LMFDB - Embedded newform 250.2.e.c.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [250,2,Mod(49,250)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(250, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("250.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$250 = 2 \cdot 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	250.e (of order $10$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,0,-6,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625$ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$5^{2}$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Root			$-0.917186 - 1.66637i$ of defining polynomial
Character	$\chi$	$=$	250.49
Dual form			250.2.e.c.199.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(1.63079 - 0.529876i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.529876 - 1.63079i) q^{6} -2.77447i q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.0483405 + 0.0351215i) q^{9} +(-2.24459 - 1.63079i) q^{11} +(-1.00788 - 1.38723i) q^{12} +(3.33732 + 4.59343i) q^{13} +(-2.24459 - 1.63079i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(4.90406 + 1.59343i) q^{17} +0.0597522i q^{18} +(-0.436451 + 1.34326i) q^{19} +(-1.47012 - 4.52458i) q^{21} +(-2.63868 + 0.857358i) q^{22} +(0.384978 - 0.529876i) q^{23} -1.71472 q^{24} +5.67779 q^{26} +(-3.08388 + 4.24459i) q^{27} +(-2.63868 + 0.857358i) q^{28} +(-1.26594 - 3.89618i) q^{29} +(-2.20239 + 6.77827i) q^{31} +1.00000i q^{32} +(-4.52458 - 1.47012i) q^{33} +(4.17164 - 3.03088i) q^{34} +(0.0483405 + 0.0351215i) q^{36} +(0.615684 + 0.847416i) q^{37} +(0.830178 + 1.14264i) q^{38} +(7.87642 + 5.72255i) q^{39} +(-7.36789 + 5.35309i) q^{41} +(-4.52458 - 1.47012i) q^{42} -9.24660i q^{43} +(-0.857358 + 2.63868i) q^{44} +(-0.202395 - 0.622907i) q^{46} +(2.63868 - 0.857358i) q^{47} +(-1.00788 + 1.38723i) q^{48} -0.697669 q^{49} +8.84181 q^{51} +(3.33732 - 4.59343i) q^{52} +(-0.500362 + 0.162577i) q^{53} +(1.62129 + 4.98982i) q^{54} +(-0.857358 + 2.63868i) q^{56} +2.42184i q^{57} +(-3.89618 - 1.26594i) q^{58} +(-3.05975 + 2.22304i) q^{59} +(8.76365 + 6.36716i) q^{61} +(4.18920 + 5.76594i) q^{62} +(0.0974433 + 0.134119i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-3.84883 + 2.79634i) q^{66} +(-4.11180 - 1.33600i) q^{67} -5.15643i q^{68} +(0.347049 - 1.06811i) q^{69} +(-4.09343 - 12.5983i) q^{71} +(0.0568277 - 0.0184644i) q^{72} +(-2.47648 + 3.40859i) q^{73} +1.04746 q^{74} +1.41238 q^{76} +(-4.52458 + 6.22754i) q^{77} +(9.25928 - 3.00852i) q^{78} +(3.05975 + 9.41695i) q^{79} +(-2.72466 + 8.38563i) q^{81} +9.10722i q^{82} +(-4.44717 - 1.44497i) q^{83} +(-3.84883 + 2.79634i) q^{84} +(-7.48066 - 5.43502i) q^{86} +(-4.12898 - 5.68305i) q^{87} +(1.63079 + 2.24459i) q^{88} +(-7.43002 - 5.39823i) q^{89} +(12.7443 - 9.25928i) q^{91} +(-0.622907 - 0.202395i) q^{92} +12.2209i q^{93} +(0.857358 - 2.63868i) q^{94} +(0.529876 + 1.63079i) q^{96} +(0.0857567 - 0.0278640i) q^{97} +(-0.410079 + 0.564426i) q^{98} +0.165781 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46}+ \cdots + 84 q^{99}+O(q^{100})$ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$ .

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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

)

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

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	1.63079	−	0.529876i	0.941538	−	0.305924i	0.202265	−	0.979331i	$-0.435170\pi$
$3$	1.63079	−	0.529876i	0.941538	−	0.305924i	0.739272	+	0.673407i	$0.235170\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	0.529876	−	1.63079i	0.216321	−	0.665768i
$7$		−	2.77447i		−	1.04865i	−0.851518	−	0.524325i	$-0.824318\pi$
$7$		−	2.77447i		−	1.04865i	0.851518	−	0.524325i	$-0.175682\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.0483405	+	0.0351215i	−0.0161135	+	0.0117072i
$10$		0			0
$11$	−2.24459	−	1.63079i	−0.676770	−	0.491702i	0.195515	−	0.980701i	$-0.437362\pi$
$11$	−2.24459	−	1.63079i	−0.676770	−	0.491702i	−0.872284	+	0.488999i	$0.837362\pi$
$12$	−1.00788	−	1.38723i	−0.290951	−	0.400460i
$13$	3.33732	+	4.59343i	0.925606	+	1.27399i	0.961549	+	0.274633i	$0.0885564\pi$
$13$	3.33732	+	4.59343i	0.925606	+	1.27399i	−0.0359433	+	0.999354i	$0.511444\pi$
$14$	−2.24459	−	1.63079i	−0.599892	−	0.435847i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.90406	+	1.59343i	1.18941	+	0.386462i	0.835854	−	0.548951i	$-0.184973\pi$
$17$	4.90406	+	1.59343i	1.18941	+	0.386462i	0.353555	+	0.935414i	$0.384973\pi$
$18$			0.0597522i			0.0140837i
$19$	−0.436451	+	1.34326i	−0.100129	+	0.308164i	−0.988556	−	0.150852i	$-0.951798\pi$
$19$	−0.436451	+	1.34326i	−0.100129	+	0.308164i	0.888428	+	0.459017i	$0.151798\pi$
$20$		0			0
$21$	−1.47012	−	4.52458i	−0.320807	−	0.987343i
$22$	−2.63868	+	0.857358i	−0.562567	+	0.182789i
$23$	0.384978	−	0.529876i	0.0802734	−	0.110487i	−0.766992	−	0.641657i	$-0.778247\pi$
$23$	0.384978	−	0.529876i	0.0802734	−	0.110487i	0.847265	+	0.531170i	$0.178247\pi$
$24$	−1.71472			−0.350015
$25$		0			0
$26$	5.67779			1.11351
$27$	−3.08388	+	4.24459i	−0.593492	+	0.816872i
$28$	−2.63868	+	0.857358i	−0.498663	+	0.162025i
$29$	−1.26594	−	3.89618i	−0.235080	−	0.723502i	−0.997111	−	0.0759609i	$-0.975798\pi$
$29$	−1.26594	−	3.89618i	−0.235080	−	0.723502i	0.762031	−	0.647541i	$-0.224202\pi$
$30$		0			0
$31$	−2.20239	+	6.77827i	−0.395562	+	1.21741i	0.532961	+	0.846140i	$0.321079\pi$
$31$	−2.20239	+	6.77827i	−0.395562	+	1.21741i	−0.928523	+	0.371274i	$0.878921\pi$
$32$			1.00000i			0.176777i
$33$	−4.52458	−	1.47012i	−0.787628	−	0.255916i
$34$	4.17164	−	3.03088i	0.715431	−	0.519791i
$35$		0			0
$36$	0.0483405	+	0.0351215i	0.00805676	+	0.00585358i
$37$	0.615684	+	0.847416i	0.101218	+	0.139314i	0.856622	−	0.515945i	$-0.172559\pi$
$37$	0.615684	+	0.847416i	0.101218	+	0.139314i	−0.755404	+	0.655260i	$0.772559\pi$
$38$	0.830178	+	1.14264i	0.134673	+	0.185361i
$39$	7.87642	+	5.72255i	1.26124	+	0.916342i
$40$		0			0
$41$	−7.36789	+	5.35309i	−1.15067	+	0.836012i	−0.988570	−	0.150762i	$-0.951827\pi$
$41$	−7.36789	+	5.35309i	−1.15067	+	0.836012i	−0.162101	+	0.986774i	$0.551827\pi$
$42$	−4.52458	−	1.47012i	−0.698157	−	0.226845i
$43$		−	9.24660i		−	1.41009i	−0.709161	−	0.705047i	$-0.750926\pi$
$43$		−	9.24660i		−	1.41009i	0.709161	−	0.705047i	$-0.249074\pi$
$44$	−0.857358	+	2.63868i	−0.129252	+	0.397795i
$45$		0			0
$46$	−0.202395	−	0.622907i	−0.0298415	−	0.0918426i
$47$	2.63868	−	0.857358i	0.384890	−	0.125058i	−0.110179	−	0.993912i	$-0.535143\pi$
$47$	2.63868	−	0.857358i	0.384890	−	0.125058i	0.495070	+	0.868853i	$0.335143\pi$
$48$	−1.00788	+	1.38723i	−0.145476	+	0.200230i
$49$	−0.697669			−0.0996670
$50$		0			0
$51$	8.84181			1.23810
$52$	3.33732	−	4.59343i	0.462803	−	0.636994i
$53$	−0.500362	+	0.162577i	−0.0687299	+	0.0223317i	−0.343180	−	0.939270i	$-0.611504\pi$
$53$	−0.500362	+	0.162577i	−0.0687299	+	0.0223317i	0.274450	+	0.961601i	$0.411504\pi$
$54$	1.62129	+	4.98982i	0.220630	+	0.679028i
$55$		0			0
$56$	−0.857358	+	2.63868i	−0.114569	+	0.352608i
$57$			2.42184i			0.320780i
$58$	−3.89618	−	1.26594i	−0.511593	−	0.166227i
$59$	−3.05975	+	2.22304i	−0.398346	+	0.289415i	−0.768867	−	0.639409i	$-0.779179\pi$
$59$	−3.05975	+	2.22304i	−0.398346	+	0.289415i	0.370521	+	0.928824i	$0.379179\pi$
$60$		0			0
$61$	8.76365	+	6.36716i	1.12207	+	0.815232i	0.984522	−	0.175263i	$-0.0560776\pi$
$61$	8.76365	+	6.36716i	1.12207	+	0.815232i	0.137549	+	0.990495i	$0.456078\pi$
$62$	4.18920	+	5.76594i	0.532029	+	0.732276i
$63$	0.0974433	+	0.134119i	0.0122767	+	0.0168974i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	−3.84883	+	2.79634i	−0.473759	+	0.344206i
$67$	−4.11180	−	1.33600i	−0.502336	−	0.163219i	0.0468778	−	0.998901i	$-0.485073\pi$
$67$	−4.11180	−	1.33600i	−0.502336	−	0.163219i	−0.549214	+	0.835682i	$0.685073\pi$
$68$		−	5.15643i		−	0.625309i
$69$	0.347049	−	1.06811i	0.0417798	−	0.128585i
$70$		0			0
$71$	−4.09343	−	12.5983i	−0.485800	−	1.49514i	−0.830819	−	0.556543i	$-0.812127\pi$
$71$	−4.09343	−	12.5983i	−0.485800	−	1.49514i	0.345018	−	0.938596i	$-0.387873\pi$
$72$	0.0568277	−	0.0184644i	0.00669721	−	0.00217606i
$73$	−2.47648	+	3.40859i	−0.289850	+	0.398945i	−0.928966	−	0.370166i	$-0.879301\pi$
$73$	−2.47648	+	3.40859i	−0.289850	+	0.398945i	0.639115	+	0.769111i	$0.279301\pi$
$74$	1.04746			0.121765
$75$		0			0
$76$	1.41238			0.162012
$77$	−4.52458	+	6.22754i	−0.515623	+	0.709695i
$78$	9.25928	−	3.00852i	1.04841	−	0.340648i
$79$	3.05975	+	9.41695i	0.344249	+	1.05949i	0.961985	+	0.273104i	$0.0880502\pi$
$79$	3.05975	+	9.41695i	0.344249	+	1.05949i	−0.617736	+	0.786386i	$0.711950\pi$
$80$		0			0
$81$	−2.72466	+	8.38563i	−0.302740	+	0.931737i
$82$			9.10722i			1.00572i
$83$	−4.44717	−	1.44497i	−0.488141	−	0.158606i	0.0545976	−	0.998508i	$-0.482612\pi$
$83$	−4.44717	−	1.44497i	−0.488141	−	0.158606i	−0.542738	+	0.839902i	$0.682612\pi$
$84$	−3.84883	+	2.79634i	−0.419942	+	0.305106i
$85$		0			0
$86$	−7.48066	−	5.43502i	−0.806660	−	0.586073i
$87$	−4.12898	−	5.68305i	−0.442673	−	0.609287i
$88$	1.63079	+	2.24459i	0.173843	+	0.239274i
$89$	−7.43002	−	5.39823i	−0.787581	−	0.572211i	0.119664	−	0.992814i	$-0.461818\pi$
$89$	−7.43002	−	5.39823i	−0.787581	−	0.572211i	−0.907245	+	0.420603i	$0.861818\pi$
$90$		0			0
$91$	12.7443	−	9.25928i	1.33597	−	0.970637i
$92$	−0.622907	−	0.202395i	−0.0649425	−	0.0211011i
$93$			12.2209i			1.26725i
$94$	0.857358	−	2.63868i	0.0884297	−	0.272159i
$95$		0			0
$96$	0.529876	+	1.63079i	0.0540803	+	0.166442i
$97$	0.0857567	−	0.0278640i	0.00870727	−	0.00282917i	−0.304660	−	0.952461i	$-0.598543\pi$
$97$	0.0857567	−	0.0278640i	0.00870727	−	0.00282917i	0.313367	+	0.949632i	$0.398543\pi$
$98$	−0.410079	+	0.564426i	−0.0414243	+	0.0570156i
$99$	0.165781			0.0166616
$100$		0			0
$101$	−7.90632			−0.786709			−0.393354	−	0.919387i	$-0.628685\pi$
$101$	−7.90632			−0.786709			−0.393354	+	0.919387i	$0.628685\pi$
$102$	5.19709	−	7.15318i	0.514588	−	0.708270i
$103$	7.45079	−	2.42091i	0.734148	−	0.238539i	0.0820014	−	0.996632i	$-0.473869\pi$
$103$	7.45079	−	2.42091i	0.734148	−	0.238539i	0.652146	+	0.758093i	$0.273869\pi$
$104$	−1.75453	−	5.39990i	−0.172046	−	0.529503i
$105$		0			0
$106$	−0.162577	+	0.500362i	−0.0157909	+	0.0485994i
$107$		−	10.2220i		−	0.988194i	−0.869407	−	0.494097i	$-0.835499\pi$
$107$		−	10.2220i		−	0.988194i	0.869407	−	0.494097i	$-0.164501\pi$
$108$	4.98982	+	1.62129i	0.480145	+	0.156009i
$109$	3.16400	−	2.29878i	0.303056	−	0.220183i	−0.425855	−	0.904791i	$-0.640027\pi$
$109$	3.16400	−	2.29878i	0.303056	−	0.220183i	0.728911	+	0.684608i	$0.240027\pi$
$110$		0			0
$111$	1.45308	+	1.05572i	0.137920	+	0.100205i
$112$	1.63079	+	2.24459i	0.154095	+	0.212094i
$113$	−3.74740	−	5.15785i	−0.352526	−	0.485210i	0.595522	−	0.803339i	$-0.296945\pi$
$113$	−3.74740	−	5.15785i	−0.352526	−	0.485210i	−0.948047	+	0.318129i	$0.896945\pi$
$114$	1.95931	+	1.42352i	0.183506	+	0.133325i
$115$		0			0
$116$	−3.31428	+	2.40797i	−0.307724	+	0.223574i
$117$	−0.322656	−	0.104837i	−0.0298295	−	0.00969220i
$118$			3.78206i			0.348167i
$119$	4.42091	−	13.6062i	0.405264	−	1.24727i
$120$		0			0
$121$	−1.02048	−	3.14070i	−0.0927706	−	0.285519i
$122$	10.3023	−	3.34742i	0.932725	−	0.303061i
$123$	−9.17902	+	12.6338i	−0.827644	+	1.13915i
$124$	7.12710			0.640032
$125$		0			0
$126$	0.165781			0.0147689
$127$	5.61272	−	7.72525i	0.498049	−	0.685505i	−0.483798	−	0.875179i	$-0.660743\pi$
$127$	5.61272	−	7.72525i	0.498049	−	0.685505i	0.981847	+	0.189674i	$0.0607432\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−4.89955	−	15.0793i	−0.431382	−	1.32766i
$130$		0			0
$131$	1.73026	−	5.32519i	0.151173	−	0.465264i	−0.846580	−	0.532262i	$-0.821342\pi$
$131$	1.73026	−	5.32519i	0.151173	−	0.465264i	0.997753	+	0.0669981i	$0.0213421\pi$
$132$			4.75742i			0.414080i
$133$	3.72682	+	1.21092i	0.323156	+	0.105000i
$134$	−3.49771	+	2.54123i	−0.302156	+	0.219529i
$135$		0			0
$136$	−4.17164	−	3.03088i	−0.357715	−	0.259895i
$137$	−4.69296	−	6.45931i	−0.400947	−	0.551856i	0.560035	−	0.828469i	$-0.310788\pi$
$137$	−4.69296	−	6.45931i	−0.400947	−	0.551856i	−0.960981	+	0.276613i	$0.910788\pi$
$138$	−0.660127	−	0.908587i	−0.0561937	−	0.0773440i
$139$	−17.8699	−	12.9832i	−1.51571	−	1.10122i	−0.963565	−	0.267473i	$-0.913811\pi$
$139$	−17.8699	−	12.9832i	−1.51571	−	1.10122i	−0.552140	−	0.833751i	$-0.686189\pi$
$140$		0			0
$141$	3.84883	−	2.79634i	0.324130	−	0.235494i
$142$	−12.5983	−	4.09343i	−1.05722	−	0.343513i
$143$		−	15.7528i		−	1.31732i
$144$	0.0184644	−	0.0568277i	0.00153870	−	0.00473564i
$145$		0			0
$146$	1.30196	+	4.00703i	0.107751	+	0.331624i
$147$	−1.13775	+	0.369678i	−0.0938402	+	0.0304905i
$148$	0.615684	−	0.847416i	0.0506089	−	0.0696572i
$149$	−4.18401			−0.342768			−0.171384	−	0.985204i	$-0.554824\pi$
$149$	−4.18401			−0.342768			−0.171384	+	0.985204i	$0.554824\pi$
$150$		0			0
$151$	−0.331561			−0.0269821			−0.0134910	−	0.999909i	$-0.504294\pi$
$151$	−0.331561			−0.0269821			−0.0134910	+	0.999909i	$0.504294\pi$
$152$	0.830178	−	1.14264i	0.0673364	−	0.0926805i
$153$	−0.293028	+	0.0952107i	−0.0236899	+	0.00769733i
$154$	2.37871	+	7.32092i	0.191682	+	0.589936i
$155$		0			0
$156$	3.00852	−	9.25928i	0.240875	−	0.741336i
$157$			3.60750i			0.287910i	0.989584	+	0.143955i	$0.0459820\pi$
$157$			3.60750i			0.287910i	−0.989584	+	0.143955i	$0.954018\pi$
$158$	9.41695	+	3.05975i	0.749172	+	0.243421i
$159$	−0.729839	+	0.530259i	−0.0578800	+	0.0420523i
$160$		0			0
$161$	−1.47012	−	1.06811i	−0.115862	−	0.0841787i
$162$	5.18260	+	7.13324i	0.407184	+	0.560440i
$163$	2.99409	+	4.12101i	0.234515	+	0.322782i	0.910013	−	0.414580i	$-0.136071\pi$
$163$	2.99409	+	4.12101i	0.234515	+	0.322782i	−0.675498	+	0.737362i	$0.736071\pi$
$164$	7.36789	+	5.35309i	0.575336	+	0.418006i
$165$		0			0
$166$	−3.78299	+	2.74850i	−0.293617	+	0.213325i
$167$	19.8418	+	6.44699i	1.53540	+	0.498883i	0.950104	−	0.311934i	$-0.100977\pi$
$167$	19.8418	+	6.44699i	1.53540	+	0.498883i	0.585300	+	0.810817i	$0.300977\pi$
$168$			4.75742i			0.367043i
$169$	−5.94464	+	18.2957i	−0.457280	+	1.40736i
$170$		0			0
$171$	−0.0260789	−	0.0802625i	−0.00199430	−	0.00613783i
$172$	−8.79404	+	2.85736i	−0.670539	+	0.217871i
$173$	7.04620	−	9.69826i	0.535713	−	0.737345i	−0.452275	−	0.891879i	$-0.649387\pi$
$173$	7.04620	−	9.69826i	0.535713	−	0.737345i	0.987988	+	0.154533i	$0.0493874\pi$
$174$	−7.02464			−0.532537
$175$		0			0
$176$	2.77447			0.209133
$177$	−3.81188	+	5.24660i	−0.286518	+	0.394359i
$178$	−8.73452	+	2.83802i	−0.654680	+	0.212718i
$179$	2.63942	+	8.12330i	0.197279	+	0.607164i	0.999942	+	0.0107309i	$0.00341581\pi$
$179$	2.63942	+	8.12330i	0.197279	+	0.607164i	−0.802663	+	0.596433i	$0.796584\pi$
$180$		0			0
$181$	2.41912	−	7.44529i	0.179812	−	0.553404i	−0.820009	−	0.572351i	$-0.806031\pi$
$181$	2.41912	−	7.44529i	0.179812	−	0.553404i	0.999820	+	0.0189471i	$0.00603140\pi$
$182$		−	15.7528i		−	1.16768i
$183$	17.6655	+	5.73987i	1.30587	+	0.424303i
$184$	−0.529876	+	0.384978i	−0.0390630	+	0.0283809i
$185$		0			0
$186$	9.88695	+	7.18329i	0.724946	+	0.526704i
$187$	−8.40906	−	11.5741i	−0.614932	−	0.846381i
$188$	−1.63079	−	2.24459i	−0.118938	−	0.163704i
$189$	11.7765	+	8.55611i	0.856613	+	0.622366i
$190$		0			0
$191$	−2.72324	+	1.97855i	−0.197047	+	0.143163i	−0.681934	−	0.731414i	$-0.738861\pi$
$191$	−2.72324	+	1.97855i	−0.197047	+	0.143163i	0.484887	+	0.874577i	$0.338861\pi$
$192$	1.63079	+	0.529876i	0.117692	+	0.0382405i
$193$			15.4211i			1.11004i	0.831839	+	0.555018i	$0.187288\pi$
$193$			15.4211i			1.11004i	−0.831839	+	0.555018i	$0.812712\pi$
$194$	0.0278640	−	0.0857567i	0.00200052	−	0.00615697i
$195$		0			0
$196$	0.215591	+	0.663522i	0.0153994	+	0.0473945i
$197$	−8.37394	+	2.72086i	−0.596619	+	0.193853i	−0.591732	−	0.806135i	$-0.701556\pi$
$197$	−8.37394	+	2.72086i	−0.596619	+	0.193853i	−0.00488692	+	0.999988i	$0.501556\pi$
$198$	0.0974433	−	0.134119i	0.00692500	−	0.00953144i
$199$	17.6222			1.24920			0.624601	−	0.780944i	$-0.285262\pi$
$199$	17.6222			1.24920			0.624601	+	0.780944i	$0.285262\pi$
$200$		0			0
$201$	−7.41340			−0.522901
$202$	−4.64722	+	6.39635i	−0.326977	+	0.450046i
$203$	−10.8098	+	3.51232i	−0.758700	+	0.246517i
$204$	−2.73227	−	8.40906i	−0.191297	−	0.588752i
$205$		0			0
$206$	2.42091	−	7.45079i	0.168673	−	0.519121i
$207$			0.0391355i			0.00272010i
$208$	−5.39990	−	1.75453i	−0.374415	−	0.121655i
$209$	3.17022	−	2.30330i	0.219289	−	0.159323i
$210$		0			0
$211$	−4.93617	−	3.58634i	−0.339820	−	0.246894i	0.404766	−	0.914420i	$-0.367353\pi$
$211$	−4.93617	−	3.58634i	−0.339820	−	0.246894i	−0.744586	+	0.667527i	$0.767353\pi$
$212$	0.309240	+	0.425633i	0.0212387	+	0.0292326i
$213$	−13.3510	−	18.3761i	−0.914798	−	1.25911i
$214$	−8.26974	−	6.00832i	−0.565308	−	0.410720i
$215$		0			0
$216$	4.24459	−	3.08388i	0.288808	−	0.209831i
$217$	18.8061	+	6.11047i	1.27664	+	0.414806i
$218$		−	3.91091i		−	0.264880i
$219$	−2.23250	+	6.87092i	−0.150858	+	0.464294i
$220$		0			0
$221$	9.04713	+	27.8442i	0.608576	+	1.87300i
$222$	1.70820	−	0.555026i	0.114647	−	0.0372509i
$223$	2.95578	−	4.06828i	0.197933	−	0.272432i	−0.698500	−	0.715610i	$-0.746149\pi$
$223$	2.95578	−	4.06828i	0.197933	−	0.272432i	0.896434	+	0.443178i	$0.146149\pi$
$224$	2.77447			0.185377
$225$		0			0
$226$	−6.37545			−0.424089
$227$	−10.4851	+	14.4314i	−0.695918	+	0.957848i	0.304069	+	0.952650i	$0.401655\pi$
$227$	−10.4851	+	14.4314i	−0.695918	+	0.957848i	−0.999986	+	0.00519840i	$0.998345\pi$
$228$	2.30330	−	0.748388i	0.152540	−	0.0495632i
$229$	6.66137	+	20.5016i	0.440195	+	1.35478i	0.887668	+	0.460485i	$0.152324\pi$
$229$	6.66137	+	20.5016i	0.440195	+	1.35478i	−0.447472	+	0.894298i	$0.647676\pi$
$230$		0			0
$231$	−4.07881	+	12.5533i	−0.268366	+	0.825946i
$232$			4.09668i			0.268960i
$233$	−13.9867	−	4.54454i	−0.916297	−	0.297723i	−0.187350	−	0.982293i	$-0.559990\pi$
$233$	−13.9867	−	4.54454i	−0.916297	−	0.297723i	−0.728947	+	0.684570i	$0.759990\pi$
$234$	−0.274467	+	0.199412i	−0.0179425	+	0.0130360i
$235$		0			0
$236$	3.05975	+	2.22304i	0.199173	+	0.144708i
$237$	9.97963	+	13.7358i	0.648247	+	0.892235i
$238$	−8.40906	−	11.5741i	−0.545079	−	0.750236i
$239$	5.61478	+	4.07938i	0.363190	+	0.263873i	0.754381	−	0.656436i	$-0.227937\pi$
$239$	5.61478	+	4.07938i	0.363190	+	0.263873i	−0.391192	+	0.920309i	$0.627937\pi$
$240$		0			0
$241$	−2.67787	+	1.94559i	−0.172497	+	0.125326i	−0.670684	−	0.741743i	$-0.733999\pi$
$241$	−2.67787	+	1.94559i	−0.172497	+	0.125326i	0.498187	+	0.867070i	$0.333999\pi$
$242$	−3.14070	−	1.02048i	−0.201892	−	0.0655987i
$243$		−	0.620870i		−	0.0398288i
$244$	3.34742	−	10.3023i	0.214296	−	0.659536i
$245$		0			0
$246$	4.82570	+	14.8520i	0.307675	+	0.946927i
$247$	−7.62672	+	2.47807i	−0.485277	+	0.157676i
$248$	4.18920	−	5.76594i	0.266015	−	0.366138i
$249$	−8.01806			−0.508124
$250$		0			0
$251$	−9.46454			−0.597397			−0.298698	−	0.954348i	$-0.596552\pi$
$251$	−9.46454			−0.597397			−0.298698	+	0.954348i	$0.596552\pi$
$252$	0.0974433	−	0.134119i	0.00613835	−	0.00844872i
$253$	−1.72823	+	0.561537i	−0.108653	+	0.0353036i
$254$	−2.95078	−	9.08158i	−0.185149	−	0.569829i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$		−	7.07963i		−	0.441615i	−0.975317	−	0.220808i	$-0.929131\pi$
$257$		−	7.07963i		−	0.441615i	0.975317	−	0.220808i	$-0.0708693\pi$
$258$	−15.0793	−	4.89955i	−0.938795	−	0.305033i
$259$	2.35113	−	1.70820i	0.146092	−	0.106142i
$260$		0			0
$261$	0.198036	+	0.143881i	0.0122581	+	0.00890604i
$262$	−3.29115	−	4.52988i	−0.203328	−	0.279857i
$263$	0.842563	+	1.15969i	0.0519547	+	0.0715095i	0.834204	−	0.551456i	$-0.185928\pi$
$263$	0.842563	+	1.15969i	0.0519547	+	0.0715095i	−0.782249	+	0.622966i	$0.785928\pi$
$264$	3.84883	+	2.79634i	0.236879	+	0.172103i
$265$		0			0
$266$	3.17022	−	2.30330i	0.194379	−	0.141225i
$267$	−14.9772	−	4.86639i	−0.916590	−	0.297818i
$268$			4.32340i			0.264094i
$269$	4.41368	−	13.5839i	0.269107	−	0.828226i	−0.721612	−	0.692298i	$-0.756598\pi$
$269$	4.41368	−	13.5839i	0.269107	−	0.828226i	0.990719	−	0.135928i	$-0.0434015\pi$
$270$		0			0
$271$	9.51325	+	29.2788i	0.577889	+	1.77856i	0.626125	+	0.779723i	$0.284640\pi$
$271$	9.51325	+	29.2788i	0.577889	+	1.77856i	−0.0482363	+	0.998836i	$0.515360\pi$
$272$	−4.90406	+	1.59343i	−0.297352	+	0.0966156i
$273$	15.8770	−	21.8529i	0.960922	−	1.32260i
$274$	−7.98414			−0.482340
$275$		0			0
$276$	−1.12307			−0.0676012
$277$	1.87485	−	2.58051i	0.112649	−	0.155048i	−0.748970	−	0.662604i	$-0.769451\pi$
$277$	1.87485	−	2.58051i	0.112649	−	0.155048i	0.861619	+	0.507556i	$0.169451\pi$
$278$	−21.0073	+	6.82570i	−1.25994	+	0.409378i
$279$	−0.131598	−	0.405017i	−0.00787856	−	0.0242477i
$280$		0			0
$281$	6.30053	−	19.3910i	0.375858	−	1.15677i	−0.567040	−	0.823690i	$-0.691912\pi$
$281$	6.30053	−	19.3910i	0.375858	−	1.15677i	0.942898	−	0.333081i	$-0.108088\pi$
$282$		−	4.75742i		−	0.283300i
$283$	12.6461	+	4.10897i	0.751733	+	0.244253i	0.659727	−	0.751506i	$-0.270672\pi$
$283$	12.6461	+	4.10897i	0.751733	+	0.244253i	0.0920063	+	0.995758i	$0.470672\pi$
$284$	−10.7167	+	7.78616i	−0.635921	+	0.462023i
$285$		0			0
$286$	−12.7443	−	9.25928i	−0.753587	−	0.547513i
$287$	14.8520	+	20.4420i	0.876684	+	1.20665i
$288$	−0.0351215	−	0.0483405i	−0.00206955	−	0.00284849i
$289$	7.75751	+	5.63616i	0.456324	+	0.331539i
$290$		0			0
$291$	0.125087	−	0.0908809i	0.00733272	−	0.00532753i
$292$	4.00703	+	1.30196i	0.234494	+	0.0761917i
$293$			26.0420i			1.52139i	0.649108	+	0.760696i	$0.275142\pi$
$293$			26.0420i			1.52139i	−0.649108	+	0.760696i	$0.724858\pi$
$294$	−0.369678	+	1.13775i	−0.0215601	+	0.0663550i
$295$		0			0
$296$	−0.323684	−	0.996198i	−0.0188138	−	0.0579028i
$297$	13.8441	−	4.49821i	0.803315	−	0.261013i
$298$	−2.45930	+	3.38494i	−0.142464	+	0.196084i
$299$	3.71874			0.215060
$300$		0			0
$301$	−25.6544			−1.47869
$302$	−0.194887	+	0.268239i	−0.0112145	+	0.0154354i
$303$	−12.8936	+	4.18937i	−0.740716	+	0.240673i
$304$	−0.436451	−	1.34326i	−0.0250322	−	0.0770411i
$305$		0			0
$306$	−0.0952107	+	0.293028i	−0.00544283	+	0.0167513i
$307$			25.1000i			1.43253i	0.697826	+	0.716267i	$0.254151\pi$
$307$			25.1000i			1.43253i	−0.697826	+	0.716267i	$0.745849\pi$
$308$	7.32092	+	2.37871i	0.417148	+	0.135540i
$309$	10.8679	−	7.89599i	0.618253	−	0.449187i
$310$		0			0
$311$	−0.585185	−	0.425162i	−0.0331828	−	0.0241087i	0.571070	−	0.820901i	$-0.306528\pi$
$311$	−0.585185	−	0.425162i	−0.0331828	−	0.0241087i	−0.604253	+	0.796792i	$0.706528\pi$
$312$	−5.72255	−	7.87642i	−0.323976	−	0.445914i
$313$	12.7057	+	17.4879i	0.718170	+	0.988477i	0.999583	+	0.0288898i	$0.00919718\pi$
$313$	12.7057	+	17.4879i	0.718170	+	0.988477i	−0.281412	+	0.959587i	$0.590803\pi$
$314$	2.91853	+	2.12043i	0.164702	+	0.119663i
$315$		0			0
$316$	8.01054	−	5.81999i	0.450628	−	0.327400i
$317$	−17.9119	−	5.81992i	−1.00603	−	0.326879i	−0.240758	−	0.970585i	$-0.577396\pi$
$317$	−17.9119	−	5.81992i	−1.00603	−	0.326879i	−0.765273	+	0.643706i	$0.777396\pi$
$318$			0.902131i			0.0505890i
$319$	−3.51232	+	10.8098i	−0.196652	+	0.605233i
$320$		0			0
$321$	−5.41637	−	16.6699i	−0.302312	−	0.930422i
$322$	−1.72823	+	0.561537i	−0.0963107	+	0.0312933i
$323$	−4.28076	+	5.89196i	−0.238188	+	0.327837i
$324$	8.81717			0.489843
$325$		0			0
$326$	5.09385			0.282122
$327$	3.94175	−	5.42535i	0.217979	−	0.300023i
$328$	8.66148	−	2.81428i	0.478250	−	0.155393i
$329$	−2.37871	−	7.32092i	−0.131143	−	0.403615i
$330$		0			0
$331$	5.21494	−	16.0499i	0.286639	−	0.882185i	−0.699263	−	0.714864i	$-0.746489\pi$
$331$	5.21494	−	16.0499i	0.286639	−	0.882185i	0.985903	−	0.167320i	$-0.0535115\pi$
$332$			4.67603i			0.256631i
$333$	−0.0595250	−	0.0193408i	−0.00326195	−	0.00105987i
$334$	16.8784	−	12.2629i	0.923546	−	0.670996i
$335$		0			0
$336$	3.84883	+	2.79634i	0.209971	+	0.152553i
$337$	−11.3749	−	15.6562i	−0.619628	−	0.852845i	0.377698	−	0.925929i	$-0.376716\pi$
$337$	−11.3749	−	15.6562i	−0.619628	−	0.852845i	−0.997326	+	0.0730841i	$0.976716\pi$
$338$	11.3074	+	15.5633i	0.615040	+	0.846530i
$339$	−8.84425	−	6.42572i	−0.480353	−	0.348997i
$340$		0			0
$341$	15.9974	−	11.6228i	0.866309	−	0.629410i
$342$	−0.0802625	−	0.0260789i	−0.00434010	−	0.00141018i
$343$		−	17.4856i		−	0.944134i
$344$	−2.85736	+	8.79404i	−0.154058	+	0.474143i
$345$		0			0
$346$	−3.70441	−	11.4010i	−0.199150	−	0.612921i
$347$	8.59630	−	2.79311i	0.461473	−	0.149942i	−0.0690480	−	0.997613i	$-0.521996\pi$
$347$	8.59630	−	2.79311i	0.461473	−	0.149942i	0.530521	+	0.847672i	$0.321996\pi$
$348$	−4.12898	+	5.68305i	−0.221337	+	0.304644i
$349$	−36.7305			−1.96614			−0.983068	−	0.183240i	$-0.941342\pi$
$349$	−36.7305			−1.96614			−0.983068	+	0.183240i	$0.941342\pi$
$350$		0			0
$351$	−29.7891			−1.59002
$352$	1.63079	−	2.24459i	0.0869214	−	0.119637i
$353$	17.4744	−	5.67779i	0.930070	−	0.302198i	0.195479	−	0.980708i	$-0.437374\pi$
$353$	17.4744	−	5.67779i	0.930070	−	0.302198i	0.734591	+	0.678510i	$0.237374\pi$
$354$	2.00402	+	6.16775i	0.106513	+	0.327812i
$355$		0			0
$356$	−2.83802	+	8.73452i	−0.150415	+	0.462928i
$357$		−	24.5313i		−	1.29834i
$358$	8.12330	+	2.63942i	0.429330	+	0.139498i
$359$	−19.7609	+	14.3572i	−1.04294	+	0.757742i	−0.970858	−	0.239657i	$-0.922965\pi$
$359$	−19.7609	+	14.3572i	−1.04294	+	0.757742i	−0.0720846	+	0.997399i	$0.522965\pi$
$360$		0			0
$361$	13.7575	+	9.99539i	0.724078	+	0.526073i
$362$	−4.60144	−	6.33334i	−0.241846	−	0.332873i
$363$	−3.32837	−	4.58111i	−0.174694	−	0.240446i
$364$	−12.7443	−	9.25928i	−0.667983	−	0.485318i
$365$		0			0
$366$	15.0272	−	10.9179i	0.785482	−	0.570686i
$367$	13.8117	+	4.48768i	0.720963	+	0.234255i	0.646441	−	0.762964i	$-0.276257\pi$
$367$	13.8117	+	4.48768i	0.720963	+	0.234255i	0.0745221	+	0.997219i	$0.476257\pi$
$368$			0.654963i			0.0341423i
$369$	0.168160	−	0.517542i	0.00875404	−	0.0269422i
$370$		0			0
$371$	0.451065	+	1.38824i	0.0234182	+	0.0720737i
$372$	11.6228	−	3.77648i	0.602615	−	0.195801i
$373$	13.6888	−	18.8410i	0.708778	−	0.975549i	−0.291044	−	0.956710i	$-0.594003\pi$
$373$	13.6888	−	18.8410i	0.708778	−	0.975549i	0.999823	−	0.0188399i	$-0.00599728\pi$
$374$	−14.3064			−0.739764
$375$		0			0
$376$	−2.77447			−0.143082
$377$	13.6719	−	18.8178i	0.704140	−	0.969166i
$378$	13.8441	−	4.49821i	0.712063	−	0.231363i
$379$	−8.84332	−	27.2169i	−0.454251	−	1.39804i	−0.872013	−	0.489483i	$-0.837185\pi$
$379$	−8.84332	−	27.2169i	−0.454251	−	1.39804i	0.417762	−	0.908556i	$-0.362815\pi$
$380$		0			0
$381$	5.05975	−	15.5723i	0.259219	−	0.797794i
$382$			3.36611i			0.172225i
$383$	15.8025	+	5.13454i	0.807469	+	0.262363i	0.683526	−	0.729927i	$-0.260446\pi$
$383$	15.8025	+	5.13454i	0.807469	+	0.262363i	0.123944	+	0.992289i	$0.460446\pi$
$384$	1.38723	−	1.00788i	0.0707920	−	0.0514334i
$385$		0			0
$386$	12.4759	+	9.06430i	0.635008	+	0.461361i
$387$	0.324754	+	0.446986i	0.0165082	+	0.0227216i
$388$	−0.0530006	−	0.0729490i	−0.00269070	−	0.00370343i
$389$	21.3392	+	15.5039i	1.08194	+	0.786077i	0.978021	−	0.208508i	$-0.0668609\pi$
$389$	21.3392	+	15.5039i	1.08194	+	0.786077i	0.103922	+	0.994585i	$0.466861\pi$
$390$		0			0
$391$	2.73227	−	1.98511i	0.138177	−	0.100391i
$392$	0.663522	+	0.215591i	0.0335129	+	0.0108890i
$393$		−	9.60109i		−	0.484311i
$394$	−2.72086	+	8.37394i	−0.137075	+	0.421873i
$395$		0			0
$396$	−0.0512290	−	0.157667i	−0.00257435	−	0.00792305i
$397$	17.0321	−	5.53406i	0.854816	−	0.277747i	0.151354	−	0.988480i	$-0.451637\pi$
$397$	17.0321	−	5.53406i	0.854816	−	0.277747i	0.703462	+	0.710733i	$0.251637\pi$
$398$	10.3580	−	14.2566i	0.519202	−	0.714620i
$399$	6.71930			0.336386
$400$		0			0
$401$	32.0164			1.59882			0.799411	−	0.600785i	$-0.205145\pi$
$401$	32.0164			1.59882			0.799411	+	0.600785i	$0.205145\pi$
$402$	−4.35749	+	5.99757i	−0.217332	+	0.299132i
$403$	−38.4856	+	12.5047i	−1.91710	+	0.622905i
$404$	2.44319	+	7.51936i	0.121553	+	0.374102i
$405$		0			0
$406$	−3.51232	+	10.8098i	−0.174314	+	0.536482i
$407$		−	2.90615i		−	0.144053i
$408$	−8.40906	−	2.73227i	−0.416311	−	0.135268i
$409$	14.5901	−	10.6003i	0.721435	−	0.524153i	−0.165407	−	0.986225i	$-0.552894\pi$
$409$	14.5901	−	10.6003i	0.721435	−	0.524153i	0.886842	+	0.462072i	$0.152894\pi$
$410$		0			0
$411$	−11.0759	−	8.04709i	−0.546332	−	0.396934i
$412$	−4.60484	−	6.33802i	−0.226864	−	0.312252i
$413$	6.16775	+	8.48918i	0.303495	+	0.417725i
$414$	0.0316613	+	0.0230033i	0.00155607	+	0.00113055i
$415$		0			0
$416$	−4.59343	+	3.33732i	−0.225211	+	0.163626i
$417$	−36.0216	−	11.7041i	−1.76398	−	0.573153i
$418$		−	3.91861i		−	0.191666i
$419$	6.03511	−	18.5742i	0.294834	−	0.907407i	−0.688443	−	0.725291i	$-0.741705\pi$
$419$	6.03511	−	18.5742i	0.294834	−	0.907407i	0.983277	−	0.182116i	$-0.0582947\pi$
$420$		0			0
$421$	−6.04242	−	18.5967i	−0.294490	−	0.906346i	−0.983392	−	0.181492i	$-0.941907\pi$
$421$	−6.04242	−	18.5967i	−0.294490	−	0.906346i	0.688903	−	0.724854i	$-0.258093\pi$
$422$	−5.80281	+	1.88545i	−0.282477	+	0.0917822i
$423$	−0.0974433	+	0.134119i	−0.00473786	+	0.00652110i
$424$	0.526111			0.0255502
$425$		0			0
$426$	−22.7142			−1.10050
$427$	17.6655	−	24.3145i	0.854893	−	1.17666i
$428$	−9.72166	+	3.15876i	−0.469914	+	0.152684i
$429$	−8.34705	−	25.6896i	−0.402999	−	1.24030i
$430$		0			0
$431$	−6.55002	+	20.1589i	−0.315503	+	0.971019i	0.660044	+	0.751227i	$0.270538\pi$
$431$	−6.55002	+	20.1589i	−0.315503	+	0.971019i	−0.975547	+	0.219792i	$0.929462\pi$
$432$		−	5.24660i		−	0.252427i
$433$	−8.13122	−	2.64199i	−0.390761	−	0.126966i	0.107045	−	0.994254i	$-0.465861\pi$
$433$	−8.13122	−	2.64199i	−0.390761	−	0.126966i	−0.497807	+	0.867288i	$0.665861\pi$
$434$	15.9974	−	11.6228i	0.767901	−	0.557913i
$435$		0			0
$436$	−3.16400	−	2.29878i	−0.151528	−	0.110091i
$437$	0.543736	+	0.748388i	0.0260104	+	0.0358003i
$438$	4.24646	+	5.84475i	0.202904	+	0.279273i
$439$	−22.7102	−	16.4999i	−1.08390	−	0.787499i	−0.105541	−	0.994415i	$-0.533657\pi$
$439$	−22.7102	−	16.4999i	−1.08390	−	0.787499i	−0.978359	+	0.206916i	$0.933657\pi$
$440$		0			0
$441$	0.0337257	−	0.0245031i	0.00160598	−	0.00116682i
$442$	27.8442	+	9.04713i	1.32441	+	0.430328i
$443$			33.0546i			1.57047i	0.619197	+	0.785236i	$0.287458\pi$
$443$			33.0546i			1.57047i	−0.619197	+	0.785236i	$0.712542\pi$
$444$	0.555026	−	1.70820i	0.0263404	−	0.0810673i
$445$		0			0
$446$	−1.55394	−	4.78254i	−0.0735813	−	0.226460i
$447$	−6.82325	+	2.21701i	−0.322729	+	0.104861i
$448$	1.63079	−	2.24459i	0.0770476	−	0.106047i
$449$	37.1628			1.75382			0.876911	−	0.480652i	$-0.159600\pi$
$449$	37.1628			1.75382			0.876911	+	0.480652i	$0.159600\pi$
$450$		0			0
$451$	25.2677			1.18981
$452$	−3.74740	+	5.15785i	−0.176263	+	0.242605i
$453$	−0.540707	+	0.175686i	−0.0254046	+	0.00825446i
$454$	5.51232	+	16.9652i	0.258706	+	0.796215i
$455$		0			0
$456$	0.748388	−	2.30330i	0.0350465	−	0.107862i
$457$			29.3139i			1.37125i	0.727956	+	0.685624i	$0.240471\pi$
$457$			29.3139i			1.37125i	−0.727956	+	0.685624i	$0.759529\pi$
$458$	20.5016	+	6.66137i	0.957976	+	0.311265i
$459$	−21.8870	+	15.9018i	−1.02160	+	0.742233i
$460$		0			0
$461$	−7.20624	−	5.23564i	−0.335628	−	0.243848i	0.407187	−	0.913345i	$-0.366510\pi$
$461$	−7.20624	−	5.23564i	−0.335628	−	0.243848i	−0.742815	+	0.669497i	$0.766510\pi$
$462$	7.75836	+	10.6785i	0.360952	+	0.496807i
$463$	−10.7430	−	14.7865i	−0.499271	−	0.687187i	0.482793	−	0.875734i	$-0.339622\pi$
$463$	−10.7430	−	14.7865i	−0.499271	−	0.687187i	−0.982064	+	0.188547i	$0.939622\pi$
$464$	3.31428	+	2.40797i	0.153862	+	0.111787i
$465$		0			0
$466$	−11.8978	+	8.64424i	−0.551154	+	0.400436i
$467$	−34.8886	−	11.3360i	−1.61445	−	0.524568i	−0.643829	−	0.765169i	$-0.722655\pi$
$467$	−34.8886	−	11.3360i	−1.61445	−	0.524568i	−0.970624	+	0.240601i	$0.922655\pi$
$468$			0.339260i			0.0156823i
$469$	−3.70670	+	11.4081i	−0.171160	+	0.526775i
$470$		0			0
$471$	1.91153	+	5.88308i	0.0880785	+	0.271078i
$472$	3.59695	−	1.16872i	0.165563	−	0.0537948i
$473$	−15.0793	+	20.7548i	−0.693346	+	0.954309i
$474$	16.9784			0.779842
$475$		0			0
$476$	−14.3064			−0.655731
$477$	0.0184778	−	0.0254325i	0.000846040	−	0.00116447i
$478$	6.60057	−	2.14465i	0.301903	−	0.0980942i
$479$	3.89046	+	11.9736i	0.177760	+	0.547088i	0.999749	−	0.0224155i	$-0.00713568\pi$
$479$	3.89046	+	11.9736i	0.177760	+	0.547088i	−0.821989	+	0.569503i	$0.807136\pi$
$480$		0			0
$481$	−1.83781	+	5.65620i	−0.0837969	+	0.257900i
$482$			3.31003i			0.150768i
$483$	−2.96343	−	0.962877i	−0.134841	−	0.0438124i
$484$	−2.67164	+	1.94106i	−0.121438	+	0.0882301i
$485$		0			0
$486$	−0.502294	−	0.364938i	−0.0227845	−	0.0165539i
$487$	10.7715	+	14.8257i	0.488103	+	0.671816i	0.980037	−	0.198816i	$-0.0637097\pi$
$487$	10.7715	+	14.8257i	0.488103	+	0.671816i	−0.491934	+	0.870633i	$0.663710\pi$
$488$	−6.36716	−	8.76365i	−0.288228	−	0.396712i
$489$	7.06635	+	5.13401i	0.319552	+	0.232168i
$490$		0			0
$491$	−17.5595	+	12.7577i	−0.792448	+	0.575747i	−0.908689	−	0.417474i	$-0.862915\pi$
$491$	−17.5595	+	12.7577i	−0.792448	+	0.575747i	0.116241	+	0.993221i	$0.462915\pi$
$492$	14.8520	+	4.82570i	0.669578	+	0.217559i
$493$		−	21.1243i		−	0.951389i
$494$	−2.47807	+	7.62672i	−0.111494	+	0.343143i
$495$		0			0
$496$	−2.20239	−	6.77827i	−0.0988904	−	0.304353i
$497$	−34.9535	+	11.3571i	−1.56788	+	0.509434i
$498$	−4.71290	+	6.48675i	−0.211190	+	0.290678i
$499$	−15.8391			−0.709055			−0.354527	−	0.935046i	$-0.615358\pi$
$499$	−15.8391			−0.709055			−0.354527	+	0.935046i	$0.615358\pi$
$500$		0			0
$501$	35.7739			1.59826
$502$	−5.56312	+	7.65697i	−0.248294	+	0.341748i
$503$	26.2044	−	8.51433i	1.16840	−	0.379635i	0.340353	−	0.940298i	$-0.389453\pi$
$503$	26.2044	−	8.51433i	1.16840	−	0.379635i	0.828044	+	0.560662i	$0.189453\pi$
$504$	−0.0512290	−	0.157667i	−0.00228192	−	0.00702303i
$505$		0			0
$506$	−0.561537	+	1.72823i	−0.0249634	+	0.0768294i
$507$			32.9864i			1.46498i
$508$	−9.08158	−	2.95078i	−0.402930	−	0.130920i
$509$	−22.3386	+	16.2300i	−0.990142	+	0.719380i	−0.959952	−	0.280164i	$-0.909611\pi$
$509$	−22.3386	+	16.2300i	−0.990142	+	0.719380i	−0.0301894	+	0.999544i	$0.509611\pi$
$510$		0			0
$511$	9.45701	+	6.87092i	0.418354	+	0.303952i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−4.35562	−	5.99499i	−0.192305	−	0.264685i
$514$	−5.72754	−	4.16130i	−0.252631	−	0.183547i
$515$		0			0
$516$	−12.8272	+	9.31951i	−0.564686	+	0.410268i
$517$	−7.32092	−	2.37871i	−0.321974	−	0.104616i
$518$		−	2.90615i		−	0.127689i
$519$	6.35200	−	19.5495i	0.278822	−	0.858126i
$520$		0			0
$521$	5.28084	+	16.2527i	0.231358	+	0.712046i	0.997584	+	0.0694747i	$0.0221323\pi$
$521$	5.28084	+	16.2527i	0.231358	+	0.712046i	−0.766226	+	0.642571i	$0.777868\pi$
$522$	0.232805	−	0.0756429i	0.0101896	−	0.00331080i
$523$	−21.3456	+	29.3796i	−0.933376	+	1.28468i	0.0251516	+	0.999684i	$0.491993\pi$
$523$	−21.3456	+	29.3796i	−0.933376	+	1.28468i	−0.958528	+	0.284999i	$0.908007\pi$
$524$	−5.59923			−0.244604
$525$		0			0
$526$	1.43345			0.0625016
$527$	−21.6013	+	29.7317i	−0.940970	+	1.29513i
$528$	4.52458	−	1.47012i	0.196907	−	0.0639789i
$529$	6.97483	+	21.4663i	0.303253	+	0.933318i
$530$		0			0
$531$	0.0698337	−	0.214926i	0.00303052	−	0.00932699i
$532$		−	3.91861i		−	0.169893i
$533$	−49.1780	−	15.9789i	−2.13014	−	0.692123i
$534$	−12.7404	+	9.25642i	−0.551330	+	0.400565i
$535$		0			0
$536$	3.49771	+	2.54123i	0.151078	+	0.109764i
$537$	8.60868	+	11.8488i	0.371492	+	0.511315i
$538$	−8.39532	−	11.5552i	−0.361948	−	0.498178i
$539$	1.56598	+	1.13775i	0.0674516	+	0.0490064i
$540$		0			0
$541$	−20.1742	+	14.6574i	−0.867355	+	0.630170i	−0.929876	−	0.367873i	$-0.880086\pi$
$541$	−20.1742	+	14.6574i	−0.867355	+	0.630170i	0.0625209	+	0.998044i	$0.480086\pi$
$542$	29.2788	+	9.51325i	1.25763	+	0.408629i
$543$		−	13.4235i		−	0.576060i
$544$	−1.59343	+	4.90406i	−0.0683176	+	0.210260i
$545$		0			0
$546$	−8.34705	−	25.6896i	−0.357221	−	1.09941i
$547$	−6.34546	+	2.06176i	−0.271312	+	0.0881547i	−0.441513	−	0.897255i	$-0.645558\pi$
$547$	−6.34546	+	2.06176i	−0.271312	+	0.0881547i	0.170201	+	0.985409i	$0.445558\pi$
$548$	−4.69296	+	6.45931i	−0.200473	+	0.275928i
$549$	−0.647264			−0.0276245
$550$		0			0
$551$	5.78609			0.246496
$552$	−0.660127	+	0.908587i	−0.0280969	+	0.0386720i
$553$	26.1270	−	8.48918i	1.11103	−	0.360997i
$554$	−0.985668	−	3.03357i	−0.0418770	−	0.128884i
$555$		0			0
$556$	−6.82570	+	21.0073i	−0.289474	+	0.890909i
$557$		−	20.4328i		−	0.865765i	−0.901450	−	0.432882i	$-0.857497\pi$
$557$		−	20.4328i		−	0.865765i	0.901450	−	0.432882i	$-0.142503\pi$
$558$	−0.405017	−	0.131598i	−0.0171457	−	0.00557098i
$559$	42.4736	−	30.8589i	1.79644	−	1.30519i
$560$		0			0
$561$	−19.8463	−	14.4192i	−0.837910	−	0.608777i
$562$	−11.9843	−	16.4950i	−0.505528	−	0.695799i
$563$	−0.354320	−	0.487680i	−0.0149328	−	0.0205532i	0.801485	−	0.598014i	$-0.204043\pi$
$563$	−0.354320	−	0.487680i	−0.0149328	−	0.0205532i	−0.816418	+	0.577461i	$0.804043\pi$
$564$	−3.84883	−	2.79634i	−0.162065	−	0.117747i
$565$		0			0
$566$	10.7574	−	7.81572i	0.452168	−	0.328519i
$567$	23.2657	+	7.55947i	0.977066	+	0.317468i
$568$			13.2466i			0.555815i
$569$	−10.4688	+	32.2195i	−0.438873	+	1.35071i	0.450192	+	0.892932i	$0.351356\pi$
$569$	−10.4688	+	32.2195i	−0.438873	+	1.35071i	−0.889065	+	0.457781i	$0.848644\pi$
$570$		0			0
$571$	−1.92521	−	5.92520i	−0.0805677	−	0.247962i	0.902657	−	0.430361i	$-0.141614\pi$
$571$	−1.92521	−	5.92520i	−0.0805677	−	0.247962i	−0.983225	+	0.182399i	$0.941614\pi$
$572$	−14.9818	+	4.86789i	−0.626422	+	0.203537i
$573$	−3.39265	+	4.66958i	−0.141730	+	0.195074i
$574$	25.2677			1.05465
$575$		0			0
$576$	−0.0597522			−0.00248967
$577$	2.22244	−	3.05893i	0.0925214	−	0.127345i	−0.760247	−	0.649634i	$-0.774922\pi$
$577$	2.22244	−	3.05893i	0.0925214	−	0.127345i	0.852768	+	0.522290i	$0.174922\pi$
$578$	9.11949	−	2.96310i	0.379321	−	0.123249i
$579$	8.17127	+	25.1486i	0.339587	+	1.04514i
$580$		0			0
$581$	−4.00903	+	12.3385i	−0.166323	+	0.511889i
$582$		−	0.154616i		−	0.00640903i
$583$	1.38824	+	0.451065i	0.0574949	+	0.0186812i
$584$	3.40859	−	2.47648i	0.141048	−	0.102478i
$585$		0			0
$586$	21.0684	+	15.3071i	0.870330	+	0.632332i
$587$	−9.61184	−	13.2296i	−0.396723	−	0.546042i	0.563195	−	0.826324i	$-0.309572\pi$
$587$	−9.61184	−	13.2296i	−0.396723	−	0.546042i	−0.959918	+	0.280282i	$0.909572\pi$
$588$	0.703169	+	0.967829i	0.0289982	+	0.0399126i
$589$	−8.14373	−	5.91676i	−0.335556	−	0.243796i
$590$		0			0
$591$	−12.2144	+	8.87430i	−0.502435	+	0.365040i
$592$	−0.996198	−	0.323684i	−0.0409435	−	0.0133033i
$593$		−	9.53314i		−	0.391479i	−0.980656	−	0.195740i	$-0.937289\pi$
$593$		−	9.53314i		−	0.391479i	0.980656	−	0.195740i	$-0.0627107\pi$
$594$	4.49821	−	13.8441i	0.184564	−	0.568030i
$595$		0			0
$596$	1.29293	+	3.97923i	0.0529605	+	0.162996i
$597$	28.7381	−	9.33756i	1.17617	−	0.382161i
$598$	2.18582	−	3.00852i	0.0893848	−	0.123028i
$599$	16.0682			0.656528			0.328264	−	0.944586i	$-0.393536\pi$
$599$	16.0682			0.656528			0.328264	+	0.944586i	$0.393536\pi$
$600$		0			0
$601$	15.0380			0.613413			0.306707	−	0.951804i	$-0.400773\pi$
$601$	15.0380			0.613413			0.306707	+	0.951804i	$0.400773\pi$
$602$	−15.0793	+	20.7548i	−0.614585	+	0.845904i
$603$	0.245689	−	0.0798292i	0.0100052	−	0.00325090i
$604$	0.102458	+	0.315333i	0.00416896	+	0.0128307i
$605$		0			0
$606$	−4.18937	+	12.8936i	−0.170182	+	0.523765i
$607$		−	44.8348i		−	1.81979i	−0.414840	−	0.909894i	$-0.636163\pi$
$607$		−	44.8348i		−	1.81979i	0.414840	−	0.909894i	$-0.363837\pi$
$608$	−1.34326	−	0.436451i	−0.0544763	−	0.0177004i
$609$	−15.7674	+	11.4557i	−0.638929	+	0.464209i
$610$		0			0
$611$	12.7443	+	9.25928i	0.515580	+	0.374590i
$612$	0.181101	+	0.249265i	0.00732059	+	0.0100759i
$613$	−9.13937	−	12.5793i	−0.369136	−	0.508072i	0.583530	−	0.812092i	$-0.301671\pi$
$613$	−9.13937	−	12.5793i	−0.369136	−	0.508072i	−0.952666	+	0.304020i	$0.901671\pi$
$614$	20.3064	+	14.7534i	0.819498	+	0.595400i
$615$		0			0
$616$	6.22754	−	4.52458i	0.250915	−	0.182300i
$617$	16.7380	+	5.43852i	0.673848	+	0.218946i	0.625900	−	0.779903i	$-0.284732\pi$
$617$	16.7380	+	5.43852i	0.673848	+	0.218946i	0.0479478	+	0.998850i	$0.484732\pi$
$618$		−	13.4335i		−	0.540373i
$619$	11.5229	−	35.4637i	0.463143	−	1.42541i	−0.398161	−	0.917316i	$-0.630351\pi$
$619$	11.5229	−	35.4637i	0.463143	−	1.42541i	0.861303	−	0.508091i	$-0.169649\pi$
$620$		0			0
$621$	1.06188	+	3.26814i	0.0426120	+	0.131146i
$622$	−0.687926	+	0.223521i	−0.0275833	+	0.00896236i
$623$	−14.9772	+	20.6144i	−0.600049	+	0.825897i
$624$	−9.73579			−0.389743
$625$		0			0
$626$	21.6163			0.863960
$627$	3.94951	−	5.43603i	0.157728	−	0.217094i
$628$	3.43094	−	1.11478i	0.136909	−	0.0444845i
$629$	1.66906	+	5.13683i	0.0665496	+	0.204819i
$630$		0			0
$631$	2.64380	−	8.13677i	0.105248	−	0.323920i	−0.884541	−	0.466463i	$-0.845528\pi$
$631$	2.64380	−	8.13677i	0.105248	−	0.323920i	0.989789	+	0.142543i	$0.0455280\pi$
$632$		−	9.90157i		−	0.393863i
$633$	−9.95017	−	3.23301i	−0.395484	−	0.128500i
$634$	−15.2367	+	11.0701i	−0.605129	+	0.439652i
$635$		0			0
$636$	0.729839	+	0.530259i	0.0289400	+	0.0210261i
$637$	−2.32834	−	3.20469i	−0.0922523	−	0.126974i
$638$	6.68083	+	9.19537i	0.264497	+	0.364048i
$639$	0.640348	+	0.465240i	0.0253318	+	0.0184046i
$640$		0			0
$641$	18.4582	−	13.4107i	0.729055	−	0.529690i	−0.160209	−	0.987083i	$-0.551217\pi$
$641$	18.4582	−	13.4107i	0.729055	−	0.529690i	0.889264	+	0.457394i	$0.151217\pi$
$642$	−16.6699	−	5.41637i	−0.657908	−	0.213767i
$643$		−	34.7745i		−	1.37137i	−0.727898	−	0.685686i	$-0.759503\pi$
$643$		−	34.7745i		−	1.37137i	0.727898	−	0.685686i	$-0.240497\pi$
$644$	−0.561537	+	1.72823i	−0.0221277	+	0.0681020i
$645$		0			0
$646$	2.25053	+	6.92641i	0.0885459	+	0.272516i
$647$	15.6526	−	5.08583i	0.615366	−	0.199945i	0.0152844	−	0.999883i	$-0.495135\pi$
$647$	15.6526	−	5.08583i	0.615366	−	0.199945i	0.600082	+	0.799939i	$0.295135\pi$
$648$	5.18260	−	7.13324i	0.203592	−	0.280220i
$649$	10.4932			0.411894
$650$		0			0
$651$	33.9066			1.32890
$652$	2.99409	−	4.12101i	0.117257	−	0.161391i
$653$	28.7306	−	9.33515i	1.12432	−	0.365313i	0.312903	−	0.949785i	$-0.398699\pi$
$653$	28.7306	−	9.33515i	1.12432	−	0.365313i	0.811414	+	0.584473i	$0.198699\pi$
$654$	−2.07230	−	6.37788i	−0.0810333	−	0.249395i
$655$		0			0
$656$	2.81428	−	8.66148i	0.109879	−	0.338174i
$657$		−	0.251751i		−	0.00982173i
$658$	−7.32092	−	2.37871i	−0.285399	−	0.0927318i
$659$	−23.0523	+	16.7485i	−0.897991	+	0.652428i	−0.937949	−	0.346773i	$-0.887277\pi$
$659$	−23.0523	+	16.7485i	−0.897991	+	0.652428i	0.0399585	+	0.999201i	$0.487277\pi$
$660$		0			0
$661$	−41.0448	−	29.8208i	−1.59646	−	1.15990i	−0.893897	−	0.448273i	$-0.852039\pi$
$661$	−41.0448	−	29.8208i	−1.59646	−	1.15990i	−0.702562	−	0.711622i	$-0.747961\pi$
$662$	−9.91941	−	13.6529i	−0.385529	−	0.530635i
$663$	29.5080	+	40.6142i	1.14599	+	1.57733i
$664$	3.78299	+	2.74850i	0.146809	+	0.106663i
$665$		0			0
$666$	−0.0506350	+	0.0367885i	−0.00196207	+	0.00142552i
$667$	−2.55185	−	0.829146i	−0.0988080	−	0.0321047i
$668$		−	20.8629i		−	0.807209i
$669$	2.66457	−	8.20070i	0.103018	−	0.317057i
$670$		0			0
$671$	−9.28730	−	28.5834i	−0.358532	−	1.10345i
$672$	4.52458	−	1.47012i	0.174539	−	0.0567113i
$673$	12.0171	−	16.5401i	0.463224	−	0.637573i	−0.511949	−	0.859016i	$-0.671077\pi$
$673$	12.0171	−	16.5401i	0.463224	−	0.637573i	0.975173	+	0.221442i	$0.0710765\pi$
$674$	−19.3521			−0.745414
$675$		0			0
$676$	19.2373			0.739894
$677$	5.01592	−	6.90383i	0.192778	−	0.265336i	−0.701676	−	0.712496i	$-0.747565\pi$
$677$	5.01592	−	6.90383i	0.192778	−	0.265336i	0.894454	+	0.447160i	$0.147565\pi$
$678$	−10.3970	+	3.37820i	−0.399296	+	0.129739i
$679$	−0.0773079	−	0.237929i	−0.00296680	−	0.00913088i
$680$		0			0
$681$	−9.45206	+	29.0904i	−0.362204	+	1.11475i
$682$		−	19.7739i		−	0.757182i
$683$	46.1913	+	15.0085i	1.76746	+	0.574283i	0.997929	−	0.0643246i	$-0.0204893\pi$
$683$	46.1913	+	15.0085i	1.76746	+	0.574283i	0.769532	+	0.638608i	$0.220489\pi$
$684$	−0.0682754	+	0.0496050i	−0.00261058	+	0.00189669i
$685$		0			0
$686$	−14.1462	−	10.2778i	−0.540103	−	0.392408i
$687$	21.7266	+	29.9041i	0.828921	+	1.14091i
$688$	5.43502	+	7.48066i	0.207208	+	0.285197i
$689$	−2.41665	−	1.75580i	−0.0920671	−	0.0668907i
$690$		0			0
$691$	−36.2501	+	26.3373i	−1.37902	+	1.00192i	−0.382048	+	0.924142i	$0.624781\pi$
$691$	−36.2501	+	26.3373i	−1.37902	+	1.00192i	−0.996971	+	0.0777740i	$0.975219\pi$
$692$	−11.4010	−	3.70441i	−0.433401	−	0.140820i
$693$		−	0.459953i		−	0.0174722i
$694$	2.79311	−	8.59630i	0.106025	−	0.326311i
$695$		0			0
$696$	2.17073	+	6.68083i	0.0822814	+	0.253236i
$697$	−44.6623	+	14.5117i	−1.69171	+	0.549669i
$698$	−21.5896	+	29.7156i	−0.817179	+	1.12475i
$699$	−25.2174			−0.953809
$700$		0			0
$701$	2.21913			0.0838152			0.0419076	−	0.999121i	$-0.486656\pi$
$701$	2.21913			0.0838152			0.0419076	+	0.999121i	$0.486656\pi$
$702$	−17.5096	+	24.0999i	−0.660857	+	0.909591i
$703$	−1.40701	+	0.457166i	−0.0530665	+	0.0172424i
$704$	−0.857358	−	2.63868i	−0.0323129	−	0.0994488i
$705$		0			0
$706$	5.67779	−	17.4744i	0.213686	−	0.657659i
$707$			21.9358i			0.824982i
$708$	6.16775	+	2.00402i	0.231798	+	0.0753158i
$709$	27.7968	−	20.1955i	1.04393	−	0.758459i	0.0728805	−	0.997341i	$-0.476781\pi$
$709$	27.7968	−	20.1955i	1.04393	−	0.758459i	0.971049	+	0.238882i	$0.0767808\pi$
$710$		0			0
$711$	−0.478647	−	0.347757i	−0.0179507	−	0.0130419i
$712$	5.39823	+	7.43002i	0.202307	+	0.278452i
$713$	2.74377	+	3.77648i	0.102755	+	0.141430i
$714$	−19.8463	−	14.4192i	−0.742728	−	0.539623i
$715$		0			0
$716$	6.91009	−	5.02047i	0.258242	−	0.187624i
$717$	11.3181	+	3.67747i	0.422682	+	0.137338i
$718$			24.4259i			0.911565i
$719$	−3.70511	+	11.4032i	−0.138177	+	0.425266i	−0.996071	−	0.0885618i	$-0.971773\pi$
$719$	−3.70511	+	11.4032i	−0.138177	+	0.425266i	0.857893	+	0.513828i	$0.171773\pi$
$720$		0			0
$721$	−6.71673	−	20.6720i	−0.250144	−	0.769864i
$722$	16.1729	−	5.25489i	0.601892	−	0.195567i
$723$	−3.33613	+	4.59179i	−0.124072	+	0.170770i
$724$	−7.82844			−0.290942
$725$		0			0
$726$	−5.66256			−0.210157
$727$	24.7944	−	34.1265i	0.919573	−	1.26568i	−0.0442177	−	0.999022i	$-0.514080\pi$
$727$	24.7944	−	34.1265i	0.919573	−	1.26568i	0.963790	−	0.266661i	$-0.0859205\pi$
$728$	−14.9818	+	4.86789i	−0.555264	+	0.180416i
$729$	−8.50295	−	26.1694i	−0.314924	−	0.969237i
$730$		0			0
$731$	14.7338	−	45.3459i	0.544948	−	1.67718i
$732$		−	18.5746i		−	0.686537i
$733$	0.306605	+	0.0996219i	0.0113247	+	0.00367962i	0.314674	−	0.949200i	$-0.398105\pi$
$733$	0.306605	+	0.0996219i	0.0113247	+	0.00367962i	−0.303349	+	0.952879i	$0.598105\pi$
$734$	11.7489	−	8.53607i	0.433660	−	0.315072i
$735$		0			0
$736$	0.529876	+	0.384978i	0.0195315	+	0.0141905i
$737$	7.05056	+	9.70427i	0.259711	+	0.357461i
$738$	−0.319859	−	0.440248i	−0.0117742	−	0.0162057i
$739$	−4.44942	−	3.23269i	−0.163674	−	0.118916i	0.502933	−	0.864325i	$-0.332254\pi$
$739$	−4.44942	−	3.23269i	−0.163674	−	0.118916i	−0.666607	+	0.745409i	$0.732254\pi$
$740$		0			0
$741$	−11.1245	+	8.08244i	−0.408670	+	0.296916i
$742$	1.38824	+	0.451065i	0.0509638	+	0.0165591i
$743$			6.03812i			0.221517i	0.993847	+	0.110759i	$0.0353280\pi$
$743$			6.03812i			0.221517i	−0.993847	+	0.110759i	$0.964672\pi$
$744$	3.77648	−	11.6228i	0.138452	−	0.426113i
$745$		0			0
$746$	−7.19662	−	22.1489i	−0.263487	−	0.810929i
$747$	0.265728	−	0.0863404i	0.00972249	−	0.00315903i
$748$	−8.40906	+	11.5741i	−0.307466	+	0.423190i
$749$	−28.3605			−1.03627
$750$		0			0
$751$	−13.5719			−0.495244			−0.247622	−	0.968857i	$-0.579649\pi$
$751$	−13.5719			−0.495244			−0.247622	+	0.968857i	$0.579649\pi$
$752$	−1.63079	+	2.24459i	−0.0594688	+	0.0818518i
$753$	−15.4347	+	5.01503i	−0.562471	+	0.182758i
$754$	−7.18776	−	22.1216i	−0.261763	−	0.805623i
$755$		0			0
$756$	4.49821	−	13.8441i	0.163598	−	0.503504i
$757$			33.0661i			1.20181i	0.799321	+	0.600904i	$0.205193\pi$
$757$			33.0661i			1.20181i	−0.799321	+	0.600904i	$0.794807\pi$
$758$	−27.2169	−	8.84332i	−0.988563	−	0.321204i
$759$	−2.52084	+	1.83150i	−0.0915008	+	0.0664792i
$760$		0			0
$761$	−4.19767	−	3.04978i	−0.152165	−	0.110555i	0.509098	−	0.860709i	$-0.329979\pi$
$761$	−4.19767	−	3.04978i	−0.152165	−	0.110555i	−0.661263	+	0.750154i	$0.729979\pi$
$762$	−9.62422	−	13.2466i	−0.348649	−	0.479874i
$763$	−6.37788	−	8.77840i	−0.230895	−	0.317799i
$764$	2.72324	+	1.97855i	0.0985233	+	0.0715814i
$765$		0			0
$766$	13.4424	−	9.76647i	0.485694	−	0.352877i
$767$	−20.4227	−	6.63575i	−0.737422	−	0.239603i
$768$		−	1.71472i		−	0.0618745i
$769$	−10.2191	+	31.4512i	−0.368511	+	1.13416i	0.579242	+	0.815156i	$0.303349\pi$
$769$	−10.2191	+	31.4512i	−0.368511	+	1.13416i	−0.947753	+	0.319005i	$0.896651\pi$
$770$		0			0
$771$	−3.75133	−	11.5454i	−0.135101	−	0.415798i
$772$	14.6663	−	4.76538i	0.527853	−	0.171510i
$773$	0.664758	−	0.914961i	0.0239097	−	0.0329088i	−0.796895	−	0.604118i	$-0.793526\pi$
$773$	0.664758	−	0.914961i	0.0239097	−	0.0329088i	0.820804	+	0.571209i	$0.193526\pi$
$774$	0.552505			0.0198594
$775$		0			0
$776$	−0.0901699			−0.00323691
$777$	2.92907	−	4.03152i	0.105080	−	0.144630i
$778$	25.0858	−	8.15086i	0.899369	−	0.292223i
$779$	−3.97485	−	12.2333i	−0.142414	−	0.438305i
$780$		0			0
$781$	−11.3571	+	34.9535i	−0.406388	+	1.25073i
$782$		−	3.37727i		−	0.120771i
$783$	20.4417	+	6.64191i	0.730526	+	0.237362i
$784$	0.564426	−	0.410079i	0.0201581	−	0.0146457i
$785$		0			0
$786$	−7.76745	−	5.64338i	−0.277056	−	0.201293i
$787$	−9.26408	−	12.7509i	−0.330229	−	0.454521i	0.611327	−	0.791378i	$-0.290636\pi$
$787$	−9.26408	−	12.7509i	−0.330229	−	0.454521i	−0.941556	+	0.336857i	$0.890636\pi$
$788$	5.17538	+	7.12330i	0.184365	+	0.253757i
$789$	1.98854	+	1.44476i	0.0707938	+	0.0514347i
$790$		0			0
$791$	−14.3103	+	10.3970i	−0.508815	+	0.369676i
$792$	−0.157667	−	0.0512290i	−0.00560244	−	0.00182034i
$793$			61.5044i			2.18409i
$794$	5.53406	−	17.0321i	0.196396	−	0.604446i
$795$		0			0
$796$	−5.44555	−	16.7597i	−0.193012	−	0.594031i
$797$	22.0071	−	7.15055i	0.779532	−	0.253285i	0.107892	−	0.994163i	$-0.465590\pi$
$797$	22.0071	−	7.15055i	0.779532	−	0.253285i	0.671640	+	0.740877i	$0.265590\pi$
$798$	3.94951	−	5.43603i	0.139811	−	0.192433i
$799$	14.3064			0.506122
$800$		0			0
$801$	0.548765			0.0193897
$802$	18.8188	−	25.9018i	0.664513	−	0.914624i
$803$	11.1174	−	3.61226i	0.392324	−	0.127474i
$804$	2.29087	+	7.05056i	0.0807927	+	0.248654i
$805$		0			0
$806$	−12.5047	+	38.4856i	−0.440460	+	1.35560i
$807$		−	24.4912i		−	0.862132i
$808$	7.51936	+	2.44319i	0.264530	+	0.0859511i
$809$	27.1345	−	19.7143i	0.953997	−	0.693119i	0.00224811	−	0.999997i	$-0.499284\pi$
$809$	27.1345	−	19.7143i	0.953997	−	0.693119i	0.951749	+	0.306878i	$0.0992844\pi$
$810$		0			0
$811$	9.67796	+	7.03145i	0.339839	+	0.246907i	0.744594	−	0.667518i	$-0.232643\pi$
$811$	9.67796	+	7.03145i	0.339839	+	0.246907i	−0.404755	+	0.914425i	$0.632643\pi$
$812$	6.68083	+	9.19537i	0.234451	+	0.322694i
$813$	31.0282	+	42.7067i	1.08821	+	1.49779i
$814$	−2.35113	−	1.70820i	−0.0824070	−	0.0598722i
$815$		0			0
$816$	−7.15318	+	5.19709i	−0.250411	+	0.181934i
$817$	12.4206	+	4.03569i	0.434540	+	0.141191i
$818$		−	18.0344i		−	0.630557i
$819$	−0.290867	+	0.895198i	−0.0101637	+	0.0312807i
$820$		0			0
$821$	−3.30466	−	10.1707i	−0.115333	−	0.354960i	0.876683	−	0.481068i	$-0.159751\pi$
$821$	−3.30466	−	10.1707i	−0.115333	−	0.354960i	−0.992016	+	0.126109i	$0.959751\pi$
$822$	−13.0205	+	4.23061i	−0.454141	+	0.147559i
$823$	7.06581	−	9.72525i	0.246299	−	0.339001i	−0.667912	−	0.744240i	$-0.732812\pi$
$823$	7.06581	−	9.72525i	0.246299	−	0.339001i	0.914211	+	0.405239i	$0.132812\pi$
$824$	−7.83422			−0.272918
$825$		0			0
$826$	10.4932			0.365105
$827$	−2.43328	+	3.34912i	−0.0846133	+	0.116460i	−0.849225	−	0.528031i	$-0.822931\pi$
$827$	−2.43328	+	3.34912i	−0.0846133	+	0.116460i	0.764612	+	0.644491i	$0.222931\pi$
$828$	0.0372200	−	0.0120935i	0.00129349	−	0.000420279i
$829$	6.28859	+	19.3543i	0.218412	+	0.672203i	0.998894	+	0.0470242i	$0.0149738\pi$
$829$	6.28859	+	19.3543i	0.218412	+	0.672203i	−0.780482	+	0.625178i	$0.785026\pi$
$830$		0			0
$831$	1.69014	−	5.20171i	0.0586303	−	0.180445i
$832$			5.67779i			0.196842i
$833$	−3.42141	−	1.11168i	−0.118545	−	0.0385175i
$834$	−30.6418	+	22.2626i	−1.06104	+	0.770890i
$835$		0			0
$836$	−3.17022	−	2.30330i	−0.109644	−	0.0796614i
$837$	−21.9791	−	30.2516i	−0.759708	−	1.04565i
$838$	−11.4795	−	15.8001i	−0.396552	−	0.545806i
$839$	2.53639	+	1.84279i	0.0875658	+	0.0636203i	0.630707	−	0.776021i	$-0.282765\pi$
$839$	2.53639	+	1.84279i	0.0875658	+	0.0636203i	−0.543141	+	0.839642i	$0.682765\pi$
$840$		0			0
$841$	9.88393	−	7.18109i	0.340825	−	0.247624i
$842$	−18.5967	−	6.04242i	−0.640883	−	0.208236i
$843$		−	34.9612i		−	1.20413i
$844$	−1.88545	+	5.80281i	−0.0648998	+	0.199741i
$845$		0			0
$846$	0.0512290	+	0.157667i	0.00176129	+	0.00542069i
$847$	−8.71378	+	2.83128i	−0.299409	+	0.0972839i
$848$	0.309240	−	0.425633i	0.0106194	−	0.0146163i
$849$	22.8004			0.782508
$850$		0			0
$851$	0.686050			0.0235175
$852$	−13.3510	+	18.3761i	−0.457399	+	0.629556i
$853$	22.2044	−	7.21464i	0.760263	−	0.247025i	0.0968717	−	0.995297i	$-0.469116\pi$
$853$	22.2044	−	7.21464i	0.760263	−	0.247025i	0.663392	+	0.748272i	$0.269116\pi$
$854$	−9.28730	−	28.5834i	−0.317805	−	0.978102i
$855$		0			0
$856$	−3.15876	+	9.72166i	−0.107964	+	0.332280i
$857$			15.3036i			0.522762i	0.965236	+	0.261381i	$0.0841779\pi$
$857$			15.3036i			0.522762i	−0.965236	+	0.261381i	$0.915822\pi$
$858$	−25.6896	−	8.34705i	−0.877028	−	0.284964i
$859$	−2.39576	+	1.74062i	−0.0817422	+	0.0593892i	−0.627906	−	0.778289i	$-0.716088\pi$
$859$	−2.39576	+	1.74062i	−0.0817422	+	0.0593892i	0.546164	+	0.837679i	$0.316088\pi$
$860$		0			0
$861$	35.0522	+	25.4669i	1.19457	+	0.867909i
$862$	12.4589	+	17.1482i	0.424351	+	0.584069i
$863$	−22.2312	−	30.5987i	−0.756760	−	1.04159i	−0.997477	−	0.0709954i	$-0.977382\pi$
$863$	−22.2312	−	30.5987i	−0.756760	−	1.04159i	0.240717	−	0.970595i	$-0.422618\pi$
$864$	−4.24459	−	3.08388i	−0.144404	−	0.104916i
$865$		0			0
$866$	−6.91683	+	5.02537i	−0.235043	+	0.170769i
$867$	15.6373	+	5.08088i	0.531072	+	0.172556i
$868$		−	19.7739i		−	0.671170i
$869$	8.48918	−	26.1270i	0.287976	−	0.886298i
$870$		0			0
$871$	−7.58555	−	23.3459i	−0.257027	−	0.791046i
$872$	−3.71950	+	1.20854i	−0.125958	+	0.0409263i
$873$	−0.00316690	+	0.00435886i	−0.000107183	+	0.000147525i
$874$	0.925059			0.0312906
$875$		0			0
$876$	7.22451			0.244094
$877$	−9.17007	+	12.6215i	−0.309651	+	0.426198i	−0.935272	−	0.353929i	$-0.884846\pi$
$877$	−9.17007	+	12.6215i	−0.309651	+	0.426198i	0.625621	+	0.780127i	$0.284846\pi$
$878$	−26.6975	+	8.67453i	−0.900996	+	0.292751i
$879$	13.7991	+	42.4691i	0.465430	+	1.43245i
$880$		0			0
$881$	0.359812	−	1.10739i	0.0121224	−	0.0373089i	−0.944812	−	0.327612i	$-0.893756\pi$
$881$	0.359812	−	1.10739i	0.0121224	−	0.0373089i	0.956935	+	0.290303i	$0.0937561\pi$
$882$		−	0.0416872i		−	0.00140368i
$883$	−46.4925	−	15.1063i	−1.56460	−	0.508368i	−0.606566	−	0.795033i	$-0.707453\pi$
$883$	−46.4925	−	15.1063i	−1.56460	−	0.508368i	−0.958031	+	0.286665i	$0.907453\pi$
$884$	23.6857	−	17.2087i	0.796636	−	0.578790i
$885$		0			0
$886$	26.7417	+	19.4290i	0.898406	+	0.652730i
$887$	−5.07195	−	6.98094i	−0.170299	−	0.234397i	0.715333	−	0.698783i	$-0.246275\pi$
$887$	−5.07195	−	6.98094i	−0.170299	−	0.234397i	−0.885633	+	0.464386i	$0.846275\pi$
$888$	−1.05572	−	1.45308i	−0.0354277	−	0.0487621i
$889$	−21.4335	−	15.5723i	−0.718855	−	0.522279i
$890$		0			0
$891$	19.7909	−	14.3790i	0.663022	−	0.481713i
$892$	−4.78254	−	1.55394i	−0.160131	−	0.0520299i
$893$			3.91861i			0.131131i
$894$	−2.21701	+	6.82325i	−0.0741479	+	0.228204i
$895$		0			0
$896$	−0.857358	−	2.63868i	−0.0286423	−	0.0881520i
$897$	6.06449	−	1.97047i	0.202487	−	0.0657921i
$898$	21.8438	−	30.0654i	0.728936	−	1.00329i
$899$	29.1975			0.973790
$900$		0			0
$901$	−2.71286			−0.0903784
$902$	14.8520	−	20.4420i	0.494516	−	0.680643i
$903$	−41.8370	+	13.5937i	−1.39225	+	0.452368i
$904$	1.97012	+	6.06342i	0.0655253	+	0.201666i
$905$		0			0
$906$	−0.175686	+	0.540707i	−0.00583679	+	0.0179638i
$907$			29.5085i			0.979815i	0.871774	+	0.489907i	$0.162969\pi$
$907$			29.5085i			0.979815i	−0.871774	+	0.489907i	$0.837031\pi$
$908$	16.9652	+	5.51232i	0.563009	+	0.182933i
$909$	0.382196	−	0.277682i	0.0126766	−	0.00921012i
$910$		0			0
$911$	31.0734	+	22.5761i	1.02951	+	0.747981i	0.968210	−	0.250139i	$-0.0804763\pi$
$911$	31.0734	+	22.5761i	1.02951	+	0.747981i	0.0612971	+	0.998120i	$0.480476\pi$
$912$	−1.42352	−	1.95931i	−0.0471374	−	0.0648791i
$913$	7.62563	+	10.4958i	0.252372	+	0.347360i
$914$	23.7155	+	17.2303i	0.784438	+	0.569928i
$915$		0			0
$916$	17.4397	−	12.6707i	0.576223	−	0.418651i
$917$	−14.7746	−	4.80055i	−0.487899	−	0.158528i
$918$			27.0538i			0.892907i
$919$	−12.8831	+	39.6500i	−0.424974	+	1.30793i	0.478046	+	0.878335i	$0.341345\pi$
$919$	−12.8831	+	39.6500i	−0.424974	+	1.30793i	−0.903020	+	0.429600i	$0.858655\pi$
$920$		0			0
$921$	13.2999	+	40.9329i	0.438247	+	1.34879i
$922$	−8.47145	+	2.75254i	−0.278992	+	0.0906501i
$923$	44.2081	−	60.8473i	1.45513	−	2.00281i
$924$	13.1993			0.434225
$925$		0			0
$926$	−18.2771			−0.600624
$927$	−0.275149	+	0.378710i	−0.00903709	+	0.0124385i
$928$	3.89618	−	1.26594i	0.127898	−	0.0415567i
$929$	−8.68484	−	26.7292i	−0.284940	−	0.876956i	−0.986417	−	0.164263i	$-0.947475\pi$
$929$	−8.68484	−	26.7292i	−0.284940	−	0.876956i	0.701476	−	0.712693i	$-0.252525\pi$
$930$		0			0
$931$	0.304498	−	0.937148i	0.00997952	−	0.0307138i
$932$			14.7065i			0.481726i
$933$	−1.17960	−	0.383274i	−0.0386183	−	0.0125478i
$934$	−29.6780	+	21.5624i	−0.971095	+	0.705542i
$935$		0			0
$936$	0.274467	+	0.199412i	0.00897124	+	0.00651799i
$937$	7.56796	+	10.4164i	0.247234	+	0.340289i	0.914540	−	0.404495i	$-0.132553\pi$
$937$	7.56796	+	10.4164i	0.247234	+	0.340289i	−0.667306	+	0.744784i	$0.732553\pi$
$938$	7.05056	+	9.70427i	0.230209	+	0.316856i
$939$	29.9868	+	21.7867i	0.978583	+	0.710982i
$940$		0			0
$941$	−8.21234	+	5.96661i	−0.267714	+	0.194506i	−0.713541	−	0.700613i	$-0.752910\pi$
$941$	−8.21234	+	5.96661i	−0.267714	+	0.194506i	0.445827	+	0.895119i	$0.352910\pi$
$942$	5.88308	+	1.91153i	0.191681	+	0.0622809i
$943$			5.96489i			0.194243i
$944$	1.16872	−	3.59695i	0.0380386	−	0.117071i
$945$		0			0
$946$	7.92764	+	24.3988i	0.257750	+	0.793273i
$947$	54.5669	−	17.7298i	1.77318	−	0.576143i	0.774760	−	0.632255i	$-0.217871\pi$
$947$	54.5669	−	17.7298i	1.77318	−	0.576143i	0.998424	+	0.0561124i	$0.0178705\pi$
$948$	9.97963	−	13.7358i	0.324123	−	0.446118i
$949$	−23.9219			−0.776538
$950$		0			0
$951$	−32.2944			−1.04722
$952$	−8.40906	+	11.5741i	−0.272539	+	0.375118i
$953$	4.91947	−	1.59843i	0.159357	−	0.0517784i	−0.228252	−	0.973602i	$-0.573301\pi$
$953$	4.91947	−	1.59843i	0.159357	−	0.0517784i	0.387609	+	0.921824i	$0.373301\pi$
$954$	−0.00971435	−	0.0298977i	−0.000314514	−	0.000967974i
$955$		0			0
$956$	2.14465	−	6.60057i	0.0693631	−	0.213478i
$957$			19.4896i			0.630010i
$958$	11.9736	+	3.89046i	0.386849	+	0.125695i
$959$	−17.9211	+	13.0205i	−0.578704	+	0.420453i
$960$		0			0
$961$	−16.0149	−	11.6355i	−0.516611	−	0.375340i
$962$	3.49572	+	4.81145i	0.112707	+	0.155127i
$963$	0.359010	+	0.494135i	0.0115689	+	0.0159233i
$964$	2.67787	+	1.94559i	0.0862484	+	0.0626631i
$965$		0			0
$966$	−2.52084	+	1.83150i	−0.0811068	+	0.0589275i
$967$	−39.3718	−	12.7927i	−1.26611	−	0.411384i	−0.402443	−	0.915445i	$-0.631839\pi$
$967$	−39.3718	−	12.7927i	−1.26611	−	0.411384i	−0.863668	+	0.504061i	$0.831839\pi$
$968$			3.30233i			0.106141i
$969$	−3.85901	+	11.8768i	−0.123969	+	0.381539i
$970$		0			0
$971$	13.3139	+	40.9761i	0.427265	+	1.31499i	0.900809	+	0.434216i	$0.142975\pi$
$971$	13.3139	+	40.9761i	0.427265	+	1.31499i	−0.473544	+	0.880770i	$0.657025\pi$
$972$	−0.590483	+	0.191859i	−0.0189397	+	0.00615389i
$973$	−36.0216	+	49.5795i	−1.15480	+	1.58944i
$974$	18.3256			0.587189
$975$		0			0
$976$	−10.8325			−0.346739
$977$	23.7826	−	32.7340i	0.760874	−	1.04725i	−0.236267	−	0.971688i	$-0.575924\pi$
$977$	23.7826	−	32.7340i	0.760874	−	1.04725i	0.997141	−	0.0755652i	$-0.0240761\pi$
$978$	8.30700	−	2.69911i	0.265628	−	0.0863079i
$979$	7.87398	+	24.2336i	0.251654	+	0.774510i
$980$		0			0
$981$	−0.0722128	+	0.222248i	−0.00230558	+	0.00709584i
$982$			21.7047i			0.692625i
$983$	−38.4023	−	12.4777i	−1.22484	−	0.397976i	−0.376000	−	0.926620i	$-0.622701\pi$
$983$	−38.4023	−	12.4777i	−1.22484	−	0.397976i	−0.848844	+	0.528644i	$0.822701\pi$
$984$	12.6338	−	9.17902i	0.402752	−	0.292616i
$985$		0			0
$986$	−17.0899	−	12.4165i	−0.544253	−	0.395423i
$987$	−7.75836	−	10.6785i	−0.246951	−	0.339899i
$988$	4.71358	+	6.48768i	0.149959	+	0.206401i
$989$	−4.89955	−	3.55973i	−0.155797	−	0.113193i
$990$		0			0
$991$	47.0391	−	34.1759i	1.49424	−	1.08563i	0.521641	−	0.853165i	$-0.325320\pi$
$991$	47.0391	−	34.1759i	1.49424	−	1.08563i	0.972604	−	0.232467i	$-0.0746798\pi$
$992$	−6.77827	−	2.20239i	−0.215210	−	0.0699261i
$993$		−	28.9374i		−	0.918300i
$994$	−11.3571	+	34.9535i	−0.360225	+	1.10866i
$995$		0			0
$996$	2.47772	+	7.62563i	0.0785095	+	0.241627i
$997$	−37.3735	+	12.1434i	−1.18363	+	0.384585i	−0.833714	−	0.552197i	$-0.813790\pi$
$997$	−37.3735	+	12.1434i	−1.18363	+	0.384585i	−0.349916	+	0.936781i	$0.613790\pi$
$998$	−9.30998	+	12.8141i	−0.294702	+	0.405623i
$999$	−5.49563			−0.173874

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.c.49.4		16
5.2	odd	4		250.2.d.d.201.1		8
5.3	odd	4		50.2.d.b.41.2	yes	8
5.4	even	2	inner	250.2.e.c.49.1		16
15.8	even	4		450.2.h.e.91.1		8
20.3	even	4		400.2.u.d.241.1		8
25.2	odd	20		250.2.d.d.51.1		8
25.6	even	5		1250.2.b.e.1249.6		8
25.8	odd	20		1250.2.a.l.1.3		4
25.11	even	5	inner	250.2.e.c.199.1		16
25.14	even	10	inner	250.2.e.c.199.4		16
25.17	odd	20		1250.2.a.f.1.2		4
25.19	even	10		1250.2.b.e.1249.3		8
25.23	odd	20		50.2.d.b.11.2	✓	8
75.23	even	20		450.2.h.e.361.1		8
100.23	even	20		400.2.u.d.161.1		8
100.67	even	20		10000.2.a.x.1.3		4
100.83	even	20		10000.2.a.t.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.2	✓	8	25.23	odd	20
50.2.d.b.41.2	yes	8	5.3	odd	4
250.2.d.d.51.1		8	25.2	odd	20
250.2.d.d.201.1		8	5.2	odd	4
250.2.e.c.49.1		16	5.4	even	2	inner
250.2.e.c.49.4		16	1.1	even	1	trivial
250.2.e.c.199.1		16	25.11	even	5	inner
250.2.e.c.199.4		16	25.14	even	10	inner
400.2.u.d.161.1		8	100.23	even	20
400.2.u.d.241.1		8	20.3	even	4
450.2.h.e.91.1		8	15.8	even	4
450.2.h.e.361.1		8	75.23	even	20
1250.2.a.f.1.2		4	25.17	odd	20
1250.2.a.l.1.3		4	25.8	odd	20
1250.2.b.e.1249.3		8	25.19	even	10
1250.2.b.e.1249.6		8	25.6	even	5
10000.2.a.t.1.2		4	100.83	even	20
10000.2.a.x.1.3		4	100.67	even	20

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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

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	250.2.e.c.49.4

Level	$250$
Weight	$2$
Character	250.49
Analytic conductor	$1.996$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$