		0			0
$160$	0.197952	+	5.19707i	0.0156495	+	0.410864i
$161$			0.644149i			0.0507661i
$162$		0			0
$163$	−3.80321	+	9.18176i	−0.297890	+	0.719171i	0.702085	+	0.712093i	$0.252253\pi$
$163$	−3.80321	+	9.18176i	−0.297890	+	0.719171i	−0.999975	+	0.00707721i	$0.997747\pi$
$164$	1.22389	−	0.0186392i	0.0955698	−	0.00145548i
$165$		0			0
$166$	−8.92914	+	9.06617i	−0.693036	+	0.703671i
$167$	19.6605	+	5.26802i	1.52138	+	0.407652i	0.920195	−	0.391460i	$-0.128030\pi$
$167$	19.6605	+	5.26802i	1.52138	+	0.407652i	0.601182	+	0.799112i	$0.294697\pi$
$168$		0			0
$169$	−12.5451	+	3.36145i	−0.965008	+	0.258573i
$170$	−2.71626	+	4.78854i	−0.208328	+	0.367264i
$171$		0			0
$172$	5.23804	−	0.770919i	0.399397	−	0.0587820i
$173$	6.80745	−	5.22354i	0.517561	−	0.397138i	−0.316685	−	0.948531i	$-0.602570\pi$
$173$	6.80745	−	5.22354i	0.517561	−	0.397138i	0.834246	+	0.551392i	$0.185903\pi$
$174$		0			0
$175$	−4.14315	−	7.17615i	−0.313193	−	0.542466i
$176$	−3.29908	−	7.32538i	−0.248678	−	0.552171i
$177$		0			0
$178$	14.6419	−	19.3855i	1.09745	−	1.45300i
$179$	−2.02726	+	4.89424i	−0.151525	+	0.365813i	−0.981355	−	0.192202i	$-0.938437\pi$
$179$	−2.02726	+	4.89424i	−0.151525	+	0.365813i	0.829831	+	0.558015i	$0.188437\pi$
$180$		0			0
$181$	16.6205	−	6.88442i	1.23539	−	0.511715i	0.333118	−	0.942885i	$-0.391899\pi$
$181$	16.6205	−	6.88442i	1.23539	−	0.511715i	0.902271	+	0.431170i	$0.141899\pi$
$182$	−0.158762	−	0.270212i	−0.0117682	−	0.0200294i
$183$		0			0
$184$	−0.902736	+	0.139892i	−0.0665505	+	0.0103130i
$185$	−1.93068	+	7.20538i	−0.141946	+	0.529750i
$186$		0			0
$187$	1.11003	−	8.43154i	0.0811737	−	0.616576i
$188$	17.2488	+	4.34139i	1.25800	+	0.316629i
$189$		0			0
$190$	4.05998	−	3.16473i	0.294542	−	0.229594i
$191$	7.06095	−	12.2299i	0.510912	−	0.884926i	−0.489008	−	0.872279i	$-0.662641\pi$
$191$	7.06095	−	12.2299i	0.510912	−	0.884926i	0.999920	−	0.0126465i	$-0.00402563\pi$
$192$		0			0
$193$	5.73584	+	9.93477i	0.412875	+	0.715121i	0.995203	−	0.0978336i	$-0.0311913\pi$
$193$	5.73584	+	9.93477i	0.412875	+	0.715121i	−0.582328	+	0.812954i	$0.697858\pi$
$194$	13.4811	+	5.46417i	0.967886	+	0.392304i
$195$		0			0
$196$	4.20854	−	4.33871i	0.300610	−	0.309908i
$197$	−11.0795	+	4.58927i	−0.789380	+	0.326972i	−0.740694	−	0.671842i	$-0.765503\pi$
$197$	−11.0795	+	4.58927i	−0.789380	+	0.326972i	−0.0486857	+	0.998814i	$0.515503\pi$
$198$		0			0
$199$	−9.49285	−	9.49285i	−0.672930	−	0.672930i	0.285460	−	0.958391i	$-0.407854\pi$
$199$	−9.49285	−	9.49285i	−0.672930	−	0.672930i	−0.958391	+	0.285460i	$0.907854\pi$
$200$	9.15714	−	7.36484i	0.647508	−	0.520773i
$201$		0			0
$202$	5.51420	−	0.0419868i	0.387978	−	0.00295418i
$203$	−0.200340	−	0.153726i	−0.0140611	−	0.0107895i
$204$		0			0
$205$	0.342538	+	0.446404i	0.0239239	+	0.0311782i
$206$	−16.5009	−	2.04470i	−1.14967	−	0.142461i
$207$		0			0
$208$	0.344206	−	0.281178i	0.0238664	−	0.0194962i
$209$	−3.97597	+	6.88658i	−0.275024	+	0.476355i
$210$		0			0
$211$	2.21223	+	16.8035i	0.152296	+	1.15680i	0.881390	+	0.472389i	$0.156608\pi$
$211$	2.21223	+	16.8035i	0.152296	+	1.15680i	−0.729094	+	0.684414i	$0.760058\pi$
$212$	3.03794	+	3.83670i	0.208646	+	0.263506i
$213$		0			0
$214$	−12.6302	−	21.4965i	−0.863382	−	1.46947i
$215$	1.72098	+	1.72098i	0.117370	+	0.117370i
$216$		0			0
$217$	13.5474	−	13.5474i	0.919660	−	0.919660i
$218$	21.3745	+	5.55321i	1.44767	+	0.376111i
$219$		0			0
$220$	1.79767	−	3.22613i	0.121199	−	0.217506i
$221$	0.466446	−	0.0614088i	0.0313766	−	0.00413081i
$222$		0			0
$223$	6.38525	+	3.68653i	0.427588	+	0.246868i	0.698319	−	0.715787i	$-0.253932\pi$
$223$	6.38525	+	3.68653i	0.427588	+	0.246868i	−0.270731	+	0.962655i	$0.587265\pi$
$224$	−9.20568	−	6.52250i	−0.615081	−	0.435803i
$225$		0			0
$226$	14.5256	−	11.3226i	0.966228	−	0.753171i
$227$	−5.33361	+	4.09262i	−0.354004	+	0.271637i	−0.770419	−	0.637538i	$-0.779953\pi$
$227$	−5.33361	+	4.09262i	−0.354004	+	0.271637i	0.416415	+	0.909175i	$0.363286\pi$
$228$		0			0
$229$	−7.55775	+	9.84945i	−0.499430	+	0.650870i	−0.973249	−	0.229752i	$-0.926208\pi$
$229$	−7.55775	+	9.84945i	−0.499430	+	0.650870i	0.473819	+	0.880622i	$0.342875\pi$
$230$	−0.299191	−	0.294669i	−0.0197281	−	0.0194299i
$231$		0			0
$232$	0.171929	−	0.314149i	0.0112877	−	0.0206249i
$233$	−17.7874	+	17.7874i	−1.16529	+	1.16529i	−0.181990	+	0.983300i	$0.558254\pi$
$233$	−17.7874	+	17.7874i	−1.16529	+	1.16529i	−0.983300	+	0.181990i	$0.941746\pi$
$234$		0			0
$235$	3.12899	+	7.55406i	0.204113	+	0.492772i
$236$	2.27280	−	5.73241i	0.147947	−	0.373148i
$237$		0			0
$238$	−4.65412	−	10.9984i	−0.301682	−	0.712922i
$239$	13.9417	−	8.04926i	0.901815	−	0.520663i	0.0240263	−	0.999711i	$-0.492351\pi$
$239$	13.9417	−	8.04926i	0.901815	−	0.520663i	0.877789	+	0.479048i	$0.159018\pi$
$240$		0			0
$241$	17.2563	+	9.96293i	1.11158	+	0.641769i	0.939237	−	0.343269i	$-0.111534\pi$
$241$	17.2563	+	9.96293i	1.11158	+	0.641769i	0.172339	+	0.985038i	$0.444867\pi$
$242$	1.21145	−	9.77654i	0.0778749	−	0.628460i
$243$		0			0
$244$	5.81296	−	7.81932i	0.372137	−	0.500581i
$245$	2.75486	+	0.362684i	0.176001	+	0.0231710i
$246$		0			0
$247$	−0.424924	−	0.113858i	−0.0270373	−	0.00724462i
$248$	21.9280	+	16.0437i	1.39243	+	1.01878i
$249$		0			0
$250$	11.5206	+	2.99311i	0.728627	+	0.189301i
$251$	5.94030	+	14.3412i	0.374948	+	0.905205i	0.992896	+	0.118986i	$0.0379644\pi$
$251$	5.94030	+	14.3412i	0.374948	+	0.905205i	−0.617948	+	0.786219i	$0.712036\pi$
$252$		0			0
$253$	0.599316	+	0.248245i	0.0376787	+	0.0156070i
$254$	10.9250	−	1.52302i	0.685496	−	0.0955626i
$255$		0			0
$256$	7.14165	−	14.3177i	0.446353	−	0.894857i
$257$	16.3222	−	9.42360i	1.01815	−	0.587828i	0.104581	−	0.994516i	$-0.466650\pi$
$257$	16.3222	−	9.42360i	1.01815	−	0.587828i	0.913567	+	0.406688i	$0.133316\pi$
$258$		0			0
$259$	−9.85099	−	12.8381i	−0.612111	−	0.797719i
$260$	0.198133	+	0.0498686i	0.0122877	+	0.00309272i
$261$		0			0
$262$	−26.1752	+	7.22766i	−1.61711	+	0.446527i
$263$	−2.04369	−	7.62714i	−0.126019	−	0.470309i	0.873855	−	0.486187i	$-0.161613\pi$
$263$	−2.04369	−	7.62714i	−0.126019	−	0.470309i	−0.999874	+	0.0158774i	$0.994946\pi$
$264$		0			0
$265$	−0.582252	+	2.17299i	−0.0357675	+	0.133486i
$266$	0.0850260	+	11.1666i	0.00521328	+	0.684669i
$267$		0			0
$268$	−19.5769	+	8.46054i	−1.19585	+	0.516810i
$269$	−21.4230	−	8.87371i	−1.30619	−	0.541040i	−0.382417	−	0.923990i	$-0.624908\pi$
$269$	−21.4230	−	8.87371i	−1.30619	−	0.541040i	−0.923769	+	0.382950i	$0.874908\pi$
$270$		0			0
$271$	17.4563			1.06039			0.530196	−	0.847875i	$-0.322118\pi$
$271$	17.4563			1.06039			0.530196	+	0.847875i	$0.322118\pi$
$272$	14.4029	−	8.91104i	0.873302	−	0.540311i
$273$		0			0
$274$	5.10322	−	2.15949i	0.308297	−	0.130460i
$275$	−8.27338	+	1.08921i	−0.498904	+	0.0656819i
$276$		0			0
$277$	0.263693	−	2.00295i	0.0158438	−	0.120345i	−0.981695	−	0.190458i	$-0.939003\pi$
$277$	0.263693	−	2.00295i	0.0158438	−	0.120345i	0.997539	+	0.0701129i	$0.0223360\pi$
$278$	13.9968	+	7.93955i	0.839470	+	0.476183i
$279$		0			0
$280$	−0.118459	−	5.18499i	−0.00707926	−	0.309862i
$281$	−26.0116	+	6.96978i	−1.55172	+	0.415782i	−0.930031	−	0.367481i	$-0.880220\pi$
$281$	−26.0116	+	6.96978i	−1.55172	+	0.415782i	−0.621690	+	0.783263i	$0.713554\pi$
$282$		0			0
$283$	7.34479	+	5.63586i	0.436603	+	0.335017i	0.803563	−	0.595220i	$-0.202935\pi$
$283$	7.34479	+	5.63586i	0.436603	+	0.335017i	−0.366961	+	0.930236i	$0.619602\pi$
$284$	−1.52289	+	2.73301i	−0.0903671	+	0.162175i
$285$		0			0
$286$	−0.312589	+	0.0435770i	−0.0184838	+	0.00257676i
$287$	−1.22062			−0.0720510
$288$		0			0
$289$	0.928068			0.0545922
$290$	0.163048	−	0.0227300i	0.00957452	−	0.00133475i
$291$		0			0
$292$	12.7282	+	7.09242i	0.744862	+	0.415053i
$293$	9.13260	+	7.00769i	0.533532	+	0.409394i	0.840081	−	0.542461i	$-0.182508\pi$
$293$	9.13260	+	7.00769i	0.533532	+	0.409394i	−0.306549	+	0.951855i	$0.599174\pi$
$294$		0			0
$295$	2.73813	−	0.733679i	0.159420	−	0.0427164i
$296$	15.8524	−	16.5937i	0.921401	−	0.964486i
$297$		0			0
$298$	−26.4622	−	15.0105i	−1.53291	−	0.869533i
$299$	−0.00468417	+	0.0355798i	−0.000270893	+	0.00205763i
$300$		0			0
$301$	−5.23454	+	0.689141i	−0.301714	+	0.0397214i
$302$	−2.87105	+	1.21492i	−0.165211	+	0.0699109i
$303$		0			0
$304$	−15.6309	+	2.54426i	−0.896491	+	0.145923i
$305$	4.47894			0.256463
$306$		0			0
$307$	−1.94912	−	0.807354i	−0.111242	−	0.0460781i	0.326368	−	0.945243i	$-0.394175\pi$
$307$	−1.94912	−	0.807354i	−0.111242	−	0.0460781i	−0.437610	+	0.899165i	$0.644175\pi$
$308$	3.17827	+	7.35422i	0.181099	+	0.419046i
$309$		0			0
$310$	0.0951010	+	12.4898i	0.00540137	+	0.709372i
$311$	−3.94549	+	14.7248i	−0.223728	+	0.834965i	0.759182	+	0.650879i	$0.225599\pi$
$311$	−3.94549	+	14.7248i	−0.223728	+	0.834965i	−0.982910	+	0.184087i	$0.941067\pi$
$312$		0			0
$313$	6.71688	+	25.0677i	0.379660	+	1.41691i	0.846415	+	0.532525i	$0.178757\pi$
$313$	6.71688	+	25.0677i	0.379660	+	1.41691i	−0.466754	+	0.884387i	$0.654577\pi$
$314$	−3.49574	+	0.965268i	−0.197276	+	0.0544732i
$315$		0			0
$316$	−8.61530	+	34.2295i	−0.484649	+	1.92556i
$317$	7.61568	+	9.92495i	0.427739	+	0.557441i	0.956651	−	0.291236i	$-0.0940665\pi$
$317$	7.61568	+	9.92495i	0.427739	+	0.557441i	−0.528912	+	0.848677i	$0.677400\pi$
$318$		0			0
$319$	−0.220234	+	0.127152i	−0.0123308	+	0.00711916i
$320$	7.24072	−	1.29206i	0.404768	−	0.0722282i
$321$		0			0
$322$	0.902240	−	0.125778i	0.0502799	−	0.00700934i
$323$	−15.4876	−	6.41516i	−0.861752	−	0.356949i
$324$		0			0
$325$	−0.176664	−	0.426505i	−0.00979957	−	0.0236583i
$326$	13.6032	+	3.53418i	0.753413	+	0.195740i
$327$		0			0
$328$	−0.265087	−	1.71063i	−0.0146370	−	0.0944535i
$329$	−17.1328	−	4.59072i	−0.944562	−	0.253095i
$330$		0			0
$331$	5.97140	+	0.786149i	0.328218	+	0.0432107i	0.292835	−	0.956163i	$-0.405401\pi$
$331$	5.97140	+	0.786149i	0.328218	+	0.0432107i	0.0353832	+	0.999374i	$0.488735\pi$
$332$	14.4422	+	10.7365i	0.792620	+	0.589242i
$333$		0			0
$334$	3.53979	−	28.5665i	0.193689	−	1.56309i
$335$	−8.49037	−	4.90192i	−0.463878	−	0.267820i
$336$		0			0
$337$	6.79715	−	3.92434i	0.370264	−	0.213772i	−0.303310	−	0.952892i	$-0.598092\pi$
$337$	6.79715	−	3.92434i	0.370264	−	0.213772i	0.673574	+	0.739120i	$0.264758\pi$
$338$	7.15787	+	16.9152i	0.389337	+	0.920064i
$339$		0			0
$340$	7.23754	+	2.86956i	0.392511	+	0.155624i
$341$	−7.38356	−	17.8255i	−0.399842	−	0.965304i
$342$		0			0
$343$	−14.1341	+	14.1341i	−0.763171	+	0.763171i
$344$	−2.10259	−	7.18623i	−0.113364	−	0.387455i
$345$		0			0
$346$	−8.64568	−	8.51502i	−0.464795	−	0.457770i
$347$	−14.4370	+	18.8146i	−0.775017	+	1.01002i	0.224352	+	0.974508i	$0.427974\pi$
$347$	−14.4370	+	18.8146i	−0.775017	+	1.01002i	−0.999369	+	0.0355141i	$0.988693\pi$
$348$		0			0
$349$	4.10745	−	3.15175i	0.219866	−	0.168709i	−0.492955	−	0.870055i	$-0.664083\pi$
$349$	4.10745	−	3.15175i	0.219866	−	0.168709i	0.712822	+	0.701345i	$0.247417\pi$
$350$	−9.24240	+	7.20441i	−0.494027	+	0.385092i
$351$		0			0
$352$	−9.61625	+	6.05129i	−0.512548	+	0.322535i
$353$	−4.00920	−	2.31471i	−0.213388	−	0.123200i	0.389497	−	0.921028i	$-0.372649\pi$
$353$	−4.00920	−	2.31471i	−0.213388	−	0.123200i	−0.602885	+	0.797828i	$0.705982\pi$
$354$		0			0
$355$	−1.42592	+	0.187727i	−0.0756802	+	0.00996349i
$356$	−30.0117	−	16.7231i	−1.59062	−	0.886325i
$357$		0			0
$358$	7.25106	+	1.88386i	0.383231	+	0.0995652i
$359$	−6.59986	+	6.59986i	−0.348328	+	0.348328i	−0.859486	−	0.511159i	$-0.829216\pi$
$359$	−6.59986	+	6.59986i	−0.348328	+	0.348328i	0.511159	+	0.859486i	$0.329216\pi$
$360$		0			0
$361$	−2.35126	−	2.35126i	−0.123751	−	0.123751i
$362$	−12.8881	−	21.9355i	−0.677385	−	1.15290i
$363$		0			0
$364$	−0.347477	+	0.275135i	−0.0182127	+	0.0144210i
$365$	0.874280	+	6.64082i	0.0457619	+	0.347596i
$366$		0			0
$367$	12.4616	−	21.5841i	0.650488	−	1.12668i	−0.332516	−	0.943098i	$-0.607898\pi$
$367$	12.4616	−	21.5841i	0.650488	−	1.12668i	0.983005	−	0.183581i	$-0.0587691\pi$
$368$	0.372213	+	1.23712i	0.0194030	+	0.0644892i
$369$		0			0
$370$	10.4693	+	1.29730i	0.544275	+	0.0674433i
$371$	−2.97086	−	3.87170i	−0.154239	−	0.201009i
$372$		0			0
$373$	−20.2126	−	15.5097i	−1.04657	−	0.803060i	−0.0657203	−	0.997838i	$-0.520935\pi$
$373$	−20.2126	−	15.5097i	−1.04657	−	0.803060i	−0.980847	+	0.194779i	$0.937601\pi$
$374$	−12.0265	+	0.0915738i	−0.621878	+	0.00473517i
$375$		0			0
$376$	2.71281	−	25.0076i	0.139903	−	1.28967i
$377$	−0.00994796	−	0.00994796i	−0.000512346	−	0.000512346i
$378$		0			0
$379$	−6.04583	+	2.50427i	−0.310554	+	0.128636i	−0.532517	−	0.846420i	$-0.678754\pi$
$379$	−6.04583	+	2.50427i	−0.310554	+	0.128636i	0.221963	+	0.975055i	$0.428754\pi$
$380$	−5.22551	−	5.06873i	−0.268063	−	0.260020i
$381$		0			0
$382$	−18.5088	−	7.50200i	−0.946993	−	0.383836i
$383$	6.29503	+	10.9033i	0.321661	+	0.557133i	0.980831	−	0.194861i	$-0.0624256\pi$
$383$	6.29503	+	10.9033i	0.321661	+	0.557133i	−0.659170	+	0.751994i	$0.729092\pi$
$384$		0			0
$385$	−1.84144	+	3.18947i	−0.0938486	+	0.162551i
$386$	12.7953	−	9.97390i	0.651265	−	0.507658i
$387$		0			0
$388$	5.02114	−	19.9495i	0.254910	−	1.01278i
$389$	0.774161	−	5.88033i	0.0392515	−	0.298145i	−0.960548	−	0.278115i	$-0.910290\pi$
$389$	0.774161	−	5.88033i	0.0392515	−	0.298145i	0.999799	−	0.0200301i	$-0.00637619\pi$
$390$		0			0
$391$	−0.353941	+	1.32093i	−0.0178996	+	0.0668022i
$392$	−6.89887	−	5.04759i	−0.348446	−	0.254942i
$393$		0			0
$394$	8.59145	+	14.6226i	0.432831	+	0.736674i
$395$	−14.9907	+	6.20935i	−0.754264	+	0.312426i
$396$		0			0
$397$	−7.21072	+	17.4082i	−0.361896	+	0.873693i	0.633127	+	0.774048i	$0.281771\pi$
$397$	−7.21072	+	17.4082i	−0.361896	+	0.873693i	−0.995023	+	0.0996456i	$0.968229\pi$
$398$	−11.4427	+	15.1499i	−0.573573	+	0.759398i
$399$		0			0
$400$	−12.1037	−	11.3880i	−0.605187	−	0.569402i
$401$	−3.48119	−	6.02959i	−0.173842	−	0.301104i	0.765918	−	0.642939i	$-0.222285\pi$
$401$	−3.48119	−	6.02959i	−0.173842	−	0.301104i	−0.939760	+	0.341835i	$0.888952\pi$
$402$		0			0
$403$	0.846813	−	0.649782i	0.0421827	−	0.0323680i
$404$	−1.13553	−	7.71538i	−0.0564946	−	0.383854i
$405$		0			0
$406$	−0.176201	+	0.310627i	−0.00874469	+	0.0154161i
$407$	−15.7409	+	4.21777i	−0.780249	+	0.209067i
$408$		0			0
$409$	−15.0275	−	4.02660i	−0.743062	−	0.199103i	−0.132623	−	0.991167i	$-0.542340\pi$
$409$	−15.0275	−	4.02660i	−0.743062	−	0.199103i	−0.610438	+	0.792064i	$0.709007\pi$
$410$	0.558379	−	0.566948i	0.0275764	−	0.0279995i
$411$		0			0
$412$	0.358069	+	23.5116i	0.0176408	+	1.15833i
$413$	−2.35326	+	5.68126i	−0.115796	+	0.279557i
$414$		0			0
$415$			8.27257i			0.406084i
$416$	−0.461048	−	0.427215i	−0.0226047	−	0.0209459i
$417$		0			0
$418$	10.4222	+	4.22433i	0.509765	+	0.206619i
$419$	−3.75071	−	28.4894i	−0.183234	−	1.39180i	−0.797794	−	0.602930i	$-0.794000\pi$
$419$	−3.75071	−	28.4894i	−0.183234	−	1.39180i	0.614560	−	0.788870i	$-0.289334\pi$
$420$		0			0
$421$	−16.1708	−	2.12893i	−0.788118	−	0.103758i	−0.274285	−	0.961648i	$-0.588441\pi$
$421$	−16.1708	−	2.12893i	−0.788118	−	0.103758i	−0.513832	+	0.857891i	$0.671775\pi$
$422$	23.1042	−	6.37970i	1.12470	−	0.310559i
$423$		0			0
$424$	4.78075	−	5.00431i	0.232174	−	0.243031i
$425$	−4.55308	−	16.9923i	−0.220857	−	0.824249i
$426$		0			0
$427$	−5.91483	+	7.70835i	−0.286239	+	0.373033i
$428$	−27.6432	+	21.8882i	−1.33619	+	1.05800i
$429$		0			0
$430$	2.07448	−	2.74656i	0.100040	−	0.132451i
$431$		−	17.6688i		−	0.851074i	−0.904941	−	0.425537i	$-0.860085\pi$
$431$		−	17.6688i		−	0.851074i	0.904941	−	0.425537i	$-0.139915\pi$
$432$		0			0
$433$			20.6124i			0.990567i	0.868731	+	0.495284i	$0.164936\pi$
$433$			20.6124i			0.990567i	−0.868731	+	0.495284i	$0.835064\pi$
$434$	−21.6208	−	16.3302i	−1.03783	−	0.783873i
$435$		0			0
$436$	3.60456	−	31.0230i	0.172627	−	1.48573i
$437$	0.778425	−	1.01446i	0.0372371	−	0.0485284i
$438$		0			0
$439$	7.93569	+	29.6164i	0.378750	+	1.41351i	0.847788	+	0.530335i	$0.177934\pi$
$439$	7.93569	+	29.6164i	0.378750	+	1.41351i	−0.469038	+	0.883178i	$0.655399\pi$
$440$	−4.86976	−	1.88800i	−0.232157	−	0.0900068i
$441$		0			0
$442$	−0.177093	−	0.641346i	−0.00842345	−	0.0305057i
$443$	18.4590	+	2.43017i	0.877013	+	0.115461i	0.555572	−	0.831468i	$-0.312499\pi$
$443$	18.4590	+	2.43017i	0.877013	+	0.115461i	0.321441	+	0.946929i	$0.395833\pi$
$444$		0			0
$445$	−2.06146	−	15.6583i	−0.0977223	−	0.742275i
$446$	3.91680	−	9.66346i	0.185466	−	0.457578i
$447$		0			0
$448$	−7.33834	+	14.1677i	−0.346704	+	0.669361i
$449$			9.64683i			0.455262i	0.973747	+	0.227631i	$0.0730980\pi$
$449$			9.64683i			0.455262i	−0.973747	+	0.227631i	$0.926902\pi$
$450$		0			0
$451$	−0.470408	+	1.13566i	−0.0221506	+	0.0534764i
$452$	−18.6956	−	18.1347i	−0.879366	−	0.852983i
$453$		0			0
$454$	6.77386	+	6.67148i	0.317913	+	0.313108i
$455$	−0.196801	−	0.0527326i	−0.00922616	−	0.00247214i
$456$		0			0
$457$	−0.731559	+	0.196021i	−0.0342209	+	0.00916945i	−0.275889	−	0.961190i	$-0.588972\pi$
$457$	−0.731559	+	0.196021i	−0.0342209	+	0.00916945i	0.241668	+	0.970359i	$0.422306\pi$
$458$	15.2716	+	8.66268i	0.713593	+	0.404780i
$459$		0			0
$460$	−0.354313	+	0.476605i	−0.0165199	+	0.0222218i
$461$	8.35536	−	6.41130i	0.389148	−	0.298604i	−0.395595	−	0.918425i	$-0.629462\pi$
$461$	8.35536	−	6.41130i	0.389148	−	0.298604i	0.784743	+	0.619821i	$0.212795\pi$
$462$		0			0
$463$	11.0847	+	19.1993i	0.515151	+	0.892267i	0.999845	+	0.0175838i	$0.00559740\pi$
$463$	11.0847	+	19.1993i	0.515151	+	0.892267i	−0.484695	+	0.874683i	$0.661069\pi$
$464$	−0.473590	−	0.179474i	−0.0219859	−	0.00833188i
$465$		0			0
$466$	28.3874	+	21.4410i	1.31502	+	0.993236i
$467$	−6.87549	+	16.5989i	−0.318160	+	0.768105i	0.681192	+	0.732105i	$0.261462\pi$
$467$	−6.87549	+	16.5989i	−0.318160	+	0.768105i	−0.999352	+	0.0360004i	$0.988538\pi$
$468$		0			0
$469$	19.6486	−	8.13871i	0.907287	−	0.375811i
$470$	9.96976	−	5.85771i	0.459871	−	0.270196i
$471$		0			0
$472$	−8.47301	−	2.06412i	−0.390002	−	0.0950089i
$473$	−1.37613	+	5.13580i	−0.0632746	+	0.236144i
$474$		0			0
$475$	−2.14705	+	16.3084i	−0.0985133	+	0.748283i
$476$	−14.4964	+	8.66646i	−0.664441	+	0.397227i
$477$		0			0
$478$	−13.9966	−	17.9560i	−0.640191	−	0.821289i
$479$	−9.30888	+	16.1234i	−0.425333	+	0.736699i	−0.996452	−	0.0841688i	$-0.973177\pi$
$479$	−9.30888	+	16.1234i	−0.425333	+	0.736699i	0.571118	+	0.820868i	$0.306510\pi$
$480$		0			0
$481$	−0.450766	−	0.780750i	−0.0205532	−	0.0355991i
$482$	10.5853	−	26.1158i	0.482145	−	1.18954i
$483$		0			0
$484$	−13.9302	+	0.212150i	−0.633193	+	0.00964320i
$485$	8.73682	−	3.61891i	0.396718	−	0.164326i
$486$		0			0
$487$	−20.7701	−	20.7701i	−0.941183	−	0.941183i	0.0571804	−	0.998364i	$-0.481789\pi$
$487$	−20.7701	−	20.7701i	−0.941183	−	0.941183i	−0.998364	+	0.0571804i	$0.981789\pi$
$488$	−12.0873	−	6.61521i	−0.547167	−	0.299457i
$489$		0			0
$490$	−0.0299201	−	3.92946i	−0.00135165	−	0.177515i
$491$	−10.7848	−	8.27545i	−0.486710	−	0.373466i	0.336060	−	0.941841i	$-0.390906\pi$
$491$	−10.7848	−	8.27545i	−0.486710	−	0.373466i	−0.822770	+	0.568375i	$0.807572\pi$
$492$		0			0
$493$	−0.326360	−	0.425320i	−0.0146985	−	0.0191555i
$494$	−0.0765058	+	0.617410i	−0.00344216	+	0.0277786i
$495$		0			0
$496$	18.1903	−	33.8467i	0.816766	−	1.51976i
$497$	1.55998	−	2.70196i	0.0699745	−	0.121199i
$498$		0			0
$499$	0.290652	+	2.20772i	0.0130114	+	0.0988310i	0.996718	−	0.0809484i	$-0.0257949\pi$
$499$	0.290652	+	2.20772i	0.0130114	+	0.0988310i	−0.983707	+	0.179779i	$0.942462\pi$
$500$	1.94281	−	16.7210i	0.0868852	−	0.747785i
$501$		0			0
$502$	18.9273	−	11.1207i	0.844766	−	0.496340i
$503$	2.56043	+	2.56043i	0.114164	+	0.114164i	0.761881	−	0.647717i	$-0.224276\pi$
$503$	2.56043	+	2.56043i	0.114164	+	0.114164i	−0.647717	+	0.761881i	$0.724276\pi$
$504$		0			0
$505$	2.53492	−	2.53492i	0.112802	−	0.112802i
$506$	0.230685	−	0.887916i	0.0102552	−	0.0394727i
$507$		0			0
$508$	−4.26648	−	15.0049i	−0.189295	−	0.665736i
$509$	−38.8541	+	5.11524i	−1.72218	+	0.226729i	−0.925786	−	0.378049i	$-0.876595\pi$
$509$	−38.8541	+	5.11524i	−1.72218	+	0.226729i	−0.796394	+	0.604778i	$0.793262\pi$
$510$		0			0
$511$	−12.5836	−	7.26512i	−0.556664	−	0.321390i
$512$	−21.4489	−	7.20737i	−0.947915	−	0.318524i
$513$		0			0
$514$	−16.3864	−	21.0219i	−0.722775	−	0.927234i
$515$	−8.57565	+	6.58033i	−0.377888	+	0.289964i
$516$		0			0
$517$	−10.8739	+	14.1712i	−0.478234	+	0.623247i
$518$	−16.0583	+	16.3048i	−0.705563	+	0.716390i
$519$		0			0
$520$	0.0311615	−	0.287256i	0.00136652	−	0.0125970i
$521$	−24.7080	+	24.7080i	−1.08248	+	1.08248i	−0.0861991	+	0.996278i	$0.527472\pi$
$521$	−24.7080	+	24.7080i	−1.08248	+	1.08248i	−0.996278	+	0.0861991i	$0.972528\pi$
$522$		0			0
$523$	4.60853	+	11.1260i	0.201517	+	0.486505i	0.992039	−	0.125928i	$-0.0401909\pi$
$523$	4.60853	+	11.1260i	0.201517	+	0.486505i	−0.790522	+	0.612433i	$0.790191\pi$
$524$	15.2346	+	35.2514i	0.665526	+	1.53997i
$525$		0			0
$526$	−10.2840	+	4.35182i	−0.448405	+	0.189748i
$527$	35.2250	−	20.3372i	1.53443	−	0.885902i
$528$		0			0
$529$	19.8282	+	11.4478i	0.862098	+	0.497732i
$530$	3.15734	+	0.391238i	0.137146	+	0.0169943i
$531$		0			0
$532$	15.6241	−	2.29951i	0.677392	−	0.0996966i
$533$	−0.0674214	−	0.00887620i	−0.00292035	−	0.000384471i
$534$		0			0
$535$	−15.6563	−	4.19509i	−0.676881	−	0.181370i
$536$	15.6731	+	25.7687i	0.676973	+	1.11304i
$537$		0			0
$538$	−8.24602	+	31.7393i	−0.355511	+	1.36838i
$539$	2.32297	+	5.60815i	0.100057	+	0.241560i
$540$		0			0
$541$	−11.1316	−	4.61087i	−0.478586	−	0.198237i	0.130331	−	0.991471i	$-0.458396\pi$
$541$	−11.1316	−	4.61087i	−0.478586	−	0.198237i	−0.608918	+	0.793234i	$0.708396\pi$
$542$	−3.40855	−	24.4504i	−0.146410	−	1.05024i
$543$		0			0
$544$	−15.2937	−	18.4336i	−0.655714	−	0.790336i
$545$	12.4335	−	7.17850i	0.532594	−	0.307493i
$546$		0			0
$547$	−20.3808	−	26.5608i	−0.871421	−	1.13566i	−0.989768	−	0.142686i	$-0.954426\pi$
$547$	−20.3808	−	26.5608i	−0.871421	−	1.13566i	0.118347	−	0.992972i	$-0.462241\pi$
$548$	−4.02120	−	6.72626i	−0.171777	−	0.287331i
$549$		0			0
$550$	3.14110	+	11.3756i	0.133937	+	0.485056i
$551$	0.129742	+	0.484203i	0.00552719	+	0.0206277i
$552$		0			0
$553$	9.11008	−	33.9993i	0.387400	−	1.44580i
$554$	−2.85695	+	0.0217537i	−0.121380	+	0.000924226i
$555$		0			0
$556$	8.38764	−	21.1551i	0.355715	−	0.897177i
$557$	40.2356	+	16.6661i	1.70484	+	0.706167i	0.999995	−	0.00319551i	$-0.00101716\pi$
$557$	40.2356	+	16.6661i	1.70484	+	0.706167i	0.704844	+	0.709363i	$0.251017\pi$
$558$		0			0
$559$	−0.294143			−0.0124409
$560$	−7.23932	+	1.17835i	−0.305917	+	0.0497946i
$561$		0			0
$562$	14.8414	+	35.0727i	0.626048	+	1.47945i
$563$	−38.7382	+	5.09998i	−1.63262	+	0.214939i	−0.890388	−	0.455202i	$-0.849567\pi$
$563$	−38.7382	+	5.09998i	−1.63262	+	0.214939i	−0.742234	+	0.670141i	$0.766234\pi$
$564$		0			0
$565$	1.56281	−	11.8707i	0.0657478	−	0.499404i
$566$	6.45981	−	11.3881i	0.271526	−	0.478677i
$567$		0			0
$568$	4.12541	+	1.59941i	0.173098	+	0.0671100i
$569$	7.10055	−	1.90259i	0.297671	−	0.0797606i	−0.106893	−	0.994271i	$-0.534090\pi$
$569$	7.10055	−	1.90259i	0.297671	−	0.0797606i	0.404563	+	0.914510i	$0.367423\pi$
$570$		0			0
$571$	−21.4398	−	16.4514i	−0.897229	−	0.688468i	0.0534745	−	0.998569i	$-0.482970\pi$
$571$	−21.4398	−	16.4514i	−0.897229	−	0.688468i	−0.950704	+	0.310101i	$0.899637\pi$
$572$	0.122074	+	0.429325i	0.00510416	+	0.0179510i
$573$		0			0
$574$	0.238341	+	1.70969i	0.00994818	+	0.0713609i
$575$	1.34187			0.0559599
$576$		0			0
$577$	39.1901			1.63150			0.815752	−	0.578402i	$-0.196323\pi$
$577$	39.1901			1.63150			0.815752	+	0.578402i	$0.196323\pi$
$578$	−0.181217	−	1.29992i	−0.00753762	−	0.0540693i
$579$		0			0
$580$	−0.0636744	−	0.223938i	−0.00264393	−	0.00929853i
$581$	−14.2373	−	10.9246i	−0.590661	−	0.453231i
$582$		0			0
$583$	−4.74714	+	1.27199i	−0.196607	+	0.0526806i
$584$	7.44880	−	19.2129i	0.308233	−	0.795034i
$585$		0			0
$586$	8.03220	−	14.1601i	0.331807	−	0.584948i
$587$	−1.72250	+	13.0837i	−0.0710950	+	0.540020i	0.918422	+	0.395602i	$0.129464\pi$
$587$	−1.72250	+	13.0837i	−0.0710950	+	0.540020i	−0.989517	+	0.144418i	$0.953869\pi$
$588$		0			0
$589$	−37.7072	+	4.96424i	−1.55370	+	0.204548i
$590$	−1.56229	−	3.69195i	−0.0643186	−	0.151995i
$591$		0			0
$592$	−26.3376	−	18.9638i	−1.08247	−	0.779408i
$593$	45.3116			1.86072			0.930362	−	0.366643i	$-0.119493\pi$
$593$	45.3116			1.86072			0.930362	+	0.366643i	$0.119493\pi$
$594$		0			0
$595$	−7.17296	−	2.97114i	−0.294063	−	0.121805i
$596$	−15.8576	+	39.9957i	−0.649554	+	1.63829i
$597$		0			0
$598$	0.0507502		0.000386427i	0.00207533		1.58022e-5i
$599$	3.22876	−	12.0499i	0.131924	−	0.492345i	−0.868068	−	0.496445i	$-0.834638\pi$
$599$	3.22876	−	12.0499i	0.131924	−	0.492345i	0.999992	+	0.00409987i	$0.00130503\pi$
$600$		0			0
$601$	2.71420	+	10.1295i	0.110714	+	0.413192i	0.998931	−	0.0462338i	$-0.0147219\pi$
$601$	2.71420	+	10.1295i	0.110714	+	0.413192i	−0.888216	+	0.459426i	$0.848055\pi$
$602$	1.98737	+	7.19730i	0.0809990	+	0.293340i
$603$		0			0
$604$	2.26231	+	3.78417i	0.0920522	+	0.153976i
$605$	−3.89874	−	5.08094i	−0.158506	−	0.206569i
$606$		0			0
$607$	31.5946	−	18.2412i	1.28239	−	0.740386i	0.305103	−	0.952319i	$-0.401309\pi$
$607$	31.5946	−	18.2412i	1.28239	−	0.740386i	0.977284	+	0.211933i	$0.0679759\pi$
$608$	6.61578	+	21.3969i	0.268305	+	0.867757i
$609$		0			0
$610$	−0.874568	−	6.27351i	−0.0354102	−	0.254007i
$611$	−0.912953	−	0.378158i	−0.0369341	−	0.0152986i
$612$		0			0
$613$	−8.89057	−	21.4637i	−0.359087	−	0.866912i	−0.995429	−	0.0955052i	$-0.969553\pi$
$613$	−8.89057	−	21.4637i	−0.359087	−	0.866912i	0.636342	−	0.771407i	$-0.280447\pi$
$614$	−0.750244	+	2.88772i	−0.0302774	+	0.116539i
$615$		0			0
$616$	9.68023	−	5.88770i	0.390028	−	0.237222i
$617$	24.4173	+	6.54261i	0.983005	+	0.263395i	0.714310	−	0.699830i	$-0.246741\pi$
$617$	24.4173	+	6.54261i	0.983005	+	0.263395i	0.268695	+	0.963225i	$0.413407\pi$
$618$		0			0
$619$	17.1114	+	2.25276i	0.687765	+	0.0905459i	0.466306	−	0.884624i	$-0.345585\pi$
$619$	17.1114	+	2.25276i	0.687765	+	0.0905459i	0.221459	+	0.975170i	$0.428918\pi$
$620$	17.4755	−	2.57199i	0.701832	−	0.103294i
$621$		0			0
$622$	21.3949	+	2.65113i	0.857859	+	0.106301i
$623$	29.6706	+	17.1303i	1.18873	+	0.686313i
$624$		0			0
$625$	−11.2890	+	6.51770i	−0.451560	+	0.260708i
$626$	33.8000	−	14.3029i	1.35092	−	0.571659i
$627$		0			0
$628$	2.03461	+	4.70790i	0.0811897	+	0.187865i
$629$	−13.1468	−	31.7393i	−0.524199	−	1.26553i
$630$		0			0
$631$	6.36119	−	6.36119i	0.253235	−	0.253235i	−0.569061	−	0.822296i	$-0.692693\pi$
$631$	6.36119	−	6.36119i	0.253235	−	0.253235i	0.822296	+	0.569061i	$0.192693\pi$
$632$	49.6264	+	5.38346i	1.97403	+	0.214142i
$633$		0			0
$634$	12.4145	−	12.6050i	0.493043	−	0.500609i
$635$	4.36548	−	5.68920i	0.173239	−	0.225769i
$636$		0			0
$637$	−0.266419	+	0.204430i	−0.0105559	+	0.00809983i
$638$	0.221102	+	0.283647i	0.00875350	+	0.0112297i
$639$		0			0
$640$	−3.22358	−	9.88956i	−0.127423	−	0.390919i
$641$	−27.8445	−	16.0760i	−1.09979	−	0.634966i	−0.163626	−	0.986522i	$-0.552319\pi$
$641$	−27.8445	−	16.0760i	−1.09979	−	0.634966i	−0.936167	+	0.351557i	$0.885652\pi$
$642$		0			0
$643$	24.6773	−	3.24883i	0.973177	−	0.128121i	0.372864	−	0.927886i	$-0.378376\pi$
$643$	24.6773	−	3.24883i	0.973177	−	0.128121i	0.600313	+	0.799765i	$0.295043\pi$
$644$	−0.352347	−	1.23918i	−0.0138844	−	0.0488305i
$645$		0			0
$646$	−5.96138	+	22.9456i	−0.234547	+	0.902782i
$647$	−32.2477	+	32.2477i	−1.26779	+	1.26779i	−0.320560	+	0.947228i	$0.603871\pi$
$647$	−32.2477	+	32.2477i	−1.26779	+	1.26779i	−0.947228	+	0.320560i	$0.896129\pi$
$648$		0			0
$649$	4.37893	+	4.37893i	0.171888	+	0.171888i
$650$	−0.562897	+	0.330729i	−0.0220786	+	0.0129722i
$651$		0			0
$652$	2.29402	−	19.7437i	0.0898408	−	0.773223i
$653$	3.50465	+	26.6205i	0.137148	+	1.04174i	0.912172	+	0.409808i	$0.134404\pi$
$653$	3.50465	+	26.6205i	0.137148	+	1.04174i	−0.775024	+	0.631932i	$0.782262\pi$
$654$		0			0
$655$	−8.82670	+	15.2883i	−0.344888	+	0.597363i
$656$	−2.34426	+	0.705320i	−0.0915279	+	0.0275381i
$657$		0			0
$658$	−3.08469	+	24.8938i	−0.120254	+	0.970461i
$659$	30.1948	+	39.3507i	1.17622	+	1.53288i	0.792992	+	0.609232i	$0.208522\pi$
$659$	30.1948	+	39.3507i	1.17622	+	1.53288i	0.383231	+	0.923653i	$0.374811\pi$
$660$		0			0
$661$	−11.4726	−	8.80327i	−0.446234	−	0.342407i	0.361075	−	0.932537i	$-0.382410\pi$
$661$	−11.4726	−	8.80327i	−0.446234	−	0.342407i	−0.807309	+	0.590130i	$0.799077\pi$
$662$	−0.0648545	−	8.51746i	−0.00252064	−	0.331040i
$663$		0			0
$664$	12.2182	−	22.3252i	0.474160	−	0.866386i
$665$	5.13337	+	5.13337i	0.199064	+	0.199064i
$666$		0			0
$667$	0.0377804	−	0.0156491i	0.00146286	−	0.000605937i
$668$	−40.7034	+	0.619893i	−1.57486	+	0.0239844i
$669$		0			0
$670$	−5.20811	+	12.8494i	−0.201207	+	0.496414i
$671$	4.89236	+	8.47382i	0.188868	+	0.327128i
$672$		0			0
$673$	8.18688	−	14.1801i	0.315581	−	0.546603i	−0.663980	−	0.747751i	$-0.731134\pi$
$673$	8.18688	−	14.1801i	0.315581	−	0.546603i	0.979561	+	0.201148i	$0.0644672\pi$
$674$	−6.82392	−	8.75428i	−0.262848	−	0.337202i
$675$		0			0
$676$	22.2949	−	13.3287i	0.857496	−	0.512642i
$677$	0.0300992	−	0.228626i	0.00115680	−	0.00878681i	−0.990857	−	0.134918i	$-0.956923\pi$
$677$	0.0300992	−	0.228626i	0.00115680	−	0.00878681i	0.992014	+	0.126132i	$0.0402561\pi$
$678$		0			0
$679$	−5.30951	+	19.8153i	−0.203760	+	0.760443i
$680$	2.60609	−	10.6977i	0.0999388	−	0.410239i
$681$		0			0
$682$	−23.5259	+	13.8226i	−0.900852	+	0.529293i
$683$	39.0929	−	16.1928i	1.49585	−	0.619601i	0.523269	−	0.852167i	$-0.324712\pi$
$683$	39.0929	−	16.1928i	1.49585	−	0.619601i	0.972581	+	0.232566i	$0.0747122\pi$
$684$		0			0
$685$	1.37859	−	3.32822i	0.0526734	−	0.127165i
$686$	22.5571	+	17.0374i	0.861233	+	0.650489i
$687$		0			0
$688$	−9.65496	+	4.34824i	−0.368092	+	0.165775i
$689$	−0.135942	−	0.235458i	−0.00517897	−	0.00897024i
$690$		0			0
$691$	−16.0959	+	12.3508i	−0.612315	+	0.469846i	−0.867764	−	0.496977i	$-0.834443\pi$
$691$	−16.0959	+	12.3508i	−0.612315	+	0.469846i	0.255449	+	0.966823i	$0.417777\pi$
$692$	−10.2385	+	13.7724i	−0.389211	+	0.523548i
$693$		0			0
$694$	29.1721	+	16.5476i	1.10736	+	0.628139i
$695$	10.1049	−	2.70760i	0.383300	−	0.102705i
$696$		0			0
$697$	−2.50307	−	0.670696i	−0.0948106	−	0.0254044i
$698$	−5.21659	−	5.13775i	−0.197451	−	0.194467i
$699$		0			0
$700$	11.8957	+	11.5388i	0.449615	+	0.436125i
$701$	17.7240	−	42.7894i	0.669425	−	1.61613i	−0.113151	−	0.993578i	$-0.536094\pi$
$701$	17.7240	−	42.7894i	0.669425	−	1.61613i	0.782575	−	0.622556i	$-0.213906\pi$
$702$		0			0
$703$			32.1230i			1.21154i
$704$	10.3535	+	12.2876i	0.390214	+	0.463106i
$705$		0			0
$706$	−2.45930	+	6.06753i	−0.0925569	+	0.228355i
$707$	1.01507	+	7.71023i	0.0381757	+	0.289973i
$708$		0			0
$709$	46.6755	+	6.14495i	1.75294	+	0.230778i	0.937480	−	0.348040i	$-0.113153\pi$
$709$	46.6755	+	6.14495i	1.75294	+	0.230778i	0.815456	+	0.578819i	$0.196486\pi$
$710$	0.541372	+	1.96059i	0.0203173	+	0.0735797i
$711$		0			0
$712$	−17.5634	+	45.3018i	−0.658217	+	1.69776i
$713$	0.803006	+	2.99686i	0.0300728	+	0.112233i
$714$		0			0
$715$	−0.124906	+	0.162781i	−0.00467122	+	0.00608766i
$716$	1.22281	−	10.5242i	0.0456984	−	0.393307i
$717$		0			0
$718$	10.5329	+	7.95552i	0.393085	+	0.296897i
$719$		−	33.7823i		−	1.25987i	−0.776649	−	0.629934i	$-0.783082\pi$
$719$		−	33.7823i		−	1.25987i	0.776649	−	0.629934i	$-0.216918\pi$
$720$		0			0
$721$		−	23.4488i		−	0.873278i
$722$	−2.83422	+	3.75245i	−0.105479	+	0.139652i
$723$		0			0
$724$	−28.2078	+	22.3352i	−1.04833	+	0.830081i
$725$	−0.320238	+	0.417342i	−0.0118933	+	0.0154997i
$726$		0			0
$727$	−3.57803	−	13.3534i	−0.132702	−	0.495250i	0.867295	−	0.497795i	$-0.165857\pi$
$727$	−3.57803	−	13.3534i	−0.132702	−	0.495250i	−0.999997	+	0.00254481i	$0.999190\pi$
$728$	0.453223	+	0.432976i	0.0167976	+	0.0160472i
$729$		0			0
$730$	9.13087	−	2.52128i	0.337949	−	0.0933167i
$731$	−11.1129	−	1.46304i	−0.411026	−	0.0541125i
$732$		0			0
$733$	−1.34275	−	10.1992i	−0.0495955	−	0.376715i	−0.998186	−	0.0602085i	$-0.980823\pi$
$733$	−1.34275	−	10.1992i	−0.0495955	−	0.376715i	0.948590	−	0.316506i	$-0.102510\pi$
$734$	−32.6654	−	13.2400i	−1.20570	−	0.488696i
$735$		0			0
$736$	1.66011	−	0.762910i	0.0611926	−	0.0281212i
$737$		−	21.4175i		−	0.788925i
$738$		0			0
$739$	17.1048	−	41.2947i	0.629211	−	1.51905i	−0.211394	−	0.977401i	$-0.567800\pi$
$739$	17.1048	−	41.2947i	0.629211	−	1.51905i	0.840605	−	0.541649i	$-0.182200\pi$
$740$	−0.227184	−	14.9174i	−0.00835146	−	0.548374i
$741$		0			0
$742$	−4.84287	+	4.91718i	−0.177787	+	0.180516i
$743$	2.76781	+	0.741632i	0.101541	+	0.0272078i	0.309232	−	0.950987i	$-0.399928\pi$
$743$	2.76781	+	0.741632i	0.101541	+	0.0272078i	−0.207691	+	0.978195i	$0.566595\pi$
$744$		0			0
$745$	−19.1042	+	5.11897i	−0.699925	+	0.187544i
$746$	−17.7771	+	31.3396i	−0.650867	+	1.14742i
$747$		0			0
$748$	2.47660	+	16.8273i	0.0905534	+	0.615268i
$749$	27.8954	−	21.4049i	1.01927	−	0.782117i
$750$		0			0
$751$	7.03768	+	12.1896i	0.256809	+	0.444806i	0.965385	−	0.260828i	$-0.0839956\pi$
$751$	7.03768	+	12.1896i	0.256809	+	0.444806i	−0.708577	+	0.705634i	$0.750662\pi$
$752$	−35.5570	+	1.08328i	−1.29663	+	0.0395032i
$753$		0			0
$754$	−0.0119913	+	0.0158763i	−0.000436699	+	0.000578179i
$755$	−0.775592	+	1.87244i	−0.0282267	+	0.0681452i
$756$		0			0
$757$	48.0034	−	19.8836i	1.74471	−	0.722683i	0.746345	−	0.665559i	$-0.231807\pi$
$757$	48.0034	−	19.8836i	1.74471	−	0.722683i	0.998367	−	0.0571241i	$-0.0181931\pi$
$758$	4.68817	+	7.97922i	0.170282	+	0.289818i
$759$		0			0
$760$	−6.07927	+	8.30893i	−0.220518	+	0.301397i
$761$	8.64150	−	32.2505i	0.313254	−	1.16908i	−0.612350	−	0.790587i	$-0.709776\pi$
$761$	8.64150	−	32.2505i	0.313254	−	1.16908i	0.925604	−	0.378493i	$-0.123558\pi$
$762$		0			0
$763$	−4.06519	+	30.8782i	−0.147170	+	1.11787i
$764$	−6.89375	+	27.3896i	−0.249407	+	0.990919i
$765$		0			0
$766$	14.0427	−	10.9463i	0.507385	−	0.395504i
$767$	−0.171296	+	0.296694i	−0.00618515	+	0.0107130i
$768$		0			0
$769$	5.70866	+	9.88770i	0.205860	+	0.356559i	0.950406	−	0.311011i	$-0.100668\pi$
$769$	5.70866	+	9.88770i	0.205860	+	0.356559i	−0.744547	+	0.667570i	$0.767334\pi$
$770$	4.82696	+	1.95647i	0.173951	+	0.0705062i
$771$		0			0
$772$	−16.4686	−	15.9745i	−0.592717	−	0.574934i
$773$	−5.85874	+	2.42677i	−0.210724	+	0.0872848i	−0.485549	−	0.874210i	$-0.661380\pi$
$773$	−5.85874	+	2.42677i	−0.210724	+	0.0872848i	0.274825	+	0.961494i	$0.411380\pi$
$774$		0			0
$775$	−28.2216	−	28.2216i	−1.01375	−	1.01375i
$776$	−28.9231	−	3.13757i	−1.03828	−	0.112632i
$777$		0			0
$778$	−8.38756	+	0.0638654i	−0.300709	+	0.00228969i
$779$	1.92234	+	1.47507i	0.0688751	+	0.0528497i
$780$		0			0
$781$	−1.91271	−	2.49269i	−0.0684421	−	0.0891955i
$782$	1.91929	+	0.237827i	0.0686338	+	0.00850469i
$783$		0			0
$784$	−5.72291	+	10.6486i	−0.204390	+	0.380308i
$785$	−1.17882	+	2.04178i	−0.0420740	+	0.0728743i
$786$		0			0
$787$	1.42466	+	10.8214i	0.0507837	+	0.385740i	0.997896	+	0.0648375i	$0.0206529\pi$
$787$	1.42466	+	10.8214i	0.0507837	+	0.385740i	−0.947112	+	0.320903i	$0.896014\pi$
$788$	18.8038	−	14.8890i	0.669857	−	0.530399i
$789$		0			0
$790$	11.6244	+	19.7845i	0.413576	+	0.703902i
$791$	18.3659	+	18.3659i	0.653017	+	0.653017i
$792$		0			0
$793$	−0.382762	+	0.382762i	−0.0135923	+	0.0135923i
$794$	25.7911	+	6.70066i	0.915293	+	0.237797i
$795$		0			0
$796$	23.4544	+	13.0693i	0.831318	+	0.463228i
$797$	22.5091	−	2.96337i	0.797312	−	0.104968i	0.279146	−	0.960249i	$-0.409948\pi$
$797$	22.5091	−	2.96337i	0.797312	−	0.104968i	0.518165	+	0.855280i	$0.326615\pi$
$798$		0			0
$799$	−32.6110	−	18.8280i	−1.15369	−	0.666086i
$800$	−13.5875	+	19.1770i	−0.480390	+	0.678009i
$801$		0			0
$802$	−7.76572	+	6.05334i	−0.274217	+	0.213751i
$803$	−11.6090	+	8.90787i	−0.409671	+	0.314352i
$804$		0			0
$805$	0.360522	−	0.469842i	0.0127067	−	0.0165597i
$806$	−1.07548	−	1.05923i	−0.0378822	−	0.0373096i
$807$		0			0
$808$	−10.5850	+	3.09702i	−0.372378	+	0.108953i
$809$	22.7074	−	22.7074i	0.798348	−	0.798348i	−0.184487	−	0.982835i	$-0.559062\pi$
$809$	22.7074	−	22.7074i	0.798348	−	0.798348i	0.982835	+	0.184487i	$0.0590624\pi$
$810$		0			0
$811$	13.7119	+	33.1034i	0.481490	+	1.16242i	0.958902	+	0.283739i	$0.0915749\pi$
$811$	13.7119	+	33.1034i	0.481490	+	1.16242i	−0.477412	+	0.878680i	$0.658425\pi$
$812$	0.469490	+	0.186145i	0.0164759	+	0.00653241i
$813$		0			0
$814$	8.98131	+	21.2243i	0.314795	+	0.743910i
$815$	7.91297	−	4.56855i	0.277179	−	0.160029i
$816$		0			0
$817$	9.07662	+	5.24039i	0.317551	+	0.183338i
$818$	−2.70563	+	21.8348i	−0.0946003	+	0.763435i
$819$		0			0
$820$	−0.903136	−	0.671400i	−0.0315389	−	0.0234463i
$821$	12.1550	+	1.60024i	0.424213	+	0.0558487i	0.339611	−	0.940566i	$-0.389705\pi$
$821$	12.1550	+	1.60024i	0.424213	+	0.0558487i	0.0846025	+	0.996415i	$0.473038\pi$
$822$		0			0
$823$	10.9127	+	2.92405i	0.380393	+	0.101926i	0.443948	−	0.896052i	$-0.353577\pi$
$823$	10.9127	+	2.92405i	0.380393	+	0.101926i	−0.0635555	+	0.997978i	$0.520244\pi$
$824$	32.8620	−	5.09246i	1.14480	−	0.177404i
$825$		0			0
$826$	8.41707	+	2.18680i	0.292867	+	0.0760883i
$827$	−3.04575	−	7.35309i	−0.105911	−	0.255692i	0.862036	−	0.506848i	$-0.169189\pi$
$827$	−3.04575	−	7.35309i	−0.105911	−	0.255692i	−0.967947	+	0.251156i	$0.919189\pi$
$828$		0			0
$829$	9.08127	+	3.76158i	0.315405	+	0.130645i	0.534770	−	0.844998i	$-0.320398\pi$
$829$	9.08127	+	3.76158i	0.315405	+	0.130645i	−0.219364	+	0.975643i	$0.570398\pi$
$830$	11.5871	−	1.61532i	0.402195	−	0.0560686i
$831$		0			0
$832$	−0.508361	+	0.729195i	−0.0176243	+	0.0252803i
$833$	−11.0823	+	6.39836i	−0.383979	+	0.221690i
$834$		0			0
$835$	−11.3919	−	14.8462i	−0.394234	−	0.513775i
$836$	3.88182	−	15.4229i	0.134256	−	0.533411i
$837$		0			0
$838$	−39.1719	+	10.8164i	−1.35317	+	0.373647i
$839$	−2.93228	−	10.9434i	−0.101233	−	0.377809i	0.896657	−	0.442726i	$-0.145988\pi$
$839$	−2.93228	−	10.9434i	−0.101233	−	0.377809i	−0.997891	+	0.0649170i	$0.979322\pi$
$840$		0			0
$841$	7.50160	−	27.9964i	0.258676	−	0.965392i
$842$	0.175629	+	23.0657i	0.00605257	+	0.794895i
$843$		0			0
$844$	−13.4472	−	31.1156i	−0.462873	−	1.07104i
$845$	11.0317	+	4.56950i	0.379504	+	0.157196i
$846$		0			0
$847$	13.8930			0.477370
$848$	−7.94287	−	5.71910i	−0.272759	−	0.196395i
$849$		0			0
$850$	−22.9116	+	9.69532i	−0.785861	+	0.332547i
$851$	2.59808	−	0.342043i	0.0890609	−	0.0117251i
$852$		0			0
$853$	−3.35298	+	25.4684i	−0.114804	+	0.872021i	0.833024	+	0.553237i	$0.186608\pi$
$853$	−3.35298	+	25.4684i	−0.114804	+	0.872021i	−0.947827	+	0.318784i	$0.896726\pi$
$854$	11.9518	+	6.77956i	0.408982	+	0.231992i
$855$		0			0
$856$	36.0557	+	34.4450i	1.23236	+	1.17731i
$857$	−6.08975	+	1.63174i	−0.208022	+	0.0557393i	−0.361325	−	0.932440i	$-0.617676\pi$
$857$	−6.08975	+	1.63174i	−0.208022	+	0.0557393i	0.153303	+	0.988179i	$0.451009\pi$
$858$		0			0
$859$	26.2644	+	20.1534i	0.896129	+	0.687624i	0.950443	−	0.310900i	$-0.100630\pi$
$859$	26.2644	+	20.1534i	0.896129	+	0.687624i	−0.0543133	+	0.998524i	$0.517297\pi$
$860$	−4.25209	−	2.36936i	−0.144995	−	0.0807944i
$861$		0			0
$862$	−24.7481	+	3.45004i	−0.842923	+	0.117509i
$863$	−13.8234			−0.470553			−0.235276	−	0.971928i	$-0.575600\pi$
$863$	−13.8234			−0.470553			−0.235276	+	0.971928i	$0.575600\pi$
$864$		0			0
$865$	−7.88889			−0.268230
$866$	28.8711	−	4.02482i	0.981080	−	0.136769i
$867$		0			0
$868$	−18.6514	+	33.4722i	−0.633071	+	1.13612i
$869$	−28.1220	−	21.5788i	−0.953974	−	0.732010i
$870$		0			0
$871$	1.14448	−	0.306662i	0.0387792	−	0.0103909i
$872$	−44.1567	+	1.00882i	−1.49534	+	0.0341631i
$873$		0			0
$874$	−1.57292	−	0.892229i	−0.0532050	−	0.0301801i
$875$	−2.19109	+	16.6430i	−0.0740722	+	0.562634i
$876$		0			0
$877$	46.1641	−	6.07762i	1.55885	−	0.205227i	0.698756	−	0.715360i	$-0.253737\pi$
$877$	46.1641	−	6.07762i	1.55885	−	0.205227i	0.860095	+	0.510133i	$0.170404\pi$
$878$	39.9332	−	16.8982i	1.34768	−	0.570288i
$879$		0			0
$880$	−1.69358	+	7.18958i	−0.0570905	+	0.242361i
$881$	6.38763			0.215205			0.107602	−	0.994194i	$-0.465683\pi$
$881$	6.38763			0.215205			0.107602	+	0.994194i	$0.465683\pi$
$882$		0			0
$883$	−31.8904	−	13.2094i	−1.07320	−	0.444532i	−0.225078	−	0.974341i	$-0.572264\pi$
$883$	−31.8904	−	13.2094i	−1.07320	−	0.444532i	−0.848117	+	0.529808i	$0.822264\pi$
$884$	−0.863734	+	0.373279i	−0.0290505	+	0.0125547i
$885$		0			0
$886$	−0.200480	−	26.3295i	−0.00673527	−	0.884555i
$887$	−7.59138	+	28.3314i	−0.254893	+	0.951275i	0.713256	+	0.700903i	$0.247220\pi$
$887$	−7.59138	+	28.3314i	−0.254893	+	0.951275i	−0.968150	+	0.250372i	$0.919447\pi$
$888$		0			0
$889$	4.02625	+	15.0262i	0.135036	+	0.503961i
$890$	−21.5296	+	5.94489i	−0.721673	+	0.199273i
$891$		0			0
$892$	−14.3001	−	3.59923i	−0.478803	−	0.120511i
$893$	21.4346	+	27.9341i	0.717281	+	0.934779i
$894$		0			0
$895$	4.21793	−	2.43522i	0.140990	−	0.0814005i
$896$	21.2772	+	7.51216i	0.710820	+	0.250964i
$897$		0			0
$898$	13.5120	−	1.88366i	0.450902	−	0.0628587i
$899$	−1.12370	−	0.465454i	−0.0374776	−	0.0155237i
$900$		0			0
$901$	−3.96482	−	9.57191i	−0.132087	−	0.318887i
$902$	1.68254	+	0.437133i	0.0560225	+	0.0145549i
$903$		0			0
$904$	−21.7501	+	29.7273i	−0.723398	+	0.988716i
$905$	−15.9761	−	4.28077i	−0.531062	−	0.142298i
$906$		0			0
$907$	−10.0567	−	1.32399i	−0.333927	−	0.0439623i	−0.0383013	−	0.999266i	$-0.512195\pi$
$907$	−10.0567	−	1.32399i	−0.333927	−	0.0439623i	−0.295625	+	0.955304i	$0.595528\pi$
$908$	8.02186	−	10.7906i	0.266215	−	0.358099i
$909$		0			0
$910$	−0.0354331	+	0.285949i	−0.00117460	+	0.00947913i
$911$	−33.5891	−	19.3927i	−1.11286	−	0.642508i	−0.173289	−	0.984871i	$-0.555440\pi$
$911$	−33.5891	−	19.3927i	−1.11286	−	0.642508i	−0.939568	+	0.342363i	$0.888773\pi$
$912$		0			0
$913$	−15.6511	+	9.03616i	−0.517975	+	0.299053i
$914$	0.417406	+	0.986396i	0.0138066	+	0.0326271i
$915$		0			0
$916$	9.15158	−	23.0819i	0.302377	−	0.762647i
$917$	−14.6551	−	35.3805i	−0.483953	−	1.16837i
$918$		0			0
$919$	−16.0260	+	16.0260i	−0.528650	+	0.528650i	−0.920170	−	0.391520i	$-0.871949\pi$
$919$	−16.0260	+	16.0260i	−0.528650	+	0.528650i	0.391520	+	0.920170i	$0.371949\pi$
$920$	0.736750	+	0.403212i	0.0242899	+	0.0132935i
$921$		0			0
$922$	−10.6116	−	10.4512i	−0.349474	−	0.344192i
$923$	0.105814	−	0.137900i	0.00348291	−	0.00453902i
$924$		0			0
$925$	−26.7439	+	20.5213i	−0.879333	+	0.674736i
$926$	24.7274	−	19.2749i	0.812594	−	0.633413i
$927$		0			0
$928$	−0.158910	+	0.698387i	−0.00521646	+	0.0229257i
$929$	−40.3656	−	23.3051i	−1.32435	−	0.764615i	−0.339933	−	0.940450i	$-0.610404\pi$
$929$	−40.3656	−	23.3051i	−1.32435	−	0.764615i	−0.984420	+	0.175835i	$0.943738\pi$
$930$		0			0
$931$	11.8632	−	1.56182i	0.388801	−	0.0511866i
$932$	24.4888	−	43.9480i	0.802156	−	1.43956i
$933$		0			0
$934$	24.5921	+	6.38914i	0.804677	+	0.209059i
$935$	−5.52868	+	5.52868i	−0.180807	+	0.180807i
$936$		0			0
$937$	−14.8752	−	14.8752i	−0.485953	−	0.485953i	0.421074	−	0.907026i	$-0.361653\pi$
$937$	−14.8752	−	14.8752i	−0.485953	−	0.485953i	−0.907026	+	0.421074i	$0.861653\pi$
$938$	−15.2363	−	25.9320i	−0.497482	−	0.846709i
$939$		0			0
$940$	−10.1514	−	12.8205i	−0.331103	−	0.418160i
$941$	5.45350	+	41.4235i	0.177779	+	1.35037i	0.814900	+	0.579602i	$0.196792\pi$
$941$	5.45350	+	41.4235i	0.177779	+	1.35037i	−0.637121	+	0.770764i	$0.719875\pi$
$942$		0			0
$943$	0.0988329	−	0.171184i	0.00321844	−	0.00557450i
$944$	−1.23669	+	12.2709i	−0.0402508	+	0.399384i
$945$		0			0
$946$	7.46226	+	0.924678i	0.242619	+	0.0300639i
$947$	3.79961	+	4.95174i	0.123471	+	0.160910i	0.850999	−	0.525168i	$-0.175998\pi$
$947$	3.79961	+	4.95174i	0.123471	+	0.160910i	−0.727528	+	0.686078i	$0.759331\pi$
$948$		0			0
$949$	−0.642226	−	0.492797i	−0.0208475	−	0.0159969i
$950$	23.2620	−	0.177124i	0.754718	−	0.00574665i
$951$		0			0
$952$	14.9694	+	18.6124i	0.485162	+	0.603231i
$953$	−1.87873	−	1.87873i	−0.0608579	−	0.0608579i	0.676023	−	0.736881i	$-0.263702\pi$
$953$	−1.87873	−	1.87873i	−0.0608579	−	0.0608579i	−0.736881	+	0.676023i	$0.763702\pi$
$954$		0			0
$955$	−11.9952	+	4.96856i	−0.388155	+	0.160779i
$956$	−22.4174	+	23.1108i	−0.725031	+	0.747456i
$957$		0			0
$958$	24.4013	+	9.89035i	0.788370	+	0.319543i
$959$	3.90739	+	6.76780i	0.126176	+	0.218544i
$960$		0			0
$961$	30.6401	−	53.0702i	0.988390	−	1.71194i
$962$	−1.00555	+	0.783825i	−0.0324204	+	0.0252715i
$963$		0			0
$964$	−38.6464	−	9.72702i	−1.24472	−	0.313286i
$965$	1.37665	−	10.4567i	0.0443159	−	0.336613i
$966$		0			0
$967$	−6.61817	+	24.6994i	−0.212826	+	0.794278i	0.774094	+	0.633070i	$0.218206\pi$
$967$	−6.61817	+	24.6994i	−0.212826	+	0.794278i	−0.986920	+	0.161208i	$0.948461\pi$
$968$	3.01720	+	19.4702i	0.0969766	+	0.625797i
$969$		0			0
$970$	−6.77486	−	11.5308i	−0.217528	−	0.370230i
$971$	21.3354	−	8.83740i	0.684684	−	0.283606i	−0.0130992	−	0.999914i	$-0.504170\pi$
$971$	21.3354	−	8.83740i	0.684684	−	0.283606i	0.697784	+	0.716309i	$0.254170\pi$
$972$		0			0
$973$	−8.68455	+	20.9663i	−0.278414	+	0.672150i
$974$	−25.0364	+	33.1477i	−0.802219	+	1.06212i
$975$		0			0
$976$	−6.90552	+	18.2220i	−0.221040	+	0.583273i
$977$	8.21825	+	14.2344i	0.262925	+	0.455400i	0.967018	−	0.254708i	$-0.0819794\pi$
$977$	8.21825	+	14.2344i	0.262925	+	0.455400i	−0.704093	+	0.710108i	$0.748646\pi$
$978$		0			0
$979$	27.3726	−	21.0038i	0.874833	−	0.671283i
$980$	−5.49803	+	0.809184i	−0.175628	+	0.0258484i
$981$		0			0
$982$	−9.48530	+	16.7218i	−0.302688	+	0.533613i
$983$	47.2731	−	12.6668i	1.50778	−	0.404008i	0.592081	−	0.805878i	$-0.298306\pi$
$983$	47.2731	−	12.6668i	1.50778	−	0.404008i	0.915696	+	0.401871i	$0.131640\pi$
$984$		0			0
$985$	10.6499	+	2.85363i	0.339334	+	0.0909243i
$986$	−0.532007	+	0.540171i	−0.0169425	+	0.0172025i
$987$		0			0
$988$	0.879726	−	0.0133978i	0.0279878	−	0.000426240i
$989$	0.327190	−	0.789907i	0.0104040	−	0.0251176i
$990$		0			0
$991$		−	36.6940i		−	1.16562i	−0.812607	−	0.582812i	$-0.801952\pi$
$991$		−	36.6940i		−	1.16562i	0.812607	−	0.582812i	$-0.198048\pi$
$992$	−50.9598	−	18.8695i	−1.61798	−	0.599108i
$993$		0			0
$994$	−4.08915	−	1.65742i	−0.129700	−	0.0525701i
$995$	1.61104	+	12.2371i	0.0510736	+	0.387942i
$996$		0			0
$997$	44.5005	+	5.85860i	1.40935	+	0.185544i	0.796490	−	0.604652i	$-0.206688\pi$
$997$	44.5005	+	5.85860i	1.40935	+	0.185544i	0.612855	+	0.790195i	$0.290021\pi$
$998$	3.03553	−	0.838191i	0.0960880	−	0.0265325i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.20		368
3.2	odd	2		288.2.bf.a.227.27	yes	368
9.4	even	3		288.2.bf.a.131.41	yes	368
9.5	odd	6	inner	864.2.bn.a.611.6		368
32.11	odd	8	inner	864.2.bn.a.683.6		368
96.11	even	8		288.2.bf.a.11.41	✓	368
288.139	odd	24		288.2.bf.a.203.27	yes	368
288.203	even	24	inner	864.2.bn.a.395.20		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.41	✓	368	96.11	even	8
288.2.bf.a.131.41	yes	368	9.4	even	3
288.2.bf.a.203.27	yes	368	288.139	odd	24
288.2.bf.a.227.27	yes	368	3.2	odd	2
864.2.bn.a.35.20		368	1.1	even	1	trivial
864.2.bn.a.395.20		368	288.203	even	24	inner
864.2.bn.a.611.6		368	9.5	odd	6	inner
864.2.bn.a.683.6		368	32.11	odd	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.195262 - 1.40067i) q^{2} +(-1.92375 + 0.546996i) q^{4} +(-0.729399 - 0.559687i) q^{5} +(1.92647 - 0.516196i) q^{7} +(1.14179 + 2.58772i) q^{8} +(-0.641512 + 1.13093i) q^{10} +(0.262162 - 1.99132i) q^{11} +(0.110163 - 0.0145032i) q^{13} +(-1.09919 - 2.59755i) q^{14} +(3.40159 - 2.10456i) q^{16} +4.23415 q^{17} +(-3.65777 - 1.51510i) q^{19} +(1.70932 + 0.677718i) q^{20} +(-2.84037 + 0.0216274i) q^{22} +(-0.0835920 + 0.311970i) q^{23} +(-1.07532 - 4.01316i) q^{25} +(-0.0418248 - 0.151470i) q^{26} +(-3.42368 + 2.04680i) q^{28} +(-0.0770779 - 0.100450i) q^{29} +(8.31926 - 4.80313i) q^{31} +(-3.61200 - 4.35356i) q^{32} +(-0.826771 - 5.93065i) q^{34} +(-1.69407 - 0.701707i) q^{35} +(-3.10495 - 7.49601i) q^{37} +(-1.40793 + 5.41917i) q^{38} +(0.615491 - 2.52653i) q^{40} +(-0.591162 - 0.158401i) q^{41} +(-2.62459 - 0.345533i) q^{43} +(0.584909 + 3.97419i) q^{44} +(0.453288 + 0.0561688i) q^{46} +(-7.70189 - 4.44669i) q^{47} +(-2.61736 + 1.51113i) q^{49} +(-5.41114 + 2.28979i) q^{50} +(-0.203992 + 0.0881591i) q^{52} +(-0.936389 - 2.26064i) q^{53} +(-1.30574 + 1.30574i) q^{55} +(3.53540 + 4.39577i) q^{56} +(-0.125647 + 0.127575i) q^{58} +(-1.87698 + 2.44612i) q^{59} +(-3.86495 + 2.96568i) q^{61} +(-8.35203 - 10.7147i) q^{62} +(-5.39261 + 5.90930i) q^{64} +(-0.0884699 - 0.0510781i) q^{65} +(10.5722 - 1.39186i) q^{67} +(-8.14544 + 2.31606i) q^{68} +(-0.652071 + 2.50985i) q^{70} +(1.10615 - 1.10615i) q^{71} +(-5.15157 - 5.15157i) q^{73} +(-9.89315 + 5.81269i) q^{74} +(7.86537 + 0.913878i) q^{76} +(-0.522863 - 3.97154i) q^{77} +(8.82426 - 15.2841i) q^{79} +(-3.65901 - 0.368763i) q^{80} +(-0.106436 + 0.858952i) q^{82} +(-5.47758 - 7.13853i) q^{83} +(-3.08839 - 2.36980i) q^{85} +(0.0285052 + 3.74364i) q^{86} +(5.45231 - 1.59527i) q^{88} +(12.1468 + 12.1468i) q^{89} +(0.204739 - 0.0848055i) q^{91} +(-0.00983634 - 0.645875i) q^{92} +(-4.72445 + 11.6561i) q^{94} +(1.81999 + 3.15232i) q^{95} +(-5.14292 + 8.90780i) q^{97} +(2.62766 + 3.37098i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

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Database

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