LMFDB - Embedded newform 1274.2.n.k.753.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(753,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.753"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,4,4,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.k.961.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} -2.41421i q^{6} -1.00000i q^{8} +(-1.41421 - 2.44949i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(-4.54026 - 2.62132i) q^{11} +(-1.20711 - 2.09077i) q^{12} +(3.00000 - 2.00000i) q^{13} +3.41421i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-2.44949 - 1.41421i) q^{18} +(0.210133 - 0.121320i) q^{19} +1.41421i q^{20} -5.24264 q^{22} +(0.792893 + 1.37333i) q^{23} +(-2.09077 - 1.20711i) q^{24} +(-1.50000 + 2.59808i) q^{25} +(1.59808 - 3.23205i) q^{26} +0.414214 q^{27} -7.41421 q^{29} +(1.70711 + 2.95680i) q^{30} +(-4.54026 - 2.62132i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-10.9612 + 6.32843i) q^{33} -6.00000i q^{34} -2.82843 q^{36} +(-2.30090 + 1.32843i) q^{37} +(0.121320 - 0.210133i) q^{38} +(-0.560220 - 8.68652i) q^{39} +(0.707107 + 1.22474i) q^{40} -9.00000i q^{41} +3.75736 q^{43} +(-4.54026 + 2.62132i) q^{44} +(3.46410 + 2.00000i) q^{45} +(1.37333 + 0.792893i) q^{46} +(-3.82282 + 2.20711i) q^{47} -2.41421 q^{48} +3.00000i q^{50} +(-7.24264 - 12.5446i) q^{51} +(-0.232051 - 3.59808i) q^{52} +(-0.707107 + 1.22474i) q^{53} +(0.358719 - 0.207107i) q^{54} +7.41421 q^{55} -0.585786i q^{57} +(-6.42090 + 3.70711i) q^{58} +(8.87039 + 5.12132i) q^{59} +(2.95680 + 1.70711i) q^{60} +(1.50000 + 2.59808i) q^{61} -5.24264 q^{62} -1.00000 q^{64} +(-2.26002 + 4.57081i) q^{65} +(-6.32843 + 10.9612i) q^{66} +(11.1713 + 6.44975i) q^{67} +(-3.00000 - 5.19615i) q^{68} +3.82843 q^{69} -3.75736i q^{71} +(-2.44949 + 1.41421i) q^{72} +(11.6786 + 6.74264i) q^{73} +(-1.32843 + 2.30090i) q^{74} +(3.62132 + 6.27231i) q^{75} -0.242641i q^{76} +(-4.82843 - 7.24264i) q^{78} +(-5.86396 - 10.1567i) q^{79} +(1.22474 + 0.707107i) q^{80} +(4.74264 - 8.21449i) q^{81} +(-4.50000 - 7.79423i) q^{82} -4.58579i q^{83} +8.48528i q^{85} +(3.25397 - 1.87868i) q^{86} +(-8.94975 + 15.5014i) q^{87} +(-2.62132 + 4.54026i) q^{88} +(9.79796 - 5.65685i) q^{89} +4.00000 q^{90} +1.58579 q^{92} +(-10.9612 + 6.32843i) q^{93} +(-2.20711 + 3.82282i) q^{94} +(-0.171573 + 0.297173i) q^{95} +(-2.09077 + 1.20711i) q^{96} +9.48528i q^{97} +14.8284i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{12} + 24 q^{13} - 4 q^{16} + 24 q^{17} - 8 q^{22} + 12 q^{23} - 12 q^{25} - 8 q^{26} - 8 q^{27} - 48 q^{29} + 8 q^{30} - 16 q^{38} + 12 q^{39} + 64 q^{43} - 8 q^{48} - 24 q^{51}+ \cdots - 24 q^{95}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^12 + 24 * q^13 - 4 * q^16 + 24 * q^17 - 8 * q^22 + 12 * q^23 - 12 * q^25 - 8 * q^26 - 8 * q^27 - 48 * q^29 + 8 * q^30 - 16 * q^38 + 12 * q^39 + 64 * q^43 - 8 * q^48 - 24 * q^51 + 12 * q^52 + 48 * q^55 + 12 * q^61 - 8 * q^62 - 8 * q^64 - 28 * q^66 - 24 * q^68 + 8 * q^69 + 12 * q^74 + 12 * q^75 - 16 * q^78 + 4 * q^79 + 4 * q^81 - 36 * q^82 - 32 * q^87 - 4 * q^88 + 32 * q^90 + 24 * q^92 - 12 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.20711	−	2.09077i	0.696923	−	1.20711i	−0.272605	−	0.962126i	$-0.587885\pi$
$3$	1.20711	−	2.09077i	0.696923	−	1.20711i	0.969528	−	0.244981i	$-0.0787816\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		−	2.41421i		−	0.985599i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	−4.54026	−	2.62132i	−1.36894	−	0.790358i	−0.378147	−	0.925745i	$-0.623439\pi$
$11$	−4.54026	−	2.62132i	−1.36894	−	0.790358i	−0.990793	+	0.135388i	$0.956772\pi$
$12$	−1.20711	−	2.09077i	−0.348462	−	0.603553i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$		0			0
$15$			3.41421i			0.881546i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	−2.44949	−	1.41421i	−0.577350	−	0.333333i
$19$	0.210133	−	0.121320i	0.0482078	−	0.0278328i	−0.475702	−	0.879606i	$-0.657806\pi$
$19$	0.210133	−	0.121320i	0.0482078	−	0.0278328i	0.523910	+	0.851774i	$0.324473\pi$
$20$			1.41421i			0.316228i
$21$		0			0
$22$	−5.24264			−1.11773
$23$	0.792893	+	1.37333i	0.165330	+	0.286359i	0.936772	−	0.349939i	$-0.113798\pi$
$23$	0.792893	+	1.37333i	0.165330	+	0.286359i	−0.771443	+	0.636299i	$0.780465\pi$
$24$	−2.09077	−	1.20711i	−0.426777	−	0.246400i
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$	1.59808	−	3.23205i	0.313409	−	0.633857i
$27$	0.414214			0.0797154
$28$		0			0
$29$	−7.41421			−1.37678			−0.688392	−	0.725338i	$-0.741683\pi$
$29$	−7.41421			−1.37678			−0.688392	+	0.725338i	$0.741683\pi$
$30$	1.70711	+	2.95680i	0.311674	+	0.539835i
$31$	−4.54026	−	2.62132i	−0.815455	−	0.470803i	0.0333918	−	0.999442i	$-0.489369\pi$
$31$	−4.54026	−	2.62132i	−0.815455	−	0.470803i	−0.848847	+	0.528639i	$0.822702\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−10.9612	+	6.32843i	−1.90809	+	1.10164i
$34$		−	6.00000i		−	1.02899i
$35$		0			0
$36$	−2.82843			−0.471405
$37$	−2.30090	+	1.32843i	−0.378266	+	0.218392i	−0.677064	−	0.735924i	$-0.736748\pi$
$37$	−2.30090	+	1.32843i	−0.378266	+	0.218392i	0.298797	+	0.954317i	$0.403414\pi$
$38$	0.121320	−	0.210133i	0.0196808	−	0.0340881i
$39$	−0.560220	−	8.68652i	−0.0897070	−	1.39096i
$40$	0.707107	+	1.22474i	0.111803	+	0.193649i
$41$		−	9.00000i		−	1.40556i	−0.711405	−	0.702782i	$-0.751941\pi$
$41$		−	9.00000i		−	1.40556i	0.711405	−	0.702782i	$-0.248059\pi$
$42$		0			0
$43$	3.75736			0.572992			0.286496	−	0.958081i	$-0.407509\pi$
$43$	3.75736			0.572992			0.286496	+	0.958081i	$0.407509\pi$
$44$	−4.54026	+	2.62132i	−0.684470	+	0.395179i
$45$	3.46410	+	2.00000i	0.516398	+	0.298142i
$46$	1.37333	+	0.792893i	0.202487	+	0.116906i
$47$	−3.82282	+	2.20711i	−0.557616	+	0.321940i	−0.752188	−	0.658949i	$-0.771001\pi$
$47$	−3.82282	+	2.20711i	−0.557616	+	0.321940i	0.194572	+	0.980888i	$0.437668\pi$
$48$	−2.41421			−0.348462
$49$		0			0
$50$			3.00000i			0.424264i
$51$	−7.24264	−	12.5446i	−1.01417	−	1.75660i
$52$	−0.232051	−	3.59808i	−0.0321797	−	0.498963i
$53$	−0.707107	+	1.22474i	−0.0971286	+	0.168232i	−0.910495	−	0.413520i	$-0.864299\pi$
$53$	−0.707107	+	1.22474i	−0.0971286	+	0.168232i	0.813366	+	0.581752i	$0.197632\pi$
$54$	0.358719	−	0.207107i	0.0488155	−	0.0281837i
$55$	7.41421			0.999732
$56$		0			0
$57$		−	0.585786i		−	0.0775893i
$58$	−6.42090	+	3.70711i	−0.843105	+	0.486767i
$59$	8.87039	+	5.12132i	1.15483	+	0.666739i	0.950059	−	0.312072i	$-0.101023\pi$
$59$	8.87039	+	5.12132i	1.15483	+	0.666739i	0.204767	+	0.978811i	$0.434356\pi$
$60$	2.95680	+	1.70711i	0.381721	+	0.220387i
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$	−5.24264			−0.665816
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.26002	+	4.57081i	−0.280321	+	0.566939i
$66$	−6.32843	+	10.9612i	−0.778976	+	1.34923i
$67$	11.1713	+	6.44975i	1.36479	+	0.787962i	0.990257	−	0.139251i	$-0.0444696\pi$
$67$	11.1713	+	6.44975i	1.36479	+	0.787962i	0.374533	+	0.927213i	$0.377803\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	3.82843			0.460888
$70$		0			0
$71$		−	3.75736i		−	0.445917i	−0.974828	−	0.222958i	$-0.928429\pi$
$71$		−	3.75736i		−	0.445917i	0.974828	−	0.222958i	$-0.0715714\pi$
$72$	−2.44949	+	1.41421i	−0.288675	+	0.166667i
$73$	11.6786	+	6.74264i	1.36688	+	0.789166i	0.990528	−	0.137312i	$-0.0438462\pi$
$73$	11.6786	+	6.74264i	1.36688	+	0.789166i	0.376348	+	0.926478i	$0.377180\pi$
$74$	−1.32843	+	2.30090i	−0.154427	+	0.267475i
$75$	3.62132	+	6.27231i	0.418154	+	0.724264i
$76$		−	0.242641i		−	0.0278328i
$77$		0			0
$78$	−4.82843	−	7.24264i	−0.546712	−	0.820068i
$79$	−5.86396	−	10.1567i	−0.659747	−	1.14272i	−0.980681	−	0.195614i	$-0.937330\pi$
$79$	−5.86396	−	10.1567i	−0.659747	−	1.14272i	0.320934	−	0.947102i	$-0.396003\pi$
$80$	1.22474	+	0.707107i	0.136931	+	0.0790569i
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$		−	4.58579i		−	0.503355i	−0.967811	−	0.251678i	$-0.919018\pi$
$83$		−	4.58579i		−	0.503355i	0.967811	−	0.251678i	$-0.0809823\pi$
$84$		0			0
$85$			8.48528i			0.920358i
$86$	3.25397	−	1.87868i	0.350884	−	0.202583i
$87$	−8.94975	+	15.5014i	−0.959514	+	1.66193i
$88$	−2.62132	+	4.54026i	−0.279434	+	0.483993i
$89$	9.79796	−	5.65685i	1.03858	−	0.599625i	0.119150	−	0.992876i	$-0.461983\pi$
$89$	9.79796	−	5.65685i	1.03858	−	0.599625i	0.919431	+	0.393251i	$0.128650\pi$
$90$	4.00000			0.421637
$91$		0			0
$92$	1.58579			0.165330
$93$	−10.9612	+	6.32843i	−1.13662	+	0.656227i
$94$	−2.20711	+	3.82282i	−0.227646	+	0.394294i
$95$	−0.171573	+	0.297173i	−0.0176030	+	0.0304893i
$96$	−2.09077	+	1.20711i	−0.213388	+	0.123200i
$97$			9.48528i			0.963084i	0.876423	+	0.481542i	$0.159923\pi$
$97$			9.48528i			0.963084i	−0.876423	+	0.481542i	$0.840077\pi$
$98$		0			0
$99$			14.8284i			1.49031i
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	4.74264	−	8.21449i	0.471910	−	0.817373i	−0.527573	−	0.849510i	$-0.676898\pi$
$101$	4.74264	−	8.21449i	0.471910	−	0.817373i	0.999483	+	0.0321369i	$0.0102312\pi$
$102$	−12.5446	−	7.24264i	−1.24210	−	0.717128i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	−2.00000	−	3.00000i	−0.196116	−	0.294174i
$105$		0			0
$106$			1.41421i			0.137361i
$107$	−5.12132	−	8.87039i	−0.495097	−	0.857533i	0.504887	−	0.863185i	$-0.331534\pi$
$107$	−5.12132	−	8.87039i	−0.495097	−	0.857533i	−0.999984	+	0.00565259i	$0.998201\pi$
$108$	0.207107	−	0.358719i	0.0199289	−	0.0345178i
$109$	7.34847	+	4.24264i	0.703856	+	0.406371i	0.808782	−	0.588109i	$-0.200127\pi$
$109$	7.34847	+	4.24264i	0.703856	+	0.406371i	−0.104926	+	0.994480i	$0.533461\pi$
$110$	6.42090	−	3.70711i	0.612209	−	0.353459i
$111$			6.41421i			0.608810i
$112$		0			0
$113$	17.1421			1.61260			0.806298	−	0.591509i	$-0.201468\pi$
$113$	17.1421			1.61260			0.806298	+	0.591509i	$0.201468\pi$
$114$	−0.292893	−	0.507306i	−0.0274320	−	0.0475136i
$115$	−1.94218	−	1.12132i	−0.181110	−	0.104564i
$116$	−3.70711	+	6.42090i	−0.344196	+	0.596165i
$117$	−9.14162	−	4.52004i	−0.845143	−	0.417878i
$118$	10.2426			0.942912
$119$		0			0
$120$	3.41421			0.311674
$121$	8.24264	+	14.2767i	0.749331	+	1.29788i
$122$	2.59808	+	1.50000i	0.235219	+	0.135804i
$123$	−18.8169	−	10.8640i	−1.69667	−	0.979570i
$124$	−4.54026	+	2.62132i	−0.407727	+	0.235402i
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	−10.7574			−0.954561			−0.477281	−	0.878751i	$-0.658377\pi$
$127$	−10.7574			−0.954561			−0.477281	+	0.878751i	$0.658377\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.53553	−	7.85578i	0.399331	−	0.691662i
$130$	0.328169	+	5.08845i	0.0287824	+	0.446286i
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$			12.6569i			1.10164i
$133$		0			0
$134$	12.8995			1.11435
$135$	−0.507306	+	0.292893i	−0.0436619	+	0.0252082i
$136$	−5.19615	−	3.00000i	−0.445566	−	0.257248i
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.956898	−	0.290424i	$-0.0937963\pi$
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.226935	+	0.973910i	$0.427130\pi$
$138$	3.31552	−	1.91421i	0.282235	−	0.162949i
$139$	−14.1421			−1.19952			−0.599760	−	0.800180i	$-0.704737\pi$
$139$	−14.1421			−1.19952			−0.599760	+	0.800180i	$0.704737\pi$
$140$		0			0
$141$			10.6569i			0.897469i
$142$	−1.87868	−	3.25397i	−0.157655	−	0.273067i
$143$	−18.8634	+	1.21656i	−1.57744	+	0.101734i
$144$	−1.41421	+	2.44949i	−0.117851	+	0.204124i
$145$	9.08052	−	5.24264i	0.754096	−	0.435378i
$146$	13.4853			1.11605
$147$		0			0
$148$			2.65685i			0.218392i
$149$	−16.8747	+	9.74264i	−1.38243	+	0.798148i	−0.992447	−	0.122673i	$-0.960854\pi$
$149$	−16.8747	+	9.74264i	−1.38243	+	0.798148i	−0.389986	+	0.920821i	$0.627520\pi$
$150$	6.27231	+	3.62132i	0.512132	+	0.295680i
$151$	17.4436	+	10.0711i	1.41954	+	0.819572i	0.996258	−	0.0864262i	$-0.0275447\pi$
$151$	17.4436	+	10.0711i	1.41954	+	0.819572i	0.423282	+	0.905998i	$0.360878\pi$
$152$	−0.121320	−	0.210133i	−0.00984038	−	0.0170440i
$153$	−16.9706			−1.37199
$154$		0			0
$155$	7.41421			0.595524
$156$	−7.80286	−	3.85810i	−0.624729	−	0.308895i
$157$	1.50000	−	2.59808i	0.119713	−	0.207349i	−0.799941	−	0.600079i	$-0.795136\pi$
$157$	1.50000	−	2.59808i	0.119713	−	0.207349i	0.919654	+	0.392730i	$0.128469\pi$
$158$	−10.1567	−	5.86396i	−0.808022	−	0.466512i
$159$	1.70711	+	2.95680i	0.135382	+	0.234489i
$160$	1.41421			0.111803
$161$		0			0
$162$		−	9.48528i		−	0.745234i
$163$	14.9941	−	8.65685i	1.17443	−	0.678057i	0.219710	−	0.975565i	$-0.429489\pi$
$163$	14.9941	−	8.65685i	1.17443	−	0.678057i	0.954719	+	0.297508i	$0.0961555\pi$
$164$	−7.79423	−	4.50000i	−0.608627	−	0.351391i
$165$	8.94975	−	15.5014i	0.696737	−	1.20678i
$166$	−2.29289	−	3.97141i	−0.177963	−	0.308241i
$167$		−	5.65685i		−	0.437741i	−0.975754	−	0.218870i	$-0.929763\pi$
$167$		−	5.65685i		−	0.437741i	0.975754	−	0.218870i	$-0.0702371\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$	4.24264	+	7.34847i	0.325396	+	0.563602i
$171$	−0.594346	−	0.343146i	−0.0454508	−	0.0262410i
$172$	1.87868	−	3.25397i	0.143248	−	0.248113i
$173$	12.2426	+	21.2049i	0.930791	+	1.61218i	0.781973	+	0.623312i	$0.214213\pi$
$173$	12.2426	+	21.2049i	0.930791	+	1.61218i	0.148818	+	0.988865i	$0.452453\pi$
$174$			17.8995i			1.35696i
$175$		0			0
$176$			5.24264i			0.395179i
$177$	21.4150	−	12.3640i	1.60965	−	0.929332i
$178$	5.65685	−	9.79796i	0.423999	−	0.734388i
$179$	5.65685	−	9.79796i	0.422813	−	0.732334i	−0.573400	−	0.819275i	$-0.694376\pi$
$179$	5.65685	−	9.79796i	0.422813	−	0.732334i	0.996213	+	0.0869415i	$0.0277093\pi$
$180$	3.46410	−	2.00000i	0.258199	−	0.149071i
$181$	16.7990			1.24866			0.624330	−	0.781161i	$-0.285372\pi$
$181$	16.7990			1.24866			0.624330	+	0.781161i	$0.285372\pi$
$182$		0			0
$183$	7.24264			0.535391
$184$	1.37333	−	0.792893i	0.101243	−	0.0584529i
$185$	1.87868	−	3.25397i	0.138123	−	0.239237i
$186$	−6.32843	+	10.9612i	−0.464023	+	0.803711i
$187$	−27.2416	+	15.7279i	−1.99210	+	1.15014i
$188$			4.41421i			0.321940i
$189$		0			0
$190$			0.343146i			0.0248944i
$191$	1.41421	+	2.44949i	0.102329	+	0.177239i	0.912644	−	0.408756i	$-0.134037\pi$
$191$	1.41421	+	2.44949i	0.102329	+	0.177239i	−0.810315	+	0.585995i	$0.800704\pi$
$192$	−1.20711	+	2.09077i	−0.0871154	+	0.150888i
$193$	−0.594346	−	0.343146i	−0.0427820	−	0.0247002i	0.478456	−	0.878111i	$-0.341196\pi$
$193$	−0.594346	−	0.343146i	−0.0427820	−	0.0247002i	−0.521238	+	0.853411i	$0.674530\pi$
$194$	4.74264	+	8.21449i	0.340502	+	0.589766i
$195$	6.82843	+	10.2426i	0.488994	+	0.733491i
$196$		0			0
$197$		−	13.9706i		−	0.995361i	−0.867360	−	0.497681i	$-0.834185\pi$
$197$		−	13.9706i		−	0.995361i	0.867360	−	0.497681i	$-0.165815\pi$
$198$	7.41421	+	12.8418i	0.526905	+	0.912627i
$199$	−3.87868	+	6.71807i	−0.274952	+	0.476231i	−0.970123	−	0.242613i	$-0.921995\pi$
$199$	−3.87868	+	6.71807i	−0.274952	+	0.476231i	0.695171	+	0.718845i	$0.255329\pi$
$200$	2.59808	+	1.50000i	0.183712	+	0.106066i
$201$	26.9699	−	15.5711i	1.90231	−	1.09830i
$202$		−	9.48528i		−	0.667382i
$203$		0			0
$204$	−14.4853			−1.01417
$205$	6.36396	+	11.0227i	0.444478	+	0.769859i
$206$		0			0
$207$	2.24264	−	3.88437i	0.155874	−	0.269982i
$208$	−3.23205	−	1.59808i	−0.224102	−	0.110807i
$209$	−1.27208			−0.0879915
$210$		0			0
$211$	−20.7279			−1.42697			−0.713485	−	0.700671i	$-0.752884\pi$
$211$	−20.7279			−1.42697			−0.713485	+	0.700671i	$0.752884\pi$
$212$	0.707107	+	1.22474i	0.0485643	+	0.0841158i
$213$	−7.85578	−	4.53553i	−0.538269	−	0.310770i
$214$	−8.87039	−	5.12132i	−0.606367	−	0.350086i
$215$	−4.60181	+	2.65685i	−0.313841	+	0.181196i
$216$		−	0.414214i		−	0.0281837i
$217$		0			0
$218$	8.48528			0.574696
$219$	28.1946	−	16.2782i	1.90522	−	1.09998i
$220$	3.70711	−	6.42090i	0.249933	−	0.432897i
$221$	−1.39230	−	21.5885i	−0.0936566	−	1.45220i
$222$	3.20711	+	5.55487i	0.215247	+	0.372819i
$223$		−	5.72792i		−	0.383570i	−0.981437	−	0.191785i	$-0.938572\pi$
$223$		−	5.72792i		−	0.383570i	0.981437	−	0.191785i	$-0.0614276\pi$
$224$		0			0
$225$	8.48528			0.565685
$226$	14.8455	−	8.57107i	0.987510	−	0.570139i
$227$	−18.0379	−	10.4142i	−1.19722	−	0.691216i	−0.237286	−	0.971440i	$-0.576258\pi$
$227$	−18.0379	−	10.4142i	−1.19722	−	0.691216i	−0.959935	+	0.280224i	$0.909591\pi$
$228$	−0.507306	−	0.292893i	−0.0335972	−	0.0193973i
$229$	−19.2627	+	11.1213i	−1.27291	+	0.734918i	−0.975535	−	0.219842i	$-0.929446\pi$
$229$	−19.2627	+	11.1213i	−1.27291	+	0.734918i	−0.297379	+	0.954760i	$0.596112\pi$
$230$	−2.24264			−0.147875
$231$		0			0
$232$			7.41421i			0.486767i
$233$	11.5711	+	20.0417i	0.758046	+	1.31297i	0.943846	+	0.330386i	$0.107179\pi$
$233$	11.5711	+	20.0417i	0.758046	+	1.31297i	−0.185800	+	0.982588i	$0.559488\pi$
$234$	−10.1769	+	0.656339i	−0.665285	+	0.0429062i
$235$	3.12132	−	5.40629i	0.203612	−	0.352667i
$236$	8.87039	−	5.12132i	0.577413	−	0.333370i
$237$	−28.3137			−1.83917
$238$		0			0
$239$		−	22.4853i		−	1.45445i	−0.686398	−	0.727226i	$-0.740809\pi$
$239$		−	22.4853i		−	1.45445i	0.686398	−	0.727226i	$-0.259191\pi$
$240$	2.95680	−	1.70711i	0.190860	−	0.110193i
$241$	−10.8126	−	6.24264i	−0.696499	−	0.402124i	0.109543	−	0.993982i	$-0.465061\pi$
$241$	−10.8126	−	6.24264i	−0.696499	−	0.402124i	−0.806042	+	0.591858i	$0.798395\pi$
$242$	14.2767	+	8.24264i	0.917739	+	0.529857i
$243$	−10.8284	−	18.7554i	−0.694644	−	1.20316i
$244$	3.00000			0.192055
$245$		0			0
$246$	−21.7279			−1.38532
$247$	0.387758	−	0.784227i	0.0246725	−	0.0498992i
$248$	−2.62132	+	4.54026i	−0.166454	+	0.288307i
$249$	−9.58783	−	5.53553i	−0.607604	−	0.350800i
$250$	−5.65685	−	9.79796i	−0.357771	−	0.619677i
$251$	−2.75736			−0.174043			−0.0870215	−	0.996206i	$-0.527735\pi$
$251$	−2.75736			−0.174043			−0.0870215	+	0.996206i	$0.527735\pi$
$252$		0			0
$253$		−	8.31371i		−	0.522678i
$254$	−9.31615	+	5.37868i	−0.584547	+	0.337488i
$255$	17.7408	+	10.2426i	1.11097	+	0.641419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.48528	−	12.9649i	−0.466919	−	0.808727i	0.532367	−	0.846514i	$-0.321303\pi$
$257$	−7.48528	−	12.9649i	−0.466919	−	0.808727i	−0.999286	+	0.0377863i	$0.987969\pi$
$258$		−	9.07107i		−	0.564740i
$259$		0			0
$260$	2.82843	+	4.24264i	0.175412	+	0.263117i
$261$	10.4853	+	18.1610i	0.649023	+	1.12414i
$262$	1.73205	+	1.00000i	0.107006	+	0.0617802i
$263$	−15.8995	+	27.5387i	−0.980405	+	1.69811i	−0.319601	+	0.947552i	$0.603549\pi$
$263$	−15.8995	+	27.5387i	−0.980405	+	1.69811i	−0.660804	+	0.750559i	$0.729784\pi$
$264$	6.32843	+	10.9612i	0.389488	+	0.674613i
$265$		−	2.00000i		−	0.122859i
$266$		0			0
$267$		−	27.3137i		−	1.67157i
$268$	11.1713	−	6.44975i	0.682395	−	0.393981i
$269$	7.25736	−	12.5701i	0.442489	−	0.766413i	−0.555385	−	0.831594i	$-0.687429\pi$
$269$	7.25736	−	12.5701i	0.442489	−	0.766413i	0.997874	+	0.0651802i	$0.0207622\pi$
$270$	−0.292893	+	0.507306i	−0.0178249	+	0.0308737i
$271$	28.3177	−	16.3492i	1.72018	−	0.993146i	0.801648	−	0.597796i	$-0.203957\pi$
$271$	28.3177	−	16.3492i	1.72018	−	0.993146i	0.918531	−	0.395350i	$-0.129377\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	16.0000			0.966595
$275$	13.6208	−	7.86396i	0.821364	−	0.474215i
$276$	1.91421	−	3.31552i	0.115222	−	0.199571i
$277$	−10.3640	+	17.9509i	−0.622710	+	1.07857i	0.366269	+	0.930509i	$0.380635\pi$
$277$	−10.3640	+	17.9509i	−0.622710	+	1.07857i	−0.988979	+	0.148056i	$0.952698\pi$
$278$	−12.2474	+	7.07107i	−0.734553	+	0.424094i
$279$			14.8284i			0.887755i
$280$		0			0
$281$			30.7279i			1.83307i	0.399950	+	0.916537i	$0.369028\pi$
$281$			30.7279i			1.83307i	−0.399950	+	0.916537i	$0.630972\pi$
$282$	5.32843	+	9.22911i	0.317303	+	0.549585i
$283$	3.62132	−	6.27231i	0.215265	−	0.372850i	−0.738089	−	0.674703i	$-0.764272\pi$
$283$	3.62132	−	6.27231i	0.215265	−	0.372850i	0.953355	+	0.301853i	$0.0976051\pi$
$284$	−3.25397	−	1.87868i	−0.193088	−	0.111479i
$285$	0.414214	+	0.717439i	0.0245359	+	0.0424974i
$286$	−15.7279	+	10.4853i	−0.930012	+	0.620008i
$287$		0			0
$288$			2.82843i			0.166667i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	5.24264	−	9.08052i	0.307858	−	0.533226i
$291$	19.8315	+	11.4497i	1.16255	+	0.671196i
$292$	11.6786	−	6.74264i	0.683438	−	0.394583i
$293$			16.6274i			0.971384i	0.874130	+	0.485692i	$0.161432\pi$
$293$			16.6274i			0.971384i	−0.874130	+	0.485692i	$0.838568\pi$
$294$		0			0
$295$	−14.4853			−0.843366
$296$	1.32843	+	2.30090i	0.0772133	+	0.133737i
$297$	−1.88064	−	1.08579i	−0.109126	−	0.0630037i
$298$	−9.74264	+	16.8747i	−0.564376	+	0.977528i
$299$	5.12534	+	2.53421i	0.296406	+	0.146557i
$300$	7.24264			0.418154
$301$		0			0
$302$	20.1421			1.15905
$303$	−11.4497	−	19.8315i	−0.657771	−	1.13929i
$304$	−0.210133	−	0.121320i	−0.0120520	−	0.00695820i
$305$	−3.67423	−	2.12132i	−0.210386	−	0.121466i
$306$	−14.6969	+	8.48528i	−0.840168	+	0.485071i
$307$			9.75736i			0.556882i	0.960453	+	0.278441i	$0.0898177\pi$
$307$			9.75736i			0.556882i	−0.960453	+	0.278441i	$0.910182\pi$
$308$		0			0
$309$		0			0
$310$	6.42090	−	3.70711i	0.364682	−	0.210550i
$311$	2.12132	−	3.67423i	0.120289	−	0.208347i	−0.799593	−	0.600543i	$-0.794951\pi$
$311$	2.12132	−	3.67423i	0.120289	−	0.208347i	0.919882	+	0.392196i	$0.128285\pi$
$312$	−8.68652	+	0.560220i	−0.491778	+	0.0317162i
$313$	−3.17157	−	5.49333i	−0.179268	−	0.310501i	0.762362	−	0.647151i	$-0.224040\pi$
$313$	−3.17157	−	5.49333i	−0.179268	−	0.310501i	−0.941630	+	0.336650i	$0.890706\pi$
$314$		−	3.00000i		−	0.169300i
$315$		0			0
$316$	−11.7279			−0.659747
$317$	3.01834	−	1.74264i	0.169527	−	0.0978765i	−0.412836	−	0.910805i	$-0.635462\pi$
$317$	3.01834	−	1.74264i	0.169527	−	0.0978765i	0.582363	+	0.812929i	$0.302128\pi$
$318$	2.95680	+	1.70711i	0.165809	+	0.0957298i
$319$	33.6625	+	19.4350i	1.88474	+	1.08815i
$320$	1.22474	−	0.707107i	0.0684653	−	0.0395285i
$321$	−24.7279			−1.38018
$322$		0			0
$323$		−	1.45584i		−	0.0810053i
$324$	−4.74264	−	8.21449i	−0.263480	−	0.456361i
$325$	0.696152	+	10.7942i	0.0386156	+	0.598756i
$326$	8.65685	−	14.9941i	0.479459	−	0.830447i
$327$	17.7408	−	10.2426i	0.981067	−	0.566419i
$328$	−9.00000			−0.496942
$329$		0			0
$330$		−	17.8995i		−	0.985335i
$331$	−1.96768	+	1.13604i	−0.108153	+	0.0624423i	−0.553101	−	0.833114i	$-0.686556\pi$
$331$	−1.96768	+	1.13604i	−0.108153	+	0.0624423i	0.444948	+	0.895557i	$0.353222\pi$
$332$	−3.97141	−	2.29289i	−0.217959	−	0.125839i
$333$	6.50794	+	3.75736i	0.356633	+	0.205902i
$334$	−2.82843	−	4.89898i	−0.154765	−	0.268060i
$335$	−18.2426			−0.996702
$336$		0			0
$337$	19.4853			1.06143			0.530715	−	0.847550i	$-0.321923\pi$
$337$	19.4853			1.06143			0.530715	+	0.847550i	$0.321923\pi$
$338$	−1.66987	−	12.8923i	−0.0908291	−	0.701249i
$339$	20.6924	−	35.8403i	1.12386	−	1.94658i
$340$	7.34847	+	4.24264i	0.398527	+	0.230089i
$341$	13.7426	+	23.8030i	0.744206	+	1.28900i
$342$	−0.686292			−0.0371104
$343$		0			0
$344$		−	3.75736i		−	0.202583i
$345$	−4.68885	+	2.70711i	−0.252439	+	0.145746i
$346$	21.2049	+	12.2426i	1.13998	+	0.658168i
$347$	−2.48528	+	4.30463i	−0.133417	+	0.231085i	−0.924992	−	0.379988i	$-0.875928\pi$
$347$	−2.48528	+	4.30463i	−0.133417	+	0.231085i	0.791575	+	0.611072i	$0.209262\pi$
$348$	8.94975	+	15.5014i	0.479757	+	0.830963i
$349$		−	8.72792i		−	0.467195i	−0.972333	−	0.233597i	$-0.924950\pi$
$349$		−	8.72792i		−	0.467195i	0.972333	−	0.233597i	$-0.0750498\pi$
$350$		0			0
$351$	1.24264	−	0.828427i	0.0663273	−	0.0442182i
$352$	2.62132	+	4.54026i	0.139717	+	0.241997i
$353$	18.1865	+	10.5000i	0.967972	+	0.558859i	0.898617	−	0.438733i	$-0.144573\pi$
$353$	18.1865	+	10.5000i	0.967972	+	0.558859i	0.0693543	+	0.997592i	$0.477906\pi$
$354$	12.3640	−	21.4150i	0.657137	−	1.13819i
$355$	2.65685	+	4.60181i	0.141011	+	0.244239i
$356$		−	11.3137i		−	0.599625i
$357$		0			0
$358$		−	11.3137i		−	0.597948i
$359$	6.71807	−	3.87868i	0.354566	−	0.204709i	−0.312128	−	0.950040i	$-0.601042\pi$
$359$	6.71807	−	3.87868i	0.354566	−	0.204709i	0.666695	+	0.745331i	$0.267709\pi$
$360$	2.00000	−	3.46410i	0.105409	−	0.182574i
$361$	−9.47056	+	16.4035i	−0.498451	+	0.863342i
$362$	14.5484	−	8.39949i	0.764644	−	0.441468i
$363$	39.7990			2.08891
$364$		0			0
$365$	−19.0711			−0.998225
$366$	6.27231	−	3.62132i	0.327859	−	0.189289i
$367$	−3.87868	+	6.71807i	−0.202465	+	0.350680i	−0.949322	−	0.314304i	$-0.898229\pi$
$367$	−3.87868	+	6.71807i	−0.202465	+	0.350680i	0.746857	+	0.664985i	$0.231562\pi$
$368$	0.792893	−	1.37333i	0.0413324	−	0.0715898i
$369$	−22.0454	+	12.7279i	−1.14764	+	0.662589i
$370$		−	3.75736i		−	0.195336i
$371$		0			0
$372$			12.6569i			0.656227i
$373$	4.36396	+	7.55860i	0.225957	+	0.391370i	0.956606	−	0.291384i	$-0.0941157\pi$
$373$	4.36396	+	7.55860i	0.225957	+	0.391370i	−0.730649	+	0.682753i	$0.760782\pi$
$374$	−15.7279	+	27.2416i	−0.813271	+	1.40863i
$375$	−23.6544	−	13.6569i	−1.22151	−	0.705237i
$376$	2.20711	+	3.82282i	0.113823	+	0.197147i
$377$	−22.2426	+	14.8284i	−1.14555	+	0.763703i
$378$		0			0
$379$			14.1421i			0.726433i	0.931705	+	0.363216i	$0.118321\pi$
$379$			14.1421i			0.726433i	−0.931705	+	0.363216i	$0.881679\pi$
$380$	0.171573	+	0.297173i	0.00880150	+	0.0152447i
$381$	−12.9853	+	22.4912i	−0.665256	+	1.15226i
$382$	2.44949	+	1.41421i	0.125327	+	0.0723575i
$383$	4.11999	−	2.37868i	0.210522	−	0.121545i	−0.391032	−	0.920377i	$-0.627882\pi$
$383$	4.11999	−	2.37868i	0.210522	−	0.121545i	0.601554	+	0.798832i	$0.294549\pi$
$384$			2.41421i			0.123200i
$385$		0			0
$386$	−0.686292			−0.0349313
$387$	−5.31371	−	9.20361i	−0.270111	−	0.467846i
$388$	8.21449	+	4.74264i	0.417028	+	0.240771i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$	11.0349	+	5.45617i	0.558774	+	0.276284i
$391$	9.51472			0.481180
$392$		0			0
$393$	4.82843			0.243562
$394$	−6.98528	−	12.0989i	−0.351913	−	0.609532i
$395$	14.3637	+	8.29289i	0.722717	+	0.417261i
$396$	12.8418	+	7.41421i	0.645324	+	0.372578i
$397$	−26.8213	+	15.4853i	−1.34612	+	0.777184i	−0.987698	−	0.156375i	$-0.950019\pi$
$397$	−26.8213	+	15.4853i	−1.34612	+	0.777184i	−0.358424	+	0.933559i	$0.616686\pi$
$398$			7.75736i			0.388841i
$399$		0			0
$400$	3.00000			0.150000
$401$	−6.24682	+	3.60660i	−0.311951	+	0.180105i	−0.647799	−	0.761811i	$-0.724310\pi$
$401$	−6.24682	+	3.60660i	−0.311951	+	0.180105i	0.335848	+	0.941916i	$0.390977\pi$
$402$	15.5711	−	26.9699i	0.776614	−	1.34514i
$403$	−18.8634	+	1.21656i	−0.939654	+	0.0606011i
$404$	−4.74264	−	8.21449i	−0.235955	−	0.408686i
$405$			13.4142i			0.666558i
$406$		0			0
$407$	13.9289			0.690432
$408$	−12.5446	+	7.24264i	−0.621051	+	0.358564i
$409$	12.1244	+	7.00000i	0.599511	+	0.346128i	0.768849	−	0.639430i	$-0.220830\pi$
$409$	12.1244	+	7.00000i	0.599511	+	0.346128i	−0.169338	+	0.985558i	$0.554163\pi$
$410$	11.0227	+	6.36396i	0.544373	+	0.314294i
$411$	33.4523	−	19.3137i	1.65008	−	0.952675i
$412$		0			0
$413$		0			0
$414$		−	4.48528i		−	0.220440i
$415$	3.24264	+	5.61642i	0.159175	+	0.275699i
$416$	−3.59808	+	0.232051i	−0.176410	+	0.0113772i
$417$	−17.0711	+	29.5680i	−0.835974	+	1.44795i
$418$	−1.10165	+	0.636039i	−0.0538836	+	0.0311097i
$419$	−1.72792			−0.0844145			−0.0422073	−	0.999109i	$-0.513439\pi$
$419$	−1.72792			−0.0844145			−0.0422073	+	0.999109i	$0.513439\pi$
$420$		0			0
$421$		−	4.02944i		−	0.196383i	−0.995168	−	0.0981914i	$-0.968694\pi$
$421$		−	4.02944i		−	0.196383i	0.995168	−	0.0981914i	$-0.0313057\pi$
$422$	−17.9509	+	10.3640i	−0.873836	+	0.504510i
$423$	10.8126	+	6.24264i	0.525725	+	0.303528i
$424$	1.22474	+	0.707107i	0.0594789	+	0.0343401i
$425$	9.00000	+	15.5885i	0.436564	+	0.756151i
$426$	−9.07107			−0.439495
$427$		0			0
$428$	−10.2426			−0.495097
$429$	−20.2266	+	40.9076i	−0.976550	+	1.97504i
$430$	−2.65685	+	4.60181i	−0.128125	+	0.221919i
$431$	−35.4815	−	20.4853i	−1.70909	−	0.986741i	−0.935694	−	0.352814i	$-0.885225\pi$
$431$	−35.4815	−	20.4853i	−1.70909	−	0.986741i	−0.773392	−	0.633927i	$-0.781442\pi$
$432$	−0.207107	−	0.358719i	−0.00996443	−	0.0172589i
$433$	28.6274			1.37575			0.687873	−	0.725831i	$-0.258545\pi$
$433$	28.6274			1.37575			0.687873	+	0.725831i	$0.258545\pi$
$434$		0			0
$435$		−	25.3137i		−	1.21370i
$436$	7.34847	−	4.24264i	0.351928	−	0.203186i
$437$	0.333226	+	0.192388i	0.0159404	+	0.00920317i
$438$	16.2782	−	28.1946i	0.777801	−	1.34719i
$439$	−6.36396	−	11.0227i	−0.303735	−	0.526085i	0.673244	−	0.739421i	$-0.264901\pi$
$439$	−6.36396	−	11.0227i	−0.303735	−	0.526085i	−0.976979	+	0.213336i	$0.931567\pi$
$440$		−	7.41421i		−	0.353459i
$441$		0			0
$442$	−12.0000	−	18.0000i	−0.570782	−	0.856173i
$443$	0.707107	+	1.22474i	0.0335957	+	0.0581894i	0.882334	−	0.470623i	$-0.155971\pi$
$443$	0.707107	+	1.22474i	0.0335957	+	0.0581894i	−0.848739	+	0.528812i	$0.822637\pi$
$444$	5.55487	+	3.20711i	0.263623	+	0.152203i
$445$	−8.00000	+	13.8564i	−0.379236	+	0.656857i
$446$	−2.86396	−	4.96053i	−0.135612	−	0.234888i
$447$			47.0416i			2.22499i
$448$		0			0
$449$		−	20.2426i		−	0.955309i	−0.878548	−	0.477655i	$-0.841487\pi$
$449$		−	20.2426i		−	0.955309i	0.878548	−	0.477655i	$-0.158513\pi$
$450$	7.34847	−	4.24264i	0.346410	−	0.200000i
$451$	−23.5919	+	40.8623i	−1.11090	+	1.92413i
$452$	8.57107	−	14.8455i	0.403149	−	0.698275i
$453$	42.1126	−	24.3137i	1.97862	−	1.14236i
$454$	−20.8284			−0.977527
$455$		0			0
$456$	−0.585786			−0.0274320
$457$	−1.52192	+	0.878680i	−0.0711923	+	0.0411029i	−0.535174	−	0.844742i	$-0.679754\pi$
$457$	−1.52192	+	0.878680i	−0.0711923	+	0.0411029i	0.463981	+	0.885845i	$0.346420\pi$
$458$	−11.1213	+	19.2627i	−0.519665	+	0.900086i
$459$	1.24264	−	2.15232i	0.0580015	−	0.100462i
$460$	−1.94218	+	1.12132i	−0.0905548	+	0.0522818i
$461$		−	10.2426i		−	0.477047i	−0.971137	−	0.238524i	$-0.923337\pi$
$461$		−	10.2426i		−	0.477047i	0.971137	−	0.238524i	$-0.0766635\pi$
$462$		0			0
$463$			21.5147i			0.999874i	0.866062	+	0.499937i	$0.166643\pi$
$463$			21.5147i			0.999874i	−0.866062	+	0.499937i	$0.833357\pi$
$464$	3.70711	+	6.42090i	0.172098	+	0.298083i
$465$	8.94975	−	15.5014i	0.415035	−	0.718861i
$466$	20.0417	+	11.5711i	0.928413	+	0.536019i
$467$	12.7279	+	22.0454i	0.588978	+	1.02014i	0.994367	+	0.105995i	$0.0338029\pi$
$467$	12.7279	+	22.0454i	0.588978	+	1.02014i	−0.405389	+	0.914144i	$0.632864\pi$
$468$	−8.48528	+	5.65685i	−0.392232	+	0.261488i
$469$		0			0
$470$		−	6.24264i		−	0.287952i
$471$	−3.62132	−	6.27231i	−0.166862	−	0.289013i
$472$	5.12132	−	8.87039i	0.235728	−	0.408293i
$473$	−17.0594	−	9.84924i	−0.784392	−	0.452869i
$474$	−24.5204	+	14.1569i	−1.12626	+	0.650246i
$475$			0.727922i			0.0333994i
$476$		0			0
$477$	4.00000			0.183147
$478$	−11.2426	−	19.4728i	−0.514226	−	0.890666i
$479$	−15.8856	−	9.17157i	−0.725833	−	0.419060i	0.0910628	−	0.995845i	$-0.470974\pi$
$479$	−15.8856	−	9.17157i	−0.725833	−	0.419060i	−0.816896	+	0.576785i	$0.804307\pi$
$480$	1.70711	−	2.95680i	0.0779184	−	0.134959i
$481$	−4.24586	+	8.58709i	−0.193594	+	0.391538i
$482$	−12.4853			−0.568689
$483$		0			0
$484$	16.4853			0.749331
$485$	−6.70711	−	11.6170i	−0.304554	−	0.527503i
$486$	−18.7554	−	10.8284i	−0.850762	−	0.491187i
$487$	18.3712	+	10.6066i	0.832477	+	0.480631i	0.854700	−	0.519122i	$-0.173741\pi$
$487$	18.3712	+	10.6066i	0.832477	+	0.480631i	−0.0222228	+	0.999753i	$0.507074\pi$
$488$	2.59808	−	1.50000i	0.117609	−	0.0679018i
$489$		−	41.7990i		−	1.89022i
$490$		0			0
$491$	−44.1838			−1.99399			−0.996993	−	0.0774952i	$-0.975308\pi$
$491$	−44.1838			−1.99399			−0.996993	+	0.0774952i	$0.975308\pi$
$492$	−18.8169	+	10.8640i	−0.848333	+	0.489785i
$493$	−22.2426	+	38.5254i	−1.00176	+	1.73510i
$494$	−0.0563050	−	0.873040i	−0.00253328	−	0.0392799i
$495$	−10.4853	−	18.1610i	−0.471278	−	0.816278i
$496$			5.24264i			0.235402i
$497$		0			0
$498$	−11.0711			−0.496106
$499$	−16.6646	+	9.62132i	−0.746011	+	0.430709i	−0.824251	−	0.566225i	$-0.808403\pi$
$499$	−16.6646	+	9.62132i	−0.746011	+	0.430709i	0.0782400	+	0.996935i	$0.475070\pi$
$500$	−9.79796	−	5.65685i	−0.438178	−	0.252982i
$501$	−11.8272	−	6.82843i	−0.528400	−	0.305072i
$502$	−2.38794	+	1.37868i	−0.106579	+	0.0615335i
$503$	38.4853			1.71597			0.857987	−	0.513671i	$-0.171715\pi$
$503$	38.4853			1.71597			0.857987	+	0.513671i	$0.171715\pi$
$504$		0			0
$505$			13.4142i			0.596925i
$506$	−4.15685	−	7.19988i	−0.184795	−	0.320074i
$507$	−19.0537	−	24.9391i	−0.846205	−	1.10759i
$508$	−5.37868	+	9.31615i	−0.238640	+	0.413337i
$509$	−19.5599	+	11.2929i	−0.866976	+	0.500549i	−0.866342	−	0.499451i	$-0.833535\pi$
$509$	−19.5599	+	11.2929i	−0.866976	+	0.500549i	−0.000633690		1.00000i	$0.500202\pi$
$510$	20.4853			0.907104
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	0.0870399	−	0.0502525i	0.00384291	−	0.00221870i
$514$	−12.9649	−	7.48528i	−0.571857	−	0.330162i
$515$		0			0
$516$	−4.53553	−	7.85578i	−0.199666	−	0.345831i
$517$	23.1421			1.01779
$518$		0			0
$519$	59.1127			2.59476
$520$	4.57081	+	2.26002i	0.200443	+	0.0991085i
$521$	11.8492	−	20.5235i	0.519125	−	0.899150i	−0.480628	−	0.876924i	$-0.659591\pi$
$521$	11.8492	−	20.5235i	0.519125	−	0.899150i	0.999753	−	0.0222260i	$-0.00707533\pi$
$522$	18.1610	+	10.4853i	0.794887	+	0.458928i
$523$	−11.3787	−	19.7085i	−0.497555	−	0.861790i	0.502441	−	0.864611i	$-0.332435\pi$
$523$	−11.3787	−	19.7085i	−0.497555	−	0.861790i	−0.999996	+	0.00282104i	$0.999102\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$			31.7990i			1.38650i
$527$	−27.2416	+	15.7279i	−1.18666	+	0.685119i
$528$	10.9612	+	6.32843i	0.477023	+	0.275409i
$529$	10.2426	−	17.7408i	0.445332	−	0.771338i
$530$	−1.00000	−	1.73205i	−0.0434372	−	0.0752355i
$531$		−	28.9706i		−	1.25722i
$532$		0			0
$533$	−18.0000	−	27.0000i	−0.779667	−	1.16950i
$534$	−13.6569	−	23.6544i	−0.590990	−	1.02362i
$535$	12.5446	+	7.24264i	0.542351	+	0.313127i
$536$	6.44975	−	11.1713i	0.278587	−	0.482526i
$537$	−13.6569	−	23.6544i	−0.589337	−	1.02076i
$538$		−	14.5147i		−	0.625774i
$539$		0			0
$540$			0.585786i			0.0252082i
$541$	26.2779	−	15.1716i	1.12978	−	0.652277i	0.185898	−	0.982569i	$-0.440481\pi$
$541$	26.2779	−	15.1716i	1.12978	−	0.652277i	0.943879	+	0.330292i	$0.107147\pi$
$542$	16.3492	−	28.3177i	0.702260	−	1.21635i
$543$	20.2782	−	35.1228i	0.870220	−	1.50726i
$544$	−5.19615	+	3.00000i	−0.222783	+	0.128624i
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−14.7279			−0.629720			−0.314860	−	0.949138i	$-0.601958\pi$
$547$	−14.7279			−0.629720			−0.314860	+	0.949138i	$0.601958\pi$
$548$	13.8564	−	8.00000i	0.591916	−	0.341743i
$549$	4.24264	−	7.34847i	0.181071	−	0.313625i
$550$	7.86396	−	13.6208i	0.335320	−	0.580792i
$551$	−1.55797	+	0.899495i	−0.0663718	+	0.0383198i
$552$		−	3.82843i		−	0.162949i
$553$		0			0
$554$			20.7279i			0.880645i
$555$	−4.53553	−	7.85578i	−0.192523	−	0.333459i
$556$	−7.07107	+	12.2474i	−0.299880	+	0.519408i
$557$	−19.4473	−	11.2279i	−0.824010	−	0.475742i	0.0277874	−	0.999614i	$-0.491154\pi$
$557$	−19.4473	−	11.2279i	−0.824010	−	0.475742i	−0.851797	+	0.523872i	$0.824487\pi$
$558$	7.41421	+	12.8418i	0.313869	+	0.543637i
$559$	11.2721	−	7.51472i	0.476758	−	0.317839i
$560$		0			0
$561$			75.9411i			3.20624i
$562$	15.3640	+	26.6112i	0.648090	+	1.12252i
$563$	8.86396	−	15.3528i	0.373571	−	0.647045i	−0.616541	−	0.787323i	$-0.711466\pi$
$563$	8.86396	−	15.3528i	0.373571	−	0.647045i	0.990112	+	0.140278i	$0.0447997\pi$
$564$	9.22911	+	5.32843i	0.388615	+	0.224367i
$565$	−20.9947	+	12.1213i	−0.883255	+	0.509948i
$566$		−	7.24264i		−	0.304431i
$567$		0			0
$568$	−3.75736			−0.157655
$569$	−1.32843	−	2.30090i	−0.0556906	−	0.0964589i	0.836836	−	0.547453i	$-0.184403\pi$
$569$	−1.32843	−	2.30090i	−0.0556906	−	0.0964589i	−0.892527	+	0.450995i	$0.851069\pi$
$570$	0.717439	+	0.414214i	0.0300502	+	0.0173495i
$571$	2.87868	−	4.98602i	0.120469	−	0.208658i	−0.799484	−	0.600688i	$-0.794893\pi$
$571$	2.87868	−	4.98602i	0.120469	−	0.208658i	0.919953	+	0.392029i	$0.128227\pi$
$572$	−8.37814	+	16.9445i	−0.350308	+	0.708484i
$573$	6.82843			0.285262
$574$		0			0
$575$	−4.75736			−0.198396
$576$	1.41421	+	2.44949i	0.0589256	+	0.102062i
$577$	−17.7408	−	10.2426i	−0.738558	−	0.426407i	0.0829867	−	0.996551i	$-0.473554\pi$
$577$	−17.7408	−	10.2426i	−0.738558	−	0.426407i	−0.821545	+	0.570144i	$0.806887\pi$
$578$	−16.4545	−	9.50000i	−0.684416	−	0.395148i
$579$	−1.43488	+	0.828427i	−0.0596315	+	0.0344283i
$580$		−	10.4853i		−	0.435378i
$581$		0			0
$582$	22.8995			0.949215
$583$	6.42090	−	3.70711i	0.265926	−	0.153533i
$584$	6.74264	−	11.6786i	0.279012	−	0.483264i
$585$	14.3923	−	0.928203i	0.595049	−	0.0383765i
$586$	8.31371	+	14.3998i	0.343436	+	0.594849i
$587$		−	8.14214i		−	0.336062i	−0.985782	−	0.168031i	$-0.946259\pi$
$587$		−	8.14214i		−	0.336062i	0.985782	−	0.168031i	$-0.0537409\pi$
$588$		0			0
$589$	−1.27208			−0.0524151
$590$	−12.5446	+	7.24264i	−0.516454	+	0.298175i
$591$	−29.2092	−	16.8640i	−1.20151	−	0.693691i
$592$	2.30090	+	1.32843i	0.0945665	+	0.0545980i
$593$	14.1026	−	8.14214i	0.579124	−	0.334357i	−0.181661	−	0.983361i	$-0.558147\pi$
$593$	14.1026	−	8.14214i	0.579124	−	0.334357i	0.760785	+	0.649004i	$0.224814\pi$
$594$	−2.17157			−0.0891007
$595$		0			0
$596$			19.4853i			0.798148i
$597$	9.36396	+	16.2189i	0.383241	+	0.663794i
$598$	5.70578	−	0.367983i	0.233327	−	0.0150479i
$599$	9.27817	−	16.0703i	0.379096	−	0.656613i	−0.611835	−	0.790985i	$-0.709568\pi$
$599$	9.27817	−	16.0703i	0.379096	−	0.656613i	0.990931	+	0.134372i	$0.0429017\pi$
$600$	6.27231	−	3.62132i	0.256066	−	0.147840i
$601$	−42.0416			−1.71491			−0.857457	−	0.514556i	$-0.827957\pi$
$601$	−42.0416			−1.71491			−0.857457	+	0.514556i	$0.827957\pi$
$602$		0			0
$603$		−	36.4853i		−	1.48580i
$604$	17.4436	−	10.0711i	0.709770	−	0.409786i
$605$	−20.1903	−	11.6569i	−0.820851	−	0.473919i
$606$	−19.8315	−	11.4497i	−0.805601	−	0.465114i
$607$	−10.0503	−	17.4075i	−0.407927	−	0.706551i	0.586730	−	0.809783i	$-0.300415\pi$
$607$	−10.0503	−	17.4075i	−0.407927	−	0.706551i	−0.994657	+	0.103232i	$0.967082\pi$
$608$	−0.242641			−0.00984038
$609$		0			0
$610$	−4.24264			−0.171780
$611$	−7.05425	+	14.2670i	−0.285384	+	0.577180i
$612$	−8.48528	+	14.6969i	−0.342997	+	0.594089i
$613$	13.2876	+	7.67157i	0.536679	+	0.309852i	0.743732	−	0.668478i	$-0.233054\pi$
$613$	13.2876	+	7.67157i	0.536679	+	0.309852i	−0.207053	+	0.978330i	$0.566387\pi$
$614$	4.87868	+	8.45012i	0.196887	+	0.341019i
$615$	30.7279			1.23907
$616$		0			0
$617$			6.72792i			0.270856i	0.990787	+	0.135428i	$0.0432409\pi$
$617$			6.72792i			0.270856i	−0.990787	+	0.135428i	$0.956759\pi$
$618$		0			0
$619$	6.71807	+	3.87868i	0.270022	+	0.155897i	0.628898	−	0.777488i	$-0.283506\pi$
$619$	6.71807	+	3.87868i	0.270022	+	0.155897i	−0.358876	+	0.933385i	$0.616840\pi$
$620$	3.70711	−	6.42090i	0.148881	−	0.257869i
$621$	0.328427	+	0.568852i	0.0131793	+	0.0228273i
$622$		−	4.24264i		−	0.170114i
$623$		0			0
$624$	−7.24264	+	4.82843i	−0.289938	+	0.193292i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−5.49333	−	3.17157i	−0.219557	−	0.126762i
$627$	−1.53553	+	2.65962i	−0.0613233	+	0.106215i
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$			15.9411i			0.635614i
$630$		0			0
$631$			33.9411i			1.35117i	0.737280	+	0.675587i	$0.236110\pi$
$631$			33.9411i			1.35117i	−0.737280	+	0.675587i	$0.763890\pi$
$632$	−10.1567	+	5.86396i	−0.404011	+	0.233256i
$633$	−25.0208	+	43.3373i	−0.994488	+	1.72250i
$634$	1.74264	−	3.01834i	0.0692091	−	0.119874i
$635$	13.1750	−	7.60660i	0.522835	−	0.301859i
$636$	3.41421			0.135382
$637$		0			0
$638$	38.8701			1.53888
$639$	−9.20361	+	5.31371i	−0.364089	+	0.210207i
$640$	0.707107	−	1.22474i	0.0279508	−	0.0484123i
$641$	−16.1569	+	27.9845i	−0.638157	+	1.10532i	0.347679	+	0.937613i	$0.386970\pi$
$641$	−16.1569	+	27.9845i	−0.638157	+	1.10532i	−0.985837	+	0.167708i	$0.946364\pi$
$642$	−21.4150	+	12.3640i	−0.845183	+	0.487967i
$643$		−	9.51472i		−	0.375224i	−0.982243	−	0.187612i	$-0.939925\pi$
$643$		−	9.51472i		−	0.375224i	0.982243	−	0.187612i	$-0.0600747\pi$
$644$		0			0
$645$			12.8284i			0.505119i
$646$	−0.727922	−	1.26080i	−0.0286397	−	0.0496054i
$647$	−11.1213	+	19.2627i	−0.437224	+	0.757295i	−0.997474	−	0.0710290i	$-0.977372\pi$
$647$	−11.1213	+	19.2627i	−0.437224	+	0.757295i	0.560250	+	0.828324i	$0.310705\pi$
$648$	−8.21449	−	4.74264i	−0.322696	−	0.186309i
$649$	−26.8492	−	46.5043i	−1.05392	−	1.82545i
$650$	6.00000	+	9.00000i	0.235339	+	0.353009i
$651$		0			0
$652$		−	17.3137i		−	0.678057i
$653$	9.36396	+	16.2189i	0.366440	+	0.634693i	0.989006	−	0.147874i	$-0.0472431\pi$
$653$	9.36396	+	16.2189i	0.366440	+	0.634693i	−0.622566	+	0.782567i	$0.713910\pi$
$654$	10.2426	−	17.7408i	0.400519	−	0.693719i
$655$	−2.44949	−	1.41421i	−0.0957095	−	0.0552579i
$656$	−7.79423	+	4.50000i	−0.304314	+	0.175695i
$657$		−	38.1421i		−	1.48807i
$658$		0			0
$659$	−38.8701			−1.51416			−0.757081	−	0.653321i	$-0.773375\pi$
$659$	−38.8701			−1.51416			−0.757081	+	0.653321i	$0.773375\pi$
$660$	−8.94975	−	15.5014i	−0.348368	−	0.603392i
$661$	34.3799	+	19.8492i	1.33722	+	0.772046i	0.986395	−	0.164394i	$-0.0525668\pi$
$661$	34.3799	+	19.8492i	1.33722	+	0.772046i	0.350828	+	0.936440i	$0.385900\pi$
$662$	−1.13604	+	1.96768i	−0.0441534	+	0.0764759i
$663$	−46.8172	−	23.1486i	−1.81823	−	0.899016i
$664$	−4.58579			−0.177963
$665$		0			0
$666$	7.51472			0.291189
$667$	−5.87868	−	10.1822i	−0.227623	−	0.394255i
$668$	−4.89898	−	2.82843i	−0.189547	−	0.109435i
$669$	−11.9758	−	6.91421i	−0.463010	−	0.267319i
$670$	−15.7986	+	9.12132i	−0.610353	+	0.352387i
$671$		−	15.7279i		−	0.607170i
$672$		0			0
$673$	17.9706			0.692714			0.346357	−	0.938103i	$-0.387419\pi$
$673$	17.9706			0.692714			0.346357	+	0.938103i	$0.387419\pi$
$674$	16.8747	−	9.74264i	0.649991	−	0.375272i
$675$	−0.621320	+	1.07616i	−0.0239146	+	0.0414214i
$676$	−7.89230	−	10.3301i	−0.303550	−	0.397313i
$677$	11.7426	+	20.3389i	0.451306	+	0.781686i	0.998467	−	0.0553418i	$-0.0176248\pi$
$677$	11.7426	+	20.3389i	0.451306	+	0.781686i	−0.547161	+	0.837027i	$0.684292\pi$
$678$		−	41.3848i		−	1.58937i
$679$		0			0
$680$	8.48528			0.325396
$681$	−43.5475	+	25.1421i	−1.66874	+	0.963449i
$682$	23.8030	+	13.7426i	0.911462	+	0.526233i
$683$	−10.5769	−	6.10660i	−0.404716	−	0.233663i	0.283801	−	0.958883i	$-0.408404\pi$
$683$	−10.5769	−	6.10660i	−0.404716	−	0.233663i	−0.688517	+	0.725221i	$0.741738\pi$
$684$	−0.594346	+	0.343146i	−0.0227254	+	0.0131205i
$685$	−22.6274			−0.864549
$686$		0			0
$687$			53.6985i			2.04872i
$688$	−1.87868	−	3.25397i	−0.0716240	−	0.124056i
$689$	0.328169	+	5.08845i	0.0125023	+	0.193854i
$690$	−2.70711	+	4.68885i	−0.103058	+	0.178501i
$691$	−4.77589	+	2.75736i	−0.181683	+	0.104895i	−0.588083	−	0.808800i	$-0.700117\pi$
$691$	−4.77589	+	2.75736i	−0.181683	+	0.104895i	0.406400	+	0.913695i	$0.366784\pi$
$692$	24.4853			0.930791
$693$		0			0
$694$			4.97056i			0.188680i
$695$	17.3205	−	10.0000i	0.657004	−	0.379322i
$696$	15.5014	+	8.94975i	0.587580	+	0.339239i
$697$	−46.7654	−	27.0000i	−1.77136	−	1.02270i
$698$	−4.36396	−	7.55860i	−0.165178	−	0.286097i
$699$	55.8701			2.11320
$700$		0			0
$701$	5.61522			0.212084			0.106042	−	0.994362i	$-0.466182\pi$
$701$	5.61522			0.212084			0.106042	+	0.994362i	$0.466182\pi$
$702$	0.661945	−	1.33876i	0.0249835	−	0.0505282i
$703$	−0.322330	+	0.558293i	−0.0121569	+	0.0210564i
$704$	4.54026	+	2.62132i	0.171117	+	0.0987947i
$705$	−7.53553	−	13.0519i	−0.283805	−	0.491564i
$706$	21.0000			0.790345
$707$		0			0
$708$		−	24.7279i		−	0.929332i
$709$	9.64937	−	5.57107i	0.362390	−	0.209226i	−0.307739	−	0.951471i	$-0.599572\pi$
$709$	9.64937	−	5.57107i	0.362390	−	0.209226i	0.670129	+	0.742245i	$0.266239\pi$
$710$	4.60181	+	2.65685i	0.172703	+	0.0997100i
$711$	−16.5858	+	28.7274i	−0.622016	+	1.07736i
$712$	−5.65685	−	9.79796i	−0.212000	−	0.367194i
$713$		−	8.31371i		−	0.311351i
$714$		0			0
$715$	22.2426	−	14.8284i	0.831828	−	0.554552i
$716$	−5.65685	−	9.79796i	−0.211407	−	0.366167i
$717$	−47.0116	−	27.1421i	−1.75568	−	1.01364i
$718$	3.87868	−	6.71807i	0.144751	−	0.250716i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		−	4.00000i		−	0.149071i
$721$		0			0
$722$			18.9411i			0.704916i
$723$	−26.1039	+	15.0711i	−0.970813	+	0.560499i
$724$	8.39949	−	14.5484i	0.312165	−	0.540685i
$725$	11.1213	−	19.2627i	0.413035	−	0.715398i
$726$	34.4669	−	19.8995i	1.27919	−	0.738540i
$727$	37.7990			1.40189			0.700943	−	0.713217i	$-0.252763\pi$
$727$	37.7990			1.40189			0.700943	+	0.713217i	$0.252763\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$	−16.5160	+	9.53553i	−0.611286	+	0.352926i
$731$	11.2721	−	19.5238i	0.416913	−	0.722114i
$732$	3.62132	−	6.27231i	0.133848	−	0.231831i
$733$	−32.0174	+	18.4853i	−1.18259	+	0.682769i	−0.956613	−	0.291363i	$-0.905891\pi$
$733$	−32.0174	+	18.4853i	−1.18259	+	0.682769i	−0.225979	+	0.974132i	$0.572558\pi$
$734$			7.75736i			0.286329i
$735$		0			0
$736$		−	1.58579i		−	0.0584529i
$737$	−33.8137	−	58.5671i	−1.24554	−	2.15735i
$738$	−12.7279	+	22.0454i	−0.468521	+	0.811503i
$739$	22.6398	+	13.0711i	0.832817	+	0.480827i	0.854816	−	0.518931i	$-0.173670\pi$
$739$	22.6398	+	13.0711i	0.832817	+	0.480827i	−0.0219993	+	0.999758i	$0.507003\pi$
$740$	−1.87868	−	3.25397i	−0.0690616	−	0.119618i
$741$	−1.17157	−	1.75736i	−0.0430388	−	0.0645582i
$742$		0			0
$743$		−	35.4558i		−	1.30075i	−0.759614	−	0.650374i	$-0.774612\pi$
$743$		−	35.4558i		−	1.30075i	0.759614	−	0.650374i	$-0.225388\pi$
$744$	6.32843	+	10.9612i	0.232011	+	0.401856i
$745$	13.7782	−	23.8645i	0.504793	−	0.874328i
$746$	7.55860	+	4.36396i	0.276740	+	0.159776i
$747$	−11.2328	+	6.48528i	−0.410988	+	0.237284i
$748$			31.4558i			1.15014i
$749$		0			0
$750$	−27.3137			−0.997356
$751$	25.1066	+	43.4859i	0.916153	+	1.58682i	0.805205	+	0.592997i	$0.202055\pi$
$751$	25.1066	+	43.4859i	0.916153	+	1.58682i	0.110948	+	0.993826i	$0.464611\pi$
$752$	3.82282	+	2.20711i	0.139404	+	0.0804849i
$753$	−3.32843	+	5.76500i	−0.121295	+	0.210088i
$754$	−11.8485	+	23.9631i	−0.431496	+	0.872685i
$755$	−28.4853			−1.03669
$756$		0			0
$757$	−2.97056			−0.107967			−0.0539835	−	0.998542i	$-0.517192\pi$
$757$	−2.97056			−0.107967			−0.0539835	+	0.998542i	$0.517192\pi$
$758$	7.07107	+	12.2474i	0.256833	+	0.444847i
$759$	−17.3821	−	10.0355i	−0.630929	−	0.364267i
$760$	0.297173	+	0.171573i	0.0107796	+	0.00622360i
$761$	−11.5045	+	6.64214i	−0.417038	+	0.240777i	−0.693809	−	0.720159i	$-0.744069\pi$
$761$	−11.5045	+	6.64214i	−0.417038	+	0.240777i	0.276771	+	0.960936i	$0.410736\pi$
$762$			25.9706i			0.940814i
$763$		0			0
$764$	2.82843			0.102329
$765$	20.7846	−	12.0000i	0.751469	−	0.433861i
$766$	2.37868	−	4.11999i	0.0859452	−	0.148861i
$767$	36.8538	−	2.37681i	1.33071	−	0.0858217i
$768$	1.20711	+	2.09077i	0.0435577	+	0.0754442i
$769$		−	7.00000i		−	0.252426i	−0.992003	−	0.126213i	$-0.959718\pi$
$769$		−	7.00000i		−	0.252426i	0.992003	−	0.126213i	$-0.0402824\pi$
$770$		0			0
$771$	−36.1421			−1.30163
$772$	−0.594346	+	0.343146i	−0.0213910	+	0.0123501i
$773$	10.6895	+	6.17157i	0.384474	+	0.221976i	0.679763	−	0.733432i	$-0.262083\pi$
$773$	10.6895	+	6.17157i	0.384474	+	0.221976i	−0.295289	+	0.955408i	$0.595416\pi$
$774$	−9.20361	−	5.31371i	−0.330817	−	0.190997i
$775$	13.6208	−	7.86396i	0.489273	−	0.282482i
$776$	9.48528			0.340502
$777$		0			0
$778$			18.0000i			0.645331i
$779$	−1.09188	−	1.89120i	−0.0391208	−	0.0677592i
$780$	12.2846	−	0.792271i	0.439859	−	0.0283679i
$781$	−9.84924	+	17.0594i	−0.352434	+	0.610433i
$782$	8.23999	−	4.75736i	0.294661	−	0.170123i
$783$	−3.07107			−0.109751
$784$		0			0
$785$			4.24264i			0.151426i
$786$	4.18154	−	2.41421i	0.149151	−	0.0861121i
$787$	−12.0734	−	6.97056i	−0.430369	−	0.248474i	0.269135	−	0.963103i	$-0.413262\pi$
$787$	−12.0734	−	6.97056i	−0.430369	−	0.248474i	−0.699504	+	0.714629i	$0.746596\pi$
$788$	−12.0989	−	6.98528i	−0.431004	−	0.248840i
$789$	38.3848	+	66.4844i	1.36653	+	2.36691i
$790$	16.5858			0.590096
$791$		0			0
$792$	14.8284			0.526905
$793$	9.69615	+	4.79423i	0.344320	+	0.170248i
$794$	−15.4853	+	26.8213i	−0.549552	+	0.951852i
$795$	−4.18154	−	2.41421i	−0.148304	−	0.0856233i
$796$	3.87868	+	6.71807i	0.137476	+	0.238116i
$797$	−8.45584			−0.299521			−0.149761	−	0.988722i	$-0.547850\pi$
$797$	−8.45584			−0.299521			−0.149761	+	0.988722i	$0.547850\pi$
$798$		0			0
$799$			26.4853i			0.936982i
$800$	2.59808	−	1.50000i	0.0918559	−	0.0530330i
$801$	−27.7128	−	16.0000i	−0.979184	−	0.565332i
$802$	−3.60660	+	6.24682i	−0.127354	+	0.220583i
$803$	−35.3492	−	61.2267i	−1.24745	−	2.16064i
$804$		−	31.1421i		−	1.09830i
$805$		0			0
$806$	−15.7279	+	10.4853i	−0.553992	+	0.369328i
$807$	−17.5208	−	30.3469i	−0.616762	−	1.06826i
$808$	−8.21449	−	4.74264i	−0.288985	−	0.166846i
$809$	−7.41421	+	12.8418i	−0.260670	+	0.451493i	−0.966420	−	0.256967i	$-0.917277\pi$
$809$	−7.41421	+	12.8418i	−0.260670	+	0.451493i	0.705750	+	0.708461i	$0.250610\pi$
$810$	6.70711	+	11.6170i	0.235664	+	0.408182i
$811$			16.0000i			0.561836i	0.959732	+	0.280918i	$0.0906389\pi$
$811$			16.0000i			0.561836i	−0.959732	+	0.280918i	$0.909361\pi$
$812$		0			0
$813$		−	78.9411i		−	2.76859i
$814$	12.0628	−	6.96447i	0.422801	−	0.244104i
$815$	−12.2426	+	21.2049i	−0.428841	+	0.742774i
$816$	−7.24264	+	12.5446i	−0.253543	+	0.439150i
$817$	0.789545	−	0.455844i	0.0276227	−	0.0159480i
$818$	14.0000			0.489499
$819$		0			0
$820$	12.7279			0.444478
$821$	2.62357	−	1.51472i	0.0915632	−	0.0528640i	−0.453519	−	0.891246i	$-0.649832\pi$
$821$	2.62357	−	1.51472i	0.0915632	−	0.0528640i	0.545082	+	0.838382i	$0.316498\pi$
$822$	19.3137	−	33.4523i	0.673643	−	1.16678i
$823$	26.5919	−	46.0585i	0.926935	−	1.60550i	0.138515	−	0.990360i	$-0.455767\pi$
$823$	26.5919	−	46.0585i	0.926935	−	1.60550i	0.788420	−	0.615138i	$-0.210900\pi$
$824$		0			0
$825$		−	37.9706i		−	1.32197i
$826$		0			0
$827$		−	37.9411i		−	1.31934i	−0.751554	−	0.659671i	$-0.770696\pi$
$827$		−	37.9411i		−	1.31934i	0.751554	−	0.659671i	$-0.229304\pi$
$828$	−2.24264	−	3.88437i	−0.0779372	−	0.134991i
$829$	4.24264	−	7.34847i	0.147353	−	0.255223i	−0.782895	−	0.622153i	$-0.786258\pi$
$829$	4.24264	−	7.34847i	0.147353	−	0.255223i	0.930248	+	0.366931i	$0.119591\pi$
$830$	5.61642	+	3.24264i	0.194949	+	0.112554i
$831$	25.0208	+	43.3373i	0.867962	+	1.50336i
$832$	−3.00000	+	2.00000i	−0.104006	+	0.0693375i
$833$		0			0
$834$			34.1421i			1.18225i
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$	−0.636039	+	1.10165i	−0.0219979	+	0.0381014i
$837$	−1.88064	−	1.08579i	−0.0650043	−	0.0375303i
$838$	−1.49642	+	0.863961i	−0.0516931	+	0.0298450i
$839$			54.8995i			1.89534i	0.319250	+	0.947671i	$0.396569\pi$
$839$			54.8995i			1.89534i	−0.319250	+	0.947671i	$0.603431\pi$
$840$		0			0
$841$	25.9706			0.895537
$842$	−2.01472	−	3.48960i	−0.0694318	−	0.120259i
$843$	64.2450	+	37.0919i	2.21272	+	1.27751i
$844$	−10.3640	+	17.9509i	−0.356742	+	0.617896i
$845$	2.36156	+	18.2325i	0.0812400	+	0.627216i
$846$	12.4853			0.429253
$847$		0			0
$848$	1.41421			0.0485643
$849$	−8.74264	−	15.1427i	−0.300047	−	0.519696i
$850$	15.5885	+	9.00000i	0.534680	+	0.308697i
$851$	−3.64874	−	2.10660i	−0.125077	−	0.0722134i
$852$	−7.85578	+	4.53553i	−0.269134	+	0.155385i
$853$		−	38.7279i		−	1.32602i	−0.748611	−	0.663009i	$-0.769279\pi$
$853$		−	38.7279i		−	1.32602i	0.748611	−	0.663009i	$-0.230721\pi$
$854$		0			0
$855$	0.970563			0.0331925
$856$	−8.87039	+	5.12132i	−0.303184	+	0.175043i
$857$	−11.8492	+	20.5235i	−0.404762	+	0.701069i	−0.994294	−	0.106676i	$-0.965979\pi$
$857$	−11.8492	+	20.5235i	−0.404762	+	0.701069i	0.589531	+	0.807745i	$0.299312\pi$
$858$	2.93703	+	45.5403i	0.100269	+	1.55472i
$859$	9.96447	+	17.2590i	0.339983	+	0.588868i	0.984429	−	0.175782i	$-0.0562453\pi$
$859$	9.96447	+	17.2590i	0.339983	+	0.588868i	−0.644446	+	0.764650i	$0.722912\pi$
$860$			5.31371i			0.181196i
$861$		0			0
$862$	−40.9706			−1.39546
$863$	−29.0246	+	16.7574i	−0.988009	+	0.570427i	−0.904679	−	0.426095i	$-0.859889\pi$
$863$	−29.0246	+	16.7574i	−0.988009	+	0.570427i	−0.0833303	+	0.996522i	$0.526556\pi$
$864$	−0.358719	−	0.207107i	−0.0122039	−	0.00704592i
$865$	−29.9882	−	17.3137i	−1.01963	−	0.588684i
$866$	24.7921	−	14.3137i	0.842469	−	0.486400i
$867$	−45.8701			−1.55783
$868$		0			0
$869$			61.4853i			2.08575i
$870$	−12.6569	−	21.9223i	−0.429108	−	0.743236i
$871$	46.4134	−	2.99334i	1.57266	−	0.101425i
$872$	4.24264	−	7.34847i	0.143674	−	0.248851i
$873$	23.2341	−	13.4142i	0.786355	−	0.454002i
$874$	0.384776			0.0130153
$875$		0			0
$876$		−	32.5563i		−	1.09998i
$877$	−31.9920	+	18.4706i	−1.08029	+	0.623707i	−0.930975	−	0.365083i	$-0.881041\pi$
$877$	−31.9920	+	18.4706i	−1.08029	+	0.623707i	−0.149316	+	0.988789i	$0.547707\pi$
$878$	−11.0227	−	6.36396i	−0.371998	−	0.214773i
$879$	34.7641	+	20.0711i	1.17256	+	0.676980i
$880$	−3.70711	−	6.42090i	−0.124967	−	0.216448i
$881$	−16.0000			−0.539054			−0.269527	−	0.962993i	$-0.586867\pi$
$881$	−16.0000			−0.539054			−0.269527	+	0.962993i	$0.586867\pi$
$882$		0			0
$883$	−45.9411			−1.54604			−0.773021	−	0.634380i	$-0.781255\pi$
$883$	−45.9411			−1.54604			−0.773021	+	0.634380i	$0.781255\pi$
$884$	−19.3923	−	9.58846i	−0.652234	−	0.322495i
$885$	−17.4853	+	30.2854i	−0.587761	+	1.01803i
$886$	1.22474	+	0.707107i	0.0411461	+	0.0237557i
$887$	21.0919	+	36.5322i	0.708196	+	1.22663i	0.965526	+	0.260308i	$0.0838241\pi$
$887$	21.0919	+	36.5322i	0.708196	+	1.22663i	−0.257330	+	0.966324i	$0.582843\pi$
$888$	6.41421			0.215247
$889$		0			0
$890$			16.0000i			0.536321i
$891$	−43.0656	+	24.8640i	−1.44275	+	0.832974i
$892$	−4.96053	−	2.86396i	−0.166091	−	0.0958925i
$893$	−0.535534	+	0.927572i	−0.0179210	+	0.0310400i
$894$	23.5208	+	40.7392i	0.786654	+	1.36252i
$895$			16.0000i			0.534821i
$896$		0			0
$897$	11.4853	−	7.65685i	0.383482	−	0.255655i
$898$	−10.1213	−	17.5306i	−0.337753	−	0.585005i
$899$	33.6625	+	19.4350i	1.12271	+	0.648195i
$900$	4.24264	−	7.34847i	0.141421	−	0.244949i
$901$	4.24264	+	7.34847i	0.141343	+	0.244813i
$902$			47.1838i			1.57105i
$903$		0			0
$904$		−	17.1421i		−	0.570139i
$905$	−20.5745	+	11.8787i	−0.683919	+	0.394861i
$906$	24.3137	−	42.1126i	0.807769	−	1.39910i
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	−0.967730	−	0.251990i	$-0.918915\pi$
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	0.702094	+	0.712084i	$0.252248\pi$
$908$	−18.0379	+	10.4142i	−0.598610	+	0.345608i
$909$	−26.8284			−0.889843
$910$		0			0
$911$	−28.2843			−0.937100			−0.468550	−	0.883437i	$-0.655223\pi$
$911$	−28.2843			−0.937100			−0.468550	+	0.883437i	$0.655223\pi$
$912$	−0.507306	+	0.292893i	−0.0167986	+	0.00969866i
$913$	−12.0208	+	20.8207i	−0.397831	+	0.689063i
$914$	−0.878680	+	1.52192i	−0.0290641	+	0.0503406i
$915$	−8.87039	+	5.12132i	−0.293246	+	0.169306i
$916$			22.2426i			0.734918i
$917$		0			0
$918$		−	2.48528i		−	0.0820265i
$919$	6.10660	+	10.5769i	0.201438	+	0.348901i	0.948992	−	0.315300i	$-0.102105\pi$
$919$	6.10660	+	10.5769i	0.201438	+	0.348901i	−0.747554	+	0.664201i	$0.768772\pi$
$920$	−1.12132	+	1.94218i	−0.0369688	+	0.0640319i
$921$	20.4004	+	11.7782i	0.672216	+	0.388104i
$922$	−5.12132	−	8.87039i	−0.168662	−	0.292131i
$923$	−7.51472	−	11.2721i	−0.247350	−	0.371025i
$924$		0			0
$925$		−	7.97056i		−	0.262070i
$926$	10.7574	+	18.6323i	0.353509	+	0.612295i
$927$		0			0
$928$	6.42090	+	3.70711i	0.210776	+	0.121692i
$929$	5.93908	−	3.42893i	0.194855	−	0.112500i	−0.399398	−	0.916777i	$-0.630781\pi$
$929$	5.93908	−	3.42893i	0.194855	−	0.112500i	0.594253	+	0.804278i	$0.297448\pi$
$930$		−	17.8995i		−	0.586948i
$931$		0			0
$932$	23.1421			0.758046
$933$	−5.12132	−	8.87039i	−0.167665	−	0.290403i
$934$	22.0454	+	12.7279i	0.721348	+	0.416470i
$935$	22.2426	−	38.5254i	0.727412	−	1.25991i
$936$	−4.52004	+	9.14162i	−0.147742	+	0.298803i
$937$	−11.6569			−0.380813			−0.190406	−	0.981705i	$-0.560981\pi$
$937$	−11.6569			−0.380813			−0.190406	+	0.981705i	$0.560981\pi$
$938$		0			0
$939$	−15.3137			−0.499744
$940$	−3.12132	−	5.40629i	−0.101806	−	0.176334i
$941$	−7.68170	−	4.43503i	−0.250416	−	0.144578i	0.369539	−	0.929215i	$-0.379516\pi$
$941$	−7.68170	−	4.43503i	−0.250416	−	0.144578i	−0.619955	+	0.784638i	$0.712849\pi$
$942$	−6.27231	−	3.62132i	−0.204363	−	0.117989i
$943$	12.3600	−	7.13604i	0.402496	−	0.232381i
$944$		−	10.2426i		−	0.333370i
$945$		0			0
$946$	−19.6985			−0.640453
$947$	21.2049	−	12.2426i	0.689066	−	0.397832i	−0.114196	−	0.993458i	$-0.536429\pi$
$947$	21.2049	−	12.2426i	0.689066	−	0.397832i	0.803262	+	0.595626i	$0.203096\pi$
$948$	−14.1569	+	24.5204i	−0.459793	+	0.796385i
$949$	48.5211	−	3.12927i	1.57506	−	0.101580i
$950$	0.363961	+	0.630399i	0.0118085	+	0.0204528i
$951$		−	8.41421i		−	0.272850i
$952$		0			0
$953$	9.17157			0.297096			0.148548	−	0.988905i	$-0.452540\pi$
$953$	9.17157			0.297096			0.148548	+	0.988905i	$0.452540\pi$
$954$	3.46410	−	2.00000i	0.112154	−	0.0647524i
$955$	−3.46410	−	2.00000i	−0.112096	−	0.0647185i
$956$	−19.4728	−	11.2426i	−0.629796	−	0.363613i
$957$	81.2684	−	46.9203i	2.62703	−	1.51672i
$958$	−18.3431			−0.592640
$959$		0			0
$960$		−	3.41421i		−	0.110193i
$961$	−1.75736	−	3.04384i	−0.0566890	−	0.0981882i
$962$	0.616525	+	9.55956i	0.0198776	+	0.308213i
$963$	−14.4853	+	25.0892i	−0.466782	+	0.808490i
$964$	−10.8126	+	6.24264i	−0.348249	+	0.201062i
$965$	0.970563			0.0312435
$966$		0			0
$967$		−	42.3431i		−	1.36166i	−0.732440	−	0.680832i	$-0.761618\pi$
$967$		−	42.3431i		−	1.36166i	0.732440	−	0.680832i	$-0.238382\pi$
$968$	14.2767	−	8.24264i	0.458870	−	0.264929i
$969$	−3.04384	−	1.75736i	−0.0977821	−	0.0564545i
$970$	−11.6170	−	6.70711i	−0.373001	−	0.215352i
$971$	−21.8345	−	37.8185i	−0.700703	−	1.21365i	−0.968220	−	0.250100i	$-0.919536\pi$
$971$	−21.8345	−	37.8185i	−0.700703	−	1.21365i	0.267517	−	0.963553i	$-0.413797\pi$
$972$	−21.6569			−0.694644
$973$		0			0
$974$	21.2132			0.679715
$975$	23.4086	+	11.5743i	0.749675	+	0.370674i
$976$	1.50000	−	2.59808i	0.0480138	−	0.0831624i
$977$	6.03668	+	3.48528i	0.193131	+	0.111504i	0.593447	−	0.804873i	$-0.297767\pi$
$977$	6.03668	+	3.48528i	0.193131	+	0.111504i	−0.400317	+	0.916377i	$0.631100\pi$
$978$	−20.8995	−	36.1990i	−0.668292	−	1.15752i
$979$	−59.3137			−1.89567
$980$		0			0
$981$		−	24.0000i		−	0.766261i
$982$	−38.2643	+	22.0919i	−1.22106	+	0.704980i
$983$	35.1844	+	20.3137i	1.12221	+	0.647907i	0.941964	−	0.335715i	$-0.108978\pi$
$983$	35.1844	+	20.3137i	1.12221	+	0.647907i	0.180244	+	0.983622i	$0.442311\pi$
$984$	−10.8640	+	18.8169i	−0.346330	+	0.599862i
$985$	9.87868	+	17.1104i	0.314761	+	0.545182i
$986$			44.4853i			1.41670i
$987$		0			0
$988$	−0.485281	−	0.727922i	−0.0154389	−	0.0231583i
$989$	2.97918	+	5.16010i	0.0947326	+	0.164082i
$990$	−18.1610	−	10.4853i	−0.577196	−	0.333244i
$991$	−2.37868	+	4.11999i	−0.0755612	+	0.130876i	−0.901330	−	0.433133i	$-0.857408\pi$
$991$	−2.37868	+	4.11999i	−0.0755612	+	0.130876i	0.825769	+	0.564009i	$0.190742\pi$
$992$	2.62132	+	4.54026i	0.0832270	+	0.144153i
$993$			5.48528i			0.174070i
$994$		0			0
$995$		−	10.9706i		−	0.347790i
$996$	−9.58783	+	5.53553i	−0.303802	+	0.175400i
$997$	−12.9853	+	22.4912i	−0.411248	+	0.712302i	−0.995027	−	0.0996105i	$-0.968240\pi$
$997$	−12.9853	+	22.4912i	−0.411248	+	0.712302i	0.583779	+	0.811913i	$0.301574\pi$
$998$	−9.62132	+	16.6646i	−0.304558	+	0.527509i
$999$	−0.953065	+	0.550253i	−0.0301537	+	0.0174092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.k.753.4		8
7.2	even	3	inner	1274.2.n.k.961.2		8
7.3	odd	6		1274.2.d.j.883.4	yes	4
7.4	even	3		1274.2.d.g.883.3	yes	4
7.5	odd	6		1274.2.n.h.961.1		8
7.6	odd	2		1274.2.n.h.753.3		8
13.12	even	2	inner	1274.2.n.k.753.2		8
91.12	odd	6		1274.2.n.h.961.3		8
91.25	even	6		1274.2.d.g.883.1	✓	4
91.38	odd	6		1274.2.d.j.883.2	yes	4
91.51	even	6	inner	1274.2.n.k.961.4		8
91.90	odd	2		1274.2.n.h.753.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1274.2.d.g.883.1	✓	4	91.25	even	6
1274.2.d.g.883.3	yes	4	7.4	even	3
1274.2.d.j.883.2	yes	4	91.38	odd	6
1274.2.d.j.883.4	yes	4	7.3	odd	6
1274.2.n.h.753.1		8	91.90	odd	2
1274.2.n.h.753.3		8	7.6	odd	2
1274.2.n.h.961.1		8	7.5	odd	6
1274.2.n.h.961.3		8	91.12	odd	6
1274.2.n.k.753.2		8	13.12	even	2	inner
1274.2.n.k.753.4		8	1.1	even	1	trivial
1274.2.n.k.961.2		8	7.2	even	3	inner
1274.2.n.k.961.4		8	91.51	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.20711 - 2.09077i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} -2.41421i q^{6} -1.00000i q^{8} +(-1.41421 - 2.44949i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(-4.54026 - 2.62132i) q^{11} +(-1.20711 - 2.09077i) q^{12} +(3.00000 - 2.00000i) q^{13} +3.41421i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-2.44949 - 1.41421i) q^{18} +(0.210133 - 0.121320i) q^{19} +1.41421i q^{20} -5.24264 q^{22} +(0.792893 + 1.37333i) q^{23} +(-2.09077 - 1.20711i) q^{24} +(-1.50000 + 2.59808i) q^{25} +(1.59808 - 3.23205i) q^{26} +0.414214 q^{27} -7.41421 q^{29} +(1.70711 + 2.95680i) q^{30} +(-4.54026 - 2.62132i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-10.9612 + 6.32843i) q^{33} -6.00000i q^{34} -2.82843 q^{36} +(-2.30090 + 1.32843i) q^{37} +(0.121320 - 0.210133i) q^{38} +(-0.560220 - 8.68652i) q^{39} +(0.707107 + 1.22474i) q^{40} -9.00000i q^{41} +3.75736 q^{43} +(-4.54026 + 2.62132i) q^{44} +(3.46410 + 2.00000i) q^{45} +(1.37333 + 0.792893i) q^{46} +(-3.82282 + 2.20711i) q^{47} -2.41421 q^{48} +3.00000i q^{50} +(-7.24264 - 12.5446i) q^{51} +(-0.232051 - 3.59808i) q^{52} +(-0.707107 + 1.22474i) q^{53} +(0.358719 - 0.207107i) q^{54} +7.41421 q^{55} -0.585786i q^{57} +(-6.42090 + 3.70711i) q^{58} +(8.87039 + 5.12132i) q^{59} +(2.95680 + 1.70711i) q^{60} +(1.50000 + 2.59808i) q^{61} -5.24264 q^{62} -1.00000 q^{64} +(-2.26002 + 4.57081i) q^{65} +(-6.32843 + 10.9612i) q^{66} +(11.1713 + 6.44975i) q^{67} +(-3.00000 - 5.19615i) q^{68} +3.82843 q^{69} -3.75736i q^{71} +(-2.44949 + 1.41421i) q^{72} +(11.6786 + 6.74264i) q^{73} +(-1.32843 + 2.30090i) q^{74} +(3.62132 + 6.27231i) q^{75} -0.242641i q^{76} +(-4.82843 - 7.24264i) q^{78} +(-5.86396 - 10.1567i) q^{79} +(1.22474 + 0.707107i) q^{80} +(4.74264 - 8.21449i) q^{81} +(-4.50000 - 7.79423i) q^{82} -4.58579i q^{83} +8.48528i q^{85} +(3.25397 - 1.87868i) q^{86} +(-8.94975 + 15.5014i) q^{87} +(-2.62132 + 4.54026i) q^{88} +(9.79796 - 5.65685i) q^{89} +4.00000 q^{90} +1.58579 q^{92} +(-10.9612 + 6.32843i) q^{93} +(-2.20711 + 3.82282i) q^{94} +(-0.171573 + 0.297173i) q^{95} +(-2.09077 + 1.20711i) q^{96} +9.48528i q^{97} +14.8284i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{12} + 24 q^{13} - 4 q^{16} + 24 q^{17} - 8 q^{22} + 12 q^{23} - 12 q^{25} - 8 q^{26} - 8 q^{27} - 48 q^{29} + 8 q^{30} - 16 q^{38} + 12 q^{39} + 64 q^{43} - 8 q^{48} - 24 q^{51}+ \cdots - 24 q^{95}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^12 + 24 * q^13 - 4 * q^16 + 24 * q^17 - 8 * q^22 + 12 * q^23 - 12 * q^25 - 8 * q^26 - 8 * q^27 - 48 * q^29 + 8 * q^30 - 16 * q^38 + 12 * q^39 + 64 * q^43 - 8 * q^48 - 24 * q^51 + 12 * q^52 + 48 * q^55 + 12 * q^61 - 8 * q^62 - 8 * q^64 - 28 * q^66 - 24 * q^68 + 8 * q^69 + 12 * q^74 + 12 * q^75 - 16 * q^78 + 4 * q^79 + 4 * q^81 - 36 * q^82 - 32 * q^87 - 4 * q^88 + 32 * q^90 + 24 * q^92 - 12 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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