LMFDB - Embedded newform 3150.2.bf.e.1151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.3
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.e.1601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +(0.570938 + 0.329631i) q^{11} -6.13514i q^{13} +(-1.05841 - 2.42482i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.43678 - 4.22062i) q^{17} +(-6.30208 + 3.63851i) q^{19} -0.659263 q^{22} +(3.98266 - 2.29939i) q^{23} +(3.06757 + 5.31319i) q^{26} +(2.12902 + 1.57075i) q^{28} +8.09526i q^{29} +(0.759345 + 0.438408i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.87356i q^{34} +(-5.05533 - 8.75609i) q^{37} +(3.63851 - 6.30208i) q^{38} -6.25234 q^{41} -9.03582 q^{43} +(0.570938 - 0.329631i) q^{44} +(-2.29939 + 3.98266i) q^{46} +(6.00136 + 10.3947i) q^{47} +(-6.82500 - 1.55542i) q^{49} +(-5.31319 - 3.06757i) q^{52} +(-10.5749 - 6.10540i) q^{53} +(-2.62916 - 0.295801i) q^{56} +(-4.04763 - 7.01070i) q^{58} +(4.06613 - 7.04274i) q^{59} +(-0.0618764 + 0.0357243i) q^{61} -0.876816 q^{62} -1.00000 q^{64} +(-0.666965 + 1.15522i) q^{67} +(-2.43678 - 4.22062i) q^{68} +2.60701i q^{71} +(-2.44571 - 1.41203i) q^{73} +(8.75609 + 5.05533i) q^{74} +7.27702i q^{76} +(-1.03554 + 1.40359i) q^{77} +(-2.88837 - 5.00280i) q^{79} +(5.41468 - 3.12617i) q^{82} +7.44660 q^{83} +(7.82525 - 4.51791i) q^{86} +(-0.329631 + 0.570938i) q^{88} +(-2.66489 - 4.61572i) q^{89} +(16.1303 + 1.81478i) q^{91} -4.59878i q^{92} +(-10.3947 - 6.00136i) q^{94} +11.4792i q^{97} +(6.68833 - 2.06547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 4 * q^7	$ 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.295801	+	2.62916i	−0.111802	+	0.993730i
$7$	−0.295801	+	2.62916i	−0.111802	+	0.993730i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	0.570938	+	0.329631i	0.172144	+	0.0993876i	0.583597	−	0.812044i	$-0.301645\pi$
$11$	0.570938	+	0.329631i	0.172144	+	0.0993876i	−0.411452	+	0.911431i	$0.634978\pi$
$12$		0			0
$13$		−	6.13514i		−	1.70158i	−0.525504	−	0.850791i	$-0.676123\pi$
$13$		−	6.13514i		−	1.70158i	0.525504	−	0.850791i	$-0.323877\pi$
$14$	−1.05841	−	2.42482i	−0.282872	−	0.648061i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.43678	−	4.22062i	0.591005	−	1.02365i	−0.403092	−	0.915160i	$-0.632064\pi$
$17$	2.43678	−	4.22062i	0.591005	−	1.02365i	0.994097	−	0.108492i	$-0.0346022\pi$
$18$		0			0
$19$	−6.30208	+	3.63851i	−1.44580	+	0.834732i	−0.998227	−	0.0595173i	$-0.981044\pi$
$19$	−6.30208	+	3.63851i	−1.44580	+	0.834732i	−0.447570	+	0.894249i	$0.647711\pi$
$20$		0			0
$21$		0			0
$22$	−0.659263			−0.140555
$23$	3.98266	−	2.29939i	0.830442	−	0.479456i	−0.0235617	−	0.999722i	$-0.507501\pi$
$23$	3.98266	−	2.29939i	0.830442	−	0.479456i	0.854004	+	0.520266i	$0.174167\pi$
$24$		0			0
$25$		0			0
$26$	3.06757	+	5.31319i	0.601600	+	1.04200i
$27$		0			0
$28$	2.12902	+	1.57075i	0.402347	+	0.296844i
$29$			8.09526i			1.50325i	0.659589	+	0.751626i	$0.270730\pi$
$29$			8.09526i			1.50325i	−0.659589	+	0.751626i	$0.729270\pi$
$30$		0			0
$31$	0.759345	+	0.438408i	0.136382	+	0.0787404i	0.566639	−	0.823966i	$-0.308243\pi$
$31$	0.759345	+	0.438408i	0.136382	+	0.0787404i	−0.430256	+	0.902707i	$0.641577\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			4.87356i			0.835808i
$35$		0			0
$36$		0			0
$37$	−5.05533	−	8.75609i	−0.831092	−	1.43949i	−0.897173	−	0.441679i	$-0.854383\pi$
$37$	−5.05533	−	8.75609i	−0.831092	−	1.43949i	0.0660818	−	0.997814i	$-0.478950\pi$
$38$	3.63851	−	6.30208i	0.590244	−	1.02233i
$39$		0			0
$40$		0			0
$41$	−6.25234			−0.976451			−0.488226	−	0.872717i	$-0.662356\pi$
$41$	−6.25234			−0.976451			−0.488226	+	0.872717i	$0.662356\pi$
$42$		0			0
$43$	−9.03582			−1.37795			−0.688975	−	0.724785i	$-0.741939\pi$
$43$	−9.03582			−1.37795			−0.688975	+	0.724785i	$0.741939\pi$
$44$	0.570938	−	0.329631i	0.0860722	−	0.0496938i
$45$		0			0
$46$	−2.29939	+	3.98266i	−0.339027	+	0.587211i
$47$	6.00136	+	10.3947i	0.875388	+	1.51622i	0.856349	+	0.516397i	$0.172727\pi$
$47$	6.00136	+	10.3947i	0.875388	+	1.51622i	0.0190383	+	0.999819i	$0.493940\pi$
$48$		0			0
$49$	−6.82500	−	1.55542i	−0.975001	−	0.222202i
$50$		0			0
$51$		0			0
$52$	−5.31319	−	3.06757i	−0.736807	−	0.425396i
$53$	−10.5749	−	6.10540i	−1.45257	−	0.838641i	−0.453943	−	0.891031i	$-0.649983\pi$
$53$	−10.5749	−	6.10540i	−1.45257	−	0.838641i	−0.998627	+	0.0523897i	$0.983316\pi$
$54$		0			0
$55$		0			0
$56$	−2.62916	−	0.295801i	−0.351337	−	0.0395280i
$57$		0			0
$58$	−4.04763	−	7.01070i	−0.531480	−	0.920550i
$59$	4.06613	−	7.04274i	0.529365	−	0.916887i	−0.470049	−	0.882640i	$-0.655764\pi$
$59$	4.06613	−	7.04274i	0.529365	−	0.916887i	0.999413	−	0.0342461i	$-0.0109030\pi$
$60$		0			0
$61$	−0.0618764	+	0.0357243i	−0.00792246	+	0.00457403i	−0.503956	−	0.863729i	$-0.668123\pi$
$61$	−0.0618764	+	0.0357243i	−0.00792246	+	0.00457403i	0.496034	+	0.868303i	$0.334789\pi$
$62$	−0.876816			−0.111356
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−0.666965	+	1.15522i	−0.0814827	+	0.141132i	−0.903887	−	0.427771i	$-0.859299\pi$
$67$	−0.666965	+	1.15522i	−0.0814827	+	0.141132i	0.822404	+	0.568903i	$0.192632\pi$
$68$	−2.43678	−	4.22062i	−0.295503	−	0.511826i
$69$		0			0
$70$		0			0
$71$			2.60701i			0.309395i	0.987962	+	0.154697i	$0.0494402\pi$
$71$			2.60701i			0.309395i	−0.987962	+	0.154697i	$0.950560\pi$
$72$		0			0
$73$	−2.44571	−	1.41203i	−0.286249	−	0.165266i	0.350000	−	0.936750i	$-0.386181\pi$
$73$	−2.44571	−	1.41203i	−0.286249	−	0.165266i	−0.636249	+	0.771484i	$0.719515\pi$
$74$	8.75609	+	5.05533i	1.01788	+	0.587670i
$75$		0			0
$76$			7.27702i			0.834732i
$77$	−1.03554	+	1.40359i	−0.118011	+	0.159953i
$78$		0			0
$79$	−2.88837	−	5.00280i	−0.324967	−	0.562859i	0.656539	−	0.754292i	$-0.272020\pi$
$79$	−2.88837	−	5.00280i	−0.324967	−	0.562859i	−0.981506	+	0.191433i	$0.938686\pi$
$80$		0			0
$81$		0			0
$82$	5.41468	−	3.12617i	0.597952	−	0.345228i
$83$	7.44660			0.817370			0.408685	−	0.912675i	$-0.365987\pi$
$83$	7.44660			0.817370			0.408685	+	0.912675i	$0.365987\pi$
$84$		0			0
$85$		0			0
$86$	7.82525	−	4.51791i	0.843819	−	0.487179i
$87$		0			0
$88$	−0.329631	+	0.570938i	−0.0351388	+	0.0608622i
$89$	−2.66489	−	4.61572i	−0.282478	−	0.489266i	0.689517	−	0.724270i	$-0.257823\pi$
$89$	−2.66489	−	4.61572i	−0.282478	−	0.489266i	−0.971994	+	0.235004i	$0.924490\pi$
$90$		0			0
$91$	16.1303	+	1.81478i	1.69091	+	0.190241i
$92$		−	4.59878i		−	0.479456i
$93$		0			0
$94$	−10.3947	−	6.00136i	−1.07213	−	0.618993i
$95$		0			0
$96$		0			0
$97$			11.4792i			1.16553i	0.812640	+	0.582766i	$0.198030\pi$
$97$			11.4792i			1.16553i	−0.812640	+	0.582766i	$0.801970\pi$
$98$	6.68833	−	2.06547i	0.675624	−	0.208644i
$99$		0			0
$100$		0			0
$101$	−7.74874	+	13.4212i	−0.771029	+	1.33546i	0.165971	+	0.986131i	$0.446924\pi$
$101$	−7.74874	+	13.4212i	−0.771029	+	1.33546i	−0.937000	+	0.349330i	$0.886409\pi$
$102$		0			0
$103$	−1.79131	+	1.03422i	−0.176503	+	0.101904i	−0.585649	−	0.810565i	$-0.699160\pi$
$103$	−1.79131	+	1.03422i	−0.176503	+	0.101904i	0.409145	+	0.912469i	$0.365827\pi$
$104$	6.13514			0.601600
$105$		0			0
$106$	12.2108			1.18602
$107$	9.43331	−	5.44632i	0.911953	−	0.526516i	0.0308937	−	0.999523i	$-0.490165\pi$
$107$	9.43331	−	5.44632i	0.911953	−	0.526516i	0.881059	+	0.473007i	$0.156831\pi$
$108$		0			0
$109$	7.17254	−	12.4232i	0.687005	−	1.18993i	−0.285797	−	0.958290i	$-0.592258\pi$
$109$	7.17254	−	12.4232i	0.687005	−	1.18993i	0.972802	−	0.231637i	$-0.0744082\pi$
$110$		0			0
$111$		0			0
$112$	2.42482	−	1.05841i	0.229124	−	0.100010i
$113$		−	11.9081i		−	1.12022i	−0.828420	−	0.560108i	$-0.810760\pi$
$113$		−	11.9081i		−	1.12022i	0.828420	−	0.560108i	$-0.189240\pi$
$114$		0			0
$115$		0			0
$116$	7.01070	+	4.04763i	0.650927	+	0.375813i
$117$		0			0
$118$			8.13225i			0.748635i
$119$	10.3759	+	7.65515i	0.951158	+	0.701747i
$120$		0			0
$121$	−5.28269	−	9.14988i	−0.480244	−	0.831807i
$122$	0.0357243	−	0.0618764i	0.00323433	−	0.00560202i
$123$		0			0
$124$	0.759345	−	0.438408i	0.0681912	−	0.0393702i
$125$		0			0
$126$		0			0
$127$	−14.6264			−1.29788			−0.648941	−	0.760839i	$-0.724788\pi$
$127$	−14.6264			−1.29788			−0.648941	+	0.760839i	$0.724788\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−1.64037	−	2.84120i	−0.143320	−	0.248237i	0.785425	−	0.618957i	$-0.212444\pi$
$131$	−1.64037	−	2.84120i	−0.143320	−	0.248237i	−0.928745	+	0.370720i	$0.879111\pi$
$132$		0			0
$133$	−7.70208	−	17.6455i	−0.667855	−	1.53006i
$134$		−	1.33393i		−	0.115234i
$135$		0			0
$136$	4.22062	+	2.43678i	0.361915	+	0.208952i
$137$	−3.03168	−	1.75034i	−0.259014	−	0.149542i	0.364871	−	0.931058i	$-0.381113\pi$
$137$	−3.03168	−	1.75034i	−0.259014	−	0.149542i	−0.623885	+	0.781516i	$0.714447\pi$
$138$		0			0
$139$		−	1.78031i		−	0.151004i	−0.997146	−	0.0755021i	$-0.975944\pi$
$139$		−	1.78031i		−	0.151004i	0.997146	−	0.0755021i	$-0.0240560\pi$
$140$		0			0
$141$		0			0
$142$	−1.30350	−	2.25773i	−0.109388	−	0.189465i
$143$	2.02234	−	3.50279i	0.169116	−	0.292918i
$144$		0			0
$145$		0			0
$146$	2.82406			0.233721
$147$		0			0
$148$	−10.1107			−0.831092
$149$	7.14910	−	4.12754i	0.585677	−	0.338141i	−0.177709	−	0.984083i	$-0.556869\pi$
$149$	7.14910	−	4.12754i	0.585677	−	0.338141i	0.763386	+	0.645942i	$0.223535\pi$
$150$		0			0
$151$	−0.463545	+	0.802883i	−0.0377227	+	0.0653377i	−0.884270	−	0.466975i	$-0.845344\pi$
$151$	−0.463545	+	0.802883i	−0.0377227	+	0.0653377i	0.846548	+	0.532313i	$0.178677\pi$
$152$	−3.63851	−	6.30208i	−0.295122	−	0.511167i
$153$		0			0
$154$	0.195010	−	1.73331i	0.0157144	−	0.139674i
$155$		0			0
$156$		0			0
$157$	−7.22480	−	4.17124i	−0.576602	−	0.332901i	0.183180	−	0.983079i	$-0.441361\pi$
$157$	−7.22480	−	4.17124i	−0.576602	−	0.332901i	−0.759782	+	0.650178i	$0.774694\pi$
$158$	5.00280	+	2.88837i	0.398001	+	0.229786i
$159$		0			0
$160$		0			0
$161$	4.86740	+	11.1512i	0.383605	+	0.878840i
$162$		0			0
$163$	−12.1525	−	21.0488i	−0.951858	−	1.64867i	−0.741400	−	0.671064i	$-0.765838\pi$
$163$	−12.1525	−	21.0488i	−0.951858	−	1.64867i	−0.210458	−	0.977603i	$-0.567496\pi$
$164$	−3.12617	+	5.41468i	−0.244113	+	0.422816i
$165$		0			0
$166$	−6.44894	+	3.72330i	−0.500535	+	0.288984i
$167$	7.48724			0.579380			0.289690	−	0.957120i	$-0.406448\pi$
$167$	7.48724			0.579380			0.289690	+	0.957120i	$0.406448\pi$
$168$		0			0
$169$	−24.6400			−1.89538
$170$		0			0
$171$		0			0
$172$	−4.51791	+	7.82525i	−0.344487	+	0.596670i
$173$	−7.12036	−	12.3328i	−0.541351	−	0.937647i	−0.998827	−	0.0484252i	$-0.984580\pi$
$173$	−7.12036	−	12.3328i	−0.541351	−	0.937647i	0.457476	−	0.889222i	$-0.348754\pi$
$174$		0			0
$175$		0			0
$176$		−	0.659263i		−	0.0496938i
$177$		0			0
$178$	4.61572	+	2.66489i	0.345963	+	0.199742i
$179$	−11.3826	−	6.57176i	−0.850777	−	0.491196i	0.0101362	−	0.999949i	$-0.496774\pi$
$179$	−11.3826	−	6.57176i	−0.850777	−	0.491196i	−0.860913	+	0.508752i	$0.830107\pi$
$180$		0			0
$181$			6.34537i			0.471648i	0.971796	+	0.235824i	$0.0757788\pi$
$181$			6.34537i			0.471648i	−0.971796	+	0.235824i	$0.924221\pi$
$182$	−14.8766	+	6.49350i	−1.10273	+	0.481331i
$183$		0			0
$184$	2.29939	+	3.98266i	0.169513	+	0.293606i
$185$		0			0
$186$		0			0
$187$	2.78250	−	1.60648i	0.203477	−	0.117477i
$188$	12.0027			0.875388
$189$		0			0
$190$		0			0
$191$	−18.8926	+	10.9077i	−1.36702	+	0.789251i	−0.990547	−	0.137175i	$-0.956198\pi$
$191$	−18.8926	+	10.9077i	−1.36702	+	0.789251i	−0.376477	+	0.926426i	$0.622865\pi$
$192$		0			0
$193$	−1.20933	+	2.09462i	−0.0870495	+	0.150774i	−0.906263	−	0.422715i	$-0.861077\pi$
$193$	−1.20933	+	2.09462i	−0.0870495	+	0.150774i	0.819213	+	0.573489i	$0.194411\pi$
$194$	−5.73958	−	9.94125i	−0.412078	−	0.713740i
$195$		0			0
$196$	−4.75953	+	5.13292i	−0.339967	+	0.366637i
$197$			6.24457i			0.444907i	0.974943	+	0.222454i	$0.0714066\pi$
$197$			6.24457i			0.444907i	−0.974943	+	0.222454i	$0.928593\pi$
$198$		0			0
$199$	−4.38388	−	2.53103i	−0.310765	−	0.179420i	0.336504	−	0.941682i	$-0.390756\pi$
$199$	−4.38388	−	2.53103i	−0.310765	−	0.179420i	−0.647269	+	0.762262i	$0.724089\pi$
$200$		0			0
$201$		0			0
$202$		−	15.4975i		−	1.09040i
$203$	−21.2838	−	2.39458i	−1.49383	−	0.168067i
$204$		0			0
$205$		0			0
$206$	1.03422	−	1.79131i	0.0720572	−	0.124807i
$207$		0			0
$208$	−5.31319	+	3.06757i	−0.368403	+	0.212698i
$209$	−4.79747			−0.331848
$210$		0			0
$211$	5.72168			0.393896			0.196948	−	0.980414i	$-0.436897\pi$
$211$	5.72168			0.393896			0.196948	+	0.980414i	$0.436897\pi$
$212$	−10.5749	+	6.10540i	−0.726285	+	0.419321i
$213$		0			0
$214$	−5.44632	+	9.43331i	−0.372303	+	0.644848i
$215$		0			0
$216$		0			0
$217$	−1.37726	+	1.86676i	−0.0934946	+	0.126724i
$218$			14.3451i			0.971572i
$219$		0			0
$220$		0			0
$221$	−25.8941	−	14.9500i	−1.74183	−	1.00564i
$222$		0			0
$223$			6.61006i			0.442642i	0.975201	+	0.221321i	$0.0710369\pi$
$223$			6.61006i			0.442642i	−0.975201	+	0.221321i	$0.928963\pi$
$224$	−1.57075	+	2.12902i	−0.104950	+	0.142251i
$225$		0			0
$226$	5.95403	+	10.3127i	0.396056	+	0.685989i
$227$	12.0278	−	20.8328i	0.798314	−	1.38272i	−0.122400	−	0.992481i	$-0.539059\pi$
$227$	12.0278	−	20.8328i	0.798314	−	1.38272i	0.920714	−	0.390239i	$-0.127608\pi$
$228$		0			0
$229$	−4.39811	+	2.53925i	−0.290635	+	0.167798i	−0.638228	−	0.769847i	$-0.720332\pi$
$229$	−4.39811	+	2.53925i	−0.290635	+	0.167798i	0.347593	+	0.937645i	$0.386999\pi$
$230$		0			0
$231$		0			0
$232$	−8.09526			−0.531480
$233$	19.1195	−	11.0386i	1.25256	−	0.723165i	0.280941	−	0.959725i	$-0.409353\pi$
$233$	19.1195	−	11.0386i	1.25256	−	0.723165i	0.971617	+	0.236560i	$0.0760201\pi$
$234$		0			0
$235$		0			0
$236$	−4.06613	−	7.04274i	−0.264682	−	0.458443i
$237$		0			0
$238$	−12.8134	−	1.44160i	−0.830568	−	0.0934451i
$239$		−	17.8556i		−	1.15498i	−0.816398	−	0.577490i	$-0.804032\pi$
$239$		−	17.8556i		−	1.15498i	0.816398	−	0.577490i	$-0.195968\pi$
$240$		0			0
$241$	18.8401	+	10.8773i	1.21360	+	0.700670i	0.963541	−	0.267562i	$-0.0862179\pi$
$241$	18.8401	+	10.8773i	1.21360	+	0.700670i	0.250055	+	0.968232i	$0.419551\pi$
$242$	9.14988	+	5.28269i	0.588177	+	0.339584i
$243$		0			0
$244$			0.0714487i			0.00457403i
$245$		0			0
$246$		0			0
$247$	22.3228	+	38.6642i	1.42036	+	2.46014i
$248$	−0.438408	+	0.759345i	−0.0278390	+	0.0482185i
$249$		0			0
$250$		0			0
$251$	−16.0445			−1.01272			−0.506361	−	0.862321i	$-0.669010\pi$
$251$	−16.0445			−1.01272			−0.506361	+	0.862321i	$0.669010\pi$
$252$		0			0
$253$	3.03181			0.190608
$254$	12.6668	−	7.31319i	0.794787	−	0.458870i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.23399	−	14.2617i	−0.513622	−	0.889620i	−0.999875	−	0.0158016i	$-0.994970\pi$
$257$	−8.23399	−	14.2617i	−0.513622	−	0.889620i	0.486253	−	0.873818i	$-0.338363\pi$
$258$		0			0
$259$	24.5166	−	10.7012i	1.52339	−	0.664943i
$260$		0			0
$261$		0			0
$262$	2.84120	+	1.64037i	0.175530	+	0.101342i
$263$	4.86760	+	2.81031i	0.300149	+	0.173291i	0.642510	−	0.766278i	$-0.277893\pi$
$263$	4.86760	+	2.81031i	0.300149	+	0.173291i	−0.342361	+	0.939569i	$0.611227\pi$
$264$		0			0
$265$		0			0
$266$	15.4929	+	11.4304i	0.949933	+	0.700843i
$267$		0			0
$268$	0.666965	+	1.15522i	0.0407414	+	0.0705661i
$269$	3.27081	−	5.66521i	0.199425	−	0.345414i	−0.748917	−	0.662664i	$-0.769426\pi$
$269$	3.27081	−	5.66521i	0.199425	−	0.345414i	0.948342	+	0.317249i	$0.102759\pi$
$270$		0			0
$271$	−16.0238	+	9.25135i	−0.973377	+	0.561980i	−0.900264	−	0.435344i	$-0.856627\pi$
$271$	−16.0238	+	9.25135i	−0.973377	+	0.561980i	−0.0731130	+	0.997324i	$0.523293\pi$
$272$	−4.87356			−0.295503
$273$		0			0
$274$	3.50069			0.211484
$275$		0			0
$276$		0			0
$277$	12.9572	−	22.4426i	0.778525	−	1.34844i	−0.154267	−	0.988029i	$-0.549302\pi$
$277$	12.9572	−	22.4426i	0.778525	−	1.34844i	0.932792	−	0.360415i	$-0.117365\pi$
$278$	0.890157	+	1.54180i	0.0533881	+	0.0924708i
$279$		0			0
$280$		0			0
$281$		−	9.24160i		−	0.551308i	−0.961257	−	0.275654i	$-0.911106\pi$
$281$		−	9.24160i		−	0.551308i	0.961257	−	0.275654i	$-0.0888943\pi$
$282$		0			0
$283$	−6.14531	−	3.54800i	−0.365301	−	0.210907i	0.306103	−	0.951999i	$-0.400975\pi$
$283$	−6.14531	−	3.54800i	−0.365301	−	0.210907i	−0.671404	+	0.741092i	$0.734308\pi$
$284$	2.25773	+	1.30350i	0.133972	+	0.0773486i
$285$		0			0
$286$			4.04467i			0.239166i
$287$	1.84944	−	16.4384i	0.109169	−	0.970329i
$288$		0			0
$289$	−3.37577	−	5.84701i	−0.198575	−	0.343942i
$290$		0			0
$291$		0			0
$292$	−2.44571	+	1.41203i	−0.143124	+	0.0826328i
$293$	8.94657			0.522664			0.261332	−	0.965249i	$-0.415838\pi$
$293$	8.94657			0.522664			0.261332	+	0.965249i	$0.415838\pi$
$294$		0			0
$295$		0			0
$296$	8.75609	−	5.05533i	0.508938	−	0.293835i
$297$		0			0
$298$	−4.12754	+	7.14910i	−0.239102	+	0.414136i
$299$	−14.1071	−	24.4342i	−0.815834	−	1.41307i
$300$		0			0
$301$	2.67280	−	23.7567i	0.154058	−	1.36931i
$302$		−	0.927090i		−	0.0533480i
$303$		0			0
$304$	6.30208	+	3.63851i	0.361449	+	0.208683i
$305$		0			0
$306$		0			0
$307$		−	7.62584i		−	0.435230i	−0.976035	−	0.217615i	$-0.930172\pi$
$307$		−	7.62584i		−	0.435230i	0.976035	−	0.217615i	$-0.0698276\pi$
$308$	0.697771	+	1.59860i	0.0397592	+	0.0910884i
$309$		0			0
$310$		0			0
$311$	−3.20348	+	5.54859i	−0.181653	+	0.314632i	−0.942443	−	0.334366i	$-0.891478\pi$
$311$	−3.20348	+	5.54859i	−0.181653	+	0.314632i	0.760791	+	0.648997i	$0.224811\pi$
$312$		0			0
$313$	−7.84360	+	4.52850i	−0.443346	+	0.255966i	−0.705016	−	0.709191i	$-0.749060\pi$
$313$	−7.84360	+	4.52850i	−0.443346	+	0.255966i	0.261670	+	0.965157i	$0.415727\pi$
$314$	8.34248			0.470793
$315$		0			0
$316$	−5.77674			−0.324967
$317$	−24.6876	+	14.2534i	−1.38660	+	0.800552i	−0.992930	−	0.118702i	$-0.962127\pi$
$317$	−24.6876	+	14.2534i	−1.38660	+	0.800552i	−0.393666	+	0.919253i	$0.628793\pi$
$318$		0			0
$319$	−2.66845	+	4.62189i	−0.149405	+	0.258776i
$320$		0			0
$321$		0			0
$322$	−9.79091	−	7.22355i	−0.545626	−	0.402553i
$323$			35.4650i			1.97332i
$324$		0			0
$325$		0			0
$326$	21.0488	+	12.1525i	1.16578	+	0.673065i
$327$		0			0
$328$		−	6.25234i		−	0.345228i
$329$	−29.1044	+	12.7038i	−1.60458	+	0.700383i
$330$		0			0
$331$	−7.53535	−	13.0516i	−0.414180	−	0.717381i	0.581162	−	0.813788i	$-0.302598\pi$
$331$	−7.53535	−	13.0516i	−0.414180	−	0.717381i	−0.995342	+	0.0964068i	$0.969265\pi$
$332$	3.72330	−	6.44894i	0.204343	−	0.353932i
$333$		0			0
$334$	−6.48414	+	3.74362i	−0.354797	+	0.204842i
$335$		0			0
$336$		0			0
$337$	−0.480936			−0.0261983			−0.0130991	−	0.999914i	$-0.504170\pi$
$337$	−0.480936			−0.0261983			−0.0130991	+	0.999914i	$0.504170\pi$
$338$	21.3389	−	12.3200i	1.16068	−	0.670119i
$339$		0			0
$340$		0			0
$341$	0.289026	+	0.500608i	0.0156516	+	0.0271094i
$342$		0			0
$343$	6.10828	−	17.4840i	0.329816	−	0.944045i
$344$		−	9.03582i		−	0.487179i
$345$		0			0
$346$	12.3328	+	7.12036i	0.663017	+	0.382793i
$347$	3.01081	+	1.73829i	0.161629	+	0.0933165i	0.578633	−	0.815588i	$-0.303586\pi$
$347$	3.01081	+	1.73829i	0.161629	+	0.0933165i	−0.417004	+	0.908905i	$0.636920\pi$
$348$		0			0
$349$		−	0.611574i		−	0.0327368i	−0.999866	−	0.0163684i	$-0.994790\pi$
$349$		−	0.611574i		−	0.0327368i	0.999866	−	0.0163684i	$-0.00521046\pi$
$350$		0			0
$351$		0			0
$352$	0.329631	+	0.570938i	0.0175694	+	0.0304311i
$353$	−10.8916	+	18.8649i	−0.579703	+	1.00407i	0.415810	+	0.909451i	$0.363498\pi$
$353$	−10.8916	+	18.8649i	−0.579703	+	1.00407i	−0.995513	+	0.0946235i	$0.969835\pi$
$354$		0			0
$355$		0			0
$356$	−5.32978			−0.282478
$357$		0			0
$358$	13.1435			0.694656
$359$	−14.0413	+	8.10672i	−0.741069	+	0.427857i	−0.822458	−	0.568826i	$-0.807398\pi$
$359$	−14.0413	+	8.10672i	−0.741069	+	0.427857i	0.0813887	+	0.996682i	$0.474064\pi$
$360$		0			0
$361$	16.9775	−	29.4059i	0.893553	−	1.54768i
$362$	−3.17268	−	5.49525i	−0.166753	−	0.288824i
$363$		0			0
$364$	9.63679	−	13.0619i	0.505105	−	0.684627i
$365$		0			0
$366$		0			0
$367$	−18.0615	−	10.4278i	−0.942802	−	0.544327i	−0.0519641	−	0.998649i	$-0.516548\pi$
$367$	−18.0615	−	10.4278i	−0.942802	−	0.544327i	−0.890837	+	0.454322i	$0.849881\pi$
$368$	−3.98266	−	2.29939i	−0.207611	−	0.119864i
$369$		0			0
$370$		0			0
$371$	19.1801	−	25.9971i	0.995784	−	1.34970i
$372$		0			0
$373$	0.702477	+	1.21673i	0.0363729	+	0.0629997i	0.883639	−	0.468169i	$-0.155086\pi$
$373$	0.702477	+	1.21673i	0.0363729	+	0.0629997i	−0.847266	+	0.531169i	$0.821753\pi$
$374$	−1.60648	+	2.78250i	−0.0830689	+	0.143880i
$375$		0			0
$376$	−10.3947	+	6.00136i	−0.536063	+	0.309496i
$377$	49.6656			2.55791
$378$		0			0
$379$	21.8729			1.12353			0.561766	−	0.827296i	$-0.310122\pi$
$379$	21.8729			1.12353			0.561766	+	0.827296i	$0.310122\pi$
$380$		0			0
$381$		0			0
$382$	10.9077	−	18.8926i	0.558085	−	0.966632i
$383$	−17.2741	−	29.9197i	−0.882666	−	1.52882i	−0.848365	−	0.529411i	$-0.822413\pi$
$383$	−17.2741	−	29.9197i	−0.882666	−	1.52882i	−0.0343009	−	0.999412i	$-0.510920\pi$
$384$		0			0
$385$		0			0
$386$		−	2.41866i		−	0.123107i
$387$		0			0
$388$	9.94125	+	5.73958i	0.504690	+	0.291383i
$389$	10.0406	+	5.79694i	0.509078	+	0.293916i	0.732455	−	0.680816i	$-0.238375\pi$
$389$	10.0406	+	5.79694i	0.509078	+	0.293916i	−0.223376	+	0.974732i	$0.571708\pi$
$390$		0			0
$391$		−	22.4124i		−	1.13344i
$392$	1.55542	−	6.82500i	0.0785604	−	0.344715i
$393$		0			0
$394$	−3.12229	−	5.40796i	−0.157299	−	0.272449i
$395$		0			0
$396$		0			0
$397$	−5.02400	+	2.90061i	−0.252147	+	0.145577i	−0.620747	−	0.784011i	$-0.713171\pi$
$397$	−5.02400	+	2.90061i	−0.252147	+	0.145577i	0.368600	+	0.929588i	$0.379837\pi$
$398$	5.06207			0.253739
$399$		0			0
$400$		0			0
$401$	17.7829	−	10.2670i	0.888036	−	0.512708i	0.0147366	−	0.999891i	$-0.495309\pi$
$401$	17.7829	−	10.2670i	0.888036	−	0.512708i	0.873300	+	0.487183i	$0.161976\pi$
$402$		0			0
$403$	2.68970	−	4.65869i	0.133983	−	0.232066i
$404$	7.74874	+	13.4212i	0.385514	+	0.667730i
$405$		0			0
$406$	19.6296	−	8.56811i	0.974199	−	0.425228i
$407$		−	6.66558i		−	0.330401i
$408$		0			0
$409$	7.85765	+	4.53662i	0.388536	+	0.224321i	0.681526	−	0.731794i	$-0.261317\pi$
$409$	7.85765	+	4.53662i	0.388536	+	0.224321i	−0.292990	+	0.956116i	$0.594650\pi$
$410$		0			0
$411$		0			0
$412$			2.06843i			0.101904i
$413$	17.3138	+	12.7738i	0.851954	+	0.628556i
$414$		0			0
$415$		0			0
$416$	3.06757	−	5.31319i	0.150400	−	0.260501i
$417$		0			0
$418$	4.15473	−	2.39873i	0.203214	−	0.117326i
$419$	5.30162			0.259001			0.129501	−	0.991579i	$-0.458663\pi$
$419$	5.30162			0.259001			0.129501	+	0.991579i	$0.458663\pi$
$420$		0			0
$421$	21.8234			1.06361			0.531804	−	0.846867i	$-0.321514\pi$
$421$	21.8234			1.06361			0.531804	+	0.846867i	$0.321514\pi$
$422$	−4.95512	+	2.86084i	−0.241211	+	0.139263i
$423$		0			0
$424$	6.10540	−	10.5749i	0.296504	−	0.513561i
$425$		0			0
$426$		0			0
$427$	−0.0756221	−	0.173250i	−0.00365961	−	0.00838417i
$428$		−	10.8926i		−	0.526516i
$429$		0			0
$430$		0			0
$431$	12.9922	+	7.50107i	0.625814	+	0.361314i	0.779129	−	0.626864i	$-0.215662\pi$
$431$	12.9922	+	7.50107i	0.625814	+	0.361314i	−0.153315	+	0.988177i	$0.548995\pi$
$432$		0			0
$433$			35.2578i			1.69438i	0.531289	+	0.847190i	$0.321708\pi$
$433$			35.2578i			1.69438i	−0.531289	+	0.847190i	$0.678292\pi$
$434$	0.259363	−	2.30529i	0.0124498	−	0.110658i
$435$		0			0
$436$	−7.17254	−	12.4232i	−0.343502	−	0.594964i
$437$	−16.7327	+	28.9819i	−0.800434	+	1.38639i
$438$		0			0
$439$	25.4755	−	14.7083i	1.21588	−	0.701988i	0.251846	−	0.967767i	$-0.418962\pi$
$439$	25.4755	−	14.7083i	1.21588	−	0.701988i	0.964034	+	0.265779i	$0.0856291\pi$
$440$		0			0
$441$		0			0
$442$	29.9000			1.42220
$443$	−25.5061	+	14.7259i	−1.21183	+	0.699651i	−0.963158	−	0.268937i	$-0.913328\pi$
$443$	−25.5061	+	14.7259i	−1.21183	+	0.699651i	−0.248673	+	0.968588i	$0.579994\pi$
$444$		0			0
$445$		0			0
$446$	−3.30503	−	5.72448i	−0.156498	−	0.271062i
$447$		0			0
$448$	0.295801	−	2.62916i	0.0139753	−	0.124216i
$449$			29.2408i			1.37996i	0.723829	+	0.689980i	$0.242381\pi$
$449$			29.2408i			1.37996i	−0.723829	+	0.689980i	$0.757619\pi$
$450$		0			0
$451$	−3.56970	−	2.06097i	−0.168091	−	0.0970471i
$452$	−10.3127	−	5.95403i	−0.485067	−	0.280054i
$453$		0			0
$454$			24.0556i			1.12899i
$455$		0			0
$456$		0			0
$457$	3.98679	+	6.90532i	0.186494	+	0.323017i	0.944079	−	0.329720i	$-0.106954\pi$
$457$	3.98679	+	6.90532i	0.186494	+	0.323017i	−0.757585	+	0.652737i	$0.773621\pi$
$458$	2.53925	−	4.39811i	0.118651	−	0.205510i
$459$		0			0
$460$		0			0
$461$	−39.9112			−1.85885			−0.929425	−	0.369012i	$-0.879696\pi$
$461$	−39.9112			−1.85885			−0.929425	+	0.369012i	$0.879696\pi$
$462$		0			0
$463$	−17.6663			−0.821021			−0.410511	−	0.911856i	$-0.634650\pi$
$463$	−17.6663			−0.821021			−0.410511	+	0.911856i	$0.634650\pi$
$464$	7.01070	−	4.04763i	0.325464	−	0.187907i
$465$		0			0
$466$	−11.0386	+	19.1195i	−0.511355	+	0.885692i
$467$	10.9757	+	19.0104i	0.507894	+	0.879698i	0.999958	+	0.00913924i	$0.00290915\pi$
$467$	10.9757	+	19.0104i	0.507894	+	0.879698i	−0.492064	+	0.870559i	$0.663758\pi$
$468$		0			0
$469$	−2.83997	−	2.09527i	−0.131137	−	0.0967507i
$470$		0			0
$471$		0			0
$472$	7.04274	+	4.06613i	0.324168	+	0.187159i
$473$	−5.15890	−	2.97849i	−0.237206	−	0.136951i
$474$		0			0
$475$		0			0
$476$	11.8175	−	5.15823i	0.541655	−	0.236427i
$477$		0			0
$478$	8.92778	+	15.4634i	0.408347	+	0.707278i
$479$	16.9834	−	29.4161i	0.775990	−	1.34405i	−0.158246	−	0.987400i	$-0.550584\pi$
$479$	16.9834	−	29.4161i	0.775990	−	1.34405i	0.934236	−	0.356655i	$-0.116083\pi$
$480$		0			0
$481$	−53.7199	+	31.0152i	−2.44942	+	1.41417i
$482$	−21.7546			−0.990897
$483$		0			0
$484$	−10.5654			−0.480244
$485$		0			0
$486$		0			0
$487$	7.42482	−	12.8602i	0.336451	−	0.582750i	−0.647312	−	0.762225i	$-0.724107\pi$
$487$	7.42482	−	12.8602i	0.336451	−	0.582750i	0.983762	+	0.179476i	$0.0574401\pi$
$488$	−0.0357243	−	0.0618764i	−0.00161716	−	0.00280101i
$489$		0			0
$490$		0			0
$491$			15.6224i			0.705029i	0.935806	+	0.352515i	$0.114673\pi$
$491$			15.6224i			0.705029i	−0.935806	+	0.352515i	$0.885327\pi$
$492$		0			0
$493$	34.1670	+	19.7264i	1.53881	+	0.888430i
$494$	−38.6642	−	22.3228i	−1.73958	−	1.00435i
$495$		0			0
$496$		−	0.876816i		−	0.0393702i
$497$	−6.85424	−	0.771153i	−0.307455	−	0.0345910i
$498$		0			0
$499$	−9.23416	−	15.9940i	−0.413378	−	0.715991i	0.581879	−	0.813275i	$-0.302318\pi$
$499$	−9.23416	−	15.9940i	−0.413378	−	0.715991i	−0.995257	+	0.0972842i	$0.968984\pi$
$500$		0			0
$501$		0			0
$502$	13.8950	−	8.02227i	0.620164	−	0.358052i
$503$	−5.46007			−0.243452			−0.121726	−	0.992564i	$-0.538843\pi$
$503$	−5.46007			−0.243452			−0.121726	+	0.992564i	$0.538843\pi$
$504$		0			0
$505$		0			0
$506$	−2.62562	+	1.51590i	−0.116723	+	0.0673901i
$507$		0			0
$508$	−7.31319	+	12.6668i	−0.324470	+	0.561999i
$509$	0.412125	+	0.713821i	0.0182671	+	0.0316396i	0.875014	−	0.484097i	$-0.160852\pi$
$509$	0.412125	+	0.713821i	0.0182671	+	0.0316396i	−0.856747	+	0.515736i	$0.827518\pi$
$510$		0			0
$511$	4.43590	−	6.01249i	0.196233	−	0.265977i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.2617	+	8.23399i	0.629056	+	0.363186i
$515$		0			0
$516$		0			0
$517$			7.91294i			0.348011i
$518$	−15.8814	+	21.5258i	−0.697787	+	0.945791i
$519$		0			0
$520$		0			0
$521$	−15.2147	+	26.3526i	−0.666566	+	1.15453i	0.312292	+	0.949986i	$0.398903\pi$
$521$	−15.2147	+	26.3526i	−0.666566	+	1.15453i	−0.978858	+	0.204541i	$0.934430\pi$
$522$		0			0
$523$	−0.196400	+	0.113392i	−0.00858799	+	0.00495828i	−0.504288	−	0.863536i	$-0.668245\pi$
$523$	−0.196400	+	0.113392i	−0.00858799	+	0.00495828i	0.495700	+	0.868494i	$0.334912\pi$
$524$	−3.28074			−0.143320
$525$		0			0
$526$	−5.62062			−0.245070
$527$	3.70071	−	2.13661i	0.161206	−	0.0930721i
$528$		0			0
$529$	−0.925602	+	1.60319i	−0.0402436	+	0.0697039i
$530$		0			0
$531$		0			0
$532$	−19.1325	−	2.15255i	−0.829498	−	0.0933247i
$533$			38.3590i			1.66151i
$534$		0			0
$535$		0			0
$536$	−1.15522	−	0.666965i	−0.0498978	−	0.0288085i
$537$		0			0
$538$			6.54163i			0.282030i
$539$	−3.38394	−	3.13778i	−0.145757	−	0.135154i
$540$		0			0
$541$	−18.5678	−	32.1603i	−0.798290	−	1.38268i	−0.920729	−	0.390204i	$-0.872405\pi$
$541$	−18.5678	−	32.1603i	−0.798290	−	1.38268i	0.122438	−	0.992476i	$-0.460929\pi$
$542$	9.25135	−	16.0238i	0.397380	−	0.688282i
$543$		0			0
$544$	4.22062	−	2.43678i	0.180958	−	0.104476i
$545$		0			0
$546$		0			0
$547$	14.2444			0.609047			0.304524	−	0.952505i	$-0.401503\pi$
$547$	14.2444			0.609047			0.304524	+	0.952505i	$0.401503\pi$
$548$	−3.03168	+	1.75034i	−0.129507	+	0.0747709i
$549$		0			0
$550$		0			0
$551$	−29.4547	−	51.0170i	−1.25481	−	2.17340i
$552$		0			0
$553$	14.0076	−	6.11416i	0.595662	−	0.260001i
$554$			25.9145i			1.10100i
$555$		0			0
$556$	−1.54180	−	0.890157i	−0.0653867	−	0.0377511i
$557$	16.3764	+	9.45492i	0.693890	+	0.400618i	0.805068	−	0.593183i	$-0.202129\pi$
$557$	16.3764	+	9.45492i	0.693890	+	0.400618i	−0.111177	+	0.993801i	$0.535462\pi$
$558$		0			0
$559$			55.4361i			2.34470i
$560$		0			0
$561$		0			0
$562$	4.62080	+	8.00346i	0.194917	+	0.337606i
$563$	−19.6538	+	34.0414i	−0.828310	+	1.43467i	0.0710537	+	0.997472i	$0.477364\pi$
$563$	−19.6538	+	34.0414i	−0.828310	+	1.43467i	−0.899363	+	0.437202i	$0.855969\pi$
$564$		0			0
$565$		0			0
$566$	7.09599			0.298267
$567$		0			0
$568$	−2.60701			−0.109388
$569$	0.768837	−	0.443888i	0.0322313	−	0.0186088i	−0.483798	−	0.875180i	$-0.660743\pi$
$569$	0.768837	−	0.443888i	0.0322313	−	0.0186088i	0.516029	+	0.856571i	$0.327410\pi$
$570$		0			0
$571$	−12.7120	+	22.0178i	−0.531981	+	0.921418i	0.467322	+	0.884087i	$0.345219\pi$
$571$	−12.7120	+	22.0178i	−0.531981	+	0.921418i	−0.999303	+	0.0373309i	$0.988114\pi$
$572$	−2.02234	−	3.50279i	−0.0845581	−	0.146459i
$573$		0			0
$574$	6.61754	+	15.1608i	0.276211	+	0.632800i
$575$		0			0
$576$		0			0
$577$	−8.90681	−	5.14235i	−0.370795	−	0.214079i	0.303010	−	0.952987i	$-0.402008\pi$
$577$	−8.90681	−	5.14235i	−0.370795	−	0.214079i	−0.673806	+	0.738908i	$0.735342\pi$
$578$	5.84701	+	3.37577i	0.243204	+	0.140414i
$579$		0			0
$580$		0			0
$581$	−2.20271	+	19.5783i	−0.0913837	+	0.812246i
$582$		0			0
$583$	−4.02506	−	6.97161i	−0.166701	−	0.288735i
$584$	1.41203	−	2.44571i	0.0584302	−	0.101204i
$585$		0			0
$586$	−7.74795	+	4.47328i	−0.320065	+	0.184790i
$587$	−25.1241			−1.03698			−0.518490	−	0.855083i	$-0.673506\pi$
$587$	−25.1241			−1.03698			−0.518490	+	0.855083i	$0.673506\pi$
$588$		0			0
$589$	−6.38061			−0.262909
$590$		0			0
$591$		0			0
$592$	−5.05533	+	8.75609i	−0.207773	+	0.359873i
$593$	−5.05492	−	8.75538i	−0.207581	−	0.359540i	0.743371	−	0.668879i	$-0.233226\pi$
$593$	−5.05492	−	8.75538i	−0.207581	−	0.359540i	−0.950952	+	0.309339i	$0.899892\pi$
$594$		0			0
$595$		0			0
$596$		−	8.25507i		−	0.338141i
$597$		0			0
$598$	24.4342	+	14.1071i	0.999189	+	0.576882i
$599$	21.6368	+	12.4920i	0.884056	+	0.510410i	0.871994	−	0.489517i	$-0.162827\pi$
$599$	21.6368	+	12.4920i	0.884056	+	0.510410i	0.0120624	+	0.999927i	$0.496160\pi$
$600$		0			0
$601$			15.2936i			0.623837i	0.950109	+	0.311919i	$0.100972\pi$
$601$			15.2936i			0.623837i	−0.950109	+	0.311919i	$0.899028\pi$
$602$	9.56361	+	21.9103i	0.389784	+	0.892996i
$603$		0			0
$604$	0.463545	+	0.802883i	0.0188614	+	0.0326689i
$605$		0			0
$606$		0			0
$607$	34.1973	−	19.7438i	1.38802	−	0.801377i	0.394932	−	0.918710i	$-0.370768\pi$
$607$	34.1973	−	19.7438i	1.38802	−	0.801377i	0.993093	+	0.117334i	$0.0374347\pi$
$608$	−7.27702			−0.295122
$609$		0			0
$610$		0			0
$611$	63.7727	−	36.8192i	2.57997	−	1.48954i
$612$		0			0
$613$	8.55968	−	14.8258i	0.345722	−	0.598809i	−0.639762	−	0.768573i	$-0.720967\pi$
$613$	8.55968	−	14.8258i	0.345722	−	0.598809i	0.985485	+	0.169764i	$0.0543006\pi$
$614$	3.81292	+	6.60417i	0.153877	+	0.266523i
$615$		0			0
$616$	−1.40359	−	1.03554i	−0.0565521	−	0.0417230i
$617$			5.80201i			0.233580i	0.993157	+	0.116790i	$0.0372605\pi$
$617$			5.80201i			0.233580i	−0.993157	+	0.116790i	$0.962740\pi$
$618$		0			0
$619$	29.5344	+	17.0517i	1.18709	+	0.685366i	0.957644	−	0.287956i	$-0.0929756\pi$
$619$	29.5344	+	17.0517i	1.18709	+	0.685366i	0.229445	+	0.973322i	$0.426309\pi$
$620$		0			0
$621$		0			0
$622$		−	6.40696i		−	0.256896i
$623$	12.9238	−	5.64109i	0.517780	−	0.226006i
$624$		0			0
$625$		0			0
$626$	4.52850	−	7.84360i	0.180995	−	0.313493i
$627$		0			0
$628$	−7.22480	+	4.17124i	−0.288301	+	0.166451i
$629$	−49.2749			−1.96472
$630$		0			0
$631$	33.1261			1.31873			0.659365	−	0.751823i	$-0.270825\pi$
$631$	33.1261			1.31873			0.659365	+	0.751823i	$0.270825\pi$
$632$	5.00280	−	2.88837i	0.199001	−	0.114893i
$633$		0			0
$634$	14.2534	−	24.6876i	0.566076	−	0.980472i
$635$		0			0
$636$		0			0
$637$	−9.54270	+	41.8724i	−0.378096	+	1.65904i
$638$		−	5.33690i		−	0.211290i
$639$		0			0
$640$		0			0
$641$	1.72685	+	0.997000i	0.0682067	+	0.0393791i	0.533716	−	0.845664i	$-0.320795\pi$
$641$	1.72685	+	0.997000i	0.0682067	+	0.0393791i	−0.465509	+	0.885043i	$0.654129\pi$
$642$		0			0
$643$			0.661676i			0.0260940i	0.999915	+	0.0130470i	$0.00415310\pi$
$643$			0.661676i			0.0260940i	−0.999915	+	0.0130470i	$0.995847\pi$
$644$	12.0910	+	1.36032i	0.476450	+	0.0536042i
$645$		0			0
$646$	−17.7325	−	30.7136i	−0.697675	−	1.20841i
$647$	9.19276	−	15.9223i	0.361405	−	0.625971i	−0.626787	−	0.779190i	$-0.715631\pi$
$647$	9.19276	−	15.9223i	0.361405	−	0.625971i	0.988192	+	0.153219i	$0.0489639\pi$
$648$		0			0
$649$	4.64302	−	2.68065i	0.182254	−	0.105225i
$650$		0			0
$651$		0			0
$652$	−24.3050			−0.951858
$653$	15.0571	−	8.69323i	0.589231	−	0.340193i	−0.175562	−	0.984468i	$-0.556174\pi$
$653$	15.0571	−	8.69323i	0.589231	−	0.340193i	0.764793	+	0.644276i	$0.222841\pi$
$654$		0			0
$655$		0			0
$656$	3.12617	+	5.41468i	0.122056	+	0.211408i
$657$		0			0
$658$	18.8533	−	25.5540i	0.734978	−	0.996200i
$659$			35.4692i			1.38168i	0.723006	+	0.690841i	$0.242760\pi$
$659$			35.4692i			1.38168i	−0.723006	+	0.690841i	$0.757240\pi$
$660$		0			0
$661$	−28.9704	−	16.7261i	−1.12682	−	0.650568i	−0.183685	−	0.982985i	$-0.558803\pi$
$661$	−28.9704	−	16.7261i	−1.12682	−	0.650568i	−0.943133	+	0.332417i	$0.892136\pi$
$662$	13.0516	+	7.53535i	0.507265	+	0.292870i
$663$		0			0
$664$			7.44660i			0.288984i
$665$		0			0
$666$		0			0
$667$	18.6142	+	32.2407i	0.720744	+	1.24836i
$668$	3.74362	−	6.48414i	0.144845	−	0.250879i
$669$		0			0
$670$		0			0
$671$	−0.0471035			−0.00181841
$672$		0			0
$673$	21.9964			0.847898			0.423949	−	0.905686i	$-0.360644\pi$
$673$	21.9964			0.847898			0.423949	+	0.905686i	$0.360644\pi$
$674$	0.416503	−	0.240468i	0.0160431	−	0.00926249i
$675$		0			0
$676$	−12.3200	+	21.3389i	−0.473846	+	0.820725i
$677$	6.18250	+	10.7084i	0.237613	+	0.411557i	0.960029	−	0.279901i	$-0.0903018\pi$
$677$	6.18250	+	10.7084i	0.237613	+	0.411557i	−0.722416	+	0.691459i	$0.756968\pi$
$678$		0			0
$679$	−30.1806	−	3.39554i	−1.15823	−	0.130309i
$680$		0			0
$681$		0			0
$682$	−0.500608	−	0.289026i	−0.0191693	−	0.0110674i
$683$	−25.9621	−	14.9892i	−0.993411	−	0.573546i	−0.0871187	−	0.996198i	$-0.527766\pi$
$683$	−25.9621	−	14.9892i	−0.993411	−	0.573546i	−0.906292	+	0.422652i	$0.861099\pi$
$684$		0			0
$685$		0			0
$686$	3.45205	+	18.1957i	0.131800	+	0.694715i
$687$		0			0
$688$	4.51791	+	7.82525i	0.172244	+	0.298335i
$689$	−37.4575	+	64.8783i	−1.42702	+	2.47167i
$690$		0			0
$691$	7.97882	−	4.60657i	0.303529	−	0.175242i	−0.340498	−	0.940245i	$-0.610596\pi$
$691$	7.97882	−	4.60657i	0.303529	−	0.175242i	0.644027	+	0.765003i	$0.277262\pi$
$692$	−14.2407			−0.541351
$693$		0			0
$694$	−3.47659			−0.131969
$695$		0			0
$696$		0			0
$697$	−15.2356	+	26.3888i	−0.577088	+	0.999546i
$698$	0.305787	+	0.529638i	0.0115742	+	0.0200471i
$699$		0			0
$700$		0			0
$701$		−	44.9022i		−	1.69593i	−0.530050	−	0.847967i	$-0.677827\pi$
$701$		−	44.9022i		−	1.69593i	0.530050	−	0.847967i	$-0.322173\pi$
$702$		0			0
$703$	63.7183	+	36.7878i	2.40318	+	1.38748i
$704$	−0.570938	−	0.329631i	−0.0215180	−	0.0124234i
$705$		0			0
$706$		−	21.7833i		−	0.819824i
$707$	−32.9945	−	24.3427i	−1.24089	−	0.915502i
$708$		0			0
$709$	−1.39264	−	2.41213i	−0.0523019	−	0.0905895i	0.838689	−	0.544610i	$-0.183322\pi$
$709$	−1.39264	−	2.41213i	−0.0523019	−	0.0905895i	−0.890991	+	0.454021i	$0.849989\pi$
$710$		0			0
$711$		0			0
$712$	4.61572	−	2.66489i	0.172981	−	0.0998709i
$713$	4.03229			0.151010
$714$		0			0
$715$		0			0
$716$	−11.3826	+	6.57176i	−0.425388	+	0.245598i
$717$		0			0
$718$	8.10672	−	14.0413i	0.302540	−	0.524015i
$719$	−13.4818	−	23.3511i	−0.502785	−	0.870849i	−0.999995	−	0.00321841i	$-0.998976\pi$
$719$	−13.4818	−	23.3511i	−0.502785	−	0.870849i	0.497210	−	0.867630i	$-0.334358\pi$
$720$		0			0
$721$	−2.18925	−	5.01558i	−0.0815319	−	0.186790i
$722$			33.9550i			1.26368i
$723$		0			0
$724$	5.49525	+	3.17268i	0.204229	+	0.117912i
$725$		0			0
$726$		0			0
$727$			29.6632i			1.10015i	0.835116	+	0.550074i	$0.185400\pi$
$727$			29.6632i			1.10015i	−0.835116	+	0.550074i	$0.814600\pi$
$728$	−1.81478	+	16.1303i	−0.0672602	+	0.597829i
$729$		0			0
$730$		0			0
$731$	−22.0183	+	38.1368i	−0.814376	+	1.41054i
$732$		0			0
$733$	19.9455	−	11.5155i	0.736704	−	0.425336i	−0.0841657	−	0.996452i	$-0.526823\pi$
$733$	19.9455	−	11.5155i	0.736704	−	0.425336i	0.820870	+	0.571116i	$0.193489\pi$
$734$	20.8556			0.769794
$735$		0			0
$736$	4.59878			0.169513
$737$	−0.761591	+	0.439705i	−0.0280536	+	0.0161967i
$738$		0			0
$739$	−17.2029	+	29.7964i	−0.632821	+	1.09608i	0.354152	+	0.935188i	$0.384770\pi$
$739$	−17.2029	+	29.7964i	−0.632821	+	1.09608i	−0.986972	+	0.160889i	$0.948564\pi$
$740$		0			0
$741$		0			0
$742$	−3.61196	+	32.1042i	−0.132599	+	1.17858i
$743$			40.6201i			1.49021i	0.666950	+	0.745103i	$0.267600\pi$
$743$			40.6201i			1.49021i	−0.666950	+	0.745103i	$0.732400\pi$
$744$		0			0
$745$		0			0
$746$	−1.21673	−	0.702477i	−0.0445475	−	0.0257195i
$747$		0			0
$748$		−	3.21295i		−	0.117477i
$749$	11.5289	+	26.4127i	0.421257	+	0.965101i
$750$		0			0
$751$	−22.8927	−	39.6513i	−0.835366	−	1.44690i	−0.893732	−	0.448601i	$-0.851922\pi$
$751$	−22.8927	−	39.6513i	−0.835366	−	1.44690i	0.0583658	−	0.998295i	$-0.481411\pi$
$752$	6.00136	−	10.3947i	0.218847	−	0.379054i
$753$		0			0
$754$	−43.0117	+	24.8328i	−1.56639	+	0.904357i
$755$		0			0
$756$		0			0
$757$	−50.7755			−1.84547			−0.922733	−	0.385440i	$-0.874050\pi$
$757$	−50.7755			−1.84547			−0.922733	+	0.385440i	$0.874050\pi$
$758$	−18.9424	+	10.9364i	−0.688021	+	0.397229i
$759$		0			0
$760$		0			0
$761$	18.0315	+	31.2316i	0.653643	+	1.13214i	0.982232	+	0.187670i	$0.0600935\pi$
$761$	18.0315	+	31.2316i	0.653643	+	1.13214i	−0.328589	+	0.944473i	$0.606573\pi$
$762$		0			0
$763$	30.5410	+	22.5326i	1.10566	+	0.815734i
$764$			21.8153i			0.789251i
$765$		0			0
$766$	29.9197	+	17.2741i	1.08104	+	0.624139i
$767$	−43.2082	−	24.9463i	−1.56016	−	0.900758i
$768$		0			0
$769$		−	17.5798i		−	0.633943i	−0.948435	−	0.316971i	$-0.897334\pi$
$769$		−	17.5798i		−	0.633943i	0.948435	−	0.316971i	$-0.102666\pi$
$770$		0			0
$771$		0			0
$772$	1.20933	+	2.09462i	0.0435248	+	0.0753871i
$773$	24.7318	−	42.8367i	0.889541	−	1.54073i	0.0491225	−	0.998793i	$-0.484358\pi$
$773$	24.7318	−	42.8367i	0.889541	−	1.54073i	0.840419	−	0.541938i	$-0.182309\pi$
$774$		0			0
$775$		0			0
$776$	−11.4792			−0.412078
$777$		0			0
$778$	−11.5939			−0.415661
$779$	39.4028	−	22.7492i	1.41175	−	0.815074i
$780$		0			0
$781$	−0.859351	+	1.48844i	−0.0307500	+	0.0532605i
$782$	11.2062	+	19.4097i	0.400733	+	0.694090i
$783$		0			0
$784$	2.06547	+	6.68833i	0.0737669	+	0.238869i
$785$		0			0
$786$		0			0
$787$	−8.38310	−	4.83998i	−0.298825	−	0.172527i	0.343090	−	0.939303i	$-0.388526\pi$
$787$	−8.38310	−	4.83998i	−0.298825	−	0.172527i	−0.641915	+	0.766776i	$0.721860\pi$
$788$	5.40796	+	3.12229i	0.192651	+	0.111227i
$789$		0			0
$790$		0			0
$791$	31.3082	+	3.52241i	1.11319	+	0.125242i
$792$		0			0
$793$	0.219174	+	0.379620i	0.00778310	+	0.0134807i
$794$	2.90061	−	5.02400i	0.102939	−	0.178295i
$795$		0			0
$796$	−4.38388	+	2.53103i	−0.155383	+	0.0897101i
$797$	15.1216			0.535636			0.267818	−	0.963470i	$-0.413697\pi$
$797$	15.1216			0.535636			0.267818	+	0.963470i	$0.413697\pi$
$798$		0			0
$799$	58.4959			2.06944
$800$		0			0
$801$		0			0
$802$	−10.2670	+	17.7829i	−0.362539	+	0.627937i
$803$	−0.930899	−	1.61236i	−0.0328507	−	0.0568991i
$804$		0			0
$805$		0			0
$806$			5.37940i			0.189481i
$807$		0			0
$808$	−13.4212	−	7.74874i	−0.472157	−	0.272600i
$809$	4.53839	+	2.62024i	0.159561	+	0.0921228i	0.577655	−	0.816281i	$-0.303968\pi$
$809$	4.53839	+	2.62024i	0.159561	+	0.0921228i	−0.418093	+	0.908404i	$0.637301\pi$
$810$		0			0
$811$			54.1101i			1.90006i	0.312154	+	0.950031i	$0.398949\pi$
$811$			54.1101i			1.90006i	−0.312154	+	0.950031i	$0.601051\pi$
$812$	−12.7157	+	17.2350i	−0.446232	+	0.604830i
$813$		0			0
$814$	3.33279	+	5.77257i	0.116814	+	0.202328i
$815$		0			0
$816$		0			0
$817$	56.9445	−	32.8769i	1.99224	−	1.15022i
$818$	−9.07323			−0.317238
$819$		0			0
$820$		0			0
$821$	23.3717	−	13.4936i	0.815677	−	0.470931i	−0.0332463	−	0.999447i	$-0.510585\pi$
$821$	23.3717	−	13.4936i	0.815677	−	0.470931i	0.848924	+	0.528516i	$0.177251\pi$
$822$		0			0
$823$	−3.12999	+	5.42130i	−0.109105	+	0.188975i	−0.915408	−	0.402528i	$-0.868132\pi$
$823$	−3.12999	+	5.42130i	−0.109105	+	0.188975i	0.806303	+	0.591502i	$0.201465\pi$
$824$	−1.03422	−	1.79131i	−0.0360286	−	0.0624034i
$825$		0			0
$826$	−21.3810	−	2.40553i	−0.743941	−	0.0836989i
$827$			32.0713i			1.11523i	0.830100	+	0.557615i	$0.188283\pi$
$827$			32.0713i			1.11523i	−0.830100	+	0.557615i	$0.811717\pi$
$828$		0			0
$829$	10.3975	+	6.00303i	0.361122	+	0.208494i	0.669573	−	0.742746i	$-0.266477\pi$
$829$	10.3975	+	6.00303i	0.361122	+	0.208494i	−0.308451	+	0.951240i	$0.599811\pi$
$830$		0			0
$831$		0			0
$832$			6.13514i			0.212698i
$833$	−23.1958	+	25.0156i	−0.803688	+	0.866738i
$834$		0			0
$835$		0			0
$836$	−2.39873	+	4.15473i	−0.0829620	+	0.143694i
$837$		0			0
$838$	−4.59134	+	2.65081i	−0.158605	+	0.0915707i
$839$	51.4896			1.77762			0.888809	−	0.458278i	$-0.151534\pi$
$839$	51.4896			1.77762			0.888809	+	0.458278i	$0.151534\pi$
$840$		0			0
$841$	−36.5332			−1.25977
$842$	−18.8996	+	10.9117i	−0.651324	+	0.376042i
$843$		0			0
$844$	2.86084	−	4.95512i	0.0984741	−	0.170562i
$845$		0			0
$846$		0			0
$847$	25.6192	−	11.1825i	0.880285	−	0.384236i
$848$			12.2108i			0.419321i
$849$		0			0
$850$		0			0
$851$	−40.2674	−	23.2484i	−1.38035	−	0.796944i
$852$		0			0
$853$			41.4695i			1.41989i	0.704258	+	0.709944i	$0.251280\pi$
$853$			41.4695i			1.41989i	−0.704258	+	0.709944i	$0.748720\pi$
$854$	0.152116	+	0.112228i	0.00520530	+	0.00384037i
$855$		0			0
$856$	5.44632	+	9.43331i	0.186152	+	0.322424i
$857$	−27.9394	+	48.3925i	−0.954393	+	1.65306i	−0.218641	+	0.975805i	$0.570163\pi$
$857$	−27.9394	+	48.3925i	−0.954393	+	1.65306i	−0.735751	+	0.677252i	$0.763171\pi$
$858$		0			0
$859$	−26.0097	+	15.0167i	−0.887440	+	0.512364i	−0.873104	−	0.487534i	$-0.837897\pi$
$859$	−26.0097	+	15.0167i	−0.887440	+	0.512364i	−0.0143355	+	0.999897i	$0.504563\pi$
$860$		0			0
$861$		0			0
$862$	−15.0021			−0.510975
$863$	−1.77218	+	1.02317i	−0.0603258	+	0.0348291i	−0.529860	−	0.848085i	$-0.677755\pi$
$863$	−1.77218	+	1.02317i	−0.0603258	+	0.0348291i	0.469534	+	0.882915i	$0.344422\pi$
$864$		0			0
$865$		0			0
$866$	−17.6289	−	30.5341i	−0.599054	−	1.03759i
$867$		0			0
$868$	0.928032	+	2.12612i	0.0314995	+	0.0721654i
$869$		−	3.80839i		−	0.129191i
$870$		0			0
$871$	7.08742	+	4.09192i	0.240148	+	0.138650i
$872$	12.4232	+	7.17254i	0.420703	+	0.242893i
$873$		0			0
$874$		−	33.4654i		−	1.13199i
$875$		0			0
$876$		0			0
$877$	5.24489	+	9.08442i	0.177107	+	0.306759i	0.940889	−	0.338716i	$-0.109993\pi$
$877$	5.24489	+	9.08442i	0.177107	+	0.306759i	−0.763781	+	0.645475i	$0.776659\pi$
$878$	−14.7083	+	25.4755i	−0.496381	+	0.859757i
$879$		0			0
$880$		0			0
$881$	44.2280			1.49008			0.745039	−	0.667021i	$-0.232431\pi$
$881$	44.2280			1.49008			0.745039	+	0.667021i	$0.232431\pi$
$882$		0			0
$883$	23.8143			0.801416			0.400708	−	0.916206i	$-0.368764\pi$
$883$	23.8143			0.801416			0.400708	+	0.916206i	$0.368764\pi$
$884$	−25.8941	+	14.9500i	−0.870914	+	0.502822i
$885$		0			0
$886$	14.7259	−	25.5061i	0.494728	−	0.856893i
$887$	15.6120	+	27.0408i	0.524200	+	0.907941i	0.999603	+	0.0281729i	$0.00896889\pi$
$887$	15.6120	+	27.0408i	0.524200	+	0.907941i	−0.475403	+	0.879768i	$0.657698\pi$
$888$		0			0
$889$	4.32649	−	38.4552i	0.145106	−	1.28974i
$890$		0			0
$891$		0			0
$892$	5.72448	+	3.30503i	0.191670	+	0.110661i
$893$	−75.6421	−	43.6720i	−2.53127	−	1.46143i
$894$		0			0
$895$		0			0
$896$	1.05841	+	2.42482i	0.0353590	+	0.0810076i
$897$		0			0
$898$	−14.6204	−	25.3233i	−0.487889	−	0.845049i
$899$	−3.54903	+	6.14710i	−0.118367	+	0.205017i
$900$		0			0
$901$	−51.5372	+	29.7550i	−1.71695	+	0.991283i
$902$	4.12193			0.137245
$903$		0			0
$904$	11.9081			0.396056
$905$		0			0
$906$		0			0
$907$	7.73076	−	13.3901i	0.256696	−	0.444610i	−0.708659	−	0.705551i	$-0.750699\pi$
$907$	7.73076	−	13.3901i	0.256696	−	0.444610i	0.965355	+	0.260941i	$0.0840328\pi$
$908$	−12.0278	−	20.8328i	−0.399157	−	0.691360i
$909$		0			0
$910$		0			0
$911$			11.7655i			0.389810i	0.980822	+	0.194905i	$0.0624398\pi$
$911$			11.7655i			0.389810i	−0.980822	+	0.194905i	$0.937560\pi$
$912$		0			0
$913$	4.25155	+	2.45463i	0.140706	+	0.0812365i
$914$	−6.90532	−	3.98679i	−0.228408	−	0.131871i
$915$		0			0
$916$			5.07850i			0.167798i
$917$	7.95521	−	3.47237i	0.262704	−	0.114668i
$918$		0			0
$919$	15.4078	+	26.6871i	0.508256	+	0.880326i	0.999954	+	0.00955987i	$0.00304305\pi$
$919$	15.4078	+	26.6871i	0.508256	+	0.880326i	−0.491698	+	0.870766i	$0.663624\pi$
$920$		0			0
$921$		0			0
$922$	34.5641	−	19.9556i	1.13831	−	0.657203i
$923$	15.9944			0.526460
$924$		0			0
$925$		0			0
$926$	15.2994	−	8.83314i	0.502771	−	0.290275i
$927$		0			0
$928$	−4.04763	+	7.01070i	−0.132870	+	0.230138i
$929$	2.44799	+	4.24005i	0.0803160	+	0.139111i	0.903386	−	0.428829i	$-0.141074\pi$
$929$	2.44799	+	4.24005i	0.0803160	+	0.139111i	−0.823070	+	0.567940i	$0.807740\pi$
$930$		0			0
$931$	48.6712	−	15.0305i	1.59513	−	0.492604i
$932$		−	22.0773i		−	0.723165i
$933$		0			0
$934$	−19.0104	−	10.9757i	−0.622040	−	0.359135i
$935$		0			0
$936$		0			0
$937$		−	28.7661i		−	0.939747i	−0.882734	−	0.469874i	$-0.844299\pi$
$937$		−	28.7661i		−	0.939747i	0.882734	−	0.469874i	$-0.155701\pi$
$938$	3.50712	+	0.394577i	0.114511	+	0.0128834i
$939$		0			0
$940$		0			0
$941$	−0.0535167	+	0.0926937i	−0.00174460	+	0.00302173i	−0.866896	−	0.498488i	$-0.833889\pi$
$941$	−0.0535167	+	0.0926937i	−0.00174460	+	0.00302173i	0.865152	+	0.501510i	$0.167222\pi$
$942$		0			0
$943$	−24.9009	+	14.3766i	−0.810886	+	0.468165i
$944$	−8.13225			−0.264682
$945$		0			0
$946$	5.95698			0.193678
$947$	12.7502	−	7.36136i	0.414327	−	0.239212i	−0.278320	−	0.960488i	$-0.589778\pi$
$947$	12.7502	−	7.36136i	0.414327	−	0.239212i	0.692647	+	0.721276i	$0.256444\pi$
$948$		0			0
$949$	−8.66301	+	15.0048i	−0.281213	+	0.487076i
$950$		0			0
$951$		0			0
$952$	−7.65515	+	10.3759i	−0.248105	+	0.336285i
$953$		−	10.5168i		−	0.340672i	−0.985386	−	0.170336i	$-0.945515\pi$
$953$		−	10.5168i		−	0.340672i	0.985386	−	0.170336i	$-0.0544852\pi$
$954$		0			0
$955$		0			0
$956$	−15.4634	−	8.92778i	−0.500121	−	0.288745i
$957$		0			0
$958$			33.9667i			1.09742i
$959$	5.49871	−	7.45304i	0.177563	−	0.240671i
$960$		0			0
$961$	−15.1156	−	26.1810i	−0.487600	−	0.844548i
$962$	31.0152	−	53.7199i	0.999970	−	1.73200i
$963$		0			0
$964$	18.8401	−	10.8773i	0.606798	−	0.350335i
$965$		0			0
$966$		0			0
$967$	8.51148			0.273711			0.136855	−	0.990591i	$-0.456300\pi$
$967$	8.51148			0.273711			0.136855	+	0.990591i	$0.456300\pi$
$968$	9.14988	−	5.28269i	0.294088	−	0.169792i
$969$		0			0
$970$		0			0
$971$	−4.49465	−	7.78496i	−0.144240	−	0.249831i	0.784849	−	0.619687i	$-0.212740\pi$
$971$	−4.49465	−	7.78496i	−0.144240	−	0.249831i	−0.929089	+	0.369856i	$0.879407\pi$
$972$		0			0
$973$	4.68074	+	0.526618i	0.150057	+	0.0168826i
$974$			14.8496i			0.475813i
$975$		0			0
$976$	0.0618764	+	0.0357243i	0.00198061	+	0.00114351i
$977$	−39.2963	−	22.6877i	−1.25720	−	0.725845i	−0.284671	−	0.958625i	$-0.591884\pi$
$977$	−39.2963	−	22.6877i	−1.25720	−	0.725845i	−0.972529	+	0.232781i	$0.925218\pi$
$978$		0			0
$979$		−	3.51372i		−	0.112299i
$980$		0			0
$981$		0			0
$982$	−7.81120	−	13.5294i	−0.249266	−	0.431741i
$983$	−12.9209	+	22.3797i	−0.412114	+	0.713802i	−0.995121	−	0.0986654i	$-0.968543\pi$
$983$	−12.9209	+	22.3797i	−0.412114	+	0.713802i	0.583007	+	0.812467i	$0.301876\pi$
$984$		0			0
$985$		0			0
$986$	−39.4527			−1.25643
$987$		0			0
$988$	44.6456			1.42036
$989$	−35.9866	+	20.7769i	−1.14431	+	0.660667i
$990$		0			0
$991$	−16.5315	+	28.6333i	−0.525139	+	0.909568i	0.474432	+	0.880292i	$0.342654\pi$
$991$	−16.5315	+	28.6333i	−0.525139	+	0.909568i	−0.999571	+	0.0292760i	$0.990680\pi$
$992$	0.438408	+	0.759345i	0.0139195	+	0.0241092i
$993$		0			0
$994$	6.32153	−	2.75928i	0.200507	−	0.0875191i
$995$		0			0
$996$		0			0
$997$	−43.2828	−	24.9894i	−1.37078	−	0.791421i	−0.379755	−	0.925087i	$-0.623992\pi$
$997$	−43.2828	−	24.9894i	−1.37078	−	0.791421i	−0.991026	+	0.133666i	$0.957325\pi$
$998$	15.9940	+	9.23416i	0.506282	+	0.292302i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.e.1151.3	yes	24
3.2	odd	2	inner	3150.2.bf.e.1151.10	yes	24
5.2	odd	4		3150.2.bp.g.899.1		24
5.3	odd	4		3150.2.bp.h.899.12		24
5.4	even	2		3150.2.bf.d.1151.10	yes	24
7.5	odd	6	inner	3150.2.bf.e.1601.10	yes	24
15.2	even	4		3150.2.bp.h.899.1		24
15.8	even	4		3150.2.bp.g.899.12		24
15.14	odd	2		3150.2.bf.d.1151.3	✓	24
21.5	even	6	inner	3150.2.bf.e.1601.3	yes	24
35.12	even	12		3150.2.bp.g.1349.12		24
35.19	odd	6		3150.2.bf.d.1601.3	yes	24
35.33	even	12		3150.2.bp.h.1349.1		24
105.47	odd	12		3150.2.bp.h.1349.12		24
105.68	odd	12		3150.2.bp.g.1349.1		24
105.89	even	6		3150.2.bf.d.1601.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.3	✓	24	15.14	odd	2
3150.2.bf.d.1151.10	yes	24	5.4	even	2
3150.2.bf.d.1601.3	yes	24	35.19	odd	6
3150.2.bf.d.1601.10	yes	24	105.89	even	6
3150.2.bf.e.1151.3	yes	24	1.1	even	1	trivial
3150.2.bf.e.1151.10	yes	24	3.2	odd	2	inner
3150.2.bf.e.1601.3	yes	24	21.5	even	6	inner
3150.2.bf.e.1601.10	yes	24	7.5	odd	6	inner
3150.2.bp.g.899.1		24	5.2	odd	4
3150.2.bp.g.899.12		24	15.8	even	4
3150.2.bp.g.1349.1		24	105.68	odd	12
3150.2.bp.g.1349.12		24	35.12	even	12
3150.2.bp.h.899.1		24	15.2	even	4
3150.2.bp.h.899.12		24	5.3	odd	4
3150.2.bp.h.1349.1		24	35.33	even	12
3150.2.bp.h.1349.12		24	105.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.295801 + 2.62916i) q^{7} +1.00000i q^{8} +(0.570938 + 0.329631i) q^{11} -6.13514i q^{13} +(-1.05841 - 2.42482i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.43678 - 4.22062i) q^{17} +(-6.30208 + 3.63851i) q^{19} -0.659263 q^{22} +(3.98266 - 2.29939i) q^{23} +(3.06757 + 5.31319i) q^{26} +(2.12902 + 1.57075i) q^{28} +8.09526i q^{29} +(0.759345 + 0.438408i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.87356i q^{34} +(-5.05533 - 8.75609i) q^{37} +(3.63851 - 6.30208i) q^{38} -6.25234 q^{41} -9.03582 q^{43} +(0.570938 - 0.329631i) q^{44} +(-2.29939 + 3.98266i) q^{46} +(6.00136 + 10.3947i) q^{47} +(-6.82500 - 1.55542i) q^{49} +(-5.31319 - 3.06757i) q^{52} +(-10.5749 - 6.10540i) q^{53} +(-2.62916 - 0.295801i) q^{56} +(-4.04763 - 7.01070i) q^{58} +(4.06613 - 7.04274i) q^{59} +(-0.0618764 + 0.0357243i) q^{61} -0.876816 q^{62} -1.00000 q^{64} +(-0.666965 + 1.15522i) q^{67} +(-2.43678 - 4.22062i) q^{68} +2.60701i q^{71} +(-2.44571 - 1.41203i) q^{73} +(8.75609 + 5.05533i) q^{74} +7.27702i q^{76} +(-1.03554 + 1.40359i) q^{77} +(-2.88837 - 5.00280i) q^{79} +(5.41468 - 3.12617i) q^{82} +7.44660 q^{83} +(7.82525 - 4.51791i) q^{86} +(-0.329631 + 0.570938i) q^{88} +(-2.66489 - 4.61572i) q^{89} +(16.1303 + 1.81478i) q^{91} -4.59878i q^{92} +(-10.3947 - 6.00136i) q^{94} +11.4792i q^{97} +(6.68833 - 2.06547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 4 * q^7	\( 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more