LMFDB - Embedded newform 3150.2.bp.g.1349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

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.bp (of order $6$, degree $2$, not 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			1349.1
Character	$\chi$	$=$	3150.1349
Dual form			3150.2.bp.g.899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.62916 + 0.295801i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.62916 + 0.295801i) q^{7} +1.00000 q^{8} +(0.570938 - 0.329631i) q^{11} -6.13514 q^{13} +(1.05841 - 2.42482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.22062 - 2.43678i) q^{17} +(6.30208 + 3.63851i) q^{19} +0.659263i q^{22} +(-2.29939 + 3.98266i) q^{23} +(3.06757 - 5.31319i) q^{26} +(1.57075 + 2.12902i) q^{28} +8.09526i q^{29} +(0.759345 - 0.438408i) q^{31} +(-0.500000 - 0.866025i) q^{32} +4.87356i q^{34} +(8.75609 + 5.05533i) q^{37} +(-6.30208 + 3.63851i) q^{38} -6.25234 q^{41} -9.03582i q^{43} +(-0.570938 - 0.329631i) q^{44} +(-2.29939 - 3.98266i) q^{46} +(-10.3947 - 6.00136i) q^{47} +(6.82500 - 1.55542i) q^{49} +(3.06757 + 5.31319i) q^{52} +(-6.10540 - 10.5749i) q^{53} +(-2.62916 + 0.295801i) q^{56} +(-7.01070 - 4.04763i) q^{58} +(-4.06613 - 7.04274i) q^{59} +(-0.0618764 - 0.0357243i) q^{61} +0.876816i q^{62} +1.00000 q^{64} +(-1.15522 + 0.666965i) q^{67} +(-4.22062 - 2.43678i) q^{68} -2.60701i q^{71} +(-1.41203 - 2.44571i) q^{73} +(-8.75609 + 5.05533i) q^{74} -7.27702i q^{76} +(-1.40359 + 1.03554i) q^{77} +(2.88837 - 5.00280i) q^{79} +(3.12617 - 5.41468i) q^{82} +7.44660i q^{83} +(7.82525 + 4.51791i) q^{86} +(0.570938 - 0.329631i) q^{88} +(2.66489 - 4.61572i) q^{89} +(16.1303 - 1.81478i) q^{91} +4.59878 q^{92} +(10.3947 - 6.00136i) q^{94} -11.4792 q^{97} +(-2.06547 + 6.68833i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.62916	+	0.295801i	−0.993730	+	0.111802i
$7$	−2.62916	+	0.295801i	−0.993730	+	0.111802i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	0.570938	−	0.329631i	0.172144	−	0.0993876i	−0.411452	−	0.911431i	$-0.634978\pi$
$11$	0.570938	−	0.329631i	0.172144	−	0.0993876i	0.583597	+	0.812044i	$0.301645\pi$
$12$		0			0
$13$	−6.13514			−1.70158			−0.850791	−	0.525504i	$-0.823877\pi$
$13$	−6.13514			−1.70158			−0.850791	+	0.525504i	$0.823877\pi$
$14$	1.05841	−	2.42482i	0.282872	−	0.648061i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.22062	−	2.43678i	1.02365	−	0.591005i	0.108492	−	0.994097i	$-0.465398\pi$
$17$	4.22062	−	2.43678i	1.02365	−	0.591005i	0.915160	+	0.403092i	$0.132064\pi$
$18$		0			0
$19$	6.30208	+	3.63851i	1.44580	+	0.834732i	0.998227	−	0.0595173i	$-0.0189562\pi$
$19$	6.30208	+	3.63851i	1.44580	+	0.834732i	0.447570	+	0.894249i	$0.352289\pi$
$20$		0			0
$21$		0			0
$22$			0.659263i			0.140555i
$23$	−2.29939	+	3.98266i	−0.479456	+	0.830442i	−0.999722	−	0.0235617i	$-0.992499\pi$
$23$	−2.29939	+	3.98266i	−0.479456	+	0.830442i	0.520266	+	0.854004i	$0.325833\pi$
$24$		0			0
$25$		0			0
$26$	3.06757	−	5.31319i	0.601600	−	1.04200i
$27$		0			0
$28$	1.57075	+	2.12902i	0.296844	+	0.402347i
$29$			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	−0.430256	−	0.902707i	$-0.641577\pi$
$31$	0.759345	−	0.438408i	0.136382	−	0.0787404i	0.566639	+	0.823966i	$0.308243\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$			4.87356i			0.835808i
$35$		0			0
$36$		0			0
$37$	8.75609	+	5.05533i	1.43949	+	0.831092i	0.997814	−	0.0660818i	$-0.0210498\pi$
$37$	8.75609	+	5.05533i	1.43949	+	0.831092i	0.441679	+	0.897173i	$0.354383\pi$
$38$	−6.30208	+	3.63851i	−1.02233	+	0.590244i
$39$		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
$43$		−	9.03582i		−	1.37795i	−0.724785	−	0.688975i	$-0.758061\pi$
$43$		−	9.03582i		−	1.37795i	0.724785	−	0.688975i	$-0.241939\pi$
$44$	−0.570938	−	0.329631i	−0.0860722	−	0.0496938i
$45$		0			0
$46$	−2.29939	−	3.98266i	−0.339027	−	0.587211i
$47$	−10.3947	−	6.00136i	−1.51622	−	0.875388i	−0.999819	−	0.0190383i	$-0.993940\pi$
$47$	−10.3947	−	6.00136i	−1.51622	−	0.875388i	−0.516397	−	0.856349i	$-0.672727\pi$
$48$		0			0
$49$	6.82500	−	1.55542i	0.975001	−	0.222202i
$50$		0			0
$51$		0			0
$52$	3.06757	+	5.31319i	0.425396	+	0.736807i
$53$	−6.10540	−	10.5749i	−0.838641	−	1.45257i	−0.891031	−	0.453943i	$-0.850017\pi$
$53$	−6.10540	−	10.5749i	−0.838641	−	1.45257i	0.0523897	−	0.998627i	$-0.483316\pi$
$54$		0			0
$55$		0			0
$56$	−2.62916	+	0.295801i	−0.351337	+	0.0395280i
$57$		0			0
$58$	−7.01070	−	4.04763i	−0.920550	−	0.531480i
$59$	−4.06613	−	7.04274i	−0.529365	−	0.916887i	−0.999413	−	0.0342461i	$-0.989097\pi$
$59$	−4.06613	−	7.04274i	−0.529365	−	0.916887i	0.470049	−	0.882640i	$-0.344236\pi$
$60$		0			0
$61$	−0.0618764	−	0.0357243i	−0.00792246	−	0.00457403i	0.496034	−	0.868303i	$-0.334789\pi$
$61$	−0.0618764	−	0.0357243i	−0.00792246	−	0.00457403i	−0.503956	+	0.863729i	$0.668123\pi$
$62$			0.876816i			0.111356i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−1.15522	+	0.666965i	−0.141132	+	0.0814827i	−0.568903	−	0.822404i	$-0.692632\pi$
$67$	−1.15522	+	0.666965i	−0.141132	+	0.0814827i	0.427771	+	0.903887i	$0.359299\pi$
$68$	−4.22062	−	2.43678i	−0.511826	−	0.295503i
$69$		0			0
$70$		0			0
$71$		−	2.60701i		−	0.309395i	−0.987962	−	0.154697i	$-0.950560\pi$
$71$		−	2.60701i		−	0.309395i	0.987962	−	0.154697i	$-0.0494402\pi$
$72$		0			0
$73$	−1.41203	−	2.44571i	−0.165266	−	0.286249i	0.771484	−	0.636249i	$-0.219515\pi$
$73$	−1.41203	−	2.44571i	−0.165266	−	0.286249i	−0.936750	+	0.350000i	$0.886181\pi$
$74$	−8.75609	+	5.05533i	−1.01788	+	0.587670i
$75$		0			0
$76$		−	7.27702i		−	0.834732i
$77$	−1.40359	+	1.03554i	−0.159953	+	0.118011i
$78$		0			0
$79$	2.88837	−	5.00280i	0.324967	−	0.562859i	−0.656539	−	0.754292i	$-0.727980\pi$
$79$	2.88837	−	5.00280i	0.324967	−	0.562859i	0.981506	+	0.191433i	$0.0613136\pi$
$80$		0			0
$81$		0			0
$82$	3.12617	−	5.41468i	0.345228	−	0.597952i
$83$			7.44660i			0.817370i	0.912675	+	0.408685i	$0.134013\pi$
$83$			7.44660i			0.817370i	−0.912675	+	0.408685i	$0.865987\pi$
$84$		0			0
$85$		0			0
$86$	7.82525	+	4.51791i	0.843819	+	0.487179i
$87$		0			0
$88$	0.570938	−	0.329631i	0.0608622	−	0.0351388i
$89$	2.66489	−	4.61572i	0.282478	−	0.489266i	−0.689517	−	0.724270i	$-0.742177\pi$
$89$	2.66489	−	4.61572i	0.282478	−	0.489266i	0.971994	+	0.235004i	$0.0755104\pi$
$90$		0			0
$91$	16.1303	−	1.81478i	1.69091	−	0.190241i
$92$	4.59878			0.479456
$93$		0			0
$94$	10.3947	−	6.00136i	1.07213	−	0.618993i
$95$		0			0
$96$		0			0
$97$	−11.4792			−1.16553			−0.582766	−	0.812640i	$-0.698030\pi$
$97$	−11.4792			−1.16553			−0.582766	+	0.812640i	$0.698030\pi$
$98$	−2.06547	+	6.68833i	−0.208644	+	0.675624i
$99$		0			0
$100$		0			0
$101$	−7.74874	−	13.4212i	−0.771029	−	1.33546i	−0.937000	−	0.349330i	$-0.886409\pi$
$101$	−7.74874	−	13.4212i	−0.771029	−	1.33546i	0.165971	−	0.986131i	$-0.446924\pi$
$102$		0			0
$103$	1.03422	−	1.79131i	0.101904	−	0.176503i	−0.810565	−	0.585649i	$-0.800840\pi$
$103$	1.03422	−	1.79131i	0.101904	−	0.176503i	0.912469	+	0.409145i	$0.134173\pi$
$104$	−6.13514			−0.601600
$105$		0			0
$106$	12.2108			1.18602
$107$	5.44632	−	9.43331i	0.526516	−	0.911953i	−0.473007	−	0.881059i	$-0.656831\pi$
$107$	5.44632	−	9.43331i	0.526516	−	0.911953i	0.999523	−	0.0308937i	$-0.00983533\pi$
$108$		0			0
$109$	−7.17254	−	12.4232i	−0.687005	−	1.18993i	−0.972802	−	0.231637i	$-0.925592\pi$
$109$	−7.17254	−	12.4232i	−0.687005	−	1.18993i	0.285797	−	0.958290i	$-0.407742\pi$
$110$		0			0
$111$		0			0
$112$	1.05841	−	2.42482i	0.100010	−	0.229124i
$113$	−11.9081			−1.12022			−0.560108	−	0.828420i	$-0.689240\pi$
$113$	−11.9081			−1.12022			−0.560108	+	0.828420i	$0.689240\pi$
$114$		0			0
$115$		0			0
$116$	7.01070	−	4.04763i	0.650927	−	0.375813i
$117$		0			0
$118$	8.13225			0.748635
$119$	−10.3759	+	7.65515i	−0.951158	+	0.701747i
$120$		0			0
$121$	−5.28269	+	9.14988i	−0.480244	+	0.831807i
$122$	0.0618764	−	0.0357243i	0.00560202	−	0.00323433i
$123$		0			0
$124$	−0.759345	−	0.438408i	−0.0681912	−	0.0393702i
$125$		0			0
$126$		0			0
$127$			14.6264i			1.29788i	0.760839	+	0.648941i	$0.224788\pi$
$127$			14.6264i			1.29788i	−0.760839	+	0.648941i	$0.775212\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−1.64037	+	2.84120i	−0.143320	+	0.248237i	−0.928745	−	0.370720i	$-0.879111\pi$
$131$	−1.64037	+	2.84120i	−0.143320	+	0.248237i	0.785425	+	0.618957i	$0.212444\pi$
$132$		0			0
$133$	−17.6455	−	7.70208i	−1.53006	−	0.667855i
$134$		−	1.33393i		−	0.115234i
$135$		0			0
$136$	4.22062	−	2.43678i	0.361915	−	0.208952i
$137$	1.75034	+	3.03168i	0.149542	+	0.259014i	0.931058	−	0.364871i	$-0.118887\pi$
$137$	1.75034	+	3.03168i	0.149542	+	0.259014i	−0.781516	+	0.623885i	$0.785553\pi$
$138$		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
$142$	2.25773	+	1.30350i	0.189465	+	0.109388i
$143$	−3.50279	+	2.02234i	−0.292918	+	0.169116i
$144$		0			0
$145$		0			0
$146$	2.82406			0.233721
$147$		0			0
$148$		−	10.1107i		−	0.831092i
$149$	−7.14910	−	4.12754i	−0.585677	−	0.338141i	0.177709	−	0.984083i	$-0.443131\pi$
$149$	−7.14910	−	4.12754i	−0.585677	−	0.338141i	−0.763386	+	0.645942i	$0.776465\pi$
$150$		0			0
$151$	−0.463545	−	0.802883i	−0.0377227	−	0.0653377i	0.846548	−	0.532313i	$-0.178677\pi$
$151$	−0.463545	−	0.802883i	−0.0377227	−	0.0653377i	−0.884270	+	0.466975i	$0.845344\pi$
$152$	6.30208	+	3.63851i	0.511167	+	0.295122i
$153$		0			0
$154$	−0.195010	−	1.73331i	−0.0157144	−	0.139674i
$155$		0			0
$156$		0			0
$157$	4.17124	+	7.22480i	0.332901	+	0.576602i	0.983079	−	0.183180i	$-0.0586391\pi$
$157$	4.17124	+	7.22480i	0.332901	+	0.576602i	−0.650178	+	0.759782i	$0.725306\pi$
$158$	2.88837	+	5.00280i	0.229786	+	0.398001i
$159$		0			0
$160$		0			0
$161$	4.86740	−	11.1512i	0.383605	−	0.878840i
$162$		0			0
$163$	−21.0488	−	12.1525i	−1.64867	−	0.951858i	−0.977603	−	0.210458i	$-0.932504\pi$
$163$	−21.0488	−	12.1525i	−1.64867	−	0.951858i	−0.671064	−	0.741400i	$-0.734162\pi$
$164$	3.12617	+	5.41468i	0.244113	+	0.422816i
$165$		0			0
$166$	−6.44894	−	3.72330i	−0.500535	−	0.288984i
$167$		−	7.48724i		−	0.579380i	−0.957120	−	0.289690i	$-0.906448\pi$
$167$		−	7.48724i		−	0.579380i	0.957120	−	0.289690i	$-0.0935523\pi$
$168$		0			0
$169$	24.6400			1.89538
$170$		0			0
$171$		0			0
$172$	−7.82525	+	4.51791i	−0.596670	+	0.344487i
$173$	−12.3328	−	7.12036i	−0.937647	−	0.541351i	−0.0484252	−	0.998827i	$-0.515420\pi$
$173$	−12.3328	−	7.12036i	−0.937647	−	0.541351i	−0.889222	+	0.457476i	$0.848754\pi$
$174$		0			0
$175$		0			0
$176$			0.659263i			0.0496938i
$177$		0			0
$178$	2.66489	+	4.61572i	0.199742	+	0.345963i
$179$	11.3826	−	6.57176i	0.850777	−	0.491196i	−0.0101362	−	0.999949i	$-0.503226\pi$
$179$	11.3826	−	6.57176i	0.850777	−	0.491196i	0.860913	+	0.508752i	$0.169893\pi$
$180$		0			0
$181$		−	6.34537i		−	0.471648i	−0.971796	−	0.235824i	$-0.924221\pi$
$181$		−	6.34537i		−	0.471648i	0.971796	−	0.235824i	$-0.0757788\pi$
$182$	−6.49350	+	14.8766i	−0.481331	+	1.10273i
$183$		0			0
$184$	−2.29939	+	3.98266i	−0.169513	+	0.293606i
$185$		0			0
$186$		0			0
$187$	1.60648	−	2.78250i	0.117477	−	0.203477i
$188$			12.0027i			0.875388i
$189$		0			0
$190$		0			0
$191$	−18.8926	−	10.9077i	−1.36702	−	0.789251i	−0.376477	−	0.926426i	$-0.622865\pi$
$191$	−18.8926	−	10.9077i	−1.36702	−	0.789251i	−0.990547	+	0.137175i	$0.956198\pi$
$192$		0			0
$193$	2.09462	−	1.20933i	0.150774	−	0.0870495i	−0.422715	−	0.906263i	$-0.638923\pi$
$193$	2.09462	−	1.20933i	0.150774	−	0.0870495i	0.573489	+	0.819213i	$0.305589\pi$
$194$	5.73958	−	9.94125i	0.412078	−	0.713740i
$195$		0			0
$196$	−4.75953	−	5.13292i	−0.339967	−	0.366637i
$197$	−6.24457			−0.444907			−0.222454	−	0.974943i	$-0.571407\pi$
$197$	−6.24457			−0.444907			−0.222454	+	0.974943i	$0.571407\pi$
$198$		0			0
$199$	4.38388	−	2.53103i	0.310765	−	0.179420i	−0.336504	−	0.941682i	$-0.609244\pi$
$199$	4.38388	−	2.53103i	0.310765	−	0.179420i	0.647269	+	0.762262i	$0.275911\pi$
$200$		0			0
$201$		0			0
$202$	15.4975			1.09040
$203$	−2.39458	−	21.2838i	−0.168067	−	1.49383i
$204$		0			0
$205$		0			0
$206$	1.03422	+	1.79131i	0.0720572	+	0.124807i
$207$		0			0
$208$	3.06757	−	5.31319i	0.212698	−	0.368403i
$209$	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	$0.436897\pi$
$212$	−6.10540	+	10.5749i	−0.419321	+	0.726285i
$213$		0			0
$214$	5.44632	+	9.43331i	0.372303	+	0.644848i
$215$		0			0
$216$		0			0
$217$	−1.86676	+	1.37726i	−0.126724	+	0.0934946i
$218$	14.3451			0.971572
$219$		0			0
$220$		0			0
$221$	−25.8941	+	14.9500i	−1.74183	+	1.00564i
$222$		0			0
$223$	6.61006			0.442642			0.221321	−	0.975201i	$-0.428963\pi$
$223$	6.61006			0.442642			0.221321	+	0.975201i	$0.428963\pi$
$224$	1.57075	+	2.12902i	0.104950	+	0.142251i
$225$		0			0
$226$	5.95403	−	10.3127i	0.396056	−	0.685989i
$227$	20.8328	−	12.0278i	1.38272	−	0.798314i	0.390239	−	0.920714i	$-0.372392\pi$
$227$	20.8328	−	12.0278i	1.38272	−	0.798314i	0.992481	+	0.122400i	$0.0390590\pi$
$228$		0			0
$229$	4.39811	+	2.53925i	0.290635	+	0.167798i	0.638228	−	0.769847i	$-0.279668\pi$
$229$	4.39811	+	2.53925i	0.290635	+	0.167798i	−0.347593	+	0.937645i	$0.613001\pi$
$230$		0			0
$231$		0			0
$232$			8.09526i			0.531480i
$233$	−11.0386	+	19.1195i	−0.723165	+	1.25256i	0.236560	+	0.971617i	$0.423980\pi$
$233$	−11.0386	+	19.1195i	−0.723165	+	1.25256i	−0.959725	+	0.280941i	$0.909353\pi$
$234$		0			0
$235$		0			0
$236$	−4.06613	+	7.04274i	−0.264682	+	0.458443i
$237$		0			0
$238$	−1.44160	−	12.8134i	−0.0934451	−	0.830568i
$239$		−	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	0.250055	−	0.968232i	$-0.419551\pi$
$241$	18.8401	−	10.8773i	1.21360	−	0.700670i	0.963541	+	0.267562i	$0.0862179\pi$
$242$	−5.28269	−	9.14988i	−0.339584	−	0.588177i
$243$		0			0
$244$			0.0714487i			0.00457403i
$245$		0			0
$246$		0			0
$247$	−38.6642	−	22.3228i	−2.46014	−	1.42036i
$248$	0.759345	−	0.438408i	0.0482185	−	0.0278390i
$249$		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
$253$			3.03181i			0.190608i
$254$	−12.6668	−	7.31319i	−0.794787	−	0.458870i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.2617	+	8.23399i	0.889620	+	0.513622i	0.873818	−	0.486253i	$-0.161637\pi$
$257$	14.2617	+	8.23399i	0.889620	+	0.513622i	0.0158016	+	0.999875i	$0.494970\pi$
$258$		0			0
$259$	−24.5166	−	10.7012i	−1.52339	−	0.664943i
$260$		0			0
$261$		0			0
$262$	−1.64037	−	2.84120i	−0.101342	−	0.175530i
$263$	2.81031	+	4.86760i	0.173291	+	0.300149i	0.939569	−	0.342361i	$-0.111227\pi$
$263$	2.81031	+	4.86760i	0.173291	+	0.300149i	−0.766278	+	0.642510i	$0.777893\pi$
$264$		0			0
$265$		0			0
$266$	15.4929	−	11.4304i	0.949933	−	0.700843i
$267$		0			0
$268$	1.15522	+	0.666965i	0.0705661	+	0.0407414i
$269$	−3.27081	−	5.66521i	−0.199425	−	0.345414i	0.748917	−	0.662664i	$-0.230574\pi$
$269$	−3.27081	−	5.66521i	−0.199425	−	0.345414i	−0.948342	+	0.317249i	$0.897241\pi$
$270$		0			0
$271$	−16.0238	−	9.25135i	−0.973377	−	0.561980i	−0.0731130	−	0.997324i	$-0.523293\pi$
$271$	−16.0238	−	9.25135i	−0.973377	−	0.561980i	−0.900264	+	0.435344i	$0.856627\pi$
$272$			4.87356i			0.295503i
$273$		0			0
$274$	−3.50069			−0.211484
$275$		0			0
$276$		0			0
$277$	22.4426	−	12.9572i	1.34844	−	0.778525i	0.360415	−	0.932792i	$-0.382635\pi$
$277$	22.4426	−	12.9572i	1.34844	−	0.778525i	0.988029	+	0.154267i	$0.0493016\pi$
$278$	1.54180	+	0.890157i	0.0924708	+	0.0533881i
$279$		0			0
$280$		0			0
$281$			9.24160i			0.551308i	0.961257	+	0.275654i	$0.0888943\pi$
$281$			9.24160i			0.551308i	−0.961257	+	0.275654i	$0.911106\pi$
$282$		0			0
$283$	−3.54800	−	6.14531i	−0.210907	−	0.365301i	0.741092	−	0.671404i	$-0.234308\pi$
$283$	−3.54800	−	6.14531i	−0.210907	−	0.365301i	−0.951999	+	0.306103i	$0.900975\pi$
$284$	−2.25773	+	1.30350i	−0.133972	+	0.0773486i
$285$		0			0
$286$		−	4.04467i		−	0.239166i
$287$	16.4384	−	1.84944i	0.970329	−	0.109169i
$288$		0			0
$289$	3.37577	−	5.84701i	0.198575	−	0.343942i
$290$		0			0
$291$		0			0
$292$	−1.41203	+	2.44571i	−0.0826328	+	0.143124i
$293$			8.94657i			0.522664i	0.965249	+	0.261332i	$0.0841617\pi$
$293$			8.94657i			0.522664i	−0.965249	+	0.261332i	$0.915838\pi$
$294$		0			0
$295$		0			0
$296$	8.75609	+	5.05533i	0.508938	+	0.293835i
$297$		0			0
$298$	7.14910	−	4.12754i	0.414136	−	0.239102i
$299$	14.1071	−	24.4342i	0.815834	−	1.41307i
$300$		0			0
$301$	2.67280	+	23.7567i	0.154058	+	1.36931i
$302$	0.927090			0.0533480
$303$		0			0
$304$	−6.30208	+	3.63851i	−0.361449	+	0.208683i
$305$		0			0
$306$		0			0
$307$	7.62584			0.435230			0.217615	−	0.976035i	$-0.430172\pi$
$307$	7.62584			0.435230			0.217615	+	0.976035i	$0.430172\pi$
$308$	1.59860	+	0.697771i	0.0910884	+	0.0397592i
$309$		0			0
$310$		0			0
$311$	−3.20348	−	5.54859i	−0.181653	−	0.314632i	0.760791	−	0.648997i	$-0.224811\pi$
$311$	−3.20348	−	5.54859i	−0.181653	−	0.314632i	−0.942443	+	0.334366i	$0.891478\pi$
$312$		0			0
$313$	4.52850	−	7.84360i	0.255966	−	0.443346i	−0.709191	−	0.705016i	$-0.750940\pi$
$313$	4.52850	−	7.84360i	0.255966	−	0.443346i	0.965157	+	0.261670i	$0.0842731\pi$
$314$	−8.34248			−0.470793
$315$		0			0
$316$	−5.77674			−0.324967
$317$	−14.2534	+	24.6876i	−0.800552	+	1.38660i	0.118702	+	0.992930i	$0.462127\pi$
$317$	−14.2534	+	24.6876i	−0.800552	+	1.38660i	−0.919253	+	0.393666i	$0.871207\pi$
$318$		0			0
$319$	2.66845	+	4.62189i	0.149405	+	0.258776i
$320$		0			0
$321$		0			0
$322$	7.22355	+	9.79091i	0.402553	+	0.545626i
$323$	35.4650			1.97332
$324$		0			0
$325$		0			0
$326$	21.0488	−	12.1525i	1.16578	−	0.673065i
$327$		0			0
$328$	−6.25234			−0.345228
$329$	29.1044	+	12.7038i	1.60458	+	0.700383i
$330$		0			0
$331$	−7.53535	+	13.0516i	−0.414180	+	0.717381i	−0.995342	−	0.0964068i	$-0.969265\pi$
$331$	−7.53535	+	13.0516i	−0.414180	+	0.717381i	0.581162	+	0.813788i	$0.302598\pi$
$332$	6.44894	−	3.72330i	0.353932	−	0.204343i
$333$		0			0
$334$	6.48414	+	3.74362i	0.354797	+	0.204842i
$335$		0			0
$336$		0			0
$337$			0.480936i			0.0261983i	0.999914	+	0.0130991i	$0.00416970\pi$
$337$			0.480936i			0.0261983i	−0.999914	+	0.0130991i	$0.995830\pi$
$338$	−12.3200	+	21.3389i	−0.670119	+	1.16068i
$339$		0			0
$340$		0			0
$341$	0.289026	−	0.500608i	0.0156516	−	0.0271094i
$342$		0			0
$343$	−17.4840	+	6.10828i	−0.944045	+	0.329816i
$344$		−	9.03582i		−	0.487179i
$345$		0			0
$346$	12.3328	−	7.12036i	0.663017	−	0.382793i
$347$	−1.73829	−	3.01081i	−0.0933165	−	0.161629i	0.815588	−	0.578633i	$-0.196414\pi$
$347$	−1.73829	−	3.01081i	−0.0933165	−	0.161629i	−0.908905	+	0.417004i	$0.863080\pi$
$348$		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
$352$	−0.570938	−	0.329631i	−0.0304311	−	0.0175694i
$353$	18.8649	−	10.8916i	1.00407	−	0.579703i	0.0946235	−	0.995513i	$-0.469835\pi$
$353$	18.8649	−	10.8916i	1.00407	−	0.579703i	0.909451	+	0.415810i	$0.136502\pi$
$354$		0			0
$355$		0			0
$356$	−5.32978			−0.282478
$357$		0			0
$358$			13.1435i			0.694656i
$359$	14.0413	+	8.10672i	0.741069	+	0.427857i	0.822458	−	0.568826i	$-0.192602\pi$
$359$	14.0413	+	8.10672i	0.741069	+	0.427857i	−0.0813887	+	0.996682i	$0.525936\pi$
$360$		0			0
$361$	16.9775	+	29.4059i	0.893553	+	1.54768i
$362$	5.49525	+	3.17268i	0.288824	+	0.166753i
$363$		0			0
$364$	−9.63679	−	13.0619i	−0.505105	−	0.684627i
$365$		0			0
$366$		0			0
$367$	10.4278	+	18.0615i	0.544327	+	0.942802i	0.998649	+	0.0519641i	$0.0165481\pi$
$367$	10.4278	+	18.0615i	0.544327	+	0.942802i	−0.454322	+	0.890837i	$0.650119\pi$
$368$	−2.29939	−	3.98266i	−0.119864	−	0.207611i
$369$		0			0
$370$		0			0
$371$	19.1801	+	25.9971i	0.995784	+	1.34970i
$372$		0			0
$373$	1.21673	+	0.702477i	0.0629997	+	0.0363729i	0.531169	−	0.847266i	$-0.321753\pi$
$373$	1.21673	+	0.702477i	0.0629997	+	0.0363729i	−0.468169	+	0.883639i	$0.655086\pi$
$374$	1.60648	+	2.78250i	0.0830689	+	0.143880i
$375$		0			0
$376$	−10.3947	−	6.00136i	−0.536063	−	0.309496i
$377$		−	49.6656i		−	2.55791i
$378$		0			0
$379$	−21.8729			−1.12353			−0.561766	−	0.827296i	$-0.689878\pi$
$379$	−21.8729			−1.12353			−0.561766	+	0.827296i	$0.689878\pi$
$380$		0			0
$381$		0			0
$382$	18.8926	−	10.9077i	0.966632	−	0.558085i
$383$	−29.9197	−	17.2741i	−1.52882	−	0.882666i	−0.999412	−	0.0343009i	$-0.989080\pi$
$383$	−29.9197	−	17.2741i	−1.52882	−	0.882666i	−0.529411	−	0.848365i	$-0.677587\pi$
$384$		0			0
$385$		0			0
$386$			2.41866i			0.123107i
$387$		0			0
$388$	5.73958	+	9.94125i	0.291383	+	0.504690i
$389$	−10.0406	+	5.79694i	−0.509078	+	0.293916i	−0.732455	−	0.680816i	$-0.761625\pi$
$389$	−10.0406	+	5.79694i	−0.509078	+	0.293916i	0.223376	+	0.974732i	$0.428292\pi$
$390$		0			0
$391$			22.4124i			1.13344i
$392$	6.82500	−	1.55542i	0.344715	−	0.0785604i
$393$		0			0
$394$	3.12229	−	5.40796i	0.157299	−	0.272449i
$395$		0			0
$396$		0			0
$397$	−2.90061	+	5.02400i	−0.145577	+	0.252147i	−0.929588	−	0.368600i	$-0.879837\pi$
$397$	−2.90061	+	5.02400i	−0.145577	+	0.252147i	0.784011	+	0.620747i	$0.213171\pi$
$398$			5.06207i			0.253739i
$399$		0			0
$400$		0			0
$401$	17.7829	+	10.2670i	0.888036	+	0.512708i	0.873300	−	0.487183i	$-0.161976\pi$
$401$	17.7829	+	10.2670i	0.888036	+	0.512708i	0.0147366	+	0.999891i	$0.495309\pi$
$402$		0			0
$403$	−4.65869	+	2.68970i	−0.232066	+	0.133983i
$404$	−7.74874	+	13.4212i	−0.385514	+	0.667730i
$405$		0			0
$406$	19.6296	+	8.56811i	0.974199	+	0.425228i
$407$	6.66558			0.330401
$408$		0			0
$409$	−7.85765	+	4.53662i	−0.388536	+	0.224321i	−0.681526	−	0.731794i	$-0.738683\pi$
$409$	−7.85765	+	4.53662i	−0.388536	+	0.224321i	0.292990	+	0.956116i	$0.405350\pi$
$410$		0			0
$411$		0			0
$412$	−2.06843			−0.101904
$413$	12.7738	+	17.3138i	0.628556	+	0.851954i
$414$		0			0
$415$		0			0
$416$	3.06757	+	5.31319i	0.150400	+	0.260501i
$417$		0			0
$418$	−2.39873	+	4.15473i	−0.117326	+	0.203214i
$419$	−5.30162			−0.259001			−0.129501	−	0.991579i	$-0.541337\pi$
$419$	−5.30162			−0.259001			−0.129501	+	0.991579i	$0.541337\pi$
$420$		0			0
$421$	21.8234			1.06361			0.531804	−	0.846867i	$-0.321514\pi$
$421$	21.8234			1.06361			0.531804	+	0.846867i	$0.321514\pi$
$422$	−2.86084	+	4.95512i	−0.139263	+	0.241211i
$423$		0			0
$424$	−6.10540	−	10.5749i	−0.296504	−	0.513561i
$425$		0			0
$426$		0			0
$427$	0.173250	+	0.0756221i	0.00838417	+	0.00365961i
$428$	−10.8926			−0.526516
$429$		0			0
$430$		0			0
$431$	12.9922	−	7.50107i	0.625814	−	0.361314i	−0.153315	−	0.988177i	$-0.548995\pi$
$431$	12.9922	−	7.50107i	0.625814	−	0.361314i	0.779129	+	0.626864i	$0.215662\pi$
$432$		0			0
$433$	35.2578			1.69438			0.847190	−	0.531289i	$-0.178292\pi$
$433$	35.2578			1.69438			0.847190	+	0.531289i	$0.178292\pi$
$434$	−0.259363	−	2.30529i	−0.0124498	−	0.110658i
$435$		0			0
$436$	−7.17254	+	12.4232i	−0.343502	+	0.594964i
$437$	−28.9819	+	16.7327i	−1.38639	+	0.800434i
$438$		0			0
$439$	−25.4755	−	14.7083i	−1.21588	−	0.701988i	−0.251846	−	0.967767i	$-0.581038\pi$
$439$	−25.4755	−	14.7083i	−1.21588	−	0.701988i	−0.964034	+	0.265779i	$0.914371\pi$
$440$		0			0
$441$		0			0
$442$		−	29.9000i		−	1.42220i
$443$	14.7259	−	25.5061i	0.699651	−	1.21183i	−0.268937	−	0.963158i	$-0.586672\pi$
$443$	14.7259	−	25.5061i	0.699651	−	1.21183i	0.968588	−	0.248673i	$-0.0799943\pi$
$444$		0			0
$445$		0			0
$446$	−3.30503	+	5.72448i	−0.156498	+	0.271062i
$447$		0			0
$448$	−2.62916	+	0.295801i	−0.124216	+	0.0139753i
$449$			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
$452$	5.95403	+	10.3127i	0.280054	+	0.485067i
$453$		0			0
$454$			24.0556i			1.12899i
$455$		0			0
$456$		0			0
$457$	−6.90532	−	3.98679i	−0.323017	−	0.186494i	0.329720	−	0.944079i	$-0.393046\pi$
$457$	−6.90532	−	3.98679i	−0.323017	−	0.186494i	−0.652737	+	0.757585i	$0.726379\pi$
$458$	−4.39811	+	2.53925i	−0.205510	+	0.118651i
$459$		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
$463$		−	17.6663i		−	0.821021i	−0.911856	−	0.410511i	$-0.865350\pi$
$463$		−	17.6663i		−	0.821021i	0.911856	−	0.410511i	$-0.134650\pi$
$464$	−7.01070	−	4.04763i	−0.325464	−	0.187907i
$465$		0			0
$466$	−11.0386	−	19.1195i	−0.511355	−	0.885692i
$467$	−19.0104	−	10.9757i	−0.879698	−	0.507894i	−0.00913924	−	0.999958i	$-0.502909\pi$
$467$	−19.0104	−	10.9757i	−0.879698	−	0.507894i	−0.870559	+	0.492064i	$0.836242\pi$
$468$		0			0
$469$	2.83997	−	2.09527i	0.131137	−	0.0967507i
$470$		0			0
$471$		0			0
$472$	−4.06613	−	7.04274i	−0.187159	−	0.324168i
$473$	−2.97849	−	5.15890i	−0.136951	−	0.237206i
$474$		0			0
$475$		0			0
$476$	11.8175	+	5.15823i	0.541655	+	0.236427i
$477$		0			0
$478$	15.4634	+	8.92778i	0.707278	+	0.408347i
$479$	−16.9834	−	29.4161i	−0.775990	−	1.34405i	−0.934236	−	0.356655i	$-0.883917\pi$
$479$	−16.9834	−	29.4161i	−0.775990	−	1.34405i	0.158246	−	0.987400i	$-0.449416\pi$
$480$		0			0
$481$	−53.7199	−	31.0152i	−2.44942	−	1.41417i
$482$			21.7546i			0.990897i
$483$		0			0
$484$	10.5654			0.480244
$485$		0			0
$486$		0			0
$487$	12.8602	−	7.42482i	0.582750	−	0.336451i	−0.179476	−	0.983762i	$-0.557440\pi$
$487$	12.8602	−	7.42482i	0.582750	−	0.336451i	0.762225	+	0.647312i	$0.224107\pi$
$488$	−0.0618764	−	0.0357243i	−0.00280101	−	0.00161716i
$489$		0			0
$490$		0			0
$491$		−	15.6224i		−	0.705029i	−0.935806	−	0.352515i	$-0.885327\pi$
$491$		−	15.6224i		−	0.705029i	0.935806	−	0.352515i	$-0.114673\pi$
$492$		0			0
$493$	19.7264	+	34.1670i	0.888430	+	1.53881i
$494$	38.6642	−	22.3228i	1.73958	−	1.00435i
$495$		0			0
$496$			0.876816i			0.0393702i
$497$	0.771153	+	6.85424i	0.0345910	+	0.307455i
$498$		0			0
$499$	9.23416	−	15.9940i	0.413378	−	0.715991i	−0.581879	−	0.813275i	$-0.697682\pi$
$499$	9.23416	−	15.9940i	0.413378	−	0.715991i	0.995257	+	0.0972842i	$0.0310156\pi$
$500$		0			0
$501$		0			0
$502$	8.02227	−	13.8950i	0.358052	−	0.620164i
$503$		−	5.46007i		−	0.243452i	−0.992564	−	0.121726i	$-0.961157\pi$
$503$		−	5.46007i		−	0.243452i	0.992564	−	0.121726i	$-0.0388430\pi$
$504$		0			0
$505$		0			0
$506$	−2.62562	−	1.51590i	−0.116723	−	0.0673901i
$507$		0			0
$508$	12.6668	−	7.31319i	0.561999	−	0.324470i
$509$	−0.412125	+	0.713821i	−0.0182671	+	0.0316396i	−0.875014	−	0.484097i	$-0.839148\pi$
$509$	−0.412125	+	0.713821i	−0.0182671	+	0.0316396i	0.856747	+	0.515736i	$0.172482\pi$
$510$		0			0
$511$	4.43590	+	6.01249i	0.196233	+	0.265977i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−14.2617	+	8.23399i	−0.629056	+	0.363186i
$515$		0			0
$516$		0			0
$517$	−7.91294			−0.348011
$518$	21.5258	−	15.8814i	0.945791	−	0.697787i
$519$		0			0
$520$		0			0
$521$	−15.2147	−	26.3526i	−0.666566	−	1.15453i	−0.978858	−	0.204541i	$-0.934430\pi$
$521$	−15.2147	−	26.3526i	−0.666566	−	1.15453i	0.312292	−	0.949986i	$-0.398903\pi$
$522$		0			0
$523$	0.113392	−	0.196400i	0.00495828	−	0.00858799i	−0.863536	−	0.504288i	$-0.831755\pi$
$523$	0.113392	−	0.196400i	0.00495828	−	0.00858799i	0.868494	+	0.495700i	$0.165088\pi$
$524$	3.28074			0.143320
$525$		0			0
$526$	−5.62062			−0.245070
$527$	2.13661	−	3.70071i	0.0930721	−	0.161206i
$528$		0			0
$529$	0.925602	+	1.60319i	0.0402436	+	0.0697039i
$530$		0			0
$531$		0			0
$532$	2.15255	+	19.1325i	0.0933247	+	0.829498i
$533$	38.3590			1.66151
$534$		0			0
$535$		0			0
$536$	−1.15522	+	0.666965i	−0.0498978	+	0.0288085i
$537$		0			0
$538$	6.54163			0.282030
$539$	3.38394	−	3.13778i	0.145757	−	0.135154i
$540$		0			0
$541$	−18.5678	+	32.1603i	−0.798290	+	1.38268i	0.122438	+	0.992476i	$0.460929\pi$
$541$	−18.5678	+	32.1603i	−0.798290	+	1.38268i	−0.920729	+	0.390204i	$0.872405\pi$
$542$	16.0238	−	9.25135i	0.688282	−	0.397380i
$543$		0			0
$544$	−4.22062	−	2.43678i	−0.180958	−	0.104476i
$545$		0			0
$546$		0			0
$547$		−	14.2444i		−	0.609047i	−0.952505	−	0.304524i	$-0.901503\pi$
$547$		−	14.2444i		−	0.609047i	0.952505	−	0.304524i	$-0.0984972\pi$
$548$	1.75034	−	3.03168i	0.0747709	−	0.129507i
$549$		0			0
$550$		0			0
$551$	−29.4547	+	51.0170i	−1.25481	+	2.17340i
$552$		0			0
$553$	−6.11416	+	14.0076i	−0.260001	+	0.595662i
$554$			25.9145i			1.10100i
$555$		0			0
$556$	−1.54180	+	0.890157i	−0.0653867	+	0.0377511i
$557$	−9.45492	−	16.3764i	−0.400618	−	0.693890i	0.593183	−	0.805068i	$-0.297871\pi$
$557$	−9.45492	−	16.3764i	−0.400618	−	0.693890i	−0.993801	+	0.111177i	$0.964538\pi$
$558$		0			0
$559$			55.4361i			2.34470i
$560$		0			0
$561$		0			0
$562$	−8.00346	−	4.62080i	−0.337606	−	0.194917i
$563$	34.0414	−	19.6538i	1.43467	−	0.828310i	0.437202	−	0.899363i	$-0.355969\pi$
$563$	34.0414	−	19.6538i	1.43467	−	0.828310i	0.997472	+	0.0710537i	$0.0226362\pi$
$564$		0			0
$565$		0			0
$566$	7.09599			0.298267
$567$		0			0
$568$		−	2.60701i		−	0.109388i
$569$	−0.768837	−	0.443888i	−0.0322313	−	0.0186088i	0.483798	−	0.875180i	$-0.339257\pi$
$569$	−0.768837	−	0.443888i	−0.0322313	−	0.0186088i	−0.516029	+	0.856571i	$0.672590\pi$
$570$		0			0
$571$	−12.7120	−	22.0178i	−0.531981	−	0.921418i	−0.999303	−	0.0373309i	$-0.988114\pi$
$571$	−12.7120	−	22.0178i	−0.531981	−	0.921418i	0.467322	−	0.884087i	$-0.345219\pi$
$572$	3.50279	+	2.02234i	0.146459	+	0.0845581i
$573$		0			0
$574$	−6.61754	+	15.1608i	−0.276211	+	0.632800i
$575$		0			0
$576$		0			0
$577$	5.14235	+	8.90681i	0.214079	+	0.370795i	0.952987	−	0.303010i	$-0.0979917\pi$
$577$	5.14235	+	8.90681i	0.214079	+	0.370795i	−0.738908	+	0.673806i	$0.764658\pi$
$578$	3.37577	+	5.84701i	0.140414	+	0.243204i
$579$		0			0
$580$		0			0
$581$	−2.20271	−	19.5783i	−0.0913837	−	0.812246i
$582$		0			0
$583$	−6.97161	−	4.02506i	−0.288735	−	0.166701i
$584$	−1.41203	−	2.44571i	−0.0584302	−	0.101204i
$585$		0			0
$586$	−7.74795	−	4.47328i	−0.320065	−	0.184790i
$587$			25.1241i			1.03698i	0.855083	+	0.518490i	$0.173506\pi$
$587$			25.1241i			1.03698i	−0.855083	+	0.518490i	$0.826494\pi$
$588$		0			0
$589$	6.38061			0.262909
$590$		0			0
$591$		0			0
$592$	−8.75609	+	5.05533i	−0.359873	+	0.207773i
$593$	−8.75538	−	5.05492i	−0.359540	−	0.207581i	0.309339	−	0.950952i	$-0.399892\pi$
$593$	−8.75538	−	5.05492i	−0.359540	−	0.207581i	−0.668879	+	0.743371i	$0.733226\pi$
$594$		0			0
$595$		0			0
$596$			8.25507i			0.338141i
$597$		0			0
$598$	14.1071	+	24.4342i	0.576882	+	0.999189i
$599$	−21.6368	+	12.4920i	−0.884056	+	0.510410i	−0.871994	−	0.489517i	$-0.837173\pi$
$599$	−21.6368	+	12.4920i	−0.884056	+	0.510410i	−0.0120624	+	0.999927i	$0.503840\pi$
$600$		0			0
$601$		−	15.2936i		−	0.623837i	−0.950109	−	0.311919i	$-0.899028\pi$
$601$		−	15.2936i		−	0.623837i	0.950109	−	0.311919i	$-0.100972\pi$
$602$	−21.9103	−	9.56361i	−0.892996	−	0.389784i
$603$		0			0
$604$	−0.463545	+	0.802883i	−0.0188614	+	0.0326689i
$605$		0			0
$606$		0			0
$607$	19.7438	−	34.1973i	0.801377	−	1.38802i	−0.117334	−	0.993093i	$-0.537435\pi$
$607$	19.7438	−	34.1973i	0.801377	−	1.38802i	0.918710	−	0.394932i	$-0.129232\pi$
$608$		−	7.27702i		−	0.295122i
$609$		0			0
$610$		0			0
$611$	63.7727	+	36.8192i	2.57997	+	1.48954i
$612$		0			0
$613$	−14.8258	+	8.55968i	−0.598809	+	0.345722i	−0.768573	−	0.639762i	$-0.779033\pi$
$613$	−14.8258	+	8.55968i	−0.598809	+	0.345722i	0.169764	+	0.985485i	$0.445699\pi$
$614$	−3.81292	+	6.60417i	−0.153877	+	0.266523i
$615$		0			0
$616$	−1.40359	+	1.03554i	−0.0565521	+	0.0417230i
$617$	−5.80201			−0.233580			−0.116790	−	0.993157i	$-0.537260\pi$
$617$	−5.80201			−0.233580			−0.116790	+	0.993157i	$0.537260\pi$
$618$		0			0
$619$	−29.5344	+	17.0517i	−1.18709	+	0.685366i	−0.957644	−	0.287956i	$-0.907024\pi$
$619$	−29.5344	+	17.0517i	−1.18709	+	0.685366i	−0.229445	+	0.973322i	$0.573691\pi$
$620$		0			0
$621$		0			0
$622$	6.40696			0.256896
$623$	−5.64109	+	12.9238i	−0.226006	+	0.517780i
$624$		0			0
$625$		0			0
$626$	4.52850	+	7.84360i	0.180995	+	0.313493i
$627$		0			0
$628$	4.17124	−	7.22480i	0.166451	−	0.288301i
$629$	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	$0.270825\pi$
$632$	2.88837	−	5.00280i	0.114893	−	0.199001i
$633$		0			0
$634$	−14.2534	−	24.6876i	−0.566076	−	0.980472i
$635$		0			0
$636$		0			0
$637$	−41.8724	+	9.54270i	−1.65904	+	0.378096i
$638$	−5.33690			−0.211290
$639$		0			0
$640$		0			0
$641$	1.72685	−	0.997000i	0.0682067	−	0.0393791i	−0.465509	−	0.885043i	$-0.654129\pi$
$641$	1.72685	−	0.997000i	0.0682067	−	0.0393791i	0.533716	+	0.845664i	$0.320795\pi$
$642$		0			0
$643$	0.661676			0.0260940			0.0130470	−	0.999915i	$-0.495847\pi$
$643$	0.661676			0.0260940			0.0130470	+	0.999915i	$0.495847\pi$
$644$	−12.0910	+	1.36032i	−0.476450	+	0.0536042i
$645$		0			0
$646$	−17.7325	+	30.7136i	−0.697675	+	1.20841i
$647$	15.9223	−	9.19276i	0.625971	−	0.361405i	−0.153219	−	0.988192i	$-0.548964\pi$
$647$	15.9223	−	9.19276i	0.625971	−	0.361405i	0.779190	+	0.626787i	$0.215631\pi$
$648$		0			0
$649$	−4.64302	−	2.68065i	−0.182254	−	0.105225i
$650$		0			0
$651$		0			0
$652$			24.3050i			0.951858i
$653$	−8.69323	+	15.0571i	−0.340193	+	0.589231i	−0.984468	−	0.175562i	$-0.943826\pi$
$653$	−8.69323	+	15.0571i	−0.340193	+	0.589231i	0.644276	+	0.764793i	$0.277159\pi$
$654$		0			0
$655$		0			0
$656$	3.12617	−	5.41468i	0.122056	−	0.211408i
$657$		0			0
$658$	−25.5540	+	18.8533i	−0.996200	+	0.734978i
$659$			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	−0.943133	−	0.332417i	$-0.892136\pi$
$661$	−28.9704	+	16.7261i	−1.12682	+	0.650568i	−0.183685	+	0.982985i	$0.558803\pi$
$662$	−7.53535	−	13.0516i	−0.292870	−	0.507265i
$663$		0			0
$664$			7.44660i			0.288984i
$665$		0			0
$666$		0			0
$667$	−32.2407	−	18.6142i	−1.24836	−	0.720744i
$668$	−6.48414	+	3.74362i	−0.250879	+	0.144845i
$669$		0			0
$670$		0			0
$671$	−0.0471035			−0.00181841
$672$		0			0
$673$			21.9964i			0.847898i	0.905686	+	0.423949i	$0.139356\pi$
$673$			21.9964i			0.847898i	−0.905686	+	0.423949i	$0.860644\pi$
$674$	−0.416503	−	0.240468i	−0.0160431	−	0.00926249i
$675$		0			0
$676$	−12.3200	−	21.3389i	−0.473846	−	0.820725i
$677$	−10.7084	−	6.18250i	−0.411557	−	0.237613i	0.279901	−	0.960029i	$-0.409698\pi$
$677$	−10.7084	−	6.18250i	−0.411557	−	0.237613i	−0.691459	+	0.722416i	$0.743032\pi$
$678$		0			0
$679$	30.1806	−	3.39554i	1.15823	−	0.130309i
$680$		0			0
$681$		0			0
$682$	0.289026	+	0.500608i	0.0110674	+	0.0191693i
$683$	−14.9892	−	25.9621i	−0.573546	−	0.993411i	−0.996198	−	0.0871187i	$-0.972234\pi$
$683$	−14.9892	−	25.9621i	−0.573546	−	0.993411i	0.422652	−	0.906292i	$-0.361099\pi$
$684$		0			0
$685$		0			0
$686$	3.45205	−	18.1957i	0.131800	−	0.694715i
$687$		0			0
$688$	7.82525	+	4.51791i	0.298335	+	0.172244i
$689$	37.4575	+	64.8783i	1.42702	+	2.47167i
$690$		0			0
$691$	7.97882	+	4.60657i	0.303529	+	0.175242i	0.644027	−	0.765003i	$-0.277262\pi$
$691$	7.97882	+	4.60657i	0.303529	+	0.175242i	−0.340498	+	0.940245i	$0.610596\pi$
$692$			14.2407i			0.541351i
$693$		0			0
$694$	3.47659			0.131969
$695$		0			0
$696$		0			0
$697$	−26.3888	+	15.2356i	−0.999546	+	0.577088i
$698$	0.529638	+	0.305787i	0.0200471	+	0.0115742i
$699$		0			0
$700$		0			0
$701$			44.9022i			1.69593i	0.530050	+	0.847967i	$0.322173\pi$
$701$			44.9022i			1.69593i	−0.530050	+	0.847967i	$0.677827\pi$
$702$		0			0
$703$	36.7878	+	63.7183i	1.38748	+	2.40318i
$704$	0.570938	−	0.329631i	0.0215180	−	0.0124234i
$705$		0			0
$706$			21.7833i			0.819824i
$707$	24.3427	+	32.9945i	0.915502	+	1.24089i
$708$		0			0
$709$	1.39264	−	2.41213i	0.0523019	−	0.0905895i	−0.838689	−	0.544610i	$-0.816678\pi$
$709$	1.39264	−	2.41213i	0.0523019	−	0.0905895i	0.890991	+	0.454021i	$0.150011\pi$
$710$		0			0
$711$		0			0
$712$	2.66489	−	4.61572i	0.0998709	−	0.172981i
$713$			4.03229i			0.151010i
$714$		0			0
$715$		0			0
$716$	−11.3826	−	6.57176i	−0.425388	−	0.245598i
$717$		0			0
$718$	−14.0413	+	8.10672i	−0.524015	+	0.302540i
$719$	13.4818	−	23.3511i	0.502785	−	0.870849i	−0.497210	−	0.867630i	$-0.665642\pi$
$719$	13.4818	−	23.3511i	0.502785	−	0.870849i	0.999995	−	0.00321841i	$-0.00102445\pi$
$720$		0			0
$721$	−2.18925	+	5.01558i	−0.0815319	+	0.186790i
$722$	−33.9550			−1.26368
$723$		0			0
$724$	−5.49525	+	3.17268i	−0.204229	+	0.117912i
$725$		0			0
$726$		0			0
$727$	−29.6632			−1.10015			−0.550074	−	0.835116i	$-0.685400\pi$
$727$	−29.6632			−1.10015			−0.550074	+	0.835116i	$0.685400\pi$
$728$	16.1303	−	1.81478i	0.597829	−	0.0672602i
$729$		0			0
$730$		0			0
$731$	−22.0183	−	38.1368i	−0.814376	−	1.41054i
$732$		0			0
$733$	−11.5155	+	19.9455i	−0.425336	+	0.736704i	−0.996452	−	0.0841657i	$-0.973177\pi$
$733$	−11.5155	+	19.9455i	−0.425336	+	0.736704i	0.571116	+	0.820870i	$0.306511\pi$
$734$	−20.8556			−0.769794
$735$		0			0
$736$	4.59878			0.169513
$737$	−0.439705	+	0.761591i	−0.0161967	+	0.0280536i
$738$		0			0
$739$	17.2029	+	29.7964i	0.632821	+	1.09608i	0.986972	+	0.160889i	$0.0514363\pi$
$739$	17.2029	+	29.7964i	0.632821	+	1.09608i	−0.354152	+	0.935188i	$0.615230\pi$
$740$		0			0
$741$		0			0
$742$	−32.1042	+	3.61196i	−1.17858	+	0.132599i
$743$	40.6201			1.49021			0.745103	−	0.666950i	$-0.232400\pi$
$743$	40.6201			1.49021			0.745103	+	0.666950i	$0.232400\pi$
$744$		0			0
$745$		0			0
$746$	−1.21673	+	0.702477i	−0.0445475	+	0.0257195i
$747$		0			0
$748$	−3.21295			−0.117477
$749$	−11.5289	+	26.4127i	−0.421257	+	0.965101i
$750$		0			0
$751$	−22.8927	+	39.6513i	−0.835366	+	1.44690i	0.0583658	+	0.998295i	$0.481411\pi$
$751$	−22.8927	+	39.6513i	−0.835366	+	1.44690i	−0.893732	+	0.448601i	$0.851922\pi$
$752$	10.3947	−	6.00136i	0.379054	−	0.218847i
$753$		0			0
$754$	43.0117	+	24.8328i	1.56639	+	0.904357i
$755$		0			0
$756$		0			0
$757$			50.7755i			1.84547i	0.385440	+	0.922733i	$0.374050\pi$
$757$			50.7755i			1.84547i	−0.385440	+	0.922733i	$0.625950\pi$
$758$	10.9364	−	18.9424i	0.397229	−	0.688021i
$759$		0			0
$760$		0			0
$761$	18.0315	−	31.2316i	0.653643	−	1.13214i	−0.328589	−	0.944473i	$-0.606573\pi$
$761$	18.0315	−	31.2316i	0.653643	−	1.13214i	0.982232	−	0.187670i	$-0.0600935\pi$
$762$		0			0
$763$	22.5326	+	30.5410i	0.815734	+	1.10566i
$764$			21.8153i			0.789251i
$765$		0			0
$766$	29.9197	−	17.2741i	1.08104	−	0.624139i
$767$	24.9463	+	43.2082i	0.900758	+	1.56016i
$768$		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
$772$	−2.09462	−	1.20933i	−0.0753871	−	0.0435248i
$773$	−42.8367	+	24.7318i	−1.54073	+	0.889541i	−0.541938	+	0.840419i	$0.682309\pi$
$773$	−42.8367	+	24.7318i	−1.54073	+	0.889541i	−0.998793	+	0.0491225i	$0.984358\pi$
$774$		0			0
$775$		0			0
$776$	−11.4792			−0.412078
$777$		0			0
$778$		−	11.5939i		−	0.415661i
$779$	−39.4028	−	22.7492i	−1.41175	−	0.815074i
$780$		0			0
$781$	−0.859351	−	1.48844i	−0.0307500	−	0.0532605i
$782$	−19.4097	−	11.2062i	−0.694090	−	0.400733i
$783$		0			0
$784$	−2.06547	+	6.68833i	−0.0737669	+	0.238869i
$785$		0			0
$786$		0			0
$787$	4.83998	+	8.38310i	0.172527	+	0.298825i	0.939303	−	0.343090i	$-0.111474\pi$
$787$	4.83998	+	8.38310i	0.172527	+	0.298825i	−0.766776	+	0.641915i	$0.778140\pi$
$788$	3.12229	+	5.40796i	0.111227	+	0.192651i
$789$		0			0
$790$		0			0
$791$	31.3082	−	3.52241i	1.11319	−	0.125242i
$792$		0			0
$793$	0.379620	+	0.219174i	0.0134807	+	0.00778310i
$794$	−2.90061	−	5.02400i	−0.102939	−	0.178295i
$795$		0			0
$796$	−4.38388	−	2.53103i	−0.155383	−	0.0897101i
$797$		−	15.1216i		−	0.535636i	−0.963470	−	0.267818i	$-0.913697\pi$
$797$		−	15.1216i		−	0.535636i	0.963470	−	0.267818i	$-0.0863026\pi$
$798$		0			0
$799$	−58.4959			−2.06944
$800$		0			0
$801$		0			0
$802$	−17.7829	+	10.2670i	−0.627937	+	0.362539i
$803$	−1.61236	−	0.930899i	−0.0568991	−	0.0328507i
$804$		0			0
$805$		0			0
$806$		−	5.37940i		−	0.189481i
$807$		0			0
$808$	−7.74874	−	13.4212i	−0.272600	−	0.472157i
$809$	−4.53839	+	2.62024i	−0.159561	+	0.0921228i	−0.577655	−	0.816281i	$-0.696032\pi$
$809$	−4.53839	+	2.62024i	−0.159561	+	0.0921228i	0.418093	+	0.908404i	$0.362699\pi$
$810$		0			0
$811$		−	54.1101i		−	1.90006i	−0.312154	−	0.950031i	$-0.601051\pi$
$811$		−	54.1101i		−	1.90006i	0.312154	−	0.950031i	$-0.398949\pi$
$812$	−17.2350	+	12.7157i	−0.604830	+	0.446232i
$813$		0			0
$814$	−3.33279	+	5.77257i	−0.116814	+	0.202328i
$815$		0			0
$816$		0			0
$817$	32.8769	−	56.9445i	1.15022	−	1.99224i
$818$		−	9.07323i		−	0.317238i
$819$		0			0
$820$		0			0
$821$	23.3717	+	13.4936i	0.815677	+	0.470931i	0.848924	−	0.528516i	$-0.177251\pi$
$821$	23.3717	+	13.4936i	0.815677	+	0.470931i	−0.0332463	+	0.999447i	$0.510585\pi$
$822$		0			0
$823$	5.42130	−	3.12999i	0.188975	−	0.109105i	−0.402528	−	0.915408i	$-0.631868\pi$
$823$	5.42130	−	3.12999i	0.188975	−	0.109105i	0.591502	+	0.806303i	$0.298535\pi$
$824$	1.03422	−	1.79131i	0.0360286	−	0.0624034i
$825$		0			0
$826$	−21.3810	+	2.40553i	−0.743941	+	0.0836989i
$827$	−32.0713			−1.11523			−0.557615	−	0.830100i	$-0.688283\pi$
$827$	−32.0713			−1.11523			−0.557615	+	0.830100i	$0.688283\pi$
$828$		0			0
$829$	−10.3975	+	6.00303i	−0.361122	+	0.208494i	−0.669573	−	0.742746i	$-0.733523\pi$
$829$	−10.3975	+	6.00303i	−0.361122	+	0.208494i	0.308451	+	0.951240i	$0.400189\pi$
$830$		0			0
$831$		0			0
$832$	−6.13514			−0.212698
$833$	25.0156	−	23.1958i	0.866738	−	0.803688i
$834$		0			0
$835$		0			0
$836$	−2.39873	−	4.15473i	−0.0829620	−	0.143694i
$837$		0			0
$838$	2.65081	−	4.59134i	0.0915707	−	0.158605i
$839$	−51.4896			−1.77762			−0.888809	−	0.458278i	$-0.848466\pi$
$839$	−51.4896			−1.77762			−0.888809	+	0.458278i	$0.848466\pi$
$840$		0			0
$841$	−36.5332			−1.25977
$842$	−10.9117	+	18.8996i	−0.376042	+	0.651324i
$843$		0			0
$844$	−2.86084	−	4.95512i	−0.0984741	−	0.170562i
$845$		0			0
$846$		0			0
$847$	11.1825	−	25.6192i	0.384236	−	0.880285i
$848$	12.2108			0.419321
$849$		0			0
$850$		0			0
$851$	−40.2674	+	23.2484i	−1.38035	+	0.796944i
$852$		0			0
$853$	41.4695			1.41989			0.709944	−	0.704258i	$-0.248720\pi$
$853$	41.4695			1.41989			0.709944	+	0.704258i	$0.248720\pi$
$854$	−0.152116	+	0.112228i	−0.00520530	+	0.00384037i
$855$		0			0
$856$	5.44632	−	9.43331i	0.186152	−	0.322424i
$857$	−48.3925	+	27.9394i	−1.65306	+	0.954393i	−0.677252	+	0.735751i	$0.736829\pi$
$857$	−48.3925	+	27.9394i	−1.65306	+	0.954393i	−0.975805	+	0.218641i	$0.929837\pi$
$858$		0			0
$859$	26.0097	+	15.0167i	0.887440	+	0.512364i	0.873104	−	0.487534i	$-0.162103\pi$
$859$	26.0097	+	15.0167i	0.887440	+	0.512364i	0.0143355	+	0.999897i	$0.495437\pi$
$860$		0			0
$861$		0			0
$862$			15.0021i			0.510975i
$863$	1.02317	−	1.77218i	0.0348291	−	0.0603258i	−0.848085	−	0.529860i	$-0.822245\pi$
$863$	1.02317	−	1.77218i	0.0348291	−	0.0603258i	0.882915	+	0.469534i	$0.155578\pi$
$864$		0			0
$865$		0			0
$866$	−17.6289	+	30.5341i	−0.599054	+	1.03759i
$867$		0			0
$868$	2.12612	+	0.928032i	0.0721654	+	0.0314995i
$869$		−	3.80839i		−	0.129191i
$870$		0			0
$871$	7.08742	−	4.09192i	0.240148	−	0.138650i
$872$	−7.17254	−	12.4232i	−0.242893	−	0.420703i
$873$		0			0
$874$		−	33.4654i		−	1.13199i
$875$		0			0
$876$		0			0
$877$	−9.08442	−	5.24489i	−0.306759	−	0.177107i	0.338716	−	0.940889i	$-0.390007\pi$
$877$	−9.08442	−	5.24489i	−0.306759	−	0.177107i	−0.645475	+	0.763781i	$0.723341\pi$
$878$	25.4755	−	14.7083i	0.859757	−	0.496381i
$879$		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
$883$			23.8143i			0.801416i	0.916206	+	0.400708i	$0.131236\pi$
$883$			23.8143i			0.801416i	−0.916206	+	0.400708i	$0.868764\pi$
$884$	25.8941	+	14.9500i	0.870914	+	0.502822i
$885$		0			0
$886$	14.7259	+	25.5061i	0.494728	+	0.856893i
$887$	−27.0408	−	15.6120i	−0.907941	−	0.524200i	−0.0281729	−	0.999603i	$-0.508969\pi$
$887$	−27.0408	−	15.6120i	−0.907941	−	0.524200i	−0.879768	+	0.475403i	$0.842302\pi$
$888$		0			0
$889$	−4.32649	−	38.4552i	−0.145106	−	1.28974i
$890$		0			0
$891$		0			0
$892$	−3.30503	−	5.72448i	−0.110661	−	0.191670i
$893$	−43.6720	−	75.6421i	−1.46143	−	2.53127i
$894$		0			0
$895$		0			0
$896$	1.05841	−	2.42482i	0.0353590	−	0.0810076i
$897$		0			0
$898$	−25.3233	−	14.6204i	−0.845049	−	0.487889i
$899$	3.54903	+	6.14710i	0.118367	+	0.205017i
$900$		0			0
$901$	−51.5372	−	29.7550i	−1.71695	−	0.991283i
$902$		−	4.12193i		−	0.137245i
$903$		0			0
$904$	−11.9081			−0.396056
$905$		0			0
$906$		0			0
$907$	13.3901	−	7.73076i	0.444610	−	0.256696i	−0.260941	−	0.965355i	$-0.584033\pi$
$907$	13.3901	−	7.73076i	0.444610	−	0.256696i	0.705551	+	0.708659i	$0.250699\pi$
$908$	−20.8328	−	12.0278i	−0.691360	−	0.399157i
$909$		0			0
$910$		0			0
$911$		−	11.7655i		−	0.389810i	−0.980822	−	0.194905i	$-0.937560\pi$
$911$		−	11.7655i		−	0.389810i	0.980822	−	0.194905i	$-0.0624398\pi$
$912$		0			0
$913$	2.45463	+	4.25155i	0.0812365	+	0.140706i
$914$	6.90532	−	3.98679i	0.228408	−	0.131871i
$915$		0			0
$916$		−	5.07850i		−	0.167798i
$917$	3.47237	−	7.95521i	0.114668	−	0.262704i
$918$		0			0
$919$	−15.4078	+	26.6871i	−0.508256	+	0.880326i	0.491698	+	0.870766i	$0.336376\pi$
$919$	−15.4078	+	26.6871i	−0.508256	+	0.880326i	−0.999954	+	0.00955987i	$0.996957\pi$
$920$		0			0
$921$		0			0
$922$	19.9556	−	34.5641i	0.657203	−	1.13831i
$923$			15.9944i			0.526460i
$924$		0			0
$925$		0			0
$926$	15.2994	+	8.83314i	0.502771	+	0.290275i
$927$		0			0
$928$	7.01070	−	4.04763i	0.230138	−	0.132870i
$929$	−2.44799	+	4.24005i	−0.0803160	+	0.139111i	−0.903386	−	0.428829i	$-0.858926\pi$
$929$	−2.44799	+	4.24005i	−0.0803160	+	0.139111i	0.823070	+	0.567940i	$0.192260\pi$
$930$		0			0
$931$	48.6712	+	15.0305i	1.59513	+	0.492604i
$932$	22.0773			0.723165
$933$		0			0
$934$	19.0104	−	10.9757i	0.622040	−	0.359135i
$935$		0			0
$936$		0			0
$937$	28.7661			0.939747			0.469874	−	0.882734i	$-0.344299\pi$
$937$	28.7661			0.939747			0.469874	+	0.882734i	$0.344299\pi$
$938$	0.394577	+	3.50712i	0.0128834	+	0.114511i
$939$		0			0
$940$		0			0
$941$	−0.0535167	−	0.0926937i	−0.00174460	−	0.00302173i	0.865152	−	0.501510i	$-0.167222\pi$
$941$	−0.0535167	−	0.0926937i	−0.00174460	−	0.00302173i	−0.866896	+	0.498488i	$0.833889\pi$
$942$		0			0
$943$	14.3766	−	24.9009i	0.468165	−	0.810886i
$944$	8.13225			0.264682
$945$		0			0
$946$	5.95698			0.193678
$947$	7.36136	−	12.7502i	0.239212	−	0.414327i	−0.721276	−	0.692647i	$-0.756444\pi$
$947$	7.36136	−	12.7502i	0.239212	−	0.414327i	0.960488	+	0.278320i	$0.0897776\pi$
$948$		0			0
$949$	8.66301	+	15.0048i	0.281213	+	0.487076i
$950$		0			0
$951$		0			0
$952$	−10.3759	+	7.65515i	−0.336285	+	0.248105i
$953$	−10.5168			−0.340672			−0.170336	−	0.985386i	$-0.554485\pi$
$953$	−10.5168			−0.340672			−0.170336	+	0.985386i	$0.554485\pi$
$954$		0			0
$955$		0			0
$956$	−15.4634	+	8.92778i	−0.500121	+	0.288745i
$957$		0			0
$958$	33.9667			1.09742
$959$	−5.49871	−	7.45304i	−0.177563	−	0.240671i
$960$		0			0
$961$	−15.1156	+	26.1810i	−0.487600	+	0.844548i
$962$	53.7199	−	31.0152i	1.73200	−	0.999970i
$963$		0			0
$964$	−18.8401	−	10.8773i	−0.606798	−	0.350335i
$965$		0			0
$966$		0			0
$967$		−	8.51148i		−	0.273711i	−0.990591	−	0.136855i	$-0.956300\pi$
$967$		−	8.51148i		−	0.273711i	0.990591	−	0.136855i	$-0.0436995\pi$
$968$	−5.28269	+	9.14988i	−0.169792	+	0.294088i
$969$		0			0
$970$		0			0
$971$	−4.49465	+	7.78496i	−0.144240	+	0.249831i	−0.929089	−	0.369856i	$-0.879407\pi$
$971$	−4.49465	+	7.78496i	−0.144240	+	0.249831i	0.784849	+	0.619687i	$0.212740\pi$
$972$		0			0
$973$	0.526618	+	4.68074i	0.0168826	+	0.150057i
$974$			14.8496i			0.475813i
$975$		0			0
$976$	0.0618764	−	0.0357243i	0.00198061	−	0.00114351i
$977$	22.6877	+	39.2963i	0.725845	+	1.25720i	0.958625	+	0.284671i	$0.0918843\pi$
$977$	22.6877	+	39.2963i	0.725845	+	1.25720i	−0.232781	+	0.972529i	$0.574782\pi$
$978$		0			0
$979$		−	3.51372i		−	0.112299i
$980$		0			0
$981$		0			0
$982$	13.5294	+	7.81120i	0.431741	+	0.249266i
$983$	22.3797	−	12.9209i	0.713802	−	0.412114i	−0.0986654	−	0.995121i	$-0.531457\pi$
$983$	22.3797	−	12.9209i	0.713802	−	0.412114i	0.812467	+	0.583007i	$0.198124\pi$
$984$		0			0
$985$		0			0
$986$	−39.4527			−1.25643
$987$		0			0
$988$			44.6456i			1.42036i
$989$	35.9866	+	20.7769i	1.14431	+	0.660667i
$990$		0			0
$991$	−16.5315	−	28.6333i	−0.525139	−	0.909568i	−0.999571	−	0.0292760i	$-0.990680\pi$
$991$	−16.5315	−	28.6333i	−0.525139	−	0.909568i	0.474432	−	0.880292i	$-0.342654\pi$
$992$	−0.759345	−	0.438408i	−0.0241092	−	0.0139195i
$993$		0			0
$994$	−6.32153	−	2.75928i	−0.200507	−	0.0875191i
$995$		0			0
$996$		0			0
$997$	24.9894	+	43.2828i	0.791421	+	1.37078i	0.925087	+	0.379755i	$0.123992\pi$
$997$	24.9894	+	43.2828i	0.791421	+	1.37078i	−0.133666	+	0.991026i	$0.542675\pi$
$998$	9.23416	+	15.9940i	0.292302	+	0.506282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.g.1349.1		24
3.2	odd	2		3150.2.bp.h.1349.1		24
5.2	odd	4		3150.2.bf.e.1601.3	yes	24
5.3	odd	4		3150.2.bf.d.1601.10	yes	24
5.4	even	2		3150.2.bp.h.1349.12		24
7.3	odd	6	inner	3150.2.bp.g.899.12		24
15.2	even	4		3150.2.bf.e.1601.10	yes	24
15.8	even	4		3150.2.bf.d.1601.3	yes	24
15.14	odd	2	inner	3150.2.bp.g.1349.12		24
21.17	even	6		3150.2.bp.h.899.12		24
35.3	even	12		3150.2.bf.d.1151.3	✓	24
35.17	even	12		3150.2.bf.e.1151.10	yes	24
35.24	odd	6		3150.2.bp.h.899.1		24
105.17	odd	12		3150.2.bf.e.1151.3	yes	24
105.38	odd	12		3150.2.bf.d.1151.10	yes	24
105.59	even	6	inner	3150.2.bp.g.899.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.3	✓	24	35.3	even	12
3150.2.bf.d.1151.10	yes	24	105.38	odd	12
3150.2.bf.d.1601.3	yes	24	15.8	even	4
3150.2.bf.d.1601.10	yes	24	5.3	odd	4
3150.2.bf.e.1151.3	yes	24	105.17	odd	12
3150.2.bf.e.1151.10	yes	24	35.17	even	12
3150.2.bf.e.1601.3	yes	24	5.2	odd	4
3150.2.bf.e.1601.10	yes	24	15.2	even	4
3150.2.bp.g.899.1		24	105.59	even	6	inner
3150.2.bp.g.899.12		24	7.3	odd	6	inner
3150.2.bp.g.1349.1		24	1.1	even	1	trivial
3150.2.bp.g.1349.12		24	15.14	odd	2	inner
3150.2.bp.h.899.1		24	35.24	odd	6
3150.2.bp.h.899.12		24	21.17	even	6
3150.2.bp.h.1349.1		24	3.2	odd	2
3150.2.bp.h.1349.12		24	5.4	even	2

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.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.62916 + 0.295801i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.62916 + 0.295801i) q^{7} +1.00000 q^{8} +(0.570938 - 0.329631i) q^{11} -6.13514 q^{13} +(1.05841 - 2.42482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.22062 - 2.43678i) q^{17} +(6.30208 + 3.63851i) q^{19} +0.659263i q^{22} +(-2.29939 + 3.98266i) q^{23} +(3.06757 - 5.31319i) q^{26} +(1.57075 + 2.12902i) q^{28} +8.09526i q^{29} +(0.759345 - 0.438408i) q^{31} +(-0.500000 - 0.866025i) q^{32} +4.87356i q^{34} +(8.75609 + 5.05533i) q^{37} +(-6.30208 + 3.63851i) q^{38} -6.25234 q^{41} -9.03582i q^{43} +(-0.570938 - 0.329631i) q^{44} +(-2.29939 - 3.98266i) q^{46} +(-10.3947 - 6.00136i) q^{47} +(6.82500 - 1.55542i) q^{49} +(3.06757 + 5.31319i) q^{52} +(-6.10540 - 10.5749i) q^{53} +(-2.62916 + 0.295801i) q^{56} +(-7.01070 - 4.04763i) q^{58} +(-4.06613 - 7.04274i) q^{59} +(-0.0618764 - 0.0357243i) q^{61} +0.876816i q^{62} +1.00000 q^{64} +(-1.15522 + 0.666965i) q^{67} +(-4.22062 - 2.43678i) q^{68} -2.60701i q^{71} +(-1.41203 - 2.44571i) q^{73} +(-8.75609 + 5.05533i) q^{74} -7.27702i q^{76} +(-1.40359 + 1.03554i) q^{77} +(2.88837 - 5.00280i) q^{79} +(3.12617 - 5.41468i) q^{82} +7.44660i q^{83} +(7.82525 + 4.51791i) q^{86} +(0.570938 - 0.329631i) q^{88} +(2.66489 - 4.61572i) q^{89} +(16.1303 - 1.81478i) q^{91} +4.59878 q^{92} +(10.3947 - 6.00136i) q^{94} -11.4792 q^{97} +(-2.06547 + 6.68833i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Introduction

L-functions

Modular forms

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Database

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